id	sid	tid	token	lemma	pos
ejpam-6524	1	1	european	european	PROPN
ejpam-6524	1	2	journal	journal	PROPN
ejpam-6524	1	3	of	of	ADP
ejpam-6524	1	4	pure	pure	ADJ
ejpam-6524	1	5	and	and	CCONJ
ejpam-6524	1	6	applied	applied	ADJ
ejpam-6524	1	7	mathematics	mathematic	NOUN
ejpam-6524	1	8	2025	2025	NUM
ejpam-6524	1	9	,	,	PUNCT
ejpam-6524	1	10	vol	vol	NOUN
ejpam-6524	1	11	.	.	PROPN
ejpam-6524	1	12	18	18	NUM
ejpam-6524	1	13	,	,	PUNCT
ejpam-6524	1	14	issue	issue	NOUN
ejpam-6524	1	15	3	3	NUM
ejpam-6524	1	16	,	,	PUNCT
ejpam-6524	1	17	article	article	NOUN
ejpam-6524	1	18	number	number	NOUN
ejpam-6524	1	19	6524	6524	NUM
ejpam-6524	1	20	issn	issn	VERB
ejpam-6524	1	21	1307	1307	NUM
ejpam-6524	1	22	-	-	SYM
ejpam-6524	1	23	5543	5543	NUM
ejpam-6524	1	24	–	–	PUNCT
ejpam-6524	1	25	ejpam.com	ejpam.com	X
ejpam-6524	1	26	published	publish	VERB
ejpam-6524	1	27	by	by	ADP
ejpam-6524	1	28	new	new	PROPN
ejpam-6524	1	29	york	york	PROPN
ejpam-6524	1	30	business	business	PROPN
ejpam-6524	1	31	global	global	ADJ
ejpam-6524	1	32	finite	finite	PROPN
ejpam-6524	1	33	elements	element	NOUN
ejpam-6524	1	34	method	method	NOUN
ejpam-6524	1	35	for	for	ADP
ejpam-6524	1	36	solving	solve	VERB
ejpam-6524	1	37	elliptic	elliptic	ADJ
ejpam-6524	1	38	and	and	CCONJ
ejpam-6524	1	39	hyperbolic	hyperbolic	ADJ
ejpam-6524	1	40	partial	partial	ADJ
ejpam-6524	1	41	differential	differential	NOUN
ejpam-6524	1	42	equations	equation	NOUN
ejpam-6524	1	43	abdulkafi	abdulkafi	PROPN
ejpam-6524	1	44	mohammed	mohammed	PROPN
ejpam-6524	1	45	saeed1,∗	saeed1,∗	PROPN
ejpam-6524	1	46	,	,	PUNCT
ejpam-6524	1	47	shahad	shahad	VERB
ejpam-6524	1	48	saleh	saleh	PROPN
ejpam-6524	1	49	ayad	ayad	PROPN
ejpam-6524	1	50	almutairi1	almutairi1	PROPN
ejpam-6524	1	51	1	1	NUM
ejpam-6524	1	52	department	department	NOUN
ejpam-6524	1	53	of	of	ADP
ejpam-6524	1	54	mathematics	mathematic	NOUN
ejpam-6524	1	55	,	,	PUNCT
ejpam-6524	1	56	college	college	NOUN
ejpam-6524	1	57	of	of	ADP
ejpam-6524	1	58	science	science	NOUN
ejpam-6524	1	59	,	,	PUNCT
ejpam-6524	1	60	qassim	qassim	PROPN
ejpam-6524	1	61	university	university	PROPN
ejpam-6524	1	62	,	,	PUNCT
ejpam-6524	1	63	buraydah	buraydah	NOUN
ejpam-6524	1	64	,	,	PUNCT
ejpam-6524	1	65	kingdom	kingdom	NOUN
ejpam-6524	1	66	of	of	ADP
ejpam-6524	1	67	saudi	saudi	PROPN
ejpam-6524	1	68	arabia	arabia	PROPN
ejpam-6524	1	69	abstract	abstract	NOUN
ejpam-6524	1	70	.	.	PUNCT
ejpam-6524	2	1	in	in	ADP
ejpam-6524	2	2	various	various	ADJ
ejpam-6524	2	3	disciplines	discipline	NOUN
ejpam-6524	2	4	of	of	ADP
ejpam-6524	2	5	engineering	engineering	NOUN
ejpam-6524	2	6	such	such	ADJ
ejpam-6524	2	7	as	as	ADP
ejpam-6524	2	8	hydrodynamics	hydrodynamic	NOUN
ejpam-6524	2	9	,	,	PUNCT
ejpam-6524	2	10	heat	heat	NOUN
ejpam-6524	2	11	conduction	conduction	NOUN
ejpam-6524	2	12	,	,	PUNCT
ejpam-6524	2	13	geomechanics	geomechanic	NOUN
ejpam-6524	2	14	,	,	PUNCT
ejpam-6524	2	15	civil	civil	ADJ
ejpam-6524	2	16	engineering	engineering	NOUN
ejpam-6524	2	17	,	,	PUNCT
ejpam-6524	2	18	nuclear	nuclear	ADJ
ejpam-6524	2	19	,	,	PUNCT
ejpam-6524	2	20	and	and	CCONJ
ejpam-6524	2	21	even	even	ADV
ejpam-6524	2	22	biomedical	biomedical	ADJ
ejpam-6524	2	23	,	,	PUNCT
ejpam-6524	2	24	the	the	DET
ejpam-6524	2	25	finite	finite	ADJ
ejpam-6524	2	26	element	element	NOUN
ejpam-6524	2	27	method	method	NOUN
ejpam-6524	2	28	(	(	PUNCT
ejpam-6524	2	29	fem	fem	NOUN
ejpam-6524	2	30	)	)	PUNCT
ejpam-6524	2	31	is	be	AUX
ejpam-6524	2	32	known	know	VERB
ejpam-6524	2	33	to	to	PART
ejpam-6524	2	34	be	be	AUX
ejpam-6524	2	35	an	an	DET
ejpam-6524	2	36	effective	effective	ADJ
ejpam-6524	2	37	and	and	CCONJ
ejpam-6524	2	38	sophisticated	sophisticated	ADJ
ejpam-6524	2	39	technique	technique	NOUN
ejpam-6524	2	40	to	to	PART
ejpam-6524	2	41	tackle	tackle	VERB
ejpam-6524	2	42	complex	complex	ADJ
ejpam-6524	2	43	computational	computational	ADJ
ejpam-6524	2	44	problems	problem	NOUN
ejpam-6524	2	45	.	.	PUNCT
ejpam-6524	3	1	the	the	DET
ejpam-6524	3	2	main	main	ADJ
ejpam-6524	3	3	idea	idea	NOUN
ejpam-6524	3	4	of	of	ADP
ejpam-6524	3	5	fem	fem	NOUN
ejpam-6524	3	6	is	be	AUX
ejpam-6524	3	7	to	to	PART
ejpam-6524	3	8	break	break	VERB
ejpam-6524	3	9	down	down	ADP
ejpam-6524	3	10	a	a	DET
ejpam-6524	3	11	complicated	complicated	ADJ
ejpam-6524	3	12	space	space	NOUN
ejpam-6524	3	13	or	or	CCONJ
ejpam-6524	3	14	domain	domain	NOUN
ejpam-6524	3	15	into	into	ADP
ejpam-6524	3	16	a	a	DET
ejpam-6524	3	17	number	number	NOUN
ejpam-6524	3	18	of	of	ADP
ejpam-6524	3	19	small	small	ADJ
ejpam-6524	3	20	,	,	PUNCT
ejpam-6524	3	21	countable	countable	ADJ
ejpam-6524	3	22	,	,	PUNCT
ejpam-6524	3	23	and	and	CCONJ
ejpam-6524	3	24	finite	finite	ADJ
ejpam-6524	3	25	elements	element	NOUN
ejpam-6524	3	26	,	,	PUNCT
ejpam-6524	3	27	or	or	CCONJ
ejpam-6524	3	28	“	"	PUNCT
ejpam-6524	3	29	finite	finite	ADJ
ejpam-6524	3	30	elements	element	NOUN
ejpam-6524	3	31	”	"	PUNCT
ejpam-6524	3	32	by	by	ADP
ejpam-6524	3	33	approximation	approximation	NOUN
ejpam-6524	3	34	methods	method	NOUN
ejpam-6524	3	35	whose	whose	DET
ejpam-6524	3	36	behavioral	behavioral	ADJ
ejpam-6524	3	37	outputs	output	NOUN
ejpam-6524	3	38	could	could	AUX
ejpam-6524	3	39	be	be	AUX
ejpam-6524	3	40	predicted	predict	VERB
ejpam-6524	3	41	using	use	VERB
ejpam-6524	3	42	simpler	simple	ADJ
ejpam-6524	3	43	equations	equation	NOUN
ejpam-6524	3	44	.	.	PUNCT
ejpam-6524	4	1	in	in	ADP
ejpam-6524	4	2	this	this	DET
ejpam-6524	4	3	work	work	NOUN
ejpam-6524	4	4	,	,	PUNCT
ejpam-6524	4	5	we	we	PRON
ejpam-6524	4	6	will	will	AUX
ejpam-6524	4	7	analyze	analyze	VERB
ejpam-6524	4	8	the	the	DET
ejpam-6524	4	9	comparison	comparison	NOUN
ejpam-6524	4	10	between	between	ADP
ejpam-6524	4	11	the	the	DET
ejpam-6524	4	12	finite	finite	ADJ
ejpam-6524	4	13	difference	difference	NOUN
ejpam-6524	4	14	method	method	NOUN
ejpam-6524	4	15	(	(	PUNCT
ejpam-6524	4	16	fdm	fdm	NOUN
ejpam-6524	4	17	)	)	PUNCT
ejpam-6524	4	18	and	and	CCONJ
ejpam-6524	4	19	fem	fem	NOUN
ejpam-6524	4	20	in	in	ADP
ejpam-6524	4	21	order	order	NOUN
ejpam-6524	4	22	to	to	PART
ejpam-6524	4	23	see	see	VERB
ejpam-6524	4	24	the	the	DET
ejpam-6524	4	25	effectiveness	effectiveness	NOUN
ejpam-6524	4	26	of	of	ADP
ejpam-6524	4	27	each	each	DET
ejpam-6524	4	28	method	method	NOUN
ejpam-6524	4	29	.	.	PUNCT
ejpam-6524	5	1	within	within	ADP
ejpam-6524	5	2	the	the	DET
ejpam-6524	5	3	scope	scope	NOUN
ejpam-6524	5	4	of	of	ADP
ejpam-6524	5	5	this	this	DET
ejpam-6524	5	6	research	research	NOUN
ejpam-6524	5	7	,	,	PUNCT
ejpam-6524	5	8	several	several	ADJ
ejpam-6524	5	9	types	type	NOUN
ejpam-6524	5	10	of	of	ADP
ejpam-6524	5	11	partial	partial	ADJ
ejpam-6524	5	12	differential	differential	ADJ
ejpam-6524	5	13	equations	equation	NOUN
ejpam-6524	5	14	(	(	PUNCT
ejpam-6524	5	15	pdes	pde	NOUN
ejpam-6524	5	16	)	)	PUNCT
ejpam-6524	5	17	will	will	AUX
ejpam-6524	5	18	be	be	AUX
ejpam-6524	5	19	solved	solve	VERB
ejpam-6524	5	20	with	with	ADP
ejpam-6524	5	21	fem	fem	NOUN
ejpam-6524	5	22	to	to	PART
ejpam-6524	5	23	estimate	estimate	VERB
ejpam-6524	5	24	a	a	DET
ejpam-6524	5	25	solution	solution	NOUN
ejpam-6524	5	26	that	that	PRON
ejpam-6524	5	27	is	be	AUX
ejpam-6524	5	28	as	as	ADV
ejpam-6524	5	29	accurate	accurate	ADJ
ejpam-6524	5	30	as	as	ADP
ejpam-6524	5	31	possible	possible	ADJ
ejpam-6524	5	32	to	to	ADP
ejpam-6524	5	33	the	the	DET
ejpam-6524	5	34	exact	exact	ADJ
ejpam-6524	5	35	answer	answer	NOUN
ejpam-6524	5	36	.	.	PUNCT
ejpam-6524	6	1	computations	computation	NOUN
ejpam-6524	6	2	will	will	AUX
ejpam-6524	6	3	be	be	AUX
ejpam-6524	6	4	completed	complete	VERB
ejpam-6524	6	5	with	with	ADP
ejpam-6524	6	6	the	the	DET
ejpam-6524	6	7	matlab	matlab	PROPN
ejpam-6524	6	8	software	software	NOUN
ejpam-6524	6	9	,	,	PUNCT
ejpam-6524	6	10	and	and	CCONJ
ejpam-6524	6	11	a	a	DET
ejpam-6524	6	12	discussion	discussion	NOUN
ejpam-6524	6	13	will	will	AUX
ejpam-6524	6	14	follow	follow	VERB
ejpam-6524	6	15	.	.	PUNCT
ejpam-6524	7	1	2020	2020	NUM
ejpam-6524	7	2	mathematics	mathematic	NOUN
ejpam-6524	7	3	subject	subject	NOUN
ejpam-6524	7	4	classifications	classification	NOUN
ejpam-6524	7	5	:	:	PUNCT
ejpam-6524	7	6	76s05	76s05	NUM
ejpam-6524	7	7	,	,	PUNCT
ejpam-6524	7	8	76d10	76d10	NUM
ejpam-6524	7	9	,	,	PUNCT
ejpam-6524	7	10	80a32	80a32	NUM
ejpam-6524	7	11	,	,	PUNCT
ejpam-6524	7	12	35q79	35q79	NUM
ejpam-6524	7	13	key	key	ADJ
ejpam-6524	7	14	words	word	NOUN
ejpam-6524	7	15	and	and	CCONJ
ejpam-6524	7	16	phrases	phrase	NOUN
ejpam-6524	7	17	:	:	PUNCT
ejpam-6524	7	18	boundary	boundary	ADJ
ejpam-6524	7	19	value	value	NOUN
ejpam-6524	7	20	problem	problem	NOUN
ejpam-6524	7	21	,	,	PUNCT
ejpam-6524	7	22	finite	finite	ADJ
ejpam-6524	7	23	difference	difference	NOUN
ejpam-6524	7	24	method	method	NOUN
ejpam-6524	7	25	,	,	PUNCT
ejpam-6524	7	26	galerkin	galerkin	PROPN
ejpam-6524	7	27	finite	finite	PROPN
ejpam-6524	7	28	element	element	PROPN
ejpam-6524	7	29	method	method	NOUN
ejpam-6524	7	30	,	,	PUNCT
ejpam-6524	7	31	poisson	poisson	PROPN
ejpam-6524	7	32	’s	’s	PART
ejpam-6524	7	33	equation	equation	NOUN
ejpam-6524	7	34	,	,	PUNCT
ejpam-6524	7	35	wave	wave	NOUN
ejpam-6524	7	36	equation	equation	NOUN
ejpam-6524	7	37	1	1	NUM
ejpam-6524	7	38	.	.	PUNCT
ejpam-6524	8	1	introduction	introduction	NOUN
ejpam-6524	8	2	physicists	physicist	NOUN
ejpam-6524	8	3	and	and	CCONJ
ejpam-6524	8	4	engineers	engineer	NOUN
ejpam-6524	8	5	apply	apply	VERB
ejpam-6524	8	6	poisson	poisson	NOUN
ejpam-6524	8	7	’s	’s	PART
ejpam-6524	8	8	equation	equation	NOUN
ejpam-6524	8	9	to	to	PART
ejpam-6524	8	10	solve	solve	VERB
ejpam-6524	8	11	problems	problem	NOUN
ejpam-6524	8	12	in	in	ADP
ejpam-6524	8	13	areas	area	NOUN
ejpam-6524	8	14	including	include	VERB
ejpam-6524	8	15	electrostatics	electrostatic	NOUN
ejpam-6524	8	16	,	,	PUNCT
ejpam-6524	8	17	magnetostatics	magnetostatic	NOUN
ejpam-6524	8	18	,	,	PUNCT
ejpam-6524	8	19	quantum	quantum	NOUN
ejpam-6524	8	20	mechanics	mechanic	NOUN
ejpam-6524	8	21	,	,	PUNCT
ejpam-6524	8	22	and	and	CCONJ
ejpam-6524	8	23	fluid	fluid	PROPN
ejpam-6524	8	24	dynamics.poisson	dynamics.poisson	PROPN
ejpam-6524	8	25	’s	’s	PART
ejpam-6524	8	26	equation	equation	NOUN
ejpam-6524	8	27	explains	explain	VERB
ejpam-6524	8	28	the	the	DET
ejpam-6524	8	29	relationship	relationship	NOUN
ejpam-6524	8	30	between	between	ADP
ejpam-6524	8	31	the	the	DET
ejpam-6524	8	32	electric	electric	ADJ
ejpam-6524	8	33	potential	potential	NOUN
ejpam-6524	8	34	and	and	CCONJ
ejpam-6524	8	35	the	the	DET
ejpam-6524	8	36	charge	charge	NOUN
ejpam-6524	8	37	distribution	distribution	NOUN
ejpam-6524	8	38	in	in	ADP
ejpam-6524	8	39	electrostatics	electrostatic	NOUN
ejpam-6524	8	40	.	.	PUNCT
ejpam-6524	9	1	it	it	PRON
ejpam-6524	9	2	links	link	VERB
ejpam-6524	9	3	the	the	DET
ejpam-6524	9	4	current	current	ADJ
ejpam-6524	9	5	distribution	distribution	NOUN
ejpam-6524	9	6	and	and	CCONJ
ejpam-6524	9	7	the	the	DET
ejpam-6524	9	8	magnetic	magnetic	ADJ
ejpam-6524	9	9	potential	potential	NOUN
ejpam-6524	9	10	in	in	ADP
ejpam-6524	9	11	magnetostatics	magnetostatic	NOUN
ejpam-6524	9	12	.	.	PUNCT
ejpam-6524	10	1	this	this	DET
ejpam-6524	10	2	equation	equation	NOUN
ejpam-6524	10	3	is	be	AUX
ejpam-6524	10	4	vital	vital	ADJ
ejpam-6524	10	5	for	for	ADP
ejpam-6524	10	6	scientists	scientist	NOUN
ejpam-6524	10	7	and	and	CCONJ
ejpam-6524	10	8	engineers	engineer	NOUN
ejpam-6524	10	9	since	since	SCONJ
ejpam-6524	10	10	it	it	PRON
ejpam-6524	10	11	aids	aid	VERB
ejpam-6524	10	12	in	in	ADP
ejpam-6524	10	13	comprehending	comprehend	VERB
ejpam-6524	10	14	how	how	SCONJ
ejpam-6524	10	15	various	various	ADJ
ejpam-6524	10	16	physical	physical	ADJ
ejpam-6524	10	17	systems	system	NOUN
ejpam-6524	10	18	behave	behave	VERB
ejpam-6524	10	19	[	[	X
ejpam-6524	10	20	1–4	1–4	NOUN
ejpam-6524	10	21	]	]	X
ejpam-6524	10	22	.	.	PUNCT
ejpam-6524	11	1	the	the	DET
ejpam-6524	11	2	wave	wave	NOUN
ejpam-6524	11	3	equation	equation	NOUN
ejpam-6524	11	4	describes	describe	VERB
ejpam-6524	11	5	the	the	DET
ejpam-6524	11	6	propagation	propagation	NOUN
ejpam-6524	11	7	of	of	ADP
ejpam-6524	11	8	sound	sound	ADJ
ejpam-6524	11	9	,	,	PUNCT
ejpam-6524	11	10	light	light	ADJ
ejpam-6524	11	11	,	,	PUNCT
ejpam-6524	11	12	water	water	NOUN
ejpam-6524	11	13	waves	wave	NOUN
ejpam-6524	11	14	,	,	PUNCT
ejpam-6524	11	15	and	and	CCONJ
ejpam-6524	11	16	other	other	ADJ
ejpam-6524	11	17	waves	wave	NOUN
ejpam-6524	11	18	through	through	ADP
ejpam-6524	11	19	various	various	ADJ
ejpam-6524	11	20	media	medium	NOUN
ejpam-6524	11	21	.	.	PUNCT
ejpam-6524	12	1	that	that	PRON
ejpam-6524	12	2	makes	make	VERB
ejpam-6524	12	3	the	the	DET
ejpam-6524	12	4	equation	equation	NOUN
ejpam-6524	12	5	useful	useful	ADJ
ejpam-6524	12	6	in	in	ADP
ejpam-6524	12	7	applied	apply	VERB
ejpam-6524	12	8	mathematics	mathematic	NOUN
ejpam-6524	12	9	,	,	PUNCT
ejpam-6524	12	10	physics	physics	NOUN
ejpam-6524	12	11	,	,	PUNCT
ejpam-6524	12	12	and	and	CCONJ
ejpam-6524	12	13	engineering	engineering	NOUN
ejpam-6524	12	14	.	.	PUNCT
ejpam-6524	13	1	this	this	DET
ejpam-6524	13	2	second	second	ADJ
ejpam-6524	13	3	-	-	PUNCT
ejpam-6524	13	4	order	order	NOUN
ejpam-6524	13	5	pde	pde	NOUN
ejpam-6524	13	6	,	,	PUNCT
ejpam-6524	13	7	also	also	ADV
ejpam-6524	13	8	known	know	VERB
ejpam-6524	13	9	as	as	ADP
ejpam-6524	13	10	the	the	DET
ejpam-6524	13	11	wave	wave	NOUN
ejpam-6524	13	12	equation	equation	NOUN
ejpam-6524	13	13	,	,	PUNCT
ejpam-6524	13	14	is	be	AUX
ejpam-6524	13	15	crucial	crucial	ADJ
ejpam-6524	13	16	for	for	ADP
ejpam-6524	13	17	analyzing	analyze	VERB
ejpam-6524	13	18	the	the	DET
ejpam-6524	13	19	dynamic	dynamic	ADJ
ejpam-6524	13	20	nature	nature	NOUN
ejpam-6524	13	21	of	of	ADP
ejpam-6524	13	22	physical	physical	ADJ
ejpam-6524	13	23	phenomena	phenomenon	NOUN
ejpam-6524	13	24	.	.	PUNCT
ejpam-6524	14	1	the	the	DET
ejpam-6524	14	2	wave	wave	NOUN
ejpam-6524	14	3	equation	equation	NOUN
ejpam-6524	14	4	is	be	AUX
ejpam-6524	14	5	vital	vital	ADJ
ejpam-6524	14	6	when	when	SCONJ
ejpam-6524	14	7	studying	study	VERB
ejpam-6524	14	8	dynamic	dynamic	ADJ
ejpam-6524	14	9	systems[5	systems[5	PROPN
ejpam-6524	14	10	,	,	PUNCT
ejpam-6524	14	11	6	6	NUM
ejpam-6524	14	12	]	]	PUNCT
ejpam-6524	14	13	.	.	PUNCT
ejpam-6524	15	1	∗corresponding	∗corresponde	VERB
ejpam-6524	15	2	author	author	NOUN
ejpam-6524	15	3	.	.	PUNCT
ejpam-6524	16	1	doi	doi	NOUN
ejpam-6524	16	2	:	:	PUNCT
ejpam-6524	16	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6524	https://doi.org/10.29020/nybg.ejpam.v18i3.6524	PROPN
ejpam-6524	16	4	email	email	NOUN
ejpam-6524	16	5	addresses	address	VERB
ejpam-6524	16	6	:	:	PUNCT
ejpam-6524	16	7	abdulkafi.ahmed@qu.edu.sa	abdulkafi.ahmed@qu.edu.sa	PROPN
ejpam-6524	16	8	(	(	PUNCT
ejpam-6524	16	9	[	[	X
ejpam-6524	16	10	abdulkafi	abdulkafi	PROPN
ejpam-6524	16	11	m.	m.	PROPN
ejpam-6524	16	12	saeed	saeed	PROPN
ejpam-6524	16	13	)	)	PUNCT
ejpam-6524	16	14	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6524	17	1	1	1	NUM
ejpam-6524	17	2	copyright	copyright	NOUN
ejpam-6524	17	3	:	:	PUNCT
ejpam-6524	17	4	©	©	PROPN
ejpam-6524	17	5	2025	2025	NUM
ejpam-6524	17	6	the	the	DET
ejpam-6524	17	7	author(s	author(s	NOUN
ejpam-6524	17	8	)	)	PUNCT
ejpam-6524	17	9	.	.	PUNCT
ejpam-6524	18	1	(	(	PUNCT
ejpam-6524	18	2	cc	cc	NOUN
ejpam-6524	18	3	by	by	ADP
ejpam-6524	18	4	-	-	PUNCT
ejpam-6524	18	5	nc	nc	PROPN
ejpam-6524	18	6	4.0	4.0	NUM
ejpam-6524	18	7	)	)	PUNCT
ejpam-6524	18	8	abdulkafi	abdulkafi	PROPN
ejpam-6524	18	9	m.	m.	PROPN
ejpam-6524	18	10	saeed	saeed	PROPN
ejpam-6524	18	11	,	,	PUNCT
ejpam-6524	18	12	shahad	shahad	PROPN
ejpam-6524	18	13	s.	s.	PROPN
ejpam-6524	18	14	almutairi	almutairi	PROPN
ejpam-6524	18	15	/	/	SYM
ejpam-6524	18	16	eur	eur	PROPN
ejpam-6524	18	17	.	.	PUNCT
ejpam-6524	19	1	j.	j.	PROPN
ejpam-6524	19	2	pure	pure	PROPN
ejpam-6524	19	3	appl	appl	PROPN
ejpam-6524	19	4	.	.	PROPN
ejpam-6524	19	5	math	math	PROPN
ejpam-6524	19	6	,	,	PUNCT
ejpam-6524	19	7	18	18	NUM
ejpam-6524	19	8	(	(	PUNCT
ejpam-6524	19	9	3	3	NUM
ejpam-6524	19	10	)	)	PUNCT
ejpam-6524	19	11	(	(	PUNCT
ejpam-6524	19	12	2025	2025	NUM
ejpam-6524	19	13	)	)	PUNCT
ejpam-6524	19	14	,	,	PUNCT
ejpam-6524	19	15	6524	6524	NUM
ejpam-6524	19	16	2	2	NUM
ejpam-6524	19	17	of	of	ADP
ejpam-6524	19	18	21	21	NUM
ejpam-6524	19	19	real	real	ADJ
ejpam-6524	19	20	-	-	PUNCT
ejpam-6524	19	21	world	world	NOUN
ejpam-6524	19	22	problems	problem	NOUN
ejpam-6524	19	23	come	come	VERB
ejpam-6524	19	24	with	with	ADP
ejpam-6524	19	25	differential	differential	ADJ
ejpam-6524	19	26	equations	equation	NOUN
ejpam-6524	19	27	that	that	PRON
ejpam-6524	19	28	are	be	AUX
ejpam-6524	19	29	complicated	complicated	ADJ
ejpam-6524	19	30	and	and	CCONJ
ejpam-6524	19	31	often	often	ADV
ejpam-6524	19	32	have	have	VERB
ejpam-6524	19	33	no	no	DET
ejpam-6524	19	34	explicit	explicit	ADJ
ejpam-6524	19	35	solution	solution	NOUN
ejpam-6524	19	36	formulas	formula	NOUN
ejpam-6524	19	37	.	.	PUNCT
ejpam-6524	20	1	when	when	SCONJ
ejpam-6524	20	2	they	they	PRON
ejpam-6524	20	3	do	do	AUX
ejpam-6524	20	4	exist	exist	VERB
ejpam-6524	20	5	,	,	PUNCT
ejpam-6524	20	6	they	they	PRON
ejpam-6524	20	7	involve	involve	VERB
ejpam-6524	20	8	integrals	integral	NOUN
ejpam-6524	20	9	that	that	PRON
ejpam-6524	20	10	have	have	VERB
ejpam-6524	20	11	to	to	PART
ejpam-6524	20	12	be	be	AUX
ejpam-6524	20	13	calculated	calculate	VERB
ejpam-6524	20	14	through	through	ADP
ejpam-6524	20	15	numerical	numerical	ADJ
ejpam-6524	20	16	quadrature	quadrature	NOUN
ejpam-6524	20	17	methods	method	NOUN
ejpam-6524	20	18	.	.	PUNCT
ejpam-6524	21	1	numerical	numerical	ADJ
ejpam-6524	21	2	analysis	analysis	NOUN
ejpam-6524	21	3	has	have	AUX
ejpam-6524	21	4	become	become	VERB
ejpam-6524	21	5	extremely	extremely	ADV
ejpam-6524	21	6	important	important	ADJ
ejpam-6524	21	7	in	in	ADP
ejpam-6524	21	8	solving	solve	VERB
ejpam-6524	21	9	differential	differential	ADJ
ejpam-6524	21	10	equations	equation	NOUN
ejpam-6524	21	11	—	—	PUNCT
ejpam-6524	21	12	under	under	ADP
ejpam-6524	21	13	specific	specific	ADJ
ejpam-6524	21	14	conditions	condition	NOUN
ejpam-6524	21	15	of	of	ADP
ejpam-6524	21	16	initial	initial	ADJ
ejpam-6524	21	17	or	or	CCONJ
ejpam-6524	21	18	boundary	boundary	ADJ
ejpam-6524	21	19	values	value	NOUN
ejpam-6524	21	20	—	—	PUNCT
ejpam-6524	21	21	making	make	VERB
ejpam-6524	21	22	this	this	DET
ejpam-6524	21	23	approach	approach	NOUN
ejpam-6524	21	24	effective	effective	ADJ
ejpam-6524	21	25	for	for	ADP
ejpam-6524	21	26	overcoming	overcome	VERB
ejpam-6524	21	27	numerous	numerous	ADJ
ejpam-6524	21	28	challenges	challenge	NOUN
ejpam-6524	21	29	.	.	PUNCT
ejpam-6524	22	1	partial	partial	ADJ
ejpam-6524	22	2	differential	differential	ADJ
ejpam-6524	22	3	equations	equation	NOUN
ejpam-6524	22	4	(	(	PUNCT
ejpam-6524	22	5	pdes	pde	NOUN
ejpam-6524	22	6	)	)	PUNCT
ejpam-6524	22	7	can	can	AUX
ejpam-6524	22	8	be	be	AUX
ejpam-6524	22	9	solved	solve	VERB
ejpam-6524	22	10	numerically	numerically	ADV
ejpam-6524	22	11	using	use	VERB
ejpam-6524	22	12	the	the	DET
ejpam-6524	22	13	finite	finite	ADJ
ejpam-6524	22	14	volume	volume	NOUN
ejpam-6524	22	15	method	method	NOUN
ejpam-6524	22	16	(	(	PUNCT
ejpam-6524	22	17	fvm	fvm	ADV
ejpam-6524	22	18	)	)	PUNCT
ejpam-6524	22	19	,	,	PUNCT
ejpam-6524	22	20	fdm	fdm	NOUN
ejpam-6524	22	21	,	,	PUNCT
ejpam-6524	22	22	and	and	CCONJ
ejpam-6524	22	23	fem	fem	NOUN
ejpam-6524	22	24	.	.	PUNCT
ejpam-6524	23	1	fdm	fdm	NOUN
ejpam-6524	23	2	creates	create	VERB
ejpam-6524	23	3	approximations	approximation	NOUN
ejpam-6524	23	4	of	of	ADP
ejpam-6524	23	5	solutions	solution	NOUN
ejpam-6524	23	6	to	to	PART
ejpam-6524	23	7	differential	differential	VERB
ejpam-6524	23	8	equations	equation	NOUN
ejpam-6524	23	9	via	via	ADP
ejpam-6524	23	10	local	local	ADJ
ejpam-6524	23	11	taylor	taylor	PROPN
ejpam-6524	23	12	series	series	PROPN
ejpam-6524	23	13	expansion	expansion	NOUN
ejpam-6524	23	14	.	.	PUNCT
ejpam-6524	24	1	when	when	SCONJ
ejpam-6524	24	2	dealing	deal	VERB
ejpam-6524	24	3	with	with	ADP
ejpam-6524	24	4	increasingly	increasingly	ADV
ejpam-6524	24	5	complex	complex	ADJ
ejpam-6524	24	6	geometries	geometry	NOUN
ejpam-6524	24	7	in	in	ADP
ejpam-6524	24	8	higher	high	ADJ
ejpam-6524	24	9	dimensions	dimension	NOUN
ejpam-6524	24	10	,	,	PUNCT
ejpam-6524	24	11	the	the	DET
ejpam-6524	24	12	topologically	topologically	PROPN
ejpam-6524	24	13	square	square	ADJ
ejpam-6524	24	14	network	network	NOUN
ejpam-6524	24	15	of	of	ADP
ejpam-6524	24	16	lines	line	NOUN
ejpam-6524	24	17	may	may	AUX
ejpam-6524	24	18	present	present	VERB
ejpam-6524	24	19	certain	certain	ADJ
ejpam-6524	24	20	challenges	challenge	NOUN
ejpam-6524	24	21	in	in	ADP
ejpam-6524	24	22	the	the	DET
ejpam-6524	24	23	discretization	discretization	NOUN
ejpam-6524	24	24	of	of	ADP
ejpam-6524	24	25	pdes	pde	NOUN
ejpam-6524	24	26	in	in	ADP
ejpam-6524	24	27	fdm	fdm	NOUN
ejpam-6524	24	28	.	.	PUNCT
ejpam-6524	25	1	these	these	DET
ejpam-6524	25	2	restrictions	restriction	NOUN
ejpam-6524	25	3	made	make	VERB
ejpam-6524	25	4	integral	integral	ADJ
ejpam-6524	25	5	-	-	PUNCT
ejpam-6524	25	6	based	base	VERB
ejpam-6524	25	7	formulations	formulation	NOUN
ejpam-6524	25	8	more	more	ADV
ejpam-6524	25	9	desirable	desirable	ADJ
ejpam-6524	25	10	,	,	PUNCT
ejpam-6524	25	11	which	which	PRON
ejpam-6524	25	12	allowed	allow	VERB
ejpam-6524	25	13	for	for	ADP
ejpam-6524	25	14	the	the	DET
ejpam-6524	25	15	creation	creation	NOUN
ejpam-6524	25	16	of	of	ADP
ejpam-6524	25	17	the	the	DET
ejpam-6524	25	18	two	two	NUM
ejpam-6524	25	19	less	less	ADV
ejpam-6524	25	20	sophisticated	sophisticated	ADJ
ejpam-6524	25	21	fvm	fvm	ADJ
ejpam-6524	25	22	and	and	CCONJ
ejpam-6524	25	23	fdm	fdm	NOUN
ejpam-6524	25	24	techniques	technique	NOUN
ejpam-6524	25	25	[	[	X
ejpam-6524	25	26	1	1	NUM
ejpam-6524	25	27	,	,	PUNCT
ejpam-6524	25	28	5	5	NUM
ejpam-6524	25	29	,	,	PUNCT
ejpam-6524	25	30	7	7	NUM
ejpam-6524	25	31	]	]	PUNCT
ejpam-6524	25	32	.	.	PUNCT
ejpam-6524	26	1	the	the	DET
ejpam-6524	26	2	primary	primary	ADJ
ejpam-6524	26	3	application	application	NOUN
ejpam-6524	26	4	of	of	ADP
ejpam-6524	26	5	fem	fem	NOUN
ejpam-6524	26	6	is	be	AUX
ejpam-6524	26	7	in	in	ADP
ejpam-6524	26	8	the	the	DET
ejpam-6524	26	9	solution	solution	NOUN
ejpam-6524	26	10	of	of	ADP
ejpam-6524	26	11	differential	differential	ADJ
ejpam-6524	26	12	equations	equation	NOUN
ejpam-6524	26	13	with	with	ADP
ejpam-6524	26	14	boundary	boundary	ADJ
ejpam-6524	26	15	conditions	condition	NOUN
ejpam-6524	26	16	.	.	PUNCT
ejpam-6524	27	1	the	the	DET
ejpam-6524	27	2	solution	solution	NOUN
ejpam-6524	27	3	is	be	AUX
ejpam-6524	27	4	calculated	calculate	VERB
ejpam-6524	27	5	by	by	ADP
ejpam-6524	27	6	partitioning	partition	VERB
ejpam-6524	27	7	the	the	DET
ejpam-6524	27	8	domain	domain	NOUN
ejpam-6524	27	9	into	into	ADP
ejpam-6524	27	10	finite	finite	ADJ
ejpam-6524	27	11	number	number	NOUN
ejpam-6524	27	12	of	of	ADP
ejpam-6524	27	13	regions	region	NOUN
ejpam-6524	27	14	,	,	PUNCT
ejpam-6524	27	15	or	or	CCONJ
ejpam-6524	27	16	elements	element	NOUN
ejpam-6524	27	17	,	,	PUNCT
ejpam-6524	27	18	and	and	CCONJ
ejpam-6524	27	19	applying	apply	VERB
ejpam-6524	27	20	basis	basis	NOUN
ejpam-6524	27	21	functions	function	NOUN
ejpam-6524	27	22	to	to	ADP
ejpam-6524	27	23	them	they	PRON
ejpam-6524	27	24	.	.	PUNCT
ejpam-6524	28	1	hydrodynamic	hydrodynamic	ADJ
ejpam-6524	28	2	and	and	CCONJ
ejpam-6524	28	3	structural	structural	ADJ
ejpam-6524	28	4	analysis	analysis	NOUN
ejpam-6524	28	5	,	,	PUNCT
ejpam-6524	28	6	as	as	ADV
ejpam-6524	28	7	well	well	ADV
ejpam-6524	28	8	as	as	ADP
ejpam-6524	28	9	multidisciplinary	multidisciplinary	ADJ
ejpam-6524	28	10	problems	problem	NOUN
ejpam-6524	28	11	are	be	AUX
ejpam-6524	28	12	some	some	PRON
ejpam-6524	28	13	of	of	ADP
ejpam-6524	28	14	the	the	DET
ejpam-6524	28	15	many	many	ADJ
ejpam-6524	28	16	fields	field	NOUN
ejpam-6524	28	17	where	where	SCONJ
ejpam-6524	28	18	fem	fem	NOUN
ejpam-6524	28	19	is	be	AUX
ejpam-6524	28	20	implemented	implement	VERB
ejpam-6524	28	21	today	today	NOUN
ejpam-6524	28	22	.	.	PUNCT
ejpam-6524	29	1	the	the	DET
ejpam-6524	29	2	reason	reason	NOUN
ejpam-6524	29	3	for	for	ADP
ejpam-6524	29	4	this	this	DET
ejpam-6524	29	5	tremendous	tremendous	ADJ
ejpam-6524	29	6	use	use	NOUN
ejpam-6524	29	7	is	be	AUX
ejpam-6524	29	8	due	due	ADJ
ejpam-6524	29	9	to	to	ADP
ejpam-6524	29	10	the	the	DET
ejpam-6524	29	11	method	method	NOUN
ejpam-6524	29	12	’s	’s	PART
ejpam-6524	29	13	precision	precision	NOUN
ejpam-6524	29	14	in	in	ADP
ejpam-6524	29	15	modeling	modeling	NOUN
ejpam-6524	29	16	and	and	CCONJ
ejpam-6524	29	17	numerically	numerically	ADV
ejpam-6524	29	18	solving	solve	VERB
ejpam-6524	29	19	intricate	intricate	ADJ
ejpam-6524	29	20	problems	problem	NOUN
ejpam-6524	29	21	.	.	PUNCT
ejpam-6524	30	1	by	by	ADP
ejpam-6524	30	2	enabling	enable	VERB
ejpam-6524	30	3	the	the	DET
ejpam-6524	30	4	simulation	simulation	NOUN
ejpam-6524	30	5	of	of	ADP
ejpam-6524	30	6	natural	natural	ADJ
ejpam-6524	30	7	phenomena	phenomenon	NOUN
ejpam-6524	30	8	and	and	CCONJ
ejpam-6524	30	9	the	the	DET
ejpam-6524	30	10	analysis	analysis	NOUN
ejpam-6524	30	11	of	of	ADP
ejpam-6524	30	12	engineering	engineering	NOUN
ejpam-6524	30	13	designs	design	NOUN
ejpam-6524	30	14	,	,	PUNCT
ejpam-6524	30	15	both	both	CCONJ
ejpam-6524	30	16	scientific	scientific	ADJ
ejpam-6524	30	17	and	and	CCONJ
ejpam-6524	30	18	engineering	engineering	NOUN
ejpam-6524	30	19	evaluation	evaluation	NOUN
ejpam-6524	30	20	are	be	AUX
ejpam-6524	30	21	possible	possible	ADJ
ejpam-6524	30	22	.	.	PUNCT
ejpam-6524	31	1	this	this	PRON
ejpam-6524	31	2	permits	permit	VERB
ejpam-6524	31	3	the	the	DET
ejpam-6524	31	4	prediction	prediction	NOUN
ejpam-6524	31	5	of	of	ADP
ejpam-6524	31	6	system	system	NOUN
ejpam-6524	31	7	performance	performance	NOUN
ejpam-6524	31	8	under	under	ADP
ejpam-6524	31	9	design	design	NOUN
ejpam-6524	31	10	conditions	condition	NOUN
ejpam-6524	31	11	and	and	CCONJ
ejpam-6524	31	12	natural	natural	ADJ
ejpam-6524	31	13	phenomena	phenomenon	NOUN
ejpam-6524	31	14	,	,	PUNCT
ejpam-6524	31	15	which	which	PRON
ejpam-6524	31	16	aids	aid	VERB
ejpam-6524	31	17	in	in	ADP
ejpam-6524	31	18	the	the	DET
ejpam-6524	31	19	development	development	NOUN
ejpam-6524	31	20	of	of	ADP
ejpam-6524	31	21	safer	safe	ADJ
ejpam-6524	31	22	,	,	PUNCT
ejpam-6524	31	23	cost	cost	NOUN
ejpam-6524	31	24	-	-	PUNCT
ejpam-6524	31	25	effective	effective	ADJ
ejpam-6524	31	26	systems	system	NOUN
ejpam-6524	31	27	.	.	PUNCT
ejpam-6524	32	1	the	the	DET
ejpam-6524	32	2	risk	risk	NOUN
ejpam-6524	32	3	of	of	ADP
ejpam-6524	32	4	disasters	disaster	NOUN
ejpam-6524	32	5	can	can	AUX
ejpam-6524	32	6	also	also	ADV
ejpam-6524	32	7	be	be	AUX
ejpam-6524	32	8	reduced	reduce	VERB
ejpam-6524	32	9	with	with	ADP
ejpam-6524	32	10	the	the	DET
ejpam-6524	32	11	aid	aid	NOUN
ejpam-6524	32	12	of	of	ADP
ejpam-6524	32	13	fem	fem	PROPN
ejpam-6524	32	14	.	.	PUNCT
ejpam-6524	33	1	the	the	DET
ejpam-6524	33	2	quality	quality	NOUN
ejpam-6524	33	3	of	of	ADP
ejpam-6524	33	4	life	life	NOUN
ejpam-6524	33	5	is	be	AUX
ejpam-6524	33	6	highly	highly	ADV
ejpam-6524	33	7	influenced	influence	VERB
ejpam-6524	33	8	by	by	ADP
ejpam-6524	33	9	the	the	DET
ejpam-6524	33	10	technology	technology	NOUN
ejpam-6524	33	11	we	we	PRON
ejpam-6524	33	12	have	have	VERB
ejpam-6524	33	13	today	today	NOUN
ejpam-6524	33	14	;	;	PUNCT
ejpam-6524	33	15	this	this	PRON
ejpam-6524	33	16	is	be	AUX
ejpam-6524	33	17	gradually	gradually	ADV
ejpam-6524	33	18	advanced	advance	VERB
ejpam-6524	33	19	by	by	ADP
ejpam-6524	33	20	a	a	DET
ejpam-6524	33	21	growing	grow	VERB
ejpam-6524	33	22	understanding	understanding	NOUN
ejpam-6524	33	23	of	of	ADP
ejpam-6524	33	24	nature	nature	NOUN
ejpam-6524	33	25	through	through	ADP
ejpam-6524	33	26	fem	fem	PROPN
ejpam-6524	33	27	’s	’s	PART
ejpam-6524	33	28	versatile	versatile	ADJ
ejpam-6524	33	29	nature	nature	NOUN
ejpam-6524	33	30	[	[	X
ejpam-6524	33	31	8	8	NUM
ejpam-6524	33	32	]	]	PUNCT
ejpam-6524	33	33	.	.	PUNCT
ejpam-6524	34	1	galerkin	galerkin	PROPN
ejpam-6524	34	2	finite	finite	PROPN
ejpam-6524	34	3	element	element	PROPN
ejpam-6524	34	4	method	method	NOUN
ejpam-6524	34	5	(	(	PUNCT
ejpam-6524	34	6	gfem	gfem	PROPN
ejpam-6524	34	7	)	)	PUNCT
ejpam-6524	34	8	is	be	AUX
ejpam-6524	34	9	formulated	formulate	VERB
ejpam-6524	34	10	as	as	ADP
ejpam-6524	34	11	a	a	DET
ejpam-6524	34	12	modification	modification	NOUN
ejpam-6524	34	13	of	of	ADP
ejpam-6524	34	14	the	the	DET
ejpam-6524	34	15	basic	basic	ADJ
ejpam-6524	34	16	process	process	NOUN
ejpam-6524	34	17	of	of	ADP
ejpam-6524	34	18	fem	fem	NOUN
ejpam-6524	34	19	,	,	PUNCT
ejpam-6524	34	20	construction	construction	NOUN
ejpam-6524	34	21	by	by	ADP
ejpam-6524	34	22	galerkin	galerkin	PROPN
ejpam-6524	34	23	’s	’s	PART
ejpam-6524	34	24	method	method	NOUN
ejpam-6524	34	25	.	.	PUNCT
ejpam-6524	35	1	it	it	PRON
ejpam-6524	35	2	is	be	AUX
ejpam-6524	35	3	simpler	simple	ADJ
ejpam-6524	35	4	than	than	ADP
ejpam-6524	35	5	other	other	ADJ
ejpam-6524	35	6	methods	method	NOUN
ejpam-6524	35	7	because	because	SCONJ
ejpam-6524	35	8	gfem	gfem	PROPN
ejpam-6524	35	9	uses	use	VERB
ejpam-6524	35	10	a	a	DET
ejpam-6524	35	11	systematic	systematic	ADJ
ejpam-6524	35	12	approach	approach	NOUN
ejpam-6524	35	13	with	with	ADP
ejpam-6524	35	14	piecewise	piecewise	NOUN
ejpam-6524	35	15	trial	trial	NOUN
ejpam-6524	35	16	functions	function	NOUN
ejpam-6524	35	17	for	for	ADP
ejpam-6524	35	18	the	the	DET
ejpam-6524	35	19	approximation	approximation	NOUN
ejpam-6524	35	20	of	of	ADP
ejpam-6524	35	21	partial	partial	ADJ
ejpam-6524	35	22	differential	differential	ADJ
ejpam-6524	35	23	equations	equation	NOUN
ejpam-6524	35	24	over	over	ADP
ejpam-6524	35	25	finite	finite	ADJ
ejpam-6524	35	26	elements	element	NOUN
ejpam-6524	35	27	[	[	X
ejpam-6524	35	28	6	6	NUM
ejpam-6524	35	29	,	,	PUNCT
ejpam-6524	35	30	9	9	NUM
ejpam-6524	35	31	,	,	PUNCT
ejpam-6524	35	32	10	10	NUM
ejpam-6524	35	33	]	]	PUNCT
ejpam-6524	35	34	.	.	PUNCT
ejpam-6524	36	1	this	this	DET
ejpam-6524	36	2	study	study	NOUN
ejpam-6524	36	3	is	be	AUX
ejpam-6524	36	4	an	an	DET
ejpam-6524	36	5	extension	extension	NOUN
ejpam-6524	36	6	of	of	ADP
ejpam-6524	36	7	the	the	DET
ejpam-6524	36	8	work	work	NOUN
ejpam-6524	36	9	done	do	VERB
ejpam-6524	36	10	by	by	ADP
ejpam-6524	36	11	s.	s.	PROPN
ejpam-6524	36	12	s.	s.	PROPN
ejpam-6524	36	13	almutairi	almutairi	PROPN
ejpam-6524	36	14	,	,	PUNCT
ejpam-6524	36	15	a.	a.	PROPN
ejpam-6524	36	16	m.	m.	PROPN
ejpam-6524	36	17	saeed	saeed	PROPN
ejpam-6524	37	1	[	[	X
ejpam-6524	37	2	11	11	NUM
ejpam-6524	37	3	]	]	PUNCT
ejpam-6524	37	4	to	to	PART
ejpam-6524	37	5	further	far	ADV
ejpam-6524	37	6	investigate	investigate	VERB
ejpam-6524	37	7	and	and	CCONJ
ejpam-6524	37	8	scrutinize	scrutinize	VERB
ejpam-6524	37	9	alternative	alternative	ADJ
ejpam-6524	37	10	approximate	approximate	ADJ
ejpam-6524	37	11	methods	method	NOUN
ejpam-6524	37	12	for	for	ADP
ejpam-6524	37	13	solving	solve	VERB
ejpam-6524	37	14	various	various	ADJ
ejpam-6524	37	15	types	type	NOUN
ejpam-6524	37	16	of	of	ADP
ejpam-6524	37	17	boundary	boundary	ADJ
ejpam-6524	37	18	value	value	NOUN
ejpam-6524	37	19	problems	problem	NOUN
ejpam-6524	37	20	.	.	PUNCT
ejpam-6524	38	1	this	this	DET
ejpam-6524	38	2	study	study	NOUN
ejpam-6524	38	3	explores	explore	VERB
ejpam-6524	38	4	the	the	DET
ejpam-6524	38	5	applications	application	NOUN
ejpam-6524	38	6	of	of	ADP
ejpam-6524	38	7	gfem	gfem	NOUN
ejpam-6524	38	8	and	and	CCONJ
ejpam-6524	38	9	compares	compare	VERB
ejpam-6524	38	10	it	it	PRON
ejpam-6524	38	11	with	with	ADP
ejpam-6524	38	12	fdm	fdm	NOUN
ejpam-6524	38	13	to	to	PART
ejpam-6524	38	14	determine	determine	VERB
ejpam-6524	38	15	which	which	DET
ejpam-6524	38	16	approach	approach	NOUN
ejpam-6524	38	17	is	be	AUX
ejpam-6524	38	18	more	more	ADV
ejpam-6524	38	19	effective	effective	ADJ
ejpam-6524	38	20	.	.	PUNCT
ejpam-6524	39	1	the	the	DET
ejpam-6524	39	2	paper	paper	NOUN
ejpam-6524	39	3	is	be	AUX
ejpam-6524	39	4	structured	structure	VERB
ejpam-6524	39	5	into	into	ADP
ejpam-6524	39	6	five	five	NUM
ejpam-6524	39	7	sections	section	NOUN
ejpam-6524	39	8	.	.	PUNCT
ejpam-6524	40	1	section	section	NOUN
ejpam-6524	40	2	2	2	NUM
ejpam-6524	40	3	provides	provide	VERB
ejpam-6524	40	4	a	a	DET
ejpam-6524	40	5	brief	brief	ADJ
ejpam-6524	40	6	overview	overview	NOUN
ejpam-6524	40	7	of	of	ADP
ejpam-6524	40	8	the	the	DET
ejpam-6524	40	9	fdm	fdm	NOUN
ejpam-6524	40	10	.	.	PUNCT
ejpam-6524	41	1	section	section	NOUN
ejpam-6524	41	2	3	3	NUM
ejpam-6524	41	3	presents	present	VERB
ejpam-6524	41	4	the	the	DET
ejpam-6524	41	5	gfem	gfem	NOUN
ejpam-6524	41	6	formulations	formulation	NOUN
ejpam-6524	41	7	for	for	ADP
ejpam-6524	41	8	solving	solve	VERB
ejpam-6524	41	9	pdes	pde	NOUN
ejpam-6524	41	10	of	of	ADP
ejpam-6524	41	11	both	both	CCONJ
ejpam-6524	41	12	elliptic	elliptic	ADJ
ejpam-6524	41	13	and	and	CCONJ
ejpam-6524	41	14	hyperbolic	hyperbolic	ADJ
ejpam-6524	41	15	types	type	NOUN
ejpam-6524	41	16	.	.	PUNCT
ejpam-6524	42	1	section	section	NOUN
ejpam-6524	42	2	4	4	NUM
ejpam-6524	42	3	discusses	discuss	VERB
ejpam-6524	42	4	numerical	numerical	ADJ
ejpam-6524	42	5	experiments	experiment	NOUN
ejpam-6524	42	6	and	and	CCONJ
ejpam-6524	42	7	compares	compare	VERB
ejpam-6524	42	8	the	the	DET
ejpam-6524	42	9	two	two	NUM
ejpam-6524	42	10	methods	method	NOUN
ejpam-6524	42	11	.	.	PUNCT
ejpam-6524	43	1	finally	finally	ADV
ejpam-6524	43	2	,	,	PUNCT
ejpam-6524	43	3	the	the	DET
ejpam-6524	43	4	paper	paper	NOUN
ejpam-6524	43	5	concludes	conclude	VERB
ejpam-6524	43	6	with	with	ADP
ejpam-6524	43	7	a	a	DET
ejpam-6524	43	8	summary	summary	NOUN
ejpam-6524	43	9	of	of	ADP
ejpam-6524	43	10	findings	finding	NOUN
ejpam-6524	43	11	and	and	CCONJ
ejpam-6524	43	12	final	final	ADJ
ejpam-6524	43	13	remarks	remark	NOUN
ejpam-6524	43	14	.	.	PUNCT
ejpam-6524	44	1	2	2	X
ejpam-6524	44	2	.	.	X
ejpam-6524	44	3	brief	brief	ADJ
ejpam-6524	44	4	description	description	NOUN
ejpam-6524	44	5	of	of	ADP
ejpam-6524	44	6	finite	finite	ADJ
ejpam-6524	44	7	difference	difference	NOUN
ejpam-6524	44	8	method	method	NOUN
ejpam-6524	44	9	fdm	fdm	NOUN
ejpam-6524	44	10	is	be	AUX
ejpam-6524	44	11	a	a	DET
ejpam-6524	44	12	numerical	numerical	ADJ
ejpam-6524	44	13	method	method	NOUN
ejpam-6524	44	14	that	that	PRON
ejpam-6524	44	15	approximates	approximate	VERB
ejpam-6524	44	16	the	the	DET
ejpam-6524	44	17	solution	solution	NOUN
ejpam-6524	44	18	of	of	ADP
ejpam-6524	44	19	differential	differential	ADJ
ejpam-6524	44	20	equations	equation	NOUN
ejpam-6524	44	21	by	by	ADP
ejpam-6524	44	22	means	mean	NOUN
ejpam-6524	44	23	of	of	ADP
ejpam-6524	44	24	discretization	discretization	NOUN
ejpam-6524	44	25	.	.	PUNCT
ejpam-6524	45	1	breaking	break	VERB
ejpam-6524	45	2	continuous	continuous	ADJ
ejpam-6524	45	3	functions	function	NOUN
ejpam-6524	45	4	into	into	ADP
ejpam-6524	45	5	discrete	discrete	ADJ
ejpam-6524	45	6	values	value	NOUN
ejpam-6524	45	7	simplifies	simplifie	NOUN
ejpam-6524	45	8	abdulkafi	abdulkafi	PROPN
ejpam-6524	45	9	m.	m.	PROPN
ejpam-6524	45	10	saeed	saeed	PROPN
ejpam-6524	45	11	,	,	PUNCT
ejpam-6524	45	12	shahad	shahad	PROPN
ejpam-6524	45	13	s.	s.	PROPN
ejpam-6524	45	14	almutairi	almutairi	PROPN
ejpam-6524	45	15	/	/	SYM
ejpam-6524	45	16	eur	eur	PROPN
ejpam-6524	45	17	.	.	PUNCT
ejpam-6524	46	1	j.	j.	PROPN
ejpam-6524	46	2	pure	pure	PROPN
ejpam-6524	46	3	appl	appl	PROPN
ejpam-6524	46	4	.	.	PROPN
ejpam-6524	46	5	math	math	PROPN
ejpam-6524	46	6	,	,	PUNCT
ejpam-6524	46	7	18	18	NUM
ejpam-6524	46	8	(	(	PUNCT
ejpam-6524	46	9	3	3	NUM
ejpam-6524	46	10	)	)	PUNCT
ejpam-6524	46	11	(	(	PUNCT
ejpam-6524	46	12	2025	2025	NUM
ejpam-6524	46	13	)	)	PUNCT
ejpam-6524	46	14	,	,	PUNCT
ejpam-6524	46	15	6524	6524	NUM
ejpam-6524	46	16	3	3	NUM
ejpam-6524	46	17	of	of	ADP
ejpam-6524	46	18	21	21	NUM
ejpam-6524	46	19	calculations	calculation	NOUN
ejpam-6524	46	20	and	and	CCONJ
ejpam-6524	46	21	enhances	enhance	VERB
ejpam-6524	46	22	various	various	ADJ
ejpam-6524	46	23	types	type	NOUN
ejpam-6524	46	24	of	of	ADP
ejpam-6524	46	25	quantitative	quantitative	ADJ
ejpam-6524	46	26	analysis	analysis	NOUN
ejpam-6524	46	27	.	.	PUNCT
ejpam-6524	47	1	this	this	DET
ejpam-6524	47	2	transformation	transformation	NOUN
ejpam-6524	47	3	makes	make	VERB
ejpam-6524	47	4	it	it	PRON
ejpam-6524	47	5	easier	easy	ADJ
ejpam-6524	47	6	to	to	PART
ejpam-6524	47	7	work	work	VERB
ejpam-6524	47	8	with	with	ADP
ejpam-6524	47	9	data	datum	NOUN
ejpam-6524	47	10	,	,	PUNCT
ejpam-6524	47	11	optimize	optimize	NOUN
ejpam-6524	47	12	processes	process	NOUN
ejpam-6524	47	13	,	,	PUNCT
ejpam-6524	47	14	and	and	CCONJ
ejpam-6524	47	15	apply	apply	VERB
ejpam-6524	47	16	computational	computational	ADJ
ejpam-6524	47	17	methods	method	NOUN
ejpam-6524	47	18	effectively	effectively	ADV
ejpam-6524	47	19	.	.	PUNCT
ejpam-6524	48	1	it	it	PRON
ejpam-6524	48	2	is	be	AUX
ejpam-6524	48	3	quite	quite	ADV
ejpam-6524	48	4	popular	popular	ADJ
ejpam-6524	48	5	in	in	ADP
ejpam-6524	48	6	various	various	ADJ
ejpam-6524	48	7	fields	field	NOUN
ejpam-6524	48	8	of	of	ADP
ejpam-6524	48	9	science	science	NOUN
ejpam-6524	48	10	and	and	CCONJ
ejpam-6524	48	11	technologie	technologie	NOUN
ejpam-6524	48	12	that	that	PRON
ejpam-6524	48	13	involve	involve	VERB
ejpam-6524	48	14	differential	differential	ADJ
ejpam-6524	48	15	equations	equation	NOUN
ejpam-6524	48	16	,	,	PUNCT
ejpam-6524	48	17	like	like	ADP
ejpam-6524	48	18	physics	physics	NOUN
ejpam-6524	48	19	,	,	PUNCT
ejpam-6524	48	20	engineering	engineering	NOUN
ejpam-6524	48	21	,	,	PUNCT
ejpam-6524	48	22	or	or	CCONJ
ejpam-6524	48	23	even	even	ADV
ejpam-6524	48	24	finance	finance	VERB
ejpam-6524	48	25	.	.	PUNCT
ejpam-6524	49	1	there	there	PRON
ejpam-6524	49	2	are	be	VERB
ejpam-6524	49	3	three	three	NUM
ejpam-6524	49	4	different	different	ADJ
ejpam-6524	49	5	kinds	kind	NOUN
ejpam-6524	49	6	of	of	ADP
ejpam-6524	49	7	finite	finite	ADJ
ejpam-6524	49	8	difference	difference	NOUN
ejpam-6524	49	9	approximations	approximation	NOUN
ejpam-6524	49	10	:	:	PUNCT
ejpam-6524	49	11	forward	forward	ADJ
ejpam-6524	49	12	distinctions	distinction	NOUN
ejpam-6524	49	13	,	,	PUNCT
ejpam-6524	49	14	backward	backward	ADJ
ejpam-6524	49	15	distinctions	distinction	NOUN
ejpam-6524	49	16	,	,	PUNCT
ejpam-6524	49	17	and	and	CCONJ
ejpam-6524	49	18	center	center	NOUN
ejpam-6524	49	19	distinctions	distinction	NOUN
ejpam-6524	49	20	.	.	PUNCT
ejpam-6524	50	1	by	by	ADP
ejpam-6524	50	2	evaluating	evaluate	VERB
ejpam-6524	50	3	the	the	DET
ejpam-6524	50	4	function	function	NOUN
ejpam-6524	50	5	at	at	ADP
ejpam-6524	50	6	two	two	NUM
ejpam-6524	50	7	future	future	ADJ
ejpam-6524	50	8	or	or	CCONJ
ejpam-6524	50	9	present	present	ADJ
ejpam-6524	50	10	values	value	NOUN
ejpam-6524	50	11	,	,	PUNCT
ejpam-6524	50	12	the	the	DET
ejpam-6524	50	13	forward	forward	ADJ
ejpam-6524	50	14	difference	difference	NOUN
ejpam-6524	50	15	approach	approach	NOUN
ejpam-6524	50	16	calculates	calculate	VERB
ejpam-6524	50	17	the	the	DET
ejpam-6524	50	18	derivative	derivative	NOUN
ejpam-6524	50	19	.	.	PUNCT
ejpam-6524	51	1	both	both	CCONJ
ejpam-6524	51	2	the	the	DET
ejpam-6524	51	3	values	value	NOUN
ejpam-6524	51	4	at	at	ADP
ejpam-6524	51	5	the	the	DET
ejpam-6524	51	6	current	current	ADJ
ejpam-6524	51	7	location	location	NOUN
ejpam-6524	51	8	and	and	CCONJ
ejpam-6524	51	9	the	the	DET
ejpam-6524	51	10	previous	previous	ADJ
ejpam-6524	51	11	one	one	NUM
ejpam-6524	51	12	are	be	AUX
ejpam-6524	51	13	of	of	ADP
ejpam-6524	51	14	interest	interest	NOUN
ejpam-6524	51	15	to	to	ADP
ejpam-6524	51	16	backward	backward	ADJ
ejpam-6524	51	17	differences	difference	NOUN
ejpam-6524	51	18	.	.	PUNCT
ejpam-6524	52	1	center	center	NOUN
ejpam-6524	52	2	is	be	AUX
ejpam-6524	52	3	more	more	ADV
ejpam-6524	52	4	accurate	accurate	ADJ
ejpam-6524	52	5	than	than	ADP
ejpam-6524	52	6	the	the	DET
ejpam-6524	52	7	others	other	NOUN
ejpam-6524	52	8	,	,	PUNCT
ejpam-6524	52	9	as	as	SCONJ
ejpam-6524	52	10	it	it	PRON
ejpam-6524	52	11	takes	take	VERB
ejpam-6524	52	12	the	the	DET
ejpam-6524	52	13	average	average	NOUN
ejpam-6524	52	14	of	of	ADP
ejpam-6524	52	15	forward	forward	ADJ
ejpam-6524	52	16	and	and	CCONJ
ejpam-6524	52	17	backward	backward	ADJ
ejpam-6524	52	18	difference	difference	NOUN
ejpam-6524	52	19	,	,	PUNCT
ejpam-6524	52	20	making	make	VERB
ejpam-6524	52	21	it	it	PRON
ejpam-6524	52	22	a	a	DET
ejpam-6524	52	23	more	more	ADV
ejpam-6524	52	24	accurate	accurate	ADJ
ejpam-6524	52	25	form	form	NOUN
ejpam-6524	52	26	of	of	ADP
ejpam-6524	52	27	approximation	approximation	NOUN
ejpam-6524	52	28	.	.	PUNCT
ejpam-6524	53	1	the	the	DET
ejpam-6524	53	2	forward	forward	ADJ
ejpam-6524	53	3	difference	difference	NOUN
ejpam-6524	53	4	method	method	NOUN
ejpam-6524	53	5	is	be	AUX
ejpam-6524	53	6	one	one	NUM
ejpam-6524	53	7	of	of	ADP
ejpam-6524	53	8	the	the	DET
ejpam-6524	53	9	numerical	numerical	ADJ
ejpam-6524	53	10	techniques	technique	NOUN
ejpam-6524	53	11	developed	develop	VERB
ejpam-6524	53	12	over	over	ADP
ejpam-6524	53	13	many	many	ADJ
ejpam-6524	53	14	decades	decade	NOUN
ejpam-6524	53	15	[	[	X
ejpam-6524	53	16	12	12	NUM
ejpam-6524	53	17	,	,	PUNCT
ejpam-6524	53	18	13	13	NUM
ejpam-6524	53	19	]	]	PUNCT
ejpam-6524	53	20	in	in	ADP
ejpam-6524	53	21	two	two	NUM
ejpam-6524	53	22	dimensions	dimension	NOUN
ejpam-6524	53	23	,	,	PUNCT
ejpam-6524	53	24	the	the	DET
ejpam-6524	53	25	poisson	poisson	NOUN
ejpam-6524	53	26	’s	’s	PART
ejpam-6524	53	27	equation	equation	NOUN
ejpam-6524	53	28	can	can	AUX
ejpam-6524	53	29	be	be	AUX
ejpam-6524	53	30	expressed	express	VERB
ejpam-6524	53	31	as	as	ADP
ejpam-6524	53	32	[	[	X
ejpam-6524	53	33	14	14	NUM
ejpam-6524	53	34	,	,	PUNCT
ejpam-6524	53	35	15	15	NUM
ejpam-6524	53	36	]	]	PUNCT
ejpam-6524	53	37	.	.	PUNCT
ejpam-6524	54	1	∂2u	∂2u	PROPN
ejpam-6524	54	2	∂x2	∂x2	PROPN
ejpam-6524	54	3	+	+	CCONJ
ejpam-6524	54	4	∂2u	∂2u	ADJ
ejpam-6524	54	5	∂y2	∂y2	NOUN
ejpam-6524	54	6	=	=	SYM
ejpam-6524	54	7	g(x	g(x	PROPN
ejpam-6524	54	8	,	,	PUNCT
ejpam-6524	54	9	y	y	NOUN
ejpam-6524	54	10	)	)	PUNCT
ejpam-6524	54	11	,	,	PUNCT
ejpam-6524	54	12	(	(	PUNCT
ejpam-6524	54	13	1	1	X
ejpam-6524	54	14	)	)	PUNCT
ejpam-6524	54	15	with	with	ADP
ejpam-6524	54	16	the	the	DET
ejpam-6524	54	17	boundary	boundary	ADJ
ejpam-6524	54	18	constraint	constraint	NOUN
ejpam-6524	54	19	u	u	NOUN
ejpam-6524	54	20	=	=	PROPN
ejpam-6524	54	21	f(x	f(x	PROPN
ejpam-6524	54	22	,	,	PUNCT
ejpam-6524	54	23	y	y	NOUN
ejpam-6524	54	24	)	)	PUNCT
ejpam-6524	54	25	along	along	ADP
ejpam-6524	54	26	the	the	DET
ejpam-6524	54	27	boundary	boundary	ADJ
ejpam-6524	54	28	c.	c.	NOUN
ejpam-6524	54	29	in	in	ADP
ejpam-6524	54	30	this	this	DET
ejpam-6524	54	31	case	case	NOUN
ejpam-6524	54	32	,	,	PUNCT
ejpam-6524	54	33	we	we	PRON
ejpam-6524	54	34	additionally	additionally	ADV
ejpam-6524	54	35	assumed	assume	VERB
ejpam-6524	54	36	that	that	SCONJ
ejpam-6524	54	37	the	the	DET
ejpam-6524	54	38	mesh	mesh	NOUN
ejpam-6524	54	39	points	point	NOUN
ejpam-6524	54	40	are	be	AUX
ejpam-6524	54	41	consistent	consistent	ADJ
ejpam-6524	54	42	across	across	ADP
ejpam-6524	54	43	the	the	DET
ejpam-6524	54	44	x	x	NOUN
ejpam-6524	54	45	and	and	CCONJ
ejpam-6524	54	46	y	y	PROPN
ejpam-6524	54	47	dimensions	dimension	NOUN
ejpam-6524	54	48	.	.	PUNCT
ejpam-6524	55	1	this	this	DET
ejpam-6524	55	2	assumption	assumption	NOUN
ejpam-6524	55	3	makes	make	VERB
ejpam-6524	55	4	it	it	PRON
ejpam-6524	55	5	possible	possible	ADJ
ejpam-6524	55	6	to	to	PART
ejpam-6524	55	7	reduce	reduce	VERB
ejpam-6524	55	8	the	the	DET
ejpam-6524	55	9	(	(	PUNCT
ejpam-6524	55	10	1	1	NUM
ejpam-6524	55	11	)	)	PUNCT
ejpam-6524	55	12	central	central	ADJ
ejpam-6524	55	13	difference	difference	NOUN
ejpam-6524	55	14	approximation	approximation	NOUN
ejpam-6524	55	15	to	to	ADP
ejpam-6524	55	16	ui	ui	PROPN
ejpam-6524	55	17	,	,	PUNCT
ejpam-6524	55	18	j	j	PROPN
ejpam-6524	56	1	=	=	NOUN
ejpam-6524	56	2	1	1	NUM
ejpam-6524	56	3	4	4	NUM
ejpam-6524	56	4	(	(	PUNCT
ejpam-6524	56	5	ui+1,j	ui+1,j	NOUN
ejpam-6524	56	6	+	+	CCONJ
ejpam-6524	56	7	ui−1,j	ui−1,j	X
ejpam-6524	56	8	+	+	CCONJ
ejpam-6524	56	9	ui	ui	NOUN
ejpam-6524	56	10	,	,	PUNCT
ejpam-6524	56	11	j+1	j+1	PROPN
ejpam-6524	56	12	+	+	PROPN
ejpam-6524	56	13	ui	ui	NOUN
ejpam-6524	56	14	,	,	PUNCT
ejpam-6524	56	15	j−1	j−1	PROPN
ejpam-6524	56	16	−	−	PROPN
ejpam-6524	56	17	h2gi	h2gi	PROPN
ejpam-6524	56	18	,	,	PUNCT
ejpam-6524	56	19	j	j	PROPN
ejpam-6524	56	20	)	)	PUNCT
ejpam-6524	56	21	,	,	PUNCT
ejpam-6524	56	22	where	where	SCONJ
ejpam-6524	56	23	gi	gi	ADP
ejpam-6524	56	24	,	,	PUNCT
ejpam-6524	56	25	j	j	PROPN
ejpam-6524	56	26	=	=	SYM
ejpam-6524	56	27	g(xi	g(xi	PROPN
ejpam-6524	56	28	,	,	PUNCT
ejpam-6524	56	29	yi	yi	PROPN
ejpam-6524	56	30	)	)	PUNCT
ejpam-6524	56	31	.	.	PUNCT
ejpam-6524	57	1	let	let	VERB
ejpam-6524	57	2	i	i	PRON
ejpam-6524	57	3	,	,	PUNCT
ejpam-6524	57	4	j	j	PROPN
ejpam-6524	57	5	=	=	SYM
ejpam-6524	57	6	0	0	NUM
ejpam-6524	57	7	,	,	PUNCT
ejpam-6524	57	8	1	1	NUM
ejpam-6524	57	9	,	,	PUNCT
ejpam-6524	57	10	2	2	NUM
ejpam-6524	57	11	,	,	PUNCT
ejpam-6524	57	12	3	3	NUM
ejpam-6524	57	13	,	,	PUNCT
ejpam-6524	57	14	4	4	NUM
ejpam-6524	57	15	and	and	CCONJ
ejpam-6524	57	16	u	u	X
ejpam-6524	58	1	=	=	NOUN
ejpam-6524	58	2	0	0	NUM
ejpam-6524	58	3	along	along	ADP
ejpam-6524	58	4	the	the	DET
ejpam-6524	58	5	boundary	boundary	ADJ
ejpam-6524	58	6	c.	c.	NOUN
ejpam-6524	58	7	for	for	ADP
ejpam-6524	58	8	j	j	PROPN
ejpam-6524	58	9	=	=	SYM
ejpam-6524	58	10	0	0	PROPN
ejpam-6524	58	11	,	,	PUNCT
ejpam-6524	58	12	1	1	NUM
ejpam-6524	58	13	,	,	PUNCT
ejpam-6524	58	14	2	2	NUM
ejpam-6524	58	15	,	,	PUNCT
ejpam-6524	58	16	3	3	NUM
ejpam-6524	58	17	,	,	PUNCT
ejpam-6524	58	18	4	4	NUM
ejpam-6524	58	19	,	,	PUNCT
ejpam-6524	58	20	then	then	ADV
ejpam-6524	58	21	ui,0	ui,0	PROPN
ejpam-6524	58	22	=	=	SYM
ejpam-6524	58	23	0	0	NUM
ejpam-6524	58	24	,	,	PUNCT
ejpam-6524	58	25	ui,4	ui,4	PROPN
ejpam-6524	58	26	=	=	SYM
ejpam-6524	58	27	0	0	NUM
ejpam-6524	58	28	,	,	PUNCT
ejpam-6524	58	29	and	and	CCONJ
ejpam-6524	58	30	u0,j	u0,j	PROPN
ejpam-6524	58	31	=	=	SYM
ejpam-6524	58	32	0	0	NUM
ejpam-6524	58	33	,	,	PUNCT
ejpam-6524	59	1	u4,j	u4,j	PROPN
ejpam-6524	59	2	=	=	SYM
ejpam-6524	59	3	0	0	X
ejpam-6524	59	4	.	.	PUNCT
ejpam-6524	60	1	when	when	SCONJ
ejpam-6524	60	2	i	i	PRON
ejpam-6524	60	3	=	=	NOUN
ejpam-6524	60	4	0	0	NUM
ejpam-6524	60	5	,	,	PUNCT
ejpam-6524	60	6	1	1	NUM
ejpam-6524	60	7	,	,	PUNCT
ejpam-6524	60	8	2	2	NUM
ejpam-6524	60	9	,	,	PUNCT
ejpam-6524	60	10	3	3	NUM
ejpam-6524	60	11	,	,	PUNCT
ejpam-6524	60	12	4	4	NUM
ejpam-6524	60	13	.	.	X
ejpam-6524	61	1	in	in	ADP
ejpam-6524	61	2	figure	figure	NOUN
ejpam-6524	61	3	1	1	NUM
ejpam-6524	61	4	,	,	PUNCT
ejpam-6524	61	5	the	the	DET
ejpam-6524	61	6	boundary	boundary	ADJ
ejpam-6524	61	7	values	value	NOUN
ejpam-6524	61	8	(	(	PUNCT
ejpam-6524	61	9	filled	fill	VERB
ejpam-6524	61	10	circles	circle	NOUN
ejpam-6524	61	11	)	)	PUNCT
ejpam-6524	61	12	are	be	AUX
ejpam-6524	61	13	displayed	display	VERB
ejpam-6524	61	14	.	.	PUNCT
ejpam-6524	62	1	figure	figure	VERB
ejpam-6524	62	2	1	1	NUM
ejpam-6524	62	3	:	:	PUNCT
ejpam-6524	62	4	fdm	fdm	NOUN
ejpam-6524	62	5	mesh	mesh	NOUN
ejpam-6524	62	6	points	point	NOUN
ejpam-6524	62	7	.	.	PUNCT
ejpam-6524	63	1	an	an	DET
ejpam-6524	63	2	example	example	NOUN
ejpam-6524	63	3	of	of	ADP
ejpam-6524	63	4	this	this	PRON
ejpam-6524	63	5	would	would	AUX
ejpam-6524	63	6	be	be	AUX
ejpam-6524	63	7	i	i	PROPN
ejpam-6524	63	8	,	,	PUNCT
ejpam-6524	63	9	j	j	PROPN
ejpam-6524	63	10	=	=	SYM
ejpam-6524	63	11	0	0	NUM
ejpam-6524	63	12	,	,	PUNCT
ejpam-6524	63	13	1	1	NUM
ejpam-6524	63	14	,	,	PUNCT
ejpam-6524	63	15	2	2	NUM
ejpam-6524	63	16	,	,	PUNCT
ejpam-6524	63	17	3	3	NUM
ejpam-6524	63	18	.	.	PUNCT
ejpam-6524	64	1	as	as	ADP
ejpam-6524	64	2	a	a	DET
ejpam-6524	64	3	result	result	NOUN
ejpam-6524	64	4	,	,	PUNCT
ejpam-6524	64	5	equation	equation	NOUN
ejpam-6524	64	6	(	(	PUNCT
ejpam-6524	64	7	1	1	X
ejpam-6524	64	8	)	)	PUNCT
ejpam-6524	64	9	transforms	transform	VERB
ejpam-6524	64	10	into	into	ADP
ejpam-6524	64	11	a	a	DET
ejpam-6524	64	12	system	system	NOUN
ejpam-6524	64	13	of	of	ADP
ejpam-6524	64	14	nine	nine	NUM
ejpam-6524	64	15	equations	equation	NOUN
ejpam-6524	64	16	with	with	ADP
ejpam-6524	64	17	nine	nine	NUM
ejpam-6524	64	18	unknowns	unknown	NOUN
ejpam-6524	64	19	.	.	PUNCT
ejpam-6524	65	1	these	these	DET
ejpam-6524	65	2	equations	equation	NOUN
ejpam-6524	65	3	can	can	AUX
ejpam-6524	65	4	be	be	AUX
ejpam-6524	65	5	represented	represent	VERB
ejpam-6524	65	6	in	in	ADP
ejpam-6524	65	7	matrix	matrix	NOUN
ejpam-6524	65	8	form	form	NOUN
ejpam-6524	65	9	for	for	ADP
ejpam-6524	65	10	a	a	DET
ejpam-6524	65	11	more	more	ADV
ejpam-6524	65	12	structured	structured	ADJ
ejpam-6524	65	13	and	and	CCONJ
ejpam-6524	65	14	efficient	efficient	ADJ
ejpam-6524	65	15	notation	notation	NOUN
ejpam-6524	65	16	.	.	PUNCT
ejpam-6524	66	1	abdulkafi	abdulkafi	PROPN
ejpam-6524	66	2	m.	m.	PROPN
ejpam-6524	66	3	saeed	saeed	PROPN
ejpam-6524	66	4	,	,	PUNCT
ejpam-6524	66	5	shahad	shahad	PROPN
ejpam-6524	66	6	s.	s.	PROPN
ejpam-6524	66	7	almutairi	almutairi	PROPN
ejpam-6524	66	8	/	/	SYM
ejpam-6524	66	9	eur	eur	PROPN
ejpam-6524	66	10	.	.	PUNCT
ejpam-6524	67	1	j.	j.	PROPN
ejpam-6524	67	2	pure	pure	PROPN
ejpam-6524	67	3	appl	appl	PROPN
ejpam-6524	67	4	.	.	PROPN
ejpam-6524	67	5	math	math	PROPN
ejpam-6524	67	6	,	,	PUNCT
ejpam-6524	67	7	18	18	NUM
ejpam-6524	67	8	(	(	PUNCT
ejpam-6524	67	9	3	3	NUM
ejpam-6524	67	10	)	)	PUNCT
ejpam-6524	67	11	(	(	PUNCT
ejpam-6524	67	12	2025	2025	NUM
ejpam-6524	67	13	)	)	PUNCT
ejpam-6524	67	14	,	,	PUNCT
ejpam-6524	67	15	6524	6524	NUM
ejpam-6524	67	16	4	4	NUM
ejpam-6524	67	17	of	of	ADP
ejpam-6524	67	18	21	21	NUM
ejpam-6524	67	19			NOUN
ejpam-6524	67	20	4	4	NUM
ejpam-6524	67	21	−1	−1	NOUN
ejpam-6524	67	22	0	0	NUM
ejpam-6524	67	23	−1	−1	NOUN
ejpam-6524	67	24	0	0	NUM
ejpam-6524	67	25	0	0	NUM
ejpam-6524	67	26	0	0	NUM
ejpam-6524	67	27	0	0	NUM
ejpam-6524	67	28	0	0	NUM
ejpam-6524	67	29	−1	−1	NOUN
ejpam-6524	67	30	4	4	NUM
ejpam-6524	67	31	−1	−1	NOUN
ejpam-6524	67	32	0	0	NUM
ejpam-6524	67	33	−1	−1	NOUN
ejpam-6524	67	34	0	0	NUM
ejpam-6524	67	35	0	0	NUM
ejpam-6524	67	36	0	0	NUM
ejpam-6524	67	37	0	0	NUM
ejpam-6524	67	38	0	0	NUM
ejpam-6524	67	39	−1	−1	NOUN
ejpam-6524	67	40	4	4	NUM
ejpam-6524	67	41	0	0	NUM
ejpam-6524	67	42	0	0	NUM
ejpam-6524	67	43	−1	−1	NOUN
ejpam-6524	67	44	0	0	NUM
ejpam-6524	67	45	0	0	NUM
ejpam-6524	67	46	0	0	NUM
ejpam-6524	67	47	−1	−1	NOUN
ejpam-6524	67	48	0	0	NUM
ejpam-6524	67	49	0	0	NUM
ejpam-6524	67	50	4	4	NUM
ejpam-6524	67	51	−1	−1	NOUN
ejpam-6524	67	52	0	0	NUM
ejpam-6524	67	53	−1	−1	NOUN
ejpam-6524	67	54	0	0	NUM
ejpam-6524	67	55	0	0	NUM
ejpam-6524	67	56	0	0	NUM
ejpam-6524	67	57	−1	−1	NOUN
ejpam-6524	67	58	0	0	NUM
ejpam-6524	67	59	−1	−1	NOUN
ejpam-6524	67	60	4	4	NUM
ejpam-6524	67	61	−1	−1	NOUN
ejpam-6524	67	62	0	0	NUM
ejpam-6524	67	63	−1	−1	NOUN
ejpam-6524	67	64	0	0	NUM
ejpam-6524	67	65	0	0	NUM
ejpam-6524	67	66	0	0	NUM
ejpam-6524	67	67	−1	−1	NOUN
ejpam-6524	67	68	0	0	NUM
ejpam-6524	67	69	−1	−1	NOUN
ejpam-6524	68	1	4	4	NUM
ejpam-6524	68	2	0	0	NUM
ejpam-6524	68	3	0	0	NUM
ejpam-6524	68	4	−1	−1	NOUN
ejpam-6524	68	5	0	0	NUM
ejpam-6524	68	6	0	0	NUM
ejpam-6524	68	7	0	0	NUM
ejpam-6524	68	8	−1	−1	NOUN
ejpam-6524	68	9	0	0	NUM
ejpam-6524	68	10	0	0	NUM
ejpam-6524	68	11	4	4	NUM
ejpam-6524	68	12	−1	−1	NOUN
ejpam-6524	68	13	0	0	NUM
ejpam-6524	68	14	0	0	NUM
ejpam-6524	68	15	0	0	NUM
ejpam-6524	68	16	0	0	NUM
ejpam-6524	68	17	0	0	NUM
ejpam-6524	68	18	−1	−1	NOUN
ejpam-6524	68	19	0	0	NUM
ejpam-6524	68	20	−1	−1	NOUN
ejpam-6524	68	21	4	4	NUM
ejpam-6524	68	22	−1	−1	NOUN
ejpam-6524	68	23	0	0	NUM
ejpam-6524	68	24	0	0	NUM
ejpam-6524	68	25	0	0	NUM
ejpam-6524	68	26	0	0	NUM
ejpam-6524	68	27	0	0	NUM
ejpam-6524	68	28	−1	−1	NOUN
ejpam-6524	68	29	0	0	NUM
ejpam-6524	68	30	−1	−1	NOUN
ejpam-6524	68	31	4	4	NUM
ejpam-6524	68	32			NOUN
ejpam-6524	68	33			VERB
ejpam-6524	69	1	u1,1	u1,1	PROPN
ejpam-6524	69	2	u1,2	u1,2	ADJ
ejpam-6524	69	3	u1,3	u1,3	NOUN
ejpam-6524	69	4	u2,1	u2,1	PROPN
ejpam-6524	70	1	u2,2	u2,2	PROPN
ejpam-6524	70	2	u2,3	u2,3	ADJ
ejpam-6524	70	3	u3,1	u3,1	NOUN
ejpam-6524	70	4	u3,2	u3,2	ADJ
ejpam-6524	70	5	u3,3	u3,3	NOUN
ejpam-6524	70	6			NOUN
ejpam-6524	70	7	=	=	PRON
ejpam-6524	70	8			VERB
ejpam-6524	70	9	−h2g1,1	−h2g1,1	NUM
ejpam-6524	70	10	−h2g1,2	−h2g1,2	NOUN
ejpam-6524	70	11	−h2g1,3	−h2g1,3	NUM
ejpam-6524	70	12	−h2g2,1	−h2g2,1	PROPN
ejpam-6524	70	13	−h2g2,2	−h2g2,2	NUM
ejpam-6524	70	14	−h2g2,3	−h2g2,3	NUM
ejpam-6524	70	15	−h2g3,1	−h2g3,1	PROPN
ejpam-6524	70	16	−h2g3,2	−h2g3,2	NOUN
ejpam-6524	70	17	−h2g3,3	−h2g3,3	PRON
ejpam-6524	70	18			PROPN
ejpam-6524	70	19	consequently	consequently	ADV
ejpam-6524	70	20	,	,	PUNCT
ejpam-6524	70	21	a	a	DET
ejpam-6524	70	22	system	system	NOUN
ejpam-6524	70	23	of	of	ADP
ejpam-6524	70	24	n	n	PRON
ejpam-6524	70	25	equations	equation	NOUN
ejpam-6524	70	26	was	be	AUX
ejpam-6524	70	27	created	create	VERB
ejpam-6524	70	28	by	by	ADP
ejpam-6524	70	29	(	(	PUNCT
ejpam-6524	70	30	1	1	NUM
ejpam-6524	70	31	)	)	PUNCT
ejpam-6524	70	32	.	.	PUNCT
ejpam-6524	71	1	here	here	ADV
ejpam-6524	71	2	,	,	PUNCT
ejpam-6524	71	3	n	n	PRON
ejpam-6524	71	4	represents	represent	VERB
ejpam-6524	71	5	the	the	DET
ejpam-6524	71	6	number	number	NOUN
ejpam-6524	71	7	of	of	ADP
ejpam-6524	71	8	subintervals	subinterval	NOUN
ejpam-6524	71	9	along	along	ADP
ejpam-6524	71	10	the	the	DET
ejpam-6524	71	11	x	x	NOUN
ejpam-6524	71	12	and	and	CCONJ
ejpam-6524	71	13	y	y	PROPN
ejpam-6524	71	14	axes	axis	NOUN
ejpam-6524	71	15	.	.	PUNCT
ejpam-6524	72	1	the	the	DET
ejpam-6524	72	2	coefficient	coefficient	NOUN
ejpam-6524	72	3	matrix	matrix	NOUN
ejpam-6524	72	4	is	be	AUX
ejpam-6524	72	5	both	both	PRON
ejpam-6524	72	6	positive	positive	ADJ
ejpam-6524	72	7	definite	definite	ADJ
ejpam-6524	72	8	and	and	CCONJ
ejpam-6524	72	9	symmetric	symmetric	ADJ
ejpam-6524	72	10	,	,	PUNCT
ejpam-6524	72	11	with	with	ADP
ejpam-6524	72	12	many	many	ADJ
ejpam-6524	72	13	elements	element	NOUN
ejpam-6524	72	14	being	be	AUX
ejpam-6524	72	15	zero	zero	NUM
ejpam-6524	72	16	,	,	PUNCT
ejpam-6524	72	17	making	make	VERB
ejpam-6524	72	18	it	it	PRON
ejpam-6524	72	19	sparse	sparse	ADJ
ejpam-6524	72	20	.	.	PUNCT
ejpam-6524	73	1	due	due	ADP
ejpam-6524	73	2	to	to	ADP
ejpam-6524	73	3	this	this	DET
ejpam-6524	73	4	sparsity	sparsity	NOUN
ejpam-6524	73	5	,	,	PUNCT
ejpam-6524	73	6	the	the	DET
ejpam-6524	73	7	system	system	NOUN
ejpam-6524	73	8	of	of	ADP
ejpam-6524	73	9	equations	equation	NOUN
ejpam-6524	73	10	is	be	AUX
ejpam-6524	73	11	best	well	ADV
ejpam-6524	73	12	solved	solve	VERB
ejpam-6524	73	13	using	use	VERB
ejpam-6524	73	14	an	an	DET
ejpam-6524	73	15	iterative	iterative	ADJ
ejpam-6524	73	16	approach	approach	NOUN
ejpam-6524	73	17	rather	rather	ADV
ejpam-6524	73	18	than	than	ADP
ejpam-6524	73	19	a	a	DET
ejpam-6524	73	20	direct	direct	ADJ
ejpam-6524	73	21	method	method	NOUN
ejpam-6524	73	22	.	.	PUNCT
ejpam-6524	74	1	we	we	PRON
ejpam-6524	74	2	consider	consider	VERB
ejpam-6524	74	3	a	a	DET
ejpam-6524	74	4	hyperbolic	hyperbolic	ADJ
ejpam-6524	74	5	pde	pde	NOUN
ejpam-6524	74	6	,	,	PUNCT
ejpam-6524	74	7	the	the	DET
ejpam-6524	74	8	numerical	numerical	ADJ
ejpam-6524	74	9	solution	solution	NOUN
ejpam-6524	74	10	to	to	ADP
ejpam-6524	74	11	the	the	DET
ejpam-6524	74	12	wave	wave	NOUN
ejpam-6524	74	13	equation	equation	NOUN
ejpam-6524	74	14	.	.	PUNCT
ejpam-6524	75	1	the	the	DET
ejpam-6524	75	2	differential	differential	ADJ
ejpam-6524	75	3	equation	equation	NOUN
ejpam-6524	75	4	provides	provide	VERB
ejpam-6524	75	5	the	the	DET
ejpam-6524	75	6	wave	wave	NOUN
ejpam-6524	75	7	equation	equation	NOUN
ejpam-6524	75	8	[	[	X
ejpam-6524	75	9	16	16	NUM
ejpam-6524	75	10	]	]	X
ejpam-6524	75	11	:	:	PUNCT
ejpam-6524	75	12	∂2u	∂2u	ADJ
ejpam-6524	75	13	∂t2	∂t2	PROPN
ejpam-6524	75	14	(	(	PUNCT
ejpam-6524	75	15	x	x	X
ejpam-6524	75	16	,	,	PUNCT
ejpam-6524	75	17	t)−	t)−	PROPN
ejpam-6524	75	18	α2∂	α2∂	PROPN
ejpam-6524	75	19	2u	2u	PROPN
ejpam-6524	75	20	∂x2	∂x2	PROPN
ejpam-6524	75	21	(	(	PUNCT
ejpam-6524	75	22	x	x	X
ejpam-6524	75	23	,	,	PUNCT
ejpam-6524	75	24	t	t	PROPN
ejpam-6524	75	25	)	)	PUNCT
ejpam-6524	75	26	=	=	SYM
ejpam-6524	75	27	0	0	NUM
ejpam-6524	75	28	,	,	PUNCT
ejpam-6524	75	29	0	0	PUNCT
ejpam-6524	75	30	<	<	X
ejpam-6524	75	31	x	x	X
ejpam-6524	75	32	<	<	X
ejpam-6524	75	33	l	l	PROPN
ejpam-6524	75	34	,	,	PUNCT
ejpam-6524	75	35	t	t	X
ejpam-6524	75	36	>	>	X
ejpam-6524	75	37	0	0	NUM
ejpam-6524	75	38	,	,	PUNCT
ejpam-6524	75	39	(	(	PUNCT
ejpam-6524	75	40	2	2	NUM
ejpam-6524	75	41	)	)	PUNCT
ejpam-6524	75	42	based	base	VERB
ejpam-6524	75	43	on	on	ADP
ejpam-6524	75	44	the	the	DET
ejpam-6524	75	45	terms	term	NOUN
ejpam-6524	75	46	u(0	u(0	PROPN
ejpam-6524	75	47	,	,	PUNCT
ejpam-6524	75	48	t	t	PROPN
ejpam-6524	75	49	)	)	PUNCT
ejpam-6524	75	50	=	=	SYM
ejpam-6524	76	1	u(l	u(l	PROPN
ejpam-6524	76	2	,	,	PUNCT
ejpam-6524	76	3	t	t	PROPN
ejpam-6524	76	4	)	)	PUNCT
ejpam-6524	76	5	=	=	SYM
ejpam-6524	76	6	0	0	NUM
ejpam-6524	76	7	,	,	PUNCT
ejpam-6524	76	8	for	for	ADP
ejpam-6524	76	9	t	t	PROPN
ejpam-6524	76	10	>	>	X
ejpam-6524	76	11	0	0	NUM
ejpam-6524	76	12	,	,	PUNCT
ejpam-6524	76	13	u(x	u(x	NOUN
ejpam-6524	76	14	,	,	PUNCT
ejpam-6524	76	15	0	0	NUM
ejpam-6524	76	16	)	)	PUNCT
ejpam-6524	76	17	=	=	SYM
ejpam-6524	76	18	f(x	f(x	PROPN
ejpam-6524	76	19	)	)	PUNCT
ejpam-6524	76	20	,	,	PUNCT
ejpam-6524	76	21	and	and	CCONJ
ejpam-6524	76	22	∂u	∂u	PROPN
ejpam-6524	76	23	∂t	∂t	PROPN
ejpam-6524	76	24	(	(	PUNCT
ejpam-6524	76	25	x	x	NOUN
ejpam-6524	76	26	,	,	PUNCT
ejpam-6524	76	27	0	0	NUM
ejpam-6524	76	28	)	)	PUNCT
ejpam-6524	76	29	=	=	SYM
ejpam-6524	76	30	g(x	g(x	NOUN
ejpam-6524	76	31	)	)	PUNCT
ejpam-6524	76	32	,	,	PUNCT
ejpam-6524	76	33	for	for	ADP
ejpam-6524	76	34	0	0	NUM
ejpam-6524	76	35	≤	≤	NUM
ejpam-6524	76	36	x	x	PUNCT
ejpam-6524	76	37	≤	≤	NUM
ejpam-6524	76	38	l	l	NOUN
ejpam-6524	76	39	,	,	PUNCT
ejpam-6524	76	40	where	where	SCONJ
ejpam-6524	76	41	α	α	NOUN
ejpam-6524	76	42	is	be	AUX
ejpam-6524	76	43	a	a	DET
ejpam-6524	76	44	constant	constant	ADJ
ejpam-6524	76	45	that	that	PRON
ejpam-6524	76	46	depends	depend	VERB
ejpam-6524	76	47	on	on	ADP
ejpam-6524	76	48	the	the	DET
ejpam-6524	76	49	problem	problem	NOUN
ejpam-6524	76	50	’s	’s	PART
ejpam-6524	76	51	physical	physical	ADJ
ejpam-6524	76	52	circumstances	circumstance	NOUN
ejpam-6524	76	53	.	.	PUNCT
ejpam-6524	77	1	to	to	PART
ejpam-6524	77	2	define	define	VERB
ejpam-6524	77	3	the	the	DET
ejpam-6524	77	4	x	x	ADJ
ejpam-6524	77	5	-	-	ADJ
ejpam-6524	77	6	axis	axis	ADJ
ejpam-6524	77	7	grid	grid	NOUN
ejpam-6524	77	8	points	point	NOUN
ejpam-6524	77	9	using	use	VERB
ejpam-6524	77	10	h	h	NOUN
ejpam-6524	77	11	=	=	PUNCT
ejpam-6524	77	12	l	l	NOUN
ejpam-6524	77	13	/	/	SYM
ejpam-6524	77	14	m	m	PROPN
ejpam-6524	77	15	,	,	PUNCT
ejpam-6524	77	16	choose	choose	VERB
ejpam-6524	77	17	an	an	DET
ejpam-6524	77	18	integer	integer	NOUN
ejpam-6524	77	19	m	m	PROPN
ejpam-6524	77	20	>	>	X
ejpam-6524	77	21	0	0	X
ejpam-6524	77	22	.	.	PUNCT
ejpam-6524	78	1	choose	choose	VERB
ejpam-6524	78	2	a	a	DET
ejpam-6524	78	3	time	time	NOUN
ejpam-6524	78	4	-	-	PUNCT
ejpam-6524	78	5	step	step	NOUN
ejpam-6524	78	6	size	size	NOUN
ejpam-6524	78	7	k	k	PROPN
ejpam-6524	78	8	>	>	X
ejpam-6524	78	9	0	0	PUNCT
ejpam-6524	78	10	as	as	ADV
ejpam-6524	78	11	well	well	ADV
ejpam-6524	78	12	.	.	PUNCT
ejpam-6524	79	1	the	the	DET
ejpam-6524	79	2	definition	definition	NOUN
ejpam-6524	79	3	of	of	ADP
ejpam-6524	79	4	the	the	DET
ejpam-6524	79	5	mesh	mesh	NOUN
ejpam-6524	79	6	points	point	NOUN
ejpam-6524	79	7	(	(	PUNCT
ejpam-6524	79	8	xi	xi	PROPN
ejpam-6524	79	9	,	,	PUNCT
ejpam-6524	79	10	tj	tj	NOUN
ejpam-6524	79	11	)	)	PUNCT
ejpam-6524	79	12	is	be	AUX
ejpam-6524	79	13	xi	xi	X
ejpam-6524	79	14	=	=	SYM
ejpam-6524	79	15	ih	ih	X
ejpam-6524	79	16	,	,	PUNCT
ejpam-6524	79	17	and	and	CCONJ
ejpam-6524	79	18	tj	tj	X
ejpam-6524	79	19	=	=	SYM
ejpam-6524	79	20	jk	jk	PROPN
ejpam-6524	79	21	,	,	PUNCT
ejpam-6524	79	22	for	for	ADP
ejpam-6524	79	23	each	each	DET
ejpam-6524	79	24	i	i	NOUN
ejpam-6524	79	25	=	=	NOUN
ejpam-6524	79	26	0	0	NUM
ejpam-6524	79	27	,	,	PUNCT
ejpam-6524	79	28	1	1	NUM
ejpam-6524	79	29	,	,	PUNCT
ejpam-6524	79	30	.	.	PUNCT
ejpam-6524	79	31	.	.	PUNCT
ejpam-6524	79	32	.	.	PUNCT
ejpam-6524	80	1	,	,	PUNCT
ejpam-6524	80	2	m	m	VERB
ejpam-6524	80	3	and	and	CCONJ
ejpam-6524	80	4	j	j	PROPN
ejpam-6524	80	5	=	=	SYM
ejpam-6524	80	6	0	0	PROPN
ejpam-6524	80	7	,	,	PUNCT
ejpam-6524	80	8	1	1	NUM
ejpam-6524	80	9	,	,	PUNCT
ejpam-6524	80	10	.	.	PUNCT
ejpam-6524	80	11	.	.	PUNCT
ejpam-6524	81	1	..	..	PUNCT
ejpam-6524	82	1	the	the	DET
ejpam-6524	82	2	wave	wave	NOUN
ejpam-6524	82	3	equation	equation	NOUN
ejpam-6524	82	4	changes	change	NOUN
ejpam-6524	82	5	to	to	ADP
ejpam-6524	82	6	(	(	PUNCT
ejpam-6524	82	7	xi	xi	PROPN
ejpam-6524	82	8	,	,	PUNCT
ejpam-6524	82	9	tj	tj	NOUN
ejpam-6524	82	10	)	)	PUNCT
ejpam-6524	82	11	at	at	ADP
ejpam-6524	82	12	any	any	DET
ejpam-6524	82	13	inner	inner	ADJ
ejpam-6524	82	14	mesh	mesh	NOUN
ejpam-6524	82	15	point	point	NOUN
ejpam-6524	82	16	.	.	PUNCT
ejpam-6524	83	1	∂2u	∂2u	ADJ
ejpam-6524	83	2	∂t2	∂t2	PROPN
ejpam-6524	83	3	(	(	PUNCT
ejpam-6524	83	4	xi	xi	X
ejpam-6524	83	5	,	,	PUNCT
ejpam-6524	83	6	tj)−	tj)−	NOUN
ejpam-6524	83	7	α2∂	α2∂	PROPN
ejpam-6524	83	8	2u	2u	PROPN
ejpam-6524	83	9	∂x2	∂x2	PROPN
ejpam-6524	83	10	(	(	PUNCT
ejpam-6524	83	11	xi	xi	PROPN
ejpam-6524	83	12	,	,	PUNCT
ejpam-6524	83	13	tj	tj	NOUN
ejpam-6524	83	14	)	)	PUNCT
ejpam-6524	83	15	=	=	SYM
ejpam-6524	83	16	0	0	X
ejpam-6524	83	17	.	.	PUNCT
ejpam-6524	84	1	(	(	PUNCT
ejpam-6524	84	2	3	3	X
ejpam-6524	84	3	)	)	PUNCT
ejpam-6524	84	4	the	the	DET
ejpam-6524	84	5	difference	difference	NOUN
ejpam-6524	84	6	technique	technique	NOUN
ejpam-6524	84	7	is	be	AUX
ejpam-6524	84	8	generated	generate	VERB
ejpam-6524	84	9	using	use	VERB
ejpam-6524	84	10	the	the	DET
ejpam-6524	84	11	centered	center	VERB
ejpam-6524	84	12	-	-	PUNCT
ejpam-6524	84	13	difference	difference	NOUN
ejpam-6524	84	14	quotient	quotient	NOUN
ejpam-6524	84	15	for	for	ADP
ejpam-6524	84	16	the	the	DET
ejpam-6524	84	17	second	second	ADJ
ejpam-6524	84	18	partial	partial	ADJ
ejpam-6524	84	19	derivatives	derivative	NOUN
ejpam-6524	84	20	given	give	VERB
ejpam-6524	84	21	by	by	ADP
ejpam-6524	84	22	∂2u	∂2u	ADJ
ejpam-6524	84	23	∂t2	∂t2	PROPN
ejpam-6524	84	24	(	(	PUNCT
ejpam-6524	84	25	xi	xi	PROPN
ejpam-6524	84	26	,	,	PUNCT
ejpam-6524	84	27	tj	tj	NOUN
ejpam-6524	84	28	)	)	PUNCT
ejpam-6524	84	29	=	=	SYM
ejpam-6524	84	30	u	u	NOUN
ejpam-6524	84	31	(	(	PUNCT
ejpam-6524	84	32	xi	xi	PROPN
ejpam-6524	84	33	,	,	PUNCT
ejpam-6524	84	34	tj+1)−	tj+1)−	PROPN
ejpam-6524	84	35	2u	2u	PROPN
ejpam-6524	84	36	(	(	PUNCT
ejpam-6524	84	37	xi	xi	PROPN
ejpam-6524	84	38	,	,	PUNCT
ejpam-6524	84	39	tj	tj	NOUN
ejpam-6524	84	40	)	)	PUNCT
ejpam-6524	85	1	+	+	NUM
ejpam-6524	85	2	u	u	SYM
ejpam-6524	85	3	(	(	PUNCT
ejpam-6524	85	4	xi	xi	PROPN
ejpam-6524	85	5	,	,	PUNCT
ejpam-6524	85	6	tj−1	tj−1	PROPN
ejpam-6524	85	7	)	)	PUNCT
ejpam-6524	85	8	k2	k2	PROPN
ejpam-6524	85	9	−	−	PROPN
ejpam-6524	85	10	k2	k2	PROPN
ejpam-6524	85	11	12	12	NUM
ejpam-6524	85	12	∂4u	∂4u	PROPN
ejpam-6524	85	13	∂t4	∂t4	NOUN
ejpam-6524	85	14	(	(	PUNCT
ejpam-6524	85	15	xi	xi	PROPN
ejpam-6524	85	16	,	,	PUNCT
ejpam-6524	85	17	µj	µj	PROPN
ejpam-6524	85	18	)	)	PUNCT
ejpam-6524	85	19	,	,	PUNCT
ejpam-6524	85	20	where	where	SCONJ
ejpam-6524	85	21	µj	µj	PROPN
ejpam-6524	85	22	∈	∈	PROPN
ejpam-6524	85	23	(	(	PUNCT
ejpam-6524	85	24	tj−1	tj−1	PROPN
ejpam-6524	85	25	,	,	PUNCT
ejpam-6524	85	26	tj+1	tj+1	NOUN
ejpam-6524	85	27	)	)	PUNCT
ejpam-6524	85	28	,	,	PUNCT
ejpam-6524	85	29	and	and	CCONJ
ejpam-6524	85	30	abdulkafi	abdulkafi	PROPN
ejpam-6524	85	31	m.	m.	PROPN
ejpam-6524	85	32	saeed	saeed	PROPN
ejpam-6524	85	33	,	,	PUNCT
ejpam-6524	85	34	shahad	shahad	PROPN
ejpam-6524	85	35	s.	s.	PROPN
ejpam-6524	85	36	almutairi	almutairi	PROPN
ejpam-6524	85	37	/	/	SYM
ejpam-6524	85	38	eur	eur	PROPN
ejpam-6524	85	39	.	.	PUNCT
ejpam-6524	86	1	j.	j.	PROPN
ejpam-6524	86	2	pure	pure	PROPN
ejpam-6524	86	3	appl	appl	PROPN
ejpam-6524	86	4	.	.	PROPN
ejpam-6524	86	5	math	math	PROPN
ejpam-6524	86	6	,	,	PUNCT
ejpam-6524	86	7	18	18	NUM
ejpam-6524	86	8	(	(	PUNCT
ejpam-6524	86	9	3	3	NUM
ejpam-6524	86	10	)	)	PUNCT
ejpam-6524	86	11	(	(	PUNCT
ejpam-6524	86	12	2025	2025	NUM
ejpam-6524	86	13	)	)	PUNCT
ejpam-6524	86	14	,	,	PUNCT
ejpam-6524	86	15	6524	6524	NUM
ejpam-6524	86	16	5	5	NUM
ejpam-6524	86	17	of	of	ADP
ejpam-6524	86	18	21	21	NUM
ejpam-6524	86	19	∂2u	∂2u	ADJ
ejpam-6524	86	20	∂x2	∂x2	PROPN
ejpam-6524	86	21	(	(	PUNCT
ejpam-6524	86	22	xi	xi	PROPN
ejpam-6524	86	23	,	,	PUNCT
ejpam-6524	86	24	tj	tj	NOUN
ejpam-6524	86	25	)	)	PUNCT
ejpam-6524	86	26	=	=	SYM
ejpam-6524	86	27	u	u	NOUN
ejpam-6524	86	28	(	(	PUNCT
ejpam-6524	86	29	xi+1	xi+1	NOUN
ejpam-6524	86	30	,	,	PUNCT
ejpam-6524	86	31	tj)−	tj)−	NOUN
ejpam-6524	86	32	2u	2u	NOUN
ejpam-6524	86	33	(	(	PUNCT
ejpam-6524	86	34	xi	xi	PROPN
ejpam-6524	86	35	,	,	PUNCT
ejpam-6524	86	36	tj	tj	NOUN
ejpam-6524	86	37	)	)	PUNCT
ejpam-6524	87	1	+	+	NUM
ejpam-6524	87	2	u	u	SYM
ejpam-6524	87	3	(	(	PUNCT
ejpam-6524	87	4	xi−1	xi−1	PROPN
ejpam-6524	87	5	,	,	PUNCT
ejpam-6524	87	6	tj	tj	NOUN
ejpam-6524	87	7	)	)	PUNCT
ejpam-6524	87	8	h2	h2	NOUN
ejpam-6524	87	9	−	−	PROPN
ejpam-6524	87	10	h2	h2	PROPN
ejpam-6524	87	11	12	12	NUM
ejpam-6524	87	12	∂4u	∂4u	NOUN
ejpam-6524	87	13	∂x4	∂x4	VERB
ejpam-6524	87	14	(	(	PUNCT
ejpam-6524	87	15	ξi	ξi	NOUN
ejpam-6524	87	16	,	,	PUNCT
ejpam-6524	87	17	tj	tj	NOUN
ejpam-6524	87	18	)	)	PUNCT
ejpam-6524	87	19	,	,	PUNCT
ejpam-6524	87	20	where	where	SCONJ
ejpam-6524	87	21	ξi	ξi	PROPN
ejpam-6524	87	22	∈	∈	PROPN
ejpam-6524	87	23	(	(	PUNCT
ejpam-6524	87	24	xi−1	xi−1	PROPN
ejpam-6524	87	25	,	,	PUNCT
ejpam-6524	87	26	xi+1	xi+1	NOUN
ejpam-6524	87	27	)	)	PUNCT
ejpam-6524	87	28	.	.	PUNCT
ejpam-6524	88	1	substituting	substitute	VERB
ejpam-6524	88	2	these	these	PRON
ejpam-6524	88	3	into	into	ADP
ejpam-6524	88	4	(	(	PUNCT
ejpam-6524	88	5	3	3	X
ejpam-6524	88	6	)	)	PUNCT
ejpam-6524	88	7	gives	give	VERB
ejpam-6524	88	8	u	u	PRON
ejpam-6524	88	9	(	(	PUNCT
ejpam-6524	88	10	xi	xi	PROPN
ejpam-6524	88	11	,	,	PUNCT
ejpam-6524	88	12	tj+1)−	tj+1)−	PROPN
ejpam-6524	88	13	2u	2u	PROPN
ejpam-6524	88	14	(	(	PUNCT
ejpam-6524	88	15	xi	xi	PROPN
ejpam-6524	88	16	,	,	PUNCT
ejpam-6524	88	17	tj	tj	NOUN
ejpam-6524	88	18	)	)	PUNCT
ejpam-6524	89	1	+	+	NUM
ejpam-6524	89	2	u	u	SYM
ejpam-6524	89	3	(	(	PUNCT
ejpam-6524	89	4	xi	xi	PROPN
ejpam-6524	89	5	,	,	PUNCT
ejpam-6524	89	6	tj−1	tj−1	PROPN
ejpam-6524	89	7	)	)	PUNCT
ejpam-6524	89	8	k2	k2	PROPN
ejpam-6524	89	9	−	−	PROPN
ejpam-6524	89	10	α2u	α2u	PROPN
ejpam-6524	89	11	(	(	PUNCT
ejpam-6524	89	12	xi+1	xi+1	NOUN
ejpam-6524	89	13	,	,	PUNCT
ejpam-6524	89	14	tj)−	tj)−	NOUN
ejpam-6524	89	15	2u	2u	NOUN
ejpam-6524	89	16	(	(	PUNCT
ejpam-6524	89	17	xi	xi	PROPN
ejpam-6524	89	18	,	,	PUNCT
ejpam-6524	89	19	tj	tj	NOUN
ejpam-6524	89	20	)	)	PUNCT
ejpam-6524	89	21	+	+	NUM
ejpam-6524	89	22	u	u	SYM
ejpam-6524	89	23	(	(	PUNCT
ejpam-6524	89	24	xi−1	xi−1	PROPN
ejpam-6524	89	25	,	,	PUNCT
ejpam-6524	89	26	tj	tj	NOUN
ejpam-6524	89	27	)	)	PUNCT
ejpam-6524	89	28	h2	h2	NOUN
ejpam-6524	89	29	=	=	SYM
ejpam-6524	89	30	1	1	NUM
ejpam-6524	89	31	12	12	NUM
ejpam-6524	89	32	[	[	PUNCT
ejpam-6524	89	33	k2	k2	ADJ
ejpam-6524	89	34	∂4u	∂4u	NOUN
ejpam-6524	89	35	∂t4	∂t4	NOUN
ejpam-6524	89	36	(	(	PUNCT
ejpam-6524	89	37	xi	xi	PROPN
ejpam-6524	89	38	,	,	PUNCT
ejpam-6524	89	39	µj)−	µj)−	NOUN
ejpam-6524	89	40	α2h2	α2h2	CCONJ
ejpam-6524	89	41	∂4u	∂4u	PROPN
ejpam-6524	89	42	∂x4	∂x4	VERB
ejpam-6524	89	43	(	(	PUNCT
ejpam-6524	89	44	ξi	ξi	NOUN
ejpam-6524	89	45	,	,	PUNCT
ejpam-6524	89	46	tj	tj	NOUN
ejpam-6524	89	47	)	)	PUNCT
ejpam-6524	89	48	]	]	PUNCT
ejpam-6524	89	49	.	.	PUNCT
ejpam-6524	90	1	ignoring	ignore	VERB
ejpam-6524	90	2	the	the	DET
ejpam-6524	90	3	incorrect	incorrect	ADJ
ejpam-6524	90	4	phrase	phrase	NOUN
ejpam-6524	90	5	τi	τi	AUX
ejpam-6524	90	6	,	,	PUNCT
ejpam-6524	90	7	j	j	PROPN
ejpam-6524	90	8	=	=	SYM
ejpam-6524	90	9	1	1	NUM
ejpam-6524	90	10	12	12	NUM
ejpam-6524	90	11	[	[	PUNCT
ejpam-6524	90	12	k2	k2	ADJ
ejpam-6524	90	13	∂4u	∂4u	NOUN
ejpam-6524	90	14	∂t4	∂t4	NOUN
ejpam-6524	90	15	(	(	PUNCT
ejpam-6524	90	16	xi	xi	PROPN
ejpam-6524	90	17	,	,	PUNCT
ejpam-6524	90	18	µj)−	µj)−	NOUN
ejpam-6524	90	19	α2h2	α2h2	CCONJ
ejpam-6524	90	20	∂4u	∂4u	PROPN
ejpam-6524	90	21	∂x4	∂x4	VERB
ejpam-6524	90	22	(	(	PUNCT
ejpam-6524	90	23	ξi	ξi	NOUN
ejpam-6524	90	24	,	,	PUNCT
ejpam-6524	90	25	tj	tj	NOUN
ejpam-6524	90	26	)	)	PUNCT
ejpam-6524	90	27	]	]	PUNCT
ejpam-6524	90	28	,	,	PUNCT
ejpam-6524	90	29	(	(	PUNCT
ejpam-6524	90	30	4	4	X
ejpam-6524	90	31	)	)	PUNCT
ejpam-6524	90	32	causes	cause	VERB
ejpam-6524	90	33	the	the	DET
ejpam-6524	90	34	distinction	distinction	NOUN
ejpam-6524	90	35	,	,	PUNCT
ejpam-6524	90	36	formula	formula	NOUN
ejpam-6524	90	37	wi	wi	PROPN
ejpam-6524	90	38	,	,	PUNCT
ejpam-6524	90	39	j+1	j+1	PROPN
ejpam-6524	90	40	−	−	PROPN
ejpam-6524	90	41	2wi	2wi	NOUN
ejpam-6524	90	42	,	,	PUNCT
ejpam-6524	90	43	j	j	PROPN
ejpam-6524	90	44	+	+	PROPN
ejpam-6524	90	45	wi	wi	PROPN
ejpam-6524	90	46	,	,	PUNCT
ejpam-6524	90	47	j−1	j−1	PROPN
ejpam-6524	90	48	k2	k2	PROPN
ejpam-6524	90	49	−	−	PROPN
ejpam-6524	90	50	α2wi+1,j	α2wi+1,j	NUM
ejpam-6524	90	51	−	−	PROPN
ejpam-6524	90	52	2wi	2wi	NOUN
ejpam-6524	90	53	,	,	PUNCT
ejpam-6524	90	54	j	j	PROPN
ejpam-6524	91	1	+	+	PUNCT
ejpam-6524	91	2	wi−1,j	wi−1,j	NOUN
ejpam-6524	91	3	h2	h2	NOUN
ejpam-6524	91	4	=	=	SYM
ejpam-6524	91	5	0	0	X
ejpam-6524	91	6	.	.	PUNCT
ejpam-6524	92	1	define	define	VERB
ejpam-6524	92	2	λ	λ	PROPN
ejpam-6524	92	3	=	=	SYM
ejpam-6524	92	4	αk	αk	PROPN
ejpam-6524	92	5	/	/	SYM
ejpam-6524	92	6	h.	h.	NOUN
ejpam-6524	93	1	the	the	DET
ejpam-6524	93	2	difference	difference	NOUN
ejpam-6524	93	3	equation	equation	NOUN
ejpam-6524	93	4	can	can	AUX
ejpam-6524	93	5	therefore	therefore	ADV
ejpam-6524	93	6	be	be	AUX
ejpam-6524	93	7	written	write	VERB
ejpam-6524	93	8	as	as	ADP
ejpam-6524	93	9	wi	wi	PROPN
ejpam-6524	93	10	,	,	PUNCT
ejpam-6524	93	11	j+1	j+1	PROPN
ejpam-6524	93	12	−	−	PROPN
ejpam-6524	93	13	2wi	2wi	NOUN
ejpam-6524	93	14	,	,	PUNCT
ejpam-6524	93	15	j	j	PROPN
ejpam-6524	93	16	+	+	CCONJ
ejpam-6524	93	17	wij−1	wij−1	NOUN
ejpam-6524	94	1	−	−	NOUN
ejpam-6524	94	2	λ2wi+1,j	λ2wi+1,j	NOUN
ejpam-6524	94	3	+	+	NOUN
ejpam-6524	94	4	2λ2wi	2λ2wi	NUM
ejpam-6524	94	5	,	,	PUNCT
ejpam-6524	94	6	j	j	PROPN
ejpam-6524	94	7	−	−	PROPN
ejpam-6524	94	8	λ2wi−1,j	λ2wi−1,j	NOUN
ejpam-6524	94	9	=	=	SYM
ejpam-6524	94	10	0	0	X
ejpam-6524	94	11	.	.	PUNCT
ejpam-6524	94	12	then	then	ADV
ejpam-6524	94	13	calculate	calculate	VERB
ejpam-6524	94	14	the	the	DET
ejpam-6524	94	15	most	most	ADV
ejpam-6524	94	16	advanced	advanced	ADJ
ejpam-6524	94	17	time	time	NOUN
ejpam-6524	94	18	-	-	PUNCT
ejpam-6524	94	19	step	step	NOUN
ejpam-6524	94	20	estimate	estimate	NOUN
ejpam-6524	94	21	,	,	PUNCT
ejpam-6524	94	22	wij+1	wij+1	NOUN
ejpam-6524	94	23	,	,	PUNCT
ejpam-6524	94	24	to	to	PART
ejpam-6524	94	25	obtain	obtain	VERB
ejpam-6524	94	26	wi	wi	PROPN
ejpam-6524	94	27	,	,	PUNCT
ejpam-6524	94	28	j+1	j+1	PROPN
ejpam-6524	94	29	=	=	SYM
ejpam-6524	94	30	2	2	NUM
ejpam-6524	94	31	(	(	PUNCT
ejpam-6524	94	32	1−	1−	NUM
ejpam-6524	94	33	λ2	λ2	NOUN
ejpam-6524	94	34	)	)	PUNCT
ejpam-6524	94	35	wi	wi	PROPN
ejpam-6524	94	36	,	,	PUNCT
ejpam-6524	94	37	j	j	PROPN
ejpam-6524	95	1	+	+	CCONJ
ejpam-6524	95	2	λ2	λ2	PROPN
ejpam-6524	95	3	(	(	PUNCT
ejpam-6524	95	4	wi+1,j	wi+1,j	NOUN
ejpam-6524	95	5	+	+	CCONJ
ejpam-6524	95	6	wi−1,j)−	wi−1,j)−	PROPN
ejpam-6524	95	7	wi	wi	PROPN
ejpam-6524	95	8	,	,	PUNCT
ejpam-6524	95	9	j−1	j−1	PROPN
ejpam-6524	95	10	.	.	PUNCT
ejpam-6524	96	1	(	(	PUNCT
ejpam-6524	96	2	5	5	NUM
ejpam-6524	96	3	)	)	PUNCT
ejpam-6524	96	4	for	for	ADP
ejpam-6524	96	5	any	any	DET
ejpam-6524	96	6	i	i	NOUN
ejpam-6524	96	7	=	=	NOUN
ejpam-6524	96	8	1	1	NUM
ejpam-6524	96	9	,	,	PUNCT
ejpam-6524	96	10	2	2	NUM
ejpam-6524	96	11	,	,	PUNCT
ejpam-6524	96	12	.	.	PUNCT
ejpam-6524	96	13	.	.	PUNCT
ejpam-6524	96	14	.	.	PUNCT
ejpam-6524	97	1	,	,	PUNCT
ejpam-6524	97	2	m	m	VERB
ejpam-6524	97	3	−	−	NOUN
ejpam-6524	97	4	1	1	NUM
ejpam-6524	97	5	and	and	CCONJ
ejpam-6524	97	6	j	j	NOUN
ejpam-6524	97	7	=	=	SYM
ejpam-6524	97	8	1	1	NUM
ejpam-6524	97	9	,	,	PUNCT
ejpam-6524	97	10	2	2	NUM
ejpam-6524	97	11	,	,	PUNCT
ejpam-6524	97	12	.	.	PUNCT
ejpam-6524	97	13	.	.	PUNCT
ejpam-6524	98	1	.	.	PUNCT
ejpam-6524	98	2	,	,	PUNCT
ejpam-6524	98	3	this	this	DET
ejpam-6524	98	4	equation	equation	NOUN
ejpam-6524	98	5	is	be	AUX
ejpam-6524	98	6	true	true	ADJ
ejpam-6524	98	7	.	.	PUNCT
ejpam-6524	99	1	the	the	DET
ejpam-6524	99	2	boundary	boundary	ADJ
ejpam-6524	99	3	conditions	condition	NOUN
ejpam-6524	99	4	give	give	VERB
ejpam-6524	99	5	w0,j	w0,j	PROPN
ejpam-6524	99	6	=	=	SYM
ejpam-6524	99	7	wm	wm	PROPN
ejpam-6524	99	8	,	,	PUNCT
ejpam-6524	99	9	j	j	PROPN
ejpam-6524	99	10	=	=	SYM
ejpam-6524	99	11	0	0	PROPN
ejpam-6524	99	12	,	,	PUNCT
ejpam-6524	99	13	for	for	ADP
ejpam-6524	99	14	each	each	DET
ejpam-6524	99	15	j	j	PROPN
ejpam-6524	99	16	=	=	SYM
ejpam-6524	99	17	1	1	NUM
ejpam-6524	99	18	,	,	PUNCT
ejpam-6524	99	19	2	2	NUM
ejpam-6524	99	20	,	,	PUNCT
ejpam-6524	99	21	3	3	NUM
ejpam-6524	99	22	,	,	PUNCT
ejpam-6524	99	23	.	.	PUNCT
ejpam-6524	99	24	.	.	PUNCT
ejpam-6524	99	25	.	.	PUNCT
ejpam-6524	100	1	,	,	PUNCT
ejpam-6524	100	2	(	(	PUNCT
ejpam-6524	100	3	6	6	NUM
ejpam-6524	100	4	)	)	PUNCT
ejpam-6524	100	5	and	and	CCONJ
ejpam-6524	100	6	the	the	DET
ejpam-6524	100	7	initial	initial	ADJ
ejpam-6524	100	8	condition	condition	NOUN
ejpam-6524	100	9	implies	imply	VERB
ejpam-6524	100	10	that	that	SCONJ
ejpam-6524	100	11	wi,0	wi,0	PROPN
ejpam-6524	100	12	=	=	SYM
ejpam-6524	100	13	f	f	PROPN
ejpam-6524	100	14	(	(	PUNCT
ejpam-6524	100	15	xi	xi	PROPN
ejpam-6524	100	16	)	)	PUNCT
ejpam-6524	100	17	,	,	PUNCT
ejpam-6524	100	18	for	for	ADP
ejpam-6524	100	19	each	each	DET
ejpam-6524	100	20	i	i	NOUN
ejpam-6524	100	21	=	=	NOUN
ejpam-6524	100	22	1	1	NUM
ejpam-6524	100	23	,	,	PUNCT
ejpam-6524	100	24	2	2	NUM
ejpam-6524	100	25	,	,	PUNCT
ejpam-6524	100	26	.	.	PUNCT
ejpam-6524	100	27	.	.	PUNCT
ejpam-6524	100	28	.	.	PUNCT
ejpam-6524	101	1	,	,	PUNCT
ejpam-6524	101	2	m−	m−	PROPN
ejpam-6524	101	3	1	1	NUM
ejpam-6524	101	4	.	.	PUNCT
ejpam-6524	102	1	this	this	DET
ejpam-6524	102	2	set	set	NOUN
ejpam-6524	102	3	of	of	ADP
ejpam-6524	102	4	equations	equation	NOUN
ejpam-6524	102	5	can	can	AUX
ejpam-6524	102	6	be	be	AUX
ejpam-6524	102	7	written	write	VERB
ejpam-6524	102	8	in	in	ADP
ejpam-6524	102	9	matrix	matrix	NOUN
ejpam-6524	102	10	form	form	NOUN
ejpam-6524	102	11	to	to	PART
ejpam-6524	102	12	give	give	VERB
ejpam-6524	102	13			PROPN
ejpam-6524	102	14	w1,j+1	w1,j+1	PROPN
ejpam-6524	102	15	w2,j+1	w2,j+1	PROPN
ejpam-6524	102	16	...	...	PUNCT
ejpam-6524	103	1	wm−1,j+1	wm−1,j+1	NOUN
ejpam-6524	103	2			NOUN
ejpam-6524	103	3	=	=	SYM
ejpam-6524	103	4			NOUN
ejpam-6524	103	5	2(1−	2(1−	NUM
ejpam-6524	103	6	λ2	λ2	NOUN
ejpam-6524	103	7	)	)	PUNCT
ejpam-6524	103	8	λ2	λ2	NOUN
ejpam-6524	103	9	0	0	NUM
ejpam-6524	103	10	·	·	PUNCT
ejpam-6524	103	11	·	·	PUNCT
ejpam-6524	103	12	·	·	PUNCT
ejpam-6524	103	13	0	0	NUM
ejpam-6524	104	1	λ2	λ2	NOUN
ejpam-6524	104	2	2(1−	2(1−	NUM
ejpam-6524	104	3	λ2	λ2	NUM
ejpam-6524	104	4	)	)	PUNCT
ejpam-6524	104	5	λ2	λ2	NOUN
ejpam-6524	104	6	·	·	PUNCT
ejpam-6524	104	7	·	·	PUNCT
ejpam-6524	104	8	·	·	PUNCT
ejpam-6524	104	9	0	0	NUM
ejpam-6524	104	10	0	0	NUM
ejpam-6524	104	11	...	...	PUNCT
ejpam-6524	104	12	·	·	PUNCT
ejpam-6524	104	13	·	·	PUNCT
ejpam-6524	104	14	·	·	PUNCT
ejpam-6524	104	15	·	·	PUNCT
ejpam-6524	104	16	·	·	PUNCT
ejpam-6524	104	17	·	·	PUNCT
ejpam-6524	104	18	...	...	PUNCT
ejpam-6524	104	19	...	...	PUNCT
ejpam-6524	104	20	.	.	PUNCT
ejpam-6524	104	21	.	.	PUNCT
ejpam-6524	104	22	.	.	PUNCT
ejpam-6524	105	1	...	...	PUNCT
ejpam-6524	105	2	0	0	NUM
ejpam-6524	106	1	...	...	PUNCT
ejpam-6524	106	2	λ2	λ2	NOUN
ejpam-6524	106	3	2(1−	2(1−	NUM
ejpam-6524	106	4	λ2	λ2	NOUN
ejpam-6524	106	5	)	)	PUNCT
ejpam-6524	106	6			PUNCT
ejpam-6524	107	1	=	=	PUNCT
ejpam-6524	107	2			PROPN
ejpam-6524	107	3	w1,j	w1,j	PROPN
ejpam-6524	107	4	w2,j	w2,j	PROPN
ejpam-6524	107	5	...	...	PUNCT
ejpam-6524	107	6	wm−1,j	wm−1,j	INTJ
ejpam-6524	107	7	−	−	PUNCT
ejpam-6524	108	1			PROPN
ejpam-6524	108	2	w1,j−1	w1,j−1	NOUN
ejpam-6524	108	3	w2,j−1	w2,j−1	NOUN
ejpam-6524	108	4	...	...	PUNCT
ejpam-6524	109	1	wm−1,j−1	wm−1,j−1	NOUN
ejpam-6524	109	2			X
ejpam-6524	109	3	(	(	PUNCT
ejpam-6524	109	4	7	7	X
ejpam-6524	109	5	)	)	PUNCT
ejpam-6524	109	6	abdulkafi	abdulkafi	PROPN
ejpam-6524	109	7	m.	m.	PROPN
ejpam-6524	109	8	saeed	saeed	PROPN
ejpam-6524	109	9	,	,	PUNCT
ejpam-6524	109	10	shahad	shahad	PROPN
ejpam-6524	109	11	s.	s.	PROPN
ejpam-6524	109	12	almutairi	almutairi	PROPN
ejpam-6524	109	13	/	/	SYM
ejpam-6524	109	14	eur	eur	PROPN
ejpam-6524	109	15	.	.	PUNCT
ejpam-6524	110	1	j.	j.	PROPN
ejpam-6524	110	2	pure	pure	PROPN
ejpam-6524	110	3	appl	appl	PROPN
ejpam-6524	110	4	.	.	PROPN
ejpam-6524	110	5	math	math	PROPN
ejpam-6524	110	6	,	,	PUNCT
ejpam-6524	110	7	18	18	NUM
ejpam-6524	110	8	(	(	PUNCT
ejpam-6524	110	9	3	3	NUM
ejpam-6524	110	10	)	)	PUNCT
ejpam-6524	110	11	(	(	PUNCT
ejpam-6524	110	12	2025	2025	NUM
ejpam-6524	110	13	)	)	PUNCT
ejpam-6524	110	14	,	,	PUNCT
ejpam-6524	110	15	6524	6524	NUM
ejpam-6524	110	16	6	6	NUM
ejpam-6524	110	17	of	of	ADP
ejpam-6524	110	18	21	21	NUM
ejpam-6524	110	19	according	accord	VERB
ejpam-6524	110	20	to	to	ADP
ejpam-6524	110	21	equations	equation	NOUN
ejpam-6524	110	22	(	(	PUNCT
ejpam-6524	110	23	4	4	NUM
ejpam-6524	110	24	)	)	PUNCT
ejpam-6524	110	25	and	and	CCONJ
ejpam-6524	110	26	(	(	PUNCT
ejpam-6524	110	27	7	7	NUM
ejpam-6524	110	28	)	)	PUNCT
ejpam-6524	110	29	,	,	PUNCT
ejpam-6524	110	30	values	value	NOUN
ejpam-6524	110	31	from	from	ADP
ejpam-6524	110	32	the	the	DET
ejpam-6524	110	33	j	j	PROPN
ejpam-6524	110	34	th	th	X
ejpam-6524	110	35	and	and	CCONJ
ejpam-6524	110	36	(	(	PUNCT
ejpam-6524	110	37	j	j	PROPN
ejpam-6524	110	38	−	−	PROPN
ejpam-6524	110	39	1	1	NUM
ejpam-6524	110	40	)	)	PUNCT
ejpam-6524	110	41	st	st	NOUN
ejpam-6524	110	42	time	time	NOUN
ejpam-6524	110	43	steps	step	NOUN
ejpam-6524	110	44	are	be	AUX
ejpam-6524	110	45	needed	need	VERB
ejpam-6524	110	46	for	for	ADP
ejpam-6524	110	47	the	the	DET
ejpam-6524	110	48	(	(	PUNCT
ejpam-6524	110	49	j	j	NOUN
ejpam-6524	110	50	+	+	CCONJ
ejpam-6524	110	51	1	1	X
ejpam-6524	110	52	)	)	PUNCT
ejpam-6524	110	53	st	st	NOUN
ejpam-6524	110	54	time	time	NOUN
ejpam-6524	110	55	step	step	NOUN
ejpam-6524	110	56	.	.	PUNCT
ejpam-6524	111	1	figure	figure	NOUN
ejpam-6524	111	2	2	2	NUM
ejpam-6524	111	3	is	be	AUX
ejpam-6524	111	4	referred	refer	VERB
ejpam-6524	111	5	to	to	ADP
ejpam-6524	111	6	.	.	PUNCT
ejpam-6524	112	1	because	because	SCONJ
ejpam-6524	112	2	(	(	PUNCT
ejpam-6524	112	3	6	6	NUM
ejpam-6524	112	4	)	)	PUNCT
ejpam-6524	112	5	gives	give	VERB
ejpam-6524	112	6	values	value	NOUN
ejpam-6524	112	7	for	for	ADP
ejpam-6524	112	8	j	j	PROPN
ejpam-6524	112	9	=	=	SYM
ejpam-6524	112	10	0	0	PROPN
ejpam-6524	112	11	,	,	PUNCT
ejpam-6524	112	12	but	but	CCONJ
ejpam-6524	112	13	the	the	DET
ejpam-6524	112	14	starting	start	VERB
ejpam-6524	112	15	-	-	PUNCT
ejpam-6524	112	16	velocity	velocity	NOUN
ejpam-6524	112	17	condition	condition	NOUN
ejpam-6524	112	18	has	have	VERB
ejpam-6524	112	19	to	to	PART
ejpam-6524	112	20	give	give	VERB
ejpam-6524	112	21	values	value	NOUN
ejpam-6524	112	22	for	for	ADP
ejpam-6524	112	23	j	j	PROPN
ejpam-6524	112	24	=	=	SYM
ejpam-6524	112	25	1	1	PROPN
ejpam-6524	112	26	,	,	PUNCT
ejpam-6524	112	27	which	which	PRON
ejpam-6524	112	28	are	be	AUX
ejpam-6524	112	29	needed	need	VERB
ejpam-6524	112	30	in	in	ADP
ejpam-6524	112	31	(	(	PUNCT
ejpam-6524	112	32	4	4	NUM
ejpam-6524	112	33	)	)	PUNCT
ejpam-6524	112	34	to	to	PART
ejpam-6524	112	35	compute	compute	VERB
ejpam-6524	112	36	wi,2	wi,2	PROPN
ejpam-6524	112	37	,	,	PUNCT
ejpam-6524	112	38	this	this	PRON
ejpam-6524	112	39	leads	lead	VERB
ejpam-6524	112	40	to	to	ADP
ejpam-6524	112	41	a	a	DET
ejpam-6524	112	42	minor	minor	ADJ
ejpam-6524	112	43	initial	initial	ADJ
ejpam-6524	112	44	problem	problem	NOUN
ejpam-6524	112	45	.	.	PUNCT
ejpam-6524	113	1	∂u	∂u	PROPN
ejpam-6524	113	2	∂t	∂t	PROPN
ejpam-6524	113	3	(	(	PUNCT
ejpam-6524	113	4	x	x	NOUN
ejpam-6524	113	5	,	,	PUNCT
ejpam-6524	113	6	0	0	NUM
ejpam-6524	113	7	)	)	PUNCT
ejpam-6524	113	8	=	=	SYM
ejpam-6524	113	9	g(x	g(x	NOUN
ejpam-6524	113	10	)	)	PUNCT
ejpam-6524	113	11	,	,	PUNCT
ejpam-6524	113	12	0	0	NUM
ejpam-6524	113	13	≤	≤	NUM
ejpam-6524	113	14	x	x	X
ejpam-6524	113	15	≤	≤	PROPN
ejpam-6524	113	16	l.	l.	NOUN
ejpam-6524	113	17	figure	figure	NOUN
ejpam-6524	113	18	2	2	NUM
ejpam-6524	113	19	:	:	PUNCT
ejpam-6524	113	20	discretization	discretization	NOUN
ejpam-6524	113	21	of	of	ADP
ejpam-6524	113	22	mesh	mesh	NOUN
ejpam-6524	113	23	points	point	NOUN
ejpam-6524	113	24	one	one	NUM
ejpam-6524	113	25	method	method	NOUN
ejpam-6524	113	26	is	be	AUX
ejpam-6524	113	27	to	to	PART
ejpam-6524	113	28	use	use	VERB
ejpam-6524	113	29	a	a	DET
ejpam-6524	113	30	forward	forward	ADJ
ejpam-6524	113	31	-	-	PUNCT
ejpam-6524	113	32	difference	difference	NOUN
ejpam-6524	113	33	approximation	approximation	NOUN
ejpam-6524	113	34	to	to	PART
ejpam-6524	113	35	replace	replace	VERB
ejpam-6524	113	36	∂u/∂t	∂u/∂t	PROPN
ejpam-6524	113	37	.	.	PUNCT
ejpam-6524	114	1	∂u	∂u	PROPN
ejpam-6524	114	2	∂t	∂t	PROPN
ejpam-6524	114	3	(	(	PUNCT
ejpam-6524	114	4	xi	xi	PROPN
ejpam-6524	114	5	,	,	PUNCT
ejpam-6524	114	6	0	0	NUM
ejpam-6524	114	7	)	)	PUNCT
ejpam-6524	114	8	=	=	SYM
ejpam-6524	114	9	u	u	NOUN
ejpam-6524	114	10	(	(	PUNCT
ejpam-6524	114	11	xi	xi	PROPN
ejpam-6524	114	12	,	,	PUNCT
ejpam-6524	114	13	t1)−	t1)−	NOUN
ejpam-6524	114	14	u	u	NOUN
ejpam-6524	114	15	(	(	PUNCT
ejpam-6524	114	16	xi	xi	PROPN
ejpam-6524	114	17	,	,	PUNCT
ejpam-6524	114	18	0	0	NUM
ejpam-6524	114	19	)	)	PUNCT
ejpam-6524	115	1	k	k	NOUN
ejpam-6524	115	2	−	−	PUNCT
ejpam-6524	115	3	k	k	PROPN
ejpam-6524	115	4	2	2	NUM
ejpam-6524	115	5	∂2u	∂2u	ADJ
ejpam-6524	115	6	∂t2	∂t2	X
ejpam-6524	115	7	(	(	PUNCT
ejpam-6524	115	8	xi	xi	PROPN
ejpam-6524	115	9	,	,	PUNCT
ejpam-6524	115	10	µ̃i	µ̃i	NUM
ejpam-6524	115	11	)	)	PUNCT
ejpam-6524	115	12	,	,	PUNCT
ejpam-6524	115	13	for	for	ADP
ejpam-6524	115	14	some	some	DET
ejpam-6524	115	15	µ̃i	µ̃i	NOUN
ejpam-6524	115	16	in	in	ADP
ejpam-6524	115	17	(	(	PUNCT
ejpam-6524	115	18	0	0	NUM
ejpam-6524	115	19	,	,	PUNCT
ejpam-6524	115	20	t1).the	t1).the	DET
ejpam-6524	115	21	equation	equation	NOUN
ejpam-6524	115	22	’s	’s	PART
ejpam-6524	115	23	u	u	NOUN
ejpam-6524	115	24	(	(	PUNCT
ejpam-6524	115	25	xi	xi	PROPN
ejpam-6524	115	26	,	,	PUNCT
ejpam-6524	115	27	t1	t1	NOUN
ejpam-6524	115	28	)	)	PUNCT
ejpam-6524	115	29	can	can	AUX
ejpam-6524	115	30	be	be	AUX
ejpam-6524	115	31	solved	solve	VERB
ejpam-6524	115	32	to	to	PART
ejpam-6524	115	33	yield	yield	VERB
ejpam-6524	115	34	u	u	PROPN
ejpam-6524	115	35	(	(	PUNCT
ejpam-6524	115	36	xi	xi	PROPN
ejpam-6524	115	37	,	,	PUNCT
ejpam-6524	115	38	t1	t1	NOUN
ejpam-6524	115	39	)	)	PUNCT
ejpam-6524	116	1	=	=	SYM
ejpam-6524	116	2	u	u	NOUN
ejpam-6524	116	3	(	(	PUNCT
ejpam-6524	116	4	xi	xi	PROPN
ejpam-6524	116	5	,	,	PUNCT
ejpam-6524	116	6	0	0	NUM
ejpam-6524	116	7	)	)	PUNCT
ejpam-6524	117	1	+	+	CCONJ
ejpam-6524	118	1	k	k	PROPN
ejpam-6524	118	2	∂u	∂u	PROPN
ejpam-6524	118	3	∂t	∂t	PROPN
ejpam-6524	118	4	(	(	PUNCT
ejpam-6524	118	5	xi	xi	PROPN
ejpam-6524	118	6	,	,	PUNCT
ejpam-6524	118	7	0	0	NUM
ejpam-6524	118	8	)	)	PUNCT
ejpam-6524	118	9	+	+	CCONJ
ejpam-6524	118	10	k2	k2	ADJ
ejpam-6524	118	11	2	2	NUM
ejpam-6524	118	12	∂2u	∂2u	PROPN
ejpam-6524	118	13	∂t2	∂t2	PROPN
ejpam-6524	118	14	(	(	PUNCT
ejpam-6524	118	15	xi	xi	PROPN
ejpam-6524	118	16	,	,	PUNCT
ejpam-6524	118	17	µ̃i	µ̃i	NUM
ejpam-6524	118	18	)	)	PUNCT
ejpam-6524	118	19	=	=	SYM
ejpam-6524	118	20	u	u	NOUN
ejpam-6524	118	21	(	(	PUNCT
ejpam-6524	118	22	xi	xi	PROPN
ejpam-6524	118	23	,	,	PUNCT
ejpam-6524	118	24	0	0	NUM
ejpam-6524	118	25	)	)	PUNCT
ejpam-6524	119	1	+	+	NUM
ejpam-6524	119	2	kg	kg	INTJ
ejpam-6524	119	3	(	(	PUNCT
ejpam-6524	119	4	xi	xi	PROPN
ejpam-6524	119	5	)	)	PUNCT
ejpam-6524	119	6	+	+	CCONJ
ejpam-6524	119	7	k2	k2	ADJ
ejpam-6524	119	8	2	2	NUM
ejpam-6524	119	9	∂2u	∂2u	PROPN
ejpam-6524	119	10	∂t2	∂t2	PROPN
ejpam-6524	119	11	(	(	PUNCT
ejpam-6524	119	12	xi	xi	PROPN
ejpam-6524	119	13	,	,	PUNCT
ejpam-6524	119	14	µ̃i	µ̃i	NUM
ejpam-6524	119	15	)	)	PUNCT
ejpam-6524	119	16	.	.	PUNCT
ejpam-6524	120	1	when	when	SCONJ
ejpam-6524	120	2	the	the	DET
ejpam-6524	120	3	truncation	truncation	NOUN
ejpam-6524	120	4	phrase	phrase	NOUN
ejpam-6524	120	5	is	be	AUX
ejpam-6524	120	6	removed	remove	VERB
ejpam-6524	120	7	,	,	PUNCT
ejpam-6524	120	8	the	the	DET
ejpam-6524	120	9	approximate	approximate	ADJ
ejpam-6524	120	10	wi,1	wi,1	PROPN
ejpam-6524	120	11	=	=	SYM
ejpam-6524	120	12	wi,0	wi,0	PROPN
ejpam-6524	120	13	+	+	CCONJ
ejpam-6524	120	14	kg	kg	INTJ
ejpam-6524	120	15	(	(	PUNCT
ejpam-6524	120	16	xi	xi	PROPN
ejpam-6524	120	17	)	)	PUNCT
ejpam-6524	120	18	,	,	PUNCT
ejpam-6524	120	19	for	for	ADP
ejpam-6524	120	20	each	each	DET
ejpam-6524	120	21	i	i	NOUN
ejpam-6524	120	22	=	=	NOUN
ejpam-6524	120	23	1	1	NUM
ejpam-6524	120	24	,	,	PUNCT
ejpam-6524	120	25	.	.	PUNCT
ejpam-6524	120	26	.	.	PUNCT
ejpam-6524	120	27	.	.	PUNCT
ejpam-6524	121	1	,	,	PUNCT
ejpam-6524	121	2	m−	m−	PROPN
ejpam-6524	121	3	1	1	NUM
ejpam-6524	121	4	.	.	PUNCT
ejpam-6524	122	1	the	the	DET
ejpam-6524	122	2	truncation	truncation	NOUN
ejpam-6524	122	3	error	error	NOUN
ejpam-6524	122	4	in	in	ADP
ejpam-6524	122	5	our	our	PRON
ejpam-6524	122	6	approximation	approximation	NOUN
ejpam-6524	122	7	is	be	AUX
ejpam-6524	122	8	only	only	ADV
ejpam-6524	122	9	o(k	o(k	NOUN
ejpam-6524	122	10	)	)	PUNCT
ejpam-6524	122	11	,	,	PUNCT
ejpam-6524	122	12	whereas	whereas	SCONJ
ejpam-6524	122	13	the	the	DET
ejpam-6524	122	14	truncation	truncation	NOUN
ejpam-6524	122	15	error	error	NOUN
ejpam-6524	122	16	in	in	ADP
ejpam-6524	122	17	(	(	PUNCT
ejpam-6524	122	18	5	5	NUM
ejpam-6524	122	19	)	)	PUNCT
ejpam-6524	122	20	is	be	AUX
ejpam-6524	122	21	o	o	NOUN
ejpam-6524	122	22	(	(	PUNCT
ejpam-6524	122	23	k2	k2	PROPN
ejpam-6524	122	24	)	)	PUNCT
ejpam-6524	122	25	.	.	PUNCT
ejpam-6524	123	1	a	a	DET
ejpam-6524	123	2	better	well	ADJ
ejpam-6524	123	3	approximation	approximation	NOUN
ejpam-6524	123	4	to	to	ADP
ejpam-6524	123	5	u	u	PROPN
ejpam-6524	123	6	(	(	PUNCT
ejpam-6524	123	7	xi	xi	PROPN
ejpam-6524	123	8	,	,	PUNCT
ejpam-6524	123	9	0	0	NUM
ejpam-6524	123	10	)	)	PUNCT
ejpam-6524	123	11	is	be	AUX
ejpam-6524	123	12	obtained	obtain	VERB
ejpam-6524	123	13	by	by	ADP
ejpam-6524	123	14	expanding	expand	VERB
ejpam-6524	123	15	in	in	ADP
ejpam-6524	123	16	t	t	PROPN
ejpam-6524	123	17	,	,	PUNCT
ejpam-6524	123	18	u	u	NOUN
ejpam-6524	123	19	(	(	PUNCT
ejpam-6524	123	20	xi	xi	PROPN
ejpam-6524	123	21	,	,	PUNCT
ejpam-6524	123	22	t1	t1	PROPN
ejpam-6524	123	23	)	)	PUNCT
ejpam-6524	123	24	is	be	AUX
ejpam-6524	123	25	a	a	DET
ejpam-6524	123	26	second	second	ADJ
ejpam-6524	123	27	maclaurin	maclaurin	NOUN
ejpam-6524	123	28	polynomial	polynomial	NOUN
ejpam-6524	123	29	.	.	PUNCT
ejpam-6524	124	1	then	then	ADV
ejpam-6524	124	2	,	,	PUNCT
ejpam-6524	124	3	u	u	PROPN
ejpam-6524	124	4	(	(	PUNCT
ejpam-6524	124	5	xi	xi	PROPN
ejpam-6524	124	6	,	,	PUNCT
ejpam-6524	124	7	t1	t1	NOUN
ejpam-6524	124	8	)	)	PUNCT
ejpam-6524	124	9	=	=	SYM
ejpam-6524	124	10	u	u	NOUN
ejpam-6524	124	11	(	(	PUNCT
ejpam-6524	124	12	xi	xi	PROPN
ejpam-6524	124	13	,	,	PUNCT
ejpam-6524	124	14	0	0	NUM
ejpam-6524	124	15	)	)	PUNCT
ejpam-6524	124	16	+	+	CCONJ
ejpam-6524	125	1	k	k	PROPN
ejpam-6524	125	2	∂u	∂u	PROPN
ejpam-6524	125	3	∂t	∂t	PROPN
ejpam-6524	125	4	(	(	PUNCT
ejpam-6524	125	5	xi	xi	PROPN
ejpam-6524	125	6	,	,	PUNCT
ejpam-6524	125	7	0	0	NUM
ejpam-6524	125	8	)	)	PUNCT
ejpam-6524	125	9	+	+	CCONJ
ejpam-6524	125	10	k2	k2	ADJ
ejpam-6524	125	11	2	2	NUM
ejpam-6524	125	12	∂2u	∂2u	PROPN
ejpam-6524	125	13	∂t2	∂t2	PROPN
ejpam-6524	125	14	(	(	PUNCT
ejpam-6524	125	15	xi	xi	PROPN
ejpam-6524	125	16	,	,	PUNCT
ejpam-6524	125	17	0	0	NUM
ejpam-6524	125	18	)	)	PUNCT
ejpam-6524	125	19	+	+	CCONJ
ejpam-6524	125	20	k3	k3	VERB
ejpam-6524	125	21	6	6	NUM
ejpam-6524	125	22	∂3u	∂3u	ADJ
ejpam-6524	125	23	∂t3	∂t3	ADJ
ejpam-6524	125	24	(	(	PUNCT
ejpam-6524	125	25	xi	xi	PROPN
ejpam-6524	125	26	,	,	PUNCT
ejpam-6524	125	27	µ̂i	µ̂i	NUM
ejpam-6524	125	28	)	)	PUNCT
ejpam-6524	125	29	,	,	PUNCT
ejpam-6524	125	30	for	for	ADP
ejpam-6524	125	31	some	some	PRON
ejpam-6524	125	32	µ̂i	µ̂i	NUM
ejpam-6524	125	33	in	in	ADP
ejpam-6524	125	34	(	(	PUNCT
ejpam-6524	125	35	0	0	NUM
ejpam-6524	125	36	,	,	PUNCT
ejpam-6524	125	37	t1	t1	NOUN
ejpam-6524	125	38	)	)	PUNCT
ejpam-6524	125	39	.	.	PUNCT
ejpam-6524	126	1	if	if	SCONJ
ejpam-6524	126	2	f	f	PRON
ejpam-6524	126	3	′′	′′	PROPN
ejpam-6524	126	4	exists	exist	VERB
ejpam-6524	126	5	,	,	PUNCT
ejpam-6524	126	6	then	then	ADV
ejpam-6524	126	7	∂2u	∂2u	ADJ
ejpam-6524	126	8	∂t2	∂t2	PROPN
ejpam-6524	126	9	(	(	PUNCT
ejpam-6524	126	10	xi	xi	PROPN
ejpam-6524	126	11	,	,	PUNCT
ejpam-6524	126	12	0	0	NUM
ejpam-6524	126	13	)	)	PUNCT
ejpam-6524	126	14	=	=	SYM
ejpam-6524	127	1	α2∂	α2∂	PROPN
ejpam-6524	127	2	2u	2u	PROPN
ejpam-6524	127	3	∂x2	∂x2	PROPN
ejpam-6524	127	4	(	(	PUNCT
ejpam-6524	127	5	xi	xi	PROPN
ejpam-6524	127	6	,	,	PUNCT
ejpam-6524	127	7	0	0	NUM
ejpam-6524	127	8	)	)	PUNCT
ejpam-6524	127	9	=	=	SYM
ejpam-6524	128	1	α2d	α2d	PROPN
ejpam-6524	128	2	2f	2f	NUM
ejpam-6524	128	3	dx2	dx2	PROPN
ejpam-6524	128	4	(	(	PUNCT
ejpam-6524	128	5	xi	xi	PROPN
ejpam-6524	128	6	)	)	PUNCT
ejpam-6524	128	7	=	=	SYM
ejpam-6524	129	1	α2f	α2f	PROPN
ejpam-6524	129	2	′′	′′	PROPN
ejpam-6524	129	3	(	(	PUNCT
ejpam-6524	129	4	xi	xi	PROPN
ejpam-6524	129	5	)	)	PUNCT
ejpam-6524	129	6	,	,	PUNCT
ejpam-6524	129	7	abdulkafi	abdulkafi	PROPN
ejpam-6524	129	8	m.	m.	PROPN
ejpam-6524	129	9	saeed	saeed	PROPN
ejpam-6524	129	10	,	,	PUNCT
ejpam-6524	129	11	shahad	shahad	PROPN
ejpam-6524	129	12	s.	s.	PROPN
ejpam-6524	129	13	almutairi	almutairi	PROPN
ejpam-6524	129	14	/	/	SYM
ejpam-6524	129	15	eur	eur	PROPN
ejpam-6524	129	16	.	.	PUNCT
ejpam-6524	130	1	j.	j.	PROPN
ejpam-6524	130	2	pure	pure	PROPN
ejpam-6524	130	3	appl	appl	PROPN
ejpam-6524	130	4	.	.	PROPN
ejpam-6524	130	5	math	math	PROPN
ejpam-6524	130	6	,	,	PUNCT
ejpam-6524	130	7	18	18	NUM
ejpam-6524	130	8	(	(	PUNCT
ejpam-6524	130	9	3	3	NUM
ejpam-6524	130	10	)	)	PUNCT
ejpam-6524	130	11	(	(	PUNCT
ejpam-6524	130	12	2025	2025	NUM
ejpam-6524	130	13	)	)	PUNCT
ejpam-6524	130	14	,	,	PUNCT
ejpam-6524	130	15	6524	6524	NUM
ejpam-6524	130	16	7	7	NUM
ejpam-6524	130	17	of	of	ADP
ejpam-6524	130	18	21	21	NUM
ejpam-6524	130	19	and	and	CCONJ
ejpam-6524	130	20	u	u	NOUN
ejpam-6524	130	21	(	(	PUNCT
ejpam-6524	130	22	xi	xi	PROPN
ejpam-6524	130	23	,	,	PUNCT
ejpam-6524	130	24	t1	t1	NOUN
ejpam-6524	130	25	)	)	PUNCT
ejpam-6524	131	1	=	=	SYM
ejpam-6524	131	2	u	u	NOUN
ejpam-6524	131	3	(	(	PUNCT
ejpam-6524	131	4	xi	xi	PROPN
ejpam-6524	131	5	,	,	PUNCT
ejpam-6524	131	6	0	0	NUM
ejpam-6524	131	7	)	)	PUNCT
ejpam-6524	132	1	+	+	NUM
ejpam-6524	132	2	kg	kg	INTJ
ejpam-6524	132	3	(	(	PUNCT
ejpam-6524	132	4	xi	xi	PROPN
ejpam-6524	132	5	)	)	PUNCT
ejpam-6524	132	6	+	+	CCONJ
ejpam-6524	132	7	α2k2	α2k2	X
ejpam-6524	132	8	2	2	NUM
ejpam-6524	132	9	f	f	X
ejpam-6524	132	10	′′	′′	PROPN
ejpam-6524	132	11	(	(	PUNCT
ejpam-6524	132	12	xi	xi	PROPN
ejpam-6524	132	13	)	)	PUNCT
ejpam-6524	132	14	+	+	CCONJ
ejpam-6524	132	15	k3	k3	VERB
ejpam-6524	132	16	6	6	NUM
ejpam-6524	132	17	∂3u	∂3u	ADJ
ejpam-6524	132	18	∂t3	∂t3	ADJ
ejpam-6524	132	19	(	(	PUNCT
ejpam-6524	132	20	xi	xi	PROPN
ejpam-6524	132	21	,	,	PUNCT
ejpam-6524	132	22	µ̂i	µ̂i	NUM
ejpam-6524	132	23	)	)	PUNCT
ejpam-6524	132	24	.	.	PUNCT
ejpam-6524	133	1	an	an	DET
ejpam-6524	133	2	estimate	estimate	NOUN
ejpam-6524	133	3	with	with	ADP
ejpam-6524	133	4	error	error	NOUN
ejpam-6524	133	5	o	o	NOUN
ejpam-6524	133	6	(	(	PUNCT
ejpam-6524	133	7	k3	k3	PROPN
ejpam-6524	133	8	)	)	PUNCT
ejpam-6524	133	9	is	be	AUX
ejpam-6524	133	10	therefore	therefore	ADV
ejpam-6524	133	11	produced	produce	VERB
ejpam-6524	133	12	:	:	PUNCT
ejpam-6524	133	13	wi1	wi1	NOUN
ejpam-6524	133	14	=	=	PUNCT
ejpam-6524	134	1	wi0	wi0	NOUN
ejpam-6524	135	1	+	+	CCONJ
ejpam-6524	135	2	kg	kg	X
ejpam-6524	135	3	(	(	PUNCT
ejpam-6524	135	4	xi	xi	PROPN
ejpam-6524	135	5	)	)	PUNCT
ejpam-6524	136	1	+	+	CCONJ
ejpam-6524	136	2	α2k2	α2k2	X
ejpam-6524	136	3	2	2	NUM
ejpam-6524	136	4	f	f	X
ejpam-6524	136	5	′′	′′	PROPN
ejpam-6524	136	6	(	(	PUNCT
ejpam-6524	136	7	xi	xi	PROPN
ejpam-6524	136	8	)	)	PUNCT
ejpam-6524	136	9	.	.	PUNCT
ejpam-6524	137	1	the	the	DET
ejpam-6524	137	2	difference	difference	NOUN
ejpam-6524	137	3	equation	equation	NOUN
ejpam-6524	137	4	can	can	AUX
ejpam-6524	137	5	be	be	AUX
ejpam-6524	137	6	used	use	VERB
ejpam-6524	137	7	if	if	SCONJ
ejpam-6524	137	8	f	f	PROPN
ejpam-6524	137	9	∈	∈	PROPN
ejpam-6524	137	10	c4[0	c4[0	PROPN
ejpam-6524	137	11	,	,	PUNCT
ejpam-6524	137	12	1	1	NUM
ejpam-6524	137	13	]	]	PUNCT
ejpam-6524	137	14	but	but	CCONJ
ejpam-6524	137	15	f	f	X
ejpam-6524	137	16	′′	′′	PROPN
ejpam-6524	137	17	(	(	PUNCT
ejpam-6524	137	18	xi	xi	PROPN
ejpam-6524	137	19	)	)	PUNCT
ejpam-6524	137	20	is	be	AUX
ejpam-6524	137	21	not	not	PART
ejpam-6524	137	22	readily	readily	ADV
ejpam-6524	137	23	available	available	ADJ
ejpam-6524	137	24	.	.	PUNCT
ejpam-6524	138	1	f	f	X
ejpam-6524	139	1	′′	′′	PROPN
ejpam-6524	139	2	(	(	PUNCT
ejpam-6524	139	3	x0	x0	PROPN
ejpam-6524	139	4	)	)	PUNCT
ejpam-6524	139	5	=	=	SYM
ejpam-6524	139	6	1	1	NUM
ejpam-6524	139	7	h2	h2	NOUN
ejpam-6524	140	1	[	[	X
ejpam-6524	140	2	f	f	X
ejpam-6524	140	3	(	(	PUNCT
ejpam-6524	140	4	x0	x0	PROPN
ejpam-6524	140	5	−	−	PROPN
ejpam-6524	141	1	h)−	h)−	PROPN
ejpam-6524	141	2	2f	2f	NUM
ejpam-6524	141	3	(	(	PUNCT
ejpam-6524	141	4	x0	x0	PROPN
ejpam-6524	141	5	)	)	PUNCT
ejpam-6524	142	1	+	+	CCONJ
ejpam-6524	142	2	f	f	X
ejpam-6524	142	3	(	(	PUNCT
ejpam-6524	142	4	x0	x0	PROPN
ejpam-6524	142	5	+	+	PROPN
ejpam-6524	142	6	h)]−	h)]−	NUM
ejpam-6524	142	7	h2	h2	PROPN
ejpam-6524	142	8	12	12	NUM
ejpam-6524	142	9	f	f	PROPN
ejpam-6524	142	10	(	(	PUNCT
ejpam-6524	142	11	4)(ξ	4)(ξ	NUM
ejpam-6524	142	12	)	)	PUNCT
ejpam-6524	142	13	,	,	PUNCT
ejpam-6524	142	14	(	(	PUNCT
ejpam-6524	142	15	8)	8)	NUM
ejpam-6524	142	16	to	to	PART
ejpam-6524	142	17	write	write	VERB
ejpam-6524	142	18	f	f	PROPN
ejpam-6524	142	19	′′	′′	PROPN
ejpam-6524	142	20	(	(	PUNCT
ejpam-6524	142	21	xi	xi	PROPN
ejpam-6524	142	22	)	)	PUNCT
ejpam-6524	142	23	=	=	SYM
ejpam-6524	142	24	f	f	PROPN
ejpam-6524	142	25	(	(	PUNCT
ejpam-6524	142	26	xi+1)−	xi+1)−	PROPN
ejpam-6524	142	27	2f	2f	NUM
ejpam-6524	142	28	(	(	PUNCT
ejpam-6524	142	29	xi	xi	X
ejpam-6524	142	30	)	)	PUNCT
ejpam-6524	142	31	+	+	NUM
ejpam-6524	142	32	f	f	X
ejpam-6524	142	33	(	(	PUNCT
ejpam-6524	142	34	xi−1	xi−1	PROPN
ejpam-6524	142	35	)	)	PUNCT
ejpam-6524	142	36	h2	h2	NOUN
ejpam-6524	142	37	−	−	PROPN
ejpam-6524	142	38	h2	h2	NOUN
ejpam-6524	142	39	12	12	NUM
ejpam-6524	142	40	f	f	NOUN
ejpam-6524	142	41	(	(	PUNCT
ejpam-6524	142	42	4	4	NUM
ejpam-6524	142	43	)	)	PUNCT
ejpam-6524	142	44	(	(	PUNCT
ejpam-6524	142	45	ξ̃i	ξ̃i	INTJ
ejpam-6524	142	46	)	)	PUNCT
ejpam-6524	142	47	,	,	PUNCT
ejpam-6524	142	48	for	for	ADP
ejpam-6524	142	49	some	some	DET
ejpam-6524	142	50	ξ̃i	ξ̃i	NOUN
ejpam-6524	142	51	in	in	ADP
ejpam-6524	142	52	(	(	PUNCT
ejpam-6524	142	53	xi−1	xi−1	PROPN
ejpam-6524	142	54	,	,	PUNCT
ejpam-6524	142	55	xi+1	xi+1	PROPN
ejpam-6524	142	56	)	)	PUNCT
ejpam-6524	142	57	.	.	PUNCT
ejpam-6524	143	1	this	this	PRON
ejpam-6524	143	2	implies	imply	VERB
ejpam-6524	143	3	that	that	SCONJ
ejpam-6524	143	4	u	u	PROPN
ejpam-6524	143	5	(	(	PUNCT
ejpam-6524	143	6	xi	xi	PROPN
ejpam-6524	143	7	,	,	PUNCT
ejpam-6524	143	8	t1	t1	NOUN
ejpam-6524	143	9	)	)	PUNCT
ejpam-6524	143	10	=	=	SYM
ejpam-6524	143	11	u	u	NOUN
ejpam-6524	143	12	(	(	PUNCT
ejpam-6524	143	13	xi	xi	PROPN
ejpam-6524	143	14	,	,	PUNCT
ejpam-6524	143	15	0	0	NUM
ejpam-6524	143	16	)	)	PUNCT
ejpam-6524	144	1	+	+	NUM
ejpam-6524	144	2	kg	kg	INTJ
ejpam-6524	144	3	(	(	PUNCT
ejpam-6524	144	4	xi	xi	PROPN
ejpam-6524	144	5	)	)	PUNCT
ejpam-6524	144	6	+	+	CCONJ
ejpam-6524	144	7	k2α2	k2α2	X
ejpam-6524	144	8	2h2	2h2	NUM
ejpam-6524	145	1	[	[	X
ejpam-6524	145	2	f	f	X
ejpam-6524	145	3	(	(	PUNCT
ejpam-6524	145	4	xi+1)−	xi+1)−	PROPN
ejpam-6524	145	5	2f	2f	NUM
ejpam-6524	145	6	(	(	PUNCT
ejpam-6524	145	7	xi	xi	X
ejpam-6524	145	8	)	)	PUNCT
ejpam-6524	145	9	+	+	NUM
ejpam-6524	145	10	f	f	X
ejpam-6524	145	11	(	(	PUNCT
ejpam-6524	145	12	xi−1	xi−1	PROPN
ejpam-6524	145	13	)	)	PUNCT
ejpam-6524	145	14	]	]	PUNCT
ejpam-6524	146	1	+	+	PUNCT
ejpam-6524	146	2	o	o	X
ejpam-6524	146	3	(	(	PUNCT
ejpam-6524	146	4	k3	k3	VERB
ejpam-6524	146	5	+	+	X
ejpam-6524	146	6	h2k2	h2k2	NOUN
ejpam-6524	146	7	)	)	PUNCT
ejpam-6524	146	8	.	.	PUNCT
ejpam-6524	147	1	because	because	SCONJ
ejpam-6524	147	2	λ	λ	X
ejpam-6524	147	3	=	=	SYM
ejpam-6524	147	4	kα	kα	PROPN
ejpam-6524	147	5	/	/	SYM
ejpam-6524	147	6	h	h	NOUN
ejpam-6524	147	7	,	,	PUNCT
ejpam-6524	147	8	we	we	PRON
ejpam-6524	147	9	can	can	AUX
ejpam-6524	147	10	write	write	VERB
ejpam-6524	147	11	this	this	PRON
ejpam-6524	147	12	as	as	ADP
ejpam-6524	147	13	u	u	PROPN
ejpam-6524	147	14	(	(	PUNCT
ejpam-6524	147	15	xi	xi	PROPN
ejpam-6524	147	16	,	,	PUNCT
ejpam-6524	147	17	t1	t1	NOUN
ejpam-6524	147	18	)	)	PUNCT
ejpam-6524	147	19	=	=	SYM
ejpam-6524	147	20	u	u	NOUN
ejpam-6524	147	21	(	(	PUNCT
ejpam-6524	147	22	xi	xi	PROPN
ejpam-6524	147	23	,	,	PUNCT
ejpam-6524	147	24	0	0	NUM
ejpam-6524	147	25	)	)	PUNCT
ejpam-6524	148	1	+	+	NUM
ejpam-6524	148	2	kg	kg	INTJ
ejpam-6524	148	3	(	(	PUNCT
ejpam-6524	148	4	xi	xi	NOUN
ejpam-6524	148	5	)	)	PUNCT
ejpam-6524	148	6	+	+	NUM
ejpam-6524	148	7	λ2	λ2	NOUN
ejpam-6524	148	8	2	2	NUM
ejpam-6524	148	9	[	[	X
ejpam-6524	148	10	f	f	X
ejpam-6524	148	11	(	(	PUNCT
ejpam-6524	148	12	xi+1)−	xi+1)−	PROPN
ejpam-6524	148	13	2f	2f	NUM
ejpam-6524	148	14	(	(	PUNCT
ejpam-6524	148	15	xi	xi	X
ejpam-6524	148	16	)	)	PUNCT
ejpam-6524	149	1	+	+	NUM
ejpam-6524	149	2	f	f	X
ejpam-6524	149	3	(	(	PUNCT
ejpam-6524	149	4	xi−1	xi−1	PROPN
ejpam-6524	149	5	)	)	PUNCT
ejpam-6524	149	6	]	]	PUNCT
ejpam-6524	150	1	+	+	PUNCT
ejpam-6524	150	2	o	o	X
ejpam-6524	150	3	(	(	PUNCT
ejpam-6524	150	4	k3	k3	VERB
ejpam-6524	150	5	+	+	CCONJ
ejpam-6524	150	6	h2k2	h2k2	NOUN
ejpam-6524	150	7	)	)	PUNCT
ejpam-6524	150	8	=	=	SYM
ejpam-6524	150	9	(	(	PUNCT
ejpam-6524	150	10	1−	1−	NUM
ejpam-6524	150	11	λ2	λ2	NOUN
ejpam-6524	150	12	)	)	PUNCT
ejpam-6524	150	13	f	f	PROPN
ejpam-6524	150	14	(	(	PUNCT
ejpam-6524	150	15	xi	xi	PROPN
ejpam-6524	150	16	)	)	PUNCT
ejpam-6524	150	17	+	+	NUM
ejpam-6524	150	18	λ2	λ2	NOUN
ejpam-6524	150	19	2	2	NUM
ejpam-6524	150	20	f	f	NOUN
ejpam-6524	150	21	(	(	PUNCT
ejpam-6524	150	22	xi+1	xi+1	NOUN
ejpam-6524	150	23	)	)	PUNCT
ejpam-6524	151	1	+	+	NUM
ejpam-6524	151	2	λ2	λ2	NOUN
ejpam-6524	151	3	2	2	NUM
ejpam-6524	151	4	f	f	NOUN
ejpam-6524	151	5	(	(	PUNCT
ejpam-6524	151	6	xi−1	xi−1	PROPN
ejpam-6524	151	7	)	)	PUNCT
ejpam-6524	152	1	+	+	NUM
ejpam-6524	152	2	kg	kg	INTJ
ejpam-6524	152	3	(	(	PUNCT
ejpam-6524	152	4	xi	xi	NOUN
ejpam-6524	152	5	)	)	PUNCT
ejpam-6524	153	1	+	+	NOUN
ejpam-6524	153	2	o	o	X
ejpam-6524	153	3	(	(	PUNCT
ejpam-6524	153	4	k3	k3	VERB
ejpam-6524	153	5	+	+	X
ejpam-6524	153	6	h2k2	h2k2	NOUN
ejpam-6524	153	7	)	)	PUNCT
ejpam-6524	153	8	.	.	PUNCT
ejpam-6524	154	1	consequently	consequently	ADV
ejpam-6524	154	2	,	,	PUNCT
ejpam-6524	154	3	the	the	DET
ejpam-6524	154	4	difference	difference	NOUN
ejpam-6524	154	5	equation	equation	NOUN
ejpam-6524	154	6	,	,	PUNCT
ejpam-6524	154	7	wi,1	wi,1	PROPN
ejpam-6524	154	8	=	=	PUNCT
ejpam-6524	154	9	(	(	PUNCT
ejpam-6524	154	10	1−	1−	NUM
ejpam-6524	154	11	λ2	λ2	NOUN
ejpam-6524	154	12	)	)	PUNCT
ejpam-6524	154	13	f	f	PROPN
ejpam-6524	154	14	(	(	PUNCT
ejpam-6524	154	15	xi	xi	PROPN
ejpam-6524	154	16	)	)	PUNCT
ejpam-6524	154	17	+	+	NUM
ejpam-6524	154	18	λ2	λ2	NOUN
ejpam-6524	154	19	2	2	NUM
ejpam-6524	154	20	f	f	NOUN
ejpam-6524	154	21	(	(	PUNCT
ejpam-6524	154	22	xi+1	xi+1	NOUN
ejpam-6524	154	23	)	)	PUNCT
ejpam-6524	155	1	+	+	NUM
ejpam-6524	155	2	λ2	λ2	NOUN
ejpam-6524	155	3	2	2	NUM
ejpam-6524	155	4	f	f	NOUN
ejpam-6524	155	5	(	(	PUNCT
ejpam-6524	155	6	xi−1	xi−1	PROPN
ejpam-6524	155	7	)	)	PUNCT
ejpam-6524	156	1	+	+	NUM
ejpam-6524	156	2	kg	kg	INTJ
ejpam-6524	156	3	(	(	PUNCT
ejpam-6524	156	4	xi	xi	PROPN
ejpam-6524	156	5	)	)	PUNCT
ejpam-6524	156	6	.	.	PUNCT
ejpam-6524	157	1	for	for	ADP
ejpam-6524	157	2	all	all	DET
ejpam-6524	157	3	i	i	PRON
ejpam-6524	157	4	=	=	NOUN
ejpam-6524	157	5	1	1	NUM
ejpam-6524	157	6	,	,	PUNCT
ejpam-6524	157	7	2	2	NUM
ejpam-6524	157	8	,	,	PUNCT
ejpam-6524	157	9	.	.	PUNCT
ejpam-6524	157	10	.	.	PUNCT
ejpam-6524	157	11	.	.	PUNCT
ejpam-6524	158	1	,	,	PUNCT
ejpam-6524	158	2	m−	m−	PROPN
ejpam-6524	158	3	1	1	NUM
ejpam-6524	158	4	,	,	PUNCT
ejpam-6524	158	5	wi,1	wi,1	PROPN
ejpam-6524	158	6	may	may	AUX
ejpam-6524	158	7	be	be	AUX
ejpam-6524	158	8	found	find	VERB
ejpam-6524	158	9	using	use	VERB
ejpam-6524	158	10	this	this	DET
ejpam-6524	158	11	method	method	NOUN
ejpam-6524	158	12	.	.	PUNCT
ejpam-6524	159	1	we	we	PRON
ejpam-6524	159	2	apply	apply	VERB
ejpam-6524	159	3	the	the	DET
ejpam-6524	159	4	system	system	NOUN
ejpam-6524	159	5	in	in	ADP
ejpam-6524	159	6	(	(	PUNCT
ejpam-6524	159	7	7	7	NUM
ejpam-6524	159	8	)	)	PUNCT
ejpam-6524	159	9	to	to	PART
ejpam-6524	159	10	determine	determine	VERB
ejpam-6524	159	11	subsequent	subsequent	ADJ
ejpam-6524	159	12	approximates	approximate	NOUN
ejpam-6524	159	13	.	.	PUNCT
ejpam-6524	160	1	3	3	X
ejpam-6524	160	2	.	.	X
ejpam-6524	160	3	formulation	formulation	NOUN
ejpam-6524	160	4	of	of	ADP
ejpam-6524	160	5	the	the	DET
ejpam-6524	160	6	finite	finite	PROPN
ejpam-6524	160	7	element	element	NOUN
ejpam-6524	160	8	method	method	NOUN
ejpam-6524	160	9	gfem	gfem	PROPN
ejpam-6524	160	10	solves	solve	VERB
ejpam-6524	160	11	differential	differential	ADJ
ejpam-6524	160	12	equations	equation	NOUN
ejpam-6524	160	13	numerically	numerically	ADV
ejpam-6524	160	14	by	by	ADP
ejpam-6524	160	15	dividing	divide	VERB
ejpam-6524	160	16	the	the	DET
ejpam-6524	160	17	domain	domain	NOUN
ejpam-6524	160	18	into	into	ADP
ejpam-6524	160	19	smaller	small	ADJ
ejpam-6524	160	20	finite	finite	ADJ
ejpam-6524	160	21	elements	element	NOUN
ejpam-6524	160	22	.	.	PUNCT
ejpam-6524	161	1	within	within	ADP
ejpam-6524	161	2	each	each	PRON
ejpam-6524	161	3	of	of	ADP
ejpam-6524	161	4	these	these	DET
ejpam-6524	161	5	elements	element	NOUN
ejpam-6524	161	6	,	,	PUNCT
ejpam-6524	161	7	the	the	DET
ejpam-6524	161	8	function	function	NOUN
ejpam-6524	161	9	is	be	AUX
ejpam-6524	161	10	approximated	approximate	VERB
ejpam-6524	161	11	using	use	VERB
ejpam-6524	161	12	piecewise	piecewise	NOUN
ejpam-6524	161	13	trial	trial	NOUN
ejpam-6524	161	14	functions	function	NOUN
ejpam-6524	161	15	,	,	PUNCT
ejpam-6524	161	16	allowing	allow	VERB
ejpam-6524	161	17	for	for	ADP
ejpam-6524	161	18	an	an	DET
ejpam-6524	161	19	efficient	efficient	ADJ
ejpam-6524	161	20	and	and	CCONJ
ejpam-6524	161	21	flexible	flexible	ADJ
ejpam-6524	161	22	solution	solution	NOUN
ejpam-6524	161	23	approach	approach	NOUN
ejpam-6524	161	24	[	[	X
ejpam-6524	161	25	17	17	NUM
ejpam-6524	161	26	,	,	PUNCT
ejpam-6524	161	27	18	18	NUM
ejpam-6524	161	28	]	]	PUNCT
ejpam-6524	161	29	.	.	PUNCT
ejpam-6524	162	1	the	the	DET
ejpam-6524	162	2	following	follow	VERB
ejpam-6524	162	3	steps	step	NOUN
ejpam-6524	162	4	make	make	VERB
ejpam-6524	162	5	up	up	ADP
ejpam-6524	162	6	the	the	DET
ejpam-6524	162	7	gfem	gfem	NOUN
ejpam-6524	162	8	for	for	ADP
ejpam-6524	162	9	solving	solve	VERB
ejpam-6524	162	10	a	a	DET
ejpam-6524	162	11	differential	differential	ADJ
ejpam-6524	162	12	equation	equation	NOUN
ejpam-6524	162	13	[	[	X
ejpam-6524	162	14	17	17	NUM
ejpam-6524	162	15	,	,	PUNCT
ejpam-6524	162	16	18	18	NUM
ejpam-6524	162	17	]	]	PUNCT
ejpam-6524	162	18	:	:	PUNCT
ejpam-6524	162	19	abdulkafi	abdulkafi	PROPN
ejpam-6524	162	20	m.	m.	PROPN
ejpam-6524	162	21	saeed	saeed	PROPN
ejpam-6524	162	22	,	,	PUNCT
ejpam-6524	162	23	shahad	shahad	PROPN
ejpam-6524	162	24	s.	s.	PROPN
ejpam-6524	162	25	almutairi	almutairi	PROPN
ejpam-6524	162	26	/	/	SYM
ejpam-6524	162	27	eur	eur	PROPN
ejpam-6524	162	28	.	.	PUNCT
ejpam-6524	163	1	j.	j.	PROPN
ejpam-6524	163	2	pure	pure	PROPN
ejpam-6524	163	3	appl	appl	PROPN
ejpam-6524	163	4	.	.	PROPN
ejpam-6524	163	5	math	math	PROPN
ejpam-6524	163	6	,	,	PUNCT
ejpam-6524	163	7	18	18	NUM
ejpam-6524	163	8	(	(	PUNCT
ejpam-6524	163	9	3	3	NUM
ejpam-6524	163	10	)	)	PUNCT
ejpam-6524	163	11	(	(	PUNCT
ejpam-6524	163	12	2025	2025	NUM
ejpam-6524	163	13	)	)	PUNCT
ejpam-6524	163	14	,	,	PUNCT
ejpam-6524	163	15	6524	6524	NUM
ejpam-6524	163	16	8	8	NUM
ejpam-6524	163	17	of	of	ADP
ejpam-6524	163	18	21	21	NUM
ejpam-6524	163	19	(	(	PUNCT
ejpam-6524	163	20	i	i	NOUN
ejpam-6524	163	21	)	)	PUNCT
ejpam-6524	163	22	the	the	DET
ejpam-6524	163	23	differential	differential	ADJ
ejpam-6524	163	24	equation	equation	NOUN
ejpam-6524	163	25	is	be	AUX
ejpam-6524	163	26	multiplied	multiply	VERB
ejpam-6524	163	27	by	by	ADP
ejpam-6524	163	28	a	a	DET
ejpam-6524	163	29	weight	weight	NOUN
ejpam-6524	163	30	function	function	NOUN
ejpam-6524	163	31	ω(x	ω(x	NOUN
ejpam-6524	163	32	)	)	PUNCT
ejpam-6524	163	33	they	they	PRON
ejpam-6524	163	34	make	make	VERB
ejpam-6524	163	35	up	up	ADP
ejpam-6524	163	36	the	the	DET
ejpam-6524	163	37	integral	integral	NOUN
ejpam-6524	163	38	for	for	ADP
ejpam-6524	163	39	the	the	DET
ejpam-6524	163	40	entire	entire	ADJ
ejpam-6524	163	41	domain	domain	NOUN
ejpam-6524	163	42	;	;	PUNCT
ejpam-6524	163	43	(	(	PUNCT
ejpam-6524	163	44	ii	ii	NOUN
ejpam-6524	163	45	)	)	PUNCT
ejpam-6524	163	46	integrate	integrate	VERB
ejpam-6524	163	47	by	by	ADP
ejpam-6524	163	48	parts	part	NOUN
ejpam-6524	163	49	if	if	SCONJ
ejpam-6524	163	50	required	require	VERB
ejpam-6524	163	51	to	to	PART
ejpam-6524	163	52	lower	lower	VERB
ejpam-6524	163	53	the	the	DET
ejpam-6524	163	54	highest	high	ADJ
ejpam-6524	163	55	order	order	NOUN
ejpam-6524	163	56	term	term	NOUN
ejpam-6524	163	57	’s	’s	PART
ejpam-6524	163	58	order	order	NOUN
ejpam-6524	163	59	;	;	PUNCT
ejpam-6524	163	60	(	(	PUNCT
ejpam-6524	163	61	iii	iii	X
ejpam-6524	163	62	)	)	PUNCT
ejpam-6524	163	63	choose	choose	VERB
ejpam-6524	163	64	the	the	DET
ejpam-6524	163	65	interpolation	interpolation	NOUN
ejpam-6524	163	66	order	order	NOUN
ejpam-6524	163	67	—	—	PUNCT
ejpam-6524	163	68	whether	whether	SCONJ
ejpam-6524	163	69	linear	linear	ADJ
ejpam-6524	163	70	,	,	PUNCT
ejpam-6524	163	71	quadratic	quadratic	ADJ
ejpam-6524	163	72	,	,	PUNCT
ejpam-6524	163	73	or	or	CCONJ
ejpam-6524	163	74	higher	high	ADJ
ejpam-6524	163	75	—	—	PUNCT
ejpam-6524	163	76	and	and	CCONJ
ejpam-6524	163	77	define	define	VERB
ejpam-6524	163	78	the	the	DET
ejpam-6524	163	79	corresponding	corresponding	ADJ
ejpam-6524	163	80	shape	shape	NOUN
ejpam-6524	163	81	functions	function	NOUN
ejpam-6524	163	82	,	,	PUNCT
ejpam-6524	163	83	ni	ni	PROPN
ejpam-6524	163	84	,	,	PUNCT
ejpam-6524	163	85	for	for	ADP
ejpam-6524	163	86	i	i	PROPN
ejpam-6524	163	87	=	=	NOUN
ejpam-6524	163	88	1	1	NUM
ejpam-6524	163	89	...	...	PUNCT
ejpam-6524	163	90	m.	m.	NOUN
ejpam-6524	163	91	using	use	VERB
ejpam-6524	163	92	the	the	DET
ejpam-6524	163	93	trial	trial	NOUN
ejpam-6524	163	94	function	function	NOUN
ejpam-6524	163	95	p	p	X
ejpam-6524	163	96	=	=	SYM
ejpam-6524	163	97	p̃(x	p̃(x	PROPN
ejpam-6524	163	98	)	)	PUNCT
ejpam-6524	164	1	=	=	PUNCT
ejpam-6524	164	2	m∑	m∑	ADP
ejpam-6524	164	3	i=1	i=1	PROPN
ejpam-6524	164	4	ni(x)pi	ni(x)pi	ADJ
ejpam-6524	164	5	,	,	PUNCT
ejpam-6524	164	6	the	the	DET
ejpam-6524	164	7	function	function	NOUN
ejpam-6524	164	8	is	be	AUX
ejpam-6524	164	9	approximated	approximate	VERB
ejpam-6524	164	10	based	base	VERB
ejpam-6524	164	11	on	on	ADP
ejpam-6524	164	12	these	these	DET
ejpam-6524	164	13	selected	select	VERB
ejpam-6524	164	14	shape	shape	NOUN
ejpam-6524	164	15	functions	function	NOUN
ejpam-6524	164	16	;	;	PUNCT
ejpam-6524	164	17	(	(	PUNCT
ejpam-6524	164	18	iv	iv	X
ejpam-6524	164	19	)	)	PUNCT
ejpam-6524	164	20	calculate	calculate	NOUN
ejpam-6524	164	21	all	all	DET
ejpam-6524	164	22	integrals	integral	NOUN
ejpam-6524	164	23	within	within	ADP
ejpam-6524	164	24	each	each	DET
ejpam-6524	164	25	element	element	NOUN
ejpam-6524	164	26	,	,	PUNCT
ejpam-6524	164	27	either	either	CCONJ
ejpam-6524	164	28	through	through	ADP
ejpam-6524	164	29	exact	exact	ADJ
ejpam-6524	164	30	analytical	analytical	ADJ
ejpam-6524	164	31	methods	method	NOUN
ejpam-6524	164	32	or	or	CCONJ
ejpam-6524	164	33	numerical	numerical	ADJ
ejpam-6524	164	34	approximation	approximation	NOUN
ejpam-6524	164	35	,	,	PUNCT
ejpam-6524	164	36	to	to	PART
ejpam-6524	164	37	establish	establish	VERB
ejpam-6524	164	38	a	a	DET
ejpam-6524	164	39	system	system	NOUN
ejpam-6524	164	40	of	of	ADP
ejpam-6524	164	41	equations	equation	NOUN
ejpam-6524	164	42	for	for	ADP
ejpam-6524	164	43	the	the	DET
ejpam-6524	164	44	unknown	unknown	ADJ
ejpam-6524	164	45	values	value	NOUN
ejpam-6524	164	46	pi′s	pi′	VERB
ejpam-6524	164	47	;	;	PUNCT
ejpam-6524	164	48	(	(	PUNCT
ejpam-6524	164	49	v	v	X
ejpam-6524	164	50	)	)	PUNCT
ejpam-6524	164	51	solve	solve	VERB
ejpam-6524	164	52	the	the	DET
ejpam-6524	164	53	system	system	NOUN
ejpam-6524	164	54	of	of	ADP
ejpam-6524	164	55	equations	equation	NOUN
ejpam-6524	164	56	to	to	PART
ejpam-6524	164	57	determine	determine	VERB
ejpam-6524	164	58	the	the	DET
ejpam-6524	164	59	unknown	unknown	ADJ
ejpam-6524	164	60	values	value	NOUN
ejpam-6524	164	61	pi′s	pi′	VERB
ejpam-6524	164	62	,	,	PUNCT
ejpam-6524	164	63	ensuring	ensure	VERB
ejpam-6524	164	64	accuracy	accuracy	NOUN
ejpam-6524	164	65	in	in	ADP
ejpam-6524	164	66	the	the	DET
ejpam-6524	164	67	numerical	numerical	ADJ
ejpam-6524	164	68	solution	solution	NOUN
ejpam-6524	164	69	process	process	NOUN
ejpam-6524	164	70	.	.	PUNCT
ejpam-6524	165	1	let	let	VERB
ejpam-6524	165	2	’s	’s	PRON
ejpam-6524	165	3	examine	examine	VERB
ejpam-6524	165	4	the	the	DET
ejpam-6524	165	5	model	model	NOUN
ejpam-6524	165	6	problem	problem	NOUN
ejpam-6524	165	7	:	:	PUNCT
ejpam-6524	165	8	poisson	poisson	PROPN
ejpam-6524	165	9	’s	’s	PART
ejpam-6524	165	10	equation	equation	NOUN
ejpam-6524	165	11	,	,	PUNCT
ejpam-6524	165	12	subject	subject	ADJ
ejpam-6524	165	13	to	to	ADP
ejpam-6524	165	14	homogeneous	homogeneous	ADJ
ejpam-6524	165	15	dirichlet	dirichlet	PROPN
ejpam-6524	165	16	boundary	boundary	ADJ
ejpam-6524	165	17	conditions	condition	NOUN
ejpam-6524	165	18	[	[	X
ejpam-6524	165	19	19	19	NUM
ejpam-6524	165	20	]	]	PUNCT
ejpam-6524	165	21	.	.	PUNCT
ejpam-6524	166	1	−∆u	−∆u	X
ejpam-6524	167	1	=	=	PUNCT
ejpam-6524	167	2	f	f	PROPN
ejpam-6524	167	3	in	in	ADP
ejpam-6524	167	4	ω	ω	PROPN
ejpam-6524	167	5	,	,	PUNCT
ejpam-6524	167	6	(	(	PUNCT
ejpam-6524	167	7	9	9	X
ejpam-6524	167	8	)	)	PUNCT
ejpam-6524	167	9	u	u	NOUN
ejpam-6524	167	10	=	=	NOUN
ejpam-6524	167	11	0	0	NUM
ejpam-6524	167	12	on	on	ADP
ejpam-6524	167	13	∂ω	∂ω	PROPN
ejpam-6524	167	14	.	.	PUNCT
ejpam-6524	168	1	in	in	ADP
ejpam-6524	168	2	this	this	DET
ejpam-6524	168	3	case	case	NOUN
ejpam-6524	168	4	,	,	PUNCT
ejpam-6524	168	5	it	it	PRON
ejpam-6524	168	6	is	be	AUX
ejpam-6524	168	7	clear	clear	ADJ
ejpam-6524	168	8	that	that	SCONJ
ejpam-6524	168	9	a	a	PRON
ejpam-6524	168	10	(	(	PUNCT
ejpam-6524	168	11	·	·	PUNCT
ejpam-6524	168	12	,	,	PUNCT
ejpam-6524	168	13	·	·	PUNCT
ejpam-6524	168	14	)	)	PUNCT
ejpam-6524	168	15	is	be	AUX
ejpam-6524	168	16	both	both	CCONJ
ejpam-6524	168	17	symmetric	symmetric	ADJ
ejpam-6524	168	18	and	and	CCONJ
ejpam-6524	168	19	bilinear	bilinear	NOUN
ejpam-6524	168	20	,	,	PUNCT
ejpam-6524	168	21	satisfying	satisfy	VERB
ejpam-6524	168	22	the	the	DET
ejpam-6524	168	23	property	property	NOUN
ejpam-6524	168	24	a(u	a(u	PROPN
ejpam-6524	168	25	,	,	PUNCT
ejpam-6524	168	26	u	u	NOUN
ejpam-6524	168	27	)	)	PUNCT
ejpam-6524	168	28	=	=	PUNCT
ejpam-6524	168	29	|u|21,ω	|u|21,ω	PUNCT
ejpam-6524	168	30	:	:	PUNCT
ejpam-6524	168	31	=	=	SYM
ejpam-6524	168	32	||u||2	||u||2	PROPN
ejpam-6524	168	33	.	.	PUNCT
ejpam-6524	169	1	furthermore	furthermore	ADV
ejpam-6524	169	2	,	,	PUNCT
ejpam-6524	169	3	when	when	SCONJ
ejpam-6524	169	4	a(u	a(u	X
ejpam-6524	169	5	,	,	PUNCT
ejpam-6524	169	6	u	u	NOUN
ejpam-6524	169	7	)	)	PUNCT
ejpam-6524	169	8	=	=	SYM
ejpam-6524	169	9	0	0	NUM
ejpam-6524	169	10	,	,	PUNCT
ejpam-6524	169	11	it	it	PRON
ejpam-6524	169	12	implies	imply	VERB
ejpam-6524	169	13	that	that	SCONJ
ejpam-6524	169	14	∇u	∇u	PROPN
ejpam-6524	169	15	=	=	SYM
ejpam-6524	169	16	0	0	NUM
ejpam-6524	169	17	,	,	PUNCT
ejpam-6524	169	18	meaning	mean	VERB
ejpam-6524	169	19	that	that	SCONJ
ejpam-6524	169	20	u	u	PRON
ejpam-6524	169	21	must	must	AUX
ejpam-6524	169	22	be	be	AUX
ejpam-6524	169	23	a	a	DET
ejpam-6524	169	24	constant	constant	ADJ
ejpam-6524	169	25	function	function	NOUN
ejpam-6524	169	26	throughout	throughout	ADP
ejpam-6524	169	27	the	the	DET
ejpam-6524	169	28	domain	domain	NOUN
ejpam-6524	169	29	.	.	PUNCT
ejpam-6524	170	1	the	the	DET
ejpam-6524	170	2	value	value	NOUN
ejpam-6524	170	3	of	of	ADP
ejpam-6524	170	4	this	this	DET
ejpam-6524	170	5	constant	constant	ADJ
ejpam-6524	170	6	should	should	AUX
ejpam-6524	170	7	be	be	AUX
ejpam-6524	170	8	zero	zero	NUM
ejpam-6524	170	9	as	as	ADP
ejpam-6524	170	10	u|γ	u|γ	NOUN
ejpam-6524	170	11	=	=	SYM
ejpam-6524	170	12	0	0	X
ejpam-6524	170	13	.	.	PUNCT
ejpam-6524	171	1	consequently	consequently	ADV
ejpam-6524	171	2	,	,	PUNCT
ejpam-6524	171	3	the	the	DET
ejpam-6524	171	4	riesz	riesz	PROPN
ejpam-6524	171	5	representation	representation	NOUN
ejpam-6524	171	6	theorem	theorem	NOUN
ejpam-6524	171	7	indicates	indicate	VERB
ejpam-6524	171	8	that	that	SCONJ
ejpam-6524	171	9	(	(	PUNCT
ejpam-6524	171	10	9	9	X
ejpam-6524	171	11	)	)	PUNCT
ejpam-6524	171	12	has	have	VERB
ejpam-6524	171	13	a	a	DET
ejpam-6524	171	14	unique	unique	ADJ
ejpam-6524	171	15	solution	solution	NOUN
ejpam-6524	171	16	since	since	SCONJ
ejpam-6524	171	17	a	a	PRON
ejpam-6524	171	18	(	(	PUNCT
ejpam-6524	171	19	·	·	PUNCT
ejpam-6524	171	20	,	,	PUNCT
ejpam-6524	171	21	·	·	PUNCT
ejpam-6524	171	22	)	)	PUNCT
ejpam-6524	171	23	forms	form	VERB
ejpam-6524	171	24	an	an	DET
ejpam-6524	171	25	inner	inner	ADJ
ejpam-6524	171	26	product	product	NOUN
ejpam-6524	171	27	on	on	ADP
ejpam-6524	171	28	v	v	NOUN
ejpam-6524	171	29	.	.	PUNCT
ejpam-6524	172	1	the	the	DET
ejpam-6524	172	2	galerkin	galerkin	ADJ
ejpam-6524	172	3	methods	method	NOUN
ejpam-6524	172	4	are	be	AUX
ejpam-6524	172	5	a	a	DET
ejpam-6524	172	6	class	class	NOUN
ejpam-6524	172	7	of	of	ADP
ejpam-6524	172	8	techniques	technique	NOUN
ejpam-6524	172	9	that	that	PRON
ejpam-6524	172	10	are	be	AUX
ejpam-6524	172	11	used	use	VERB
ejpam-6524	172	12	to	to	PART
ejpam-6524	172	13	estimate	estimate	VERB
ejpam-6524	172	14	the	the	DET
ejpam-6524	172	15	solution	solution	NOUN
ejpam-6524	172	16	to	to	ADP
ejpam-6524	172	17	(	(	PUNCT
ejpam-6524	172	18	9	9	NUM
ejpam-6524	172	19	)	)	PUNCT
ejpam-6524	172	20	.	.	PUNCT
ejpam-6524	173	1	let	let	VERB
ejpam-6524	173	2	vh	vh	PROPN
ejpam-6524	173	3	⊂	⊂	PROPN
ejpam-6524	173	4	v	v	AUX
ejpam-6524	173	5	be	be	AUX
ejpam-6524	173	6	a	a	DET
ejpam-6524	173	7	finite	finite	ADJ
ejpam-6524	173	8	dimensional	dimensional	ADJ
ejpam-6524	173	9	subspace	subspace	NOUN
ejpam-6524	173	10	.	.	PUNCT
ejpam-6524	174	1	limit	limit	VERB
ejpam-6524	174	2	the	the	DET
ejpam-6524	174	3	variational	variational	ADJ
ejpam-6524	174	4	formulation	formulation	NOUN
ejpam-6524	174	5	to	to	ADP
ejpam-6524	174	6	the	the	DET
ejpam-6524	174	7	subspace	subspace	PROPN
ejpam-6524	174	8	vh	vh	PROPN
ejpam-6524	174	9	,	,	PUNCT
ejpam-6524	174	10	meaning	mean	VERB
ejpam-6524	174	11	that	that	SCONJ
ejpam-6524	174	12	the	the	DET
ejpam-6524	174	13	goal	goal	NOUN
ejpam-6524	174	14	is	be	AUX
ejpam-6524	174	15	to	to	PART
ejpam-6524	174	16	find	find	VERB
ejpam-6524	174	17	uh	uh	INTJ
ejpam-6524	174	18	∈	∈	NOUN
ejpam-6524	174	19	v	v	ADP
ejpam-6524	174	20	such	such	ADJ
ejpam-6524	174	21	that	that	SCONJ
ejpam-6524	174	22	it	it	PRON
ejpam-6524	174	23	satisfies	satisfy	VERB
ejpam-6524	174	24	the	the	DET
ejpam-6524	174	25	given	give	VERB
ejpam-6524	174	26	conditions	condition	NOUN
ejpam-6524	174	27	within	within	ADP
ejpam-6524	174	28	this	this	DET
ejpam-6524	174	29	restricted	restricted	ADJ
ejpam-6524	174	30	space	space	NOUN
ejpam-6524	174	31	.	.	PUNCT
ejpam-6524	175	1	a(u	a(u	NOUN
ejpam-6524	175	2	,	,	PUNCT
ejpam-6524	175	3	v	v	NOUN
ejpam-6524	175	4	)	)	PUNCT
ejpam-6524	175	5	=	=	SYM
ejpam-6524	175	6	(	(	PUNCT
ejpam-6524	175	7	f	f	X
ejpam-6524	175	8	,	,	PUNCT
ejpam-6524	175	9	v	v	NOUN
ejpam-6524	175	10	)	)	PUNCT
ejpam-6524	175	11	,	,	PUNCT
ejpam-6524	175	12	for	for	ADP
ejpam-6524	175	13	all	all	DET
ejpam-6524	175	14	v	v	ADP
ejpam-6524	175	15	∈	∈	PROPN
ejpam-6524	175	16	v	v	NOUN
ejpam-6524	175	17	,	,	PUNCT
ejpam-6524	175	18	(	(	PUNCT
ejpam-6524	175	19	10	10	NUM
ejpam-6524	175	20	)	)	PUNCT
ejpam-6524	175	21	where	where	SCONJ
ejpam-6524	175	22	a(u	a(u	PROPN
ejpam-6524	175	23	,	,	PUNCT
ejpam-6524	175	24	v	v	NOUN
ejpam-6524	175	25	)	)	PUNCT
ejpam-6524	175	26	=	=	SYM
ejpam-6524	176	1	∫	∫	PROPN
ejpam-6524	176	2	ω	ω	PROPN
ejpam-6524	176	3	∇u∇v	∇u∇v	NUM
ejpam-6524	176	4	dx	dx	PROPN
ejpam-6524	176	5	,	,	PUNCT
ejpam-6524	176	6	(	(	PUNCT
ejpam-6524	176	7	f	f	X
ejpam-6524	176	8	,	,	PUNCT
ejpam-6524	176	9	v	v	NOUN
ejpam-6524	176	10	)	)	PUNCT
ejpam-6524	176	11	=	=	SYM
ejpam-6524	177	1	∫	∫	PROPN
ejpam-6524	177	2	ω	ω	NUM
ejpam-6524	177	3	fv	fv	PROPN
ejpam-6524	177	4	dx	dx	PROPN
ejpam-6524	177	5	for	for	ADP
ejpam-6524	177	6	all	all	DET
ejpam-6524	177	7	f	f	PROPN
ejpam-6524	177	8	∈	∈	PROPN
ejpam-6524	177	9	l2(ω	l2(ω	PROPN
ejpam-6524	177	10	)	)	PUNCT
ejpam-6524	177	11	.	.	PUNCT
ejpam-6524	178	1	(	(	PUNCT
ejpam-6524	178	2	11	11	X
ejpam-6524	178	3	)	)	PUNCT
ejpam-6524	178	4	it	it	PRON
ejpam-6524	178	5	is	be	AUX
ejpam-6524	178	6	evident	evident	ADJ
ejpam-6524	178	7	that	that	SCONJ
ejpam-6524	178	8	in	in	ADP
ejpam-6524	178	9	this	this	DET
ejpam-6524	178	10	scenario	scenario	NOUN
ejpam-6524	178	11	,	,	PUNCT
ejpam-6524	178	12	a	a	PRON
ejpam-6524	178	13	(	(	PUNCT
ejpam-6524	178	14	·	·	PUNCT
ejpam-6524	178	15	,	,	PUNCT
ejpam-6524	178	16	·	·	PUNCT
ejpam-6524	178	17	)	)	PUNCT
ejpam-6524	178	18	is	be	AUX
ejpam-6524	178	19	symmetric	symmetric	ADJ
ejpam-6524	178	20	and	and	CCONJ
ejpam-6524	178	21	bilinear	bilinear	NOUN
ejpam-6524	178	22	,	,	PUNCT
ejpam-6524	178	23	and	and	CCONJ
ejpam-6524	178	24	a(u	a(u	PROPN
ejpam-6524	178	25	,	,	PUNCT
ejpam-6524	178	26	u	u	NOUN
ejpam-6524	178	27	)	)	PUNCT
ejpam-6524	178	28	=	=	PUNCT
ejpam-6524	178	29	|u|21,ω	|u|21,ω	PUNCT
ejpam-6524	178	30	:	:	PUNCT
ejpam-6524	178	31	=	=	SYM
ejpam-6524	178	32	||u||2	||u||2	PROPN
ejpam-6524	178	33	moreover	moreover	ADV
ejpam-6524	178	34	,	,	PUNCT
ejpam-6524	178	35	a(u	a(u	PROPN
ejpam-6524	178	36	,	,	PUNCT
ejpam-6524	178	37	u	u	NOUN
ejpam-6524	178	38	)	)	PUNCT
ejpam-6524	178	39	=	=	SYM
ejpam-6524	178	40	0	0	NUM
ejpam-6524	178	41	suggests	suggest	VERB
ejpam-6524	178	42	that	that	SCONJ
ejpam-6524	178	43	∇u	∇u	PROPN
ejpam-6524	178	44	=	=	SYM
ejpam-6524	178	45	0	0	NUM
ejpam-6524	178	46	,	,	PUNCT
ejpam-6524	178	47	and	and	CCONJ
ejpam-6524	178	48	as	as	ADP
ejpam-6524	178	49	a	a	DET
ejpam-6524	178	50	result	result	NOUN
ejpam-6524	178	51	,	,	PUNCT
ejpam-6524	178	52	u	u	NOUN
ejpam-6524	178	53	is	be	AUX
ejpam-6524	178	54	constant	constant	ADJ
ejpam-6524	178	55	.	.	PUNCT
ejpam-6524	179	1	since	since	SCONJ
ejpam-6524	179	2	u|γ	u|γ	PUNCT
ejpam-6524	179	3	=	=	SYM
ejpam-6524	179	4	0	0	PROPN
ejpam-6524	179	5	,	,	PUNCT
ejpam-6524	179	6	this	this	DET
ejpam-6524	179	7	constant	constant	ADJ
ejpam-6524	179	8	’s	’s	PART
ejpam-6524	179	9	value	value	NOUN
ejpam-6524	179	10	should	should	AUX
ejpam-6524	179	11	be	be	AUX
ejpam-6524	179	12	0	0	NUM
ejpam-6524	179	13	.	.	PUNCT
ejpam-6524	180	1	consequently	consequently	ADV
ejpam-6524	180	2	,	,	PUNCT
ejpam-6524	180	3	the	the	DET
ejpam-6524	180	4	riesz	riesz	PROPN
ejpam-6524	180	5	representation	representation	NOUN
ejpam-6524	180	6	theorem	theorem	NOUN
ejpam-6524	180	7	indicates	indicate	VERB
ejpam-6524	180	8	that	that	SCONJ
ejpam-6524	180	9	(	(	PUNCT
ejpam-6524	180	10	9	9	X
ejpam-6524	180	11	)	)	PUNCT
ejpam-6524	180	12	has	have	VERB
ejpam-6524	180	13	a	a	DET
ejpam-6524	180	14	unique	unique	ADJ
ejpam-6524	180	15	solution	solution	NOUN
ejpam-6524	180	16	since	since	SCONJ
ejpam-6524	180	17	a	a	PRON
ejpam-6524	180	18	(	(	PUNCT
ejpam-6524	180	19	·	·	PUNCT
ejpam-6524	180	20	,	,	PUNCT
ejpam-6524	180	21	·	·	PUNCT
ejpam-6524	180	22	)	)	PUNCT
ejpam-6524	180	23	forms	form	VERB
ejpam-6524	180	24	an	an	DET
ejpam-6524	180	25	inner	inner	ADJ
ejpam-6524	180	26	product	product	NOUN
ejpam-6524	180	27	on	on	ADP
ejpam-6524	180	28	v	v	NOUN
ejpam-6524	180	29	.	.	PUNCT
ejpam-6524	181	1	the	the	DET
ejpam-6524	181	2	galerkin	galerkin	ADJ
ejpam-6524	181	3	methods	method	NOUN
ejpam-6524	181	4	are	be	AUX
ejpam-6524	181	5	a	a	DET
ejpam-6524	181	6	class	class	NOUN
ejpam-6524	181	7	of	of	ADP
ejpam-6524	181	8	techniques	technique	NOUN
ejpam-6524	181	9	that	that	PRON
ejpam-6524	181	10	are	be	AUX
ejpam-6524	181	11	used	use	VERB
ejpam-6524	181	12	to	to	PART
ejpam-6524	181	13	estimate	estimate	VERB
ejpam-6524	181	14	the	the	DET
ejpam-6524	181	15	solution	solution	NOUN
ejpam-6524	181	16	to	to	ADP
ejpam-6524	181	17	(	(	PUNCT
ejpam-6524	181	18	9	9	NUM
ejpam-6524	181	19	)	)	PUNCT
ejpam-6524	181	20	.	.	PUNCT
ejpam-6524	182	1	let	let	VERB
ejpam-6524	182	2	vh	vh	PROPN
ejpam-6524	182	3	⊂	⊂	PROPN
ejpam-6524	182	4	v	v	AUX
ejpam-6524	182	5	be	be	AUX
ejpam-6524	182	6	a	a	DET
ejpam-6524	182	7	subspace	subspace	NOUN
ejpam-6524	182	8	of	of	ADP
ejpam-6524	182	9	finite	finite	ADJ
ejpam-6524	182	10	dimensions	dimension	NOUN
ejpam-6524	182	11	.	.	PUNCT
ejpam-6524	183	1	find	find	VERB
ejpam-6524	183	2	uh	uh	INTJ
ejpam-6524	183	3	∈	∈	PROPN
ejpam-6524	183	4	v	v	PROPN
ejpam-6524	183	5	s.t	s.t	PROPN
ejpam-6524	183	6	.	.	PUNCT
ejpam-6524	183	7	by	by	ADP
ejpam-6524	183	8	restricting	restrict	VERB
ejpam-6524	183	9	the	the	DET
ejpam-6524	183	10	variational	variational	ADJ
ejpam-6524	183	11	form	form	NOUN
ejpam-6524	183	12	in	in	ADP
ejpam-6524	183	13	the	the	DET
ejpam-6524	183	14	subspace	subspace	PROPN
ejpam-6524	183	15	vh	vh	PROPN
ejpam-6524	183	16	.	.	PROPN
ejpam-6524	183	17	a(uh	a(uh	PROPN
ejpam-6524	183	18	,	,	PUNCT
ejpam-6524	183	19	vh	vh	PROPN
ejpam-6524	183	20	)	)	PUNCT
ejpam-6524	183	21	=	=	PUNCT
ejpam-6524	184	1	(	(	PUNCT
ejpam-6524	184	2	f	f	X
ejpam-6524	184	3	,	,	PUNCT
ejpam-6524	184	4	vh	vh	PROPN
ejpam-6524	184	5	)	)	PUNCT
ejpam-6524	184	6	,	,	PUNCT
ejpam-6524	184	7	for	for	ADP
ejpam-6524	184	8	all	all	DET
ejpam-6524	184	9	vh	vh	NOUN
ejpam-6524	184	10	∈	∈	PROPN
ejpam-6524	184	11	v.	v.	PROPN
ejpam-6524	184	12	(	(	PUNCT
ejpam-6524	184	13	12	12	NUM
ejpam-6524	184	14	)	)	PUNCT
ejpam-6524	184	15	abdulkafi	abdulkafi	PROPN
ejpam-6524	184	16	m.	m.	PROPN
ejpam-6524	184	17	saeed	saeed	PROPN
ejpam-6524	184	18	,	,	PUNCT
ejpam-6524	184	19	shahad	shahad	PROPN
ejpam-6524	184	20	s.	s.	PROPN
ejpam-6524	184	21	almutairi	almutairi	PROPN
ejpam-6524	184	22	/	/	SYM
ejpam-6524	184	23	eur	eur	PROPN
ejpam-6524	184	24	.	.	PUNCT
ejpam-6524	185	1	j.	j.	PROPN
ejpam-6524	185	2	pure	pure	PROPN
ejpam-6524	185	3	appl	appl	PROPN
ejpam-6524	185	4	.	.	PROPN
ejpam-6524	185	5	math	math	PROPN
ejpam-6524	185	6	,	,	PUNCT
ejpam-6524	185	7	18	18	NUM
ejpam-6524	185	8	(	(	PUNCT
ejpam-6524	185	9	3	3	NUM
ejpam-6524	185	10	)	)	PUNCT
ejpam-6524	185	11	(	(	PUNCT
ejpam-6524	185	12	2025	2025	NUM
ejpam-6524	185	13	)	)	PUNCT
ejpam-6524	185	14	,	,	PUNCT
ejpam-6524	185	15	6524	6524	NUM
ejpam-6524	185	16	9	9	NUM
ejpam-6524	185	17	of	of	ADP
ejpam-6524	185	18	21	21	NUM
ejpam-6524	185	19	vh	vh	NOUN
ejpam-6524	185	20	=	=	SYM
ejpam-6524	185	21	span{φ1	span{φ1	ADJ
ejpam-6524	185	22	,	,	PUNCT
ejpam-6524	185	23	φ2	φ2	PROPN
ejpam-6524	185	24	,	,	PUNCT
ejpam-6524	185	25	...	...	PUNCT
ejpam-6524	185	26	,	,	PUNCT
ejpam-6524	185	27	φn	φn	ADP
ejpam-6524	185	28	}	}	PUNCT
ejpam-6524	185	29	allows	allow	VERB
ejpam-6524	185	30	us	we	PRON
ejpam-6524	185	31	to	to	ADP
ejpam-6524	185	32	every	every	DET
ejpam-6524	185	33	function	function	NOUN
ejpam-6524	185	34	v	v	ADP
ejpam-6524	185	35	∈	∈	PROPN
ejpam-6524	185	36	vh	vh	NOUN
ejpam-6524	185	37	has	have	VERB
ejpam-6524	185	38	a	a	DET
ejpam-6524	185	39	unique	unique	ADJ
ejpam-6524	185	40	representation	representation	NOUN
ejpam-6524	185	41	:	:	PUNCT
ejpam-6524	185	42	to	to	PART
ejpam-6524	185	43	calculate	calculate	VERB
ejpam-6524	185	44	v	v	NOUN
ejpam-6524	185	45	=	=	PUNCT
ejpam-6524	185	46	∑n	∑n	PROPN
ejpam-6524	185	47	i=1	i=1	PROPN
ejpam-6524	185	48	viφi	viφi	PROPN
ejpam-6524	185	49	as	as	ADP
ejpam-6524	185	50	a	a	DET
ejpam-6524	185	51	result	result	NOUN
ejpam-6524	185	52	,	,	PUNCT
ejpam-6524	185	53	one	one	PRON
ejpam-6524	185	54	can	can	AUX
ejpam-6524	185	55	define	define	VERB
ejpam-6524	185	56	an	an	DET
ejpam-6524	185	57	isomorphism	isomorphism	NOUN
ejpam-6524	185	58	.	.	PUNCT
ejpam-6524	186	1	vh	vh	PROPN
ejpam-6524	186	2	∼=	∼=	PROPN
ejpam-6524	186	3	rn	rn	PROPN
ejpam-6524	186	4	by	by	ADP
ejpam-6524	186	5	v	v	NOUN
ejpam-6524	186	6	=	=	SYM
ejpam-6524	186	7	n∑	n∑	PROPN
ejpam-6524	186	8	i=1	i=1	PROPN
ejpam-6524	187	1	viφi	viφi	NOUN
ejpam-6524	188	1	←→	←→	PROPN
ejpam-6524	188	2	v	v	NOUN
ejpam-6524	188	3	=	=	PUNCT
ejpam-6524	188	4	(	(	PUNCT
ejpam-6524	188	5	v1	v1	PROPN
ejpam-6524	188	6	,	,	PUNCT
ejpam-6524	188	7	...	...	PUNCT
ejpam-6524	188	8	,	,	PUNCT
ejpam-6524	188	9	vn	vn	PROPN
ejpam-6524	188	10	)	)	PUNCT
ejpam-6524	188	11	t	t	PROPN
ejpam-6524	188	12	.	.	PUNCT
ejpam-6524	189	1	we	we	PRON
ejpam-6524	189	2	then	then	ADV
ejpam-6524	189	3	refer	refer	VERB
ejpam-6524	189	4	to	to	ADP
ejpam-6524	189	5	v	v	NOUN
ejpam-6524	189	6	as	as	ADP
ejpam-6524	189	7	the	the	DET
ejpam-6524	189	8	coordinate	coordinate	NOUN
ejpam-6524	189	9	vector	vector	NOUN
ejpam-6524	189	10	of	of	ADP
ejpam-6524	189	11	v	v	NOUN
ejpam-6524	189	12	with	with	ADP
ejpam-6524	189	13	regard	regard	NOUN
ejpam-6524	189	14	to	to	ADP
ejpam-6524	189	15	the	the	DET
ejpam-6524	189	16	basis	basis	NOUN
ejpam-6524	189	17	{	{	PUNCT
ejpam-6524	189	18	φ}ni=1	φ}ni=1	NOUN
ejpam-6524	189	19	.	.	PUNCT
ejpam-6524	190	1	we	we	PRON
ejpam-6524	190	2	present	present	VERB
ejpam-6524	190	3	the	the	DET
ejpam-6524	190	4	stiffness	stiffness	ADJ
ejpam-6524	190	5	matrix	matrix	NOUN
ejpam-6524	190	6	after	after	ADP
ejpam-6524	190	7	introducing	introduce	VERB
ejpam-6524	190	8	the	the	DET
ejpam-6524	190	9	elasticity	elasticity	NOUN
ejpam-6524	190	10	language	language	NOUN
ejpam-6524	190	11	.	.	PUNCT
ejpam-6524	191	1	a	a	PRON
ejpam-6524	191	2	=	=	SYM
ejpam-6524	191	3	(	(	PUNCT
ejpam-6524	191	4	aij)n	aij)n	PROPN
ejpam-6524	191	5	x	x	SYM
ejpam-6524	191	6	n	n	X
ejpam-6524	191	7	with	with	ADP
ejpam-6524	191	8	aij	aij	PROPN
ejpam-6524	191	9	=	=	SYM
ejpam-6524	191	10	a(φi	a(φi	PROPN
ejpam-6524	191	11	,	,	PUNCT
ejpam-6524	191	12	φj	φj	NOUN
ejpam-6524	191	13	)	)	PUNCT
ejpam-6524	191	14	,	,	PUNCT
ejpam-6524	191	15	and	and	CCONJ
ejpam-6524	191	16	the	the	DET
ejpam-6524	191	17	load	load	NOUN
ejpam-6524	191	18	vector	vector	NOUN
ejpam-6524	191	19	f	f	PROPN
ejpam-6524	191	20	=	=	PUNCT
ejpam-6524	191	21	{	{	PUNCT
ejpam-6524	191	22	⟨f	⟨f	X
ejpam-6524	191	23	,	,	PUNCT
ejpam-6524	191	24	φ⟩}nk=1	φ⟩}nk=1	PROPN
ejpam-6524	191	25	∈	∈	PROPN
ejpam-6524	191	26	rn	rn	PROPN
ejpam-6524	191	27	.	.	PUNCT
ejpam-6524	192	1	the	the	DET
ejpam-6524	192	2	following	follow	VERB
ejpam-6524	192	3	linear	linear	ADJ
ejpam-6524	192	4	algebraic	algebraic	ADJ
ejpam-6524	192	5	system	system	NOUN
ejpam-6524	192	6	can	can	AUX
ejpam-6524	192	7	therefore	therefore	ADV
ejpam-6524	192	8	be	be	AUX
ejpam-6524	192	9	used	use	VERB
ejpam-6524	192	10	to	to	PART
ejpam-6524	192	11	formulate	formulate	VERB
ejpam-6524	192	12	the	the	DET
ejpam-6524	192	13	variational	variational	ADJ
ejpam-6524	192	14	(	(	PUNCT
ejpam-6524	192	15	12	12	NUM
ejpam-6524	192	16	)	)	PUNCT
ejpam-6524	192	17	on	on	ADP
ejpam-6524	192	18	vh	vh	PROPN
ejpam-6524	192	19	.	.	PROPN
ejpam-6524	192	20	au	au	PROPN
ejpam-6524	193	1	=	=	PROPN
ejpam-6524	193	2	f.	f.	PROPN
ejpam-6524	193	3	the	the	DET
ejpam-6524	193	4	a	a	PROPN
ejpam-6524	193	5	(	(	PUNCT
ejpam-6524	193	6	·	·	PUNCT
ejpam-6524	193	7	,	,	PUNCT
ejpam-6524	193	8	·	·	PUNCT
ejpam-6524	193	9	)	)	PUNCT
ejpam-6524	193	10	-inner	-inner	NOUN
ejpam-6524	193	11	product	product	NOUN
ejpam-6524	193	12	of	of	ADP
ejpam-6524	193	13	two	two	NUM
ejpam-6524	193	14	functions	function	NOUN
ejpam-6524	193	15	,	,	PUNCT
ejpam-6524	193	16	vu	vu	PROPN
ejpam-6524	193	17	∈	∈	PROPN
ejpam-6524	193	18	vh	vh	PROPN
ejpam-6524	193	19	is	be	AUX
ejpam-6524	193	20	realized	realize	VERB
ejpam-6524	193	21	via	via	ADP
ejpam-6524	193	22	the	the	DET
ejpam-6524	193	23	matrix	matrix	NOUN
ejpam-6524	193	24	product	product	NOUN
ejpam-6524	193	25	by	by	ADP
ejpam-6524	193	26	definition	definition	NOUN
ejpam-6524	193	27	.	.	PUNCT
ejpam-6524	194	1	a(uh	a(uh	PROPN
ejpam-6524	194	2	,	,	PUNCT
ejpam-6524	194	3	vh	vh	PROPN
ejpam-6524	194	4	)	)	PUNCT
ejpam-6524	194	5	=	=	SYM
ejpam-6524	195	1	a	a	PRON
ejpam-6524	195	2	(	(	PUNCT
ejpam-6524	195	3	∑	∑	PROPN
ejpam-6524	195	4	i	i	PRON
ejpam-6524	195	5	uiφi	uiφi	PRON
ejpam-6524	195	6	,	,	PUNCT
ejpam-6524	195	7	∑	∑	ADV
ejpam-6524	195	8	vjφj	vjφj	ADJ
ejpam-6524	195	9	)	)	PUNCT
ejpam-6524	195	10	=	=	PUNCT
ejpam-6524	196	1	∑	∑	PUNCT
ejpam-6524	196	2	i	i	PROPN
ejpam-6524	196	3	,	,	PUNCT
ejpam-6524	196	4	j	j	PROPN
ejpam-6524	196	5	a(φi	a(φi	PROPN
ejpam-6524	196	6	,	,	PUNCT
ejpam-6524	196	7	φj)uivj	φj)uivj	NOUN
ejpam-6524	196	8	=	=	PUNCT
ejpam-6524	196	9	vtau	vtau	NOUN
ejpam-6524	196	10	.	.	PUNCT
ejpam-6524	197	1	therefore	therefore	ADV
ejpam-6524	197	2	,	,	PUNCT
ejpam-6524	197	3	for	for	ADP
ejpam-6524	197	4	any	any	DET
ejpam-6524	197	5	vector	vector	NOUN
ejpam-6524	197	6	u	u	PROPN
ejpam-6524	197	7	∈	∈	PROPN
ejpam-6524	197	8	rn	rn	PROPN
ejpam-6524	197	9	,	,	PUNCT
ejpam-6524	197	10	utau	utau	PROPN
ejpam-6524	197	11	=	=	SYM
ejpam-6524	197	12	a(u	a(u	PROPN
ejpam-6524	197	13	,	,	PUNCT
ejpam-6524	197	14	u	u	NOUN
ejpam-6524	197	15	)	)	PUNCT
ejpam-6524	197	16	≥	≥	NOUN
ejpam-6524	197	17	0	0	NUM
ejpam-6524	197	18	and	and	CCONJ
ejpam-6524	197	19	equals	equal	VERB
ejpam-6524	197	20	0	0	PUNCT
ejpam-6524	198	1	if	if	SCONJ
ejpam-6524	198	2	and	and	CCONJ
ejpam-6524	198	3	only	only	ADV
ejpam-6524	198	4	if	if	SCONJ
ejpam-6524	198	5	u	u	NOUN
ejpam-6524	198	6	is	be	AUX
ejpam-6524	198	7	zero	zero	NUM
ejpam-6524	198	8	.	.	PUNCT
ejpam-6524	199	1	namely	namely	ADV
ejpam-6524	199	2	,	,	PUNCT
ejpam-6524	199	3	a	a	PRON
ejpam-6524	199	4	is	be	AUX
ejpam-6524	199	5	an	an	DET
ejpam-6524	199	6	spd	spd	NOUN
ejpam-6524	199	7	matrix	matrix	NOUN
ejpam-6524	199	8	,	,	PUNCT
ejpam-6524	199	9	and	and	CCONJ
ejpam-6524	199	10	thus	thus	ADV
ejpam-6524	199	11	the	the	DET
ejpam-6524	199	12	solution	solution	NOUN
ejpam-6524	199	13	u	u	X
ejpam-6524	199	14	=	=	PUNCT
ejpam-6524	199	15	a−1f	a−1f	PROPN
ejpam-6524	199	16	exists	exist	VERB
ejpam-6524	199	17	and	and	CCONJ
ejpam-6524	199	18	is	be	AUX
ejpam-6524	199	19	unique	unique	ADJ
ejpam-6524	199	20	.	.	PUNCT
ejpam-6524	200	1	once	once	SCONJ
ejpam-6524	200	2	we	we	PRON
ejpam-6524	200	3	get	get	VERB
ejpam-6524	200	4	the	the	DET
ejpam-6524	200	5	coefficient	coefficient	NOUN
ejpam-6524	200	6	vector	vector	PROPN
ejpam-6524	200	7	u	u	PROPN
ejpam-6524	200	8	,	,	PUNCT
ejpam-6524	200	9	we	we	PRON
ejpam-6524	200	10	can	can	AUX
ejpam-6524	200	11	use	use	VERB
ejpam-6524	200	12	a	a	DET
ejpam-6524	200	13	linear	linear	ADJ
ejpam-6524	200	14	combination	combination	NOUN
ejpam-6524	200	15	of	of	ADP
ejpam-6524	200	16	basis	basis	NOUN
ejpam-6524	200	17	functions	function	NOUN
ejpam-6524	200	18	to	to	PART
ejpam-6524	200	19	generate	generate	VERB
ejpam-6524	200	20	uh	uh	INTJ
ejpam-6524	200	21	.	.	PUNCT
ejpam-6524	201	1	a	a	DET
ejpam-6524	201	2	well	well	ADV
ejpam-6524	201	3	-	-	PUNCT
ejpam-6524	201	4	known	know	VERB
ejpam-6524	201	5	and	and	CCONJ
ejpam-6524	201	6	frequently	frequently	ADV
ejpam-6524	201	7	applied	apply	VERB
ejpam-6524	201	8	example	example	NOUN
ejpam-6524	201	9	of	of	ADP
ejpam-6524	201	10	galerkin	galerkin	ADJ
ejpam-6524	201	11	methods	method	NOUN
ejpam-6524	201	12	is	be	AUX
ejpam-6524	201	13	the	the	DET
ejpam-6524	201	14	fem	fem	NOUN
ejpam-6524	201	15	,	,	PUNCT
ejpam-6524	201	16	which	which	PRON
ejpam-6524	201	17	builds	build	VERB
ejpam-6524	201	18	a	a	DET
ejpam-6524	201	19	finite	finite	ADJ
ejpam-6524	201	20	-	-	ADJ
ejpam-6524	201	21	dimensional	dimensional	ADJ
ejpam-6524	201	22	subspace	subspace	NOUN
ejpam-6524	201	23	vh	vh	PROPN
ejpam-6524	201	24	from	from	ADP
ejpam-6524	201	25	domain	domain	NOUN
ejpam-6524	201	26	triangulations	triangulation	NOUN
ejpam-6524	201	27	τh	τh	ADP
ejpam-6524	201	28	.	.	PUNCT
ejpam-6524	202	1	the	the	DET
ejpam-6524	202	2	domain	domain	NOUN
ejpam-6524	202	3	’s	’s	PART
ejpam-6524	202	4	decomposition	decomposition	NOUN
ejpam-6524	202	5	into	into	ADP
ejpam-6524	202	6	a	a	DET
ejpam-6524	202	7	limited	limited	ADJ
ejpam-6524	202	8	number	number	NOUN
ejpam-6524	202	9	of	of	ADP
ejpam-6524	202	10	pieces	piece	NOUN
ejpam-6524	202	11	is	be	AUX
ejpam-6524	202	12	the	the	DET
ejpam-6524	202	13	source	source	NOUN
ejpam-6524	202	14	of	of	ADP
ejpam-6524	202	15	the	the	DET
ejpam-6524	202	16	name	name	NOUN
ejpam-6524	202	17	.	.	PUNCT
ejpam-6524	203	1	piecewise	piecewise	NOUN
ejpam-6524	203	2	polynomials	polynomial	NOUN
ejpam-6524	203	3	are	be	AUX
ejpam-6524	203	4	commonly	commonly	ADV
ejpam-6524	203	5	used	use	VERB
ejpam-6524	203	6	to	to	PART
ejpam-6524	203	7	define	define	VERB
ejpam-6524	203	8	a	a	DET
ejpam-6524	203	9	finite	finite	ADJ
ejpam-6524	203	10	dimensional	dimensional	ADJ
ejpam-6524	203	11	space	space	NOUN
ejpam-6524	203	12	.	.	PUNCT
ejpam-6524	204	1	the	the	DET
ejpam-6524	204	2	scalar	scalar	ADJ
ejpam-6524	204	3	wave	wave	NOUN
ejpam-6524	204	4	equation	equation	NOUN
ejpam-6524	204	5	that	that	PRON
ejpam-6524	204	6	models	model	VERB
ejpam-6524	204	7	the	the	DET
ejpam-6524	204	8	propagation	propagation	NOUN
ejpam-6524	204	9	of	of	ADP
ejpam-6524	204	10	acoustic	acoustic	ADJ
ejpam-6524	204	11	waves	wave	NOUN
ejpam-6524	204	12	in	in	ADP
ejpam-6524	204	13	a	a	DET
ejpam-6524	204	14	bounded	bounded	ADJ
ejpam-6524	204	15	domain	domain	NOUN
ejpam-6524	204	16	ω3	ω3	NOUN
ejpam-6524	204	17	with	with	ADP
ejpam-6524	204	18	boundary	boundary	ADJ
ejpam-6524	204	19	γ	γ	X
ejpam-6524	204	20	is	be	AUX
ejpam-6524	204	21	examined	examine	VERB
ejpam-6524	204	22	:	:	PUNCT
ejpam-6524	204	23	[	[	X
ejpam-6524	204	24	20–22	20–22	NUM
ejpam-6524	204	25	]	]	SYM
ejpam-6524	204	26	.	.	PUNCT
ejpam-6524	204	27	1	1	NUM
ejpam-6524	204	28	c(x)2	c(x)2	NOUN
ejpam-6524	204	29	∂2u	∂2u	ADJ
ejpam-6524	204	30	∂t2	∂t2	PROPN
ejpam-6524	204	31	−	−	ADP
ejpam-6524	204	32	△	△	X
ejpam-6524	204	33	u	u	NOUN
ejpam-6524	204	34	=	=	NOUN
ejpam-6524	204	35	0	0	NUM
ejpam-6524	204	36	,	,	PUNCT
ejpam-6524	204	37	in	in	ADP
ejpam-6524	204	38	ω×	ω×	PROPN
ejpam-6524	204	39	(	(	PUNCT
ejpam-6524	204	40	0	0	NUM
ejpam-6524	204	41	,	,	PUNCT
ejpam-6524	204	42	t	t	NOUN
ejpam-6524	204	43	)	)	PUNCT
ejpam-6524	204	44	,	,	PUNCT
ejpam-6524	204	45	u	u	NOUN
ejpam-6524	204	46	(	(	PUNCT
ejpam-6524	204	47	·	·	PUNCT
ejpam-6524	204	48	,	,	PUNCT
ejpam-6524	204	49	0	0	NUM
ejpam-6524	204	50	)	)	PUNCT
ejpam-6524	204	51	=	=	SYM
ejpam-6524	204	52	0	0	NUM
ejpam-6524	204	53	,	,	PUNCT
ejpam-6524	204	54	∂u	∂u	PROPN
ejpam-6524	204	55	∂t	∂t	PROPN
ejpam-6524	204	56	(	(	PUNCT
ejpam-6524	204	57	·	·	PUNCT
ejpam-6524	204	58	,	,	PUNCT
ejpam-6524	204	59	0	0	NUM
ejpam-6524	204	60	)	)	PUNCT
ejpam-6524	205	1	=	=	SYM
ejpam-6524	205	2	f	f	X
ejpam-6524	205	3	,	,	PUNCT
ejpam-6524	205	4	in	in	ADP
ejpam-6524	205	5	ω	ω	NUM
ejpam-6524	205	6	,	,	PUNCT
ejpam-6524	205	7	∂nu|γ1	∂nu|γ1	NOUN
ejpam-6524	205	8	=	=	SYM
ejpam-6524	205	9	0	0	NUM
ejpam-6524	205	10	,	,	PUNCT
ejpam-6524	205	11	on	on	ADP
ejpam-6524	205	12	γ×	γ×	PROPN
ejpam-6524	205	13	(	(	PUNCT
ejpam-6524	205	14	0	0	NUM
ejpam-6524	205	15	,	,	PUNCT
ejpam-6524	205	16	t	t	NOUN
ejpam-6524	205	17	)	)	PUNCT
ejpam-6524	205	18	.	.	PUNCT
ejpam-6524	206	1	(	(	PUNCT
ejpam-6524	206	2	13	13	NUM
ejpam-6524	206	3	)	)	PUNCT
ejpam-6524	206	4	where	where	SCONJ
ejpam-6524	206	5	t	t	PROPN
ejpam-6524	206	6	is	be	AUX
ejpam-6524	206	7	the	the	DET
ejpam-6524	206	8	time	time	NOUN
ejpam-6524	206	9	variable	variable	NOUN
ejpam-6524	206	10	,	,	PUNCT
ejpam-6524	206	11	t	t	PROPN
ejpam-6524	206	12	is	be	AUX
ejpam-6524	206	13	a	a	DET
ejpam-6524	206	14	final	final	ADJ
ejpam-6524	206	15	time	time	NOUN
ejpam-6524	206	16	,	,	PUNCT
ejpam-6524	206	17	and	and	CCONJ
ejpam-6524	206	18	f	f	PROPN
ejpam-6524	206	19	is	be	AUX
ejpam-6524	206	20	a	a	DET
ejpam-6524	206	21	load	load	NOUN
ejpam-6524	206	22	vector	vector	NOUN
ejpam-6524	206	23	.	.	PUNCT
ejpam-6524	207	1	u(x	u(x	PROPN
ejpam-6524	207	2	,	,	PUNCT
ejpam-6524	207	3	t	t	PROPN
ejpam-6524	207	4	)	)	PUNCT
ejpam-6524	207	5	is	be	AUX
ejpam-6524	207	6	the	the	DET
ejpam-6524	207	7	pressure	pressure	NOUN
ejpam-6524	207	8	,	,	PUNCT
ejpam-6524	207	9	and	and	CCONJ
ejpam-6524	207	10	c(x	c(x	NOUN
ejpam-6524	207	11	)	)	PUNCT
ejpam-6524	207	12	is	be	AUX
ejpam-6524	207	13	the	the	DET
ejpam-6524	207	14	wave	wave	NOUN
ejpam-6524	207	15	speed	speed	NOUN
ejpam-6524	207	16	based	base	VERB
ejpam-6524	207	17	on	on	ADP
ejpam-6524	207	18	x	x	X
ejpam-6524	207	19	=	=	SYM
ejpam-6524	207	20	(	(	PUNCT
ejpam-6524	207	21	x1	x1	PROPN
ejpam-6524	207	22	,	,	PUNCT
ejpam-6524	207	23	x2	x2	PROPN
ejpam-6524	207	24	,	,	PUNCT
ejpam-6524	207	25	x3	x3	ADJ
ejpam-6524	207	26	)	)	PUNCT
ejpam-6524	207	27	∈	∈	PROPN
ejpam-6524	207	28	ω	ω	X
ejpam-6524	207	29	.	.	PUNCT
ejpam-6524	208	1	we	we	PRON
ejpam-6524	208	2	now	now	ADV
ejpam-6524	208	3	use	use	VERB
ejpam-6524	208	4	continuous	continuous	ADJ
ejpam-6524	208	5	piecewise	piecewise	NOUN
ejpam-6524	208	6	linear	linear	NOUN
ejpam-6524	208	7	functions	function	NOUN
ejpam-6524	208	8	in	in	ADP
ejpam-6524	208	9	space	space	NOUN
ejpam-6524	208	10	and	and	CCONJ
ejpam-6524	208	11	time	time	NOUN
ejpam-6524	208	12	to	to	PART
ejpam-6524	208	13	build	build	VERB
ejpam-6524	208	14	a	a	DET
ejpam-6524	208	15	fem	fem	NOUN
ejpam-6524	208	16	for	for	ADP
ejpam-6524	208	17	(	(	PUNCT
ejpam-6524	208	18	13	13	NUM
ejpam-6524	208	19	)	)	PUNCT
ejpam-6524	208	20	.	.	PUNCT
ejpam-6524	209	1	the	the	DET
ejpam-6524	209	2	standard	standard	ADJ
ejpam-6524	209	3	method	method	NOUN
ejpam-6524	209	4	for	for	ADP
ejpam-6524	209	5	discretizing	discretize	VERB
ejpam-6524	209	6	ω×	ω×	PROPN
ejpam-6524	209	7	(	(	PUNCT
ejpam-6524	209	8	0	0	NUM
ejpam-6524	209	9	,	,	PUNCT
ejpam-6524	209	10	t	t	PROPN
ejpam-6524	209	11	)	)	PUNCT
ejpam-6524	209	12	is	be	AUX
ejpam-6524	209	13	to	to	PART
ejpam-6524	209	14	use	use	VERB
ejpam-6524	209	15	kh	kh	PROPN
ejpam-6524	209	16	=	=	PRON
ejpam-6524	209	17	{	{	PUNCT
ejpam-6524	209	18	k	k	X
ejpam-6524	209	19	}	}	PUNCT
ejpam-6524	209	20	to	to	PART
ejpam-6524	209	21	partition	partition	VERB
ejpam-6524	209	22	the	the	DET
ejpam-6524	209	23	domain	domain	NOUN
ejpam-6524	209	24	ω	ω	NOUN
ejpam-6524	209	25	into	into	ADP
ejpam-6524	209	26	tetrahedra	tetrahedron	NOUN
ejpam-6524	209	27	k(h	k(h	PROPN
ejpam-6524	209	28	=	=	SYM
ejpam-6524	209	29	h(x	h(x	PROPN
ejpam-6524	209	30	)	)	PUNCT
ejpam-6524	209	31	,	,	PUNCT
ejpam-6524	209	32	where	where	SCONJ
ejpam-6524	209	33	jk	jk	PROPN
ejpam-6524	209	34	=	=	PRON
ejpam-6524	209	35	{	{	PUNCT
ejpam-6524	209	36	j	j	NOUN
ejpam-6524	209	37	}	}	PUNCT
ejpam-6524	209	38	is	be	AUX
ejpam-6524	209	39	a	a	DET
ejpam-6524	209	40	partition	partition	NOUN
ejpam-6524	209	41	of	of	ADP
ejpam-6524	209	42	the	the	DET
ejpam-6524	209	43	time	time	NOUN
ejpam-6524	209	44	interval	interval	NOUN
ejpam-6524	209	45	(	(	PUNCT
ejpam-6524	209	46	0	0	NUM
ejpam-6524	209	47	,	,	PUNCT
ejpam-6524	209	48	t	t	NOUN
ejpam-6524	209	49	)	)	PUNCT
ejpam-6524	209	50	into	into	ADP
ejpam-6524	209	51	time	time	NOUN
ejpam-6524	209	52	intervals	interval	NOUN
ejpam-6524	209	53	j	j	PROPN
ejpam-6524	210	1	=	=	PRON
ejpam-6524	210	2	(	(	PUNCT
ejpam-6524	210	3	tk−1	tk−1	PROPN
ejpam-6524	210	4	,	,	PUNCT
ejpam-6524	210	5	tk	tk	PROPN
ejpam-6524	210	6	)	)	PUNCT
ejpam-6524	210	7	.k	.k	PUNCT
ejpam-6524	211	1	=	=	PUNCT
ejpam-6524	211	2	1	1	NUM
ejpam-6524	211	3	,	,	PUNCT
ejpam-6524	211	4	.	.	PUNCT
ejpam-6524	211	5	.	.	PUNCT
ejpam-6524	212	1	.	.	PUNCT
ejpam-6524	213	1	,	,	PUNCT
ejpam-6524	213	2	n	n	X
ejpam-6524	213	3	,	,	PUNCT
ejpam-6524	213	4	of	of	ADP
ejpam-6524	213	5	uniform	uniform	ADJ
ejpam-6524	213	6	length	length	NOUN
ejpam-6524	213	7	τ	τ	PROPN
ejpam-6524	213	8	=	=	SYM
ejpam-6524	213	9	tk	tk	PROPN
ejpam-6524	213	10	−	−	PROPN
ejpam-6524	213	11	tk−1	tk−1	PROPN
ejpam-6524	213	12	.	.	PUNCT
ejpam-6524	214	1	abdulkafi	abdulkafi	PROPN
ejpam-6524	214	2	m.	m.	PROPN
ejpam-6524	214	3	saeed	saeed	PROPN
ejpam-6524	214	4	,	,	PUNCT
ejpam-6524	214	5	shahad	shahad	PROPN
ejpam-6524	214	6	s.	s.	PROPN
ejpam-6524	214	7	almutairi	almutairi	PROPN
ejpam-6524	214	8	/	/	SYM
ejpam-6524	214	9	eur	eur	PROPN
ejpam-6524	214	10	.	.	PUNCT
ejpam-6524	215	1	j.	j.	PROPN
ejpam-6524	215	2	pure	pure	PROPN
ejpam-6524	215	3	appl	appl	PROPN
ejpam-6524	215	4	.	.	PROPN
ejpam-6524	215	5	math	math	PROPN
ejpam-6524	215	6	,	,	PUNCT
ejpam-6524	215	7	18	18	NUM
ejpam-6524	215	8	(	(	PUNCT
ejpam-6524	215	9	3	3	NUM
ejpam-6524	215	10	)	)	PUNCT
ejpam-6524	215	11	(	(	PUNCT
ejpam-6524	215	12	2025	2025	NUM
ejpam-6524	215	13	)	)	PUNCT
ejpam-6524	215	14	,	,	PUNCT
ejpam-6524	215	15	6524	6524	NUM
ejpam-6524	215	16	10	10	NUM
ejpam-6524	215	17	of	of	ADP
ejpam-6524	215	18	21	21	NUM
ejpam-6524	215	19	the	the	DET
ejpam-6524	215	20	finite	finite	PROPN
ejpam-6524	215	21	element	element	NOUN
ejpam-6524	215	22	approach	approach	NOUN
ejpam-6524	215	23	for	for	ADP
ejpam-6524	215	24	(	(	PUNCT
ejpam-6524	215	25	13	13	NUM
ejpam-6524	215	26	)	)	PUNCT
ejpam-6524	215	27	is	be	AUX
ejpam-6524	215	28	formulated	formulate	VERB
ejpam-6524	215	29	by	by	ADP
ejpam-6524	215	30	introducing	introduce	VERB
ejpam-6524	215	31	the	the	DET
ejpam-6524	215	32	finite	finite	ADJ
ejpam-6524	215	33	element	element	NOUN
ejpam-6524	215	34	space	space	NOUN
ejpam-6524	215	35	w	w	PROPN
ejpam-6524	215	36	u	u	PROPN
ejpam-6524	215	37	h	h	NOUN
ejpam-6524	215	38	,	,	PUNCT
ejpam-6524	215	39	which	which	PRON
ejpam-6524	215	40	is	be	AUX
ejpam-6524	215	41	defined	define	VERB
ejpam-6524	215	42	as	as	SCONJ
ejpam-6524	215	43	follows	follow	VERB
ejpam-6524	215	44	:	:	PUNCT
ejpam-6524	215	45	w	w	NOUN
ejpam-6524	215	46	u	u	NOUN
ejpam-6524	215	47	:	:	PUNCT
ejpam-6524	215	48	=	=	SYM
ejpam-6524	215	49	{	{	PUNCT
ejpam-6524	215	50	u	u	NOUN
ejpam-6524	215	51	∈	∈	PROPN
ejpam-6524	215	52	h1(ω×	h1(ω×	PROPN
ejpam-6524	215	53	j	j	PROPN
ejpam-6524	215	54	)	)	PUNCT
ejpam-6524	215	55	:	:	PUNCT
ejpam-6524	215	56	u	u	NOUN
ejpam-6524	215	57	(	(	PUNCT
ejpam-6524	215	58	·	·	PUNCT
ejpam-6524	215	59	,	,	PUNCT
ejpam-6524	215	60	0	0	NUM
ejpam-6524	215	61	)	)	PUNCT
ejpam-6524	215	62	=	=	SYM
ejpam-6524	215	63	0	0	NUM
ejpam-6524	215	64	,	,	PUNCT
ejpam-6524	215	65	∂nu|γ	∂nu|γ	X
ejpam-6524	215	66	=	=	SYM
ejpam-6524	215	67	0	0	NUM
ejpam-6524	215	68	}	}	PUNCT
ejpam-6524	215	69	,	,	PUNCT
ejpam-6524	215	70	w	w	NOUN
ejpam-6524	215	71	u	u	NOUN
ejpam-6524	215	72	h	h	NOUN
ejpam-6524	215	73	:	:	PUNCT
ejpam-6524	215	74	=	=	SYM
ejpam-6524	215	75	{	{	PUNCT
ejpam-6524	215	76	u	u	NOUN
ejpam-6524	215	77	∈w	∈w	VERB
ejpam-6524	215	78	u	u	NOUN
ejpam-6524	215	79	:	:	PUNCT
ejpam-6524	215	80	u|k×j	u|k×j	PROPN
ejpam-6524	215	81	∈	∈	PROPN
ejpam-6524	215	82	p1(k)×	p1(k)×	NOUN
ejpam-6524	215	83	p1(j),∀k	p1(j),∀k	PROPN
ejpam-6524	215	84	∈	∈	PROPN
ejpam-6524	216	1	kh,∀j	kh,∀j	PROPN
ejpam-6524	216	2	∈	∈	PROPN
ejpam-6524	216	3	jk	jk	PROPN
ejpam-6524	216	4	}	}	PUNCT
ejpam-6524	216	5	.	.	PUNCT
ejpam-6524	217	1	(	(	PUNCT
ejpam-6524	217	2	14	14	NUM
ejpam-6524	217	3	)	)	PUNCT
ejpam-6524	217	4	the	the	DET
ejpam-6524	217	5	set	set	NOUN
ejpam-6524	217	6	of	of	ADP
ejpam-6524	217	7	piecewise	piecewise	NOUN
ejpam-6524	217	8	linear	linear	NOUN
ejpam-6524	217	9	functions	function	NOUN
ejpam-6524	217	10	on	on	ADP
ejpam-6524	217	11	k	k	PROPN
ejpam-6524	217	12	and	and	CCONJ
ejpam-6524	217	13	j	j	PROPN
ejpam-6524	217	14	,	,	PUNCT
ejpam-6524	217	15	respectively	respectively	ADV
ejpam-6524	217	16	,	,	PUNCT
ejpam-6524	217	17	is	be	AUX
ejpam-6524	217	18	denoted	denote	VERB
ejpam-6524	217	19	by	by	ADP
ejpam-6524	217	20	p1(k	p1(k	NOUN
ejpam-6524	217	21	)	)	PUNCT
ejpam-6524	217	22	and	and	CCONJ
ejpam-6524	217	23	p1(j	p1(j	VERB
ejpam-6524	217	24	)	)	PUNCT
ejpam-6524	217	25	.	.	PUNCT
ejpam-6524	218	1	we	we	PRON
ejpam-6524	218	2	use	use	VERB
ejpam-6524	218	3	cg(1	cg(1	NOUN
ejpam-6524	218	4	)	)	PUNCT
ejpam-6524	218	5	in	in	ADP
ejpam-6524	218	6	space	space	NOUN
ejpam-6524	218	7	and	and	CCONJ
ejpam-6524	218	8	time	time	NOUN
ejpam-6524	218	9	to	to	PART
ejpam-6524	218	10	construct	construct	VERB
ejpam-6524	218	11	a	a	DET
ejpam-6524	218	12	discrete	discrete	ADJ
ejpam-6524	218	13	scheme	scheme	NOUN
ejpam-6524	218	14	,	,	PUNCT
ejpam-6524	218	15	and	and	CCONJ
ejpam-6524	218	16	we	we	PRON
ejpam-6524	218	17	look	look	VERB
ejpam-6524	218	18	for	for	ADP
ejpam-6524	218	19	a	a	DET
ejpam-6524	218	20	discrete	discrete	ADJ
ejpam-6524	218	21	solution	solution	NOUN
ejpam-6524	218	22	in	in	ADP
ejpam-6524	218	23	the	the	DET
ejpam-6524	218	24	space	space	NOUN
ejpam-6524	218	25	w	w	PROPN
ejpam-6524	218	26	u	u	PROPN
ejpam-6524	218	27	h	h	NOUN
ejpam-6524	218	28	for	for	ADP
ejpam-6524	218	29	u	u	NOUN
ejpam-6524	218	30	spanned	span	VERB
ejpam-6524	218	31	by	by	ADP
ejpam-6524	218	32	the	the	DET
ejpam-6524	218	33	functions	function	NOUN
ejpam-6524	218	34	.	.	PUNCT
ejpam-6524	219	1	u(x	u(x	PROPN
ejpam-6524	219	2	,	,	PUNCT
ejpam-6524	219	3	t	t	PROPN
ejpam-6524	219	4	)	)	PUNCT
ejpam-6524	219	5	=	=	SYM
ejpam-6524	220	1	n∑	n∑	PROPN
ejpam-6524	220	2	l=0	l=0	PROPN
ejpam-6524	220	3	m∑	m∑	VERB
ejpam-6524	220	4	i=1	i=1	PROPN
ejpam-6524	220	5	uliφi(x)ψl(t	uliφi(x)ψl(t	NOUN
ejpam-6524	220	6	)	)	PUNCT
ejpam-6524	220	7	.	.	PUNCT
ejpam-6524	221	1	(	(	PUNCT
ejpam-6524	221	2	15	15	NUM
ejpam-6524	221	3	)	)	PUNCT
ejpam-6524	221	4	in	in	ADP
ejpam-6524	221	5	space	space	NOUN
ejpam-6524	221	6	and	and	CCONJ
ejpam-6524	221	7	time	time	NOUN
ejpam-6524	221	8	,	,	PUNCT
ejpam-6524	221	9	the	the	DET
ejpam-6524	221	10	typical	typical	ADJ
ejpam-6524	221	11	continuous	continuous	ADJ
ejpam-6524	221	12	piecewise	piecewise	NOUN
ejpam-6524	221	13	linear	linear	NOUN
ejpam-6524	221	14	functions	function	NOUN
ejpam-6524	221	15	φi(x	φi(x	NUM
ejpam-6524	221	16	)	)	PUNCT
ejpam-6524	221	17	and	and	CCONJ
ejpam-6524	221	18	ψl(t	ψl(t	NOUN
ejpam-6524	221	19	)	)	PUNCT
ejpam-6524	221	20	are	be	AUX
ejpam-6524	221	21	represented	represent	VERB
ejpam-6524	221	22	,	,	PUNCT
ejpam-6524	221	23	respectively	respectively	ADV
ejpam-6524	221	24	.	.	PUNCT
ejpam-6524	222	1	the	the	DET
ejpam-6524	222	2	system	system	NOUN
ejpam-6524	222	3	of	of	ADP
ejpam-6524	222	4	linear	linear	PROPN
ejpam-6524	222	5	equations	equation	NOUN
ejpam-6524	222	6	that	that	PRON
ejpam-6524	222	7	results	result	VERB
ejpam-6524	222	8	from	from	ADP
ejpam-6524	222	9	substituting	substitute	VERB
ejpam-6524	222	10	this	this	PRON
ejpam-6524	222	11	into	into	ADP
ejpam-6524	222	12	(	(	PUNCT
ejpam-6524	222	13	13	13	NUM
ejpam-6524	222	14	)	)	PUNCT
ejpam-6524	222	15	is	be	AUX
ejpam-6524	222	16	as	as	SCONJ
ejpam-6524	222	17	follows	follow	VERB
ejpam-6524	222	18	:	:	PUNCT
ejpam-6524	222	19	m	m	VERB
ejpam-6524	222	20	(	(	PUNCT
ejpam-6524	222	21	uk+1	uk+1	ADP
ejpam-6524	222	22	−	−	PROPN
ejpam-6524	222	23	2uk	2uk	NOUN
ejpam-6524	222	24	+	+	CCONJ
ejpam-6524	222	25	uk−1	uk−1	ADJ
ejpam-6524	222	26	)	)	PUNCT
ejpam-6524	222	27	=	=	SYM
ejpam-6524	223	1	τ2f	τ2f	PUNCT
ejpam-6524	223	2	k	k	PROPN
ejpam-6524	224	1	−	−	NOUN
ejpam-6524	224	2	τ2a	τ2a	NOUN
ejpam-6524	224	3	(	(	PUNCT
ejpam-6524	224	4	1	1	NUM
ejpam-6524	224	5	6	6	NUM
ejpam-6524	224	6	uk−1	uk−1	ADJ
ejpam-6524	224	7	+	+	CCONJ
ejpam-6524	224	8	2	2	NUM
ejpam-6524	224	9	3	3	NUM
ejpam-6524	224	10	uk	uk	NOUN
ejpam-6524	224	11	+	+	CCONJ
ejpam-6524	224	12	1	1	NUM
ejpam-6524	224	13	6	6	NUM
ejpam-6524	224	14	uk+1	uk+1	X
ejpam-6524	224	15	)	)	PUNCT
ejpam-6524	224	16	,	,	PUNCT
ejpam-6524	224	17	k	k	X
ejpam-6524	225	1	=	=	SYM
ejpam-6524	225	2	1	1	NUM
ejpam-6524	225	3	,	,	PUNCT
ejpam-6524	225	4	.	.	PUNCT
ejpam-6524	225	5	.	.	PUNCT
ejpam-6524	226	1	.	.	PUNCT
ejpam-6524	227	1	,	,	PUNCT
ejpam-6524	228	1	n	n	CCONJ
ejpam-6524	228	2	−	−	PROPN
ejpam-6524	228	3	1	1	NUM
ejpam-6524	228	4	,	,	PUNCT
ejpam-6524	228	5	(	(	PUNCT
ejpam-6524	228	6	16	16	NUM
ejpam-6524	228	7	)	)	PUNCT
ejpam-6524	228	8	with	with	ADP
ejpam-6524	228	9	initial	initial	ADJ
ejpam-6524	228	10	conditions	condition	NOUN
ejpam-6524	228	11	:	:	PUNCT
ejpam-6524	228	12	u(0	u(0	NOUN
ejpam-6524	228	13	)	)	PUNCT
ejpam-6524	228	14	=	=	SYM
ejpam-6524	229	1	∂u	∂u	PROPN
ejpam-6524	229	2	∂t	∂t	PROPN
ejpam-6524	229	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6524	229	4	t=0	t=0	VERB
ejpam-6524	229	5	=	=	NOUN
ejpam-6524	229	6	0	0	X
ejpam-6524	229	7	.	.	PUNCT
ejpam-6524	230	1	here	here	ADV
ejpam-6524	230	2	,	,	PUNCT
ejpam-6524	230	3	f	f	PROPN
ejpam-6524	230	4	k	k	PROPN
ejpam-6524	230	5	is	be	AUX
ejpam-6524	230	6	the	the	DET
ejpam-6524	230	7	load	load	NOUN
ejpam-6524	230	8	vector	vector	NOUN
ejpam-6524	230	9	at	at	ADP
ejpam-6524	230	10	time	time	NOUN
ejpam-6524	230	11	level	level	PROPN
ejpam-6524	230	12	tk	tk	PROPN
ejpam-6524	230	13	,	,	PUNCT
ejpam-6524	230	14	wherek	wherek	NOUN
ejpam-6524	230	15	=	=	SYM
ejpam-6524	230	16	1	1	NUM
ejpam-6524	230	17	,	,	PUNCT
ejpam-6524	230	18	2	2	NUM
ejpam-6524	230	19	,	,	PUNCT
ejpam-6524	230	20	3	3	NUM
ejpam-6524	230	21	.	.	PUNCT
ejpam-6524	230	22	.	.	PUNCT
ejpam-6524	231	1	.	.	PUNCT
ejpam-6524	232	1	,	,	PUNCT
ejpam-6524	232	2	mathbfu	mathbfu	PROPN
ejpam-6524	232	3	is	be	AUX
ejpam-6524	232	4	the	the	DET
ejpam-6524	232	5	unknown	unknown	ADJ
ejpam-6524	232	6	discrete	discrete	ADJ
ejpam-6524	232	7	field	field	NOUN
ejpam-6524	232	8	values	value	NOUN
ejpam-6524	232	9	of	of	ADP
ejpam-6524	232	10	u	u	NOUN
ejpam-6524	232	11	,	,	PUNCT
ejpam-6524	232	12	m	m	VERB
ejpam-6524	232	13	is	be	AUX
ejpam-6524	232	14	the	the	DET
ejpam-6524	232	15	mass	mass	ADJ
ejpam-6524	232	16	matrix	matrix	NOUN
ejpam-6524	232	17	in	in	ADP
ejpam-6524	232	18	space	space	NOUN
ejpam-6524	232	19	,	,	PUNCT
ejpam-6524	232	20	a	a	PRON
ejpam-6524	232	21	is	be	AUX
ejpam-6524	232	22	the	the	DET
ejpam-6524	232	23	stiffness	stiffness	ADJ
ejpam-6524	232	24	matrix	matrix	NOUN
ejpam-6524	232	25	,	,	PUNCT
ejpam-6524	232	26	and	and	CCONJ
ejpam-6524	232	27	τ	τ	PROPN
ejpam-6524	232	28	is	be	AUX
ejpam-6524	232	29	the	the	DET
ejpam-6524	232	30	time	time	NOUN
ejpam-6524	232	31	step	step	NOUN
ejpam-6524	232	32	.	.	PUNCT
ejpam-6524	233	1	for	for	ADP
ejpam-6524	233	2	each	each	DET
ejpam-6524	233	3	element	element	NOUN
ejpam-6524	233	4	e	e	NOUN
ejpam-6524	233	5	,	,	PUNCT
ejpam-6524	233	6	the	the	DET
ejpam-6524	233	7	explicit	explicit	ADJ
ejpam-6524	233	8	formulas	formula	NOUN
ejpam-6524	233	9	for	for	ADP
ejpam-6524	233	10	the	the	DET
ejpam-6524	233	11	entries	entry	NOUN
ejpam-6524	233	12	in	in	ADP
ejpam-6524	233	13	system	system	NOUN
ejpam-6524	233	14	(	(	PUNCT
ejpam-6524	233	15	16	16	NUM
ejpam-6524	233	16	)	)	PUNCT
ejpam-6524	233	17	can	can	AUX
ejpam-6524	233	18	be	be	AUX
ejpam-6524	233	19	provided	provide	VERB
ejpam-6524	233	20	as	as	SCONJ
ejpam-6524	233	21	follows	follow	VERB
ejpam-6524	233	22	:	:	PUNCT
ejpam-6524	233	23	m	m	VERB
ejpam-6524	233	24	e	e	X
ejpam-6524	233	25	i	i	PRON
ejpam-6524	233	26	,	,	PUNCT
ejpam-6524	233	27	j	j	PROPN
ejpam-6524	234	1	=	=	PRON
ejpam-6524	234	2	(	(	PUNCT
ejpam-6524	234	3	1	1	NUM
ejpam-6524	234	4	c2	c2	PROPN
ejpam-6524	234	5	φi	φi	ADP
ejpam-6524	234	6	,	,	PUNCT
ejpam-6524	234	7	φj	φj	NOUN
ejpam-6524	234	8	)	)	PUNCT
ejpam-6524	234	9	e	e	NOUN
ejpam-6524	234	10	,	,	PUNCT
ejpam-6524	234	11	ke	ke	PROPN
ejpam-6524	234	12	i	i	PROPN
ejpam-6524	234	13	,	,	PUNCT
ejpam-6524	234	14	j	j	PROPN
ejpam-6524	234	15	=	=	PRON
ejpam-6524	234	16	(	(	PUNCT
ejpam-6524	234	17	∇φi,∇φj)e	∇φi,∇φj)e	PROPN
ejpam-6524	234	18	,	,	PUNCT
ejpam-6524	234	19	f	f	PROPN
ejpam-6524	234	20	e	e	X
ejpam-6524	234	21	j	j	PROPN
ejpam-6524	234	22	=	=	SYM
ejpam-6524	234	23	(	(	PUNCT
ejpam-6524	234	24	f	f	X
ejpam-6524	234	25	,	,	PUNCT
ejpam-6524	234	26	φj)e	φj)e	PROPN
ejpam-6524	234	27	.	.	PUNCT
ejpam-6524	235	1	where	where	SCONJ
ejpam-6524	235	2	the	the	DET
ejpam-6524	235	3	l2(e	l2(e	NOUN
ejpam-6524	235	4	)	)	PUNCT
ejpam-6524	235	5	scalar	scalar	ADJ
ejpam-6524	235	6	product	product	NOUN
ejpam-6524	235	7	is	be	AUX
ejpam-6524	235	8	indicated	indicate	VERB
ejpam-6524	235	9	by	by	ADP
ejpam-6524	235	10	(	(	PUNCT
ejpam-6524	235	11	.	.	PUNCT
ejpam-6524	235	12	,	,	PUNCT
ejpam-6524	235	13	.)e	.)e	PROPN
ejpam-6524	235	14	.	.	PUNCT
ejpam-6524	236	1	the	the	DET
ejpam-6524	236	2	contribution	contribution	NOUN
ejpam-6524	236	3	of	of	ADP
ejpam-6524	236	4	element	element	NOUN
ejpam-6524	236	5	e	e	PROPN
ejpam-6524	236	6	to	to	ADP
ejpam-6524	236	7	the	the	DET
ejpam-6524	236	8	global	global	ADJ
ejpam-6524	236	9	assembled	assemble	VERB
ejpam-6524	236	10	matrix	matrix	NOUN
ejpam-6524	236	11	in	in	ADP
ejpam-6524	236	12	space	space	NOUN
ejpam-6524	236	13	m	m	VERB
ejpam-6524	236	14	is	be	AUX
ejpam-6524	236	15	represented	represent	VERB
ejpam-6524	236	16	by	by	ADP
ejpam-6524	236	17	the	the	DET
ejpam-6524	236	18	matrix	matrix	NOUN
ejpam-6524	236	19	me	i	PRON
ejpam-6524	236	20	,	,	PUNCT
ejpam-6524	236	21	while	while	SCONJ
ejpam-6524	236	22	the	the	DET
ejpam-6524	236	23	contribution	contribution	NOUN
ejpam-6524	236	24	of	of	ADP
ejpam-6524	236	25	element	element	NOUN
ejpam-6524	236	26	e	e	PROPN
ejpam-6524	236	27	to	to	ADP
ejpam-6524	236	28	the	the	DET
ejpam-6524	236	29	global	global	ADJ
ejpam-6524	236	30	assembled	assemble	VERB
ejpam-6524	236	31	matrix	matrix	NOUN
ejpam-6524	236	32	k	k	NOUN
ejpam-6524	236	33	is	be	AUX
ejpam-6524	236	34	represented	represent	VERB
ejpam-6524	236	35	by	by	ADP
ejpam-6524	236	36	the	the	DET
ejpam-6524	236	37	matrix	matrix	NOUN
ejpam-6524	236	38	ke	ke	NOUN
ejpam-6524	236	39	.	.	PUNCT
ejpam-6524	237	1	w	w	NOUN
ejpam-6524	237	2	u	u	NOUN
ejpam-6524	237	3	h	h	NOUN
ejpam-6524	237	4	is	be	AUX
ejpam-6524	237	5	a	a	DET
ejpam-6524	237	6	vector	vector	NOUN
ejpam-6524	237	7	space	space	NOUN
ejpam-6524	237	8	with	with	ADP
ejpam-6524	237	9	finite	finite	ADJ
ejpam-6524	237	10	dimensions	dimension	NOUN
ejpam-6524	237	11	,	,	PUNCT
ejpam-6524	237	12	dimw	dimw	VERB
ejpam-6524	237	13	u	u	NOUN
ejpam-6524	237	14	h	h	NOUN
ejpam-6524	237	15	=	=	NOUN
ejpam-6524	237	16	m	m	X
ejpam-6524	237	17	×n	×n	PRON
ejpam-6524	237	18	,	,	PUNCT
ejpam-6524	237	19	with	with	ADP
ejpam-6524	237	20	a	a	DET
ejpam-6524	237	21	basis	basis	NOUN
ejpam-6524	237	22	consisting	consist	VERB
ejpam-6524	237	23	of	of	ADP
ejpam-6524	237	24	the	the	DET
ejpam-6524	237	25	standard	standard	ADJ
ejpam-6524	237	26	continuous	continuous	ADJ
ejpam-6524	237	27	piecewise	piecewise	NOUN
ejpam-6524	237	28	linear	linear	NOUN
ejpam-6524	237	29	functions	function	NOUN
ejpam-6524	237	30	{	{	PUNCT
ejpam-6524	237	31	φi}mi=1	φi}mi=1	VERB
ejpam-6524	237	32	in	in	ADP
ejpam-6524	237	33	space	space	NOUN
ejpam-6524	237	34	and	and	CCONJ
ejpam-6524	237	35	hat	hat	NOUN
ejpam-6524	237	36	functions	function	NOUN
ejpam-6524	237	37	{	{	PUNCT
ejpam-6524	237	38	ψl}nl=1	ψl}nl=1	VERB
ejpam-6524	237	39	in	in	ADP
ejpam-6524	237	40	time	time	NOUN
ejpam-6524	237	41	,	,	PUNCT
ejpam-6524	237	42	where	where	SCONJ
ejpam-6524	237	43	:	:	PUNCT
ejpam-6524	237	44	abdulkafi	abdulkafi	PROPN
ejpam-6524	237	45	m.	m.	PROPN
ejpam-6524	237	46	saeed	saeed	PROPN
ejpam-6524	237	47	,	,	PUNCT
ejpam-6524	237	48	shahad	shahad	PROPN
ejpam-6524	237	49	s.	s.	PROPN
ejpam-6524	237	50	almutairi	almutairi	PROPN
ejpam-6524	237	51	/	/	SYM
ejpam-6524	237	52	eur	eur	PROPN
ejpam-6524	237	53	.	.	PUNCT
ejpam-6524	238	1	j.	j.	PROPN
ejpam-6524	238	2	pure	pure	PROPN
ejpam-6524	238	3	appl	appl	PROPN
ejpam-6524	238	4	.	.	PROPN
ejpam-6524	238	5	math	math	PROPN
ejpam-6524	238	6	,	,	PUNCT
ejpam-6524	238	7	18	18	NUM
ejpam-6524	238	8	(	(	PUNCT
ejpam-6524	238	9	3	3	NUM
ejpam-6524	238	10	)	)	PUNCT
ejpam-6524	238	11	(	(	PUNCT
ejpam-6524	238	12	2025	2025	NUM
ejpam-6524	238	13	)	)	PUNCT
ejpam-6524	238	14	,	,	PUNCT
ejpam-6524	238	15	6524	6524	NUM
ejpam-6524	238	16	11	11	NUM
ejpam-6524	238	17	of	of	ADP
ejpam-6524	238	18	21	21	NUM
ejpam-6524	238	19	figure	figure	NOUN
ejpam-6524	238	20	3	3	NUM
ejpam-6524	238	21	:	:	PUNCT
ejpam-6524	238	22	discretization	discretization	NOUN
ejpam-6524	238	23	of	of	ADP
ejpam-6524	238	24	ψ(t	ψ(t	PROPN
ejpam-6524	238	25	)	)	PUNCT
ejpam-6524	238	26	ψl(t	ψl(t	NOUN
ejpam-6524	238	27	)	)	PUNCT
ejpam-6524	238	28	=	=	SYM
ejpam-6524	239	1			NUM
ejpam-6524	239	2	0	0	NUM
ejpam-6524	239	3	,	,	PUNCT
ejpam-6524	239	4	if	if	SCONJ
ejpam-6524	239	5	t	t	PROPN
ejpam-6524	239	6	/∈	/∈	PUNCT
ejpam-6524	240	1	[	[	X
ejpam-6524	240	2	tl−1	tl−1	NOUN
ejpam-6524	240	3	,	,	PUNCT
ejpam-6524	240	4	tl+1	tl+1	PROPN
ejpam-6524	240	5	]	]	PUNCT
ejpam-6524	240	6	,	,	PUNCT
ejpam-6524	240	7	t−tl−1	t−tl−1	PRON
ejpam-6524	240	8	ti−tl−1	ti−tl−1	NOUN
ejpam-6524	240	9	,	,	PUNCT
ejpam-6524	240	10	if	if	SCONJ
ejpam-6524	240	11	t	t	PROPN
ejpam-6524	240	12	∈	∈	PROPN
ejpam-6524	240	13	[	[	X
ejpam-6524	240	14	tl−1	tl−1	NOUN
ejpam-6524	240	15	,	,	PUNCT
ejpam-6524	240	16	tl	tl	PROPN
ejpam-6524	240	17	]	]	PUNCT
ejpam-6524	240	18	,	,	PUNCT
ejpam-6524	240	19	tl+1−t	tl+1−t	NOUN
ejpam-6524	240	20	tl+1−tl	tl+1−tl	NOUN
ejpam-6524	240	21	,	,	PUNCT
ejpam-6524	240	22	if	if	SCONJ
ejpam-6524	240	23	t	t	PROPN
ejpam-6524	240	24	∈	∈	PROPN
ejpam-6524	241	1	[	[	X
ejpam-6524	241	2	tl	tl	PROPN
ejpam-6524	241	3	,	,	PUNCT
ejpam-6524	241	4	tl+1	tl+1	PROPN
ejpam-6524	241	5	]	]	PUNCT
ejpam-6524	241	6	.	.	PUNCT
ejpam-6524	242	1	(	(	PUNCT
ejpam-6524	242	2	17	17	NUM
ejpam-6524	242	3	)	)	PUNCT
ejpam-6524	242	4	the	the	DET
ejpam-6524	242	5	discrete	discrete	ADJ
ejpam-6524	242	6	system	system	NOUN
ejpam-6524	242	7	of	of	ADP
ejpam-6524	242	8	equations	equation	NOUN
ejpam-6524	242	9	using	use	VERB
ejpam-6524	242	10	basis	basis	NOUN
ejpam-6524	242	11	of	of	ADP
ejpam-6524	242	12	functions	function	NOUN
ejpam-6524	242	13	{	{	PUNCT
ejpam-6524	242	14	φi}mi=1	φi}mi=1	VERB
ejpam-6524	242	15	in	in	ADP
ejpam-6524	242	16	space	space	NOUN
ejpam-6524	242	17	and	and	CCONJ
ejpam-6524	242	18	{	{	PUNCT
ejpam-6524	242	19	ψl}nl=1	ψl}nl=1	VERB
ejpam-6524	242	20	in	in	ADP
ejpam-6524	242	21	time	time	NOUN
ejpam-6524	242	22	we	we	PRON
ejpam-6524	242	23	have	have	VERB
ejpam-6524	242	24	:	:	PUNCT
ejpam-6524	242	25	uh	uh	INTJ
ejpam-6524	242	26	=	=	SYM
ejpam-6524	242	27	∑n	∑n	PROPN
ejpam-6524	242	28	l=0	l=0	PROPN
ejpam-6524	242	29	∑m	∑m	PROPN
ejpam-6524	243	1	i=1	i=1	PROPN
ejpam-6524	243	2	u	u	PROPN
ejpam-6524	243	3	l	l	NOUN
ejpam-6524	243	4	hiφi(x)ψl(t	hiφi(x)ψl(t	PROPN
ejpam-6524	243	5	)	)	PUNCT
ejpam-6524	243	6	.	.	PUNCT
ejpam-6524	244	1	substituting	substitute	VERB
ejpam-6524	244	2	into	into	ADP
ejpam-6524	244	3	(	(	PUNCT
ejpam-6524	244	4	13	13	NUM
ejpam-6524	244	5	)	)	PUNCT
ejpam-6524	244	6	we	we	PRON
ejpam-6524	244	7	get	get	VERB
ejpam-6524	244	8	:	:	PUNCT
ejpam-6524	244	9	−	−	PROPN
ejpam-6524	245	1	n∑	n∑	X
ejpam-6524	246	1	l=0	l=0	PROPN
ejpam-6524	247	1	m∑	m∑	VERB
ejpam-6524	248	1	i=1	i=1	PROPN
ejpam-6524	249	1	ul	ul	INTJ
ejpam-6524	249	2	hl	hl	NOUN
ejpam-6524	250	1	i	i	PRON
ejpam-6524	250	2	∫	∫	PROPN
ejpam-6524	251	1	ω	ω	PROPN
ejpam-6524	251	2	1	1	NUM
ejpam-6524	251	3	c2	c2	PROPN
ejpam-6524	251	4	φi(x	φi(x	NUM
ejpam-6524	251	5	)	)	PUNCT
ejpam-6524	251	6	∫	∫	PROPN
ejpam-6524	251	7	tl+1	tl+1	PROPN
ejpam-6524	251	8	tl−1	tl−1	PROPN
ejpam-6524	251	9	∂ψl(t	∂ψl(t	PROPN
ejpam-6524	251	10	)	)	PUNCT
ejpam-6524	252	1	∂t	∂t	PROPN
ejpam-6524	252	2	∂v(x	∂v(x	PROPN
ejpam-6524	252	3	,	,	PUNCT
ejpam-6524	252	4	t	t	PROPN
ejpam-6524	252	5	)	)	PUNCT
ejpam-6524	252	6	∂t	∂t	PROPN
ejpam-6524	252	7	dxdt	dxdt	NOUN
ejpam-6524	252	8	+	+	CCONJ
ejpam-6524	252	9	n∑	n∑	X
ejpam-6524	252	10	l=0	l=0	PROPN
ejpam-6524	252	11	m∑	m∑	VERB
ejpam-6524	252	12	i=1	i=1	PROPN
ejpam-6524	253	1	ulhi	ulhi	PROPN
ejpam-6524	253	2	∫	∫	PROPN
ejpam-6524	253	3	ω	ω	NUM
ejpam-6524	253	4	∫	∫	PROPN
ejpam-6524	253	5	tl+1	tl+1	PROPN
ejpam-6524	253	6	tl−1	tl−1	PROPN
ejpam-6524	253	7	∇φi(x)∇v(x	∇φi(x)∇v(x	VERB
ejpam-6524	253	8	,	,	PUNCT
ejpam-6524	253	9	t)ψl(t)dxdt	t)ψl(t)dxdt	X
ejpam-6524	254	1	=	=	SYM
ejpam-6524	254	2	∫	∫	PROPN
ejpam-6524	254	3	ω	ω	NUM
ejpam-6524	254	4	∫	∫	PROPN
ejpam-6524	254	5	t	t	PROPN
ejpam-6524	254	6	0	0	NUM
ejpam-6524	254	7	f(x)v(x	f(x)v(x	NOUN
ejpam-6524	254	8	,	,	PUNCT
ejpam-6524	254	9	t)dxdt	t)dxdt	NOUN
ejpam-6524	254	10	∀v	∀v	NOUN
ejpam-6524	254	11	∈w	∈w	VERB
ejpam-6524	254	12	u	u	NOUN
ejpam-6524	254	13	h	h	NOUN
ejpam-6524	254	14	.	.	PUNCT
ejpam-6524	255	1	we	we	PRON
ejpam-6524	255	2	take	take	VERB
ejpam-6524	255	3	v(x	v(x	PROPN
ejpam-6524	255	4	,	,	PUNCT
ejpam-6524	255	5	t	t	PROPN
ejpam-6524	255	6	)	)	PUNCT
ejpam-6524	255	7	=	=	SYM
ejpam-6524	255	8	φj(x)ψm(t	φj(x)ψm(t	NOUN
ejpam-6524	255	9	)	)	PUNCT
ejpam-6524	255	10	and	and	CCONJ
ejpam-6524	255	11	get	get	VERB
ejpam-6524	255	12	:	:	PUNCT
ejpam-6524	255	13	−	−	PROPN
ejpam-6524	256	1	n∑	n∑	X
ejpam-6524	256	2	l=0	l=0	PROPN
ejpam-6524	256	3	m∑	m∑	VERB
ejpam-6524	256	4	i=1	i=1	PROPN
ejpam-6524	257	1	ulhi	ulhi	PROPN
ejpam-6524	257	2	∫	∫	PROPN
ejpam-6524	257	3	ω	ω	NUM
ejpam-6524	257	4	1	1	NUM
ejpam-6524	257	5	c2	c2	PROPN
ejpam-6524	257	6	φi(x)φj(x	φi(x)φj(x	PROPN
ejpam-6524	257	7	)	)	PUNCT
ejpam-6524	257	8	∫	∫	PROPN
ejpam-6524	257	9	tl+1	tl+1	PROPN
ejpam-6524	257	10	tl−1	tl−1	PROPN
ejpam-6524	257	11	∂ψl(t	∂ψl(t	PROPN
ejpam-6524	257	12	)	)	PUNCT
ejpam-6524	258	1	∂t	∂t	PROPN
ejpam-6524	258	2	∂ψm(t	∂ψm(t	PROPN
ejpam-6524	258	3	)	)	PUNCT
ejpam-6524	259	1	∂t	∂t	PROPN
ejpam-6524	259	2	dxdt	dxdt	NOUN
ejpam-6524	259	3	+	+	CCONJ
ejpam-6524	259	4	n∑	n∑	X
ejpam-6524	259	5	l=0	l=0	PROPN
ejpam-6524	259	6	m∑	m∑	VERB
ejpam-6524	259	7	i=1	i=1	PROPN
ejpam-6524	260	1	ulhi	ulhi	PROPN
ejpam-6524	260	2	∫	∫	PROPN
ejpam-6524	260	3	ω	ω	PROPN
ejpam-6524	260	4	∇φi(x)∇φj(x	∇φi(x)∇φj(x	PROPN
ejpam-6524	260	5	)	)	PUNCT
ejpam-6524	261	1	∫	∫	PROPN
ejpam-6524	262	1	tl+1	tl+1	PROPN
ejpam-6524	262	2	tl−1	tl−1	PROPN
ejpam-6524	262	3	ψl(t)ψm(t)dxdt	ψl(t)ψm(t)dxdt	PROPN
ejpam-6524	262	4	=	=	SYM
ejpam-6524	262	5	∫	∫	PROPN
ejpam-6524	263	1	ω	ω	NUM
ejpam-6524	263	2	∫	∫	PROPN
ejpam-6524	263	3	t	t	PROPN
ejpam-6524	263	4	0	0	NUM
ejpam-6524	263	5	f(x)v(x	f(x)v(x	NOUN
ejpam-6524	263	6	,	,	PUNCT
ejpam-6524	263	7	t)dxdt	t)dxdt	NOUN
ejpam-6524	263	8	∀v	∀v	NOUN
ejpam-6524	263	9	∈w	∈w	VERB
ejpam-6524	263	10	u	u	NOUN
ejpam-6524	263	11	h	h	NOUN
ejpam-6524	263	12	.	.	PUNCT
ejpam-6524	264	1	(	(	PUNCT
ejpam-6524	264	2	18	18	NUM
ejpam-6524	264	3	)	)	PUNCT
ejpam-6524	264	4	the	the	DET
ejpam-6524	264	5	vector	vector	NOUN
ejpam-6524	264	6	of	of	ADP
ejpam-6524	264	7	unknown	unknown	ADJ
ejpam-6524	264	8	coefficients	coefficient	NOUN
ejpam-6524	264	9	is	be	AUX
ejpam-6524	264	10	represented	represent	VERB
ejpam-6524	264	11	by	by	ADP
ejpam-6524	264	12	u	u	NOUN
ejpam-6524	264	13	=	=	NOUN
ejpam-6524	264	14	ulhi	ulhi	PROPN
ejpam-6524	264	15	,	,	PUNCT
ejpam-6524	264	16	m	m	VERB
ejpam-6524	264	17	=	=	SYM
ejpam-6524	264	18	(	(	PUNCT
ejpam-6524	264	19	mij	mij	NOUN
ejpam-6524	264	20	)	)	PUNCT
ejpam-6524	264	21	,	,	PUNCT
ejpam-6524	264	22	and	and	CCONJ
ejpam-6524	264	23	a	a	DET
ejpam-6524	264	24	=	=	X
ejpam-6524	264	25	(	(	PUNCT
ejpam-6524	264	26	aij	aij	PROPN
ejpam-6524	264	27	)	)	PUNCT
ejpam-6524	264	28	,	,	PUNCT
ejpam-6524	264	29	are	be	AUX
ejpam-6524	264	30	stiffness	stiffness	ADJ
ejpam-6524	264	31	and	and	CCONJ
ejpam-6524	264	32	mass	mass	ADJ
ejpam-6524	264	33	matrices	matrix	NOUN
ejpam-6524	264	34	.	.	PUNCT
ejpam-6524	265	1	accordingly	accordingly	ADV
ejpam-6524	265	2	,	,	PUNCT
ejpam-6524	265	3	m	m	VERB
ejpam-6524	265	4	×m	×m	NOUN
ejpam-6524	265	5	in	in	ADP
ejpam-6524	265	6	space	space	NOUN
ejpam-6524	265	7	,	,	PUNCT
ejpam-6524	265	8	with	with	ADP
ejpam-6524	265	9	coefficients	coefficient	NOUN
ejpam-6524	265	10	mij	mij	X
ejpam-6524	265	11	=	=	SYM
ejpam-6524	265	12	∫	∫	PROPN
ejpam-6524	265	13	ω	ω	NUM
ejpam-6524	265	14	φi(x)φj(x)dx	φi(x)φj(x)dx	PROPN
ejpam-6524	265	15	,	,	PUNCT
ejpam-6524	265	16	aij	aij	PROPN
ejpam-6524	265	17	=	=	SYM
ejpam-6524	265	18	∫	∫	PROPN
ejpam-6524	265	19	ω	ω	NOUN
ejpam-6524	265	20	∇φi(x)∇φj(x)dx	∇φi(x)∇φj(x)dx	ADJ
ejpam-6524	265	21	.	.	PUNCT
ejpam-6524	266	1	k	k	X
ejpam-6524	266	2	=	=	PRON
ejpam-6524	266	3	(	(	PUNCT
ejpam-6524	266	4	klm	klm	PROPN
ejpam-6524	266	5	)	)	PUNCT
ejpam-6524	266	6	,	,	PUNCT
ejpam-6524	266	7	p	p	NOUN
ejpam-6524	266	8	=	=	SYM
ejpam-6524	266	9	(	(	PUNCT
ejpam-6524	266	10	plm	plm	PROPN
ejpam-6524	266	11	)	)	PUNCT
ejpam-6524	266	12	are	be	AUX
ejpam-6524	266	13	matrices	matrix	NOUN
ejpam-6524	266	14	of	of	ADP
ejpam-6524	266	15	mass	mass	NOUN
ejpam-6524	266	16	and	and	CCONJ
ejpam-6524	266	17	stiffness	stiffness	NOUN
ejpam-6524	266	18	.	.	PUNCT
ejpam-6524	267	1	n	n	CCONJ
ejpam-6524	267	2	×n	×n	PRON
ejpam-6524	267	3	with	with	ADP
ejpam-6524	267	4	coefficients	coefficient	NOUN
ejpam-6524	267	5	in	in	ADP
ejpam-6524	267	6	time	time	NOUN
ejpam-6524	267	7	abdulkafi	abdulkafi	PROPN
ejpam-6524	267	8	m.	m.	PROPN
ejpam-6524	267	9	saeed	saeed	PROPN
ejpam-6524	267	10	,	,	PUNCT
ejpam-6524	267	11	shahad	shahad	PROPN
ejpam-6524	267	12	s.	s.	PROPN
ejpam-6524	267	13	almutairi	almutairi	PROPN
ejpam-6524	267	14	/	/	SYM
ejpam-6524	267	15	eur	eur	PROPN
ejpam-6524	267	16	.	.	PUNCT
ejpam-6524	268	1	j.	j.	PROPN
ejpam-6524	268	2	pure	pure	PROPN
ejpam-6524	268	3	appl	appl	PROPN
ejpam-6524	268	4	.	.	PROPN
ejpam-6524	268	5	math	math	PROPN
ejpam-6524	268	6	,	,	PUNCT
ejpam-6524	268	7	18	18	NUM
ejpam-6524	268	8	(	(	PUNCT
ejpam-6524	268	9	3	3	NUM
ejpam-6524	268	10	)	)	PUNCT
ejpam-6524	268	11	(	(	PUNCT
ejpam-6524	268	12	2025	2025	NUM
ejpam-6524	268	13	)	)	PUNCT
ejpam-6524	268	14	,	,	PUNCT
ejpam-6524	268	15	6524	6524	NUM
ejpam-6524	268	16	12	12	NUM
ejpam-6524	268	17	of	of	ADP
ejpam-6524	268	18	21	21	NUM
ejpam-6524	268	19	klm	klm	NOUN
ejpam-6524	268	20	=	=	SYM
ejpam-6524	268	21	∫	∫	PROPN
ejpam-6524	268	22	tl+1	tl+1	PROPN
ejpam-6524	268	23	tl−1	tl−1	PROPN
ejpam-6524	268	24	∂ψl(t	∂ψl(t	PROPN
ejpam-6524	268	25	)	)	PUNCT
ejpam-6524	268	26	∂t	∂t	PROPN
ejpam-6524	268	27	∂ψm(t	∂ψm(t	PROPN
ejpam-6524	268	28	)	)	PUNCT
ejpam-6524	269	1	∂t	∂t	PROPN
ejpam-6524	269	2	dt	dt	PROPN
ejpam-6524	269	3	,	,	PUNCT
ejpam-6524	269	4	klm	klm	PROPN
ejpam-6524	269	5	=	=	SYM
ejpam-6524	270	1	∫	∫	PROPN
ejpam-6524	270	2	tl+1	tl+1	PROPN
ejpam-6524	270	3	tl−1	tl−1	PROPN
ejpam-6524	270	4	ψl(t)ψm(t)dt	ψl(t)ψm(t)dt	PROPN
ejpam-6524	270	5	,	,	PUNCT
ejpam-6524	270	6	as	as	ADV
ejpam-6524	270	7	well	well	ADV
ejpam-6524	270	8	as	as	ADP
ejpam-6524	270	9	the	the	DET
ejpam-6524	270	10	load	load	NOUN
ejpam-6524	270	11	vector	vector	NOUN
ejpam-6524	270	12	b	b	PROPN
ejpam-6524	270	13	=	=	PUNCT
ejpam-6524	270	14	(	(	PUNCT
ejpam-6524	270	15	bjm	bjm	NOUN
ejpam-6524	270	16	)	)	PUNCT
ejpam-6524	270	17	with	with	ADP
ejpam-6524	270	18	coefficients	coefficient	NOUN
ejpam-6524	270	19	bjm	bjm	PROPN
ejpam-6524	271	1	=	=	SYM
ejpam-6524	271	2	∫	∫	PROPN
ejpam-6524	271	3	ω	ω	NUM
ejpam-6524	271	4	∫	∫	PROPN
ejpam-6524	271	5	tl+1	tl+1	PROPN
ejpam-6524	271	6	tl−1	tl−1	PROPN
ejpam-6524	271	7	f(x)φj(x)ψm(t)dxdt	f(x)φj(x)ψm(t)dxdt	PROPN
ejpam-6524	271	8	.	.	PUNCT
ejpam-6524	272	1	k	k	PROPN
ejpam-6524	272	2	=	=	PRON
ejpam-6524	272	3	(	(	PUNCT
ejpam-6524	272	4	klm	klm	PROPN
ejpam-6524	272	5	)	)	PUNCT
ejpam-6524	272	6	and	and	CCONJ
ejpam-6524	272	7	p	p	NOUN
ejpam-6524	272	8	=	=	SYM
ejpam-6524	272	9	(	(	PUNCT
ejpam-6524	272	10	plm	plm	PROPN
ejpam-6524	272	11	)	)	PUNCT
ejpam-6524	272	12	are	be	AUX
ejpam-6524	272	13	first	first	ADV
ejpam-6524	272	14	calculated	calculate	VERB
ejpam-6524	272	15	.	.	PUNCT
ejpam-6524	273	1	as	as	SCONJ
ejpam-6524	273	2	you	you	PRON
ejpam-6524	273	3	can	can	AUX
ejpam-6524	273	4	see	see	VERB
ejpam-6524	273	5	,	,	PUNCT
ejpam-6524	273	6	klm	klm	PROPN
ejpam-6524	273	7	=	=	SYM
ejpam-6524	273	8	0	0	NUM
ejpam-6524	273	9	,	,	PUNCT
ejpam-6524	273	10	plm	plm	X
ejpam-6524	273	11	=	=	SYM
ejpam-6524	273	12	0	0	PUNCT
ejpam-6524	274	1	unless	unless	SCONJ
ejpam-6524	274	2	when	when	SCONJ
ejpam-6524	274	3	l	l	PROPN
ejpam-6524	274	4	=	=	SYM
ejpam-6524	274	5	m−	m−	PROPN
ejpam-6524	274	6	1	1	NUM
ejpam-6524	274	7	,	,	PUNCT
ejpam-6524	274	8	l	l	NOUN
ejpam-6524	274	9	=	=	SYM
ejpam-6524	274	10	m	m	PROPN
ejpam-6524	274	11	,	,	PUNCT
ejpam-6524	274	12	l	l	NOUN
ejpam-6524	274	13	=	=	PUNCT
ejpam-6524	274	14	m+	m+	NUM
ejpam-6524	274	15	1	1	NUM
ejpam-6524	274	16	.	.	PUNCT
ejpam-6524	274	17	using	use	VERB
ejpam-6524	274	18	the	the	DET
ejpam-6524	274	19	test	test	NOUN
ejpam-6524	274	20	function	function	NOUN
ejpam-6524	274	21	specification	specification	NOUN
ejpam-6524	274	22	(	(	PUNCT
ejpam-6524	274	23	17	17	NUM
ejpam-6524	274	24	)	)	PUNCT
ejpam-6524	274	25	,	,	PUNCT
ejpam-6524	274	26	we	we	PRON
ejpam-6524	274	27	calculate	calculate	VERB
ejpam-6524	274	28	the	the	DET
ejpam-6524	274	29	first	first	ADJ
ejpam-6524	274	30	diagonal	diagonal	ADJ
ejpam-6524	274	31	elements	element	NOUN
ejpam-6524	274	32	kll	kll	X
ejpam-6524	274	33	:	:	PUNCT
ejpam-6524	275	1	kll	kll	PROPN
ejpam-6524	276	1	=	=	SYM
ejpam-6524	276	2	∫	∫	PROPN
ejpam-6524	276	3	tl+1	tl+1	PROPN
ejpam-6524	276	4	tl−1	tl−1	PROPN
ejpam-6524	276	5	ψ′	ψ′	PROPN
ejpam-6524	276	6	l(t)ψ	l(t)ψ	NOUN
ejpam-6524	276	7	′	′	NOUN
ejpam-6524	276	8	l(t)dt	l(t)dt	NOUN
ejpam-6524	277	1	=	=	SYM
ejpam-6524	277	2	∫	∫	PROPN
ejpam-6524	277	3	tl	tl	PROPN
ejpam-6524	277	4	tl−1	tl−1	PROPN
ejpam-6524	277	5	(	(	PUNCT
ejpam-6524	277	6	1	1	NUM
ejpam-6524	277	7	τ	τ	PROPN
ejpam-6524	277	8	)	)	PUNCT
ejpam-6524	277	9	2	2	NUM
ejpam-6524	277	10	dt+	dt+	NOUN
ejpam-6524	277	11	∫	∫	NOUN
ejpam-6524	278	1	tl+1	tl+1	PROPN
ejpam-6524	278	2	tl	tl	PROPN
ejpam-6524	278	3	(	(	PUNCT
ejpam-6524	278	4	−1	−1	NOUN
ejpam-6524	278	5	τ	τ	PROPN
ejpam-6524	278	6	)	)	PUNCT
ejpam-6524	278	7	2	2	NUM
ejpam-6524	278	8	dt	dt	NOUN
ejpam-6524	278	9	=	=	SYM
ejpam-6524	278	10	2	2	NUM
ejpam-6524	278	11	τ	τ	PROPN
ejpam-6524	278	12	,	,	PUNCT
ejpam-6524	278	13	pll	pll	PROPN
ejpam-6524	278	14	=	=	SYM
ejpam-6524	278	15	∫	∫	PROPN
ejpam-6524	278	16	tl+1	tl+1	PROPN
ejpam-6524	278	17	tl−1	tl−1	PROPN
ejpam-6524	278	18	ψl(t)ψl(t)dt	ψl(t)ψl(t)dt	PROPN
ejpam-6524	278	19	=	=	PUNCT
ejpam-6524	278	20	∫	∫	PROPN
ejpam-6524	278	21	tl	tl	PROPN
ejpam-6524	278	22	tl−1	tl−1	PROPN
ejpam-6524	278	23	(	(	PUNCT
ejpam-6524	278	24	t−	t−	PROPN
ejpam-6524	278	25	tl−1	tl−1	PROPN
ejpam-6524	278	26	τ	τ	PROPN
ejpam-6524	278	27	)	)	PUNCT
ejpam-6524	278	28	2	2	NUM
ejpam-6524	278	29	dt+	dt+	NOUN
ejpam-6524	278	30	∫	∫	NOUN
ejpam-6524	278	31	tl+1	tl+1	PROPN
ejpam-6524	278	32	tl	tl	PROPN
ejpam-6524	279	1	(	(	PUNCT
ejpam-6524	279	2	tl+1	tl+1	PROPN
ejpam-6524	279	3	−	−	PROPN
ejpam-6524	279	4	t	t	PROPN
ejpam-6524	279	5	τ	τ	PROPN
ejpam-6524	279	6	)	)	PUNCT
ejpam-6524	279	7	2	2	NUM
ejpam-6524	279	8	dt	dt	NOUN
ejpam-6524	279	9	=	=	SYM
ejpam-6524	279	10	2	2	NUM
ejpam-6524	279	11	3	3	NUM
ejpam-6524	279	12	τ	τ	X
ejpam-6524	279	13	.	.	PUNCT
ejpam-6524	280	1	similarly	similarly	ADV
ejpam-6524	280	2	,	,	PUNCT
ejpam-6524	280	3	the	the	DET
ejpam-6524	280	4	other	other	ADJ
ejpam-6524	280	5	elements	element	NOUN
ejpam-6524	280	6	can	can	AUX
ejpam-6524	280	7	be	be	AUX
ejpam-6524	280	8	written	write	VERB
ejpam-6524	280	9	as	as	ADP
ejpam-6524	280	10	kl	kl	PROPN
ejpam-6524	280	11	,	,	PUNCT
ejpam-6524	280	12	l+1	l+1	PROPN
ejpam-6524	281	1	=	=	SYM
ejpam-6524	282	1	∫	∫	PROPN
ejpam-6524	282	2	tl+1	tl+1	PROPN
ejpam-6524	282	3	tl−1	tl−1	PROPN
ejpam-6524	282	4	ψ′	ψ′	PART
ejpam-6524	282	5	l(t)ψ	l(t)ψ	NOUN
ejpam-6524	282	6	′	′	NUM
ejpam-6524	282	7	l+1(t)dt	l+1(t)dt	PROPN
ejpam-6524	282	8	=	=	SYM
ejpam-6524	282	9	∫	∫	PROPN
ejpam-6524	282	10	tl+1	tl+1	PROPN
ejpam-6524	282	11	tl	tl	PROPN
ejpam-6524	282	12	−1	−1	NOUN
ejpam-6524	282	13	τ	τ	PROPN
ejpam-6524	282	14	1	1	NUM
ejpam-6524	282	15	τ	τ	NOUN
ejpam-6524	282	16	dt	dt	NOUN
ejpam-6524	282	17	=	=	SYM
ejpam-6524	282	18	−1	−1	NOUN
ejpam-6524	282	19	τ	τ	PROPN
ejpam-6524	282	20	,	,	PUNCT
ejpam-6524	282	21	kl−1,l	kl−1,l	PROPN
ejpam-6524	283	1	=	=	PUNCT
ejpam-6524	283	2	∫	∫	PROPN
ejpam-6524	283	3	tl+1	tl+1	PROPN
ejpam-6524	283	4	tl−1	tl−1	NOUN
ejpam-6524	283	5	ψ′	ψ′	PART
ejpam-6524	284	1	l−1(t)ψ	l−1(t)ψ	ADJ
ejpam-6524	284	2	′	′	NOUN
ejpam-6524	284	3	l(t)dt	l(t)dt	NOUN
ejpam-6524	284	4	=	=	SYM
ejpam-6524	284	5	∫	∫	PROPN
ejpam-6524	284	6	tl	tl	PROPN
ejpam-6524	284	7	tl−1	tl−1	PROPN
ejpam-6524	284	8	−1	−1	NOUN
ejpam-6524	284	9	τ	τ	PROPN
ejpam-6524	284	10	1	1	NUM
ejpam-6524	284	11	τ	τ	NOUN
ejpam-6524	284	12	dt	dt	NOUN
ejpam-6524	284	13	=	=	SYM
ejpam-6524	284	14	−1	−1	NOUN
ejpam-6524	284	15	τ	τ	PROPN
ejpam-6524	284	16	.	.	PUNCT
ejpam-6524	285	1	abdulkafi	abdulkafi	PROPN
ejpam-6524	285	2	m.	m.	PROPN
ejpam-6524	285	3	saeed	saeed	PROPN
ejpam-6524	285	4	,	,	PUNCT
ejpam-6524	285	5	shahad	shahad	PROPN
ejpam-6524	285	6	s.	s.	PROPN
ejpam-6524	285	7	almutairi	almutairi	PROPN
ejpam-6524	285	8	/	/	SYM
ejpam-6524	285	9	eur	eur	PROPN
ejpam-6524	285	10	.	.	PUNCT
ejpam-6524	286	1	j.	j.	PROPN
ejpam-6524	286	2	pure	pure	PROPN
ejpam-6524	286	3	appl	appl	PROPN
ejpam-6524	286	4	.	.	PROPN
ejpam-6524	286	5	math	math	PROPN
ejpam-6524	286	6	,	,	PUNCT
ejpam-6524	286	7	18	18	NUM
ejpam-6524	286	8	(	(	PUNCT
ejpam-6524	286	9	3	3	NUM
ejpam-6524	286	10	)	)	PUNCT
ejpam-6524	286	11	(	(	PUNCT
ejpam-6524	286	12	2025	2025	NUM
ejpam-6524	286	13	)	)	PUNCT
ejpam-6524	286	14	,	,	PUNCT
ejpam-6524	286	15	6524	6524	NUM
ejpam-6524	286	16	13	13	NUM
ejpam-6524	286	17	of	of	ADP
ejpam-6524	286	18	21	21	NUM
ejpam-6524	286	19	pl	pl	NOUN
ejpam-6524	286	20	,	,	PUNCT
ejpam-6524	286	21	l+1	l+1	PART
ejpam-6524	286	22	=	=	SYM
ejpam-6524	286	23	∫	∫	PROPN
ejpam-6524	286	24	tl+1	tl+1	PROPN
ejpam-6524	286	25	tl−1	tl−1	PROPN
ejpam-6524	286	26	ψl(t)ψl+1(t)dt	ψl(t)ψl+1(t)dt	PROPN
ejpam-6524	286	27	=	=	SYM
ejpam-6524	286	28	∫	∫	PROPN
ejpam-6524	286	29	tl	tl	PROPN
ejpam-6524	286	30	tl−1	tl−1	PROPN
ejpam-6524	286	31	(	(	PUNCT
ejpam-6524	286	32	t−	t−	PROPN
ejpam-6524	286	33	tl−1	tl−1	PROPN
ejpam-6524	286	34	τ	τ	PROPN
ejpam-6524	286	35	)	)	PUNCT
ejpam-6524	286	36	·	·	PUNCT
ejpam-6524	287	1	(	(	PUNCT
ejpam-6524	287	2	t−	t−	PROPN
ejpam-6524	287	3	tl	tl	PROPN
ejpam-6524	287	4	τ	τ	PROPN
ejpam-6524	287	5	)	)	PUNCT
ejpam-6524	288	1	dt	dt	NOUN
ejpam-6524	289	1	=	=	NOUN
ejpam-6524	289	2	1	1	NUM
ejpam-6524	289	3	6	6	NUM
ejpam-6524	289	4	τ	τ	PROPN
ejpam-6524	289	5	,	,	PUNCT
ejpam-6524	289	6	pl−1,l	pl−1,l	PROPN
ejpam-6524	289	7	=	=	SYM
ejpam-6524	289	8	∫	∫	PROPN
ejpam-6524	289	9	tl+1	tl+1	PROPN
ejpam-6524	289	10	tl−1	tl−1	NOUN
ejpam-6524	289	11	ψl−1(t)ψl(t)dt	ψl−1(t)ψl(t)dt	PUNCT
ejpam-6524	289	12	=	=	SYM
ejpam-6524	290	1	∫	∫	PROPN
ejpam-6524	291	1	tl+1	tl+1	PROPN
ejpam-6524	291	2	tl	tl	PROPN
ejpam-6524	291	3	(	(	PUNCT
ejpam-6524	291	4	tl+1	tl+1	PROPN
ejpam-6524	292	1	−	−	PROPN
ejpam-6524	292	2	t	t	PROPN
ejpam-6524	292	3	τ	τ	PROPN
ejpam-6524	292	4	)	)	PUNCT
ejpam-6524	292	5	·	·	PUNCT
ejpam-6524	293	1	(	(	PUNCT
ejpam-6524	293	2	tl	tl	PROPN
ejpam-6524	293	3	−	−	PROPN
ejpam-6524	294	1	t	t	PROPN
ejpam-6524	294	2	τ	τ	PROPN
ejpam-6524	294	3	)	)	PUNCT
ejpam-6524	294	4	dt	dt	NOUN
ejpam-6524	295	1	=	=	NOUN
ejpam-6524	295	2	1	1	NUM
ejpam-6524	295	3	6	6	NUM
ejpam-6524	295	4	τ	τ	X
ejpam-6524	295	5	.	.	PUNCT
ejpam-6524	296	1	(	(	PUNCT
ejpam-6524	296	2	19	19	NUM
ejpam-6524	296	3	)	)	PUNCT
ejpam-6524	296	4	verification	verification	NOUN
ejpam-6524	296	5	:	:	PUNCT
ejpam-6524	296	6	in	in	ADP
ejpam-6524	296	7	(	(	PUNCT
ejpam-6524	296	8	19	19	NUM
ejpam-6524	296	9	)	)	PUNCT
ejpam-6524	296	10	,	,	PUNCT
ejpam-6524	296	11	write	write	VERB
ejpam-6524	296	12	(	(	PUNCT
ejpam-6524	296	13	17	17	NUM
ejpam-6524	296	14	)	)	PUNCT
ejpam-6524	296	15	for	for	ADP
ejpam-6524	296	16	ψl+1	ψl+1	X
ejpam-6524	296	17	and	and	CCONJ
ejpam-6524	296	18	ψl−1	ψl−1	PROPN
ejpam-6524	296	19	.	.	PUNCT
ejpam-6524	297	1	using	use	VERB
ejpam-6524	297	2	the	the	DET
ejpam-6524	297	3	same	same	ADJ
ejpam-6524	297	4	method	method	NOUN
ejpam-6524	297	5	,	,	PUNCT
ejpam-6524	297	6	we	we	PRON
ejpam-6524	297	7	calculate	calculate	VERB
ejpam-6524	297	8	the	the	DET
ejpam-6524	297	9	coefficients	coefficient	NOUN
ejpam-6524	297	10	of	of	ADP
ejpam-6524	297	11	b	b	NOUN
ejpam-6524	297	12	to	to	PART
ejpam-6524	297	13	obtain	obtain	VERB
ejpam-6524	297	14	:	:	PUNCT
ejpam-6524	297	15	bjm	bjm	PROPN
ejpam-6524	297	16	=	=	SYM
ejpam-6524	297	17	∫	∫	PROPN
ejpam-6524	297	18	ω	ω	NUM
ejpam-6524	297	19	∫	∫	PROPN
ejpam-6524	297	20	tm+1	tm+1	PROPN
ejpam-6524	297	21	tm−1	tm−1	PROPN
ejpam-6524	297	22	f(x)φj(x)ψm(t)dxdt	f(x)φj(x)ψm(t)dxdt	PROPN
ejpam-6524	297	23	=	=	SYM
ejpam-6524	297	24	∫	∫	PROPN
ejpam-6524	297	25	ω	ω	PROPN
ejpam-6524	297	26	f(x)φj(x	f(x)φj(x	PROPN
ejpam-6524	297	27	)	)	PUNCT
ejpam-6524	297	28	∫	∫	PROPN
ejpam-6524	298	1	tm	tm	PROPN
ejpam-6524	298	2	tm−1	tm−1	NOUN
ejpam-6524	298	3	t−	t−	PROPN
ejpam-6524	298	4	tm−1	tm−1	NOUN
ejpam-6524	298	5	τ	τ	PROPN
ejpam-6524	298	6	dxdt	dxdt	NOUN
ejpam-6524	298	7	+	+	CCONJ
ejpam-6524	298	8	∫	∫	PROPN
ejpam-6524	298	9	ω	ω	NUM
ejpam-6524	298	10	f(x)φj(x	f(x)φj(x	PROPN
ejpam-6524	298	11	)	)	PUNCT
ejpam-6524	298	12	∫	∫	PROPN
ejpam-6524	299	1	tm+1	tm+1	PROPN
ejpam-6524	299	2	tm	tm	PROPN
ejpam-6524	299	3	tm+1	tm+1	PROPN
ejpam-6524	299	4	−	−	PROPN
ejpam-6524	299	5	t	t	PROPN
ejpam-6524	299	6	τ	τ	PROPN
ejpam-6524	299	7	dxdt	dxdt	NOUN
ejpam-6524	300	1	≈	≈	PROPN
ejpam-6524	300	2	τ	τ	PROPN
ejpam-6524	300	3	∫	∫	PROPN
ejpam-6524	300	4	ω	ω	PROPN
ejpam-6524	300	5	f	f	PROPN
ejpam-6524	300	6	(	(	PUNCT
ejpam-6524	300	7	xj)φj(x)dx	xj)φj(x)dx	PROPN
ejpam-6524	300	8	.	.	PUNCT
ejpam-6524	301	1	the	the	DET
ejpam-6524	301	2	system	system	NOUN
ejpam-6524	301	3	of	of	ADP
ejpam-6524	301	4	linear	linear	PROPN
ejpam-6524	301	5	equations	equation	NOUN
ejpam-6524	301	6	(	(	PUNCT
ejpam-6524	301	7	16	16	NUM
ejpam-6524	301	8	)	)	PUNCT
ejpam-6524	301	9	is	be	AUX
ejpam-6524	301	10	obtained	obtain	VERB
ejpam-6524	301	11	by	by	ADP
ejpam-6524	301	12	substituting	substitute	VERB
ejpam-6524	301	13	estimated	estimate	VERB
ejpam-6524	301	14	coefficients	coefficient	NOUN
ejpam-6524	301	15	to	to	ADP
ejpam-6524	301	16	(	(	PUNCT
ejpam-6524	301	17	18	18	NUM
ejpam-6524	301	18	):	):	PUNCT
ejpam-6524	301	19	m	m	AUX
ejpam-6524	301	20	(	(	PUNCT
ejpam-6524	301	21	uk+1	uk+1	X
ejpam-6524	301	22	−2uk	−2uk	X
ejpam-6524	301	23	+	+	CCONJ
ejpam-6524	301	24	uk−1	uk−1	ADJ
ejpam-6524	301	25	)	)	PUNCT
ejpam-6524	302	1	=	=	SYM
ejpam-6524	302	2	τ2f	τ2f	PUNCT
ejpam-6524	303	1	k	k	PROPN
ejpam-6524	304	1	−	−	NOUN
ejpam-6524	304	2	τ2a	τ2a	NOUN
ejpam-6524	304	3	(	(	PUNCT
ejpam-6524	304	4	1	1	NUM
ejpam-6524	304	5	6	6	NUM
ejpam-6524	304	6	uk−1	uk−1	ADJ
ejpam-6524	304	7	+	+	CCONJ
ejpam-6524	304	8	2	2	NUM
ejpam-6524	304	9	3	3	NUM
ejpam-6524	304	10	uk	uk	NOUN
ejpam-6524	304	11	+	+	CCONJ
ejpam-6524	304	12	1	1	NUM
ejpam-6524	304	13	6	6	NUM
ejpam-6524	304	14	uk+1	uk+1	X
ejpam-6524	304	15	)	)	PUNCT
ejpam-6524	304	16	,	,	PUNCT
ejpam-6524	304	17	k	k	X
ejpam-6524	305	1	=	=	SYM
ejpam-6524	305	2	1	1	NUM
ejpam-6524	305	3	,	,	PUNCT
ejpam-6524	305	4	.	.	PUNCT
ejpam-6524	305	5	.	.	PUNCT
ejpam-6524	306	1	.	.	PUNCT
ejpam-6524	307	1	,	,	PUNCT
ejpam-6524	308	1	n	n	CCONJ
ejpam-6524	308	2	−	−	PROPN
ejpam-6524	308	3	1	1	NUM
ejpam-6524	308	4	.	.	PUNCT
ejpam-6524	309	1	(	(	PUNCT
ejpam-6524	309	2	20	20	NUM
ejpam-6524	309	3	)	)	PUNCT
ejpam-6524	309	4	to	to	PART
ejpam-6524	309	5	get	get	VERB
ejpam-6524	309	6	an	an	DET
ejpam-6524	309	7	explicit	explicit	ADJ
ejpam-6524	309	8	approach	approach	NOUN
ejpam-6524	309	9	,	,	PUNCT
ejpam-6524	309	10	m	m	VERB
ejpam-6524	309	11	is	be	AUX
ejpam-6524	309	12	approximated	approximate	VERB
ejpam-6524	309	13	using	use	VERB
ejpam-6524	309	14	the	the	DET
ejpam-6524	309	15	lumped	lump	VERB
ejpam-6524	309	16	mass	mass	NOUN
ejpam-6524	309	17	matrix	matrix	NOUN
ejpam-6524	309	18	ml	ml	NOUN
ejpam-6524	309	19	in	in	ADP
ejpam-6524	309	20	space	space	NOUN
ejpam-6524	309	21	,	,	PUNCT
ejpam-6524	309	22	the	the	DET
ejpam-6524	309	23	diagonal	diagonal	ADJ
ejpam-6524	309	24	approximation	approximation	NOUN
ejpam-6524	309	25	obtained	obtain	VERB
ejpam-6524	309	26	by	by	ADP
ejpam-6524	309	27	taking	take	VERB
ejpam-6524	309	28	the	the	DET
ejpam-6524	309	29	row	row	NOUN
ejpam-6524	309	30	sum	sum	NOUN
ejpam-6524	309	31	of	of	ADP
ejpam-6524	309	32	m	m	PROPN
ejpam-6524	309	33	,	,	PUNCT
ejpam-6524	309	34	and	and	CCONJ
ejpam-6524	309	35	mass	mass	ADJ
ejpam-6524	309	36	lumping	lump	VERB
ejpam-6524	309	37	in	in	ADP
ejpam-6524	309	38	time	time	NOUN
ejpam-6524	309	39	by	by	ADP
ejpam-6524	309	40	replacing	replace	VERB
ejpam-6524	309	41	the	the	DET
ejpam-6524	309	42	terms	term	NOUN
ejpam-6524	309	43	1	1	NUM
ejpam-6524	309	44	6u	6u	NUM
ejpam-6524	309	45	k−1	k−1	PROPN
ejpam-6524	309	46	+	+	PROPN
ejpam-6524	309	47	2	2	NUM
ejpam-6524	309	48	3u	3u	NUM
ejpam-6524	309	49	k+	k+	NOUN
ejpam-6524	309	50	1	1	NUM
ejpam-6524	309	51	6u	6u	NUM
ejpam-6524	309	52	k+1	k+1	X
ejpam-6524	309	53	by	by	ADP
ejpam-6524	309	54	uk	uk	PROPN
ejpam-6524	309	55	and	and	CCONJ
ejpam-6524	309	56	(	(	PUNCT
ejpam-6524	309	57	20	20	NUM
ejpam-6524	309	58	)	)	PUNCT
ejpam-6524	309	59	is	be	AUX
ejpam-6524	309	60	multiplied	multiply	VERB
ejpam-6524	309	61	by	by	ADP
ejpam-6524	309	62	(	(	PUNCT
ejpam-6524	309	63	ml	ml	ADJ
ejpam-6524	309	64	)	)	PUNCT
ejpam-6524	309	65	−1	−1	NOUN
ejpam-6524	309	66	to	to	PART
ejpam-6524	309	67	produce	produce	VERB
ejpam-6524	309	68	an	an	DET
ejpam-6524	309	69	effective	effective	ADJ
ejpam-6524	309	70	explicit	explicit	ADJ
ejpam-6524	309	71	formulation	formulation	NOUN
ejpam-6524	309	72	:	:	PUNCT
ejpam-6524	310	1	uk+1	uk+1	PROPN
ejpam-6524	310	2	=	=	SYM
ejpam-6524	310	3	τ2f	τ2f	PUNCT
ejpam-6524	310	4	k	k	PROPN
ejpam-6524	311	1	+	+	CCONJ
ejpam-6524	311	2	2uk	2uk	ADJ
ejpam-6524	312	1	−	−	X
ejpam-6524	312	2	τ2	τ2	NOUN
ejpam-6524	312	3	(	(	PUNCT
ejpam-6524	312	4	ml	ml	ADJ
ejpam-6524	312	5	)	)	PUNCT
ejpam-6524	312	6	−1	−1	NOUN
ejpam-6524	312	7	kuk	kuk	PROPN
ejpam-6524	312	8	−	−	PROPN
ejpam-6524	312	9	uk−1	uk−1	PROPN
ejpam-6524	312	10	,	,	PUNCT
ejpam-6524	312	11	k	k	PROPN
ejpam-6524	312	12	=	=	SYM
ejpam-6524	312	13	1	1	NUM
ejpam-6524	312	14	,	,	PUNCT
ejpam-6524	312	15	.	.	PUNCT
ejpam-6524	312	16	.	.	PUNCT
ejpam-6524	312	17	.	.	PUNCT
ejpam-6524	312	18	,	,	PUNCT
ejpam-6524	313	1	n	n	CCONJ
ejpam-6524	313	2	−	−	PROPN
ejpam-6524	313	3	1	1	NUM
ejpam-6524	313	4	.	.	PUNCT
ejpam-6524	313	5	(	(	PUNCT
ejpam-6524	313	6	21	21	NUM
ejpam-6524	313	7	)	)	PUNCT
ejpam-6524	313	8	abdulkafi	abdulkafi	PROPN
ejpam-6524	313	9	m.	m.	PROPN
ejpam-6524	313	10	saeed	saeed	PROPN
ejpam-6524	313	11	,	,	PUNCT
ejpam-6524	313	12	shahad	shahad	PROPN
ejpam-6524	313	13	s.	s.	PROPN
ejpam-6524	313	14	almutairi	almutairi	PROPN
ejpam-6524	313	15	/	/	SYM
ejpam-6524	313	16	eur	eur	PROPN
ejpam-6524	313	17	.	.	PUNCT
ejpam-6524	314	1	j.	j.	PROPN
ejpam-6524	314	2	pure	pure	PROPN
ejpam-6524	314	3	appl	appl	PROPN
ejpam-6524	314	4	.	.	PROPN
ejpam-6524	314	5	math	math	PROPN
ejpam-6524	314	6	,	,	PUNCT
ejpam-6524	314	7	18	18	NUM
ejpam-6524	314	8	(	(	PUNCT
ejpam-6524	314	9	3	3	NUM
ejpam-6524	314	10	)	)	PUNCT
ejpam-6524	314	11	(	(	PUNCT
ejpam-6524	314	12	2025	2025	NUM
ejpam-6524	314	13	)	)	PUNCT
ejpam-6524	314	14	,	,	PUNCT
ejpam-6524	314	15	6524	6524	NUM
ejpam-6524	314	16	14	14	NUM
ejpam-6524	314	17	of	of	ADP
ejpam-6524	314	18	21	21	NUM
ejpam-6524	314	19	4	4	NUM
ejpam-6524	314	20	.	.	PUNCT
ejpam-6524	314	21	numerical	numerical	ADJ
ejpam-6524	314	22	experiments	experiment	NOUN
ejpam-6524	314	23	example	example	VERB
ejpam-6524	314	24	1	1	X
ejpam-6524	314	25	.	.	PUNCT
ejpam-6524	315	1	this	this	DET
ejpam-6524	315	2	experiment	experiment	NOUN
ejpam-6524	315	3	have	have	AUX
ejpam-6524	315	4	been	be	AUX
ejpam-6524	315	5	done	do	VERB
ejpam-6524	315	6	by	by	ADP
ejpam-6524	315	7	s.	s.	PROPN
ejpam-6524	315	8	s.	s.	PROPN
ejpam-6524	315	9	almutairi	almutairi	PROPN
ejpam-6524	315	10	,	,	PUNCT
ejpam-6524	315	11	a.	a.	PROPN
ejpam-6524	315	12	m.	m.	PROPN
ejpam-6524	315	13	saeed	saeed	PROPN
ejpam-6524	316	1	[	[	X
ejpam-6524	316	2	11	11	NUM
ejpam-6524	316	3	]	]	PUNCT
ejpam-6524	316	4	but	but	CCONJ
ejpam-6524	316	5	we	we	PRON
ejpam-6524	316	6	extended	extend	VERB
ejpam-6524	316	7	it	it	PRON
ejpam-6524	316	8	to	to	ADP
ejpam-6524	316	9	additional	additional	ADJ
ejpam-6524	316	10	points	point	NOUN
ejpam-6524	316	11	to	to	PART
ejpam-6524	316	12	ensure	ensure	VERB
ejpam-6524	316	13	the	the	DET
ejpam-6524	316	14	accuracy	accuracy	NOUN
ejpam-6524	316	15	of	of	ADP
ejpam-6524	316	16	the	the	DET
ejpam-6524	316	17	method	method	NOUN
ejpam-6524	316	18	.	.	PUNCT
ejpam-6524	317	1	∂2u	∂2u	PROPN
ejpam-6524	317	2	∂x2	∂x2	PROPN
ejpam-6524	317	3	+	+	CCONJ
ejpam-6524	317	4	∂2u	∂2u	ADJ
ejpam-6524	317	5	∂y2	∂y2	NUM
ejpam-6524	317	6	=	=	PUNCT
ejpam-6524	318	1	xy	xy	INTJ
ejpam-6524	318	2	.	.	PUNCT
ejpam-6524	319	1	(	(	PUNCT
ejpam-6524	319	2	22	22	NUM
ejpam-6524	319	3	)	)	PUNCT
ejpam-6524	319	4	depending	depend	VERB
ejpam-6524	319	5	on	on	ADP
ejpam-6524	319	6	the	the	DET
ejpam-6524	319	7	boundary	boundary	ADJ
ejpam-6524	319	8	conditions	condition	NOUN
ejpam-6524	319	9	u(x	u(x	NOUN
ejpam-6524	319	10	,	,	PUNCT
ejpam-6524	319	11	0	0	NUM
ejpam-6524	319	12	)	)	PUNCT
ejpam-6524	319	13	=	=	SYM
ejpam-6524	319	14	0	0	NUM
ejpam-6524	319	15	,	,	PUNCT
ejpam-6524	319	16	u(x	u(x	NOUN
ejpam-6524	319	17	,	,	PUNCT
ejpam-6524	319	18	2	2	NUM
ejpam-6524	319	19	)	)	PUNCT
ejpam-6524	319	20	=	=	SYM
ejpam-6524	319	21	0	0	NUM
ejpam-6524	319	22	,	,	PUNCT
ejpam-6524	319	23	u(0	u(0	PROPN
ejpam-6524	319	24	,	,	PUNCT
ejpam-6524	319	25	y	y	PROPN
ejpam-6524	319	26	)	)	PUNCT
ejpam-6524	319	27	=	=	SYM
ejpam-6524	319	28	0	0	NUM
ejpam-6524	319	29	,	,	PUNCT
ejpam-6524	319	30	u(2	u(2	PROPN
ejpam-6524	319	31	,	,	PUNCT
ejpam-6524	319	32	y	y	PROPN
ejpam-6524	319	33	)	)	PUNCT
ejpam-6524	319	34	=	=	NOUN
ejpam-6524	320	1	0	0	X
ejpam-6524	320	2	.	.	PUNCT
ejpam-6524	321	1	with	with	ADP
ejpam-6524	321	2	the	the	DET
ejpam-6524	321	3	exact	exact	ADJ
ejpam-6524	321	4	solution	solution	NOUN
ejpam-6524	321	5	of	of	ADP
ejpam-6524	321	6	the	the	DET
ejpam-6524	321	7	pde	pde	NOUN
ejpam-6524	321	8	is	be	AUX
ejpam-6524	321	9	u	u	NOUN
ejpam-6524	321	10	=	=	PUNCT
ejpam-6524	321	11	∑	∑	PUNCT
ejpam-6524	321	12	m≥1	m≥1	PROPN
ejpam-6524	321	13	∑	∑	PUNCT
ejpam-6524	321	14	n≥1	n≥1	VERB
ejpam-6524	321	15	−16	−16	PROPN
ejpam-6524	321	16	π2	π2	NOUN
ejpam-6524	321	17	(	(	PUNCT
ejpam-6524	321	18	−1)n+m	−1)n+m	PROPN
ejpam-6524	321	19	nmλnm	nmλnm	ADJ
ejpam-6524	321	20	sin	sin	NOUN
ejpam-6524	321	21	(	(	PUNCT
ejpam-6524	321	22	nπx	nπx	NOUN
ejpam-6524	321	23	2	2	NUM
ejpam-6524	321	24	)	)	PUNCT
ejpam-6524	321	25	sin	sin	NOUN
ejpam-6524	321	26	(	(	PUNCT
ejpam-6524	321	27	mπy	mπy	NOUN
ejpam-6524	321	28	2	2	NUM
ejpam-6524	321	29	)	)	PUNCT
ejpam-6524	321	30	.	.	PUNCT
ejpam-6524	322	1	(	(	PUNCT
ejpam-6524	322	2	23	23	NUM
ejpam-6524	322	3	)	)	PUNCT
ejpam-6524	322	4	table	table	NOUN
ejpam-6524	322	5	1	1	NUM
ejpam-6524	322	6	:	:	PUNCT
ejpam-6524	322	7	a	a	DET
ejpam-6524	322	8	comparison	comparison	NOUN
ejpam-6524	322	9	of	of	ADP
ejpam-6524	322	10	the	the	DET
ejpam-6524	322	11	approximation	approximation	NOUN
ejpam-6524	322	12	solutions	solution	NOUN
ejpam-6524	322	13	obtained	obtain	VERB
ejpam-6524	322	14	using	use	VERB
ejpam-6524	322	15	fdm	fdm	NOUN
ejpam-6524	322	16	and	and	CCONJ
ejpam-6524	322	17	gfem	gfem	PROPN
ejpam-6524	322	18	,	,	PUNCT
ejpam-6524	322	19	alongside	alongside	ADP
ejpam-6524	322	20	the	the	DET
ejpam-6524	322	21	analytical	analytical	ADJ
ejpam-6524	322	22	solution	solution	NOUN
ejpam-6524	322	23	of	of	ADP
ejpam-6524	322	24	the	the	DET
ejpam-6524	322	25	given	give	VERB
ejpam-6524	322	26	problem	problem	NOUN
ejpam-6524	322	27	.	.	PUNCT
ejpam-6524	323	1	nodes	node	NOUN
ejpam-6524	323	2	fdm	fdm	VERB
ejpam-6524	323	3	gfem	gfem	ADJ
ejpam-6524	323	4	analytical	analytical	ADJ
ejpam-6524	323	5	solution	solution	NOUN
ejpam-6524	323	6	1	1	NUM
ejpam-6524	323	7	0	0	NUM
ejpam-6524	323	8	0	0	NUM
ejpam-6524	323	9	0	0	NUM
ejpam-6524	323	10	2	2	NUM
ejpam-6524	323	11	−0.0684455218855219	−0.0684455218855219	ADP
ejpam-6524	323	12	−0.066074304273125	−0.066074304273125	NOUN
ejpam-6524	323	13	−0.0679026913	−0.0679026913	X
ejpam-6524	323	14	3	3	NUM
ejpam-6524	323	15	−0.119349193976091	−0.119349193976091	NOUN
ejpam-6524	323	16	−0.122668821548822	−0.122668821548822	NOUN
ejpam-6524	323	17	−0.1226832533	−0.1226832533	X
ejpam-6524	323	18	4	4	NUM
ejpam-6524	323	19	−0.11477288471148	−0.11477288471148	NOUN
ejpam-6524	323	20	−0.117143703703704	−0.117143703703704	NUM
ejpam-6524	323	21	−0.1176222268	−0.1176222268	NUM
ejpam-6524	323	22	5	5	NUM
ejpam-6524	323	23	−0.119349193976091	−0.119349193976091	NOUN
ejpam-6524	323	24	−0.122668821548822	−0.122668821548822	NOUN
ejpam-6524	323	25	−0.1226832533	−0.1226832533	X
ejpam-6524	323	26	6	6	NUM
ejpam-6524	323	27	−0.146756094276094	−0.146756094276094	NUM
ejpam-6524	323	28	−0.14343667851387	−0.14343667851387	PROPN
ejpam-6524	323	29	-0.1473700856	-0.1473700856	NOUN
ejpam-6524	323	30	7	7	NUM
ejpam-6524	323	31	−0.216687033077673	−0.216687033077673	NOUN
ejpam-6524	323	32	−0.221429225589226	−0.221429225589226	NUM
ejpam-6524	323	33	−0.222990496	−0.222990496	NOUN
ejpam-6524	323	34	8	8	NUM
ejpam-6524	323	35	-0.216574276094276	-0.216574276094276	NOUN
ejpam-6524	323	36	-0.213255170322128	-0.213255170322128	NOUN
ejpam-6524	323	37	-0.2194532299	-0.2194532299	NOUN
ejpam-6524	323	38	9	9	NUM
ejpam-6524	323	39	−0.213255170322128	−0.213255170322128	NOUN
ejpam-6524	323	40	−0.216574276094276	−0.216574276094276	X
ejpam-6524	323	41	−0.2194532299	−0.2194532299	X
ejpam-6524	323	42	10	10	NUM
ejpam-6524	323	43	-0.240081885521885	-0.240081885521885	X
ejpam-6524	323	44	-0.237711277602432	-0.237711277602432	PROPN
ejpam-6524	323	45	-0.2512047163	-0.2512047163	PROPN
ejpam-6524	324	1	11	11	NUM
ejpam-6524	324	2	-0.267567407407407	-0.267567407407407	NOUN
ejpam-6524	324	3	-0.262825492159407	-0.262825492159407	NOUN
ejpam-6524	324	4	-0.2707333253	-0.2707333253	VERB
ejpam-6524	324	5	12	12	NUM
ejpam-6524	324	6	-0.262825492159407	-0.262825492159407	NOUN
ejpam-6524	324	7	-0.267567407407407	-0.267567407407407	X
ejpam-6524	324	8	-0.2707333253	-0.2707333253	VERB
ejpam-6524	324	9	13	13	NUM
ejpam-6524	324	10	-0.273941548821549	-0.273941548821549	NOUN
ejpam-6524	324	11	-0.270622555204864	-0.270622555204864	NOUN
ejpam-6524	325	1	-0.2809825828	-0.2809825828	VERB
ejpam-6524	326	1	14	14	NUM
ejpam-6524	326	2	-0.329065589225589	-0.329065589225589	NOUN
ejpam-6524	326	3	-0.324323898288515	-0.324323898288515	NOUN
ejpam-6524	326	4	-0.3354518272	-0.3354518272	NOUN
ejpam-6524	326	5	table	table	NOUN
ejpam-6524	326	6	1	1	NUM
ejpam-6524	326	7	presents	present	VERB
ejpam-6524	326	8	the	the	DET
ejpam-6524	326	9	approximate	approximate	ADJ
ejpam-6524	326	10	solutions	solution	NOUN
ejpam-6524	326	11	obtained	obtain	VERB
ejpam-6524	326	12	using	use	VERB
ejpam-6524	326	13	gfem	gfem	NOUN
ejpam-6524	326	14	and	and	CCONJ
ejpam-6524	326	15	fdm	fdm	NOUN
ejpam-6524	326	16	,	,	PUNCT
ejpam-6524	326	17	alongside	alongside	ADP
ejpam-6524	326	18	the	the	DET
ejpam-6524	326	19	analytical	analytical	ADJ
ejpam-6524	326	20	solution	solution	NOUN
ejpam-6524	326	21	of	of	ADP
ejpam-6524	326	22	the	the	DET
ejpam-6524	326	23	proposed	propose	VERB
ejpam-6524	326	24	problem	problem	NOUN
ejpam-6524	326	25	.	.	PUNCT
ejpam-6524	327	1	the	the	DET
ejpam-6524	327	2	results	result	NOUN
ejpam-6524	327	3	indicate	indicate	VERB
ejpam-6524	327	4	that	that	SCONJ
ejpam-6524	327	5	gfem	gfem	NOUN
ejpam-6524	327	6	performs	perform	VERB
ejpam-6524	327	7	better	well	ADV
ejpam-6524	327	8	than	than	ADP
ejpam-6524	327	9	fdm	fdm	NOUN
ejpam-6524	327	10	,	,	PUNCT
ejpam-6524	327	11	as	as	SCONJ
ejpam-6524	327	12	its	its	PRON
ejpam-6524	327	13	approximations	approximation	NOUN
ejpam-6524	327	14	are	be	AUX
ejpam-6524	327	15	closer	close	ADJ
ejpam-6524	327	16	to	to	ADP
ejpam-6524	327	17	the	the	DET
ejpam-6524	327	18	analytical	analytical	ADJ
ejpam-6524	327	19	solution	solution	NOUN
ejpam-6524	327	20	.	.	PUNCT
ejpam-6524	328	1	this	this	PRON
ejpam-6524	328	2	is	be	AUX
ejpam-6524	328	3	because	because	SCONJ
ejpam-6524	328	4	gfem	gfem	NOUN
ejpam-6524	328	5	relies	rely	VERB
ejpam-6524	328	6	on	on	ADP
ejpam-6524	328	7	a	a	DET
ejpam-6524	328	8	solid	solid	ADJ
ejpam-6524	328	9	mathematical	mathematical	ADJ
ejpam-6524	328	10	foundation	foundation	NOUN
ejpam-6524	328	11	,	,	PUNCT
ejpam-6524	328	12	using	use	VERB
ejpam-6524	328	13	weighted	weight	VERB
ejpam-6524	328	14	residuals	residual	NOUN
ejpam-6524	328	15	and	and	CCONJ
ejpam-6524	328	16	carefully	carefully	ADV
ejpam-6524	328	17	chosen	choose	VERB
ejpam-6524	328	18	basis	basis	NOUN
ejpam-6524	328	19	functions	function	NOUN
ejpam-6524	328	20	to	to	PART
ejpam-6524	328	21	minimize	minimize	VERB
ejpam-6524	328	22	errors	error	NOUN
ejpam-6524	328	23	.	.	PUNCT
ejpam-6524	329	1	it	it	PRON
ejpam-6524	329	2	’s	’	VERB
ejpam-6524	329	3	especially	especially	ADV
ejpam-6524	329	4	effective	effective	ADJ
ejpam-6524	329	5	for	for	ADP
ejpam-6524	329	6	handling	handle	VERB
ejpam-6524	329	7	complex	complex	ADJ
ejpam-6524	329	8	geometries	geometry	NOUN
ejpam-6524	329	9	and	and	CCONJ
ejpam-6524	329	10	localized	localize	VERB
ejpam-6524	329	11	phenomena	phenomenon	NOUN
ejpam-6524	329	12	,	,	PUNCT
ejpam-6524	329	13	making	make	VERB
ejpam-6524	329	14	it	it	PRON
ejpam-6524	329	15	ideal	ideal	ADJ
ejpam-6524	329	16	for	for	ADP
ejpam-6524	329	17	simulations	simulation	NOUN
ejpam-6524	329	18	that	that	PRON
ejpam-6524	329	19	demand	demand	VERB
ejpam-6524	329	20	precision	precision	NOUN
ejpam-6524	329	21	.	.	PUNCT
ejpam-6524	330	1	on	on	ADP
ejpam-6524	330	2	the	the	DET
ejpam-6524	330	3	other	other	ADJ
ejpam-6524	330	4	hand	hand	NOUN
ejpam-6524	330	5	,	,	PUNCT
ejpam-6524	330	6	fdm	fdm	NOUN
ejpam-6524	330	7	is	be	AUX
ejpam-6524	330	8	straightforward	straightforward	ADJ
ejpam-6524	330	9	and	and	CCONJ
ejpam-6524	330	10	computationally	computationally	ADV
ejpam-6524	330	11	efficient	efficient	ADJ
ejpam-6524	330	12	,	,	PUNCT
ejpam-6524	330	13	but	but	CCONJ
ejpam-6524	330	14	its	its	PRON
ejpam-6524	330	15	accuracy	accuracy	NOUN
ejpam-6524	330	16	depends	depend	VERB
ejpam-6524	330	17	heavily	heavily	ADV
ejpam-6524	330	18	on	on	ADP
ejpam-6524	330	19	maintaining	maintain	VERB
ejpam-6524	330	20	a	a	DET
ejpam-6524	330	21	structured	structured	ADJ
ejpam-6524	330	22	mesh	mesh	NOUN
ejpam-6524	330	23	.	.	PUNCT
ejpam-6524	331	1	this	this	PRON
ejpam-6524	331	2	can	can	AUX
ejpam-6524	331	3	lead	lead	VERB
ejpam-6524	331	4	to	to	ADP
ejpam-6524	331	5	larger	large	ADJ
ejpam-6524	331	6	discretization	discretization	NOUN
ejpam-6524	331	7	errors	error	NOUN
ejpam-6524	331	8	,	,	PUNCT
ejpam-6524	331	9	especially	especially	ADV
ejpam-6524	331	10	in	in	ADP
ejpam-6524	331	11	cases	case	NOUN
ejpam-6524	331	12	where	where	SCONJ
ejpam-6524	331	13	the	the	DET
ejpam-6524	331	14	problem	problem	NOUN
ejpam-6524	331	15	involves	involve	VERB
ejpam-6524	331	16	irregular	irregular	ADJ
ejpam-6524	331	17	domains	domain	NOUN
ejpam-6524	331	18	or	or	CCONJ
ejpam-6524	331	19	varying	vary	VERB
ejpam-6524	331	20	material	material	NOUN
ejpam-6524	331	21	properties	property	NOUN
ejpam-6524	331	22	.	.	PUNCT
ejpam-6524	332	1	because	because	SCONJ
ejpam-6524	332	2	of	of	ADP
ejpam-6524	332	3	this	this	DET
ejpam-6524	332	4	limitation	limitation	NOUN
ejpam-6524	332	5	,	,	PUNCT
ejpam-6524	332	6	fdm	fdm	NOUN
ejpam-6524	332	7	may	may	AUX
ejpam-6524	332	8	not	not	PART
ejpam-6524	332	9	be	be	AUX
ejpam-6524	332	10	the	the	DET
ejpam-6524	332	11	best	good	ADJ
ejpam-6524	332	12	choice	choice	NOUN
ejpam-6524	332	13	when	when	SCONJ
ejpam-6524	332	14	high	high	ADJ
ejpam-6524	332	15	precision	precision	NOUN
ejpam-6524	332	16	is	be	AUX
ejpam-6524	332	17	required	require	VERB
ejpam-6524	332	18	.	.	PUNCT
ejpam-6524	333	1	simply	simply	ADV
ejpam-6524	333	2	put	put	VERB
ejpam-6524	333	3	,	,	PUNCT
ejpam-6524	333	4	gfem	gfem	PROPN
ejpam-6524	333	5	stands	stand	VERB
ejpam-6524	333	6	out	out	ADP
ejpam-6524	333	7	because	because	SCONJ
ejpam-6524	333	8	of	of	ADP
ejpam-6524	333	9	its	its	PRON
ejpam-6524	333	10	adaptability	adaptability	NOUN
ejpam-6524	333	11	abdulkafi	abdulkafi	PROPN
ejpam-6524	333	12	m.	m.	PROPN
ejpam-6524	333	13	saeed	saeed	PROPN
ejpam-6524	333	14	,	,	PUNCT
ejpam-6524	333	15	shahad	shahad	PROPN
ejpam-6524	333	16	s.	s.	PROPN
ejpam-6524	333	17	almutairi	almutairi	PROPN
ejpam-6524	333	18	/	/	SYM
ejpam-6524	333	19	eur	eur	PROPN
ejpam-6524	333	20	.	.	PUNCT
ejpam-6524	334	1	j.	j.	PROPN
ejpam-6524	334	2	pure	pure	PROPN
ejpam-6524	334	3	appl	appl	PROPN
ejpam-6524	334	4	.	.	PROPN
ejpam-6524	334	5	math	math	PROPN
ejpam-6524	334	6	,	,	PUNCT
ejpam-6524	334	7	18	18	NUM
ejpam-6524	334	8	(	(	PUNCT
ejpam-6524	334	9	3	3	NUM
ejpam-6524	334	10	)	)	PUNCT
ejpam-6524	334	11	(	(	PUNCT
ejpam-6524	334	12	2025	2025	NUM
ejpam-6524	334	13	)	)	PUNCT
ejpam-6524	334	14	,	,	PUNCT
ejpam-6524	334	15	6524	6524	NUM
ejpam-6524	334	16	15	15	NUM
ejpam-6524	334	17	of	of	ADP
ejpam-6524	334	18	21	21	NUM
ejpam-6524	334	19	and	and	CCONJ
ejpam-6524	334	20	accuracy	accuracy	NOUN
ejpam-6524	334	21	,	,	PUNCT
ejpam-6524	334	22	making	make	VERB
ejpam-6524	334	23	it	it	PRON
ejpam-6524	334	24	a	a	DET
ejpam-6524	334	25	better	well	ADJ
ejpam-6524	334	26	choice	choice	NOUN
ejpam-6524	334	27	for	for	ADP
ejpam-6524	334	28	solving	solve	VERB
ejpam-6524	334	29	differential	differential	ADJ
ejpam-6524	334	30	equations	equation	NOUN
ejpam-6524	334	31	in	in	ADP
ejpam-6524	334	32	situations	situation	NOUN
ejpam-6524	334	33	where	where	SCONJ
ejpam-6524	334	34	precision	precision	NOUN
ejpam-6524	334	35	matters	matter	VERB
ejpam-6524	334	36	most	most	ADV
ejpam-6524	334	37	.	.	PUNCT
ejpam-6524	335	1	figure	figure	VERB
ejpam-6524	335	2	4	4	NUM
ejpam-6524	335	3	:	:	PUNCT
ejpam-6524	335	4	graph	graph	NOUN
ejpam-6524	335	5	representing	represent	VERB
ejpam-6524	335	6	the	the	DET
ejpam-6524	335	7	numerical	numerical	ADJ
ejpam-6524	335	8	solution	solution	NOUN
ejpam-6524	335	9	of	of	ADP
ejpam-6524	335	10	the	the	DET
ejpam-6524	335	11	poisson	poisson	NOUN
ejpam-6524	335	12	equation	equation	NOUN
ejpam-6524	335	13	computed	compute	VERB
ejpam-6524	335	14	using	use	VERB
ejpam-6524	335	15	fdm	fdm	NOUN
ejpam-6524	335	16	.	.	PUNCT
ejpam-6524	336	1	figure	figure	VERB
ejpam-6524	336	2	5	5	NUM
ejpam-6524	336	3	:	:	PUNCT
ejpam-6524	336	4	graph	graph	NOUN
ejpam-6524	336	5	representing	represent	VERB
ejpam-6524	336	6	the	the	DET
ejpam-6524	336	7	numerical	numerical	ADJ
ejpam-6524	336	8	solution	solution	NOUN
ejpam-6524	336	9	of	of	ADP
ejpam-6524	336	10	the	the	DET
ejpam-6524	336	11	poisson	poisson	NOUN
ejpam-6524	336	12	equation	equation	NOUN
ejpam-6524	336	13	computed	compute	VERB
ejpam-6524	336	14	using	use	VERB
ejpam-6524	336	15	gfem	gfem	PROPN
ejpam-6524	336	16	.	.	PUNCT
ejpam-6524	337	1	abdulkafi	abdulkafi	PROPN
ejpam-6524	337	2	m.	m.	PROPN
ejpam-6524	337	3	saeed	saeed	PROPN
ejpam-6524	337	4	,	,	PUNCT
ejpam-6524	337	5	shahad	shahad	PROPN
ejpam-6524	337	6	s.	s.	PROPN
ejpam-6524	337	7	almutairi	almutairi	PROPN
ejpam-6524	337	8	/	/	SYM
ejpam-6524	337	9	eur	eur	PROPN
ejpam-6524	337	10	.	.	PUNCT
ejpam-6524	338	1	j.	j.	PROPN
ejpam-6524	338	2	pure	pure	PROPN
ejpam-6524	338	3	appl	appl	PROPN
ejpam-6524	338	4	.	.	PROPN
ejpam-6524	338	5	math	math	PROPN
ejpam-6524	338	6	,	,	PUNCT
ejpam-6524	338	7	18	18	NUM
ejpam-6524	338	8	(	(	PUNCT
ejpam-6524	338	9	3	3	NUM
ejpam-6524	338	10	)	)	PUNCT
ejpam-6524	338	11	(	(	PUNCT
ejpam-6524	338	12	2025	2025	NUM
ejpam-6524	338	13	)	)	PUNCT
ejpam-6524	338	14	,	,	PUNCT
ejpam-6524	338	15	6524	6524	NUM
ejpam-6524	338	16	16	16	NUM
ejpam-6524	338	17	of	of	ADP
ejpam-6524	338	18	21	21	NUM
ejpam-6524	338	19	figure	figure	NOUN
ejpam-6524	338	20	6	6	NUM
ejpam-6524	338	21	:	:	PUNCT
ejpam-6524	338	22	graph	graph	NOUN
ejpam-6524	338	23	representing	represent	VERB
ejpam-6524	338	24	the	the	DET
ejpam-6524	338	25	analytical	analytical	ADJ
ejpam-6524	338	26	solution	solution	NOUN
ejpam-6524	338	27	.	.	PUNCT
ejpam-6524	339	1	figures	figure	NOUN
ejpam-6524	339	2	4	4	NUM
ejpam-6524	339	3	,	,	PUNCT
ejpam-6524	339	4	5	5	NUM
ejpam-6524	339	5	and	and	CCONJ
ejpam-6524	339	6	6	6	NUM
ejpam-6524	339	7	clearly	clearly	ADV
ejpam-6524	339	8	show	show	VERB
ejpam-6524	339	9	the	the	DET
ejpam-6524	339	10	numerical	numerical	ADJ
ejpam-6524	339	11	solution	solution	NOUN
ejpam-6524	339	12	of	of	ADP
ejpam-6524	339	13	poisson	poisson	NOUN
ejpam-6524	339	14	’s	’s	PART
ejpam-6524	339	15	equation	equation	NOUN
ejpam-6524	339	16	using	use	VERB
ejpam-6524	339	17	fdm	fdm	NOUN
ejpam-6524	339	18	,	,	PUNCT
ejpam-6524	339	19	fem	fem	NOUN
ejpam-6524	339	20	,	,	PUNCT
ejpam-6524	339	21	and	and	CCONJ
ejpam-6524	339	22	analytical	analytical	ADJ
ejpam-6524	339	23	solution	solution	NOUN
ejpam-6524	339	24	.	.	PUNCT
ejpam-6524	340	1	example	example	NOUN
ejpam-6524	340	2	2	2	NUM
ejpam-6524	340	3	.	.	X
ejpam-6524	340	4	consider	consider	VERB
ejpam-6524	340	5	wave	wave	NOUN
ejpam-6524	340	6	equation	equation	NOUN
ejpam-6524	340	7	∂2u	∂2u	ADJ
ejpam-6524	340	8	∂t2	∂t2	PROPN
ejpam-6524	340	9	=	=	SYM
ejpam-6524	340	10	c2	c2	PROPN
ejpam-6524	340	11	(	(	PUNCT
ejpam-6524	340	12	∂2u	∂2u	PROPN
ejpam-6524	340	13	∂x2	∂x2	PROPN
ejpam-6524	340	14	+	+	CCONJ
ejpam-6524	340	15	∂2u	∂2u	ADJ
ejpam-6524	340	16	∂y2	∂y2	PROPN
ejpam-6524	340	17	)	)	PUNCT
ejpam-6524	340	18	,	,	PUNCT
ejpam-6524	340	19	with	with	ADP
ejpam-6524	340	20	boundary	boundary	ADJ
ejpam-6524	340	21	conditions	condition	NOUN
ejpam-6524	340	22	u(0	u(0	PROPN
ejpam-6524	340	23	,	,	PUNCT
ejpam-6524	340	24	y	y	PROPN
ejpam-6524	340	25	,	,	PUNCT
ejpam-6524	340	26	t	t	PROPN
ejpam-6524	340	27	)	)	PUNCT
ejpam-6524	340	28	=	=	SYM
ejpam-6524	340	29	u(a	u(a	PROPN
ejpam-6524	340	30	,	,	PUNCT
ejpam-6524	340	31	y	y	PROPN
ejpam-6524	340	32	,	,	PUNCT
ejpam-6524	340	33	t	t	PROPN
ejpam-6524	340	34	)	)	PUNCT
ejpam-6524	340	35	=	=	SYM
ejpam-6524	340	36	0	0	NUM
ejpam-6524	340	37	,	,	PUNCT
ejpam-6524	340	38	0	0	NUM
ejpam-6524	340	39	≤	≤	NUM
ejpam-6524	340	40	y	y	PROPN
ejpam-6524	340	41	≤	≤	PROPN
ejpam-6524	340	42	b	b	PROPN
ejpam-6524	340	43	,	,	PUNCT
ejpam-6524	340	44	t	t	PROPN
ejpam-6524	340	45	>	>	X
ejpam-6524	340	46	0	0	NUM
ejpam-6524	340	47	,	,	PUNCT
ejpam-6524	340	48	u(x	u(x	NOUN
ejpam-6524	340	49	,	,	PUNCT
ejpam-6524	340	50	0	0	NUM
ejpam-6524	340	51	,	,	PUNCT
ejpam-6524	340	52	t	t	PROPN
ejpam-6524	340	53	)	)	PUNCT
ejpam-6524	340	54	=	=	SYM
ejpam-6524	341	1	u(x	u(x	PROPN
ejpam-6524	341	2	,	,	PUNCT
ejpam-6524	341	3	b	b	NOUN
ejpam-6524	341	4	,	,	PUNCT
ejpam-6524	341	5	t	t	PROPN
ejpam-6524	341	6	)	)	PUNCT
ejpam-6524	341	7	=	=	SYM
ejpam-6524	341	8	0	0	NUM
ejpam-6524	341	9	,	,	PUNCT
ejpam-6524	341	10	0	0	NUM
ejpam-6524	341	11	≤	≤	NUM
ejpam-6524	341	12	x	x	SYM
ejpam-6524	341	13	≤	≤	NUM
ejpam-6524	341	14	a	a	PRON
ejpam-6524	341	15	,	,	PUNCT
ejpam-6524	341	16	t	t	X
ejpam-6524	341	17	>	>	X
ejpam-6524	341	18	0	0	PROPN
ejpam-6524	341	19	.	.	PUNCT
ejpam-6524	342	1	and	and	CCONJ
ejpam-6524	342	2	initial	initial	ADJ
ejpam-6524	342	3	conditions	condition	NOUN
ejpam-6524	342	4	u(x	u(x	NOUN
ejpam-6524	342	5	,	,	PUNCT
ejpam-6524	342	6	y	y	NOUN
ejpam-6524	342	7	,	,	PUNCT
ejpam-6524	342	8	0	0	NUM
ejpam-6524	342	9	)	)	PUNCT
ejpam-6524	342	10	=	=	SYM
ejpam-6524	342	11	f(x	f(x	PROPN
ejpam-6524	342	12	,	,	PUNCT
ejpam-6524	342	13	y	y	PROPN
ejpam-6524	342	14	)	)	PUNCT
ejpam-6524	342	15	,	,	PUNCT
ejpam-6524	342	16	(	(	PUNCT
ejpam-6524	342	17	x	x	X
ejpam-6524	342	18	,	,	PUNCT
ejpam-6524	342	19	y	y	NOUN
ejpam-6524	342	20	)	)	PUNCT
ejpam-6524	342	21	∈	∈	PROPN
ejpam-6524	342	22	r	r	NOUN
ejpam-6524	342	23	,	,	PUNCT
ejpam-6524	342	24	u(x	u(x	PROPN
ejpam-6524	342	25	,	,	PUNCT
ejpam-6524	342	26	y	y	PROPN
ejpam-6524	342	27	,	,	PUNCT
ejpam-6524	342	28	0	0	NUM
ejpam-6524	342	29	)	)	PUNCT
ejpam-6524	342	30	=	=	SYM
ejpam-6524	343	1	g(x	g(x	NOUN
ejpam-6524	343	2	,	,	PUNCT
ejpam-6524	343	3	y	y	NOUN
ejpam-6524	343	4	)	)	PUNCT
ejpam-6524	343	5	,	,	PUNCT
ejpam-6524	343	6	(	(	PUNCT
ejpam-6524	343	7	x	x	X
ejpam-6524	343	8	,	,	PUNCT
ejpam-6524	343	9	y	y	PROPN
ejpam-6524	343	10	)	)	PUNCT
ejpam-6524	343	11	∈	∈	PROPN
ejpam-6524	343	12	r.	r.	NOUN
ejpam-6524	343	13	the	the	DET
ejpam-6524	343	14	general	general	ADJ
ejpam-6524	343	15	solution	solution	NOUN
ejpam-6524	343	16	is	be	AUX
ejpam-6524	343	17	u(x	u(x	NOUN
ejpam-6524	343	18	,	,	PUNCT
ejpam-6524	343	19	y	y	PROPN
ejpam-6524	343	20	,	,	PUNCT
ejpam-6524	343	21	t	t	PROPN
ejpam-6524	343	22	)	)	PUNCT
ejpam-6524	343	23	=	=	NOUN
ejpam-6524	344	1	∞∑	∞∑	NUM
ejpam-6524	344	2	n=1	n=1	ADP
ejpam-6524	344	3	∞∑	∞∑	PROPN
ejpam-6524	344	4	m=1	m=1	PROPN
ejpam-6524	344	5	sin	sin	NOUN
ejpam-6524	344	6	(	(	PUNCT
ejpam-6524	344	7	mπ	mπ	NOUN
ejpam-6524	344	8	a	a	DET
ejpam-6524	344	9	x	x	NOUN
ejpam-6524	344	10	)	)	PUNCT
ejpam-6524	344	11	sin	sin	NOUN
ejpam-6524	344	12	(	(	PUNCT
ejpam-6524	344	13	nπ	nπ	NOUN
ejpam-6524	344	14	b	b	PROPN
ejpam-6524	344	15	y)(bmn	y)(bmn	PROPN
ejpam-6524	344	16	cos(c	cos(c	PROPN
ejpam-6524	344	17	2	2	NUM
ejpam-6524	344	18	√	√	PROPN
ejpam-6524	344	19	(	(	PUNCT
ejpam-6524	344	20	mπ	mπ	NOUN
ejpam-6524	344	21	a	a	PRON
ejpam-6524	344	22	)	)	PUNCT
ejpam-6524	344	23	2	2	NUM
ejpam-6524	344	24	+	+	CCONJ
ejpam-6524	344	25	(	(	PUNCT
ejpam-6524	344	26	nπ	nπ	NOUN
ejpam-6524	344	27	b	b	PROPN
ejpam-6524	344	28	)	)	PUNCT
ejpam-6524	344	29	2t)+b∗	2t)+b∗	PROPN
ejpam-6524	344	30	mn	mn	PROPN
ejpam-6524	344	31	sin(c	sin(c	PROPN
ejpam-6524	344	32	2	2	NUM
ejpam-6524	344	33	√	√	PROPN
ejpam-6524	344	34	(	(	PUNCT
ejpam-6524	344	35	mπ	mπ	NOUN
ejpam-6524	344	36	a	a	PRON
ejpam-6524	344	37	)	)	PUNCT
ejpam-6524	344	38	2	2	NUM
ejpam-6524	344	39	+	+	CCONJ
ejpam-6524	344	40	(	(	PUNCT
ejpam-6524	344	41	nπ	nπ	NOUN
ejpam-6524	344	42	b	b	PROPN
ejpam-6524	344	43	)	)	PUNCT
ejpam-6524	344	44	2	2	NUM
ejpam-6524	344	45	t	t	NOUN
ejpam-6524	344	46	)	)	PUNCT
ejpam-6524	344	47	)	)	PUNCT
ejpam-6524	344	48	.	.	PUNCT
ejpam-6524	345	1	(	(	PUNCT
ejpam-6524	345	2	24	24	NUM
ejpam-6524	345	3	)	)	PUNCT
ejpam-6524	345	4	abdulkafi	abdulkafi	PROPN
ejpam-6524	345	5	m.	m.	PROPN
ejpam-6524	345	6	saeed	saeed	PROPN
ejpam-6524	345	7	,	,	PUNCT
ejpam-6524	345	8	shahad	shahad	PROPN
ejpam-6524	345	9	s.	s.	PROPN
ejpam-6524	345	10	almutairi	almutairi	PROPN
ejpam-6524	345	11	/	/	SYM
ejpam-6524	345	12	eur	eur	PROPN
ejpam-6524	345	13	.	.	PUNCT
ejpam-6524	346	1	j.	j.	PROPN
ejpam-6524	346	2	pure	pure	PROPN
ejpam-6524	346	3	appl	appl	PROPN
ejpam-6524	346	4	.	.	PROPN
ejpam-6524	346	5	math	math	PROPN
ejpam-6524	346	6	,	,	PUNCT
ejpam-6524	346	7	18	18	NUM
ejpam-6524	346	8	(	(	PUNCT
ejpam-6524	346	9	3	3	NUM
ejpam-6524	346	10	)	)	PUNCT
ejpam-6524	346	11	(	(	PUNCT
ejpam-6524	346	12	2025	2025	NUM
ejpam-6524	346	13	)	)	PUNCT
ejpam-6524	346	14	,	,	PUNCT
ejpam-6524	346	15	6524	6524	NUM
ejpam-6524	346	16	17	17	NUM
ejpam-6524	346	17	of	of	ADP
ejpam-6524	346	18	21	21	NUM
ejpam-6524	346	19	table	table	NOUN
ejpam-6524	346	20	2	2	NUM
ejpam-6524	346	21	:	:	PUNCT
ejpam-6524	346	22	comparison	comparison	NOUN
ejpam-6524	346	23	results	result	NOUN
ejpam-6524	346	24	of	of	ADP
ejpam-6524	346	25	the	the	DET
ejpam-6524	346	26	approximation	approximation	NOUN
ejpam-6524	346	27	solution	solution	NOUN
ejpam-6524	346	28	fdm	fdm	NOUN
ejpam-6524	346	29	and	and	CCONJ
ejpam-6524	346	30	analytical	analytical	ADJ
ejpam-6524	346	31	solution	solution	NOUN
ejpam-6524	346	32	.	.	PUNCT
ejpam-6524	347	1	x	x	PUNCT
ejpam-6524	347	2	y	y	PROPN
ejpam-6524	347	3	analytical	analytical	ADJ
ejpam-6524	347	4	solution	solution	NOUN
ejpam-6524	347	5	fdm	fdm	VERB
ejpam-6524	347	6	0.15789	0.15789	NUM
ejpam-6524	347	7	0.15789	0.15789	NUM
ejpam-6524	347	8	−0.091701	−0.091701	NOUN
ejpam-6524	347	9	−0.095024	−0.095024	NUM
ejpam-6524	347	10	0.78947	0.78947	NUM
ejpam-6524	347	11	1.1053	1.1053	NUM
ejpam-6524	347	12	-3.117	-3.117	NUM
ejpam-6524	347	13	-3.0759	-3.0759	NOUN
ejpam-6524	347	14	0.94737	0.94737	NUM
ejpam-6524	347	15	0.63158	0.63158	NUM
ejpam-6524	347	16	-2.3209	-2.3209	NOUN
ejpam-6524	347	17	-2.2537	-2.2537	VERB
ejpam-6524	347	18	1.1053	1.1053	NUM
ejpam-6524	347	19	1.4211	1.4211	NUM
ejpam-6524	347	20	-4.3357	-4.3357	NOUN
ejpam-6524	347	21	-4.3143	-4.3143	NOUN
ejpam-6524	347	22	1.5789	1.5789	NUM
ejpam-6524	347	23	0.47368	0.47368	NUM
ejpam-6524	347	24	-2.1181	-2.1181	NOUN
ejpam-6524	347	25	-2.0426	-2.0426	NOUN
ejpam-6524	348	1	1.7368	1.7368	NUM
ejpam-6524	348	2	2.5263	2.5263	NUM
ejpam-6524	348	3	-2.0561	-2.0561	NOUN
ejpam-6524	348	4	-1.9891	-1.9891	NOUN
ejpam-6524	349	1	2.0526	2.0526	NUM
ejpam-6524	349	2	2.3684	2.3684	NUM
ejpam-6524	349	3	-2.3209	-2.3209	NOUN
ejpam-6524	349	4	-2.2537	-2.2537	VERB
ejpam-6524	349	5	2.3684	2.3684	NUM
ejpam-6524	349	6	1.8947	1.8947	NUM
ejpam-6524	349	7	-2.5588	-2.5588	NOUN
ejpam-6524	349	8	-2.4973	-2.4973	NOUN
ejpam-6524	349	9	2.8421	2.8421	NUM
ejpam-6524	349	10	1.2632	1.2632	NUM
ejpam-6524	349	11	-0.64947	-0.64947	NOUN
ejpam-6524	349	12	-0.66045	-0.66045	VERB
ejpam-6524	349	13	the	the	DET
ejpam-6524	349	14	error	error	NOUN
ejpam-6524	349	15	of	of	ADP
ejpam-6524	349	16	fdm	fdm	NOUN
ejpam-6524	349	17	are	be	AUX
ejpam-6524	349	18	l1	l1	PROPN
ejpam-6524	349	19	error	error	NOUN
ejpam-6524	349	20	:	:	PUNCT
ejpam-6524	349	21	0.031623	0.031623	NUM
ejpam-6524	349	22	,	,	PUNCT
ejpam-6524	349	23	l2	l2	NOUN
ejpam-6524	349	24	error	error	NOUN
ejpam-6524	349	25	:	:	PUNCT
ejpam-6524	349	26	0.041968	0.041968	NUM
ejpam-6524	349	27	and	and	CCONJ
ejpam-6524	349	28	l∞	l∞	NOUN
ejpam-6524	349	29	error	error	NOUN
ejpam-6524	349	30	:	:	PUNCT
ejpam-6524	349	31	0.083343	0.083343	NUM
ejpam-6524	349	32	.	.	PUNCT
ejpam-6524	350	1	figure	figure	NOUN
ejpam-6524	350	2	7	7	NUM
ejpam-6524	350	3	:	:	PUNCT
ejpam-6524	350	4	comparison	comparison	NOUN
ejpam-6524	350	5	of	of	ADP
ejpam-6524	350	6	the	the	DET
ejpam-6524	350	7	analytical	analytical	ADJ
ejpam-6524	350	8	solution	solution	NOUN
ejpam-6524	350	9	and	and	CCONJ
ejpam-6524	350	10	the	the	DET
ejpam-6524	350	11	fdm	fdm	NOUN
ejpam-6524	350	12	approximation	approximation	NOUN
ejpam-6524	350	13	solution	solution	NOUN
ejpam-6524	350	14	for	for	ADP
ejpam-6524	350	15	wave	wave	NOUN
ejpam-6524	350	16	equation	equation	NOUN
ejpam-6524	350	17	table	table	NOUN
ejpam-6524	350	18	3	3	NUM
ejpam-6524	350	19	:	:	PUNCT
ejpam-6524	350	20	comparison	comparison	NOUN
ejpam-6524	350	21	results	result	NOUN
ejpam-6524	350	22	of	of	ADP
ejpam-6524	350	23	the	the	DET
ejpam-6524	350	24	approximation	approximation	NOUN
ejpam-6524	350	25	solution	solution	NOUN
ejpam-6524	350	26	gfem	gfem	NOUN
ejpam-6524	350	27	and	and	CCONJ
ejpam-6524	350	28	analytical	analytical	ADJ
ejpam-6524	350	29	solution	solution	NOUN
ejpam-6524	350	30	.	.	PUNCT
ejpam-6524	351	1	x	x	PUNCT
ejpam-6524	351	2	y	y	PROPN
ejpam-6524	351	3	analytical	analytical	ADJ
ejpam-6524	351	4	solution	solution	NOUN
ejpam-6524	351	5	gfem	gfem	VERB
ejpam-6524	351	6	0.15	0.15	NUM
ejpam-6524	351	7	1.95	1.95	NUM
ejpam-6524	351	8	-0.56165	-0.56165	NOUN
ejpam-6524	351	9	-0.56281	-0.56281	NOUN
ejpam-6524	351	10	0.225	0.225	NUM
ejpam-6524	351	11	0.075	0.075	NUM
ejpam-6524	351	12	-0.061833	-0.061833	PUNCT
ejpam-6524	352	1	-0.062814	-0.062814	PROPN
ejpam-6524	352	2	0.9	0.9	NUM
ejpam-6524	352	3	2.85	2.85	NUM
ejpam-6524	352	4	-0.50533	-0.50533	NOUN
ejpam-6524	352	5	-0.50546	-0.50546	VERB
ejpam-6524	352	6	1.2	1.2	NUM
ejpam-6524	352	7	2.7	2.7	NUM
ejpam-6524	352	8	-1.2571	-1.2571	NOUN
ejpam-6524	352	9	-1.2247	-1.2247	PROPN
ejpam-6524	352	10	1.575	1.575	NUM
ejpam-6524	352	11	0.075	0.075	NUM
ejpam-6524	352	12	-0.30975	-0.30975	NOUN
ejpam-6524	352	13	-0.31918	-0.31918	PROPN
ejpam-6524	352	14	1.95	1.95	NUM
ejpam-6524	352	15	2.85	2.85	NUM
ejpam-6524	352	16	-0.56165	-0.56165	NOUN
ejpam-6524	352	17	-0.56281	-0.56281	NOUN
ejpam-6524	352	18	2.025	2.025	NUM
ejpam-6524	352	19	0.825	0.825	NUM
ejpam-6524	352	20	-2.9906	-2.9906	NOUN
ejpam-6524	352	21	-2.9721	-2.9721	NOUN
ejpam-6524	353	1	2.325	2.325	NUM
ejpam-6524	353	2	1.425	1.425	NUM
ejpam-6524	353	3	-2.9808	-2.9808	NOUN
ejpam-6524	353	4	-2.9531	-2.9531	NOUN
ejpam-6524	354	1	2.775	2.775	NUM
ejpam-6524	354	2	1.125	1.125	NUM
ejpam-6524	354	3	-0.89784	-0.89784	NOUN
ejpam-6524	354	4	-0.88465	-0.88465	VERB
ejpam-6524	354	5	the	the	DET
ejpam-6524	354	6	errors	error	NOUN
ejpam-6524	354	7	of	of	ADP
ejpam-6524	354	8	fem	fem	NOUN
ejpam-6524	354	9	are	be	AUX
ejpam-6524	354	10	l1	l1	PROPN
ejpam-6524	354	11	error	error	NOUN
ejpam-6524	354	12	:	:	PUNCT
ejpam-6524	354	13	2.722e-05	2.722e-05	NUM
ejpam-6524	354	14	,	,	PUNCT
ejpam-6524	354	15	l2	l2	NOUN
ejpam-6524	354	16	error	error	NOUN
ejpam-6524	354	17	:	:	PUNCT
ejpam-6524	354	18	0.00099633	0.00099633	NUM
ejpam-6524	354	19	and	and	CCONJ
ejpam-6524	354	20	l∞	l∞	NOUN
ejpam-6524	354	21	error	error	NOUN
ejpam-6524	354	22	:	:	PUNCT
ejpam-6524	354	23	abdulkafi	abdulkafi	PROPN
ejpam-6524	354	24	m.	m.	PROPN
ejpam-6524	354	25	saeed	saeed	PROPN
ejpam-6524	354	26	,	,	PUNCT
ejpam-6524	354	27	shahad	shahad	PROPN
ejpam-6524	354	28	s.	s.	PROPN
ejpam-6524	354	29	almutairi	almutairi	PROPN
ejpam-6524	354	30	/	/	SYM
ejpam-6524	354	31	eur	eur	PROPN
ejpam-6524	354	32	.	.	PUNCT
ejpam-6524	355	1	j.	j.	PROPN
ejpam-6524	355	2	pure	pure	PROPN
ejpam-6524	355	3	appl	appl	PROPN
ejpam-6524	355	4	.	.	PROPN
ejpam-6524	355	5	math	math	PROPN
ejpam-6524	355	6	,	,	PUNCT
ejpam-6524	355	7	18	18	NUM
ejpam-6524	355	8	(	(	PUNCT
ejpam-6524	355	9	3	3	NUM
ejpam-6524	355	10	)	)	PUNCT
ejpam-6524	355	11	(	(	PUNCT
ejpam-6524	355	12	2025	2025	NUM
ejpam-6524	355	13	)	)	PUNCT
ejpam-6524	355	14	,	,	PUNCT
ejpam-6524	355	15	6524	6524	NUM
ejpam-6524	355	16	18	18	NUM
ejpam-6524	355	17	of	of	ADP
ejpam-6524	355	18	21	21	NUM
ejpam-6524	355	19	0.056977	0.056977	NUM
ejpam-6524	355	20	.	.	PUNCT
ejpam-6524	356	1	figure	figure	NOUN
ejpam-6524	356	2	8	8	NUM
ejpam-6524	356	3	:	:	PUNCT
ejpam-6524	356	4	comparison	comparison	NOUN
ejpam-6524	356	5	of	of	ADP
ejpam-6524	356	6	the	the	DET
ejpam-6524	356	7	analytical	analytical	ADJ
ejpam-6524	356	8	solution	solution	NOUN
ejpam-6524	356	9	and	and	CCONJ
ejpam-6524	356	10	the	the	DET
ejpam-6524	356	11	gfem	gfem	PROPN
ejpam-6524	356	12	approximation	approximation	NOUN
ejpam-6524	356	13	solution	solution	NOUN
ejpam-6524	356	14	for	for	ADP
ejpam-6524	356	15	wave	wave	NOUN
ejpam-6524	356	16	equation	equation	NOUN
ejpam-6524	356	17	the	the	DET
ejpam-6524	356	18	gfem	gfem	NOUN
ejpam-6524	356	19	exhibits	exhibit	VERB
ejpam-6524	356	20	lower	low	ADJ
ejpam-6524	356	21	error	error	NOUN
ejpam-6524	356	22	rates	rate	NOUN
ejpam-6524	356	23	than	than	ADP
ejpam-6524	356	24	the	the	DET
ejpam-6524	356	25	fdm	fdm	NOUN
ejpam-6524	356	26	,	,	PUNCT
ejpam-6524	356	27	which	which	PRON
ejpam-6524	356	28	suggests	suggest	VERB
ejpam-6524	356	29	that	that	SCONJ
ejpam-6524	356	30	the	the	DET
ejpam-6524	356	31	gfem	gfem	NOUN
ejpam-6524	356	32	is	be	AUX
ejpam-6524	356	33	more	more	ADV
ejpam-6524	356	34	reliable	reliable	ADJ
ejpam-6524	356	35	for	for	ADP
ejpam-6524	356	36	solving	solve	VERB
ejpam-6524	356	37	these	these	DET
ejpam-6524	356	38	kinds	kind	NOUN
ejpam-6524	356	39	of	of	ADP
ejpam-6524	356	40	equations	equation	NOUN
ejpam-6524	356	41	,	,	PUNCT
ejpam-6524	356	42	according	accord	VERB
ejpam-6524	356	43	to	to	ADP
ejpam-6524	356	44	tables	table	NOUN
ejpam-6524	356	45	2	2	NUM
ejpam-6524	356	46	and	and	CCONJ
ejpam-6524	356	47	3	3	NUM
ejpam-6524	356	48	.	.	PUNCT
ejpam-6524	357	1	in	in	ADP
ejpam-6524	357	2	response	response	NOUN
ejpam-6524	357	3	,	,	PUNCT
ejpam-6524	357	4	this	this	DET
ejpam-6524	357	5	study	study	NOUN
ejpam-6524	357	6	suggests	suggest	VERB
ejpam-6524	357	7	using	use	VERB
ejpam-6524	357	8	gfem	gfem	PROPN
ejpam-6524	357	9	as	as	ADP
ejpam-6524	357	10	a	a	DET
ejpam-6524	357	11	substitute	substitute	NOUN
ejpam-6524	357	12	for	for	ADP
ejpam-6524	357	13	elliptic	elliptic	ADJ
ejpam-6524	357	14	and	and	CCONJ
ejpam-6524	357	15	hyperbolic	hyperbolic	ADJ
ejpam-6524	357	16	type	type	NOUN
ejpam-6524	357	17	pdes	pde	NOUN
ejpam-6524	357	18	.	.	PUNCT
ejpam-6524	358	1	also	also	ADV
ejpam-6524	358	2	figures	figure	VERB
ejpam-6524	358	3	7	7	NUM
ejpam-6524	358	4	and	and	CCONJ
ejpam-6524	358	5	8	8	NUM
ejpam-6524	358	6	clearly	clearly	ADV
ejpam-6524	358	7	demonstrate	demonstrate	VERB
ejpam-6524	358	8	that	that	SCONJ
ejpam-6524	358	9	the	the	DET
ejpam-6524	358	10	gfem	gfem	NOUN
ejpam-6524	358	11	solution	solution	NOUN
ejpam-6524	358	12	agrees	agree	VERB
ejpam-6524	358	13	more	more	ADV
ejpam-6524	358	14	closely	closely	ADV
ejpam-6524	358	15	with	with	ADP
ejpam-6524	358	16	the	the	DET
ejpam-6524	358	17	analytical	analytical	ADJ
ejpam-6524	358	18	solution	solution	NOUN
ejpam-6524	358	19	than	than	ADP
ejpam-6524	358	20	fdm	fdm	NOUN
ejpam-6524	358	21	.	.	PUNCT
ejpam-6524	359	1	figure	figure	NOUN
ejpam-6524	359	2	9	9	NUM
ejpam-6524	359	3	:	:	PUNCT
ejpam-6524	359	4	graph	graph	NOUN
ejpam-6524	359	5	of	of	ADP
ejpam-6524	359	6	the	the	DET
ejpam-6524	359	7	numerical	numerical	ADJ
ejpam-6524	359	8	solution	solution	NOUN
ejpam-6524	359	9	of	of	ADP
ejpam-6524	359	10	wave	wave	NOUN
ejpam-6524	359	11	equation	equation	NOUN
ejpam-6524	359	12	using	use	VERB
ejpam-6524	359	13	fdm	fdm	NOUN
ejpam-6524	359	14	.	.	PUNCT
ejpam-6524	360	1	abdulkafi	abdulkafi	PROPN
ejpam-6524	360	2	m.	m.	PROPN
ejpam-6524	360	3	saeed	saeed	PROPN
ejpam-6524	360	4	,	,	PUNCT
ejpam-6524	360	5	shahad	shahad	PROPN
ejpam-6524	360	6	s.	s.	PROPN
ejpam-6524	360	7	almutairi	almutairi	PROPN
ejpam-6524	360	8	/	/	SYM
ejpam-6524	360	9	eur	eur	PROPN
ejpam-6524	360	10	.	.	PUNCT
ejpam-6524	361	1	j.	j.	PROPN
ejpam-6524	361	2	pure	pure	PROPN
ejpam-6524	361	3	appl	appl	PROPN
ejpam-6524	361	4	.	.	PROPN
ejpam-6524	361	5	math	math	PROPN
ejpam-6524	361	6	,	,	PUNCT
ejpam-6524	361	7	18	18	NUM
ejpam-6524	361	8	(	(	PUNCT
ejpam-6524	361	9	3	3	NUM
ejpam-6524	361	10	)	)	PUNCT
ejpam-6524	361	11	(	(	PUNCT
ejpam-6524	361	12	2025	2025	NUM
ejpam-6524	361	13	)	)	PUNCT
ejpam-6524	361	14	,	,	PUNCT
ejpam-6524	361	15	6524	6524	NUM
ejpam-6524	361	16	19	19	NUM
ejpam-6524	361	17	of	of	ADP
ejpam-6524	361	18	21	21	NUM
ejpam-6524	361	19	figure	figure	NOUN
ejpam-6524	361	20	10	10	NUM
ejpam-6524	361	21	:	:	PUNCT
ejpam-6524	361	22	graph	graph	NOUN
ejpam-6524	361	23	of	of	ADP
ejpam-6524	361	24	the	the	DET
ejpam-6524	361	25	numerical	numerical	ADJ
ejpam-6524	361	26	solution	solution	NOUN
ejpam-6524	361	27	of	of	ADP
ejpam-6524	361	28	wave	wave	NOUN
ejpam-6524	361	29	equation	equation	NOUN
ejpam-6524	361	30	using	use	VERB
ejpam-6524	361	31	gfem	gfem	PROPN
ejpam-6524	361	32	.	.	PUNCT
ejpam-6524	362	1	figure	figure	VERB
ejpam-6524	362	2	11	11	NUM
ejpam-6524	362	3	:	:	PUNCT
ejpam-6524	362	4	graph	graph	NOUN
ejpam-6524	362	5	of	of	ADP
ejpam-6524	362	6	the	the	DET
ejpam-6524	362	7	analytical	analytical	ADJ
ejpam-6524	362	8	solution	solution	NOUN
ejpam-6524	362	9	of	of	ADP
ejpam-6524	362	10	wave	wave	NOUN
ejpam-6524	362	11	equation	equation	NOUN
ejpam-6524	362	12	.	.	PUNCT
ejpam-6524	363	1	figures	figure	NOUN
ejpam-6524	363	2	9	9	NUM
ejpam-6524	363	3	,	,	PUNCT
ejpam-6524	363	4	10	10	NUM
ejpam-6524	363	5	,	,	PUNCT
ejpam-6524	363	6	and	and	CCONJ
ejpam-6524	363	7	11	11	NUM
ejpam-6524	363	8	display	display	VERB
ejpam-6524	363	9	the	the	DET
ejpam-6524	363	10	solutions	solution	NOUN
ejpam-6524	363	11	of	of	ADP
ejpam-6524	363	12	the	the	DET
ejpam-6524	363	13	wave	wave	NOUN
ejpam-6524	363	14	equation	equation	NOUN
ejpam-6524	363	15	obtained	obtain	VERB
ejpam-6524	363	16	using	use	VERB
ejpam-6524	363	17	the	the	DET
ejpam-6524	363	18	fdm	fdm	NOUN
ejpam-6524	363	19	,	,	PUNCT
ejpam-6524	363	20	gfem	gfem	NOUN
ejpam-6524	363	21	,	,	PUNCT
ejpam-6524	363	22	and	and	CCONJ
ejpam-6524	363	23	the	the	DET
ejpam-6524	363	24	analytical	analytical	ADJ
ejpam-6524	363	25	solution	solution	NOUN
ejpam-6524	363	26	.	.	PUNCT
ejpam-6524	364	1	the	the	DET
ejpam-6524	364	2	results	result	NOUN
ejpam-6524	364	3	show	show	VERB
ejpam-6524	364	4	that	that	SCONJ
ejpam-6524	364	5	the	the	DET
ejpam-6524	364	6	gfem	gfem	NOUN
ejpam-6524	364	7	achieves	achieve	VERB
ejpam-6524	364	8	higher	high	ADJ
ejpam-6524	364	9	accuracy	accuracy	NOUN
ejpam-6524	364	10	compared	compare	VERB
ejpam-6524	364	11	to	to	ADP
ejpam-6524	364	12	the	the	DET
ejpam-6524	364	13	fdm	fdm	NOUN
ejpam-6524	364	14	when	when	SCONJ
ejpam-6524	364	15	applied	apply	VERB
ejpam-6524	364	16	to	to	ADP
ejpam-6524	364	17	the	the	DET
ejpam-6524	364	18	wave	wave	NOUN
ejpam-6524	364	19	equation	equation	NOUN
ejpam-6524	364	20	.	.	PUNCT
ejpam-6524	365	1	based	base	VERB
ejpam-6524	365	2	on	on	ADP
ejpam-6524	365	3	these	these	DET
ejpam-6524	365	4	findings	finding	NOUN
ejpam-6524	365	5	,	,	PUNCT
ejpam-6524	365	6	we	we	PRON
ejpam-6524	365	7	conclude	conclude	VERB
ejpam-6524	365	8	that	that	SCONJ
ejpam-6524	365	9	gfem	gfem	NOUN
ejpam-6524	365	10	provides	provide	VERB
ejpam-6524	365	11	more	more	ADV
ejpam-6524	365	12	precise	precise	ADJ
ejpam-6524	365	13	and	and	CCONJ
ejpam-6524	365	14	stable	stable	ADJ
ejpam-6524	365	15	solutions	solution	NOUN
ejpam-6524	365	16	,	,	PUNCT
ejpam-6524	365	17	making	make	VERB
ejpam-6524	365	18	it	it	PRON
ejpam-6524	365	19	a	a	DET
ejpam-6524	365	20	more	more	ADV
ejpam-6524	365	21	effective	effective	ADJ
ejpam-6524	365	22	choice	choice	NOUN
ejpam-6524	365	23	for	for	ADP
ejpam-6524	365	24	solving	solve	VERB
ejpam-6524	365	25	elliptic	elliptic	ADJ
ejpam-6524	365	26	and	and	CCONJ
ejpam-6524	365	27	hyperbolic	hyperbolic	ADJ
ejpam-6524	365	28	pdes	pde	NOUN
ejpam-6524	365	29	.	.	PUNCT
ejpam-6524	366	1	abdulkafi	abdulkafi	PROPN
ejpam-6524	366	2	m.	m.	PROPN
ejpam-6524	366	3	saeed	saeed	PROPN
ejpam-6524	366	4	,	,	PUNCT
ejpam-6524	366	5	shahad	shahad	PROPN
ejpam-6524	366	6	s.	s.	PROPN
ejpam-6524	366	7	almutairi	almutairi	PROPN
ejpam-6524	366	8	/	/	SYM
ejpam-6524	366	9	eur	eur	PROPN
ejpam-6524	366	10	.	.	PUNCT
ejpam-6524	367	1	j.	j.	PROPN
ejpam-6524	367	2	pure	pure	PROPN
ejpam-6524	367	3	appl	appl	PROPN
ejpam-6524	367	4	.	.	PROPN
ejpam-6524	367	5	math	math	PROPN
ejpam-6524	367	6	,	,	PUNCT
ejpam-6524	367	7	18	18	NUM
ejpam-6524	367	8	(	(	PUNCT
ejpam-6524	367	9	3	3	NUM
ejpam-6524	367	10	)	)	PUNCT
ejpam-6524	367	11	(	(	PUNCT
ejpam-6524	367	12	2025	2025	NUM
ejpam-6524	367	13	)	)	PUNCT
ejpam-6524	367	14	,	,	PUNCT
ejpam-6524	367	15	6524	6524	NUM
ejpam-6524	367	16	20	20	NUM
ejpam-6524	367	17	of	of	ADP
ejpam-6524	367	18	21	21	NUM
ejpam-6524	367	19	5	5	NUM
ejpam-6524	367	20	.	.	PUNCT
ejpam-6524	367	21	conclusion	conclusion	NOUN
ejpam-6524	367	22	in	in	ADP
ejpam-6524	367	23	this	this	DET
ejpam-6524	367	24	paper	paper	NOUN
ejpam-6524	367	25	,	,	PUNCT
ejpam-6524	367	26	poisson	poisson	PROPN
ejpam-6524	367	27	’s	’s	PART
ejpam-6524	367	28	equation	equation	NOUN
ejpam-6524	367	29	and	and	CCONJ
ejpam-6524	367	30	the	the	DET
ejpam-6524	367	31	wave	wave	NOUN
ejpam-6524	367	32	equation	equation	NOUN
ejpam-6524	367	33	have	have	AUX
ejpam-6524	367	34	been	be	AUX
ejpam-6524	367	35	solved	solve	VERB
ejpam-6524	367	36	using	use	VERB
ejpam-6524	367	37	the	the	DET
ejpam-6524	367	38	gfem	gfem	NOUN
ejpam-6524	367	39	.	.	PUNCT
ejpam-6524	368	1	to	to	PART
ejpam-6524	368	2	assess	assess	VERB
ejpam-6524	368	3	its	its	PRON
ejpam-6524	368	4	effectiveness	effectiveness	NOUN
ejpam-6524	368	5	relative	relative	ADJ
ejpam-6524	368	6	to	to	ADP
ejpam-6524	368	7	the	the	DET
ejpam-6524	368	8	fdm	fdm	NOUN
ejpam-6524	368	9	,	,	PUNCT
ejpam-6524	368	10	several	several	ADJ
ejpam-6524	368	11	numerical	numerical	ADJ
ejpam-6524	368	12	experiments	experiment	NOUN
ejpam-6524	368	13	.	.	PUNCT
ejpam-6524	369	1	the	the	DET
ejpam-6524	369	2	results	result	NOUN
ejpam-6524	369	3	consistently	consistently	ADV
ejpam-6524	369	4	indicate	indicate	VERB
ejpam-6524	369	5	that	that	SCONJ
ejpam-6524	369	6	gfem	gfem	NOUN
ejpam-6524	369	7	achieves	achieve	VERB
ejpam-6524	369	8	superior	superior	ADJ
ejpam-6524	369	9	accuracy	accuracy	NOUN
ejpam-6524	369	10	,	,	PUNCT
ejpam-6524	369	11	particularly	particularly	ADV
ejpam-6524	369	12	in	in	ADP
ejpam-6524	369	13	capturing	capture	VERB
ejpam-6524	369	14	fine	fine	ADJ
ejpam-6524	369	15	wave	wave	NOUN
ejpam-6524	369	16	structures	structure	NOUN
ejpam-6524	369	17	and	and	CCONJ
ejpam-6524	369	18	handling	handle	VERB
ejpam-6524	369	19	boundary	boundary	ADJ
ejpam-6524	369	20	conditions	condition	NOUN
ejpam-6524	369	21	with	with	ADP
ejpam-6524	369	22	greater	great	ADJ
ejpam-6524	369	23	stability	stability	NOUN
ejpam-6524	369	24	.	.	PUNCT
ejpam-6524	370	1	this	this	DET
ejpam-6524	370	2	improved	improved	ADJ
ejpam-6524	370	3	performance	performance	NOUN
ejpam-6524	370	4	is	be	AUX
ejpam-6524	370	5	most	most	ADV
ejpam-6524	370	6	evident	evident	ADJ
ejpam-6524	370	7	in	in	ADP
ejpam-6524	370	8	scenarios	scenario	NOUN
ejpam-6524	370	9	involving	involve	VERB
ejpam-6524	370	10	complex	complex	ADJ
ejpam-6524	370	11	geometries	geometry	NOUN
ejpam-6524	370	12	and	and	CCONJ
ejpam-6524	370	13	high	high	ADJ
ejpam-6524	370	14	-	-	PUNCT
ejpam-6524	370	15	frequency	frequency	NOUN
ejpam-6524	370	16	wave	wave	NOUN
ejpam-6524	370	17	propagation	propagation	NOUN
ejpam-6524	370	18	,	,	PUNCT
ejpam-6524	370	19	where	where	SCONJ
ejpam-6524	370	20	fdm	fdm	NOUN
ejpam-6524	370	21	tends	tend	VERB
ejpam-6524	370	22	to	to	PART
ejpam-6524	370	23	suffer	suffer	VERB
ejpam-6524	370	24	from	from	ADP
ejpam-6524	370	25	numerical	numerical	ADJ
ejpam-6524	370	26	dispersion	dispersion	NOUN
ejpam-6524	370	27	and	and	CCONJ
ejpam-6524	370	28	phase	phase	NOUN
ejpam-6524	370	29	errors	error	NOUN
ejpam-6524	370	30	.	.	PUNCT
ejpam-6524	371	1	based	base	VERB
ejpam-6524	371	2	on	on	ADP
ejpam-6524	371	3	these	these	DET
ejpam-6524	371	4	findings	finding	NOUN
ejpam-6524	371	5	,	,	PUNCT
ejpam-6524	371	6	we	we	PRON
ejpam-6524	371	7	conclude	conclude	VERB
ejpam-6524	371	8	that	that	SCONJ
ejpam-6524	371	9	gfem	gfem	PROPN
ejpam-6524	371	10	presents	present	VERB
ejpam-6524	371	11	a	a	DET
ejpam-6524	371	12	reliable	reliable	ADJ
ejpam-6524	371	13	and	and	CCONJ
ejpam-6524	371	14	efficient	efficient	ADJ
ejpam-6524	371	15	alternative	alternative	NOUN
ejpam-6524	371	16	for	for	ADP
ejpam-6524	371	17	solving	solve	VERB
ejpam-6524	371	18	both	both	CCONJ
ejpam-6524	371	19	elliptic	elliptic	ADJ
ejpam-6524	371	20	and	and	CCONJ
ejpam-6524	371	21	hyperbolic	hyperbolic	ADJ
ejpam-6524	371	22	partial	partial	ADJ
ejpam-6524	371	23	differential	differential	NOUN
ejpam-6524	371	24	equations	equation	NOUN
ejpam-6524	371	25	.	.	PUNCT
ejpam-6524	372	1	furthermore	furthermore	ADV
ejpam-6524	372	2	,	,	PUNCT
ejpam-6524	372	3	given	give	VERB
ejpam-6524	372	4	its	its	PRON
ejpam-6524	372	5	flexibility	flexibility	NOUN
ejpam-6524	372	6	in	in	ADP
ejpam-6524	372	7	mesh	mesh	NOUN
ejpam-6524	372	8	adaptation	adaptation	NOUN
ejpam-6524	372	9	and	and	CCONJ
ejpam-6524	372	10	compatibility	compatibility	NOUN
ejpam-6524	372	11	with	with	ADP
ejpam-6524	372	12	higher	high	ADJ
ejpam-6524	372	13	-	-	PUNCT
ejpam-6524	372	14	order	order	NOUN
ejpam-6524	372	15	basis	basis	NOUN
ejpam-6524	372	16	functions	function	NOUN
ejpam-6524	372	17	,	,	PUNCT
ejpam-6524	372	18	gfem	gfem	PROPN
ejpam-6524	372	19	holds	hold	VERB
ejpam-6524	372	20	strong	strong	ADJ
ejpam-6524	372	21	potential	potential	NOUN
ejpam-6524	372	22	for	for	ADP
ejpam-6524	372	23	broader	broad	ADJ
ejpam-6524	372	24	applications	application	NOUN
ejpam-6524	372	25	in	in	ADP
ejpam-6524	372	26	engineering	engineering	NOUN
ejpam-6524	372	27	,	,	PUNCT
ejpam-6524	372	28	fluid	fluid	ADJ
ejpam-6524	372	29	dynamics	dynamic	NOUN
ejpam-6524	372	30	,	,	PUNCT
ejpam-6524	372	31	material	material	NOUN
ejpam-6524	372	32	science	science	NOUN
ejpam-6524	372	33	,	,	PUNCT
ejpam-6524	372	34	and	and	CCONJ
ejpam-6524	372	35	other	other	ADJ
ejpam-6524	372	36	computational	computational	ADJ
ejpam-6524	372	37	fields	field	NOUN
ejpam-6524	372	38	that	that	PRON
ejpam-6524	372	39	require	require	VERB
ejpam-6524	372	40	robust	robust	ADJ
ejpam-6524	372	41	and	and	CCONJ
ejpam-6524	372	42	precise	precise	ADJ
ejpam-6524	372	43	numerical	numerical	ADJ
ejpam-6524	372	44	modeling	modeling	NOUN
ejpam-6524	372	45	.	.	PUNCT
ejpam-6524	373	1	acknowledgements	acknowledgement	NOUN
ejpam-6524	373	2	the	the	DET
ejpam-6524	373	3	authors	author	NOUN
ejpam-6524	373	4	gratefully	gratefully	ADV
ejpam-6524	373	5	acknowledge	acknowledge	VERB
ejpam-6524	373	6	qassim	qassim	PROPN
ejpam-6524	373	7	university	university	PROPN
ejpam-6524	373	8	,	,	PUNCT
ejpam-6524	373	9	represented	represent	VERB
ejpam-6524	373	10	by	by	ADP
ejpam-6524	373	11	the	the	DET
ejpam-6524	373	12	deanship	deanship	NOUN
ejpam-6524	373	13	of	of	ADP
ejpam-6524	373	14	graduate	graduate	NOUN
ejpam-6524	373	15	studies	study	NOUN
ejpam-6524	373	16	and	and	CCONJ
ejpam-6524	373	17	scientific	scientific	ADJ
ejpam-6524	373	18	research	research	NOUN
ejpam-6524	373	19	,	,	PUNCT
ejpam-6524	373	20	on	on	ADP
ejpam-6524	373	21	the	the	DET
ejpam-6524	373	22	financial	financial	ADJ
ejpam-6524	373	23	support	support	NOUN
ejpam-6524	373	24	for	for	ADP
ejpam-6524	373	25	this	this	DET
ejpam-6524	373	26	research	research	NOUN
ejpam-6524	373	27	under	under	ADP
ejpam-6524	373	28	the	the	DET
ejpam-6524	373	29	number	number	NOUN
ejpam-6524	373	30	(	(	PUNCT
ejpam-6524	373	31	qu	qu	PROPN
ejpam-6524	373	32	-	-	PROPN
ejpam-6524	373	33	j	j	NOUN
ejpam-6524	373	34	-	-	PUNCT
ejpam-6524	373	35	pg-2	pg-2	NOUN
ejpam-6524	373	36	-	-	PUNCT
ejpam-6524	373	37	202553051	202553051	NUM
ejpam-6524	373	38	)	)	PUNCT
ejpam-6524	373	39	during	during	ADP
ejpam-6524	373	40	the	the	DET
ejpam-6524	373	41	academic	academic	ADJ
ejpam-6524	373	42	year	year	NOUN
ejpam-6524	373	43	1446	1446	NUM
ejpam-6524	373	44	ah	ah	INTJ
ejpam-6524	373	45	/	/	SYM
ejpam-6524	373	46	2024	2024	NUM
ejpam-6524	373	47	ad	ad	NOUN
ejpam-6524	373	48	.	.	PUNCT
ejpam-6524	374	1	references	reference	NOUN
ejpam-6524	374	2	[	[	X
ejpam-6524	374	3	1	1	X
ejpam-6524	374	4	]	]	PUNCT
ejpam-6524	374	5	a	a	DET
ejpam-6524	374	6	quarteroni	quarteroni	NOUN
ejpam-6524	374	7	.	.	PUNCT
ejpam-6524	375	1	numerical	numerical	ADJ
ejpam-6524	375	2	approximation	approximation	NOUN
ejpam-6524	375	3	of	of	ADP
ejpam-6524	375	4	partial	partial	ADJ
ejpam-6524	375	5	differential	differential	ADJ
ejpam-6524	375	6	equations	equation	NOUN
ejpam-6524	375	7	.	.	PUNCT
ejpam-6524	376	1	berlin	berlin	PROPN
ejpam-6524	376	2	;	;	PUNCT
ejpam-6524	376	3	new	new	PROPN
ejpam-6524	376	4	york	york	PROPN
ejpam-6524	376	5	:	:	PUNCT
ejpam-6524	376	6	springer	springer	NOUN
ejpam-6524	376	7	-	-	PUNCT
ejpam-6524	376	8	verlag	verlag	PROPN
ejpam-6524	376	9	,	,	PUNCT
ejpam-6524	376	10	1994	1994	NUM
ejpam-6524	376	11	.	.	PUNCT
ejpam-6524	377	1	[	[	X
ejpam-6524	377	2	2	2	NUM
ejpam-6524	377	3	]	]	PUNCT
ejpam-6524	377	4	g	g	PROPN
ejpam-6524	377	5	smith	smith	PROPN
ejpam-6524	377	6	.	.	PUNCT
ejpam-6524	378	1	numerical	numerical	ADJ
ejpam-6524	378	2	solution	solution	NOUN
ejpam-6524	378	3	of	of	ADP
ejpam-6524	378	4	partial	partial	ADJ
ejpam-6524	378	5	differential	differential	NOUN
ejpam-6524	378	6	equations	equation	NOUN
ejpam-6524	378	7	:	:	PUNCT
ejpam-6524	378	8	finite	finite	ADJ
ejpam-6524	378	9	difference	difference	NOUN
ejpam-6524	378	10	methods	method	NOUN
ejpam-6524	378	11	.	.	PUNCT
ejpam-6524	379	1	clarendon	clarendon	PROPN
ejpam-6524	379	2	press	press	PROPN
ejpam-6524	379	3	,	,	PUNCT
ejpam-6524	379	4	1985	1985	NUM
ejpam-6524	379	5	.	.	PUNCT
ejpam-6524	380	1	[	[	X
ejpam-6524	380	2	3	3	X
ejpam-6524	380	3	]	]	X
ejpam-6524	380	4	kh	kh	PROPN
ejpam-6524	380	5	.	.	PUNCT
ejpam-6524	380	6	lotfy	lotfy	PROPN
ejpam-6524	380	7	.	.	PUNCT
ejpam-6524	381	1	two	two	NUM
ejpam-6524	381	2	temperature	temperature	NOUN
ejpam-6524	381	3	generalized	generalize	VERB
ejpam-6524	381	4	magneto	magneto	NOUN
ejpam-6524	381	5	-	-	PUNCT
ejpam-6524	381	6	thermoelastic	thermoelastic	ADJ
ejpam-6524	381	7	interactions	interaction	NOUN
ejpam-6524	381	8	in	in	ADP
ejpam-6524	381	9	an	an	DET
ejpam-6524	381	10	elastic	elastic	ADJ
ejpam-6524	381	11	medium	medium	NOUN
ejpam-6524	381	12	under	under	ADP
ejpam-6524	381	13	three	three	NUM
ejpam-6524	381	14	theories	theory	NOUN
ejpam-6524	381	15	.	.	PUNCT
ejpam-6524	382	1	applied	apply	VERB
ejpam-6524	382	2	mathematics	mathematic	NOUN
ejpam-6524	382	3	and	and	CCONJ
ejpam-6524	382	4	computation	computation	NOUN
ejpam-6524	382	5	,	,	PUNCT
ejpam-6524	382	6	227:871	227:871	NOUN
ejpam-6524	382	7	–	–	PUNCT
ejpam-6524	382	8	888	888	NUM
ejpam-6524	382	9	,	,	PUNCT
ejpam-6524	382	10	2014	2014	NUM
ejpam-6524	382	11	.	.	PUNCT
ejpam-6524	383	1	[	[	X
ejpam-6524	383	2	4	4	NUM
ejpam-6524	383	3	]	]	X
ejpam-6524	383	4	kh	kh	PROPN
ejpam-6524	383	5	.	.	PROPN
ejpam-6524	383	6	lotfy	lotfy	PROPN
ejpam-6524	383	7	,	,	PUNCT
ejpam-6524	383	8	a.a	a.a	PROPN
ejpam-6524	383	9	.	.	PROPN
ejpam-6524	383	10	el	el	PROPN
ejpam-6524	383	11	-	-	PUNCT
ejpam-6524	383	12	bary	bary	PROPN
ejpam-6524	383	13	,	,	PUNCT
ejpam-6524	383	14	w.	w.	PROPN
ejpam-6524	383	15	hassan	hassan	PROPN
ejpam-6524	383	16	,	,	PUNCT
ejpam-6524	383	17	a.r	a.r	PROPN
ejpam-6524	383	18	.	.	PROPN
ejpam-6524	383	19	alharbi	alharbi	PROPN
ejpam-6524	383	20	,	,	PUNCT
ejpam-6524	383	21	and	and	CCONJ
ejpam-6524	383	22	m.b	m.b	PROPN
ejpam-6524	383	23	.	.	PROPN
ejpam-6524	383	24	almatrafi	almatrafi	PROPN
ejpam-6524	383	25	.	.	PUNCT
ejpam-6524	384	1	electromagnetic	electromagnetic	ADJ
ejpam-6524	384	2	and	and	CCONJ
ejpam-6524	384	3	thomson	thomson	NOUN
ejpam-6524	384	4	effects	effect	NOUN
ejpam-6524	384	5	during	during	ADP
ejpam-6524	384	6	photothermal	photothermal	ADJ
ejpam-6524	384	7	transport	transport	NOUN
ejpam-6524	384	8	process	process	NOUN
ejpam-6524	384	9	of	of	ADP
ejpam-6524	384	10	a	a	DET
ejpam-6524	384	11	rotator	rotator	NOUN
ejpam-6524	384	12	semiconductor	semiconductor	NOUN
ejpam-6524	384	13	medium	medium	NOUN
ejpam-6524	384	14	under	under	ADP
ejpam-6524	384	15	hydrostatic	hydrostatic	ADJ
ejpam-6524	384	16	initial	initial	ADJ
ejpam-6524	384	17	stress	stress	NOUN
ejpam-6524	384	18	.	.	PUNCT
ejpam-6524	385	1	results	result	NOUN
ejpam-6524	385	2	in	in	ADP
ejpam-6524	385	3	physics	physics	NOUN
ejpam-6524	385	4	,	,	PUNCT
ejpam-6524	385	5	16:102983	16:102983	NUM
ejpam-6524	385	6	,	,	PUNCT
ejpam-6524	385	7	2020	2020	NUM
ejpam-6524	385	8	.	.	PUNCT
ejpam-6524	386	1	[	[	X
ejpam-6524	386	2	5	5	NUM
ejpam-6524	386	3	]	]	SYM
ejpam-6524	386	4	b	b	PROPN
ejpam-6524	386	5	szabo	szabo	PROPN
ejpam-6524	386	6	and	and	CCONJ
ejpam-6524	386	7	i	i	PROPN
ejpam-6524	386	8	babuska	babuska	PROPN
ejpam-6524	386	9	.	.	PUNCT
ejpam-6524	387	1	finite	finite	PROPN
ejpam-6524	387	2	element	element	NOUN
ejpam-6524	387	3	analysis	analysis	NOUN
ejpam-6524	387	4	:	:	PUNCT
ejpam-6524	387	5	method	method	NOUN
ejpam-6524	387	6	,	,	PUNCT
ejpam-6524	387	7	verification	verification	NOUN
ejpam-6524	387	8	and	and	CCONJ
ejpam-6524	387	9	validation	validation	NOUN
ejpam-6524	387	10	.	.	PUNCT
ejpam-6524	388	1	wiley	wiley	PROPN
ejpam-6524	388	2	,	,	PUNCT
ejpam-6524	388	3	2021	2021	NUM
ejpam-6524	388	4	.	.	PUNCT
ejpam-6524	389	1	[	[	X
ejpam-6524	389	2	6	6	NUM
ejpam-6524	389	3	]	]	PUNCT
ejpam-6524	389	4	t	t	PROPN
ejpam-6524	389	5	hughes	hughe	NOUN
ejpam-6524	389	6	.	.	PUNCT
ejpam-6524	390	1	the	the	DET
ejpam-6524	390	2	finite	finite	PROPN
ejpam-6524	390	3	element	element	NOUN
ejpam-6524	390	4	method	method	NOUN
ejpam-6524	390	5	:	:	PUNCT
ejpam-6524	390	6	linear	linear	ADJ
ejpam-6524	390	7	static	static	ADJ
ejpam-6524	390	8	and	and	CCONJ
ejpam-6524	390	9	dynamic	dynamic	ADJ
ejpam-6524	390	10	finite	finite	NOUN
ejpam-6524	390	11	element	element	NOUN
ejpam-6524	390	12	analysis	analysis	NOUN
ejpam-6524	390	13	.	.	PUNCT
ejpam-6524	391	1	mineola	mineola	PROPN
ejpam-6524	391	2	,	,	PUNCT
ejpam-6524	391	3	ny	ny	PROPN
ejpam-6524	391	4	:	:	PUNCT
ejpam-6524	391	5	dover	dover	PROPN
ejpam-6524	391	6	publications	publication	NOUN
ejpam-6524	391	7	,	,	PUNCT
ejpam-6524	391	8	2000	2000	NUM
ejpam-6524	391	9	.	.	PUNCT
ejpam-6524	392	1	[	[	X
ejpam-6524	392	2	7	7	NUM
ejpam-6524	392	3	]	]	X
ejpam-6524	392	4	e	e	X
ejpam-6524	392	5	cheney	cheney	NOUN
ejpam-6524	392	6	and	and	CCONJ
ejpam-6524	392	7	d	d	PROPN
ejpam-6524	392	8	kincaid	kincaid	PROPN
ejpam-6524	392	9	.	.	PUNCT
ejpam-6524	393	1	numerical	numerical	PROPN
ejpam-6524	393	2	mathematics	mathematics	PROPN
ejpam-6524	393	3	and	and	CCONJ
ejpam-6524	393	4	computing	computing	NOUN
ejpam-6524	393	5	.	.	PUNCT
ejpam-6524	394	1	pacific	pacific	PROPN
ejpam-6524	394	2	grove	grove	PROPN
ejpam-6524	394	3	,	,	PUNCT
ejpam-6524	394	4	ca	can	AUX
ejpam-6524	394	5	:	:	PUNCT
ejpam-6524	394	6	brooks	brooks	PROPN
ejpam-6524	394	7	/	/	SYM
ejpam-6524	394	8	cole	cole	PROPN
ejpam-6524	394	9	pub	pub	NOUN
ejpam-6524	394	10	.	.	PUNCT
ejpam-6524	395	1	co	co	NOUN
ejpam-6524	395	2	,	,	PUNCT
ejpam-6524	395	3	1999	1999	NUM
ejpam-6524	395	4	.	.	PUNCT
ejpam-6524	396	1	[	[	X
ejpam-6524	396	2	8	8	NUM
ejpam-6524	396	3	]	]	X
ejpam-6524	396	4	o	o	NOUN
ejpam-6524	396	5	zienkiewicz	zienkiewicz	NOUN
ejpam-6524	396	6	.	.	PUNCT
ejpam-6524	397	1	the	the	DET
ejpam-6524	397	2	finite	finite	PROPN
ejpam-6524	397	3	element	element	NOUN
ejpam-6524	397	4	method	method	NOUN
ejpam-6524	397	5	.	.	PUNCT
ejpam-6524	398	1	singapore	singapore	PROPN
ejpam-6524	398	2	:	:	PUNCT
ejpam-6524	398	3	mcgraw	mcgraw	PROPN
ejpam-6524	398	4	-	-	PUNCT
ejpam-6524	398	5	hill	hill	NOUN
ejpam-6524	398	6	,	,	PUNCT
ejpam-6524	398	7	1989	1989	NUM
ejpam-6524	398	8	.	.	PUNCT
ejpam-6524	399	1	[	[	X
ejpam-6524	399	2	9	9	NUM
ejpam-6524	399	3	]	]	X
ejpam-6524	399	4	o	o	NOUN
ejpam-6524	399	5	zienkiewicz	zienkiewicz	NOUN
ejpam-6524	399	6	,	,	PUNCT
ejpam-6524	399	7	r	r	PROPN
ejpam-6524	399	8	taylor	taylor	PROPN
ejpam-6524	399	9	,	,	PUNCT
ejpam-6524	399	10	and	and	CCONJ
ejpam-6524	399	11	j	j	PROPN
ejpam-6524	399	12	zhu	zhu	PROPN
ejpam-6524	399	13	.	.	PUNCT
ejpam-6524	400	1	the	the	DET
ejpam-6524	400	2	finite	finite	PROPN
ejpam-6524	400	3	element	element	NOUN
ejpam-6524	400	4	method	method	NOUN
ejpam-6524	400	5	:	:	PUNCT
ejpam-6524	400	6	its	its	PRON
ejpam-6524	400	7	basis	basis	NOUN
ejpam-6524	400	8	and	and	CCONJ
ejpam-6524	400	9	fundamentals	fundamental	NOUN
ejpam-6524	400	10	.	.	PUNCT
ejpam-6524	401	1	elsevier	elsevier	PROPN
ejpam-6524	401	2	science	science	PROPN
ejpam-6524	401	3	,	,	PUNCT
ejpam-6524	401	4	2005	2005	NUM
ejpam-6524	401	5	.	.	PUNCT
ejpam-6524	402	1	abdulkafi	abdulkafi	PROPN
ejpam-6524	402	2	m.	m.	PROPN
ejpam-6524	402	3	saeed	saeed	PROPN
ejpam-6524	402	4	,	,	PUNCT
ejpam-6524	402	5	shahad	shahad	PROPN
ejpam-6524	402	6	s.	s.	PROPN
ejpam-6524	402	7	almutairi	almutairi	PROPN
ejpam-6524	402	8	/	/	SYM
ejpam-6524	402	9	eur	eur	PROPN
ejpam-6524	402	10	.	.	PUNCT
ejpam-6524	403	1	j.	j.	PROPN
ejpam-6524	403	2	pure	pure	PROPN
ejpam-6524	403	3	appl	appl	PROPN
ejpam-6524	403	4	.	.	PROPN
ejpam-6524	403	5	math	math	PROPN
ejpam-6524	403	6	,	,	PUNCT
ejpam-6524	403	7	18	18	NUM
ejpam-6524	403	8	(	(	PUNCT
ejpam-6524	403	9	3	3	NUM
ejpam-6524	403	10	)	)	PUNCT
ejpam-6524	403	11	(	(	PUNCT
ejpam-6524	403	12	2025	2025	NUM
ejpam-6524	403	13	)	)	PUNCT
ejpam-6524	403	14	,	,	PUNCT
ejpam-6524	403	15	6524	6524	NUM
ejpam-6524	403	16	21	21	NUM
ejpam-6524	403	17	of	of	ADP
ejpam-6524	403	18	21	21	NUM
ejpam-6524	404	1	[	[	SYM
ejpam-6524	404	2	10	10	NUM
ejpam-6524	404	3	]	]	X
ejpam-6524	404	4	s	s	PART
ejpam-6524	404	5	brenner	brenner	NOUN
ejpam-6524	404	6	and	and	CCONJ
ejpam-6524	404	7	r	r	PROPN
ejpam-6524	404	8	scott	scott	PROPN
ejpam-6524	404	9	.	.	PUNCT
ejpam-6524	405	1	the	the	DET
ejpam-6524	405	2	mathematical	mathematical	ADJ
ejpam-6524	405	3	theory	theory	NOUN
ejpam-6524	405	4	of	of	ADP
ejpam-6524	405	5	finite	finite	ADJ
ejpam-6524	405	6	element	element	NOUN
ejpam-6524	405	7	methods	method	NOUN
ejpam-6524	405	8	.	.	PUNCT
ejpam-6524	406	1	springer	springer	PROPN
ejpam-6524	406	2	new	new	PROPN
ejpam-6524	406	3	york	york	PROPN
ejpam-6524	406	4	,	,	PUNCT
ejpam-6524	406	5	2007	2007	NUM
ejpam-6524	406	6	.	.	PUNCT
ejpam-6524	407	1	[	[	X
ejpam-6524	407	2	11	11	NUM
ejpam-6524	407	3	]	]	PUNCT
ejpam-6524	407	4	a	a	DET
ejpam-6524	407	5	shahad	shahad	NOUN
ejpam-6524	407	6	and	and	CCONJ
ejpam-6524	407	7	s	s	VERB
ejpam-6524	407	8	abdulkafi	abdulkafi	NOUN
ejpam-6524	407	9	.	.	PUNCT
ejpam-6524	408	1	a	a	DET
ejpam-6524	408	2	comparative	comparative	ADJ
ejpam-6524	408	3	study	study	NOUN
ejpam-6524	408	4	of	of	ADP
ejpam-6524	408	5	finite	finite	ADJ
ejpam-6524	408	6	difference	difference	NOUN
ejpam-6524	408	7	and	and	CCONJ
ejpam-6524	408	8	galerkin	galerkin	PROPN
ejpam-6524	408	9	finite	finite	PROPN
ejpam-6524	408	10	element	element	NOUN
ejpam-6524	408	11	methods	method	NOUN
ejpam-6524	408	12	for	for	ADP
ejpam-6524	408	13	solving	solve	VERB
ejpam-6524	408	14	boundary	boundary	ADJ
ejpam-6524	408	15	value	value	NOUN
ejpam-6524	408	16	problems	problem	NOUN
ejpam-6524	408	17	.	.	PUNCT
ejpam-6524	409	1	european	european	ADJ
ejpam-6524	409	2	journal	journal	PROPN
ejpam-6524	409	3	of	of	ADP
ejpam-6524	409	4	pure	pure	ADJ
ejpam-6524	409	5	and	and	CCONJ
ejpam-6524	409	6	applied	applied	ADJ
ejpam-6524	409	7	mathematics	mathematic	NOUN
ejpam-6524	409	8	,	,	PUNCT
ejpam-6524	409	9	18(2):5895	18(2):5895	NUM
ejpam-6524	409	10	,	,	PUNCT
ejpam-6524	409	11	2025	2025	NUM
ejpam-6524	409	12	.	.	PUNCT
ejpam-6524	410	1	[	[	X
ejpam-6524	410	2	12	12	NUM
ejpam-6524	410	3	]	]	X
ejpam-6524	410	4	p	p	NOUN
ejpam-6524	410	5	causon	causon	NOUN
ejpam-6524	410	6	and	and	CCONJ
ejpam-6524	410	7	p	p	PROPN
ejpam-6524	410	8	mingham	mingham	NOUN
ejpam-6524	410	9	.	.	PUNCT
ejpam-6524	411	1	introductory	introductory	ADJ
ejpam-6524	411	2	finite	finite	ADJ
ejpam-6524	411	3	difference	difference	NOUN
ejpam-6524	411	4	methods	method	NOUN
ejpam-6524	411	5	for	for	ADP
ejpam-6524	411	6	pdes	pde	NOUN
ejpam-6524	411	7	.	.	PUNCT
ejpam-6524	412	1	bookboon	bookboon	NOUN
ejpam-6524	412	2	,	,	PUNCT
ejpam-6524	412	3	2010	2010	NUM
ejpam-6524	412	4	.	.	PUNCT
ejpam-6524	413	1	[	[	X
ejpam-6524	413	2	13	13	NUM
ejpam-6524	413	3	]	]	SYM
ejpam-6524	413	4	u	u	NOUN
ejpam-6524	413	5	yashkun	yashkun	NOUN
ejpam-6524	413	6	and	and	CCONJ
ejpam-6524	413	7	m	m	PROPN
ejpam-6524	413	8	chandio	chandio	NOUN
ejpam-6524	413	9	.	.	PUNCT
ejpam-6524	414	1	finite	finite	ADJ
ejpam-6524	414	2	difference	difference	NOUN
ejpam-6524	414	3	method	method	NOUN
ejpam-6524	414	4	with	with	ADP
ejpam-6524	414	5	dirichlet	dirichlet	PROPN
ejpam-6524	414	6	problems	problem	NOUN
ejpam-6524	414	7	of	of	ADP
ejpam-6524	414	8	2d	2d	NUM
ejpam-6524	414	9	laplace	laplace	NOUN
ejpam-6524	414	10	’s	’s	PART
ejpam-6524	414	11	equation	equation	NOUN
ejpam-6524	414	12	in	in	ADP
ejpam-6524	414	13	elliptic	elliptic	ADJ
ejpam-6524	414	14	domain	domain	NOUN
ejpam-6524	414	15	.	.	PUNCT
ejpam-6524	415	1	pakistan	pakistan	PROPN
ejpam-6524	415	2	journal	journal	PROPN
ejpam-6524	415	3	of	of	ADP
ejpam-6524	415	4	engineering	engineering	NOUN
ejpam-6524	415	5	technology	technology	NOUN
ejpam-6524	415	6	and	and	CCONJ
ejpam-6524	415	7	science	science	NOUN
ejpam-6524	415	8	(	(	PUNCT
ejpam-6524	415	9	pjets	pjet	NOUN
ejpam-6524	415	10	)	)	PUNCT
ejpam-6524	415	11	,	,	PUNCT
ejpam-6524	415	12	6(2):136–144	6(2):136–144	NOUN
ejpam-6524	415	13	,	,	PUNCT
ejpam-6524	415	14	2016	2016	NUM
ejpam-6524	415	15	.	.	PUNCT
ejpam-6524	416	1	[	[	X
ejpam-6524	416	2	14	14	NUM
ejpam-6524	416	3	]	]	X
ejpam-6524	416	4	s	s	PART
ejpam-6524	416	5	abdulkafi	abdulkafi	NOUN
ejpam-6524	416	6	.	.	PUNCT
ejpam-6524	417	1	improved	improve	VERB
ejpam-6524	417	2	rotated	rotate	VERB
ejpam-6524	417	3	finite	finite	ADJ
ejpam-6524	417	4	difference	difference	NOUN
ejpam-6524	417	5	method	method	NOUN
ejpam-6524	417	6	for	for	ADP
ejpam-6524	417	7	solving	solve	VERB
ejpam-6524	417	8	fractional	fractional	ADJ
ejpam-6524	417	9	elliptic	elliptic	ADJ
ejpam-6524	417	10	partial	partial	ADJ
ejpam-6524	417	11	differential	differential	NOUN
ejpam-6524	417	12	equations	equation	NOUN
ejpam-6524	417	13	.	.	PUNCT
ejpam-6524	418	1	american	american	ADJ
ejpam-6524	418	2	scientific	scientific	ADJ
ejpam-6524	418	3	research	research	PROPN
ejpam-6524	418	4	journal	journal	NOUN
ejpam-6524	418	5	for	for	ADP
ejpam-6524	418	6	engineering	engineering	NOUN
ejpam-6524	418	7	,	,	PUNCT
ejpam-6524	418	8	technology	technology	NOUN
ejpam-6524	418	9	,	,	PUNCT
ejpam-6524	418	10	and	and	CCONJ
ejpam-6524	418	11	sciences	science	NOUN
ejpam-6524	418	12	(	(	PUNCT
ejpam-6524	418	13	asrjets	asrjet	NOUN
ejpam-6524	418	14	)	)	PUNCT
ejpam-6524	418	15	,	,	PUNCT
ejpam-6524	418	16	26(1):261–270	26(1):261–270	NUM
ejpam-6524	418	17	,	,	PUNCT
ejpam-6524	418	18	2016	2016	NUM
ejpam-6524	418	19	.	.	PUNCT
ejpam-6524	419	1	[	[	X
ejpam-6524	419	2	15	15	NUM
ejpam-6524	419	3	]	]	X
ejpam-6524	419	4	p	p	X
ejpam-6524	419	5	zhou	zhou	PROPN
ejpam-6524	419	6	.	.	PUNCT
ejpam-6524	420	1	finite	finite	ADJ
ejpam-6524	420	2	difference	difference	NOUN
ejpam-6524	420	3	method	method	NOUN
ejpam-6524	420	4	,	,	PUNCT
ejpam-6524	420	5	pages	page	NOUN
ejpam-6524	420	6	63–94	63–94	NUM
ejpam-6524	420	7	.	.	PUNCT
ejpam-6524	421	1	springer	springer	PROPN
ejpam-6524	421	2	berlin	berlin	PROPN
ejpam-6524	421	3	heidelberg	heidelberg	PROPN
ejpam-6524	421	4	,	,	PUNCT
ejpam-6524	421	5	berlin	berlin	PROPN
ejpam-6524	421	6	,	,	PUNCT
ejpam-6524	421	7	heidelberg	heidelberg	PROPN
ejpam-6524	421	8	,	,	PUNCT
ejpam-6524	421	9	1993	1993	NUM
ejpam-6524	421	10	.	.	PUNCT
ejpam-6524	422	1	[	[	X
ejpam-6524	422	2	16	16	NUM
ejpam-6524	422	3	]	]	X
ejpam-6524	422	4	r.	r.	PROPN
ejpam-6524	422	5	burden	burden	PROPN
ejpam-6524	422	6	and	and	CCONJ
ejpam-6524	422	7	j.	j.	PROPN
ejpam-6524	422	8	faires	faires	PROPN
ejpam-6524	422	9	.	.	PUNCT
ejpam-6524	423	1	numerical	numerical	ADJ
ejpam-6524	423	2	analysis	analysis	NOUN
ejpam-6524	423	3	.	.	PUNCT
ejpam-6524	424	1	pws	pws	NOUN
ejpam-6524	424	2	-	-	PUNCT
ejpam-6524	424	3	kent	kent	PROPN
ejpam-6524	424	4	publishing	publishing	PROPN
ejpam-6524	424	5	company	company	NOUN
ejpam-6524	424	6	,	,	PUNCT
ejpam-6524	424	7	1989	1989	NUM
ejpam-6524	424	8	.	.	PUNCT
ejpam-6524	425	1	[	[	X
ejpam-6524	425	2	17	17	NUM
ejpam-6524	425	3	]	]	X
ejpam-6524	425	4	h	h	NOUN
ejpam-6524	425	5	grosshans	grosshan	NOUN
ejpam-6524	425	6	,	,	PUNCT
ejpam-6524	425	7	s	s	VERB
ejpam-6524	425	8	gopireddy	gopireddy	NOUN
ejpam-6524	425	9	,	,	PUNCT
ejpam-6524	425	10	r	r	NOUN
ejpam-6524	425	11	humza	humza	NOUN
ejpam-6524	425	12	,	,	PUNCT
ejpam-6524	425	13	and	and	CCONJ
ejpam-6524	425	14	e	e	NOUN
ejpam-6524	425	15	gutheil	gutheil	NOUN
ejpam-6524	425	16	.	.	PUNCT
ejpam-6524	426	1	modeling	modeling	NOUN
ejpam-6524	426	2	and	and	CCONJ
ejpam-6524	426	3	simulation	simulation	NOUN
ejpam-6524	426	4	of	of	ADP
ejpam-6524	426	5	single	single	ADJ
ejpam-6524	426	6	particle	particle	NOUN
ejpam-6524	426	7	and	and	CCONJ
ejpam-6524	426	8	spray	spray	VERB
ejpam-6524	426	9	drying	dry	VERB
ejpam-6524	426	10	of	of	ADP
ejpam-6524	426	11	pvpand	pvpand	NOUN
ejpam-6524	426	12	mannitol	mannitol	NOUN
ejpam-6524	426	13	-	-	PUNCT
ejpam-6524	426	14	water	water	NOUN
ejpam-6524	426	15	in	in	ADP
ejpam-6524	426	16	hot	hot	ADJ
ejpam-6524	426	17	air	air	NOUN
ejpam-6524	426	18	.	.	PUNCT
ejpam-6524	427	1	springer	springer	NOUN
ejpam-6524	427	2	,	,	PUNCT
ejpam-6524	427	3	cham	cham	PROPN
ejpam-6524	427	4	,	,	PUNCT
ejpam-6524	427	5	pages	page	NOUN
ejpam-6524	427	6	309–339	309–339	NUM
ejpam-6524	427	7	,	,	PUNCT
ejpam-6524	427	8	2016	2016	NUM
ejpam-6524	427	9	.	.	PUNCT
ejpam-6524	428	1	[	[	X
ejpam-6524	428	2	18	18	NUM
ejpam-6524	428	3	]	]	X
ejpam-6524	428	4	j	j	PROPN
ejpam-6524	428	5	west	west	PROPN
ejpam-6524	428	6	and	and	CCONJ
ejpam-6524	428	7	linster	linster	PROPN
ejpam-6524	428	8	.	.	PUNCT
ejpam-6524	429	1	the	the	DET
ejpam-6524	429	2	evolution	evolution	NOUN
ejpam-6524	429	3	of	of	ADP
ejpam-6524	429	4	fuzzy	fuzzy	ADJ
ejpam-6524	429	5	rules	rule	NOUN
ejpam-6524	429	6	in	in	ADP
ejpam-6524	429	7	two	two	NUM
ejpam-6524	429	8	-	-	PUNCT
ejpam-6524	429	9	player	player	NOUN
ejpam-6524	429	10	games	game	NOUN
ejpam-6524	429	11	.	.	PUNCT
ejpam-6524	430	1	southern	southern	ADJ
ejpam-6524	430	2	economic	economic	ADJ
ejpam-6524	430	3	journal	journal	NOUN
ejpam-6524	430	4	,	,	PUNCT
ejpam-6524	430	5	69(3):705–717	69(3):705–717	PROPN
ejpam-6524	430	6	,	,	PUNCT
ejpam-6524	430	7	2003	2003	NUM
ejpam-6524	430	8	.	.	PUNCT
ejpam-6524	431	1	[	[	X
ejpam-6524	431	2	19	19	NUM
ejpam-6524	431	3	]	]	X
ejpam-6524	431	4	p	p	NOUN
ejpam-6524	431	5	ciarlet	ciarlet	NOUN
ejpam-6524	431	6	.	.	PUNCT
ejpam-6524	432	1	the	the	DET
ejpam-6524	432	2	finite	finite	PROPN
ejpam-6524	432	3	element	element	NOUN
ejpam-6524	432	4	method	method	NOUN
ejpam-6524	432	5	for	for	ADP
ejpam-6524	432	6	elliptic	elliptic	ADJ
ejpam-6524	432	7	problems	problem	NOUN
ejpam-6524	432	8	.	.	PUNCT
ejpam-6524	433	1	studies	study	NOUN
ejpam-6524	433	2	in	in	ADP
ejpam-6524	433	3	mathematics	mathematic	NOUN
ejpam-6524	433	4	and	and	CCONJ
ejpam-6524	433	5	its	its	PRON
ejpam-6524	433	6	applications	application	NOUN
ejpam-6524	433	7	.	.	PUNCT
ejpam-6524	434	1	north	north	NOUN
ejpam-6524	434	2	holland	holland	PROPN
ejpam-6524	434	3	,	,	PUNCT
ejpam-6524	434	4	1978	1978	NUM
ejpam-6524	434	5	.	.	PUNCT
ejpam-6524	435	1	[	[	X
ejpam-6524	435	2	20	20	NUM
ejpam-6524	435	3	]	]	X
ejpam-6524	435	4	g	g	PROPN
ejpam-6524	435	5	michael	michael	PROPN
ejpam-6524	435	6	b	b	PROPN
ejpam-6524	435	7	wolfgang	wolfgang	PROPN
ejpam-6524	435	8	and	and	CCONJ
ejpam-6524	435	9	r	r	NOUN
ejpam-6524	435	10	rolf	rolf	NOUN
ejpam-6524	435	11	.	.	PUNCT
ejpam-6524	436	1	adaptive	adaptive	ADJ
ejpam-6524	436	2	galerkin	galerkin	PROPN
ejpam-6524	436	3	finite	finite	PROPN
ejpam-6524	436	4	element	element	NOUN
ejpam-6524	436	5	methods	method	NOUN
ejpam-6524	436	6	for	for	ADP
ejpam-6524	436	7	the	the	DET
ejpam-6524	436	8	wave	wave	NOUN
ejpam-6524	436	9	equation	equation	NOUN
ejpam-6524	436	10	.	.	PUNCT
ejpam-6524	437	1	computational	computational	ADJ
ejpam-6524	437	2	methods	method	NOUN
ejpam-6524	437	3	in	in	ADP
ejpam-6524	437	4	applied	applied	ADJ
ejpam-6524	437	5	mathematics	mathematic	NOUN
ejpam-6524	437	6	,	,	PUNCT
ejpam-6524	437	7	10(1):3–48	10(1):3–48	NUM
ejpam-6524	437	8	,	,	PUNCT
ejpam-6524	437	9	2010	2010	NUM
ejpam-6524	437	10	.	.	PUNCT
ejpam-6524	438	1	[	[	X
ejpam-6524	438	2	21	21	NUM
ejpam-6524	438	3	]	]	SYM
ejpam-6524	438	4	b	b	X
ejpam-6524	438	5	klaus	klaus	PROPN
ejpam-6524	438	6	-	-	PUNCT
ejpam-6524	438	7	jurgen	jurgen	PROPN
ejpam-6524	438	8	h	h	PROPN
ejpam-6524	438	9	seounghyun	seounghyun	PROPN
ejpam-6524	438	10	.	.	PUNCT
ejpam-6524	439	1	a	a	DET
ejpam-6524	439	2	finite	finite	ADJ
ejpam-6524	439	3	element	element	NOUN
ejpam-6524	439	4	method	method	NOUN
ejpam-6524	439	5	enriched	enrich	VERB
ejpam-6524	439	6	for	for	ADP
ejpam-6524	439	7	wave	wave	NOUN
ejpam-6524	439	8	propagation	propagation	NOUN
ejpam-6524	439	9	problems	problem	NOUN
ejpam-6524	439	10	.	.	PUNCT
ejpam-6524	440	1	computers	computer	NOUN
ejpam-6524	440	2	and	and	CCONJ
ejpam-6524	440	3	structures	structure	NOUN
ejpam-6524	440	4	,	,	PUNCT
ejpam-6524	440	5	94(1):1–12	94(1):1–12	NUM
ejpam-6524	440	6	,	,	PUNCT
ejpam-6524	440	7	2012	2012	NUM
ejpam-6524	440	8	.	.	PUNCT
ejpam-6524	441	1	[	[	X
ejpam-6524	441	2	22	22	NUM
ejpam-6524	441	3	]	]	X
ejpam-6524	441	4	j	j	PROPN
ejpam-6524	441	5	kim	kim	PROPN
ejpam-6524	441	6	and	and	CCONJ
ejpam-6524	441	7	k	k	PROPN
ejpam-6524	441	8	bai	bai	PROPN
ejpam-6524	441	9	.	.	PUNCT
ejpam-6524	442	1	a	a	DET
ejpam-6524	442	2	finite	finite	ADJ
ejpam-6524	442	3	element	element	NOUN
ejpam-6524	442	4	method	method	NOUN
ejpam-6524	442	5	for	for	ADP
ejpam-6524	442	6	two	two	NUM
ejpam-6524	442	7	-	-	PUNCT
ejpam-6524	442	8	dimensional	dimensional	ADJ
ejpam-6524	442	9	water	water	NOUN
ejpam-6524	442	10	-	-	PUNCT
ejpam-6524	442	11	wave	wave	NOUN
ejpam-6524	442	12	problems	problem	NOUN
ejpam-6524	442	13	.	.	PUNCT
ejpam-6524	443	1	international	international	ADJ
ejpam-6524	443	2	journal	journal	PROPN
ejpam-6524	443	3	for	for	ADP
ejpam-6524	443	4	numerical	numerical	ADJ
ejpam-6524	443	5	methods	method	NOUN
ejpam-6524	443	6	in	in	ADP
ejpam-6524	443	7	fluids	fluid	NOUN
ejpam-6524	443	8	,	,	PUNCT
ejpam-6524	443	9	30(1):105–122	30(1):105–122	PROPN
ejpam-6524	443	10	,	,	PUNCT
ejpam-6524	443	11	1999	1999	NUM
ejpam-6524	443	12	.	.	PUNCT