id	sid	tid	token	lemma	pos
cana-5535	1	1	communications	communication	NOUN
cana-5535	1	2	on	on	ADP
cana-5535	1	3	applied	apply	VERB
cana-5535	1	4	nonlinear	nonlinear	ADJ
cana-5535	1	5	analysis	analysis	NOUN
cana-5535	1	6	issn	issn	NOUN
cana-5535	1	7	:	:	PUNCT
cana-5535	1	8	1074	1074	NUM
cana-5535	1	9	-	-	PUNCT
cana-5535	1	10	133x	133x	NUM
cana-5535	1	11	vol	vol	VERB
cana-5535	1	12	32	32	NUM
cana-5535	1	13	no	no	NOUN
cana-5535	1	14	.	.	PUNCT
cana-5535	2	1	10s	10	NOUN
cana-5535	2	2	(	(	PUNCT
cana-5535	2	3	2025	2025	NUM
cana-5535	2	4	)	)	PUNCT
cana-5535	2	5	2580	2580	NUM
cana-5535	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5535	2	7	numerical	numerical	ADJ
cana-5535	2	8	method	method	NOUN
cana-5535	2	9	for	for	ADP
cana-5535	2	10	the	the	DET
cana-5535	2	11	solution	solution	NOUN
cana-5535	2	12	of	of	ADP
cana-5535	2	13	integro	integro	ADJ
cana-5535	2	14	-	-	PUNCT
cana-5535	2	15	differential	differential	NOUN
cana-5535	2	16	equations	equation	NOUN
cana-5535	2	17	of	of	ADP
cana-5535	2	18	the	the	DET
cana-5535	2	19	second	second	ADJ
cana-5535	2	20	kind	kind	NOUN
cana-5535	2	21	dilmi	dilmi	NOUN
cana-5535	2	22	.	.	PUNCT
cana-5535	3	1	mustapha	mustapha	PROPN
cana-5535	3	2	college	college	PROPN
cana-5535	3	3	of	of	ADP
cana-5535	3	4	mathematics	mathematics	PROPN
cana-5535	3	5	and	and	CCONJ
cana-5535	3	6	computer	computer	NOUN
cana-5535	3	7	science	science	NOUN
cana-5535	3	8	,	,	PUNCT
cana-5535	3	9	university	university	NOUN
cana-5535	3	10	pole	pole	NOUN
cana-5535	3	11	,	,	PUNCT
cana-5535	3	12	road	road	NOUN
cana-5535	3	13	bordj	bordj	PROPN
cana-5535	3	14	bou	bou	PROPN
cana-5535	3	15	arreridj	arreridj	PROPN
cana-5535	3	16	,	,	PUNCT
cana-5535	3	17	m’sila	m’sila	PROPN
cana-5535	3	18	28000	28000	NUM
cana-5535	3	19	algeria	algeria	PROPN
cana-5535	3	20	moustafa.dilmi@univ-msila.dz	moustafa.dilmi@univ-msila.dz	PROPN
cana-5535	3	21	article	article	NOUN
cana-5535	3	22	history	history	NOUN
cana-5535	3	23	:	:	PUNCT
cana-5535	3	24	received	receive	VERB
cana-5535	3	25	:	:	PUNCT
cana-5535	3	26	12	12	NUM
cana-5535	3	27	-	-	SYM
cana-5535	3	28	01	01	NUM
cana-5535	3	29	-	-	PUNCT
cana-5535	3	30	2025	2025	NUM
cana-5535	3	31	revised	revise	VERB
cana-5535	3	32	:	:	PUNCT
cana-5535	3	33	15	15	NUM
cana-5535	3	34	-	-	NUM
cana-5535	3	35	02	02	NUM
cana-5535	3	36	-	-	PUNCT
cana-5535	3	37	2025	2025	NUM
cana-5535	3	38	accepted	accept	VERB
cana-5535	3	39	:	:	PUNCT
cana-5535	3	40	01	01	NUM
cana-5535	3	41	-	-	SYM
cana-5535	3	42	03	03	NUM
cana-5535	3	43	-	-	PUNCT
cana-5535	3	44	2025	2025	NUM
cana-5535	3	45	abstract	abstract	NOUN
cana-5535	3	46	:	:	PUNCT
cana-5535	3	47	the	the	DET
cana-5535	3	48	purpose	purpose	NOUN
cana-5535	3	49	of	of	ADP
cana-5535	3	50	this	this	DET
cana-5535	3	51	work	work	NOUN
cana-5535	3	52	is	be	AUX
cana-5535	3	53	to	to	PART
cana-5535	3	54	search	search	VERB
cana-5535	3	55	for	for	ADP
cana-5535	3	56	an	an	DET
cana-5535	3	57	approximate	approximate	ADJ
cana-5535	3	58	solution	solution	NOUN
cana-5535	3	59	to	to	ADP
cana-5535	3	60	the	the	DET
cana-5535	3	61	fredholm	fredholm	NOUN
cana-5535	3	62	and	and	CCONJ
cana-5535	3	63	volterra	volterra	NOUN
cana-5535	3	64	integro	integro	PROPN
cana-5535	3	65	-	-	PUNCT
cana-5535	3	66	differential	differential	NOUN
cana-5535	3	67	equations	equation	NOUN
cana-5535	3	68	using	use	VERB
cana-5535	3	69	genocchi	genocchi	PROPN
cana-5535	3	70	polynomials	polynomial	NOUN
cana-5535	3	71	,	,	PUNCT
cana-5535	3	72	replacing	replace	VERB
cana-5535	3	73	the	the	DET
cana-5535	3	74	initial	initial	ADJ
cana-5535	3	75	conditions	condition	NOUN
cana-5535	3	76	if	if	SCONJ
cana-5535	3	77	necessary	necessary	ADJ
cana-5535	3	78	,	,	PUNCT
cana-5535	3	79	where	where	SCONJ
cana-5535	3	80	the	the	DET
cana-5535	3	81	integrals	integral	NOUN
cana-5535	3	82	can	can	AUX
cana-5535	3	83	be	be	AUX
cana-5535	3	84	calculated	calculate	VERB
cana-5535	3	85	using	use	VERB
cana-5535	3	86	numerical	numerical	ADJ
cana-5535	3	87	methods	method	NOUN
cana-5535	3	88	,	,	PUNCT
cana-5535	3	89	in	in	ADP
cana-5535	3	90	order	order	NOUN
cana-5535	3	91	to	to	PART
cana-5535	3	92	obtain	obtain	VERB
cana-5535	3	93	a	a	DET
cana-5535	3	94	variation	variation	NOUN
cana-5535	3	95	problem	problem	NOUN
cana-5535	3	96	and	and	CCONJ
cana-5535	3	97	reduce	reduce	VERB
cana-5535	3	98	it	it	PRON
cana-5535	3	99	to	to	ADP
cana-5535	3	100	a	a	DET
cana-5535	3	101	linear	linear	ADJ
cana-5535	3	102	system	system	NOUN
cana-5535	3	103	,	,	PUNCT
cana-5535	3	104	where	where	SCONJ
cana-5535	3	105	its	its	PRON
cana-5535	3	106	solution	solution	NOUN
cana-5535	3	107	is	be	AUX
cana-5535	3	108	to	to	PART
cana-5535	3	109	find	find	VERB
cana-5535	3	110	the	the	DET
cana-5535	3	111	coefficients	coefficient	NOUN
cana-5535	3	112	of	of	ADP
cana-5535	3	113	the	the	DET
cana-5535	3	114	function	function	NOUN
cana-5535	3	115	.	.	PUNCT
cana-5535	4	1	unknowns	unknown	NOUN
cana-5535	4	2	and	and	CCONJ
cana-5535	4	3	then	then	ADV
cana-5535	4	4	solve	solve	VERB
cana-5535	4	5	the	the	DET
cana-5535	4	6	equation	equation	NOUN
cana-5535	4	7	.	.	PUNCT
cana-5535	5	1	the	the	DET
cana-5535	5	2	convergence	convergence	NOUN
cana-5535	5	3	and	and	CCONJ
cana-5535	5	4	effectiveness	effectiveness	NOUN
cana-5535	5	5	of	of	ADP
cana-5535	5	6	this	this	DET
cana-5535	5	7	method	method	NOUN
cana-5535	5	8	are	be	AUX
cana-5535	5	9	confirmed	confirm	VERB
cana-5535	5	10	by	by	ADP
cana-5535	5	11	numerical	numerical	ADJ
cana-5535	5	12	examples	example	NOUN
cana-5535	5	13	that	that	PRON
cana-5535	5	14	will	will	AUX
cana-5535	5	15	be	be	AUX
cana-5535	5	16	presented	present	VERB
cana-5535	5	17	.	.	PUNCT
cana-5535	6	1	keywords	keyword	NOUN
cana-5535	6	2	:	:	PUNCT
cana-5535	6	3	integro	integro	ADJ
cana-5535	6	4	-	-	PUNCT
cana-5535	6	5	differential	differential	NOUN
cana-5535	6	6	equations	equation	NOUN
cana-5535	6	7	,	,	PUNCT
cana-5535	6	8	numerical	numerical	ADJ
cana-5535	6	9	method	method	NOUN
cana-5535	6	10	,	,	PUNCT
cana-5535	6	11	genocchi	genocchi	PROPN
cana-5535	6	12	polynomials	polynomial	VERB
cana-5535	6	13	.	.	PUNCT
cana-5535	7	1	1	1	X
cana-5535	7	2	.	.	X
cana-5535	7	3	introduction	introduction	NOUN
cana-5535	7	4	integro	integro	ADJ
cana-5535	7	5	-	-	PUNCT
cana-5535	7	6	differential	differential	NOUN
cana-5535	7	7	equations	equation	NOUN
cana-5535	7	8	are	be	AUX
cana-5535	7	9	considered	consider	VERB
cana-5535	7	10	one	one	NUM
cana-5535	7	11	of	of	ADP
cana-5535	7	12	the	the	DET
cana-5535	7	13	most	most	ADV
cana-5535	7	14	important	important	ADJ
cana-5535	7	15	fields	field	NOUN
cana-5535	7	16	in	in	ADP
cana-5535	7	17	mathematical	mathematical	ADJ
cana-5535	7	18	disciplines	discipline	NOUN
cana-5535	7	19	,	,	PUNCT
cana-5535	7	20	for	for	ADP
cana-5535	7	21	example	example	NOUN
cana-5535	7	22	pure	pure	ADJ
cana-5535	7	23	mathematics	mathematic	NOUN
cana-5535	7	24	and	and	CCONJ
cana-5535	7	25	applied	apply	VERB
cana-5535	7	26	mathematics	mathematic	NOUN
cana-5535	7	27	.	.	PUNCT
cana-5535	8	1	integro	integro	ADJ
cana-5535	8	2	-	-	PUNCT
cana-5535	8	3	differential	differential	NOUN
cana-5535	8	4	equations	equation	NOUN
cana-5535	8	5	linear	linear	VERB
cana-5535	8	6	and	and	CCONJ
cana-5535	8	7	non	non	ADJ
cana-5535	8	8	linear	linear	PROPN
cana-5535	8	9	have	have	VERB
cana-5535	8	10	a	a	DET
cana-5535	8	11	very	very	ADV
cana-5535	8	12	important	important	ADJ
cana-5535	8	13	role	role	NOUN
cana-5535	8	14	in	in	ADP
cana-5535	8	15	modern	modern	ADJ
cana-5535	8	16	science	science	NOUN
cana-5535	8	17	and	and	CCONJ
cana-5535	8	18	technology	technology	NOUN
cana-5535	8	19	such	such	ADJ
cana-5535	8	20	as	as	ADP
cana-5535	8	21	heat	heat	NOUN
cana-5535	8	22	transfer	transfer	NOUN
cana-5535	8	23	,	,	PUNCT
cana-5535	8	24	diffusion	diffusion	NOUN
cana-5535	8	25	processes	process	NOUN
cana-5535	8	26	,	,	PUNCT
cana-5535	8	27	mechanics	mechanic	NOUN
cana-5535	8	28	,	,	PUNCT
cana-5535	8	29	biological	biological	ADJ
cana-5535	8	30	species	specie	NOUN
cana-5535	8	31	,	,	PUNCT
cana-5535	8	32	and	and	CCONJ
cana-5535	8	33	many	many	ADJ
cana-5535	8	34	other	other	ADJ
cana-5535	8	35	fields	field	NOUN
cana-5535	8	36	.	.	PUNCT
cana-5535	9	1	to	to	PART
cana-5535	9	2	learn	learn	VERB
cana-5535	9	3	more	more	ADJ
cana-5535	9	4	about	about	ADP
cana-5535	9	5	the	the	DET
cana-5535	9	6	sources	source	NOUN
cana-5535	9	7	in	in	ADP
cana-5535	9	8	which	which	PRON
cana-5535	9	9	these	these	DET
cana-5535	9	10	types	type	NOUN
cana-5535	9	11	of	of	ADP
cana-5535	9	12	equations	equation	NOUN
cana-5535	9	13	are	be	AUX
cana-5535	9	14	studied	study	VERB
cana-5535	9	15	in	in	ADP
cana-5535	9	16	applications	application	NOUN
cana-5535	9	17	of	of	ADP
cana-5535	9	18	physics	physics	NOUN
cana-5535	9	19	,	,	PUNCT
cana-5535	9	20	biology	biology	NOUN
cana-5535	9	21	,	,	PUNCT
cana-5535	9	22	and	and	CCONJ
cana-5535	9	23	engineering	engineering	NOUN
cana-5535	9	24	,	,	PUNCT
cana-5535	9	25	as	as	ADV
cana-5535	9	26	well	well	ADV
cana-5535	9	27	as	as	ADP
cana-5535	9	28	in	in	ADP
cana-5535	9	29	books	book	NOUN
cana-5535	9	30	on	on	ADP
cana-5535	9	31	advanced	advanced	ADJ
cana-5535	9	32	integral	integral	ADJ
cana-5535	9	33	equations	equation	NOUN
cana-5535	9	34	.	.	PUNCT
cana-5535	10	1	references	reference	NOUN
cana-5535	10	2	can	can	AUX
cana-5535	10	3	be	be	AUX
cana-5535	10	4	found	find	VERB
cana-5535	10	5	[	[	X
cana-5535	10	6	4	4	NUM
cana-5535	10	7	,	,	PUNCT
cana-5535	10	8	10	10	NUM
cana-5535	10	9	,	,	PUNCT
cana-5535	10	10	11	11	NUM
cana-5535	10	11	,	,	PUNCT
cana-5535	10	12	15	15	NUM
cana-5535	10	13	]	]	PUNCT
cana-5535	10	14	.	.	PUNCT
cana-5535	11	1	the	the	DET
cana-5535	11	2	numerical	numerical	ADJ
cana-5535	11	3	solution	solution	NOUN
cana-5535	11	4	of	of	ADP
cana-5535	11	5	second	second	ADJ
cana-5535	11	6	order	order	NOUN
cana-5535	11	7	integro	integro	ADJ
cana-5535	11	8	-	-	PUNCT
cana-5535	11	9	differential	differential	NOUN
cana-5535	11	10	equations	equation	NOUN
cana-5535	11	11	with	with	ADP
cana-5535	11	12	the	the	DET
cana-5535	11	13	boundary	boundary	ADJ
cana-5535	11	14	conditions	condition	NOUN
cana-5535	11	15	of	of	ADP
cana-5535	11	16	the	the	DET
cana-5535	11	17	fredholm	fredholm	NOUN
cana-5535	11	18	and	and	CCONJ
cana-5535	11	19	volterra	volterra	NOUN
cana-5535	11	20	equations	equation	NOUN
cana-5535	11	21	and	and	CCONJ
cana-5535	11	22	other	other	ADJ
cana-5535	11	23	equations	equation	NOUN
cana-5535	11	24	related	relate	VERB
cana-5535	11	25	to	to	ADP
cana-5535	11	26	this	this	DET
cana-5535	11	27	type	type	NOUN
cana-5535	11	28	of	of	ADP
cana-5535	11	29	equations	equation	NOUN
cana-5535	11	30	has	have	AUX
cana-5535	11	31	been	be	AUX
cana-5535	11	32	done	do	VERB
cana-5535	11	33	by	by	ADP
cana-5535	11	34	some	some	DET
cana-5535	11	35	authors	author	NOUN
cana-5535	11	36	.	.	PUNCT
cana-5535	12	1	for	for	ADP
cana-5535	12	2	example	example	NOUN
cana-5535	12	3	,	,	PUNCT
cana-5535	12	4	the	the	DET
cana-5535	12	5	authors	author	NOUN
cana-5535	12	6	in	in	ADP
cana-5535	12	7	[	[	X
cana-5535	12	8	4	4	NUM
cana-5535	12	9	]	]	PUNCT
cana-5535	12	10	discussed	discuss	VERB
cana-5535	12	11	the	the	DET
cana-5535	12	12	chebyshev	chebyshev	NOUN
cana-5535	12	13	collocation	collocation	NOUN
cana-5535	12	14	method	method	NOUN
cana-5535	12	15	for	for	ADP
cana-5535	12	16	the	the	DET
cana-5535	12	17	solution	solution	NOUN
cana-5535	12	18	of	of	ADP
cana-5535	12	19	linear	linear	PROPN
cana-5535	12	20	integro	integro	ADJ
cana-5535	12	21	-	-	PUNCT
cana-5535	12	22	differential	differential	NOUN
cana-5535	12	23	equations	equation	NOUN
cana-5535	12	24	,	,	PUNCT
cana-5535	12	25	which	which	PRON
cana-5535	12	26	is	be	AUX
cana-5535	12	27	the	the	DET
cana-5535	12	28	compact	compact	ADJ
cana-5535	12	29	finite	finite	ADJ
cana-5535	12	30	difference	difference	NOUN
cana-5535	12	31	method	method	NOUN
cana-5535	12	32	,	,	PUNCT
cana-5535	12	33	and	and	CCONJ
cana-5535	12	34	the	the	DET
cana-5535	12	35	monotonic	monotonic	ADJ
cana-5535	12	36	iterative	iterative	NOUN
cana-5535	12	37	sequence	sequence	NOUN
cana-5535	12	38	method	method	NOUN
cana-5535	12	39	for	for	ADP
cana-5535	12	40	solving	solve	VERB
cana-5535	12	41	the	the	DET
cana-5535	12	42	second	second	ADJ
cana-5535	12	43	order	order	NOUN
cana-5535	12	44	volterra	volterra	PROPN
cana-5535	12	45	integro	integro	PROPN
cana-5535	12	46	-	-	PUNCT
cana-5535	12	47	differential	differential	NOUN
cana-5535	12	48	equation	equation	NOUN
cana-5535	12	49	was	be	AUX
cana-5535	12	50	implemented	implement	VERB
cana-5535	12	51	in	in	ADP
cana-5535	12	52	[	[	X
cana-5535	12	53	5	5	NUM
cana-5535	12	54	,	,	PUNCT
cana-5535	12	55	27	27	NUM
cana-5535	12	56	]	]	PUNCT
cana-5535	12	57	.	.	PUNCT
cana-5535	13	1	however	however	ADV
cana-5535	13	2	,	,	PUNCT
cana-5535	13	3	a	a	DET
cana-5535	13	4	sequential	sequential	ADJ
cana-5535	13	5	solution	solution	NOUN
cana-5535	13	6	of	of	ADP
cana-5535	13	7	second	second	ADJ
cana-5535	13	8	order	order	NOUN
cana-5535	13	9	integro	integro	ADJ
cana-5535	13	10	-	-	PUNCT
cana-5535	13	11	differential	differential	NOUN
cana-5535	13	12	equations	equation	NOUN
cana-5535	13	13	with	with	ADP
cana-5535	13	14	boundary	boundary	ADJ
cana-5535	13	15	conditions	condition	NOUN
cana-5535	13	16	of	of	ADP
cana-5535	13	17	fredholm	fredholm	NOUN
cana-5535	13	18	and	and	CCONJ
cana-5535	13	19	volterra	volterra	NOUN
cana-5535	13	20	types	type	NOUN
cana-5535	13	21	by	by	ADP
cana-5535	13	22	the	the	DET
cana-5535	13	23	homotopy	homotopy	NOUN
cana-5535	13	24	analysis	analysis	NOUN
cana-5535	13	25	method	method	NOUN
cana-5535	13	26	was	be	AUX
cana-5535	13	27	also	also	ADV
cana-5535	13	28	considered	consider	VERB
cana-5535	13	29	in	in	ADP
cana-5535	13	30	[	[	X
cana-5535	13	31	16	16	NUM
cana-5535	13	32	]	]	PUNCT
cana-5535	13	33	.	.	PUNCT
cana-5535	14	1	accordingly	accordingly	ADV
cana-5535	14	2	,	,	PUNCT
cana-5535	14	3	this	this	DET
cana-5535	14	4	work	work	NOUN
cana-5535	14	5	aims	aim	VERB
cana-5535	14	6	to	to	PART
cana-5535	14	7	find	find	VERB
cana-5535	14	8	approximate	approximate	ADJ
cana-5535	14	9	solutions	solution	NOUN
cana-5535	14	10	to	to	PART
cana-5535	14	11	fredholm	fredholm	VERB
cana-5535	14	12	and	and	CCONJ
cana-5535	14	13	volterra	volterra	PROPN
cana-5535	14	14	linear	linear	PROPN
cana-5535	14	15	integro	integro	PROPN
cana-5535	14	16	-	-	PUNCT
cana-5535	14	17	differential	differential	NOUN
cana-5535	14	18	equations	equation	NOUN
cana-5535	14	19	of	of	ADP
cana-5535	14	20	the	the	DET
cana-5535	14	21	second	second	ADJ
cana-5535	14	22	type	type	NOUN
cana-5535	14	23	using	use	VERB
cana-5535	14	24	polynomials	polynomial	NOUN
cana-5535	14	25	of	of	ADP
cana-5535	14	26	the	the	DET
cana-5535	14	27	genocchi	genocchi	PROPN
cana-5535	14	28	type	type	NOUN
cana-5535	14	29	with	with	ADP
cana-5535	14	30	the	the	DET
cana-5535	14	31	numerique	numerique	ADJ
cana-5535	14	32	method	method	NOUN
cana-5535	14	33	and	and	CCONJ
cana-5535	14	34	then	then	ADV
cana-5535	14	35	compare	compare	VERB
cana-5535	14	36	the	the	DET
cana-5535	14	37	approximate	approximate	ADJ
cana-5535	14	38	solutions	solution	NOUN
cana-5535	14	39	with	with	ADP
cana-5535	14	40	the	the	DET
cana-5535	14	41	exact	exact	ADJ
cana-5535	14	42	solutions	solution	NOUN
cana-5535	14	43	to	to	PART
cana-5535	14	44	see	see	VERB
cana-5535	14	45	the	the	DET
cana-5535	14	46	effectiveness	effectiveness	NOUN
cana-5535	14	47	of	of	ADP
cana-5535	14	48	the	the	DET
cana-5535	14	49	method	method	NOUN
cana-5535	14	50	through	through	ADP
cana-5535	14	51	the	the	DET
cana-5535	14	52	examples	example	NOUN
cana-5535	14	53	that	that	PRON
cana-5535	14	54	we	we	PRON
cana-5535	14	55	will	will	AUX
cana-5535	14	56	present	present	VERB
cana-5535	14	57	.	.	PUNCT
cana-5535	15	1	2	2	X
cana-5535	15	2	.	.	X
cana-5535	15	3	genocchi	genocchi	PROPN
cana-5535	15	4	polynomial	polynomial	ADJ
cana-5535	15	5	method	method	NOUN
cana-5535	15	6	for	for	ADP
cana-5535	15	7	i.d.e	i.d.e	NOUN
cana-5535	15	8	consider	consider	VERB
cana-5535	15	9	the	the	DET
cana-5535	15	10	following	follow	VERB
cana-5535	15	11	integro	integro	ADJ
cana-5535	15	12	-	-	PUNCT
cana-5535	15	13	differential	differential	NOUN
cana-5535	15	14	equation	equation	NOUN
cana-5535	15	15	𝑦	𝑦	NOUN
cana-5535	15	16	′(𝑥	′(𝑥	NOUN
cana-5535	15	17	)	)	PUNCT
cana-5535	15	18	=	=	SYM
cana-5535	15	19	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5535	15	20	)	)	PUNCT
cana-5535	15	21	+	+	NUM
cana-5535	15	22	∫	∫	PROPN
cana-5535	15	23	𝑘(𝑥	𝑘(𝑥	PROPN
cana-5535	15	24	,	,	PUNCT
cana-5535	15	25	𝑡)𝑦(𝑡	𝑡)𝑦(𝑡	NOUN
cana-5535	15	26	)	)	PUNCT
cana-5535	15	27	𝑥	𝑥	PRON
cana-5535	15	28	𝑎	𝑎	NOUN
cana-5535	15	29	𝑑𝑡	𝑑𝑡	ADP
cana-5535	15	30	(	(	PUNCT
cana-5535	15	31	1	1	NUM
cana-5535	15	32	)	)	PUNCT
cana-5535	15	33	communications	communication	NOUN
cana-5535	15	34	on	on	ADP
cana-5535	15	35	applied	apply	VERB
cana-5535	15	36	nonlinear	nonlinear	ADJ
cana-5535	15	37	analysis	analysis	NOUN
cana-5535	15	38	issn	issn	NOUN
cana-5535	15	39	:	:	PUNCT
cana-5535	15	40	1074	1074	NUM
cana-5535	15	41	-	-	PUNCT
cana-5535	15	42	133x	133x	NUM
cana-5535	15	43	vol	vol	VERB
cana-5535	15	44	32	32	NUM
cana-5535	15	45	no	no	NOUN
cana-5535	15	46	.	.	PUNCT
cana-5535	16	1	10s	10	NOUN
cana-5535	16	2	(	(	PUNCT
cana-5535	16	3	2025	2025	NUM
cana-5535	16	4	)	)	PUNCT
cana-5535	16	5	2581	2581	NUM
cana-5535	16	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5535	16	7	𝑦(𝑎	𝑦(𝑎	NOUN
cana-5535	16	8	)	)	PUNCT
cana-5535	17	1	=	=	NOUN
cana-5535	17	2	∝	∝	NOUN
cana-5535	17	3	where	where	SCONJ
cana-5535	17	4	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5535	17	5	)	)	PUNCT
cana-5535	17	6	and	and	CCONJ
cana-5535	17	7	𝑘(𝑥	𝑘(𝑥	PROPN
cana-5535	17	8	,	,	PUNCT
cana-5535	17	9	𝑡	𝑡	X
cana-5535	17	10	)	)	PUNCT
cana-5535	17	11	are	be	AUX
cana-5535	17	12	known	know	VERB
cana-5535	17	13	functions	function	NOUN
cana-5535	17	14	,	,	PUNCT
cana-5535	17	15	while	while	SCONJ
cana-5535	17	16	𝑦(𝑥	𝑦(𝑥	NOUN
cana-5535	17	17	)	)	PUNCT
cana-5535	17	18	is	be	AUX
cana-5535	17	19	the	the	DET
cana-5535	17	20	unknown	unknown	ADJ
cana-5535	17	21	function	function	NOUN
cana-5535	17	22	to	to	PART
cana-5535	17	23	be	be	AUX
cana-5535	17	24	determined	determine	VERB
cana-5535	17	25	.	.	PUNCT
cana-5535	18	1	the	the	DET
cana-5535	18	2	method	method	NOUN
cana-5535	18	3	under	under	ADP
cana-5535	18	4	consideration	consideration	NOUN
cana-5535	18	5	employs	employ	VERB
cana-5535	18	6	genocchi	genocchi	PROPN
cana-5535	18	7	polynomials	polynomial	NOUN
cana-5535	18	8	,	,	PUNCT
cana-5535	18	9	as	as	SCONJ
cana-5535	18	10	thoroughly	thoroughly	ADV
cana-5535	18	11	discussed	discuss	VERB
cana-5535	18	12	in	in	ADP
cana-5535	18	13	references	reference	NOUN
cana-5535	18	14	[	[	X
cana-5535	18	15	12	12	NUM
cana-5535	18	16	,	,	PUNCT
cana-5535	18	17	13	13	NUM
cana-5535	18	18	,	,	PUNCT
cana-5535	18	19	14	14	NUM
cana-5535	18	20	,	,	PUNCT
cana-5535	18	21	22	22	NUM
cana-5535	18	22	]	]	PUNCT
cana-5535	18	23	.	.	PUNCT
cana-5535	19	1	these	these	DET
cana-5535	19	2	polynomials	polynomial	NOUN
cana-5535	19	3	are	be	AUX
cana-5535	19	4	used	use	VERB
cana-5535	19	5	as	as	ADP
cana-5535	19	6	a	a	DET
cana-5535	19	7	basis	basis	NOUN
cana-5535	19	8	to	to	PART
cana-5535	19	9	approximate	approximate	VERB
cana-5535	19	10	the	the	DET
cana-5535	19	11	solution	solution	NOUN
cana-5535	19	12	over	over	ADP
cana-5535	19	13	a	a	DET
cana-5535	19	14	closed	closed	ADJ
cana-5535	19	15	and	and	CCONJ
cana-5535	19	16	finite	finite	ADJ
cana-5535	19	17	interval	interval	NOUN
cana-5535	19	18	.	.	PUNCT
cana-5535	20	1	it	it	PRON
cana-5535	20	2	is	be	AUX
cana-5535	20	3	assumed	assume	VERB
cana-5535	20	4	that	that	SCONJ
cana-5535	20	5	𝑦𝑛(𝑥	𝑦𝑛(𝑥	NOUN
cana-5535	20	6	)	)	PUNCT
cana-5535	20	7	=	=	SYM
cana-5535	21	1	∑	∑	PUNCT
cana-5535	21	2	𝛽𝑖	𝛽𝑖	VERB
cana-5535	21	3	𝑛	𝑛	PRON
cana-5535	21	4	𝑖=0	𝑖=0	PROPN
cana-5535	21	5	𝐺𝑖(𝑥	𝐺𝑖(𝑥	PROPN
cana-5535	21	6	)	)	PUNCT
cana-5535	21	7	=	=	SYM
cana-5535	21	8	∑	∑	PUNCT
cana-5535	21	9	𝛽𝑖	𝛽𝑖	VERB
cana-5535	22	1	𝑛	𝑛	DET
cana-5535	22	2	𝑖=0	𝑖=0	PUNCT
cana-5535	22	3	𝐺𝑖	𝐺𝑖	PROPN
cana-5535	22	4	(	(	PUNCT
cana-5535	22	5	𝑥−𝑎	𝑥−𝑎	PROPN
cana-5535	22	6	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	22	7	)	)	PUNCT
cana-5535	22	8	(	(	PUNCT
cana-5535	22	9	2	2	X
cana-5535	22	10	)	)	PUNCT
cana-5535	22	11	where	where	SCONJ
cana-5535	22	12	𝐺𝑖	𝐺𝑖	PROPN
cana-5535	22	13	(	(	PUNCT
cana-5535	22	14	𝑥−𝑎	𝑥−𝑎	PROPN
cana-5535	22	15	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	22	16	)	)	PUNCT
cana-5535	22	17	is	be	AUX
cana-5535	22	18	shifted	shift	VERB
cana-5535	22	19	genocchi	genocchi	PROPN
cana-5535	22	20	polynomial	polynomial	PROPN
cana-5535	22	21	at	at	ADP
cana-5535	22	22	[	[	X
cana-5535	22	23	𝑎	𝑎	X
cana-5535	22	24	,	,	PUNCT
cana-5535	22	25	𝑏	𝑏	NOUN
cana-5535	22	26	]	]	PUNCT
cana-5535	22	27	note	note	NOUN
cana-5535	22	28	that	that	SCONJ
cana-5535	22	29	when	when	SCONJ
cana-5535	22	30	we	we	PRON
cana-5535	22	31	take	take	VERB
cana-5535	22	32	the	the	DET
cana-5535	22	33	value	value	NOUN
cana-5535	22	34	𝑥	𝑥	NOUN
cana-5535	22	35	=	=	SYM
cana-5535	22	36	𝑎	𝑎	X
cana-5535	22	37	we	we	PRON
cana-5535	22	38	get	get	VERB
cana-5535	22	39	𝑥−𝑎	𝑥−𝑎	NOUN
cana-5535	22	40	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	22	41	=	=	SYM
cana-5535	22	42	0	0	NUM
cana-5535	22	43	,	,	PUNCT
cana-5535	22	44	and	and	CCONJ
cana-5535	22	45	when	when	SCONJ
cana-5535	22	46	𝑥	𝑥	PROPN
cana-5535	22	47	=	=	SYM
cana-5535	22	48	𝑏	𝑏	NOUN
cana-5535	22	49	we	we	PRON
cana-5535	22	50	get	get	VERB
cana-5535	22	51	𝑥−𝑎	𝑥−𝑎	NOUN
cana-5535	22	52	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	22	53	=	=	SYM
cana-5535	23	1	1	1	X
cana-5535	23	2	.	.	PUNCT
cana-5535	24	1	so	so	ADV
cana-5535	24	2	we	we	PRON
cana-5535	24	3	have	have	VERB
cana-5535	24	4	𝑦	𝑦	NOUN
cana-5535	24	5	′(𝑥	′(𝑥	NUM
cana-5535	24	6	)	)	PUNCT
cana-5535	25	1	=	=	VERB
cana-5535	25	2	𝑦𝑛	𝑦𝑛	ADP
cana-5535	25	3	′	′	NUM
cana-5535	25	4	(	(	PUNCT
cana-5535	25	5	𝑥	𝑥	NOUN
cana-5535	25	6	)	)	PUNCT
cana-5535	25	7	=	=	SYM
cana-5535	25	8	∑	∑	PUNCT
cana-5535	25	9	(	(	PUNCT
cana-5535	25	10	1	1	NUM
cana-5535	25	11	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	25	12	)	)	PUNCT
cana-5535	26	1	𝑛	𝑛	DET
cana-5535	26	2	𝑖=0	𝑖=0	PROPN
cana-5535	26	3	𝛽𝑖𝐺𝑖	𝛽𝑖𝐺𝑖	ADJ
cana-5535	26	4	′	′	NUM
cana-5535	27	1	(	(	PUNCT
cana-5535	27	2	𝑥−𝑎	𝑥−𝑎	PROPN
cana-5535	27	3	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	27	4	)	)	PUNCT
cana-5535	27	5	(	(	PUNCT
cana-5535	27	6	3	3	X
cana-5535	27	7	)	)	PUNCT
cana-5535	27	8	substituting	substitute	VERB
cana-5535	27	9	(	(	PUNCT
cana-5535	27	10	2	2	NUM
cana-5535	27	11	)	)	PUNCT
cana-5535	27	12	and	and	CCONJ
cana-5535	27	13	(	(	PUNCT
cana-5535	27	14	3	3	X
cana-5535	27	15	)	)	PUNCT
cana-5535	27	16	into	into	ADP
cana-5535	27	17	(	(	PUNCT
cana-5535	27	18	1	1	NUM
cana-5535	27	19	)	)	PUNCT
cana-5535	27	20	,	,	PUNCT
cana-5535	27	21	results	result	VERB
cana-5535	27	22	in	in	ADP
cana-5535	27	23	∑	∑	PROPN
cana-5535	27	24	(	(	PUNCT
cana-5535	27	25	1	1	NUM
cana-5535	27	26	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	27	27	)	)	PUNCT
cana-5535	27	28	𝑛	𝑛	DET
cana-5535	27	29	𝑖=0	𝑖=0	PROPN
cana-5535	27	30	𝛽𝑖𝐺𝑖	𝛽𝑖𝐺𝑖	ADJ
cana-5535	27	31	′	′	NUM
cana-5535	28	1	(	(	PUNCT
cana-5535	28	2	𝑥−𝑎	𝑥−𝑎	PROPN
cana-5535	28	3	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	28	4	)	)	PUNCT
cana-5535	29	1	=	=	SYM
cana-5535	29	2	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5535	29	3	)	)	PUNCT
cana-5535	30	1	+	+	NUM
cana-5535	30	2	∫	∫	PROPN
cana-5535	30	3	𝑘(𝑥	𝑘(𝑥	PROPN
cana-5535	30	4	,	,	PUNCT
cana-5535	30	5	𝑡	𝑡	PROPN
cana-5535	30	6	)	)	PUNCT
cana-5535	30	7	𝑥	𝑥	PROPN
cana-5535	30	8	𝑎	𝑎	X
cana-5535	30	9	∑	∑	PUNCT
cana-5535	30	10	𝛽𝑖𝐺𝑖	𝛽𝑖𝐺𝑖	PROPN
cana-5535	30	11	(	(	PUNCT
cana-5535	30	12	𝑡−𝑎	𝑡−𝑎	PROPN
cana-5535	30	13	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	30	14	)	)	PUNCT
cana-5535	30	15	𝑛	𝑛	PRON
cana-5535	30	16	𝑖=0	𝑖=0	PROPN
cana-5535	30	17	𝑑𝑡	𝑑𝑡	ADP
cana-5535	30	18	=	=	PUNCT
cana-5535	30	19	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5535	30	20	)	)	PUNCT
cana-5535	30	21	+	+	CCONJ
cana-5535	30	22	∑	∑	PUNCT
cana-5535	30	23	𝛽𝑖	𝛽𝑖	VERB
cana-5535	30	24	𝑛	𝑛	DET
cana-5535	30	25	𝑖=0	𝑖=0	PROPN
cana-5535	30	26	∫	∫	PROPN
cana-5535	30	27	𝑘(𝑥	𝑘(𝑥	PROPN
cana-5535	30	28	,	,	PUNCT
cana-5535	30	29	𝑡)𝐺𝑖	𝑡)𝐺𝑖	NOUN
cana-5535	31	1	𝑥	𝑥	X
cana-5535	31	2	𝑎	𝑎	X
cana-5535	31	3	(	(	PUNCT
cana-5535	31	4	𝑡−𝑎	𝑡−𝑎	PUNCT
cana-5535	31	5	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	31	6	)	)	PUNCT
cana-5535	31	7	𝑑𝑡	𝑑𝑡	ADP
cana-5535	31	8	(	(	PUNCT
cana-5535	31	9	4	4	NUM
cana-5535	31	10	)	)	PUNCT
cana-5535	31	11	to	to	PART
cana-5535	31	12	determine	determine	VERB
cana-5535	31	13	unknown	unknown	ADJ
cana-5535	31	14	coefficients	coefficient	NOUN
cana-5535	31	15	𝛽𝑖	𝛽𝑖	VERB
cana-5535	31	16	,	,	PUNCT
cana-5535	31	17	we	we	PRON
cana-5535	31	18	use	use	VERB
cana-5535	31	19	the	the	DET
cana-5535	31	20	method	method	NOUN
cana-5535	31	21	technique	technique	NOUN
cana-5535	31	22	by	by	ADP
cana-5535	31	23	multiplying	multiply	VERB
cana-5535	31	24	equation	equation	NOUN
cana-5535	31	25	(	(	PUNCT
cana-5535	31	26	4	4	NUM
cana-5535	31	27	)	)	PUNCT
cana-5535	31	28	by	by	ADP
cana-5535	31	29	𝐺𝑗	𝐺𝑗	PROPN
cana-5535	31	30	(	(	PUNCT
cana-5535	31	31	𝑡−𝑎	𝑡−𝑎	PUNCT
cana-5535	31	32	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	31	33	)	)	PUNCT
cana-5535	31	34	and	and	CCONJ
cana-5535	31	35	then	then	ADV
cana-5535	31	36	integrating	integrate	VERB
cana-5535	31	37	with	with	ADP
cana-5535	31	38	respect	respect	NOUN
cana-5535	31	39	to	to	ADP
cana-5535	31	40	𝑥	𝑥	PRON
cana-5535	31	41	from	from	ADP
cana-5535	31	42	0	0	NUM
cana-5535	31	43	to	to	ADP
cana-5535	31	44	1	1	NUM
cana-5535	31	45	.	.	PUNCT
cana-5535	32	1	so	so	ADV
cana-5535	32	2	we	we	PRON
cana-5535	32	3	have	have	AUX
cana-5535	32	4	∑	∑	ADV
cana-5535	32	5	(	(	PUNCT
cana-5535	32	6	1	1	NUM
cana-5535	32	7	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	32	8	)	)	PUNCT
cana-5535	32	9	𝑛	𝑛	DET
cana-5535	32	10	𝑖=0	𝑖=0	PROPN
cana-5535	32	11	𝛽𝑖	𝛽𝑖	VERB
cana-5535	32	12	∫	∫	PROPN
cana-5535	32	13	𝐺𝑖	𝐺𝑖	VERB
cana-5535	32	14	′1	′1	SYM
cana-5535	32	15	0	0	NUM
cana-5535	32	16	(	(	PUNCT
cana-5535	32	17	𝑥−𝑎	𝑥−𝑎	PROPN
cana-5535	32	18	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	32	19	)	)	PUNCT
cana-5535	33	1	𝐺𝑗	𝐺𝑗	PROPN
cana-5535	33	2	(	(	PUNCT
cana-5535	33	3	𝑥−𝑎	𝑥−𝑎	PROPN
cana-5535	33	4	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	33	5	)	)	PUNCT
cana-5535	33	6	𝑑𝑥	𝑑𝑥	NOUN
cana-5535	33	7	=	=	VERB
cana-5535	33	8	∫	∫	NOUN
cana-5535	33	9	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5535	33	10	)	)	PUNCT
cana-5535	33	11	1	1	NUM
cana-5535	33	12	0	0	X
cana-5535	33	13	𝐺𝑗	𝐺𝑗	PROPN
cana-5535	33	14	(	(	PUNCT
cana-5535	33	15	𝑥−𝑎	𝑥−𝑎	PROPN
cana-5535	33	16	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	33	17	)	)	PUNCT
cana-5535	33	18	𝑑𝑥	𝑑𝑥	VERB
cana-5535	33	19	+	+	NUM
cana-5535	33	20	∫	∫	PROPN
cana-5535	33	21	[	[	X
cana-5535	33	22	∑	∑	INTJ
cana-5535	33	23	𝛽𝑖	𝛽𝑖	VERB
cana-5535	33	24	∫	∫	PROPN
cana-5535	33	25	𝑘(𝑥	𝑘(𝑥	PROPN
cana-5535	33	26	,	,	PUNCT
cana-5535	33	27	𝑡)𝐺𝑖	𝑡)𝐺𝑖	PROPN
cana-5535	33	28	(	(	PUNCT
cana-5535	33	29	𝑡−𝑎	𝑡−𝑎	PROPN
cana-5535	33	30	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	33	31	)	)	PUNCT
cana-5535	33	32	𝑑𝑡	𝑑𝑡	ADP
cana-5535	33	33	𝑥	𝑥	DET
cana-5535	33	34	𝑎	𝑎	NOUN
cana-5535	33	35	𝑛	𝑛	PROPN
cana-5535	33	36	𝑖=0	𝑖=0	PROPN
cana-5535	33	37	]	]	PUNCT
cana-5535	33	38	1	1	NUM
cana-5535	33	39	0	0	X
cana-5535	33	40	𝐺𝑗	𝐺𝑗	PROPN
cana-5535	33	41	(	(	PUNCT
cana-5535	33	42	𝑥−𝑎	𝑥−𝑎	PROPN
cana-5535	33	43	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	33	44	)	)	PUNCT
cana-5535	33	45	𝑑𝑥	𝑑𝑥	VERB
cana-5535	33	46	(	(	PUNCT
cana-5535	33	47	5	5	NUM
cana-5535	33	48	)	)	PUNCT
cana-5535	33	49	for	for	ADP
cana-5535	33	50	=	=	NOUN
cana-5535	33	51	0,1	0,1	NUM
cana-5535	33	52	,	,	PUNCT
cana-5535	33	53	…	…	PUNCT
cana-5535	33	54	,	,	PUNCT
cana-5535	33	55	𝑛	𝑛	NOUN
cana-5535	33	56	,	,	PUNCT
cana-5535	33	57	or	or	CCONJ
cana-5535	33	58	equivalently	equivalently	ADV
cana-5535	33	59	∑	∑	PUNCT
cana-5535	33	60	(	(	PUNCT
cana-5535	33	61	1	1	NUM
cana-5535	33	62	𝑏−𝑎	𝑏−𝑎	ADV
cana-5535	33	63	)	)	PUNCT
cana-5535	33	64	𝛽𝑖	𝛽𝑖	CCONJ
cana-5535	33	65	𝑛	𝑛	DET
cana-5535	33	66	𝑖=0	𝑖=0	PROPN
cana-5535	33	67	∫	∫	PROPN
cana-5535	34	1	𝐺𝑖	𝐺𝑖	VERB
cana-5535	34	2	′1	′1	SYM
cana-5535	34	3	0	0	NUM
cana-5535	34	4	(	(	PUNCT
cana-5535	34	5	𝑥−𝑎	𝑥−𝑎	PROPN
cana-5535	34	6	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	34	7	)	)	PUNCT
cana-5535	35	1	𝐺𝑗	𝐺𝑗	PROPN
cana-5535	35	2	(	(	PUNCT
cana-5535	35	3	𝑥−𝑎	𝑥−𝑎	PROPN
cana-5535	35	4	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	35	5	)	)	PUNCT
cana-5535	35	6	𝑑𝑥	𝑑𝑥	NOUN
cana-5535	35	7	=	=	VERB
cana-5535	35	8	∫	∫	NOUN
cana-5535	35	9	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5535	35	10	)	)	PUNCT
cana-5535	35	11	1	1	NUM
cana-5535	35	12	0	0	X
cana-5535	35	13	𝐺𝑗	𝐺𝑗	PROPN
cana-5535	35	14	(	(	PUNCT
cana-5535	35	15	𝑥−𝑎	𝑥−𝑎	PROPN
cana-5535	35	16	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	35	17	)	)	PUNCT
cana-5535	35	18	𝑑𝑥	𝑑𝑥	VERB
cana-5535	35	19	+	+	CCONJ
cana-5535	35	20	∑	∑	PUNCT
cana-5535	35	21	𝛽𝑖	𝛽𝑖	VERB
cana-5535	35	22	𝑛	𝑛	DET
cana-5535	35	23	𝑖=0	𝑖=0	PROPN
cana-5535	35	24	∫	∫	PROPN
cana-5535	36	1	[	[	X
cana-5535	36	2	∫	∫	PROPN
cana-5535	36	3	𝑘(𝑥	𝑘(𝑥	PROPN
cana-5535	36	4	,	,	PUNCT
cana-5535	36	5	𝑡)𝐺𝑖	𝑡)𝐺𝑖	PROPN
cana-5535	36	6	(	(	PUNCT
cana-5535	36	7	𝑡−𝑎	𝑡−𝑎	PROPN
cana-5535	36	8	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	36	9	)	)	PUNCT
cana-5535	36	10	𝑑𝑡	𝑑𝑡	ADP
cana-5535	36	11	𝑥	𝑥	PRON
cana-5535	36	12	𝑎	𝑎	X
cana-5535	36	13	]	]	SYM
cana-5535	36	14	1	1	NUM
cana-5535	36	15	0	0	X
cana-5535	36	16	𝐺𝑗	𝐺𝑗	PROPN
cana-5535	36	17	(	(	PUNCT
cana-5535	36	18	𝑥−𝑎	𝑥−𝑎	PROPN
cana-5535	36	19	𝑏−𝑎	𝑏−𝑎	PROPN
cana-5535	36	20	)	)	PUNCT
cana-5535	36	21	𝑑𝑥	𝑑𝑥	VERB
cana-5535	36	22	(	(	PUNCT
cana-5535	36	23	6	6	NUM
cana-5535	36	24	)	)	PUNCT
cana-5535	36	25	if	if	SCONJ
cana-5535	36	26	necessary	necessary	ADJ
cana-5535	36	27	,	,	PUNCT
cana-5535	36	28	the	the	DET
cana-5535	36	29	integrals	integral	NOUN
cana-5535	36	30	can	can	AUX
cana-5535	36	31	be	be	AUX
cana-5535	36	32	evaluated	evaluate	VERB
cana-5535	36	33	using	use	VERB
cana-5535	36	34	numerical	numerical	ADJ
cana-5535	36	35	techniques	technique	NOUN
cana-5535	36	36	.	.	PUNCT
cana-5535	37	1	this	this	DET
cana-5535	37	2	process	process	NOUN
cana-5535	37	3	results	result	VERB
cana-5535	37	4	in	in	ADP
cana-5535	37	5	a	a	DET
cana-5535	37	6	system	system	NOUN
cana-5535	37	7	of	of	ADP
cana-5535	37	8	linear	linear	PROPN
cana-5535	37	9	equations	equation	NOUN
cana-5535	37	10	involving	involve	VERB
cana-5535	37	11	the	the	DET
cana-5535	37	12	unknown	unknown	ADJ
cana-5535	37	13	coefficients	coefficient	NOUN
cana-5535	37	14	{	{	PUNCT
cana-5535	37	15	𝛽0	𝛽0	NOUN
cana-5535	37	16	,	,	PUNCT
cana-5535	37	17	𝛽1	𝛽1	NOUN
cana-5535	37	18	,	,	PUNCT
cana-5535	37	19	…	…	PUNCT
cana-5535	37	20	,	,	PUNCT
cana-5535	37	21	𝛽𝑛	𝛽𝑛	NOUN
cana-5535	37	22	}	}	PUNCT
cana-5535	37	23	.	.	PUNCT
cana-5535	38	1	in	in	ADP
cana-5535	38	2	many	many	ADJ
cana-5535	38	3	studies	study	NOUN
cana-5535	38	4	,	,	PUNCT
cana-5535	38	5	researchers	researcher	NOUN
cana-5535	38	6	incorporate	incorporate	VERB
cana-5535	38	7	the	the	DET
cana-5535	38	8	initial	initial	ADJ
cana-5535	38	9	condition	condition	NOUN
cana-5535	38	10	by	by	ADP
cana-5535	38	11	directly	directly	ADV
cana-5535	38	12	substituting	substitute	VERB
cana-5535	38	13	it	it	PRON
cana-5535	38	14	into	into	ADP
cana-5535	38	15	the	the	DET
cana-5535	38	16	system	system	NOUN
cana-5535	38	17	.	.	PUNCT
cana-5535	39	1	𝑦(𝑎	𝑦(𝑎	NOUN
cana-5535	39	2	)	)	PUNCT
cana-5535	40	1	=	=	NOUN
cana-5535	40	2	∝	∝	PROPN
cana-5535	40	3	⇒	⇒	VERB
cana-5535	40	4	∑	∑	PROPN
cana-5535	40	5	𝛽𝑖𝐺𝑖	𝛽𝑖𝐺𝑖	PROPN
cana-5535	40	6	𝑛	𝑛	DET
cana-5535	40	7	𝑖=0	𝑖=0	PROPN
cana-5535	40	8	(	(	PUNCT
cana-5535	40	9	𝑎−𝑎	𝑎−𝑎	NOUN
cana-5535	40	10	𝑏−𝑎	𝑏−𝑎	ADV
cana-5535	40	11	)	)	PUNCT
cana-5535	41	1	=	=	PUNCT
cana-5535	41	2	∑	∑	PUNCT
cana-5535	41	3	𝛽𝑖𝐺𝑖	𝛽𝑖𝐺𝑖	PROPN
cana-5535	41	4	𝑛	𝑛	PRON
cana-5535	41	5	𝑖=0	𝑖=0	PROPN
cana-5535	41	6	(	(	PUNCT
cana-5535	41	7	0	0	NUM
cana-5535	41	8	)	)	PUNCT
cana-5535	42	1	=	=	NOUN
cana-5535	42	2	∝	∝	NOUN
cana-5535	42	3	(	(	PUNCT
cana-5535	42	4	7	7	X
cana-5535	42	5	)	)	PUNCT
cana-5535	42	6	maintaining	maintain	VERB
cana-5535	42	7	an	an	DET
cana-5535	42	8	equal	equal	ADJ
cana-5535	42	9	number	number	NOUN
cana-5535	42	10	of	of	ADP
cana-5535	42	11	equations	equation	NOUN
cana-5535	42	12	in	in	ADP
cana-5535	42	13	the	the	DET
cana-5535	42	14	previously	previously	ADV
cana-5535	42	15	constructed	construct	VERB
cana-5535	42	16	linear	linear	NOUN
cana-5535	42	17	system	system	NOUN
cana-5535	42	18	,	,	PUNCT
cana-5535	42	19	the	the	DET
cana-5535	42	20	unknown	unknown	ADJ
cana-5535	42	21	coefficients	coefficient	NOUN
cana-5535	42	22	are	be	AUX
cana-5535	42	23	determined	determine	VERB
cana-5535	42	24	by	by	ADP
cana-5535	42	25	simultaneously	simultaneously	ADV
cana-5535	42	26	solving	solve	VERB
cana-5535	42	27	equations	equation	NOUN
cana-5535	42	28	(	(	PUNCT
cana-5535	42	29	6	6	NUM
cana-5535	42	30	)	)	PUNCT
cana-5535	42	31	and	and	CCONJ
cana-5535	42	32	(	(	PUNCT
cana-5535	42	33	7	7	NUM
cana-5535	42	34	)	)	PUNCT
cana-5535	42	35	.	.	PUNCT
cana-5535	43	1	once	once	ADV
cana-5535	43	2	obtained	obtain	VERB
cana-5535	43	3	,	,	PUNCT
cana-5535	43	4	these	these	DET
cana-5535	43	5	values	value	NOUN
cana-5535	43	6	are	be	AUX
cana-5535	43	7	substituted	substitute	VERB
cana-5535	43	8	into	into	ADP
cana-5535	43	9	equation	equation	NOUN
cana-5535	43	10	(	(	PUNCT
cana-5535	43	11	2	2	NUM
cana-5535	43	12	)	)	PUNCT
cana-5535	43	13	to	to	PART
cana-5535	43	14	derive	derive	VERB
cana-5535	43	15	an	an	DET
cana-5535	43	16	approximate	approximate	ADJ
cana-5535	43	17	solution	solution	NOUN
cana-5535	43	18	to	to	ADP
cana-5535	43	19	the	the	DET
cana-5535	43	20	original	original	ADJ
cana-5535	43	21	equation	equation	NOUN
cana-5535	43	22	(	(	PUNCT
cana-5535	43	23	1	1	NUM
cana-5535	43	24	)	)	PUNCT
cana-5535	43	25	.	.	PUNCT
cana-5535	44	1	communications	communication	NOUN
cana-5535	44	2	on	on	ADP
cana-5535	44	3	applied	apply	VERB
cana-5535	44	4	nonlinear	nonlinear	ADJ
cana-5535	44	5	analysis	analysis	NOUN
cana-5535	44	6	issn	issn	NOUN
cana-5535	44	7	:	:	PUNCT
cana-5535	44	8	1074	1074	NUM
cana-5535	44	9	-	-	PUNCT
cana-5535	44	10	133x	133x	NUM
cana-5535	44	11	vol	vol	VERB
cana-5535	44	12	32	32	NUM
cana-5535	44	13	no	no	NOUN
cana-5535	44	14	.	.	PUNCT
cana-5535	45	1	10s	10	NOUN
cana-5535	45	2	(	(	PUNCT
cana-5535	45	3	2025	2025	NUM
cana-5535	45	4	)	)	PUNCT
cana-5535	45	5	2582	2582	NUM
cana-5535	45	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5535	45	7	3	3	X
cana-5535	45	8	.	.	X
cana-5535	46	1	genocchi	genocchi	PROPN
cana-5535	46	2	polynomials	polynomial	NOUN
cana-5535	46	3	and	and	CCONJ
cana-5535	46	4	their	their	PRON
cana-5535	46	5	properties	property	NOUN
cana-5535	46	6	the	the	DET
cana-5535	46	7	classical	classical	ADJ
cana-5535	46	8	genocchi	genocchi	NOUN
cana-5535	46	9	polynomial	polynomial	ADJ
cana-5535	46	10	𝐺𝑛(𝑥	𝐺𝑛(𝑥	NOUN
cana-5535	46	11	)	)	PUNCT
cana-5535	46	12	is	be	AUX
cana-5535	46	13	usually	usually	ADV
cana-5535	46	14	defined	define	VERB
cana-5535	46	15	by	by	ADP
cana-5535	46	16	means	mean	NOUN
cana-5535	46	17	of	of	ADP
cana-5535	46	18	the	the	DET
cana-5535	46	19	exponential	exponential	ADJ
cana-5535	46	20	generating	generating	NOUN
cana-5535	46	21	functions	function	NOUN
cana-5535	46	22	2𝑡𝑒𝑥𝑡	2𝑡𝑒𝑥𝑡	NUM
cana-5535	46	23	𝑒𝑡	𝑒𝑡	NOUN
cana-5535	46	24	+	+	CCONJ
cana-5535	46	25	1	1	NUM
cana-5535	46	26	=	=	SYM
cana-5535	46	27	∑𝐺𝑛(𝑥	∑𝐺𝑛(𝑥	NOUN
cana-5535	46	28	)	)	PUNCT
cana-5535	47	1	+	+	NOUN
cana-5535	47	2	∞	∞	PROPN
cana-5535	47	3	𝑛=0	𝑛=0	NOUN
cana-5535	47	4	𝑡𝑛	𝑡𝑛	X
cana-5535	47	5	𝑛	𝑛	VERB
cana-5535	47	6	!	!	PUNCT
cana-5535	47	7	where	where	SCONJ
cana-5535	47	8	𝐺𝑛(𝑥	𝐺𝑛(𝑥	NOUN
cana-5535	47	9	)	)	PUNCT
cana-5535	47	10	is	be	AUX
cana-5535	47	11	the	the	DET
cana-5535	47	12	genocchi	genocchi	PROPN
cana-5535	47	13	polynomial	polynomial	NOUN
cana-5535	47	14	of	of	ADP
cana-5535	47	15	degree	degree	NOUN
cana-5535	47	16	𝑛	𝑛	PROPN
cana-5535	47	17	and	and	CCONJ
cana-5535	47	18	is	be	AUX
cana-5535	47	19	given	give	VERB
cana-5535	47	20	by	by	ADP
cana-5535	47	21	𝐺𝑛(𝑥	𝐺𝑛(𝑥	NOUN
cana-5535	47	22	)	)	PUNCT
cana-5535	47	23	=	=	PUNCT
cana-5535	47	24	∑	∑	PROPN
cana-5535	47	25	(	(	PUNCT
cana-5535	47	26	𝑛	𝑛	PRON
cana-5535	47	27	𝑘	𝑘	NOUN
cana-5535	47	28	)	)	PUNCT
cana-5535	47	29	𝐺𝑛−𝑘(𝑥	𝐺𝑛−𝑘(𝑥	PROPN
cana-5535	47	30	)	)	PUNCT
cana-5535	47	31	𝑛	𝑛	NOUN
cana-5535	47	32	𝑘=0	𝑘=0	ADP
cana-5535	47	33	𝑥𝑘	𝑥𝑘	X
cana-5535	47	34	𝐺𝑛−𝑘.	𝐺𝑛−𝑘.	PRON
cana-5535	47	35	is	be	AUX
cana-5535	47	36	the	the	DET
cana-5535	47	37	genocchi	genocchi	PROPN
cana-5535	47	38	number	number	NOUN
cana-5535	47	39	.	.	PUNCT
cana-5535	48	1	some	some	PRON
cana-5535	48	2	of	of	ADP
cana-5535	48	3	the	the	DET
cana-5535	48	4	important	important	ADJ
cana-5535	48	5	properties	property	NOUN
cana-5535	48	6	of	of	ADP
cana-5535	48	7	these	these	DET
cana-5535	48	8	polynomials	polynomial	NOUN
cana-5535	48	9	include	include	VERB
cana-5535	48	10	{	{	PUNCT
cana-5535	48	11	∫𝐺𝑝(𝑥)𝐺𝑞(𝑥	∫𝐺𝑝(𝑥)𝐺𝑞(𝑥	NOUN
cana-5535	48	12	)	)	PUNCT
cana-5535	48	13	1	1	NUM
cana-5535	48	14	0	0	NUM
cana-5535	48	15	𝑑𝑥	𝑑𝑥	NOUN
cana-5535	48	16	=	=	SYM
cana-5535	48	17	2(−1)𝑝𝑝	2(−1)𝑝𝑝	NUM
cana-5535	48	18	!	!	PUNCT
cana-5535	49	1	𝑞	𝑞	X
cana-5535	49	2	!	!	PUNCT
cana-5535	49	3	(	(	PUNCT
cana-5535	49	4	𝑝	𝑝	PROPN
cana-5535	49	5	+	+	NUM
cana-5535	49	6	𝑞	𝑞	NOUN
cana-5535	49	7	)	)	PUNCT
cana-5535	49	8	!	!	PUNCT
cana-5535	50	1	𝐺𝑝+𝑞	𝐺𝑝+𝑞	PROPN
cana-5535	50	2	,	,	PUNCT
cana-5535	50	3	𝑝	𝑝	PROPN
cana-5535	50	4	,	,	PUNCT
cana-5535	50	5	𝑞	𝑞	PROPN
cana-5535	50	6	∈	∈	PROPN
cana-5535	50	7	ℕ	ℕ	PROPN
cana-5535	50	8	∗	∗	VERB
cana-5535	50	9	𝑑𝐺𝑝(𝑥	𝑑𝐺𝑝(𝑥	NOUN
cana-5535	50	10	)	)	PUNCT
cana-5535	50	11	𝑑𝑥	𝑑𝑥	VERB
cana-5535	50	12	=	=	SYM
cana-5535	50	13	𝑛𝐺𝑛−1(𝑥	𝑛𝐺𝑛−1(𝑥	NUM
cana-5535	50	14	)	)	PUNCT
cana-5535	50	15	,	,	PUNCT
cana-5535	50	16	𝑝	𝑝	PROPN
cana-5535	50	17	∈	∈	PROPN
cana-5535	50	18	ℕ	ℕ	PROPN
cana-5535	50	19	∗	∗	NOUN
cana-5535	50	20	𝐺𝑝(1	𝐺𝑝(1	NOUN
cana-5535	50	21	)	)	PUNCT
cana-5535	51	1	+	+	CCONJ
cana-5535	51	2	𝐺𝑞(0	𝐺𝑞(0	ADJ
cana-5535	51	3	)	)	PUNCT
cana-5535	51	4	=	=	SYM
cana-5535	51	5	0	0	NUM
cana-5535	51	6	,	,	PUNCT
cana-5535	51	7	𝑝	𝑝	PROPN
cana-5535	51	8	∈	∈	PROPN
cana-5535	51	9	ℕ	ℕ	PROPN
cana-5535	51	10	∗	∗	NOUN
cana-5535	51	11	4	4	NUM
cana-5535	51	12	.	.	PUNCT
cana-5535	51	13	numerical	numerical	ADJ
cana-5535	51	14	examples	example	NOUN
cana-5535	51	15	in	in	ADP
cana-5535	51	16	this	this	DET
cana-5535	51	17	section	section	NOUN
cana-5535	51	18	,	,	PUNCT
cana-5535	51	19	we	we	PRON
cana-5535	51	20	intend	intend	VERB
cana-5535	51	21	to	to	PART
cana-5535	51	22	show	show	VERB
cana-5535	51	23	the	the	DET
cana-5535	51	24	efficiency	efficiency	NOUN
cana-5535	51	25	of	of	ADP
cana-5535	51	26	the	the	DET
cana-5535	51	27	method	method	NOUN
cana-5535	51	28	for	for	ADP
cana-5535	51	29	solving	solve	VERB
cana-5535	51	30	fredholm	fredholm	NOUN
cana-5535	51	31	and	and	CCONJ
cana-5535	51	32	volterra	volterra	NOUN
cana-5535	51	33	integro	integro	PROPN
cana-5535	51	34	-	-	PUNCT
cana-5535	51	35	differential	differential	NOUN
cana-5535	51	36	equations	equation	NOUN
cana-5535	51	37	of	of	ADP
cana-5535	51	38	the	the	DET
cana-5535	51	39	second	second	ADJ
cana-5535	51	40	kind	kind	NOUN
cana-5535	51	41	by	by	ADP
cana-5535	51	42	genocchi	genocchi	PROPN
cana-5535	51	43	polynomials	polynomial	NOUN
cana-5535	51	44	by	by	ADP
cana-5535	51	45	presenting	present	VERB
cana-5535	51	46	six	six	NUM
cana-5535	51	47	illustrative	illustrative	ADJ
cana-5535	51	48	examples	example	NOUN
cana-5535	51	49	.	.	PUNCT
cana-5535	52	1	the	the	DET
cana-5535	52	2	absolute	absolute	ADJ
cana-5535	52	3	error	error	NOUN
cana-5535	52	4	for	for	ADP
cana-5535	52	5	this	this	DET
cana-5535	52	6	formulation	formulation	NOUN
cana-5535	52	7	is	be	AUX
cana-5535	52	8	need	need	NOUN
cana-5535	52	9	by	by	ADP
cana-5535	52	10	𝐸(𝑥	𝐸(𝑥	NOUN
cana-5535	52	11	)	)	PUNCT
cana-5535	52	12	=	=	SYM
cana-5535	52	13	|𝑦(𝑥	|𝑦(𝑥	PROPN
cana-5535	52	14	)	)	PUNCT
cana-5535	52	15	−	−	PROPN
cana-5535	52	16	𝑦𝑛(𝑥)|	𝑦𝑛(𝑥)|	PUNCT
cana-5535	52	17	.	.	PUNCT
cana-5535	53	1	example	example	NOUN
cana-5535	54	1	1	1	NUM
cana-5535	54	2	.	.	PUNCT
cana-5535	54	3	let	let	VERB
cana-5535	54	4	us	we	PRON
cana-5535	54	5	consider	consider	VERB
cana-5535	54	6	the	the	DET
cana-5535	54	7	linear	linear	ADJ
cana-5535	54	8	integro	integro	ADJ
cana-5535	54	9	-	-	PUNCT
cana-5535	54	10	differential	differential	NOUN
cana-5535	54	11	equation	equation	NOUN
cana-5535	54	12	of	of	ADP
cana-5535	54	13	volterra	volterra	NOUN
cana-5535	54	14	.	.	PUNCT
cana-5535	55	1	𝑦′(𝑥	𝑦′(𝑥	VERB
cana-5535	55	2	)	)	PUNCT
cana-5535	55	3	=	=	SYM
cana-5535	55	4	2	2	NUM
cana-5535	55	5	−	−	NOUN
cana-5535	55	6	𝑥2	𝑥2	NOUN
cana-5535	55	7	4	4	NUM
cana-5535	55	8	+	+	NOUN
cana-5535	55	9	1	1	NUM
cana-5535	55	10	4	4	NUM
cana-5535	55	11	∫	∫	NOUN
cana-5535	55	12	𝑦(𝑡)𝑑𝑡	𝑦(𝑡)𝑑𝑡	NOUN
cana-5535	55	13	𝑥	𝑥	NOUN
cana-5535	55	14	0	0	NUM
cana-5535	55	15	with	with	ADP
cana-5535	55	16	the	the	DET
cana-5535	55	17	initial	initial	ADJ
cana-5535	55	18	condition	condition	NOUN
cana-5535	55	19	𝑦(0	𝑦(0	PROPN
cana-5535	55	20	)	)	PUNCT
cana-5535	55	21	=	=	SYM
cana-5535	55	22	0	0	NUM
cana-5535	56	1	where	where	SCONJ
cana-5535	56	2	the	the	DET
cana-5535	56	3	function	function	NOUN
cana-5535	56	4	𝑦(𝑥	𝑦(𝑥	NOUN
cana-5535	56	5	)	)	PUNCT
cana-5535	56	6	=	=	SYM
cana-5535	57	1	2𝑥	2𝑥	NOUN
cana-5535	57	2	is	be	AUX
cana-5535	57	3	the	the	DET
cana-5535	57	4	exact	exact	ADJ
cana-5535	57	5	solution	solution	NOUN
cana-5535	57	6	.	.	PUNCT
cana-5535	58	1	the	the	DET
cana-5535	58	2	approximate	approximate	ADJ
cana-5535	58	3	solution	solution	NOUN
cana-5535	58	4	𝑦𝑛(𝑥	𝑦𝑛(𝑥	NOUN
cana-5535	58	5	)	)	PUNCT
cana-5535	58	6	of	of	ADP
cana-5535	58	7	𝑦(𝑥	𝑦(𝑥	NOUN
cana-5535	58	8	)	)	PUNCT
cana-5535	58	9	is	be	AUX
cana-5535	58	10	obtained	obtain	VERB
cana-5535	58	11	by	by	ADP
cana-5535	58	12	the	the	DET
cana-5535	58	13	genocchi	genocchi	PROPN
cana-5535	58	14	polynomial	polynomial	ADJ
cana-5535	58	15	method	method	NOUN
cana-5535	58	16	.	.	PUNCT
cana-5535	59	1	communications	communication	NOUN
cana-5535	59	2	on	on	ADP
cana-5535	59	3	applied	apply	VERB
cana-5535	59	4	nonlinear	nonlinear	ADJ
cana-5535	59	5	analysis	analysis	NOUN
cana-5535	59	6	issn	issn	NOUN
cana-5535	59	7	:	:	PUNCT
cana-5535	59	8	1074	1074	NUM
cana-5535	59	9	-	-	PUNCT
cana-5535	59	10	133x	133x	NUM
cana-5535	59	11	vol	vol	VERB
cana-5535	59	12	32	32	NUM
cana-5535	59	13	no	no	NOUN
cana-5535	59	14	.	.	PUNCT
cana-5535	60	1	10s	10	NOUN
cana-5535	60	2	(	(	PUNCT
cana-5535	60	3	2025	2025	NUM
cana-5535	60	4	)	)	PUNCT
cana-5535	60	5	2583	2583	NUM
cana-5535	60	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5535	60	7	figure	figure	NOUN
cana-5535	60	8	1	1	NUM
cana-5535	60	9	.	.	PUNCT
cana-5535	61	1	graph	graph	NOUN
cana-5535	61	2	for	for	ADP
cana-5535	61	3	example	example	NOUN
cana-5535	61	4	1	1	NUM
cana-5535	61	5	example	example	NOUN
cana-5535	61	6	2	2	NUM
cana-5535	61	7	.	.	PUNCT
cana-5535	62	1	let	let	VERB
cana-5535	62	2	us	we	PRON
cana-5535	62	3	consider	consider	VERB
cana-5535	62	4	the	the	DET
cana-5535	62	5	linear	linear	ADJ
cana-5535	62	6	integro	integro	ADJ
cana-5535	62	7	-	-	PUNCT
cana-5535	62	8	differential	differential	NOUN
cana-5535	62	9	equation	equation	NOUN
cana-5535	62	10	of	of	ADP
cana-5535	62	11	volterra	volterra	NOUN
cana-5535	62	12	.	.	PUNCT
cana-5535	63	1	𝑦′(𝑥	𝑦′(𝑥	VERB
cana-5535	63	2	)	)	PUNCT
cana-5535	63	3	=	=	SYM
cana-5535	64	1	1	1	NUM
cana-5535	64	2	−	−	PROPN
cana-5535	64	3	2𝑥	2𝑥	PROPN
cana-5535	64	4	sin(𝑥	sin(𝑥	PROPN
cana-5535	64	5	)	)	PUNCT
cana-5535	64	6	+	+	NUM
cana-5535	64	7	∫	∫	PROPN
cana-5535	64	8	𝑦(𝑡	𝑦(𝑡	NUM
cana-5535	64	9	)	)	PUNCT
cana-5535	64	10	𝑥	𝑥	NOUN
cana-5535	64	11	0	0	NUM
cana-5535	64	12	𝑑𝑡	𝑑𝑡	ADP
cana-5535	64	13	with	with	ADP
cana-5535	64	14	the	the	DET
cana-5535	64	15	initial	initial	ADJ
cana-5535	64	16	condition	condition	NOUN
cana-5535	64	17	𝑦(0	𝑦(0	PROPN
cana-5535	64	18	)	)	PUNCT
cana-5535	64	19	=	=	SYM
cana-5535	64	20	0	0	NUM
cana-5535	65	1	the	the	DET
cana-5535	65	2	exact	exact	ADJ
cana-5535	65	3	solution	solution	NOUN
cana-5535	65	4	is	be	AUX
cana-5535	65	5	given	give	VERB
cana-5535	65	6	by	by	ADP
cana-5535	65	7	𝑦(𝑥	𝑦(𝑥	NOUN
cana-5535	65	8	)	)	PUNCT
cana-5535	65	9	=	=	SYM
cana-5535	65	10	𝑥	𝑥	DET
cana-5535	65	11	cos(𝑥	cos(𝑥	PROPN
cana-5535	65	12	)	)	PUNCT
cana-5535	65	13	the	the	DET
cana-5535	65	14	approximate	approximate	ADJ
cana-5535	65	15	solution	solution	NOUN
cana-5535	65	16	𝑦𝑛(𝑥	𝑦𝑛(𝑥	NOUN
cana-5535	65	17	)	)	PUNCT
cana-5535	65	18	of	of	ADP
cana-5535	65	19	𝑦(𝑥	𝑦(𝑥	NOUN
cana-5535	65	20	)	)	PUNCT
cana-5535	65	21	is	be	AUX
cana-5535	65	22	obtained	obtain	VERB
cana-5535	65	23	by	by	ADP
cana-5535	65	24	the	the	DET
cana-5535	65	25	genocchi	genocchi	PROPN
cana-5535	65	26	polynomial	polynomial	ADJ
cana-5535	65	27	method	method	NOUN
cana-5535	65	28	.	.	PUNCT
cana-5535	66	1	figure	figure	NOUN
cana-5535	66	2	2	2	NUM
cana-5535	66	3	.	.	PUNCT
cana-5535	66	4	graph	graph	NOUN
cana-5535	66	5	for	for	ADP
cana-5535	66	6	example	example	NOUN
cana-5535	66	7	2	2	NUM
cana-5535	66	8	0	0	NUM
cana-5535	66	9	0.1	0.1	NUM
cana-5535	66	10	0.2	0.2	NUM
cana-5535	66	11	0.3	0.3	NUM
cana-5535	66	12	0.4	0.4	NUM
cana-5535	66	13	0.5	0.5	NUM
cana-5535	66	14	0.6	0.6	NUM
cana-5535	66	15	0.7	0.7	NUM
cana-5535	66	16	0.8	0.8	NUM
cana-5535	66	17	0.9	0.9	NUM
cana-5535	66	18	1	1	NUM
cana-5535	66	19	0	0	NUM
cana-5535	66	20	0.2	0.2	NUM
cana-5535	66	21	0.4	0.4	NUM
cana-5535	66	22	0.6	0.6	NUM
cana-5535	66	23	0.8	0.8	NUM
cana-5535	66	24	1	1	NUM
cana-5535	66	25	1.2	1.2	NUM
cana-5535	66	26	1.4	1.4	NUM
cana-5535	66	27	1.6	1.6	NUM
cana-5535	66	28	1.8	1.8	NUM
cana-5535	66	29	2	2	NUM
cana-5535	66	30	x	x	SYM
cana-5535	66	31	y	y	PROPN
cana-5535	66	32	exacte	exacte	PROPN
cana-5535	66	33	solution	solution	PROPN
cana-5535	66	34	approx	approx	PROPN
cana-5535	66	35	.	.	PUNCT
cana-5535	67	1	solution	solution	NOUN
cana-5535	67	2	0	0	NUM
cana-5535	67	3	0.1	0.1	NUM
cana-5535	67	4	0.2	0.2	NUM
cana-5535	67	5	0.3	0.3	NUM
cana-5535	67	6	0.4	0.4	NUM
cana-5535	67	7	0.5	0.5	NUM
cana-5535	67	8	0.6	0.6	NUM
cana-5535	67	9	0.7	0.7	NUM
cana-5535	67	10	0.8	0.8	NUM
cana-5535	67	11	0.9	0.9	NUM
cana-5535	67	12	1	1	NUM
cana-5535	67	13	0	0	NUM
cana-5535	67	14	0.1	0.1	NUM
cana-5535	67	15	0.2	0.2	NUM
cana-5535	67	16	0.3	0.3	NUM
cana-5535	67	17	0.4	0.4	NUM
cana-5535	67	18	0.5	0.5	NUM
cana-5535	67	19	0.6	0.6	NUM
cana-5535	67	20	0.7	0.7	NUM
cana-5535	67	21	x	x	SYM
cana-5535	67	22	y	y	PROPN
cana-5535	67	23	exacte	exacte	PROPN
cana-5535	67	24	solution	solution	PROPN
cana-5535	67	25	approx	approx	PROPN
cana-5535	67	26	.	.	PUNCT
cana-5535	68	1	solution	solution	NOUN
cana-5535	68	2	communications	communication	NOUN
cana-5535	68	3	on	on	ADP
cana-5535	68	4	applied	apply	VERB
cana-5535	68	5	nonlinear	nonlinear	ADJ
cana-5535	68	6	analysis	analysis	NOUN
cana-5535	68	7	issn	issn	NOUN
cana-5535	68	8	:	:	PUNCT
cana-5535	68	9	1074	1074	NUM
cana-5535	68	10	-	-	PUNCT
cana-5535	68	11	133x	133x	NUM
cana-5535	68	12	vol	vol	VERB
cana-5535	68	13	32	32	NUM
cana-5535	68	14	no	no	NOUN
cana-5535	68	15	.	.	PUNCT
cana-5535	69	1	10s	10	NOUN
cana-5535	69	2	(	(	PUNCT
cana-5535	69	3	2025	2025	NUM
cana-5535	69	4	)	)	PUNCT
cana-5535	69	5	2584	2584	NUM
cana-5535	69	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5535	69	7	example	example	NOUN
cana-5535	70	1	3	3	X
cana-5535	70	2	.	.	PUNCT
cana-5535	70	3	let	let	VERB
cana-5535	70	4	us	we	PRON
cana-5535	70	5	consider	consider	VERB
cana-5535	70	6	the	the	DET
cana-5535	70	7	linear	linear	ADJ
cana-5535	70	8	integro	integro	ADJ
cana-5535	70	9	-	-	PUNCT
cana-5535	70	10	differential	differential	NOUN
cana-5535	70	11	equation	equation	NOUN
cana-5535	70	12	of	of	ADP
cana-5535	70	13	fredholm	fredholm	NOUN
cana-5535	70	14	𝑦′(𝑥	𝑦′(𝑥	PROPN
cana-5535	70	15	)	)	PUNCT
cana-5535	70	16	=	=	SYM
cana-5535	71	1	3𝑒3𝑥	3𝑒3𝑥	NOUN
cana-5535	71	2	−	−	NOUN
cana-5535	71	3	1	1	NUM
cana-5535	71	4	3	3	NUM
cana-5535	71	5	(	(	PUNCT
cana-5535	71	6	2𝑒3	2𝑒3	NUM
cana-5535	71	7	+	+	SYM
cana-5535	71	8	1)𝑥	1)𝑥	NUM
cana-5535	71	9	+	+	CCONJ
cana-5535	71	10	∫	∫	PROPN
cana-5535	71	11	3𝑥𝑡𝑦(𝑡	3𝑥𝑡𝑦(𝑡	NUM
cana-5535	71	12	)	)	PUNCT
cana-5535	71	13	1	1	NUM
cana-5535	71	14	0	0	NUM
cana-5535	71	15	𝑑𝑡	𝑑𝑡	ADP
cana-5535	71	16	with	with	ADP
cana-5535	71	17	the	the	DET
cana-5535	71	18	initial	initial	ADJ
cana-5535	71	19	condition	condition	NOUN
cana-5535	71	20	𝑦(0	𝑦(0	PROPN
cana-5535	71	21	)	)	PUNCT
cana-5535	71	22	=	=	PUNCT
cana-5535	72	1	1	1	NUM
cana-5535	72	2	the	the	DET
cana-5535	72	3	exact	exact	ADJ
cana-5535	72	4	solution	solution	NOUN
cana-5535	72	5	is	be	AUX
cana-5535	72	6	given	give	VERB
cana-5535	72	7	by	by	ADP
cana-5535	72	8	𝑦(𝑥	𝑦(𝑥	NOUN
cana-5535	72	9	)	)	PUNCT
cana-5535	72	10	=	=	PRON
cana-5535	72	11	𝑒3𝑥	𝑒3𝑥	VERB
cana-5535	72	12	the	the	DET
cana-5535	72	13	approximate	approximate	ADJ
cana-5535	72	14	solution	solution	NOUN
cana-5535	72	15	𝑦𝑛(𝑥	𝑦𝑛(𝑥	NOUN
cana-5535	72	16	)	)	PUNCT
cana-5535	72	17	of	of	ADP
cana-5535	72	18	𝑦(𝑥	𝑦(𝑥	NOUN
cana-5535	72	19	)	)	PUNCT
cana-5535	72	20	is	be	AUX
cana-5535	72	21	obtained	obtain	VERB
cana-5535	72	22	by	by	ADP
cana-5535	72	23	the	the	DET
cana-5535	72	24	genocchi	genocchi	PROPN
cana-5535	72	25	polynomial	polynomial	ADJ
cana-5535	72	26	method	method	NOUN
cana-5535	72	27	.	.	PUNCT
cana-5535	73	1	figure	figure	NOUN
cana-5535	73	2	3	3	NUM
cana-5535	73	3	.	.	PUNCT
cana-5535	73	4	graph	graph	NOUN
cana-5535	73	5	for	for	ADP
cana-5535	73	6	example	example	NOUN
cana-5535	73	7	3	3	NUM
cana-5535	73	8	example	example	NOUN
cana-5535	73	9	4	4	NUM
cana-5535	73	10	.	.	PUNCT
cana-5535	74	1	let	let	VERB
cana-5535	74	2	us	we	PRON
cana-5535	74	3	consider	consider	VERB
cana-5535	74	4	the	the	DET
cana-5535	74	5	linear	linear	ADJ
cana-5535	74	6	integro	integro	ADJ
cana-5535	74	7	-	-	PUNCT
cana-5535	74	8	differential	differential	NOUN
cana-5535	74	9	equation	equation	NOUN
cana-5535	74	10	of	of	ADP
cana-5535	74	11	fredholm	fredholm	NOUN
cana-5535	74	12	.	.	PUNCT
cana-5535	75	1	𝑦′(𝑥	𝑦′(𝑥	VERB
cana-5535	75	2	)	)	PUNCT
cana-5535	75	3	=	=	SYM
cana-5535	75	4	3	3	NUM
cana-5535	75	5	+	+	NUM
cana-5535	75	6	6𝑥	6𝑥	NOUN
cana-5535	75	7	+	+	CCONJ
cana-5535	75	8	∫𝑥𝑡	∫𝑥𝑡	VERB
cana-5535	75	9	1	1	NUM
cana-5535	75	10	0	0	NUM
cana-5535	75	11	𝑦(𝑡)𝑑𝑡	𝑦(𝑡)𝑑𝑡	PUNCT
cana-5535	75	12	with	with	ADP
cana-5535	75	13	the	the	DET
cana-5535	75	14	initial	initial	ADJ
cana-5535	75	15	condition	condition	NOUN
cana-5535	75	16	𝑦(0	𝑦(0	PROPN
cana-5535	75	17	)	)	PUNCT
cana-5535	76	1	=	=	SYM
cana-5535	76	2	0	0	NUM
cana-5535	77	1	the	the	DET
cana-5535	77	2	exact	exact	ADJ
cana-5535	77	3	solution	solution	NOUN
cana-5535	77	4	is	be	AUX
cana-5535	77	5	given	give	VERB
cana-5535	77	6	by	by	ADP
cana-5535	77	7	𝑦(𝑥	𝑦(𝑥	NOUN
cana-5535	77	8	)	)	PUNCT
cana-5535	77	9	=	=	SYM
cana-5535	77	10	3𝑥	3𝑥	NOUN
cana-5535	77	11	+	+	CCONJ
cana-5535	77	12	4𝑥2	4𝑥2	NUM
cana-5535	77	13	the	the	DET
cana-5535	77	14	approximate	approximate	ADJ
cana-5535	77	15	solution	solution	NOUN
cana-5535	77	16	𝑦𝑛(𝑥	𝑦𝑛(𝑥	NOUN
cana-5535	77	17	)	)	PUNCT
cana-5535	77	18	of	of	ADP
cana-5535	77	19	𝑦(𝑥	𝑦(𝑥	NOUN
cana-5535	77	20	)	)	PUNCT
cana-5535	77	21	is	be	AUX
cana-5535	77	22	obtained	obtain	VERB
cana-5535	77	23	by	by	ADP
cana-5535	77	24	the	the	DET
cana-5535	77	25	genocchi	genocchi	PROPN
cana-5535	77	26	polynomial	polynomial	ADJ
cana-5535	77	27	method	method	NOUN
cana-5535	77	28	.	.	PUNCT
cana-5535	78	1	0	0	NUM
cana-5535	78	2	0.1	0.1	NUM
cana-5535	78	3	0.2	0.2	NUM
cana-5535	78	4	0.3	0.3	NUM
cana-5535	78	5	0.4	0.4	NUM
cana-5535	78	6	0.5	0.5	NUM
cana-5535	78	7	0.6	0.6	NUM
cana-5535	78	8	0.7	0.7	NUM
cana-5535	78	9	0.8	0.8	NUM
cana-5535	78	10	0.9	0.9	NUM
cana-5535	78	11	1	1	NUM
cana-5535	78	12	0	0	NUM
cana-5535	78	13	5	5	NUM
cana-5535	78	14	10	10	NUM
cana-5535	78	15	15	15	NUM
cana-5535	78	16	20	20	NUM
cana-5535	78	17	25	25	NUM
cana-5535	78	18	x	x	SYM
cana-5535	78	19	y	y	PROPN
cana-5535	78	20	exacte	exacte	PROPN
cana-5535	78	21	solution	solution	PROPN
cana-5535	78	22	approx	approx	PROPN
cana-5535	78	23	.	.	PUNCT
cana-5535	79	1	solution	solution	NOUN
cana-5535	79	2	communications	communication	NOUN
cana-5535	79	3	on	on	ADP
cana-5535	79	4	applied	apply	VERB
cana-5535	79	5	nonlinear	nonlinear	ADJ
cana-5535	79	6	analysis	analysis	NOUN
cana-5535	79	7	issn	issn	NOUN
cana-5535	79	8	:	:	PUNCT
cana-5535	79	9	1074	1074	NUM
cana-5535	79	10	-	-	PUNCT
cana-5535	79	11	133x	133x	NUM
cana-5535	79	12	vol	vol	VERB
cana-5535	79	13	32	32	NUM
cana-5535	79	14	no	no	NOUN
cana-5535	79	15	.	.	PUNCT
cana-5535	80	1	10s	10	NOUN
cana-5535	80	2	(	(	PUNCT
cana-5535	80	3	2025	2025	NUM
cana-5535	80	4	)	)	PUNCT
cana-5535	80	5	2585	2585	NUM
cana-5535	80	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5535	80	7	figure	figure	NOUN
cana-5535	80	8	4	4	NUM
cana-5535	80	9	.	.	PUNCT
cana-5535	81	1	graph	graph	NOUN
cana-5535	81	2	for	for	ADP
cana-5535	81	3	example	example	NOUN
cana-5535	81	4	4	4	NUM
cana-5535	81	5	example	example	NOUN
cana-5535	81	6	5	5	NUM
cana-5535	81	7	.	.	X
cana-5535	82	1	consider	consider	VERB
cana-5535	82	2	linear	linear	PROPN
cana-5535	82	3	volterra	volterra	PROPN
cana-5535	82	4	integro	integro	PROPN
cana-5535	82	5	-	-	PUNCT
cana-5535	82	6	differential	differential	NOUN
cana-5535	82	7	equation	equation	NOUN
cana-5535	82	8	of	of	ADP
cana-5535	82	9	second	second	ADJ
cana-5535	82	10	kind	kind	NOUN
cana-5535	82	11	𝑦′′(𝑥	𝑦′′(𝑥	NOUN
cana-5535	82	12	)	)	PUNCT
cana-5535	82	13	=	=	SYM
cana-5535	83	1	𝑥	𝑥	PROPN
cana-5535	83	2	+	+	CCONJ
cana-5535	83	3	∫(𝑥	∫(𝑥	PROPN
cana-5535	83	4	−	−	NOUN
cana-5535	83	5	𝑡)𝑦(𝑡	𝑡)𝑦(𝑡	NOUN
cana-5535	83	6	)	)	PUNCT
cana-5535	83	7	𝑥	𝑥	NOUN
cana-5535	83	8	0	0	NUM
cana-5535	83	9	𝑑𝑡	𝑑𝑡	ADP
cana-5535	83	10	with	with	ADP
cana-5535	83	11	the	the	DET
cana-5535	83	12	initial	initial	ADJ
cana-5535	83	13	condition	condition	NOUN
cana-5535	83	14	𝑦(0	𝑦(0	PROPN
cana-5535	83	15	)	)	PUNCT
cana-5535	83	16	=	=	SYM
cana-5535	83	17	0	0	NUM
cana-5535	83	18	,	,	PUNCT
cana-5535	83	19	𝑦′(0	𝑦′(0	NOUN
cana-5535	83	20	)	)	PUNCT
cana-5535	83	21	=	=	SYM
cana-5535	83	22	1	1	NUM
cana-5535	83	23	where	where	SCONJ
cana-5535	83	24	the	the	DET
cana-5535	83	25	function	function	NOUN
cana-5535	83	26	𝑦(𝑥	𝑦(𝑥	PROPN
cana-5535	83	27	)	)	PUNCT
cana-5535	83	28	=	=	PUNCT
cana-5535	83	29	sinh	sinh	NOUN
cana-5535	83	30	(	(	PUNCT
cana-5535	83	31	𝑥	𝑥	NOUN
cana-5535	83	32	)	)	PUNCT
cana-5535	83	33	is	be	AUX
cana-5535	83	34	the	the	DET
cana-5535	83	35	exact	exact	ADJ
cana-5535	83	36	solution	solution	NOUN
cana-5535	83	37	the	the	DET
cana-5535	83	38	approximate	approximate	ADJ
cana-5535	83	39	solution	solution	NOUN
cana-5535	83	40	𝑦𝑛(𝑥	𝑦𝑛(𝑥	NOUN
cana-5535	83	41	)	)	PUNCT
cana-5535	83	42	of	of	ADP
cana-5535	83	43	𝑦(𝑥	𝑦(𝑥	NOUN
cana-5535	83	44	)	)	PUNCT
cana-5535	83	45	is	be	AUX
cana-5535	83	46	obtained	obtain	VERB
cana-5535	83	47	by	by	ADP
cana-5535	83	48	the	the	DET
cana-5535	83	49	genocchi	genocchi	PROPN
cana-5535	83	50	polynomial	polynomial	ADJ
cana-5535	83	51	method	method	NOUN
cana-5535	83	52	.	.	PUNCT
cana-5535	84	1	figure	figure	NOUN
cana-5535	84	2	5	5	NUM
cana-5535	84	3	.	.	PUNCT
cana-5535	84	4	graph	graph	NOUN
cana-5535	84	5	for	for	ADP
cana-5535	84	6	example	example	NOUN
cana-5535	84	7	5	5	NUM
cana-5535	84	8	0	0	NUM
cana-5535	84	9	0.1	0.1	NUM
cana-5535	84	10	0.2	0.2	NUM
cana-5535	84	11	0.3	0.3	NUM
cana-5535	84	12	0.4	0.4	NUM
cana-5535	84	13	0.5	0.5	NUM
cana-5535	84	14	0.6	0.6	NUM
cana-5535	84	15	0.7	0.7	NUM
cana-5535	84	16	0.8	0.8	NUM
cana-5535	84	17	0.9	0.9	NUM
cana-5535	84	18	1	1	NUM
cana-5535	84	19	0	0	NUM
cana-5535	84	20	1	1	NUM
cana-5535	84	21	2	2	NUM
cana-5535	84	22	3	3	NUM
cana-5535	84	23	4	4	NUM
cana-5535	84	24	5	5	NUM
cana-5535	84	25	6	6	NUM
cana-5535	84	26	7	7	NUM
cana-5535	84	27	x	x	SYM
cana-5535	84	28	y	y	PROPN
cana-5535	84	29	exacte	exacte	PROPN
cana-5535	84	30	solution	solution	PROPN
cana-5535	84	31	approx	approx	PROPN
cana-5535	84	32	.	.	PUNCT
cana-5535	85	1	solution	solution	NOUN
cana-5535	85	2	0	0	NUM
cana-5535	85	3	0.1	0.1	NUM
cana-5535	85	4	0.2	0.2	NUM
cana-5535	85	5	0.3	0.3	NUM
cana-5535	85	6	0.4	0.4	NUM
cana-5535	85	7	0.5	0.5	NUM
cana-5535	85	8	0.6	0.6	NUM
cana-5535	85	9	0.7	0.7	NUM
cana-5535	85	10	0.8	0.8	NUM
cana-5535	85	11	0.9	0.9	NUM
cana-5535	85	12	1	1	NUM
cana-5535	85	13	0	0	NUM
cana-5535	85	14	0.2	0.2	NUM
cana-5535	85	15	0.4	0.4	NUM
cana-5535	85	16	0.6	0.6	NUM
cana-5535	85	17	0.8	0.8	NUM
cana-5535	85	18	1	1	NUM
cana-5535	85	19	1.2	1.2	NUM
cana-5535	85	20	1.4	1.4	NUM
cana-5535	85	21	x	x	SYM
cana-5535	85	22	y	y	PROPN
cana-5535	85	23	exacte	exacte	PROPN
cana-5535	85	24	solution	solution	PROPN
cana-5535	85	25	approx	approx	PROPN
cana-5535	85	26	.	.	PUNCT
cana-5535	86	1	solution	solution	NOUN
cana-5535	86	2	communications	communication	NOUN
cana-5535	86	3	on	on	ADP
cana-5535	86	4	applied	apply	VERB
cana-5535	86	5	nonlinear	nonlinear	ADJ
cana-5535	86	6	analysis	analysis	NOUN
cana-5535	86	7	issn	issn	NOUN
cana-5535	86	8	:	:	PUNCT
cana-5535	86	9	1074	1074	NUM
cana-5535	86	10	-	-	PUNCT
cana-5535	86	11	133x	133x	NUM
cana-5535	86	12	vol	vol	VERB
cana-5535	86	13	32	32	NUM
cana-5535	86	14	no	no	NOUN
cana-5535	86	15	.	.	PUNCT
cana-5535	87	1	10s	10	NOUN
cana-5535	87	2	(	(	PUNCT
cana-5535	87	3	2025	2025	NUM
cana-5535	87	4	)	)	PUNCT
cana-5535	87	5	2586	2586	NUM
cana-5535	87	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5535	87	7	example	example	NOUN
cana-5535	87	8	6	6	NUM
cana-5535	87	9	.	.	PUNCT
cana-5535	87	10	consider	consider	VERB
cana-5535	87	11	the	the	DET
cana-5535	87	12	integro	integro	ADJ
cana-5535	87	13	-	-	PUNCT
cana-5535	87	14	differential	differential	NOUN
cana-5535	87	15	equation	equation	NOUN
cana-5535	87	16	𝑦′(𝑥	𝑦′(𝑥	PROPN
cana-5535	87	17	)	)	PUNCT
cana-5535	87	18	=	=	SYM
cana-5535	88	1	−	−	PROPN
cana-5535	88	2	cos(2𝜋𝑥	cos(2𝜋𝑥	NUM
cana-5535	88	3	)	)	PUNCT
cana-5535	88	4	−	−	PROPN
cana-5535	88	5	2𝜋	2𝜋	NUM
cana-5535	88	6	sin(2𝜋𝑥	sin(2𝜋𝑥	NOUN
cana-5535	88	7	)	)	PUNCT
cana-5535	88	8	−	−	NOUN
cana-5535	88	9	1	1	NUM
cana-5535	88	10	2	2	NUM
cana-5535	88	11	sin(4𝜋𝑥	sin(4𝜋𝑥	NUM
cana-5535	88	12	)	)	PUNCT
cana-5535	88	13	+	+	NUM
cana-5535	88	14	∫	∫	PROPN
cana-5535	88	15	sin(4𝜋𝑥	sin(4𝜋𝑥	X
cana-5535	88	16	+	+	CCONJ
cana-5535	88	17	2𝜋𝑡	2𝜋𝑡	NOUN
cana-5535	88	18	)	)	PUNCT
cana-5535	88	19	𝑦(𝑡	𝑦(𝑡	NUM
cana-5535	88	20	)	)	PUNCT
cana-5535	88	21	1	1	NUM
cana-5535	88	22	0	0	NUM
cana-5535	88	23	𝑑𝑡	𝑑𝑡	ADP
cana-5535	88	24	with	with	ADP
cana-5535	88	25	the	the	DET
cana-5535	88	26	initial	initial	ADJ
cana-5535	88	27	condition	condition	NOUN
cana-5535	88	28	𝑦(0	𝑦(0	PROPN
cana-5535	88	29	)	)	PUNCT
cana-5535	89	1	=	=	SYM
cana-5535	89	2	1	1	NUM
cana-5535	89	3	,	,	PUNCT
cana-5535	89	4	where	where	SCONJ
cana-5535	89	5	the	the	DET
cana-5535	89	6	function	function	NOUN
cana-5535	89	7	𝑦(𝑥	𝑦(𝑥	NOUN
cana-5535	89	8	)	)	PUNCT
cana-5535	89	9	=	=	SYM
cana-5535	89	10	cos	cos	X
cana-5535	89	11	(	(	PUNCT
cana-5535	89	12	2𝜋𝑥	2𝜋𝑥	NOUN
cana-5535	89	13	)	)	PUNCT
cana-5535	89	14	is	be	AUX
cana-5535	89	15	the	the	DET
cana-5535	89	16	exact	exact	ADJ
cana-5535	89	17	solution	solution	NOUN
cana-5535	89	18	the	the	DET
cana-5535	89	19	approximate	approximate	ADJ
cana-5535	89	20	solution	solution	NOUN
cana-5535	89	21	𝑦𝑛(𝑥	𝑦𝑛(𝑥	NOUN
cana-5535	89	22	)	)	PUNCT
cana-5535	89	23	of	of	ADP
cana-5535	89	24	𝑦(𝑥	𝑦(𝑥	NOUN
cana-5535	89	25	)	)	PUNCT
cana-5535	89	26	is	be	AUX
cana-5535	89	27	obtained	obtain	VERB
cana-5535	89	28	by	by	ADP
cana-5535	89	29	the	the	DET
cana-5535	89	30	genocchi	genocchi	PROPN
cana-5535	89	31	polynomial	polynomial	ADJ
cana-5535	89	32	method	method	NOUN
cana-5535	89	33	.	.	PUNCT
cana-5535	90	1	figure	figure	NOUN
cana-5535	90	2	6	6	NUM
cana-5535	90	3	.	.	PUNCT
cana-5535	91	1	graph	graph	NOUN
cana-5535	91	2	for	for	ADP
cana-5535	91	3	example	example	NOUN
cana-5535	91	4	6	6	NUM
cana-5535	91	5	conclusion	conclusion	NOUN
cana-5535	91	6	this	this	DET
cana-5535	91	7	article	article	NOUN
cana-5535	91	8	deals	deal	VERB
cana-5535	91	9	with	with	ADP
cana-5535	91	10	the	the	DET
cana-5535	91	11	numerical	numerical	ADJ
cana-5535	91	12	solution	solution	NOUN
cana-5535	91	13	of	of	ADP
cana-5535	91	14	first	first	ADJ
cana-5535	91	15	order	order	NOUN
cana-5535	91	16	fredholm	fredholm	NOUN
cana-5535	91	17	and	and	CCONJ
cana-5535	91	18	volterra	volterra	NOUN
cana-5535	91	19	integrodifferential	integrodifferential	ADJ
cana-5535	91	20	equations	equation	NOUN
cana-5535	91	21	of	of	ADP
cana-5535	91	22	the	the	DET
cana-5535	91	23	second	second	ADJ
cana-5535	91	24	kind	kind	NOUN
cana-5535	91	25	,	,	PUNCT
cana-5535	91	26	using	use	VERB
cana-5535	91	27	the	the	DET
cana-5535	91	28	method	method	NOUN
cana-5535	91	29	technique	technique	NOUN
cana-5535	91	30	by	by	ADP
cana-5535	91	31	means	mean	NOUN
cana-5535	91	32	of	of	ADP
cana-5535	91	33	genocchi	genocchi	PROPN
cana-5535	91	34	polynomials	polynomial	NOUN
cana-5535	91	35	.	.	PUNCT
cana-5535	92	1	this	this	DET
cana-5535	92	2	technique	technique	NOUN
cana-5535	92	3	was	be	AUX
cana-5535	92	4	tested	test	VERB
cana-5535	92	5	on	on	ADP
cana-5535	92	6	six	six	NUM
cana-5535	92	7	examples	example	NOUN
cana-5535	92	8	shown	show	VERB
cana-5535	92	9	in	in	ADP
cana-5535	92	10	the	the	DET
cana-5535	92	11	obtained	obtain	VERB
cana-5535	92	12	figures	figure	NOUN
cana-5535	92	13	,	,	PUNCT
cana-5535	92	14	and	and	CCONJ
cana-5535	92	15	the	the	DET
cana-5535	92	16	results	result	NOUN
cana-5535	92	17	were	be	AUX
cana-5535	92	18	satisfactory	satisfactory	ADJ
cana-5535	92	19	and	and	CCONJ
cana-5535	92	20	the	the	DET
cana-5535	92	21	method	method	NOUN
cana-5535	92	22	was	be	AUX
cana-5535	92	23	quite	quite	ADV
cana-5535	92	24	effective	effective	ADJ
cana-5535	92	25	.	.	PUNCT
cana-5535	93	1	in	in	ADP
cana-5535	93	2	addition	addition	NOUN
cana-5535	93	3	,	,	PUNCT
cana-5535	93	4	this	this	DET
cana-5535	93	5	method	method	NOUN
cana-5535	93	6	can	can	AUX
cana-5535	93	7	be	be	AUX
cana-5535	93	8	applied	apply	VERB
cana-5535	93	9	to	to	ADP
cana-5535	93	10	high	high	ADJ
cana-5535	93	11	order	order	NOUN
cana-5535	93	12	fredholm	fredholm	NOUN
cana-5535	93	13	and	and	CCONJ
cana-5535	93	14	volterra	volterra	NOUN
cana-5535	93	15	integro	integro	PROPN
cana-5535	93	16	-	-	PUNCT
cana-5535	93	17	differential	differential	NOUN
cana-5535	93	18	equations	equation	NOUN
cana-5535	93	19	of	of	ADP
cana-5535	93	20	the	the	DET
cana-5535	93	21	second	second	ADJ
cana-5535	93	22	kind	kind	NOUN
cana-5535	93	23	,	,	PUNCT
cana-5535	93	24	where	where	SCONJ
cana-5535	93	25	the	the	DET
cana-5535	93	26	matlab	matlab	PROPN
cana-5535	93	27	program	program	NOUN
cana-5535	93	28	is	be	AUX
cana-5535	93	29	used	use	VERB
cana-5535	93	30	to	to	PART
cana-5535	93	31	obtain	obtain	VERB
cana-5535	93	32	approximate	approximate	ADJ
cana-5535	93	33	solutions	solution	NOUN
cana-5535	93	34	.	.	PUNCT
cana-5535	94	1	this	this	DET
cana-5535	94	2	technique	technique	NOUN
cana-5535	94	3	will	will	AUX
cana-5535	94	4	be	be	AUX
cana-5535	94	5	applied	apply	VERB
cana-5535	94	6	in	in	ADP
cana-5535	94	7	the	the	DET
cana-5535	94	8	future	future	NOUN
cana-5535	94	9	to	to	ADP
cana-5535	94	10	fractional	fractional	ADJ
cana-5535	94	11	integro	integro	ADJ
cana-5535	94	12	-	-	PUNCT
cana-5535	94	13	differential	differential	NOUN
cana-5535	94	14	equations	equation	NOUN
cana-5535	94	15	and	and	CCONJ
cana-5535	94	16	nonlinear	nonlinear	ADJ
cana-5535	94	17	integro	integro	ADJ
cana-5535	94	18	-	-	PUNCT
cana-5535	94	19	differential	differential	NOUN
cana-5535	94	20	equations	equation	NOUN
cana-5535	94	21	.	.	PUNCT
cana-5535	95	1	refrences	refrence	VERB
cana-5535	95	2	[	[	X
cana-5535	95	3	1	1	NUM
cana-5535	95	4	]	]	PUNCT
cana-5535	95	5	a.	a.	NOUN
cana-5535	95	6	adawi	adawi	PROPN
cana-5535	95	7	,	,	PUNCT
cana-5535	95	8	f.	f.	PROPN
cana-5535	95	9	awawdeh	awawdeh	PROPN
cana-5535	95	10	,	,	PUNCT
cana-5535	95	11	a	a	DET
cana-5535	95	12	numerical	numerical	ADJ
cana-5535	95	13	method	method	NOUN
cana-5535	95	14	for	for	ADP
cana-5535	95	15	solving	solve	VERB
cana-5535	95	16	linear	linear	ADJ
cana-5535	95	17	integral	integral	ADJ
cana-5535	95	18	equations	equation	NOUN
cana-5535	95	19	,	,	PUNCT
cana-5535	95	20	int	int	NOUN
cana-5535	95	21	.	.	PUNCT
cana-5535	96	1	j.	j.	PROPN
cana-5535	96	2	contemp	contemp	PROPN
cana-5535	96	3	.	.	PUNCT
cana-5535	97	1	mathematics	mathematic	NOUN
cana-5535	97	2	sciences	science	NOUN
cana-5535	97	3	,	,	PUNCT
cana-5535	97	4	10	10	NUM
cana-5535	97	5	,	,	PUNCT
cana-5535	97	6	(	(	PUNCT
cana-5535	97	7	2009	2009	NUM
cana-5535	97	8	)	)	PUNCT
cana-5535	97	9	pp	pp	ADP
cana-5535	97	10	485	485	NUM
cana-5535	97	11	-	-	SYM
cana-5535	97	12	496	496	NUM
cana-5535	97	13	.	.	PUNCT
cana-5535	98	1	[	[	X
cana-5535	98	2	2	2	X
cana-5535	98	3	]	]	PUNCT
cana-5535	98	4	k.	k.	PROPN
cana-5535	98	5	atkinson	atkinson	PROPN
cana-5535	98	6	,	,	PUNCT
cana-5535	98	7	the	the	DET
cana-5535	98	8	numerical	numerical	ADJ
cana-5535	98	9	solution	solution	NOUN
cana-5535	98	10	of	of	ADP
cana-5535	98	11	integral	integral	ADJ
cana-5535	98	12	equations	equation	NOUN
cana-5535	98	13	of	of	ADP
cana-5535	98	14	the	the	DET
cana-5535	98	15	second	second	ADJ
cana-5535	98	16	kind	kind	NOUN
cana-5535	98	17	,	,	PUNCT
cana-5535	98	18	the	the	DET
cana-5535	98	19	press	press	NOUN
cana-5535	98	20	syndicate	syndicate	NOUN
cana-5535	98	21	of	of	ADP
cana-5535	98	22	the	the	DET
cana-5535	98	23	university	university	PROPN
cana-5535	98	24	of	of	ADP
cana-5535	98	25	cambridge	cambridge	PROPN
cana-5535	98	26	,	,	PUNCT
cana-5535	98	27	united	united	ADJ
cana-5535	98	28	kingdom	kingdom	PROPN
cana-5535	98	29	,	,	PUNCT
cana-5535	98	30	1997	1997	NUM
cana-5535	98	31	.	.	PUNCT
cana-5535	99	1	[	[	X
cana-5535	99	2	3	3	X
cana-5535	99	3	]	]	X
cana-5535	99	4	s.	s.	PROPN
cana-5535	99	5	aggarwal	aggarwal	PROPN
cana-5535	99	6	,	,	PUNCT
cana-5535	99	7	n.	n.	PROPN
cana-5535	99	8	sharma	sharma	PROPN
cana-5535	99	9	,	,	PUNCT
cana-5535	99	10	r.	r.	PROPN
cana-5535	99	11	chauhan	chauhan	PROPN
cana-5535	99	12	.	.	PUNCT
cana-5535	99	13	solution	solution	NOUN
cana-5535	99	14	of	of	ADP
cana-5535	99	15	linear	linear	PROPN
cana-5535	99	16	volterra	volterra	PROPN
cana-5535	99	17	integro	integro	PROPN
cana-5535	99	18	-	-	PUNCT
cana-5535	99	19	differential	differential	NOUN
cana-5535	99	20	equations	equation	NOUN
cana-5535	99	21	of	of	ADP
cana-5535	99	22	second	second	ADJ
cana-5535	99	23	kind	kind	NOUN
cana-5535	99	24	using	use	VERB
cana-5535	99	25	mahgoub	mahgoub	NOUN
cana-5535	99	26	transform	transform	VERB
cana-5535	99	27	.	.	PUNCT
cana-5535	100	1	international	international	ADJ
cana-5535	100	2	journal	journal	NOUN
cana-5535	100	3	of	of	ADP
cana-5535	100	4	latest	late	ADJ
cana-5535	100	5	0	0	NUM
cana-5535	100	6	0.1	0.1	NUM
cana-5535	100	7	0.2	0.2	NUM
cana-5535	100	8	0.3	0.3	NUM
cana-5535	100	9	0.4	0.4	NUM
cana-5535	100	10	0.5	0.5	NUM
cana-5535	100	11	0.6	0.6	NUM
cana-5535	100	12	0.7	0.7	NUM
cana-5535	100	13	0.8	0.8	NUM
cana-5535	100	14	0.9	0.9	NUM
cana-5535	100	15	1	1	NUM
cana-5535	100	16	-1	-1	SYM
cana-5535	100	17	-0.5	-0.5	X
cana-5535	100	18	0	0	NUM
cana-5535	100	19	0.5	0.5	NUM
cana-5535	100	20	1	1	NUM
cana-5535	100	21	1.5	1.5	NUM
cana-5535	100	22	x	x	SYM
cana-5535	100	23	y	y	PROPN
cana-5535	100	24	exacte	exacte	PROPN
cana-5535	100	25	solution	solution	PROPN
cana-5535	100	26	approx	approx	PROPN
cana-5535	100	27	.	.	PUNCT
cana-5535	101	1	solution	solution	NOUN
cana-5535	101	2	communications	communication	NOUN
cana-5535	101	3	on	on	ADP
cana-5535	101	4	applied	apply	VERB
cana-5535	101	5	nonlinear	nonlinear	ADJ
cana-5535	101	6	analysis	analysis	NOUN
cana-5535	101	7	issn	issn	NOUN
cana-5535	101	8	:	:	PUNCT
cana-5535	101	9	1074	1074	NUM
cana-5535	101	10	-	-	PUNCT
cana-5535	101	11	133x	133x	NUM
cana-5535	101	12	vol	vol	VERB
cana-5535	101	13	32	32	NUM
cana-5535	101	14	no	no	NOUN
cana-5535	101	15	.	.	PUNCT
cana-5535	102	1	10s	10	NOUN
cana-5535	102	2	(	(	PUNCT
cana-5535	102	3	2025	2025	NUM
cana-5535	102	4	)	)	PUNCT
cana-5535	102	5	2587	2587	NUM
cana-5535	102	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5535	102	7	technology	technology	NOUN
cana-5535	102	8	in	in	ADP
cana-5535	102	9	engineering	engineering	NOUN
cana-5535	102	10	,	,	PUNCT
cana-5535	102	11	management	management	NOUN
cana-5535	102	12	&	&	CCONJ
cana-5535	102	13	applied	apply	VERB
cana-5535	102	14	science	science	NOUN
cana-5535	102	15	.	.	PUNCT
cana-5535	103	1	volume	volume	PROPN
cana-5535	103	2	vii	vii	PROPN
cana-5535	103	3	,	,	PUNCT
cana-5535	103	4	issue	issue	NOUN
cana-5535	103	5	v	v	ADP
cana-5535	103	6	,	,	PUNCT
cana-5535	103	7	(	(	PUNCT
cana-5535	103	8	2018	2018	NUM
cana-5535	103	9	)	)	PUNCT
cana-5535	103	10	173	173	NUM
cana-5535	103	11	-	-	SYM
cana-5535	103	12	176	176	NUM
cana-5535	103	13	.	.	PUNCT
cana-5535	104	1	[	[	X
cana-5535	104	2	4	4	NUM
cana-5535	104	3	]	]	PUNCT
cana-5535	104	4	a.	a.	NOUN
cana-5535	104	5	akyuz	akyuz	NOUN
cana-5535	104	6	and	and	CCONJ
cana-5535	104	7	m.	m.	NOUN
cana-5535	104	8	sezer	sezer	PROPN
cana-5535	104	9	.	.	PUNCT
cana-5535	105	1	a	a	DET
cana-5535	105	2	chebyshev	chebyshev	NOUN
cana-5535	105	3	collocation	collocation	NOUN
cana-5535	105	4	method	method	NOUN
cana-5535	105	5	for	for	ADP
cana-5535	105	6	the	the	DET
cana-5535	105	7	solution	solution	NOUN
cana-5535	105	8	of	of	ADP
cana-5535	105	9	linear	linear	ADJ
cana-5535	105	10	integrodifferential	integrodifferential	ADJ
cana-5535	105	11	equations	equation	NOUN
cana-5535	105	12	,	,	PUNCT
cana-5535	105	13	int	int	NOUN
cana-5535	105	14	.	.	PUNCT
cana-5535	106	1	j.	j.	PROPN
cana-5535	106	2	comput	comput	PROPN
cana-5535	106	3	math	math	PROPN
cana-5535	106	4	.	.	PUNCT
cana-5535	107	1	vol	vol	NOUN
cana-5535	107	2	.	.	PROPN
cana-5535	108	1	27	27	NUM
cana-5535	108	2	,	,	PUNCT
cana-5535	108	3	no	no	INTJ
cana-5535	108	4	.	.	NOUN
cana-5535	108	5	4	4	NUM
cana-5535	108	6	,	,	PUNCT
cana-5535	108	7	(	(	PUNCT
cana-5535	108	8	1999	1999	NUM
cana-5535	108	9	)	)	PUNCT
cana-5535	108	10	.	.	PUNCT
cana-5535	109	1	[	[	X
cana-5535	109	2	5	5	NUM
cana-5535	109	3	]	]	PUNCT
cana-5535	109	4	q.	q.	PROPN
cana-5535	109	5	m.	m.	PROPN
cana-5535	109	6	al	al	PROPN
cana-5535	109	7	-	-	PUNCT
cana-5535	109	8	mdallal	mdallal	PROPN
cana-5535	109	9	,	,	PUNCT
cana-5535	109	10	monotone	monotone	ADJ
cana-5535	109	11	iterative	iterative	NOUN
cana-5535	109	12	sequences	sequence	NOUN
cana-5535	109	13	for	for	ADP
cana-5535	109	14	nonlinear	nonlinear	ADJ
cana-5535	109	15	integro	integro	ADJ
cana-5535	109	16	-	-	PUNCT
cana-5535	109	17	differential	differential	NOUN
cana-5535	109	18	equations	equation	NOUN
cana-5535	109	19	of	of	ADP
cana-5535	109	20	second	second	ADJ
cana-5535	109	21	order	order	NOUN
cana-5535	109	22	,	,	PUNCT
cana-5535	109	23	nonlinear	nonlinear	ADJ
cana-5535	109	24	analysis	analysis	NOUN
cana-5535	109	25	,	,	PUNCT
cana-5535	109	26	12	12	NUM
cana-5535	109	27	(	(	PUNCT
cana-5535	109	28	2011	2011	NUM
cana-5535	109	29	)	)	PUNCT
cana-5535	109	30	,	,	PUNCT
cana-5535	110	1	no	no	INTJ
cana-5535	110	2	.	.	NOUN
cana-5535	110	3	6	6	NUM
cana-5535	110	4	,	,	PUNCT
cana-5535	110	5	3665	3665	NUM
cana-5535	110	6	-	-	SYM
cana-5535	110	7	3673	3673	NUM
cana-5535	110	8	.	.	PUNCT
cana-5535	111	1	[	[	X
cana-5535	111	2	6	6	NUM
cana-5535	111	3	]	]	X
cana-5535	111	4	e.	e.	PROPN
cana-5535	111	5	babolian	babolian	PROPN
cana-5535	111	6	,	,	PUNCT
cana-5535	111	7	a.	a.	NOUN
cana-5535	111	8	davari	davari	PROPN
cana-5535	111	9	,	,	PUNCT
cana-5535	111	10	numerical	numerical	ADJ
cana-5535	111	11	implementation	implementation	NOUN
cana-5535	111	12	of	of	ADP
cana-5535	111	13	adomian	adomian	ADJ
cana-5535	111	14	decomposition	decomposition	NOUN
cana-5535	111	15	method	method	NOUN
cana-5535	111	16	for	for	ADP
cana-5535	111	17	linear	linear	PROPN
cana-5535	111	18	volterra	volterra	PROPN
cana-5535	111	19	integral	integral	ADJ
cana-5535	111	20	equations	equation	NOUN
cana-5535	111	21	of	of	ADP
cana-5535	111	22	the	the	DET
cana-5535	111	23	second	second	ADJ
cana-5535	111	24	kind	kind	NOUN
cana-5535	111	25	,	,	PUNCT
cana-5535	111	26	app	app	PROPN
cana-5535	111	27	.	.	PROPN
cana-5535	111	28	math	math	PROPN
cana-5535	111	29	.	.	PUNCT
cana-5535	112	1	comput	comput	NOUN
cana-5535	112	2	,	,	PUNCT
cana-5535	112	3	165	165	NUM
cana-5535	112	4	(	(	PUNCT
cana-5535	112	5	2005	2005	NUM
cana-5535	112	6	)	)	PUNCT
cana-5535	112	7	223227	223227	NUM
cana-5535	112	8	.	.	PUNCT
cana-5535	113	1	[	[	X
cana-5535	113	2	7	7	X
cana-5535	113	3	]	]	X
cana-5535	113	4	m.	m.	NOUN
cana-5535	113	5	djalil	djalil	PROPN
cana-5535	113	6	,	,	PUNCT
cana-5535	113	7	h.	h.	PROPN
cana-5535	113	8	souidan	souidan	PROPN
cana-5535	113	9	,	,	PUNCT
cana-5535	113	10	w.	w.	PROPN
cana-5535	113	11	souidan	souidan	PROPN
cana-5535	113	12	,	,	PUNCT
cana-5535	113	13	approximate	approximate	ADJ
cana-5535	113	14	solution	solution	NOUN
cana-5535	113	15	of	of	ADP
cana-5535	113	16	linear	linear	PROPN
cana-5535	113	17	volterra	volterra	PROPN
cana-5535	113	18	integrodifferential	integrodifferential	ADJ
cana-5535	113	19	equation	equation	NOUN
cana-5535	113	20	by	by	ADP
cana-5535	113	21	touchard	touchard	NOUN
cana-5535	113	22	polynomials	polynomial	NOUN
cana-5535	113	23	method	method	VERB
cana-5535	113	24	,	,	PUNCT
cana-5535	113	25	(	(	PUNCT
cana-5535	113	26	wjsm	wjsm	ADJ
cana-5535	113	27	)	)	PUNCT
cana-5535	113	28	11(2	11(2	NUM
cana-5535	113	29	)	)	PUNCT
cana-5535	113	30	,	,	PUNCT
cana-5535	113	31	(	(	PUNCT
cana-5535	113	32	2018	2018	NUM
cana-5535	113	33	)	)	PUNCT
cana-5535	113	34	,	,	PUNCT
cana-5535	113	35	29	29	NUM
cana-5535	113	36	-	-	SYM
cana-5535	113	37	41	41	NUM
cana-5535	114	1	[	[	X
cana-5535	114	2	8	8	NUM
cana-5535	114	3	]	]	PUNCT
cana-5535	114	4	a.	a.	NOUN
cana-5535	114	5	jerri	jerri	PROPN
cana-5535	114	6	.	.	PUNCT
cana-5535	115	1	introduction	introduction	NOUN
cana-5535	115	2	to	to	ADP
cana-5535	115	3	integral	integral	ADJ
cana-5535	115	4	equations	equation	NOUN
cana-5535	115	5	with	with	ADP
cana-5535	115	6	applications	application	NOUN
cana-5535	115	7	.	.	PUNCT
cana-5535	116	1	john	john	PROPN
cana-5535	116	2	wiley	wiley	PROPN
cana-5535	116	3	and	and	CCONJ
cana-5535	116	4	sons	son	NOUN
cana-5535	116	5	,	,	PUNCT
cana-5535	116	6	inc	inc	PROPN
cana-5535	116	7	,	,	PUNCT
cana-5535	116	8	1999	1999	NUM
cana-5535	116	9	.	.	PUNCT
cana-5535	117	1	[	[	X
cana-5535	117	2	9	9	NUM
cana-5535	117	3	]	]	PUNCT
cana-5535	117	4	j.	j.	PROPN
cana-5535	117	5	he	he	PROPN
cana-5535	117	6	,	,	PUNCT
cana-5535	117	7	homotopy	homotopy	VERB
cana-5535	117	8	perturbation	perturbation	NOUN
cana-5535	117	9	technique	technique	NOUN
cana-5535	117	10	,	,	PUNCT
cana-5535	117	11	comput	comput	NOUN
cana-5535	117	12	,	,	PUNCT
cana-5535	117	13	methods	method	NOUN
cana-5535	117	14	appl	appl	PROPN
cana-5535	117	15	.	.	PROPN
cana-5535	117	16	mech	mech	PROPN
cana-5535	117	17	.	.	PUNCT
cana-5535	118	1	engrg	engrg	PROPN
cana-5535	118	2	,	,	PUNCT
cana-5535	118	3	178	178	NUM
cana-5535	118	4	(	(	PUNCT
cana-5535	118	5	1999	1999	NUM
cana-5535	118	6	)	)	PUNCT
cana-5535	118	7	257	257	NUM
cana-5535	118	8	-	-	SYM
cana-5535	118	9	262	262	NUM
cana-5535	118	10	.	.	PUNCT
cana-5535	119	1	[	[	X
cana-5535	119	2	10	10	NUM
cana-5535	119	3	]	]	X
cana-5535	119	4	a.	a.	PROPN
cana-5535	119	5	hossein	hossein	PROPN
cana-5535	119	6	,	,	PUNCT
cana-5535	119	7	a	a	DET
cana-5535	119	8	new	new	ADJ
cana-5535	119	9	analytical	analytical	ADJ
cana-5535	119	10	method	method	NOUN
cana-5535	119	11	for	for	ADP
cana-5535	119	12	solving	solve	VERB
cana-5535	119	13	systems	system	NOUN
cana-5535	119	14	of	of	ADP
cana-5535	119	15	linear	linear	PROPN
cana-5535	119	16	integro	integro	ADJ
cana-5535	119	17	-	-	PUNCT
cana-5535	119	18	differential	differential	NOUN
cana-5535	119	19	equations	equation	NOUN
cana-5535	119	20	,	,	PUNCT
cana-5535	119	21	journal	journal	NOUN
cana-5535	119	22	of	of	ADP
cana-5535	119	23	king	king	NOUN
cana-5535	119	24	saud	saud	PROPN
cana-5535	119	25	universityscience	universityscience	NOUN
cana-5535	119	26	(	(	PUNCT
cana-5535	119	27	2011	2011	NUM
cana-5535	119	28	)	)	PUNCT
cana-5535	119	29	,	,	PUNCT
cana-5535	119	30	23	23	NUM
cana-5535	119	31	,	,	PUNCT
cana-5535	119	32	349	349	NUM
cana-5535	119	33	-	-	SYM
cana-5535	119	34	353	353	NUM
cana-5535	119	35	.	.	PUNCT
cana-5535	120	1	[	[	X
cana-5535	120	2	11	11	NUM
cana-5535	120	3	]	]	PUNCT
cana-5535	120	4	s.	s.	PROPN
cana-5535	120	5	m.	m.	PROPN
cana-5535	120	6	hosseini	hosseini	PROPN
cana-5535	120	7	and	and	CCONJ
cana-5535	120	8	s.	s.	PROPN
cana-5535	120	9	shamord	shamord	PROPN
cana-5535	120	10	,	,	PUNCT
cana-5535	120	11	numerical	numerical	ADJ
cana-5535	120	12	piecewise	piecewise	PROPN
cana-5535	120	13	approximate	approximate	ADJ
cana-5535	120	14	solution	solution	NOUN
cana-5535	120	15	of	of	ADP
cana-5535	120	16	fredholm	fredholm	ADJ
cana-5535	120	17	integro	integro	ADJ
cana-5535	120	18	-	-	PUNCT
cana-5535	120	19	differential	differential	NOUN
cana-5535	120	20	equations	equation	NOUN
cana-5535	120	21	by	by	ADP
cana-5535	120	22	the	the	DET
cana-5535	120	23	tau	tau	PROPN
cana-5535	120	24	method	method	NOUN
cana-5535	120	25	,	,	PUNCT
cana-5535	120	26	app	app	PROPN
cana-5535	120	27	.	.	PROPN
cana-5535	120	28	math	math	PROPN
cana-5535	120	29	.	.	PUNCT
cana-5535	121	1	model	model	PROPN
cana-5535	121	2	29(2005)1005	29(2005)1005	PROPN
cana-5535	121	3	-	-	SYM
cana-5535	121	4	1021	1021	NUM
cana-5535	121	5	.	.	PUNCT
cana-5535	122	1	isah	isah	PROPN
cana-5535	122	2	,	,	PUNCT
cana-5535	122	3	c.	c.	PROPN
cana-5535	122	4	phang	phang	PROPN
cana-5535	122	5	.	.	PUNCT
cana-5535	123	1	operational	operational	ADJ
cana-5535	123	2	matrix	matrix	NOUN
cana-5535	123	3	based	base	VERB
cana-5535	123	4	on	on	ADP
cana-5535	123	5	genocchi	genocchi	PROPN
cana-5535	123	6	polynomials	polynomial	NOUN
cana-5535	123	7	for	for	ADP
cana-5535	123	8	solution	solution	NOUN
cana-5535	123	9	of	of	ADP
cana-5535	123	10	delay	delay	NOUN
cana-5535	123	11	differential	differential	ADJ
cana-5535	123	12	equations	equation	NOUN
cana-5535	123	13	.	.	PUNCT
cana-5535	124	1	ain	ain	PROPN
cana-5535	124	2	shams	sham	VERB
cana-5535	124	3	engineering	engineering	NOUN
cana-5535	124	4	journal	journal	NOUN
cana-5535	124	5	,	,	PUNCT
cana-5535	124	6	2017	2017	NUM
cana-5535	124	7	.	.	PUNCT
cana-5535	125	1	[	[	X
cana-5535	125	2	12	12	NUM
cana-5535	125	3	]	]	PUNCT
cana-5535	125	4	a.	a.	NOUN
cana-5535	125	5	isah	isah	PROPN
cana-5535	125	6	,	,	PUNCT
cana-5535	125	7	c.	c.	PROPN
cana-5535	125	8	phang	phang	PROPN
cana-5535	125	9	.	.	PUNCT
cana-5535	126	1	operational	operational	ADJ
cana-5535	126	2	matrix	matrix	NOUN
cana-5535	126	3	based	base	VERB
cana-5535	126	4	on	on	ADP
cana-5535	126	5	genocchi	genocchi	PROPN
cana-5535	126	6	polynomials	polynomial	NOUN
cana-5535	126	7	for	for	ADP
cana-5535	126	8	solution	solution	NOUN
cana-5535	126	9	of	of	ADP
cana-5535	126	10	delay	delay	NOUN
cana-5535	126	11	differential	differential	ADJ
cana-5535	126	12	equations	equation	NOUN
cana-5535	126	13	.	.	PUNCT
cana-5535	127	1	ain	ain	PROPN
cana-5535	127	2	shams	sham	VERB
cana-5535	127	3	engineering	engineering	NOUN
cana-5535	127	4	journal	journal	NOUN
cana-5535	127	5	,	,	PUNCT
cana-5535	127	6	2017	2017	NUM
cana-5535	127	7	.	.	PUNCT
cana-5535	128	1	[	[	X
cana-5535	128	2	13	13	NUM
cana-5535	128	3	]	]	PUNCT
cana-5535	128	4	a.	a.	NOUN
cana-5535	128	5	isah	isah	PROPN
cana-5535	128	6	,	,	PUNCT
cana-5535	128	7	c.	c.	PROPN
cana-5535	128	8	phang	phang	PROPN
cana-5535	128	9	.	.	PUNCT
cana-5535	129	1	genocchi	genocchi	PROPN
cana-5535	129	2	wavelet	wavelet	NOUN
cana-5535	129	3	-	-	PUNCT
cana-5535	129	4	like	like	ADJ
cana-5535	129	5	operational	operational	ADJ
cana-5535	129	6	matrix	matrix	NOUN
cana-5535	129	7	and	and	CCONJ
cana-5535	129	8	its	its	PRON
cana-5535	129	9	application	application	NOUN
cana-5535	129	10	for	for	ADP
cana-5535	129	11	solving	solve	VERB
cana-5535	129	12	non	non	ADJ
cana-5535	129	13	-	-	ADJ
cana-5535	129	14	linear	linear	ADJ
cana-5535	129	15	fractional	fractional	ADJ
cana-5535	129	16	differential	differential	NOUN
cana-5535	129	17	equations	equation	NOUN
cana-5535	129	18	.	.	PUNCT
cana-5535	130	1	open	open	ADJ
cana-5535	130	2	physics	physics	PROPN
cana-5535	130	3	,	,	PUNCT
cana-5535	130	4	vol	vol	NOUN
cana-5535	130	5	.	.	PROPN
cana-5535	130	6	14	14	NUM
cana-5535	130	7	,	,	PUNCT
cana-5535	130	8	no	no	INTJ
cana-5535	130	9	.	.	NOUN
cana-5535	130	10	1	1	NUM
cana-5535	130	11	,	,	PUNCT
cana-5535	130	12	pp	pp	ADJ
cana-5535	130	13	.	.	PUNCT
cana-5535	131	1	463	463	NUM
cana-5535	131	2	-	-	SYM
cana-5535	131	3	472	472	NUM
cana-5535	131	4	,	,	PUNCT
cana-5535	131	5	2016	2016	NUM
cana-5535	131	6	.	.	PUNCT
cana-5535	132	1	[	[	X
cana-5535	132	2	14	14	NUM
cana-5535	132	3	]	]	PUNCT
cana-5535	132	4	t.	t.	PROPN
cana-5535	132	5	kim	kim	PROPN
cana-5535	132	6	.	.	PUNCT
cana-5535	133	1	some	some	DET
cana-5535	133	2	identities	identity	NOUN
cana-5535	133	3	for	for	ADP
cana-5535	133	4	the	the	DET
cana-5535	133	5	bernoulli	bernoulli	NOUN
cana-5535	133	6	,	,	PUNCT
cana-5535	133	7	the	the	DET
cana-5535	133	8	euler	euler	NOUN
cana-5535	133	9	and	and	CCONJ
cana-5535	133	10	the	the	DET
cana-5535	133	11	genocchi	genocchi	PROPN
cana-5535	133	12	numbers	number	NOUN
cana-5535	133	13	and	and	CCONJ
cana-5535	133	14	polynomials	polynomial	NOUN
cana-5535	133	15	.	.	PUNCT
cana-5535	134	1	advanced	advanced	ADJ
cana-5535	134	2	studies	study	NOUN
cana-5535	134	3	in	in	ADP
cana-5535	134	4	contemporary	contemporary	ADJ
cana-5535	134	5	mathematics	mathematic	NOUN
cana-5535	134	6	,	,	PUNCT
cana-5535	134	7	vol	vol	NOUN
cana-5535	134	8	.	.	PROPN
cana-5535	134	9	20	20	NUM
cana-5535	134	10	,	,	PUNCT
cana-5535	134	11	no	no	INTJ
cana-5535	134	12	.	.	NOUN
cana-5535	134	13	1	1	NUM
cana-5535	134	14	,	,	PUNCT
cana-5535	134	15	pp	pp	ADJ
cana-5535	134	16	.	.	PUNCT
cana-5535	135	1	23	23	NUM
cana-5535	135	2	-	-	SYM
cana-5535	135	3	28	28	NUM
cana-5535	135	4	,	,	PUNCT
cana-5535	135	5	2010	2010	NUM
cana-5535	135	6	.	.	PUNCT
cana-5535	136	1	[	[	X
cana-5535	136	2	15	15	NUM
cana-5535	136	3	]	]	X
cana-5535	136	4	m.	m.	NOUN
cana-5535	136	5	khanian	khanian	PROPN
cana-5535	136	6	,	,	PUNCT
cana-5535	136	7	a.	a.	NOUN
cana-5535	136	8	davari	davari	PROPN
cana-5535	136	9	.	.	PUNCT
cana-5535	137	1	solution	solution	NOUN
cana-5535	137	2	of	of	ADP
cana-5535	137	3	system	system	NOUN
cana-5535	137	4	of	of	ADP
cana-5535	137	5	fredholm	fredholm	ADJ
cana-5535	137	6	integro	integro	ADJ
cana-5535	137	7	-	-	PUNCT
cana-5535	137	8	differential	differential	NOUN
cana-5535	137	9	equations	equation	NOUN
cana-5535	137	10	by	by	ADP
cana-5535	137	11	adomain	adomain	NOUN
cana-5535	137	12	decomposition	decomposition	NOUN
cana-5535	137	13	method	method	NOUN
cana-5535	137	14	,	,	PUNCT
cana-5535	137	15	australian	australian	ADJ
cana-5535	137	16	journal	journal	NOUN
cana-5535	137	17	of	of	ADP
cana-5535	137	18	basic	basic	ADJ
cana-5535	137	19	and	and	CCONJ
cana-5535	137	20	applied	apply	VERB
cana-5535	137	21	science	science	NOUN
cana-5535	137	22	,	,	PUNCT
cana-5535	137	23	vol	vol	NOUN
cana-5535	137	24	.	.	PROPN
cana-5535	137	25	5	5	NUM
cana-5535	137	26	,	,	PUNCT
cana-5535	137	27	no	no	INTJ
cana-5535	137	28	.	.	NOUN
cana-5535	137	29	12	12	NUM
cana-5535	137	30	,	,	PUNCT
cana-5535	137	31	(	(	PUNCT
cana-5535	137	32	2011	2011	NUM
cana-5535	137	33	)	)	PUNCT
cana-5535	137	34	,	,	PUNCT
cana-5535	137	35	2356	2356	NUM
cana-5535	137	36	-	-	SYM
cana-5535	137	37	2361	2361	NUM
cana-5535	137	38	.	.	PUNCT
cana-5535	138	1	[	[	X
cana-5535	138	2	16	16	NUM
cana-5535	138	3	]	]	PUNCT
cana-5535	138	4	s.	s.	PROPN
cana-5535	138	5	j.	j.	PROPN
cana-5535	138	6	liao	liao	PROPN
cana-5535	138	7	.	.	PROPN
cana-5535	139	1	beyond	beyond	ADP
cana-5535	139	2	perturbation	perturbation	NOUN
cana-5535	139	3	:	:	PUNCT
cana-5535	139	4	introduction	introduction	NOUN
cana-5535	139	5	to	to	ADP
cana-5535	139	6	the	the	DET
cana-5535	139	7	homotopy	homotopy	NOUN
cana-5535	139	8	analysis	analysis	NOUN
cana-5535	139	9	methods	method	NOUN
cana-5535	139	10	,	,	PUNCT
cana-5535	139	11	chapman	chapman	PROPN
cana-5535	139	12	&	&	CCONJ
cana-5535	139	13	hall	hall	PROPN
cana-5535	139	14	,	,	PUNCT
cana-5535	139	15	boca	boca	PROPN
cana-5535	139	16	raton	raton	PROPN
cana-5535	139	17	,	,	PUNCT
cana-5535	139	18	fla	fla	PROPN
cana-5535	139	19	,	,	PUNCT
cana-5535	139	20	usa	usa	PROPN
cana-5535	139	21	,	,	PUNCT
cana-5535	139	22	2003	2003	NUM
cana-5535	139	23	.	.	PUNCT
cana-5535	140	1	[	[	X
cana-5535	140	2	17	17	NUM
cana-5535	140	3	]	]	PUNCT
cana-5535	140	4	k.	k.	PROPN
cana-5535	140	5	maleknejad	maleknejad	PROPN
cana-5535	140	6	,	,	PUNCT
cana-5535	140	7	n.	n.	PROPN
cana-5535	140	8	aghazadeh	aghazadeh	PROPN
cana-5535	140	9	.	.	PUNCT
cana-5535	141	1	numerical	numerical	ADJ
cana-5535	141	2	solution	solution	NOUN
cana-5535	141	3	of	of	ADP
cana-5535	141	4	volterra	volterra	PROPN
cana-5535	141	5	integral	integral	ADJ
cana-5535	141	6	equations	equation	NOUN
cana-5535	141	7	of	of	ADP
cana-5535	141	8	the	the	DET
cana-5535	141	9	second	second	ADJ
cana-5535	141	10	kind	kind	NOUN
cana-5535	141	11	with	with	ADP
cana-5535	141	12	convolution	convolution	NOUN
cana-5535	141	13	kernel	kernel	NOUN
cana-5535	141	14	by	by	ADP
cana-5535	141	15	using	use	VERB
cana-5535	141	16	taylor	taylor	PROPN
cana-5535	141	17	-	-	PUNCT
cana-5535	141	18	series	series	NOUN
cana-5535	141	19	expansion	expansion	NOUN
cana-5535	141	20	method	method	NOUN
cana-5535	141	21	,	,	PUNCT
cana-5535	141	22	appl	appl	PROPN
cana-5535	141	23	.	.	PROPN
cana-5535	141	24	math	math	PROPN
cana-5535	141	25	.	.	PUNCT
cana-5535	142	1	comput	comput	NOUN
cana-5535	142	2	,	,	PUNCT
cana-5535	142	3	161	161	NUM
cana-5535	142	4	,	,	PUNCT
cana-5535	142	5	(	(	PUNCT
cana-5535	142	6	2005	2005	NUM
cana-5535	142	7	)	)	PUNCT
cana-5535	142	8	915	915	NUM
cana-5535	142	9	-	-	SYM
cana-5535	142	10	922	922	NUM
cana-5535	142	11	.	.	PUNCT
cana-5535	143	1	[	[	X
cana-5535	143	2	18	18	NUM
cana-5535	143	3	]	]	PUNCT
cana-5535	143	4	k.	k.	PROPN
cana-5535	143	5	maleknejad	maleknejad	PROPN
cana-5535	143	6	,	,	PUNCT
cana-5535	143	7	k.	k.	PROPN
cana-5535	143	8	nouri	nouri	PROPN
cana-5535	143	9	,	,	PUNCT
cana-5535	143	10	m.	m.	NOUN
cana-5535	143	11	yousefi	yousefi	PROPN
cana-5535	143	12	.	.	PUNCT
cana-5535	144	1	discussion	discussion	NOUN
cana-5535	144	2	on	on	ADP
cana-5535	144	3	convergence	convergence	NOUN
cana-5535	144	4	of	of	ADP
cana-5535	144	5	legendre	legendre	PROPN
cana-5535	144	6	polynomial	polynomial	PROPN
cana-5535	144	7	for	for	ADP
cana-5535	144	8	numerical	numerical	ADJ
cana-5535	144	9	solution	solution	NOUN
cana-5535	144	10	of	of	ADP
cana-5535	144	11	integral	integral	ADJ
cana-5535	144	12	equations	equation	NOUN
cana-5535	144	13	,	,	PUNCT
cana-5535	144	14	applied	apply	VERB
cana-5535	144	15	mathematics	mathematic	NOUN
cana-5535	144	16	and	and	CCONJ
cana-5535	144	17	computation	computation	NOUN
cana-5535	144	18	,	,	PUNCT
cana-5535	144	19	193	193	NUM
cana-5535	144	20	,	,	PUNCT
cana-5535	144	21	(	(	PUNCT
cana-5535	144	22	2007	2007	NUM
cana-5535	144	23	)	)	PUNCT
cana-5535	144	24	,	,	PUNCT
cana-5535	144	25	335	335	NUM
cana-5535	144	26	-	-	SYM
cana-5535	144	27	339	339	NUM
cana-5535	144	28	.	.	PUNCT
cana-5535	145	1	[	[	X
cana-5535	145	2	19	19	NUM
cana-5535	145	3	]	]	PUNCT
cana-5535	145	4	m.	m.	NOUN
cana-5535	145	5	nadir	nadir	NOUN
cana-5535	145	6	.	.	PUNCT
cana-5535	146	1	cours	cours	PROPN
cana-5535	146	2	sur	sur	PROPN
cana-5535	146	3	les	les	PROPN
cana-5535	146	4	équations	équations	PROPN
cana-5535	146	5	intégrales	intégrale	NOUN
cana-5535	146	6	,	,	PUNCT
cana-5535	146	7	université	université	PROPN
cana-5535	146	8	m'sila	m'sila	PROPN
cana-5535	146	9	2008	2008	NUM
cana-5535	146	10	.	.	PUNCT
cana-5535	147	1	communications	communication	NOUN
cana-5535	147	2	on	on	ADP
cana-5535	147	3	applied	apply	VERB
cana-5535	147	4	nonlinear	nonlinear	ADJ
cana-5535	147	5	analysis	analysis	NOUN
cana-5535	147	6	issn	issn	NOUN
cana-5535	147	7	:	:	PUNCT
cana-5535	147	8	1074	1074	NUM
cana-5535	147	9	-	-	PUNCT
cana-5535	147	10	133x	133x	NUM
cana-5535	147	11	vol	vol	VERB
cana-5535	147	12	32	32	NUM
cana-5535	147	13	no	no	NOUN
cana-5535	147	14	.	.	PUNCT
cana-5535	148	1	10s	10	NOUN
cana-5535	148	2	(	(	PUNCT
cana-5535	148	3	2025	2025	NUM
cana-5535	148	4	)	)	PUNCT
cana-5535	148	5	2588	2588	NUM
cana-5535	148	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5535	149	1	[	[	X
cana-5535	149	2	20	20	NUM
cana-5535	149	3	]	]	PUNCT
cana-5535	149	4	m.	m.	NOUN
cana-5535	149	5	nadir	nadir	NOUN
cana-5535	149	6	.	.	PUNCT
cana-5535	150	1	solving	solve	VERB
cana-5535	150	2	fredholm	fredholm	NOUN
cana-5535	150	3	integral	integral	ADJ
cana-5535	150	4	equations	equation	NOUN
cana-5535	150	5	with	with	ADP
cana-5535	150	6	application	application	NOUN
cana-5535	150	7	of	of	ADP
cana-5535	150	8	the	the	DET
cana-5535	150	9	four	four	NUM
cana-5535	150	10	chebyshev	chebyshev	NOUN
cana-5535	150	11	polynomials	polynomial	NOUN
cana-5535	150	12	,	,	PUNCT
cana-5535	150	13	in	in	ADP
cana-5535	150	14	journal	journal	NOUN
cana-5535	150	15	of	of	ADP
cana-5535	150	16	approximation	approximation	NOUN
cana-5535	150	17	theory	theory	NOUN
cana-5535	150	18	and	and	CCONJ
cana-5535	150	19	applied	apply	VERB
cana-5535	150	20	mathematics	mathematic	NOUN
cana-5535	150	21	,	,	PUNCT
cana-5535	150	22	4	4	NUM
cana-5535	150	23	,	,	PUNCT
cana-5535	150	24	(	(	PUNCT
cana-5535	150	25	2014	2014	NUM
cana-5535	150	26	)	)	PUNCT
cana-5535	150	27	,	,	PUNCT
cana-5535	150	28	pp	pp	ADP
cana-5535	150	29	37	37	NUM
cana-5535	150	30	-	-	SYM
cana-5535	150	31	44	44	NUM
cana-5535	150	32	.	.	PUNCT
cana-5535	151	1	[	[	X
cana-5535	151	2	21	21	NUM
cana-5535	151	3	]	]	PUNCT
cana-5535	151	4	m.	m.	NOUN
cana-5535	151	5	nadir	nadir	PROPN
cana-5535	151	6	,	,	PUNCT
cana-5535	151	7	d.	d.	PROPN
cana-5535	151	8	mustapha	mustapha	PROPN
cana-5535	151	9	.	.	PUNCT
cana-5535	151	10	euler	euler	PROPN
cana-5535	151	11	series	series	PROPN
cana-5535	151	12	solutions	solution	NOUN
cana-5535	151	13	for	for	ADP
cana-5535	151	14	linear	linear	ADJ
cana-5535	151	15	integral	integral	ADJ
cana-5535	151	16	equations	equation	NOUN
cana-5535	151	17	ajmaa	ajmaa	VERB
cana-5535	151	18	,	,	PUNCT
cana-5535	151	19	vol	vol	NOUN
cana-5535	151	20	.	.	PROPN
cana-5535	152	1	14	14	NUM
cana-5535	152	2	,	,	PUNCT
cana-5535	152	3	no	no	INTJ
cana-5535	152	4	.	.	NOUN
cana-5535	152	5	2	2	NUM
cana-5535	152	6	,	,	PUNCT
cana-5535	152	7	art	art	NOUN
cana-5535	152	8	.	.	PUNCT
cana-5535	153	1	11	11	NUM
cana-5535	153	2	,	,	PUNCT
cana-5535	153	3	(	(	PUNCT
cana-5535	153	4	2017	2017	NUM
cana-5535	153	5	)	)	PUNCT
cana-5535	153	6	pp	pp	ADP
cana-5535	153	7	1	1	NUM
cana-5535	153	8	-	-	SYM
cana-5535	153	9	7	7	NUM
cana-5535	153	10	.	.	PUNCT
cana-5535	154	1	[	[	X
cana-5535	154	2	22	22	NUM
cana-5535	154	3	]	]	X
cana-5535	154	4	c.	c.	PROPN
cana-5535	154	5	phang	phang	PROPN
cana-5535	154	6	,	,	PUNCT
cana-5535	154	7	n.	n.	PROPN
cana-5535	154	8	f.	f.	PROPN
cana-5535	154	9	ismail	ismail	PROPN
cana-5535	154	10	,	,	PUNCT
cana-5535	154	11	a.	a.	NOUN
cana-5535	154	12	isah	isah	PROPN
cana-5535	154	13	,	,	PUNCT
cana-5535	154	14	and	and	CCONJ
cana-5535	154	15	j.	j.	PROPN
cana-5535	154	16	r.	r.	PROPN
cana-5535	154	17	loh	loh	PROPN
cana-5535	154	18	.	.	PUNCT
cana-5535	155	1	a	a	DET
cana-5535	155	2	new	new	ADJ
cana-5535	155	3	efficient	efficient	ADJ
cana-5535	155	4	numerical	numerical	ADJ
cana-5535	155	5	scheme	scheme	NOUN
cana-5535	155	6	for	for	ADP
cana-5535	155	7	solving	solve	VERB
cana-5535	155	8	fractional	fractional	ADJ
cana-5535	155	9	optimal	optimal	ADJ
cana-5535	155	10	control	control	NOUN
cana-5535	155	11	problems	problem	NOUN
cana-5535	155	12	via	via	ADP
cana-5535	155	13	a	a	DET
cana-5535	155	14	genocchi	genocchi	PROPN
cana-5535	155	15	operational	operational	ADJ
cana-5535	155	16	matrix	matrix	NOUN
cana-5535	155	17	of	of	ADP
cana-5535	155	18	integration	integration	NOUN
cana-5535	155	19	.	.	PUNCT
cana-5535	156	1	journal	journal	NOUN
cana-5535	156	2	of	of	ADP
cana-5535	156	3	vibration	vibration	NOUN
cana-5535	156	4	and	and	CCONJ
cana-5535	156	5	control	control	NOUN
cana-5535	156	6	,	,	PUNCT
cana-5535	156	7	2017	2017	NUM
cana-5535	156	8	.	.	PUNCT
cana-5535	157	1	[	[	X
cana-5535	157	2	23	23	NUM
cana-5535	157	3	]	]	PUNCT
cana-5535	157	4	m.	m.	NOUN
cana-5535	157	5	rahman	rahman	PROPN
cana-5535	157	6	.	.	PUNCT
cana-5535	158	1	mathematical	mathematical	ADJ
cana-5535	158	2	methods	method	NOUN
cana-5535	158	3	with	with	ADP
cana-5535	158	4	application	application	NOUN
cana-5535	158	5	,	,	PUNCT
cana-5535	158	6	wit	wit	ADJ
cana-5535	158	7	press	press	PROPN
cana-5535	158	8	,	,	PUNCT
cana-5535	158	9	southampton	southampton	PROPN
cana-5535	158	10	,	,	PUNCT
cana-5535	158	11	uk	uk	PROPN
cana-5535	158	12	,	,	PUNCT
cana-5535	158	13	pp	pp	ADJ
cana-5535	158	14	.	.	PUNCT
cana-5535	158	15	456	456	NUM
cana-5535	158	16	,	,	PUNCT
cana-5535	158	17	2000	2000	NUM
cana-5535	158	18	.	.	PUNCT
cana-5535	159	1	[	[	X
cana-5535	159	2	24	24	NUM
cana-5535	159	3	]	]	X
cana-5535	159	4	s.	s.	PROPN
cana-5535	159	5	roman	roman	PROPN
cana-5535	159	6	,	,	PUNCT
cana-5535	159	7	the	the	DET
cana-5535	159	8	umbral	umbral	ADJ
cana-5535	159	9	calculus	calculus	NOUN
cana-5535	159	10	.	.	PUNCT
cana-5535	160	1	208	208	NUM
cana-5535	160	2	dover	dover	PROPN
cana-5535	160	3	publications	publications	PROPN
cana-5535	160	4	usa	usa	PROPN
cana-5535	160	5	,	,	PUNCT
cana-5535	160	6	2005	2005	NUM
cana-5535	160	7	.	.	PUNCT
cana-5535	161	1	[	[	X
cana-5535	161	2	25	25	NUM
cana-5535	161	3	]	]	X
cana-5535	161	4	s.	s.	PROPN
cana-5535	161	5	wang	wang	PROPN
cana-5535	161	6	,	,	PUNCT
cana-5535	161	7	j.h	j.h	PROPN
cana-5535	161	8	.	.	PUNCT
cana-5535	162	1	he	he	PRON
cana-5535	162	2	.	.	PUNCT
cana-5535	163	1	variational	variational	ADJ
cana-5535	163	2	iteration	iteration	NOUN
cana-5535	163	3	method	method	NOUN
cana-5535	163	4	for	for	ADP
cana-5535	163	5	solving	solve	VERB
cana-5535	163	6	integro	integro	ADJ
cana-5535	163	7	-	-	PUNCT
cana-5535	163	8	differential	differential	NOUN
cana-5535	163	9	equations	equation	NOUN
cana-5535	163	10	.	.	PUNCT
cana-5535	164	1	phys	phy	NOUN
cana-5535	164	2	.	.	PUNCT
cana-5535	165	1	lett	lett	PROPN
cana-5535	165	2	.	.	PROPN
cana-5535	165	3	,	,	PUNCT
cana-5535	165	4	a	a	DET
cana-5535	165	5	367	367	NUM
cana-5535	165	6	(	(	PUNCT
cana-5535	165	7	2007	2007	NUM
cana-5535	165	8	)	)	PUNCT
cana-5535	165	9	188	188	NUM
cana-5535	165	10	-	-	SYM
cana-5535	165	11	191	191	NUM
cana-5535	165	12	.	.	PUNCT
cana-5535	166	1	[	[	X
cana-5535	166	2	26	26	NUM
cana-5535	166	3	]	]	PUNCT
cana-5535	166	4	a.m.	a.m.	NOUN
cana-5535	166	5	wazwaz	wazwaz	PROPN
cana-5535	166	6	.	.	PUNCT
cana-5535	167	1	a	a	DET
cana-5535	167	2	reliable	reliable	ADJ
cana-5535	167	3	algorithm	algorithm	NOUN
cana-5535	167	4	for	for	ADP
cana-5535	167	5	solving	solve	VERB
cana-5535	167	6	boundary	boundary	ADJ
cana-5535	167	7	value	value	NOUN
cana-5535	167	8	problems	problem	NOUN
cana-5535	167	9	for	for	ADP
cana-5535	167	10	higher	high	ADJ
cana-5535	167	11	-	-	PUNCT
cana-5535	167	12	order	order	NOUN
cana-5535	167	13	integro	integro	ADJ
cana-5535	167	14	-	-	PUNCT
cana-5535	167	15	differential	differential	NOUN
cana-5535	167	16	equations	equation	NOUN
cana-5535	167	17	,	,	PUNCT
cana-5535	167	18	applied	apply	VERB
cana-5535	167	19	mathematical	mathematical	ADJ
cana-5535	167	20	and	and	CCONJ
cana-5535	167	21	computation	computation	NOUN
cana-5535	167	22	,	,	PUNCT
cana-5535	167	23	118	118	NUM
cana-5535	167	24	(	(	PUNCT
cana-5535	167	25	2001	2001	NUM
cana-5535	167	26	)	)	PUNCT
cana-5535	167	27	,	,	PUNCT
cana-5535	167	28	327	327	NUM
cana-5535	167	29	-	-	SYM
cana-5535	167	30	342	342	NUM
cana-5535	167	31	.	.	PUNCT
cana-5535	168	1	[	[	X
cana-5535	168	2	27	27	NUM
cana-5535	168	3	]	]	X
cana-5535	168	4	l.h	l.h	PROPN
cana-5535	168	5	.	.	PROPN
cana-5535	168	6	yang	yang	PROPN
cana-5535	168	7	,	,	PUNCT
cana-5535	168	8	y.	y.	PROPN
cana-5535	168	9	lin	lin	PROPN
cana-5535	168	10	.	.	PUNCT
cana-5535	169	1	reproducing	reproduce	VERB
cana-5535	169	2	kernel	kernel	NOUN
cana-5535	169	3	methods	method	NOUN
cana-5535	169	4	for	for	ADP
cana-5535	169	5	solving	solve	VERB
cana-5535	169	6	linear	linear	ADJ
cana-5535	169	7	initial	initial	ADJ
cana-5535	169	8	boundary	boundary	ADJ
cana-5535	169	9	-	-	PUNCT
cana-5535	169	10	value	value	NOUN
cana-5535	169	11	problems	problem	NOUN
cana-5535	169	12	,	,	PUNCT
cana-5535	169	13	electronic	electronic	ADJ
cana-5535	169	14	journal	journal	NOUN
cana-5535	169	15	of	of	ADP
cana-5535	169	16	differential	differential	ADJ
cana-5535	169	17	equations	equation	NOUN
cana-5535	169	18	,	,	PUNCT
cana-5535	169	19	(	(	PUNCT
cana-5535	169	20	2008	2008	NUM
cana-5535	169	21	)	)	PUNCT
cana-5535	169	22	,	,	PUNCT
cana-5535	169	23	1	1	NUM
cana-5535	169	24	-	-	SYM
cana-5535	169	25	11	11	NUM
cana-5535	169	26	.	.	PUNCT