id	sid	tid	token	lemma	pos
cana-1729	1	1	communications	communication	NOUN
cana-1729	1	2	on	on	ADP
cana-1729	1	3	applied	apply	VERB
cana-1729	1	4	nonlinear	nonlinear	ADJ
cana-1729	1	5	analysis	analysis	NOUN
cana-1729	1	6	issn	issn	NOUN
cana-1729	1	7	:	:	PUNCT
cana-1729	1	8	1074	1074	NUM
cana-1729	1	9	-	-	PUNCT
cana-1729	1	10	133x	133x	NUM
cana-1729	1	11	vol	vol	NOUN
cana-1729	1	12	32	32	NUM
cana-1729	1	13	no	no	NOUN
cana-1729	1	14	.	.	NOUN
cana-1729	1	15	2	2	NUM
cana-1729	1	16	(	(	PUNCT
cana-1729	1	17	2025	2025	NUM
cana-1729	1	18	)	)	PUNCT
cana-1729	1	19	151	151	NUM
cana-1729	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1729	1	21	numerical	numerical	ADJ
cana-1729	1	22	solution	solution	NOUN
cana-1729	1	23	of	of	ADP
cana-1729	1	24	one	one	NUM
cana-1729	1	25	-	-	PUNCT
cana-1729	1	26	dimensional	dimensional	ADJ
cana-1729	1	27	advection	advection	NOUN
cana-1729	1	28	-	-	PUNCT
cana-1729	1	29	diffusion	diffusion	NOUN
cana-1729	1	30	equation	equation	NOUN
cana-1729	1	31	using	use	VERB
cana-1729	1	32	radial	radial	ADJ
cana-1729	1	33	basis	basis	NOUN
cana-1729	1	34	function	function	NOUN
cana-1729	1	35	method	method	NOUN
cana-1729	1	36	of	of	ADP
cana-1729	1	37	lines	line	NOUN
cana-1729	1	38	shrikrishna	shrikrishna	VERB
cana-1729	1	39	dasari	dasari	PROPN
cana-1729	1	40	1	1	NUM
cana-1729	1	41	,	,	PUNCT
cana-1729	1	42	amit	amit	PROPN
cana-1729	1	43	parikh	parikh	PROPN
cana-1729	1	44	2	2	NUM
cana-1729	1	45	1	1	NUM
cana-1729	1	46	department	department	NOUN
cana-1729	1	47	of	of	ADP
cana-1729	1	48	mathematics	mathematic	NOUN
cana-1729	1	49	,	,	PUNCT
cana-1729	1	50	mehsana	mehsana	PROPN
cana-1729	1	51	urban	urban	PROPN
cana-1729	1	52	institute	institute	PROPN
cana-1729	1	53	of	of	ADP
cana-1729	1	54	sciences	sciences	PROPN
cana-1729	1	55	,	,	PUNCT
cana-1729	1	56	ganpat	ganpat	PROPN
cana-1729	1	57	university	university	NOUN
cana-1729	1	58	,	,	PUNCT
cana-1729	1	59	mehsana	mehsana	NOUN
cana-1729	1	60	,	,	PUNCT
cana-1729	1	61	gujarat-384012	gujarat-384012	NOUN
cana-1729	1	62	,	,	PUNCT
cana-1729	1	63	india	india	PROPN
cana-1729	1	64	(	(	PUNCT
cana-1729	1	65	e	e	NOUN
cana-1729	1	66	-	-	NOUN
cana-1729	1	67	mail	mail	NOUN
cana-1729	1	68	:	:	PUNCT
cana-1729	1	69	shrikrishna.dasari@sakec.ac.in	shrikrishna.dasari@sakec.ac.in	NUM
cana-1729	1	70	)	)	PUNCT
cana-1729	1	71	orcid	orcid	NOUN
cana-1729	1	72	:	:	PUNCT
cana-1729	1	73	0000	0000	NUM
cana-1729	1	74	-	-	PUNCT
cana-1729	1	75	0001	0001	NUM
cana-1729	1	76	-	-	PUNCT
cana-1729	1	77	8638	8638	NUM
cana-1729	1	78	-	-	SYM
cana-1729	1	79	0398	0398	NUM
cana-1729	1	80	2	2	NUM
cana-1729	1	81	department	department	NOUN
cana-1729	1	82	of	of	ADP
cana-1729	1	83	mathematics	mathematic	NOUN
cana-1729	1	84	,	,	PUNCT
cana-1729	1	85	mehsana	mehsana	PROPN
cana-1729	1	86	urban	urban	PROPN
cana-1729	1	87	institute	institute	PROPN
cana-1729	1	88	of	of	ADP
cana-1729	1	89	sciences	sciences	PROPN
cana-1729	1	90	,	,	PUNCT
cana-1729	1	91	ganpat	ganpat	PROPN
cana-1729	1	92	university	university	NOUN
cana-1729	1	93	,	,	PUNCT
cana-1729	1	94	mehsana	mehsana	NOUN
cana-1729	1	95	,	,	PUNCT
cana-1729	1	96	gujarat-384012	gujarat-384012	NOUN
cana-1729	1	97	,	,	PUNCT
cana-1729	1	98	india	india	PROPN
cana-1729	1	99	(	(	PUNCT
cana-1729	1	100	e	e	NOUN
cana-1729	1	101	-	-	NOUN
cana-1729	1	102	mail	mail	NOUN
cana-1729	1	103	:	:	PUNCT
cana-1729	1	104	amit.parikh.maths@gmail.com	amit.parikh.maths@gmail.com	X
cana-1729	1	105	)	)	PUNCT
cana-1729	1	106	orcid	orcid	NOUN
cana-1729	1	107	:	:	PUNCT
cana-1729	1	108	0000	0000	NUM
cana-1729	1	109	-	-	PUNCT
cana-1729	1	110	0002	0002	NUM
cana-1729	1	111	-	-	PUNCT
cana-1729	1	112	9711	9711	NUM
cana-1729	1	113	-	-	PUNCT
cana-1729	1	114	9627	9627	NUM
cana-1729	1	115	article	article	NOUN
cana-1729	1	116	history	history	NOUN
cana-1729	1	117	:	:	PUNCT
cana-1729	1	118	received	receive	VERB
cana-1729	1	119	:	:	PUNCT
cana-1729	1	120	26	26	NUM
cana-1729	1	121	-	-	SYM
cana-1729	1	122	07	07	NUM
cana-1729	1	123	-	-	PUNCT
cana-1729	1	124	2024	2024	NUM
cana-1729	1	125	revised	revise	VERB
cana-1729	1	126	:	:	PUNCT
cana-1729	1	127	08	08	NUM
cana-1729	1	128	-	-	SYM
cana-1729	1	129	09	09	NUM
cana-1729	1	130	-	-	PUNCT
cana-1729	1	131	2024	2024	NUM
cana-1729	1	132	accepted	accept	VERB
cana-1729	1	133	:	:	PUNCT
cana-1729	1	134	17	17	NUM
cana-1729	1	135	-	-	SYM
cana-1729	1	136	09	09	NUM
cana-1729	1	137	-	-	PUNCT
cana-1729	1	138	2024	2024	NUM
cana-1729	1	139	abstract	abstract	NOUN
cana-1729	1	140	:	:	PUNCT
cana-1729	1	141	the	the	DET
cana-1729	1	142	research	research	NOUN
cana-1729	1	143	article	article	NOUN
cana-1729	1	144	proposes	propose	VERB
cana-1729	1	145	a	a	DET
cana-1729	1	146	numerical	numerical	ADJ
cana-1729	1	147	solution	solution	NOUN
cana-1729	1	148	for	for	ADP
cana-1729	1	149	the	the	DET
cana-1729	1	150	one	one	NUM
cana-1729	1	151	-	-	PUNCT
cana-1729	1	152	dimensional	dimensional	ADJ
cana-1729	1	153	advection	advection	NOUN
cana-1729	1	154	-	-	PUNCT
cana-1729	1	155	diffusion	diffusion	NOUN
cana-1729	1	156	equation	equation	NOUN
cana-1729	1	157	using	use	VERB
cana-1729	1	158	the	the	DET
cana-1729	1	159	radial	radial	ADJ
cana-1729	1	160	basis	basis	NOUN
cana-1729	1	161	function	function	NOUN
cana-1729	1	162	(	(	PUNCT
cana-1729	1	163	rbf	rbf	PROPN
cana-1729	1	164	)	)	PUNCT
cana-1729	1	165	method	method	NOUN
cana-1729	1	166	of	of	ADP
cana-1729	1	167	lines	line	NOUN
cana-1729	1	168	.	.	PUNCT
cana-1729	2	1	the	the	DET
cana-1729	2	2	approach	approach	NOUN
cana-1729	2	3	utilizes	utilize	VERB
cana-1729	2	4	the	the	DET
cana-1729	2	5	asymmetric	asymmetric	ADJ
cana-1729	2	6	multiquadric	multiquadric	ADJ
cana-1729	2	7	collocation	collocation	NOUN
cana-1729	2	8	method	method	NOUN
cana-1729	2	9	for	for	ADP
cana-1729	2	10	spatial	spatial	ADJ
cana-1729	2	11	discretization	discretization	NOUN
cana-1729	2	12	,	,	PUNCT
cana-1729	2	13	resulting	result	VERB
cana-1729	2	14	in	in	ADP
cana-1729	2	15	a	a	DET
cana-1729	2	16	system	system	NOUN
cana-1729	2	17	of	of	ADP
cana-1729	2	18	ordinary	ordinary	ADJ
cana-1729	2	19	differential	differential	ADJ
cana-1729	2	20	equations	equation	NOUN
cana-1729	2	21	(	(	PUNCT
cana-1729	2	22	odes	ode	NOUN
cana-1729	2	23	)	)	PUNCT
cana-1729	2	24	in	in	ADP
cana-1729	2	25	time	time	NOUN
cana-1729	2	26	.	.	PUNCT
cana-1729	3	1	the	the	DET
cana-1729	3	2	fourth	fourth	ADJ
cana-1729	3	3	-	-	PUNCT
cana-1729	3	4	order	order	NOUN
cana-1729	3	5	runge	runge	NOUN
cana-1729	3	6	-	-	PUNCT
cana-1729	3	7	kutta	kutta	NOUN
cana-1729	3	8	(	(	PUNCT
cana-1729	3	9	rk	rk	NOUN
cana-1729	3	10	)	)	PUNCT
cana-1729	3	11	method	method	NOUN
cana-1729	3	12	is	be	AUX
cana-1729	3	13	then	then	ADV
cana-1729	3	14	applied	apply	VERB
cana-1729	3	15	to	to	PART
cana-1729	3	16	solve	solve	VERB
cana-1729	3	17	this	this	DET
cana-1729	3	18	system	system	NOUN
cana-1729	3	19	.	.	PUNCT
cana-1729	4	1	the	the	DET
cana-1729	4	2	method	method	NOUN
cana-1729	4	3	is	be	AUX
cana-1729	4	4	illustrated	illustrate	VERB
cana-1729	4	5	by	by	ADP
cana-1729	4	6	solving	solve	VERB
cana-1729	4	7	selected	select	VERB
cana-1729	4	8	problems	problem	NOUN
cana-1729	4	9	and	and	CCONJ
cana-1729	4	10	comparing	compare	VERB
cana-1729	4	11	the	the	DET
cana-1729	4	12	results	result	NOUN
cana-1729	4	13	to	to	PART
cana-1729	4	14	exact	exact	ADJ
cana-1729	4	15	solutions	solution	NOUN
cana-1729	4	16	,	,	PUNCT
cana-1729	4	17	highlighting	highlight	VERB
cana-1729	4	18	its	its	PRON
cana-1729	4	19	effectiveness	effectiveness	NOUN
cana-1729	4	20	.	.	PUNCT
cana-1729	5	1	the	the	DET
cana-1729	5	2	algorithm	algorithm	NOUN
cana-1729	5	3	is	be	AUX
cana-1729	5	4	user	user	NOUN
cana-1729	5	5	-	-	PUNCT
cana-1729	5	6	friendly	friendly	ADJ
cana-1729	5	7	,	,	PUNCT
cana-1729	5	8	accurate	accurate	ADJ
cana-1729	5	9	,	,	PUNCT
cana-1729	5	10	and	and	CCONJ
cana-1729	5	11	suitable	suitable	ADJ
cana-1729	5	12	for	for	ADP
cana-1729	5	13	onedimensional	onedimensional	ADJ
cana-1729	5	14	linear	linear	ADJ
cana-1729	5	15	diffusion	diffusion	NOUN
cana-1729	5	16	problems	problem	NOUN
cana-1729	5	17	with	with	ADP
cana-1729	5	18	complex	complex	ADJ
cana-1729	5	19	initial	initial	ADJ
cana-1729	5	20	and	and	CCONJ
cana-1729	5	21	boundary	boundary	ADJ
cana-1729	5	22	conditions	condition	NOUN
cana-1729	5	23	,	,	PUNCT
cana-1729	5	24	offering	offer	VERB
cana-1729	5	25	a	a	DET
cana-1729	5	26	new	new	ADJ
cana-1729	5	27	perspective	perspective	NOUN
cana-1729	5	28	in	in	ADP
cana-1729	5	29	computational	computational	ADJ
cana-1729	5	30	physics	physics	NOUN
cana-1729	5	31	and	and	CCONJ
cana-1729	5	32	numerical	numerical	ADJ
cana-1729	5	33	analysis	analysis	NOUN
cana-1729	5	34	.	.	PUNCT
cana-1729	6	1	keywords	keyword	NOUN
cana-1729	6	2	:	:	PUNCT
cana-1729	6	3	advection	advection	NOUN
cana-1729	6	4	-	-	PUNCT
cana-1729	6	5	diffusion	diffusion	NOUN
cana-1729	6	6	equation	equation	NOUN
cana-1729	6	7	,	,	PUNCT
cana-1729	6	8	collocation	collocation	NOUN
cana-1729	6	9	method	method	NOUN
cana-1729	6	10	,	,	PUNCT
cana-1729	6	11	method	method	NOUN
cana-1729	6	12	of	of	ADP
cana-1729	6	13	lines	line	NOUN
cana-1729	6	14	,	,	PUNCT
cana-1729	6	15	radial	radial	ADJ
cana-1729	6	16	basis	basis	NOUN
cana-1729	6	17	function	function	NOUN
cana-1729	6	18	,	,	PUNCT
cana-1729	6	19	shape	shape	NOUN
cana-1729	6	20	parameter	parameter	NOUN
cana-1729	6	21	.	.	PUNCT
cana-1729	7	1	introduction	introduction	NOUN
cana-1729	7	2	the	the	DET
cana-1729	7	3	unsteady	unsteady	ADJ
cana-1729	7	4	linear	linear	ADJ
cana-1729	7	5	1	1	NUM
cana-1729	7	6	-	-	PUNCT
cana-1729	7	7	d	d	NOUN
cana-1729	7	8	advection	advection	NOUN
cana-1729	7	9	-	-	PUNCT
cana-1729	7	10	diffusion	diffusion	NOUN
cana-1729	7	11	equation	equation	NOUN
cana-1729	7	12	is	be	AUX
cana-1729	7	13	a	a	DET
cana-1729	7	14	significant	significant	ADJ
cana-1729	7	15	area	area	NOUN
cana-1729	7	16	of	of	ADP
cana-1729	7	17	research	research	NOUN
cana-1729	7	18	in	in	ADP
cana-1729	7	19	various	various	ADJ
cana-1729	7	20	fields	field	NOUN
cana-1729	7	21	,	,	PUNCT
cana-1729	7	22	including	include	VERB
cana-1729	7	23	environmental	environmental	ADJ
cana-1729	7	24	engineering	engineering	NOUN
cana-1729	7	25	,	,	PUNCT
cana-1729	7	26	hydrology	hydrology	NOUN
cana-1729	7	27	,	,	PUNCT
cana-1729	7	28	and	and	CCONJ
cana-1729	7	29	mathematical	mathematical	ADJ
cana-1729	7	30	modelling	modelling	NOUN
cana-1729	7	31	.	.	PUNCT
cana-1729	8	1	analysis	analysis	NOUN
cana-1729	8	2	of	of	ADP
cana-1729	8	3	the	the	DET
cana-1729	8	4	numerical	numerical	ADJ
cana-1729	8	5	and	and	CCONJ
cana-1729	8	6	analytical	analytical	ADJ
cana-1729	8	7	solutions	solution	NOUN
cana-1729	8	8	to	to	ADP
cana-1729	8	9	this	this	DET
cana-1729	8	10	problem	problem	NOUN
cana-1729	8	11	has	have	AUX
cana-1729	8	12	been	be	AUX
cana-1729	8	13	done	do	VERB
cana-1729	8	14	in	in	ADP
cana-1729	8	15	several	several	ADJ
cana-1729	8	16	papers	paper	NOUN
cana-1729	8	17	.	.	PUNCT
cana-1729	9	1	analytical	analytical	ADJ
cana-1729	9	2	solutions	solution	NOUN
cana-1729	9	3	for	for	ADP
cana-1729	9	4	the	the	DET
cana-1729	9	5	one	one	NUM
cana-1729	9	6	-	-	PUNCT
cana-1729	9	7	dimensional	dimensional	ADJ
cana-1729	9	8	advection	advection	NOUN
cana-1729	9	9	-	-	PUNCT
cana-1729	9	10	diffusion	diffusion	NOUN
cana-1729	9	11	equation	equation	NOUN
cana-1729	9	12	with	with	ADP
cana-1729	9	13	temporally	temporally	ADV
cana-1729	9	14	dependent	dependent	ADJ
cana-1729	9	15	coefficients	coefficient	NOUN
cana-1729	9	16	are	be	AUX
cana-1729	9	17	shown	show	VERB
cana-1729	9	18	in	in	ADP
cana-1729	9	19	a	a	DET
cana-1729	9	20	work	work	NOUN
cana-1729	9	21	by	by	ADP
cana-1729	9	22	jaiswal	jaiswal	PROPN
cana-1729	9	23	et	et	PROPN
cana-1729	9	24	al	al	PROPN
cana-1729	9	25	.	.	PROPN
cana-1729	10	1	(	(	PUNCT
cana-1729	10	2	2011	2011	NUM
cana-1729	10	3	)	)	PUNCT
cana-1729	10	4	.	.	PUNCT
cana-1729	11	1	the	the	DET
cana-1729	11	2	solute	solute	ADJ
cana-1729	11	3	dispersion	dispersion	NOUN
cana-1729	11	4	parameter	parameter	NOUN
cana-1729	11	5	is	be	AUX
cana-1729	11	6	time	time	NOUN
cana-1729	11	7	-	-	PUNCT
cana-1729	11	8	dependent	dependent	ADJ
cana-1729	11	9	when	when	SCONJ
cana-1729	11	10	the	the	DET
cana-1729	11	11	flow	flow	NOUN
cana-1729	11	12	domain	domain	NOUN
cana-1729	11	13	is	be	AUX
cana-1729	11	14	uniform	uniform	ADJ
cana-1729	11	15	;	;	PUNCT
cana-1729	11	16	both	both	DET
cana-1729	11	17	parameters	parameter	NOUN
cana-1729	11	18	are	be	AUX
cana-1729	11	19	time	time	NOUN
cana-1729	11	20	-	-	PUNCT
cana-1729	11	21	dependent	dependent	ADJ
cana-1729	11	22	;	;	PUNCT
cana-1729	11	23	and	and	CCONJ
cana-1729	11	24	the	the	DET
cana-1729	11	25	former	former	ADJ
cana-1729	11	26	is	be	AUX
cana-1729	11	27	uniform	uniform	ADJ
cana-1729	11	28	,	,	PUNCT
cana-1729	11	29	and	and	CCONJ
cana-1729	11	30	the	the	DET
cana-1729	11	31	latter	latter	ADJ
cana-1729	11	32	is	be	AUX
cana-1729	11	33	time	time	NOUN
cana-1729	11	34	-	-	PUNCT
cana-1729	11	35	dependent	dependent	ADJ
cana-1729	11	36	.	.	PUNCT
cana-1729	12	1	these	these	PRON
cana-1729	12	2	are	be	AUX
cana-1729	12	3	the	the	DET
cana-1729	12	4	three	three	NUM
cana-1729	12	5	scenarios	scenario	NOUN
cana-1729	12	6	that	that	SCONJ
cana-1729	12	7	the	the	DET
cana-1729	12	8	authors	author	NOUN
cana-1729	12	9	address	address	VERB
cana-1729	12	10	.	.	PUNCT
cana-1729	13	1	the	the	DET
cana-1729	13	2	time	time	NOUN
cana-1729	13	3	-	-	PUNCT
cana-1729	13	4	dependent	dependent	ADJ
cana-1729	13	5	onedimensional	onedimensional	ADJ
cana-1729	13	6	linear	linear	ADJ
cana-1729	13	7	advection	advection	NOUN
cana-1729	13	8	-	-	PUNCT
cana-1729	13	9	diffusion	diffusion	NOUN
cana-1729	13	10	equation	equation	NOUN
cana-1729	13	11	is	be	AUX
cana-1729	13	12	solved	solve	VERB
cana-1729	13	13	analytically	analytically	ADV
cana-1729	13	14	by	by	ADP
cana-1729	13	15	mojtabi	mojtabi	PROPN
cana-1729	13	16	and	and	CCONJ
cana-1729	13	17	deville	deville	PROPN
cana-1729	13	18	(	(	PUNCT
cana-1729	13	19	2015	2015	NUM
cana-1729	13	20	)	)	PUNCT
cana-1729	13	21	using	use	VERB
cana-1729	13	22	variable	variable	ADJ
cana-1729	13	23	separation	separation	NOUN
cana-1729	13	24	and	and	CCONJ
cana-1729	13	25	numerically	numerically	ADV
cana-1729	13	26	by	by	ADP
cana-1729	13	27	employing	employ	VERB
cana-1729	13	28	the	the	DET
cana-1729	13	29	finite	finite	ADJ
cana-1729	13	30	element	element	NOUN
cana-1729	13	31	approach	approach	NOUN
cana-1729	13	32	.	.	PUNCT
cana-1729	14	1	the	the	DET
cana-1729	14	2	study	study	NOUN
cana-1729	14	3	notes	note	VERB
cana-1729	14	4	that	that	SCONJ
cana-1729	14	5	the	the	DET
cana-1729	14	6	analytical	analytical	ADJ
cana-1729	14	7	solution	solution	NOUN
cana-1729	14	8	behaves	behave	VERB
cana-1729	14	9	badly	badly	ADV
cana-1729	14	10	and	and	CCONJ
cana-1729	14	11	is	be	AUX
cana-1729	14	12	more	more	ADV
cana-1729	14	13	difficult	difficult	ADJ
cana-1729	14	14	to	to	PART
cana-1729	14	15	assess	assess	VERB
cana-1729	14	16	when	when	SCONJ
cana-1729	14	17	advection	advection	NOUN
cana-1729	14	18	takes	take	VERB
cana-1729	14	19	over	over	ADP
cana-1729	14	20	.	.	PUNCT
cana-1729	15	1	gane	gane	NOUN
cana-1729	15	2	(	(	PUNCT
cana-1729	15	3	2000	2000	NUM
cana-1729	15	4	)	)	PUNCT
cana-1729	15	5	looked	look	VERB
cana-1729	15	6	on	on	ADP
cana-1729	15	7	the	the	DET
cana-1729	15	8	use	use	NOUN
cana-1729	15	9	of	of	ADP
cana-1729	15	10	characteristics	characteristic	NOUN
cana-1729	15	11	-	-	PUNCT
cana-1729	15	12	based	base	VERB
cana-1729	15	13	methods	method	NOUN
cana-1729	15	14	and	and	CCONJ
cana-1729	15	15	finite	finite	ADJ
cana-1729	15	16	difference	difference	NOUN
cana-1729	15	17	approaches	approach	NOUN
cana-1729	15	18	to	to	PART
cana-1729	15	19	solve	solve	VERB
cana-1729	15	20	the	the	DET
cana-1729	15	21	advection	advection	NOUN
cana-1729	15	22	problem	problem	NOUN
cana-1729	15	23	.	.	PUNCT
cana-1729	16	1	in	in	ADP
cana-1729	16	2	a	a	DET
cana-1729	16	3	longitudinal	longitudinal	ADJ
cana-1729	16	4	finite	finite	NOUN
cana-1729	16	5	initially	initially	ADV
cana-1729	16	6	solute	solute	VERB
cana-1729	16	7	-	-	PUNCT
cana-1729	16	8	free	free	ADJ
cana-1729	16	9	domain	domain	NOUN
cana-1729	16	10	,	,	PUNCT
cana-1729	16	11	kumar	kumar	PROPN
cana-1729	16	12	et	et	PROPN
cana-1729	16	13	al	al	PROPN
cana-1729	16	14	.	.	PROPN
cana-1729	17	1	(	(	PUNCT
cana-1729	17	2	2009	2009	NUM
cana-1729	17	3	)	)	PUNCT
cana-1729	17	4	discovered	discover	VERB
cana-1729	17	5	analytical	analytical	ADJ
cana-1729	17	6	solutions	solution	NOUN
cana-1729	17	7	for	for	ADP
cana-1729	17	8	the	the	DET
cana-1729	17	9	one	one	NUM
cana-1729	17	10	-	-	PUNCT
cana-1729	17	11	dimensional	dimensional	ADJ
cana-1729	17	12	advection	advection	NOUN
cana-1729	17	13	-	-	PUNCT
cana-1729	17	14	diffusion	diffusion	NOUN
cana-1729	17	15	equation	equation	NOUN
cana-1729	17	16	with	with	ADP
cana-1729	17	17	variable	variable	ADJ
cana-1729	17	18	coefficients	coefficient	NOUN
cana-1729	17	19	.	.	PUNCT
cana-1729	18	1	when	when	SCONJ
cana-1729	18	2	dispersion	dispersion	NOUN
cana-1729	18	3	is	be	AUX
cana-1729	18	4	proportional	proportional	ADJ
cana-1729	18	5	to	to	ADP
cana-1729	18	6	the	the	DET
cana-1729	18	7	same	same	ADJ
cana-1729	18	8	linearly	linearly	ADV
cana-1729	18	9	interpolated	interpolate	VERB
cana-1729	18	10	velocity	velocity	NOUN
cana-1729	18	11	,	,	PUNCT
cana-1729	18	12	the	the	DET
cana-1729	18	13	study	study	NOUN
cana-1729	18	14	compares	compare	VERB
cana-1729	18	15	the	the	DET
cana-1729	18	16	analytical	analytical	ADJ
cana-1729	18	17	&	&	CCONJ
cana-1729	18	18	numerical	numerical	PROPN
cana-1729	18	19	solutions	solution	NOUN
cana-1729	18	20	.	.	PUNCT
cana-1729	19	1	three	three	NUM
cana-1729	19	2	numerical	numerical	ADJ
cana-1729	19	3	techniques	technique	NOUN
cana-1729	19	4	for	for	ADP
cana-1729	19	5	solving	solve	VERB
cana-1729	19	6	the	the	DET
cana-1729	19	7	onecommunications	onecommunication	NOUN
cana-1729	19	8	on	on	ADP
cana-1729	19	9	applied	apply	VERB
cana-1729	19	10	nonlinear	nonlinear	ADJ
cana-1729	19	11	analysis	analysis	NOUN
cana-1729	19	12	issn	issn	NOUN
cana-1729	19	13	:	:	PUNCT
cana-1729	19	14	1074	1074	NUM
cana-1729	19	15	-	-	PUNCT
cana-1729	19	16	133x	133x	NUM
cana-1729	19	17	vol	vol	NOUN
cana-1729	19	18	32	32	NUM
cana-1729	19	19	no	no	NOUN
cana-1729	19	20	.	.	NOUN
cana-1729	19	21	2	2	NUM
cana-1729	19	22	(	(	PUNCT
cana-1729	19	23	2025	2025	NUM
cana-1729	19	24	)	)	PUNCT
cana-1729	19	25	152	152	NUM
cana-1729	19	26	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1729	19	27	dimensional	dimensional	ADJ
cana-1729	19	28	advection	advection	NOUN
cana-1729	19	29	-	-	PUNCT
cana-1729	19	30	diffusion	diffusion	NOUN
cana-1729	19	31	problem	problem	NOUN
cana-1729	19	32	with	with	ADP
cana-1729	19	33	constant	constant	ADJ
cana-1729	19	34	coefficients	coefficient	NOUN
cana-1729	19	35	are	be	AUX
cana-1729	19	36	compared	compare	VERB
cana-1729	19	37	by	by	ADP
cana-1729	19	38	appadu	appadu	ADJ
cana-1729	19	39	(	(	PUNCT
cana-1729	19	40	2013	2013	NUM
cana-1729	19	41	)	)	PUNCT
cana-1729	19	42	.	.	PUNCT
cana-1729	20	1	the	the	DET
cana-1729	20	2	lax	lax	PROPN
cana-1729	20	3	-	-	PUNCT
cana-1729	20	4	wendroff	wendroff	NOUN
cana-1729	20	5	scheme	scheme	NOUN
cana-1729	20	6	,	,	PUNCT
cana-1729	20	7	the	the	DET
cana-1729	20	8	crank	crank	NOUN
cana-1729	20	9	-	-	PUNCT
cana-1729	20	10	nicolson	nicolson	PROPN
cana-1729	20	11	scheme	scheme	NOUN
cana-1729	20	12	,	,	PUNCT
cana-1729	20	13	and	and	CCONJ
cana-1729	20	14	a	a	DET
cana-1729	20	15	nonstandard	nonstandard	ADJ
cana-1729	20	16	finite	finite	ADJ
cana-1729	20	17	difference	difference	NOUN
cana-1729	20	18	scheme	scheme	NOUN
cana-1729	20	19	are	be	AUX
cana-1729	20	20	some	some	PRON
cana-1729	20	21	of	of	ADP
cana-1729	20	22	the	the	DET
cana-1729	20	23	techniques	technique	NOUN
cana-1729	20	24	used	use	VERB
cana-1729	20	25	.	.	PUNCT
cana-1729	21	1	according	accord	VERB
cana-1729	21	2	to	to	ADP
cana-1729	21	3	the	the	DET
cana-1729	21	4	study	study	NOUN
cana-1729	21	5	,	,	PUNCT
cana-1729	21	6	for	for	ADP
cana-1729	21	7	specific	specific	ADJ
cana-1729	21	8	values	value	NOUN
cana-1729	21	9	of	of	ADP
cana-1729	21	10	space	space	NOUN
cana-1729	21	11	and	and	CCONJ
cana-1729	21	12	time	time	NOUN
cana-1729	21	13	step	step	NOUN
cana-1729	21	14	sizes	size	NOUN
cana-1729	21	15	,	,	PUNCT
cana-1729	21	16	the	the	DET
cana-1729	21	17	lax	lax	NOUN
cana-1729	21	18	-	-	PUNCT
cana-1729	21	19	wendroff	wendroff	NOUN
cana-1729	21	20	and	and	CCONJ
cana-1729	21	21	nonstandard	nonstandard	ADJ
cana-1729	21	22	finite	finite	ADJ
cana-1729	21	23	difference	difference	NOUN
cana-1729	21	24	schemes	scheme	NOUN
cana-1729	21	25	yield	yield	VERB
cana-1729	21	26	excellent	excellent	ADJ
cana-1729	21	27	approximations	approximation	NOUN
cana-1729	21	28	for	for	ADP
cana-1729	21	29	the	the	DET
cana-1729	21	30	1d	1d	NUM
cana-1729	21	31	advection	advection	NOUN
cana-1729	21	32	-	-	PUNCT
cana-1729	21	33	diffusion	diffusion	NOUN
cana-1729	21	34	equation	equation	NOUN
cana-1729	21	35	.	.	PUNCT
cana-1729	22	1	the	the	DET
cana-1729	22	2	hybrid	hybrid	ADJ
cana-1729	22	3	nature	nature	NOUN
cana-1729	22	4	of	of	ADP
cana-1729	22	5	the	the	DET
cana-1729	22	6	transport	transport	NOUN
cana-1729	22	7	equation	equation	NOUN
cana-1729	22	8	has	have	VERB
cana-1729	22	9	numerical	numerical	ADJ
cana-1729	22	10	implications	implication	NOUN
cana-1729	22	11	that	that	PRON
cana-1729	22	12	result	result	VERB
cana-1729	22	13	in	in	ADP
cana-1729	22	14	problems	problem	NOUN
cana-1729	22	15	that	that	PRON
cana-1729	22	16	are	be	AUX
cana-1729	22	17	dominated	dominate	VERB
cana-1729	22	18	by	by	ADP
cana-1729	22	19	advection	advection	NOUN
cana-1729	22	20	or	or	CCONJ
cana-1729	22	21	diffusion	diffusion	NOUN
cana-1729	22	22	,	,	PUNCT
cana-1729	22	23	as	as	SCONJ
cana-1729	22	24	discussed	discuss	VERB
cana-1729	22	25	by	by	ADP
cana-1729	22	26	szymkiewicz	szymkiewicz	PROPN
cana-1729	22	27	(	(	PUNCT
cana-1729	22	28	2010	2010	NUM
cana-1729	22	29	)	)	PUNCT
cana-1729	22	30	.	.	PUNCT
cana-1729	23	1	the	the	DET
cana-1729	23	2	author	author	NOUN
cana-1729	23	3	provides	provide	VERB
cana-1729	23	4	algorithms	algorithm	NOUN
cana-1729	23	5	based	base	VERB
cana-1729	23	6	on	on	ADP
cana-1729	23	7	the	the	DET
cana-1729	23	8	splitting	splitting	NOUN
cana-1729	23	9	approach	approach	NOUN
cana-1729	23	10	,	,	PUNCT
cana-1729	23	11	the	the	DET
cana-1729	23	12	finite	finite	ADJ
cana-1729	23	13	difference	difference	NOUN
cana-1729	23	14	and	and	CCONJ
cana-1729	23	15	the	the	DET
cana-1729	23	16	finite	finite	ADJ
cana-1729	23	17	element	element	NOUN
cana-1729	23	18	methods	method	NOUN
cana-1729	23	19	for	for	ADP
cana-1729	23	20	solving	solve	VERB
cana-1729	23	21	the	the	DET
cana-1729	23	22	1d	1d	NUM
cana-1729	23	23	advection	advection	NOUN
cana-1729	23	24	-	-	PUNCT
cana-1729	23	25	diffusion	diffusion	NOUN
cana-1729	23	26	problem	problem	NOUN
cana-1729	23	27	.	.	PUNCT
cana-1729	24	1	the	the	DET
cana-1729	24	2	study	study	NOUN
cana-1729	24	3	highlights	highlight	VERB
cana-1729	24	4	how	how	SCONJ
cana-1729	24	5	the	the	DET
cana-1729	24	6	diffusion	diffusion	NOUN
cana-1729	24	7	in	in	ADP
cana-1729	24	8	the	the	DET
cana-1729	24	9	numerical	numerical	ADJ
cana-1729	24	10	solution	solution	NOUN
cana-1729	24	11	is	be	AUX
cana-1729	24	12	equivalent	equivalent	ADJ
cana-1729	24	13	to	to	ADP
cana-1729	24	14	that	that	PRON
cana-1729	24	15	in	in	ADP
cana-1729	24	16	the	the	DET
cana-1729	24	17	physical	physical	ADJ
cana-1729	24	18	world	world	NOUN
cana-1729	24	19	.	.	PUNCT
cana-1729	25	1	convection	convection	NOUN
cana-1729	25	2	-	-	PUNCT
cana-1729	25	3	diffusion	diffusion	NOUN
cana-1729	25	4	equations	equation	NOUN
cana-1729	25	5	are	be	AUX
cana-1729	25	6	solved	solve	VERB
cana-1729	25	7	by	by	ADP
cana-1729	25	8	mittal	mittal	NOUN
cana-1729	25	9	and	and	CCONJ
cana-1729	25	10	jain	jain	PROPN
cana-1729	25	11	(	(	PUNCT
cana-1729	25	12	2010	2010	NUM
cana-1729	25	13	)	)	PUNCT
cana-1729	25	14	using	use	VERB
cana-1729	25	15	the	the	DET
cana-1729	25	16	redefined	redefine	VERB
cana-1729	25	17	cubic	cubic	ADJ
cana-1729	25	18	bsplines	bspline	NOUN
cana-1729	25	19	and	and	CCONJ
cana-1729	25	20	the	the	DET
cana-1729	25	21	collocation	collocation	NOUN
cana-1729	25	22	method	method	NOUN
cana-1729	25	23	.	.	PUNCT
cana-1729	26	1	karahan	karahan	PROPN
cana-1729	26	2	(	(	PUNCT
cana-1729	26	3	2006	2006	NUM
cana-1729	26	4	)	)	PUNCT
cana-1729	26	5	solves	solve	VERB
cana-1729	26	6	the	the	DET
cana-1729	26	7	advection	advection	NOUN
cana-1729	26	8	-	-	PUNCT
cana-1729	26	9	diffusion	diffusion	NOUN
cana-1729	26	10	equation	equation	NOUN
cana-1729	26	11	using	use	VERB
cana-1729	26	12	implicit	implicit	ADJ
cana-1729	26	13	finite	finite	ADJ
cana-1729	26	14	difference	difference	NOUN
cana-1729	26	15	methods	method	NOUN
cana-1729	26	16	.	.	PUNCT
cana-1729	27	1	this	this	DET
cana-1729	27	2	study	study	NOUN
cana-1729	27	3	's	's	PART
cana-1729	27	4	primary	primary	ADJ
cana-1729	27	5	goal	goal	NOUN
cana-1729	27	6	is	be	AUX
cana-1729	27	7	to	to	PART
cana-1729	27	8	provide	provide	VERB
cana-1729	27	9	a	a	DET
cana-1729	27	10	straightforward	straightforward	ADJ
cana-1729	27	11	,	,	PUNCT
cana-1729	27	12	reliable	reliable	ADJ
cana-1729	27	13	,	,	PUNCT
cana-1729	27	14	and	and	CCONJ
cana-1729	27	15	user	user	NOUN
cana-1729	27	16	-	-	PUNCT
cana-1729	27	17	friendly	friendly	ADJ
cana-1729	27	18	meshless	meshless	ADJ
cana-1729	27	19	technique	technique	NOUN
cana-1729	27	20	.	.	PUNCT
cana-1729	28	1	the	the	DET
cana-1729	28	2	structure	structure	NOUN
cana-1729	28	3	of	of	ADP
cana-1729	28	4	the	the	DET
cana-1729	28	5	paper	paper	NOUN
cana-1729	28	6	is	be	AUX
cana-1729	28	7	as	as	ADV
cana-1729	28	8	under	under	ADV
cana-1729	28	9	.	.	PUNCT
cana-1729	29	1	the	the	DET
cana-1729	29	2	problem	problem	NOUN
cana-1729	29	3	statement	statement	NOUN
cana-1729	29	4	is	be	AUX
cana-1729	29	5	provided	provide	VERB
cana-1729	29	6	in	in	ADP
cana-1729	29	7	section	section	NOUN
cana-1729	29	8	2	2	NUM
cana-1729	29	9	.	.	PUNCT
cana-1729	30	1	in	in	ADP
cana-1729	30	2	section	section	NOUN
cana-1729	30	3	3	3	NUM
cana-1729	30	4	,	,	PUNCT
cana-1729	30	5	the	the	DET
cana-1729	30	6	rbf	rbf	PROPN
cana-1729	30	7	approximation	approximation	NOUN
cana-1729	30	8	is	be	AUX
cana-1729	30	9	presented	present	VERB
cana-1729	30	10	.	.	PUNCT
cana-1729	31	1	in	in	ADP
cana-1729	31	2	section	section	NOUN
cana-1729	31	3	4	4	NUM
cana-1729	31	4	,	,	PUNCT
cana-1729	31	5	the	the	DET
cana-1729	31	6	asymmetric	asymmetric	ADJ
cana-1729	31	7	multiquadric	multiquadric	ADJ
cana-1729	31	8	collocation	collocation	NOUN
cana-1729	31	9	method	method	NOUN
cana-1729	31	10	is	be	AUX
cana-1729	31	11	introduced	introduce	VERB
cana-1729	31	12	.	.	PUNCT
cana-1729	32	1	the	the	DET
cana-1729	32	2	section	section	NOUN
cana-1729	32	3	5	5	NUM
cana-1729	32	4	deals	deal	NOUN
cana-1729	32	5	with	with	ADP
cana-1729	32	6	the	the	DET
cana-1729	32	7	error	error	NOUN
cana-1729	32	8	estimation	estimation	NOUN
cana-1729	32	9	.	.	PUNCT
cana-1729	33	1	two	two	NUM
cana-1729	33	2	test	test	NOUN
cana-1729	33	3	problems	problem	NOUN
cana-1729	33	4	are	be	AUX
cana-1729	33	5	addressed	address	VERB
cana-1729	33	6	in	in	ADP
cana-1729	33	7	section	section	NOUN
cana-1729	33	8	6	6	NUM
cana-1729	33	9	.	.	PUNCT
cana-1729	34	1	in	in	ADP
cana-1729	34	2	section	section	NOUN
cana-1729	34	3	7	7	NUM
cana-1729	34	4	,	,	PUNCT
cana-1729	34	5	the	the	DET
cana-1729	34	6	closing	closing	NOUN
cana-1729	34	7	thoughts	thought	NOUN
cana-1729	34	8	are	be	AUX
cana-1729	34	9	discussed	discuss	VERB
cana-1729	34	10	.	.	PUNCT
cana-1729	35	1	1	1	NUM
cana-1729	35	2	.	.	X
cana-1729	35	3	1	1	NUM
cana-1729	35	4	-	-	PUNCT
cana-1729	35	5	d	d	NOUN
cana-1729	35	6	advection	advection	NOUN
cana-1729	35	7	-	-	PUNCT
cana-1729	35	8	diffusion	diffusion	NOUN
cana-1729	35	9	equation	equation	NOUN
cana-1729	35	10	the	the	DET
cana-1729	35	11	one	one	NUM
cana-1729	35	12	-	-	PUNCT
cana-1729	35	13	dimensional	dimensional	ADJ
cana-1729	35	14	advection	advection	NOUN
cana-1729	35	15	-	-	PUNCT
cana-1729	35	16	diffusion	diffusion	NOUN
cana-1729	35	17	is	be	AUX
cana-1729	35	18	given	give	VERB
cana-1729	35	19	by	by	ADP
cana-1729	35	20	(	(	PUNCT
cana-1729	35	21	hundsdorfer	hundsdorfer	NOUN
cana-1729	35	22	and	and	CCONJ
cana-1729	35	23	verwer	verwer	NOUN
cana-1729	35	24	2003	2003	NUM
cana-1729	35	25	)	)	PUNCT
cana-1729	36	1	∂u	∂u	PROPN
cana-1729	36	2	∂t	∂t	PROPN
cana-1729	36	3	+	+	CCONJ
cana-1729	36	4	α	α	NOUN
cana-1729	36	5	∂u	∂u	NOUN
cana-1729	36	6	∂x	∂x	NOUN
cana-1729	36	7	=	=	PUNCT
cana-1729	36	8	γ	γ	PROPN
cana-1729	36	9	∂2u	∂2u	PROPN
cana-1729	36	10	∂x2	∂x2	PROPN
cana-1729	36	11	;	;	PUNCT
cana-1729	36	12	0	0	NUM
cana-1729	36	13	≤	≤	NUM
cana-1729	36	14	x	x	SYM
cana-1729	36	15	≤	≤	NUM
cana-1729	36	16	l	l	NOUN
cana-1729	36	17	,	,	PUNCT
cana-1729	36	18	0	0	PUNCT
cana-1729	36	19	<	<	X
cana-1729	36	20	t	t	X
cana-1729	36	21	≤	≤	PROPN
cana-1729	36	22	t	t	PROPN
cana-1729	36	23	(	(	PUNCT
cana-1729	36	24	2.1	2.1	NUM
cana-1729	36	25	)	)	PUNCT
cana-1729	36	26	with	with	ADP
cana-1729	36	27	initial	initial	ADJ
cana-1729	36	28	condition	condition	NOUN
cana-1729	36	29	𝑢(𝑥	𝑢(𝑥	PROPN
cana-1729	36	30	,	,	PUNCT
cana-1729	36	31	0	0	NUM
cana-1729	36	32	)	)	PUNCT
cana-1729	36	33	=	=	SYM
cana-1729	36	34	𝜑(𝑥	𝜑(𝑥	NOUN
cana-1729	36	35	)	)	PUNCT
cana-1729	36	36	;	;	PUNCT
cana-1729	36	37	0	0	NUM
cana-1729	36	38	≤	≤	NUM
cana-1729	36	39	𝑥	𝑥	PRON
cana-1729	36	40	≤	≤	PROPN
cana-1729	36	41	𝐿	𝐿	PROPN
cana-1729	36	42	(	(	PUNCT
cana-1729	36	43	2.2	2.2	NUM
cana-1729	36	44	)	)	PUNCT
cana-1729	36	45	and	and	CCONJ
cana-1729	36	46	the	the	DET
cana-1729	36	47	boundary	boundary	ADJ
cana-1729	36	48	conditions	condition	NOUN
cana-1729	36	49	are	be	AUX
cana-1729	36	50	𝑢(0	𝑢(0	PROPN
cana-1729	36	51	,	,	PUNCT
cana-1729	36	52	𝑡	𝑡	NOUN
cana-1729	36	53	)	)	PUNCT
cana-1729	36	54	=	=	SYM
cana-1729	36	55	𝜑1(𝑡	𝜑1(𝑡	PROPN
cana-1729	36	56	)	)	PUNCT
cana-1729	36	57	;	;	PUNCT
cana-1729	36	58	𝑢(𝐿	𝑢(𝐿	X
cana-1729	36	59	,	,	PUNCT
cana-1729	36	60	𝑡	𝑡	X
cana-1729	36	61	)	)	PUNCT
cana-1729	36	62	=	=	SYM
cana-1729	36	63	𝜑2(𝑡	𝜑2(𝑡	PROPN
cana-1729	36	64	)	)	PUNCT
cana-1729	36	65	;	;	PUNCT
cana-1729	36	66	0	0	NUM
cana-1729	37	1	<	<	X
cana-1729	37	2	𝑡	𝑡	PROPN
cana-1729	37	3	≤	≤	ADJ
cana-1729	37	4	𝑇	𝑇	PROPN
cana-1729	37	5	(	(	PUNCT
cana-1729	37	6	2.3	2.3	NUM
cana-1729	37	7	)	)	PUNCT
cana-1729	37	8	where	where	SCONJ
cana-1729	37	9	𝛼	𝛼	VERB
cana-1729	37	10	and	and	CCONJ
cana-1729	37	11	𝛾	𝛾	PROPN
cana-1729	37	12	are	be	AUX
cana-1729	37	13	positive	positive	ADJ
cana-1729	37	14	constants	constant	NOUN
cana-1729	37	15	and	and	CCONJ
cana-1729	37	16	they	they	PRON
cana-1729	37	17	represent	represent	VERB
cana-1729	37	18	the	the	DET
cana-1729	37	19	advection	advection	NOUN
cana-1729	37	20	speed	speed	NOUN
cana-1729	37	21	and	and	CCONJ
cana-1729	37	22	diffusion	diffusion	NOUN
cana-1729	37	23	coefficients	coefficient	NOUN
cana-1729	37	24	respectively	respectively	ADV
cana-1729	37	25	.	.	PUNCT
cana-1729	38	1	the	the	DET
cana-1729	38	2	functions	function	NOUN
cana-1729	38	3	𝜑(𝑥	𝜑(𝑥	NOUN
cana-1729	38	4	)	)	PUNCT
cana-1729	38	5	,	,	PUNCT
cana-1729	38	6	𝜑1(𝑡	𝜑1(𝑡	CCONJ
cana-1729	38	7	)	)	PUNCT
cana-1729	38	8	and	and	CCONJ
cana-1729	38	9	𝜑2(𝑡	𝜑2(𝑡	PROPN
cana-1729	38	10	)	)	PUNCT
cana-1729	38	11	are	be	AUX
cana-1729	38	12	the	the	DET
cana-1729	38	13	known	know	VERB
cana-1729	38	14	functions	function	NOUN
cana-1729	38	15	with	with	ADP
cana-1729	38	16	sufficiently	sufficiently	ADV
cana-1729	38	17	smoothness	smoothness	ADJ
cana-1729	38	18	.	.	PUNCT
cana-1729	39	1	the	the	DET
cana-1729	39	2	suggested	suggest	VERB
cana-1729	39	3	approach	approach	NOUN
cana-1729	39	4	is	be	AUX
cana-1729	39	5	used	use	VERB
cana-1729	39	6	to	to	ADP
cana-1729	39	7	the	the	DET
cana-1729	39	8	solution	solution	NOUN
cana-1729	39	9	of	of	ADP
cana-1729	39	10	equations	equation	NOUN
cana-1729	39	11	(	(	PUNCT
cana-1729	39	12	2.1)–(2.3	2.1)–(2.3	NUM
cana-1729	39	13	)	)	PUNCT
cana-1729	39	14	.	.	PUNCT
cana-1729	40	1	after	after	ADP
cana-1729	40	2	completing	complete	VERB
cana-1729	40	3	the	the	DET
cana-1729	40	4	spatial	spatial	ADJ
cana-1729	40	5	discretization	discretization	NOUN
cana-1729	40	6	,	,	PUNCT
cana-1729	40	7	a	a	DET
cana-1729	40	8	typical	typical	ADJ
cana-1729	40	9	ode	ode	PROPN
cana-1729	40	10	solver	solver	NOUN
cana-1729	40	11	in	in	ADP
cana-1729	40	12	matlab	matlab	PROPN
cana-1729	40	13	is	be	AUX
cana-1729	40	14	used	use	VERB
cana-1729	40	15	to	to	PART
cana-1729	40	16	solve	solve	VERB
cana-1729	40	17	the	the	DET
cana-1729	40	18	resulting	result	VERB
cana-1729	40	19	system	system	NOUN
cana-1729	40	20	of	of	ADP
cana-1729	40	21	odes	ode	NOUN
cana-1729	40	22	using	use	VERB
cana-1729	40	23	the	the	DET
cana-1729	40	24	method	method	NOUN
cana-1729	40	25	of	of	ADP
cana-1729	40	26	lines	line	NOUN
cana-1729	40	27	approach	approach	NOUN
cana-1729	40	28	.	.	PUNCT
cana-1729	41	1	2	2	X
cana-1729	41	2	.	.	X
cana-1729	41	3	radial	radial	ADJ
cana-1729	41	4	basis	basis	NOUN
cana-1729	41	5	approximation	approximation	NOUN
cana-1729	41	6	rbfs	rbfs	NOUN
cana-1729	41	7	are	be	AUX
cana-1729	41	8	a	a	DET
cana-1729	41	9	class	class	NOUN
cana-1729	41	10	of	of	ADP
cana-1729	41	11	functions	function	NOUN
cana-1729	41	12	that	that	PRON
cana-1729	41	13	are	be	AUX
cana-1729	41	14	defined	define	VERB
cana-1729	41	15	as	as	ADP
cana-1729	41	16	a	a	DET
cana-1729	41	17	function	function	NOUN
cana-1729	41	18	of	of	ADP
cana-1729	41	19	the	the	DET
cana-1729	41	20	distance	distance	NOUN
cana-1729	41	21	between	between	ADP
cana-1729	41	22	a	a	DET
cana-1729	41	23	point	point	NOUN
cana-1729	41	24	and	and	CCONJ
cana-1729	41	25	a	a	DET
cana-1729	41	26	set	set	NOUN
cana-1729	41	27	of	of	ADP
cana-1729	41	28	fixed	fix	VERB
cana-1729	41	29	points	point	NOUN
cana-1729	41	30	called	call	VERB
cana-1729	41	31	centres	centre	NOUN
cana-1729	41	32	(	(	PUNCT
cana-1729	41	33	larsson	larsson	PROPN
cana-1729	41	34	and	and	CCONJ
cana-1729	41	35	fornberg	fornberg	PROPN
cana-1729	41	36	2003	2003	NUM
cana-1729	41	37	)	)	PUNCT
cana-1729	41	38	.	.	PUNCT
cana-1729	42	1	the	the	DET
cana-1729	42	2	most	most	ADV
cana-1729	42	3	used	use	VERB
cana-1729	42	4	rbf	rbf	PROPN
cana-1729	42	5	is	be	AUX
cana-1729	42	6	the	the	DET
cana-1729	42	7	gaussian	gaussian	PROPN
cana-1729	42	8	rbf	rbf	PROPN
cana-1729	42	9	,	,	PUNCT
cana-1729	42	10	which	which	PRON
cana-1729	42	11	is	be	AUX
cana-1729	42	12	defined	define	VERB
cana-1729	42	13	as	as	ADP
cana-1729	42	14	follows	follow	VERB
cana-1729	42	15	:	:	PUNCT
cana-1729	42	16	∅(𝑥	∅(𝑥	NUM
cana-1729	42	17	)	)	PUNCT
cana-1729	42	18	=	=	SYM
cana-1729	42	19	𝑒−𝜖2𝑟2	𝑒−𝜖2𝑟2	PROPN
cana-1729	42	20	,	,	PUNCT
cana-1729	42	21	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	ADJ
cana-1729	42	22	𝑟	𝑟	NOUN
cana-1729	42	23	=	=	PUNCT
cana-1729	42	24	‖𝑥	‖𝑥	NOUN
cana-1729	42	25	−	−	NOUN
cana-1729	42	26	𝑐‖	𝑐‖	NOUN
cana-1729	42	27	(	(	PUNCT
cana-1729	42	28	3.1	3.1	NUM
cana-1729	42	29	)	)	PUNCT
cana-1729	42	30	where	where	SCONJ
cana-1729	42	31	∅(𝑥	∅(𝑥	NOUN
cana-1729	42	32	)	)	PUNCT
cana-1729	42	33	is	be	AUX
cana-1729	42	34	the	the	DET
cana-1729	42	35	value	value	NOUN
cana-1729	42	36	of	of	ADP
cana-1729	42	37	the	the	DET
cana-1729	42	38	rbf	rbf	PROPN
cana-1729	42	39	at	at	ADP
cana-1729	42	40	point	point	NOUN
cana-1729	42	41	x	x	X
cana-1729	42	42	,	,	PUNCT
cana-1729	42	43	c	c	PROPN
cana-1729	42	44	is	be	AUX
cana-1729	42	45	the	the	DET
cana-1729	42	46	centre	centre	NOUN
cana-1729	42	47	of	of	ADP
cana-1729	42	48	the	the	DET
cana-1729	42	49	rbf	rbf	PROPN
cana-1729	42	50	,	,	PUNCT
cana-1729	42	51	𝜖	𝜖	PROPN
cana-1729	42	52	is	be	AUX
cana-1729	42	53	the	the	DET
cana-1729	42	54	shape	shape	NOUN
cana-1729	42	55	parameter	parameter	NOUN
cana-1729	42	56	,	,	PUNCT
cana-1729	42	57	and	and	CCONJ
cana-1729	42	58	‖𝑥	‖𝑥	NOUN
cana-1729	42	59	−	−	PROPN
cana-1729	42	60	𝑐‖	𝑐‖	NOUN
cana-1729	42	61	is	be	AUX
cana-1729	42	62	the	the	DET
cana-1729	42	63	euclidean	euclidean	ADJ
cana-1729	42	64	distance	distance	NOUN
cana-1729	42	65	between	between	ADP
cana-1729	42	66	x	x	PROPN
cana-1729	42	67	and	and	CCONJ
cana-1729	42	68	c.	c.	PROPN
cana-1729	42	69	communications	communication	NOUN
cana-1729	42	70	on	on	ADP
cana-1729	42	71	applied	apply	VERB
cana-1729	42	72	nonlinear	nonlinear	ADJ
cana-1729	42	73	analysis	analysis	NOUN
cana-1729	42	74	issn	issn	NOUN
cana-1729	42	75	:	:	PUNCT
cana-1729	42	76	1074	1074	NUM
cana-1729	42	77	-	-	PUNCT
cana-1729	42	78	133x	133x	NUM
cana-1729	42	79	vol	vol	NOUN
cana-1729	42	80	32	32	NUM
cana-1729	42	81	no	no	NOUN
cana-1729	42	82	.	.	NOUN
cana-1729	42	83	2	2	NUM
cana-1729	42	84	(	(	PUNCT
cana-1729	42	85	2025	2025	NUM
cana-1729	42	86	)	)	PUNCT
cana-1729	42	87	153	153	NUM
cana-1729	42	88	https://internationalpubls.com	https://internationalpubls.com	X
cana-1729	42	89	rbfs	rbfs	NOUN
cana-1729	42	90	can	can	AUX
cana-1729	42	91	be	be	AUX
cana-1729	42	92	used	use	VERB
cana-1729	42	93	for	for	ADP
cana-1729	42	94	function	function	NOUN
cana-1729	42	95	approximation	approximation	NOUN
cana-1729	42	96	by	by	ADP
cana-1729	42	97	constructing	construct	VERB
cana-1729	42	98	a	a	DET
cana-1729	42	99	linear	linear	ADJ
cana-1729	42	100	combination	combination	NOUN
cana-1729	42	101	of	of	ADP
cana-1729	42	102	rbfs	rbfs	NOUN
cana-1729	42	103	centred	centre	VERB
cana-1729	42	104	at	at	ADP
cana-1729	42	105	different	different	ADJ
cana-1729	42	106	points	point	NOUN
cana-1729	42	107	(	(	PUNCT
cana-1729	42	108	larsson	larsson	PROPN
cana-1729	42	109	and	and	CCONJ
cana-1729	42	110	fornberg	fornberg	PROPN
cana-1729	42	111	2003	2003	NUM
cana-1729	42	112	)	)	PUNCT
cana-1729	42	113	.	.	PUNCT
cana-1729	43	1	this	this	DET
cana-1729	43	2	linear	linear	ADJ
cana-1729	43	3	combination	combination	NOUN
cana-1729	43	4	is	be	AUX
cana-1729	43	5	given	give	VERB
cana-1729	43	6	by	by	ADP
cana-1729	43	7	:	:	PUNCT
cana-1729	43	8	𝑓(𝑥	𝑓(𝑥	NOUN
cana-1729	43	9	)	)	PUNCT
cana-1729	43	10	=	=	PUNCT
cana-1729	44	1	∑	∑	PUNCT
cana-1729	44	2	𝛼𝑖𝜑(‖𝑥	𝛼𝑖𝜑(‖𝑥	PRON
cana-1729	44	3	−	−	NOUN
cana-1729	44	4	𝑐𝑖‖	𝑐𝑖‖	ADJ
cana-1729	44	5	)	)	PUNCT
cana-1729	44	6	𝑁	𝑁	PROPN
cana-1729	44	7	𝑖=1	𝑖=1	PROPN
cana-1729	44	8	(	(	PUNCT
cana-1729	44	9	3.2	3.2	NUM
cana-1729	44	10	)	)	PUNCT
cana-1729	44	11	where	where	SCONJ
cana-1729	44	12	n	n	PRON
cana-1729	44	13	is	be	AUX
cana-1729	44	14	the	the	DET
cana-1729	44	15	number	number	NOUN
cana-1729	44	16	of	of	ADP
cana-1729	44	17	rbfs	rbfs	NOUN
cana-1729	44	18	used	use	VERB
cana-1729	44	19	in	in	ADP
cana-1729	44	20	the	the	DET
cana-1729	44	21	approximation	approximation	NOUN
cana-1729	44	22	,	,	PUNCT
cana-1729	44	23	f(x	f(x	PROPN
cana-1729	44	24	)	)	PUNCT
cana-1729	44	25	is	be	AUX
cana-1729	44	26	the	the	DET
cana-1729	44	27	approximated	approximated	ADJ
cana-1729	44	28	function	function	NOUN
cana-1729	44	29	,	,	PUNCT
cana-1729	44	30	𝛼𝑖	𝛼𝑖	PROPN
cana-1729	44	31	is	be	AUX
cana-1729	44	32	the	the	DET
cana-1729	44	33	weight	weight	NOUN
cana-1729	44	34	associated	associate	VERB
cana-1729	44	35	with	with	ADP
cana-1729	44	36	the	the	DET
cana-1729	44	37	i	i	PROPN
cana-1729	44	38	-	-	PUNCT
cana-1729	44	39	th	th	X
cana-1729	44	40	rbf	rbf	PROPN
cana-1729	44	41	,	,	PUNCT
cana-1729	44	42	and	and	CCONJ
cana-1729	44	43	𝑐𝑖	𝑐𝑖	NOUN
cana-1729	44	44	is	be	AUX
cana-1729	44	45	the	the	DET
cana-1729	44	46	center	center	NOUN
cana-1729	44	47	of	of	ADP
cana-1729	44	48	the	the	DET
cana-1729	44	49	i	i	PROPN
cana-1729	44	50	-	-	PUNCT
cana-1729	44	51	th	th	X
cana-1729	44	52	rbf	rbf	PROPN
cana-1729	44	53	.	.	PUNCT
cana-1729	45	1	by	by	ADP
cana-1729	45	2	minimizing	minimize	VERB
cana-1729	45	3	the	the	DET
cana-1729	45	4	difference	difference	NOUN
cana-1729	45	5	between	between	ADP
cana-1729	45	6	the	the	DET
cana-1729	45	7	approximated	approximated	ADJ
cana-1729	45	8	function	function	NOUN
cana-1729	45	9	and	and	CCONJ
cana-1729	45	10	the	the	DET
cana-1729	45	11	actual	actual	ADJ
cana-1729	45	12	function	function	NOUN
cana-1729	45	13	at	at	ADP
cana-1729	45	14	a	a	DET
cana-1729	45	15	set	set	NOUN
cana-1729	45	16	of	of	ADP
cana-1729	45	17	training	training	NOUN
cana-1729	45	18	points	point	NOUN
cana-1729	45	19	,	,	PUNCT
cana-1729	45	20	the	the	DET
cana-1729	45	21	weights	weight	NOUN
cana-1729	45	22	𝛼𝑖	𝛼𝑖	PROPN
cana-1729	45	23	can	can	AUX
cana-1729	45	24	be	be	AUX
cana-1729	45	25	found	find	VERB
cana-1729	45	26	(	(	PUNCT
cana-1729	45	27	dasari	dasari	NOUN
cana-1729	45	28	and	and	CCONJ
cana-1729	45	29	parikh	parikh	PROPN
cana-1729	45	30	2023	2023	NUM
cana-1729	45	31	)	)	PUNCT
cana-1729	45	32	.	.	PUNCT
cana-1729	46	1	the	the	DET
cana-1729	46	2	most	most	ADV
cana-1729	46	3	used	used	ADJ
cana-1729	46	4	rbfs	rbfs	NOUN
cana-1729	46	5	are	be	AUX
cana-1729	46	6	given	give	VERB
cana-1729	46	7	in	in	ADP
cana-1729	46	8	table	table	NOUN
cana-1729	46	9	1	1	NUM
cana-1729	46	10	(	(	PUNCT
cana-1729	46	11	larsson	larsson	PROPN
cana-1729	46	12	and	and	CCONJ
cana-1729	46	13	fornberg	fornberg	PROPN
cana-1729	46	14	2003	2003	NUM
cana-1729	46	15	)	)	PUNCT
cana-1729	46	16	.	.	PUNCT
cana-1729	47	1	table	table	NOUN
cana-1729	47	2	1	1	NUM
cana-1729	47	3	.	.	PUNCT
cana-1729	48	1	the	the	DET
cana-1729	48	2	frequently	frequently	ADV
cana-1729	48	3	used	use	VERB
cana-1729	48	4	radial	radial	ADJ
cana-1729	48	5	basis	basis	NOUN
cana-1729	48	6	functions	function	NOUN
cana-1729	48	7	type	type	NOUN
cana-1729	48	8	of	of	ADP
cana-1729	48	9	rbf	rbf	PROPN
cana-1729	48	10	definition	definition	NOUN
cana-1729	48	11	inverse	inverse	NOUN
cana-1729	48	12	multiquadric	multiquadric	NOUN
cana-1729	48	13	1/√1	1/√1	PROPN
cana-1729	49	1	+	+	CCONJ
cana-1729	50	1	𝜀2𝑟2	𝜀2𝑟2	PROPN
cana-1729	50	2	inverse	inverse	NOUN
cana-1729	50	3	quadric	quadric	PROPN
cana-1729	50	4	1/(1	1/(1	PROPN
cana-1729	50	5	+	+	CCONJ
cana-1729	50	6	𝜀2𝑟2	𝜀2𝑟2	NOUN
cana-1729	50	7	)	)	PUNCT
cana-1729	50	8	multiquadric	multiquadric	NOUN
cana-1729	50	9	√1	√1	PROPN
cana-1729	51	1	+	+	CCONJ
cana-1729	51	2	𝜀2𝑟2	𝜀2𝑟2	PROPN
cana-1729	51	3	gaussian	gaussian	PROPN
cana-1729	51	4	𝑒−𝜀2𝑟2	𝑒−𝜀2𝑟2	PROPN
cana-1729	51	5	spline	spline	NOUN
cana-1729	51	6	(	(	PUNCT
cana-1729	51	7	polyharmonic	polyharmonic	NOUN
cana-1729	51	8	)	)	PUNCT
cana-1729	51	9	𝑟𝑘	𝑟𝑘	NOUN
cana-1729	51	10	,	,	PUNCT
cana-1729	51	11	𝑘	𝑘	NOUN
cana-1729	51	12	=	=	NOUN
cana-1729	51	13	1,3,5	1,3,5	NUM
cana-1729	51	14	,	,	PUNCT
cana-1729	51	15	−	−	PROPN
cana-1729	51	16	−	−	PROPN
cana-1729	51	17	spline	spline	NOUN
cana-1729	51	18	(	(	PUNCT
cana-1729	51	19	thin	thin	ADJ
cana-1729	51	20	plate	plate	NOUN
cana-1729	51	21	)	)	PUNCT
cana-1729	51	22	𝑟2log	𝑟2log	PUNCT
cana-1729	51	23	(	(	PUNCT
cana-1729	51	24	𝑟	𝑟	NOUN
cana-1729	51	25	)	)	PUNCT
cana-1729	51	26	where	where	SCONJ
cana-1729	51	27	𝑟	𝑟	X
cana-1729	51	28	𝑖𝑠	𝑖𝑠	ADP
cana-1729	51	29	𝑡ℎ𝑒	𝑡ℎ𝑒	ADJ
cana-1729	51	30	𝐸𝑢𝑐𝑙𝑖𝑑𝑒𝑎𝑛	𝐸𝑢𝑐𝑙𝑖𝑑𝑒𝑎𝑛	PROPN
cana-1729	51	31	𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒	𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒	VERB
cana-1729	51	32	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-1729	51	33	𝜀	𝜀	PROPN
cana-1729	51	34	is	be	AUX
cana-1729	51	35	a	a	DET
cana-1729	51	36	shape	shape	NOUN
cana-1729	51	37	parameter	parameter	NOUN
cana-1729	51	38	for	for	ADP
cana-1729	51	39	scaling	scale	VERB
cana-1729	51	40	the	the	DET
cana-1729	51	41	radial	radial	ADJ
cana-1729	51	42	kernel	kernel	NOUN
cana-1729	51	43	's	's	PART
cana-1729	51	44	input	input	NOUN
cana-1729	51	45	.	.	PUNCT
cana-1729	52	1	3	3	X
cana-1729	52	2	.	.	X
cana-1729	52	3	asymmetric	asymmetric	ADJ
cana-1729	52	4	multiquadric	multiquadric	ADJ
cana-1729	52	5	collocation	collocation	NOUN
cana-1729	52	6	method	method	NOUN
cana-1729	52	7	we	we	PRON
cana-1729	52	8	consider	consider	VERB
cana-1729	52	9	the	the	DET
cana-1729	52	10	time	time	NOUN
cana-1729	52	11	-	-	PUNCT
cana-1729	52	12	dependent	dependent	ADJ
cana-1729	52	13	linear	linear	ADJ
cana-1729	52	14	boundary	boundary	ADJ
cana-1729	52	15	value	value	NOUN
cana-1729	52	16	problem	problem	NOUN
cana-1729	52	17	as	as	SCONJ
cana-1729	52	18	follows	follow	VERB
cana-1729	53	1	𝜕𝑢	𝜕𝑢	NOUN
cana-1729	53	2	𝜕𝑡	𝜕𝑡	NOUN
cana-1729	53	3	=	=	SYM
cana-1729	53	4	𝓛𝑢	𝓛𝑢	PROPN
cana-1729	53	5	,	,	PUNCT
cana-1729	53	6	𝑖𝑛	𝑖𝑛	PROPN
cana-1729	53	7	ω	ω	PROPN
cana-1729	53	8	(	(	PUNCT
cana-1729	53	9	4.1	4.1	NUM
cana-1729	53	10	)	)	PUNCT
cana-1729	53	11	subject	subject	NOUN
cana-1729	53	12	to	to	ADP
cana-1729	53	13	boundary	boundary	ADJ
cana-1729	53	14	operator	operator	NOUN
cana-1729	53	15	𝓑	𝓑	ADP
cana-1729	53	16	𝑖𝑛	𝑖𝑛	INTJ
cana-1729	54	1	𝜕ω	𝜕ω	PROPN
cana-1729	54	2	(	(	PUNCT
cana-1729	54	3	4.2	4.2	NUM
cana-1729	54	4	)	)	PUNCT
cana-1729	54	5	where	where	SCONJ
cana-1729	54	6	𝓛	𝓛	PROPN
cana-1729	54	7	is	be	AUX
cana-1729	54	8	a	a	DET
cana-1729	54	9	linear	linear	ADJ
cana-1729	54	10	differential	differential	NOUN
cana-1729	54	11	operator	operator	NOUN
cana-1729	54	12	,	,	PUNCT
cana-1729	54	13	𝓑	𝓑	PROPN
cana-1729	54	14	is	be	AUX
cana-1729	54	15	a	a	DET
cana-1729	54	16	boundary	boundary	ADJ
cana-1729	54	17	operator	operator	NOUN
cana-1729	54	18	,	,	PUNCT
cana-1729	54	19	ω	ω	PROPN
cana-1729	54	20	is	be	AUX
cana-1729	54	21	the	the	DET
cana-1729	54	22	bounded	bounded	ADJ
cana-1729	54	23	domain	domain	NOUN
cana-1729	54	24	and	and	CCONJ
cana-1729	54	25	𝜕ω	𝜕ω	PROPN
cana-1729	54	26	is	be	AUX
cana-1729	54	27	the	the	DET
cana-1729	54	28	boundary	boundary	ADJ
cana-1729	54	29	domain	domain	NOUN
cana-1729	54	30	.	.	PUNCT
cana-1729	55	1	let	let	VERB
cana-1729	55	2	the	the	DET
cana-1729	55	3	approximate	approximate	ADJ
cana-1729	55	4	solution	solution	NOUN
cana-1729	55	5	of	of	ADP
cana-1729	55	6	(	(	PUNCT
cana-1729	55	7	4.1	4.1	NUM
cana-1729	55	8	)	)	PUNCT
cana-1729	55	9	&	&	CCONJ
cana-1729	55	10	(	(	PUNCT
cana-1729	55	11	4.2	4.2	NUM
cana-1729	55	12	)	)	PUNCT
cana-1729	55	13	in	in	ADP
cana-1729	55	14	terms	term	NOUN
cana-1729	55	15	of	of	ADP
cana-1729	55	16	rbfs	rbfs	NOUN
cana-1729	55	17	be	be	AUX
cana-1729	55	18	𝑢(𝑥	𝑢(𝑥	PROPN
cana-1729	55	19	)	)	PUNCT
cana-1729	56	1	=	=	PUNCT
cana-1729	56	2	∑	∑	PUNCT
cana-1729	56	3	𝛼𝑖	𝛼𝑖	PART
cana-1729	56	4	𝑛	𝑛	PRON
cana-1729	56	5	𝑖=1	𝑖=1	PROPN
cana-1729	56	6	𝜙(𝑟𝑖	𝜙(𝑟𝑖	NOUN
cana-1729	56	7	)	)	PUNCT
cana-1729	56	8	(	(	PUNCT
cana-1729	56	9	4.3	4.3	NUM
cana-1729	56	10	)	)	PUNCT
cana-1729	56	11	where	where	SCONJ
cana-1729	56	12	𝜙	𝜙	NOUN
cana-1729	56	13	is	be	AUX
cana-1729	56	14	an	an	DET
cana-1729	56	15	rbf	rbf	PROPN
cana-1729	56	16	,	,	PUNCT
cana-1729	56	17	𝑟𝑖	𝑟𝑖	ADV
cana-1729	56	18	=	=	SYM
cana-1729	56	19	‖𝑥	‖𝑥	NOUN
cana-1729	56	20	−	−	NOUN
cana-1729	56	21	𝑥𝑖‖	𝑥𝑖‖	PROPN
cana-1729	56	22	is	be	AUX
cana-1729	56	23	the	the	DET
cana-1729	56	24	euclidean	euclidean	ADJ
cana-1729	56	25	distance	distance	NOUN
cana-1729	56	26	between	between	ADP
cana-1729	56	27	two	two	NUM
cana-1729	56	28	points	point	NOUN
cana-1729	56	29	,	,	PUNCT
cana-1729	56	30	𝑥𝑖	𝑥𝑖	PROPN
cana-1729	56	31	is	be	AUX
cana-1729	56	32	the	the	DET
cana-1729	56	33	center	center	NOUN
cana-1729	56	34	of	of	ADP
cana-1729	56	35	the	the	DET
cana-1729	56	36	rbf	rbf	PROPN
cana-1729	56	37	,	,	PUNCT
cana-1729	56	38	𝛼𝑖	𝛼𝑖	PROPN
cana-1729	56	39	are	be	AUX
cana-1729	56	40	constants	constant	NOUN
cana-1729	56	41	to	to	PART
cana-1729	56	42	be	be	AUX
cana-1729	56	43	calculated	calculate	VERB
cana-1729	56	44	by	by	ADP
cana-1729	56	45	collocation	collocation	NOUN
cana-1729	56	46	.	.	PUNCT
cana-1729	57	1	in	in	ADP
cana-1729	57	2	the	the	DET
cana-1729	57	3	present	present	ADJ
cana-1729	57	4	paper	paper	NOUN
cana-1729	57	5	,	,	PUNCT
cana-1729	57	6	we	we	PRON
cana-1729	57	7	use	use	VERB
cana-1729	57	8	the	the	DET
cana-1729	57	9	multiquadric	multiquadric	ADJ
cana-1729	57	10	rbf	rbf	PROPN
cana-1729	57	11	which	which	PRON
cana-1729	57	12	is	be	AUX
cana-1729	57	13	given	give	VERB
cana-1729	57	14	by	by	ADP
cana-1729	57	15	𝜙(𝑟	𝜙(𝑟	NOUN
cana-1729	57	16	)	)	PUNCT
cana-1729	57	17	=	=	PUNCT
cana-1729	57	18	√1	√1	PROPN
cana-1729	58	1	+	+	CCONJ
cana-1729	58	2	𝑐2𝑟2	𝑐2𝑟2	X
cana-1729	58	3	where	where	SCONJ
cana-1729	58	4	c	c	NOUN
cana-1729	58	5	is	be	AUX
cana-1729	58	6	a	a	DET
cana-1729	58	7	shape	shape	NOUN
cana-1729	58	8	parameter	parameter	NOUN
cana-1729	58	9	which	which	PRON
cana-1729	58	10	controls	control	VERB
cana-1729	58	11	the	the	DET
cana-1729	58	12	steepness	steepness	NOUN
cana-1729	58	13	of	of	ADP
cana-1729	58	14	the	the	DET
cana-1729	58	15	shape	shape	NOUN
cana-1729	58	16	function	function	NOUN
cana-1729	58	17	.	.	PUNCT
cana-1729	59	1	communications	communication	NOUN
cana-1729	59	2	on	on	ADP
cana-1729	59	3	applied	apply	VERB
cana-1729	59	4	nonlinear	nonlinear	ADJ
cana-1729	59	5	analysis	analysis	NOUN
cana-1729	59	6	issn	issn	NOUN
cana-1729	59	7	:	:	PUNCT
cana-1729	59	8	1074	1074	NUM
cana-1729	59	9	-	-	PUNCT
cana-1729	59	10	133x	133x	NUM
cana-1729	59	11	vol	vol	NOUN
cana-1729	59	12	32	32	NUM
cana-1729	59	13	no	no	NOUN
cana-1729	59	14	.	.	NOUN
cana-1729	59	15	2	2	NUM
cana-1729	59	16	(	(	PUNCT
cana-1729	59	17	2025	2025	NUM
cana-1729	59	18	)	)	PUNCT
cana-1729	59	19	154	154	NUM
cana-1729	59	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1729	59	21	let	let	VERB
cana-1729	59	22	𝑁𝐼	𝑁𝐼	PROPN
cana-1729	59	23	be	be	AUX
cana-1729	59	24	the	the	DET
cana-1729	59	25	set	set	NOUN
cana-1729	59	26	of	of	ADP
cana-1729	59	27	nodes	node	NOUN
cana-1729	59	28	interior	interior	ADJ
cana-1729	59	29	to	to	ADP
cana-1729	59	30	the	the	DET
cana-1729	59	31	solution	solution	NOUN
cana-1729	59	32	domain	domain	NOUN
cana-1729	59	33	i.e.	i.e.	X
cana-1729	59	34	𝑥𝑗	𝑥𝑗	PROPN
cana-1729	59	35	∈	∈	PROPN
cana-1729	59	36	ω	ω	PROPN
cana-1729	59	37	,	,	PUNCT
cana-1729	59	38	let	let	VERB
cana-1729	59	39	𝑁𝐵	𝑁𝐵	PROPN
cana-1729	59	40	be	be	AUX
cana-1729	59	41	the	the	DET
cana-1729	59	42	set	set	NOUN
cana-1729	59	43	of	of	ADP
cana-1729	59	44	distinct	distinct	ADJ
cana-1729	59	45	nodes	node	NOUN
cana-1729	59	46	on	on	ADP
cana-1729	59	47	the	the	DET
cana-1729	59	48	boundary	boundary	NOUN
cana-1729	59	49	i.e.	i.e.	X
cana-1729	59	50	,	,	PUNCT
cana-1729	59	51	𝑥𝑗	𝑥𝑗	PROPN
cana-1729	59	52	∈	∈	PROPN
cana-1729	59	53	𝜕ω	𝜕ω	PROPN
cana-1729	59	54	.	.	PUNCT
cana-1729	60	1	now	now	ADV
cana-1729	60	2	,	,	PUNCT
cana-1729	60	3	applying	apply	VERB
cana-1729	60	4	the	the	DET
cana-1729	60	5	operator	operator	NOUN
cana-1729	60	6	𝓛	𝓛	NOUN
cana-1729	60	7	to	to	ADP
cana-1729	60	8	equation	equation	NOUN
cana-1729	60	9	(	(	PUNCT
cana-1729	60	10	4.3	4.3	NUM
cana-1729	60	11	)	)	PUNCT
cana-1729	60	12	and	and	CCONJ
cana-1729	60	13	by	by	ADP
cana-1729	60	14	multiquadric	multiquadric	ADJ
cana-1729	60	15	collocation	collocation	NOUN
cana-1729	60	16	at	at	ADP
cana-1729	60	17	the	the	DET
cana-1729	60	18	𝑁𝐼	𝑁𝐼	PROPN
cana-1729	60	19	interior	interior	ADJ
cana-1729	60	20	centers	center	NOUN
cana-1729	60	21	,	,	PUNCT
cana-1729	60	22	we	we	PRON
cana-1729	60	23	get	get	VERB
cana-1729	60	24	𝓛𝑢(𝑥𝑖	𝓛𝑢(𝑥𝑖	ADJ
cana-1729	60	25	)	)	PUNCT
cana-1729	60	26	=	=	SYM
cana-1729	60	27	∑	∑	PUNCT
cana-1729	60	28	𝛼𝑗𝓛	𝛼𝑗𝓛	PROPN
cana-1729	60	29	𝑛	𝑛	PRON
cana-1729	60	30	𝑗=1	𝑗=1	PROPN
cana-1729	60	31	𝜙(‖𝑥𝑖	𝜙(‖𝑥𝑖	PROPN
cana-1729	60	32	−	−	PROPN
cana-1729	60	33	𝑥𝑗‖	𝑥𝑗‖	PROPN
cana-1729	60	34	)	)	PUNCT
cana-1729	60	35	;	;	PUNCT
cana-1729	61	1	𝑖	𝑖	X
cana-1729	61	2	=	=	SYM
cana-1729	61	3	1	1	NUM
cana-1729	61	4	,	,	PUNCT
cana-1729	61	5	…	…	PUNCT
cana-1729	61	6	,	,	PUNCT
cana-1729	61	7	𝑁𝐼	𝑁𝐼	PROPN
cana-1729	61	8	(	(	PUNCT
cana-1729	61	9	4.4	4.4	NUM
cana-1729	61	10	)	)	PUNCT
cana-1729	61	11	now	now	ADV
cana-1729	61	12	,	,	PUNCT
cana-1729	61	13	applying	apply	VERB
cana-1729	61	14	the	the	DET
cana-1729	61	15	operator	operator	NOUN
cana-1729	61	16	𝓑	𝓑	ADP
cana-1729	61	17	to	to	ADP
cana-1729	61	18	equation	equation	NOUN
cana-1729	61	19	(	(	PUNCT
cana-1729	61	20	4.3	4.3	NUM
cana-1729	61	21	)	)	PUNCT
cana-1729	61	22	and	and	CCONJ
cana-1729	61	23	by	by	ADP
cana-1729	61	24	multiquadric	multiquadric	ADJ
cana-1729	61	25	collocation	collocation	NOUN
cana-1729	61	26	at	at	ADP
cana-1729	61	27	the	the	DET
cana-1729	61	28	𝑁𝐵	𝑁𝐵	PROPN
cana-1729	61	29	boundary	boundary	ADJ
cana-1729	61	30	centers	center	NOUN
cana-1729	61	31	,	,	PUNCT
cana-1729	61	32	we	we	PRON
cana-1729	61	33	get	get	AUX
cana-1729	61	34	𝓑𝑢(𝑥𝑖	𝓑𝑢(𝑥𝑖	VERB
cana-1729	61	35	)	)	PUNCT
cana-1729	62	1	=	=	PUNCT
cana-1729	62	2	∑	∑	PUNCT
cana-1729	62	3	𝛼𝑗𝓑	𝛼𝑗𝓑	X
cana-1729	62	4	𝑛	𝑛	DET
cana-1729	62	5	𝑗=1	𝑗=1	PROPN
cana-1729	62	6	𝜙(‖𝑥𝑖	𝜙(‖𝑥𝑖	PROPN
cana-1729	62	7	−	−	PROPN
cana-1729	62	8	𝑥𝑗‖	𝑥𝑗‖	PROPN
cana-1729	62	9	)	)	PUNCT
cana-1729	62	10	;	;	PUNCT
cana-1729	62	11	𝑖	𝑖	X
cana-1729	62	12	=	=	PUNCT
cana-1729	62	13	𝑁𝐼+1	𝑁𝐼+1	PROPN
cana-1729	62	14	,	,	PUNCT
cana-1729	62	15	…	…	PUNCT
cana-1729	62	16	,	,	PUNCT
cana-1729	62	17	𝑁	𝑁	PROPN
cana-1729	62	18	(	(	PUNCT
cana-1729	62	19	4.5	4.5	NUM
cana-1729	62	20	)	)	PUNCT
cana-1729	62	21	the	the	DET
cana-1729	62	22	matrix	matrix	NOUN
cana-1729	62	23	form	form	NOUN
cana-1729	62	24	of	of	ADP
cana-1729	62	25	the	the	DET
cana-1729	62	26	right	right	ADJ
cana-1729	62	27	-	-	PUNCT
cana-1729	62	28	hand	hand	NOUN
cana-1729	62	29	sides	side	NOUN
cana-1729	62	30	of	of	ADP
cana-1729	62	31	equations	equation	NOUN
cana-1729	62	32	(	(	PUNCT
cana-1729	62	33	4.4	4.4	NUM
cana-1729	62	34	)	)	PUNCT
cana-1729	62	35	&	&	CCONJ
cana-1729	62	36	(	(	PUNCT
cana-1729	62	37	4.5	4.5	NUM
cana-1729	62	38	)	)	PUNCT
cana-1729	62	39	can	can	AUX
cana-1729	62	40	be	be	AUX
cana-1729	62	41	written	write	VERB
cana-1729	62	42	as	as	ADP
cana-1729	62	43	𝑯𝛼	𝑯𝛼	PROPN
cana-1729	62	44	where	where	SCONJ
cana-1729	62	45	𝑯	𝑯	PROPN
cana-1729	62	46	is	be	AUX
cana-1729	62	47	the	the	DET
cana-1729	62	48	evaluation	evaluation	NOUN
cana-1729	62	49	matrix	matrix	NOUN
cana-1729	62	50	which	which	PRON
cana-1729	62	51	discretizes	discretize	VERB
cana-1729	62	52	the	the	DET
cana-1729	62	53	pde	pde	NOUN
cana-1729	62	54	and	and	CCONJ
cana-1729	62	55	has	have	VERB
cana-1729	62	56	the	the	DET
cana-1729	62	57	following	follow	VERB
cana-1729	62	58	form	form	NOUN
cana-1729	62	59	𝐻	𝐻	NOUN
cana-1729	62	60	=	=	PUNCT
cana-1729	63	1	[	[	PUNCT
cana-1729	63	2	𝓛𝜙	𝓛𝜙	PROPN
cana-1729	63	3	𝓑𝜙	𝓑𝜙	PROPN
cana-1729	63	4	]	]	PUNCT
cana-1729	63	5	(	(	PUNCT
cana-1729	63	6	4.6	4.6	NUM
cana-1729	63	7	)	)	PUNCT
cana-1729	63	8	the	the	DET
cana-1729	63	9	elements	element	NOUN
cana-1729	63	10	of	of	ADP
cana-1729	63	11	𝓛𝜙	𝓛𝜙	PROPN
cana-1729	63	12	&	&	CCONJ
cana-1729	63	13	𝓑𝜙	𝓑𝜙	PROPN
cana-1729	63	14	are	be	AUX
cana-1729	63	15	(	(	PUNCT
cana-1729	63	16	𝓛𝜙)𝑖𝑗	𝓛𝜙)𝑖𝑗	NOUN
cana-1729	63	17	=	=	PUNCT
cana-1729	63	18	𝓛𝜙(‖𝑥𝑖	𝓛𝜙(‖𝑥𝑖	NOUN
cana-1729	63	19	−	−	PROPN
cana-1729	63	20	𝑥𝑗‖	𝑥𝑗‖	PROPN
cana-1729	63	21	)	)	PUNCT
cana-1729	63	22	,	,	PUNCT
cana-1729	63	23	𝑖	𝑖	NOUN
cana-1729	63	24	=	=	SYM
cana-1729	63	25	1	1	NUM
cana-1729	63	26	,	,	PUNCT
cana-1729	63	27	…	…	PUNCT
cana-1729	63	28	,	,	PUNCT
cana-1729	63	29	𝑁𝐼	𝑁𝐼	PROPN
cana-1729	63	30	,	,	PUNCT
cana-1729	63	31	𝑗	𝑗	NOUN
cana-1729	63	32	=	=	SYM
cana-1729	63	33	1	1	NUM
cana-1729	63	34	,	,	PUNCT
cana-1729	63	35	…	…	PUNCT
cana-1729	63	36	,	,	PUNCT
cana-1729	63	37	𝑁	𝑁	PROPN
cana-1729	63	38	(	(	PUNCT
cana-1729	63	39	4.7	4.7	NUM
cana-1729	63	40	)	)	PUNCT
cana-1729	63	41	(	(	PUNCT
cana-1729	63	42	𝓑𝜙)𝑖𝑗	𝓑𝜙)𝑖𝑗	NOUN
cana-1729	63	43	=	=	NOUN
cana-1729	63	44	𝓑𝜙(‖𝑥𝑖	𝓑𝜙(‖𝑥𝑖	NOUN
cana-1729	63	45	−	−	PROPN
cana-1729	63	46	𝑥𝑗‖	𝑥𝑗‖	PROPN
cana-1729	63	47	)	)	PUNCT
cana-1729	63	48	,	,	PUNCT
cana-1729	63	49	𝑖	𝑖	X
cana-1729	64	1	=	=	SYM
cana-1729	64	2	𝑁𝐼+1	𝑁𝐼+1	PROPN
cana-1729	64	3	,	,	PUNCT
cana-1729	64	4	…	…	PUNCT
cana-1729	64	5	,	,	PUNCT
cana-1729	64	6	𝑁	𝑁	PROPN
cana-1729	64	7	,	,	PUNCT
cana-1729	64	8	𝑗	𝑗	NOUN
cana-1729	64	9	=	=	SYM
cana-1729	64	10	1	1	NUM
cana-1729	64	11	,	,	PUNCT
cana-1729	64	12	…	…	PUNCT
cana-1729	64	13	,	,	PUNCT
cana-1729	64	14	𝑁	𝑁	PROPN
cana-1729	64	15	(	(	PUNCT
cana-1729	64	16	4.8	4.8	NUM
cana-1729	64	17	)	)	PUNCT
cana-1729	64	18	now	now	ADV
cana-1729	64	19	,	,	PUNCT
cana-1729	64	20	collocating	collocate	VERB
cana-1729	64	21	equation	equation	NOUN
cana-1729	64	22	(	(	PUNCT
cana-1729	64	23	4.3	4.3	NUM
cana-1729	64	24	)	)	PUNCT
cana-1729	64	25	,	,	PUNCT
cana-1729	64	26	the	the	DET
cana-1729	64	27	matrix	matrix	NOUN
cana-1729	64	28	form	form	NOUN
cana-1729	64	29	is	be	AUX
cana-1729	64	30	𝑢	𝑢	ADJ
cana-1729	64	31	=	=	SYM
cana-1729	64	32	𝐵𝛼	𝐵𝛼	PROPN
cana-1729	64	33	(	(	PUNCT
cana-1729	64	34	4.9	4.9	NUM
cana-1729	64	35	)	)	PUNCT
cana-1729	64	36	where	where	SCONJ
cana-1729	64	37	the	the	DET
cana-1729	64	38	elements	element	NOUN
cana-1729	64	39	of	of	ADP
cana-1729	64	40	𝐵	𝐵	NOUN
cana-1729	64	41	are	be	AUX
cana-1729	64	42	𝑏𝑖𝑗	𝑏𝑖𝑗	ADP
cana-1729	64	43	=	=	SYM
cana-1729	64	44	𝜙(‖𝑥𝑖	𝜙(‖𝑥𝑖	NOUN
cana-1729	64	45	−	−	NOUN
cana-1729	64	46	𝑥𝑗	𝑥𝑗	PROPN
cana-1729	64	47	‖	‖	PROPN
cana-1729	64	48	since	since	SCONJ
cana-1729	64	49	𝐵	𝐵	NOUN
cana-1729	64	50	is	be	AUX
cana-1729	64	51	invertible	invertible	ADJ
cana-1729	64	52	for	for	ADP
cana-1729	64	53	multiquadric	multiquadric	ADJ
cana-1729	64	54	rbf	rbf	PROPN
cana-1729	64	55	(	(	PUNCT
cana-1729	64	56	michelli	michelli	PROPN
cana-1729	64	57	1984	1984	NUM
cana-1729	64	58	)	)	PUNCT
cana-1729	64	59	,	,	PUNCT
cana-1729	64	60	we	we	PRON
cana-1729	64	61	have	have	VERB
cana-1729	64	62	𝛼	𝛼	NOUN
cana-1729	64	63	=	=	PUNCT
cana-1729	64	64	𝐵−1𝑢	𝐵−1𝑢	PROPN
cana-1729	64	65	(	(	PUNCT
cana-1729	64	66	4.10	4.10	NUM
cana-1729	64	67	)	)	PUNCT
cana-1729	64	68	therefore	therefore	ADV
cana-1729	64	69	,	,	PUNCT
cana-1729	64	70	the	the	DET
cana-1729	64	71	matrix	matrix	NOUN
cana-1729	64	72	that	that	PRON
cana-1729	64	73	discretizes	discretize	VERB
cana-1729	64	74	the	the	DET
cana-1729	64	75	pde	pde	NOUN
cana-1729	64	76	in	in	ADP
cana-1729	64	77	space	space	NOUN
cana-1729	64	78	is	be	AUX
cana-1729	64	79	the	the	DET
cana-1729	64	80	differentiation	differentiation	NOUN
cana-1729	64	81	matrix	matrix	NOUN
cana-1729	64	82	(	(	PUNCT
cana-1729	64	83	sarra	sarra	PROPN
cana-1729	64	84	and	and	CCONJ
cana-1729	64	85	kansa	kansa	PROPN
cana-1729	64	86	2009	2009	NUM
cana-1729	64	87	)	)	PUNCT
cana-1729	64	88	,	,	PUNCT
cana-1729	64	89	which	which	PRON
cana-1729	64	90	now	now	ADV
cana-1729	64	91	can	can	AUX
cana-1729	64	92	be	be	AUX
cana-1729	64	93	written	write	VERB
cana-1729	64	94	as	as	ADP
cana-1729	64	95	𝐷	𝐷	NOUN
cana-1729	64	96	=	=	PUNCT
cana-1729	64	97	𝐻𝐵−1	𝐻𝐵−1	NOUN
cana-1729	64	98	(	(	PUNCT
cana-1729	64	99	4.11	4.11	NUM
cana-1729	64	100	)	)	PUNCT
cana-1729	64	101	thus	thus	ADV
cana-1729	64	102	,	,	PUNCT
cana-1729	64	103	after	after	SCONJ
cana-1729	64	104	the	the	DET
cana-1729	64	105	space	space	NOUN
cana-1729	64	106	discretization	discretization	NOUN
cana-1729	64	107	the	the	DET
cana-1729	64	108	pde	pde	NOUN
cana-1729	64	109	(	(	PUNCT
cana-1729	64	110	4.1	4.1	NUM
cana-1729	64	111	)	)	PUNCT
cana-1729	64	112	becomes	become	VERB
cana-1729	64	113	𝑑𝑢	𝑑𝑢	INTJ
cana-1729	64	114	𝑑𝑡	𝑑𝑡	ADP
cana-1729	64	115	=	=	SYM
cana-1729	64	116	𝓛𝑢	𝓛𝑢	PROPN
cana-1729	64	117	≈	≈	PROPN
cana-1729	64	118	𝐷𝑢	𝐷𝑢	PROPN
cana-1729	64	119	(	(	PUNCT
cana-1729	64	120	4.12	4.12	NUM
cana-1729	64	121	)	)	PUNCT
cana-1729	64	122	which	which	PRON
cana-1729	64	123	is	be	AUX
cana-1729	64	124	a	a	DET
cana-1729	64	125	system	system	NOUN
cana-1729	64	126	of	of	ADP
cana-1729	64	127	odes	ode	NOUN
cana-1729	64	128	in	in	ADP
cana-1729	64	129	time	time	NOUN
cana-1729	64	130	and	and	CCONJ
cana-1729	64	131	can	can	AUX
cana-1729	64	132	be	be	AUX
cana-1729	64	133	solved	solve	VERB
cana-1729	64	134	by	by	ADP
cana-1729	64	135	any	any	DET
cana-1729	64	136	standard	standard	ADJ
cana-1729	64	137	ode	ode	PROPN
cana-1729	64	138	solver	solver	NOUN
cana-1729	64	139	,	,	PUNCT
cana-1729	64	140	this	this	DET
cana-1729	64	141	strategy	strategy	NOUN
cana-1729	64	142	is	be	AUX
cana-1729	64	143	commonly	commonly	ADV
cana-1729	64	144	known	know	VERB
cana-1729	64	145	as	as	ADP
cana-1729	64	146	method	method	NOUN
cana-1729	64	147	of	of	ADP
cana-1729	64	148	lines	line	NOUN
cana-1729	64	149	approach	approach	NOUN
cana-1729	64	150	.	.	PUNCT
cana-1729	65	1	4	4	X
cana-1729	65	2	.	.	X
cana-1729	65	3	error	error	NOUN
cana-1729	65	4	estimates	estimate	NOUN
cana-1729	65	5	we	we	PRON
cana-1729	65	6	employ	employ	VERB
cana-1729	65	7	the	the	DET
cana-1729	65	8	following	follow	VERB
cana-1729	65	9	errors	error	NOUN
cana-1729	65	10	to	to	PART
cana-1729	65	11	verify	verify	VERB
cana-1729	65	12	the	the	DET
cana-1729	65	13	proposed	propose	VERB
cana-1729	65	14	method	method	NOUN
cana-1729	65	15	's	's	PART
cana-1729	65	16	accuracy	accuracy	NOUN
cana-1729	65	17	and	and	CCONJ
cana-1729	65	18	validity	validity	NOUN
cana-1729	65	19	.	.	PUNCT
cana-1729	66	1	𝐿2	𝐿2	NOUN
cana-1729	66	2	error	error	NOUN
cana-1729	66	3	norm	norm	NOUN
cana-1729	66	4	:	:	PUNCT
cana-1729	66	5	𝐿2	𝐿2	PROPN
cana-1729	66	6	=	=	PUNCT
cana-1729	66	7	√∑|𝑢𝑗	√∑|𝑢𝑗	NOUN
cana-1729	66	8	−	−	NOUN
cana-1729	66	9	𝑈𝑗|	𝑈𝑗|	NOUN
cana-1729	66	10	2	2	NUM
cana-1729	66	11	𝑁	𝑁	PROPN
cana-1729	66	12	𝑗=1	𝑗=1	PROPN
cana-1729	66	13	(	(	PUNCT
cana-1729	66	14	5.1	5.1	NUM
cana-1729	66	15	)	)	PUNCT
cana-1729	66	16	communications	communication	NOUN
cana-1729	66	17	on	on	ADP
cana-1729	66	18	applied	apply	VERB
cana-1729	66	19	nonlinear	nonlinear	ADJ
cana-1729	66	20	analysis	analysis	NOUN
cana-1729	66	21	issn	issn	NOUN
cana-1729	66	22	:	:	PUNCT
cana-1729	66	23	1074	1074	NUM
cana-1729	66	24	-	-	PUNCT
cana-1729	66	25	133x	133x	NUM
cana-1729	66	26	vol	vol	NOUN
cana-1729	66	27	32	32	NUM
cana-1729	66	28	no	no	NOUN
cana-1729	66	29	.	.	NOUN
cana-1729	66	30	2	2	NUM
cana-1729	66	31	(	(	PUNCT
cana-1729	66	32	2025	2025	NUM
cana-1729	66	33	)	)	PUNCT
cana-1729	66	34	155	155	NUM
cana-1729	66	35	https://internationalpubls.com	https://internationalpubls.com	X
cana-1729	66	36	𝐿∞	𝐿∞	NOUN
cana-1729	66	37	error	error	NOUN
cana-1729	66	38	norm	norm	NOUN
cana-1729	66	39	:	:	PUNCT
cana-1729	66	40	𝐿∞	𝐿∞	NOUN
cana-1729	66	41	=	=	PUNCT
cana-1729	67	1	max	max	PROPN
cana-1729	67	2	𝑗	𝑗	INTJ
cana-1729	67	3	|𝑢𝑗	|𝑢𝑗	NOUN
cana-1729	67	4	−	−	NOUN
cana-1729	67	5	𝑈𝑗|	𝑈𝑗|	NOUN
cana-1729	67	6	(	(	PUNCT
cana-1729	67	7	5.2	5.2	NUM
cana-1729	67	8	)	)	PUNCT
cana-1729	67	9	root	root	NOUN
cana-1729	67	10	mean	mean	ADJ
cana-1729	67	11	square	square	NOUN
cana-1729	67	12	error	error	NOUN
cana-1729	67	13	:	:	PUNCT
cana-1729	67	14	𝑅𝑀𝑆	𝑅𝑀𝑆	PROPN
cana-1729	67	15	=	=	SYM
cana-1729	67	16	1	1	NUM
cana-1729	67	17	𝑁	𝑁	PROPN
cana-1729	67	18	√∑|𝑢𝑗	√∑|𝑢𝑗	NOUN
cana-1729	67	19	−	−	NOUN
cana-1729	67	20	𝑈𝑗|	𝑈𝑗|	NOUN
cana-1729	67	21	2	2	NUM
cana-1729	67	22	𝑁	𝑁	PROPN
cana-1729	67	23	𝑗=1	𝑗=1	PROPN
cana-1729	67	24	(	(	PUNCT
cana-1729	67	25	5.3	5.3	NUM
cana-1729	67	26	)	)	PUNCT
cana-1729	67	27	5	5	NUM
cana-1729	67	28	.	.	NOUN
cana-1729	67	29	results	result	NOUN
cana-1729	67	30	and	and	CCONJ
cana-1729	67	31	discussions	discussion	NOUN
cana-1729	67	32	we	we	PRON
cana-1729	67	33	demonstrate	demonstrate	VERB
cana-1729	67	34	the	the	DET
cana-1729	67	35	numerical	numerical	ADJ
cana-1729	67	36	solutions	solution	NOUN
cana-1729	67	37	for	for	ADP
cana-1729	67	38	the	the	DET
cana-1729	67	39	two	two	NUM
cana-1729	67	40	problems	problem	NOUN
cana-1729	67	41	using	use	VERB
cana-1729	67	42	the	the	DET
cana-1729	67	43	proposed	propose	VERB
cana-1729	67	44	method	method	NOUN
cana-1729	67	45	in	in	ADP
cana-1729	67	46	this	this	DET
cana-1729	67	47	section	section	NOUN
cana-1729	67	48	.	.	PUNCT
cana-1729	68	1	problem	problem	NOUN
cana-1729	68	2	1	1	NUM
cana-1729	68	3	:	:	PUNCT
cana-1729	68	4	the	the	DET
cana-1729	68	5	exact	exact	ADJ
cana-1729	68	6	solution	solution	NOUN
cana-1729	68	7	of	of	ADP
cana-1729	68	8	the	the	DET
cana-1729	68	9	following	follow	VERB
cana-1729	68	10	equation	equation	NOUN
cana-1729	68	11	𝜕𝑢	𝜕𝑢	NOUN
cana-1729	69	1	𝜕𝑡	𝜕𝑡	NOUN
cana-1729	69	2	+	+	CCONJ
cana-1729	69	3	𝛼	𝛼	NOUN
cana-1729	69	4	𝜕𝑢	𝜕𝑢	NOUN
cana-1729	69	5	𝜕𝑥	𝜕𝑥	NOUN
cana-1729	69	6	=	=	PUNCT
cana-1729	69	7	𝛾	𝛾	ADP
cana-1729	69	8	𝜕2𝑢	𝜕2𝑢	PROPN
cana-1729	69	9	𝜕𝑥2	𝜕𝑥2	NOUN
cana-1729	69	10	;	;	PUNCT
cana-1729	69	11	0	0	NUM
cana-1729	69	12	≤	≤	NUM
cana-1729	69	13	𝑥	𝑥	PUNCT
cana-1729	69	14	≤	≤	NUM
cana-1729	69	15	1	1	NUM
cana-1729	69	16	,	,	PUNCT
cana-1729	69	17	0	0	NUM
cana-1729	69	18	≤	≤	NUM
cana-1729	69	19	𝑡	𝑡	PROPN
cana-1729	69	20	≤	≤	ADJ
cana-1729	69	21	𝑇	𝑇	PROPN
cana-1729	69	22	(	(	PUNCT
cana-1729	69	23	6.1	6.1	NUM
cana-1729	69	24	)	)	PUNCT
cana-1729	69	25	with	with	ADP
cana-1729	69	26	𝛼	𝛼	NOUN
cana-1729	69	27	=	=	SYM
cana-1729	69	28	3.5	3.5	NUM
cana-1729	69	29	,	,	PUNCT
cana-1729	69	30	𝛾	𝛾	PROPN
cana-1729	69	31	=	=	SYM
cana-1729	69	32	0.022	0.022	NUM
cana-1729	69	33	is	be	AUX
cana-1729	69	34	given	give	VERB
cana-1729	69	35	by	by	ADP
cana-1729	69	36	(	(	PUNCT
cana-1729	69	37	ismail	ismail	PROPN
cana-1729	69	38	et	et	PROPN
cana-1729	69	39	al	al	PROPN
cana-1729	69	40	.	.	PROPN
cana-1729	69	41	2004	2004	NUM
cana-1729	69	42	)	)	PUNCT
cana-1729	69	43	𝑢(𝑥	𝑢(𝑥	PROPN
cana-1729	69	44	,	,	PUNCT
cana-1729	69	45	𝑡	𝑡	X
cana-1729	69	46	)	)	PUNCT
cana-1729	69	47	=	=	SYM
cana-1729	69	48	𝑒(𝑎𝑥+𝑏𝑡	𝑒(𝑎𝑥+𝑏𝑡	X
cana-1729	69	49	)	)	PUNCT
cana-1729	69	50	(	(	PUNCT
cana-1729	69	51	6.2	6.2	NUM
cana-1729	69	52	)	)	PUNCT
cana-1729	69	53	the	the	DET
cana-1729	69	54	initial	initial	ADJ
cana-1729	69	55	and	and	CCONJ
cana-1729	69	56	boundary	boundary	ADJ
cana-1729	69	57	conditions	condition	NOUN
cana-1729	69	58	can	can	AUX
cana-1729	69	59	be	be	AUX
cana-1729	69	60	obtained	obtain	VERB
cana-1729	69	61	from	from	ADP
cana-1729	69	62	the	the	DET
cana-1729	69	63	exact	exact	ADJ
cana-1729	69	64	solution	solution	NOUN
cana-1729	69	65	.	.	PUNCT
cana-1729	70	1	by	by	ADP
cana-1729	70	2	taking	take	VERB
cana-1729	70	3	𝑎	𝑎	NOUN
cana-1729	70	4	=	=	NOUN
cana-1729	70	5	0.02854797991928	0.02854797991928	NUM
cana-1729	70	6	,	,	PUNCT
cana-1729	70	7	𝑏	𝑏	PROPN
cana-1729	70	8	=	=	SYM
cana-1729	70	9	−0.0999	−0.0999	NOUN
cana-1729	70	10	,	,	PUNCT
cana-1729	70	11	𝑁	𝑁	PROPN
cana-1729	70	12	=	=	SYM
cana-1729	70	13	55	55	NUM
cana-1729	70	14	,	,	PUNCT
cana-1729	70	15	𝑠ℎ𝑎𝑝𝑒	𝑠ℎ𝑎𝑝𝑒	NOUN
cana-1729	70	16	𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟	𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟	NOUN
cana-1729	70	17	=	=	PUNCT
cana-1729	70	18	10	10	NUM
cana-1729	70	19	the	the	DET
cana-1729	70	20	proposed	propose	VERB
cana-1729	70	21	method	method	NOUN
cana-1729	70	22	is	be	AUX
cana-1729	70	23	used	use	VERB
cana-1729	70	24	.	.	PUNCT
cana-1729	71	1	the	the	DET
cana-1729	71	2	results	result	NOUN
cana-1729	71	3	are	be	AUX
cana-1729	71	4	calculated	calculate	VERB
cana-1729	71	5	at	at	ADP
cana-1729	71	6	various	various	ADJ
cana-1729	71	7	time	time	NOUN
cana-1729	71	8	intervals	interval	NOUN
cana-1729	71	9	.	.	PUNCT
cana-1729	72	1	table	table	NOUN
cana-1729	72	2	2	2	NUM
cana-1729	72	3	presents	present	VERB
cana-1729	72	4	the	the	DET
cana-1729	72	5	various	various	ADJ
cana-1729	72	6	error	error	NOUN
cana-1729	72	7	norms	norm	NOUN
cana-1729	72	8	.	.	PUNCT
cana-1729	73	1	the	the	DET
cana-1729	73	2	fig	fig	NOUN
cana-1729	73	3	.	.	PUNCT
cana-1729	74	1	1	1	NUM
cana-1729	74	2	presents	present	VERB
cana-1729	74	3	a	a	DET
cana-1729	74	4	graphical	graphical	ADJ
cana-1729	74	5	comparison	comparison	NOUN
cana-1729	74	6	between	between	ADP
cana-1729	74	7	the	the	DET
cana-1729	74	8	exact	exact	ADJ
cana-1729	74	9	and	and	CCONJ
cana-1729	74	10	approximate	approximate	ADJ
cana-1729	74	11	solutions	solution	NOUN
cana-1729	74	12	of	of	ADP
cana-1729	74	13	the	the	DET
cana-1729	74	14	one	one	NUM
cana-1729	74	15	-	-	PUNCT
cana-1729	74	16	dimensional	dimensional	ADJ
cana-1729	74	17	advection	advection	NOUN
cana-1729	74	18	-	-	PUNCT
cana-1729	74	19	diffusion	diffusion	NOUN
cana-1729	74	20	equation	equation	NOUN
cana-1729	74	21	at	at	ADP
cana-1729	74	22	three	three	NUM
cana-1729	74	23	different	different	ADJ
cana-1729	74	24	time	time	NOUN
cana-1729	74	25	points	point	NOUN
cana-1729	74	26	𝑎𝑡	𝑎𝑡	ADP
cana-1729	74	27	𝑡	𝑡	PROPN
cana-1729	74	28	=	=	SYM
cana-1729	74	29	1	1	NUM
cana-1729	74	30	,	,	PUNCT
cana-1729	74	31	𝑡	𝑡	PROPN
cana-1729	74	32	=	=	SYM
cana-1729	74	33	2	2	NUM
cana-1729	74	34	&	&	CCONJ
cana-1729	74	35	𝑡	𝑡	PROPN
cana-1729	74	36	=	=	PROPN
cana-1729	74	37	3	3	X
cana-1729	74	38	.	.	PUNCT
cana-1729	75	1	the	the	DET
cana-1729	75	2	figure	figure	NOUN
cana-1729	75	3	clearly	clearly	ADV
cana-1729	75	4	shows	show	VERB
cana-1729	75	5	that	that	SCONJ
cana-1729	75	6	the	the	DET
cana-1729	75	7	approximate	approximate	ADJ
cana-1729	75	8	solution	solution	NOUN
cana-1729	75	9	obtained	obtain	VERB
cana-1729	75	10	via	via	ADP
cana-1729	75	11	the	the	DET
cana-1729	75	12	radial	radial	ADJ
cana-1729	75	13	basis	basis	NOUN
cana-1729	75	14	function	function	NOUN
cana-1729	75	15	method	method	NOUN
cana-1729	75	16	of	of	ADP
cana-1729	75	17	lines	line	NOUN
cana-1729	75	18	(	(	PUNCT
cana-1729	75	19	rbfml	rbfml	ADV
cana-1729	75	20	)	)	PUNCT
cana-1729	75	21	method	method	NOUN
cana-1729	75	22	closely	closely	ADV
cana-1729	75	23	matches	match	VERB
cana-1729	75	24	the	the	DET
cana-1729	75	25	exact	exact	ADJ
cana-1729	75	26	solution	solution	NOUN
cana-1729	75	27	at	at	ADP
cana-1729	75	28	all	all	ADV
cana-1729	75	29	displayed	display	VERB
cana-1729	75	30	time	time	NOUN
cana-1729	75	31	points	point	NOUN
cana-1729	75	32	.	.	PUNCT
cana-1729	76	1	this	this	PRON
cana-1729	76	2	demonstrates	demonstrate	VERB
cana-1729	76	3	the	the	DET
cana-1729	76	4	accuracy	accuracy	NOUN
cana-1729	76	5	and	and	CCONJ
cana-1729	76	6	effectiveness	effectiveness	NOUN
cana-1729	76	7	of	of	ADP
cana-1729	76	8	the	the	DET
cana-1729	76	9	rbf	rbf	PROPN
cana-1729	76	10	-	-	PUNCT
cana-1729	76	11	ml	ml	PROPN
cana-1729	76	12	method	method	NOUN
cana-1729	76	13	for	for	ADP
cana-1729	76	14	solving	solve	VERB
cana-1729	76	15	the	the	DET
cana-1729	76	16	one	one	NUM
cana-1729	76	17	-	-	PUNCT
cana-1729	76	18	dimensional	dimensional	ADJ
cana-1729	76	19	advectiondiffusion	advectiondiffusion	NOUN
cana-1729	76	20	equation	equation	NOUN
cana-1729	76	21	.	.	PUNCT
cana-1729	77	1	the	the	DET
cana-1729	77	2	fig	fig	NOUN
cana-1729	77	3	.	.	PUNCT
cana-1729	78	1	2	2	NUM
cana-1729	78	2	visualizes	visualize	VERB
cana-1729	78	3	the	the	DET
cana-1729	78	4	solution	solution	NOUN
cana-1729	78	5	𝑢(𝑥	𝑢(𝑥	PROPN
cana-1729	78	6	,	,	PUNCT
cana-1729	78	7	𝑡	𝑡	X
cana-1729	78	8	)	)	PUNCT
cana-1729	78	9	=	=	SYM
cana-1729	78	10	𝑒(𝑎𝑥+𝑏𝑡	𝑒(𝑎𝑥+𝑏𝑡	X
cana-1729	78	11	)	)	PUNCT
cana-1729	78	12	of	of	ADP
cana-1729	78	13	the	the	DET
cana-1729	78	14	pde	pde	NOUN
cana-1729	78	15	.	.	PUNCT
cana-1729	79	1	the	the	DET
cana-1729	79	2	graph	graph	NOUN
cana-1729	79	3	’s	’s	PART
cana-1729	79	4	surface	surface	NOUN
cana-1729	79	5	shows	show	VERB
cana-1729	79	6	how	how	SCONJ
cana-1729	79	7	𝑢(𝑥	𝑢(𝑥	PROPN
cana-1729	79	8	,	,	PUNCT
cana-1729	79	9	𝑡	𝑡	NOUN
cana-1729	79	10	)	)	PUNCT
cana-1729	79	11	changes	change	NOUN
cana-1729	79	12	exponentially	exponentially	ADV
cana-1729	79	13	over	over	ADP
cana-1729	79	14	space	space	NOUN
cana-1729	79	15	and	and	CCONJ
cana-1729	79	16	time	time	NOUN
cana-1729	79	17	,	,	PUNCT
cana-1729	79	18	with	with	ADP
cana-1729	79	19	the	the	DET
cana-1729	79	20	specific	specific	ADJ
cana-1729	79	21	form	form	NOUN
cana-1729	79	22	of	of	ADP
cana-1729	79	23	this	this	DET
cana-1729	79	24	change	change	NOUN
cana-1729	79	25	depending	depend	VERB
cana-1729	79	26	on	on	ADP
cana-1729	79	27	the	the	DET
cana-1729	79	28	values	value	NOUN
cana-1729	79	29	of	of	ADP
cana-1729	79	30	𝑎	𝑎	PROPN
cana-1729	79	31	&	&	CCONJ
cana-1729	79	32	𝑏.	𝑏.	VERB
cana-1729	79	33	the	the	DET
cana-1729	79	34	color	color	NOUN
cana-1729	79	35	coding	code	VERB
cana-1729	79	36	highlights	highlight	NOUN
cana-1729	79	37	the	the	DET
cana-1729	79	38	magnitude	magnitude	NOUN
cana-1729	79	39	of	of	ADP
cana-1729	79	40	𝑢(𝑥	𝑢(𝑥	PROPN
cana-1729	79	41	,	,	PUNCT
cana-1729	79	42	𝑡	𝑡	PROPN
cana-1729	79	43	)	)	PUNCT
cana-1729	79	44	at	at	ADP
cana-1729	79	45	different	different	ADJ
cana-1729	79	46	points	point	NOUN
cana-1729	79	47	,	,	PUNCT
cana-1729	79	48	indicating	indicate	VERB
cana-1729	79	49	areas	area	NOUN
cana-1729	79	50	of	of	ADP
cana-1729	79	51	higher	high	ADJ
cana-1729	79	52	and	and	CCONJ
cana-1729	79	53	lower	low	ADJ
cana-1729	79	54	values	value	NOUN
cana-1729	79	55	.	.	PUNCT
cana-1729	80	1	figure	figure	NOUN
cana-1729	80	2	1	1	NUM
cana-1729	80	3	.	.	PUNCT
cana-1729	80	4	exact	exact	ADJ
cana-1729	80	5	vs	vs	ADP
cana-1729	80	6	approximate	approximate	ADJ
cana-1729	80	7	solution	solution	NOUN
cana-1729	80	8	of	of	ADP
cana-1729	80	9	problem	problem	NOUN
cana-1729	80	10	1	1	NUM
cana-1729	80	11	at	at	ADP
cana-1729	80	12	𝑡	𝑡	PROPN
cana-1729	80	13	=	=	SYM
cana-1729	80	14	1.0,2.0	1.0,2.0	NUM
cana-1729	80	15	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-1729	80	16	3.0	3.0	NUM
cana-1729	80	17	figure	figure	NOUN
cana-1729	80	18	2	2	NUM
cana-1729	80	19	.	.	NOUN
cana-1729	80	20	3	3	NUM
cana-1729	80	21	-	-	SYM
cana-1729	80	22	d	d	NOUN
cana-1729	80	23	profile	profile	NOUN
cana-1729	80	24	of	of	ADP
cana-1729	80	25	the	the	DET
cana-1729	80	26	exact	exact	ADJ
cana-1729	80	27	solution	solution	NOUN
cana-1729	80	28	of	of	ADP
cana-1729	80	29	problem	problem	NOUN
cana-1729	80	30	1	1	NUM
cana-1729	80	31	for	for	ADP
cana-1729	80	32	𝑎	𝑎	PROPN
cana-1729	80	33	=	=	SYM
cana-1729	80	34	1	1	NUM
cana-1729	80	35	&	&	CCONJ
cana-1729	80	36	𝑏	𝑏	NOUN
cana-1729	80	37	=	=	SYM
cana-1729	80	38	1	1	NUM
cana-1729	80	39	communications	communication	NOUN
cana-1729	80	40	on	on	ADP
cana-1729	80	41	applied	apply	VERB
cana-1729	80	42	nonlinear	nonlinear	ADJ
cana-1729	80	43	analysis	analysis	NOUN
cana-1729	80	44	issn	issn	NOUN
cana-1729	80	45	:	:	PUNCT
cana-1729	80	46	1074	1074	NUM
cana-1729	80	47	-	-	PUNCT
cana-1729	80	48	133x	133x	NUM
cana-1729	80	49	vol	vol	NOUN
cana-1729	80	50	32	32	NUM
cana-1729	80	51	no	no	NOUN
cana-1729	80	52	.	.	NOUN
cana-1729	80	53	2	2	NUM
cana-1729	80	54	(	(	PUNCT
cana-1729	80	55	2025	2025	NUM
cana-1729	80	56	)	)	PUNCT
cana-1729	81	1	156	156	NUM
cana-1729	81	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1729	81	3	table	table	NOUN
cana-1729	81	4	2	2	NUM
cana-1729	81	5	.	.	PUNCT
cana-1729	82	1	different	different	ADJ
cana-1729	82	2	error	error	NOUN
cana-1729	82	3	norms	norm	NOUN
cana-1729	82	4	for	for	ADP
cana-1729	82	5	problem	problem	NOUN
cana-1729	82	6	1	1	NUM
cana-1729	82	7	t	t	NOUN
cana-1729	82	8	𝐿2	𝐿2	PROPN
cana-1729	82	9	𝐿∞	𝐿∞	NOUN
cana-1729	82	10	rms	rm	VERB
cana-1729	82	11	1	1	NUM
cana-1729	82	12	7.8120e-04	7.8120e-04	NUM
cana-1729	82	13	1.1193e-04	1.1193e-04	NUM
cana-1729	82	14	1.0534e-04	1.0534e-04	NUM
cana-1729	82	15	2	2	NUM
cana-1729	82	16	7.0690e-04	7.0690e-04	NUM
cana-1729	82	17	1.0129e-04	1.0129e-04	NUM
cana-1729	82	18	9.5319e-05	9.5319e-05	NUM
cana-1729	82	19	3	3	NUM
cana-1729	82	20	5.8494e-04	5.8494e-04	NUM
cana-1729	82	21	8.4253e-05	8.4253e-05	NUM
cana-1729	82	22	7.8874e-05	7.8874e-05	NUM
cana-1729	82	23	4	4	NUM
cana-1729	82	24	5.2933e-04	5.2933e-04	NUM
cana-1729	82	25	7.6243e-05	7.6243e-05	NUM
cana-1729	82	26	7.1375e-05	7.1375e-05	NUM
cana-1729	82	27	5	5	NUM
cana-1729	82	28	4.7901e-04	4.7901e-04	NUM
cana-1729	82	29	6.8994e-05	6.8994e-05	NUM
cana-1729	82	30	6.4589e-05	6.4589e-05	NUM
cana-1729	82	31	problem	problem	NOUN
cana-1729	82	32	2	2	NUM
cana-1729	82	33	:	:	PUNCT
cana-1729	82	34	the	the	DET
cana-1729	82	35	exact	exact	ADJ
cana-1729	82	36	solution	solution	NOUN
cana-1729	82	37	of	of	ADP
cana-1729	82	38	the	the	DET
cana-1729	82	39	following	follow	VERB
cana-1729	82	40	equation	equation	NOUN
cana-1729	82	41	𝜕𝑢	𝜕𝑢	NOUN
cana-1729	83	1	𝜕𝑡	𝜕𝑡	NOUN
cana-1729	83	2	+	+	CCONJ
cana-1729	83	3	𝛼	𝛼	NOUN
cana-1729	83	4	𝜕𝑢	𝜕𝑢	NOUN
cana-1729	83	5	𝜕𝑥	𝜕𝑥	NOUN
cana-1729	83	6	=	=	PUNCT
cana-1729	83	7	𝛾	𝛾	ADP
cana-1729	83	8	𝜕2𝑢	𝜕2𝑢	PROPN
cana-1729	83	9	𝜕𝑥2	𝜕𝑥2	NOUN
cana-1729	83	10	;	;	PUNCT
cana-1729	83	11	0	0	NUM
cana-1729	83	12	≤	≤	NUM
cana-1729	83	13	𝑥	𝑥	PUNCT
cana-1729	83	14	≤	≤	NUM
cana-1729	83	15	1	1	NUM
cana-1729	83	16	,	,	PUNCT
cana-1729	83	17	0	0	NUM
cana-1729	83	18	≤	≤	NUM
cana-1729	83	19	𝑡	𝑡	PROPN
cana-1729	83	20	≤	≤	ADJ
cana-1729	83	21	𝑇	𝑇	PROPN
cana-1729	83	22	(	(	PUNCT
cana-1729	83	23	6.3	6.3	NUM
cana-1729	83	24	)	)	PUNCT
cana-1729	83	25	with	with	ADP
cana-1729	83	26	𝛼	𝛼	NOUN
cana-1729	83	27	=	=	SYM
cana-1729	83	28	1.0	1.0	NUM
cana-1729	83	29	,	,	PUNCT
cana-1729	83	30	𝛾	𝛾	AUX
cana-1729	83	31	=	=	NOUN
cana-1729	83	32	0.01	0.01	NUM
cana-1729	83	33	is	be	AUX
cana-1729	83	34	given	give	VERB
cana-1729	83	35	by	by	ADP
cana-1729	83	36	(	(	PUNCT
cana-1729	83	37	dehghan	dehghan	PROPN
cana-1729	83	38	2004	2004	NUM
cana-1729	83	39	)	)	PUNCT
cana-1729	84	1	𝑢(𝑥	𝑢(𝑥	PROPN
cana-1729	84	2	,	,	PUNCT
cana-1729	84	3	𝑡	𝑡	X
cana-1729	84	4	)	)	PUNCT
cana-1729	84	5	=	=	PUNCT
cana-1729	84	6	0.025	0.025	NUM
cana-1729	84	7	√0.000625	√0.000625	ADV
cana-1729	84	8	+	+	CCONJ
cana-1729	84	9	0.02𝑡	0.02𝑡	NUM
cana-1729	84	10	𝑒	𝑒	X
cana-1729	84	11	(	(	PUNCT
cana-1729	84	12	𝑥+0.5−𝑡)2	𝑥+0.5−𝑡)2	X
cana-1729	84	13	(	(	PUNCT
cana-1729	84	14	0.00125	0.00125	NUM
cana-1729	84	15	+	+	NOUN
cana-1729	84	16	0.04𝑡	0.04𝑡	NUM
cana-1729	84	17	)	)	PUNCT
cana-1729	84	18	(	(	PUNCT
cana-1729	84	19	6.4	6.4	NUM
cana-1729	84	20	)	)	PUNCT
cana-1729	84	21	the	the	DET
cana-1729	84	22	initial	initial	ADJ
cana-1729	84	23	and	and	CCONJ
cana-1729	84	24	boundary	boundary	ADJ
cana-1729	84	25	conditions	condition	NOUN
cana-1729	84	26	can	can	AUX
cana-1729	84	27	be	be	AUX
cana-1729	84	28	obtained	obtain	VERB
cana-1729	84	29	from	from	ADP
cana-1729	84	30	the	the	DET
cana-1729	84	31	exact	exact	ADJ
cana-1729	84	32	solution	solution	NOUN
cana-1729	84	33	.	.	PUNCT
cana-1729	85	1	we	we	PRON
cana-1729	85	2	take	take	VERB
cana-1729	85	3	𝑁	𝑁	PROPN
cana-1729	85	4	=	=	SYM
cana-1729	85	5	55	55	NUM
cana-1729	85	6	,	,	PUNCT
cana-1729	85	7	𝑠ℎ𝑎𝑝𝑒	𝑠ℎ𝑎𝑝𝑒	NOUN
cana-1729	85	8	𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟	𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟	NOUN
cana-1729	85	9	=	=	PUNCT
cana-1729	85	10	10	10	NUM
cana-1729	85	11	.	.	PUNCT
cana-1729	86	1	the	the	DET
cana-1729	86	2	outcomes	outcome	NOUN
cana-1729	86	3	are	be	AUX
cana-1729	86	4	calculated	calculate	VERB
cana-1729	86	5	at	at	ADP
cana-1729	86	6	various	various	ADJ
cana-1729	86	7	time	time	NOUN
cana-1729	86	8	intervals	interval	NOUN
cana-1729	86	9	.	.	PUNCT
cana-1729	87	1	table	table	NOUN
cana-1729	87	2	3	3	NUM
cana-1729	87	3	presents	present	VERB
cana-1729	87	4	the	the	DET
cana-1729	87	5	various	various	ADJ
cana-1729	87	6	error	error	NOUN
cana-1729	87	7	norms	norm	NOUN
cana-1729	87	8	.	.	PUNCT
cana-1729	88	1	the	the	DET
cana-1729	88	2	fig	fig	NOUN
cana-1729	88	3	.	.	PUNCT
cana-1729	88	4	2	2	NUM
cana-1729	88	5	shows	show	VERB
cana-1729	88	6	a	a	DET
cana-1729	88	7	comparison	comparison	NOUN
cana-1729	88	8	between	between	ADP
cana-1729	88	9	the	the	DET
cana-1729	88	10	exact	exact	ADJ
cana-1729	88	11	and	and	CCONJ
cana-1729	88	12	approximate	approximate	ADJ
cana-1729	88	13	solutions	solution	NOUN
cana-1729	88	14	of	of	ADP
cana-1729	88	15	the	the	DET
cana-1729	88	16	one	one	NUM
cana-1729	88	17	-	-	PUNCT
cana-1729	88	18	dimensional	dimensional	ADJ
cana-1729	88	19	advection	advection	NOUN
cana-1729	88	20	-	-	PUNCT
cana-1729	88	21	diffusion	diffusion	NOUN
cana-1729	88	22	equation	equation	NOUN
cana-1729	88	23	at	at	ADP
cana-1729	88	24	three	three	NUM
cana-1729	88	25	different	different	ADJ
cana-1729	88	26	time	time	NOUN
cana-1729	88	27	points	point	NOUN
cana-1729	88	28	𝑎𝑡	𝑎𝑡	ADP
cana-1729	88	29	𝑡	𝑡	X
cana-1729	88	30	=	=	PROPN
cana-1729	88	31	0.8	0.8	NUM
cana-1729	88	32	,	,	PUNCT
cana-1729	88	33	𝑡	𝑡	X
cana-1729	88	34	=	=	SYM
cana-1729	88	35	1.0	1.0	NUM
cana-1729	88	36	&	&	CCONJ
cana-1729	88	37	𝑡	𝑡	PROPN
cana-1729	88	38	=	=	PROPN
cana-1729	88	39	1.2	1.2	NUM
cana-1729	88	40	.	.	PUNCT
cana-1729	89	1	the	the	DET
cana-1729	89	2	figure	figure	NOUN
cana-1729	89	3	demonstrates	demonstrate	VERB
cana-1729	89	4	that	that	SCONJ
cana-1729	89	5	the	the	DET
cana-1729	89	6	approximate	approximate	ADJ
cana-1729	89	7	solution	solution	NOUN
cana-1729	89	8	obtained	obtain	VERB
cana-1729	89	9	using	use	VERB
cana-1729	89	10	the	the	DET
cana-1729	89	11	radial	radial	ADJ
cana-1729	89	12	basis	basis	NOUN
cana-1729	89	13	function	function	NOUN
cana-1729	89	14	method	method	NOUN
cana-1729	89	15	of	of	ADP
cana-1729	89	16	lines	line	NOUN
cana-1729	89	17	(	(	PUNCT
cana-1729	89	18	rbf	rbf	PROPN
cana-1729	89	19	-	-	PUNCT
cana-1729	89	20	ml	ml	NOUN
cana-1729	89	21	)	)	PUNCT
cana-1729	89	22	closely	closely	ADV
cana-1729	89	23	matches	match	VERB
cana-1729	89	24	the	the	DET
cana-1729	89	25	exact	exact	ADJ
cana-1729	89	26	solution	solution	NOUN
cana-1729	89	27	at	at	ADP
cana-1729	89	28	all	all	DET
cana-1729	89	29	three	three	NUM
cana-1729	89	30	time	time	NOUN
cana-1729	89	31	points	point	NOUN
cana-1729	89	32	.	.	PUNCT
cana-1729	90	1	the	the	DET
cana-1729	90	2	fig	fig	NOUN
cana-1729	90	3	.	.	PUNCT
cana-1729	90	4	3	3	NUM
cana-1729	90	5	provides	provide	VERB
cana-1729	90	6	a	a	DET
cana-1729	90	7	visualization	visualization	NOUN
cana-1729	90	8	of	of	ADP
cana-1729	90	9	how	how	SCONJ
cana-1729	90	10	the	the	DET
cana-1729	90	11	solution	solution	NOUN
cana-1729	90	12	𝑢(𝑥.	𝑢(𝑥.	X
cana-1729	90	13	𝑡	𝑡	NOUN
cana-1729	90	14	)	)	PUNCT
cana-1729	90	15	of	of	ADP
cana-1729	90	16	the	the	DET
cana-1729	90	17	pde	pde	NOUN
cana-1729	90	18	evolves	evolve	VERB
cana-1729	90	19	over	over	ADP
cana-1729	90	20	space	space	NOUN
cana-1729	90	21	and	and	CCONJ
cana-1729	90	22	time	time	NOUN
cana-1729	90	23	.	.	PUNCT
cana-1729	91	1	initially	initially	ADV
cana-1729	91	2	,	,	PUNCT
cana-1729	91	3	𝑢(𝑥	𝑢(𝑥	PROPN
cana-1729	91	4	,	,	PUNCT
cana-1729	91	5	0	0	NUM
cana-1729	91	6	)	)	PUNCT
cana-1729	91	7	is	be	AUX
cana-1729	91	8	concentrated	concentrate	VERB
cana-1729	91	9	around	around	ADP
cana-1729	91	10	𝑥	𝑥	PROPN
cana-1729	91	11	=	=	SYM
cana-1729	91	12	0.5	0.5	NUM
cana-1729	91	13	.	.	PUNCT
cana-1729	92	1	as	as	ADP
cana-1729	92	2	time	time	NOUN
cana-1729	92	3	increases	increase	NOUN
cana-1729	92	4	,	,	PUNCT
cana-1729	92	5	the	the	DET
cana-1729	92	6	peak	peak	NOUN
cana-1729	92	7	value	value	NOUN
cana-1729	92	8	decreases	decrease	NOUN
cana-1729	92	9	and	and	CCONJ
cana-1729	92	10	shifts	shift	NOUN
cana-1729	92	11	towards	towards	ADP
cana-1729	92	12	larger	large	ADJ
cana-1729	92	13	𝑥	𝑥	PROPN
cana-1729	92	14	values	value	NOUN
cana-1729	92	15	,	,	PUNCT
cana-1729	92	16	indicating	indicate	VERB
cana-1729	92	17	both	both	DET
cana-1729	92	18	diffusion	diffusion	NOUN
cana-1729	92	19	(	(	PUNCT
cana-1729	92	20	spreading	spread	VERB
cana-1729	92	21	out	out	ADP
cana-1729	92	22	)	)	PUNCT
cana-1729	92	23	and	and	CCONJ
cana-1729	92	24	advection	advection	NOUN
cana-1729	92	25	(	(	PUNCT
cana-1729	92	26	shifting	shifting	NOUN
cana-1729	92	27	)	)	PUNCT
cana-1729	92	28	of	of	ADP
cana-1729	92	29	the	the	DET
cana-1729	92	30	initial	initial	ADJ
cana-1729	92	31	peak	peak	NOUN
cana-1729	92	32	.	.	PUNCT
cana-1729	93	1	the	the	DET
cana-1729	93	2	color	color	NOUN
cana-1729	93	3	coding	code	VERB
cana-1729	93	4	highlights	highlight	NOUN
cana-1729	93	5	the	the	DET
cana-1729	93	6	magnitude	magnitude	NOUN
cana-1729	93	7	of	of	ADP
cana-1729	93	8	𝑢(𝑥	𝑢(𝑥	PROPN
cana-1729	93	9	,	,	PUNCT
cana-1729	93	10	𝑡	𝑡	PROPN
cana-1729	93	11	)	)	PUNCT
cana-1729	93	12	at	at	ADP
cana-1729	93	13	different	different	ADJ
cana-1729	93	14	points	point	NOUN
cana-1729	93	15	,	,	PUNCT
cana-1729	93	16	with	with	ADP
cana-1729	93	17	the	the	DET
cana-1729	93	18	highest	high	ADJ
cana-1729	93	19	value	value	NOUN
cana-1729	93	20	around	around	ADP
cana-1729	93	21	0.25	0.25	NUM
cana-1729	93	22	at	at	ADP
cana-1729	93	23	𝑡	𝑡	PROPN
cana-1729	93	24	=	=	NOUN
cana-1729	93	25	0	0	NUM
cana-1729	93	26	near	near	ADP
cana-1729	93	27	𝑥	𝑥	NOUN
cana-1729	93	28	=	=	SYM
cana-1729	93	29	0.5	0.5	NUM
cana-1729	93	30	and	and	CCONJ
cana-1729	93	31	decreasing	decrease	VERB
cana-1729	93	32	over	over	ADP
cana-1729	93	33	time	time	NOUN
cana-1729	93	34	.	.	PUNCT
cana-1729	94	1	figure	figure	VERB
cana-1729	94	2	3	3	NUM
cana-1729	94	3	.	.	PUNCT
cana-1729	94	4	exact	exact	ADJ
cana-1729	94	5	vs	vs	ADP
cana-1729	94	6	approximate	approximate	ADJ
cana-1729	94	7	solution	solution	NOUN
cana-1729	94	8	of	of	ADP
cana-1729	94	9	problem	problem	NOUN
cana-1729	94	10	2	2	NUM
cana-1729	94	11	at	at	ADP
cana-1729	94	12	𝑡	𝑡	PROPN
cana-1729	94	13	=	=	PROPN
cana-1729	94	14	0.8,1.0	0.8,1.0	PROPN
cana-1729	94	15	&	&	CCONJ
cana-1729	94	16	1.2	1.2	NUM
cana-1729	94	17	figure	figure	NOUN
cana-1729	94	18	4	4	NUM
cana-1729	94	19	.	.	NOUN
cana-1729	94	20	3	3	NUM
cana-1729	94	21	-	-	SYM
cana-1729	94	22	d	d	NOUN
cana-1729	94	23	profile	profile	NOUN
cana-1729	94	24	of	of	ADP
cana-1729	94	25	the	the	DET
cana-1729	94	26	exact	exact	ADJ
cana-1729	94	27	solution	solution	NOUN
cana-1729	94	28	of	of	ADP
cana-1729	94	29	problem	problem	NOUN
cana-1729	94	30	2	2	NUM
cana-1729	94	31	communications	communication	NOUN
cana-1729	94	32	on	on	ADP
cana-1729	94	33	applied	apply	VERB
cana-1729	94	34	nonlinear	nonlinear	ADJ
cana-1729	94	35	analysis	analysis	NOUN
cana-1729	94	36	issn	issn	NOUN
cana-1729	94	37	:	:	PUNCT
cana-1729	94	38	1074	1074	NUM
cana-1729	94	39	-	-	PUNCT
cana-1729	94	40	133x	133x	NUM
cana-1729	94	41	vol	vol	NOUN
cana-1729	94	42	32	32	NUM
cana-1729	94	43	no	no	NOUN
cana-1729	94	44	.	.	NOUN
cana-1729	94	45	2	2	NUM
cana-1729	94	46	(	(	PUNCT
cana-1729	94	47	2025	2025	NUM
cana-1729	94	48	)	)	PUNCT
cana-1729	94	49	157	157	NUM
cana-1729	94	50	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1729	94	51	table	table	NOUN
cana-1729	94	52	3	3	NUM
cana-1729	94	53	.	.	PUNCT
cana-1729	95	1	different	different	ADJ
cana-1729	95	2	error	error	NOUN
cana-1729	95	3	norms	norm	NOUN
cana-1729	95	4	for	for	ADP
cana-1729	95	5	problem	problem	NOUN
cana-1729	95	6	2	2	NUM
cana-1729	95	7	t	t	NOUN
cana-1729	95	8	𝐿2	𝐿2	PROPN
cana-1729	95	9	𝐿∞	𝐿∞	NOUN
cana-1729	95	10	rms	rm	VERB
cana-1729	95	11	0.6	0.6	NUM
cana-1729	95	12	6.5364e-04	6.5364e-04	NUM
cana-1729	95	13	1.9390e-04	1.9390e-04	NUM
cana-1729	95	14	8.8136e-05	8.8136e-05	NUM
cana-1729	95	15	0.8	0.8	NUM
cana-1729	95	16	5.8509e-04	5.8509e-04	NUM
cana-1729	95	17	1.4811e-04	1.4811e-04	NUM
cana-1729	95	18	7.8894e-05	7.8894e-05	NUM
cana-1729	95	19	1.0	1.0	NUM
cana-1729	95	20	4.9723e-04	4.9723e-04	NUM
cana-1729	95	21	1.1992e-04	1.1992e-04	NUM
cana-1729	95	22	6.7047e-05	6.7047e-05	NUM
cana-1729	95	23	1.2	1.2	NUM
cana-1729	95	24	4.1710e-04	4.1710e-04	NUM
cana-1729	95	25	1.0083e-04	1.0083e-04	NUM
cana-1729	95	26	5.6242e-05	5.6242e-05	NUM
cana-1729	95	27	1.4	1.4	NUM
cana-1729	95	28	2.9361e-04	2.9361e-04	NUM
cana-1729	95	29	8.7017e-05	8.7017e-05	NUM
cana-1729	95	30	3.9591e-05	3.9591e-05	NUM
cana-1729	95	31	6	6	NUM
cana-1729	95	32	.	.	PUNCT
cana-1729	95	33	conclusion	conclusion	NOUN
cana-1729	95	34	in	in	ADP
cana-1729	95	35	this	this	DET
cana-1729	95	36	research	research	NOUN
cana-1729	95	37	,	,	PUNCT
cana-1729	95	38	we	we	PRON
cana-1729	95	39	proposed	propose	VERB
cana-1729	95	40	a	a	DET
cana-1729	95	41	numerical	numerical	ADJ
cana-1729	95	42	solution	solution	NOUN
cana-1729	95	43	for	for	ADP
cana-1729	95	44	the	the	DET
cana-1729	95	45	one	one	NUM
cana-1729	95	46	-	-	PUNCT
cana-1729	95	47	dimensional	dimensional	ADJ
cana-1729	95	48	advection	advection	NOUN
cana-1729	95	49	-	-	PUNCT
cana-1729	95	50	diffusion	diffusion	NOUN
cana-1729	95	51	equation	equation	NOUN
cana-1729	95	52	using	use	VERB
cana-1729	95	53	the	the	DET
cana-1729	95	54	radial	radial	ADJ
cana-1729	95	55	basis	basis	NOUN
cana-1729	95	56	function	function	NOUN
cana-1729	95	57	(	(	PUNCT
cana-1729	95	58	rbf	rbf	PROPN
cana-1729	95	59	)	)	PUNCT
cana-1729	95	60	method	method	NOUN
cana-1729	95	61	of	of	ADP
cana-1729	95	62	lines	line	NOUN
cana-1729	95	63	(	(	PUNCT
cana-1729	95	64	mol	mol	NOUN
cana-1729	95	65	)	)	PUNCT
cana-1729	95	66	.	.	PUNCT
cana-1729	96	1	the	the	DET
cana-1729	96	2	asymmetric	asymmetric	ADJ
cana-1729	96	3	multiquadric	multiquadric	ADJ
cana-1729	96	4	collocation	collocation	NOUN
cana-1729	96	5	method	method	NOUN
cana-1729	96	6	was	be	AUX
cana-1729	96	7	applied	apply	VERB
cana-1729	96	8	for	for	ADP
cana-1729	96	9	spatial	spatial	ADJ
cana-1729	96	10	discretization	discretization	NOUN
cana-1729	96	11	,	,	PUNCT
cana-1729	96	12	and	and	CCONJ
cana-1729	96	13	the	the	DET
cana-1729	96	14	fourth	fourth	ADJ
cana-1729	96	15	-	-	PUNCT
cana-1729	96	16	order	order	NOUN
cana-1729	96	17	rungekutta	rungekutta	NOUN
cana-1729	96	18	method	method	NOUN
cana-1729	96	19	was	be	AUX
cana-1729	96	20	utilized	utilize	VERB
cana-1729	96	21	to	to	PART
cana-1729	96	22	solve	solve	VERB
cana-1729	96	23	the	the	DET
cana-1729	96	24	resulting	result	VERB
cana-1729	96	25	system	system	NOUN
cana-1729	96	26	of	of	ADP
cana-1729	96	27	ordinary	ordinary	ADJ
cana-1729	96	28	differential	differential	ADJ
cana-1729	96	29	equations	equation	NOUN
cana-1729	96	30	.	.	PUNCT
cana-1729	97	1	the	the	DET
cana-1729	97	2	numerical	numerical	ADJ
cana-1729	97	3	results	result	NOUN
cana-1729	97	4	for	for	ADP
cana-1729	97	5	the	the	DET
cana-1729	97	6	two	two	NUM
cana-1729	97	7	test	test	NOUN
cana-1729	97	8	problems	problem	NOUN
cana-1729	97	9	demonstrated	demonstrate	VERB
cana-1729	97	10	that	that	SCONJ
cana-1729	97	11	the	the	DET
cana-1729	97	12	rbf	rbf	PROPN
cana-1729	97	13	-	-	PUNCT
cana-1729	97	14	mol	mol	PROPN
cana-1729	97	15	approach	approach	NOUN
cana-1729	97	16	closely	closely	ADV
cana-1729	97	17	approximates	approximate	VERB
cana-1729	97	18	the	the	DET
cana-1729	97	19	exact	exact	ADJ
cana-1729	97	20	solutions	solution	NOUN
cana-1729	97	21	,	,	PUNCT
cana-1729	97	22	with	with	ADP
cana-1729	97	23	a	a	DET
cana-1729	97	24	high	high	ADJ
cana-1729	97	25	degree	degree	NOUN
cana-1729	97	26	of	of	ADP
cana-1729	97	27	accuracy	accuracy	NOUN
cana-1729	97	28	across	across	ADP
cana-1729	97	29	various	various	ADJ
cana-1729	97	30	time	time	NOUN
cana-1729	97	31	intervals	interval	NOUN
cana-1729	97	32	.	.	PUNCT
cana-1729	98	1	the	the	DET
cana-1729	98	2	proposed	propose	VERB
cana-1729	98	3	method	method	NOUN
cana-1729	98	4	shows	show	VERB
cana-1729	98	5	significant	significant	ADJ
cana-1729	98	6	potential	potential	NOUN
cana-1729	98	7	for	for	ADP
cana-1729	98	8	solving	solve	VERB
cana-1729	98	9	linear	linear	ADJ
cana-1729	98	10	advection	advection	NOUN
cana-1729	98	11	-	-	PUNCT
cana-1729	98	12	diffusion	diffusion	NOUN
cana-1729	98	13	problems	problem	NOUN
cana-1729	98	14	with	with	ADP
cana-1729	98	15	complex	complex	ADJ
cana-1729	98	16	initial	initial	ADJ
cana-1729	98	17	and	and	CCONJ
cana-1729	98	18	boundary	boundary	ADJ
cana-1729	98	19	conditions	condition	NOUN
cana-1729	98	20	.	.	PUNCT
cana-1729	99	1	the	the	DET
cana-1729	99	2	accuracy	accuracy	NOUN
cana-1729	99	3	,	,	PUNCT
cana-1729	99	4	flexibility	flexibility	NOUN
cana-1729	99	5	,	,	PUNCT
cana-1729	99	6	and	and	CCONJ
cana-1729	99	7	ease	ease	NOUN
cana-1729	99	8	of	of	ADP
cana-1729	99	9	implementation	implementation	NOUN
cana-1729	99	10	make	make	VERB
cana-1729	99	11	this	this	DET
cana-1729	99	12	approach	approach	NOUN
cana-1729	99	13	a	a	DET
cana-1729	99	14	valuable	valuable	ADJ
cana-1729	99	15	tool	tool	NOUN
cana-1729	99	16	in	in	ADP
cana-1729	99	17	computational	computational	ADJ
cana-1729	99	18	physics	physics	NOUN
cana-1729	99	19	and	and	CCONJ
cana-1729	99	20	numerical	numerical	ADJ
cana-1729	99	21	analysis	analysis	NOUN
cana-1729	99	22	.	.	PUNCT
cana-1729	100	1	additionally	additionally	ADV
cana-1729	100	2	,	,	PUNCT
cana-1729	100	3	the	the	DET
cana-1729	100	4	method	method	NOUN
cana-1729	100	5	's	's	PART
cana-1729	100	6	capability	capability	NOUN
cana-1729	100	7	to	to	PART
cana-1729	100	8	handle	handle	VERB
cana-1729	100	9	problems	problem	NOUN
cana-1729	100	10	dominated	dominate	VERB
cana-1729	100	11	by	by	ADP
cana-1729	100	12	both	both	DET
cana-1729	100	13	advection	advection	NOUN
cana-1729	100	14	and	and	CCONJ
cana-1729	100	15	diffusion	diffusion	NOUN
cana-1729	100	16	highlights	highlight	NOUN
cana-1729	100	17	its	its	PRON
cana-1729	100	18	versatility	versatility	NOUN
cana-1729	100	19	.	.	PUNCT
cana-1729	101	1	future	future	ADJ
cana-1729	101	2	research	research	NOUN
cana-1729	101	3	may	may	AUX
cana-1729	101	4	focus	focus	VERB
cana-1729	101	5	on	on	ADP
cana-1729	101	6	extending	extend	VERB
cana-1729	101	7	this	this	DET
cana-1729	101	8	method	method	NOUN
cana-1729	101	9	to	to	ADP
cana-1729	101	10	higher	higher	ADV
cana-1729	101	11	-	-	PUNCT
cana-1729	101	12	dimensional	dimensional	ADJ
cana-1729	101	13	problems	problem	NOUN
cana-1729	101	14	or	or	CCONJ
cana-1729	101	15	exploring	explore	VERB
cana-1729	101	16	its	its	PRON
cana-1729	101	17	application	application	NOUN
cana-1729	101	18	to	to	ADP
cana-1729	101	19	nonlinear	nonlinear	ADJ
cana-1729	101	20	advection	advection	NOUN
cana-1729	101	21	-	-	PUNCT
cana-1729	101	22	diffusion	diffusion	NOUN
cana-1729	101	23	equations	equation	NOUN
cana-1729	101	24	.	.	PUNCT
cana-1729	102	1	references	reference	NOUN
cana-1729	102	2	[	[	X
cana-1729	102	3	1	1	X
cana-1729	102	4	]	]	PUNCT
cana-1729	102	5	d.	d.	PROPN
cana-1729	102	6	k.	k.	PROPN
cana-1729	102	7	jaiswal	jaiswal	PROPN
cana-1729	102	8	,	,	PUNCT
cana-1729	102	9	a.	a.	PROPN
cana-1729	102	10	kumar	kumar	PROPN
cana-1729	102	11	,	,	PUNCT
cana-1729	102	12	r.	r.	PROPN
cana-1729	102	13	r.	r.	PROPN
cana-1729	102	14	yadav	yadav	PROPN
cana-1729	102	15	,	,	PUNCT
cana-1729	102	16	analytical	analytical	ADJ
cana-1729	102	17	solution	solution	NOUN
cana-1729	102	18	to	to	ADP
cana-1729	102	19	the	the	DET
cana-1729	102	20	one	one	NUM
cana-1729	102	21	-	-	PUNCT
cana-1729	102	22	dimensional	dimensional	ADJ
cana-1729	102	23	advection	advection	NOUN
cana-1729	102	24	-	-	PUNCT
cana-1729	102	25	diffusion	diffusion	NOUN
cana-1729	102	26	equation	equation	NOUN
cana-1729	102	27	with	with	ADP
cana-1729	102	28	temporally	temporally	ADV
cana-1729	102	29	dependent	dependent	ADJ
cana-1729	102	30	coefficients	coefficient	NOUN
cana-1729	102	31	,	,	PUNCT
cana-1729	102	32	journal	journal	NOUN
cana-1729	102	33	of	of	ADP
cana-1729	102	34	water	water	NOUN
cana-1729	102	35	resource	resource	NOUN
cana-1729	102	36	and	and	CCONJ
cana-1729	102	37	protection	protection	NOUN
cana-1729	102	38	,	,	PUNCT
cana-1729	102	39	3	3	NUM
cana-1729	102	40	(	(	PUNCT
cana-1729	102	41	2011	2011	NUM
cana-1729	102	42	)	)	PUNCT
cana-1729	102	43	,	,	PUNCT
cana-1729	102	44	76	76	NUM
cana-1729	102	45	-	-	SYM
cana-1729	102	46	84	84	NUM
cana-1729	102	47	.	.	PUNCT
cana-1729	103	1	[	[	X
cana-1729	103	2	2	2	NUM
cana-1729	103	3	]	]	PUNCT
cana-1729	103	4	a.	a.	NOUN
cana-1729	103	5	mojtabi	mojtabi	PROPN
cana-1729	103	6	,	,	PUNCT
cana-1729	103	7	m.	m.	NOUN
cana-1729	103	8	o.	o.	PROPN
cana-1729	103	9	deville	deville	PROPN
cana-1729	103	10	,	,	PUNCT
cana-1729	103	11	one	one	NUM
cana-1729	103	12	-	-	PUNCT
cana-1729	103	13	dimensional	dimensional	ADJ
cana-1729	103	14	linear	linear	ADJ
cana-1729	103	15	advection	advection	NOUN
cana-1729	103	16	-	-	PUNCT
cana-1729	103	17	diffusion	diffusion	NOUN
cana-1729	103	18	equation	equation	NOUN
cana-1729	103	19	:	:	PUNCT
cana-1729	103	20	analytical	analytical	ADJ
cana-1729	103	21	and	and	CCONJ
cana-1729	103	22	finite	finite	ADJ
cana-1729	103	23	element	element	NOUN
cana-1729	103	24	solutions	solution	NOUN
cana-1729	103	25	,	,	PUNCT
cana-1729	103	26	computers	computer	NOUN
cana-1729	103	27	&	&	CCONJ
cana-1729	103	28	fluids	fluid	NOUN
cana-1729	103	29	,	,	PUNCT
cana-1729	103	30	107	107	NUM
cana-1729	103	31	(	(	PUNCT
cana-1729	103	32	2015	2015	NUM
cana-1729	103	33	)	)	PUNCT
cana-1729	103	34	,	,	PUNCT
cana-1729	103	35	189	189	NUM
cana-1729	103	36	-	-	SYM
cana-1729	103	37	195	195	NUM
cana-1729	103	38	.	.	PUNCT
cana-1729	104	1	[	[	X
cana-1729	104	2	3	3	X
cana-1729	104	3	]	]	PUNCT
cana-1729	104	4	s.	s.	PROPN
cana-1729	104	5	gane	gane	PROPN
cana-1729	104	6	,	,	PUNCT
cana-1729	104	7	solution	solution	NOUN
cana-1729	104	8	of	of	ADP
cana-1729	104	9	the	the	DET
cana-1729	104	10	advection	advection	NOUN
cana-1729	104	11	equation	equation	NOUN
cana-1729	104	12	using	use	VERB
cana-1729	104	13	finite	finite	ADJ
cana-1729	104	14	difference	difference	NOUN
cana-1729	104	15	schemes	scheme	NOUN
cana-1729	104	16	and	and	CCONJ
cana-1729	104	17	the	the	DET
cana-1729	104	18	method	method	NOUN
cana-1729	104	19	of	of	ADP
cana-1729	104	20	characteristics	characteristic	NOUN
cana-1729	104	21	,	,	PUNCT
cana-1729	104	22	phd	phd	NOUN
cana-1729	104	23	thesis	thesis	NOUN
cana-1729	104	24	,	,	PUNCT
cana-1729	104	25	university	university	NOUN
cana-1729	104	26	of	of	ADP
cana-1729	104	27	glasgow	glasgow	PROPN
cana-1729	104	28	,	,	PUNCT
cana-1729	104	29	(	(	PUNCT
cana-1729	104	30	2000	2000	NUM
cana-1729	104	31	)	)	PUNCT
cana-1729	104	32	.	.	PUNCT
cana-1729	105	1	[	[	X
cana-1729	105	2	4	4	NUM
cana-1729	105	3	]	]	PUNCT
cana-1729	105	4	a.	a.	NOUN
cana-1729	105	5	kumar	kumar	PROPN
cana-1729	105	6	,	,	PUNCT
cana-1729	105	7	d.	d.	PROPN
cana-1729	105	8	k.	k.	PROPN
cana-1729	105	9	jaiswal	jaiswal	PROPN
cana-1729	105	10	,	,	PUNCT
cana-1729	105	11	n.	n.	PROPN
cana-1729	105	12	kumar	kumar	PROPN
cana-1729	105	13	,	,	PUNCT
cana-1729	105	14	analytical	analytical	ADJ
cana-1729	105	15	solutions	solution	NOUN
cana-1729	105	16	of	of	ADP
cana-1729	105	17	one	one	NUM
cana-1729	105	18	-	-	PUNCT
cana-1729	105	19	dimensional	dimensional	ADJ
cana-1729	105	20	advection	advection	NOUN
cana-1729	105	21	–	–	PUNCT
cana-1729	105	22	diffusion	diffusion	NOUN
cana-1729	105	23	equation	equation	NOUN
cana-1729	105	24	with	with	ADP
cana-1729	105	25	variable	variable	ADJ
cana-1729	105	26	coefficients	coefficient	NOUN
cana-1729	105	27	in	in	ADP
cana-1729	105	28	a	a	DET
cana-1729	105	29	finite	finite	ADJ
cana-1729	105	30	domain	domain	NOUN
cana-1729	105	31	,	,	PUNCT
cana-1729	105	32	journal	journal	NOUN
cana-1729	105	33	of	of	ADP
cana-1729	105	34	earth	earth	NOUN
cana-1729	105	35	system	system	NOUN
cana-1729	105	36	science	science	NOUN
cana-1729	105	37	,	,	PUNCT
cana-1729	105	38	118	118	NUM
cana-1729	105	39	(	(	PUNCT
cana-1729	105	40	2009	2009	NUM
cana-1729	105	41	)	)	PUNCT
cana-1729	105	42	,	,	PUNCT
cana-1729	105	43	539	539	NUM
cana-1729	105	44	-	-	SYM
cana-1729	105	45	549	549	NUM
cana-1729	105	46	.	.	PUNCT
cana-1729	106	1	[	[	X
cana-1729	106	2	5	5	NUM
cana-1729	106	3	]	]	PUNCT
cana-1729	106	4	a.	a.	PROPN
cana-1729	106	5	r.	r.	PROPN
cana-1729	106	6	appadu	appadu	PROPN
cana-1729	106	7	,	,	PUNCT
cana-1729	106	8	numerical	numerical	ADJ
cana-1729	106	9	solution	solution	NOUN
cana-1729	106	10	of	of	ADP
cana-1729	106	11	the	the	DET
cana-1729	106	12	1d	1d	NUM
cana-1729	106	13	advection	advection	NOUN
cana-1729	106	14	-	-	PUNCT
cana-1729	106	15	diffusion	diffusion	NOUN
cana-1729	106	16	equation	equation	NOUN
cana-1729	106	17	using	use	VERB
cana-1729	106	18	standard	standard	ADJ
cana-1729	106	19	and	and	CCONJ
cana-1729	106	20	nonstandard	nonstandard	ADJ
cana-1729	106	21	finite	finite	ADJ
cana-1729	106	22	difference	difference	NOUN
cana-1729	106	23	schemes	scheme	NOUN
cana-1729	106	24	,	,	PUNCT
cana-1729	106	25	journal	journal	NOUN
cana-1729	106	26	of	of	ADP
cana-1729	106	27	applied	apply	VERB
cana-1729	106	28	mathematics	mathematic	NOUN
cana-1729	106	29	,	,	PUNCT
cana-1729	106	30	2013	2013	NUM
cana-1729	106	31	(	(	PUNCT
cana-1729	106	32	2013	2013	NUM
cana-1729	106	33	)	)	PUNCT
cana-1729	106	34	,	,	PUNCT
cana-1729	106	35	734374	734374	NUM
cana-1729	106	36	.	.	PUNCT
cana-1729	107	1	[	[	X
cana-1729	107	2	6	6	NUM
cana-1729	107	3	]	]	PUNCT
cana-1729	107	4	r.	r.	PROPN
cana-1729	107	5	szymkiewicz	szymkiewicz	PROPN
cana-1729	107	6	,	,	PUNCT
cana-1729	107	7	numerical	numerical	ADJ
cana-1729	107	8	solution	solution	NOUN
cana-1729	107	9	of	of	ADP
cana-1729	107	10	the	the	DET
cana-1729	107	11	advection	advection	NOUN
cana-1729	107	12	-	-	PUNCT
cana-1729	107	13	diffusion	diffusion	NOUN
cana-1729	107	14	equation	equation	NOUN
cana-1729	107	15	,	,	PUNCT
cana-1729	107	16	in	in	ADP
cana-1729	107	17	:	:	PUNCT
cana-1729	107	18	numerical	numerical	ADJ
cana-1729	107	19	modeling	modeling	NOUN
cana-1729	107	20	in	in	ADP
cana-1729	107	21	open	open	ADJ
cana-1729	107	22	channel	channel	NOUN
cana-1729	107	23	hydraulics	hydraulic	NOUN
cana-1729	107	24	.	.	PUNCT
cana-1729	108	1	water	water	NOUN
cana-1729	108	2	science	science	NOUN
cana-1729	108	3	and	and	CCONJ
cana-1729	108	4	technology	technology	NOUN
cana-1729	108	5	library	library	NOUN
cana-1729	108	6	,	,	PUNCT
cana-1729	108	7	vol	vol	NOUN
cana-1729	108	8	83	83	NUM
cana-1729	108	9	.	.	PUNCT
cana-1729	108	10	springer	springer	NOUN
cana-1729	108	11	,	,	PUNCT
cana-1729	108	12	dordrecht	dordrecht	PROPN
cana-1729	108	13	,	,	PUNCT
cana-1729	108	14	(	(	PUNCT
cana-1729	108	15	2010	2010	NUM
cana-1729	108	16	)	)	PUNCT
cana-1729	108	17	.	.	PUNCT
cana-1729	109	1	[	[	X
cana-1729	109	2	7	7	X
cana-1729	109	3	]	]	X
cana-1729	109	4	r.	r.	PROPN
cana-1729	109	5	c.	c.	PROPN
cana-1729	109	6	mittal	mittal	PROPN
cana-1729	109	7	,	,	PUNCT
cana-1729	109	8	r.	r.	PROPN
cana-1729	109	9	k.	k.	PROPN
cana-1729	109	10	jain	jain	PROPN
cana-1729	109	11	,	,	PUNCT
cana-1729	109	12	redefined	redefine	VERB
cana-1729	109	13	cubic	cubic	ADJ
cana-1729	109	14	b	b	NOUN
cana-1729	109	15	-	-	PUNCT
cana-1729	109	16	splines	spline	NOUN
cana-1729	109	17	collocation	collocation	NOUN
cana-1729	109	18	method	method	NOUN
cana-1729	109	19	for	for	ADP
cana-1729	109	20	solving	solve	VERB
cana-1729	109	21	convection	convection	NOUN
cana-1729	109	22	-	-	PUNCT
cana-1729	109	23	diffusion	diffusion	NOUN
cana-1729	109	24	equations	equation	NOUN
cana-1729	109	25	,	,	PUNCT
cana-1729	109	26	applied	apply	VERB
cana-1729	109	27	mathematical	mathematical	ADJ
cana-1729	109	28	modelling	modelling	NOUN
cana-1729	109	29	,	,	PUNCT
cana-1729	109	30	36	36	NUM
cana-1729	109	31	(	(	PUNCT
cana-1729	109	32	2012	2012	NUM
cana-1729	109	33	)	)	PUNCT
cana-1729	109	34	,	,	PUNCT
cana-1729	109	35	5555	5555	NUM
cana-1729	109	36	-	-	SYM
cana-1729	109	37	5573	5573	NUM
cana-1729	109	38	.	.	PUNCT
cana-1729	110	1	[	[	X
cana-1729	110	2	8	8	NUM
cana-1729	110	3	]	]	X
cana-1729	110	4	h.	h.	PROPN
cana-1729	110	5	karahan	karahan	PROPN
cana-1729	110	6	,	,	PUNCT
cana-1729	110	7	implicit	implicit	ADJ
cana-1729	110	8	finite	finite	ADJ
cana-1729	110	9	difference	difference	NOUN
cana-1729	110	10	techniques	technique	NOUN
cana-1729	110	11	for	for	ADP
cana-1729	110	12	the	the	DET
cana-1729	110	13	advection	advection	NOUN
cana-1729	110	14	-	-	PUNCT
cana-1729	110	15	diffusion	diffusion	NOUN
cana-1729	110	16	equation	equation	NOUN
cana-1729	110	17	using	use	VERB
cana-1729	110	18	spreadsheets	spreadsheet	NOUN
cana-1729	110	19	,	,	PUNCT
cana-1729	110	20	advances	advance	NOUN
cana-1729	110	21	in	in	ADP
cana-1729	110	22	engineering	engineering	NOUN
cana-1729	110	23	software	software	NOUN
cana-1729	110	24	,	,	PUNCT
cana-1729	110	25	37	37	NUM
cana-1729	110	26	(	(	PUNCT
cana-1729	110	27	2006	2006	NUM
cana-1729	110	28	)	)	PUNCT
cana-1729	110	29	,	,	PUNCT
cana-1729	110	30	601	601	NUM
cana-1729	110	31	-	-	NOUN
cana-1729	110	32	608	608	NUM
cana-1729	110	33	.	.	PUNCT
cana-1729	111	1	[	[	X
cana-1729	111	2	9	9	NUM
cana-1729	111	3	]	]	PUNCT
cana-1729	111	4	w.	w.	NOUN
cana-1729	111	5	hundsdorfer	hundsdorfer	PROPN
cana-1729	111	6	,	,	PUNCT
cana-1729	111	7	j.	j.	PROPN
cana-1729	111	8	verwer	verwer	PROPN
cana-1729	111	9	,	,	PUNCT
cana-1729	111	10	numerical	numerical	ADJ
cana-1729	111	11	solution	solution	NOUN
cana-1729	111	12	of	of	ADP
cana-1729	111	13	time	time	NOUN
cana-1729	111	14	-	-	PUNCT
cana-1729	111	15	dependent	dependent	ADJ
cana-1729	111	16	advection	advection	NOUN
cana-1729	111	17	-	-	PUNCT
cana-1729	111	18	diffusion	diffusion	NOUN
cana-1729	111	19	-	-	PUNCT
cana-1729	111	20	reaction	reaction	NOUN
cana-1729	111	21	equations	equation	NOUN
cana-1729	111	22	,	,	PUNCT
cana-1729	111	23	springer	springer	NOUN
cana-1729	111	24	,	,	PUNCT
cana-1729	111	25	berlin	berlin	PROPN
cana-1729	111	26	,	,	PUNCT
cana-1729	111	27	heidelberg	heidelberg	PROPN
cana-1729	111	28	,	,	PUNCT
cana-1729	111	29	(	(	PUNCT
cana-1729	111	30	2003	2003	NUM
cana-1729	111	31	)	)	PUNCT
cana-1729	111	32	.	.	PUNCT
cana-1729	112	1	[	[	X
cana-1729	112	2	10	10	NUM
cana-1729	112	3	]	]	X
cana-1729	112	4	e.	e.	PROPN
cana-1729	112	5	larsson	larsson	PROPN
cana-1729	112	6	,	,	PUNCT
cana-1729	112	7	b.	b.	PROPN
cana-1729	112	8	fornberg	fornberg	PROPN
cana-1729	112	9	,	,	PUNCT
cana-1729	112	10	a	a	DET
cana-1729	112	11	numerical	numerical	ADJ
cana-1729	112	12	study	study	NOUN
cana-1729	112	13	of	of	ADP
cana-1729	112	14	some	some	DET
cana-1729	112	15	radial	radial	ADJ
cana-1729	112	16	basis	basis	NOUN
cana-1729	112	17	function	function	NOUN
cana-1729	112	18	-	-	PUNCT
cana-1729	112	19	based	base	VERB
cana-1729	112	20	solution	solution	NOUN
cana-1729	112	21	methods	method	NOUN
cana-1729	112	22	for	for	ADP
cana-1729	112	23	elliptic	elliptic	ADJ
cana-1729	112	24	pdes	pde	NOUN
cana-1729	112	25	,	,	PUNCT
cana-1729	112	26	computers	computer	NOUN
cana-1729	112	27	&	&	CCONJ
cana-1729	112	28	mathematics	mathematics	PROPN
cana-1729	112	29	with	with	ADP
cana-1729	112	30	applications	application	NOUN
cana-1729	112	31	,	,	PUNCT
cana-1729	112	32	46	46	NUM
cana-1729	112	33	(	(	PUNCT
cana-1729	112	34	2003	2003	NUM
cana-1729	112	35	)	)	PUNCT
cana-1729	112	36	,	,	PUNCT
cana-1729	112	37	891	891	NUM
cana-1729	112	38	-	-	SYM
cana-1729	112	39	902	902	NUM
cana-1729	112	40	.	.	PUNCT
cana-1729	113	1	[	[	X
cana-1729	113	2	11	11	NUM
cana-1729	113	3	]	]	PUNCT
cana-1729	113	4	s.	s.	PROPN
cana-1729	113	5	dasari	dasari	PROPN
cana-1729	113	6	,	,	PUNCT
cana-1729	113	7	a.	a.	NOUN
cana-1729	113	8	parikh	parikh	PROPN
cana-1729	113	9	,	,	PUNCT
cana-1729	113	10	meshless	meshless	ADJ
cana-1729	113	11	radial	radial	ADJ
cana-1729	113	12	basis	basis	NOUN
cana-1729	113	13	function	function	NOUN
cana-1729	113	14	pseudo	pseudo	NOUN
cana-1729	113	15	-	-	ADJ
cana-1729	113	16	spectral	spectral	ADJ
cana-1729	113	17	method	method	NOUN
cana-1729	113	18	for	for	ADP
cana-1729	113	19	solving	solve	VERB
cana-1729	113	20	non	non	ADJ
cana-1729	113	21	-	-	ADJ
cana-1729	113	22	linear	linear	ADJ
cana-1729	113	23	kdv	kdv	NOUN
cana-1729	113	24	equation	equation	NOUN
cana-1729	113	25	,	,	PUNCT
cana-1729	113	26	communications	communication	NOUN
cana-1729	113	27	in	in	ADP
cana-1729	113	28	mathematics	mathematic	NOUN
cana-1729	113	29	and	and	CCONJ
cana-1729	113	30	applications	application	NOUN
cana-1729	113	31	,	,	PUNCT
cana-1729	113	32	14	14	NUM
cana-1729	113	33	(	(	PUNCT
cana-1729	113	34	2023	2023	NUM
cana-1729	113	35	)	)	PUNCT
cana-1729	113	36	,	,	PUNCT
cana-1729	113	37	1153	1153	NUM
cana-1729	113	38	-	-	SYM
cana-1729	113	39	1160	1160	NUM
cana-1729	113	40	.	.	PUNCT
cana-1729	114	1	communications	communication	NOUN
cana-1729	114	2	on	on	ADP
cana-1729	114	3	applied	apply	VERB
cana-1729	114	4	nonlinear	nonlinear	ADJ
cana-1729	114	5	analysis	analysis	NOUN
cana-1729	114	6	issn	issn	NOUN
cana-1729	114	7	:	:	PUNCT
cana-1729	114	8	1074	1074	NUM
cana-1729	114	9	-	-	PUNCT
cana-1729	114	10	133x	133x	NUM
cana-1729	114	11	vol	vol	NOUN
cana-1729	114	12	32	32	NUM
cana-1729	114	13	no	no	NOUN
cana-1729	114	14	.	.	NOUN
cana-1729	114	15	2	2	NUM
cana-1729	114	16	(	(	PUNCT
cana-1729	114	17	2025	2025	NUM
cana-1729	114	18	)	)	PUNCT
cana-1729	114	19	158	158	NUM
cana-1729	114	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1729	115	1	[	[	X
cana-1729	115	2	12	12	NUM
cana-1729	115	3	]	]	X
cana-1729	115	4	c.	c.	PROPN
cana-1729	115	5	a.	a.	PROPN
cana-1729	115	6	michelli	michelli	PROPN
cana-1729	115	7	,	,	PUNCT
cana-1729	115	8	interpolation	interpolation	NOUN
cana-1729	115	9	of	of	ADP
cana-1729	115	10	scattered	scatter	VERB
cana-1729	115	11	data	datum	NOUN
cana-1729	115	12	:	:	PUNCT
cana-1729	115	13	distance	distance	NOUN
cana-1729	115	14	matrices	matrix	NOUN
cana-1729	115	15	and	and	CCONJ
cana-1729	115	16	conditionally	conditionally	ADV
cana-1729	115	17	positive	positive	ADJ
cana-1729	115	18	definite	definite	ADJ
cana-1729	115	19	functions	function	NOUN
cana-1729	115	20	,	,	PUNCT
cana-1729	115	21	in	in	ADP
cana-1729	115	22	:	:	PUNCT
cana-1729	115	23	approximation	approximation	NOUN
cana-1729	115	24	theory	theory	NOUN
cana-1729	115	25	and	and	CCONJ
cana-1729	115	26	spline	spline	NOUN
cana-1729	115	27	functions	function	NOUN
cana-1729	115	28	,	,	PUNCT
cana-1729	115	29	nato	nato	PROPN
cana-1729	115	30	asi	asi	PROPN
cana-1729	115	31	series	series	PROPN
cana-1729	115	32	,	,	PUNCT
cana-1729	115	33	vol	vol	NOUN
cana-1729	115	34	136	136	NUM
cana-1729	115	35	.	.	PUNCT
cana-1729	116	1	springer	springer	NOUN
cana-1729	116	2	,	,	PUNCT
cana-1729	116	3	dordrecht	dordrecht	PROPN
cana-1729	116	4	,	,	PUNCT
cana-1729	116	5	(	(	PUNCT
cana-1729	116	6	1984	1984	NUM
cana-1729	116	7	)	)	PUNCT
cana-1729	116	8	.	.	PUNCT
cana-1729	117	1	[	[	X
cana-1729	117	2	13	13	NUM
cana-1729	117	3	]	]	PUNCT
cana-1729	117	4	s.	s.	PROPN
cana-1729	117	5	a.	a.	PROPN
cana-1729	117	6	sarra	sarra	PROPN
cana-1729	117	7	,	,	PUNCT
cana-1729	117	8	e.	e.	PROPN
cana-1729	117	9	j.	j.	PROPN
cana-1729	117	10	kansa	kansa	PROPN
cana-1729	117	11	,	,	PUNCT
cana-1729	117	12	multiquadric	multiquadric	ADJ
cana-1729	117	13	radial	radial	ADJ
cana-1729	117	14	basis	basis	NOUN
cana-1729	117	15	function	function	NOUN
cana-1729	117	16	approximation	approximation	NOUN
cana-1729	117	17	methods	method	NOUN
cana-1729	117	18	for	for	ADP
cana-1729	117	19	the	the	DET
cana-1729	117	20	numerical	numerical	ADJ
cana-1729	117	21	solution	solution	NOUN
cana-1729	117	22	of	of	ADP
cana-1729	117	23	partial	partial	ADJ
cana-1729	117	24	differential	differential	NOUN
cana-1729	117	25	equations	equation	NOUN
cana-1729	117	26	,	,	PUNCT
cana-1729	117	27	advances	advance	NOUN
cana-1729	117	28	in	in	ADP
cana-1729	117	29	computational	computational	ADJ
cana-1729	117	30	mechanics	mechanic	NOUN
cana-1729	117	31	,	,	PUNCT
cana-1729	117	32	2	2	NUM
cana-1729	117	33	(	(	PUNCT
cana-1729	117	34	2009	2009	NUM
cana-1729	117	35	)	)	PUNCT
cana-1729	117	36	,	,	PUNCT
cana-1729	117	37	220	220	NUM
cana-1729	117	38	.	.	PUNCT
cana-1729	118	1	[	[	X
cana-1729	118	2	14	14	NUM
cana-1729	118	3	]	]	X
cana-1729	118	4	h.	h.	PROPN
cana-1729	118	5	n.	n.	PROPN
cana-1729	118	6	a.	a.	PROPN
cana-1729	118	7	ismail	ismail	PROPN
cana-1729	118	8	,	,	PUNCT
cana-1729	118	9	e.	e.	PROPN
cana-1729	118	10	m.	m.	PROPN
cana-1729	118	11	e.	e.	PROPN
cana-1729	118	12	elbarbary	elbarbary	PROPN
cana-1729	118	13	,	,	PUNCT
cana-1729	118	14	g.	g.	PROPN
cana-1729	118	15	s.	s.	PROPN
cana-1729	118	16	e.	e.	PROPN
cana-1729	118	17	salem	salem	PROPN
cana-1729	118	18	,	,	PUNCT
cana-1729	118	19	restrictive	restrictive	ADJ
cana-1729	118	20	taylor	taylor	PROPN
cana-1729	118	21	's	's	PART
cana-1729	118	22	approximation	approximation	NOUN
cana-1729	118	23	for	for	ADP
cana-1729	118	24	solving	solve	VERB
cana-1729	118	25	convectiondiffusion	convectiondiffusion	NOUN
cana-1729	118	26	equation	equation	NOUN
cana-1729	118	27	,	,	PUNCT
cana-1729	118	28	applied	apply	VERB
cana-1729	118	29	mathematics	mathematic	NOUN
cana-1729	118	30	and	and	CCONJ
cana-1729	118	31	computation	computation	NOUN
cana-1729	118	32	,	,	PUNCT
cana-1729	118	33	147	147	NUM
cana-1729	118	34	(	(	PUNCT
cana-1729	118	35	2004	2004	NUM
cana-1729	118	36	)	)	PUNCT
cana-1729	118	37	,	,	PUNCT
cana-1729	118	38	355	355	NUM
cana-1729	118	39	-	-	SYM
cana-1729	118	40	363	363	NUM
cana-1729	118	41	.	.	PUNCT
cana-1729	119	1	[	[	X
cana-1729	119	2	15	15	NUM
cana-1729	119	3	]	]	X
cana-1729	119	4	m.	m.	NOUN
cana-1729	119	5	dehghan	dehghan	PROPN
cana-1729	119	6	,	,	PUNCT
cana-1729	119	7	weighted	weight	VERB
cana-1729	119	8	finite	finite	ADJ
cana-1729	119	9	difference	difference	NOUN
cana-1729	119	10	techniques	technique	NOUN
cana-1729	119	11	for	for	ADP
cana-1729	119	12	the	the	DET
cana-1729	119	13	one	one	NUM
cana-1729	119	14	-	-	PUNCT
cana-1729	119	15	dimensional	dimensional	ADJ
cana-1729	119	16	advection	advection	NOUN
cana-1729	119	17	-	-	PUNCT
cana-1729	119	18	diffusion	diffusion	NOUN
cana-1729	119	19	equation	equation	NOUN
cana-1729	119	20	,	,	PUNCT
cana-1729	119	21	applied	apply	VERB
cana-1729	119	22	mathematics	mathematic	NOUN
cana-1729	119	23	and	and	CCONJ
cana-1729	119	24	computation	computation	NOUN
cana-1729	119	25	,	,	PUNCT
cana-1729	119	26	147	147	NUM
cana-1729	119	27	(	(	PUNCT
cana-1729	119	28	2004	2004	NUM
cana-1729	119	29	)	)	PUNCT
cana-1729	119	30	,	,	PUNCT
cana-1729	119	31	307	307	NUM
cana-1729	119	32	-	-	SYM
cana-1729	119	33	319	319	NUM
cana-1729	119	34	.	.	PUNCT