id	sid	tid	token	lemma	pos
cana-4456	1	1	communications	communication	NOUN
cana-4456	1	2	on	on	ADP
cana-4456	1	3	applied	apply	VERB
cana-4456	1	4	nonlinear	nonlinear	ADJ
cana-4456	1	5	analysis	analysis	NOUN
cana-4456	1	6	issn	issn	NOUN
cana-4456	1	7	:	:	PUNCT
cana-4456	1	8	1074	1074	NUM
cana-4456	1	9	-	-	PUNCT
cana-4456	1	10	133x	133x	NUM
cana-4456	1	11	vol	vol	NOUN
cana-4456	1	12	32	32	NUM
cana-4456	1	13	no	no	NOUN
cana-4456	1	14	.	.	PUNCT
cana-4456	2	1	9s	9s	NUM
cana-4456	2	2	(	(	PUNCT
cana-4456	2	3	2025	2025	NUM
cana-4456	2	4	)	)	PUNCT
cana-4456	2	5	2167	2167	NUM
cana-4456	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	2	7	artificial	artificial	ADJ
cana-4456	2	8	viscosity	viscosity	NOUN
cana-4456	2	9	stabilization	stabilization	NOUN
cana-4456	2	10	of	of	ADP
cana-4456	2	11	meshless	meshless	ADJ
cana-4456	2	12	methods	method	NOUN
cana-4456	2	13	for	for	ADP
cana-4456	2	14	shallow	shallow	ADJ
cana-4456	2	15	water	water	NOUN
cana-4456	2	16	flows	flow	NOUN
cana-4456	2	17	in	in	ADP
cana-4456	2	18	channels	channel	NOUN
cana-4456	2	19	mariam	mariam	PROPN
cana-4456	2	20	ijerch1	ijerch1	PROPN
cana-4456	2	21	,	,	PUNCT
cana-4456	2	22	mohamed	mohamed	PROPN
cana-4456	2	23	sadik2	sadik2	PROPN
cana-4456	2	24	1engineering	1engineering	NUM
cana-4456	2	25	sciences	science	NOUN
cana-4456	2	26	laboratory	laboratory	NOUN
cana-4456	2	27	,	,	PUNCT
cana-4456	2	28	faculty	faculty	NOUN
cana-4456	2	29	of	of	ADP
cana-4456	2	30	sciences	science	NOUN
cana-4456	2	31	,	,	PUNCT
cana-4456	2	32	agadir	agadir	PROPN
cana-4456	2	33	,	,	PUNCT
cana-4456	2	34	ibn	ibn	PROPN
cana-4456	2	35	zohr	zohr	NOUN
cana-4456	2	36	university	university	PROPN
cana-4456	2	37	,	,	PUNCT
cana-4456	2	38	morocco	morocco	PROPN
cana-4456	2	39	(	(	PUNCT
cana-4456	2	40	email	email	NOUN
cana-4456	2	41	:	:	PUNCT
cana-4456	2	42	mariam.ijerch@edu.uiz.ac.ma	mariam.ijerch@edu.uiz.ac.ma	NOUN
cana-4456	2	43	)	)	PUNCT
cana-4456	2	44	2engineering	2engineering	NUM
cana-4456	2	45	sciences	science	NOUN
cana-4456	2	46	laboratory	laboratory	NOUN
cana-4456	2	47	,	,	PUNCT
cana-4456	2	48	faculty	faculty	NOUN
cana-4456	2	49	of	of	ADP
cana-4456	2	50	sciences	science	NOUN
cana-4456	2	51	,	,	PUNCT
cana-4456	2	52	agadir	agadir	PROPN
cana-4456	2	53	,	,	PUNCT
cana-4456	2	54	ibn	ibn	PROPN
cana-4456	2	55	zohr	zohr	NOUN
cana-4456	2	56	university	university	PROPN
cana-4456	2	57	,	,	PUNCT
cana-4456	2	58	morocco	morocco	PROPN
cana-4456	2	59	(	(	PUNCT
cana-4456	2	60	email	email	NOUN
cana-4456	2	61	:	:	PUNCT
cana-4456	2	62	m.sadik@uiz.ac.ma	m.sadik@uiz.ac.ma	NOUN
cana-4456	2	63	)	)	PUNCT
cana-4456	2	64	article	article	NOUN
cana-4456	2	65	history	history	NOUN
cana-4456	2	66	:	:	PUNCT
cana-4456	2	67	received	receive	VERB
cana-4456	2	68	:	:	PUNCT
cana-4456	2	69	12	12	NUM
cana-4456	2	70	-	-	SYM
cana-4456	2	71	01	01	NUM
cana-4456	2	72	-	-	PUNCT
cana-4456	2	73	2025	2025	NUM
cana-4456	2	74	revised	revise	VERB
cana-4456	2	75	:	:	PUNCT
cana-4456	2	76	15	15	NUM
cana-4456	2	77	-	-	NUM
cana-4456	2	78	02	02	NUM
cana-4456	2	79	-	-	PUNCT
cana-4456	2	80	2025	2025	NUM
cana-4456	2	81	accepted	accept	VERB
cana-4456	2	82	:	:	PUNCT
cana-4456	2	83	01	01	NUM
cana-4456	2	84	-	-	SYM
cana-4456	2	85	03	03	NUM
cana-4456	2	86	-	-	PUNCT
cana-4456	2	87	2025	2025	NUM
cana-4456	2	88	abstract	abstract	NOUN
cana-4456	2	89	:	:	PUNCT
cana-4456	2	90	the	the	DET
cana-4456	2	91	purpose	purpose	NOUN
cana-4456	2	92	of	of	ADP
cana-4456	2	93	this	this	DET
cana-4456	2	94	paper	paper	NOUN
cana-4456	2	95	is	be	AUX
cana-4456	2	96	to	to	PART
cana-4456	2	97	present	present	VERB
cana-4456	2	98	an	an	DET
cana-4456	2	99	efficient	efficient	ADJ
cana-4456	2	100	localized	localize	VERB
cana-4456	2	101	meshless	meshless	ADJ
cana-4456	2	102	methods	method	NOUN
cana-4456	2	103	based	base	VERB
cana-4456	2	104	on	on	ADP
cana-4456	2	105	radial	radial	ADJ
cana-4456	2	106	basis	basis	NOUN
cana-4456	2	107	functions	function	NOUN
cana-4456	2	108	to	to	PART
cana-4456	2	109	accurately	accurately	ADV
cana-4456	2	110	analyze	analyze	VERB
cana-4456	2	111	the	the	DET
cana-4456	2	112	shallow	shallow	ADJ
cana-4456	2	113	water	water	NOUN
cana-4456	2	114	equations	equation	NOUN
cana-4456	2	115	(	(	PUNCT
cana-4456	2	116	swes	swes	X
cana-4456	2	117	)	)	PUNCT
cana-4456	2	118	in	in	ADP
cana-4456	2	119	open	open	ADJ
cana-4456	2	120	channels	channel	NOUN
cana-4456	2	121	.	.	PUNCT
cana-4456	3	1	it	it	PRON
cana-4456	3	2	is	be	AUX
cana-4456	3	3	a	a	DET
cana-4456	3	4	hyperbolic	hyperbolic	ADJ
cana-4456	3	5	system	system	NOUN
cana-4456	3	6	of	of	ADP
cana-4456	3	7	first	first	ADJ
cana-4456	3	8	-	-	PUNCT
cana-4456	3	9	order	order	NOUN
cana-4456	3	10	nonlinear	nonlinear	ADJ
cana-4456	3	11	partial	partial	ADJ
cana-4456	3	12	differential	differential	NOUN
cana-4456	3	13	equations	equation	NOUN
cana-4456	3	14	.	.	PUNCT
cana-4456	4	1	due	due	ADP
cana-4456	4	2	to	to	ADP
cana-4456	4	3	their	their	PRON
cana-4456	4	4	classification	classification	NOUN
cana-4456	4	5	as	as	ADP
cana-4456	4	6	advection	advection	NOUN
cana-4456	4	7	equations	equation	NOUN
cana-4456	4	8	,	,	PUNCT
cana-4456	4	9	they	they	PRON
cana-4456	4	10	allow	allow	VERB
cana-4456	4	11	for	for	ADP
cana-4456	4	12	discontinuous	discontinuous	ADJ
cana-4456	4	13	solutions	solution	NOUN
cana-4456	4	14	,	,	PUNCT
cana-4456	4	15	often	often	ADV
cana-4456	4	16	characterized	characterize	VERB
cana-4456	4	17	by	by	ADP
cana-4456	4	18	shock	shock	NOUN
cana-4456	4	19	behaviour	behaviour	NOUN
cana-4456	4	20	in	in	ADP
cana-4456	4	21	simulations	simulation	NOUN
cana-4456	4	22	.	.	PUNCT
cana-4456	5	1	therefore	therefore	ADV
cana-4456	5	2	,	,	PUNCT
cana-4456	5	3	the	the	DET
cana-4456	5	4	development	development	NOUN
cana-4456	5	5	of	of	ADP
cana-4456	5	6	an	an	DET
cana-4456	5	7	efficient	efficient	ADJ
cana-4456	5	8	and	and	CCONJ
cana-4456	5	9	accurate	accurate	ADJ
cana-4456	5	10	numerical	numerical	ADJ
cana-4456	5	11	model	model	NOUN
cana-4456	5	12	for	for	ADP
cana-4456	5	13	analyzing	analyze	VERB
cana-4456	5	14	the	the	DET
cana-4456	5	15	swes	swe	NOUN
cana-4456	5	16	holds	hold	VERB
cana-4456	5	17	critical	critical	ADJ
cana-4456	5	18	importance	importance	NOUN
cana-4456	5	19	in	in	ADP
cana-4456	5	20	scientific	scientific	ADJ
cana-4456	5	21	research	research	NOUN
cana-4456	5	22	.	.	PUNCT
cana-4456	6	1	to	to	PART
cana-4456	6	2	address	address	VERB
cana-4456	6	3	non	non	ADJ
cana-4456	6	4	-	-	ADJ
cana-4456	6	5	physical	physical	ADJ
cana-4456	6	6	oscillations	oscillation	NOUN
cana-4456	6	7	near	near	ADP
cana-4456	6	8	discontinuities	discontinuity	NOUN
cana-4456	6	9	,	,	PUNCT
cana-4456	6	10	we	we	PRON
cana-4456	6	11	developed	develop	VERB
cana-4456	6	12	a	a	DET
cana-4456	6	13	technique	technique	NOUN
cana-4456	6	14	involving	involve	VERB
cana-4456	6	15	artificial	artificial	ADJ
cana-4456	6	16	viscosity	viscosity	NOUN
cana-4456	6	17	,	,	PUNCT
cana-4456	6	18	which	which	PRON
cana-4456	6	19	is	be	AUX
cana-4456	6	20	integrated	integrate	VERB
cana-4456	6	21	with	with	ADP
cana-4456	6	22	the	the	DET
cana-4456	6	23	local	local	ADJ
cana-4456	6	24	meshless	meshless	ADJ
cana-4456	6	25	methods	method	NOUN
cana-4456	6	26	for	for	ADP
cana-4456	6	27	spatial	spatial	ADJ
cana-4456	6	28	discretization	discretization	NOUN
cana-4456	6	29	of	of	ADP
cana-4456	6	30	the	the	DET
cana-4456	6	31	swes	swes	NOUN
cana-4456	6	32	,	,	PUNCT
cana-4456	6	33	while	while	SCONJ
cana-4456	6	34	temporal	temporal	ADJ
cana-4456	6	35	discretization	discretization	NOUN
cana-4456	6	36	is	be	AUX
cana-4456	6	37	achieved	achieve	VERB
cana-4456	6	38	using	use	VERB
cana-4456	6	39	the	the	DET
cana-4456	6	40	fourth	fourth	ADJ
cana-4456	6	41	-	-	PUNCT
cana-4456	6	42	order	order	NOUN
cana-4456	6	43	runge	runge	NOUN
cana-4456	6	44	-	-	PUNCT
cana-4456	6	45	kutta	kutta	NOUN
cana-4456	6	46	method	method	NOUN
cana-4456	6	47	.	.	PUNCT
cana-4456	7	1	a	a	DET
cana-4456	7	2	series	series	NOUN
cana-4456	7	3	of	of	ADP
cana-4456	7	4	experiments	experiment	NOUN
cana-4456	7	5	has	have	AUX
cana-4456	7	6	been	be	AUX
cana-4456	7	7	conducted	conduct	VERB
cana-4456	7	8	to	to	PART
cana-4456	7	9	evaluate	evaluate	VERB
cana-4456	7	10	the	the	DET
cana-4456	7	11	effectiveness	effectiveness	NOUN
cana-4456	7	12	and	and	CCONJ
cana-4456	7	13	accuracy	accuracy	NOUN
cana-4456	7	14	of	of	ADP
cana-4456	7	15	the	the	DET
cana-4456	7	16	suggested	suggest	VERB
cana-4456	7	17	methods	method	NOUN
cana-4456	7	18	.	.	PUNCT
cana-4456	8	1	these	these	DET
cana-4456	8	2	experiments	experiment	NOUN
cana-4456	8	3	included	include	VERB
cana-4456	8	4	examining	examine	VERB
cana-4456	8	5	flow	flow	NOUN
cana-4456	8	6	at	at	ADP
cana-4456	8	7	a	a	DET
cana-4456	8	8	steady	steady	ADJ
cana-4456	8	9	state	state	NOUN
cana-4456	8	10	with	with	ADP
cana-4456	8	11	and	and	CCONJ
cana-4456	8	12	without	without	ADP
cana-4456	8	13	friction	friction	NOUN
cana-4456	8	14	,	,	PUNCT
cana-4456	8	15	as	as	ADV
cana-4456	8	16	well	well	ADV
cana-4456	8	17	as	as	ADP
cana-4456	8	18	studying	study	VERB
cana-4456	8	19	the	the	DET
cana-4456	8	20	dam	dam	NOUN
cana-4456	8	21	-	-	PUNCT
cana-4456	8	22	break	break	NOUN
cana-4456	8	23	scenario	scenario	NOUN
cana-4456	8	24	on	on	ADP
cana-4456	8	25	a	a	DET
cana-4456	8	26	wet	wet	ADJ
cana-4456	8	27	bed	bed	NOUN
cana-4456	8	28	.	.	PUNCT
cana-4456	9	1	the	the	DET
cana-4456	9	2	results	result	NOUN
cana-4456	9	3	compared	compare	VERB
cana-4456	9	4	with	with	ADP
cana-4456	9	5	analytical	analytical	ADJ
cana-4456	9	6	solutions	solution	NOUN
cana-4456	9	7	,	,	PUNCT
cana-4456	9	8	demonstrate	demonstrate	VERB
cana-4456	9	9	that	that	SCONJ
cana-4456	9	10	the	the	DET
cana-4456	9	11	artificial	artificial	ADJ
cana-4456	9	12	viscosity	viscosity	NOUN
cana-4456	9	13	combined	combine	VERB
cana-4456	9	14	with	with	ADP
cana-4456	9	15	the	the	DET
cana-4456	9	16	proposed	propose	VERB
cana-4456	9	17	methods	method	NOUN
cana-4456	9	18	proficiently	proficiently	ADV
cana-4456	9	19	capture	capture	VERB
cana-4456	9	20	shocks	shock	NOUN
cana-4456	9	21	and	and	CCONJ
cana-4456	9	22	effectively	effectively	ADV
cana-4456	9	23	handles	handle	VERB
cana-4456	9	24	discontinuous	discontinuous	ADJ
cana-4456	9	25	flow	flow	NOUN
cana-4456	9	26	by	by	ADP
cana-4456	9	27	introducing	introduce	VERB
cana-4456	9	28	an	an	DET
cana-4456	9	29	appropriate	appropriate	ADJ
cana-4456	9	30	viscosity	viscosity	NOUN
cana-4456	9	31	coefficient	coefficient	NOUN
cana-4456	9	32	into	into	ADP
cana-4456	9	33	the	the	DET
cana-4456	9	34	equations	equation	NOUN
cana-4456	9	35	.	.	PUNCT
cana-4456	10	1	overall	overall	ADV
cana-4456	10	2	,	,	PUNCT
cana-4456	10	3	the	the	DET
cana-4456	10	4	results	result	NOUN
cana-4456	10	5	are	be	AUX
cana-4456	10	6	satisfactory	satisfactory	ADJ
cana-4456	10	7	and	and	CCONJ
cana-4456	10	8	show	show	VERB
cana-4456	10	9	good	good	ADJ
cana-4456	10	10	agreement	agreement	NOUN
cana-4456	10	11	.	.	PUNCT
cana-4456	11	1	keywords	keyword	NOUN
cana-4456	11	2	:	:	PUNCT
cana-4456	11	3	shallow	shallow	ADJ
cana-4456	11	4	water	water	NOUN
cana-4456	11	5	equations	equation	NOUN
cana-4456	11	6	,	,	PUNCT
cana-4456	11	7	open	open	ADJ
cana-4456	11	8	channel	channel	NOUN
cana-4456	11	9	,	,	PUNCT
cana-4456	11	10	radial	radial	ADJ
cana-4456	11	11	basis	basis	NOUN
cana-4456	11	12	function	function	NOUN
cana-4456	11	13	partition	partition	NOUN
cana-4456	11	14	of	of	ADP
cana-4456	11	15	unity	unity	NOUN
cana-4456	11	16	method	method	NOUN
cana-4456	11	17	(	(	PUNCT
cana-4456	11	18	rbf	rbf	PROPN
cana-4456	11	19	-	-	PROPN
cana-4456	11	20	pum	pum	PROPN
cana-4456	11	21	)	)	PUNCT
cana-4456	11	22	,	,	PUNCT
cana-4456	11	23	radial	radial	ADJ
cana-4456	11	24	basis	basis	NOUN
cana-4456	11	25	function	function	NOUN
cana-4456	11	26	finite	finite	NOUN
cana-4456	11	27	difference	difference	NOUN
cana-4456	11	28	(	(	PUNCT
cana-4456	11	29	rbf	rbf	PROPN
cana-4456	11	30	-	-	PUNCT
cana-4456	11	31	fd	fd	PROPN
cana-4456	11	32	)	)	PUNCT
cana-4456	11	33	method	method	NOUN
cana-4456	11	34	,	,	PUNCT
cana-4456	11	35	qr	qr	NOUN
cana-4456	11	36	factorization	factorization	NOUN
cana-4456	11	37	.	.	PUNCT
cana-4456	12	1	1	1	X
cana-4456	12	2	.	.	X
cana-4456	12	3	introduction	introduction	NOUN
cana-4456	12	4	the	the	DET
cana-4456	12	5	shallow	shallow	ADJ
cana-4456	12	6	water	water	NOUN
cana-4456	12	7	equations	equation	NOUN
cana-4456	12	8	(	(	PUNCT
cana-4456	12	9	swes	swes	PROPN
cana-4456	12	10	)	)	PUNCT
cana-4456	12	11	were	be	AUX
cana-4456	12	12	first	first	ADV
cana-4456	12	13	proposed	propose	VERB
cana-4456	12	14	in	in	ADP
cana-4456	12	15	1871	1871	NUM
cana-4456	12	16	by	by	ADP
cana-4456	12	17	saint	saint	NOUN
cana-4456	12	18	-	-	PUNCT
cana-4456	12	19	venant	venant	NOUN
cana-4456	13	1	[	[	X
cana-4456	13	2	1	1	NUM
cana-4456	13	3	]	]	PUNCT
cana-4456	13	4	to	to	PART
cana-4456	13	5	describe	describe	VERB
cana-4456	13	6	various	various	ADJ
cana-4456	13	7	applications	application	NOUN
cana-4456	13	8	in	in	ADP
cana-4456	13	9	ocean	ocean	NOUN
cana-4456	13	10	and	and	CCONJ
cana-4456	13	11	hydraulic	hydraulic	ADJ
cana-4456	13	12	engineering	engineering	NOUN
cana-4456	13	13	,	,	PUNCT
cana-4456	13	14	such	such	ADJ
cana-4456	13	15	as	as	ADP
cana-4456	13	16	coastal	coastal	ADJ
cana-4456	13	17	flow	flow	NOUN
cana-4456	13	18	,	,	PUNCT
cana-4456	13	19	open	open	ADJ
cana-4456	13	20	-	-	PUNCT
cana-4456	13	21	channel	channel	NOUN
cana-4456	13	22	flow	flow	NOUN
cana-4456	13	23	in	in	ADP
cana-4456	13	24	natural	natural	ADJ
cana-4456	13	25	rivers	river	NOUN
cana-4456	13	26	and	and	CCONJ
cana-4456	13	27	prismatic	prismatic	ADJ
cana-4456	13	28	channels	channel	NOUN
cana-4456	13	29	,	,	PUNCT
cana-4456	13	30	flood	flood	NOUN
cana-4456	13	31	waves	wave	NOUN
cana-4456	13	32	,	,	PUNCT
cana-4456	13	33	failure	failure	NOUN
cana-4456	13	34	of	of	ADP
cana-4456	13	35	dams	dam	NOUN
cana-4456	13	36	,	,	PUNCT
cana-4456	13	37	etc	etc	X
cana-4456	13	38	.	.	X
cana-4456	14	1	under	under	ADP
cana-4456	14	2	some	some	DET
cana-4456	14	3	essential	essential	ADJ
cana-4456	14	4	assumptions	assumption	NOUN
cana-4456	14	5	[	[	X
cana-4456	14	6	2	2	NUM
cana-4456	14	7	]	]	PUNCT
cana-4456	14	8	,	,	PUNCT
cana-4456	14	9	the	the	DET
cana-4456	14	10	swes	swe	NOUN
cana-4456	14	11	are	be	AUX
cana-4456	14	12	derived	derive	VERB
cana-4456	14	13	by	by	ADP
cana-4456	14	14	three	three	NUM
cana-4456	14	15	-	-	PUNCT
cana-4456	14	16	dimensional	dimensional	ADJ
cana-4456	14	17	navier	navier	NOUN
cana-4456	14	18	-	-	PUNCT
cana-4456	14	19	stokes	stoke	NOUN
cana-4456	14	20	equations	equation	NOUN
cana-4456	14	21	where	where	SCONJ
cana-4456	14	22	the	the	DET
cana-4456	14	23	horizontal	horizontal	ADJ
cana-4456	14	24	wave	wave	NOUN
cana-4456	14	25	length	length	NOUN
cana-4456	14	26	is	be	AUX
cana-4456	14	27	much	much	ADV
cana-4456	14	28	larger	large	ADJ
cana-4456	14	29	than	than	ADP
cana-4456	14	30	the	the	DET
cana-4456	14	31	depth	depth	NOUN
cana-4456	14	32	of	of	ADP
cana-4456	14	33	the	the	DET
cana-4456	14	34	fluid	fluid	NOUN
cana-4456	14	35	.	.	PUNCT
cana-4456	15	1	swes	swe	NOUN
cana-4456	15	2	form	form	VERB
cana-4456	15	3	a	a	DET
cana-4456	15	4	system	system	NOUN
cana-4456	15	5	of	of	ADP
cana-4456	15	6	non	non	ADJ
cana-4456	15	7	-	-	ADJ
cana-4456	15	8	linear	linear	ADJ
cana-4456	15	9	hyperbolic	hyperbolic	ADJ
cana-4456	15	10	partial	partial	ADJ
cana-4456	15	11	differential	differential	NOUN
cana-4456	15	12	equations	equation	NOUN
cana-4456	15	13	(	(	PUNCT
cana-4456	15	14	pdes	pde	NOUN
cana-4456	15	15	)	)	PUNCT
cana-4456	15	16	governed	govern	VERB
cana-4456	15	17	by	by	ADP
cana-4456	15	18	conservation	conservation	NOUN
cana-4456	15	19	of	of	ADP
cana-4456	15	20	mass	mass	NOUN
cana-4456	15	21	and	and	CCONJ
cana-4456	15	22	balance	balance	NOUN
cana-4456	15	23	of	of	ADP
cana-4456	15	24	momentum	momentum	NOUN
cana-4456	15	25	.	.	PUNCT
cana-4456	16	1	the	the	DET
cana-4456	16	2	critical	critical	ADJ
cana-4456	16	3	problem	problem	NOUN
cana-4456	16	4	in	in	ADP
cana-4456	16	5	solving	solve	VERB
cana-4456	16	6	this	this	DET
cana-4456	16	7	system	system	NOUN
cana-4456	16	8	of	of	ADP
cana-4456	16	9	equations	equation	NOUN
cana-4456	16	10	is	be	AUX
cana-4456	16	11	the	the	DET
cana-4456	16	12	spurious	spurious	ADJ
cana-4456	16	13	oscillation	oscillation	NOUN
cana-4456	16	14	happens	happen	VERB
cana-4456	16	15	in	in	ADP
cana-4456	16	16	the	the	DET
cana-4456	16	17	discontinuous	discontinuous	ADJ
cana-4456	16	18	areas	area	NOUN
cana-4456	16	19	such	such	ADJ
cana-4456	16	20	as	as	ADP
cana-4456	16	21	shock	shock	NOUN
cana-4456	16	22	waves	wave	NOUN
cana-4456	16	23	,	,	PUNCT
cana-4456	16	24	dam	dam	NOUN
cana-4456	16	25	break	break	NOUN
cana-4456	16	26	,	,	PUNCT
cana-4456	16	27	or	or	CCONJ
cana-4456	16	28	hydraulic	hydraulic	ADJ
cana-4456	16	29	jump	jump	NOUN
cana-4456	16	30	problems	problem	NOUN
cana-4456	16	31	.	.	PUNCT
cana-4456	17	1	the	the	DET
cana-4456	17	2	analytical	analytical	ADJ
cana-4456	17	3	solution	solution	NOUN
cana-4456	17	4	for	for	ADP
cana-4456	17	5	these	these	DET
cana-4456	17	6	problems	problem	NOUN
cana-4456	17	7	is	be	AUX
cana-4456	17	8	only	only	ADV
cana-4456	17	9	available	available	ADJ
cana-4456	17	10	for	for	ADP
cana-4456	17	11	a	a	DET
cana-4456	17	12	limited	limited	ADJ
cana-4456	17	13	number	number	NOUN
cana-4456	17	14	of	of	ADP
cana-4456	17	15	special	special	ADJ
cana-4456	17	16	cases	case	NOUN
cana-4456	17	17	[	[	X
cana-4456	17	18	3	3	NUM
cana-4456	17	19	]	]	PUNCT
cana-4456	17	20	.	.	PUNCT
cana-4456	18	1	therefore	therefore	ADV
cana-4456	18	2	it	it	PRON
cana-4456	18	3	is	be	AUX
cana-4456	18	4	significant	significant	ADJ
cana-4456	18	5	to	to	PART
cana-4456	18	6	develop	develop	VERB
cana-4456	18	7	a	a	DET
cana-4456	18	8	reliable	reliable	ADJ
cana-4456	18	9	and	and	CCONJ
cana-4456	18	10	accurate	accurate	ADJ
cana-4456	18	11	numerical	numerical	ADJ
cana-4456	18	12	solver	solver	NOUN
cana-4456	18	13	.	.	PUNCT
cana-4456	19	1	mailto:mariam.ijerch@edu.uiz.ac.ma	mailto:mariam.ijerch@edu.uiz.ac.ma	PROPN
cana-4456	19	2	mailto:m.sadik@uiz.ac.ma	mailto:m.sadik@uiz.ac.ma	PROPN
cana-4456	19	3	communications	communication	NOUN
cana-4456	19	4	on	on	ADP
cana-4456	19	5	applied	apply	VERB
cana-4456	19	6	nonlinear	nonlinear	ADJ
cana-4456	19	7	analysis	analysis	NOUN
cana-4456	19	8	issn	issn	NOUN
cana-4456	19	9	:	:	PUNCT
cana-4456	19	10	1074	1074	NUM
cana-4456	19	11	-	-	PUNCT
cana-4456	19	12	133x	133x	NUM
cana-4456	19	13	vol	vol	NOUN
cana-4456	19	14	32	32	NUM
cana-4456	19	15	no	no	NOUN
cana-4456	19	16	.	.	PUNCT
cana-4456	20	1	9s	9s	NUM
cana-4456	20	2	(	(	PUNCT
cana-4456	20	3	2025	2025	NUM
cana-4456	20	4	)	)	PUNCT
cana-4456	20	5	2168	2168	NUM
cana-4456	20	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	20	7	in	in	ADP
cana-4456	20	8	the	the	DET
cana-4456	20	9	past	past	ADJ
cana-4456	20	10	decades	decade	NOUN
cana-4456	20	11	,	,	PUNCT
cana-4456	20	12	plenty	plenty	NOUN
cana-4456	20	13	of	of	ADP
cana-4456	20	14	mesh	mesh	NOUN
cana-4456	20	15	-	-	PUNCT
cana-4456	20	16	based	base	VERB
cana-4456	20	17	numerical	numerical	ADJ
cana-4456	20	18	models	model	NOUN
cana-4456	20	19	have	have	AUX
cana-4456	20	20	been	be	AUX
cana-4456	20	21	developed	develop	VERB
cana-4456	20	22	for	for	ADP
cana-4456	20	23	solving	solve	VERB
cana-4456	20	24	the	the	DET
cana-4456	20	25	swes	swe	NOUN
cana-4456	20	26	,	,	PUNCT
cana-4456	20	27	such	such	ADJ
cana-4456	20	28	as	as	ADP
cana-4456	20	29	the	the	DET
cana-4456	20	30	finite	finite	ADJ
cana-4456	20	31	difference	difference	NOUN
cana-4456	20	32	method	method	NOUN
cana-4456	20	33	(	(	PUNCT
cana-4456	20	34	fdm	fdm	NOUN
cana-4456	20	35	)	)	PUNCT
cana-4456	21	1	[	[	X
cana-4456	21	2	4	4	NUM
cana-4456	21	3	]	]	PUNCT
cana-4456	21	4	,	,	PUNCT
cana-4456	21	5	finite	finite	PROPN
cana-4456	21	6	element	element	NOUN
cana-4456	21	7	method	method	NOUN
cana-4456	21	8	(	(	PUNCT
cana-4456	21	9	fem	fem	NOUN
cana-4456	21	10	)	)	PUNCT
cana-4456	22	1	[	[	X
cana-4456	22	2	5	5	NUM
cana-4456	22	3	]	]	PUNCT
cana-4456	22	4	,	,	PUNCT
cana-4456	22	5	and	and	CCONJ
cana-4456	22	6	finite	finite	ADJ
cana-4456	22	7	volume	volume	NOUN
cana-4456	22	8	method	method	NOUN
cana-4456	22	9	(	(	PUNCT
cana-4456	22	10	fvm	fvm	ADV
cana-4456	22	11	)	)	PUNCT
cana-4456	23	1	[	[	X
cana-4456	23	2	6	6	NUM
cana-4456	23	3	,	,	PUNCT
cana-4456	23	4	7	7	NUM
cana-4456	23	5	]	]	PUNCT
cana-4456	23	6	.	.	PUNCT
cana-4456	24	1	however	however	ADV
cana-4456	24	2	,	,	PUNCT
cana-4456	24	3	for	for	ADP
cana-4456	24	4	multidimensional	multidimensional	ADJ
cana-4456	24	5	problems	problem	NOUN
cana-4456	24	6	defined	define	VERB
cana-4456	24	7	on	on	ADP
cana-4456	24	8	a	a	DET
cana-4456	24	9	complex	complex	ADJ
cana-4456	24	10	geometries	geometry	NOUN
cana-4456	24	11	,	,	PUNCT
cana-4456	24	12	mesh	mesh	NOUN
cana-4456	24	13	generation	generation	NOUN
cana-4456	24	14	have	have	VERB
cana-4456	24	15	a	a	DET
cana-4456	24	16	common	common	ADJ
cana-4456	24	17	difficulty	difficulty	NOUN
cana-4456	24	18	that	that	SCONJ
cana-4456	24	19	it	it	PRON
cana-4456	24	20	is	be	AUX
cana-4456	24	21	a	a	DET
cana-4456	24	22	time	time	NOUN
cana-4456	24	23	-	-	PUNCT
cana-4456	24	24	consuming	consume	VERB
cana-4456	24	25	and	and	CCONJ
cana-4456	24	26	their	their	PRON
cana-4456	24	27	performance	performance	NOUN
cana-4456	24	28	depends	depend	VERB
cana-4456	24	29	on	on	ADP
cana-4456	24	30	the	the	DET
cana-4456	24	31	quality	quality	NOUN
cana-4456	24	32	of	of	ADP
cana-4456	24	33	the	the	DET
cana-4456	24	34	mesh	mesh	NOUN
cana-4456	24	35	.	.	PUNCT
cana-4456	25	1	to	to	PART
cana-4456	25	2	overcome	overcome	VERB
cana-4456	25	3	these	these	DET
cana-4456	25	4	difficulties	difficulty	NOUN
cana-4456	25	5	,	,	PUNCT
cana-4456	25	6	many	many	ADJ
cana-4456	25	7	researchers	researcher	NOUN
cana-4456	25	8	have	have	AUX
cana-4456	25	9	paid	pay	VERB
cana-4456	25	10	attention	attention	NOUN
cana-4456	25	11	to	to	PART
cana-4456	25	12	use	use	VERB
cana-4456	25	13	the	the	DET
cana-4456	25	14	newly	newly	ADV
cana-4456	25	15	developed	develop	VERB
cana-4456	25	16	meshless	meshless	ADJ
cana-4456	25	17	method	method	NOUN
cana-4456	25	18	as	as	ADP
cana-4456	25	19	the	the	DET
cana-4456	25	20	promising	promising	ADJ
cana-4456	25	21	alternative	alternative	NOUN
cana-4456	25	22	to	to	ADP
cana-4456	25	23	traditional	traditional	ADJ
cana-4456	25	24	methods	method	NOUN
cana-4456	25	25	which	which	PRON
cana-4456	25	26	have	have	AUX
cana-4456	25	27	been	be	AUX
cana-4456	25	28	employed	employ	VERB
cana-4456	25	29	to	to	PART
cana-4456	25	30	analyse	analyse	VERB
cana-4456	25	31	various	various	ADJ
cana-4456	25	32	problems	problem	NOUN
cana-4456	25	33	.	.	PUNCT
cana-4456	26	1	the	the	DET
cana-4456	26	2	meshless	meshless	ADJ
cana-4456	26	3	methods	method	NOUN
cana-4456	26	4	were	be	AUX
cana-4456	26	5	also	also	ADV
cana-4456	26	6	adopted	adopt	VERB
cana-4456	26	7	to	to	PART
cana-4456	26	8	solve	solve	VERB
cana-4456	26	9	swes	swe	NOUN
cana-4456	26	10	by	by	ADP
cana-4456	26	11	many	many	ADJ
cana-4456	26	12	scholars	scholar	NOUN
cana-4456	26	13	.	.	PUNCT
cana-4456	27	1	among	among	ADP
cana-4456	27	2	them	they	PRON
cana-4456	27	3	,	,	PUNCT
cana-4456	27	4	the	the	DET
cana-4456	27	5	development	development	NOUN
cana-4456	27	6	of	of	ADP
cana-4456	27	7	meshless	meshless	ADJ
cana-4456	27	8	methods	method	NOUN
cana-4456	27	9	based	base	VERB
cana-4456	27	10	on	on	ADP
cana-4456	27	11	radial	radial	ADJ
cana-4456	27	12	basis	basis	NOUN
cana-4456	27	13	functions	function	NOUN
cana-4456	27	14	(	(	PUNCT
cana-4456	27	15	rbfs	rbfs	NOUN
cana-4456	27	16	)	)	PUNCT
cana-4456	27	17	,	,	PUNCT
cana-4456	27	18	such	such	ADJ
cana-4456	27	19	as	as	ADP
cana-4456	27	20	multiquadric	multiquadric	ADJ
cana-4456	27	21	method	method	NOUN
cana-4456	27	22	[	[	X
cana-4456	27	23	8	8	NUM
cana-4456	27	24	]	]	PUNCT
cana-4456	27	25	,	,	PUNCT
cana-4456	27	26	compactly	compactly	ADV
cana-4456	27	27	supported	support	VERB
cana-4456	27	28	rbf	rbf	PROPN
cana-4456	27	29	(	(	PUNCT
cana-4456	27	30	csrbf	csrbf	PROPN
cana-4456	27	31	)	)	PUNCT
cana-4456	28	1	[	[	X
cana-4456	28	2	9	9	NUM
cana-4456	28	3	]	]	PUNCT
cana-4456	28	4	,	,	PUNCT
cana-4456	28	5	local	local	ADJ
cana-4456	28	6	radial	radial	ADJ
cana-4456	28	7	basis	basis	NOUN
cana-4456	28	8	function	function	NOUN
cana-4456	28	9	based	base	VERB
cana-4456	28	10	differential	differential	ADJ
cana-4456	28	11	quadrature	quadrature	NOUN
cana-4456	28	12	method	method	NOUN
cana-4456	28	13	(	(	PUNCT
cana-4456	28	14	lrbfdqm	lrbfdqm	NOUN
cana-4456	28	15	)	)	PUNCT
cana-4456	29	1	[	[	X
cana-4456	29	2	10	10	NUM
cana-4456	29	3	]	]	PUNCT
cana-4456	29	4	,	,	PUNCT
cana-4456	29	5	extrapolated	extrapolate	VERB
cana-4456	29	6	local	local	ADJ
cana-4456	29	7	radial	radial	ADJ
cana-4456	29	8	basis	basis	NOUN
cana-4456	29	9	functions	function	NOUN
cana-4456	29	10	collocation	collocation	NOUN
cana-4456	29	11	method	method	NOUN
cana-4456	29	12	(	(	PUNCT
cana-4456	29	13	elrbfcm	elrbfcm	X
cana-4456	29	14	)	)	PUNCT
cana-4456	30	1	[	[	X
cana-4456	30	2	11	11	NUM
cana-4456	30	3	]	]	PUNCT
cana-4456	30	4	,	,	PUNCT
cana-4456	30	5	and	and	CCONJ
cana-4456	30	6	others	other	NOUN
cana-4456	30	7	.	.	PUNCT
cana-4456	31	1	the	the	DET
cana-4456	31	2	main	main	ADJ
cana-4456	31	3	advantages	advantage	NOUN
cana-4456	31	4	of	of	ADP
cana-4456	31	5	rbf	rbf	PROPN
cana-4456	31	6	-	-	PUNCT
cana-4456	31	7	based	base	VERB
cana-4456	31	8	methods	method	NOUN
cana-4456	31	9	for	for	ADP
cana-4456	31	10	solving	solve	VERB
cana-4456	31	11	partial	partial	ADJ
cana-4456	31	12	differential	differential	ADJ
cana-4456	31	13	equations	equation	NOUN
cana-4456	31	14	lie	lie	VERB
cana-4456	31	15	in	in	ADP
cana-4456	31	16	their	their	PRON
cana-4456	31	17	simplicity	simplicity	NOUN
cana-4456	31	18	,	,	PUNCT
cana-4456	31	19	flexibility	flexibility	NOUN
cana-4456	31	20	,	,	PUNCT
cana-4456	31	21	and	and	CCONJ
cana-4456	31	22	applicability	applicability	NOUN
cana-4456	31	23	to	to	ADP
cana-4456	31	24	various	various	ADJ
cana-4456	31	25	pdes	pde	NOUN
cana-4456	31	26	.	.	PUNCT
cana-4456	32	1	they	they	PRON
cana-4456	32	2	are	be	AUX
cana-4456	32	3	particularly	particularly	ADV
cana-4456	32	4	effective	effective	ADJ
cana-4456	32	5	in	in	ADP
cana-4456	32	6	handling	handle	VERB
cana-4456	32	7	high	high	ADJ
cana-4456	32	8	-	-	PUNCT
cana-4456	32	9	dimensional	dimensional	ADJ
cana-4456	32	10	problems	problem	NOUN
cana-4456	32	11	with	with	ADP
cana-4456	32	12	complex	complex	ADJ
cana-4456	32	13	geometries	geometry	NOUN
cana-4456	32	14	.	.	PUNCT
cana-4456	33	1	since	since	SCONJ
cana-4456	33	2	the	the	DET
cana-4456	33	3	shallow	shallow	ADJ
cana-4456	33	4	water	water	NOUN
cana-4456	33	5	equations	equation	NOUN
cana-4456	33	6	are	be	AUX
cana-4456	33	7	a	a	DET
cana-4456	33	8	hyperbolic	hyperbolic	ADJ
cana-4456	33	9	non	non	ADJ
cana-4456	33	10	-	-	ADJ
cana-4456	33	11	linear	linear	ADJ
cana-4456	33	12	partial	partial	ADJ
cana-4456	33	13	differential	differential	NOUN
cana-4456	33	14	equations	equation	NOUN
cana-4456	33	15	,	,	PUNCT
cana-4456	33	16	the	the	DET
cana-4456	33	17	information	information	NOUN
cana-4456	33	18	of	of	ADP
cana-4456	33	19	characteristic	characteristic	ADJ
cana-4456	33	20	and	and	CCONJ
cana-4456	33	21	the	the	DET
cana-4456	33	22	correct	correct	ADJ
cana-4456	33	23	directions	direction	NOUN
cana-4456	33	24	of	of	ADP
cana-4456	33	25	wave	wave	NOUN
cana-4456	33	26	transmission	transmission	NOUN
cana-4456	33	27	are	be	AUX
cana-4456	33	28	quite	quite	ADV
cana-4456	33	29	important	important	ADJ
cana-4456	33	30	to	to	ADP
cana-4456	33	31	numerical	numerical	PROPN
cana-4456	33	32	simulation	simulation	PROPN
cana-4456	33	33	.	.	PUNCT
cana-4456	34	1	the	the	DET
cana-4456	34	2	first	first	ADJ
cana-4456	34	3	author	author	NOUN
cana-4456	34	4	who	who	PRON
cana-4456	34	5	introduced	introduce	VERB
cana-4456	34	6	the	the	DET
cana-4456	34	7	radial	radial	ADJ
cana-4456	34	8	basis	basis	NOUN
cana-4456	34	9	functions	function	NOUN
cana-4456	34	10	method	method	NOUN
cana-4456	34	11	in	in	ADP
cana-4456	34	12	the	the	DET
cana-4456	34	13	field	field	NOUN
cana-4456	34	14	of	of	ADP
cana-4456	34	15	pdes	pde	NOUN
cana-4456	34	16	was	be	AUX
cana-4456	34	17	kansa	kansa	VERB
cana-4456	34	18	in	in	ADP
cana-4456	34	19	1990	1990	NUM
cana-4456	34	20	[	[	X
cana-4456	34	21	12	12	NUM
cana-4456	34	22	,	,	PUNCT
cana-4456	34	23	13	13	NUM
cana-4456	34	24	]	]	PUNCT
cana-4456	34	25	.	.	PUNCT
cana-4456	35	1	he	he	PRON
cana-4456	35	2	developed	develop	VERB
cana-4456	35	3	the	the	DET
cana-4456	35	4	global	global	ADJ
cana-4456	35	5	rbf	rbf	PROPN
cana-4456	35	6	method	method	NOUN
cana-4456	35	7	which	which	PRON
cana-4456	35	8	is	be	AUX
cana-4456	35	9	a	a	DET
cana-4456	35	10	numerical	numerical	ADJ
cana-4456	35	11	method	method	NOUN
cana-4456	35	12	that	that	PRON
cana-4456	35	13	gives	give	VERB
cana-4456	35	14	an	an	DET
cana-4456	35	15	approximate	approximate	ADJ
cana-4456	35	16	solution	solution	NOUN
cana-4456	35	17	for	for	ADP
cana-4456	35	18	pdes	pde	NOUN
cana-4456	35	19	.	.	PUNCT
cana-4456	36	1	it	it	PRON
cana-4456	36	2	can	can	AUX
cana-4456	36	3	be	be	AUX
cana-4456	36	4	considered	consider	VERB
cana-4456	36	5	as	as	ADP
cana-4456	36	6	one	one	NUM
cana-4456	36	7	of	of	ADP
cana-4456	36	8	the	the	DET
cana-4456	36	9	collocation	collocation	NOUN
cana-4456	36	10	methods	method	NOUN
cana-4456	36	11	which	which	PRON
cana-4456	36	12	are	be	AUX
cana-4456	36	13	efficient	efficient	ADJ
cana-4456	36	14	and	and	CCONJ
cana-4456	36	15	expected	expect	VERB
cana-4456	36	16	to	to	PART
cana-4456	36	17	produce	produce	VERB
cana-4456	36	18	spectral	spectral	ADJ
cana-4456	36	19	accuracy	accuracy	NOUN
cana-4456	36	20	for	for	ADP
cana-4456	36	21	the	the	DET
cana-4456	36	22	numerical	numerical	ADJ
cana-4456	36	23	solution	solution	NOUN
cana-4456	36	24	.	.	PUNCT
cana-4456	37	1	however	however	ADV
cana-4456	37	2	,	,	PUNCT
cana-4456	37	3	the	the	DET
cana-4456	37	4	infinitely	infinitely	ADV
cana-4456	37	5	smooth	smooth	ADJ
cana-4456	37	6	rbfs	rbfs	NOUN
cana-4456	37	7	(	(	PUNCT
cana-4456	37	8	table	table	NOUN
cana-4456	37	9	1	1	NUM
cana-4456	37	10	)	)	PUNCT
cana-4456	37	11	produce	produce	VERB
cana-4456	37	12	dense	dense	ADJ
cana-4456	37	13	matrices	matrix	NOUN
cana-4456	37	14	thus	thus	ADV
cana-4456	37	15	ill	ill	ADV
cana-4456	37	16	-	-	PUNCT
cana-4456	37	17	conditioned	condition	VERB
cana-4456	37	18	matrices	matrix	NOUN
cana-4456	37	19	,	,	PUNCT
cana-4456	37	20	especially	especially	ADV
cana-4456	37	21	for	for	ADP
cana-4456	37	22	the	the	DET
cana-4456	37	23	parameter	parameter	NOUN
cana-4456	37	24	values	value	NOUN
cana-4456	37	25	that	that	PRON
cana-4456	37	26	lead	lead	VERB
cana-4456	37	27	to	to	ADP
cana-4456	37	28	the	the	DET
cana-4456	37	29	highest	high	ADJ
cana-4456	37	30	accuracy	accuracy	NOUN
cana-4456	37	31	.	.	PUNCT
cana-4456	38	1	to	to	PART
cana-4456	38	2	overcome	overcome	VERB
cana-4456	38	3	this	this	DET
cana-4456	38	4	issue	issue	NOUN
cana-4456	38	5	,	,	PUNCT
cana-4456	38	6	it	it	PRON
cana-4456	38	7	is	be	AUX
cana-4456	38	8	essential	essential	ADJ
cana-4456	38	9	to	to	PART
cana-4456	38	10	introduce	introduce	VERB
cana-4456	38	11	certain	certain	ADJ
cana-4456	38	12	locality	locality	NOUN
cana-4456	38	13	in	in	ADP
cana-4456	38	14	the	the	DET
cana-4456	38	15	system	system	NOUN
cana-4456	38	16	to	to	PART
cana-4456	38	17	be	be	AUX
cana-4456	38	18	solved	solve	VERB
cana-4456	38	19	.	.	PUNCT
cana-4456	39	1	not	not	PART
cana-4456	39	2	only	only	ADV
cana-4456	39	3	the	the	DET
cana-4456	39	4	conditioning	conditioning	NOUN
cana-4456	39	5	will	will	AUX
cana-4456	39	6	be	be	AUX
cana-4456	39	7	improved	improve	VERB
cana-4456	39	8	,	,	PUNCT
cana-4456	39	9	but	but	CCONJ
cana-4456	39	10	also	also	ADV
cana-4456	39	11	the	the	DET
cana-4456	39	12	accuracy	accuracy	NOUN
cana-4456	39	13	of	of	ADP
cana-4456	39	14	the	the	DET
cana-4456	39	15	numerical	numerical	ADJ
cana-4456	39	16	solution	solution	NOUN
cana-4456	39	17	will	will	AUX
cana-4456	39	18	be	be	AUX
cana-4456	39	19	guaranteed	guarantee	VERB
cana-4456	39	20	.	.	PUNCT
cana-4456	40	1	in	in	ADP
cana-4456	40	2	this	this	DET
cana-4456	40	3	context	context	NOUN
cana-4456	40	4	,	,	PUNCT
cana-4456	40	5	we	we	PRON
cana-4456	40	6	conducted	conduct	VERB
cana-4456	40	7	our	our	PRON
cana-4456	40	8	studies	study	NOUN
cana-4456	40	9	using	use	VERB
cana-4456	40	10	local	local	ADJ
cana-4456	40	11	and	and	CCONJ
cana-4456	40	12	stable	stable	ADJ
cana-4456	40	13	meshless	meshless	ADJ
cana-4456	40	14	methods	method	NOUN
cana-4456	40	15	in	in	ADP
cana-4456	40	16	addition	addition	NOUN
cana-4456	40	17	to	to	ADP
cana-4456	40	18	kansa	kansa	PROPN
cana-4456	40	19	's	's	PART
cana-4456	40	20	method	method	NOUN
cana-4456	40	21	to	to	PART
cana-4456	40	22	solve	solve	VERB
cana-4456	40	23	swes	swes	NOUN
cana-4456	40	24	.	.	PUNCT
cana-4456	41	1	one	one	NUM
cana-4456	41	2	such	such	ADJ
cana-4456	41	3	method	method	NOUN
cana-4456	41	4	is	be	AUX
cana-4456	41	5	the	the	DET
cana-4456	41	6	rbf	rbf	PROPN
cana-4456	41	7	finite	finite	PROPN
cana-4456	41	8	difference	difference	NOUN
cana-4456	41	9	method	method	NOUN
cana-4456	41	10	(	(	PUNCT
cana-4456	41	11	rbf	rbf	PROPN
cana-4456	41	12	-	-	PUNCT
cana-4456	41	13	fd	fd	PROPN
cana-4456	41	14	)	)	PUNCT
cana-4456	41	15	,	,	PUNCT
cana-4456	41	16	first	first	ADV
cana-4456	41	17	described	describe	VERB
cana-4456	41	18	in	in	ADP
cana-4456	41	19	[	[	X
cana-4456	41	20	14	14	NUM
cana-4456	41	21	]	]	PUNCT
cana-4456	41	22	in	in	ADP
cana-4456	41	23	2000	2000	NUM
cana-4456	41	24	.	.	PUNCT
cana-4456	42	1	the	the	DET
cana-4456	42	2	idea	idea	NOUN
cana-4456	42	3	of	of	ADP
cana-4456	42	4	this	this	DET
cana-4456	42	5	method	method	NOUN
cana-4456	42	6	is	be	AUX
cana-4456	42	7	to	to	PART
cana-4456	42	8	form	form	VERB
cana-4456	42	9	computational	computational	ADJ
cana-4456	42	10	stencils	stencil	NOUN
cana-4456	42	11	,	,	PUNCT
cana-4456	42	12	similar	similar	ADJ
cana-4456	42	13	to	to	ADP
cana-4456	42	14	those	those	PRON
cana-4456	42	15	in	in	ADP
cana-4456	42	16	finite	finite	ADJ
cana-4456	42	17	difference	difference	NOUN
cana-4456	42	18	method	method	NOUN
cana-4456	42	19	,	,	PUNCT
cana-4456	42	20	by	by	ADP
cana-4456	42	21	constructing	construct	VERB
cana-4456	42	22	derivative	derivative	ADJ
cana-4456	42	23	discretizations	discretization	NOUN
cana-4456	42	24	based	base	VERB
cana-4456	42	25	on	on	ADP
cana-4456	42	26	rbf	rbf	PROPN
cana-4456	42	27	interpolants	interpolant	NOUN
cana-4456	42	28	on	on	ADP
cana-4456	42	29	localized	localized	ADJ
cana-4456	42	30	node	node	NOUN
cana-4456	42	31	sets	set	NOUN
cana-4456	42	32	[	[	X
cana-4456	42	33	15	15	NUM
cana-4456	42	34	]	]	PUNCT
cana-4456	42	35	.	.	PUNCT
cana-4456	43	1	another	another	DET
cana-4456	43	2	localized	localized	ADJ
cana-4456	43	3	method	method	NOUN
cana-4456	43	4	is	be	AUX
cana-4456	43	5	the	the	DET
cana-4456	43	6	rbf	rbf	PROPN
cana-4456	43	7	partition	partition	NOUN
cana-4456	43	8	of	of	ADP
cana-4456	43	9	unity	unity	NOUN
cana-4456	43	10	method	method	NOUN
cana-4456	43	11	(	(	PUNCT
cana-4456	43	12	rbf	rbf	PROPN
cana-4456	43	13	-	-	PROPN
cana-4456	43	14	pum	pum	PROPN
cana-4456	43	15	)	)	PUNCT
cana-4456	43	16	which	which	PRON
cana-4456	43	17	is	be	AUX
cana-4456	43	18	based	base	VERB
cana-4456	43	19	on	on	ADP
cana-4456	43	20	approximating	approximate	VERB
cana-4456	43	21	the	the	DET
cana-4456	43	22	solution	solution	NOUN
cana-4456	43	23	of	of	ADP
cana-4456	43	24	pdes	pde	NOUN
cana-4456	43	25	in	in	ADP
cana-4456	43	26	a	a	DET
cana-4456	43	27	regular	regular	ADJ
cana-4456	43	28	covering	covering	NOUN
cana-4456	43	29	of	of	ADP
cana-4456	43	30	overlapping	overlap	VERB
cana-4456	43	31	subdomains	subdomain	NOUN
cana-4456	43	32	and	and	CCONJ
cana-4456	43	33	then	then	ADV
cana-4456	43	34	patching	patch	VERB
cana-4456	43	35	up	up	ADP
cana-4456	43	36	the	the	DET
cana-4456	43	37	local	local	ADJ
cana-4456	43	38	solutions	solution	NOUN
cana-4456	43	39	using	use	VERB
cana-4456	43	40	the	the	DET
cana-4456	43	41	partition	partition	NOUN
cana-4456	43	42	of	of	ADP
cana-4456	43	43	unity	unity	NOUN
cana-4456	43	44	principle	principle	NOUN
cana-4456	43	45	[	[	X
cana-4456	43	46	16	16	NUM
cana-4456	43	47	,	,	PUNCT
cana-4456	43	48	17	17	NUM
cana-4456	43	49	]	]	PUNCT
cana-4456	43	50	.	.	PUNCT
cana-4456	44	1	the	the	DET
cana-4456	44	2	rbf	rbf	PROPN
cana-4456	44	3	-	-	PUNCT
cana-4456	44	4	pum	pum	PROPN
cana-4456	44	5	,	,	PUNCT
cana-4456	44	6	increasing	increase	VERB
cana-4456	44	7	the	the	DET
cana-4456	44	8	sparsity	sparsity	NOUN
cana-4456	44	9	of	of	ADP
cana-4456	44	10	linear	linear	PROPN
cana-4456	44	11	systems	system	NOUN
cana-4456	44	12	,	,	PUNCT
cana-4456	44	13	enables	enable	VERB
cana-4456	44	14	us	we	PRON
cana-4456	44	15	to	to	PART
cana-4456	44	16	offer	offer	VERB
cana-4456	44	17	significant	significant	ADJ
cana-4456	44	18	savings	saving	NOUN
cana-4456	44	19	in	in	ADP
cana-4456	44	20	the	the	DET
cana-4456	44	21	computational	computational	ADJ
cana-4456	44	22	time	time	NOUN
cana-4456	44	23	,	,	PUNCT
cana-4456	44	24	but	but	CCONJ
cana-4456	44	25	in	in	ADP
cana-4456	44	26	order	order	NOUN
cana-4456	44	27	to	to	PART
cana-4456	44	28	guarantee	guarantee	VERB
cana-4456	44	29	the	the	DET
cana-4456	44	30	stability	stability	NOUN
cana-4456	44	31	of	of	ADP
cana-4456	44	32	the	the	DET
cana-4456	44	33	solution	solution	NOUN
cana-4456	44	34	,	,	PUNCT
cana-4456	44	35	as	as	ADP
cana-4456	44	36	𝜀	𝜀	NOUN
cana-4456	44	37	⟶	⟶	NOUN
cana-4456	44	38	0	0	NUM
cana-4456	44	39	(	(	PUNCT
cana-4456	44	40	called	call	VERB
cana-4456	44	41	flat	flat	ADJ
cana-4456	44	42	limit	limit	NOUN
cana-4456	44	43	regime	regime	NOUN
cana-4456	44	44	)	)	PUNCT
cana-4456	44	45	,	,	PUNCT
cana-4456	44	46	a	a	DET
cana-4456	44	47	stable	stable	ADJ
cana-4456	44	48	evaluation	evaluation	NOUN
cana-4456	44	49	algorithm	algorithm	NOUN
cana-4456	44	50	is	be	AUX
cana-4456	44	51	employed	employ	VERB
cana-4456	44	52	.	.	PUNCT
cana-4456	45	1	the	the	DET
cana-4456	45	2	stable	stable	ADJ
cana-4456	45	3	rbf	rbf	PROPN
cana-4456	45	4	-	-	PUNCT
cana-4456	45	5	qr	qr	PROPN
cana-4456	45	6	algorithm	algorithm	NOUN
cana-4456	45	7	bypasses	bypass	VERB
cana-4456	45	8	some	some	DET
cana-4456	45	9	limitations	limitation	NOUN
cana-4456	45	10	,	,	PUNCT
cana-4456	45	11	including	include	VERB
cana-4456	45	12	complications	complication	NOUN
cana-4456	45	13	related	relate	VERB
cana-4456	45	14	to	to	ADP
cana-4456	45	15	the	the	DET
cana-4456	45	16	selection	selection	NOUN
cana-4456	45	17	of	of	ADP
cana-4456	45	18	𝜀	𝜀	PROPN
cana-4456	45	19	,	,	PUNCT
cana-4456	45	20	ill	ill	ADJ
cana-4456	45	21	-	-	PUNCT
cana-4456	45	22	conditioning	conditioning	NOUN
cana-4456	45	23	of	of	ADP
cana-4456	45	24	rbf	rbf	PROPN
cana-4456	45	25	-	-	PUNCT
cana-4456	45	26	pum	pum	PROPN
cana-4456	45	27	matrices	matrix	NOUN
cana-4456	45	28	.	.	PUNCT
cana-4456	46	1	the	the	DET
cana-4456	46	2	main	main	ADJ
cana-4456	46	3	logic	logic	NOUN
cana-4456	46	4	behind	behind	ADP
cana-4456	46	5	the	the	DET
cana-4456	46	6	rbf	rbf	PROPN
cana-4456	46	7	-	-	PUNCT
cana-4456	46	8	qr	qr	PROPN
cana-4456	46	9	method	method	NOUN
cana-4456	46	10	is	be	AUX
cana-4456	46	11	to	to	PART
cana-4456	46	12	replace	replace	VERB
cana-4456	46	13	the	the	DET
cana-4456	46	14	bad	bad	ADJ
cana-4456	46	15	basis	basis	NOUN
cana-4456	46	16	(	(	PUNCT
cana-4456	46	17	ill	ill	ADV
cana-4456	46	18	-	-	PUNCT
cana-4456	46	19	conditioned	condition	VERB
cana-4456	46	20	)	)	PUNCT
cana-4456	46	21	with	with	ADP
cana-4456	46	22	a	a	DET
cana-4456	46	23	good	good	ADJ
cana-4456	46	24	one	one	NOUN
cana-4456	46	25	that	that	PRON
cana-4456	46	26	can	can	AUX
cana-4456	46	27	span	span	VERB
cana-4456	46	28	the	the	DET
cana-4456	46	29	same	same	ADJ
cana-4456	46	30	space	space	NOUN
cana-4456	46	31	[	[	X
cana-4456	46	32	18	18	NUM
cana-4456	46	33	,	,	PUNCT
cana-4456	46	34	19	19	NUM
cana-4456	46	35	]	]	PUNCT
cana-4456	46	36	.	.	PUNCT
cana-4456	47	1	the	the	DET
cana-4456	47	2	rbf	rbf	PROPN
cana-4456	47	3	methods	method	NOUN
cana-4456	47	4	that	that	PRON
cana-4456	47	5	we	we	PRON
cana-4456	47	6	investigate	investigate	VERB
cana-4456	47	7	are	be	AUX
cana-4456	47	8	:	:	PUNCT
cana-4456	47	9	the	the	DET
cana-4456	47	10	rbf	rbf	PROPN
cana-4456	47	11	generated	generate	VERB
cana-4456	47	12	finite	finite	PROPN
cana-4456	47	13	difference(rbf	difference(rbf	PROPN
cana-4456	47	14	-	-	PUNCT
cana-4456	47	15	fd	fd	PROPN
cana-4456	47	16	)	)	PUNCT
cana-4456	47	17	method	method	NOUN
cana-4456	47	18	,	,	PUNCT
cana-4456	47	19	the	the	DET
cana-4456	47	20	rbf	rbf	PROPN
cana-4456	47	21	partition	partition	NOUN
cana-4456	47	22	of	of	ADP
cana-4456	47	23	unity	unity	NOUN
cana-4456	47	24	method	method	NOUN
cana-4456	47	25	(	(	PUNCT
cana-4456	47	26	rbf	rbf	PROPN
cana-4456	47	27	-	-	PROPN
cana-4456	47	28	pum	pum	PROPN
cana-4456	47	29	)	)	PUNCT
cana-4456	47	30	and	and	CCONJ
cana-4456	47	31	kansa	kansa	PROPN
cana-4456	47	32	's	's	PART
cana-4456	47	33	method	method	NOUN
cana-4456	47	34	.	.	PUNCT
cana-4456	48	1	the	the	DET
cana-4456	48	2	first	first	ADJ
cana-4456	48	3	two	two	NUM
cana-4456	48	4	methods	method	NOUN
cana-4456	48	5	are	be	AUX
cana-4456	48	6	localized	localize	VERB
cana-4456	48	7	such	such	ADJ
cana-4456	48	8	that	that	SCONJ
cana-4456	48	9	the	the	DET
cana-4456	48	10	final	final	ADJ
cana-4456	48	11	system	system	NOUN
cana-4456	48	12	of	of	ADP
cana-4456	48	13	equations	equation	NOUN
cana-4456	48	14	is	be	AUX
cana-4456	48	15	sparse	sparse	ADJ
cana-4456	48	16	,	,	PUNCT
cana-4456	48	17	and	and	CCONJ
cana-4456	48	18	the	the	DET
cana-4456	48	19	third	third	ADJ
cana-4456	48	20	method	method	NOUN
cana-4456	48	21	is	be	AUX
cana-4456	48	22	global	global	ADJ
cana-4456	48	23	and	and	CCONJ
cana-4456	48	24	gives	give	VERB
cana-4456	48	25	a	a	DET
cana-4456	48	26	dense	dense	ADJ
cana-4456	48	27	system	system	NOUN
cana-4456	48	28	of	of	ADP
cana-4456	48	29	equations	equation	NOUN
cana-4456	48	30	.	.	PUNCT
cana-4456	49	1	it	it	PRON
cana-4456	49	2	is	be	AUX
cana-4456	49	3	known	know	VERB
cana-4456	49	4	,	,	PUNCT
cana-4456	49	5	based	base	VERB
cana-4456	49	6	on	on	ADP
cana-4456	49	7	numerical	numerical	ADJ
cana-4456	49	8	experiments	experiment	NOUN
cana-4456	49	9	,	,	PUNCT
cana-4456	49	10	that	that	SCONJ
cana-4456	49	11	all	all	DET
cana-4456	49	12	three	three	NUM
cana-4456	49	13	methods	method	NOUN
cana-4456	49	14	in	in	ADP
cana-4456	49	15	general	general	ADJ
cana-4456	49	16	are	be	AUX
cana-4456	49	17	unstable	unstable	ADJ
cana-4456	49	18	when	when	SCONJ
cana-4456	49	19	computing	compute	VERB
cana-4456	49	20	collocated	collocate	VERB
cana-4456	49	21	solutions	solution	NOUN
cana-4456	49	22	to	to	ADP
cana-4456	49	23	time	time	NOUN
cana-4456	49	24	-	-	PUNCT
cana-4456	49	25	dependent	dependent	ADJ
cana-4456	49	26	conservation	conservation	NOUN
cana-4456	49	27	laws	law	NOUN
cana-4456	49	28	without	without	ADP
cana-4456	49	29	communications	communication	NOUN
cana-4456	49	30	on	on	ADP
cana-4456	49	31	applied	apply	VERB
cana-4456	49	32	nonlinear	nonlinear	ADJ
cana-4456	49	33	analysis	analysis	NOUN
cana-4456	49	34	issn	issn	NOUN
cana-4456	49	35	:	:	PUNCT
cana-4456	49	36	1074	1074	NUM
cana-4456	49	37	-	-	PUNCT
cana-4456	49	38	133x	133x	NUM
cana-4456	49	39	vol	vol	NOUN
cana-4456	49	40	32	32	NUM
cana-4456	49	41	no	no	NOUN
cana-4456	49	42	.	.	PUNCT
cana-4456	50	1	9s	9s	NUM
cana-4456	50	2	(	(	PUNCT
cana-4456	50	3	2025	2025	NUM
cana-4456	50	4	)	)	PUNCT
cana-4456	50	5	2169	2169	NUM
cana-4456	50	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	50	7	additional	additional	ADJ
cana-4456	50	8	stabilization	stabilization	NOUN
cana-4456	50	9	[	[	X
cana-4456	50	10	20	20	NUM
cana-4456	50	11	]	]	PUNCT
cana-4456	50	12	.	.	PUNCT
cana-4456	51	1	in	in	ADP
cana-4456	51	2	[	[	X
cana-4456	51	3	21	21	NUM
cana-4456	51	4	]	]	PUNCT
cana-4456	51	5	,	,	PUNCT
cana-4456	51	6	the	the	DET
cana-4456	51	7	author	author	NOUN
cana-4456	51	8	suggests	suggest	VERB
cana-4456	51	9	activating	activate	VERB
cana-4456	51	10	artificial	artificial	ADJ
cana-4456	51	11	viscosity	viscosity	NOUN
cana-4456	51	12	in	in	ADP
cana-4456	51	13	the	the	DET
cana-4456	51	14	time	time	NOUN
cana-4456	51	15	domain	domain	NOUN
cana-4456	51	16	rather	rather	ADV
cana-4456	51	17	than	than	ADP
cana-4456	51	18	in	in	ADP
cana-4456	51	19	localized	localized	ADJ
cana-4456	51	20	regions	region	NOUN
cana-4456	51	21	of	of	ADP
cana-4456	51	22	space	space	NOUN
cana-4456	51	23	and	and	CCONJ
cana-4456	51	24	using	use	VERB
cana-4456	51	25	hyperviscosity	hyperviscosity	NOUN
cana-4456	51	26	provides	provide	VERB
cana-4456	51	27	an	an	DET
cana-4456	51	28	elegant	elegant	ADJ
cana-4456	51	29	approach	approach	NOUN
cana-4456	51	30	to	to	PART
cana-4456	51	31	spatially	spatially	ADV
cana-4456	51	32	selecting	select	VERB
cana-4456	51	33	the	the	DET
cana-4456	51	34	diffusion	diffusion	NOUN
cana-4456	51	35	effect	effect	NOUN
cana-4456	51	36	based	base	VERB
cana-4456	51	37	on	on	ADP
cana-4456	51	38	supplementing	supplement	VERB
cana-4456	51	39	the	the	DET
cana-4456	51	40	numerical	numerical	ADJ
cana-4456	51	41	scheme	scheme	NOUN
cana-4456	51	42	by	by	ADP
cana-4456	51	43	a	a	DET
cana-4456	51	44	hyperviscosity	hyperviscosity	NOUN
cana-4456	51	45	term	term	NOUN
cana-4456	51	46	.	.	PUNCT
cana-4456	52	1	hyperviscosity	hyperviscosity	NOUN
cana-4456	52	2	was	be	AUX
cana-4456	52	3	first	first	ADV
cana-4456	52	4	introduced	introduce	VERB
cana-4456	52	5	to	to	ADP
cana-4456	52	6	spectral	spectral	ADJ
cana-4456	52	7	methods	method	NOUN
cana-4456	52	8	in	in	ADP
cana-4456	52	9	1998	1998	NUM
cana-4456	52	10	by	by	ADP
cana-4456	52	11	ma	ma	PROPN
cana-4456	52	12	under	under	ADP
cana-4456	52	13	the	the	DET
cana-4456	52	14	name	name	NOUN
cana-4456	52	15	(	(	PUNCT
cana-4456	52	16	super)spectral	super)spectral	ADJ
cana-4456	52	17	viscosity	viscosity	NOUN
cana-4456	52	18	[	[	X
cana-4456	52	19	22	22	NUM
cana-4456	52	20	]	]	PUNCT
cana-4456	52	21	.	.	PUNCT
cana-4456	53	1	despite	despite	SCONJ
cana-4456	53	2	the	the	DET
cana-4456	53	3	promising	promising	ADJ
cana-4456	53	4	analytical	analytical	ADJ
cana-4456	53	5	results	result	NOUN
cana-4456	53	6	demonstrated	demonstrate	VERB
cana-4456	53	7	by	by	ADP
cana-4456	53	8	ma	ma	PROPN
cana-4456	53	9	,	,	PUNCT
cana-4456	53	10	the	the	DET
cana-4456	53	11	method	method	NOUN
cana-4456	53	12	was	be	AUX
cana-4456	53	13	never	never	ADV
cana-4456	53	14	widely	widely	ADV
cana-4456	53	15	adopted	adopt	VERB
cana-4456	53	16	and	and	CCONJ
cana-4456	53	17	has	have	AUX
cana-4456	53	18	only	only	ADV
cana-4456	53	19	been	be	AUX
cana-4456	53	20	mentioned	mention	VERB
cana-4456	53	21	in	in	ADP
cana-4456	53	22	a	a	DET
cana-4456	53	23	few	few	ADJ
cana-4456	53	24	research	research	NOUN
cana-4456	53	25	papers	paper	NOUN
cana-4456	53	26	where	where	SCONJ
cana-4456	53	27	it	it	PRON
cana-4456	53	28	was	be	AUX
cana-4456	53	29	applied	apply	VERB
cana-4456	53	30	to	to	ADP
cana-4456	53	31	the	the	DET
cana-4456	53	32	navier	navier	NOUN
cana-4456	53	33	-	-	PUNCT
cana-4456	53	34	stokes	stoke	NOUN
cana-4456	53	35	equations	equation	NOUN
cana-4456	53	36	.	.	PUNCT
cana-4456	54	1	the	the	DET
cana-4456	54	2	meshless	meshless	ADJ
cana-4456	54	3	community	community	NOUN
cana-4456	54	4	first	first	ADV
cana-4456	54	5	adopted	adopt	VERB
cana-4456	54	6	spectral	spectral	ADJ
cana-4456	54	7	viscosity	viscosity	NOUN
cana-4456	54	8	,	,	PUNCT
cana-4456	54	9	now	now	ADV
cana-4456	54	10	called	call	VERB
cana-4456	54	11	hyperviscosity	hyperviscosity	NOUN
cana-4456	54	12	,	,	PUNCT
cana-4456	54	13	in	in	ADP
cana-4456	54	14	2011	2011	NUM
cana-4456	54	15	when	when	SCONJ
cana-4456	54	16	fornberg	fornberg	PROPN
cana-4456	54	17	[	[	X
cana-4456	54	18	20	20	NUM
cana-4456	54	19	]	]	PUNCT
cana-4456	54	20	demonstrated	demonstrate	VERB
cana-4456	54	21	that	that	SCONJ
cana-4456	54	22	hyperviscosity	hyperviscosity	NOUN
cana-4456	54	23	could	could	AUX
cana-4456	54	24	stabilize	stabilize	VERB
cana-4456	54	25	time	time	NOUN
cana-4456	54	26	-	-	PUNCT
cana-4456	54	27	stepping	step	VERB
cana-4456	54	28	schemes	scheme	NOUN
cana-4456	54	29	by	by	ADP
cana-4456	54	30	shifting	shift	VERB
cana-4456	54	31	spurious	spurious	ADJ
cana-4456	54	32	eigenvalues	eigenvalue	NOUN
cana-4456	54	33	into	into	ADP
cana-4456	54	34	the	the	DET
cana-4456	54	35	stable	stable	ADJ
cana-4456	54	36	region	region	NOUN
cana-4456	54	37	.	.	PUNCT
cana-4456	55	1	subsequently	subsequently	ADV
cana-4456	55	2	,	,	PUNCT
cana-4456	55	3	hyperviscosity	hyperviscosity	PROPN
cana-4456	55	4	was	be	AUX
cana-4456	55	5	applied	apply	VERB
cana-4456	55	6	to	to	ADP
cana-4456	55	7	a	a	DET
cana-4456	55	8	variety	variety	NOUN
cana-4456	55	9	of	of	ADP
cana-4456	55	10	fluid	fluid	ADJ
cana-4456	55	11	dynamics	dynamic	NOUN
cana-4456	55	12	cases	case	NOUN
cana-4456	55	13	[	[	X
cana-4456	55	14	23	23	NUM
cana-4456	55	15	,	,	PUNCT
cana-4456	55	16	24	24	NUM
cana-4456	55	17	]	]	PUNCT
cana-4456	55	18	.	.	PUNCT
cana-4456	56	1	initially	initially	ADV
cana-4456	56	2	,	,	PUNCT
cana-4456	56	3	the	the	DET
cana-4456	56	4	parameters	parameter	NOUN
cana-4456	56	5	of	of	ADP
cana-4456	56	6	hyperviscosity	hyperviscosity	NOUN
cana-4456	56	7	were	be	AUX
cana-4456	56	8	only	only	ADV
cana-4456	56	9	briefly	briefly	ADV
cana-4456	56	10	mentioned	mention	VERB
cana-4456	56	11	and	and	CCONJ
cana-4456	56	12	included	include	VERB
cana-4456	56	13	a	a	DET
cana-4456	56	14	large	large	ADJ
cana-4456	56	15	number	number	NOUN
cana-4456	56	16	of	of	ADP
cana-4456	56	17	empirical	empirical	ADJ
cana-4456	56	18	approximations	approximation	NOUN
cana-4456	56	19	.	.	PUNCT
cana-4456	57	1	recently	recently	ADV
cana-4456	57	2	,	,	PUNCT
cana-4456	57	3	new	new	ADJ
cana-4456	57	4	artificial	artificial	ADJ
cana-4456	57	5	hyperviscosity	hyperviscosity	NOUN
cana-4456	57	6	formulations	formulation	NOUN
cana-4456	57	7	have	have	AUX
cana-4456	57	8	been	be	AUX
cana-4456	57	9	proposed	propose	VERB
cana-4456	57	10	in	in	ADP
cana-4456	57	11	the	the	DET
cana-4456	57	12	literature	literature	NOUN
cana-4456	57	13	[	[	X
cana-4456	57	14	25	25	NUM
cana-4456	57	15	]	]	PUNCT
cana-4456	57	16	,	,	PUNCT
cana-4456	57	17	which	which	PRON
cana-4456	57	18	are	be	AUX
cana-4456	57	19	very	very	ADV
cana-4456	57	20	effective	effective	ADJ
cana-4456	57	21	for	for	ADP
cana-4456	57	22	rbf	rbf	PROPN
cana-4456	57	23	-	-	PUNCT
cana-4456	57	24	fd	fd	PROPN
cana-4456	57	25	methods	method	NOUN
cana-4456	57	26	for	for	ADP
cana-4456	57	27	solving	solve	VERB
cana-4456	57	28	surface	surface	NOUN
cana-4456	57	29	convection	convection	NOUN
cana-4456	57	30	-	-	PUNCT
cana-4456	57	31	diffusion	diffusion	NOUN
cana-4456	57	32	equations	equation	NOUN
cana-4456	57	33	and	and	CCONJ
cana-4456	57	34	for	for	ADP
cana-4456	57	35	nonlinear	nonlinear	ADJ
cana-4456	57	36	conservation	conservation	NOUN
cana-4456	57	37	laws	law	NOUN
cana-4456	57	38	[	[	X
cana-4456	57	39	26	26	NUM
cana-4456	57	40	]	]	PUNCT
cana-4456	57	41	.	.	PUNCT
cana-4456	58	1	additionally	additionally	ADV
cana-4456	58	2	,	,	PUNCT
cana-4456	58	3	meshless	meshless	ADJ
cana-4456	58	4	schemes	scheme	NOUN
cana-4456	58	5	combined	combine	VERB
cana-4456	58	6	with	with	ADP
cana-4456	58	7	hyperviscosity	hyperviscosity	NOUN
cana-4456	58	8	technique	technique	NOUN
cana-4456	58	9	have	have	AUX
cana-4456	58	10	been	be	AUX
cana-4456	58	11	proposed	propose	VERB
cana-4456	58	12	to	to	ADP
cana-4456	58	13	the	the	DET
cana-4456	58	14	authors	author	NOUN
cana-4456	58	15	'	'	PART
cana-4456	58	16	knowledge	knowledge	NOUN
cana-4456	58	17	such	such	ADJ
cana-4456	58	18	in	in	ADP
cana-4456	58	19	[	[	X
cana-4456	58	20	27	27	NUM
cana-4456	58	21	]	]	PUNCT
cana-4456	58	22	used	use	VERB
cana-4456	58	23	the	the	DET
cana-4456	58	24	rbf	rbf	PROPN
cana-4456	58	25	-	-	PUNCT
cana-4456	58	26	based	base	VERB
cana-4456	58	27	method	method	NOUN
cana-4456	58	28	for	for	ADP
cana-4456	58	29	solving	solve	VERB
cana-4456	58	30	the	the	DET
cana-4456	58	31	shallow	shallow	ADJ
cana-4456	58	32	water	water	NOUN
cana-4456	58	33	equations	equation	NOUN
cana-4456	58	34	to	to	PART
cana-4456	58	35	capture	capture	VERB
cana-4456	58	36	shocks	shock	NOUN
cana-4456	58	37	.	.	PUNCT
cana-4456	59	1	moreover	moreover	ADV
cana-4456	59	2	,	,	PUNCT
cana-4456	59	3	hyperviscosity	hyperviscosity	NOUN
cana-4456	59	4	and	and	CCONJ
cana-4456	59	5	its	its	PRON
cana-4456	59	6	connection	connection	NOUN
cana-4456	59	7	to	to	ADP
cana-4456	59	8	the	the	DET
cana-4456	59	9	stability	stability	NOUN
cana-4456	59	10	of	of	ADP
cana-4456	59	11	the	the	DET
cana-4456	59	12	rbf	rbf	PROPN
cana-4456	59	13	partition	partition	NOUN
cana-4456	59	14	of	of	ADP
cana-4456	59	15	unity	unity	NOUN
cana-4456	59	16	(	(	PUNCT
cana-4456	59	17	rbf	rbf	PROPN
cana-4456	59	18	-	-	PUNCT
cana-4456	59	19	pu	pu	PROPN
cana-4456	59	20	)	)	PUNCT
cana-4456	59	21	method	method	NOUN
cana-4456	59	22	was	be	AUX
cana-4456	59	23	only	only	ADV
cana-4456	59	24	well	well	ADV
cana-4456	59	25	established	establish	VERB
cana-4456	59	26	by	by	ADP
cana-4456	59	27	the	the	DET
cana-4456	59	28	work	work	NOUN
cana-4456	59	29	of	of	ADP
cana-4456	59	30	liu	liu	PROPN
cana-4456	59	31	et	et	PROPN
cana-4456	59	32	al	al	PROPN
cana-4456	59	33	.	.	PUNCT
cana-4456	60	1	[	[	X
cana-4456	60	2	28	28	NUM
cana-4456	60	3	]	]	PUNCT
cana-4456	60	4	,	,	PUNCT
cana-4456	60	5	who	who	PRON
cana-4456	60	6	showed	show	VERB
cana-4456	60	7	that	that	SCONJ
cana-4456	60	8	the	the	DET
cana-4456	60	9	hyperviscosity	hyperviscosity	NOUN
cana-4456	60	10	improve	improve	VERB
cana-4456	60	11	the	the	DET
cana-4456	60	12	stability	stability	NOUN
cana-4456	60	13	of	of	ADP
cana-4456	60	14	the	the	DET
cana-4456	60	15	rbf	rbf	PROPN
cana-4456	60	16	-	-	PROPN
cana-4456	60	17	pu	pu	PROPN
cana-4456	60	18	method	method	NOUN
cana-4456	60	19	for	for	ADP
cana-4456	60	20	solving	solve	VERB
cana-4456	60	21	convection	convection	NOUN
cana-4456	60	22	-	-	PUNCT
cana-4456	60	23	diffusion	diffusion	NOUN
cana-4456	60	24	equations	equation	NOUN
cana-4456	60	25	on	on	ADP
cana-4456	60	26	surfaces	surface	NOUN
cana-4456	60	27	.	.	PUNCT
cana-4456	61	1	therefore	therefore	ADV
cana-4456	61	2	,	,	PUNCT
cana-4456	61	3	we	we	PRON
cana-4456	61	4	suggested	suggest	VERB
cana-4456	61	5	to	to	PART
cana-4456	61	6	combine	combine	VERB
cana-4456	61	7	the	the	DET
cana-4456	61	8	rbf	rbf	PROPN
cana-4456	61	9	-	-	PROPN
cana-4456	61	10	fd	fd	PROPN
cana-4456	61	11	(	(	PUNCT
cana-4456	61	12	using	use	VERB
cana-4456	61	13	inverse	inverse	ADJ
cana-4456	61	14	multiquadratic	multiquadratic	ADJ
cana-4456	61	15	function	function	NOUN
cana-4456	61	16	)	)	PUNCT
cana-4456	61	17	and	and	CCONJ
cana-4456	61	18	rbf	rbf	PROPN
cana-4456	61	19	-	-	PUNCT
cana-4456	61	20	pum	pum	PROPN
cana-4456	61	21	-	-	PUNCT
cana-4456	61	22	qr	qr	PROPN
cana-4456	61	23	with	with	ADP
cana-4456	61	24	hyperviscosty	hyperviscosty	NOUN
cana-4456	61	25	technique	technique	NOUN
cana-4456	61	26	in	in	ADP
cana-4456	61	27	order	order	NOUN
cana-4456	61	28	to	to	PART
cana-4456	61	29	establish	establish	VERB
cana-4456	61	30	a	a	DET
cana-4456	61	31	localized	localize	VERB
cana-4456	61	32	numerical	numerical	ADJ
cana-4456	61	33	meshless	meshless	ADJ
cana-4456	61	34	model	model	NOUN
cana-4456	61	35	which	which	PRON
cana-4456	61	36	can	can	AUX
cana-4456	61	37	accurately	accurately	ADV
cana-4456	61	38	and	and	CCONJ
cana-4456	61	39	effectively	effectively	ADV
cana-4456	61	40	solve	solve	VERB
cana-4456	61	41	the	the	DET
cana-4456	61	42	swes	swes	NOUN
cana-4456	61	43	.	.	PUNCT
cana-4456	62	1	this	this	DET
cana-4456	62	2	paper	paper	NOUN
cana-4456	62	3	is	be	AUX
cana-4456	62	4	organized	organize	VERB
cana-4456	62	5	as	as	SCONJ
cana-4456	62	6	follows	follow	VERB
cana-4456	62	7	.	.	PUNCT
cana-4456	63	1	in	in	ADP
cana-4456	63	2	section	section	NOUN
cana-4456	63	3	2	2	NUM
cana-4456	63	4	,	,	PUNCT
cana-4456	63	5	the	the	DET
cana-4456	63	6	governing	govern	VERB
cana-4456	63	7	equations	equation	NOUN
cana-4456	63	8	and	and	CCONJ
cana-4456	63	9	some	some	DET
cana-4456	63	10	properties	property	NOUN
cana-4456	63	11	are	be	AUX
cana-4456	63	12	explained	explain	VERB
cana-4456	63	13	.	.	PUNCT
cana-4456	64	1	the	the	DET
cana-4456	64	2	kansa	kansa	PROPN
cana-4456	64	3	's	's	PART
cana-4456	64	4	method	method	NOUN
cana-4456	64	5	,	,	PUNCT
cana-4456	64	6	rbf	rbf	PROPN
cana-4456	64	7	-	-	PUNCT
cana-4456	64	8	fd	fd	PROPN
cana-4456	64	9	method	method	NOUN
cana-4456	64	10	and	and	CCONJ
cana-4456	64	11	rbf	rbf	PROPN
cana-4456	64	12	-	-	PROPN
cana-4456	64	13	pum	pum	PROPN
cana-4456	64	14	with	with	ADP
cana-4456	64	15	qr	qr	PROPN
cana-4456	64	16	factorization	factorization	NOUN
cana-4456	64	17	with	with	ADP
cana-4456	64	18	hyperviscosity	hyperviscosity	NOUN
cana-4456	64	19	technique	technique	NOUN
cana-4456	64	20	is	be	AUX
cana-4456	64	21	presented	present	VERB
cana-4456	64	22	in	in	ADP
cana-4456	64	23	section	section	NOUN
cana-4456	64	24	3	3	NUM
cana-4456	64	25	.	.	PUNCT
cana-4456	65	1	then	then	ADV
cana-4456	65	2	,	,	PUNCT
cana-4456	65	3	two	two	NUM
cana-4456	65	4	challenging	challenging	ADJ
cana-4456	65	5	tests	test	NOUN
cana-4456	65	6	are	be	AUX
cana-4456	65	7	adopted	adopt	VERB
cana-4456	65	8	to	to	PART
cana-4456	65	9	evaluate	evaluate	VERB
cana-4456	65	10	the	the	DET
cana-4456	65	11	accuracy	accuracy	NOUN
cana-4456	65	12	and	and	CCONJ
cana-4456	65	13	stability	stability	NOUN
cana-4456	65	14	of	of	ADP
cana-4456	65	15	the	the	DET
cana-4456	65	16	numerical	numerical	ADJ
cana-4456	65	17	methods	method	NOUN
cana-4456	65	18	in	in	ADP
cana-4456	65	19	section	section	NOUN
cana-4456	65	20	4	4	NUM
cana-4456	65	21	.	.	PUNCT
cana-4456	66	1	finally	finally	ADV
cana-4456	66	2	,	,	PUNCT
cana-4456	66	3	some	some	DET
cana-4456	66	4	conclusions	conclusion	NOUN
cana-4456	66	5	are	be	AUX
cana-4456	66	6	given	give	VERB
cana-4456	66	7	in	in	ADP
cana-4456	66	8	section	section	NOUN
cana-4456	66	9	5	5	NUM
cana-4456	66	10	.	.	NOUN
cana-4456	66	11	2	2	NUM
cana-4456	66	12	.	.	X
cana-4456	66	13	governing	govern	VERB
cana-4456	66	14	equations	equation	NOUN
cana-4456	66	15	and	and	CCONJ
cana-4456	66	16	properties	property	NOUN
cana-4456	66	17	saint	saint	NOUN
cana-4456	66	18	-	-	PUNCT
cana-4456	66	19	venant	venant	NOUN
cana-4456	67	1	[	[	X
cana-4456	67	2	1	1	NUM
cana-4456	67	3	]	]	PUNCT
cana-4456	67	4	introduced	introduce	VERB
cana-4456	67	5	the	the	DET
cana-4456	67	6	mathematical	mathematical	ADJ
cana-4456	67	7	model	model	NOUN
cana-4456	67	8	for	for	ADP
cana-4456	67	9	shallow	shallow	ADJ
cana-4456	67	10	water	water	NOUN
cana-4456	67	11	,	,	PUNCT
cana-4456	67	12	known	know	VERB
cana-4456	67	13	as	as	ADP
cana-4456	67	14	saint	saint	NOUN
cana-4456	67	15	-	-	PUNCT
cana-4456	67	16	venant	venant	NOUN
cana-4456	67	17	's	's	PART
cana-4456	67	18	equations	equation	NOUN
cana-4456	67	19	or	or	CCONJ
cana-4456	67	20	shallow	shallow	ADJ
cana-4456	67	21	water	water	NOUN
cana-4456	67	22	equations	equation	NOUN
cana-4456	67	23	(	(	PUNCT
cana-4456	67	24	swes	swes	PROPN
cana-4456	67	25	)	)	PUNCT
cana-4456	67	26	.	.	PUNCT
cana-4456	68	1	these	these	DET
cana-4456	68	2	equations	equation	NOUN
cana-4456	68	3	are	be	AUX
cana-4456	68	4	based	base	VERB
cana-4456	68	5	on	on	ADP
cana-4456	68	6	fundamental	fundamental	ADJ
cana-4456	68	7	physical	physical	ADJ
cana-4456	68	8	principles	principle	NOUN
cana-4456	68	9	,	,	PUNCT
cana-4456	68	10	specifically	specifically	ADV
cana-4456	68	11	the	the	DET
cana-4456	68	12	laws	law	NOUN
cana-4456	68	13	of	of	ADP
cana-4456	68	14	mass	mass	ADJ
cana-4456	68	15	conservation	conservation	NOUN
cana-4456	68	16	and	and	CCONJ
cana-4456	68	17	momentum	momentum	NOUN
cana-4456	68	18	conservation	conservation	NOUN
cana-4456	68	19	.	.	PUNCT
cana-4456	69	1	the	the	DET
cana-4456	69	2	model	model	NOUN
cana-4456	69	3	is	be	AUX
cana-4456	69	4	applicable	applicable	ADJ
cana-4456	69	5	to	to	ADP
cana-4456	69	6	free	free	VERB
cana-4456	69	7	surface	surface	NOUN
cana-4456	69	8	flows	flow	NOUN
cana-4456	69	9	when	when	SCONJ
cana-4456	69	10	the	the	DET
cana-4456	69	11	horizontal	horizontal	ADJ
cana-4456	69	12	scales	scale	NOUN
cana-4456	69	13	of	of	ADP
cana-4456	69	14	water	water	NOUN
cana-4456	69	15	mass	mass	NOUN
cana-4456	69	16	significantly	significantly	ADV
cana-4456	69	17	exceed	exceed	VERB
cana-4456	69	18	the	the	DET
cana-4456	69	19	vertical	vertical	ADJ
cana-4456	69	20	scale	scale	NOUN
cana-4456	69	21	and	and	CCONJ
cana-4456	69	22	the	the	DET
cana-4456	69	23	flow	flow	NOUN
cana-4456	69	24	in	in	ADP
cana-4456	69	25	the	the	DET
cana-4456	69	26	vertical	vertical	ADJ
cana-4456	69	27	direction	direction	NOUN
cana-4456	69	28	is	be	AUX
cana-4456	69	29	negligible	negligible	ADJ
cana-4456	69	30	.	.	PUNCT
cana-4456	70	1	the	the	DET
cana-4456	70	2	water	water	NOUN
cana-4456	70	3	density	density	NOUN
cana-4456	70	4	in	in	ADP
cana-4456	70	5	our	our	PRON
cana-4456	70	6	model	model	NOUN
cana-4456	70	7	is	be	AUX
cana-4456	70	8	considered	consider	VERB
cana-4456	70	9	to	to	PART
cana-4456	70	10	be	be	AUX
cana-4456	70	11	constant	constant	ADJ
cana-4456	70	12	and	and	CCONJ
cana-4456	70	13	coriolis	coriolis	PROPN
cana-4456	70	14	force	force	NOUN
cana-4456	70	15	is	be	AUX
cana-4456	70	16	neglected	neglect	VERB
cana-4456	70	17	.	.	PUNCT
cana-4456	71	1	as	as	SCONJ
cana-4456	71	2	the	the	DET
cana-4456	71	3	source	source	NOUN
cana-4456	71	4	terms	term	VERB
cana-4456	71	5	the	the	DET
cana-4456	71	6	bed	bed	NOUN
cana-4456	71	7	slope	slope	NOUN
cana-4456	71	8	term	term	NOUN
cana-4456	71	9	and	and	CCONJ
cana-4456	71	10	bed	bed	NOUN
cana-4456	71	11	friction	friction	NOUN
cana-4456	71	12	term	term	NOUN
cana-4456	71	13	are	be	AUX
cana-4456	71	14	considered	consider	VERB
cana-4456	71	15	.	.	PUNCT
cana-4456	72	1	the	the	DET
cana-4456	72	2	equations	equation	NOUN
cana-4456	72	3	of	of	ADP
cana-4456	72	4	interest	interest	NOUN
cana-4456	72	5	consist	consist	NOUN
cana-4456	72	6	of	of	ADP
cana-4456	72	7	the	the	DET
cana-4456	72	8	following	follow	VERB
cana-4456	72	9	system	system	NOUN
cana-4456	72	10	:	:	PUNCT
cana-4456	72	11	{	{	PUNCT
cana-4456	72	12	𝜕𝑡ℎ	𝜕𝑡ℎ	PUNCT
cana-4456	72	13	+	+	PUNCT
cana-4456	72	14	𝜕𝑥𝑞	𝜕𝑥𝑞	PUNCT
cana-4456	73	1	=	=	NOUN
cana-4456	73	2	0	0	NUM
cana-4456	73	3	,	,	PUNCT
cana-4456	73	4	𝜕𝑡𝑞	𝜕𝑡𝑞	PUNCT
cana-4456	74	1	+	+	CCONJ
cana-4456	74	2	𝜕𝑥	𝜕𝑥	X
cana-4456	74	3	(	(	PUNCT
cana-4456	74	4	𝑞2	𝑞2	NOUN
cana-4456	74	5	ℎ	ℎ	PART
cana-4456	74	6	+	+	NOUN
cana-4456	74	7	1	1	NUM
cana-4456	74	8	2	2	NUM
cana-4456	74	9	𝑔ℎ2	𝑔ℎ2	NOUN
cana-4456	74	10	)	)	PUNCT
cana-4456	74	11	=	=	PUNCT
cana-4456	75	1	𝑔ℎ𝑆𝑏	𝑔ℎ𝑆𝑏	INTJ
cana-4456	75	2	−	−	X
cana-4456	75	3	𝑆𝑓	𝑆𝑓	PROPN
cana-4456	75	4	,	,	PUNCT
cana-4456	75	5	(	(	PUNCT
cana-4456	75	6	1	1	X
cana-4456	75	7	)	)	PUNCT
cana-4456	75	8	where	where	SCONJ
cana-4456	75	9	ℎ(𝑥	ℎ(𝑥	NOUN
cana-4456	75	10	,	,	PUNCT
cana-4456	75	11	𝑡	𝑡	NOUN
cana-4456	75	12	)	)	PUNCT
cana-4456	75	13	is	be	AUX
cana-4456	75	14	the	the	DET
cana-4456	75	15	height	height	NOUN
cana-4456	75	16	of	of	ADP
cana-4456	75	17	the	the	DET
cana-4456	75	18	water	water	NOUN
cana-4456	75	19	,	,	PUNCT
cana-4456	75	20	𝑢(𝑥	𝑢(𝑥	PROPN
cana-4456	75	21	,	,	PUNCT
cana-4456	75	22	𝑡	𝑡	PROPN
cana-4456	75	23	)	)	PUNCT
cana-4456	75	24	is	be	AUX
cana-4456	75	25	the	the	DET
cana-4456	75	26	flow	flow	NOUN
cana-4456	75	27	velocity	velocity	NOUN
cana-4456	75	28	,	,	PUNCT
cana-4456	75	29	𝑞(𝑥	𝑞(𝑥	PROPN
cana-4456	75	30	,	,	PUNCT
cana-4456	75	31	𝑡	𝑡	NOUN
cana-4456	75	32	)	)	PUNCT
cana-4456	75	33	=	=	SYM
cana-4456	75	34	ℎ(𝑥	ℎ(𝑥	NOUN
cana-4456	75	35	,	,	PUNCT
cana-4456	75	36	𝑡)𝑢(𝑥	𝑡)𝑢(𝑥	NOUN
cana-4456	75	37	,	,	PUNCT
cana-4456	75	38	𝑡	𝑡	NOUN
cana-4456	75	39	)	)	PUNCT
cana-4456	75	40	is	be	AUX
cana-4456	75	41	the	the	DET
cana-4456	75	42	flow	flow	NOUN
cana-4456	75	43	discharge	discharge	NOUN
cana-4456	75	44	and	and	CCONJ
cana-4456	75	45	𝑔	𝑔	PROPN
cana-4456	75	46	is	be	AUX
cana-4456	75	47	the	the	DET
cana-4456	75	48	acceleration	acceleration	NOUN
cana-4456	75	49	due	due	ADP
cana-4456	75	50	to	to	ADP
cana-4456	75	51	gravity	gravity	NOUN
cana-4456	75	52	.	.	PUNCT
cana-4456	76	1	concerning	concern	VERB
cana-4456	76	2	the	the	DET
cana-4456	76	3	source	source	NOUN
cana-4456	76	4	terms	term	NOUN
cana-4456	76	5	,	,	PUNCT
cana-4456	76	6	𝑆𝑏	𝑆𝑏	PROPN
cana-4456	76	7	=	=	PUNCT
cana-4456	76	8	−𝜕𝑥𝑏	−𝜕𝑥𝑏	SCONJ
cana-4456	76	9	is	be	AUX
cana-4456	76	10	the	the	DET
cana-4456	76	11	bed	bed	NOUN
cana-4456	76	12	slope	slope	NOUN
cana-4456	76	13	where	where	SCONJ
cana-4456	76	14	𝑏	𝑏	NOUN
cana-4456	76	15	:	:	PUNCT
cana-4456	76	16	ℝ	ℝ	PROPN
cana-4456	76	17	→	→	SYM
cana-4456	76	18	ℝ+	ℝ+	PUNCT
cana-4456	76	19	is	be	AUX
cana-4456	76	20	a	a	DET
cana-4456	76	21	given	give	VERB
cana-4456	76	22	smooth	smooth	ADJ
cana-4456	76	23	function	function	NOUN
cana-4456	76	24	which	which	PRON
cana-4456	76	25	describes	describe	VERB
cana-4456	76	26	the	the	DET
cana-4456	76	27	topography	topography	NOUN
cana-4456	76	28	and	and	CCONJ
cana-4456	76	29	𝑆𝑓	𝑆𝑓	PROPN
cana-4456	76	30	is	be	AUX
cana-4456	76	31	communications	communication	NOUN
cana-4456	76	32	on	on	ADP
cana-4456	76	33	applied	apply	VERB
cana-4456	76	34	nonlinear	nonlinear	ADJ
cana-4456	76	35	analysis	analysis	NOUN
cana-4456	76	36	issn	issn	NOUN
cana-4456	76	37	:	:	PUNCT
cana-4456	76	38	1074	1074	NUM
cana-4456	76	39	-	-	PUNCT
cana-4456	76	40	133x	133x	NUM
cana-4456	76	41	vol	vol	NOUN
cana-4456	76	42	32	32	NUM
cana-4456	76	43	no	no	NOUN
cana-4456	76	44	.	.	PUNCT
cana-4456	77	1	9s	9s	NUM
cana-4456	77	2	(	(	PUNCT
cana-4456	77	3	2025	2025	NUM
cana-4456	77	4	)	)	PUNCT
cana-4456	77	5	2170	2170	NUM
cana-4456	77	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	78	1	the	the	DET
cana-4456	78	2	friction	friction	NOUN
cana-4456	78	3	term	term	NOUN
cana-4456	78	4	,	,	PUNCT
cana-4456	78	5	it	it	PRON
cana-4456	78	6	is	be	AUX
cana-4456	78	7	a	a	DET
cana-4456	78	8	given	give	VERB
cana-4456	78	9	function	function	NOUN
cana-4456	78	10	of	of	ADP
cana-4456	78	11	ℎ	ℎ	PROPN
cana-4456	78	12	and	and	CCONJ
cana-4456	78	13	𝑢	𝑢	NOUN
cana-4456	78	14	,	,	PUNCT
cana-4456	78	15	two	two	NUM
cana-4456	78	16	examples	example	NOUN
cana-4456	78	17	widely	widely	ADV
cana-4456	78	18	used	use	VERB
cana-4456	78	19	in	in	ADP
cana-4456	78	20	hydrology	hydrology	NOUN
cana-4456	78	21	are	be	AUX
cana-4456	78	22	the	the	DET
cana-4456	78	23	manning	manning	NOUN
cana-4456	78	24	and	and	CCONJ
cana-4456	78	25	the	the	DET
cana-4456	78	26	darcy	darcy	NOUN
cana-4456	78	27	-	-	PUNCT
cana-4456	78	28	weisbach	weisbach	NOUN
cana-4456	78	29	friction	friction	NOUN
cana-4456	78	30	laws	law	NOUN
cana-4456	78	31	,	,	PUNCT
cana-4456	78	32	which	which	PRON
cana-4456	78	33	are	be	AUX
cana-4456	78	34	given	give	VERB
cana-4456	78	35	respectively	respectively	ADV
cana-4456	78	36	by	by	ADP
cana-4456	78	37	𝑆𝑓	𝑆𝑓	PROPN
cana-4456	78	38	=	=	SYM
cana-4456	78	39	𝐶𝑓𝑔	𝐶𝑓𝑔	PROPN
cana-4456	78	40	𝑢|𝑢|	𝑢|𝑢|	NOUN
cana-4456	78	41	ℎ	ℎ	NOUN
cana-4456	78	42	1	1	NUM
cana-4456	78	43	3	3	NUM
cana-4456	78	44	=	=	SYM
cana-4456	78	45	𝐶𝑓𝑔	𝐶𝑓𝑔	PROPN
cana-4456	78	46	𝑞|𝑞|	𝑞|𝑞|	NOUN
cana-4456	78	47	ℎ	ℎ	PROPN
cana-4456	78	48	7	7	NUM
cana-4456	78	49	3	3	NUM
cana-4456	78	50	,	,	PUNCT
cana-4456	78	51	  	  	SPACE
cana-4456	78	52	(	(	PUNCT
cana-4456	78	53	2	2	NUM
cana-4456	78	54	)	)	PUNCT
cana-4456	78	55	where	where	SCONJ
cana-4456	78	56	𝐶𝑓	𝐶𝑓	NOUN
cana-4456	78	57	  	  	SPACE
cana-4456	78	58	=	=	SYM
cana-4456	78	59	 	 	SPACE
cana-4456	78	60	𝑛2	𝑛2	NOUN
cana-4456	78	61	,	,	PUNCT
cana-4456	78	62	 	 	SPACE
cana-4456	78	63	𝑛	𝑛	PROPN
cana-4456	78	64	is	be	AUX
cana-4456	78	65	manning	man	VERB
cana-4456	78	66	's	's	PART
cana-4456	78	67	coefficient	coefficient	NOUN
cana-4456	78	68	.	.	PUNCT
cana-4456	79	1	𝑆𝑓	𝑆𝑓	NOUN
cana-4456	79	2	=	=	PUNCT
cana-4456	79	3	𝐶𝑓𝑔𝑢|𝑢|	𝐶𝑓𝑔𝑢|𝑢|	PROPN
cana-4456	79	4	=	=	PUNCT
cana-4456	79	5	𝐶𝑓𝑔	𝐶𝑓𝑔	PROPN
cana-4456	79	6	𝑞|𝑞|	𝑞|𝑞|	NOUN
cana-4456	79	7	ℎ2	ℎ2	NOUN
cana-4456	79	8	,	,	PUNCT
cana-4456	79	9	(	(	PUNCT
cana-4456	79	10	3	3	X
cana-4456	79	11	)	)	PUNCT
cana-4456	79	12	where	where	SCONJ
cana-4456	79	13	𝐶𝑓	𝐶𝑓	NOUN
cana-4456	79	14	=	=	PUNCT
cana-4456	79	15	𝑓	𝑓	DET
cana-4456	79	16	8𝑔	8𝑔	NOUN
cana-4456	79	17	,	,	PUNCT
cana-4456	79	18	𝑓	𝑓	PRON
cana-4456	79	19	is	be	AUX
cana-4456	79	20	dimensionless	dimensionless	ADJ
cana-4456	79	21	coefficient	coefficient	NOUN
cana-4456	79	22	.	.	PUNCT
cana-4456	80	1	in	in	ADP
cana-4456	80	2	order	order	NOUN
cana-4456	80	3	to	to	PART
cana-4456	80	4	emphasize	emphasize	VERB
cana-4456	80	5	the	the	DET
cana-4456	80	6	properties	property	NOUN
cana-4456	80	7	of	of	ADP
cana-4456	80	8	(	(	PUNCT
cana-4456	80	9	1	1	NUM
cana-4456	80	10	)	)	PUNCT
cana-4456	80	11	without	without	ADP
cana-4456	80	12	friction	friction	NOUN
cana-4456	80	13	,	,	PUNCT
cana-4456	80	14	we	we	PRON
cana-4456	80	15	rewrite	rewrite	VERB
cana-4456	80	16	the	the	DET
cana-4456	80	17	one	one	NUM
cana-4456	80	18	-	-	PUNCT
cana-4456	80	19	dimensional	dimensional	ADJ
cana-4456	80	20	equations	equation	NOUN
cana-4456	80	21	in	in	ADP
cana-4456	80	22	quasilinear	quasilinear	NOUN
cana-4456	80	23	form	form	NOUN
cana-4456	80	24	∂t𝐐	∂t𝐐	PROPN
cana-4456	80	25	+	+	CCONJ
cana-4456	80	26	a(𝐐	a(𝐐	NOUN
cana-4456	80	27	)	)	PUNCT
cana-4456	80	28	∂xq	∂xq	PROPN
cana-4456	80	29	=	=	SYM
cana-4456	80	30	s(𝐐	s(𝐐	PROPN
cana-4456	80	31	)	)	PUNCT
cana-4456	80	32	,	,	PUNCT
cana-4456	80	33	(	(	PUNCT
cana-4456	80	34	4	4	X
cana-4456	80	35	)	)	PUNCT
cana-4456	80	36	with	with	ADP
cana-4456	80	37	𝑸	𝑸	PROPN
cana-4456	80	38	=	=	PUNCT
cana-4456	80	39	(	(	PUNCT
cana-4456	80	40	ℎ	ℎ	X
cana-4456	80	41	𝑞	𝑞	PROPN
cana-4456	80	42	)	)	PUNCT
cana-4456	80	43	,	,	PUNCT
cana-4456	80	44	a(𝐐	a(𝐐	NUM
cana-4456	80	45	)	)	PUNCT
cana-4456	81	1	=	=	PRON
cana-4456	81	2	(	(	PUNCT
cana-4456	81	3	0	0	NUM
cana-4456	81	4	1	1	NUM
cana-4456	81	5	−𝑢2	−𝑢2	NOUN
cana-4456	81	6	+	+	CCONJ
cana-4456	81	7	𝑔ℎ	𝑔ℎ	ADJ
cana-4456	81	8	2𝑢	2𝑢	NUM
cana-4456	81	9	)	)	PUNCT
cana-4456	81	10	,	,	PUNCT
cana-4456	81	11	𝑆(𝑸	𝑆(𝑸	NOUN
cana-4456	81	12	)	)	PUNCT
cana-4456	81	13	=	=	PUNCT
cana-4456	81	14	(	(	PUNCT
cana-4456	81	15	0	0	NUM
cana-4456	81	16	−gh	−gh	PROPN
cana-4456	81	17	∂xb	∂xb	PROPN
cana-4456	81	18	)	)	PUNCT
cana-4456	81	19	.	.	PUNCT
cana-4456	82	1	(	(	PUNCT
cana-4456	82	2	5	5	X
cana-4456	82	3	)	)	PUNCT
cana-4456	82	4	when	when	SCONJ
cana-4456	82	5	ℎ	ℎ	X
cana-4456	82	6	>	>	X
cana-4456	82	7	0	0	PROPN
cana-4456	82	8	,	,	PUNCT
cana-4456	82	9	the	the	DET
cana-4456	82	10	system	system	NOUN
cana-4456	82	11	is	be	AUX
cana-4456	82	12	strict	strict	ADJ
cana-4456	82	13	hyperbolic	hyperbolic	ADJ
cana-4456	82	14	with	with	ADP
cana-4456	82	15	the	the	DET
cana-4456	82	16	eigenvalues	eigenvalue	NOUN
cana-4456	82	17	of	of	ADP
cana-4456	82	18	𝐴	𝐴	PROPN
cana-4456	82	19	are	be	AUX
cana-4456	82	20	given	give	VERB
cana-4456	82	21	by	by	ADP
cana-4456	82	22	𝜆1	𝜆1	PROPN
cana-4456	82	23	=	=	PUNCT
cana-4456	82	24	𝑢	𝑢	NOUN
cana-4456	82	25	−	−	PROPN
cana-4456	82	26	√𝑔ℎ	√𝑔ℎ	PROPN
cana-4456	82	27	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-4456	82	28	𝜆2	𝜆2	NOUN
cana-4456	82	29	=	=	SYM
cana-4456	82	30	𝑢	𝑢	PROPN
cana-4456	82	31	+	+	X
cana-4456	82	32	√𝑔ℎ.	√𝑔ℎ.	X
cana-4456	82	33	(	(	PUNCT
cana-4456	82	34	6	6	NUM
cana-4456	82	35	)	)	PUNCT
cana-4456	82	36	these	these	DET
cana-4456	82	37	eigenvalues	eigenvalue	NOUN
cana-4456	82	38	represent	represent	VERB
cana-4456	82	39	the	the	DET
cana-4456	82	40	wave	wave	NOUN
cana-4456	82	41	speeds	speed	NOUN
cana-4456	82	42	which	which	PRON
cana-4456	82	43	are	be	AUX
cana-4456	82	44	basic	basic	ADJ
cana-4456	82	45	characteristics	characteristic	NOUN
cana-4456	82	46	of	of	ADP
cana-4456	82	47	the	the	DET
cana-4456	82	48	flow	flow	NOUN
cana-4456	82	49	.	.	PUNCT
cana-4456	83	1	when	when	SCONJ
cana-4456	83	2	ℎ	ℎ	X
cana-4456	83	3	=	=	SYM
cana-4456	83	4	0	0	NUM
cana-4456	83	5	(	(	PUNCT
cana-4456	83	6	dry	dry	ADJ
cana-4456	83	7	zone	zone	NOUN
cana-4456	83	8	)	)	PUNCT
cana-4456	83	9	the	the	DET
cana-4456	83	10	eigenvalues	eigenvalue	NOUN
cana-4456	83	11	coincide	coincide	NOUN
cana-4456	83	12	and	and	CCONJ
cana-4456	83	13	the	the	DET
cana-4456	83	14	system	system	NOUN
cana-4456	83	15	looses	loose	VERB
cana-4456	83	16	hyperbolicity	hyperbolicity	NOUN
cana-4456	83	17	.	.	PUNCT
cana-4456	84	1	for	for	ADP
cana-4456	84	2	considering	consider	VERB
cana-4456	84	3	the	the	DET
cana-4456	84	4	wellposed	wellpose	VERB
cana-4456	84	5	problem	problem	NOUN
cana-4456	84	6	in	in	ADP
cana-4456	84	7	1d	1d	NUM
cana-4456	84	8	described	describe	VERB
cana-4456	84	9	by	by	ADP
cana-4456	84	10	the	the	DET
cana-4456	84	11	swes	swes	NOUN
cana-4456	84	12	,	,	PUNCT
cana-4456	84	13	the	the	DET
cana-4456	84	14	number	number	NOUN
cana-4456	84	15	of	of	ADP
cana-4456	84	16	boundary	boundary	ADJ
cana-4456	84	17	conditions	condition	NOUN
cana-4456	84	18	should	should	AUX
cana-4456	84	19	be	be	AUX
cana-4456	84	20	confirmed	confirm	VERB
cana-4456	84	21	by	by	ADP
cana-4456	84	22	the	the	DET
cana-4456	84	23	froude	froude	ADJ
cana-4456	84	24	number	number	NOUN
cana-4456	84	25	fr	fr	NOUN
cana-4456	85	1	=	=	PUNCT
cana-4456	85	2	|𝑢|	|𝑢|	PROPN
cana-4456	85	3	√𝑔ℎ	√𝑔ℎ	PROPN
cana-4456	85	4	.	.	PUNCT
cana-4456	86	1	(	(	PUNCT
cana-4456	86	2	7	7	X
cana-4456	86	3	)	)	PUNCT
cana-4456	86	4	if	if	SCONJ
cana-4456	86	5	fr	fr	PROPN
cana-4456	86	6	<	<	X
cana-4456	86	7	1	1	NUM
cana-4456	86	8	the	the	DET
cana-4456	86	9	flow	flow	NOUN
cana-4456	86	10	is	be	AUX
cana-4456	86	11	considered	consider	VERB
cana-4456	86	12	subcritical	subcritical	ADJ
cana-4456	86	13	,	,	PUNCT
cana-4456	86	14	indicating	indicate	VERB
cana-4456	86	15	the	the	DET
cana-4456	86	16	presence	presence	NOUN
cana-4456	86	17	of	of	ADP
cana-4456	86	18	one	one	NUM
cana-4456	86	19	positive	positive	ADJ
cana-4456	86	20	and	and	CCONJ
cana-4456	86	21	one	one	NUM
cana-4456	86	22	negative	negative	ADJ
cana-4456	86	23	eigenvalue	eigenvalue	NOUN
cana-4456	86	24	.	.	PUNCT
cana-4456	87	1	in	in	ADP
cana-4456	87	2	such	such	ADJ
cana-4456	87	3	cases	case	NOUN
cana-4456	87	4	,	,	PUNCT
cana-4456	87	5	it	it	PRON
cana-4456	87	6	is	be	AUX
cana-4456	87	7	necessary	necessary	ADJ
cana-4456	87	8	to	to	PART
cana-4456	87	9	define	define	VERB
cana-4456	87	10	one	one	NUM
cana-4456	87	11	boundary	boundary	ADJ
cana-4456	87	12	value	value	NOUN
cana-4456	87	13	on	on	ADP
cana-4456	87	14	the	the	DET
cana-4456	87	15	left	left	NOUN
cana-4456	87	16	and	and	CCONJ
cana-4456	87	17	another	another	PRON
cana-4456	87	18	on	on	ADP
cana-4456	87	19	the	the	DET
cana-4456	87	20	right	right	NOUN
cana-4456	87	21	.	.	PUNCT
cana-4456	88	1	on	on	ADP
cana-4456	88	2	the	the	DET
cana-4456	88	3	other	other	ADJ
cana-4456	88	4	hand	hand	NOUN
cana-4456	88	5	,	,	PUNCT
cana-4456	88	6	when	when	SCONJ
cana-4456	88	7	fr	fr	PROPN
cana-4456	88	8	>	>	X
cana-4456	88	9	1	1	NUM
cana-4456	88	10	then	then	ADV
cana-4456	88	11	the	the	DET
cana-4456	88	12	flow	flow	NOUN
cana-4456	88	13	is	be	AUX
cana-4456	88	14	supercritical	supercritical	ADJ
cana-4456	88	15	which	which	PRON
cana-4456	88	16	means	mean	VERB
cana-4456	88	17	that	that	SCONJ
cana-4456	88	18	two	two	NUM
cana-4456	88	19	values	value	NOUN
cana-4456	88	20	have	have	VERB
cana-4456	88	21	to	to	PART
cana-4456	88	22	be	be	AUX
cana-4456	88	23	specified	specify	VERB
cana-4456	88	24	at	at	ADP
cana-4456	88	25	one	one	NUM
cana-4456	88	26	of	of	ADP
cana-4456	88	27	the	the	DET
cana-4456	88	28	boundaries	boundary	NOUN
cana-4456	88	29	depending	depend	VERB
cana-4456	88	30	on	on	ADP
cana-4456	88	31	the	the	DET
cana-4456	88	32	sign	sign	NOUN
cana-4456	88	33	of	of	ADP
cana-4456	88	34	the	the	DET
cana-4456	88	35	velocity	velocity	NOUN
cana-4456	88	36	.	.	PUNCT
cana-4456	89	1	a	a	DET
cana-4456	89	2	transcritical	transcritical	ADJ
cana-4456	89	3	regime	regime	NOUN
cana-4456	89	4	can	can	AUX
cana-4456	89	5	exist	exist	VERB
cana-4456	89	6	in	in	ADP
cana-4456	89	7	the	the	DET
cana-4456	89	8	solution	solution	NOUN
cana-4456	89	9	if	if	SCONJ
cana-4456	89	10	parts	part	NOUN
cana-4456	89	11	of	of	ADP
cana-4456	89	12	the	the	DET
cana-4456	89	13	flow	flow	NOUN
cana-4456	89	14	are	be	AUX
cana-4456	89	15	subcritical	subcritical	ADJ
cana-4456	89	16	and	and	CCONJ
cana-4456	89	17	other	other	ADJ
cana-4456	89	18	parts	part	NOUN
cana-4456	89	19	are	be	AUX
cana-4456	89	20	supercritical	supercritical	ADJ
cana-4456	89	21	.	.	PUNCT
cana-4456	90	1	2.1	2.1	NUM
cana-4456	90	2	hyperviscosity	hyperviscosity	NOUN
cana-4456	90	3	technique	technique	NOUN
cana-4456	90	4	although	although	SCONJ
cana-4456	90	5	the	the	DET
cana-4456	90	6	global	global	ADJ
cana-4456	90	7	stability	stability	NOUN
cana-4456	90	8	theory	theory	NOUN
cana-4456	90	9	of	of	ADP
cana-4456	90	10	rbf	rbf	PROPN
cana-4456	90	11	-	-	PUNCT
cana-4456	90	12	fd	fd	PROPN
cana-4456	90	13	and	and	CCONJ
cana-4456	90	14	rbf	rbf	PROPN
cana-4456	90	15	-	-	PUNCT
cana-4456	90	16	pum	pum	PROPN
cana-4456	90	17	methods	method	NOUN
cana-4456	90	18	is	be	AUX
cana-4456	90	19	largely	largely	ADV
cana-4456	90	20	undeveloped	undeveloped	ADJ
cana-4456	90	21	,	,	PUNCT
cana-4456	90	22	fornberg	fornberg	NOUN
cana-4456	90	23	and	and	CCONJ
cana-4456	90	24	lehto	lehto	NOUN
cana-4456	90	25	[	[	X
cana-4456	90	26	20	20	NUM
cana-4456	90	27	]	]	PUNCT
cana-4456	90	28	proposed	propose	VERB
cana-4456	90	29	a	a	DET
cana-4456	90	30	practical	practical	ADJ
cana-4456	90	31	method	method	NOUN
cana-4456	90	32	to	to	PART
cana-4456	90	33	correct	correct	VERB
cana-4456	90	34	the	the	DET
cana-4456	90	35	spectra	spectra	NOUN
cana-4456	90	36	of	of	ADP
cana-4456	90	37	rbf	rbf	PROPN
cana-4456	90	38	-	-	PUNCT
cana-4456	90	39	fd	fd	PROPN
cana-4456	90	40	differentiation	differentiation	NOUN
cana-4456	90	41	matrices	matrix	NOUN
cana-4456	90	42	for	for	ADP
cana-4456	90	43	hyperbolic	hyperbolic	ADJ
cana-4456	90	44	operators	operator	NOUN
cana-4456	90	45	on	on	ADP
cana-4456	90	46	the	the	DET
cana-4456	90	47	sphere	sphere	NOUN
cana-4456	90	48	by	by	ADP
cana-4456	90	49	introducing	introduce	VERB
cana-4456	90	50	artificial	artificial	ADJ
cana-4456	90	51	hyperviscosity	hyperviscosity	NOUN
cana-4456	90	52	.	.	PUNCT
cana-4456	91	1	their	their	PRON
cana-4456	91	2	approach	approach	NOUN
cana-4456	91	3	effectively	effectively	ADV
cana-4456	91	4	shifted	shift	VERB
cana-4456	91	5	rogue	rogue	NOUN
cana-4456	91	6	eigenvalues	eigenvalue	NOUN
cana-4456	91	7	to	to	ADP
cana-4456	91	8	the	the	DET
cana-4456	91	9	left	left	ADJ
cana-4456	91	10	half	half	NOUN
cana-4456	91	11	of	of	ADP
cana-4456	91	12	the	the	DET
cana-4456	91	13	complex	complex	ADJ
cana-4456	91	14	plane	plane	NOUN
cana-4456	91	15	.	.	PUNCT
cana-4456	92	1	this	this	DET
cana-4456	92	2	issue	issue	NOUN
cana-4456	92	3	is	be	AUX
cana-4456	92	4	also	also	ADV
cana-4456	92	5	caused	cause	VERB
cana-4456	92	6	by	by	ADP
cana-4456	92	7	using	use	VERB
cana-4456	92	8	large	large	ADJ
cana-4456	92	9	rbf	rbf	PROPN
cana-4456	92	10	-	-	PUNCT
cana-4456	92	11	fd	fd	PROPN
cana-4456	92	12	stencils	stencil	NOUN
cana-4456	92	13	,	,	PUNCT
cana-4456	92	14	where	where	SCONJ
cana-4456	92	15	increasing	increase	VERB
cana-4456	92	16	the	the	DET
cana-4456	92	17	stencil	stencil	PROPN
cana-4456	92	18	size	size	NOUN
cana-4456	92	19	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	NOUN
cana-4456	92	20	enhances	enhance	VERB
cana-4456	92	21	the	the	DET
cana-4456	92	22	accuracy	accuracy	NOUN
cana-4456	92	23	of	of	ADP
cana-4456	92	24	the	the	DET
cana-4456	92	25	approximation	approximation	NOUN
cana-4456	92	26	.	.	PUNCT
cana-4456	93	1	based	base	VERB
cana-4456	93	2	on	on	ADP
cana-4456	93	3	the	the	DET
cana-4456	93	4	above	above	ADJ
cana-4456	93	5	analysis	analysis	NOUN
cana-4456	93	6	,	,	PUNCT
cana-4456	93	7	we	we	PRON
cana-4456	93	8	will	will	AUX
cana-4456	93	9	use	use	VERB
cana-4456	93	10	the	the	DET
cana-4456	93	11	kansa	kansa	PROPN
cana-4456	93	12	,	,	PUNCT
cana-4456	93	13	rbf	rbf	PROPN
cana-4456	93	14	-	-	PUNCT
cana-4456	93	15	fd	fd	PROPN
cana-4456	93	16	,	,	PUNCT
cana-4456	93	17	and	and	CCONJ
cana-4456	93	18	rbf	rbf	PROPN
cana-4456	93	19	-	-	PUNCT
cana-4456	93	20	pum	pum	PROPN
cana-4456	93	21	methods	method	NOUN
cana-4456	93	22	combined	combine	VERB
cana-4456	93	23	with	with	ADP
cana-4456	93	24	an	an	DET
cana-4456	93	25	artificial	artificial	ADJ
cana-4456	93	26	hyperviscosity	hyperviscosity	NOUN
cana-4456	93	27	formulation	formulation	NOUN
cana-4456	93	28	to	to	PART
cana-4456	93	29	solve	solve	VERB
cana-4456	93	30	the	the	DET
cana-4456	93	31	shallow	shallow	ADJ
cana-4456	93	32	water	water	NOUN
cana-4456	93	33	equations	equation	NOUN
cana-4456	93	34	,	,	PUNCT
cana-4456	93	35	where	where	SCONJ
cana-4456	93	36	the	the	DET
cana-4456	93	37	convection	convection	NOUN
cana-4456	93	38	term	term	NOUN
cana-4456	93	39	dominates	dominate	VERB
cana-4456	93	40	and	and	CCONJ
cana-4456	93	41	leads	lead	VERB
cana-4456	93	42	to	to	ADP
cana-4456	93	43	non	non	ADJ
cana-4456	93	44	-	-	ADJ
cana-4456	93	45	physical	physical	ADJ
cana-4456	93	46	oscillations	oscillation	NOUN
cana-4456	93	47	that	that	PRON
cana-4456	93	48	would	would	AUX
cana-4456	93	49	otherwise	otherwise	ADV
cana-4456	93	50	amplify	amplify	VERB
cana-4456	93	51	with	with	ADP
cana-4456	93	52	time	time	NOUN
cana-4456	93	53	.	.	PUNCT
cana-4456	94	1	communications	communication	NOUN
cana-4456	94	2	on	on	ADP
cana-4456	94	3	applied	apply	VERB
cana-4456	94	4	nonlinear	nonlinear	ADJ
cana-4456	94	5	analysis	analysis	NOUN
cana-4456	94	6	issn	issn	NOUN
cana-4456	94	7	:	:	PUNCT
cana-4456	94	8	1074	1074	NUM
cana-4456	94	9	-	-	PUNCT
cana-4456	94	10	133x	133x	NUM
cana-4456	94	11	vol	vol	NOUN
cana-4456	94	12	32	32	NUM
cana-4456	94	13	no	no	NOUN
cana-4456	94	14	.	.	PUNCT
cana-4456	95	1	9s	9s	NUM
cana-4456	95	2	(	(	PUNCT
cana-4456	95	3	2025	2025	NUM
cana-4456	95	4	)	)	PUNCT
cana-4456	95	5	2171	2171	NUM
cana-4456	96	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	96	2	stabilization	stabilization	NOUN
cana-4456	96	3	of	of	ADP
cana-4456	96	4	the	the	DET
cana-4456	96	5	methods	method	NOUN
cana-4456	96	6	is	be	AUX
cana-4456	96	7	achieved	achieve	VERB
cana-4456	96	8	by	by	ADP
cana-4456	96	9	applying	apply	VERB
cana-4456	96	10	a	a	DET
cana-4456	96	11	hyperviscosity	hyperviscosity	NOUN
cana-4456	96	12	as	as	ADP
cana-4456	96	13	a	a	DET
cana-4456	96	14	filter	filter	NOUN
cana-4456	96	15	to	to	ADP
cana-4456	96	16	the	the	DET
cana-4456	96	17	right	right	ADJ
cana-4456	96	18	hand	hand	NOUN
cana-4456	96	19	side	side	NOUN
cana-4456	96	20	of	of	ADP
cana-4456	96	21	the	the	DET
cana-4456	96	22	model	model	NOUN
cana-4456	96	23	,	,	PUNCT
cana-4456	96	24	the	the	DET
cana-4456	96	25	equation	equation	NOUN
cana-4456	96	26	solved	solve	VERB
cana-4456	96	27	takes	take	VERB
cana-4456	96	28	the	the	DET
cana-4456	96	29	form	form	NOUN
cana-4456	96	30	𝜕𝑡𝑸	𝜕𝑡𝑸	NUM
cana-4456	96	31	=	=	SYM
cana-4456	96	32	−𝐹(𝑸	−𝐹(𝑸	X
cana-4456	96	33	)	)	PUNCT
cana-4456	97	1	+	+	CCONJ
cana-4456	97	2	𝑆(𝑸	𝑆(𝑸	NOUN
cana-4456	97	3	)	)	PUNCT
cana-4456	97	4	+	+	CCONJ
cana-4456	97	5	𝐻(𝑸	𝐻(𝑸	ADJ
cana-4456	97	6	)	)	PUNCT
cana-4456	97	7	,	,	PUNCT
cana-4456	97	8	(	(	PUNCT
cana-4456	97	9	8)	8)	NUM
cana-4456	97	10	where	where	SCONJ
cana-4456	97	11	𝑸	𝑸	NOUN
cana-4456	97	12	=	=	SYM
cana-4456	97	13	(	(	PUNCT
cana-4456	97	14	ℎ	ℎ	X
cana-4456	97	15	𝑞	𝑞	PROPN
cana-4456	97	16	)	)	PUNCT
cana-4456	97	17	,	,	PUNCT
cana-4456	97	18	f(𝐐	f(𝐐	NOUN
cana-4456	97	19	)	)	PUNCT
cana-4456	97	20	=	=	PRON
cana-4456	97	21	(	(	PUNCT
cana-4456	97	22	𝜕𝑥𝑞	𝜕𝑥𝑞	X
cana-4456	97	23	𝜕𝑥	𝜕𝑥	X
cana-4456	97	24	(	(	PUNCT
cana-4456	97	25	𝑞2	𝑞2	NOUN
cana-4456	97	26	ℎ	ℎ	PART
cana-4456	97	27	+	+	NOUN
cana-4456	97	28	1	1	NUM
cana-4456	97	29	2	2	NUM
cana-4456	97	30	𝑔ℎ2	𝑔ℎ2	NOUN
cana-4456	97	31	)	)	PUNCT
cana-4456	97	32	)	)	PUNCT
cana-4456	97	33	,	,	PUNCT
cana-4456	97	34	𝑆(𝑸	𝑆(𝑸	NOUN
cana-4456	97	35	)	)	PUNCT
cana-4456	97	36	=	=	PUNCT
cana-4456	98	1	(	(	PUNCT
cana-4456	98	2	0	0	NUM
cana-4456	98	3	𝑔ℎ𝑆𝑏−𝑆𝑓	𝑔ℎ𝑆𝑏−𝑆𝑓	PROPN
cana-4456	98	4	)	)	PUNCT
cana-4456	98	5	,	,	PUNCT
cana-4456	98	6	(	(	PUNCT
cana-4456	98	7	9	9	X
cana-4456	98	8	)	)	PUNCT
cana-4456	99	1	and	and	CCONJ
cana-4456	99	2	𝐻	𝐻	PROPN
cana-4456	99	3	is	be	AUX
cana-4456	99	4	the	the	DET
cana-4456	99	5	hyperviscosity	hyperviscosity	NOUN
cana-4456	99	6	filter	filter	NOUN
cana-4456	99	7	defined	define	VERB
cana-4456	99	8	by	by	ADP
cana-4456	99	9	𝐻	𝐻	PROPN
cana-4456	99	10	=	=	PUNCT
cana-4456	99	11	𝜇	𝜇	ADP
cana-4456	99	12	𝜕2𝑘	𝜕2𝑘	PROPN
cana-4456	99	13	𝜕𝑥2𝑘	𝜕𝑥2𝑘	PROPN
cana-4456	99	14	,	,	PUNCT
cana-4456	99	15	(	(	PUNCT
cana-4456	99	16	10	10	NUM
cana-4456	99	17	)	)	PUNCT
cana-4456	99	18	where	where	SCONJ
cana-4456	99	19	𝜇	𝜇	ADP
cana-4456	99	20	∈	∈	PROPN
cana-4456	99	21	𝑅	𝑅	PROPN
cana-4456	99	22	and	and	CCONJ
cana-4456	99	23	𝑘	𝑘	PRON
cana-4456	99	24	∈	∈	NOUN
cana-4456	99	25	𝑁∗	𝑁∗	VERB
cana-4456	99	26	small	small	ADJ
cana-4456	99	27	numbers	number	NOUN
cana-4456	99	28	that	that	PRON
cana-4456	99	29	must	must	AUX
cana-4456	99	30	be	be	AUX
cana-4456	99	31	selected	select	VERB
cana-4456	99	32	.	.	PUNCT
cana-4456	100	1	the	the	DET
cana-4456	100	2	constant	constant	ADJ
cana-4456	100	3	μ	μ	PROPN
cana-4456	100	4	has	have	VERB
cana-4456	100	5	to	to	PART
cana-4456	100	6	be	be	AUX
cana-4456	100	7	selected	select	VERB
cana-4456	100	8	carefully	carefully	ADV
cana-4456	100	9	to	to	PART
cana-4456	100	10	provide	provide	VERB
cana-4456	100	11	enough	enough	ADJ
cana-4456	100	12	stabilisation	stabilisation	NOUN
cana-4456	100	13	without	without	ADP
cana-4456	100	14	ruining	ruin	VERB
cana-4456	100	15	the	the	DET
cana-4456	100	16	solution	solution	NOUN
cana-4456	100	17	[	[	X
cana-4456	100	18	20	20	NUM
cana-4456	100	19	,	,	PUNCT
cana-4456	100	20	23	23	NUM
cana-4456	100	21	]	]	PUNCT
cana-4456	100	22	.	.	PUNCT
cana-4456	101	1	there	there	PRON
cana-4456	101	2	is	be	VERB
cana-4456	101	3	no	no	DET
cana-4456	101	4	broad	broad	ADJ
cana-4456	101	5	consensus	consensus	NOUN
cana-4456	101	6	in	in	ADP
cana-4456	101	7	the	the	DET
cana-4456	101	8	literature	literature	NOUN
cana-4456	101	9	with	with	ADP
cana-4456	101	10	an	an	DET
cana-4456	101	11	abundance	abundance	NOUN
cana-4456	101	12	of	of	ADP
cana-4456	101	13	proposed	propose	VERB
cana-4456	101	14	estimates	estimate	NOUN
cana-4456	101	15	and	and	CCONJ
cana-4456	101	16	scalings	scaling	NOUN
cana-4456	101	17	for	for	ADP
cana-4456	101	18	the	the	DET
cana-4456	101	19	constant	constant	ADJ
cana-4456	101	20	μ	μ	NOUN
cana-4456	101	21	.	.	PUNCT
cana-4456	102	1	however	however	ADV
cana-4456	102	2	,	,	PUNCT
cana-4456	102	3	there	there	PRON
cana-4456	102	4	are	be	VERB
cana-4456	102	5	many	many	ADJ
cana-4456	102	6	studies	study	NOUN
cana-4456	102	7	suggesting	suggest	VERB
cana-4456	102	8	that	that	SCONJ
cana-4456	102	9	the	the	DET
cana-4456	102	10	hyperviscosity	hyperviscosity	NOUN
cana-4456	102	11	parameter	parameter	NOUN
cana-4456	102	12	should	should	AUX
cana-4456	102	13	be	be	AUX
cana-4456	102	14	chosen	choose	VERB
cana-4456	102	15	through	through	ADP
cana-4456	102	16	trial	trial	NOUN
cana-4456	102	17	and	and	CCONJ
cana-4456	102	18	error	error	NOUN
cana-4456	102	19	.	.	PUNCT
cana-4456	103	1	fornberg	fornberg	PROPN
cana-4456	103	2	and	and	CCONJ
cana-4456	103	3	lehto	lehto	NOUN
cana-4456	104	1	[	[	X
cana-4456	104	2	20	20	NUM
cana-4456	104	3	]	]	PUNCT
cana-4456	104	4	provide	provide	VERB
cana-4456	104	5	suggestions	suggestion	NOUN
cana-4456	104	6	for	for	ADP
cana-4456	104	7	selecting	select	VERB
cana-4456	104	8	μ	μ	NOUN
cana-4456	104	9	in	in	ADP
cana-4456	104	10	the	the	DET
cana-4456	104	11	rbf	rbf	PROPN
cana-4456	104	12	-	-	PUNCT
cana-4456	104	13	fd	fd	PROPN
cana-4456	104	14	method	method	NOUN
cana-4456	104	15	,	,	PUNCT
cana-4456	104	16	they	they	PRON
cana-4456	104	17	found	find	VERB
cana-4456	104	18	scaling	scale	VERB
cana-4456	104	19	𝜇	𝜇	ADP
cana-4456	104	20	~	~	PUNCT
cana-4456	104	21	𝑁−2𝑘	𝑁−2𝑘	PROPN
cana-4456	104	22	worked	work	VERB
cana-4456	104	23	well	well	ADV
cana-4456	104	24	,	,	PUNCT
cana-4456	104	25	where	where	SCONJ
cana-4456	104	26	n	n	PRON
cana-4456	104	27	is	be	AUX
cana-4456	104	28	the	the	DET
cana-4456	104	29	total	total	ADJ
cana-4456	104	30	number	number	NOUN
cana-4456	104	31	of	of	ADP
cana-4456	104	32	nodes	node	NOUN
cana-4456	104	33	in	in	ADP
cana-4456	104	34	the	the	DET
cana-4456	104	35	domain	domain	NOUN
cana-4456	104	36	.	.	PUNCT
cana-4456	105	1	then	then	ADV
cana-4456	105	2	,	,	PUNCT
cana-4456	105	3	in	in	ADP
cana-4456	105	4	[	[	X
cana-4456	105	5	23	23	NUM
cana-4456	105	6	]	]	PUNCT
cana-4456	105	7	,	,	PUNCT
cana-4456	105	8	flyer	flyer	NOUN
cana-4456	105	9	et	et	PROPN
cana-4456	105	10	al	al	PROPN
cana-4456	105	11	.	.	PROPN
cana-4456	105	12	empirically	empirically	ADV
cana-4456	105	13	computed	compute	VERB
cana-4456	105	14	μ	μ	PROPN
cana-4456	105	15	and	and	CCONJ
cana-4456	105	16	k	k	PROPN
cana-4456	105	17	for	for	ADP
cana-4456	105	18	the	the	DET
cana-4456	105	19	shallow	shallow	ADJ
cana-4456	105	20	water	water	NOUN
cana-4456	105	21	equations	equation	NOUN
cana-4456	105	22	on	on	ADP
cana-4456	105	23	the	the	DET
cana-4456	105	24	sphere	sphere	NOUN
cana-4456	105	25	.	.	PUNCT
cana-4456	106	1	they	they	PRON
cana-4456	106	2	found	find	VERB
cana-4456	106	3	experimentally	experimentally	ADV
cana-4456	106	4	that	that	SCONJ
cana-4456	106	5	for	for	ADP
cana-4456	106	6	given	give	VERB
cana-4456	106	7	values	value	NOUN
cana-4456	106	8	of	of	ADP
cana-4456	106	9	n	n	CCONJ
cana-4456	106	10	,	,	PUNCT
cana-4456	106	11	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	NOUN
cana-4456	106	12	and	and	CCONJ
cana-4456	106	13	𝜀	𝜀	PROPN
cana-4456	106	14	,	,	PUNCT
cana-4456	106	15	choosing	choose	VERB
cana-4456	106	16	𝜇	𝜇	ADP
cana-4456	106	17	=	=	PUNCT
cana-4456	106	18	𝜇𝑐𝑁−𝑘	𝜇𝑐𝑁−𝑘	PROPN
cana-4456	106	19	where	where	SCONJ
cana-4456	106	20	𝜇𝑐	𝜇𝑐	NOUN
cana-4456	106	21	ranging	range	VERB
cana-4456	106	22	from	from	ADP
cana-4456	106	23	o(1	o(1	NOUN
cana-4456	106	24	)	)	PUNCT
cana-4456	106	25	to	to	ADP
cana-4456	106	26	o(10−2	o(10−2	NOUN
cana-4456	106	27	)	)	PUNCT
cana-4456	106	28	provides	provide	VERB
cana-4456	106	29	stability	stability	NOUN
cana-4456	106	30	with	with	ADP
cana-4456	106	31	good	good	ADJ
cana-4456	106	32	accuracy	accuracy	NOUN
cana-4456	106	33	for	for	ADP
cana-4456	106	34	pdes	pde	NOUN
cana-4456	106	35	.	.	PUNCT
cana-4456	107	1	in	in	ADP
cana-4456	107	2	this	this	DET
cana-4456	107	3	paper	paper	NOUN
cana-4456	107	4	,	,	PUNCT
cana-4456	107	5	we	we	PRON
cana-4456	107	6	experimentally	experimentally	ADV
cana-4456	107	7	determine	determine	VERB
cana-4456	107	8	the	the	DET
cana-4456	107	9	hyperviscosity	hyperviscosity	NOUN
cana-4456	107	10	parameter	parameter	NOUN
cana-4456	107	11	through	through	ADP
cana-4456	107	12	trial	trial	NOUN
cana-4456	107	13	and	and	CCONJ
cana-4456	107	14	error	error	NOUN
cana-4456	107	15	,	,	PUNCT
cana-4456	107	16	the	the	DET
cana-4456	107	17	order	order	NOUN
cana-4456	107	18	k	k	PROPN
cana-4456	107	19	set	set	VERB
cana-4456	107	20	to	to	ADP
cana-4456	107	21	one	one	NUM
cana-4456	107	22	,	,	PUNCT
cana-4456	107	23	drawing	draw	VERB
cana-4456	107	24	on	on	ADP
cana-4456	107	25	the	the	DET
cana-4456	107	26	work	work	NOUN
cana-4456	107	27	of	of	ADP
cana-4456	107	28	dehghan	dehghan	PROPN
cana-4456	107	29	and	and	CCONJ
cana-4456	107	30	abbaszadeh	abbaszadeh	X
cana-4456	107	31	[	[	X
cana-4456	107	32	29	29	NUM
cana-4456	107	33	]	]	PUNCT
cana-4456	107	34	,	,	PUNCT
cana-4456	107	35	who	who	PRON
cana-4456	107	36	used	use	VERB
cana-4456	107	37	a	a	DET
cana-4456	107	38	value	value	NOUN
cana-4456	107	39	of	of	ADP
cana-4456	107	40	10−3	10−3	NUM
cana-4456	107	41	to	to	PART
cana-4456	107	42	stabilize	stabilize	VERB
cana-4456	107	43	their	their	PRON
cana-4456	107	44	method	method	NOUN
cana-4456	107	45	for	for	ADP
cana-4456	107	46	the	the	DET
cana-4456	107	47	dam	dam	NOUN
cana-4456	107	48	break	break	NOUN
cana-4456	107	49	problem	problem	NOUN
cana-4456	107	50	.	.	PUNCT
cana-4456	108	1	we	we	PRON
cana-4456	108	2	also	also	ADV
cana-4456	108	3	reference	reference	VERB
cana-4456	108	4	[	[	X
cana-4456	108	5	27	27	NUM
cana-4456	108	6	]	]	PUNCT
cana-4456	108	7	,	,	PUNCT
cana-4456	108	8	where	where	SCONJ
cana-4456	108	9	values	value	NOUN
cana-4456	108	10	ranging	range	VERB
cana-4456	108	11	from	from	ADP
cana-4456	108	12	0.01	0.01	NUM
cana-4456	108	13	to	to	PART
cana-4456	108	14	0.5	0.5	NUM
cana-4456	108	15	were	be	AUX
cana-4456	108	16	employed	employ	VERB
cana-4456	108	17	with	with	ADP
cana-4456	108	18	an	an	DET
cana-4456	108	19	order	order	NOUN
cana-4456	108	20	k	k	PROPN
cana-4456	108	21	set	set	VERB
cana-4456	108	22	to	to	ADP
cana-4456	108	23	one	one	NUM
cana-4456	108	24	,	,	PUNCT
cana-4456	108	25	and	and	CCONJ
cana-4456	108	26	[	[	X
cana-4456	108	27	30	30	NUM
cana-4456	108	28	]	]	PUNCT
cana-4456	108	29	,	,	PUNCT
cana-4456	108	30	where	where	SCONJ
cana-4456	108	31	a	a	DET
cana-4456	108	32	small	small	ADJ
cana-4456	108	33	value	value	NOUN
cana-4456	108	34	around	around	ADP
cana-4456	108	35	10−5	10−5	NUM
cana-4456	108	36	was	be	AUX
cana-4456	108	37	deliberately	deliberately	ADV
cana-4456	108	38	chosen	choose	VERB
cana-4456	108	39	with	with	ADP
cana-4456	108	40	the	the	DET
cana-4456	108	41	same	same	ADJ
cana-4456	108	42	order	order	NOUN
cana-4456	108	43	k.	k.	NOUN
cana-4456	109	1	3	3	X
cana-4456	109	2	.	.	PUNCT
cana-4456	109	3	numerical	numerical	ADJ
cana-4456	109	4	methods	method	NOUN
cana-4456	109	5	3.1	3.1	NUM
cana-4456	109	6	kansa	kansa	PROPN
cana-4456	109	7	method	method	PROPN
cana-4456	109	8	first	first	ADV
cana-4456	109	9	,	,	PUNCT
cana-4456	109	10	we	we	PRON
cana-4456	109	11	introduce	introduce	VERB
cana-4456	109	12	the	the	DET
cana-4456	109	13	well	well	ADV
cana-4456	109	14	-	-	PUNCT
cana-4456	109	15	known	know	VERB
cana-4456	109	16	kansa	kansa	PROPN
cana-4456	109	17	method	method	NOUN
cana-4456	109	18	[	[	X
cana-4456	109	19	12	12	NUM
cana-4456	109	20	,	,	PUNCT
cana-4456	109	21	13	13	NUM
cana-4456	109	22	]	]	PUNCT
cana-4456	109	23	.	.	PUNCT
cana-4456	110	1	it	it	PRON
cana-4456	110	2	is	be	AUX
cana-4456	110	3	also	also	ADV
cana-4456	110	4	referred	refer	VERB
cana-4456	110	5	to	to	ADP
cana-4456	110	6	as	as	ADP
cana-4456	110	7	radial	radial	ADJ
cana-4456	110	8	basis	basis	NOUN
cana-4456	110	9	function	function	NOUN
cana-4456	110	10	collocation	collocation	NOUN
cana-4456	110	11	method	method	NOUN
cana-4456	110	12	(	(	PUNCT
cana-4456	110	13	rbfcm	rbfcm	NOUN
cana-4456	110	14	)	)	PUNCT
cana-4456	110	15	.	.	PUNCT
cana-4456	111	1	the	the	DET
cana-4456	111	2	main	main	ADJ
cana-4456	111	3	idea	idea	NOUN
cana-4456	111	4	of	of	ADP
cana-4456	111	5	the	the	DET
cana-4456	111	6	method	method	NOUN
cana-4456	111	7	is	be	AUX
cana-4456	111	8	approximating	approximate	VERB
cana-4456	111	9	the	the	DET
cana-4456	111	10	solution	solution	NOUN
cana-4456	111	11	in	in	ADP
cana-4456	111	12	terms	term	NOUN
cana-4456	111	13	of	of	ADP
cana-4456	111	14	linear	linear	ADJ
cana-4456	111	15	combination	combination	NOUN
cana-4456	111	16	of	of	ADP
cana-4456	111	17	infinitely	infinitely	ADV
cana-4456	111	18	differentiable	differentiable	ADJ
cana-4456	111	19	radial	radial	ADJ
cana-4456	111	20	basis	basis	NOUN
cana-4456	111	21	functions	function	NOUN
cana-4456	111	22	(	(	PUNCT
cana-4456	111	23	rbfs	rbfs	NOUN
cana-4456	111	24	)	)	PUNCT
cana-4456	111	25	𝜑	𝜑	NOUN
cana-4456	111	26	which	which	PRON
cana-4456	111	27	are	be	AUX
cana-4456	111	28	listed	list	VERB
cana-4456	111	29	in	in	ADP
cana-4456	111	30	table	table	NOUN
cana-4456	111	31	1	1	NUM
cana-4456	111	32	,	,	PUNCT
cana-4456	111	33	this	this	DET
cana-4456	111	34	functions	function	NOUN
cana-4456	111	35	depends	depend	VERB
cana-4456	111	36	only	only	ADV
cana-4456	111	37	on	on	ADP
cana-4456	111	38	the	the	DET
cana-4456	111	39	distance	distance	NOUN
cana-4456	111	40	to	to	ADP
cana-4456	111	41	a	a	DET
cana-4456	111	42	center	center	NOUN
cana-4456	111	43	point	point	NOUN
cana-4456	111	44	and	and	CCONJ
cana-4456	111	45	shape	shape	NOUN
cana-4456	111	46	parameter	parameter	NOUN
cana-4456	111	47	𝜀.	𝜀.	VERB
cana-4456	111	48	this	this	DET
cana-4456	111	49	method	method	NOUN
cana-4456	111	50	is	be	AUX
cana-4456	111	51	particularly	particularly	ADV
cana-4456	111	52	useful	useful	ADJ
cana-4456	111	53	for	for	ADP
cana-4456	111	54	solving	solve	VERB
cana-4456	111	55	pdes	pde	NOUN
cana-4456	111	56	in	in	ADP
cana-4456	111	57	complex	complex	ADJ
cana-4456	111	58	geometries	geometry	NOUN
cana-4456	111	59	with	with	ADP
cana-4456	111	60	irregularly	irregularly	ADV
cana-4456	111	61	distributed	distribute	VERB
cana-4456	111	62	points	point	NOUN
cana-4456	111	63	,	,	PUNCT
cana-4456	111	64	offering	offer	VERB
cana-4456	111	65	an	an	DET
cana-4456	111	66	efficient	efficient	ADJ
cana-4456	111	67	and	and	CCONJ
cana-4456	111	68	flexible	flexible	ADJ
cana-4456	111	69	numerical	numerical	ADJ
cana-4456	111	70	technique	technique	NOUN
cana-4456	111	71	.	.	PUNCT
cana-4456	112	1	however	however	ADV
cana-4456	112	2	,	,	PUNCT
cana-4456	112	3	the	the	DET
cana-4456	112	4	main	main	ADJ
cana-4456	112	5	disadvantage	disadvantage	NOUN
cana-4456	112	6	of	of	ADP
cana-4456	112	7	the	the	DET
cana-4456	112	8	method	method	NOUN
cana-4456	112	9	is	be	AUX
cana-4456	112	10	that	that	SCONJ
cana-4456	112	11	it	it	PRON
cana-4456	112	12	represents	represent	VERB
cana-4456	112	13	the	the	DET
cana-4456	112	14	discretization	discretization	NOUN
cana-4456	112	15	of	of	ADP
cana-4456	112	16	the	the	DET
cana-4456	112	17	pde	pde	NOUN
cana-4456	112	18	as	as	ADP
cana-4456	112	19	a	a	DET
cana-4456	112	20	dense	dense	ADJ
cana-4456	112	21	matrix	matrix	NOUN
cana-4456	112	22	.	.	PUNCT
cana-4456	113	1	these	these	DET
cana-4456	113	2	matrices	matrix	NOUN
cana-4456	113	3	are	be	AUX
cana-4456	113	4	communications	communication	NOUN
cana-4456	113	5	on	on	ADP
cana-4456	113	6	applied	apply	VERB
cana-4456	113	7	nonlinear	nonlinear	ADJ
cana-4456	113	8	analysis	analysis	NOUN
cana-4456	113	9	issn	issn	NOUN
cana-4456	113	10	:	:	PUNCT
cana-4456	113	11	1074	1074	NUM
cana-4456	113	12	-	-	PUNCT
cana-4456	113	13	133x	133x	NUM
cana-4456	113	14	vol	vol	NOUN
cana-4456	113	15	32	32	NUM
cana-4456	114	1	no	no	NOUN
cana-4456	114	2	.	.	PUNCT
cana-4456	115	1	9s	9s	NUM
cana-4456	115	2	(	(	PUNCT
cana-4456	115	3	2025	2025	NUM
cana-4456	115	4	)	)	PUNCT
cana-4456	115	5	2172	2172	NUM
cana-4456	115	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	115	7	extremely	extremely	ADV
cana-4456	115	8	sensitive	sensitive	ADJ
cana-4456	115	9	to	to	ADP
cana-4456	115	10	the	the	DET
cana-4456	115	11	choice	choice	NOUN
cana-4456	115	12	of	of	ADP
cana-4456	115	13	the	the	DET
cana-4456	115	14	shape	shape	NOUN
cana-4456	115	15	parameter	parameter	NOUN
cana-4456	115	16	for	for	ADP
cana-4456	115	17	the	the	DET
cana-4456	115	18	rbfs	rbfs	NOUN
cana-4456	115	19	,	,	PUNCT
cana-4456	115	20	which	which	PRON
cana-4456	115	21	makes	make	VERB
cana-4456	115	22	it	it	PRON
cana-4456	115	23	difficult	difficult	ADJ
cana-4456	115	24	to	to	PART
cana-4456	115	25	solve	solve	VERB
cana-4456	115	26	problems	problem	NOUN
cana-4456	115	27	with	with	ADP
cana-4456	115	28	a	a	DET
cana-4456	115	29	large	large	ADJ
cana-4456	115	30	number	number	NOUN
cana-4456	115	31	of	of	ADP
cana-4456	115	32	unknowns	unknown	NOUN
cana-4456	115	33	.	.	PUNCT
cana-4456	116	1	this	this	PRON
cana-4456	116	2	occurs	occur	VERB
cana-4456	116	3	because	because	SCONJ
cana-4456	116	4	in	in	ADP
cana-4456	116	5	the	the	DET
cana-4456	116	6	use	use	NOUN
cana-4456	116	7	of	of	ADP
cana-4456	116	8	rbf	rbf	PROPN
cana-4456	116	9	interpolation	interpolation	NOUN
cana-4456	116	10	and	and	CCONJ
cana-4456	116	11	add	add	VERB
cana-4456	116	12	more	more	ADJ
cana-4456	116	13	nodes	node	NOUN
cana-4456	116	14	,	,	PUNCT
cana-4456	116	15	the	the	DET
cana-4456	116	16	matrices	matrix	NOUN
cana-4456	116	17	involved	involve	VERB
cana-4456	116	18	become	become	VERB
cana-4456	116	19	less	less	ADV
cana-4456	116	20	stable	stable	ADJ
cana-4456	116	21	.	.	PUNCT
cana-4456	117	1	this	this	PRON
cana-4456	117	2	is	be	AUX
cana-4456	117	3	especially	especially	ADV
cana-4456	117	4	true	true	ADJ
cana-4456	117	5	when	when	SCONJ
cana-4456	117	6	a	a	DET
cana-4456	117	7	poor	poor	ADJ
cana-4456	117	8	choice	choice	NOUN
cana-4456	117	9	has	have	AUX
cana-4456	117	10	been	be	AUX
cana-4456	117	11	made	make	VERB
cana-4456	117	12	when	when	SCONJ
cana-4456	117	13	designating	designate	VERB
cana-4456	117	14	the	the	DET
cana-4456	117	15	rbf	rbf	PROPN
cana-4456	117	16	centers	center	NOUN
cana-4456	117	17	,	,	PUNCT
cana-4456	117	18	and	and	CCONJ
cana-4456	117	19	also	also	ADV
cana-4456	117	20	when	when	SCONJ
cana-4456	117	21	infinitely	infinitely	ADV
cana-4456	117	22	smooth	smooth	ADJ
cana-4456	117	23	basis	basis	NOUN
cana-4456	117	24	functions	function	NOUN
cana-4456	117	25	are	be	AUX
cana-4456	117	26	used	use	VERB
cana-4456	117	27	with	with	ADP
cana-4456	117	28	associated	associated	ADJ
cana-4456	117	29	shape	shape	NOUN
cana-4456	117	30	parameters	parameter	NOUN
cana-4456	117	31	set	set	VERB
cana-4456	117	32	to	to	ADP
cana-4456	117	33	extreme	extreme	ADJ
cana-4456	117	34	values	value	NOUN
cana-4456	117	35	.	.	PUNCT
cana-4456	118	1	to	to	PART
cana-4456	118	2	have	have	VERB
cana-4456	118	3	more	more	ADJ
cana-4456	118	4	details	detail	NOUN
cana-4456	118	5	on	on	ADP
cana-4456	118	6	the	the	DET
cana-4456	118	7	theoretical	theoretical	ADJ
cana-4456	118	8	background	background	NOUN
cana-4456	118	9	,	,	PUNCT
cana-4456	118	10	we	we	PRON
cana-4456	118	11	refer	refer	VERB
cana-4456	118	12	the	the	DET
cana-4456	118	13	reader	reader	NOUN
cana-4456	118	14	to	to	ADP
cana-4456	118	15	[	[	X
cana-4456	118	16	35	35	NUM
cana-4456	118	17	,	,	PUNCT
cana-4456	118	18	36	36	NUM
cana-4456	118	19	]	]	PUNCT
cana-4456	118	20	.	.	PUNCT
cana-4456	119	1	table	table	NOUN
cana-4456	119	2	1	1	NUM
cana-4456	119	3	.	.	PUNCT
cana-4456	119	4	infinitely	infinitely	ADV
cana-4456	119	5	smooth	smooth	ADJ
cana-4456	119	6	rbfs	rbfs	NOUN
cana-4456	119	7	multiquadric	multiquadric	ADJ
cana-4456	119	8	inverse	inverse	NOUN
cana-4456	119	9	multiquadratic	multiquadratic	ADJ
cana-4456	119	10	inverse	inverse	NOUN
cana-4456	119	11	quadratic	quadratic	ADJ
cana-4456	119	12	gaussian	gaussian	NOUN
cana-4456	119	13	(	(	PUNCT
cana-4456	119	14	𝟏	𝟏	NUM
cana-4456	119	15	+	+	CCONJ
cana-4456	119	16	𝝐𝟐𝒓𝟐	𝝐𝟐𝒓𝟐	X
cana-4456	119	17	)	)	PUNCT
cana-4456	120	1	𝟏	𝟏	NUM
cana-4456	120	2	𝟐	𝟐	NUM
cana-4456	120	3	(	(	PUNCT
cana-4456	120	4	𝟏	𝟏	NUM
cana-4456	120	5	+	+	CCONJ
cana-4456	120	6	𝝐𝟐𝒓𝟐	𝝐𝟐𝒓𝟐	X
cana-4456	120	7	)	)	PUNCT
cana-4456	120	8	−𝟏	−𝟏	NOUN
cana-4456	120	9	𝟐	𝟐	NUM
cana-4456	120	10	(	(	PUNCT
cana-4456	120	11	𝟏	𝟏	NUM
cana-4456	120	12	+	+	NUM
cana-4456	120	13	𝝐𝟐𝒓𝟐)−𝟏	𝝐𝟐𝒓𝟐)−𝟏	PROPN
cana-4456	120	14	𝒆−𝝐𝟐𝒓𝟐	𝒆−𝝐𝟐𝒓𝟐	ADP
cana-4456	120	15	3.1.1	3.1.1	NUM
cana-4456	120	16	method	method	NOUN
cana-4456	120	17	’s	’s	PART
cana-4456	120	18	principle	principle	NOUN
cana-4456	120	19	in	in	ADP
cana-4456	120	20	this	this	DET
cana-4456	120	21	section	section	NOUN
cana-4456	120	22	,	,	PUNCT
cana-4456	120	23	we	we	PRON
cana-4456	120	24	introduce	introduce	VERB
cana-4456	120	25	the	the	DET
cana-4456	120	26	general	general	ADJ
cana-4456	120	27	notation	notation	NOUN
cana-4456	120	28	and	and	CCONJ
cana-4456	120	29	quantities	quantity	NOUN
cana-4456	120	30	we	we	PRON
cana-4456	120	31	need	need	VERB
cana-4456	120	32	for	for	ADP
cana-4456	120	33	rbf	rbf	PROPN
cana-4456	120	34	approximation	approximation	NOUN
cana-4456	120	35	of	of	ADP
cana-4456	120	36	swes	swes	NOUN
cana-4456	120	37	.	.	PUNCT
cana-4456	121	1	assume	assume	VERB
cana-4456	121	2	that	that	SCONJ
cana-4456	121	3	x	x	PRON
cana-4456	121	4	=	=	PRON
cana-4456	121	5	{	{	PUNCT
cana-4456	121	6	𝑥1	𝑥1	NOUN
cana-4456	121	7	,	,	PUNCT
cana-4456	121	8	𝑥2	𝑥2	NOUN
cana-4456	121	9	,	,	PUNCT
cana-4456	121	10	.	.	PUNCT
cana-4456	121	11	.	.	PUNCT
cana-4456	121	12	.	.	PUNCT
cana-4456	122	1	,	,	PUNCT
cana-4456	122	2	𝑥𝑁	𝑥𝑁	NOUN
cana-4456	122	3	}	}	PUNCT
cana-4456	122	4	is	be	AUX
cana-4456	122	5	a	a	DET
cana-4456	122	6	set	set	NOUN
cana-4456	122	7	of	of	ADP
cana-4456	122	8	distinct	distinct	ADJ
cana-4456	122	9	points	point	NOUN
cana-4456	122	10	in	in	ADP
cana-4456	122	11	ω	ω	PROPN
cana-4456	122	12	⊂	⊂	PROPN
cana-4456	123	1	ℝ𝑑.	ℝ𝑑.	NOUN
cana-4456	123	2	we	we	PRON
cana-4456	123	3	start	start	VERB
cana-4456	123	4	from	from	ADP
cana-4456	123	5	given	give	VERB
cana-4456	123	6	an	an	DET
cana-4456	123	7	interpolant	interpolant	NOUN
cana-4456	123	8	𝐼𝑢	𝐼𝑢	PROPN
cana-4456	123	9	that	that	PRON
cana-4456	123	10	approximates	approximate	VERB
cana-4456	123	11	a	a	DET
cana-4456	123	12	function	function	NOUN
cana-4456	123	13	𝑢	𝑢	PART
cana-4456	123	14	:	:	PUNCT
cana-4456	123	15	𝐼𝑢(𝑥	𝐼𝑢(𝑥	NOUN
cana-4456	123	16	)	)	PUNCT
cana-4456	124	1	=	=	PUNCT
cana-4456	124	2	∑	∑	PUNCT
cana-4456	124	3	𝜆𝑖	𝜆𝑖	VERB
cana-4456	124	4	𝑛	𝑛	PRON
cana-4456	124	5	𝑖=1	𝑖=1	PROPN
cana-4456	124	6	𝜑(‖𝑥	𝜑(‖𝑥	PUNCT
cana-4456	124	7	−	−	PROPN
cana-4456	124	8	𝑥𝑖‖	𝑥𝑖‖	PROPN
cana-4456	124	9	)	)	PUNCT
cana-4456	124	10	,	,	PUNCT
cana-4456	124	11	𝑥	𝑥	PRON
cana-4456	124	12	∈	∈	PROPN
cana-4456	124	13	𝛺	𝛺	PROPN
cana-4456	124	14	,	,	PUNCT
cana-4456	124	15	(	(	PUNCT
cana-4456	124	16	11	11	NUM
cana-4456	124	17	)	)	PUNCT
cana-4456	124	18	where	where	SCONJ
cana-4456	124	19	𝜆𝑖	𝜆𝑖	PROPN
cana-4456	124	20	∈	∈	PROPN
cana-4456	124	21	ℝ	ℝ	PROPN
cana-4456	124	22	are	be	AUX
cana-4456	124	23	the	the	DET
cana-4456	124	24	unknown	unknown	ADJ
cana-4456	124	25	coefficient	coefficient	NOUN
cana-4456	124	26	to	to	PART
cana-4456	124	27	be	be	AUX
cana-4456	124	28	determined	determine	VERB
cana-4456	124	29	and	and	CCONJ
cana-4456	124	30	𝜑	𝜑	NOUN
cana-4456	124	31	can	can	AUX
cana-4456	124	32	be	be	AUX
cana-4456	124	33	any	any	DET
cana-4456	124	34	radial	radial	ADJ
cana-4456	124	35	basis	basis	NOUN
cana-4456	124	36	function	function	NOUN
cana-4456	124	37	such	such	ADJ
cana-4456	124	38	in	in	ADP
cana-4456	124	39	table	table	NOUN
cana-4456	124	40	1	1	NUM
cana-4456	124	41	,	,	PUNCT
cana-4456	124	42	the	the	DET
cana-4456	124	43	shape	shape	NOUN
cana-4456	124	44	parameter	parameter	NOUN
cana-4456	124	45	𝜀	𝜀	PROPN
cana-4456	124	46	appearing	appear	VERB
cana-4456	124	47	in	in	ADP
cana-4456	124	48	the	the	DET
cana-4456	124	49	rbfs	rbfs	NOUN
cana-4456	124	50	dictates	dictate	VERB
cana-4456	124	51	the	the	DET
cana-4456	124	52	flatness	flatness	NOUN
cana-4456	124	53	of	of	ADP
cana-4456	124	54	the	the	DET
cana-4456	124	55	radial	radial	ADJ
cana-4456	124	56	basis	basis	NOUN
cana-4456	124	57	function	function	NOUN
cana-4456	124	58	and	and	CCONJ
cana-4456	124	59	plays	play	VERB
cana-4456	124	60	a	a	DET
cana-4456	124	61	key	key	ADJ
cana-4456	124	62	role	role	NOUN
cana-4456	124	63	in	in	ADP
cana-4456	124	64	the	the	DET
cana-4456	124	65	convergence	convergence	NOUN
cana-4456	124	66	rate	rate	NOUN
cana-4456	124	67	of	of	ADP
cana-4456	124	68	the	the	DET
cana-4456	124	69	approximations	approximation	NOUN
cana-4456	124	70	and	and	CCONJ
cana-4456	124	71	the	the	DET
cana-4456	124	72	condition	condition	NOUN
cana-4456	124	73	number	number	NOUN
cana-4456	124	74	of	of	ADP
cana-4456	124	75	the	the	DET
cana-4456	124	76	coefficient	coefficient	NOUN
cana-4456	124	77	matrices	matrix	NOUN
cana-4456	124	78	.	.	PUNCT
cana-4456	125	1	by	by	ADP
cana-4456	125	2	applying	apply	VERB
cana-4456	125	3	the	the	DET
cana-4456	125	4	interpolation	interpolation	NOUN
cana-4456	125	5	criteria	criterion	NOUN
cana-4456	125	6	𝐼𝑢(𝑥𝑗	𝐼𝑢(𝑥𝑗	NOUN
cana-4456	125	7	)	)	PUNCT
cana-4456	125	8	=	=	SYM
cana-4456	125	9	𝑢(𝑥𝑗	𝑢(𝑥𝑗	NOUN
cana-4456	125	10	)	)	PUNCT
cana-4456	125	11	,	,	PUNCT
cana-4456	125	12	the	the	DET
cana-4456	125	13	coefficient	coefficient	NOUN
cana-4456	125	14	𝜆𝑗	𝜆𝑗	X
cana-4456	125	15	,	,	PUNCT
cana-4456	125	16	𝑗	𝑗	PROPN
cana-4456	125	17	=	=	ADJ
cana-4456	125	18	1	1	NUM
cana-4456	125	19	,	,	PUNCT
cana-4456	125	20	.	.	PUNCT
cana-4456	125	21	.	.	PUNCT
cana-4456	126	1	.	.	PUNCT
cana-4456	127	1	,	,	PUNCT
cana-4456	127	2	𝑁	𝑁	PROPN
cana-4456	127	3	is	be	AUX
cana-4456	127	4	discovered	discover	VERB
cana-4456	127	5	.	.	PUNCT
cana-4456	128	1	and	and	CCONJ
cana-4456	128	2	we	we	PRON
cana-4456	128	3	obtain	obtain	VERB
cana-4456	128	4	a	a	DET
cana-4456	128	5	linear	linear	ADJ
cana-4456	128	6	system	system	NOUN
cana-4456	128	7	as	as	SCONJ
cana-4456	128	8	follow	follow	VERB
cana-4456	128	9	:	:	PUNCT
cana-4456	128	10	a	a	DET
cana-4456	128	11	�	�	NOUN
cana-4456	128	12	̅	̅	NOUN
cana-4456	128	13	�	�	NOUN
cana-4456	128	14	=	=	SYM
cana-4456	128	15	𝑈	𝑈	PROPN
cana-4456	128	16	,	,	PUNCT
cana-4456	128	17	(	(	PUNCT
cana-4456	128	18	12	12	NUM
cana-4456	128	19	)	)	PUNCT
cana-4456	128	20	where	where	SCONJ
cana-4456	128	21	𝐴	𝐴	PROPN
cana-4456	128	22	=	=	SYM
cana-4456	128	23	(	(	PUNCT
cana-4456	128	24	𝜑(‖𝑥1	𝜑(‖𝑥1	NOUN
cana-4456	128	25	−	−	NOUN
cana-4456	128	26	𝑥1‖	𝑥1‖	PROPN
cana-4456	128	27	)	)	PUNCT
cana-4456	128	28	⋯	⋯	NOUN
cana-4456	128	29	𝜑(‖𝑥1	𝜑(‖𝑥1	NOUN
cana-4456	128	30	−	−	PROPN
cana-4456	128	31	𝑥𝑁‖	𝑥𝑁‖	NOUN
cana-4456	128	32	)	)	PUNCT
cana-4456	128	33	⋮	⋮	NOUN
cana-4456	128	34	⋱	⋱	PUNCT
cana-4456	128	35	⋮	⋮	NOUN
cana-4456	128	36	𝜑(‖𝑥𝑁	𝜑(‖𝑥𝑁	NOUN
cana-4456	128	37	−	−	PROPN
cana-4456	128	38	𝑥1‖	𝑥1‖	PROPN
cana-4456	128	39	)	)	PUNCT
cana-4456	129	1	⋯	⋯	VERB
cana-4456	129	2	𝜑(‖𝑥𝑁	𝜑(‖𝑥𝑁	NOUN
cana-4456	129	3	−	−	PROPN
cana-4456	129	4	𝑥𝑁‖	𝑥𝑁‖	NOUN
cana-4456	129	5	)	)	PUNCT
cana-4456	129	6	)	)	PUNCT
cana-4456	129	7	,	,	PUNCT
cana-4456	129	8	(	(	PUNCT
cana-4456	129	9	13	13	NUM
cana-4456	129	10	)	)	PUNCT
cana-4456	129	11	�	�	NOUN
cana-4456	129	12	̅	̅	NOUN
cana-4456	129	13	�	�	NOUN
cana-4456	129	14	=	=	PUNCT
cana-4456	130	1	[	[	X
cana-4456	130	2	𝜆1	𝜆1	NOUN
cana-4456	130	3	,	,	PUNCT
cana-4456	130	4	𝜆2	𝜆2	PROPN
cana-4456	130	5	,	,	PUNCT
cana-4456	130	6	…	…	PUNCT
cana-4456	130	7	,	,	PUNCT
cana-4456	130	8	𝜆𝑁]𝑇	𝜆𝑁]𝑇	PROPN
cana-4456	130	9	,	,	PUNCT
cana-4456	130	10	u	u	NOUN
cana-4456	130	11	=	=	X
cana-4456	131	1	[	[	X
cana-4456	131	2	𝑢(𝑥1	𝑢(𝑥1	ADJ
cana-4456	131	3	)	)	PUNCT
cana-4456	131	4	,	,	PUNCT
cana-4456	131	5	𝑢(𝑥2	𝑢(𝑥2	NOUN
cana-4456	131	6	)	)	PUNCT
cana-4456	131	7	,	,	PUNCT
cana-4456	131	8	…	…	PUNCT
cana-4456	131	9	,	,	PUNCT
cana-4456	131	10	𝑢(𝑥𝑁)]𝑇.	𝑢(𝑥𝑁)]𝑇.	PROPN
cana-4456	131	11	(	(	PUNCT
cana-4456	131	12	14	14	NUM
cana-4456	131	13	)	)	PUNCT
cana-4456	131	14	when	when	SCONJ
cana-4456	131	15	solving	solve	VERB
cana-4456	131	16	pde	pde	NOUN
cana-4456	131	17	,	,	PUNCT
cana-4456	131	18	we	we	PRON
cana-4456	131	19	prefer	prefer	VERB
cana-4456	131	20	to	to	PART
cana-4456	131	21	work	work	VERB
cana-4456	131	22	with	with	ADP
cana-4456	131	23	the	the	DET
cana-4456	131	24	discrete	discrete	ADJ
cana-4456	131	25	approximate	approximate	NOUN
cana-4456	131	26	instead	instead	ADV
cana-4456	131	27	of	of	ADP
cana-4456	131	28	the	the	DET
cana-4456	131	29	coefficients	coefficient	NOUN
cana-4456	131	30	.	.	PUNCT
cana-4456	132	1	from	from	ADP
cana-4456	132	2	(	(	PUNCT
cana-4456	132	3	11	11	NUM
cana-4456	132	4	)	)	PUNCT
cana-4456	132	5	and	and	CCONJ
cana-4456	132	6	(	(	PUNCT
cana-4456	132	7	12	12	NUM
cana-4456	132	8	)	)	PUNCT
cana-4456	132	9	we	we	PRON
cana-4456	132	10	can	can	AUX
cana-4456	132	11	write	write	VERB
cana-4456	132	12	𝐼𝑢(𝑥	𝐼𝑢(𝑥	NOUN
cana-4456	132	13	)	)	PUNCT
cana-4456	132	14	=	=	SYM
cana-4456	132	15	�	�	PROPN
cana-4456	132	16	̅	̅	NOUN
cana-4456	132	17	�	�	NOUN
cana-4456	132	18	(𝑥)𝐴−1𝑈	(𝑥)𝐴−1𝑈	PUNCT
cana-4456	132	19	=	=	SYM
cana-4456	132	20	𝐷(𝑥)𝑈	𝐷(𝑥)𝑈	X
cana-4456	132	21	,	,	PUNCT
cana-4456	132	22	(	(	PUNCT
cana-4456	132	23	15	15	X
cana-4456	132	24	)	)	PUNCT
cana-4456	132	25	communications	communication	NOUN
cana-4456	132	26	on	on	ADP
cana-4456	132	27	applied	apply	VERB
cana-4456	132	28	nonlinear	nonlinear	ADJ
cana-4456	132	29	analysis	analysis	NOUN
cana-4456	132	30	issn	issn	NOUN
cana-4456	132	31	:	:	PUNCT
cana-4456	132	32	1074	1074	NUM
cana-4456	132	33	-	-	PUNCT
cana-4456	132	34	133x	133x	NUM
cana-4456	132	35	vol	vol	NOUN
cana-4456	132	36	32	32	NUM
cana-4456	132	37	no	no	NOUN
cana-4456	132	38	.	.	PUNCT
cana-4456	133	1	9s	9s	NUM
cana-4456	133	2	(	(	PUNCT
cana-4456	133	3	2025	2025	NUM
cana-4456	133	4	)	)	PUNCT
cana-4456	133	5	2173	2173	NUM
cana-4456	133	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	133	7	where	where	SCONJ
cana-4456	133	8	�	�	NOUN
cana-4456	133	9	̅	̅	VERB
cana-4456	133	10	�	�	NOUN
cana-4456	133	11	(𝑥	(𝑥	NOUN
cana-4456	133	12	)	)	PUNCT
cana-4456	133	13	=	=	PUNCT
cana-4456	134	1	[	[	X
cana-4456	134	2	𝜑	𝜑	X
cana-4456	134	3	(	(	PUNCT
cana-4456	134	4	∥	∥	X
cana-4456	134	5	𝑥	𝑥	PRON
cana-4456	134	6	−	−	PROPN
cana-4456	134	7	𝑥1	𝑥1	NOUN
cana-4456	134	8	∥	∥	NOUN
cana-4456	134	9	)	)	PUNCT
cana-4456	134	10	,	,	PUNCT
cana-4456	134	11	𝜑	𝜑	PROPN
cana-4456	134	12	(	(	PUNCT
cana-4456	134	13	∥	∥	X
cana-4456	134	14	𝑥	𝑥	PRON
cana-4456	134	15	−	−	NOUN
cana-4456	134	16	𝑥2	𝑥2	NOUN
cana-4456	134	17	∥	∥	NUM
cana-4456	134	18	)	)	PUNCT
cana-4456	134	19	,	,	PUNCT
cana-4456	134	20	…	…	PUNCT
cana-4456	134	21	,	,	PUNCT
cana-4456	134	22	𝜑	𝜑	X
cana-4456	134	23	(	(	PUNCT
cana-4456	134	24	∥	∥	X
cana-4456	134	25	𝑥	𝑥	PRON
cana-4456	134	26	−	−	NOUN
cana-4456	134	27	𝑥𝑁	𝑥𝑁	NOUN
cana-4456	134	28	∥	∥	NOUN
cana-4456	134	29	)	)	PUNCT
cana-4456	134	30	]	]	PUNCT
cana-4456	134	31	and	and	CCONJ
cana-4456	134	32	𝐷	𝐷	PROPN
cana-4456	134	33	=	=	PUNCT
cana-4456	134	34	�	�	PROPN
cana-4456	134	35	̅	̅	NOUN
cana-4456	134	36	�	�	NOUN
cana-4456	134	37	𝐴−1	𝐴−1	NOUN
cana-4456	134	38	.	.	PUNCT
cana-4456	134	39	micchlli	micchlli	PROPN
cana-4456	135	1	[	[	X
cana-4456	135	2	37	37	NUM
cana-4456	135	3	]	]	PUNCT
cana-4456	135	4	proved	prove	VERB
cana-4456	135	5	that	that	SCONJ
cana-4456	135	6	the	the	DET
cana-4456	135	7	strict	strict	ADJ
cana-4456	135	8	positive	positive	ADJ
cana-4456	135	9	definiteness	definiteness	NOUN
cana-4456	135	10	of	of	ADP
cana-4456	135	11	an	an	DET
cana-4456	135	12	rbf	rbf	PROPN
cana-4456	135	13	listed	list	VERB
cana-4456	135	14	in	in	ADP
cana-4456	135	15	table	table	NOUN
cana-4456	135	16	1	1	NUM
cana-4456	135	17	guarantees	guarantee	VERB
cana-4456	135	18	that	that	SCONJ
cana-4456	135	19	the	the	DET
cana-4456	135	20	interpolation	interpolation	NOUN
cana-4456	135	21	matrix	matrix	NOUN
cana-4456	135	22	a	a	DET
cana-4456	135	23	in	in	ADP
cana-4456	135	24	(	(	PUNCT
cana-4456	135	25	13	13	NUM
cana-4456	135	26	)	)	PUNCT
cana-4456	135	27	is	be	AUX
cana-4456	135	28	also	also	ADV
cana-4456	135	29	positive	positive	ADJ
cana-4456	135	30	definite	definite	ADJ
cana-4456	135	31	,	,	PUNCT
cana-4456	135	32	and	and	CCONJ
cana-4456	135	33	thus	thus	ADV
cana-4456	135	34	invertible	invertible	ADJ
cana-4456	135	35	.	.	PUNCT
cana-4456	136	1	because	because	SCONJ
cana-4456	136	2	our	our	PRON
cana-4456	136	3	final	final	ADJ
cana-4456	136	4	target	target	NOUN
cana-4456	136	5	is	be	AUX
cana-4456	136	6	to	to	PART
cana-4456	136	7	solve	solve	VERB
cana-4456	136	8	pdes	pde	NOUN
cana-4456	136	9	,	,	PUNCT
cana-4456	136	10	we	we	PRON
cana-4456	136	11	apply	apply	VERB
cana-4456	136	12	a	a	DET
cana-4456	136	13	linear	linear	ADJ
cana-4456	136	14	differential	differential	NOUN
cana-4456	136	15	operator	operator	NOUN
cana-4456	136	16	𝐿	𝐿	PROPN
cana-4456	136	17	to	to	ADP
cana-4456	136	18	the	the	DET
cana-4456	136	19	rbf	rbf	PROPN
cana-4456	136	20	approximation	approximation	NOUN
cana-4456	136	21	,	,	PUNCT
cana-4456	136	22	we	we	PRON
cana-4456	136	23	get	get	VERB
cana-4456	136	24	(	(	PUNCT
cana-4456	136	25	𝐼𝑢)𝐿(𝑥	𝐼𝑢)𝐿(𝑥	ADJ
cana-4456	136	26	)	)	PUNCT
cana-4456	136	27	=	=	SYM
cana-4456	136	28	�	�	NOUN
cana-4456	136	29	̅	̅	NOUN
cana-4456	136	30	�	�	NOUN
cana-4456	136	31	𝐿(𝑥)𝐴−1𝑈	𝐿(𝑥)𝐴−1𝑈	NOUN
cana-4456	136	32	=	=	SYM
cana-4456	136	33	𝐷𝐿(𝑥)𝑈	𝐷𝐿(𝑥)𝑈	NOUN
cana-4456	136	34	,	,	PUNCT
cana-4456	136	35	(	(	PUNCT
cana-4456	136	36	16	16	NUM
cana-4456	136	37	)	)	PUNCT
cana-4456	136	38	where	where	SCONJ
cana-4456	136	39	𝐷𝐿	𝐷𝐿	PROPN
cana-4456	136	40	=	=	SYM
cana-4456	136	41	�	�	PROPN
cana-4456	136	42	̅	̅	NOUN
cana-4456	136	43	�	�	NOUN
cana-4456	136	44	𝐿𝐴−1	𝐿𝐴−1	NOUN
cana-4456	136	45	is	be	AUX
cana-4456	136	46	known	know	VERB
cana-4456	136	47	as	as	ADP
cana-4456	136	48	a	a	DET
cana-4456	136	49	differentiation	differentiation	NOUN
cana-4456	136	50	matrix	matrix	NOUN
cana-4456	136	51	.	.	PUNCT
cana-4456	137	1	3.1.2	3.1.2	NUM
cana-4456	137	2	spatial	spatial	ADJ
cana-4456	137	3	discretization	discretization	NOUN
cana-4456	137	4	of	of	ADP
cana-4456	137	5	swes	swe	NOUN
cana-4456	137	6	using	use	VERB
cana-4456	137	7	kansa	kansa	PROPN
cana-4456	137	8	method	method	NOUN
cana-4456	137	9	in	in	ADP
cana-4456	137	10	this	this	DET
cana-4456	137	11	section	section	NOUN
cana-4456	137	12	,	,	PUNCT
cana-4456	137	13	we	we	PRON
cana-4456	137	14	will	will	AUX
cana-4456	137	15	describe	describe	VERB
cana-4456	137	16	the	the	DET
cana-4456	137	17	implementation	implementation	NOUN
cana-4456	137	18	of	of	ADP
cana-4456	137	19	kansa	kansa	PROPN
cana-4456	137	20	method	method	PROPN
cana-4456	137	21	for	for	ADP
cana-4456	137	22	shallow	shallow	ADJ
cana-4456	137	23	water	water	NOUN
cana-4456	137	24	equations	equation	NOUN
cana-4456	137	25	.	.	PUNCT
cana-4456	138	1	let	let	VERB
cana-4456	138	2	{	{	PUNCT
cana-4456	138	3	𝑥1	𝑥1	NOUN
cana-4456	138	4	,	,	PUNCT
cana-4456	138	5	𝑥2	𝑥2	NOUN
cana-4456	138	6	,	,	PUNCT
cana-4456	138	7	.	.	PUNCT
cana-4456	138	8	.	.	PUNCT
cana-4456	138	9	.	.	PUNCT
cana-4456	139	1	,	,	PUNCT
cana-4456	139	2	𝑥𝑁	𝑥𝑁	NOUN
cana-4456	139	3	}	}	PUNCT
cana-4456	139	4	be	be	AUX
cana-4456	139	5	a	a	DET
cana-4456	139	6	set	set	NOUN
cana-4456	139	7	of	of	ADP
cana-4456	139	8	scattered	scatter	VERB
cana-4456	139	9	nodes	node	NOUN
cana-4456	139	10	considered	consider	VERB
cana-4456	139	11	in	in	ADP
cana-4456	139	12	the	the	DET
cana-4456	139	13	study	study	NOUN
cana-4456	139	14	area	area	NOUN
cana-4456	139	15	.	.	PUNCT
cana-4456	140	1	using	use	VERB
cana-4456	140	2	(	(	PUNCT
cana-4456	140	3	16	16	NUM
cana-4456	140	4	)	)	PUNCT
cana-4456	140	5	,	,	PUNCT
cana-4456	140	6	the	the	DET
cana-4456	140	7	first	first	ADJ
cana-4456	140	8	and	and	CCONJ
cana-4456	140	9	second	second	ADJ
cana-4456	140	10	spatial	spatial	ADJ
cana-4456	140	11	derivatives	derivative	NOUN
cana-4456	140	12	of	of	ADP
cana-4456	140	13	a	a	DET
cana-4456	140	14	function	function	NOUN
cana-4456	140	15	𝑸(𝑥	𝑸(𝑥	NOUN
cana-4456	140	16	,	,	PUNCT
cana-4456	140	17	𝑡	𝑡	PROPN
cana-4456	140	18	)	)	PUNCT
cana-4456	140	19	can	can	AUX
cana-4456	140	20	be	be	AUX
cana-4456	140	21	expressed	express	VERB
cana-4456	140	22	as	as	SCONJ
cana-4456	140	23	follows	follow	VERB
cana-4456	140	24	:	:	PUNCT
cana-4456	140	25	𝜕𝑸(𝑥,𝑡	𝜕𝑸(𝑥,𝑡	ADJ
cana-4456	140	26	)	)	PUNCT
cana-4456	140	27	𝜕𝑥	𝜕𝑥	NOUN
cana-4456	141	1	=	=	SYM
cana-4456	142	1	𝐷𝑥𝑸(𝑥	𝐷𝑥𝑸(𝑥	PROPN
cana-4456	142	2	,	,	PUNCT
cana-4456	142	3	𝑡	𝑡	NOUN
cana-4456	142	4	)	)	PUNCT
cana-4456	142	5	,	,	PUNCT
cana-4456	142	6	𝜕2𝑸(𝑥,𝑡	𝜕2𝑸(𝑥,𝑡	NOUN
cana-4456	142	7	)	)	PUNCT
cana-4456	142	8	𝜕𝑥2	𝜕𝑥2	NOUN
cana-4456	142	9	=	=	PUNCT
cana-4456	143	1	𝐷𝑥𝑥𝑸(𝑥	𝐷𝑥𝑥𝑸(𝑥	PROPN
cana-4456	143	2	,	,	PUNCT
cana-4456	143	3	𝑡	𝑡	NOUN
cana-4456	143	4	)	)	PUNCT
cana-4456	143	5	,	,	PUNCT
cana-4456	143	6	(	(	PUNCT
cana-4456	143	7	17	17	NUM
cana-4456	143	8	)	)	PUNCT
cana-4456	143	9	where	where	SCONJ
cana-4456	143	10	𝐷𝑥	𝐷𝑥	PROPN
cana-4456	143	11	and	and	CCONJ
cana-4456	143	12	𝐷𝑥𝑥	𝐷𝑥𝑥	PROPN
cana-4456	143	13	are	be	AUX
cana-4456	143	14	first	first	ADJ
cana-4456	143	15	and	and	CCONJ
cana-4456	143	16	second	second	ADJ
cana-4456	143	17	derivative	derivative	ADJ
cana-4456	143	18	matrices	matrix	NOUN
cana-4456	143	19	with	with	ADP
cana-4456	143	20	respect	respect	NOUN
cana-4456	143	21	to	to	ADP
cana-4456	143	22	𝑥	𝑥	PRON
cana-4456	143	23	.	.	PUNCT
cana-4456	144	1	the	the	DET
cana-4456	144	2	system	system	NOUN
cana-4456	144	3	(	(	PUNCT
cana-4456	144	4	8)	8)	NUM
cana-4456	144	5	is	be	AUX
cana-4456	144	6	approximated	approximate	VERB
cana-4456	144	7	by	by	ADP
cana-4456	144	8	the	the	DET
cana-4456	144	9	following	follow	VERB
cana-4456	144	10	equivalent	equivalent	ADJ
cana-4456	144	11	system	system	NOUN
cana-4456	144	12	:	:	PUNCT
cana-4456	144	13	𝜕𝑡𝑸	𝜕𝑡𝑸	NUM
cana-4456	144	14	=	=	PUNCT
cana-4456	144	15	−	−	NUM
cana-4456	144	16	�	�	NOUN
cana-4456	144	17	̅	̅	NOUN
cana-4456	144	18	�	�	NOUN
cana-4456	144	19	(𝑸	(𝑸	NUM
cana-4456	144	20	)	)	PUNCT
cana-4456	144	21	+	+	NUM
cana-4456	144	22	𝑆̅(𝑸	𝑆̅(𝑸	NOUN
cana-4456	144	23	)	)	PUNCT
cana-4456	144	24	+	+	CCONJ
cana-4456	144	25	�	�	NOUN
cana-4456	144	26	̅	̅	NOUN
cana-4456	144	27	�	�	PROPN
cana-4456	144	28	(𝑸	(𝑸	NUM
cana-4456	144	29	)	)	PUNCT
cana-4456	144	30	,	,	PUNCT
cana-4456	144	31	(	(	PUNCT
cana-4456	144	32	18	18	NUM
cana-4456	144	33	)	)	PUNCT
cana-4456	144	34	where	where	SCONJ
cana-4456	144	35	�	�	NOUN
cana-4456	144	36	̅	̅	NOUN
cana-4456	144	37	�	�	NOUN
cana-4456	144	38	is	be	AUX
cana-4456	144	39	the	the	DET
cana-4456	144	40	convective	convective	ADJ
cana-4456	144	41	flux	flux	NOUN
cana-4456	144	42	,	,	PUNCT
cana-4456	144	43	�	�	PROPN
cana-4456	144	44	̅	̅	NOUN
cana-4456	144	45	�	�	NOUN
cana-4456	144	46	contains	contain	VERB
cana-4456	144	47	the	the	DET
cana-4456	144	48	hyperviscosity	hyperviscosity	NOUN
cana-4456	144	49	and	and	CCONJ
cana-4456	144	50	𝑆̅	𝑆̅	NOUN
cana-4456	144	51	is	be	AUX
cana-4456	144	52	the	the	DET
cana-4456	144	53	source	source	NOUN
cana-4456	144	54	term	term	NOUN
cana-4456	144	55	due	due	ADP
cana-4456	144	56	to	to	ADP
cana-4456	144	57	bottom	bottom	ADJ
cana-4456	144	58	elevator	elevator	NOUN
cana-4456	144	59	.	.	PUNCT
cana-4456	145	1	using	use	VERB
cana-4456	145	2	the	the	DET
cana-4456	145	3	kansa	kansa	PROPN
cana-4456	145	4	method	method	NOUN
cana-4456	145	5	,	,	PUNCT
cana-4456	145	6	we	we	PRON
cana-4456	145	7	obtain	obtain	VERB
cana-4456	145	8	𝐹	𝐹	PROPN
cana-4456	145	9	̅(𝑸	̅(𝑸	ADV
cana-4456	145	10	)	)	PUNCT
cana-4456	146	1	=	=	PRON
cana-4456	147	1	(	(	PUNCT
cana-4456	147	2	𝐷𝑥𝑞	𝐷𝑥𝑞	INTJ
cana-4456	147	3	𝐷𝑥	𝐷𝑥	PROPN
cana-4456	147	4	(	(	PUNCT
cana-4456	147	5	𝑞2	𝑞2	NOUN
cana-4456	147	6	ℎ	ℎ	PART
cana-4456	147	7	+	+	NOUN
cana-4456	147	8	1	1	NUM
cana-4456	147	9	2	2	NUM
cana-4456	147	10	𝑔ℎ2	𝑔ℎ2	NOUN
cana-4456	147	11	)	)	PUNCT
cana-4456	147	12	)	)	PUNCT
cana-4456	147	13	,	,	PUNCT
cana-4456	147	14	𝑆	𝑆	PROPN
cana-4456	147	15	̅(𝑸	̅(𝑸	PROPN
cana-4456	147	16	)	)	PUNCT
cana-4456	147	17	=	=	PUNCT
cana-4456	148	1	(	(	PUNCT
cana-4456	148	2	0	0	NUM
cana-4456	148	3	−𝑔ℎ𝐷𝑥𝑏	−𝑔ℎ𝐷𝑥𝑏	NUM
cana-4456	148	4	)	)	PUNCT
cana-4456	148	5	,	,	PUNCT
cana-4456	148	6	𝐻	𝐻	PROPN
cana-4456	148	7	̅̅	̅̅	NOUN
cana-4456	148	8	̅(𝑸	̅(𝑸	PUNCT
cana-4456	148	9	)	)	PUNCT
cana-4456	148	10	=	=	PUNCT
cana-4456	149	1	(	(	PUNCT
cana-4456	149	2	𝜇𝐷𝑥𝑥ℎ	𝜇𝐷𝑥𝑥ℎ	PROPN
cana-4456	149	3	𝜇𝐷𝑥𝑥𝑞	𝜇𝐷𝑥𝑥𝑞	PROPN
cana-4456	149	4	)	)	PUNCT
cana-4456	149	5	,	,	PUNCT
cana-4456	149	6	(	(	PUNCT
cana-4456	149	7	19	19	NUM
cana-4456	149	8	)	)	PUNCT
cana-4456	149	9	equivalent	equivalent	ADJ
cana-4456	149	10	to	to	ADP
cana-4456	149	11	𝜕𝑡𝑸	𝜕𝑡𝑸	NUM
cana-4456	149	12	=	=	PUNCT
cana-4456	149	13	𝑅𝐻𝑆𝑘𝑎𝑛𝑠𝑎(𝑸	𝑅𝐻𝑆𝑘𝑎𝑛𝑠𝑎(𝑸	X
cana-4456	149	14	)	)	PUNCT
cana-4456	150	1	where	where	SCONJ
cana-4456	150	2	𝑅𝐻𝑆𝑘𝑎𝑛𝑠𝑎(𝑸	𝑅𝐻𝑆𝑘𝑎𝑛𝑠𝑎(𝑸	VERB
cana-4456	150	3	)	)	PUNCT
cana-4456	150	4	=	=	SYM
cana-4456	150	5	−	−	NUM
cana-4456	150	6	�	�	NOUN
cana-4456	150	7	̅	̅	NOUN
cana-4456	150	8	�	�	NOUN
cana-4456	150	9	(𝑸	(𝑸	NUM
cana-4456	150	10	)	)	PUNCT
cana-4456	150	11	+	+	NUM
cana-4456	150	12	𝑆̅(𝑸	𝑆̅(𝑸	NOUN
cana-4456	150	13	)	)	PUNCT
cana-4456	151	1	+	+	CCONJ
cana-4456	151	2	�	�	NOUN
cana-4456	151	3	̅	̅	NOUN
cana-4456	151	4	�	�	NOUN
cana-4456	151	5	(𝑸	(𝑸	NUM
cana-4456	151	6	)	)	PUNCT
cana-4456	151	7	.	.	PUNCT
cana-4456	152	1	(	(	PUNCT
cana-4456	152	2	20	20	NUM
cana-4456	152	3	)	)	PUNCT
cana-4456	152	4	3.2	3.2	NUM
cana-4456	152	5	radial	radial	ADJ
cana-4456	152	6	basis	basis	NOUN
cana-4456	152	7	function	function	NOUN
cana-4456	152	8	finite	finite	NOUN
cana-4456	152	9	difference	difference	NOUN
cana-4456	152	10	method	method	NOUN
cana-4456	152	11	(	(	PUNCT
cana-4456	152	12	rbf	rbf	PROPN
cana-4456	152	13	-	-	PUNCT
cana-4456	152	14	fd	fd	PROPN
cana-4456	152	15	)	)	PUNCT
cana-4456	152	16	first	first	ADV
cana-4456	152	17	introduced	introduce	VERB
cana-4456	152	18	by	by	ADP
cana-4456	152	19	tolstykh	tolstykh	PROPN
cana-4456	152	20	[	[	X
cana-4456	152	21	14	14	NUM
cana-4456	152	22	]	]	PUNCT
cana-4456	152	23	,	,	PUNCT
cana-4456	152	24	rbf	rbf	PROPN
cana-4456	152	25	-	-	PUNCT
cana-4456	152	26	fd	fd	PROPN
cana-4456	152	27	formulas	formula	NOUN
cana-4456	152	28	are	be	AUX
cana-4456	152	29	derived	derive	VERB
cana-4456	152	30	through	through	ADP
cana-4456	152	31	rbf	rbf	PROPN
cana-4456	152	32	interpolation	interpolation	NOUN
cana-4456	152	33	over	over	ADP
cana-4456	152	34	local	local	ADJ
cana-4456	152	35	sets	set	NOUN
cana-4456	152	36	of	of	ADP
cana-4456	152	37	nodes	node	NOUN
cana-4456	152	38	on	on	ADP
cana-4456	152	39	the	the	DET
cana-4456	152	40	surface	surface	NOUN
cana-4456	152	41	.	.	PUNCT
cana-4456	153	1	this	this	DET
cana-4456	153	2	type	type	NOUN
cana-4456	153	3	of	of	ADP
cana-4456	153	4	method	method	NOUN
cana-4456	153	5	is	be	AUX
cana-4456	153	6	conceptually	conceptually	ADV
cana-4456	153	7	similar	similar	ADJ
cana-4456	153	8	to	to	ADP
cana-4456	153	9	the	the	DET
cana-4456	153	10	standard	standard	ADJ
cana-4456	153	11	finite	finite	ADJ
cana-4456	153	12	difference	difference	NOUN
cana-4456	153	13	(	(	PUNCT
cana-4456	153	14	fd	fd	PROPN
cana-4456	153	15	)	)	PUNCT
cana-4456	153	16	.	.	PUNCT
cana-4456	154	1	the	the	DET
cana-4456	154	2	fundamental	fundamental	ADJ
cana-4456	154	3	principle	principle	NOUN
cana-4456	154	4	underlying	underlie	VERB
cana-4456	154	5	rbf	rbf	PROPN
cana-4456	154	6	-	-	PUNCT
cana-4456	154	7	fd	fd	PROPN
cana-4456	154	8	revolves	revolve	VERB
cana-4456	154	9	around	around	ADP
cana-4456	154	10	the	the	DET
cana-4456	154	11	approximation	approximation	NOUN
cana-4456	154	12	of	of	ADP
cana-4456	154	13	the	the	DET
cana-4456	154	14	differential	differential	ADJ
cana-4456	154	15	operator	operator	NOUN
cana-4456	154	16	for	for	ADP
cana-4456	154	17	solutions	solution	NOUN
cana-4456	154	18	at	at	ADP
cana-4456	154	19	interior	interior	ADJ
cana-4456	154	20	nodes	node	NOUN
cana-4456	154	21	.	.	PUNCT
cana-4456	155	1	the	the	DET
cana-4456	155	2	approximation	approximation	NOUN
cana-4456	155	3	is	be	AUX
cana-4456	155	4	achieved	achieve	VERB
cana-4456	155	5	by	by	ADP
cana-4456	155	6	means	mean	NOUN
cana-4456	155	7	of	of	ADP
cana-4456	155	8	a	a	DET
cana-4456	155	9	linear	linear	ADJ
cana-4456	155	10	combination	combination	NOUN
cana-4456	155	11	of	of	ADP
cana-4456	155	12	function	function	NOUN
cana-4456	155	13	values	value	NOUN
cana-4456	155	14	at	at	ADP
cana-4456	155	15	the	the	DET
cana-4456	155	16	neighbouring	neighbouring	ADJ
cana-4456	155	17	node	node	NOUN
cana-4456	155	18	locations	location	NOUN
cana-4456	155	19	and	and	CCONJ
cana-4456	155	20	then	then	ADV
cana-4456	155	21	determining	determine	VERB
cana-4456	155	22	the	the	DET
cana-4456	155	23	rbf	rbf	PROPN
cana-4456	155	24	-	-	PUNCT
cana-4456	155	25	fd	fd	VERB
cana-4456	155	26	weights	weight	NOUN
cana-4456	155	27	by	by	ADP
cana-4456	155	28	assuming	assume	VERB
cana-4456	155	29	that	that	SCONJ
cana-4456	155	30	the	the	DET
cana-4456	155	31	approximations	approximation	NOUN
cana-4456	155	32	become	become	VERB
cana-4456	155	33	exact	exact	ADJ
cana-4456	155	34	for	for	ADP
cana-4456	155	35	all	all	DET
cana-4456	155	36	rbfs	rbfs	NOUN
cana-4456	155	37	that	that	PRON
cana-4456	155	38	are	be	AUX
cana-4456	155	39	centred	centre	VERB
cana-4456	155	40	at	at	ADP
cana-4456	155	41	the	the	DET
cana-4456	155	42	neighbouring	neighbouring	ADJ
cana-4456	155	43	nodes	node	NOUN
cana-4456	155	44	,	,	PUNCT
cana-4456	155	45	as	as	SCONJ
cana-4456	155	46	opposed	oppose	VERB
cana-4456	155	47	to	to	ADP
cana-4456	155	48	the	the	DET
cana-4456	155	49	standard	standard	NOUN
cana-4456	155	50	fd	fd	PROPN
cana-4456	155	51	,	,	PUNCT
cana-4456	155	52	which	which	PRON
cana-4456	155	53	focuses	focus	VERB
cana-4456	155	54	on	on	ADP
cana-4456	155	55	approximating	approximate	VERB
cana-4456	155	56	polynomials	polynomial	NOUN
cana-4456	155	57	for	for	ADP
cana-4456	155	58	the	the	DET
cana-4456	155	59	same	same	ADJ
cana-4456	155	60	nodes	node	NOUN
cana-4456	155	61	sets	set	VERB
cana-4456	155	62	.	.	PUNCT
cana-4456	156	1	after	after	ADP
cana-4456	156	2	performing	perform	VERB
cana-4456	156	3	calculations	calculation	NOUN
cana-4456	156	4	at	at	ADP
cana-4456	156	5	all	all	DET
cana-4456	156	6	interior	interior	ADJ
cana-4456	156	7	nodes	node	NOUN
cana-4456	156	8	,	,	PUNCT
cana-4456	156	9	the	the	DET
cana-4456	156	10	approximate	approximate	ADJ
cana-4456	156	11	solution	solution	NOUN
cana-4456	156	12	communications	communication	NOUN
cana-4456	156	13	on	on	ADP
cana-4456	156	14	applied	apply	VERB
cana-4456	156	15	nonlinear	nonlinear	ADJ
cana-4456	156	16	analysis	analysis	NOUN
cana-4456	156	17	issn	issn	NOUN
cana-4456	156	18	:	:	PUNCT
cana-4456	156	19	1074	1074	NUM
cana-4456	156	20	-	-	PUNCT
cana-4456	156	21	133x	133x	NUM
cana-4456	156	22	vol	vol	NOUN
cana-4456	156	23	32	32	NUM
cana-4456	156	24	no	no	NOUN
cana-4456	156	25	.	.	PUNCT
cana-4456	157	1	9s	9s	NUM
cana-4456	157	2	(	(	PUNCT
cana-4456	157	3	2025	2025	NUM
cana-4456	157	4	)	)	PUNCT
cana-4456	157	5	2174	2174	NUM
cana-4456	158	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	158	2	can	can	AUX
cana-4456	158	3	be	be	AUX
cana-4456	158	4	computed	compute	VERB
cana-4456	158	5	from	from	ADP
cana-4456	158	6	the	the	DET
cana-4456	158	7	associated	associated	ADJ
cana-4456	158	8	linear	linear	NOUN
cana-4456	158	9	system	system	NOUN
cana-4456	158	10	of	of	ADP
cana-4456	158	11	equations	equation	NOUN
cana-4456	158	12	,	,	PUNCT
cana-4456	158	13	for	for	ADP
cana-4456	158	14	which	which	PRON
cana-4456	158	15	the	the	DET
cana-4456	158	16	rbf	rbf	PROPN
cana-4456	158	17	-	-	PUNCT
cana-4456	158	18	fd	fd	PROPN
cana-4456	158	19	system	system	NOUN
cana-4456	158	20	matrix	matrix	NOUN
cana-4456	158	21	is	be	AUX
cana-4456	158	22	sparse	sparse	ADJ
cana-4456	158	23	,	,	PUNCT
cana-4456	158	24	thus	thus	ADV
cana-4456	158	25	can	can	AUX
cana-4456	158	26	be	be	AUX
cana-4456	158	27	effectively	effectively	ADV
cana-4456	158	28	inverted	invert	VERB
cana-4456	158	29	.	.	PUNCT
cana-4456	159	1	3.2.1	3.2.1	NUM
cana-4456	159	2	method	method	NOUN
cana-4456	159	3	’s	’s	PART
cana-4456	159	4	principle	principle	NOUN
cana-4456	159	5	we	we	PRON
cana-4456	159	6	will	will	AUX
cana-4456	159	7	next	next	ADV
cana-4456	159	8	present	present	VERB
cana-4456	159	9	an	an	DET
cana-4456	159	10	outline	outline	NOUN
cana-4456	159	11	of	of	ADP
cana-4456	159	12	the	the	DET
cana-4456	159	13	rbf	rbf	PROPN
cana-4456	159	14	along	along	ADP
cana-4456	159	15	with	with	ADP
cana-4456	159	16	finite	finite	ADJ
cana-4456	159	17	-	-	NOUN
cana-4456	159	18	difference	difference	NOUN
cana-4456	159	19	(	(	PUNCT
cana-4456	159	20	rbf	rbf	PROPN
cana-4456	159	21	-	-	PUNCT
cana-4456	159	22	fd	fd	ADJ
cana-4456	159	23	)	)	PUNCT
cana-4456	159	24	formulation	formulation	NOUN
cana-4456	159	25	.	.	PUNCT
cana-4456	160	1	let	let	VERB
cana-4456	160	2	x	x	PUNCT
cana-4456	160	3	=	=	PRON
cana-4456	160	4	{	{	PUNCT
cana-4456	160	5	𝑥1	𝑥1	NOUN
cana-4456	160	6	,	,	PUNCT
cana-4456	160	7	𝑥2	𝑥2	NOUN
cana-4456	160	8	,	,	PUNCT
cana-4456	160	9	.	.	PUNCT
cana-4456	160	10	.	.	PUNCT
cana-4456	160	11	.	.	PUNCT
cana-4456	161	1	,	,	PUNCT
cana-4456	161	2	𝑥𝑁	𝑥𝑁	NOUN
cana-4456	161	3	}	}	PUNCT
cana-4456	161	4	is	be	AUX
cana-4456	161	5	a	a	DET
cana-4456	161	6	set	set	NOUN
cana-4456	161	7	of	of	ADP
cana-4456	161	8	distinct	distinct	ADJ
cana-4456	161	9	points	point	NOUN
cana-4456	161	10	in	in	ADP
cana-4456	161	11	ω	ω	PROPN
cana-4456	161	12	⊂	⊂	PROPN
cana-4456	162	1	ℝ𝑑	ℝ𝑑	PROPN
cana-4456	162	2	and	and	CCONJ
cana-4456	162	3	let	let	VERB
cana-4456	162	4	𝐼(𝑥𝑗	𝐼(𝑥𝑗	NOUN
cana-4456	162	5	)	)	PUNCT
cana-4456	163	1	=	=	PRON
cana-4456	163	2	{	{	PUNCT
cana-4456	163	3	𝑥1	𝑥1	NOUN
cana-4456	163	4	𝑗	𝑗	NOUN
cana-4456	163	5	,	,	PUNCT
cana-4456	163	6	𝑥2	𝑥2	NOUN
cana-4456	163	7	𝑗	𝑗	NOUN
cana-4456	163	8	,	,	PUNCT
cana-4456	163	9	…	…	PUNCT
cana-4456	163	10	,	,	PUNCT
cana-4456	163	11	𝑥𝑛𝑙𝑜𝑐	𝑥𝑛𝑙𝑜𝑐	NOUN
cana-4456	163	12	𝑗	𝑗	AUX
cana-4456	163	13	}	}	PUNCT
cana-4456	163	14	be	be	AUX
cana-4456	163	15	a	a	DET
cana-4456	163	16	set	set	NOUN
cana-4456	163	17	of	of	ADP
cana-4456	163	18	points	point	NOUN
cana-4456	163	19	to	to	PART
cana-4456	163	20	form	form	VERB
cana-4456	163	21	a	a	DET
cana-4456	163	22	stencil	stencil	NOUN
cana-4456	163	23	weight	weight	NOUN
cana-4456	163	24	at	at	ADP
cana-4456	163	25	𝑥𝑗	𝑥𝑗	PROPN
cana-4456	163	26	.	.	PUNCT
cana-4456	164	1	note	note	VERB
cana-4456	164	2	that	that	SCONJ
cana-4456	164	3	the	the	DET
cana-4456	164	4	number	number	NOUN
cana-4456	164	5	of	of	ADP
cana-4456	164	6	points	point	NOUN
cana-4456	164	7	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	164	8	in	in	ADP
cana-4456	164	9	each	each	DET
cana-4456	164	10	stencil	stencil	NOUN
cana-4456	164	11	is	be	AUX
cana-4456	164	12	either	either	CCONJ
cana-4456	164	13	constant	constant	ADJ
cana-4456	164	14	or	or	CCONJ
cana-4456	164	15	vary	vary	VERB
cana-4456	164	16	with	with	ADP
cana-4456	164	17	𝑗	𝑗	INTJ
cana-4456	164	18	,	,	PUNCT
cana-4456	164	19	without	without	ADP
cana-4456	164	20	loss	loss	NOUN
cana-4456	164	21	of	of	ADP
cana-4456	164	22	generality	generality	NOUN
cana-4456	164	23	we	we	PRON
cana-4456	164	24	suppose	suppose	VERB
cana-4456	164	25	that	that	SCONJ
cana-4456	164	26	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	NOUN
cana-4456	164	27	is	be	AUX
cana-4456	164	28	constant	constant	ADJ
cana-4456	164	29	.	.	PUNCT
cana-4456	165	1	in	in	ADP
cana-4456	165	2	rbf	rbf	PROPN
cana-4456	165	3	-	-	PUNCT
cana-4456	165	4	fd	fd	PROPN
cana-4456	165	5	,	,	PUNCT
cana-4456	165	6	any	any	DET
cana-4456	165	7	linear	linear	ADJ
cana-4456	165	8	differential	differential	NOUN
cana-4456	165	9	operator	operator	NOUN
cana-4456	165	10	𝐿	𝐿	PROPN
cana-4456	165	11	that	that	PRON
cana-4456	165	12	acts	act	VERB
cana-4456	165	13	on	on	ADP
cana-4456	165	14	𝑢(𝑥	𝑢(𝑥	PROPN
cana-4456	165	15	)	)	PUNCT
cana-4456	165	16	evaluated	evaluate	VERB
cana-4456	165	17	at	at	ADP
cana-4456	165	18	𝑥𝑗	𝑥𝑗	PROPN
cana-4456	165	19	can	can	AUX
cana-4456	165	20	be	be	AUX
cana-4456	165	21	approximated	approximate	VERB
cana-4456	165	22	by	by	ADP
cana-4456	165	23	a	a	DET
cana-4456	165	24	linear	linear	ADJ
cana-4456	165	25	weighted	weight	VERB
cana-4456	165	26	combination	combination	NOUN
cana-4456	165	27	of	of	ADP
cana-4456	165	28	the	the	DET
cana-4456	165	29	function	function	NOUN
cana-4456	165	30	values	value	NOUN
cana-4456	165	31	at	at	ADP
cana-4456	165	32	the	the	DET
cana-4456	165	33	points	point	NOUN
cana-4456	165	34	of	of	ADP
cana-4456	165	35	𝐼(𝑥𝑗	𝐼(𝑥𝑗	NOUN
cana-4456	165	36	)	)	PUNCT
cana-4456	165	37	,	,	PUNCT
cana-4456	165	38	i.e.	i.e.	X
cana-4456	165	39	𝐿𝑢(𝑥𝑗	𝐿𝑢(𝑥𝑗	NOUN
cana-4456	165	40	)	)	PUNCT
cana-4456	166	1	≈	≈	NOUN
cana-4456	166	2	∑	∑	PUNCT
cana-4456	166	3	𝜔𝑘	𝜔𝑘	ADP
cana-4456	166	4	(	(	PUNCT
cana-4456	166	5	𝑗)𝑛𝑙𝑜𝑐	𝑗)𝑛𝑙𝑜𝑐	NOUN
cana-4456	166	6	𝑘=1	𝑘=1	PRON
cana-4456	166	7	𝑢(𝑥𝑘	𝑢(𝑥𝑘	PROPN
cana-4456	166	8	(	(	PUNCT
cana-4456	166	9	𝑗	𝑗	NOUN
cana-4456	166	10	)	)	PUNCT
cana-4456	166	11	)	)	PUNCT
cana-4456	166	12	.	.	PUNCT
cana-4456	167	1	(	(	PUNCT
cana-4456	167	2	21	21	NUM
cana-4456	167	3	)	)	PUNCT
cana-4456	167	4	the	the	DET
cana-4456	167	5	rbf	rbf	PROPN
cana-4456	167	6	-	-	PUNCT
cana-4456	167	7	fd	fd	PROPN
cana-4456	167	8	weights	weight	NOUN
cana-4456	167	9	𝜔𝑘	𝜔𝑘	X
cana-4456	167	10	(	(	PUNCT
cana-4456	167	11	𝑗	𝑗	NOUN
cana-4456	167	12	)	)	PUNCT
cana-4456	167	13	,	,	PUNCT
cana-4456	167	14	𝑘	𝑘	X
cana-4456	167	15	=	=	SYM
cana-4456	167	16	1	1	NUM
cana-4456	167	17	,	,	PUNCT
cana-4456	167	18	…	…	PUNCT
cana-4456	167	19	,	,	PUNCT
cana-4456	167	20	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	167	21	are	be	AUX
cana-4456	167	22	computed	compute	VERB
cana-4456	167	23	by	by	ADP
cana-4456	167	24	assuming	assume	VERB
cana-4456	167	25	the	the	DET
cana-4456	167	26	approximations	approximation	NOUN
cana-4456	167	27	(	(	PUNCT
cana-4456	167	28	21	21	NUM
cana-4456	167	29	)	)	PUNCT
cana-4456	167	30	become	become	VERB
cana-4456	167	31	exact	exact	ADJ
cana-4456	167	32	for	for	ADP
cana-4456	167	33	all	all	DET
cana-4456	167	34	rbfs	rbfs	NOUN
cana-4456	167	35	𝜑	𝜑	X
cana-4456	167	36	(	(	PUNCT
cana-4456	167	37	table	table	NOUN
cana-4456	167	38	1	1	NUM
cana-4456	167	39	)	)	PUNCT
cana-4456	167	40	that	that	PRON
cana-4456	167	41	are	be	AUX
cana-4456	167	42	centred	centre	VERB
cana-4456	167	43	at	at	ADP
cana-4456	167	44	the	the	DET
cana-4456	167	45	nodes	node	NOUN
cana-4456	167	46	𝑥𝑖	𝑥𝑖	X
cana-4456	167	47	(	(	PUNCT
cana-4456	167	48	𝑗	𝑗	NOUN
cana-4456	167	49	)	)	PUNCT
cana-4456	167	50	,	,	PUNCT
cana-4456	167	51	𝑖	𝑖	NOUN
cana-4456	167	52	=	=	SYM
cana-4456	167	53	1	1	NUM
cana-4456	167	54	,	,	PUNCT
cana-4456	167	55	…	…	PUNCT
cana-4456	167	56	,	,	PUNCT
cana-4456	167	57	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	167	58	,	,	PUNCT
cana-4456	167	59	i.e.	i.e.	X
cana-4456	167	60	,	,	PUNCT
cana-4456	167	61	we	we	PRON
cana-4456	167	62	assume	assume	VERB
cana-4456	167	63	that	that	SCONJ
cana-4456	167	64	(	(	PUNCT
cana-4456	167	65	21	21	NUM
cana-4456	167	66	)	)	PUNCT
cana-4456	167	67	becomes	become	VERB
cana-4456	167	68	exact	exact	ADJ
cana-4456	167	69	for	for	ADP
cana-4456	167	70	function	function	NOUN
cana-4456	167	71	𝑢(𝑥𝑗	𝑢(𝑥𝑗	NOUN
cana-4456	167	72	)	)	PUNCT
cana-4456	167	73	=	=	PUNCT
cana-4456	167	74	𝜑(∥	𝜑(∥	PROPN
cana-4456	167	75	𝑥	𝑥	PRON
cana-4456	167	76	−	−	X
cana-4456	167	77	𝑥𝑖	𝑥𝑖	PROPN
cana-4456	167	78	(	(	PUNCT
cana-4456	167	79	𝑗	𝑗	NOUN
cana-4456	167	80	)	)	PUNCT
cana-4456	167	81	∥)|	∥)|	PROPN
cana-4456	167	82	𝑥=𝑥𝑗	𝑥=𝑥𝑗	PROPN
cana-4456	167	83	,	,	PUNCT
cana-4456	167	84	𝑖	𝑖	PROPN
cana-4456	167	85	=	=	NOUN
cana-4456	167	86	1	1	NUM
cana-4456	167	87	,	,	PUNCT
cana-4456	167	88	…	…	PUNCT
cana-4456	167	89	,	,	PUNCT
cana-4456	167	90	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	167	91	,	,	PUNCT
cana-4456	167	92	this	this	DET
cana-4456	167	93	assumption	assumption	NOUN
cana-4456	167	94	leads	lead	VERB
cana-4456	167	95	to	to	ADP
cana-4456	167	96	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	X
cana-4456	167	97	×	×	NOUN
cana-4456	167	98	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	167	99	linear	linear	NOUN
cana-4456	167	100	system	system	NOUN
cana-4456	167	101	:	:	PUNCT
cana-4456	167	102	(	(	PUNCT
cana-4456	167	103	𝜑	𝜑	X
cana-4456	167	104	(	(	PUNCT
cana-4456	167	105	‖𝑥1	‖𝑥1	NOUN
cana-4456	167	106	(	(	PUNCT
cana-4456	167	107	𝑗	𝑗	NOUN
cana-4456	167	108	)	)	PUNCT
cana-4456	167	109	−	−	PROPN
cana-4456	167	110	𝑥1	𝑥1	PROPN
cana-4456	167	111	(	(	PUNCT
cana-4456	167	112	𝑗)‖	𝑗)‖	NOUN
cana-4456	167	113	)	)	PUNCT
cana-4456	167	114	⋯	⋯	NOUN
cana-4456	167	115	𝜑	𝜑	NOUN
cana-4456	167	116	(	(	PUNCT
cana-4456	167	117	‖𝑥1	‖𝑥1	NOUN
cana-4456	167	118	(	(	PUNCT
cana-4456	167	119	𝑗	𝑗	NOUN
cana-4456	167	120	)	)	PUNCT
cana-4456	168	1	−	−	NOUN
cana-4456	168	2	𝑥𝑛𝑙𝑜𝑐	𝑥𝑛𝑙𝑜𝑐	NOUN
cana-4456	168	3	(	(	PUNCT
cana-4456	168	4	𝑗	𝑗	NOUN
cana-4456	168	5	)	)	PUNCT
cana-4456	168	6	‖	‖	ADJ
cana-4456	168	7	)	)	PUNCT
cana-4456	168	8	⋮	⋮	NOUN
cana-4456	168	9	⋱	⋱	PUNCT
cana-4456	168	10	⋮	⋮	NOUN
cana-4456	168	11	𝜑	𝜑	X
cana-4456	168	12	(	(	PUNCT
cana-4456	168	13	‖𝑥𝑛𝑙𝑜𝑐	‖𝑥𝑛𝑙𝑜𝑐	NOUN
cana-4456	168	14	(	(	PUNCT
cana-4456	168	15	𝑗	𝑗	NOUN
cana-4456	168	16	)	)	PUNCT
cana-4456	168	17	−	−	PROPN
cana-4456	168	18	𝑥1	𝑥1	PROPN
cana-4456	168	19	(	(	PUNCT
cana-4456	168	20	𝑗)‖	𝑗)‖	NOUN
cana-4456	168	21	)	)	PUNCT
cana-4456	168	22	⋯	⋯	NOUN
cana-4456	168	23	𝜑	𝜑	NOUN
cana-4456	168	24	(	(	PUNCT
cana-4456	168	25	‖𝑥𝑛𝑙𝑜𝑐	‖𝑥𝑛𝑙𝑜𝑐	NOUN
cana-4456	168	26	(	(	PUNCT
cana-4456	168	27	𝑗	𝑗	NOUN
cana-4456	168	28	)	)	PUNCT
cana-4456	168	29	−	−	NOUN
cana-4456	169	1	𝑥𝑛𝑙𝑜𝑐	𝑥𝑛𝑙𝑜𝑐	NOUN
cana-4456	169	2	(	(	PUNCT
cana-4456	169	3	𝑗	𝑗	NOUN
cana-4456	169	4	)	)	PUNCT
cana-4456	169	5	‖	‖	NUM
cana-4456	169	6	)	)	PUNCT
cana-4456	169	7	)	)	PUNCT
cana-4456	170	1	(	(	PUNCT
cana-4456	170	2	𝜔1	𝜔1	ADJ
cana-4456	170	3	(	(	PUNCT
cana-4456	170	4	𝑗	𝑗	NOUN
cana-4456	170	5	)	)	PUNCT
cana-4456	170	6	⋮	⋮	NOUN
cana-4456	170	7	𝜔𝑛𝑙𝑜𝑐	𝜔𝑛𝑙𝑜𝑐	NOUN
cana-4456	170	8	(	(	PUNCT
cana-4456	170	9	𝑗	𝑗	NOUN
cana-4456	170	10	)	)	PUNCT
cana-4456	170	11	)	)	PUNCT
cana-4456	171	1	=	=	PRON
cana-4456	171	2	(	(	PUNCT
cana-4456	171	3	𝐿𝜑(∥𝑥	𝐿𝜑(∥𝑥	PROPN
cana-4456	171	4	−	−	PROPN
cana-4456	171	5	𝑥1	𝑥1	PROPN
cana-4456	171	6	(	(	PUNCT
cana-4456	171	7	𝑗	𝑗	PROPN
cana-4456	171	8	)	)	PUNCT
cana-4456	171	9	∥)|	∥)|	PROPN
cana-4456	171	10	𝑥=𝑥𝑗	𝑥=𝑥𝑗	PROPN
cana-4456	171	11	⋮	⋮	PROPN
cana-4456	171	12	𝐿𝜑(∥𝑥	𝐿𝜑(∥𝑥	PROPN
cana-4456	172	1	−	−	PROPN
cana-4456	172	2	𝑥𝑛𝑙𝑜𝑐	𝑥𝑛𝑙𝑜𝑐	NOUN
cana-4456	172	3	(	(	PUNCT
cana-4456	172	4	𝑗	𝑗	NOUN
cana-4456	172	5	)	)	PUNCT
cana-4456	172	6	∥)|	∥)|	PROPN
cana-4456	172	7	𝑥=𝑥𝑗	𝑥=𝑥𝑗	PROPN
cana-4456	172	8	)	)	PUNCT
cana-4456	172	9	(	(	PUNCT
cana-4456	172	10	22	22	X
cana-4456	172	11	)	)	PUNCT
cana-4456	172	12	note	note	NOUN
cana-4456	172	13	that	that	SCONJ
cana-4456	172	14	the	the	DET
cana-4456	172	15	system	system	NOUN
cana-4456	172	16	matrix	matrix	NOUN
cana-4456	172	17	is	be	AUX
cana-4456	172	18	invertible	invertible	ADJ
cana-4456	172	19	due	due	ADP
cana-4456	172	20	to	to	ADP
cana-4456	172	21	the	the	DET
cana-4456	172	22	properties	property	NOUN
cana-4456	172	23	of	of	ADP
cana-4456	172	24	the	the	DET
cana-4456	172	25	rbfs	rbfs	NOUN
cana-4456	172	26	mentioned	mention	VERB
cana-4456	172	27	before	before	ADV
cana-4456	172	28	.	.	PUNCT
cana-4456	173	1	therefore	therefore	ADV
cana-4456	173	2	,	,	PUNCT
cana-4456	173	3	the	the	DET
cana-4456	173	4	rbf	rbf	PROPN
cana-4456	173	5	-	-	PUNCT
cana-4456	173	6	fd	fd	ADJ
cana-4456	173	7	weights	weight	NOUN
cana-4456	173	8	can	can	AUX
cana-4456	173	9	always	always	ADV
cana-4456	173	10	be	be	AUX
cana-4456	173	11	calculated	calculate	VERB
cana-4456	173	12	.	.	PUNCT
cana-4456	174	1	to	to	PART
cana-4456	174	2	obtain	obtain	VERB
cana-4456	174	3	the	the	DET
cana-4456	174	4	rbf	rbf	PROPN
cana-4456	174	5	-	-	PUNCT
cana-4456	174	6	fd	fd	ADJ
cana-4456	174	7	weights	weight	NOUN
cana-4456	174	8	,	,	PUNCT
cana-4456	174	9	we	we	PRON
cana-4456	174	10	have	have	VERB
cana-4456	174	11	to	to	PART
cana-4456	174	12	solve	solve	VERB
cana-4456	174	13	the	the	DET
cana-4456	174	14	system	system	NOUN
cana-4456	174	15	(	(	PUNCT
cana-4456	174	16	22	22	NUM
cana-4456	174	17	)	)	PUNCT
cana-4456	174	18	for	for	ADP
cana-4456	174	19	each	each	DET
cana-4456	174	20	stencil	stencil	PROPN
cana-4456	174	21	center	center	PROPN
cana-4456	174	22	𝑥𝑗	𝑥𝑗	PROPN
cana-4456	174	23	,	,	PUNCT
cana-4456	174	24	𝑗	𝑗	PROPN
cana-4456	174	25	=	=	SYM
cana-4456	174	26	1	1	NUM
cana-4456	174	27	,	,	PUNCT
cana-4456	174	28	…	…	PUNCT
cana-4456	174	29	,	,	PUNCT
cana-4456	174	30	𝑁	𝑁	PROPN
cana-4456	174	31	to	to	PART
cana-4456	174	32	form	form	VERB
cana-4456	174	33	𝑁	𝑁	PROPN
cana-4456	174	34	rows	row	NOUN
cana-4456	174	35	of	of	ADP
cana-4456	174	36	the	the	DET
cana-4456	174	37	differentiation	differentiation	NOUN
cana-4456	174	38	matrix	matrix	NOUN
cana-4456	174	39	denoted	denote	VERB
cana-4456	174	40	by	by	ADP
cana-4456	174	41	𝑊𝐿	𝑊𝐿	PROPN
cana-4456	174	42	where	where	SCONJ
cana-4456	174	43	𝐿	𝐿	PROPN
cana-4456	174	44	refer	refer	VERB
cana-4456	174	45	to	to	ADP
cana-4456	174	46	a	a	DET
cana-4456	174	47	linear	linear	ADJ
cana-4456	174	48	differential	differential	NOUN
cana-4456	174	49	operator	operator	NOUN
cana-4456	174	50	that	that	PRON
cana-4456	174	51	acts	act	VERB
cana-4456	174	52	on	on	ADP
cana-4456	174	53	solutions	solution	NOUN
cana-4456	174	54	,	,	PUNCT
cana-4456	174	55	𝑊𝐿	𝑊𝐿	PROPN
cana-4456	174	56	is	be	AUX
cana-4456	174	57	a	a	DET
cana-4456	174	58	sparse	sparse	ADJ
cana-4456	174	59	matrix	matrix	NOUN
cana-4456	174	60	and	and	CCONJ
cana-4456	174	61	contains	contain	VERB
cana-4456	174	62	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	PROPN
cana-4456	174	63	non	non	ADJ
cana-4456	174	64	-	-	ADJ
cana-4456	174	65	zero	zero	NUM
cana-4456	174	66	elements	element	NOUN
cana-4456	174	67	per	per	ADP
cana-4456	174	68	row	row	NOUN
cana-4456	174	69	.	.	PUNCT
cana-4456	175	1	when	when	SCONJ
cana-4456	175	2	solving	solve	VERB
cana-4456	175	3	pde	pde	NOUN
cana-4456	175	4	,	,	PUNCT
cana-4456	175	5	we	we	PRON
cana-4456	175	6	apply	apply	VERB
cana-4456	175	7	a	a	DET
cana-4456	175	8	similar	similar	ADJ
cana-4456	175	9	procedure	procedure	NOUN
cana-4456	175	10	of	of	ADP
cana-4456	175	11	what	what	PRON
cana-4456	175	12	has	have	AUX
cana-4456	175	13	done	do	VERB
cana-4456	175	14	for	for	ADP
cana-4456	175	15	kansa	kansa	PROPN
cana-4456	175	16	method	method	NOUN
cana-4456	175	17	.	.	PUNCT
cana-4456	176	1	after	after	ADP
cana-4456	176	2	obtaining	obtain	VERB
cana-4456	176	3	the	the	DET
cana-4456	176	4	weights	weight	NOUN
cana-4456	176	5	,	,	PUNCT
cana-4456	176	6	we	we	PRON
cana-4456	176	7	use	use	VERB
cana-4456	176	8	the	the	DET
cana-4456	176	9	approximation	approximation	NOUN
cana-4456	176	10	equation	equation	NOUN
cana-4456	176	11	(	(	PUNCT
cana-4456	176	12	21	21	NUM
cana-4456	176	13	)	)	PUNCT
cana-4456	176	14	to	to	PART
cana-4456	176	15	conclude	conclude	VERB
cana-4456	176	16	an	an	DET
cana-4456	176	17	approximate	approximate	ADJ
cana-4456	176	18	solution	solution	NOUN
cana-4456	176	19	for	for	ADP
cana-4456	176	20	the	the	DET
cana-4456	176	21	pde	pde	NOUN
cana-4456	176	22	.	.	PUNCT
cana-4456	177	1	3.2.2	3.2.2	NUM
cana-4456	177	2	spatial	spatial	ADJ
cana-4456	177	3	discretization	discretization	NOUN
cana-4456	177	4	of	of	ADP
cana-4456	177	5	swes	swe	NOUN
cana-4456	177	6	using	use	VERB
cana-4456	177	7	rbf	rbf	PROPN
cana-4456	177	8	-	-	PUNCT
cana-4456	177	9	fd	fd	PROPN
cana-4456	177	10	method	method	NOUN
cana-4456	177	11	in	in	ADP
cana-4456	177	12	this	this	DET
cana-4456	177	13	section	section	NOUN
cana-4456	177	14	,	,	PUNCT
cana-4456	177	15	we	we	PRON
cana-4456	177	16	will	will	AUX
cana-4456	177	17	present	present	VERB
cana-4456	177	18	implementation	implementation	NOUN
cana-4456	177	19	details	detail	NOUN
cana-4456	177	20	on	on	ADP
cana-4456	177	21	the	the	DET
cana-4456	177	22	computational	computational	ADJ
cana-4456	177	23	of	of	ADP
cana-4456	177	24	rbf	rbf	PROPN
cana-4456	177	25	-	-	PUNCT
cana-4456	177	26	fd	fd	PROPN
cana-4456	177	27	formulation	formulation	NOUN
cana-4456	177	28	for	for	ADP
cana-4456	177	29	solving	solve	VERB
cana-4456	177	30	equations	equation	NOUN
cana-4456	177	31	(	(	PUNCT
cana-4456	177	32	1	1	NUM
cana-4456	177	33	)	)	PUNCT
cana-4456	177	34	.	.	PUNCT
cana-4456	178	1	let	let	VERB
cana-4456	178	2	{	{	PUNCT
cana-4456	178	3	𝑥1	𝑥1	NOUN
cana-4456	178	4	,	,	PUNCT
cana-4456	178	5	𝑥2	𝑥2	NOUN
cana-4456	178	6	,	,	PUNCT
cana-4456	178	7	.	.	PUNCT
cana-4456	178	8	.	.	PUNCT
cana-4456	178	9	.	.	PUNCT
cana-4456	179	1	,	,	PUNCT
cana-4456	179	2	𝑥𝑁	𝑥𝑁	NOUN
cana-4456	179	3	}	}	PUNCT
cana-4456	179	4	be	be	AUX
cana-4456	179	5	a	a	DET
cana-4456	179	6	set	set	NOUN
cana-4456	179	7	of	of	ADP
cana-4456	179	8	scattered	scatter	VERB
cana-4456	179	9	nodes	node	NOUN
cana-4456	179	10	.	.	PUNCT
cana-4456	180	1	using	use	VERB
cana-4456	180	2	(	(	PUNCT
cana-4456	180	3	21	21	NUM
cana-4456	180	4	)	)	PUNCT
cana-4456	180	5	,	,	PUNCT
cana-4456	180	6	the	the	DET
cana-4456	180	7	first	first	ADJ
cana-4456	180	8	and	and	CCONJ
cana-4456	180	9	second	second	ADJ
cana-4456	180	10	spatial	spatial	ADJ
cana-4456	180	11	derivatives	derivative	NOUN
cana-4456	180	12	of	of	ADP
cana-4456	180	13	a	a	DET
cana-4456	180	14	function	function	NOUN
cana-4456	180	15	𝑸(𝑥	𝑸(𝑥	NOUN
cana-4456	180	16	,	,	PUNCT
cana-4456	180	17	𝑡	𝑡	PROPN
cana-4456	180	18	)	)	PUNCT
cana-4456	180	19	can	can	AUX
cana-4456	180	20	be	be	AUX
cana-4456	180	21	expressed	express	VERB
cana-4456	180	22	as	as	SCONJ
cana-4456	180	23	follows	follow	VERB
cana-4456	180	24	:	:	PUNCT
cana-4456	180	25	𝜕𝑸(𝑥𝑗,𝑡	𝜕𝑸(𝑥𝑗,𝑡	PROPN
cana-4456	180	26	)	)	PUNCT
cana-4456	180	27	𝜕𝑥	𝜕𝑥	NOUN
cana-4456	180	28	=	=	PUNCT
cana-4456	180	29	∑	∑	PUNCT
cana-4456	180	30	𝜕	𝜕	NOUN
cana-4456	180	31	𝜔𝑘	𝜔𝑘	X
cana-4456	180	32	(	(	PUNCT
cana-4456	180	33	𝑗	𝑗	NOUN
cana-4456	180	34	)	)	PUNCT
cana-4456	180	35	𝜕𝑥	𝜕𝑥	X
cana-4456	180	36	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	X
cana-4456	181	1	𝑘=1	𝑘=1	PRON
cana-4456	181	2	𝑸(𝑥𝑘	𝑸(𝑥𝑘	PROPN
cana-4456	181	3	(	(	PUNCT
cana-4456	181	4	𝑗	𝑗	NOUN
cana-4456	181	5	)	)	PUNCT
cana-4456	181	6	,	,	PUNCT
cana-4456	181	7	𝑡	𝑡	PROPN
cana-4456	181	8	)	)	PUNCT
cana-4456	181	9	,	,	PUNCT
cana-4456	181	10	𝜕2𝑸(𝑥𝑗,𝑡	𝜕2𝑸(𝑥𝑗,𝑡	PROPN
cana-4456	181	11	)	)	PUNCT
cana-4456	181	12	𝜕𝑥2	𝜕𝑥2	NOUN
cana-4456	181	13	=	=	PUNCT
cana-4456	182	1	∑	∑	PUNCT
cana-4456	182	2	𝜕2𝜔𝑘	𝜕2𝜔𝑘	PROPN
cana-4456	182	3	(	(	PUNCT
cana-4456	182	4	𝑗	𝑗	NOUN
cana-4456	182	5	)	)	PUNCT
cana-4456	182	6	𝜕𝑥2	𝜕𝑥2	NOUN
cana-4456	182	7	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	182	8	𝑘=1	𝑘=1	X
cana-4456	182	9	𝑸(𝑥𝑘	𝑸(𝑥𝑘	PROPN
cana-4456	182	10	(	(	PUNCT
cana-4456	182	11	𝑗	𝑗	NOUN
cana-4456	182	12	)	)	PUNCT
cana-4456	182	13	,	,	PUNCT
cana-4456	182	14	𝑡	𝑡	PROPN
cana-4456	182	15	)	)	PUNCT
cana-4456	182	16	,	,	PUNCT
cana-4456	182	17	𝑗	𝑗	NOUN
cana-4456	183	1	=	=	SYM
cana-4456	183	2	1	1	NUM
cana-4456	183	3	,	,	PUNCT
cana-4456	183	4	…	…	PUNCT
cana-4456	183	5	,	,	PUNCT
cana-4456	183	6	𝑁	𝑁	PROPN
cana-4456	183	7	(	(	PUNCT
cana-4456	183	8	23	23	NUM
cana-4456	183	9	)	)	PUNCT
cana-4456	183	10	communications	communication	NOUN
cana-4456	183	11	on	on	ADP
cana-4456	183	12	applied	apply	VERB
cana-4456	183	13	nonlinear	nonlinear	ADJ
cana-4456	183	14	analysis	analysis	NOUN
cana-4456	183	15	issn	issn	NOUN
cana-4456	183	16	:	:	PUNCT
cana-4456	183	17	1074	1074	NUM
cana-4456	183	18	-	-	PUNCT
cana-4456	183	19	133x	133x	NUM
cana-4456	183	20	vol	vol	NOUN
cana-4456	183	21	32	32	NUM
cana-4456	183	22	no	no	NOUN
cana-4456	183	23	.	.	PUNCT
cana-4456	184	1	9s	9s	NUM
cana-4456	184	2	(	(	PUNCT
cana-4456	184	3	2025	2025	NUM
cana-4456	184	4	)	)	PUNCT
cana-4456	184	5	2175	2175	NUM
cana-4456	184	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	185	1	after	after	ADP
cana-4456	185	2	collocating	collocate	VERB
cana-4456	185	3	the	the	DET
cana-4456	185	4	points	point	NOUN
cana-4456	185	5	,	,	PUNCT
cana-4456	185	6	we	we	PRON
cana-4456	185	7	obtain	obtain	VERB
cana-4456	185	8	𝜕𝑸(𝑥,𝑡	𝜕𝑸(𝑥,𝑡	ADJ
cana-4456	185	9	)	)	PUNCT
cana-4456	185	10	𝜕𝑥	𝜕𝑥	NOUN
cana-4456	185	11	=	=	SYM
cana-4456	185	12	𝑊𝑥𝑸(𝑥	𝑊𝑥𝑸(𝑥	PROPN
cana-4456	185	13	,	,	PUNCT
cana-4456	185	14	𝑡	𝑡	NOUN
cana-4456	185	15	)	)	PUNCT
cana-4456	185	16	,	,	PUNCT
cana-4456	185	17	𝜕2𝑸(𝑥,𝑡	𝜕2𝑸(𝑥,𝑡	NOUN
cana-4456	185	18	)	)	PUNCT
cana-4456	185	19	𝜕𝑥2	𝜕𝑥2	NOUN
cana-4456	185	20	=	=	SYM
cana-4456	185	21	𝑊𝑥𝑥𝑸(𝑥	𝑊𝑥𝑥𝑸(𝑥	PROPN
cana-4456	185	22	,	,	PUNCT
cana-4456	185	23	𝑡	𝑡	NOUN
cana-4456	185	24	)	)	PUNCT
cana-4456	185	25	,	,	PUNCT
cana-4456	185	26	(	(	PUNCT
cana-4456	185	27	24	24	NUM
cana-4456	185	28	)	)	PUNCT
cana-4456	185	29	where	where	SCONJ
cana-4456	185	30	𝑊𝑥	𝑊𝑥	NOUN
cana-4456	185	31	and	and	CCONJ
cana-4456	185	32	𝑊𝑥𝑥	𝑊𝑥𝑥	PROPN
cana-4456	185	33	are	be	AUX
cana-4456	185	34	first	first	ADJ
cana-4456	185	35	and	and	CCONJ
cana-4456	185	36	second	second	ADJ
cana-4456	185	37	derivative	derivative	ADJ
cana-4456	185	38	matrices	matrix	NOUN
cana-4456	185	39	with	with	ADP
cana-4456	185	40	respect	respect	NOUN
cana-4456	185	41	to	to	ADP
cana-4456	185	42	𝑥	𝑥	PRON
cana-4456	185	43	.	.	PUNCT
cana-4456	186	1	the	the	DET
cana-4456	186	2	system	system	NOUN
cana-4456	186	3	(	(	PUNCT
cana-4456	186	4	8)	8)	NUM
cana-4456	186	5	is	be	AUX
cana-4456	186	6	approximated	approximate	VERB
cana-4456	186	7	by	by	ADP
cana-4456	186	8	the	the	DET
cana-4456	186	9	following	follow	VERB
cana-4456	186	10	equivalent	equivalent	ADJ
cana-4456	186	11	system	system	NOUN
cana-4456	186	12	:	:	PUNCT
cana-4456	186	13	𝜕𝑡𝑸	𝜕𝑡𝑸	NUM
cana-4456	186	14	=	=	PUNCT
cana-4456	186	15	−	−	NUM
cana-4456	186	16	�	�	NOUN
cana-4456	186	17	̅	̅	NOUN
cana-4456	186	18	�	�	NOUN
cana-4456	186	19	(𝑸	(𝑸	NUM
cana-4456	186	20	)	)	PUNCT
cana-4456	186	21	+	+	NUM
cana-4456	186	22	𝑆̅(𝑸	𝑆̅(𝑸	NOUN
cana-4456	186	23	)	)	PUNCT
cana-4456	186	24	+	+	CCONJ
cana-4456	186	25	�	�	NOUN
cana-4456	186	26	̅	̅	NOUN
cana-4456	186	27	�	�	PROPN
cana-4456	186	28	(𝑸	(𝑸	NUM
cana-4456	186	29	)	)	PUNCT
cana-4456	186	30	,	,	PUNCT
cana-4456	186	31	(	(	PUNCT
cana-4456	186	32	25	25	NUM
cana-4456	186	33	)	)	PUNCT
cana-4456	186	34	using	use	VERB
cana-4456	186	35	the	the	DET
cana-4456	186	36	rbf	rbf	PROPN
cana-4456	186	37	-	-	PUNCT
cana-4456	186	38	fd	fd	PROPN
cana-4456	186	39	method	method	NOUN
cana-4456	186	40	to	to	PART
cana-4456	186	41	perform	perform	VERB
cana-4456	186	42	numerical	numerical	ADJ
cana-4456	186	43	evaluation	evaluation	NOUN
cana-4456	186	44	,	,	PUNCT
cana-4456	186	45	we	we	PRON
cana-4456	186	46	obtain	obtain	VERB
cana-4456	186	47	𝐹	𝐹	PROPN
cana-4456	186	48	̅(𝑸	̅(𝑸	ADV
cana-4456	186	49	)	)	PUNCT
cana-4456	186	50	=	=	PUNCT
cana-4456	187	1	(	(	PUNCT
cana-4456	187	2	𝑊𝑥𝑞	𝑊𝑥𝑞	PROPN
cana-4456	187	3	𝑊𝑥	𝑊𝑥	PROPN
cana-4456	187	4	(	(	PUNCT
cana-4456	187	5	𝑞2	𝑞2	NOUN
cana-4456	187	6	ℎ	ℎ	PART
cana-4456	187	7	+	+	NOUN
cana-4456	187	8	1	1	NUM
cana-4456	187	9	2	2	NUM
cana-4456	187	10	𝑔ℎ2	𝑔ℎ2	NOUN
cana-4456	187	11	)	)	PUNCT
cana-4456	187	12	)	)	PUNCT
cana-4456	187	13	,	,	PUNCT
cana-4456	187	14	𝑆	𝑆	PROPN
cana-4456	187	15	̅(𝑸	̅(𝑸	PROPN
cana-4456	187	16	)	)	PUNCT
cana-4456	187	17	=	=	PUNCT
cana-4456	187	18	(	(	PUNCT
cana-4456	187	19	0	0	NUM
cana-4456	187	20	−𝑔ℎ𝑊𝑥𝑏	−𝑔ℎ𝑊𝑥𝑏	NOUN
cana-4456	187	21	)	)	PUNCT
cana-4456	187	22	,	,	PUNCT
cana-4456	187	23	𝐻	𝐻	PROPN
cana-4456	187	24	̅̅	̅̅	NOUN
cana-4456	187	25	̅(𝑸	̅(𝑸	PUNCT
cana-4456	187	26	)	)	PUNCT
cana-4456	187	27	=	=	PUNCT
cana-4456	187	28	(	(	PUNCT
cana-4456	187	29	𝜇𝑊𝑥𝑥ℎ	𝜇𝑊𝑥𝑥ℎ	PROPN
cana-4456	187	30	𝜇𝑊𝑥𝑥𝑞	𝜇𝑊𝑥𝑥𝑞	PROPN
cana-4456	187	31	)	)	PUNCT
cana-4456	187	32	,	,	PUNCT
cana-4456	187	33	(	(	PUNCT
cana-4456	187	34	26	26	NUM
cana-4456	187	35	)	)	PUNCT
cana-4456	187	36	equivalent	equivalent	ADJ
cana-4456	187	37	to	to	ADP
cana-4456	187	38	𝜕𝑡𝑸	𝜕𝑡𝑸	NUM
cana-4456	187	39	=	=	SYM
cana-4456	187	40	𝑅𝐻𝑆𝑅𝐵𝐹−𝐹𝐷(𝑸	𝑅𝐻𝑆𝑅𝐵𝐹−𝐹𝐷(𝑸	NOUN
cana-4456	187	41	)	)	PUNCT
cana-4456	187	42	,	,	PUNCT
cana-4456	187	43	where	where	SCONJ
cana-4456	187	44	𝑅𝐻𝑆𝑅𝐵𝐹−𝐹𝐷(𝑸	𝑅𝐻𝑆𝑅𝐵𝐹−𝐹𝐷(𝑸	NOUN
cana-4456	187	45	)	)	PUNCT
cana-4456	187	46	=	=	SYM
cana-4456	188	1	−	−	NUM
cana-4456	188	2	�	�	NOUN
cana-4456	188	3	̅	̅	NOUN
cana-4456	188	4	�	�	NOUN
cana-4456	188	5	(𝑸	(𝑸	NUM
cana-4456	188	6	)	)	PUNCT
cana-4456	188	7	+	+	NUM
cana-4456	188	8	𝑆̅(𝑸	𝑆̅(𝑸	NOUN
cana-4456	188	9	)	)	PUNCT
cana-4456	188	10	+	+	CCONJ
cana-4456	188	11	�	�	NOUN
cana-4456	188	12	̅	̅	NOUN
cana-4456	188	13	�	�	NOUN
cana-4456	188	14	(𝑸	(𝑸	NUM
cana-4456	188	15	)	)	PUNCT
cana-4456	188	16	.	.	PUNCT
cana-4456	189	1	(	(	PUNCT
cana-4456	189	2	27	27	NUM
cana-4456	189	3	)	)	SYM
cana-4456	189	4	3.3	3.3	NUM
cana-4456	189	5	radial	radial	ADJ
cana-4456	189	6	basis	basis	NOUN
cana-4456	189	7	function	function	NOUN
cana-4456	189	8	partition	partition	NOUN
cana-4456	189	9	of	of	ADP
cana-4456	189	10	unity	unity	NOUN
cana-4456	189	11	method	method	NOUN
cana-4456	189	12	(	(	PUNCT
cana-4456	189	13	rbf	rbf	PROPN
cana-4456	189	14	-	-	PUNCT
cana-4456	189	15	pum	pum	PROPN
cana-4456	189	16	)	)	PUNCT
cana-4456	189	17	the	the	DET
cana-4456	189	18	partition	partition	NOUN
cana-4456	189	19	of	of	ADP
cana-4456	189	20	unity	unity	NOUN
cana-4456	189	21	method	method	NOUN
cana-4456	189	22	(	(	PUNCT
cana-4456	189	23	pum	pum	PROPN
cana-4456	189	24	)	)	PUNCT
cana-4456	189	25	was	be	AUX
cana-4456	189	26	first	first	ADV
cana-4456	189	27	proposed	propose	VERB
cana-4456	189	28	by	by	ADP
cana-4456	189	29	babuška	babuška	PROPN
cana-4456	189	30	and	and	CCONJ
cana-4456	189	31	melenk	melenk	NOUN
cana-4456	190	1	[	[	X
cana-4456	190	2	31	31	NUM
cana-4456	190	3	]	]	PUNCT
cana-4456	191	1	and	and	CCONJ
cana-4456	191	2	applied	apply	VERB
cana-4456	191	3	the	the	DET
cana-4456	191	4	method	method	NOUN
cana-4456	191	5	to	to	PART
cana-4456	191	6	solve	solve	VERB
cana-4456	191	7	pdes	pde	NOUN
cana-4456	191	8	.	.	PUNCT
cana-4456	192	1	the	the	DET
cana-4456	192	2	main	main	ADJ
cana-4456	192	3	idea	idea	NOUN
cana-4456	192	4	of	of	ADP
cana-4456	192	5	rbf	rbf	PROPN
cana-4456	192	6	-	-	PROPN
cana-4456	192	7	pum	pum	PROPN
cana-4456	192	8	is	be	AUX
cana-4456	192	9	to	to	PART
cana-4456	192	10	subdivide	subdivide	VERB
cana-4456	192	11	the	the	DET
cana-4456	192	12	domain	domain	NOUN
cana-4456	192	13	into	into	ADP
cana-4456	192	14	overlapping	overlap	VERB
cana-4456	192	15	subdomains	subdomain	NOUN
cana-4456	192	16	or	or	CCONJ
cana-4456	192	17	patches	patch	NOUN
cana-4456	192	18	in	in	ADP
cana-4456	192	19	which	which	PRON
cana-4456	192	20	we	we	PRON
cana-4456	192	21	construct	construct	VERB
cana-4456	192	22	the	the	DET
cana-4456	192	23	local	local	ADJ
cana-4456	192	24	rbf	rbf	PROPN
cana-4456	192	25	approximation	approximation	NOUN
cana-4456	192	26	on	on	ADP
cana-4456	192	27	each	each	DET
cana-4456	192	28	patches	patch	NOUN
cana-4456	192	29	,	,	PUNCT
cana-4456	192	30	then	then	ADV
cana-4456	192	31	the	the	DET
cana-4456	192	32	global	global	ADJ
cana-4456	192	33	solution	solution	NOUN
cana-4456	192	34	is	be	AUX
cana-4456	192	35	given	give	VERB
cana-4456	192	36	by	by	ADP
cana-4456	192	37	the	the	DET
cana-4456	192	38	sum	sum	NOUN
cana-4456	192	39	of	of	ADP
cana-4456	192	40	these	these	DET
cana-4456	192	41	local	local	ADJ
cana-4456	192	42	approximations	approximation	NOUN
cana-4456	192	43	multiplied	multiply	VERB
cana-4456	192	44	by	by	ADP
cana-4456	192	45	partition	partition	NOUN
cana-4456	192	46	of	of	ADP
cana-4456	192	47	unity	unity	NOUN
cana-4456	192	48	weight	weight	NOUN
cana-4456	192	49	functions	function	NOUN
cana-4456	192	50	.	.	PUNCT
cana-4456	193	1	3.3.1	3.3.1	NUM
cana-4456	193	2	method	method	NOUN
cana-4456	193	3	’s	’s	PART
cana-4456	193	4	principle	principle	NOUN
cana-4456	193	5	let	let	VERB
cana-4456	193	6	{	{	PUNCT
cana-4456	193	7	ω𝑖	ω𝑖	NOUN
cana-4456	193	8	}	}	PUNCT
cana-4456	193	9	𝑖=1	𝑖=1	PROPN
cana-4456	193	10	𝑛𝑝	𝑛𝑝	AUX
cana-4456	193	11	be	be	AUX
cana-4456	193	12	an	an	DET
cana-4456	193	13	open	open	ADJ
cana-4456	193	14	covering	covering	NOUN
cana-4456	193	15	of	of	ADP
cana-4456	193	16	an	an	DET
cana-4456	193	17	open	open	ADJ
cana-4456	193	18	set	set	NOUN
cana-4456	193	19	𝛺	𝛺	NOUN
cana-4456	193	20	i.e.	i.e.	X
cana-4456	193	21	,	,	PUNCT
cana-4456	193	22	𝛺	𝛺	ADP
cana-4456	193	23	⊆	⊆	NUM
cana-4456	193	24	⋃	⋃	SCONJ
cana-4456	193	25	𝛺𝑖	𝛺𝑖	PROPN
cana-4456	193	26	𝑛𝑝	𝑛𝑝	ADP
cana-4456	193	27	𝑖=1	𝑖=1	PROPN
cana-4456	193	28	.	.	PUNCT
cana-4456	194	1	the	the	DET
cana-4456	194	2	rbf	rbf	PROPN
cana-4456	194	3	-	-	PUNCT
cana-4456	194	4	pum	pum	PROPN
cana-4456	194	5	is	be	AUX
cana-4456	194	6	a	a	DET
cana-4456	194	7	localized	localized	ADJ
cana-4456	194	8	method	method	NOUN
cana-4456	194	9	based	base	VERB
cana-4456	194	10	on	on	ADP
cana-4456	194	11	subdividing	subdivide	VERB
cana-4456	194	12	the	the	DET
cana-4456	194	13	domain	domain	NOUN
cana-4456	194	14	𝛺	𝛺	NOUN
cana-4456	194	15	on	on	ADP
cana-4456	194	16	np	np	PROPN
cana-4456	194	17	patches	patch	NOUN
cana-4456	194	18	𝛺1	𝛺1	PROPN
cana-4456	194	19	,	,	PUNCT
cana-4456	194	20	…	…	PUNCT
cana-4456	194	21	,	,	PUNCT
cana-4456	195	1	𝛺𝑛𝑝	𝛺𝑛𝑝	NOUN
cana-4456	195	2	.	.	PUNCT
cana-4456	196	1	first	first	ADV
cana-4456	196	2	,	,	PUNCT
cana-4456	196	3	we	we	PRON
cana-4456	196	4	define	define	VERB
cana-4456	196	5	a	a	DET
cana-4456	196	6	partition	partition	NOUN
cana-4456	196	7	of	of	ADP
cana-4456	196	8	unity	unity	NOUN
cana-4456	196	9	functions	function	NOUN
cana-4456	196	10	{	{	PUNCT
cana-4456	196	11	𝜔𝑖}𝑖=1	𝜔𝑖}𝑖=1	ADJ
cana-4456	196	12	𝑛𝑝	𝑛𝑝	NOUN
cana-4456	196	13	subordinated	subordinate	VERB
cana-4456	196	14	to	to	ADP
cana-4456	196	15	the	the	DET
cana-4456	196	16	covering	covering	NOUN
cana-4456	196	17	{	{	PUNCT
cana-4456	196	18	ω𝑖	ω𝑖	PROPN
cana-4456	196	19	}	}	PUNCT
cana-4456	196	20	𝑖=1	𝑖=1	PROPN
cana-4456	196	21	𝑛𝑝	𝑛𝑝	ADP
cana-4456	196	22	such	such	ADJ
cana-4456	196	23	that	that	PRON
cana-4456	196	24	∑	∑	PROPN
cana-4456	196	25	𝜔𝑖(𝑥	𝜔𝑖(𝑥	PUNCT
cana-4456	196	26	)	)	PUNCT
cana-4456	196	27	=	=	SYM
cana-4456	196	28	1	1	NUM
cana-4456	196	29	,	,	PUNCT
cana-4456	196	30	𝑥	𝑥	PRON
cana-4456	196	31	∈	∈	PROPN
cana-4456	196	32	ω	ω	PROPN
cana-4456	196	33	,	,	PUNCT
cana-4456	196	34	𝑛𝑝	𝑛𝑝	ADP
cana-4456	196	35	𝑖=1	𝑖=1	PROPN
cana-4456	196	36	(	(	PUNCT
cana-4456	196	37	28	28	NUM
cana-4456	196	38	)	)	PUNCT
cana-4456	196	39	where	where	SCONJ
cana-4456	196	40	the	the	DET
cana-4456	196	41	weight	weight	NOUN
cana-4456	196	42	function	function	NOUN
cana-4456	196	43	𝜔𝑖	𝜔𝑖	ADP
cana-4456	196	44	∶	∶	NOUN
cana-4456	196	45	𝛺𝑖	𝛺𝑖	PROPN
cana-4456	196	46	→	→	SYM
cana-4456	196	47	ℝ	ℝ	PROPN
cana-4456	196	48	is	be	AUX
cana-4456	196	49	compactly	compactly	ADV
cana-4456	196	50	supported	support	VERB
cana-4456	196	51	,	,	PUNCT
cana-4456	196	52	non	non	ADJ
cana-4456	196	53	-	-	ADJ
cana-4456	196	54	negative	negative	ADJ
cana-4456	196	55	and	and	CCONJ
cana-4456	196	56	continuous	continuous	ADJ
cana-4456	196	57	.	.	PUNCT
cana-4456	197	1	for	for	ADP
cana-4456	197	2	each	each	DET
cana-4456	197	3	patch	patch	NOUN
cana-4456	197	4	we	we	PRON
cana-4456	197	5	may	may	AUX
cana-4456	197	6	thus	thus	ADV
cana-4456	197	7	construct	construct	VERB
cana-4456	197	8	a	a	DET
cana-4456	197	9	local	local	ADJ
cana-4456	197	10	rbf	rbf	PROPN
cana-4456	197	11	interpolant	interpolant	NOUN
cana-4456	197	12	𝐼𝑢	𝐼𝑢	PROPN
cana-4456	197	13	𝑖	𝑖	SYM
cana-4456	197	14	∶	∶	NOUN
cana-4456	197	15	𝛺𝑖	𝛺𝑖	PROPN
cana-4456	197	16	→	→	SYM
cana-4456	197	17	ℝ	ℝ	PROPN
cana-4456	197	18	of	of	ADP
cana-4456	197	19	the	the	DET
cana-4456	197	20	form	form	NOUN
cana-4456	197	21	:	:	PUNCT
cana-4456	197	22	𝐼𝑢	𝐼𝑢	ADP
cana-4456	197	23	𝑖	𝑖	SYM
cana-4456	197	24	(	(	PUNCT
cana-4456	197	25	𝑥	𝑥	NOUN
cana-4456	197	26	)	)	PUNCT
cana-4456	197	27	=	=	SYM
cana-4456	197	28	∑	∑	PROPN
cana-4456	197	29	𝜆𝑗	𝜆𝑗	X
cana-4456	197	30	𝑖𝑛𝑖	𝑖𝑛𝑖	VERB
cana-4456	197	31	𝑗=1	𝑗=1	PROPN
cana-4456	198	1	𝜑(‖𝑥	𝜑(‖𝑥	CCONJ
cana-4456	198	2	−	−	NUM
cana-4456	198	3	𝑥𝑗	𝑥𝑗	PRON
cana-4456	198	4	𝑖‖	𝑖‖	PROPN
cana-4456	198	5	)	)	PUNCT
cana-4456	198	6	,	,	PUNCT
cana-4456	198	7	(	(	PUNCT
cana-4456	198	8	29	29	NUM
cana-4456	198	9	)	)	PUNCT
cana-4456	198	10	where	where	SCONJ
cana-4456	198	11	𝑛𝑖	𝑛𝑖	PROPN
cana-4456	198	12	is	be	AUX
cana-4456	198	13	the	the	DET
cana-4456	198	14	number	number	NOUN
cana-4456	198	15	of	of	ADP
cana-4456	198	16	nodes	node	NOUN
cana-4456	198	17	in	in	ADP
cana-4456	198	18	ωi	ωi	PROPN
cana-4456	198	19	.	.	PUNCT
cana-4456	199	1	therefore	therefore	ADV
cana-4456	199	2	,	,	PUNCT
cana-4456	199	3	the	the	DET
cana-4456	199	4	global	global	PROPN
cana-4456	199	5	rbf	rbf	PROPN
cana-4456	199	6	-	-	PROPN
cana-4456	199	7	pum	pum	PROPN
cana-4456	199	8	interpolant	interpolant	NOUN
cana-4456	199	9	is	be	AUX
cana-4456	199	10	defined	define	VERB
cana-4456	199	11	as	as	ADP
cana-4456	199	12	communications	communication	NOUN
cana-4456	199	13	on	on	ADP
cana-4456	199	14	applied	apply	VERB
cana-4456	199	15	nonlinear	nonlinear	ADJ
cana-4456	199	16	analysis	analysis	NOUN
cana-4456	199	17	issn	issn	NOUN
cana-4456	199	18	:	:	PUNCT
cana-4456	199	19	1074	1074	NUM
cana-4456	199	20	-	-	PUNCT
cana-4456	199	21	133x	133x	NUM
cana-4456	199	22	vol	vol	NOUN
cana-4456	199	23	32	32	NUM
cana-4456	199	24	no	no	NOUN
cana-4456	199	25	.	.	PUNCT
cana-4456	200	1	9s	9s	NUM
cana-4456	200	2	(	(	PUNCT
cana-4456	200	3	2025	2025	NUM
cana-4456	200	4	)	)	PUNCT
cana-4456	200	5	2176	2176	NUM
cana-4456	200	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	200	7	𝐼𝑢(𝑥	𝐼𝑢(𝑥	NOUN
cana-4456	200	8	)	)	PUNCT
cana-4456	200	9	=	=	PUNCT
cana-4456	200	10	∑	∑	PUNCT
cana-4456	200	11	𝜔𝑖(𝑥)𝐼𝑢	𝜔𝑖(𝑥)𝐼𝑢	X
cana-4456	200	12	𝑖	𝑖	X
cana-4456	200	13	(	(	PUNCT
cana-4456	200	14	𝑥	𝑥	NOUN
cana-4456	200	15	)	)	PUNCT
cana-4456	200	16	𝑛𝑝	𝑛𝑝	ADP
cana-4456	200	17	𝑖=1	𝑖=1	PROPN
cana-4456	200	18	=	=	SYM
cana-4456	200	19	∑	∑	NOUN
cana-4456	200	20	𝜔𝑖(𝑥	𝜔𝑖(𝑥	PUNCT
cana-4456	200	21	)	)	PUNCT
cana-4456	200	22	𝑛𝑝	𝑛𝑝	ADP
cana-4456	200	23	𝑖=1	𝑖=1	PROPN
cana-4456	200	24	∑	∑	PROPN
cana-4456	200	25	𝜆𝑗	𝜆𝑗	PROPN
cana-4456	200	26	𝑖𝑛𝑖	𝑖𝑛𝑖	VERB
cana-4456	200	27	𝑗=1	𝑗=1	PROPN
cana-4456	201	1	𝜑(‖𝑥	𝜑(‖𝑥	CCONJ
cana-4456	201	2	−	−	NUM
cana-4456	201	3	𝑥𝑗	𝑥𝑗	PRON
cana-4456	201	4	𝑖‖	𝑖‖	PROPN
cana-4456	201	5	)	)	PUNCT
cana-4456	201	6	,	,	PUNCT
cana-4456	201	7	𝑥	𝑥	PROPN
cana-4456	201	8	∈	∈	PROPN
cana-4456	201	9	ω	ω	PROPN
cana-4456	201	10	,	,	PUNCT
cana-4456	201	11	(	(	PUNCT
cana-4456	201	12	30	30	NUM
cana-4456	201	13	)	)	PUNCT
cana-4456	201	14	by	by	ADP
cana-4456	201	15	enforcing	enforce	VERB
cana-4456	201	16	the	the	DET
cana-4456	201	17	interpolation	interpolation	NOUN
cana-4456	201	18	condition	condition	NOUN
cana-4456	201	19	,	,	PUNCT
cana-4456	201	20	we	we	PRON
cana-4456	201	21	have	have	VERB
cana-4456	201	22	the	the	DET
cana-4456	201	23	following	follow	VERB
cana-4456	201	24	form	form	NOUN
cana-4456	201	25	of	of	ADP
cana-4456	201	26	the	the	DET
cana-4456	201	27	global	global	ADJ
cana-4456	201	28	interpolant	interpolant	NOUN
cana-4456	201	29	[	[	X
cana-4456	201	30	32	32	NUM
cana-4456	201	31	]	]	X
cana-4456	201	32	𝑈	𝑈	PROPN
cana-4456	201	33	=	=	PUNCT
cana-4456	201	34	∑	∑	PROPN
cana-4456	201	35	𝑅𝑖𝑊𝑖	𝑅𝑖𝑊𝑖	ADP
cana-4456	201	36	𝑛𝑝	𝑛𝑝	ADP
cana-4456	201	37	𝑖=1	𝑖=1	PROPN
cana-4456	201	38	𝐴𝑖𝜆𝑖,̅̅	𝐴𝑖𝜆𝑖,̅̅	NUM
cana-4456	201	39	̅	̅	NOUN
cana-4456	201	40	(	(	PUNCT
cana-4456	201	41	31	31	NUM
cana-4456	201	42	)	)	PUNCT
cana-4456	201	43	where	where	SCONJ
cana-4456	201	44	𝑈	𝑈	PROPN
cana-4456	201	45	is	be	AUX
cana-4456	201	46	a	a	DET
cana-4456	201	47	vector	vector	NOUN
cana-4456	201	48	containing	contain	VERB
cana-4456	201	49	the	the	DET
cana-4456	201	50	global	global	ADJ
cana-4456	201	51	solution	solution	NOUN
cana-4456	201	52	at𝑥𝑘	at𝑥𝑘	NOUN
cana-4456	201	53	,	,	PUNCT
cana-4456	201	54	𝑘	𝑘	X
cana-4456	201	55	=	=	SYM
cana-4456	201	56	1	1	NUM
cana-4456	201	57	,	,	PUNCT
cana-4456	201	58	…	…	PUNCT
cana-4456	201	59	,	,	PUNCT
cana-4456	201	60	𝑁	𝑁	PROPN
cana-4456	201	61	,	,	PUNCT
cana-4456	201	62	𝑅𝑖	𝑅𝑖	PROPN
cana-4456	201	63	is	be	AUX
cana-4456	201	64	a	a	DET
cana-4456	201	65	permutation	permutation	NOUN
cana-4456	201	66	projection	projection	NOUN
cana-4456	201	67	operator	operator	NOUN
cana-4456	201	68	which	which	PRON
cana-4456	201	69	maps	map	VERB
cana-4456	201	70	the	the	DET
cana-4456	201	71	local	local	ADJ
cana-4456	201	72	index	index	NOUN
cana-4456	201	73	set	set	VERB
cana-4456	201	74	into	into	ADP
cana-4456	201	75	the	the	DET
cana-4456	201	76	global	global	ADJ
cana-4456	201	77	one	one	NOUN
cana-4456	201	78	,	,	PUNCT
cana-4456	201	79	𝑊𝑖	𝑊𝑖	PROPN
cana-4456	201	80	is	be	AUX
cana-4456	201	81	a	a	DET
cana-4456	201	82	diagonal	diagonal	ADJ
cana-4456	201	83	matrix	matrix	NOUN
cana-4456	201	84	with	with	ADP
cana-4456	201	85	element	element	NOUN
cana-4456	201	86	𝜔𝑖(𝑥	𝜔𝑖(𝑥	PUNCT
cana-4456	201	87	)	)	PUNCT
cana-4456	201	88	on	on	ADP
cana-4456	201	89	it	it	PRON
cana-4456	201	90	and	and	CCONJ
cana-4456	201	91	𝐴𝑖	𝐴𝑖	PROPN
cana-4456	201	92	is	be	AUX
cana-4456	201	93	the	the	DET
cana-4456	201	94	local	local	ADJ
cana-4456	201	95	rbf	rbf	PROPN
cana-4456	201	96	matrix	matrix	NOUN
cana-4456	201	97	.	.	PUNCT
cana-4456	202	1	the	the	DET
cana-4456	202	2	weight	weight	NOUN
cana-4456	202	3	function	function	NOUN
cana-4456	202	4	𝜔𝑖	𝜔𝑖	PART
cana-4456	202	5	are	be	AUX
cana-4456	202	6	constructed	construct	VERB
cana-4456	202	7	using	use	VERB
cana-4456	202	8	shepard	shepard	NOUN
cana-4456	202	9	’s	’s	PART
cana-4456	202	10	method	method	NOUN
cana-4456	202	11	[	[	X
cana-4456	202	12	33	33	NUM
cana-4456	202	13	]	]	PUNCT
cana-4456	202	14	𝜔𝑖(𝑥	𝜔𝑖(𝑥	PUNCT
cana-4456	202	15	)	)	PUNCT
cana-4456	202	16	=	=	SYM
cana-4456	202	17	𝜓𝑖(𝑥	𝜓𝑖(𝑥	X
cana-4456	202	18	)	)	PUNCT
cana-4456	202	19	∑	∑	ADV
cana-4456	202	20	𝜓𝑙(𝑥	𝜓𝑙(𝑥	X
cana-4456	202	21	)	)	PUNCT
cana-4456	202	22	𝑛𝑝	𝑛𝑝	ADP
cana-4456	202	23	𝑙=1	𝑙=1	PROPN
cana-4456	202	24	,	,	PUNCT
cana-4456	202	25	𝑖	𝑖	SYM
cana-4456	202	26	=	=	SYM
cana-4456	202	27	1	1	NUM
cana-4456	202	28	,	,	PUNCT
cana-4456	202	29	…	…	PUNCT
cana-4456	202	30	,	,	PUNCT
cana-4456	202	31	𝑛𝑝	𝑛𝑝	X
cana-4456	202	32	(	(	PUNCT
cana-4456	202	33	32	32	NUM
cana-4456	202	34	)	)	PUNCT
cana-4456	202	35	where	where	SCONJ
cana-4456	202	36	𝜓(𝑥	𝜓(𝑥	ADV
cana-4456	202	37	)	)	PUNCT
cana-4456	202	38	is	be	AUX
cana-4456	202	39	compactly	compactly	ADV
cana-4456	202	40	supported	support	VERB
cana-4456	202	41	function	function	NOUN
cana-4456	202	42	with	with	ADP
cana-4456	202	43	support	support	NOUN
cana-4456	202	44	on	on	ADP
cana-4456	202	45	𝛺𝑖	𝛺𝑖	PROPN
cana-4456	202	46	.	.	PUNCT
cana-4456	203	1	we	we	PRON
cana-4456	203	2	have	have	AUX
cana-4456	203	3	used	use	VERB
cana-4456	203	4	the	the	DET
cana-4456	203	5	following	follow	VERB
cana-4456	203	6	compactly	compactly	ADV
cana-4456	203	7	supported	support	VERB
cana-4456	203	8	wendland	wendland	NOUN
cana-4456	203	9	function	function	NOUN
cana-4456	203	10	[	[	X
cana-4456	203	11	34	34	NUM
cana-4456	203	12	]	]	SYM
cana-4456	203	13	𝜓(𝑟	𝜓(𝑟	NOUN
cana-4456	203	14	)	)	PUNCT
cana-4456	203	15	=	=	PRON
cana-4456	203	16	{	{	PUNCT
cana-4456	203	17	(	(	PUNCT
cana-4456	203	18	1	1	NUM
cana-4456	203	19	−	−	NOUN
cana-4456	203	20	𝑟)2(32𝑟3	𝑟)2(32𝑟3	NOUN
cana-4456	204	1	+	+	CCONJ
cana-4456	204	2	25𝑟2	25𝑟2	NUM
cana-4456	205	1	+	+	CCONJ
cana-4456	205	2	8𝑟	8𝑟	ADJ
cana-4456	205	3	+	+	CCONJ
cana-4456	205	4	1	1	NUM
cana-4456	205	5	)	)	PUNCT
cana-4456	205	6	0	0	NUM
cana-4456	206	1	≤	≤	NUM
cana-4456	206	2	𝑟	𝑟	X
cana-4456	206	3	≤	≤	NUM
cana-4456	206	4	1	1	NUM
cana-4456	206	5	,	,	PUNCT
cana-4456	206	6	0	0	NUM
cana-4456	206	7	𝑟	𝑟	NOUN
cana-4456	206	8	>	>	SYM
cana-4456	206	9	1	1	NUM
cana-4456	206	10	in	in	ADP
cana-4456	206	11	this	this	DET
cana-4456	206	12	paper	paper	NOUN
cana-4456	206	13	,	,	PUNCT
cana-4456	206	14	we	we	PRON
cana-4456	206	15	will	will	AUX
cana-4456	206	16	use	use	VERB
cana-4456	206	17	circular	circular	ADJ
cana-4456	206	18	patches	patch	NOUN
cana-4456	206	19	due	due	ADP
cana-4456	206	20	to	to	ADP
cana-4456	206	21	their	their	PRON
cana-4456	206	22	flexibility	flexibility	NOUN
cana-4456	206	23	in	in	ADP
cana-4456	206	24	practice	practice	NOUN
cana-4456	206	25	.	.	PUNCT
cana-4456	207	1	thus	thus	ADV
cana-4456	207	2	,	,	PUNCT
cana-4456	207	3	the	the	DET
cana-4456	207	4	wendland	wendland	NOUN
cana-4456	207	5	functions	function	NOUN
cana-4456	207	6	will	will	AUX
cana-4456	207	7	be	be	AUX
cana-4456	207	8	scaled	scale	VERB
cana-4456	207	9	to	to	PART
cana-4456	207	10	get	get	VERB
cana-4456	207	11	𝜓𝑖(𝑥	𝜓𝑖(𝑥	X
cana-4456	207	12	)	)	PUNCT
cana-4456	207	13	=	=	SYM
cana-4456	207	14	𝜓	𝜓	PROPN
cana-4456	207	15	(	(	PUNCT
cana-4456	207	16	‖𝑥−𝜉𝑖‖	‖𝑥−𝜉𝑖‖	X
cana-4456	207	17	𝜌𝑖	𝜌𝑖	ADP
cana-4456	207	18	)	)	PUNCT
cana-4456	207	19	,	,	PUNCT
cana-4456	207	20	𝑖	𝑖	NOUN
cana-4456	207	21	=	=	SYM
cana-4456	207	22	1	1	NUM
cana-4456	207	23	,	,	PUNCT
cana-4456	207	24	…	…	PUNCT
cana-4456	207	25	,	,	PUNCT
cana-4456	207	26	𝑛𝑝	𝑛𝑝	X
cana-4456	207	27	(	(	PUNCT
cana-4456	207	28	33	33	NUM
cana-4456	207	29	)	)	PUNCT
cana-4456	207	30	where	where	SCONJ
cana-4456	207	31	𝜉𝑖	𝜉𝑖	ADV
cana-4456	207	32	and	and	CCONJ
cana-4456	207	33	𝜌𝑖	𝜌𝑖	ADP
cana-4456	207	34	are	be	AUX
cana-4456	207	35	,	,	PUNCT
cana-4456	207	36	respectively	respectively	ADV
cana-4456	207	37	,	,	PUNCT
cana-4456	207	38	the	the	DET
cana-4456	207	39	centres	centre	NOUN
cana-4456	207	40	and	and	CCONJ
cana-4456	207	41	the	the	DET
cana-4456	207	42	radii	radius	NOUN
cana-4456	207	43	of	of	ADP
cana-4456	207	44	patches	patch	NOUN
cana-4456	207	45	𝛺𝑖	𝛺𝑖	PROPN
cana-4456	207	46	,	,	PUNCT
cana-4456	207	47	𝑖	𝑖	NOUN
cana-4456	207	48	=	=	SYM
cana-4456	207	49	1	1	NUM
cana-4456	207	50	,	,	PUNCT
cana-4456	207	51	…	…	PUNCT
cana-4456	207	52	,	,	PUNCT
cana-4456	207	53	𝑛𝑝.	𝑛𝑝.	VERB
cana-4456	207	54	let	let	VERB
cana-4456	207	55	𝑢𝑘	𝑢𝑘	PRON
cana-4456	207	56	𝑖	𝑖	PART
cana-4456	207	57	be	be	AUX
cana-4456	207	58	the	the	DET
cana-4456	207	59	value	value	NOUN
cana-4456	207	60	of	of	ADP
cana-4456	207	61	local	local	ADJ
cana-4456	207	62	solution	solution	NOUN
cana-4456	207	63	at	at	ADP
cana-4456	207	64	the	the	DET
cana-4456	207	65	node	node	PROPN
cana-4456	207	66	𝑥𝑘	𝑥𝑘	X
cana-4456	207	67	located	locate	VERB
cana-4456	207	68	in	in	ADP
cana-4456	207	69	𝛺𝑖.	𝛺𝑖.	PROPN
cana-4456	207	70	because	because	SCONJ
cana-4456	207	71	our	our	PRON
cana-4456	207	72	final	final	ADJ
cana-4456	207	73	target	target	NOUN
cana-4456	207	74	is	be	AUX
cana-4456	207	75	to	to	PART
cana-4456	207	76	solve	solve	VERB
cana-4456	207	77	pdes	pde	NOUN
cana-4456	207	78	,	,	PUNCT
cana-4456	207	79	the	the	DET
cana-4456	207	80	problem	problem	NOUN
cana-4456	207	81	here	here	ADV
cana-4456	207	82	is	be	AUX
cana-4456	207	83	that	that	SCONJ
cana-4456	207	84	there	there	PRON
cana-4456	207	85	would	would	AUX
cana-4456	207	86	be	be	AUX
cana-4456	207	87	more	more	ADV
cana-4456	207	88	unknown	unknown	ADJ
cana-4456	207	89	than	than	ADP
cana-4456	207	90	equations	equation	NOUN
cana-4456	207	91	.	.	PUNCT
cana-4456	208	1	this	this	PRON
cana-4456	208	2	can	can	AUX
cana-4456	208	3	be	be	AUX
cana-4456	208	4	fixed	fix	VERB
cana-4456	208	5	by	by	ADP
cana-4456	208	6	requiring	require	VERB
cana-4456	208	7	the	the	DET
cana-4456	208	8	local	local	ADJ
cana-4456	208	9	solutions	solution	NOUN
cana-4456	208	10	𝑢𝑘	𝑢𝑘	ADP
cana-4456	208	11	𝑖	𝑖	X
cana-4456	208	12	to	to	PART
cana-4456	208	13	coincide	coincide	VERB
cana-4456	208	14	with	with	ADP
cana-4456	208	15	the	the	DET
cana-4456	208	16	global	global	ADJ
cana-4456	208	17	one	one	NUM
cana-4456	208	18	.	.	PUNCT
cana-4456	209	1	the	the	DET
cana-4456	209	2	interpolation	interpolation	NOUN
cana-4456	209	3	property	property	NOUN
cana-4456	209	4	implies	imply	VERB
cana-4456	209	5	that	that	SCONJ
cana-4456	209	6	𝑢𝑖	𝑢𝑖	ADP
cana-4456	209	7	=	=	SYM
cana-4456	209	8	𝐴𝑖𝜆	𝐴𝑖𝜆	PROPN
cana-4456	209	9	�	�	PROPN
cana-4456	209	10	̅	̅	NOUN
cana-4456	209	11	�	�	PROPN
cana-4456	209	12	⇒	⇒	PROPN
cana-4456	209	13	𝜆	𝜆	PROPN
cana-4456	209	14	�	�	PROPN
cana-4456	209	15	̅	̅	NOUN
cana-4456	209	16	�	�	NOUN
cana-4456	209	17	=	=	SYM
cana-4456	209	18	𝐴𝑖	𝐴𝑖	PROPN
cana-4456	209	19	−1𝑢𝑖	−1𝑢𝑖	X
cana-4456	209	20	(	(	PUNCT
cana-4456	209	21	34	34	NUM
cana-4456	209	22	)	)	PUNCT
cana-4456	209	23	therefore	therefore	ADV
cana-4456	209	24	,	,	PUNCT
cana-4456	209	25	the	the	DET
cana-4456	209	26	approximation	approximation	NOUN
cana-4456	209	27	of	of	ADP
cana-4456	209	28	any	any	DET
cana-4456	209	29	linear	linear	ADJ
cana-4456	209	30	differential	differential	NOUN
cana-4456	209	31	operator	operator	NOUN
cana-4456	209	32	𝐿	𝐿	PROPN
cana-4456	209	33	can	can	AUX
cana-4456	209	34	be	be	AUX
cana-4456	209	35	derived	derive	VERB
cana-4456	209	36	𝐿𝑈	𝐿𝑈	PROPN
cana-4456	209	37	=	=	SYM
cana-4456	209	38	∑	∑	PUNCT
cana-4456	209	39	𝑅𝑖𝐿(𝑊𝑖	𝑅𝑖𝐿(𝑊𝑖	VERB
cana-4456	209	40	𝑛𝑝	𝑛𝑝	NUM
cana-4456	209	41	𝑖=1	𝑖=1	PROPN
cana-4456	209	42	𝐴𝑖)𝜆𝑖̅̅	𝐴𝑖)𝜆𝑖̅̅	PROPN
cana-4456	209	43	̅̅	̅̅	PROPN
cana-4456	209	44	(	(	PUNCT
cana-4456	209	45	35	35	NUM
cana-4456	209	46	)	)	PUNCT
cana-4456	209	47	=	=	PUNCT
cana-4456	209	48	∑	∑	AUX
cana-4456	209	49	𝑅𝑖𝐿(𝑊𝑖	𝑅𝑖𝐿(𝑊𝑖	VERB
cana-4456	209	50	𝑛𝑝	𝑛𝑝	ADP
cana-4456	209	51	𝑖=1	𝑖=1	PROPN
cana-4456	209	52	𝐴𝑖)𝐴𝑖	𝐴𝑖)𝐴𝑖	X
cana-4456	209	53	−1𝑢𝑖	−1𝑢𝑖	NUM
cana-4456	209	54	(	(	PUNCT
cana-4456	209	55	36	36	NUM
cana-4456	209	56	)	)	PUNCT
cana-4456	209	57	=	=	SYM
cana-4456	209	58	∑	∑	PUNCT
cana-4456	209	59	𝑅𝑖𝐷𝐿	𝑅𝑖𝐷𝐿	NOUN
cana-4456	209	60	𝑖𝑛𝑝	𝑖𝑛𝑝	VERB
cana-4456	209	61	𝑖=1	𝑖=1	NUM
cana-4456	209	62	𝑢𝑖	𝑢𝑖	NOUN
cana-4456	209	63	(	(	PUNCT
cana-4456	209	64	37	37	NUM
cana-4456	209	65	)	)	PUNCT
cana-4456	209	66	communications	communication	NOUN
cana-4456	209	67	on	on	ADP
cana-4456	209	68	applied	apply	VERB
cana-4456	209	69	nonlinear	nonlinear	ADJ
cana-4456	209	70	analysis	analysis	NOUN
cana-4456	209	71	issn	issn	NOUN
cana-4456	209	72	:	:	PUNCT
cana-4456	209	73	1074	1074	NUM
cana-4456	209	74	-	-	PUNCT
cana-4456	209	75	133x	133x	NUM
cana-4456	209	76	vol	vol	NOUN
cana-4456	209	77	32	32	NUM
cana-4456	209	78	no	no	NOUN
cana-4456	209	79	.	.	PUNCT
cana-4456	210	1	9s	9s	NUM
cana-4456	210	2	(	(	PUNCT
cana-4456	210	3	2025	2025	NUM
cana-4456	210	4	)	)	PUNCT
cana-4456	210	5	2177	2177	NUM
cana-4456	210	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	210	7	where	where	SCONJ
cana-4456	210	8	𝐷𝐿	𝐷𝐿	PROPN
cana-4456	210	9	𝑖	𝑖	VERB
cana-4456	210	10	is	be	AUX
cana-4456	210	11	a	a	DET
cana-4456	210	12	local	local	ADJ
cana-4456	210	13	differentiation	differentiation	NOUN
cana-4456	210	14	matrix	matrix	NOUN
cana-4456	210	15	which	which	PRON
cana-4456	210	16	defined	define	VERB
cana-4456	210	17	as	as	ADP
cana-4456	210	18	𝐷𝐿	𝐷𝐿	PROPN
cana-4456	210	19	𝑖	𝑖	NOUN
cana-4456	210	20	=	=	NOUN
cana-4456	210	21	𝐿(𝑊𝑖𝐴𝑖)𝐴𝑖	𝐿(𝑊𝑖𝐴𝑖)𝐴𝑖	NOUN
cana-4456	210	22	−1	−1	NOUN
cana-4456	210	23	.	.	PUNCT
cana-4456	211	1	3.2.2	3.2.2	NUM
cana-4456	211	2	spatial	spatial	ADJ
cana-4456	211	3	discretization	discretization	NOUN
cana-4456	211	4	of	of	ADP
cana-4456	211	5	swes	swe	NOUN
cana-4456	211	6	using	use	VERB
cana-4456	211	7	rbf	rbf	PROPN
cana-4456	211	8	-	-	PROPN
cana-4456	211	9	pum	pum	PROPN
cana-4456	211	10	we	we	PRON
cana-4456	211	11	intend	intend	VERB
cana-4456	211	12	to	to	PART
cana-4456	211	13	illustrate	illustrate	VERB
cana-4456	211	14	the	the	DET
cana-4456	211	15	discretization	discretization	NOUN
cana-4456	211	16	of	of	ADP
cana-4456	211	17	rbf	rbf	PROPN
cana-4456	211	18	–	–	PUNCT
cana-4456	211	19	pu	pu	PROPN
cana-4456	211	20	method	method	NOUN
cana-4456	211	21	for	for	ADP
cana-4456	211	22	the	the	DET
cana-4456	211	23	shallow	shallow	ADJ
cana-4456	211	24	water	water	NOUN
cana-4456	211	25	equations	equation	NOUN
cana-4456	211	26	.	.	PUNCT
cana-4456	212	1	let	let	VERB
cana-4456	212	2	{	{	PUNCT
cana-4456	212	3	𝑥1	𝑥1	NOUN
cana-4456	212	4	,	,	PUNCT
cana-4456	212	5	𝑥2	𝑥2	NOUN
cana-4456	212	6	,	,	PUNCT
cana-4456	212	7	.	.	PUNCT
cana-4456	212	8	.	.	PUNCT
cana-4456	212	9	.	.	PUNCT
cana-4456	213	1	,	,	PUNCT
cana-4456	213	2	𝑥𝑁	𝑥𝑁	NOUN
cana-4456	213	3	}	}	PUNCT
cana-4456	213	4	be	be	AUX
cana-4456	213	5	a	a	DET
cana-4456	213	6	set	set	NOUN
cana-4456	213	7	of	of	ADP
cana-4456	213	8	𝑁	𝑁	PROPN
cana-4456	213	9	distinct	distinct	ADJ
cana-4456	213	10	points	point	NOUN
cana-4456	213	11	.	.	PUNCT
cana-4456	214	1	using	use	VERB
cana-4456	214	2	(	(	PUNCT
cana-4456	214	3	35	35	NUM
cana-4456	214	4	)	)	PUNCT
cana-4456	214	5	,	,	PUNCT
cana-4456	214	6	the	the	DET
cana-4456	214	7	first	first	ADJ
cana-4456	214	8	and	and	CCONJ
cana-4456	214	9	second	second	ADJ
cana-4456	214	10	spatial	spatial	ADJ
cana-4456	214	11	derivatives	derivative	NOUN
cana-4456	214	12	of	of	ADP
cana-4456	214	13	a	a	DET
cana-4456	214	14	function	function	NOUN
cana-4456	214	15	𝑸(𝑥	𝑸(𝑥	NOUN
cana-4456	214	16	,	,	PUNCT
cana-4456	214	17	𝑡	𝑡	PROPN
cana-4456	214	18	)	)	PUNCT
cana-4456	214	19	can	can	AUX
cana-4456	214	20	be	be	AUX
cana-4456	214	21	expressed	express	VERB
cana-4456	214	22	as	as	SCONJ
cana-4456	214	23	follows	follow	VERB
cana-4456	214	24	:	:	PUNCT
cana-4456	214	25	𝜕𝑸(𝑥,𝑡	𝜕𝑸(𝑥,𝑡	ADJ
cana-4456	214	26	)	)	PUNCT
cana-4456	214	27	𝜕𝑥	𝜕𝑥	NOUN
cana-4456	214	28	=	=	PUNCT
cana-4456	214	29	∑	∑	PUNCT
cana-4456	214	30	𝑅𝑖𝐷𝑥	𝑅𝑖𝐷𝑥	PROPN
cana-4456	214	31	𝑖𝑛𝑝	𝑖𝑛𝑝	VERB
cana-4456	214	32	𝑖=1	𝑖=1	PUNCT
cana-4456	215	1	𝑸𝑖	𝑸𝑖	PROPN
cana-4456	215	2	,	,	PUNCT
cana-4456	215	3	𝜕2𝑸(𝑥,𝑡	𝜕2𝑸(𝑥,𝑡	ADJ
cana-4456	215	4	)	)	PUNCT
cana-4456	215	5	𝜕𝑥2	𝜕𝑥2	NOUN
cana-4456	216	1	=	=	PUNCT
cana-4456	216	2	∑	∑	PUNCT
cana-4456	216	3	𝑅𝑖𝐷𝑥𝑥	𝑅𝑖𝐷𝑥𝑥	PROPN
cana-4456	216	4	𝑖𝑛𝑝	𝑖𝑛𝑝	VERB
cana-4456	216	5	𝑖=1	𝑖=1	PUNCT
cana-4456	217	1	𝑸𝑖	𝑸𝑖	PROPN
cana-4456	217	2	,	,	PUNCT
cana-4456	217	3	(	(	PUNCT
cana-4456	217	4	38	38	NUM
cana-4456	217	5	)	)	PUNCT
cana-4456	217	6	hence	hence	ADV
cana-4456	217	7	,	,	PUNCT
cana-4456	217	8	the	the	DET
cana-4456	217	9	global	global	ADJ
cana-4456	217	10	differentiation	differentiation	NOUN
cana-4456	217	11	matrices	matrix	NOUN
cana-4456	217	12	𝐷𝑥	𝐷𝑥	PROPN
cana-4456	217	13	̅̅	̅̅	NOUN
cana-4456	217	14	̅̅	̅̅	PROPN
cana-4456	217	15	and	and	CCONJ
cana-4456	217	16	𝐷𝑥𝑥	𝐷𝑥𝑥	PROPN
cana-4456	217	17	̅̅	̅̅	NOUN
cana-4456	217	18	̅̅	̅̅	NOUN
cana-4456	217	19	̅	̅	NOUN
cana-4456	217	20	is	be	AUX
cana-4456	217	21	computed	compute	VERB
cana-4456	217	22	by	by	ADP
cana-4456	217	23	assembling	assemble	VERB
cana-4456	217	24	the	the	DET
cana-4456	217	25	above	above	ADJ
cana-4456	217	26	local	local	ADJ
cana-4456	217	27	matrices	matrix	NOUN
cana-4456	217	28	into	into	ADP
cana-4456	217	29	the	the	DET
cana-4456	217	30	global	global	ADJ
cana-4456	217	31	one	one	NOUN
cana-4456	217	32	,	,	PUNCT
cana-4456	217	33	(	(	PUNCT
cana-4456	217	34	38	38	NUM
cana-4456	217	35	)	)	PUNCT
cana-4456	217	36	becomes	become	VERB
cana-4456	217	37	𝜕𝑸(𝑥,𝑡	𝜕𝑸(𝑥,𝑡	NOUN
cana-4456	217	38	)	)	PUNCT
cana-4456	217	39	𝜕𝑥	𝜕𝑥	NOUN
cana-4456	218	1	=	=	SYM
cana-4456	219	1	𝐷𝑥	𝐷𝑥	PROPN
cana-4456	219	2	̅̅	̅̅	NOUN
cana-4456	219	3	̅̅	̅̅	PROPN
cana-4456	219	4	𝑸(𝑥	𝑸(𝑥	PROPN
cana-4456	219	5	,	,	PUNCT
cana-4456	219	6	𝑡	𝑡	PROPN
cana-4456	219	7	)	)	PUNCT
cana-4456	219	8	,	,	PUNCT
cana-4456	219	9	𝜕2𝑸(𝑥,𝑡	𝜕2𝑸(𝑥,𝑡	NOUN
cana-4456	219	10	)	)	PUNCT
cana-4456	219	11	𝜕𝑥2	𝜕𝑥2	NOUN
cana-4456	219	12	=	=	SYM
cana-4456	220	1	𝐷𝑥𝑥	𝐷𝑥𝑥	PROPN
cana-4456	220	2	̅̅	̅̅	NOUN
cana-4456	220	3	̅̅	̅̅	PROPN
cana-4456	220	4	̅𝑸(𝑥	̅𝑸(𝑥	PROPN
cana-4456	220	5	,	,	PUNCT
cana-4456	220	6	𝑡	𝑡	PROPN
cana-4456	220	7	)	)	PUNCT
cana-4456	220	8	,	,	PUNCT
cana-4456	220	9	(	(	PUNCT
cana-4456	220	10	39	39	NUM
cana-4456	220	11	)	)	PUNCT
cana-4456	220	12	the	the	DET
cana-4456	220	13	system	system	NOUN
cana-4456	220	14	(	(	PUNCT
cana-4456	220	15	8)	8)	NUM
cana-4456	220	16	is	be	AUX
cana-4456	220	17	approximated	approximate	VERB
cana-4456	220	18	by	by	ADP
cana-4456	220	19	the	the	DET
cana-4456	220	20	following	follow	VERB
cana-4456	220	21	equivalent	equivalent	ADJ
cana-4456	220	22	system	system	NOUN
cana-4456	220	23	𝜕𝑡𝑸	𝜕𝑡𝑸	NUM
cana-4456	220	24	=	=	PUNCT
cana-4456	220	25	−	−	NUM
cana-4456	220	26	�	�	NOUN
cana-4456	220	27	̅	̅	NOUN
cana-4456	220	28	�	�	NOUN
cana-4456	220	29	(𝑸	(𝑸	NUM
cana-4456	220	30	)	)	PUNCT
cana-4456	220	31	+	+	NUM
cana-4456	220	32	𝑆̅(𝑸	𝑆̅(𝑸	NOUN
cana-4456	220	33	)	)	PUNCT
cana-4456	220	34	+	+	CCONJ
cana-4456	220	35	�	�	NOUN
cana-4456	220	36	̅	̅	NOUN
cana-4456	220	37	�	�	NOUN
cana-4456	220	38	(𝑸	(𝑸	NUM
cana-4456	220	39	)	)	PUNCT
cana-4456	220	40	.	.	PUNCT
cana-4456	221	1	(	(	PUNCT
cana-4456	221	2	40	40	NUM
cana-4456	221	3	)	)	PUNCT
cana-4456	221	4	using	use	VERB
cana-4456	221	5	the	the	DET
cana-4456	221	6	rbf	rbf	PROPN
cana-4456	221	7	-	-	PUNCT
cana-4456	221	8	pum	pum	PROPN
cana-4456	221	9	to	to	PART
cana-4456	221	10	perform	perform	VERB
cana-4456	221	11	numerical	numerical	ADJ
cana-4456	221	12	evaluation	evaluation	NOUN
cana-4456	221	13	,	,	PUNCT
cana-4456	221	14	we	we	PRON
cana-4456	221	15	obtain	obtain	VERB
cana-4456	221	16	𝐹	𝐹	PROPN
cana-4456	221	17	̅(𝑸	̅(𝑸	ADV
cana-4456	221	18	)	)	PUNCT
cana-4456	221	19	=	=	SYM
cana-4456	222	1	(	(	PUNCT
cana-4456	222	2	𝐷𝑥	𝐷𝑥	PROPN
cana-4456	222	3	̅̅	̅̅	PROPN
cana-4456	222	4	̅̅	̅̅	PROPN
cana-4456	222	5	𝑞	𝑞	PROPN
cana-4456	222	6	𝐷𝑥	𝐷𝑥	PROPN
cana-4456	222	7	̅̅	̅̅	PROPN
cana-4456	222	8	̅̅	̅̅	PROPN
cana-4456	222	9	(	(	PUNCT
cana-4456	222	10	𝑞2	𝑞2	NOUN
cana-4456	222	11	ℎ	ℎ	PART
cana-4456	222	12	+	+	NOUN
cana-4456	222	13	1	1	NUM
cana-4456	222	14	2	2	NUM
cana-4456	222	15	𝑔ℎ2	𝑔ℎ2	NOUN
cana-4456	222	16	)	)	PUNCT
cana-4456	222	17	)	)	PUNCT
cana-4456	222	18	,	,	PUNCT
cana-4456	222	19	𝑆	𝑆	PROPN
cana-4456	222	20	̅(𝑸	̅(𝑸	PROPN
cana-4456	222	21	)	)	PUNCT
cana-4456	222	22	=	=	PUNCT
cana-4456	222	23	(	(	PUNCT
cana-4456	222	24	0	0	NUM
cana-4456	222	25	−𝑔ℎ𝐷𝑥	−𝑔ℎ𝐷𝑥	NOUN
cana-4456	222	26	̅̅	̅̅	PROPN
cana-4456	222	27	̅̅	̅̅	PROPN
cana-4456	222	28	𝑏	𝑏	PROPN
cana-4456	222	29	)	)	PUNCT
cana-4456	222	30	,	,	PUNCT
cana-4456	222	31	𝐻	𝐻	PROPN
cana-4456	222	32	̅̅	̅̅	NOUN
cana-4456	222	33	̅(𝑸	̅(𝑸	PUNCT
cana-4456	222	34	)	)	PUNCT
cana-4456	222	35	=	=	PUNCT
cana-4456	223	1	(	(	PUNCT
cana-4456	223	2	𝜇𝐷𝑥𝑥	𝜇𝐷𝑥𝑥	PROPN
cana-4456	223	3	̅̅	̅̅	PROPN
cana-4456	223	4	̅̅	̅̅	PROPN
cana-4456	223	5	̅̅	̅̅	PROPN
cana-4456	223	6	ℎ	ℎ	PROPN
cana-4456	224	1	𝜇𝐷𝑥𝑥	𝜇𝐷𝑥𝑥	PROPN
cana-4456	224	2	̅̅	̅̅	PROPN
cana-4456	224	3	̅̅	̅̅	PROPN
cana-4456	224	4	̅̅	̅̅	PROPN
cana-4456	224	5	𝑞	𝑞	PROPN
cana-4456	224	6	)	)	PUNCT
cana-4456	224	7	,	,	PUNCT
cana-4456	224	8	(	(	PUNCT
cana-4456	224	9	41	41	NUM
cana-4456	224	10	)	)	PUNCT
cana-4456	224	11	equivalent	equivalent	ADJ
cana-4456	224	12	to	to	ADP
cana-4456	224	13	𝜕𝑡𝑸	𝜕𝑡𝑸	PROPN
cana-4456	224	14	=	=	PUNCT
cana-4456	224	15	𝑅𝐻𝑆𝑅𝐵𝐹−𝑃𝑈𝑀(𝑸	𝑅𝐻𝑆𝑅𝐵𝐹−𝑃𝑈𝑀(𝑸	PROPN
cana-4456	224	16	)	)	PUNCT
cana-4456	224	17	,	,	PUNCT
cana-4456	224	18	where	where	SCONJ
cana-4456	224	19	𝑅𝐻𝑆𝑅𝐵𝐹−𝑃𝑈𝑀(𝑸	𝑅𝐻𝑆𝑅𝐵𝐹−𝑃𝑈𝑀(𝑸	NOUN
cana-4456	224	20	)	)	PUNCT
cana-4456	224	21	=	=	PUNCT
cana-4456	225	1	−	−	NUM
cana-4456	225	2	�	�	NOUN
cana-4456	225	3	̅	̅	NOUN
cana-4456	225	4	�	�	NOUN
cana-4456	225	5	(𝑸	(𝑸	NUM
cana-4456	225	6	)	)	PUNCT
cana-4456	225	7	+	+	NUM
cana-4456	225	8	𝑆̅(𝑸	𝑆̅(𝑸	NOUN
cana-4456	225	9	)	)	PUNCT
cana-4456	225	10	+	+	CCONJ
cana-4456	225	11	�	�	NOUN
cana-4456	225	12	̅	̅	NOUN
cana-4456	225	13	�	�	NOUN
cana-4456	225	14	(𝑸	(𝑸	NUM
cana-4456	225	15	)	)	PUNCT
cana-4456	225	16	.	.	PUNCT
cana-4456	226	1	(	(	PUNCT
cana-4456	226	2	42	42	NUM
cana-4456	226	3	)	)	PUNCT
cana-4456	226	4	3.4	3.4	NUM
cana-4456	226	5	rbf	rbf	PROPN
cana-4456	226	6	-	-	PUNCT
cana-4456	226	7	pum	pum	PROPN
cana-4456	226	8	with	with	ADP
cana-4456	226	9	qr	qr	PROPN
cana-4456	226	10	factorization	factorization	NOUN
cana-4456	226	11	(	(	PUNCT
cana-4456	226	12	rbf	rbf	PROPN
cana-4456	226	13	-	-	PUNCT
cana-4456	226	14	pum	pum	PROPN
cana-4456	226	15	-	-	PUNCT
cana-4456	226	16	qr	qr	NOUN
cana-4456	226	17	)	)	PUNCT
cana-4456	226	18	it	it	PRON
cana-4456	226	19	is	be	AUX
cana-4456	226	20	well	well	ADV
cana-4456	226	21	known	know	VERB
cana-4456	226	22	that	that	SCONJ
cana-4456	226	23	the	the	DET
cana-4456	226	24	use	use	NOUN
cana-4456	226	25	of	of	ADP
cana-4456	226	26	infinitely	infinitely	ADV
cana-4456	226	27	smooth	smooth	ADJ
cana-4456	226	28	rbfs	rbfs	NOUN
cana-4456	226	29	(	(	PUNCT
cana-4456	226	30	table	table	NOUN
cana-4456	226	31	1	1	NUM
cana-4456	226	32	)	)	PUNCT
cana-4456	226	33	can	can	AUX
cana-4456	226	34	provide	provide	VERB
cana-4456	226	35	spectral	spectral	ADJ
cana-4456	226	36	accuracy	accuracy	NOUN
cana-4456	226	37	for	for	ADP
cana-4456	226	38	solving	solve	VERB
cana-4456	226	39	pdes	pde	NOUN
cana-4456	226	40	.	.	PUNCT
cana-4456	227	1	as	as	SCONJ
cana-4456	227	2	mentioned	mention	VERB
cana-4456	227	3	previously	previously	ADV
cana-4456	227	4	,	,	PUNCT
cana-4456	227	5	this	this	DET
cana-4456	227	6	type	type	NOUN
cana-4456	227	7	of	of	ADP
cana-4456	227	8	rbfs	rbfs	NOUN
cana-4456	227	9	is	be	AUX
cana-4456	227	10	usually	usually	ADV
cana-4456	227	11	formulated	formulate	VERB
cana-4456	227	12	by	by	ADP
cana-4456	227	13	including	include	VERB
cana-4456	227	14	a	a	DET
cana-4456	227	15	free	free	ADJ
cana-4456	227	16	shape	shape	NOUN
cana-4456	227	17	parameter	parameter	NOUN
cana-4456	227	18	𝜀	𝜀	PROPN
cana-4456	227	19	,	,	PUNCT
cana-4456	227	20	which	which	PRON
cana-4456	227	21	is	be	AUX
cana-4456	227	22	generally	generally	ADV
cana-4456	227	23	applied	apply	VERB
cana-4456	227	24	to	to	PART
cana-4456	227	25	control	control	VERB
cana-4456	227	26	the	the	DET
cana-4456	227	27	fatness	fatness	NOUN
cana-4456	227	28	of	of	ADP
cana-4456	227	29	the	the	DET
cana-4456	227	30	functions	function	NOUN
cana-4456	227	31	.	.	PUNCT
cana-4456	228	1	decreasing	decrease	VERB
cana-4456	228	2	𝜀	𝜀	NOUN
cana-4456	228	3	often	often	ADV
cana-4456	228	4	improves	improve	VERB
cana-4456	228	5	the	the	DET
cana-4456	228	6	accuracy	accuracy	NOUN
cana-4456	228	7	of	of	ADP
cana-4456	228	8	approximation	approximation	NOUN
cana-4456	228	9	.	.	PUNCT
cana-4456	229	1	however	however	ADV
cana-4456	229	2	,	,	PUNCT
cana-4456	229	3	mathematical	mathematical	ADJ
cana-4456	229	4	investigations	investigation	NOUN
cana-4456	229	5	show	show	VERB
cana-4456	229	6	that	that	SCONJ
cana-4456	229	7	when	when	SCONJ
cana-4456	229	8	𝜀	𝜀	X
cana-4456	229	9	→	→	SYM
cana-4456	229	10	0	0	NUM
cana-4456	229	11	(	(	PUNCT
cana-4456	229	12	flat	flat	ADJ
cana-4456	229	13	limit	limit	NOUN
cana-4456	229	14	region	region	NOUN
cana-4456	229	15	)	)	PUNCT
cana-4456	229	16	,	,	PUNCT
cana-4456	229	17	the	the	DET
cana-4456	229	18	rbf	rbf	PROPN
cana-4456	229	19	methods	method	NOUN
cana-4456	229	20	suffers	suffer	VERB
cana-4456	229	21	from	from	ADP
cana-4456	229	22	severe	severe	ADJ
cana-4456	229	23	ill	ill	ADJ
cana-4456	229	24	-	-	PUNCT
cana-4456	229	25	conditioning	conditioning	NOUN
cana-4456	229	26	.	.	PUNCT
cana-4456	230	1	therefore	therefore	ADV
cana-4456	230	2	,	,	PUNCT
cana-4456	230	3	rbfpum	rbfpum	NOUN
cana-4456	230	4	requires	require	VERB
cana-4456	230	5	a	a	DET
cana-4456	230	6	stable	stable	ADJ
cana-4456	230	7	evaluation	evaluation	NOUN
cana-4456	230	8	method	method	NOUN
cana-4456	230	9	to	to	PART
cana-4456	230	10	converge	converge	VERB
cana-4456	230	11	as	as	ADP
cana-4456	230	12	𝜀	𝜀	PROPN
cana-4456	230	13	→	→	SYM
cana-4456	230	14	0	0	NUM
cana-4456	231	1	[	[	X
cana-4456	231	2	38	38	NUM
cana-4456	231	3	,	,	PUNCT
cana-4456	231	4	39	39	NUM
cana-4456	231	5	]	]	PUNCT
cana-4456	231	6	.	.	PUNCT
cana-4456	232	1	the	the	DET
cana-4456	232	2	obvious	obvious	ADJ
cana-4456	232	3	question	question	NOUN
cana-4456	232	4	becomes	become	VERB
cana-4456	232	5	how	how	SCONJ
cana-4456	232	6	to	to	PART
cana-4456	232	7	devise	devise	VERB
cana-4456	232	8	algorithms	algorithm	NOUN
cana-4456	232	9	that	that	PRON
cana-4456	232	10	balance	balance	VERB
cana-4456	232	11	numerical	numerical	ADJ
cana-4456	232	12	stability	stability	NOUN
cana-4456	232	13	and	and	CCONJ
cana-4456	232	14	computational	computational	ADJ
cana-4456	232	15	efficiency	efficiency	NOUN
cana-4456	232	16	when	when	SCONJ
cana-4456	232	17	dealing	deal	VERB
cana-4456	232	18	with	with	ADP
cana-4456	232	19	small	small	ADJ
cana-4456	232	20	values	value	NOUN
cana-4456	232	21	of	of	ADP
cana-4456	232	22	ε	ε	PROPN
cana-4456	232	23	.	.	PUNCT
cana-4456	233	1	this	this	PRON
cana-4456	233	2	was	be	AUX
cana-4456	233	3	the	the	DET
cana-4456	233	4	subject	subject	NOUN
cana-4456	233	5	of	of	ADP
cana-4456	233	6	many	many	ADJ
cana-4456	233	7	papers	paper	NOUN
cana-4456	233	8	published	publish	VERB
cana-4456	233	9	during	during	ADP
cana-4456	233	10	the	the	DET
cana-4456	233	11	last	last	ADJ
cana-4456	233	12	two	two	NUM
cana-4456	233	13	decades	decade	NOUN
cana-4456	233	14	(	(	PUNCT
cana-4456	233	15	e.g.	e.g.	ADV
cana-4456	233	16	[	[	X
cana-4456	233	17	40	40	NUM
cana-4456	233	18	,	,	PUNCT
cana-4456	233	19	41	41	NUM
cana-4456	233	20	,	,	PUNCT
cana-4456	233	21	42	42	NUM
cana-4456	233	22	]	]	PUNCT
cana-4456	233	23	)	)	PUNCT
cana-4456	233	24	.	.	PUNCT
cana-4456	234	1	communications	communication	NOUN
cana-4456	234	2	on	on	ADP
cana-4456	234	3	applied	apply	VERB
cana-4456	234	4	nonlinear	nonlinear	ADJ
cana-4456	234	5	analysis	analysis	NOUN
cana-4456	234	6	issn	issn	NOUN
cana-4456	234	7	:	:	PUNCT
cana-4456	234	8	1074	1074	NUM
cana-4456	234	9	-	-	PUNCT
cana-4456	234	10	133x	133x	NUM
cana-4456	234	11	vol	vol	NOUN
cana-4456	234	12	32	32	NUM
cana-4456	234	13	no	no	NOUN
cana-4456	234	14	.	.	PUNCT
cana-4456	235	1	9s	9s	NUM
cana-4456	235	2	(	(	PUNCT
cana-4456	235	3	2025	2025	NUM
cana-4456	235	4	)	)	PUNCT
cana-4456	235	5	2178	2178	NUM
cana-4456	235	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	236	1	in	in	ADP
cana-4456	236	2	order	order	NOUN
cana-4456	236	3	to	to	PART
cana-4456	236	4	use	use	VERB
cana-4456	236	5	small	small	ADJ
cana-4456	236	6	values	value	NOUN
cana-4456	236	7	of	of	ADP
cana-4456	236	8	the	the	DET
cana-4456	236	9	shape	shape	NOUN
cana-4456	236	10	parameter	parameter	NOUN
cana-4456	236	11	in	in	ADP
cana-4456	236	12	rbf	rbf	PROPN
cana-4456	236	13	-	-	PROPN
cana-4456	236	14	pum	pum	PROPN
cana-4456	236	15	,	,	PUNCT
cana-4456	236	16	we	we	PRON
cana-4456	236	17	consider	consider	VERB
cana-4456	236	18	the	the	DET
cana-4456	236	19	rbf	rbf	PROPN
cana-4456	236	20	-	-	PUNCT
cana-4456	236	21	qr	qr	PROPN
cana-4456	236	22	algorithm	algorithm	NOUN
cana-4456	236	23	[	[	X
cana-4456	236	24	40	40	NUM
cana-4456	236	25	]	]	PUNCT
cana-4456	236	26	.	.	PUNCT
cana-4456	237	1	the	the	DET
cana-4456	237	2	essential	essential	ADJ
cana-4456	237	3	concept	concept	NOUN
cana-4456	237	4	behind	behind	ADP
cana-4456	237	5	the	the	DET
cana-4456	237	6	rbf	rbf	PROPN
cana-4456	237	7	-	-	PUNCT
cana-4456	237	8	qr	qr	PROPN
cana-4456	237	9	algorithm	algorithm	NOUN
cana-4456	237	10	is	be	AUX
cana-4456	237	11	finding	find	VERB
cana-4456	237	12	a	a	DET
cana-4456	237	13	way	way	NOUN
cana-4456	237	14	to	to	PART
cana-4456	237	15	form	form	VERB
cana-4456	237	16	a	a	DET
cana-4456	237	17	well	well	ADV
cana-4456	237	18	conditioned	condition	VERB
cana-4456	237	19	basis	basis	NOUN
cana-4456	237	20	in	in	ADP
cana-4456	237	21	the	the	DET
cana-4456	237	22	same	same	ADJ
cana-4456	237	23	function	function	NOUN
cana-4456	237	24	space	space	NOUN
cana-4456	237	25	spanned	span	VERB
cana-4456	237	26	by	by	ADP
cana-4456	237	27	a	a	DET
cana-4456	237	28	finite	finite	ADJ
cana-4456	237	29	set	set	NOUN
cana-4456	237	30	of	of	ADP
cana-4456	237	31	nearly	nearly	ADV
cana-4456	237	32	flat	flat	ADJ
cana-4456	237	33	rbfs	rbfs	NOUN
cana-4456	237	34	[	[	X
cana-4456	237	35	41	41	NUM
cana-4456	237	36	]	]	PUNCT
cana-4456	237	37	.	.	PUNCT
cana-4456	238	1	the	the	DET
cana-4456	238	2	change	change	NOUN
cana-4456	238	3	of	of	ADP
cana-4456	238	4	basis	basis	NOUN
cana-4456	238	5	will	will	AUX
cana-4456	238	6	allow	allow	VERB
cana-4456	238	7	to	to	PART
cana-4456	238	8	remove	remove	VERB
cana-4456	238	9	the	the	DET
cana-4456	238	10	ill	ill	ADJ
cana-4456	238	11	-	-	PUNCT
cana-4456	238	12	conditioning	conditioning	NOUN
cana-4456	238	13	issue	issue	NOUN
cana-4456	238	14	while	while	SCONJ
cana-4456	238	15	maintaining	maintain	VERB
cana-4456	238	16	the	the	DET
cana-4456	238	17	same	same	ADJ
cana-4456	238	18	accuracy	accuracy	NOUN
cana-4456	238	19	or	or	CCONJ
cana-4456	238	20	even	even	ADV
cana-4456	238	21	better	well	ADJ
cana-4456	238	22	one	one	NUM
cana-4456	238	23	.	.	PUNCT
cana-4456	239	1	the	the	DET
cana-4456	239	2	construction	construction	NOUN
cana-4456	239	3	of	of	ADP
cana-4456	239	4	the	the	DET
cana-4456	239	5	new	new	ADJ
cana-4456	239	6	basis	basis	NOUN
cana-4456	239	7	was	be	AUX
cana-4456	239	8	done	do	VERB
cana-4456	239	9	by	by	ADP
cana-4456	239	10	expanding	expand	VERB
cana-4456	239	11	the	the	DET
cana-4456	239	12	gaussian	gaussian	NOUN
cana-4456	239	13	rbf	rbf	PROPN
cana-4456	239	14	(	(	PUNCT
cana-4456	239	15	table	table	NOUN
cana-4456	239	16	(	(	PUNCT
cana-4456	239	17	1	1	NUM
cana-4456	239	18	)	)	PUNCT
cana-4456	239	19	)	)	PUNCT
cana-4456	239	20	on	on	ADP
cana-4456	239	21	chebyshev	chebyshev	NOUN
cana-4456	239	22	polynomials	polynomial	NOUN
cana-4456	239	23	in	in	ADP
cana-4456	239	24	one	one	NUM
cana-4456	239	25	dimension	dimension	NOUN
cana-4456	239	26	,	,	PUNCT
cana-4456	239	27	on	on	ADP
cana-4456	239	28	chebyshev	chebyshev	NOUN
cana-4456	239	29	polynomials	polynomial	NOUN
cana-4456	239	30	and	and	CCONJ
cana-4456	239	31	trigonometric	trigonometric	ADJ
cana-4456	239	32	functions	function	NOUN
cana-4456	239	33	in	in	ADP
cana-4456	239	34	two	two	NUM
cana-4456	239	35	dimensions	dimension	NOUN
cana-4456	239	36	and	and	CCONJ
cana-4456	239	37	on	on	ADP
cana-4456	239	38	a	a	DET
cana-4456	239	39	combination	combination	NOUN
cana-4456	239	40	between	between	ADP
cana-4456	239	41	chebyshev	chebyshev	NOUN
cana-4456	239	42	polynomials	polynomial	NOUN
cana-4456	239	43	and	and	CCONJ
cana-4456	239	44	spherical	spherical	ADJ
cana-4456	239	45	harmonics	harmonic	NOUN
cana-4456	239	46	in	in	ADP
cana-4456	239	47	three	three	NUM
cana-4456	239	48	dimensions	dimension	NOUN
cana-4456	239	49	.	.	PUNCT
cana-4456	240	1	the	the	DET
cana-4456	240	2	new	new	ADJ
cana-4456	240	3	basis	basis	NOUN
cana-4456	240	4	derived	derive	VERB
cana-4456	240	5	from	from	ADP
cana-4456	240	6	rbf	rbf	PROPN
cana-4456	240	7	-	-	PUNCT
cana-4456	240	8	qr	qr	PROPN
cana-4456	240	9	algorithm	algorithm	NOUN
cana-4456	240	10	spans	span	VERB
cana-4456	240	11	the	the	DET
cana-4456	240	12	same	same	ADJ
cana-4456	240	13	approximation	approximation	NOUN
cana-4456	240	14	space	space	NOUN
cana-4456	240	15	as	as	ADP
cana-4456	240	16	the	the	DET
cana-4456	240	17	gaussian	gaussian	ADJ
cana-4456	240	18	basis	basis	NOUN
cana-4456	240	19	which	which	PRON
cana-4456	240	20	produce	produce	VERB
cana-4456	240	21	an	an	DET
cana-4456	240	22	accurate	accurate	ADJ
cana-4456	240	23	numerical	numerical	ADJ
cana-4456	240	24	solutions	solution	NOUN
cana-4456	240	25	and	and	CCONJ
cana-4456	240	26	bypasses	bypass	VERB
cana-4456	240	27	some	some	DET
cana-4456	240	28	limitations	limitation	NOUN
cana-4456	240	29	,	,	PUNCT
cana-4456	240	30	including	include	VERB
cana-4456	240	31	complications	complication	NOUN
cana-4456	240	32	related	relate	VERB
cana-4456	240	33	to	to	ADP
cana-4456	240	34	the	the	DET
cana-4456	240	35	selection	selection	NOUN
cana-4456	240	36	of	of	ADP
cana-4456	240	37	ε	ε	PROPN
cana-4456	240	38	,	,	PUNCT
cana-4456	240	39	ill	ill	ADJ
cana-4456	240	40	-	-	PUNCT
cana-4456	240	41	conditioning	conditioning	NOUN
cana-4456	240	42	of	of	ADP
cana-4456	240	43	rbf	rbf	PROPN
cana-4456	240	44	-	-	PUNCT
cana-4456	240	45	pum	pum	PROPN
cana-4456	240	46	matrices	matrix	NOUN
cana-4456	240	47	.	.	PUNCT
cana-4456	241	1	to	to	PART
cana-4456	241	2	have	have	VERB
cana-4456	241	3	more	more	ADJ
cana-4456	241	4	details	detail	NOUN
cana-4456	241	5	on	on	ADP
cana-4456	241	6	the	the	DET
cana-4456	241	7	construction	construction	NOUN
cana-4456	241	8	of	of	ADP
cana-4456	241	9	the	the	DET
cana-4456	241	10	new	new	ADJ
cana-4456	241	11	basis	basis	NOUN
cana-4456	241	12	,	,	PUNCT
cana-4456	241	13	we	we	PRON
cana-4456	241	14	refer	refer	VERB
cana-4456	241	15	the	the	DET
cana-4456	241	16	reader	reader	NOUN
cana-4456	241	17	to	to	ADP
cana-4456	241	18	[	[	X
cana-4456	241	19	40	40	NUM
cana-4456	241	20	]	]	PUNCT
cana-4456	241	21	.	.	PUNCT
cana-4456	242	1	3.5	3.5	NUM
cana-4456	242	2	temporal	temporal	ADJ
cana-4456	242	3	discretization	discretization	NOUN
cana-4456	242	4	of	of	ADP
cana-4456	242	5	the	the	DET
cana-4456	242	6	numerical	numerical	ADJ
cana-4456	242	7	methods	method	NOUN
cana-4456	242	8	to	to	PART
cana-4456	242	9	achieve	achieve	VERB
cana-4456	242	10	a	a	DET
cana-4456	242	11	higher	high	ADJ
cana-4456	242	12	order	order	NOUN
cana-4456	242	13	of	of	ADP
cana-4456	242	14	accuracy	accuracy	NOUN
cana-4456	242	15	,	,	PUNCT
cana-4456	242	16	it	it	PRON
cana-4456	242	17	is	be	AUX
cana-4456	242	18	sensible	sensible	ADJ
cana-4456	242	19	to	to	PART
cana-4456	242	20	use	use	VERB
cana-4456	242	21	a	a	DET
cana-4456	242	22	high	high	ADJ
cana-4456	242	23	order	order	NOUN
cana-4456	242	24	time	time	NOUN
cana-4456	242	25	discretization	discretization	NOUN
cana-4456	242	26	as	as	ADV
cana-4456	242	27	well	well	ADV
cana-4456	242	28	.	.	PUNCT
cana-4456	243	1	the	the	DET
cana-4456	243	2	ode	ode	PROPN
cana-4456	243	3	systems	system	NOUN
cana-4456	243	4	(	(	PUNCT
cana-4456	243	5	20	20	NUM
cana-4456	243	6	)	)	PUNCT
cana-4456	243	7	,	,	PUNCT
cana-4456	243	8	(	(	PUNCT
cana-4456	243	9	21	21	NUM
cana-4456	243	10	)	)	PUNCT
cana-4456	243	11	,	,	PUNCT
cana-4456	243	12	(	(	PUNCT
cana-4456	243	13	42	42	NUM
cana-4456	243	14	)	)	PUNCT
cana-4456	243	15	are	be	AUX
cana-4456	243	16	integrated	integrate	VERB
cana-4456	243	17	in	in	ADP
cana-4456	243	18	time	time	NOUN
cana-4456	243	19	using	use	VERB
cana-4456	243	20	the	the	DET
cana-4456	243	21	fourth	fourth	ADJ
cana-4456	243	22	order	order	NOUN
cana-4456	243	23	runge	runge	NOUN
cana-4456	243	24	-	-	PUNCT
cana-4456	243	25	kutta	kutta	NOUN
cana-4456	243	26	scheme	scheme	NOUN
cana-4456	243	27	.	.	PUNCT
cana-4456	244	1	the	the	DET
cana-4456	244	2	procedure	procedure	NOUN
cana-4456	244	3	to	to	PART
cana-4456	244	4	advance	advance	VERB
cana-4456	244	5	the	the	DET
cana-4456	244	6	solution	solution	NOUN
cana-4456	244	7	from	from	ADP
cana-4456	244	8	the	the	DET
cana-4456	244	9	time	time	NOUN
cana-4456	244	10	𝑡𝑛	𝑡𝑛	NOUN
cana-4456	244	11	to	to	ADP
cana-4456	244	12	the	the	DET
cana-4456	244	13	next	next	ADJ
cana-4456	244	14	time	time	NOUN
cana-4456	244	15	𝑡𝑛+1	𝑡𝑛+1	NUM
cana-4456	244	16	is	be	AUX
cana-4456	244	17	carried	carry	VERB
cana-4456	244	18	out	out	ADP
cana-4456	244	19	as	as	ADP
cana-4456	244	20	𝑘1	𝑘1	PROPN
cana-4456	244	21	=	=	SYM
cana-4456	244	22	∆𝑡	∆𝑡	PROPN
cana-4456	244	23	𝑅𝐻𝑆(𝑸𝑛	𝑅𝐻𝑆(𝑸𝑛	NOUN
cana-4456	244	24	)	)	PUNCT
cana-4456	244	25	,	,	PUNCT
cana-4456	244	26	𝑘2	𝑘2	PROPN
cana-4456	244	27	=	=	PUNCT
cana-4456	244	28	∆𝑡	∆𝑡	PROPN
cana-4456	244	29	𝑅𝐻𝑆	𝑅𝐻𝑆	NOUN
cana-4456	244	30	(	(	PUNCT
cana-4456	244	31	𝑸𝑛	𝑸𝑛	NOUN
cana-4456	244	32	+	+	NOUN
cana-4456	244	33	1	1	NUM
cana-4456	244	34	2	2	NUM
cana-4456	244	35	𝑘1	𝑘1	NOUN
cana-4456	244	36	)	)	PUNCT
cana-4456	244	37	,	,	PUNCT
cana-4456	245	1	𝑘3	𝑘3	PROPN
cana-4456	245	2	=	=	PUNCT
cana-4456	245	3	∆𝑡	∆𝑡	PROPN
cana-4456	245	4	𝑅𝐻𝑆	𝑅𝐻𝑆	NOUN
cana-4456	245	5	(	(	PUNCT
cana-4456	245	6	𝑸𝑛	𝑸𝑛	NOUN
cana-4456	245	7	+	+	NOUN
cana-4456	245	8	1	1	NUM
cana-4456	245	9	2	2	NUM
cana-4456	245	10	𝑘2	𝑘2	NOUN
cana-4456	245	11	)	)	PUNCT
cana-4456	245	12	,	,	PUNCT
cana-4456	245	13	𝑘4	𝑘4	PROPN
cana-4456	245	14	=	=	SYM
cana-4456	245	15	∆𝑡	∆𝑡	PROPN
cana-4456	245	16	𝑅𝐻𝑆(𝑸𝑛	𝑅𝐻𝑆(𝑸𝑛	PROPN
cana-4456	245	17	+	+	CCONJ
cana-4456	245	18	𝑘3	𝑘3	PROPN
cana-4456	245	19	)	)	PUNCT
cana-4456	245	20	,	,	PUNCT
cana-4456	245	21	𝑸𝑛+1	𝑸𝑛+1	X
cana-4456	245	22	=	=	SYM
cana-4456	245	23	𝑸𝑛	𝑸𝑛	NOUN
cana-4456	245	24	+	+	NUM
cana-4456	245	25	1	1	NUM
cana-4456	245	26	6	6	NUM
cana-4456	245	27	(	(	PUNCT
cana-4456	245	28	𝑘1	𝑘1	PROPN
cana-4456	245	29	+	+	CCONJ
cana-4456	245	30	2𝑘2	2𝑘2	NUM
cana-4456	245	31	+	+	CCONJ
cana-4456	245	32	2𝑘3	2𝑘3	NUM
cana-4456	245	33	+	+	NUM
cana-4456	245	34	𝑘4	𝑘4	PROPN
cana-4456	245	35	)	)	PUNCT
cana-4456	245	36	,	,	PUNCT
cana-4456	245	37	(	(	PUNCT
cana-4456	245	38	43	43	NUM
cana-4456	245	39	)	)	PUNCT
cana-4456	245	40	where	where	SCONJ
cana-4456	245	41	𝑅𝐻𝑆	𝑅𝐻𝑆	NOUN
cana-4456	245	42	can	can	AUX
cana-4456	245	43	be	be	AUX
cana-4456	245	44	𝑅𝐻𝑆𝑘𝑎𝑛𝑠𝑎	𝑅𝐻𝑆𝑘𝑎𝑛𝑠𝑎	ADJ
cana-4456	245	45	or	or	CCONJ
cana-4456	245	46	𝑅𝐻𝑆𝑅𝐵𝐹−𝐹𝐷	𝑅𝐻𝑆𝑅𝐵𝐹−𝐹𝐷	PUNCT
cana-4456	245	47	or𝑅𝐻𝑆𝑅𝐵𝐹−𝑃𝑈𝑀	or𝑅𝐻𝑆𝑅𝐵𝐹−𝑃𝑈𝑀	PROPN
cana-4456	245	48	,	,	PUNCT
cana-4456	245	49	𝑛	𝑛	PROPN
cana-4456	245	50	represents	represent	VERB
cana-4456	245	51	the	the	DET
cana-4456	245	52	time	time	NOUN
cana-4456	245	53	level	level	NOUN
cana-4456	245	54	and	and	CCONJ
cana-4456	245	55	𝛥𝑡	𝛥𝑡	PROPN
cana-4456	245	56	is	be	AUX
cana-4456	245	57	the	the	DET
cana-4456	245	58	time	time	NOUN
cana-4456	245	59	step	step	NOUN
cana-4456	245	60	,	,	PUNCT
cana-4456	245	61	this	this	PRON
cana-4456	245	62	needs	need	VERB
cana-4456	245	63	to	to	PART
cana-4456	245	64	be	be	AUX
cana-4456	245	65	chosen	choose	VERB
cana-4456	245	66	carefully	carefully	ADV
cana-4456	245	67	to	to	PART
cana-4456	245	68	guarantee	guarantee	VERB
cana-4456	245	69	the	the	DET
cana-4456	245	70	stability	stability	NOUN
cana-4456	245	71	of	of	ADP
cana-4456	245	72	the	the	DET
cana-4456	245	73	scheme	scheme	NOUN
cana-4456	245	74	.	.	PUNCT
cana-4456	246	1	in	in	ADP
cana-4456	246	2	all	all	DET
cana-4456	246	3	our	our	PRON
cana-4456	246	4	simulations	simulation	NOUN
cana-4456	246	5	,	,	PUNCT
cana-4456	246	6	we	we	PRON
cana-4456	246	7	chose	choose	VERB
cana-4456	246	8	𝛥𝑡	𝛥𝑡	ADP
cana-4456	246	9	using	use	VERB
cana-4456	246	10	the	the	DET
cana-4456	246	11	following	follow	VERB
cana-4456	246	12	formula	formula	NOUN
cana-4456	246	13	:	:	PUNCT
cana-4456	246	14	∆𝑡	∆𝑡	NOUN
cana-4456	246	15	=	=	PUNCT
cana-4456	246	16	𝐶𝐹𝐿	𝐶𝐹𝐿	VERB
cana-4456	246	17	𝑑𝑚𝑖𝑛	𝑑𝑚𝑖𝑛	PROPN
cana-4456	246	18	max	max	PROPN
cana-4456	246	19	(	(	PUNCT
cana-4456	246	20	|𝑢|+√𝑔ℎ	|𝑢|+√𝑔ℎ	NOUN
cana-4456	246	21	)	)	PUNCT
cana-4456	246	22	,	,	PUNCT
cana-4456	246	23	(	(	PUNCT
cana-4456	246	24	44	44	NUM
cana-4456	246	25	)	)	PUNCT
cana-4456	246	26	where	where	SCONJ
cana-4456	246	27	𝑑𝑚𝑖𝑛	𝑑𝑚𝑖𝑛	PROPN
cana-4456	246	28	denotes	denote	VERB
cana-4456	246	29	the	the	DET
cana-4456	246	30	smallest	small	ADJ
cana-4456	246	31	nodal	nodal	NOUN
cana-4456	246	32	distance	distance	NOUN
cana-4456	246	33	between	between	ADP
cana-4456	246	34	collocation	collocation	NOUN
cana-4456	246	35	points	point	NOUN
cana-4456	246	36	and	and	CCONJ
cana-4456	246	37	𝐶𝐹𝐿	𝐶𝐹𝐿	NOUN
cana-4456	246	38	is	be	AUX
cana-4456	246	39	the	the	DET
cana-4456	246	40	courant	courant	ADJ
cana-4456	246	41	number	number	NOUN
cana-4456	246	42	such	such	ADJ
cana-4456	246	43	that	that	SCONJ
cana-4456	246	44	0	0	NUM
cana-4456	246	45	<	<	X
cana-4456	246	46	𝐶𝐹𝐿	𝐶𝐹𝐿	VERB
cana-4456	246	47	<	<	X
cana-4456	246	48	1	1	NUM
cana-4456	246	49	.	.	PUNCT
cana-4456	247	1	in	in	ADP
cana-4456	247	2	the	the	DET
cana-4456	247	3	following	following	NOUN
cana-4456	247	4	,	,	PUNCT
cana-4456	247	5	algorithm	algorithm	NOUN
cana-4456	247	6	1	1	NUM
cana-4456	247	7	and	and	CCONJ
cana-4456	247	8	algorithm	algorithm	PROPN
cana-4456	247	9	2	2	NUM
cana-4456	247	10	illustrates	illustrate	VERB
cana-4456	247	11	the	the	DET
cana-4456	247	12	full	full	ADJ
cana-4456	247	13	discretization	discretization	NOUN
cana-4456	247	14	of	of	ADP
cana-4456	247	15	the	the	DET
cana-4456	247	16	swes	swe	NOUN
cana-4456	247	17	using	use	VERB
cana-4456	247	18	rbf	rbf	PROPN
cana-4456	247	19	-	-	PUNCT
cana-4456	247	20	fd	fd	PROPN
cana-4456	247	21	method	method	NOUN
cana-4456	247	22	and	and	CCONJ
cana-4456	247	23	rbf	rbf	PROPN
cana-4456	247	24	-	-	PUNCT
cana-4456	247	25	pum	pum	PROPN
cana-4456	247	26	-	-	PUNCT
cana-4456	247	27	qr	qr	PROPN
cana-4456	247	28	method	method	NOUN
cana-4456	247	29	,	,	PUNCT
cana-4456	247	30	respectively	respectively	ADV
cana-4456	247	31	.	.	PUNCT
cana-4456	248	1	communications	communication	NOUN
cana-4456	248	2	on	on	ADP
cana-4456	248	3	applied	apply	VERB
cana-4456	248	4	nonlinear	nonlinear	ADJ
cana-4456	248	5	analysis	analysis	NOUN
cana-4456	248	6	issn	issn	NOUN
cana-4456	248	7	:	:	PUNCT
cana-4456	248	8	1074	1074	NUM
cana-4456	248	9	-	-	PUNCT
cana-4456	248	10	133x	133x	NUM
cana-4456	248	11	vol	vol	NOUN
cana-4456	248	12	32	32	NUM
cana-4456	248	13	no	no	NOUN
cana-4456	248	14	.	.	PUNCT
cana-4456	249	1	9s	9s	NUM
cana-4456	249	2	(	(	PUNCT
cana-4456	249	3	2025	2025	NUM
cana-4456	249	4	)	)	PUNCT
cana-4456	249	5	2179	2179	NUM
cana-4456	250	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	250	2	algorithm	algorithm	NOUN
cana-4456	250	3	1	1	NUM
cana-4456	250	4	full	full	ADJ
cana-4456	250	5	discretization	discretization	NOUN
cana-4456	250	6	of	of	ADP
cana-4456	250	7	1d	1d	NUM
cana-4456	250	8	swes	swe	NOUN
cana-4456	250	9	using	use	VERB
cana-4456	250	10	rbf	rbf	PROPN
cana-4456	250	11	-	-	PUNCT
cana-4456	250	12	fd	fd	PROPN
cana-4456	250	13	method	method	NOUN
cana-4456	250	14	1	1	NUM
cana-4456	250	15	:	:	PUNCT
cana-4456	250	16	enter	enter	VERB
cana-4456	250	17	the	the	DET
cana-4456	250	18	required	require	VERB
cana-4456	250	19	simulation	simulation	NOUN
cana-4456	250	20	parameters	parameter	NOUN
cana-4456	250	21	,	,	PUNCT
cana-4456	250	22	i.e	i.e	PROPN
cana-4456	250	23	𝑵	𝑵	PROPN
cana-4456	250	24	,	,	PUNCT
cana-4456	250	25	𝝁	𝝁	PRON
cana-4456	250	26	,	,	PUNCT
cana-4456	250	27	𝒏𝒍𝒐𝒄	𝒏𝒍𝒐𝒄	VERB
cana-4456	250	28	,	,	PUNCT
cana-4456	250	29	𝑻	𝑻	PROPN
cana-4456	250	30	,	,	PUNCT
cana-4456	250	31	𝒏𝒕	𝒏𝒕	NOUN
cana-4456	250	32	.	.	PUNCT
cana-4456	250	33	..	..	PUNCT
cana-4456	251	1	2	2	X
cana-4456	251	2	:	:	PUNCT
cana-4456	251	3	construct	construct	VERB
cana-4456	251	4	the	the	DET
cana-4456	251	5	rbf	rbf	PROPN
cana-4456	251	6	-	-	PUNCT
cana-4456	251	7	fd	fd	PROPN
cana-4456	251	8	differentiation	differentiation	NOUN
cana-4456	251	9	matrices	matrix	NOUN
cana-4456	251	10	:	:	PUNCT
cana-4456	251	11	a	a	X
cana-4456	251	12	:	:	PUNCT
cana-4456	251	13	specify	specify	VERB
cana-4456	251	14	the	the	DET
cana-4456	251	15	computational	computational	ADJ
cana-4456	251	16	domain	domain	NOUN
cana-4456	251	17	𝜴.	𝜴.	PROPN
cana-4456	251	18	b	b	PROPN
cana-4456	251	19	:	:	PUNCT
cana-4456	251	20	generate	generate	VERB
cana-4456	251	21	a	a	DET
cana-4456	251	22	set	set	NOUN
cana-4456	251	23	of	of	ADP
cana-4456	251	24	collocation	collocation	NOUN
cana-4456	251	25	points	point	NOUN
cana-4456	251	26	(	(	PUNCT
cana-4456	251	27	nodes	node	NOUN
cana-4456	251	28	)	)	PUNCT
cana-4456	251	29	{	{	PUNCT
cana-4456	251	30	𝒙𝒊}𝒊=𝟏	𝒙𝒊}𝒊=𝟏	NOUN
cana-4456	251	31	𝑵	𝑵	PROPN
cana-4456	251	32	in	in	ADP
cana-4456	251	33	the	the	DET
cana-4456	251	34	domain	domain	NOUN
cana-4456	251	35	𝜴.	𝜴.	PROPN
cana-4456	251	36	c	c	NOUN
cana-4456	251	37	:	:	PUNCT
cana-4456	251	38	choose	choose	VERB
cana-4456	251	39	an	an	DET
cana-4456	251	40	rbf	rbf	PROPN
cana-4456	251	41	𝝋	𝝋	PROPN
cana-4456	251	42	and	and	CCONJ
cana-4456	251	43	determine	determine	VERB
cana-4456	251	44	the	the	DET
cana-4456	251	45	shape	shape	NOUN
cana-4456	251	46	parameter	parameter	NOUN
cana-4456	251	47	𝜺.	𝜺.	PROPN
cana-4456	252	1	d	d	X
cana-4456	252	2	:	:	PUNCT
cana-4456	252	3	for	for	SCONJ
cana-4456	252	4	each	each	DET
cana-4456	252	5	node	node	PROPN
cana-4456	252	6	𝒙𝒊	𝒙𝒊	PROPN
cana-4456	252	7	,	,	PUNCT
cana-4456	252	8	find	find	VERB
cana-4456	252	9	a	a	DET
cana-4456	252	10	stencil	stencil	NOUN
cana-4456	252	11	of	of	ADP
cana-4456	252	12	neighboring	neighboring	NOUN
cana-4456	252	13	nodes	node	NOUN
cana-4456	252	14	{	{	PUNCT
cana-4456	252	15	𝒙𝟏	𝒙𝟏	NOUN
cana-4456	252	16	𝒊	𝒊	NOUN
cana-4456	252	17	,	,	PUNCT
cana-4456	252	18	𝒙𝟐	𝒙𝟐	NOUN
cana-4456	252	19	𝒊	𝒊	NOUN
cana-4456	252	20	,	,	PUNCT
cana-4456	252	21	…	…	PUNCT
cana-4456	252	22	,	,	PUNCT
cana-4456	252	23	𝒙𝒏𝒍𝒐𝒄	𝒙𝒏𝒍𝒐𝒄	NOUN
cana-4456	252	24	𝒊	𝒊	X
cana-4456	252	25	}	}	PUNCT
cana-4456	252	26	.	.	PUNCT
cana-4456	253	1	e	e	NOUN
cana-4456	253	2	:	:	PUNCT
cana-4456	253	3	form	form	VERB
cana-4456	253	4	a	a	DET
cana-4456	253	5	local	local	ADJ
cana-4456	253	6	rbf	rbf	PROPN
cana-4456	253	7	interpolation	interpolation	NOUN
cana-4456	253	8	matrix	matrix	NOUN
cana-4456	253	9	using	use	VERB
cana-4456	253	10	the	the	DET
cana-4456	253	11	stencil	stencil	PROPN
cana-4456	253	12	nodes	node	NOUN
cana-4456	253	13	.	.	PUNCT
cana-4456	254	1	f	f	X
cana-4456	254	2	:	:	PUNCT
cana-4456	254	3	construct	construct	VERB
cana-4456	254	4	the	the	DET
cana-4456	254	5	differentiation	differentiation	NOUN
cana-4456	254	6	matrices	matrix	NOUN
cana-4456	254	7	𝑾𝒙	𝑾𝒙	PROPN
cana-4456	254	8	and	and	CCONJ
cana-4456	254	9	𝑾𝒙𝒙	𝑾𝒙𝒙	PROPN
cana-4456	254	10	by	by	ADP
cana-4456	254	11	differentiating	differentiate	VERB
cana-4456	254	12	the	the	DET
cana-4456	254	13	rbfs	rbfs	NOUN
cana-4456	254	14	and	and	CCONJ
cana-4456	254	15	solving	solving	NOUN
cana-4456	254	16	for	for	ADP
cana-4456	254	17	the	the	DET
cana-4456	254	18	weights	weight	NOUN
cana-4456	254	19	the	the	DET
cana-4456	254	20	system	system	NOUN
cana-4456	254	21	(	(	PUNCT
cana-4456	254	22	22	22	NUM
cana-4456	254	23	)	)	PUNCT
cana-4456	254	24	.	.	PUNCT
cana-4456	255	1	3	3	X
cana-4456	255	2	:	:	PUNCT
cana-4456	255	3	make	make	VERB
cana-4456	255	4	the	the	DET
cana-4456	255	5	right	right	ADJ
cana-4456	255	6	hand	hand	NOUN
cana-4456	255	7	side	side	NOUN
cana-4456	255	8	of	of	ADP
cana-4456	255	9	ode	ode	PROPN
cana-4456	255	10	obtained	obtain	VERB
cana-4456	255	11	:	:	PUNCT
cana-4456	255	12	𝑹𝑯𝑺𝒉	𝑹𝑯𝑺𝒉	PROPN
cana-4456	255	13	=	=	SYM
cana-4456	255	14	@(𝒉	@(𝒉	PROPN
cana-4456	255	15	,	,	PUNCT
cana-4456	255	16	𝒒	𝒒	PROPN
cana-4456	255	17	)	)	PUNCT
cana-4456	255	18	−	−	PROPN
cana-4456	256	1	𝑾𝒙𝒒	𝑾𝒙𝒒	PROPN
cana-4456	256	2	+	+	PROPN
cana-4456	256	3	𝝁𝑾𝒙𝒙𝒉	𝝁𝑾𝒙𝒙𝒉	PROPN
cana-4456	256	4	(	(	PUNCT
cana-4456	256	5	45.a	45.a	NUM
cana-4456	256	6	)	)	PUNCT
cana-4456	256	7	𝑹𝑯𝑺𝒒	𝑹𝑯𝑺𝒒	PROPN
cana-4456	256	8	=	=	SYM
cana-4456	256	9	@(𝒉	@(𝒉	PROPN
cana-4456	256	10	,	,	PUNCT
cana-4456	256	11	𝒒	𝒒	PROPN
cana-4456	256	12	)	)	PUNCT
cana-4456	256	13	−	−	PROPN
cana-4456	257	1	𝑾𝒙	𝑾𝒙	PROPN
cana-4456	257	2	(	(	PUNCT
cana-4456	257	3	𝒒𝟐	𝒒𝟐	AUX
cana-4456	257	4	𝒉	𝒉	VERB
cana-4456	257	5	+	+	CCONJ
cana-4456	257	6	𝟏	𝟏	NUM
cana-4456	257	7	𝟐	𝟐	NUM
cana-4456	257	8	𝒈𝒉𝟐	𝒈𝒉𝟐	PROPN
cana-4456	257	9	)	)	PUNCT
cana-4456	257	10	−𝒈(𝒉.	−𝒈(𝒉.	PROPN
cana-4456	257	11	𝑾𝒙𝒃	𝑾𝒙𝒃	PROPN
cana-4456	257	12	)	)	PUNCT
cana-4456	257	13	+	+	CCONJ
cana-4456	257	14	𝝁𝑾𝒙𝒙𝒒	𝝁𝑾𝒙𝒙𝒒	PROPN
cana-4456	257	15	(	(	PUNCT
cana-4456	257	16	45.b	45.b	NUM
cana-4456	257	17	)	)	PUNCT
cana-4456	257	18	4	4	NUM
cana-4456	257	19	:	:	PUNCT
cana-4456	257	20	enter	enter	VERB
cana-4456	257	21	initial	initial	ADJ
cana-4456	257	22	condition	condition	NOUN
cana-4456	257	23	.	.	PUNCT
cana-4456	258	1	5	5	NUM
cana-4456	258	2	:	:	PUNCT
cana-4456	258	3	for	for	ADP
cana-4456	258	4	𝒋	𝒋	NOUN
cana-4456	258	5	=	=	SYM
cana-4456	258	6	𝟏	𝟏	NUM
cana-4456	258	7	:	:	PUNCT
cana-4456	258	8	𝒏𝒕	𝒏𝒕	ADP
cana-4456	258	9	do	do	VERB
cana-4456	258	10	6	6	NUM
cana-4456	258	11	:	:	PUNCT
cana-4456	258	12	𝒕	𝒕	PROPN
cana-4456	258	13	=	=	PUNCT
cana-4456	258	14	𝒋.	𝒋.	NOUN
cana-4456	258	15	𝒅𝒕	𝒅𝒕	ADJ
cana-4456	258	16	7	7	NUM
cana-4456	258	17	:	:	PUNCT
cana-4456	258	18	𝒌𝟏	𝒌𝟏	NOUN
cana-4456	258	19	=	=	SYM
cana-4456	258	20	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	258	21	𝑹𝑯𝑺𝒉(𝒉	𝑹𝑯𝑺𝒉(𝒉	ADJ
cana-4456	258	22	,	,	PUNCT
cana-4456	258	23	𝒒	𝒒	NOUN
cana-4456	258	24	)	)	PUNCT
cana-4456	258	25	𝒌𝟏	𝒌𝟏	NOUN
cana-4456	258	26	=	=	SYM
cana-4456	258	27	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	258	28	𝑹𝑯𝑺𝒒(𝒉	𝑹𝑯𝑺𝒒(𝒉	NOUN
cana-4456	258	29	,	,	PUNCT
cana-4456	258	30	𝒒	𝒒	NOUN
cana-4456	258	31	)	)	PUNCT
cana-4456	258	32	8	8	NUM
cana-4456	258	33	:	:	PUNCT
cana-4456	258	34	𝒌𝟐	𝒌𝟐	NOUN
cana-4456	258	35	=	=	PUNCT
cana-4456	258	36	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	258	37	𝑹𝑯𝑺𝒉(𝒉	𝑹𝑯𝑺𝒉(𝒉	NOUN
cana-4456	258	38	+	+	CCONJ
cana-4456	258	39	𝒌𝟏	𝒌𝟏	PROPN
cana-4456	258	40	𝟐	𝟐	NUM
cana-4456	258	41	,	,	PUNCT
cana-4456	258	42	𝒒	𝒒	X
cana-4456	258	43	)	)	PUNCT
cana-4456	258	44	𝒌𝟐	𝒌𝟐	NOUN
cana-4456	258	45	=	=	SYM
cana-4456	258	46	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	258	47	𝑹𝑯𝑺𝒒(𝒉	𝑹𝑯𝑺𝒒(𝒉	NOUN
cana-4456	258	48	,	,	PUNCT
cana-4456	258	49	𝒒	𝒒	X
cana-4456	259	1	+	+	NUM
cana-4456	259	2	𝒌𝟏	𝒌𝟏	NOUN
cana-4456	259	3	𝟐	𝟐	NUM
cana-4456	259	4	)	)	PUNCT
cana-4456	259	5	9	9	NUM
cana-4456	259	6	:	:	PUNCT
cana-4456	259	7	𝒌𝟑	𝒌𝟑	NOUN
cana-4456	259	8	=	=	SYM
cana-4456	259	9	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	259	10	𝑹𝑯𝑺𝒉(𝒉	𝑹𝑯𝑺𝒉(𝒉	NOUN
cana-4456	259	11	+	+	CCONJ
cana-4456	259	12	𝒌𝟐	𝒌𝟐	PROPN
cana-4456	259	13	𝟐	𝟐	NUM
cana-4456	259	14	,	,	PUNCT
cana-4456	259	15	𝒒	𝒒	NOUN
cana-4456	259	16	)	)	PUNCT
cana-4456	259	17	𝒌𝟑	𝒌𝟑	NOUN
cana-4456	259	18	=	=	SYM
cana-4456	259	19	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	259	20	𝑹𝑯𝑺𝒒(𝒉	𝑹𝑯𝑺𝒒(𝒉	NOUN
cana-4456	259	21	,	,	PUNCT
cana-4456	259	22	𝒒	𝒒	PROPN
cana-4456	259	23	+	+	CCONJ
cana-4456	259	24	𝒌𝟐	𝒌𝟐	NOUN
cana-4456	259	25	𝟐	𝟐	NUM
cana-4456	259	26	)	)	PUNCT
cana-4456	259	27	10	10	NUM
cana-4456	259	28	:	:	PUNCT
cana-4456	259	29	𝒌𝟒	𝒌𝟒	ADJ
cana-4456	259	30	=	=	PUNCT
cana-4456	259	31	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	259	32	𝑹𝑯𝑺𝒉(𝒉	𝑹𝑯𝑺𝒉(𝒉	NOUN
cana-4456	259	33	+	+	CCONJ
cana-4456	259	34	𝒌𝟑	𝒌𝟑	NOUN
cana-4456	259	35	,	,	PUNCT
cana-4456	259	36	𝒒	𝒒	NOUN
cana-4456	259	37	)	)	PUNCT
cana-4456	259	38	𝒌𝟒	𝒌𝟒	ADJ
cana-4456	259	39	=	=	PUNCT
cana-4456	259	40	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	259	41	𝑹𝑯𝑺𝒒(𝒉	𝑹𝑯𝑺𝒒(𝒉	NOUN
cana-4456	259	42	,	,	PUNCT
cana-4456	259	43	𝒒	𝒒	X
cana-4456	259	44	+	+	NUM
cana-4456	259	45	𝒌𝟑	𝒌𝟑	NOUN
cana-4456	259	46	)	)	PUNCT
cana-4456	259	47	11	11	NUM
cana-4456	259	48	:	:	PUNCT
cana-4456	259	49	𝒉	𝒉	X
cana-4456	259	50	=	=	SYM
cana-4456	259	51	𝒉	𝒉	PROPN
cana-4456	259	52	+	+	CCONJ
cana-4456	259	53	𝟏	𝟏	NUM
cana-4456	259	54	𝟔	𝟔	NUM
cana-4456	259	55	(	(	PUNCT
cana-4456	259	56	𝒌𝟏	𝒌𝟏	NOUN
cana-4456	259	57	+	+	CCONJ
cana-4456	259	58	𝟐𝒌𝟐	𝟐𝒌𝟐	PUNCT
cana-4456	259	59	+	+	NUM
cana-4456	259	60	𝟐𝒌𝟑	𝟐𝒌𝟑	PUNCT
cana-4456	259	61	+	+	CCONJ
cana-4456	259	62	𝒌𝟒	𝒌𝟒	ADJ
cana-4456	259	63	)	)	PUNCT
cana-4456	259	64	𝒒	𝒒	PROPN
cana-4456	259	65	=	=	SYM
cana-4456	259	66	𝒒	𝒒	PROPN
cana-4456	259	67	+	+	NUM
cana-4456	259	68	𝟏	𝟏	NUM
cana-4456	259	69	𝟔	𝟔	NUM
cana-4456	259	70	(	(	PUNCT
cana-4456	259	71	𝒌𝟏	𝒌𝟏	NOUN
cana-4456	259	72	+	+	CCONJ
cana-4456	259	73	𝟐𝒌𝟐	𝟐𝒌𝟐	PUNCT
cana-4456	259	74	+	+	NUM
cana-4456	259	75	𝟐𝒌𝟑	𝟐𝒌𝟑	PUNCT
cana-4456	259	76	+	+	CCONJ
cana-4456	259	77	𝒌𝟒	𝒌𝟒	ADJ
cana-4456	259	78	)	)	PUNCT
cana-4456	259	79	12	12	NUM
cana-4456	259	80	:	:	PUNCT
cana-4456	259	81	apply	apply	VERB
cana-4456	259	82	boundary	boundary	ADJ
cana-4456	259	83	condition	condition	NOUN
cana-4456	259	84	.	.	PUNCT
cana-4456	260	1	13	13	NUM
cana-4456	260	2	:	:	PUNCT
cana-4456	260	3	end	end	NOUN
cana-4456	260	4	14	14	NUM
cana-4456	260	5	:	:	PUNCT
cana-4456	260	6	compute	compute	NOUN
cana-4456	260	7	error	error	NOUN
cana-4456	260	8	.	.	PUNCT
cana-4456	261	1	algorithm	algorithm	NOUN
cana-4456	261	2	1	1	NUM
cana-4456	261	3	full	full	ADJ
cana-4456	261	4	discretization	discretization	NOUN
cana-4456	261	5	of	of	ADP
cana-4456	261	6	1d	1d	NUM
cana-4456	261	7	swes	swe	NOUN
cana-4456	261	8	using	use	VERB
cana-4456	261	9	rbf	rbf	PROPN
cana-4456	261	10	-	-	PUNCT
cana-4456	261	11	pum	pum	PROPN
cana-4456	261	12	-	-	PUNCT
cana-4456	261	13	qr	qr	PROPN
cana-4456	261	14	method	method	NOUN
cana-4456	261	15	1	1	NUM
cana-4456	261	16	:	:	PUNCT
cana-4456	261	17	enter	enter	VERB
cana-4456	261	18	the	the	DET
cana-4456	261	19	required	require	VERB
cana-4456	261	20	simulation	simulation	NOUN
cana-4456	261	21	parameters	parameter	NOUN
cana-4456	261	22	,	,	PUNCT
cana-4456	261	23	i.e	i.e	PROPN
cana-4456	261	24	𝑵	𝑵	PROPN
cana-4456	261	25	,	,	PUNCT
cana-4456	261	26	𝝁	𝝁	PRON
cana-4456	261	27	,	,	PUNCT
cana-4456	261	28	𝒏𝒑	𝒏𝒑	INTJ
cana-4456	261	29	,	,	PUNCT
cana-4456	261	30	𝑻	𝑻	PROPN
cana-4456	261	31	,	,	PUNCT
cana-4456	261	32	𝒏𝒕	𝒏𝒕	NOUN
cana-4456	261	33	.	.	PUNCT
cana-4456	261	34	..	..	PUNCT
cana-4456	262	1	2	2	X
cana-4456	262	2	:	:	PUNCT
cana-4456	262	3	construct	construct	VERB
cana-4456	262	4	the	the	DET
cana-4456	262	5	rbf	rbf	PROPN
cana-4456	262	6	-	-	PUNCT
cana-4456	262	7	pum	pum	PROPN
cana-4456	262	8	-	-	PUNCT
cana-4456	262	9	qr	qr	NOUN
cana-4456	262	10	differentiation	differentiation	NOUN
cana-4456	262	11	matrices	matrix	NOUN
cana-4456	262	12	:	:	PUNCT
cana-4456	262	13	a	a	X
cana-4456	262	14	:	:	PUNCT
cana-4456	262	15	specify	specify	VERB
cana-4456	262	16	the	the	DET
cana-4456	262	17	computational	computational	ADJ
cana-4456	262	18	domain	domain	NOUN
cana-4456	262	19	𝜴.	𝜴.	PROPN
cana-4456	262	20	b	b	PROPN
cana-4456	262	21	:	:	PUNCT
cana-4456	262	22	generate	generate	VERB
cana-4456	262	23	a	a	DET
cana-4456	262	24	set	set	NOUN
cana-4456	262	25	of	of	ADP
cana-4456	262	26	collocation	collocation	NOUN
cana-4456	262	27	points	point	NOUN
cana-4456	262	28	(	(	PUNCT
cana-4456	262	29	nodes	node	NOUN
cana-4456	262	30	)	)	PUNCT
cana-4456	262	31	{	{	PUNCT
cana-4456	262	32	𝒙𝒊}𝒊=𝟏	𝒙𝒊}𝒊=𝟏	NOUN
cana-4456	262	33	𝑵	𝑵	PROPN
cana-4456	262	34	in	in	ADP
cana-4456	262	35	the	the	DET
cana-4456	262	36	domain	domain	NOUN
cana-4456	262	37	𝜴.	𝜴.	PROPN
cana-4456	262	38	c	c	PROPN
cana-4456	262	39	:	:	PUNCT
cana-4456	262	40	divide	divide	VERB
cana-4456	262	41	the	the	DET
cana-4456	262	42	domain	domain	NOUN
cana-4456	262	43	into	into	ADP
cana-4456	262	44	overlapping	overlap	VERB
cana-4456	262	45	subdomains	subdomain	NOUN
cana-4456	262	46	{	{	PUNCT
cana-4456	262	47	ω𝒊}𝒊=𝟏	ω𝒊}𝒊=𝟏	NOUN
cana-4456	262	48	𝒏𝒑	𝒏𝒑	ADP
cana-4456	262	49	such	such	ADJ
cana-4456	262	50	that	that	SCONJ
cana-4456	262	51	𝜴	𝜴	PROPN
cana-4456	262	52	⊆	⊆	NUM
cana-4456	262	53	⋃	⋃	ADP
cana-4456	262	54	𝜴𝒊	𝜴𝒊	PROPN
cana-4456	262	55	𝒏𝒑	𝒏𝒑	ADP
cana-4456	262	56	𝒊=𝟏	𝒊=𝟏	NOUN
cana-4456	262	57	.	.	PUNCT
cana-4456	263	1	d	d	X
cana-4456	263	2	:	:	PUNCT
cana-4456	263	3	for	for	SCONJ
cana-4456	263	4	each	each	DET
cana-4456	263	5	subdomain	subdomain	NOUN
cana-4456	263	6	ω𝒊	ω𝒊	PART
cana-4456	263	7	,	,	PUNCT
cana-4456	263	8	select	select	VERB
cana-4456	263	9	a	a	DET
cana-4456	263	10	set	set	NOUN
cana-4456	263	11	of	of	ADP
cana-4456	263	12	nodes	node	NOUN
cana-4456	263	13	{	{	PUNCT
cana-4456	263	14	𝒙𝒋	𝒙𝒋	NOUN
cana-4456	263	15	𝒊}𝒋=𝟏	𝒊}𝒋=𝟏	PROPN
cana-4456	263	16	𝒏𝒊	𝒏𝒊	ADP
cana-4456	263	17	within	within	ADP
cana-4456	263	18	ω𝒊	ω𝒊	PRON
cana-4456	263	19	.	.	PUNCT
cana-4456	264	1	e	e	X
cana-4456	264	2	:	:	PUNCT
cana-4456	264	3	for	for	ADP
cana-4456	264	4	each	each	DET
cana-4456	264	5	point	point	NOUN
cana-4456	264	6	{	{	PUNCT
cana-4456	264	7	𝒙𝒋	𝒙𝒋	PROPN
cana-4456	264	8	𝒊}𝒋=𝟏	𝒊}𝒋=𝟏	PROPN
cana-4456	264	9	𝒏𝒊	𝒏𝒊	ADP
cana-4456	264	10	,	,	PUNCT
cana-4456	264	11	define	define	VERB
cana-4456	264	12	the	the	DET
cana-4456	264	13	partition	partition	NOUN
cana-4456	264	14	of	of	ADP
cana-4456	264	15	unity	unity	NOUN
cana-4456	264	16	using	use	VERB
cana-4456	264	17	shepard	shepard	NOUN
cana-4456	264	18	’s	’s	PART
cana-4456	264	19	method	method	NOUN
cana-4456	264	20	(	(	PUNCT
cana-4456	264	21	32	32	NUM
cana-4456	264	22	)	)	PUNCT
cana-4456	264	23	.	.	PUNCT
cana-4456	265	1	f	f	X
cana-4456	265	2	:	:	PUNCT
cana-4456	265	3	construct	construct	VERB
cana-4456	265	4	the	the	DET
cana-4456	265	5	differentiation	differentiation	NOUN
cana-4456	265	6	matrices	matrix	NOUN
cana-4456	265	7	𝑫𝒙	𝑫𝒙	PROPN
cana-4456	265	8	̅̅	̅̅	NOUN
cana-4456	265	9	̅̅	̅̅	PROPN
cana-4456	265	10	and	and	CCONJ
cana-4456	265	11	𝑫𝒙𝒙	𝑫𝒙𝒙	PROPN
cana-4456	265	12	̅̅	̅̅	PROPN
cana-4456	265	13	̅̅	̅̅	PROPN
cana-4456	265	14	̅̅	̅̅	PROPN
cana-4456	265	15	using	use	VERB
cana-4456	265	16	the	the	DET
cana-4456	265	17	differentiation	differentiation	NOUN
cana-4456	265	18	weights	weight	NOUN
cana-4456	265	19	obtained	obtain	VERB
cana-4456	265	20	from	from	ADP
cana-4456	265	21	the	the	DET
cana-4456	265	22	qr	qr	NOUN
cana-4456	265	23	factorization	factorization	NOUN
cana-4456	265	24	of	of	ADP
cana-4456	265	25	the	the	DET
cana-4456	265	26	local	local	ADJ
cana-4456	265	27	rbf	rbf	PROPN
cana-4456	265	28	-	-	PUNCT
cana-4456	265	29	pum	pum	PROPN
cana-4456	265	30	systems	system	NOUN
cana-4456	265	31	,	,	PUNCT
cana-4456	265	32	specifically	specifically	ADV
cana-4456	265	33	using	use	VERB
cana-4456	265	34	gaussian	gaussian	ADJ
cana-4456	265	35	rbfs	rbfs	NOUN
cana-4456	265	36	[	[	X
cana-4456	265	37	40	40	NUM
cana-4456	265	38	]	]	PUNCT
cana-4456	265	39	.	.	PUNCT
cana-4456	266	1	communications	communication	NOUN
cana-4456	266	2	on	on	ADP
cana-4456	266	3	applied	apply	VERB
cana-4456	266	4	nonlinear	nonlinear	ADJ
cana-4456	266	5	analysis	analysis	NOUN
cana-4456	266	6	issn	issn	NOUN
cana-4456	266	7	:	:	PUNCT
cana-4456	266	8	1074	1074	NUM
cana-4456	266	9	-	-	PUNCT
cana-4456	266	10	133x	133x	NUM
cana-4456	266	11	vol	vol	NOUN
cana-4456	266	12	32	32	NUM
cana-4456	266	13	no	no	NOUN
cana-4456	266	14	.	.	PUNCT
cana-4456	267	1	9s	9s	NUM
cana-4456	267	2	(	(	PUNCT
cana-4456	267	3	2025	2025	NUM
cana-4456	267	4	)	)	PUNCT
cana-4456	267	5	2180	2180	NUM
cana-4456	267	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	267	7	3	3	NUM
cana-4456	267	8	:	:	PUNCT
cana-4456	267	9	make	make	VERB
cana-4456	267	10	the	the	DET
cana-4456	267	11	right	right	ADJ
cana-4456	267	12	hand	hand	NOUN
cana-4456	267	13	side	side	NOUN
cana-4456	267	14	of	of	ADP
cana-4456	267	15	ode	ode	PROPN
cana-4456	267	16	obtained	obtain	VERB
cana-4456	267	17	:	:	PUNCT
cana-4456	267	18	𝑹𝑯𝑺𝒉	𝑹𝑯𝑺𝒉	PROPN
cana-4456	267	19	=	=	SYM
cana-4456	267	20	@(𝒉	@(𝒉	PROPN
cana-4456	267	21	,	,	PUNCT
cana-4456	267	22	𝒒	𝒒	PROPN
cana-4456	267	23	)	)	PUNCT
cana-4456	267	24	−	−	PROPN
cana-4456	268	1	𝑫𝒙	𝑫𝒙	PROPN
cana-4456	268	2	̅̅	̅̅	PROPN
cana-4456	268	3	̅̅	̅̅	PROPN
cana-4456	268	4	𝒒	𝒒	PROPN
cana-4456	269	1	+	+	CCONJ
cana-4456	269	2	𝝁𝑫𝒙𝒙	𝝁𝑫𝒙𝒙	PROPN
cana-4456	269	3	̅̅	̅̅	PROPN
cana-4456	269	4	̅̅	̅̅	PROPN
cana-4456	269	5	̅̅	̅̅	PROPN
cana-4456	269	6	𝒉	𝒉	PROPN
cana-4456	269	7	(	(	PUNCT
cana-4456	269	8	46.a	46.a	NUM
cana-4456	269	9	)	)	PUNCT
cana-4456	269	10	𝑹𝑯𝑺𝒒	𝑹𝑯𝑺𝒒	PROPN
cana-4456	269	11	=	=	SYM
cana-4456	269	12	@(𝒉	@(𝒉	PROPN
cana-4456	269	13	,	,	PUNCT
cana-4456	269	14	𝒒	𝒒	PROPN
cana-4456	269	15	)	)	PUNCT
cana-4456	269	16	−	−	PROPN
cana-4456	270	1	𝑫𝒙	𝑫𝒙	PROPN
cana-4456	270	2	̅̅	̅̅	PROPN
cana-4456	270	3	̅̅	̅̅	PROPN
cana-4456	270	4	(	(	PUNCT
cana-4456	270	5	𝒒𝟐	𝒒𝟐	AUX
cana-4456	270	6	𝒉	𝒉	VERB
cana-4456	270	7	+	+	CCONJ
cana-4456	270	8	𝟏	𝟏	NUM
cana-4456	270	9	𝟐	𝟐	NUM
cana-4456	270	10	𝒈𝒉𝟐	𝒈𝒉𝟐	PROPN
cana-4456	270	11	)	)	PUNCT
cana-4456	270	12	−	−	NOUN
cana-4456	270	13	𝒈(𝒉.	𝒈(𝒉.	X
cana-4456	271	1	𝑫𝒙	𝑫𝒙	PROPN
cana-4456	271	2	̅̅	̅̅	PROPN
cana-4456	271	3	̅̅	̅̅	PROPN
cana-4456	271	4	𝒃	𝒃	NOUN
cana-4456	271	5	)	)	PUNCT
cana-4456	272	1	+	+	CCONJ
cana-4456	272	2	𝝁𝑫𝒙𝒙	𝝁𝑫𝒙𝒙	PROPN
cana-4456	272	3	̅̅	̅̅	PROPN
cana-4456	272	4	̅̅	̅̅	PROPN
cana-4456	272	5	̅̅	̅̅	PROPN
cana-4456	272	6	𝒒	𝒒	X
cana-4456	272	7	(	(	PUNCT
cana-4456	272	8	46.b	46.b	NUM
cana-4456	272	9	)	)	PUNCT
cana-4456	272	10	4	4	NUM
cana-4456	272	11	:	:	PUNCT
cana-4456	272	12	enter	enter	VERB
cana-4456	272	13	initial	initial	ADJ
cana-4456	272	14	condition	condition	NOUN
cana-4456	272	15	.	.	PUNCT
cana-4456	273	1	5	5	NUM
cana-4456	273	2	:	:	PUNCT
cana-4456	273	3	for	for	ADP
cana-4456	273	4	𝒋	𝒋	NOUN
cana-4456	273	5	=	=	SYM
cana-4456	273	6	𝟏	𝟏	NUM
cana-4456	273	7	:	:	PUNCT
cana-4456	273	8	𝒏𝒕	𝒏𝒕	ADP
cana-4456	273	9	do	do	VERB
cana-4456	273	10	6	6	NUM
cana-4456	273	11	:	:	PUNCT
cana-4456	273	12	𝒕	𝒕	PROPN
cana-4456	273	13	=	=	PUNCT
cana-4456	273	14	𝒋.	𝒋.	NOUN
cana-4456	273	15	𝒅𝒕	𝒅𝒕	ADJ
cana-4456	273	16	7	7	NUM
cana-4456	273	17	:	:	PUNCT
cana-4456	273	18	𝒌𝟏	𝒌𝟏	NOUN
cana-4456	273	19	=	=	SYM
cana-4456	273	20	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	273	21	𝑹𝑯𝑺𝒉(𝒉	𝑹𝑯𝑺𝒉(𝒉	ADJ
cana-4456	273	22	,	,	PUNCT
cana-4456	273	23	𝒒	𝒒	NOUN
cana-4456	273	24	)	)	PUNCT
cana-4456	273	25	𝒌𝟏	𝒌𝟏	NOUN
cana-4456	273	26	=	=	SYM
cana-4456	273	27	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	273	28	𝑹𝑯𝑺𝒒(𝒉	𝑹𝑯𝑺𝒒(𝒉	NOUN
cana-4456	273	29	,	,	PUNCT
cana-4456	273	30	𝒒	𝒒	NOUN
cana-4456	273	31	)	)	PUNCT
cana-4456	273	32	8	8	NUM
cana-4456	273	33	:	:	PUNCT
cana-4456	273	34	𝒌𝟐	𝒌𝟐	NOUN
cana-4456	273	35	=	=	PUNCT
cana-4456	273	36	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	273	37	𝑹𝑯𝑺𝒉(𝒉	𝑹𝑯𝑺𝒉(𝒉	NOUN
cana-4456	273	38	+	+	CCONJ
cana-4456	273	39	𝒌𝟏	𝒌𝟏	PROPN
cana-4456	273	40	𝟐	𝟐	NUM
cana-4456	273	41	,	,	PUNCT
cana-4456	273	42	𝒒	𝒒	X
cana-4456	273	43	)	)	PUNCT
cana-4456	273	44	𝒌𝟐	𝒌𝟐	NOUN
cana-4456	273	45	=	=	SYM
cana-4456	273	46	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	273	47	𝑹𝑯𝑺𝒒(𝒉	𝑹𝑯𝑺𝒒(𝒉	NOUN
cana-4456	273	48	,	,	PUNCT
cana-4456	273	49	𝒒	𝒒	X
cana-4456	274	1	+	+	NUM
cana-4456	274	2	𝒌𝟏	𝒌𝟏	NOUN
cana-4456	274	3	𝟐	𝟐	NUM
cana-4456	274	4	)	)	PUNCT
cana-4456	274	5	9	9	NUM
cana-4456	274	6	:	:	PUNCT
cana-4456	274	7	𝒌𝟑	𝒌𝟑	NOUN
cana-4456	274	8	=	=	SYM
cana-4456	274	9	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	274	10	𝑹𝑯𝑺𝒉(𝒉	𝑹𝑯𝑺𝒉(𝒉	NOUN
cana-4456	274	11	+	+	CCONJ
cana-4456	274	12	𝒌𝟐	𝒌𝟐	PROPN
cana-4456	274	13	𝟐	𝟐	NUM
cana-4456	274	14	,	,	PUNCT
cana-4456	274	15	𝒒	𝒒	NOUN
cana-4456	274	16	)	)	PUNCT
cana-4456	274	17	𝒌𝟑	𝒌𝟑	NOUN
cana-4456	274	18	=	=	SYM
cana-4456	274	19	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	274	20	𝑹𝑯𝑺𝒒(𝒉	𝑹𝑯𝑺𝒒(𝒉	NOUN
cana-4456	274	21	,	,	PUNCT
cana-4456	274	22	𝒒	𝒒	PROPN
cana-4456	274	23	+	+	CCONJ
cana-4456	274	24	𝒌𝟐	𝒌𝟐	NOUN
cana-4456	274	25	𝟐	𝟐	NUM
cana-4456	274	26	)	)	PUNCT
cana-4456	274	27	10	10	NUM
cana-4456	274	28	:	:	PUNCT
cana-4456	274	29	𝒌𝟒	𝒌𝟒	ADJ
cana-4456	274	30	=	=	PUNCT
cana-4456	274	31	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	274	32	𝑹𝑯𝑺𝒉(𝒉	𝑹𝑯𝑺𝒉(𝒉	NOUN
cana-4456	274	33	+	+	CCONJ
cana-4456	274	34	𝒌𝟑	𝒌𝟑	NOUN
cana-4456	274	35	,	,	PUNCT
cana-4456	274	36	𝒒	𝒒	NOUN
cana-4456	274	37	)	)	PUNCT
cana-4456	274	38	𝒌𝟒	𝒌𝟒	ADJ
cana-4456	274	39	=	=	PUNCT
cana-4456	274	40	𝒅𝒕.	𝒅𝒕.	NOUN
cana-4456	274	41	𝑹𝑯𝑺𝒒(𝒉	𝑹𝑯𝑺𝒒(𝒉	NOUN
cana-4456	274	42	,	,	PUNCT
cana-4456	274	43	𝒒	𝒒	X
cana-4456	274	44	+	+	NUM
cana-4456	274	45	𝒌𝟑	𝒌𝟑	NOUN
cana-4456	274	46	)	)	PUNCT
cana-4456	274	47	11	11	NUM
cana-4456	274	48	:	:	PUNCT
cana-4456	274	49	𝒉	𝒉	X
cana-4456	274	50	=	=	SYM
cana-4456	274	51	𝒉	𝒉	PROPN
cana-4456	274	52	+	+	CCONJ
cana-4456	274	53	𝟏	𝟏	NUM
cana-4456	274	54	𝟔	𝟔	NUM
cana-4456	274	55	(	(	PUNCT
cana-4456	274	56	𝒌𝟏	𝒌𝟏	NOUN
cana-4456	274	57	+	+	CCONJ
cana-4456	274	58	𝟐𝒌𝟐	𝟐𝒌𝟐	PUNCT
cana-4456	274	59	+	+	NUM
cana-4456	274	60	𝟐𝒌𝟑	𝟐𝒌𝟑	PUNCT
cana-4456	274	61	+	+	CCONJ
cana-4456	274	62	𝒌𝟒	𝒌𝟒	ADJ
cana-4456	274	63	)	)	PUNCT
cana-4456	274	64	𝒒	𝒒	PROPN
cana-4456	274	65	=	=	SYM
cana-4456	274	66	𝒒	𝒒	PROPN
cana-4456	274	67	+	+	NUM
cana-4456	274	68	𝟏	𝟏	NUM
cana-4456	274	69	𝟔	𝟔	NUM
cana-4456	274	70	(	(	PUNCT
cana-4456	274	71	𝒌𝟏	𝒌𝟏	NOUN
cana-4456	274	72	+	+	CCONJ
cana-4456	274	73	𝟐𝒌𝟐	𝟐𝒌𝟐	PUNCT
cana-4456	274	74	+	+	NUM
cana-4456	274	75	𝟐𝒌𝟑	𝟐𝒌𝟑	PUNCT
cana-4456	274	76	+	+	CCONJ
cana-4456	274	77	𝒌𝟒	𝒌𝟒	ADJ
cana-4456	274	78	)	)	PUNCT
cana-4456	274	79	12	12	NUM
cana-4456	274	80	:	:	PUNCT
cana-4456	274	81	apply	apply	VERB
cana-4456	274	82	boundary	boundary	ADJ
cana-4456	274	83	condition	condition	NOUN
cana-4456	274	84	.	.	PUNCT
cana-4456	275	1	13	13	NUM
cana-4456	275	2	:	:	PUNCT
cana-4456	275	3	end	end	NOUN
cana-4456	275	4	14	14	NUM
cana-4456	275	5	:	:	PUNCT
cana-4456	275	6	compute	compute	NOUN
cana-4456	275	7	error	error	NOUN
cana-4456	275	8	.	.	PUNCT
cana-4456	276	1	3.6	3.6	NUM
cana-4456	276	2	friction	friction	NOUN
cana-4456	276	3	source	source	NOUN
cana-4456	276	4	term	term	NOUN
cana-4456	276	5	discretization	discretization	VERB
cana-4456	276	6	the	the	DET
cana-4456	276	7	non	non	ADJ
cana-4456	276	8	-	-	ADJ
cana-4456	276	9	linear	linear	ADJ
cana-4456	276	10	nature	nature	NOUN
cana-4456	276	11	of	of	ADP
cana-4456	276	12	the	the	DET
cana-4456	276	13	friction	friction	NOUN
cana-4456	276	14	terms	term	NOUN
cana-4456	276	15	(	(	PUNCT
cana-4456	276	16	2	2	NUM
cana-4456	276	17	)	)	PUNCT
cana-4456	276	18	,	,	PUNCT
cana-4456	276	19	(	(	PUNCT
cana-4456	276	20	3	3	X
cana-4456	276	21	)	)	PUNCT
cana-4456	276	22	and	and	CCONJ
cana-4456	276	23	their	their	PRON
cana-4456	276	24	interactions	interaction	NOUN
cana-4456	276	25	with	with	ADP
cana-4456	276	26	other	other	ADJ
cana-4456	276	27	source	source	NOUN
cana-4456	276	28	terms	term	NOUN
cana-4456	276	29	remains	remain	VERB
cana-4456	276	30	to	to	PART
cana-4456	276	31	be	be	AUX
cana-4456	276	32	a	a	DET
cana-4456	276	33	challenge	challenge	NOUN
cana-4456	276	34	for	for	ADP
cana-4456	276	35	developing	develop	VERB
cana-4456	276	36	numerically	numerically	ADV
cana-4456	276	37	accurate	accurate	ADJ
cana-4456	276	38	and	and	CCONJ
cana-4456	276	39	stable	stable	ADJ
cana-4456	276	40	schemes	scheme	NOUN
cana-4456	276	41	to	to	PART
cana-4456	276	42	solve	solve	VERB
cana-4456	276	43	the	the	DET
cana-4456	276	44	swes	swe	NOUN
cana-4456	276	45	for	for	ADP
cana-4456	276	46	simulating	simulate	VERB
cana-4456	276	47	very	very	ADV
cana-4456	276	48	shallow	shallow	ADJ
cana-4456	276	49	flows	flow	NOUN
cana-4456	276	50	as	as	SCONJ
cana-4456	276	51	found	find	VERB
cana-4456	276	52	in	in	ADP
cana-4456	276	53	the	the	DET
cana-4456	276	54	applications	application	NOUN
cana-4456	276	55	involving	involve	VERB
cana-4456	276	56	overland	overland	NOUN
cana-4456	276	57	flows	flow	NOUN
cana-4456	276	58	and	and	CCONJ
cana-4456	276	59	wet	wet	ADJ
cana-4456	276	60	/	/	SYM
cana-4456	276	61	dry	dry	ADJ
cana-4456	276	62	fronts	front	NOUN
cana-4456	276	63	.	.	PUNCT
cana-4456	277	1	indeed	indeed	ADV
cana-4456	277	2	,	,	PUNCT
cana-4456	277	3	the	the	DET
cana-4456	277	4	friction	friction	NOUN
cana-4456	277	5	term	term	NOUN
cana-4456	277	6	actually	actually	ADV
cana-4456	277	7	dominates	dominate	VERB
cana-4456	277	8	the	the	DET
cana-4456	277	9	stability	stability	NOUN
cana-4456	277	10	of	of	ADP
cana-4456	277	11	a	a	DET
cana-4456	277	12	numerical	numerical	ADJ
cana-4456	277	13	scheme	scheme	NOUN
cana-4456	277	14	.	.	PUNCT
cana-4456	278	1	in	in	ADP
cana-4456	278	2	particular	particular	ADJ
cana-4456	278	3	,	,	PUNCT
cana-4456	278	4	when	when	SCONJ
cana-4456	278	5	the	the	DET
cana-4456	278	6	water	water	NOUN
cana-4456	278	7	depth	depth	NOUN
cana-4456	278	8	becomes	become	VERB
cana-4456	278	9	very	very	ADV
cana-4456	278	10	small	small	ADJ
cana-4456	278	11	,	,	PUNCT
cana-4456	278	12	the	the	DET
cana-4456	278	13	friction	friction	NOUN
cana-4456	278	14	formulations	formulation	NOUN
cana-4456	278	15	may	may	AUX
cana-4456	278	16	lead	lead	VERB
cana-4456	278	17	to	to	ADP
cana-4456	278	18	an	an	DET
cana-4456	278	19	exaggerated	exaggerated	ADJ
cana-4456	278	20	force	force	NOUN
cana-4456	278	21	that	that	PRON
cana-4456	278	22	can	can	AUX
cana-4456	278	23	even	even	ADV
cana-4456	278	24	reverse	reverse	VERB
cana-4456	278	25	the	the	DET
cana-4456	278	26	flow	flow	NOUN
cana-4456	278	27	,	,	PUNCT
cana-4456	278	28	which	which	PRON
cana-4456	278	29	is	be	AUX
cana-4456	278	30	obviously	obviously	ADV
cana-4456	278	31	physically	physically	ADV
cana-4456	278	32	incorrect	incorrect	ADJ
cana-4456	278	33	[	[	X
cana-4456	278	34	43	43	NUM
cana-4456	278	35	]	]	PUNCT
cana-4456	278	36	.	.	PUNCT
cana-4456	279	1	to	to	PART
cana-4456	279	2	deal	deal	VERB
cana-4456	279	3	with	with	ADP
cana-4456	279	4	this	this	DET
cana-4456	279	5	problem	problem	NOUN
cana-4456	279	6	,	,	PUNCT
cana-4456	279	7	at	at	ADP
cana-4456	279	8	the	the	DET
cana-4456	279	9	beginning	beginning	NOUN
cana-4456	279	10	of	of	ADP
cana-4456	279	11	each	each	DET
cana-4456	279	12	step	step	NOUN
cana-4456	279	13	of	of	ADP
cana-4456	279	14	the	the	DET
cana-4456	279	15	runge	runge	NOUN
cana-4456	279	16	-	-	PUNCT
cana-4456	279	17	kutta	kutta	NOUN
cana-4456	279	18	scheme	scheme	NOUN
cana-4456	279	19	,	,	PUNCT
cana-4456	279	20	the	the	DET
cana-4456	279	21	friction	friction	NOUN
cana-4456	279	22	effect	effect	NOUN
cana-4456	279	23	is	be	AUX
cana-4456	279	24	evaluated	evaluate	VERB
cana-4456	279	25	and	and	CCONJ
cana-4456	279	26	used	use	VERB
cana-4456	279	27	implicitly	implicitly	ADV
cana-4456	279	28	by	by	ADP
cana-4456	279	29	the	the	DET
cana-4456	279	30	splitting	splitting	NOUN
cana-4456	279	31	method	method	NOUN
cana-4456	279	32	described	describe	VERB
cana-4456	279	33	by	by	ADP
cana-4456	279	34	[	[	X
cana-4456	279	35	27	27	NUM
cana-4456	279	36	,	,	PUNCT
cana-4456	279	37	43	43	NUM
cana-4456	279	38	]	]	PUNCT
cana-4456	279	39	,	,	PUNCT
cana-4456	279	40	and	and	CCONJ
cana-4456	279	41	it	it	PRON
cana-4456	279	42	is	be	AUX
cana-4456	279	43	equivalent	equivalent	ADJ
cana-4456	279	44	to	to	PART
cana-4456	279	45	solve	solve	VERB
cana-4456	279	46	the	the	DET
cana-4456	279	47	following	follow	VERB
cana-4456	279	48	ordinary	ordinary	ADJ
cana-4456	279	49	differential	differential	ADJ
cana-4456	279	50	equations	equation	NOUN
cana-4456	279	51	𝜕𝑞	𝜕𝑞	VERB
cana-4456	279	52	𝜕𝑡	𝜕𝑡	NOUN
cana-4456	279	53	=	=	PUNCT
cana-4456	280	1	𝑆𝑓	𝑆𝑓	NOUN
cana-4456	280	2	.	.	PUNCT
cana-4456	281	1	(	(	PUNCT
cana-4456	281	2	47	47	NUM
cana-4456	281	3	)	)	PUNCT
cana-4456	281	4	since	since	SCONJ
cana-4456	281	5	the	the	DET
cana-4456	281	6	friction	friction	NOUN
cana-4456	281	7	term	term	NOUN
cana-4456	281	8	is	be	AUX
cana-4456	281	9	only	only	ADV
cana-4456	281	10	involved	involve	VERB
cana-4456	281	11	in	in	ADP
cana-4456	281	12	the	the	DET
cana-4456	281	13	momentum	momentum	NOUN
cana-4456	281	14	equation	equation	NOUN
cana-4456	281	15	,	,	PUNCT
cana-4456	281	16	only	only	ADV
cana-4456	281	17	the	the	DET
cana-4456	281	18	flow	flow	NOUN
cana-4456	281	19	rates	rate	NOUN
cana-4456	281	20	need	need	VERB
cana-4456	281	21	to	to	PART
cana-4456	281	22	be	be	AUX
cana-4456	281	23	evaluated	evaluate	VERB
cana-4456	281	24	.	.	PUNCT
cana-4456	282	1	the	the	DET
cana-4456	282	2	above	above	ADJ
cana-4456	282	3	equation	equation	NOUN
cana-4456	282	4	is	be	AUX
cana-4456	282	5	then	then	ADV
cana-4456	282	6	discretized	discretize	VERB
cana-4456	282	7	by	by	ADP
cana-4456	282	8	a	a	DET
cana-4456	282	9	full	full	ADJ
cana-4456	282	10	implicit	implicit	ADJ
cana-4456	282	11	method	method	NOUN
cana-4456	282	12	as	as	ADP
cana-4456	282	13	:	:	PUNCT
cana-4456	282	14	𝑞𝑛+1−𝑞𝑛	𝑞𝑛+1−𝑞𝑛	PROPN
cana-4456	282	15	∆𝑡	∆𝑡	PROPN
cana-4456	283	1	=	=	PUNCT
cana-4456	284	1	𝑆𝑓	𝑆𝑓	PROPN
cana-4456	284	2	𝑛+1	𝑛+1	PROPN
cana-4456	284	3	,	,	PUNCT
cana-4456	284	4	(	(	PUNCT
cana-4456	284	5	48	48	NUM
cana-4456	284	6	)	)	PUNCT
cana-4456	284	7	communications	communication	NOUN
cana-4456	284	8	on	on	ADP
cana-4456	284	9	applied	apply	VERB
cana-4456	284	10	nonlinear	nonlinear	ADJ
cana-4456	284	11	analysis	analysis	NOUN
cana-4456	284	12	issn	issn	NOUN
cana-4456	284	13	:	:	PUNCT
cana-4456	284	14	1074	1074	NUM
cana-4456	284	15	-	-	PUNCT
cana-4456	284	16	133x	133x	NUM
cana-4456	284	17	vol	vol	NOUN
cana-4456	284	18	32	32	NUM
cana-4456	284	19	no	no	NOUN
cana-4456	284	20	.	.	PUNCT
cana-4456	285	1	9s	9s	NUM
cana-4456	285	2	(	(	PUNCT
cana-4456	285	3	2025	2025	NUM
cana-4456	285	4	)	)	PUNCT
cana-4456	285	5	2181	2181	NUM
cana-4456	285	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	285	7	where	where	SCONJ
cana-4456	285	8	the	the	DET
cana-4456	285	9	friction	friction	NOUN
cana-4456	285	10	term	term	NOUN
cana-4456	285	11	𝑆𝑓	𝑆𝑓	PROPN
cana-4456	285	12	𝑛+1	𝑛+1	PROPN
cana-4456	285	13	may	may	AUX
cana-4456	285	14	be	be	AUX
cana-4456	285	15	expressed	express	VERB
cana-4456	285	16	using	use	VERB
cana-4456	285	17	a	a	DET
cana-4456	285	18	taylor	taylor	PROPN
cana-4456	285	19	series	series	NOUN
cana-4456	285	20	as	as	ADP
cana-4456	285	21	𝑆𝑓	𝑆𝑓	PROPN
cana-4456	285	22	𝑛+1	𝑛+1	X
cana-4456	285	23	=	=	PUNCT
cana-4456	285	24	𝑆𝑓	𝑆𝑓	PROPN
cana-4456	285	25	𝑛	𝑛	PROPN
cana-4456	285	26	+	+	CCONJ
cana-4456	285	27	(	(	PUNCT
cana-4456	285	28	𝜕𝑆𝑓	𝜕𝑆𝑓	ADV
cana-4456	285	29	𝜕𝑞	𝜕𝑞	PROPN
cana-4456	285	30	)	)	PUNCT
cana-4456	285	31	𝑛	𝑛	PRON
cana-4456	285	32	∆𝑞	∆𝑞	PROPN
cana-4456	285	33	+	+	CCONJ
cana-4456	285	34	𝑜(∆𝑞2	𝑜(∆𝑞2	NOUN
cana-4456	285	35	)	)	PUNCT
cana-4456	285	36	,	,	PUNCT
cana-4456	285	37	(	(	PUNCT
cana-4456	285	38	49	49	NUM
cana-4456	285	39	)	)	PUNCT
cana-4456	285	40	where	where	SCONJ
cana-4456	285	41	∆𝑞	∆𝑞	PROPN
cana-4456	285	42	=	=	SYM
cana-4456	285	43	𝑞𝑛+1	𝑞𝑛+1	PROPN
cana-4456	285	44	−	−	PROPN
cana-4456	285	45	𝑞𝑛.	𝑞𝑛.	PROPN
cana-4456	285	46	ignoring	ignore	VERB
cana-4456	285	47	the	the	DET
cana-4456	285	48	higher	high	ADJ
cana-4456	285	49	-	-	PUNCT
cana-4456	285	50	order	order	NOUN
cana-4456	285	51	terms	term	NOUN
cana-4456	285	52	and	and	CCONJ
cana-4456	285	53	substituting	substitute	VERB
cana-4456	285	54	the	the	DET
cana-4456	285	55	above	above	ADJ
cana-4456	285	56	equation	equation	NOUN
cana-4456	285	57	into	into	ADP
cana-4456	285	58	(	(	PUNCT
cana-4456	285	59	48	48	NUM
cana-4456	285	60	)	)	PUNCT
cana-4456	285	61	lead	lead	NOUN
cana-4456	285	62	to	to	ADP
cana-4456	285	63	the	the	DET
cana-4456	285	64	following	follow	VERB
cana-4456	285	65	formula	formula	NOUN
cana-4456	285	66	for	for	ADP
cana-4456	285	67	updating	update	VERB
cana-4456	285	68	water	water	NOUN
cana-4456	285	69	discharge	discharge	NOUN
cana-4456	285	70	𝑞	𝑞	NOUN
cana-4456	285	71	at	at	ADP
cana-4456	285	72	the	the	DET
cana-4456	285	73	new	new	ADJ
cana-4456	285	74	time	time	NOUN
cana-4456	285	75	step	step	NOUN
cana-4456	285	76	:	:	PUNCT
cana-4456	285	77	𝑞𝑛+1	𝑞𝑛+1	PROPN
cana-4456	285	78	=	=	PUNCT
cana-4456	285	79	𝑞𝑛	𝑞𝑛	PROPN
cana-4456	285	80	+	+	PROPN
cana-4456	285	81	∆𝑡	∆𝑡	PROPN
cana-4456	286	1	𝑆𝑓	𝑆𝑓	NOUN
cana-4456	286	2	𝑛	𝑛	ADP
cana-4456	286	3	1−∆𝑡	1−∆𝑡	NUM
cana-4456	286	4	(	(	PUNCT
cana-4456	286	5	𝜕𝑆𝑓	𝜕𝑆𝑓	ADV
cana-4456	286	6	𝜕𝑞	𝜕𝑞	NOUN
cana-4456	286	7	)	)	PUNCT
cana-4456	286	8	𝑛	𝑛	PROPN
cana-4456	286	9	(	(	PUNCT
cana-4456	286	10	50	50	NUM
cana-4456	286	11	)	)	PUNCT
cana-4456	286	12	=	=	PUNCT
cana-4456	286	13	𝑞𝑛	𝑞𝑛	PROPN
cana-4456	286	14	+	+	NOUN
cana-4456	286	15	∆𝑡	∆𝑡	PROPN
cana-4456	286	16	(	(	PUNCT
cana-4456	286	17	𝑆𝑓	𝑆𝑓	NOUN
cana-4456	286	18	𝐷	𝐷	PROPN
cana-4456	286	19	)	)	PUNCT
cana-4456	286	20	𝑛	𝑛	PROPN
cana-4456	286	21	=	=	PUNCT
cana-4456	286	22	𝑞𝑛	𝑞𝑛	PROPN
cana-4456	286	23	+	+	CCONJ
cana-4456	286	24	∆𝑡𝐹	∆𝑡𝐹	PROPN
cana-4456	286	25	,	,	PUNCT
cana-4456	286	26	(	(	PUNCT
cana-4456	286	27	51	51	NUM
cana-4456	286	28	)	)	PUNCT
cana-4456	286	29	where	where	SCONJ
cana-4456	286	30	𝐷	𝐷	NOUN
cana-4456	286	31	=	=	PUNCT
cana-4456	286	32	{	{	PUNCT
cana-4456	286	33	1	1	NUM
cana-4456	286	34	+	+	NUM
cana-4456	286	35	2∆𝑡	2∆𝑡	NOUN
cana-4456	286	36	(	(	PUNCT
cana-4456	286	37	𝑔𝑛2|𝑢|	𝑔𝑛2|𝑢|	NUM
cana-4456	286	38	ℎ	ℎ	PROPN
cana-4456	286	39	4	4	NUM
cana-4456	286	40	3	3	NUM
cana-4456	286	41	)	)	PUNCT
cana-4456	286	42	1	1	NUM
cana-4456	286	43	+	+	NUM
cana-4456	286	44	2∆𝑡	2∆𝑡	NOUN
cana-4456	286	45	(	(	PUNCT
cana-4456	286	46	𝑓|𝑢|	𝑓|𝑢|	NOUN
cana-4456	286	47	8ℎ	8ℎ	NOUN
cana-4456	286	48	)	)	PUNCT
cana-4456	286	49	(	(	PUNCT
cana-4456	286	50	52	52	NUM
cana-4456	286	51	)	)	PUNCT
cana-4456	286	52	𝐷	𝐷	NOUN
cana-4456	286	53	is	be	AUX
cana-4456	286	54	the	the	DET
cana-4456	286	55	coefficient	coefficient	NOUN
cana-4456	286	56	derived	derive	VERB
cana-4456	286	57	for	for	ADP
cana-4456	286	58	a	a	DET
cana-4456	286	59	full	full	ADJ
cana-4456	286	60	implicit	implicit	ADJ
cana-4456	286	61	scheme	scheme	NOUN
cana-4456	286	62	where	where	SCONJ
cana-4456	286	63	the	the	DET
cana-4456	286	64	first	first	ADJ
cana-4456	286	65	line	line	NOUN
cana-4456	286	66	is	be	AUX
cana-4456	286	67	for	for	ADP
cana-4456	286	68	manning	man	VERB
cana-4456	286	69	law	law	NOUN
cana-4456	286	70	and	and	CCONJ
cana-4456	286	71	the	the	DET
cana-4456	286	72	second	second	ADJ
cana-4456	286	73	line	line	NOUN
cana-4456	286	74	is	be	AUX
cana-4456	286	75	for	for	ADP
cana-4456	286	76	darcy	darcy	NOUN
cana-4456	286	77	-	-	PUNCT
cana-4456	286	78	weisbach	weisbach	NOUN
cana-4456	286	79	law	law	NOUN
cana-4456	286	80	and	and	CCONJ
cana-4456	286	81	𝐹	𝐹	PROPN
cana-4456	286	82	is	be	AUX
cana-4456	286	83	the	the	DET
cana-4456	286	84	friction	friction	NOUN
cana-4456	286	85	source	source	NOUN
cana-4456	286	86	term	term	NOUN
cana-4456	286	87	including	include	VERB
cana-4456	286	88	the	the	DET
cana-4456	286	89	implicit	implicit	ADJ
cana-4456	286	90	coefficient	coefficient	NOUN
cana-4456	286	91	.	.	PUNCT
cana-4456	287	1	this	this	DET
cana-4456	287	2	updated	update	VERB
cana-4456	287	3	water	water	NOUN
cana-4456	287	4	discharge	discharge	NOUN
cana-4456	287	5	is	be	AUX
cana-4456	287	6	used	use	VERB
cana-4456	287	7	as	as	ADP
cana-4456	287	8	an	an	DET
cana-4456	287	9	initial	initial	ADJ
cana-4456	287	10	condition	condition	NOUN
cana-4456	287	11	for	for	ADP
cana-4456	287	12	the	the	DET
cana-4456	287	13	operators	operator	NOUN
cana-4456	287	14	in	in	ADP
cana-4456	287	15	equation	equation	NOUN
cana-4456	287	16	(	(	PUNCT
cana-4456	287	17	43	43	NUM
cana-4456	287	18	)	)	PUNCT
cana-4456	287	19	.	.	PUNCT
cana-4456	288	1	4	4	X
cana-4456	288	2	.	.	X
cana-4456	288	3	numerical	numerical	ADJ
cana-4456	288	4	results	result	NOUN
cana-4456	288	5	in	in	ADP
cana-4456	288	6	order	order	NOUN
cana-4456	288	7	to	to	PART
cana-4456	288	8	verify	verify	VERB
cana-4456	288	9	the	the	DET
cana-4456	288	10	feasibility	feasibility	NOUN
cana-4456	288	11	and	and	CCONJ
cana-4456	288	12	the	the	DET
cana-4456	288	13	ability	ability	NOUN
cana-4456	288	14	of	of	ADP
cana-4456	288	15	the	the	DET
cana-4456	288	16	proposed	propose	VERB
cana-4456	288	17	methods	method	NOUN
cana-4456	288	18	combined	combine	VERB
cana-4456	288	19	with	with	ADP
cana-4456	288	20	artificial	artificial	ADJ
cana-4456	288	21	viscosity	viscosity	NOUN
cana-4456	288	22	to	to	PART
cana-4456	288	23	solve	solve	VERB
cana-4456	288	24	the	the	DET
cana-4456	288	25	problem	problem	NOUN
cana-4456	288	26	with	with	ADP
cana-4456	288	27	strong	strong	ADJ
cana-4456	288	28	discontinuity	discontinuity	NOUN
cana-4456	288	29	appears	appear	VERB
cana-4456	288	30	in	in	ADP
cana-4456	288	31	swes	swes	NOUN
cana-4456	288	32	,	,	PUNCT
cana-4456	288	33	we	we	PRON
cana-4456	288	34	present	present	VERB
cana-4456	288	35	sets	set	NOUN
cana-4456	288	36	of	of	ADP
cana-4456	288	37	numerical	numerical	ADJ
cana-4456	288	38	tests	test	NOUN
cana-4456	288	39	,	,	PUNCT
cana-4456	288	40	including	include	VERB
cana-4456	288	41	various	various	ADJ
cana-4456	288	42	frictionless	frictionless	ADJ
cana-4456	288	43	steady	steady	ADJ
cana-4456	288	44	-	-	PUNCT
cana-4456	288	45	state	state	NOUN
cana-4456	288	46	solutions	solution	NOUN
cana-4456	288	47	,	,	PUNCT
cana-4456	288	48	transient	transient	ADJ
cana-4456	288	49	solutions	solution	NOUN
cana-4456	288	50	and	and	CCONJ
cana-4456	288	51	steady	steady	ADJ
cana-4456	288	52	-	-	PUNCT
cana-4456	288	53	state	state	NOUN
cana-4456	288	54	solutions	solution	NOUN
cana-4456	288	55	with	with	ADP
cana-4456	288	56	friction	friction	NOUN
cana-4456	288	57	to	to	PART
cana-4456	288	58	address	address	VERB
cana-4456	288	59	different	different	ADJ
cana-4456	288	60	numerical	numerical	ADJ
cana-4456	288	61	challenges	challenge	NOUN
cana-4456	288	62	.	.	PUNCT
cana-4456	289	1	these	these	DET
cana-4456	289	2	problems	problem	NOUN
cana-4456	289	3	are	be	AUX
cana-4456	289	4	widely	widely	ADV
cana-4456	289	5	used	use	VERB
cana-4456	289	6	to	to	PART
cana-4456	289	7	test	test	VERB
cana-4456	289	8	numerical	numerical	ADJ
cana-4456	289	9	algorithms	algorithm	NOUN
cana-4456	289	10	for	for	ADP
cana-4456	289	11	the	the	DET
cana-4456	289	12	swes	swe	NOUN
cana-4456	289	13	(	(	PUNCT
cana-4456	289	14	e.g.	e.g.	ADV
cana-4456	289	15	[	[	X
cana-4456	289	16	44	44	NUM
cana-4456	289	17	,	,	PUNCT
cana-4456	289	18	45	45	NUM
cana-4456	289	19	,	,	PUNCT
cana-4456	289	20	51	51	NUM
cana-4456	289	21	]	]	PUNCT
cana-4456	289	22	)	)	PUNCT
cana-4456	289	23	.	.	PUNCT
cana-4456	290	1	the	the	DET
cana-4456	290	2	goal	goal	NOUN
cana-4456	290	3	of	of	ADP
cana-4456	290	4	the	the	DET
cana-4456	290	5	first	first	PROPN
cana-4456	290	6	numerical	numerical	ADJ
cana-4456	290	7	test	test	NOUN
cana-4456	290	8	is	be	AUX
cana-4456	290	9	to	to	PART
cana-4456	290	10	assess	assess	VERB
cana-4456	290	11	the	the	DET
cana-4456	290	12	ability	ability	NOUN
cana-4456	290	13	of	of	ADP
cana-4456	290	14	the	the	DET
cana-4456	290	15	suggested	suggest	VERB
cana-4456	290	16	schemes	scheme	NOUN
cana-4456	290	17	to	to	PART
cana-4456	290	18	capture	capture	VERB
cana-4456	290	19	steady	steady	ADJ
cana-4456	290	20	state	state	NOUN
cana-4456	290	21	solutions	solution	NOUN
cana-4456	290	22	,	,	PUNCT
cana-4456	290	23	in	in	ADP
cana-4456	290	24	addition	addition	NOUN
cana-4456	290	25	to	to	ADP
cana-4456	290	26	preserving	preserve	VERB
cana-4456	290	27	them	they	PRON
cana-4456	290	28	.	.	PUNCT
cana-4456	291	1	the	the	DET
cana-4456	291	2	second	second	ADJ
cana-4456	291	3	numerical	numerical	ADJ
cana-4456	291	4	example	example	NOUN
cana-4456	291	5	is	be	AUX
cana-4456	291	6	performed	perform	VERB
cana-4456	291	7	to	to	PART
cana-4456	291	8	test	test	VERB
cana-4456	291	9	if	if	SCONJ
cana-4456	291	10	the	the	DET
cana-4456	291	11	numerical	numerical	ADJ
cana-4456	291	12	methods	method	NOUN
cana-4456	291	13	catches	catch	VERB
cana-4456	291	14	the	the	DET
cana-4456	291	15	transitory	transitory	ADJ
cana-4456	291	16	behaviour	behaviour	NOUN
cana-4456	291	17	and	and	CCONJ
cana-4456	291	18	shock	shock	NOUN
cana-4456	291	19	behaviour	behaviour	NOUN
cana-4456	291	20	of	of	ADP
cana-4456	291	21	the	the	DET
cana-4456	291	22	solution	solution	NOUN
cana-4456	291	23	properly	properly	ADV
cana-4456	291	24	.	.	PUNCT
cana-4456	292	1	the	the	DET
cana-4456	292	2	third	third	PROPN
cana-4456	292	3	numerical	numerical	PROPN
cana-4456	292	4	test	test	NOUN
cana-4456	292	5	verifies	verifie	NOUN
cana-4456	292	6	the	the	DET
cana-4456	292	7	accuracy	accuracy	NOUN
cana-4456	292	8	of	of	ADP
cana-4456	292	9	the	the	DET
cana-4456	292	10	proposed	propose	VERB
cana-4456	292	11	methods	method	NOUN
cana-4456	292	12	in	in	ADP
cana-4456	292	13	preserving	preserve	VERB
cana-4456	292	14	moving	move	VERB
cana-4456	292	15	steady	steady	ADJ
cana-4456	292	16	states	state	NOUN
cana-4456	292	17	that	that	PRON
cana-4456	292	18	involve	involve	VERB
cana-4456	292	19	both	both	DET
cana-4456	292	20	topography	topography	NOUN
cana-4456	292	21	and	and	CCONJ
cana-4456	292	22	friction	friction	NOUN
cana-4456	292	23	.	.	PUNCT
cana-4456	293	1	the	the	DET
cana-4456	293	2	following	follow	VERB
cana-4456	293	3	parameters	parameter	NOUN
cana-4456	293	4	are	be	AUX
cana-4456	293	5	defined	define	VERB
cana-4456	293	6	:	:	PUNCT
cana-4456	293	7	𝑁	𝑁	PROPN
cana-4456	293	8	is	be	AUX
cana-4456	293	9	the	the	DET
cana-4456	293	10	total	total	ADJ
cana-4456	293	11	number	number	NOUN
cana-4456	293	12	of	of	ADP
cana-4456	293	13	nodes	node	NOUN
cana-4456	293	14	in	in	ADP
cana-4456	293	15	the	the	DET
cana-4456	293	16	whole	whole	ADJ
cana-4456	293	17	computational	computational	ADJ
cana-4456	293	18	domain	domain	NOUN
cana-4456	293	19	,	,	PUNCT
cana-4456	293	20	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	PROPN
cana-4456	293	21	is	be	AUX
cana-4456	293	22	the	the	DET
cana-4456	293	23	stencil	stencil	PROPN
cana-4456	293	24	number	number	NOUN
cana-4456	293	25	of	of	ADP
cana-4456	293	26	the	the	DET
cana-4456	293	27	rbf	rbf	PROPN
cana-4456	293	28	-	-	PUNCT
cana-4456	293	29	fd	fd	PROPN
cana-4456	293	30	method	method	NOUN
cana-4456	293	31	based	base	VERB
cana-4456	293	32	on	on	ADP
cana-4456	293	33	the	the	DET
cana-4456	293	34	inverse	inverse	NOUN
cana-4456	293	35	multiquadric	multiquadric	ADJ
cana-4456	293	36	radial	radial	ADJ
cana-4456	293	37	basis	basis	NOUN
cana-4456	293	38	function	function	NOUN
cana-4456	293	39	,	,	PUNCT
cana-4456	293	40	the	the	DET
cana-4456	293	41	optimal	optimal	ADJ
cana-4456	293	42	shape	shape	NOUN
cana-4456	293	43	parameter	parameter	NOUN
cana-4456	293	44	𝜀	𝜀	PROPN
cana-4456	293	45	is	be	AUX
cana-4456	293	46	selected	select	VERB
cana-4456	293	47	using	use	VERB
cana-4456	293	48	the	the	DET
cana-4456	293	49	computed	computed	ADJ
cana-4456	293	50	error	error	NOUN
cana-4456	293	51	of	of	ADP
cana-4456	293	52	the	the	DET
cana-4456	293	53	approximate	approximate	ADJ
cana-4456	293	54	solutions	solution	NOUN
cana-4456	293	55	,	,	PUNCT
cana-4456	293	56	𝑛𝑝	𝑛𝑝	X
cana-4456	293	57	is	be	AUX
cana-4456	293	58	the	the	DET
cana-4456	293	59	number	number	NOUN
cana-4456	293	60	of	of	ADP
cana-4456	293	61	patch	patch	NOUN
cana-4456	293	62	of	of	ADP
cana-4456	293	63	the	the	DET
cana-4456	293	64	rbf	rbf	PROPN
cana-4456	293	65	-	-	PUNCT
cana-4456	293	66	pum	pum	PROPN
cana-4456	293	67	-	-	PUNCT
cana-4456	293	68	qr	qr	PROPN
cana-4456	293	69	method	method	NOUN
cana-4456	293	70	.	.	PUNCT
cana-4456	294	1	for	for	ADP
cana-4456	294	2	kansa	kansa	PROPN
cana-4456	294	3	method	method	NOUN
cana-4456	294	4	based	base	VERB
cana-4456	294	5	on	on	ADP
cana-4456	294	6	the	the	DET
cana-4456	294	7	multiquadric	multiquadric	ADJ
cana-4456	294	8	radial	radial	ADJ
cana-4456	294	9	basis	basis	NOUN
cana-4456	294	10	function	function	NOUN
cana-4456	294	11	,	,	PUNCT
cana-4456	294	12	the	the	DET
cana-4456	294	13	shape	shape	NOUN
cana-4456	294	14	parameter	parameter	NOUN
cana-4456	294	15	𝜀	𝜀	PROPN
cana-4456	294	16	=	=	SYM
cana-4456	294	17	𝜀0√𝑁	𝜀0√𝑁	PROPN
cana-4456	294	18	𝑑𝑚𝑖𝑛	𝑑𝑚𝑖𝑛	PROPN
cana-4456	294	19	in	in	ADP
cana-4456	294	20	which	which	PRON
cana-4456	294	21	𝑑𝑚𝑖𝑛	𝑑𝑚𝑖𝑛	PROPN
cana-4456	294	22	is	be	AUX
cana-4456	294	23	the	the	DET
cana-4456	294	24	minimum	minimum	ADJ
cana-4456	294	25	distance	distance	NOUN
cana-4456	294	26	between	between	ADP
cana-4456	294	27	two	two	NUM
cana-4456	294	28	nodes	node	NOUN
cana-4456	294	29	and	and	CCONJ
cana-4456	294	30	10−4	10−4	NUM
cana-4456	294	31	≤	≤	NOUN
cana-4456	294	32	𝜀0	𝜀0	VERB
cana-4456	294	33	≤	≤	ADJ
cana-4456	294	34	10−1	10−1	PROPN
cana-4456	295	1	[	[	X
cana-4456	295	2	46	46	NUM
cana-4456	295	3	]	]	PUNCT
cana-4456	295	4	and	and	CCONJ
cana-4456	295	5	𝑇	𝑇	PROPN
cana-4456	295	6	is	be	AUX
cana-4456	295	7	the	the	DET
cana-4456	295	8	terminal	terminal	ADJ
cana-4456	295	9	time	time	NOUN
cana-4456	295	10	of	of	ADP
cana-4456	295	11	the	the	DET
cana-4456	295	12	simulation	simulation	NOUN
cana-4456	295	13	.	.	PUNCT
cana-4456	296	1	to	to	PART
cana-4456	296	2	show	show	VERB
cana-4456	296	3	the	the	DET
cana-4456	296	4	advantages	advantage	NOUN
cana-4456	296	5	of	of	ADP
cana-4456	296	6	the	the	DET
cana-4456	296	7	methods	method	NOUN
cana-4456	296	8	in	in	ADP
cana-4456	296	9	terms	term	NOUN
cana-4456	296	10	of	of	ADP
cana-4456	296	11	accuracy	accuracy	NOUN
cana-4456	296	12	,	,	PUNCT
cana-4456	296	13	we	we	PRON
cana-4456	296	14	compute	compute	VERB
cana-4456	296	15	the	the	DET
cana-4456	296	16	relative	relative	ADJ
cana-4456	296	17	error	error	NOUN
cana-4456	296	18	as	as	SCONJ
cana-4456	296	19	follows	follow	VERB
cana-4456	296	20	:	:	PUNCT
cana-4456	296	21	communications	communication	NOUN
cana-4456	296	22	on	on	ADP
cana-4456	296	23	applied	apply	VERB
cana-4456	296	24	nonlinear	nonlinear	ADJ
cana-4456	296	25	analysis	analysis	NOUN
cana-4456	296	26	issn	issn	NOUN
cana-4456	296	27	:	:	PUNCT
cana-4456	296	28	1074	1074	NUM
cana-4456	296	29	-	-	PUNCT
cana-4456	296	30	133x	133x	NUM
cana-4456	296	31	vol	vol	NOUN
cana-4456	296	32	32	32	NUM
cana-4456	296	33	no	no	NOUN
cana-4456	296	34	.	.	PUNCT
cana-4456	297	1	9s	9s	NUM
cana-4456	297	2	(	(	PUNCT
cana-4456	297	3	2025	2025	NUM
cana-4456	297	4	)	)	PUNCT
cana-4456	297	5	2182	2182	NUM
cana-4456	297	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	298	1	𝐸𝑟𝑟	𝐸𝑟𝑟	PROPN
cana-4456	298	2	=	=	SYM
cana-4456	298	3	√1	√1	PROPN
cana-4456	298	4	𝑁	𝑁	PROPN
cana-4456	298	5	∑	∑	PROPN
cana-4456	298	6	(	(	PUNCT
cana-4456	298	7	𝑸𝑛𝑢𝑚(𝑥𝑖,𝑡)−𝑸𝑎𝑛𝑎(𝑥𝑖,𝑡	𝑸𝑛𝑢𝑚(𝑥𝑖,𝑡)−𝑸𝑎𝑛𝑎(𝑥𝑖,𝑡	PROPN
cana-4456	298	8	)	)	PUNCT
cana-4456	298	9	𝑸𝑎𝑛𝑎(𝑥𝑖,𝑡	𝑸𝑎𝑛𝑎(𝑥𝑖,𝑡	NOUN
cana-4456	298	10	)	)	PUNCT
cana-4456	298	11	)	)	PUNCT
cana-4456	299	1	2	2	NUM
cana-4456	299	2	𝑁	𝑁	PROPN
cana-4456	299	3	𝑖=1	𝑖=1	PROPN
cana-4456	299	4	,	,	PUNCT
cana-4456	299	5	(	(	PUNCT
cana-4456	299	6	53	53	NUM
cana-4456	299	7	)	)	PUNCT
cana-4456	299	8	where	where	SCONJ
cana-4456	299	9	𝑸𝑛𝑢𝑚	𝑸𝑛𝑢𝑚	PROPN
cana-4456	299	10	and	and	CCONJ
cana-4456	299	11	𝑸𝑎𝑛𝑎	𝑸𝑎𝑛𝑎	PROPN
cana-4456	299	12	are	be	AUX
cana-4456	299	13	respectively	respectively	ADV
cana-4456	299	14	,	,	PUNCT
cana-4456	299	15	the	the	DET
cana-4456	299	16	numerical	numerical	ADJ
cana-4456	299	17	and	and	CCONJ
cana-4456	299	18	analytical	analytical	ADJ
cana-4456	299	19	solutions	solution	NOUN
cana-4456	299	20	.	.	PUNCT
cana-4456	300	1	in	in	ADP
cana-4456	300	2	all	all	DET
cana-4456	300	3	our	our	PRON
cana-4456	300	4	computations	computation	NOUN
cana-4456	300	5	a	a	DET
cana-4456	300	6	fixed	fix	VERB
cana-4456	300	7	courant	courant	ADJ
cana-4456	300	8	number	number	NOUN
cana-4456	300	9	𝐶𝐹𝐿	𝐶𝐹𝐿	VERB
cana-4456	300	10	=	=	SYM
cana-4456	300	11	0.5	0.5	NUM
cana-4456	300	12	.	.	PUNCT
cana-4456	301	1	the	the	DET
cana-4456	301	2	numerical	numerical	ADJ
cana-4456	301	3	tests	test	NOUN
cana-4456	301	4	are	be	AUX
cana-4456	301	5	performed	perform	VERB
cana-4456	301	6	on	on	ADP
cana-4456	301	7	a	a	DET
cana-4456	301	8	core	core	NOUN
cana-4456	301	9	cpu	cpu	NOUN
cana-4456	301	10	i5	i5	ADV
cana-4456	301	11	2.11gh	2.11gh	NUM
cana-4456	301	12	computer	computer	NOUN
cana-4456	301	13	in	in	ADP
cana-4456	301	14	a	a	DET
cana-4456	301	15	matlab	matlab	PROPN
cana-4456	301	16	2018a	2018a	NOUN
cana-4456	301	17	tools	tool	NOUN
cana-4456	301	18	.	.	PUNCT
cana-4456	302	1	4.1	4.1	NUM
cana-4456	302	2	test	test	NOUN
cana-4456	302	3	1	1	NUM
cana-4456	302	4	:	:	PUNCT
cana-4456	302	5	steady	steady	ADJ
cana-4456	302	6	flow	flow	NOUN
cana-4456	302	7	over	over	ADP
cana-4456	302	8	a	a	DET
cana-4456	302	9	bump	bump	NOUN
cana-4456	302	10	according	accord	VERB
cana-4456	302	11	to	to	ADP
cana-4456	302	12	[	[	X
cana-4456	302	13	47	47	NUM
cana-4456	302	14	]	]	PUNCT
cana-4456	302	15	,	,	PUNCT
cana-4456	302	16	the	the	DET
cana-4456	302	17	source	source	NOUN
cana-4456	302	18	term	term	NOUN
cana-4456	302	19	appears	appear	VERB
cana-4456	302	20	in	in	ADP
cana-4456	302	21	(	(	PUNCT
cana-4456	302	22	8)	8)	NUM
cana-4456	302	23	is	be	AUX
cana-4456	302	24	a	a	DET
cana-4456	302	25	crucial	crucial	ADJ
cana-4456	302	26	point	point	NOUN
cana-4456	302	27	in	in	ADP
cana-4456	302	28	preserving	preserve	VERB
cana-4456	302	29	steady	steady	ADJ
cana-4456	302	30	states	state	NOUN
cana-4456	302	31	.	.	PUNCT
cana-4456	303	1	in	in	ADP
cana-4456	303	2	order	order	NOUN
cana-4456	303	3	to	to	PART
cana-4456	303	4	prove	prove	VERB
cana-4456	303	5	the	the	DET
cana-4456	303	6	ability	ability	NOUN
cana-4456	303	7	of	of	ADP
cana-4456	303	8	the	the	DET
cana-4456	303	9	proposed	propose	VERB
cana-4456	303	10	methods	method	NOUN
cana-4456	303	11	to	to	PART
cana-4456	303	12	catch	catch	VERB
cana-4456	303	13	these	these	DET
cana-4456	303	14	states	state	NOUN
cana-4456	303	15	,	,	PUNCT
cana-4456	303	16	we	we	PRON
cana-4456	303	17	apply	apply	VERB
cana-4456	303	18	the	the	DET
cana-4456	303	19	schemes	scheme	NOUN
cana-4456	303	20	to	to	ADP
cana-4456	303	21	a	a	DET
cana-4456	303	22	series	series	NOUN
cana-4456	303	23	of	of	ADP
cana-4456	303	24	benchmark	benchmark	NOUN
cana-4456	303	25	cases	case	NOUN
cana-4456	303	26	of	of	ADP
cana-4456	303	27	different	different	ADJ
cana-4456	303	28	boundary	boundary	ADJ
cana-4456	303	29	and	and	CCONJ
cana-4456	303	30	initial	initial	ADJ
cana-4456	303	31	conditions	condition	NOUN
cana-4456	303	32	[	[	X
cana-4456	303	33	48	48	NUM
cana-4456	303	34	]	]	PUNCT
cana-4456	303	35	.	.	PUNCT
cana-4456	304	1	these	these	DET
cana-4456	304	2	benchmarks	benchmark	NOUN
cana-4456	304	3	have	have	AUX
cana-4456	304	4	been	be	AUX
cana-4456	304	5	derived	derive	VERB
cana-4456	304	6	by	by	ADP
cana-4456	304	7	considering	consider	VERB
cana-4456	304	8	the	the	DET
cana-4456	304	9	bernoulli	bernoulli	PROPN
cana-4456	304	10	equation	equation	NOUN
cana-4456	304	11	that	that	PRON
cana-4456	304	12	governs	govern	VERB
cana-4456	304	13	the	the	DET
cana-4456	304	14	steady	steady	ADJ
cana-4456	304	15	state	state	NOUN
cana-4456	304	16	solutions	solution	NOUN
cana-4456	304	17	of	of	ADP
cana-4456	304	18	the	the	DET
cana-4456	304	19	shallowwater	shallowwater	ADJ
cana-4456	304	20	equations	equation	NOUN
cana-4456	304	21	with	with	ADP
cana-4456	304	22	non	non	ADJ
cana-4456	304	23	-	-	ADJ
cana-4456	304	24	flat	flat	ADJ
cana-4456	304	25	topography	topography	NOUN
cana-4456	304	26	and	and	CCONJ
cana-4456	304	27	a	a	DET
cana-4456	304	28	vanishing	vanish	VERB
cana-4456	304	29	friction	friction	NOUN
cana-4456	304	30	contribution	contribution	NOUN
cana-4456	304	31	,	,	PUNCT
cana-4456	304	32	the	the	DET
cana-4456	304	33	experiments	experiment	NOUN
cana-4456	304	34	from	from	ADP
cana-4456	304	35	[	[	X
cana-4456	304	36	48	48	NUM
cana-4456	304	37	]	]	PUNCT
cana-4456	304	38	are	be	AUX
cana-4456	304	39	called	call	VERB
cana-4456	304	40	the	the	DET
cana-4456	304	41	subcritical	subcritical	ADJ
cana-4456	304	42	flow	flow	NOUN
cana-4456	304	43	,	,	PUNCT
cana-4456	304	44	the	the	DET
cana-4456	304	45	transcritical	transcritical	ADJ
cana-4456	304	46	flow	flow	NOUN
cana-4456	304	47	without	without	ADP
cana-4456	304	48	shock	shock	NOUN
cana-4456	304	49	and	and	CCONJ
cana-4456	304	50	the	the	DET
cana-4456	304	51	transcritical	transcritical	ADJ
cana-4456	304	52	flow	flow	NOUN
cana-4456	304	53	with	with	ADP
cana-4456	304	54	shock	shock	NOUN
cana-4456	304	55	.	.	PUNCT
cana-4456	305	1	the	the	DET
cana-4456	305	2	computational	computational	ADJ
cana-4456	305	3	domain	domain	NOUN
cana-4456	305	4	is	be	AUX
cana-4456	305	5	a	a	DET
cana-4456	305	6	rectangular	rectangular	ADJ
cana-4456	305	7	channel	channel	NOUN
cana-4456	305	8	with	with	ADP
cana-4456	305	9	𝐿	𝐿	PROPN
cana-4456	305	10	=	=	PROPN
cana-4456	305	11	25	25	NUM
cana-4456	305	12	𝑚	𝑚	NOUN
cana-4456	305	13	in	in	ADP
cana-4456	305	14	length	length	NOUN
cana-4456	305	15	.	.	PUNCT
cana-4456	306	1	the	the	DET
cana-4456	306	2	inflow	inflow	NOUN
cana-4456	306	3	and	and	CCONJ
cana-4456	306	4	outflow	outflow	ADJ
cana-4456	306	5	boundary	boundary	ADJ
cana-4456	306	6	conditions	condition	NOUN
cana-4456	306	7	are	be	AUX
cana-4456	306	8	imposed	impose	VERB
cana-4456	306	9	along	along	ADP
cana-4456	306	10	the	the	DET
cana-4456	306	11	left	left	NOUN
cana-4456	306	12	and	and	CCONJ
cana-4456	306	13	the	the	DET
cana-4456	306	14	right	right	ADJ
cana-4456	306	15	boundary	boundary	ADJ
cana-4456	306	16	segments	segment	NOUN
cana-4456	306	17	,	,	PUNCT
cana-4456	306	18	respectively	respectively	ADV
cana-4456	306	19	.	.	PUNCT
cana-4456	307	1	the	the	DET
cana-4456	307	2	bed	bed	NOUN
cana-4456	307	3	elevation	elevation	NOUN
cana-4456	307	4	of	of	ADP
cana-4456	307	5	a	a	DET
cana-4456	307	6	bump	bump	NOUN
cana-4456	307	7	is	be	AUX
cana-4456	307	8	defined	define	VERB
cana-4456	307	9	as	as	SCONJ
cana-4456	307	10	follows	follow	VERB
cana-4456	307	11	:	:	PUNCT
cana-4456	307	12	𝑏(𝑥	𝑏(𝑥	NOUN
cana-4456	307	13	)	)	PUNCT
cana-4456	307	14	=	=	PRON
cana-4456	308	1	{	{	PUNCT
cana-4456	308	2	0.2	0.2	NUM
cana-4456	308	3	−	−	NOUN
cana-4456	308	4	0.05(𝑥	0.05(𝑥	NOUN
cana-4456	308	5	−	−	NOUN
cana-4456	308	6	10)2	10)2	NUM
cana-4456	308	7	8𝑚	8𝑚	NOUN
cana-4456	308	8	<	<	X
cana-4456	308	9	𝑥	𝑥	X
cana-4456	308	10	<	<	X
cana-4456	308	11	12𝑚	12𝑚	ADJ
cana-4456	308	12	0	0	NUM
cana-4456	308	13	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒.	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒.	NOUN
cana-4456	308	14	(	(	PUNCT
cana-4456	308	15	54	54	NUM
cana-4456	308	16	)	)	PUNCT
cana-4456	308	17	the	the	DET
cana-4456	308	18	boundary	boundary	ADJ
cana-4456	308	19	conditions	condition	NOUN
cana-4456	308	20	are	be	AUX
cana-4456	308	21	defined	define	VERB
cana-4456	308	22	in	in	ADP
cana-4456	308	23	terms	term	NOUN
cana-4456	308	24	of	of	ADP
cana-4456	308	25	two	two	NUM
cana-4456	308	26	quantities	quantity	NOUN
cana-4456	308	27	,	,	PUNCT
cana-4456	308	28	𝑞0	𝑞0	NOUN
cana-4456	308	29	and	and	CCONJ
cana-4456	308	30	ℎ𝐿	ℎ𝐿	ADV
cana-4456	308	31	,	,	PUNCT
cana-4456	308	32	whose	whose	DET
cana-4456	308	33	values	value	NOUN
cana-4456	308	34	vary	vary	VERB
cana-4456	308	35	depending	depend	VERB
cana-4456	308	36	on	on	ADP
cana-4456	308	37	the	the	DET
cana-4456	308	38	specific	specific	ADJ
cana-4456	308	39	experiment	experiment	NOUN
cana-4456	308	40	being	be	AUX
cana-4456	308	41	analysed	analyse	VERB
cana-4456	308	42	:	:	PUNCT
cana-4456	308	43	•	•	NOUN
cana-4456	308	44	on	on	ADP
cana-4456	308	45	the	the	DET
cana-4456	308	46	left	left	ADJ
cana-4456	308	47	boundary	boundary	NOUN
cana-4456	308	48	,	,	PUNCT
cana-4456	308	49	the	the	DET
cana-4456	308	50	water	water	NOUN
cana-4456	308	51	height	height	NOUN
cana-4456	308	52	satisfies	satisfy	VERB
cana-4456	308	53	a	a	DET
cana-4456	308	54	homogeneous	homogeneous	ADJ
cana-4456	308	55	neumann	neumann	PROPN
cana-4456	308	56	condition	condition	NOUN
cana-4456	308	57	and	and	CCONJ
cana-4456	308	58	the	the	DET
cana-4456	308	59	discharge	discharge	NOUN
cana-4456	308	60	is	be	AUX
cana-4456	308	61	set	set	VERB
cana-4456	308	62	to	to	ADP
cana-4456	308	63	a	a	DET
cana-4456	308	64	specific	specific	ADJ
cana-4456	308	65	𝑞0	𝑞0	NOUN
cana-4456	308	66	.	.	PUNCT
cana-4456	309	1	•	•	NUM
cana-4456	309	2	on	on	ADP
cana-4456	309	3	the	the	DET
cana-4456	309	4	right	right	ADJ
cana-4456	309	5	boundary	boundary	NOUN
cana-4456	309	6	,	,	PUNCT
cana-4456	309	7	the	the	DET
cana-4456	309	8	water	water	NOUN
cana-4456	309	9	height	height	NOUN
cana-4456	309	10	is	be	AUX
cana-4456	309	11	set	set	VERB
cana-4456	309	12	to	to	ADP
cana-4456	309	13	ℎ𝐿	ℎ𝐿	ADV
cana-4456	309	14	when	when	SCONJ
cana-4456	309	15	the	the	DET
cana-4456	309	16	flow	flow	NOUN
cana-4456	309	17	is	be	AUX
cana-4456	309	18	subcritical	subcritical	ADJ
cana-4456	309	19	(	(	PUNCT
cana-4456	309	20	and	and	CCONJ
cana-4456	309	21	a	a	DET
cana-4456	309	22	homogeneous	homogeneous	ADJ
cana-4456	309	23	neumann	neumann	PROPN
cana-4456	309	24	boundary	boundary	ADJ
cana-4456	309	25	condition	condition	NOUN
cana-4456	309	26	is	be	AUX
cana-4456	309	27	prescribed	prescribe	VERB
cana-4456	309	28	otherwise	otherwise	ADV
cana-4456	309	29	)	)	PUNCT
cana-4456	309	30	,	,	PUNCT
cana-4456	309	31	and	and	CCONJ
cana-4456	309	32	the	the	DET
cana-4456	309	33	discharge	discharge	NOUN
cana-4456	309	34	follows	follow	VERB
cana-4456	309	35	a	a	DET
cana-4456	309	36	homogeneous	homogeneous	ADJ
cana-4456	309	37	neumann	neumann	PROPN
cana-4456	309	38	boundary	boundary	ADJ
cana-4456	309	39	condition	condition	NOUN
cana-4456	309	40	.	.	PUNCT
cana-4456	310	1	in	in	ADP
cana-4456	310	2	addition	addition	NOUN
cana-4456	310	3	,	,	PUNCT
cana-4456	310	4	the	the	DET
cana-4456	310	5	initial	initial	ADJ
cana-4456	310	6	conditions	condition	NOUN
cana-4456	310	7	set	set	VERB
cana-4456	310	8	to	to	ADP
cana-4456	310	9	ℎ(𝑥	ℎ(𝑥	NUM
cana-4456	310	10	)	)	PUNCT
cana-4456	310	11	+	+	SYM
cana-4456	310	12	𝑏(𝑥	𝑏(𝑥	NOUN
cana-4456	310	13	)	)	PUNCT
cana-4456	311	1	=	=	PUNCT
cana-4456	311	2	ℎ𝐿𝑚	ℎ𝐿𝑚	ADP
cana-4456	311	3	and	and	CCONJ
cana-4456	311	4	𝑞(𝑥	𝑞(𝑥	NUM
cana-4456	311	5	)	)	PUNCT
cana-4456	312	1	=	=	PUNCT
cana-4456	312	2	0𝑚2/𝑠	0𝑚2/𝑠	PROPN
cana-4456	312	3	throughout	throughout	ADP
cana-4456	312	4	the	the	DET
cana-4456	312	5	domain	domain	NOUN
cana-4456	312	6	.	.	PUNCT
cana-4456	313	1	all	all	DET
cana-4456	313	2	these	these	DET
cana-4456	313	3	results	result	NOUN
cana-4456	313	4	are	be	AUX
cana-4456	313	5	frictionless	frictionless	ADJ
cana-4456	313	6	and	and	CCONJ
cana-4456	313	7	displayed	display	VERB
cana-4456	313	8	at	at	ADP
cana-4456	313	9	𝑇	𝑇	PROPN
cana-4456	313	10	=	=	SYM
cana-4456	313	11	200𝑠	200𝑠	PROPN
cana-4456	313	12	using𝑁	using𝑁	PROPN
cana-4456	313	13	=	=	SYM
cana-4456	313	14	1001	1001	NUM
cana-4456	313	15	,	,	PUNCT
cana-4456	313	16	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	313	17	=	=	SYM
cana-4456	313	18	100	100	NUM
cana-4456	313	19	and	and	CCONJ
cana-4456	313	20	𝑛𝑝	𝑛𝑝	NOUN
cana-4456	313	21	=	=	SYM
cana-4456	313	22	300	300	NUM
cana-4456	313	23	,	,	PUNCT
cana-4456	313	24	the	the	DET
cana-4456	313	25	analytical	analytical	ADJ
cana-4456	313	26	solutions	solution	NOUN
cana-4456	313	27	are	be	AUX
cana-4456	313	28	also	also	ADV
cana-4456	313	29	plotted	plot	VERB
cana-4456	313	30	within	within	ADP
cana-4456	313	31	the	the	DET
cana-4456	313	32	obtained	obtain	VERB
cana-4456	313	33	numerical	numerical	ADJ
cana-4456	313	34	results	result	NOUN
cana-4456	313	35	.	.	PUNCT
cana-4456	314	1	4.1.1	4.1.1	NUM
cana-4456	314	2	subcritical	subcritical	ADJ
cana-4456	314	3	flow	flow	NOUN
cana-4456	314	4	for	for	ADP
cana-4456	314	5	this	this	DET
cana-4456	314	6	test	test	NOUN
cana-4456	314	7	,	,	PUNCT
cana-4456	314	8	a	a	DET
cana-4456	314	9	discharge	discharge	NOUN
cana-4456	314	10	of	of	ADP
cana-4456	314	11	𝑞0	𝑞0	NOUN
cana-4456	314	12	=	=	NOUN
cana-4456	314	13	4.42𝑚2/𝑠	4.42𝑚2/𝑠	NOUN
cana-4456	314	14	and	and	CCONJ
cana-4456	314	15	the	the	DET
cana-4456	314	16	constant	constant	ADJ
cana-4456	314	17	water	water	NOUN
cana-4456	314	18	surface	surface	NOUN
cana-4456	314	19	level	level	NOUN
cana-4456	314	20	of	of	ADP
cana-4456	314	21	the	the	DET
cana-4456	314	22	water	water	NOUN
cana-4456	314	23	level	level	NOUN
cana-4456	314	24	ℎ𝐿	ℎ𝐿	ADV
cana-4456	314	25	=	=	SYM
cana-4456	314	26	2𝑚	2𝑚	NOUN
cana-4456	314	27	are	be	AUX
cana-4456	314	28	set	set	VERB
cana-4456	314	29	as	as	ADP
cana-4456	314	30	upstream	upstream	ADJ
cana-4456	314	31	and	and	CCONJ
cana-4456	314	32	downstream	downstream	ADJ
cana-4456	314	33	boundary	boundary	ADJ
cana-4456	314	34	conditions	condition	NOUN
cana-4456	314	35	,	,	PUNCT
cana-4456	314	36	respectively	respectively	ADV
cana-4456	314	37	.	.	PUNCT
cana-4456	315	1	the	the	DET
cana-4456	315	2	steady	steady	ADJ
cana-4456	315	3	-	-	PUNCT
cana-4456	315	4	state	state	NOUN
cana-4456	315	5	numerical	numerical	ADJ
cana-4456	315	6	solutions	solution	NOUN
cana-4456	315	7	of	of	ADP
cana-4456	315	8	water	water	NOUN
cana-4456	315	9	height	height	NOUN
cana-4456	315	10	ℎ	ℎ	NOUN
cana-4456	315	11	and	and	CCONJ
cana-4456	315	12	discharge	discharge	VERB
cana-4456	315	13	𝑞	𝑞	PRON
cana-4456	315	14	compared	compare	VERB
cana-4456	315	15	with	with	ADP
cana-4456	315	16	the	the	DET
cana-4456	315	17	analytical	analytical	ADJ
cana-4456	315	18	solution	solution	NOUN
cana-4456	315	19	[	[	X
cana-4456	315	20	48	48	NUM
cana-4456	315	21	]	]	PUNCT
cana-4456	315	22	are	be	AUX
cana-4456	315	23	plotted	plot	VERB
cana-4456	315	24	in	in	ADP
cana-4456	315	25	figure	figure	NOUN
cana-4456	315	26	1	1	NUM
cana-4456	315	27	.	.	PUNCT
cana-4456	316	1	the	the	DET
cana-4456	316	2	numerical	numerical	ADJ
cana-4456	316	3	examples	example	NOUN
cana-4456	316	4	are	be	AUX
cana-4456	316	5	performed	perform	VERB
cana-4456	316	6	for	for	ADP
cana-4456	316	7	kansa	kansa	PROPN
cana-4456	316	8	method	method	PROPN
cana-4456	316	9	using	use	VERB
cana-4456	316	10	𝜇	𝜇	ADP
cana-4456	316	11	=	=	SYM
cana-4456	316	12	8	8	NUM
cana-4456	316	13	×	×	NOUN
cana-4456	316	14	10−3	10−3	NUM
cana-4456	316	15	,	,	PUNCT
cana-4456	316	16	for	for	SCONJ
cana-4456	316	17	communications	communication	NOUN
cana-4456	316	18	on	on	ADP
cana-4456	316	19	applied	apply	VERB
cana-4456	316	20	nonlinear	nonlinear	ADJ
cana-4456	316	21	analysis	analysis	NOUN
cana-4456	316	22	issn	issn	NOUN
cana-4456	316	23	:	:	PUNCT
cana-4456	316	24	1074	1074	NUM
cana-4456	316	25	-	-	PUNCT
cana-4456	316	26	133x	133x	NUM
cana-4456	316	27	vol	vol	NOUN
cana-4456	316	28	32	32	NUM
cana-4456	317	1	no	no	NOUN
cana-4456	317	2	.	.	PUNCT
cana-4456	318	1	9s	9s	NUM
cana-4456	318	2	(	(	PUNCT
cana-4456	318	3	2025	2025	NUM
cana-4456	318	4	)	)	PUNCT
cana-4456	318	5	2183	2183	NUM
cana-4456	318	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	319	1	rbf	rbf	PROPN
cana-4456	319	2	-	-	PUNCT
cana-4456	319	3	pum	pum	PROPN
cana-4456	319	4	-	-	PUNCT
cana-4456	319	5	qr	qr	PROPN
cana-4456	319	6	method	method	NOUN
cana-4456	319	7	using	use	VERB
cana-4456	319	8	𝜇	𝜇	ADP
cana-4456	319	9	=	=	SYM
cana-4456	319	10	8	8	NUM
cana-4456	319	11	×	×	NOUN
cana-4456	319	12	10−3	10−3	NUM
cana-4456	319	13	,	,	PUNCT
cana-4456	319	14	and	and	CCONJ
cana-4456	319	15	for	for	ADP
cana-4456	319	16	rbf	rbf	PROPN
cana-4456	319	17	-	-	PUNCT
cana-4456	319	18	fd	fd	PROPN
cana-4456	319	19	method	method	NOUN
cana-4456	319	20	using	use	VERB
cana-4456	319	21	𝜇	𝜇	ADP
cana-4456	319	22	=	=	PROPN
cana-4456	319	23	2	2	NUM
cana-4456	319	24	×	×	NOUN
cana-4456	319	25	10−3	10−3	NUM
cana-4456	319	26	with	with	ADP
cana-4456	319	27	the	the	DET
cana-4456	319	28	optimal	optimal	ADJ
cana-4456	319	29	shape	shape	NOUN
cana-4456	319	30	parameter	parameter	NOUN
cana-4456	319	31	𝜀	𝜀	NOUN
cana-4456	319	32	=	=	SYM
cana-4456	319	33	5	5	NUM
cana-4456	319	34	.	.	PUNCT
cana-4456	320	1	the	the	DET
cana-4456	320	2	selection	selection	NOUN
cana-4456	320	3	of	of	ADP
cana-4456	320	4	an	an	DET
cana-4456	320	5	optimal	optimal	ADJ
cana-4456	320	6	shape	shape	NOUN
cana-4456	320	7	parameter	parameter	NOUN
cana-4456	320	8	𝜀	𝜀	PROPN
cana-4456	320	9	and	and	CCONJ
cana-4456	320	10	the	the	DET
cana-4456	320	11	viscosity	viscosity	NOUN
cana-4456	320	12	coefficient	coefficient	NOUN
cana-4456	320	13	𝜇	𝜇	ADP
cana-4456	320	14	in	in	ADP
cana-4456	320	15	all	all	DET
cana-4456	320	16	tests	test	NOUN
cana-4456	320	17	in	in	ADP
cana-4456	320	18	this	this	DET
cana-4456	320	19	paper	paper	NOUN
cana-4456	320	20	was	be	AUX
cana-4456	320	21	made	make	VERB
cana-4456	320	22	using	use	VERB
cana-4456	320	23	trial	trial	NOUN
cana-4456	320	24	and	and	CCONJ
cana-4456	320	25	error	error	NOUN
cana-4456	320	26	strategy	strategy	NOUN
cana-4456	320	27	.	.	PUNCT
cana-4456	321	1	the	the	DET
cana-4456	321	2	strategy	strategy	NOUN
cana-4456	321	3	is	be	AUX
cana-4456	321	4	to	to	PART
cana-4456	321	5	perform	perform	VERB
cana-4456	321	6	a	a	DET
cana-4456	321	7	series	series	NOUN
cana-4456	321	8	of	of	ADP
cana-4456	321	9	experiments	experiment	NOUN
cana-4456	321	10	by	by	ADP
cana-4456	321	11	varying	vary	VERB
cana-4456	321	12	the	the	DET
cana-4456	321	13	values	value	NOUN
cana-4456	321	14	of	of	ADP
cana-4456	321	15	the	the	DET
cana-4456	321	16	shape	shape	NOUN
cana-4456	321	17	parameter	parameter	NOUN
cana-4456	321	18	or	or	CCONJ
cana-4456	321	19	viscosity	viscosity	NOUN
cana-4456	321	20	coefficient	coefficient	NOUN
cana-4456	321	21	,	,	PUNCT
cana-4456	321	22	and	and	CCONJ
cana-4456	321	23	then	then	ADV
cana-4456	321	24	pick	pick	VERB
cana-4456	321	25	the	the	DET
cana-4456	321	26	best	good	ADJ
cana-4456	321	27	one	one	NUM
cana-4456	321	28	corresponding	correspond	VERB
cana-4456	321	29	to	to	ADP
cana-4456	321	30	the	the	DET
cana-4456	321	31	smallest	small	ADJ
cana-4456	321	32	error	error	NOUN
cana-4456	321	33	.	.	PUNCT
cana-4456	322	1	in	in	ADP
cana-4456	322	2	figure	figure	NOUN
cana-4456	322	3	1	1	NUM
cana-4456	322	4	,	,	PUNCT
cana-4456	322	5	it	it	PRON
cana-4456	322	6	is	be	AUX
cana-4456	322	7	evident	evident	ADJ
cana-4456	322	8	that	that	SCONJ
cana-4456	322	9	the	the	DET
cana-4456	322	10	impact	impact	NOUN
cana-4456	322	11	of	of	ADP
cana-4456	322	12	a	a	DET
cana-4456	322	13	bump	bump	NOUN
cana-4456	322	14	in	in	ADP
cana-4456	322	15	subcritical	subcritical	ADJ
cana-4456	322	16	flow	flow	NOUN
cana-4456	322	17	is	be	AUX
cana-4456	322	18	clearly	clearly	ADV
cana-4456	322	19	observable	observable	ADJ
cana-4456	322	20	and	and	CCONJ
cana-4456	322	21	the	the	DET
cana-4456	322	22	model	model	NOUN
cana-4456	322	23	can	can	AUX
cana-4456	322	24	well	well	ADV
cana-4456	322	25	capture	capture	VERB
cana-4456	322	26	the	the	DET
cana-4456	322	27	drop	drop	NOUN
cana-4456	322	28	of	of	ADP
cana-4456	322	29	the	the	DET
cana-4456	322	30	water	water	NOUN
cana-4456	322	31	surface	surface	NOUN
cana-4456	322	32	elevation	elevation	NOUN
cana-4456	322	33	at	at	ADP
cana-4456	322	34	the	the	DET
cana-4456	322	35	bump	bump	NOUN
cana-4456	322	36	.	.	PUNCT
cana-4456	323	1	a	a	DET
cana-4456	323	2	more	more	ADV
cana-4456	323	3	detailed	detailed	ADJ
cana-4456	323	4	analysis	analysis	NOUN
cana-4456	323	5	of	of	ADP
cana-4456	323	6	the	the	DET
cana-4456	323	7	numerical	numerical	ADJ
cana-4456	323	8	error	error	NOUN
cana-4456	323	9	is	be	AUX
cana-4456	323	10	listed	list	VERB
cana-4456	323	11	in	in	ADP
cana-4456	323	12	table	table	NOUN
cana-4456	323	13	2	2	NUM
cana-4456	323	14	.	.	PUNCT
cana-4456	323	15	figure	figure	NOUN
cana-4456	323	16	2	2	NUM
cana-4456	323	17	shows	show	VERB
cana-4456	323	18	the	the	DET
cana-4456	323	19	computed	computed	ADJ
cana-4456	323	20	𝐿2	𝐿2	NOUN
cana-4456	323	21	error	error	NOUN
cana-4456	323	22	for	for	ADP
cana-4456	323	23	different	different	ADJ
cana-4456	323	24	values	value	NOUN
cana-4456	323	25	of	of	ADP
cana-4456	323	26	the	the	DET
cana-4456	323	27	viscosity	viscosity	NOUN
cana-4456	323	28	coefficient	coefficient	NOUN
cana-4456	323	29	𝜇.	𝜇.	ADV
cana-4456	323	30	from	from	ADP
cana-4456	323	31	figure	figure	NOUN
cana-4456	323	32	2	2	NUM
cana-4456	323	33	,	,	PUNCT
cana-4456	323	34	we	we	PRON
cana-4456	323	35	remark	remark	VERB
cana-4456	323	36	that	that	SCONJ
cana-4456	323	37	for	for	ADP
cana-4456	323	38	kansa	kansa	PROPN
cana-4456	323	39	method	method	VERB
cana-4456	323	40	the	the	DET
cana-4456	323	41	minimum	minimum	NOUN
cana-4456	323	42	error	error	NOUN
cana-4456	323	43	is	be	AUX
cana-4456	323	44	for	for	SCONJ
cana-4456	323	45	obtained	obtain	VERB
cana-4456	323	46	around	around	ADP
cana-4456	323	47	𝜇	𝜇	ADP
cana-4456	323	48	=	=	PROPN
cana-4456	323	49	10−3	10−3	NUM
cana-4456	323	50	,	,	PUNCT
cana-4456	323	51	for	for	ADP
cana-4456	323	52	rbf	rbf	PROPN
cana-4456	323	53	-	-	PUNCT
cana-4456	323	54	fd	fd	PROPN
cana-4456	323	55	method	method	NOUN
cana-4456	323	56	𝜇	𝜇	ADP
cana-4456	323	57	=	=	PROPN
cana-4456	323	58	10−2	10−2	NUM
cana-4456	323	59	and	and	CCONJ
cana-4456	323	60	for	for	ADP
cana-4456	323	61	rbf	rbf	PROPN
cana-4456	323	62	-	-	PUNCT
cana-4456	323	63	pum	pum	PROPN
cana-4456	323	64	-	-	PUNCT
cana-4456	323	65	qr	qr	PROPN
cana-4456	323	66	method	method	NOUN
cana-4456	323	67	𝜇	𝜇	ADP
cana-4456	323	68	=	=	PROPN
cana-4456	323	69	10−3	10−3	NUM
cana-4456	323	70	.	.	PUNCT
cana-4456	324	1	we	we	PRON
cana-4456	324	2	make	make	VERB
cana-4456	324	3	a	a	DET
cana-4456	324	4	error	error	NOUN
cana-4456	324	5	analysis	analysis	NOUN
cana-4456	324	6	for	for	ADP
cana-4456	324	7	the	the	DET
cana-4456	324	8	subcritical	subcritical	ADJ
cana-4456	324	9	flow	flow	NOUN
cana-4456	324	10	problem	problem	NOUN
cana-4456	324	11	using	use	VERB
cana-4456	324	12	rbf	rbf	PROPN
cana-4456	324	13	-	-	PUNCT
cana-4456	324	14	fd	fd	PROPN
cana-4456	324	15	method	method	NOUN
cana-4456	324	16	(	(	PUNCT
cana-4456	324	17	see	see	VERB
cana-4456	324	18	figure	figure	NOUN
cana-4456	324	19	3	3	NUM
cana-4456	324	20	(	(	PUNCT
cana-4456	324	21	a	a	NOUN
cana-4456	324	22	)	)	PUNCT
cana-4456	324	23	)	)	PUNCT
cana-4456	324	24	.	.	PUNCT
cana-4456	325	1	four	four	NUM
cana-4456	325	2	different	different	ADJ
cana-4456	325	3	stencil	stencil	NOUN
cana-4456	325	4	sizes	size	NOUN
cana-4456	325	5	are	be	AUX
cana-4456	325	6	used	use	VERB
cana-4456	325	7	,	,	PUNCT
cana-4456	325	8	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	325	9	=	=	SYM
cana-4456	325	10	20	20	NUM
cana-4456	325	11	,	,	PUNCT
cana-4456	325	12	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	325	13	=	=	SYM
cana-4456	325	14	100	100	NUM
cana-4456	325	15	and	and	CCONJ
cana-4456	325	16	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	325	17	=	=	NOUN
cana-4456	325	18	150	150	NUM
cana-4456	325	19	.	.	PUNCT
cana-4456	326	1	the	the	DET
cana-4456	326	2	result	result	NOUN
cana-4456	326	3	seen	see	VERB
cana-4456	326	4	in	in	ADP
cana-4456	326	5	figure	figure	NOUN
cana-4456	326	6	3	3	NUM
cana-4456	326	7	(	(	PUNCT
cana-4456	326	8	a	a	PRON
cana-4456	326	9	)	)	PUNCT
cana-4456	326	10	plotted	plot	VERB
cana-4456	326	11	in	in	ADP
cana-4456	326	12	logarithmic	logarithmic	ADJ
cana-4456	326	13	scales	scale	NOUN
cana-4456	326	14	,	,	PUNCT
cana-4456	326	15	where	where	SCONJ
cana-4456	326	16	the	the	DET
cana-4456	326	17	𝐿2	𝐿2	NOUN
cana-4456	326	18	-	-	PUNCT
cana-4456	326	19	norm	norm	NOUN
cana-4456	326	20	of	of	ADP
cana-4456	326	21	the	the	DET
cana-4456	326	22	numerical	numerical	ADJ
cana-4456	326	23	error	error	NOUN
cana-4456	326	24	is	be	AUX
cana-4456	326	25	plotted	plot	VERB
cana-4456	326	26	against	against	ADP
cana-4456	326	27	the	the	DET
cana-4456	326	28	grid	grid	NOUN
cana-4456	326	29	size	size	NOUN
cana-4456	326	30	,	,	PUNCT
cana-4456	326	31	we	we	PRON
cana-4456	326	32	display	display	VERB
cana-4456	326	33	in	in	ADP
cana-4456	326	34	figure	figure	NOUN
cana-4456	326	35	3	3	NUM
cana-4456	326	36	(	(	PUNCT
cana-4456	326	37	b	b	NOUN
cana-4456	326	38	)	)	PUNCT
cana-4456	326	39	the	the	DET
cana-4456	326	40	error	error	NOUN
cana-4456	326	41	of	of	ADP
cana-4456	326	42	the	the	DET
cana-4456	326	43	numerical	numerical	ADJ
cana-4456	326	44	solution	solution	NOUN
cana-4456	326	45	at	at	ADP
cana-4456	326	46	𝑇	𝑇	PROPN
cana-4456	326	47	=	=	PUNCT
cana-4456	326	48	200	200	NUM
cana-4456	326	49	seconds	second	NOUN
cana-4456	326	50	in	in	ADP
cana-4456	326	51	terms	term	NOUN
cana-4456	326	52	of	of	ADP
cana-4456	326	53	the	the	DET
cana-4456	326	54	shape	shape	NOUN
cana-4456	326	55	parameter	parameter	NOUN
cana-4456	326	56	in	in	ADP
cana-4456	326	57	order	order	NOUN
cana-4456	326	58	to	to	PART
cana-4456	326	59	show	show	VERB
cana-4456	326	60	that	that	SCONJ
cana-4456	326	61	stable	stable	ADJ
cana-4456	326	62	computations	computation	NOUN
cana-4456	326	63	were	be	AUX
cana-4456	326	64	achieved	achieve	VERB
cana-4456	326	65	for	for	ADP
cana-4456	326	66	𝜀	𝜀	NOUN
cana-4456	326	67	=	=	SYM
cana-4456	326	68	5	5	NUM
cana-4456	326	69	.	.	PUNCT
cana-4456	327	1	the	the	DET
cana-4456	327	2	computed	compute	VERB
cana-4456	327	3	solutions	solution	NOUN
cana-4456	327	4	are	be	AUX
cana-4456	327	5	oscillation	oscillation	NOUN
cana-4456	327	6	-	-	PUNCT
cana-4456	327	7	free	free	ADJ
cana-4456	327	8	which	which	PRON
cana-4456	327	9	demonstrates	demonstrate	VERB
cana-4456	327	10	the	the	DET
cana-4456	327	11	ability	ability	NOUN
cana-4456	327	12	of	of	ADP
cana-4456	327	13	the	the	DET
cana-4456	327	14	proposed	propose	VERB
cana-4456	327	15	methods	method	NOUN
cana-4456	327	16	to	to	PART
cana-4456	327	17	accurately	accurately	ADV
cana-4456	327	18	capture	capture	VERB
cana-4456	327	19	steady	steady	ADJ
cana-4456	327	20	state	state	NOUN
cana-4456	327	21	solutions	solution	NOUN
cana-4456	327	22	.	.	PUNCT
cana-4456	328	1	table	table	NOUN
cana-4456	328	2	2	2	NUM
cana-4456	328	3	.	.	X
cana-4456	328	4	error	error	NOUN
cana-4456	328	5	comparison	comparison	NOUN
cana-4456	328	6	of	of	ADP
cana-4456	328	7	water	water	NOUN
cana-4456	328	8	level	level	NOUN
cana-4456	328	9	and	and	CCONJ
cana-4456	328	10	discharge	discharge	VERB
cana-4456	328	11	for	for	ADP
cana-4456	328	12	different	different	ADJ
cana-4456	328	13	flow	flow	NOUN
cana-4456	328	14	conditions	condition	NOUN
cana-4456	328	15	(	(	PUNCT
cana-4456	328	16	subcritical	subcritical	ADJ
cana-4456	328	17	,	,	PUNCT
cana-4456	328	18	transcritical	transcritical	ADJ
cana-4456	328	19	without	without	ADP
cana-4456	328	20	shock	shock	NOUN
cana-4456	328	21	and	and	CCONJ
cana-4456	328	22	transcritical	transcritical	ADJ
cana-4456	328	23	with	with	ADP
cana-4456	328	24	shock	shock	NOUN
cana-4456	328	25	)	)	PUNCT
cana-4456	328	26	using	use	VERB
cana-4456	328	27	kansa	kansa	PROPN
cana-4456	328	28	,	,	PUNCT
cana-4456	328	29	rbf	rbf	PROPN
cana-4456	328	30	-	-	PUNCT
cana-4456	328	31	fd	fd	PROPN
cana-4456	328	32	and	and	CCONJ
cana-4456	328	33	rbf	rbf	PROPN
cana-4456	328	34	-	-	PUNCT
cana-4456	328	35	pum	pum	PROPN
cana-4456	328	36	-	-	PUNCT
cana-4456	328	37	qr	qr	NOUN
cana-4456	328	38	methods	method	NOUN
cana-4456	328	39	.	.	PUNCT
cana-4456	329	1	kansa	kansa	PROPN
cana-4456	329	2	rbf	rbf	PROPN
cana-4456	329	3	-	-	PUNCT
cana-4456	329	4	fd	fd	PROPN
cana-4456	329	5	rbf	rbf	PROPN
cana-4456	329	6	-	-	PUNCT
cana-4456	329	7	pum	pum	PROPN
cana-4456	329	8	-	-	PUNCT
cana-4456	329	9	qr	qr	NOUN
cana-4456	329	10	water	water	NOUN
cana-4456	329	11	height	height	NOUN
cana-4456	329	12	ℎ[𝑚	ℎ[𝑚	PROPN
cana-4456	329	13	]	]	PUNCT
cana-4456	329	14	6.73	6.73	NUM
cana-4456	329	15	×	×	NOUN
cana-4456	329	16	10−6	10−6	NUM
cana-4456	329	17	3.94	3.94	NUM
cana-4456	329	18	×	×	NOUN
cana-4456	329	19	10−6	10−6	NUM
cana-4456	329	20	1.38	1.38	NUM
cana-4456	329	21	×	×	NOUN
cana-4456	329	22	10−6	10−6	NUM
cana-4456	329	23	subcritical	subcritical	ADJ
cana-4456	329	24	discharge	discharge	NOUN
cana-4456	329	25	𝑞[𝑚2/𝑠	𝑞[𝑚2/𝑠	NOUN
cana-4456	329	26	]	]	X
cana-4456	329	27	7	7	NUM
cana-4456	329	28	.	.	NUM
cana-4456	329	29	02	02	NUM
cana-4456	329	30	×	×	NOUN
cana-4456	329	31	10−6	10−6	NUM
cana-4456	329	32	4.21	4.21	NUM
cana-4456	329	33	×	×	NOUN
cana-4456	329	34	10−6	10−6	NUM
cana-4456	329	35	1.05	1.05	NUM
cana-4456	329	36	×	×	NOUN
cana-4456	329	37	10−6	10−6	NUM
cana-4456	329	38	water	water	NOUN
cana-4456	329	39	height	height	NOUN
cana-4456	329	40	ℎ[𝑚	ℎ[𝑚	PROPN
cana-4456	329	41	]	]	PUNCT
cana-4456	329	42	3.99	3.99	NUM
cana-4456	329	43	×	×	NOUN
cana-4456	329	44	10−5	10−5	NUM
cana-4456	329	45	1.95	1.95	NUM
cana-4456	329	46	×	×	NOUN
cana-4456	329	47	10−5	10−5	NUM
cana-4456	329	48	1.26	1.26	NUM
cana-4456	329	49	×	×	NOUN
cana-4456	329	50	10−5	10−5	NUM
cana-4456	329	51	transcritical	transcritical	ADJ
cana-4456	329	52	without	without	ADP
cana-4456	329	53	shock	shock	NOUN
cana-4456	329	54	discharge	discharge	NOUN
cana-4456	329	55	𝑞[𝑚2/𝑠	𝑞[𝑚2/𝑠	NOUN
cana-4456	329	56	]	]	X
cana-4456	329	57	1	1	NUM
cana-4456	329	58	.	.	SYM
cana-4456	329	59	88	88	NUM
cana-4456	329	60	×	×	NOUN
cana-4456	329	61	10−5	10−5	NUM
cana-4456	329	62	1.06	1.06	NUM
cana-4456	329	63	×	×	NOUN
cana-4456	329	64	10−5	10−5	NUM
cana-4456	329	65	6.90	6.90	NUM
cana-4456	329	66	×	×	NOUN
cana-4456	329	67	10−6	10−6	NUM
cana-4456	329	68	water	water	NOUN
cana-4456	329	69	height	height	NOUN
cana-4456	329	70	ℎ[𝑚	ℎ[𝑚	PROPN
cana-4456	329	71	]	]	PUNCT
cana-4456	329	72	4.70	4.70	NUM
cana-4456	329	73	×	×	NOUN
cana-4456	329	74	10−4	10−4	NUM
cana-4456	329	75	4.51	4.51	NUM
cana-4456	329	76	×	×	NOUN
cana-4456	329	77	10−4	10−4	NUM
cana-4456	329	78	4.40	4.40	NUM
cana-4456	329	79	×	×	NOUN
cana-4456	329	80	10−4	10−4	NUM
cana-4456	329	81	transcritical	transcritical	ADJ
cana-4456	329	82	with	with	ADP
cana-4456	329	83	shock	shock	NOUN
cana-4456	329	84	discharge	discharge	NOUN
cana-4456	329	85	𝑞[𝑚2/𝑠	𝑞[𝑚2/𝑠	NOUN
cana-4456	329	86	]	]	X
cana-4456	329	87	3.50×	3.50×	NUM
cana-4456	329	88	10−4	10−4	NUM
cana-4456	329	89	2.50	2.50	NUM
cana-4456	329	90	×	×	NOUN
cana-4456	329	91	10−4	10−4	NUM
cana-4456	329	92	3.10	3.10	NUM
cana-4456	329	93	×	×	NOUN
cana-4456	329	94	10−4	10−4	NUM
cana-4456	329	95	communications	communication	NOUN
cana-4456	329	96	on	on	ADP
cana-4456	329	97	applied	apply	VERB
cana-4456	329	98	nonlinear	nonlinear	ADJ
cana-4456	329	99	analysis	analysis	NOUN
cana-4456	329	100	issn	issn	NOUN
cana-4456	329	101	:	:	PUNCT
cana-4456	329	102	1074	1074	NUM
cana-4456	329	103	-	-	PUNCT
cana-4456	329	104	133x	133x	NUM
cana-4456	329	105	vol	vol	NOUN
cana-4456	329	106	32	32	NUM
cana-4456	329	107	no	no	NOUN
cana-4456	329	108	.	.	PUNCT
cana-4456	330	1	9s	9s	NUM
cana-4456	330	2	(	(	PUNCT
cana-4456	330	3	2025	2025	NUM
cana-4456	330	4	)	)	PUNCT
cana-4456	330	5	2184	2184	NUM
cana-4456	331	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	331	2	(	(	PUNCT
cana-4456	331	3	a	a	X
cana-4456	331	4	)	)	PUNCT
cana-4456	331	5	kansa	kansa	PROPN
cana-4456	331	6	method	method	NOUN
cana-4456	331	7	(	(	PUNCT
cana-4456	331	8	b	b	NOUN
cana-4456	331	9	)	)	PUNCT
cana-4456	331	10	rbf	rbf	PROPN
cana-4456	331	11	-	-	PUNCT
cana-4456	331	12	fd	fd	PROPN
cana-4456	331	13	method	method	NOUN
cana-4456	331	14	(	(	PUNCT
cana-4456	331	15	c	c	NOUN
cana-4456	331	16	)	)	PUNCT
cana-4456	331	17	rbf	rbf	PROPN
cana-4456	331	18	-	-	PUNCT
cana-4456	331	19	pum	pum	PROPN
cana-4456	331	20	-	-	PUNCT
cana-4456	331	21	qr	qr	PROPN
cana-4456	331	22	method	method	NOUN
cana-4456	331	23	figure	figure	NOUN
cana-4456	331	24	1	1	NUM
cana-4456	331	25	.	.	PUNCT
cana-4456	331	26	subcritical	subcritical	ADJ
cana-4456	331	27	flow	flow	NOUN
cana-4456	331	28	over	over	ADP
cana-4456	331	29	a	a	DET
cana-4456	331	30	bump	bump	NOUN
cana-4456	331	31	using	use	VERB
cana-4456	331	32	(	(	PUNCT
cana-4456	331	33	a	a	PRON
cana-4456	331	34	)	)	PUNCT
cana-4456	331	35	kansa	kansa	PROPN
cana-4456	331	36	,	,	PUNCT
cana-4456	331	37	(	(	PUNCT
cana-4456	331	38	b	b	X
cana-4456	331	39	)	)	PUNCT
cana-4456	331	40	rbf	rbf	PROPN
cana-4456	331	41	-	-	PUNCT
cana-4456	331	42	fd	fd	PROPN
cana-4456	331	43	,	,	PUNCT
cana-4456	331	44	and	and	CCONJ
cana-4456	331	45	(	(	PUNCT
cana-4456	331	46	c	c	X
cana-4456	331	47	)	)	PUNCT
cana-4456	331	48	rbf	rbf	PROPN
cana-4456	331	49	-	-	PUNCT
cana-4456	331	50	pum	pum	PROPN
cana-4456	331	51	-	-	PUNCT
cana-4456	331	52	qr	qr	NOUN
cana-4456	331	53	at	at	ADP
cana-4456	331	54	t	t	PROPN
cana-4456	331	55	=	=	NUM
cana-4456	331	56	200	200	NUM
cana-4456	331	57	seconds	second	NOUN
cana-4456	331	58	4.1.2	4.1.2	NUM
cana-4456	331	59	transcritical	transcritical	ADJ
cana-4456	331	60	flow	flow	NOUN
cana-4456	331	61	without	without	ADP
cana-4456	331	62	shock	shock	NOUN
cana-4456	331	63	in	in	ADP
cana-4456	331	64	this	this	DET
cana-4456	331	65	case	case	NOUN
cana-4456	331	66	,	,	PUNCT
cana-4456	331	67	the	the	DET
cana-4456	331	68	upstream	upstream	ADJ
cana-4456	331	69	inflow	inflow	NOUN
cana-4456	331	70	of	of	ADP
cana-4456	331	71	the	the	DET
cana-4456	331	72	discharge	discharge	NOUN
cana-4456	331	73	𝑞0	𝑞0	NOUN
cana-4456	331	74	=	=	SYM
cana-4456	331	75	1.53𝑚2/𝑠	1.53𝑚2/𝑠	NUM
cana-4456	331	76	is	be	AUX
cana-4456	331	77	imposed	impose	VERB
cana-4456	331	78	and	and	CCONJ
cana-4456	331	79	a	a	DET
cana-4456	331	80	downstream	downstream	ADJ
cana-4456	331	81	condition	condition	NOUN
cana-4456	331	82	for	for	ADP
cana-4456	331	83	the	the	DET
cana-4456	331	84	height	height	NOUN
cana-4456	331	85	ℎ𝐿	ℎ𝐿	ADV
cana-4456	331	86	=	=	SYM
cana-4456	331	87	0.40𝑚	0.40𝑚	PROPN
cana-4456	331	88	only	only	ADV
cana-4456	331	89	if	if	SCONJ
cana-4456	331	90	the	the	DET
cana-4456	331	91	flow	flow	NOUN
cana-4456	331	92	is	be	AUX
cana-4456	331	93	subcritical	subcritical	ADJ
cana-4456	331	94	.	.	PUNCT
cana-4456	332	1	if	if	SCONJ
cana-4456	332	2	the	the	DET
cana-4456	332	3	flow	flow	NOUN
cana-4456	332	4	is	be	AUX
cana-4456	332	5	supercritical	supercritical	ADJ
cana-4456	332	6	,	,	PUNCT
cana-4456	332	7	no	no	DET
cana-4456	332	8	condition	condition	NOUN
cana-4456	332	9	is	be	AUX
cana-4456	332	10	imposed	impose	VERB
cana-4456	332	11	.	.	PUNCT
cana-4456	333	1	the	the	DET
cana-4456	333	2	numerical	numerical	ADJ
cana-4456	333	3	examples	example	NOUN
cana-4456	333	4	are	be	AUX
cana-4456	333	5	performed	perform	VERB
cana-4456	333	6	for	for	ADP
cana-4456	333	7	kansa	kansa	PROPN
cana-4456	333	8	method	method	PROPN
cana-4456	333	9	using	use	VERB
cana-4456	333	10	𝜇	𝜇	ADP
cana-4456	333	11	=	=	PROPN
cana-4456	333	12	7	7	NUM
cana-4456	333	13	×	×	NOUN
cana-4456	333	14	10−3	10−3	NUM
cana-4456	333	15	,	,	PUNCT
cana-4456	333	16	for	for	ADP
cana-4456	333	17	rbf	rbf	PROPN
cana-4456	333	18	-	-	PUNCT
cana-4456	333	19	fd	fd	PROPN
cana-4456	333	20	method	method	NOUN
cana-4456	333	21	using	use	VERB
cana-4456	333	22	𝜇	𝜇	ADP
cana-4456	333	23	=	=	PROPN
cana-4456	333	24	4	4	NUM
cana-4456	333	25	×	×	NOUN
cana-4456	333	26	10−3	10−3	NUM
cana-4456	333	27	,	,	PUNCT
cana-4456	333	28	the	the	DET
cana-4456	333	29	optimal	optimal	ADJ
cana-4456	333	30	shape	shape	NOUN
cana-4456	333	31	parameter	parameter	NOUN
cana-4456	333	32	𝜀	𝜀	PROPN
cana-4456	333	33	=	=	SYM
cana-4456	333	34	7	7	NUM
cana-4456	333	35	and	and	CCONJ
cana-4456	333	36	for	for	ADP
cana-4456	333	37	rbf	rbf	PROPN
cana-4456	333	38	-	-	PUNCT
cana-4456	333	39	pum	pum	PROPN
cana-4456	333	40	-	-	PUNCT
cana-4456	333	41	qr	qr	PROPN
cana-4456	333	42	method	method	NOUN
cana-4456	333	43	using	use	VERB
cana-4456	333	44	𝜇	𝜇	ADP
cana-4456	333	45	=	=	PROPN
cana-4456	333	46	10−3	10−3	NUM
cana-4456	333	47	.	.	PUNCT
cana-4456	334	1	as	as	SCONJ
cana-4456	334	2	shown	show	VERB
cana-4456	334	3	in	in	ADP
cana-4456	334	4	figure	figure	NOUN
cana-4456	334	5	4	4	NUM
cana-4456	334	6	,	,	PUNCT
cana-4456	334	7	the	the	DET
cana-4456	334	8	water	water	NOUN
cana-4456	334	9	height	height	NOUN
cana-4456	334	10	and	and	CCONJ
cana-4456	334	11	discharge	discharge	NOUN
cana-4456	334	12	are	be	AUX
cana-4456	334	13	compared	compare	VERB
cana-4456	334	14	with	with	ADP
cana-4456	334	15	the	the	DET
cana-4456	334	16	analytical	analytical	ADJ
cana-4456	334	17	solution	solution	NOUN
cana-4456	334	18	[	[	X
cana-4456	334	19	48	48	NUM
cana-4456	334	20	]	]	PUNCT
cana-4456	334	21	,	,	PUNCT
cana-4456	334	22	which	which	PRON
cana-4456	334	23	can	can	AUX
cana-4456	334	24	be	be	AUX
cana-4456	334	25	observed	observe	VERB
cana-4456	334	26	that	that	SCONJ
cana-4456	334	27	the	the	DET
cana-4456	334	28	water	water	NOUN
cana-4456	334	29	surface	surface	NOUN
cana-4456	334	30	drops	drop	VERB
cana-4456	334	31	significantly	significantly	ADV
cana-4456	334	32	as	as	SCONJ
cana-4456	334	33	the	the	DET
cana-4456	334	34	flow	flow	NOUN
cana-4456	334	35	passes	pass	VERB
cana-4456	334	36	through	through	ADP
cana-4456	334	37	the	the	DET
cana-4456	334	38	bump	bump	NOUN
cana-4456	334	39	.	.	PUNCT
cana-4456	335	1	the	the	DET
cana-4456	335	2	transcritical	transcritical	ADJ
cana-4456	335	3	flow	flow	NOUN
cana-4456	335	4	happened	happen	VERB
cana-4456	335	5	nearby	nearby	ADP
cana-4456	335	6	the	the	DET
cana-4456	335	7	bump	bump	NOUN
cana-4456	335	8	,	,	PUNCT
cana-4456	335	9	since	since	SCONJ
cana-4456	335	10	the	the	DET
cana-4456	335	11	subcritical	subcritical	ADJ
cana-4456	335	12	flow	flow	NOUN
cana-4456	335	13	is	be	AUX
cana-4456	335	14	at	at	ADP
cana-4456	335	15	the	the	DET
cana-4456	335	16	upstream	upstream	NOUN
cana-4456	335	17	and	and	CCONJ
cana-4456	335	18	the	the	DET
cana-4456	335	19	supercritical	supercritical	ADJ
cana-4456	335	20	flow	flow	NOUN
cana-4456	335	21	is	be	AUX
cana-4456	335	22	at	at	ADP
cana-4456	335	23	the	the	DET
cana-4456	335	24	downstream	downstream	NOUN
cana-4456	335	25	.	.	PUNCT
cana-4456	336	1	the	the	DET
cana-4456	336	2	errors	error	NOUN
cana-4456	336	3	of	of	ADP
cana-4456	336	4	water	water	NOUN
cana-4456	336	5	height	height	NOUN
cana-4456	336	6	ℎ	ℎ	NOUN
cana-4456	336	7	and	and	CCONJ
cana-4456	336	8	communications	communication	NOUN
cana-4456	336	9	on	on	ADP
cana-4456	336	10	applied	apply	VERB
cana-4456	336	11	nonlinear	nonlinear	ADJ
cana-4456	336	12	analysis	analysis	NOUN
cana-4456	336	13	issn	issn	NOUN
cana-4456	336	14	:	:	PUNCT
cana-4456	336	15	1074	1074	NUM
cana-4456	336	16	-	-	PUNCT
cana-4456	336	17	133x	133x	NUM
cana-4456	336	18	vol	vol	NOUN
cana-4456	336	19	32	32	NUM
cana-4456	336	20	no	no	NOUN
cana-4456	336	21	.	.	PUNCT
cana-4456	337	1	9s	9s	NUM
cana-4456	337	2	(	(	PUNCT
cana-4456	337	3	2025	2025	NUM
cana-4456	337	4	)	)	PUNCT
cana-4456	337	5	2185	2185	NUM
cana-4456	338	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	338	2	discharge	discharge	NOUN
cana-4456	338	3	𝑞	𝑞	X
cana-4456	338	4	are	be	AUX
cana-4456	338	5	listed	list	VERB
cana-4456	338	6	in	in	ADP
cana-4456	338	7	table	table	NOUN
cana-4456	338	8	2	2	NUM
cana-4456	338	9	.	.	PUNCT
cana-4456	339	1	it	it	PRON
cana-4456	339	2	can	can	AUX
cana-4456	339	3	be	be	AUX
cana-4456	339	4	clearly	clearly	ADV
cana-4456	339	5	seen	see	VERB
cana-4456	339	6	that	that	SCONJ
cana-4456	339	7	the	the	DET
cana-4456	339	8	numerical	numerical	ADJ
cana-4456	339	9	and	and	CCONJ
cana-4456	339	10	analytical	analytical	ADJ
cana-4456	339	11	solutions	solution	NOUN
cana-4456	339	12	are	be	AUX
cana-4456	339	13	in	in	ADP
cana-4456	339	14	good	good	ADJ
cana-4456	339	15	agreement	agreement	NOUN
cana-4456	339	16	.	.	PUNCT
cana-4456	340	1	(	(	PUNCT
cana-4456	340	2	a	a	X
cana-4456	340	3	)	)	PUNCT
cana-4456	340	4	kansa	kansa	PROPN
cana-4456	340	5	method	method	NOUN
cana-4456	340	6	(	(	PUNCT
cana-4456	340	7	b	b	NOUN
cana-4456	340	8	)	)	PUNCT
cana-4456	340	9	rbf	rbf	PROPN
cana-4456	340	10	-	-	PUNCT
cana-4456	340	11	fd	fd	PROPN
cana-4456	340	12	method	method	NOUN
cana-4456	340	13	(	(	PUNCT
cana-4456	340	14	c	c	NOUN
cana-4456	340	15	)	)	PUNCT
cana-4456	340	16	rbf	rbf	PROPN
cana-4456	340	17	-	-	PUNCT
cana-4456	340	18	pum	pum	PROPN
cana-4456	340	19	-	-	PUNCT
cana-4456	340	20	qr	qr	PROPN
cana-4456	340	21	method	method	NOUN
cana-4456	340	22	figure	figure	NOUN
cana-4456	340	23	2	2	NUM
cana-4456	340	24	.	.	PUNCT
cana-4456	340	25	𝐿2	𝐿2	NOUN
cana-4456	340	26	error	error	NOUN
cana-4456	340	27	as	as	ADP
cana-4456	340	28	a	a	DET
cana-4456	340	29	function	function	NOUN
cana-4456	340	30	of	of	ADP
cana-4456	340	31	the	the	DET
cana-4456	340	32	viscosity	viscosity	NOUN
cana-4456	340	33	coefficient	coefficient	NOUN
cana-4456	340	34	for	for	ADP
cana-4456	340	35	the	the	DET
cana-4456	340	36	”	"	PUNCT
cana-4456	340	37	subcritical	subcritical	ADJ
cana-4456	340	38	flow	flow	NOUN
cana-4456	340	39	”	"	PUNCT
cana-4456	340	40	problem	problem	NOUN
cana-4456	340	41	for	for	ADP
cana-4456	340	42	(	(	PUNCT
cana-4456	340	43	a	a	X
cana-4456	340	44	)	)	PUNCT
cana-4456	340	45	kansa	kansa	PROPN
cana-4456	340	46	,	,	PUNCT
cana-4456	340	47	(	(	PUNCT
cana-4456	340	48	b	b	X
cana-4456	340	49	)	)	PUNCT
cana-4456	340	50	rbf	rbf	PROPN
cana-4456	340	51	-	-	PUNCT
cana-4456	340	52	fd	fd	PROPN
cana-4456	340	53	,	,	PUNCT
cana-4456	340	54	and	and	CCONJ
cana-4456	340	55	(	(	PUNCT
cana-4456	340	56	c	c	X
cana-4456	340	57	)	)	PUNCT
cana-4456	340	58	rbf	rbf	PROPN
cana-4456	340	59	-	-	PUNCT
cana-4456	340	60	pum	pum	PROPN
cana-4456	340	61	-	-	PUNCT
cana-4456	340	62	qr	qr	NOUN
cana-4456	340	63	at	at	ADP
cana-4456	340	64	t	t	PROPN
cana-4456	340	65	=	=	NUM
cana-4456	340	66	200	200	NUM
cana-4456	340	67	seconds	second	NOUN
cana-4456	340	68	communications	communication	NOUN
cana-4456	340	69	on	on	ADP
cana-4456	340	70	applied	apply	VERB
cana-4456	340	71	nonlinear	nonlinear	ADJ
cana-4456	340	72	analysis	analysis	NOUN
cana-4456	340	73	issn	issn	NOUN
cana-4456	340	74	:	:	PUNCT
cana-4456	340	75	1074	1074	NUM
cana-4456	340	76	-	-	PUNCT
cana-4456	340	77	133x	133x	NUM
cana-4456	340	78	vol	vol	NOUN
cana-4456	340	79	32	32	NUM
cana-4456	340	80	no	no	NOUN
cana-4456	340	81	.	.	PUNCT
cana-4456	341	1	9s	9s	NUM
cana-4456	341	2	(	(	PUNCT
cana-4456	341	3	2025	2025	NUM
cana-4456	341	4	)	)	PUNCT
cana-4456	341	5	2186	2186	NUM
cana-4456	341	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	341	7	(	(	PUNCT
cana-4456	341	8	a	a	NOUN
cana-4456	341	9	)	)	PUNCT
cana-4456	341	10	(	(	PUNCT
cana-4456	341	11	b	b	X
cana-4456	341	12	)	)	PUNCT
cana-4456	341	13	figure	figure	NOUN
cana-4456	341	14	3	3	NUM
cana-4456	341	15	.	.	PUNCT
cana-4456	342	1	(	(	PUNCT
cana-4456	342	2	a	a	X
cana-4456	342	3	)	)	PUNCT
cana-4456	342	4	𝐿2	𝐿2	PROPN
cana-4456	342	5	errors	error	NOUN
cana-4456	342	6	of	of	ADP
cana-4456	342	7	the	the	DET
cana-4456	342	8	rbf	rbf	PROPN
cana-4456	342	9	-	-	PUNCT
cana-4456	342	10	fd	fd	PROPN
cana-4456	342	11	method	method	NOUN
cana-4456	342	12	for	for	ADP
cana-4456	342	13	solving	solve	VERB
cana-4456	342	14	”	"	PUNCT
cana-4456	342	15	subcritical	subcritical	ADJ
cana-4456	342	16	flow	flow	NOUN
cana-4456	342	17	”	"	PUNCT
cana-4456	342	18	problem	problem	NOUN
cana-4456	342	19	using	use	VERB
cana-4456	342	20	𝜇	𝜇	ADP
cana-4456	342	21	=	=	SYM
cana-4456	342	22	8	8	NUM
cana-4456	342	23	×	×	NOUN
cana-4456	342	24	10−3	10−3	NUM
cana-4456	342	25	.	.	PUNCT
cana-4456	343	1	(	(	PUNCT
cana-4456	343	2	b	b	X
cana-4456	343	3	)	)	PUNCT
cana-4456	343	4	𝐿2	𝐿2	NOUN
cana-4456	343	5	error	error	NOUN
cana-4456	343	6	in	in	ADP
cana-4456	343	7	terms	term	NOUN
cana-4456	343	8	of	of	ADP
cana-4456	343	9	the	the	DET
cana-4456	343	10	shape	shape	NOUN
cana-4456	343	11	parameter	parameter	NOUN
cana-4456	343	12	𝜀.	𝜀.	VERB
cana-4456	343	13	4.1.3	4.1.3	NUM
cana-4456	343	14	transcritical	transcritical	ADJ
cana-4456	343	15	flow	flow	NOUN
cana-4456	343	16	with	with	ADP
cana-4456	343	17	shock	shock	NOUN
cana-4456	343	18	this	this	DET
cana-4456	343	19	case	case	NOUN
cana-4456	343	20	is	be	AUX
cana-4456	343	21	similar	similar	ADJ
cana-4456	343	22	to	to	ADP
cana-4456	343	23	the	the	DET
cana-4456	343	24	previous	previous	ADJ
cana-4456	343	25	one	one	NOUN
cana-4456	343	26	but	but	CCONJ
cana-4456	343	27	with	with	ADP
cana-4456	343	28	different	different	ADJ
cana-4456	343	29	boundary	boundary	ADJ
cana-4456	343	30	conditions	condition	NOUN
cana-4456	343	31	.	.	PUNCT
cana-4456	344	1	here	here	ADV
cana-4456	344	2	,	,	PUNCT
cana-4456	344	3	a	a	DET
cana-4456	344	4	discharge	discharge	NOUN
cana-4456	344	5	of	of	ADP
cana-4456	344	6	𝑞0	𝑞0	NOUN
cana-4456	344	7	=	=	SYM
cana-4456	344	8	0.18𝑚2/𝑠	0.18𝑚2/𝑠	PROPN
cana-4456	344	9	is	be	AUX
cana-4456	344	10	imposed	impose	VERB
cana-4456	344	11	as	as	ADP
cana-4456	344	12	the	the	DET
cana-4456	344	13	upstream	upstream	ADJ
cana-4456	344	14	boundary	boundary	ADJ
cana-4456	344	15	condition	condition	NOUN
cana-4456	344	16	and	and	CCONJ
cana-4456	344	17	a	a	DET
cana-4456	344	18	water	water	NOUN
cana-4456	344	19	level	level	NOUN
cana-4456	344	20	of	of	ADP
cana-4456	344	21	ℎ𝐿	ℎ𝐿	NOUN
cana-4456	344	22	=	=	SYM
cana-4456	344	23	0.33𝑚	0.33𝑚	NOUN
cana-4456	344	24	as	as	ADP
cana-4456	344	25	the	the	DET
cana-4456	344	26	downstream	downstream	ADJ
cana-4456	344	27	boundary	boundary	ADJ
cana-4456	344	28	condition	condition	NOUN
cana-4456	344	29	;	;	PUNCT
cana-4456	344	30	the	the	DET
cana-4456	344	31	flow	flow	NOUN
cana-4456	344	32	regime	regime	NOUN
cana-4456	344	33	changed	change	VERB
cana-4456	344	34	from	from	ADP
cana-4456	344	35	subcritical	subcritical	ADJ
cana-4456	344	36	flow	flow	NOUN
cana-4456	344	37	to	to	ADP
cana-4456	344	38	supercritical	supercritical	ADJ
cana-4456	344	39	flow	flow	NOUN
cana-4456	344	40	and	and	CCONJ
cana-4456	344	41	back	back	ADV
cana-4456	344	42	to	to	ADP
cana-4456	344	43	subcritical	subcritical	ADJ
cana-4456	344	44	flow	flow	NOUN
cana-4456	344	45	with	with	ADP
cana-4456	344	46	a	a	DET
cana-4456	344	47	hydraulic	hydraulic	ADJ
cana-4456	344	48	jump	jump	NOUN
cana-4456	344	49	over	over	ADP
cana-4456	344	50	the	the	DET
cana-4456	344	51	bump	bump	NOUN
cana-4456	344	52	.	.	PUNCT
cana-4456	345	1	for	for	ADP
cana-4456	345	2	this	this	DET
cana-4456	345	3	numerical	numerical	ADJ
cana-4456	345	4	test	test	NOUN
cana-4456	345	5	,	,	PUNCT
cana-4456	345	6	we	we	PRON
cana-4456	345	7	used	use	VERB
cana-4456	345	8	the	the	DET
cana-4456	345	9	following	follow	VERB
cana-4456	345	10	parameters	parameter	NOUN
cana-4456	345	11	𝜇	𝜇	ADP
cana-4456	345	12	=	=	PROPN
cana-4456	345	13	8	8	NUM
cana-4456	345	14	×	×	NOUN
cana-4456	345	15	10−3	10−3	NUM
cana-4456	345	16	,	,	PUNCT
cana-4456	345	17	𝜇	𝜇	ADP
cana-4456	345	18	=	=	SYM
cana-4456	345	19	6	6	NUM
cana-4456	345	20	×	×	NOUN
cana-4456	345	21	10−3	10−3	NUM
cana-4456	345	22	and	and	CCONJ
cana-4456	345	23	𝜇	𝜇	X
cana-4456	345	24	=	=	SYM
cana-4456	345	25	9	9	NUM
cana-4456	345	26	×	×	NOUN
cana-4456	345	27	10−3	10−3	NUM
cana-4456	345	28	,	,	PUNCT
cana-4456	345	29	for	for	ADP
cana-4456	345	30	kansa	kansa	PROPN
cana-4456	345	31	,	,	PUNCT
cana-4456	345	32	rbf	rbf	PROPN
cana-4456	345	33	-	-	PUNCT
cana-4456	345	34	fd	fd	PROPN
cana-4456	345	35	,	,	PUNCT
cana-4456	345	36	rbf	rbf	PROPN
cana-4456	345	37	-	-	PUNCT
cana-4456	345	38	pum	pum	PROPN
cana-4456	345	39	-	-	PUNCT
cana-4456	345	40	qr	qr	NOUN
cana-4456	345	41	methods	method	NOUN
cana-4456	345	42	respectively	respectively	ADV
cana-4456	345	43	.	.	PUNCT
cana-4456	346	1	in	in	ADP
cana-4456	346	2	our	our	PRON
cana-4456	346	3	simulation	simulation	NOUN
cana-4456	346	4	,	,	PUNCT
cana-4456	346	5	we	we	PRON
cana-4456	346	6	set	set	VERB
cana-4456	346	7	the	the	DET
cana-4456	346	8	shape	shape	NOUN
cana-4456	346	9	parameter	parameter	NOUN
cana-4456	346	10	𝜀	𝜀	PROPN
cana-4456	346	11	=	=	SYM
cana-4456	346	12	5	5	NUM
cana-4456	346	13	.	.	PUNCT
cana-4456	346	14	figure	figure	NOUN
cana-4456	346	15	5	5	NUM
cana-4456	346	16	,	,	PUNCT
cana-4456	346	17	shows	show	VERB
cana-4456	346	18	the	the	DET
cana-4456	346	19	numerical	numerical	ADJ
cana-4456	346	20	solutions	solution	NOUN
cana-4456	346	21	concerning	concern	VERB
cana-4456	346	22	the	the	DET
cana-4456	346	23	water	water	NOUN
cana-4456	346	24	height	height	NOUN
cana-4456	346	25	and	and	CCONJ
cana-4456	346	26	discharge	discharge	VERB
cana-4456	346	27	,	,	PUNCT
cana-4456	346	28	compared	compare	VERB
cana-4456	346	29	with	with	ADP
cana-4456	346	30	the	the	DET
cana-4456	346	31	analytical	analytical	ADJ
cana-4456	346	32	solution	solution	NOUN
cana-4456	346	33	.	.	PUNCT
cana-4456	347	1	however	however	ADV
cana-4456	347	2	,	,	PUNCT
cana-4456	347	3	near	near	ADP
cana-4456	347	4	the	the	DET
cana-4456	347	5	jump	jump	NOUN
cana-4456	347	6	discontinuity	discontinuity	NOUN
cana-4456	347	7	we	we	PRON
cana-4456	347	8	can	can	AUX
cana-4456	347	9	observe	observe	VERB
cana-4456	347	10	differences	difference	NOUN
cana-4456	347	11	that	that	PRON
cana-4456	347	12	are	be	AUX
cana-4456	347	13	even	even	ADV
cana-4456	347	14	more	more	ADV
cana-4456	347	15	clear	clear	ADJ
cana-4456	347	16	when	when	SCONJ
cana-4456	347	17	we	we	PRON
cana-4456	347	18	compare	compare	VERB
cana-4456	347	19	analytical	analytical	ADJ
cana-4456	347	20	and	and	CCONJ
cana-4456	347	21	numerical	numerical	ADJ
cana-4456	347	22	discharge	discharge	NOUN
cana-4456	347	23	.	.	PUNCT
cana-4456	348	1	a	a	DET
cana-4456	348	2	more	more	ADV
cana-4456	348	3	quantitative	quantitative	ADJ
cana-4456	348	4	analysis	analysis	NOUN
cana-4456	348	5	of	of	ADP
cana-4456	348	6	the	the	DET
cana-4456	348	7	accuracy	accuracy	NOUN
cana-4456	348	8	is	be	AUX
cana-4456	348	9	listed	list	VERB
cana-4456	348	10	in	in	ADP
cana-4456	348	11	table	table	NOUN
cana-4456	348	12	1	1	NUM
cana-4456	348	13	,	,	PUNCT
cana-4456	348	14	we	we	PRON
cana-4456	348	15	observe	observe	VERB
cana-4456	348	16	that	that	SCONJ
cana-4456	348	17	capturing	capture	VERB
cana-4456	348	18	the	the	DET
cana-4456	348	19	discharge	discharge	NOUN
cana-4456	348	20	𝑞	𝑞	X
cana-4456	348	21	correctly	correctly	ADV
cana-4456	348	22	in	in	ADP
cana-4456	348	23	the	the	DET
cana-4456	348	24	kansa	kansa	PROPN
cana-4456	348	25	method	method	NOUN
cana-4456	348	26	is	be	AUX
cana-4456	348	27	more	more	ADV
cana-4456	348	28	difficult	difficult	ADJ
cana-4456	348	29	than	than	ADP
cana-4456	348	30	in	in	ADP
cana-4456	348	31	the	the	DET
cana-4456	348	32	other	other	ADJ
cana-4456	348	33	methods	method	NOUN
cana-4456	348	34	.	.	PUNCT
cana-4456	349	1	from	from	ADP
cana-4456	349	2	the	the	DET
cana-4456	349	3	results	result	NOUN
cana-4456	349	4	and	and	CCONJ
cana-4456	349	5	comparisons	comparison	NOUN
cana-4456	349	6	in	in	ADP
cana-4456	349	7	this	this	DET
cana-4456	349	8	example	example	NOUN
cana-4456	349	9	,	,	PUNCT
cana-4456	349	10	the	the	DET
cana-4456	349	11	merits	merit	NOUN
cana-4456	349	12	of	of	ADP
cana-4456	349	13	the	the	DET
cana-4456	349	14	proposed	propose	VERB
cana-4456	349	15	meshless	meshless	ADJ
cana-4456	349	16	methods	method	NOUN
cana-4456	349	17	are	be	AUX
cana-4456	349	18	verified	verify	VERB
cana-4456	349	19	.	.	PUNCT
cana-4456	350	1	4.2	4.2	NUM
cana-4456	350	2	test	test	NOUN
cana-4456	350	3	2	2	NUM
cana-4456	350	4	:	:	PUNCT
cana-4456	350	5	dam	dam	NOUN
cana-4456	350	6	break	break	NOUN
cana-4456	350	7	problem	problem	NOUN
cana-4456	350	8	the	the	DET
cana-4456	350	9	dam	dam	NOUN
cana-4456	350	10	-	-	PUNCT
cana-4456	350	11	break	break	NOUN
cana-4456	350	12	problem	problem	NOUN
cana-4456	350	13	is	be	AUX
cana-4456	350	14	the	the	DET
cana-4456	350	15	most	most	ADV
cana-4456	350	16	commonly	commonly	ADV
cana-4456	350	17	investigated	investigate	VERB
cana-4456	350	18	problem	problem	NOUN
cana-4456	350	19	and	and	CCONJ
cana-4456	350	20	have	have	AUX
cana-4456	350	21	also	also	ADV
cana-4456	350	22	become	become	VERB
cana-4456	350	23	the	the	DET
cana-4456	350	24	standard	standard	ADJ
cana-4456	350	25	test	test	NOUN
cana-4456	350	26	scenario	scenario	NOUN
cana-4456	350	27	for	for	ADP
cana-4456	350	28	numerical	numerical	ADJ
cana-4456	350	29	methods	method	NOUN
cana-4456	350	30	for	for	ADP
cana-4456	350	31	shallow	shallow	ADJ
cana-4456	350	32	water	water	NOUN
cana-4456	350	33	equations	equation	NOUN
cana-4456	350	34	.	.	PUNCT
cana-4456	351	1	toro	toro	PROPN
cana-4456	352	1	[	[	X
cana-4456	352	2	49	49	NUM
cana-4456	352	3	]	]	PUNCT
cana-4456	352	4	has	have	AUX
cana-4456	352	5	the	the	DET
cana-4456	352	6	dam	dam	NOUN
cana-4456	352	7	-	-	PUNCT
cana-4456	352	8	break	break	NOUN
cana-4456	352	9	communications	communication	NOUN
cana-4456	352	10	on	on	ADP
cana-4456	352	11	applied	apply	VERB
cana-4456	352	12	nonlinear	nonlinear	ADJ
cana-4456	352	13	analysis	analysis	NOUN
cana-4456	352	14	issn	issn	NOUN
cana-4456	352	15	:	:	PUNCT
cana-4456	352	16	1074	1074	NUM
cana-4456	352	17	-	-	PUNCT
cana-4456	352	18	133x	133x	NUM
cana-4456	352	19	vol	vol	NOUN
cana-4456	352	20	32	32	NUM
cana-4456	352	21	no	no	NOUN
cana-4456	352	22	.	.	PUNCT
cana-4456	353	1	9s	9s	NUM
cana-4456	353	2	(	(	PUNCT
cana-4456	353	3	2025	2025	NUM
cana-4456	353	4	)	)	PUNCT
cana-4456	353	5	2187	2187	NUM
cana-4456	353	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	353	7	(	(	PUNCT
cana-4456	353	8	a	a	X
cana-4456	353	9	)	)	PUNCT
cana-4456	353	10	kansa	kansa	PROPN
cana-4456	353	11	method	method	NOUN
cana-4456	353	12	(	(	PUNCT
cana-4456	353	13	b	b	NOUN
cana-4456	353	14	)	)	PUNCT
cana-4456	353	15	rbf	rbf	PROPN
cana-4456	353	16	-	-	PUNCT
cana-4456	353	17	fd	fd	PROPN
cana-4456	353	18	method	method	NOUN
cana-4456	353	19	(	(	PUNCT
cana-4456	353	20	c	c	NOUN
cana-4456	353	21	)	)	PUNCT
cana-4456	353	22	rbf	rbf	PROPN
cana-4456	353	23	-	-	PUNCT
cana-4456	353	24	pum	pum	PROPN
cana-4456	353	25	-	-	PUNCT
cana-4456	353	26	qr	qr	PROPN
cana-4456	353	27	method	method	NOUN
cana-4456	353	28	figure	figure	NOUN
cana-4456	353	29	4	4	NUM
cana-4456	353	30	.	.	PUNCT
cana-4456	353	31	transcritical	transcritical	ADJ
cana-4456	353	32	flow	flow	NOUN
cana-4456	353	33	without	without	ADP
cana-4456	353	34	shock	shock	NOUN
cana-4456	353	35	over	over	ADP
cana-4456	353	36	a	a	DET
cana-4456	353	37	bump	bump	NOUN
cana-4456	353	38	using	use	VERB
cana-4456	353	39	(	(	PUNCT
cana-4456	353	40	a	a	PRON
cana-4456	353	41	)	)	PUNCT
cana-4456	353	42	kansa	kansa	PROPN
cana-4456	353	43	,	,	PUNCT
cana-4456	353	44	(	(	PUNCT
cana-4456	353	45	b	b	X
cana-4456	353	46	)	)	PUNCT
cana-4456	353	47	rbf	rbf	PROPN
cana-4456	353	48	-	-	PUNCT
cana-4456	353	49	fd	fd	PROPN
cana-4456	353	50	,	,	PUNCT
cana-4456	353	51	and	and	CCONJ
cana-4456	353	52	(	(	PUNCT
cana-4456	353	53	c	c	NOUN
cana-4456	353	54	)	)	PUNCT
cana-4456	353	55	rbfpum	rbfpum	NOUN
cana-4456	353	56	-	-	PUNCT
cana-4456	353	57	qr	qr	PROPN
cana-4456	353	58	at	at	ADP
cana-4456	353	59	t	t	PROPN
cana-4456	353	60	=	=	NUM
cana-4456	353	61	200	200	NUM
cana-4456	353	62	seconds	second	NOUN
cana-4456	353	63	in	in	ADP
cana-4456	353	64	high	high	ADJ
cana-4456	353	65	regard	regard	NOUN
cana-4456	353	66	,	,	PUNCT
cana-4456	353	67	because	because	SCONJ
cana-4456	353	68	its	its	PRON
cana-4456	353	69	solution	solution	NOUN
cana-4456	353	70	includes	include	VERB
cana-4456	353	71	both	both	CCONJ
cana-4456	353	72	continuous	continuous	ADJ
cana-4456	353	73	and	and	CCONJ
cana-4456	353	74	discontinuous	discontinuous	ADJ
cana-4456	353	75	solutions	solution	NOUN
cana-4456	353	76	at	at	ADP
cana-4456	353	77	the	the	DET
cana-4456	353	78	same	same	ADJ
cana-4456	353	79	time	time	NOUN
cana-4456	353	80	,	,	PUNCT
cana-4456	353	81	and	and	CCONJ
cana-4456	353	82	several	several	ADJ
cana-4456	353	83	researches	research	NOUN
cana-4456	353	84	have	have	AUX
cana-4456	353	85	shown	show	VERB
cana-4456	353	86	that	that	SCONJ
cana-4456	353	87	the	the	DET
cana-4456	353	88	shallow	shallow	ADJ
cana-4456	353	89	water	water	NOUN
cana-4456	353	90	equations	equation	NOUN
cana-4456	353	91	are	be	AUX
cana-4456	353	92	suitable	suitable	ADJ
cana-4456	353	93	for	for	ADP
cana-4456	353	94	the	the	DET
cana-4456	353	95	representation	representation	NOUN
cana-4456	353	96	of	of	ADP
cana-4456	353	97	dam	dam	NOUN
cana-4456	353	98	-	-	PUNCT
cana-4456	353	99	break	break	NOUN
cana-4456	353	100	flows	flow	VERB
cana-4456	354	1	e.g.	e.g.	ADV
cana-4456	354	2	[	[	X
cana-4456	354	3	3	3	NUM
cana-4456	354	4	,	,	PUNCT
cana-4456	354	5	50	50	NUM
cana-4456	354	6	,	,	PUNCT
cana-4456	354	7	51	51	NUM
cana-4456	354	8	]	]	PUNCT
cana-4456	354	9	and	and	CCONJ
cana-4456	354	10	thus	thus	ADV
cana-4456	354	11	,	,	PUNCT
cana-4456	354	12	in	in	ADP
cana-4456	354	13	order	order	NOUN
cana-4456	354	14	to	to	PART
cana-4456	354	15	examine	examine	VERB
cana-4456	354	16	the	the	DET
cana-4456	354	17	capability	capability	NOUN
cana-4456	354	18	of	of	ADP
cana-4456	354	19	the	the	DET
cana-4456	354	20	proposed	propose	VERB
cana-4456	354	21	methods	method	NOUN
cana-4456	354	22	considering	consider	VERB
cana-4456	354	23	artificial	artificial	ADJ
cana-4456	354	24	viscosity	viscosity	NOUN
cana-4456	354	25	term	term	NOUN
cana-4456	354	26	to	to	PART
cana-4456	354	27	solve	solve	VERB
cana-4456	354	28	the	the	DET
cana-4456	354	29	problem	problem	NOUN
cana-4456	354	30	of	of	ADP
cana-4456	354	31	discontinuous	discontinuous	ADJ
cana-4456	354	32	initial	initial	ADJ
cana-4456	354	33	condition	condition	NOUN
cana-4456	354	34	,	,	PUNCT
cana-4456	354	35	we	we	PRON
cana-4456	354	36	consider	consider	VERB
cana-4456	354	37	dam	dam	NOUN
cana-4456	354	38	-	-	PUNCT
cana-4456	354	39	break	break	NOUN
cana-4456	354	40	test	test	NOUN
cana-4456	354	41	is	be	AUX
cana-4456	354	42	adopted	adopt	VERB
cana-4456	354	43	as	as	ADP
cana-4456	354	44	the	the	DET
cana-4456	354	45	second	second	ADJ
cana-4456	354	46	test	test	NOUN
cana-4456	354	47	.	.	PUNCT
cana-4456	355	1	the	the	DET
cana-4456	355	2	one	one	NUM
cana-4456	355	3	-	-	PUNCT
cana-4456	355	4	dimensional	dimensional	ADJ
cana-4456	355	5	dam	dam	NOUN
cana-4456	355	6	break	break	NOUN
cana-4456	355	7	is	be	AUX
cana-4456	355	8	an	an	DET
cana-4456	355	9	initial	initial	ADJ
cana-4456	355	10	value	value	NOUN
cana-4456	355	11	problem	problem	NOUN
cana-4456	355	12	consisting	consist	VERB
cana-4456	355	13	of	of	ADP
cana-4456	355	14	two	two	NUM
cana-4456	355	15	still	still	ADV
cana-4456	355	16	bodies	body	NOUN
cana-4456	355	17	of	of	ADP
cana-4456	355	18	water	water	NOUN
cana-4456	355	19	of	of	ADP
cana-4456	355	20	different	different	ADJ
cana-4456	355	21	heights	height	NOUN
cana-4456	355	22	.	.	PUNCT
cana-4456	356	1	the	the	DET
cana-4456	356	2	upstream	upstream	ADJ
cana-4456	356	3	body	body	NOUN
cana-4456	356	4	(	(	PUNCT
cana-4456	356	5	the	the	DET
cana-4456	356	6	reservoir	reservoir	NOUN
cana-4456	356	7	)	)	PUNCT
cana-4456	356	8	is	be	AUX
cana-4456	356	9	separated	separate	VERB
cana-4456	356	10	from	from	ADP
cana-4456	356	11	the	the	DET
cana-4456	356	12	downstream	downstream	ADJ
cana-4456	356	13	body	body	NOUN
cana-4456	356	14	of	of	ADP
cana-4456	356	15	water	water	NOUN
cana-4456	356	16	by	by	ADP
cana-4456	356	17	a	a	DET
cana-4456	356	18	partition	partition	NOUN
cana-4456	356	19	that	that	PRON
cana-4456	356	20	is	be	AUX
cana-4456	356	21	instantaneously	instantaneously	ADV
cana-4456	356	22	removed	remove	VERB
cana-4456	356	23	at	at	ADP
cana-4456	356	24	time	time	NOUN
cana-4456	356	25	𝑡	𝑡	X
cana-4456	356	26	=	=	NOUN
cana-4456	356	27	0	0	NUM
cana-4456	356	28	seconds	second	NOUN
cana-4456	356	29	.	.	PUNCT
cana-4456	357	1	the	the	DET
cana-4456	357	2	two	two	NUM
cana-4456	357	3	bodies	body	NOUN
cana-4456	357	4	of	of	ADP
cana-4456	357	5	water	water	NOUN
cana-4456	357	6	are	be	AUX
cana-4456	357	7	allowed	allow	VERB
cana-4456	357	8	to	to	PART
cana-4456	357	9	interact	interact	VERB
cana-4456	357	10	under	under	ADP
cana-4456	357	11	the	the	DET
cana-4456	357	12	force	force	NOUN
cana-4456	357	13	of	of	ADP
cana-4456	357	14	gravity	gravity	NOUN
cana-4456	357	15	.	.	PUNCT
cana-4456	358	1	we	we	PRON
cana-4456	358	2	consider	consider	VERB
cana-4456	358	3	the	the	DET
cana-4456	358	4	dam	dam	NOUN
cana-4456	358	5	-	-	PUNCT
cana-4456	358	6	break	break	NOUN
cana-4456	358	7	problem	problem	NOUN
cana-4456	358	8	in	in	ADP
cana-4456	358	9	a	a	DET
cana-4456	358	10	rectangular	rectangular	ADJ
cana-4456	358	11	channel	channel	NOUN
cana-4456	358	12	with	with	ADP
cana-4456	358	13	flat	flat	ADJ
cana-4456	358	14	bottom	bottom	NOUN
cana-4456	358	15	,	,	PUNCT
cana-4456	358	16	𝑏(𝑥	𝑏(𝑥	NOUN
cana-4456	358	17	)	)	PUNCT
cana-4456	358	18	=	=	SYM
cana-4456	358	19	0	0	NUM
cana-4456	358	20	and	and	CCONJ
cana-4456	358	21	frictionless	frictionless	NOUN
cana-4456	358	22	.	.	PUNCT
cana-4456	359	1	the	the	DET
cana-4456	359	2	channel	channel	NOUN
cana-4456	359	3	is	be	AUX
cana-4456	359	4	of	of	ADP
cana-4456	359	5	length	length	NOUN
cana-4456	359	6	10𝑚	10𝑚	NOUN
cana-4456	359	7	and	and	CCONJ
cana-4456	359	8	the	the	DET
cana-4456	359	9	initial	initial	ADJ
cana-4456	359	10	conditions	condition	NOUN
cana-4456	359	11	are	be	AUX
cana-4456	359	12	given	give	VERB
cana-4456	359	13	by	by	ADP
cana-4456	359	14	communications	communication	NOUN
cana-4456	359	15	on	on	ADP
cana-4456	359	16	applied	apply	VERB
cana-4456	359	17	nonlinear	nonlinear	ADJ
cana-4456	359	18	analysis	analysis	NOUN
cana-4456	359	19	issn	issn	NOUN
cana-4456	359	20	:	:	PUNCT
cana-4456	359	21	1074	1074	NUM
cana-4456	359	22	-	-	PUNCT
cana-4456	359	23	133x	133x	NUM
cana-4456	359	24	vol	vol	NOUN
cana-4456	359	25	32	32	NUM
cana-4456	359	26	no	no	NOUN
cana-4456	359	27	.	.	PUNCT
cana-4456	360	1	9s	9s	NUM
cana-4456	360	2	(	(	PUNCT
cana-4456	360	3	2025	2025	NUM
cana-4456	360	4	)	)	PUNCT
cana-4456	360	5	2188	2188	NUM
cana-4456	360	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	360	7	(	(	PUNCT
cana-4456	360	8	a	a	X
cana-4456	360	9	)	)	PUNCT
cana-4456	360	10	kansa	kansa	PROPN
cana-4456	360	11	method	method	NOUN
cana-4456	360	12	(	(	PUNCT
cana-4456	360	13	b	b	NOUN
cana-4456	360	14	)	)	PUNCT
cana-4456	360	15	rbf	rbf	PROPN
cana-4456	360	16	-	-	PUNCT
cana-4456	360	17	fd	fd	PROPN
cana-4456	360	18	method	method	NOUN
cana-4456	360	19	(	(	PUNCT
cana-4456	360	20	c	c	NOUN
cana-4456	360	21	)	)	PUNCT
cana-4456	360	22	rbf	rbf	PROPN
cana-4456	360	23	-	-	PUNCT
cana-4456	360	24	pum	pum	PROPN
cana-4456	360	25	-	-	PUNCT
cana-4456	360	26	qr	qr	PROPN
cana-4456	360	27	method	method	NOUN
cana-4456	360	28	figure	figure	NOUN
cana-4456	360	29	5	5	NUM
cana-4456	360	30	.	.	PUNCT
cana-4456	360	31	transcritical	transcritical	ADJ
cana-4456	360	32	flow	flow	NOUN
cana-4456	360	33	with	with	ADP
cana-4456	360	34	shock	shock	NOUN
cana-4456	360	35	over	over	ADP
cana-4456	360	36	a	a	DET
cana-4456	360	37	bump	bump	NOUN
cana-4456	360	38	using	use	VERB
cana-4456	360	39	(	(	PUNCT
cana-4456	360	40	a	a	PRON
cana-4456	360	41	)	)	PUNCT
cana-4456	360	42	kansa	kansa	PROPN
cana-4456	360	43	,	,	PUNCT
cana-4456	360	44	(	(	PUNCT
cana-4456	360	45	b	b	X
cana-4456	360	46	)	)	PUNCT
cana-4456	360	47	rbf	rbf	PROPN
cana-4456	360	48	-	-	PUNCT
cana-4456	360	49	fd	fd	PROPN
cana-4456	360	50	,	,	PUNCT
cana-4456	360	51	and	and	CCONJ
cana-4456	360	52	(	(	PUNCT
cana-4456	360	53	c	c	NOUN
cana-4456	360	54	)	)	PUNCT
cana-4456	360	55	rbfpum	rbfpum	NOUN
cana-4456	360	56	-	-	PUNCT
cana-4456	360	57	qr	qr	PROPN
cana-4456	360	58	at	at	ADP
cana-4456	360	59	t	t	PROPN
cana-4456	360	60	=	=	NUM
cana-4456	360	61	200	200	NUM
cana-4456	360	62	seconds	second	NOUN
cana-4456	360	63	𝑞(𝑥	𝑞(𝑥	PROPN
cana-4456	360	64	,	,	PUNCT
cana-4456	360	65	0	0	NUM
cana-4456	360	66	)	)	PUNCT
cana-4456	360	67	=	=	SYM
cana-4456	360	68	0	0	NUM
cana-4456	360	69	and	and	CCONJ
cana-4456	360	70	ℎ(𝑥	ℎ(𝑥	NOUN
cana-4456	360	71	,	,	PUNCT
cana-4456	360	72	0	0	NUM
cana-4456	360	73	)	)	PUNCT
cana-4456	360	74	=	=	NOUN
cana-4456	360	75	{	{	PUNCT
cana-4456	360	76	0.005	0.005	NUM
cana-4456	360	77	𝑥	𝑥	NOUN
cana-4456	360	78	<	<	X
cana-4456	360	79	5𝑚	5𝑚	NUM
cana-4456	360	80	0.001	0.001	NUM
cana-4456	360	81	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	NOUN
cana-4456	360	82	(	(	PUNCT
cana-4456	360	83	55	55	NUM
cana-4456	360	84	)	)	PUNCT
cana-4456	360	85	as	as	ADP
cana-4456	360	86	boundary	boundary	ADJ
cana-4456	360	87	conditions	condition	NOUN
cana-4456	360	88	,	,	PUNCT
cana-4456	360	89	a	a	DET
cana-4456	360	90	zero	zero	NUM
cana-4456	360	91	discharge	discharge	NOUN
cana-4456	360	92	and	and	CCONJ
cana-4456	360	93	a	a	DET
cana-4456	360	94	free	free	ADJ
cana-4456	360	95	boundary	boundary	NOUN
cana-4456	360	96	are	be	AUX
cana-4456	360	97	considered	consider	VERB
cana-4456	360	98	at	at	ADP
cana-4456	360	99	the	the	DET
cana-4456	360	100	left	left	ADJ
cana-4456	360	101	and	and	CCONJ
cana-4456	360	102	right	right	ADJ
cana-4456	360	103	ends	end	NOUN
cana-4456	360	104	of	of	ADP
cana-4456	360	105	the	the	DET
cana-4456	360	106	channel	channel	NOUN
cana-4456	360	107	.	.	PUNCT
cana-4456	361	1	the	the	DET
cana-4456	361	2	analytical	analytical	ADJ
cana-4456	361	3	solution	solution	NOUN
cana-4456	361	4	for	for	ADP
cana-4456	361	5	this	this	DET
cana-4456	361	6	simple	simple	ADJ
cana-4456	361	7	dam	dam	NOUN
cana-4456	361	8	break	break	NOUN
cana-4456	361	9	test	test	NOUN
cana-4456	361	10	consists	consist	VERB
cana-4456	361	11	of	of	ADP
cana-4456	361	12	a	a	DET
cana-4456	361	13	backward	backward	ADJ
cana-4456	361	14	propagating	propagate	VERB
cana-4456	361	15	rarefaction	rarefaction	NOUN
cana-4456	361	16	and	and	CCONJ
cana-4456	361	17	a	a	DET
cana-4456	361	18	forward	forward	ADV
cana-4456	361	19	-	-	PUNCT
cana-4456	361	20	moving	move	VERB
cana-4456	361	21	shock	shock	NOUN
cana-4456	361	22	wave	wave	NOUN
cana-4456	361	23	[	[	X
cana-4456	361	24	49	49	NUM
cana-4456	361	25	]	]	PUNCT
cana-4456	361	26	.	.	PUNCT
cana-4456	362	1	the	the	DET
cana-4456	362	2	comparison	comparison	NOUN
cana-4456	362	3	of	of	ADP
cana-4456	362	4	the	the	DET
cana-4456	362	5	numerical	numerical	ADJ
cana-4456	362	6	results	result	NOUN
cana-4456	362	7	at	at	ADP
cana-4456	362	8	𝑇	𝑇	PROPN
cana-4456	362	9	=	=	SYM
cana-4456	362	10	2	2	NUM
cana-4456	362	11	,	,	PUNCT
cana-4456	362	12	4	4	NUM
cana-4456	362	13	,	,	PUNCT
cana-4456	362	14	6	6	NUM
cana-4456	362	15	𝑠	𝑠	NOUN
cana-4456	362	16	are	be	AUX
cana-4456	362	17	displayed	display	VERB
cana-4456	362	18	in	in	ADP
cana-4456	362	19	figure	figure	NOUN
cana-4456	362	20	6	6	NUM
cana-4456	362	21	for	for	ADP
cana-4456	362	22	rbf	rbf	PROPN
cana-4456	362	23	-	-	PUNCT
cana-4456	362	24	fd	fd	PROPN
cana-4456	362	25	method	method	NOUN
cana-4456	362	26	using	use	VERB
cana-4456	362	27	𝜇	𝜇	ADP
cana-4456	362	28	=	=	SYM
cana-4456	362	29	2	2	NUM
cana-4456	362	30	×	×	NOUN
cana-4456	362	31	10−4	10−4	NUM
cana-4456	362	32	and	and	CCONJ
cana-4456	362	33	the	the	DET
cana-4456	362	34	optimal	optimal	ADJ
cana-4456	362	35	shape	shape	NOUN
cana-4456	362	36	parameter	parameter	NOUN
cana-4456	362	37	𝜀	𝜀	PROPN
cana-4456	362	38	=	=	SYM
cana-4456	362	39	12	12	NUM
cana-4456	362	40	.	.	PUNCT
cana-4456	362	41	table	table	NOUN
cana-4456	362	42	3	3	NUM
cana-4456	362	43	depicts	depict	VERB
cana-4456	362	44	the	the	DET
cana-4456	362	45	error	error	NOUN
cana-4456	362	46	comparison	comparison	NOUN
cana-4456	362	47	of	of	ADP
cana-4456	362	48	water	water	NOUN
cana-4456	362	49	height	height	NOUN
cana-4456	362	50	ℎ	ℎ	NOUN
cana-4456	362	51	and	and	CCONJ
cana-4456	362	52	discharg	discharg	NOUN
cana-4456	362	53	communications	communication	NOUN
cana-4456	362	54	on	on	ADP
cana-4456	362	55	applied	apply	VERB
cana-4456	362	56	nonlinear	nonlinear	ADJ
cana-4456	362	57	analysis	analysis	NOUN
cana-4456	362	58	issn	issn	NOUN
cana-4456	362	59	:	:	PUNCT
cana-4456	362	60	1074	1074	NUM
cana-4456	362	61	-	-	PUNCT
cana-4456	362	62	133x	133x	NUM
cana-4456	362	63	vol	vol	NOUN
cana-4456	362	64	32	32	NUM
cana-4456	362	65	no	no	NOUN
cana-4456	362	66	.	.	PUNCT
cana-4456	363	1	9s	9s	NUM
cana-4456	363	2	(	(	PUNCT
cana-4456	363	3	2025	2025	NUM
cana-4456	363	4	)	)	PUNCT
cana-4456	363	5	2189	2189	NUM
cana-4456	364	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	364	2	table	table	NOUN
cana-4456	364	3	2	2	NUM
cana-4456	364	4	.	.	X
cana-4456	364	5	error	error	NOUN
cana-4456	364	6	comparison	comparison	NOUN
cana-4456	364	7	of	of	ADP
cana-4456	364	8	water	water	NOUN
cana-4456	364	9	level	level	NOUN
cana-4456	364	10	and	and	CCONJ
cana-4456	364	11	discharge	discharge	VERB
cana-4456	364	12	for	for	ADP
cana-4456	364	13	dam	dam	NOUN
cana-4456	364	14	break	break	NOUN
cana-4456	364	15	problem	problem	NOUN
cana-4456	364	16	over	over	ADP
cana-4456	364	17	a	a	DET
cana-4456	364	18	wet	wet	ADJ
cana-4456	364	19	bed	bed	NOUN
cana-4456	364	20	.	.	PUNCT
cana-4456	365	1	kansa	kansa	PROPN
cana-4456	366	1	rbf	rbf	PROPN
cana-4456	366	2	-	-	PUNCT
cana-4456	366	3	fd	fd	PROPN
cana-4456	366	4	rbf	rbf	PROPN
cana-4456	366	5	-	-	PUNCT
cana-4456	366	6	pum	pum	PROPN
cana-4456	366	7	-	-	PUNCT
cana-4456	366	8	qr	qr	NOUN
cana-4456	366	9	water	water	NOUN
cana-4456	366	10	height	height	NOUN
cana-4456	366	11	ℎ[𝑚	ℎ[𝑚	PROPN
cana-4456	366	12	]	]	PUNCT
cana-4456	366	13	3.07	3.07	NUM
cana-4456	366	14	×	×	NOUN
cana-4456	366	15	10−4	10−4	NUM
cana-4456	366	16	1.71	1.71	NUM
cana-4456	366	17	×	×	NOUN
cana-4456	366	18	10−4	10−4	NUM
cana-4456	366	19	2.10	2.10	NUM
cana-4456	366	20	×	×	NOUN
cana-4456	366	21	10−4	10−4	NUM
cana-4456	366	22	discharge	discharge	NOUN
cana-4456	366	23	𝑞[𝑚2/𝑠	𝑞[𝑚2/𝑠	NOUN
cana-4456	366	24	]	]	X
cana-4456	366	25	1.48×	1.48×	NUM
cana-4456	366	26	10−3	10−3	NUM
cana-4456	366	27	9.76	9.76	NUM
cana-4456	366	28	×	×	NOUN
cana-4456	366	29	10−4	10−4	NUM
cana-4456	366	30	8.85	8.85	NUM
cana-4456	366	31	×	×	NOUN
cana-4456	366	32	10−4	10−4	NUM
cana-4456	366	33	figure	figure	NOUN
cana-4456	366	34	6	6	NUM
cana-4456	366	35	:	:	PUNCT
cana-4456	366	36	dam	dam	NOUN
cana-4456	366	37	-	-	PUNCT
cana-4456	366	38	break	break	NOUN
cana-4456	366	39	on	on	ADP
cana-4456	366	40	wet	wet	ADJ
cana-4456	366	41	bed	bed	NOUN
cana-4456	366	42	using	use	VERB
cana-4456	366	43	rbf	rbf	PROPN
cana-4456	366	44	-	-	PUNCT
cana-4456	366	45	fd	fd	PROPN
cana-4456	366	46	method	method	NOUN
cana-4456	366	47	at	at	ADP
cana-4456	366	48	𝑇	𝑇	PROPN
cana-4456	366	49	=	=	SYM
cana-4456	366	50	2	2	NUM
cana-4456	366	51	,	,	PUNCT
cana-4456	366	52	4	4	NUM
cana-4456	366	53	,	,	PUNCT
cana-4456	366	54	6	6	NUM
cana-4456	366	55	𝑠	𝑠	NOUN
cana-4456	366	56	,	,	PUNCT
cana-4456	366	57	top	top	ADJ
cana-4456	366	58	:	:	PUNCT
cana-4456	366	59	water	water	NOUN
cana-4456	366	60	height	height	NOUN
cana-4456	366	61	,	,	PUNCT
cana-4456	366	62	bottom	bottom	ADJ
cana-4456	366	63	:	:	PUNCT
cana-4456	366	64	discharge	discharge	VERB
cana-4456	366	65	.	.	PUNCT
cana-4456	367	1	for	for	ADP
cana-4456	367	2	all	all	DET
cana-4456	367	3	rbf	rbf	PROPN
cana-4456	367	4	-	-	PUNCT
cana-4456	367	5	based	base	VERB
cana-4456	367	6	methods	method	NOUN
cana-4456	367	7	.	.	PUNCT
cana-4456	368	1	the	the	DET
cana-4456	368	2	results	result	NOUN
cana-4456	368	3	show	show	VERB
cana-4456	368	4	that	that	SCONJ
cana-4456	368	5	the	the	DET
cana-4456	368	6	proposed	propose	VERB
cana-4456	368	7	meshless	meshless	ADJ
cana-4456	368	8	numerical	numerical	ADJ
cana-4456	368	9	methods	method	NOUN
cana-4456	368	10	with	with	ADP
cana-4456	368	11	hyperviscosity	hyperviscosity	NOUN
cana-4456	368	12	has	have	VERB
cana-4456	368	13	ability	ability	NOUN
cana-4456	368	14	of	of	ADP
cana-4456	368	15	shock	shock	NOUN
cana-4456	368	16	capturing	capturing	NOUN
cana-4456	368	17	and	and	CCONJ
cana-4456	368	18	provides	provide	VERB
cana-4456	368	19	stability	stability	NOUN
cana-4456	368	20	in	in	ADP
cana-4456	368	21	dealing	deal	VERB
cana-4456	368	22	with	with	ADP
cana-4456	368	23	problems	problem	NOUN
cana-4456	368	24	with	with	ADP
cana-4456	368	25	discontinuous	discontinuous	ADJ
cana-4456	368	26	flow	flow	NOUN
cana-4456	368	27	.	.	PUNCT
cana-4456	369	1	additionally	additionally	ADV
cana-4456	369	2	,	,	PUNCT
cana-4456	369	3	figure	figure	VERB
cana-4456	369	4	7	7	NUM
cana-4456	369	5	shows	show	VERB
cana-4456	369	6	the	the	DET
cana-4456	369	7	computed	computed	ADJ
cana-4456	369	8	𝐿2	𝐿2	NOUN
cana-4456	369	9	error	error	NOUN
cana-4456	369	10	for	for	ADP
cana-4456	369	11	different	different	ADJ
cana-4456	369	12	values	value	NOUN
cana-4456	369	13	of	of	ADP
cana-4456	369	14	the	the	DET
cana-4456	369	15	viscosity	viscosity	NOUN
cana-4456	369	16	coefficient	coefficient	NOUN
cana-4456	369	17	𝜇	𝜇	ADP
cana-4456	369	18	,	,	PUNCT
cana-4456	369	19	this	this	DET
cana-4456	369	20	coefficient	coefficient	NOUN
cana-4456	369	21	controls	control	VERB
cana-4456	369	22	the	the	DET
cana-4456	369	23	accuracy	accuracy	NOUN
cana-4456	369	24	of	of	ADP
cana-4456	369	25	the	the	DET
cana-4456	369	26	method	method	NOUN
cana-4456	369	27	where	where	SCONJ
cana-4456	369	28	small	small	ADJ
cana-4456	369	29	values	value	NOUN
cana-4456	369	30	are	be	AUX
cana-4456	369	31	expected	expect	VERB
cana-4456	369	32	to	to	PART
cana-4456	369	33	provide	provide	VERB
cana-4456	369	34	accurate	accurate	ADJ
cana-4456	369	35	solutions	solution	NOUN
cana-4456	369	36	,	,	PUNCT
cana-4456	369	37	and	and	CCONJ
cana-4456	369	38	should	should	AUX
cana-4456	369	39	be	be	AUX
cana-4456	369	40	a	a	DET
cana-4456	369	41	limit	limit	NOUN
cana-4456	369	42	value	value	NOUN
cana-4456	369	43	of	of	ADP
cana-4456	369	44	around	around	ADP
cana-4456	369	45	10−4	10−4	NUM
cana-4456	369	46	to	to	PART
cana-4456	369	47	avoid	avoid	VERB
cana-4456	369	48	instability	instability	NOUN
cana-4456	369	49	issues	issue	NOUN
cana-4456	369	50	.	.	PUNCT
cana-4456	370	1	another	another	DET
cana-4456	370	2	consequence	consequence	NOUN
cana-4456	370	3	is	be	AUX
cana-4456	370	4	that	that	SCONJ
cana-4456	370	5	the	the	DET
cana-4456	370	6	accuracy	accuracy	NOUN
cana-4456	370	7	of	of	ADP
cana-4456	370	8	rbf	rbf	PROPN
cana-4456	370	9	-	-	PUNCT
cana-4456	370	10	fd	fd	PROPN
cana-4456	370	11	method	method	NOUN
cana-4456	370	12	does	do	AUX
cana-4456	370	13	not	not	PART
cana-4456	370	14	indefinitely	indefinitely	ADV
cana-4456	370	15	increase	increase	VERB
cana-4456	370	16	with	with	ADP
cana-4456	370	17	stencil	stencil	PROPN
cana-4456	370	18	size	size	NOUN
cana-4456	370	19	𝑛𝑙𝑜𝑐.	𝑛𝑙𝑜𝑐.	NOUN
cana-4456	370	20	as	as	SCONJ
cana-4456	370	21	shown	show	VERB
cana-4456	370	22	in	in	ADP
cana-4456	370	23	figure	figure	NOUN
cana-4456	370	24	8	8	NUM
cana-4456	370	25	(	(	PUNCT
cana-4456	370	26	left	leave	VERB
cana-4456	370	27	)	)	PUNCT
cana-4456	370	28	the	the	DET
cana-4456	370	29	stencil	stencil	PROPN
cana-4456	370	30	size	size	NOUN
cana-4456	370	31	has	have	VERB
cana-4456	370	32	no	no	DET
cana-4456	370	33	bearing	bearing	NOUN
cana-4456	370	34	on	on	ADP
cana-4456	370	35	accuracy	accuracy	NOUN
cana-4456	370	36	,	,	PUNCT
cana-4456	370	37	hence	hence	ADV
cana-4456	370	38	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	370	39	=	=	SYM
cana-4456	370	40	100	100	NUM
cana-4456	370	41	is	be	AUX
cana-4456	370	42	the	the	DET
cana-4456	370	43	stencil	stencil	PROPN
cana-4456	370	44	size	size	NOUN
cana-4456	370	45	chosen	choose	VERB
cana-4456	370	46	for	for	ADP
cana-4456	370	47	this	this	DET
cana-4456	370	48	test	test	NOUN
cana-4456	370	49	case	case	NOUN
cana-4456	370	50	.	.	PUNCT
cana-4456	371	1	with	with	ADP
cana-4456	371	2	𝜇	𝜇	ADP
cana-4456	371	3	=	=	PROPN
cana-4456	371	4	10−4	10−4	PROPN
cana-4456	371	5	,	,	PUNCT
cana-4456	371	6	we	we	PRON
cana-4456	371	7	display	display	VERB
cana-4456	371	8	in	in	ADP
cana-4456	371	9	figure	figure	NOUN
cana-4456	371	10	8	8	NUM
cana-4456	371	11	(	(	PUNCT
cana-4456	371	12	right	right	ADJ
cana-4456	371	13	)	)	PUNCT
cana-4456	371	14	the	the	DET
cana-4456	371	15	curve	curve	NOUN
cana-4456	371	16	of	of	ADP
cana-4456	371	17	the	the	DET
cana-4456	371	18	𝐿2	𝐿2	NOUN
cana-4456	371	19	in	in	ADP
cana-4456	371	20	terms	term	NOUN
cana-4456	371	21	of	of	ADP
cana-4456	371	22	the	the	DET
cana-4456	371	23	shape	shape	NOUN
cana-4456	371	24	parameter	parameter	NOUN
cana-4456	371	25	ε	ε	PROPN
cana-4456	371	26	,	,	PUNCT
cana-4456	371	27	we	we	PRON
cana-4456	371	28	remark	remark	VERB
cana-4456	371	29	that	that	SCONJ
cana-4456	371	30	the	the	DET
cana-4456	371	31	minimum	minimum	NOUN
cana-4456	371	32	error	error	NOUN
cana-4456	371	33	is	be	AUX
cana-4456	371	34	obtained	obtain	VERB
cana-4456	371	35	for	for	ADP
cana-4456	371	36	𝜀	𝜀	NOUN
cana-4456	371	37	=	=	SYM
cana-4456	371	38	12	12	NUM
cana-4456	371	39	.	.	PUNCT
cana-4456	372	1	from	from	ADP
cana-4456	372	2	this	this	DET
cana-4456	372	3	study	study	NOUN
cana-4456	372	4	,	,	PUNCT
cana-4456	372	5	we	we	PRON
cana-4456	372	6	can	can	AUX
cana-4456	372	7	note	note	VERB
cana-4456	372	8	that	that	SCONJ
cana-4456	372	9	increasing	increase	VERB
cana-4456	372	10	the	the	DET
cana-4456	372	11	number	number	NOUN
cana-4456	372	12	of	of	ADP
cana-4456	372	13	points	point	NOUN
cana-4456	372	14	per	per	ADP
cana-4456	372	15	stencil	stencil	PROPN
cana-4456	372	16	leads	lead	VERB
cana-4456	372	17	to	to	ADP
cana-4456	372	18	enhanced	enhanced	ADJ
cana-4456	372	19	accuracy	accuracy	NOUN
cana-4456	372	20	.	.	PUNCT
cana-4456	373	1	communications	communication	NOUN
cana-4456	373	2	on	on	ADP
cana-4456	373	3	applied	apply	VERB
cana-4456	373	4	nonlinear	nonlinear	ADJ
cana-4456	373	5	analysis	analysis	NOUN
cana-4456	373	6	issn	issn	NOUN
cana-4456	373	7	:	:	PUNCT
cana-4456	373	8	1074	1074	NUM
cana-4456	373	9	-	-	PUNCT
cana-4456	373	10	133x	133x	NUM
cana-4456	373	11	vol	vol	NOUN
cana-4456	373	12	32	32	NUM
cana-4456	373	13	no	no	NOUN
cana-4456	373	14	.	.	PUNCT
cana-4456	374	1	9s	9s	NUM
cana-4456	374	2	(	(	PUNCT
cana-4456	374	3	2025	2025	NUM
cana-4456	374	4	)	)	PUNCT
cana-4456	374	5	2190	2190	NUM
cana-4456	374	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	374	7	4.3	4.3	NUM
cana-4456	374	8	test	test	NOUN
cana-4456	374	9	3	3	NUM
cana-4456	374	10	:	:	PUNCT
cana-4456	374	11	steady	steady	ADJ
cana-4456	374	12	flow	flow	NOUN
cana-4456	374	13	with	with	ADP
cana-4456	374	14	friction	friction	NOUN
cana-4456	374	15	(	(	PUNCT
cana-4456	374	16	a	a	X
cana-4456	374	17	)	)	PUNCT
cana-4456	374	18	kansa	kansa	PROPN
cana-4456	374	19	method	method	NOUN
cana-4456	374	20	(	(	PUNCT
cana-4456	374	21	b	b	NOUN
cana-4456	374	22	)	)	PUNCT
cana-4456	374	23	rbf	rbf	PROPN
cana-4456	374	24	-	-	PUNCT
cana-4456	374	25	fd	fd	PROPN
cana-4456	374	26	method	method	NOUN
cana-4456	374	27	(	(	PUNCT
cana-4456	374	28	c	c	NOUN
cana-4456	374	29	)	)	PUNCT
cana-4456	374	30	rbf	rbf	PROPN
cana-4456	374	31	-	-	PUNCT
cana-4456	374	32	pum	pum	PROPN
cana-4456	374	33	-	-	PUNCT
cana-4456	374	34	qr	qr	PROPN
cana-4456	374	35	method	method	NOUN
cana-4456	374	36	figure	figure	NOUN
cana-4456	374	37	7	7	NUM
cana-4456	374	38	.	.	PUNCT
cana-4456	375	1	𝐿2	𝐿2	NOUN
cana-4456	375	2	error	error	NOUN
cana-4456	375	3	as	as	ADP
cana-4456	375	4	a	a	DET
cana-4456	375	5	function	function	NOUN
cana-4456	375	6	of	of	ADP
cana-4456	375	7	the	the	DET
cana-4456	375	8	viscosity	viscosity	NOUN
cana-4456	375	9	coefficient	coefficient	NOUN
cana-4456	375	10	for	for	ADP
cana-4456	375	11	the	the	DET
cana-4456	375	12	”	"	PUNCT
cana-4456	375	13	dam	dam	NOUN
cana-4456	375	14	-	-	PUNCT
cana-4456	375	15	break	break	NOUN
cana-4456	375	16	”	"	PUNCT
cana-4456	375	17	problem	problem	NOUN
cana-4456	375	18	for	for	ADP
cana-4456	375	19	(	(	PUNCT
cana-4456	375	20	a	a	X
cana-4456	375	21	)	)	PUNCT
cana-4456	375	22	kansa	kansa	PROPN
cana-4456	375	23	,	,	PUNCT
cana-4456	375	24	(	(	PUNCT
cana-4456	375	25	b	b	X
cana-4456	375	26	)	)	PUNCT
cana-4456	375	27	rbf	rbf	PROPN
cana-4456	375	28	-	-	PUNCT
cana-4456	375	29	fd	fd	PROPN
cana-4456	375	30	,	,	PUNCT
cana-4456	375	31	and	and	CCONJ
cana-4456	375	32	(	(	PUNCT
cana-4456	375	33	c	c	X
cana-4456	375	34	)	)	PUNCT
cana-4456	375	35	rbf	rbf	PROPN
cana-4456	375	36	-	-	PUNCT
cana-4456	375	37	pum	pum	PROPN
cana-4456	375	38	-	-	PUNCT
cana-4456	375	39	qr	qr	NOUN
cana-4456	375	40	at	at	ADP
cana-4456	375	41	t	t	PROPN
cana-4456	375	42	=	=	NUM
cana-4456	375	43	6	6	NUM
cana-4456	375	44	seconds	second	NOUN
cana-4456	375	45	communications	communication	NOUN
cana-4456	375	46	on	on	ADP
cana-4456	375	47	applied	apply	VERB
cana-4456	375	48	nonlinear	nonlinear	ADJ
cana-4456	375	49	analysis	analysis	NOUN
cana-4456	375	50	issn	issn	NOUN
cana-4456	375	51	:	:	PUNCT
cana-4456	375	52	1074	1074	NUM
cana-4456	375	53	-	-	PUNCT
cana-4456	375	54	133x	133x	NUM
cana-4456	375	55	vol	vol	NOUN
cana-4456	375	56	32	32	NUM
cana-4456	375	57	no	no	NOUN
cana-4456	375	58	.	.	PUNCT
cana-4456	376	1	9s	9s	NUM
cana-4456	376	2	(	(	PUNCT
cana-4456	376	3	2025	2025	NUM
cana-4456	376	4	)	)	PUNCT
cana-4456	376	5	2191	2191	NUM
cana-4456	376	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	376	7	(	(	PUNCT
cana-4456	376	8	a	a	NOUN
cana-4456	376	9	)	)	PUNCT
cana-4456	376	10	(	(	PUNCT
cana-4456	376	11	b	b	X
cana-4456	376	12	)	)	PUNCT
cana-4456	376	13	figure	figure	NOUN
cana-4456	376	14	8	8	NUM
cana-4456	376	15	.	.	PUNCT
cana-4456	377	1	(	(	PUNCT
cana-4456	377	2	a	a	X
cana-4456	377	3	)	)	PUNCT
cana-4456	377	4	𝐿2	𝐿2	PROPN
cana-4456	377	5	errors	error	NOUN
cana-4456	377	6	of	of	ADP
cana-4456	377	7	the	the	DET
cana-4456	377	8	rbf	rbf	PROPN
cana-4456	377	9	-	-	PUNCT
cana-4456	377	10	fd	fd	PROPN
cana-4456	377	11	method	method	NOUN
cana-4456	377	12	for	for	ADP
cana-4456	377	13	solving	solve	VERB
cana-4456	377	14	”	"	PUNCT
cana-4456	377	15	dam	dam	NOUN
cana-4456	377	16	-	-	PUNCT
cana-4456	377	17	break	break	NOUN
cana-4456	377	18	”	"	PUNCT
cana-4456	377	19	problem	problem	NOUN
cana-4456	377	20	with	with	ADP
cana-4456	377	21	respect	respect	NOUN
cana-4456	377	22	to	to	ADP
cana-4456	377	23	the	the	DET
cana-4456	377	24	number	number	NOUN
cana-4456	377	25	of	of	ADP
cana-4456	377	26	stencils	stencil	NOUN
cana-4456	377	27	using	use	VERB
cana-4456	377	28	𝜇	𝜇	ADP
cana-4456	377	29	=	=	PROPN
cana-4456	377	30	2	2	NUM
cana-4456	377	31	×	×	NOUN
cana-4456	377	32	10−4	10−4	NUM
cana-4456	377	33	.	.	PUNCT
cana-4456	378	1	(	(	PUNCT
cana-4456	378	2	b	b	X
cana-4456	378	3	)	)	PUNCT
cana-4456	378	4	𝐿2	𝐿2	NOUN
cana-4456	378	5	error	error	NOUN
cana-4456	378	6	in	in	ADP
cana-4456	378	7	terms	term	NOUN
cana-4456	378	8	of	of	ADP
cana-4456	378	9	the	the	DET
cana-4456	378	10	shape	shape	NOUN
cana-4456	378	11	parameter	parameter	NOUN
cana-4456	378	12	𝜀.	𝜀.	VERB
cana-4456	378	13	the	the	DET
cana-4456	378	14	solutions	solution	NOUN
cana-4456	378	15	presented	present	VERB
cana-4456	378	16	in	in	ADP
cana-4456	378	17	this	this	DET
cana-4456	378	18	section	section	NOUN
cana-4456	378	19	are	be	AUX
cana-4456	378	20	more	more	ADV
cana-4456	378	21	intricate	intricate	ADJ
cana-4456	378	22	than	than	ADP
cana-4456	378	23	those	those	PRON
cana-4456	378	24	in	in	ADP
cana-4456	378	25	the	the	DET
cana-4456	378	26	previous	previous	ADJ
cana-4456	378	27	section	section	NOUN
cana-4456	378	28	4.1	4.1	NUM
cana-4456	378	29	-	-	SYM
cana-4456	378	30	4.2	4.2	NUM
cana-4456	378	31	due	due	ADP
cana-4456	378	32	to	to	ADP
cana-4456	378	33	the	the	DET
cana-4456	378	34	variability	variability	NOUN
cana-4456	378	35	of	of	ADP
cana-4456	378	36	the	the	DET
cana-4456	378	37	topography	topography	NOUN
cana-4456	378	38	near	near	ADP
cana-4456	378	39	the	the	DET
cana-4456	378	40	boundaries	boundary	NOUN
cana-4456	378	41	.	.	PUNCT
cana-4456	379	1	consequently	consequently	ADV
cana-4456	379	2	,	,	PUNCT
cana-4456	379	3	they	they	PRON
cana-4456	379	4	provide	provide	VERB
cana-4456	379	5	a	a	DET
cana-4456	379	6	more	more	ADV
cana-4456	379	7	rigorous	rigorous	ADJ
cana-4456	379	8	validation	validation	NOUN
cana-4456	379	9	of	of	ADP
cana-4456	379	10	the	the	DET
cana-4456	379	11	boundary	boundary	ADJ
cana-4456	379	12	conditions	condition	NOUN
cana-4456	379	13	.	.	PUNCT
cana-4456	380	1	when	when	SCONJ
cana-4456	380	2	𝑆𝑓	𝑆𝑓	PROPN
cana-4456	380	3	=	=	SYM
cana-4456	380	4	0	0	PUNCT
cana-4456	380	5	(	(	PUNCT
cana-4456	380	6	indicating	indicate	VERB
cana-4456	380	7	bottom	bottom	ADJ
cana-4456	380	8	friction	friction	NOUN
cana-4456	380	9	)	)	PUNCT
cana-4456	380	10	,	,	PUNCT
cana-4456	380	11	the	the	DET
cana-4456	380	12	following	follow	VERB
cana-4456	380	13	solutions	solution	NOUN
cana-4456	380	14	can	can	AUX
cana-4456	380	15	verify	verify	VERB
cana-4456	380	16	if	if	SCONJ
cana-4456	380	17	the	the	DET
cana-4456	380	18	friction	friction	NOUN
cana-4456	380	19	terms	term	NOUN
cana-4456	380	20	are	be	AUX
cana-4456	380	21	implemented	implement	VERB
cana-4456	380	22	correctly	correctly	ADV
cana-4456	380	23	to	to	PART
cana-4456	380	24	maintain	maintain	VERB
cana-4456	380	25	steady	steady	ADJ
cana-4456	380	26	states	state	NOUN
cana-4456	380	27	.	.	PUNCT
cana-4456	381	1	these	these	DET
cana-4456	381	2	solutions	solution	NOUN
cana-4456	381	3	are	be	AUX
cana-4456	381	4	derived	derive	VERB
cana-4456	381	5	using	use	VERB
cana-4456	381	6	the	the	DET
cana-4456	381	7	procedure	procedure	NOUN
cana-4456	381	8	introduced	introduce	VERB
cana-4456	381	9	by	by	ADP
cana-4456	381	10	i.	i.	PROPN
cana-4456	381	11	macdonald	macdonald	PROPN
cana-4456	382	1	[	[	X
cana-4456	382	2	52	52	NUM
cana-4456	382	3	,	,	PUNCT
cana-4456	382	4	53	53	NUM
cana-4456	382	5	]	]	PUNCT
cana-4456	382	6	:	:	PUNCT
cana-4456	382	7	given	give	VERB
cana-4456	382	8	the	the	DET
cana-4456	382	9	water	water	NOUN
cana-4456	382	10	depth	depth	NOUN
cana-4456	382	11	profile	profile	NOUN
cana-4456	382	12	and	and	CCONJ
cana-4456	382	13	the	the	DET
cana-4456	382	14	discharge	discharge	NOUN
cana-4456	382	15	,	,	PUNCT
cana-4456	382	16	the	the	DET
cana-4456	382	17	corresponding	corresponding	ADJ
cana-4456	382	18	topography	topography	NOUN
cana-4456	382	19	is	be	AUX
cana-4456	382	20	subsequently	subsequently	ADV
cana-4456	382	21	computed	compute	VERB
cana-4456	382	22	.	.	PUNCT
cana-4456	383	1	the	the	DET
cana-4456	383	2	three	three	NUM
cana-4456	383	3	selected	select	VERB
cana-4456	383	4	solutions	solution	NOUN
cana-4456	383	5	illustrate	illustrate	VERB
cana-4456	383	6	the	the	DET
cana-4456	383	7	efficacy	efficacy	NOUN
cana-4456	383	8	of	of	ADP
cana-4456	383	9	the	the	DET
cana-4456	383	10	scheme	scheme	NOUN
cana-4456	383	11	in	in	ADP
cana-4456	383	12	addressing	address	VERB
cana-4456	383	13	stationary	stationary	ADJ
cana-4456	383	14	states	state	NOUN
cana-4456	383	15	induced	induce	VERB
cana-4456	383	16	by	by	ADP
cana-4456	383	17	the	the	DET
cana-4456	383	18	topography	topography	NOUN
cana-4456	383	19	and	and	CCONJ
cana-4456	383	20	by	by	ADP
cana-4456	383	21	friction	friction	NOUN
cana-4456	383	22	under	under	ADP
cana-4456	383	23	a	a	DET
cana-4456	383	24	wide	wide	ADJ
cana-4456	383	25	range	range	NOUN
cana-4456	383	26	of	of	ADP
cana-4456	383	27	flow	flow	NOUN
cana-4456	383	28	conditions	condition	NOUN
cana-4456	383	29	.	.	PUNCT
cana-4456	384	1	at	at	ADP
cana-4456	384	2	steady	steady	ADJ
cana-4456	384	3	states	state	NOUN
cana-4456	384	4	,	,	PUNCT
cana-4456	384	5	we	we	PRON
cana-4456	384	6	have	have	VERB
cana-4456	384	7	𝜕𝑡ℎ	𝜕𝑡ℎ	PROPN
cana-4456	384	8	=	=	SYM
cana-4456	384	9	𝜕𝑡𝑢	𝜕𝑡𝑢	NOUN
cana-4456	384	10	=	=	SYM
cana-4456	384	11	𝜕𝑡𝑞	𝜕𝑡𝑞	NOUN
cana-4456	385	1	=	=	NOUN
cana-4456	385	2	0	0	NUM
cana-4456	385	3	,	,	PUNCT
cana-4456	385	4	thus	thus	ADV
cana-4456	385	5	the	the	DET
cana-4456	385	6	mass	mass	ADJ
cana-4456	385	7	-	-	PUNCT
cana-4456	385	8	conservation	conservation	NOUN
cana-4456	385	9	equation	equation	NOUN
cana-4456	385	10	gives	give	VERB
cana-4456	385	11	𝑞	𝑞	NOUN
cana-4456	385	12	=	=	NOUN
cana-4456	385	13	constant	constant	ADJ
cana-4456	385	14	and	and	CCONJ
cana-4456	385	15	we	we	PRON
cana-4456	385	16	get	get	VERB
cana-4456	385	17	the	the	DET
cana-4456	385	18	equation	equation	NOUN
cana-4456	385	19	𝜕𝑥𝑏	𝜕𝑥𝑏	PUNCT
cana-4456	386	1	=	=	PUNCT
cana-4456	386	2	(	(	PUNCT
cana-4456	386	3	𝑞2	𝑞2	NOUN
cana-4456	386	4	𝑔ℎ3	𝑔ℎ3	VERB
cana-4456	386	5	−	−	NOUN
cana-4456	386	6	1	1	NUM
cana-4456	386	7	)	)	PUNCT
cana-4456	386	8	𝜕𝑥ℎ	𝜕𝑥ℎ	PUNCT
cana-4456	387	1	+	+	CCONJ
cana-4456	387	2	𝑆𝑓.	𝑆𝑓.	PROPN
cana-4456	387	3	(	(	PUNCT
cana-4456	387	4	56	56	NUM
cana-4456	387	5	)	)	PUNCT
cana-4456	387	6	where	where	SCONJ
cana-4456	387	7	𝑆𝑓	𝑆𝑓	PROPN
cana-4456	387	8	depends	depend	VERB
cana-4456	387	9	on	on	ADP
cana-4456	387	10	the	the	DET
cana-4456	387	11	friction	friction	NOUN
cana-4456	387	12	law	law	NOUN
cana-4456	387	13	chosen	choose	VERB
cana-4456	387	14	.	.	PUNCT
cana-4456	388	1	from	from	ADP
cana-4456	388	2	this	this	DET
cana-4456	388	3	relation	relation	NOUN
cana-4456	388	4	,	,	PUNCT
cana-4456	388	5	one	one	PRON
cana-4456	388	6	can	can	AUX
cana-4456	388	7	make	make	VERB
cana-4456	388	8	as	as	ADP
cana-4456	388	9	many	many	ADJ
cana-4456	388	10	solutions	solution	NOUN
cana-4456	388	11	as	as	SCONJ
cana-4456	388	12	needed	need	VERB
cana-4456	388	13	.	.	PUNCT
cana-4456	389	1	in	in	ADP
cana-4456	389	2	this	this	DET
cana-4456	389	3	section	section	NOUN
cana-4456	389	4	,	,	PUNCT
cana-4456	389	5	we	we	PRON
cana-4456	389	6	present	present	VERB
cana-4456	389	7	a	a	DET
cana-4456	389	8	few	few	ADJ
cana-4456	389	9	of	of	ADP
cana-4456	389	10	these	these	DET
cana-4456	389	11	solutions	solution	NOUN
cana-4456	389	12	obtained	obtain	VERB
cana-4456	389	13	for	for	ADP
cana-4456	389	14	specific	specific	ADJ
cana-4456	389	15	value	value	NOUN
cana-4456	389	16	of	of	ADP
cana-4456	389	17	the	the	DET
cana-4456	389	18	domain	domain	NOUN
cana-4456	389	19	length	length	NOUN
cana-4456	389	20	𝐿	𝐿	PROPN
cana-4456	389	21	and	and	CCONJ
cana-4456	389	22	fixed	fix	VERB
cana-4456	389	23	parameters	parameter	NOUN
cana-4456	389	24	,	,	PUNCT
cana-4456	389	25	such	such	ADJ
cana-4456	389	26	as	as	ADP
cana-4456	389	27	the	the	DET
cana-4456	389	28	friction	friction	NOUN
cana-4456	389	29	law	law	NOUN
cana-4456	389	30	and	and	CCONJ
cana-4456	389	31	its	its	PRON
cana-4456	389	32	coefficient	coefficient	NOUN
cana-4456	389	33	.	.	PUNCT
cana-4456	390	1	the	the	DET
cana-4456	390	2	water	water	NOUN
cana-4456	390	3	height	height	NOUN
cana-4456	390	4	profile	profile	NOUN
cana-4456	390	5	and	and	CCONJ
cana-4456	390	6	the	the	DET
cana-4456	390	7	discharge	discharge	NOUN
cana-4456	390	8	are	be	AUX
cana-4456	390	9	provided	provide	VERB
cana-4456	390	10	,	,	PUNCT
cana-4456	390	11	and	and	CCONJ
cana-4456	390	12	the	the	DET
cana-4456	390	13	corresponding	corresponding	ADJ
cana-4456	390	14	topographies	topography	NOUN
cana-4456	390	15	are	be	AUX
cana-4456	390	16	computed	compute	VERB
cana-4456	390	17	by	by	ADP
cana-4456	390	18	solving	solve	VERB
cana-4456	390	19	the	the	DET
cana-4456	390	20	equation	equation	NOUN
cana-4456	390	21	(	(	PUNCT
cana-4456	390	22	56	56	NUM
cana-4456	390	23	)	)	PUNCT
cana-4456	390	24	with	with	ADP
cana-4456	390	25	a	a	DET
cana-4456	390	26	high	high	ADJ
cana-4456	390	27	order	order	NOUN
cana-4456	390	28	iterative	iterative	NOUN
cana-4456	390	29	method	method	NOUN
cana-4456	390	30	[	[	X
cana-4456	390	31	51	51	NUM
cana-4456	390	32	]	]	PUNCT
cana-4456	390	33	.	.	PUNCT
cana-4456	391	1	in	in	ADP
cana-4456	391	2	the	the	DET
cana-4456	391	3	following	follow	VERB
cana-4456	391	4	computations	computation	NOUN
cana-4456	391	5	,	,	PUNCT
cana-4456	391	6	the	the	DET
cana-4456	391	7	initial	initial	ADJ
cana-4456	391	8	conditions	condition	NOUN
cana-4456	391	9	set	set	VERB
cana-4456	391	10	to	to	ADP
cana-4456	391	11	ℎ(𝑥	ℎ(𝑥	NUM
cana-4456	391	12	)	)	PUNCT
cana-4456	391	13	+	+	SYM
cana-4456	391	14	𝑏(𝑥	𝑏(𝑥	NOUN
cana-4456	391	15	)	)	PUNCT
cana-4456	391	16	=	=	SYM
cana-4456	391	17	0	0	NUM
cana-4456	391	18	,	,	PUNCT
cana-4456	391	19	𝑞(𝑥	𝑞(𝑥	PROPN
cana-4456	391	20	)	)	PUNCT
cana-4456	391	21	=	=	SYM
cana-4456	391	22	0	0	NUM
cana-4456	391	23	and	and	CCONJ
cana-4456	391	24	all	all	DET
cana-4456	391	25	results	result	NOUN
cana-4456	391	26	are	be	AUX
cana-4456	391	27	displayed	display	VERB
cana-4456	391	28	at	at	ADP
cana-4456	391	29	𝑇	𝑇	PROPN
cana-4456	391	30	=	=	SYM
cana-4456	391	31	1500𝑠	1500𝑠	NOUN
cana-4456	391	32	using	use	VERB
cana-4456	391	33	𝑁	𝑁	PROPN
cana-4456	391	34	=	=	SYM
cana-4456	391	35	801	801	NUM
cana-4456	391	36	,	,	PUNCT
cana-4456	391	37	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	391	38	=	=	SYM
cana-4456	391	39	100	100	NUM
cana-4456	391	40	and	and	CCONJ
cana-4456	391	41	𝑛𝑝	𝑛𝑝	NOUN
cana-4456	391	42	=	=	NUM
cana-4456	391	43	400	400	NUM
cana-4456	391	44	.	.	PUNCT
cana-4456	392	1	the	the	DET
cana-4456	392	2	analytical	analytical	ADJ
cana-4456	392	3	solutions	solution	NOUN
cana-4456	392	4	shown	show	VERB
cana-4456	392	5	in	in	ADP
cana-4456	392	6	[	[	X
cana-4456	392	7	51	51	NUM
cana-4456	392	8	]	]	PUNCT
cana-4456	392	9	are	be	AUX
cana-4456	392	10	also	also	ADV
cana-4456	392	11	plotted	plot	VERB
cana-4456	392	12	within	within	ADP
cana-4456	392	13	the	the	DET
cana-4456	392	14	obtained	obtain	VERB
cana-4456	392	15	numerical	numerical	ADJ
cana-4456	392	16	results	result	NOUN
cana-4456	392	17	.	.	PUNCT
cana-4456	393	1	communications	communication	NOUN
cana-4456	393	2	on	on	ADP
cana-4456	393	3	applied	apply	VERB
cana-4456	393	4	nonlinear	nonlinear	ADJ
cana-4456	393	5	analysis	analysis	NOUN
cana-4456	393	6	issn	issn	NOUN
cana-4456	393	7	:	:	PUNCT
cana-4456	393	8	1074	1074	NUM
cana-4456	393	9	-	-	PUNCT
cana-4456	393	10	133x	133x	NUM
cana-4456	393	11	vol	vol	NOUN
cana-4456	393	12	32	32	NUM
cana-4456	393	13	no	no	NOUN
cana-4456	393	14	.	.	PUNCT
cana-4456	394	1	9s	9s	NUM
cana-4456	394	2	(	(	PUNCT
cana-4456	394	3	2025	2025	NUM
cana-4456	394	4	)	)	PUNCT
cana-4456	394	5	2192	2192	NUM
cana-4456	394	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	394	7	4.3.1	4.3.1	NUM
cana-4456	394	8	subcritical	subcritical	ADJ
cana-4456	394	9	flow	flow	NOUN
cana-4456	394	10	we	we	PRON
cana-4456	394	11	consider	consider	VERB
cana-4456	394	12	a	a	DET
cana-4456	394	13	𝐿	𝐿	NOUN
cana-4456	394	14	=	=	NOUN
cana-4456	394	15	1000	1000	NUM
cana-4456	394	16	𝑚	𝑚	ADP
cana-4456	394	17	long	long	ADJ
cana-4456	394	18	channel	channel	NOUN
cana-4456	394	19	with	with	ADP
cana-4456	394	20	a	a	DET
cana-4456	394	21	discharge	discharge	NOUN
cana-4456	394	22	of	of	ADP
cana-4456	394	23	q	q	NOUN
cana-4456	395	1	=	=	NOUN
cana-4456	395	2	2𝑚2/𝑠.	2𝑚2/𝑠.	NUM
cana-4456	395	3	the	the	DET
cana-4456	395	4	flow	flow	NOUN
cana-4456	395	5	is	be	AUX
cana-4456	395	6	subcritical	subcritical	ADJ
cana-4456	395	7	at	at	ADP
cana-4456	395	8	inflow	inflow	NOUN
cana-4456	395	9	and	and	CCONJ
cana-4456	395	10	is	be	AUX
cana-4456	395	11	subcritical	subcritical	ADJ
cana-4456	395	12	at	at	ADP
cana-4456	395	13	outflow	outflow	NOUN
cana-4456	395	14	with	with	ADP
cana-4456	395	15	depth	depth	NOUN
cana-4456	395	16	ℎ𝑎𝑛𝑎(1000	ℎ𝑎𝑛𝑎(1000	NOUN
cana-4456	395	17	)	)	PUNCT
cana-4456	396	1	=	=	PUNCT
cana-4456	396	2	0.748409	0.748409	NUM
cana-4456	396	3	𝑚	𝑚	X
cana-4456	396	4	where	where	SCONJ
cana-4456	396	5	ℎ𝑎𝑛𝑎	ℎ𝑎𝑛𝑎	NOUN
cana-4456	396	6	is	be	AUX
cana-4456	396	7	analytical	analytical	ADJ
cana-4456	396	8	solution	solution	NOUN
cana-4456	396	9	.	.	PUNCT
cana-4456	397	1	the	the	DET
cana-4456	397	2	manning	man	VERB
cana-4456	397	3	coefficient	coefficient	NOUN
cana-4456	397	4	for	for	ADP
cana-4456	397	5	the	the	DET
cana-4456	397	6	channel	channel	NOUN
cana-4456	397	7	is	be	AUX
cana-4456	397	8	𝑛	𝑛	PRON
cana-4456	397	9	=	=	PRON
cana-4456	397	10	0.033𝑚−1/3𝑠.	0.033𝑚−1/3𝑠.	NOUN
cana-4456	397	11	the	the	DET
cana-4456	397	12	boundary	boundary	ADJ
cana-4456	397	13	conditions	condition	NOUN
cana-4456	397	14	set	set	VERB
cana-4456	397	15	to	to	PART
cana-4456	397	16	{	{	PUNCT
cana-4456	397	17	𝑞(𝑥	𝑞(𝑥	PROPN
cana-4456	397	18	)	)	PUNCT
cana-4456	397	19	=	=	SYM
cana-4456	398	1	2	2	NUM
cana-4456	398	2	𝑥	𝑥	NOUN
cana-4456	398	3	=	=	SYM
cana-4456	398	4	0	0	X
cana-4456	398	5	ℎ(𝑥	ℎ(𝑥	NUM
cana-4456	398	6	)	)	PUNCT
cana-4456	398	7	=	=	SYM
cana-4456	398	8	ℎ𝑎𝑛𝑎(1000	ℎ𝑎𝑛𝑎(1000	X
cana-4456	398	9	)	)	PUNCT
cana-4456	398	10	𝑥	𝑥	NOUN
cana-4456	398	11	=	=	SYM
cana-4456	398	12	𝐿	𝐿	PROPN
cana-4456	398	13	(	(	PUNCT
cana-4456	398	14	57	57	NUM
cana-4456	398	15	)	)	PUNCT
cana-4456	398	16	the	the	DET
cana-4456	398	17	water	water	NOUN
cana-4456	398	18	depth	depth	NOUN
cana-4456	398	19	and	and	CCONJ
cana-4456	398	20	discharge	discharge	NOUN
cana-4456	398	21	are	be	AUX
cana-4456	398	22	shown	show	VERB
cana-4456	398	23	in	in	ADP
cana-4456	398	24	figure	figure	NOUN
cana-4456	398	25	9	9	NUM
cana-4456	398	26	for	for	ADP
cana-4456	398	27	kansa	kansa	PROPN
cana-4456	398	28	,	,	PUNCT
cana-4456	398	29	rbf	rbf	PROPN
cana-4456	398	30	-	-	PUNCT
cana-4456	398	31	fd	fd	PROPN
cana-4456	398	32	with	with	ADP
cana-4456	398	33	an	an	DET
cana-4456	398	34	optimal	optimal	ADJ
cana-4456	398	35	shape	shape	NOUN
cana-4456	398	36	parameter	parameter	NOUN
cana-4456	398	37	ε	ε	PROPN
cana-4456	398	38	=	=	PUNCT
cana-4456	398	39	0.25	0.25	NUM
cana-4456	398	40	and	and	CCONJ
cana-4456	398	41	rbf	rbf	PROPN
cana-4456	398	42	-	-	PUNCT
cana-4456	398	43	pum	pum	PROPN
cana-4456	398	44	-	-	PUNCT
cana-4456	398	45	qr	qr	NOUN
cana-4456	398	46	methods	method	NOUN
cana-4456	398	47	using	use	VERB
cana-4456	398	48	𝜇	𝜇	ADP
cana-4456	398	49	=	=	PROPN
cana-4456	398	50	10−1	10−1	PROPN
cana-4456	398	51	in	in	ADP
cana-4456	398	52	all	all	DET
cana-4456	398	53	cases	case	NOUN
cana-4456	398	54	.	.	PUNCT
cana-4456	399	1	the	the	DET
cana-4456	399	2	numerical	numerical	ADJ
cana-4456	399	3	solutions	solution	NOUN
cana-4456	399	4	is	be	AUX
cana-4456	399	5	very	very	ADV
cana-4456	399	6	close	close	ADJ
cana-4456	399	7	to	to	ADP
cana-4456	399	8	the	the	DET
cana-4456	399	9	analytical	analytical	ADJ
cana-4456	399	10	solution	solution	NOUN
cana-4456	399	11	,	,	PUNCT
cana-4456	399	12	and	and	CCONJ
cana-4456	399	13	we	we	PRON
cana-4456	399	14	obtained	obtain	VERB
cana-4456	399	15	very	very	ADV
cana-4456	399	16	satisfying	satisfying	ADJ
cana-4456	399	17	results	result	NOUN
cana-4456	399	18	in	in	ADP
cana-4456	399	19	the	the	DET
cana-4456	399	20	approximation	approximation	NOUN
cana-4456	399	21	of	of	ADP
cana-4456	399	22	the	the	DET
cana-4456	399	23	steady	steady	ADJ
cana-4456	399	24	discharge	discharge	NOUN
cana-4456	399	25	and	and	CCONJ
cana-4456	399	26	water	water	NOUN
cana-4456	399	27	height	height	NOUN
cana-4456	399	28	as	as	SCONJ
cana-4456	399	29	illustrated	illustrate	VERB
cana-4456	399	30	in	in	ADP
cana-4456	399	31	table	table	NOUN
cana-4456	399	32	4	4	NUM
cana-4456	399	33	.	.	PUNCT
cana-4456	399	34	figure	figure	VERB
cana-4456	399	35	10	10	NUM
cana-4456	399	36	shows	show	VERB
cana-4456	399	37	the	the	DET
cana-4456	399	38	computed	computed	ADJ
cana-4456	399	39	𝐿2	𝐿2	NOUN
cana-4456	399	40	error	error	NOUN
cana-4456	399	41	for	for	ADP
cana-4456	399	42	different	different	ADJ
cana-4456	399	43	values	value	NOUN
cana-4456	399	44	of	of	ADP
cana-4456	399	45	the	the	DET
cana-4456	399	46	viscosity	viscosity	NOUN
cana-4456	399	47	coefficient	coefficient	NOUN
cana-4456	399	48	𝜇.	𝜇.	ADV
cana-4456	399	49	from	from	ADP
cana-4456	399	50	figure	figure	NOUN
cana-4456	399	51	10	10	NUM
cana-4456	399	52	,	,	PUNCT
cana-4456	399	53	we	we	PRON
cana-4456	399	54	remark	remark	VERB
cana-4456	399	55	that	that	SCONJ
cana-4456	399	56	for	for	ADP
cana-4456	399	57	kansa	kansa	PROPN
cana-4456	399	58	method	method	VERB
cana-4456	399	59	the	the	DET
cana-4456	399	60	minimum	minimum	NOUN
cana-4456	399	61	error	error	NOUN
cana-4456	399	62	is	be	AUX
cana-4456	399	63	for	for	SCONJ
cana-4456	399	64	obtained	obtain	VERB
cana-4456	399	65	around	around	ADP
cana-4456	399	66	𝜇	𝜇	ADP
cana-4456	399	67	=	=	PROPN
cana-4456	399	68	10−1	10−1	NUM
cana-4456	399	69	,	,	PUNCT
cana-4456	399	70	for	for	ADP
cana-4456	399	71	rbf	rbf	PROPN
cana-4456	399	72	-	-	PUNCT
cana-4456	399	73	fd	fd	PROPN
cana-4456	399	74	method	method	NOUN
cana-4456	399	75	𝜇	𝜇	ADP
cana-4456	399	76	=	=	PROPN
cana-4456	399	77	10−1	10−1	PROPN
cana-4456	399	78	and	and	CCONJ
cana-4456	399	79	for	for	ADP
cana-4456	399	80	rbfpum	rbfpum	NOUN
cana-4456	399	81	-	-	PUNCT
cana-4456	399	82	qr	qr	PROPN
cana-4456	399	83	method	method	NOUN
cana-4456	399	84	𝜇	𝜇	ADP
cana-4456	399	85	=	=	PROPN
cana-4456	399	86	10−1	10−1	NUM
cana-4456	399	87	.	.	PUNCT
cana-4456	400	1	we	we	PRON
cana-4456	400	2	make	make	VERB
cana-4456	400	3	an	an	DET
cana-4456	400	4	error	error	NOUN
cana-4456	400	5	analysis	analysis	NOUN
cana-4456	400	6	for	for	ADP
cana-4456	400	7	the	the	DET
cana-4456	400	8	subcritical	subcritical	ADJ
cana-4456	400	9	flow	flow	NOUN
cana-4456	400	10	problem	problem	NOUN
cana-4456	400	11	using	use	VERB
cana-4456	400	12	rbffd	rbffd	NOUN
cana-4456	400	13	method	method	NOUN
cana-4456	400	14	(	(	PUNCT
cana-4456	400	15	see	see	VERB
cana-4456	400	16	figure	figure	NOUN
cana-4456	400	17	11	11	NUM
cana-4456	400	18	(	(	PUNCT
cana-4456	400	19	a	a	NOUN
cana-4456	400	20	)	)	PUNCT
cana-4456	400	21	)	)	PUNCT
cana-4456	400	22	.	.	PUNCT
cana-4456	401	1	four	four	NUM
cana-4456	401	2	different	different	ADJ
cana-4456	401	3	stencil	stencil	NOUN
cana-4456	401	4	sizes	size	NOUN
cana-4456	401	5	are	be	AUX
cana-4456	401	6	used	use	VERB
cana-4456	401	7	,	,	PUNCT
cana-4456	401	8	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	401	9	=	=	SYM
cana-4456	401	10	20	20	NUM
cana-4456	401	11	,	,	PUNCT
cana-4456	401	12	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	401	13	=	=	SYM
cana-4456	401	14	100	100	NUM
cana-4456	401	15	and	and	CCONJ
cana-4456	401	16	𝑛𝑙𝑜𝑐	𝑛𝑙𝑜𝑐	VERB
cana-4456	401	17	=	=	NOUN
cana-4456	401	18	150	150	NUM
cana-4456	401	19	.	.	PUNCT
cana-4456	402	1	the	the	DET
cana-4456	402	2	result	result	NOUN
cana-4456	402	3	in	in	ADP
cana-4456	402	4	seen	see	VERB
cana-4456	402	5	in	in	ADP
cana-4456	402	6	figure	figure	NOUN
cana-4456	402	7	11	11	NUM
cana-4456	402	8	(	(	PUNCT
cana-4456	402	9	a	a	X
cana-4456	402	10	)	)	PUNCT
cana-4456	402	11	plotted	plot	VERB
cana-4456	402	12	in	in	ADP
cana-4456	402	13	logarithmic	logarithmic	ADJ
cana-4456	402	14	scales	scale	NOUN
cana-4456	402	15	,	,	PUNCT
cana-4456	402	16	where	where	SCONJ
cana-4456	402	17	the	the	DET
cana-4456	402	18	𝐿2	𝐿2	NOUN
cana-4456	402	19	-	-	PUNCT
cana-4456	402	20	norm	norm	NOUN
cana-4456	402	21	of	of	ADP
cana-4456	402	22	the	the	DET
cana-4456	402	23	numerical	numerical	ADJ
cana-4456	402	24	error	error	NOUN
cana-4456	402	25	is	be	AUX
cana-4456	402	26	plotted	plot	VERB
cana-4456	402	27	against	against	ADP
cana-4456	402	28	the	the	DET
cana-4456	402	29	grid	grid	NOUN
cana-4456	402	30	size	size	NOUN
cana-4456	402	31	,	,	PUNCT
cana-4456	402	32	we	we	PRON
cana-4456	402	33	display	display	VERB
cana-4456	402	34	in	in	ADP
cana-4456	402	35	figure	figure	NOUN
cana-4456	402	36	11	11	NUM
cana-4456	402	37	(	(	PUNCT
cana-4456	402	38	b	b	NOUN
cana-4456	402	39	)	)	PUNCT
cana-4456	402	40	the	the	DET
cana-4456	402	41	error	error	NOUN
cana-4456	402	42	of	of	ADP
cana-4456	402	43	the	the	DET
cana-4456	402	44	numerical	numerical	ADJ
cana-4456	402	45	solution	solution	NOUN
cana-4456	402	46	at	at	ADP
cana-4456	402	47	𝑇	𝑇	PROPN
cana-4456	402	48	=	=	SYM
cana-4456	402	49	1500	1500	NUM
cana-4456	402	50	seconds	second	NOUN
cana-4456	402	51	in	in	ADP
cana-4456	402	52	terms	term	NOUN
cana-4456	402	53	of	of	ADP
cana-4456	402	54	the	the	DET
cana-4456	402	55	shape	shape	NOUN
cana-4456	402	56	parameter	parameter	NOUN
cana-4456	402	57	in	in	ADP
cana-4456	402	58	order	order	NOUN
cana-4456	402	59	to	to	PART
cana-4456	402	60	show	show	VERB
cana-4456	402	61	that	that	SCONJ
cana-4456	402	62	stable	stable	ADJ
cana-4456	402	63	computations	computation	NOUN
cana-4456	402	64	were	be	AUX
cana-4456	402	65	achieved	achieve	VERB
cana-4456	402	66	for	for	ADP
cana-4456	402	67	𝜀	𝜀	NOUN
cana-4456	402	68	=	=	PROPN
cana-4456	402	69	0.25	0.25	NUM
cana-4456	402	70	.	.	PUNCT
cana-4456	403	1	from	from	ADP
cana-4456	403	2	the	the	DET
cana-4456	403	3	results	result	NOUN
cana-4456	403	4	and	and	CCONJ
cana-4456	403	5	comparisons	comparison	NOUN
cana-4456	403	6	in	in	ADP
cana-4456	403	7	this	this	DET
cana-4456	403	8	example	example	NOUN
cana-4456	403	9	,	,	PUNCT
cana-4456	403	10	the	the	DET
cana-4456	403	11	merits	merit	NOUN
cana-4456	403	12	of	of	ADP
cana-4456	403	13	the	the	DET
cana-4456	403	14	proposed	propose	VERB
cana-4456	403	15	meshless	meshless	ADJ
cana-4456	403	16	method	method	NOUN
cana-4456	403	17	are	be	AUX
cana-4456	403	18	verified	verify	VERB
cana-4456	403	19	.	.	PUNCT
cana-4456	404	1	4.3.2	4.3.2	NUM
cana-4456	404	2	supercritical	supercritical	ADJ
cana-4456	404	3	flow	flow	NOUN
cana-4456	404	4	considering	consider	VERB
cana-4456	404	5	a	a	DET
cana-4456	404	6	1000	1000	NUM
cana-4456	404	7	𝑚	𝑚	ADP
cana-4456	404	8	long	long	ADJ
cana-4456	404	9	computational	computational	ADJ
cana-4456	404	10	domain	domain	NOUN
cana-4456	404	11	with	with	ADP
cana-4456	404	12	a	a	DET
cana-4456	404	13	discharge	discharge	NOUN
cana-4456	404	14	of	of	ADP
cana-4456	404	15	q	q	NOUN
cana-4456	404	16	=	=	SYM
cana-4456	404	17	2𝑚2/𝑠	2𝑚2/𝑠	NUM
cana-4456	404	18	.	.	PUNCT
cana-4456	405	1	the	the	DET
cana-4456	405	2	flow	flow	NOUN
cana-4456	405	3	is	be	AUX
cana-4456	405	4	supercritical	supercritical	ADJ
cana-4456	405	5	at	at	ADP
cana-4456	405	6	inflow	inflow	NOUN
cana-4456	405	7	with	with	ADP
cana-4456	405	8	depth	depth	NOUN
cana-4456	405	9	ℎ𝑎𝑛𝑎(0	ℎ𝑎𝑛𝑎(0	NOUN
cana-4456	405	10	)	)	PUNCT
cana-4456	406	1	=	=	PUNCT
cana-4456	406	2	0.741599	0.741599	NUM
cana-4456	406	3	𝑚	𝑚	NOUN
cana-4456	406	4	and	and	CCONJ
cana-4456	406	5	is	be	AUX
cana-4456	406	6	supercritical	supercritical	ADJ
cana-4456	406	7	at	at	ADP
cana-4456	406	8	outflow	outflow	NOUN
cana-4456	406	9	.	.	PUNCT
cana-4456	407	1	the	the	DET
cana-4456	407	2	manning	man	VERB
cana-4456	407	3	coefficient	coefficient	NOUN
cana-4456	407	4	for	for	ADP
cana-4456	407	5	the	the	DET
cana-4456	407	6	channel	channel	NOUN
cana-4456	407	7	is	be	AUX
cana-4456	407	8	𝑛	𝑛	PRON
cana-4456	407	9	=	=	PUNCT
cana-4456	407	10	0.0218𝑚−1/3𝑠.	0.0218𝑚−1/3𝑠.	NOUN
cana-4456	408	1	the	the	DET
cana-4456	408	2	boundary	boundary	ADJ
cana-4456	408	3	conditions	condition	NOUN
cana-4456	408	4	set	set	VERB
cana-4456	408	5	to	to	PART
cana-4456	408	6	{	{	PUNCT
cana-4456	408	7	𝑞(𝑥	𝑞(𝑥	PROPN
cana-4456	408	8	)	)	PUNCT
cana-4456	408	9	=	=	SYM
cana-4456	408	10	2	2	NUM
cana-4456	408	11	,	,	PUNCT
cana-4456	408	12	ℎ(𝑥	ℎ(𝑥	NUM
cana-4456	408	13	)	)	PUNCT
cana-4456	408	14	=	=	SYM
cana-4456	408	15	ℎ𝑎𝑛𝑎(0	ℎ𝑎𝑛𝑎(0	NOUN
cana-4456	408	16	)	)	PUNCT
cana-4456	409	1	𝑥	𝑥	NOUN
cana-4456	409	2	=	=	SYM
cana-4456	409	3	0	0	NUM
cana-4456	409	4	,	,	PUNCT
cana-4456	409	5	𝑓𝑟𝑒𝑒	𝑓𝑟𝑒𝑒	NOUN
cana-4456	409	6	𝑥	𝑥	NOUN
cana-4456	409	7	=	=	SYM
cana-4456	409	8	𝐿.	𝐿.	PROPN
cana-4456	409	9	(	(	PUNCT
cana-4456	409	10	58	58	NUM
cana-4456	409	11	)	)	PUNCT
cana-4456	409	12	the	the	DET
cana-4456	409	13	initial	initial	ADJ
cana-4456	409	14	free	free	ADJ
cana-4456	409	15	surface	surface	NOUN
cana-4456	409	16	is	be	AUX
cana-4456	409	17	set	set	VERB
cana-4456	409	18	to	to	ADP
cana-4456	409	19	zero	zero	NUM
cana-4456	409	20	on	on	ADP
cana-4456	409	21	the	the	DET
cana-4456	409	22	whole	whole	ADJ
cana-4456	409	23	domain	domain	NOUN
cana-4456	409	24	.	.	PUNCT
cana-4456	410	1	we	we	PRON
cana-4456	410	2	show	show	VERB
cana-4456	410	3	on	on	ADP
cana-4456	410	4	figure	figure	NOUN
cana-4456	410	5	12	12	NUM
cana-4456	410	6	the	the	DET
cana-4456	410	7	steady	steady	ADJ
cana-4456	410	8	state	state	NOUN
cana-4456	410	9	water	water	NOUN
cana-4456	410	10	free	free	ADJ
cana-4456	410	11	surface	surface	NOUN
cana-4456	410	12	and	and	CCONJ
cana-4456	410	13	discharge	discharge	VERB
cana-4456	410	14	at	at	ADP
cana-4456	410	15	𝑇	𝑇	PROPN
cana-4456	410	16	=	=	PUNCT
cana-4456	410	17	1500𝑠	1500𝑠	NOUN
cana-4456	410	18	and	and	CCONJ
cana-4456	410	19	we	we	PRON
cana-4456	410	20	observe	observe	VERB
cana-4456	410	21	very	very	ADV
cana-4456	410	22	close	close	ADJ
cana-4456	410	23	agreement	agreement	NOUN
cana-4456	410	24	between	between	ADP
cana-4456	410	25	numerical	numerical	ADJ
cana-4456	410	26	results	result	NOUN
cana-4456	410	27	and	and	CCONJ
cana-4456	410	28	the	the	DET
cana-4456	410	29	reference	reference	NOUN
cana-4456	410	30	solution	solution	NOUN
cana-4456	410	31	.	.	PUNCT
cana-4456	411	1	the	the	DET
cana-4456	411	2	numerical	numerical	ADJ
cana-4456	411	3	examples	example	NOUN
cana-4456	411	4	are	be	AUX
cana-4456	411	5	performed	perform	VERB
cana-4456	411	6	for	for	ADP
cana-4456	411	7	kansa	kansa	PROPN
cana-4456	411	8	,	,	PUNCT
cana-4456	411	9	rbf	rbf	PROPN
cana-4456	411	10	-	-	PUNCT
cana-4456	411	11	fd	fd	PROPN
cana-4456	411	12	with	with	ADP
cana-4456	411	13	an	an	DET
cana-4456	411	14	optimal	optimal	ADJ
cana-4456	411	15	shape	shape	NOUN
cana-4456	411	16	parameter	parameter	NOUN
cana-4456	411	17	𝜀	𝜀	NOUN
cana-4456	411	18	=	=	SYM
cana-4456	411	19	0.1	0.1	NUM
cana-4456	411	20	and	and	CCONJ
cana-4456	411	21	rbf	rbf	PROPN
cana-4456	411	22	-	-	PUNCT
cana-4456	411	23	pum	pum	PROPN
cana-4456	411	24	-	-	PUNCT
cana-4456	411	25	qr	qr	NOUN
cana-4456	411	26	methods	method	NOUN
cana-4456	411	27	using	use	VERB
cana-4456	411	28	𝜇	𝜇	ADP
cana-4456	411	29	=	=	PROPN
cana-4456	411	30	10−1	10−1	PROPN
cana-4456	411	31	for	for	ADP
cana-4456	411	32	all	all	DET
cana-4456	411	33	cases	case	NOUN
cana-4456	411	34	.	.	PUNCT
cana-4456	412	1	the	the	DET
cana-4456	412	2	error	error	NOUN
cana-4456	412	3	of	of	ADP
cana-4456	412	4	converged	converge	VERB
cana-4456	412	5	results	result	NOUN
cana-4456	412	6	by	by	ADP
cana-4456	412	7	different	different	ADJ
cana-4456	412	8	schemes	scheme	NOUN
cana-4456	412	9	are	be	AUX
cana-4456	412	10	listed	list	VERB
cana-4456	412	11	in	in	ADP
cana-4456	412	12	table	table	NOUN
cana-4456	412	13	4	4	NUM
cana-4456	412	14	.	.	PUNCT
cana-4456	412	15	communications	communication	NOUN
cana-4456	412	16	on	on	ADP
cana-4456	412	17	applied	apply	VERB
cana-4456	412	18	nonlinear	nonlinear	ADJ
cana-4456	412	19	analysis	analysis	NOUN
cana-4456	412	20	issn	issn	NOUN
cana-4456	412	21	:	:	PUNCT
cana-4456	412	22	1074	1074	NUM
cana-4456	412	23	-	-	PUNCT
cana-4456	412	24	133x	133x	NUM
cana-4456	412	25	vol	vol	NOUN
cana-4456	412	26	32	32	NUM
cana-4456	413	1	no	no	NOUN
cana-4456	413	2	.	.	PUNCT
cana-4456	414	1	9s	9s	NUM
cana-4456	414	2	(	(	PUNCT
cana-4456	414	3	2025	2025	NUM
cana-4456	414	4	)	)	PUNCT
cana-4456	414	5	2193	2193	NUM
cana-4456	414	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	414	7	4.3.3	4.3.3	NUM
cana-4456	414	8	supercritical	supercritical	ADJ
cana-4456	414	9	to	to	ADP
cana-4456	414	10	subcritical	subcritical	ADJ
cana-4456	414	11	flow	flow	NOUN
cana-4456	414	12	we	we	PRON
cana-4456	414	13	consider	consider	VERB
cana-4456	414	14	a	a	DET
cana-4456	414	15	discharge	discharge	NOUN
cana-4456	414	16	of	of	ADP
cana-4456	414	17	q	q	NOUN
cana-4456	414	18	=	=	SYM
cana-4456	414	19	2𝑚2/𝑠.	2𝑚2/𝑠.	NUM
cana-4456	414	20	again	again	ADV
cana-4456	414	21	,	,	PUNCT
cana-4456	414	22	the	the	DET
cana-4456	414	23	initial	initial	ADJ
cana-4456	414	24	free	free	ADJ
cana-4456	414	25	surface	surface	NOUN
cana-4456	414	26	and	and	CCONJ
cana-4456	414	27	discharge	discharge	NOUN
cana-4456	414	28	are	be	AUX
cana-4456	414	29	set	set	VERB
cana-4456	414	30	to	to	ADP
cana-4456	414	31	zero	zero	NUM
cana-4456	414	32	on	on	ADP
cana-4456	414	33	the	the	DET
cana-4456	414	34	whole	whole	ADJ
cana-4456	414	35	domain	domain	NOUN
cana-4456	414	36	.	.	PUNCT
cana-4456	415	1	the	the	DET
cana-4456	415	2	flow	flow	NOUN
cana-4456	415	3	is	be	AUX
cana-4456	415	4	supercritical	supercritical	ADJ
cana-4456	415	5	at	at	ADP
cana-4456	415	6	inflow	inflow	NOUN
cana-4456	415	7	with	with	ADP
cana-4456	415	8	depth	depth	NOUN
cana-4456	415	9	ℎ𝑎𝑛𝑎(0	ℎ𝑎𝑛𝑎(0	NOUN
cana-4456	415	10	)	)	PUNCT
cana-4456	416	1	=	=	SYM
cana-4456	416	2	0.543853𝑚	0.543853𝑚	PROPN
cana-4456	416	3	and	and	CCONJ
cana-4456	416	4	is	be	AUX
cana-4456	416	5	table	table	NOUN
cana-4456	416	6	4	4	NUM
cana-4456	416	7	.	.	PUNCT
cana-4456	416	8	error	error	NOUN
cana-4456	416	9	comparison	comparison	NOUN
cana-4456	416	10	of	of	ADP
cana-4456	416	11	water	water	NOUN
cana-4456	416	12	level	level	NOUN
cana-4456	416	13	and	and	CCONJ
cana-4456	416	14	discharge	discharge	VERB
cana-4456	416	15	for	for	ADP
cana-4456	416	16	different	different	ADJ
cana-4456	416	17	flow	flow	NOUN
cana-4456	416	18	conditions	condition	NOUN
cana-4456	416	19	(	(	PUNCT
cana-4456	416	20	subcritical	subcritical	ADJ
cana-4456	416	21	,	,	PUNCT
cana-4456	416	22	supercritical	supercritical	ADJ
cana-4456	416	23	and	and	CCONJ
cana-4456	416	24	supercritical	supercritical	ADJ
cana-4456	416	25	to	to	ADP
cana-4456	416	26	subcritical	subcritical	ADJ
cana-4456	416	27	)	)	PUNCT
cana-4456	416	28	with	with	ADP
cana-4456	416	29	friction	friction	NOUN
cana-4456	416	30	using	use	VERB
cana-4456	416	31	kansa	kansa	PROPN
cana-4456	416	32	,	,	PUNCT
cana-4456	416	33	rbf	rbf	PROPN
cana-4456	416	34	-	-	PUNCT
cana-4456	416	35	fd	fd	PROPN
cana-4456	416	36	and	and	CCONJ
cana-4456	416	37	rbf	rbf	PROPN
cana-4456	416	38	-	-	PUNCT
cana-4456	416	39	pum	pum	PROPN
cana-4456	416	40	-	-	PUNCT
cana-4456	416	41	qr	qr	NOUN
cana-4456	416	42	methods	method	NOUN
cana-4456	416	43	.	.	PUNCT
cana-4456	417	1	kansa	kansa	PROPN
cana-4456	417	2	rbf	rbf	PROPN
cana-4456	417	3	-	-	PUNCT
cana-4456	417	4	fd	fd	PROPN
cana-4456	417	5	rbf	rbf	PROPN
cana-4456	417	6	-	-	PUNCT
cana-4456	417	7	pum	pum	PROPN
cana-4456	417	8	-	-	PUNCT
cana-4456	417	9	qr	qr	NOUN
cana-4456	417	10	water	water	NOUN
cana-4456	417	11	height	height	NOUN
cana-4456	417	12	ℎ[𝑚	ℎ[𝑚	PROPN
cana-4456	417	13	]	]	PUNCT
cana-4456	417	14	2.66	2.66	NUM
cana-4456	417	15	×	×	NOUN
cana-4456	417	16	10−4	10−4	NUM
cana-4456	417	17	2.29	2.29	NUM
cana-4456	417	18	×	×	NOUN
cana-4456	417	19	10−4	10−4	NUM
cana-4456	417	20	2.55	2.55	NUM
cana-4456	417	21	×	×	NOUN
cana-4456	417	22	10−4	10−4	NUM
cana-4456	417	23	subcritical	subcritical	ADJ
cana-4456	417	24	discharge	discharge	NOUN
cana-4456	417	25	𝑞[𝑚2/𝑠	𝑞[𝑚2/𝑠	NOUN
cana-4456	417	26	]	]	X
cana-4456	417	27	1.85	1.85	NUM
cana-4456	417	28	×	×	NOUN
cana-4456	417	29	10−4	10−4	NUM
cana-4456	417	30	1.39	1.39	NUM
cana-4456	417	31	×	×	NOUN
cana-4456	417	32	10−4	10−4	NUM
cana-4456	417	33	1.82	1.82	NUM
cana-4456	417	34	×	×	NOUN
cana-4456	417	35	10−4	10−4	NUM
cana-4456	417	36	water	water	NOUN
cana-4456	417	37	height	height	NOUN
cana-4456	417	38	ℎ[𝑚	ℎ[𝑚	PROPN
cana-4456	417	39	]	]	PUNCT
cana-4456	417	40	8.88	8.88	NUM
cana-4456	417	41	×	×	NOUN
cana-4456	417	42	10−5	10−5	NUM
cana-4456	417	43	1.07	1.07	NUM
cana-4456	417	44	×	×	NOUN
cana-4456	417	45	10−5	10−5	NUM
cana-4456	417	46	8.65	8.65	NUM
cana-4456	417	47	×	×	NOUN
cana-4456	417	48	10−5	10−5	NUM
cana-4456	417	49	supercritical	supercritical	ADJ
cana-4456	417	50	discharge	discharge	NOUN
cana-4456	417	51	𝑞[𝑚2/𝑠	𝑞[𝑚2/𝑠	NOUN
cana-4456	417	52	]	]	X
cana-4456	417	53	9.55	9.55	NUM
cana-4456	417	54	×	×	NOUN
cana-4456	417	55	10−5	10−5	NUM
cana-4456	417	56	7.83	7.83	NUM
cana-4456	417	57	×	×	NOUN
cana-4456	417	58	10−5	10−5	NUM
cana-4456	417	59	6.04	6.04	NUM
cana-4456	417	60	×	×	NOUN
cana-4456	417	61	10−6	10−6	NUM
cana-4456	417	62	water	water	NOUN
cana-4456	417	63	height	height	NOUN
cana-4456	417	64	ℎ[𝑚	ℎ[𝑚	PROPN
cana-4456	417	65	]	]	X
cana-4456	417	66	6.45	6.45	NUM
cana-4456	417	67	×	×	NOUN
cana-4456	417	68	10−4	10−4	NUM
cana-4456	417	69	8.31	8.31	NUM
cana-4456	417	70	×	×	NOUN
cana-4456	417	71	10−4	10−4	NUM
cana-4456	417	72	5.20	5.20	NUM
cana-4456	417	73	×	×	NOUN
cana-4456	417	74	10−4	10−4	NUM
cana-4456	417	75	supercritical	supercritical	ADJ
cana-4456	417	76	to	to	ADP
cana-4456	417	77	subcritical	subcritical	ADJ
cana-4456	417	78	discharge	discharge	NOUN
cana-4456	417	79	𝑞[𝑚2/𝑠	𝑞[𝑚2/𝑠	NOUN
cana-4456	417	80	]	]	X
cana-4456	417	81	2.83	2.83	NUM
cana-4456	417	82	×	×	NOUN
cana-4456	417	83	10−4	10−4	NUM
cana-4456	417	84	3.21	3.21	NUM
cana-4456	417	85	×	×	NOUN
cana-4456	417	86	10−4	10−4	NUM
cana-4456	417	87	2.50	2.50	NUM
cana-4456	417	88	×	×	NOUN
cana-4456	417	89	10−4	10−4	NUM
cana-4456	417	90	subcritical	subcritical	NOUN
cana-4456	417	91	at	at	ADP
cana-4456	417	92	outflow	outflow	NOUN
cana-4456	417	93	with	with	ADP
cana-4456	417	94	depth	depth	NOUN
cana-4456	417	95	ℎ𝑎𝑛𝑎(1000	ℎ𝑎𝑛𝑎(1000	NOUN
cana-4456	417	96	)	)	PUNCT
cana-4456	418	1	=	=	PUNCT
cana-4456	419	1	1.334899	1.334899	NUM
cana-4456	419	2	m	m	NOUN
cana-4456	419	3	.	.	PUNCT
cana-4456	420	1	the	the	DET
cana-4456	420	2	manning	man	VERB
cana-4456	420	3	coefficient	coefficient	NOUN
cana-4456	420	4	for	for	ADP
cana-4456	420	5	the	the	DET
cana-4456	420	6	channel	channel	NOUN
cana-4456	420	7	is	be	AUX
cana-4456	420	8	𝑛	𝑛	PRON
cana-4456	420	9	=	=	PUNCT
cana-4456	420	10	0.0218𝑚−1/3𝑠.	0.0218𝑚−1/3𝑠.	NOUN
cana-4456	421	1	the	the	DET
cana-4456	421	2	boundary	boundary	ADJ
cana-4456	421	3	conditions	condition	NOUN
cana-4456	421	4	set	set	VERB
cana-4456	421	5	to	to	PART
cana-4456	421	6	{	{	PUNCT
cana-4456	421	7	𝑞(𝑥	𝑞(𝑥	PROPN
cana-4456	421	8	)	)	PUNCT
cana-4456	421	9	=	=	SYM
cana-4456	421	10	2	2	NUM
cana-4456	421	11	,	,	PUNCT
cana-4456	421	12	ℎ(𝑥	ℎ(𝑥	NUM
cana-4456	421	13	)	)	PUNCT
cana-4456	421	14	=	=	SYM
cana-4456	421	15	ℎ𝑎𝑛𝑎(0	ℎ𝑎𝑛𝑎(0	NOUN
cana-4456	421	16	)	)	PUNCT
cana-4456	422	1	𝑥	𝑥	NOUN
cana-4456	422	2	=	=	SYM
cana-4456	422	3	0	0	NUM
cana-4456	422	4	,	,	PUNCT
cana-4456	422	5	ℎ(𝑥	ℎ(𝑥	NUM
cana-4456	422	6	)	)	PUNCT
cana-4456	422	7	=	=	SYM
cana-4456	422	8	ℎ𝑎𝑛𝑎(1000	ℎ𝑎𝑛𝑎(1000	X
cana-4456	422	9	)	)	PUNCT
cana-4456	422	10	𝑥	𝑥	NOUN
cana-4456	423	1	=	=	SYM
cana-4456	423	2	𝐿.	𝐿.	PROPN
cana-4456	423	3	(	(	PUNCT
cana-4456	423	4	59	59	NUM
cana-4456	423	5	)	)	PUNCT
cana-4456	423	6	the	the	DET
cana-4456	423	7	water	water	NOUN
cana-4456	423	8	depth	depth	NOUN
cana-4456	423	9	and	and	CCONJ
cana-4456	423	10	discharge	discharge	NOUN
cana-4456	423	11	are	be	AUX
cana-4456	423	12	shown	show	VERB
cana-4456	423	13	in	in	ADP
cana-4456	423	14	figure	figure	NOUN
cana-4456	423	15	13	13	NUM
cana-4456	423	16	for	for	ADP
cana-4456	423	17	kansa	kansa	PROPN
cana-4456	423	18	,	,	PUNCT
cana-4456	423	19	rbf	rbf	PROPN
cana-4456	423	20	-	-	PUNCT
cana-4456	423	21	fd	fd	PROPN
cana-4456	423	22	𝜀	𝜀	PROPN
cana-4456	423	23	=	=	SYM
cana-4456	423	24	0.1	0.1	NUM
cana-4456	423	25	and	and	CCONJ
cana-4456	423	26	rbf	rbf	PROPN
cana-4456	423	27	-	-	PUNCT
cana-4456	423	28	pumqr	pumqr	NOUN
cana-4456	423	29	methods	method	NOUN
cana-4456	423	30	using	use	VERB
cana-4456	423	31	𝜇	𝜇	ADP
cana-4456	423	32	=	=	PROPN
cana-4456	423	33	10−1	10−1	NUM
cana-4456	423	34	.	.	PUNCT
cana-4456	424	1	we	we	PRON
cana-4456	424	2	can	can	AUX
cana-4456	424	3	clearly	clearly	ADV
cana-4456	424	4	see	see	VERB
cana-4456	424	5	that	that	SCONJ
cana-4456	424	6	the	the	DET
cana-4456	424	7	flow	flow	NOUN
cana-4456	424	8	accurately	accurately	ADV
cana-4456	424	9	converges	converge	VERB
cana-4456	424	10	towards	towards	ADP
cana-4456	424	11	the	the	DET
cana-4456	424	12	steady	steady	ADJ
cana-4456	424	13	state	state	NOUN
cana-4456	424	14	and	and	CCONJ
cana-4456	424	15	that	that	SCONJ
cana-4456	424	16	the	the	DET
cana-4456	424	17	shock	shock	NOUN
cana-4456	424	18	location	location	NOUN
cana-4456	424	19	is	be	AUX
cana-4456	424	20	accurately	accurately	ADV
cana-4456	424	21	computed	compute	VERB
cana-4456	424	22	.	.	PUNCT
cana-4456	425	1	the	the	DET
cana-4456	425	2	comparison	comparison	NOUN
cana-4456	425	3	of	of	ADP
cana-4456	425	4	the	the	DET
cana-4456	425	5	relative	relative	ADJ
cana-4456	425	6	error	error	NOUN
cana-4456	425	7	of	of	ADP
cana-4456	425	8	the	the	DET
cana-4456	425	9	results	result	NOUN
cana-4456	425	10	by	by	ADP
cana-4456	425	11	kansa	kansa	PROPN
cana-4456	425	12	,	,	PUNCT
cana-4456	425	13	rbf	rbf	PROPN
cana-4456	425	14	-	-	PUNCT
cana-4456	425	15	fd	fd	PROPN
cana-4456	425	16	and	and	CCONJ
cana-4456	425	17	rbf	rbf	PROPN
cana-4456	425	18	-	-	PUNCT
cana-4456	425	19	pum	pum	PROPN
cana-4456	425	20	-	-	PUNCT
cana-4456	425	21	qr	qr	PROPN
cana-4456	425	22	methods	method	NOUN
cana-4456	425	23	is	be	AUX
cana-4456	425	24	shown	show	VERB
cana-4456	425	25	in	in	ADP
cana-4456	425	26	table	table	NOUN
cana-4456	425	27	4	4	NUM
cana-4456	425	28	.	.	NOUN
cana-4456	425	29	5	5	NUM
cana-4456	425	30	.	.	X
cana-4456	425	31	conclusion	conclusion	NOUN
cana-4456	425	32	in	in	ADP
cana-4456	425	33	this	this	DET
cana-4456	425	34	paper	paper	NOUN
cana-4456	425	35	,	,	PUNCT
cana-4456	425	36	the	the	DET
cana-4456	425	37	shallow	shallow	ADJ
cana-4456	425	38	water	water	NOUN
cana-4456	425	39	equations	equation	NOUN
cana-4456	425	40	is	be	AUX
cana-4456	425	41	presented	present	VERB
cana-4456	425	42	to	to	PART
cana-4456	425	43	simulate	simulate	VERB
cana-4456	425	44	the	the	DET
cana-4456	425	45	one	one	NUM
cana-4456	425	46	-	-	PUNCT
cana-4456	425	47	dimensional	dimensional	ADJ
cana-4456	425	48	flow	flow	NOUN
cana-4456	425	49	of	of	ADP
cana-4456	425	50	water	water	NOUN
cana-4456	425	51	in	in	ADP
cana-4456	425	52	channels	channel	NOUN
cana-4456	425	53	.	.	PUNCT
cana-4456	426	1	the	the	DET
cana-4456	426	2	resulting	result	VERB
cana-4456	426	3	system	system	NOUN
cana-4456	426	4	is	be	AUX
cana-4456	426	5	solved	solve	VERB
cana-4456	426	6	numerically	numerically	ADV
cana-4456	426	7	using	use	VERB
cana-4456	426	8	a	a	DET
cana-4456	426	9	globally	globally	ADV
cana-4456	426	10	,	,	PUNCT
cana-4456	426	11	localized	localized	ADJ
cana-4456	426	12	and	and	CCONJ
cana-4456	426	13	stable	stable	ADJ
cana-4456	426	14	meshless	meshless	ADJ
cana-4456	426	15	methods	method	NOUN
cana-4456	426	16	based	base	VERB
cana-4456	426	17	on	on	ADP
cana-4456	426	18	radial	radial	ADJ
cana-4456	426	19	basis	basis	NOUN
cana-4456	426	20	functions	function	NOUN
cana-4456	426	21	.	.	PUNCT
cana-4456	427	1	in	in	ADP
cana-4456	427	2	order	order	NOUN
cana-4456	427	3	to	to	PART
cana-4456	427	4	stabilize	stabilize	VERB
cana-4456	427	5	these	these	DET
cana-4456	427	6	methods	method	NOUN
cana-4456	427	7	and	and	CCONJ
cana-4456	427	8	minimize	minimize	VERB
cana-4456	427	9	the	the	DET
cana-4456	427	10	nonphysical	nonphysical	ADJ
cana-4456	427	11	numerical	numerical	ADJ
cana-4456	427	12	oscillations	oscillation	NOUN
cana-4456	427	13	near	near	ADP
cana-4456	427	14	the	the	DET
cana-4456	427	15	discontinuities	discontinuity	NOUN
cana-4456	427	16	which	which	PRON
cana-4456	427	17	can	can	AUX
cana-4456	427	18	solve	solve	VERB
cana-4456	427	19	the	the	DET
cana-4456	427	20	strong	strong	ADJ
cana-4456	427	21	discontinuity	discontinuity	NOUN
cana-4456	427	22	communications	communication	NOUN
cana-4456	427	23	on	on	ADP
cana-4456	427	24	applied	apply	VERB
cana-4456	427	25	nonlinear	nonlinear	ADJ
cana-4456	427	26	analysis	analysis	NOUN
cana-4456	427	27	issn	issn	NOUN
cana-4456	427	28	:	:	PUNCT
cana-4456	427	29	1074	1074	NUM
cana-4456	427	30	-	-	PUNCT
cana-4456	427	31	133x	133x	NUM
cana-4456	427	32	vol	vol	NOUN
cana-4456	427	33	32	32	NUM
cana-4456	427	34	no	no	NOUN
cana-4456	427	35	.	.	PUNCT
cana-4456	428	1	9s	9s	NUM
cana-4456	428	2	(	(	PUNCT
cana-4456	428	3	2025	2025	NUM
cana-4456	428	4	)	)	PUNCT
cana-4456	428	5	2194	2194	NUM
cana-4456	429	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	429	2	problem	problem	NOUN
cana-4456	429	3	in	in	ADP
cana-4456	429	4	swes	swes	NOUN
cana-4456	429	5	,	,	PUNCT
cana-4456	429	6	an	an	DET
cana-4456	429	7	artificial	artificial	ADJ
cana-4456	429	8	viscosity	viscosity	NOUN
cana-4456	429	9	(	(	PUNCT
cana-4456	429	10	hyperviscosity	hyperviscosity	NOUN
cana-4456	429	11	)	)	PUNCT
cana-4456	429	12	technique	technique	NOUN
cana-4456	429	13	is	be	AUX
cana-4456	429	14	implemented	implement	VERB
cana-4456	429	15	.	.	PUNCT
cana-4456	430	1	in	in	ADP
cana-4456	430	2	kansa	kansa	PROPN
cana-4456	430	3	’s	’s	PART
cana-4456	430	4	method	method	VERB
cana-4456	430	5	the	the	DET
cana-4456	430	6	system	system	NOUN
cana-4456	430	7	to	to	PART
cana-4456	430	8	be	be	AUX
cana-4456	430	9	solved	solve	VERB
cana-4456	430	10	is	be	AUX
cana-4456	430	11	dense	dense	ADJ
cana-4456	430	12	and	and	CCONJ
cana-4456	430	13	therefore	therefore	ADV
cana-4456	430	14	it	it	PRON
cana-4456	430	15	was	be	AUX
cana-4456	430	16	necessary	necessary	ADJ
cana-4456	430	17	to	to	PART
cana-4456	430	18	refer	refer	VERB
cana-4456	430	19	to	to	ADP
cana-4456	430	20	localized	localize	VERB
cana-4456	430	21	meshless	meshless	ADJ
cana-4456	430	22	methods	method	NOUN
cana-4456	430	23	such	such	ADJ
cana-4456	430	24	as	as	ADP
cana-4456	430	25	rbf	rbf	PROPN
cana-4456	430	26	-	-	PUNCT
cana-4456	430	27	fd	fd	PROPN
cana-4456	430	28	and	and	CCONJ
cana-4456	430	29	rbf	rbf	PROPN
cana-4456	430	30	-	-	PROPN
cana-4456	430	31	pum	pum	PROPN
cana-4456	430	32	in	in	ADP
cana-4456	430	33	order	order	NOUN
cana-4456	430	34	to	to	PART
cana-4456	430	35	present	present	VERB
cana-4456	430	36	sparsity	sparsity	NOUN
cana-4456	430	37	and	and	CCONJ
cana-4456	430	38	locality	locality	NOUN
cana-4456	430	39	.	.	PUNCT
cana-4456	431	1	the	the	DET
cana-4456	431	2	problem	problem	NOUN
cana-4456	431	3	of	of	ADP
cana-4456	431	4	choosing	choose	VERB
cana-4456	431	5	any	any	DET
cana-4456	431	6	value	value	NOUN
cana-4456	431	7	of	of	ADP
cana-4456	431	8	shape	shape	NOUN
cana-4456	431	9	parameter	parameter	NOUN
cana-4456	431	10	ε	ε	PROPN
cana-4456	431	11	from	from	ADP
cana-4456	431	12	the	the	DET
cana-4456	431	13	flat	flat	ADJ
cana-4456	431	14	limit	limit	NOUN
cana-4456	431	15	region	region	NOUN
cana-4456	431	16	which	which	PRON
cana-4456	431	17	affect	affect	VERB
cana-4456	431	18	the	the	DET
cana-4456	431	19	accuracy	accuracy	NOUN
cana-4456	431	20	of	of	ADP
cana-4456	431	21	the	the	DET
cana-4456	431	22	solution	solution	NOUN
cana-4456	431	23	can	can	AUX
cana-4456	431	24	be	be	AUX
cana-4456	431	25	handled	handle	VERB
cana-4456	431	26	by	by	ADP
cana-4456	431	27	combining	combine	VERB
cana-4456	431	28	the	the	DET
cana-4456	431	29	rbf	rbf	PROPN
cana-4456	431	30	-	-	PUNCT
cana-4456	431	31	pum	pum	PROPN
cana-4456	431	32	with	with	ADP
cana-4456	431	33	rbf	rbf	PROPN
cana-4456	431	34	-	-	PUNCT
cana-4456	431	35	qr	qr	PROPN
cana-4456	431	36	approach	approach	NOUN
cana-4456	431	37	.	.	PUNCT
cana-4456	432	1	the	the	DET
cana-4456	432	2	proposed	propose	VERB
cana-4456	432	3	meshless	meshless	ADJ
cana-4456	432	4	methods	method	NOUN
cana-4456	432	5	with	with	ADP
cana-4456	432	6	hyperviscosity	hyperviscosity	NOUN
cana-4456	432	7	has	have	AUX
cana-4456	432	8	been	be	AUX
cana-4456	432	9	tested	test	VERB
cana-4456	432	10	on	on	ADP
cana-4456	432	11	systems	system	NOUN
cana-4456	432	12	of	of	ADP
cana-4456	432	13	shallow	shallow	ADJ
cana-4456	432	14	water	water	NOUN
cana-4456	432	15	equations	equation	NOUN
cana-4456	432	16	at	at	ADP
cana-4456	432	17	different	different	ADJ
cana-4456	432	18	flow	flow	NOUN
cana-4456	432	19	regimes	regime	NOUN
cana-4456	432	20	.	.	PUNCT
cana-4456	433	1	the	the	DET
cana-4456	433	2	obtained	obtain	VERB
cana-4456	433	3	results	result	NOUN
cana-4456	433	4	indicate	indicate	VERB
cana-4456	433	5	good	good	ADJ
cana-4456	433	6	shock	shock	NOUN
cana-4456	433	7	resolution	resolution	NOUN
cana-4456	433	8	with	with	ADP
cana-4456	433	9	high	high	ADJ
cana-4456	433	10	(	(	PUNCT
cana-4456	433	11	a	a	X
cana-4456	433	12	)	)	PUNCT
cana-4456	433	13	kansa	kansa	PROPN
cana-4456	433	14	method	method	NOUN
cana-4456	433	15	(	(	PUNCT
cana-4456	433	16	b	b	NOUN
cana-4456	433	17	)	)	PUNCT
cana-4456	433	18	rbf	rbf	PROPN
cana-4456	433	19	-	-	PUNCT
cana-4456	433	20	fd	fd	PROPN
cana-4456	433	21	method	method	NOUN
cana-4456	433	22	(	(	PUNCT
cana-4456	433	23	c	c	NOUN
cana-4456	433	24	)	)	PUNCT
cana-4456	433	25	rbf	rbf	PROPN
cana-4456	433	26	-	-	PUNCT
cana-4456	433	27	pum	pum	PROPN
cana-4456	433	28	-	-	PUNCT
cana-4456	433	29	qr	qr	PROPN
cana-4456	433	30	method	method	NOUN
cana-4456	433	31	figure	figure	NOUN
cana-4456	433	32	9	9	NUM
cana-4456	433	33	.	.	PUNCT
cana-4456	433	34	subcritical	subcritical	ADJ
cana-4456	433	35	flow	flow	NOUN
cana-4456	433	36	using	use	VERB
cana-4456	433	37	(	(	PUNCT
cana-4456	433	38	a	a	PRON
cana-4456	433	39	)	)	PUNCT
cana-4456	433	40	kansa	kansa	PROPN
cana-4456	433	41	,	,	PUNCT
cana-4456	433	42	(	(	PUNCT
cana-4456	433	43	b	b	X
cana-4456	433	44	)	)	PUNCT
cana-4456	433	45	rbf	rbf	PROPN
cana-4456	433	46	-	-	PUNCT
cana-4456	433	47	fd	fd	PROPN
cana-4456	433	48	,	,	PUNCT
cana-4456	433	49	and	and	CCONJ
cana-4456	433	50	(	(	PUNCT
cana-4456	433	51	c	c	X
cana-4456	433	52	)	)	PUNCT
cana-4456	433	53	rbf	rbf	PROPN
cana-4456	433	54	-	-	PUNCT
cana-4456	433	55	pum	pum	PROPN
cana-4456	433	56	-	-	PUNCT
cana-4456	433	57	qr	qr	NOUN
cana-4456	433	58	methods	method	NOUN
cana-4456	433	59	at	at	ADP
cana-4456	433	60	t	t	PROPN
cana-4456	433	61	=	=	SYM
cana-4456	433	62	1500	1500	NUM
cana-4456	433	63	seconds	second	NOUN
cana-4456	433	64	with	with	ADP
cana-4456	433	65	manning	man	VERB
cana-4456	433	66	friction	friction	NOUN
cana-4456	433	67	𝑛	𝑛	PRON
cana-4456	433	68	=	=	SYM
cana-4456	433	69	0.033𝑚−1/3𝑠.	0.033𝑚−1/3𝑠.	NOUN
cana-4456	433	70	accuracy	accuracy	NOUN
cana-4456	433	71	in	in	ADP
cana-4456	433	72	smooth	smooth	ADJ
cana-4456	433	73	regions	region	NOUN
cana-4456	433	74	,	,	PUNCT
cana-4456	433	75	and	and	CCONJ
cana-4456	433	76	the	the	DET
cana-4456	433	77	convergence	convergence	NOUN
cana-4456	433	78	to	to	ADP
cana-4456	433	79	the	the	DET
cana-4456	433	80	correct	correct	ADJ
cana-4456	433	81	steady	steady	ADJ
cana-4456	433	82	state	state	NOUN
cana-4456	433	83	solution	solution	NOUN
cana-4456	433	84	has	have	AUX
cana-4456	433	85	been	be	AUX
cana-4456	433	86	clearly	clearly	ADV
cana-4456	433	87	verified	verify	VERB
cana-4456	433	88	in	in	ADP
cana-4456	433	89	flow	flow	NOUN
cana-4456	433	90	over	over	ADP
cana-4456	433	91	a	a	DET
cana-4456	433	92	non	non	ADJ
cana-4456	433	93	-	-	ADJ
cana-4456	433	94	flat	flat	ADJ
cana-4456	433	95	bottom	bottom	NOUN
cana-4456	433	96	,	,	PUNCT
cana-4456	433	97	which	which	PRON
cana-4456	433	98	confirm	confirm	VERB
cana-4456	433	99	the	the	DET
cana-4456	433	100	numerical	numerical	ADJ
cana-4456	433	101	stability	stability	NOUN
cana-4456	433	102	and	and	CCONJ
cana-4456	433	103	computational	computational	ADJ
cana-4456	433	104	communications	communication	NOUN
cana-4456	433	105	on	on	ADP
cana-4456	433	106	applied	apply	VERB
cana-4456	433	107	nonlinear	nonlinear	ADJ
cana-4456	433	108	analysis	analysis	NOUN
cana-4456	433	109	issn	issn	NOUN
cana-4456	433	110	:	:	PUNCT
cana-4456	433	111	1074	1074	NUM
cana-4456	433	112	-	-	PUNCT
cana-4456	433	113	133x	133x	NUM
cana-4456	433	114	vol	vol	NOUN
cana-4456	433	115	32	32	NUM
cana-4456	433	116	no	no	NOUN
cana-4456	433	117	.	.	PUNCT
cana-4456	434	1	9s	9s	NUM
cana-4456	434	2	(	(	PUNCT
cana-4456	434	3	2025	2025	NUM
cana-4456	434	4	)	)	PUNCT
cana-4456	434	5	2195	2195	NUM
cana-4456	434	6	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-4456	434	7	accuracy	accuracy	NOUN
cana-4456	434	8	.	.	PUNCT
cana-4456	435	1	additionally	additionally	ADV
cana-4456	435	2	,	,	PUNCT
cana-4456	435	3	the	the	DET
cana-4456	435	4	main	main	ADJ
cana-4456	435	5	challenge	challenge	NOUN
cana-4456	435	6	encountered	encounter	VERB
cana-4456	435	7	was	be	AUX
cana-4456	435	8	the	the	DET
cana-4456	435	9	selection	selection	NOUN
cana-4456	435	10	of	of	ADP
cana-4456	435	11	hyperviscosity	hyperviscosity	NOUN
cana-4456	435	12	parameters	parameter	NOUN
cana-4456	435	13	,	,	PUNCT
cana-4456	435	14	particularly	particularly	ADV
cana-4456	435	15	the	the	DET
cana-4456	435	16	constant	constant	ADJ
cana-4456	435	17	μ	μ	NOUN
cana-4456	435	18	and	and	CCONJ
cana-4456	435	19	its	its	PRON
cana-4456	435	20	scaling	scaling	NOUN
cana-4456	435	21	relations	relation	NOUN
cana-4456	435	22	,	,	PUNCT
cana-4456	435	23	to	to	PART
cana-4456	435	24	ensure	ensure	VERB
cana-4456	435	25	adequate	adequate	ADJ
cana-4456	435	26	stabilization	stabilization	NOUN
cana-4456	435	27	across	across	ADP
cana-4456	435	28	a	a	DET
cana-4456	435	29	wide	wide	ADJ
cana-4456	435	30	range	range	NOUN
cana-4456	435	31	of	of	ADP
cana-4456	435	32	flow	flow	NOUN
cana-4456	435	33	regimes	regime	NOUN
cana-4456	435	34	and	and	CCONJ
cana-4456	435	35	discretization	discretization	NOUN
cana-4456	435	36	densities	density	NOUN
cana-4456	435	37	.	.	PUNCT
cana-4456	436	1	while	while	SCONJ
cana-4456	436	2	our	our	PRON
cana-4456	436	3	numerical	numerical	ADJ
cana-4456	436	4	computations	computation	NOUN
cana-4456	436	5	have	have	AUX
cana-4456	436	6	been	be	AUX
cana-4456	436	7	limited	limit	VERB
cana-4456	436	8	to	to	ADP
cana-4456	436	9	one	one	NUM
cana-4456	436	10	-	-	PUNCT
cana-4456	436	11	dimensional	dimensional	ADJ
cana-4456	436	12	shallow	shallow	ADJ
cana-4456	436	13	water	water	NOUN
cana-4456	436	14	problems	problem	NOUN
cana-4456	436	15	,	,	PUNCT
cana-4456	436	16	the	the	DET
cana-4456	436	17	current	current	ADJ
cana-4456	436	18	meshless	meshless	ADV
cana-4456	436	19	-	-	PUNCT
cana-4456	436	20	based	base	VERB
cana-4456	436	21	rbf	rbf	PROPN
cana-4456	436	22	methods	method	NOUN
cana-4456	436	23	can	can	AUX
cana-4456	436	24	be	be	AUX
cana-4456	436	25	readily	readily	ADV
cana-4456	436	26	extended	extend	VERB
cana-4456	436	27	to	to	ADP
cana-4456	436	28	two	two	NUM
cana-4456	436	29	-	-	PUNCT
cana-4456	436	30	dimensional	dimensional	ADJ
cana-4456	436	31	shallow	shallow	ADJ
cana-4456	436	32	water	water	NOUN
cana-4456	436	33	problems	problem	NOUN
cana-4456	436	34	incorporating	incorporate	VERB
cana-4456	436	35	source	source	NOUN
cana-4456	436	36	terms	term	NOUN
cana-4456	436	37	.	.	PUNCT
cana-4456	437	1	these	these	DET
cana-4456	437	2	extensions	extension	NOUN
cana-4456	437	3	,	,	PUNCT
cana-4456	437	4	along	along	ADP
cana-4456	437	5	with	with	ADP
cana-4456	437	6	other	other	ADJ
cana-4456	437	7	related	related	ADJ
cana-4456	437	8	issues	issue	NOUN
cana-4456	437	9	,	,	PUNCT
cana-4456	437	10	will	will	AUX
cana-4456	437	11	be	be	AUX
cana-4456	437	12	the	the	DET
cana-4456	437	13	focus	focus	NOUN
cana-4456	437	14	of	of	ADP
cana-4456	437	15	future	future	ADJ
cana-4456	437	16	investigations	investigation	NOUN
cana-4456	437	17	.	.	PUNCT
cana-4456	438	1	(	(	PUNCT
cana-4456	438	2	a	a	X
cana-4456	438	3	)	)	PUNCT
cana-4456	438	4	kansa	kansa	PROPN
cana-4456	438	5	method	method	NOUN
cana-4456	438	6	(	(	PUNCT
cana-4456	438	7	b	b	NOUN
cana-4456	438	8	)	)	PUNCT
cana-4456	438	9	rbf	rbf	PROPN
cana-4456	438	10	-	-	PUNCT
cana-4456	438	11	fd	fd	PROPN
cana-4456	438	12	method	method	NOUN
cana-4456	438	13	(	(	PUNCT
cana-4456	438	14	c	c	NOUN
cana-4456	438	15	)	)	PUNCT
cana-4456	438	16	rbf	rbf	PROPN
cana-4456	438	17	-	-	PUNCT
cana-4456	438	18	pum	pum	PROPN
cana-4456	438	19	-	-	PUNCT
cana-4456	438	20	qr	qr	PROPN
cana-4456	438	21	method	method	NOUN
cana-4456	438	22	figure	figure	NOUN
cana-4456	438	23	10	10	NUM
cana-4456	438	24	.	.	PUNCT
cana-4456	439	1	𝐿2	𝐿2	PROPN
cana-4456	439	2	error	error	NOUN
cana-4456	439	3	as	as	ADP
cana-4456	439	4	a	a	DET
cana-4456	439	5	function	function	NOUN
cana-4456	439	6	of	of	ADP
cana-4456	439	7	the	the	DET
cana-4456	439	8	viscosity	viscosity	NOUN
cana-4456	439	9	coefficient	coefficient	NOUN
cana-4456	439	10	for	for	ADP
cana-4456	439	11	the	the	DET
cana-4456	439	12	”	"	PUNCT
cana-4456	439	13	subcritical	subcritical	ADJ
cana-4456	439	14	flow	flow	NOUN
cana-4456	439	15	”	"	PUNCT
cana-4456	439	16	problem	problem	NOUN
cana-4456	439	17	for	for	ADP
cana-4456	439	18	(	(	PUNCT
cana-4456	439	19	a	a	X
cana-4456	439	20	)	)	PUNCT
cana-4456	439	21	kansa	kansa	PROPN
cana-4456	439	22	,	,	PUNCT
cana-4456	439	23	(	(	PUNCT
cana-4456	439	24	b	b	X
cana-4456	439	25	)	)	PUNCT
cana-4456	439	26	rbf	rbf	PROPN
cana-4456	439	27	-	-	PUNCT
cana-4456	439	28	fd	fd	PROPN
cana-4456	439	29	,	,	PUNCT
cana-4456	439	30	and	and	CCONJ
cana-4456	439	31	(	(	PUNCT
cana-4456	439	32	c	c	X
cana-4456	439	33	)	)	PUNCT
cana-4456	439	34	rbf	rbf	PROPN
cana-4456	439	35	-	-	PUNCT
cana-4456	439	36	pum	pum	PROPN
cana-4456	439	37	-	-	PUNCT
cana-4456	439	38	qr	qr	NOUN
cana-4456	439	39	at	at	ADP
cana-4456	439	40	t	t	PROPN
cana-4456	439	41	=	=	SYM
cana-4456	439	42	1500	1500	NUM
cana-4456	439	43	seconds	second	NOUN
cana-4456	439	44	communications	communication	NOUN
cana-4456	439	45	on	on	ADP
cana-4456	439	46	applied	apply	VERB
cana-4456	439	47	nonlinear	nonlinear	ADJ
cana-4456	439	48	analysis	analysis	NOUN
cana-4456	439	49	issn	issn	NOUN
cana-4456	439	50	:	:	PUNCT
cana-4456	439	51	1074	1074	NUM
cana-4456	439	52	-	-	PUNCT
cana-4456	439	53	133x	133x	NUM
cana-4456	439	54	vol	vol	NOUN
cana-4456	439	55	32	32	NUM
cana-4456	439	56	no	no	NOUN
cana-4456	439	57	.	.	PUNCT
cana-4456	440	1	9s	9s	NUM
cana-4456	440	2	(	(	PUNCT
cana-4456	440	3	2025	2025	NUM
cana-4456	440	4	)	)	PUNCT
cana-4456	440	5	2196	2196	NUM
cana-4456	440	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	440	7	(	(	PUNCT
cana-4456	440	8	a	a	NOUN
cana-4456	440	9	)	)	PUNCT
cana-4456	440	10	(	(	PUNCT
cana-4456	440	11	b	b	X
cana-4456	440	12	)	)	PUNCT
cana-4456	440	13	figure	figure	NOUN
cana-4456	440	14	11	11	NUM
cana-4456	440	15	.	.	PUNCT
cana-4456	441	1	(	(	PUNCT
cana-4456	441	2	a	a	X
cana-4456	441	3	)	)	PUNCT
cana-4456	441	4	𝐿2	𝐿2	PROPN
cana-4456	441	5	errors	error	NOUN
cana-4456	441	6	of	of	ADP
cana-4456	441	7	the	the	DET
cana-4456	441	8	rbf	rbf	PROPN
cana-4456	441	9	-	-	PUNCT
cana-4456	441	10	fd	fd	PROPN
cana-4456	441	11	method	method	NOUN
cana-4456	441	12	for	for	ADP
cana-4456	441	13	solving	solve	VERB
cana-4456	441	14	”	"	PUNCT
cana-4456	441	15	subcritical	subcritical	ADJ
cana-4456	441	16	flow	flow	NOUN
cana-4456	441	17	”	"	PUNCT
cana-4456	441	18	problem	problem	NOUN
cana-4456	441	19	with	with	ADP
cana-4456	441	20	respect	respect	NOUN
cana-4456	441	21	to	to	ADP
cana-4456	441	22	the	the	DET
cana-4456	441	23	number	number	NOUN
cana-4456	441	24	of	of	ADP
cana-4456	441	25	stencils	stencil	NOUN
cana-4456	441	26	using	use	VERB
cana-4456	441	27	𝜇	𝜇	ADP
cana-4456	441	28	=	=	PROPN
cana-4456	441	29	10−1	10−1	NUM
cana-4456	441	30	.	.	PUNCT
cana-4456	442	1	(	(	PUNCT
cana-4456	442	2	b	b	X
cana-4456	442	3	)	)	PUNCT
cana-4456	442	4	𝐿2	𝐿2	NOUN
cana-4456	442	5	error	error	NOUN
cana-4456	442	6	in	in	ADP
cana-4456	442	7	terms	term	NOUN
cana-4456	442	8	of	of	ADP
cana-4456	442	9	the	the	DET
cana-4456	442	10	shape	shape	NOUN
cana-4456	442	11	parameter	parameter	NOUN
cana-4456	442	12	𝜀.	𝜀.	NOUN
cana-4456	442	13	(	(	PUNCT
cana-4456	442	14	a	a	X
cana-4456	442	15	)	)	PUNCT
cana-4456	442	16	kansa	kansa	PROPN
cana-4456	442	17	method	method	NOUN
cana-4456	442	18	(	(	PUNCT
cana-4456	442	19	b	b	NOUN
cana-4456	442	20	)	)	PUNCT
cana-4456	442	21	rbf	rbf	PROPN
cana-4456	442	22	-	-	PUNCT
cana-4456	442	23	fd	fd	PROPN
cana-4456	442	24	method	method	NOUN
cana-4456	442	25	communications	communication	NOUN
cana-4456	442	26	on	on	ADP
cana-4456	442	27	applied	apply	VERB
cana-4456	442	28	nonlinear	nonlinear	ADJ
cana-4456	442	29	analysis	analysis	NOUN
cana-4456	442	30	issn	issn	NOUN
cana-4456	442	31	:	:	PUNCT
cana-4456	442	32	1074	1074	NUM
cana-4456	442	33	-	-	PUNCT
cana-4456	442	34	133x	133x	NUM
cana-4456	442	35	vol	vol	NOUN
cana-4456	442	36	32	32	NUM
cana-4456	442	37	no	no	NOUN
cana-4456	442	38	.	.	PUNCT
cana-4456	443	1	9s	9s	NUM
cana-4456	443	2	(	(	PUNCT
cana-4456	443	3	2025	2025	NUM
cana-4456	443	4	)	)	PUNCT
cana-4456	443	5	2197	2197	NUM
cana-4456	443	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	443	7	(	(	PUNCT
cana-4456	443	8	c	c	NOUN
cana-4456	443	9	)	)	PUNCT
cana-4456	443	10	rbf	rbf	PROPN
cana-4456	443	11	-	-	PUNCT
cana-4456	443	12	pum	pum	PROPN
cana-4456	443	13	-	-	PUNCT
cana-4456	443	14	qr	qr	PROPN
cana-4456	443	15	method	method	NOUN
cana-4456	443	16	figure	figure	NOUN
cana-4456	443	17	12	12	NUM
cana-4456	443	18	.	.	PUNCT
cana-4456	444	1	supercritical	supercritical	ADJ
cana-4456	444	2	flow	flow	NOUN
cana-4456	444	3	using	use	VERB
cana-4456	444	4	(	(	PUNCT
cana-4456	444	5	a	a	PRON
cana-4456	444	6	)	)	PUNCT
cana-4456	444	7	kansa	kansa	PROPN
cana-4456	444	8	,	,	PUNCT
cana-4456	444	9	(	(	PUNCT
cana-4456	444	10	b	b	X
cana-4456	444	11	)	)	PUNCT
cana-4456	444	12	rbf	rbf	PROPN
cana-4456	444	13	-	-	PUNCT
cana-4456	444	14	fd	fd	PROPN
cana-4456	444	15	,	,	PUNCT
cana-4456	444	16	and	and	CCONJ
cana-4456	444	17	(	(	PUNCT
cana-4456	444	18	c	c	X
cana-4456	444	19	)	)	PUNCT
cana-4456	444	20	rbf	rbf	PROPN
cana-4456	444	21	-	-	PUNCT
cana-4456	444	22	pum	pum	PROPN
cana-4456	444	23	-	-	PUNCT
cana-4456	444	24	qr	qr	NOUN
cana-4456	444	25	methods	method	NOUN
cana-4456	444	26	at	at	ADP
cana-4456	444	27	t	t	PROPN
cana-4456	444	28	=	=	SYM
cana-4456	444	29	1500	1500	NUM
cana-4456	444	30	seconds	second	NOUN
cana-4456	444	31	with	with	ADP
cana-4456	444	32	manning	man	VERB
cana-4456	444	33	friction	friction	NOUN
cana-4456	444	34	𝑛	𝑛	PRON
cana-4456	444	35	=	=	SYM
cana-4456	444	36	0.0218𝑚−1/3𝑠.	0.0218𝑚−1/3𝑠.	NOUN
cana-4456	444	37	(	(	PUNCT
cana-4456	444	38	a	a	X
cana-4456	444	39	)	)	PUNCT
cana-4456	444	40	kansa	kansa	PROPN
cana-4456	444	41	method	method	NOUN
cana-4456	444	42	(	(	PUNCT
cana-4456	444	43	b	b	NOUN
cana-4456	444	44	)	)	PUNCT
cana-4456	444	45	rbf	rbf	PROPN
cana-4456	444	46	-	-	PUNCT
cana-4456	444	47	fd	fd	PROPN
cana-4456	444	48	method	method	NOUN
cana-4456	444	49	(	(	PUNCT
cana-4456	444	50	c	c	NOUN
cana-4456	444	51	)	)	PUNCT
cana-4456	444	52	rbf	rbf	PROPN
cana-4456	444	53	-	-	PUNCT
cana-4456	444	54	pum	pum	PROPN
cana-4456	444	55	-	-	PUNCT
cana-4456	444	56	qr	qr	PROPN
cana-4456	444	57	method	method	NOUN
cana-4456	444	58	figure	figure	NOUN
cana-4456	444	59	13	13	NUM
cana-4456	444	60	.	.	PUNCT
cana-4456	445	1	supercritical	supercritical	ADJ
cana-4456	445	2	to	to	ADP
cana-4456	445	3	subcritical	subcritical	ADJ
cana-4456	445	4	flow	flow	NOUN
cana-4456	445	5	using	use	VERB
cana-4456	445	6	(	(	PUNCT
cana-4456	445	7	a	a	PRON
cana-4456	445	8	)	)	PUNCT
cana-4456	445	9	kansa	kansa	PROPN
cana-4456	445	10	,	,	PUNCT
cana-4456	445	11	(	(	PUNCT
cana-4456	445	12	b	b	X
cana-4456	445	13	)	)	PUNCT
cana-4456	445	14	rbf	rbf	PROPN
cana-4456	445	15	-	-	PUNCT
cana-4456	445	16	fd	fd	PROPN
cana-4456	445	17	,	,	PUNCT
cana-4456	445	18	and	and	CCONJ
cana-4456	445	19	(	(	PUNCT
cana-4456	445	20	c	c	X
cana-4456	445	21	)	)	PUNCT
cana-4456	445	22	rbf	rbf	PROPN
cana-4456	445	23	-	-	PUNCT
cana-4456	445	24	pum	pum	PROPN
cana-4456	445	25	-	-	PUNCT
cana-4456	445	26	qr	qr	NOUN
cana-4456	445	27	methods	method	NOUN
cana-4456	445	28	at	at	ADP
cana-4456	445	29	t	t	PROPN
cana-4456	445	30	=	=	SYM
cana-4456	445	31	1500	1500	NUM
cana-4456	445	32	seconds	second	NOUN
cana-4456	445	33	with	with	ADP
cana-4456	445	34	manning	man	VERB
cana-4456	445	35	friction	friction	NOUN
cana-4456	445	36	𝑛	𝑛	PRON
cana-4456	445	37	=	=	SYM
cana-4456	445	38	0.0218𝑚−1/3𝑠.	0.0218𝑚−1/3𝑠.	NOUN
cana-4456	445	39	communications	communication	NOUN
cana-4456	445	40	on	on	ADP
cana-4456	445	41	applied	apply	VERB
cana-4456	445	42	nonlinear	nonlinear	ADJ
cana-4456	445	43	analysis	analysis	NOUN
cana-4456	445	44	issn	issn	NOUN
cana-4456	445	45	:	:	PUNCT
cana-4456	445	46	1074	1074	NUM
cana-4456	445	47	-	-	PUNCT
cana-4456	445	48	133x	133x	NUM
cana-4456	445	49	vol	vol	NOUN
cana-4456	445	50	32	32	NUM
cana-4456	446	1	no	no	NOUN
cana-4456	446	2	.	.	PUNCT
cana-4456	447	1	9s	9s	NUM
cana-4456	447	2	(	(	PUNCT
cana-4456	447	3	2025	2025	NUM
cana-4456	447	4	)	)	PUNCT
cana-4456	447	5	2198	2198	NUM
cana-4456	448	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	448	2	refrences	refrence	VERB
cana-4456	448	3	[	[	X
cana-4456	448	4	1	1	X
cana-4456	448	5	]	]	X
cana-4456	448	6	a.b	a.b	PROPN
cana-4456	448	7	.	.	PROPN
cana-4456	448	8	de	de	PROPN
cana-4456	448	9	saint	saint	PROPN
cana-4456	448	10	-	-	PUNCT
cana-4456	448	11	venant	venant	NOUN
cana-4456	448	12	,	,	PUNCT
cana-4456	448	13	théorie	théorie	PROPN
cana-4456	448	14	du	du	PROPN
cana-4456	448	15	mouvement	mouvement	PROPN
cana-4456	448	16	non	non	PROPN
cana-4456	448	17	permanent	permanent	PROPN
cana-4456	448	18	des	des	X
cana-4456	448	19	eaux	eaux	X
cana-4456	448	20	,	,	PUNCT
cana-4456	448	21	avec	avec	X
cana-4456	448	22	application	application	PROPN
cana-4456	448	23	aux	aux	PROPN
cana-4456	448	24	crues	crues	PROPN
cana-4456	448	25	des	des	PROPN
cana-4456	448	26	rivières	rivières	PROPN
cana-4456	448	27	et	et	PROPN
cana-4456	448	28	a	a	DET
cana-4456	448	29	l'introduction	l'introduction	NOUN
cana-4456	448	30	de	de	ADP
cana-4456	448	31	marées	marées	PROPN
cana-4456	448	32	dans	dans	PROPN
cana-4456	448	33	leurs	leur	NOUN
cana-4456	448	34	lits	lits	PROPN
cana-4456	448	35	,	,	PUNCT
cana-4456	448	36	comptes	compte	VERB
cana-4456	448	37	rendus	rendus	PROPN
cana-4456	448	38	de	de	PROPN
cana-4456	448	39	l'académie	l'académie	PROPN
cana-4456	448	40	des	des	PROPN
cana-4456	448	41	sciences	sciences	PROPN
cana-4456	448	42	de	de	X
cana-4456	448	43	paris	paris	PROPN
cana-4456	448	44	73	73	NUM
cana-4456	448	45	,	,	PUNCT
cana-4456	448	46	147	147	NUM
cana-4456	448	47	-	-	SYM
cana-4456	448	48	-154	-154	NOUN
cana-4456	448	49	and	and	CCONJ
cana-4456	448	50	237	237	NUM
cana-4456	448	51	-	-	SYM
cana-4456	448	52	240	240	NUM
cana-4456	448	53	(	(	PUNCT
cana-4456	448	54	1871	1871	NUM
cana-4456	448	55	)	)	PUNCT
cana-4456	448	56	.	.	PUNCT
cana-4456	449	1	[	[	X
cana-4456	449	2	2	2	X
cana-4456	449	3	]	]	X
cana-4456	449	4	m.h	m.h	PROPN
cana-4456	449	5	.	.	PROPN
cana-4456	449	6	chaudhry	chaudhry	PROPN
cana-4456	449	7	,	,	PUNCT
cana-4456	449	8	open	open	ADJ
cana-4456	449	9	-	-	PUNCT
cana-4456	449	10	channel	channel	NOUN
cana-4456	449	11	flow	flow	NOUN
cana-4456	449	12	,	,	PUNCT
cana-4456	449	13	boston	boston	PROPN
cana-4456	449	14	,	,	PUNCT
cana-4456	449	15	ma	ma	PROPN
cana-4456	449	16	:	:	PUNCT
cana-4456	449	17	springer	springer	NOUN
cana-4456	449	18	us	us	PROPN
cana-4456	449	19	(	(	PUNCT
cana-4456	449	20	2008	2008	NUM
cana-4456	449	21	)	)	PUNCT
cana-4456	449	22	.	.	PUNCT
cana-4456	450	1	[	[	X
cana-4456	450	2	3	3	X
cana-4456	450	3	]	]	X
cana-4456	450	4	o.	o.	NOUN
cana-4456	450	5	delestre	delestre	PROPN
cana-4456	450	6	,	,	PUNCT
cana-4456	450	7	c.	c.	PROPN
cana-4456	450	8	lucas	lucas	PROPN
cana-4456	450	9	,	,	PUNCT
cana-4456	450	10	p.a	p.a	PROPN
cana-4456	450	11	.	.	PROPN
cana-4456	450	12	ksinant	ksinant	PROPN
cana-4456	450	13	,	,	PUNCT
cana-4456	450	14	f.	f.	PROPN
cana-4456	450	15	darboux	darboux	NOUN
cana-4456	450	16	,	,	PUNCT
cana-4456	450	17	c.	c.	NOUN
cana-4456	450	18	laguerre	laguerre	PROPN
cana-4456	450	19	,	,	PUNCT
cana-4456	450	20	et	et	PROPN
cana-4456	450	21	al	al	PROPN
cana-4456	450	22	.	.	PROPN
cana-4456	450	23	,	,	PUNCT
cana-4456	450	24	swashes	swash	VERB
cana-4456	450	25	:	:	PUNCT
cana-4456	450	26	a	a	DET
cana-4456	450	27	compilation	compilation	NOUN
cana-4456	450	28	of	of	ADP
cana-4456	450	29	shallow	shallow	ADJ
cana-4456	450	30	water	water	NOUN
cana-4456	450	31	analytic	analytic	ADJ
cana-4456	450	32	solutions	solution	NOUN
cana-4456	450	33	for	for	ADP
cana-4456	450	34	hydraulic	hydraulic	ADJ
cana-4456	450	35	and	and	CCONJ
cana-4456	450	36	environmental	environmental	ADJ
cana-4456	450	37	studies	study	NOUN
cana-4456	450	38	,	,	PUNCT
cana-4456	450	39	international	international	ADJ
cana-4456	450	40	journal	journal	NOUN
cana-4456	450	41	for	for	ADP
cana-4456	450	42	numerical	numerical	ADJ
cana-4456	450	43	methods	method	NOUN
cana-4456	450	44	in	in	ADP
cana-4456	450	45	fluids	fluid	NOUN
cana-4456	450	46	72(3	72(3	NUM
cana-4456	450	47	)	)	PUNCT
cana-4456	450	48	,	,	PUNCT
cana-4456	450	49	269	269	NUM
cana-4456	450	50	-	-	SYM
cana-4456	450	51	300	300	NUM
cana-4456	450	52	(	(	PUNCT
cana-4456	450	53	2013	2013	NUM
cana-4456	450	54	)	)	PUNCT
cana-4456	450	55	.	.	PUNCT
cana-4456	451	1	[	[	X
cana-4456	451	2	4	4	X
cana-4456	451	3	]	]	X
cana-4456	451	4	y.	y.	PROPN
cana-4456	451	5	xing	xing	PROPN
cana-4456	451	6	,	,	PUNCT
cana-4456	451	7	c.w	c.w	PROPN
cana-4456	451	8	.	.	PROPN
cana-4456	451	9	shu	shu	PROPN
cana-4456	451	10	,	,	PUNCT
cana-4456	451	11	solution	solution	NOUN
cana-4456	451	12	of	of	ADP
cana-4456	451	13	shallow	shallow	ADJ
cana-4456	451	14	-	-	PUNCT
cana-4456	451	15	water	water	NOUN
cana-4456	451	16	equations	equation	NOUN
cana-4456	451	17	using	use	VERB
cana-4456	451	18	least	least	ADJ
cana-4456	451	19	-	-	PUNCT
cana-4456	451	20	squares	square	NOUN
cana-4456	451	21	finite	finite	ADJ
cana-4456	451	22	-	-	ADJ
cana-4456	451	23	element	element	ADJ
cana-4456	451	24	method	method	NOUN
cana-4456	451	25	,	,	PUNCT
cana-4456	451	26	journal	journal	NOUN
cana-4456	451	27	of	of	ADP
cana-4456	451	28	computational	computational	ADJ
cana-4456	451	29	physics	physics	NOUN
cana-4456	451	30	208(1	208(1	NUM
cana-4456	451	31	)	)	PUNCT
cana-4456	451	32	,	,	PUNCT
cana-4456	451	33	206	206	NUM
cana-4456	451	34	-	-	SYM
cana-4456	451	35	227	227	NUM
cana-4456	451	36	(	(	PUNCT
cana-4456	451	37	2005	2005	NUM
cana-4456	451	38	)	)	PUNCT
cana-4456	451	39	.	.	PUNCT
cana-4456	452	1	[	[	X
cana-4456	452	2	5	5	NUM
cana-4456	452	3	]	]	X
cana-4456	452	4	s.j	s.j	PROPN
cana-4456	452	5	.	.	PROPN
cana-4456	452	6	liang	liang	PROPN
cana-4456	452	7	,	,	PUNCT
cana-4456	452	8	j.h	j.h	PROPN
cana-4456	452	9	.	.	PROPN
cana-4456	452	10	tang	tang	PROPN
cana-4456	452	11	,	,	PUNCT
cana-4456	452	12	m.s	m.s	PROPN
cana-4456	452	13	.	.	PROPN
cana-4456	452	14	wu	wu	PROPN
cana-4456	452	15	,	,	PUNCT
cana-4456	452	16	high	high	ADJ
cana-4456	452	17	order	order	NOUN
cana-4456	452	18	finite	finite	ADJ
cana-4456	452	19	difference	difference	NOUN
cana-4456	452	20	weno	weno	NOUN
cana-4456	452	21	schemes	scheme	NOUN
cana-4456	452	22	with	with	ADP
cana-4456	452	23	the	the	DET
cana-4456	452	24	exact	exact	ADJ
cana-4456	452	25	conservation	conservation	NOUN
cana-4456	452	26	property	property	NOUN
cana-4456	452	27	for	for	ADP
cana-4456	452	28	the	the	DET
cana-4456	452	29	shallow	shallow	ADJ
cana-4456	452	30	water	water	NOUN
cana-4456	452	31	equations	equation	NOUN
cana-4456	452	32	,	,	PUNCT
cana-4456	452	33	acta	acta	PROPN
cana-4456	452	34	mechanica	mechanica	PROPN
cana-4456	452	35	sinica	sinica	PROPN
cana-4456	452	36	24	24	NUM
cana-4456	452	37	,	,	PUNCT
cana-4456	452	38	523	523	NUM
cana-4456	452	39	-	-	SYM
cana-4456	452	40	532	532	NUM
cana-4456	452	41	(	(	PUNCT
cana-4456	452	42	2008	2008	NUM
cana-4456	452	43	)	)	PUNCT
cana-4456	452	44	.	.	PUNCT
cana-4456	453	1	[	[	X
cana-4456	453	2	6	6	NUM
cana-4456	453	3	]	]	SYM
cana-4456	453	4	s.n	s.n	PROPN
cana-4456	453	5	.	.	PROPN
cana-4456	453	6	kuiry	kuiry	PROPN
cana-4456	453	7	,	,	PUNCT
cana-4456	453	8	k.	k.	PROPN
cana-4456	453	9	pramanik	pramanik	PROPN
cana-4456	453	10	,	,	PUNCT
cana-4456	453	11	d.	d.	PROPN
cana-4456	453	12	sen	sen	PROPN
cana-4456	453	13	,	,	PUNCT
cana-4456	453	14	finite	finite	ADJ
cana-4456	453	15	volume	volume	NOUN
cana-4456	453	16	model	model	NOUN
cana-4456	453	17	for	for	ADP
cana-4456	453	18	shallow	shallow	ADJ
cana-4456	453	19	water	water	NOUN
cana-4456	453	20	equations	equation	NOUN
cana-4456	453	21	with	with	ADP
cana-4456	453	22	improved	improved	ADJ
cana-4456	453	23	treatment	treatment	NOUN
cana-4456	453	24	of	of	ADP
cana-4456	453	25	source	source	NOUN
cana-4456	453	26	terms	term	NOUN
cana-4456	453	27	,	,	PUNCT
cana-4456	453	28	journal	journal	NOUN
cana-4456	453	29	of	of	ADP
cana-4456	453	30	hydraulic	hydraulic	ADJ
cana-4456	453	31	engineering	engineering	NOUN
cana-4456	453	32	134(2	134(2	NUM
cana-4456	453	33	)	)	PUNCT
cana-4456	453	34	,	,	PUNCT
cana-4456	453	35	231	231	NUM
cana-4456	453	36	-	-	SYM
cana-4456	453	37	242	242	NUM
cana-4456	453	38	(	(	PUNCT
cana-4456	453	39	2008	2008	NUM
cana-4456	453	40	)	)	PUNCT
cana-4456	453	41	.	.	PUNCT
cana-4456	454	1	[	[	X
cana-4456	454	2	7	7	X
cana-4456	454	3	]	]	X
cana-4456	454	4	g.h	g.h	PROPN
cana-4456	454	5	.	.	PROPN
cana-4456	454	6	duenas	duenas	PROPN
cana-4456	454	7	,	,	PUNCT
cana-4456	454	8	a.	a.	PROPN
cana-4456	454	9	beljadid	beljadid	VERB
cana-4456	454	10	,	,	PUNCT
cana-4456	454	11	a	a	DET
cana-4456	454	12	central	central	ADJ
cana-4456	454	13	-	-	PUNCT
cana-4456	454	14	upwind	upwind	NOUN
cana-4456	454	15	scheme	scheme	NOUN
cana-4456	454	16	with	with	ADP
cana-4456	454	17	artificial	artificial	ADJ
cana-4456	454	18	viscosity	viscosity	NOUN
cana-4456	454	19	for	for	ADP
cana-4456	454	20	shallow	shallow	ADJ
cana-4456	454	21	-	-	PUNCT
cana-4456	454	22	water	water	NOUN
cana-4456	454	23	flows	flow	NOUN
cana-4456	454	24	in	in	ADP
cana-4456	454	25	channels	channel	NOUN
cana-4456	454	26	,	,	PUNCT
cana-4456	454	27	advances	advance	NOUN
cana-4456	454	28	in	in	ADP
cana-4456	454	29	water	water	NOUN
cana-4456	454	30	resources	resource	NOUN
cana-4456	454	31	96	96	NUM
cana-4456	454	32	,	,	PUNCT
cana-4456	454	33	323–338	323–338	NUM
cana-4456	454	34	(	(	PUNCT
cana-4456	454	35	2016	2016	NUM
cana-4456	454	36	)	)	PUNCT
cana-4456	454	37	.	.	PUNCT
cana-4456	455	1	[	[	X
cana-4456	455	2	8	8	NUM
cana-4456	455	3	]	]	X
cana-4456	455	4	y.c	y.c	PROPN
cana-4456	455	5	.	.	PROPN
cana-4456	455	6	hon	hon	PROPN
cana-4456	455	7	,	,	PUNCT
cana-4456	455	8	k.f	k.f	PROPN
cana-4456	455	9	.	.	PROPN
cana-4456	455	10	cheung	cheung	PROPN
cana-4456	455	11	,	,	PUNCT
cana-4456	455	12	x.z	x.z	PROPN
cana-4456	455	13	.	.	PROPN
cana-4456	455	14	mao	mao	PROPN
cana-4456	455	15	,	,	PUNCT
cana-4456	455	16	e.j	e.j	PROPN
cana-4456	455	17	.	.	PROPN
cana-4456	455	18	kansa	kansa	PROPN
cana-4456	455	19	,	,	PUNCT
cana-4456	455	20	multiquadric	multiquadric	ADJ
cana-4456	455	21	solution	solution	NOUN
cana-4456	455	22	for	for	ADP
cana-4456	455	23	shallow	shallow	ADJ
cana-4456	455	24	water	water	NOUN
cana-4456	455	25	equations	equation	NOUN
cana-4456	455	26	,	,	PUNCT
cana-4456	455	27	journal	journal	NOUN
cana-4456	455	28	of	of	ADP
cana-4456	455	29	hydraulic	hydraulic	ADJ
cana-4456	455	30	engineering	engineering	NOUN
cana-4456	455	31	125	125	NUM
cana-4456	455	32	,	,	PUNCT
cana-4456	455	33	524	524	NUM
cana-4456	455	34	-	-	SYM
cana-4456	455	35	533	533	NUM
cana-4456	455	36	(	(	PUNCT
cana-4456	455	37	1999	1999	NUM
cana-4456	455	38	)	)	PUNCT
cana-4456	455	39	.	.	PUNCT
cana-4456	456	1	[	[	X
cana-4456	456	2	9	9	NUM
cana-4456	456	3	]	]	SYM
cana-4456	456	4	s.m	s.m	PROPN
cana-4456	456	5	.	.	PROPN
cana-4456	456	6	wong	wong	PROPN
cana-4456	456	7	,	,	PUNCT
cana-4456	456	8	y.c	y.c	PROPN
cana-4456	456	9	.	.	PROPN
cana-4456	456	10	hon	hon	PROPN
cana-4456	456	11	,	,	PUNCT
cana-4456	456	12	m.a	m.a	PROPN
cana-4456	456	13	.	.	PROPN
cana-4456	456	14	golberg	golberg	PROPN
cana-4456	456	15	,	,	PUNCT
cana-4456	456	16	compactly	compactly	ADV
cana-4456	456	17	supported	support	VERB
cana-4456	456	18	radial	radial	ADJ
cana-4456	456	19	basis	basis	NOUN
cana-4456	456	20	functions	function	NOUN
cana-4456	456	21	for	for	ADP
cana-4456	456	22	shallow	shallow	ADJ
cana-4456	456	23	water	water	NOUN
cana-4456	456	24	equations	equation	NOUN
cana-4456	456	25	.	.	PUNCT
cana-4456	457	1	applied	apply	VERB
cana-4456	457	2	mathematics	mathematic	NOUN
cana-4456	457	3	and	and	CCONJ
cana-4456	457	4	computation	computation	NOUN
cana-4456	457	5	127	127	NUM
cana-4456	457	6	,	,	PUNCT
cana-4456	457	7	79	79	NUM
cana-4456	457	8	-	-	SYM
cana-4456	457	9	101	101	NUM
cana-4456	457	10	(	(	PUNCT
cana-4456	457	11	2002	2002	NUM
cana-4456	457	12	)	)	PUNCT
cana-4456	457	13	.	.	PUNCT
cana-4456	458	1	[	[	X
cana-4456	458	2	10	10	NUM
cana-4456	458	3	]	]	X
cana-4456	458	4	s.m	s.m	PROPN
cana-4456	458	5	.	.	PROPN
cana-4456	458	6	wong	wong	PROPN
cana-4456	458	7	,	,	PUNCT
cana-4456	458	8	y.c	y.c	PROPN
cana-4456	458	9	.	.	PROPN
cana-4456	458	10	hon	hon	PROPN
cana-4456	458	11	,	,	PUNCT
cana-4456	458	12	m.a	m.a	PROPN
cana-4456	458	13	.	.	PROPN
cana-4456	458	14	golberg	golberg	PROPN
cana-4456	458	15	,	,	PUNCT
cana-4456	458	16	compactly	compactly	ADV
cana-4456	458	17	supported	support	VERB
cana-4456	458	18	radial	radial	ADJ
cana-4456	458	19	basis	basis	NOUN
cana-4456	458	20	functions	function	NOUN
cana-4456	458	21	for	for	ADP
cana-4456	458	22	shallow	shallow	ADJ
cana-4456	458	23	water	water	NOUN
cana-4456	458	24	equations	equation	NOUN
cana-4456	458	25	.	.	PUNCT
cana-4456	459	1	applied	apply	VERB
cana-4456	459	2	mathematics	mathematic	NOUN
cana-4456	459	3	and	and	CCONJ
cana-4456	459	4	computation	computation	NOUN
cana-4456	459	5	127	127	NUM
cana-4456	459	6	,	,	PUNCT
cana-4456	459	7	79	79	NUM
cana-4456	459	8	-	-	SYM
cana-4456	459	9	101	101	NUM
cana-4456	459	10	(	(	PUNCT
cana-4456	459	11	2002	2002	NUM
cana-4456	459	12	)	)	PUNCT
cana-4456	459	13	.	.	PUNCT
cana-4456	460	1	[	[	X
cana-4456	460	2	11	11	NUM
cana-4456	460	3	]	]	X
cana-4456	460	4	e.j	e.j	PROPN
cana-4456	460	5	.	.	PROPN
cana-4456	460	6	kansa	kansa	PROPN
cana-4456	460	7	,	,	PUNCT
cana-4456	460	8	multiquadrics-{a	multiquadrics-{a	AUX
cana-4456	460	9	}	}	PUNCT
cana-4456	460	10	scattered	scatter	VERB
cana-4456	460	11	data	datum	NOUN
cana-4456	460	12	approximation	approximation	NOUN
cana-4456	460	13	scheme	scheme	NOUN
cana-4456	460	14	with	with	ADP
cana-4456	460	15	applications	application	NOUN
cana-4456	460	16	to	to	ADP
cana-4456	460	17	computational	computational	ADJ
cana-4456	460	18	fluid	fluid	NOUN
cana-4456	460	19	-	-	PUNCT
cana-4456	460	20	dynamics-{ii	dynamics-{ii	NOUN
cana-4456	460	21	}	}	PUNCT
cana-4456	460	22	solutions	solution	NOUN
cana-4456	460	23	to	to	PART
cana-4456	460	24	parabolic	parabolic	VERB
cana-4456	460	25	,	,	PUNCT
cana-4456	460	26	hyperbolic	hyperbolic	ADJ
cana-4456	460	27	and	and	CCONJ
cana-4456	460	28	elliptic	elliptic	ADJ
cana-4456	460	29	partial	partial	ADJ
cana-4456	460	30	differential	differential	NOUN
cana-4456	460	31	equations	equation	NOUN
cana-4456	460	32	,	,	PUNCT
cana-4456	460	33	computers	computer	NOUN
cana-4456	460	34	and	and	CCONJ
cana-4456	460	35	mathematics	mathematic	NOUN
cana-4456	460	36	with	with	ADP
cana-4456	460	37	applications	application	NOUN
cana-4456	460	38	19(8	19(8	NUM
cana-4456	460	39	)	)	PUNCT
cana-4456	460	40	,	,	PUNCT
cana-4456	460	41	147	147	NUM
cana-4456	460	42	-	-	SYM
cana-4456	460	43	161	161	NUM
cana-4456	460	44	(	(	PUNCT
cana-4456	460	45	1990	1990	NUM
cana-4456	460	46	)	)	PUNCT
cana-4456	460	47	.	.	PUNCT
cana-4456	461	1	[	[	X
cana-4456	461	2	12	12	NUM
cana-4456	461	3	]	]	PUNCT
cana-4456	461	4	a.	a.	NOUN
cana-4456	461	5	tolstykh	tolstykh	PROPN
cana-4456	461	6	,	,	PUNCT
cana-4456	461	7	d.	d.	PROPN
cana-4456	461	8	shirobokov	shirobokov	PROPN
cana-4456	461	9	,	,	PUNCT
cana-4456	461	10	on	on	ADP
cana-4456	461	11	using	use	VERB
cana-4456	461	12	radial	radial	ADJ
cana-4456	461	13	basis	basis	NOUN
cana-4456	461	14	functions	function	NOUN
cana-4456	461	15	in	in	ADP
cana-4456	461	16	a	a	DET
cana-4456	461	17	finite	finite	ADJ
cana-4456	461	18	difference	difference	NOUN
cana-4456	461	19	mode	mode	NOUN
cana-4456	461	20	with	with	ADP
cana-4456	461	21	applications	application	NOUN
cana-4456	461	22	to	to	ADP
cana-4456	461	23	elasticity	elasticity	NOUN
cana-4456	461	24	problems	problem	NOUN
cana-4456	461	25	,	,	PUNCT
cana-4456	461	26	computational	computational	ADJ
cana-4456	461	27	mechanics	mechanic	NOUN
cana-4456	461	28	33	33	NUM
cana-4456	461	29	,	,	PUNCT
cana-4456	461	30	68	68	NUM
cana-4456	461	31	-	-	SYM
cana-4456	461	32	79	79	NUM
cana-4456	461	33	(	(	PUNCT
cana-4456	461	34	2003	2003	NUM
cana-4456	461	35	)	)	PUNCT
cana-4456	461	36	.	.	PUNCT
cana-4456	462	1	[	[	X
cana-4456	462	2	13	13	NUM
cana-4456	462	3	]	]	X
cana-4456	462	4	b.	b.	PROPN
cana-4456	462	5	fornberg	fornberg	PROPN
cana-4456	462	6	,	,	PUNCT
cana-4456	462	7	n.	n.	NOUN
cana-4456	462	8	flyer	flyer	NOUN
cana-4456	462	9	,	,	PUNCT
cana-4456	462	10	a	a	DET
cana-4456	462	11	primer	primer	NOUN
cana-4456	462	12	on	on	ADP
cana-4456	462	13	radial	radial	ADJ
cana-4456	462	14	basis	basis	NOUN
cana-4456	462	15	functions	function	NOUN
cana-4456	462	16	with	with	ADP
cana-4456	462	17	applications	application	NOUN
cana-4456	462	18	to	to	ADP
cana-4456	462	19	the	the	DET
cana-4456	462	20	geosciences	geoscience	NOUN
cana-4456	462	21	}	}	PUNCT
cana-4456	462	22	,	,	PUNCT
cana-4456	462	23	cbms	cbms	ADJ
cana-4456	462	24	-	-	PUNCT
cana-4456	462	25	nsf	nsf	ADJ
cana-4456	462	26	regional	regional	ADJ
cana-4456	462	27	conference	conference	NOUN
cana-4456	462	28	series	series	NOUN
cana-4456	462	29	in	in	ADP
cana-4456	462	30	applied	applied	ADJ
cana-4456	462	31	mathematics	mathematic	NOUN
cana-4456	462	32	,	,	PUNCT
cana-4456	462	33	society	society	NOUN
cana-4456	462	34	for	for	ADP
cana-4456	462	35	industrial	industrial	ADJ
cana-4456	462	36	and	and	CCONJ
cana-4456	462	37	applied	applied	ADJ
cana-4456	462	38	mathematics	mathematic	NOUN
cana-4456	462	39	(	(	PUNCT
cana-4456	462	40	siam	siam	NOUN
cana-4456	462	41	)	)	PUNCT
cana-4456	462	42	,	,	PUNCT
cana-4456	462	43	(	(	PUNCT
cana-4456	462	44	2015	2015	NUM
cana-4456	462	45	)	)	PUNCT
cana-4456	462	46	.	.	PUNCT
cana-4456	463	1	[	[	X
cana-4456	463	2	14	14	NUM
cana-4456	463	3	]	]	X
cana-4456	463	4	e.	e.	PROPN
cana-4456	463	5	ben	ben	PROPN
cana-4456	463	6	-	-	PUNCT
cana-4456	463	7	ahmed	ahmed	PROPN
cana-4456	463	8	,	,	PUNCT
cana-4456	463	9	m.	m.	NOUN
cana-4456	463	10	sadik	sadik	PROPN
cana-4456	463	11	and	and	CCONJ
cana-4456	463	12	m.	m.	NOUN
cana-4456	463	13	wakrim	wakrim	PROPN
cana-4456	463	14	,	,	PUNCT
cana-4456	463	15	radial	radial	ADJ
cana-4456	463	16	basis	basis	NOUN
cana-4456	463	17	function	function	NOUN
cana-4456	463	18	partition	partition	NOUN
cana-4456	463	19	of	of	ADP
cana-4456	463	20	unity	unity	NOUN
cana-4456	463	21	method	method	NOUN
cana-4456	463	22	for	for	ADP
cana-4456	463	23	modelling	model	VERB
cana-4456	463	24	water	water	NOUN
cana-4456	463	25	flow	flow	NOUN
cana-4456	463	26	in	in	ADP
cana-4456	463	27	porous	porous	ADJ
cana-4456	463	28	media	medium	NOUN
cana-4456	463	29	,	,	PUNCT
cana-4456	463	30	computers	computer	NOUN
cana-4456	463	31	and	and	CCONJ
cana-4456	463	32	mathematics	mathematic	NOUN
cana-4456	463	33	with	with	ADP
cana-4456	463	34	applications	application	NOUN
cana-4456	463	35	8(75	8(75	NUM
cana-4456	463	36	)	)	PUNCT
cana-4456	463	37	,	,	PUNCT
cana-4456	463	38	2925	2925	NUM
cana-4456	463	39	-	-	SYM
cana-4456	463	40	2941	2941	NUM
cana-4456	463	41	(	(	PUNCT
cana-4456	463	42	2018	2018	NUM
cana-4456	463	43	)	)	PUNCT
cana-4456	463	44	.	.	PUNCT
cana-4456	464	1	[	[	X
cana-4456	464	2	15	15	X
cana-4456	464	3	]	]	X
cana-4456	464	4	v.	v.	CCONJ
cana-4456	464	5	shcherbakov	shcherbakov	PROPN
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cana-4456	464	7	e.	e.	PROPN
cana-4456	464	8	larsson	larsson	PROPN
cana-4456	464	9	,	,	PUNCT
cana-4456	464	10	radial	radial	ADJ
cana-4456	464	11	basis	basis	NOUN
cana-4456	464	12	function	function	NOUN
cana-4456	464	13	partition	partition	NOUN
cana-4456	464	14	of	of	ADP
cana-4456	464	15	unity	unity	NOUN
cana-4456	464	16	methods	method	NOUN
cana-4456	464	17	for	for	ADP
cana-4456	464	18	pricing	price	VERB
cana-4456	464	19	vanilla	vanilla	NOUN
cana-4456	464	20	basket	basket	NOUN
cana-4456	464	21	options	option	NOUN
cana-4456	464	22	,	,	PUNCT
cana-4456	464	23	computers	computer	NOUN
cana-4456	464	24	and	and	CCONJ
cana-4456	464	25	mathematics	mathematic	NOUN
cana-4456	464	26	with	with	ADP
cana-4456	464	27	applications	application	NOUN
cana-4456	464	28	71(1	71(1	NOUN
cana-4456	464	29	)	)	PUNCT
cana-4456	464	30	,	,	PUNCT
cana-4456	464	31	185	185	NUM
cana-4456	464	32	-	-	SYM
cana-4456	464	33	200	200	NUM
cana-4456	464	34	(	(	PUNCT
cana-4456	464	35	2016	2016	NUM
cana-4456	464	36	)	)	PUNCT
cana-4456	464	37	.	.	PUNCT
cana-4456	465	1	[	[	X
cana-4456	465	2	16	16	NUM
cana-4456	465	3	]	]	X
cana-4456	465	4	e.	e.	PROPN
cana-4456	465	5	ben	ben	PROPN
cana-4456	465	6	-	-	PUNCT
cana-4456	465	7	ahmed	ahmed	PROPN
cana-4456	465	8	,	,	PUNCT
cana-4456	465	9	m.	m.	NOUN
cana-4456	465	10	sadik	sadik	PROPN
cana-4456	465	11	and	and	CCONJ
cana-4456	465	12	m.	m.	PROPN
cana-4456	465	13	wakrim	wakrim	PROPN
cana-4456	465	14	,	,	PUNCT
cana-4456	465	15	rbfpum	rbfpum	NOUN
cana-4456	465	16	with	with	ADP
cana-4456	465	17	qr	qr	NOUN
cana-4456	465	18	factorization	factorization	NOUN
cana-4456	465	19	for	for	ADP
cana-4456	465	20	solving	solve	VERB
cana-4456	465	21	water	water	NOUN
cana-4456	465	22	flow	flow	NOUN
cana-4456	465	23	problem	problem	NOUN
cana-4456	465	24	in	in	ADP
cana-4456	465	25	multilayered	multilayered	ADJ
cana-4456	465	26	soil	soil	NOUN
cana-4456	465	27	,	,	PUNCT
cana-4456	465	28	international	international	ADJ
cana-4456	465	29	journal	journal	NOUN
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cana-4456	465	32	sciences	sciences	PROPN
cana-4456	465	33	and	and	CCONJ
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cana-4456	465	37	(	(	PUNCT
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cana-4456	465	39	)	)	PUNCT
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cana-4456	466	1	[	[	X
cana-4456	466	2	17	17	NUM
cana-4456	466	3	]	]	X
cana-4456	466	4	e.	e.	PROPN
cana-4456	466	5	ben	ben	PROPN
cana-4456	466	6	-	-	PUNCT
cana-4456	466	7	ahmed	ahmed	PROPN
cana-4456	466	8	,	,	PUNCT
cana-4456	466	9	m.	m.	NOUN
cana-4456	466	10	sadik	sadik	PROPN
cana-4456	466	11	and	and	CCONJ
cana-4456	466	12	m.	m.	PROPN
cana-4456	466	13	wakrim	wakrim	PROPN
cana-4456	466	14	,	,	PUNCT
cana-4456	466	15	a	a	DET
cana-4456	466	16	stable	stable	ADJ
cana-4456	466	17	radial	radial	ADJ
cana-4456	466	18	basis	basis	NOUN
cana-4456	466	19	function	function	NOUN
cana-4456	466	20	partition	partition	NOUN
cana-4456	466	21	of	of	ADP
cana-4456	466	22	unity	unity	NOUN
cana-4456	466	23	method	method	NOUN
cana-4456	466	24	with	with	ADP
cana-4456	466	25	d	d	ADJ
cana-4456	466	26	-	-	ADJ
cana-4456	466	27	rectangular	rectangular	ADJ
cana-4456	466	28	patches	patch	NOUN
cana-4456	466	29	for	for	ADP
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cana-4456	466	31	water	water	NOUN
cana-4456	466	32	flow	flow	NOUN
cana-4456	466	33	in	in	ADP
cana-4456	466	34	porous	porous	ADJ
cana-4456	466	35	media	medium	NOUN
cana-4456	466	36	,	,	PUNCT
cana-4456	466	37	journal	journal	NOUN
cana-4456	466	38	of	of	ADP
cana-4456	466	39	scientific	scientific	ADJ
cana-4456	466	40	computing	computing	NOUN
cana-4456	466	41	84	84	NUM
cana-4456	466	42	,	,	PUNCT
cana-4456	466	43	(	(	PUNCT
cana-4456	466	44	2020	2020	NUM
cana-4456	466	45	)	)	PUNCT
cana-4456	466	46	.	.	PUNCT
cana-4456	467	1	communications	communication	NOUN
cana-4456	467	2	on	on	ADP
cana-4456	467	3	applied	apply	VERB
cana-4456	467	4	nonlinear	nonlinear	ADJ
cana-4456	467	5	analysis	analysis	NOUN
cana-4456	467	6	issn	issn	NOUN
cana-4456	467	7	:	:	PUNCT
cana-4456	467	8	1074	1074	NUM
cana-4456	467	9	-	-	PUNCT
cana-4456	467	10	133x	133x	NUM
cana-4456	467	11	vol	vol	NOUN
cana-4456	467	12	32	32	NUM
cana-4456	467	13	no	no	NOUN
cana-4456	467	14	.	.	PUNCT
cana-4456	468	1	9s	9s	NUM
cana-4456	468	2	(	(	PUNCT
cana-4456	468	3	2025	2025	NUM
cana-4456	468	4	)	)	PUNCT
cana-4456	468	5	2199	2199	NUM
cana-4456	468	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	469	1	[	[	X
cana-4456	469	2	18	18	NUM
cana-4456	469	3	]	]	X
cana-4456	469	4	b.	b.	PROPN
cana-4456	469	5	fornberg	fornberg	PROPN
cana-4456	469	6	,	,	PUNCT
cana-4456	469	7	e.	e.	PROPN
cana-4456	469	8	lehto	lehto	PROPN
cana-4456	469	9	,	,	PUNCT
cana-4456	469	10	stabilization	stabilization	NOUN
cana-4456	469	11	of	of	ADP
cana-4456	469	12	rbf	rbf	PROPN
cana-4456	469	13	-	-	PUNCT
cana-4456	469	14	generated	generate	VERB
cana-4456	469	15	finite	finite	ADJ
cana-4456	469	16	difference	difference	NOUN
cana-4456	469	17	methods	method	NOUN
cana-4456	469	18	for	for	ADP
cana-4456	469	19	convective	convective	ADJ
cana-4456	469	20	pdes	pde	NOUN
cana-4456	469	21	,	,	PUNCT
cana-4456	469	22	journal	journal	NOUN
cana-4456	469	23	of	of	ADP
cana-4456	469	24	computational	computational	ADJ
cana-4456	469	25	physics	physics	NOUN
cana-4456	469	26	230	230	NUM
cana-4456	469	27	,	,	PUNCT
cana-4456	469	28	2270	2270	NUM
cana-4456	469	29	-	-	SYM
cana-4456	469	30	2285	2285	NUM
cana-4456	469	31	(	(	PUNCT
cana-4456	469	32	2011	2011	NUM
cana-4456	469	33	)	)	PUNCT
cana-4456	469	34	.	.	PUNCT
cana-4456	470	1	[	[	X
cana-4456	470	2	19	19	NUM
cana-4456	470	3	]	]	X
cana-4456	470	4	d.	d.	PROPN
cana-4456	470	5	stevens	stevens	PROPN
cana-4456	470	6	,	,	PUNCT
cana-4456	470	7	h.	h.	PROPN
cana-4456	470	8	power	power	PROPN
cana-4456	470	9	,	,	PUNCT
cana-4456	470	10	the	the	DET
cana-4456	470	11	radial	radial	ADJ
cana-4456	470	12	basis	basis	NOUN
cana-4456	470	13	function	function	NOUN
cana-4456	470	14	finite	finite	NOUN
cana-4456	470	15	collocation	collocation	NOUN
cana-4456	470	16	approach	approach	NOUN
cana-4456	470	17	for	for	ADP
cana-4456	470	18	capturing	capture	VERB
cana-4456	470	19	sharp	sharp	ADJ
cana-4456	470	20	fronts	front	NOUN
cana-4456	470	21	in	in	ADP
cana-4456	470	22	time	time	NOUN
cana-4456	470	23	dependent	dependent	ADJ
cana-4456	470	24	advection	advection	NOUN
cana-4456	470	25	problems	problem	NOUN
cana-4456	470	26	,	,	PUNCT
cana-4456	470	27	journal	journal	NOUN
cana-4456	470	28	of	of	ADP
cana-4456	470	29	computational	computational	ADJ
cana-4456	470	30	physics	physics	NOUN
cana-4456	470	31	298	298	NUM
cana-4456	470	32	,	,	PUNCT
cana-4456	470	33	423	423	NUM
cana-4456	470	34	-	-	SYM
cana-4456	470	35	445	445	NUM
cana-4456	470	36	(	(	PUNCT
cana-4456	470	37	2015	2015	NUM
cana-4456	470	38	)	)	PUNCT
cana-4456	470	39	.	.	PUNCT
cana-4456	471	1	[	[	X
cana-4456	471	2	20	20	NUM
cana-4456	471	3	]	]	PUNCT
cana-4456	471	4	h.	h.	PROPN
cana-4456	471	5	ma	ma	PROPN
cana-4456	471	6	,	,	PUNCT
cana-4456	471	7	chebyshev	chebyshev	PROPN
cana-4456	471	8	-	-	PUNCT
cana-4456	471	9	legendre	legendre	PROPN
cana-4456	471	10	super	super	PROPN
cana-4456	471	11	spectral	spectral	ADJ
cana-4456	471	12	viscosity	viscosity	NOUN
cana-4456	471	13	method	method	NOUN
cana-4456	471	14	for	for	ADP
cana-4456	471	15	nonlinear	nonlinear	ADJ
cana-4456	471	16	conservation	conservation	NOUN
cana-4456	471	17	laws	law	NOUN
cana-4456	471	18	,	,	PUNCT
cana-4456	471	19	siam	siam	PROPN
cana-4456	471	20	journal	journal	NOUN
cana-4456	471	21	of	of	ADP
cana-4456	471	22	numerical	numerical	ADJ
cana-4456	471	23	analysis	analysis	NOUN
cana-4456	471	24	35	35	NUM
cana-4456	471	25	,	,	PUNCT
cana-4456	471	26	893	893	NUM
cana-4456	471	27	-	-	SYM
cana-4456	471	28	908	908	NUM
cana-4456	471	29	(	(	PUNCT
cana-4456	471	30	1998	1998	NUM
cana-4456	471	31	)	)	PUNCT
cana-4456	471	32	.	.	PUNCT
cana-4456	472	1	[	[	X
cana-4456	472	2	21	21	NUM
cana-4456	472	3	]	]	X
cana-4456	472	4	n.	n.	NOUN
cana-4456	472	5	flyer	flyer	NOUN
cana-4456	472	6	,	,	PUNCT
cana-4456	472	7	e.	e.	PROPN
cana-4456	472	8	lehto	lehto	PROPN
cana-4456	472	9	,	,	PUNCT
cana-4456	472	10	s.	s.	PROPN
cana-4456	472	11	blaise	blaise	PROPN
cana-4456	472	12	,	,	PUNCT
cana-4456	472	13	g.b	g.b	PROPN
cana-4456	472	14	.	.	PROPN
cana-4456	472	15	wright	wright	PROPN
cana-4456	472	16	,	,	PUNCT
cana-4456	472	17	a.	a.	PROPN
cana-4456	472	18	st	st	PROPN
cana-4456	472	19	-	-	PUNCT
cana-4456	472	20	cyr	cyr	PROPN
cana-4456	472	21	,	,	PUNCT
cana-4456	472	22	a	a	DET
cana-4456	472	23	guide	guide	NOUN
cana-4456	472	24	to	to	ADP
cana-4456	472	25	rbf	rbf	PROPN
cana-4456	472	26	-	-	PUNCT
cana-4456	472	27	generated	generate	VERB
cana-4456	472	28	finite	finite	ADJ
cana-4456	472	29	differences	difference	NOUN
cana-4456	472	30	for	for	ADP
cana-4456	472	31	nonlinear	nonlinear	ADJ
cana-4456	472	32	transport	transport	NOUN
cana-4456	472	33	:	:	PUNCT
cana-4456	472	34	shallow	shallow	ADJ
cana-4456	472	35	water	water	NOUN
cana-4456	472	36	simulations	simulation	NOUN
cana-4456	472	37	on	on	ADP
cana-4456	472	38	a	a	DET
cana-4456	472	39	sphere	sphere	NOUN
cana-4456	472	40	,	,	PUNCT
cana-4456	472	41	journal	journal	NOUN
cana-4456	472	42	of	of	ADP
cana-4456	472	43	computational	computational	ADJ
cana-4456	472	44	physics	physic	NOUN
cana-4456	472	45	231	231	NUM
cana-4456	472	46	,	,	PUNCT
cana-4456	472	47	4078	4078	NUM
cana-4456	472	48	-	-	SYM
cana-4456	472	49	4095	4095	NUM
cana-4456	472	50	(	(	PUNCT
cana-4456	472	51	2012	2012	NUM
cana-4456	472	52	)	)	PUNCT
cana-4456	472	53	.	.	PUNCT
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cana-4456	473	2	22	22	NUM
cana-4456	473	3	]	]	X
cana-4456	473	4	n.	n.	NOUN
cana-4456	473	5	flyer	flyer	NOUN
cana-4456	473	6	,	,	PUNCT
cana-4456	473	7	g.a	g.a	PROPN
cana-4456	473	8	.	.	PROPN
cana-4456	473	9	barnett	barnett	PROPN
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cana-4456	473	11	l.j	l.j	PROPN
cana-4456	473	12	.	.	PROPN
cana-4456	473	13	wicker	wicker	PROPN
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cana-4456	473	15	enhancing	enhance	VERB
cana-4456	473	16	finite	finite	ADJ
cana-4456	473	17	differences	difference	NOUN
cana-4456	473	18	with	with	ADP
cana-4456	473	19	radial	radial	ADJ
cana-4456	473	20	basis	basis	NOUN
cana-4456	473	21	functions	function	NOUN
cana-4456	473	22	:	:	PUNCT
cana-4456	473	23	experiments	experiment	NOUN
cana-4456	473	24	on	on	ADP
cana-4456	473	25	the	the	DET
cana-4456	473	26	navier	navier	NOUN
cana-4456	473	27	–	–	PUNCT
cana-4456	473	28	stokes	stoke	NOUN
cana-4456	473	29	equations	equation	NOUN
cana-4456	473	30	,	,	PUNCT
cana-4456	473	31	journal	journal	NOUN
cana-4456	473	32	of	of	ADP
cana-4456	473	33	computational	computational	ADJ
cana-4456	473	34	physics	physic	NOUN
cana-4456	473	35	316	316	NUM
cana-4456	473	36	,	,	PUNCT
cana-4456	473	37	39	39	NUM
cana-4456	473	38	-	-	SYM
cana-4456	473	39	62	62	NUM
cana-4456	473	40	(	(	PUNCT
cana-4456	473	41	2016	2016	NUM
cana-4456	473	42	)	)	PUNCT
cana-4456	473	43	.	.	PUNCT
cana-4456	474	1	[	[	X
cana-4456	474	2	23	23	X
cana-4456	474	3	]	]	X
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cana-4456	474	5	shankar	shankar	PROPN
cana-4456	474	6	,	,	PUNCT
cana-4456	474	7	g.b	g.b	PROPN
cana-4456	474	8	.	.	PROPN
cana-4456	474	9	wright	wright	PROPN
cana-4456	474	10	,	,	PUNCT
cana-4456	474	11	a.	a.	PROPN
cana-4456	474	12	narayan	narayan	PROPN
cana-4456	474	13	,	,	PUNCT
cana-4456	474	14	a	a	DET
cana-4456	474	15	robust	robust	ADJ
cana-4456	474	16	hyperviscosity	hyperviscosity	NOUN
cana-4456	474	17	formulation	formulation	NOUN
cana-4456	474	18	for	for	ADP
cana-4456	474	19	stable	stable	ADJ
cana-4456	474	20	rbf	rbf	PROPN
cana-4456	474	21	-	-	PUNCT
cana-4456	474	22	fd	fd	PROPN
cana-4456	474	23	discretizations	discretization	NOUN
cana-4456	474	24	of	of	ADP
cana-4456	474	25	advection	advection	NOUN
cana-4456	474	26	-	-	PUNCT
cana-4456	474	27	diffusion	diffusion	NOUN
cana-4456	474	28	-	-	PUNCT
cana-4456	474	29	reaction	reaction	NOUN
cana-4456	474	30	equations	equation	NOUN
cana-4456	474	31	on	on	ADP
cana-4456	474	32	manifolds	manifold	NOUN
cana-4456	474	33	,	,	PUNCT
cana-4456	474	34	siam	siam	ADJ
cana-4456	474	35	journal	journal	NOUN
cana-4456	474	36	on	on	ADP
cana-4456	474	37	scientific	scientific	ADJ
cana-4456	474	38	computing	computing	NOUN
cana-4456	474	39	42	42	NUM
cana-4456	474	40	,	,	PUNCT
cana-4456	474	41	a2371	a2371	PROPN
cana-4456	474	42	-	-	PUNCT
cana-4456	474	43	a2401	a2401	PROPN
cana-4456	474	44	(	(	PUNCT
cana-4456	474	45	2020	2020	NUM
cana-4456	474	46	)	)	PUNCT
cana-4456	474	47	.	.	PUNCT
cana-4456	475	1	[	[	X
cana-4456	475	2	24	24	NUM
cana-4456	475	3	]	]	PUNCT
cana-4456	475	4	i.	i.	PROPN
cana-4456	475	5	tominec	tominec	PROPN
cana-4456	475	6	,	,	PUNCT
cana-4456	475	7	m.	m.	NOUN
cana-4456	475	8	nazarov	nazarov	PROPN
cana-4456	475	9	,	,	PUNCT
cana-4456	475	10	residual	residual	ADJ
cana-4456	475	11	viscosity	viscosity	NOUN
cana-4456	475	12	stabilized	stabilize	VERB
cana-4456	475	13	rbf	rbf	PROPN
cana-4456	475	14	-	-	PUNCT
cana-4456	475	15	fd	fd	ADJ
cana-4456	475	16	methods	method	NOUN
cana-4456	475	17	for	for	ADP
cana-4456	475	18	solving	solve	VERB
cana-4456	475	19	nonlinear	nonlinear	ADJ
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cana-4456	475	21	laws	law	NOUN
cana-4456	475	22	,	,	PUNCT
cana-4456	475	23	journal	journal	NOUN
cana-4456	475	24	of	of	ADP
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cana-4456	475	26	computing	computing	NOUN
cana-4456	475	27	94	94	NUM
cana-4456	475	28	,	,	PUNCT
cana-4456	475	29	(	(	PUNCT
cana-4456	475	30	2022	2022	NUM
cana-4456	475	31	)	)	PUNCT
cana-4456	475	32	.	.	PUNCT
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cana-4456	476	3	]	]	PUNCT
cana-4456	476	4	m.	m.	NOUN
cana-4456	476	5	al	al	PROPN
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cana-4456	476	7	,	,	PUNCT
cana-4456	476	8	e.	e.	PROPN
cana-4456	476	9	chaabelasri	chaabelasri	PROPN
cana-4456	476	10	,	,	PUNCT
cana-4456	476	11	balanced	balance	VERB
cana-4456	476	12	meshless	meshless	ADJ
cana-4456	476	13	method	method	NOUN
cana-4456	476	14	for	for	ADP
cana-4456	476	15	numerical	numerical	ADJ
cana-4456	476	16	simulation	simulation	NOUN
cana-4456	476	17	of	of	ADP
cana-4456	476	18	pollutant	pollutant	ADJ
cana-4456	476	19	transport	transport	NOUN
cana-4456	476	20	by	by	ADP
cana-4456	476	21	shallow	shallow	ADJ
cana-4456	476	22	water	water	NOUN
cana-4456	476	23	flow	flow	NOUN
cana-4456	476	24	over	over	ADP
cana-4456	476	25	irregular	irregular	ADJ
cana-4456	476	26	bed	bed	NOUN
cana-4456	476	27	:	:	PUNCT
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cana-4456	476	29	in	in	ADP
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cana-4456	476	32	of	of	ADP
cana-4456	476	33	gibraltar	gibraltar	NOUN
cana-4456	476	34	,	,	PUNCT
cana-4456	476	35	applied	apply	VERB
cana-4456	476	36	sciences	science	NOUN
cana-4456	476	37	12	12	NUM
cana-4456	476	38	,	,	PUNCT
cana-4456	476	39	6849	6849	NUM
cana-4456	476	40	(	(	PUNCT
cana-4456	476	41	2022	2022	NUM
cana-4456	476	42	)	)	PUNCT
cana-4456	476	43	.	.	PUNCT
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cana-4456	477	3	]	]	X
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cana-4456	477	7	y.	y.	PROPN
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cana-4456	477	10	x.	x.	NOUN
cana-4456	477	11	feng	feng	PROPN
cana-4456	477	12	,	,	PUNCT
cana-4456	477	13	a	a	DET
cana-4456	477	14	stable	stable	ADJ
cana-4456	477	15	radial	radial	ADJ
cana-4456	477	16	basis	basis	NOUN
cana-4456	477	17	function	function	NOUN
cana-4456	477	18	partition	partition	NOUN
cana-4456	477	19	of	of	ADP
cana-4456	477	20	unity	unity	NOUN
cana-4456	477	21	method	method	NOUN
cana-4456	477	22	for	for	ADP
cana-4456	477	23	solving	solve	VERB
cana-4456	477	24	convection	convection	NOUN
cana-4456	477	25	-	-	PUNCT
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cana-4456	477	27	equations	equation	NOUN
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cana-4456	477	29	surfaces	surface	NOUN
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cana-4456	477	32	analysis	analysis	NOUN
cana-4456	477	33	with	with	ADP
cana-4456	477	34	boundary	boundary	ADJ
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cana-4456	477	36	155	155	NUM
cana-4456	477	37	,	,	PUNCT
cana-4456	477	38	148	148	NUM
cana-4456	477	39	-	-	SYM
cana-4456	477	40	159	159	NUM
cana-4456	477	41	(	(	PUNCT
cana-4456	477	42	2023	2023	NUM
cana-4456	477	43	)	)	PUNCT
cana-4456	477	44	.	.	PUNCT
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cana-4456	478	2	27	27	NUM
cana-4456	478	3	]	]	PUNCT
cana-4456	478	4	m.	m.	NOUN
cana-4456	478	5	dehghan	dehghan	PROPN
cana-4456	478	6	,	,	PUNCT
cana-4456	478	7	m.	m.	NOUN
cana-4456	478	8	abbaszadeh	abbaszadeh	PROPN
cana-4456	478	9	,	,	PUNCT
cana-4456	478	10	the	the	DET
cana-4456	478	11	use	use	NOUN
cana-4456	478	12	of	of	ADP
cana-4456	478	13	proper	proper	ADJ
cana-4456	478	14	orthogonal	orthogonal	ADJ
cana-4456	478	15	decomposition	decomposition	NOUN
cana-4456	478	16	(	(	PUNCT
cana-4456	478	17	pod	pod	NOUN
cana-4456	478	18	)	)	PUNCT
cana-4456	478	19	meshless	meshless	ADJ
cana-4456	478	20	rbffd	rbffd	NOUN
cana-4456	478	21	technique	technique	NOUN
cana-4456	478	22	to	to	PART
cana-4456	478	23	simulate	simulate	VERB
cana-4456	478	24	the	the	DET
cana-4456	478	25	shallow	shallow	ADJ
cana-4456	478	26	water	water	NOUN
cana-4456	478	27	equations	equation	NOUN
cana-4456	478	28	,	,	PUNCT
cana-4456	478	29	journal	journal	NOUN
cana-4456	478	30	of	of	ADP
cana-4456	478	31	computational	computational	ADJ
cana-4456	478	32	physics	physic	NOUN
cana-4456	478	33	351	351	NUM
cana-4456	478	34	,	,	PUNCT
cana-4456	478	35	478	478	NUM
cana-4456	478	36	-	-	SYM
cana-4456	478	37	510	510	NUM
cana-4456	478	38	(	(	PUNCT
cana-4456	478	39	2017	2017	NUM
cana-4456	478	40	)	)	PUNCT
cana-4456	478	41	.	.	PUNCT
cana-4456	479	1	[	[	X
cana-4456	479	2	28	28	NUM
cana-4456	479	3	]	]	X
cana-4456	479	4	j.	j.	PROPN
cana-4456	479	5	borggaard	borggaard	ADV
cana-4456	479	6	,	,	PUNCT
cana-4456	479	7	t.	t.	PROPN
cana-4456	479	8	iliescu	iliescu	PROPN
cana-4456	479	9	,	,	PUNCT
cana-4456	479	10	z.	z.	PROPN
cana-4456	479	11	wang	wang	PROPN
cana-4456	479	12	,	,	PUNCT
cana-4456	479	13	artificial	artificial	ADJ
cana-4456	479	14	viscosity	viscosity	NOUN
cana-4456	479	15	proper	proper	ADJ
cana-4456	479	16	orthogonal	orthogonal	ADJ
cana-4456	479	17	decomposition	decomposition	NOUN
cana-4456	479	18	,	,	PUNCT
cana-4456	479	19	mathematical	mathematical	ADJ
cana-4456	479	20	and	and	CCONJ
cana-4456	479	21	computer	computer	NOUN
cana-4456	479	22	modelling	model	VERB
cana-4456	479	23	53	53	NUM
cana-4456	479	24	,	,	PUNCT
cana-4456	479	25	269	269	NUM
cana-4456	479	26	-	-	SYM
cana-4456	479	27	279	279	NUM
cana-4456	479	28	(	(	PUNCT
cana-4456	479	29	2011	2011	NUM
cana-4456	479	30	)	)	PUNCT
cana-4456	479	31	.	.	PUNCT
cana-4456	480	1	[	[	X
cana-4456	480	2	29	29	NUM
cana-4456	480	3	]	]	X
cana-4456	480	4	i.	i.	NOUN
cana-4456	480	5	babuska	babuska	PROPN
cana-4456	480	6	and	and	CCONJ
cana-4456	480	7	j.m.~melenk	j.m.~melenk	PROPN
cana-4456	480	8	,	,	PUNCT
cana-4456	480	9	the	the	DET
cana-4456	480	10	partition	partition	NOUN
cana-4456	480	11	of	of	ADP
cana-4456	480	12	unity	unity	NOUN
cana-4456	480	13	method	method	NOUN
cana-4456	480	14	,	,	PUNCT
cana-4456	480	15	international	international	ADJ
cana-4456	480	16	journal	journal	NOUN
cana-4456	480	17	for	for	ADP
cana-4456	480	18	numerical	numerical	ADJ
cana-4456	480	19	methods	method	NOUN
cana-4456	480	20	in	in	ADP
cana-4456	480	21	engineering	engineer	VERB
cana-4456	480	22	40(4	40(4	NUM
cana-4456	480	23	)	)	PUNCT
cana-4456	480	24	,	,	PUNCT
cana-4456	480	25	727	727	NUM
cana-4456	480	26	-	-	SYM
cana-4456	480	27	758	758	NUM
cana-4456	480	28	(	(	PUNCT
cana-4456	480	29	1998	1998	NUM
cana-4456	480	30	)	)	PUNCT
cana-4456	480	31	.	.	PUNCT
cana-4456	481	1	[	[	X
cana-4456	481	2	30	30	NUM
cana-4456	481	3	]	]	X
cana-4456	481	4	v.	v.	CCONJ
cana-4456	481	5	shcherbakov	shcherbakov	PROPN
cana-4456	481	6	,	,	PUNCT
cana-4456	481	7	e.	e.	PROPN
cana-4456	481	8	larsson	larsson	PROPN
cana-4456	481	9	,	,	PUNCT
cana-4456	481	10	radial	radial	ADJ
cana-4456	481	11	basis	basis	NOUN
cana-4456	481	12	function	function	NOUN
cana-4456	481	13	partition	partition	NOUN
cana-4456	481	14	of	of	ADP
cana-4456	481	15	unity	unity	NOUN
cana-4456	481	16	methods	method	NOUN
cana-4456	481	17	for	for	ADP
cana-4456	481	18	pricing	price	VERB
cana-4456	481	19	vanilla	vanilla	NOUN
cana-4456	481	20	basket	basket	NOUN
cana-4456	481	21	options	option	NOUN
cana-4456	481	22	,	,	PUNCT
cana-4456	481	23	computers	computer	NOUN
cana-4456	481	24	and	and	CCONJ
cana-4456	481	25	mathematics	mathematic	NOUN
cana-4456	481	26	with	with	ADP
cana-4456	481	27	applications	application	NOUN
cana-4456	481	28	71	71	NUM
cana-4456	481	29	,	,	PUNCT
cana-4456	481	30	185	185	NUM
cana-4456	481	31	-	-	SYM
cana-4456	481	32	200	200	NUM
cana-4456	481	33	(	(	PUNCT
cana-4456	481	34	2016	2016	NUM
cana-4456	481	35	)	)	PUNCT
cana-4456	481	36	.	.	PUNCT
cana-4456	482	1	[	[	X
cana-4456	482	2	31	31	NUM
cana-4456	482	3	]	]	X
cana-4456	482	4	d.	d.	PROPN
cana-4456	482	5	shepard	shepard	PROPN
cana-4456	482	6	,	,	PUNCT
cana-4456	482	7	a	a	DET
cana-4456	482	8	two	two	NUM
cana-4456	482	9	-	-	PUNCT
cana-4456	482	10	dimensional	dimensional	ADJ
cana-4456	482	11	interpolation	interpolation	NOUN
cana-4456	482	12	function	function	NOUN
cana-4456	482	13	for	for	ADP
cana-4456	482	14	irregularly	irregularly	ADV
cana-4456	482	15	-	-	PUNCT
cana-4456	482	16	spaced	space	VERB
cana-4456	482	17	data	datum	NOUN
cana-4456	482	18	,	,	PUNCT
cana-4456	482	19	in	in	ADP
cana-4456	482	20	:	:	PUNCT
cana-4456	482	21	proceedings	proceeding	NOUN
cana-4456	482	22	of	of	ADP
cana-4456	482	23	the	the	DET
cana-4456	482	24	23rd	23rd	PROPN
cana-4456	482	25	acm	acm	PROPN
cana-4456	482	26	national	national	PROPN
cana-4456	482	27	conference	conference	NOUN
cana-4456	482	28	,	,	PUNCT
cana-4456	482	29	517	517	NUM
cana-4456	482	30	-	-	SYM
cana-4456	482	31	524	524	NUM
cana-4456	482	32	(	(	PUNCT
cana-4456	482	33	1968	1968	NUM
cana-4456	482	34	)	)	PUNCT
cana-4456	482	35	.	.	PUNCT
cana-4456	483	1	[	[	X
cana-4456	483	2	32	32	NUM
cana-4456	483	3	]	]	PUNCT
cana-4456	483	4	h.	h.	PROPN
cana-4456	483	5	wendland	wendland	PROPN
cana-4456	483	6	,	,	PUNCT
cana-4456	483	7	piecewise	piecewise	NOUN
cana-4456	483	8	polynomial	polynomial	ADJ
cana-4456	483	9	,	,	PUNCT
cana-4456	483	10	positive	positive	ADJ
cana-4456	483	11	definite	definite	ADJ
cana-4456	483	12	and	and	CCONJ
cana-4456	483	13	compactly	compactly	ADV
cana-4456	483	14	supported	support	VERB
cana-4456	483	15	radial	radial	ADJ
cana-4456	483	16	functions	function	NOUN
cana-4456	483	17	of	of	ADP
cana-4456	483	18	minimal	minimal	ADJ
cana-4456	483	19	degree	degree	NOUN
cana-4456	483	20	,	,	PUNCT
cana-4456	483	21	advances	advance	NOUN
cana-4456	483	22	in	in	ADP
cana-4456	483	23	computational	computational	ADJ
cana-4456	483	24	mathematics	mathematic	NOUN
cana-4456	483	25	4(1	4(1	NOUN
cana-4456	483	26	)	)	PUNCT
cana-4456	483	27	,	,	PUNCT
cana-4456	483	28	389	389	NUM
cana-4456	483	29	-	-	SYM
cana-4456	483	30	396	396	NUM
cana-4456	483	31	(	(	PUNCT
cana-4456	483	32	1995	1995	NUM
cana-4456	483	33	)	)	PUNCT
cana-4456	483	34	.	.	PUNCT
cana-4456	484	1	[	[	X
cana-4456	484	2	33	33	NUM
cana-4456	484	3	]	]	X
cana-4456	484	4	m.d	m.d	PROPN
cana-4456	484	5	.	.	PROPN
cana-4456	484	6	buhmann	buhmann	PROPN
cana-4456	484	7	,	,	PUNCT
cana-4456	484	8	radial	radial	ADJ
cana-4456	484	9	basis	basis	NOUN
cana-4456	484	10	functions	function	NOUN
cana-4456	484	11	:	:	PUNCT
cana-4456	484	12	theory	theory	NOUN
cana-4456	484	13	and	and	CCONJ
cana-4456	484	14	implementation	implementation	NOUN
cana-4456	484	15	,	,	PUNCT
cana-4456	484	16	cambridge	cambridge	PROPN
cana-4456	484	17	university	university	PROPN
cana-4456	484	18	press	press	PROPN
cana-4456	484	19	,	,	PUNCT
cana-4456	484	20	cambridge	cambridge	PROPN
cana-4456	484	21	(	(	PUNCT
cana-4456	484	22	2003	2003	NUM
cana-4456	484	23	)	)	PUNCT
cana-4456	484	24	.	.	PUNCT
cana-4456	485	1	[	[	X
cana-4456	485	2	34	34	NUM
cana-4456	485	3	]	]	X
cana-4456	485	4	h.	h.	PROPN
cana-4456	485	5	wendland	wendland	PROPN
cana-4456	485	6	,	,	PUNCT
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cana-4456	485	8	data	data	NOUN
cana-4456	485	9	approximation	approximation	NOUN
cana-4456	485	10	,	,	PUNCT
cana-4456	485	11	cambridge	cambridge	PROPN
cana-4456	485	12	university	university	PROPN
cana-4456	485	13	press	press	PROPN
cana-4456	485	14	,	,	PUNCT
cana-4456	485	15	cambridge	cambridge	PROPN
cana-4456	485	16	(	(	PUNCT
cana-4456	485	17	2005	2005	NUM
cana-4456	485	18	)	)	PUNCT
cana-4456	485	19	.	.	PUNCT
cana-4456	486	1	communications	communication	NOUN
cana-4456	486	2	on	on	ADP
cana-4456	486	3	applied	apply	VERB
cana-4456	486	4	nonlinear	nonlinear	ADJ
cana-4456	486	5	analysis	analysis	NOUN
cana-4456	486	6	issn	issn	NOUN
cana-4456	486	7	:	:	PUNCT
cana-4456	486	8	1074	1074	NUM
cana-4456	486	9	-	-	PUNCT
cana-4456	486	10	133x	133x	NUM
cana-4456	486	11	vol	vol	NOUN
cana-4456	486	12	32	32	NUM
cana-4456	486	13	no	no	NOUN
cana-4456	486	14	.	.	PUNCT
cana-4456	487	1	9s	9s	NUM
cana-4456	487	2	(	(	PUNCT
cana-4456	487	3	2025	2025	NUM
cana-4456	487	4	)	)	PUNCT
cana-4456	487	5	2200	2200	NUM
cana-4456	487	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4456	488	1	[	[	X
cana-4456	488	2	35	35	NUM
cana-4456	488	3	]	]	X
cana-4456	488	4	c.a	c.a	PROPN
cana-4456	488	5	.	.	PROPN
cana-4456	488	6	micchelli	micchelli	PROPN
cana-4456	488	7	,	,	PUNCT
cana-4456	488	8	interpolation	interpolation	NOUN
cana-4456	488	9	of	of	ADP
cana-4456	488	10	scattered	scatter	VERB
cana-4456	488	11	data	datum	NOUN
cana-4456	488	12	:	:	PUNCT
cana-4456	488	13	distance	distance	NOUN
cana-4456	488	14	matrices	matrix	NOUN
cana-4456	488	15	and	and	CCONJ
cana-4456	488	16	conditionally	conditionally	ADV
cana-4456	488	17	positive	positive	ADJ
cana-4456	488	18	definite	definite	ADJ
cana-4456	488	19	functions	function	NOUN
cana-4456	488	20	,	,	PUNCT
cana-4456	488	21	constructive	constructive	ADJ
cana-4456	488	22	approximation	approximation	NOUN
cana-4456	488	23	2	2	NUM
cana-4456	488	24	,	,	PUNCT
cana-4456	488	25	11	11	NUM
cana-4456	488	26	-	-	SYM
cana-4456	488	27	22	22	NUM
cana-4456	488	28	(	(	PUNCT
cana-4456	488	29	1986	1986	NUM
cana-4456	488	30	)	)	PUNCT
cana-4456	488	31	.	.	PUNCT
cana-4456	489	1	[	[	X
cana-4456	489	2	36	36	NUM
cana-4456	489	3	]	]	X
cana-4456	489	4	e.	e.	PROPN
cana-4456	489	5	larsson	larsson	PROPN
cana-4456	489	6	,	,	PUNCT
cana-4456	489	7	v.	v.	ADP
cana-4456	489	8	shcherbakov	shcherbakov	PROPN
cana-4456	489	9	,	,	PUNCT
cana-4456	489	10	a.	a.	PROPN
cana-4456	489	11	heryudono	heryudono	PROPN
cana-4456	489	12	,	,	PUNCT
cana-4456	489	13	a	a	DET
cana-4456	489	14	least	least	ADJ
cana-4456	489	15	squares	square	NOUN
cana-4456	489	16	radial	radial	ADJ
cana-4456	489	17	basis	basis	NOUN
cana-4456	489	18	function	function	NOUN
cana-4456	489	19	partition	partition	NOUN
cana-4456	489	20	of	of	ADP
cana-4456	489	21	unity	unity	NOUN
cana-4456	489	22	method	method	NOUN
cana-4456	489	23	for	for	ADP
cana-4456	489	24	solving	solve	VERB
cana-4456	489	25	pdes	pde	NOUN
cana-4456	489	26	,	,	PUNCT
cana-4456	489	27	siam	siam	ADJ
cana-4456	489	28	journal	journal	NOUN
cana-4456	489	29	on	on	ADP
cana-4456	489	30	scientific	scientific	ADJ
cana-4456	489	31	computing	computing	NOUN
cana-4456	489	32	39	39	NUM
cana-4456	489	33	,	,	PUNCT
cana-4456	489	34	a2538	a2538	NOUN
cana-4456	489	35	-	-	PUNCT
cana-4456	489	36	a2563	a2563	VERB
cana-4456	489	37	(	(	PUNCT
cana-4456	489	38	2017	2017	NUM
cana-4456	489	39	)	)	PUNCT
cana-4456	489	40	.	.	PUNCT
cana-4456	490	1	[	[	X
cana-4456	490	2	37	37	NUM
cana-4456	490	3	]	]	PUNCT
cana-4456	490	4	a.	a.	NOUN
cana-4456	490	5	heryudono	heryudono	PROPN
cana-4456	490	6	,	,	PUNCT
cana-4456	490	7	e.	e.	PROPN
cana-4456	490	8	larsson	larsson	PROPN
cana-4456	490	9	,	,	PUNCT
cana-4456	490	10	a.	a.	NOUN
cana-4456	490	11	ramage	ramage	PROPN
cana-4456	490	12	,	,	PUNCT
cana-4456	490	13	l.	l.	PROPN
cana-4456	490	14	von	von	PROPN
cana-4456	490	15	sydow	sydow	PROPN
cana-4456	490	16	,	,	PUNCT
cana-4456	490	17	preconditioning	precondition	VERB
cana-4456	490	18	for	for	ADP
cana-4456	490	19	radial	radial	ADJ
cana-4456	490	20	basis	basis	NOUN
cana-4456	490	21	function	function	NOUN
cana-4456	490	22	partition	partition	NOUN
cana-4456	490	23	of	of	ADP
cana-4456	490	24	unity	unity	NOUN
cana-4456	490	25	methods	method	NOUN
cana-4456	490	26	,	,	PUNCT
cana-4456	490	27	journal	journal	NOUN
cana-4456	490	28	of	of	ADP
cana-4456	490	29	scientific	scientific	ADJ
cana-4456	490	30	computing	computing	NOUN
cana-4456	490	31	67	67	NUM
cana-4456	490	32	,	,	PUNCT
cana-4456	490	33	1089	1089	NUM
cana-4456	490	34	-	-	SYM
cana-4456	490	35	1109	1109	NUM
cana-4456	490	36	(	(	PUNCT
cana-4456	490	37	2016	2016	NUM
cana-4456	490	38	)	)	PUNCT
cana-4456	490	39	.	.	PUNCT
cana-4456	491	1	[	[	X
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cana-4456	491	3	]	]	PUNCT
cana-4456	491	4	b.	b.	PROPN
cana-4456	491	5	forenberg	forenberg	PROPN
cana-4456	491	6	,	,	PUNCT
cana-4456	491	7	e.	e.	PROPN
cana-4456	491	8	larsson	larsson	PROPN
cana-4456	491	9	,	,	PUNCT
cana-4456	491	10	n.	n.	NOUN
cana-4456	491	11	flyer	flyer	NOUN
cana-4456	491	12	,	,	PUNCT
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cana-4456	491	15	with	with	ADP
cana-4456	491	16	gaussian	gaussian	ADJ
cana-4456	491	17	radial	radial	ADJ
cana-4456	491	18	basis	basis	NOUN
cana-4456	491	19	functions	function	NOUN
cana-4456	491	20	,	,	PUNCT
cana-4456	491	21	siam	siam	ADJ
cana-4456	491	22	journal	journal	NOUN
cana-4456	491	23	on	on	ADP
cana-4456	491	24	scientific	scientific	ADJ
cana-4456	491	25	computing	computing	NOUN
cana-4456	491	26	33	33	NUM
cana-4456	491	27	,	,	PUNCT
cana-4456	491	28	869	869	NUM
cana-4456	491	29	-	-	SYM
cana-4456	491	30	892	892	NUM
cana-4456	491	31	(	(	PUNCT
cana-4456	491	32	2011	2011	NUM
cana-4456	491	33	)	)	PUNCT
cana-4456	491	34	.	.	PUNCT
cana-4456	492	1	[	[	X
cana-4456	492	2	39	39	NUM
cana-4456	492	3	]	]	PUNCT
cana-4456	492	4	b.	b.	PROPN
cana-4456	492	5	forenberg	forenberg	PROPN
cana-4456	492	6	,	,	PUNCT
cana-4456	492	7	c.	c.	PROPN
cana-4456	492	8	piret	piret	PROPN
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cana-4456	492	10	a	a	DET
cana-4456	492	11	stable	stable	ADJ
cana-4456	492	12	algorithm	algorithm	NOUN
cana-4456	492	13	for	for	ADP
cana-4456	492	14	flat	flat	ADJ
cana-4456	492	15	radial	radial	ADJ
cana-4456	492	16	basis	basis	NOUN
cana-4456	492	17	functions	function	NOUN
cana-4456	492	18	on	on	ADP
cana-4456	492	19	a	a	DET
cana-4456	492	20	sphere	sphere	NOUN
cana-4456	492	21	,	,	PUNCT
cana-4456	492	22	siam	siam	ADJ
cana-4456	492	23	journal	journal	NOUN
cana-4456	492	24	on	on	ADP
cana-4456	492	25	scientific	scientific	ADJ
cana-4456	492	26	computing	computing	NOUN
cana-4456	492	27	33	33	NUM
cana-4456	492	28	,	,	PUNCT
cana-4456	492	29	60	60	NUM
cana-4456	492	30	-	-	SYM
cana-4456	492	31	80	80	NUM
cana-4456	492	32	(	(	PUNCT
cana-4456	492	33	2008	2008	NUM
cana-4456	492	34	)	)	PUNCT
cana-4456	492	35	.	.	PUNCT
cana-4456	493	1	[	[	X
cana-4456	493	2	40	40	NUM
cana-4456	493	3	]	]	PUNCT
cana-4456	493	4	b.	b.	PROPN
cana-4456	493	5	fornberg	fornberg	PROPN
cana-4456	493	6	,	,	PUNCT
cana-4456	493	7	g.	g.	PROPN
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cana-4456	493	9	,	,	PUNCT
cana-4456	493	10	stable	stable	ADJ
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cana-4456	493	12	of	of	ADP
cana-4456	493	13	multiquadric	multiquadric	ADJ
cana-4456	493	14	interpolants	interpolant	NOUN
cana-4456	493	15	for	for	ADP
cana-4456	493	16	all	all	DET
cana-4456	493	17	values	value	NOUN
cana-4456	493	18	of	of	ADP
cana-4456	493	19	the	the	DET
cana-4456	493	20	shape	shape	NOUN
cana-4456	493	21	parameter	parameter	NOUN
cana-4456	493	22	.	.	PUNCT
cana-4456	494	1	computers	computer	NOUN
cana-4456	494	2	and	and	CCONJ
cana-4456	494	3	mathematics	mathematic	NOUN
cana-4456	494	4	with	with	ADP
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cana-4456	494	6	48	48	NUM
cana-4456	494	7	,	,	PUNCT
cana-4456	494	8	853	853	NUM
cana-4456	494	9	-	-	SYM
cana-4456	494	10	867	867	NUM
cana-4456	494	11	(	(	PUNCT
cana-4456	494	12	2004	2004	NUM
cana-4456	494	13	)	)	PUNCT
cana-4456	495	1	[	[	X
cana-4456	495	2	41	41	NUM
cana-4456	495	3	]	]	X
cana-4456	495	4	q.	q.	PROPN
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cana-4456	495	6	,	,	PUNCT
cana-4456	495	7	f.	f.	PROPN
cana-4456	495	8	marche	marche	PROPN
cana-4456	495	9	,	,	PUNCT
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cana-4456	495	12	of	of	ADP
cana-4456	495	13	well	well	ADV
cana-4456	495	14	-	-	PUNCT
cana-4456	495	15	balanced	balance	VERB
cana-4456	495	16	shallow	shallow	ADJ
cana-4456	495	17	water	water	NOUN
cana-4456	495	18	equations	equation	NOUN
cana-4456	495	19	with	with	ADP
cana-4456	495	20	complex	complex	ADJ
cana-4456	495	21	source	source	NOUN
cana-4456	495	22	terms	term	NOUN
cana-4456	495	23	,	,	PUNCT
cana-4456	495	24	advances	advance	NOUN
cana-4456	495	25	in	in	ADP
cana-4456	495	26	water	water	NOUN
cana-4456	495	27	resources	resource	NOUN
cana-4456	495	28	32	32	NUM
cana-4456	495	29	,	,	PUNCT
cana-4456	495	30	873	873	NUM
cana-4456	495	31	-	-	SYM
cana-4456	495	32	884	884	NUM
cana-4456	495	33	(	(	PUNCT
cana-4456	495	34	2009	2009	NUM
cana-4456	495	35	)	)	PUNCT
cana-4456	495	36	.	.	PUNCT
cana-4456	496	1	[	[	X
cana-4456	496	2	42	42	NUM
cana-4456	496	3	]	]	PUNCT
cana-4456	496	4	t.	t.	PROPN
cana-4456	496	5	zhang	zhang	PROPN
cana-4456	496	6	,	,	PUNCT
cana-4456	496	7	c.x	c.x	PROPN
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cana-4456	496	14	c.	c.	PROPN
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cana-4456	496	17	x.m	x.m	PROPN
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cana-4456	496	24	artificial	artificial	ADJ
cana-4456	496	25	viscosity	viscosity	NOUN
cana-4456	496	26	technology	technology	NOUN
cana-4456	496	27	combined	combine	VERB
cana-4456	496	28	with	with	ADP
cana-4456	496	29	local	local	ADJ
cana-4456	496	30	radial	radial	ADJ
cana-4456	496	31	point	point	NOUN
cana-4456	496	32	interpolation	interpolation	NOUN
cana-4456	496	33	method	method	NOUN
cana-4456	496	34	for	for	ADP
cana-4456	496	35	2d	2d	NUM
cana-4456	496	36	shallow	shallow	ADJ
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cana-4456	496	39	,	,	PUNCT
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cana-4456	496	41	analysis	analysis	NOUN
cana-4456	496	42	with	with	ADP
cana-4456	496	43	boundary	boundary	ADJ
cana-4456	496	44	element	element	NOUN
cana-4456	496	45	133	133	NUM
cana-4456	496	46	,	,	PUNCT
cana-4456	496	47	303	303	NUM
cana-4456	496	48	-	-	SYM
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cana-4456	496	50	(	(	PUNCT
cana-4456	496	51	2021	2021	NUM
cana-4456	496	52	)	)	PUNCT
cana-4456	496	53	.	.	PUNCT
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cana-4456	497	3	]	]	X
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cana-4456	497	6	,	,	PUNCT
cana-4456	497	7	s.n	s.n	PROPN
cana-4456	497	8	.	.	PROPN
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cana-4456	497	11	s.	s.	PROPN
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cana-4456	497	14	a	a	DET
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cana-4456	497	16	-	-	PUNCT
cana-4456	497	17	capturing	capture	VERB
cana-4456	497	18	meshless	meshless	ADJ
cana-4456	497	19	method	method	NOUN
cana-4456	497	20	for	for	ADP
cana-4456	497	21	solving	solve	VERB
cana-4456	497	22	the	the	DET
cana-4456	497	23	onedimensional	onedimensional	ADJ
cana-4456	497	24	saint	saint	PROPN
cana-4456	497	25	-	-	PUNCT
cana-4456	497	26	venant	venant	NOUN
cana-4456	497	27	equations	equation	NOUN
cana-4456	497	28	on	on	ADP
cana-4456	497	29	a	a	DET
cana-4456	497	30	highly	highly	ADV
cana-4456	497	31	variable	variable	ADJ
cana-4456	497	32	topography	topography	NOUN
cana-4456	497	33	,	,	PUNCT
cana-4456	497	34	journal	journal	NOUN
cana-4456	497	35	of	of	ADP
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cana-4456	497	38	,	,	PUNCT
cana-4456	497	39	17	17	NUM
cana-4456	497	40	-	-	SYM
cana-4456	497	41	18	18	NUM
cana-4456	497	42	(	(	PUNCT
cana-4456	497	43	2023	2023	NUM
cana-4456	497	44	)	)	PUNCT
cana-4456	497	45	.	.	PUNCT
cana-4456	498	1	[	[	X
cana-4456	498	2	44	44	NUM
cana-4456	498	3	]	]	PUNCT
cana-4456	498	4	s.	s.	PROPN
cana-4456	498	5	sarra	sarra	PROPN
cana-4456	498	6	,	,	PUNCT
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cana-4456	498	9	radial	radial	ADJ
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cana-4456	498	11	function	function	NOUN
cana-4456	498	12	method	method	NOUN
cana-4456	498	13	for	for	ADP
cana-4456	498	14	advection	advection	NOUN
cana-4456	498	15	-	-	PUNCT
cana-4456	498	16	diffusion	diffusion	NOUN
cana-4456	498	17	-	-	PUNCT
cana-4456	498	18	reaction	reaction	NOUN
cana-4456	498	19	equations	equation	NOUN
cana-4456	498	20	on	on	ADP
cana-4456	498	21	complexly	complexly	ADJ
cana-4456	498	22	shaped	shape	VERB
cana-4456	498	23	domains	domain	NOUN
cana-4456	498	24	.	.	PUNCT
cana-4456	499	1	applied	apply	VERB
cana-4456	499	2	mathematics	mathematic	NOUN
cana-4456	499	3	and	and	CCONJ
cana-4456	499	4	computation	computation	NOUN
cana-4456	499	5	218	218	NUM
cana-4456	499	6	,	,	PUNCT
cana-4456	499	7	9853	9853	NUM
cana-4456	499	8	-	-	SYM
cana-4456	499	9	9865	9865	NUM
cana-4456	499	10	(	(	PUNCT
cana-4456	499	11	2012	2012	NUM
cana-4456	499	12	)	)	PUNCT
cana-4456	499	13	.	.	PUNCT
cana-4456	500	1	[	[	X
cana-4456	500	2	45	45	NUM
cana-4456	500	3	]	]	PUNCT
cana-4456	500	4	a.	a.	NOUN
cana-4456	500	5	bermudez	bermudez	PROPN
cana-4456	500	6	,	,	PUNCT
cana-4456	500	7	m.e	m.e	PROPN
cana-4456	500	8	.	.	PROPN
cana-4456	500	9	vazquez	vazquez	PROPN
cana-4456	500	10	,	,	PUNCT
cana-4456	500	11	upwind	upwind	NOUN
cana-4456	500	12	methods	method	NOUN
cana-4456	500	13	for	for	ADP
cana-4456	500	14	hyperbolic	hyperbolic	ADJ
cana-4456	500	15	conservation	conservation	NOUN
cana-4456	500	16	laws	law	NOUN
cana-4456	500	17	with	with	ADP
cana-4456	500	18	source	source	NOUN
cana-4456	500	19	terms	term	NOUN
cana-4456	500	20	,	,	PUNCT
cana-4456	500	21	computers	computer	NOUN
cana-4456	500	22	and	and	CCONJ
cana-4456	500	23	fluids	fluid	NOUN
cana-4456	500	24	23(8	23(8	NOUN
cana-4456	500	25	)	)	PUNCT
cana-4456	500	26	,	,	PUNCT
cana-4456	500	27	1049	1049	NUM
cana-4456	500	28	-	-	SYM
cana-4456	500	29	1071	1071	NUM
cana-4456	500	30	(	(	PUNCT
cana-4456	500	31	1994	1994	NUM
cana-4456	500	32	)	)	PUNCT
cana-4456	500	33	.	.	PUNCT
cana-4456	501	1	[	[	X
cana-4456	501	2	46	46	NUM
cana-4456	501	3	]	]	X
cana-4456	501	4	n.	n.	NOUN
cana-4456	501	5	goutal	goutal	PROPN
cana-4456	501	6	,	,	PUNCT
cana-4456	501	7	f.	f.	PROPN
cana-4456	501	8	maurel	maurel	PROPN
cana-4456	501	9	,	,	PUNCT
cana-4456	501	10	electriciteé	electriciteé	PROPN
cana-4456	501	11	de	de	PROPN
cana-4456	501	12	france	france	PROPN
cana-4456	501	13	service	service	PROPN
cana-4456	501	14	applications	application	NOUN
cana-4456	501	15	de	de	X
cana-4456	501	16	l'electriciteé	l'electriciteé	PROPN
cana-4456	501	17	et	et	PROPN
cana-4456	501	18	environnement	environnement	PROPN
cana-4456	501	19	&	&	CCONJ
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cana-4456	501	21	on	on	ADP
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cana-4456	501	23	-	-	PUNCT
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cana-4456	501	25	wave	wave	NOUN
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cana-4456	501	27	,	,	PUNCT
cana-4456	501	28	in	in	ADP
cana-4456	501	29	:	:	PUNCT
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cana-4456	501	31	of	of	ADP
cana-4456	501	32	the	the	DET
cana-4456	501	33	2nd	2nd	ADJ
cana-4456	501	34	workshop	workshop	NOUN
cana-4456	501	35	on	on	ADP
cana-4456	501	36	dam	dam	NOUN
cana-4456	501	37	-	-	PUNCT
cana-4456	501	38	break	break	NOUN
cana-4456	501	39	wave	wave	NOUN
cana-4456	501	40	simulation	simulation	NOUN
cana-4456	501	41	,	,	PUNCT
cana-4456	501	42	direction	direction	NOUN
cana-4456	501	43	des	des	PROPN
cana-4456	501	44	études	études	PROPN
cana-4456	501	45	et	et	NOUN
cana-4456	501	46	recherches	recherche	NOUN
cana-4456	501	47	,	,	PUNCT
cana-4456	501	48	electricité	electricité	PROPN
cana-4456	501	49	de	de	X
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cana-4456	501	52	(	(	PUNCT
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cana-4456	501	54	)	)	PUNCT
cana-4456	501	55	.	.	PUNCT
cana-4456	502	1	[	[	X
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cana-4456	502	3	]	]	X
cana-4456	502	4	e.f	e.f	PROPN
cana-4456	502	5	.	.	PROPN
cana-4456	502	6	toro	toro	PROPN
cana-4456	502	7	,	,	PUNCT
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cana-4456	502	9	-	-	PUNCT
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cana-4456	502	12	for	for	ADP
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cana-4456	502	14	-	-	PUNCT
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cana-4456	502	16	shallow	shallow	ADJ
cana-4456	502	17	flows	flow	NOUN
cana-4456	502	18	,	,	PUNCT
cana-4456	502	19	wiley	wiley	NOUN
cana-4456	502	20	and	and	CCONJ
cana-4456	502	21	sons	son	NOUN
cana-4456	502	22	(	(	PUNCT
cana-4456	502	23	2001	2001	NUM
cana-4456	502	24	)	)	PUNCT
cana-4456	502	25	.	.	PUNCT
cana-4456	503	1	[	[	X
cana-4456	503	2	48	48	NUM
cana-4456	503	3	]	]	PUNCT
cana-4456	503	4	benkhaldoun	benkhaldoun	NOUN
cana-4456	503	5	.	.	PUNCT
cana-4456	504	1	f	f	X
cana-4456	504	2	,	,	PUNCT
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cana-4456	504	4	.	.	PUNCT
cana-4456	505	1	m	m	PROPN
cana-4456	505	2	,	,	PUNCT
cana-4456	505	3	a	a	DET
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cana-4456	505	5	finite	finite	ADJ
cana-4456	505	6	volume	volume	NOUN
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cana-4456	505	8	for	for	ADP
cana-4456	505	9	the	the	DET
cana-4456	505	10	shallow	shallow	ADJ
cana-4456	505	11	water	water	NOUN
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cana-4456	505	13	,	,	PUNCT
cana-4456	505	14	journal	journal	NOUN
cana-4456	505	15	of	of	ADP
cana-4456	505	16	computational	computational	ADJ
cana-4456	505	17	and	and	CCONJ
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cana-4456	505	19	mathematics	mathematic	NOUN
cana-4456	505	20	234	234	NUM
cana-4456	505	21	,	,	PUNCT
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cana-4456	505	23	-	-	SYM
cana-4456	505	24	72	72	NUM
cana-4456	505	25	(	(	PUNCT
cana-4456	505	26	2010	2010	NUM
cana-4456	505	27	)	)	PUNCT
cana-4456	505	28	.	.	PUNCT
cana-4456	506	1	[	[	X
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cana-4456	506	6	,	,	PUNCT
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cana-4456	506	8	du	du	PROPN
cana-4456	506	9	ruisselement	ruisselement	PROPN
cana-4456	506	10	d'eau	d'eau	PROPN
cana-4456	506	11	de	de	PROPN
cana-4456	506	12	pluie	pluie	PROPN
cana-4456	506	13	sur	sur	PROPN
cana-4456	506	14	des	des	PROPN
cana-4456	506	15	surfaces	surface	NOUN
cana-4456	506	16	agricoles	agricole	NOUN
cana-4456	506	17	,	,	PUNCT
cana-4456	506	18	phd	phd	NOUN
cana-4456	506	19	thesis	thesis	NOUN
cana-4456	506	20	(	(	PUNCT
cana-4456	506	21	2010	2010	NUM
cana-4456	506	22	)	)	PUNCT
cana-4456	506	23	.	.	PUNCT
cana-4456	507	1	[	[	X
cana-4456	507	2	50	50	NUM
cana-4456	507	3	]	]	PUNCT
cana-4456	507	4	i.	i.	PROPN
cana-4456	507	5	macdonald	macdonald	PROPN
cana-4456	507	6	,	,	PUNCT
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cana-4456	507	14	flow	flow	NOUN
cana-4456	507	15	,	,	PUNCT
cana-4456	507	16	phd	phd	NOUN
cana-4456	507	17	thesis	thesis	NOUN
cana-4456	507	18	,	,	PUNCT
cana-4456	507	19	university	university	NOUN
cana-4456	507	20	of	of	ADP
cana-4456	507	21	reading	read	VERB
cana-4456	507	22	department	department	PROPN
cana-4456	507	23	of	of	ADP
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cana-4456	507	25	(	(	PUNCT
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cana-4456	507	27	)	)	PUNCT
cana-4456	507	28	.	.	PUNCT
cana-4456	508	1	[	[	X
cana-4456	508	2	51	51	NUM
cana-4456	508	3	]	]	X
cana-4456	508	4	i.	i.	PROPN
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cana-4456	508	6	,	,	PUNCT
cana-4456	508	7	m.j	m.j	PROPN
cana-4456	508	8	.	.	PROPN
cana-4456	508	9	baines	baine	NOUN
cana-4456	508	10	,	,	PUNCT
cana-4456	508	11	n.k	n.k	PROPN
cana-4456	508	12	.	.	PROPN
cana-4456	508	13	nichols	nichols	PROPN
cana-4456	508	14	,	,	PUNCT
cana-4456	508	15	p.g	p.g	PROPN
cana-4456	508	16	.	.	PROPN
cana-4456	508	17	samuels	samuels	PROPN
cana-4456	508	18	.	.	PUNCT
cana-4456	508	19	analytic	analytic	ADJ
cana-4456	508	20	benchmark	benchmark	NOUN
cana-4456	508	21	solutions	solution	NOUN
cana-4456	508	22	for	for	ADP
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cana-4456	508	24	flows	flow	NOUN
cana-4456	508	25	.	.	PUNCT
cana-4456	509	1	journal	journal	PROPN
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cana-4456	509	3	hydraulic	hydraulic	ADJ
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cana-4456	509	5	123(11	123(11	NUM
cana-4456	509	6	)	)	PUNCT
cana-4456	509	7	,	,	PUNCT
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cana-4456	509	10	1045	1045	NUM
cana-4456	509	11	(	(	PUNCT
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cana-4456	509	13	)	)	PUNCT
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