id	sid	tid	token	lemma	pos
cana-6069	1	1	communications	communication	NOUN
cana-6069	1	2	on	on	ADP
cana-6069	1	3	applied	apply	VERB
cana-6069	1	4	nonlinear	nonlinear	ADJ
cana-6069	1	5	analysis	analysis	NOUN
cana-6069	1	6	issn	issn	NOUN
cana-6069	1	7	:	:	PUNCT
cana-6069	1	8	1074	1074	NUM
cana-6069	1	9	-	-	PUNCT
cana-6069	1	10	133x	133x	NUM
cana-6069	1	11	vol	vol	VERB
cana-6069	1	12	32	32	NUM
cana-6069	1	13	no.10s	no.10s	PROPN
cana-6069	1	14	y	y	PROPN
cana-6069	1	15	(	(	PUNCT
cana-6069	1	16	2025	2025	NUM
cana-6069	1	17	)	)	PUNCT
cana-6069	1	18	3308	3308	NUM
cana-6069	1	19	three	three	NUM
cana-6069	1	20	-	-	PUNCT
cana-6069	1	21	dimensional	dimensional	ADJ
cana-6069	1	22	nonlinear	nonlinear	ADJ
cana-6069	1	23	fredholm	fredholm	ADJ
cana-6069	1	24	integral	integral	ADJ
cana-6069	1	25	equation	equation	NOUN
cana-6069	1	26	of	of	ADP
cana-6069	1	27	the	the	DET
cana-6069	1	28	second	second	ADJ
cana-6069	1	29	kind	kind	NOUN
cana-6069	1	30	solved	solve	VERB
cana-6069	1	31	by	by	ADP
cana-6069	1	32	comparing	compare	VERB
cana-6069	1	33	fibonacci	fibonacci	NOUN
cana-6069	1	34	collocation	collocation	NOUN
cana-6069	1	35	method	method	NOUN
cana-6069	1	36	and	and	CCONJ
cana-6069	1	37	hermitegalerkin	hermitegalerkin	X
cana-6069	1	38	method	method	PROPN
cana-6069	1	39	m.	m.	PROPN
cana-6069	1	40	h.	h.	PROPN
cana-6069	1	41	ahmed	ahmed	PROPN
cana-6069	1	42	and	and	CCONJ
cana-6069	1	43	s.	s.	PROPN
cana-6069	1	44	h.	h.	PROPN
cana-6069	1	45	aljahdali	aljahdali	PROPN
cana-6069	1	46	taibah	taibah	PROPN
cana-6069	1	47	university	university	PROPN
cana-6069	1	48	,	,	PUNCT
cana-6069	1	49	college	college	NOUN
cana-6069	1	50	of	of	ADP
cana-6069	1	51	science	science	NOUN
cana-6069	1	52	,	,	PUNCT
cana-6069	1	53	department	department	NOUN
cana-6069	1	54	of	of	ADP
cana-6069	1	55	mathematics	mathematic	NOUN
cana-6069	1	56	,	,	PUNCT
cana-6069	1	57	p.o.box	p.o.box	PROPN
cana-6069	1	58	344	344	NUM
cana-6069	1	59	,	,	PUNCT
cana-6069	1	60	madinah,3002	madinah,3002	NOUN
cana-6069	1	61	,	,	PUNCT
cana-6069	1	62	saudi	saudi	PROPN
cana-6069	1	63	arabia	arabia	PROPN
cana-6069	1	64	.	.	PUNCT
cana-6069	2	1	article	article	PROPN
cana-6069	2	2	history	history	NOUN
cana-6069	2	3	:	:	PUNCT
cana-6069	2	4	received	receive	VERB
cana-6069	2	5	:	:	PUNCT
cana-6069	2	6	01/01/2025	01/01/2025	NUM
cana-6069	2	7	revised	revise	VERB
cana-6069	2	8	:	:	PUNCT
cana-6069	2	9	06/02/2025	06/02/2025	NUM
cana-6069	2	10	accepted	accept	VERB
cana-6069	2	11	:	:	PUNCT
cana-6069	2	12	10/03/2025	10/03/2025	NUM
cana-6069	2	13	abstract	abstract	NOUN
cana-6069	2	14	:	:	PUNCT
cana-6069	2	15	in	in	ADP
cana-6069	2	16	this	this	DET
cana-6069	2	17	article	article	NOUN
cana-6069	2	18	,	,	PUNCT
cana-6069	2	19	we	we	PRON
cana-6069	2	20	present	present	VERB
cana-6069	2	21	the	the	DET
cana-6069	2	22	numerical	numerical	ADJ
cana-6069	2	23	solutions	solution	NOUN
cana-6069	2	24	of	of	ADP
cana-6069	2	25	three	three	NUM
cana-6069	2	26	-	-	PUNCT
cana-6069	2	27	dimensional	dimensional	ADJ
cana-6069	2	28	nonlinear	nonlinear	ADJ
cana-6069	2	29	fredholm	fredholm	ADJ
cana-6069	2	30	integral	integral	ADJ
cana-6069	2	31	equations	equation	NOUN
cana-6069	2	32	using	use	VERB
cana-6069	2	33	two	two	NUM
cana-6069	2	34	different	different	ADJ
cana-6069	2	35	polynomial	polynomial	ADJ
cana-6069	2	36	-	-	PUNCT
cana-6069	2	37	based	base	VERB
cana-6069	2	38	approaches	approach	NOUN
cana-6069	2	39	.	.	PUNCT
cana-6069	3	1	the	the	DET
cana-6069	3	2	first	first	ADJ
cana-6069	3	3	method	method	NOUN
cana-6069	3	4	employs	employ	VERB
cana-6069	3	5	fibonacci	fibonacci	NOUN
cana-6069	3	6	polynomials	polynomial	NOUN
cana-6069	3	7	within	within	ADP
cana-6069	3	8	the	the	DET
cana-6069	3	9	collocation	collocation	NOUN
cana-6069	3	10	method	method	NOUN
cana-6069	3	11	,	,	PUNCT
cana-6069	3	12	while	while	SCONJ
cana-6069	3	13	the	the	DET
cana-6069	3	14	second	second	ADJ
cana-6069	3	15	method	method	NOUN
cana-6069	3	16	applies	apply	VERB
cana-6069	3	17	hermite	hermite	ADJ
cana-6069	3	18	polynomials	polynomial	VERB
cana-6069	3	19	through	through	ADP
cana-6069	3	20	the	the	DET
cana-6069	3	21	galerkin	galerkin	ADJ
cana-6069	3	22	projection	projection	NOUN
cana-6069	3	23	technique	technique	NOUN
cana-6069	3	24	.	.	PUNCT
cana-6069	4	1	a	a	DET
cana-6069	4	2	comparative	comparative	ADJ
cana-6069	4	3	study	study	NOUN
cana-6069	4	4	between	between	ADP
cana-6069	4	5	the	the	DET
cana-6069	4	6	two	two	NUM
cana-6069	4	7	proposed	propose	VERB
cana-6069	4	8	approaches	approach	NOUN
cana-6069	4	9	is	be	AUX
cana-6069	4	10	carried	carry	VERB
cana-6069	4	11	out	out	ADP
cana-6069	4	12	,	,	PUNCT
cana-6069	4	13	and	and	CCONJ
cana-6069	4	14	the	the	DET
cana-6069	4	15	obtained	obtain	VERB
cana-6069	4	16	results	result	NOUN
cana-6069	4	17	are	be	AUX
cana-6069	4	18	also	also	ADV
cana-6069	4	19	contrasted	contrast	VERB
cana-6069	4	20	with	with	ADP
cana-6069	4	21	those	those	PRON
cana-6069	4	22	available	available	ADJ
cana-6069	4	23	in	in	ADP
cana-6069	4	24	related	related	ADJ
cana-6069	4	25	works	work	NOUN
cana-6069	4	26	.	.	PUNCT
cana-6069	5	1	the	the	DET
cana-6069	5	2	numerical	numerical	ADJ
cana-6069	5	3	results	result	NOUN
cana-6069	5	4	are	be	AUX
cana-6069	5	5	illustrated	illustrate	VERB
cana-6069	5	6	in	in	ADP
cana-6069	5	7	a	a	DET
cana-6069	5	8	series	series	NOUN
cana-6069	5	9	of	of	ADP
cana-6069	5	10	tables	table	NOUN
cana-6069	5	11	and	and	CCONJ
cana-6069	5	12	figures	figure	NOUN
cana-6069	5	13	,	,	PUNCT
cana-6069	5	14	demonstrating	demonstrate	VERB
cana-6069	5	15	the	the	DET
cana-6069	5	16	efficiency	efficiency	NOUN
cana-6069	5	17	and	and	CCONJ
cana-6069	5	18	accuracy	accuracy	NOUN
cana-6069	5	19	of	of	ADP
cana-6069	5	20	the	the	DET
cana-6069	5	21	methods	method	NOUN
cana-6069	5	22	.	.	PUNCT
cana-6069	6	1	introduction	introduction	NOUN
cana-6069	6	2	:	:	PUNCT
cana-6069	6	3	the	the	DET
cana-6069	6	4	three	three	NUM
cana-6069	6	5	-	-	PUNCT
cana-6069	6	6	dimensional	dimensional	ADJ
cana-6069	6	7	nonlinear	nonlinear	ADJ
cana-6069	6	8	fredholm	fredholm	ADJ
cana-6069	6	9	integral	integral	ADJ
cana-6069	6	10	equations	equation	NOUN
cana-6069	6	11	(	(	PUNCT
cana-6069	6	12	3dnlfies	3dnlfie	NOUN
cana-6069	6	13	)	)	PUNCT
cana-6069	6	14	of	of	ADP
cana-6069	6	15	the	the	DET
cana-6069	6	16	second	second	ADJ
cana-6069	6	17	kind	kind	NOUN
cana-6069	6	18	are	be	AUX
cana-6069	6	19	fundamental	fundamental	ADJ
cana-6069	6	20	tools	tool	NOUN
cana-6069	6	21	in	in	ADP
cana-6069	6	22	modelling	model	VERB
cana-6069	6	23	a	a	DET
cana-6069	6	24	wide	wide	ADJ
cana-6069	6	25	range	range	NOUN
cana-6069	6	26	of	of	ADP
cana-6069	6	27	problems	problem	NOUN
cana-6069	6	28	in	in	ADP
cana-6069	6	29	applied	applied	ADJ
cana-6069	6	30	mathematics	mathematic	NOUN
cana-6069	6	31	,	,	PUNCT
cana-6069	6	32	physics	physics	NOUN
cana-6069	6	33	,	,	PUNCT
cana-6069	6	34	and	and	CCONJ
cana-6069	6	35	engineering	engineering	NOUN
cana-6069	6	36	.	.	PUNCT
cana-6069	7	1	these	these	DET
cana-6069	7	2	equations	equation	NOUN
cana-6069	7	3	naturally	naturally	ADV
cana-6069	7	4	arise	arise	VERB
cana-6069	7	5	in	in	ADP
cana-6069	7	6	mathematical	mathematical	ADJ
cana-6069	7	7	models	model	NOUN
cana-6069	7	8	of	of	ADP
cana-6069	7	9	electromagnetic	electromagnetic	ADJ
cana-6069	7	10	scattering	scattering	NOUN
cana-6069	7	11	,	,	PUNCT
cana-6069	7	12	quantum	quantum	ADJ
cana-6069	7	13	mechanics	mechanic	NOUN
cana-6069	7	14	,	,	PUNCT
cana-6069	7	15	heat	heat	NOUN
cana-6069	7	16	transfer	transfer	NOUN
cana-6069	7	17	,	,	PUNCT
cana-6069	7	18	and	and	CCONJ
cana-6069	7	19	population	population	NOUN
cana-6069	7	20	dynamics	dynamic	NOUN
cana-6069	7	21	[	[	X
cana-6069	7	22	6	6	NUM
cana-6069	7	23	,	,	PUNCT
cana-6069	7	24	12	12	NUM
cana-6069	7	25	,	,	PUNCT
cana-6069	7	26	14	14	NUM
cana-6069	7	27	]	]	PUNCT
cana-6069	7	28	.	.	PUNCT
cana-6069	8	1	in	in	ADP
cana-6069	8	2	three	three	NUM
cana-6069	8	3	dimensions	dimension	NOUN
cana-6069	8	4	,	,	PUNCT
cana-6069	8	5	the	the	DET
cana-6069	8	6	nonlinear	nonlinear	ADJ
cana-6069	8	7	structure	structure	NOUN
cana-6069	8	8	combined	combine	VERB
cana-6069	8	9	with	with	ADP
cana-6069	8	10	the	the	DET
cana-6069	8	11	multi	multi	ADJ
cana-6069	8	12	-	-	ADJ
cana-6069	8	13	variable	variable	ADJ
cana-6069	8	14	kernel	kernel	NOUN
cana-6069	8	15	makes	make	VERB
cana-6069	8	16	analytical	analytical	ADJ
cana-6069	8	17	solutions	solution	NOUN
cana-6069	8	18	intractable	intractable	ADJ
cana-6069	8	19	,	,	PUNCT
cana-6069	8	20	which	which	PRON
cana-6069	8	21	emphasizes	emphasize	VERB
cana-6069	8	22	the	the	DET
cana-6069	8	23	importance	importance	NOUN
cana-6069	8	24	of	of	ADP
cana-6069	8	25	developing	develop	VERB
cana-6069	8	26	efficient	efficient	ADJ
cana-6069	8	27	and	and	CCONJ
cana-6069	8	28	accurate	accurate	ADJ
cana-6069	8	29	numerical	numerical	ADJ
cana-6069	8	30	methods	method	NOUN
cana-6069	8	31	.	.	PUNCT
cana-6069	9	1	it	it	PRON
cana-6069	9	2	is	be	AUX
cana-6069	9	3	worth	worth	ADJ
cana-6069	9	4	mentioning	mention	VERB
cana-6069	9	5	that	that	SCONJ
cana-6069	9	6	several	several	ADJ
cana-6069	9	7	recent	recent	ADJ
cana-6069	9	8	studies	study	NOUN
cana-6069	9	9	have	have	AUX
cana-6069	9	10	applied	apply	VERB
cana-6069	9	11	second	second	ADJ
cana-6069	9	12	-	-	PUNCT
cana-6069	9	13	kind	kind	NOUN
cana-6069	9	14	fredholm	fredholm	NOUN
cana-6069	9	15	integral	integral	ADJ
cana-6069	9	16	equations	equation	NOUN
cana-6069	9	17	to	to	ADP
cana-6069	9	18	advanced	advanced	ADJ
cana-6069	9	19	fields	field	NOUN
cana-6069	9	20	such	such	ADJ
cana-6069	9	21	as	as	ADP
cana-6069	9	22	electromagnetic	electromagnetic	ADJ
cana-6069	9	23	wave	wave	NOUN
cana-6069	9	24	propagation	propagation	NOUN
cana-6069	9	25	in	in	ADP
cana-6069	9	26	dielectric	dielectric	ADJ
cana-6069	9	27	gratings	grating	NOUN
cana-6069	9	28	.	.	PUNCT
cana-6069	10	1	for	for	ADP
cana-6069	10	2	example	example	NOUN
cana-6069	10	3	,	,	PUNCT
cana-6069	10	4	the	the	DET
cana-6069	10	5	paper	paper	NOUN
cana-6069	10	6	[	[	X
cana-6069	10	7	15	15	NUM
cana-6069	10	8	]	]	PUNCT
cana-6069	10	9	presents	present	VERB
cana-6069	10	10	a	a	DET
cana-6069	10	11	volume	volume	NOUN
cana-6069	10	12	integral	integral	ADJ
cana-6069	10	13	equation	equation	NOUN
cana-6069	10	14	(	(	PUNCT
cana-6069	10	15	vie	vie	NOUN
cana-6069	10	16	)	)	PUNCT
cana-6069	10	17	formulation	formulation	NOUN
cana-6069	10	18	combined	combine	VERB
cana-6069	10	19	with	with	ADP
cana-6069	10	20	the	the	DET
cana-6069	10	21	galerkin	galerkin	ADJ
cana-6069	10	22	method	method	NOUN
cana-6069	10	23	,	,	PUNCT
cana-6069	10	24	which	which	PRON
cana-6069	10	25	enables	enable	VERB
cana-6069	10	26	stable	stable	ADJ
cana-6069	10	27	and	and	CCONJ
cana-6069	10	28	ac	ac	ADJ
cana-6069	10	29	curate	curate	NOUN
cana-6069	10	30	solutions	solution	NOUN
cana-6069	10	31	for	for	ADP
cana-6069	10	32	the	the	DET
cana-6069	10	33	scattering	scatter	VERB
cana-6069	10	34	phenomena	phenomenon	NOUN
cana-6069	10	35	in	in	ADP
cana-6069	10	36	multilayer	multilayer	ADJ
cana-6069	10	37	dielectric	dielectric	ADJ
cana-6069	10	38	gratings	grating	NOUN
cana-6069	10	39	.	.	PUNCT
cana-6069	11	1	this	this	DET
cana-6069	11	2	work	work	NOUN
cana-6069	11	3	highlights	highlight	VERB
cana-6069	11	4	the	the	DET
cana-6069	11	5	significance	significance	NOUN
cana-6069	11	6	of	of	ADP
cana-6069	11	7	numerical	numerical	ADJ
cana-6069	11	8	techniques	technique	NOUN
cana-6069	11	9	based	base	VERB
cana-6069	11	10	on	on	ADP
cana-6069	11	11	integral	integral	ADJ
cana-6069	11	12	equations	equation	NOUN
cana-6069	11	13	in	in	ADP
cana-6069	11	14	addressing	address	VERB
cana-6069	11	15	complex	complex	ADJ
cana-6069	11	16	and	and	CCONJ
cana-6069	11	17	practical	practical	ADJ
cana-6069	11	18	problems	problem	NOUN
cana-6069	11	19	in	in	ADP
cana-6069	11	20	physics	physics	NOUN
cana-6069	11	21	and	and	CCONJ
cana-6069	11	22	applied	apply	VERB
cana-6069	11	23	mathematics	mathematic	NOUN
cana-6069	11	24	,	,	PUNCT
cana-6069	11	25	which	which	PRON
cana-6069	11	26	is	be	AUX
cana-6069	11	27	in	in	ADP
cana-6069	11	28	line	line	NOUN
cana-6069	11	29	with	with	ADP
cana-6069	11	30	our	our	PRON
cana-6069	11	31	research	research	NOUN
cana-6069	11	32	focus	focus	NOUN
cana-6069	11	33	on	on	ADP
cana-6069	11	34	developing	develop	VERB
cana-6069	11	35	numerical	numerical	ADJ
cana-6069	11	36	approaches	approach	NOUN
cana-6069	11	37	for	for	ADP
cana-6069	11	38	solving	solve	VERB
cana-6069	11	39	nonlinear	nonlinear	ADJ
cana-6069	11	40	fredholm	fredholm	ADJ
cana-6069	11	41	integral	integral	ADJ
cana-6069	11	42	equations	equation	NOUN
cana-6069	11	43	[	[	X
cana-6069	11	44	9	9	NUM
cana-6069	11	45	]	]	PUNCT
cana-6069	11	46	.	.	PUNCT
cana-6069	12	1	objectives	objective	NOUN
cana-6069	12	2	:	:	PUNCT
cana-6069	12	3	this	this	DET
cana-6069	12	4	paper	paper	NOUN
cana-6069	12	5	consists	consist	VERB
cana-6069	12	6	of	of	ADP
cana-6069	12	7	five	five	NUM
cana-6069	12	8	sections	section	NOUN
cana-6069	12	9	:	:	PUNCT
cana-6069	12	10	an	an	DET
cana-6069	12	11	introduction	introduction	NOUN
cana-6069	12	12	and	and	CCONJ
cana-6069	12	13	definition	definition	NOUN
cana-6069	12	14	of	of	ADP
cana-6069	12	15	the	the	DET
cana-6069	12	16	3dnlfies	3dnlfies	PROPN
cana-6069	12	17	,	,	PUNCT
cana-6069	12	18	a	a	DET
cana-6069	12	19	statement	statement	NOUN
cana-6069	12	20	of	of	ADP
cana-6069	12	21	objectives	objective	NOUN
cana-6069	12	22	,	,	PUNCT
cana-6069	12	23	a	a	DET
cana-6069	12	24	review	review	NOUN
cana-6069	12	25	of	of	ADP
cana-6069	12	26	fibonacci	fibonacci	PROPN
cana-6069	12	27	and	and	CCONJ
cana-6069	12	28	hermite	hermite	ADJ
cana-6069	12	29	polynomials	polynomial	NOUN
cana-6069	12	30	with	with	ADP
cana-6069	12	31	the	the	DET
cana-6069	12	32	application	application	NOUN
cana-6069	12	33	of	of	ADP
cana-6069	12	34	the	the	DET
cana-6069	12	35	fibonacci	fibonacci	NOUN
cana-6069	12	36	collocation	collocation	NOUN
cana-6069	12	37	and	and	CCONJ
cana-6069	12	38	hermite	hermite	ADJ
cana-6069	12	39	–	–	PUNCT
cana-6069	12	40	galerkin	galerkin	ADJ
cana-6069	12	41	methods	method	NOUN
cana-6069	12	42	,	,	PUNCT
cana-6069	12	43	results	result	NOUN
cana-6069	12	44	including	include	VERB
cana-6069	12	45	existence	existence	NOUN
cana-6069	12	46	and	and	CCONJ
cana-6069	12	47	uniqueness	uniqueness	NOUN
cana-6069	12	48	proofs	proof	NOUN
cana-6069	12	49	and	and	CCONJ
cana-6069	12	50	numerical	numerical	ADJ
cana-6069	12	51	comparisons	comparison	NOUN
cana-6069	12	52	,	,	PUNCT
cana-6069	12	53	and	and	CCONJ
cana-6069	12	54	finally	finally	ADV
cana-6069	12	55	a	a	DET
cana-6069	12	56	discussion	discussion	NOUN
cana-6069	12	57	analysing	analyse	VERB
cana-6069	12	58	the	the	DET
cana-6069	12	59	accuracy	accuracy	NOUN
cana-6069	12	60	and	and	CCONJ
cana-6069	12	61	efficiency	efficiency	NOUN
cana-6069	12	62	of	of	ADP
cana-6069	12	63	the	the	DET
cana-6069	12	64	methods	method	NOUN
cana-6069	12	65	.	.	PUNCT
cana-6069	13	1	methods	method	NOUN
cana-6069	13	2	:	:	PUNCT
cana-6069	13	3	we	we	PRON
cana-6069	13	4	employed	employ	VERB
cana-6069	13	5	the	the	DET
cana-6069	13	6	fibonacci	fibonacci	NOUN
cana-6069	13	7	collocation	collocation	NOUN
cana-6069	13	8	method	method	NOUN
cana-6069	13	9	and	and	CCONJ
cana-6069	13	10	the	the	DET
cana-6069	13	11	hermite	hermite	ADJ
cana-6069	13	12	–	–	PUNCT
cana-6069	13	13	galerkin	galerkin	ADJ
cana-6069	13	14	method	method	NOUN
cana-6069	13	15	to	to	PART
cana-6069	13	16	solve	solve	VERB
cana-6069	13	17	3d	3d	NUM
cana-6069	13	18	-	-	PUNCT
cana-6069	13	19	nlfies	nlfie	NOUN
cana-6069	13	20	.	.	PUNCT
cana-6069	14	1	results	result	NOUN
cana-6069	14	2	:	:	PUNCT
cana-6069	14	3	established	establish	VERB
cana-6069	14	4	the	the	DET
cana-6069	14	5	existence	existence	NOUN
cana-6069	14	6	and	and	CCONJ
cana-6069	14	7	uniqueness	uniqueness	NOUN
cana-6069	14	8	of	of	ADP
cana-6069	14	9	the	the	DET
cana-6069	14	10	solution	solution	NOUN
cana-6069	14	11	for	for	ADP
cana-6069	14	12	the	the	DET
cana-6069	14	13	3d	3d	NOUN
cana-6069	14	14	-	-	PUNCT
cana-6069	14	15	nlfie	nlfie	NOUN
cana-6069	14	16	and	and	CCONJ
cana-6069	14	17	obtained	obtain	VERB
cana-6069	14	18	numerical	numerical	ADJ
cana-6069	14	19	solutions	solution	NOUN
cana-6069	14	20	using	use	VERB
cana-6069	14	21	matlab	matlab	NOUN
cana-6069	14	22	by	by	ADP
cana-6069	14	23	applying	apply	VERB
cana-6069	14	24	both	both	DET
cana-6069	14	25	methods	method	NOUN
cana-6069	14	26	.	.	PUNCT
cana-6069	15	1	a	a	DET
cana-6069	15	2	comparative	comparative	ADJ
cana-6069	15	3	communications	communication	NOUN
cana-6069	15	4	on	on	ADP
cana-6069	15	5	applied	apply	VERB
cana-6069	15	6	nonlinear	nonlinear	ADJ
cana-6069	15	7	analysis	analysis	NOUN
cana-6069	15	8	issn	issn	NOUN
cana-6069	15	9	:	:	PUNCT
cana-6069	15	10	1074	1074	NUM
cana-6069	15	11	-	-	PUNCT
cana-6069	15	12	133x	133x	NUM
cana-6069	15	13	vol	vol	VERB
cana-6069	15	14	32	32	NUM
cana-6069	15	15	no.10s	no.10s	PROPN
cana-6069	15	16	y	y	PROPN
cana-6069	15	17	(	(	PUNCT
cana-6069	15	18	2025	2025	NUM
cana-6069	15	19	)	)	PUNCT
cana-6069	15	20	3309	3309	NUM
cana-6069	15	21	analysis	analysis	NOUN
cana-6069	15	22	was	be	AUX
cana-6069	15	23	then	then	ADV
cana-6069	15	24	conducted	conduct	VERB
cana-6069	15	25	between	between	ADP
cana-6069	15	26	the	the	DET
cana-6069	15	27	two	two	NUM
cana-6069	15	28	methods	method	NOUN
cana-6069	15	29	,	,	PUNCT
cana-6069	15	30	and	and	CCONJ
cana-6069	15	31	the	the	DET
cana-6069	15	32	results	result	NOUN
cana-6069	15	33	were	be	AUX
cana-6069	15	34	reported	report	VERB
cana-6069	15	35	in	in	ADP
cana-6069	15	36	previous	previous	ADJ
cana-6069	15	37	studies	study	NOUN
cana-6069	15	38	[	[	X
cana-6069	15	39	7,8	7,8	NUM
cana-6069	15	40	]	]	PUNCT
cana-6069	15	41	.	.	PUNCT
cana-6069	16	1	conclusions	conclusion	NOUN
cana-6069	16	2	:	:	PUNCT
cana-6069	16	3	the	the	DET
cana-6069	16	4	results	result	NOUN
cana-6069	16	5	demonstrated	demonstrate	VERB
cana-6069	16	6	that	that	SCONJ
cana-6069	16	7	the	the	DET
cana-6069	16	8	fibonacci	fibonacci	NOUN
cana-6069	16	9	collocation	collocation	NOUN
cana-6069	16	10	method	method	NOUN
cana-6069	16	11	consistently	consistently	ADV
cana-6069	16	12	outperformed	outperform	VERB
cana-6069	16	13	the	the	DET
cana-6069	16	14	hermite	hermite	ADJ
cana-6069	16	15	–	–	PUNCT
cana-6069	16	16	galerkin	galerkin	ADJ
cana-6069	16	17	method	method	NOUN
cana-6069	16	18	for	for	ADP
cana-6069	16	19	different	different	ADJ
cana-6069	16	20	values	value	NOUN
cana-6069	16	21	of	of	ADP
cana-6069	16	22	𝑁	𝑁	PROPN
cana-6069	16	23	,	,	PUNCT
cana-6069	16	24	achieving	achieve	VERB
cana-6069	16	25	higher	high	ADJ
cana-6069	16	26	accuracy	accuracy	NOUN
cana-6069	16	27	and	and	CCONJ
cana-6069	16	28	lower	low	ADJ
cana-6069	16	29	numerical	numerical	ADJ
cana-6069	16	30	errors	error	NOUN
cana-6069	16	31	across	across	ADP
cana-6069	16	32	most	most	ADJ
cana-6069	16	33	test	test	NOUN
cana-6069	16	34	points	point	NOUN
cana-6069	16	35	.	.	PUNCT
cana-6069	17	1	this	this	DET
cana-6069	17	2	highlights	highlight	VERB
cana-6069	17	3	the	the	DET
cana-6069	17	4	effectiveness	effectiveness	NOUN
cana-6069	17	5	of	of	ADP
cana-6069	17	6	the	the	DET
cana-6069	17	7	fibonacci	fibonacci	NOUN
cana-6069	17	8	approach	approach	NOUN
cana-6069	17	9	in	in	ADP
cana-6069	17	10	improving	improve	VERB
cana-6069	17	11	convergence	convergence	NOUN
cana-6069	17	12	and	and	CCONJ
cana-6069	17	13	solution	solution	NOUN
cana-6069	17	14	quality	quality	NOUN
cana-6069	17	15	compared	compare	VERB
cana-6069	17	16	to	to	ADP
cana-6069	17	17	the	the	DET
cana-6069	17	18	hermite	hermite	ADJ
cana-6069	17	19	–	–	PUNCT
cana-6069	17	20	galerkin	galerkin	ADJ
cana-6069	17	21	method	method	NOUN
cana-6069	17	22	under	under	ADP
cana-6069	17	23	the	the	DET
cana-6069	17	24	same	same	ADJ
cana-6069	17	25	number	number	NOUN
cana-6069	17	26	of	of	ADP
cana-6069	17	27	𝑁.	𝑁.	PROPN
cana-6069	17	28	keywords	keyword	NOUN
cana-6069	17	29	:	:	PUNCT
cana-6069	17	30	three	three	NUM
cana-6069	17	31	-	-	PUNCT
cana-6069	17	32	dimensional	dimensional	ADJ
cana-6069	17	33	nonlinear	nonlinear	ADJ
cana-6069	17	34	fredholm	fredholm	ADJ
cana-6069	17	35	integral	integral	ADJ
cana-6069	17	36	equations	equation	NOUN
cana-6069	17	37	;	;	PUNCT
cana-6069	17	38	fibonacci	fibonacci	NOUN
cana-6069	17	39	polynomials	polynomial	NOUN
cana-6069	17	40	;	;	PUNCT
cana-6069	17	41	hermite	hermite	ADJ
cana-6069	17	42	polynomials	polynomial	NOUN
cana-6069	17	43	;	;	PUNCT
cana-6069	17	44	collocation	collocation	NOUN
cana-6069	17	45	method	method	NOUN
cana-6069	17	46	;	;	PUNCT
cana-6069	17	47	galerkin	galerkin	X
cana-6069	17	48	method	method	NOUN
cana-6069	17	49	1	1	NUM
cana-6069	17	50	.	.	PUNCT
cana-6069	17	51	introduction	introduction	NOUN
cana-6069	17	52	a	a	DET
cana-6069	17	53	general	general	ADJ
cana-6069	17	54	form	form	NOUN
cana-6069	17	55	of	of	ADP
cana-6069	17	56	the	the	DET
cana-6069	17	57	three	three	NUM
cana-6069	17	58	-	-	PUNCT
cana-6069	17	59	dimensional	dimensional	ADJ
cana-6069	17	60	nonlinear	nonlinear	ADJ
cana-6069	17	61	fredholm	fredholm	ADJ
cana-6069	17	62	integral	integral	ADJ
cana-6069	17	63	equation	equation	NOUN
cana-6069	17	64	of	of	ADP
cana-6069	17	65	the	the	DET
cana-6069	17	66	second	second	ADJ
cana-6069	17	67	kind	kind	NOUN
cana-6069	17	68	can	can	AUX
cana-6069	17	69	be	be	AUX
cana-6069	17	70	written	write	VERB
cana-6069	17	71	as	as	ADP
cana-6069	17	72	𝑢(𝑥1	𝑢(𝑥1	ADV
cana-6069	17	73	,	,	PUNCT
cana-6069	17	74	𝑦1	𝑦1	NOUN
cana-6069	17	75	,	,	PUNCT
cana-6069	17	76	𝑧1	𝑧1	NOUN
cana-6069	17	77	)	)	PUNCT
cana-6069	17	78	−	−	PUNCT
cana-6069	18	1	𝜆	𝜆	PRON
cana-6069	18	2	∫	∫	PROPN
cana-6069	18	3	∫	∫	PROPN
cana-6069	18	4	∫	∫	PROPN
cana-6069	18	5	𝑘(𝑥1	𝑘(𝑥1	PROPN
cana-6069	18	6	,	,	PUNCT
cana-6069	18	7	𝑦1	𝑦1	PROPN
cana-6069	18	8	,	,	PUNCT
cana-6069	18	9	𝑧1	𝑧1	NOUN
cana-6069	18	10	,	,	PUNCT
cana-6069	18	11	𝑠1	𝑠1	PROPN
cana-6069	18	12	,	,	PUNCT
cana-6069	18	13	𝑡1	𝑡1	NOUN
cana-6069	18	14	,	,	PUNCT
cana-6069	18	15	𝑟1	𝑟1	NOUN
cana-6069	18	16	)	)	PUNCT
cana-6069	18	17	𝑄(𝑢(𝑠1	𝑄(𝑢(𝑠1	PROPN
cana-6069	18	18	,	,	PUNCT
cana-6069	18	19	𝑡1	𝑡1	NOUN
cana-6069	18	20	,	,	PUNCT
cana-6069	18	21	𝑟1))𝑑𝑠1	𝑟1))𝑑𝑠1	NUM
cana-6069	18	22	𝑑𝑡1	𝑑𝑡1	NOUN
cana-6069	18	23	𝑑𝑟1	𝑑𝑟1	X
cana-6069	18	24	𝑓	𝑓	PROPN
cana-6069	18	25	𝑒	𝑒	PROPN
cana-6069	18	26	𝑑	𝑑	PROPN
cana-6069	18	27	𝑐	𝑐	NOUN
cana-6069	18	28	𝑏	𝑏	PROPN
cana-6069	18	29	𝑎	𝑎	PROPN
cana-6069	18	30	=	=	PUNCT
cana-6069	18	31	𝑔(𝑥1	𝑔(𝑥1	NOUN
cana-6069	18	32	,	,	PUNCT
cana-6069	18	33	𝑦1	𝑦1	NOUN
cana-6069	18	34	,	,	PUNCT
cana-6069	18	35	𝑧1	𝑧1	NOUN
cana-6069	18	36	)	)	PUNCT
cana-6069	18	37	,	,	PUNCT
cana-6069	18	38	∀	∀	X
cana-6069	18	39	(	(	PUNCT
cana-6069	18	40	𝑥1	𝑥1	NOUN
cana-6069	18	41	,	,	PUNCT
cana-6069	18	42	𝑦1	𝑦1	NOUN
cana-6069	18	43	,	,	PUNCT
cana-6069	18	44	𝑧1	𝑧1	PROPN
cana-6069	18	45	)	)	PUNCT
cana-6069	18	46	∈	∈	PROPN
cana-6069	18	47	𝐷	𝐷	PROPN
cana-6069	18	48	(	(	PUNCT
cana-6069	18	49	1	1	NUM
cana-6069	18	50	)	)	PUNCT
cana-6069	18	51	where	where	SCONJ
cana-6069	18	52	𝑢	𝑢	PRON
cana-6069	18	53	is	be	AUX
cana-6069	18	54	the	the	DET
cana-6069	18	55	unknown	unknown	ADJ
cana-6069	18	56	function	function	NOUN
cana-6069	18	57	.	.	PUNCT
cana-6069	19	1	in	in	ADP
cana-6069	19	2	domain	domain	NOUN
cana-6069	19	3	𝐷	𝐷	PROPN
cana-6069	19	4	is	be	AUX
cana-6069	19	5	usually	usually	ADV
cana-6069	19	6	taken	take	VERB
cana-6069	19	7	as	as	ADP
cana-6069	19	8	unit	unit	NOUN
cana-6069	19	9	cube	cube	NOUN
cana-6069	19	10	[	[	X
cana-6069	19	11	0,1]3	0,1]3	NUM
cana-6069	19	12	,	,	PUNCT
cana-6069	19	13	𝑘(𝑥1	𝑘(𝑥1	NOUN
cana-6069	19	14	,	,	PUNCT
cana-6069	19	15	𝑦1	𝑦1	NOUN
cana-6069	19	16	,	,	PUNCT
cana-6069	19	17	𝑧1	𝑧1	NOUN
cana-6069	19	18	,	,	PUNCT
cana-6069	19	19	𝑠1	𝑠1	PROPN
cana-6069	19	20	,	,	PUNCT
cana-6069	19	21	𝑡1	𝑡1	NOUN
cana-6069	19	22	,	,	PUNCT
cana-6069	19	23	𝑟1	𝑟1	NOUN
cana-6069	19	24	)	)	PUNCT
cana-6069	19	25	is	be	AUX
cana-6069	19	26	the	the	DET
cana-6069	19	27	kernel	kernel	PROPN
cana-6069	19	28	function	function	NOUN
cana-6069	19	29	and	and	CCONJ
cana-6069	19	30	g	g	NOUN
cana-6069	19	31	is	be	AUX
cana-6069	19	32	a	a	DET
cana-6069	19	33	given	give	VERB
cana-6069	19	34	source	source	NOUN
cana-6069	19	35	function	function	NOUN
cana-6069	19	36	in	in	ADP
cana-6069	19	37	domain	domain	NOUN
cana-6069	19	38	𝐷	𝐷	PROPN
cana-6069	19	39	×	×	NOUN
cana-6069	19	40	𝐷	𝐷	PROPN
cana-6069	19	41	and	and	CCONJ
cana-6069	19	42	𝐷.	𝐷.	PROPN
cana-6069	19	43	depending	depend	VERB
cana-6069	19	44	on	on	ADP
cana-6069	19	45	the	the	DET
cana-6069	19	46	properties	property	NOUN
cana-6069	19	47	of	of	ADP
cana-6069	19	48	the	the	DET
cana-6069	19	49	kernel	kernel	NOUN
cana-6069	19	50	(	(	PUNCT
cana-6069	19	51	continuous	continuous	ADJ
cana-6069	19	52	,	,	PUNCT
cana-6069	19	53	symmetric	symmetric	ADJ
cana-6069	19	54	,	,	PUNCT
cana-6069	19	55	degenerate	degenerate	ADJ
cana-6069	19	56	,	,	PUNCT
cana-6069	19	57	or	or	CCONJ
cana-6069	19	58	singular	singular	PROPN
cana-6069	19	59	)	)	PUNCT
cana-6069	19	60	,	,	PUNCT
cana-6069	19	61	the	the	DET
cana-6069	19	62	complexity	complexity	NOUN
cana-6069	19	63	of	of	ADP
cana-6069	19	64	both	both	DET
cana-6069	19	65	analysis	analysis	NOUN
cana-6069	19	66	and	and	CCONJ
cana-6069	19	67	computation	computation	NOUN
cana-6069	19	68	varies	vary	VERB
cana-6069	19	69	significantly	significantly	ADV
cana-6069	19	70	[	[	X
cana-6069	19	71	12	12	NUM
cana-6069	19	72	]	]	PUNCT
cana-6069	19	73	.	.	PUNCT
cana-6069	20	1	several	several	ADJ
cana-6069	20	2	numerical	numerical	ADJ
cana-6069	20	3	approaches	approach	NOUN
cana-6069	20	4	have	have	AUX
cana-6069	20	5	been	be	AUX
cana-6069	20	6	developed	develop	VERB
cana-6069	20	7	for	for	ADP
cana-6069	20	8	solving	solve	VERB
cana-6069	20	9	3d	3d	NOUN
cana-6069	20	10	-	-	PUNCT
cana-6069	20	11	nlfies	nlfie	NOUN
cana-6069	20	12	.	.	PUNCT
cana-6069	21	1	basseem	basseem	VERB
cana-6069	22	1	[	[	X
cana-6069	22	2	1	1	NUM
cana-6069	22	3	]	]	PUNCT
cana-6069	22	4	implemented	implement	VERB
cana-6069	22	5	the	the	DET
cana-6069	22	6	degenerate	degenerate	ADJ
cana-6069	22	7	kernel	kernel	NOUN
cana-6069	22	8	technique	technique	NOUN
cana-6069	22	9	to	to	ADP
cana-6069	22	10	approximate	approximate	ADJ
cana-6069	22	11	solutions	solution	NOUN
cana-6069	22	12	of	of	ADP
cana-6069	22	13	three	three	NUM
cana-6069	22	14	-	-	PUNCT
cana-6069	22	15	dimensional	dimensional	ADJ
cana-6069	22	16	nonlinear	nonlinear	ADJ
cana-6069	22	17	integral	integral	ADJ
cana-6069	22	18	equa	equa	NOUN
cana-6069	22	19	tions	tion	NOUN
cana-6069	22	20	.	.	PUNCT
cana-6069	23	1	kazemi	kazemi	PROPN
cana-6069	23	2	et	et	PROPN
cana-6069	23	3	al	al	PROPN
cana-6069	23	4	.	.	PUNCT
cana-6069	24	1	[	[	X
cana-6069	24	2	8	8	NUM
cana-6069	24	3	]	]	PUNCT
cana-6069	24	4	introduced	introduce	VERB
cana-6069	24	5	a	a	DET
cana-6069	24	6	haar	haar	NOUN
cana-6069	24	7	wavelet	wavelet	NOUN
cana-6069	24	8	-	-	PUNCT
cana-6069	24	9	based	base	VERB
cana-6069	24	10	procedure	procedure	NOUN
cana-6069	24	11	for	for	ADP
cana-6069	24	12	solving	solve	VERB
cana-6069	24	13	such	such	ADJ
cana-6069	24	14	equations	equation	NOUN
cana-6069	24	15	,	,	PUNCT
cana-6069	24	16	while	while	SCONJ
cana-6069	24	17	maleknejad	maleknejad	PROPN
cana-6069	24	18	et	et	PROPN
cana-6069	24	19	al	al	PROPN
cana-6069	24	20	.	.	PUNCT
cana-6069	25	1	[	[	X
cana-6069	25	2	10	10	NUM
cana-6069	25	3	]	]	PUNCT
cana-6069	25	4	employed	employ	VERB
cana-6069	25	5	bernstein	bernstein	PROPN
cana-6069	25	6	polynomials	polynomial	NOUN
cana-6069	25	7	for	for	ADP
cana-6069	25	8	the	the	DET
cana-6069	25	9	numerical	numerical	ADJ
cana-6069	25	10	solution	solution	NOUN
cana-6069	25	11	of	of	ADP
cana-6069	25	12	two	two	NUM
cana-6069	25	13	-	-	PUNCT
cana-6069	25	14	dimensional	dimensional	ADJ
cana-6069	25	15	nonlinear	nonlinear	ADJ
cana-6069	25	16	fredholm	fredholm	ADJ
cana-6069	25	17	integral	integral	ADJ
cana-6069	25	18	equations	equation	NOUN
cana-6069	25	19	,	,	PUNCT
cana-6069	25	20	which	which	PRON
cana-6069	25	21	was	be	AUX
cana-6069	25	22	later	later	ADV
cana-6069	25	23	extended	extend	VERB
cana-6069	25	24	to	to	ADP
cana-6069	25	25	higher	high	ADJ
cana-6069	25	26	dimensions	dimension	NOUN
cana-6069	25	27	.	.	PUNCT
cana-6069	26	1	these	these	DET
cana-6069	26	2	contributions	contribution	NOUN
cana-6069	26	3	demonstrate	demonstrate	VERB
cana-6069	26	4	the	the	DET
cana-6069	26	5	continuous	continuous	ADJ
cana-6069	26	6	effort	effort	NOUN
cana-6069	26	7	to	to	PART
cana-6069	26	8	establish	establish	VERB
cana-6069	26	9	reliable	reliable	ADJ
cana-6069	26	10	approximation	approximation	NOUN
cana-6069	26	11	schemes	scheme	NOUN
cana-6069	26	12	for	for	ADP
cana-6069	26	13	threedimensional	threedimensional	ADJ
cana-6069	26	14	nonlinear	nonlinear	ADJ
cana-6069	26	15	integral	integral	ADJ
cana-6069	26	16	equations	equation	NOUN
cana-6069	26	17	.	.	PUNCT
cana-6069	27	1	in	in	ADP
cana-6069	27	2	this	this	DET
cana-6069	27	3	study	study	NOUN
cana-6069	27	4	,	,	PUNCT
cana-6069	27	5	we	we	PRON
cana-6069	27	6	employ	employ	VERB
cana-6069	27	7	and	and	CCONJ
cana-6069	27	8	compare	compare	VERB
cana-6069	27	9	two	two	NUM
cana-6069	27	10	polynomial	polynomial	ADJ
cana-6069	27	11	-	-	PUNCT
cana-6069	27	12	based	base	VERB
cana-6069	27	13	approximation	approximation	NOUN
cana-6069	27	14	techniques	technique	NOUN
cana-6069	27	15	:	:	PUNCT
cana-6069	27	16	the	the	DET
cana-6069	27	17	fibonacci	fibonacci	NOUN
cana-6069	27	18	collocation	collocation	NOUN
cana-6069	27	19	method	method	NOUN
cana-6069	27	20	and	and	CCONJ
cana-6069	27	21	the	the	DET
cana-6069	27	22	hermite	hermite	ADJ
cana-6069	27	23	–	–	PUNCT
cana-6069	27	24	galerkin	galerkin	ADJ
cana-6069	27	25	method	method	NOUN
cana-6069	27	26	.	.	PUNCT
cana-6069	28	1	fibonacci	fibonacci	NOUN
cana-6069	28	2	polynomials	polynomial	NOUN
cana-6069	28	3	,	,	PUNCT
cana-6069	28	4	derived	derive	VERB
cana-6069	28	5	from	from	ADP
cana-6069	28	6	general	general	ADJ
cana-6069	28	7	izations	ization	NOUN
cana-6069	28	8	of	of	ADP
cana-6069	28	9	the	the	DET
cana-6069	28	10	fibonacci	fibonacci	NOUN
cana-6069	28	11	sequence	sequence	NOUN
cana-6069	28	12	,	,	PUNCT
cana-6069	28	13	have	have	AUX
cana-6069	28	14	shown	show	VERB
cana-6069	28	15	promising	promising	ADJ
cana-6069	28	16	results	result	NOUN
cana-6069	28	17	in	in	ADP
cana-6069	28	18	solving	solve	VERB
cana-6069	28	19	various	various	ADJ
cana-6069	28	20	types	type	NOUN
cana-6069	28	21	of	of	ADP
cana-6069	28	22	integral	integral	ADJ
cana-6069	28	23	and	and	CCONJ
cana-6069	28	24	differential	differential	ADJ
cana-6069	28	25	equations	equation	NOUN
cana-6069	28	26	.	.	PUNCT
cana-6069	29	1	hermite	hermite	ADJ
cana-6069	29	2	polynomials	polynomial	NOUN
cana-6069	29	3	,	,	PUNCT
cana-6069	29	4	with	with	ADP
cana-6069	29	5	their	their	PRON
cana-6069	29	6	well	well	ADV
cana-6069	29	7	-	-	PUNCT
cana-6069	29	8	known	know	VERB
cana-6069	29	9	orthogonality	orthogonality	NOUN
cana-6069	29	10	properties	property	NOUN
cana-6069	29	11	,	,	PUNCT
cana-6069	29	12	are	be	AUX
cana-6069	29	13	widely	widely	ADV
cana-6069	29	14	applied	apply	VERB
cana-6069	29	15	in	in	ADP
cana-6069	29	16	galerkin	galerkin	ADJ
cana-6069	29	17	-	-	PUNCT
cana-6069	29	18	type	type	NOUN
cana-6069	29	19	schemes	scheme	NOUN
cana-6069	29	20	for	for	ADP
cana-6069	29	21	integral	integral	ADJ
cana-6069	29	22	equations	equation	NOUN
cana-6069	29	23	.	.	PUNCT
cana-6069	30	1	we	we	PRON
cana-6069	30	2	further	far	ADV
cana-6069	30	3	compare	compare	VERB
cana-6069	30	4	our	our	PRON
cana-6069	30	5	results	result	NOUN
cana-6069	30	6	with	with	ADP
cana-6069	30	7	three	three	NUM
cana-6069	30	8	other	other	ADJ
cana-6069	30	9	numerical	numerical	ADJ
cana-6069	30	10	methods	method	NOUN
cana-6069	30	11	available	available	ADJ
cana-6069	30	12	in	in	ADP
cana-6069	30	13	the	the	DET
cana-6069	30	14	literature	literature	NOUN
cana-6069	30	15	[	[	X
cana-6069	30	16	1,7,8	1,7,8	NUM
cana-6069	30	17	]	]	PUNCT
cana-6069	30	18	.	.	PUNCT
cana-6069	31	1	2	2	X
cana-6069	31	2	.	.	X
cana-6069	31	3	objectives	objective	VERB
cana-6069	31	4	the	the	DET
cana-6069	31	5	remainder	remainder	NOUN
cana-6069	31	6	of	of	ADP
cana-6069	31	7	this	this	DET
cana-6069	31	8	paper	paper	NOUN
cana-6069	31	9	is	be	AUX
cana-6069	31	10	organized	organize	VERB
cana-6069	31	11	as	as	SCONJ
cana-6069	31	12	follows	follow	VERB
cana-6069	31	13	.	.	PUNCT
cana-6069	32	1	section	section	NOUN
cana-6069	32	2	1	1	NUM
cana-6069	32	3	presents	present	VERB
cana-6069	32	4	an	an	DET
cana-6069	32	5	introduction	introduction	NOUN
cana-6069	32	6	and	and	CCONJ
cana-6069	32	7	a	a	DET
cana-6069	32	8	formal	formal	ADJ
cana-6069	32	9	definition	definition	NOUN
cana-6069	32	10	of	of	ADP
cana-6069	32	11	the	the	DET
cana-6069	32	12	3d	3d	NOUN
cana-6069	32	13	-	-	PUNCT
cana-6069	32	14	nlfies	nlfie	NOUN
cana-6069	32	15	.	.	PUNCT
cana-6069	33	1	section	section	NOUN
cana-6069	33	2	2	2	NUM
cana-6069	33	3	outlines	outline	VERB
cana-6069	33	4	the	the	DET
cana-6069	33	5	content	content	NOUN
cana-6069	33	6	and	and	CCONJ
cana-6069	33	7	purpose	purpose	NOUN
cana-6069	33	8	of	of	ADP
cana-6069	33	9	each	each	DET
cana-6069	33	10	section	section	NOUN
cana-6069	33	11	of	of	ADP
cana-6069	33	12	the	the	DET
cana-6069	33	13	study	study	NOUN
cana-6069	33	14	.	.	PUNCT
cana-6069	34	1	in	in	ADP
cana-6069	34	2	section	section	NOUN
cana-6069	34	3	3	3	NUM
cana-6069	34	4	reviews	review	VERB
cana-6069	34	5	the	the	DET
cana-6069	34	6	fibonacci	fibonacci	NOUN
cana-6069	34	7	and	and	CCONJ
cana-6069	34	8	hermite	hermite	ADJ
cana-6069	34	9	polynomials	polynomial	NOUN
cana-6069	34	10	,	,	PUNCT
cana-6069	34	11	discusses	discuss	VERB
cana-6069	34	12	some	some	PRON
cana-6069	34	13	of	of	ADP
cana-6069	34	14	their	their	PRON
cana-6069	34	15	key	key	ADJ
cana-6069	34	16	properties	property	NOUN
cana-6069	34	17	,	,	PUNCT
cana-6069	34	18	and	and	CCONJ
cana-6069	34	19	demonstrates	demonstrate	VERB
cana-6069	34	20	the	the	DET
cana-6069	34	21	application	application	NOUN
cana-6069	34	22	of	of	ADP
cana-6069	34	23	the	the	DET
cana-6069	34	24	fibonacci	fibonacci	NOUN
cana-6069	34	25	collocation	collocation	NOUN
cana-6069	34	26	method	method	NOUN
cana-6069	34	27	and	and	CCONJ
cana-6069	34	28	the	the	DET
cana-6069	34	29	hermite	hermite	ADJ
cana-6069	34	30	–	–	PUNCT
cana-6069	34	31	galerkin	galerkin	ADJ
cana-6069	34	32	method	method	NOUN
cana-6069	34	33	to	to	ADP
cana-6069	34	34	the	the	DET
cana-6069	34	35	3d	3d	NUM
cana-6069	34	36	-	-	PUNCT
cana-6069	34	37	nlfies	nlfie	NOUN
cana-6069	34	38	.	.	PUNCT
cana-6069	35	1	section	section	NOUN
cana-6069	35	2	4	4	NUM
cana-6069	35	3	establishes	establish	VERB
cana-6069	35	4	the	the	DET
cana-6069	35	5	existence	existence	NOUN
cana-6069	35	6	and	and	CCONJ
cana-6069	35	7	uniqueness	uniqueness	NOUN
cana-6069	35	8	of	of	ADP
cana-6069	35	9	the	the	DET
cana-6069	35	10	solution	solution	NOUN
cana-6069	35	11	for	for	ADP
cana-6069	35	12	the	the	DET
cana-6069	35	13	nonlinear	nonlinear	ADJ
cana-6069	35	14	three	three	NUM
cana-6069	35	15	-	-	PUNCT
cana-6069	35	16	dimensional	dimensional	ADJ
cana-6069	35	17	fredholm	fredholm	NOUN
cana-6069	35	18	integral	integral	ADJ
cana-6069	35	19	equation	equation	NOUN
cana-6069	35	20	and	and	CCONJ
cana-6069	35	21	applies	apply	VERB
cana-6069	35	22	the	the	DET
cana-6069	35	23	two	two	NUM
cana-6069	35	24	methods	method	NOUN
cana-6069	35	25	to	to	ADP
cana-6069	35	26	several	several	ADJ
cana-6069	35	27	illustrative	illustrative	ADJ
cana-6069	35	28	examples	example	NOUN
cana-6069	35	29	,	,	PUNCT
cana-6069	35	30	followed	follow	VERB
cana-6069	35	31	by	by	ADP
cana-6069	35	32	a	a	DET
cana-6069	35	33	comparison	comparison	NOUN
cana-6069	35	34	with	with	ADP
cana-6069	35	35	results	result	NOUN
cana-6069	35	36	reported	report	VERB
cana-6069	35	37	in	in	ADP
cana-6069	35	38	previous	previous	ADJ
cana-6069	35	39	studies	study	NOUN
cana-6069	35	40	.	.	PUNCT
cana-6069	36	1	finally	finally	ADV
cana-6069	36	2	,	,	PUNCT
cana-6069	36	3	section	section	NOUN
cana-6069	36	4	5	5	NUM
cana-6069	36	5	provides	provide	VERB
cana-6069	36	6	a	a	DET
cana-6069	36	7	critical	critical	ADJ
cana-6069	36	8	analysis	analysis	NOUN
cana-6069	36	9	of	of	ADP
cana-6069	36	10	the	the	DET
cana-6069	36	11	obtained	obtain	VERB
cana-6069	36	12	results	result	NOUN
cana-6069	36	13	,	,	PUNCT
cana-6069	36	14	highlighting	highlight	VERB
cana-6069	36	15	the	the	DET
cana-6069	36	16	efficiency	efficiency	NOUN
cana-6069	36	17	and	and	CCONJ
cana-6069	36	18	accuracy	accuracy	NOUN
cana-6069	36	19	of	of	ADP
cana-6069	36	20	the	the	DET
cana-6069	36	21	proposed	propose	VERB
cana-6069	36	22	methods	method	NOUN
cana-6069	36	23	in	in	ADP
cana-6069	36	24	comparison	comparison	NOUN
cana-6069	36	25	with	with	ADP
cana-6069	36	26	other	other	ADJ
cana-6069	36	27	techniques	technique	NOUN
cana-6069	36	28	.	.	PUNCT
cana-6069	37	1	3	3	X
cana-6069	37	2	.	.	X
cana-6069	37	3	methods	method	NOUN
cana-6069	37	4	3.1	3.1	NUM
cana-6069	37	5	fibonacci	fibonacci	NOUN
cana-6069	37	6	polynomials	polynomial	NOUN
cana-6069	37	7	.	.	PUNCT
cana-6069	38	1	[	[	X
cana-6069	38	2	2–5	2–5	X
cana-6069	38	3	]	]	X
cana-6069	38	4	leonardo	leonardo	NOUN
cana-6069	38	5	of	of	ADP
cana-6069	38	6	pisa	pisa	PROPN
cana-6069	38	7	,	,	PUNCT
cana-6069	38	8	commonly	commonly	ADV
cana-6069	38	9	known	know	VERB
cana-6069	38	10	as	as	ADP
cana-6069	38	11	fibonacci	fibonacci	NOUN
cana-6069	38	12	,	,	PUNCT
cana-6069	38	13	was	be	AUX
cana-6069	38	14	an	an	DET
cana-6069	38	15	italian	italian	ADJ
cana-6069	38	16	mathematician	mathematician	NOUN
cana-6069	38	17	from	from	ADP
cana-6069	38	18	the	the	DET
cana-6069	38	19	13𝑡ℎ	13𝑡ℎ	ADJ
cana-6069	38	20	century	century	NOUN
cana-6069	38	21	.	.	PUNCT
cana-6069	39	1	in	in	ADP
cana-6069	39	2	1202	1202	NUM
cana-6069	39	3	,	,	PUNCT
cana-6069	39	4	he	he	PRON
cana-6069	39	5	communications	communication	VERB
cana-6069	39	6	on	on	ADP
cana-6069	39	7	applied	apply	VERB
cana-6069	39	8	nonlinear	nonlinear	ADJ
cana-6069	39	9	analysis	analysis	NOUN
cana-6069	39	10	issn	issn	NOUN
cana-6069	39	11	:	:	PUNCT
cana-6069	39	12	1074	1074	NUM
cana-6069	39	13	-	-	PUNCT
cana-6069	39	14	133x	133x	NUM
cana-6069	39	15	vol	vol	VERB
cana-6069	39	16	32	32	NUM
cana-6069	39	17	no.10s	no.10s	PROPN
cana-6069	39	18	y	y	PROPN
cana-6069	39	19	(	(	PUNCT
cana-6069	39	20	2025	2025	NUM
cana-6069	39	21	)	)	PUNCT
cana-6069	39	22	3310	3310	NUM
cana-6069	39	23	posed	pose	VERB
cana-6069	39	24	and	and	CCONJ
cana-6069	39	25	solved	solve	VERB
cana-6069	39	26	a	a	DET
cana-6069	39	27	problem	problem	NOUN
cana-6069	39	28	related	relate	VERB
cana-6069	39	29	to	to	ADP
cana-6069	39	30	the	the	DET
cana-6069	39	31	growth	growth	NOUN
cana-6069	39	32	of	of	ADP
cana-6069	39	33	a	a	DET
cana-6069	39	34	rabbit	rabbit	NOUN
cana-6069	39	35	population	population	NOUN
cana-6069	39	36	under	under	ADP
cana-6069	39	37	idealized	idealized	ADJ
cana-6069	39	38	conditions	condition	NOUN
cana-6069	39	39	.	.	PUNCT
cana-6069	40	1	the	the	DET
cana-6069	40	2	resulting	result	VERB
cana-6069	40	3	sequence	sequence	NOUN
cana-6069	40	4	is	be	AUX
cana-6069	40	5	now	now	ADV
cana-6069	40	6	known	know	VERB
cana-6069	40	7	as	as	ADP
cana-6069	40	8	the	the	DET
cana-6069	40	9	fibonacci	fibonacci	NOUN
cana-6069	40	10	numbers	number	NOUN
cana-6069	40	11	:	:	PUNCT
cana-6069	40	12	0,1,1,2,3,5,8	0,1,1,2,3,5,8	NUM
cana-6069	40	13	,	,	PUNCT
cana-6069	40	14	⋯	⋯	VERB
cana-6069	40	15	this	this	DET
cana-6069	40	16	sequence	sequence	NOUN
cana-6069	40	17	gained	gain	VERB
cana-6069	40	18	widespread	widespread	ADJ
cana-6069	40	19	attention	attention	NOUN
cana-6069	40	20	for	for	ADP
cana-6069	40	21	its	its	PRON
cana-6069	40	22	elegant	elegant	ADJ
cana-6069	40	23	structure	structure	NOUN
cana-6069	40	24	and	and	CCONJ
cana-6069	40	25	natural	natural	ADJ
cana-6069	40	26	occurrence	occurrence	NOUN
cana-6069	40	27	in	in	ADP
cana-6069	40	28	various	various	ADJ
cana-6069	40	29	scientific	scientific	ADJ
cana-6069	40	30	phenomena	phenomenon	NOUN
cana-6069	40	31	.	.	PUNCT
cana-6069	41	1	in	in	ADP
cana-6069	41	2	1883	1883	NUM
cana-6069	41	3	,	,	PUNCT
cana-6069	41	4	belgian	belgian	ADJ
cana-6069	41	5	mathematician	mathematician	ADJ
cana-6069	41	6	eugene	eugene	PROPN
cana-6069	41	7	charles	charles	PROPN
cana-6069	41	8	catalan	catalan	PROPN
cana-6069	41	9	and	and	CCONJ
cana-6069	41	10	german	german	ADJ
cana-6069	41	11	mathematician	mathematician	PROPN
cana-6069	41	12	e.	e.	PROPN
cana-6069	41	13	jacobsthal	jacobsthal	PROPN
cana-6069	41	14	studied	study	VERB
cana-6069	41	15	broader	broad	ADJ
cana-6069	41	16	classes	class	NOUN
cana-6069	41	17	of	of	ADP
cana-6069	41	18	polynomials	polynomial	NOUN
cana-6069	41	19	inspired	inspire	VERB
cana-6069	41	20	by	by	ADP
cana-6069	41	21	fibonacci	fibonacci	NOUN
cana-6069	41	22	numbers	number	NOUN
cana-6069	41	23	.	.	PUNCT
cana-6069	42	1	these	these	PRON
cana-6069	42	2	are	be	AUX
cana-6069	42	3	known	know	VERB
cana-6069	42	4	as	as	ADP
cana-6069	42	5	fibonacci	fibonacci	NOUN
cana-6069	42	6	polynomials	polynomial	NOUN
cana-6069	42	7	,	,	PUNCT
cana-6069	42	8	typically	typically	ADV
cana-6069	42	9	denoted	denote	VERB
cana-6069	42	10	by	by	ADP
cana-6069	42	11	𝐹𝑛(𝑥1).this	𝐹𝑛(𝑥1).this	DET
cana-6069	42	12	class	class	NOUN
cana-6069	42	13	of	of	ADP
cana-6069	42	14	polynomials	polynomial	NOUN
cana-6069	42	15	plays	play	VERB
cana-6069	42	16	a	a	DET
cana-6069	42	17	significant	significant	ADJ
cana-6069	42	18	role	role	NOUN
cana-6069	42	19	in	in	ADP
cana-6069	42	20	both	both	CCONJ
cana-6069	42	21	theoretical	theoretical	ADJ
cana-6069	42	22	and	and	CCONJ
cana-6069	42	23	applied	applied	ADJ
cana-6069	42	24	mathematics	mathematic	NOUN
cana-6069	42	25	.	.	PUNCT
cana-6069	43	1	numerous	numerous	ADJ
cana-6069	43	2	properties	property	NOUN
cana-6069	43	3	and	and	CCONJ
cana-6069	43	4	identities	identity	NOUN
cana-6069	43	5	involving	involve	VERB
cana-6069	43	6	𝐹𝑛(𝑥1	𝐹𝑛(𝑥1	NOUN
cana-6069	43	7	)	)	PUNCT
cana-6069	43	8	  	  	SPACE
cana-6069	43	9	have	have	AUX
cana-6069	43	10	been	be	AUX
cana-6069	43	11	studied	study	VERB
cana-6069	43	12	due	due	ADP
cana-6069	43	13	to	to	ADP
cana-6069	43	14	their	their	PRON
cana-6069	43	15	wide	wide	ADJ
cana-6069	43	16	applicability	applicability	NOUN
cana-6069	43	17	.	.	PUNCT
cana-6069	44	1	fibonacci	fibonacci	NOUN
cana-6069	44	2	polynomials	polynomial	NOUN
cana-6069	44	3	also	also	ADV
cana-6069	44	4	appear	appear	VERB
cana-6069	44	5	in	in	ADP
cana-6069	44	6	the	the	DET
cana-6069	44	7	solution	solution	NOUN
cana-6069	44	8	of	of	ADP
cana-6069	44	9	second	second	ADJ
cana-6069	44	10	-	-	PUNCT
cana-6069	44	11	order	order	NOUN
cana-6069	44	12	ordinary	ordinary	ADJ
cana-6069	44	13	differential	differential	ADJ
cana-6069	44	14	equations	equation	NOUN
cana-6069	44	15	:	:	PUNCT
cana-6069	44	16	𝑑2𝑦1	𝑑2𝑦1	X
cana-6069	44	17	𝑑𝑥1	𝑑𝑥1	ADJ
cana-6069	44	18	2	2	NUM
cana-6069	44	19	−	−	PROPN
cana-6069	44	20	𝑥1	𝑥1	NOUN
cana-6069	44	21	𝑑𝑦1	𝑑𝑦1	PROPN
cana-6069	44	22	𝑑𝑥1	𝑑𝑥1	PROPN
cana-6069	45	1	−	−	PROPN
cana-6069	46	1	𝑦1	𝑦1	NOUN
cana-6069	46	2	=	=	SYM
cana-6069	46	3	0	0	NUM
cana-6069	46	4	,	,	PUNCT
cana-6069	46	5	whose	whose	DET
cana-6069	46	6	solution	solution	NOUN
cana-6069	46	7	for	for	ADP
cana-6069	46	8	𝑛	𝑛	NOUN
cana-6069	46	9	  	  	SPACE
cana-6069	46	10	∈	∈	NOUN
cana-6069	46	11	 	 	SPACE
cana-6069	46	12	𝑁0is	𝑁0is	NOUN
cana-6069	46	13	:	:	PUNCT
cana-6069	46	14	𝐹𝑛(𝑥1	𝐹𝑛(𝑥1	NUM
cana-6069	46	15	)	)	PUNCT
cana-6069	46	16	=	=	SYM
cana-6069	47	1	1	1	NUM
cana-6069	47	2	𝛼	𝛼	NOUN
cana-6069	47	3	−	−	PROPN
cana-6069	47	4	𝛽	𝛽	NOUN
cana-6069	47	5	 	 	SPACE
cana-6069	47	6	(	(	PUNCT
cana-6069	47	7	𝛼𝑛	𝛼𝑛	PROPN
cana-6069	47	8	−	−	PROPN
cana-6069	47	9	𝛽𝑛	𝛽𝑛	PROPN
cana-6069	47	10	)	)	PUNCT
cana-6069	47	11	,	,	PUNCT
cana-6069	47	12	where	where	SCONJ
cana-6069	47	13	𝛼	𝛼	X
cana-6069	47	14	=	=	NOUN
cana-6069	47	15	  	  	SPACE
cana-6069	47	16	𝑥1	𝑥1	PROPN
cana-6069	47	17	+	+	CCONJ
cana-6069	47	18	√𝑥1	√𝑥1	PROPN
cana-6069	47	19	2	2	NUM
cana-6069	47	20	+	+	CCONJ
cana-6069	47	21	4	4	NUM
cana-6069	47	22	2	2	NUM
cana-6069	47	23	,	,	PUNCT
cana-6069	47	24	  	  	SPACE
cana-6069	47	25	𝛽	𝛽	NOUN
cana-6069	47	26	=	=	PUNCT
cana-6069	47	27	  	  	SPACE
cana-6069	47	28	𝑥1	𝑥1	PROPN
cana-6069	47	29	−	−	PROPN
cana-6069	47	30	√𝑥1	√𝑥1	PROPN
cana-6069	47	31	2	2	NUM
cana-6069	47	32	+	+	CCONJ
cana-6069	47	33	4	4	NUM
cana-6069	47	34	2	2	NUM
cana-6069	47	35	  	  	SPACE
cana-6069	47	36	an	an	DET
cana-6069	47	37	explicit	explicit	ADJ
cana-6069	47	38	representation	representation	NOUN
cana-6069	47	39	of	of	ADP
cana-6069	47	40	fibonacci	fibonacci	NOUN
cana-6069	47	41	polynomials	polynomial	NOUN
cana-6069	47	42	is	be	AUX
cana-6069	47	43	given	give	VERB
cana-6069	47	44	as	as	SCONJ
cana-6069	47	45	follows	follow	VERB
cana-6069	47	46	,	,	PUNCT
cana-6069	47	47	:	:	PUNCT
cana-6069	47	48	𝐹𝑛+1(𝑥1	𝐹𝑛+1(𝑥1	X
cana-6069	47	49	)	)	PUNCT
cana-6069	47	50	=	=	SYM
cana-6069	47	51	  	  	SPACE
cana-6069	47	52	∑	∑	PROPN
cana-6069	47	53	(	(	PUNCT
cana-6069	47	54	𝑛	𝑛	PRON
cana-6069	47	55	−	−	PROPN
cana-6069	47	56	𝑘	𝑘	PROPN
cana-6069	47	57	𝑘	𝑘	NOUN
cana-6069	47	58	)	)	PUNCT
cana-6069	47	59	[	[	PUNCT
cana-6069	47	60	𝑛	𝑛	PROPN
cana-6069	47	61	2	2	NUM
cana-6069	47	62	]	]	PUNCT
cana-6069	47	63	𝑘=0	𝑘=0	PROPN
cana-6069	47	64	𝑥1	𝑥1	VERB
cana-6069	47	65	𝑛−2𝑘	𝑛−2𝑘	PRON
cana-6069	47	66	,	,	PUNCT
cana-6069	47	67	𝑛	𝑛	PRON
cana-6069	47	68	≥	≥	NOUN
cana-6069	47	69	0	0	NUM
cana-6069	47	70	.	.	PUNCT
cana-6069	48	1	the	the	DET
cana-6069	48	2	first	first	ADJ
cana-6069	48	3	few	few	ADJ
cana-6069	48	4	terms	term	NOUN
cana-6069	48	5	are	be	AUX
cana-6069	48	6	:	:	PUNCT
cana-6069	48	7	𝐹1(𝑥1	𝐹1(𝑥1	X
cana-6069	48	8	)	)	PUNCT
cana-6069	48	9	=	=	SYM
cana-6069	48	10	1	1	NUM
cana-6069	48	11	,	,	PUNCT
cana-6069	48	12	𝐹2(𝑥1	𝐹2(𝑥1	NUM
cana-6069	48	13	)	)	PUNCT
cana-6069	48	14	=	=	SYM
cana-6069	48	15	 	 	SPACE
cana-6069	48	16	𝑥1	𝑥1	NOUN
cana-6069	48	17	,	,	PUNCT
cana-6069	48	18	𝐹3(𝑥1	𝐹3(𝑥1	NOUN
cana-6069	48	19	)	)	PUNCT
cana-6069	48	20	=	=	SYM
cana-6069	48	21	 	 	SPACE
cana-6069	48	22	𝑥1	𝑥1	NOUN
cana-6069	48	23	2	2	NUM
cana-6069	48	24	+	+	CCONJ
cana-6069	48	25	1	1	NUM
cana-6069	48	26	,	,	PUNCT
cana-6069	48	27	𝐹4(𝑥1	𝐹4(𝑥1	ADJ
cana-6069	48	28	)	)	PUNCT
cana-6069	48	29	=	=	PUNCT
cana-6069	48	30	 	 	SPACE
cana-6069	48	31	𝑥1	𝑥1	NOUN
cana-6069	48	32	3	3	NUM
cana-6069	48	33	+	+	CCONJ
cana-6069	48	34	2𝑥1	2𝑥1	NUM
cana-6069	48	35	,	,	PUNCT
cana-6069	48	36	𝐹5(𝑥1	𝐹5(𝑥1	ADJ
cana-6069	48	37	)	)	PUNCT
cana-6069	48	38	=	=	PUNCT
cana-6069	48	39	 	 	SPACE
cana-6069	48	40	𝑥1	𝑥1	NOUN
cana-6069	48	41	4	4	NUM
cana-6069	48	42	+	+	CCONJ
cana-6069	48	43	3𝑥1	3𝑥1	NUM
cana-6069	48	44	2	2	NUM
cana-6069	48	45	+	+	NUM
cana-6069	48	46	1	1	NUM
cana-6069	48	47	,	,	PUNCT
cana-6069	48	48	in	in	ADP
cana-6069	48	49	what	what	PRON
cana-6069	48	50	follows	follow	VERB
cana-6069	48	51	,	,	PUNCT
cana-6069	48	52	we	we	PRON
cana-6069	48	53	present	present	VERB
cana-6069	48	54	some	some	DET
cana-6069	48	55	fundamental	fundamental	ADJ
cana-6069	48	56	properties	property	NOUN
cana-6069	48	57	of	of	ADP
cana-6069	48	58	fibonacci	fibonacci	NOUN
cana-6069	48	59	polynomials	polynomial	NOUN
cana-6069	48	60	:	:	PUNCT
cana-6069	48	61	properties	property	NOUN
cana-6069	48	62	of	of	ADP
cana-6069	48	63	fibonacci	fibonacci	NOUN
cana-6069	48	64	polynomials	polynomial	NOUN
cana-6069	48	65	.	.	PUNCT
cana-6069	49	1	(	(	PUNCT
cana-6069	49	2	recurrence	recurrence	NOUN
cana-6069	49	3	relation	relation	NOUN
cana-6069	49	4	)	)	PUNCT
cana-6069	49	5	fibonacci	fibonacci	NOUN
cana-6069	49	6	polynomials	polynomial	NOUN
cana-6069	49	7	satisfy	satisfy	VERB
cana-6069	49	8	the	the	DET
cana-6069	49	9	recurrence	recurrence	NOUN
cana-6069	49	10	relation	relation	NOUN
cana-6069	49	11	:	:	PUNCT
cana-6069	49	12	𝐹𝑛+2(𝑥1	𝐹𝑛+2(𝑥1	X
cana-6069	49	13	)	)	PUNCT
cana-6069	49	14	=	=	SYM
cana-6069	49	15	𝑥1𝐹𝑛+1(𝑥1	𝑥1𝐹𝑛+1(𝑥1	NUM
cana-6069	49	16	)	)	PUNCT
cana-6069	49	17	+	+	NUM
cana-6069	49	18	𝐹𝑛(𝑥1	𝐹𝑛(𝑥1	NUM
cana-6069	49	19	)	)	PUNCT
cana-6069	49	20	,	,	PUNCT
cana-6069	49	21	with	with	ADP
cana-6069	49	22	:	:	PUNCT
cana-6069	49	23	𝐹1(𝑥1	𝐹1(𝑥1	X
cana-6069	49	24	)	)	PUNCT
cana-6069	49	25	=	=	SYM
cana-6069	49	26	1	1	NUM
cana-6069	49	27	,	,	PUNCT
cana-6069	49	28	  	  	SPACE
cana-6069	49	29	𝐹2(𝑥1	𝐹2(𝑥1	PRON
cana-6069	49	30	)	)	PUNCT
cana-6069	49	31	=	=	SYM
cana-6069	49	32	 	 	SPACE
cana-6069	49	33	𝑥1	𝑥1	NOUN
cana-6069	49	34	.	.	PROPN
cana-6069	50	1	notably	notably	ADV
cana-6069	50	2	:	:	PUNCT
cana-6069	50	3	if	if	SCONJ
cana-6069	50	4	𝑥1	𝑥1	NOUN
cana-6069	50	5	=	=	NOUN
cana-6069	50	6	1	1	NUM
cana-6069	50	7	then	then	ADV
cana-6069	50	8	𝐹𝑛(1	𝐹𝑛(1	PROPN
cana-6069	50	9	)	)	PUNCT
cana-6069	50	10	=	=	SYM
cana-6069	51	1	𝐹𝑛+1	𝐹𝑛+1	ADJ
cana-6069	51	2	,	,	PUNCT
cana-6069	51	3	if	if	SCONJ
cana-6069	51	4	𝑥1	𝑥1	NOUN
cana-6069	51	5	=	=	SYM
cana-6069	51	6	0	0	PROPN
cana-6069	51	7	then	then	ADV
cana-6069	51	8	𝐹2𝑛(0	𝐹2𝑛(0	NOUN
cana-6069	51	9	)	)	PUNCT
cana-6069	51	10	=	=	SYM
cana-6069	51	11	0	0	NUM
cana-6069	51	12	for	for	ADP
cana-6069	51	13	𝑛	𝑛	NOUN
cana-6069	51	14	=	=	SYM
cana-6069	51	15	1,2	1,2	NUM
cana-6069	51	16	,	,	PUNCT
cana-6069	51	17	…	…	PUNCT
cana-6069	51	18	(	(	PUNCT
cana-6069	51	19	extrema	extrema	X
cana-6069	51	20	)	)	PUNCT
cana-6069	51	21	the	the	DET
cana-6069	51	22	extrema	extrema	NOUN
cana-6069	51	23	of	of	ADP
cana-6069	51	24	𝐹𝑛(𝑥1	𝐹𝑛(𝑥1	NOUN
cana-6069	51	25	)	)	PUNCT
cana-6069	51	26	over	over	ADP
cana-6069	51	27	[	[	X
cana-6069	51	28	𝑎	𝑎	X
cana-6069	51	29	,	,	PUNCT
cana-6069	51	30	𝑏	𝑏	NOUN
cana-6069	51	31	]	]	PUNCT
cana-6069	51	32	are	be	AUX
cana-6069	51	33	:	:	PUNCT
cana-6069	51	34	𝑥1𝑘	𝑥1𝑘	PROPN
cana-6069	51	35	=	=	PUNCT
cana-6069	52	1	𝑎	𝑎	PROPN
cana-6069	52	2	+	+	NOUN
cana-6069	52	3	𝑏	𝑏	NOUN
cana-6069	52	4	−	−	PROPN
cana-6069	52	5	𝑎	𝑎	PROPN
cana-6069	52	6	𝑛	𝑛	NOUN
cana-6069	52	7	+	+	NUM
cana-6069	52	8	1	1	NUM
cana-6069	52	9	𝑘	𝑘	NOUN
cana-6069	52	10	,	,	PUNCT
cana-6069	52	11	  	  	SPACE
cana-6069	52	12	𝑘	𝑘	NOUN
cana-6069	52	13	=	=	SYM
cana-6069	52	14	1,2	1,2	NUM
cana-6069	52	15	,	,	PUNCT
cana-6069	52	16	…	…	PUNCT
cana-6069	52	17	,	,	PUNCT
cana-6069	52	18	𝑛	𝑛	PRON
cana-6069	52	19	+	+	NOUN
cana-6069	52	20	1	1	NUM
cana-6069	52	21	.	.	X
cana-6069	52	22	(	(	PUNCT
cana-6069	52	23	generating	generate	VERB
cana-6069	52	24	function	function	NOUN
cana-6069	52	25	)	)	PUNCT
cana-6069	53	1	the	the	DET
cana-6069	53	2	generating	generate	VERB
cana-6069	53	3	function	function	NOUN
cana-6069	53	4	is	be	AUX
cana-6069	53	5	given	give	VERB
cana-6069	53	6	by	by	ADP
cana-6069	53	7	:	:	PUNCT
cana-6069	53	8	communications	communication	NOUN
cana-6069	53	9	on	on	ADP
cana-6069	53	10	applied	apply	VERB
cana-6069	53	11	nonlinear	nonlinear	ADJ
cana-6069	53	12	analysis	analysis	NOUN
cana-6069	53	13	issn	issn	NOUN
cana-6069	53	14	:	:	PUNCT
cana-6069	53	15	1074	1074	NUM
cana-6069	53	16	-	-	PUNCT
cana-6069	53	17	133x	133x	NUM
cana-6069	53	18	vol	vol	VERB
cana-6069	53	19	32	32	NUM
cana-6069	53	20	no.10s	no.10s	PROPN
cana-6069	53	21	y	y	PROPN
cana-6069	53	22	(	(	PUNCT
cana-6069	53	23	2025	2025	NUM
cana-6069	53	24	)	)	PUNCT
cana-6069	53	25	3311	3311	NUM
cana-6069	53	26	∑	∑	PROPN
cana-6069	53	27	𝐹𝑛(𝑥1)𝑧1	𝐹𝑛(𝑥1)𝑧1	PROPN
cana-6069	53	28	𝑛	𝑛	PRON
cana-6069	53	29	∞	∞	NUM
cana-6069	53	30	𝑛=0	𝑛=0	PROPN
cana-6069	53	31	=	=	SYM
cana-6069	53	32	1	1	NUM
cana-6069	53	33	1	1	NUM
cana-6069	53	34	−	−	NOUN
cana-6069	53	35	𝑥1𝑧1	𝑥1𝑧1	ADJ
cana-6069	53	36	−	−	PROPN
cana-6069	53	37	𝑧1	𝑧1	NOUN
cana-6069	53	38	2	2	NUM
cana-6069	53	39	.	.	PUNCT
cana-6069	54	1	(	(	PUNCT
cana-6069	54	2	evenness	evenness	NOUN
cana-6069	54	3	and	and	CCONJ
cana-6069	54	4	oddness	oddness	ADJ
cana-6069	54	5	)	)	PUNCT
cana-6069	54	6	𝐹1(𝑥1	𝐹1(𝑥1	X
cana-6069	54	7	)	)	PUNCT
cana-6069	54	8	 	 	SPACE
cana-6069	54	9	is	be	AUX
cana-6069	54	10	even	even	ADV
cana-6069	54	11	when	when	SCONJ
cana-6069	54	12	𝑛	𝑛	PROPN
cana-6069	54	13	is	be	AUX
cana-6069	54	14	odd	odd	ADJ
cana-6069	54	15	,	,	PUNCT
cana-6069	54	16	and	and	CCONJ
cana-6069	54	17	odd	odd	ADJ
cana-6069	54	18	when	when	SCONJ
cana-6069	54	19	𝑛	𝑛	PROPN
cana-6069	54	20	is	be	AUX
cana-6069	54	21	even	even	ADV
cana-6069	54	22	.	.	PUNCT
cana-6069	55	1	3.2	3.2	NUM
cana-6069	55	2	hermite	hermite	ADJ
cana-6069	55	3	polynomials	polynomial	VERB
cana-6069	55	4	[	[	X
cana-6069	55	5	11,13,17	11,13,17	NUM
cana-6069	55	6	]	]	PUNCT
cana-6069	55	7	.	.	PUNCT
cana-6069	56	1	hermite	hermite	ADJ
cana-6069	56	2	polynomials	polynomial	NOUN
cana-6069	56	3	,	,	PUNCT
cana-6069	56	4	widely	widely	ADV
cana-6069	56	5	used	use	VERB
cana-6069	56	6	in	in	ADP
cana-6069	56	7	both	both	CCONJ
cana-6069	56	8	pure	pure	ADJ
cana-6069	56	9	and	and	CCONJ
cana-6069	56	10	applied	applied	ADJ
cana-6069	56	11	mathematics	mathematic	NOUN
cana-6069	56	12	,	,	PUNCT
cana-6069	56	13	have	have	VERB
cana-6069	56	14	a	a	DET
cana-6069	56	15	rich	rich	ADJ
cana-6069	56	16	historical	historical	ADJ
cana-6069	56	17	back	back	NOUN
cana-6069	56	18	ground	ground	NOUN
cana-6069	56	19	.	.	PUNCT
cana-6069	57	1	while	while	SCONJ
cana-6069	57	2	a	a	DET
cana-6069	57	3	form	form	NOUN
cana-6069	57	4	of	of	ADP
cana-6069	57	5	these	these	DET
cana-6069	57	6	polynomials	polynomial	NOUN
cana-6069	57	7	was	be	AUX
cana-6069	57	8	introduced	introduce	VERB
cana-6069	57	9	by	by	ADP
cana-6069	57	10	pierre	pierre	PROPN
cana-6069	57	11	-	-	PUNCT
cana-6069	57	12	simon	simon	PROPN
cana-6069	57	13	laplace	laplace	PROPN
cana-6069	57	14	as	as	ADV
cana-6069	57	15	early	early	ADV
cana-6069	57	16	as	as	ADP
cana-6069	57	17	1810	1810	NUM
cana-6069	57	18	,	,	PUNCT
cana-6069	57	19	it	it	PRON
cana-6069	57	20	was	be	AUX
cana-6069	57	21	charles	charles	PROPN
cana-6069	57	22	hermite	hermite	PROPN
cana-6069	57	23	who	who	PRON
cana-6069	57	24	later	later	ADV
cana-6069	57	25	provided	provide	VERB
cana-6069	57	26	a	a	DET
cana-6069	57	27	formal	formal	ADJ
cana-6069	57	28	definition	definition	NOUN
cana-6069	57	29	for	for	ADP
cana-6069	57	30	a	a	DET
cana-6069	57	31	broader	broad	ADJ
cana-6069	57	32	class	class	NOUN
cana-6069	57	33	of	of	ADP
cana-6069	57	34	what	what	PRON
cana-6069	57	35	are	be	AUX
cana-6069	57	36	now	now	ADV
cana-6069	57	37	known	know	VERB
cana-6069	57	38	as	as	ADP
cana-6069	57	39	generalized	generalize	VERB
cana-6069	57	40	hermite	hermite	ADJ
cana-6069	57	41	polynomials	polynomial	NOUN
cana-6069	57	42	—	—	PUNCT
cana-6069	57	43	an	an	DET
cana-6069	57	44	extension	extension	NOUN
cana-6069	57	45	that	that	PRON
cana-6069	57	46	remains	remain	VERB
cana-6069	57	47	relatively	relatively	ADV
cana-6069	57	48	underexplored	underexplored	ADJ
cana-6069	57	49	compared	compare	VERB
cana-6069	57	50	to	to	ADP
cana-6069	57	51	the	the	DET
cana-6069	57	52	classical	classical	ADJ
cana-6069	57	53	case	case	NOUN
cana-6069	57	54	.	.	PUNCT
cana-6069	58	1	hermite	hermite	ADJ
cana-6069	58	2	polynomials	polynomial	NOUN
cana-6069	58	3	have	have	AUX
cana-6069	58	4	gained	gain	VERB
cana-6069	58	5	significant	significant	ADJ
cana-6069	58	6	importance	importance	NOUN
cana-6069	58	7	in	in	ADP
cana-6069	58	8	recent	recent	ADJ
cana-6069	58	9	decades	decade	NOUN
cana-6069	58	10	due	due	ADP
cana-6069	58	11	to	to	ADP
cana-6069	58	12	their	their	PRON
cana-6069	58	13	applications	application	NOUN
cana-6069	58	14	in	in	ADP
cana-6069	58	15	quantum	quantum	ADJ
cana-6069	58	16	mechanics	mechanic	NOUN
cana-6069	58	17	,	,	PUNCT
cana-6069	58	18	engineering	engineering	NOUN
cana-6069	58	19	,	,	PUNCT
cana-6069	58	20	physics	physics	NOUN
cana-6069	58	21	,	,	PUNCT
cana-6069	58	22	and	and	CCONJ
cana-6069	58	23	various	various	ADJ
cana-6069	58	24	other	other	ADJ
cana-6069	58	25	scientific	scientific	ADJ
cana-6069	58	26	disciplines	discipline	NOUN
cana-6069	58	27	.	.	PUNCT
cana-6069	59	1	their	their	PRON
cana-6069	59	2	mathematical	mathematical	ADJ
cana-6069	59	3	utility	utility	NOUN
cana-6069	59	4	and	and	CCONJ
cana-6069	59	5	orthogonality	orthogonality	NOUN
cana-6069	59	6	properties	property	NOUN
cana-6069	59	7	make	make	VERB
cana-6069	59	8	them	they	PRON
cana-6069	59	9	essential	essential	ADJ
cana-6069	59	10	tools	tool	NOUN
cana-6069	59	11	in	in	ADP
cana-6069	59	12	the	the	DET
cana-6069	59	13	analysis	analysis	NOUN
cana-6069	59	14	of	of	ADP
cana-6069	59	15	complex	complex	ADJ
cana-6069	59	16	systems	system	NOUN
cana-6069	59	17	.	.	PUNCT
cana-6069	60	1	the	the	DET
cana-6069	60	2	classical	classical	ADJ
cana-6069	60	3	hermite	hermite	ADJ
cana-6069	60	4	polynomials	polynomial	NOUN
cana-6069	60	5	arise	arise	VERB
cana-6069	60	6	as	as	ADP
cana-6069	60	7	solutions	solution	NOUN
cana-6069	60	8	to	to	ADP
cana-6069	60	9	the	the	DET
cana-6069	60	10	second	second	ADJ
cana-6069	60	11	-	-	PUNCT
cana-6069	60	12	order	order	NOUN
cana-6069	60	13	linear	linear	NOUN
cana-6069	60	14	differential	differential	NOUN
cana-6069	60	15	equation	equation	NOUN
cana-6069	60	16	defined	define	VERB
cana-6069	60	17	on	on	ADP
cana-6069	60	18	the	the	DET
cana-6069	60	19	interval	interval	NOUN
cana-6069	60	20	(	(	PUNCT
cana-6069	60	21	−∞	−∞	NOUN
cana-6069	60	22	,	,	PUNCT
cana-6069	60	23	 	 	SPACE
cana-6069	60	24	∞	∞	NUM
cana-6069	60	25	)	)	PUNCT
cana-6069	60	26	,	,	PUNCT
cana-6069	60	27	given	give	VERB
cana-6069	60	28	by	by	ADP
cana-6069	60	29	:	:	PUNCT
cana-6069	60	30	𝑑2𝑦1	𝑑2𝑦1	NUM
cana-6069	60	31	𝑑𝑥1	𝑑𝑥1	ADJ
cana-6069	60	32	2	2	NUM
cana-6069	60	33	−	−	PROPN
cana-6069	60	34	2𝑥1	2𝑥1	NUM
cana-6069	60	35	𝑑𝑦1	𝑑𝑦1	NOUN
cana-6069	60	36	𝑑𝑥1	𝑑𝑥1	PROPN
cana-6069	61	1	+	+	CCONJ
cana-6069	61	2	2𝑛𝑦1	2𝑛𝑦1	NUM
cana-6069	61	3	=	=	SYM
cana-6069	61	4	0	0	NUM
cana-6069	61	5	,	,	PUNCT
cana-6069	61	6	where	where	SCONJ
cana-6069	61	7	𝑛	𝑛	PRON
cana-6069	61	8	≥	≥	NOUN
cana-6069	61	9	0	0	NUM
cana-6069	61	10	.	.	PUNCT
cana-6069	62	1	the	the	DET
cana-6069	62	2	solution	solution	NOUN
cana-6069	62	3	corresponding	correspond	VERB
cana-6069	62	4	to	to	ADP
cana-6069	62	5	a	a	DET
cana-6069	62	6	given	give	VERB
cana-6069	62	7	𝑛	𝑛	PROPN
cana-6069	62	8	is	be	AUX
cana-6069	62	9	denoted	denote	VERB
cana-6069	62	10	by	by	ADP
cana-6069	62	11	𝐻𝑛(𝑥1	𝐻𝑛(𝑥1	ADJ
cana-6069	62	12	)	)	PUNCT
cana-6069	62	13	and	and	CCONJ
cana-6069	62	14	is	be	AUX
cana-6069	62	15	referred	refer	VERB
cana-6069	62	16	to	to	ADP
cana-6069	62	17	as	as	ADP
cana-6069	62	18	hermite	hermite	ADJ
cana-6069	62	19	polynomial	polynomial	NOUN
cana-6069	62	20	of	of	ADP
cana-6069	62	21	degree	degree	NOUN
cana-6069	62	22	𝑛.	𝑛.	NOUN
cana-6069	62	23	as	as	ADP
cana-6069	62	24	with	with	ADP
cana-6069	62	25	other	other	ADJ
cana-6069	62	26	families	family	NOUN
cana-6069	62	27	of	of	ADP
cana-6069	62	28	classical	classical	ADJ
cana-6069	62	29	orthogonal	orthogonal	ADJ
cana-6069	62	30	polynomials	polynomial	NOUN
cana-6069	62	31	,	,	PUNCT
cana-6069	62	32	hermite	hermite	ADJ
cana-6069	62	33	polynomials	polynomial	NOUN
cana-6069	62	34	can	can	AUX
cana-6069	62	35	be	be	AUX
cana-6069	62	36	introduced	introduce	VERB
cana-6069	62	37	and	and	CCONJ
cana-6069	62	38	derived	derive	VERB
cana-6069	62	39	through	through	ADP
cana-6069	62	40	various	various	ADJ
cana-6069	62	41	equivalent	equivalent	ADJ
cana-6069	62	42	formulations	formulation	NOUN
cana-6069	62	43	,	,	PUNCT
cana-6069	62	44	including	include	VERB
cana-6069	62	45	differential	differential	ADJ
cana-6069	62	46	equations	equation	NOUN
cana-6069	62	47	,	,	PUNCT
cana-6069	62	48	generating	generating	NOUN
cana-6069	62	49	functions	function	NOUN
cana-6069	62	50	,	,	PUNCT
cana-6069	62	51	and	and	CCONJ
cana-6069	62	52	recurrence	recurrence	NOUN
cana-6069	62	53	relations.in	relations.in	X
cana-6069	63	1	what	what	PRON
cana-6069	63	2	follows	follow	VERB
cana-6069	63	3	,	,	PUNCT
cana-6069	63	4	we	we	PRON
cana-6069	63	5	present	present	VERB
cana-6069	63	6	some	some	DET
cana-6069	63	7	fundamental	fundamental	ADJ
cana-6069	63	8	properties	property	NOUN
cana-6069	63	9	of	of	ADP
cana-6069	63	10	hermite	hermite	ADJ
cana-6069	63	11	polynomials	polynomial	NOUN
cana-6069	63	12	.	.	PUNCT
cana-6069	64	1	properties	property	NOUN
cana-6069	64	2	of	of	ADP
cana-6069	64	3	the	the	DET
cana-6069	64	4	hermite	hermite	ADJ
cana-6069	64	5	polynomials	polynomial	NOUN
cana-6069	64	6	.	.	PUNCT
cana-6069	65	1	(	(	PUNCT
cana-6069	65	2	rodrigues	rodrigues	PROPN
cana-6069	65	3	’	'	PUNCT
cana-6069	65	4	formula	formula	NOUN
cana-6069	65	5	)	)	PUNCT
cana-6069	66	1	hermite	hermite	PROPN
cana-6069	66	2	polynomials	polynomial	VERB
cana-6069	66	3	𝐻𝑛(𝑥1	𝐻𝑛(𝑥1	ADV
cana-6069	66	4	)	)	PUNCT
cana-6069	66	5	can	can	AUX
cana-6069	66	6	be	be	AUX
cana-6069	66	7	expressed	express	VERB
cana-6069	66	8	using	use	VERB
cana-6069	66	9	rodrigues	rodrigue	NOUN
cana-6069	66	10	’	'	PUNCT
cana-6069	66	11	formula	formula	NOUN
cana-6069	66	12	,	,	PUNCT
cana-6069	66	13	which	which	PRON
cana-6069	66	14	involves	involve	VERB
cana-6069	66	15	repeated	repeat	VERB
cana-6069	66	16	differentiation	differentiation	NOUN
cana-6069	66	17	of	of	ADP
cana-6069	66	18	the	the	DET
cana-6069	66	19	gaussian	gaussian	ADJ
cana-6069	66	20	function	function	NOUN
cana-6069	66	21	.	.	PUNCT
cana-6069	67	1	the	the	DET
cana-6069	67	2	formula	formula	NOUN
cana-6069	67	3	is	be	AUX
cana-6069	67	4	given	give	VERB
cana-6069	67	5	by	by	ADP
cana-6069	67	6	:	:	PUNCT
cana-6069	67	7	𝐻𝑛(𝑥1	𝐻𝑛(𝑥1	X
cana-6069	67	8	)	)	PUNCT
cana-6069	67	9	=	=	SYM
cana-6069	67	10	(	(	PUNCT
cana-6069	67	11	−1)𝑛𝑒𝑥1	−1)𝑛𝑒𝑥1	SYM
cana-6069	67	12	2	2	NUM
cana-6069	67	13	𝑑𝑛	𝑑𝑛	NOUN
cana-6069	67	14	𝑑𝑥1	𝑑𝑥1	ADJ
cana-6069	67	15	𝑛	𝑛	VERB
cana-6069	67	16	(	(	PUNCT
cana-6069	67	17	𝑒−𝑥1	𝑒−𝑥1	NOUN
cana-6069	67	18	2	2	NUM
cana-6069	67	19	)	)	PUNCT
cana-6069	67	20	,	,	PUNCT
cana-6069	67	21	for	for	ADP
cana-6069	67	22	𝑛	𝑛	NOUN
cana-6069	67	23	=	=	SYM
cana-6069	67	24	0,1,2,3	0,1,2,3	NUM
cana-6069	67	25	,	,	PUNCT
cana-6069	67	26	…	…	PUNCT
cana-6069	67	27	.	.	PUNCT
cana-6069	67	28	  	  	SPACE
cana-6069	68	1	the	the	DET
cana-6069	68	2	first	first	ADJ
cana-6069	68	3	few	few	ADJ
cana-6069	68	4	hermite	hermite	ADJ
cana-6069	68	5	polynomials	polynomial	NOUN
cana-6069	68	6	in	in	ADP
cana-6069	68	7	terms	term	NOUN
cana-6069	68	8	of	of	ADP
cana-6069	68	9	𝑥1are	𝑥1are	NUM
cana-6069	68	10	:	:	PUNCT
cana-6069	68	11	𝐻0(𝑥1	𝐻0(𝑥1	ADJ
cana-6069	68	12	)	)	PUNCT
cana-6069	68	13	=	=	SYM
cana-6069	68	14	1	1	NUM
cana-6069	68	15	,	,	PUNCT
cana-6069	68	16	𝐻1(𝑥1	𝐻1(𝑥1	PROPN
cana-6069	68	17	)	)	PUNCT
cana-6069	68	18	=	=	PUNCT
cana-6069	68	19	 	 	SPACE
cana-6069	68	20	2𝑥1	2𝑥1	NUM
cana-6069	68	21	,	,	PUNCT
cana-6069	68	22	𝐻2(𝑥1	𝐻2(𝑥1	NOUN
cana-6069	68	23	)	)	PUNCT
cana-6069	68	24	=	=	SYM
cana-6069	68	25	 	 	SPACE
cana-6069	68	26	4𝑥1	4𝑥1	NUM
cana-6069	68	27	2	2	NUM
cana-6069	68	28	−	−	ADP
cana-6069	68	29	2	2	NUM
cana-6069	68	30	,	,	PUNCT
cana-6069	68	31	𝐻3(𝑥1	𝐻3(𝑥1	X
cana-6069	68	32	)	)	PUNCT
cana-6069	68	33	=	=	PUNCT
cana-6069	68	34	 	 	SPACE
cana-6069	68	35	8𝑥1	8𝑥1	NUM
cana-6069	68	36	3	3	NUM
cana-6069	68	37	−	−	PROPN
cana-6069	68	38	12𝑥1	12𝑥1	NUM
cana-6069	68	39	,	,	PUNCT
cana-6069	68	40	𝐻4(𝑥1	𝐻4(𝑥1	PROPN
cana-6069	68	41	)	)	PUNCT
cana-6069	68	42	=	=	PUNCT
cana-6069	68	43	 	 	SPACE
cana-6069	69	1	16𝑥1	16𝑥1	NUM
cana-6069	69	2	4	4	NUM
cana-6069	69	3	−	−	NOUN
cana-6069	69	4	48𝑥1	48𝑥1	NUM
cana-6069	69	5	2	2	NUM
cana-6069	69	6	+	+	NUM
cana-6069	69	7	12	12	NUM
cana-6069	69	8	,	,	PUNCT
cana-6069	69	9	𝐻5(𝑥1	𝐻5(𝑥1	NOUN
cana-6069	69	10	)	)	PUNCT
cana-6069	69	11	=	=	SYM
cana-6069	69	12	 	 	SPACE
cana-6069	70	1	32𝑥1	32𝑥1	NUM
cana-6069	70	2	5	5	NUM
cana-6069	70	3	−	−	PROPN
cana-6069	70	4	160𝑥1	160𝑥1	NUM
cana-6069	70	5	3	3	NUM
cana-6069	70	6	+	+	SYM
cana-6069	70	7	120	120	NUM
cana-6069	70	8	,	,	PUNCT
cana-6069	70	9	𝐻6(𝑥1	𝐻6(𝑥1	ADJ
cana-6069	70	10	)	)	PUNCT
cana-6069	70	11	=	=	PUNCT
cana-6069	70	12	 	 	SPACE
cana-6069	71	1	64𝑥1	64𝑥1	NUM
cana-6069	71	2	6	6	NUM
cana-6069	71	3	−	−	NOUN
cana-6069	71	4	480𝑥1	480𝑥1	NUM
cana-6069	71	5	4	4	NUM
cana-6069	71	6	+	+	NUM
cana-6069	71	7	720𝑥1	720𝑥1	NUM
cana-6069	71	8	2	2	NUM
cana-6069	71	9	−	−	PROPN
cana-6069	71	10	120	120	NUM
cana-6069	71	11	,	,	PUNCT
cana-6069	71	12	(	(	PUNCT
cana-6069	71	13	recurrence	recurrence	NOUN
cana-6069	71	14	relation	relation	NOUN
cana-6069	71	15	)	)	PUNCT
cana-6069	71	16	the	the	DET
cana-6069	71	17	fundamental	fundamental	ADJ
cana-6069	71	18	recurrence	recurrence	NOUN
cana-6069	71	19	relation	relation	NOUN
cana-6069	71	20	of	of	ADP
cana-6069	71	21	𝐻𝑛(𝑥1	𝐻𝑛(𝑥1	NOUN
cana-6069	71	22	)	)	PUNCT
cana-6069	71	23	is	be	AUX
cana-6069	71	24	:	:	PUNCT
cana-6069	71	25	𝐻𝑛+2(𝑥1	𝐻𝑛+2(𝑥1	X
cana-6069	71	26	)	)	PUNCT
cana-6069	71	27	=	=	SYM
cana-6069	71	28	2𝑥1𝐻𝑛+1(𝑥1	2𝑥1𝐻𝑛+1(𝑥1	X
cana-6069	71	29	)	)	PUNCT
cana-6069	71	30	−	−	PROPN
cana-6069	71	31	2𝑛𝐻𝑛(𝑥1	2𝑛𝐻𝑛(𝑥1	NUM
cana-6069	71	32	)	)	PUNCT
cana-6069	71	33	,	,	PUNCT
cana-6069	71	34	for	for	ADP
cana-6069	71	35	𝑛	𝑛	NOUN
cana-6069	71	36	=	=	SYM
cana-6069	71	37	0,1,2,3	0,1,2,3	NUM
cana-6069	71	38	,	,	PUNCT
cana-6069	71	39	…	…	PUNCT
cana-6069	71	40	 	 	SPACE
cana-6069	71	41	,	,	PUNCT
cana-6069	71	42	which	which	PRON
cana-6069	71	43	can	can	AUX
cana-6069	71	44	generate	generate	VERB
cana-6069	71	45	𝐻𝑛(𝑥1	𝐻𝑛(𝑥1	ADJ
cana-6069	71	46	)	)	PUNCT
cana-6069	71	47	efficiently	efficiently	ADV
cana-6069	71	48	and	and	CCONJ
cana-6069	71	49	easily	easily	ADV
cana-6069	71	50	with	with	ADP
cana-6069	71	51	the	the	DET
cana-6069	71	52	initial	initial	ADJ
cana-6069	71	53	terms	term	NOUN
cana-6069	71	54	:	:	PUNCT
cana-6069	71	55	𝐻0(𝑥1	𝐻0(𝑥1	ADJ
cana-6069	71	56	)	)	PUNCT
cana-6069	71	57	=	=	SYM
cana-6069	71	58	1	1	NUM
cana-6069	71	59	,	,	PUNCT
cana-6069	71	60	𝐻1(𝑥1	𝐻1(𝑥1	PROPN
cana-6069	71	61	)	)	PUNCT
cana-6069	71	62	=	=	PUNCT
cana-6069	71	63	 	 	SPACE
cana-6069	71	64	2𝑥1	2𝑥1	NUM
cana-6069	71	65	.	.	PUNCT
cana-6069	72	1	(	(	PUNCT
cana-6069	72	2	orthogonality	orthogonality	NOUN
cana-6069	72	3	)	)	PUNCT
cana-6069	72	4	hermite	hermite	PROPN
cana-6069	72	5	polynomials	polynomial	VERB
cana-6069	72	6	𝐻𝑛(𝑥1	𝐻𝑛(𝑥1	ADJ
cana-6069	72	7	)	)	PUNCT
cana-6069	72	8	form	form	NOUN
cana-6069	72	9	an	an	DET
cana-6069	72	10	orthogonal	orthogonal	ADJ
cana-6069	72	11	set	set	NOUN
cana-6069	72	12	on	on	ADP
cana-6069	72	13	the	the	DET
cana-6069	72	14	interval	interval	NOUN
cana-6069	72	15	[	[	X
cana-6069	72	16	−∞	−∞	NOUN
cana-6069	72	17	,	,	PUNCT
cana-6069	72	18	∞	∞	PROPN
cana-6069	72	19	]	]	PUNCT
cana-6069	72	20	with	with	ADP
cana-6069	72	21	respect	respect	NOUN
cana-6069	72	22	to	to	ADP
cana-6069	72	23	the	the	DET
cana-6069	72	24	weight	weight	NOUN
cana-6069	72	25	communications	communication	NOUN
cana-6069	72	26	on	on	ADP
cana-6069	72	27	applied	apply	VERB
cana-6069	72	28	nonlinear	nonlinear	ADJ
cana-6069	72	29	analysis	analysis	NOUN
cana-6069	72	30	issn	issn	NOUN
cana-6069	72	31	:	:	PUNCT
cana-6069	72	32	1074	1074	NUM
cana-6069	72	33	-	-	PUNCT
cana-6069	72	34	133x	133x	NUM
cana-6069	72	35	vol	vol	VERB
cana-6069	72	36	32	32	NUM
cana-6069	72	37	no.10s	no.10s	PROPN
cana-6069	72	38	y	y	PROPN
cana-6069	72	39	(	(	PUNCT
cana-6069	72	40	2025	2025	NUM
cana-6069	72	41	)	)	PUNCT
cana-6069	72	42	3312	3312	NUM
cana-6069	72	43	function	function	NOUN
cana-6069	72	44	𝑒−𝑥1	𝑒−𝑥1	NOUN
cana-6069	72	45	2	2	NUM
cana-6069	72	46	.	.	PUNCT
cana-6069	73	1	this	this	PRON
cana-6069	73	2	means	mean	VERB
cana-6069	73	3	:	:	PUNCT
cana-6069	73	4	⟨𝐻𝑚(𝑥1	⟨𝐻𝑚(𝑥1	X
cana-6069	73	5	)	)	PUNCT
cana-6069	73	6	,	,	PUNCT
cana-6069	73	7	𝐻𝑛(𝑥1)⟩	𝐻𝑛(𝑥1)⟩	NOUN
cana-6069	73	8	=	=	SYM
cana-6069	73	9	∫	∫	PROPN
cana-6069	73	10	𝑒−𝑥1	𝑒−𝑥1	NOUN
cana-6069	73	11	2	2	NUM
cana-6069	73	12	𝐻𝑚(𝑥1)𝐻𝑛(𝑥1)𝑑𝑥1	𝐻𝑚(𝑥1)𝐻𝑛(𝑥1)𝑑𝑥1	X
cana-6069	73	13	∞	∞	PROPN
cana-6069	73	14	−∞	−∞	X
cana-6069	73	15	=	=	X
cana-6069	73	16	{	{	PUNCT
cana-6069	73	17	0	0	NUM
cana-6069	73	18	,	,	PUNCT
cana-6069	73	19	𝑚	𝑚	ADP
cana-6069	73	20	≠	≠	NOUN
cana-6069	73	21	𝑛	𝑛	DET
cana-6069	73	22	2𝑛𝜋	2𝑛𝜋	NOUN
cana-6069	73	23	1	1	NUM
cana-6069	73	24	2𝑛	2𝑛	NUM
cana-6069	73	25	!	!	PUNCT
cana-6069	73	26	,	,	PUNCT
cana-6069	73	27	𝑚	𝑚	X
cana-6069	73	28	=	=	SYM
cana-6069	73	29	𝑛	𝑛	PROPN
cana-6069	73	30	,	,	PUNCT
cana-6069	73	31	(	(	PUNCT
cana-6069	73	32	generating	generate	VERB
cana-6069	73	33	function	function	NOUN
cana-6069	73	34	)	)	PUNCT
cana-6069	73	35	the	the	DET
cana-6069	73	36	generating	generate	VERB
cana-6069	73	37	function	function	NOUN
cana-6069	73	38	for	for	ADP
cana-6069	73	39	𝐻𝑛(𝑥1	𝐻𝑛(𝑥1	NOUN
cana-6069	73	40	)	)	PUNCT
cana-6069	73	41	is	be	AUX
cana-6069	73	42	𝑒−𝑧1	𝑒−𝑧1	PRON
cana-6069	73	43	2	2	NUM
cana-6069	73	44	+	+	PROPN
cana-6069	73	45	2𝑧1𝑥1	2𝑧1𝑥1	NOUN
cana-6069	73	46	=	=	SYM
cana-6069	73	47	∑	∑	PUNCT
cana-6069	73	48	𝐻𝑛(𝑥1	𝐻𝑛(𝑥1	ADJ
cana-6069	73	49	)	)	PUNCT
cana-6069	73	50	𝑧1	𝑧1	NOUN
cana-6069	73	51	𝑛	𝑛	DET
cana-6069	73	52	𝑛	𝑛	NOUN
cana-6069	73	53	!	!	PUNCT
cana-6069	73	54	∞	∞	NUM
cana-6069	73	55	𝑛=0	𝑛=0	PROPN
cana-6069	73	56	.	.	PUNCT
cana-6069	74	1	oddness	oddness	ADJ
cana-6069	74	2	and	and	CCONJ
cana-6069	74	3	evenness	evenness	NOUN
cana-6069	74	4	it	it	PRON
cana-6069	74	5	is	be	AUX
cana-6069	74	6	clear	clear	ADJ
cana-6069	74	7	that	that	SCONJ
cana-6069	74	8	the	the	DET
cana-6069	74	9	polynomial	polynomial	ADJ
cana-6069	74	10	𝐻𝑛(𝑥1	𝐻𝑛(𝑥1	NOUN
cana-6069	74	11	)	)	PUNCT
cana-6069	74	12	is	be	AUX
cana-6069	74	13	even	even	ADV
cana-6069	74	14	or	or	CCONJ
cana-6069	74	15	odd	odd	ADJ
cana-6069	74	16	in	in	ADP
cana-6069	74	17	𝑥1	𝑥1	NOUN
cana-6069	74	18	,	,	PUNCT
cana-6069	74	19	according	accord	VERB
cana-6069	74	20	to	to	ADP
cana-6069	74	21	whether	whether	SCONJ
cana-6069	74	22	𝑛	𝑛	PRON
cana-6069	74	23	is	be	AUX
cana-6069	74	24	even	even	ADV
cana-6069	74	25	or	or	CCONJ
cana-6069	74	26	odd	odd	ADJ
cana-6069	74	27	.	.	PUNCT
cana-6069	74	28	3.3	3.3	NUM
cana-6069	74	29	fibonacci	fibonacci	NOUN
cana-6069	74	30	collocation	collocation	NOUN
cana-6069	74	31	method	method	NOUN
cana-6069	74	32	:	:	PUNCT
cana-6069	74	33	consider	consider	VERB
cana-6069	74	34	the	the	PRON
cana-6069	74	35	which	which	PRON
cana-6069	74	36	is	be	AUX
cana-6069	74	37	represented	represent	VERB
cana-6069	74	38	the	the	DET
cana-6069	74	39	approximate	approximate	ADJ
cana-6069	74	40	solution	solution	NOUN
cana-6069	74	41	:	:	PUNCT
cana-6069	75	1	𝑢𝑁(𝑥1	𝑢𝑁(𝑥1	X
cana-6069	75	2	,	,	PUNCT
cana-6069	75	3	𝑦1	𝑦1	NOUN
cana-6069	75	4	,	,	PUNCT
cana-6069	75	5	𝑧1	𝑧1	PROPN
cana-6069	75	6	)	)	PUNCT
cana-6069	76	1	≈	≈	PROPN
cana-6069	76	2	∑	∑	PROPN
cana-6069	76	3	∑	∑	PROPN
cana-6069	76	4	∑	∑	PROPN
cana-6069	76	5	𝑐𝑖𝑗𝑘𝐹𝑖(𝑥1)𝐹𝑗(𝑦1)𝐹𝑘(𝑧1	𝑐𝑖𝑗𝑘𝐹𝑖(𝑥1)𝐹𝑗(𝑦1)𝐹𝑘(𝑧1	PROPN
cana-6069	76	6	)	)	PUNCT
cana-6069	76	7	𝑁+1	𝑁+1	PUNCT
cana-6069	77	1	𝑘=1	𝑘=1	NOUN
cana-6069	77	2	𝑁+1	𝑁+1	NUM
cana-6069	78	1	𝑗=1	𝑗=1	PROPN
cana-6069	78	2	𝑁+1	𝑁+1	NUM
cana-6069	78	3	𝑖=1	𝑖=1	PUNCT
cana-6069	78	4	.	.	PUNCT
cana-6069	79	1	(	(	PUNCT
cana-6069	79	2	2	2	X
cana-6069	79	3	)	)	PUNCT
cana-6069	79	4	where	where	SCONJ
cana-6069	79	5	𝐹𝑖	𝐹𝑖	PROPN
cana-6069	79	6	(	(	PUNCT
cana-6069	79	7	𝑥1	𝑥1	NOUN
cana-6069	79	8	)	)	PUNCT
cana-6069	79	9	,	,	PUNCT
cana-6069	79	10	𝐹𝑗(𝑦1	𝐹𝑗(𝑦1	PROPN
cana-6069	79	11	)	)	PUNCT
cana-6069	79	12	and	and	CCONJ
cana-6069	79	13	𝐹𝑘(𝑧1	𝐹𝑘(𝑧1	NOUN
cana-6069	79	14	)	)	PUNCT
cana-6069	79	15	are	be	AUX
cana-6069	79	16	fibonacci	fibonacci	NOUN
cana-6069	79	17	polynomial	polynomial	ADJ
cana-6069	79	18	of	of	ADP
cana-6069	79	19	degree	degree	NOUN
cana-6069	79	20	𝑖	𝑖	NOUN
cana-6069	79	21	,	,	PUNCT
cana-6069	79	22	𝑗	𝑗	PROPN
cana-6069	79	23	,	,	PUNCT
cana-6069	79	24	𝑘	𝑘	NOUN
cana-6069	79	25	,	,	PUNCT
cana-6069	79	26	𝑐𝑖𝑗𝑘	𝑐𝑖𝑗𝑘	VERB
cana-6069	79	27	the	the	DET
cana-6069	79	28	coefficients	coefficient	NOUN
cana-6069	79	29	are	be	AUX
cana-6069	79	30	determined	determine	VERB
cana-6069	79	31	choose	choose	VERB
cana-6069	79	32	the	the	DET
cana-6069	79	33	collocation	collocation	NOUN
cana-6069	79	34	points	point	NOUN
cana-6069	79	35	(	(	PUNCT
cana-6069	79	36	𝑥𝑛	𝑥𝑛	PROPN
cana-6069	79	37	,	,	PUNCT
cana-6069	79	38	𝑦𝑚	𝑦𝑚	PROPN
cana-6069	79	39	,	,	PUNCT
cana-6069	79	40	𝑧𝑙	𝑧𝑙	PROPN
cana-6069	79	41	)	)	PUNCT
cana-6069	79	42	by	by	ADP
cana-6069	79	43	dividing	divide	VERB
cana-6069	79	44	the	the	DET
cana-6069	79	45	intervals	interval	NOUN
cana-6069	79	46	[	[	X
cana-6069	79	47	𝑎	𝑎	X
cana-6069	79	48	,	,	PUNCT
cana-6069	79	49	𝑏	𝑏	NOUN
cana-6069	79	50	]	]	PUNCT
cana-6069	79	51	,	,	PUNCT
cana-6069	80	1	[	[	X
cana-6069	80	2	𝑐	𝑐	X
cana-6069	80	3	,	,	PUNCT
cana-6069	80	4	𝑑	𝑑	NOUN
cana-6069	80	5	]	]	PUNCT
cana-6069	80	6	and	and	CCONJ
cana-6069	80	7	[	[	X
cana-6069	80	8	𝑒	𝑒	X
cana-6069	80	9	,	,	PUNCT
cana-6069	80	10	𝑓	𝑓	X
cana-6069	80	11	]	]	PUNCT
cana-6069	80	12	into	into	ADP
cana-6069	80	13	𝑁	𝑁	PROPN
cana-6069	80	14	+	+	NOUN
cana-6069	80	15	1	1	NUM
cana-6069	80	16	,	,	PUNCT
cana-6069	80	17	respectively	respectively	ADV
cana-6069	80	18	:	:	PUNCT
cana-6069	80	19	𝑥1𝑛	𝑥1𝑛	PUNCT
cana-6069	80	20	=	=	SYM
cana-6069	80	21	𝑎	𝑎	X
cana-6069	80	22	+	+	X
cana-6069	80	23	(	(	PUNCT
cana-6069	80	24	𝑏	𝑏	PROPN
cana-6069	80	25	−	−	PROPN
cana-6069	80	26	𝑎	𝑎	NOUN
cana-6069	80	27	)	)	PUNCT
cana-6069	80	28	𝑁	𝑁	PROPN
cana-6069	80	29	+	+	CCONJ
cana-6069	80	30	1	1	NUM
cana-6069	80	31	𝑛	𝑛	NOUN
cana-6069	80	32	,	,	PUNCT
cana-6069	80	33	𝑦1𝑚	𝑦1𝑚	SCONJ
cana-6069	80	34	=	=	SYM
cana-6069	80	35	𝑐	𝑐	PROPN
cana-6069	80	36	+	+	PUNCT
cana-6069	80	37	(	(	PUNCT
cana-6069	80	38	𝑑	𝑑	PROPN
cana-6069	80	39	−	−	PROPN
cana-6069	80	40	𝑐	𝑐	NOUN
cana-6069	80	41	)	)	PUNCT
cana-6069	80	42	𝑁	𝑁	NOUN
cana-6069	80	43	+	+	NOUN
cana-6069	80	44	1	1	NUM
cana-6069	80	45	𝑚	𝑚	NOUN
cana-6069	80	46	,	,	PUNCT
cana-6069	80	47	𝑧1𝑙	𝑧1𝑙	VERB
cana-6069	80	48	=	=	SYM
cana-6069	80	49	𝑒	𝑒	PROPN
cana-6069	81	1	+	+	PUNCT
cana-6069	81	2	(	(	PUNCT
cana-6069	81	3	𝑓	𝑓	DET
cana-6069	81	4	−	−	NOUN
cana-6069	81	5	𝑒	𝑒	NOUN
cana-6069	81	6	)	)	PUNCT
cana-6069	81	7	𝑁	𝑁	NOUN
cana-6069	81	8	+	+	CCONJ
cana-6069	81	9	1	1	NUM
cana-6069	81	10	𝑙	𝑙	NUM
cana-6069	81	11	,	,	PUNCT
cana-6069	81	12	𝑛	𝑛	PROPN
cana-6069	81	13	,	,	PUNCT
cana-6069	81	14	𝑚	𝑚	PROPN
cana-6069	81	15	,	,	PUNCT
cana-6069	81	16	𝑙	𝑙	X
cana-6069	81	17	=	=	SYM
cana-6069	81	18	1,2	1,2	NUM
cana-6069	81	19	,	,	PUNCT
cana-6069	81	20	.	.	PUNCT
cana-6069	81	21	.	.	PUNCT
cana-6069	82	1	.	.	PUNCT
cana-6069	83	1	,	,	PUNCT
cana-6069	84	1	𝑁	𝑁	PROPN
cana-6069	84	2	+	+	NOUN
cana-6069	84	3	1	1	NUM
cana-6069	84	4	.	.	PUNCT
cana-6069	84	5	(	(	PUNCT
cana-6069	84	6	3	3	X
cana-6069	84	7	)	)	PUNCT
cana-6069	84	8	first	first	ADV
cana-6069	84	9	substituting	substitute	VERB
cana-6069	84	10	eq.(2	eq.(2	NOUN
cana-6069	84	11	)	)	PUNCT
cana-6069	84	12	into	into	ADP
cana-6069	84	13	three	three	NUM
cana-6069	84	14	-	-	PUNCT
cana-6069	84	15	dimensional	dimensional	ADJ
cana-6069	84	16	nonlinear	nonlinear	ADJ
cana-6069	84	17	fredholm	fredholm	ADJ
cana-6069	84	18	integral	integral	ADJ
cana-6069	84	19	equations	equation	NOUN
cana-6069	84	20	(	(	PUNCT
cana-6069	84	21	1	1	X
cana-6069	84	22	)	)	PUNCT
cana-6069	84	23	at	at	ADP
cana-6069	84	24	use	use	VERB
cana-6069	84	25	the	the	DET
cana-6069	84	26	collocation	collocation	NOUN
cana-6069	84	27	points	point	NOUN
cana-6069	84	28	(	(	PUNCT
cana-6069	84	29	𝑥𝑛	𝑥𝑛	NOUN
cana-6069	84	30	,	,	PUNCT
cana-6069	84	31	𝑦𝑚	𝑦𝑚	INTJ
cana-6069	84	32	,	,	PUNCT
cana-6069	84	33	𝑧𝑙	𝑧𝑙	PROPN
cana-6069	84	34	):	):	PUNCT
cana-6069	84	35	∑	∑	ADV
cana-6069	84	36	∑	∑	PROPN
cana-6069	84	37	∑	∑	PROPN
cana-6069	84	38	𝑐𝑖𝑗𝑘𝐹𝑖(𝑥1)𝐹𝑗(𝑦1)𝐹𝑘(𝑧1	𝑐𝑖𝑗𝑘𝐹𝑖(𝑥1)𝐹𝑗(𝑦1)𝐹𝑘(𝑧1	PROPN
cana-6069	84	39	)	)	PUNCT
cana-6069	84	40	𝑁+1	𝑁+1	PUNCT
cana-6069	85	1	𝑘=1	𝑘=1	NOUN
cana-6069	85	2	𝑁+1	𝑁+1	NUM
cana-6069	86	1	𝑗=1	𝑗=1	PROPN
cana-6069	86	2	𝑁+1	𝑁+1	PUNCT
cana-6069	86	3	𝑖=1	𝑖=1	PUNCT
cana-6069	87	1	−	−	PROPN
cana-6069	88	1	𝜆	𝜆	DET
cana-6069	88	2	∫	∫	PROPN
cana-6069	88	3	∫	∫	PROPN
cana-6069	88	4	∫	∫	PROPN
cana-6069	88	5	𝑘(𝑥1	𝑘(𝑥1	PROPN
cana-6069	88	6	,	,	PUNCT
cana-6069	88	7	𝑦1	𝑦1	PROPN
cana-6069	88	8	,	,	PUNCT
cana-6069	88	9	𝑧1	𝑧1	NOUN
cana-6069	88	10	,	,	PUNCT
cana-6069	88	11	𝑠1	𝑠1	PROPN
cana-6069	88	12	,	,	PUNCT
cana-6069	88	13	𝑡1	𝑡1	NOUN
cana-6069	88	14	,	,	PUNCT
cana-6069	88	15	𝑟1	𝑟1	NOUN
cana-6069	88	16	)	)	PUNCT
cana-6069	88	17	𝑄	𝑄	PROPN
cana-6069	89	1	𝑓	𝑓	ADV
cana-6069	89	2	𝑒	𝑒	PROPN
cana-6069	89	3	𝑑	𝑑	PROPN
cana-6069	89	4	𝑐	𝑐	NOUN
cana-6069	89	5	𝑏	𝑏	PROPN
cana-6069	89	6	𝑎	𝑎	PROPN
cana-6069	89	7	(	(	PUNCT
cana-6069	89	8	∑	∑	PROPN
cana-6069	89	9	∑	∑	PROPN
cana-6069	89	10	∑	∑	PROPN
cana-6069	89	11	𝑐𝑖𝑗𝑘𝐹𝑖(𝑥1)𝐹𝑗(𝑦1)𝐹𝑘(𝑧1	𝑐𝑖𝑗𝑘𝐹𝑖(𝑥1)𝐹𝑗(𝑦1)𝐹𝑘(𝑧1	PROPN
cana-6069	89	12	)	)	PUNCT
cana-6069	89	13	𝑁+1	𝑁+1	PUNCT
cana-6069	90	1	𝑘=1	𝑘=1	NOUN
cana-6069	90	2	𝑁+1	𝑁+1	NUM
cana-6069	91	1	𝑗=1	𝑗=1	PROPN
cana-6069	91	2	𝑁+1	𝑁+1	NUM
cana-6069	91	3	𝑖=1	𝑖=1	PUNCT
cana-6069	91	4	.	.	PUNCT
cana-6069	91	5	)	)	PUNCT
cana-6069	92	1	𝑑𝑠1	𝑑𝑠1	PROPN
cana-6069	92	2	𝑑𝑡1	𝑑𝑡1	PROPN
cana-6069	92	3	𝑑𝑟1	𝑑𝑟1	X
cana-6069	92	4	=	=	SYM
cana-6069	92	5	𝑔(𝑥1	𝑔(𝑥1	X
cana-6069	92	6	,	,	PUNCT
cana-6069	92	7	𝑦1	𝑦1	NOUN
cana-6069	92	8	,	,	PUNCT
cana-6069	92	9	𝑧1	𝑧1	NOUN
cana-6069	92	10	)	)	PUNCT
cana-6069	92	11	.	.	PUNCT
cana-6069	93	1	(	(	PUNCT
cana-6069	93	2	4	4	X
cana-6069	93	3	)	)	PUNCT
cana-6069	93	4	then	then	ADV
cana-6069	93	5	the	the	DET
cana-6069	93	6	coefficients	coefficient	NOUN
cana-6069	93	7	𝑐𝑖𝑗𝑘	𝑐𝑖𝑗𝑘	PROPN
cana-6069	93	8	are	be	AUX
cana-6069	93	9	determined	determine	VERB
cana-6069	93	10	by	by	ADP
cana-6069	93	11	solving	solve	VERB
cana-6069	93	12	the	the	DET
cana-6069	93	13	nonlinear	nonlinear	ADJ
cana-6069	93	14	system	system	NOUN
cana-6069	93	15	of	of	ADP
cana-6069	93	16	matrix	matrix	NOUN
cana-6069	93	17	iteratively	iteratively	ADV
cana-6069	93	18	:	:	PUNCT
cana-6069	93	19	𝐴	𝐴	PROPN
cana-6069	93	20	⋅	⋅	PROPN
cana-6069	93	21	𝑐	𝑐	PROPN
cana-6069	93	22	=	=	SYM
cana-6069	93	23	𝐵	𝐵	PROPN
cana-6069	93	24	where	where	SCONJ
cana-6069	93	25	𝐴	𝐴	PROPN
cana-6069	93	26	is	be	AUX
cana-6069	93	27	a	a	DET
cana-6069	93	28	matrix	matrix	NOUN
cana-6069	93	29	of	of	ADP
cana-6069	93	30	size	size	NOUN
cana-6069	93	31	(	(	PUNCT
cana-6069	93	32	𝑁	𝑁	PROPN
cana-6069	93	33	+	+	PROPN
cana-6069	93	34	1)3	1)3	PROPN
cana-6069	93	35	×	×	NOUN
cana-6069	93	36	(	(	PUNCT
cana-6069	93	37	𝑁	𝑁	PROPN
cana-6069	93	38	+	+	PROPN
cana-6069	93	39	1)3	1)3	PROPN
cana-6069	93	40	,	,	PUNCT
cana-6069	93	41	b	b	PROPN
cana-6069	93	42	is	be	AUX
cana-6069	93	43	a	a	DET
cana-6069	93	44	matrix	matrix	NOUN
cana-6069	93	45	of	of	ADP
cana-6069	93	46	size	size	NOUN
cana-6069	93	47	(	(	PUNCT
cana-6069	93	48	𝑁	𝑁	PROPN
cana-6069	93	49	+	+	PROPN
cana-6069	93	50	1)3	1)3	PROPN
cana-6069	93	51	×	×	NOUN
cana-6069	93	52	1	1	NUM
cana-6069	93	53	and	and	CCONJ
cana-6069	93	54	𝑐	𝑐	PROPN
cana-6069	93	55	is	be	AUX
cana-6069	93	56	a	a	DET
cana-6069	93	57	matrix	matrix	NOUN
cana-6069	93	58	of	of	ADP
cana-6069	93	59	size	size	NOUN
cana-6069	93	60	(	(	PUNCT
cana-6069	93	61	𝑁	𝑁	PROPN
cana-6069	93	62	+	+	PROPN
cana-6069	93	63	1)3	1)3	PROPN
cana-6069	93	64	×	×	NOUN
cana-6069	93	65	1	1	NUM
cana-6069	93	66	defined	define	VERB
cana-6069	93	67	by	by	ADP
cana-6069	93	68	[	[	X
cana-6069	93	69	𝑐111	𝑐111	PROPN
cana-6069	93	70	𝑐112	𝑐112	PROPN
cana-6069	93	71	…	…	PUNCT
cana-6069	93	72	𝑐(𝑁+1)3	𝑐(𝑁+1)3	NOUN
cana-6069	93	73	]	]	PUNCT
cana-6069	93	74	𝑇	𝑇	PROPN
cana-6069	93	75	.	.	PUNCT
cana-6069	94	1	thus	thus	ADV
cana-6069	94	2	we	we	PRON
cana-6069	94	3	have	have	AUX
cana-6069	94	4	obtained	obtain	VERB
cana-6069	94	5	a	a	DET
cana-6069	94	6	nonlinear	nonlinear	ADJ
cana-6069	94	7	system	system	NOUN
cana-6069	94	8	of	of	ADP
cana-6069	94	9	equations	equation	NOUN
cana-6069	94	10	which	which	PRON
cana-6069	94	11	contains	contain	VERB
cana-6069	94	12	(	(	PUNCT
cana-6069	94	13	𝑁	𝑁	PROPN
cana-6069	94	14	+	+	CCONJ
cana-6069	94	15	1)2	1)2	NUM
cana-6069	94	16	unknown	unknown	ADJ
cana-6069	94	17	coefficients	coefficient	NOUN
cana-6069	94	18	.	.	PUNCT
cana-6069	95	1	solving	solve	VERB
cana-6069	95	2	this	this	DET
cana-6069	95	3	system	system	NOUN
cana-6069	95	4	to	to	PART
cana-6069	95	5	obtain	obtain	VERB
cana-6069	95	6	the	the	DET
cana-6069	95	7	values	value	NOUN
cana-6069	95	8	of	of	ADP
cana-6069	95	9	these	these	DET
cana-6069	95	10	coefficients	coefficient	NOUN
cana-6069	95	11	,	,	PUNCT
cana-6069	95	12	we	we	PRON
cana-6069	95	13	arrive	arrive	VERB
cana-6069	95	14	at	at	ADP
cana-6069	95	15	the	the	DET
cana-6069	95	16	approximate	approximate	ADJ
cana-6069	95	17	solution	solution	NOUN
cana-6069	95	18	𝑢𝑁(𝑥1	𝑢𝑁(𝑥1	PROPN
cana-6069	95	19	,	,	PUNCT
cana-6069	95	20	𝑦1	𝑦1	PROPN
cana-6069	95	21	,	,	PUNCT
cana-6069	95	22	𝑧1	𝑧1	NOUN
cana-6069	95	23	)	)	PUNCT
cana-6069	95	24	.	.	PUNCT
cana-6069	96	1	3.4	3.4	NUM
cana-6069	96	2	hermite	hermite	ADJ
cana-6069	96	3	–	–	PUNCT
cana-6069	96	4	galerkin	galerkin	ADJ
cana-6069	96	5	method	method	NOUN
cana-6069	96	6	.	.	PUNCT
cana-6069	96	7	.consider	.consider	PUNCT
cana-6069	97	1	the	the	DET
cana-6069	97	2	which	which	PRON
cana-6069	97	3	is	be	AUX
cana-6069	97	4	represented	represent	VERB
cana-6069	97	5	the	the	DET
cana-6069	97	6	approximate	approximate	ADJ
cana-6069	97	7	solution	solution	NOUN
cana-6069	97	8	:	:	PUNCT
cana-6069	97	9	𝑢𝑁(𝑥1	𝑢𝑁(𝑥1	ADJ
cana-6069	97	10	,	,	PUNCT
cana-6069	97	11	𝑦1	𝑦1	NOUN
cana-6069	97	12	,	,	PUNCT
cana-6069	97	13	𝑧1	𝑧1	NOUN
cana-6069	97	14	)	)	PUNCT
cana-6069	98	1	≈	≈	PROPN
cana-6069	98	2	∑	∑	PROPN
cana-6069	98	3	∑	∑	PROPN
cana-6069	98	4	∑	∑	INTJ
cana-6069	98	5	𝑐𝑖𝑗𝑘𝐻𝑖(𝑥1)𝐻𝑗(𝑦1)𝐻𝑘(𝑧1	𝑐𝑖𝑗𝑘𝐻𝑖(𝑥1)𝐻𝑗(𝑦1)𝐻𝑘(𝑧1	PROPN
cana-6069	98	6	)	)	PUNCT
cana-6069	98	7	𝑁+1	𝑁+1	PUNCT
cana-6069	99	1	𝑘=1	𝑘=1	NOUN
cana-6069	99	2	𝑁+1	𝑁+1	NUM
cana-6069	100	1	𝑗=1	𝑗=1	PROPN
cana-6069	100	2	𝑁+1	𝑁+1	NUM
cana-6069	100	3	𝑖=1	𝑖=1	PUNCT
cana-6069	100	4	.	.	PUNCT
cana-6069	101	1	(	(	PUNCT
cana-6069	101	2	5	5	NUM
cana-6069	101	3	)	)	PUNCT
cana-6069	101	4	where	where	SCONJ
cana-6069	101	5	𝐻𝑖	𝐻𝑖	PROPN
cana-6069	101	6	(	(	PUNCT
cana-6069	101	7	𝑥1	𝑥1	NOUN
cana-6069	101	8	)	)	PUNCT
cana-6069	101	9	,	,	PUNCT
cana-6069	101	10	𝐻𝑗(𝑦1	𝐻𝑗(𝑦1	PROPN
cana-6069	101	11	)	)	PUNCT
cana-6069	101	12	and	and	CCONJ
cana-6069	101	13	𝐻𝑘(𝑧1	𝐻𝑘(𝑧1	NOUN
cana-6069	101	14	)	)	PUNCT
cana-6069	101	15	are	be	AUX
cana-6069	101	16	hermite	hermite	ADJ
cana-6069	101	17	polynomial	polynomial	ADJ
cana-6069	101	18	,	,	PUNCT
cana-6069	101	19	𝑐𝑖𝑗𝑘	𝑐𝑖𝑗𝑘	ADP
cana-6069	101	20	the	the	DET
cana-6069	101	21	coefficients	coefficient	NOUN
cana-6069	101	22	are	be	AUX
cana-6069	101	23	determined	determine	VERB
cana-6069	101	24	.	.	PUNCT
cana-6069	102	1	first	first	ADJ
cana-6069	102	2	substituting	substitute	VERB
cana-6069	102	3	eq.(5	eq.(5	NOUN
cana-6069	102	4	)	)	PUNCT
cana-6069	102	5	into	into	ADP
cana-6069	102	6	three	three	NUM
cana-6069	102	7	-	-	PUNCT
cana-6069	102	8	dimensional	dimensional	ADJ
cana-6069	102	9	nonlinear	nonlinear	ADJ
cana-6069	102	10	fredholm	fredholm	ADJ
cana-6069	102	11	integral	integral	ADJ
cana-6069	102	12	equations	equation	NOUN
cana-6069	102	13	eq.(1	eq.(1	ADJ
cana-6069	102	14	)	)	PUNCT
cana-6069	102	15	and	and	CCONJ
cana-6069	102	16	applying	apply	VERB
cana-6069	102	17	the	the	DET
cana-6069	102	18	galerkin	galerkin	ADJ
cana-6069	102	19	condition	condition	NOUN
cana-6069	102	20	leads	lead	VERB
cana-6069	102	21	to	to	ADP
cana-6069	102	22	the	the	DET
cana-6069	102	23	following	follow	VERB
cana-6069	102	24	equation	equation	NOUN
cana-6069	102	25	:	:	PUNCT
cana-6069	103	1	∫	∫	PROPN
cana-6069	103	2	∫	∫	PROPN
cana-6069	103	3	∫	∫	PROPN
cana-6069	103	4	∑	∑	PROPN
cana-6069	103	5	∑	∑	PROPN
cana-6069	103	6	∑	∑	PUNCT
cana-6069	103	7	𝑐𝑖𝑗𝑘𝐻𝑖(𝑥1)𝐻𝑗(𝑦1)𝐻𝑘(𝑧1)𝐻𝑞(𝑥1)𝐻𝑝(𝑦1)𝐻𝑣(𝑧1	𝑐𝑖𝑗𝑘𝐻𝑖(𝑥1)𝐻𝑗(𝑦1)𝐻𝑘(𝑧1)𝐻𝑞(𝑥1)𝐻𝑝(𝑦1)𝐻𝑣(𝑧1	VERB
cana-6069	103	8	)	)	PUNCT
cana-6069	103	9	𝑑𝑥1𝑑𝑦1𝑑𝑧1	𝑑𝑥1𝑑𝑦1𝑑𝑧1	NOUN
cana-6069	103	10	𝑁+1	𝑁+1	PUNCT
cana-6069	104	1	𝑘=1	𝑘=1	NOUN
cana-6069	104	2	𝑁+1	𝑁+1	NUM
cana-6069	105	1	𝑗=1	𝑗=1	PROPN
cana-6069	105	2	𝑁+1	𝑁+1	PUNCT
cana-6069	105	3	𝑖=1	𝑖=1	PUNCT
cana-6069	106	1	𝑓	𝑓	PRON
cana-6069	106	2	𝑒	𝑒	PROPN
cana-6069	106	3	𝑑	𝑑	PROPN
cana-6069	106	4	𝑐	𝑐	NOUN
cana-6069	106	5	𝑏	𝑏	PROPN
cana-6069	106	6	𝑎	𝑎	PRON
cana-6069	106	7	−	−	PROPN
cana-6069	106	8	∫	∫	PROPN
cana-6069	106	9	∫	∫	PROPN
cana-6069	106	10	∫	∫	PROPN
cana-6069	106	11	(	(	PUNCT
cana-6069	106	12	𝑊)𝐻𝑞(𝑥1)𝐻𝑝(𝑦1)𝐻𝑣(𝑧1	𝑊)𝐻𝑞(𝑥1)𝐻𝑝(𝑦1)𝐻𝑣(𝑧1	PROPN
cana-6069	106	13	)	)	PUNCT
cana-6069	106	14	𝑑𝑥1	𝑑𝑥1	ADJ
cana-6069	107	1	𝑑𝑦1	𝑑𝑦1	PROPN
cana-6069	107	2	𝑑𝑧1	𝑑𝑧1	NOUN
cana-6069	108	1	𝑓	𝑓	PRON
cana-6069	108	2	𝑒	𝑒	PROPN
cana-6069	108	3	𝑑	𝑑	PROPN
cana-6069	108	4	𝑐	𝑐	NOUN
cana-6069	108	5	𝑏	𝑏	PROPN
cana-6069	108	6	𝑎	𝑎	PROPN
cana-6069	108	7	=	=	PUNCT
cana-6069	108	8	∫	∫	PROPN
cana-6069	108	9	∫	∫	PROPN
cana-6069	108	10	∫	∫	PROPN
cana-6069	108	11	𝑔(𝑥1	𝑔(𝑥1	PROPN
cana-6069	108	12	,	,	PUNCT
cana-6069	108	13	𝑦1	𝑦1	PROPN
cana-6069	108	14	,	,	PUNCT
cana-6069	108	15	𝑧1)𝐻𝑞(𝑥1)𝐻𝑝(𝑦1)𝐻𝑣(𝑧1	𝑧1)𝐻𝑞(𝑥1)𝐻𝑝(𝑦1)𝐻𝑣(𝑧1	PROPN
cana-6069	108	16	)	)	PUNCT
cana-6069	108	17	𝑑𝑥1	𝑑𝑥1	ADJ
cana-6069	108	18	𝑑𝑦1	𝑑𝑦1	PROPN
cana-6069	108	19	𝑑𝑧1	𝑑𝑧1	NOUN
cana-6069	108	20	𝑓	𝑓	PRON
cana-6069	108	21	𝑒	𝑒	PROPN
cana-6069	108	22	𝑑	𝑑	PROPN
cana-6069	108	23	𝑐	𝑐	PROPN
cana-6069	108	24	𝑏	𝑏	PROPN
cana-6069	108	25	𝑎	𝑎	PROPN
cana-6069	108	26	(	(	PUNCT
cana-6069	108	27	6	6	NUM
cana-6069	108	28	)	)	PUNCT
cana-6069	108	29	communications	communication	NOUN
cana-6069	108	30	on	on	ADP
cana-6069	108	31	applied	apply	VERB
cana-6069	108	32	nonlinear	nonlinear	ADJ
cana-6069	108	33	analysis	analysis	NOUN
cana-6069	108	34	issn	issn	NOUN
cana-6069	108	35	:	:	PUNCT
cana-6069	108	36	1074	1074	NUM
cana-6069	108	37	-	-	PUNCT
cana-6069	108	38	133x	133x	NUM
cana-6069	108	39	vol	vol	VERB
cana-6069	108	40	32	32	NUM
cana-6069	108	41	no.10s	no.10s	PROPN
cana-6069	108	42	y	y	PROPN
cana-6069	108	43	(	(	PUNCT
cana-6069	108	44	2025	2025	NUM
cana-6069	108	45	)	)	PUNCT
cana-6069	108	46	3313	3313	NUM
cana-6069	108	47	where	where	SCONJ
cana-6069	108	48	𝑊	𝑊	PROPN
cana-6069	108	49	=	=	SYM
cana-6069	108	50	𝜆	𝜆	PRON
cana-6069	108	51	∫	∫	PROPN
cana-6069	108	52	∫	∫	PROPN
cana-6069	108	53	∫	∫	PROPN
cana-6069	108	54	𝑘(𝑥1	𝑘(𝑥1	PROPN
cana-6069	108	55	,	,	PUNCT
cana-6069	108	56	𝑦1	𝑦1	NOUN
cana-6069	108	57	,	,	PUNCT
cana-6069	108	58	𝑧1	𝑧1	NOUN
cana-6069	108	59	,	,	PUNCT
cana-6069	108	60	𝑠1	𝑠1	PROPN
cana-6069	108	61	,	,	PUNCT
cana-6069	108	62	𝑡1	𝑡1	NOUN
cana-6069	108	63	,	,	PUNCT
cana-6069	108	64	𝑟1	𝑟1	NOUN
cana-6069	108	65	)	)	PUNCT
cana-6069	108	66	𝑓	𝑓	PRON
cana-6069	108	67	𝑒	𝑒	PROPN
cana-6069	108	68	𝑑	𝑑	PROPN
cana-6069	108	69	𝑐	𝑐	PROPN
cana-6069	108	70	𝑏	𝑏	PROPN
cana-6069	108	71	𝑎	𝑎	PRON
cana-6069	108	72	𝑄	𝑄	PROPN
cana-6069	108	73	(	(	PUNCT
cana-6069	108	74	∑	∑	PROPN
cana-6069	108	75	∑	∑	PROPN
cana-6069	108	76	∑	∑	PROPN
cana-6069	108	77	𝑐𝑖𝑗𝑘𝐻𝑖(𝑥1)𝐻𝑗(𝑦1)𝐻𝑘(𝑧1	𝑐𝑖𝑗𝑘𝐻𝑖(𝑥1)𝐻𝑗(𝑦1)𝐻𝑘(𝑧1	PROPN
cana-6069	108	78	)	)	PUNCT
cana-6069	108	79	.	.	PUNCT
cana-6069	108	80	𝑁+1	𝑁+1	PUNCT
cana-6069	109	1	𝑘=1	𝑘=1	NOUN
cana-6069	109	2	𝑁+1	𝑁+1	NUM
cana-6069	110	1	𝑗=1	𝑗=1	PROPN
cana-6069	110	2	𝑁+1	𝑁+1	NUM
cana-6069	110	3	𝑖=1	𝑖=1	PUNCT
cana-6069	110	4	)	)	PUNCT
cana-6069	110	5	𝑑𝑠1	𝑑𝑠1	PROPN
cana-6069	110	6	𝑑𝑡1	𝑑𝑡1	PROPN
cana-6069	110	7	𝑑𝑟1	𝑑𝑟1	X
cana-6069	110	8	for	for	ADP
cana-6069	110	9	all	all	DET
cana-6069	110	10	𝑞	𝑞	PROPN
cana-6069	110	11	,	,	PUNCT
cana-6069	110	12	𝑝	𝑝	PROPN
cana-6069	110	13	,	,	PUNCT
cana-6069	110	14	𝑣	𝑣	X
cana-6069	110	15	=	=	SYM
cana-6069	110	16	1	1	NUM
cana-6069	110	17	,	,	PUNCT
cana-6069	110	18	2	2	NUM
cana-6069	110	19	,	,	PUNCT
cana-6069	110	20	…	…	PUNCT
cana-6069	110	21	,	,	PUNCT
cana-6069	111	1	𝑁	𝑁	PROPN
cana-6069	111	2	+	+	NOUN
cana-6069	111	3	1	1	NUM
cana-6069	111	4	.	.	PUNCT
cana-6069	112	1	the	the	DET
cana-6069	112	2	coefficients	coefficient	NOUN
cana-6069	112	3	𝑐𝑖𝑗𝑘	𝑐𝑖𝑗𝑘	PROPN
cana-6069	112	4	are	be	AUX
cana-6069	112	5	determined	determine	VERB
cana-6069	112	6	by	by	ADP
cana-6069	112	7	solving	solve	VERB
cana-6069	112	8	the	the	DET
cana-6069	112	9	nonlinear	nonlinear	ADJ
cana-6069	112	10	system	system	NOUN
cana-6069	112	11	of	of	ADP
cana-6069	112	12	matrix	matrix	NOUN
cana-6069	112	13	iteratively	iteratively	ADV
cana-6069	112	14	:	:	PUNCT
cana-6069	112	15	𝐴	𝐴	PROPN
cana-6069	112	16	⋅	⋅	PROPN
cana-6069	112	17	𝑐	𝑐	PROPN
cana-6069	112	18	=	=	SYM
cana-6069	112	19	𝐵	𝐵	PROPN
cana-6069	112	20	where	where	SCONJ
cana-6069	112	21	𝐴	𝐴	PROPN
cana-6069	112	22	is	be	AUX
cana-6069	112	23	a	a	DET
cana-6069	112	24	matrix	matrix	NOUN
cana-6069	112	25	of	of	ADP
cana-6069	112	26	size	size	NOUN
cana-6069	112	27	(	(	PUNCT
cana-6069	112	28	𝑁	𝑁	PROPN
cana-6069	112	29	+	+	PROPN
cana-6069	112	30	1)3	1)3	PROPN
cana-6069	112	31	×	×	NOUN
cana-6069	112	32	(	(	PUNCT
cana-6069	112	33	𝑁	𝑁	PROPN
cana-6069	112	34	+	+	PROPN
cana-6069	112	35	1)3	1)3	PROPN
cana-6069	112	36	,	,	PUNCT
cana-6069	112	37	𝐵	𝐵	NOUN
cana-6069	112	38	is	be	AUX
cana-6069	112	39	a	a	DET
cana-6069	112	40	matrix	matrix	NOUN
cana-6069	112	41	of	of	ADP
cana-6069	112	42	size	size	NOUN
cana-6069	112	43	(	(	PUNCT
cana-6069	112	44	𝑁	𝑁	PROPN
cana-6069	112	45	+	+	PROPN
cana-6069	112	46	1)3	1)3	PROPN
cana-6069	112	47	×	×	NOUN
cana-6069	112	48	1	1	NUM
cana-6069	112	49	and	and	CCONJ
cana-6069	112	50	𝑐	𝑐	PROPN
cana-6069	112	51	is	be	AUX
cana-6069	112	52	a	a	DET
cana-6069	112	53	matrix	matrix	NOUN
cana-6069	112	54	of	of	ADP
cana-6069	112	55	size	size	NOUN
cana-6069	112	56	(	(	PUNCT
cana-6069	112	57	𝑁	𝑁	PROPN
cana-6069	112	58	+	+	PROPN
cana-6069	112	59	1)3	1)3	PROPN
cana-6069	112	60	×	×	NOUN
cana-6069	112	61	1	1	NUM
cana-6069	112	62	defined	define	VERB
cana-6069	112	63	by	by	ADP
cana-6069	112	64	[	[	X
cana-6069	112	65	𝑐111	𝑐111	PROPN
cana-6069	112	66	𝑐112	𝑐112	PROPN
cana-6069	112	67	…	…	PUNCT
cana-6069	112	68	𝑐(𝑁+1)3	𝑐(𝑁+1)3	NOUN
cana-6069	112	69	]	]	PUNCT
cana-6069	112	70	𝑇	𝑇	PROPN
cana-6069	113	1	.thus	.thus	ADV
cana-6069	113	2	,	,	PUNCT
cana-6069	113	3	we	we	PRON
cana-6069	113	4	have	have	AUX
cana-6069	113	5	obtained	obtain	VERB
cana-6069	113	6	a	a	DET
cana-6069	113	7	nonlinear	nonlinear	ADJ
cana-6069	113	8	system	system	NOUN
cana-6069	113	9	of	of	ADP
cana-6069	113	10	equations	equation	NOUN
cana-6069	113	11	which	which	PRON
cana-6069	113	12	contains	contain	VERB
cana-6069	113	13	(	(	PUNCT
cana-6069	113	14	𝑁	𝑁	PROPN
cana-6069	113	15	+	+	CCONJ
cana-6069	113	16	1)2	1)2	NUM
cana-6069	113	17	unknown	unknown	ADJ
cana-6069	113	18	coefficients	coefficient	NOUN
cana-6069	113	19	.	.	PUNCT
cana-6069	114	1	solving	solve	VERB
cana-6069	114	2	this	this	DET
cana-6069	114	3	system	system	NOUN
cana-6069	114	4	to	to	PART
cana-6069	114	5	obtain	obtain	VERB
cana-6069	114	6	the	the	DET
cana-6069	114	7	values	value	NOUN
cana-6069	114	8	of	of	ADP
cana-6069	114	9	these	these	DET
cana-6069	114	10	coefficients	coefficient	NOUN
cana-6069	114	11	,	,	PUNCT
cana-6069	114	12	we	we	PRON
cana-6069	114	13	arrive	arrive	VERB
cana-6069	114	14	at	at	ADP
cana-6069	114	15	the	the	DET
cana-6069	114	16	approximate	approximate	ADJ
cana-6069	114	17	solution	solution	NOUN
cana-6069	114	18	𝑢𝑁(𝑥1	𝑢𝑁(𝑥1	PROPN
cana-6069	114	19	,	,	PUNCT
cana-6069	114	20	𝑦1	𝑦1	PROPN
cana-6069	114	21	,	,	PUNCT
cana-6069	114	22	𝑧1	𝑧1	NOUN
cana-6069	114	23	)	)	PUNCT
cana-6069	114	24	.	.	PUNCT
cana-6069	115	1	4	4	X
cana-6069	115	2	.	.	X
cana-6069	115	3	results	result	VERB
cana-6069	115	4	4.1	4.1	NUM
cana-6069	115	5	existence	existence	NOUN
cana-6069	115	6	and	and	CCONJ
cana-6069	115	7	uniqueness	uniqueness	NOUN
cana-6069	115	8	of	of	ADP
cana-6069	115	9	solution	solution	NOUN
cana-6069	115	10	for	for	ADP
cana-6069	115	11	three	three	NUM
cana-6069	115	12	-	-	PUNCT
cana-6069	115	13	dimensional	dimensional	ADJ
cana-6069	115	14	nonlinear	nonlinear	ADJ
cana-6069	115	15	fredholm	fredholm	ADJ
cana-6069	115	16	integral	integral	ADJ
cana-6069	115	17	equation	equation	NOUN
cana-6069	115	18	we	we	PRON
cana-6069	115	19	consider	consider	VERB
cana-6069	115	20	the	the	DET
cana-6069	115	21	nonlinear	nonlinear	ADJ
cana-6069	115	22	fredholm	fredholm	ADJ
cana-6069	115	23	integral	integral	ADJ
cana-6069	115	24	equation	equation	NOUN
cana-6069	115	25	in	in	ADP
cana-6069	115	26	three	three	NUM
cana-6069	115	27	dimensions	dimension	NOUN
cana-6069	115	28	eq(1	eq(1	NOUN
cana-6069	115	29	):	):	PUNCT
cana-6069	115	30	𝑢(𝑥1	𝑢(𝑥1	ADV
cana-6069	115	31	,	,	PUNCT
cana-6069	115	32	𝑦1	𝑦1	NOUN
cana-6069	115	33	,	,	PUNCT
cana-6069	115	34	𝑧1	𝑧1	NOUN
cana-6069	115	35	)	)	PUNCT
cana-6069	115	36	−	−	PUNCT
cana-6069	116	1	𝜆	𝜆	PRON
cana-6069	116	2	∫	∫	PROPN
cana-6069	116	3	∫	∫	PROPN
cana-6069	116	4	∫	∫	PROPN
cana-6069	116	5	𝑘(𝑥1	𝑘(𝑥1	PROPN
cana-6069	116	6	,	,	PUNCT
cana-6069	116	7	𝑦1	𝑦1	PROPN
cana-6069	116	8	,	,	PUNCT
cana-6069	116	9	𝑧1	𝑧1	NOUN
cana-6069	116	10	,	,	PUNCT
cana-6069	116	11	𝑠1	𝑠1	PROPN
cana-6069	116	12	,	,	PUNCT
cana-6069	116	13	𝑡1	𝑡1	NOUN
cana-6069	116	14	,	,	PUNCT
cana-6069	116	15	𝑟1	𝑟1	NOUN
cana-6069	116	16	)	)	PUNCT
cana-6069	116	17	𝑄(𝑢(𝑠1	𝑄(𝑢(𝑠1	PROPN
cana-6069	116	18	,	,	PUNCT
cana-6069	116	19	𝑡1	𝑡1	NOUN
cana-6069	116	20	,	,	PUNCT
cana-6069	116	21	𝑟1))𝑑𝑠1	𝑟1))𝑑𝑠1	NUM
cana-6069	116	22	𝑑𝑡1	𝑑𝑡1	NOUN
cana-6069	116	23	𝑑𝑟1	𝑑𝑟1	X
cana-6069	116	24	𝑓	𝑓	PROPN
cana-6069	116	25	𝑒	𝑒	PROPN
cana-6069	116	26	𝑑	𝑑	PROPN
cana-6069	116	27	𝑐	𝑐	NOUN
cana-6069	116	28	𝑏	𝑏	PROPN
cana-6069	116	29	𝑎	𝑎	PROPN
cana-6069	116	30	=	=	PUNCT
cana-6069	116	31	𝑔(𝑥1	𝑔(𝑥1	NOUN
cana-6069	116	32	,	,	PUNCT
cana-6069	116	33	𝑦1	𝑦1	NOUN
cana-6069	116	34	,	,	PUNCT
cana-6069	116	35	𝑧1	𝑧1	NOUN
cana-6069	116	36	)	)	PUNCT
cana-6069	116	37	,	,	PUNCT
cana-6069	116	38	where	where	SCONJ
cana-6069	116	39	the	the	DET
cana-6069	116	40	domain	domain	NOUN
cana-6069	116	41	𝐷	𝐷	NOUN
cana-6069	116	42	=	=	PUNCT
cana-6069	117	1	[	[	X
cana-6069	117	2	𝑎	𝑎	X
cana-6069	117	3	,	,	PUNCT
cana-6069	117	4	𝑏	𝑏	NOUN
cana-6069	117	5	]	]	X
cana-6069	117	6	×	×	NOUN
cana-6069	117	7	[	[	X
cana-6069	117	8	𝑐	𝑐	NOUN
cana-6069	117	9	,	,	PUNCT
cana-6069	117	10	𝑑	𝑑	NOUN
cana-6069	117	11	]	]	X
cana-6069	117	12	×	×	NOUN
cana-6069	118	1	[	[	X
cana-6069	118	2	𝑒	𝑒	X
cana-6069	118	3	,	,	PUNCT
cana-6069	118	4	𝑓	𝑓	X
cana-6069	118	5	]	]	X
cana-6069	118	6	,	,	PUNCT
cana-6069	118	7	and	and	CCONJ
cana-6069	118	8	𝑄	𝑄	PRON
cana-6069	118	9	is	be	AUX
cana-6069	118	10	a	a	DET
cana-6069	118	11	nonlinear	nonlinear	ADJ
cana-6069	118	12	function	function	NOUN
cana-6069	118	13	.	.	PUNCT
cana-6069	119	1	theorem	theorem	NOUN
cana-6069	119	2	1	1	NUM
cana-6069	119	3	.	.	PUNCT
cana-6069	120	1	let	let	VERB
cana-6069	120	2	𝑋	𝑋	PROPN
cana-6069	120	3	=	=	SYM
cana-6069	120	4	𝐶([𝑎	𝐶([𝑎	PROPN
cana-6069	120	5	,	,	PUNCT
cana-6069	120	6	𝑏	𝑏	NOUN
cana-6069	120	7	]	]	X
cana-6069	120	8	×	×	NOUN
cana-6069	120	9	[	[	X
cana-6069	120	10	𝑐	𝑐	NOUN
cana-6069	120	11	,	,	PUNCT
cana-6069	120	12	𝑑	𝑑	NOUN
cana-6069	120	13	]	]	X
cana-6069	120	14	×	×	NOUN
cana-6069	121	1	[	[	X
cana-6069	121	2	𝑒	𝑒	X
cana-6069	121	3	,	,	PUNCT
cana-6069	121	4	𝑓	𝑓	X
cana-6069	121	5	]	]	X
cana-6069	121	6	)	)	PUNCT
cana-6069	121	7	be	be	AUX
cana-6069	121	8	the	the	DET
cana-6069	121	9	banach	banach	NOUN
cana-6069	121	10	space	space	NOUN
cana-6069	121	11	of	of	ADP
cana-6069	121	12	continuous	continuous	ADJ
cana-6069	121	13	functions	function	NOUN
cana-6069	121	14	𝑢(𝑥1	𝑢(𝑥1	ADV
cana-6069	121	15	,	,	PUNCT
cana-6069	121	16	𝑦1	𝑦1	NOUN
cana-6069	121	17	,	,	PUNCT
cana-6069	121	18	𝑧1	𝑧1	NOUN
cana-6069	121	19	)	)	PUNCT
cana-6069	121	20	,	,	PUNCT
cana-6069	121	21	equipped	equip	VERB
cana-6069	121	22	with	with	ADP
cana-6069	121	23	the	the	DET
cana-6069	121	24	supremum	supremum	ADJ
cana-6069	121	25	norm	norm	NOUN
cana-6069	121	26	:	:	PUNCT
cana-6069	121	27	‖𝑢‖	‖𝑢‖	PROPN
cana-6069	121	28	=	=	SYM
cana-6069	121	29	𝑠𝑢𝑝(𝑥1,𝑦1,𝑧1)∈[𝑐,𝑑]×[𝑒,𝑓]|𝑢(𝑥1	𝑠𝑢𝑝(𝑥1,𝑦1,𝑧1)∈[𝑐,𝑑]×[𝑒,𝑓]|𝑢(𝑥1	PROPN
cana-6069	121	30	,	,	PUNCT
cana-6069	121	31	𝑦	𝑦	NOUN
cana-6069	121	32	1	1	NUM
cana-6069	121	33	,	,	PUNCT
cana-6069	121	34	𝑧1)|	𝑧1)|	X
cana-6069	121	35	.	.	PUNCT
cana-6069	122	1	assume	assume	VERB
cana-6069	122	2	that	that	SCONJ
cana-6069	122	3	:	:	PUNCT
cana-6069	122	4	(	(	PUNCT
cana-6069	122	5	1	1	X
cana-6069	122	6	)	)	PUNCT
cana-6069	122	7	the	the	DET
cana-6069	122	8	kernel	kernel	PROPN
cana-6069	122	9	𝑘(𝑥1	𝑘(𝑥1	PROPN
cana-6069	122	10	,	,	PUNCT
cana-6069	122	11	𝑦1	𝑦1	NOUN
cana-6069	122	12	,	,	PUNCT
cana-6069	122	13	𝑧1	𝑧1	NOUN
cana-6069	122	14	,	,	PUNCT
cana-6069	122	15	𝑠1	𝑠1	PROPN
cana-6069	122	16	,	,	PUNCT
cana-6069	122	17	𝑡1	𝑡1	NOUN
cana-6069	122	18	,	,	PUNCT
cana-6069	122	19	𝑟1	𝑟1	NOUN
cana-6069	122	20	)	)	PUNCT
cana-6069	122	21	is	be	AUX
cana-6069	122	22	continuous	continuous	ADJ
cana-6069	122	23	on	on	ADP
cana-6069	122	24	𝐷	𝐷	PROPN
cana-6069	122	25	×	×	PROPN
cana-6069	122	26	𝐷	𝐷	PROPN
cana-6069	122	27	,	,	PUNCT
cana-6069	122	28	(	(	PUNCT
cana-6069	122	29	2	2	X
cana-6069	122	30	)	)	PUNCT
cana-6069	122	31	the	the	DET
cana-6069	122	32	function	function	NOUN
cana-6069	122	33	𝑄	𝑄	PROPN
cana-6069	122	34	:	:	PUNCT
cana-6069	122	35	𝑅	𝑅	PROPN
cana-6069	122	36	⟶	⟶	NOUN
cana-6069	122	37	𝑅	𝑅	PROPN
cana-6069	122	38	satisfies	satisfy	VERB
cana-6069	122	39	a	a	DET
cana-6069	122	40	lipschitz	lipschitz	NOUN
cana-6069	122	41	condition	condition	NOUN
cana-6069	122	42	:	:	PUNCT
cana-6069	122	43	|𝑄(𝑢	|𝑄(𝑢	NUM
cana-6069	122	44	)	)	PUNCT
cana-6069	122	45	−	−	PROPN
cana-6069	123	1	𝑄(𝑣)|	𝑄(𝑣)|	PROPN
cana-6069	123	2	≤	≤	PROPN
cana-6069	123	3	𝐿|𝑢	𝐿|𝑢	VERB
cana-6069	123	4	−	−	PROPN
cana-6069	123	5	𝑣|	𝑣|	PROPN
cana-6069	123	6	∀𝑢	∀𝑢	PROPN
cana-6069	123	7	,	,	PUNCT
cana-6069	123	8	𝑣	𝑣	PROPN
cana-6069	123	9	∈	∈	PROPN
cana-6069	123	10	𝑅	𝑅	PROPN
cana-6069	123	11	,	,	PUNCT
cana-6069	123	12	(	(	PUNCT
cana-6069	123	13	3	3	X
cana-6069	123	14	)	)	PUNCT
cana-6069	123	15	the	the	DET
cana-6069	123	16	constant	constant	ADJ
cana-6069	123	17	𝐶	𝐶	PROPN
cana-6069	123	18	=	=	SYM
cana-6069	123	19	𝐿𝑀	𝐿𝑀	PROPN
cana-6069	123	20	<	<	X
cana-6069	123	21	1	1	NUM
cana-6069	123	22	,	,	PUNCT
cana-6069	123	23	where	where	SCONJ
cana-6069	123	24	𝑀	𝑀	PROPN
cana-6069	123	25	=	=	PROPN
cana-6069	123	26	𝑠𝑢𝑝(𝑥1,𝑦1,𝑧1)∈d	𝑠𝑢𝑝(𝑥1,𝑦1,𝑧1)∈d	PROPN
cana-6069	123	27	∫	∫	PROPN
cana-6069	123	28	∫	∫	PROPN
cana-6069	123	29	∫	∫	PROPN
cana-6069	123	30	|𝑘(𝑥1	|𝑘(𝑥1	PROPN
cana-6069	123	31	,	,	PUNCT
cana-6069	123	32	𝑦1	𝑦1	NOUN
cana-6069	123	33	,	,	PUNCT
cana-6069	123	34	𝑧1	𝑧1	NOUN
cana-6069	123	35	,	,	PUNCT
cana-6069	123	36	𝑠1	𝑠1	PROPN
cana-6069	123	37	,	,	PUNCT
cana-6069	123	38	𝑡1	𝑡1	PROPN
cana-6069	123	39	,	,	PUNCT
cana-6069	123	40	𝑟1)|𝑑𝑠1	𝑟1)|𝑑𝑠1	PROPN
cana-6069	123	41	𝑑𝑡1𝑑𝑟1	𝑑𝑡1𝑑𝑟1	NOUN
cana-6069	123	42	.	.	PUNCT
cana-6069	124	1	𝑓	𝑓	PRON
cana-6069	124	2	𝑒	𝑒	PROPN
cana-6069	124	3	𝑑	𝑑	PROPN
cana-6069	124	4	𝑐	𝑐	PROPN
cana-6069	124	5	𝑏	𝑏	PROPN
cana-6069	124	6	𝑎	𝑎	NOUN
cana-6069	124	7	then	then	ADV
cana-6069	124	8	,	,	PUNCT
cana-6069	124	9	the	the	DET
cana-6069	124	10	integral	integral	ADJ
cana-6069	124	11	equation	equation	NOUN
cana-6069	124	12	has	have	VERB
cana-6069	124	13	a	a	DET
cana-6069	124	14	unique	unique	ADJ
cana-6069	124	15	solution	solution	NOUN
cana-6069	124	16	𝑢∗	𝑢∗	NOUN
cana-6069	124	17	∈	∈	PROPN
cana-6069	124	18	𝑋.	𝑋.	PROPN
cana-6069	124	19	proof	proof	NOUN
cana-6069	124	20	.	.	PUNCT
cana-6069	125	1	define	define	VERB
cana-6069	125	2	the	the	DET
cana-6069	125	3	operator	operator	NOUN
cana-6069	125	4	𝑇	𝑇	PROPN
cana-6069	125	5	∶	∶	NOUN
cana-6069	125	6	𝑋	𝑋	NOUN
cana-6069	125	7	→	→	PUNCT
cana-6069	125	8	𝑋	𝑋	NOUN
cana-6069	125	9	by	by	ADP
cana-6069	125	10	(	(	PUNCT
cana-6069	125	11	𝑇𝑢)(𝑥1	𝑇𝑢)(𝑥1	ADJ
cana-6069	125	12	,	,	PUNCT
cana-6069	125	13	𝑦1	𝑦1	NOUN
cana-6069	125	14	,	,	PUNCT
cana-6069	125	15	𝑧1	𝑧1	NOUN
cana-6069	125	16	)	)	PUNCT
cana-6069	125	17	=	=	SYM
cana-6069	125	18	𝑔(𝑥1	𝑔(𝑥1	X
cana-6069	125	19	,	,	PUNCT
cana-6069	125	20	𝑦1	𝑦1	NOUN
cana-6069	125	21	,	,	PUNCT
cana-6069	125	22	𝑧1	𝑧1	NOUN
cana-6069	125	23	)	)	PUNCT
cana-6069	126	1	+	+	CCONJ
cana-6069	126	2	∫	∫	PROPN
cana-6069	126	3	∫	∫	PROPN
cana-6069	126	4	∫	∫	PROPN
cana-6069	126	5	𝑘(𝑥1	𝑘(𝑥1	PROPN
cana-6069	126	6	,	,	PUNCT
cana-6069	126	7	𝑦1	𝑦1	NOUN
cana-6069	126	8	,	,	PUNCT
cana-6069	126	9	𝑧1	𝑧1	NOUN
cana-6069	126	10	,	,	PUNCT
cana-6069	126	11	𝑠1	𝑠1	PROPN
cana-6069	126	12	,	,	PUNCT
cana-6069	126	13	𝑡1	𝑡1	NOUN
cana-6069	126	14	,	,	PUNCT
cana-6069	126	15	𝑟1	𝑟1	NOUN
cana-6069	126	16	)	)	PUNCT
cana-6069	126	17	𝑄(𝑢(𝑠1	𝑄(𝑢(𝑠1	PROPN
cana-6069	126	18	,	,	PUNCT
cana-6069	126	19	𝑡1	𝑡1	NOUN
cana-6069	126	20	,	,	PUNCT
cana-6069	126	21	𝑟1))𝑑𝑠1	𝑟1))𝑑𝑠1	NUM
cana-6069	126	22	𝑑𝑡1	𝑑𝑡1	NOUN
cana-6069	126	23	𝑑𝑟1	𝑑𝑟1	X
cana-6069	126	24	𝑓	𝑓	PROPN
cana-6069	126	25	𝑒	𝑒	PROPN
cana-6069	126	26	𝑑	𝑑	PROPN
cana-6069	126	27	𝑐	𝑐	PROPN
cana-6069	126	28	𝑏	𝑏	PROPN
cana-6069	126	29	𝑎	𝑎	NOUN
cana-6069	126	30	let	let	NOUN
cana-6069	126	31	𝑢	𝑢	NOUN
cana-6069	126	32	,	,	PUNCT
cana-6069	126	33	𝑣	𝑣	PRON
cana-6069	126	34	∈	∈	PROPN
cana-6069	126	35	𝑋.	𝑋.	PROPN
cana-6069	126	36	then	then	ADV
cana-6069	126	37	|(𝑇𝑢)(𝑥1	|(𝑇𝑢)(𝑥1	NOUN
cana-6069	126	38	,	,	PUNCT
cana-6069	126	39	𝑦1	𝑦1	NOUN
cana-6069	126	40	,	,	PUNCT
cana-6069	126	41	𝑧1	𝑧1	NOUN
cana-6069	126	42	)	)	PUNCT
cana-6069	126	43	−	−	PROPN
cana-6069	126	44	(	(	PUNCT
cana-6069	126	45	𝑇𝑣)(𝑥1	𝑇𝑣)(𝑥1	ADJ
cana-6069	126	46	,	,	PUNCT
cana-6069	126	47	𝑦1	𝑦1	NOUN
cana-6069	126	48	,	,	PUNCT
cana-6069	126	49	𝑧1)|	𝑧1)|	NOUN
cana-6069	126	50	=	=	SYM
cana-6069	126	51	|∫	|∫	PROPN
cana-6069	126	52	∫	∫	PROPN
cana-6069	126	53	∫	∫	PROPN
cana-6069	126	54	𝑘(𝑥1	𝑘(𝑥1	PROPN
cana-6069	126	55	,	,	PUNCT
cana-6069	126	56	𝑦1	𝑦1	NOUN
cana-6069	126	57	,	,	PUNCT
cana-6069	126	58	𝑧1	𝑧1	NOUN
cana-6069	126	59	,	,	PUNCT
cana-6069	126	60	𝑠1	𝑠1	PROPN
cana-6069	126	61	,	,	PUNCT
cana-6069	126	62	𝑡1	𝑡1	NOUN
cana-6069	126	63	,	,	PUNCT
cana-6069	126	64	𝑟1	𝑟1	NOUN
cana-6069	126	65	)	)	PUNCT
cana-6069	126	66	𝑓	𝑓	PRON
cana-6069	126	67	𝑒	𝑒	PROPN
cana-6069	126	68	𝑑	𝑑	PROPN
cana-6069	126	69	𝑐	𝑐	PROPN
cana-6069	126	70	𝑏	𝑏	PROPN
cana-6069	126	71	𝑎	𝑎	PRON
cana-6069	126	72	[	[	PUNCT
cana-6069	126	73	𝑄(𝑢(𝑠1	𝑄(𝑢(𝑠1	PROPN
cana-6069	126	74	,	,	PUNCT
cana-6069	126	75	𝑡1	𝑡1	NOUN
cana-6069	126	76	,	,	PUNCT
cana-6069	126	77	𝑟1	𝑟1	NOUN
cana-6069	126	78	)	)	PUNCT
cana-6069	126	79	)	)	PUNCT
cana-6069	127	1	−	−	PROPN
cana-6069	127	2	𝑄(𝑣(𝑠1	𝑄(𝑣(𝑠1	NOUN
cana-6069	127	3	,	,	PUNCT
cana-6069	127	4	𝑡1	𝑡1	NOUN
cana-6069	127	5	,	,	PUNCT
cana-6069	127	6	𝑟1))]𝑑𝑠1	𝑟1))]𝑑𝑠1	NOUN
cana-6069	127	7	𝑑𝑡1	𝑑𝑡1	NOUN
cana-6069	127	8	𝑑𝑟1|	𝑑𝑟1|	PROPN
cana-6069	127	9	≤	≤	PUNCT
cana-6069	128	1	𝐿	𝐿	PROPN
cana-6069	128	2	∫	∫	PROPN
cana-6069	128	3	∫	∫	PROPN
cana-6069	128	4	∫	∫	PROPN
cana-6069	128	5	|𝑘(𝑥1	|𝑘(𝑥1	PROPN
cana-6069	128	6	,	,	PUNCT
cana-6069	128	7	𝑦1	𝑦1	NOUN
cana-6069	128	8	,	,	PUNCT
cana-6069	128	9	𝑧1	𝑧1	NOUN
cana-6069	128	10	,	,	PUNCT
cana-6069	128	11	𝑠1	𝑠1	PROPN
cana-6069	128	12	,	,	PUNCT
cana-6069	128	13	𝑡1	𝑡1	PROPN
cana-6069	128	14	,	,	PUNCT
cana-6069	128	15	𝑟1)|	𝑟1)|	PROPN
cana-6069	128	16	𝑓	𝑓	PROPN
cana-6069	128	17	𝑒	𝑒	PROPN
cana-6069	128	18	𝑑	𝑑	PROPN
cana-6069	128	19	𝑐	𝑐	PROPN
cana-6069	128	20	𝑏	𝑏	PROPN
cana-6069	128	21	𝑎	𝑎	PRON
cana-6069	128	22	⋅	⋅	PROPN
cana-6069	128	23	|𝑢(𝑠1	|𝑢(𝑠1	ADJ
cana-6069	128	24	,	,	PUNCT
cana-6069	128	25	𝑡1	𝑡1	NOUN
cana-6069	128	26	,	,	PUNCT
cana-6069	128	27	𝑟1	𝑟1	NOUN
cana-6069	128	28	)	)	PUNCT
cana-6069	128	29	−	−	PROPN
cana-6069	128	30	𝑣(𝑠1	𝑣(𝑠1	NOUN
cana-6069	128	31	,	,	PUNCT
cana-6069	128	32	𝑡1	𝑡1	NOUN
cana-6069	128	33	,	,	PUNCT
cana-6069	128	34	𝑟1)|𝑑𝑠1	𝑟1)|𝑑𝑠1	NOUN
cana-6069	128	35	𝑑𝑡1𝑑𝑟1	𝑑𝑡1𝑑𝑟1	PROPN
cana-6069	128	36	≤	≤	PROPN
cana-6069	128	37	𝐿	𝐿	PROPN
cana-6069	128	38	∫	∫	PROPN
cana-6069	128	39	∫	∫	PROPN
cana-6069	128	40	∫	∫	PROPN
cana-6069	128	41	|𝑘(𝑥1	|𝑘(𝑥1	PROPN
cana-6069	128	42	,	,	PUNCT
cana-6069	128	43	𝑦1	𝑦1	NOUN
cana-6069	128	44	,	,	PUNCT
cana-6069	128	45	𝑧1	𝑧1	NOUN
cana-6069	128	46	,	,	PUNCT
cana-6069	128	47	𝑠1	𝑠1	PROPN
cana-6069	128	48	,	,	PUNCT
cana-6069	128	49	𝑡1	𝑡1	PROPN
cana-6069	128	50	,	,	PUNCT
cana-6069	128	51	𝑟1)|	𝑟1)|	PROPN
cana-6069	128	52	𝑓	𝑓	PROPN
cana-6069	128	53	𝑒	𝑒	PROPN
cana-6069	128	54	𝑑	𝑑	PROPN
cana-6069	128	55	𝑐	𝑐	PROPN
cana-6069	128	56	𝑏	𝑏	PROPN
cana-6069	128	57	𝑎	𝑎	VERB
cana-6069	128	58	𝑑𝑠1	𝑑𝑠1	NOUN
cana-6069	128	59	𝑑𝑡1𝑑𝑟1	𝑑𝑡1𝑑𝑟1	PROPN
cana-6069	128	60	⋅	⋅	PROPN
cana-6069	128	61	‖𝑢	‖𝑢	PART
cana-6069	128	62	−	−	NUM
cana-6069	128	63	𝑣‖.	𝑣‖.	NOUN
cana-6069	128	64	communications	communication	NOUN
cana-6069	128	65	on	on	ADP
cana-6069	128	66	applied	apply	VERB
cana-6069	128	67	nonlinear	nonlinear	ADJ
cana-6069	128	68	analysis	analysis	NOUN
cana-6069	128	69	issn	issn	NOUN
cana-6069	128	70	:	:	PUNCT
cana-6069	128	71	1074	1074	NUM
cana-6069	128	72	-	-	PUNCT
cana-6069	128	73	133x	133x	NUM
cana-6069	128	74	vol	vol	VERB
cana-6069	128	75	32	32	NUM
cana-6069	128	76	no.10s	no.10s	PROPN
cana-6069	128	77	y	y	PROPN
cana-6069	128	78	(	(	PUNCT
cana-6069	128	79	2025	2025	NUM
cana-6069	128	80	)	)	PUNCT
cana-6069	128	81	3314	3314	NUM
cana-6069	128	82	taking	take	VERB
cana-6069	128	83	the	the	DET
cana-6069	128	84	supremum	supremum	ADJ
cana-6069	128	85	over	over	ADP
cana-6069	128	86	(	(	PUNCT
cana-6069	128	87	𝑥1	𝑥1	NOUN
cana-6069	128	88	,	,	PUNCT
cana-6069	128	89	𝑦1	𝑦1	NOUN
cana-6069	128	90	,	,	PUNCT
cana-6069	128	91	𝑧1	𝑧1	NOUN
cana-6069	128	92	)	)	PUNCT
cana-6069	128	93	∈	∈	PROPN
cana-6069	128	94	𝐷	𝐷	PROPN
cana-6069	128	95	,	,	PUNCT
cana-6069	128	96	𝑤𝑒	𝑤𝑒	PROPN
cana-6069	128	97	𝑔𝑒𝑡	𝑔𝑒𝑡	NOUN
cana-6069	128	98	:	:	PUNCT
cana-6069	128	99	‖𝑇𝑢	‖𝑇𝑢	ADJ
cana-6069	128	100	−	−	NOUN
cana-6069	128	101	𝑇𝑣‖	𝑇𝑣‖	NOUN
cana-6069	128	102	≤	≤	PROPN
cana-6069	128	103	𝐿𝑀‖𝑢	𝐿𝑀‖𝑢	NOUN
cana-6069	128	104	−	−	ADP
cana-6069	128	105	𝑣‖	𝑣‖	NOUN
cana-6069	128	106	=	=	PUNCT
cana-6069	128	107	𝐶‖𝑢	𝐶‖𝑢	ADJ
cana-6069	128	108	−	−	PROPN
cana-6069	128	109	𝑣‖.	𝑣‖.	NOUN
cana-6069	128	110	since	since	SCONJ
cana-6069	128	111	𝐶	𝐶	PROPN
cana-6069	128	112	<	<	X
cana-6069	128	113	1	1	NUM
cana-6069	128	114	,	,	PUNCT
cana-6069	128	115	the	the	DET
cana-6069	128	116	operator	operator	NOUN
cana-6069	128	117	t	t	NOUN
cana-6069	128	118	is	be	AUX
cana-6069	128	119	a	a	DET
cana-6069	128	120	contraction	contraction	NOUN
cana-6069	128	121	.	.	PUNCT
cana-6069	129	1	by	by	ADP
cana-6069	129	2	banach	banach	NOUN
cana-6069	129	3	's	's	PART
cana-6069	129	4	fixed	fix	VERB
cana-6069	129	5	point	point	NOUN
cana-6069	129	6	theorem	theorem	VERB
cana-6069	129	7	,	,	PUNCT
cana-6069	129	8	there	there	PRON
cana-6069	129	9	exists	exist	VERB
cana-6069	129	10	a	a	DET
cana-6069	129	11	unique	unique	ADJ
cana-6069	129	12	fixed	fix	VERB
cana-6069	129	13	point	point	NOUN
cana-6069	129	14	𝑢∗	𝑢∗	NOUN
cana-6069	129	15	∈	∈	NOUN
cana-6069	129	16	𝑋	𝑋	NOUN
cana-6069	129	17	such	such	ADJ
cana-6069	129	18	that	that	DET
cana-6069	129	19	𝑇𝑢∗	𝑇𝑢∗	NOUN
cana-6069	129	20	=	=	SYM
cana-6069	129	21	𝑢∗	𝑢∗	NOUN
cana-6069	129	22	,	,	PUNCT
cana-6069	129	23	i.e	i.e	PRON
cana-6069	129	24	,	,	PUNCT
cana-6069	129	25	𝑢∗is	𝑢∗i	VERB
cana-6069	129	26	the	the	DET
cana-6069	129	27	unique	unique	ADJ
cana-6069	129	28	solution	solution	NOUN
cana-6069	129	29	of	of	ADP
cana-6069	129	30	the	the	DET
cana-6069	129	31	integral	integral	ADJ
cana-6069	129	32	equation	equation	NOUN
cana-6069	129	33	.	.	PUNCT
cana-6069	130	1	□	□	PUNCT
cana-6069	130	2	4.2	4.2	NUM
cana-6069	130	3	numerical	numerical	ADJ
cana-6069	130	4	examples	example	NOUN
cana-6069	130	5	we	we	PRON
cana-6069	130	6	present	present	VERB
cana-6069	130	7	the	the	DET
cana-6069	130	8	numerical	numerical	ADJ
cana-6069	130	9	results	result	NOUN
cana-6069	130	10	for	for	ADP
cana-6069	130	11	the	the	DET
cana-6069	130	12	three	three	NUM
cana-6069	130	13	-	-	PUNCT
cana-6069	130	14	dimensional	dimensional	ADJ
cana-6069	130	15	nonlinear	nonlinear	ADJ
cana-6069	130	16	fredholm	fredholm	ADJ
cana-6069	130	17	integral	integral	ADJ
cana-6069	130	18	equations	equation	NOUN
cana-6069	130	19	.	.	PUNCT
cana-6069	131	1	tables	table	NOUN
cana-6069	131	2	containing	contain	VERB
cana-6069	131	3	the	the	DET
cana-6069	131	4	approximate	approximate	ADJ
cana-6069	131	5	solution	solution	NOUN
cana-6069	131	6	values	value	NOUN
cana-6069	131	7	are	be	AUX
cana-6069	131	8	provided	provide	VERB
cana-6069	131	9	,	,	PUNCT
cana-6069	131	10	along	along	ADP
cana-6069	131	11	with	with	ADP
cana-6069	131	12	three	three	NUM
cana-6069	131	13	-	-	PUNCT
cana-6069	131	14	dimensional	dimensional	ADJ
cana-6069	131	15	graphical	graphical	ADJ
cana-6069	131	16	representations	representation	NOUN
cana-6069	131	17	of	of	ADP
cana-6069	131	18	the	the	DET
cana-6069	131	19	solutions	solution	NOUN
cana-6069	131	20	obtained	obtain	VERB
cana-6069	131	21	using	use	VERB
cana-6069	131	22	matlab	matlab	PROPN
cana-6069	131	23	.	.	PUNCT
cana-6069	132	1	the	the	DET
cana-6069	132	2	results	result	NOUN
cana-6069	132	3	are	be	AUX
cana-6069	132	4	derived	derive	VERB
cana-6069	132	5	by	by	ADP
cana-6069	132	6	employing	employ	VERB
cana-6069	132	7	the	the	DET
cana-6069	132	8	proposed	propose	VERB
cana-6069	132	9	fibonacci	fibonacci	NOUN
cana-6069	132	10	and	and	CCONJ
cana-6069	132	11	hermite	hermite	ADJ
cana-6069	132	12	-	-	PUNCT
cana-6069	132	13	galerkin	galerkin	ADJ
cana-6069	132	14	methods	method	NOUN
cana-6069	132	15	and	and	CCONJ
cana-6069	132	16	further	far	ADV
cana-6069	132	17	compared	compare	VERB
cana-6069	132	18	with	with	ADP
cana-6069	132	19	the	the	DET
cana-6069	132	20	other	other	ADJ
cana-6069	132	21	methods	method	NOUN
cana-6069	132	22	discussed	discuss	VERB
cana-6069	132	23	earlier	early	ADV
cana-6069	132	24	.	.	PUNCT
cana-6069	133	1	example1	example1	PROPN
cana-6069	133	2	.	.	PUNCT
cana-6069	134	1	consider	consider	VERB
cana-6069	134	2	the	the	DET
cana-6069	134	3	following	follow	VERB
cana-6069	134	4	3d	3d	NOUN
cana-6069	134	5	-	-	PUNCT
cana-6069	134	6	nfie	nfie	PROPN
cana-6069	135	1	[	[	X
cana-6069	135	2	7,8	7,8	NUM
cana-6069	135	3	]	]	PUNCT
cana-6069	135	4	:	:	PUNCT
cana-6069	135	5	𝑢(𝑥1	𝑢(𝑥1	ADV
cana-6069	135	6	,	,	PUNCT
cana-6069	135	7	𝑦1	𝑦1	NOUN
cana-6069	135	8	,	,	PUNCT
cana-6069	135	9	𝑧1	𝑧1	NOUN
cana-6069	135	10	)	)	PUNCT
cana-6069	135	11	=	=	SYM
cana-6069	135	12	𝑔(𝑥1	𝑔(𝑥1	X
cana-6069	135	13	,	,	PUNCT
cana-6069	135	14	𝑦1	𝑦1	NOUN
cana-6069	135	15	,	,	PUNCT
cana-6069	135	16	𝑧1	𝑧1	NOUN
cana-6069	135	17	)	)	PUNCT
cana-6069	135	18	+	+	CCONJ
cana-6069	135	19	∫	∫	PROPN
cana-6069	135	20	∫	∫	PROPN
cana-6069	135	21	∫	∫	PROPN
cana-6069	135	22	1	1	NUM
cana-6069	135	23	100	100	NUM
cana-6069	135	24	1	1	NUM
cana-6069	135	25	0	0	NUM
cana-6069	135	26	1	1	NUM
cana-6069	135	27	0	0	NUM
cana-6069	135	28	1	1	NUM
cana-6069	135	29	0	0	NUM
cana-6069	135	30	𝑥1	𝑥1	NOUN
cana-6069	135	31	2𝑠1(𝑡1	2𝑠1(𝑡1	NUM
cana-6069	135	32	2	2	NUM
cana-6069	135	33	+	+	SYM
cana-6069	135	34	𝑦1)𝑟1𝑧1𝑢2(𝑠1	𝑦1)𝑟1𝑧1𝑢2(𝑠1	PROPN
cana-6069	135	35	,	,	PUNCT
cana-6069	135	36	𝑡1	𝑡1	NOUN
cana-6069	135	37	,	,	PUNCT
cana-6069	135	38	𝑟1	𝑟1	NOUN
cana-6069	135	39	)	)	PUNCT
cana-6069	135	40	𝑑𝑠1	𝑑𝑠1	PROPN
cana-6069	135	41	𝑑𝑡1	𝑑𝑡1	PROPN
cana-6069	135	42	𝑑𝑟1	𝑑𝑟1	PROPN
cana-6069	135	43	,	,	PUNCT
cana-6069	135	44	(	(	PUNCT
cana-6069	135	45	𝑥1	𝑥1	NOUN
cana-6069	135	46	,	,	PUNCT
cana-6069	135	47	𝑦1	𝑦1	NOUN
cana-6069	135	48	,	,	PUNCT
cana-6069	135	49	𝑧1	𝑧1	NOUN
cana-6069	135	50	)	)	PUNCT
cana-6069	135	51	∈	∈	PROPN
cana-6069	136	1	[	[	X
cana-6069	136	2	0,1]3	0,1]3	NUM
cana-6069	136	3	(	(	PUNCT
cana-6069	136	4	7	7	NUM
cana-6069	136	5	)	)	PUNCT
cana-6069	136	6	where	where	SCONJ
cana-6069	136	7	𝑔(𝑥1	𝑔(𝑥1	NOUN
cana-6069	136	8	,	,	PUNCT
cana-6069	136	9	𝑦1	𝑦1	NOUN
cana-6069	136	10	,	,	PUNCT
cana-6069	136	11	𝑧1	𝑧1	NOUN
cana-6069	136	12	)	)	PUNCT
cana-6069	136	13	=	=	SYM
cana-6069	136	14	𝑥1	𝑥1	NOUN
cana-6069	136	15	2𝑦1	2𝑦1	NUM
cana-6069	136	16	2𝑧1	2𝑧1	NUM
cana-6069	136	17	−	−	DET
cana-6069	136	18	1	1	NUM
cana-6069	136	19	16800	16800	NUM
cana-6069	136	20	𝑥1	𝑥1	NOUN
cana-6069	136	21	2𝑧1	2𝑧1	NUM
cana-6069	136	22	−	−	PROPN
cana-6069	136	23	1	1	NUM
cana-6069	136	24	12000	12000	NUM
cana-6069	136	25	𝑥1	𝑥1	NOUN
cana-6069	136	26	2𝑦1𝑧1	2𝑦1𝑧1	NUM
cana-6069	136	27	,	,	PUNCT
cana-6069	136	28	and	and	CCONJ
cana-6069	136	29	exact	exact	ADJ
cana-6069	136	30	solution	solution	NOUN
cana-6069	136	31	is	be	AUX
cana-6069	136	32	𝑢(𝑥1	𝑢(𝑥1	ADV
cana-6069	136	33	,	,	PUNCT
cana-6069	136	34	𝑦1	𝑦1	NOUN
cana-6069	136	35	,	,	PUNCT
cana-6069	136	36	𝑧1	𝑧1	NOUN
cana-6069	136	37	)	)	PUNCT
cana-6069	136	38	=	=	SYM
cana-6069	136	39	𝑥1	𝑥1	NOUN
cana-6069	136	40	2𝑦1	2𝑦1	NUM
cana-6069	136	41	2𝑧1	2𝑧1	NUM
cana-6069	136	42	.	.	PUNCT
cana-6069	137	1	the	the	DET
cana-6069	137	2	comparison	comparison	NOUN
cana-6069	137	3	of	of	ADP
cana-6069	137	4	absolute	absolute	ADJ
cana-6069	137	5	errors	error	NOUN
cana-6069	137	6	of	of	ADP
cana-6069	137	7	equation(7	equation(7	PROPN
cana-6069	137	8	)	)	PUNCT
cana-6069	137	9	for	for	ADP
cana-6069	137	10	different	different	ADJ
cana-6069	137	11	values	value	NOUN
cana-6069	137	12	of	of	ADP
cana-6069	137	13	(	(	PUNCT
cana-6069	137	14	𝑥1	𝑥1	NOUN
cana-6069	137	15	,	,	PUNCT
cana-6069	137	16	𝑦1	𝑦1	NOUN
cana-6069	137	17	,	,	PUNCT
cana-6069	137	18	𝑧1	𝑧1	NOUN
cana-6069	137	19	)	)	PUNCT
cana-6069	137	20	,	,	PUNCT
cana-6069	137	21	between	between	ADP
cana-6069	137	22	fibonacci	fibonacci	NOUN
cana-6069	137	23	collocation	collocation	NOUN
cana-6069	137	24	(	(	PUNCT
cana-6069	137	25	fc	fc	INTJ
cana-6069	137	26	)	)	PUNCT
cana-6069	137	27	,	,	PUNCT
cana-6069	137	28	hermite	hermite	PROPN
cana-6069	137	29	–	–	PUNCT
cana-6069	137	30	galerkin	galerkin	PROPN
cana-6069	137	31	(	(	PUNCT
cana-6069	137	32	h	h	NOUN
cana-6069	137	33	-	-	PUNCT
cana-6069	137	34	g	g	NOUN
cana-6069	137	35	)	)	PUNCT
cana-6069	137	36	methods	method	NOUN
cana-6069	137	37	with	with	ADP
cana-6069	137	38	n=2	n=2	PRON
cana-6069	137	39	,	,	PUNCT
cana-6069	137	40	the	the	DET
cana-6069	137	41	successive	successive	ADJ
cana-6069	137	42	approximations	approximation	NOUN
cana-6069	137	43	method	method	NOUN
cana-6069	137	44	at	at	ADP
cana-6069	137	45	n=10	n=10	NOUN
cana-6069	137	46	[	[	X
cana-6069	137	47	8	8	NUM
cana-6069	137	48	]	]	PUNCT
cana-6069	137	49	,	,	PUNCT
cana-6069	137	50	and	and	CCONJ
cana-6069	137	51	the	the	DET
cana-6069	137	52	haar	haar	PROPN
cana-6069	137	53	wavelet	wavelet	NOUN
cana-6069	137	54	method	method	NOUN
cana-6069	137	55	at	at	ADP
cana-6069	137	56	2n=8	2n=8	PROPN
cana-6069	137	57	[	[	X
cana-6069	137	58	7	7	NUM
cana-6069	137	59	]	]	PUNCT
cana-6069	137	60	,	,	PUNCT
cana-6069	137	61	are	be	AUX
cana-6069	137	62	presented	present	VERB
cana-6069	137	63	in	in	ADP
cana-6069	137	64	table	table	NOUN
cana-6069	137	65	(	(	PUNCT
cana-6069	137	66	1	1	NUM
cana-6069	137	67	)	)	PUNCT
cana-6069	137	68	.	.	PUNCT
cana-6069	138	1	figures	figure	NOUN
cana-6069	138	2	(	(	PUNCT
cana-6069	138	3	1	1	NUM
cana-6069	138	4	)	)	PUNCT
cana-6069	138	5	and	and	CCONJ
cana-6069	138	6	(	(	PUNCT
cana-6069	138	7	2	2	X
cana-6069	138	8	)	)	PUNCT
cana-6069	138	9	show	show	VERB
cana-6069	138	10	the	the	DET
cana-6069	138	11	absolute	absolute	ADJ
cana-6069	138	12	error	error	NOUN
cana-6069	138	13	distribution	distribution	NOUN
cana-6069	138	14	obtained	obtain	VERB
cana-6069	138	15	by	by	ADP
cana-6069	138	16	both	both	DET
cana-6069	138	17	methods	method	NOUN
cana-6069	138	18	.	.	PUNCT
cana-6069	139	1	table	table	NOUN
cana-6069	139	2	1	1	NUM
cana-6069	139	3	.	.	PUNCT
cana-6069	139	4	numerical	numerical	ADJ
cana-6069	139	5	results	result	NOUN
cana-6069	139	6	for	for	ADP
cana-6069	139	7	example	example	NOUN
cana-6069	139	8	1	1	NUM
cana-6069	139	9	,	,	PUNCT
cana-6069	139	10	𝑧1	𝑧1	NOUN
cana-6069	139	11	=	=	SYM
cana-6069	139	12	0.5	0.5	NUM
cana-6069	139	13	(	(	PUNCT
cana-6069	139	14	𝑥1	𝑥1	NOUN
cana-6069	139	15	,	,	PUNCT
cana-6069	139	16	𝑦1	𝑦1	NOUN
cana-6069	139	17	,	,	PUNCT
cana-6069	139	18	𝑧1	𝑧1	NOUN
cana-6069	139	19	)	)	PUNCT
cana-6069	139	20	fibonacci	fibonacci	NOUN
cana-6069	139	21	collocation	collocation	NOUN
cana-6069	139	22	method	method	NOUN
cana-6069	139	23	𝑁	𝑁	PROPN
cana-6069	139	24	=	=	SYM
cana-6069	139	25	2	2	NUM
cana-6069	139	26	hermite	hermite	ADJ
cana-6069	139	27	-	-	PUNCT
cana-6069	139	28	galerkin	galerkin	ADJ
cana-6069	139	29	method	method	NOUN
cana-6069	139	30	𝑁	𝑁	PROPN
cana-6069	139	31	=	=	SYM
cana-6069	139	32	2	2	NUM
cana-6069	139	33	method	method	NOUN
cana-6069	139	34	of	of	ADP
cana-6069	139	35	[	[	X
cana-6069	139	36	8	8	NUM
cana-6069	139	37	]	]	PUNCT
cana-6069	139	38	with	with	ADP
cana-6069	139	39	𝑁	𝑁	PROPN
cana-6069	139	40	=	=	SYM
cana-6069	139	41	10	10	NUM
cana-6069	139	42	method	method	NOUN
cana-6069	139	43	of	of	ADP
cana-6069	139	44	[	[	X
cana-6069	139	45	7	7	NUM
cana-6069	139	46	]	]	PUNCT
cana-6069	139	47	with	with	ADP
cana-6069	139	48	2𝑁	2𝑁	NOUN
cana-6069	139	49	=	=	SYM
cana-6069	139	50	8	8	NUM
cana-6069	139	51	(	(	PUNCT
cana-6069	139	52	0,0,0	0,0,0	NOUN
cana-6069	139	53	)	)	PUNCT
cana-6069	139	54	1.4727	1.4727	NUM
cana-6069	139	55	×	×	NOUN
cana-6069	139	56	10−11	10−11	NUM
cana-6069	139	57	8.729	8.729	NUM
cana-6069	139	58	×	×	NOUN
cana-6069	139	59	10−9	10−9	NUM
cana-6069	139	60	0	0	NUM
cana-6069	139	61	.	.	NOUN
cana-6069	139	62	0	0	NUM
cana-6069	139	63	.	.	PUNCT
cana-6069	140	1	(	(	PUNCT
cana-6069	140	2	0.1,0.1,0.1	0.1,0.1,0.1	NOUN
cana-6069	140	3	)	)	PUNCT
cana-6069	140	4	3.9781	3.9781	NUM
cana-6069	140	5	×	×	NOUN
cana-6069	140	6	10−12	10−12	NOUN
cana-6069	140	7	2.3279	2.3279	NUM
cana-6069	140	8	×	×	NOUN
cana-6069	140	9	10−9	10−9	NUM
cana-6069	140	10	1.549	1.549	NUM
cana-6069	140	11	×	×	NOUN
cana-6069	140	12	10−9	10−9	NUM
cana-6069	140	13	3.51	3.51	NUM
cana-6069	140	14	×	×	NOUN
cana-6069	140	15	10−9	10−9	NUM
cana-6069	140	16	(	(	PUNCT
cana-6069	140	17	0.2,0.2,0.2	0.2,0.2,0.2	NUM
cana-6069	140	18	)	)	PUNCT
cana-6069	140	19	7.7772	7.7772	NUM
cana-6069	140	20	×	×	NOUN
cana-6069	140	21	10−13	10−13	PROPN
cana-6069	140	22	5.6042	5.6042	NUM
cana-6069	140	23	×	×	NOUN
cana-6069	140	24	10−11	10−11	NUM
cana-6069	140	25	1.345	1.345	NUM
cana-6069	140	26	×	×	NOUN
cana-6069	140	27	10−8	10−8	NUM
cana-6069	140	28	3.075	3.075	NUM
cana-6069	140	29	×	×	NOUN
cana-6069	140	30	10−8	10−8	NUM
cana-6069	140	31	(	(	PUNCT
cana-6069	140	32	0.3,0.3,0.3	0.3,0.3,0.3	NUM
cana-6069	140	33	)	)	PUNCT
cana-6069	140	34	3.7868	3.7868	NUM
cana-6069	140	35	×	×	NOUN
cana-6069	140	36	10−13	10−13	NUM
cana-6069	140	37	4.2694	4.2694	NUM
cana-6069	140	38	×	×	NOUN
cana-6069	140	39	10−10	10−10	NUM
cana-6069	140	40	4.9181	4.9181	NUM
cana-6069	140	41	×	×	NOUN
cana-6069	140	42	10−8	10−8	NUM
cana-6069	140	43	1.127	1.127	NUM
cana-6069	140	44	×	×	NOUN
cana-6069	140	45	10−7	10−7	NUM
cana-6069	140	46	(	(	PUNCT
cana-6069	140	47	0.4,0.4,0.4	0.4,0.4,0.4	NUM
cana-6069	140	48	)	)	PUNCT
cana-6069	140	49	6.0653	6.0653	NUM
cana-6069	140	50	×	×	NOUN
cana-6069	140	51	10−13	10−13	NUM
cana-6069	140	52	1.6048	1.6048	NUM
cana-6069	140	53	×	×	NOUN
cana-6069	140	54	10−9	10−9	NUM
cana-6069	140	55	1.2552	1.2552	NUM
cana-6069	140	56	×	×	NOUN
cana-6069	140	57	10−7	10−7	NUM
cana-6069	140	58	2.884	2.884	NUM
cana-6069	140	59	×	×	NOUN
cana-6069	140	60	10−7	10−7	NUM
cana-6069	140	61	(	(	PUNCT
cana-6069	140	62	0.5,0.5,0.5	0.5,0.5,0.5	NUM
cana-6069	140	63	)	)	PUNCT
cana-6069	140	64	1.1211	1.1211	NUM
cana-6069	140	65	×	×	NOUN
cana-6069	140	66	10−12	10−12	NOUN
cana-6069	140	67	2.2105	2.2105	NUM
cana-6069	140	68	×	×	NOUN
cana-6069	140	69	10−9	10−9	NUM
cana-6069	140	70	2.6264	2.6264	NUM
cana-6069	140	71	×	×	NOUN
cana-6069	140	72	10−7	10−7	NUM
cana-6069	140	73	6.0474	6.0474	NUM
cana-6069	140	74	×	×	NOUN
cana-6069	140	75	10−7	10−7	NUM
cana-6069	140	76	(	(	PUNCT
cana-6069	140	77	0.6,0.6,0.6	0.6,0.6,0.6	NUM
cana-6069	140	78	)	)	PUNCT
cana-6069	140	79	2.6918	2.6918	NUM
cana-6069	140	80	×	×	NOUN
cana-6069	140	81	10−12	10−12	NOUN
cana-6069	140	82	1.7484	1.7484	NUM
cana-6069	140	83	×	×	NOUN
cana-6069	140	84	10−9	10−9	NUM
cana-6069	140	85	4.8404	4.8404	NUM
cana-6069	140	86	×	×	NOUN
cana-6069	140	87	10−7	10−7	NUM
cana-6069	140	88	1.116	1.116	NUM
cana-6069	140	89	×	×	NOUN
cana-6069	140	90	10−6	10−6	NUM
cana-6069	140	91	(	(	PUNCT
cana-6069	140	92	0.7,0.7,0.7	0.7,0.7,0.7	NUM
cana-6069	140	93	)	)	PUNCT
cana-6069	140	94	6.4935	6.4935	NUM
cana-6069	140	95	×	×	NOUN
cana-6069	140	96	10−12	10−12	NOUN
cana-6069	140	97	6.5454	6.5454	NUM
cana-6069	140	98	×	×	NOUN
cana-6069	140	99	10−10	10−10	NUM
cana-6069	140	100	8.1658	8.1658	NUM
cana-6069	140	101	×	×	NOUN
cana-6069	140	102	10−7	10−7	NUM
cana-6069	140	103	1.886	1.886	NUM
cana-6069	140	104	×	×	NOUN
cana-6069	140	105	10−6	10−6	NUM
cana-6069	140	106	(	(	PUNCT
cana-6069	140	107	0.8,0.8,0.8	0.8,0.8,0.8	NUM
cana-6069	140	108	)	)	PUNCT
cana-6069	140	109	1.3411	1.3411	NUM
cana-6069	140	110	×	×	NOUN
cana-6069	140	111	10−11	10−11	NUM
cana-6069	140	112	3.3782	3.3782	NUM
cana-6069	140	113	×	×	NOUN
cana-6069	140	114	10−11	10−11	NUM
cana-6069	140	115	1.2905	1.2905	NUM
cana-6069	140	116	×	×	NOUN
cana-6069	140	117	10−6	10−6	NUM
cana-6069	140	118	2.9856	2.9856	NUM
cana-6069	140	119	×	×	NOUN
cana-6069	140	120	10−6	10−6	NUM
cana-6069	140	121	(	(	PUNCT
cana-6069	140	122	0.9,0.9,0.9	0.9,0.9,0.9	NOUN
cana-6069	140	123	)	)	PUNCT
cana-6069	140	124	2.3367	2.3367	NUM
cana-6069	140	125	×	×	NOUN
cana-6069	140	126	10−11	10−11	NUM
cana-6069	140	127	6.1231	6.1231	NUM
cana-6069	140	128	×	×	NOUN
cana-6069	140	129	10−10	10−10	NUM
cana-6069	140	130	1.9393	1.9393	NUM
cana-6069	140	131	×	×	NOUN
cana-6069	140	132	10−6	10−6	NUM
cana-6069	140	133	4.4936	4.4936	NUM
cana-6069	140	134	×	×	NOUN
cana-6069	140	135	10−6	10−6	NUM
cana-6069	140	136	(	(	PUNCT
cana-6069	140	137	1.0,1.0,1.0	1.0,1.0,1.0	NUM
cana-6069	140	138	)	)	PUNCT
cana-6069	140	139	3.4658	3.4658	NUM
cana-6069	140	140	×	×	NOUN
cana-6069	140	141	10−11	10−11	NOUN
cana-6069	140	142	2.3253	2.3253	NUM
cana-6069	140	143	×	×	NOUN
cana-6069	140	144	10−9	10−9	NUM
cana-6069	140	145	2.8000	2.8000	NUM
cana-6069	140	146	×	×	NOUN
cana-6069	140	147	10−6	10−6	NUM
cana-6069	140	148	6.4936	6.4936	NUM
cana-6069	140	149	×	×	NOUN
cana-6069	140	150	10−6	10−6	NUM
cana-6069	140	151	.	.	PUNCT
cana-6069	141	1	figure	figure	NOUN
cana-6069	141	2	1	1	NUM
cana-6069	141	3	.	.	PUNCT
cana-6069	141	4	absolute	absolute	ADJ
cana-6069	141	5	error	error	NOUN
cana-6069	141	6	of	of	ADP
cana-6069	141	7	example	example	NOUN
cana-6069	141	8	1	1	NUM
cana-6069	141	9	by	by	ADP
cana-6069	141	10	fc	fc	PROPN
cana-6069	141	11	method	method	NOUN
cana-6069	141	12	,	,	PUNCT
cana-6069	141	13	𝑁	𝑁	PROPN
cana-6069	141	14	=	=	SYM
cana-6069	141	15	2	2	NUM
cana-6069	141	16	,	,	PUNCT
cana-6069	141	17	and	and	CCONJ
cana-6069	141	18	𝑧1	𝑧1	NOUN
cana-6069	141	19	=	=	SYM
cana-6069	141	20	0.5	0.5	NUM
cana-6069	141	21	.	.	PUNCT
cana-6069	142	1	communications	communication	NOUN
cana-6069	142	2	on	on	ADP
cana-6069	142	3	applied	apply	VERB
cana-6069	142	4	nonlinear	nonlinear	ADJ
cana-6069	142	5	analysis	analysis	NOUN
cana-6069	142	6	issn	issn	NOUN
cana-6069	142	7	:	:	PUNCT
cana-6069	142	8	1074	1074	NUM
cana-6069	142	9	-	-	PUNCT
cana-6069	142	10	133x	133x	NUM
cana-6069	142	11	vol	vol	VERB
cana-6069	142	12	32	32	NUM
cana-6069	142	13	no.10s	no.10s	PROPN
cana-6069	142	14	y	y	PROPN
cana-6069	142	15	(	(	PUNCT
cana-6069	142	16	2025	2025	NUM
cana-6069	142	17	)	)	PUNCT
cana-6069	142	18	3315	3315	NUM
cana-6069	142	19	example	example	NOUN
cana-6069	143	1	2	2	NUM
cana-6069	143	2	.	.	X
cana-6069	143	3	consider	consider	VERB
cana-6069	143	4	the	the	DET
cana-6069	143	5	following	follow	VERB
cana-6069	143	6	3d	3d	NOUN
cana-6069	143	7	-	-	PUNCT
cana-6069	143	8	nfie	nfie	PUNCT
cana-6069	144	1	[	[	X
cana-6069	144	2	8	8	NUM
cana-6069	144	3	]	]	X
cana-6069	144	4	:	:	PUNCT
cana-6069	144	5	𝑢(𝑥1	𝑢(𝑥1	ADV
cana-6069	144	6	,	,	PUNCT
cana-6069	144	7	𝑦1	𝑦1	NOUN
cana-6069	144	8	,	,	PUNCT
cana-6069	144	9	𝑧1	𝑧1	NOUN
cana-6069	144	10	)	)	PUNCT
cana-6069	144	11	=	=	SYM
cana-6069	144	12	𝑔(𝑥1	𝑔(𝑥1	X
cana-6069	144	13	,	,	PUNCT
cana-6069	144	14	𝑦1	𝑦1	NOUN
cana-6069	144	15	,	,	PUNCT
cana-6069	144	16	𝑧1	𝑧1	NOUN
cana-6069	144	17	)	)	PUNCT
cana-6069	145	1	+	+	CCONJ
cana-6069	145	2	∫	∫	PROPN
cana-6069	145	3	∫	∫	PROPN
cana-6069	145	4	∫	∫	PROPN
cana-6069	145	5	𝑥1	𝑥1	PROPN
cana-6069	145	6	2	2	NUM
cana-6069	145	7	1	1	NUM
cana-6069	145	8	0	0	NUM
cana-6069	145	9	1	1	NUM
cana-6069	145	10	0	0	NUM
cana-6069	145	11	1	1	NUM
cana-6069	145	12	0	0	NUM
cana-6069	145	13	𝑦1𝑧1𝑡1𝑟1	𝑦1𝑧1𝑡1𝑟1	PROPN
cana-6069	145	14	𝑠𝑖𝑛(𝑠1)𝑢3(𝑠1	𝑠𝑖𝑛(𝑠1)𝑢3(𝑠1	PROPN
cana-6069	145	15	,	,	PUNCT
cana-6069	145	16	𝑡1	𝑡1	NOUN
cana-6069	145	17	,	,	PUNCT
cana-6069	145	18	𝑟1	𝑟1	NOUN
cana-6069	145	19	)	)	PUNCT
cana-6069	145	20	𝑑𝑠1	𝑑𝑠1	PROPN
cana-6069	145	21	𝑑𝑡1	𝑑𝑡1	PROPN
cana-6069	145	22	𝑑𝑟1	𝑑𝑟1	PROPN
cana-6069	145	23	,	,	PUNCT
cana-6069	145	24	(	(	PUNCT
cana-6069	145	25	𝑥1	𝑥1	NOUN
cana-6069	145	26	,	,	PUNCT
cana-6069	145	27	𝑦1	𝑦1	NOUN
cana-6069	145	28	,	,	PUNCT
cana-6069	145	29	𝑧1	𝑧1	NOUN
cana-6069	145	30	)	)	PUNCT
cana-6069	145	31	∈	∈	PROPN
cana-6069	146	1	[	[	X
cana-6069	146	2	0,1]3	0,1]3	NUM
cana-6069	146	3	(	(	PUNCT
cana-6069	146	4	8)	8)	NUM
cana-6069	146	5	where	where	SCONJ
cana-6069	146	6	𝑔(𝑥1	𝑔(𝑥1	NOUN
cana-6069	146	7	,	,	PUNCT
cana-6069	146	8	𝑦1	𝑦1	NOUN
cana-6069	146	9	,	,	PUNCT
cana-6069	146	10	𝑧1	𝑧1	NOUN
cana-6069	146	11	)	)	PUNCT
cana-6069	146	12	=	=	PUNCT
cana-6069	146	13	𝑦1𝑧1𝑐𝑜𝑠(𝑥1	𝑦1𝑧1𝑐𝑜𝑠(𝑥1	PROPN
cana-6069	146	14	)	)	PUNCT
cana-6069	146	15	−	−	PROPN
cana-6069	146	16	1	1	NUM
cana-6069	146	17	100	100	NUM
cana-6069	146	18	𝑥1	𝑥1	NOUN
cana-6069	146	19	2𝑦1𝑧1	2𝑦1𝑧1	NOUN
cana-6069	146	20	−	−	PROPN
cana-6069	146	21	1	1	NUM
cana-6069	146	22	100	100	NUM
cana-6069	146	23	𝑥1	𝑥1	NOUN
cana-6069	146	24	2𝑦1𝑧1𝑐𝑜𝑠4(1	2𝑦1𝑧1𝑐𝑜𝑠4(1	NUM
cana-6069	146	25	)	)	PUNCT
cana-6069	146	26	,	,	PUNCT
cana-6069	146	27	and	and	CCONJ
cana-6069	146	28	the	the	DET
cana-6069	146	29	exact	exact	ADJ
cana-6069	146	30	solution	solution	NOUN
cana-6069	146	31	is	be	AUX
cana-6069	146	32	𝑢(𝑥1	𝑢(𝑥1	ADJ
cana-6069	146	33	,	,	PUNCT
cana-6069	146	34	𝑦1	𝑦1	NOUN
cana-6069	146	35	,	,	PUNCT
cana-6069	146	36	𝑧1	𝑧1	PROPN
cana-6069	146	37	)	)	PUNCT
cana-6069	147	1	=	=	SYM
cana-6069	147	2	𝑦1	𝑦1	NOUN
cana-6069	147	3	+	+	CCONJ
cana-6069	147	4	𝑧1𝑐𝑜𝑠	𝑧1𝑐𝑜𝑠	PROPN
cana-6069	147	5	(	(	PUNCT
cana-6069	147	6	𝑥1	𝑥1	NOUN
cana-6069	147	7	)	)	PUNCT
cana-6069	147	8	.	.	PUNCT
cana-6069	148	1	table	table	NOUN
cana-6069	148	2	(	(	PUNCT
cana-6069	148	3	2	2	NUM
cana-6069	148	4	)	)	PUNCT
cana-6069	148	5	presents	present	VERB
cana-6069	148	6	the	the	DET
cana-6069	148	7	absolute	absolute	ADJ
cana-6069	148	8	error	error	NOUN
cana-6069	148	9	of	of	ADP
cana-6069	148	10	equation	equation	NOUN
cana-6069	148	11	(	(	PUNCT
cana-6069	148	12	8)	8)	NUM
cana-6069	148	13	for	for	ADP
cana-6069	148	14	different	different	ADJ
cana-6069	148	15	values	value	NOUN
cana-6069	148	16	of	of	ADP
cana-6069	148	17	(	(	PUNCT
cana-6069	148	18	𝑥1	𝑥1	NOUN
cana-6069	148	19	,	,	PUNCT
cana-6069	148	20	𝑦1	𝑦1	NOUN
cana-6069	148	21	,	,	PUNCT
cana-6069	148	22	𝑧1	𝑧1	NOUN
cana-6069	148	23	)	)	PUNCT
cana-6069	148	24	,	,	PUNCT
cana-6069	148	25	between	between	ADP
cana-6069	148	26	fibonacci	fibonacci	NOUN
cana-6069	148	27	collocation	collocation	NOUN
cana-6069	148	28	(	(	PUNCT
cana-6069	148	29	fc	fc	INTJ
cana-6069	148	30	)	)	PUNCT
cana-6069	148	31	,	,	PUNCT
cana-6069	148	32	hermite	hermite	PROPN
cana-6069	148	33	–	–	PUNCT
cana-6069	148	34	galerkin	galerkin	PROPN
cana-6069	148	35	(	(	PUNCT
cana-6069	148	36	hg	hg	NOUN
cana-6069	148	37	)	)	PUNCT
cana-6069	148	38	methods	method	NOUN
cana-6069	148	39	with	with	ADP
cana-6069	148	40	n=6	n=6	NOUN
cana-6069	148	41	,	,	PUNCT
cana-6069	148	42	the	the	DET
cana-6069	148	43	successive	successive	ADJ
cana-6069	148	44	approximations	approximation	NOUN
cana-6069	148	45	method	method	NOUN
cana-6069	148	46	at	at	ADP
cana-6069	148	47	n=10	n=10	NOUN
cana-6069	148	48	[	[	X
cana-6069	148	49	8	8	NUM
cana-6069	148	50	]	]	PUNCT
cana-6069	148	51	figures	figure	NOUN
cana-6069	148	52	(	(	PUNCT
cana-6069	148	53	3)–(4	3)–(4	NUM
cana-6069	148	54	)	)	PUNCT
cana-6069	148	55	illustrate	illustrate	VERB
cana-6069	148	56	the	the	DET
cana-6069	148	57	absolute	absolute	ADJ
cana-6069	148	58	errors	error	NOUN
cana-6069	148	59	obtained	obtain	VERB
cana-6069	148	60	by	by	ADP
cana-6069	148	61	both	both	DET
cana-6069	148	62	methods	method	NOUN
cana-6069	148	63	.	.	PUNCT
cana-6069	149	1	table	table	NOUN
cana-6069	149	2	2	2	NUM
cana-6069	149	3	.	.	PUNCT
cana-6069	149	4	numerical	numerical	ADJ
cana-6069	149	5	results	result	NOUN
cana-6069	149	6	for	for	ADP
cana-6069	149	7	example	example	NOUN
cana-6069	149	8	2	2	NUM
cana-6069	149	9	,	,	PUNCT
cana-6069	149	10	𝑧1	𝑧1	NOUN
cana-6069	149	11	=	=	SYM
cana-6069	149	12	0.5	0.5	NUM
cana-6069	149	13	(	(	PUNCT
cana-6069	149	14	𝑥1	𝑥1	NOUN
cana-6069	149	15	,	,	PUNCT
cana-6069	149	16	𝑦1	𝑦1	NOUN
cana-6069	149	17	,	,	PUNCT
cana-6069	149	18	𝑧1	𝑧1	NOUN
cana-6069	149	19	)	)	PUNCT
cana-6069	149	20	fibonacci	fibonacci	NOUN
cana-6069	149	21	collocation	collocation	NOUN
cana-6069	149	22	method	method	NOUN
cana-6069	149	23	𝑁	𝑁	PROPN
cana-6069	149	24	=	=	SYM
cana-6069	149	25	4	4	NUM
cana-6069	149	26	fibonacci	fibonacci	NOUN
cana-6069	149	27	collocation	collocation	NOUN
cana-6069	149	28	method	method	NOUN
cana-6069	149	29	𝑁	𝑁	PROPN
cana-6069	149	30	=	=	SYM
cana-6069	149	31	6	6	NUM
cana-6069	149	32	hermite	hermite	ADJ
cana-6069	149	33	-	-	PUNCT
cana-6069	149	34	galerkin	galerkin	ADJ
cana-6069	149	35	method	method	NOUN
cana-6069	149	36	𝑁	𝑁	PROPN
cana-6069	149	37	=	=	SYM
cana-6069	149	38	4	4	NUM
cana-6069	149	39	hermite	hermite	ADJ
cana-6069	149	40	-	-	PUNCT
cana-6069	149	41	galerkin	galerkin	ADJ
cana-6069	149	42	method	method	NOUN
cana-6069	149	43	𝑁	𝑁	PROPN
cana-6069	149	44	=	=	SYM
cana-6069	149	45	6	6	NUM
cana-6069	149	46	method	method	NOUN
cana-6069	149	47	of	of	ADP
cana-6069	149	48	[	[	X
cana-6069	149	49	8	8	NUM
cana-6069	149	50	]	]	PUNCT
cana-6069	149	51	with	with	ADP
cana-6069	149	52	𝑁	𝑁	PROPN
cana-6069	149	53	=	=	SYM
cana-6069	149	54	10	10	NUM
cana-6069	149	55	(	(	PUNCT
cana-6069	149	56	0,0,0	0,0,0	NOUN
cana-6069	149	57	)	)	PUNCT
cana-6069	149	58	3.3736	3.3736	NUM
cana-6069	149	59	×	×	NOUN
cana-6069	149	60	10−10	10−10	PROPN
cana-6069	149	61	2.5886	2.5886	NUM
cana-6069	149	62	×	×	NOUN
cana-6069	149	63	10−7	10−7	NUM
cana-6069	149	64	2.5387	2.5387	NUM
cana-6069	149	65	×	×	NOUN
cana-6069	149	66	10−2	10−2	NUM
cana-6069	149	67	1.0534	1.0534	NUM
cana-6069	149	68	×	×	NOUN
cana-6069	149	69	10−1	10−1	PROPN
cana-6069	149	70	0	0	NUM
cana-6069	149	71	.	.	PUNCT
cana-6069	150	1	(	(	PUNCT
cana-6069	150	2	0.1,0.1,0.1	0.1,0.1,0.1	NOUN
cana-6069	150	3	)	)	PUNCT
cana-6069	150	4	3.863	3.863	NUM
cana-6069	150	5	×	×	NOUN
cana-6069	150	6	10−7	10−7	NUM
cana-6069	150	7	2.6904	2.6904	NUM
cana-6069	150	8	×	×	NOUN
cana-6069	150	9	10−11	10−11	NUM
cana-6069	150	10	1.367	1.367	NUM
cana-6069	150	11	×	×	NOUN
cana-6069	150	12	10−3	10−3	NUM
cana-6069	150	13	2.822	2.822	NUM
cana-6069	150	14	×	×	NOUN
cana-6069	150	15	10−3	10−3	NUM
cana-6069	150	16	1.9452	1.9452	NUM
cana-6069	150	17	×	×	NOUN
cana-6069	150	18	10−9	10−9	NUM
cana-6069	150	19	(	(	PUNCT
cana-6069	150	20	0.2,0.2,0.2	0.2,0.2,0.2	NUM
cana-6069	150	21	)	)	PUNCT
cana-6069	150	22	2.6101	2.6101	NUM
cana-6069	150	23	×	×	NOUN
cana-6069	150	24	10−9	10−9	NUM
cana-6069	150	25	2.9308	2.9308	NUM
cana-6069	150	26	×	×	NOUN
cana-6069	150	27	10−9	10−9	NUM
cana-6069	150	28	1.5613	1.5613	NUM
cana-6069	150	29	×	×	NOUN
cana-6069	150	30	10−3	10−3	NUM
cana-6069	150	31	6.1957	6.1957	NUM
cana-6069	150	32	×	×	NOUN
cana-6069	150	33	10−3	10−3	NUM
cana-6069	150	34	3.1124	3.1124	NUM
cana-6069	150	35	×	×	NOUN
cana-6069	150	36	10−8	10−8	NUM
cana-6069	150	37	(	(	PUNCT
cana-6069	150	38	0.3,0.3,0.3	0.3,0.3,0.3	NUM
cana-6069	150	39	)	)	PUNCT
cana-6069	150	40	3.9605	3.9605	NUM
cana-6069	150	41	×	×	NOUN
cana-6069	150	42	10−7	10−7	NUM
cana-6069	150	43	1.2532	1.2532	NUM
cana-6069	150	44	×	×	NOUN
cana-6069	150	45	10−8	10−8	NUM
cana-6069	150	46	2.1344	2.1344	NUM
cana-6069	150	47	×	×	NOUN
cana-6069	150	48	10−3	10−3	NUM
cana-6069	150	49	2.6484	2.6484	NUM
cana-6069	150	50	×	×	NOUN
cana-6069	150	51	10−3	10−3	NUM
cana-6069	150	52	1.5756	1.5756	NUM
cana-6069	150	53	×	×	NOUN
cana-6069	150	54	10−7	10−7	NUM
cana-6069	150	55	(	(	PUNCT
cana-6069	150	56	0.4,0.4,0.4	0.4,0.4,0.4	NUM
cana-6069	150	57	)	)	PUNCT
cana-6069	150	58	4.1756	4.1756	NUM
cana-6069	150	59	×	×	NOUN
cana-6069	150	60	10−8	10−8	NUM
cana-6069	150	61	3.9765	3.9765	NUM
cana-6069	150	62	×	×	NOUN
cana-6069	150	63	10−8	10−8	NUM
cana-6069	150	64	1.5719	1.5719	NUM
cana-6069	150	65	×	×	NOUN
cana-6069	150	66	10−2	10−2	NUM
cana-6069	150	67	2.2452	2.2452	NUM
cana-6069	150	68	×	×	NOUN
cana-6069	150	69	10−2	10−2	NUM
cana-6069	150	70	4.9799	4.9799	NUM
cana-6069	150	71	×	×	NOUN
cana-6069	150	72	10−7	10−7	NUM
cana-6069	150	73	(	(	PUNCT
cana-6069	150	74	0.5,0.5,0.5	0.5,0.5,0.5	NUM
cana-6069	150	75	)	)	PUNCT
cana-6069	150	76	6.1579	6.1579	NUM
cana-6069	150	77	×	×	NOUN
cana-6069	150	78	10−7	10−7	NUM
cana-6069	150	79	9.7949	9.7949	NUM
cana-6069	150	80	×	×	NOUN
cana-6069	150	81	10−8	10−8	NUM
cana-6069	150	82	2.4358	2.4358	NUM
cana-6069	150	83	×	×	NOUN
cana-6069	150	84	10−2	10−2	NUM
cana-6069	150	85	4.4104	4.4104	NUM
cana-6069	150	86	×	×	NOUN
cana-6069	150	87	10−2	10−2	NUM
cana-6069	150	88	1.2158	1.2158	NUM
cana-6069	150	89	×	×	NOUN
cana-6069	150	90	10−6	10−6	NUM
cana-6069	150	91	(	(	PUNCT
cana-6069	150	92	0.6,0.6,0.6	0.6,0.6,0.6	NUM
cana-6069	150	93	)	)	PUNCT
cana-6069	150	94	2.1135	2.1135	NUM
cana-6069	150	95	×	×	NOUN
cana-6069	150	96	10−7	10−7	NUM
cana-6069	150	97	2.0196	2.0196	NUM
cana-6069	150	98	×	×	NOUN
cana-6069	150	99	10−7	10−7	NUM
cana-6069	150	100	1.4499	1.4499	NUM
cana-6069	150	101	×	×	NOUN
cana-6069	150	102	10−2	10−2	NUM
cana-6069	150	103	1.369	1.369	NUM
cana-6069	150	104	×	×	NOUN
cana-6069	150	105	10−2	10−2	NUM
cana-6069	150	106	2.521	2.521	NUM
cana-6069	150	107	×	×	NOUN
cana-6069	150	108	10−6	10−6	NUM
cana-6069	150	109	(	(	PUNCT
cana-6069	150	110	0.7,0.7,0.7	0.7,0.7,0.7	NUM
cana-6069	150	111	)	)	PUNCT
cana-6069	150	112	6.6599	6.6599	NUM
cana-6069	150	113	×	×	NOUN
cana-6069	150	114	10−7	10−7	NUM
cana-6069	150	115	3.7446	3.7446	NUM
cana-6069	150	116	×	×	NOUN
cana-6069	150	117	10−7	10−7	NUM
cana-6069	150	118	6.0005	6.0005	NUM
cana-6069	150	119	×	×	NOUN
cana-6069	150	120	10−4	10−4	NUM
cana-6069	150	121	2.5634	2.5634	NUM
cana-6069	150	122	×	×	PROPN
cana-6069	150	123	10−3	10−3	NUM
cana-6069	150	124	4.6706	4.6706	NUM
cana-6069	150	125	×	×	NOUN
cana-6069	150	126	10−6	10−6	NUM
cana-6069	150	127	(	(	PUNCT
cana-6069	150	128	0.8,0.8,0.8	0.8,0.8,0.8	NUM
cana-6069	150	129	)	)	PUNCT
cana-6069	150	130	6.6795	6.6795	NUM
cana-6069	150	131	×	×	NOUN
cana-6069	150	132	10−7	10−7	NUM
cana-6069	150	133	6.4132	6.4132	NUM
cana-6069	150	134	×	×	NOUN
cana-6069	150	135	10−7	10−7	NUM
cana-6069	150	136	3.7639	3.7639	NUM
cana-6069	150	137	×	×	PROPN
cana-6069	150	138	10−3	10−3	NUM
cana-6069	150	139	8.2663	8.2663	NUM
cana-6069	150	140	×	×	PROPN
cana-6069	150	141	10−3	10−3	NUM
cana-6069	150	142	7.9678	7.9678	NUM
cana-6069	150	143	×	×	NOUN
cana-6069	150	144	10−6	10−6	NUM
cana-6069	150	145	(	(	PUNCT
cana-6069	150	146	0.9,0.9,0.9	0.9,0.9,0.9	NOUN
cana-6069	150	147	)	)	PUNCT
cana-6069	150	148	5.3352	5.3352	NUM
cana-6069	150	149	×	×	NOUN
cana-6069	150	150	10−6	10−6	NUM
cana-6069	150	151	1.0188	1.0188	NUM
cana-6069	150	152	×	×	NOUN
cana-6069	150	153	10−6	10−6	NUM
cana-6069	150	154	5.2081	5.2081	NUM
cana-6069	150	155	×	×	NOUN
cana-6069	150	156	10−3	10−3	NUM
cana-6069	150	157	8.7402	8.7402	NUM
cana-6069	150	158	×	×	NOUN
cana-6069	150	159	10−3	10−3	NUM
cana-6069	150	160	1.2763	1.2763	NUM
cana-6069	150	161	×	×	NOUN
cana-6069	150	162	10−5	10−5	NUM
cana-6069	150	163	(	(	PUNCT
cana-6069	150	164	1.0,1.0,1.0	1.0,1.0,1.0	NUM
cana-6069	150	165	)	)	PUNCT
cana-6069	150	166	1.6307	1.6307	NUM
cana-6069	150	167	×	×	NOUN
cana-6069	150	168	10−6	10−6	NUM
cana-6069	150	169	1.5608	1.5608	NUM
cana-6069	150	170	×	×	NOUN
cana-6069	150	171	10−6	10−6	NUM
cana-6069	150	172	7.4386	7.4386	NUM
cana-6069	150	173	×	×	NOUN
cana-6069	150	174	10−3	10−3	NUM
cana-6069	150	175	1.1347	1.1347	NUM
cana-6069	150	176	×	×	NOUN
cana-6069	150	177	10−1	10−1	NUM
cana-6069	150	178	1.9452	1.9452	NUM
cana-6069	150	179	×	×	NOUN
cana-6069	150	180	10−5	10−5	NUM
cana-6069	150	181	figure	figure	NOUN
cana-6069	150	182	2	2	NUM
cana-6069	150	183	.	.	PUNCT
cana-6069	150	184	absolute	absolute	ADJ
cana-6069	150	185	error	error	NOUN
cana-6069	150	186	of	of	ADP
cana-6069	150	187	example	example	NOUN
cana-6069	150	188	1	1	NUM
cana-6069	150	189	by	by	ADP
cana-6069	150	190	hg	hg	PROPN
cana-6069	150	191	method	method	NOUN
cana-6069	150	192	,	,	PUNCT
cana-6069	150	193	𝑁	𝑁	PROPN
cana-6069	150	194	=	=	SYM
cana-6069	150	195	2	2	NUM
cana-6069	150	196	,	,	PUNCT
cana-6069	150	197	and	and	CCONJ
cana-6069	150	198	𝑧1	𝑧1	NOUN
cana-6069	150	199	=	=	SYM
cana-6069	150	200	0.5	0.5	NUM
cana-6069	150	201	.	.	PUNCT
cana-6069	151	1	communications	communication	NOUN
cana-6069	151	2	on	on	ADP
cana-6069	151	3	applied	apply	VERB
cana-6069	151	4	nonlinear	nonlinear	ADJ
cana-6069	151	5	analysis	analysis	NOUN
cana-6069	151	6	issn	issn	NOUN
cana-6069	151	7	:	:	PUNCT
cana-6069	151	8	1074	1074	NUM
cana-6069	151	9	-	-	PUNCT
cana-6069	151	10	133x	133x	NUM
cana-6069	151	11	vol	vol	VERB
cana-6069	151	12	32	32	NUM
cana-6069	151	13	no.10s	no.10s	PROPN
cana-6069	151	14	y	y	PROPN
cana-6069	151	15	(	(	PUNCT
cana-6069	151	16	2025	2025	NUM
cana-6069	151	17	)	)	PUNCT
cana-6069	151	18	3316	3316	NUM
cana-6069	151	19	example	example	NOUN
cana-6069	152	1	3	3	NUM
cana-6069	152	2	.	.	X
cana-6069	152	3	consider	consider	VERB
cana-6069	152	4	the	the	DET
cana-6069	152	5	following	follow	VERB
cana-6069	152	6	3d	3d	NOUN
cana-6069	152	7	-	-	PUNCT
cana-6069	152	8	nfie	nfie	PROPN
cana-6069	153	1	[	[	X
cana-6069	153	2	7	7	NUM
cana-6069	153	3	]	]	X
cana-6069	153	4	:	:	PUNCT
cana-6069	153	5	𝑢(𝑥1	𝑢(𝑥1	ADV
cana-6069	153	6	,	,	PUNCT
cana-6069	153	7	𝑦1	𝑦1	NOUN
cana-6069	153	8	,	,	PUNCT
cana-6069	153	9	𝑧1	𝑧1	NOUN
cana-6069	153	10	)	)	PUNCT
cana-6069	153	11	=	=	SYM
cana-6069	153	12	𝑔(𝑥1	𝑔(𝑥1	X
cana-6069	153	13	,	,	PUNCT
cana-6069	153	14	𝑦1	𝑦1	NOUN
cana-6069	153	15	,	,	PUNCT
cana-6069	153	16	𝑧1	𝑧1	NOUN
cana-6069	153	17	)	)	PUNCT
cana-6069	154	1	+	+	CCONJ
cana-6069	154	2	∫	∫	PROPN
cana-6069	154	3	∫	∫	PROPN
cana-6069	154	4	∫	∫	PROPN
cana-6069	154	5	𝑥1	𝑥1	PROPN
cana-6069	154	6	2	2	NUM
cana-6069	154	7	1	1	NUM
cana-6069	154	8	0	0	NUM
cana-6069	154	9	1	1	NUM
cana-6069	154	10	0	0	NUM
cana-6069	154	11	1	1	NUM
cana-6069	154	12	0	0	NUM
cana-6069	154	13	𝑡1	𝑡1	NOUN
cana-6069	154	14	𝑐𝑜𝑠(𝑧1	𝑐𝑜𝑠(𝑧1	NOUN
cana-6069	154	15	)	)	PUNCT
cana-6069	154	16	𝑠𝑖𝑛(𝑠1)𝑢3(𝑠1	𝑠𝑖𝑛(𝑠1)𝑢3(𝑠1	NOUN
cana-6069	154	17	,	,	PUNCT
cana-6069	154	18	𝑡1	𝑡1	NOUN
cana-6069	154	19	,	,	PUNCT
cana-6069	154	20	𝑟1	𝑟1	NOUN
cana-6069	154	21	)	)	PUNCT
cana-6069	154	22	𝑑𝑠1	𝑑𝑠1	PROPN
cana-6069	154	23	𝑑𝑡1	𝑑𝑡1	PROPN
cana-6069	154	24	𝑑𝑟1	𝑑𝑟1	PROPN
cana-6069	154	25	,	,	PUNCT
cana-6069	154	26	(	(	PUNCT
cana-6069	154	27	𝑥1	𝑥1	NOUN
cana-6069	154	28	,	,	PUNCT
cana-6069	154	29	𝑦1	𝑦1	NOUN
cana-6069	154	30	,	,	PUNCT
cana-6069	154	31	𝑧1	𝑧1	NOUN
cana-6069	154	32	)	)	PUNCT
cana-6069	154	33	∈	∈	PROPN
cana-6069	155	1	[	[	X
cana-6069	155	2	0,1]3	0,1]3	NUM
cana-6069	155	3	,	,	PUNCT
cana-6069	155	4	(	(	PUNCT
cana-6069	155	5	9	9	NUM
cana-6069	155	6	)	)	PUNCT
cana-6069	155	7	where	where	SCONJ
cana-6069	155	8	𝑔(𝑥1	𝑔(𝑥1	NOUN
cana-6069	155	9	,	,	PUNCT
cana-6069	155	10	𝑦1	𝑦1	NOUN
cana-6069	155	11	,	,	PUNCT
cana-6069	155	12	𝑧1	𝑧1	NOUN
cana-6069	155	13	)	)	PUNCT
cana-6069	155	14	=	=	SYM
cana-6069	155	15	𝑦1𝑧1𝑐𝑜𝑠2(𝑥1	𝑦1𝑧1𝑐𝑜𝑠2(𝑥1	X
cana-6069	155	16	)	)	PUNCT
cana-6069	155	17	+	+	CCONJ
cana-6069	155	18	1	1	NUM
cana-6069	155	19	140	140	NUM
cana-6069	155	20	𝑥1	𝑥1	NOUN
cana-6069	155	21	2	2	NUM
cana-6069	155	22	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
cana-6069	155	23	(	(	PUNCT
cana-6069	155	24	𝑧1)(𝑐𝑜𝑠7(1	𝑧1)(𝑐𝑜𝑠7(1	NOUN
cana-6069	155	25	)	)	PUNCT
cana-6069	155	26	−	−	PROPN
cana-6069	156	1	1	1	NUM
cana-6069	156	2	)	)	PUNCT
cana-6069	156	3	,	,	PUNCT
cana-6069	156	4	and	and	CCONJ
cana-6069	156	5	the	the	DET
cana-6069	156	6	exact	exact	ADJ
cana-6069	156	7	solution	solution	NOUN
cana-6069	156	8	is	be	AUX
cana-6069	156	9	𝑢(𝑥1	𝑢(𝑥1	ADJ
cana-6069	156	10	,	,	PUNCT
cana-6069	156	11	𝑦1	𝑦1	NOUN
cana-6069	156	12	,	,	PUNCT
cana-6069	156	13	𝑧1	𝑧1	PROPN
cana-6069	156	14	)	)	PUNCT
cana-6069	157	1	=	=	SYM
cana-6069	157	2	𝑦1	𝑦1	PROPN
cana-6069	157	3	+	+	CCONJ
cana-6069	157	4	𝑧1𝑐𝑜𝑠2(𝑥1	𝑧1𝑐𝑜𝑠2(𝑥1	PROPN
cana-6069	157	5	)	)	PUNCT
cana-6069	157	6	.	.	PUNCT
cana-6069	158	1	table	table	NOUN
cana-6069	158	2	(	(	PUNCT
cana-6069	158	3	3	3	X
cana-6069	158	4	)	)	PUNCT
cana-6069	158	5	shows	show	VERB
cana-6069	158	6	the	the	DET
cana-6069	158	7	comparison	comparison	NOUN
cana-6069	158	8	of	of	ADP
cana-6069	158	9	the	the	DET
cana-6069	158	10	absolute	absolute	ADJ
cana-6069	158	11	error	error	NOUN
cana-6069	158	12	of	of	ADP
cana-6069	158	13	equation	equation	NOUN
cana-6069	158	14	(	(	PUNCT
cana-6069	158	15	9	9	X
cana-6069	158	16	)	)	PUNCT
cana-6069	158	17	using	use	VERB
cana-6069	158	18	hermite	hermite	ADJ
cana-6069	158	19	–	–	PUNCT
cana-6069	158	20	galerkin	galerkin	PROPN
cana-6069	158	21	(	(	PUNCT
cana-6069	158	22	hg	hg	NOUN
cana-6069	158	23	)	)	PUNCT
cana-6069	158	24	and	and	CCONJ
cana-6069	158	25	fibonacci	fibonacci	NOUN
cana-6069	158	26	collocation	collocation	NOUN
cana-6069	158	27	(	(	PUNCT
cana-6069	158	28	fc	fc	X
cana-6069	158	29	)	)	PUNCT
cana-6069	158	30	methods	method	NOUN
cana-6069	158	31	for	for	ADP
cana-6069	158	32	various	various	ADJ
cana-6069	158	33	values	value	NOUN
cana-6069	158	34	of	of	ADP
cana-6069	158	35	(	(	PUNCT
cana-6069	158	36	𝑥1	𝑥1	NOUN
cana-6069	158	37	,	,	PUNCT
cana-6069	158	38	𝑦1	𝑦1	NOUN
cana-6069	158	39	,	,	PUNCT
cana-6069	158	40	𝑧1	𝑧1	PROPN
cana-6069	158	41	)	)	PUNCT
cana-6069	158	42	.	.	PUNCT
cana-6069	159	1	figures	figure	NOUN
cana-6069	159	2	(	(	PUNCT
cana-6069	159	3	5)&(6	5)&(6	NUM
cana-6069	159	4	)	)	PUNCT
cana-6069	159	5	illustrate	illustrate	VERB
cana-6069	159	6	the	the	DET
cana-6069	159	7	absolute	absolute	ADJ
cana-6069	159	8	errors	error	NOUN
cana-6069	159	9	obtained	obtain	VERB
cana-6069	159	10	by	by	ADP
cana-6069	159	11	both	both	DET
cana-6069	159	12	methods	method	NOUN
cana-6069	159	13	.	.	PUNCT
cana-6069	160	1	a	a	DET
cana-6069	160	2	comparison	comparison	NOUN
cana-6069	160	3	with	with	ADP
cana-6069	160	4	the	the	DET
cana-6069	160	5	haar	haar	PROPN
cana-6069	160	6	wavelet	wavelet	NOUN
cana-6069	160	7	method	method	NOUN
cana-6069	160	8	at	at	ADP
cana-6069	160	9	2𝑁	2𝑁	NOUN
cana-6069	160	10	=	=	PUNCT
cana-6069	160	11	32	32	NUM
cana-6069	161	1	[	[	X
cana-6069	161	2	7	7	NUM
cana-6069	161	3	]	]	PUNCT
cana-6069	161	4	.	.	PUNCT
cana-6069	162	1	table	table	NOUN
cana-6069	162	2	3	3	NUM
cana-6069	162	3	.	.	PUNCT
cana-6069	162	4	numerical	numerical	ADJ
cana-6069	162	5	results	result	NOUN
cana-6069	162	6	for	for	ADP
cana-6069	162	7	example	example	NOUN
cana-6069	162	8	3	3	NUM
cana-6069	162	9	,	,	PUNCT
cana-6069	162	10	𝑧1	𝑧1	NOUN
cana-6069	162	11	=	=	SYM
cana-6069	162	12	0.5	0.5	NUM
cana-6069	162	13	(	(	PUNCT
cana-6069	162	14	𝑥1	𝑥1	NOUN
cana-6069	162	15	,	,	PUNCT
cana-6069	162	16	𝑦1	𝑦1	NOUN
cana-6069	162	17	,	,	PUNCT
cana-6069	162	18	𝑧1	𝑧1	NOUN
cana-6069	162	19	)	)	PUNCT
cana-6069	162	20	fibonacci	fibonacci	NOUN
cana-6069	162	21	collocation	collocation	NOUN
cana-6069	162	22	method	method	NOUN
cana-6069	162	23	𝑁	𝑁	PROPN
cana-6069	162	24	=	=	SYM
cana-6069	162	25	6	6	NUM
cana-6069	162	26	hermite	hermite	ADJ
cana-6069	162	27	-	-	PUNCT
cana-6069	162	28	galerkin	galerkin	ADJ
cana-6069	162	29	method	method	NOUN
cana-6069	162	30	𝑁	𝑁	PROPN
cana-6069	162	31	=	=	SYM
cana-6069	162	32	6	6	NUM
cana-6069	162	33	method	method	NOUN
cana-6069	162	34	of	of	ADP
cana-6069	162	35	[	[	X
cana-6069	162	36	7	7	NUM
cana-6069	162	37	]	]	PUNCT
cana-6069	162	38	with	with	ADP
cana-6069	162	39	2𝑁	2𝑁	NOUN
cana-6069	162	40	=	=	SYM
cana-6069	162	41	32	32	NUM
cana-6069	162	42	(	(	PUNCT
cana-6069	162	43	0,0,0	0,0,0	NOUN
cana-6069	162	44	)	)	PUNCT
cana-6069	162	45	6.3588	6.3588	NUM
cana-6069	162	46	×	×	NOUN
cana-6069	162	47	10−7	10−7	NUM
cana-6069	162	48	2.7131	2.7131	NUM
cana-6069	162	49	×	×	NOUN
cana-6069	162	50	10−1	10−1	PROPN
cana-6069	162	51	0	0	NUM
cana-6069	162	52	.	.	PUNCT
cana-6069	163	1	(	(	PUNCT
cana-6069	163	2	0.1,0.1,0.1	0.1,0.1,0.1	NOUN
cana-6069	163	3	)	)	PUNCT
cana-6069	163	4	1.0895	1.0895	NUM
cana-6069	163	5	×	×	NOUN
cana-6069	163	6	10−7	10−7	NUM
cana-6069	163	7	7.1995	7.1995	NUM
cana-6069	163	8	×	×	NOUN
cana-6069	163	9	10−3	10−3	NUM
cana-6069	163	10	1.1244	1.1244	NUM
cana-6069	163	11	×	×	NOUN
cana-6069	163	12	10−8	10−8	NUM
cana-6069	163	13	(	(	PUNCT
cana-6069	163	14	0.2,0.2,0.2	0.2,0.2,0.2	NUM
cana-6069	163	15	)	)	PUNCT
cana-6069	163	16	2.9425	2.9425	NUM
cana-6069	163	17	×	×	NOUN
cana-6069	163	18	10−9	10−9	NUM
cana-6069	163	19	1.5717	1.5717	NUM
cana-6069	163	20	×	×	NOUN
cana-6069	163	21	10−2	10−2	NUM
cana-6069	163	22	4.4304	4.4304	NUM
cana-6069	163	23	×	×	NOUN
cana-6069	163	24	10−8	10−8	NUM
cana-6069	163	25	figure	figure	NOUN
cana-6069	163	26	3	3	NUM
cana-6069	163	27	.	.	PUNCT
cana-6069	163	28	absolute	absolute	ADJ
cana-6069	163	29	error	error	NOUN
cana-6069	163	30	of	of	ADP
cana-6069	163	31	example	example	NOUN
cana-6069	163	32	2	2	NUM
cana-6069	163	33	by	by	ADP
cana-6069	163	34	fc	fc	PROPN
cana-6069	163	35	method	method	NOUN
cana-6069	163	36	,	,	PUNCT
cana-6069	163	37	𝑁	𝑁	PROPN
cana-6069	163	38	=	=	SYM
cana-6069	163	39	6	6	NUM
cana-6069	163	40	,	,	PUNCT
cana-6069	163	41	and	and	CCONJ
cana-6069	163	42	𝑧1	𝑧1	NOUN
cana-6069	163	43	=	=	SYM
cana-6069	163	44	0.5	0.5	NUM
cana-6069	163	45	.	.	PUNCT
cana-6069	163	46	figure	figure	NOUN
cana-6069	163	47	4	4	NUM
cana-6069	163	48	.	.	PUNCT
cana-6069	164	1	absolute	absolute	ADJ
cana-6069	164	2	error	error	NOUN
cana-6069	164	3	of	of	ADP
cana-6069	164	4	example	example	NOUN
cana-6069	164	5	2	2	NUM
cana-6069	164	6	by	by	ADP
cana-6069	164	7	hg	hg	PROPN
cana-6069	164	8	method	method	NOUN
cana-6069	164	9	,	,	PUNCT
cana-6069	164	10	𝑁	𝑁	PROPN
cana-6069	164	11	=	=	SYM
cana-6069	164	12	6	6	NUM
cana-6069	164	13	,	,	PUNCT
cana-6069	164	14	and	and	CCONJ
cana-6069	164	15	𝑧1	𝑧1	NOUN
cana-6069	164	16	=	=	SYM
cana-6069	164	17	0.5	0.5	NUM
cana-6069	164	18	.	.	PUNCT
cana-6069	165	1	communications	communication	NOUN
cana-6069	165	2	on	on	ADP
cana-6069	165	3	applied	apply	VERB
cana-6069	165	4	nonlinear	nonlinear	ADJ
cana-6069	165	5	analysis	analysis	NOUN
cana-6069	165	6	issn	issn	NOUN
cana-6069	165	7	:	:	PUNCT
cana-6069	165	8	1074	1074	NUM
cana-6069	165	9	-	-	PUNCT
cana-6069	165	10	133x	133x	NUM
cana-6069	165	11	vol	vol	VERB
cana-6069	165	12	32	32	NUM
cana-6069	165	13	no.10s	no.10s	PROPN
cana-6069	165	14	y	y	PROPN
cana-6069	165	15	(	(	PUNCT
cana-6069	165	16	2025	2025	NUM
cana-6069	165	17	)	)	PUNCT
cana-6069	165	18	3317	3317	NUM
cana-6069	165	19	(	(	PUNCT
cana-6069	165	20	0.3,0.3,0.3	0.3,0.3,0.3	NUM
cana-6069	165	21	)	)	PUNCT
cana-6069	165	22	5.5898	5.5898	NUM
cana-6069	165	23	×	×	NOUN
cana-6069	165	24	10−8	10−8	NUM
cana-6069	165	25	6.4034	6.4034	NUM
cana-6069	165	26	×	×	NOUN
cana-6069	165	27	10−3	10−3	NUM
cana-6069	165	28	9.7169	9.7169	NUM
cana-6069	165	29	×	×	NOUN
cana-6069	165	30	10−8	10−8	NUM
cana-6069	165	31	(	(	PUNCT
cana-6069	165	32	0.4,0.4,0.4	0.4,0.4,0.4	NUM
cana-6069	165	33	)	)	PUNCT
cana-6069	165	34	6.3907	6.3907	NUM
cana-6069	165	35	×	×	NOUN
cana-6069	165	36	10−8	10−8	NUM
cana-6069	165	37	5.7392	5.7392	NUM
cana-6069	165	38	×	×	NOUN
cana-6069	165	39	10−2	10−2	NUM
cana-6069	165	40	1.6654	1.6654	NUM
cana-6069	165	41	×	×	NOUN
cana-6069	165	42	10−7	10−7	NUM
cana-6069	165	43	(	(	PUNCT
cana-6069	165	44	0.5,0.5,0.5	0.5,0.5,0.5	NUM
cana-6069	165	45	)	)	PUNCT
cana-6069	165	46	1.4021	1.4021	NUM
cana-6069	165	47	×	×	NOUN
cana-6069	165	48	10−8	10−8	NUM
cana-6069	165	49	1.1352	1.1352	NUM
cana-6069	165	50	×	×	NOUN
cana-6069	165	51	10−1	10−1	NUM
cana-6069	165	52	2.4794	2.4794	NUM
cana-6069	165	53	×	×	NOUN
cana-6069	165	54	10−7	10−7	NUM
cana-6069	165	55	(	(	PUNCT
cana-6069	165	56	0.6,0.6,0.6	0.6,0.6,0.6	NUM
cana-6069	165	57	)	)	PUNCT
cana-6069	165	58	1.2999	1.2999	NUM
cana-6069	165	59	×	×	NOUN
cana-6069	165	60	10−7	10−7	NUM
cana-6069	165	61	3.6224	3.6224	NUM
cana-6069	165	62	×	×	NOUN
cana-6069	165	63	10−2	10−2	NUM
cana-6069	165	64	3.3578	3.3578	NUM
cana-6069	165	65	×	×	NOUN
cana-6069	165	66	10−7	10−7	NUM
cana-6069	165	67	(	(	PUNCT
cana-6069	165	68	0.7,0.7,0.7	0.7,0.7,0.7	NUM
cana-6069	165	69	)	)	PUNCT
cana-6069	165	70	1.9685	1.9685	NUM
cana-6069	165	71	×	×	NOUN
cana-6069	165	72	10−7	10−7	NUM
cana-6069	165	73	3.5896	3.5896	NUM
cana-6069	165	74	×	×	NOUN
cana-6069	165	75	10−3	10−3	NUM
cana-6069	165	76	4.2354	4.2354	NUM
cana-6069	165	77	×	×	NOUN
cana-6069	165	78	10−7	10−7	NUM
cana-6069	165	79	(	(	PUNCT
cana-6069	165	80	0.8,0.8,0.8	0.8,0.8,0.8	NUM
cana-6069	165	81	)	)	PUNCT
cana-6069	165	82	4.7301	4.7301	NUM
cana-6069	165	83	×	×	NOUN
cana-6069	165	84	10−8	10−8	NUM
cana-6069	165	85	1.4785	1.4785	NUM
cana-6069	165	86	×	×	NOUN
cana-6069	165	87	10−2	10−2	NUM
cana-6069	165	88	5.0391	5.0391	NUM
cana-6069	165	89	×	×	NOUN
cana-6069	165	90	10−7	10−7	NUM
cana-6069	165	91	(	(	PUNCT
cana-6069	165	92	0.9,0.9,0.9	0.9,0.9,0.9	NUM
cana-6069	165	93	)	)	PUNCT
cana-6069	165	94	8.6554	8.6554	NUM
cana-6069	165	95	×	×	NOUN
cana-6069	165	96	10−7	10−7	NUM
cana-6069	165	97	1.0595	1.0595	NUM
cana-6069	165	98	×	×	NOUN
cana-6069	165	99	10−2	10−2	NUM
cana-6069	165	100	5.6902	5.6902	NUM
cana-6069	165	101	×	×	NOUN
cana-6069	165	102	10−7	10−7	NUM
cana-6069	165	103	(	(	PUNCT
cana-6069	165	104	1.0,1.0,1.0	1.0,1.0,1.0	NUM
cana-6069	165	105	)	)	PUNCT
cana-6069	165	106	2.3595	2.3595	NUM
cana-6069	165	107	×	×	NOUN
cana-6069	165	108	10−7	10−7	NUM
cana-6069	165	109	3.1193	3.1193	NUM
cana-6069	165	110	×	×	NOUN
cana-6069	165	111	10−1	10−1	NUM
cana-6069	165	112	6.1061	6.1061	NUM
cana-6069	165	113	×	×	NOUN
cana-6069	165	114	10−7	10−7	NUM
cana-6069	165	115	5	5	NUM
cana-6069	165	116	.	.	PUNCT
cana-6069	165	117	discussion	discussion	NOUN
cana-6069	165	118	in	in	ADP
cana-6069	165	119	this	this	DET
cana-6069	165	120	article	article	NOUN
cana-6069	165	121	,	,	PUNCT
cana-6069	165	122	we	we	PRON
cana-6069	165	123	have	have	AUX
cana-6069	165	124	obtained	obtain	VERB
cana-6069	165	125	the	the	DET
cana-6069	165	126	numerical	numerical	ADJ
cana-6069	165	127	solutions	solution	NOUN
cana-6069	165	128	of	of	ADP
cana-6069	165	129	3d	3d	NOUN
cana-6069	165	130	-	-	PUNCT
cana-6069	165	131	nfies	nfie	NOUN
cana-6069	165	132	using	use	VERB
cana-6069	165	133	two	two	NUM
cana-6069	165	134	different	different	ADJ
cana-6069	165	135	polynomial	polynomial	ADJ
cana-6069	165	136	-	-	PUNCT
cana-6069	165	137	based	base	VERB
cana-6069	165	138	approaches	approach	NOUN
cana-6069	165	139	:	:	PUNCT
cana-6069	165	140	the	the	DET
cana-6069	165	141	fibonacci	fibonacci	NOUN
cana-6069	165	142	collocation	collocation	NOUN
cana-6069	165	143	method	method	NOUN
cana-6069	165	144	and	and	CCONJ
cana-6069	165	145	the	the	DET
cana-6069	165	146	hermite	hermite	ADJ
cana-6069	165	147	–	–	PUNCT
cana-6069	165	148	galerkin	galerkin	ADJ
cana-6069	165	149	method	method	NOUN
cana-6069	165	150	.	.	PUNCT
cana-6069	166	1	adetailed	adetaile	VERB
cana-6069	166	2	comparison	comparison	NOUN
cana-6069	166	3	between	between	ADP
cana-6069	166	4	the	the	DET
cana-6069	166	5	two	two	NUM
cana-6069	166	6	techniques	technique	NOUN
cana-6069	166	7	has	have	AUX
cana-6069	166	8	been	be	AUX
cana-6069	166	9	carried	carry	VERB
cana-6069	166	10	out	out	ADP
cana-6069	166	11	,	,	PUNCT
cana-6069	166	12	and	and	CCONJ
cana-6069	166	13	the	the	DET
cana-6069	166	14	results	result	NOUN
cana-6069	166	15	demonstrate	demonstrate	VERB
cana-6069	166	16	that	that	SCONJ
cana-6069	166	17	the	the	DET
cana-6069	166	18	fibonacci	fibonacci	NOUN
cana-6069	166	19	approach	approach	NOUN
cana-6069	166	20	provides	provide	VERB
cana-6069	166	21	better	well	ADJ
cana-6069	166	22	accuracy	accuracy	NOUN
cana-6069	166	23	than	than	ADP
cana-6069	166	24	the	the	DET
cana-6069	166	25	hermite	hermite	ADJ
cana-6069	166	26	–	–	PUNCT
cana-6069	166	27	galerkin	galerkin	ADJ
cana-6069	166	28	method	method	NOUN
cana-6069	166	29	.	.	PUNCT
cana-6069	167	1	furthermore	furthermore	ADV
cana-6069	167	2	,	,	PUNCT
cana-6069	167	3	when	when	SCONJ
cana-6069	167	4	compared	compare	VERB
cana-6069	167	5	with	with	ADP
cana-6069	167	6	other	other	ADJ
cana-6069	167	7	methods	method	NOUN
cana-6069	167	8	reported	report	VERB
cana-6069	167	9	in	in	ADP
cana-6069	167	10	the	the	DET
cana-6069	167	11	literature	literature	NOUN
cana-6069	167	12	[	[	X
cana-6069	167	13	7,8	7,8	NUM
cana-6069	167	14	]	]	PUNCT
cana-6069	167	15	.	.	PUNCT
cana-6069	168	1	in	in	ADP
cana-6069	168	2	the	the	DET
cana-6069	168	3	third	third	ADJ
cana-6069	168	4	example	example	NOUN
cana-6069	168	5	,	,	PUNCT
cana-6069	168	6	the	the	DET
cana-6069	168	7	haar	haar	PROPN
cana-6069	168	8	wavelet	wavelet	NOUN
cana-6069	168	9	method	method	NOUN
cana-6069	168	10	reaches	reach	VERB
cana-6069	168	11	its	its	PRON
cana-6069	168	12	maximum	maximum	ADJ
cana-6069	168	13	error	error	NOUN
cana-6069	168	14	of	of	ADP
cana-6069	168	15	1.1244	1.1244	NUM
cana-6069	168	16	×	×	NOUN
cana-6069	168	17	10−8	10−8	NUM
cana-6069	168	18	at	at	ADP
cana-6069	168	19	2n=32	2n=32	PROPN
cana-6069	169	1	[	[	X
cana-6069	169	2	8	8	NUM
cana-6069	169	3	]	]	PUNCT
cana-6069	169	4	,	,	PUNCT
cana-6069	169	5	whereas	whereas	SCONJ
cana-6069	169	6	the	the	DET
cana-6069	169	7	fibonacci	fibonacci	NOUN
cana-6069	169	8	method	method	PROPN
cana-6069	169	9	yields	yield	VERB
cana-6069	169	10	a	a	DET
cana-6069	169	11	significantly	significantly	ADV
cana-6069	169	12	smaller	small	ADJ
cana-6069	169	13	error	error	NOUN
cana-6069	169	14	of	of	ADP
cana-6069	169	15	2.9425	2.9425	NUM
cana-6069	169	16	×	×	NOUN
cana-6069	169	17	10−9	10−9	NUM
cana-6069	169	18	at	at	ADP
cana-6069	169	19	𝑁	𝑁	PROPN
cana-6069	169	20	=	=	SYM
cana-6069	169	21	6	6	NUM
cana-6069	169	22	,	,	PUNCT
cana-6069	169	23	in	in	ADP
cana-6069	169	24	the	the	DET
cana-6069	169	25	second	second	ADJ
cana-6069	169	26	example	example	NOUN
cana-6069	169	27	,	,	PUNCT
cana-6069	169	28	the	the	DET
cana-6069	169	29	fibonacci	fibonacci	NOUN
cana-6069	169	30	method	method	NOUN
cana-6069	169	31	also	also	ADV
cana-6069	169	32	achieves	achieve	VERB
cana-6069	169	33	an	an	DET
cana-6069	169	34	error	error	NOUN
cana-6069	169	35	of	of	ADP
cana-6069	169	36	2.6904	2.6904	NUM
cana-6069	169	37	×	×	NOUN
cana-6069	169	38	10−11	10−11	NUM
cana-6069	169	39	at	at	ADP
cana-6069	169	40	𝑁	𝑁	PROPN
cana-6069	169	41	=	=	SYM
cana-6069	169	42	6	6	NUM
cana-6069	169	43	,	,	PUNCT
cana-6069	169	44	which	which	PRON
cana-6069	169	45	is	be	AUX
cana-6069	169	46	lower	low	ADJ
cana-6069	169	47	than	than	ADP
cana-6069	169	48	that	that	PRON
cana-6069	169	49	obtained	obtain	VERB
cana-6069	169	50	by	by	ADP
cana-6069	169	51	the	the	DET
cana-6069	169	52	successive	successive	ADJ
cana-6069	169	53	approximations	approximation	NOUN
cana-6069	169	54	method	method	NOUN
cana-6069	169	55	,	,	PUNCT
cana-6069	169	56	which	which	PRON
cana-6069	169	57	records	record	VERB
cana-6069	169	58	an	an	DET
cana-6069	169	59	error	error	NOUN
cana-6069	169	60	of	of	ADP
cana-6069	169	61	1.9452	1.9452	NUM
cana-6069	169	62	×	×	NOUN
cana-6069	169	63	10−9	10−9	NUM
cana-6069	169	64	at	at	ADP
cana-6069	169	65	𝑁	𝑁	PROPN
cana-6069	169	66	=	=	SYM
cana-6069	169	67	10	10	NUM
cana-6069	169	68	.	.	PUNCT
cana-6069	170	1	in	in	ADP
cana-6069	170	2	the	the	DET
cana-6069	170	3	first	first	ADJ
cana-6069	170	4	example	example	NOUN
cana-6069	170	5	,	,	PUNCT
cana-6069	170	6	the	the	DET
cana-6069	170	7	fibonacci	fibonacci	NOUN
cana-6069	170	8	method	method	NOUN
cana-6069	170	9	outperforms	outperform	VERB
cana-6069	170	10	both	both	DET
cana-6069	170	11	methods	method	NOUN
cana-6069	170	12	,	,	PUNCT
cana-6069	170	13	achieving	achieve	VERB
cana-6069	170	14	the	the	DET
cana-6069	170	15	smallest	small	ADJ
cana-6069	170	16	error	error	NOUN
cana-6069	170	17	3.7868	3.7868	NUM
cana-6069	170	18	×	×	NOUN
cana-6069	170	19	10−13	10−13	NOUN
cana-6069	170	20	at	at	ADP
cana-6069	170	21	𝑁	𝑁	PROPN
cana-6069	170	22	=	=	SYM
cana-6069	170	23	2	2	NUM
cana-6069	170	24	.	.	PUNCT
cana-6069	171	1	the	the	DET
cana-6069	171	2	fibonacci	fibonacci	NOUN
cana-6069	171	3	method	method	NOUN
cana-6069	171	4	still	still	ADV
cana-6069	171	5	outperforms	outperform	VERB
cana-6069	171	6	them	they	PRON
cana-6069	171	7	,	,	PUNCT
cana-6069	171	8	achieving	achieve	VERB
cana-6069	171	9	higher	high	ADJ
cana-6069	171	10	accuracy	accuracy	NOUN
cana-6069	171	11	with	with	ADP
cana-6069	171	12	a	a	DET
cana-6069	171	13	smaller	small	ADJ
cana-6069	171	14	number	number	NOUN
cana-6069	171	15	of	of	ADP
cana-6069	171	16	basis	basis	NOUN
cana-6069	171	17	functions	function	NOUN
cana-6069	171	18	𝑁.	𝑁.	PROPN
cana-6069	171	19	this	this	DET
cana-6069	171	20	highlights	highlight	NOUN
cana-6069	171	21	the	the	DET
cana-6069	171	22	efficiency	efficiency	NOUN
cana-6069	171	23	and	and	CCONJ
cana-6069	171	24	effectiveness	effectiveness	NOUN
cana-6069	171	25	of	of	ADP
cana-6069	171	26	the	the	DET
cana-6069	171	27	fibonacci	fibonacci	NOUN
cana-6069	171	28	collocation	collocation	NOUN
cana-6069	171	29	scheme	scheme	NOUN
cana-6069	171	30	in	in	ADP
cana-6069	171	31	solving	solve	VERB
cana-6069	171	32	such	such	ADJ
cana-6069	171	33	classes	class	NOUN
cana-6069	171	34	of	of	ADP
cana-6069	171	35	integral	integral	ADJ
cana-6069	171	36	equations	equation	NOUN
cana-6069	171	37	.	.	PUNCT
cana-6069	172	1	all	all	DET
cana-6069	172	2	computations	computation	NOUN
cana-6069	172	3	and	and	CCONJ
cana-6069	172	4	implementations	implementation	NOUN
cana-6069	172	5	are	be	AUX
cana-6069	172	6	performed	perform	VERB
cana-6069	172	7	using	use	VERB
cana-6069	172	8	matlab	matlab	PROPN
cana-6069	172	9	.	.	PUNCT
cana-6069	173	1	references	reference	NOUN
cana-6069	173	2	[	[	X
cana-6069	173	3	1	1	NUM
cana-6069	173	4	]	]	PUNCT
cana-6069	173	5	basseem	basseem	NOUN
cana-6069	173	6	,	,	PUNCT
cana-6069	173	7	b.	b.	PROPN
cana-6069	173	8	(	(	PUNCT
cana-6069	173	9	2015	2015	NUM
cana-6069	173	10	)	)	PUNCT
cana-6069	173	11	.	.	PUNCT
cana-6069	174	1	numerical	numerical	ADJ
cana-6069	174	2	solution	solution	NOUN
cana-6069	174	3	of	of	ADP
cana-6069	174	4	three	three	NUM
cana-6069	174	5	-	-	PUNCT
cana-6069	174	6	dimensional	dimensional	ADJ
cana-6069	174	7	nonlinear	nonlinear	ADJ
cana-6069	174	8	integral	integral	ADJ
cana-6069	174	9	equations	equation	NOUN
cana-6069	174	10	using	use	VERB
cana-6069	174	11	degenerate	degenerate	ADJ
cana-6069	174	12	kernel	kernel	NOUN
cana-6069	174	13	technique	technique	NOUN
cana-6069	174	14	.	.	PUNCT
cana-6069	175	1	university	university	NOUN
cana-6069	175	2	journal	journal	NOUN
cana-6069	175	3	of	of	ADP
cana-6069	175	4	integral	integral	ADJ
cana-6069	175	5	equations	equation	NOUN
cana-6069	175	6	,	,	PUNCT
cana-6069	175	7	3	3	NUM
cana-6069	175	8	,	,	PUNCT
cana-6069	175	9	6–15	6–15	PROPN
cana-6069	175	10	.	.	PUNCT
cana-6069	176	1	figure	figure	NOUN
cana-6069	176	2	5	5	NUM
cana-6069	176	3	.	.	PUNCT
cana-6069	177	1	absolute	absolute	ADJ
cana-6069	177	2	error	error	NOUN
cana-6069	177	3	of	of	ADP
cana-6069	177	4	example	example	NOUN
cana-6069	177	5	3	3	NUM
cana-6069	177	6	by	by	ADP
cana-6069	177	7	fc	fc	PROPN
cana-6069	177	8	method	method	NOUN
cana-6069	177	9	,	,	PUNCT
cana-6069	177	10	𝑁	𝑁	PROPN
cana-6069	177	11	=	=	SYM
cana-6069	177	12	6	6	NUM
cana-6069	177	13	,	,	PUNCT
cana-6069	177	14	and	and	CCONJ
cana-6069	177	15	𝑧1	𝑧1	NOUN
cana-6069	177	16	=	=	SYM
cana-6069	177	17	0.5	0.5	NUM
cana-6069	177	18	.	.	PUNCT
cana-6069	177	19	figure	figure	NOUN
cana-6069	177	20	6	6	NUM
cana-6069	177	21	.	.	PUNCT
cana-6069	178	1	absolute	absolute	ADJ
cana-6069	178	2	error	error	NOUN
cana-6069	178	3	of	of	ADP
cana-6069	178	4	example	example	NOUN
cana-6069	178	5	3	3	NUM
cana-6069	178	6	by	by	ADP
cana-6069	178	7	hg	hg	PROPN
cana-6069	178	8	method	method	NOUN
cana-6069	178	9	,	,	PUNCT
cana-6069	178	10	𝑁	𝑁	PROPN
cana-6069	178	11	=	=	SYM
cana-6069	178	12	6	6	NUM
cana-6069	178	13	,	,	PUNCT
cana-6069	178	14	and	and	CCONJ
cana-6069	178	15	𝑧1	𝑧1	NOUN
cana-6069	178	16	=	=	SYM
cana-6069	178	17	0.5	0.5	NUM
cana-6069	178	18	.	.	PUNCT
cana-6069	179	1	communications	communication	NOUN
cana-6069	179	2	on	on	ADP
cana-6069	179	3	applied	apply	VERB
cana-6069	179	4	nonlinear	nonlinear	ADJ
cana-6069	179	5	analysis	analysis	NOUN
cana-6069	179	6	issn	issn	NOUN
cana-6069	179	7	:	:	PUNCT
cana-6069	179	8	1074	1074	NUM
cana-6069	179	9	-	-	PUNCT
cana-6069	179	10	133x	133x	NUM
cana-6069	179	11	vol	vol	VERB
cana-6069	179	12	32	32	NUM
cana-6069	179	13	no.10s	no.10s	PROPN
cana-6069	179	14	y	y	PROPN
cana-6069	179	15	(	(	PUNCT
cana-6069	179	16	2025	2025	NUM
cana-6069	179	17	)	)	PUNCT
cana-6069	179	18	3318	3318	NUM
cana-6069	180	1	[	[	X
cana-6069	180	2	2	2	NUM
cana-6069	180	3	]	]	X
cana-6069	180	4	el	el	PROPN
cana-6069	180	5	-	-	PUNCT
cana-6069	180	6	mikkawy	mikkawy	PROPN
cana-6069	180	7	,	,	PUNCT
cana-6069	180	8	m.	m.	NOUN
cana-6069	180	9	,	,	PUNCT
cana-6069	180	10	&	&	CCONJ
cana-6069	180	11	sogabe	sogabe	PROPN
cana-6069	180	12	,	,	PUNCT
cana-6069	180	13	t.	t.	PROPN
cana-6069	180	14	(	(	PUNCT
cana-6069	180	15	2010	2010	NUM
cana-6069	180	16	)	)	PUNCT
cana-6069	180	17	.	.	PUNCT
cana-6069	181	1	a	a	DET
cana-6069	181	2	new	new	ADJ
cana-6069	181	3	family	family	NOUN
cana-6069	181	4	of	of	ADP
cana-6069	181	5	k	k	PROPN
cana-6069	181	6	-	-	PUNCT
cana-6069	181	7	fibonacci	fibonacci	NOUN
cana-6069	181	8	numbers	number	NOUN
cana-6069	181	9	.	.	PUNCT
cana-6069	182	1	applied	apply	VERB
cana-6069	182	2	mathematics	mathematic	NOUN
cana-6069	182	3	and	and	CCONJ
cana-6069	182	4	computation	computation	NOUN
cana-6069	182	5	,	,	PUNCT
cana-6069	182	6	215(12	215(12	NUM
cana-6069	182	7	)	)	PUNCT
cana-6069	182	8	,	,	PUNCT
cana-6069	182	9	4456–4461	4456–4461	NUM
cana-6069	182	10	.	.	PUNCT
cana-6069	183	1	[	[	X
cana-6069	183	2	3	3	NUM
cana-6069	183	3	]	]	X
cana-6069	183	4	falcon	falcon	PROPN
cana-6069	183	5	,	,	PUNCT
cana-6069	183	6	s.	s.	PROPN
cana-6069	183	7	,	,	PUNCT
cana-6069	183	8	&	&	CCONJ
cana-6069	183	9	plaza	plaza	PROPN
cana-6069	183	10	,	,	PUNCT
cana-6069	183	11	´	´	PROPN
cana-6069	183	12	a.	a.	NOUN
cana-6069	183	13	(	(	PUNCT
cana-6069	183	14	2007	2007	NUM
cana-6069	183	15	)	)	PUNCT
cana-6069	183	16	.	.	PUNCT
cana-6069	184	1	the	the	DET
cana-6069	184	2	k	k	PROPN
cana-6069	184	3	-	-	PUNCT
cana-6069	184	4	fibonacci	fibonacci	NOUN
cana-6069	184	5	sequence	sequence	NOUN
cana-6069	184	6	and	and	CCONJ
cana-6069	184	7	the	the	DET
cana-6069	184	8	pascal	pascal	ADJ
cana-6069	184	9	2	2	NUM
cana-6069	184	10	-	-	PUNCT
cana-6069	184	11	triangle	triangle	NOUN
cana-6069	184	12	.	.	PUNCT
cana-6069	185	1	chaos	chaos	NOUN
cana-6069	185	2	,	,	PUNCT
cana-6069	185	3	solitons	soliton	NOUN
cana-6069	185	4	&	&	CCONJ
cana-6069	185	5	fractals	fractal	NOUN
cana-6069	185	6	,	,	PUNCT
cana-6069	185	7	33(1	33(1	NUM
cana-6069	185	8	)	)	PUNCT
cana-6069	185	9	,	,	PUNCT
cana-6069	185	10	38–49	38–49	NUM
cana-6069	185	11	.	.	PUNCT
cana-6069	186	1	[	[	X
cana-6069	186	2	4	4	NUM
cana-6069	186	3	]	]	X
cana-6069	186	4	falcon	falcon	PROPN
cana-6069	186	5	,	,	PUNCT
cana-6069	186	6	s.	s.	PROPN
cana-6069	186	7	,	,	PUNCT
cana-6069	186	8	&	&	CCONJ
cana-6069	186	9	plaza	plaza	PROPN
cana-6069	186	10	,	,	PUNCT
cana-6069	186	11	a.	a.	NOUN
cana-6069	186	12	(	(	PUNCT
cana-6069	186	13	2009	2009	NUM
cana-6069	186	14	)	)	PUNCT
cana-6069	186	15	.	.	PUNCT
cana-6069	187	1	on	on	ADP
cana-6069	187	2	k	k	PROPN
cana-6069	187	3	-	-	PUNCT
cana-6069	187	4	fibonacci	fibonacci	NOUN
cana-6069	187	5	sequences	sequence	NOUN
cana-6069	187	6	and	and	CCONJ
cana-6069	187	7	polynomials	polynomial	NOUN
cana-6069	187	8	and	and	CCONJ
cana-6069	187	9	their	their	PRON
cana-6069	187	10	derivatives	derivative	NOUN
cana-6069	187	11	.	.	PUNCT
cana-6069	188	1	chaos	chaos	NOUN
cana-6069	188	2	,	,	PUNCT
cana-6069	188	3	solitons	soliton	NOUN
cana-6069	188	4	&	&	CCONJ
cana-6069	188	5	fractals	fractal	NOUN
cana-6069	188	6	,	,	PUNCT
cana-6069	188	7	39(3	39(3	NUM
cana-6069	188	8	)	)	PUNCT
cana-6069	188	9	,	,	PUNCT
cana-6069	188	10	1005–1019	1005–1019	NUM
cana-6069	188	11	.	.	PUNCT
cana-6069	189	1	[	[	X
cana-6069	189	2	5	5	NUM
cana-6069	189	3	]	]	X
cana-6069	189	4	grimm	grimm	NOUN
cana-6069	189	5	,	,	PUNCT
cana-6069	189	6	r.	r.	PROPN
cana-6069	189	7	e.	e.	PROPN
cana-6069	189	8	(	(	PUNCT
cana-6069	189	9	1973	1973	NUM
cana-6069	189	10	)	)	PUNCT
cana-6069	189	11	.	.	PUNCT
cana-6069	190	1	the	the	DET
cana-6069	190	2	autobiography	autobiography	NOUN
cana-6069	190	3	of	of	ADP
cana-6069	190	4	leonardo	leonardo	PROPN
cana-6069	190	5	pisano	pisano	PROPN
cana-6069	190	6	.	.	PUNCT
cana-6069	191	1	the	the	DET
cana-6069	191	2	fibonacci	fibonacci	PROPN
cana-6069	191	3	quarterly	quarterly	ADV
cana-6069	191	4	,	,	PUNCT
cana-6069	191	5	11(1	11(1	NUM
cana-6069	191	6	)	)	PUNCT
cana-6069	191	7	,	,	PUNCT
cana-6069	191	8	99–104	99–104	PROPN
cana-6069	191	9	.	.	PUNCT
cana-6069	192	1	[	[	X
cana-6069	192	2	6	6	NUM
cana-6069	192	3	]	]	X
cana-6069	192	4	hursan	hursan	PROPN
cana-6069	192	5	,	,	PUNCT
cana-6069	192	6	g.	g.	PROPN
cana-6069	192	7	,	,	PUNCT
cana-6069	192	8	zhdanov	zhdanov	PROPN
cana-6069	192	9	,	,	PUNCT
cana-6069	192	10	m.	m.	PROPN
cana-6069	192	11	s.	s.	PROPN
cana-6069	192	12	(	(	PUNCT
cana-6069	192	13	2002	2002	NUM
cana-6069	192	14	)	)	PUNCT
cana-6069	192	15	.	.	PUNCT
cana-6069	193	1	contraction	contraction	NOUN
cana-6069	193	2	integral	integral	ADJ
cana-6069	193	3	equation	equation	NOUN
cana-6069	193	4	method	method	NOUN
cana-6069	193	5	in	in	ADP
cana-6069	193	6	three	three	NUM
cana-6069	193	7	-	-	PUNCT
cana-6069	193	8	dimensional	dimensional	ADJ
cana-6069	193	9	electromagnetic	electromagnetic	ADJ
cana-6069	193	10	modeling	modeling	NOUN
cana-6069	193	11	.	.	PUNCT
cana-6069	194	1	radio	radio	NOUN
cana-6069	194	2	science	science	NOUN
cana-6069	194	3	,	,	PUNCT
cana-6069	194	4	37(6	37(6	NUM
cana-6069	194	5	)	)	PUNCT
cana-6069	194	6	,	,	PUNCT
cana-6069	194	7	1	1	NUM
cana-6069	194	8	-	-	SYM
cana-6069	194	9	13	13	NUM
cana-6069	194	10	.	.	PUNCT
cana-6069	195	1	[	[	X
cana-6069	195	2	7	7	NUM
cana-6069	195	3	]	]	SYM
cana-6069	195	4	kazemi	kazemi	PROPN
cana-6069	195	5	,	,	PUNCT
cana-6069	195	6	m.	m.	NOUN
cana-6069	195	7	,	,	PUNCT
cana-6069	195	8	torkashvand	torkashvand	NOUN
cana-6069	195	9	,	,	PUNCT
cana-6069	195	10	v.	v.	PROPN
cana-6069	195	11	,	,	PUNCT
cana-6069	195	12	ezzati	ezzati	PROPN
cana-6069	195	13	,	,	PUNCT
cana-6069	195	14	r.	r.	PROPN
cana-6069	195	15	(	(	PUNCT
cana-6069	195	16	2021	2021	NUM
cana-6069	195	17	)	)	PUNCT
cana-6069	195	18	.	.	PUNCT
cana-6069	196	1	a	a	DET
cana-6069	196	2	new	new	ADJ
cana-6069	196	3	method	method	NOUN
cana-6069	196	4	for	for	ADP
cana-6069	196	5	solving	solve	VERB
cana-6069	196	6	three	three	NUM
cana-6069	196	7	-	-	PUNCT
cana-6069	196	8	dimensional	dimensional	ADJ
cana-6069	196	9	nonlinear	nonlinear	ADJ
cana-6069	196	10	fredholm	fredholm	ADJ
cana-6069	196	11	integral	integral	ADJ
cana-6069	196	12	equations	equation	NOUN
cana-6069	196	13	by	by	ADP
cana-6069	196	14	haar	haar	PROPN
cana-6069	196	15	wavelet	wavelet	PROPN
cana-6069	196	16	.	.	PUNCT
cana-6069	197	1	international	international	ADJ
cana-6069	197	2	journal	journal	PROPN
cana-6069	197	3	of	of	ADP
cana-6069	197	4	nonlinear	nonlinear	ADJ
cana-6069	197	5	analysis	analysis	NOUN
cana-6069	197	6	and	and	CCONJ
cana-6069	197	7	applications	application	NOUN
cana-6069	197	8	,	,	PUNCT
cana-6069	197	9	12(2	12(2	NUM
cana-6069	197	10	)	)	PUNCT
cana-6069	197	11	,	,	PUNCT
cana-6069	197	12	115	115	NUM
cana-6069	197	13	-	-	SYM
cana-6069	197	14	133	133	NUM
cana-6069	197	15	.	.	PUNCT
cana-6069	198	1	[	[	X
cana-6069	198	2	8	8	NUM
cana-6069	198	3	]	]	X
cana-6069	198	4	kazemi	kazemi	PROPN
cana-6069	198	5	,	,	PUNCT
cana-6069	198	6	m.	m.	NOUN
cana-6069	198	7	(	(	PUNCT
cana-6069	198	8	2021	2021	NUM
cana-6069	198	9	)	)	PUNCT
cana-6069	198	10	.	.	PUNCT
cana-6069	199	1	approximating	approximate	VERB
cana-6069	199	2	the	the	DET
cana-6069	199	3	solution	solution	NOUN
cana-6069	199	4	of	of	ADP
cana-6069	199	5	three	three	NUM
cana-6069	199	6	-	-	PUNCT
cana-6069	199	7	dimensional	dimensional	ADJ
cana-6069	199	8	nonlinear	nonlinear	ADJ
cana-6069	199	9	fredholm	fredholm	ADJ
cana-6069	199	10	integral	integral	ADJ
cana-6069	199	11	equations	equation	NOUN
cana-6069	199	12	.	.	PUNCT
cana-6069	200	1	journal	journal	NOUN
cana-6069	200	2	of	of	ADP
cana-6069	200	3	computational	computational	ADJ
cana-6069	200	4	and	and	CCONJ
cana-6069	200	5	applied	applied	ADJ
cana-6069	200	6	mathematics	mathematic	NOUN
cana-6069	200	7	,	,	PUNCT
cana-6069	200	8	395	395	NUM
cana-6069	200	9	,	,	PUNCT
cana-6069	200	10	113590	113590	NUM
cana-6069	200	11	.	.	PUNCT
cana-6069	201	1	[	[	X
cana-6069	201	2	9	9	NUM
cana-6069	201	3	]	]	SYM
cana-6069	201	4	mahdy	mahdy	NOUN
cana-6069	201	5	,	,	PUNCT
cana-6069	201	6	a.	a.	NOUN
cana-6069	201	7	m.	m.	NOUN
cana-6069	201	8	,	,	PUNCT
cana-6069	201	9	nagdy	nagdy	NOUN
cana-6069	201	10	,	,	PUNCT
cana-6069	201	11	a.	a.	PROPN
cana-6069	201	12	s.	s.	PROPN
cana-6069	201	13	,	,	PUNCT
cana-6069	201	14	hashem	hashem	PROPN
cana-6069	201	15	,	,	PUNCT
cana-6069	201	16	k.	k.	PROPN
cana-6069	201	17	m.	m.	PROPN
cana-6069	201	18	,	,	PUNCT
cana-6069	201	19	mohamed	mohamed	PROPN
cana-6069	201	20	,	,	PUNCT
cana-6069	201	21	d.	d.	PROPN
cana-6069	201	22	s.	s.	PROPN
cana-6069	201	23	(	(	PUNCT
cana-6069	201	24	2023	2023	NUM
cana-6069	201	25	)	)	PUNCT
cana-6069	201	26	.	.	PUNCT
cana-6069	202	1	a	a	DET
cana-6069	202	2	computational	computational	ADJ
cana-6069	202	3	technique	technique	NOUN
cana-6069	202	4	for	for	ADP
cana-6069	202	5	solving	solve	VERB
cana-6069	202	6	three	three	NUM
cana-6069	202	7	dimensional	dimensional	ADJ
cana-6069	202	8	mixed	mixed	ADJ
cana-6069	202	9	volterra	volterra	NOUN
cana-6069	202	10	–	–	PUNCT
cana-6069	202	11	fredholm	fredholm	ADJ
cana-6069	202	12	integral	integral	ADJ
cana-6069	202	13	equations	equation	NOUN
cana-6069	202	14	.	.	PUNCT
cana-6069	203	1	fractal	fractal	PROPN
cana-6069	203	2	and	and	CCONJ
cana-6069	203	3	fractional	fractional	ADJ
cana-6069	203	4	,	,	PUNCT
cana-6069	203	5	7(2	7(2	NUM
cana-6069	203	6	)	)	PUNCT
cana-6069	203	7	,	,	PUNCT
cana-6069	203	8	196	196	NUM
cana-6069	203	9	.	.	PUNCT
cana-6069	204	1	[	[	X
cana-6069	204	2	10	10	NUM
cana-6069	204	3	]	]	X
cana-6069	204	4	maleknejad	maleknejad	PROPN
cana-6069	204	5	,	,	PUNCT
cana-6069	204	6	k.	k.	PROPN
cana-6069	204	7	,	,	PUNCT
cana-6069	204	8	almasieh	almasieh	PROPN
cana-6069	204	9	,	,	PUNCT
cana-6069	204	10	h.	h.	PROPN
cana-6069	204	11	,	,	PUNCT
cana-6069	204	12	&	&	CCONJ
cana-6069	204	13	hashemizadeh	hashemizadeh	PROPN
cana-6069	204	14	,	,	PUNCT
cana-6069	204	15	e.	e.	PROPN
cana-6069	204	16	(	(	PUNCT
cana-6069	204	17	2012	2012	NUM
cana-6069	204	18	)	)	PUNCT
cana-6069	204	19	.	.	PUNCT
cana-6069	205	1	bernstein	bernstein	PROPN
cana-6069	205	2	polynomials	polynomial	VERB
cana-6069	205	3	for	for	ADP
cana-6069	205	4	solving	solve	VERB
cana-6069	205	5	a	a	DET
cana-6069	205	6	class	class	NOUN
cana-6069	205	7	of	of	ADP
cana-6069	205	8	nonlinear	nonlinear	ADJ
cana-6069	205	9	two	two	NUM
cana-6069	205	10	-	-	PUNCT
cana-6069	205	11	dimensional	dimensional	ADJ
cana-6069	205	12	fredholm	fredholm	ADJ
cana-6069	205	13	integral	integral	ADJ
cana-6069	205	14	equations	equation	NOUN
cana-6069	205	15	.	.	PUNCT
cana-6069	206	1	international	international	ADJ
cana-6069	206	2	journal	journal	PROPN
cana-6069	206	3	of	of	ADP
cana-6069	206	4	nonlinear	nonlinear	ADJ
cana-6069	206	5	analysis	analysis	NOUN
cana-6069	206	6	and	and	CCONJ
cana-6069	206	7	applications	application	NOUN
cana-6069	206	8	,	,	PUNCT
cana-6069	206	9	12(2	12(2	NUM
cana-6069	206	10	)	)	PUNCT
cana-6069	206	11	,	,	PUNCT
cana-6069	206	12	115–133	115–133	NUM
cana-6069	206	13	.	.	PUNCT
cana-6069	207	1	[	[	X
cana-6069	207	2	11	11	NUM
cana-6069	207	3	]	]	X
cana-6069	207	4	ogola	ogola	PROPN
cana-6069	207	5	,	,	PUNCT
cana-6069	207	6	j.	j.	PROPN
cana-6069	207	7	a.	a.	PROPN
cana-6069	207	8	(	(	PUNCT
cana-6069	207	9	2020	2020	NUM
cana-6069	207	10	)	)	PUNCT
cana-6069	207	11	.	.	PUNCT
cana-6069	208	1	numerical	numerical	ADJ
cana-6069	208	2	solutions	solution	NOUN
cana-6069	208	3	of	of	ADP
cana-6069	208	4	fredholm	fredholm	ADJ
cana-6069	208	5	integral	integral	ADJ
cana-6069	208	6	equations	equation	NOUN
cana-6069	208	7	of	of	ADP
cana-6069	208	8	the	the	DET
cana-6069	208	9	second	second	ADJ
cana-6069	208	10	kind	kind	NOUN
cana-6069	208	11	.	.	PUNCT
cana-6069	209	1	research	research	NOUN
cana-6069	209	2	report	report	NOUN
cana-6069	209	3	in	in	ADP
cana-6069	209	4	math	math	NOUN
cana-6069	209	5	ematics	ematic	NOUN
cana-6069	209	6	,	,	PUNCT
cana-6069	209	7	no	no	INTJ
cana-6069	209	8	.	.	NOUN
cana-6069	209	9	30	30	NUM
cana-6069	209	10	,	,	PUNCT
cana-6069	209	11	university	university	NOUN
cana-6069	209	12	of	of	ADP
cana-6069	209	13	nairobi	nairobi	PROPN
cana-6069	209	14	.	.	PUNCT
cana-6069	210	1	[	[	X
cana-6069	210	2	12	12	NUM
cana-6069	210	3	]	]	X
cana-6069	210	4	rahman	rahman	PROPN
cana-6069	210	5	,	,	PUNCT
cana-6069	210	6	m.	m.	NOUN
cana-6069	210	7	(	(	PUNCT
cana-6069	210	8	2007	2007	NUM
cana-6069	210	9	)	)	PUNCT
cana-6069	210	10	.	.	PUNCT
cana-6069	211	1	integral	integral	ADJ
cana-6069	211	2	equations	equation	NOUN
cana-6069	211	3	and	and	CCONJ
cana-6069	211	4	their	their	PRON
cana-6069	211	5	applications	application	NOUN
cana-6069	211	6	.	.	PUNCT
cana-6069	212	1	wit	wit	ADJ
cana-6069	212	2	press	press	NOUN
cana-6069	212	3	.	.	PUNCT
cana-6069	213	1	[	[	X
cana-6069	213	2	13	13	NUM
cana-6069	213	3	]	]	X
cana-6069	213	4	rahman	rahman	PROPN
cana-6069	213	5	,	,	PUNCT
cana-6069	213	6	m.	m.	NOUN
cana-6069	213	7	m.	m.	NOUN
cana-6069	213	8	(	(	PUNCT
cana-6069	213	9	2013	2013	NUM
cana-6069	213	10	,	,	PUNCT
cana-6069	213	11	july	july	PROPN
cana-6069	213	12	)	)	PUNCT
cana-6069	213	13	.	.	PUNCT
cana-6069	214	1	numerical	numerical	ADJ
cana-6069	214	2	solutions	solution	NOUN
cana-6069	214	3	of	of	ADP
cana-6069	214	4	volterra	volterra	PROPN
cana-6069	214	5	integral	integral	ADJ
cana-6069	214	6	equations	equation	NOUN
cana-6069	214	7	using	use	VERB
cana-6069	214	8	galerkin	galerkin	ADJ
cana-6069	214	9	method	method	NOUN
cana-6069	214	10	with	with	ADP
cana-6069	214	11	hermite	hermite	ADJ
cana-6069	214	12	polynomials	polynomial	NOUN
cana-6069	214	13	.	.	PUNCT
cana-6069	215	1	in	in	ADP
cana-6069	215	2	proceedings	proceeding	NOUN
cana-6069	215	3	of	of	ADP
cana-6069	215	4	the	the	DET
cana-6069	215	5	international	international	ADJ
cana-6069	215	6	conference	conference	NOUN
cana-6069	215	7	on	on	ADP
cana-6069	215	8	applied	apply	VERB
cana-6069	215	9	mathematics	mathematic	NOUN
cana-6069	215	10	and	and	CCONJ
cana-6069	215	11	computational	computational	ADJ
cana-6069	215	12	methods	method	NOUN
cana-6069	215	13	in	in	ADP
cana-6069	215	14	engineering	engineering	NOUN
cana-6069	215	15	.	.	PUNCT
cana-6069	216	1	[	[	X
cana-6069	216	2	14	14	NUM
cana-6069	216	3	]	]	SYM
cana-6069	216	4	sadri	sadri	ADJ
cana-6069	216	5	,	,	PUNCT
cana-6069	216	6	k.	k.	PROPN
cana-6069	216	7	,	,	PUNCT
cana-6069	216	8	amini	amini	PROPN
cana-6069	216	9	,	,	PUNCT
cana-6069	216	10	a.	a.	PROPN
cana-6069	216	11	,	,	PUNCT
cana-6069	216	12	cheng	cheng	PROPN
cana-6069	216	13	,	,	PUNCT
cana-6069	216	14	c.	c.	PROPN
cana-6069	216	15	(	(	PUNCT
cana-6069	216	16	2017	2017	NUM
cana-6069	216	17	)	)	PUNCT
cana-6069	216	18	.	.	PUNCT
cana-6069	217	1	low	low	ADJ
cana-6069	217	2	cost	cost	PROPN
cana-6069	217	3	numerical	numerical	ADJ
cana-6069	217	4	solution	solution	NOUN
cana-6069	217	5	for	for	ADP
cana-6069	217	6	three	three	NUM
cana-6069	217	7	-	-	PUNCT
cana-6069	217	8	dimensional	dimensional	ADJ
cana-6069	217	9	linear	linear	NOUN
cana-6069	217	10	and	and	CCONJ
cana-6069	217	11	nonlinear	nonlinear	ADJ
cana-6069	217	12	integral	integral	ADJ
cana-6069	217	13	equations	equation	NOUN
cana-6069	217	14	via	via	ADP
cana-6069	217	15	three	three	NUM
cana-6069	217	16	-	-	PUNCT
cana-6069	217	17	dimensional	dimensional	ADJ
cana-6069	217	18	jacobi	jacobi	NOUN
cana-6069	217	19	polynomials	polynomial	NOUN
cana-6069	217	20	.	.	PUNCT
cana-6069	218	1	journal	journal	NOUN
cana-6069	218	2	of	of	ADP
cana-6069	218	3	computational	computational	ADJ
cana-6069	218	4	and	and	CCONJ
cana-6069	218	5	applied	applied	ADJ
cana-6069	218	6	mathematics	mathematic	NOUN
cana-6069	218	7	,	,	PUNCT
cana-6069	218	8	319	319	NUM
cana-6069	218	9	,	,	PUNCT
cana-6069	218	10	493	493	NUM
cana-6069	218	11	-	-	SYM
cana-6069	218	12	513	513	NUM
cana-6069	218	13	.	.	PUNCT
cana-6069	219	1	[	[	X
cana-6069	219	2	15	15	NUM
cana-6069	219	3	]	]	X
cana-6069	219	4	tsitsas	tsitsa	NOUN
cana-6069	219	5	,	,	PUNCT
cana-6069	219	6	n.	n.	PROPN
cana-6069	219	7	l.	l.	PROPN
cana-6069	219	8	(	(	PUNCT
cana-6069	219	9	2021	2021	NUM
cana-6069	219	10	)	)	PUNCT
cana-6069	219	11	.	.	PUNCT
cana-6069	220	1	second	second	ADJ
cana-6069	220	2	-	-	PUNCT
cana-6069	220	3	kind	kind	NOUN
cana-6069	220	4	fredholm	fredholm	ADJ
cana-6069	220	5	integral	integral	ADJ
cana-6069	220	6	-	-	PUNCT
cana-6069	220	7	equation	equation	NOUN
cana-6069	220	8	analysis	analysis	NOUN
cana-6069	220	9	of	of	ADP
cana-6069	220	10	scattering	scatter	VERB
cana-6069	220	11	by	by	ADP
cana-6069	220	12	layered	layered	ADJ
cana-6069	220	13	dielectric	dielectric	ADJ
cana-6069	220	14	gratings	grating	NOUN
cana-6069	220	15	.	.	PUNCT
cana-6069	221	1	iet	iet	PROPN
cana-6069	221	2	microwaves	microwave	NOUN
cana-6069	221	3	,	,	PUNCT
cana-6069	221	4	antennas	antennas	NOUN
cana-6069	221	5	propagation	propagation	NOUN
cana-6069	221	6	,	,	PUNCT
cana-6069	221	7	15(10	15(10	NUM
cana-6069	221	8	)	)	PUNCT
cana-6069	221	9	,	,	PUNCT
cana-6069	221	10	1194	1194	NUM
cana-6069	221	11	-	-	SYM
cana-6069	221	12	1205	1205	NUM
cana-6069	221	13	.	.	PUNCT
cana-6069	222	1	[	[	X
cana-6069	222	2	16	16	NUM
cana-6069	222	3	]	]	X
cana-6069	222	4	wongyat	wongyat	NOUN
cana-6069	222	5	,	,	PUNCT
cana-6069	222	6	t.	t.	PROPN
cana-6069	222	7	,	,	PUNCT
cana-6069	222	8	sintunavarat	sintunavarat	NOUN
cana-6069	222	9	,	,	PUNCT
cana-6069	222	10	w.	w.	PROPN
cana-6069	222	11	(	(	PUNCT
cana-6069	222	12	2017	2017	NUM
cana-6069	222	13	)	)	PUNCT
cana-6069	222	14	.	.	PUNCT
cana-6069	223	1	the	the	DET
cana-6069	223	2	existence	existence	NOUN
cana-6069	223	3	and	and	CCONJ
cana-6069	223	4	uniqueness	uniqueness	NOUN
cana-6069	223	5	of	of	ADP
cana-6069	223	6	the	the	DET
cana-6069	223	7	solution	solution	NOUN
cana-6069	223	8	for	for	ADP
cana-6069	223	9	nonlinear	nonlinear	ADJ
cana-6069	223	10	fredholm	fredholm	NOUN
cana-6069	223	11	and	and	CCONJ
cana-6069	223	12	volterra	volterra	PROPN
cana-6069	223	13	integral	integral	ADJ
cana-6069	223	14	equations	equation	NOUN
cana-6069	223	15	together	together	ADV
cana-6069	223	16	with	with	ADP
cana-6069	223	17	nonlinear	nonlinear	ADJ
cana-6069	223	18	fractional	fractional	ADJ
cana-6069	223	19	differential	differential	ADJ
cana-6069	223	20	equations	equation	NOUN
cana-6069	223	21	via	via	ADP
cana-6069	223	22	w	w	NOUN
cana-6069	223	23	-	-	PUNCT
cana-6069	223	24	distances	distance	NOUN
cana-6069	223	25	.	.	PUNCT
cana-6069	224	1	advances	advance	NOUN
cana-6069	224	2	in	in	ADP
cana-6069	224	3	dif	dif	X
cana-6069	224	4	ference	ference	NOUN
cana-6069	224	5	equations	equation	NOUN
cana-6069	224	6	,	,	PUNCT
cana-6069	224	7	2017(1	2017(1	NUM
cana-6069	224	8	)	)	PUNCT
cana-6069	224	9	,	,	PUNCT
cana-6069	224	10	211	211	NUM
cana-6069	224	11	.	.	PUNCT
cana-6069	225	1	[	[	X
cana-6069	225	2	17	17	NUM
cana-6069	225	3	]	]	PUNCT
cana-6069	225	4	yal¸cınba¸s	yal¸cınba¸s	PROPN
cana-6069	225	5	,	,	PUNCT
cana-6069	225	6	s.	s.	PROPN
cana-6069	225	7	,	,	PUNCT
cana-6069	225	8	&	&	CCONJ
cana-6069	225	9	aynig¨ul	aynig¨ul	PROPN
cana-6069	225	10	,	,	PUNCT
cana-6069	225	11	m.	m.	NOUN
cana-6069	225	12	(	(	PUNCT
cana-6069	225	13	2011	2011	NUM
cana-6069	225	14	)	)	PUNCT
cana-6069	225	15	.	.	PUNCT
cana-6069	226	1	hermite	hermite	PROPN
cana-6069	226	2	series	series	PROPN
cana-6069	226	3	solutions	solution	NOUN
cana-6069	226	4	of	of	ADP
cana-6069	226	5	linear	linear	ADJ
cana-6069	226	6	fredholm	fredholm	ADJ
cana-6069	226	7	integral	integral	ADJ
cana-6069	226	8	equations	equation	NOUN
cana-6069	226	9	.	.	PUNCT
cana-6069	227	1	mathematical	mathematical	ADJ
cana-6069	227	2	and	and	CCONJ
cana-6069	227	3	computational	computational	ADJ
cana-6069	227	4	applications	application	NOUN
cana-6069	227	5	,	,	PUNCT
cana-6069	227	6	16(2	16(2	NUM
cana-6069	227	7	)	)	PUNCT
cana-6069	227	8	,	,	PUNCT
cana-6069	227	9	497–506	497–506	NUM
cana-6069	227	10	.	.	PUNCT