id	sid	tid	token	lemma	pos
ejpam-6969	1	1	european	european	PROPN
ejpam-6969	1	2	journal	journal	PROPN
ejpam-6969	1	3	of	of	ADP
ejpam-6969	1	4	pure	pure	ADJ
ejpam-6969	1	5	and	and	CCONJ
ejpam-6969	1	6	applied	applied	ADJ
ejpam-6969	1	7	mathematics	mathematic	NOUN
ejpam-6969	1	8	2025	2025	NUM
ejpam-6969	1	9	,	,	PUNCT
ejpam-6969	1	10	vol	vol	NOUN
ejpam-6969	1	11	.	.	PROPN
ejpam-6969	1	12	18	18	NUM
ejpam-6969	1	13	,	,	PUNCT
ejpam-6969	1	14	issue	issue	NOUN
ejpam-6969	1	15	4	4	NUM
ejpam-6969	1	16	,	,	PUNCT
ejpam-6969	1	17	article	article	NOUN
ejpam-6969	1	18	number	number	NOUN
ejpam-6969	1	19	6969	6969	NUM
ejpam-6969	1	20	issn	issn	VERB
ejpam-6969	1	21	1307	1307	NUM
ejpam-6969	1	22	-	-	SYM
ejpam-6969	1	23	5543	5543	NUM
ejpam-6969	1	24	–	–	PUNCT
ejpam-6969	1	25	ejpam.com	ejpam.com	X
ejpam-6969	1	26	published	publish	VERB
ejpam-6969	1	27	by	by	ADP
ejpam-6969	1	28	new	new	PROPN
ejpam-6969	1	29	york	york	PROPN
ejpam-6969	1	30	business	business	PROPN
ejpam-6969	1	31	global	global	PROPN
ejpam-6969	1	32	a	a	DET
ejpam-6969	1	33	comparative	comparative	ADJ
ejpam-6969	1	34	study	study	NOUN
ejpam-6969	1	35	of	of	ADP
ejpam-6969	1	36	bernoulli	bernoulli	NOUN
ejpam-6969	1	37	collocation	collocation	NOUN
ejpam-6969	1	38	and	and	CCONJ
ejpam-6969	1	39	hermite	hermite	ADJ
ejpam-6969	1	40	-	-	PUNCT
ejpam-6969	1	41	galerkin	galerkin	ADJ
ejpam-6969	1	42	methods	method	NOUN
ejpam-6969	1	43	for	for	ADP
ejpam-6969	1	44	solving	solve	VERB
ejpam-6969	1	45	two	two	NUM
ejpam-6969	1	46	-	-	PUNCT
ejpam-6969	1	47	dimensional	dimensional	ADJ
ejpam-6969	1	48	nonlinear	nonlinear	ADJ
ejpam-6969	1	49	volterra	volterra	NOUN
ejpam-6969	1	50	integral	integral	ADJ
ejpam-6969	1	51	equations	equation	NOUN
ejpam-6969	1	52	of	of	ADP
ejpam-6969	1	53	the	the	DET
ejpam-6969	1	54	second	second	ADJ
ejpam-6969	1	55	kind	kind	NOUN
ejpam-6969	1	56	m.	m.	NOUN
ejpam-6969	1	57	h.	h.	PROPN
ejpam-6969	1	58	ahmed1,∗	ahmed1,∗	PROPN
ejpam-6969	1	59	,	,	PUNCT
ejpam-6969	1	60	a.	a.	NOUN
ejpam-6969	1	61	m.	m.	NOUN
ejpam-6969	1	62	aljabri1	aljabri1	PROPN
ejpam-6969	1	63	1	1	NUM
ejpam-6969	1	64	taibah	taibah	NOUN
ejpam-6969	1	65	university	university	NOUN
ejpam-6969	1	66	,	,	PUNCT
ejpam-6969	1	67	college	college	NOUN
ejpam-6969	1	68	of	of	ADP
ejpam-6969	1	69	science	science	NOUN
ejpam-6969	1	70	,	,	PUNCT
ejpam-6969	1	71	department	department	NOUN
ejpam-6969	1	72	of	of	ADP
ejpam-6969	1	73	mathematics	mathematics	PROPN
ejpam-6969	1	74	,	,	PUNCT
ejpam-6969	1	75	p.o	p.o	PROPN
ejpam-6969	1	76	.	.	PROPN
ejpam-6969	1	77	box	box	PROPN
ejpam-6969	1	78	344	344	NUM
ejpam-6969	1	79	,	,	PUNCT
ejpam-6969	1	80	madinah	madinah	PROPN
ejpam-6969	1	81	,	,	PUNCT
ejpam-6969	1	82	3002	3002	NUM
ejpam-6969	1	83	saudi	saudi	PROPN
ejpam-6969	1	84	arabia	arabia	PROPN
ejpam-6969	1	85	abstract	abstract	NOUN
ejpam-6969	1	86	.	.	PUNCT
ejpam-6969	2	1	this	this	DET
ejpam-6969	2	2	article	article	NOUN
ejpam-6969	2	3	is	be	AUX
ejpam-6969	2	4	devoted	devote	VERB
ejpam-6969	2	5	to	to	ADP
ejpam-6969	2	6	the	the	DET
ejpam-6969	2	7	presentation	presentation	NOUN
ejpam-6969	2	8	of	of	ADP
ejpam-6969	2	9	two	two	NUM
ejpam-6969	2	10	numerical	numerical	ADJ
ejpam-6969	2	11	methods	method	NOUN
ejpam-6969	2	12	which	which	PRON
ejpam-6969	2	13	give	give	VERB
ejpam-6969	2	14	the	the	DET
ejpam-6969	2	15	solution	solution	NOUN
ejpam-6969	2	16	of	of	ADP
ejpam-6969	2	17	a	a	DET
ejpam-6969	2	18	two	two	NUM
ejpam-6969	2	19	-	-	PUNCT
ejpam-6969	2	20	dimensional	dimensional	ADJ
ejpam-6969	2	21	nonlinear	nonlinear	ADJ
ejpam-6969	2	22	volterra	volterra	NOUN
ejpam-6969	2	23	integral	integral	ADJ
ejpam-6969	2	24	equation	equation	NOUN
ejpam-6969	2	25	of	of	ADP
ejpam-6969	2	26	the	the	DET
ejpam-6969	2	27	second	second	ADJ
ejpam-6969	2	28	kind	kind	NOUN
ejpam-6969	2	29	.	.	PUNCT
ejpam-6969	3	1	the	the	DET
ejpam-6969	3	2	first	first	ADJ
ejpam-6969	3	3	method	method	NOUN
ejpam-6969	3	4	,	,	PUNCT
ejpam-6969	3	5	bernoulli	bernoulli	NOUN
ejpam-6969	3	6	collocation	collocation	NOUN
ejpam-6969	3	7	,	,	PUNCT
ejpam-6969	3	8	depend	depend	VERB
ejpam-6969	3	9	on	on	ADP
ejpam-6969	3	10	approximating	approximate	VERB
ejpam-6969	3	11	the	the	DET
ejpam-6969	3	12	unknown	unknown	ADJ
ejpam-6969	3	13	function	function	NOUN
ejpam-6969	3	14	using	use	VERB
ejpam-6969	3	15	bernoulli	bernoulli	NOUN
ejpam-6969	3	16	polynomials	polynomial	NOUN
ejpam-6969	3	17	,	,	PUNCT
ejpam-6969	3	18	while	while	SCONJ
ejpam-6969	3	19	applying	apply	VERB
ejpam-6969	3	20	the	the	DET
ejpam-6969	3	21	collocation	collocation	NOUN
ejpam-6969	3	22	technique	technique	NOUN
ejpam-6969	3	23	at	at	ADP
ejpam-6969	3	24	shifted	shift	VERB
ejpam-6969	3	25	chebyshev	chebyshev	PROPN
ejpam-6969	3	26	points	point	NOUN
ejpam-6969	3	27	over	over	ADP
ejpam-6969	3	28	the	the	DET
ejpam-6969	3	29	interval	interval	NOUN
ejpam-6969	3	30	[	[	X
ejpam-6969	3	31	0,1	0,1	NUM
ejpam-6969	3	32	]	]	PUNCT
ejpam-6969	3	33	.	.	PUNCT
ejpam-6969	4	1	the	the	DET
ejpam-6969	4	2	second	second	ADJ
ejpam-6969	4	3	method	method	NOUN
ejpam-6969	4	4	,	,	PUNCT
ejpam-6969	4	5	hermite	hermite	ADJ
ejpam-6969	4	6	-	-	PUNCT
ejpam-6969	4	7	galerkin	galerkin	ADJ
ejpam-6969	4	8	method	method	NOUN
ejpam-6969	4	9	,	,	PUNCT
ejpam-6969	4	10	relies	rely	VERB
ejpam-6969	4	11	on	on	ADP
ejpam-6969	4	12	constructing	construct	VERB
ejpam-6969	4	13	an	an	DET
ejpam-6969	4	14	operational	operational	ADJ
ejpam-6969	4	15	matrices	matrix	NOUN
ejpam-6969	4	16	and	and	CCONJ
ejpam-6969	4	17	applying	apply	VERB
ejpam-6969	4	18	the	the	DET
ejpam-6969	4	19	galerkin	galerkin	ADJ
ejpam-6969	4	20	projection	projection	NOUN
ejpam-6969	4	21	,	,	PUNCT
ejpam-6969	4	22	which	which	PRON
ejpam-6969	4	23	we	we	PRON
ejpam-6969	4	24	have	have	VERB
ejpam-6969	4	25	a	a	DET
ejpam-6969	4	26	system	system	NOUN
ejpam-6969	4	27	of	of	ADP
ejpam-6969	4	28	nonlinear	nonlinear	ADJ
ejpam-6969	4	29	algebraic	algebraic	ADJ
ejpam-6969	4	30	equations	equation	NOUN
ejpam-6969	4	31	from	from	ADP
ejpam-6969	4	32	volterra	volterra	PROPN
ejpam-6969	4	33	integral	integral	ADJ
ejpam-6969	4	34	equation	equation	NOUN
ejpam-6969	4	35	.	.	PUNCT
ejpam-6969	5	1	discussion	discussion	NOUN
ejpam-6969	5	2	on	on	ADP
ejpam-6969	5	3	the	the	DET
ejpam-6969	5	4	existence	existence	NOUN
ejpam-6969	5	5	and	and	CCONJ
ejpam-6969	5	6	uniqueness	uniqueness	NOUN
ejpam-6969	5	7	of	of	ADP
ejpam-6969	5	8	the	the	DET
ejpam-6969	5	9	solution	solution	NOUN
ejpam-6969	5	10	is	be	AUX
ejpam-6969	5	11	provided	provide	VERB
ejpam-6969	5	12	.	.	PUNCT
ejpam-6969	6	1	finally	finally	ADV
ejpam-6969	6	2	,	,	PUNCT
ejpam-6969	6	3	the	the	DET
ejpam-6969	6	4	effect	effect	NOUN
ejpam-6969	6	5	of	of	ADP
ejpam-6969	6	6	that	that	PRON
ejpam-6969	6	7	two	two	NUM
ejpam-6969	6	8	numerical	numerical	ADJ
ejpam-6969	6	9	methods	method	NOUN
ejpam-6969	6	10	is	be	AUX
ejpam-6969	6	11	described	describe	VERB
ejpam-6969	6	12	.	.	PUNCT
ejpam-6969	7	1	to	to	PART
ejpam-6969	7	2	illustrate	illustrate	VERB
ejpam-6969	7	3	the	the	DET
ejpam-6969	7	4	previously	previously	ADV
ejpam-6969	7	5	described	describe	VERB
ejpam-6969	7	6	methods	method	NOUN
ejpam-6969	7	7	,	,	PUNCT
ejpam-6969	7	8	several	several	ADJ
ejpam-6969	7	9	numerical	numerical	ADJ
ejpam-6969	7	10	examples	example	NOUN
ejpam-6969	7	11	are	be	AUX
ejpam-6969	7	12	provided	provide	VERB
ejpam-6969	7	13	.	.	PUNCT
ejpam-6969	8	1	numerical	numerical	PROPN
ejpam-6969	8	2	results	result	NOUN
ejpam-6969	8	3	show	show	VERB
ejpam-6969	8	4	that	that	SCONJ
ejpam-6969	8	5	the	the	DET
ejpam-6969	8	6	bernoulli	bernoulli	PROPN
ejpam-6969	8	7	collocation	collocation	NOUN
ejpam-6969	8	8	method	method	NOUN
ejpam-6969	8	9	consistently	consistently	ADV
ejpam-6969	8	10	provides	provide	VERB
ejpam-6969	8	11	more	more	ADV
ejpam-6969	8	12	accurate	accurate	ADJ
ejpam-6969	8	13	and	and	CCONJ
ejpam-6969	8	14	efficient	efficient	ADJ
ejpam-6969	8	15	results	result	NOUN
ejpam-6969	8	16	than	than	ADP
ejpam-6969	8	17	the	the	DET
ejpam-6969	8	18	hermite	hermite	ADJ
ejpam-6969	8	19	–	–	PUNCT
ejpam-6969	8	20	galerkin	galerkin	ADJ
ejpam-6969	8	21	method	method	NOUN
ejpam-6969	8	22	for	for	ADP
ejpam-6969	8	23	the	the	DET
ejpam-6969	8	24	same	same	ADJ
ejpam-6969	8	25	number	number	NOUN
ejpam-6969	8	26	of	of	ADP
ejpam-6969	8	27	collocation	collocation	NOUN
ejpam-6969	8	28	points	point	NOUN
ejpam-6969	8	29	.	.	PUNCT
ejpam-6969	9	1	comparisons	comparison	NOUN
ejpam-6969	9	2	with	with	ADP
ejpam-6969	9	3	previously	previously	ADV
ejpam-6969	9	4	published	publish	VERB
ejpam-6969	9	5	approaches	approach	NOUN
ejpam-6969	9	6	further	far	ADV
ejpam-6969	9	7	demonstrate	demonstrate	VERB
ejpam-6969	9	8	the	the	DET
ejpam-6969	9	9	superiority	superiority	NOUN
ejpam-6969	9	10	of	of	ADP
ejpam-6969	9	11	the	the	DET
ejpam-6969	9	12	proposed	propose	VERB
ejpam-6969	9	13	methods	method	NOUN
ejpam-6969	9	14	in	in	ADP
ejpam-6969	9	15	terms	term	NOUN
ejpam-6969	9	16	of	of	ADP
ejpam-6969	9	17	convergence	convergence	NOUN
ejpam-6969	9	18	and	and	CCONJ
ejpam-6969	9	19	stability	stability	NOUN
ejpam-6969	9	20	.	.	PUNCT
ejpam-6969	10	1	2020	2020	NUM
ejpam-6969	10	2	mathematics	mathematic	NOUN
ejpam-6969	10	3	subject	subject	NOUN
ejpam-6969	10	4	classifications	classification	NOUN
ejpam-6969	10	5	:	:	PUNCT
ejpam-6969	10	6	11b39	11b39	NUM
ejpam-6969	10	7	,	,	PUNCT
ejpam-6969	10	8	45b05	45b05	NUM
ejpam-6969	10	9	,	,	PUNCT
ejpam-6969	10	10	45d05	45d05	NUM
ejpam-6969	10	11	,	,	PUNCT
ejpam-6969	10	12	65r20	65r20	NUM
ejpam-6969	10	13	key	key	ADJ
ejpam-6969	10	14	words	word	NOUN
ejpam-6969	10	15	and	and	CCONJ
ejpam-6969	10	16	phrases	phrase	NOUN
ejpam-6969	10	17	:	:	PUNCT
ejpam-6969	10	18	non	non	ADJ
ejpam-6969	10	19	-	-	ADJ
ejpam-6969	10	20	linear	linear	ADJ
ejpam-6969	10	21	two	two	NUM
ejpam-6969	10	22	-	-	PUNCT
ejpam-6969	10	23	dimensional	dimensional	ADJ
ejpam-6969	10	24	volterra	volterra	NOUN
ejpam-6969	10	25	integral	integral	ADJ
ejpam-6969	10	26	equations	equation	NOUN
ejpam-6969	10	27	,	,	PUNCT
ejpam-6969	10	28	bernoulli	bernoulli	NOUN
ejpam-6969	10	29	polynomials	polynomial	NOUN
ejpam-6969	10	30	,	,	PUNCT
ejpam-6969	10	31	shifted	shift	VERB
ejpam-6969	10	32	chebyshev	chebyshev	NOUN
ejpam-6969	10	33	points	point	NOUN
ejpam-6969	10	34	,	,	PUNCT
ejpam-6969	10	35	hermite	hermite	ADJ
ejpam-6969	10	36	polynomials	polynomial	NOUN
ejpam-6969	10	37	and	and	CCONJ
ejpam-6969	10	38	galerkin	galerkin	ADJ
ejpam-6969	10	39	method	method	NOUN
ejpam-6969	10	40	1	1	NUM
ejpam-6969	10	41	.	.	PUNCT
ejpam-6969	11	1	introduction	introduction	NOUN
ejpam-6969	11	2	volterra	volterra	PROPN
ejpam-6969	11	3	integral	integral	ADJ
ejpam-6969	11	4	equations	equation	NOUN
ejpam-6969	11	5	(	(	PUNCT
ejpam-6969	11	6	vies	vie	NOUN
ejpam-6969	11	7	)	)	PUNCT
ejpam-6969	11	8	,	,	PUNCT
ejpam-6969	11	9	particularly	particularly	ADV
ejpam-6969	11	10	in	in	ADP
ejpam-6969	11	11	two	two	NUM
ejpam-6969	11	12	dimensions	dimension	NOUN
ejpam-6969	11	13	,	,	PUNCT
ejpam-6969	11	14	serve	serve	VERB
ejpam-6969	11	15	as	as	ADP
ejpam-6969	11	16	an	an	DET
ejpam-6969	11	17	effective	effective	ADJ
ejpam-6969	11	18	tool	tool	NOUN
ejpam-6969	11	19	for	for	ADP
ejpam-6969	11	20	modeling	model	VERB
ejpam-6969	11	21	various	various	ADJ
ejpam-6969	11	22	phenomena	phenomenon	NOUN
ejpam-6969	11	23	in	in	ADP
ejpam-6969	11	24	physical	physical	ADJ
ejpam-6969	11	25	and	and	CCONJ
ejpam-6969	11	26	engineering	engineering	NOUN
ejpam-6969	11	27	sciences	science	NOUN
ejpam-6969	11	28	.	.	PUNCT
ejpam-6969	12	1	for	for	ADP
ejpam-6969	12	2	instance	instance	NOUN
ejpam-6969	12	3	,	,	PUNCT
ejpam-6969	12	4	(	(	PUNCT
ejpam-6969	12	5	vies	vie	NOUN
ejpam-6969	12	6	)	)	PUNCT
ejpam-6969	12	7	are	be	AUX
ejpam-6969	12	8	used	use	VERB
ejpam-6969	12	9	to	to	PART
ejpam-6969	12	10	describe	describe	VERB
ejpam-6969	12	11	viscoelastic	viscoelastic	ADJ
ejpam-6969	12	12	rods	rod	NOUN
ejpam-6969	12	13	and	and	CCONJ
ejpam-6969	12	14	plates	plate	NOUN
ejpam-6969	12	15	,	,	PUNCT
ejpam-6969	12	16	where	where	SCONJ
ejpam-6969	12	17	stress	stress	NOUN
ejpam-6969	12	18	depends	depend	VERB
ejpam-6969	12	19	on	on	ADP
ejpam-6969	12	20	the	the	DET
ejpam-6969	12	21	full	full	ADJ
ejpam-6969	12	22	strain	strain	NOUN
ejpam-6969	12	23	history	history	NOUN
ejpam-6969	13	1	[	[	X
ejpam-6969	13	2	1	1	NUM
ejpam-6969	13	3	]	]	PUNCT
ejpam-6969	13	4	,	,	PUNCT
ejpam-6969	13	5	and	and	CCONJ
ejpam-6969	13	6	nonlinear	nonlinear	ADJ
ejpam-6969	13	7	viscoelastic	viscoelastic	ADJ
ejpam-6969	13	8	solids	solid	NOUN
ejpam-6969	13	9	[	[	X
ejpam-6969	13	10	2	2	NUM
ejpam-6969	13	11	]	]	PUNCT
ejpam-6969	13	12	,	,	PUNCT
ejpam-6969	13	13	highlighting	highlight	VERB
ejpam-6969	13	14	their	their	PRON
ejpam-6969	13	15	relevance	relevance	NOUN
ejpam-6969	13	16	in	in	ADP
ejpam-6969	13	17	modeling	model	VERB
ejpam-6969	13	18	real	real	ADJ
ejpam-6969	13	19	-	-	PUNCT
ejpam-6969	13	20	world	world	NOUN
ejpam-6969	13	21	materials	material	NOUN
ejpam-6969	13	22	and	and	CCONJ
ejpam-6969	13	23	systems	system	NOUN
ejpam-6969	13	24	.	.	PUNCT
ejpam-6969	14	1	these	these	DET
ejpam-6969	14	2	equations	equation	NOUN
ejpam-6969	14	3	have	have	AUX
ejpam-6969	14	4	attracted	attract	VERB
ejpam-6969	14	5	considerable	considerable	ADJ
ejpam-6969	14	6	∗corresponding	∗corresponding	NOUN
ejpam-6969	14	7	author	author	NOUN
ejpam-6969	14	8	.	.	PUNCT
ejpam-6969	15	1	doi	doi	NOUN
ejpam-6969	15	2	:	:	PUNCT
ejpam-6969	15	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6969	https://doi.org/10.29020/nybg.ejpam.v18i4.6969	PART
ejpam-6969	15	4	email	email	NOUN
ejpam-6969	15	5	addresses	address	NOUN
ejpam-6969	15	6	:	:	PUNCT
ejpam-6969	15	7	mramadan@taibahu.edu.sa	mramadan@taibahu.edu.sa	PROPN
ejpam-6969	15	8	(	(	PUNCT
ejpam-6969	15	9	m.	m.	PROPN
ejpam-6969	15	10	h.	h.	PROPN
ejpam-6969	15	11	ahmed	ahmed	PROPN
ejpam-6969	15	12	)	)	PUNCT
ejpam-6969	15	13	,	,	PUNCT
ejpam-6969	15	14	asmazaljabrii@gmail.com	asmazaljabrii@gmail.com	X
ejpam-6969	16	1	(	(	PUNCT
ejpam-6969	16	2	a.	a.	NOUN
ejpam-6969	16	3	m.	m.	PROPN
ejpam-6969	16	4	aljabri	aljabri	PROPN
ejpam-6969	16	5	)	)	PUNCT
ejpam-6969	16	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6969	17	1	1	1	NUM
ejpam-6969	17	2	copyright	copyright	NOUN
ejpam-6969	17	3	:	:	PUNCT
ejpam-6969	17	4	©	©	PROPN
ejpam-6969	17	5	2025	2025	NUM
ejpam-6969	17	6	the	the	DET
ejpam-6969	17	7	author(s	author(s	NOUN
ejpam-6969	17	8	)	)	PUNCT
ejpam-6969	17	9	.	.	PUNCT
ejpam-6969	18	1	(	(	PUNCT
ejpam-6969	18	2	cc	cc	NOUN
ejpam-6969	18	3	by	by	ADP
ejpam-6969	18	4	-	-	PUNCT
ejpam-6969	18	5	nc	nc	PROPN
ejpam-6969	18	6	4.0	4.0	NUM
ejpam-6969	18	7	)	)	PUNCT
ejpam-6969	18	8	m.	m.	NOUN
ejpam-6969	18	9	h.	h.	PROPN
ejpam-6969	18	10	ahmed	ahmed	PROPN
ejpam-6969	18	11	,	,	PUNCT
ejpam-6969	18	12	a.	a.	NOUN
ejpam-6969	18	13	m.	m.	PROPN
ejpam-6969	18	14	aljabri	aljabri	PROPN
ejpam-6969	18	15	/	/	SYM
ejpam-6969	18	16	eur	eur	PROPN
ejpam-6969	18	17	.	.	PUNCT
ejpam-6969	19	1	j.	j.	PROPN
ejpam-6969	19	2	pure	pure	PROPN
ejpam-6969	19	3	appl	appl	PROPN
ejpam-6969	19	4	.	.	PROPN
ejpam-6969	19	5	math	math	PROPN
ejpam-6969	19	6	,	,	PUNCT
ejpam-6969	19	7	18	18	NUM
ejpam-6969	19	8	(	(	PUNCT
ejpam-6969	19	9	4	4	NUM
ejpam-6969	19	10	)	)	PUNCT
ejpam-6969	19	11	(	(	PUNCT
ejpam-6969	19	12	2025	2025	NUM
ejpam-6969	19	13	)	)	PUNCT
ejpam-6969	19	14	,	,	PUNCT
ejpam-6969	19	15	6969	6969	NUM
ejpam-6969	19	16	2	2	NUM
ejpam-6969	19	17	of	of	ADP
ejpam-6969	19	18	16	16	NUM
ejpam-6969	19	19	attention	attention	NOUN
ejpam-6969	19	20	in	in	ADP
ejpam-6969	19	21	both	both	CCONJ
ejpam-6969	19	22	theoretical	theoretical	ADJ
ejpam-6969	19	23	analysis	analysis	NOUN
ejpam-6969	19	24	and	and	CCONJ
ejpam-6969	19	25	the	the	DET
ejpam-6969	19	26	development	development	NOUN
ejpam-6969	19	27	of	of	ADP
ejpam-6969	19	28	accurate	accurate	ADJ
ejpam-6969	19	29	and	and	CCONJ
ejpam-6969	19	30	efficient	efficient	ADJ
ejpam-6969	19	31	numerical	numerical	ADJ
ejpam-6969	19	32	methods	method	NOUN
ejpam-6969	19	33	for	for	ADP
ejpam-6969	19	34	their	their	PRON
ejpam-6969	19	35	solution	solution	NOUN
ejpam-6969	19	36	[	[	X
ejpam-6969	19	37	3–5	3–5	NOUN
ejpam-6969	19	38	]	]	PUNCT
ejpam-6969	19	39	.	.	PUNCT
ejpam-6969	20	1	in	in	ADP
ejpam-6969	20	2	the	the	DET
ejpam-6969	20	3	present	present	ADJ
ejpam-6969	20	4	study	study	NOUN
ejpam-6969	20	5	,	,	PUNCT
ejpam-6969	20	6	we	we	PRON
ejpam-6969	20	7	examine	examine	VERB
ejpam-6969	20	8	the	the	DET
ejpam-6969	20	9	following	follow	VERB
ejpam-6969	20	10	two	two	NUM
ejpam-6969	20	11	-	-	PUNCT
ejpam-6969	20	12	dimensional	dimensional	ADJ
ejpam-6969	20	13	nonlinear	nonlinear	ADJ
ejpam-6969	20	14	volterra	volterra	NOUN
ejpam-6969	20	15	integral	integral	ADJ
ejpam-6969	20	16	equation	equation	NOUN
ejpam-6969	20	17	of	of	ADP
ejpam-6969	20	18	the	the	DET
ejpam-6969	20	19	second	second	ADJ
ejpam-6969	20	20	kind	kind	NOUN
ejpam-6969	20	21	:	:	PUNCT
ejpam-6969	20	22	u(χ	u(χ	PROPN
ejpam-6969	20	23	,	,	PUNCT
ejpam-6969	20	24	t	t	PROPN
ejpam-6969	20	25	)	)	PUNCT
ejpam-6969	20	26	=	=	SYM
ejpam-6969	20	27	f(χ	f(χ	PROPN
ejpam-6969	20	28	,	,	PUNCT
ejpam-6969	20	29	t	t	PROPN
ejpam-6969	20	30	)	)	PUNCT
ejpam-6969	21	1	+	+	NUM
ejpam-6969	22	1	λ	λ	PROPN
ejpam-6969	22	2	∫	∫	PROPN
ejpam-6969	22	3	t	t	PROPN
ejpam-6969	22	4	0	0	NUM
ejpam-6969	22	5	∫	∫	PROPN
ejpam-6969	23	1	χ	χ	X
ejpam-6969	23	2	0	0	PROPN
ejpam-6969	23	3	k(χ	k(χ	PROPN
ejpam-6969	23	4	,	,	PUNCT
ejpam-6969	23	5	t	t	PROPN
ejpam-6969	23	6	,	,	PUNCT
ejpam-6969	23	7	s	s	PROPN
ejpam-6969	23	8	,	,	PUNCT
ejpam-6969	23	9	y	y	PROPN
ejpam-6969	23	10	,	,	PUNCT
ejpam-6969	23	11	u(s	u(s	PROPN
ejpam-6969	23	12	,	,	PUNCT
ejpam-6969	23	13	y	y	NOUN
ejpam-6969	23	14	)	)	PUNCT
ejpam-6969	23	15	)	)	PUNCT
ejpam-6969	23	16	ds	ds	PROPN
ejpam-6969	23	17	dy	dy	NOUN
ejpam-6969	23	18	,	,	PUNCT
ejpam-6969	23	19	χ	χ	X
ejpam-6969	23	20	,	,	PUNCT
ejpam-6969	23	21	t	t	PROPN
ejpam-6969	23	22	∈	∈	PROPN
ejpam-6969	24	1	[	[	X
ejpam-6969	24	2	0	0	NUM
ejpam-6969	24	3	,	,	PUNCT
ejpam-6969	24	4	1	1	NUM
ejpam-6969	24	5	]	]	PUNCT
ejpam-6969	24	6	,	,	PUNCT
ejpam-6969	24	7	(	(	PUNCT
ejpam-6969	24	8	1	1	X
ejpam-6969	24	9	)	)	PUNCT
ejpam-6969	24	10	where	where	SCONJ
ejpam-6969	24	11	u(χ	u(χ	PROPN
ejpam-6969	24	12	,	,	PUNCT
ejpam-6969	24	13	t	t	PROPN
ejpam-6969	24	14	)	)	PUNCT
ejpam-6969	24	15	is	be	AUX
ejpam-6969	24	16	the	the	DET
ejpam-6969	24	17	unknown	unknown	ADJ
ejpam-6969	24	18	function	function	NOUN
ejpam-6969	24	19	defined	define	VERB
ejpam-6969	24	20	on	on	ADP
ejpam-6969	24	21	the	the	DET
ejpam-6969	24	22	domain	domain	NOUN
ejpam-6969	25	1	d	d	NOUN
ejpam-6969	25	2	=	=	PUNCT
ejpam-6969	26	1	[	[	X
ejpam-6969	26	2	0	0	NUM
ejpam-6969	26	3	,	,	PUNCT
ejpam-6969	26	4	1]×	1]×	NUM
ejpam-6969	26	5	[	[	X
ejpam-6969	26	6	0	0	NUM
ejpam-6969	26	7	,	,	PUNCT
ejpam-6969	26	8	1	1	NUM
ejpam-6969	26	9	]	]	PUNCT
ejpam-6969	26	10	,	,	PUNCT
ejpam-6969	26	11	and	and	CCONJ
ejpam-6969	26	12	f(χ	f(χ	PROPN
ejpam-6969	26	13	,	,	PUNCT
ejpam-6969	26	14	t	t	PROPN
ejpam-6969	26	15	)	)	PUNCT
ejpam-6969	26	16	,	,	PUNCT
ejpam-6969	26	17	k(χ	k(χ	PROPN
ejpam-6969	26	18	,	,	PUNCT
ejpam-6969	26	19	t	t	PROPN
ejpam-6969	26	20	,	,	PUNCT
ejpam-6969	26	21	s	s	PROPN
ejpam-6969	26	22	,	,	PUNCT
ejpam-6969	26	23	y	y	PROPN
ejpam-6969	26	24	,	,	PUNCT
ejpam-6969	26	25	u(s	u(s	PROPN
ejpam-6969	26	26	,	,	PUNCT
ejpam-6969	26	27	y	y	NOUN
ejpam-6969	26	28	)	)	PUNCT
ejpam-6969	26	29	)	)	PUNCT
ejpam-6969	26	30	are	be	AUX
ejpam-6969	26	31	assumed	assume	VERB
ejpam-6969	26	32	to	to	PART
ejpam-6969	26	33	be	be	AUX
ejpam-6969	26	34	known	know	VERB
ejpam-6969	26	35	analytical	analytical	ADJ
ejpam-6969	26	36	functions	function	NOUN
ejpam-6969	26	37	.	.	PUNCT
ejpam-6969	27	1	many	many	ADJ
ejpam-6969	27	2	numerical	numerical	ADJ
ejpam-6969	27	3	methods	method	NOUN
ejpam-6969	27	4	have	have	AUX
ejpam-6969	27	5	been	be	AUX
ejpam-6969	27	6	developed	develop	VERB
ejpam-6969	27	7	to	to	PART
ejpam-6969	27	8	solve	solve	VERB
ejpam-6969	27	9	two	two	NUM
ejpam-6969	27	10	-	-	PUNCT
ejpam-6969	27	11	dimensional	dimensional	ADJ
ejpam-6969	27	12	volterra	volterra	NOUN
ejpam-6969	27	13	integral	integral	ADJ
ejpam-6969	27	14	equations	equation	NOUN
ejpam-6969	27	15	due	due	ADP
ejpam-6969	27	16	to	to	ADP
ejpam-6969	27	17	the	the	DET
ejpam-6969	27	18	difficulty	difficulty	NOUN
ejpam-6969	27	19	of	of	ADP
ejpam-6969	27	20	obtaining	obtain	VERB
ejpam-6969	27	21	analytical	analytical	ADJ
ejpam-6969	27	22	solutions	solution	NOUN
ejpam-6969	27	23	.	.	PUNCT
ejpam-6969	28	1	for	for	ADP
ejpam-6969	28	2	example	example	NOUN
ejpam-6969	28	3	,	,	PUNCT
ejpam-6969	28	4	several	several	ADJ
ejpam-6969	28	5	numerical	numerical	ADJ
ejpam-6969	28	6	techniques	technique	NOUN
ejpam-6969	28	7	have	have	AUX
ejpam-6969	28	8	been	be	AUX
ejpam-6969	28	9	proposed	propose	VERB
ejpam-6969	28	10	for	for	ADP
ejpam-6969	28	11	these	these	DET
ejpam-6969	28	12	equations	equation	NOUN
ejpam-6969	28	13	,	,	PUNCT
ejpam-6969	28	14	including	include	VERB
ejpam-6969	28	15	the	the	DET
ejpam-6969	28	16	chebysheve	chebysheve	NOUN
ejpam-6969	28	17	polynomials	polynomial	NOUN
ejpam-6969	28	18	as	as	ADP
ejpam-6969	28	19	the	the	DET
ejpam-6969	28	20	basis	basis	NOUN
ejpam-6969	28	21	in	in	ADP
ejpam-6969	28	22	the	the	DET
ejpam-6969	28	23	collocation	collocation	NOUN
ejpam-6969	28	24	method	method	NOUN
ejpam-6969	28	25	[	[	X
ejpam-6969	28	26	6	6	NUM
ejpam-6969	28	27	]	]	PUNCT
ejpam-6969	28	28	,	,	PUNCT
ejpam-6969	28	29	differential	differential	ADJ
ejpam-6969	28	30	transformation	transformation	NOUN
ejpam-6969	28	31	method	method	NOUN
ejpam-6969	29	1	[	[	X
ejpam-6969	29	2	7	7	NUM
ejpam-6969	29	3	]	]	PUNCT
ejpam-6969	29	4	,	,	PUNCT
ejpam-6969	29	5	reproducing	reproduce	VERB
ejpam-6969	29	6	kernel	kernel	NOUN
ejpam-6969	29	7	function	function	NOUN
ejpam-6969	29	8	method	method	NOUN
ejpam-6969	29	9	[	[	X
ejpam-6969	29	10	8	8	NUM
ejpam-6969	29	11	]	]	PUNCT
ejpam-6969	29	12	,	,	PUNCT
ejpam-6969	29	13	legendre	legendre	PROPN
ejpam-6969	29	14	polynomials	polynomial	NOUN
ejpam-6969	29	15	method	method	VERB
ejpam-6969	29	16	[	[	X
ejpam-6969	29	17	9	9	NUM
ejpam-6969	29	18	]	]	PUNCT
ejpam-6969	29	19	,	,	PUNCT
ejpam-6969	29	20	rationalized	rationalize	VERB
ejpam-6969	29	21	haar	haar	NOUN
ejpam-6969	29	22	functions	function	NOUN
ejpam-6969	29	23	[	[	X
ejpam-6969	29	24	10	10	NUM
ejpam-6969	29	25	]	]	PUNCT
ejpam-6969	29	26	and	and	CCONJ
ejpam-6969	29	27	two	two	NUM
ejpam-6969	29	28	-	-	PUNCT
ejpam-6969	29	29	dimensional	dimensional	ADJ
ejpam-6969	29	30	block	block	NOUN
ejpam-6969	29	31	-	-	PUNCT
ejpam-6969	29	32	pulse	pulse	NOUN
ejpam-6969	29	33	functions	function	NOUN
ejpam-6969	29	34	[	[	X
ejpam-6969	29	35	11	11	NUM
ejpam-6969	29	36	,	,	PUNCT
ejpam-6969	29	37	12	12	NUM
ejpam-6969	29	38	]	]	PUNCT
ejpam-6969	29	39	.	.	PUNCT
ejpam-6969	30	1	in	in	ADP
ejpam-6969	30	2	[	[	X
ejpam-6969	30	3	13	13	NUM
ejpam-6969	30	4	]	]	PUNCT
ejpam-6969	30	5	,	,	PUNCT
ejpam-6969	30	6	a	a	DET
ejpam-6969	30	7	numerical	numerical	ADJ
ejpam-6969	30	8	method	method	NOUN
ejpam-6969	30	9	was	be	AUX
ejpam-6969	30	10	presented	present	VERB
ejpam-6969	30	11	for	for	ADP
ejpam-6969	30	12	solving	solve	VERB
ejpam-6969	30	13	a	a	DET
ejpam-6969	30	14	class	class	NOUN
ejpam-6969	30	15	of	of	ADP
ejpam-6969	30	16	nonlinear	nonlinear	ADJ
ejpam-6969	30	17	two	two	NUM
ejpam-6969	30	18	-	-	PUNCT
ejpam-6969	30	19	dimensional	dimensional	ADJ
ejpam-6969	30	20	integral	integral	ADJ
ejpam-6969	30	21	equations	equation	NOUN
ejpam-6969	30	22	using	use	VERB
ejpam-6969	30	23	bernoulli	bernoulli	NOUN
ejpam-6969	30	24	polynomials	polynomial	NOUN
ejpam-6969	30	25	.	.	PUNCT
ejpam-6969	31	1	the	the	DET
ejpam-6969	31	2	approach	approach	NOUN
ejpam-6969	31	3	relies	rely	VERB
ejpam-6969	31	4	on	on	ADP
ejpam-6969	31	5	constructing	construct	VERB
ejpam-6969	31	6	an	an	DET
ejpam-6969	31	7	operational	operational	ADJ
ejpam-6969	31	8	matrix	matrix	NOUN
ejpam-6969	31	9	of	of	ADP
ejpam-6969	31	10	bernoulli	bernoulli	NOUN
ejpam-6969	31	11	polynomials	polynomial	NOUN
ejpam-6969	31	12	,	,	PUNCT
ejpam-6969	31	13	resulting	result	VERB
ejpam-6969	31	14	in	in	ADP
ejpam-6969	31	15	an	an	DET
ejpam-6969	31	16	efficient	efficient	ADJ
ejpam-6969	31	17	and	and	CCONJ
ejpam-6969	31	18	accurate	accurate	ADJ
ejpam-6969	31	19	approximation	approximation	NOUN
ejpam-6969	31	20	scheme	scheme	NOUN
ejpam-6969	31	21	.	.	PUNCT
ejpam-6969	32	1	in	in	ADP
ejpam-6969	32	2	[	[	X
ejpam-6969	32	3	14	14	NUM
ejpam-6969	32	4	]	]	X
ejpam-6969	32	5	,	,	PUNCT
ejpam-6969	32	6	a	a	DET
ejpam-6969	32	7	numerical	numerical	ADJ
ejpam-6969	32	8	scheme	scheme	NOUN
ejpam-6969	32	9	based	base	VERB
ejpam-6969	32	10	on	on	ADP
ejpam-6969	32	11	shifted	shift	VERB
ejpam-6969	32	12	jacobi	jacobi	PROPN
ejpam-6969	32	13	operational	operational	ADJ
ejpam-6969	32	14	matrices	matrix	NOUN
ejpam-6969	32	15	combined	combine	VERB
ejpam-6969	32	16	with	with	ADP
ejpam-6969	32	17	the	the	DET
ejpam-6969	32	18	collocation	collocation	NOUN
ejpam-6969	32	19	method	method	NOUN
ejpam-6969	32	20	was	be	AUX
ejpam-6969	32	21	developed	develop	VERB
ejpam-6969	32	22	to	to	PART
ejpam-6969	32	23	solve	solve	VERB
ejpam-6969	32	24	two	two	NUM
ejpam-6969	32	25	-	-	PUNCT
ejpam-6969	32	26	dimensional	dimensional	ADJ
ejpam-6969	32	27	nonlinear	nonlinear	ADJ
ejpam-6969	32	28	fractional	fractional	ADJ
ejpam-6969	32	29	volterra	volterra	NOUN
ejpam-6969	32	30	and	and	CCONJ
ejpam-6969	32	31	fredholm	fredholm	VERB
ejpam-6969	32	32	integral	integral	ADJ
ejpam-6969	32	33	equations	equation	NOUN
ejpam-6969	32	34	.	.	PUNCT
ejpam-6969	33	1	this	this	DET
ejpam-6969	33	2	method	method	NOUN
ejpam-6969	33	3	effectively	effectively	ADV
ejpam-6969	33	4	handles	handle	VERB
ejpam-6969	33	5	fractional	fractional	ADJ
ejpam-6969	33	6	orders	order	NOUN
ejpam-6969	33	7	while	while	SCONJ
ejpam-6969	33	8	maintaining	maintain	VERB
ejpam-6969	33	9	high	high	ADJ
ejpam-6969	33	10	accuracy	accuracy	NOUN
ejpam-6969	33	11	.	.	PUNCT
ejpam-6969	34	1	the	the	DET
ejpam-6969	34	2	authors	author	NOUN
ejpam-6969	34	3	of	of	ADP
ejpam-6969	34	4	[	[	X
ejpam-6969	34	5	15	15	NUM
ejpam-6969	34	6	]	]	PUNCT
ejpam-6969	34	7	introduced	introduce	VERB
ejpam-6969	34	8	a	a	DET
ejpam-6969	34	9	laguerre	laguerre	NOUN
ejpam-6969	34	10	wavelet	wavelet	NOUN
ejpam-6969	34	11	-	-	PUNCT
ejpam-6969	34	12	based	base	VERB
ejpam-6969	34	13	method	method	NOUN
ejpam-6969	34	14	for	for	ADP
ejpam-6969	34	15	solving	solve	VERB
ejpam-6969	34	16	two	two	NUM
ejpam-6969	34	17	-	-	PUNCT
ejpam-6969	34	18	dimensional	dimensional	ADJ
ejpam-6969	34	19	nonlinear	nonlinear	ADJ
ejpam-6969	34	20	integral	integral	ADJ
ejpam-6969	34	21	equations	equation	NOUN
ejpam-6969	34	22	.	.	PUNCT
ejpam-6969	35	1	their	their	PRON
ejpam-6969	35	2	work	work	NOUN
ejpam-6969	35	3	included	include	VERB
ejpam-6969	35	4	a	a	DET
ejpam-6969	35	5	detailed	detailed	ADJ
ejpam-6969	35	6	convergence	convergence	NOUN
ejpam-6969	35	7	analysis	analysis	NOUN
ejpam-6969	35	8	that	that	PRON
ejpam-6969	35	9	confirmed	confirm	VERB
ejpam-6969	35	10	the	the	DET
ejpam-6969	35	11	method	method	NOUN
ejpam-6969	35	12	’s	’s	PART
ejpam-6969	35	13	accuracy	accuracy	NOUN
ejpam-6969	35	14	and	and	CCONJ
ejpam-6969	35	15	efficiency	efficiency	NOUN
ejpam-6969	35	16	.	.	PUNCT
ejpam-6969	36	1	moreover	moreover	ADV
ejpam-6969	36	2	,	,	PUNCT
ejpam-6969	36	3	in	in	ADP
ejpam-6969	36	4	[	[	X
ejpam-6969	36	5	16	16	NUM
ejpam-6969	36	6	]	]	X
ejpam-6969	36	7	,	,	PUNCT
ejpam-6969	36	8	a	a	DET
ejpam-6969	36	9	numerical	numerical	ADJ
ejpam-6969	36	10	method	method	NOUN
ejpam-6969	36	11	using	use	VERB
ejpam-6969	36	12	radial	radial	ADJ
ejpam-6969	36	13	basis	basis	NOUN
ejpam-6969	36	14	functions	function	NOUN
ejpam-6969	36	15	(	(	PUNCT
ejpam-6969	36	16	rbfs	rbfs	NOUN
ejpam-6969	36	17	)	)	PUNCT
ejpam-6969	36	18	was	be	AUX
ejpam-6969	36	19	developed	develop	VERB
ejpam-6969	36	20	to	to	PART
ejpam-6969	36	21	solve	solve	VERB
ejpam-6969	36	22	nonlinear	nonlinear	ADJ
ejpam-6969	36	23	two	two	NUM
ejpam-6969	36	24	-	-	PUNCT
ejpam-6969	36	25	dimensional	dimensional	ADJ
ejpam-6969	36	26	volterra	volterra	NOUN
ejpam-6969	36	27	integral	integral	ADJ
ejpam-6969	36	28	equations	equation	NOUN
ejpam-6969	36	29	of	of	ADP
ejpam-6969	36	30	the	the	DET
ejpam-6969	36	31	second	second	ADJ
ejpam-6969	36	32	kind	kind	NOUN
ejpam-6969	36	33	on	on	ADP
ejpam-6969	36	34	non	non	ADJ
ejpam-6969	36	35	-	-	ADJ
ejpam-6969	36	36	rectangular	rectangular	ADJ
ejpam-6969	36	37	domains	domain	NOUN
ejpam-6969	36	38	.	.	PUNCT
ejpam-6969	37	1	the	the	DET
ejpam-6969	37	2	method	method	NOUN
ejpam-6969	37	3	exhibits	exhibit	VERB
ejpam-6969	37	4	strong	strong	ADJ
ejpam-6969	37	5	flexibility	flexibility	NOUN
ejpam-6969	37	6	in	in	ADP
ejpam-6969	37	7	dealing	deal	VERB
ejpam-6969	37	8	with	with	ADP
ejpam-6969	37	9	complex	complex	ADJ
ejpam-6969	37	10	geometries	geometry	NOUN
ejpam-6969	37	11	while	while	SCONJ
ejpam-6969	37	12	preserving	preserve	VERB
ejpam-6969	37	13	computational	computational	ADJ
ejpam-6969	37	14	accuracy	accuracy	NOUN
ejpam-6969	37	15	.	.	PUNCT
ejpam-6969	38	1	however	however	ADV
ejpam-6969	38	2	,	,	PUNCT
ejpam-6969	38	3	the	the	DET
ejpam-6969	38	4	field	field	NOUN
ejpam-6969	38	5	of	of	ADP
ejpam-6969	38	6	integral	integral	ADJ
ejpam-6969	38	7	equations	equation	NOUN
ejpam-6969	38	8	is	be	AUX
ejpam-6969	38	9	closely	closely	ADV
ejpam-6969	38	10	related	relate	VERB
ejpam-6969	38	11	to	to	ADP
ejpam-6969	38	12	the	the	DET
ejpam-6969	38	13	solution	solution	NOUN
ejpam-6969	38	14	of	of	ADP
ejpam-6969	38	15	a	a	DET
ejpam-6969	38	16	wide	wide	ADJ
ejpam-6969	38	17	class	class	NOUN
ejpam-6969	38	18	of	of	ADP
ejpam-6969	38	19	differential	differential	NOUN
ejpam-6969	38	20	models	model	NOUN
ejpam-6969	38	21	,	,	PUNCT
ejpam-6969	38	22	including	include	VERB
ejpam-6969	38	23	fractional	fractional	ADJ
ejpam-6969	38	24	ones	one	NOUN
ejpam-6969	38	25	,	,	PUNCT
ejpam-6969	38	26	as	as	SCONJ
ejpam-6969	38	27	they	they	PRON
ejpam-6969	38	28	share	share	VERB
ejpam-6969	38	29	both	both	DET
ejpam-6969	38	30	challenges	challenge	NOUN
ejpam-6969	38	31	and	and	CCONJ
ejpam-6969	38	32	advanced	advanced	ADJ
ejpam-6969	38	33	numerical	numerical	ADJ
ejpam-6969	38	34	techniques	technique	NOUN
ejpam-6969	38	35	.	.	PUNCT
ejpam-6969	39	1	several	several	ADJ
ejpam-6969	39	2	numerical	numerical	ADJ
ejpam-6969	39	3	[	[	X
ejpam-6969	39	4	17	17	NUM
ejpam-6969	39	5	]	]	PUNCT
ejpam-6969	39	6	,	,	PUNCT
ejpam-6969	39	7	analytical	analytical	ADJ
ejpam-6969	39	8	[	[	X
ejpam-6969	39	9	18	18	NUM
ejpam-6969	39	10	]	]	PUNCT
ejpam-6969	39	11	,	,	PUNCT
ejpam-6969	39	12	and	and	CCONJ
ejpam-6969	39	13	semi	semi	ADJ
ejpam-6969	39	14	-	-	ADJ
ejpam-6969	39	15	analytical	analytical	ADJ
ejpam-6969	39	16	techniques	technique	NOUN
ejpam-6969	39	17	have	have	AUX
ejpam-6969	39	18	been	be	AUX
ejpam-6969	39	19	developed	develop	VERB
ejpam-6969	39	20	for	for	ADP
ejpam-6969	39	21	solving	solve	VERB
ejpam-6969	39	22	differential	differential	ADJ
ejpam-6969	39	23	equations	equation	NOUN
ejpam-6969	39	24	,	,	PUNCT
ejpam-6969	39	25	particularly	particularly	ADV
ejpam-6969	39	26	focusing	focus	VERB
ejpam-6969	39	27	on	on	ADP
ejpam-6969	39	28	accurate	accurate	ADJ
ejpam-6969	39	29	differentiation	differentiation	NOUN
ejpam-6969	39	30	[	[	X
ejpam-6969	39	31	19–21	19–21	NUM
ejpam-6969	39	32	]	]	PUNCT
ejpam-6969	39	33	.	.	PUNCT
ejpam-6969	40	1	these	these	DET
ejpam-6969	40	2	studies	study	NOUN
ejpam-6969	40	3	provide	provide	VERB
ejpam-6969	40	4	a	a	DET
ejpam-6969	40	5	foundational	foundational	ADJ
ejpam-6969	40	6	background	background	NOUN
ejpam-6969	40	7	for	for	ADP
ejpam-6969	40	8	extending	extend	VERB
ejpam-6969	40	9	such	such	ADJ
ejpam-6969	40	10	methods	method	NOUN
ejpam-6969	40	11	to	to	ADP
ejpam-6969	40	12	more	more	ADV
ejpam-6969	40	13	complex	complex	ADJ
ejpam-6969	40	14	problems	problem	NOUN
ejpam-6969	40	15	,	,	PUNCT
ejpam-6969	40	16	including	include	VERB
ejpam-6969	40	17	volterra	volterra	PROPN
ejpam-6969	40	18	integral	integral	ADJ
ejpam-6969	40	19	equations	equation	NOUN
ejpam-6969	40	20	.	.	PUNCT
ejpam-6969	41	1	in	in	ADP
ejpam-6969	41	2	this	this	DET
ejpam-6969	41	3	work	work	NOUN
ejpam-6969	41	4	,	,	PUNCT
ejpam-6969	41	5	we	we	PRON
ejpam-6969	41	6	propose	propose	VERB
ejpam-6969	41	7	two	two	NUM
ejpam-6969	41	8	numerical	numerical	ADJ
ejpam-6969	41	9	methods	method	NOUN
ejpam-6969	41	10	for	for	ADP
ejpam-6969	41	11	solving	solve	VERB
ejpam-6969	41	12	a	a	DET
ejpam-6969	41	13	nonlinear	nonlinear	ADJ
ejpam-6969	41	14	two	two	NUM
ejpam-6969	41	15	-	-	PUNCT
ejpam-6969	41	16	dimensional	dimensional	ADJ
ejpam-6969	41	17	volterra	volterra	NOUN
ejpam-6969	41	18	integral	integral	ADJ
ejpam-6969	41	19	equation	equation	NOUN
ejpam-6969	41	20	.	.	PUNCT
ejpam-6969	42	1	the	the	DET
ejpam-6969	42	2	first	first	ADJ
ejpam-6969	42	3	method	method	NOUN
ejpam-6969	42	4	,	,	PUNCT
ejpam-6969	42	5	bernoulli	bernoulli	NOUN
ejpam-6969	42	6	collocation	collocation	NOUN
ejpam-6969	42	7	,	,	PUNCT
ejpam-6969	42	8	is	be	AUX
ejpam-6969	42	9	based	base	VERB
ejpam-6969	42	10	on	on	ADP
ejpam-6969	42	11	approximating	approximate	VERB
ejpam-6969	42	12	the	the	DET
ejpam-6969	42	13	unknown	unknown	ADJ
ejpam-6969	42	14	function	function	NOUN
ejpam-6969	42	15	using	use	VERB
ejpam-6969	42	16	bernoulli	bernoulli	NOUN
ejpam-6969	42	17	polynomials	polynomial	NOUN
ejpam-6969	42	18	,	,	PUNCT
ejpam-6969	42	19	while	while	SCONJ
ejpam-6969	42	20	applying	apply	VERB
ejpam-6969	42	21	the	the	DET
ejpam-6969	42	22	collocation	collocation	NOUN
ejpam-6969	42	23	technique	technique	NOUN
ejpam-6969	42	24	at	at	ADP
ejpam-6969	42	25	shifted	shift	VERB
ejpam-6969	42	26	chebyshev	chebyshev	PROPN
ejpam-6969	42	27	points	point	NOUN
ejpam-6969	42	28	over	over	ADP
ejpam-6969	42	29	the	the	DET
ejpam-6969	42	30	interval	interval	NOUN
ejpam-6969	42	31	[	[	X
ejpam-6969	42	32	0,1	0,1	NUM
ejpam-6969	42	33	]	]	PUNCT
ejpam-6969	42	34	.	.	PUNCT
ejpam-6969	43	1	the	the	DET
ejpam-6969	43	2	integral	integral	ADJ
ejpam-6969	43	3	equation	equation	NOUN
ejpam-6969	43	4	is	be	AUX
ejpam-6969	43	5	then	then	ADV
ejpam-6969	43	6	transformed	transform	VERB
ejpam-6969	43	7	into	into	ADP
ejpam-6969	43	8	a	a	DET
ejpam-6969	43	9	system	system	NOUN
ejpam-6969	43	10	of	of	ADP
ejpam-6969	43	11	nonlinear	nonlinear	ADJ
ejpam-6969	43	12	algebraic	algebraic	ADJ
ejpam-6969	43	13	equations	equation	NOUN
ejpam-6969	43	14	.	.	PUNCT
ejpam-6969	44	1	the	the	DET
ejpam-6969	44	2	second	second	ADJ
ejpam-6969	44	3	method	method	NOUN
ejpam-6969	44	4	,	,	PUNCT
ejpam-6969	44	5	hermite	hermite	PROPN
ejpam-6969	44	6	-	-	PUNCT
ejpam-6969	44	7	galerkin	galerkin	ADJ
ejpam-6969	44	8	,	,	PUNCT
ejpam-6969	44	9	relies	rely	VERB
ejpam-6969	44	10	on	on	ADP
ejpam-6969	44	11	approximating	approximate	VERB
ejpam-6969	44	12	the	the	DET
ejpam-6969	44	13	solution	solution	NOUN
ejpam-6969	44	14	using	use	VERB
ejpam-6969	44	15	hermite	hermite	ADJ
ejpam-6969	44	16	functions	function	NOUN
ejpam-6969	44	17	and	and	CCONJ
ejpam-6969	44	18	applying	apply	VERB
ejpam-6969	44	19	the	the	DET
ejpam-6969	44	20	galerkin	galerkin	ADJ
ejpam-6969	44	21	projection	projection	NOUN
ejpam-6969	44	22	,	,	PUNCT
ejpam-6969	44	23	which	which	PRON
ejpam-6969	44	24	also	also	ADV
ejpam-6969	44	25	reduces	reduce	VERB
ejpam-6969	44	26	the	the	DET
ejpam-6969	44	27	integral	integral	ADJ
ejpam-6969	44	28	equation	equation	NOUN
ejpam-6969	44	29	to	to	ADP
ejpam-6969	44	30	a	a	DET
ejpam-6969	44	31	system	system	NOUN
ejpam-6969	44	32	of	of	ADP
ejpam-6969	44	33	nonlinear	nonlinear	ADJ
ejpam-6969	44	34	algebraic	algebraic	ADJ
ejpam-6969	44	35	equations	equation	NOUN
ejpam-6969	44	36	.	.	PUNCT
ejpam-6969	45	1	the	the	DET
ejpam-6969	45	2	outline	outline	NOUN
ejpam-6969	45	3	of	of	ADP
ejpam-6969	45	4	this	this	DET
ejpam-6969	45	5	paper	paper	NOUN
ejpam-6969	45	6	is	be	AUX
ejpam-6969	45	7	as	as	SCONJ
ejpam-6969	45	8	follows	follow	VERB
ejpam-6969	45	9	:	:	PUNCT
ejpam-6969	45	10	in	in	ADP
ejpam-6969	45	11	section	section	NOUN
ejpam-6969	45	12	2	2	NUM
ejpam-6969	45	13	,	,	PUNCT
ejpam-6969	45	14	we	we	PRON
ejpam-6969	45	15	review	review	VERB
ejpam-6969	45	16	some	some	DET
ejpam-6969	45	17	fundamental	fundamental	ADJ
ejpam-6969	45	18	formulations	formulation	NOUN
ejpam-6969	45	19	and	and	CCONJ
ejpam-6969	45	20	properties	property	NOUN
ejpam-6969	45	21	of	of	ADP
ejpam-6969	45	22	bernoulli	bernoulli	PROPN
ejpam-6969	45	23	and	and	CCONJ
ejpam-6969	45	24	hermite	hermite	ADJ
ejpam-6969	45	25	polynomials	polynomial	NOUN
ejpam-6969	45	26	.	.	PUNCT
ejpam-6969	46	1	section	section	NOUN
ejpam-6969	46	2	3	3	NUM
ejpam-6969	46	3	is	be	AUX
ejpam-6969	46	4	devoted	devoted	ADJ
ejpam-6969	46	5	m.	m.	PROPN
ejpam-6969	46	6	h.	h.	PROPN
ejpam-6969	46	7	ahmed	ahmed	PROPN
ejpam-6969	46	8	,	,	PUNCT
ejpam-6969	46	9	a.	a.	NOUN
ejpam-6969	46	10	m.	m.	PROPN
ejpam-6969	46	11	aljabri	aljabri	PROPN
ejpam-6969	46	12	/	/	SYM
ejpam-6969	46	13	eur	eur	PROPN
ejpam-6969	46	14	.	.	PUNCT
ejpam-6969	47	1	j.	j.	PROPN
ejpam-6969	47	2	pure	pure	PROPN
ejpam-6969	47	3	appl	appl	PROPN
ejpam-6969	47	4	.	.	PROPN
ejpam-6969	47	5	math	math	PROPN
ejpam-6969	47	6	,	,	PUNCT
ejpam-6969	47	7	18	18	NUM
ejpam-6969	47	8	(	(	PUNCT
ejpam-6969	47	9	4	4	NUM
ejpam-6969	47	10	)	)	PUNCT
ejpam-6969	47	11	(	(	PUNCT
ejpam-6969	47	12	2025	2025	NUM
ejpam-6969	47	13	)	)	PUNCT
ejpam-6969	47	14	,	,	PUNCT
ejpam-6969	47	15	6969	6969	NUM
ejpam-6969	47	16	3	3	NUM
ejpam-6969	47	17	of	of	ADP
ejpam-6969	47	18	16	16	NUM
ejpam-6969	47	19	to	to	ADP
ejpam-6969	47	20	the	the	DET
ejpam-6969	47	21	existence	existence	NOUN
ejpam-6969	47	22	and	and	CCONJ
ejpam-6969	47	23	uniqueness	uniqueness	NOUN
ejpam-6969	47	24	of	of	ADP
ejpam-6969	47	25	the	the	DET
ejpam-6969	47	26	solution	solution	NOUN
ejpam-6969	47	27	of	of	ADP
ejpam-6969	47	28	the	the	DET
ejpam-6969	47	29	integral	integral	ADJ
ejpam-6969	47	30	equation	equation	NOUN
ejpam-6969	47	31	.	.	PUNCT
ejpam-6969	48	1	in	in	ADP
ejpam-6969	48	2	section	section	NOUN
ejpam-6969	48	3	4	4	NUM
ejpam-6969	48	4	,	,	PUNCT
ejpam-6969	48	5	we	we	PRON
ejpam-6969	48	6	present	present	VERB
ejpam-6969	48	7	computational	computational	ADJ
ejpam-6969	48	8	methods	method	NOUN
ejpam-6969	48	9	for	for	ADP
ejpam-6969	48	10	solving	solve	VERB
ejpam-6969	48	11	the	the	DET
ejpam-6969	48	12	two	two	NUM
ejpam-6969	48	13	-	-	PUNCT
ejpam-6969	48	14	dimensional	dimensional	ADJ
ejpam-6969	48	15	volterra	volterra	NOUN
ejpam-6969	48	16	integral	integral	ADJ
ejpam-6969	48	17	equation	equation	NOUN
ejpam-6969	48	18	(	(	PUNCT
ejpam-6969	48	19	1	1	X
ejpam-6969	48	20	)	)	PUNCT
ejpam-6969	48	21	using	use	VERB
ejpam-6969	48	22	both	both	PRON
ejpam-6969	48	23	bernoulli	bernoulli	NOUN
ejpam-6969	48	24	collocation	collocation	NOUN
ejpam-6969	48	25	method	method	NOUN
ejpam-6969	48	26	and	and	CCONJ
ejpam-6969	48	27	hermite	hermite	ADJ
ejpam-6969	48	28	-	-	PUNCT
ejpam-6969	48	29	galerkin	galerkin	ADJ
ejpam-6969	48	30	method	method	NOUN
ejpam-6969	48	31	.	.	PUNCT
ejpam-6969	49	1	comparison	comparison	NOUN
ejpam-6969	49	2	of	of	ADP
ejpam-6969	49	3	results	result	NOUN
ejpam-6969	49	4	are	be	AUX
ejpam-6969	49	5	found	find	VERB
ejpam-6969	49	6	in	in	ADP
ejpam-6969	49	7	some	some	DET
ejpam-6969	49	8	numerical	numerical	ADJ
ejpam-6969	49	9	examples	example	NOUN
ejpam-6969	49	10	which	which	PRON
ejpam-6969	49	11	provided	provide	VERB
ejpam-6969	49	12	in	in	ADP
ejpam-6969	49	13	section	section	NOUN
ejpam-6969	49	14	5	5	NUM
ejpam-6969	49	15	.	.	PUNCT
ejpam-6969	50	1	the	the	DET
ejpam-6969	50	2	results	result	NOUN
ejpam-6969	50	3	are	be	AUX
ejpam-6969	50	4	discussed	discuss	VERB
ejpam-6969	50	5	in	in	ADP
ejpam-6969	50	6	section	section	NOUN
ejpam-6969	50	7	6	6	NUM
ejpam-6969	50	8	.	.	PUNCT
ejpam-6969	51	1	finally	finally	ADV
ejpam-6969	51	2	,	,	PUNCT
ejpam-6969	51	3	the	the	DET
ejpam-6969	51	4	paper	paper	NOUN
ejpam-6969	51	5	is	be	AUX
ejpam-6969	51	6	concluded	conclude	VERB
ejpam-6969	51	7	in	in	ADP
ejpam-6969	51	8	section	section	NOUN
ejpam-6969	51	9	7	7	NUM
ejpam-6969	51	10	.	.	PUNCT
ejpam-6969	52	1	these	these	DET
ejpam-6969	52	2	previously	previously	ADV
ejpam-6969	52	3	proposed	propose	VERB
ejpam-6969	52	4	methods	method	NOUN
ejpam-6969	52	5	provide	provide	VERB
ejpam-6969	52	6	a	a	DET
ejpam-6969	52	7	foundation	foundation	NOUN
ejpam-6969	52	8	and	and	CCONJ
ejpam-6969	52	9	motivation	motivation	NOUN
ejpam-6969	52	10	for	for	ADP
ejpam-6969	52	11	the	the	DET
ejpam-6969	52	12	present	present	ADJ
ejpam-6969	52	13	study	study	NOUN
ejpam-6969	52	14	,	,	PUNCT
ejpam-6969	52	15	which	which	PRON
ejpam-6969	52	16	focuses	focus	VERB
ejpam-6969	52	17	on	on	ADP
ejpam-6969	52	18	bernoulli	bernoulli	NOUN
ejpam-6969	52	19	collocation	collocation	NOUN
ejpam-6969	52	20	and	and	CCONJ
ejpam-6969	52	21	hermite	hermite	ADJ
ejpam-6969	52	22	–	–	PUNCT
ejpam-6969	52	23	galerkin	galerkin	ADJ
ejpam-6969	52	24	approaches	approach	NOUN
ejpam-6969	52	25	as	as	ADP
ejpam-6969	52	26	efficient	efficient	ADJ
ejpam-6969	52	27	alternatives	alternative	NOUN
ejpam-6969	52	28	for	for	ADP
ejpam-6969	52	29	solving	solve	VERB
ejpam-6969	52	30	two	two	NUM
ejpam-6969	52	31	-	-	PUNCT
ejpam-6969	52	32	dimensional	dimensional	ADJ
ejpam-6969	52	33	nonlinear	nonlinear	ADJ
ejpam-6969	52	34	volterra	volterra	NOUN
ejpam-6969	52	35	integral	integral	ADJ
ejpam-6969	52	36	equations	equation	NOUN
ejpam-6969	52	37	.	.	PUNCT
ejpam-6969	53	1	2	2	X
ejpam-6969	53	2	.	.	X
ejpam-6969	53	3	some	some	DET
ejpam-6969	53	4	definitions	definition	NOUN
ejpam-6969	53	5	and	and	CCONJ
ejpam-6969	53	6	properties	property	NOUN
ejpam-6969	53	7	2.1	2.1	NUM
ejpam-6969	53	8	.	.	PUNCT
ejpam-6969	54	1	bernoulli	bernoulli	PROPN
ejpam-6969	54	2	polynomials	polynomial	VERB
ejpam-6969	54	3	bernoulli	bernoulli	NOUN
ejpam-6969	54	4	polynomials	polynomial	NOUN
ejpam-6969	54	5	were	be	AUX
ejpam-6969	54	6	introduced	introduce	VERB
ejpam-6969	54	7	by	by	ADP
ejpam-6969	54	8	jacob	jacob	PROPN
ejpam-6969	54	9	bernoulli	bernoulli	PROPN
ejpam-6969	54	10	and	and	CCONJ
ejpam-6969	54	11	later	later	ADV
ejpam-6969	54	12	generalized	generalize	VERB
ejpam-6969	54	13	by	by	ADP
ejpam-6969	54	14	euler	euler	NOUN
ejpam-6969	54	15	to	to	ADP
ejpam-6969	54	16	arbitrary	arbitrary	ADJ
ejpam-6969	54	17	values	value	NOUN
ejpam-6969	54	18	of	of	ADP
ejpam-6969	54	19	the	the	DET
ejpam-6969	54	20	variable	variable	NOUN
ejpam-6969	55	1	[	[	X
ejpam-6969	55	2	22–24	22–24	NUM
ejpam-6969	55	3	]	]	PUNCT
ejpam-6969	55	4	.	.	PUNCT
ejpam-6969	56	1	the	the	DET
ejpam-6969	56	2	generating	generate	VERB
ejpam-6969	56	3	function	function	NOUN
ejpam-6969	56	4	of	of	ADP
ejpam-6969	56	5	bernoulli	bernoulli	PROPN
ejpam-6969	56	6	polynomials	polynomial	NOUN
ejpam-6969	56	7	bn	bn	INTJ
ejpam-6969	56	8	(	(	PUNCT
ejpam-6969	56	9	χ	χ	X
ejpam-6969	56	10	)	)	PUNCT
ejpam-6969	56	11	is	be	AUX
ejpam-6969	56	12	given	give	VERB
ejpam-6969	56	13	by	by	ADP
ejpam-6969	56	14	z1e	z1e	NOUN
ejpam-6969	56	15	χz1	χz1	NOUN
ejpam-6969	56	16	ez1	ez1	NOUN
ejpam-6969	56	17	−	−	NOUN
ejpam-6969	56	18	1	1	NUM
ejpam-6969	56	19	=	=	PUNCT
ejpam-6969	56	20	∞∑	∞∑	PRON
ejpam-6969	56	21	n=0	n=0	NUM
ejpam-6969	56	22	bn	bn	NOUN
ejpam-6969	56	23	(	(	PUNCT
ejpam-6969	56	24	χ	χ	NOUN
ejpam-6969	56	25	)	)	PUNCT
ejpam-6969	56	26	zn1	zn1	NOUN
ejpam-6969	56	27	n	n	NOUN
ejpam-6969	56	28	!	!	PUNCT
ejpam-6969	56	29	,	,	PUNCT
ejpam-6969	56	30	|z1|	|z1|	NOUN
ejpam-6969	56	31	<	<	X
ejpam-6969	56	32	2π	2π	NOUN
ejpam-6969	56	33	,	,	PUNCT
ejpam-6969	56	34	(	(	PUNCT
ejpam-6969	56	35	2	2	X
ejpam-6969	56	36	)	)	PUNCT
ejpam-6969	56	37	the	the	DET
ejpam-6969	56	38	bernoulli	bernoulli	PROPN
ejpam-6969	56	39	numbers	number	NOUN
ejpam-6969	56	40	bn	bn	INTJ
ejpam-6969	56	41	:	:	PUNCT
ejpam-6969	56	42	=	=	SYM
ejpam-6969	56	43	bn	bn	ADJ
ejpam-6969	56	44	(	(	PUNCT
ejpam-6969	56	45	0	0	NUM
ejpam-6969	56	46	)	)	PUNCT
ejpam-6969	56	47	are	be	AUX
ejpam-6969	56	48	defined	define	VERB
ejpam-6969	56	49	via	via	ADP
ejpam-6969	56	50	the	the	DET
ejpam-6969	56	51	generating	generate	VERB
ejpam-6969	56	52	function	function	NOUN
ejpam-6969	56	53	z1	z1	NOUN
ejpam-6969	56	54	ez1	ez1	NOUN
ejpam-6969	56	55	−	−	NOUN
ejpam-6969	56	56	1	1	NUM
ejpam-6969	56	57	=	=	NOUN
ejpam-6969	56	58	∞∑	∞∑	NUM
ejpam-6969	56	59	n=0	n=0	NUM
ejpam-6969	56	60	bn	bn	ADP
ejpam-6969	56	61	zn1	zn1	NOUN
ejpam-6969	56	62	n	n	NOUN
ejpam-6969	56	63	!	!	PUNCT
ejpam-6969	57	1	,	,	PUNCT
ejpam-6969	57	2	|z1|	|z1|	NOUN
ejpam-6969	57	3	<	<	X
ejpam-6969	57	4	2π	2π	NOUN
ejpam-6969	57	5	.	.	PUNCT
ejpam-6969	58	1	(	(	PUNCT
ejpam-6969	58	2	3	3	X
ejpam-6969	58	3	)	)	PUNCT
ejpam-6969	58	4	from	from	ADP
ejpam-6969	58	5	this	this	PRON
ejpam-6969	58	6	,	,	PUNCT
ejpam-6969	58	7	the	the	DET
ejpam-6969	58	8	bernoulli	bernoulli	PROPN
ejpam-6969	58	9	polynomials	polynomial	VERB
ejpam-6969	58	10	bn	bn	INTJ
ejpam-6969	58	11	(	(	PUNCT
ejpam-6969	58	12	χ	χ	X
ejpam-6969	58	13	)	)	PUNCT
ejpam-6969	58	14	can	can	AUX
ejpam-6969	58	15	be	be	AUX
ejpam-6969	58	16	expressed	express	VERB
ejpam-6969	58	17	as	as	ADP
ejpam-6969	58	18	bn	bn	ADJ
ejpam-6969	58	19	(	(	PUNCT
ejpam-6969	58	20	χ	χ	NOUN
ejpam-6969	58	21	)	)	PUNCT
ejpam-6969	58	22	=	=	SYM
ejpam-6969	58	23	n∑	n∑	NOUN
ejpam-6969	58	24	k=0	k=0	PROPN
ejpam-6969	58	25	(	(	PUNCT
ejpam-6969	58	26	n	n	X
ejpam-6969	58	27	k	k	PROPN
ejpam-6969	58	28	)	)	PUNCT
ejpam-6969	58	29	bkχ	bkχ	PROPN
ejpam-6969	58	30	n−k	n−k	PROPN
ejpam-6969	58	31	.	.	PUNCT
ejpam-6969	59	1	(	(	PUNCT
ejpam-6969	59	2	4	4	X
ejpam-6969	59	3	)	)	PUNCT
ejpam-6969	59	4	they	they	PRON
ejpam-6969	59	5	satisfy	satisfy	VERB
ejpam-6969	59	6	the	the	DET
ejpam-6969	59	7	identity	identity	NOUN
ejpam-6969	59	8	bn	bn	NOUN
ejpam-6969	59	9	(	(	PUNCT
ejpam-6969	59	10	χ+	χ+	PROPN
ejpam-6969	59	11	1)−bn	1)−bn	NUM
ejpam-6969	59	12	(	(	PUNCT
ejpam-6969	59	13	χ	χ	NOUN
ejpam-6969	59	14	)	)	PUNCT
ejpam-6969	60	1	=	=	SYM
ejpam-6969	60	2	nχn−1	nχn−1	PROPN
ejpam-6969	60	3	,	,	PUNCT
ejpam-6969	60	4	n	n	PROPN
ejpam-6969	60	5	∈	∈	PROPN
ejpam-6969	60	6	n0	n0	PROPN
ejpam-6969	60	7	,	,	PUNCT
ejpam-6969	60	8	(	(	PUNCT
ejpam-6969	60	9	5	5	NUM
ejpam-6969	60	10	)	)	PUNCT
ejpam-6969	60	11	which	which	PRON
ejpam-6969	60	12	implies	imply	VERB
ejpam-6969	60	13	that	that	SCONJ
ejpam-6969	61	1	bn	bn	INTJ
ejpam-6969	61	2	(	(	PUNCT
ejpam-6969	61	3	0	0	NUM
ejpam-6969	61	4	)	)	PUNCT
ejpam-6969	61	5	=	=	SYM
ejpam-6969	61	6	bn	bn	X
ejpam-6969	61	7	(	(	PUNCT
ejpam-6969	61	8	1	1	NUM
ejpam-6969	61	9	)	)	PUNCT
ejpam-6969	61	10	,	,	PUNCT
ejpam-6969	61	11	n	n	PROPN
ejpam-6969	61	12	∈	∈	PROPN
ejpam-6969	61	13	n	n	CCONJ
ejpam-6969	61	14	\	\	NOUN
ejpam-6969	61	15	{	{	PUNCT
ejpam-6969	61	16	1	1	NUM
ejpam-6969	61	17	}	}	PUNCT
ejpam-6969	61	18	.	.	PUNCT
ejpam-6969	62	1	(	(	PUNCT
ejpam-6969	62	2	6	6	X
ejpam-6969	62	3	)	)	PUNCT
ejpam-6969	62	4	substituting	substitute	VERB
ejpam-6969	62	5	χ	χ	NOUN
ejpam-6969	62	6	=	=	SYM
ejpam-6969	62	7	1	1	NUM
ejpam-6969	62	8	into	into	ADP
ejpam-6969	62	9	(	(	PUNCT
ejpam-6969	62	10	4	4	NUM
ejpam-6969	62	11	)	)	PUNCT
ejpam-6969	62	12	,	,	PUNCT
ejpam-6969	62	13	and	and	CCONJ
ejpam-6969	62	14	using	use	VERB
ejpam-6969	62	15	(	(	PUNCT
ejpam-6969	62	16	6	6	NUM
ejpam-6969	62	17	)	)	PUNCT
ejpam-6969	62	18	,	,	PUNCT
ejpam-6969	62	19	yields	yield	VERB
ejpam-6969	62	20	bn	bn	NOUN
ejpam-6969	62	21	=	=	SYM
ejpam-6969	62	22	n∑	n∑	PROPN
ejpam-6969	62	23	k=0	k=0	PROPN
ejpam-6969	62	24	(	(	PUNCT
ejpam-6969	62	25	n	n	X
ejpam-6969	62	26	k	k	PROPN
ejpam-6969	62	27	)	)	PUNCT
ejpam-6969	62	28	bk	bk	PROPN
ejpam-6969	62	29	.	.	PUNCT
ejpam-6969	63	1	(	(	PUNCT
ejpam-6969	63	2	7	7	X
ejpam-6969	63	3	)	)	PUNCT
ejpam-6969	63	4	these	these	DET
ejpam-6969	63	5	polynomials	polynomial	NOUN
ejpam-6969	63	6	satisfy	satisfy	VERB
ejpam-6969	63	7	several	several	ADJ
ejpam-6969	63	8	important	important	ADJ
ejpam-6969	63	9	identities	identity	NOUN
ejpam-6969	63	10	,	,	PUNCT
ejpam-6969	63	11	such	such	ADJ
ejpam-6969	63	12	as	as	ADP
ejpam-6969	63	13	b′	b′	NUM
ejpam-6969	63	14	n	n	NOUN
ejpam-6969	63	15	(	(	PUNCT
ejpam-6969	63	16	χ	χ	X
ejpam-6969	63	17	)	)	PUNCT
ejpam-6969	63	18	=	=	SYM
ejpam-6969	63	19	nbn−1(χ	nbn−1(χ	NOUN
ejpam-6969	63	20	)	)	PUNCT
ejpam-6969	63	21	,	,	PUNCT
ejpam-6969	63	22	n	n	PRON
ejpam-6969	63	23	≥	≥	NOUN
ejpam-6969	63	24	1	1	NUM
ejpam-6969	63	25	,	,	PUNCT
ejpam-6969	63	26	m.	m.	NOUN
ejpam-6969	63	27	h.	h.	PROPN
ejpam-6969	63	28	ahmed	ahmed	PROPN
ejpam-6969	63	29	,	,	PUNCT
ejpam-6969	63	30	a.	a.	NOUN
ejpam-6969	63	31	m.	m.	PROPN
ejpam-6969	63	32	aljabri	aljabri	PROPN
ejpam-6969	63	33	/	/	SYM
ejpam-6969	63	34	eur	eur	PROPN
ejpam-6969	63	35	.	.	PUNCT
ejpam-6969	64	1	j.	j.	PROPN
ejpam-6969	64	2	pure	pure	PROPN
ejpam-6969	64	3	appl	appl	PROPN
ejpam-6969	64	4	.	.	PROPN
ejpam-6969	64	5	math	math	PROPN
ejpam-6969	64	6	,	,	PUNCT
ejpam-6969	64	7	18	18	NUM
ejpam-6969	64	8	(	(	PUNCT
ejpam-6969	64	9	4	4	NUM
ejpam-6969	64	10	)	)	PUNCT
ejpam-6969	64	11	(	(	PUNCT
ejpam-6969	64	12	2025	2025	NUM
ejpam-6969	64	13	)	)	PUNCT
ejpam-6969	64	14	,	,	PUNCT
ejpam-6969	64	15	6969	6969	NUM
ejpam-6969	64	16	4	4	NUM
ejpam-6969	64	17	of	of	ADP
ejpam-6969	64	18	16∫	16∫	NUM
ejpam-6969	64	19	1	1	NUM
ejpam-6969	64	20	0	0	NUM
ejpam-6969	64	21	bn	bn	NOUN
ejpam-6969	64	22	(	(	PUNCT
ejpam-6969	64	23	χ	χ	NOUN
ejpam-6969	64	24	)	)	PUNCT
ejpam-6969	64	25	dχ	dχ	NOUN
ejpam-6969	64	26	=	=	SYM
ejpam-6969	64	27	0	0	PROPN
ejpam-6969	64	28	,	,	PUNCT
ejpam-6969	64	29	n	n	PRON
ejpam-6969	64	30	≥	≥	NOUN
ejpam-6969	64	31	1	1	NUM
ejpam-6969	64	32	,	,	PUNCT
ejpam-6969	64	33	bn	bn	ADJ
ejpam-6969	64	34	(	(	PUNCT
ejpam-6969	64	35	χ+	χ+	PROPN
ejpam-6969	64	36	1)−bn	1)−bn	NUM
ejpam-6969	64	37	(	(	PUNCT
ejpam-6969	64	38	χ	χ	NOUN
ejpam-6969	64	39	)	)	PUNCT
ejpam-6969	64	40	=	=	SYM
ejpam-6969	64	41	nχn−1	nχn−1	PROPN
ejpam-6969	64	42	,	,	PUNCT
ejpam-6969	64	43	n	n	PRON
ejpam-6969	64	44	≥	≥	NOUN
ejpam-6969	64	45	1	1	NUM
ejpam-6969	64	46	,	,	PUNCT
ejpam-6969	64	47	and	and	CCONJ
ejpam-6969	64	48	bn	bn	INTJ
ejpam-6969	64	49	(	(	PUNCT
ejpam-6969	64	50	1−	1−	NUM
ejpam-6969	64	51	χ	χ	NOUN
ejpam-6969	64	52	)	)	PUNCT
ejpam-6969	64	53	=	=	SYM
ejpam-6969	64	54	(	(	PUNCT
ejpam-6969	64	55	−1)nbn	−1)nbn	PROPN
ejpam-6969	64	56	(	(	PUNCT
ejpam-6969	64	57	χ	χ	NOUN
ejpam-6969	64	58	)	)	PUNCT
ejpam-6969	64	59	.	.	PUNCT
ejpam-6969	65	1	the	the	DET
ejpam-6969	65	2	first	first	ADJ
ejpam-6969	65	3	five	five	NUM
ejpam-6969	65	4	bernoulli	bernoulli	NOUN
ejpam-6969	65	5	polynomials	polynomial	NOUN
ejpam-6969	65	6	are	be	AUX
ejpam-6969	65	7	b0(χ	b0(χ	NOUN
ejpam-6969	65	8	)	)	PUNCT
ejpam-6969	65	9	=	=	SYM
ejpam-6969	65	10	1	1	NUM
ejpam-6969	65	11	,	,	PUNCT
ejpam-6969	65	12	b1(χ	b1(χ	PROPN
ejpam-6969	65	13	)	)	PUNCT
ejpam-6969	65	14	=	=	NOUN
ejpam-6969	65	15	χ−	χ−	NOUN
ejpam-6969	65	16	1	1	NUM
ejpam-6969	65	17	2	2	NUM
ejpam-6969	65	18	,	,	PUNCT
ejpam-6969	65	19	b2(χ	b2(χ	NOUN
ejpam-6969	65	20	)	)	PUNCT
ejpam-6969	66	1	=	=	SYM
ejpam-6969	66	2	χ2	χ2	PROPN
ejpam-6969	66	3	−	−	PROPN
ejpam-6969	66	4	χ+	χ+	PROPN
ejpam-6969	66	5	1	1	NUM
ejpam-6969	66	6	6	6	NUM
ejpam-6969	66	7	,	,	PUNCT
ejpam-6969	66	8	b3(χ	b3(χ	NOUN
ejpam-6969	66	9	)	)	PUNCT
ejpam-6969	66	10	=	=	PUNCT
ejpam-6969	66	11	χ3	χ3	NOUN
ejpam-6969	66	12	−	−	NOUN
ejpam-6969	66	13	3	3	NUM
ejpam-6969	66	14	2	2	NUM
ejpam-6969	66	15	χ2	χ2	NOUN
ejpam-6969	66	16	+	+	CCONJ
ejpam-6969	66	17	1	1	NUM
ejpam-6969	66	18	2	2	NUM
ejpam-6969	66	19	χ	χ	NOUN
ejpam-6969	66	20	,	,	PUNCT
ejpam-6969	66	21	b4(χ	b4(χ	NOUN
ejpam-6969	66	22	)	)	PUNCT
ejpam-6969	66	23	=	=	SYM
ejpam-6969	66	24	χ4	χ4	NOUN
ejpam-6969	66	25	−	−	PROPN
ejpam-6969	66	26	2χ3	2χ3	NUM
ejpam-6969	67	1	+	+	CCONJ
ejpam-6969	67	2	χ2	χ2	PROPN
ejpam-6969	67	3	−	−	PROPN
ejpam-6969	67	4	1	1	NUM
ejpam-6969	67	5	30	30	NUM
ejpam-6969	67	6	.	.	PUNCT
ejpam-6969	68	1	2.2	2.2	NUM
ejpam-6969	68	2	.	.	PUNCT
ejpam-6969	69	1	hermite	hermite	PROPN
ejpam-6969	69	2	polynomials	polynomial	VERB
ejpam-6969	69	3	hermite	hermite	ADJ
ejpam-6969	69	4	polynomials	polynomial	NOUN
ejpam-6969	69	5	were	be	AUX
ejpam-6969	69	6	first	first	ADV
ejpam-6969	69	7	introduced	introduce	VERB
ejpam-6969	69	8	in	in	ADP
ejpam-6969	69	9	1810	1810	NUM
ejpam-6969	69	10	by	by	ADP
ejpam-6969	69	11	pierre	pierre	PROPN
ejpam-6969	69	12	-	-	PUNCT
ejpam-6969	69	13	simon	simon	PROPN
ejpam-6969	69	14	laplace	laplace	PROPN
ejpam-6969	69	15	.	.	PUNCT
ejpam-6969	70	1	however	however	ADV
ejpam-6969	70	2	,	,	PUNCT
ejpam-6969	70	3	it	it	PRON
ejpam-6969	70	4	was	be	AUX
ejpam-6969	70	5	charles	charles	PROPN
ejpam-6969	70	6	hermite	hermite	PROPN
ejpam-6969	70	7	who	who	PRON
ejpam-6969	70	8	later	later	ADV
ejpam-6969	70	9	defined	define	VERB
ejpam-6969	70	10	a	a	DET
ejpam-6969	70	11	more	more	ADV
ejpam-6969	70	12	generalized	generalized	ADJ
ejpam-6969	70	13	class	class	NOUN
ejpam-6969	70	14	of	of	ADP
ejpam-6969	70	15	hermite	hermite	ADJ
ejpam-6969	70	16	polynomials	polynomial	NOUN
ejpam-6969	70	17	,	,	PUNCT
ejpam-6969	70	18	which	which	PRON
ejpam-6969	70	19	remain	remain	VERB
ejpam-6969	70	20	less	less	ADV
ejpam-6969	70	21	known	know	VERB
ejpam-6969	70	22	compared	compare	VERB
ejpam-6969	70	23	to	to	ADP
ejpam-6969	70	24	the	the	DET
ejpam-6969	70	25	standard	standard	ADJ
ejpam-6969	70	26	form	form	NOUN
ejpam-6969	70	27	,	,	PUNCT
ejpam-6969	70	28	despite	despite	SCONJ
ejpam-6969	70	29	their	their	PRON
ejpam-6969	70	30	significance	significance	NOUN
ejpam-6969	70	31	.	.	PUNCT
ejpam-6969	71	1	these	these	DET
ejpam-6969	71	2	polynomials	polynomial	NOUN
ejpam-6969	71	3	have	have	AUX
ejpam-6969	71	4	emerged	emerge	VERB
ejpam-6969	71	5	as	as	ADP
ejpam-6969	71	6	a	a	DET
ejpam-6969	71	7	fundamental	fundamental	ADJ
ejpam-6969	71	8	tool	tool	NOUN
ejpam-6969	71	9	in	in	ADP
ejpam-6969	71	10	both	both	CCONJ
ejpam-6969	71	11	pure	pure	ADJ
ejpam-6969	71	12	and	and	CCONJ
ejpam-6969	71	13	applied	applied	ADJ
ejpam-6969	71	14	mathematics	mathematic	NOUN
ejpam-6969	71	15	.	.	PUNCT
ejpam-6969	72	1	their	their	PRON
ejpam-6969	72	2	relevance	relevance	NOUN
ejpam-6969	72	3	has	have	AUX
ejpam-6969	72	4	recently	recently	ADV
ejpam-6969	72	5	increased	increase	VERB
ejpam-6969	72	6	due	due	ADP
ejpam-6969	72	7	to	to	ADP
ejpam-6969	72	8	their	their	PRON
ejpam-6969	72	9	applications	application	NOUN
ejpam-6969	72	10	in	in	ADP
ejpam-6969	72	11	quantum	quantum	ADJ
ejpam-6969	72	12	mechanics	mechanic	NOUN
ejpam-6969	72	13	,	,	PUNCT
ejpam-6969	72	14	engineering	engineering	NOUN
ejpam-6969	72	15	,	,	PUNCT
ejpam-6969	72	16	physics	physics	NOUN
ejpam-6969	72	17	,	,	PUNCT
ejpam-6969	72	18	and	and	CCONJ
ejpam-6969	72	19	other	other	ADJ
ejpam-6969	72	20	scientific	scientific	ADJ
ejpam-6969	72	21	fields	field	NOUN
ejpam-6969	72	22	.	.	PUNCT
ejpam-6969	73	1	hermite	hermite	ADJ
ejpam-6969	73	2	polynomials	polynomial	NOUN
ejpam-6969	73	3	form	form	VERB
ejpam-6969	73	4	a	a	DET
ejpam-6969	73	5	set	set	NOUN
ejpam-6969	73	6	of	of	ADP
ejpam-6969	73	7	mutually	mutually	ADV
ejpam-6969	73	8	orthogonal	orthogonal	ADJ
ejpam-6969	73	9	functions	function	NOUN
ejpam-6969	73	10	with	with	ADP
ejpam-6969	73	11	respect	respect	NOUN
ejpam-6969	73	12	to	to	ADP
ejpam-6969	73	13	the	the	DET
ejpam-6969	73	14	weight	weight	NOUN
ejpam-6969	73	15	function	function	NOUN
ejpam-6969	73	16	e−χ2	e−χ2	VERB
ejpam-6969	73	17	over	over	ADP
ejpam-6969	73	18	the	the	DET
ejpam-6969	73	19	interval	interval	NOUN
ejpam-6969	73	20	(	(	PUNCT
ejpam-6969	73	21	−∞,∞	−∞,∞	VERB
ejpam-6969	73	22	)	)	PUNCT
ejpam-6969	74	1	[	[	X
ejpam-6969	74	2	23	23	NUM
ejpam-6969	74	3	,	,	PUNCT
ejpam-6969	74	4	25	25	NUM
ejpam-6969	74	5	,	,	PUNCT
ejpam-6969	74	6	26	26	NUM
ejpam-6969	74	7	]	]	PUNCT
ejpam-6969	74	8	.	.	PUNCT
ejpam-6969	75	1	they	they	PRON
ejpam-6969	75	2	can	can	AUX
ejpam-6969	75	3	be	be	AUX
ejpam-6969	75	4	generated	generate	VERB
ejpam-6969	75	5	using	use	VERB
ejpam-6969	75	6	the	the	DET
ejpam-6969	75	7	rodrigues	rodrigues	PROPN
ejpam-6969	75	8	formula	formula	NOUN
ejpam-6969	75	9	:	:	PUNCT
ejpam-6969	75	10	hn(χ	hn(χ	X
ejpam-6969	75	11	)	)	PUNCT
ejpam-6969	76	1	=	=	SYM
ejpam-6969	76	2	(	(	PUNCT
ejpam-6969	76	3	−1)neχ2	−1)neχ2	NUM
ejpam-6969	76	4	dn	dn	NOUN
ejpam-6969	76	5	dχn	dχn	PROPN
ejpam-6969	76	6	(	(	PUNCT
ejpam-6969	76	7	e−χ2	e−χ2	PROPN
ejpam-6969	76	8	)	)	PUNCT
ejpam-6969	76	9	,	,	PUNCT
ejpam-6969	76	10	n	n	NOUN
ejpam-6969	76	11	=	=	SYM
ejpam-6969	76	12	0	0	NUM
ejpam-6969	76	13	,	,	PUNCT
ejpam-6969	76	14	1	1	NUM
ejpam-6969	76	15	,	,	PUNCT
ejpam-6969	76	16	2	2	NUM
ejpam-6969	76	17	,	,	PUNCT
ejpam-6969	76	18	.	.	PUNCT
ejpam-6969	76	19	.	.	PUNCT
ejpam-6969	76	20	.	.	PUNCT
ejpam-6969	77	1	the	the	DET
ejpam-6969	77	2	first	first	ADJ
ejpam-6969	77	3	few	few	ADJ
ejpam-6969	77	4	hermite	hermite	ADJ
ejpam-6969	77	5	polynomials	polynomial	NOUN
ejpam-6969	77	6	are	be	AUX
ejpam-6969	77	7	given	give	VERB
ejpam-6969	77	8	by	by	ADP
ejpam-6969	77	9	h0(χ	h0(χ	NOUN
ejpam-6969	77	10	)	)	PUNCT
ejpam-6969	77	11	=	=	SYM
ejpam-6969	77	12	1	1	NUM
ejpam-6969	77	13	,	,	PUNCT
ejpam-6969	77	14	h1(χ	h1(χ	PROPN
ejpam-6969	77	15	)	)	PUNCT
ejpam-6969	77	16	=	=	NOUN
ejpam-6969	77	17	2χ	2χ	NUM
ejpam-6969	77	18	,	,	PUNCT
ejpam-6969	77	19	h2(χ	h2(χ	NOUN
ejpam-6969	77	20	)	)	PUNCT
ejpam-6969	77	21	=	=	SYM
ejpam-6969	77	22	4χ2	4χ2	NUM
ejpam-6969	77	23	−	−	NOUN
ejpam-6969	77	24	2	2	NUM
ejpam-6969	77	25	,	,	PUNCT
ejpam-6969	77	26	h3(χ	h3(χ	NUM
ejpam-6969	77	27	)	)	PUNCT
ejpam-6969	77	28	=	=	SYM
ejpam-6969	77	29	8χ3	8χ3	NUM
ejpam-6969	77	30	−	−	NOUN
ejpam-6969	77	31	12χ	12χ	NOUN
ejpam-6969	77	32	,	,	PUNCT
ejpam-6969	77	33	h4(χ	h4(χ	NOUN
ejpam-6969	77	34	)	)	PUNCT
ejpam-6969	77	35	=	=	SYM
ejpam-6969	78	1	16χ4	16χ4	NUM
ejpam-6969	78	2	−	−	NUM
ejpam-6969	78	3	48χ2	48χ2	NUM
ejpam-6969	79	1	+	+	CCONJ
ejpam-6969	79	2	12	12	NUM
ejpam-6969	79	3	,	,	PUNCT
ejpam-6969	79	4	h5(χ	h5(χ	AUX
ejpam-6969	79	5	)	)	PUNCT
ejpam-6969	79	6	=	=	SYM
ejpam-6969	80	1	32χ5	32χ5	NUM
ejpam-6969	80	2	−	−	NUM
ejpam-6969	80	3	160χ3	160χ3	NUM
ejpam-6969	80	4	+	+	NUM
ejpam-6969	80	5	120χ	120χ	PROPN
ejpam-6969	80	6	.	.	PUNCT
ejpam-6969	81	1	these	these	DET
ejpam-6969	81	2	polynomials	polynomial	NOUN
ejpam-6969	81	3	satisfy	satisfy	VERB
ejpam-6969	81	4	several	several	ADJ
ejpam-6969	81	5	important	important	ADJ
ejpam-6969	81	6	identities	identity	NOUN
ejpam-6969	81	7	.	.	PUNCT
ejpam-6969	82	1	the	the	DET
ejpam-6969	82	2	derivative	derivative	NOUN
ejpam-6969	82	3	of	of	ADP
ejpam-6969	82	4	hn(χ	hn(χ	NOUN
ejpam-6969	82	5	)	)	PUNCT
ejpam-6969	82	6	is	be	AUX
ejpam-6969	82	7	given	give	VERB
ejpam-6969	82	8	by	by	ADP
ejpam-6969	82	9	h	h	PROPN
ejpam-6969	82	10	′	′	NUM
ejpam-6969	82	11	n(χ	n(χ	NOUN
ejpam-6969	82	12	)	)	PUNCT
ejpam-6969	82	13	=	=	SYM
ejpam-6969	82	14	2nhn−1(χ	2nhn−1(χ	NUM
ejpam-6969	82	15	)	)	PUNCT
ejpam-6969	82	16	,	,	PUNCT
ejpam-6969	82	17	n	n	PRON
ejpam-6969	82	18	≥	≥	NOUN
ejpam-6969	82	19	1	1	NUM
ejpam-6969	82	20	.	.	PUNCT
ejpam-6969	82	21	m.	m.	PROPN
ejpam-6969	82	22	h.	h.	PROPN
ejpam-6969	82	23	ahmed	ahmed	PROPN
ejpam-6969	82	24	,	,	PUNCT
ejpam-6969	82	25	a.	a.	NOUN
ejpam-6969	82	26	m.	m.	PROPN
ejpam-6969	82	27	aljabri	aljabri	PROPN
ejpam-6969	82	28	/	/	SYM
ejpam-6969	82	29	eur	eur	PROPN
ejpam-6969	82	30	.	.	PUNCT
ejpam-6969	83	1	j.	j.	PROPN
ejpam-6969	83	2	pure	pure	PROPN
ejpam-6969	83	3	appl	appl	PROPN
ejpam-6969	83	4	.	.	PROPN
ejpam-6969	83	5	math	math	PROPN
ejpam-6969	83	6	,	,	PUNCT
ejpam-6969	83	7	18	18	NUM
ejpam-6969	83	8	(	(	PUNCT
ejpam-6969	83	9	4	4	NUM
ejpam-6969	83	10	)	)	PUNCT
ejpam-6969	83	11	(	(	PUNCT
ejpam-6969	83	12	2025	2025	NUM
ejpam-6969	83	13	)	)	PUNCT
ejpam-6969	83	14	,	,	PUNCT
ejpam-6969	83	15	6969	6969	NUM
ejpam-6969	83	16	5	5	NUM
ejpam-6969	83	17	of	of	ADP
ejpam-6969	83	18	16	16	NUM
ejpam-6969	83	19	they	they	PRON
ejpam-6969	83	20	also	also	ADV
ejpam-6969	83	21	satisfy	satisfy	VERB
ejpam-6969	83	22	a	a	DET
ejpam-6969	83	23	recurrence	recurrence	NOUN
ejpam-6969	83	24	relation	relation	NOUN
ejpam-6969	83	25	hn+1(χ)−	hn+1(χ)−	NOUN
ejpam-6969	83	26	2χhn(χ	2χhn(χ	NUM
ejpam-6969	83	27	)	)	PUNCT
ejpam-6969	83	28	=	=	SYM
ejpam-6969	83	29	−2nhn−1(χ	−2nhn−1(χ	NOUN
ejpam-6969	83	30	)	)	PUNCT
ejpam-6969	83	31	,	,	PUNCT
ejpam-6969	83	32	n	n	NOUN
ejpam-6969	83	33	=	=	SYM
ejpam-6969	83	34	1	1	NUM
ejpam-6969	83	35	,	,	PUNCT
ejpam-6969	83	36	2	2	NUM
ejpam-6969	83	37	,	,	PUNCT
ejpam-6969	83	38	.	.	PUNCT
ejpam-6969	83	39	.	.	PUNCT
ejpam-6969	83	40	.	.	PUNCT
ejpam-6969	84	1	moreover	moreover	ADV
ejpam-6969	84	2	,	,	PUNCT
ejpam-6969	84	3	they	they	PRON
ejpam-6969	84	4	exhibit	exhibit	VERB
ejpam-6969	84	5	symmetry	symmetry	NOUN
ejpam-6969	84	6	properties	property	NOUN
ejpam-6969	84	7	based	base	VERB
ejpam-6969	84	8	on	on	ADP
ejpam-6969	84	9	the	the	DET
ejpam-6969	84	10	parity	parity	NOUN
ejpam-6969	84	11	of	of	ADP
ejpam-6969	84	12	n	n	PRON
ejpam-6969	84	13	hn(−χ	hn(−χ	NOUN
ejpam-6969	84	14	)	)	PUNCT
ejpam-6969	85	1	=	=	SYM
ejpam-6969	85	2	(	(	PUNCT
ejpam-6969	85	3	−1)nhn(χ	−1)nhn(χ	NOUN
ejpam-6969	85	4	)	)	PUNCT
ejpam-6969	85	5	.	.	PUNCT
ejpam-6969	86	1	with	with	ADP
ejpam-6969	86	2	respect	respect	NOUN
ejpam-6969	86	3	to	to	ADP
ejpam-6969	86	4	orthogonality	orthogonality	NOUN
ejpam-6969	86	5	,	,	PUNCT
ejpam-6969	86	6	hermite	hermite	ADJ
ejpam-6969	86	7	polynomials	polynomial	NOUN
ejpam-6969	86	8	satisfy	satisfy	VERB
ejpam-6969	86	9	the	the	DET
ejpam-6969	86	10	following	follow	VERB
ejpam-6969	86	11	inner	inner	ADJ
ejpam-6969	86	12	product	product	NOUN
ejpam-6969	86	13	identity	identity	NOUN
ejpam-6969	86	14	over	over	ADP
ejpam-6969	86	15	the	the	DET
ejpam-6969	86	16	entire	entire	ADJ
ejpam-6969	86	17	real	real	NOUN
ejpam-6969	86	18	line∫	line∫	VERB
ejpam-6969	86	19	∞	∞	PROPN
ejpam-6969	86	20	−∞	−∞	ADP
ejpam-6969	86	21	e−χ2	e−χ2	PROPN
ejpam-6969	86	22	hm(χ)hn(χ	hm(χ)hn(χ	NOUN
ejpam-6969	86	23	)	)	PUNCT
ejpam-6969	86	24	dχ	dχ	NOUN
ejpam-6969	86	25	=	=	SYM
ejpam-6969	86	26	{	{	PUNCT
ejpam-6969	86	27	0	0	NUM
ejpam-6969	86	28	,	,	PUNCT
ejpam-6969	86	29	m	m	VERB
ejpam-6969	86	30	̸=	̸=	PROPN
ejpam-6969	86	31	n	n	CCONJ
ejpam-6969	86	32	,	,	PUNCT
ejpam-6969	86	33	2n	2n	NUM
ejpam-6969	86	34	√	√	NUM
ejpam-6969	86	35	π	π	PROPN
ejpam-6969	86	36	n	n	CCONJ
ejpam-6969	86	37	!	!	PUNCT
ejpam-6969	86	38	,	,	PUNCT
ejpam-6969	86	39	m	m	VERB
ejpam-6969	86	40	=	=	PUNCT
ejpam-6969	86	41	n.	n.	NOUN
ejpam-6969	86	42	3	3	X
ejpam-6969	86	43	.	.	PUNCT
ejpam-6969	86	44	existence	existence	NOUN
ejpam-6969	86	45	and	and	CCONJ
ejpam-6969	86	46	uniqueness	uniqueness	NOUN
ejpam-6969	86	47	of	of	ADP
ejpam-6969	86	48	the	the	DET
ejpam-6969	86	49	solution	solution	NOUN
ejpam-6969	86	50	of	of	ADP
ejpam-6969	86	51	the	the	DET
ejpam-6969	86	52	integral	integral	ADJ
ejpam-6969	86	53	equation	equation	NOUN
ejpam-6969	86	54	first	first	ADV
ejpam-6969	86	55	,	,	PUNCT
ejpam-6969	86	56	we	we	PRON
ejpam-6969	86	57	need	need	VERB
ejpam-6969	86	58	to	to	PART
ejpam-6969	86	59	prove	prove	VERB
ejpam-6969	86	60	the	the	DET
ejpam-6969	86	61	existence	existence	NOUN
ejpam-6969	86	62	and	and	CCONJ
ejpam-6969	86	63	uniqueness	uniqueness	NOUN
ejpam-6969	86	64	of	of	ADP
ejpam-6969	86	65	the	the	DET
ejpam-6969	86	66	solution	solution	NOUN
ejpam-6969	86	67	of	of	ADP
ejpam-6969	86	68	(	(	PUNCT
ejpam-6969	86	69	1	1	NUM
ejpam-6969	86	70	)	)	PUNCT
ejpam-6969	86	71	.	.	PUNCT
ejpam-6969	87	1	to	to	ADP
ejpam-6969	87	2	this	this	DET
ejpam-6969	87	3	end	end	NOUN
ejpam-6969	87	4	,	,	PUNCT
ejpam-6969	87	5	we	we	PRON
ejpam-6969	87	6	employ	employ	VERB
ejpam-6969	87	7	the	the	DET
ejpam-6969	87	8	banach	banach	ADV
ejpam-6969	87	9	fixed	fix	VERB
ejpam-6969	87	10	point	point	NOUN
ejpam-6969	87	11	theorem	theorem	VERB
ejpam-6969	87	12	.	.	PUNCT
ejpam-6969	87	13	theorem	theorem	NOUN
ejpam-6969	87	14	1	1	NUM
ejpam-6969	87	15	.	.	PUNCT
ejpam-6969	88	1	let	let	VERB
ejpam-6969	88	2	(	(	PUNCT
ejpam-6969	88	3	c(d	c(d	PROPN
ejpam-6969	88	4	)	)	PUNCT
ejpam-6969	88	5	,	,	PUNCT
ejpam-6969	88	6	∥·∥	∥·∥	PROPN
ejpam-6969	88	7	)	)	PUNCT
ejpam-6969	88	8	as	as	ADP
ejpam-6969	88	9	the	the	DET
ejpam-6969	88	10	banach	banach	NOUN
ejpam-6969	88	11	space	space	NOUN
ejpam-6969	88	12	for	for	ADP
ejpam-6969	88	13	continuous	continuous	ADJ
ejpam-6969	88	14	real	real	ADV
ejpam-6969	88	15	-	-	PUNCT
ejpam-6969	88	16	valued	value	VERB
ejpam-6969	88	17	functions	function	NOUN
ejpam-6969	88	18	on	on	ADP
ejpam-6969	88	19	d	d	PROPN
ejpam-6969	88	20	,	,	PUNCT
ejpam-6969	88	21	with	with	ADP
ejpam-6969	88	22	norm	norm	NOUN
ejpam-6969	88	23	∥u∥	∥u∥	NOUN
ejpam-6969	88	24	=	=	SYM
ejpam-6969	88	25	max	max	PROPN
ejpam-6969	88	26	(	(	PUNCT
ejpam-6969	88	27	χ	χ	NOUN
ejpam-6969	88	28	,	,	PUNCT
ejpam-6969	88	29	t)∈d	t)∈d	X
ejpam-6969	88	30	|u(χ	|u(χ	PROPN
ejpam-6969	88	31	,	,	PUNCT
ejpam-6969	88	32	t)|	t)|	PROPN
ejpam-6969	88	33	.	.	PUNCT
ejpam-6969	89	1	assume	assume	VERB
ejpam-6969	89	2	that	that	SCONJ
ejpam-6969	89	3	the	the	DET
ejpam-6969	89	4	function	function	NOUN
ejpam-6969	89	5	f(χ	f(χ	PROPN
ejpam-6969	89	6	,	,	PUNCT
ejpam-6969	89	7	t	t	PROPN
ejpam-6969	89	8	)	)	PUNCT
ejpam-6969	89	9	is	be	AUX
ejpam-6969	89	10	continuous	continuous	ADJ
ejpam-6969	89	11	on	on	ADP
ejpam-6969	89	12	d	d	PROPN
ejpam-6969	89	13	,	,	PUNCT
ejpam-6969	89	14	and	and	CCONJ
ejpam-6969	89	15	the	the	DET
ejpam-6969	89	16	kernel	kernel	PROPN
ejpam-6969	89	17	k(χ	k(χ	PROPN
ejpam-6969	89	18	,	,	PUNCT
ejpam-6969	89	19	t	t	PROPN
ejpam-6969	89	20	,	,	PUNCT
ejpam-6969	89	21	s	s	PROPN
ejpam-6969	89	22	,	,	PUNCT
ejpam-6969	89	23	y	y	PROPN
ejpam-6969	89	24	,	,	PUNCT
ejpam-6969	89	25	u	u	NOUN
ejpam-6969	89	26	)	)	PUNCT
ejpam-6969	89	27	is	be	AUX
ejpam-6969	89	28	continuous	continuous	ADJ
ejpam-6969	89	29	on	on	ADP
ejpam-6969	89	30	d	d	X
ejpam-6969	89	31	×d	×d	NOUN
ejpam-6969	89	32	×	×	NOUN
ejpam-6969	89	33	r	r	NOUN
ejpam-6969	89	34	,	,	PUNCT
ejpam-6969	89	35	and	and	CCONJ
ejpam-6969	89	36	satisfies	satisfy	VERB
ejpam-6969	89	37	the	the	DET
ejpam-6969	89	38	lipschitz	lipschitz	NOUN
ejpam-6969	89	39	condition	condition	NOUN
ejpam-6969	89	40	in	in	ADP
ejpam-6969	89	41	the	the	DET
ejpam-6969	89	42	fifth	fifth	ADJ
ejpam-6969	89	43	argument	argument	NOUN
ejpam-6969	89	44	|k(χ	|k(χ	PROPN
ejpam-6969	89	45	,	,	PUNCT
ejpam-6969	89	46	t	t	PROPN
ejpam-6969	89	47	,	,	PUNCT
ejpam-6969	89	48	s	s	PROPN
ejpam-6969	89	49	,	,	PUNCT
ejpam-6969	89	50	y	y	PROPN
ejpam-6969	89	51	,	,	PUNCT
ejpam-6969	89	52	u)−k(χ	u)−k(χ	PROPN
ejpam-6969	89	53	,	,	PUNCT
ejpam-6969	89	54	t	t	PROPN
ejpam-6969	89	55	,	,	PUNCT
ejpam-6969	89	56	s	s	PROPN
ejpam-6969	89	57	,	,	PUNCT
ejpam-6969	89	58	y	y	PROPN
ejpam-6969	89	59	,	,	PUNCT
ejpam-6969	89	60	v)|	v)|	VERB
ejpam-6969	89	61	≤	≤	ADJ
ejpam-6969	89	62	l|u−	l|u−	X
ejpam-6969	89	63	v|	v|	NOUN
ejpam-6969	89	64	for	for	ADP
ejpam-6969	89	65	all	all	PRON
ejpam-6969	89	66	(	(	PUNCT
ejpam-6969	89	67	χ	χ	NOUN
ejpam-6969	89	68	,	,	PUNCT
ejpam-6969	89	69	t	t	PROPN
ejpam-6969	89	70	,	,	PUNCT
ejpam-6969	89	71	s	s	PROPN
ejpam-6969	89	72	,	,	PUNCT
ejpam-6969	89	73	y	y	NOUN
ejpam-6969	89	74	)	)	PUNCT
ejpam-6969	89	75	∈	∈	PROPN
ejpam-6969	90	1	d	d	NOUN
ejpam-6969	90	2	×d	×d	NOUN
ejpam-6969	90	3	and	and	CCONJ
ejpam-6969	90	4	all	all	DET
ejpam-6969	90	5	u	u	NOUN
ejpam-6969	90	6	,	,	PUNCT
ejpam-6969	90	7	v	v	NOUN
ejpam-6969	90	8	∈	∈	NOUN
ejpam-6969	90	9	r	r	NOUN
ejpam-6969	90	10	,	,	PUNCT
ejpam-6969	90	11	with	with	ADP
ejpam-6969	90	12	a	a	DET
ejpam-6969	90	13	constant	constant	ADJ
ejpam-6969	90	14	l	l	NOUN
ejpam-6969	90	15	>	>	X
ejpam-6969	90	16	0	0	X
ejpam-6969	90	17	.	.	PUNCT
ejpam-6969	91	1	if	if	SCONJ
ejpam-6969	91	2	α	α	PRON
ejpam-6969	91	3	=	=	X
ejpam-6969	91	4	|λ|l	|λ|l	ADP
ejpam-6969	91	5	<	<	X
ejpam-6969	91	6	1	1	NUM
ejpam-6969	91	7	,	,	PUNCT
ejpam-6969	91	8	and	and	CCONJ
ejpam-6969	91	9	0	0	NUM
ejpam-6969	91	10	<	<	X
ejpam-6969	91	11	α	α	X
ejpam-6969	91	12	<	<	X
ejpam-6969	91	13	1	1	NUM
ejpam-6969	91	14	then	then	ADV
ejpam-6969	91	15	the	the	DET
ejpam-6969	91	16	integral	integral	ADJ
ejpam-6969	91	17	equation	equation	NOUN
ejpam-6969	91	18	(	(	PUNCT
ejpam-6969	91	19	1	1	X
ejpam-6969	91	20	)	)	PUNCT
ejpam-6969	91	21	has	have	VERB
ejpam-6969	91	22	a	a	DET
ejpam-6969	91	23	unique	unique	ADJ
ejpam-6969	91	24	solution	solution	NOUN
ejpam-6969	91	25	u	u	PROPN
ejpam-6969	91	26	∈	∈	PROPN
ejpam-6969	91	27	c(d	c(d	PROPN
ejpam-6969	91	28	)	)	PUNCT
ejpam-6969	91	29	.	.	PUNCT
ejpam-6969	92	1	proof	proof	NOUN
ejpam-6969	92	2	.	.	PUNCT
ejpam-6969	93	1	define	define	VERB
ejpam-6969	93	2	the	the	DET
ejpam-6969	93	3	operator	operator	NOUN
ejpam-6969	93	4	t	t	PROPN
ejpam-6969	93	5	on	on	ADP
ejpam-6969	93	6	c(d	c(d	PROPN
ejpam-6969	93	7	)	)	PUNCT
ejpam-6969	93	8	by	by	ADP
ejpam-6969	93	9	(	(	PUNCT
ejpam-6969	93	10	tu)(χ	tu)(χ	PROPN
ejpam-6969	93	11	,	,	PUNCT
ejpam-6969	93	12	t	t	PROPN
ejpam-6969	93	13	)	)	PUNCT
ejpam-6969	93	14	=	=	SYM
ejpam-6969	93	15	f(χ	f(χ	PROPN
ejpam-6969	93	16	,	,	PUNCT
ejpam-6969	93	17	t	t	PROPN
ejpam-6969	93	18	)	)	PUNCT
ejpam-6969	94	1	+	+	NUM
ejpam-6969	95	1	λ	λ	PROPN
ejpam-6969	95	2	∫	∫	PROPN
ejpam-6969	95	3	t	t	PROPN
ejpam-6969	95	4	0	0	NUM
ejpam-6969	95	5	∫	∫	PROPN
ejpam-6969	96	1	χ	χ	X
ejpam-6969	96	2	0	0	PROPN
ejpam-6969	96	3	k(χ	k(χ	PROPN
ejpam-6969	96	4	,	,	PUNCT
ejpam-6969	96	5	t	t	PROPN
ejpam-6969	96	6	,	,	PUNCT
ejpam-6969	96	7	s	s	PROPN
ejpam-6969	96	8	,	,	PUNCT
ejpam-6969	96	9	y	y	PROPN
ejpam-6969	96	10	,	,	PUNCT
ejpam-6969	96	11	u(s	u(s	PROPN
ejpam-6969	96	12	,	,	PUNCT
ejpam-6969	96	13	y	y	NOUN
ejpam-6969	96	14	)	)	PUNCT
ejpam-6969	96	15	)	)	PUNCT
ejpam-6969	96	16	ds	ds	NOUN
ejpam-6969	96	17	dy	dy	NOUN
ejpam-6969	96	18	.	.	PUNCT
ejpam-6969	97	1	we	we	PRON
ejpam-6969	97	2	aim	aim	VERB
ejpam-6969	97	3	to	to	PART
ejpam-6969	97	4	show	show	VERB
ejpam-6969	97	5	that	that	SCONJ
ejpam-6969	97	6	t	t	PROPN
ejpam-6969	97	7	is	be	AUX
ejpam-6969	97	8	a	a	DET
ejpam-6969	97	9	contraction	contraction	NOUN
ejpam-6969	97	10	on	on	ADP
ejpam-6969	97	11	c(d	c(d	PROPN
ejpam-6969	97	12	)	)	PUNCT
ejpam-6969	97	13	.	.	PUNCT
ejpam-6969	98	1	for	for	ADP
ejpam-6969	98	2	any	any	DET
ejpam-6969	98	3	u	u	NOUN
ejpam-6969	98	4	,	,	PUNCT
ejpam-6969	98	5	v	v	PROPN
ejpam-6969	98	6	∈	∈	PROPN
ejpam-6969	98	7	c(d	c(d	PROPN
ejpam-6969	98	8	)	)	PUNCT
ejpam-6969	98	9	,	,	PUNCT
ejpam-6969	98	10	we	we	PRON
ejpam-6969	98	11	have	have	VERB
ejpam-6969	98	12	∥tu−	∥tu−	NOUN
ejpam-6969	98	13	tv∥	tv∥	NOUN
ejpam-6969	99	1	=	=	SYM
ejpam-6969	99	2	max	max	PROPN
ejpam-6969	99	3	(	(	PUNCT
ejpam-6969	99	4	χ	χ	NOUN
ejpam-6969	99	5	,	,	PUNCT
ejpam-6969	99	6	t)∈d	t)∈d	X
ejpam-6969	99	7	|(tu)(χ	|(tu)(χ	X
ejpam-6969	99	8	,	,	PUNCT
ejpam-6969	99	9	t)−	t)−	PROPN
ejpam-6969	99	10	(	(	PUNCT
ejpam-6969	99	11	tv)(χ	tv)(χ	ADV
ejpam-6969	99	12	,	,	PUNCT
ejpam-6969	99	13	t)|	t)|	NOUN
ejpam-6969	99	14	=	=	SYM
ejpam-6969	99	15	max	max	PROPN
ejpam-6969	99	16	(	(	PUNCT
ejpam-6969	99	17	χ	χ	NOUN
ejpam-6969	99	18	,	,	PUNCT
ejpam-6969	99	19	t)∈d	t)∈d	NUM
ejpam-6969	99	20	∣∣∣∣λ	∣∣∣∣λ	NOUN
ejpam-6969	100	1	∫	∫	PROPN
ejpam-6969	100	2	t	t	PROPN
ejpam-6969	100	3	0	0	NUM
ejpam-6969	100	4	∫	∫	PROPN
ejpam-6969	101	1	χ	χ	X
ejpam-6969	101	2	0	0	PUNCT
ejpam-6969	102	1	[	[	X
ejpam-6969	102	2	k(χ	k(χ	PROPN
ejpam-6969	102	3	,	,	PUNCT
ejpam-6969	102	4	t	t	PROPN
ejpam-6969	102	5	,	,	PUNCT
ejpam-6969	102	6	s	s	PROPN
ejpam-6969	102	7	,	,	PUNCT
ejpam-6969	102	8	y	y	PROPN
ejpam-6969	102	9	,	,	PUNCT
ejpam-6969	102	10	u(s	u(s	PROPN
ejpam-6969	102	11	,	,	PUNCT
ejpam-6969	102	12	y))−k(χ	y))−k(χ	PROPN
ejpam-6969	102	13	,	,	PUNCT
ejpam-6969	102	14	t	t	PROPN
ejpam-6969	102	15	,	,	PUNCT
ejpam-6969	102	16	s	s	PROPN
ejpam-6969	102	17	,	,	PUNCT
ejpam-6969	102	18	y	y	PROPN
ejpam-6969	102	19	,	,	PUNCT
ejpam-6969	102	20	v(s	v(s	PROPN
ejpam-6969	102	21	,	,	PUNCT
ejpam-6969	102	22	y	y	NOUN
ejpam-6969	102	23	)	)	PUNCT
ejpam-6969	102	24	)	)	PUNCT
ejpam-6969	102	25	]	]	PUNCT
ejpam-6969	102	26	ds	ds	NOUN
ejpam-6969	102	27	dy	dy	NOUN
ejpam-6969	102	28	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6969	102	29	≤	≤	PUNCT
ejpam-6969	102	30	|λ|	|λ|	PROPN
ejpam-6969	102	31	max	max	PROPN
ejpam-6969	102	32	(	(	PUNCT
ejpam-6969	102	33	χ	χ	X
ejpam-6969	102	34	,	,	PUNCT
ejpam-6969	102	35	t)∈d	t)∈d	NUM
ejpam-6969	102	36	∫	∫	NOUN
ejpam-6969	102	37	t	t	NOUN
ejpam-6969	102	38	0	0	NUM
ejpam-6969	102	39	∫	∫	PROPN
ejpam-6969	103	1	χ	χ	X
ejpam-6969	103	2	0	0	PROPN
ejpam-6969	103	3	|k(χ	|k(χ	PROPN
ejpam-6969	103	4	,	,	PUNCT
ejpam-6969	103	5	t	t	PROPN
ejpam-6969	103	6	,	,	PUNCT
ejpam-6969	103	7	s	s	PROPN
ejpam-6969	103	8	,	,	PUNCT
ejpam-6969	103	9	y	y	PROPN
ejpam-6969	103	10	,	,	PUNCT
ejpam-6969	103	11	u(s	u(s	PROPN
ejpam-6969	103	12	,	,	PUNCT
ejpam-6969	103	13	y))−k(χ	y))−k(χ	PROPN
ejpam-6969	103	14	,	,	PUNCT
ejpam-6969	103	15	t	t	PROPN
ejpam-6969	103	16	,	,	PUNCT
ejpam-6969	103	17	s	s	PROPN
ejpam-6969	103	18	,	,	PUNCT
ejpam-6969	103	19	y	y	PROPN
ejpam-6969	103	20	,	,	PUNCT
ejpam-6969	103	21	v(s	v(s	PROPN
ejpam-6969	103	22	,	,	PUNCT
ejpam-6969	103	23	y))|	y))|	PROPN
ejpam-6969	103	24	ds	ds	PROPN
ejpam-6969	103	25	dy	dy	X
ejpam-6969	103	26	≤	≤	NUM
ejpam-6969	103	27	|λ|l	|λ|l	ADP
ejpam-6969	103	28	max	max	PROPN
ejpam-6969	103	29	(	(	PUNCT
ejpam-6969	103	30	χ	χ	X
ejpam-6969	103	31	,	,	PUNCT
ejpam-6969	103	32	t)∈d	t)∈d	NUM
ejpam-6969	103	33	∫	∫	NOUN
ejpam-6969	103	34	t	t	NOUN
ejpam-6969	103	35	0	0	NUM
ejpam-6969	103	36	∫	∫	PROPN
ejpam-6969	104	1	χ	χ	X
ejpam-6969	104	2	0	0	PROPN
ejpam-6969	104	3	|u(s	|u(s	PROPN
ejpam-6969	104	4	,	,	PUNCT
ejpam-6969	104	5	y)−	y)−	PROPN
ejpam-6969	104	6	v(s	v(s	PROPN
ejpam-6969	104	7	,	,	PUNCT
ejpam-6969	104	8	y)|	y)|	PROPN
ejpam-6969	104	9	ds	ds	NOUN
ejpam-6969	104	10	dy	dy	X
ejpam-6969	104	11	≤	≤	PROPN
ejpam-6969	104	12	|λ|l∥u−	|λ|l∥u−	PROPN
ejpam-6969	104	13	v∥	v∥	PROPN
ejpam-6969	104	14	max	max	PROPN
ejpam-6969	104	15	(	(	PUNCT
ejpam-6969	104	16	χ	χ	X
ejpam-6969	104	17	,	,	PUNCT
ejpam-6969	104	18	t)∈d	t)∈d	NUM
ejpam-6969	104	19	∫	∫	NOUN
ejpam-6969	105	1	t	t	NOUN
ejpam-6969	105	2	0	0	NUM
ejpam-6969	105	3	∫	∫	PROPN
ejpam-6969	105	4	χ	χ	X
ejpam-6969	105	5	0	0	NUM
ejpam-6969	105	6	ds	ds	NOUN
ejpam-6969	105	7	dy	dy	NOUN
ejpam-6969	105	8	=	=	SYM
ejpam-6969	105	9	|λ|l∥u−	|λ|l∥u−	PROPN
ejpam-6969	105	10	v∥	v∥	PROPN
ejpam-6969	105	11	max	max	PROPN
ejpam-6969	105	12	(	(	PUNCT
ejpam-6969	105	13	χ	χ	ADP
ejpam-6969	105	14	,	,	PUNCT
ejpam-6969	105	15	t)∈d	t)∈d	NUM
ejpam-6969	105	16	χ	χ	PRON
ejpam-6969	106	1	t	t	NOUN
ejpam-6969	106	2	=	=	SYM
ejpam-6969	106	3	α∥u−	α∥u−	PROPN
ejpam-6969	106	4	v∥.	v∥.	PROPN
ejpam-6969	106	5	m.	m.	NOUN
ejpam-6969	106	6	h.	h.	PROPN
ejpam-6969	106	7	ahmed	ahmed	PROPN
ejpam-6969	106	8	,	,	PUNCT
ejpam-6969	106	9	a.	a.	NOUN
ejpam-6969	106	10	m.	m.	PROPN
ejpam-6969	106	11	aljabri	aljabri	PROPN
ejpam-6969	106	12	/	/	SYM
ejpam-6969	106	13	eur	eur	PROPN
ejpam-6969	106	14	.	.	PUNCT
ejpam-6969	107	1	j.	j.	PROPN
ejpam-6969	107	2	pure	pure	PROPN
ejpam-6969	107	3	appl	appl	PROPN
ejpam-6969	107	4	.	.	PROPN
ejpam-6969	107	5	math	math	PROPN
ejpam-6969	107	6	,	,	PUNCT
ejpam-6969	107	7	18	18	NUM
ejpam-6969	107	8	(	(	PUNCT
ejpam-6969	107	9	4	4	NUM
ejpam-6969	107	10	)	)	PUNCT
ejpam-6969	107	11	(	(	PUNCT
ejpam-6969	107	12	2025	2025	NUM
ejpam-6969	107	13	)	)	PUNCT
ejpam-6969	107	14	,	,	PUNCT
ejpam-6969	107	15	6969	6969	NUM
ejpam-6969	107	16	6	6	NUM
ejpam-6969	107	17	of	of	ADP
ejpam-6969	107	18	16	16	NUM
ejpam-6969	107	19	since	since	SCONJ
ejpam-6969	107	20	α	α	X
ejpam-6969	107	21	=	=	PUNCT
ejpam-6969	107	22	|λ|l	|λ|l	PROPN
ejpam-6969	107	23	<	<	X
ejpam-6969	107	24	1	1	NUM
ejpam-6969	107	25	,	,	PUNCT
ejpam-6969	107	26	the	the	DET
ejpam-6969	107	27	operator	operator	NOUN
ejpam-6969	107	28	t	t	NOUN
ejpam-6969	107	29	is	be	AUX
ejpam-6969	107	30	a	a	DET
ejpam-6969	107	31	contraction	contraction	NOUN
ejpam-6969	107	32	.	.	PUNCT
ejpam-6969	108	1	therefore	therefore	ADV
ejpam-6969	108	2	,	,	PUNCT
ejpam-6969	108	3	by	by	ADP
ejpam-6969	108	4	the	the	DET
ejpam-6969	108	5	banach	banach	ADV
ejpam-6969	108	6	fixed	fix	VERB
ejpam-6969	108	7	point	point	NOUN
ejpam-6969	108	8	theorem	theorem	VERB
ejpam-6969	108	9	,	,	PUNCT
ejpam-6969	108	10	t	t	PROPN
ejpam-6969	108	11	has	have	VERB
ejpam-6969	108	12	a	a	DET
ejpam-6969	108	13	unique	unique	ADJ
ejpam-6969	108	14	fixed	fix	VERB
ejpam-6969	108	15	point	point	NOUN
ejpam-6969	108	16	u	u	PROPN
ejpam-6969	108	17	∈	∈	PROPN
ejpam-6969	108	18	c(d	c(d	PROPN
ejpam-6969	108	19	)	)	PUNCT
ejpam-6969	108	20	,	,	PUNCT
ejpam-6969	108	21	which	which	PRON
ejpam-6969	108	22	is	be	AUX
ejpam-6969	108	23	the	the	DET
ejpam-6969	108	24	unique	unique	ADJ
ejpam-6969	108	25	solution	solution	NOUN
ejpam-6969	108	26	of	of	ADP
ejpam-6969	108	27	the	the	DET
ejpam-6969	108	28	integral	integral	ADJ
ejpam-6969	108	29	equation	equation	NOUN
ejpam-6969	108	30	.	.	PUNCT
ejpam-6969	109	1	to	to	PART
ejpam-6969	109	2	illustrate	illustrate	VERB
ejpam-6969	109	3	the	the	DET
ejpam-6969	109	4	convergence	convergence	NOUN
ejpam-6969	109	5	,	,	PUNCT
ejpam-6969	109	6	s.bazm	s.bazm	NOUN
ejpam-6969	109	7	studied	study	VERB
ejpam-6969	109	8	the	the	DET
ejpam-6969	109	9	bernoulli	bernoulli	NOUN
ejpam-6969	109	10	polynomials	polynomial	NOUN
ejpam-6969	109	11	for	for	ADP
ejpam-6969	109	12	integral	integral	ADJ
ejpam-6969	109	13	equations	equation	NOUN
ejpam-6969	109	14	[	[	X
ejpam-6969	109	15	27	27	NUM
ejpam-6969	109	16	]	]	PUNCT
ejpam-6969	109	17	,	,	PUNCT
ejpam-6969	109	18	while	while	SCONJ
ejpam-6969	109	19	mao	mao	PROPN
ejpam-6969	109	20	and	and	CCONJ
ejpam-6969	109	21	shen	shen	PROPN
ejpam-6969	109	22	analyzed	analyze	VERB
ejpam-6969	109	23	the	the	DET
ejpam-6969	109	24	hermite	hermite	ADJ
ejpam-6969	109	25	–	–	PUNCT
ejpam-6969	109	26	galerkin	galerkin	ADJ
ejpam-6969	109	27	method	method	NOUN
ejpam-6969	109	28	for	for	ADP
ejpam-6969	109	29	fractional	fractional	ADJ
ejpam-6969	109	30	pdes	pde	NOUN
ejpam-6969	109	31	[	[	X
ejpam-6969	109	32	25	25	NUM
ejpam-6969	109	33	]	]	PUNCT
ejpam-6969	109	34	.	.	PUNCT
ejpam-6969	110	1	4	4	X
ejpam-6969	110	2	.	.	X
ejpam-6969	110	3	description	description	NOUN
ejpam-6969	110	4	of	of	ADP
ejpam-6969	110	5	the	the	DET
ejpam-6969	110	6	methods	method	NOUN
ejpam-6969	110	7	in	in	ADP
ejpam-6969	110	8	this	this	DET
ejpam-6969	110	9	section	section	NOUN
ejpam-6969	110	10	,	,	PUNCT
ejpam-6969	110	11	we	we	PRON
ejpam-6969	110	12	solve	solve	VERB
ejpam-6969	110	13	eq.(1	eq.(1	ADV
ejpam-6969	110	14	)	)	PUNCT
ejpam-6969	110	15	using	use	VERB
ejpam-6969	110	16	bernoulli	bernoulli	NOUN
ejpam-6969	110	17	collocation	collocation	NOUN
ejpam-6969	110	18	method	method	NOUN
ejpam-6969	110	19	and	and	CCONJ
ejpam-6969	110	20	hermite	hermite	ADJ
ejpam-6969	110	21	galerkin	galerkin	PROPN
ejpam-6969	110	22	method	method	NOUN
ejpam-6969	110	23	.	.	PUNCT
ejpam-6969	111	1	4.1	4.1	NUM
ejpam-6969	111	2	.	.	PUNCT
ejpam-6969	112	1	bernoulli	bernoulli	NOUN
ejpam-6969	112	2	collocation	collocation	NOUN
ejpam-6969	112	3	method	method	NOUN
ejpam-6969	112	4	in	in	ADP
ejpam-6969	112	5	this	this	DET
ejpam-6969	112	6	method	method	NOUN
ejpam-6969	113	1	,	,	PUNCT
ejpam-6969	113	2	we	we	PRON
ejpam-6969	113	3	approximate	approximate	VERB
ejpam-6969	113	4	the	the	DET
ejpam-6969	113	5	unknown	unknown	ADJ
ejpam-6969	113	6	function	function	NOUN
ejpam-6969	113	7	ũ(χ	ũ(χ	PROPN
ejpam-6969	113	8	,	,	PUNCT
ejpam-6969	113	9	t	t	PROPN
ejpam-6969	113	10	)	)	PUNCT
ejpam-6969	113	11	in	in	ADP
ejpam-6969	113	12	equation	equation	NOUN
ejpam-6969	113	13	(	(	PUNCT
ejpam-6969	113	14	1	1	X
ejpam-6969	113	15	)	)	PUNCT
ejpam-6969	113	16	using	use	VERB
ejpam-6969	113	17	a	a	DET
ejpam-6969	113	18	double	double	ADJ
ejpam-6969	113	19	series	series	NOUN
ejpam-6969	113	20	expansion	expansion	NOUN
ejpam-6969	113	21	of	of	ADP
ejpam-6969	113	22	the	the	DET
ejpam-6969	113	23	form	form	NOUN
ejpam-6969	113	24	ũ(χ	ũ(χ	PROPN
ejpam-6969	113	25	,	,	PUNCT
ejpam-6969	113	26	t	t	PROPN
ejpam-6969	113	27	)	)	PUNCT
ejpam-6969	113	28	=	=	PUNCT
ejpam-6969	114	1	∞∑	∞∑	NUM
ejpam-6969	114	2	i=0	i=0	PROPN
ejpam-6969	114	3	∞∑	∞∑	PROPN
ejpam-6969	114	4	j=0	j=0	PROPN
ejpam-6969	114	5	aijbi(χ)bj(t	aijbi(χ)bj(t	PROPN
ejpam-6969	114	6	)	)	PUNCT
ejpam-6969	114	7	,	,	PUNCT
ejpam-6969	114	8	(	(	PUNCT
ejpam-6969	114	9	8)	8)	NUM
ejpam-6969	114	10	where	where	SCONJ
ejpam-6969	114	11	bi(χ	bi(χ	NOUN
ejpam-6969	114	12	)	)	PUNCT
ejpam-6969	114	13	and	and	CCONJ
ejpam-6969	114	14	bj(t	bj(t	NUM
ejpam-6969	114	15	)	)	PUNCT
ejpam-6969	114	16	are	be	AUX
ejpam-6969	114	17	bernoulli	bernoulli	NOUN
ejpam-6969	114	18	polynomials	polynomial	NOUN
ejpam-6969	114	19	and	and	CCONJ
ejpam-6969	114	20	the	the	DET
ejpam-6969	114	21	unknown	unknown	ADJ
ejpam-6969	114	22	coefficients	coefficient	NOUN
ejpam-6969	114	23	aij	aij	PROPN
ejpam-6969	114	24	are	be	AUX
ejpam-6969	114	25	be	be	AUX
ejpam-6969	114	26	determined	determine	VERB
ejpam-6969	114	27	.	.	PUNCT
ejpam-6969	115	1	this	this	DET
ejpam-6969	115	2	representation	representation	NOUN
ejpam-6969	115	3	is	be	AUX
ejpam-6969	115	4	then	then	ADV
ejpam-6969	115	5	used	use	VERB
ejpam-6969	115	6	to	to	PART
ejpam-6969	115	7	construct	construct	VERB
ejpam-6969	115	8	the	the	DET
ejpam-6969	115	9	approximate	approximate	ADJ
ejpam-6969	115	10	solution	solution	NOUN
ejpam-6969	115	11	as	as	SCONJ
ejpam-6969	115	12	follows	follow	VERB
ejpam-6969	115	13	.	.	PUNCT
ejpam-6969	116	1	by	by	ADP
ejpam-6969	116	2	truncating	truncate	VERB
ejpam-6969	116	3	the	the	DET
ejpam-6969	116	4	infinite	infinite	ADJ
ejpam-6969	116	5	series	series	NOUN
ejpam-6969	116	6	in	in	ADP
ejpam-6969	116	7	equation	equation	NOUN
ejpam-6969	116	8	(	(	PUNCT
ejpam-6969	116	9	8)	8)	NUM
ejpam-6969	116	10	,	,	PUNCT
ejpam-6969	116	11	we	we	PRON
ejpam-6969	116	12	obtain	obtain	VERB
ejpam-6969	116	13	the	the	DET
ejpam-6969	116	14	following	follow	VERB
ejpam-6969	116	15	finite	finite	ADJ
ejpam-6969	116	16	approximation	approximation	NOUN
ejpam-6969	116	17	ũ(χ	ũ(χ	PROPN
ejpam-6969	116	18	,	,	PUNCT
ejpam-6969	116	19	t	t	PROPN
ejpam-6969	116	20	)	)	PUNCT
ejpam-6969	117	1	≈	≈	PROPN
ejpam-6969	117	2	n−1∑	n−1∑	PROPN
ejpam-6969	117	3	i=0	i=0	PROPN
ejpam-6969	117	4	n−1∑	n−1∑	NUM
ejpam-6969	117	5	j=0	j=0	PROPN
ejpam-6969	117	6	aijbi(χ)bj(t	aijbi(χ)bj(t	PROPN
ejpam-6969	117	7	)	)	PUNCT
ejpam-6969	117	8	,	,	PUNCT
ejpam-6969	117	9	(	(	PUNCT
ejpam-6969	117	10	9	9	X
ejpam-6969	117	11	)	)	PUNCT
ejpam-6969	117	12	where	where	SCONJ
ejpam-6969	117	13	n	n	PRON
ejpam-6969	117	14	−	−	PROPN
ejpam-6969	117	15	1	1	NUM
ejpam-6969	117	16	is	be	AUX
ejpam-6969	117	17	the	the	DET
ejpam-6969	117	18	chosen	choose	VERB
ejpam-6969	117	19	degree	degree	NOUN
ejpam-6969	117	20	of	of	ADP
ejpam-6969	117	21	approximation	approximation	NOUN
ejpam-6969	117	22	in	in	ADP
ejpam-6969	117	23	both	both	DET
ejpam-6969	117	24	variables	variable	NOUN
ejpam-6969	117	25	.	.	PUNCT
ejpam-6969	118	1	substituting	substitute	VERB
ejpam-6969	118	2	from	from	ADP
ejpam-6969	118	3	(	(	PUNCT
ejpam-6969	118	4	9	9	NUM
ejpam-6969	118	5	)	)	PUNCT
ejpam-6969	118	6	into	into	ADP
ejpam-6969	118	7	(	(	PUNCT
ejpam-6969	118	8	1	1	X
ejpam-6969	118	9	)	)	PUNCT
ejpam-6969	118	10	we	we	PRON
ejpam-6969	118	11	get	get	VERB
ejpam-6969	118	12	n−1∑	n−1∑	NUM
ejpam-6969	118	13	i=0	i=0	PROPN
ejpam-6969	118	14	n−1∑	n−1∑	PROPN
ejpam-6969	118	15	j=0	j=0	PROPN
ejpam-6969	118	16	aijbi(χ)bj(t	aijbi(χ)bj(t	PROPN
ejpam-6969	118	17	)	)	PUNCT
ejpam-6969	118	18	=	=	SYM
ejpam-6969	118	19	f(χ	f(χ	PROPN
ejpam-6969	118	20	,	,	PUNCT
ejpam-6969	118	21	t	t	PROPN
ejpam-6969	118	22	)	)	PUNCT
ejpam-6969	118	23	+	+	NUM
ejpam-6969	119	1	λ	λ	PROPN
ejpam-6969	119	2	∫	∫	PROPN
ejpam-6969	119	3	t	t	PROPN
ejpam-6969	119	4	0	0	NUM
ejpam-6969	119	5	∫	∫	PROPN
ejpam-6969	120	1	χ	χ	X
ejpam-6969	120	2	0	0	NUM
ejpam-6969	121	1	k	k	PROPN
ejpam-6969	121	2	χ	χ	PROPN
ejpam-6969	121	3	,	,	PUNCT
ejpam-6969	121	4	t	t	PROPN
ejpam-6969	121	5	,	,	PUNCT
ejpam-6969	121	6	s	s	PROPN
ejpam-6969	121	7	,	,	PUNCT
ejpam-6969	121	8	y	y	PROPN
ejpam-6969	121	9	,	,	PUNCT
ejpam-6969	121	10	n−1∑	n−1∑	PROPN
ejpam-6969	121	11	i=0	i=0	PROPN
ejpam-6969	121	12	n−1∑	n−1∑	NUM
ejpam-6969	121	13	j=0	j=0	PROPN
ejpam-6969	121	14	aijbi(s)bj(y	aijbi(s)bj(y	PROPN
ejpam-6969	121	15	)	)	PUNCT
ejpam-6969	121	16			PROPN
ejpam-6969	121	17	ds	ds	ADJ
ejpam-6969	121	18	dy	dy	X
ejpam-6969	121	19	.	.	PUNCT
ejpam-6969	122	1	(	(	PUNCT
ejpam-6969	122	2	10	10	NUM
ejpam-6969	122	3	)	)	PUNCT
ejpam-6969	122	4	the	the	DET
ejpam-6969	122	5	unknown	unknown	ADJ
ejpam-6969	122	6	function	function	NOUN
ejpam-6969	122	7	ũ(χ	ũ(χ	PROPN
ejpam-6969	122	8	,	,	PUNCT
ejpam-6969	122	9	t	t	PROPN
ejpam-6969	122	10	)	)	PUNCT
ejpam-6969	122	11	is	be	AUX
ejpam-6969	122	12	approximated	approximate	VERB
ejpam-6969	122	13	using	use	VERB
ejpam-6969	122	14	bernoulli	bernoulli	NOUN
ejpam-6969	122	15	polynomials	polynomial	NOUN
ejpam-6969	122	16	as	as	ADP
ejpam-6969	122	17	basis	basis	NOUN
ejpam-6969	122	18	functions	function	NOUN
ejpam-6969	122	19	,	,	PUNCT
ejpam-6969	122	20	while	while	SCONJ
ejpam-6969	122	21	the	the	DET
ejpam-6969	122	22	collocation	collocation	NOUN
ejpam-6969	122	23	points	point	VERB
ejpam-6969	122	24	χ	χ	PRON
ejpam-6969	122	25	l	l	NOUN
ejpam-6969	122	26	,	,	PUNCT
ejpam-6969	122	27	t	t	PROPN
ejpam-6969	122	28	f	f	PROPN
ejpam-6969	122	29	are	be	AUX
ejpam-6969	122	30	chosen	choose	VERB
ejpam-6969	122	31	as	as	ADP
ejpam-6969	122	32	shifted	shift	VERB
ejpam-6969	122	33	chebyshev	chebyshev	NOUN
ejpam-6969	122	34	points	point	NOUN
ejpam-6969	122	35	on	on	ADP
ejpam-6969	122	36	the	the	DET
ejpam-6969	122	37	interval	interval	NOUN
ejpam-6969	122	38	[	[	X
ejpam-6969	122	39	0	0	NUM
ejpam-6969	122	40	,	,	PUNCT
ejpam-6969	122	41	1	1	NUM
ejpam-6969	122	42	]	]	PUNCT
ejpam-6969	122	43	,	,	PUNCT
ejpam-6969	122	44	given	give	VERB
ejpam-6969	122	45	by	by	ADP
ejpam-6969	122	46	χ	χ	PROPN
ejpam-6969	122	47	l	l	NOUN
ejpam-6969	122	48	=	=	SYM
ejpam-6969	122	49	1	1	NUM
ejpam-6969	122	50	2	2	NUM
ejpam-6969	122	51	(	(	PUNCT
ejpam-6969	122	52	1	1	NUM
ejpam-6969	123	1	+	+	CCONJ
ejpam-6969	123	2	cos	cos	X
ejpam-6969	123	3	(	(	PUNCT
ejpam-6969	123	4	(	(	PUNCT
ejpam-6969	123	5	2l	2l	NUM
ejpam-6969	123	6	−	−	PROPN
ejpam-6969	123	7	1)π	1)π	NUM
ejpam-6969	123	8	2n	2n	NUM
ejpam-6969	123	9	)	)	PUNCT
ejpam-6969	123	10	)	)	PUNCT
ejpam-6969	123	11	,	,	PUNCT
ejpam-6969	123	12	t	t	PROPN
ejpam-6969	123	13	f	f	PROPN
ejpam-6969	123	14	=	=	SYM
ejpam-6969	123	15	1	1	NUM
ejpam-6969	123	16	2	2	NUM
ejpam-6969	123	17	(	(	PUNCT
ejpam-6969	123	18	1	1	NUM
ejpam-6969	123	19	+	+	CCONJ
ejpam-6969	123	20	cos	cos	X
ejpam-6969	123	21	(	(	PUNCT
ejpam-6969	123	22	(	(	PUNCT
ejpam-6969	123	23	2f	2f	NUM
ejpam-6969	123	24	−	−	NUM
ejpam-6969	123	25	1)π	1)π	NUM
ejpam-6969	123	26	2n	2n	NUM
ejpam-6969	123	27	)	)	PUNCT
ejpam-6969	123	28	)	)	PUNCT
ejpam-6969	123	29	,	,	PUNCT
ejpam-6969	123	30	l	l	NOUN
ejpam-6969	123	31	,	,	PUNCT
ejpam-6969	123	32	f	f	PROPN
ejpam-6969	123	33	=	=	SYM
ejpam-6969	123	34	1	1	NUM
ejpam-6969	123	35	,	,	PUNCT
ejpam-6969	123	36	2	2	NUM
ejpam-6969	123	37	,	,	PUNCT
ejpam-6969	123	38	.	.	PUNCT
ejpam-6969	123	39	.	.	PUNCT
ejpam-6969	123	40	.	.	PUNCT
ejpam-6969	124	1	,	,	PUNCT
ejpam-6969	124	2	n.	n.	NOUN
ejpam-6969	124	3	(	(	PUNCT
ejpam-6969	124	4	11	11	NUM
ejpam-6969	124	5	)	)	PUNCT
ejpam-6969	124	6	m.	m.	NOUN
ejpam-6969	124	7	h.	h.	PROPN
ejpam-6969	124	8	ahmed	ahmed	PROPN
ejpam-6969	124	9	,	,	PUNCT
ejpam-6969	124	10	a.	a.	NOUN
ejpam-6969	124	11	m.	m.	PROPN
ejpam-6969	124	12	aljabri	aljabri	PROPN
ejpam-6969	124	13	/	/	SYM
ejpam-6969	124	14	eur	eur	PROPN
ejpam-6969	124	15	.	.	PUNCT
ejpam-6969	125	1	j.	j.	PROPN
ejpam-6969	125	2	pure	pure	PROPN
ejpam-6969	125	3	appl	appl	PROPN
ejpam-6969	125	4	.	.	PROPN
ejpam-6969	125	5	math	math	PROPN
ejpam-6969	125	6	,	,	PUNCT
ejpam-6969	125	7	18	18	NUM
ejpam-6969	125	8	(	(	PUNCT
ejpam-6969	125	9	4	4	NUM
ejpam-6969	125	10	)	)	PUNCT
ejpam-6969	125	11	(	(	PUNCT
ejpam-6969	125	12	2025	2025	NUM
ejpam-6969	125	13	)	)	PUNCT
ejpam-6969	125	14	,	,	PUNCT
ejpam-6969	125	15	6969	6969	NUM
ejpam-6969	125	16	7	7	NUM
ejpam-6969	125	17	of	of	ADP
ejpam-6969	125	18	16	16	NUM
ejpam-6969	125	19	equation	equation	NOUN
ejpam-6969	125	20	(	(	PUNCT
ejpam-6969	125	21	10	10	NUM
ejpam-6969	125	22	)	)	PUNCT
ejpam-6969	125	23	can	can	AUX
ejpam-6969	125	24	be	be	AUX
ejpam-6969	125	25	represented	represent	VERB
ejpam-6969	125	26	as	as	ADP
ejpam-6969	125	27	n−1∑	n−1∑	PROPN
ejpam-6969	125	28	i=0	i=0	PROPN
ejpam-6969	125	29	n−1∑	n−1∑	NUM
ejpam-6969	125	30	j=0	j=0	VERB
ejpam-6969	125	31	aijbi(χl	aijbi(χl	ADV
ejpam-6969	125	32	)	)	PUNCT
ejpam-6969	125	33	bj(tf	bj(tf	PROPN
ejpam-6969	125	34	)	)	PUNCT
ejpam-6969	126	1	=	=	PUNCT
ejpam-6969	127	1	f(χ	f(χ	PROPN
ejpam-6969	127	2	l	l	PROPN
ejpam-6969	127	3	,	,	PUNCT
ejpam-6969	127	4	t	t	PROPN
ejpam-6969	127	5	f	f	PROPN
ejpam-6969	127	6	)	)	PUNCT
ejpam-6969	128	1	+	+	NOUN
ejpam-6969	128	2	λ	λ	X
ejpam-6969	128	3	∫	∫	PROPN
ejpam-6969	128	4	t	t	PROPN
ejpam-6969	128	5	f	f	PROPN
ejpam-6969	128	6	0	0	NUM
ejpam-6969	128	7	∫	∫	PROPN
ejpam-6969	128	8	χ	χ	PRON
ejpam-6969	128	9	l	l	NOUN
ejpam-6969	128	10	0	0	PUNCT
ejpam-6969	128	11	k	k	ADJ
ejpam-6969	128	12	χ	χ	PROPN
ejpam-6969	128	13	l	l	NOUN
ejpam-6969	128	14	,	,	PUNCT
ejpam-6969	128	15	t	t	PROPN
ejpam-6969	128	16	f	f	PROPN
ejpam-6969	128	17	,	,	PUNCT
ejpam-6969	128	18	s	s	PROPN
ejpam-6969	128	19	,	,	PUNCT
ejpam-6969	128	20	y	y	PROPN
ejpam-6969	128	21	,	,	PUNCT
ejpam-6969	128	22	n−1∑	n−1∑	PROPN
ejpam-6969	128	23	i=0	i=0	PROPN
ejpam-6969	128	24	n−1∑	n−1∑	NUM
ejpam-6969	128	25	j=0	j=0	PROPN
ejpam-6969	128	26	aijbi(s)bj(y	aijbi(s)bj(y	PROPN
ejpam-6969	128	27	)	)	PUNCT
ejpam-6969	128	28			PROPN
ejpam-6969	128	29	ds	ds	ADJ
ejpam-6969	128	30	dy	dy	NOUN
ejpam-6969	128	31	.	.	PUNCT
ejpam-6969	129	1	(	(	PUNCT
ejpam-6969	129	2	12	12	NUM
ejpam-6969	129	3	)	)	PUNCT
ejpam-6969	129	4	by	by	ADP
ejpam-6969	129	5	substituting	substitute	VERB
ejpam-6969	129	6	the	the	DET
ejpam-6969	129	7	collocation	collocation	NOUN
ejpam-6969	129	8	points	point	NOUN
ejpam-6969	129	9	defined	define	VERB
ejpam-6969	129	10	in	in	ADP
ejpam-6969	129	11	(	(	PUNCT
ejpam-6969	129	12	11	11	NUM
ejpam-6969	129	13	)	)	PUNCT
ejpam-6969	129	14	into	into	ADP
ejpam-6969	129	15	equation	equation	NOUN
ejpam-6969	129	16	(	(	PUNCT
ejpam-6969	129	17	10	10	NUM
ejpam-6969	129	18	)	)	PUNCT
ejpam-6969	129	19	,	,	PUNCT
ejpam-6969	129	20	we	we	PRON
ejpam-6969	129	21	obtain	obtain	VERB
ejpam-6969	129	22	a	a	DET
ejpam-6969	129	23	system	system	NOUN
ejpam-6969	129	24	of	of	ADP
ejpam-6969	129	25	nonlinear	nonlinear	ADJ
ejpam-6969	129	26	algebraic	algebraic	ADJ
ejpam-6969	129	27	equations	equation	NOUN
ejpam-6969	129	28	containing	contain	VERB
ejpam-6969	129	29	n2	n2	ADJ
ejpam-6969	129	30	unknown	unknown	ADJ
ejpam-6969	129	31	coefficients	coefficient	NOUN
ejpam-6969	129	32	aij	aij	PROPN
ejpam-6969	129	33	,	,	PUNCT
ejpam-6969	129	34	with	with	ADP
ejpam-6969	129	35	indices	index	NOUN
ejpam-6969	129	36	i	i	PRON
ejpam-6969	129	37	,	,	PUNCT
ejpam-6969	129	38	j	j	PROPN
ejpam-6969	129	39	=	=	SYM
ejpam-6969	129	40	0	0	NUM
ejpam-6969	129	41	,	,	PUNCT
ejpam-6969	129	42	1	1	NUM
ejpam-6969	129	43	,	,	PUNCT
ejpam-6969	129	44	...	...	PUNCT
ejpam-6969	129	45	,	,	PUNCT
ejpam-6969	129	46	n	n	CCONJ
ejpam-6969	129	47	−	−	PROPN
ejpam-6969	129	48	1	1	NUM
ejpam-6969	129	49	.	.	PUNCT
ejpam-6969	130	1	in	in	ADP
ejpam-6969	130	2	this	this	DET
ejpam-6969	130	3	study	study	NOUN
ejpam-6969	130	4	,	,	PUNCT
ejpam-6969	130	5	n	n	PROPN
ejpam-6969	130	6	=	=	NUM
ejpam-6969	130	7	6	6	NUM
ejpam-6969	130	8	was	be	AUX
ejpam-6969	130	9	chosen	choose	VERB
ejpam-6969	130	10	as	as	SCONJ
ejpam-6969	130	11	it	it	PRON
ejpam-6969	130	12	provides	provide	VERB
ejpam-6969	130	13	sufficient	sufficient	ADJ
ejpam-6969	130	14	accuracy	accuracy	NOUN
ejpam-6969	130	15	while	while	SCONJ
ejpam-6969	130	16	keeping	keep	VERB
ejpam-6969	130	17	the	the	DET
ejpam-6969	130	18	computational	computational	ADJ
ejpam-6969	130	19	cost	cost	NOUN
ejpam-6969	130	20	reasonable	reasonable	ADJ
ejpam-6969	130	21	.	.	PUNCT
ejpam-6969	131	1	all	all	DET
ejpam-6969	131	2	double	double	ADJ
ejpam-6969	131	3	integrals	integral	NOUN
ejpam-6969	131	4	,	,	PUNCT
ejpam-6969	131	5	including	include	VERB
ejpam-6969	131	6	the	the	DET
ejpam-6969	131	7	nonlinear	nonlinear	ADJ
ejpam-6969	131	8	terms	term	NOUN
ejpam-6969	131	9	containing	contain	VERB
ejpam-6969	131	10	the	the	DET
ejpam-6969	131	11	kernel	kernel	PROPN
ejpam-6969	131	12	k	k	PROPN
ejpam-6969	131	13	,	,	PUNCT
ejpam-6969	131	14	are	be	AUX
ejpam-6969	131	15	numerically	numerically	ADV
ejpam-6969	131	16	evaluated	evaluate	VERB
ejpam-6969	131	17	using	use	VERB
ejpam-6969	131	18	matlab	matlab	PROPN
ejpam-6969	131	19	’s	’s	PART
ejpam-6969	131	20	integral2	integral2	PROPN
ejpam-6969	131	21	function	function	NOUN
ejpam-6969	131	22	(	(	PUNCT
ejpam-6969	131	23	adaptive	adaptive	ADJ
ejpam-6969	131	24	quadrature	quadrature	NOUN
ejpam-6969	131	25	method	method	NOUN
ejpam-6969	131	26	)	)	PUNCT
ejpam-6969	131	27	.	.	PUNCT
ejpam-6969	132	1	the	the	DET
ejpam-6969	132	2	resulting	result	VERB
ejpam-6969	132	3	nonlinear	nonlinear	ADJ
ejpam-6969	132	4	system	system	NOUN
ejpam-6969	132	5	is	be	AUX
ejpam-6969	132	6	solved	solve	VERB
ejpam-6969	132	7	iteratively	iteratively	ADV
ejpam-6969	132	8	using	use	VERB
ejpam-6969	132	9	the	the	DET
ejpam-6969	132	10	picard	picard	NOUN
ejpam-6969	132	11	iteration	iteration	NOUN
ejpam-6969	132	12	method	method	NOUN
ejpam-6969	132	13	with	with	ADP
ejpam-6969	132	14	a	a	DET
ejpam-6969	132	15	convergence	convergence	NOUN
ejpam-6969	132	16	tolerance	tolerance	NOUN
ejpam-6969	132	17	of	of	ADP
ejpam-6969	132	18	1×	1×	NUM
ejpam-6969	132	19	10−6	10−6	NUM
ejpam-6969	132	20	,	,	PUNCT
ejpam-6969	132	21	with	with	ADP
ejpam-6969	132	22	a	a	DET
ejpam-6969	132	23	maximum	maximum	ADJ
ejpam-6969	132	24	limit	limit	NOUN
ejpam-6969	132	25	of	of	ADP
ejpam-6969	132	26	10	10	NUM
ejpam-6969	132	27	iterations	iteration	NOUN
ejpam-6969	132	28	to	to	PART
ejpam-6969	132	29	ensure	ensure	VERB
ejpam-6969	132	30	numerical	numerical	ADJ
ejpam-6969	132	31	stability	stability	NOUN
ejpam-6969	132	32	,	,	PUNCT
ejpam-6969	132	33	leading	lead	VERB
ejpam-6969	132	34	to	to	ADP
ejpam-6969	132	35	the	the	DET
ejpam-6969	132	36	approximate	approximate	ADJ
ejpam-6969	132	37	solution	solution	NOUN
ejpam-6969	132	38	ũ(χ	ũ(χ	PROPN
ejpam-6969	132	39	,	,	PUNCT
ejpam-6969	132	40	t	t	PROPN
ejpam-6969	132	41	)	)	PUNCT
ejpam-6969	132	42	.	.	PUNCT
ejpam-6969	133	1	4.2	4.2	NUM
ejpam-6969	133	2	.	.	PUNCT
ejpam-6969	134	1	hermite	hermite	PROPN
ejpam-6969	134	2	galerkin	galerkin	PROPN
ejpam-6969	134	3	method	method	NOUN
ejpam-6969	134	4	assume	assume	VERB
ejpam-6969	134	5	that	that	SCONJ
ejpam-6969	134	6	ũ(χ	ũ(χ	PROPN
ejpam-6969	134	7	,	,	PUNCT
ejpam-6969	134	8	t	t	PROPN
ejpam-6969	134	9	)	)	PUNCT
ejpam-6969	134	10	is	be	AUX
ejpam-6969	134	11	an	an	DET
ejpam-6969	134	12	approximate	approximate	ADJ
ejpam-6969	134	13	solution	solution	NOUN
ejpam-6969	134	14	of	of	ADP
ejpam-6969	134	15	the	the	DET
ejpam-6969	134	16	two	two	NUM
ejpam-6969	134	17	-	-	PUNCT
ejpam-6969	134	18	dimensional	dimensional	ADJ
ejpam-6969	134	19	volterra	volterra	NOUN
ejpam-6969	134	20	integral	integral	ADJ
ejpam-6969	134	21	equation	equation	NOUN
ejpam-6969	134	22	(	(	PUNCT
ejpam-6969	134	23	1	1	NUM
ejpam-6969	134	24	)	)	PUNCT
ejpam-6969	134	25	.	.	PUNCT
ejpam-6969	135	1	the	the	DET
ejpam-6969	135	2	galerkin	galerkin	ADJ
ejpam-6969	135	3	method	method	NOUN
ejpam-6969	135	4	with	with	ADP
ejpam-6969	135	5	hermite	hermite	ADJ
ejpam-6969	135	6	polynomials	polynomial	NOUN
ejpam-6969	135	7	is	be	AUX
ejpam-6969	135	8	applied	apply	VERB
ejpam-6969	135	9	,	,	PUNCT
ejpam-6969	135	10	yielding	yield	VERB
ejpam-6969	135	11	the	the	DET
ejpam-6969	135	12	following	follow	VERB
ejpam-6969	135	13	approximation	approximation	NOUN
ejpam-6969	135	14	ũ(χ	ũ(χ	PROPN
ejpam-6969	135	15	,	,	PUNCT
ejpam-6969	135	16	t	t	PROPN
ejpam-6969	135	17	)	)	PUNCT
ejpam-6969	136	1	≈	≈	PROPN
ejpam-6969	136	2	n−1∑	n−1∑	PROPN
ejpam-6969	136	3	i=0	i=0	PROPN
ejpam-6969	136	4	n−1∑	n−1∑	NUM
ejpam-6969	136	5	j=0	j=0	PROPN
ejpam-6969	136	6	cijhi(χ)hj(t	cijhi(χ)hj(t	PROPN
ejpam-6969	136	7	)	)	PUNCT
ejpam-6969	136	8	,	,	PUNCT
ejpam-6969	136	9	(	(	PUNCT
ejpam-6969	136	10	13	13	NUM
ejpam-6969	136	11	)	)	PUNCT
ejpam-6969	136	12	where	where	SCONJ
ejpam-6969	136	13	the	the	DET
ejpam-6969	136	14	hermite	hermite	ADJ
ejpam-6969	136	15	polynomials	polynomial	NOUN
ejpam-6969	136	16	are	be	AUX
ejpam-6969	136	17	hi(χ	hi(χ	NOUN
ejpam-6969	136	18	)	)	PUNCT
ejpam-6969	136	19	and	and	CCONJ
ejpam-6969	136	20	hj(t	hj(t	NUM
ejpam-6969	136	21	)	)	PUNCT
ejpam-6969	136	22	and	and	CCONJ
ejpam-6969	136	23	the	the	DET
ejpam-6969	136	24	unknown	unknown	ADJ
ejpam-6969	136	25	hermite	hermite	ADJ
ejpam-6969	136	26	coefficients	coefficient	NOUN
ejpam-6969	136	27	cij	cij	PROPN
ejpam-6969	136	28	are	be	AUX
ejpam-6969	136	29	to	to	PART
ejpam-6969	136	30	be	be	AUX
ejpam-6969	136	31	determined	determine	VERB
ejpam-6969	136	32	.	.	PUNCT
ejpam-6969	137	1	from	from	ADP
ejpam-6969	137	2	the	the	DET
ejpam-6969	137	3	right	right	ADJ
ejpam-6969	137	4	-	-	PUNCT
ejpam-6969	137	5	hand	hand	NOUN
ejpam-6969	137	6	side	side	NOUN
ejpam-6969	137	7	of	of	ADP
ejpam-6969	137	8	equation	equation	NOUN
ejpam-6969	137	9	(	(	PUNCT
ejpam-6969	137	10	13	13	NUM
ejpam-6969	137	11	)	)	PUNCT
ejpam-6969	137	12	and	and	CCONJ
ejpam-6969	137	13	substituting	substitute	VERB
ejpam-6969	137	14	into	into	ADP
ejpam-6969	137	15	equation	equation	NOUN
ejpam-6969	137	16	(	(	PUNCT
ejpam-6969	137	17	1	1	NUM
ejpam-6969	137	18	)	)	PUNCT
ejpam-6969	137	19	,	,	PUNCT
ejpam-6969	137	20	we	we	PRON
ejpam-6969	137	21	obtain	obtain	VERB
ejpam-6969	137	22	n−1∑	n−1∑	NOUN
ejpam-6969	138	1	i=0	i=0	PROPN
ejpam-6969	138	2	n−1∑	n−1∑	PROPN
ejpam-6969	138	3	j=0	j=0	PROPN
ejpam-6969	138	4	cijhi(χ)hj(t	cijhi(χ)hj(t	PROPN
ejpam-6969	138	5	)	)	PUNCT
ejpam-6969	138	6	=	=	SYM
ejpam-6969	138	7	f(χ	f(χ	PROPN
ejpam-6969	138	8	,	,	PUNCT
ejpam-6969	138	9	t	t	PROPN
ejpam-6969	138	10	)	)	PUNCT
ejpam-6969	138	11	+	+	X
ejpam-6969	138	12	η(χ	η(χ	PROPN
ejpam-6969	138	13	,	,	PUNCT
ejpam-6969	138	14	t	t	PROPN
ejpam-6969	138	15	)	)	PUNCT
ejpam-6969	138	16	,	,	PUNCT
ejpam-6969	138	17	(	(	PUNCT
ejpam-6969	138	18	14	14	NUM
ejpam-6969	138	19	)	)	PUNCT
ejpam-6969	138	20	where	where	SCONJ
ejpam-6969	138	21	η(χ	η(χ	PROPN
ejpam-6969	138	22	,	,	PUNCT
ejpam-6969	138	23	t	t	PROPN
ejpam-6969	138	24	)	)	PUNCT
ejpam-6969	138	25	=	=	PUNCT
ejpam-6969	139	1	λ	λ	X
ejpam-6969	139	2	∫	∫	PROPN
ejpam-6969	139	3	t	t	PROPN
ejpam-6969	139	4	0	0	NUM
ejpam-6969	139	5	∫	∫	PROPN
ejpam-6969	140	1	χ	χ	X
ejpam-6969	140	2	0	0	NUM
ejpam-6969	140	3	k	k	PROPN
ejpam-6969	140	4	χ	χ	PROPN
ejpam-6969	140	5	,	,	PUNCT
ejpam-6969	140	6	t	t	PROPN
ejpam-6969	140	7	,	,	PUNCT
ejpam-6969	140	8	s	s	PROPN
ejpam-6969	140	9	,	,	PUNCT
ejpam-6969	140	10	y	y	PROPN
ejpam-6969	140	11	,	,	PUNCT
ejpam-6969	140	12	n−1∑	n−1∑	PROPN
ejpam-6969	140	13	i=0	i=0	PROPN
ejpam-6969	140	14	n−1∑	n−1∑	NUM
ejpam-6969	140	15	j=0	j=0	PROPN
ejpam-6969	140	16	cijhi(s)hj(y	cijhi(s)hj(y	PROPN
ejpam-6969	140	17	)	)	PUNCT
ejpam-6969	140	18			PROPN
ejpam-6969	140	19	ds	ds	ADJ
ejpam-6969	140	20	dy	dy	NOUN
ejpam-6969	140	21	.	.	PUNCT
ejpam-6969	140	22	multiplying	multiply	VERB
ejpam-6969	140	23	equation	equation	NOUN
ejpam-6969	140	24	(	(	PUNCT
ejpam-6969	140	25	14	14	NUM
ejpam-6969	140	26	)	)	PUNCT
ejpam-6969	140	27	by	by	ADP
ejpam-6969	140	28	hb(χ)hr(t	hb(χ)hr(t	NOUN
ejpam-6969	140	29	)	)	PUNCT
ejpam-6969	140	30	,	,	PUNCT
ejpam-6969	140	31	also	also	ADV
ejpam-6969	140	32	integrating	integrate	VERB
ejpam-6969	140	33	both	both	DET
ejpam-6969	140	34	sides	side	NOUN
ejpam-6969	140	35	of	of	ADP
ejpam-6969	140	36	equation	equation	NOUN
ejpam-6969	140	37	(	(	PUNCT
ejpam-6969	140	38	14	14	NUM
ejpam-6969	140	39	)	)	PUNCT
ejpam-6969	140	40	with	with	ADP
ejpam-6969	140	41	respect	respect	NOUN
ejpam-6969	140	42	to	to	ADP
ejpam-6969	140	43	χ	χ	NOUN
ejpam-6969	140	44	and	and	CCONJ
ejpam-6969	140	45	t	t	PROPN
ejpam-6969	140	46	over	over	ADP
ejpam-6969	140	47	[	[	X
ejpam-6969	140	48	0	0	NUM
ejpam-6969	140	49	,	,	PUNCT
ejpam-6969	140	50	1	1	NUM
ejpam-6969	140	51	]	]	PUNCT
ejpam-6969	140	52	,	,	PUNCT
ejpam-6969	140	53	for	for	ADP
ejpam-6969	140	54	b	b	NOUN
ejpam-6969	140	55	,	,	PUNCT
ejpam-6969	140	56	r	r	NOUN
ejpam-6969	140	57	=	=	SYM
ejpam-6969	140	58	0	0	NUM
ejpam-6969	140	59	,	,	PUNCT
ejpam-6969	140	60	1	1	NUM
ejpam-6969	140	61	,	,	PUNCT
ejpam-6969	140	62	.	.	PUNCT
ejpam-6969	140	63	.	.	PUNCT
ejpam-6969	140	64	.	.	PUNCT
ejpam-6969	141	1	,	,	PUNCT
ejpam-6969	141	2	n	n	CCONJ
ejpam-6969	141	3	−	−	PROPN
ejpam-6969	141	4	1	1	NUM
ejpam-6969	141	5	,	,	PUNCT
ejpam-6969	141	6	we	we	PRON
ejpam-6969	141	7	have	have	VERB
ejpam-6969	141	8	the	the	DET
ejpam-6969	141	9	following	following	NOUN
ejpam-6969	141	10	.	.	PUNCT
ejpam-6969	142	1	n−1∑	n−1∑	NUM
ejpam-6969	142	2	i=0	i=0	PROPN
ejpam-6969	142	3	n−1∑	n−1∑	NUM
ejpam-6969	142	4	j=0	j=0	PROPN
ejpam-6969	142	5	cij	cij	PROPN
ejpam-6969	142	6	∫	∫	PROPN
ejpam-6969	142	7	1	1	NUM
ejpam-6969	142	8	0	0	NUM
ejpam-6969	142	9	∫	∫	PROPN
ejpam-6969	142	10	1	1	NUM
ejpam-6969	142	11	0	0	NUM
ejpam-6969	142	12	hi(χ)hj(t)hb(χ)hr(t	hi(χ)hj(t)hb(χ)hr(t	PROPN
ejpam-6969	142	13	)	)	PUNCT
ejpam-6969	142	14	dχ	dχ	NOUN
ejpam-6969	142	15	dt	dt	NOUN
ejpam-6969	143	1	=	=	SYM
ejpam-6969	143	2	∫	∫	PROPN
ejpam-6969	143	3	1	1	NUM
ejpam-6969	143	4	0	0	NUM
ejpam-6969	143	5	∫	∫	PROPN
ejpam-6969	143	6	1	1	NUM
ejpam-6969	143	7	0	0	NUM
ejpam-6969	143	8	f(χ	f(χ	PROPN
ejpam-6969	143	9	,	,	PUNCT
ejpam-6969	143	10	t)hb(χ)hr(t	t)hb(χ)hr(t	NOUN
ejpam-6969	143	11	)	)	PUNCT
ejpam-6969	143	12	dχ	dχ	NOUN
ejpam-6969	143	13	dt	dt	NOUN
ejpam-6969	144	1	+	+	CCONJ
ejpam-6969	144	2	∫	∫	PROPN
ejpam-6969	144	3	1	1	NUM
ejpam-6969	144	4	0	0	NUM
ejpam-6969	144	5	∫	∫	PROPN
ejpam-6969	144	6	1	1	NUM
ejpam-6969	144	7	0	0	NUM
ejpam-6969	144	8	η(χ	η(χ	NUM
ejpam-6969	144	9	,	,	PUNCT
ejpam-6969	144	10	t)hb(χ)hr(t	t)hb(χ)hr(t	NOUN
ejpam-6969	144	11	)	)	PUNCT
ejpam-6969	144	12	dχ	dχ	NOUN
ejpam-6969	144	13	dt	dt	PROPN
ejpam-6969	144	14	.	.	PUNCT
ejpam-6969	145	1	(	(	PUNCT
ejpam-6969	145	2	15	15	NUM
ejpam-6969	145	3	)	)	PUNCT
ejpam-6969	145	4	m.	m.	NOUN
ejpam-6969	145	5	h.	h.	PROPN
ejpam-6969	145	6	ahmed	ahmed	PROPN
ejpam-6969	145	7	,	,	PUNCT
ejpam-6969	145	8	a.	a.	NOUN
ejpam-6969	145	9	m.	m.	PROPN
ejpam-6969	145	10	aljabri	aljabri	PROPN
ejpam-6969	145	11	/	/	SYM
ejpam-6969	145	12	eur	eur	PROPN
ejpam-6969	145	13	.	.	PUNCT
ejpam-6969	146	1	j.	j.	PROPN
ejpam-6969	146	2	pure	pure	PROPN
ejpam-6969	146	3	appl	appl	PROPN
ejpam-6969	146	4	.	.	PROPN
ejpam-6969	146	5	math	math	PROPN
ejpam-6969	146	6	,	,	PUNCT
ejpam-6969	146	7	18	18	NUM
ejpam-6969	146	8	(	(	PUNCT
ejpam-6969	146	9	4	4	NUM
ejpam-6969	146	10	)	)	PUNCT
ejpam-6969	146	11	(	(	PUNCT
ejpam-6969	146	12	2025	2025	NUM
ejpam-6969	146	13	)	)	PUNCT
ejpam-6969	146	14	,	,	PUNCT
ejpam-6969	146	15	6969	6969	NUM
ejpam-6969	146	16	8	8	NUM
ejpam-6969	146	17	of	of	ADP
ejpam-6969	146	18	16	16	NUM
ejpam-6969	146	19	by	by	ADP
ejpam-6969	146	20	substituting	substitute	VERB
ejpam-6969	146	21	all	all	DET
ejpam-6969	146	22	combinations	combination	NOUN
ejpam-6969	146	23	of	of	ADP
ejpam-6969	146	24	b	b	NOUN
ejpam-6969	146	25	,	,	PUNCT
ejpam-6969	146	26	r	r	NOUN
ejpam-6969	146	27	=	=	SYM
ejpam-6969	146	28	0	0	NUM
ejpam-6969	146	29	,	,	PUNCT
ejpam-6969	146	30	1	1	NUM
ejpam-6969	146	31	,	,	PUNCT
ejpam-6969	146	32	.	.	PUNCT
ejpam-6969	146	33	.	.	PUNCT
ejpam-6969	147	1	.	.	PUNCT
ejpam-6969	148	1	,	,	PUNCT
ejpam-6969	149	1	n	n	CCONJ
ejpam-6969	149	2	−	−	PROPN
ejpam-6969	149	3	1	1	NUM
ejpam-6969	149	4	into	into	ADP
ejpam-6969	149	5	equation	equation	NOUN
ejpam-6969	149	6	(	(	PUNCT
ejpam-6969	149	7	15	15	NUM
ejpam-6969	149	8	)	)	PUNCT
ejpam-6969	149	9	,	,	PUNCT
ejpam-6969	149	10	we	we	PRON
ejpam-6969	149	11	obtain	obtain	VERB
ejpam-6969	149	12	a	a	DET
ejpam-6969	149	13	system	system	NOUN
ejpam-6969	149	14	of	of	ADP
ejpam-6969	149	15	n2	n2	ADJ
ejpam-6969	149	16	nonlinear	nonlinear	ADJ
ejpam-6969	149	17	algebraic	algebraic	ADJ
ejpam-6969	149	18	equations	equation	NOUN
ejpam-6969	149	19	involving	involve	VERB
ejpam-6969	149	20	the	the	DET
ejpam-6969	149	21	unknown	unknown	ADJ
ejpam-6969	149	22	hermite	hermite	ADJ
ejpam-6969	149	23	coefficients	coefficient	VERB
ejpam-6969	149	24	cij	cij	PROPN
ejpam-6969	149	25	.	.	PUNCT
ejpam-6969	150	1	in	in	ADP
ejpam-6969	150	2	this	this	DET
ejpam-6969	150	3	work	work	NOUN
ejpam-6969	150	4	,	,	PUNCT
ejpam-6969	150	5	n	n	NOUN
ejpam-6969	150	6	=	=	NUM
ejpam-6969	150	7	6	6	NUM
ejpam-6969	150	8	is	be	AUX
ejpam-6969	150	9	chosen	choose	VERB
ejpam-6969	150	10	to	to	PART
ejpam-6969	150	11	balance	balance	VERB
ejpam-6969	150	12	computational	computational	ADJ
ejpam-6969	150	13	efficiency	efficiency	NOUN
ejpam-6969	150	14	and	and	CCONJ
ejpam-6969	150	15	accuracy	accuracy	NOUN
ejpam-6969	150	16	.	.	PUNCT
ejpam-6969	151	1	all	all	DET
ejpam-6969	151	2	double	double	ADJ
ejpam-6969	151	3	integrals	integral	NOUN
ejpam-6969	151	4	appearing	appear	VERB
ejpam-6969	151	5	in	in	ADP
ejpam-6969	151	6	the	the	DET
ejpam-6969	151	7	formulation	formulation	NOUN
ejpam-6969	151	8	are	be	AUX
ejpam-6969	151	9	numerically	numerically	ADV
ejpam-6969	151	10	evaluated	evaluate	VERB
ejpam-6969	151	11	using	use	VERB
ejpam-6969	151	12	matlab	matlab	PROPN
ejpam-6969	151	13	’s	’s	PART
ejpam-6969	151	14	integral2	integral2	PROPN
ejpam-6969	151	15	function	function	NOUN
ejpam-6969	151	16	.	.	PUNCT
ejpam-6969	152	1	the	the	DET
ejpam-6969	152	2	resulting	result	VERB
ejpam-6969	152	3	nonlinear	nonlinear	ADJ
ejpam-6969	152	4	system	system	NOUN
ejpam-6969	152	5	is	be	AUX
ejpam-6969	152	6	solved	solve	VERB
ejpam-6969	152	7	iteratively	iteratively	ADV
ejpam-6969	152	8	using	use	VERB
ejpam-6969	152	9	the	the	DET
ejpam-6969	152	10	picard	picard	NOUN
ejpam-6969	152	11	iteration	iteration	NOUN
ejpam-6969	152	12	method	method	NOUN
ejpam-6969	152	13	with	with	ADP
ejpam-6969	152	14	a	a	DET
ejpam-6969	152	15	convergence	convergence	NOUN
ejpam-6969	152	16	tolerance	tolerance	NOUN
ejpam-6969	152	17	of	of	ADP
ejpam-6969	152	18	1	1	NUM
ejpam-6969	152	19	×	×	NOUN
ejpam-6969	152	20	10−6	10−6	NUM
ejpam-6969	152	21	,	,	PUNCT
ejpam-6969	152	22	leading	lead	VERB
ejpam-6969	152	23	to	to	ADP
ejpam-6969	152	24	the	the	DET
ejpam-6969	152	25	approximate	approximate	ADJ
ejpam-6969	152	26	solution	solution	NOUN
ejpam-6969	152	27	ũ(χ	ũ(χ	PROPN
ejpam-6969	152	28	,	,	PUNCT
ejpam-6969	152	29	t	t	PROPN
ejpam-6969	152	30	)	)	PUNCT
ejpam-6969	152	31	.	.	PUNCT
ejpam-6969	153	1	5	5	X
ejpam-6969	153	2	.	.	X
ejpam-6969	153	3	numerical	numerical	ADJ
ejpam-6969	153	4	examples	example	NOUN
ejpam-6969	153	5	to	to	PART
ejpam-6969	153	6	illustrate	illustrate	VERB
ejpam-6969	153	7	the	the	DET
ejpam-6969	153	8	previously	previously	ADV
ejpam-6969	153	9	described	describe	VERB
ejpam-6969	153	10	methods	method	NOUN
ejpam-6969	153	11	,	,	PUNCT
ejpam-6969	153	12	several	several	ADJ
ejpam-6969	153	13	numerical	numerical	ADJ
ejpam-6969	153	14	examples	example	NOUN
ejpam-6969	153	15	of	of	ADP
ejpam-6969	153	16	the	the	DET
ejpam-6969	153	17	twodimensional	twodimensional	PROPN
ejpam-6969	153	18	nonlinear	nonlinear	PROPN
ejpam-6969	153	19	volterra	volterra	PROPN
ejpam-6969	153	20	integral	integral	ADJ
ejpam-6969	153	21	equation	equation	NOUN
ejpam-6969	153	22	(	(	PUNCT
ejpam-6969	153	23	2d	2d	NOUN
ejpam-6969	153	24	-	-	PUNCT
ejpam-6969	153	25	nvie	nvie	NOUN
ejpam-6969	153	26	)	)	PUNCT
ejpam-6969	153	27	are	be	AUX
ejpam-6969	153	28	provided	provide	VERB
ejpam-6969	153	29	.	.	PUNCT
ejpam-6969	154	1	the	the	DET
ejpam-6969	154	2	results	result	NOUN
ejpam-6969	154	3	were	be	AUX
ejpam-6969	154	4	obtained	obtain	VERB
ejpam-6969	154	5	using	use	VERB
ejpam-6969	154	6	matlab	matlab	PROPN
ejpam-6969	154	7	r2025a	r2025a	PROPN
ejpam-6969	154	8	.	.	PROPN
ejpam-6969	154	9	example	example	NOUN
ejpam-6969	154	10	1	1	NUM
ejpam-6969	154	11	.	.	X
ejpam-6969	154	12	consider	consider	VERB
ejpam-6969	154	13	the	the	DET
ejpam-6969	154	14	following	follow	VERB
ejpam-6969	154	15	2d	2d	NOUN
ejpam-6969	154	16	-	-	PUNCT
ejpam-6969	154	17	nvie	nvie	NOUN
ejpam-6969	154	18	[	[	X
ejpam-6969	154	19	8	8	NUM
ejpam-6969	154	20	,	,	PUNCT
ejpam-6969	154	21	28	28	NUM
ejpam-6969	154	22	]	]	PUNCT
ejpam-6969	154	23	:	:	PUNCT
ejpam-6969	154	24	u(χ	u(χ	PROPN
ejpam-6969	154	25	,	,	PUNCT
ejpam-6969	154	26	t	t	PROPN
ejpam-6969	154	27	)	)	PUNCT
ejpam-6969	155	1	=	=	SYM
ejpam-6969	155	2	f(χ	f(χ	PROPN
ejpam-6969	155	3	,	,	PUNCT
ejpam-6969	155	4	t	t	PROPN
ejpam-6969	155	5	)	)	PUNCT
ejpam-6969	156	1	+	+	CCONJ
ejpam-6969	157	1	∫	∫	PROPN
ejpam-6969	157	2	t	t	PROPN
ejpam-6969	157	3	0	0	NUM
ejpam-6969	157	4	∫	∫	PROPN
ejpam-6969	157	5	χ	χ	X
ejpam-6969	157	6	0	0	NUM
ejpam-6969	157	7	(	(	PUNCT
ejpam-6969	157	8	χs2	χs2	NOUN
ejpam-6969	157	9	+	+	CCONJ
ejpam-6969	157	10	cos	cos	PROPN
ejpam-6969	157	11	y)u2(s	y)u2(s	PROPN
ejpam-6969	157	12	,	,	PUNCT
ejpam-6969	157	13	y	y	NOUN
ejpam-6969	157	14	)	)	PUNCT
ejpam-6969	157	15	ds	ds	NOUN
ejpam-6969	157	16	dy	dy	NOUN
ejpam-6969	157	17	χ	χ	NOUN
ejpam-6969	157	18	,	,	PUNCT
ejpam-6969	157	19	t	t	PROPN
ejpam-6969	157	20	∈	∈	PROPN
ejpam-6969	158	1	[	[	X
ejpam-6969	158	2	0	0	NUM
ejpam-6969	158	3	,	,	PUNCT
ejpam-6969	158	4	1	1	NUM
ejpam-6969	158	5	]	]	PUNCT
ejpam-6969	158	6	,	,	PUNCT
ejpam-6969	158	7	(	(	PUNCT
ejpam-6969	158	8	16	16	NUM
ejpam-6969	158	9	)	)	PUNCT
ejpam-6969	159	1	where	where	SCONJ
ejpam-6969	159	2	f(χ	f(χ	PROPN
ejpam-6969	159	3	,	,	PUNCT
ejpam-6969	159	4	t	t	PROPN
ejpam-6969	159	5	)	)	PUNCT
ejpam-6969	159	6	=	=	SYM
ejpam-6969	159	7	χ	χ	DET
ejpam-6969	159	8	sin	sin	NOUN
ejpam-6969	159	9	t(1−	t(1−	VERB
ejpam-6969	159	10	1	1	NUM
ejpam-6969	159	11	9	9	NUM
ejpam-6969	159	12	χ2	χ2	PROPN
ejpam-6969	159	13	sin2	sin2	PROPN
ejpam-6969	159	14	t	t	PROPN
ejpam-6969	159	15	)	)	PUNCT
ejpam-6969	159	16	+	+	CCONJ
ejpam-6969	159	17	1	1	NUM
ejpam-6969	159	18	10	10	NUM
ejpam-6969	159	19	χ6	χ6	NOUN
ejpam-6969	159	20	(	(	PUNCT
ejpam-6969	159	21	1	1	NUM
ejpam-6969	159	22	2	2	NUM
ejpam-6969	159	23	sin	sin	NOUN
ejpam-6969	159	24	2t−	2t−	PROPN
ejpam-6969	159	25	t	t	NOUN
ejpam-6969	159	26	)	)	PUNCT
ejpam-6969	159	27	,	,	PUNCT
ejpam-6969	159	28	and	and	CCONJ
ejpam-6969	159	29	exact	exact	ADJ
ejpam-6969	159	30	solution	solution	NOUN
ejpam-6969	159	31	is	be	AUX
ejpam-6969	159	32	u(χ	u(χ	ADJ
ejpam-6969	159	33	,	,	PUNCT
ejpam-6969	159	34	t	t	PROPN
ejpam-6969	159	35	)	)	PUNCT
ejpam-6969	160	1	=	=	SYM
ejpam-6969	161	1	χ	χ	DET
ejpam-6969	161	2	sin	sin	NOUN
ejpam-6969	161	3	t.	t.	PROPN
ejpam-6969	161	4	the	the	DET
ejpam-6969	161	5	comparison	comparison	NOUN
ejpam-6969	161	6	of	of	ADP
ejpam-6969	161	7	absolute	absolute	ADJ
ejpam-6969	161	8	errors	error	NOUN
ejpam-6969	161	9	of	of	ADP
ejpam-6969	161	10	equation	equation	NOUN
ejpam-6969	161	11	(	(	PUNCT
ejpam-6969	161	12	16	16	NUM
ejpam-6969	161	13	)	)	PUNCT
ejpam-6969	161	14	for	for	ADP
ejpam-6969	161	15	various	various	ADJ
ejpam-6969	161	16	values	value	NOUN
ejpam-6969	161	17	of	of	ADP
ejpam-6969	161	18	χ	χ	PROPN
ejpam-6969	161	19	and	and	CCONJ
ejpam-6969	161	20	t	t	PROPN
ejpam-6969	161	21	,	,	PUNCT
ejpam-6969	161	22	with	with	ADP
ejpam-6969	161	23	using	use	VERB
ejpam-6969	161	24	bernoulli	bernoulli	NOUN
ejpam-6969	161	25	collocation	collocation	NOUN
ejpam-6969	161	26	(	(	PUNCT
ejpam-6969	161	27	bc	bc	PROPN
ejpam-6969	161	28	)	)	PUNCT
ejpam-6969	161	29	,	,	PUNCT
ejpam-6969	161	30	hermite	hermite	PROPN
ejpam-6969	161	31	–	–	PUNCT
ejpam-6969	161	32	galerkin	galerkin	PROPN
ejpam-6969	161	33	(	(	PUNCT
ejpam-6969	161	34	hg	hg	NOUN
ejpam-6969	161	35	)	)	PUNCT
ejpam-6969	161	36	methods	method	NOUN
ejpam-6969	161	37	with	with	ADP
ejpam-6969	161	38	n	n	NOUN
ejpam-6969	161	39	=	=	SYM
ejpam-6969	161	40	6	6	NUM
ejpam-6969	161	41	,	,	PUNCT
ejpam-6969	161	42	the	the	DET
ejpam-6969	161	43	reproducing	reproduce	VERB
ejpam-6969	161	44	kernel	kernel	NOUN
ejpam-6969	161	45	space	space	NOUN
ejpam-6969	161	46	[	[	X
ejpam-6969	161	47	8	8	NUM
ejpam-6969	161	48	]	]	PUNCT
ejpam-6969	161	49	with	with	ADP
ejpam-6969	161	50	n	n	NOUN
ejpam-6969	161	51	=	=	SYM
ejpam-6969	161	52	30	30	NUM
ejpam-6969	161	53	and	and	CCONJ
ejpam-6969	161	54	the	the	DET
ejpam-6969	161	55	taylor	taylor	PROPN
ejpam-6969	161	56	collocation	collocation	NOUN
ejpam-6969	161	57	method	method	NOUN
ejpam-6969	161	58	[	[	X
ejpam-6969	161	59	28	28	NUM
ejpam-6969	161	60	]	]	PUNCT
ejpam-6969	161	61	with	with	ADP
ejpam-6969	161	62	n	n	PROPN
ejpam-6969	161	63	=	=	SYM
ejpam-6969	161	64	64	64	NUM
ejpam-6969	161	65	,	,	PUNCT
ejpam-6969	161	66	is	be	AUX
ejpam-6969	161	67	presented	present	VERB
ejpam-6969	161	68	in	in	ADP
ejpam-6969	161	69	table	table	NOUN
ejpam-6969	161	70	(	(	PUNCT
ejpam-6969	161	71	1	1	NUM
ejpam-6969	161	72	)	)	PUNCT
ejpam-6969	161	73	.	.	PUNCT
ejpam-6969	162	1	figures	figure	NOUN
ejpam-6969	162	2	(	(	PUNCT
ejpam-6969	162	3	1	1	NUM
ejpam-6969	162	4	)	)	PUNCT
ejpam-6969	162	5	and	and	CCONJ
ejpam-6969	162	6	(	(	PUNCT
ejpam-6969	162	7	2	2	X
ejpam-6969	162	8	)	)	PUNCT
ejpam-6969	162	9	show	show	VERB
ejpam-6969	162	10	the	the	DET
ejpam-6969	162	11	absolute	absolute	ADJ
ejpam-6969	162	12	error	error	NOUN
ejpam-6969	162	13	distributions	distribution	NOUN
ejpam-6969	162	14	obtained	obtain	VERB
ejpam-6969	162	15	by	by	ADP
ejpam-6969	162	16	these	these	DET
ejpam-6969	162	17	methods	method	NOUN
ejpam-6969	162	18	.	.	PUNCT
ejpam-6969	163	1	table	table	NOUN
ejpam-6969	163	2	2	2	NUM
ejpam-6969	163	3	shows	show	VERB
ejpam-6969	163	4	the	the	DET
ejpam-6969	163	5	absolute	absolute	ADJ
ejpam-6969	163	6	errors	error	NOUN
ejpam-6969	163	7	of	of	ADP
ejpam-6969	163	8	equation	equation	NOUN
ejpam-6969	163	9	(	(	PUNCT
ejpam-6969	163	10	16	16	NUM
ejpam-6969	163	11	)	)	PUNCT
ejpam-6969	163	12	for	for	ADP
ejpam-6969	163	13	(	(	PUNCT
ejpam-6969	163	14	χ	χ	NOUN
ejpam-6969	163	15	,	,	PUNCT
ejpam-6969	163	16	t	t	PROPN
ejpam-6969	163	17	)	)	PUNCT
ejpam-6969	163	18	=	=	PUNCT
ejpam-6969	163	19	(	(	PUNCT
ejpam-6969	163	20	0.5	0.5	NUM
ejpam-6969	163	21	,	,	PUNCT
ejpam-6969	163	22	0.5	0.5	NUM
ejpam-6969	163	23	)	)	PUNCT
ejpam-6969	163	24	using	use	VERB
ejpam-6969	163	25	bc	bc	PROPN
ejpam-6969	163	26	and	and	CCONJ
ejpam-6969	163	27	hg	hg	NOUN
ejpam-6969	163	28	methods	method	NOUN
ejpam-6969	163	29	at	at	ADP
ejpam-6969	163	30	different	different	ADJ
ejpam-6969	163	31	n	n	NOUN
ejpam-6969	163	32	.	.	PUNCT
ejpam-6969	164	1	the	the	DET
ejpam-6969	164	2	errors	error	NOUN
ejpam-6969	164	3	decrease	decrease	VERB
ejpam-6969	164	4	as	as	ADP
ejpam-6969	164	5	n	n	DET
ejpam-6969	164	6	increases	increase	NOUN
ejpam-6969	164	7	,	,	PUNCT
ejpam-6969	164	8	with	with	ADP
ejpam-6969	164	9	bc	bc	PROPN
ejpam-6969	164	10	converging	converge	VERB
ejpam-6969	164	11	much	much	ADV
ejpam-6969	164	12	faster	fast	ADV
ejpam-6969	164	13	than	than	ADP
ejpam-6969	164	14	hg	hg	PROPN
ejpam-6969	164	15	due	due	ADP
ejpam-6969	164	16	to	to	ADP
ejpam-6969	164	17	the	the	DET
ejpam-6969	164	18	latter	latter	ADJ
ejpam-6969	164	19	’s	’s	PART
ejpam-6969	164	20	higher	high	ADJ
ejpam-6969	164	21	computational	computational	ADJ
ejpam-6969	164	22	cost	cost	NOUN
ejpam-6969	164	23	from	from	ADP
ejpam-6969	164	24	nested	nested	ADJ
ejpam-6969	164	25	integrals	integral	NOUN
ejpam-6969	164	26	.	.	PUNCT
ejpam-6969	165	1	figure	figure	NOUN
ejpam-6969	165	2	3	3	NUM
ejpam-6969	165	3	illustrates	illustrate	VERB
ejpam-6969	165	4	the	the	DET
ejpam-6969	165	5	same	same	ADJ
ejpam-6969	165	6	trend	trend	NOUN
ejpam-6969	165	7	visually	visually	ADV
ejpam-6969	165	8	.	.	PUNCT
ejpam-6969	166	1	therefore	therefore	ADV
ejpam-6969	166	2	,	,	PUNCT
ejpam-6969	166	3	n	n	PROPN
ejpam-6969	166	4	=	=	NUM
ejpam-6969	166	5	6	6	NUM
ejpam-6969	166	6	was	be	AUX
ejpam-6969	166	7	chosen	choose	VERB
ejpam-6969	166	8	as	as	ADP
ejpam-6969	166	9	a	a	DET
ejpam-6969	166	10	suitable	suitable	ADJ
ejpam-6969	166	11	compromise	compromise	NOUN
ejpam-6969	166	12	between	between	ADP
ejpam-6969	166	13	accuracy	accuracy	NOUN
ejpam-6969	166	14	and	and	CCONJ
ejpam-6969	166	15	efficiency	efficiency	NOUN
ejpam-6969	166	16	.	.	PUNCT
ejpam-6969	167	1	figure	figure	VERB
ejpam-6969	167	2	1	1	NUM
ejpam-6969	167	3	:	:	PUNCT
ejpam-6969	167	4	absolute	absolute	ADJ
ejpam-6969	167	5	error	error	NOUN
ejpam-6969	167	6	of	of	ADP
ejpam-6969	167	7	example	example	NOUN
ejpam-6969	167	8	1	1	NUM
ejpam-6969	167	9	by	by	ADP
ejpam-6969	167	10	the	the	DET
ejpam-6969	167	11	bc	bc	PROPN
ejpam-6969	167	12	method	method	NOUN
ejpam-6969	167	13	,	,	PUNCT
ejpam-6969	167	14	n	n	NOUN
ejpam-6969	167	15	=	=	SYM
ejpam-6969	167	16	6	6	NUM
ejpam-6969	167	17	.	.	PUNCT
ejpam-6969	167	18	figure	figure	NOUN
ejpam-6969	167	19	2	2	NUM
ejpam-6969	167	20	:	:	PUNCT
ejpam-6969	167	21	absolute	absolute	ADJ
ejpam-6969	167	22	error	error	NOUN
ejpam-6969	167	23	for	for	ADP
ejpam-6969	167	24	example	example	NOUN
ejpam-6969	167	25	1	1	NUM
ejpam-6969	167	26	by	by	ADP
ejpam-6969	167	27	hg	hg	PROPN
ejpam-6969	167	28	method	method	NOUN
ejpam-6969	167	29	,	,	PUNCT
ejpam-6969	167	30	n	n	NOUN
ejpam-6969	167	31	=	=	SYM
ejpam-6969	167	32	6	6	NUM
ejpam-6969	167	33	.	.	PUNCT
ejpam-6969	167	34	m.	m.	PROPN
ejpam-6969	167	35	h.	h.	PROPN
ejpam-6969	167	36	ahmed	ahmed	PROPN
ejpam-6969	167	37	,	,	PUNCT
ejpam-6969	167	38	a.	a.	NOUN
ejpam-6969	167	39	m.	m.	PROPN
ejpam-6969	167	40	aljabri	aljabri	PROPN
ejpam-6969	167	41	/	/	SYM
ejpam-6969	167	42	eur	eur	PROPN
ejpam-6969	167	43	.	.	PUNCT
ejpam-6969	168	1	j.	j.	PROPN
ejpam-6969	168	2	pure	pure	PROPN
ejpam-6969	168	3	appl	appl	PROPN
ejpam-6969	168	4	.	.	PROPN
ejpam-6969	168	5	math	math	PROPN
ejpam-6969	168	6	,	,	PUNCT
ejpam-6969	168	7	18	18	NUM
ejpam-6969	168	8	(	(	PUNCT
ejpam-6969	168	9	4	4	NUM
ejpam-6969	168	10	)	)	PUNCT
ejpam-6969	168	11	(	(	PUNCT
ejpam-6969	168	12	2025	2025	NUM
ejpam-6969	168	13	)	)	PUNCT
ejpam-6969	168	14	,	,	PUNCT
ejpam-6969	168	15	6969	6969	NUM
ejpam-6969	168	16	9	9	NUM
ejpam-6969	168	17	of	of	ADP
ejpam-6969	168	18	16	16	NUM
ejpam-6969	168	19	(	(	PUNCT
ejpam-6969	168	20	χ	χ	NOUN
ejpam-6969	168	21	,	,	PUNCT
ejpam-6969	168	22	t	t	PROPN
ejpam-6969	168	23	)	)	PUNCT
ejpam-6969	168	24	=	=	PUNCT
ejpam-6969	168	25	(	(	PUNCT
ejpam-6969	168	26	1	1	NUM
ejpam-6969	168	27	2p	2p	NUM
ejpam-6969	168	28	,	,	PUNCT
ejpam-6969	168	29	1	1	NUM
ejpam-6969	168	30	2p	2p	NUM
ejpam-6969	168	31	)	)	PUNCT
ejpam-6969	168	32	bernoulli	bernoulli	NOUN
ejpam-6969	168	33	collocation	collocation	NOUN
ejpam-6969	168	34	method	method	NOUN
ejpam-6969	168	35	n	n	PROPN
ejpam-6969	168	36	=	=	SYM
ejpam-6969	168	37	6	6	NUM
ejpam-6969	168	38	hermitegalerkin	hermitegalerkin	X
ejpam-6969	168	39	method	method	NOUN
ejpam-6969	168	40	n	n	PROPN
ejpam-6969	168	41	=	=	SYM
ejpam-6969	168	42	6	6	NUM
ejpam-6969	168	43	method	method	NOUN
ejpam-6969	168	44	of	of	ADP
ejpam-6969	168	45	[	[	X
ejpam-6969	168	46	8	8	NUM
ejpam-6969	168	47	]	]	PUNCT
ejpam-6969	168	48	with	with	ADP
ejpam-6969	168	49	n	n	NOUN
ejpam-6969	168	50	=	=	SYM
ejpam-6969	168	51	30	30	NUM
ejpam-6969	168	52	method	method	NOUN
ejpam-6969	168	53	of	of	ADP
ejpam-6969	168	54	[	[	X
ejpam-6969	168	55	28	28	NUM
ejpam-6969	168	56	]	]	PUNCT
ejpam-6969	168	57	with	with	ADP
ejpam-6969	168	58	n	n	NOUN
ejpam-6969	168	59	=	=	SYM
ejpam-6969	168	60	m	m	NOUN
ejpam-6969	168	61	=	=	NOUN
ejpam-6969	168	62	64	64	NUM
ejpam-6969	168	63	p	p	NOUN
ejpam-6969	168	64	=	=	SYM
ejpam-6969	168	65	1	1	NUM
ejpam-6969	168	66	1.61×	1.61×	NUM
ejpam-6969	168	67	10−7	10−7	NUM
ejpam-6969	169	1	3.70×	3.70×	NUM
ejpam-6969	169	2	10−5	10−5	NUM
ejpam-6969	169	3	6.0×	6.0×	NUM
ejpam-6969	169	4	10−5	10−5	NUM
ejpam-6969	169	5	3.45×	3.45×	NUM
ejpam-6969	169	6	10−7	10−7	NUM
ejpam-6969	169	7	p	p	X
ejpam-6969	169	8	=	=	SYM
ejpam-6969	169	9	2	2	NUM
ejpam-6969	169	10	7.54×	7.54×	NUM
ejpam-6969	169	11	10−8	10−8	NUM
ejpam-6969	169	12	5.56×	5.56×	NUM
ejpam-6969	169	13	10−5	10−5	NUM
ejpam-6969	169	14	1.29×	1.29×	NUM
ejpam-6969	169	15	10−4	10−4	NUM
ejpam-6969	169	16	1.28×	1.28×	NUM
ejpam-6969	169	17	10−10	10−10	NUM
ejpam-6969	169	18	p	p	NOUN
ejpam-6969	169	19	=	=	SYM
ejpam-6969	169	20	3	3	NUM
ejpam-6969	169	21	1.33×	1.33×	NUM
ejpam-6969	169	22	10−8	10−8	NUM
ejpam-6969	169	23	8.06×	8.06×	NUM
ejpam-6969	169	24	10−5	10−5	NUM
ejpam-6969	169	25	7.0×	7.0×	NUM
ejpam-6969	169	26	10−5	10−5	NUM
ejpam-6969	169	27	2.22×	2.22×	NUM
ejpam-6969	169	28	10−11	10−11	NOUN
ejpam-6969	170	1	p	p	NOUN
ejpam-6969	170	2	=	=	SYM
ejpam-6969	170	3	4	4	NUM
ejpam-6969	170	4	1.77×	1.77×	NUM
ejpam-6969	170	5	10−8	10−8	NUM
ejpam-6969	170	6	1.0×	1.0×	NUM
ejpam-6969	170	7	10−4	10−4	NUM
ejpam-6969	170	8	5.33×	5.33×	NUM
ejpam-6969	170	9	10−5	10−5	NUM
ejpam-6969	170	10	1.67×	1.67×	NUM
ejpam-6969	170	11	10−13	10−13	PROPN
ejpam-6969	170	12	p	p	NOUN
ejpam-6969	170	13	=	=	SYM
ejpam-6969	170	14	5	5	NUM
ejpam-6969	170	15	4.69×	4.69×	NUM
ejpam-6969	170	16	10−9	10−9	NUM
ejpam-6969	170	17	3.54×	3.54×	NUM
ejpam-6969	170	18	10−5	10−5	NUM
ejpam-6969	170	19	5.959×	5.959×	NUM
ejpam-6969	170	20	10−5	10−5	NUM
ejpam-6969	170	21	3.23×	3.23×	NUM
ejpam-6969	170	22	10−13	10−13	NOUN
ejpam-6969	170	23	p	p	X
ejpam-6969	170	24	=	=	PROPN
ejpam-6969	170	25	6	6	NUM
ejpam-6969	170	26	2.93×	2.93×	NUM
ejpam-6969	170	27	10−10	10−10	NUM
ejpam-6969	170	28	4.33×	4.33×	NUM
ejpam-6969	170	29	10−5	10−5	NUM
ejpam-6969	170	30	7.4588×	7.4588×	NUM
ejpam-6969	170	31	10−4	10−4	NUM
ejpam-6969	170	32	9.42×	9.42×	NUM
ejpam-6969	170	33	10−15	10−15	NUM
ejpam-6969	170	34	table	table	NOUN
ejpam-6969	170	35	1	1	NUM
ejpam-6969	170	36	:	:	PUNCT
ejpam-6969	170	37	numerical	numerical	ADJ
ejpam-6969	170	38	results	result	NOUN
ejpam-6969	170	39	for	for	ADP
ejpam-6969	170	40	example	example	NOUN
ejpam-6969	170	41	1	1	NUM
ejpam-6969	170	42	.	.	PUNCT
ejpam-6969	171	1	n	n	PROPN
ejpam-6969	171	2	bc	bc	PROPN
ejpam-6969	171	3	method	method	PROPN
ejpam-6969	171	4	hg	hg	PROPN
ejpam-6969	171	5	method	method	VERB
ejpam-6969	171	6	2	2	NUM
ejpam-6969	171	7	1.5726×	1.5726×	NUM
ejpam-6969	171	8	10−2	10−2	NUM
ejpam-6969	171	9	1.0118×	1.0118×	NUM
ejpam-6969	171	10	10−2	10−2	NUM
ejpam-6969	171	11	4	4	NUM
ejpam-6969	171	12	7.7782×	7.7782×	NUM
ejpam-6969	171	13	10−5	10−5	NUM
ejpam-6969	171	14	5.3089×	5.3089×	NUM
ejpam-6969	171	15	10−5	10−5	NUM
ejpam-6969	171	16	6	6	NUM
ejpam-6969	171	17	1.6191×	1.6191×	NUM
ejpam-6969	171	18	10−7	10−7	NUM
ejpam-6969	171	19	3.7095×	3.7095×	NUM
ejpam-6969	171	20	10−5	10−5	NUM
ejpam-6969	171	21	7	7	NUM
ejpam-6969	171	22	6.0440×	6.0440×	NOUN
ejpam-6969	171	23	10−11	10−11	NUM
ejpam-6969	171	24	6.9195×	6.9195×	NUM
ejpam-6969	171	25	10−5	10−5	NUM
ejpam-6969	171	26	table	table	NOUN
ejpam-6969	171	27	2	2	NUM
ejpam-6969	171	28	:	:	PUNCT
ejpam-6969	171	29	effect	effect	NOUN
ejpam-6969	171	30	of	of	ADP
ejpam-6969	171	31	n	n	PROPN
ejpam-6969	171	32	on	on	ADP
ejpam-6969	171	33	the	the	DET
ejpam-6969	171	34	absolute	absolute	ADJ
ejpam-6969	171	35	error	error	NOUN
ejpam-6969	171	36	for	for	ADP
ejpam-6969	171	37	(	(	PUNCT
ejpam-6969	171	38	χ	χ	NOUN
ejpam-6969	171	39	,	,	PUNCT
ejpam-6969	171	40	t	t	PROPN
ejpam-6969	171	41	)	)	PUNCT
ejpam-6969	171	42	=	=	PUNCT
ejpam-6969	171	43	(	(	PUNCT
ejpam-6969	171	44	0.5	0.5	NUM
ejpam-6969	171	45	,	,	PUNCT
ejpam-6969	171	46	0.5	0.5	NUM
ejpam-6969	171	47	)	)	PUNCT
ejpam-6969	171	48	.	.	PUNCT
ejpam-6969	172	1	figure	figure	VERB
ejpam-6969	172	2	3	3	NUM
ejpam-6969	172	3	:	:	PUNCT
ejpam-6969	172	4	effect	effect	NOUN
ejpam-6969	172	5	of	of	ADP
ejpam-6969	172	6	n	n	PROPN
ejpam-6969	172	7	on	on	ADP
ejpam-6969	172	8	the	the	DET
ejpam-6969	172	9	absolute	absolute	ADJ
ejpam-6969	172	10	error	error	NOUN
ejpam-6969	172	11	for	for	ADP
ejpam-6969	172	12	(	(	PUNCT
ejpam-6969	172	13	χ	χ	NOUN
ejpam-6969	172	14	,	,	PUNCT
ejpam-6969	172	15	t	t	PROPN
ejpam-6969	172	16	)	)	PUNCT
ejpam-6969	172	17	=	=	PUNCT
ejpam-6969	172	18	(	(	PUNCT
ejpam-6969	172	19	0.5	0.5	NUM
ejpam-6969	172	20	,	,	PUNCT
ejpam-6969	172	21	0.5	0.5	NUM
ejpam-6969	172	22	)	)	PUNCT
ejpam-6969	172	23	.	.	PUNCT
ejpam-6969	173	1	example	example	NOUN
ejpam-6969	174	1	2	2	NUM
ejpam-6969	174	2	.	.	PUNCT
ejpam-6969	174	3	let	let	VERB
ejpam-6969	174	4	us	we	PRON
ejpam-6969	174	5	present	present	VERB
ejpam-6969	174	6	the	the	DET
ejpam-6969	174	7	following	follow	VERB
ejpam-6969	174	8	2d	2d	NOUN
ejpam-6969	174	9	-	-	PUNCT
ejpam-6969	174	10	nvie	nvie	NOUN
ejpam-6969	175	1	[	[	X
ejpam-6969	175	2	10	10	NUM
ejpam-6969	175	3	]	]	X
ejpam-6969	175	4	:	:	PUNCT
ejpam-6969	175	5	u(χ	u(χ	PROPN
ejpam-6969	175	6	,	,	PUNCT
ejpam-6969	175	7	t	t	PROPN
ejpam-6969	175	8	)	)	PUNCT
ejpam-6969	175	9	=	=	SYM
ejpam-6969	175	10	f(χ	f(χ	PROPN
ejpam-6969	175	11	,	,	PUNCT
ejpam-6969	175	12	t	t	PROPN
ejpam-6969	175	13	)	)	PUNCT
ejpam-6969	176	1	+	+	CCONJ
ejpam-6969	177	1	∫	∫	PROPN
ejpam-6969	177	2	t	t	PROPN
ejpam-6969	177	3	0	0	NUM
ejpam-6969	177	4	∫	∫	PROPN
ejpam-6969	177	5	χ	χ	X
ejpam-6969	177	6	0	0	NUM
ejpam-6969	177	7	u2(s	u2(s	PROPN
ejpam-6969	177	8	,	,	PUNCT
ejpam-6969	177	9	y	y	NOUN
ejpam-6969	177	10	)	)	PUNCT
ejpam-6969	177	11	ds	ds	NOUN
ejpam-6969	177	12	dy	dy	NOUN
ejpam-6969	177	13	χ	χ	NOUN
ejpam-6969	177	14	,	,	PUNCT
ejpam-6969	177	15	t	t	PROPN
ejpam-6969	177	16	∈	∈	PROPN
ejpam-6969	178	1	[	[	X
ejpam-6969	178	2	0	0	NUM
ejpam-6969	178	3	,	,	PUNCT
ejpam-6969	178	4	1	1	NUM
ejpam-6969	178	5	]	]	PUNCT
ejpam-6969	178	6	,	,	PUNCT
ejpam-6969	178	7	(	(	PUNCT
ejpam-6969	178	8	17	17	NUM
ejpam-6969	178	9	)	)	PUNCT
ejpam-6969	178	10	m.	m.	NOUN
ejpam-6969	178	11	h.	h.	PROPN
ejpam-6969	178	12	ahmed	ahmed	PROPN
ejpam-6969	178	13	,	,	PUNCT
ejpam-6969	178	14	a.	a.	NOUN
ejpam-6969	178	15	m.	m.	PROPN
ejpam-6969	178	16	aljabri	aljabri	PROPN
ejpam-6969	178	17	/	/	SYM
ejpam-6969	178	18	eur	eur	PROPN
ejpam-6969	178	19	.	.	PUNCT
ejpam-6969	179	1	j.	j.	PROPN
ejpam-6969	179	2	pure	pure	PROPN
ejpam-6969	179	3	appl	appl	PROPN
ejpam-6969	179	4	.	.	PROPN
ejpam-6969	179	5	math	math	PROPN
ejpam-6969	179	6	,	,	PUNCT
ejpam-6969	179	7	18	18	NUM
ejpam-6969	179	8	(	(	PUNCT
ejpam-6969	179	9	4	4	NUM
ejpam-6969	179	10	)	)	PUNCT
ejpam-6969	179	11	(	(	PUNCT
ejpam-6969	179	12	2025	2025	NUM
ejpam-6969	179	13	)	)	PUNCT
ejpam-6969	179	14	,	,	PUNCT
ejpam-6969	179	15	6969	6969	NUM
ejpam-6969	179	16	10	10	NUM
ejpam-6969	179	17	of	of	ADP
ejpam-6969	179	18	16	16	NUM
ejpam-6969	180	1	where	where	SCONJ
ejpam-6969	180	2	f(χ	f(χ	PROPN
ejpam-6969	180	3	,	,	PUNCT
ejpam-6969	180	4	t	t	PROPN
ejpam-6969	180	5	)	)	PUNCT
ejpam-6969	180	6	=	=	SYM
ejpam-6969	180	7	χ2	χ2	PROPN
ejpam-6969	180	8	+	+	CCONJ
ejpam-6969	180	9	t2	t2	PROPN
ejpam-6969	180	10	−	−	PROPN
ejpam-6969	180	11	1	1	NUM
ejpam-6969	180	12	45	45	NUM
ejpam-6969	180	13	χt(9χ4	χt(9χ4	NOUN
ejpam-6969	180	14	+	+	CCONJ
ejpam-6969	180	15	10χ2t2	10χ2t2	NOUN
ejpam-6969	180	16	+	+	CCONJ
ejpam-6969	180	17	9t4	9t4	NUM
ejpam-6969	180	18	)	)	PUNCT
ejpam-6969	180	19	,	,	PUNCT
ejpam-6969	180	20	and	and	CCONJ
ejpam-6969	180	21	the	the	DET
ejpam-6969	180	22	exact	exact	ADJ
ejpam-6969	180	23	solution	solution	NOUN
ejpam-6969	180	24	is	be	AUX
ejpam-6969	180	25	u(χ	u(χ	ADJ
ejpam-6969	180	26	,	,	PUNCT
ejpam-6969	180	27	t	t	PROPN
ejpam-6969	180	28	)	)	PUNCT
ejpam-6969	180	29	=	=	SYM
ejpam-6969	180	30	χ2	χ2	PROPN
ejpam-6969	180	31	+	+	CCONJ
ejpam-6969	180	32	t2	t2	PROPN
ejpam-6969	180	33	.	.	PUNCT
ejpam-6969	181	1	table	table	NOUN
ejpam-6969	181	2	(	(	PUNCT
ejpam-6969	181	3	3	3	X
ejpam-6969	181	4	)	)	PUNCT
ejpam-6969	181	5	presents	present	VERB
ejpam-6969	181	6	the	the	DET
ejpam-6969	181	7	absolute	absolute	ADJ
ejpam-6969	181	8	errors	error	NOUN
ejpam-6969	181	9	of	of	ADP
ejpam-6969	181	10	equation	equation	NOUN
ejpam-6969	181	11	(	(	PUNCT
ejpam-6969	181	12	17	17	NUM
ejpam-6969	181	13	)	)	PUNCT
ejpam-6969	181	14	calculated	calculate	VERB
ejpam-6969	181	15	using	use	VERB
ejpam-6969	181	16	the	the	DET
ejpam-6969	181	17	bernoulli	bernoulli	NOUN
ejpam-6969	181	18	collocation	collocation	NOUN
ejpam-6969	181	19	(	(	PUNCT
ejpam-6969	181	20	bc	bc	PROPN
ejpam-6969	181	21	)	)	PUNCT
ejpam-6969	181	22	and	and	CCONJ
ejpam-6969	181	23	hermite	hermite	ADJ
ejpam-6969	181	24	–	–	PUNCT
ejpam-6969	181	25	galerkin	galerkin	ADJ
ejpam-6969	181	26	(	(	PUNCT
ejpam-6969	181	27	hg	hg	NOUN
ejpam-6969	181	28	)	)	PUNCT
ejpam-6969	181	29	methods	method	NOUN
ejpam-6969	181	30	for	for	ADP
ejpam-6969	181	31	various	various	ADJ
ejpam-6969	181	32	values	value	NOUN
ejpam-6969	181	33	of	of	ADP
ejpam-6969	181	34	χ	χ	NOUN
ejpam-6969	181	35	and	and	CCONJ
ejpam-6969	181	36	t.	t.	NOUN
ejpam-6969	181	37	figures	figure	NOUN
ejpam-6969	181	38	(	(	PUNCT
ejpam-6969	181	39	4)–(5	4)–(5	NOUN
ejpam-6969	181	40	)	)	PUNCT
ejpam-6969	181	41	illustrate	illustrate	VERB
ejpam-6969	181	42	the	the	DET
ejpam-6969	181	43	absolute	absolute	ADJ
ejpam-6969	181	44	error	error	NOUN
ejpam-6969	181	45	distributions	distribution	NOUN
ejpam-6969	181	46	obtained	obtain	VERB
ejpam-6969	181	47	by	by	ADP
ejpam-6969	181	48	these	these	DET
ejpam-6969	181	49	methods	method	NOUN
ejpam-6969	181	50	.	.	PUNCT
ejpam-6969	182	1	furthermore	furthermore	ADV
ejpam-6969	182	2	,	,	PUNCT
ejpam-6969	182	3	a	a	DET
ejpam-6969	182	4	comparison	comparison	NOUN
ejpam-6969	182	5	with	with	ADP
ejpam-6969	182	6	the	the	DET
ejpam-6969	182	7	rationalized	rationalize	VERB
ejpam-6969	182	8	haar	haar	NOUN
ejpam-6969	182	9	functions	function	NOUN
ejpam-6969	182	10	method	method	NOUN
ejpam-6969	182	11	[	[	X
ejpam-6969	182	12	10	10	NUM
ejpam-6969	182	13	]	]	PUNCT
ejpam-6969	182	14	with	with	ADP
ejpam-6969	182	15	n	n	NOUN
ejpam-6969	182	16	=	=	SYM
ejpam-6969	182	17	32	32	NUM
ejpam-6969	182	18	is	be	AUX
ejpam-6969	182	19	also	also	ADV
ejpam-6969	182	20	included	include	VERB
ejpam-6969	182	21	.	.	PUNCT
ejpam-6969	183	1	(	(	PUNCT
ejpam-6969	183	2	χ	χ	X
ejpam-6969	183	3	,	,	PUNCT
ejpam-6969	183	4	t	t	PROPN
ejpam-6969	183	5	)	)	PUNCT
ejpam-6969	183	6	=	=	PUNCT
ejpam-6969	183	7	(	(	PUNCT
ejpam-6969	183	8	1	1	NUM
ejpam-6969	183	9	2p	2p	NUM
ejpam-6969	183	10	,	,	PUNCT
ejpam-6969	183	11	1	1	NUM
ejpam-6969	183	12	2p	2p	NUM
ejpam-6969	183	13	)	)	PUNCT
ejpam-6969	183	14	bernoulli	bernoulli	NOUN
ejpam-6969	183	15	collocation	collocation	NOUN
ejpam-6969	183	16	method	method	NOUN
ejpam-6969	183	17	n	n	PROPN
ejpam-6969	183	18	=	=	SYM
ejpam-6969	183	19	6	6	NUM
ejpam-6969	183	20	hermitegalerkin	hermitegalerkin	X
ejpam-6969	183	21	method	method	NOUN
ejpam-6969	183	22	n	n	PROPN
ejpam-6969	183	23	=	=	SYM
ejpam-6969	183	24	6	6	NUM
ejpam-6969	183	25	method	method	NOUN
ejpam-6969	183	26	of	of	ADP
ejpam-6969	183	27	[	[	X
ejpam-6969	183	28	10	10	NUM
ejpam-6969	183	29	]	]	PUNCT
ejpam-6969	183	30	with	with	ADP
ejpam-6969	183	31	n	n	NOUN
ejpam-6969	183	32	=	=	SYM
ejpam-6969	183	33	32	32	NUM
ejpam-6969	183	34	p	p	NOUN
ejpam-6969	183	35	=	=	NOUN
ejpam-6969	183	36	2	2	NUM
ejpam-6969	183	37	5.37×	5.37×	NUM
ejpam-6969	183	38	10−12	10−12	NOUN
ejpam-6969	183	39	6.92×	6.92×	NUM
ejpam-6969	183	40	10−5	10−5	NUM
ejpam-6969	183	41	5.90×	5.90×	NUM
ejpam-6969	183	42	10−5	10−5	NUM
ejpam-6969	183	43	p	p	X
ejpam-6969	183	44	=	=	SYM
ejpam-6969	183	45	3	3	NUM
ejpam-6969	183	46	1.34×	1.34×	NUM
ejpam-6969	183	47	10−12	10−12	PROPN
ejpam-6969	183	48	5.06×	5.06×	NUM
ejpam-6969	183	49	10−5	10−5	NUM
ejpam-6969	183	50	9.06×	9.06×	NUM
ejpam-6969	183	51	10−7	10−7	NUM
ejpam-6969	183	52	p	p	NOUN
ejpam-6969	183	53	=	=	SYM
ejpam-6969	183	54	4	4	NUM
ejpam-6969	183	55	1.15×	1.15×	NUM
ejpam-6969	183	56	10−12	10−12	NOUN
ejpam-6969	183	57	9.52×	9.52×	NUM
ejpam-6969	183	58	10−6	10−6	NUM
ejpam-6969	183	59	1.29×	1.29×	NUM
ejpam-6969	183	60	10−8	10−8	NUM
ejpam-6969	183	61	p	p	NOUN
ejpam-6969	183	62	=	=	SYM
ejpam-6969	183	63	5	5	NUM
ejpam-6969	183	64	5.70×	5.70×	NUM
ejpam-6969	183	65	10−13	10−13	NUM
ejpam-6969	183	66	2.49×	2.49×	NUM
ejpam-6969	183	67	10−4	10−4	PROPN
ejpam-6969	183	68	1.43×	1.43×	NUM
ejpam-6969	183	69	10−10	10−10	NUM
ejpam-6969	183	70	p	p	NOUN
ejpam-6969	183	71	=	=	SYM
ejpam-6969	183	72	6	6	NUM
ejpam-6969	183	73	1.62×	1.62×	NUM
ejpam-6969	183	74	10−13	10−13	PROPN
ejpam-6969	183	75	4.67×	4.67×	NUM
ejpam-6969	183	76	10−4	10−4	NUM
ejpam-6969	183	77	2.00×	2.00×	NUM
ejpam-6969	183	78	10−12	10−12	NOUN
ejpam-6969	183	79	table	table	NOUN
ejpam-6969	183	80	3	3	NUM
ejpam-6969	183	81	:	:	PUNCT
ejpam-6969	183	82	numerical	numerical	ADJ
ejpam-6969	183	83	results	result	NOUN
ejpam-6969	183	84	for	for	ADP
ejpam-6969	183	85	example	example	NOUN
ejpam-6969	183	86	2	2	NUM
ejpam-6969	183	87	.	.	X
ejpam-6969	183	88	figure	figure	VERB
ejpam-6969	183	89	4	4	NUM
ejpam-6969	183	90	:	:	PUNCT
ejpam-6969	183	91	absolute	absolute	ADJ
ejpam-6969	183	92	error	error	NOUN
ejpam-6969	183	93	of	of	ADP
ejpam-6969	183	94	example	example	NOUN
ejpam-6969	183	95	2	2	NUM
ejpam-6969	183	96	by	by	ADP
ejpam-6969	183	97	the	the	DET
ejpam-6969	183	98	bc	bc	PROPN
ejpam-6969	183	99	method	method	NOUN
ejpam-6969	183	100	with	with	ADP
ejpam-6969	183	101	n	n	NOUN
ejpam-6969	183	102	=	=	SYM
ejpam-6969	183	103	6	6	NUM
ejpam-6969	183	104	.	.	PUNCT
ejpam-6969	183	105	figure	figure	NOUN
ejpam-6969	183	106	5	5	NUM
ejpam-6969	183	107	:	:	PUNCT
ejpam-6969	183	108	absolute	absolute	ADJ
ejpam-6969	183	109	error	error	NOUN
ejpam-6969	183	110	for	for	ADP
ejpam-6969	183	111	example	example	NOUN
ejpam-6969	183	112	2	2	NUM
ejpam-6969	183	113	by	by	ADP
ejpam-6969	183	114	the	the	DET
ejpam-6969	183	115	hg	hg	PROPN
ejpam-6969	183	116	method	method	NOUN
ejpam-6969	183	117	with	with	ADP
ejpam-6969	183	118	n	n	NOUN
ejpam-6969	183	119	=	=	SYM
ejpam-6969	183	120	6	6	NUM
ejpam-6969	183	121	.	.	NOUN
ejpam-6969	183	122	example	example	NOUN
ejpam-6969	183	123	3	3	X
ejpam-6969	183	124	.	.	PUNCT
ejpam-6969	184	1	let	let	VERB
ejpam-6969	184	2	us	we	PRON
ejpam-6969	184	3	present	present	VERB
ejpam-6969	184	4	the	the	DET
ejpam-6969	184	5	following	follow	VERB
ejpam-6969	184	6	2d	2d	NOUN
ejpam-6969	184	7	-	-	PUNCT
ejpam-6969	184	8	nvie	nvie	NOUN
ejpam-6969	184	9	[	[	X
ejpam-6969	184	10	29	29	NUM
ejpam-6969	184	11	]	]	NUM
ejpam-6969	184	12	:	:	PUNCT
ejpam-6969	184	13	u(χ	u(χ	PROPN
ejpam-6969	184	14	,	,	PUNCT
ejpam-6969	184	15	t	t	PROPN
ejpam-6969	184	16	)	)	PUNCT
ejpam-6969	184	17	=	=	SYM
ejpam-6969	184	18	f(χ	f(χ	PROPN
ejpam-6969	184	19	,	,	PUNCT
ejpam-6969	184	20	t	t	PROPN
ejpam-6969	184	21	)	)	PUNCT
ejpam-6969	185	1	+	+	CCONJ
ejpam-6969	186	1	∫	∫	PROPN
ejpam-6969	186	2	t	t	PROPN
ejpam-6969	186	3	0	0	NUM
ejpam-6969	186	4	∫	∫	PROPN
ejpam-6969	186	5	χ	χ	X
ejpam-6969	186	6	0	0	NUM
ejpam-6969	186	7	(	(	PUNCT
ejpam-6969	186	8	χ+	χ+	PROPN
ejpam-6969	186	9	t)eu(s	t)eu(s	ADJ
ejpam-6969	186	10	,	,	PUNCT
ejpam-6969	186	11	y	y	NOUN
ejpam-6969	186	12	)	)	PUNCT
ejpam-6969	186	13	ds	ds	NOUN
ejpam-6969	186	14	dy	dy	NOUN
ejpam-6969	186	15	χ	χ	NOUN
ejpam-6969	186	16	,	,	PUNCT
ejpam-6969	186	17	t	t	PROPN
ejpam-6969	186	18	∈	∈	PROPN
ejpam-6969	187	1	[	[	X
ejpam-6969	187	2	0	0	NUM
ejpam-6969	187	3	,	,	PUNCT
ejpam-6969	187	4	1	1	NUM
ejpam-6969	187	5	]	]	PUNCT
ejpam-6969	187	6	,	,	PUNCT
ejpam-6969	187	7	(	(	PUNCT
ejpam-6969	187	8	18	18	NUM
ejpam-6969	187	9	)	)	PUNCT
ejpam-6969	187	10	m.	m.	NOUN
ejpam-6969	187	11	h.	h.	PROPN
ejpam-6969	187	12	ahmed	ahmed	PROPN
ejpam-6969	187	13	,	,	PUNCT
ejpam-6969	187	14	a.	a.	NOUN
ejpam-6969	187	15	m.	m.	PROPN
ejpam-6969	187	16	aljabri	aljabri	PROPN
ejpam-6969	187	17	/	/	SYM
ejpam-6969	187	18	eur	eur	PROPN
ejpam-6969	187	19	.	.	PUNCT
ejpam-6969	188	1	j.	j.	PROPN
ejpam-6969	188	2	pure	pure	PROPN
ejpam-6969	188	3	appl	appl	PROPN
ejpam-6969	188	4	.	.	PROPN
ejpam-6969	188	5	math	math	PROPN
ejpam-6969	188	6	,	,	PUNCT
ejpam-6969	188	7	18	18	NUM
ejpam-6969	188	8	(	(	PUNCT
ejpam-6969	188	9	4	4	NUM
ejpam-6969	188	10	)	)	PUNCT
ejpam-6969	188	11	(	(	PUNCT
ejpam-6969	188	12	2025	2025	NUM
ejpam-6969	188	13	)	)	PUNCT
ejpam-6969	188	14	,	,	PUNCT
ejpam-6969	188	15	6969	6969	NUM
ejpam-6969	188	16	11	11	NUM
ejpam-6969	188	17	of	of	ADP
ejpam-6969	188	18	16	16	NUM
ejpam-6969	188	19	where	where	SCONJ
ejpam-6969	188	20	f(χ	f(χ	PROPN
ejpam-6969	188	21	,	,	PUNCT
ejpam-6969	188	22	t	t	PROPN
ejpam-6969	188	23	)	)	PUNCT
ejpam-6969	188	24	=	=	PUNCT
ejpam-6969	189	1	(	(	PUNCT
ejpam-6969	189	2	χ+	χ+	NUM
ejpam-6969	189	3	t)(eχ	t)(eχ	NOUN
ejpam-6969	189	4	+	+	CCONJ
ejpam-6969	189	5	et	et	NOUN
ejpam-6969	189	6	−	−	NOUN
ejpam-6969	189	7	e(χ+t	e(χ+t	NOUN
ejpam-6969	189	8	)	)	PUNCT
ejpam-6969	189	9	)	)	PUNCT
ejpam-6969	189	10	.	.	PUNCT
ejpam-6969	190	1	the	the	DET
ejpam-6969	190	2	exact	exact	ADJ
ejpam-6969	190	3	solution	solution	NOUN
ejpam-6969	190	4	is	be	AUX
ejpam-6969	190	5	given	give	VERB
ejpam-6969	190	6	by	by	ADP
ejpam-6969	190	7	u(χ	u(χ	PROPN
ejpam-6969	190	8	,	,	PUNCT
ejpam-6969	190	9	t	t	PROPN
ejpam-6969	190	10	)	)	PUNCT
ejpam-6969	190	11	=	=	SYM
ejpam-6969	191	1	χ+	χ+	PRON
ejpam-6969	191	2	t.	t.	NOUN
ejpam-6969	191	3	table	table	NOUN
ejpam-6969	191	4	(	(	PUNCT
ejpam-6969	191	5	4	4	X
ejpam-6969	191	6	)	)	PUNCT
ejpam-6969	191	7	shows	show	VERB
ejpam-6969	191	8	the	the	DET
ejpam-6969	191	9	comparison	comparison	NOUN
ejpam-6969	191	10	of	of	ADP
ejpam-6969	191	11	the	the	DET
ejpam-6969	191	12	absolute	absolute	ADJ
ejpam-6969	191	13	errors	error	NOUN
ejpam-6969	191	14	of	of	ADP
ejpam-6969	191	15	equation	equation	NOUN
ejpam-6969	191	16	(	(	PUNCT
ejpam-6969	191	17	18	18	NUM
ejpam-6969	191	18	)	)	PUNCT
ejpam-6969	191	19	calculated	calculate	VERB
ejpam-6969	191	20	using	use	VERB
ejpam-6969	191	21	the	the	DET
ejpam-6969	191	22	bernoulli	bernoulli	NOUN
ejpam-6969	191	23	collocation	collocation	NOUN
ejpam-6969	191	24	(	(	PUNCT
ejpam-6969	191	25	bc	bc	PROPN
ejpam-6969	191	26	)	)	PUNCT
ejpam-6969	191	27	and	and	CCONJ
ejpam-6969	191	28	hermite	hermite	ADJ
ejpam-6969	191	29	–	–	PUNCT
ejpam-6969	191	30	galerkin	galerkin	ADJ
ejpam-6969	191	31	(	(	PUNCT
ejpam-6969	191	32	hg	hg	NOUN
ejpam-6969	191	33	)	)	PUNCT
ejpam-6969	191	34	methods	method	NOUN
ejpam-6969	191	35	for	for	ADP
ejpam-6969	191	36	various	various	ADJ
ejpam-6969	191	37	values	value	NOUN
ejpam-6969	191	38	of	of	ADP
ejpam-6969	191	39	χ	χ	NOUN
ejpam-6969	191	40	and	and	CCONJ
ejpam-6969	191	41	t.	t.	NOUN
ejpam-6969	191	42	figures	figure	NOUN
ejpam-6969	191	43	(	(	PUNCT
ejpam-6969	191	44	6)–(7	6)–(7	NUM
ejpam-6969	191	45	)	)	PUNCT
ejpam-6969	191	46	illustrate	illustrate	VERB
ejpam-6969	191	47	the	the	DET
ejpam-6969	191	48	absolute	absolute	ADJ
ejpam-6969	191	49	error	error	NOUN
ejpam-6969	191	50	distributions	distribution	NOUN
ejpam-6969	191	51	obtained	obtain	VERB
ejpam-6969	191	52	by	by	ADP
ejpam-6969	191	53	these	these	DET
ejpam-6969	191	54	methods	method	NOUN
ejpam-6969	191	55	.	.	PUNCT
ejpam-6969	192	1	a	a	DET
ejpam-6969	192	2	comparison	comparison	NOUN
ejpam-6969	192	3	with	with	ADP
ejpam-6969	192	4	the	the	DET
ejpam-6969	192	5	extrapolation	extrapolation	NOUN
ejpam-6969	192	6	method	method	NOUN
ejpam-6969	192	7	[	[	X
ejpam-6969	192	8	29	29	NUM
ejpam-6969	192	9	]	]	PUNCT
ejpam-6969	192	10	for	for	ADP
ejpam-6969	192	11	m	m	PROPN
ejpam-6969	192	12	=	=	SYM
ejpam-6969	192	13	n	n	PROPN
ejpam-6969	192	14	=	=	SYM
ejpam-6969	192	15	26	26	NUM
ejpam-6969	192	16	is	be	AUX
ejpam-6969	192	17	also	also	ADV
ejpam-6969	192	18	provided	provide	VERB
ejpam-6969	192	19	.	.	PUNCT
ejpam-6969	193	1	(	(	PUNCT
ejpam-6969	193	2	χ	χ	X
ejpam-6969	193	3	,	,	PUNCT
ejpam-6969	193	4	t	t	PROPN
ejpam-6969	193	5	)	)	PUNCT
ejpam-6969	193	6	bernoulli	bernoulli	NOUN
ejpam-6969	193	7	collocation	collocation	NOUN
ejpam-6969	193	8	method	method	NOUN
ejpam-6969	193	9	n	n	PROPN
ejpam-6969	193	10	=	=	SYM
ejpam-6969	193	11	6	6	NUM
ejpam-6969	193	12	hermitegalerkin	hermitegalerkin	X
ejpam-6969	193	13	method	method	NOUN
ejpam-6969	193	14	n	n	PROPN
ejpam-6969	193	15	=	=	SYM
ejpam-6969	193	16	6	6	NUM
ejpam-6969	193	17	method	method	NOUN
ejpam-6969	193	18	of	of	ADP
ejpam-6969	193	19	[	[	X
ejpam-6969	193	20	29	29	NUM
ejpam-6969	193	21	]	]	PUNCT
ejpam-6969	193	22	with	with	ADP
ejpam-6969	193	23	m	m	PROPN
ejpam-6969	193	24	=	=	SYM
ejpam-6969	193	25	n	n	PROPN
ejpam-6969	193	26	=	=	SYM
ejpam-6969	193	27	26	26	NUM
ejpam-6969	193	28	(	(	PUNCT
ejpam-6969	193	29	0.1	0.1	NUM
ejpam-6969	193	30	,	,	PUNCT
ejpam-6969	193	31	0.1	0.1	NUM
ejpam-6969	193	32	)	)	PUNCT
ejpam-6969	193	33	1.87×	1.87×	NUM
ejpam-6969	193	34	10−11	10−11	NUM
ejpam-6969	193	35	5.24×	5.24×	NUM
ejpam-6969	193	36	10−6	10−6	NUM
ejpam-6969	193	37	1.5×	1.5×	NUM
ejpam-6969	193	38	10−7	10−7	NUM
ejpam-6969	193	39	(	(	PUNCT
ejpam-6969	193	40	0.2	0.2	NUM
ejpam-6969	193	41	,	,	PUNCT
ejpam-6969	193	42	0.2	0.2	NUM
ejpam-6969	193	43	)	)	PUNCT
ejpam-6969	193	44	4.52×	4.52×	NUM
ejpam-6969	193	45	10−12	10−12	PROPN
ejpam-6969	193	46	4.36×	4.36×	NUM
ejpam-6969	193	47	10−5	10−5	NUM
ejpam-6969	193	48	1.5×	1.5×	NUM
ejpam-6969	193	49	10−6	10−6	NUM
ejpam-6969	193	50	(	(	PUNCT
ejpam-6969	193	51	0.3	0.3	NUM
ejpam-6969	193	52	,	,	PUNCT
ejpam-6969	193	53	0.3	0.3	NUM
ejpam-6969	193	54	)	)	PUNCT
ejpam-6969	193	55	2.58×	2.58×	NUM
ejpam-6969	193	56	10−11	10−11	NUM
ejpam-6969	193	57	8.14×	8.14×	NUM
ejpam-6969	193	58	10−6	10−6	NUM
ejpam-6969	194	1	6.4×	6.4×	NUM
ejpam-6969	194	2	10−6	10−6	NUM
ejpam-6969	194	3	(	(	PUNCT
ejpam-6969	194	4	0.4	0.4	NUM
ejpam-6969	194	5	,	,	PUNCT
ejpam-6969	194	6	0.4	0.4	NUM
ejpam-6969	194	7	)	)	PUNCT
ejpam-6969	194	8	3.73×	3.73×	NUM
ejpam-6969	194	9	10−12	10−12	NOUN
ejpam-6969	194	10	1.91×	1.91×	NUM
ejpam-6969	194	11	10−5	10−5	NUM
ejpam-6969	194	12	1.9×	1.9×	NUM
ejpam-6969	194	13	10−5	10−5	NUM
ejpam-6969	194	14	(	(	PUNCT
ejpam-6969	194	15	0.5	0.5	NUM
ejpam-6969	194	16	,	,	PUNCT
ejpam-6969	194	17	0.5	0.5	NUM
ejpam-6969	194	18	)	)	PUNCT
ejpam-6969	194	19	3.98×	3.98×	NUM
ejpam-6969	194	20	10−11	10−11	NUM
ejpam-6969	194	21	1.67×	1.67×	NUM
ejpam-6969	194	22	10−5	10−5	NUM
ejpam-6969	194	23	4.7×	4.7×	PROPN
ejpam-6969	194	24	10−5	10−5	NUM
ejpam-6969	194	25	(	(	PUNCT
ejpam-6969	194	26	0.6	0.6	NUM
ejpam-6969	194	27	,	,	PUNCT
ejpam-6969	194	28	0.6	0.6	NUM
ejpam-6969	194	29	)	)	PUNCT
ejpam-6969	194	30	8.77×	8.77×	NUM
ejpam-6969	194	31	10−11	10−11	NUM
ejpam-6969	194	32	3.09×	3.09×	NUM
ejpam-6969	194	33	10−5	10−5	NUM
ejpam-6969	194	34	1.0×	1.0×	NUM
ejpam-6969	194	35	10−4	10−4	NUM
ejpam-6969	194	36	(	(	PUNCT
ejpam-6969	194	37	0.7	0.7	NUM
ejpam-6969	194	38	,	,	PUNCT
ejpam-6969	194	39	0.7	0.7	NUM
ejpam-6969	194	40	)	)	PUNCT
ejpam-6969	194	41	2.83×	2.83×	NUM
ejpam-6969	194	42	10−11	10−11	NUM
ejpam-6969	195	1	5.62×	5.62×	NUM
ejpam-6969	195	2	10−5	10−5	NUM
ejpam-6969	195	3	2.0×	2.0×	NUM
ejpam-6969	195	4	10−4	10−4	NUM
ejpam-6969	195	5	(	(	PUNCT
ejpam-6969	195	6	0.8	0.8	NUM
ejpam-6969	195	7	,	,	PUNCT
ejpam-6969	195	8	0.8	0.8	NUM
ejpam-6969	195	9	)	)	PUNCT
ejpam-6969	196	1	6.36×	6.36×	NUM
ejpam-6969	196	2	10−12	10−12	NOUN
ejpam-6969	196	3	5.79×	5.79×	NUM
ejpam-6969	196	4	10−5	10−5	NUM
ejpam-6969	196	5	3.8×	3.8×	NUM
ejpam-6969	196	6	10−4	10−4	NUM
ejpam-6969	196	7	(	(	PUNCT
ejpam-6969	196	8	0.9	0.9	NUM
ejpam-6969	196	9	,	,	PUNCT
ejpam-6969	196	10	0.9	0.9	NUM
ejpam-6969	196	11	)	)	PUNCT
ejpam-6969	196	12	2.01×	2.01×	NUM
ejpam-6969	196	13	10−9	10−9	NUM
ejpam-6969	196	14	1.5×	1.5×	NUM
ejpam-6969	196	15	10−4	10−4	NUM
ejpam-6969	196	16	6.8×	6.8×	NUM
ejpam-6969	196	17	10−4	10−4	NUM
ejpam-6969	196	18	table	table	NOUN
ejpam-6969	196	19	4	4	NUM
ejpam-6969	196	20	:	:	PUNCT
ejpam-6969	196	21	numerical	numerical	ADJ
ejpam-6969	196	22	results	result	NOUN
ejpam-6969	196	23	for	for	ADP
ejpam-6969	196	24	example	example	NOUN
ejpam-6969	196	25	3	3	NUM
ejpam-6969	196	26	.	.	X
ejpam-6969	196	27	figure	figure	VERB
ejpam-6969	196	28	6	6	NUM
ejpam-6969	196	29	:	:	PUNCT
ejpam-6969	196	30	absolute	absolute	ADJ
ejpam-6969	196	31	error	error	NOUN
ejpam-6969	196	32	for	for	ADP
ejpam-6969	196	33	example	example	NOUN
ejpam-6969	196	34	3	3	NUM
ejpam-6969	196	35	by	by	ADP
ejpam-6969	196	36	the	the	DET
ejpam-6969	196	37	bc	bc	PROPN
ejpam-6969	196	38	method	method	NOUN
ejpam-6969	196	39	with	with	ADP
ejpam-6969	196	40	n	n	NOUN
ejpam-6969	196	41	=	=	SYM
ejpam-6969	196	42	6	6	NUM
ejpam-6969	196	43	.	.	PUNCT
ejpam-6969	196	44	figure	figure	VERB
ejpam-6969	196	45	7	7	NUM
ejpam-6969	196	46	:	:	PUNCT
ejpam-6969	196	47	absolute	absolute	ADJ
ejpam-6969	196	48	error	error	NOUN
ejpam-6969	196	49	for	for	ADP
ejpam-6969	196	50	example	example	NOUN
ejpam-6969	196	51	3	3	NUM
ejpam-6969	196	52	by	by	ADP
ejpam-6969	196	53	hg	hg	PROPN
ejpam-6969	196	54	method	method	NOUN
ejpam-6969	196	55	with	with	ADP
ejpam-6969	196	56	n	n	NOUN
ejpam-6969	196	57	=	=	SYM
ejpam-6969	196	58	6	6	NUM
ejpam-6969	196	59	.	.	PUNCT
ejpam-6969	196	60	m.	m.	PROPN
ejpam-6969	196	61	h.	h.	PROPN
ejpam-6969	196	62	ahmed	ahmed	PROPN
ejpam-6969	196	63	,	,	PUNCT
ejpam-6969	196	64	a.	a.	NOUN
ejpam-6969	196	65	m.	m.	PROPN
ejpam-6969	196	66	aljabri	aljabri	PROPN
ejpam-6969	196	67	/	/	SYM
ejpam-6969	196	68	eur	eur	PROPN
ejpam-6969	196	69	.	.	PUNCT
ejpam-6969	197	1	j.	j.	PROPN
ejpam-6969	197	2	pure	pure	PROPN
ejpam-6969	197	3	appl	appl	PROPN
ejpam-6969	197	4	.	.	PROPN
ejpam-6969	197	5	math	math	PROPN
ejpam-6969	197	6	,	,	PUNCT
ejpam-6969	197	7	18	18	NUM
ejpam-6969	197	8	(	(	PUNCT
ejpam-6969	197	9	4	4	NUM
ejpam-6969	197	10	)	)	PUNCT
ejpam-6969	197	11	(	(	PUNCT
ejpam-6969	197	12	2025	2025	NUM
ejpam-6969	197	13	)	)	PUNCT
ejpam-6969	197	14	,	,	PUNCT
ejpam-6969	197	15	6969	6969	NUM
ejpam-6969	197	16	12	12	NUM
ejpam-6969	197	17	of	of	ADP
ejpam-6969	197	18	16	16	NUM
ejpam-6969	197	19	6	6	NUM
ejpam-6969	197	20	.	.	PUNCT
ejpam-6969	197	21	results	result	NOUN
ejpam-6969	197	22	and	and	CCONJ
ejpam-6969	197	23	discussion	discussion	NOUN
ejpam-6969	197	24	as	as	SCONJ
ejpam-6969	197	25	shown	show	VERB
ejpam-6969	197	26	in	in	ADP
ejpam-6969	197	27	the	the	DET
ejpam-6969	197	28	numerical	numerical	ADJ
ejpam-6969	197	29	results	result	NOUN
ejpam-6969	197	30	for	for	ADP
ejpam-6969	197	31	the	the	DET
ejpam-6969	197	32	three	three	NUM
ejpam-6969	197	33	test	test	NOUN
ejpam-6969	197	34	examples	example	NOUN
ejpam-6969	197	35	(	(	PUNCT
ejpam-6969	197	36	tables	table	NOUN
ejpam-6969	197	37	(	(	PUNCT
ejpam-6969	197	38	1)–(4	1)–(4	NUM
ejpam-6969	197	39	)	)	PUNCT
ejpam-6969	197	40	and	and	CCONJ
ejpam-6969	197	41	figures	figure	NOUN
ejpam-6969	197	42	(	(	PUNCT
ejpam-6969	197	43	1)–(7	1)–(7	NUM
ejpam-6969	197	44	)	)	PUNCT
ejpam-6969	197	45	)	)	PUNCT
ejpam-6969	197	46	,	,	PUNCT
ejpam-6969	197	47	the	the	DET
ejpam-6969	197	48	bernoulli	bernoulli	NOUN
ejpam-6969	197	49	collocation	collocation	NOUN
ejpam-6969	197	50	(	(	PUNCT
ejpam-6969	197	51	bc	bc	PROPN
ejpam-6969	197	52	)	)	PUNCT
ejpam-6969	197	53	method	method	NOUN
ejpam-6969	197	54	provides	provide	VERB
ejpam-6969	197	55	smaller	small	ADJ
ejpam-6969	197	56	absolute	absolute	ADJ
ejpam-6969	197	57	errors	error	NOUN
ejpam-6969	197	58	compared	compare	VERB
ejpam-6969	197	59	to	to	ADP
ejpam-6969	197	60	the	the	DET
ejpam-6969	197	61	hermite	hermite	PROPN
ejpam-6969	197	62	–	–	PUNCT
ejpam-6969	197	63	galerkin	galerkin	PROPN
ejpam-6969	197	64	(	(	PUNCT
ejpam-6969	197	65	hg	hg	NOUN
ejpam-6969	197	66	)	)	PUNCT
ejpam-6969	197	67	method	method	NOUN
ejpam-6969	197	68	.	.	PUNCT
ejpam-6969	198	1	although	although	SCONJ
ejpam-6969	198	2	n	n	NOUN
ejpam-6969	198	3	=	=	SYM
ejpam-6969	198	4	6	6	NUM
ejpam-6969	198	5	was	be	AUX
ejpam-6969	198	6	generally	generally	ADV
ejpam-6969	198	7	selected	select	VERB
ejpam-6969	198	8	as	as	ADP
ejpam-6969	198	9	a	a	DET
ejpam-6969	198	10	suitable	suitable	ADJ
ejpam-6969	198	11	compromise	compromise	NOUN
ejpam-6969	198	12	between	between	ADP
ejpam-6969	198	13	accuracy	accuracy	NOUN
ejpam-6969	198	14	and	and	CCONJ
ejpam-6969	198	15	computational	computational	ADJ
ejpam-6969	198	16	cost	cost	NOUN
ejpam-6969	198	17	,	,	PUNCT
ejpam-6969	198	18	a	a	DET
ejpam-6969	198	19	higher	high	ADJ
ejpam-6969	198	20	value	value	NOUN
ejpam-6969	198	21	of	of	ADP
ejpam-6969	198	22	n	n	PROPN
ejpam-6969	198	23	(	(	PUNCT
ejpam-6969	198	24	e.g.	e.g.	ADV
ejpam-6969	198	25	,	,	PUNCT
ejpam-6969	198	26	n	n	NOUN
ejpam-6969	198	27	=	=	SYM
ejpam-6969	198	28	7	7	NUM
ejpam-6969	198	29	in	in	ADP
ejpam-6969	198	30	example	example	NOUN
ejpam-6969	198	31	(	(	PUNCT
ejpam-6969	198	32	1	1	NUM
ejpam-6969	198	33	)	)	PUNCT
ejpam-6969	198	34	)	)	PUNCT
ejpam-6969	198	35	was	be	AUX
ejpam-6969	198	36	occasionally	occasionally	ADV
ejpam-6969	198	37	used	use	VERB
ejpam-6969	198	38	to	to	PART
ejpam-6969	198	39	investigate	investigate	VERB
ejpam-6969	198	40	the	the	DET
ejpam-6969	198	41	error	error	NOUN
ejpam-6969	198	42	behavior	behavior	NOUN
ejpam-6969	198	43	.	.	PUNCT
ejpam-6969	199	1	the	the	DET
ejpam-6969	199	2	computational	computational	ADJ
ejpam-6969	199	3	cost	cost	NOUN
ejpam-6969	199	4	of	of	ADP
ejpam-6969	199	5	the	the	DET
ejpam-6969	199	6	hg	hg	PROPN
ejpam-6969	199	7	method	method	NOUN
ejpam-6969	199	8	increases	increase	VERB
ejpam-6969	199	9	significantly	significantly	ADV
ejpam-6969	199	10	with	with	ADP
ejpam-6969	199	11	n	n	CCONJ
ejpam-6969	199	12	due	due	ADP
ejpam-6969	199	13	to	to	ADP
ejpam-6969	199	14	the	the	DET
ejpam-6969	199	15	evaluation	evaluation	NOUN
ejpam-6969	199	16	of	of	ADP
ejpam-6969	199	17	multiple	multiple	ADJ
ejpam-6969	199	18	nested	nested	ADJ
ejpam-6969	199	19	integrals	integral	NOUN
ejpam-6969	199	20	.	.	PUNCT
ejpam-6969	200	1	the	the	DET
ejpam-6969	200	2	numerical	numerical	ADJ
ejpam-6969	200	3	results	result	NOUN
ejpam-6969	200	4	indicate	indicate	VERB
ejpam-6969	200	5	that	that	SCONJ
ejpam-6969	200	6	the	the	DET
ejpam-6969	200	7	bc	bc	PROPN
ejpam-6969	200	8	method	method	NOUN
ejpam-6969	200	9	consistently	consistently	ADV
ejpam-6969	200	10	outperforms	outperform	VERB
ejpam-6969	200	11	the	the	DET
ejpam-6969	200	12	hg	hg	NOUN
ejpam-6969	200	13	method	method	NOUN
ejpam-6969	200	14	.	.	PUNCT
ejpam-6969	201	1	this	this	DET
ejpam-6969	201	2	superiority	superiority	NOUN
ejpam-6969	201	3	is	be	AUX
ejpam-6969	201	4	mainly	mainly	ADV
ejpam-6969	201	5	due	due	ADJ
ejpam-6969	201	6	to	to	ADP
ejpam-6969	201	7	the	the	DET
ejpam-6969	201	8	better	well	ADJ
ejpam-6969	201	9	conditioning	conditioning	NOUN
ejpam-6969	201	10	of	of	ADP
ejpam-6969	201	11	the	the	DET
ejpam-6969	201	12	bc	bc	PROPN
ejpam-6969	201	13	formulation	formulation	NOUN
ejpam-6969	201	14	and	and	CCONJ
ejpam-6969	201	15	the	the	DET
ejpam-6969	201	16	suitability	suitability	NOUN
ejpam-6969	201	17	of	of	ADP
ejpam-6969	201	18	the	the	DET
ejpam-6969	201	19	bernoulli	bernoulli	PROPN
ejpam-6969	201	20	basis	basis	NOUN
ejpam-6969	201	21	functions	function	NOUN
ejpam-6969	201	22	for	for	ADP
ejpam-6969	201	23	smooth	smooth	ADJ
ejpam-6969	201	24	nonlinear	nonlinear	ADJ
ejpam-6969	201	25	kernels	kernel	NOUN
ejpam-6969	201	26	,	,	PUNCT
ejpam-6969	201	27	which	which	PRON
ejpam-6969	201	28	leads	lead	VERB
ejpam-6969	201	29	to	to	ADP
ejpam-6969	201	30	faster	fast	ADJ
ejpam-6969	201	31	convergence	convergence	NOUN
ejpam-6969	201	32	and	and	CCONJ
ejpam-6969	201	33	reduced	reduce	VERB
ejpam-6969	201	34	numerical	numerical	ADJ
ejpam-6969	201	35	oscillations	oscillation	NOUN
ejpam-6969	201	36	.	.	PUNCT
ejpam-6969	202	1	7	7	X
ejpam-6969	202	2	.	.	X
ejpam-6969	202	3	conclusions	conclusion	NOUN
ejpam-6969	202	4	in	in	ADP
ejpam-6969	202	5	this	this	DET
ejpam-6969	202	6	article	article	NOUN
ejpam-6969	202	7	,	,	PUNCT
ejpam-6969	202	8	we	we	PRON
ejpam-6969	202	9	employed	employ	VERB
ejpam-6969	202	10	bernoulli	bernoulli	NOUN
ejpam-6969	202	11	collocation	collocation	NOUN
ejpam-6969	202	12	and	and	CCONJ
ejpam-6969	202	13	hermite	hermite	ADJ
ejpam-6969	202	14	–	–	PUNCT
ejpam-6969	202	15	galerkin	galerkin	ADJ
ejpam-6969	202	16	methods	method	NOUN
ejpam-6969	202	17	to	to	PART
ejpam-6969	202	18	approximate	approximate	VERB
ejpam-6969	202	19	the	the	DET
ejpam-6969	202	20	solution	solution	NOUN
ejpam-6969	202	21	of	of	ADP
ejpam-6969	202	22	two	two	NUM
ejpam-6969	202	23	-	-	PUNCT
ejpam-6969	202	24	dimensional	dimensional	ADJ
ejpam-6969	202	25	nonlinear	nonlinear	ADJ
ejpam-6969	202	26	volterra	volterra	NOUN
ejpam-6969	202	27	integral	integral	ADJ
ejpam-6969	202	28	equations	equation	NOUN
ejpam-6969	202	29	.	.	PUNCT
ejpam-6969	203	1	numerical	numerical	PROPN
ejpam-6969	203	2	results	result	NOUN
ejpam-6969	203	3	show	show	VERB
ejpam-6969	203	4	that	that	SCONJ
ejpam-6969	203	5	the	the	DET
ejpam-6969	203	6	bernoulli	bernoulli	PROPN
ejpam-6969	203	7	collocation	collocation	NOUN
ejpam-6969	203	8	method	method	NOUN
ejpam-6969	203	9	consistently	consistently	ADV
ejpam-6969	203	10	provides	provide	VERB
ejpam-6969	203	11	more	more	ADV
ejpam-6969	203	12	accurate	accurate	ADJ
ejpam-6969	203	13	and	and	CCONJ
ejpam-6969	203	14	efficient	efficient	ADJ
ejpam-6969	203	15	results	result	NOUN
ejpam-6969	203	16	than	than	ADP
ejpam-6969	203	17	the	the	DET
ejpam-6969	203	18	hermite	hermite	ADJ
ejpam-6969	203	19	–	–	PUNCT
ejpam-6969	203	20	galerkin	galerkin	ADJ
ejpam-6969	203	21	method	method	NOUN
ejpam-6969	203	22	for	for	ADP
ejpam-6969	203	23	the	the	DET
ejpam-6969	203	24	same	same	ADJ
ejpam-6969	203	25	number	number	NOUN
ejpam-6969	203	26	of	of	ADP
ejpam-6969	203	27	points	point	NOUN
ejpam-6969	203	28	n	n	X
ejpam-6969	203	29	.	.	PUNCT
ejpam-6969	204	1	in	in	ADP
ejpam-6969	204	2	our	our	PRON
ejpam-6969	204	3	computations	computation	NOUN
ejpam-6969	204	4	,	,	PUNCT
ejpam-6969	204	5	we	we	PRON
ejpam-6969	204	6	used	use	VERB
ejpam-6969	204	7	n	n	NOUN
ejpam-6969	204	8	=	=	NUM
ejpam-6969	204	9	6	6	NUM
ejpam-6969	204	10	,	,	PUNCT
ejpam-6969	204	11	as	as	ADP
ejpam-6969	204	12	increasing	increase	VERB
ejpam-6969	204	13	n	n	CCONJ
ejpam-6969	204	14	for	for	ADP
ejpam-6969	204	15	the	the	DET
ejpam-6969	204	16	hermite	hermite	ADJ
ejpam-6969	204	17	–	–	PUNCT
ejpam-6969	204	18	galerkin	galerkin	ADJ
ejpam-6969	204	19	method	method	NOUN
ejpam-6969	204	20	is	be	AUX
ejpam-6969	204	21	difficult	difficult	ADJ
ejpam-6969	204	22	due	due	ADP
ejpam-6969	204	23	to	to	ADP
ejpam-6969	204	24	the	the	DET
ejpam-6969	204	25	complexity	complexity	NOUN
ejpam-6969	204	26	of	of	ADP
ejpam-6969	204	27	its	its	PRON
ejpam-6969	204	28	integrals	integral	NOUN
ejpam-6969	204	29	,	,	PUNCT
ejpam-6969	204	30	while	while	SCONJ
ejpam-6969	204	31	the	the	DET
ejpam-6969	204	32	bernoulli	bernoulli	NOUN
ejpam-6969	204	33	collocation	collocation	NOUN
ejpam-6969	204	34	method	method	NOUN
ejpam-6969	204	35	handles	handle	VERB
ejpam-6969	204	36	larger	large	ADJ
ejpam-6969	204	37	n	n	PRON
ejpam-6969	204	38	more	more	ADV
ejpam-6969	204	39	efficiently	efficiently	ADV
ejpam-6969	204	40	.	.	PUNCT
ejpam-6969	205	1	comparisons	comparison	NOUN
ejpam-6969	205	2	with	with	ADP
ejpam-6969	205	3	previously	previously	ADV
ejpam-6969	205	4	published	publish	VERB
ejpam-6969	205	5	methods	method	NOUN
ejpam-6969	205	6	,	,	PUNCT
ejpam-6969	205	7	such	such	ADJ
ejpam-6969	205	8	as	as	ADP
ejpam-6969	205	9	the	the	DET
ejpam-6969	205	10	reproducing	reproduce	VERB
ejpam-6969	205	11	kernel	kernel	NOUN
ejpam-6969	205	12	space	space	NOUN
ejpam-6969	205	13	[	[	X
ejpam-6969	205	14	8	8	NUM
ejpam-6969	205	15	]	]	PUNCT
ejpam-6969	205	16	,	,	PUNCT
ejpam-6969	205	17	taylor	taylor	NOUN
ejpam-6969	205	18	collocation	collocation	NOUN
ejpam-6969	206	1	[	[	X
ejpam-6969	206	2	28	28	NUM
ejpam-6969	206	3	]	]	PUNCT
ejpam-6969	206	4	,	,	PUNCT
ejpam-6969	206	5	rationalized	rationalize	VERB
ejpam-6969	206	6	haar	haar	NOUN
ejpam-6969	206	7	functions	function	NOUN
ejpam-6969	206	8	[	[	X
ejpam-6969	206	9	10	10	NUM
ejpam-6969	206	10	]	]	PUNCT
ejpam-6969	206	11	,	,	PUNCT
ejpam-6969	206	12	and	and	CCONJ
ejpam-6969	206	13	extrapolation	extrapolation	NOUN
ejpam-6969	206	14	methods	method	NOUN
ejpam-6969	206	15	[	[	X
ejpam-6969	206	16	29	29	NUM
ejpam-6969	206	17	]	]	PUNCT
ejpam-6969	206	18	,	,	PUNCT
ejpam-6969	206	19	further	far	ADV
ejpam-6969	206	20	demonstrate	demonstrate	VERB
ejpam-6969	206	21	the	the	DET
ejpam-6969	206	22	superiority	superiority	NOUN
ejpam-6969	206	23	of	of	ADP
ejpam-6969	206	24	our	our	PRON
ejpam-6969	206	25	approaches	approach	NOUN
ejpam-6969	206	26	.	.	PUNCT
ejpam-6969	207	1	the	the	DET
ejpam-6969	207	2	better	well	ADJ
ejpam-6969	207	3	performance	performance	NOUN
ejpam-6969	207	4	of	of	ADP
ejpam-6969	207	5	the	the	DET
ejpam-6969	207	6	bernoulli	bernoulli	NOUN
ejpam-6969	207	7	collocation	collocation	NOUN
ejpam-6969	207	8	method	method	NOUN
ejpam-6969	207	9	is	be	AUX
ejpam-6969	207	10	mainly	mainly	ADV
ejpam-6969	207	11	due	due	ADJ
ejpam-6969	207	12	to	to	ADP
ejpam-6969	207	13	the	the	DET
ejpam-6969	207	14	suitability	suitability	NOUN
ejpam-6969	207	15	of	of	ADP
ejpam-6969	207	16	the	the	DET
ejpam-6969	207	17	bernoulli	bernoulli	PROPN
ejpam-6969	207	18	basis	basis	NOUN
ejpam-6969	207	19	functions	function	NOUN
ejpam-6969	207	20	for	for	ADP
ejpam-6969	207	21	smooth	smooth	ADJ
ejpam-6969	207	22	nonlinear	nonlinear	ADJ
ejpam-6969	207	23	kernels	kernel	NOUN
ejpam-6969	207	24	and	and	CCONJ
ejpam-6969	207	25	improved	improved	ADJ
ejpam-6969	207	26	conditioning	conditioning	NOUN
ejpam-6969	207	27	,	,	PUNCT
ejpam-6969	207	28	leading	lead	VERB
ejpam-6969	207	29	to	to	ADP
ejpam-6969	207	30	faster	fast	ADJ
ejpam-6969	207	31	convergence	convergence	NOUN
ejpam-6969	207	32	and	and	CCONJ
ejpam-6969	207	33	reduced	reduce	VERB
ejpam-6969	207	34	numerical	numerical	ADJ
ejpam-6969	207	35	oscillations	oscillation	NOUN
ejpam-6969	207	36	.	.	PUNCT
ejpam-6969	208	1	furthermore	furthermore	ADV
ejpam-6969	208	2	,	,	PUNCT
ejpam-6969	208	3	the	the	DET
ejpam-6969	208	4	present	present	ADJ
ejpam-6969	208	5	work	work	NOUN
ejpam-6969	208	6	can	can	AUX
ejpam-6969	208	7	be	be	AUX
ejpam-6969	208	8	extended	extend	VERB
ejpam-6969	208	9	to	to	ADP
ejpam-6969	208	10	fractional	fractional	ADJ
ejpam-6969	208	11	-	-	PUNCT
ejpam-6969	208	12	order	order	NOUN
ejpam-6969	208	13	versions	version	NOUN
ejpam-6969	208	14	of	of	ADP
ejpam-6969	208	15	two	two	NUM
ejpam-6969	208	16	-	-	PUNCT
ejpam-6969	208	17	dimensional	dimensional	ADJ
ejpam-6969	208	18	volterra	volterra	NOUN
ejpam-6969	208	19	integral	integral	ADJ
ejpam-6969	208	20	equations	equation	NOUN
ejpam-6969	208	21	to	to	PART
ejpam-6969	208	22	capture	capture	VERB
ejpam-6969	208	23	memory	memory	NOUN
ejpam-6969	208	24	and	and	CCONJ
ejpam-6969	208	25	nonlocal	nonlocal	ADJ
ejpam-6969	208	26	effects	effect	NOUN
ejpam-6969	208	27	,	,	PUNCT
ejpam-6969	208	28	as	as	SCONJ
ejpam-6969	208	29	illustrated	illustrate	VERB
ejpam-6969	208	30	in	in	ADP
ejpam-6969	208	31	related	related	ADJ
ejpam-6969	208	32	studies	study	NOUN
ejpam-6969	208	33	[	[	X
ejpam-6969	208	34	19	19	NUM
ejpam-6969	208	35	,	,	PUNCT
ejpam-6969	208	36	30	30	NUM
ejpam-6969	208	37	]	]	PUNCT
ejpam-6969	208	38	.	.	PUNCT
ejpam-6969	209	1	acknowledgements	acknowledgement	NOUN
ejpam-6969	209	2	the	the	DET
ejpam-6969	209	3	authors	author	NOUN
ejpam-6969	209	4	are	be	AUX
ejpam-6969	209	5	deeply	deeply	ADV
ejpam-6969	209	6	grateful	grateful	ADJ
ejpam-6969	209	7	to	to	ADP
ejpam-6969	209	8	the	the	DET
ejpam-6969	209	9	editor	editor	NOUN
ejpam-6969	209	10	and	and	CCONJ
ejpam-6969	209	11	anonymous	anonymous	ADJ
ejpam-6969	209	12	reviewers	reviewer	NOUN
ejpam-6969	209	13	for	for	ADP
ejpam-6969	209	14	their	their	PRON
ejpam-6969	209	15	valuable	valuable	ADJ
ejpam-6969	209	16	comments	comment	NOUN
ejpam-6969	209	17	,	,	PUNCT
ejpam-6969	209	18	insightful	insightful	ADJ
ejpam-6969	209	19	suggestions	suggestion	NOUN
ejpam-6969	209	20	,	,	PUNCT
ejpam-6969	209	21	and	and	CCONJ
ejpam-6969	209	22	constructive	constructive	ADJ
ejpam-6969	209	23	recommendations	recommendation	NOUN
ejpam-6969	209	24	that	that	PRON
ejpam-6969	209	25	greatly	greatly	ADV
ejpam-6969	209	26	improved	improve	VERB
ejpam-6969	209	27	the	the	DET
ejpam-6969	209	28	quality	quality	NOUN
ejpam-6969	209	29	and	and	CCONJ
ejpam-6969	209	30	organization	organization	NOUN
ejpam-6969	209	31	of	of	ADP
ejpam-6969	209	32	this	this	DET
ejpam-6969	209	33	manuscript	manuscript	NOUN
ejpam-6969	209	34	.	.	PUNCT
ejpam-6969	210	1	competing	compete	VERB
ejpam-6969	210	2	interests	interest	NOUN
ejpam-6969	210	3	:	:	PUNCT
ejpam-6969	210	4	the	the	DET
ejpam-6969	210	5	authors	author	NOUN
ejpam-6969	210	6	declare	declare	VERB
ejpam-6969	210	7	that	that	SCONJ
ejpam-6969	210	8	they	they	PRON
ejpam-6969	210	9	have	have	VERB
ejpam-6969	210	10	no	no	DET
ejpam-6969	210	11	conflicts	conflict	NOUN
ejpam-6969	210	12	of	of	ADP
ejpam-6969	210	13	interest	interest	NOUN
ejpam-6969	210	14	regarding	regard	VERB
ejpam-6969	210	15	the	the	DET
ejpam-6969	210	16	publication	publication	NOUN
ejpam-6969	210	17	of	of	ADP
ejpam-6969	210	18	this	this	DET
ejpam-6969	210	19	work	work	NOUN
ejpam-6969	210	20	.	.	PUNCT
ejpam-6969	211	1	m.	m.	NOUN
ejpam-6969	211	2	h.	h.	PROPN
ejpam-6969	211	3	ahmed	ahmed	PROPN
ejpam-6969	211	4	,	,	PUNCT
ejpam-6969	211	5	a.	a.	NOUN
ejpam-6969	211	6	m.	m.	PROPN
ejpam-6969	211	7	aljabri	aljabri	PROPN
ejpam-6969	211	8	/	/	SYM
ejpam-6969	211	9	eur	eur	PROPN
ejpam-6969	211	10	.	.	PUNCT
ejpam-6969	212	1	j.	j.	PROPN
ejpam-6969	212	2	pure	pure	PROPN
ejpam-6969	212	3	appl	appl	PROPN
ejpam-6969	212	4	.	.	PROPN
ejpam-6969	212	5	math	math	PROPN
ejpam-6969	212	6	,	,	PUNCT
ejpam-6969	212	7	18	18	NUM
ejpam-6969	212	8	(	(	PUNCT
ejpam-6969	212	9	4	4	NUM
ejpam-6969	212	10	)	)	PUNCT
ejpam-6969	212	11	(	(	PUNCT
ejpam-6969	212	12	2025	2025	NUM
ejpam-6969	212	13	)	)	PUNCT
ejpam-6969	212	14	,	,	PUNCT
ejpam-6969	212	15	6969	6969	NUM
ejpam-6969	212	16	13	13	NUM
ejpam-6969	212	17	of	of	ADP
ejpam-6969	212	18	16	16	NUM
ejpam-6969	212	19	references	reference	NOUN
ejpam-6969	212	20	[	[	X
ejpam-6969	212	21	1	1	NUM
ejpam-6969	212	22	]	]	X
ejpam-6969	212	23	richard	richard	PROPN
ejpam-6969	212	24	d	d	PROPN
ejpam-6969	212	25	noren	noren	PROPN
ejpam-6969	212	26	.	.	PUNCT
ejpam-6969	213	1	a	a	DET
ejpam-6969	213	2	linear	linear	PROPN
ejpam-6969	213	3	volterra	volterra	NOUN
ejpam-6969	213	4	integro	integro	PROPN
ejpam-6969	213	5	-	-	PUNCT
ejpam-6969	213	6	differential	differential	NOUN
ejpam-6969	213	7	equation	equation	NOUN
ejpam-6969	213	8	for	for	ADP
ejpam-6969	213	9	viscoelastic	viscoelastic	ADJ
ejpam-6969	213	10	rods	rod	NOUN
ejpam-6969	213	11	and	and	CCONJ
ejpam-6969	213	12	plates	plate	NOUN
ejpam-6969	213	13	.	.	PUNCT
ejpam-6969	214	1	quarterly	quarterly	ADV
ejpam-6969	214	2	of	of	ADP
ejpam-6969	214	3	applied	applied	ADJ
ejpam-6969	214	4	mathematics	mathematic	NOUN
ejpam-6969	214	5	,	,	PUNCT
ejpam-6969	214	6	45(3):503–514	45(3):503–514	NOUN
ejpam-6969	214	7	,	,	PUNCT
ejpam-6969	214	8	1987	1987	NUM
ejpam-6969	214	9	.	.	PUNCT
ejpam-6969	215	1	[	[	X
ejpam-6969	215	2	2	2	NUM
ejpam-6969	215	3	]	]	PUNCT
ejpam-6969	215	4	a25126821197	a25126821197	NOUN
ejpam-6969	215	5	wineman	wineman	NOUN
ejpam-6969	215	6	.	.	PUNCT
ejpam-6969	216	1	nonlinear	nonlinear	ADJ
ejpam-6969	216	2	viscoelastic	viscoelastic	ADJ
ejpam-6969	216	3	solids	solid	NOUN
ejpam-6969	216	4	—	—	PUNCT
ejpam-6969	216	5	a	a	DET
ejpam-6969	216	6	review	review	NOUN
ejpam-6969	216	7	.	.	PUNCT
ejpam-6969	217	1	mathematics	mathematic	NOUN
ejpam-6969	217	2	and	and	CCONJ
ejpam-6969	217	3	mechanics	mechanic	NOUN
ejpam-6969	217	4	of	of	ADP
ejpam-6969	217	5	solids	solid	NOUN
ejpam-6969	217	6	,	,	PUNCT
ejpam-6969	217	7	14(3):300–366	14(3):300–366	PROPN
ejpam-6969	217	8	,	,	PUNCT
ejpam-6969	217	9	2009	2009	NUM
ejpam-6969	217	10	.	.	PUNCT
ejpam-6969	218	1	[	[	X
ejpam-6969	218	2	3	3	NUM
ejpam-6969	218	3	]	]	PUNCT
ejpam-6969	218	4	faheem	faheem	NOUN
ejpam-6969	218	5	khan	khan	PROPN
ejpam-6969	218	6	,	,	PUNCT
ejpam-6969	218	7	muhammad	muhammad	PROPN
ejpam-6969	218	8	omar	omar	PROPN
ejpam-6969	218	9	,	,	PUNCT
ejpam-6969	218	10	and	and	CCONJ
ejpam-6969	218	11	zafar	zafar	PROPN
ejpam-6969	218	12	ullah	ullah	PROPN
ejpam-6969	218	13	.	.	PUNCT
ejpam-6969	218	14	discretization	discretization	NOUN
ejpam-6969	218	15	method	method	NOUN
ejpam-6969	218	16	for	for	ADP
ejpam-6969	218	17	the	the	DET
ejpam-6969	218	18	numerical	numerical	ADJ
ejpam-6969	218	19	solution	solution	NOUN
ejpam-6969	218	20	of	of	ADP
ejpam-6969	218	21	2d	2d	PROPN
ejpam-6969	218	22	volterra	volterra	NOUN
ejpam-6969	218	23	integral	integral	ADJ
ejpam-6969	218	24	equation	equation	NOUN
ejpam-6969	218	25	based	base	VERB
ejpam-6969	218	26	on	on	ADP
ejpam-6969	218	27	two	two	NUM
ejpam-6969	218	28	-	-	PUNCT
ejpam-6969	218	29	dimensional	dimensional	ADJ
ejpam-6969	218	30	bernstein	bernstein	PROPN
ejpam-6969	218	31	polynomial	polynomial	PROPN
ejpam-6969	218	32	.	.	PUNCT
ejpam-6969	219	1	aip	aip	PROPN
ejpam-6969	219	2	advances	advance	NOUN
ejpam-6969	219	3	,	,	PUNCT
ejpam-6969	219	4	8(12	8(12	NUM
ejpam-6969	219	5	)	)	PUNCT
ejpam-6969	219	6	,	,	PUNCT
ejpam-6969	219	7	2018	2018	NUM
ejpam-6969	219	8	.	.	PUNCT
ejpam-6969	220	1	[	[	X
ejpam-6969	220	2	4	4	X
ejpam-6969	220	3	]	]	X
ejpam-6969	220	4	pouria	pouria	NOUN
ejpam-6969	220	5	assari	assari	NOUN
ejpam-6969	220	6	and	and	CCONJ
ejpam-6969	220	7	mehdi	mehdi	PROPN
ejpam-6969	220	8	dehghan	dehghan	PROPN
ejpam-6969	220	9	.	.	PUNCT
ejpam-6969	221	1	a	a	DET
ejpam-6969	221	2	meshless	meshless	ADJ
ejpam-6969	221	3	local	local	ADJ
ejpam-6969	221	4	discrete	discrete	ADJ
ejpam-6969	221	5	galerkin	galerkin	NOUN
ejpam-6969	221	6	(	(	PUNCT
ejpam-6969	221	7	mldg	mldg	NOUN
ejpam-6969	221	8	)	)	PUNCT
ejpam-6969	221	9	scheme	scheme	NOUN
ejpam-6969	221	10	for	for	ADP
ejpam-6969	221	11	numerically	numerically	ADV
ejpam-6969	221	12	solving	solve	VERB
ejpam-6969	221	13	two	two	NUM
ejpam-6969	221	14	-	-	PUNCT
ejpam-6969	221	15	dimensional	dimensional	ADJ
ejpam-6969	221	16	nonlinear	nonlinear	ADJ
ejpam-6969	221	17	volterra	volterra	NOUN
ejpam-6969	221	18	integral	integral	ADJ
ejpam-6969	221	19	equations	equation	NOUN
ejpam-6969	221	20	.	.	PUNCT
ejpam-6969	222	1	applied	apply	VERB
ejpam-6969	222	2	mathematics	mathematic	NOUN
ejpam-6969	222	3	and	and	CCONJ
ejpam-6969	222	4	computation	computation	NOUN
ejpam-6969	222	5	,	,	PUNCT
ejpam-6969	222	6	350:249–265	350:249–265	NUM
ejpam-6969	222	7	,	,	PUNCT
ejpam-6969	222	8	2019	2019	NUM
ejpam-6969	222	9	.	.	PUNCT
ejpam-6969	223	1	[	[	X
ejpam-6969	223	2	5	5	NUM
ejpam-6969	223	3	]	]	X
ejpam-6969	223	4	manochehr	manochehr	PROPN
ejpam-6969	223	5	kazemi	kazemi	PROPN
ejpam-6969	223	6	.	.	PUNCT
ejpam-6969	224	1	an	an	DET
ejpam-6969	224	2	iterative	iterative	NOUN
ejpam-6969	224	3	method	method	NOUN
ejpam-6969	224	4	for	for	ADP
ejpam-6969	224	5	solving	solve	VERB
ejpam-6969	224	6	two	two	NUM
ejpam-6969	224	7	dimensional	dimensional	ADJ
ejpam-6969	224	8	nonlinear	nonlinear	ADJ
ejpam-6969	224	9	volterra	volterra	NOUN
ejpam-6969	224	10	integral	integral	ADJ
ejpam-6969	224	11	equations	equation	NOUN
ejpam-6969	224	12	.	.	PUNCT
ejpam-6969	225	1	analytical	analytical	ADJ
ejpam-6969	225	2	and	and	CCONJ
ejpam-6969	225	3	numerical	numerical	ADJ
ejpam-6969	225	4	solutions	solution	NOUN
ejpam-6969	225	5	for	for	ADP
ejpam-6969	225	6	nonlinear	nonlinear	ADJ
ejpam-6969	225	7	equations	equation	NOUN
ejpam-6969	225	8	,	,	PUNCT
ejpam-6969	225	9	6(1):41–57	6(1):41–57	NUM
ejpam-6969	225	10	,	,	PUNCT
ejpam-6969	225	11	2021	2021	NUM
ejpam-6969	225	12	.	.	PUNCT
ejpam-6969	226	1	[	[	X
ejpam-6969	226	2	6	6	NUM
ejpam-6969	226	3	]	]	PUNCT
ejpam-6969	226	4	zakieh	zakieh	PROPN
ejpam-6969	226	5	avazzadeh	avazzadeh	PROPN
ejpam-6969	226	6	and	and	CCONJ
ejpam-6969	226	7	mohammad	mohammad	PROPN
ejpam-6969	226	8	heydari	heydari	PROPN
ejpam-6969	226	9	.	.	PUNCT
ejpam-6969	227	1	chebyshev	chebyshev	PROPN
ejpam-6969	227	2	polynomials	polynomial	NOUN
ejpam-6969	227	3	for	for	ADP
ejpam-6969	227	4	solving	solve	VERB
ejpam-6969	227	5	two	two	NUM
ejpam-6969	227	6	dimensional	dimensional	ADJ
ejpam-6969	227	7	linear	linear	NOUN
ejpam-6969	227	8	and	and	CCONJ
ejpam-6969	227	9	nonlinear	nonlinear	ADJ
ejpam-6969	227	10	integral	integral	ADJ
ejpam-6969	227	11	equations	equation	NOUN
ejpam-6969	227	12	of	of	ADP
ejpam-6969	227	13	the	the	DET
ejpam-6969	227	14	second	second	ADJ
ejpam-6969	227	15	kind	kind	NOUN
ejpam-6969	227	16	.	.	PUNCT
ejpam-6969	228	1	computational	computational	ADJ
ejpam-6969	228	2	&	&	CCONJ
ejpam-6969	228	3	applied	applied	ADJ
ejpam-6969	228	4	mathematics	mathematic	NOUN
ejpam-6969	228	5	,	,	PUNCT
ejpam-6969	228	6	31:127–142	31:127–142	PROPN
ejpam-6969	228	7	,	,	PUNCT
ejpam-6969	228	8	2012	2012	NUM
ejpam-6969	228	9	.	.	PUNCT
ejpam-6969	229	1	[	[	X
ejpam-6969	229	2	7	7	X
ejpam-6969	229	3	]	]	X
ejpam-6969	229	4	a	a	DET
ejpam-6969	229	5	tari	tari	NOUN
ejpam-6969	229	6	,	,	PUNCT
ejpam-6969	229	7	my	my	PRON
ejpam-6969	229	8	rahimi	rahimi	NOUN
ejpam-6969	229	9	,	,	PUNCT
ejpam-6969	229	10	s	s	NOUN
ejpam-6969	229	11	shahmorad	shahmorad	NOUN
ejpam-6969	229	12	,	,	PUNCT
ejpam-6969	229	13	and	and	CCONJ
ejpam-6969	229	14	f	f	PROPN
ejpam-6969	229	15	talati	talati	NOUN
ejpam-6969	229	16	.	.	PUNCT
ejpam-6969	230	1	solving	solve	VERB
ejpam-6969	230	2	a	a	DET
ejpam-6969	230	3	class	class	NOUN
ejpam-6969	230	4	of	of	ADP
ejpam-6969	230	5	two	two	NUM
ejpam-6969	230	6	-	-	PUNCT
ejpam-6969	230	7	dimensional	dimensional	ADJ
ejpam-6969	230	8	linear	linear	NOUN
ejpam-6969	230	9	and	and	CCONJ
ejpam-6969	230	10	nonlinear	nonlinear	ADJ
ejpam-6969	230	11	volterra	volterra	PROPN
ejpam-6969	230	12	integral	integral	ADJ
ejpam-6969	230	13	equations	equation	NOUN
ejpam-6969	230	14	by	by	ADP
ejpam-6969	230	15	the	the	DET
ejpam-6969	230	16	differential	differential	ADJ
ejpam-6969	230	17	transform	transform	NOUN
ejpam-6969	230	18	method	method	NOUN
ejpam-6969	230	19	.	.	PUNCT
ejpam-6969	231	1	journal	journal	NOUN
ejpam-6969	231	2	of	of	ADP
ejpam-6969	231	3	computational	computational	ADJ
ejpam-6969	231	4	and	and	CCONJ
ejpam-6969	231	5	applied	applied	ADJ
ejpam-6969	231	6	mathematics	mathematic	NOUN
ejpam-6969	231	7	,	,	PUNCT
ejpam-6969	231	8	228(1):70–76	228(1):70–76	NUM
ejpam-6969	231	9	,	,	PUNCT
ejpam-6969	231	10	2009	2009	NUM
ejpam-6969	231	11	.	.	PUNCT
ejpam-6969	232	1	[	[	X
ejpam-6969	232	2	8	8	NUM
ejpam-6969	232	3	]	]	X
ejpam-6969	232	4	a	a	DET
ejpam-6969	232	5	fazli	fazli	NOUN
ejpam-6969	232	6	,	,	PUNCT
ejpam-6969	232	7	t	t	NOUN
ejpam-6969	232	8	allahviranloo	allahviranloo	NOUN
ejpam-6969	232	9	,	,	PUNCT
ejpam-6969	232	10	and	and	CCONJ
ejpam-6969	232	11	sh	sh	PROPN
ejpam-6969	232	12	javadi	javadi	PROPN
ejpam-6969	232	13	.	.	PUNCT
ejpam-6969	233	1	numerical	numerical	ADJ
ejpam-6969	233	2	solution	solution	NOUN
ejpam-6969	233	3	of	of	ADP
ejpam-6969	233	4	nonlinear	nonlinear	ADJ
ejpam-6969	233	5	twodimensional	twodimensional	PROPN
ejpam-6969	233	6	volterra	volterra	PROPN
ejpam-6969	233	7	integral	integral	ADJ
ejpam-6969	233	8	equation	equation	NOUN
ejpam-6969	233	9	of	of	ADP
ejpam-6969	233	10	the	the	DET
ejpam-6969	233	11	second	second	ADJ
ejpam-6969	233	12	kind	kind	NOUN
ejpam-6969	233	13	in	in	ADP
ejpam-6969	233	14	the	the	DET
ejpam-6969	233	15	reproducing	reproduce	VERB
ejpam-6969	233	16	kernel	kernel	NOUN
ejpam-6969	233	17	space	space	NOUN
ejpam-6969	233	18	.	.	PUNCT
ejpam-6969	234	1	mathematical	mathematical	ADJ
ejpam-6969	234	2	sciences	sciences	PROPN
ejpam-6969	234	3	,	,	PUNCT
ejpam-6969	234	4	11(2):139–144	11(2):139–144	NUM
ejpam-6969	234	5	,	,	PUNCT
ejpam-6969	234	6	2017	2017	NUM
ejpam-6969	234	7	.	.	PUNCT
ejpam-6969	235	1	[	[	X
ejpam-6969	235	2	9	9	NUM
ejpam-6969	235	3	]	]	X
ejpam-6969	235	4	somayeh	somayeh	NOUN
ejpam-6969	235	5	nemati	nemati	PROPN
ejpam-6969	235	6	,	,	PUNCT
ejpam-6969	235	7	pedro	pedro	PROPN
ejpam-6969	235	8	miguel	miguel	PROPN
ejpam-6969	235	9	lima	lima	PROPN
ejpam-6969	235	10	,	,	PUNCT
ejpam-6969	235	11	and	and	CCONJ
ejpam-6969	235	12	yadollah	yadollah	PROPN
ejpam-6969	235	13	ordokhani	ordokhani	PROPN
ejpam-6969	235	14	.	.	PUNCT
ejpam-6969	236	1	numerical	numerical	ADJ
ejpam-6969	236	2	solution	solution	NOUN
ejpam-6969	236	3	of	of	ADP
ejpam-6969	236	4	a	a	DET
ejpam-6969	236	5	class	class	NOUN
ejpam-6969	236	6	of	of	ADP
ejpam-6969	236	7	two	two	NUM
ejpam-6969	236	8	-	-	PUNCT
ejpam-6969	236	9	dimensional	dimensional	ADJ
ejpam-6969	236	10	nonlinear	nonlinear	ADJ
ejpam-6969	236	11	volterra	volterra	NOUN
ejpam-6969	236	12	integral	integral	ADJ
ejpam-6969	236	13	equations	equation	NOUN
ejpam-6969	236	14	using	use	VERB
ejpam-6969	236	15	legendre	legendre	PROPN
ejpam-6969	236	16	polynomials	polynomial	NOUN
ejpam-6969	236	17	.	.	PUNCT
ejpam-6969	237	1	journal	journal	NOUN
ejpam-6969	237	2	of	of	ADP
ejpam-6969	237	3	computational	computational	ADJ
ejpam-6969	237	4	and	and	CCONJ
ejpam-6969	237	5	applied	applied	ADJ
ejpam-6969	237	6	mathematics	mathematic	NOUN
ejpam-6969	237	7	,	,	PUNCT
ejpam-6969	237	8	242:53–69	242:53–69	NUM
ejpam-6969	237	9	,	,	PUNCT
ejpam-6969	237	10	2013	2013	NUM
ejpam-6969	237	11	.	.	PUNCT
ejpam-6969	238	1	[	[	X
ejpam-6969	238	2	10	10	NUM
ejpam-6969	238	3	]	]	X
ejpam-6969	238	4	majid	majid	PROPN
ejpam-6969	238	5	erfanian	erfanian	PROPN
ejpam-6969	238	6	and	and	CCONJ
ejpam-6969	238	7	hamed	hamed	ADJ
ejpam-6969	238	8	zeidabadi	zeidabadi	NOUN
ejpam-6969	238	9	.	.	PUNCT
ejpam-6969	239	1	solving	solve	VERB
ejpam-6969	239	2	two	two	NUM
ejpam-6969	239	3	-	-	PUNCT
ejpam-6969	239	4	dimensional	dimensional	ADJ
ejpam-6969	239	5	nonlinear	nonlinear	ADJ
ejpam-6969	239	6	volterra	volterra	NOUN
ejpam-6969	239	7	integral	integral	ADJ
ejpam-6969	239	8	equations	equation	NOUN
ejpam-6969	239	9	using	use	VERB
ejpam-6969	239	10	rationalized	rationalize	VERB
ejpam-6969	239	11	haar	haar	NOUN
ejpam-6969	239	12	functions	function	NOUN
ejpam-6969	239	13	.	.	PUNCT
ejpam-6969	240	1	international	international	ADJ
ejpam-6969	240	2	journal	journal	PROPN
ejpam-6969	240	3	of	of	ADP
ejpam-6969	240	4	nonlinear	nonlinear	ADJ
ejpam-6969	240	5	analysis	analysis	NOUN
ejpam-6969	240	6	and	and	CCONJ
ejpam-6969	240	7	applications	application	NOUN
ejpam-6969	240	8	,	,	PUNCT
ejpam-6969	240	9	14(8):95–105	14(8):95–105	NUM
ejpam-6969	240	10	,	,	PUNCT
ejpam-6969	240	11	2023	2023	NUM
ejpam-6969	240	12	.	.	PUNCT
ejpam-6969	241	1	[	[	X
ejpam-6969	241	2	11	11	NUM
ejpam-6969	241	3	]	]	SYM
ejpam-6969	241	4	esmail	esmail	ADJ
ejpam-6969	241	5	babolian	babolian	NOUN
ejpam-6969	241	6	,	,	PUNCT
ejpam-6969	241	7	khosrow	khosrow	NOUN
ejpam-6969	241	8	maleknejad	maleknejad	PROPN
ejpam-6969	241	9	,	,	PUNCT
ejpam-6969	241	10	mohammad	mohammad	PROPN
ejpam-6969	241	11	mordad	mordad	PROPN
ejpam-6969	241	12	,	,	PUNCT
ejpam-6969	241	13	and	and	CCONJ
ejpam-6969	241	14	bijan	bijan	PROPN
ejpam-6969	241	15	rahimi	rahimi	NOUN
ejpam-6969	241	16	.	.	PUNCT
ejpam-6969	242	1	a	a	DET
ejpam-6969	242	2	numerical	numerical	ADJ
ejpam-6969	242	3	method	method	NOUN
ejpam-6969	242	4	for	for	ADP
ejpam-6969	242	5	solving	solve	VERB
ejpam-6969	242	6	fredholm	fredholm	NOUN
ejpam-6969	242	7	–	–	PUNCT
ejpam-6969	242	8	volterra	volterra	NOUN
ejpam-6969	242	9	integral	integral	ADJ
ejpam-6969	242	10	equations	equation	NOUN
ejpam-6969	242	11	in	in	ADP
ejpam-6969	242	12	two	two	NUM
ejpam-6969	242	13	-	-	PUNCT
ejpam-6969	242	14	dimensional	dimensional	ADJ
ejpam-6969	242	15	spaces	space	NOUN
ejpam-6969	242	16	using	use	VERB
ejpam-6969	242	17	block	block	NOUN
ejpam-6969	242	18	pulse	pulse	NOUN
ejpam-6969	242	19	functions	function	NOUN
ejpam-6969	242	20	and	and	CCONJ
ejpam-6969	242	21	an	an	DET
ejpam-6969	242	22	operational	operational	ADJ
ejpam-6969	242	23	matrix	matrix	NOUN
ejpam-6969	242	24	.	.	PUNCT
ejpam-6969	243	1	journal	journal	NOUN
ejpam-6969	243	2	of	of	ADP
ejpam-6969	243	3	computational	computational	ADJ
ejpam-6969	243	4	and	and	CCONJ
ejpam-6969	243	5	applied	applied	ADJ
ejpam-6969	243	6	mathematics	mathematic	NOUN
ejpam-6969	243	7	,	,	PUNCT
ejpam-6969	243	8	235(14):3965–3971	235(14):3965–3971	NUM
ejpam-6969	243	9	,	,	PUNCT
ejpam-6969	243	10	2011	2011	NUM
ejpam-6969	243	11	.	.	PUNCT
ejpam-6969	244	1	[	[	X
ejpam-6969	244	2	12	12	NUM
ejpam-6969	244	3	]	]	X
ejpam-6969	244	4	mohsen	mohsen	PROPN
ejpam-6969	244	5	jalalian	jalalian	PROPN
ejpam-6969	244	6	,	,	PUNCT
ejpam-6969	244	7	kawa	kawa	PROPN
ejpam-6969	244	8	wali	wali	PROPN
ejpam-6969	244	9	ali	ali	PROPN
ejpam-6969	244	10	,	,	PUNCT
ejpam-6969	244	11	sarkawt	sarkawt	PROPN
ejpam-6969	244	12	raouf	raouf	PROPN
ejpam-6969	244	13	qadir	qadir	PROPN
ejpam-6969	244	14	,	,	PUNCT
ejpam-6969	244	15	and	and	CCONJ
ejpam-6969	244	16	mohamad	mohamad	PROPN
ejpam-6969	244	17	reza	reza	PROPN
ejpam-6969	244	18	jalalian	jalalian	PROPN
ejpam-6969	244	19	.	.	PUNCT
ejpam-6969	245	1	a	a	DET
ejpam-6969	245	2	numerical	numerical	ADJ
ejpam-6969	245	3	method	method	NOUN
ejpam-6969	245	4	based	base	VERB
ejpam-6969	245	5	on	on	ADP
ejpam-6969	245	6	the	the	DET
ejpam-6969	245	7	radial	radial	ADJ
ejpam-6969	245	8	basis	basis	NOUN
ejpam-6969	245	9	functions	function	NOUN
ejpam-6969	245	10	for	for	ADP
ejpam-6969	245	11	solving	solve	VERB
ejpam-6969	245	12	nonlinear	nonlinear	ADJ
ejpam-6969	245	13	twodimensional	twodimensional	ADJ
ejpam-6969	245	14	volterra	volterra	NOUN
ejpam-6969	245	15	integral	integral	ADJ
ejpam-6969	245	16	equations	equation	NOUN
ejpam-6969	245	17	of	of	ADP
ejpam-6969	245	18	the	the	DET
ejpam-6969	245	19	second	second	ADJ
ejpam-6969	245	20	kind	kind	NOUN
ejpam-6969	245	21	on	on	ADP
ejpam-6969	245	22	non	non	ADJ
ejpam-6969	245	23	-	-	ADJ
ejpam-6969	245	24	rectangular	rectangular	ADJ
ejpam-6969	245	25	domains	domain	NOUN
ejpam-6969	245	26	.	.	PUNCT
ejpam-6969	245	27	journal	journal	PROPN
ejpam-6969	245	28	of	of	ADP
ejpam-6969	245	29	mathematical	mathematical	ADJ
ejpam-6969	245	30	modeling	modeling	NOUN
ejpam-6969	245	31	,	,	PUNCT
ejpam-6969	245	32	12(4):687–705	12(4):687–705	NUM
ejpam-6969	245	33	,	,	PUNCT
ejpam-6969	245	34	2024	2024	NUM
ejpam-6969	245	35	.	.	PUNCT
ejpam-6969	246	1	[	[	X
ejpam-6969	246	2	13	13	NUM
ejpam-6969	246	3	]	]	PUNCT
ejpam-6969	246	4	sohrab	sohrab	NOUN
ejpam-6969	246	5	bazm	bazm	PROPN
ejpam-6969	246	6	.	.	PUNCT
ejpam-6969	247	1	numerical	numerical	ADJ
ejpam-6969	247	2	solution	solution	NOUN
ejpam-6969	247	3	of	of	ADP
ejpam-6969	247	4	a	a	DET
ejpam-6969	247	5	class	class	NOUN
ejpam-6969	247	6	of	of	ADP
ejpam-6969	247	7	nonlinear	nonlinear	ADJ
ejpam-6969	247	8	two	two	NUM
ejpam-6969	247	9	-	-	PUNCT
ejpam-6969	247	10	dimensional	dimensional	ADJ
ejpam-6969	247	11	integral	integral	ADJ
ejpam-6969	247	12	equations	equation	NOUN
ejpam-6969	247	13	using	use	VERB
ejpam-6969	247	14	bernoulli	bernoulli	NOUN
ejpam-6969	247	15	polynomials	polynomial	NOUN
ejpam-6969	247	16	.	.	PUNCT
ejpam-6969	248	1	sahand	sahand	NOUN
ejpam-6969	248	2	communications	communication	NOUN
ejpam-6969	248	3	in	in	ADP
ejpam-6969	248	4	mathematical	mathematical	ADJ
ejpam-6969	248	5	analysis	analysis	NOUN
ejpam-6969	248	6	,	,	PUNCT
ejpam-6969	248	7	3(1):37–51	3(1):37–51	NUM
ejpam-6969	248	8	,	,	PUNCT
ejpam-6969	248	9	2016	2016	NUM
ejpam-6969	248	10	.	.	PUNCT
ejpam-6969	249	1	[	[	X
ejpam-6969	249	2	14	14	NUM
ejpam-6969	249	3	]	]	X
ejpam-6969	249	4	jalil	jalil	PROPN
ejpam-6969	249	5	rashidinia	rashidinia	PROPN
ejpam-6969	249	6	,	,	PUNCT
ejpam-6969	249	7	tahereh	tahereh	VERB
ejpam-6969	249	8	eftekhari	eftekhari	NOUN
ejpam-6969	249	9	,	,	PUNCT
ejpam-6969	249	10	and	and	CCONJ
ejpam-6969	249	11	khosrow	khosrow	PROPN
ejpam-6969	249	12	maleknejad	maleknejad	PROPN
ejpam-6969	249	13	.	.	PUNCT
ejpam-6969	250	1	numerical	numerical	ADJ
ejpam-6969	250	2	solutions	solution	NOUN
ejpam-6969	250	3	of	of	ADP
ejpam-6969	250	4	two	two	NUM
ejpam-6969	250	5	-	-	PUNCT
ejpam-6969	250	6	dimensional	dimensional	ADJ
ejpam-6969	250	7	nonlinear	nonlinear	ADJ
ejpam-6969	250	8	fractional	fractional	ADJ
ejpam-6969	250	9	volterra	volterra	NOUN
ejpam-6969	250	10	and	and	CCONJ
ejpam-6969	250	11	fredholm	fredholm	VERB
ejpam-6969	250	12	integral	integral	ADJ
ejpam-6969	250	13	equations	equation	NOUN
ejpam-6969	250	14	using	use	VERB
ejpam-6969	250	15	m.	m.	PROPN
ejpam-6969	250	16	h.	h.	PROPN
ejpam-6969	250	17	ahmed	ahmed	PROPN
ejpam-6969	250	18	,	,	PUNCT
ejpam-6969	250	19	a.	a.	NOUN
ejpam-6969	250	20	m.	m.	PROPN
ejpam-6969	250	21	aljabri	aljabri	PROPN
ejpam-6969	250	22	/	/	SYM
ejpam-6969	250	23	eur	eur	PROPN
ejpam-6969	250	24	.	.	PUNCT
ejpam-6969	251	1	j.	j.	PROPN
ejpam-6969	251	2	pure	pure	PROPN
ejpam-6969	251	3	appl	appl	PROPN
ejpam-6969	251	4	.	.	PROPN
ejpam-6969	251	5	math	math	PROPN
ejpam-6969	251	6	,	,	PUNCT
ejpam-6969	251	7	18	18	NUM
ejpam-6969	251	8	(	(	PUNCT
ejpam-6969	251	9	4	4	NUM
ejpam-6969	251	10	)	)	PUNCT
ejpam-6969	251	11	(	(	PUNCT
ejpam-6969	251	12	2025	2025	NUM
ejpam-6969	251	13	)	)	PUNCT
ejpam-6969	251	14	,	,	PUNCT
ejpam-6969	251	15	6969	6969	NUM
ejpam-6969	251	16	14	14	NUM
ejpam-6969	251	17	of	of	ADP
ejpam-6969	251	18	16	16	NUM
ejpam-6969	251	19	shifted	shift	VERB
ejpam-6969	251	20	jacobi	jacobi	PROPN
ejpam-6969	251	21	operational	operational	ADJ
ejpam-6969	251	22	matrices	matrix	NOUN
ejpam-6969	251	23	via	via	ADP
ejpam-6969	251	24	collocation	collocation	NOUN
ejpam-6969	251	25	method	method	NOUN
ejpam-6969	251	26	.	.	PUNCT
ejpam-6969	252	1	journal	journal	NOUN
ejpam-6969	252	2	of	of	ADP
ejpam-6969	252	3	king	king	PROPN
ejpam-6969	252	4	saud	saud	PROPN
ejpam-6969	252	5	university	university	PROPN
ejpam-6969	252	6	-	-	PUNCT
ejpam-6969	252	7	science	science	NOUN
ejpam-6969	252	8	,	,	PUNCT
ejpam-6969	252	9	33(1):101244	33(1):101244	NOUN
ejpam-6969	252	10	,	,	PUNCT
ejpam-6969	252	11	2021	2021	NUM
ejpam-6969	252	12	.	.	PUNCT
ejpam-6969	253	1	[	[	X
ejpam-6969	253	2	15	15	NUM
ejpam-6969	253	3	]	]	X
ejpam-6969	253	4	k	k	PROPN
ejpam-6969	253	5	maleknejad	maleknejad	PROPN
ejpam-6969	253	6	and	and	CCONJ
ejpam-6969	253	7	m	m	PROPN
ejpam-6969	253	8	soleiman	soleiman	NOUN
ejpam-6969	253	9	dehkordi	dehkordi	PROPN
ejpam-6969	253	10	.	.	PUNCT
ejpam-6969	254	1	numerical	numerical	ADJ
ejpam-6969	254	2	solutions	solution	NOUN
ejpam-6969	254	3	of	of	ADP
ejpam-6969	254	4	two	two	NUM
ejpam-6969	254	5	-	-	PUNCT
ejpam-6969	254	6	dimensional	dimensional	ADJ
ejpam-6969	254	7	nonlinear	nonlinear	ADJ
ejpam-6969	254	8	integral	integral	ADJ
ejpam-6969	254	9	equations	equation	NOUN
ejpam-6969	254	10	via	via	ADP
ejpam-6969	254	11	laguerre	laguerre	NOUN
ejpam-6969	254	12	wavelet	wavelet	NOUN
ejpam-6969	254	13	method	method	NOUN
ejpam-6969	254	14	with	with	ADP
ejpam-6969	254	15	convergence	convergence	NOUN
ejpam-6969	254	16	analysis	analysis	NOUN
ejpam-6969	254	17	.	.	PUNCT
ejpam-6969	255	1	applied	apply	VERB
ejpam-6969	255	2	mathematics	mathematic	NOUN
ejpam-6969	255	3	-	-	PUNCT
ejpam-6969	255	4	a	a	DET
ejpam-6969	255	5	journal	journal	NOUN
ejpam-6969	255	6	of	of	ADP
ejpam-6969	255	7	chinese	chinese	ADJ
ejpam-6969	255	8	universities	university	NOUN
ejpam-6969	255	9	,	,	PUNCT
ejpam-6969	255	10	36(1):83–98	36(1):83–98	NUM
ejpam-6969	255	11	,	,	PUNCT
ejpam-6969	255	12	2021	2021	NUM
ejpam-6969	255	13	.	.	PUNCT
ejpam-6969	256	1	[	[	X
ejpam-6969	256	2	16	16	NUM
ejpam-6969	256	3	]	]	X
ejpam-6969	256	4	k	k	PROPN
ejpam-6969	256	5	maleknejad	maleknejad	PROPN
ejpam-6969	256	6	,	,	PUNCT
ejpam-6969	256	7	s	s	PART
ejpam-6969	256	8	sohrabi	sohrabi	NOUN
ejpam-6969	256	9	,	,	PUNCT
ejpam-6969	256	10	and	and	CCONJ
ejpam-6969	256	11	b	b	X
ejpam-6969	256	12	baranji	baranji	X
ejpam-6969	256	13	.	.	PUNCT
ejpam-6969	257	1	application	application	NOUN
ejpam-6969	257	2	of	of	ADP
ejpam-6969	257	3	2d	2d	NOUN
ejpam-6969	257	4	-	-	PUNCT
ejpam-6969	257	5	bpfs	bpfs	NOUN
ejpam-6969	257	6	to	to	PART
ejpam-6969	257	7	nonlinear	nonlinear	ADJ
ejpam-6969	257	8	integral	integral	ADJ
ejpam-6969	257	9	equations	equation	NOUN
ejpam-6969	257	10	.	.	PUNCT
ejpam-6969	258	1	communications	communication	NOUN
ejpam-6969	258	2	in	in	ADP
ejpam-6969	258	3	nonlinear	nonlinear	ADJ
ejpam-6969	258	4	science	science	NOUN
ejpam-6969	258	5	and	and	CCONJ
ejpam-6969	258	6	numerical	numerical	PROPN
ejpam-6969	258	7	simulation	simulation	PROPN
ejpam-6969	258	8	,	,	PUNCT
ejpam-6969	258	9	15(3):527–535	15(3):527–535	PROPN
ejpam-6969	258	10	,	,	PUNCT
ejpam-6969	258	11	2010	2010	NUM
ejpam-6969	258	12	.	.	PUNCT
ejpam-6969	259	1	[	[	X
ejpam-6969	259	2	17	17	NUM
ejpam-6969	259	3	]	]	PUNCT
ejpam-6969	259	4	emad	emad	NOUN
ejpam-6969	259	5	a	a	DET
ejpam-6969	259	6	az	az	PROPN
ejpam-6969	259	7	-	-	PUNCT
ejpam-6969	259	8	zo’bi	zo’bi	PROPN
ejpam-6969	259	9	and	and	CCONJ
ejpam-6969	259	10	kamel	kamel	PROPN
ejpam-6969	259	11	al	al	PROPN
ejpam-6969	259	12	-	-	PUNCT
ejpam-6969	259	13	khaled	khaled	PROPN
ejpam-6969	259	14	.	.	PUNCT
ejpam-6969	260	1	a	a	DET
ejpam-6969	260	2	new	new	ADJ
ejpam-6969	260	3	convergence	convergence	NOUN
ejpam-6969	260	4	proof	proof	NOUN
ejpam-6969	260	5	of	of	ADP
ejpam-6969	260	6	the	the	DET
ejpam-6969	260	7	adomian	adomian	NOUN
ejpam-6969	260	8	decomposition	decomposition	NOUN
ejpam-6969	260	9	method	method	NOUN
ejpam-6969	260	10	for	for	ADP
ejpam-6969	260	11	a	a	DET
ejpam-6969	260	12	mixed	mixed	ADJ
ejpam-6969	260	13	hyperbolic	hyperbolic	ADJ
ejpam-6969	260	14	elliptic	elliptic	ADJ
ejpam-6969	260	15	system	system	NOUN
ejpam-6969	260	16	of	of	ADP
ejpam-6969	260	17	conservation	conservation	NOUN
ejpam-6969	260	18	laws	law	NOUN
ejpam-6969	260	19	.	.	PUNCT
ejpam-6969	261	1	applied	apply	VERB
ejpam-6969	261	2	mathematics	mathematic	NOUN
ejpam-6969	261	3	and	and	CCONJ
ejpam-6969	261	4	computation	computation	NOUN
ejpam-6969	261	5	,	,	PUNCT
ejpam-6969	261	6	217(8):4248–4256	217(8):4248–4256	PROPN
ejpam-6969	261	7	,	,	PUNCT
ejpam-6969	261	8	2010	2010	NUM
ejpam-6969	261	9	.	.	PUNCT
ejpam-6969	262	1	[	[	X
ejpam-6969	262	2	18	18	NUM
ejpam-6969	262	3	]	]	SYM
ejpam-6969	262	4	ea	ea	PROPN
ejpam-6969	262	5	az	az	PROPN
ejpam-6969	262	6	-	-	PROPN
ejpam-6969	262	7	zo’bi	zo’bi	PROPN
ejpam-6969	262	8	.	.	PUNCT
ejpam-6969	263	1	a	a	DET
ejpam-6969	263	2	reliable	reliable	ADJ
ejpam-6969	263	3	analytic	analytic	ADJ
ejpam-6969	263	4	study	study	NOUN
ejpam-6969	263	5	for	for	ADP
ejpam-6969	263	6	higher	high	ADJ
ejpam-6969	263	7	-	-	PUNCT
ejpam-6969	263	8	dimensional	dimensional	ADJ
ejpam-6969	263	9	telegraph	telegraph	NOUN
ejpam-6969	263	10	equation	equation	NOUN
ejpam-6969	263	11	.	.	PUNCT
ejpam-6969	264	1	j.	j.	PROPN
ejpam-6969	264	2	math	math	PROPN
ejpam-6969	264	3	.	.	PUNCT
ejpam-6969	265	1	comput	comput	NOUN
ejpam-6969	265	2	.	.	PUNCT
ejpam-6969	266	1	sci	sci	PROPN
ejpam-6969	266	2	,	,	PUNCT
ejpam-6969	266	3	18(4):423–429	18(4):423–429	PROPN
ejpam-6969	266	4	,	,	PUNCT
ejpam-6969	266	5	2018	2018	NUM
ejpam-6969	266	6	.	.	PUNCT
ejpam-6969	267	1	[	[	X
ejpam-6969	267	2	19	19	NUM
ejpam-6969	267	3	]	]	X
ejpam-6969	267	4	emad	emad	PROPN
ejpam-6969	267	5	az	az	PROPN
ejpam-6969	267	6	-	-	PROPN
ejpam-6969	267	7	zo’bi	zo’bi	PROPN
ejpam-6969	267	8	,	,	PUNCT
ejpam-6969	267	9	lanre	lanre	NOUN
ejpam-6969	267	10	akinyemi	akinyemi	NOUN
ejpam-6969	267	11	,	,	PUNCT
ejpam-6969	267	12	and	and	CCONJ
ejpam-6969	267	13	ahmed	ahmed	PROPN
ejpam-6969	267	14	o	o	PROPN
ejpam-6969	267	15	alleddawi	alleddawi	PROPN
ejpam-6969	267	16	.	.	PUNCT
ejpam-6969	268	1	construction	construction	NOUN
ejpam-6969	268	2	of	of	ADP
ejpam-6969	268	3	optical	optical	ADJ
ejpam-6969	268	4	solitons	soliton	NOUN
ejpam-6969	268	5	for	for	ADP
ejpam-6969	268	6	conformable	conformable	ADJ
ejpam-6969	268	7	generalized	generalized	ADJ
ejpam-6969	268	8	model	model	NOUN
ejpam-6969	268	9	in	in	ADP
ejpam-6969	268	10	nonlinear	nonlinear	ADJ
ejpam-6969	268	11	media	medium	NOUN
ejpam-6969	268	12	.	.	PUNCT
ejpam-6969	269	1	modern	modern	ADJ
ejpam-6969	269	2	physics	physics	NOUN
ejpam-6969	269	3	letters	letters	PROPN
ejpam-6969	269	4	b	b	PROPN
ejpam-6969	269	5	,	,	PUNCT
ejpam-6969	269	6	35(24):2150409	35(24):2150409	NUM
ejpam-6969	269	7	,	,	PUNCT
ejpam-6969	269	8	2021	2021	NUM
ejpam-6969	269	9	.	.	PUNCT
ejpam-6969	270	1	[	[	X
ejpam-6969	270	2	20	20	NUM
ejpam-6969	270	3	]	]	X
ejpam-6969	270	4	jamil	jamil	PROPN
ejpam-6969	270	5	abbas	abbas	PROPN
ejpam-6969	270	6	haider	haider	PROPN
ejpam-6969	270	7	,	,	PUNCT
ejpam-6969	270	8	shahbaz	shahbaz	PROPN
ejpam-6969	270	9	ahmad	ahmad	PROPN
ejpam-6969	270	10	,	,	PUNCT
ejpam-6969	270	11	hassan	hassan	PROPN
ejpam-6969	270	12	ali	ali	PROPN
ejpam-6969	270	13	ghazwani	ghazwani	PROPN
ejpam-6969	270	14	,	,	PUNCT
ejpam-6969	270	15	mohamed	mohamed	PROPN
ejpam-6969	270	16	hussien	hussien	PROPN
ejpam-6969	270	17	,	,	PUNCT
ejpam-6969	270	18	musawa	musawa	PROPN
ejpam-6969	270	19	yahya	yahya	PROPN
ejpam-6969	270	20	almusawa	almusawa	NOUN
ejpam-6969	270	21	,	,	PUNCT
ejpam-6969	270	22	and	and	CCONJ
ejpam-6969	270	23	emad	emad	NOUN
ejpam-6969	270	24	a	a	DET
ejpam-6969	270	25	az	az	PROPN
ejpam-6969	270	26	-	-	PUNCT
ejpam-6969	270	27	zo’bi	zo’bi	PROPN
ejpam-6969	270	28	.	.	PUNCT
ejpam-6969	270	29	results	result	VERB
ejpam-6969	270	30	validation	validation	NOUN
ejpam-6969	270	31	by	by	ADP
ejpam-6969	270	32	using	use	VERB
ejpam-6969	270	33	finite	finite	ADJ
ejpam-6969	270	34	volume	volume	NOUN
ejpam-6969	270	35	method	method	NOUN
ejpam-6969	270	36	for	for	ADP
ejpam-6969	270	37	the	the	DET
ejpam-6969	270	38	blood	blood	NOUN
ejpam-6969	270	39	flow	flow	NOUN
ejpam-6969	270	40	with	with	ADP
ejpam-6969	270	41	magnetohydrodynamics	magnetohydrodynamic	NOUN
ejpam-6969	270	42	and	and	CCONJ
ejpam-6969	270	43	hybrid	hybrid	NOUN
ejpam-6969	270	44	nanofluids	nanofluid	NOUN
ejpam-6969	270	45	.	.	PUNCT
ejpam-6969	271	1	modern	modern	ADJ
ejpam-6969	271	2	physics	physics	NOUN
ejpam-6969	271	3	letters	letters	PROPN
ejpam-6969	271	4	b	b	PROPN
ejpam-6969	271	5	,	,	PUNCT
ejpam-6969	271	6	38(24):2450208	38(24):2450208	NUM
ejpam-6969	271	7	,	,	PUNCT
ejpam-6969	271	8	2024	2024	NUM
ejpam-6969	271	9	.	.	PUNCT
ejpam-6969	272	1	[	[	X
ejpam-6969	272	2	21	21	NUM
ejpam-6969	272	3	]	]	PUNCT
ejpam-6969	272	4	shumaila	shumaila	PROPN
ejpam-6969	272	5	kanwal	kanwal	PROPN
ejpam-6969	272	6	,	,	PUNCT
ejpam-6969	272	7	syed	syed	ADJ
ejpam-6969	272	8	asif	asif	PROPN
ejpam-6969	272	9	ali	ali	PROPN
ejpam-6969	272	10	shah	shah	PROPN
ejpam-6969	272	11	,	,	PUNCT
ejpam-6969	272	12	abdul	abdul	PROPN
ejpam-6969	272	13	bariq	bariq	PROPN
ejpam-6969	272	14	,	,	PUNCT
ejpam-6969	272	15	bagh	bagh	PROPN
ejpam-6969	272	16	ali	ali	PROPN
ejpam-6969	272	17	,	,	PUNCT
ejpam-6969	272	18	adham	adham	PROPN
ejpam-6969	272	19	e	e	PROPN
ejpam-6969	272	20	ragab	ragab	PROPN
ejpam-6969	272	21	,	,	PUNCT
ejpam-6969	272	22	and	and	CCONJ
ejpam-6969	272	23	emad	emad	NOUN
ejpam-6969	272	24	a	a	DET
ejpam-6969	272	25	az	az	PROPN
ejpam-6969	272	26	-	-	PUNCT
ejpam-6969	272	27	zo’bi	zo’bi	PROPN
ejpam-6969	272	28	.	.	PUNCT
ejpam-6969	272	29	insight	insight	NOUN
ejpam-6969	272	30	into	into	ADP
ejpam-6969	272	31	the	the	DET
ejpam-6969	272	32	dynamics	dynamic	NOUN
ejpam-6969	272	33	of	of	ADP
ejpam-6969	272	34	heat	heat	NOUN
ejpam-6969	272	35	and	and	CCONJ
ejpam-6969	272	36	mass	mass	NOUN
ejpam-6969	272	37	transfer	transfer	NOUN
ejpam-6969	272	38	in	in	ADP
ejpam-6969	272	39	nanofluid	nanofluid	ADJ
ejpam-6969	272	40	flow	flow	NOUN
ejpam-6969	272	41	with	with	ADP
ejpam-6969	272	42	linear	linear	ADJ
ejpam-6969	272	43	/	/	SYM
ejpam-6969	272	44	nonlinear	nonlinear	ADJ
ejpam-6969	272	45	mixed	mixed	ADJ
ejpam-6969	272	46	convection	convection	NOUN
ejpam-6969	272	47	,	,	PUNCT
ejpam-6969	272	48	thermal	thermal	ADJ
ejpam-6969	272	49	radiation	radiation	NOUN
ejpam-6969	272	50	,	,	PUNCT
ejpam-6969	272	51	and	and	CCONJ
ejpam-6969	272	52	activation	activation	NOUN
ejpam-6969	272	53	energy	energy	NOUN
ejpam-6969	272	54	effects	effect	NOUN
ejpam-6969	272	55	over	over	ADP
ejpam-6969	272	56	the	the	DET
ejpam-6969	272	57	rotating	rotate	VERB
ejpam-6969	272	58	disk	disk	NOUN
ejpam-6969	272	59	.	.	PUNCT
ejpam-6969	273	1	scientific	scientific	ADJ
ejpam-6969	273	2	reports	report	NOUN
ejpam-6969	273	3	,	,	PUNCT
ejpam-6969	273	4	13(1):23031	13(1):23031	NUM
ejpam-6969	273	5	,	,	PUNCT
ejpam-6969	273	6	2023	2023	NUM
ejpam-6969	273	7	.	.	PUNCT
ejpam-6969	274	1	[	[	X
ejpam-6969	274	2	22	22	NUM
ejpam-6969	274	3	]	]	X
ejpam-6969	274	4	da	da	ADJ
ejpam-6969	274	5	-	-	PUNCT
ejpam-6969	274	6	qian	qian	PROPN
ejpam-6969	274	7	lu	lu	PROPN
ejpam-6969	274	8	and	and	CCONJ
ejpam-6969	274	9	qiu	qiu	PROPN
ejpam-6969	274	10	-	-	PUNCT
ejpam-6969	274	11	ming	ming	PROPN
ejpam-6969	274	12	luo	luo	PROPN
ejpam-6969	274	13	.	.	PUNCT
ejpam-6969	275	1	some	some	DET
ejpam-6969	275	2	generalizations	generalization	NOUN
ejpam-6969	275	3	of	of	ADP
ejpam-6969	275	4	2d	2d	NUM
ejpam-6969	275	5	bernoulli	bernoulli	NOUN
ejpam-6969	275	6	polynomials	polynomial	NOUN
ejpam-6969	275	7	.	.	PUNCT
ejpam-6969	276	1	journal	journal	PROPN
ejpam-6969	276	2	of	of	ADP
ejpam-6969	276	3	inequalities	inequality	NOUN
ejpam-6969	276	4	and	and	CCONJ
ejpam-6969	276	5	applications	application	NOUN
ejpam-6969	276	6	,	,	PUNCT
ejpam-6969	276	7	2013(1):110	2013(1):110	NUM
ejpam-6969	276	8	,	,	PUNCT
ejpam-6969	276	9	2013	2013	NUM
ejpam-6969	276	10	.	.	PUNCT
ejpam-6969	277	1	[	[	X
ejpam-6969	277	2	23	23	NUM
ejpam-6969	277	3	]	]	PUNCT
ejpam-6969	277	4	doaa	doaa	PROPN
ejpam-6969	277	5	shokry	shokry	PROPN
ejpam-6969	277	6	mohamed	mohamed	PROPN
ejpam-6969	277	7	and	and	CCONJ
ejpam-6969	277	8	dina	dina	PROPN
ejpam-6969	277	9	mohamed	mohamed	PROPN
ejpam-6969	277	10	abdessami	abdessami	PROPN
ejpam-6969	277	11	.	.	PUNCT
ejpam-6969	278	1	a	a	DET
ejpam-6969	278	2	comparison	comparison	NOUN
ejpam-6969	278	3	between	between	ADP
ejpam-6969	278	4	bernoulli	bernoulli	NOUN
ejpam-6969	278	5	-	-	PUNCT
ejpam-6969	278	6	collocation	collocation	NOUN
ejpam-6969	278	7	method	method	NOUN
ejpam-6969	278	8	and	and	CCONJ
ejpam-6969	278	9	hermite	hermite	ADJ
ejpam-6969	278	10	-	-	PUNCT
ejpam-6969	278	11	galerkin	galerkin	ADJ
ejpam-6969	278	12	method	method	NOUN
ejpam-6969	278	13	for	for	ADP
ejpam-6969	278	14	solving	solve	VERB
ejpam-6969	278	15	twodimensional	twodimensional	ADJ
ejpam-6969	278	16	mixed	mixed	ADJ
ejpam-6969	278	17	volterra	volterra	NOUN
ejpam-6969	278	18	-	-	PUNCT
ejpam-6969	278	19	fredholm	fredholm	NOUN
ejpam-6969	278	20	singular	singular	ADJ
ejpam-6969	278	21	integral	integral	ADJ
ejpam-6969	278	22	equations	equation	NOUN
ejpam-6969	278	23	.	.	PUNCT
ejpam-6969	279	1	transactions	transaction	NOUN
ejpam-6969	279	2	of	of	ADP
ejpam-6969	279	3	a.	a.	NOUN
ejpam-6969	279	4	razmadze	razmadze	PROPN
ejpam-6969	279	5	mathematical	mathematical	PROPN
ejpam-6969	279	6	institute	institute	PROPN
ejpam-6969	279	7	,	,	PUNCT
ejpam-6969	279	8	175(2	175(2	NUM
ejpam-6969	279	9	)	)	PUNCT
ejpam-6969	279	10	,	,	PUNCT
ejpam-6969	279	11	2021	2021	NUM
ejpam-6969	279	12	.	.	PUNCT
ejpam-6969	280	1	[	[	X
ejpam-6969	280	2	24	24	NUM
ejpam-6969	280	3	]	]	X
ejpam-6969	280	4	don	don	PROPN
ejpam-6969	280	5	zagier	zagier	NOUN
ejpam-6969	280	6	.	.	PUNCT
ejpam-6969	281	1	curious	curious	ADJ
ejpam-6969	281	2	and	and	CCONJ
ejpam-6969	281	3	exotic	exotic	ADJ
ejpam-6969	281	4	identities	identity	NOUN
ejpam-6969	281	5	for	for	ADP
ejpam-6969	281	6	bernoulli	bernoulli	NOUN
ejpam-6969	281	7	numbers	number	NOUN
ejpam-6969	281	8	.	.	PUNCT
ejpam-6969	282	1	max	max	PROPN
ejpam-6969	282	2	planck	planck	PROPN
ejpam-6969	282	3	insitute	insitute	PROPN
ejpam-6969	282	4	for	for	ADP
ejpam-6969	282	5	mathematics	mathematics	PROPN
ejpam-6969	282	6	,	,	PUNCT
ejpam-6969	282	7	bonn	bonn	PROPN
ejpam-6969	282	8	,	,	PUNCT
ejpam-6969	282	9	germany	germany	PROPN
ejpam-6969	282	10	,	,	PUNCT
ejpam-6969	282	11	nd	nd	PRON
ejpam-6969	282	12	,	,	PUNCT
ejpam-6969	282	13	2014	2014	NUM
ejpam-6969	282	14	.	.	PUNCT
ejpam-6969	283	1	[	[	X
ejpam-6969	283	2	25	25	NUM
ejpam-6969	283	3	]	]	PUNCT
ejpam-6969	283	4	zhiping	zhiping	NOUN
ejpam-6969	283	5	mao	mao	PROPN
ejpam-6969	283	6	and	and	CCONJ
ejpam-6969	283	7	jie	jie	PROPN
ejpam-6969	283	8	shen	shen	PROPN
ejpam-6969	283	9	.	.	PUNCT
ejpam-6969	284	1	hermite	hermite	ADJ
ejpam-6969	284	2	spectral	spectral	ADJ
ejpam-6969	284	3	methods	method	NOUN
ejpam-6969	284	4	for	for	ADP
ejpam-6969	284	5	fractional	fractional	ADJ
ejpam-6969	284	6	pdes	pde	NOUN
ejpam-6969	284	7	in	in	ADP
ejpam-6969	284	8	unbounded	unbounded	ADJ
ejpam-6969	284	9	domains	domain	NOUN
ejpam-6969	284	10	.	.	PUNCT
ejpam-6969	285	1	siam	siam	PROPN
ejpam-6969	285	2	journal	journal	PROPN
ejpam-6969	285	3	on	on	ADP
ejpam-6969	285	4	scientific	scientific	ADJ
ejpam-6969	285	5	computing	computing	NOUN
ejpam-6969	285	6	,	,	PUNCT
ejpam-6969	285	7	39(5):a1928	39(5):a1928	PROPN
ejpam-6969	285	8	–	–	PUNCT
ejpam-6969	285	9	a1950	a1950	PROPN
ejpam-6969	285	10	,	,	PUNCT
ejpam-6969	285	11	2017	2017	NUM
ejpam-6969	285	12	.	.	PUNCT
ejpam-6969	286	1	[	[	X
ejpam-6969	286	2	26	26	NUM
ejpam-6969	286	3	]	]	PUNCT
ejpam-6969	286	4	changtao	changtao	PROPN
ejpam-6969	286	5	sheng	sheng	PROPN
ejpam-6969	286	6	,	,	PUNCT
ejpam-6969	286	7	suna	suna	PROPN
ejpam-6969	286	8	ma	ma	PROPN
ejpam-6969	286	9	,	,	PUNCT
ejpam-6969	286	10	huiyuan	huiyuan	PROPN
ejpam-6969	286	11	li	li	PROPN
ejpam-6969	286	12	,	,	PUNCT
ejpam-6969	286	13	li	li	PROPN
ejpam-6969	286	14	-	-	PROPN
ejpam-6969	286	15	lian	lian	ADJ
ejpam-6969	286	16	wang	wang	PROPN
ejpam-6969	286	17	,	,	PUNCT
ejpam-6969	286	18	and	and	CCONJ
ejpam-6969	286	19	lueling	luele	VERB
ejpam-6969	286	20	jia	jia	PROPN
ejpam-6969	286	21	.	.	PROPN
ejpam-6969	286	22	generalised	generalise	VERB
ejpam-6969	286	23	hermite	hermite	ADJ
ejpam-6969	286	24	functions	function	NOUN
ejpam-6969	286	25	and	and	CCONJ
ejpam-6969	286	26	their	their	PRON
ejpam-6969	286	27	applications	application	NOUN
ejpam-6969	286	28	in	in	ADP
ejpam-6969	286	29	spectral	spectral	ADJ
ejpam-6969	286	30	approximations	approximation	NOUN
ejpam-6969	286	31	.	.	PUNCT
ejpam-6969	287	1	in	in	ADP
ejpam-6969	287	2	other	other	ADJ
ejpam-6969	287	3	words	word	NOUN
ejpam-6969	287	4	,	,	PUNCT
ejpam-6969	287	5	1(2):1–3	1(2):1–3	NUM
ejpam-6969	287	6	,	,	PUNCT
ejpam-6969	287	7	2020	2020	NUM
ejpam-6969	287	8	.	.	PUNCT
ejpam-6969	288	1	[	[	X
ejpam-6969	288	2	27	27	NUM
ejpam-6969	288	3	]	]	X
ejpam-6969	288	4	sohrab	sohrab	NOUN
ejpam-6969	288	5	bazm	bazm	PROPN
ejpam-6969	288	6	.	.	PUNCT
ejpam-6969	289	1	bernoulli	bernoulli	PROPN
ejpam-6969	289	2	polynomials	polynomial	NOUN
ejpam-6969	289	3	for	for	ADP
ejpam-6969	289	4	the	the	DET
ejpam-6969	289	5	numerical	numerical	ADJ
ejpam-6969	289	6	solution	solution	NOUN
ejpam-6969	289	7	of	of	ADP
ejpam-6969	289	8	some	some	DET
ejpam-6969	289	9	classes	class	NOUN
ejpam-6969	289	10	of	of	ADP
ejpam-6969	289	11	linear	linear	PROPN
ejpam-6969	289	12	and	and	CCONJ
ejpam-6969	289	13	nonlinear	nonlinear	ADJ
ejpam-6969	289	14	integral	integral	ADJ
ejpam-6969	289	15	equations	equation	NOUN
ejpam-6969	289	16	.	.	PUNCT
ejpam-6969	290	1	journal	journal	NOUN
ejpam-6969	290	2	of	of	ADP
ejpam-6969	290	3	computational	computational	ADJ
ejpam-6969	290	4	and	and	CCONJ
ejpam-6969	290	5	applied	applied	ADJ
ejpam-6969	290	6	mathematics	mathematic	NOUN
ejpam-6969	290	7	,	,	PUNCT
ejpam-6969	290	8	275:44–60	275:44–60	NOUN
ejpam-6969	290	9	,	,	PUNCT
ejpam-6969	290	10	2015	2015	NUM
ejpam-6969	290	11	.	.	PUNCT
ejpam-6969	291	1	[	[	X
ejpam-6969	291	2	28	28	NUM
ejpam-6969	291	3	]	]	X
ejpam-6969	291	4	hafida	hafida	PROPN
ejpam-6969	291	5	laib	laib	PROPN
ejpam-6969	291	6	,	,	PUNCT
ejpam-6969	291	7	aissa	aissa	PROPN
ejpam-6969	291	8	boulmerka	boulmerka	PROPN
ejpam-6969	291	9	,	,	PUNCT
ejpam-6969	291	10	azzeddine	azzeddine	PROPN
ejpam-6969	291	11	bellour	bellour	PROPN
ejpam-6969	291	12	,	,	PUNCT
ejpam-6969	291	13	and	and	CCONJ
ejpam-6969	291	14	fouzia	fouzia	PROPN
ejpam-6969	291	15	birem	birem	VERB
ejpam-6969	291	16	.	.	PUNCT
ejpam-6969	292	1	numerical	numerical	ADJ
ejpam-6969	292	2	solution	solution	NOUN
ejpam-6969	292	3	of	of	ADP
ejpam-6969	292	4	two	two	NUM
ejpam-6969	292	5	-	-	PUNCT
ejpam-6969	292	6	dimensional	dimensional	ADJ
ejpam-6969	292	7	linear	linear	NOUN
ejpam-6969	292	8	and	and	CCONJ
ejpam-6969	292	9	nonlinear	nonlinear	ADJ
ejpam-6969	292	10	volterra	volterra	PROPN
ejpam-6969	292	11	integral	integral	ADJ
ejpam-6969	292	12	equations	equation	NOUN
ejpam-6969	292	13	using	use	VERB
ejpam-6969	292	14	taylor	taylor	PROPN
ejpam-6969	292	15	collocation	collocation	NOUN
ejpam-6969	292	16	method	method	NOUN
ejpam-6969	292	17	.	.	PUNCT
ejpam-6969	293	1	journal	journal	NOUN
ejpam-6969	293	2	of	of	ADP
ejpam-6969	293	3	computational	computational	ADJ
ejpam-6969	293	4	and	and	CCONJ
ejpam-6969	293	5	applied	applied	ADJ
ejpam-6969	293	6	mathematics	mathematic	NOUN
ejpam-6969	293	7	,	,	PUNCT
ejpam-6969	293	8	417:114537	417:114537	NUM
ejpam-6969	293	9	,	,	PUNCT
ejpam-6969	293	10	m.	m.	NOUN
ejpam-6969	293	11	h.	h.	PROPN
ejpam-6969	293	12	ahmed	ahmed	PROPN
ejpam-6969	293	13	,	,	PUNCT
ejpam-6969	293	14	a.	a.	NOUN
ejpam-6969	293	15	m.	m.	PROPN
ejpam-6969	293	16	aljabri	aljabri	PROPN
ejpam-6969	293	17	/	/	SYM
ejpam-6969	293	18	eur	eur	PROPN
ejpam-6969	293	19	.	.	PUNCT
ejpam-6969	294	1	j.	j.	PROPN
ejpam-6969	294	2	pure	pure	PROPN
ejpam-6969	294	3	appl	appl	PROPN
ejpam-6969	294	4	.	.	PROPN
ejpam-6969	294	5	math	math	PROPN
ejpam-6969	294	6	,	,	PUNCT
ejpam-6969	294	7	18	18	NUM
ejpam-6969	294	8	(	(	PUNCT
ejpam-6969	294	9	4	4	NUM
ejpam-6969	294	10	)	)	PUNCT
ejpam-6969	294	11	(	(	PUNCT
ejpam-6969	294	12	2025	2025	NUM
ejpam-6969	294	13	)	)	PUNCT
ejpam-6969	294	14	,	,	PUNCT
ejpam-6969	294	15	6969	6969	NUM
ejpam-6969	294	16	15	15	NUM
ejpam-6969	294	17	of	of	ADP
ejpam-6969	294	18	16	16	NUM
ejpam-6969	294	19	2023	2023	NUM
ejpam-6969	294	20	.	.	PUNCT
ejpam-6969	295	1	[	[	X
ejpam-6969	295	2	29	29	NUM
ejpam-6969	295	3	]	]	X
ejpam-6969	295	4	yubin	yubin	PROPN
ejpam-6969	295	5	pan	pan	PROPN
ejpam-6969	295	6	and	and	CCONJ
ejpam-6969	295	7	jin	jin	PROPN
ejpam-6969	295	8	huang	huang	PROPN
ejpam-6969	295	9	.	.	PUNCT
ejpam-6969	295	10	extrapolation	extrapolation	NOUN
ejpam-6969	295	11	method	method	NOUN
ejpam-6969	295	12	for	for	ADP
ejpam-6969	295	13	solving	solve	VERB
ejpam-6969	295	14	two	two	NUM
ejpam-6969	295	15	-	-	PUNCT
ejpam-6969	295	16	dimensional	dimensional	ADJ
ejpam-6969	295	17	volterral	volterral	ADJ
ejpam-6969	295	18	integral	integral	ADJ
ejpam-6969	295	19	equations	equation	NOUN
ejpam-6969	295	20	of	of	ADP
ejpam-6969	295	21	the	the	DET
ejpam-6969	295	22	second	second	ADJ
ejpam-6969	295	23	kind	kind	NOUN
ejpam-6969	295	24	.	.	PUNCT
ejpam-6969	295	25	applied	apply	VERB
ejpam-6969	295	26	mathematics	mathematic	NOUN
ejpam-6969	295	27	and	and	CCONJ
ejpam-6969	295	28	computation	computation	NOUN
ejpam-6969	295	29	,	,	PUNCT
ejpam-6969	295	30	367:124784	367:124784	NUM
ejpam-6969	295	31	,	,	PUNCT
ejpam-6969	295	32	2020	2020	NUM
ejpam-6969	295	33	.	.	PUNCT
ejpam-6969	296	1	[	[	X
ejpam-6969	296	2	30	30	NUM
ejpam-6969	296	3	]	]	X
ejpam-6969	296	4	mohammad	mohammad	PROPN
ejpam-6969	296	5	a	a	PROPN
ejpam-6969	296	6	al	al	PROPN
ejpam-6969	296	7	zubi	zubi	PROPN
ejpam-6969	296	8	,	,	PUNCT
ejpam-6969	296	9	kallekh	kallekh	ADJ
ejpam-6969	296	10	afef	afef	NOUN
ejpam-6969	296	11	,	,	PUNCT
ejpam-6969	296	12	and	and	CCONJ
ejpam-6969	296	13	emad	emad	NOUN
ejpam-6969	296	14	a	a	DET
ejpam-6969	296	15	az	az	PROPN
ejpam-6969	296	16	-	-	PUNCT
ejpam-6969	296	17	zo’bi	zo’bi	PROPN
ejpam-6969	296	18	.	.	PUNCT
ejpam-6969	297	1	assorted	assort	VERB
ejpam-6969	297	2	spatial	spatial	ADJ
ejpam-6969	297	3	optical	optical	ADJ
ejpam-6969	297	4	dynamics	dynamic	NOUN
ejpam-6969	297	5	of	of	ADP
ejpam-6969	297	6	a	a	DET
ejpam-6969	297	7	generalized	generalize	VERB
ejpam-6969	297	8	fractional	fractional	ADJ
ejpam-6969	297	9	quadruple	quadruple	NOUN
ejpam-6969	297	10	nematic	nematic	ADJ
ejpam-6969	297	11	liquid	liquid	NOUN
ejpam-6969	297	12	crystal	crystal	NOUN
ejpam-6969	297	13	system	system	NOUN
ejpam-6969	297	14	in	in	ADP
ejpam-6969	297	15	nonlocal	nonlocal	ADJ
ejpam-6969	297	16	media	medium	NOUN
ejpam-6969	297	17	.	.	PUNCT
ejpam-6969	298	1	symmetry	symmetry	NOUN
ejpam-6969	298	2	,	,	PUNCT
ejpam-6969	298	3	16(6):778	16(6):778	PROPN
ejpam-6969	298	4	,	,	PUNCT
ejpam-6969	298	5	2024	2024	NUM
ejpam-6969	298	6	.	.	PUNCT
ejpam-6969	299	1	m.	m.	NOUN
ejpam-6969	299	2	h.	h.	PROPN
ejpam-6969	299	3	ahmed	ahmed	PROPN
ejpam-6969	299	4	,	,	PUNCT
ejpam-6969	299	5	a.	a.	NOUN
ejpam-6969	299	6	m.	m.	PROPN
ejpam-6969	299	7	aljabri	aljabri	PROPN
ejpam-6969	299	8	/	/	SYM
ejpam-6969	299	9	eur	eur	PROPN
ejpam-6969	299	10	.	.	PUNCT
ejpam-6969	300	1	j.	j.	PROPN
ejpam-6969	300	2	pure	pure	PROPN
ejpam-6969	300	3	appl	appl	PROPN
ejpam-6969	300	4	.	.	PROPN
ejpam-6969	300	5	math	math	PROPN
ejpam-6969	300	6	,	,	PUNCT
ejpam-6969	300	7	18	18	NUM
ejpam-6969	300	8	(	(	PUNCT
ejpam-6969	300	9	4	4	NUM
ejpam-6969	300	10	)	)	PUNCT
ejpam-6969	300	11	(	(	PUNCT
ejpam-6969	300	12	2025	2025	NUM
ejpam-6969	300	13	)	)	PUNCT
ejpam-6969	300	14	,	,	PUNCT
ejpam-6969	300	15	6969	6969	NUM
ejpam-6969	300	16	16	16	NUM
ejpam-6969	300	17	of	of	ADP
ejpam-6969	300	18	16	16	NUM
ejpam-6969	300	19	appendix	appendix	VERB
ejpam-6969	300	20	a.	a.	NOUN
ejpam-6969	300	21	implementation	implementation	NOUN
ejpam-6969	300	22	of	of	ADP
ejpam-6969	300	23	the	the	DET
ejpam-6969	300	24	bernoulli	bernoulli	NOUN
ejpam-6969	300	25	collocation	collocation	NOUN
ejpam-6969	300	26	method	method	NOUN
ejpam-6969	300	27	algorithm	algorithm	NOUN
ejpam-6969	300	28	1	1	NUM
ejpam-6969	300	29	bernoulli	bernoulli	NOUN
ejpam-6969	300	30	collocation	collocation	NOUN
ejpam-6969	300	31	maximum	maximum	ADJ
ejpam-6969	300	32	degree	degree	NOUN
ejpam-6969	300	33	n	n	NOUN
ejpam-6969	300	34	;	;	PUNCT
ejpam-6969	300	35	tolerance	tolerance	NOUN
ejpam-6969	300	36	tol	tol	NOUN
ejpam-6969	300	37	;	;	PUNCT
ejpam-6969	300	38	maximum	maximum	ADJ
ejpam-6969	300	39	iterations	iteration	NOUN
ejpam-6969	300	40	imax	imax	NOUN
ejpam-6969	300	41	;	;	PUNCT
ejpam-6969	300	42	nonlinear	nonlinear	ADJ
ejpam-6969	300	43	function	function	NOUN
ejpam-6969	300	44	g(u	g(u	PROPN
ejpam-6969	300	45	)	)	PUNCT
ejpam-6969	300	46	.	.	PUNCT
ejpam-6969	301	1	1	1	X
ejpam-6969	301	2	.	.	X
ejpam-6969	301	3	initialize	initialize	VERB
ejpam-6969	301	4	c(0	c(0	NOUN
ejpam-6969	301	5	)	)	PUNCT
ejpam-6969	301	6	(	(	PUNCT
ejpam-6969	301	7	coefficient	coefficient	NOUN
ejpam-6969	301	8	vector	vector	NOUN
ejpam-6969	301	9	)	)	PUNCT
ejpam-6969	301	10	to	to	ADP
ejpam-6969	301	11	zeros	zero	NOUN
ejpam-6969	301	12	(	(	PUNCT
ejpam-6969	301	13	or	or	CCONJ
ejpam-6969	301	14	a	a	DET
ejpam-6969	301	15	suitable	suitable	ADJ
ejpam-6969	301	16	initial	initial	ADJ
ejpam-6969	301	17	guess	guess	NOUN
ejpam-6969	301	18	)	)	PUNCT
ejpam-6969	301	19	.	.	PUNCT
ejpam-6969	302	1	2	2	X
ejpam-6969	302	2	.	.	X
ejpam-6969	302	3	define	define	VERB
ejpam-6969	302	4	collocation	collocation	NOUN
ejpam-6969	302	5	points	point	NOUN
ejpam-6969	302	6	xi	xi	PROPN
ejpam-6969	302	7	,	,	PUNCT
ejpam-6969	302	8	tj	tj	NOUN
ejpam-6969	302	9	using	use	VERB
ejpam-6969	302	10	chebyshev	chebyshev	NOUN
ejpam-6969	302	11	roots	root	NOUN
ejpam-6969	302	12	:	:	PUNCT
ejpam-6969	302	13	xpoints	xpoint	NOUN
ejpam-6969	302	14	=	=	NOUN
ejpam-6969	302	15	1	1	NUM
ejpam-6969	302	16	2	2	NUM
ejpam-6969	302	17	[	[	PUNCT
ejpam-6969	302	18	cos	cos	X
ejpam-6969	302	19	(	(	PUNCT
ejpam-6969	302	20	(	(	PUNCT
ejpam-6969	302	21	2i−1)π	2i−1)π	NUM
ejpam-6969	302	22	2n	2n	NUM
ejpam-6969	302	23	)	)	PUNCT
ejpam-6969	303	1	+	+	CCONJ
ejpam-6969	303	2	1	1	NUM
ejpam-6969	303	3	]	]	PUNCT
ejpam-6969	303	4	.	.	PUNCT
ejpam-6969	304	1	3	3	X
ejpam-6969	304	2	.	.	X
ejpam-6969	304	3	generate	generate	VERB
ejpam-6969	304	4	bernoulli	bernoulli	PROPN
ejpam-6969	304	5	basis	basis	NOUN
ejpam-6969	304	6	functions	function	NOUN
ejpam-6969	304	7	bk(x	bk(x	NOUN
ejpam-6969	304	8	)	)	PUNCT
ejpam-6969	304	9	for	for	ADP
ejpam-6969	304	10	k	k	PROPN
ejpam-6969	304	11	=	=	SYM
ejpam-6969	304	12	0	0	PROPN
ejpam-6969	304	13	,	,	PUNCT
ejpam-6969	304	14	.	.	PUNCT
ejpam-6969	304	15	.	.	PUNCT
ejpam-6969	305	1	.	.	PUNCT
ejpam-6969	306	1	,	,	PUNCT
ejpam-6969	307	1	n	n	CCONJ
ejpam-6969	307	2	−	−	PROPN
ejpam-6969	307	3	1	1	NUM
ejpam-6969	307	4	.	.	PUNCT
ejpam-6969	308	1	for	for	ADP
ejpam-6969	308	2	k	k	PROPN
ejpam-6969	308	3	=	=	SYM
ejpam-6969	308	4	1	1	NUM
ejpam-6969	308	5	to	to	ADP
ejpam-6969	308	6	imax	imax	PROPN
ejpam-6969	308	7	do	do	VERB
ejpam-6969	308	8	4	4	NUM
ejpam-6969	308	9	.	.	PUNCT
ejpam-6969	308	10	compute	compute	VERB
ejpam-6969	308	11	the	the	DET
ejpam-6969	308	12	approximate	approximate	ADJ
ejpam-6969	308	13	solution	solution	NOUN
ejpam-6969	308	14	u(k−1)(s	u(k−1)(s	NOUN
ejpam-6969	308	15	,	,	PUNCT
ejpam-6969	308	16	y	y	NOUN
ejpam-6969	308	17	)	)	PUNCT
ejpam-6969	308	18	from	from	ADP
ejpam-6969	308	19	the	the	DET
ejpam-6969	308	20	previous	previous	ADJ
ejpam-6969	308	21	iteration	iteration	NOUN
ejpam-6969	308	22	using	use	VERB
ejpam-6969	308	23	c(k−1	c(k−1	NOUN
ejpam-6969	308	24	):	):	PUNCT
ejpam-6969	308	25	u(k−1)(s	u(k−1)(s	NOUN
ejpam-6969	308	26	,	,	PUNCT
ejpam-6969	308	27	y	y	NOUN
ejpam-6969	308	28	)	)	PUNCT
ejpam-6969	308	29	=	=	SYM
ejpam-6969	308	30	∑n−1	∑n−1	ADP
ejpam-6969	308	31	m=0	m=0	PROPN
ejpam-6969	308	32	∑n−1	∑n−1	PROPN
ejpam-6969	308	33	n=0	n=0	X
ejpam-6969	308	34	c	c	PROPN
ejpam-6969	308	35	(	(	PUNCT
ejpam-6969	308	36	k−1	k−1	PROPN
ejpam-6969	308	37	)	)	PUNCT
ejpam-6969	308	38	m	m	PROPN
ejpam-6969	308	39	,	,	PUNCT
ejpam-6969	308	40	n	n	CCONJ
ejpam-6969	308	41	bm(s)bn(y	bm(s)bn(y	PROPN
ejpam-6969	308	42	)	)	PUNCT
ejpam-6969	308	43	.	.	PUNCT
ejpam-6969	309	1	5	5	X
ejpam-6969	309	2	.	.	X
ejpam-6969	309	3	initialize	initialize	VERB
ejpam-6969	309	4	the	the	DET
ejpam-6969	309	5	system	system	NOUN
ejpam-6969	309	6	matrices	matrix	NOUN
ejpam-6969	309	7	for	for	ADP
ejpam-6969	309	8	the	the	DET
ejpam-6969	309	9	current	current	ADJ
ejpam-6969	309	10	iteration	iteration	NOUN
ejpam-6969	309	11	:	:	PUNCT
ejpam-6969	309	12	a(k	a(k	NUM
ejpam-6969	309	13	)	)	PUNCT
ejpam-6969	309	14	←	←	PROPN
ejpam-6969	309	15	zeros(n2	zeros(n2	PROPN
ejpam-6969	309	16	,	,	PUNCT
ejpam-6969	309	17	n2	n2	ADJ
ejpam-6969	309	18	)	)	PUNCT
ejpam-6969	309	19	,	,	PUNCT
ejpam-6969	309	20	f	f	PROPN
ejpam-6969	309	21	(	(	PUNCT
ejpam-6969	309	22	k	k	NOUN
ejpam-6969	309	23	)	)	PUNCT
ejpam-6969	309	24	←	←	PROPN
ejpam-6969	309	25	zeros(n2	zeros(n2	X
ejpam-6969	309	26	,	,	PUNCT
ejpam-6969	309	27	1	1	NUM
ejpam-6969	309	28	)	)	PUNCT
ejpam-6969	309	29	.	.	PUNCT
ejpam-6969	310	1	6	6	X
ejpam-6969	310	2	.	.	X
ejpam-6969	310	3	assemble	assemble	VERB
ejpam-6969	310	4	the	the	DET
ejpam-6969	310	5	system	system	NOUN
ejpam-6969	310	6	at	at	ADP
ejpam-6969	310	7	each	each	DET
ejpam-6969	310	8	collocation	collocation	NOUN
ejpam-6969	310	9	point	point	NOUN
ejpam-6969	310	10	(	(	PUNCT
ejpam-6969	310	11	xi	xi	PROPN
ejpam-6969	310	12	,	,	PUNCT
ejpam-6969	310	13	tj	tj	NOUN
ejpam-6969	310	14	)	)	PUNCT
ejpam-6969	310	15	for	for	ADP
ejpam-6969	310	16	i	i	PRON
ejpam-6969	310	17	,	,	PUNCT
ejpam-6969	310	18	j	j	PROPN
ejpam-6969	310	19	=	=	SYM
ejpam-6969	310	20	1	1	NUM
ejpam-6969	310	21	,	,	PUNCT
ejpam-6969	310	22	.	.	PUNCT
ejpam-6969	310	23	.	.	PUNCT
ejpam-6969	311	1	.	.	PUNCT
ejpam-6969	312	1	,	,	PUNCT
ejpam-6969	312	2	n	n	X
ejpam-6969	312	3	(	(	PUNCT
ejpam-6969	312	4	total	total	ADJ
ejpam-6969	312	5	n2	n2	ADJ
ejpam-6969	312	6	points	point	NOUN
ejpam-6969	312	7	):	):	PUNCT
ejpam-6969	312	8	for	for	ADP
ejpam-6969	312	9	i	i	PRON
ejpam-6969	312	10	=	=	NOUN
ejpam-6969	312	11	1	1	NUM
ejpam-6969	312	12	to	to	PART
ejpam-6969	312	13	n	n	PRON
ejpam-6969	312	14	do	do	AUX
ejpam-6969	312	15	for	for	ADP
ejpam-6969	312	16	j	j	PROPN
ejpam-6969	312	17	=	=	SYM
ejpam-6969	312	18	1	1	NUM
ejpam-6969	312	19	to	to	PART
ejpam-6969	312	20	n	n	PRON
ejpam-6969	312	21	do	do	AUX
ejpam-6969	312	22	a.	a.	NOUN
ejpam-6969	312	23	compute	compute	VERB
ejpam-6969	312	24	the	the	DET
ejpam-6969	312	25	integral	integral	NOUN
ejpam-6969	312	26	of	of	ADP
ejpam-6969	312	27	the	the	DET
ejpam-6969	312	28	known	known	ADJ
ejpam-6969	312	29	non	non	ADJ
ejpam-6969	312	30	-	-	ADJ
ejpam-6969	312	31	linear	linear	ADJ
ejpam-6969	312	32	term	term	NOUN
ejpam-6969	312	33	(	(	PUNCT
ejpam-6969	312	34	from	from	ADP
ejpam-6969	312	35	the	the	DET
ejpam-6969	312	36	previous	previous	ADJ
ejpam-6969	312	37	approximation	approximation	NOUN
ejpam-6969	312	38	u(k−1	u(k−1	PROPN
ejpam-6969	312	39	)	)	PUNCT
ejpam-6969	312	40	):	):	PUNCT
ejpam-6969	312	41	j	j	PROPN
ejpam-6969	312	42	(	(	PUNCT
ejpam-6969	312	43	k−1	k−1	PROPN
ejpam-6969	312	44	)	)	PUNCT
ejpam-6969	312	45	i	i	PROPN
ejpam-6969	312	46	,	,	PUNCT
ejpam-6969	312	47	j	j	PROPN
ejpam-6969	313	1	=	=	SYM
ejpam-6969	313	2	λ	λ	PROPN
ejpam-6969	313	3	∫	∫	PROPN
ejpam-6969	313	4	tj	tj	PROPN
ejpam-6969	313	5	0	0	PROPN
ejpam-6969	313	6	∫	∫	PROPN
ejpam-6969	313	7	xi	xi	X
ejpam-6969	313	8	0	0	PUNCT
ejpam-6969	313	9	k(xi	k(xi	PROPN
ejpam-6969	313	10	,	,	PUNCT
ejpam-6969	313	11	tj	tj	X
ejpam-6969	313	12	,	,	PUNCT
ejpam-6969	313	13	s	s	PROPN
ejpam-6969	313	14	,	,	PUNCT
ejpam-6969	313	15	y	y	PROPN
ejpam-6969	313	16	,	,	PUNCT
ejpam-6969	313	17	u	u	PROPN
ejpam-6969	313	18	(	(	PUNCT
ejpam-6969	313	19	k−1)(s	k−1)(s	PROPN
ejpam-6969	313	20	,	,	PUNCT
ejpam-6969	313	21	y	y	PROPN
ejpam-6969	313	22	)	)	PUNCT
ejpam-6969	313	23	)	)	PUNCT
ejpam-6969	313	24	ds	ds	PROPN
ejpam-6969	313	25	dy	dy	X
ejpam-6969	313	26	b.	b.	PROPN
ejpam-6969	313	27	define	define	VERB
ejpam-6969	313	28	the	the	DET
ejpam-6969	313	29	right	right	ADJ
ejpam-6969	313	30	-	-	PUNCT
ejpam-6969	313	31	hand	hand	NOUN
ejpam-6969	313	32	side	side	NOUN
ejpam-6969	313	33	vector	vector	NOUN
ejpam-6969	313	34	f	f	NOUN
ejpam-6969	313	35	:	:	PUNCT
ejpam-6969	313	36	f	f	PROPN
ejpam-6969	313	37	(	(	PUNCT
ejpam-6969	313	38	k	k	NOUN
ejpam-6969	313	39	)	)	PUNCT
ejpam-6969	313	40	(	(	PUNCT
ejpam-6969	313	41	i−1)n+j	i−1)n+j	PROPN
ejpam-6969	313	42	=	=	SYM
ejpam-6969	313	43	f(xi	f(xi	PROPN
ejpam-6969	313	44	,	,	PUNCT
ejpam-6969	313	45	tj	tj	NOUN
ejpam-6969	313	46	)	)	PUNCT
ejpam-6969	313	47	+	+	NUM
ejpam-6969	313	48	j	j	PROPN
ejpam-6969	313	49	(	(	PUNCT
ejpam-6969	313	50	k−1	k−1	PROPN
ejpam-6969	313	51	)	)	PUNCT
ejpam-6969	313	52	i	i	PROPN
ejpam-6969	313	53	,	,	PUNCT
ejpam-6969	313	54	j	j	PROPN
ejpam-6969	313	55	c.	c.	PROPN
ejpam-6969	313	56	define	define	VERB
ejpam-6969	313	57	the	the	DET
ejpam-6969	313	58	system	system	NOUN
ejpam-6969	313	59	matrix	matrix	NOUN
ejpam-6969	313	60	a	a	PRON
ejpam-6969	313	61	(	(	PUNCT
ejpam-6969	313	62	which	which	PRON
ejpam-6969	313	63	remains	remain	VERB
ejpam-6969	313	64	constant	constant	ADJ
ejpam-6969	313	65	for	for	ADP
ejpam-6969	313	66	the	the	DET
ejpam-6969	313	67	bernoulli	bernoulli	PROPN
ejpam-6969	313	68	basis	basis	NOUN
ejpam-6969	313	69	):	):	PUNCT
ejpam-6969	313	70	a	a	DET
ejpam-6969	313	71	(	(	PUNCT
ejpam-6969	313	72	k	k	NOUN
ejpam-6969	313	73	)	)	PUNCT
ejpam-6969	313	74	(	(	PUNCT
ejpam-6969	313	75	i−1)n+j	i−1)n+j	NOUN
ejpam-6969	313	76	,	,	PUNCT
ejpam-6969	313	77	mn+n	mn+n	NOUN
ejpam-6969	313	78	=	=	SYM
ejpam-6969	313	79	bm(xi)bn(tj	bm(xi)bn(tj	NOUN
ejpam-6969	313	80	)	)	PUNCT
ejpam-6969	313	81	7	7	NUM
ejpam-6969	313	82	.	.	X
ejpam-6969	314	1	solve	solve	VERB
ejpam-6969	314	2	the	the	DET
ejpam-6969	314	3	linear	linear	ADJ
ejpam-6969	314	4	system	system	NOUN
ejpam-6969	314	5	for	for	ADP
ejpam-6969	314	6	the	the	DET
ejpam-6969	314	7	new	new	ADJ
ejpam-6969	314	8	coefficients	coefficient	NOUN
ejpam-6969	314	9	:	:	PUNCT
ejpam-6969	314	10	c(k	c(k	PROPN
ejpam-6969	314	11	)	)	PUNCT
ejpam-6969	314	12	←	←	PROPN
ejpam-6969	314	13	(	(	PUNCT
ejpam-6969	314	14	a(k))−1f	a(k))−1f	X
ejpam-6969	314	15	(	(	PUNCT
ejpam-6969	314	16	k	k	NOUN
ejpam-6969	314	17	)	)	PUNCT
ejpam-6969	314	18	.	.	PUNCT
ejpam-6969	315	1	8	8	X
ejpam-6969	315	2	.	.	X
ejpam-6969	315	3	check	check	NOUN
ejpam-6969	315	4	for	for	ADP
ejpam-6969	315	5	convergence	convergence	NOUN
ejpam-6969	315	6	:	:	PUNCT
ejpam-6969	315	7	if	if	SCONJ
ejpam-6969	315	8	∥c(k	∥c(k	ADJ
ejpam-6969	315	9	)	)	PUNCT
ejpam-6969	315	10	−	−	PROPN
ejpam-6969	316	1	c(k−1)∥∞	c(k−1)∥∞	NOUN
ejpam-6969	316	2	<	<	X
ejpam-6969	316	3	tol	tol	NOUN
ejpam-6969	316	4	then	then	ADV
ejpam-6969	316	5	return	return	VERB
ejpam-6969	316	6	c(k	c(k	NOUN
ejpam-6969	316	7	)	)	PUNCT
ejpam-6969	316	8	and	and	CCONJ
ejpam-6969	316	9	break	break	NOUN
ejpam-6969	316	10	.	.	PUNCT
ejpam-6969	317	1	9	9	X
ejpam-6969	317	2	.	.	X
ejpam-6969	317	3	update	update	VERB
ejpam-6969	317	4	the	the	DET
ejpam-6969	317	5	coefficients	coefficient	NOUN
ejpam-6969	317	6	:	:	PUNCT
ejpam-6969	317	7	c(k−1	c(k−1	X
ejpam-6969	317	8	)	)	PUNCT
ejpam-6969	317	9	←	←	PROPN
ejpam-6969	317	10	c(k	c(k	PROPN
ejpam-6969	317	11	)	)	PUNCT
ejpam-6969	317	12	.	.	PUNCT