id	sid	tid	token	lemma	pos
ejpam-5024	1	1	european	european	PROPN
ejpam-5024	1	2	journal	journal	PROPN
ejpam-5024	1	3	of	of	ADP
ejpam-5024	1	4	pure	pure	ADJ
ejpam-5024	1	5	and	and	CCONJ
ejpam-5024	1	6	applied	apply	VERB
ejpam-5024	1	7	mathematics	mathematic	NOUN
ejpam-5024	1	8	vol	vol	NOUN
ejpam-5024	1	9	.	.	PROPN
ejpam-5024	2	1	17	17	NUM
ejpam-5024	2	2	,	,	PUNCT
ejpam-5024	2	3	no	no	INTJ
ejpam-5024	2	4	.	.	NOUN
ejpam-5024	2	5	1	1	NUM
ejpam-5024	2	6	,	,	PUNCT
ejpam-5024	2	7	2024	2024	NUM
ejpam-5024	2	8	,	,	PUNCT
ejpam-5024	2	9	286	286	NUM
ejpam-5024	2	10	-	-	SYM
ejpam-5024	2	11	299	299	NUM
ejpam-5024	2	12	issn	issn	PROPN
ejpam-5024	2	13	1307	1307	NUM
ejpam-5024	2	14	-	-	SYM
ejpam-5024	2	15	5543	5543	NUM
ejpam-5024	2	16	–	–	PUNCT
ejpam-5024	2	17	ejpam.com	ejpam.com	X
ejpam-5024	2	18	published	publish	VERB
ejpam-5024	2	19	by	by	ADP
ejpam-5024	2	20	new	new	PROPN
ejpam-5024	2	21	york	york	PROPN
ejpam-5024	2	22	business	business	PROPN
ejpam-5024	2	23	global	global	PROPN
ejpam-5024	2	24	numerical	numerical	PROPN
ejpam-5024	2	25	simulation	simulation	PROPN
ejpam-5024	2	26	of	of	ADP
ejpam-5024	2	27	initial	initial	ADJ
ejpam-5024	2	28	value	value	NOUN
ejpam-5024	2	29	problem	problem	NOUN
ejpam-5024	2	30	of	of	ADP
ejpam-5024	2	31	integro	integro	ADJ
ejpam-5024	2	32	-	-	PUNCT
ejpam-5024	2	33	differential	differential	NOUN
ejpam-5024	2	34	equation	equation	NOUN
ejpam-5024	2	35	models	model	NOUN
ejpam-5024	2	36	f.	f.	PROPN
ejpam-5024	2	37	m.	m.	PROPN
ejpam-5024	2	38	alharbi1	alharbi1	PROPN
ejpam-5024	2	39	,	,	PUNCT
ejpam-5024	2	40	s.	s.	PROPN
ejpam-5024	2	41	s.	s.	PROPN
ejpam-5024	2	42	althubiti2,∗	althubiti2,∗	PROPN
ejpam-5024	2	43	1	1	NUM
ejpam-5024	2	44	mathematics	mathematic	NOUN
ejpam-5024	2	45	department	department	NOUN
ejpam-5024	2	46	,	,	PUNCT
ejpam-5024	2	47	faculty	faculty	NOUN
ejpam-5024	2	48	of	of	ADP
ejpam-5024	2	49	sciences	science	NOUN
ejpam-5024	2	50	,	,	PUNCT
ejpam-5024	2	51	umm	umm	INTJ
ejpam-5024	2	52	al	al	PROPN
ejpam-5024	2	53	-	-	PUNCT
ejpam-5024	2	54	quraa	quraa	PROPN
ejpam-5024	2	55	university	university	PROPN
ejpam-5024	2	56	,	,	PUNCT
ejpam-5024	2	57	makkah	makkah	PROPN
ejpam-5024	2	58	,	,	PUNCT
ejpam-5024	2	59	saudi	saudi	PROPN
ejpam-5024	2	60	arabia	arabia	PROPN
ejpam-5024	2	61	abstract	abstract	NOUN
ejpam-5024	2	62	.	.	PUNCT
ejpam-5024	3	1	in	in	ADP
ejpam-5024	3	2	this	this	DET
ejpam-5024	3	3	article	article	NOUN
ejpam-5024	3	4	,	,	PUNCT
ejpam-5024	3	5	the	the	DET
ejpam-5024	3	6	volterra	volterra	NOUN
ejpam-5024	3	7	-	-	PUNCT
ejpam-5024	3	8	fredholm	fredholm	NOUN
ejpam-5024	3	9	integral	integral	ADJ
ejpam-5024	3	10	equation	equation	NOUN
ejpam-5024	3	11	is	be	AUX
ejpam-5024	3	12	derived	derive	VERB
ejpam-5024	3	13	from	from	ADP
ejpam-5024	3	14	an	an	DET
ejpam-5024	3	15	initial	initial	ADJ
ejpam-5024	3	16	value	value	NOUN
ejpam-5024	3	17	problem	problem	NOUN
ejpam-5024	3	18	of	of	ADP
ejpam-5024	3	19	kind	kind	ADJ
ejpam-5024	3	20	integro	integro	ADJ
ejpam-5024	3	21	-	-	PUNCT
ejpam-5024	3	22	differential	differential	NOUN
ejpam-5024	3	23	equation	equation	NOUN
ejpam-5024	3	24	.	.	PUNCT
ejpam-5024	4	1	we	we	PRON
ejpam-5024	4	2	discuss	discuss	VERB
ejpam-5024	4	3	the	the	DET
ejpam-5024	4	4	existence	existence	NOUN
ejpam-5024	4	5	and	and	CCONJ
ejpam-5024	4	6	uniqueness	uniqueness	NOUN
ejpam-5024	4	7	of	of	ADP
ejpam-5024	4	8	the	the	DET
ejpam-5024	4	9	solution	solution	NOUN
ejpam-5024	4	10	to	to	ADP
ejpam-5024	4	11	the	the	DET
ejpam-5024	4	12	problem	problem	NOUN
ejpam-5024	4	13	in	in	ADP
ejpam-5024	4	14	hilbert	hilbert	NOUN
ejpam-5024	4	15	space	space	NOUN
ejpam-5024	4	16	.	.	PUNCT
ejpam-5024	5	1	a	a	DET
ejpam-5024	5	2	numerical	numerical	ADJ
ejpam-5024	5	3	method	method	NOUN
ejpam-5024	5	4	is	be	AUX
ejpam-5024	5	5	used	use	VERB
ejpam-5024	5	6	to	to	PART
ejpam-5024	5	7	reduce	reduce	VERB
ejpam-5024	5	8	this	this	DET
ejpam-5024	5	9	type	type	NOUN
ejpam-5024	5	10	of	of	ADP
ejpam-5024	5	11	equation	equation	NOUN
ejpam-5024	5	12	to	to	ADP
ejpam-5024	5	13	the	the	DET
ejpam-5024	5	14	system	system	NOUN
ejpam-5024	5	15	of	of	ADP
ejpam-5024	5	16	fredholm	fredholm	ADJ
ejpam-5024	5	17	integral	integral	ADJ
ejpam-5024	5	18	equations	equation	NOUN
ejpam-5024	5	19	of	of	ADP
ejpam-5024	5	20	the	the	DET
ejpam-5024	5	21	second	second	ADJ
ejpam-5024	5	22	kind	kind	NOUN
ejpam-5024	5	23	.	.	PUNCT
ejpam-5024	6	1	in	in	ADP
ejpam-5024	6	2	light	light	NOUN
ejpam-5024	6	3	of	of	ADP
ejpam-5024	6	4	this	this	PRON
ejpam-5024	6	5	,	,	PUNCT
ejpam-5024	6	6	the	the	DET
ejpam-5024	6	7	collocation	collocation	NOUN
ejpam-5024	6	8	method	method	NOUN
ejpam-5024	6	9	and	and	CCONJ
ejpam-5024	6	10	the	the	DET
ejpam-5024	6	11	galerkin	galerkin	ADJ
ejpam-5024	6	12	method	method	NOUN
ejpam-5024	6	13	are	be	AUX
ejpam-5024	6	14	used	use	VERB
ejpam-5024	6	15	to	to	PART
ejpam-5024	6	16	solve	solve	VERB
ejpam-5024	6	17	the	the	DET
ejpam-5024	6	18	system	system	NOUN
ejpam-5024	6	19	of	of	ADP
ejpam-5024	6	20	second	second	ADJ
ejpam-5024	6	21	-	-	PUNCT
ejpam-5024	6	22	order	order	NOUN
ejpam-5024	6	23	fredholm	fredholm	NOUN
ejpam-5024	6	24	integral	integral	ADJ
ejpam-5024	6	25	equations	equation	NOUN
ejpam-5024	6	26	and	and	CCONJ
ejpam-5024	6	27	calculate	calculate	VERB
ejpam-5024	6	28	the	the	DET
ejpam-5024	6	29	error	error	NOUN
ejpam-5024	6	30	in	in	ADP
ejpam-5024	6	31	each	each	DET
ejpam-5024	6	32	case	case	NOUN
ejpam-5024	6	33	.	.	PUNCT
ejpam-5024	7	1	finally	finally	ADV
ejpam-5024	7	2	,	,	PUNCT
ejpam-5024	7	3	the	the	DET
ejpam-5024	7	4	approximate	approximate	ADJ
ejpam-5024	7	5	and	and	CCONJ
ejpam-5024	7	6	exact	exact	ADJ
ejpam-5024	7	7	solutions	solution	NOUN
ejpam-5024	7	8	are	be	AUX
ejpam-5024	7	9	plotted	plot	VERB
ejpam-5024	7	10	on	on	ADP
ejpam-5024	7	11	the	the	DET
ejpam-5024	7	12	same	same	ADJ
ejpam-5024	7	13	coordinate	coordinate	NOUN
ejpam-5024	7	14	plane	plane	NOUN
ejpam-5024	7	15	using	use	VERB
ejpam-5024	7	16	matlab	matlab	PROPN
ejpam-5024	7	17	code	code	PROPN
ejpam-5024	7	18	(	(	PUNCT
ejpam-5024	7	19	2022	2022	NUM
ejpam-5024	7	20	)	)	PUNCT
ejpam-5024	7	21	.	.	PUNCT
ejpam-5024	8	1	2020	2020	NUM
ejpam-5024	8	2	mathematics	mathematic	NOUN
ejpam-5024	8	3	subject	subject	NOUN
ejpam-5024	8	4	classifications	classification	NOUN
ejpam-5024	8	5	:	:	PUNCT
ejpam-5024	8	6	34k05,45e20	34k05,45e20	NUM
ejpam-5024	8	7	key	key	ADJ
ejpam-5024	8	8	words	word	NOUN
ejpam-5024	8	9	and	and	CCONJ
ejpam-5024	8	10	phrases	phrase	NOUN
ejpam-5024	8	11	:	:	PUNCT
ejpam-5024	8	12	integro	integro	ADJ
ejpam-5024	8	13	-	-	PUNCT
ejpam-5024	8	14	differential	differential	NOUN
ejpam-5024	8	15	equations	equation	NOUN
ejpam-5024	8	16	ide	ide	NOUN
ejpam-5024	8	17	,	,	PUNCT
ejpam-5024	8	18	volterra	volterra	NOUN
ejpam-5024	8	19	-	-	PUNCT
ejpam-5024	8	20	fredholm	fredholm	NOUN
ejpam-5024	8	21	integral	integral	ADJ
ejpam-5024	8	22	equation	equation	NOUN
ejpam-5024	8	23	v	v	NOUN
ejpam-5024	8	24	-	-	PUNCT
ejpam-5024	8	25	fie	fie	ADJ
ejpam-5024	8	26	,	,	PUNCT
ejpam-5024	8	27	system	system	NOUN
ejpam-5024	8	28	of	of	ADP
ejpam-5024	8	29	second	second	ADJ
ejpam-5024	8	30	-	-	PUNCT
ejpam-5024	8	31	order	order	NOUN
ejpam-5024	8	32	fredholm	fredholm	NOUN
ejpam-5024	8	33	integral	integral	ADJ
ejpam-5024	8	34	equations	equation	NOUN
ejpam-5024	8	35	sfies	sfie	NOUN
ejpam-5024	8	36	,	,	PUNCT
ejpam-5024	8	37	collocation	collocation	NOUN
ejpam-5024	8	38	method	method	NOUN
ejpam-5024	8	39	and	and	CCONJ
ejpam-5024	8	40	galerkin	galerkin	ADJ
ejpam-5024	8	41	method	method	NOUN
ejpam-5024	8	42	1	1	NUM
ejpam-5024	8	43	.	.	PUNCT
ejpam-5024	9	1	introduction	introduction	NOUN
ejpam-5024	9	2	integro	integro	ADJ
ejpam-5024	9	3	-	-	PUNCT
ejpam-5024	9	4	differential	differential	NOUN
ejpam-5024	9	5	equations	equation	NOUN
ejpam-5024	9	6	ide	ide	NOUN
ejpam-5024	9	7	have	have	AUX
ejpam-5024	9	8	garnered	garner	VERB
ejpam-5024	9	9	growing	grow	VERB
ejpam-5024	9	10	interest	interest	NOUN
ejpam-5024	9	11	from	from	ADP
ejpam-5024	9	12	the	the	DET
ejpam-5024	9	13	mathematical	mathematical	ADJ
ejpam-5024	9	14	and	and	CCONJ
ejpam-5024	9	15	physics	physics	NOUN
ejpam-5024	9	16	communities	community	NOUN
ejpam-5024	9	17	.	.	PUNCT
ejpam-5024	10	1	these	these	DET
ejpam-5024	10	2	equations	equation	NOUN
ejpam-5024	10	3	appear	appear	VERB
ejpam-5024	10	4	often	often	ADV
ejpam-5024	10	5	in	in	ADP
ejpam-5024	10	6	a	a	DET
ejpam-5024	10	7	wide	wide	ADJ
ejpam-5024	10	8	range	range	NOUN
ejpam-5024	10	9	of	of	ADP
ejpam-5024	10	10	application	application	NOUN
ejpam-5024	10	11	domains	domain	NOUN
ejpam-5024	10	12	including	include	VERB
ejpam-5024	10	13	engineering	engineering	NOUN
ejpam-5024	10	14	,	,	PUNCT
ejpam-5024	10	15	mechanics	mechanic	NOUN
ejpam-5024	10	16	,	,	PUNCT
ejpam-5024	10	17	elastic	elastic	ADJ
ejpam-5024	10	18	theory	theory	NOUN
ejpam-5024	10	19	,	,	PUNCT
ejpam-5024	10	20	probability	probability	NOUN
ejpam-5024	10	21	theory	theory	NOUN
ejpam-5024	10	22	,	,	PUNCT
ejpam-5024	10	23	and	and	CCONJ
ejpam-5024	10	24	mathematical	mathematical	ADJ
ejpam-5024	10	25	physics	physics	NOUN
ejpam-5024	10	26	.	.	PUNCT
ejpam-5024	11	1	also	also	ADV
ejpam-5024	11	2	,	,	PUNCT
ejpam-5024	11	3	arise	arise	VERB
ejpam-5024	11	4	in	in	ADP
ejpam-5024	11	5	fluid	fluid	ADJ
ejpam-5024	11	6	dynamics	dynamic	NOUN
ejpam-5024	11	7	,	,	PUNCT
ejpam-5024	11	8	such	such	ADJ
ejpam-5024	11	9	as	as	ADP
ejpam-5024	11	10	the	the	DET
ejpam-5024	11	11	glass	glass	NOUN
ejpam-5024	11	12	-	-	PUNCT
ejpam-5024	11	13	forming	form	VERB
ejpam-5024	11	14	process	process	NOUN
ejpam-5024	11	15	and	and	CCONJ
ejpam-5024	11	16	nano	nano	NOUN
ejpam-5024	11	17	-	-	PUNCT
ejpam-5024	11	18	hydrodynamics	hydrodynamic	NOUN
ejpam-5024	11	19	,	,	PUNCT
ejpam-5024	11	20	falling	fall	VERB
ejpam-5024	11	21	condensation	condensation	NOUN
ejpam-5024	11	22	,	,	PUNCT
ejpam-5024	11	23	biological	biological	ADJ
ejpam-5024	11	24	models	model	NOUN
ejpam-5024	11	25	,	,	PUNCT
ejpam-5024	11	26	chemical	chemical	NOUN
ejpam-5024	11	27	kinetics	kinetic	NOUN
ejpam-5024	11	28	,	,	PUNCT
ejpam-5024	11	29	ecology	ecology	NOUN
ejpam-5024	11	30	,	,	PUNCT
ejpam-5024	11	31	and	and	CCONJ
ejpam-5024	11	32	control	control	NOUN
ejpam-5024	11	33	theory	theory	NOUN
ejpam-5024	11	34	in	in	ADP
ejpam-5024	11	35	financial	financial	ADJ
ejpam-5024	11	36	mathematics	mathematic	NOUN
ejpam-5024	11	37	,	,	PUNCT
ejpam-5024	11	38	space	space	NOUN
ejpam-5024	11	39	systems	system	NOUN
ejpam-5024	11	40	,	,	PUNCT
ejpam-5024	11	41	and	and	CCONJ
ejpam-5024	11	42	industrial	industrial	ADJ
ejpam-5024	11	43	mathematics	mathematic	NOUN
ejpam-5024	11	44	.	.	PUNCT
ejpam-5024	12	1	see	see	VERB
ejpam-5024	12	2	[	[	X
ejpam-5024	12	3	12][10][15	12][10][15	NUM
ejpam-5024	12	4	]	]	X
ejpam-5024	12	5	.	.	PUNCT
ejpam-5024	13	1	recently	recently	ADV
ejpam-5024	13	2	,	,	PUNCT
ejpam-5024	13	3	the	the	DET
ejpam-5024	13	4	authors	author	NOUN
ejpam-5024	13	5	have	have	AUX
ejpam-5024	13	6	used	use	VERB
ejpam-5024	13	7	various	various	ADJ
ejpam-5024	13	8	methods	method	NOUN
ejpam-5024	13	9	to	to	PART
ejpam-5024	13	10	display	display	VERB
ejpam-5024	13	11	the	the	DET
ejpam-5024	13	12	numerical	numerical	ADJ
ejpam-5024	13	13	or	or	CCONJ
ejpam-5024	13	14	analytical	analytical	ADJ
ejpam-5024	13	15	solutions	solution	NOUN
ejpam-5024	13	16	of	of	ADP
ejpam-5024	13	17	ides	ide	NOUN
ejpam-5024	13	18	.	.	PUNCT
ejpam-5024	14	1	therefore	therefore	ADV
ejpam-5024	14	2	,	,	PUNCT
ejpam-5024	14	3	many	many	ADJ
ejpam-5024	14	4	authors	author	NOUN
ejpam-5024	14	5	worked	work	VERB
ejpam-5024	14	6	on	on	ADP
ejpam-5024	14	7	semianalytical	semianalytical	ADJ
ejpam-5024	14	8	methods	method	NOUN
ejpam-5024	14	9	such	such	ADJ
ejpam-5024	14	10	as	as	ADP
ejpam-5024	14	11	sequential	sequential	ADJ
ejpam-5024	14	12	taylor	taylor	PROPN
ejpam-5024	14	13	expansion	expansion	NOUN
ejpam-5024	14	14	method	method	NOUN
ejpam-5024	14	15	,	,	PUNCT
ejpam-5024	14	16	see	see	VERB
ejpam-5024	14	17	[	[	X
ejpam-5024	14	18	2][13	2][13	NOUN
ejpam-5024	14	19	]	]	PUNCT
ejpam-5024	14	20	,	,	PUNCT
ejpam-5024	14	21	bessel	bessel	ADJ
ejpam-5024	14	22	collocation	collocation	NOUN
ejpam-5024	14	23	method	method	NOUN
ejpam-5024	14	24	,	,	PUNCT
ejpam-5024	14	25	see[17	see[17	PROPN
ejpam-5024	14	26	]	]	PUNCT
ejpam-5024	14	27	,	,	PUNCT
ejpam-5024	14	28	the	the	DET
ejpam-5024	14	29	variational	variational	ADJ
ejpam-5024	14	30	iteration	iteration	NOUN
ejpam-5024	14	31	method	method	NOUN
ejpam-5024	14	32	,	,	PUNCT
ejpam-5024	14	33	see[14	see[14	PROPN
ejpam-5024	14	34	]	]	PUNCT
ejpam-5024	14	35	,	,	PUNCT
ejpam-5024	14	36	haar	haar	PROPN
ejpam-5024	14	37	functions	function	NOUN
ejpam-5024	14	38	method	method	NOUN
ejpam-5024	14	39	,	,	PUNCT
ejpam-5024	14	40	see[5][3	see[5][3	PROPN
ejpam-5024	14	41	]	]	X
ejpam-5024	14	42	,	,	PUNCT
ejpam-5024	14	43	legendre	legendre	PROPN
ejpam-5024	14	44	-	-	PUNCT
ejpam-5024	14	45	spectral	spectral	ADJ
ejpam-5024	14	46	method	method	NOUN
ejpam-5024	14	47	,	,	PUNCT
ejpam-5024	14	48	see[16	see[16	PROPN
ejpam-5024	14	49	]	]	PUNCT
ejpam-5024	15	1	[	[	X
ejpam-5024	15	2	11	11	NUM
ejpam-5024	15	3	]	]	PUNCT
ejpam-5024	15	4	,	,	PUNCT
ejpam-5024	15	5	multi	multi	ADJ
ejpam-5024	15	6	-	-	ADJ
ejpam-5024	15	7	wave	wave	ADJ
ejpam-5024	15	8	legendre	legendre	PROPN
ejpam-5024	15	9	method	method	PROPN
ejpam-5024	15	10	,	,	PUNCT
ejpam-5024	15	11	see	see	VERB
ejpam-5024	15	12	[	[	X
ejpam-5024	15	13	9	9	NUM
ejpam-5024	15	14	]	]	PUNCT
ejpam-5024	15	15	,	,	PUNCT
ejpam-5024	15	16	legendre	legendre	PROPN
ejpam-5024	15	17	matrix	matrix	NOUN
ejpam-5024	15	18	method	method	NOUN
ejpam-5024	15	19	,	,	PUNCT
ejpam-5024	15	20	see	see	VERB
ejpam-5024	15	21	[	[	X
ejpam-5024	15	22	18	18	NUM
ejpam-5024	15	23	]	]	PUNCT
ejpam-5024	15	24	and	and	CCONJ
ejpam-5024	15	25	differential	differential	ADJ
ejpam-5024	15	26	transform	transform	NOUN
ejpam-5024	15	27	method	method	NOUN
ejpam-5024	15	28	,	,	PUNCT
ejpam-5024	15	29	see	see	VERB
ejpam-5024	15	30	[	[	X
ejpam-5024	15	31	4	4	NUM
ejpam-5024	15	32	]	]	PUNCT
ejpam-5024	15	33	.	.	PUNCT
ejpam-5024	16	1	in	in	ADP
ejpam-5024	16	2	this	this	DET
ejpam-5024	16	3	article	article	NOUN
ejpam-5024	16	4	,	,	PUNCT
ejpam-5024	16	5	we	we	PRON
ejpam-5024	16	6	study	study	VERB
ejpam-5024	16	7	the	the	DET
ejpam-5024	16	8	numerical	numerical	ADJ
ejpam-5024	16	9	solutions	solution	NOUN
ejpam-5024	16	10	for	for	ADP
ejpam-5024	16	11	ides	ide	NOUN
ejpam-5024	16	12	of	of	ADP
ejpam-5024	16	13	order	order	NOUN
ejpam-5024	16	14	two	two	NUM
ejpam-5024	16	15	.	.	PUNCT
ejpam-5024	17	1	∗corresponding	∗corresponde	VERB
ejpam-5024	17	2	author	author	NOUN
ejpam-5024	17	3	.	.	PUNCT
ejpam-5024	18	1	doi	doi	NOUN
ejpam-5024	18	2	:	:	PUNCT
ejpam-5024	18	3	https://doi.org/10.29020/nybg.ejpam.v17i1.5024	https://doi.org/10.29020/nybg.ejpam.v17i1.5024	NOUN
ejpam-5024	18	4	email	email	NOUN
ejpam-5024	18	5	addresses	address	VERB
ejpam-5024	18	6	:	:	PUNCT
ejpam-5024	18	7	fmharbi@uqu.edu.sa	fmharbi@uqu.edu.sa	PROPN
ejpam-5024	18	8	(	(	PUNCT
ejpam-5024	18	9	f.	f.	PROPN
ejpam-5024	18	10	m.	m.	PROPN
ejpam-5024	18	11	alharbi	alharbi	PROPN
ejpam-5024	18	12	)	)	PUNCT
ejpam-5024	18	13	,	,	PUNCT
ejpam-5024	18	14	sharifah.althubiti10@gmail.com	sharifah.althubiti10@gmail.com	X
ejpam-5024	18	15	(	(	PUNCT
ejpam-5024	18	16	s.	s.	PROPN
ejpam-5024	18	17	s.	s.	PROPN
ejpam-5024	18	18	althubiti	althubiti	PROPN
ejpam-5024	18	19	)	)	PUNCT
ejpam-5024	18	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5024	19	1	286	286	NUM
ejpam-5024	19	2	©	©	ADP
ejpam-5024	19	3	2024	2024	NUM
ejpam-5024	19	4	ejpam	ejpam	NOUN
ejpam-5024	19	5	all	all	DET
ejpam-5024	19	6	rights	right	NOUN
ejpam-5024	19	7	reserved	reserve	VERB
ejpam-5024	19	8	.	.	PUNCT
ejpam-5024	20	1	f.	f.	PROPN
ejpam-5024	20	2	m.	m.	PROPN
ejpam-5024	20	3	alharbi	alharbi	PROPN
ejpam-5024	20	4	,	,	PUNCT
ejpam-5024	20	5	s.	s.	PROPN
ejpam-5024	20	6	s.	s.	PROPN
ejpam-5024	20	7	althubiti	althubiti	PROPN
ejpam-5024	20	8	/	/	SYM
ejpam-5024	20	9	eur	eur	PROPN
ejpam-5024	20	10	.	.	PUNCT
ejpam-5024	21	1	j.	j.	PROPN
ejpam-5024	21	2	pure	pure	PROPN
ejpam-5024	21	3	appl	appl	PROPN
ejpam-5024	21	4	.	.	PROPN
ejpam-5024	21	5	math	math	PROPN
ejpam-5024	21	6	,	,	PUNCT
ejpam-5024	21	7	17	17	NUM
ejpam-5024	21	8	(	(	PUNCT
ejpam-5024	21	9	1	1	NUM
ejpam-5024	21	10	)	)	PUNCT
ejpam-5024	21	11	(	(	PUNCT
ejpam-5024	21	12	2024	2024	NUM
ejpam-5024	21	13	)	)	PUNCT
ejpam-5024	21	14	,	,	PUNCT
ejpam-5024	21	15	286	286	NUM
ejpam-5024	21	16	-	-	SYM
ejpam-5024	21	17	299	299	NUM
ejpam-5024	21	18	287	287	NUM
ejpam-5024	21	19	2	2	NUM
ejpam-5024	21	20	.	.	PUNCT
ejpam-5024	22	1	formulation	formulation	NOUN
ejpam-5024	22	2	of	of	ADP
ejpam-5024	22	3	the	the	DET
ejpam-5024	22	4	problem	problem	NOUN
ejpam-5024	22	5	consider	consider	VERB
ejpam-5024	22	6	the	the	DET
ejpam-5024	22	7	ide	ide	NOUN
ejpam-5024	22	8	,	,	PUNCT
ejpam-5024	22	9	µy′′(t	µy′′(t	NOUN
ejpam-5024	22	10	)	)	PUNCT
ejpam-5024	23	1	+	+	ADV
ejpam-5024	23	2	b1y	b1y	ADP
ejpam-5024	23	3	′(t	′(t	NOUN
ejpam-5024	23	4	)	)	PUNCT
ejpam-5024	24	1	+	+	NOUN
ejpam-5024	24	2	b2y(t	b2y(t	PROPN
ejpam-5024	24	3	)	)	PUNCT
ejpam-5024	25	1	+	+	CCONJ
ejpam-5024	25	2	∫	∫	PROPN
ejpam-5024	25	3	a	a	DET
ejpam-5024	25	4	0	0	PUNCT
ejpam-5024	25	5	k(t	k(t	NOUN
ejpam-5024	25	6	,	,	PUNCT
ejpam-5024	25	7	τ)y(τ)dτ	τ)y(τ)dτ	NOUN
ejpam-5024	25	8	=	=	SYM
ejpam-5024	25	9	f(t	f(t	PROPN
ejpam-5024	25	10	)	)	PUNCT
ejpam-5024	25	11	(	(	PUNCT
ejpam-5024	25	12	1	1	X
ejpam-5024	25	13	)	)	PUNCT
ejpam-5024	25	14	with	with	ADP
ejpam-5024	25	15	initial	initial	ADJ
ejpam-5024	25	16	conditions	condition	NOUN
ejpam-5024	25	17	:	:	PUNCT
ejpam-5024	25	18	y′(0	y′(0	NOUN
ejpam-5024	25	19	)	)	PUNCT
ejpam-5024	25	20	=	=	PROPN
ejpam-5024	25	21	q1	q1	PROPN
ejpam-5024	25	22	y(0	y(0	PROPN
ejpam-5024	25	23	)	)	PUNCT
ejpam-5024	25	24	=	=	PRON
ejpam-5024	26	1	q0	q0	NOUN
ejpam-5024	26	2	(	(	PUNCT
ejpam-5024	26	3	2	2	NUM
ejpam-5024	26	4	)	)	PUNCT
ejpam-5024	26	5	where	where	SCONJ
ejpam-5024	26	6	:	:	PUNCT
ejpam-5024	26	7	y′′(t	y′′(t	VERB
ejpam-5024	26	8	)	)	PUNCT
ejpam-5024	26	9	=	=	SYM
ejpam-5024	26	10	d2y	d2y	PROPN
ejpam-5024	26	11	dt2	dt2	PROPN
ejpam-5024	26	12	and	and	CCONJ
ejpam-5024	26	13	y(t	y(t	NUM
ejpam-5024	26	14	)	)	PUNCT
ejpam-5024	26	15	is	be	AUX
ejpam-5024	26	16	the	the	DET
ejpam-5024	26	17	unknown	unknown	ADJ
ejpam-5024	26	18	function	function	NOUN
ejpam-5024	26	19	in	in	ADP
ejpam-5024	26	20	the	the	DET
ejpam-5024	26	21	hilbert	hilbert	NOUN
ejpam-5024	26	22	space	space	NOUN
ejpam-5024	26	23	and	and	CCONJ
ejpam-5024	26	24	it	it	PRON
ejpam-5024	26	25	is	be	AUX
ejpam-5024	26	26	continuous	continuous	ADJ
ejpam-5024	26	27	with	with	ADP
ejpam-5024	26	28	its	its	PRON
ejpam-5024	26	29	derivatives	derivative	NOUN
ejpam-5024	26	30	.	.	PUNCT
ejpam-5024	27	1	the	the	DET
ejpam-5024	27	2	parameters	parameter	NOUN
ejpam-5024	27	3	µ	µ	VERB
ejpam-5024	27	4	may	may	AUX
ejpam-5024	27	5	have	have	VERB
ejpam-5024	27	6	a	a	DET
ejpam-5024	27	7	physical	physical	ADJ
ejpam-5024	27	8	meaning	meaning	NOUN
ejpam-5024	27	9	.	.	PUNCT
ejpam-5024	28	1	the	the	DET
ejpam-5024	28	2	known	know	VERB
ejpam-5024	28	3	function	function	NOUN
ejpam-5024	28	4	f(t	f(t	NOUN
ejpam-5024	28	5	)	)	PUNCT
ejpam-5024	28	6	is	be	AUX
ejpam-5024	28	7	continuous	continuous	ADJ
ejpam-5024	28	8	.	.	PUNCT
ejpam-5024	29	1	the	the	DET
ejpam-5024	29	2	k(t	k(t	PROPN
ejpam-5024	29	3	,	,	PUNCT
ejpam-5024	29	4	τ	τ	X
ejpam-5024	29	5	)	)	PUNCT
ejpam-5024	29	6	is	be	AUX
ejpam-5024	29	7	the	the	DET
ejpam-5024	29	8	ide	ide	NOUN
ejpam-5024	29	9	’s	’s	PART
ejpam-5024	29	10	kernel	kernel	NOUN
ejpam-5024	29	11	which	which	PRON
ejpam-5024	29	12	is	be	AUX
ejpam-5024	29	13	a	a	DET
ejpam-5024	29	14	continuous	continuous	ADJ
ejpam-5024	29	15	function	function	NOUN
ejpam-5024	29	16	or	or	CCONJ
ejpam-5024	29	17	at	at	ADP
ejpam-5024	29	18	least	least	ADJ
ejpam-5024	29	19	satisfies	satisfy	VERB
ejpam-5024	29	20	fredholm	fredholm	NOUN
ejpam-5024	29	21	’s	’s	PART
ejpam-5024	29	22	condition	condition	NOUN
ejpam-5024	29	23	.	.	PUNCT
ejpam-5024	30	1	b1	b1	NOUN
ejpam-5024	30	2	and	and	CCONJ
ejpam-5024	30	3	b2	b2	NOUN
ejpam-5024	30	4	are	be	AUX
ejpam-5024	30	5	known	know	VERB
ejpam-5024	30	6	continuous	continuous	ADJ
ejpam-5024	30	7	functions	function	NOUN
ejpam-5024	30	8	in	in	ADP
ejpam-5024	30	9	the	the	DET
ejpam-5024	30	10	class	class	NOUN
ejpam-5024	30	11	space	space	NOUN
ejpam-5024	30	12	l2[0	l2[0	PROPN
ejpam-5024	30	13	,	,	PUNCT
ejpam-5024	30	14	a	a	X
ejpam-5024	30	15	]	]	X
ejpam-5024	30	16	with	with	ADP
ejpam-5024	30	17	their	their	PRON
ejpam-5024	30	18	derivatives	derivative	NOUN
ejpam-5024	30	19	.	.	PUNCT
ejpam-5024	31	1	to	to	PART
ejpam-5024	31	2	solve	solve	VERB
ejpam-5024	31	3	the	the	DET
ejpam-5024	31	4	ide	ide	NOUN
ejpam-5024	31	5	,	,	PUNCT
ejpam-5024	31	6	we	we	PRON
ejpam-5024	31	7	must	must	AUX
ejpam-5024	31	8	transform	transform	VERB
ejpam-5024	31	9	it	it	PRON
ejpam-5024	31	10	into	into	ADP
ejpam-5024	31	11	a	a	DET
ejpam-5024	31	12	volterra	volterra	NOUN
ejpam-5024	31	13	-	-	PUNCT
ejpam-5024	31	14	fredholm	fredholm	NOUN
ejpam-5024	31	15	integral	integral	ADJ
ejpam-5024	31	16	equation	equation	NOUN
ejpam-5024	31	17	v	v	NOUN
ejpam-5024	31	18	-	-	PUNCT
ejpam-5024	31	19	fie	fie	NOUN
ejpam-5024	31	20	.	.	PUNCT
ejpam-5024	32	1	then	then	ADV
ejpam-5024	32	2	the	the	DET
ejpam-5024	32	3	existence	existence	NOUN
ejpam-5024	32	4	of	of	ADP
ejpam-5024	32	5	a	a	DET
ejpam-5024	32	6	unique	unique	ADJ
ejpam-5024	32	7	solution	solution	NOUN
ejpam-5024	32	8	of	of	ADP
ejpam-5024	32	9	the	the	DET
ejpam-5024	32	10	equation	equation	NOUN
ejpam-5024	32	11	(	(	PUNCT
ejpam-5024	32	12	2.1	2.1	NUM
ejpam-5024	32	13	)	)	PUNCT
ejpam-5024	32	14	under	under	ADP
ejpam-5024	32	15	the	the	DET
ejpam-5024	32	16	given	give	VERB
ejpam-5024	32	17	conditions	condition	NOUN
ejpam-5024	32	18	(	(	PUNCT
ejpam-5024	32	19	2.2	2.2	NUM
ejpam-5024	32	20	)	)	PUNCT
ejpam-5024	32	21	is	be	AUX
ejpam-5024	32	22	provided	provide	VERB
ejpam-5024	32	23	.	.	PUNCT
ejpam-5024	33	1	the	the	DET
ejpam-5024	33	2	essential	essential	ADJ
ejpam-5024	33	3	requirements	requirement	NOUN
ejpam-5024	33	4	that	that	PRON
ejpam-5024	33	5	ensure	ensure	VERB
ejpam-5024	33	6	the	the	DET
ejpam-5024	33	7	result	result	NOUN
ejpam-5024	33	8	is	be	AUX
ejpam-5024	33	9	unique	unique	ADJ
ejpam-5024	33	10	.	.	PUNCT
ejpam-5024	34	1	see[1	see[1	X
ejpam-5024	34	2	]	]	PUNCT
ejpam-5024	34	3	.	.	PUNCT
ejpam-5024	35	1	after	after	ADP
ejpam-5024	35	2	that	that	PRON
ejpam-5024	35	3	,	,	PUNCT
ejpam-5024	35	4	by	by	ADP
ejpam-5024	35	5	using	use	VERB
ejpam-5024	35	6	algebraic	algebraic	ADJ
ejpam-5024	35	7	techniques	technique	NOUN
ejpam-5024	35	8	,	,	PUNCT
ejpam-5024	35	9	we	we	PRON
ejpam-5024	35	10	reduce	reduce	VERB
ejpam-5024	35	11	the	the	DET
ejpam-5024	35	12	v	v	NOUN
ejpam-5024	35	13	-	-	PUNCT
ejpam-5024	35	14	fie	fie	NOUN
ejpam-5024	35	15	to	to	ADP
ejpam-5024	35	16	an	an	DET
ejpam-5024	35	17	aliner	aliner	NOUN
ejpam-5024	35	18	system	system	NOUN
ejpam-5024	35	19	of	of	ADP
ejpam-5024	35	20	fredholm	fredholm	ADJ
ejpam-5024	35	21	integral	integral	ADJ
ejpam-5024	35	22	equation	equation	NOUN
ejpam-5024	35	23	sfies	sfie	NOUN
ejpam-5024	35	24	.	.	PUNCT
ejpam-5024	36	1	the	the	DET
ejpam-5024	36	2	collocation	collocation	NOUN
ejpam-5024	36	3	and	and	CCONJ
ejpam-5024	36	4	galerkin	galerkin	ADJ
ejpam-5024	36	5	methods	method	NOUN
ejpam-5024	36	6	are	be	AUX
ejpam-5024	36	7	used	use	VERB
ejpam-5024	36	8	to	to	PART
ejpam-5024	36	9	generate	generate	VERB
ejpam-5024	36	10	a	a	DET
ejpam-5024	36	11	numerical	numerical	ADJ
ejpam-5024	36	12	solution	solution	NOUN
ejpam-5024	36	13	of	of	ADP
ejpam-5024	36	14	a	a	DET
ejpam-5024	36	15	linear	linear	ADJ
ejpam-5024	36	16	system	system	NOUN
ejpam-5024	36	17	of	of	ADP
ejpam-5024	36	18	algebraic	algebraic	ADJ
ejpam-5024	36	19	equations	equation	NOUN
ejpam-5024	36	20	.	.	PUNCT
ejpam-5024	37	1	which	which	PRON
ejpam-5024	37	2	are	be	AUX
ejpam-5024	37	3	then	then	ADV
ejpam-5024	37	4	solved	solve	VERB
ejpam-5024	37	5	using	use	VERB
ejpam-5024	37	6	numerical	numerical	ADJ
ejpam-5024	37	7	methods	method	NOUN
ejpam-5024	37	8	.	.	PUNCT
ejpam-5024	38	1	furthermore	furthermore	ADV
ejpam-5024	38	2	,	,	PUNCT
ejpam-5024	38	3	in	in	ADP
ejpam-5024	38	4	each	each	DET
ejpam-5024	38	5	method	method	NOUN
ejpam-5024	38	6	,	,	PUNCT
ejpam-5024	38	7	the	the	DET
ejpam-5024	38	8	estimating	estimate	VERB
ejpam-5024	38	9	error	error	NOUN
ejpam-5024	38	10	is	be	AUX
ejpam-5024	38	11	computed	compute	VERB
ejpam-5024	38	12	and	and	CCONJ
ejpam-5024	38	13	plotted	plot	VERB
ejpam-5024	38	14	.	.	PUNCT
ejpam-5024	39	1	see[7	see[7	PROPN
ejpam-5024	39	2	]	]	PUNCT
ejpam-5024	39	3	assume	assume	VERB
ejpam-5024	39	4	that	that	SCONJ
ejpam-5024	39	5	,	,	PUNCT
ejpam-5024	39	6	y′′(t	y′′(t	VERB
ejpam-5024	39	7	)	)	PUNCT
ejpam-5024	39	8	=	=	SYM
ejpam-5024	39	9	g(t	g(t	PROPN
ejpam-5024	39	10	)	)	PUNCT
ejpam-5024	39	11	(	(	PUNCT
ejpam-5024	39	12	3	3	X
ejpam-5024	39	13	)	)	PUNCT
ejpam-5024	39	14	integrating	integrate	VERB
ejpam-5024	39	15	equation	equation	NOUN
ejpam-5024	39	16	(	(	PUNCT
ejpam-5024	39	17	2.3	2.3	NUM
ejpam-5024	39	18	)	)	PUNCT
ejpam-5024	39	19	two	two	NUM
ejpam-5024	39	20	times	time	NOUN
ejpam-5024	39	21	.	.	PUNCT
ejpam-5024	40	1	to	to	PART
ejpam-5024	40	2	follow	follow	VERB
ejpam-5024	40	3	,	,	PUNCT
ejpam-5024	40	4	y(t	y(t	NUM
ejpam-5024	40	5	)	)	PUNCT
ejpam-5024	41	1	=	=	SYM
ejpam-5024	42	1	∫	∫	PROPN
ejpam-5024	42	2	t	t	PROPN
ejpam-5024	42	3	0	0	NUM
ejpam-5024	42	4	(	(	PUNCT
ejpam-5024	42	5	t−	t−	PROPN
ejpam-5024	42	6	x)g(x)dx+	x)g(x)dx+	PROPN
ejpam-5024	42	7	tq1	tq1	PROPN
ejpam-5024	43	1	+	+	CCONJ
ejpam-5024	43	2	q0	q0	PROPN
ejpam-5024	43	3	(	(	PUNCT
ejpam-5024	43	4	4	4	X
ejpam-5024	43	5	)	)	PUNCT
ejpam-5024	43	6	using	use	VERB
ejpam-5024	43	7	the	the	DET
ejpam-5024	43	8	preceding	precede	VERB
ejpam-5024	43	9	results	result	NOUN
ejpam-5024	43	10	from	from	ADP
ejpam-5024	43	11	equation	equation	NOUN
ejpam-5024	43	12	(	(	PUNCT
ejpam-5024	43	13	2.1	2.1	NUM
ejpam-5024	43	14	)	)	PUNCT
ejpam-5024	43	15	,	,	PUNCT
ejpam-5024	43	16	µg(t	µg(t	ADP
ejpam-5024	43	17	)	)	PUNCT
ejpam-5024	44	1	+	+	CCONJ
ejpam-5024	45	1	∫	∫	PROPN
ejpam-5024	45	2	t	t	NOUN
ejpam-5024	45	3	0	0	NUM
ejpam-5024	45	4	ϕ(t	ϕ(t	PROPN
ejpam-5024	45	5	,	,	PUNCT
ejpam-5024	45	6	x)g(x)dx+	x)g(x)dx+	PROPN
ejpam-5024	45	7	∫	∫	PROPN
ejpam-5024	45	8	a	a	DET
ejpam-5024	45	9	0	0	NUM
ejpam-5024	45	10	ψ(t	ψ(t	NOUN
ejpam-5024	45	11	,	,	PUNCT
ejpam-5024	45	12	τ)g(x)dx	τ)g(x)dx	NOUN
ejpam-5024	45	13	=	=	SYM
ejpam-5024	45	14	f	f	PROPN
ejpam-5024	45	15	(	(	PUNCT
ejpam-5024	45	16	t	t	PROPN
ejpam-5024	45	17	)	)	PUNCT
ejpam-5024	45	18	(	(	PUNCT
ejpam-5024	45	19	5	5	NUM
ejpam-5024	45	20	)	)	PUNCT
ejpam-5024	45	21	where	where	SCONJ
ejpam-5024	45	22	,	,	PUNCT
ejpam-5024	45	23	ϕ(t	ϕ(t	PROPN
ejpam-5024	45	24	,	,	PUNCT
ejpam-5024	45	25	x	x	X
ejpam-5024	45	26	)	)	PUNCT
ejpam-5024	45	27	=	=	SYM
ejpam-5024	45	28	b1	b1	NOUN
ejpam-5024	45	29	+	+	CCONJ
ejpam-5024	45	30	(	(	PUNCT
ejpam-5024	45	31	t−	t−	PROPN
ejpam-5024	45	32	x)b2	x)b2	PROPN
ejpam-5024	45	33	(	(	PUNCT
ejpam-5024	45	34	6	6	NUM
ejpam-5024	45	35	)	)	PUNCT
ejpam-5024	45	36	ψ(t	ψ(t	PROPN
ejpam-5024	45	37	,	,	PUNCT
ejpam-5024	45	38	τ	τ	X
ejpam-5024	45	39	)	)	PUNCT
ejpam-5024	45	40	=	=	SYM
ejpam-5024	46	1	∫	∫	PROPN
ejpam-5024	46	2	t	t	NOUN
ejpam-5024	46	3	0	0	NUM
ejpam-5024	46	4	k(t	k(t	NOUN
ejpam-5024	46	5	,	,	PUNCT
ejpam-5024	46	6	τ)(τ	τ)(τ	PROPN
ejpam-5024	46	7	−	−	PROPN
ejpam-5024	47	1	x)dτ	x)dτ	PROPN
ejpam-5024	47	2	(	(	PUNCT
ejpam-5024	47	3	7	7	NUM
ejpam-5024	47	4	)	)	PUNCT
ejpam-5024	47	5	f	f	NOUN
ejpam-5024	47	6	(	(	PUNCT
ejpam-5024	47	7	x	x	X
ejpam-5024	47	8	)	)	PUNCT
ejpam-5024	48	1	=	=	SYM
ejpam-5024	48	2	f(x)−	f(x)−	PROPN
ejpam-5024	49	1	[	[	X
ejpam-5024	49	2	b1q1	b1q1	X
ejpam-5024	49	3	+	+	NOUN
ejpam-5024	49	4	b2tq1	b2tq1	NOUN
ejpam-5024	49	5	+	+	NOUN
ejpam-5024	49	6	b2q0]−	b2q0]−	NOUN
ejpam-5024	49	7	[	[	PUNCT
ejpam-5024	49	8	∫	∫	PROPN
ejpam-5024	49	9	a	a	DET
ejpam-5024	49	10	0	0	NUM
ejpam-5024	49	11	k(t	k(t	NOUN
ejpam-5024	49	12	,	,	PUNCT
ejpam-5024	49	13	τ)(tq1	τ)(tq1	PUNCT
ejpam-5024	50	1	+	+	CCONJ
ejpam-5024	50	2	q0)dτ	q0)dτ	NOUN
ejpam-5024	50	3	]	]	X
ejpam-5024	50	4	(	(	PUNCT
ejpam-5024	50	5	8)	8)	NUM
ejpam-5024	50	6	in	in	ADP
ejpam-5024	50	7	the	the	DET
ejpam-5024	50	8	space	space	NOUN
ejpam-5024	50	9	l2[0	l2[0	PROPN
ejpam-5024	50	10	,	,	PUNCT
ejpam-5024	50	11	a	a	DET
ejpam-5024	50	12	]	]	X
ejpam-5024	50	13	×	×	NOUN
ejpam-5024	50	14	c[0	c[0	PROPN
ejpam-5024	50	15	,	,	PUNCT
ejpam-5024	50	16	t	t	X
ejpam-5024	50	17	]	]	PUNCT
ejpam-5024	50	18	,	,	PUNCT
ejpam-5024	50	19	t	t	X
ejpam-5024	50	20	<	<	X
ejpam-5024	50	21	∞	∞	PROPN
ejpam-5024	50	22	t	t	PROPN
ejpam-5024	50	23	,	,	PUNCT
ejpam-5024	50	24	τ	τ	PROPN
ejpam-5024	50	25	∈	∈	PROPN
ejpam-5024	50	26	[	[	X
ejpam-5024	50	27	0	0	NUM
ejpam-5024	50	28	,	,	PUNCT
ejpam-5024	50	29	a	a	DET
ejpam-5024	50	30	]	]	X
ejpam-5024	50	31	,	,	PUNCT
ejpam-5024	50	32	equation	equation	NOUN
ejpam-5024	50	33	(	(	PUNCT
ejpam-5024	50	34	2.5	2.5	NUM
ejpam-5024	50	35	)	)	PUNCT
ejpam-5024	50	36	is	be	AUX
ejpam-5024	50	37	known	know	VERB
ejpam-5024	50	38	as	as	ADP
ejpam-5024	50	39	the	the	DET
ejpam-5024	50	40	v	v	NOUN
ejpam-5024	50	41	-	-	PUNCT
ejpam-5024	50	42	fie	fie	NOUN
ejpam-5024	50	43	.	.	PUNCT
ejpam-5024	51	1	where	where	SCONJ
ejpam-5024	51	2	the	the	DET
ejpam-5024	51	3	fredholm	fredholm	ADJ
ejpam-5024	51	4	integral	integral	ADJ
ejpam-5024	51	5	term	term	NOUN
ejpam-5024	51	6	is	be	AUX
ejpam-5024	51	7	positive	positive	ADJ
ejpam-5024	51	8	and	and	CCONJ
ejpam-5024	51	9	continuous	continuous	ADJ
ejpam-5024	51	10	kernel	kernel	NOUN
ejpam-5024	51	11	ψ(t	ψ(t	PROPN
ejpam-5024	51	12	,	,	PUNCT
ejpam-5024	51	13	τ	τ	X
ejpam-5024	51	14	)	)	PUNCT
ejpam-5024	51	15	.	.	PUNCT
ejpam-5024	52	1	while	while	SCONJ
ejpam-5024	52	2	the	the	DET
ejpam-5024	52	3	volterra	volterra	NOUN
ejpam-5024	52	4	integral	integral	ADJ
ejpam-5024	52	5	term	term	NOUN
ejpam-5024	52	6	is	be	AUX
ejpam-5024	52	7	considered	consider	VERB
ejpam-5024	52	8	in	in	ADP
ejpam-5024	52	9	time	time	NOUN
ejpam-5024	52	10	with	with	ADP
ejpam-5024	52	11	a	a	DET
ejpam-5024	52	12	positive	positive	ADJ
ejpam-5024	52	13	continuous	continuous	ADJ
ejpam-5024	52	14	kernel	kernel	NOUN
ejpam-5024	52	15	ϕ(t	ϕ(t	PROPN
ejpam-5024	52	16	,	,	PUNCT
ejpam-5024	52	17	x	x	NOUN
ejpam-5024	52	18	)	)	PUNCT
ejpam-5024	52	19	for	for	ADP
ejpam-5024	52	20	all	all	DET
ejpam-5024	52	21	t	t	PROPN
ejpam-5024	52	22	,	,	PUNCT
ejpam-5024	52	23	x	x	X
ejpam-5024	52	24	∈	∈	PROPN
ejpam-5024	53	1	[	[	X
ejpam-5024	53	2	0	0	NUM
ejpam-5024	53	3	,	,	PUNCT
ejpam-5024	53	4	t	t	X
ejpam-5024	53	5	]	]	PUNCT
ejpam-5024	53	6	,	,	PUNCT
ejpam-5024	53	7	t	t	X
ejpam-5024	53	8	<	<	X
ejpam-5024	53	9	∞.	∞.	PROPN
ejpam-5024	53	10	the	the	DET
ejpam-5024	53	11	free	free	ADJ
ejpam-5024	53	12	term	term	NOUN
ejpam-5024	53	13	f	f	PROPN
ejpam-5024	53	14	(	(	PUNCT
ejpam-5024	53	15	x	x	PROPN
ejpam-5024	53	16	,	,	PUNCT
ejpam-5024	53	17	t	t	PROPN
ejpam-5024	53	18	)	)	PUNCT
ejpam-5024	53	19	is	be	AUX
ejpam-5024	53	20	the	the	DET
ejpam-5024	53	21	surface	surface	NOUN
ejpam-5024	53	22	integral	integral	ADJ
ejpam-5024	53	23	equation	equation	NOUN
ejpam-5024	53	24	(	(	PUNCT
ejpam-5024	53	25	2.5	2.5	NUM
ejpam-5024	53	26	)	)	PUNCT
ejpam-5024	53	27	and	and	CCONJ
ejpam-5024	53	28	it	it	PRON
ejpam-5024	53	29	is	be	AUX
ejpam-5024	53	30	a	a	DET
ejpam-5024	53	31	known	know	VERB
ejpam-5024	53	32	continuous	continuous	ADJ
ejpam-5024	53	33	function	function	NOUN
ejpam-5024	53	34	in	in	ADP
ejpam-5024	53	35	the	the	DET
ejpam-5024	53	36	space	space	NOUN
ejpam-5024	53	37	l2[a	l2[a	NOUN
ejpam-5024	53	38	,	,	PUNCT
ejpam-5024	53	39	b	b	X
ejpam-5024	53	40	]	]	X
ejpam-5024	53	41	f.	f.	PROPN
ejpam-5024	53	42	m.	m.	PROPN
ejpam-5024	53	43	alharbi	alharbi	PROPN
ejpam-5024	53	44	,	,	PUNCT
ejpam-5024	53	45	s.	s.	PROPN
ejpam-5024	53	46	s.	s.	PROPN
ejpam-5024	53	47	althubiti	althubiti	PROPN
ejpam-5024	53	48	/	/	SYM
ejpam-5024	53	49	eur	eur	PROPN
ejpam-5024	53	50	.	.	PUNCT
ejpam-5024	54	1	j.	j.	PROPN
ejpam-5024	54	2	pure	pure	PROPN
ejpam-5024	54	3	appl	appl	PROPN
ejpam-5024	54	4	.	.	PROPN
ejpam-5024	54	5	math	math	PROPN
ejpam-5024	54	6	,	,	PUNCT
ejpam-5024	54	7	17	17	NUM
ejpam-5024	54	8	(	(	PUNCT
ejpam-5024	54	9	1	1	NUM
ejpam-5024	54	10	)	)	PUNCT
ejpam-5024	54	11	(	(	PUNCT
ejpam-5024	54	12	2024	2024	NUM
ejpam-5024	54	13	)	)	PUNCT
ejpam-5024	54	14	,	,	PUNCT
ejpam-5024	54	15	286	286	NUM
ejpam-5024	54	16	-	-	SYM
ejpam-5024	54	17	299	299	NUM
ejpam-5024	54	18	288	288	NUM
ejpam-5024	54	19	2.1	2.1	NUM
ejpam-5024	54	20	.	.	PUNCT
ejpam-5024	55	1	the	the	DET
ejpam-5024	55	2	main	main	ADJ
ejpam-5024	55	3	conditions	condition	NOUN
ejpam-5024	55	4	in	in	ADP
ejpam-5024	55	5	order	order	NOUN
ejpam-5024	55	6	to	to	PART
ejpam-5024	55	7	ensure	ensure	VERB
ejpam-5024	55	8	a	a	DET
ejpam-5024	55	9	unique	unique	ADJ
ejpam-5024	55	10	solution	solution	NOUN
ejpam-5024	55	11	to	to	ADP
ejpam-5024	55	12	equation(2.1	equation(2.1	NOUN
ejpam-5024	55	13	)	)	PUNCT
ejpam-5024	55	14	,	,	PUNCT
ejpam-5024	55	15	we	we	PRON
ejpam-5024	55	16	assume	assume	VERB
ejpam-5024	55	17	the	the	DET
ejpam-5024	55	18	following	follow	VERB
ejpam-5024	55	19	conditions	condition	NOUN
ejpam-5024	55	20	must	must	AUX
ejpam-5024	55	21	be	be	AUX
ejpam-5024	55	22	satisfies	satisfie	NOUN
ejpam-5024	55	23	:	:	PUNCT
ejpam-5024	55	24	(	(	PUNCT
ejpam-5024	55	25	i	i	NOUN
ejpam-5024	55	26	)	)	PUNCT
ejpam-5024	55	27	the	the	DET
ejpam-5024	55	28	kernel	kernel	NOUN
ejpam-5024	55	29	of	of	ADP
ejpam-5024	55	30	the	the	DET
ejpam-5024	55	31	integral	integral	ADJ
ejpam-5024	55	32	term	term	NOUN
ejpam-5024	55	33	k(t	k(t	PROPN
ejpam-5024	55	34	,	,	PUNCT
ejpam-5024	55	35	τ	τ	X
ejpam-5024	55	36	)	)	PUNCT
ejpam-5024	55	37	must	must	AUX
ejpam-5024	55	38	be	be	AUX
ejpam-5024	55	39	continuous	continuous	ADJ
ejpam-5024	55	40	or	or	CCONJ
ejpam-5024	55	41	at	at	ADP
ejpam-5024	55	42	least	least	ADJ
ejpam-5024	55	43	satisfy	satisfy	VERB
ejpam-5024	55	44	the	the	DET
ejpam-5024	55	45	fredholm	fredholm	NOUN
ejpam-5024	55	46	condition	condition	NOUN
ejpam-5024	55	47	.	.	PUNCT
ejpam-5024	56	1	|	|	ADV
ejpam-5024	56	2	∫	∫	PROPN
ejpam-5024	56	3	a	a	DET
ejpam-5024	56	4	0	0	NUM
ejpam-5024	56	5	∫	∫	NOUN
ejpam-5024	57	1	a	a	DET
ejpam-5024	57	2	0	0	NUM
ejpam-5024	57	3	k2(t	k2(t	PROPN
ejpam-5024	57	4	,	,	PUNCT
ejpam-5024	57	5	τ)dtdτ	τ)dtdτ	PUNCT
ejpam-5024	57	6	|	|	ADV
ejpam-5024	57	7	1	1	NUM
ejpam-5024	57	8	2≤	2≤	NUM
ejpam-5024	57	9	α	α	PROPN
ejpam-5024	57	10	α	α	PROPN
ejpam-5024	57	11	is	be	AUX
ejpam-5024	57	12	constant	constant	ADJ
ejpam-5024	57	13	.	.	PUNCT
ejpam-5024	58	1	(	(	PUNCT
ejpam-5024	58	2	ii	ii	NOUN
ejpam-5024	58	3	)	)	PUNCT
ejpam-5024	58	4	for	for	ADP
ejpam-5024	58	5	the	the	DET
ejpam-5024	58	6	constants	constant	NOUN
ejpam-5024	58	7	a1	a1	NOUN
ejpam-5024	58	8	,	,	PUNCT
ejpam-5024	58	9	a2	a2	PROPN
ejpam-5024	58	10	the	the	DET
ejpam-5024	58	11	given	give	VERB
ejpam-5024	58	12	continuous	continuous	ADJ
ejpam-5024	58	13	functions	function	NOUN
ejpam-5024	58	14	b1(t	b1(t	NOUN
ejpam-5024	58	15	)	)	PUNCT
ejpam-5024	58	16	,	,	PUNCT
ejpam-5024	58	17	b2(t	b2(t	PROPN
ejpam-5024	58	18	)	)	PUNCT
ejpam-5024	58	19	satisfies	satisfy	VERB
ejpam-5024	58	20	the	the	DET
ejpam-5024	58	21	following	follow	VERB
ejpam-5024	58	22	conditions	condition	NOUN
ejpam-5024	58	23	:	:	PUNCT
ejpam-5024	58	24	|	|	ADV
ejpam-5024	58	25	b1(t	b1(t	SYM
ejpam-5024	58	26	)	)	PUNCT
ejpam-5024	58	27	|≤	|≤	PROPN
ejpam-5024	58	28	a1	a1	NOUN
ejpam-5024	58	29	,	,	PUNCT
ejpam-5024	58	30	|	|	ADV
ejpam-5024	58	31	b2(t	b2(t	NOUN
ejpam-5024	58	32	)	)	PUNCT
ejpam-5024	58	33	|≤	|≤	PROPN
ejpam-5024	58	34	a2	a2	PROPN
ejpam-5024	58	35	(	(	PUNCT
ejpam-5024	58	36	iii	iii	NOUN
ejpam-5024	58	37	)	)	PUNCT
ejpam-5024	58	38	the	the	DET
ejpam-5024	58	39	norm	norm	NOUN
ejpam-5024	58	40	of	of	ADP
ejpam-5024	58	41	surtace	surtace	ADJ
ejpam-5024	58	42	function	function	PROPN
ejpam-5024	58	43	f(x	f(x	PROPN
ejpam-5024	58	44	)	)	PUNCT
ejpam-5024	58	45	is	be	AUX
ejpam-5024	58	46	defined	define	VERB
ejpam-5024	58	47	as	as	ADP
ejpam-5024	58	48	:	:	PUNCT
ejpam-5024	58	49	∥	∥	PROPN
ejpam-5024	58	50	f(x	f(x	PROPN
ejpam-5024	58	51	)	)	PUNCT
ejpam-5024	58	52	∥=	∥=	NOUN
ejpam-5024	58	53	[	[	PUNCT
ejpam-5024	58	54	∫	∫	PROPN
ejpam-5024	58	55	a	a	DET
ejpam-5024	58	56	0	0	NUM
ejpam-5024	58	57	f2(x)dx	f2(x)dx	ADJ
ejpam-5024	58	58	]	]	X
ejpam-5024	58	59	1	1	NUM
ejpam-5024	58	60	2	2	NUM
ejpam-5024	58	61	≤	≤	NUM
ejpam-5024	58	62	γ	γ	NOUN
ejpam-5024	58	63	,	,	PUNCT
ejpam-5024	58	64	γ	γ	PROPN
ejpam-5024	58	65	is	be	AUX
ejpam-5024	58	66	constant	constant	ADJ
ejpam-5024	58	67	.	.	PUNCT
ejpam-5024	59	1	(	(	PUNCT
ejpam-5024	59	2	iv	iv	X
ejpam-5024	59	3	)	)	PUNCT
ejpam-5024	59	4	the	the	DET
ejpam-5024	59	5	unknown	unknown	ADJ
ejpam-5024	59	6	function	function	NOUN
ejpam-5024	59	7	y(t	y(t	PROPN
ejpam-5024	59	8	)	)	PUNCT
ejpam-5024	59	9	in	in	ADP
ejpam-5024	59	10	the	the	DET
ejpam-5024	59	11	hilbert	hilbert	PROPN
ejpam-5024	59	12	space	space	PROPN
ejpam-5024	59	13	l2[0	l2[0	PROPN
ejpam-5024	59	14	,	,	PUNCT
ejpam-5024	59	15	a	a	PRON
ejpam-5024	59	16	]	]	PUNCT
ejpam-5024	59	17	behaves	behave	NOUN
ejpam-5024	59	18	as	as	ADP
ejpam-5024	59	19	the	the	DET
ejpam-5024	59	20	given	give	VERB
ejpam-5024	59	21	function	function	NOUN
ejpam-5024	59	22	f(t	f(t	NOUN
ejpam-5024	59	23	)	)	PUNCT
ejpam-5024	59	24	2.2	2.2	NUM
ejpam-5024	59	25	.	.	PUNCT
ejpam-5024	60	1	the	the	DET
ejpam-5024	60	2	normality	normality	NOUN
ejpam-5024	60	3	and	and	CCONJ
ejpam-5024	60	4	continuity	continuity	NOUN
ejpam-5024	60	5	of	of	ADP
ejpam-5024	60	6	the	the	DET
ejpam-5024	60	7	integral	integral	ADJ
ejpam-5024	60	8	operator	operator	NOUN
ejpam-5024	60	9	:	:	PUNCT
ejpam-5024	60	10	theorem	theorem	NOUN
ejpam-5024	60	11	1	1	NUM
ejpam-5024	60	12	.	.	PUNCT
ejpam-5024	61	1	the	the	DET
ejpam-5024	61	2	integral	integral	ADJ
ejpam-5024	61	3	equation	equation	NOUN
ejpam-5024	61	4	(	(	PUNCT
ejpam-5024	61	5	2.1	2.1	NUM
ejpam-5024	61	6	)	)	PUNCT
ejpam-5024	61	7	under	under	ADP
ejpam-5024	61	8	the	the	DET
ejpam-5024	61	9	previous	previous	ADJ
ejpam-5024	61	10	conditions	condition	NOUN
ejpam-5024	61	11	(	(	PUNCT
ejpam-5024	61	12	i)-(iv	i)-(iv	X
ejpam-5024	61	13	)	)	PUNCT
ejpam-5024	61	14	has	have	VERB
ejpam-5024	61	15	a	a	DET
ejpam-5024	61	16	distinct	distinct	ADJ
ejpam-5024	61	17	solution	solution	NOUN
ejpam-5024	61	18	.	.	PUNCT
ejpam-5024	62	1	proof	proof	NOUN
ejpam-5024	62	2	:	:	PUNCT
ejpam-5024	62	3	to	to	PART
ejpam-5024	62	4	prove	prove	VERB
ejpam-5024	62	5	the	the	DET
ejpam-5024	62	6	existence	existence	NOUN
ejpam-5024	62	7	of	of	ADP
ejpam-5024	62	8	a	a	DET
ejpam-5024	62	9	unique	unique	ADJ
ejpam-5024	62	10	solution	solution	NOUN
ejpam-5024	62	11	of	of	ADP
ejpam-5024	62	12	equation	equation	NOUN
ejpam-5024	62	13	(	(	PUNCT
ejpam-5024	62	14	2.5	2.5	NUM
ejpam-5024	62	15	)	)	PUNCT
ejpam-5024	62	16	,	,	PUNCT
ejpam-5024	62	17	we	we	PRON
ejpam-5024	62	18	use	use	VERB
ejpam-5024	62	19	the	the	DET
ejpam-5024	62	20	normality	normality	NOUN
ejpam-5024	62	21	and	and	CCONJ
ejpam-5024	62	22	continuity	continuity	NOUN
ejpam-5024	62	23	of	of	ADP
ejpam-5024	62	24	the	the	DET
ejpam-5024	62	25	mixed	mixed	ADJ
ejpam-5024	62	26	integral	integral	ADJ
ejpam-5024	62	27	equation	equation	NOUN
ejpam-5024	62	28	.	.	PUNCT
ejpam-5024	63	1	for	for	ADP
ejpam-5024	63	2	this	this	PRON
ejpam-5024	63	3	,	,	PUNCT
ejpam-5024	63	4	the	the	DET
ejpam-5024	63	5	integral	integral	ADJ
ejpam-5024	63	6	equation	equation	NOUN
ejpam-5024	63	7	(	(	PUNCT
ejpam-5024	63	8	2.5	2.5	NUM
ejpam-5024	63	9	)	)	PUNCT
ejpam-5024	63	10	can	can	AUX
ejpam-5024	63	11	be	be	AUX
ejpam-5024	63	12	written	write	VERB
ejpam-5024	63	13	in	in	ADP
ejpam-5024	63	14	the	the	DET
ejpam-5024	63	15	integral	integral	ADJ
ejpam-5024	63	16	operator	operator	NOUN
ejpam-5024	63	17	form	form	NOUN
ejpam-5024	63	18	:	:	PUNCT
ejpam-5024	63	19	w̄g(t	w̄g(t	ADJ
ejpam-5024	63	20	)	)	PUNCT
ejpam-5024	63	21	=	=	SYM
ejpam-5024	63	22	f	f	PROPN
ejpam-5024	63	23	(	(	PUNCT
ejpam-5024	63	24	t	t	PROPN
ejpam-5024	63	25	)	)	PUNCT
ejpam-5024	63	26	+	+	NOUN
ejpam-5024	63	27	wg(t	wg(t	ADJ
ejpam-5024	63	28	)	)	PUNCT
ejpam-5024	63	29	(	(	PUNCT
ejpam-5024	63	30	9	9	NUM
ejpam-5024	63	31	)	)	PUNCT
ejpam-5024	63	32	wg(t	wg(t	NOUN
ejpam-5024	63	33	)	)	PUNCT
ejpam-5024	63	34	=	=	SYM
ejpam-5024	63	35	ψg(x	ψg(x	X
ejpam-5024	63	36	)	)	PUNCT
ejpam-5024	64	1	+	+	CCONJ
ejpam-5024	64	2	ϕg(x	ϕg(x	NUM
ejpam-5024	64	3	)	)	PUNCT
ejpam-5024	64	4	(	(	PUNCT
ejpam-5024	64	5	10	10	NUM
ejpam-5024	64	6	)	)	PUNCT
ejpam-5024	64	7	ψg(t	ψg(t	NOUN
ejpam-5024	64	8	)	)	PUNCT
ejpam-5024	64	9	=	=	SYM
ejpam-5024	65	1	−	−	PROPN
ejpam-5024	65	2	1	1	NUM
ejpam-5024	65	3	µ	µ	X
ejpam-5024	65	4	∫	∫	NOUN
ejpam-5024	65	5	a	a	DET
ejpam-5024	65	6	0	0	NUM
ejpam-5024	66	1	|	|	NOUN
ejpam-5024	66	2	(	(	PUNCT
ejpam-5024	66	3	t−	t−	PROPN
ejpam-5024	66	4	x	x	NOUN
ejpam-5024	66	5	)	)	PUNCT
ejpam-5024	66	6	|	|	ADV
ejpam-5024	66	7	g(x)dx	g(x)dx	VERB
ejpam-5024	66	8	(	(	PUNCT
ejpam-5024	66	9	11	11	NUM
ejpam-5024	66	10	)	)	PUNCT
ejpam-5024	66	11	ϕg(t	ϕg(t	NOUN
ejpam-5024	66	12	)	)	PUNCT
ejpam-5024	67	1	=	=	SYM
ejpam-5024	68	1	−	−	PROPN
ejpam-5024	68	2	1	1	NUM
ejpam-5024	68	3	µ	µ	PRON
ejpam-5024	68	4	∫	∫	PROPN
ejpam-5024	68	5	t	t	NOUN
ejpam-5024	68	6	0	0	NUM
ejpam-5024	69	1	ϕ(t	ϕ(t	NUM
ejpam-5024	69	2	,	,	PUNCT
ejpam-5024	69	3	x)g(x)dx	x)g(x)dx	PROPN
ejpam-5024	69	4	(	(	PUNCT
ejpam-5024	69	5	12	12	NUM
ejpam-5024	69	6	)	)	PUNCT
ejpam-5024	69	7	if	if	SCONJ
ejpam-5024	69	8	conditions	condition	NOUN
ejpam-5024	69	9	(	(	PUNCT
ejpam-5024	69	10	i)-(iii	i)-(iii	NOUN
ejpam-5024	69	11	)	)	PUNCT
ejpam-5024	69	12	are	be	AUX
ejpam-5024	69	13	satisfied	satisfied	ADJ
ejpam-5024	69	14	,	,	PUNCT
ejpam-5024	69	15	then	then	ADV
ejpam-5024	69	16	we	we	PRON
ejpam-5024	69	17	have	have	AUX
ejpam-5024	69	18	respectively	respectively	ADV
ejpam-5024	69	19	found	find	VERB
ejpam-5024	69	20	:	:	PUNCT
ejpam-5024	69	21	(	(	PUNCT
ejpam-5024	69	22	a	a	X
ejpam-5024	69	23	)	)	PUNCT
ejpam-5024	69	24	there	there	PRON
ejpam-5024	69	25	exists	exist	VERB
ejpam-5024	69	26	a	a	DET
ejpam-5024	69	27	constant	constant	ADJ
ejpam-5024	69	28	ωψ	ωψ	NOUN
ejpam-5024	69	29	,	,	PUNCT
ejpam-5024	69	30	such	such	ADJ
ejpam-5024	69	31	that:[∫	that:[∫	NOUN
ejpam-5024	69	32	a	a	DET
ejpam-5024	69	33	0	0	NUM
ejpam-5024	69	34	∫	∫	NOUN
ejpam-5024	69	35	a	a	DET
ejpam-5024	69	36	0	0	PUNCT
ejpam-5024	69	37	ψ2(|t−	ψ2(|t−	SYM
ejpam-5024	69	38	τ	τ	X
ejpam-5024	69	39	|)dτdt	|)dτdt	X
ejpam-5024	69	40	]	]	SYM
ejpam-5024	69	41	1	1	NUM
ejpam-5024	69	42	2	2	NUM
ejpam-5024	69	43	≤	≤	NOUN
ejpam-5024	69	44	ωψ	ωψ	ADP
ejpam-5024	69	45	(	(	PUNCT
ejpam-5024	69	46	13	13	NUM
ejpam-5024	69	47	)	)	PUNCT
ejpam-5024	69	48	f.	f.	PROPN
ejpam-5024	69	49	m.	m.	PROPN
ejpam-5024	69	50	alharbi	alharbi	PROPN
ejpam-5024	69	51	,	,	PUNCT
ejpam-5024	69	52	s.	s.	PROPN
ejpam-5024	69	53	s.	s.	PROPN
ejpam-5024	69	54	althubiti	althubiti	PROPN
ejpam-5024	69	55	/	/	SYM
ejpam-5024	69	56	eur	eur	PROPN
ejpam-5024	69	57	.	.	PUNCT
ejpam-5024	70	1	j.	j.	PROPN
ejpam-5024	70	2	pure	pure	PROPN
ejpam-5024	70	3	appl	appl	PROPN
ejpam-5024	70	4	.	.	PROPN
ejpam-5024	70	5	math	math	PROPN
ejpam-5024	70	6	,	,	PUNCT
ejpam-5024	70	7	17	17	NUM
ejpam-5024	70	8	(	(	PUNCT
ejpam-5024	70	9	1	1	NUM
ejpam-5024	70	10	)	)	PUNCT
ejpam-5024	70	11	(	(	PUNCT
ejpam-5024	70	12	2024	2024	NUM
ejpam-5024	70	13	)	)	PUNCT
ejpam-5024	70	14	,	,	PUNCT
ejpam-5024	70	15	286	286	NUM
ejpam-5024	70	16	-	-	SYM
ejpam-5024	70	17	299	299	NUM
ejpam-5024	70	18	289	289	NUM
ejpam-5024	70	19	to	to	PART
ejpam-5024	70	20	obtain	obtain	VERB
ejpam-5024	70	21	this	this	PRON
ejpam-5024	70	22	,	,	PUNCT
ejpam-5024	70	23	we	we	PRON
ejpam-5024	70	24	take	take	VERB
ejpam-5024	70	25	the	the	DET
ejpam-5024	70	26	norm	norm	NOUN
ejpam-5024	70	27	of	of	ADP
ejpam-5024	70	28	equation	equation	NOUN
ejpam-5024	70	29	(	(	PUNCT
ejpam-5024	70	30	2.7	2.7	NUM
ejpam-5024	70	31	)	)	PUNCT
ejpam-5024	70	32	and	and	CCONJ
ejpam-5024	70	33	apply	apply	VERB
ejpam-5024	70	34	the	the	DET
ejpam-5024	70	35	cauchy	cauchy	PROPN
ejpam-5024	70	36	-	-	PUNCT
ejpam-5024	70	37	schwarz	schwarz	PROPN
ejpam-5024	70	38	inequality	inequality	NOUN
ejpam-5024	70	39	.	.	PUNCT
ejpam-5024	71	1	∥ψ(t	∥ψ(t	PROPN
ejpam-5024	71	2	,	,	PUNCT
ejpam-5024	71	3	τ)∥	τ)∥	PUNCT
ejpam-5024	71	4	≤	≤	NUM
ejpam-5024	71	5	1	1	NUM
ejpam-5024	71	6	µ	µ	SYM
ejpam-5024	71	7	∥∥∥∥∥	∥∥∥∥∥	PROPN
ejpam-5024	71	8	∫	∫	PROPN
ejpam-5024	71	9	a	a	DET
ejpam-5024	71	10	0	0	NUM
ejpam-5024	71	11	(	(	PUNCT
ejpam-5024	71	12	k2(t	k2(t	PROPN
ejpam-5024	71	13	,	,	PUNCT
ejpam-5024	71	14	τ)dτ	τ)dτ	ADJ
ejpam-5024	71	15	)	)	PUNCT
ejpam-5024	71	16	1	1	NUM
ejpam-5024	71	17	2	2	NUM
ejpam-5024	71	18	(	(	PUNCT
ejpam-5024	71	19	∫	∫	PROPN
ejpam-5024	71	20	a	a	PRON
ejpam-5024	71	21	0	0	NUM
ejpam-5024	72	1	(	(	PUNCT
ejpam-5024	72	2	τ	τ	PROPN
ejpam-5024	72	3	−	−	PROPN
ejpam-5024	72	4	x)2dτ	x)2dτ	PROPN
ejpam-5024	72	5	)	)	PUNCT
ejpam-5024	72	6	1	1	NUM
ejpam-5024	72	7	2	2	NUM
ejpam-5024	72	8	∥∥∥∥∥	∥∥∥∥∥	X
ejpam-5024	72	9	(	(	PUNCT
ejpam-5024	72	10	14	14	NUM
ejpam-5024	72	11	)	)	PUNCT
ejpam-5024	72	12	by	by	ADP
ejpam-5024	72	13	using	use	VERB
ejpam-5024	72	14	condition	condition	NOUN
ejpam-5024	72	15	(	(	PUNCT
ejpam-5024	72	16	i	i	NOUN
ejpam-5024	72	17	)	)	PUNCT
ejpam-5024	72	18	,	,	PUNCT
ejpam-5024	72	19	we	we	PRON
ejpam-5024	72	20	get	get	VERB
ejpam-5024	72	21	:	:	PUNCT
ejpam-5024	72	22	∥ψ(t	∥ψ(t	PROPN
ejpam-5024	72	23	,	,	PUNCT
ejpam-5024	72	24	τ)∥	τ)∥	PUNCT
ejpam-5024	72	25	≤	≤	NUM
ejpam-5024	72	26	α	α	PROPN
ejpam-5024	72	27	µ	µ	X
ejpam-5024	72	28	(	(	PUNCT
ejpam-5024	72	29	∫	∫	PROPN
ejpam-5024	72	30	a	a	PRON
ejpam-5024	72	31	0	0	NUM
ejpam-5024	73	1	[	[	PUNCT
ejpam-5024	73	2	−x3	−x3	PROPN
ejpam-5024	73	3	−	−	PROPN
ejpam-5024	73	4	3ax2	3ax2	NUM
ejpam-5024	73	5	+	+	SYM
ejpam-5024	73	6	3a2x−	3a2x−	NUM
ejpam-5024	73	7	a3	a3	NOUN
ejpam-5024	73	8	3	3	NUM
ejpam-5024	73	9	]	]	PUNCT
ejpam-5024	73	10	dt	dt	X
ejpam-5024	73	11	)	)	PUNCT
ejpam-5024	73	12	1	1	NUM
ejpam-5024	73	13	2	2	NUM
ejpam-5024	73	14	(	(	PUNCT
ejpam-5024	73	15	15	15	NUM
ejpam-5024	73	16	)	)	PUNCT
ejpam-5024	73	17	hence	hence	ADV
ejpam-5024	73	18	∥ψ(|t−	∥ψ(|t−	PROPN
ejpam-5024	73	19	τ	τ	PROPN
ejpam-5024	73	20	|)∥	|)∥	PROPN
ejpam-5024	73	21	≤	≤	NOUN
ejpam-5024	73	22	α	α	PROPN
ejpam-5024	73	23	µ	µ	X
ejpam-5024	73	24	(	(	PUNCT
ejpam-5024	73	25	a4	a4	PROPN
ejpam-5024	73	26	12	12	NUM
ejpam-5024	73	27	)	)	PUNCT
ejpam-5024	73	28	1	1	NUM
ejpam-5024	73	29	2	2	NUM
ejpam-5024	73	30	=	=	SYM
ejpam-5024	73	31	ωψ	ωψ	ADP
ejpam-5024	73	32	<	<	X
ejpam-5024	73	33	1	1	NUM
ejpam-5024	73	34	(	(	PUNCT
ejpam-5024	73	35	16	16	NUM
ejpam-5024	73	36	)	)	PUNCT
ejpam-5024	73	37	(	(	PUNCT
ejpam-5024	73	38	b	b	X
ejpam-5024	73	39	)	)	PUNCT
ejpam-5024	73	40	there	there	PRON
ejpam-5024	73	41	exists	exist	VERB
ejpam-5024	73	42	a	a	DET
ejpam-5024	73	43	constant	constant	ADJ
ejpam-5024	73	44	ωϕ	ωϕ	ADP
ejpam-5024	73	45	such	such	ADJ
ejpam-5024	73	46	that	that	SCONJ
ejpam-5024	73	47	,	,	PUNCT
ejpam-5024	73	48	∥ϕ(t	∥ϕ(t	PROPN
ejpam-5024	73	49	,	,	PUNCT
ejpam-5024	73	50	x)∥	x)∥	SYM
ejpam-5024	73	51	≤	≤	NUM
ejpam-5024	73	52	ωϕ	ωϕ	NUM
ejpam-5024	73	53	,	,	PUNCT
ejpam-5024	73	54	(	(	PUNCT
ejpam-5024	73	55	17	17	NUM
ejpam-5024	73	56	)	)	PUNCT
ejpam-5024	73	57	taking	take	VERB
ejpam-5024	73	58	the	the	DET
ejpam-5024	73	59	norm	norm	NOUN
ejpam-5024	73	60	of	of	ADP
ejpam-5024	73	61	equation	equation	NOUN
ejpam-5024	73	62	(	(	PUNCT
ejpam-5024	73	63	2.6	2.6	NUM
ejpam-5024	73	64	)	)	PUNCT
ejpam-5024	73	65	and	and	CCONJ
ejpam-5024	73	66	applying	apply	VERB
ejpam-5024	73	67	condition	condition	NOUN
ejpam-5024	73	68	(	(	PUNCT
ejpam-5024	73	69	ii	ii	NOUN
ejpam-5024	73	70	)	)	PUNCT
ejpam-5024	73	71	,	,	PUNCT
ejpam-5024	73	72	we	we	PRON
ejpam-5024	73	73	get	get	VERB
ejpam-5024	73	74	:	:	PUNCT
ejpam-5024	73	75	∥ϕ(t	∥ϕ(t	ADJ
ejpam-5024	73	76	,	,	PUNCT
ejpam-5024	73	77	x)∥	x)∥	SYM
ejpam-5024	73	78	≤	≤	NUM
ejpam-5024	73	79	1	1	NUM
ejpam-5024	73	80	µ	µ	PRON
ejpam-5024	73	81	[	[	X
ejpam-5024	73	82	|b1|+	|b1|+	NOUN
ejpam-5024	73	83	|b2|∥(t−	|b2|∥(t−	NOUN
ejpam-5024	73	84	x)∥	x)∥	X
ejpam-5024	73	85	]	]	X
ejpam-5024	73	86	≤	≤	NUM
ejpam-5024	73	87	1	1	NUM
ejpam-5024	73	88	µ	µ	X
ejpam-5024	73	89	(	(	PUNCT
ejpam-5024	73	90	a1	a1	NOUN
ejpam-5024	73	91	+	+	NOUN
ejpam-5024	73	92	a2∥t∥	a2∥t∥	NOUN
ejpam-5024	73	93	)	)	PUNCT
ejpam-5024	73	94	≤	≤	NUM
ejpam-5024	73	95	1	1	NUM
ejpam-5024	73	96	µ	µ	NOUN
ejpam-5024	73	97	(	(	PUNCT
ejpam-5024	73	98	a1	a1	PROPN
ejpam-5024	73	99	+	+	PROPN
ejpam-5024	73	100	a2	a2	PROPN
ejpam-5024	73	101	(	(	PUNCT
ejpam-5024	73	102	a3	a3	NOUN
ejpam-5024	73	103	3	3	NUM
ejpam-5024	73	104	)	)	PUNCT
ejpam-5024	73	105	1	1	NUM
ejpam-5024	73	106	2	2	NUM
ejpam-5024	73	107	)	)	PUNCT
ejpam-5024	73	108	≤	≤	NOUN
ejpam-5024	73	109	ωϕ	ωϕ	PRON
ejpam-5024	73	110	<	<	X
ejpam-5024	73	111	1	1	NUM
ejpam-5024	73	112	(	(	PUNCT
ejpam-5024	73	113	18	18	NUM
ejpam-5024	73	114	)	)	PUNCT
ejpam-5024	73	115	(	(	PUNCT
ejpam-5024	73	116	c	c	X
ejpam-5024	73	117	)	)	PUNCT
ejpam-5024	73	118	there	there	PRON
ejpam-5024	73	119	exists	exist	VERB
ejpam-5024	73	120	a	a	DET
ejpam-5024	73	121	constant	constant	ADJ
ejpam-5024	73	122	ωf	ωf	ADP
ejpam-5024	73	123	such	such	ADJ
ejpam-5024	73	124	that	that	SCONJ
ejpam-5024	73	125	∥f	∥f	PROPN
ejpam-5024	73	126	(	(	PUNCT
ejpam-5024	73	127	x)∥	x)∥	NOUN
ejpam-5024	73	128	≤	≤	NUM
ejpam-5024	73	129	ωf	ωf	PROPN
ejpam-5024	73	130	(	(	PUNCT
ejpam-5024	73	131	19	19	NUM
ejpam-5024	73	132	)	)	PUNCT
ejpam-5024	73	133	where	where	SCONJ
ejpam-5024	73	134	1	1	NUM
ejpam-5024	73	135	µ	µ	NOUN
ejpam-5024	73	136	∥f(x)∥	∥f(x)∥	NOUN
ejpam-5024	73	137	≤	≤	NUM
ejpam-5024	73	138	γ	γ	X
ejpam-5024	73	139	<	<	X
ejpam-5024	73	140	1	1	NUM
ejpam-5024	73	141	(	(	PUNCT
ejpam-5024	73	142	20	20	NUM
ejpam-5024	73	143	)	)	SYM
ejpam-5024	73	144	1	1	NUM
ejpam-5024	73	145	µ	µ	X
ejpam-5024	73	146	∥(b1q1	∥(b1q1	X
ejpam-5024	74	1	+	+	NOUN
ejpam-5024	74	2	b2q0	b2q0	PROPN
ejpam-5024	74	3	+	+	NOUN
ejpam-5024	74	4	b2q1t)∥	b2q1t)∥	X
ejpam-5024	74	5	≤	≤	VERB
ejpam-5024	74	6	ϵ	ϵ	X
ejpam-5024	74	7	<	<	X
ejpam-5024	74	8	1	1	NUM
ejpam-5024	74	9	(	(	PUNCT
ejpam-5024	74	10	21	21	NUM
ejpam-5024	74	11	)	)	PUNCT
ejpam-5024	74	12	1	1	NUM
ejpam-5024	74	13	µ	µ	X
ejpam-5024	74	14	∥	∥	X
ejpam-5024	74	15	[	[	PUNCT
ejpam-5024	74	16	∫	∫	PROPN
ejpam-5024	74	17	a	a	PRON
ejpam-5024	74	18	0	0	NUM
ejpam-5024	74	19	k(t	k(t	NOUN
ejpam-5024	74	20	,	,	PUNCT
ejpam-5024	74	21	τ)(tq1	τ)(tq1	PUNCT
ejpam-5024	75	1	+	+	CCONJ
ejpam-5024	75	2	q0)dτ	q0)dτ	NOUN
ejpam-5024	75	3	]	]	X
ejpam-5024	75	4	∥	∥	PUNCT
ejpam-5024	75	5	≤	≤	NUM
ejpam-5024	75	6	α	α	PROPN
ejpam-5024	75	7	µ	µ	X
ejpam-5024	75	8	(	(	PUNCT
ejpam-5024	75	9	q0	q0	PROPN
ejpam-5024	75	10	+	+	NUM
ejpam-5024	75	11	q1	q1	PROPN
ejpam-5024	75	12	(	(	PUNCT
ejpam-5024	75	13	a3	a3	NOUN
ejpam-5024	75	14	3	3	NUM
ejpam-5024	75	15	)	)	PUNCT
ejpam-5024	75	16	1	1	NUM
ejpam-5024	75	17	2	2	NUM
ejpam-5024	75	18	)	)	PUNCT
ejpam-5024	75	19	=	=	PUNCT
ejpam-5024	76	1	σ	σ	X
ejpam-5024	76	2	<	<	X
ejpam-5024	76	3	1	1	NUM
ejpam-5024	76	4	(	(	PUNCT
ejpam-5024	76	5	22	22	NUM
ejpam-5024	76	6	)	)	PUNCT
ejpam-5024	76	7	ωf	ωf	PROPN
ejpam-5024	76	8	=	=	PUNCT
ejpam-5024	76	9	(	(	PUNCT
ejpam-5024	76	10	γ	γ	X
ejpam-5024	76	11	+	+	SYM
ejpam-5024	76	12	ϵ+	ϵ+	X
ejpam-5024	76	13	σ	σ	NOUN
ejpam-5024	76	14	)	)	PUNCT
ejpam-5024	76	15	(	(	PUNCT
ejpam-5024	76	16	23	23	X
ejpam-5024	76	17	)	)	PUNCT
ejpam-5024	76	18	theorem	theorem	NOUN
ejpam-5024	76	19	2	2	NUM
ejpam-5024	76	20	.	.	PUNCT
ejpam-5024	77	1	if	if	SCONJ
ejpam-5024	77	2	conditions	condition	NOUN
ejpam-5024	77	3	(	(	PUNCT
ejpam-5024	77	4	a)-(c	a)-(c	NOUN
ejpam-5024	77	5	)	)	PUNCT
ejpam-5024	77	6	are	be	AUX
ejpam-5024	77	7	satisfied	satisfied	ADJ
ejpam-5024	77	8	,	,	PUNCT
ejpam-5024	77	9	and	and	CCONJ
ejpam-5024	77	10	the	the	DET
ejpam-5024	77	11	integration	integration	NOUN
ejpam-5024	77	12	factor	factor	NOUN
ejpam-5024	77	13	(	(	PUNCT
ejpam-5024	77	14	2.9	2.9	NUM
ejpam-5024	77	15	)	)	PUNCT
ejpam-5024	77	16	is	be	AUX
ejpam-5024	77	17	normal	normal	ADJ
ejpam-5024	77	18	and	and	CCONJ
ejpam-5024	77	19	continuous	continuous	ADJ
ejpam-5024	77	20	,	,	PUNCT
ejpam-5024	77	21	then	then	ADV
ejpam-5024	77	22	equation	equation	NOUN
ejpam-5024	77	23	(	(	PUNCT
ejpam-5024	77	24	2.5	2.5	NUM
ejpam-5024	77	25	)	)	PUNCT
ejpam-5024	77	26	has	have	VERB
ejpam-5024	77	27	a	a	DET
ejpam-5024	77	28	unique	unique	ADJ
ejpam-5024	77	29	solution	solution	NOUN
ejpam-5024	77	30	in	in	ADP
ejpam-5024	77	31	banach	banach	NOUN
ejpam-5024	77	32	space	space	NOUN
ejpam-5024	77	33	l2	l2	NOUN
ejpam-5024	78	1	[	[	X
ejpam-5024	78	2	0	0	NUM
ejpam-5024	78	3	,	,	PUNCT
ejpam-5024	78	4	a	a	PRON
ejpam-5024	78	5	]	]	X
ejpam-5024	78	6	,	,	PUNCT
ejpam-5024	78	7	under	under	ADP
ejpam-5024	78	8	the	the	DET
ejpam-5024	78	9	condition	condition	NOUN
ejpam-5024	78	10	,	,	PUNCT
ejpam-5024	78	11	|λ|	|λ|	PROPN
ejpam-5024	78	12	≤	≤	NOUN
ejpam-5024	78	13	1−	1−	NUM
ejpam-5024	78	14	ωϕ	ωϕ	PRON
ejpam-5024	78	15	ωψ	ωψ	ADP
ejpam-5024	78	16	(	(	PUNCT
ejpam-5024	78	17	24	24	NUM
ejpam-5024	78	18	)	)	PUNCT
ejpam-5024	78	19	f.	f.	PROPN
ejpam-5024	78	20	m.	m.	PROPN
ejpam-5024	78	21	alharbi	alharbi	PROPN
ejpam-5024	78	22	,	,	PUNCT
ejpam-5024	78	23	s.	s.	PROPN
ejpam-5024	78	24	s.	s.	PROPN
ejpam-5024	78	25	althubiti	althubiti	PROPN
ejpam-5024	78	26	/	/	SYM
ejpam-5024	78	27	eur	eur	PROPN
ejpam-5024	78	28	.	.	PUNCT
ejpam-5024	79	1	j.	j.	PROPN
ejpam-5024	79	2	pure	pure	PROPN
ejpam-5024	79	3	appl	appl	PROPN
ejpam-5024	79	4	.	.	PROPN
ejpam-5024	79	5	math	math	PROPN
ejpam-5024	79	6	,	,	PUNCT
ejpam-5024	79	7	17	17	NUM
ejpam-5024	79	8	(	(	PUNCT
ejpam-5024	79	9	1	1	NUM
ejpam-5024	79	10	)	)	PUNCT
ejpam-5024	79	11	(	(	PUNCT
ejpam-5024	79	12	2024	2024	NUM
ejpam-5024	79	13	)	)	PUNCT
ejpam-5024	79	14	,	,	PUNCT
ejpam-5024	79	15	286	286	NUM
ejpam-5024	79	16	-	-	SYM
ejpam-5024	79	17	299	299	NUM
ejpam-5024	79	18	290	290	NUM
ejpam-5024	79	19	proof	proof	NOUN
ejpam-5024	79	20	:	:	PUNCT
ejpam-5024	79	21	we	we	PRON
ejpam-5024	79	22	establish	establish	VERB
ejpam-5024	79	23	the	the	DET
ejpam-5024	79	24	normality	normality	NOUN
ejpam-5024	79	25	and	and	CCONJ
ejpam-5024	79	26	continuity	continuity	NOUN
ejpam-5024	79	27	of	of	ADP
ejpam-5024	79	28	the	the	DET
ejpam-5024	79	29	integral	integral	ADJ
ejpam-5024	79	30	operator	operator	NOUN
ejpam-5024	79	31	(	(	PUNCT
ejpam-5024	79	32	2.9	2.9	NUM
ejpam-5024	79	33	)	)	PUNCT
ejpam-5024	79	34	.	.	PUNCT
ejpam-5024	80	1	(	(	PUNCT
ejpam-5024	80	2	a	a	X
ejpam-5024	80	3	)	)	PUNCT
ejpam-5024	80	4	for	for	ADP
ejpam-5024	80	5	the	the	DET
ejpam-5024	80	6	normality	normality	NOUN
ejpam-5024	80	7	of	of	ADP
ejpam-5024	80	8	the	the	DET
ejpam-5024	80	9	integral	integral	ADJ
ejpam-5024	80	10	operator	operator	NOUN
ejpam-5024	80	11	wg	wg	PROPN
ejpam-5024	80	12	,	,	PUNCT
ejpam-5024	80	13	we	we	PRON
ejpam-5024	80	14	write	write	VERB
ejpam-5024	80	15	:	:	PUNCT
ejpam-5024	80	16	∥wg∥	∥wg∥	NOUN
ejpam-5024	81	1	≤	≤	NUM
ejpam-5024	81	2	−1	−1	NOUN
ejpam-5024	81	3	µ	µ	X
ejpam-5024	81	4	[	[	PUNCT
ejpam-5024	81	5	∥∥∥∥∫	∥∥∥∥∫	NOUN
ejpam-5024	81	6	t	t	NOUN
ejpam-5024	81	7	0	0	NUM
ejpam-5024	82	1	ϕ(t	ϕ(t	NUM
ejpam-5024	82	2	,	,	PUNCT
ejpam-5024	82	3	x)g(x)dx	x)g(x)dx	ADJ
ejpam-5024	82	4	∥∥∥∥+	∥∥∥∥+	NOUN
ejpam-5024	82	5	∥∥∥∥∫	∥∥∥∥∫	VERB
ejpam-5024	82	6	a	a	DET
ejpam-5024	82	7	0	0	NUM
ejpam-5024	82	8	ψ(|t−	ψ(|t−	PROPN
ejpam-5024	82	9	x|)g(x)dx	x|)g(x)dx	PROPN
ejpam-5024	82	10	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5024	82	11	]	]	PUNCT
ejpam-5024	82	12	.	.	PUNCT
ejpam-5024	83	1	(	(	PUNCT
ejpam-5024	83	2	25	25	NUM
ejpam-5024	83	3	)	)	PUNCT
ejpam-5024	83	4	then	then	ADV
ejpam-5024	83	5	,	,	PUNCT
ejpam-5024	83	6	∥ϕg(x)∥	∥ϕg(x)∥	VERB
ejpam-5024	83	7	≤	≤	NUM
ejpam-5024	83	8	1	1	NUM
ejpam-5024	83	9	µ	µ	X
ejpam-5024	83	10	(	(	PUNCT
ejpam-5024	83	11	a1	a1	VERB
ejpam-5024	83	12	+	+	NOUN
ejpam-5024	83	13	a2∥t∥)∥g(x)∥	a2∥t∥)∥g(x)∥	X
ejpam-5024	83	14	≤	≤	NUM
ejpam-5024	83	15	1	1	NUM
ejpam-5024	83	16	µ	µ	NOUN
ejpam-5024	83	17	(	(	PUNCT
ejpam-5024	83	18	a1	a1	PROPN
ejpam-5024	83	19	+	+	PROPN
ejpam-5024	83	20	a2	a2	PROPN
ejpam-5024	83	21	(	(	PUNCT
ejpam-5024	83	22	a3	a3	NOUN
ejpam-5024	83	23	3	3	NUM
ejpam-5024	83	24	)	)	PUNCT
ejpam-5024	83	25	1	1	NUM
ejpam-5024	83	26	2	2	NUM
ejpam-5024	83	27	)	)	PUNCT
ejpam-5024	83	28	∥g(x)∥	∥g(x)∥	PROPN
ejpam-5024	83	29	,	,	PUNCT
ejpam-5024	83	30	(	(	PUNCT
ejpam-5024	83	31	26	26	NUM
ejpam-5024	83	32	)	)	PUNCT
ejpam-5024	83	33	which	which	PRON
ejpam-5024	83	34	can	can	AUX
ejpam-5024	83	35	be	be	AUX
ejpam-5024	83	36	adapted	adapt	VERB
ejpam-5024	83	37	as	as	ADP
ejpam-5024	83	38	:	:	PUNCT
ejpam-5024	83	39	∥ϕg(x)∥	∥ϕg(x)∥	NOUN
ejpam-5024	83	40	≤	≤	NUM
ejpam-5024	83	41	ωϕ∥g(x)∥	ωϕ∥g(x)∥	NOUN
ejpam-5024	83	42	,	,	PUNCT
ejpam-5024	83	43	.	.	PUNCT
ejpam-5024	84	1	(	(	PUNCT
ejpam-5024	84	2	27	27	NUM
ejpam-5024	84	3	)	)	PUNCT
ejpam-5024	84	4	also	also	ADV
ejpam-5024	84	5	,	,	PUNCT
ejpam-5024	84	6	∥ψg(x)∥	∥ψg(x)∥	NOUN
ejpam-5024	84	7	≤	≤	NUM
ejpam-5024	84	8	∥∥∥∥∫	∥∥∥∥∫	VERB
ejpam-5024	84	9	a	a	DET
ejpam-5024	84	10	0	0	NUM
ejpam-5024	84	11	ψ(|t−	ψ(|t−	PROPN
ejpam-5024	84	12	x|)g(x)dx	x|)g(x)dx	PROPN
ejpam-5024	84	13	∥∥∥∥	∥∥∥∥	NUM
ejpam-5024	84	14	.	.	PUNCT
ejpam-5024	85	1	(	(	PUNCT
ejpam-5024	85	2	28	28	NUM
ejpam-5024	85	3	)	)	PUNCT
ejpam-5024	85	4	by	by	ADP
ejpam-5024	85	5	using	use	VERB
ejpam-5024	85	6	condition	condition	NOUN
ejpam-5024	85	7	(	(	PUNCT
ejpam-5024	85	8	a	a	X
ejpam-5024	85	9	)	)	PUNCT
ejpam-5024	85	10	,	,	PUNCT
ejpam-5024	85	11	we	we	PRON
ejpam-5024	85	12	get	get	VERB
ejpam-5024	85	13	:	:	PUNCT
ejpam-5024	85	14	∥ψg(x	∥ψg(x	PRON
ejpam-5024	85	15	)	)	PUNCT
ejpam-5024	85	16	∥≤	∥≤	VERB
ejpam-5024	85	17	ωψ∥	ωψ∥	PROPN
ejpam-5024	85	18	g(x)∥	g(x)∥	NOUN
ejpam-5024	85	19	,	,	PUNCT
ejpam-5024	85	20	(	(	PUNCT
ejpam-5024	85	21	29	29	NUM
ejpam-5024	85	22	)	)	PUNCT
ejpam-5024	85	23	and	and	CCONJ
ejpam-5024	85	24	them	they	PRON
ejpam-5024	85	25	,	,	PUNCT
ejpam-5024	85	26	∥wg(x)∥	∥wg(x)∥	VERB
ejpam-5024	85	27	≤	≤	NUM
ejpam-5024	85	28	χ∥g(x)∥	χ∥g(x)∥	NOUN
ejpam-5024	85	29	,	,	PUNCT
ejpam-5024	85	30	χ	χ	NOUN
ejpam-5024	85	31	=	=	X
ejpam-5024	85	32	(	(	PUNCT
ejpam-5024	85	33	ωϕ	ωϕ	ADP
ejpam-5024	85	34	+	+	ADJ
ejpam-5024	85	35	ωψ	ωψ	NOUN
ejpam-5024	85	36	)	)	PUNCT
ejpam-5024	85	37	.	.	PUNCT
ejpam-5024	86	1	(	(	PUNCT
ejpam-5024	86	2	30	30	NUM
ejpam-5024	86	3	)	)	PUNCT
ejpam-5024	86	4	so	so	ADV
ejpam-5024	86	5	,	,	PUNCT
ejpam-5024	86	6	w	w	NOUN
ejpam-5024	86	7	is	be	AUX
ejpam-5024	86	8	a	a	DET
ejpam-5024	86	9	norm	norm	NOUN
ejpam-5024	86	10	operator	operator	NOUN
ejpam-5024	86	11	that	that	PRON
ejpam-5024	86	12	leads	lead	VERB
ejpam-5024	86	13	straight	straight	ADV
ejpam-5024	86	14	to	to	ADP
ejpam-5024	86	15	the	the	DET
ejpam-5024	86	16	normality	normality	NOUN
ejpam-5024	86	17	of	of	ADP
ejpam-5024	86	18	the	the	DET
ejpam-5024	86	19	operator	operator	NOUN
ejpam-5024	86	20	w̄	w̄	NOUN
ejpam-5024	86	21	after	after	ADP
ejpam-5024	86	22	applying	apply	VERB
ejpam-5024	86	23	condition	condition	NOUN
ejpam-5024	86	24	(	(	PUNCT
ejpam-5024	86	25	c	c	NOUN
ejpam-5024	86	26	)	)	PUNCT
ejpam-5024	86	27	.	.	PUNCT
ejpam-5024	87	1	(	(	PUNCT
ejpam-5024	87	2	b	b	X
ejpam-5024	87	3	)	)	PUNCT
ejpam-5024	87	4	we	we	PRON
ejpam-5024	87	5	assume	assume	VERB
ejpam-5024	87	6	that	that	SCONJ
ejpam-5024	87	7	the	the	DET
ejpam-5024	87	8	two	two	NUM
ejpam-5024	87	9	potential	potential	ADJ
ejpam-5024	87	10	functions	function	NOUN
ejpam-5024	87	11	g1(x	g1(x	NOUN
ejpam-5024	87	12	)	)	PUNCT
ejpam-5024	87	13	,	,	PUNCT
ejpam-5024	87	14	g2(x	g2(x	PROPN
ejpam-5024	87	15	)	)	PUNCT
ejpam-5024	87	16	in	in	ADP
ejpam-5024	87	17	the	the	DET
ejpam-5024	87	18	helbert	helbert	NOUN
ejpam-5024	87	19	space	space	NOUN
ejpam-5024	87	20	,	,	PUNCT
ejpam-5024	87	21	then	then	ADV
ejpam-5024	87	22	,	,	PUNCT
ejpam-5024	87	23	∥∥w̄	∥∥w̄	X
ejpam-5024	87	24	(	(	PUNCT
ejpam-5024	87	25	g1	g1	PROPN
ejpam-5024	87	26	−	−	PROPN
ejpam-5024	87	27	g2	g2	PROPN
ejpam-5024	87	28	)	)	PUNCT
ejpam-5024	87	29	∥∥	∥∥	PROPN
ejpam-5024	87	30	≤	≤	PROPN
ejpam-5024	87	31	∥∥∥∥∫	∥∥∥∥∫	VERB
ejpam-5024	87	32	t	t	NOUN
ejpam-5024	87	33	0	0	NUM
ejpam-5024	88	1	ϕ(t	ϕ(t	NUM
ejpam-5024	88	2	,	,	PUNCT
ejpam-5024	88	3	x	x	X
ejpam-5024	88	4	)	)	PUNCT
ejpam-5024	88	5	(	(	PUNCT
ejpam-5024	88	6	g1(x)−	g1(x)−	PROPN
ejpam-5024	88	7	g2(x	g2(x	PROPN
ejpam-5024	88	8	)	)	PUNCT
ejpam-5024	88	9	)	)	PUNCT
ejpam-5024	88	10	dx	dx	PROPN
ejpam-5024	88	11	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5024	89	1	+	+	CCONJ
ejpam-5024	89	2	∥∥∥∥∫	∥∥∥∥∫	VERB
ejpam-5024	89	3	a	a	DET
ejpam-5024	89	4	0	0	NUM
ejpam-5024	89	5	ψ(|t−	ψ(|t−	PROPN
ejpam-5024	89	6	x|	x|	PROPN
ejpam-5024	89	7	)	)	PUNCT
ejpam-5024	89	8	(	(	PUNCT
ejpam-5024	89	9	g1(x)−	g1(x)−	PROPN
ejpam-5024	89	10	g2(x	g2(x	PROPN
ejpam-5024	89	11	)	)	PUNCT
ejpam-5024	89	12	)	)	PUNCT
ejpam-5024	89	13	dx	dx	PROPN
ejpam-5024	89	14	∥∥∥∥	∥∥∥∥	NUM
ejpam-5024	89	15	.	.	PUNCT
ejpam-5024	90	1	(	(	PUNCT
ejpam-5024	90	2	31	31	NUM
ejpam-5024	90	3	)	)	PUNCT
ejpam-5024	90	4	using	use	VERB
ejpam-5024	90	5	conditions	condition	NOUN
ejpam-5024	90	6	(	(	PUNCT
ejpam-5024	90	7	a	a	X
ejpam-5024	90	8	)	)	PUNCT
ejpam-5024	90	9	and	and	CCONJ
ejpam-5024	90	10	(	(	PUNCT
ejpam-5024	90	11	b	b	NOUN
ejpam-5024	90	12	)	)	PUNCT
ejpam-5024	90	13	,	,	PUNCT
ejpam-5024	90	14	we	we	PRON
ejpam-5024	90	15	get:∥∥w̄	get:∥∥w̄	X
ejpam-5024	90	16	(	(	PUNCT
ejpam-5024	90	17	g1	g1	PROPN
ejpam-5024	90	18	−	−	PROPN
ejpam-5024	90	19	g2	g2	PROPN
ejpam-5024	90	20	)	)	PUNCT
ejpam-5024	90	21	∥∥	∥∥	PROPN
ejpam-5024	90	22	≤	≤	NOUN
ejpam-5024	91	1	χ	χ	DET
ejpam-5024	91	2	∥g1(x)−	∥g1(x)−	PROPN
ejpam-5024	91	3	g2(x)∥	g2(x)∥	PROPN
ejpam-5024	91	4	.	.	PUNCT
ejpam-5024	92	1	(	(	PUNCT
ejpam-5024	92	2	32	32	NUM
ejpam-5024	92	3	)	)	PUNCT
ejpam-5024	92	4	that	that	PRON
ejpam-5024	92	5	proves	prove	VERB
ejpam-5024	92	6	w̄	w̄	NOUN
ejpam-5024	92	7	is	be	AUX
ejpam-5024	92	8	a	a	DET
ejpam-5024	92	9	continuous	continuous	ADJ
ejpam-5024	92	10	operator	operator	NOUN
ejpam-5024	92	11	,	,	PUNCT
ejpam-5024	92	12	then	then	ADV
ejpam-5024	92	13	,	,	PUNCT
ejpam-5024	92	14	by	by	ADP
ejpam-5024	92	15	using	use	VERB
ejpam-5024	92	16	the	the	DET
ejpam-5024	92	17	condition	condition	NOUN
ejpam-5024	92	18	χ	χ	ADP
ejpam-5024	92	19	<	<	X
ejpam-5024	92	20	1	1	NUM
ejpam-5024	92	21	,	,	PUNCT
ejpam-5024	92	22	we	we	PRON
ejpam-5024	92	23	deduce	deduce	VERB
ejpam-5024	92	24	that	that	SCONJ
ejpam-5024	92	25	w̄	w̄	NOUN
ejpam-5024	92	26	is	be	AUX
ejpam-5024	92	27	a	a	DET
ejpam-5024	92	28	contraction	contraction	NOUN
ejpam-5024	92	29	operator	operator	NOUN
ejpam-5024	92	30	,	,	PUNCT
ejpam-5024	92	31	and	and	CCONJ
ejpam-5024	92	32	it	it	PRON
ejpam-5024	92	33	has	have	VERB
ejpam-5024	92	34	a	a	DET
ejpam-5024	92	35	unique	unique	ADJ
ejpam-5024	92	36	solution	solution	NOUN
ejpam-5024	92	37	.	.	PUNCT
ejpam-5024	93	1	2.3	2.3	NUM
ejpam-5024	93	2	.	.	PUNCT
ejpam-5024	93	3	system	system	NOUN
ejpam-5024	93	4	of	of	ADP
ejpam-5024	93	5	fredholm	fredholm	ADJ
ejpam-5024	93	6	integral	integral	ADJ
ejpam-5024	93	7	equations	equation	NOUN
ejpam-5024	93	8	sfies	sfie	VERB
ejpam-5024	93	9	the	the	DET
ejpam-5024	93	10	quadratic	quadratic	ADJ
ejpam-5024	93	11	method	method	NOUN
ejpam-5024	93	12	has	have	VERB
ejpam-5024	93	13	wide	wide	ADJ
ejpam-5024	93	14	application	application	NOUN
ejpam-5024	93	15	in	in	ADP
ejpam-5024	93	16	mathematical	mathematical	ADJ
ejpam-5024	93	17	and	and	CCONJ
ejpam-5024	93	18	physics	physics	NOUN
ejpam-5024	93	19	problems	problem	NOUN
ejpam-5024	93	20	,	,	PUNCT
ejpam-5024	93	21	where	where	SCONJ
ejpam-5024	93	22	the	the	DET
ejpam-5024	93	23	eigenvalues	eigenvalue	NOUN
ejpam-5024	93	24	and	and	CCONJ
ejpam-5024	93	25	eigenfunctions	eigenfunction	NOUN
ejpam-5024	93	26	of	of	ADP
ejpam-5024	93	27	integral	integral	ADJ
ejpam-5024	93	28	equations	equation	NOUN
ejpam-5024	93	29	are	be	AUX
ejpam-5024	93	30	often	often	ADV
ejpam-5024	93	31	studied	study	VERB
ejpam-5024	93	32	and	and	CCONJ
ejpam-5024	93	33	discussed	discuss	VERB
ejpam-5024	93	34	.	.	PUNCT
ejpam-5024	94	1	it	it	PRON
ejpam-5024	94	2	also	also	ADV
ejpam-5024	94	3	has	have	VERB
ejpam-5024	94	4	wide	wide	ADJ
ejpam-5024	94	5	applications	application	NOUN
ejpam-5024	94	6	in	in	ADP
ejpam-5024	94	7	applied	applied	ADJ
ejpam-5024	94	8	sciences	science	NOUN
ejpam-5024	94	9	,	,	PUNCT
ejpam-5024	94	10	especially	especially	ADV
ejpam-5024	94	11	in	in	ADP
ejpam-5024	94	12	the	the	DET
ejpam-5024	94	13	theory	theory	NOUN
ejpam-5024	94	14	of	of	ADP
ejpam-5024	94	15	elasticity	elasticity	NOUN
ejpam-5024	94	16	,	,	PUNCT
ejpam-5024	94	17	mixed	mixed	ADJ
ejpam-5024	94	18	problems	problem	NOUN
ejpam-5024	94	19	in	in	ADP
ejpam-5024	94	20	the	the	DET
ejpam-5024	94	21	fluid	fluid	NOUN
ejpam-5024	94	22	of	of	ADP
ejpam-5024	94	23	mechanics	mechanic	NOUN
ejpam-5024	94	24	,	,	PUNCT
ejpam-5024	94	25	and	and	CCONJ
ejpam-5024	94	26	communication	communication	NOUN
ejpam-5024	94	27	problems	problem	NOUN
ejpam-5024	94	28	.	.	PUNCT
ejpam-5024	95	1	this	this	DET
ejpam-5024	95	2	numerical	numerical	ADJ
ejpam-5024	95	3	technique	technique	NOUN
ejpam-5024	95	4	will	will	AUX
ejpam-5024	95	5	be	be	AUX
ejpam-5024	95	6	applied	apply	VERB
ejpam-5024	95	7	in	in	ADP
ejpam-5024	95	8	this	this	DET
ejpam-5024	95	9	section	section	NOUN
ejpam-5024	95	10	to	to	PART
ejpam-5024	95	11	reduce	reduce	VERB
ejpam-5024	95	12	v	v	NOUN
ejpam-5024	95	13	-	-	PUNCT
ejpam-5024	95	14	fies	fie	NOUN
ejpam-5024	95	15	to	to	ADP
ejpam-5024	95	16	linear	linear	PROPN
ejpam-5024	95	17	sfies	sfie	NOUN
ejpam-5024	95	18	.	.	PUNCT
ejpam-5024	96	1	f.	f.	PROPN
ejpam-5024	96	2	m.	m.	PROPN
ejpam-5024	96	3	alharbi	alharbi	PROPN
ejpam-5024	96	4	,	,	PUNCT
ejpam-5024	96	5	s.	s.	PROPN
ejpam-5024	96	6	s.	s.	PROPN
ejpam-5024	96	7	althubiti	althubiti	PROPN
ejpam-5024	96	8	/	/	SYM
ejpam-5024	96	9	eur	eur	PROPN
ejpam-5024	96	10	.	.	PUNCT
ejpam-5024	97	1	j.	j.	PROPN
ejpam-5024	97	2	pure	pure	PROPN
ejpam-5024	97	3	appl	appl	PROPN
ejpam-5024	97	4	.	.	PROPN
ejpam-5024	97	5	math	math	PROPN
ejpam-5024	97	6	,	,	PUNCT
ejpam-5024	97	7	17	17	NUM
ejpam-5024	97	8	(	(	PUNCT
ejpam-5024	97	9	1	1	NUM
ejpam-5024	97	10	)	)	PUNCT
ejpam-5024	97	11	(	(	PUNCT
ejpam-5024	97	12	2024	2024	NUM
ejpam-5024	97	13	)	)	PUNCT
ejpam-5024	97	14	,	,	PUNCT
ejpam-5024	97	15	286	286	NUM
ejpam-5024	97	16	-	-	SYM
ejpam-5024	97	17	299	299	NUM
ejpam-5024	97	18	291	291	NUM
ejpam-5024	97	19	consider	consider	NOUN
ejpam-5024	97	20	,	,	PUNCT
ejpam-5024	97	21	µg(t	µg(t	ADJ
ejpam-5024	97	22	)	)	PUNCT
ejpam-5024	97	23	=	=	SYM
ejpam-5024	97	24	f	f	X
ejpam-5024	97	25	(	(	PUNCT
ejpam-5024	97	26	t	t	PROPN
ejpam-5024	97	27	)	)	PUNCT
ejpam-5024	98	1	+	+	CCONJ
ejpam-5024	99	1	∫	∫	PROPN
ejpam-5024	99	2	t	t	NOUN
ejpam-5024	99	3	0	0	NUM
ejpam-5024	99	4	ϕ(t	ϕ(t	PROPN
ejpam-5024	99	5	,	,	PUNCT
ejpam-5024	99	6	x)g(x)dx+	x)g(x)dx+	PROPN
ejpam-5024	99	7	∫	∫	PROPN
ejpam-5024	99	8	a	a	DET
ejpam-5024	99	9	0	0	NUM
ejpam-5024	99	10	ψ(t	ψ(t	PROPN
ejpam-5024	99	11	,	,	PUNCT
ejpam-5024	99	12	τ)g(x)dx	τ)g(x)dx	NOUN
ejpam-5024	99	13	(	(	PUNCT
ejpam-5024	99	14	33	33	NUM
ejpam-5024	99	15	)	)	PUNCT
ejpam-5024	99	16	divide	divide	VERB
ejpam-5024	99	17	the	the	DET
ejpam-5024	99	18	interval	interval	NOUN
ejpam-5024	99	19	[	[	X
ejpam-5024	99	20	0	0	NUM
ejpam-5024	99	21	,	,	PUNCT
ejpam-5024	99	22	t	t	NOUN
ejpam-5024	99	23	]	]	PUNCT
ejpam-5024	99	24	as	as	ADP
ejpam-5024	99	25	0	0	NUM
ejpam-5024	99	26	=	=	SYM
ejpam-5024	99	27	t0	t0	PROPN
ejpam-5024	99	28	≤	≤	NUM
ejpam-5024	99	29	t1	t1	NOUN
ejpam-5024	99	30	≤	≤	PUNCT
ejpam-5024	99	31	·	·	PUNCT
ejpam-5024	99	32	·	·	PUNCT
ejpam-5024	99	33	·	·	PUNCT
ejpam-5024	100	1	≤	≤	NUM
ejpam-5024	100	2	tn	tn	NOUN
ejpam-5024	100	3	=	=	SYM
ejpam-5024	100	4	t	t	PROPN
ejpam-5024	100	5	.	.	PUNCT
ejpam-5024	101	1	using	use	VERB
ejpam-5024	101	2	the	the	DET
ejpam-5024	101	3	quadrature	quadrature	NOUN
ejpam-5024	101	4	formula	formula	NOUN
ejpam-5024	101	5	,	,	PUNCT
ejpam-5024	101	6	equation	equation	NOUN
ejpam-5024	101	7	(	(	PUNCT
ejpam-5024	101	8	4.1	4.1	NUM
ejpam-5024	101	9	)	)	PUNCT
ejpam-5024	101	10	becomes:∫	becomes:∫	NOUN
ejpam-5024	101	11	t	t	NOUN
ejpam-5024	101	12	0	0	NUM
ejpam-5024	102	1	ϕ(t	ϕ(t	NUM
ejpam-5024	102	2	,	,	PUNCT
ejpam-5024	102	3	x)g(x)dx	x)g(x)dx	PROPN
ejpam-5024	102	4	=	=	SYM
ejpam-5024	102	5	n∑	n∑	PROPN
ejpam-5024	102	6	m=0	m=0	PROPN
ejpam-5024	102	7	umϕ(tn	umϕ(tn	PROPN
ejpam-5024	102	8	,	,	PUNCT
ejpam-5024	102	9	xm)g(xm	xm)g(xm	NUM
ejpam-5024	102	10	)	)	PUNCT
ejpam-5024	102	11	(	(	PUNCT
ejpam-5024	102	12	34	34	NUM
ejpam-5024	102	13	)	)	PUNCT
ejpam-5024	102	14	where	where	SCONJ
ejpam-5024	102	15	n	n	NOUN
ejpam-5024	102	16	=	=	SYM
ejpam-5024	102	17	0	0	NUM
ejpam-5024	102	18	,	,	PUNCT
ejpam-5024	102	19	1	1	NUM
ejpam-5024	102	20	,	,	PUNCT
ejpam-5024	102	21	2	2	NUM
ejpam-5024	102	22	,	,	PUNCT
ejpam-5024	102	23	·	·	PUNCT
ejpam-5024	102	24	·	·	PUNCT
ejpam-5024	102	25	·	·	PUNCT
ejpam-5024	102	26	,	,	PUNCT
ejpam-5024	102	27	n	n	CCONJ
ejpam-5024	102	28	−	−	PROPN
ejpam-5024	102	29	1	1	NUM
ejpam-5024	102	30	,	,	PUNCT
ejpam-5024	102	31	and	and	CCONJ
ejpam-5024	102	32	u0	u0	ADJ
ejpam-5024	102	33	=	=	NOUN
ejpam-5024	102	34	1	1	NUM
ejpam-5024	102	35	2h0	2h0	NUM
ejpam-5024	102	36	,	,	PUNCT
ejpam-5024	102	37	un	un	PROPN
ejpam-5024	102	38	=	=	PROPN
ejpam-5024	102	39	1	1	NUM
ejpam-5024	102	40	2hn	2hn	NOUN
ejpam-5024	102	41	,	,	PUNCT
ejpam-5024	102	42	ui	ui	PROPN
ejpam-5024	103	1	=	=	PUNCT
ejpam-5024	103	2	hi	hi	PROPN
ejpam-5024	103	3	,	,	PUNCT
ejpam-5024	103	4	(	(	PUNCT
ejpam-5024	103	5	i	i	PRON
ejpam-5024	103	6	̸=	̸=	PROPN
ejpam-5024	103	7	0	0	NUM
ejpam-5024	103	8	,	,	PUNCT
ejpam-5024	103	9	n	n	CCONJ
ejpam-5024	103	10	)	)	PUNCT
ejpam-5024	103	11	.	.	PUNCT
ejpam-5024	104	1	using	use	VERB
ejpam-5024	104	2	(	(	PUNCT
ejpam-5024	104	3	2.34	2.34	NUM
ejpam-5024	104	4	)	)	PUNCT
ejpam-5024	104	5	in	in	ADP
ejpam-5024	104	6	(	(	PUNCT
ejpam-5024	104	7	2.33	2.33	NUM
ejpam-5024	104	8	)	)	PUNCT
ejpam-5024	104	9	,	,	PUNCT
ejpam-5024	104	10	we	we	PRON
ejpam-5024	104	11	have	have	VERB
ejpam-5024	104	12	:	:	PUNCT
ejpam-5024	104	13	g(t	g(t	X
ejpam-5024	104	14	)	)	PUNCT
ejpam-5024	105	1	=	=	SYM
ejpam-5024	105	2	f	f	X
ejpam-5024	105	3	(	(	PUNCT
ejpam-5024	105	4	t	t	PROPN
ejpam-5024	105	5	)	)	PUNCT
ejpam-5024	105	6	+	+	CCONJ
ejpam-5024	105	7	∫	∫	PROPN
ejpam-5024	105	8	a	a	DET
ejpam-5024	105	9	0	0	PUNCT
ejpam-5024	105	10	ψ(t	ψ(t	PROPN
ejpam-5024	105	11	,	,	PUNCT
ejpam-5024	105	12	τ)g(x)dx+	τ)g(x)dx+	PROPN
ejpam-5024	105	13	n∑	n∑	PROPN
ejpam-5024	105	14	m=0	m=0	PROPN
ejpam-5024	105	15	umϕ	umϕ	PROPN
ejpam-5024	105	16	(	(	PUNCT
ejpam-5024	105	17	tn	tn	PROPN
ejpam-5024	105	18	,	,	PUNCT
ejpam-5024	105	19	xm	xm	PROPN
ejpam-5024	105	20	)	)	PUNCT
ejpam-5024	105	21	g(xm	g(xm	PROPN
ejpam-5024	105	22	)	)	PUNCT
ejpam-5024	105	23	(	(	PUNCT
ejpam-5024	105	24	35	35	NUM
ejpam-5024	105	25	)	)	PUNCT
ejpam-5024	105	26	then	then	ADV
ejpam-5024	105	27	:	:	PUNCT
ejpam-5024	105	28	gn	gn	PROPN
ejpam-5024	105	29	=	=	PUNCT
ejpam-5024	105	30	yn(t	yn(t	PROPN
ejpam-5024	105	31	)	)	PUNCT
ejpam-5024	106	1	+	+	CCONJ
ejpam-5024	106	2	∫	∫	PROPN
ejpam-5024	106	3	a	a	DET
ejpam-5024	106	4	0	0	NUM
ejpam-5024	106	5	ψ(t	ψ(t	NOUN
ejpam-5024	106	6	,	,	PUNCT
ejpam-5024	106	7	τ)gn(x)dx	τ)gn(x)dx	NOUN
ejpam-5024	106	8	(	(	PUNCT
ejpam-5024	106	9	36	36	NUM
ejpam-5024	106	10	)	)	PUNCT
ejpam-5024	106	11	where	where	SCONJ
ejpam-5024	106	12	yn(t	yn(t	X
ejpam-5024	106	13	)	)	PUNCT
ejpam-5024	106	14	=	=	PUNCT
ejpam-5024	106	15	fn(t	fn(t	X
ejpam-5024	106	16	)	)	PUNCT
ejpam-5024	107	1	+	+	CCONJ
ejpam-5024	107	2	∑n	∑n	PROPN
ejpam-5024	107	3	m=0	m=0	PROPN
ejpam-5024	107	4	umϕ	umϕ	PROPN
ejpam-5024	107	5	(	(	PUNCT
ejpam-5024	107	6	tn	tn	PROPN
ejpam-5024	107	7	,	,	PUNCT
ejpam-5024	107	8	xm	xm	PROPN
ejpam-5024	107	9	)	)	PUNCT
ejpam-5024	107	10	g(xm	g(xm	NOUN
ejpam-5024	107	11	)	)	PUNCT
ejpam-5024	107	12	,	,	PUNCT
ejpam-5024	107	13	n	n	NOUN
ejpam-5024	107	14	=	=	SYM
ejpam-5024	107	15	0	0	NUM
ejpam-5024	107	16	,	,	PUNCT
ejpam-5024	107	17	1	1	NUM
ejpam-5024	107	18	,	,	PUNCT
ejpam-5024	107	19	·	·	PUNCT
ejpam-5024	107	20	·	·	PUNCT
ejpam-5024	107	21	·	·	PUNCT
ejpam-5024	107	22	,	,	PUNCT
ejpam-5024	107	23	n	n	X
ejpam-5024	107	24	.	.	PUNCT
ejpam-5024	108	1	formula	formula	NOUN
ejpam-5024	108	2	(	(	PUNCT
ejpam-5024	108	3	2.36	2.36	NUM
ejpam-5024	108	4	)	)	PUNCT
ejpam-5024	108	5	represents	represent	VERB
ejpam-5024	108	6	a	a	DET
ejpam-5024	108	7	sfies	sfie	NOUN
ejpam-5024	108	8	,	,	PUNCT
ejpam-5024	108	9	and	and	CCONJ
ejpam-5024	108	10	we	we	PRON
ejpam-5024	108	11	have	have	VERB
ejpam-5024	108	12	n	n	NUM
ejpam-5024	108	13	unknown	unknown	ADJ
ejpam-5024	108	14	functions	function	NOUN
ejpam-5024	108	15	gn(t	gn(t	PRON
ejpam-5024	108	16	)	)	PUNCT
ejpam-5024	108	17	corresponding	correspond	VERB
ejpam-5024	108	18	to	to	ADP
ejpam-5024	108	19	time	time	NOUN
ejpam-5024	108	20	interval	interval	NOUN
ejpam-5024	108	21	[	[	X
ejpam-5024	108	22	0	0	NUM
ejpam-5024	108	23	,	,	PUNCT
ejpam-5024	108	24	t	t	X
ejpam-5024	108	25	]	]	PUNCT
ejpam-5024	108	26	.	.	PUNCT
ejpam-5024	109	1	3	3	X
ejpam-5024	109	2	.	.	X
ejpam-5024	109	3	numerical	numerical	ADJ
ejpam-5024	109	4	methods	method	NOUN
ejpam-5024	109	5	in	in	ADP
ejpam-5024	109	6	this	this	DET
ejpam-5024	109	7	section	section	NOUN
ejpam-5024	109	8	,	,	PUNCT
ejpam-5024	109	9	the	the	DET
ejpam-5024	109	10	collocation	collocation	NOUN
ejpam-5024	109	11	method	method	NOUN
ejpam-5024	109	12	and	and	CCONJ
ejpam-5024	109	13	galerkin	galerkin	ADJ
ejpam-5024	109	14	method	method	NOUN
ejpam-5024	109	15	are	be	AUX
ejpam-5024	109	16	used	use	VERB
ejpam-5024	109	17	to	to	PART
ejpam-5024	109	18	solve	solve	VERB
ejpam-5024	109	19	v	v	NOUN
ejpam-5024	109	20	-	-	PUNCT
ejpam-5024	109	21	fie	fie	NOUN
ejpam-5024	109	22	of	of	ADP
ejpam-5024	109	23	the	the	DET
ejpam-5024	109	24	second	second	ADJ
ejpam-5024	109	25	kind	kind	NOUN
ejpam-5024	109	26	.	.	PUNCT
ejpam-5024	110	1	3.1	3.1	NUM
ejpam-5024	110	2	.	.	PUNCT
ejpam-5024	110	3	collocation	collocation	NOUN
ejpam-5024	110	4	method	method	NOUN
ejpam-5024	110	5	to	to	PART
ejpam-5024	110	6	find	find	VERB
ejpam-5024	110	7	the	the	DET
ejpam-5024	110	8	solution	solution	NOUN
ejpam-5024	110	9	to	to	ADP
ejpam-5024	110	10	equation	equation	NOUN
ejpam-5024	110	11	(	(	PUNCT
ejpam-5024	110	12	2.5	2.5	NUM
ejpam-5024	110	13	)	)	PUNCT
ejpam-5024	110	14	,	,	PUNCT
ejpam-5024	110	15	use	use	VERB
ejpam-5024	110	16	the	the	DET
ejpam-5024	110	17	collocation	collocation	NOUN
ejpam-5024	110	18	method	method	NOUN
ejpam-5024	110	19	.	.	PUNCT
ejpam-5024	111	1	we	we	PRON
ejpam-5024	111	2	approximate	approximate	VERB
ejpam-5024	111	3	the	the	DET
ejpam-5024	111	4	unidentified	unidentified	ADJ
ejpam-5024	111	5	function	function	NOUN
ejpam-5024	111	6	g(x	g(x	NOUN
ejpam-5024	111	7	)	)	PUNCT
ejpam-5024	111	8	by	by	ADP
ejpam-5024	111	9	using	use	VERB
ejpam-5024	111	10	the	the	DET
ejpam-5024	111	11	function	function	NOUN
ejpam-5024	111	12	li(x	li(x	NOUN
ejpam-5024	111	13	)	)	PUNCT
ejpam-5024	111	14	.	.	PUNCT
ejpam-5024	112	1	s(t	s(t	PROPN
ejpam-5024	112	2	,	,	PUNCT
ejpam-5024	112	3	xi	xi	X
ejpam-5024	112	4	)	)	PUNCT
ejpam-5024	112	5	=	=	SYM
ejpam-5024	113	1	n∑	n∑	NOUN
ejpam-5024	113	2	i=1	i=1	PROPN
ejpam-5024	114	1	cili(x	cili(x	PROPN
ejpam-5024	114	2	)	)	PUNCT
ejpam-5024	114	3	(	(	PUNCT
ejpam-5024	114	4	37	37	NUM
ejpam-5024	114	5	)	)	PUNCT
ejpam-5024	114	6	given	give	VERB
ejpam-5024	114	7	a	a	DET
ejpam-5024	114	8	set	set	NOUN
ejpam-5024	114	9	of	of	ADP
ejpam-5024	114	10	n	n	CCONJ
ejpam-5024	114	11	linearly	linearly	ADV
ejpam-5024	114	12	independent	independent	ADJ
ejpam-5024	114	13	functions	function	NOUN
ejpam-5024	114	14	l1(x	l1(x	NOUN
ejpam-5024	114	15	)	)	PUNCT
ejpam-5024	114	16	,	,	PUNCT
ejpam-5024	114	17	l2(x	l2(x	PROPN
ejpam-5024	114	18	)	)	PUNCT
ejpam-5024	114	19	,	,	PUNCT
ejpam-5024	114	20	.	.	PUNCT
ejpam-5024	114	21	.	.	PUNCT
ejpam-5024	114	22	.	.	PUNCT
ejpam-5024	115	1	,	,	PUNCT
ejpam-5024	115	2	ln	ln	X
ejpam-5024	115	3	(	(	PUNCT
ejpam-5024	115	4	x	x	X
ejpam-5024	115	5	)	)	PUNCT
ejpam-5024	115	6	defined	define	VERB
ejpam-5024	115	7	on	on	ADP
ejpam-5024	115	8	the	the	DET
ejpam-5024	115	9	interval	interval	NOUN
ejpam-5024	115	10	(	(	PUNCT
ejpam-5024	115	11	0	0	NUM
ejpam-5024	115	12	,	,	PUNCT
ejpam-5024	115	13	a	a	DET
ejpam-5024	115	14	)	)	PUNCT
ejpam-5024	115	15	.	.	PUNCT
ejpam-5024	116	1	therefore	therefore	ADV
ejpam-5024	116	2	,	,	PUNCT
ejpam-5024	116	3	we	we	PRON
ejpam-5024	116	4	have	have	VERB
ejpam-5024	116	5	:	:	PUNCT
ejpam-5024	116	6	µsn(t	µsn(t	X
ejpam-5024	116	7	)	)	PUNCT
ejpam-5024	117	1	≈	≈	PROPN
ejpam-5024	117	2	f	f	PROPN
ejpam-5024	117	3	(	(	PUNCT
ejpam-5024	117	4	t	t	PROPN
ejpam-5024	117	5	,	,	PUNCT
ejpam-5024	117	6	xi	xi	PROPN
ejpam-5024	117	7	)	)	PUNCT
ejpam-5024	118	1	+	+	CCONJ
ejpam-5024	118	2	∫	∫	PROPN
ejpam-5024	118	3	a	a	DET
ejpam-5024	118	4	0	0	NUM
ejpam-5024	118	5	ψ(t	ψ(t	PROPN
ejpam-5024	118	6	,	,	PUNCT
ejpam-5024	118	7	x)sn(x)dx+	x)sn(x)dx+	ADJ
ejpam-5024	118	8	n−1∑	n−1∑	PROPN
ejpam-5024	118	9	m=0	m=0	PROPN
ejpam-5024	118	10	umϕjmsn(x	umϕjmsn(x	PROPN
ejpam-5024	118	11	)	)	PUNCT
ejpam-5024	119	1	+	+	CCONJ
ejpam-5024	119	2	ϵ	ϵ	X
ejpam-5024	119	3	(	(	PUNCT
ejpam-5024	119	4	x	x	NOUN
ejpam-5024	119	5	,	,	PUNCT
ejpam-5024	119	6	c1(t	c1(t	NOUN
ejpam-5024	119	7	)	)	PUNCT
ejpam-5024	119	8	,	,	PUNCT
ejpam-5024	119	9	c2(t	c2(t	PROPN
ejpam-5024	119	10	)	)	PUNCT
ejpam-5024	119	11	,	,	PUNCT
ejpam-5024	119	12	.	.	PUNCT
ejpam-5024	119	13	.	.	PUNCT
ejpam-5024	119	14	.	.	PUNCT
ejpam-5024	120	1	,	,	PUNCT
ejpam-5024	120	2	cn	cn	PROPN
ejpam-5024	120	3	(	(	PUNCT
ejpam-5024	120	4	t	t	PROPN
ejpam-5024	120	5	)	)	PUNCT
ejpam-5024	121	1	+	+	NOUN
ejpam-5024	121	2	r	r	NOUN
ejpam-5024	121	3	(	(	PUNCT
ejpam-5024	121	4	hp+1	hp+1	NOUN
ejpam-5024	121	5	i	i	NOUN
ejpam-5024	121	6	)	)	PUNCT
ejpam-5024	121	7	)	)	PUNCT
ejpam-5024	121	8	.j	.j	NOUN
ejpam-5024	122	1	=	=	PUNCT
ejpam-5024	122	2	0	0	NUM
ejpam-5024	122	3	,	,	PUNCT
ejpam-5024	122	4	1	1	NUM
ejpam-5024	122	5	,	,	PUNCT
ejpam-5024	122	6	.	.	PUNCT
ejpam-5024	122	7	.	.	PUNCT
ejpam-5024	123	1	.	.	PUNCT
ejpam-5024	124	1	,	,	PUNCT
ejpam-5024	124	2	n	n	X
ejpam-5024	124	3	(	(	PUNCT
ejpam-5024	124	4	38	38	NUM
ejpam-5024	124	5	)	)	PUNCT
ejpam-5024	124	6	f.	f.	PROPN
ejpam-5024	124	7	m.	m.	PROPN
ejpam-5024	124	8	alharbi	alharbi	PROPN
ejpam-5024	124	9	,	,	PUNCT
ejpam-5024	124	10	s.	s.	PROPN
ejpam-5024	124	11	s.	s.	PROPN
ejpam-5024	124	12	althubiti	althubiti	PROPN
ejpam-5024	124	13	/	/	SYM
ejpam-5024	124	14	eur	eur	PROPN
ejpam-5024	124	15	.	.	PUNCT
ejpam-5024	125	1	j.	j.	PROPN
ejpam-5024	125	2	pure	pure	PROPN
ejpam-5024	125	3	appl	appl	PROPN
ejpam-5024	125	4	.	.	PROPN
ejpam-5024	125	5	math	math	PROPN
ejpam-5024	125	6	,	,	PUNCT
ejpam-5024	125	7	17	17	NUM
ejpam-5024	125	8	(	(	PUNCT
ejpam-5024	125	9	1	1	NUM
ejpam-5024	125	10	)	)	PUNCT
ejpam-5024	125	11	(	(	PUNCT
ejpam-5024	125	12	2024	2024	NUM
ejpam-5024	125	13	)	)	PUNCT
ejpam-5024	125	14	,	,	PUNCT
ejpam-5024	125	15	286	286	NUM
ejpam-5024	125	16	-	-	SYM
ejpam-5024	125	17	299	299	NUM
ejpam-5024	125	18	292	292	NUM
ejpam-5024	125	19	of	of	ADP
ejpam-5024	125	20	course	course	NOUN
ejpam-5024	125	21	,	,	PUNCT
ejpam-5024	125	22	if	if	SCONJ
ejpam-5024	125	23	the	the	DET
ejpam-5024	125	24	approximate	approximate	ADJ
ejpam-5024	125	25	solution	solution	NOUN
ejpam-5024	125	26	(	(	PUNCT
ejpam-5024	125	27	3.1	3.1	NUM
ejpam-5024	125	28	)	)	PUNCT
ejpam-5024	125	29	is	be	AUX
ejpam-5024	125	30	substituted	substitute	VERB
ejpam-5024	125	31	with	with	ADP
ejpam-5024	125	32	(	(	PUNCT
ejpam-5024	125	33	2.36	2.36	NUM
ejpam-5024	125	34	)	)	PUNCT
ejpam-5024	125	35	for	for	ADP
ejpam-5024	125	36	the	the	DET
ejpam-5024	125	37	function	function	NOUN
ejpam-5024	125	38	g(t	g(t	PROPN
ejpam-5024	125	39	,	,	PUNCT
ejpam-5024	125	40	x	x	X
ejpam-5024	125	41	)	)	PUNCT
ejpam-5024	125	42	,	,	PUNCT
ejpam-5024	125	43	there	there	PRON
ejpam-5024	125	44	would	would	AUX
ejpam-5024	125	45	inevitably	inevitably	ADV
ejpam-5024	125	46	be	be	AUX
ejpam-5024	125	47	an	an	DET
ejpam-5024	125	48	error	error	NOUN
ejpam-5024	125	49	denoted	denote	VERB
ejpam-5024	125	50	as	as	ADP
ejpam-5024	125	51	ε	ε	PROPN
ejpam-5024	125	52	(	(	PUNCT
ejpam-5024	125	53	x	x	NOUN
ejpam-5024	125	54	,	,	PUNCT
ejpam-5024	125	55	c1(t	c1(t	NOUN
ejpam-5024	125	56	)	)	PUNCT
ejpam-5024	125	57	,	,	PUNCT
ejpam-5024	125	58	c2(t	c2(t	PROPN
ejpam-5024	125	59	)	)	PUNCT
ejpam-5024	125	60	,	,	PUNCT
ejpam-5024	125	61	.	.	PUNCT
ejpam-5024	125	62	.	.	PUNCT
ejpam-5024	126	1	.	.	PUNCT
ejpam-5024	127	1	,	,	PUNCT
ejpam-5024	127	2	cn	cn	PROPN
ejpam-5024	127	3	(	(	PUNCT
ejpam-5024	127	4	t	t	PROPN
ejpam-5024	127	5	)	)	PUNCT
ejpam-5024	127	6	)	)	PUNCT
ejpam-5024	127	7	.	.	PUNCT
ejpam-5024	128	1	the	the	DET
ejpam-5024	128	2	extent	extent	NOUN
ejpam-5024	128	3	of	of	ADP
ejpam-5024	128	4	this	this	DET
ejpam-5024	128	5	error	error	NOUN
ejpam-5024	128	6	is	be	AUX
ejpam-5024	128	7	dependent	dependent	ADJ
ejpam-5024	128	8	on	on	ADP
ejpam-5024	128	9	the	the	DET
ejpam-5024	128	10	selection	selection	NOUN
ejpam-5024	128	11	of	of	ADP
ejpam-5024	128	12	coefficients	coefficient	NOUN
ejpam-5024	128	13	in	in	ADP
ejpam-5024	128	14	the	the	DET
ejpam-5024	128	15	formula	formula	NOUN
ejpam-5024	128	16	.	.	PUNCT
ejpam-5024	129	1	the	the	DET
ejpam-5024	129	2	value	value	NOUN
ejpam-5024	129	3	of	of	ADP
ejpam-5024	129	4	x	x	PROPN
ejpam-5024	129	5	is	be	AUX
ejpam-5024	129	6	selected	select	VERB
ejpam-5024	129	7	.	.	PUNCT
ejpam-5024	130	1	given	give	VERB
ejpam-5024	130	2	that	that	PRON
ejpam-5024	130	3	x	x	PRON
ejpam-5024	130	4	is	be	AUX
ejpam-5024	130	5	equal	equal	ADJ
ejpam-5024	130	6	to	to	ADP
ejpam-5024	130	7	xi	xi	PROPN
ejpam-5024	130	8	for	for	ADP
ejpam-5024	130	9	i	i	PRON
ejpam-5024	130	10	ranging	range	VERB
ejpam-5024	130	11	from	from	ADP
ejpam-5024	130	12	0	0	NUM
ejpam-5024	130	13	to	to	ADP
ejpam-5024	130	14	n	n	PROPN
ejpam-5024	130	15	,	,	PUNCT
ejpam-5024	130	16	we	we	PRON
ejpam-5024	130	17	may	may	AUX
ejpam-5024	130	18	express	express	VERB
ejpam-5024	130	19	this	this	PRON
ejpam-5024	130	20	as	as	ADP
ejpam-5024	130	21	:	:	PUNCT
ejpam-5024	130	22	µ	µ	NUM
ejpam-5024	130	23	n∑	n∑	NOUN
ejpam-5024	130	24	i=1	i=1	PROPN
ejpam-5024	130	25	cili(x	cili(x	PROPN
ejpam-5024	130	26	)	)	PUNCT
ejpam-5024	131	1	≈	≈	PROPN
ejpam-5024	131	2	f	f	PROPN
ejpam-5024	131	3	(	(	PUNCT
ejpam-5024	131	4	t	t	PROPN
ejpam-5024	131	5	,	,	PUNCT
ejpam-5024	131	6	xi	xi	PROPN
ejpam-5024	131	7	)	)	PUNCT
ejpam-5024	132	1	+	+	CCONJ
ejpam-5024	132	2	∫	∫	PROPN
ejpam-5024	132	3	a	a	DET
ejpam-5024	132	4	0	0	NUM
ejpam-5024	132	5	ψ(t	ψ(t	PROPN
ejpam-5024	132	6	,	,	PUNCT
ejpam-5024	132	7	x	x	NOUN
ejpam-5024	132	8	)	)	PUNCT
ejpam-5024	132	9	n∑	n∑	NOUN
ejpam-5024	133	1	i=1	i=1	PROPN
ejpam-5024	133	2	cili(x)dx	cili(x)dx	VERB
ejpam-5024	133	3	+	+	CCONJ
ejpam-5024	133	4	n−1∑	n−1∑	PROPN
ejpam-5024	133	5	m=0	m=0	PROPN
ejpam-5024	133	6	umϕjm	umϕjm	PROPN
ejpam-5024	133	7	n∑	n∑	PROPN
ejpam-5024	133	8	i=1	i=1	PROPN
ejpam-5024	133	9	cili(x	cili(x	PROPN
ejpam-5024	133	10	)	)	PUNCT
ejpam-5024	134	1	+	+	CCONJ
ejpam-5024	134	2	ϵ	ϵ	X
ejpam-5024	134	3	(	(	PUNCT
ejpam-5024	134	4	x	x	NOUN
ejpam-5024	134	5	,	,	PUNCT
ejpam-5024	134	6	c1(t	c1(t	NOUN
ejpam-5024	134	7	)	)	PUNCT
ejpam-5024	134	8	,	,	PUNCT
ejpam-5024	134	9	c2(t	c2(t	PROPN
ejpam-5024	134	10	)	)	PUNCT
ejpam-5024	134	11	,	,	PUNCT
ejpam-5024	134	12	.	.	PUNCT
ejpam-5024	134	13	.	.	PUNCT
ejpam-5024	134	14	.	.	PUNCT
ejpam-5024	135	1	,	,	PUNCT
ejpam-5024	135	2	cn	cn	PROPN
ejpam-5024	135	3	(	(	PUNCT
ejpam-5024	135	4	t	t	PROPN
ejpam-5024	135	5	)	)	PUNCT
ejpam-5024	136	1	+	+	NOUN
ejpam-5024	136	2	r	r	NOUN
ejpam-5024	136	3	(	(	PUNCT
ejpam-5024	136	4	hp+1	hp+1	NOUN
ejpam-5024	136	5	i	i	NOUN
ejpam-5024	136	6	)	)	PUNCT
ejpam-5024	136	7	)	)	PUNCT
ejpam-5024	136	8	,	,	PUNCT
ejpam-5024	136	9	j	j	PROPN
ejpam-5024	136	10	=	=	SYM
ejpam-5024	136	11	1	1	NUM
ejpam-5024	136	12	,	,	PUNCT
ejpam-5024	136	13	.	.	PUNCT
ejpam-5024	136	14	.	.	PUNCT
ejpam-5024	137	1	.	.	PUNCT
ejpam-5024	138	1	,	,	PUNCT
ejpam-5024	138	2	n	n	X
ejpam-5024	138	3	(	(	PUNCT
ejpam-5024	138	4	39	39	NUM
ejpam-5024	138	5	)	)	PUNCT
ejpam-5024	138	6	for	for	ADP
ejpam-5024	138	7	determining	determine	VERB
ejpam-5024	138	8	the	the	DET
ejpam-5024	138	9	coefficients	coefficient	NOUN
ejpam-5024	138	10	c1	c1	PROPN
ejpam-5024	138	11	(	(	PUNCT
ejpam-5024	138	12	ti	ti	NOUN
ejpam-5024	138	13	)	)	PUNCT
ejpam-5024	138	14	,	,	PUNCT
ejpam-5024	138	15	c2	c2	PROPN
ejpam-5024	138	16	(	(	PUNCT
ejpam-5024	138	17	ti	ti	NOUN
ejpam-5024	138	18	)	)	PUNCT
ejpam-5024	138	19	,	,	PUNCT
ejpam-5024	138	20	.	.	PUNCT
ejpam-5024	138	21	.	.	PUNCT
ejpam-5024	139	1	.	.	PUNCT
ejpam-5024	140	1	,	,	PUNCT
ejpam-5024	140	2	cn	cn	X
ejpam-5024	140	3	(	(	PUNCT
ejpam-5024	140	4	ti	ti	NOUN
ejpam-5024	140	5	)	)	PUNCT
ejpam-5024	140	6	of	of	ADP
ejpam-5024	140	7	the	the	DET
ejpam-5024	140	8	approximate	approximate	ADJ
ejpam-5024	140	9	solution	solution	NOUN
ejpam-5024	140	10	sn	sn	PROPN
ejpam-5024	140	11	(	(	PUNCT
ejpam-5024	140	12	xj	xj	PROPN
ejpam-5024	140	13	)	)	PUNCT
ejpam-5024	140	14	,	,	PUNCT
ejpam-5024	140	15	as	as	SCONJ
ejpam-5024	140	16	given	give	VERB
ejpam-5024	140	17	in	in	ADP
ejpam-5024	140	18	equation	equation	NOUN
ejpam-5024	140	19	(	(	PUNCT
ejpam-5024	140	20	3.1	3.1	NUM
ejpam-5024	140	21	)	)	PUNCT
ejpam-5024	140	22	,	,	PUNCT
ejpam-5024	140	23	using	use	VERB
ejpam-5024	140	24	n	n	ADP
ejpam-5024	140	25	linearly	linearly	ADV
ejpam-5024	140	26	independent	independent	ADJ
ejpam-5024	140	27	functions	function	NOUN
ejpam-5024	140	28	l1(x	l1(x	NOUN
ejpam-5024	140	29	)	)	PUNCT
ejpam-5024	140	30	,	,	PUNCT
ejpam-5024	140	31	l2(x	l2(x	PROPN
ejpam-5024	140	32	)	)	PUNCT
ejpam-5024	140	33	,	,	PUNCT
ejpam-5024	140	34	.	.	PUNCT
ejpam-5024	140	35	.	.	PUNCT
ejpam-5024	141	1	.	.	PUNCT
ejpam-5024	142	1	,	,	PUNCT
ejpam-5024	142	2	ln(x	ln(x	X
ejpam-5024	142	3	)	)	PUNCT
ejpam-5024	142	4	defined	define	VERB
ejpam-5024	142	5	on	on	ADP
ejpam-5024	142	6	the	the	DET
ejpam-5024	142	7	numerical	numerical	ADJ
ejpam-5024	142	8	interval	interval	NOUN
ejpam-5024	142	9	[	[	X
ejpam-5024	142	10	0	0	NUM
ejpam-5024	142	11	,	,	PUNCT
ejpam-5024	142	12	a	a	PRON
ejpam-5024	142	13	]	]	X
ejpam-5024	142	14	.	.	PUNCT
ejpam-5024	143	1	hence	hence	ADV
ejpam-5024	143	2	,	,	PUNCT
ejpam-5024	143	3	we	we	PRON
ejpam-5024	143	4	need	need	VERB
ejpam-5024	143	5	to	to	PART
ejpam-5024	143	6	carry	carry	VERB
ejpam-5024	143	7	out	out	ADP
ejpam-5024	143	8	the	the	DET
ejpam-5024	143	9	process	process	NOUN
ejpam-5024	143	10	of	of	ADP
ejpam-5024	143	11	integration	integration	NOUN
ejpam-5024	143	12	and	and	CCONJ
ejpam-5024	143	13	subsequently	subsequently	ADV
ejpam-5024	143	14	replace	replace	VERB
ejpam-5024	143	15	x	x	PUNCT
ejpam-5024	143	16	with	with	ADP
ejpam-5024	143	17	x1	x1	PROPN
ejpam-5024	143	18	,	,	PUNCT
ejpam-5024	143	19	x2	x2	PROPN
ejpam-5024	143	20	,	,	PUNCT
ejpam-5024	143	21	.	.	PUNCT
ejpam-5024	143	22	.	.	PUNCT
ejpam-5024	143	23	.	.	PUNCT
ejpam-5024	144	1	,	,	PUNCT
ejpam-5024	144	2	xn	xn	PROPN
ejpam-5024	144	3	to	to	PART
ejpam-5024	144	4	identify	identify	VERB
ejpam-5024	144	5	the	the	DET
ejpam-5024	144	6	points	point	NOUN
ejpam-5024	144	7	at	at	ADP
ejpam-5024	144	8	which	which	PRON
ejpam-5024	144	9	the	the	DET
ejpam-5024	144	10	error	error	NOUN
ejpam-5024	144	11	ϵ	ϵ	X
ejpam-5024	144	12	(	(	PUNCT
ejpam-5024	144	13	x	x	NOUN
ejpam-5024	144	14	,	,	PUNCT
ejpam-5024	144	15	c1(t	c1(t	NOUN
ejpam-5024	144	16	)	)	PUNCT
ejpam-5024	144	17	,	,	PUNCT
ejpam-5024	144	18	c2(t	c2(t	PROPN
ejpam-5024	144	19	)	)	PUNCT
ejpam-5024	144	20	,	,	PUNCT
ejpam-5024	144	21	.	.	PUNCT
ejpam-5024	144	22	.	.	PUNCT
ejpam-5024	145	1	.	.	PUNCT
ejpam-5024	146	1	,	,	PUNCT
ejpam-5024	146	2	cn	cn	PROPN
ejpam-5024	146	3	(	(	PUNCT
ejpam-5024	146	4	t	t	PROPN
ejpam-5024	146	5	)	)	PUNCT
ejpam-5024	146	6	)	)	PUNCT
ejpam-5024	146	7	becomes	become	VERB
ejpam-5024	146	8	zero	zero	NUM
ejpam-5024	146	9	.	.	PUNCT
ejpam-5024	147	1	by	by	ADP
ejpam-5024	147	2	substituting	substitute	VERB
ejpam-5024	147	3	the	the	DET
ejpam-5024	147	4	equation	equation	NOUN
ejpam-5024	147	5	(	(	PUNCT
ejpam-5024	147	6	3.1	3.1	NUM
ejpam-5024	147	7	)	)	PUNCT
ejpam-5024	147	8	into	into	ADP
ejpam-5024	147	9	equation	equation	NOUN
ejpam-5024	147	10	(	(	PUNCT
ejpam-5024	147	11	3.2	3.2	NUM
ejpam-5024	147	12	)	)	PUNCT
ejpam-5024	147	13	,	,	PUNCT
ejpam-5024	147	14	we	we	PRON
ejpam-5024	147	15	obtain	obtain	VERB
ejpam-5024	147	16	:	:	PUNCT
ejpam-5024	147	17	µ	µ	NUM
ejpam-5024	147	18	n∑	n∑	X
ejpam-5024	147	19	i=1	i=1	PROPN
ejpam-5024	148	1	cili(x	cili(x	PROPN
ejpam-5024	148	2	)	)	PUNCT
ejpam-5024	149	1	≈	≈	PROPN
ejpam-5024	149	2	f	f	PROPN
ejpam-5024	149	3	(	(	PUNCT
ejpam-5024	149	4	t	t	PROPN
ejpam-5024	149	5	,	,	PUNCT
ejpam-5024	149	6	xi	xi	PROPN
ejpam-5024	149	7	)	)	PUNCT
ejpam-5024	150	1	+	+	CCONJ
ejpam-5024	150	2	∫	∫	PROPN
ejpam-5024	150	3	a	a	DET
ejpam-5024	150	4	0	0	NUM
ejpam-5024	150	5	ψ(t	ψ(t	PROPN
ejpam-5024	150	6	,	,	PUNCT
ejpam-5024	150	7	x	x	NOUN
ejpam-5024	150	8	)	)	PUNCT
ejpam-5024	150	9	n∑	n∑	PROPN
ejpam-5024	151	1	i=1	i=1	PROPN
ejpam-5024	151	2	cili(x)dx+	cili(x)dx+	ADJ
ejpam-5024	151	3	n−1∑	n−1∑	PROPN
ejpam-5024	151	4	m=0	m=0	PROPN
ejpam-5024	151	5	umϕjm	umϕjm	PROPN
ejpam-5024	151	6	n∑	n∑	PROPN
ejpam-5024	151	7	i=1	i=1	PROPN
ejpam-5024	152	1	cili(x	cili(x	PROPN
ejpam-5024	152	2	)	)	PUNCT
ejpam-5024	153	1	+	+	CCONJ
ejpam-5024	153	2	ϵ	ϵ	X
ejpam-5024	153	3	(	(	PUNCT
ejpam-5024	153	4	x	x	NOUN
ejpam-5024	153	5	,	,	PUNCT
ejpam-5024	153	6	c1(t	c1(t	NOUN
ejpam-5024	153	7	)	)	PUNCT
ejpam-5024	153	8	,	,	PUNCT
ejpam-5024	153	9	c2(t	c2(t	PROPN
ejpam-5024	153	10	)	)	PUNCT
ejpam-5024	153	11	,	,	PUNCT
ejpam-5024	153	12	.	.	PUNCT
ejpam-5024	153	13	.	.	PUNCT
ejpam-5024	153	14	.	.	PUNCT
ejpam-5024	154	1	,	,	PUNCT
ejpam-5024	154	2	cn	cn	PROPN
ejpam-5024	154	3	(	(	PUNCT
ejpam-5024	154	4	t	t	PROPN
ejpam-5024	154	5	)	)	PUNCT
ejpam-5024	155	1	+	+	NOUN
ejpam-5024	155	2	r	r	NOUN
ejpam-5024	155	3	(	(	PUNCT
ejpam-5024	155	4	hp+1	hp+1	NOUN
ejpam-5024	155	5	i	i	NOUN
ejpam-5024	155	6	)	)	PUNCT
ejpam-5024	155	7	)	)	PUNCT
ejpam-5024	155	8	,	,	PUNCT
ejpam-5024	155	9	j	j	PROPN
ejpam-5024	155	10	=	=	SYM
ejpam-5024	155	11	1	1	NUM
ejpam-5024	155	12	,	,	PUNCT
ejpam-5024	155	13	.	.	PUNCT
ejpam-5024	155	14	.	.	PUNCT
ejpam-5024	156	1	.	.	PUNCT
ejpam-5024	157	1	,	,	PUNCT
ejpam-5024	157	2	n	n	CCONJ
ejpam-5024	157	3	this	this	PRON
ejpam-5024	157	4	gives	give	VERB
ejpam-5024	157	5	us	we	PRON
ejpam-5024	157	6	:	:	PUNCT
ejpam-5024	157	7	µ	µ	NUM
ejpam-5024	157	8	n∑	n∑	NOUN
ejpam-5024	157	9	i=1	i=1	PROPN
ejpam-5024	158	1	cili(x	cili(x	PROPN
ejpam-5024	158	2	)	)	PUNCT
ejpam-5024	159	1	≈	≈	PROPN
ejpam-5024	159	2	f	f	PROPN
ejpam-5024	159	3	(	(	PUNCT
ejpam-5024	159	4	t	t	PROPN
ejpam-5024	159	5	,	,	PUNCT
ejpam-5024	159	6	xi	xi	PROPN
ejpam-5024	159	7	)	)	PUNCT
ejpam-5024	160	1	+	+	NUM
ejpam-5024	160	2	n∑	n∑	PROPN
ejpam-5024	160	3	i=1	i=1	PROPN
ejpam-5024	160	4	ci	ci	PROPN
ejpam-5024	160	5	∫	∫	PROPN
ejpam-5024	160	6	a	a	DET
ejpam-5024	160	7	0	0	PUNCT
ejpam-5024	160	8	ψ(t	ψ(t	PROPN
ejpam-5024	160	9	,	,	PUNCT
ejpam-5024	160	10	x)li(x)dx	x)li(x)dx	PROPN
ejpam-5024	160	11	+	+	CCONJ
ejpam-5024	160	12	n−1∑	n−1∑	PROPN
ejpam-5024	160	13	m=0	m=0	PROPN
ejpam-5024	160	14	n∑	n∑	PROPN
ejpam-5024	160	15	i=1	i=1	PROPN
ejpam-5024	161	1	umϕjmcili(x	umϕjmcili(x	NOUN
ejpam-5024	161	2	)	)	PUNCT
ejpam-5024	162	1	+	+	CCONJ
ejpam-5024	162	2	ϵ	ϵ	X
ejpam-5024	162	3	(	(	PUNCT
ejpam-5024	162	4	x	x	NOUN
ejpam-5024	162	5	,	,	PUNCT
ejpam-5024	162	6	c1(t	c1(t	NOUN
ejpam-5024	162	7	)	)	PUNCT
ejpam-5024	162	8	,	,	PUNCT
ejpam-5024	162	9	c2(t	c2(t	PROPN
ejpam-5024	162	10	)	)	PUNCT
ejpam-5024	162	11	,	,	PUNCT
ejpam-5024	162	12	.	.	PUNCT
ejpam-5024	162	13	.	.	PUNCT
ejpam-5024	162	14	.	.	PUNCT
ejpam-5024	163	1	,	,	PUNCT
ejpam-5024	163	2	cn	cn	PROPN
ejpam-5024	163	3	(	(	PUNCT
ejpam-5024	163	4	t	t	PROPN
ejpam-5024	163	5	)	)	PUNCT
ejpam-5024	164	1	+	+	NOUN
ejpam-5024	164	2	r	r	NOUN
ejpam-5024	164	3	(	(	PUNCT
ejpam-5024	164	4	hp+1	hp+1	NOUN
ejpam-5024	164	5	i	i	NOUN
ejpam-5024	164	6	)	)	PUNCT
ejpam-5024	164	7	)	)	PUNCT
ejpam-5024	164	8	,	,	PUNCT
ejpam-5024	164	9	j	j	PROPN
ejpam-5024	164	10	=	=	SYM
ejpam-5024	164	11	0	0	PROPN
ejpam-5024	164	12	,	,	PUNCT
ejpam-5024	164	13	.	.	PUNCT
ejpam-5024	164	14	.	.	PUNCT
ejpam-5024	165	1	.	.	PUNCT
ejpam-5024	166	1	,	,	PUNCT
ejpam-5024	166	2	n	n	PRON
ejpam-5024	166	3	see[6	see[6	NOUN
ejpam-5024	166	4	,	,	PUNCT
ejpam-5024	166	5	7	7	NUM
ejpam-5024	166	6	]	]	SYM
ejpam-5024	166	7	3.2	3.2	NUM
ejpam-5024	166	8	.	.	PUNCT
ejpam-5024	167	1	galerkin	galerkin	PROPN
ejpam-5024	167	2	method	method	VERB
ejpam-5024	167	3	the	the	DET
ejpam-5024	167	4	galerkin	galerkin	ADJ
ejpam-5024	167	5	method	method	NOUN
ejpam-5024	167	6	is	be	AUX
ejpam-5024	167	7	used	use	VERB
ejpam-5024	167	8	to	to	PART
ejpam-5024	167	9	obtain	obtain	VERB
ejpam-5024	167	10	an	an	DET
ejpam-5024	167	11	approximate	approximate	ADJ
ejpam-5024	167	12	solution	solution	NOUN
ejpam-5024	167	13	to	to	ADP
ejpam-5024	167	14	equation	equation	NOUN
ejpam-5024	167	15	(	(	PUNCT
ejpam-5024	167	16	2.36	2.36	NUM
ejpam-5024	167	17	)	)	PUNCT
ejpam-5024	167	18	.	.	PUNCT
ejpam-5024	168	1	the	the	DET
ejpam-5024	168	2	approach	approach	NOUN
ejpam-5024	168	3	sets	set	VERB
ejpam-5024	168	4	the	the	DET
ejpam-5024	168	5	necessary	necessary	ADJ
ejpam-5024	168	6	conditions	condition	NOUN
ejpam-5024	168	7	for	for	ADP
ejpam-5024	168	8	calculating	calculate	VERB
ejpam-5024	168	9	a	a	DET
ejpam-5024	168	10	set	set	NOUN
ejpam-5024	168	11	of	of	ADP
ejpam-5024	168	12	n	n	DET
ejpam-5024	168	13	coefficients	coefficient	NOUN
ejpam-5024	168	14	,	,	PUNCT
ejpam-5024	168	15	as	as	SCONJ
ejpam-5024	168	16	stated	state	VERB
ejpam-5024	168	17	in	in	ADP
ejpam-5024	168	18	equation	equation	NOUN
ejpam-5024	168	19	(	(	PUNCT
ejpam-5024	168	20	3.1	3.1	NUM
ejpam-5024	168	21	)	)	PUNCT
ejpam-5024	168	22	.	.	PUNCT
ejpam-5024	169	1	by	by	ADP
ejpam-5024	169	2	introducing	introduce	VERB
ejpam-5024	169	3	the	the	DET
ejpam-5024	169	4	error	error	NOUN
ejpam-5024	169	5	ε	ε	NOUN
ejpam-5024	169	6	(	(	PUNCT
ejpam-5024	169	7	x	x	NOUN
ejpam-5024	169	8	,	,	PUNCT
ejpam-5024	169	9	c1(t	c1(t	NOUN
ejpam-5024	169	10	)	)	PUNCT
ejpam-5024	169	11	,	,	PUNCT
ejpam-5024	169	12	c2(t	c2(t	PROPN
ejpam-5024	169	13	)	)	PUNCT
ejpam-5024	169	14	,	,	PUNCT
ejpam-5024	169	15	.	.	PUNCT
ejpam-5024	169	16	.	.	PUNCT
ejpam-5024	169	17	.	.	PUNCT
ejpam-5024	170	1	,	,	PUNCT
ejpam-5024	170	2	cn	cn	PROPN
ejpam-5024	170	3	(	(	PUNCT
ejpam-5024	170	4	t	t	PROPN
ejpam-5024	170	5	)	)	PUNCT
ejpam-5024	170	6	)	)	PUNCT
ejpam-5024	170	7	in	in	ADP
ejpam-5024	170	8	equation	equation	NOUN
ejpam-5024	170	9	(	(	PUNCT
ejpam-5024	170	10	3.2	3.2	NUM
ejpam-5024	170	11	)	)	PUNCT
ejpam-5024	170	12	which	which	PRON
ejpam-5024	170	13	is	be	AUX
ejpam-5024	170	14	perpendicular	perpendicular	ADJ
ejpam-5024	170	15	to	to	ADP
ejpam-5024	170	16	n	n	CCONJ
ejpam-5024	170	17	linearly	linearly	ADV
ejpam-5024	170	18	independent	independent	ADJ
ejpam-5024	170	19	functions	function	NOUN
ejpam-5024	170	20	l1(x	l1(x	NOUN
ejpam-5024	170	21	)	)	PUNCT
ejpam-5024	170	22	,	,	PUNCT
ejpam-5024	170	23	l2(x	l2(x	PROPN
ejpam-5024	170	24	)	)	PUNCT
ejpam-5024	170	25	,	,	PUNCT
ejpam-5024	170	26	.	.	PUNCT
ejpam-5024	170	27	.	.	PUNCT
ejpam-5024	171	1	.	.	PUNCT
ejpam-5024	172	1	,	,	PUNCT
ejpam-5024	172	2	ln	ln	X
ejpam-5024	172	3	(	(	PUNCT
ejpam-5024	172	4	x	x	X
ejpam-5024	172	5	)	)	PUNCT
ejpam-5024	172	6	on	on	ADP
ejpam-5024	172	7	the	the	DET
ejpam-5024	172	8	f.	f.	PROPN
ejpam-5024	172	9	m.	m.	PROPN
ejpam-5024	172	10	alharbi	alharbi	PROPN
ejpam-5024	172	11	,	,	PUNCT
ejpam-5024	172	12	s.	s.	PROPN
ejpam-5024	172	13	s.	s.	PROPN
ejpam-5024	172	14	althubiti	althubiti	PROPN
ejpam-5024	172	15	/	/	SYM
ejpam-5024	172	16	eur	eur	PROPN
ejpam-5024	172	17	.	.	PUNCT
ejpam-5024	173	1	j.	j.	PROPN
ejpam-5024	173	2	pure	pure	PROPN
ejpam-5024	173	3	appl	appl	PROPN
ejpam-5024	173	4	.	.	PROPN
ejpam-5024	173	5	math	math	PROPN
ejpam-5024	173	6	,	,	PUNCT
ejpam-5024	173	7	17	17	NUM
ejpam-5024	173	8	(	(	PUNCT
ejpam-5024	173	9	1	1	NUM
ejpam-5024	173	10	)	)	PUNCT
ejpam-5024	173	11	(	(	PUNCT
ejpam-5024	173	12	2024	2024	NUM
ejpam-5024	173	13	)	)	PUNCT
ejpam-5024	173	14	,	,	PUNCT
ejpam-5024	173	15	286	286	NUM
ejpam-5024	173	16	-	-	SYM
ejpam-5024	173	17	299	299	NUM
ejpam-5024	173	18	293	293	NUM
ejpam-5024	173	19	interval	interval	NOUN
ejpam-5024	173	20	(	(	PUNCT
ejpam-5024	173	21	0	0	NUM
ejpam-5024	173	22	,	,	PUNCT
ejpam-5024	173	23	a	a	PRON
ejpam-5024	173	24	)	)	PUNCT
ejpam-5024	173	25	,	,	PUNCT
ejpam-5024	173	26	i.e.	i.e.	X
ejpam-5024	173	27	∫	∫	PROPN
ejpam-5024	173	28	a	a	DET
ejpam-5024	173	29	0	0	NUM
ejpam-5024	173	30	lj(x)ϵ(x	lj(x)ϵ(x	PROPN
ejpam-5024	173	31	,	,	PUNCT
ejpam-5024	173	32	c1(t	c1(t	NOUN
ejpam-5024	173	33	)	)	PUNCT
ejpam-5024	173	34	,	,	PUNCT
ejpam-5024	173	35	c2(t	c2(t	PROPN
ejpam-5024	173	36	)	)	PUNCT
ejpam-5024	173	37	)	)	PUNCT
ejpam-5024	173	38	,	,	PUNCT
ejpam-5024	173	39	.	.	PUNCT
ejpam-5024	173	40	.	.	PUNCT
ejpam-5024	174	1	.	.	PUNCT
ejpam-5024	175	1	,	,	PUNCT
ejpam-5024	175	2	cn	cn	INTJ
ejpam-5024	175	3	(	(	PUNCT
ejpam-5024	175	4	t)dx	t)dx	PROPN
ejpam-5024	175	5	=	=	SYM
ejpam-5024	175	6	0	0	PUNCT
ejpam-5024	175	7	(	(	PUNCT
ejpam-5024	175	8	40	40	NUM
ejpam-5024	175	9	)	)	PUNCT
ejpam-5024	175	10	then	then	ADV
ejpam-5024	175	11	from	from	ADP
ejpam-5024	175	12	(	(	PUNCT
ejpam-5024	175	13	2.34	2.34	NUM
ejpam-5024	175	14	)	)	PUNCT
ejpam-5024	175	15	,	,	PUNCT
ejpam-5024	175	16	we	we	PRON
ejpam-5024	175	17	have	have	VERB
ejpam-5024	175	18	µ	µ	PRON
ejpam-5024	175	19	n∑	n∑	NOUN
ejpam-5024	175	20	i=1	i=1	PROPN
ejpam-5024	176	1	cili(x)−	cili(x)−	PROPN
ejpam-5024	176	2	∫	∫	PROPN
ejpam-5024	176	3	a	a	DET
ejpam-5024	176	4	0	0	NUM
ejpam-5024	176	5	ψ(t	ψ(t	PROPN
ejpam-5024	176	6	,	,	PUNCT
ejpam-5024	176	7	x	x	NOUN
ejpam-5024	176	8	)	)	PUNCT
ejpam-5024	176	9	n∑	n∑	PROPN
ejpam-5024	177	1	i=1	i=1	PROPN
ejpam-5024	178	1	cili(x)dx−	cili(x)dx−	PROPN
ejpam-5024	178	2	n−1∑	n−1∑	PROPN
ejpam-5024	179	1	m=0	m=0	PROPN
ejpam-5024	179	2	umϕjm	umϕjm	PROPN
ejpam-5024	179	3	n∑	n∑	PROPN
ejpam-5024	179	4	i=1	i=1	PROPN
ejpam-5024	179	5	cili(x	cili(x	PROPN
ejpam-5024	179	6	)	)	PUNCT
ejpam-5024	180	1	+	+	CCONJ
ejpam-5024	180	2	ϵ	ϵ	X
ejpam-5024	180	3	(	(	PUNCT
ejpam-5024	180	4	x	x	NOUN
ejpam-5024	180	5	,	,	PUNCT
ejpam-5024	180	6	c1(t	c1(t	NOUN
ejpam-5024	180	7	)	)	PUNCT
ejpam-5024	180	8	,	,	PUNCT
ejpam-5024	180	9	c2(t	c2(t	PROPN
ejpam-5024	180	10	)	)	PUNCT
ejpam-5024	180	11	,	,	PUNCT
ejpam-5024	180	12	.	.	PUNCT
ejpam-5024	180	13	.	.	PUNCT
ejpam-5024	180	14	.	.	PUNCT
ejpam-5024	181	1	,	,	PUNCT
ejpam-5024	181	2	cn	cn	PROPN
ejpam-5024	181	3	(	(	PUNCT
ejpam-5024	181	4	t	t	PROPN
ejpam-5024	181	5	)	)	PUNCT
ejpam-5024	182	1	+	+	NOUN
ejpam-5024	182	2	r	r	NOUN
ejpam-5024	182	3	(	(	PUNCT
ejpam-5024	182	4	hp+1	hp+1	NOUN
ejpam-5024	182	5	i	i	NOUN
ejpam-5024	182	6	)	)	PUNCT
ejpam-5024	182	7	)	)	PUNCT
ejpam-5024	183	1	=	=	SYM
ejpam-5024	183	2	f	f	PROPN
ejpam-5024	183	3	(	(	PUNCT
ejpam-5024	183	4	t	t	PROPN
ejpam-5024	183	5	)	)	PUNCT
ejpam-5024	183	6	(	(	PUNCT
ejpam-5024	183	7	41	41	NUM
ejpam-5024	183	8	)	)	PUNCT
ejpam-5024	183	9	then	then	ADV
ejpam-5024	183	10	the	the	DET
ejpam-5024	183	11	galerkin	galerkin	ADJ
ejpam-5024	183	12	equations	equation	NOUN
ejpam-5024	183	13	are	be	AUX
ejpam-5024	183	14	obtained	obtain	VERB
ejpam-5024	183	15	by	by	ADP
ejpam-5024	183	16	multiplying	multiply	VERB
ejpam-5024	183	17	both	both	DET
ejpam-5024	183	18	sides	side	NOUN
ejpam-5024	183	19	of	of	ADP
ejpam-5024	183	20	(	(	PUNCT
ejpam-5024	183	21	3.5	3.5	NUM
ejpam-5024	183	22	)	)	PUNCT
ejpam-5024	183	23	by	by	ADP
ejpam-5024	183	24	lj(x	lj(x	NOUN
ejpam-5024	183	25	)	)	PUNCT
ejpam-5024	183	26	and	and	CCONJ
ejpam-5024	183	27	then	then	ADV
ejpam-5024	183	28	integrating	integrate	VERB
ejpam-5024	183	29	with	with	ADP
ejpam-5024	183	30	respect	respect	NOUN
ejpam-5024	183	31	to	to	ADP
ejpam-5024	183	32	x	x	PUNCT
ejpam-5024	183	33	from	from	ADP
ejpam-5024	183	34	0	0	NUM
ejpam-5024	183	35	to	to	ADP
ejpam-5024	183	36	a	a	PRON
ejpam-5024	183	37	,	,	PUNCT
ejpam-5024	183	38	we	we	PRON
ejpam-5024	183	39	obtain	obtain	VERB
ejpam-5024	183	40	n∑	n∑	PROPN
ejpam-5024	183	41	i=1	i=1	PROPN
ejpam-5024	184	1	ci	ci	PROPN
ejpam-5024	184	2	∫	∫	PROPN
ejpam-5024	184	3	a	a	DET
ejpam-5024	184	4	0	0	NUM
ejpam-5024	185	1	[	[	PUNCT
ejpam-5024	185	2	µli(x)−	µli(x)−	PROPN
ejpam-5024	185	3	∫	∫	PROPN
ejpam-5024	185	4	a	a	DET
ejpam-5024	185	5	0	0	NUM
ejpam-5024	185	6	ψ(t	ψ(t	PROPN
ejpam-5024	185	7	,	,	PUNCT
ejpam-5024	185	8	x)li(x)dx−	x)li(x)dx−	PUNCT
ejpam-5024	186	1	n−1∑	n−1∑	NUM
ejpam-5024	186	2	m=0	m=0	PROPN
ejpam-5024	186	3	umϕjmli(x	umϕjmli(x	PROPN
ejpam-5024	186	4	)	)	PUNCT
ejpam-5024	186	5	]	]	PUNCT
ejpam-5024	187	1	li(x)dx	li(x)dx	NOUN
ejpam-5024	187	2	(	(	PUNCT
ejpam-5024	187	3	42	42	NUM
ejpam-5024	187	4	)	)	PUNCT
ejpam-5024	187	5	=	=	VERB
ejpam-5024	188	1	∫	∫	PROPN
ejpam-5024	188	2	a	a	PRON
ejpam-5024	189	1	0	0	NUM
ejpam-5024	189	2	f	f	NOUN
ejpam-5024	189	3	(	(	PUNCT
ejpam-5024	189	4	t)li(x)dx	t)li(x)dx	INTJ
ejpam-5024	189	5	(	(	PUNCT
ejpam-5024	189	6	43	43	NUM
ejpam-5024	189	7	)	)	PUNCT
ejpam-5024	189	8	the	the	DET
ejpam-5024	189	9	unknown	unknown	ADJ
ejpam-5024	189	10	parameters	parameter	NOUN
ejpam-5024	189	11	ci	ci	PROPN
ejpam-5024	189	12	are	be	AUX
ejpam-5024	189	13	determined	determine	VERB
ejpam-5024	189	14	by	by	ADP
ejpam-5024	189	15	solving	solve	VERB
ejpam-5024	189	16	the	the	DET
ejpam-5024	189	17	system	system	NOUN
ejpam-5024	189	18	of	of	ADP
ejpam-5024	189	19	equations	equation	NOUN
ejpam-5024	189	20	mentioned	mention	VERB
ejpam-5024	189	21	above	above	ADV
ejpam-5024	189	22	and	and	CCONJ
ejpam-5024	189	23	inserting	insert	VERB
ejpam-5024	189	24	these	these	DET
ejpam-5024	189	25	values	value	NOUN
ejpam-5024	189	26	of	of	ADP
ejpam-5024	189	27	parameters	parameter	NOUN
ejpam-5024	189	28	in	in	ADP
ejpam-5024	189	29	trial	trial	NOUN
ejpam-5024	189	30	functions	function	NOUN
ejpam-5024	189	31	.	.	PUNCT
ejpam-5024	190	1	we	we	PRON
ejpam-5024	190	2	obtain	obtain	VERB
ejpam-5024	190	3	an	an	DET
ejpam-5024	190	4	approximate	approximate	ADJ
ejpam-5024	190	5	solution	solution	NOUN
ejpam-5024	190	6	,	,	PUNCT
ejpam-5024	190	7	denoted	denote	VERB
ejpam-5024	190	8	as	as	ADP
ejpam-5024	190	9	gh	gh	PROPN
ejpam-5024	190	10	,	,	PUNCT
ejpam-5024	190	11	of	of	ADP
ejpam-5024	190	12	the	the	DET
ejpam-5024	190	13	v	v	NOUN
ejpam-5024	190	14	-	-	PUNCT
ejpam-5024	190	15	fie	fie	NOUN
ejpam-5024	190	16	.see	.see	PUNCT
ejpam-5024	191	1	[	[	X
ejpam-5024	191	2	7	7	NUM
ejpam-5024	191	3	,	,	PUNCT
ejpam-5024	191	4	8	8	NUM
ejpam-5024	191	5	]	]	SYM
ejpam-5024	191	6	4	4	NUM
ejpam-5024	191	7	.	.	PUNCT
ejpam-5024	191	8	applications	application	NOUN
ejpam-5024	191	9	.	.	PUNCT
ejpam-5024	192	1	consider	consider	VERB
ejpam-5024	192	2	the	the	DET
ejpam-5024	192	3	following	follow	VERB
ejpam-5024	192	4	applications	application	NOUN
ejpam-5024	192	5	:	:	PUNCT
ejpam-5024	192	6	application	application	NOUN
ejpam-5024	192	7	(	(	PUNCT
ejpam-5024	192	8	1	1	X
ejpam-5024	192	9	)	)	PUNCT
ejpam-5024	192	10	consider	consider	VERB
ejpam-5024	192	11	the	the	DET
ejpam-5024	192	12	ivp	ivp	NOUN
ejpam-5024	192	13	,	,	PUNCT
ejpam-5024	192	14	y′′(t	y′′(t	VERB
ejpam-5024	192	15	)	)	PUNCT
ejpam-5024	192	16	=	=	SYM
ejpam-5024	192	17	2−	2−	NUM
ejpam-5024	192	18	cos	cos	NOUN
ejpam-5024	192	19	t+	t+	PUNCT
ejpam-5024	192	20	∫	∫	PROPN
ejpam-5024	192	21	π	π	PROPN
ejpam-5024	192	22	0	0	NUM
ejpam-5024	192	23	ty(t)dt	ty(t)dt	PROPN
ejpam-5024	192	24	(	(	PUNCT
ejpam-5024	192	25	44	44	NUM
ejpam-5024	192	26	)	)	PUNCT
ejpam-5024	192	27	under	under	ADP
ejpam-5024	192	28	the	the	DET
ejpam-5024	192	29	initial	initial	ADJ
ejpam-5024	192	30	conditions	condition	NOUN
ejpam-5024	192	31	y′(0	y′(0	NOUN
ejpam-5024	192	32	)	)	PUNCT
ejpam-5024	192	33	=	=	SYM
ejpam-5024	192	34	0	0	X
ejpam-5024	192	35	y(0	y(0	PROPN
ejpam-5024	192	36	)	)	PUNCT
ejpam-5024	192	37	=	=	SYM
ejpam-5024	192	38	0	0	PUNCT
ejpam-5024	193	1	(	(	PUNCT
ejpam-5024	193	2	45	45	NUM
ejpam-5024	193	3	)	)	PUNCT
ejpam-5024	193	4	the	the	DET
ejpam-5024	193	5	exact	exact	ADJ
ejpam-5024	193	6	solution	solution	NOUN
ejpam-5024	193	7	is	be	AUX
ejpam-5024	193	8	y(t	y(t	NUM
ejpam-5024	193	9	)	)	PUNCT
ejpam-5024	194	1	=	=	PUNCT
ejpam-5024	194	2	|	|	ADV
ejpam-5024	194	3	cos	cos	PROPN
ejpam-5024	194	4	t|	t|	PROPN
ejpam-5024	194	5	.	.	PUNCT
ejpam-5024	195	1	after	after	ADP
ejpam-5024	195	2	converting	convert	VERB
ejpam-5024	195	3	it	it	PRON
ejpam-5024	195	4	to	to	ADP
ejpam-5024	195	5	v	v	NOUN
ejpam-5024	195	6	-	-	PUNCT
ejpam-5024	195	7	fie	fie	NOUN
ejpam-5024	195	8	we	we	PRON
ejpam-5024	195	9	get	get	VERB
ejpam-5024	195	10	:	:	PUNCT
ejpam-5024	196	1	ϕ(t)−	ϕ(t)−	PROPN
ejpam-5024	196	2	∫	∫	PROPN
ejpam-5024	196	3	π	π	NOUN
ejpam-5024	196	4	0	0	NUM
ejpam-5024	196	5	ψ(x)ϕ(x)dx	ψ(x)ϕ(x)dx	NOUN
ejpam-5024	196	6	=	=	SYM
ejpam-5024	196	7	f	f	X
ejpam-5024	196	8	(	(	PUNCT
ejpam-5024	196	9	t	t	PROPN
ejpam-5024	196	10	)	)	PUNCT
ejpam-5024	196	11	where	where	SCONJ
ejpam-5024	196	12	,	,	PUNCT
ejpam-5024	196	13	ψ(x	ψ(x	PROPN
ejpam-5024	196	14	)	)	PUNCT
ejpam-5024	196	15	=	=	SYM
ejpam-5024	197	1	∫	∫	PROPN
ejpam-5024	197	2	t	t	NOUN
ejpam-5024	197	3	0	0	NUM
ejpam-5024	198	1	t(t−	t(t−	PROPN
ejpam-5024	198	2	x)dt	x)dt	PROPN
ejpam-5024	198	3	f	f	PROPN
ejpam-5024	198	4	(	(	PUNCT
ejpam-5024	198	5	x	x	NOUN
ejpam-5024	198	6	)	)	PUNCT
ejpam-5024	198	7	=	=	SYM
ejpam-5024	198	8	2−	2−	NUM
ejpam-5024	198	9	cos	cos	ADP
ejpam-5024	198	10	t.	t.	PROPN
ejpam-5024	198	11	(	(	PUNCT
ejpam-5024	198	12	46	46	NUM
ejpam-5024	198	13	)	)	PUNCT
ejpam-5024	198	14	f.	f.	PROPN
ejpam-5024	198	15	m.	m.	PROPN
ejpam-5024	198	16	alharbi	alharbi	PROPN
ejpam-5024	198	17	,	,	PUNCT
ejpam-5024	198	18	s.	s.	PROPN
ejpam-5024	198	19	s.	s.	PROPN
ejpam-5024	198	20	althubiti	althubiti	PROPN
ejpam-5024	198	21	/	/	SYM
ejpam-5024	198	22	eur	eur	PROPN
ejpam-5024	198	23	.	.	PUNCT
ejpam-5024	199	1	j.	j.	PROPN
ejpam-5024	199	2	pure	pure	PROPN
ejpam-5024	199	3	appl	appl	PROPN
ejpam-5024	199	4	.	.	PROPN
ejpam-5024	199	5	math	math	PROPN
ejpam-5024	199	6	,	,	PUNCT
ejpam-5024	199	7	17	17	NUM
ejpam-5024	199	8	(	(	PUNCT
ejpam-5024	199	9	1	1	NUM
ejpam-5024	199	10	)	)	PUNCT
ejpam-5024	199	11	(	(	PUNCT
ejpam-5024	199	12	2024	2024	NUM
ejpam-5024	199	13	)	)	PUNCT
ejpam-5024	199	14	,	,	PUNCT
ejpam-5024	199	15	286	286	NUM
ejpam-5024	199	16	-	-	SYM
ejpam-5024	199	17	299	299	NUM
ejpam-5024	199	18	294	294	NUM
ejpam-5024	199	19	•	•	NOUN
ejpam-5024	199	20	using	use	VERB
ejpam-5024	199	21	collocation	collocation	NOUN
ejpam-5024	199	22	method	method	NOUN
ejpam-5024	199	23	let	let	VERB
ejpam-5024	199	24	us	we	PRON
ejpam-5024	199	25	consider	consider	VERB
ejpam-5024	199	26	the	the	DET
ejpam-5024	199	27	approximate	approximate	ADJ
ejpam-5024	199	28	answer	answer	VERB
ejpam-5024	199	29	the	the	DET
ejpam-5024	199	30	equation	equation	NOUN
ejpam-5024	199	31	(	(	PUNCT
ejpam-5024	199	32	4.1	4.1	NUM
ejpam-5024	199	33	)	)	PUNCT
ejpam-5024	199	34	,	,	PUNCT
ejpam-5024	199	35	as	as	ADP
ejpam-5024	199	36	the	the	DET
ejpam-5024	199	37	three	three	NUM
ejpam-5024	199	38	independent	independent	ADJ
ejpam-5024	199	39	functions	function	NOUN
ejpam-5024	199	40	,	,	PUNCT
ejpam-5024	199	41	l0(t	l0(t	X
ejpam-5024	199	42	)	)	PUNCT
ejpam-5024	199	43	=	=	SYM
ejpam-5024	199	44	1	1	NUM
ejpam-5024	199	45	,	,	PUNCT
ejpam-5024	199	46	l1	l1	PROPN
ejpam-5024	199	47	=	=	SYM
ejpam-5024	199	48	t	t	PROPN
ejpam-5024	199	49	,	,	PUNCT
ejpam-5024	199	50	l2(t	l2(t	PROPN
ejpam-5024	199	51	)	)	PUNCT
ejpam-5024	199	52	=	=	PUNCT
ejpam-5024	199	53	|cos(t)|	|cos(t)|	NOUN
ejpam-5024	199	54	.	.	PUNCT
ejpam-5024	200	1	by	by	ADP
ejpam-5024	200	2	substituting	substitute	VERB
ejpam-5024	200	3	these	these	DET
ejpam-5024	200	4	functions	function	NOUN
ejpam-5024	200	5	into	into	ADP
ejpam-5024	200	6	equation	equation	NOUN
ejpam-5024	200	7	(	(	PUNCT
ejpam-5024	200	8	4.3	4.3	NUM
ejpam-5024	200	9	)	)	PUNCT
ejpam-5024	200	10	and	and	CCONJ
ejpam-5024	200	11	then	then	ADV
ejpam-5024	200	12	solving	solve	VERB
ejpam-5024	200	13	the	the	DET
ejpam-5024	200	14	resulting	result	VERB
ejpam-5024	200	15	equation	equation	NOUN
ejpam-5024	200	16	when	when	SCONJ
ejpam-5024	200	17	t	t	PROPN
ejpam-5024	200	18	=	=	SYM
ejpam-5024	200	19	0	0	NUM
ejpam-5024	200	20	,	,	PUNCT
ejpam-5024	200	21	π2	π2	X
ejpam-5024	200	22	,	,	PUNCT
ejpam-5024	200	23	π	π	X
ejpam-5024	200	24	,	,	PUNCT
ejpam-5024	200	25	we	we	PRON
ejpam-5024	200	26	get	get	VERB
ejpam-5024	200	27	:	:	PUNCT
ejpam-5024	200	28	c0	c0	PROPN
ejpam-5024	200	29	=	=	PUNCT
ejpam-5024	200	30	−1.34404356	−1.34404356	PROPN
ejpam-5024	200	31	c1	c1	NOUN
ejpam-5024	200	32	=	=	PROPN
ejpam-5024	200	33	0.382981562	0.382981562	NUM
ejpam-5024	200	34	c2	c2	PROPN
ejpam-5024	200	35	=	=	PROPN
ejpam-5024	200	36	2.34404356	2.34404356	NUM
ejpam-5024	200	37	therefore	therefore	ADV
ejpam-5024	200	38	,	,	PUNCT
ejpam-5024	200	39	the	the	DET
ejpam-5024	200	40	approximate	approximate	ADJ
ejpam-5024	200	41	solution	solution	NOUN
ejpam-5024	200	42	is	be	AUX
ejpam-5024	200	43	s1(t	s1(t	X
ejpam-5024	200	44	)	)	PUNCT
ejpam-5024	200	45	=	=	SYM
ejpam-5024	201	1	−1.34404356	−1.34404356	NOUN
ejpam-5024	201	2	+	+	CCONJ
ejpam-5024	201	3	0.382981562t+	0.382981562t+	X
ejpam-5024	201	4	2.34404356|cos(t)|	2.34404356|cos(t)|	NUM
ejpam-5024	201	5	.	.	PUNCT
ejpam-5024	202	1	•	•	NOUN
ejpam-5024	202	2	using	use	VERB
ejpam-5024	202	3	galerkin	galerkin	ADJ
ejpam-5024	202	4	method	method	NOUN
ejpam-5024	202	5	as	as	ADP
ejpam-5024	202	6	the	the	DET
ejpam-5024	202	7	same	same	ADJ
ejpam-5024	202	8	consideration	consideration	NOUN
ejpam-5024	202	9	independent	independent	ADJ
ejpam-5024	202	10	approximate	approximate	ADJ
ejpam-5024	202	11	solution	solution	NOUN
ejpam-5024	202	12	and	and	CCONJ
ejpam-5024	202	13	the	the	DET
ejpam-5024	202	14	same	same	ADJ
ejpam-5024	202	15	arbitrary	arbitrary	ADJ
ejpam-5024	202	16	points	point	NOUN
ejpam-5024	202	17	in	in	ADP
ejpam-5024	202	18	the	the	DET
ejpam-5024	202	19	collocation	collocation	NOUN
ejpam-5024	202	20	method	method	NOUN
ejpam-5024	202	21	,	,	PUNCT
ejpam-5024	202	22	we	we	PRON
ejpam-5024	202	23	get	get	VERB
ejpam-5024	202	24	,	,	PUNCT
ejpam-5024	202	25	c0	c0	PROPN
ejpam-5024	202	26	=	=	PROPN
ejpam-5024	202	27	−1.32446935	−1.32446935	PROPN
ejpam-5024	202	28	c1	c1	NOUN
ejpam-5024	202	29	=	=	PROPN
ejpam-5024	203	1	0.332647197	0.332647197	NUM
ejpam-5024	204	1	c2	c2	PROPN
ejpam-5024	204	2	=	=	SYM
ejpam-5024	204	3	2.18043309	2.18043309	NUM
ejpam-5024	204	4	therefore	therefore	ADV
ejpam-5024	204	5	,	,	PUNCT
ejpam-5024	204	6	the	the	DET
ejpam-5024	204	7	approximate	approximate	ADJ
ejpam-5024	204	8	solution	solution	NOUN
ejpam-5024	204	9	:	:	PUNCT
ejpam-5024	204	10	s2(t	s2(t	X
ejpam-5024	204	11	)	)	PUNCT
ejpam-5024	204	12	=	=	SYM
ejpam-5024	204	13	−1.32446935	−1.32446935	PROPN
ejpam-5024	204	14	+	+	CCONJ
ejpam-5024	204	15	0.332647197t+	0.332647197t+	NUM
ejpam-5024	204	16	2.18043309|cos(t)|	2.18043309|cos(t)|	NUM
ejpam-5024	204	17	.	.	PUNCT
ejpam-5024	205	1	the	the	DET
ejpam-5024	205	2	following	follow	VERB
ejpam-5024	205	3	figures	figure	NOUN
ejpam-5024	205	4	discuss	discuss	VERB
ejpam-5024	205	5	the	the	DET
ejpam-5024	205	6	shape	shape	NOUN
ejpam-5024	205	7	of	of	ADP
ejpam-5024	205	8	the	the	DET
ejpam-5024	205	9	numerical	numerical	ADJ
ejpam-5024	205	10	solution	solution	NOUN
ejpam-5024	205	11	of	of	ADP
ejpam-5024	205	12	the	the	DET
ejpam-5024	205	13	two	two	NUM
ejpam-5024	205	14	methods	method	NOUN
ejpam-5024	205	15	and	and	CCONJ
ejpam-5024	205	16	the	the	DET
ejpam-5024	205	17	relation	relation	NOUN
ejpam-5024	205	18	between	between	ADP
ejpam-5024	205	19	the	the	DET
ejpam-5024	205	20	estimating	estimate	VERB
ejpam-5024	205	21	errors	error	NOUN
ejpam-5024	205	22	that	that	PRON
ejpam-5024	205	23	were	be	AUX
ejpam-5024	205	24	obtained	obtain	VERB
ejpam-5024	205	25	.	.	PUNCT
ejpam-5024	206	1	f.	f.	PROPN
ejpam-5024	206	2	m.	m.	PROPN
ejpam-5024	206	3	alharbi	alharbi	PROPN
ejpam-5024	206	4	,	,	PUNCT
ejpam-5024	206	5	s.	s.	PROPN
ejpam-5024	206	6	s.	s.	PROPN
ejpam-5024	206	7	althubiti	althubiti	PROPN
ejpam-5024	206	8	/	/	SYM
ejpam-5024	206	9	eur	eur	PROPN
ejpam-5024	206	10	.	.	PUNCT
ejpam-5024	207	1	j.	j.	PROPN
ejpam-5024	207	2	pure	pure	PROPN
ejpam-5024	207	3	appl	appl	PROPN
ejpam-5024	207	4	.	.	PROPN
ejpam-5024	207	5	math	math	PROPN
ejpam-5024	207	6	,	,	PUNCT
ejpam-5024	207	7	17	17	NUM
ejpam-5024	207	8	(	(	PUNCT
ejpam-5024	207	9	1	1	NUM
ejpam-5024	207	10	)	)	PUNCT
ejpam-5024	207	11	(	(	PUNCT
ejpam-5024	207	12	2024	2024	NUM
ejpam-5024	207	13	)	)	PUNCT
ejpam-5024	207	14	,	,	PUNCT
ejpam-5024	207	15	286	286	NUM
ejpam-5024	207	16	-	-	SYM
ejpam-5024	207	17	299	299	NUM
ejpam-5024	207	18	295	295	NUM
ejpam-5024	207	19	figure	figure	NOUN
ejpam-5024	207	20	1	1	NUM
ejpam-5024	207	21	:	:	PUNCT
ejpam-5024	207	22	the	the	DET
ejpam-5024	207	23	relation	relation	NOUN
ejpam-5024	207	24	between	between	ADP
ejpam-5024	207	25	the	the	DET
ejpam-5024	207	26	exact	exact	ADJ
ejpam-5024	207	27	solution	solution	NOUN
ejpam-5024	207	28	and	and	CCONJ
ejpam-5024	207	29	numerical	numerical	ADJ
ejpam-5024	207	30	solution	solution	NOUN
ejpam-5024	207	31	in	in	ADP
ejpam-5024	207	32	collocation	collocation	NOUN
ejpam-5024	207	33	approximate	approximate	ADJ
ejpam-5024	207	34	.	.	PUNCT
ejpam-5024	208	1	figure	figure	VERB
ejpam-5024	208	2	2	2	NUM
ejpam-5024	208	3	:	:	PUNCT
ejpam-5024	208	4	relation	relation	NOUN
ejpam-5024	208	5	between	between	ADP
ejpam-5024	208	6	the	the	DET
ejpam-5024	208	7	exact	exact	ADJ
ejpam-5024	208	8	solution	solution	NOUN
ejpam-5024	208	9	and	and	CCONJ
ejpam-5024	208	10	numerical	numerical	ADJ
ejpam-5024	208	11	solution	solution	NOUN
ejpam-5024	208	12	in	in	ADP
ejpam-5024	208	13	galerkin	galerkin	PROPN
ejpam-5024	208	14	approximate	approximate	NOUN
ejpam-5024	208	15	.	.	PUNCT
ejpam-5024	209	1	figure	figure	VERB
ejpam-5024	209	2	3	3	NUM
ejpam-5024	209	3	:	:	PUNCT
ejpam-5024	209	4	the	the	DET
ejpam-5024	209	5	relation	relation	NOUN
ejpam-5024	209	6	between	between	ADP
ejpam-5024	209	7	estimating	estimate	VERB
ejpam-5024	209	8	error	error	NOUN
ejpam-5024	209	9	of	of	ADP
ejpam-5024	209	10	collocation	collocation	NOUN
ejpam-5024	209	11	approximate	approximate	ADJ
ejpam-5024	209	12	and	and	CCONJ
ejpam-5024	209	13	galerkin	galerkin	ADJ
ejpam-5024	209	14	approximate	approximate	NOUN
ejpam-5024	209	15	.	.	PUNCT
ejpam-5024	210	1	application	application	NOUN
ejpam-5024	210	2	(	(	PUNCT
ejpam-5024	210	3	2	2	X
ejpam-5024	210	4	)	)	PUNCT
ejpam-5024	210	5	consider	consider	VERB
ejpam-5024	210	6	the	the	DET
ejpam-5024	210	7	ivp	ivp	NOUN
ejpam-5024	210	8	,	,	PUNCT
ejpam-5024	210	9	y′′(t	y′′(t	VERB
ejpam-5024	210	10	)	)	PUNCT
ejpam-5024	210	11	=	=	SYM
ejpam-5024	211	1	1−	1−	NUM
ejpam-5024	211	2	e+	e+	VERB
ejpam-5024	211	3	et	et	NOUN
ejpam-5024	211	4	+	+	CCONJ
ejpam-5024	211	5	∫	∫	PROPN
ejpam-5024	211	6	1	1	NUM
ejpam-5024	211	7	0	0	NUM
ejpam-5024	211	8	y(t)dt	y(t)dt	PROPN
ejpam-5024	211	9	(	(	PUNCT
ejpam-5024	211	10	47	47	NUM
ejpam-5024	211	11	)	)	PUNCT
ejpam-5024	211	12	under	under	ADP
ejpam-5024	211	13	the	the	DET
ejpam-5024	211	14	initial	initial	ADJ
ejpam-5024	211	15	conditions	condition	NOUN
ejpam-5024	211	16	y′(0	y′(0	NOUN
ejpam-5024	211	17	)	)	PUNCT
ejpam-5024	211	18	=	=	SYM
ejpam-5024	211	19	1	1	NUM
ejpam-5024	211	20	y(0	y(0	PROPN
ejpam-5024	211	21	)	)	PUNCT
ejpam-5024	211	22	=	=	SYM
ejpam-5024	211	23	1	1	NUM
ejpam-5024	211	24	(	(	PUNCT
ejpam-5024	211	25	48	48	NUM
ejpam-5024	211	26	)	)	PUNCT
ejpam-5024	211	27	the	the	DET
ejpam-5024	211	28	exact	exact	ADJ
ejpam-5024	211	29	solution	solution	NOUN
ejpam-5024	211	30	is	be	AUX
ejpam-5024	211	31	y(t	y(t	PROPN
ejpam-5024	211	32	)	)	PUNCT
ejpam-5024	212	1	=	=	SYM
ejpam-5024	212	2	et	et	NOUN
ejpam-5024	212	3	after	after	ADP
ejpam-5024	212	4	converting	convert	VERB
ejpam-5024	212	5	it	it	PRON
ejpam-5024	212	6	to	to	ADP
ejpam-5024	212	7	f	f	PROPN
ejpam-5024	212	8	-	-	PUNCT
ejpam-5024	212	9	vie	vie	VERB
ejpam-5024	212	10	we	we	PRON
ejpam-5024	212	11	get	get	VERB
ejpam-5024	212	12	:	:	PUNCT
ejpam-5024	212	13	f.	f.	PROPN
ejpam-5024	212	14	m.	m.	PROPN
ejpam-5024	212	15	alharbi	alharbi	PROPN
ejpam-5024	212	16	,	,	PUNCT
ejpam-5024	212	17	s.	s.	PROPN
ejpam-5024	212	18	s.	s.	PROPN
ejpam-5024	212	19	althubiti	althubiti	PROPN
ejpam-5024	212	20	/	/	SYM
ejpam-5024	212	21	eur	eur	PROPN
ejpam-5024	212	22	.	.	PUNCT
ejpam-5024	213	1	j.	j.	PROPN
ejpam-5024	213	2	pure	pure	PROPN
ejpam-5024	213	3	appl	appl	PROPN
ejpam-5024	213	4	.	.	PROPN
ejpam-5024	213	5	math	math	PROPN
ejpam-5024	213	6	,	,	PUNCT
ejpam-5024	213	7	17	17	NUM
ejpam-5024	213	8	(	(	PUNCT
ejpam-5024	213	9	1	1	NUM
ejpam-5024	213	10	)	)	PUNCT
ejpam-5024	213	11	(	(	PUNCT
ejpam-5024	213	12	2024	2024	NUM
ejpam-5024	213	13	)	)	PUNCT
ejpam-5024	213	14	,	,	PUNCT
ejpam-5024	213	15	286	286	NUM
ejpam-5024	213	16	-	-	SYM
ejpam-5024	213	17	299	299	NUM
ejpam-5024	213	18	296	296	NUM
ejpam-5024	213	19	ϕ(t)−	ϕ(t)−	PROPN
ejpam-5024	213	20	∫	∫	PROPN
ejpam-5024	213	21	1	1	NUM
ejpam-5024	213	22	0	0	NUM
ejpam-5024	213	23	ψ(x)ϕ(x)dx	ψ(x)ϕ(x)dx	NOUN
ejpam-5024	213	24	=	=	SYM
ejpam-5024	213	25	f	f	X
ejpam-5024	213	26	(	(	PUNCT
ejpam-5024	213	27	x	x	X
ejpam-5024	213	28	)	)	PUNCT
ejpam-5024	213	29	where	where	SCONJ
ejpam-5024	213	30	,	,	PUNCT
ejpam-5024	213	31	ψ(x	ψ(x	PROPN
ejpam-5024	213	32	)	)	PUNCT
ejpam-5024	213	33	=	=	SYM
ejpam-5024	214	1	∫	∫	PROPN
ejpam-5024	214	2	t	t	PROPN
ejpam-5024	214	3	0	0	NUM
ejpam-5024	214	4	(	(	PUNCT
ejpam-5024	214	5	t−	t−	PROPN
ejpam-5024	214	6	x)dtf	x)dtf	PROPN
ejpam-5024	214	7	(	(	PUNCT
ejpam-5024	214	8	x	x	X
ejpam-5024	214	9	)	)	PUNCT
ejpam-5024	214	10	=	=	SYM
ejpam-5024	214	11	5	5	NUM
ejpam-5024	214	12	2	2	NUM
ejpam-5024	214	13	−	−	NOUN
ejpam-5024	214	14	e+	e+	PUNCT
ejpam-5024	214	15	et	et	X
ejpam-5024	214	16	.	.	PUNCT
ejpam-5024	215	1	(	(	PUNCT
ejpam-5024	215	2	49	49	NUM
ejpam-5024	215	3	)	)	PUNCT
ejpam-5024	215	4	•	•	NOUN
ejpam-5024	215	5	using	use	VERB
ejpam-5024	215	6	collocation	collocation	NOUN
ejpam-5024	215	7	method	method	NOUN
ejpam-5024	215	8	let	let	VERB
ejpam-5024	215	9	us	we	PRON
ejpam-5024	215	10	consider	consider	VERB
ejpam-5024	215	11	the	the	DET
ejpam-5024	215	12	approximate	approximate	ADJ
ejpam-5024	215	13	answer	answer	VERB
ejpam-5024	215	14	the	the	DET
ejpam-5024	215	15	equation	equation	NOUN
ejpam-5024	215	16	(	(	PUNCT
ejpam-5024	215	17	4.1	4.1	NUM
ejpam-5024	215	18	)	)	PUNCT
ejpam-5024	215	19	,	,	PUNCT
ejpam-5024	215	20	as	as	ADP
ejpam-5024	215	21	the	the	DET
ejpam-5024	215	22	three	three	NUM
ejpam-5024	215	23	independent	independent	ADJ
ejpam-5024	215	24	functions	function	NOUN
ejpam-5024	215	25	,	,	PUNCT
ejpam-5024	215	26	l0(t	l0(t	X
ejpam-5024	215	27	)	)	PUNCT
ejpam-5024	215	28	=	=	SYM
ejpam-5024	215	29	1	1	NUM
ejpam-5024	215	30	,	,	PUNCT
ejpam-5024	215	31	l1	l1	PROPN
ejpam-5024	215	32	=	=	SYM
ejpam-5024	215	33	t	t	PROPN
ejpam-5024	215	34	,	,	PUNCT
ejpam-5024	215	35	l2(t	l2(t	PROPN
ejpam-5024	215	36	)	)	PUNCT
ejpam-5024	215	37	=	=	SYM
ejpam-5024	215	38	t2	t2	NOUN
ejpam-5024	215	39	.	.	PUNCT
ejpam-5024	216	1	by	by	ADP
ejpam-5024	216	2	substituting	substitute	VERB
ejpam-5024	216	3	these	these	DET
ejpam-5024	216	4	functions	function	NOUN
ejpam-5024	216	5	into	into	ADP
ejpam-5024	216	6	equation	equation	NOUN
ejpam-5024	216	7	(	(	PUNCT
ejpam-5024	216	8	4.6	4.6	NUM
ejpam-5024	216	9	)	)	PUNCT
ejpam-5024	216	10	and	and	CCONJ
ejpam-5024	216	11	then	then	ADV
ejpam-5024	216	12	solving	solve	VERB
ejpam-5024	216	13	the	the	DET
ejpam-5024	216	14	resulting	result	VERB
ejpam-5024	216	15	equation	equation	NOUN
ejpam-5024	216	16	when	when	SCONJ
ejpam-5024	216	17	t	t	PROPN
ejpam-5024	216	18	=	=	SYM
ejpam-5024	216	19	0	0	NUM
ejpam-5024	216	20	,	,	PUNCT
ejpam-5024	216	21	π2	π2	X
ejpam-5024	216	22	,	,	PUNCT
ejpam-5024	216	23	π	π	X
ejpam-5024	216	24	,	,	PUNCT
ejpam-5024	216	25	we	we	PRON
ejpam-5024	216	26	get	get	VERB
ejpam-5024	216	27	:	:	PUNCT
ejpam-5024	216	28	c0	c0	PROPN
ejpam-5024	216	29	=	=	SYM
ejpam-5024	216	30	0.7817181715	0.7817181715	NUM
ejpam-5024	216	31	c1	c1	NOUN
ejpam-5024	216	32	=	=	PUNCT
ejpam-5024	216	33	−0.267748300	−0.267748300	NUM
ejpam-5024	216	34	c2	c2	PROPN
ejpam-5024	216	35	=	=	PROPN
ejpam-5024	216	36	1.98603013	1.98603013	NUM
ejpam-5024	216	37	therefore	therefore	ADV
ejpam-5024	216	38	,	,	PUNCT
ejpam-5024	216	39	the	the	DET
ejpam-5024	216	40	approximate	approximate	ADJ
ejpam-5024	216	41	solution	solution	NOUN
ejpam-5024	216	42	is	be	AUX
ejpam-5024	216	43	s2(t	s2(t	PROPN
ejpam-5024	216	44	)	)	PUNCT
ejpam-5024	216	45	=	=	SYM
ejpam-5024	216	46	0.7817181715−	0.7817181715−	NOUN
ejpam-5024	216	47	0.267748300t+	0.267748300t+	NUM
ejpam-5024	216	48	1.98603013t2	1.98603013t2	NUM
ejpam-5024	216	49	.	.	PUNCT
ejpam-5024	217	1	•	•	NOUN
ejpam-5024	217	2	using	use	VERB
ejpam-5024	217	3	galerkin	galerkin	ADJ
ejpam-5024	217	4	method	method	NOUN
ejpam-5024	217	5	as	as	ADP
ejpam-5024	217	6	the	the	DET
ejpam-5024	217	7	same	same	ADJ
ejpam-5024	217	8	consideration	consideration	NOUN
ejpam-5024	217	9	independent	independent	ADJ
ejpam-5024	217	10	approximate	approximate	ADJ
ejpam-5024	217	11	solution	solution	NOUN
ejpam-5024	217	12	and	and	CCONJ
ejpam-5024	217	13	the	the	DET
ejpam-5024	217	14	same	same	ADJ
ejpam-5024	217	15	arbitrary	arbitrary	ADJ
ejpam-5024	217	16	points	point	NOUN
ejpam-5024	217	17	in	in	ADP
ejpam-5024	217	18	the	the	DET
ejpam-5024	217	19	collocation	collocation	NOUN
ejpam-5024	217	20	method	method	NOUN
ejpam-5024	217	21	,	,	PUNCT
ejpam-5024	217	22	we	we	PRON
ejpam-5024	217	23	get	get	VERB
ejpam-5024	217	24	,	,	PUNCT
ejpam-5024	217	25	c0	c0	PROPN
ejpam-5024	217	26	=	=	SYM
ejpam-5024	217	27	0.844299425	0.844299425	NUM
ejpam-5024	217	28	c1	c1	NOUN
ejpam-5024	217	29	=	=	PUNCT
ejpam-5024	218	1	−0.370315407	−0.370315407	X
ejpam-5024	218	2	c2	c2	PROPN
ejpam-5024	218	3	=	=	SYM
ejpam-5024	218	4	1.90695998	1.90695998	NUM
ejpam-5024	218	5	therefore	therefore	ADV
ejpam-5024	218	6	,	,	PUNCT
ejpam-5024	218	7	the	the	DET
ejpam-5024	218	8	approximate	approximate	ADJ
ejpam-5024	218	9	solution	solution	NOUN
ejpam-5024	218	10	:	:	PUNCT
ejpam-5024	218	11	s2(t	s2(t	X
ejpam-5024	218	12	)	)	PUNCT
ejpam-5024	219	1	=	=	NOUN
ejpam-5024	219	2	0.844299425−	0.844299425−	NUM
ejpam-5024	219	3	0.370315407t+	0.370315407t+	PROPN
ejpam-5024	219	4	1.90695998t2	1.90695998t2	NUM
ejpam-5024	219	5	.	.	PUNCT
ejpam-5024	220	1	the	the	DET
ejpam-5024	220	2	results	result	NOUN
ejpam-5024	220	3	are	be	AUX
ejpam-5024	220	4	shown	show	VERB
ejpam-5024	220	5	in	in	ADP
ejpam-5024	220	6	figure	figure	NOUN
ejpam-5024	220	7	4	4	NUM
ejpam-5024	220	8	and	and	CCONJ
ejpam-5024	220	9	5	5	NUM
ejpam-5024	220	10	for	for	ADP
ejpam-5024	220	11	n	n	NOUN
ejpam-5024	220	12	=	=	SYM
ejpam-5024	220	13	6	6	NUM
ejpam-5024	220	14	.	.	PUNCT
ejpam-5024	220	15	f.	f.	PROPN
ejpam-5024	220	16	m.	m.	PROPN
ejpam-5024	220	17	alharbi	alharbi	PROPN
ejpam-5024	220	18	,	,	PUNCT
ejpam-5024	220	19	s.	s.	PROPN
ejpam-5024	220	20	s.	s.	PROPN
ejpam-5024	220	21	althubiti	althubiti	PROPN
ejpam-5024	220	22	/	/	SYM
ejpam-5024	220	23	eur	eur	PROPN
ejpam-5024	220	24	.	.	PUNCT
ejpam-5024	221	1	j.	j.	PROPN
ejpam-5024	221	2	pure	pure	PROPN
ejpam-5024	221	3	appl	appl	PROPN
ejpam-5024	221	4	.	.	PROPN
ejpam-5024	221	5	math	math	PROPN
ejpam-5024	221	6	,	,	PUNCT
ejpam-5024	221	7	17	17	NUM
ejpam-5024	221	8	(	(	PUNCT
ejpam-5024	221	9	1	1	NUM
ejpam-5024	221	10	)	)	PUNCT
ejpam-5024	221	11	(	(	PUNCT
ejpam-5024	221	12	2024	2024	NUM
ejpam-5024	221	13	)	)	PUNCT
ejpam-5024	221	14	,	,	PUNCT
ejpam-5024	221	15	286	286	NUM
ejpam-5024	221	16	-	-	SYM
ejpam-5024	221	17	299	299	NUM
ejpam-5024	221	18	297	297	NUM
ejpam-5024	221	19	figure	figure	NOUN
ejpam-5024	221	20	4	4	NUM
ejpam-5024	221	21	:	:	PUNCT
ejpam-5024	221	22	the	the	DET
ejpam-5024	221	23	relation	relation	NOUN
ejpam-5024	221	24	between	between	ADP
ejpam-5024	221	25	the	the	DET
ejpam-5024	221	26	exact	exact	ADJ
ejpam-5024	221	27	solution	solution	NOUN
ejpam-5024	221	28	and	and	CCONJ
ejpam-5024	221	29	numerical	numerical	ADJ
ejpam-5024	221	30	solution	solution	NOUN
ejpam-5024	221	31	in	in	ADP
ejpam-5024	221	32	collocation	collocation	NOUN
ejpam-5024	221	33	approximate	approximate	ADJ
ejpam-5024	221	34	.	.	PUNCT
ejpam-5024	222	1	figure	figure	VERB
ejpam-5024	222	2	5	5	NUM
ejpam-5024	222	3	:	:	PUNCT
ejpam-5024	222	4	relation	relation	NOUN
ejpam-5024	222	5	between	between	ADP
ejpam-5024	222	6	the	the	DET
ejpam-5024	222	7	exact	exact	ADJ
ejpam-5024	222	8	solution	solution	NOUN
ejpam-5024	222	9	and	and	CCONJ
ejpam-5024	222	10	numerical	numerical	ADJ
ejpam-5024	222	11	solution	solution	NOUN
ejpam-5024	222	12	in	in	ADP
ejpam-5024	222	13	galerkin	galerkin	PROPN
ejpam-5024	222	14	approximate	approximate	NOUN
ejpam-5024	222	15	.	.	PUNCT
ejpam-5024	223	1	figure	figure	VERB
ejpam-5024	223	2	6	6	NUM
ejpam-5024	223	3	:	:	PUNCT
ejpam-5024	223	4	the	the	DET
ejpam-5024	223	5	relation	relation	NOUN
ejpam-5024	223	6	between	between	ADP
ejpam-5024	223	7	estimating	estimate	VERB
ejpam-5024	223	8	error	error	NOUN
ejpam-5024	223	9	of	of	ADP
ejpam-5024	223	10	collocation	collocation	NOUN
ejpam-5024	223	11	approximate	approximate	ADJ
ejpam-5024	223	12	and	and	CCONJ
ejpam-5024	223	13	galerkin	galerkin	ADJ
ejpam-5024	223	14	approximate	approximate	NOUN
ejpam-5024	223	15	.	.	PUNCT
ejpam-5024	224	1	5	5	X
ejpam-5024	224	2	.	.	X
ejpam-5024	224	3	conclusion	conclusion	NOUN
ejpam-5024	224	4	in	in	ADP
ejpam-5024	224	5	this	this	DET
ejpam-5024	224	6	study	study	NOUN
ejpam-5024	224	7	,	,	PUNCT
ejpam-5024	224	8	we	we	PRON
ejpam-5024	224	9	focus	focus	VERB
ejpam-5024	224	10	on	on	ADP
ejpam-5024	224	11	the	the	DET
ejpam-5024	224	12	initial	initial	ADJ
ejpam-5024	224	13	value	value	NOUN
ejpam-5024	224	14	problem	problem	NOUN
ejpam-5024	224	15	of	of	ADP
ejpam-5024	224	16	a	a	DET
ejpam-5024	224	17	linear	linear	ADJ
ejpam-5024	224	18	integro	integro	ADJ
ejpam-5024	224	19	-	-	PUNCT
ejpam-5024	224	20	differentail	differentail	NOUN
ejpam-5024	224	21	equation	equation	NOUN
ejpam-5024	224	22	with	with	ADP
ejpam-5024	224	23	a	a	DET
ejpam-5024	224	24	continuous	continuous	ADJ
ejpam-5024	224	25	kernel	kernel	NOUN
ejpam-5024	224	26	,	,	PUNCT
ejpam-5024	224	27	or	or	CCONJ
ejpam-5024	224	28	at	at	ADP
ejpam-5024	224	29	least	least	ADJ
ejpam-5024	224	30	satisfy	satisfy	VERB
ejpam-5024	224	31	the	the	DET
ejpam-5024	224	32	fredholm	fredholm	NOUN
ejpam-5024	224	33	condition	condition	NOUN
ejpam-5024	224	34	.	.	PUNCT
ejpam-5024	225	1	by	by	ADP
ejpam-5024	225	2	converting	convert	VERB
ejpam-5024	225	3	the	the	DET
ejpam-5024	225	4	studding	stud	VERB
ejpam-5024	225	5	equation	equation	NOUN
ejpam-5024	225	6	to	to	ADP
ejpam-5024	225	7	a	a	DET
ejpam-5024	225	8	volterra	volterra	NOUN
ejpam-5024	225	9	-	-	PUNCT
ejpam-5024	225	10	fredholm	fredholm	NOUN
ejpam-5024	225	11	integral	integral	ADJ
ejpam-5024	225	12	equation	equation	NOUN
ejpam-5024	225	13	of	of	ADP
ejpam-5024	225	14	the	the	DET
ejpam-5024	225	15	second	second	ADJ
ejpam-5024	225	16	kind	kind	NOUN
ejpam-5024	225	17	it	it	PRON
ejpam-5024	225	18	transforms	transform	VERB
ejpam-5024	225	19	into	into	ADP
ejpam-5024	225	20	a	a	DET
ejpam-5024	225	21	linear	linear	ADJ
ejpam-5024	225	22	system	system	NOUN
ejpam-5024	225	23	of	of	ADP
ejpam-5024	225	24	fredholm	fredholm	ADJ
ejpam-5024	225	25	integral	integral	ADJ
ejpam-5024	225	26	equations	equation	NOUN
ejpam-5024	225	27	.	.	PUNCT
ejpam-5024	226	1	the	the	DET
ejpam-5024	226	2	collocation	collocation	NOUN
ejpam-5024	226	3	method	method	NOUN
ejpam-5024	226	4	and	and	CCONJ
ejpam-5024	226	5	the	the	DET
ejpam-5024	226	6	galerkin	galerkin	ADJ
ejpam-5024	226	7	method	method	NOUN
ejpam-5024	226	8	are	be	AUX
ejpam-5024	226	9	used	use	VERB
ejpam-5024	226	10	to	to	PART
ejpam-5024	226	11	efficiently	efficiently	ADV
ejpam-5024	226	12	discretize	discretize	VERB
ejpam-5024	226	13	the	the	DET
ejpam-5024	226	14	integral	integral	ADJ
ejpam-5024	226	15	equations	equation	NOUN
ejpam-5024	226	16	using	use	VERB
ejpam-5024	226	17	a	a	DET
ejpam-5024	226	18	set	set	NOUN
ejpam-5024	226	19	of	of	ADP
ejpam-5024	226	20	points	point	NOUN
ejpam-5024	226	21	.	.	PUNCT
ejpam-5024	227	1	we	we	PRON
ejpam-5024	227	2	discuss	discuss	VERB
ejpam-5024	227	3	the	the	DET
ejpam-5024	227	4	error	error	NOUN
ejpam-5024	227	5	estimates	estimate	NOUN
ejpam-5024	227	6	associated	associate	VERB
ejpam-5024	227	7	with	with	ADP
ejpam-5024	227	8	both	both	DET
ejpam-5024	227	9	methods	method	NOUN
ejpam-5024	227	10	.	.	PUNCT
ejpam-5024	228	1	references	reference	NOUN
ejpam-5024	228	2	298	298	NUM
ejpam-5024	228	3	references	reference	NOUN
ejpam-5024	228	4	[	[	X
ejpam-5024	228	5	1	1	NUM
ejpam-5024	228	6	]	]	X
ejpam-5024	228	7	fm	fm	PROPN
ejpam-5024	228	8	alharbi	alharbi	PROPN
ejpam-5024	228	9	and	and	CCONJ
ejpam-5024	228	10	ma	ma	PROPN
ejpam-5024	228	11	abdou	abdou	PROPN
ejpam-5024	228	12	.	.	PROPN
ejpam-5024	229	1	boundary	boundary	ADJ
ejpam-5024	229	2	and	and	CCONJ
ejpam-5024	229	3	initial	initial	ADJ
ejpam-5024	229	4	value	value	NOUN
ejpam-5024	229	5	problems	problem	NOUN
ejpam-5024	229	6	and	and	CCONJ
ejpam-5024	229	7	integral	integral	ADJ
ejpam-5024	229	8	operator	operator	NOUN
ejpam-5024	229	9	.	.	PUNCT
ejpam-5024	230	1	adv	adv	PROPN
ejpam-5024	230	2	.	.	PROPN
ejpam-5024	230	3	differ	differ	VERB
ejpam-5024	230	4	.	.	PUNCT
ejpam-5024	231	1	equ	equ	PROPN
ejpam-5024	231	2	.	.	PUNCT
ejpam-5024	231	3	control	control	PROPN
ejpam-5024	231	4	process	process	NOUN
ejpam-5024	231	5	,	,	PUNCT
ejpam-5024	231	6	19	19	NUM
ejpam-5024	231	7	,	,	PUNCT
ejpam-5024	231	8	2018	2018	NUM
ejpam-5024	231	9	.	.	PUNCT
ejpam-5024	232	1	[	[	X
ejpam-5024	232	2	2	2	X
ejpam-5024	232	3	]	]	PUNCT
ejpam-5024	232	4	azizallah	azizallah	PROPN
ejpam-5024	232	5	alvandi	alvandi	PROPN
ejpam-5024	232	6	and	and	CCONJ
ejpam-5024	232	7	mahmoud	mahmoud	PROPN
ejpam-5024	232	8	paripour	paripour	NOUN
ejpam-5024	232	9	.	.	PUNCT
ejpam-5024	233	1	reproducing	reproduce	VERB
ejpam-5024	233	2	kernel	kernel	PROPN
ejpam-5024	233	3	method	method	NOUN
ejpam-5024	233	4	with	with	ADP
ejpam-5024	233	5	taylor	taylor	PROPN
ejpam-5024	233	6	expansion	expansion	NOUN
ejpam-5024	233	7	for	for	ADP
ejpam-5024	233	8	linear	linear	PROPN
ejpam-5024	233	9	volterra	volterra	PROPN
ejpam-5024	233	10	integro	integro	PROPN
ejpam-5024	233	11	-	-	PUNCT
ejpam-5024	233	12	differential	differential	NOUN
ejpam-5024	233	13	equations	equation	NOUN
ejpam-5024	233	14	.	.	PUNCT
ejpam-5024	234	1	communications	communication	NOUN
ejpam-5024	234	2	in	in	ADP
ejpam-5024	234	3	numerical	numerical	ADJ
ejpam-5024	234	4	analysis	analysis	NOUN
ejpam-5024	234	5	,	,	PUNCT
ejpam-5024	234	6	1	1	NUM
ejpam-5024	234	7	,	,	PUNCT
ejpam-5024	234	8	2017	2017	NUM
ejpam-5024	234	9	.	.	PUNCT
ejpam-5024	235	1	[	[	X
ejpam-5024	235	2	3	3	NUM
ejpam-5024	235	3	]	]	X
ejpam-5024	235	4	rohul	rohul	PROPN
ejpam-5024	235	5	amin	amin	PROPN
ejpam-5024	235	6	,	,	PUNCT
ejpam-5024	235	7	ibrahim	ibrahim	PROPN
ejpam-5024	235	8	mahariq	mahariq	PROPN
ejpam-5024	235	9	,	,	PUNCT
ejpam-5024	235	10	kamal	kamal	PROPN
ejpam-5024	235	11	shah	shah	PROPN
ejpam-5024	235	12	,	,	PUNCT
ejpam-5024	235	13	muhammad	muhammad	PROPN
ejpam-5024	235	14	awais	awais	PROPN
ejpam-5024	235	15	,	,	PUNCT
ejpam-5024	235	16	and	and	CCONJ
ejpam-5024	235	17	fahmi	fahmi	NOUN
ejpam-5024	235	18	elsayed	elsaye	VERB
ejpam-5024	235	19	.	.	PUNCT
ejpam-5024	236	1	numerical	numerical	ADJ
ejpam-5024	236	2	solution	solution	NOUN
ejpam-5024	236	3	of	of	ADP
ejpam-5024	236	4	the	the	DET
ejpam-5024	236	5	second	second	ADJ
ejpam-5024	236	6	order	order	NOUN
ejpam-5024	236	7	linear	linear	ADJ
ejpam-5024	236	8	and	and	CCONJ
ejpam-5024	236	9	nonlinear	nonlinear	ADJ
ejpam-5024	236	10	integro	integro	ADJ
ejpam-5024	236	11	-	-	PUNCT
ejpam-5024	236	12	differential	differential	NOUN
ejpam-5024	236	13	equations	equation	NOUN
ejpam-5024	236	14	using	use	VERB
ejpam-5024	236	15	haar	haar	PROPN
ejpam-5024	236	16	wavelet	wavelet	NOUN
ejpam-5024	236	17	method	method	NOUN
ejpam-5024	236	18	.	.	PUNCT
ejpam-5024	237	1	arab	arab	PROPN
ejpam-5024	237	2	journal	journal	PROPN
ejpam-5024	237	3	of	of	ADP
ejpam-5024	237	4	basic	basic	ADJ
ejpam-5024	237	5	and	and	CCONJ
ejpam-5024	237	6	applied	applied	ADJ
ejpam-5024	237	7	sciences	science	NOUN
ejpam-5024	237	8	,	,	PUNCT
ejpam-5024	237	9	28	28	NUM
ejpam-5024	237	10	,	,	PUNCT
ejpam-5024	237	11	2021	2021	NUM
ejpam-5024	237	12	.	.	PUNCT
ejpam-5024	238	1	[	[	X
ejpam-5024	238	2	4	4	NUM
ejpam-5024	238	3	]	]	PUNCT
ejpam-5024	238	4	aytac	aytac	PROPN
ejpam-5024	238	5	arikoglu	arikoglu	NOUN
ejpam-5024	238	6	and	and	CCONJ
ejpam-5024	238	7	ibrahim	ibrahim	PROPN
ejpam-5024	238	8	ozkol	ozkol	PROPN
ejpam-5024	238	9	.	.	PUNCT
ejpam-5024	239	1	solutions	solution	NOUN
ejpam-5024	239	2	of	of	ADP
ejpam-5024	239	3	integral	integral	ADJ
ejpam-5024	239	4	and	and	CCONJ
ejpam-5024	239	5	integro	integro	ADJ
ejpam-5024	239	6	-	-	PUNCT
ejpam-5024	239	7	differential	differential	NOUN
ejpam-5024	239	8	equation	equation	NOUN
ejpam-5024	239	9	systems	system	NOUN
ejpam-5024	239	10	by	by	ADP
ejpam-5024	239	11	using	use	VERB
ejpam-5024	239	12	differential	differential	ADJ
ejpam-5024	239	13	transform	transform	NOUN
ejpam-5024	239	14	method	method	NOUN
ejpam-5024	239	15	.	.	PUNCT
ejpam-5024	240	1	computers	computer	NOUN
ejpam-5024	240	2	&	&	CCONJ
ejpam-5024	240	3	mathematics	mathematics	PROPN
ejpam-5024	240	4	with	with	ADP
ejpam-5024	240	5	applications	application	NOUN
ejpam-5024	240	6	,	,	PUNCT
ejpam-5024	240	7	56	56	NUM
ejpam-5024	240	8	,	,	PUNCT
ejpam-5024	240	9	2008	2008	NUM
ejpam-5024	240	10	.	.	PUNCT
ejpam-5024	241	1	[	[	X
ejpam-5024	241	2	5	5	X
ejpam-5024	241	3	]	]	X
ejpam-5024	241	4	imran	imran	PROPN
ejpam-5024	241	5	aziz	aziz	PROPN
ejpam-5024	241	6	et	et	PROPN
ejpam-5024	241	7	al	al	PROPN
ejpam-5024	241	8	.	.	PUNCT
ejpam-5024	242	1	new	new	ADJ
ejpam-5024	242	2	algorithms	algorithm	NOUN
ejpam-5024	242	3	for	for	ADP
ejpam-5024	242	4	the	the	DET
ejpam-5024	242	5	numerical	numerical	ADJ
ejpam-5024	242	6	solution	solution	NOUN
ejpam-5024	242	7	of	of	ADP
ejpam-5024	242	8	nonlinear	nonlinear	ADJ
ejpam-5024	242	9	fredholm	fredholm	NOUN
ejpam-5024	242	10	and	and	CCONJ
ejpam-5024	242	11	volterra	volterra	PROPN
ejpam-5024	242	12	integral	integral	ADJ
ejpam-5024	242	13	equations	equation	NOUN
ejpam-5024	242	14	using	use	VERB
ejpam-5024	242	15	haar	haar	PROPN
ejpam-5024	242	16	wavelets	wavelet	NOUN
ejpam-5024	242	17	.	.	PUNCT
ejpam-5024	243	1	journal	journal	NOUN
ejpam-5024	243	2	of	of	ADP
ejpam-5024	243	3	computational	computational	ADJ
ejpam-5024	243	4	and	and	CCONJ
ejpam-5024	243	5	applied	applied	ADJ
ejpam-5024	243	6	mathematics	mathematic	NOUN
ejpam-5024	243	7	,	,	PUNCT
ejpam-5024	243	8	239	239	NUM
ejpam-5024	243	9	,	,	PUNCT
ejpam-5024	243	10	2013	2013	NUM
ejpam-5024	243	11	.	.	PUNCT
ejpam-5024	244	1	[	[	X
ejpam-5024	244	2	6	6	NUM
ejpam-5024	244	3	]	]	X
ejpam-5024	244	4	angelamaria	angelamaria	PROPN
ejpam-5024	244	5	cardone	cardone	PROPN
ejpam-5024	244	6	,	,	PUNCT
ejpam-5024	244	7	dajana	dajana	PROPN
ejpam-5024	244	8	conte	conte	PROPN
ejpam-5024	244	9	,	,	PUNCT
ejpam-5024	244	10	raffaele	raffaele	PROPN
ejpam-5024	244	11	d’ambrosio	d’ambrosio	PROPN
ejpam-5024	244	12	,	,	PUNCT
ejpam-5024	244	13	and	and	CCONJ
ejpam-5024	244	14	beatrice	beatrice	PROPN
ejpam-5024	244	15	paternoster	paternoster	PROPN
ejpam-5024	244	16	.	.	PUNCT
ejpam-5024	245	1	collocation	collocation	NOUN
ejpam-5024	245	2	methods	method	NOUN
ejpam-5024	245	3	for	for	ADP
ejpam-5024	245	4	volterra	volterra	NOUN
ejpam-5024	245	5	integral	integral	ADJ
ejpam-5024	245	6	and	and	CCONJ
ejpam-5024	245	7	integro	integro	ADJ
ejpam-5024	245	8	-	-	PUNCT
ejpam-5024	245	9	differential	differential	NOUN
ejpam-5024	245	10	equations	equation	NOUN
ejpam-5024	245	11	:	:	PUNCT
ejpam-5024	245	12	a	a	DET
ejpam-5024	245	13	review	review	NOUN
ejpam-5024	245	14	.	.	PUNCT
ejpam-5024	246	1	axioms	axiom	NOUN
ejpam-5024	246	2	,	,	PUNCT
ejpam-5024	246	3	7	7	NUM
ejpam-5024	246	4	,	,	PUNCT
ejpam-5024	246	5	2018	2018	NUM
ejpam-5024	246	6	.	.	PUNCT
ejpam-5024	247	1	[	[	X
ejpam-5024	247	2	7	7	X
ejpam-5024	247	3	]	]	PUNCT
ejpam-5024	247	4	fatheah	fatheah	NOUN
ejpam-5024	247	5	ahmad	ahmad	PROPN
ejpam-5024	247	6	hendi	hendi	PROPN
ejpam-5024	247	7	and	and	CCONJ
ejpam-5024	247	8	abeer	abeer	PROPN
ejpam-5024	247	9	majed	majed	PROPN
ejpam-5024	247	10	albugami	albugami	PROPN
ejpam-5024	247	11	.	.	PUNCT
ejpam-5024	248	1	numerical	numerical	ADJ
ejpam-5024	248	2	solution	solution	NOUN
ejpam-5024	248	3	for	for	ADP
ejpam-5024	248	4	fredholm	fredholm	NOUN
ejpam-5024	248	5	–	–	PUNCT
ejpam-5024	248	6	volterra	volterra	NOUN
ejpam-5024	248	7	integral	integral	ADJ
ejpam-5024	248	8	equation	equation	NOUN
ejpam-5024	248	9	of	of	ADP
ejpam-5024	248	10	the	the	DET
ejpam-5024	248	11	second	second	ADJ
ejpam-5024	248	12	kind	kind	NOUN
ejpam-5024	248	13	by	by	ADP
ejpam-5024	248	14	using	use	VERB
ejpam-5024	248	15	collocation	collocation	NOUN
ejpam-5024	248	16	and	and	CCONJ
ejpam-5024	248	17	galerkin	galerkin	ADJ
ejpam-5024	248	18	methods	method	NOUN
ejpam-5024	248	19	.	.	PUNCT
ejpam-5024	249	1	journal	journal	PROPN
ejpam-5024	249	2	of	of	ADP
ejpam-5024	249	3	king	king	PROPN
ejpam-5024	249	4	saud	saud	PROPN
ejpam-5024	249	5	university	university	PROPN
ejpam-5024	249	6	-	-	PUNCT
ejpam-5024	249	7	science	science	NOUN
ejpam-5024	249	8	,	,	PUNCT
ejpam-5024	249	9	22	22	NUM
ejpam-5024	249	10	,	,	PUNCT
ejpam-5024	249	11	2010	2010	NUM
ejpam-5024	249	12	.	.	PUNCT
ejpam-5024	250	1	[	[	X
ejpam-5024	250	2	8	8	NUM
ejpam-5024	250	3	]	]	X
ejpam-5024	250	4	k	k	X
ejpam-5024	250	5	issa	issa	PROPN
ejpam-5024	250	6	and	and	CCONJ
ejpam-5024	250	7	f	f	PROPN
ejpam-5024	250	8	salehi	salehi	PROPN
ejpam-5024	250	9	.	.	PUNCT
ejpam-5024	251	1	approximate	approximate	ADJ
ejpam-5024	251	2	solution	solution	NOUN
ejpam-5024	251	3	of	of	ADP
ejpam-5024	251	4	perturbed	perturb	VERB
ejpam-5024	251	5	volterra	volterra	NOUN
ejpam-5024	251	6	-	-	PUNCT
ejpam-5024	251	7	fredholm	fredholm	NOUN
ejpam-5024	251	8	integrodifferential	integrodifferential	ADJ
ejpam-5024	251	9	equations	equation	NOUN
ejpam-5024	251	10	by	by	ADP
ejpam-5024	251	11	chebyshev	chebyshev	NOUN
ejpam-5024	251	12	-	-	PUNCT
ejpam-5024	251	13	galerkin	galerkin	ADJ
ejpam-5024	251	14	method	method	NOUN
ejpam-5024	251	15	.	.	PUNCT
ejpam-5024	252	1	journal	journal	NOUN
ejpam-5024	252	2	of	of	ADP
ejpam-5024	252	3	mathematics	mathematic	NOUN
ejpam-5024	252	4	,	,	PUNCT
ejpam-5024	252	5	2017	2017	NUM
ejpam-5024	252	6	,	,	PUNCT
ejpam-5024	252	7	2017	2017	NUM
ejpam-5024	252	8	.	.	PUNCT
ejpam-5024	253	1	[	[	X
ejpam-5024	253	2	9	9	X
ejpam-5024	253	3	]	]	X
ejpam-5024	253	4	imran	imran	PROPN
ejpam-5024	253	5	khan	khan	PROPN
ejpam-5024	253	6	,	,	PUNCT
ejpam-5024	253	7	muhammad	muhammad	PROPN
ejpam-5024	253	8	asif	asif	PROPN
ejpam-5024	253	9	,	,	PUNCT
ejpam-5024	253	10	rohul	rohul	PROPN
ejpam-5024	253	11	amin	amin	PROPN
ejpam-5024	253	12	,	,	PUNCT
ejpam-5024	253	13	qasem	qasem	PROPN
ejpam-5024	253	14	al	al	PROPN
ejpam-5024	253	15	-	-	PUNCT
ejpam-5024	253	16	mdallal	mdallal	PROPN
ejpam-5024	253	17	,	,	PUNCT
ejpam-5024	253	18	and	and	CCONJ
ejpam-5024	253	19	fahd	fahd	PROPN
ejpam-5024	253	20	jarad	jarad	PROPN
ejpam-5024	253	21	.	.	PUNCT
ejpam-5024	254	1	on	on	ADP
ejpam-5024	254	2	a	a	DET
ejpam-5024	254	3	new	new	ADJ
ejpam-5024	254	4	method	method	NOUN
ejpam-5024	254	5	for	for	ADP
ejpam-5024	254	6	finding	find	VERB
ejpam-5024	254	7	numerical	numerical	ADJ
ejpam-5024	254	8	solutions	solution	NOUN
ejpam-5024	254	9	to	to	ADP
ejpam-5024	254	10	integro	integro	ADJ
ejpam-5024	254	11	-	-	PUNCT
ejpam-5024	254	12	differential	differential	NOUN
ejpam-5024	254	13	equations	equation	NOUN
ejpam-5024	254	14	based	base	VERB
ejpam-5024	254	15	on	on	ADP
ejpam-5024	254	16	legendre	legendre	PROPN
ejpam-5024	254	17	multi	multi	PROPN
ejpam-5024	254	18	-	-	ADJ
ejpam-5024	254	19	wavelets	wavelets	ADJ
ejpam-5024	254	20	collocation	collocation	NOUN
ejpam-5024	254	21	.	.	PUNCT
ejpam-5024	255	1	alexandria	alexandria	PROPN
ejpam-5024	255	2	engineering	engineering	PROPN
ejpam-5024	255	3	journal	journal	PROPN
ejpam-5024	255	4	,	,	PUNCT
ejpam-5024	255	5	61	61	NUM
ejpam-5024	255	6	,	,	PUNCT
ejpam-5024	255	7	2022	2022	NUM
ejpam-5024	255	8	.	.	PUNCT
ejpam-5024	256	1	[	[	X
ejpam-5024	256	2	10	10	NUM
ejpam-5024	256	3	]	]	X
ejpam-5024	256	4	vangipuram	vangipuram	PROPN
ejpam-5024	256	5	lakshmikantham	lakshmikantham	NOUN
ejpam-5024	256	6	.	.	PUNCT
ejpam-5024	257	1	theory	theory	NOUN
ejpam-5024	257	2	of	of	ADP
ejpam-5024	257	3	integro	integro	ADJ
ejpam-5024	257	4	-	-	PUNCT
ejpam-5024	257	5	differential	differential	NOUN
ejpam-5024	257	6	equations	equation	NOUN
ejpam-5024	257	7	,	,	PUNCT
ejpam-5024	257	8	volume	volume	NOUN
ejpam-5024	257	9	1	1	NUM
ejpam-5024	257	10	.	.	PUNCT
ejpam-5024	257	11	crc	crc	PROPN
ejpam-5024	257	12	press	press	PROPN
ejpam-5024	257	13	,	,	PUNCT
ejpam-5024	257	14	1995	1995	NUM
ejpam-5024	257	15	.	.	PUNCT
ejpam-5024	258	1	[	[	X
ejpam-5024	258	2	11	11	NUM
ejpam-5024	258	3	]	]	X
ejpam-5024	258	4	mahmoud	mahmoud	PROPN
ejpam-5024	258	5	lotfi	lotfi	PROPN
ejpam-5024	258	6	and	and	CCONJ
ejpam-5024	258	7	amjad	amjad	PROPN
ejpam-5024	258	8	alipanah	alipanah	PROPN
ejpam-5024	258	9	.	.	PUNCT
ejpam-5024	259	1	legendre	legendre	PROPN
ejpam-5024	259	2	spectral	spectral	PROPN
ejpam-5024	259	3	element	element	PROPN
ejpam-5024	259	4	method	method	NOUN
ejpam-5024	259	5	for	for	ADP
ejpam-5024	259	6	solving	solve	VERB
ejpam-5024	259	7	volterra	volterra	NOUN
ejpam-5024	259	8	-	-	PUNCT
ejpam-5024	259	9	integro	integro	PROPN
ejpam-5024	259	10	differential	differential	ADJ
ejpam-5024	259	11	equations	equation	NOUN
ejpam-5024	259	12	.	.	PUNCT
ejpam-5024	260	1	results	result	NOUN
ejpam-5024	260	2	in	in	ADP
ejpam-5024	260	3	applied	applied	ADJ
ejpam-5024	260	4	mathematics	mathematic	NOUN
ejpam-5024	260	5	,	,	PUNCT
ejpam-5024	260	6	7	7	NUM
ejpam-5024	260	7	,	,	PUNCT
ejpam-5024	260	8	2020	2020	NUM
ejpam-5024	260	9	.	.	PUNCT
ejpam-5024	261	1	[	[	X
ejpam-5024	261	2	12	12	NUM
ejpam-5024	261	3	]	]	X
ejpam-5024	261	4	allen	allen	PROPN
ejpam-5024	261	5	c	c	PROPN
ejpam-5024	261	6	pipkin	pipkin	PROPN
ejpam-5024	261	7	.	.	PUNCT
ejpam-5024	262	1	a	a	DET
ejpam-5024	262	2	course	course	NOUN
ejpam-5024	262	3	on	on	ADP
ejpam-5024	262	4	integral	integral	ADJ
ejpam-5024	262	5	equations	equation	NOUN
ejpam-5024	262	6	.	.	PUNCT
ejpam-5024	263	1	number	number	NOUN
ejpam-5024	263	2	9	9	NUM
ejpam-5024	263	3	.	.	PUNCT
ejpam-5024	263	4	springer	springer	NOUN
ejpam-5024	263	5	science	science	PROPN
ejpam-5024	263	6	&	&	CCONJ
ejpam-5024	263	7	business	business	NOUN
ejpam-5024	263	8	media	medium	NOUN
ejpam-5024	263	9	,	,	PUNCT
ejpam-5024	263	10	1991	1991	NUM
ejpam-5024	263	11	.	.	PUNCT
ejpam-5024	264	1	references	reference	NOUN
ejpam-5024	264	2	299	299	NUM
ejpam-5024	264	3	[	[	X
ejpam-5024	264	4	13	13	NUM
ejpam-5024	264	5	]	]	X
ejpam-5024	264	6	j	j	PROPN
ejpam-5024	264	7	rashidinia	rashidinia	PROPN
ejpam-5024	264	8	and	and	CCONJ
ejpam-5024	264	9	a	a	DET
ejpam-5024	264	10	tahmasebi	tahmasebi	NOUN
ejpam-5024	264	11	.	.	PUNCT
ejpam-5024	265	1	taylor	taylor	PROPN
ejpam-5024	265	2	series	series	PROPN
ejpam-5024	265	3	method	method	NOUN
ejpam-5024	265	4	for	for	ADP
ejpam-5024	265	5	the	the	DET
ejpam-5024	265	6	system	system	NOUN
ejpam-5024	265	7	of	of	ADP
ejpam-5024	265	8	linear	linear	PROPN
ejpam-5024	265	9	volterra	volterra	PROPN
ejpam-5024	265	10	integro	integro	PROPN
ejpam-5024	265	11	-	-	PUNCT
ejpam-5024	265	12	differential	differential	NOUN
ejpam-5024	265	13	equations	equation	NOUN
ejpam-5024	265	14	.	.	PUNCT
ejpam-5024	266	1	system	system	NOUN
ejpam-5024	266	2	,	,	PUNCT
ejpam-5024	266	3	50	50	NUM
ejpam-5024	266	4	,	,	PUNCT
ejpam-5024	266	5	2012	2012	NUM
ejpam-5024	266	6	.	.	PUNCT
ejpam-5024	267	1	[	[	X
ejpam-5024	267	2	14	14	NUM
ejpam-5024	267	3	]	]	X
ejpam-5024	267	4	jafar	jafar	PROPN
ejpam-5024	267	5	saberi	saberi	PROPN
ejpam-5024	267	6	-	-	PUNCT
ejpam-5024	267	7	nadjafi	nadjafi	PROPN
ejpam-5024	267	8	and	and	CCONJ
ejpam-5024	267	9	mohamadreza	mohamadreza	NOUN
ejpam-5024	267	10	tamamgar	tamamgar	NOUN
ejpam-5024	267	11	.	.	PUNCT
ejpam-5024	268	1	the	the	DET
ejpam-5024	268	2	variational	variational	ADJ
ejpam-5024	268	3	iteration	iteration	NOUN
ejpam-5024	268	4	method	method	NOUN
ejpam-5024	268	5	:	:	PUNCT
ejpam-5024	268	6	a	a	DET
ejpam-5024	268	7	highly	highly	ADV
ejpam-5024	268	8	promising	promising	ADJ
ejpam-5024	268	9	method	method	NOUN
ejpam-5024	268	10	for	for	ADP
ejpam-5024	268	11	solving	solve	VERB
ejpam-5024	268	12	the	the	DET
ejpam-5024	268	13	system	system	NOUN
ejpam-5024	268	14	of	of	ADP
ejpam-5024	268	15	integro	integro	ADJ
ejpam-5024	268	16	-	-	PUNCT
ejpam-5024	268	17	differential	differential	NOUN
ejpam-5024	268	18	equations	equation	NOUN
ejpam-5024	268	19	.	.	PUNCT
ejpam-5024	269	1	computers	computer	NOUN
ejpam-5024	269	2	mathematics	mathematic	NOUN
ejpam-5024	269	3	with	with	ADP
ejpam-5024	269	4	applications	application	NOUN
ejpam-5024	269	5	,	,	PUNCT
ejpam-5024	269	6	56	56	NUM
ejpam-5024	269	7	,	,	PUNCT
ejpam-5024	269	8	2008	2008	NUM
ejpam-5024	269	9	.	.	PUNCT
ejpam-5024	270	1	[	[	X
ejpam-5024	270	2	15	15	NUM
ejpam-5024	270	3	]	]	X
ejpam-5024	270	4	abdul	abdul	PROPN
ejpam-5024	270	5	-	-	PUNCT
ejpam-5024	270	6	majid	majid	PROPN
ejpam-5024	270	7	wazwaz	wazwaz	NOUN
ejpam-5024	270	8	.	.	PUNCT
ejpam-5024	271	1	first	first	ADJ
ejpam-5024	271	2	course	course	NOUN
ejpam-5024	271	3	in	in	ADP
ejpam-5024	271	4	integral	integral	ADJ
ejpam-5024	271	5	equations	equation	NOUN
ejpam-5024	271	6	,	,	PUNCT
ejpam-5024	271	7	a.	a.	NOUN
ejpam-5024	271	8	world	world	NOUN
ejpam-5024	271	9	scientific	scientific	ADJ
ejpam-5024	271	10	publishing	publishing	NOUN
ejpam-5024	271	11	company	company	NOUN
ejpam-5024	271	12	,	,	PUNCT
ejpam-5024	271	13	2015	2015	NUM
ejpam-5024	271	14	.	.	PUNCT
ejpam-5024	272	1	[	[	X
ejpam-5024	272	2	16	16	NUM
ejpam-5024	272	3	]	]	X
ejpam-5024	272	4	yunxia	yunxia	PROPN
ejpam-5024	272	5	wei	wei	PROPN
ejpam-5024	272	6	and	and	CCONJ
ejpam-5024	272	7	yanping	yanpe	VERB
ejpam-5024	272	8	chen	chen	PROPN
ejpam-5024	272	9	.	.	PUNCT
ejpam-5024	273	1	convergence	convergence	NOUN
ejpam-5024	273	2	analysis	analysis	NOUN
ejpam-5024	273	3	of	of	ADP
ejpam-5024	273	4	the	the	DET
ejpam-5024	273	5	legendre	legendre	PROPN
ejpam-5024	273	6	spectral	spectral	ADJ
ejpam-5024	273	7	collocation	collocation	NOUN
ejpam-5024	273	8	methods	method	NOUN
ejpam-5024	273	9	for	for	ADP
ejpam-5024	273	10	second	second	ADJ
ejpam-5024	273	11	order	order	NOUN
ejpam-5024	273	12	volterra	volterra	PROPN
ejpam-5024	273	13	integro	integro	PROPN
ejpam-5024	273	14	-	-	PUNCT
ejpam-5024	273	15	differential	differential	NOUN
ejpam-5024	273	16	equations	equation	NOUN
ejpam-5024	273	17	.	.	PUNCT
ejpam-5024	274	1	numerical	numerical	PROPN
ejpam-5024	274	2	mathematics	mathematics	PROPN
ejpam-5024	274	3	:	:	PUNCT
ejpam-5024	274	4	theory	theory	NOUN
ejpam-5024	274	5	,	,	PUNCT
ejpam-5024	274	6	methods	method	NOUN
ejpam-5024	274	7	and	and	CCONJ
ejpam-5024	274	8	applications	application	NOUN
ejpam-5024	274	9	,	,	PUNCT
ejpam-5024	274	10	4	4	NUM
ejpam-5024	274	11	,	,	PUNCT
ejpam-5024	274	12	2011	2011	NUM
ejpam-5024	274	13	.	.	PUNCT
ejpam-5024	275	1	[	[	X
ejpam-5024	275	2	17	17	NUM
ejpam-5024	275	3	]	]	X
ejpam-5024	275	4	şuayip	şuayip	NOUN
ejpam-5024	275	5	yüzbaşı	yüzbaşı	NOUN
ejpam-5024	275	6	.	.	PUNCT
ejpam-5024	276	1	improved	improve	VERB
ejpam-5024	276	2	bessel	bessel	ADJ
ejpam-5024	276	3	collocation	collocation	NOUN
ejpam-5024	276	4	method	method	NOUN
ejpam-5024	276	5	for	for	ADP
ejpam-5024	276	6	linear	linear	PROPN
ejpam-5024	276	7	volterra	volterra	PROPN
ejpam-5024	276	8	integrodifferential	integrodifferential	ADJ
ejpam-5024	276	9	equations	equation	NOUN
ejpam-5024	276	10	with	with	ADP
ejpam-5024	276	11	piecewise	piecewise	NOUN
ejpam-5024	276	12	intervals	interval	NOUN
ejpam-5024	276	13	and	and	CCONJ
ejpam-5024	276	14	application	application	NOUN
ejpam-5024	276	15	of	of	ADP
ejpam-5024	276	16	a	a	DET
ejpam-5024	276	17	volterra	volterra	NOUN
ejpam-5024	276	18	population	population	NOUN
ejpam-5024	276	19	model	model	NOUN
ejpam-5024	276	20	.	.	PUNCT
ejpam-5024	277	1	applied	apply	VERB
ejpam-5024	277	2	mathematical	mathematical	ADJ
ejpam-5024	277	3	modelling	modelling	NOUN
ejpam-5024	277	4	,	,	PUNCT
ejpam-5024	277	5	40	40	NUM
ejpam-5024	277	6	,	,	PUNCT
ejpam-5024	277	7	2016	2016	NUM
ejpam-5024	277	8	.	.	PUNCT
ejpam-5024	278	1	[	[	X
ejpam-5024	278	2	18	18	NUM
ejpam-5024	278	3	]	]	X
ejpam-5024	278	4	şuayip	şuayip	NOUN
ejpam-5024	278	5	yüzbaşı	yüzbaşı	NOUN
ejpam-5024	278	6	,	,	PUNCT
ejpam-5024	278	7	mehmet	mehmet	PROPN
ejpam-5024	278	8	sezer	sezer	PROPN
ejpam-5024	278	9	,	,	PUNCT
ejpam-5024	278	10	and	and	CCONJ
ejpam-5024	278	11	bayram	bayram	PROPN
ejpam-5024	278	12	kemancı	kemancı	PROPN
ejpam-5024	278	13	.	.	PUNCT
ejpam-5024	279	1	numerical	numerical	ADJ
ejpam-5024	279	2	solutions	solution	NOUN
ejpam-5024	279	3	of	of	ADP
ejpam-5024	279	4	integrodifferential	integrodifferential	ADJ
ejpam-5024	279	5	equations	equation	NOUN
ejpam-5024	279	6	and	and	CCONJ
ejpam-5024	279	7	application	application	NOUN
ejpam-5024	279	8	of	of	ADP
ejpam-5024	279	9	a	a	DET
ejpam-5024	279	10	population	population	NOUN
ejpam-5024	279	11	model	model	NOUN
ejpam-5024	279	12	with	with	ADP
ejpam-5024	279	13	an	an	DET
ejpam-5024	279	14	improved	improved	ADJ
ejpam-5024	279	15	legendre	legendre	NOUN
ejpam-5024	279	16	method	method	NOUN
ejpam-5024	279	17	.	.	PUNCT
ejpam-5024	280	1	applied	apply	VERB
ejpam-5024	280	2	mathematical	mathematical	ADJ
ejpam-5024	280	3	modelling	modelling	NOUN
ejpam-5024	280	4	,	,	PUNCT
ejpam-5024	280	5	37	37	NUM
ejpam-5024	280	6	,	,	PUNCT
ejpam-5024	280	7	2013	2013	NUM
ejpam-5024	280	8	.	.	PUNCT