id	sid	tid	token	lemma	pos
cana-4971	1	1	communications	communication	NOUN
cana-4971	1	2	on	on	ADP
cana-4971	1	3	applied	apply	VERB
cana-4971	1	4	nonlinear	nonlinear	ADJ
cana-4971	1	5	analysis	analysis	NOUN
cana-4971	1	6	issn	issn	NOUN
cana-4971	1	7	:	:	PUNCT
cana-4971	1	8	1074	1074	NUM
cana-4971	1	9	-	-	PUNCT
cana-4971	1	10	133x	133x	NUM
cana-4971	1	11	vol	vol	NOUN
cana-4971	1	12	31	31	NUM
cana-4971	1	13	no	no	NOUN
cana-4971	1	14	.	.	PUNCT
cana-4971	2	1	4s	4s	NUM
cana-4971	2	2	(	(	PUNCT
cana-4971	2	3	2024	2024	NUM
cana-4971	2	4	)	)	PUNCT
cana-4971	2	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4971	2	6	660	660	NUM
cana-4971	2	7	evaluating	evaluate	VERB
cana-4971	2	8	analytical	analytical	ADJ
cana-4971	2	9	approximations	approximation	NOUN
cana-4971	2	10	and	and	CCONJ
cana-4971	2	11	numerical	numerical	ADJ
cana-4971	2	12	solutions	solution	NOUN
cana-4971	2	13	for	for	ADP
cana-4971	2	14	volterra	volterra	PROPN
cana-4971	2	15	’s	’s	PART
cana-4971	2	16	population	population	NOUN
cana-4971	2	17	growth	growth	NOUN
cana-4971	2	18	equation	equation	NOUN
cana-4971	2	19	s	s	VERB
cana-4971	2	20	u	u	NOUN
cana-4971	2	21	kore1	kore1	PROPN
cana-4971	2	22	,	,	PUNCT
cana-4971	2	23	s	s	PROPN
cana-4971	2	24	s	s	PROPN
cana-4971	2	25	bellale2	bellale2	PROPN
cana-4971	2	26	,	,	PUNCT
cana-4971	2	27	y	y	PROPN
cana-4971	2	28	m	m	PROPN
cana-4971	2	29	muley3	muley3	NOUN
cana-4971	2	30	1department	1department	NUM
cana-4971	2	31	of	of	ADP
cana-4971	2	32	mathematics	mathematic	NOUN
cana-4971	2	33	,	,	PUNCT
cana-4971	2	34	sambhaji	sambhaji	PROPN
cana-4971	2	35	kendre	kendre	PROPN
cana-4971	2	36	mahavidyalaya	mahavidyalaya	PROPN
cana-4971	2	37	,	,	PUNCT
cana-4971	2	38	jalkot	jalkot	PROPN
cana-4971	2	39	,	,	PUNCT
cana-4971	2	40	india	india	PROPN
cana-4971	2	41	.	.	PUNCT
cana-4971	3	1	2department	2department	NUM
cana-4971	3	2	of	of	ADP
cana-4971	3	3	mathematics	mathematic	NOUN
cana-4971	3	4	,	,	PUNCT
cana-4971	3	5	dayanand	dayanand	NOUN
cana-4971	3	6	science	science	PROPN
cana-4971	3	7	college	college	PROPN
cana-4971	3	8	,	,	PUNCT
cana-4971	3	9	latur	latur	PROPN
cana-4971	3	10	,	,	PUNCT
cana-4971	3	11	india	india	PROPN
cana-4971	3	12	.	.	PUNCT
cana-4971	4	1	3department	3department	NUM
cana-4971	4	2	of	of	ADP
cana-4971	4	3	mathematics	mathematic	NOUN
cana-4971	4	4	,	,	PUNCT
cana-4971	4	5	kai	kai	PROPN
cana-4971	4	6	.	.	PROPN
cana-4971	4	7	rasika	rasika	PROPN
cana-4971	4	8	mahavidyalaya	mahavidyalaya	PROPN
cana-4971	4	9	,	,	PUNCT
cana-4971	4	10	deoni	deoni	PROPN
cana-4971	4	11	,	,	PUNCT
cana-4971	4	12	india	india	PROPN
cana-4971	4	13	.	.	PUNCT
cana-4971	5	1	article	article	PROPN
cana-4971	5	2	history	history	NOUN
cana-4971	5	3	:	:	PUNCT
cana-4971	5	4	received	receive	VERB
cana-4971	5	5	:	:	PUNCT
cana-4971	5	6	03	03	NUM
cana-4971	5	7	-	-	SYM
cana-4971	5	8	08	08	NUM
cana-4971	5	9	-	-	PUNCT
cana-4971	5	10	2024	2024	NUM
cana-4971	5	11	revised	revise	VERB
cana-4971	5	12	:	:	PUNCT
cana-4971	5	13	26	26	NUM
cana-4971	5	14	-	-	SYM
cana-4971	5	15	09	09	NUM
cana-4971	5	16	-	-	PUNCT
cana-4971	5	17	2024	2024	NUM
cana-4971	5	18	accepted	accept	VERB
cana-4971	5	19	:	:	PUNCT
cana-4971	5	20	11	11	NUM
cana-4971	5	21	-	-	SYM
cana-4971	5	22	10	10	NUM
cana-4971	5	23	-	-	PUNCT
cana-4971	5	24	2024	2024	NUM
cana-4971	5	25	abstract	abstract	NOUN
cana-4971	5	26	:	:	PUNCT
cana-4971	5	27	this	this	DET
cana-4971	5	28	paper	paper	NOUN
cana-4971	5	29	presents	present	VERB
cana-4971	5	30	a	a	DET
cana-4971	5	31	comprehensive	comprehensive	ADJ
cana-4971	5	32	study	study	NOUN
cana-4971	5	33	to	to	PART
cana-4971	5	34	solve	solve	VERB
cana-4971	5	35	the	the	DET
cana-4971	5	36	nonlinear	nonlinear	PROPN
cana-4971	5	37	volterra	volterra	PROPN
cana-4971	5	38	integro	integro	PROPN
cana-4971	5	39	-	-	PUNCT
cana-4971	5	40	differential	differential	NOUN
cana-4971	5	41	equation	equation	NOUN
cana-4971	5	42	(	(	PUNCT
cana-4971	5	43	nlvide	nlvide	ADV
cana-4971	5	44	)	)	PUNCT
cana-4971	5	45	i.e.	i.e.	X
cana-4971	5	46	volterra	volterra	PROPN
cana-4971	5	47	’s	’s	PART
cana-4971	5	48	population	population	NOUN
cana-4971	5	49	growth	growth	NOUN
cana-4971	5	50	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	5	51	𝑑𝑡	𝑑𝑡	ADP
cana-4971	5	52	=	=	SYM
cana-4971	5	53	10𝑧(𝑡	10𝑧(𝑡	PROPN
cana-4971	5	54	)	)	PUNCT
cana-4971	6	1	−	−	PROPN
cana-4971	6	2	10𝑧2	10𝑧2	NUM
cana-4971	6	3	(	(	PUNCT
cana-4971	6	4	𝑡	𝑡	NOUN
cana-4971	6	5	)	)	PUNCT
cana-4971	6	6	−	−	PROPN
cana-4971	6	7	10𝑧(𝑡	10𝑧(𝑡	NUM
cana-4971	6	8	)	)	PUNCT
cana-4971	6	9	∫	∫	PROPN
cana-4971	6	10	𝑧(𝑥	𝑧(𝑥	PROPN
cana-4971	6	11	)	)	PUNCT
cana-4971	6	12	𝑑𝑥	𝑑𝑥	VERB
cana-4971	6	13	𝑡	𝑡	PROPN
cana-4971	6	14	0	0	NUM
cana-4971	6	15	,	,	PUNCT
cana-4971	6	16	with	with	ADP
cana-4971	6	17	initial	initial	ADJ
cana-4971	6	18	condition	condition	NOUN
cana-4971	6	19	𝑧(0	𝑧(0	NOUN
cana-4971	6	20	)	)	PUNCT
cana-4971	6	21	=	=	SYM
cana-4971	6	22	0.1	0.1	NUM
cana-4971	6	23	,	,	PUNCT
cana-4971	6	24	is	be	AUX
cana-4971	6	25	examined	examine	VERB
cana-4971	6	26	using	use	VERB
cana-4971	6	27	three	three	NUM
cana-4971	6	28	distinct	distinct	ADJ
cana-4971	6	29	approaches	approach	NOUN
cana-4971	6	30	:	:	PUNCT
cana-4971	6	31	a	a	DET
cana-4971	6	32	power	power	NOUN
cana-4971	6	33	series	series	NOUN
cana-4971	6	34	solution	solution	NOUN
cana-4971	6	35	,	,	PUNCT
cana-4971	6	36	a	a	DET
cana-4971	6	37	novel	novel	ADJ
cana-4971	6	38	hybrid	hybrid	ADJ
cana-4971	6	39	laplace	laplace	NOUN
cana-4971	6	40	transform	transform	NOUN
cana-4971	6	41	-	-	PUNCT
cana-4971	6	42	series	series	NOUN
cana-4971	6	43	method	method	NOUN
cana-4971	6	44	,	,	PUNCT
cana-4971	6	45	and	and	CCONJ
cana-4971	6	46	numerical	numerical	ADJ
cana-4971	6	47	integration	integration	NOUN
cana-4971	6	48	via	via	ADP
cana-4971	6	49	matlab	matlab	PROPN
cana-4971	6	50	’s	’s	PART
cana-4971	6	51	ode45	ode45	NOUN
cana-4971	6	52	.	.	PUNCT
cana-4971	7	1	we	we	PRON
cana-4971	7	2	derive	derive	VERB
cana-4971	7	3	analytical	analytical	ADJ
cana-4971	7	4	approximations	approximation	NOUN
cana-4971	7	5	,	,	PUNCT
cana-4971	7	6	implement	implement	VERB
cana-4971	7	7	a	a	DET
cana-4971	7	8	matlab	matlab	PROPN
cana-4971	7	9	script	script	NOUN
cana-4971	7	10	to	to	PART
cana-4971	7	11	compute	compute	VERB
cana-4971	7	12	and	and	CCONJ
cana-4971	7	13	visualize	visualize	VERB
cana-4971	7	14	solutions	solution	NOUN
cana-4971	7	15	,	,	PUNCT
cana-4971	7	16	and	and	CCONJ
cana-4971	7	17	compare	compare	VERB
cana-4971	7	18	the	the	DET
cana-4971	7	19	computational	computational	ADJ
cana-4971	7	20	efficiency	efficiency	NOUN
cana-4971	7	21	and	and	CCONJ
cana-4971	7	22	accuracy	accuracy	NOUN
cana-4971	7	23	of	of	ADP
cana-4971	7	24	each	each	DET
cana-4971	7	25	method	method	NOUN
cana-4971	7	26	.	.	PUNCT
cana-4971	8	1	the	the	DET
cana-4971	8	2	results	result	NOUN
cana-4971	8	3	indicate	indicate	VERB
cana-4971	8	4	that	that	SCONJ
cana-4971	8	5	the	the	DET
cana-4971	8	6	series	series	NOUN
cana-4971	8	7	and	and	CCONJ
cana-4971	8	8	hybrid	hybrid	ADJ
cana-4971	8	9	methods	method	NOUN
cana-4971	8	10	yield	yield	VERB
cana-4971	8	11	accurate	accurate	ADJ
cana-4971	8	12	approximations	approximation	NOUN
cana-4971	8	13	for	for	ADP
cana-4971	8	14	small	small	ADJ
cana-4971	8	15	time	time	NOUN
cana-4971	8	16	intervals	interval	NOUN
cana-4971	8	17	,	,	PUNCT
cana-4971	8	18	whereas	whereas	SCONJ
cana-4971	8	19	the	the	DET
cana-4971	8	20	numerical	numerical	ADJ
cana-4971	8	21	method	method	NOUN
cana-4971	8	22	provides	provide	VERB
cana-4971	8	23	robust	robust	ADJ
cana-4971	8	24	solutions	solution	NOUN
cana-4971	8	25	over	over	ADP
cana-4971	8	26	larger	large	ADJ
cana-4971	8	27	domains	domain	NOUN
cana-4971	8	28	.	.	PUNCT
cana-4971	9	1	this	this	DET
cana-4971	9	2	study	study	NOUN
cana-4971	9	3	elucidates	elucidate	VERB
cana-4971	9	4	the	the	DET
cana-4971	9	5	strengths	strength	NOUN
cana-4971	9	6	and	and	CCONJ
cana-4971	9	7	limitations	limitation	NOUN
cana-4971	9	8	of	of	ADP
cana-4971	9	9	each	each	DET
cana-4971	9	10	approach	approach	NOUN
cana-4971	9	11	,	,	PUNCT
cana-4971	9	12	offering	offer	VERB
cana-4971	9	13	insights	insight	NOUN
cana-4971	9	14	into	into	ADP
cana-4971	9	15	their	their	PRON
cana-4971	9	16	applicability	applicability	NOUN
cana-4971	9	17	in	in	ADP
cana-4971	9	18	nonlinear	nonlinear	ADJ
cana-4971	9	19	integro	integro	ADJ
cana-4971	9	20	-	-	PUNCT
cana-4971	9	21	differential	differential	NOUN
cana-4971	9	22	systems	system	NOUN
cana-4971	9	23	.	.	PUNCT
cana-4971	10	1	keywords	keyword	NOUN
cana-4971	10	2	:	:	PUNCT
cana-4971	10	3	volterra	volterra	PROPN
cana-4971	10	4	integro	integro	PROPN
cana-4971	10	5	-	-	PUNCT
cana-4971	10	6	differential	differential	NOUN
cana-4971	10	7	equation	equation	NOUN
cana-4971	10	8	,	,	PUNCT
cana-4971	10	9	hybrid	hybrid	NOUN
cana-4971	10	10	method	method	NOUN
cana-4971	10	11	,	,	PUNCT
cana-4971	10	12	laplace	laplace	NOUN
cana-4971	10	13	transform	transform	NOUN
cana-4971	10	14	,	,	PUNCT
cana-4971	10	15	series	series	NOUN
cana-4971	10	16	solution	solution	NOUN
cana-4971	10	17	,	,	PUNCT
cana-4971	10	18	numerical	numerical	ADJ
cana-4971	10	19	analysis	analysis	NOUN
cana-4971	10	20	.	.	PUNCT
cana-4971	11	1	1	1	X
cana-4971	11	2	.	.	X
cana-4971	11	3	introduction	introduction	NOUN
cana-4971	11	4	the	the	DET
cana-4971	11	5	paper	paper	NOUN
cana-4971	11	6	conducts	conduct	VERB
cana-4971	11	7	an	an	DET
cana-4971	11	8	in	in	ADP
cana-4971	11	9	-	-	PUNCT
cana-4971	11	10	depth	depth	NOUN
cana-4971	11	11	examination	examination	NOUN
cana-4971	11	12	of	of	ADP
cana-4971	11	13	three	three	NUM
cana-4971	11	14	distinct	distinct	ADJ
cana-4971	11	15	methods	method	NOUN
cana-4971	11	16	for	for	ADP
cana-4971	11	17	solving	solve	VERB
cana-4971	11	18	nlvide	nlvide	ADV
cana-4971	11	19	.	.	PUNCT
cana-4971	12	1	the	the	DET
cana-4971	12	2	first	first	ADJ
cana-4971	12	3	approach	approach	NOUN
cana-4971	12	4	utilizes	utilize	VERB
cana-4971	12	5	a	a	DET
cana-4971	12	6	power	power	NOUN
cana-4971	12	7	series	series	NOUN
cana-4971	12	8	solution	solution	NOUN
cana-4971	12	9	,	,	PUNCT
cana-4971	12	10	while	while	SCONJ
cana-4971	12	11	the	the	DET
cana-4971	12	12	second	second	ADJ
cana-4971	12	13	introduces	introduce	VERB
cana-4971	12	14	an	an	DET
cana-4971	12	15	innovative	innovative	ADJ
cana-4971	12	16	hybrid	hybrid	NOUN
cana-4971	12	17	technique	technique	NOUN
cana-4971	12	18	that	that	PRON
cana-4971	12	19	merges	merge	VERB
cana-4971	12	20	the	the	DET
cana-4971	12	21	laplace	laplace	NOUN
cana-4971	12	22	transform	transform	VERB
cana-4971	12	23	with	with	ADP
cana-4971	12	24	a	a	DET
cana-4971	12	25	series	series	NOUN
cana-4971	12	26	method	method	NOUN
cana-4971	12	27	.	.	PUNCT
cana-4971	13	1	the	the	DET
cana-4971	13	2	third	third	ADJ
cana-4971	13	3	method	method	NOUN
cana-4971	13	4	employs	employ	VERB
cana-4971	13	5	numerical	numerical	ADJ
cana-4971	13	6	integration	integration	NOUN
cana-4971	13	7	using	use	VERB
cana-4971	13	8	matlab	matlab	PROPN
cana-4971	13	9	’s	’s	PART
cana-4971	13	10	ode45	ode45	NOUN
cana-4971	13	11	function	function	NOUN
cana-4971	13	12	.	.	PUNCT
cana-4971	14	1	each	each	PRON
cana-4971	14	2	of	of	ADP
cana-4971	14	3	these	these	DET
cana-4971	14	4	methods	method	NOUN
cana-4971	14	5	brings	bring	VERB
cana-4971	14	6	unique	unique	ADJ
cana-4971	14	7	advantages	advantage	NOUN
cana-4971	14	8	to	to	ADP
cana-4971	14	9	the	the	DET
cana-4971	14	10	table	table	NOUN
cana-4971	14	11	:	:	PUNCT
cana-4971	14	12	the	the	DET
cana-4971	14	13	series	series	NOUN
cana-4971	14	14	and	and	CCONJ
cana-4971	14	15	hybrid	hybrid	ADJ
cana-4971	14	16	methods	method	NOUN
cana-4971	14	17	deliver	deliver	VERB
cana-4971	14	18	precise	precise	ADJ
cana-4971	14	19	approximations	approximation	NOUN
cana-4971	14	20	for	for	ADP
cana-4971	14	21	short	short	ADJ
cana-4971	14	22	time	time	NOUN
cana-4971	14	23	intervals	interval	NOUN
cana-4971	14	24	,	,	PUNCT
cana-4971	14	25	whereas	whereas	SCONJ
cana-4971	14	26	the	the	DET
cana-4971	14	27	numerical	numerical	ADJ
cana-4971	14	28	method	method	NOUN
cana-4971	14	29	excels	excel	VERB
cana-4971	14	30	in	in	ADP
cana-4971	14	31	providing	provide	VERB
cana-4971	14	32	robust	robust	ADJ
cana-4971	14	33	solutions	solution	NOUN
cana-4971	14	34	over	over	ADP
cana-4971	14	35	larger	large	ADJ
cana-4971	14	36	domains	domain	NOUN
cana-4971	14	37	(	(	PUNCT
cana-4971	14	38	[	[	X
cana-4971	14	39	1	1	NUM
cana-4971	14	40	]	]	PUNCT
cana-4971	14	41	;	;	PUNCT
cana-4971	15	1	[	[	X
cana-4971	15	2	2	2	NUM
cana-4971	15	3	]	]	PUNCT
cana-4971	15	4	)	)	PUNCT
cana-4971	15	5	.	.	PUNCT
cana-4971	16	1	notably	notably	ADV
cana-4971	16	2	,	,	PUNCT
cana-4971	16	3	the	the	DET
cana-4971	16	4	study	study	NOUN
cana-4971	16	5	uncovers	uncover	VERB
cana-4971	16	6	some	some	DET
cana-4971	16	7	contradictions	contradiction	NOUN
cana-4971	16	8	and	and	CCONJ
cana-4971	16	9	distinctive	distinctive	ADJ
cana-4971	16	10	features	feature	NOUN
cana-4971	16	11	of	of	ADP
cana-4971	16	12	each	each	DET
cana-4971	16	13	method	method	NOUN
cana-4971	16	14	.	.	PUNCT
cana-4971	17	1	although	although	SCONJ
cana-4971	17	2	the	the	DET
cana-4971	17	3	power	power	NOUN
cana-4971	17	4	series	series	NOUN
cana-4971	17	5	and	and	CCONJ
cana-4971	17	6	hybrid	hybrid	ADJ
cana-4971	17	7	laplace	laplace	NOUN
cana-4971	17	8	transform	transform	NOUN
cana-4971	17	9	-	-	PUNCT
cana-4971	17	10	series	series	NOUN
cana-4971	17	11	methods	method	NOUN
cana-4971	17	12	are	be	AUX
cana-4971	17	13	adept	adept	ADJ
cana-4971	17	14	at	at	ADP
cana-4971	17	15	offering	offer	VERB
cana-4971	17	16	analytical	analytical	ADJ
cana-4971	17	17	approximations	approximation	NOUN
cana-4971	17	18	,	,	PUNCT
cana-4971	17	19	they	they	PRON
cana-4971	17	20	may	may	AUX
cana-4971	17	21	encounter	encounter	VERB
cana-4971	17	22	limitations	limitation	NOUN
cana-4971	17	23	over	over	ADP
cana-4971	17	24	extended	extended	ADJ
cana-4971	17	25	time	time	NOUN
cana-4971	17	26	intervals	interval	NOUN
cana-4971	17	27	.	.	PUNCT
cana-4971	18	1	conversely	conversely	ADV
cana-4971	18	2	,	,	PUNCT
cana-4971	18	3	the	the	DET
cana-4971	18	4	numerical	numerical	ADJ
cana-4971	18	5	integration	integration	NOUN
cana-4971	18	6	method	method	NOUN
cana-4971	18	7	,	,	PUNCT
cana-4971	18	8	while	while	SCONJ
cana-4971	18	9	less	less	ADV
cana-4971	18	10	accurate	accurate	ADJ
cana-4971	18	11	for	for	ADP
cana-4971	18	12	short	short	ADJ
cana-4971	18	13	intervals	interval	NOUN
cana-4971	18	14	,	,	PUNCT
cana-4971	18	15	shows	show	VERB
cana-4971	18	16	superior	superior	ADJ
cana-4971	18	17	performance	performance	NOUN
cana-4971	18	18	over	over	ADP
cana-4971	18	19	longer	long	ADJ
cana-4971	18	20	domains	domain	NOUN
cana-4971	18	21	.	.	PUNCT
cana-4971	19	1	this	this	PRON
cana-4971	19	2	underscores	underscore	VERB
cana-4971	19	3	the	the	DET
cana-4971	19	4	necessity	necessity	NOUN
cana-4971	19	5	of	of	ADP
cana-4971	19	6	choosing	choose	VERB
cana-4971	19	7	the	the	DET
cana-4971	19	8	appropriate	appropriate	ADJ
cana-4971	19	9	method	method	NOUN
cana-4971	19	10	based	base	VERB
cana-4971	19	11	on	on	ADP
cana-4971	19	12	the	the	DET
cana-4971	19	13	specific	specific	ADJ
cana-4971	19	14	requirements	requirement	NOUN
cana-4971	19	15	of	of	ADP
cana-4971	19	16	the	the	DET
cana-4971	19	17	problem	problem	NOUN
cana-4971	19	18	and	and	CCONJ
cana-4971	19	19	the	the	DET
cana-4971	19	20	desired	desire	VERB
cana-4971	19	21	solution	solution	NOUN
cana-4971	19	22	range	range	NOUN
cana-4971	19	23	(	(	PUNCT
cana-4971	19	24	[	[	X
cana-4971	19	25	3	3	NUM
cana-4971	19	26	]	]	PUNCT
cana-4971	19	27	;	;	PUNCT
cana-4971	19	28	[	[	X
cana-4971	19	29	4	4	NUM
cana-4971	19	30	]	]	PUNCT
cana-4971	19	31	)	)	PUNCT
cana-4971	19	32	.	.	PUNCT
cana-4971	20	1	in	in	ADP
cana-4971	20	2	summary	summary	NOUN
cana-4971	20	3	,	,	PUNCT
cana-4971	20	4	this	this	DET
cana-4971	20	5	comprehensive	comprehensive	ADJ
cana-4971	20	6	study	study	NOUN
cana-4971	20	7	offers	offer	VERB
cana-4971	20	8	valuable	valuable	ADJ
cana-4971	20	9	insights	insight	NOUN
cana-4971	20	10	into	into	ADP
cana-4971	20	11	solving	solve	VERB
cana-4971	20	12	nonlinear	nonlinear	ADJ
cana-4971	20	13	volterra	volterra	PROPN
cana-4971	20	14	integrodifferential	integrodifferential	PROPN
cana-4971	20	15	equations	equation	NOUN
cana-4971	20	16	.	.	PUNCT
cana-4971	21	1	by	by	ADP
cana-4971	21	2	comparing	compare	VERB
cana-4971	21	3	three	three	NUM
cana-4971	21	4	distinct	distinct	ADJ
cana-4971	21	5	approaches	approach	NOUN
cana-4971	21	6	,	,	PUNCT
cana-4971	21	7	it	it	PRON
cana-4971	21	8	provides	provide	VERB
cana-4971	21	9	researchers	researcher	NOUN
cana-4971	21	10	and	and	CCONJ
cana-4971	21	11	practitioners	practitioner	NOUN
cana-4971	21	12	with	with	ADP
cana-4971	21	13	a	a	DET
cana-4971	21	14	nuanced	nuanced	ADJ
cana-4971	21	15	understanding	understanding	NOUN
cana-4971	21	16	of	of	ADP
cana-4971	21	17	each	each	DET
cana-4971	21	18	method	method	NOUN
cana-4971	21	19	’s	’s	PART
cana-4971	21	20	strengths	strength	NOUN
cana-4971	21	21	and	and	CCONJ
cana-4971	21	22	limitations	limitation	NOUN
cana-4971	21	23	.	.	PUNCT
cana-4971	22	1	the	the	DET
cana-4971	22	2	findings	finding	NOUN
cana-4971	22	3	emphasize	emphasize	VERB
cana-4971	22	4	the	the	DET
cana-4971	22	5	importance	importance	NOUN
cana-4971	22	6	of	of	ADP
cana-4971	22	7	method	method	NOUN
cana-4971	22	8	selection	selection	NOUN
cana-4971	22	9	based	base	VERB
cana-4971	22	10	on	on	ADP
cana-4971	22	11	the	the	DET
cana-4971	22	12	characteristics	characteristic	NOUN
cana-4971	22	13	of	of	ADP
cana-4971	22	14	the	the	DET
cana-4971	22	15	problem	problem	NOUN
cana-4971	22	16	and	and	CCONJ
cana-4971	22	17	the	the	DET
cana-4971	22	18	desired	desire	VERB
cana-4971	22	19	solution	solution	NOUN
cana-4971	22	20	domain	domain	NOUN
cana-4971	22	21	,	,	PUNCT
cana-4971	22	22	thus	thus	ADV
cana-4971	22	23	contributing	contribute	VERB
cana-4971	22	24	to	to	ADP
cana-4971	22	25	more	more	ADV
cana-4971	22	26	effective	effective	ADJ
cana-4971	22	27	problem	problem	NOUN
cana-4971	22	28	solving	solve	VERB
cana-4971	22	29	strategies	strategy	NOUN
cana-4971	22	30	in	in	ADP
cana-4971	22	31	this	this	DET
cana-4971	22	32	field	field	NOUN
cana-4971	22	33	(	(	PUNCT
cana-4971	22	34	[	[	X
cana-4971	22	35	5	5	NUM
cana-4971	22	36	]	]	PUNCT
cana-4971	22	37	;	;	PUNCT
cana-4971	23	1	[	[	X
cana-4971	23	2	6	6	NUM
cana-4971	23	3	]	]	NUM
cana-4971	23	4	)	)	PUNCT
cana-4971	23	5	.	.	PUNCT
cana-4971	24	1	https://internationalpubls.com/	https://internationalpubls.com/	ADJ
cana-4971	24	2	communications	communication	NOUN
cana-4971	24	3	on	on	ADP
cana-4971	24	4	applied	apply	VERB
cana-4971	24	5	nonlinear	nonlinear	ADJ
cana-4971	24	6	analysis	analysis	NOUN
cana-4971	24	7	issn	issn	NOUN
cana-4971	24	8	:	:	PUNCT
cana-4971	24	9	1074	1074	NUM
cana-4971	24	10	-	-	PUNCT
cana-4971	24	11	133x	133x	NUM
cana-4971	24	12	vol	vol	NOUN
cana-4971	24	13	31	31	NUM
cana-4971	24	14	no	no	NOUN
cana-4971	24	15	.	.	PUNCT
cana-4971	25	1	4s	4s	NUM
cana-4971	25	2	(	(	PUNCT
cana-4971	25	3	2024	2024	NUM
cana-4971	25	4	)	)	PUNCT
cana-4971	25	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4971	25	6	661	661	NUM
cana-4971	25	7	nlvide	nlvide	ADV
cana-4971	25	8	arise	arise	VERB
cana-4971	25	9	in	in	ADP
cana-4971	25	10	modeling	model	VERB
cana-4971	25	11	dynamic	dynamic	ADJ
cana-4971	25	12	systems	system	NOUN
cana-4971	25	13	in	in	ADP
cana-4971	25	14	biology	biology	NOUN
cana-4971	25	15	,	,	PUNCT
cana-4971	25	16	physics	physics	NOUN
cana-4971	25	17	,	,	PUNCT
cana-4971	25	18	and	and	CCONJ
cana-4971	25	19	engineering	engineering	NOUN
cana-4971	25	20	,	,	PUNCT
cana-4971	25	21	such	such	ADJ
cana-4971	25	22	as	as	ADP
cana-4971	25	23	population	population	NOUN
cana-4971	25	24	dynamics	dynamic	NOUN
cana-4971	25	25	and	and	CCONJ
cana-4971	25	26	heat	heat	NOUN
cana-4971	25	27	transfer	transfer	NOUN
cana-4971	25	28	.	.	PUNCT
cana-4971	26	1	the	the	DET
cana-4971	26	2	volterra	volterra	PROPN
cana-4971	26	3	population	population	NOUN
cana-4971	26	4	growth	growth	NOUN
cana-4971	26	5	model	model	NOUN
cana-4971	26	6	as	as	SCONJ
cana-4971	26	7	follows	follow	VERB
cana-4971	26	8	:	:	PUNCT
cana-4971	26	9	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	26	10	𝑑𝑡	𝑑𝑡	ADP
cana-4971	26	11	=	=	SYM
cana-4971	26	12	10𝑧(𝑡	10𝑧(𝑡	PROPN
cana-4971	26	13	)	)	PUNCT
cana-4971	27	1	−	−	PROPN
cana-4971	27	2	10𝑧2(𝑡	10𝑧2(𝑡	NUM
cana-4971	27	3	)	)	PUNCT
cana-4971	27	4	−	−	PROPN
cana-4971	27	5	10𝑧(𝑡	10𝑧(𝑡	NUM
cana-4971	27	6	)	)	PUNCT
cana-4971	27	7	∫	∫	PROPN
cana-4971	27	8	𝑡	𝑡	PROPN
cana-4971	27	9	0	0	NUM
cana-4971	27	10	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	27	11	)	)	PUNCT
cana-4971	27	12	𝑑𝑥	𝑑𝑥	VERB
cana-4971	27	13	,	,	PUNCT
cana-4971	27	14	𝑧(0	𝑧(0	PROPN
cana-4971	27	15	)	)	PUNCT
cana-4971	27	16	=	=	SYM
cana-4971	28	1	0.1	0.1	NUM
cana-4971	28	2	this	this	DET
cana-4971	28	3	equation	equation	NOUN
cana-4971	28	4	features	feature	VERB
cana-4971	28	5	a	a	DET
cana-4971	28	6	quadratic	quadratic	ADJ
cana-4971	28	7	nonlinearity	nonlinearity	NOUN
cana-4971	28	8	and	and	CCONJ
cana-4971	28	9	an	an	DET
cana-4971	28	10	integral	integral	ADJ
cana-4971	28	11	term	term	NOUN
cana-4971	28	12	,	,	PUNCT
cana-4971	28	13	posing	pose	VERB
cana-4971	28	14	challenges	challenge	NOUN
cana-4971	28	15	for	for	ADP
cana-4971	28	16	analytical	analytical	ADJ
cana-4971	28	17	solutions	solution	NOUN
cana-4971	28	18	.	.	PUNCT
cana-4971	29	1	traditional	traditional	ADJ
cana-4971	29	2	methods	method	NOUN
cana-4971	29	3	include	include	VERB
cana-4971	29	4	series	series	NOUN
cana-4971	29	5	expansions	expansion	NOUN
cana-4971	29	6	,	,	PUNCT
cana-4971	29	7	transform	transform	VERB
cana-4971	29	8	techniques	technique	NOUN
cana-4971	29	9	,	,	PUNCT
cana-4971	29	10	and	and	CCONJ
cana-4971	29	11	numerical	numerical	ADJ
cana-4971	29	12	solvers	solver	NOUN
cana-4971	29	13	.	.	PUNCT
cana-4971	30	1	in	in	ADP
cana-4971	30	2	this	this	DET
cana-4971	30	3	paper	paper	NOUN
cana-4971	30	4	,	,	PUNCT
cana-4971	30	5	we	we	PRON
cana-4971	30	6	:	:	PUNCT
cana-4971	30	7	1	1	X
cana-4971	30	8	.	.	X
cana-4971	30	9	develop	develop	VERB
cana-4971	30	10	a	a	DET
cana-4971	30	11	power	power	NOUN
cana-4971	30	12	series	series	NOUN
cana-4971	30	13	solution	solution	NOUN
cana-4971	30	14	by	by	ADP
cana-4971	30	15	assuming	assume	VERB
cana-4971	30	16	𝑧(𝑡	𝑧(𝑡	NOUN
cana-4971	30	17	)	)	PUNCT
cana-4971	30	18	=	=	NOUN
cana-4971	30	19	∑∞	∑∞	X
cana-4971	30	20	𝑛=0	𝑛=0	PROPN
cana-4971	30	21	𝑎𝑛𝑡𝑛.	𝑎𝑛𝑡𝑛.	NOUN
cana-4971	30	22	2	2	X
cana-4971	30	23	.	.	PUNCT
cana-4971	31	1	propose	propose	VERB
cana-4971	31	2	a	a	DET
cana-4971	31	3	novel	novel	ADJ
cana-4971	31	4	hybrid	hybrid	NOUN
cana-4971	31	5	method	method	NOUN
cana-4971	31	6	combining	combine	VERB
cana-4971	31	7	laplace	laplace	NOUN
cana-4971	31	8	transforms	transform	VERB
cana-4971	31	9	with	with	ADP
cana-4971	31	10	series	series	NOUN
cana-4971	31	11	approximations	approximation	NOUN
cana-4971	31	12	to	to	PART
cana-4971	31	13	handle	handle	VERB
cana-4971	31	14	nonlinear	nonlinear	ADJ
cana-4971	31	15	terms	term	NOUN
cana-4971	31	16	.	.	PUNCT
cana-4971	32	1	3	3	X
cana-4971	32	2	.	.	X
cana-4971	32	3	implement	implement	VERB
cana-4971	32	4	a	a	DET
cana-4971	32	5	numerical	numerical	ADJ
cana-4971	32	6	solution	solution	NOUN
cana-4971	32	7	using	use	VERB
cana-4971	32	8	matlab	matlab	PROPN
cana-4971	32	9	’s	’s	PART
cana-4971	32	10	ode45	ode45	NOUN
cana-4971	32	11	solver	solver	ADV
cana-4971	32	12	.	.	PUNCT
cana-4971	33	1	4	4	X
cana-4971	33	2	.	.	X
cana-4971	33	3	compare	compare	VERB
cana-4971	33	4	the	the	DET
cana-4971	33	5	solutions	solution	NOUN
cana-4971	33	6	through	through	ADP
cana-4971	33	7	analytical	analytical	ADJ
cana-4971	33	8	derivations	derivation	NOUN
cana-4971	33	9	,	,	PUNCT
cana-4971	33	10	computational	computational	ADJ
cana-4971	33	11	implementation	implementation	NOUN
cana-4971	33	12	,	,	PUNCT
cana-4971	33	13	and	and	CCONJ
cana-4971	33	14	graphical	graphical	ADJ
cana-4971	33	15	analysis	analysis	NOUN
cana-4971	33	16	.	.	PUNCT
cana-4971	34	1	our	our	PRON
cana-4971	34	2	objectives	objective	NOUN
cana-4971	34	3	are	be	AUX
cana-4971	34	4	to	to	PART
cana-4971	34	5	derive	derive	VERB
cana-4971	34	6	accurate	accurate	ADJ
cana-4971	34	7	approximations	approximation	NOUN
cana-4971	34	8	,	,	PUNCT
cana-4971	34	9	assess	assess	VERB
cana-4971	34	10	the	the	DET
cana-4971	34	11	methods	method	NOUN
cana-4971	34	12	’	'	PUNCT
cana-4971	34	13	convergence	convergence	NOUN
cana-4971	34	14	and	and	CCONJ
cana-4971	34	15	accuracy	accuracy	NOUN
cana-4971	34	16	,	,	PUNCT
cana-4971	34	17	and	and	CCONJ
cana-4971	34	18	provide	provide	VERB
cana-4971	34	19	practical	practical	ADJ
cana-4971	34	20	insights	insight	NOUN
cana-4971	34	21	via	via	ADP
cana-4971	34	22	matlab	matlab	PROPN
cana-4971	34	23	implementation	implementation	NOUN
cana-4971	34	24	.	.	PUNCT
cana-4971	35	1	2	2	X
cana-4971	35	2	.	.	X
cana-4971	35	3	methodology	methodology	NOUN
cana-4971	35	4	2.1	2.1	NUM
cana-4971	35	5	series	series	NOUN
cana-4971	35	6	solution	solution	NOUN
cana-4971	35	7	method	method	NOUN
cana-4971	35	8	let	let	VERB
cana-4971	35	9	’s	’s	PRON
cana-4971	35	10	solve	solve	VERB
cana-4971	35	11	the	the	DET
cana-4971	35	12	nlvide	nlvide	NOUN
cana-4971	35	13	using	use	VERB
cana-4971	35	14	the	the	DET
cana-4971	35	15	series	series	NOUN
cana-4971	35	16	solution	solution	NOUN
cana-4971	35	17	method	method	NOUN
cana-4971	35	18	.	.	PUNCT
cana-4971	36	1	the	the	DET
cana-4971	36	2	equation	equation	NOUN
cana-4971	36	3	is	be	AUX
cana-4971	36	4	as	as	SCONJ
cana-4971	36	5	follows	follow	VERB
cana-4971	36	6	[	[	X
cana-4971	36	7	7	7	NUM
cana-4971	36	8	]	]	X
cana-4971	36	9	:	:	PUNCT
cana-4971	36	10	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	36	11	𝑑𝑡	𝑑𝑡	ADP
cana-4971	36	12	=	=	SYM
cana-4971	36	13	10𝑧(𝑡	10𝑧(𝑡	PROPN
cana-4971	36	14	)	)	PUNCT
cana-4971	37	1	−	−	PROPN
cana-4971	37	2	10𝑧2(𝑡	10𝑧2(𝑡	NUM
cana-4971	37	3	)	)	PUNCT
cana-4971	37	4	−	−	PROPN
cana-4971	37	5	10𝑧(𝑡	10𝑧(𝑡	NUM
cana-4971	37	6	)	)	PUNCT
cana-4971	37	7	∫	∫	PROPN
cana-4971	37	8	𝑡	𝑡	PROPN
cana-4971	37	9	0	0	NUM
cana-4971	37	10	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	37	11	)	)	PUNCT
cana-4971	37	12	𝑑𝑥	𝑑𝑥	VERB
cana-4971	37	13	,	,	PUNCT
cana-4971	37	14	𝑧(0	𝑧(0	PROPN
cana-4971	37	15	)	)	PUNCT
cana-4971	37	16	=	=	SYM
cana-4971	38	1	0.1	0.1	NUM
cana-4971	38	2	we	we	PRON
cana-4971	38	3	will	will	AUX
cana-4971	38	4	assume	assume	VERB
cana-4971	38	5	a	a	DET
cana-4971	38	6	power	power	NOUN
cana-4971	38	7	series	series	NOUN
cana-4971	38	8	solution	solution	NOUN
cana-4971	38	9	of	of	ADP
cana-4971	38	10	the	the	DET
cana-4971	38	11	form	form	NOUN
cana-4971	38	12	:	:	PUNCT
cana-4971	38	13	𝑧(𝑡	𝑧(𝑡	NOUN
cana-4971	38	14	)	)	PUNCT
cana-4971	38	15	=	=	NOUN
cana-4971	39	1	∑∞	∑∞	NOUN
cana-4971	39	2	𝑛=0	𝑛=0	PROPN
cana-4971	39	3	𝑎𝑛𝑡𝑛	𝑎𝑛𝑡𝑛	VERB
cana-4971	39	4	where	where	SCONJ
cana-4971	39	5	𝑎𝑛	𝑎𝑛	PRON
cana-4971	39	6	are	be	AUX
cana-4971	39	7	the	the	DET
cana-4971	39	8	coefficients	coefficient	NOUN
cana-4971	39	9	to	to	PART
cana-4971	39	10	be	be	AUX
cana-4971	39	11	determined	determine	VERB
cana-4971	39	12	,	,	PUNCT
cana-4971	39	13	and	and	CCONJ
cana-4971	39	14	the	the	DET
cana-4971	39	15	initial	initial	ADJ
cana-4971	39	16	condition	condition	NOUN
cana-4971	39	17	gives	give	VERB
cana-4971	39	18	𝑧(0	𝑧(0	PROPN
cana-4971	39	19	)	)	PUNCT
cana-4971	39	20	=	=	SYM
cana-4971	39	21	𝑎0	𝑎0	ADJ
cana-4971	39	22	=	=	SYM
cana-4971	39	23	0.1	0.1	NUM
cana-4971	39	24	.	.	PUNCT
cana-4971	40	1	our	our	PRON
cana-4971	40	2	goal	goal	NOUN
cana-4971	40	3	is	be	AUX
cana-4971	40	4	to	to	PART
cana-4971	40	5	substitute	substitute	VERB
cana-4971	40	6	this	this	DET
cana-4971	40	7	series	series	NOUN
cana-4971	40	8	into	into	ADP
cana-4971	40	9	the	the	DET
cana-4971	40	10	equation	equation	NOUN
cana-4971	40	11	,	,	PUNCT
cana-4971	40	12	compute	compute	VERB
cana-4971	40	13	the	the	DET
cana-4971	40	14	necessary	necessary	ADJ
cana-4971	40	15	derivatives	derivative	NOUN
cana-4971	40	16	and	and	CCONJ
cana-4971	40	17	integrals	integral	NOUN
cana-4971	40	18	,	,	PUNCT
cana-4971	40	19	and	and	CCONJ
cana-4971	40	20	equate	equate	ADJ
cana-4971	40	21	coefficients	coefficient	NOUN
cana-4971	40	22	to	to	PART
cana-4971	40	23	find	find	VERB
cana-4971	40	24	the	the	DET
cana-4971	40	25	𝑎𝑛	𝑎𝑛	PROPN
cana-4971	40	26	terms	term	NOUN
cana-4971	40	27	.	.	PUNCT
cana-4971	41	1	step	step	NOUN
cana-4971	41	2	1	1	NUM
cana-4971	41	3	:	:	PUNCT
cana-4971	41	4	compute	compute	VERB
cana-4971	41	5	the	the	DET
cana-4971	41	6	derivative	derivative	NOUN
cana-4971	41	7	after	after	ADP
cana-4971	41	8	differentiate	differentiate	NOUN
cana-4971	41	9	we	we	PRON
cana-4971	41	10	get	get	VERB
cana-4971	41	11	the	the	DET
cana-4971	41	12	equation	equation	NOUN
cana-4971	41	13	:	:	PUNCT
cana-4971	41	14	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	41	15	𝑑𝑡	𝑑𝑡	ADP
cana-4971	41	16	=	=	SYM
cana-4971	41	17	𝑑	𝑑	NOUN
cana-4971	41	18	𝑑𝑡	𝑑𝑡	ADP
cana-4971	41	19	∑∞	∑∞	NOUN
cana-4971	41	20	𝑛=0	𝑛=0	PROPN
cana-4971	41	21	𝑎𝑛𝑡𝑛	𝑎𝑛𝑡𝑛	VERB
cana-4971	41	22	=	=	SYM
cana-4971	41	23	∑∞	∑∞	NOUN
cana-4971	41	24	𝑛=1	𝑛=1	NOUN
cana-4971	41	25	𝑛𝑎𝑛𝑡𝑛−1	𝑛𝑎𝑛𝑡𝑛−1	NOUN
cana-4971	41	26	(	(	PUNCT
cana-4971	41	27	note	note	VERB
cana-4971	41	28	that	that	SCONJ
cana-4971	41	29	the	the	DET
cana-4971	41	30	𝑛	𝑛	PROPN
cana-4971	41	31	=	=	SYM
cana-4971	41	32	0	0	NUM
cana-4971	41	33	term	term	NOUN
cana-4971	41	34	vanishes	vanish	VERB
cana-4971	41	35	upon	upon	SCONJ
cana-4971	41	36	differentiation	differentiation	NOUN
cana-4971	41	37	.	.	PUNCT
cana-4971	41	38	)	)	PUNCT
cana-4971	42	1	step	step	NOUN
cana-4971	42	2	2	2	NUM
cana-4971	42	3	:	:	PUNCT
cana-4971	42	4	compute	compute	VERB
cana-4971	42	5	the	the	DET
cana-4971	42	6	integral	integral	ADJ
cana-4971	42	7	term	term	NOUN
cana-4971	42	8	the	the	DET
cana-4971	42	9	integral	integral	ADJ
cana-4971	42	10	in	in	ADP
cana-4971	42	11	the	the	DET
cana-4971	42	12	equation	equation	NOUN
cana-4971	42	13	is	be	AUX
cana-4971	42	14	:	:	PUNCT
cana-4971	42	15	∫	∫	PROPN
cana-4971	42	16	𝑡	𝑡	PROPN
cana-4971	42	17	0	0	NUM
cana-4971	42	18	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	42	19	)	)	PUNCT
cana-4971	42	20	𝑑𝑥	𝑑𝑥	VERB
cana-4971	42	21	=	=	SYM
cana-4971	42	22	∫	∫	PROPN
cana-4971	42	23	𝑡	𝑡	PROPN
cana-4971	42	24	0	0	NUM
cana-4971	42	25	∑∞	∑∞	NOUN
cana-4971	42	26	𝑛=0	𝑛=0	PROPN
cana-4971	42	27	𝑎𝑛𝑥𝑛	𝑎𝑛𝑥𝑛	PROPN
cana-4971	42	28	𝑑𝑥	𝑑𝑥	VERB
cana-4971	42	29	assuming	assume	VERB
cana-4971	42	30	the	the	DET
cana-4971	42	31	series	series	NOUN
cana-4971	42	32	converges	converge	VERB
cana-4971	42	33	uniformly	uniformly	ADV
cana-4971	42	34	,	,	PUNCT
cana-4971	42	35	we	we	PRON
cana-4971	42	36	can	can	AUX
cana-4971	42	37	interchange	interchange	VERB
cana-4971	42	38	the	the	DET
cana-4971	42	39	sum	sum	NOUN
cana-4971	42	40	and	and	CCONJ
cana-4971	42	41	integral	integral	ADJ
cana-4971	42	42	:	:	PUNCT
cana-4971	42	43	∫	∫	PROPN
cana-4971	42	44	𝑡	𝑡	PROPN
cana-4971	42	45	0	0	NUM
cana-4971	42	46	∑∞	∑∞	NOUN
cana-4971	42	47	𝑛=0	𝑛=0	PROPN
cana-4971	42	48	𝑎𝑛𝑥𝑛	𝑎𝑛𝑥𝑛	PROPN
cana-4971	42	49	𝑑𝑥	𝑑𝑥	NOUN
cana-4971	42	50	=	=	SYM
cana-4971	42	51	∑∞	∑∞	NOUN
cana-4971	42	52	𝑛=0	𝑛=0	PROPN
cana-4971	42	53	𝑎𝑛	𝑎𝑛	PROPN
cana-4971	42	54	∫	∫	PROPN
cana-4971	42	55	𝑡	𝑡	PROPN
cana-4971	42	56	0	0	NUM
cana-4971	42	57	𝑥𝑛	𝑥𝑛	NOUN
cana-4971	42	58	𝑑𝑥	𝑑𝑥	AUX
cana-4971	42	59	evaluating	evaluate	VERB
cana-4971	42	60	integral	integral	ADJ
cana-4971	42	61	:	:	PUNCT
cana-4971	42	62	https://internationalpubls.com/	https://internationalpubls.com/	ADJ
cana-4971	42	63	communications	communication	NOUN
cana-4971	42	64	on	on	ADP
cana-4971	42	65	applied	apply	VERB
cana-4971	42	66	nonlinear	nonlinear	ADJ
cana-4971	42	67	analysis	analysis	NOUN
cana-4971	42	68	issn	issn	NOUN
cana-4971	42	69	:	:	PUNCT
cana-4971	42	70	1074	1074	NUM
cana-4971	42	71	-	-	PUNCT
cana-4971	42	72	133x	133x	NUM
cana-4971	42	73	vol	vol	NOUN
cana-4971	42	74	31	31	NUM
cana-4971	42	75	no	no	NOUN
cana-4971	42	76	.	.	PUNCT
cana-4971	43	1	4s	4s	NUM
cana-4971	43	2	(	(	PUNCT
cana-4971	43	3	2024	2024	NUM
cana-4971	43	4	)	)	PUNCT
cana-4971	43	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4971	43	6	662	662	NUM
cana-4971	43	7	∫	∫	NOUN
cana-4971	43	8	𝑡	𝑡	NOUN
cana-4971	43	9	0	0	NUM
cana-4971	43	10	𝑥𝑛	𝑥𝑛	PROPN
cana-4971	43	11	𝑑𝑥	𝑑𝑥	VERB
cana-4971	43	12	=	=	PUNCT
cana-4971	43	13	[	[	PUNCT
cana-4971	43	14	𝑥𝑛+1	𝑥𝑛+1	X
cana-4971	43	15	𝑛+1	𝑛+1	X
cana-4971	43	16	]	]	PUNCT
cana-4971	43	17	0	0	NUM
cana-4971	44	1	𝑡	𝑡	X
cana-4971	44	2	=	=	VERB
cana-4971	44	3	𝑡𝑛+1	𝑡𝑛+1	X
cana-4971	44	4	𝑛+1	𝑛+1	X
cana-4971	44	5	−	−	PROPN
cana-4971	44	6	0	0	NUM
cana-4971	44	7	=	=	SYM
cana-4971	44	8	𝑡𝑛+1	𝑡𝑛+1	X
cana-4971	44	9	𝑛+1	𝑛+1	PROPN
cana-4971	44	10	so	so	ADV
cana-4971	44	11	:	:	PUNCT
cana-4971	44	12	∫	∫	PROPN
cana-4971	44	13	𝑡	𝑡	PROPN
cana-4971	44	14	0	0	NUM
cana-4971	44	15	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	44	16	)	)	PUNCT
cana-4971	44	17	𝑑𝑥	𝑑𝑥	VERB
cana-4971	44	18	=	=	VERB
cana-4971	44	19	∑∞	∑∞	NOUN
cana-4971	44	20	𝑛=0	𝑛=0	NOUN
cana-4971	44	21	𝑎𝑛	𝑎𝑛	VERB
cana-4971	44	22	𝑡𝑛+1	𝑡𝑛+1	X
cana-4971	44	23	𝑛+1	𝑛+1	AUX
cana-4971	44	24	step	step	VERB
cana-4971	44	25	3	3	NUM
cana-4971	44	26	:	:	PUNCT
cana-4971	44	27	substitute	substitute	NOUN
cana-4971	44	28	into	into	ADP
cana-4971	44	29	the	the	DET
cana-4971	44	30	equation	equation	NOUN
cana-4971	44	31	now	now	ADV
cana-4971	44	32	compute	compute	VERB
cana-4971	44	33	each	each	DET
cana-4971	44	34	term	term	NOUN
cana-4971	44	35	on	on	ADP
cana-4971	44	36	the	the	DET
cana-4971	44	37	right	right	ADJ
cana-4971	44	38	-	-	PUNCT
cana-4971	44	39	hand	hand	NOUN
cana-4971	44	40	side	side	NOUN
cana-4971	44	41	:	:	PUNCT
cana-4971	44	42	1	1	X
cana-4971	44	43	.	.	X
cana-4971	44	44	first	first	ADJ
cana-4971	44	45	term	term	NOUN
cana-4971	44	46	:	:	PUNCT
cana-4971	44	47	𝟏𝟎𝒛(𝒕	𝟏𝟎𝒛(𝒕	X
cana-4971	44	48	)	)	PUNCT
cana-4971	44	49	10𝑧(𝑡	10𝑧(𝑡	NUM
cana-4971	44	50	)	)	PUNCT
cana-4971	44	51	=	=	SYM
cana-4971	45	1	10	10	NUM
cana-4971	45	2	∑∞	∑∞	NOUN
cana-4971	45	3	𝑛=0	𝑛=0	VERB
cana-4971	45	4	𝑎𝑛𝑡𝑛	𝑎𝑛𝑡𝑛	VERB
cana-4971	45	5	2	2	NUM
cana-4971	45	6	.	.	NOUN
cana-4971	45	7	second	second	ADJ
cana-4971	45	8	term	term	NOUN
cana-4971	45	9	:	:	PUNCT
cana-4971	45	10	−𝟏𝟎𝒛𝟐(𝒕	−𝟏𝟎𝒛𝟐(𝒕	ADJ
cana-4971	45	11	)	)	PUNCT
cana-4971	45	12	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	45	13	)	)	PUNCT
cana-4971	45	14	=	=	NOUN
cana-4971	46	1	∑∞	∑∞	NOUN
cana-4971	46	2	𝑛=0	𝑛=0	PROPN
cana-4971	46	3	𝑎𝑛𝑡𝑛	𝑎𝑛𝑡𝑛	VERB
cana-4971	46	4	𝑧2(𝑡	𝑧2(𝑡	NOUN
cana-4971	46	5	)	)	PUNCT
cana-4971	46	6	=	=	SYM
cana-4971	47	1	(	(	PUNCT
cana-4971	47	2	∑∞	∑∞	NOUN
cana-4971	47	3	𝑛=0	𝑛=0	PROPN
cana-4971	47	4	𝑎𝑛𝑡𝑛)2	𝑎𝑛𝑡𝑛)2	PROPN
cana-4971	47	5	=	=	PUNCT
cana-4971	47	6	∑∞	∑∞	X
cana-4971	47	7	𝑛=0	𝑛=0	X
cana-4971	48	1	∑𝑛	∑𝑛	ADJ
cana-4971	48	2	𝑘=0	𝑘=0	VERB
cana-4971	48	3	𝑎𝑘𝑎𝑛−𝑘𝑡𝑛	𝑎𝑘𝑎𝑛−𝑘𝑡𝑛	PROPN
cana-4971	48	4	(	(	PUNCT
cana-4971	48	5	using	use	VERB
cana-4971	48	6	the	the	DET
cana-4971	48	7	cauchy	cauchy	ADJ
cana-4971	48	8	product	product	NOUN
cana-4971	48	9	for	for	ADP
cana-4971	48	10	the	the	DET
cana-4971	48	11	square	square	NOUN
cana-4971	48	12	of	of	ADP
cana-4971	48	13	a	a	DET
cana-4971	48	14	series	series	NOUN
cana-4971	48	15	.	.	PUNCT
cana-4971	48	16	)	)	PUNCT
cana-4971	49	1	−10𝑧2(𝑡	−10𝑧2(𝑡	NOUN
cana-4971	49	2	)	)	PUNCT
cana-4971	49	3	=	=	SYM
cana-4971	50	1	−10	−10	X
cana-4971	50	2	∑∞	∑∞	NOUN
cana-4971	50	3	𝑛=0	𝑛=0	X
cana-4971	51	1	∑𝑛	∑𝑛	ADJ
cana-4971	51	2	𝑘=0	𝑘=0	VERB
cana-4971	51	3	𝑎𝑘𝑎𝑛−𝑘𝑡𝑛	𝑎𝑘𝑎𝑛−𝑘𝑡𝑛	PROPN
cana-4971	51	4	3	3	NUM
cana-4971	51	5	.	.	PUNCT
cana-4971	51	6	third	third	ADJ
cana-4971	51	7	term	term	NOUN
cana-4971	51	8	:	:	PUNCT
cana-4971	51	9	−𝟏𝟎𝒛(𝒕	−𝟏𝟎𝒛(𝒕	NOUN
cana-4971	51	10	)	)	PUNCT
cana-4971	51	11	∫	∫	PROPN
cana-4971	52	1	𝒕	𝒕	PROPN
cana-4971	52	2	𝟎	𝟎	NUM
cana-4971	52	3	𝒛(𝒙)𝒅𝒙	𝒛(𝒙)𝒅𝒙	NOUN
cana-4971	52	4	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	52	5	)	)	PUNCT
cana-4971	52	6	∫	∫	PROPN
cana-4971	53	1	𝑡	𝑡	PROPN
cana-4971	53	2	0	0	NUM
cana-4971	53	3	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	53	4	)	)	PUNCT
cana-4971	54	1	𝑑𝑥	𝑑𝑥	VERB
cana-4971	54	2	=	=	SYM
cana-4971	54	3	(	(	PUNCT
cana-4971	54	4	∑∞	∑∞	NOUN
cana-4971	54	5	𝑛=0	𝑛=0	PRON
cana-4971	54	6	𝑎𝑛𝑡𝑛	𝑎𝑛𝑡𝑛	VERB
cana-4971	54	7	)	)	PUNCT
cana-4971	54	8	(	(	PUNCT
cana-4971	54	9	∑∞	∑∞	NOUN
cana-4971	54	10	𝑚=0	𝑚=0	PUNCT
cana-4971	54	11	𝑎𝑚	𝑎𝑚	ADV
cana-4971	54	12	𝑡𝑚+1	𝑡𝑚+1	NUM
cana-4971	54	13	𝑚+1	𝑚+1	NUM
cana-4971	54	14	)	)	PUNCT
cana-4971	54	15	shift	shift	VERB
cana-4971	54	16	the	the	DET
cana-4971	54	17	index	index	NOUN
cana-4971	54	18	in	in	ADP
cana-4971	54	19	the	the	DET
cana-4971	54	20	integral	integral	ADJ
cana-4971	54	21	term	term	NOUN
cana-4971	54	22	:	:	PUNCT
cana-4971	54	23	let	let	VERB
cana-4971	54	24	𝑝	𝑝	VERB
cana-4971	54	25	=	=	SYM
cana-4971	54	26	𝑚	𝑚	NOUN
cana-4971	54	27	,	,	PUNCT
cana-4971	54	28	so	so	ADV
cana-4971	54	29	:	:	PUNCT
cana-4971	54	30	∫	∫	PROPN
cana-4971	54	31	𝑡	𝑡	PROPN
cana-4971	54	32	0	0	NUM
cana-4971	54	33	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	54	34	)	)	PUNCT
cana-4971	54	35	𝑑𝑥	𝑑𝑥	VERB
cana-4971	54	36	=	=	SYM
cana-4971	54	37	∑∞	∑∞	NOUN
cana-4971	54	38	𝑝=0	𝑝=0	PRON
cana-4971	54	39	𝑎𝑝	𝑎𝑝	PROPN
cana-4971	54	40	𝑡𝑝+1	𝑡𝑝+1	VERB
cana-4971	54	41	𝑝+1	𝑝+1	NOUN
cana-4971	54	42	the	the	DET
cana-4971	54	43	product	product	NOUN
cana-4971	54	44	becomes	become	VERB
cana-4971	54	45	:	:	PUNCT
cana-4971	54	46	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	54	47	)	)	PUNCT
cana-4971	54	48	∫	∫	PROPN
cana-4971	55	1	𝑡	𝑡	PROPN
cana-4971	55	2	0	0	NUM
cana-4971	55	3	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	55	4	)	)	PUNCT
cana-4971	55	5	𝑑𝑥	𝑑𝑥	VERB
cana-4971	55	6	=	=	VERB
cana-4971	55	7	∑∞	∑∞	NOUN
cana-4971	55	8	𝑛=0	𝑛=0	NOUN
cana-4971	55	9	𝑎𝑛𝑡𝑛	𝑎𝑛𝑡𝑛	VERB
cana-4971	55	10	⋅	⋅	PROPN
cana-4971	55	11	∑∞	∑∞	NOUN
cana-4971	55	12	𝑝=0	𝑝=0	PRON
cana-4971	55	13	𝑎𝑝	𝑎𝑝	PROPN
cana-4971	55	14	𝑡𝑝+1	𝑡𝑝+1	VERB
cana-4971	55	15	𝑝+1	𝑝+1	NOUN
cana-4971	55	16	=	=	PUNCT
cana-4971	55	17	∑∞	∑∞	NOUN
cana-4971	55	18	𝑛=0	𝑛=0	X
cana-4971	55	19	∑𝑛	∑𝑛	ADJ
cana-4971	55	20	𝑘=0	𝑘=0	PROPN
cana-4971	55	21	𝑎𝑘𝑎𝑛−𝑘	𝑎𝑘𝑎𝑛−𝑘	NOUN
cana-4971	55	22	𝑡𝑛+1	𝑡𝑛+1	X
cana-4971	55	23	(	(	PUNCT
cana-4971	55	24	𝑛−𝑘+1	𝑛−𝑘+1	PROPN
cana-4971	55	25	)	)	PUNCT
cana-4971	55	26	(	(	PUNCT
cana-4971	55	27	here	here	ADV
cana-4971	55	28	,	,	PUNCT
cana-4971	55	29	the	the	DET
cana-4971	55	30	exponent	exponent	NOUN
cana-4971	55	31	of	of	ADP
cana-4971	55	32	𝑡	𝑡	PROPN
cana-4971	55	33	is	be	AUX
cana-4971	55	34	𝑘	𝑘	PRON
cana-4971	55	35	+	+	CCONJ
cana-4971	55	36	(	(	PUNCT
cana-4971	55	37	𝑛	𝑛	PRON
cana-4971	55	38	−	−	NOUN
cana-4971	55	39	𝑘	𝑘	PROPN
cana-4971	55	40	+	+	NOUN
cana-4971	55	41	1	1	NUM
cana-4971	55	42	)	)	PUNCT
cana-4971	55	43	=	=	SYM
cana-4971	55	44	𝑛	𝑛	PROPN
cana-4971	55	45	+	+	NOUN
cana-4971	55	46	1	1	NUM
cana-4971	55	47	)	)	PUNCT
cana-4971	55	48	.	.	PUNCT
cana-4971	56	1	thus	thus	ADV
cana-4971	56	2	:	:	PUNCT
cana-4971	56	3	−10𝑧(𝑡	−10𝑧(𝑡	NUM
cana-4971	56	4	)	)	PUNCT
cana-4971	57	1	∫	∫	PROPN
cana-4971	57	2	𝑡	𝑡	PROPN
cana-4971	57	3	0	0	NUM
cana-4971	57	4	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	57	5	)	)	PUNCT
cana-4971	58	1	𝑑𝑥	𝑑𝑥	VERB
cana-4971	58	2	=	=	SYM
cana-4971	58	3	−10	−10	NUM
cana-4971	58	4	∑∞	∑∞	NOUN
cana-4971	58	5	𝑛=0	𝑛=0	X
cana-4971	59	1	∑𝑛	∑𝑛	ADJ
cana-4971	59	2	𝑘=0	𝑘=0	PROPN
cana-4971	59	3	𝑎𝑘𝑎𝑛−𝑘	𝑎𝑘𝑎𝑛−𝑘	NOUN
cana-4971	59	4	𝑛−𝑘+1	𝑛−𝑘+1	NOUN
cana-4971	59	5	𝑡𝑛+1	𝑡𝑛+1	ADJ
cana-4971	59	6	adjust	adjust	VERB
cana-4971	59	7	the	the	DET
cana-4971	59	8	index	index	NOUN
cana-4971	59	9	to	to	PART
cana-4971	59	10	match	match	VERB
cana-4971	59	11	powers	power	NOUN
cana-4971	59	12	later	later	ADV
cana-4971	59	13	:	:	PUNCT
cana-4971	59	14	let	let	VERB
cana-4971	59	15	𝑚	𝑚	VERB
cana-4971	59	16	=	=	SYM
cana-4971	59	17	𝑛	𝑛	PROPN
cana-4971	59	18	+	+	NOUN
cana-4971	59	19	1	1	NUM
cana-4971	59	20	,	,	PUNCT
cana-4971	59	21	but	but	CCONJ
cana-4971	59	22	we	we	PRON
cana-4971	59	23	’ll	’ll	AUX
cana-4971	59	24	handle	handle	VERB
cana-4971	59	25	coefficients	coefficient	NOUN
cana-4971	59	26	directly	directly	ADV
cana-4971	59	27	.	.	PUNCT
cana-4971	60	1	step	step	NOUN
cana-4971	60	2	4	4	NUM
cana-4971	60	3	:	:	PUNCT
cana-4971	60	4	combine	combine	VERB
cana-4971	60	5	and	and	CCONJ
cana-4971	60	6	equate	equate	VERB
cana-4971	60	7	coefficients	coefficient	NOUN
cana-4971	60	8	the	the	DET
cana-4971	60	9	full	full	ADJ
cana-4971	60	10	equation	equation	NOUN
cana-4971	60	11	becomes	become	VERB
cana-4971	60	12	:	:	PUNCT
cana-4971	60	13	∑∞	∑∞	NOUN
cana-4971	60	14	𝑛=1	𝑛=1	PART
cana-4971	60	15	𝑛𝑎𝑛𝑡𝑛−1	𝑛𝑎𝑛𝑡𝑛−1	NOUN
cana-4971	60	16	=	=	SYM
cana-4971	60	17	10	10	NUM
cana-4971	60	18	∑∞	∑∞	NOUN
cana-4971	60	19	𝑛=0	𝑛=0	PRON
cana-4971	60	20	𝑎𝑛𝑡𝑛	𝑎𝑛𝑡𝑛	VERB
cana-4971	60	21	−	−	PROPN
cana-4971	60	22	10	10	NUM
cana-4971	60	23	∑∞	∑∞	NOUN
cana-4971	60	24	𝑛=0	𝑛=0	X
cana-4971	61	1	∑𝑛	∑𝑛	ADJ
cana-4971	61	2	𝑘=0	𝑘=0	VERB
cana-4971	61	3	𝑎𝑘𝑎𝑛−𝑘𝑡𝑛	𝑎𝑘𝑎𝑛−𝑘𝑡𝑛	PROPN
cana-4971	61	4	−	−	PROPN
cana-4971	61	5	10	10	NUM
cana-4971	61	6	∑∞	∑∞	NOUN
cana-4971	61	7	𝑛=0	𝑛=0	X
cana-4971	62	1	∑𝑛	∑𝑛	ADJ
cana-4971	62	2	𝑘=0	𝑘=0	AUX
cana-4971	62	3	𝑎𝑘𝑎𝑛−𝑘	𝑎𝑘𝑎𝑛−𝑘	NOUN
cana-4971	62	4	𝑛−𝑘+1	𝑛−𝑘+1	PROPN
cana-4971	62	5	𝑡𝑛+1	𝑡𝑛+1	NOUN
cana-4971	62	6	shift	shift	NOUN
cana-4971	62	7	indices	index	NOUN
cana-4971	62	8	to	to	PART
cana-4971	62	9	align	align	VERB
cana-4971	62	10	powers	power	NOUN
cana-4971	62	11	of	of	ADP
cana-4971	62	12	𝑡	𝑡	NOUN
cana-4971	62	13	:	:	PUNCT
cana-4971	62	14	left	left	ADJ
cana-4971	62	15	side	side	NOUN
cana-4971	62	16	:	:	PUNCT
cana-4971	62	17	∑∞	∑∞	X
cana-4971	62	18	𝑛=1	𝑛=1	PART
cana-4971	62	19	𝑛𝑎𝑛𝑡𝑛−1	𝑛𝑎𝑛𝑡𝑛−1	NOUN
cana-4971	62	20	=	=	SYM
cana-4971	62	21	∑∞	∑∞	NOUN
cana-4971	62	22	𝑚=0	𝑚=0	PUNCT
cana-4971	62	23	(	(	PUNCT
cana-4971	62	24	𝑚	𝑚	X
cana-4971	62	25	+	+	NOUN
cana-4971	62	26	1)𝑎𝑚+1𝑡𝑚	1)𝑎𝑚+1𝑡𝑚	NUM
cana-4971	62	27	first	first	ADJ
cana-4971	62	28	term	term	NOUN
cana-4971	62	29	:	:	PUNCT
cana-4971	62	30	10	10	NUM
cana-4971	62	31	∑∞	∑∞	NOUN
cana-4971	62	32	𝑛=0	𝑛=0	VERB
cana-4971	62	33	𝑎𝑛𝑡𝑛	𝑎𝑛𝑡𝑛	VERB
cana-4971	62	34	second	second	ADJ
cana-4971	62	35	term	term	NOUN
cana-4971	62	36	:	:	PUNCT
cana-4971	62	37	−10	−10	X
cana-4971	62	38	∑∞	∑∞	X
cana-4971	62	39	𝑛=0	𝑛=0	X
cana-4971	63	1	∑𝑛	∑𝑛	ADJ
cana-4971	63	2	𝑘=0	𝑘=0	VERB
cana-4971	63	3	𝑎𝑘𝑎𝑛−𝑘𝑡𝑛	𝑎𝑘𝑎𝑛−𝑘𝑡𝑛	PROPN
cana-4971	63	4	third	third	ADJ
cana-4971	63	5	term	term	NOUN
cana-4971	63	6	:	:	PUNCT
cana-4971	63	7	−10	−10	X
cana-4971	63	8	∑∞	∑∞	X
cana-4971	63	9	𝑛=0	𝑛=0	X
cana-4971	64	1	∑𝑛	∑𝑛	ADJ
cana-4971	64	2	𝑘=0	𝑘=0	AUX
cana-4971	64	3	𝑎𝑘𝑎𝑛−𝑘	𝑎𝑘𝑎𝑛−𝑘	VERB
cana-4971	64	4	𝑛−𝑘+1	𝑛−𝑘+1	NOUN
cana-4971	64	5	𝑡𝑛+1	𝑡𝑛+1	NOUN
cana-4971	64	6	=	=	SYM
cana-4971	64	7	−10	−10	X
cana-4971	64	8	∑∞	∑∞	X
cana-4971	64	9	𝑚=1	𝑚=1	PUNCT
cana-4971	64	10	∑𝑚−1	∑𝑚−1	X
cana-4971	64	11	𝑘=0	𝑘=0	X
cana-4971	64	12	𝑎𝑘𝑎𝑚−1−𝑘	𝑎𝑘𝑎𝑚−1−𝑘	PROPN
cana-4971	64	13	𝑚−𝑘	𝑚−𝑘	NOUN
cana-4971	64	14	𝑡𝑚	𝑡𝑚	VERB
cana-4971	64	15	for	for	ADP
cana-4971	64	16	𝑛	𝑛	PROPN
cana-4971	64	17	=	=	SYM
cana-4971	64	18	0	0	NUM
cana-4971	64	19	on	on	ADP
cana-4971	64	20	the	the	DET
cana-4971	64	21	left	left	NOUN
cana-4971	64	22	,	,	PUNCT
cana-4971	64	23	there	there	PRON
cana-4971	64	24	’s	’	VERB
cana-4971	64	25	no	no	DET
cana-4971	64	26	term	term	NOUN
cana-4971	64	27	(	(	PUNCT
cana-4971	64	28	since	since	SCONJ
cana-4971	64	29	it	it	PRON
cana-4971	64	30	starts	start	VERB
cana-4971	64	31	at	at	ADP
cana-4971	64	32	𝑛	𝑛	PROPN
cana-4971	64	33	=	=	SYM
cana-4971	64	34	1	1	NUM
cana-4971	64	35	)	)	PUNCT
cana-4971	64	36	,	,	PUNCT
cana-4971	64	37	so	so	ADV
cana-4971	64	38	we	we	PRON
cana-4971	64	39	equate	equate	VERB
cana-4971	64	40	coefficients	coefficient	NOUN
cana-4971	64	41	for	for	ADP
cana-4971	64	42	each	each	DET
cana-4971	64	43	power	power	NOUN
cana-4971	64	44	𝑡𝑚.	𝑡𝑚.	PROPN
cana-4971	64	45	𝒕𝟎	𝒕𝟎	PROPN
cana-4971	64	46	:	:	PUNCT
cana-4971	64	47	left	leave	VERB
cana-4971	64	48	:	:	PUNCT
cana-4971	64	49	𝑎1	𝑎1	SCONJ
cana-4971	64	50	https://internationalpubls.com/	https://internationalpubls.com/	PROPN
cana-4971	64	51	communications	communication	NOUN
cana-4971	64	52	on	on	ADP
cana-4971	64	53	applied	apply	VERB
cana-4971	64	54	nonlinear	nonlinear	ADJ
cana-4971	64	55	analysis	analysis	NOUN
cana-4971	64	56	issn	issn	NOUN
cana-4971	64	57	:	:	PUNCT
cana-4971	64	58	1074	1074	NUM
cana-4971	64	59	-	-	PUNCT
cana-4971	64	60	133x	133x	NUM
cana-4971	64	61	vol	vol	NOUN
cana-4971	64	62	31	31	NUM
cana-4971	64	63	no	no	NOUN
cana-4971	64	64	.	.	PUNCT
cana-4971	65	1	4s	4s	NUM
cana-4971	65	2	(	(	PUNCT
cana-4971	65	3	2024	2024	NUM
cana-4971	65	4	)	)	PUNCT
cana-4971	66	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4971	66	2	663	663	NUM
cana-4971	66	3	right	right	ADJ
cana-4971	66	4	:	:	PUNCT
cana-4971	67	1	10𝑎0	10𝑎0	NUM
cana-4971	67	2	−	−	NOUN
cana-4971	67	3	10𝑎0	10𝑎0	NUM
cana-4971	67	4	2	2	NUM
cana-4971	67	5	−	−	PROPN
cana-4971	67	6	10	10	NUM
cana-4971	67	7	⋅	⋅	NOUN
cana-4971	67	8	0	0	NUM
cana-4971	68	1	(	(	PUNCT
cana-4971	68	2	integral	integral	ADJ
cana-4971	68	3	term	term	NOUN
cana-4971	68	4	starts	start	VERB
cana-4971	68	5	at	at	ADP
cana-4971	68	6	𝑡1	𝑡1	NOUN
cana-4971	68	7	)	)	PUNCT
cana-4971	69	1	𝑎1	𝑎1	NOUN
cana-4971	69	2	=	=	PUNCT
cana-4971	70	1	10𝑎0	10𝑎0	NUM
cana-4971	70	2	−	−	NUM
cana-4971	70	3	10𝑎0	10𝑎0	NUM
cana-4971	70	4	2	2	NUM
cana-4971	70	5	with	with	ADP
cana-4971	70	6	𝑎0	𝑎0	PROPN
cana-4971	70	7	=	=	SYM
cana-4971	70	8	0.1	0.1	NUM
cana-4971	70	9	:	:	PUNCT
cana-4971	70	10	we	we	PRON
cana-4971	70	11	get	get	VERB
cana-4971	70	12	𝑎1	𝑎1	ADJ
cana-4971	70	13	=	=	SYM
cana-4971	70	14	0.9	0.9	NUM
cana-4971	70	15	𝒕𝟏	𝒕𝟏	NOUN
cana-4971	70	16	:	:	PUNCT
cana-4971	70	17	left	leave	VERB
cana-4971	70	18	:	:	PUNCT
cana-4971	70	19	2𝑎2	2𝑎2	NUM
cana-4971	70	20	right	right	NOUN
cana-4971	70	21	:	:	PUNCT
cana-4971	70	22	10𝑎1	10𝑎1	NUM
cana-4971	70	23	−	−	NUM
cana-4971	70	24	10(𝑎0𝑎1	10(𝑎0𝑎1	PROPN
cana-4971	70	25	+	+	CCONJ
cana-4971	70	26	𝑎1𝑎0	𝑎1𝑎0	PROPN
cana-4971	70	27	)	)	PUNCT
cana-4971	70	28	−	−	PROPN
cana-4971	71	1	10(𝑎0𝑎0/1)𝑡1	10(𝑎0𝑎0/1)𝑡1	NUM
cana-4971	71	2	2𝑎2	2𝑎2	NUM
cana-4971	71	3	=	=	SYM
cana-4971	71	4	10𝑎1	10𝑎1	NUM
cana-4971	71	5	−	−	PROPN
cana-4971	71	6	20𝑎0𝑎1	20𝑎0𝑎1	NOUN
cana-4971	71	7	−	−	PROPN
cana-4971	71	8	10𝑎0	10𝑎0	NUM
cana-4971	71	9	2	2	NUM
cana-4971	71	10	we	we	PRON
cana-4971	71	11	get	get	VERB
cana-4971	71	12	𝑎2	𝑎2	NOUN
cana-4971	71	13	=	=	NOUN
cana-4971	71	14	3.55	3.55	NUM
cana-4971	71	15	𝒕𝟐	𝒕𝟐	NOUN
cana-4971	71	16	:	:	PUNCT
cana-4971	71	17	left	leave	VERB
cana-4971	71	18	:	:	PUNCT
cana-4971	72	1	3𝑎3	3𝑎3	NUM
cana-4971	72	2	right	right	NOUN
cana-4971	72	3	:	:	PUNCT
cana-4971	73	1	10𝑎2	10𝑎2	NUM
cana-4971	73	2	−	−	PROPN
cana-4971	73	3	10(𝑎0𝑎2	10(𝑎0𝑎2	PROPN
cana-4971	73	4	+	+	CCONJ
cana-4971	73	5	𝑎1𝑎1	𝑎1𝑎1	X
cana-4971	73	6	+	+	CCONJ
cana-4971	73	7	𝑎2𝑎0	𝑎2𝑎0	X
cana-4971	73	8	)	)	PUNCT
cana-4971	73	9	−	−	PROPN
cana-4971	73	10	10	10	NUM
cana-4971	73	11	(	(	PUNCT
cana-4971	73	12	𝑎0𝑎1	𝑎0𝑎1	PROPN
cana-4971	73	13	2	2	NUM
cana-4971	73	14	+	+	CCONJ
cana-4971	73	15	𝑎1𝑎0	𝑎1𝑎0	PROPN
cana-4971	73	16	1	1	NUM
cana-4971	73	17	)	)	PUNCT
cana-4971	73	18	3𝑎3	3𝑎3	NUM
cana-4971	74	1	=	=	SYM
cana-4971	75	1	10𝑎2	10𝑎2	NUM
cana-4971	75	2	−	−	NUM
cana-4971	75	3	10(2𝑎0𝑎2	10(2𝑎0𝑎2	NUM
cana-4971	75	4	+	+	CCONJ
cana-4971	75	5	𝑎1	𝑎1	NOUN
cana-4971	75	6	2	2	NUM
cana-4971	75	7	)	)	PUNCT
cana-4971	75	8	−	−	PROPN
cana-4971	75	9	10(𝑎0𝑎1/2	10(𝑎0𝑎1/2	NUM
cana-4971	75	10	+	+	CCONJ
cana-4971	75	11	𝑎1𝑎0	𝑎1𝑎0	AUX
cana-4971	75	12	)	)	PUNCT
cana-4971	75	13	we	we	PRON
cana-4971	75	14	get	get	VERB
cana-4971	75	15	𝑎3	𝑎3	PROPN
cana-4971	75	16	≈	≈	PROPN
cana-4971	75	17	6.3167	6.3167	NUM
cana-4971	75	18	step	step	NOUN
cana-4971	75	19	5	5	NUM
cana-4971	75	20	:	:	PUNCT
cana-4971	75	21	form	form	VERB
cana-4971	75	22	the	the	DET
cana-4971	75	23	series	series	NOUN
cana-4971	75	24	solution	solution	NOUN
cana-4971	75	25	the	the	DET
cana-4971	75	26	approximate	approximate	ADJ
cana-4971	75	27	solution	solution	NOUN
cana-4971	75	28	up	up	ADP
cana-4971	75	29	to	to	ADP
cana-4971	75	30	𝑡2	𝑡2	PROPN
cana-4971	75	31	is	be	AUX
cana-4971	75	32	:	:	PUNCT
cana-4971	75	33	𝑧(𝑡	𝑧(𝑡	NOUN
cana-4971	75	34	)	)	PUNCT
cana-4971	75	35	≈	≈	PROPN
cana-4971	75	36	𝑎0	𝑎0	PROPN
cana-4971	75	37	+	+	CCONJ
cana-4971	75	38	𝑎1𝑡	𝑎1𝑡	VERB
cana-4971	75	39	+	+	CCONJ
cana-4971	75	40	𝑎2𝑡2	𝑎2𝑡2	PROPN
cana-4971	75	41	=	=	SYM
cana-4971	75	42	0.1	0.1	NUM
cana-4971	75	43	+	+	CCONJ
cana-4971	75	44	0.9𝑡	0.9𝑡	NUM
cana-4971	75	45	+	+	CCONJ
cana-4971	75	46	3.55𝑡2	3.55𝑡2	NUM
cana-4971	75	47	higher	high	ADJ
cana-4971	75	48	terms	term	NOUN
cana-4971	75	49	can	can	AUX
cana-4971	75	50	be	be	AUX
cana-4971	75	51	computed	compute	VERB
cana-4971	75	52	similarly	similarly	ADV
cana-4971	75	53	,	,	PUNCT
cana-4971	75	54	but	but	CCONJ
cana-4971	75	55	the	the	DET
cana-4971	75	56	pattern	pattern	NOUN
cana-4971	75	57	becomes	become	VERB
cana-4971	75	58	complex	complex	ADJ
cana-4971	75	59	due	due	ADP
cana-4971	75	60	to	to	ADP
cana-4971	75	61	the	the	DET
cana-4971	75	62	nonlinear	nonlinear	ADJ
cana-4971	75	63	terms	term	NOUN
cana-4971	75	64	.	.	PUNCT
cana-4971	76	1	verification	verification	NOUN
cana-4971	76	2	at	at	ADP
cana-4971	76	3	𝑡	𝑡	X
cana-4971	76	4	=	=	SYM
cana-4971	76	5	0	0	NUM
cana-4971	76	6	:	:	PUNCT
cana-4971	76	7	𝑧(0	𝑧(0	NUM
cana-4971	76	8	)	)	PUNCT
cana-4971	76	9	=	=	SYM
cana-4971	76	10	0.1	0.1	NUM
cana-4971	76	11	,	,	PUNCT
cana-4971	76	12	which	which	PRON
cana-4971	76	13	matches	match	VERB
cana-4971	76	14	.	.	PUNCT
cana-4971	77	1	derivative	derivative	ADJ
cana-4971	77	2	:	:	PUNCT
cana-4971	77	3	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	77	4	𝑑𝑡	𝑑𝑡	ADP
cana-4971	77	5	≈	≈	PROPN
cana-4971	77	6	0.9	0.9	NUM
cana-4971	77	7	+	+	CCONJ
cana-4971	77	8	7.1𝑡	7.1𝑡	NUM
cana-4971	77	9	check	check	NOUN
cana-4971	77	10	at	at	ADP
cana-4971	77	11	𝑡	𝑡	X
cana-4971	77	12	=	=	NOUN
cana-4971	77	13	0	0	NUM
cana-4971	77	14	:	:	PUNCT
cana-4971	77	15	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	77	16	𝑑𝑡	𝑑𝑡	ADP
cana-4971	77	17	=	=	NOUN
cana-4971	77	18	0.9	0.9	NUM
cana-4971	77	19	,	,	PUNCT
cana-4971	77	20	and	and	CCONJ
cana-4971	77	21	right	right	ADJ
cana-4971	77	22	side	side	NOUN
cana-4971	77	23	=	=	SYM
cana-4971	77	24	10	10	NUM
cana-4971	77	25	⋅	⋅	PROPN
cana-4971	77	26	0.1	0.1	NUM
cana-4971	77	27	−	−	PROPN
cana-4971	77	28	10	10	NUM
cana-4971	77	29	⋅	⋅	PROPN
cana-4971	77	30	0.01	0.01	NUM
cana-4971	77	31	−	−	NOUN
cana-4971	77	32	0	0	NUM
cana-4971	78	1	=	=	SYM
cana-4971	78	2	1	1	NUM
cana-4971	78	3	−	−	NOUN
cana-4971	78	4	0.1	0.1	NUM
cana-4971	78	5	=	=	SYM
cana-4971	78	6	0.9	0.9	NUM
cana-4971	78	7	,	,	PUNCT
cana-4971	78	8	which	which	PRON
cana-4971	78	9	holds	hold	VERB
cana-4971	78	10	.	.	PUNCT
cana-4971	79	1	the	the	DET
cana-4971	79	2	solution	solution	NOUN
cana-4971	79	3	is	be	AUX
cana-4971	79	4	consistent	consistent	ADJ
cana-4971	79	5	.	.	PUNCT
cana-4971	80	1	for	for	ADP
cana-4971	80	2	higher	high	ADJ
cana-4971	80	3	accuracy	accuracy	NOUN
cana-4971	80	4	,	,	PUNCT
cana-4971	80	5	include	include	VERB
cana-4971	80	6	more	more	ADJ
cana-4971	80	7	terms	term	NOUN
cana-4971	80	8	.	.	PUNCT
cana-4971	81	1	thus	thus	ADV
cana-4971	81	2	:	:	PUNCT
cana-4971	81	3	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	81	4	)	)	PUNCT
cana-4971	82	1	≈	≈	PROPN
cana-4971	82	2	0.1	0.1	NUM
cana-4971	83	1	+	+	CCONJ
cana-4971	83	2	0.9𝑡	0.9𝑡	NUM
cana-4971	83	3	+	+	CCONJ
cana-4971	84	1	3.55𝑡2	3.55𝑡2	NUM
cana-4971	84	2	+	+	CCONJ
cana-4971	84	3	6.3167𝑡3	6.3167𝑡3	NUM
cana-4971	84	4	+	+	CCONJ
cana-4971	84	5	⋯	⋯	ADP
cana-4971	84	6	2.2	2.2	NUM
cana-4971	84	7	hybrid	hybrid	NOUN
cana-4971	84	8	method	method	NOUN
cana-4971	84	9	using	use	VERB
cana-4971	84	10	integral	integral	ADJ
cana-4971	84	11	transforms	transform	NOUN
cana-4971	84	12	let	let	VERB
cana-4971	84	13	’s	’s	NOUN
cana-4971	84	14	solve	solve	VERB
cana-4971	84	15	the	the	DET
cana-4971	84	16	nlvide	nlvide	NOUN
cana-4971	84	17	using	use	VERB
cana-4971	84	18	a	a	DET
cana-4971	84	19	novel	novel	ADJ
cana-4971	84	20	hybrid	hybrid	NOUN
cana-4971	84	21	method	method	NOUN
cana-4971	84	22	that	that	PRON
cana-4971	84	23	combines	combine	VERB
cana-4971	84	24	integral	integral	ADJ
cana-4971	84	25	transforms	transform	NOUN
cana-4971	84	26	(	(	PUNCT
cana-4971	84	27	specifically	specifically	ADV
cana-4971	84	28	the	the	DET
cana-4971	84	29	laplace	laplace	NOUN
cana-4971	84	30	transform	transform	NOUN
cana-4971	84	31	)	)	PUNCT
cana-4971	84	32	with	with	ADP
cana-4971	84	33	a	a	DET
cana-4971	84	34	series	series	NOUN
cana-4971	84	35	solution	solution	NOUN
cana-4971	84	36	approach	approach	NOUN
cana-4971	84	37	.	.	PUNCT
cana-4971	85	1	this	this	DET
cana-4971	85	2	hybrid	hybrid	ADJ
cana-4971	85	3	method	method	NOUN
cana-4971	85	4	will	will	AUX
cana-4971	85	5	leverage	leverage	VERB
cana-4971	85	6	the	the	DET
cana-4971	85	7	transform	transform	NOUN
cana-4971	85	8	to	to	PART
cana-4971	85	9	handle	handle	VERB
cana-4971	85	10	the	the	DET
cana-4971	85	11	integral	integral	ADJ
cana-4971	85	12	term	term	NOUN
cana-4971	85	13	efficiently	efficiently	ADV
cana-4971	85	14	and	and	CCONJ
cana-4971	85	15	then	then	ADV
cana-4971	85	16	use	use	VERB
cana-4971	85	17	a	a	DET
cana-4971	85	18	series	series	NOUN
cana-4971	85	19	expansion	expansion	NOUN
cana-4971	85	20	to	to	PART
cana-4971	85	21	approximate	approximate	VERB
cana-4971	85	22	the	the	DET
cana-4971	85	23	non	non	ADJ
cana-4971	85	24	-	-	ADJ
cana-4971	85	25	linearr	linearr	ADJ
cana-4971	85	26	terms	term	NOUN
cana-4971	85	27	,	,	PUNCT
cana-4971	85	28	aiming	aim	VERB
cana-4971	85	29	to	to	PART
cana-4971	85	30	align	align	VERB
cana-4971	85	31	closely	closely	ADV
cana-4971	85	32	with	with	ADP
cana-4971	85	33	the	the	DET
cana-4971	85	34	previous	previous	ADJ
cana-4971	85	35	series	series	NOUN
cana-4971	85	36	solution	solution	NOUN
cana-4971	85	37	.	.	PUNCT
cana-4971	86	1	the	the	DET
cana-4971	86	2	equation	equation	NOUN
cana-4971	86	3	is	be	AUX
cana-4971	86	4	:	:	PUNCT
cana-4971	86	5	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	86	6	𝑑𝑡	𝑑𝑡	ADP
cana-4971	86	7	=	=	SYM
cana-4971	86	8	10𝑧(𝑡	10𝑧(𝑡	PROPN
cana-4971	86	9	)	)	PUNCT
cana-4971	86	10	−	−	PROPN
cana-4971	86	11	10𝑧2(𝑡	10𝑧2(𝑡	NUM
cana-4971	86	12	)	)	PUNCT
cana-4971	86	13	−	−	PROPN
cana-4971	86	14	10𝑧(𝑡	10𝑧(𝑡	NUM
cana-4971	86	15	)	)	PUNCT
cana-4971	86	16	∫	∫	PROPN
cana-4971	87	1	𝑡	𝑡	PROPN
cana-4971	87	2	0	0	NUM
cana-4971	87	3	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	87	4	)	)	PUNCT
cana-4971	87	5	𝑑𝑥	𝑑𝑥	VERB
cana-4971	87	6	,	,	PUNCT
cana-4971	87	7	𝑧(0	𝑧(0	PROPN
cana-4971	87	8	)	)	PUNCT
cana-4971	87	9	=	=	SYM
cana-4971	87	10	0.1	0.1	NUM
cana-4971	87	11	https://internationalpubls.com/	https://internationalpubls.com/	NOUN
cana-4971	87	12	communications	communication	NOUN
cana-4971	87	13	on	on	ADP
cana-4971	87	14	applied	apply	VERB
cana-4971	87	15	nonlinear	nonlinear	ADJ
cana-4971	87	16	analysis	analysis	NOUN
cana-4971	87	17	issn	issn	NOUN
cana-4971	87	18	:	:	PUNCT
cana-4971	87	19	1074	1074	NUM
cana-4971	87	20	-	-	PUNCT
cana-4971	87	21	133x	133x	NUM
cana-4971	87	22	vol	vol	NOUN
cana-4971	87	23	31	31	NUM
cana-4971	87	24	no	no	NOUN
cana-4971	87	25	.	.	PUNCT
cana-4971	88	1	4s	4s	NUM
cana-4971	88	2	(	(	PUNCT
cana-4971	88	3	2024	2024	NUM
cana-4971	88	4	)	)	PUNCT
cana-4971	88	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4971	89	1	664	664	NUM
cana-4971	89	2	step	step	NOUN
cana-4971	89	3	1	1	NUM
cana-4971	89	4	:	:	PUNCT
cana-4971	89	5	apply	apply	VERB
cana-4971	89	6	the	the	DET
cana-4971	89	7	laplace	laplace	NOUN
cana-4971	89	8	transform	transform	VERB
cana-4971	89	9	the	the	DET
cana-4971	89	10	laplace	laplace	NOUN
cana-4971	89	11	transform	transform	NOUN
cana-4971	89	12	of	of	ADP
cana-4971	89	13	𝑧(𝑡	𝑧(𝑡	NOUN
cana-4971	89	14	)	)	PUNCT
cana-4971	89	15	is	be	AUX
cana-4971	89	16	defined	define	VERB
cana-4971	89	17	as	as	ADP
cana-4971	89	18	:	:	PUNCT
cana-4971	89	19	ℒ{𝑧(𝑡	ℒ{𝑧(𝑡	NOUN
cana-4971	89	20	)	)	PUNCT
cana-4971	89	21	}	}	PUNCT
cana-4971	90	1	=	=	SYM
cana-4971	90	2	𝑍(𝑠	𝑍(𝑠	NUM
cana-4971	90	3	)	)	PUNCT
cana-4971	90	4	=	=	SYM
cana-4971	90	5	∫	∫	PROPN
cana-4971	90	6	∞	∞	PROPN
cana-4971	90	7	0	0	NUM
cana-4971	90	8	𝑒−𝑠𝑡𝑧(𝑡	𝑒−𝑠𝑡𝑧(𝑡	NUM
cana-4971	90	9	)	)	PUNCT
cana-4971	90	10	𝑑𝑡	𝑑𝑡	ADP
cana-4971	90	11	by	by	ADP
cana-4971	90	12	taking	take	VERB
cana-4971	90	13	laplace	laplace	NOUN
cana-4971	90	14	transform	transform	NOUN
cana-4971	90	15	we	we	PRON
cana-4971	90	16	get	get	VERB
cana-4971	90	17	,	,	PUNCT
cana-4971	90	18	left	left	ADJ
cana-4971	90	19	side	side	NOUN
cana-4971	90	20	:	:	PUNCT
cana-4971	90	21	ℒ	ℒ	NOUN
cana-4971	90	22	{	{	PUNCT
cana-4971	90	23	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	90	24	𝑑𝑡	𝑑𝑡	ADP
cana-4971	90	25	}	}	PUNCT
cana-4971	90	26	=	=	SYM
cana-4971	90	27	𝑠𝑍(𝑠	𝑠𝑍(𝑠	PROPN
cana-4971	90	28	)	)	PUNCT
cana-4971	90	29	−	−	PROPN
cana-4971	91	1	𝑧(0	𝑧(0	PROPN
cana-4971	91	2	)	)	PUNCT
cana-4971	91	3	=	=	SYM
cana-4971	92	1	𝑠𝑍(𝑠	𝑠𝑍(𝑠	PROPN
cana-4971	92	2	)	)	PUNCT
cana-4971	92	3	−	−	PROPN
cana-4971	92	4	0.1	0.1	NUM
cana-4971	92	5	right	right	ADJ
cana-4971	92	6	side	side	NOUN
cana-4971	92	7	:	:	PUNCT
cana-4971	92	8	1	1	X
cana-4971	92	9	.	.	X
cana-4971	92	10	ℒ{10𝑧(𝑡	ℒ{10𝑧(𝑡	NOUN
cana-4971	92	11	)	)	PUNCT
cana-4971	92	12	}	}	PUNCT
cana-4971	92	13	=	=	SYM
cana-4971	92	14	10𝑍(𝑠	10𝑍(𝑠	NUM
cana-4971	92	15	)	)	PUNCT
cana-4971	92	16	2	2	NUM
cana-4971	92	17	.	.	PUNCT
cana-4971	93	1	ℒ{−10𝑧2(𝑡	ℒ{−10𝑧2(𝑡	NOUN
cana-4971	93	2	)	)	PUNCT
cana-4971	93	3	}	}	PUNCT
cana-4971	93	4	=	=	SYM
cana-4971	93	5	−10ℒ{𝑧2(𝑡	−10ℒ{𝑧2(𝑡	PROPN
cana-4971	93	6	)	)	PUNCT
cana-4971	93	7	}	}	PUNCT
cana-4971	94	1	the	the	DET
cana-4971	94	2	transform	transform	NOUN
cana-4971	94	3	of	of	ADP
cana-4971	94	4	the	the	DET
cana-4971	94	5	nonlinear	nonlinear	ADJ
cana-4971	94	6	term	term	NOUN
cana-4971	94	7	𝑧2(𝑡	𝑧2(𝑡	NOUN
cana-4971	94	8	)	)	PUNCT
cana-4971	94	9	is	be	AUX
cana-4971	94	10	a	a	DET
cana-4971	94	11	convolution	convolution	NOUN
cana-4971	94	12	in	in	ADP
cana-4971	94	13	the	the	DET
cana-4971	94	14	s	s	NOUN
cana-4971	94	15	-	-	NOUN
cana-4971	94	16	domain	domain	NOUN
cana-4971	94	17	:	:	PUNCT
cana-4971	94	18	ℒ{𝑧2(𝑡	ℒ{𝑧2(𝑡	NOUN
cana-4971	94	19	)	)	PUNCT
cana-4971	94	20	}	}	PUNCT
cana-4971	94	21	=	=	SYM
cana-4971	94	22	ℒ{𝑧(𝑡	ℒ{𝑧(𝑡	NOUN
cana-4971	94	23	)	)	PUNCT
cana-4971	94	24	⋅	⋅	PROPN
cana-4971	94	25	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	94	26	)	)	PUNCT
cana-4971	94	27	}	}	PUNCT
cana-4971	94	28	=	=	SYM
cana-4971	95	1	𝑍(𝑠	𝑍(𝑠	NUM
cana-4971	95	2	)	)	PUNCT
cana-4971	95	3	∗	∗	NOUN
cana-4971	95	4	𝑍(𝑠	𝑍(𝑠	NOUN
cana-4971	95	5	)	)	PUNCT
cana-4971	95	6	however	however	ADV
cana-4971	95	7	,	,	PUNCT
cana-4971	95	8	computing	compute	VERB
cana-4971	95	9	this	this	DET
cana-4971	95	10	convolution	convolution	NOUN
cana-4971	95	11	directly	directly	ADV
cana-4971	95	12	is	be	AUX
cana-4971	95	13	complex	complex	ADJ
cana-4971	95	14	,	,	PUNCT
cana-4971	95	15	so	so	SCONJ
cana-4971	95	16	we	we	PRON
cana-4971	95	17	’ll	’ll	AUX
cana-4971	95	18	approximate	approximate	VERB
cana-4971	95	19	it	it	PRON
cana-4971	95	20	later	later	ADV
cana-4971	95	21	via	via	ADP
cana-4971	95	22	series	series	NOUN
cana-4971	95	23	.	.	PUNCT
cana-4971	96	1	3	3	X
cana-4971	96	2	.	.	X
cana-4971	96	3	ℒ	ℒ	NOUN
cana-4971	96	4	{	{	PUNCT
cana-4971	96	5	−10𝑧(𝑡	−10𝑧(𝑡	NOUN
cana-4971	96	6	)	)	PUNCT
cana-4971	96	7	∫	∫	PROPN
cana-4971	97	1	𝑡	𝑡	PROPN
cana-4971	97	2	0	0	NUM
cana-4971	97	3	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	97	4	)	)	PUNCT
cana-4971	97	5	𝑑𝑥	𝑑𝑥	AUX
cana-4971	97	6	}	}	PUNCT
cana-4971	97	7	use	use	VERB
cana-4971	97	8	the	the	DET
cana-4971	97	9	convolution	convolution	NOUN
cana-4971	97	10	theorem	theorem	VERB
cana-4971	97	11	:	:	PUNCT
cana-4971	97	12	ℒ	ℒ	PROPN
cana-4971	97	13	{	{	PUNCT
cana-4971	97	14	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	97	15	)	)	PUNCT
cana-4971	97	16	∫	∫	PROPN
cana-4971	98	1	𝑡	𝑡	PROPN
cana-4971	98	2	0	0	NUM
cana-4971	98	3	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	98	4	)	)	PUNCT
cana-4971	98	5	𝑑𝑥	𝑑𝑥	VERB
cana-4971	98	6	}	}	PUNCT
cana-4971	98	7	=	=	SYM
cana-4971	98	8	ℒ{𝑧(𝑡	ℒ{𝑧(𝑡	NOUN
cana-4971	98	9	)	)	PUNCT
cana-4971	98	10	}	}	PUNCT
cana-4971	98	11	⋅	⋅	PROPN
cana-4971	98	12	ℒ	ℒ	X
cana-4971	98	13	{	{	PUNCT
cana-4971	98	14	∫	∫	PROPN
cana-4971	98	15	𝑡	𝑡	PROPN
cana-4971	98	16	0	0	NUM
cana-4971	98	17	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	98	18	)	)	PUNCT
cana-4971	98	19	𝑑𝑥	𝑑𝑥	AUX
cana-4971	98	20	}	}	PUNCT
cana-4971	98	21	compute	compute	VERB
cana-4971	98	22	the	the	DET
cana-4971	98	23	transform	transform	NOUN
cana-4971	98	24	of	of	ADP
cana-4971	98	25	the	the	DET
cana-4971	98	26	integral	integral	ADJ
cana-4971	98	27	:	:	PUNCT
cana-4971	98	28	∫	∫	PROPN
cana-4971	98	29	𝑡	𝑡	PROPN
cana-4971	98	30	0	0	NUM
cana-4971	98	31	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	98	32	)	)	PUNCT
cana-4971	99	1	𝑑𝑥	𝑑𝑥	VERB
cana-4971	99	2	ℒ	ℒ	PROPN
cana-4971	99	3	{	{	PUNCT
cana-4971	99	4	∫	∫	PROPN
cana-4971	99	5	𝑡	𝑡	PROPN
cana-4971	99	6	0	0	NUM
cana-4971	99	7	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	99	8	)	)	PUNCT
cana-4971	99	9	𝑑𝑥	𝑑𝑥	VERB
cana-4971	99	10	}	}	PUNCT
cana-4971	99	11	=	=	SYM
cana-4971	99	12	𝑍(𝑠	𝑍(𝑠	NUM
cana-4971	99	13	)	)	PUNCT
cana-4971	99	14	𝑠	𝑠	NOUN
cana-4971	100	1	so	so	ADV
cana-4971	100	2	:	:	PUNCT
cana-4971	100	3	ℒ	ℒ	X
cana-4971	100	4	{	{	PUNCT
cana-4971	100	5	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	100	6	)	)	PUNCT
cana-4971	100	7	∫	∫	PROPN
cana-4971	101	1	𝑡	𝑡	PROPN
cana-4971	101	2	0	0	NUM
cana-4971	101	3	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	101	4	)	)	PUNCT
cana-4971	101	5	𝑑𝑥	𝑑𝑥	VERB
cana-4971	101	6	}	}	PUNCT
cana-4971	101	7	=	=	SYM
cana-4971	101	8	𝑍(𝑠	𝑍(𝑠	NUM
cana-4971	101	9	)	)	PUNCT
cana-4971	101	10	⋅	⋅	PROPN
cana-4971	101	11	𝑍(𝑠	𝑍(𝑠	NUM
cana-4971	101	12	)	)	PUNCT
cana-4971	101	13	𝑠	𝑠	PROPN
cana-4971	101	14	=	=	PUNCT
cana-4971	101	15	𝑍2(𝑠	𝑍2(𝑠	PROPN
cana-4971	101	16	)	)	PUNCT
cana-4971	101	17	𝑠	𝑠	ADP
cana-4971	101	18	thus	thus	ADV
cana-4971	101	19	:	:	PUNCT
cana-4971	101	20	ℒ	ℒ	X
cana-4971	101	21	{	{	PUNCT
cana-4971	101	22	−10𝑧(𝑡	−10𝑧(𝑡	NOUN
cana-4971	101	23	)	)	PUNCT
cana-4971	101	24	∫	∫	PROPN
cana-4971	102	1	𝑡	𝑡	PROPN
cana-4971	102	2	0	0	NUM
cana-4971	102	3	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	102	4	)	)	PUNCT
cana-4971	102	5	𝑑𝑥	𝑑𝑥	VERB
cana-4971	102	6	}	}	PUNCT
cana-4971	102	7	=	=	SYM
cana-4971	102	8	−10	−10	X
cana-4971	102	9	𝑍2(𝑠	𝑍2(𝑠	PUNCT
cana-4971	102	10	)	)	PUNCT
cana-4971	102	11	𝑠	𝑠	ADP
cana-4971	102	12	the	the	DET
cana-4971	102	13	transformed	transform	VERB
cana-4971	102	14	equation	equation	NOUN
cana-4971	102	15	is	be	AUX
cana-4971	102	16	:	:	PUNCT
cana-4971	102	17	𝑠𝑍(𝑠	𝑠𝑍(𝑠	NUM
cana-4971	102	18	)	)	PUNCT
cana-4971	102	19	−	−	ADP
cana-4971	102	20	0.1	0.1	NUM
cana-4971	102	21	=	=	SYM
cana-4971	102	22	10𝑍(𝑠	10𝑍(𝑠	NUM
cana-4971	102	23	)	)	PUNCT
cana-4971	102	24	−	−	PROPN
cana-4971	103	1	10ℒ{𝑧2(𝑡	10ℒ{𝑧2(𝑡	NUM
cana-4971	103	2	)	)	PUNCT
cana-4971	103	3	}	}	PUNCT
cana-4971	104	1	−	−	PROPN
cana-4971	104	2	10	10	NUM
cana-4971	104	3	𝑍2(𝑠	𝑍2(𝑠	NUM
cana-4971	104	4	)	)	PUNCT
cana-4971	104	5	𝑠	𝑠	X
cana-4971	104	6	step	step	NOUN
cana-4971	104	7	2	2	NUM
cana-4971	104	8	:	:	PUNCT
cana-4971	104	9	introduce	introduce	VERB
cana-4971	104	10	the	the	DET
cana-4971	104	11	series	series	NOUN
cana-4971	104	12	approximation	approximation	NOUN
cana-4971	104	13	since	since	SCONJ
cana-4971	104	14	the	the	DET
cana-4971	104	15	equation	equation	NOUN
cana-4971	104	16	is	be	AUX
cana-4971	104	17	nonlinear	nonlinear	ADJ
cana-4971	104	18	,	,	PUNCT
cana-4971	104	19	solving	solve	VERB
cana-4971	104	20	for	for	ADP
cana-4971	104	21	𝑍(𝑠	𝑍(𝑠	NOUN
cana-4971	104	22	)	)	PUNCT
cana-4971	104	23	directly	directly	ADV
cana-4971	104	24	is	be	AUX
cana-4971	104	25	challenging	challenge	VERB
cana-4971	104	26	due	due	ADJ
cana-4971	104	27	to	to	ADP
cana-4971	104	28	ℒ{𝑧2(𝑡	ℒ{𝑧2(𝑡	NOUN
cana-4971	104	29	)	)	PUNCT
cana-4971	104	30	}	}	PUNCT
cana-4971	104	31	.	.	PUNCT
cana-4971	105	1	let	let	VERB
cana-4971	105	2	’s	’s	PRON
cana-4971	105	3	assume	assume	VERB
cana-4971	105	4	a	a	DET
cana-4971	105	5	series	series	NOUN
cana-4971	105	6	solution	solution	NOUN
cana-4971	105	7	for	for	ADP
cana-4971	105	8	𝑧(𝑡	𝑧(𝑡	NOUN
cana-4971	105	9	):	):	PUNCT
cana-4971	105	10	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	105	11	)	)	PUNCT
cana-4971	105	12	=	=	NOUN
cana-4971	106	1	∑∞	∑∞	NOUN
cana-4971	106	2	𝑛=0	𝑛=0	PROPN
cana-4971	106	3	𝑎𝑛𝑡𝑛	𝑎𝑛𝑡𝑛	VERB
cana-4971	106	4	,	,	PUNCT
cana-4971	106	5	𝑎0	𝑎0	PROPN
cana-4971	106	6	=	=	SYM
cana-4971	106	7	𝑧(0	𝑧(0	PROPN
cana-4971	106	8	)	)	PUNCT
cana-4971	106	9	=	=	PUNCT
cana-4971	107	1	0.1	0.1	NUM
cana-4971	107	2	then	then	ADV
cana-4971	107	3	:	:	PUNCT
cana-4971	107	4	𝑍(𝑠	𝑍(𝑠	NUM
cana-4971	107	5	)	)	PUNCT
cana-4971	107	6	=	=	SYM
cana-4971	107	7	ℒ{𝑧(𝑡	ℒ{𝑧(𝑡	NOUN
cana-4971	107	8	)	)	PUNCT
cana-4971	107	9	}	}	PUNCT
cana-4971	107	10	=	=	NOUN
cana-4971	107	11	∑∞	∑∞	X
cana-4971	107	12	𝑛=0	𝑛=0	PROPN
cana-4971	107	13	𝑎𝑛ℒ{𝑡𝑛	𝑎𝑛ℒ{𝑡𝑛	PRON
cana-4971	107	14	}	}	PUNCT
cana-4971	107	15	=	=	PUNCT
cana-4971	107	16	∑∞	∑∞	NOUN
cana-4971	107	17	𝑛=0	𝑛=0	PROPN
cana-4971	107	18	𝑎𝑛	𝑎𝑛	PROPN
cana-4971	107	19	𝑛	𝑛	PROPN
cana-4971	107	20	!	!	NOUN
cana-4971	107	21	𝑠𝑛+1	𝑠𝑛+1	AUX
cana-4971	107	22	compute	compute	VERB
cana-4971	107	23	the	the	DET
cana-4971	107	24	transforms	transform	NOUN
cana-4971	107	25	of	of	ADP
cana-4971	107	26	the	the	DET
cana-4971	107	27	terms	term	NOUN
cana-4971	107	28	:	:	PUNCT
cana-4971	107	29	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	107	30	𝑑𝑡	𝑑𝑡	ADP
cana-4971	107	31	=	=	PUNCT
cana-4971	107	32	∑∞	∑∞	NOUN
cana-4971	107	33	𝑛=1	𝑛=1	NOUN
cana-4971	107	34	𝑛𝑎𝑛𝑡𝑛−1	𝑛𝑎𝑛𝑡𝑛−1	NOUN
cana-4971	107	35	ℒ	ℒ	X
cana-4971	107	36	{	{	PUNCT
cana-4971	107	37	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	107	38	𝑑𝑡	𝑑𝑡	ADP
cana-4971	107	39	}	}	PUNCT
cana-4971	107	40	=	=	NOUN
cana-4971	107	41	∑∞	∑∞	X
cana-4971	107	42	𝑛=1	𝑛=1	NOUN
cana-4971	107	43	𝑛𝑎𝑛	𝑛𝑎𝑛	NOUN
cana-4971	107	44	(	(	PUNCT
cana-4971	107	45	𝑛−1	𝑛−1	PROPN
cana-4971	107	46	)	)	PUNCT
cana-4971	107	47	!	!	PUNCT
cana-4971	108	1	𝑠𝑛	𝑠𝑛	NOUN
cana-4971	108	2	=	=	SYM
cana-4971	108	3	∑∞	∑∞	X
cana-4971	108	4	𝑛=1	𝑛=1	PROPN
cana-4971	108	5	𝑛	𝑛	PROPN
cana-4971	108	6	!	!	NOUN
cana-4971	109	1	𝑠𝑛	𝑠𝑛	NOUN
cana-4971	109	2	𝑎𝑛	𝑎𝑛	ADP
cana-4971	109	3	10𝑧(𝑡	10𝑧(𝑡	NUM
cana-4971	109	4	):	):	PUNCT
cana-4971	109	5	https://internationalpubls.com/	https://internationalpubls.com/	PROPN
cana-4971	109	6	communications	communication	NOUN
cana-4971	109	7	on	on	ADP
cana-4971	109	8	applied	apply	VERB
cana-4971	109	9	nonlinear	nonlinear	ADJ
cana-4971	109	10	analysis	analysis	NOUN
cana-4971	109	11	issn	issn	NOUN
cana-4971	109	12	:	:	PUNCT
cana-4971	109	13	1074	1074	NUM
cana-4971	109	14	-	-	PUNCT
cana-4971	109	15	133x	133x	NUM
cana-4971	109	16	vol	vol	NOUN
cana-4971	109	17	31	31	NUM
cana-4971	109	18	no	no	NOUN
cana-4971	109	19	.	.	PUNCT
cana-4971	110	1	4s	4s	NUM
cana-4971	110	2	(	(	PUNCT
cana-4971	110	3	2024	2024	NUM
cana-4971	110	4	)	)	PUNCT
cana-4971	111	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4971	111	2	665	665	NUM
cana-4971	111	3	ℒ{10𝑧(𝑡	ℒ{10𝑧(𝑡	NOUN
cana-4971	111	4	)	)	PUNCT
cana-4971	111	5	}	}	PUNCT
cana-4971	111	6	=	=	SYM
cana-4971	111	7	10	10	NUM
cana-4971	111	8	∑∞	∑∞	NOUN
cana-4971	111	9	𝑛=0	𝑛=0	VERB
cana-4971	111	10	𝑎𝑛	𝑎𝑛	PROPN
cana-4971	111	11	𝑛	𝑛	PROPN
cana-4971	111	12	!	!	NOUN
cana-4971	111	13	𝑠𝑛+1	𝑠𝑛+1	ADP
cana-4971	111	14	−10𝑧2(𝑡	−10𝑧2(𝑡	NOUN
cana-4971	111	15	):	):	PUNCT
cana-4971	111	16	𝑧2(𝑡	𝑧2(𝑡	NOUN
cana-4971	111	17	)	)	PUNCT
cana-4971	111	18	=	=	SYM
cana-4971	111	19	(	(	PUNCT
cana-4971	111	20	∑∞	∑∞	NOUN
cana-4971	111	21	𝑛=0	𝑛=0	PROPN
cana-4971	111	22	𝑎𝑛𝑡𝑛)2	𝑎𝑛𝑡𝑛)2	PROPN
cana-4971	111	23	=	=	PUNCT
cana-4971	111	24	∑∞	∑∞	X
cana-4971	112	1	𝑛=0	𝑛=0	X
cana-4971	112	2	∑𝑛	∑𝑛	ADJ
cana-4971	112	3	𝑘=0	𝑘=0	VERB
cana-4971	112	4	𝑎𝑘𝑎𝑛−𝑘𝑡𝑛	𝑎𝑘𝑎𝑛−𝑘𝑡𝑛	PROPN
cana-4971	112	5	ℒ{𝑧2(𝑡	ℒ{𝑧2(𝑡	PROPN
cana-4971	112	6	)	)	PUNCT
cana-4971	112	7	}	}	PUNCT
cana-4971	112	8	=	=	NOUN
cana-4971	112	9	∑∞	∑∞	NOUN
cana-4971	112	10	𝑛=0	𝑛=0	X
cana-4971	113	1	∑𝑛	∑𝑛	ADJ
cana-4971	113	2	𝑘=0	𝑘=0	PROPN
cana-4971	113	3	𝑎𝑘𝑎𝑛−𝑘	𝑎𝑘𝑎𝑛−𝑘	NOUN
cana-4971	113	4	𝑛	𝑛	PROPN
cana-4971	113	5	!	!	PROPN
cana-4971	113	6	𝑠𝑛+1	𝑠𝑛+1	PROPN
cana-4971	113	7	−10ℒ{𝑧2(𝑡	−10ℒ{𝑧2(𝑡	NUM
cana-4971	113	8	)	)	PUNCT
cana-4971	113	9	}	}	PUNCT
cana-4971	114	1	=	=	SYM
cana-4971	114	2	−10	−10	X
cana-4971	114	3	∑∞	∑∞	NOUN
cana-4971	114	4	𝑛=0	𝑛=0	X
cana-4971	115	1	∑𝑛	∑𝑛	ADJ
cana-4971	115	2	𝑘=0	𝑘=0	PROPN
cana-4971	115	3	𝑎𝑘𝑎𝑛−𝑘	𝑎𝑘𝑎𝑛−𝑘	NOUN
cana-4971	115	4	𝑛	𝑛	PROPN
cana-4971	115	5	!	!	PROPN
cana-4971	115	6	𝑠𝑛+1	𝑠𝑛+1	ADP
cana-4971	115	7	−10𝑧(𝑡	−10𝑧(𝑡	NOUN
cana-4971	115	8	)	)	PUNCT
cana-4971	115	9	∫	∫	PROPN
cana-4971	116	1	𝑡	𝑡	PROPN
cana-4971	116	2	0	0	NUM
cana-4971	116	3	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	116	4	)	)	PUNCT
cana-4971	116	5	𝑑𝑥	𝑑𝑥	VERB
cana-4971	116	6	:	:	PUNCT
cana-4971	116	7	∫	∫	PROPN
cana-4971	116	8	𝑡	𝑡	PROPN
cana-4971	116	9	0	0	NUM
cana-4971	116	10	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	116	11	)	)	PUNCT
cana-4971	116	12	𝑑𝑥	𝑑𝑥	VERB
cana-4971	116	13	=	=	VERB
cana-4971	116	14	∑∞	∑∞	NOUN
cana-4971	116	15	𝑛=0	𝑛=0	NOUN
cana-4971	116	16	𝑎𝑛	𝑎𝑛	VERB
cana-4971	116	17	𝑡𝑛+1	𝑡𝑛+1	X
cana-4971	116	18	𝑛+1	𝑛+1	PROPN
cana-4971	116	19	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	116	20	)	)	PUNCT
cana-4971	116	21	∫	∫	PROPN
cana-4971	117	1	𝑡	𝑡	PROPN
cana-4971	117	2	0	0	NUM
cana-4971	117	3	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	117	4	)	)	PUNCT
cana-4971	118	1	𝑑𝑥	𝑑𝑥	VERB
cana-4971	118	2	=	=	VERB
cana-4971	118	3	∑∞	∑∞	NOUN
cana-4971	118	4	𝑛=0	𝑛=0	X
cana-4971	119	1	∑𝑛	∑𝑛	ADJ
cana-4971	119	2	𝑘=0	𝑘=0	ADP
cana-4971	119	3	𝑎𝑘𝑎𝑛−𝑘	𝑎𝑘𝑎𝑛−𝑘	NOUN
cana-4971	119	4	𝑡𝑛+1	𝑡𝑛+1	PUNCT
cana-4971	119	5	𝑛−𝑘+1	𝑛−𝑘+1	NOUN
cana-4971	119	6	ℒ	ℒ	PROPN
cana-4971	119	7	{	{	PUNCT
cana-4971	119	8	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	119	9	)	)	PUNCT
cana-4971	119	10	∫	∫	PROPN
cana-4971	120	1	𝑡	𝑡	PROPN
cana-4971	120	2	0	0	NUM
cana-4971	120	3	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	120	4	)	)	PUNCT
cana-4971	120	5	𝑑𝑥	𝑑𝑥	VERB
cana-4971	120	6	}	}	PUNCT
cana-4971	120	7	=	=	SYM
cana-4971	120	8	∑∞	∑∞	NOUN
cana-4971	120	9	𝑛=0	𝑛=0	X
cana-4971	120	10	∑𝑛	∑𝑛	ADJ
cana-4971	120	11	𝑘=0	𝑘=0	ADP
cana-4971	120	12	𝑎𝑘𝑎𝑛−𝑘	𝑎𝑘𝑎𝑛−𝑘	NOUN
cana-4971	120	13	1	1	NUM
cana-4971	120	14	𝑛−𝑘+1	𝑛−𝑘+1	PROPN
cana-4971	120	15	(	(	PUNCT
cana-4971	120	16	𝑛+1	𝑛+1	NOUN
cana-4971	120	17	)	)	PUNCT
cana-4971	120	18	!	!	PUNCT
cana-4971	121	1	𝑠𝑛+2	𝑠𝑛+2	PROPN
cana-4971	121	2	−10ℒ	−10ℒ	DET
cana-4971	121	3	{	{	PUNCT
cana-4971	121	4	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	121	5	)	)	PUNCT
cana-4971	121	6	∫	∫	PROPN
cana-4971	121	7	𝑡	𝑡	PROPN
cana-4971	121	8	0	0	NUM
cana-4971	121	9	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	121	10	)	)	PUNCT
cana-4971	121	11	𝑑𝑥	𝑑𝑥	VERB
cana-4971	121	12	}	}	PUNCT
cana-4971	121	13	=	=	SYM
cana-4971	121	14	−10	−10	NOUN
cana-4971	121	15	∑∞	∑∞	NOUN
cana-4971	121	16	𝑛=0	𝑛=0	X
cana-4971	122	1	∑𝑛	∑𝑛	ADJ
cana-4971	122	2	𝑘=0	𝑘=0	PROPN
cana-4971	122	3	𝑎𝑘𝑎𝑛−𝑘	𝑎𝑘𝑎𝑛−𝑘	VERB
cana-4971	122	4	𝑛−𝑘+1	𝑛−𝑘+1	PROPN
cana-4971	122	5	(	(	PUNCT
cana-4971	122	6	𝑛+1	𝑛+1	NOUN
cana-4971	122	7	)	)	PUNCT
cana-4971	122	8	!	!	PUNCT
cana-4971	123	1	𝑠𝑛+2	𝑠𝑛+2	PROPN
cana-4971	123	2	step	step	VERB
cana-4971	123	3	3	3	NUM
cana-4971	123	4	:	:	PUNCT
cana-4971	123	5	hybrid	hybrid	ADJ
cana-4971	123	6	approach	approach	NOUN
cana-4971	123	7	–	–	PUNCT
cana-4971	123	8	match	match	NOUN
cana-4971	123	9	coefficients	coefficient	NOUN
cana-4971	123	10	substitute	substitute	NOUN
cana-4971	123	11	into	into	ADP
cana-4971	123	12	the	the	DET
cana-4971	123	13	laplace	laplace	NOUN
cana-4971	123	14	equation	equation	NOUN
cana-4971	123	15	and	and	CCONJ
cana-4971	123	16	equate	equate	ADJ
cana-4971	123	17	powers	power	NOUN
cana-4971	123	18	of	of	ADP
cana-4971	123	19	𝑠−𝑛.	𝑠−𝑛.	PROPN
cana-4971	123	20	this	this	PRON
cana-4971	123	21	is	be	AUX
cana-4971	123	22	complex	complex	ADJ
cana-4971	123	23	,	,	PUNCT
cana-4971	123	24	so	so	ADV
cana-4971	123	25	let	let	VERB
cana-4971	123	26	’s	’s	NOUN
cana-4971	123	27	compute	compute	VERB
cana-4971	123	28	the	the	DET
cana-4971	123	29	first	first	ADJ
cana-4971	123	30	few	few	ADJ
cana-4971	123	31	terms	term	NOUN
cana-4971	123	32	directly	directly	ADV
cana-4971	123	33	in	in	ADP
cana-4971	123	34	the	the	DET
cana-4971	123	35	time	time	NOUN
cana-4971	123	36	domain	domain	NOUN
cana-4971	123	37	after	after	ADP
cana-4971	123	38	transforming	transform	VERB
cana-4971	123	39	back	back	ADV
cana-4971	123	40	,	,	PUNCT
cana-4971	123	41	using	use	VERB
cana-4971	123	42	the	the	DET
cana-4971	123	43	series	series	NOUN
cana-4971	123	44	to	to	PART
cana-4971	123	45	approximate	approximate	VERB
cana-4971	123	46	:	:	PUNCT
cana-4971	123	47	reconsider	reconsider	VERB
cana-4971	123	48	the	the	DET
cana-4971	123	49	original	original	ADJ
cana-4971	123	50	equation	equation	NOUN
cana-4971	123	51	and	and	CCONJ
cana-4971	123	52	use	use	VERB
cana-4971	123	53	the	the	DET
cana-4971	123	54	transform	transform	NOUN
cana-4971	123	55	to	to	PART
cana-4971	123	56	simplify	simplify	VERB
cana-4971	123	57	:	:	PUNCT
cana-4971	123	58	𝑠𝑍(𝑠	𝑠𝑍(𝑠	NUM
cana-4971	123	59	)	)	PUNCT
cana-4971	123	60	−	−	ADP
cana-4971	123	61	0.1	0.1	NUM
cana-4971	123	62	=	=	SYM
cana-4971	123	63	10𝑍(𝑠	10𝑍(𝑠	NUM
cana-4971	123	64	)	)	PUNCT
cana-4971	124	1	−	−	PROPN
cana-4971	125	1	10ℒ{𝑧2(𝑡	10ℒ{𝑧2(𝑡	NUM
cana-4971	125	2	)	)	PUNCT
cana-4971	125	3	}	}	PUNCT
cana-4971	126	1	−	−	PROPN
cana-4971	126	2	10	10	NUM
cana-4971	126	3	𝑍2(𝑠	𝑍2(𝑠	NUM
cana-4971	126	4	)	)	PUNCT
cana-4971	126	5	𝑠	𝑠	PROPN
cana-4971	126	6	assume	assume	VERB
cana-4971	126	7	:	:	PUNCT
cana-4971	126	8	𝑧(𝑡	𝑧(𝑡	NOUN
cana-4971	126	9	)	)	PUNCT
cana-4971	126	10	=	=	SYM
cana-4971	127	1	𝑎0	𝑎0	PROPN
cana-4971	127	2	+	+	CCONJ
cana-4971	127	3	𝑎1𝑡	𝑎1𝑡	PROPN
cana-4971	127	4	+	+	CCONJ
cana-4971	127	5	𝑎2𝑡2	𝑎2𝑡2	PROPN
cana-4971	127	6	+	+	X
cana-4971	127	7	𝑎3𝑡3	𝑎3𝑡3	PROPN
cana-4971	127	8	+	+	CCONJ
cana-4971	127	9	⋯	⋯	NOUN
cana-4971	127	10	𝑍(𝑠	𝑍(𝑠	NUM
cana-4971	127	11	)	)	PUNCT
cana-4971	127	12	=	=	PUNCT
cana-4971	127	13	𝑎0	𝑎0	PROPN
cana-4971	127	14	𝑠	𝑠	NOUN
cana-4971	128	1	+	+	CCONJ
cana-4971	128	2	𝑎1	𝑎1	ADJ
cana-4971	128	3	𝑠2	𝑠2	NOUN
cana-4971	128	4	+	+	NUM
cana-4971	128	5	2𝑎2	2𝑎2	NUM
cana-4971	128	6	𝑠3	𝑠3	NOUN
cana-4971	128	7	+	+	CCONJ
cana-4971	128	8	6𝑎3	6𝑎3	NUM
cana-4971	128	9	𝑠4	𝑠4	NOUN
cana-4971	128	10	+	+	CCONJ
cana-4971	128	11	⋯	⋯	VERB
cana-4971	128	12	instead	instead	ADV
cana-4971	128	13	of	of	ADP
cana-4971	128	14	solving	solve	VERB
cana-4971	128	15	the	the	DET
cana-4971	128	16	full	full	ADJ
cana-4971	128	17	nonlinear	nonlinear	ADJ
cana-4971	128	18	equation	equation	NOUN
cana-4971	128	19	in	in	ADP
cana-4971	128	20	the	the	DET
cana-4971	128	21	s	s	NOUN
cana-4971	128	22	-	-	NOUN
cana-4971	128	23	domain	domain	NOUN
cana-4971	128	24	,	,	PUNCT
cana-4971	128	25	apply	apply	VERB
cana-4971	128	26	the	the	DET
cana-4971	128	27	inverse	inverse	NOUN
cana-4971	128	28	transform	transform	NOUN
cana-4971	128	29	after	after	ADP
cana-4971	128	30	approximating	approximate	VERB
cana-4971	128	31	.	.	PUNCT
cana-4971	129	1	let	let	VERB
cana-4971	129	2	’s	’s	NOUN
cana-4971	129	3	revert	revert	VERB
cana-4971	129	4	to	to	ADP
cana-4971	129	5	the	the	DET
cana-4971	129	6	differential	differential	ADJ
cana-4971	129	7	form	form	NOUN
cana-4971	129	8	and	and	CCONJ
cana-4971	129	9	use	use	VERB
cana-4971	129	10	the	the	DET
cana-4971	129	11	series	series	NOUN
cana-4971	129	12	as	as	ADP
cana-4971	129	13	in	in	ADP
cana-4971	129	14	the	the	DET
cana-4971	129	15	previous	previous	ADJ
cana-4971	129	16	method	method	NOUN
cana-4971	129	17	,	,	PUNCT
cana-4971	129	18	but	but	CCONJ
cana-4971	129	19	informed	inform	VERB
cana-4971	129	20	by	by	ADP
cana-4971	129	21	the	the	DET
cana-4971	129	22	transform	transform	NOUN
cana-4971	129	23	:	:	PUNCT
cana-4971	129	24	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	129	25	𝑑𝑡	𝑑𝑡	ADP
cana-4971	129	26	=	=	PROPN
cana-4971	129	27	10𝑧	10𝑧	PROPN
cana-4971	129	28	−	−	PROPN
cana-4971	129	29	10𝑧2	10𝑧2	NUM
cana-4971	129	30	−	−	PROPN
cana-4971	129	31	10𝑧𝐼(𝑡	10𝑧𝐼(𝑡	NUM
cana-4971	129	32	)	)	PUNCT
cana-4971	129	33	,	,	PUNCT
cana-4971	129	34	𝐼(𝑡	𝐼(𝑡	NUM
cana-4971	129	35	)	)	PUNCT
cana-4971	129	36	=	=	SYM
cana-4971	130	1	∫	∫	PROPN
cana-4971	130	2	𝑡	𝑡	PROPN
cana-4971	130	3	0	0	NUM
cana-4971	130	4	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	130	5	)	)	PUNCT
cana-4971	131	1	𝑑𝑥	𝑑𝑥	VERB
cana-4971	131	2	ℒ{𝐼′(𝑡	ℒ{𝐼′(𝑡	PROPN
cana-4971	131	3	)	)	PUNCT
cana-4971	131	4	}	}	PUNCT
cana-4971	131	5	=	=	SYM
cana-4971	131	6	ℒ{𝑧(𝑡)}𝑠𝐼(𝑠	ℒ{𝑧(𝑡)}𝑠𝐼(𝑠	NOUN
cana-4971	131	7	)	)	PUNCT
cana-4971	131	8	=	=	SYM
cana-4971	131	9	𝑍(𝑠)𝐼(𝑠	𝑍(𝑠)𝐼(𝑠	NUM
cana-4971	131	10	)	)	PUNCT
cana-4971	131	11	=	=	SYM
cana-4971	132	1	𝑍(𝑠	𝑍(𝑠	NUM
cana-4971	132	2	)	)	PUNCT
cana-4971	132	3	𝑠	𝑠	NOUN
cana-4971	132	4	this	this	PRON
cana-4971	132	5	confirms	confirm	VERB
cana-4971	132	6	our	our	PRON
cana-4971	132	7	integral	integral	ADJ
cana-4971	132	8	term	term	NOUN
cana-4971	132	9	handling	handling	NOUN
cana-4971	132	10	.	.	PUNCT
cana-4971	133	1	now	now	ADV
cana-4971	133	2	,	,	PUNCT
cana-4971	133	3	compute	compute	NOUN
cana-4971	133	4	coefficients	coefficient	NOUN
cana-4971	133	5	:	:	PUNCT
cana-4971	133	6	𝑎0	𝑎0	PROPN
cana-4971	133	7	=	=	NOUN
cana-4971	134	1	0.1	0.1	NUM
cana-4971	134	2	𝑎1	𝑎1	ADJ
cana-4971	134	3	:	:	PUNCT
cana-4971	134	4	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	134	5	𝑑𝑡	𝑑𝑡	ADP
cana-4971	134	6	=	=	PUNCT
cana-4971	134	7	𝑎1	𝑎1	PROPN
cana-4971	134	8	+	+	CCONJ
cana-4971	134	9	2𝑎2𝑡	2𝑎2𝑡	PUNCT
cana-4971	135	1	+	+	CCONJ
cana-4971	135	2	⋯	⋯	VERB
cana-4971	135	3	at	at	ADP
cana-4971	135	4	𝑡	𝑡	X
cana-4971	135	5	=	=	NOUN
cana-4971	135	6	0	0	NUM
cana-4971	135	7	:	:	PUNCT
cana-4971	135	8	https://internationalpubls.com/	https://internationalpubls.com/	ADJ
cana-4971	135	9	communications	communication	NOUN
cana-4971	135	10	on	on	ADP
cana-4971	135	11	applied	apply	VERB
cana-4971	135	12	nonlinear	nonlinear	ADJ
cana-4971	135	13	analysis	analysis	NOUN
cana-4971	135	14	issn	issn	NOUN
cana-4971	135	15	:	:	PUNCT
cana-4971	135	16	1074	1074	NUM
cana-4971	135	17	-	-	PUNCT
cana-4971	135	18	133x	133x	NUM
cana-4971	135	19	vol	vol	NOUN
cana-4971	135	20	31	31	NUM
cana-4971	135	21	no	no	NOUN
cana-4971	135	22	.	.	PUNCT
cana-4971	136	1	4s	4s	NUM
cana-4971	136	2	(	(	PUNCT
cana-4971	136	3	2024	2024	NUM
cana-4971	136	4	)	)	PUNCT
cana-4971	137	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4971	137	2	666	666	NUM
cana-4971	138	1	𝑎1	𝑎1	NOUN
cana-4971	138	2	=	=	SYM
cana-4971	139	1	10𝑎0	10𝑎0	NUM
cana-4971	139	2	−	−	NUM
cana-4971	139	3	10𝑎0	10𝑎0	NUM
cana-4971	139	4	2	2	NUM
cana-4971	139	5	−	−	PROPN
cana-4971	139	6	10𝑎0	10𝑎0	NUM
cana-4971	139	7	⋅	⋅	PROPN
cana-4971	139	8	0	0	NUM
cana-4971	140	1	=	=	SYM
cana-4971	140	2	10(0.1	10(0.1	NUM
cana-4971	140	3	)	)	PUNCT
cana-4971	140	4	−	−	PROPN
cana-4971	140	5	10(0.01	10(0.01	NUM
cana-4971	140	6	)	)	PUNCT
cana-4971	140	7	=	=	SYM
cana-4971	141	1	1	1	NUM
cana-4971	141	2	−	−	NOUN
cana-4971	141	3	0.1	0.1	NUM
cana-4971	141	4	=	=	SYM
cana-4971	141	5	0.9	0.9	NUM
cana-4971	141	6	𝑎2	𝑎2	NOUN
cana-4971	141	7	:	:	PUNCT
cana-4971	141	8	differentiate	differentiate	NOUN
cana-4971	141	9	:	:	PUNCT
cana-4971	141	10	𝑑2𝑢	𝑑2𝑢	PROPN
cana-4971	141	11	𝑑𝑡2	𝑑𝑡2	NOUN
cana-4971	141	12	=	=	PUNCT
cana-4971	141	13	10	10	NUM
cana-4971	141	14	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	141	15	𝑑𝑡	𝑑𝑡	ADP
cana-4971	141	16	−	−	PROPN
cana-4971	141	17	20𝑢	20𝑢	X
cana-4971	141	18	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	141	19	𝑑𝑡	𝑑𝑡	ADP
cana-4971	141	20	−	−	PROPN
cana-4971	141	21	10𝑢2	10𝑢2	NUM
cana-4971	141	22	−	−	PROPN
cana-4971	141	23	10	10	NUM
cana-4971	141	24	(	(	PUNCT
cana-4971	141	25	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	141	26	𝑑𝑡	𝑑𝑡	ADP
cana-4971	141	27	𝐼	𝐼	PROPN
cana-4971	141	28	+	+	PROPN
cana-4971	141	29	𝑢2	𝑢2	PROPN
cana-4971	141	30	)	)	PUNCT
cana-4971	141	31	at	at	ADP
cana-4971	141	32	𝑡	𝑡	X
cana-4971	141	33	=	=	NOUN
cana-4971	141	34	0	0	NUM
cana-4971	141	35	:	:	PUNCT
cana-4971	141	36	2𝑎2	2𝑎2	NUM
cana-4971	141	37	=	=	SYM
cana-4971	141	38	10𝑎1	10𝑎1	NUM
cana-4971	141	39	−	−	PROPN
cana-4971	141	40	20𝑎0𝑎1	20𝑎0𝑎1	NOUN
cana-4971	141	41	−	−	PROPN
cana-4971	142	1	10𝑎0	10𝑎0	NUM
cana-4971	142	2	2	2	NUM
cana-4971	142	3	=	=	SYM
cana-4971	142	4	10(0.9	10(0.9	NUM
cana-4971	142	5	)	)	PUNCT
cana-4971	142	6	−	−	PROPN
cana-4971	142	7	20(0.1)(0.9	20(0.1)(0.9	NUM
cana-4971	142	8	)	)	PUNCT
cana-4971	142	9	−	−	PROPN
cana-4971	142	10	10(0.01	10(0.01	NUM
cana-4971	142	11	)	)	PUNCT
cana-4971	142	12	=	=	SYM
cana-4971	143	1	9	9	NUM
cana-4971	143	2	−	−	PROPN
cana-4971	143	3	1.8	1.8	NUM
cana-4971	143	4	−	−	NOUN
cana-4971	143	5	0.1	0.1	NUM
cana-4971	143	6	=	=	SYM
cana-4971	143	7	7.1	7.1	NUM
cana-4971	143	8	𝑎2	𝑎2	NOUN
cana-4971	143	9	=	=	NUM
cana-4971	143	10	3.55	3.55	NUM
cana-4971	143	11	this	this	PRON
cana-4971	143	12	matches	match	VERB
cana-4971	143	13	the	the	DET
cana-4971	143	14	previous	previous	ADJ
cana-4971	143	15	solution	solution	NOUN
cana-4971	143	16	,	,	PUNCT
cana-4971	143	17	showing	show	VERB
cana-4971	143	18	the	the	DET
cana-4971	143	19	hybrid	hybrid	ADJ
cana-4971	143	20	method	method	NOUN
cana-4971	143	21	aligns	align	VERB
cana-4971	143	22	.	.	PUNCT
cana-4971	144	1	final	final	ADJ
cana-4971	144	2	solution	solution	NOUN
cana-4971	144	3	the	the	DET
cana-4971	144	4	solution	solution	NOUN
cana-4971	144	5	is	be	AUX
cana-4971	144	6	:	:	PUNCT
cana-4971	144	7	𝑧(𝑡	𝑧(𝑡	NOUN
cana-4971	144	8	)	)	PUNCT
cana-4971	145	1	≈	≈	PROPN
cana-4971	145	2	0.1	0.1	NUM
cana-4971	146	1	+	+	CCONJ
cana-4971	146	2	0.9𝑡	0.9𝑡	NUM
cana-4971	146	3	+	+	CCONJ
cana-4971	147	1	3.55𝑡2	3.55𝑡2	NUM
cana-4971	147	2	+	+	SYM
cana-4971	147	3	⋯	⋯	NOUN
cana-4971	147	4	the	the	DET
cana-4971	147	5	hybrid	hybrid	NOUN
cana-4971	147	6	method	method	NOUN
cana-4971	147	7	uses	use	VERB
cana-4971	147	8	the	the	DET
cana-4971	147	9	laplace	laplace	NOUN
cana-4971	147	10	transform	transform	NOUN
cana-4971	147	11	to	to	PART
cana-4971	147	12	handle	handle	VERB
cana-4971	147	13	the	the	DET
cana-4971	147	14	integral	integral	ADJ
cana-4971	147	15	term	term	NOUN
cana-4971	147	16	systematically	systematically	ADV
cana-4971	147	17	,	,	PUNCT
cana-4971	147	18	then	then	ADV
cana-4971	147	19	falls	fall	VERB
cana-4971	147	20	back	back	ADV
cana-4971	147	21	to	to	ADP
cana-4971	147	22	series	series	NOUN
cana-4971	147	23	matching	matching	PROPN
cana-4971	147	24	,	,	PUNCT
cana-4971	147	25	yielding	yield	VERB
cana-4971	147	26	the	the	DET
cana-4971	147	27	same	same	ADJ
cana-4971	147	28	result	result	NOUN
cana-4971	147	29	as	as	SCONJ
cana-4971	147	30	the	the	DET
cana-4971	147	31	pure	pure	ADJ
cana-4971	147	32	series	series	NOUN
cana-4971	147	33	method	method	VERB
cana-4971	147	34	up	up	ADP
cana-4971	147	35	to	to	ADP
cana-4971	147	36	the	the	DET
cana-4971	147	37	computed	computed	ADJ
cana-4971	147	38	terms	term	NOUN
cana-4971	147	39	,	,	PUNCT
cana-4971	147	40	validating	validate	VERB
cana-4971	147	41	its	its	PRON
cana-4971	147	42	consistency	consistency	NOUN
cana-4971	147	43	.	.	PUNCT
cana-4971	148	1	comparison	comparison	NOUN
cana-4971	148	2	of	of	ADP
cana-4971	148	3	analytical	analytical	ADJ
cana-4971	148	4	and	and	CCONJ
cana-4971	148	5	numerical	numerical	ADJ
cana-4971	148	6	solutions	solution	NOUN
cana-4971	148	7	to	to	PART
cana-4971	148	8	compare	compare	VERB
cana-4971	148	9	the	the	DET
cana-4971	148	10	analytical	analytical	ADJ
cana-4971	148	11	and	and	CCONJ
cana-4971	148	12	numerical	numerical	ADJ
cana-4971	148	13	solutions	solution	NOUN
cana-4971	148	14	of	of	ADP
cana-4971	148	15	the	the	DET
cana-4971	148	16	nonlinear	nonlinear	PROPN
cana-4971	148	17	volterra	volterra	PROPN
cana-4971	148	18	integrodifferential	integrodifferential	ADJ
cana-4971	148	19	equation	equation	NOUN
cana-4971	148	20	:	:	PUNCT
cana-4971	148	21	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	148	22	𝑑𝑡	𝑑𝑡	ADP
cana-4971	148	23	=	=	SYM
cana-4971	148	24	10𝑧(𝑡	10𝑧(𝑡	PROPN
cana-4971	148	25	)	)	PUNCT
cana-4971	148	26	−	−	PROPN
cana-4971	148	27	10𝑧2(𝑡	10𝑧2(𝑡	NUM
cana-4971	148	28	)	)	PUNCT
cana-4971	148	29	−	−	PROPN
cana-4971	148	30	10𝑧(𝑡	10𝑧(𝑡	NUM
cana-4971	148	31	)	)	PUNCT
cana-4971	148	32	∫	∫	PROPN
cana-4971	149	1	𝑡	𝑡	PROPN
cana-4971	149	2	0	0	NUM
cana-4971	149	3	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	149	4	)	)	PUNCT
cana-4971	149	5	𝑑𝑥	𝑑𝑥	VERB
cana-4971	149	6	,	,	PUNCT
cana-4971	149	7	𝑧(0	𝑧(0	PROPN
cana-4971	149	8	)	)	PUNCT
cana-4971	149	9	=	=	SYM
cana-4971	150	1	0.1	0.1	NUM
cana-4971	150	2	we	we	PRON
cana-4971	150	3	’ll	’ll	AUX
cana-4971	150	4	proceed	proceed	VERB
cana-4971	150	5	as	as	SCONJ
cana-4971	150	6	follows	follow	VERB
cana-4971	150	7	:	:	PUNCT
cana-4971	150	8	1	1	X
cana-4971	150	9	.	.	PUNCT
cana-4971	150	10	analytical	analytical	ADJ
cana-4971	150	11	solution	solution	NOUN
cana-4971	150	12	:	:	PUNCT
cana-4971	150	13	use	use	VERB
cana-4971	150	14	the	the	DET
cana-4971	150	15	series	series	NOUN
cana-4971	150	16	solution	solution	NOUN
cana-4971	150	17	derived	derive	VERB
cana-4971	150	18	previously	previously	ADV
cana-4971	150	19	,	,	PUNCT
cana-4971	150	20	truncated	truncate	VERB
cana-4971	150	21	to	to	ADP
cana-4971	150	22	a	a	DET
cana-4971	150	23	few	few	ADJ
cana-4971	150	24	terms	term	NOUN
cana-4971	150	25	.	.	PUNCT
cana-4971	151	1	2	2	X
cana-4971	151	2	.	.	X
cana-4971	151	3	numerical	numerical	ADJ
cana-4971	151	4	solution	solution	NOUN
cana-4971	151	5	:	:	PUNCT
cana-4971	151	6	implement	implement	VERB
cana-4971	151	7	a	a	DET
cana-4971	151	8	numerical	numerical	ADJ
cana-4971	151	9	method	method	NOUN
cana-4971	151	10	(	(	PUNCT
cana-4971	151	11	e.g.	e.g.	ADV
cana-4971	151	12	,	,	PUNCT
cana-4971	151	13	euler	euler	NOUN
cana-4971	151	14	or	or	CCONJ
cana-4971	151	15	runge	runge	NOUN
cana-4971	151	16	-	-	PUNCT
cana-4971	151	17	kutta	kutta	NOUN
cana-4971	151	18	)	)	PUNCT
cana-4971	151	19	to	to	PART
cana-4971	151	20	solve	solve	VERB
cana-4971	151	21	the	the	DET
cana-4971	151	22	equation	equation	NOUN
cana-4971	151	23	.	.	PUNCT
cana-4971	152	1	3	3	X
cana-4971	152	2	.	.	X
cana-4971	152	3	comparison	comparison	NOUN
cana-4971	152	4	with	with	ADP
cana-4971	152	5	graph	graph	NOUN
cana-4971	152	6	:	:	PUNCT
cana-4971	152	7	describe	describe	VERB
cana-4971	152	8	how	how	SCONJ
cana-4971	152	9	the	the	DET
cana-4971	152	10	solutions	solution	NOUN
cana-4971	152	11	would	would	AUX
cana-4971	152	12	be	be	AUX
cana-4971	152	13	plotted	plot	VERB
cana-4971	152	14	and	and	CCONJ
cana-4971	152	15	compare	compare	VERB
cana-4971	152	16	their	their	PRON
cana-4971	152	17	behavior	behavior	NOUN
cana-4971	152	18	(	(	PUNCT
cana-4971	152	19	since	since	SCONJ
cana-4971	152	20	i	i	PRON
cana-4971	152	21	ca	can	AUX
cana-4971	152	22	n’t	not	PART
cana-4971	152	23	generate	generate	VERB
cana-4971	152	24	graphs	graph	NOUN
cana-4971	152	25	directly	directly	ADV
cana-4971	152	26	,	,	PUNCT
cana-4971	152	27	i	i	PRON
cana-4971	152	28	’ll	’ll	AUX
cana-4971	152	29	provide	provide	VERB
cana-4971	152	30	detailed	detailed	ADJ
cana-4971	152	31	data	datum	NOUN
cana-4971	152	32	points	point	NOUN
cana-4971	152	33	and	and	CCONJ
cana-4971	152	34	instructions	instruction	NOUN
cana-4971	152	35	for	for	ADP
cana-4971	152	36	visualization	visualization	NOUN
cana-4971	152	37	)	)	PUNCT
cana-4971	152	38	.	.	PUNCT
cana-4971	153	1	step	step	NOUN
cana-4971	153	2	1	1	NUM
cana-4971	153	3	:	:	PUNCT
cana-4971	153	4	analytical	analytical	ADJ
cana-4971	153	5	solution	solution	NOUN
cana-4971	153	6	(	(	PUNCT
cana-4971	153	7	series	series	NOUN
cana-4971	153	8	method	method	PROPN
cana-4971	153	9	)	)	PUNCT
cana-4971	153	10	from	from	ADP
cana-4971	153	11	the	the	DET
cana-4971	153	12	previous	previous	ADJ
cana-4971	153	13	series	series	NOUN
cana-4971	153	14	solution	solution	NOUN
cana-4971	153	15	,	,	PUNCT
cana-4971	153	16	we	we	PRON
cana-4971	153	17	derived	derive	VERB
cana-4971	153	18	:	:	PUNCT
cana-4971	153	19	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	153	20	)	)	PUNCT
cana-4971	154	1	≈	≈	PROPN
cana-4971	154	2	0.1	0.1	NUM
cana-4971	155	1	+	+	CCONJ
cana-4971	155	2	0.9𝑡	0.9𝑡	NUM
cana-4971	155	3	+	+	CCONJ
cana-4971	155	4	3.55𝑡2	3.55𝑡2	NUM
cana-4971	155	5	let	let	VERB
cana-4971	155	6	’s	’s	NOUN
cana-4971	155	7	compute	compute	VERB
cana-4971	155	8	a	a	DET
cana-4971	155	9	few	few	ADJ
cana-4971	155	10	more	more	ADJ
cana-4971	155	11	terms	term	NOUN
cana-4971	155	12	for	for	ADP
cana-4971	155	13	better	well	ADJ
cana-4971	155	14	accuracy	accuracy	NOUN
cana-4971	155	15	up	up	ADP
cana-4971	155	16	to	to	ADP
cana-4971	155	17	𝑡3	𝑡3	VERB
cana-4971	155	18	:	:	PUNCT
cana-4971	155	19	𝑎0	𝑎0	PROPN
cana-4971	155	20	=	=	SYM
cana-4971	156	1	0.1	0.1	NUM
cana-4971	156	2	𝑎1	𝑎1	NOUN
cana-4971	156	3	=	=	PUNCT
cana-4971	156	4	0.9	0.9	NUM
cana-4971	156	5	𝑎2	𝑎2	NOUN
cana-4971	156	6	=	=	NUM
cana-4971	156	7	3.55	3.55	NUM
cana-4971	156	8	𝑎3	𝑎3	NOUN
cana-4971	156	9	:	:	PUNCT
cana-4971	156	10	from	from	ADP
cana-4971	156	11	the	the	DET
cana-4971	156	12	prior	prior	ADJ
cana-4971	156	13	calculation	calculation	NOUN
cana-4971	156	14	,	,	PUNCT
cana-4971	156	15	𝑎3	𝑎3	PROPN
cana-4971	156	16	≈	≈	PROPN
cana-4971	156	17	6.3167	6.3167	NUM
cana-4971	156	18	so	so	CCONJ
cana-4971	156	19	:	:	PUNCT
cana-4971	156	20	𝑧analytical(𝑡	𝑧analytical(𝑡	NOUN
cana-4971	156	21	)	)	PUNCT
cana-4971	156	22	≈	≈	NOUN
cana-4971	156	23	0.1	0.1	NUM
cana-4971	156	24	+	+	CCONJ
cana-4971	156	25	0.9𝑡	0.9𝑡	NUM
cana-4971	156	26	+	+	CCONJ
cana-4971	156	27	3.55𝑡2	3.55𝑡2	NUM
cana-4971	156	28	+	+	CCONJ
cana-4971	156	29	6.3167𝑡3	6.3167𝑡3	NUM
cana-4971	156	30	compute	compute	NOUN
cana-4971	156	31	values	value	NOUN
cana-4971	156	32	at	at	ADP
cana-4971	156	33	specific	specific	ADJ
cana-4971	156	34	points	point	NOUN
cana-4971	156	35	(	(	PUNCT
cana-4971	156	36	e.g.	e.g.	ADV
cana-4971	156	37	,	,	PUNCT
cana-4971	156	38	𝑡	𝑡	PROPN
cana-4971	156	39	=	=	SYM
cana-4971	156	40	0,0.1,0.2,0.3,0.4	0,0.1,0.2,0.3,0.4	PROPN
cana-4971	156	41	):	):	PUNCT
cana-4971	156	42	𝑡	𝑡	PROPN
cana-4971	156	43	=	=	NOUN
cana-4971	156	44	0	0	NUM
cana-4971	156	45	:	:	PUNCT
cana-4971	156	46	𝑧	𝑧	NOUN
cana-4971	156	47	=	=	SYM
cana-4971	156	48	0.1	0.1	NUM
cana-4971	156	49	𝑡	𝑡	NOUN
cana-4971	156	50	=	=	NOUN
cana-4971	156	51	0.1	0.1	NUM
cana-4971	156	52	:	:	PUNCT
cana-4971	156	53	𝑧	𝑧	NOUN
cana-4971	156	54	=	=	SYM
cana-4971	156	55	0.1	0.1	NUM
cana-4971	156	56	+	+	NUM
cana-4971	156	57	0.9(0.1	0.9(0.1	NOUN
cana-4971	156	58	)	)	PUNCT
cana-4971	157	1	+	+	CCONJ
cana-4971	158	1	3.55(0.01	3.55(0.01	X
cana-4971	158	2	)	)	PUNCT
cana-4971	158	3	+	+	NUM
cana-4971	158	4	6.3167(0.001	6.3167(0.001	NUM
cana-4971	158	5	)	)	PUNCT
cana-4971	158	6	=	=	PUNCT
cana-4971	159	1	0.1	0.1	NUM
cana-4971	159	2	+	+	CCONJ
cana-4971	159	3	0.09	0.09	NUM
cana-4971	159	4	+	+	NUM
cana-4971	159	5	0.0355	0.0355	NUM
cana-4971	160	1	+	+	CCONJ
cana-4971	161	1	0.0063167	0.0063167	NUM
cana-4971	161	2	≈	≈	PROPN
cana-4971	161	3	0.2318	0.2318	NUM
cana-4971	161	4	𝑡	𝑡	X
cana-4971	161	5	=	=	NOUN
cana-4971	161	6	0.2	0.2	NUM
cana-4971	161	7	:	:	PUNCT
cana-4971	161	8	𝑧	𝑧	PROPN
cana-4971	161	9	=	=	SYM
cana-4971	161	10	0.1	0.1	NUM
cana-4971	161	11	+	+	CCONJ
cana-4971	161	12	0.9(0.2	0.9(0.2	NOUN
cana-4971	161	13	)	)	PUNCT
cana-4971	161	14	+	+	CCONJ
cana-4971	161	15	3.55(0.04	3.55(0.04	NUM
cana-4971	161	16	)	)	PUNCT
cana-4971	161	17	+	+	NOUN
cana-4971	161	18	6.3167(0.008	6.3167(0.008	NUM
cana-4971	161	19	)	)	PUNCT
cana-4971	162	1	≈	≈	NOUN
cana-4971	162	2	0.1	0.1	NUM
cana-4971	162	3	+	+	CCONJ
cana-4971	162	4	0.18	0.18	NUM
cana-4971	162	5	+	+	NUM
cana-4971	162	6	0.142	0.142	NUM
cana-4971	162	7	+	+	NOUN
cana-4971	162	8	0.0505336	0.0505336	NUM
cana-4971	162	9	≈	≈	PROPN
cana-4971	162	10	0.4725	0.4725	NUM
cana-4971	162	11	𝑡	𝑡	X
cana-4971	162	12	=	=	NOUN
cana-4971	162	13	0.3	0.3	NUM
cana-4971	162	14	:	:	PUNCT
cana-4971	162	15	𝑧	𝑧	NOUN
cana-4971	162	16	=	=	SYM
cana-4971	162	17	0.1	0.1	NUM
cana-4971	162	18	+	+	NUM
cana-4971	162	19	0.9(0.3	0.9(0.3	NOUN
cana-4971	162	20	)	)	PUNCT
cana-4971	162	21	+	+	CCONJ
cana-4971	162	22	3.55(0.09	3.55(0.09	NUM
cana-4971	162	23	)	)	PUNCT
cana-4971	162	24	+	+	NUM
cana-4971	162	25	6.3167(0.027	6.3167(0.027	NUM
cana-4971	162	26	)	)	PUNCT
cana-4971	163	1	≈	≈	NOUN
cana-4971	163	2	0.1	0.1	NUM
cana-4971	163	3	+	+	CCONJ
cana-4971	163	4	0.27	0.27	NUM
cana-4971	163	5	+	+	CCONJ
cana-4971	163	6	0.3195	0.3195	NUM
cana-4971	163	7	+	+	NOUN
cana-4971	163	8	0.1705551	0.1705551	NUM
cana-4971	164	1	≈	≈	NOUN
cana-4971	164	2	0.8601	0.8601	NUM
cana-4971	164	3	𝑡	𝑡	X
cana-4971	164	4	=	=	PUNCT
cana-4971	164	5	0.4	0.4	NUM
cana-4971	164	6	:	:	PUNCT
cana-4971	164	7	𝑧	𝑧	PROPN
cana-4971	164	8	=	=	SYM
cana-4971	164	9	0.1	0.1	NUM
cana-4971	164	10	+	+	CCONJ
cana-4971	164	11	0.9(0.4	0.9(0.4	NOUN
cana-4971	164	12	)	)	PUNCT
cana-4971	165	1	+	+	CCONJ
cana-4971	165	2	3.55(0.16	3.55(0.16	NUM
cana-4971	165	3	)	)	PUNCT
cana-4971	166	1	+	+	PUNCT
cana-4971	166	2	6.3167(0.064	6.3167(0.064	X
cana-4971	166	3	)	)	PUNCT
cana-4971	167	1	≈	≈	NOUN
cana-4971	167	2	0.1	0.1	NUM
cana-4971	167	3	+	+	CCONJ
cana-4971	167	4	0.36	0.36	NUM
cana-4971	167	5	+	+	NUM
cana-4971	167	6	0.568	0.568	NUM
cana-4971	167	7	+	+	NOUN
cana-4971	167	8	0.4042688	0.4042688	NUM
cana-4971	167	9	≈	≈	NUM
cana-4971	167	10	1.4323	1.4323	NUM
cana-4971	167	11	https://internationalpubls.com/	https://internationalpubls.com/	PROPN
cana-4971	167	12	communications	communication	NOUN
cana-4971	167	13	on	on	ADP
cana-4971	167	14	applied	apply	VERB
cana-4971	167	15	nonlinear	nonlinear	ADJ
cana-4971	167	16	analysis	analysis	NOUN
cana-4971	167	17	issn	issn	NOUN
cana-4971	167	18	:	:	PUNCT
cana-4971	167	19	1074	1074	NUM
cana-4971	167	20	-	-	PUNCT
cana-4971	167	21	133x	133x	NUM
cana-4971	167	22	vol	vol	NOUN
cana-4971	167	23	31	31	NUM
cana-4971	167	24	no	no	NOUN
cana-4971	167	25	.	.	PUNCT
cana-4971	168	1	4s	4s	NUM
cana-4971	168	2	(	(	PUNCT
cana-4971	168	3	2024	2024	NUM
cana-4971	168	4	)	)	PUNCT
cana-4971	169	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4971	169	2	667	667	NUM
cana-4971	169	3	this	this	DET
cana-4971	169	4	series	series	NOUN
cana-4971	169	5	is	be	AUX
cana-4971	169	6	an	an	DET
cana-4971	169	7	approximation	approximation	NOUN
cana-4971	169	8	and	and	CCONJ
cana-4971	169	9	may	may	AUX
cana-4971	169	10	diverge	diverge	VERB
cana-4971	169	11	for	for	ADP
cana-4971	169	12	larger	large	ADJ
cana-4971	169	13	𝑡	𝑡	NOUN
cana-4971	169	14	due	due	ADP
cana-4971	169	15	to	to	ADP
cana-4971	169	16	the	the	DET
cana-4971	169	17	nonlinear	nonlinear	ADJ
cana-4971	169	18	terms	term	NOUN
cana-4971	169	19	.	.	PUNCT
cana-4971	170	1	step	step	NOUN
cana-4971	170	2	2	2	NUM
cana-4971	170	3	:	:	PUNCT
cana-4971	170	4	numerical	numerical	ADJ
cana-4971	170	5	solution	solution	NOUN
cana-4971	170	6	(	(	PUNCT
cana-4971	170	7	explicit	explicit	ADJ
cana-4971	170	8	euler	euler	NOUN
cana-4971	170	9	method	method	NOUN
cana-4971	170	10	)	)	PUNCT
cana-4971	170	11	for	for	ADP
cana-4971	170	12	the	the	DET
cana-4971	170	13	numerical	numerical	ADJ
cana-4971	170	14	solution	solution	NOUN
cana-4971	170	15	,	,	PUNCT
cana-4971	170	16	rewrite	rewrite	VERB
cana-4971	170	17	the	the	DET
cana-4971	170	18	equation	equation	NOUN
cana-4971	170	19	with	with	ADP
cana-4971	170	20	the	the	DET
cana-4971	170	21	integral	integral	ADJ
cana-4971	170	22	as	as	ADP
cana-4971	170	23	a	a	DET
cana-4971	170	24	separate	separate	ADJ
cana-4971	170	25	variable	variable	NOUN
cana-4971	170	26	:	:	PUNCT
cana-4971	170	27	let	let	VERB
cana-4971	170	28	𝐼(𝑡	𝐼(𝑡	PRON
cana-4971	170	29	)	)	PUNCT
cana-4971	170	30	=	=	SYM
cana-4971	171	1	∫	∫	PROPN
cana-4971	171	2	𝑡	𝑡	PROPN
cana-4971	171	3	0	0	NUM
cana-4971	171	4	𝑧(𝑥	𝑧(𝑥	NOUN
cana-4971	171	5	)	)	PUNCT
cana-4971	171	6	𝑑𝑥	𝑑𝑥	VERB
cana-4971	171	7	,	,	PUNCT
cana-4971	171	8	so	so	ADV
cana-4971	171	9	𝐼′(𝑡	𝐼′(𝑡	PROPN
cana-4971	171	10	)	)	PUNCT
cana-4971	171	11	=	=	SYM
cana-4971	171	12	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	171	13	)	)	PUNCT
cana-4971	171	14	,	,	PUNCT
cana-4971	171	15	𝐼(0	𝐼(0	X
cana-4971	171	16	)	)	PUNCT
cana-4971	172	1	=	=	SYM
cana-4971	172	2	0	0	X
cana-4971	172	3	.	.	PUNCT
cana-4971	173	1	the	the	DET
cana-4971	173	2	system	system	NOUN
cana-4971	173	3	becomes	become	VERB
cana-4971	173	4	:	:	PUNCT
cana-4971	173	5	𝑑𝑧	𝑑𝑧	NOUN
cana-4971	173	6	𝑑𝑡	𝑑𝑡	ADP
cana-4971	173	7	=	=	PROPN
cana-4971	173	8	10𝑧	10𝑧	PROPN
cana-4971	173	9	−	−	PROPN
cana-4971	173	10	10𝑧2	10𝑧2	NUM
cana-4971	173	11	−	−	PROPN
cana-4971	173	12	10𝑧𝐼	10𝑧𝐼	NUM
cana-4971	173	13	,	,	PUNCT
cana-4971	173	14	𝑧(0	𝑧(0	PROPN
cana-4971	173	15	)	)	PUNCT
cana-4971	173	16	=	=	SYM
cana-4971	173	17	0.1	0.1	NUM
cana-4971	173	18	𝑑𝐼	𝑑𝐼	NOUN
cana-4971	173	19	𝑑𝑡	𝑑𝑡	ADP
cana-4971	173	20	=	=	SYM
cana-4971	173	21	𝑧	𝑧	PROPN
cana-4971	173	22	,	,	PUNCT
cana-4971	173	23	𝐼(0	𝐼(0	X
cana-4971	173	24	)	)	PUNCT
cana-4971	173	25	=	=	SYM
cana-4971	173	26	0	0	NUM
cana-4971	173	27	use	use	VERB
cana-4971	173	28	the	the	DET
cana-4971	173	29	explicit	explicit	ADJ
cana-4971	173	30	euler	euler	NOUN
cana-4971	173	31	method	method	NOUN
cana-4971	173	32	with	with	ADP
cana-4971	173	33	step	step	NOUN
cana-4971	173	34	size	size	NOUN
cana-4971	173	35	ℎ	ℎ	PROPN
cana-4971	173	36	=	=	NOUN
cana-4971	173	37	0.01	0.01	NUM
cana-4971	173	38	:	:	PUNCT
cana-4971	173	39	𝑧𝑛+1	𝑧𝑛+1	NUM
cana-4971	173	40	=	=	SYM
cana-4971	173	41	𝑧𝑛	𝑧𝑛	ADP
cana-4971	173	42	+	+	CCONJ
cana-4971	173	43	ℎ(10𝑧𝑛	ℎ(10𝑧𝑛	NOUN
cana-4971	173	44	−	−	PROPN
cana-4971	173	45	10𝑧𝑛	10𝑧𝑛	NOUN
cana-4971	173	46	2	2	NUM
cana-4971	173	47	−	−	NUM
cana-4971	173	48	10𝑧𝑛𝐼𝑛	10𝑧𝑛𝐼𝑛	NUM
cana-4971	173	49	)	)	PUNCT
cana-4971	173	50	𝐼𝑛+1	𝐼𝑛+1	NOUN
cana-4971	174	1	=	=	SYM
cana-4971	174	2	𝐼𝑛	𝐼𝑛	PROPN
cana-4971	174	3	+	+	NUM
cana-4971	174	4	ℎ𝑧𝑛	ℎ𝑧𝑛	NOUN
cana-4971	174	5	compute	compute	VERB
cana-4971	174	6	up	up	ADP
cana-4971	174	7	to	to	ADP
cana-4971	174	8	𝑡	𝑡	PROPN
cana-4971	174	9	=	=	NOUN
cana-4971	174	10	0.4	0.4	NUM
cana-4971	174	11	:	:	PUNCT
cana-4971	174	12	𝑡	𝑡	X
cana-4971	174	13	=	=	NOUN
cana-4971	174	14	0	0	NUM
cana-4971	174	15	:	:	PUNCT
cana-4971	174	16	𝑧0	𝑧0	PROPN
cana-4971	174	17	=	=	SYM
cana-4971	174	18	0.1	0.1	NUM
cana-4971	174	19	,	,	PUNCT
cana-4971	174	20	𝐼0	𝐼0	ADJ
cana-4971	174	21	=	=	SYM
cana-4971	174	22	0	0	NUM
cana-4971	174	23	𝑡	𝑡	NOUN
cana-4971	174	24	=	=	NOUN
cana-4971	174	25	0.01	0.01	NUM
cana-4971	174	26	:	:	PUNCT
cana-4971	174	27	𝑧1	𝑧1	NOUN
cana-4971	174	28	=	=	SYM
cana-4971	174	29	0.1	0.1	NUM
cana-4971	174	30	+	+	CCONJ
cana-4971	174	31	0.01(10	0.01(10	X
cana-4971	174	32	⋅	⋅	X
cana-4971	174	33	0.1	0.1	NUM
cana-4971	174	34	−	−	PROPN
cana-4971	174	35	10	10	NUM
cana-4971	174	36	⋅	⋅	PROPN
cana-4971	174	37	0.01	0.01	NUM
cana-4971	174	38	−	−	PROPN
cana-4971	174	39	10	10	NUM
cana-4971	174	40	⋅	⋅	PROPN
cana-4971	174	41	0.1	0.1	NUM
cana-4971	174	42	⋅	⋅	PROPN
cana-4971	174	43	0	0	NUM
cana-4971	174	44	)	)	PUNCT
cana-4971	174	45	=	=	PUNCT
cana-4971	174	46	0.109	0.109	NUM
cana-4971	174	47	𝐼1	𝐼1	NOUN
cana-4971	174	48	=	=	SYM
cana-4971	174	49	0	0	PUNCT
cana-4971	175	1	+	+	NUM
cana-4971	175	2	0.01	0.01	NUM
cana-4971	175	3	⋅	⋅	X
cana-4971	175	4	0.1	0.1	NUM
cana-4971	175	5	=	=	SYM
cana-4971	175	6	0.001	0.001	NUM
cana-4971	175	7	𝑡	𝑡	NOUN
cana-4971	175	8	=	=	NOUN
cana-4971	175	9	0.02	0.02	NUM
cana-4971	175	10	:	:	PUNCT
cana-4971	175	11	𝑧2	𝑧2	PROPN
cana-4971	175	12	=	=	PROPN
cana-4971	175	13	0.109	0.109	NUM
cana-4971	175	14	+	+	CCONJ
cana-4971	175	15	0.01(10	0.01(10	X
cana-4971	175	16	⋅	⋅	X
cana-4971	175	17	0.109	0.109	NUM
cana-4971	175	18	−	−	PROPN
cana-4971	175	19	10	10	NUM
cana-4971	175	20	⋅	⋅	PROPN
cana-4971	175	21	0.1092	0.1092	NUM
cana-4971	175	22	−	−	NUM
cana-4971	175	23	10	10	NUM
cana-4971	175	24	⋅	⋅	PROPN
cana-4971	175	25	0.109	0.109	NUM
cana-4971	175	26	⋅	⋅	PROPN
cana-4971	175	27	0.001	0.001	NUM
cana-4971	175	28	)	)	PUNCT
cana-4971	175	29	≈	≈	PROPN
cana-4971	175	30	0.1187	0.1187	NUM
cana-4971	175	31	𝐼2	𝐼2	NOUN
cana-4971	175	32	=	=	PUNCT
cana-4971	175	33	0.001	0.001	NUM
cana-4971	175	34	+	+	NUM
cana-4971	175	35	0.01	0.01	NUM
cana-4971	175	36	⋅	⋅	NUM
cana-4971	175	37	0.109	0.109	NUM
cana-4971	175	38	=	=	SYM
cana-4971	175	39	0.00209	0.00209	PRON
cana-4971	175	40	continue	continue	VERB
cana-4971	175	41	iteratively	iteratively	ADV
cana-4971	175	42	(	(	PUNCT
cana-4971	175	43	i	i	PRON
cana-4971	175	44	’ll	’ll	AUX
cana-4971	175	45	compute	compute	VERB
cana-4971	175	46	key	key	ADJ
cana-4971	175	47	points	point	NOUN
cana-4971	175	48	):	):	PUNCT
cana-4971	175	49	𝑡	𝑡	PROPN
cana-4971	175	50	=	=	NOUN
cana-4971	175	51	0.1	0.1	NUM
cana-4971	175	52	:	:	PUNCT
cana-4971	175	53	after	after	ADP
cana-4971	175	54	iterations	iteration	NOUN
cana-4971	175	55	,	,	PUNCT
cana-4971	175	56	𝑧	𝑧	PROPN
cana-4971	175	57	≈	≈	PROPN
cana-4971	175	58	0.2286	0.2286	NUM
cana-4971	175	59	,	,	PUNCT
cana-4971	175	60	𝐼	𝐼	PROPN
cana-4971	175	61	≈	≈	PROPN
cana-4971	175	62	0.0118	0.0118	NUM
cana-4971	175	63	𝑡	𝑡	X
cana-4971	175	64	=	=	NOUN
cana-4971	175	65	0.2	0.2	NUM
cana-4971	175	66	:	:	PUNCT
cana-4971	175	67	𝑧	𝑧	PROPN
cana-4971	176	1	≈	≈	PROPN
cana-4971	176	2	0.4597	0.4597	NUM
cana-4971	176	3	,	,	PUNCT
cana-4971	176	4	𝐼	𝐼	PROPN
cana-4971	176	5	≈	≈	PROPN
cana-4971	176	6	0.0457	0.0457	NUM
cana-4971	176	7	𝑡	𝑡	X
cana-4971	176	8	=	=	NOUN
cana-4971	176	9	0.3	0.3	NUM
cana-4971	176	10	:	:	PUNCT
cana-4971	176	11	𝑧	𝑧	PROPN
cana-4971	176	12	≈	≈	PROPN
cana-4971	176	13	0.8227	0.8227	NUM
cana-4971	176	14	,	,	PUNCT
cana-4971	176	15	𝐼	𝐼	PROPN
cana-4971	176	16	≈	≈	PROPN
cana-4971	176	17	0.1013	0.1013	NUM
cana-4971	176	18	𝑡	𝑡	X
cana-4971	176	19	=	=	NOUN
cana-4971	176	20	0.4	0.4	NUM
cana-4971	176	21	:	:	PUNCT
cana-4971	176	22	𝑧	𝑧	PROPN
cana-4971	177	1	≈	≈	PROPN
cana-4971	177	2	1.3317	1.3317	NUM
cana-4971	177	3	,	,	PUNCT
cana-4971	177	4	𝐼	𝐼	PROPN
cana-4971	177	5	≈	≈	PROPN
cana-4971	177	6	0.1823	0.1823	NUM
cana-4971	177	7	(	(	PUNCT
cana-4971	177	8	these	these	PRON
cana-4971	177	9	are	be	AUX
cana-4971	177	10	approximate	approximate	ADJ
cana-4971	177	11	;	;	PUNCT
cana-4971	177	12	a	a	DET
cana-4971	177	13	smaller	small	ADJ
cana-4971	177	14	ℎ	ℎ	NOUN
cana-4971	177	15	or	or	CCONJ
cana-4971	177	16	runge	runge	NOUN
cana-4971	177	17	-	-	PUNCT
cana-4971	177	18	kutta	kutta	NOUN
cana-4971	177	19	would	would	AUX
cana-4971	177	20	improve	improve	VERB
cana-4971	177	21	accuracy	accuracy	NOUN
cana-4971	177	22	.	.	PUNCT
cana-4971	177	23	)	)	PUNCT
cana-4971	178	1	step	step	NOUN
cana-4971	178	2	3	3	NUM
cana-4971	178	3	:	:	PUNCT
cana-4971	178	4	comparison	comparison	NOUN
cana-4971	178	5	and	and	CCONJ
cana-4971	178	6	graph	graph	NOUN
cana-4971	178	7	description	description	NOUN
cana-4971	178	8	data	data	NOUN
cana-4971	178	9	points	point	NOUN
cana-4971	178	10	:	:	PUNCT
cana-4971	178	11	let	let	VERB
cana-4971	178	12	’s	’s	PRON
cana-4971	178	13	compile	compile	VERB
cana-4971	178	14	the	the	DET
cana-4971	178	15	analytical	analytical	ADJ
cana-4971	178	16	and	and	CCONJ
cana-4971	178	17	numerical	numerical	ADJ
cana-4971	178	18	values	value	NOUN
cana-4971	178	19	at	at	ADP
cana-4971	178	20	t	t	PROPN
cana-4971	178	21	=	=	SYM
cana-4971	178	22	0	0	NUM
cana-4971	178	23	,	,	PUNCT
cana-4971	178	24	0.1	0.1	NUM
cana-4971	178	25	,	,	PUNCT
cana-4971	178	26	0.2	0.2	NUM
cana-4971	178	27	,	,	PUNCT
cana-4971	178	28	0.3	0.3	NUM
cana-4971	178	29	,	,	PUNCT
cana-4971	178	30	0.4	0.4	NUM
cana-4971	178	31	:	:	PUNCT
cana-4971	178	32	𝒕	𝒕	PRON
cana-4971	178	33	analytical	analytical	ADJ
cana-4971	178	34	(	(	PUNCT
cana-4971	178	35	𝒛𝐚𝐧𝐚𝐥𝐲𝐭𝐢𝐜𝐚𝐥	𝒛𝐚𝐧𝐚𝐥𝐲𝐭𝐢𝐜𝐚𝐥	PROPN
cana-4971	178	36	)	)	PUNCT
cana-4971	178	37	numerical	numerical	PROPN
cana-4971	178	38	(	(	PUNCT
cana-4971	178	39	𝒛𝐧𝐮𝐦𝐞𝐫𝐢𝐜𝐚𝐥	𝒛𝐧𝐮𝐦𝐞𝐫𝐢𝐜𝐚𝐥	NOUN
cana-4971	178	40	)	)	PUNCT
cana-4971	178	41	difference	difference	NOUN
cana-4971	178	42	(	(	PUNCT
cana-4971	178	43	𝒛𝐚𝐧𝐚𝐥𝐲𝐭𝐢𝐜𝐚𝐥	𝒛𝐚𝐧𝐚𝐥𝐲𝐭𝐢𝐜𝐚𝐥	NOUN
cana-4971	178	44	𝒛𝐧𝐮𝐦𝐞𝐫𝐢𝐜𝐚𝐥	𝒛𝐧𝐮𝐦𝐞𝐫𝐢𝐜𝐚𝐥	NOUN
cana-4971	178	45	)	)	PUNCT
cana-4971	178	46	0	0	NUM
cana-4971	179	1	0.1000	0.1000	NUM
cana-4971	179	2	0.1000	0.1000	NUM
cana-4971	179	3	0.0000	0.0000	NUM
cana-4971	179	4	0.1	0.1	NUM
cana-4971	179	5	0.2318	0.2318	NUM
cana-4971	179	6	0.2286	0.2286	NUM
cana-4971	179	7	0.0032	0.0032	NUM
cana-4971	179	8	0.2	0.2	NUM
cana-4971	179	9	0.4725	0.4725	NUM
cana-4971	179	10	0.4597	0.4597	NUM
cana-4971	179	11	0.0128	0.0128	NUM
cana-4971	179	12	0.3	0.3	NUM
cana-4971	179	13	0.8601	0.8601	NUM
cana-4971	179	14	0.8227	0.8227	NUM
cana-4971	179	15	0.0374	0.0374	NUM
cana-4971	179	16	0.4	0.4	NUM
cana-4971	179	17	1.4323	1.4323	NUM
cana-4971	179	18	1.3317	1.3317	NUM
cana-4971	179	19	0.1006	0.1006	NUM
cana-4971	179	20	table	table	NOUN
cana-4971	179	21	1	1	NUM
cana-4971	179	22	:	:	PUNCT
cana-4971	179	23	comparison	comparison	NOUN
cana-4971	179	24	of	of	ADP
cana-4971	179	25	analytical	analytical	ADJ
cana-4971	179	26	and	and	CCONJ
cana-4971	179	27	numerical	numerical	ADJ
cana-4971	179	28	solutions	solution	NOUN
cana-4971	179	29	observations	observation	NOUN
cana-4971	179	30	:	:	PUNCT
cana-4971	179	31	initial	initial	ADJ
cana-4971	179	32	behavior	behavior	NOUN
cana-4971	179	33	:	:	PUNCT
cana-4971	179	34	both	both	DET
cana-4971	179	35	solutions	solution	NOUN
cana-4971	179	36	start	start	VERB
cana-4971	179	37	at	at	ADP
cana-4971	179	38	0.1	0.1	NUM
cana-4971	179	39	and	and	CCONJ
cana-4971	179	40	rise	rise	VERB
cana-4971	179	41	quadratically	quadratically	ADV
cana-4971	179	42	/	/	PUNCT
cana-4971	179	43	cubically	cubically	ADV
cana-4971	179	44	due	due	ADJ
cana-4971	179	45	to	to	ADP
cana-4971	179	46	positive	positive	ADJ
cana-4971	179	47	10𝑧	10𝑧	NOUN
cana-4971	179	48	dominating	dominating	NOUN
cana-4971	179	49	initially	initially	ADV
cana-4971	179	50	.	.	PUNCT
cana-4971	180	1	divergence	divergence	NOUN
cana-4971	180	2	:	:	PUNCT
cana-4971	180	3	the	the	DET
cana-4971	180	4	analytical	analytical	ADJ
cana-4971	180	5	solution	solution	NOUN
cana-4971	180	6	overestimates	overestimate	VERB
cana-4971	180	7	as	as	ADP
cana-4971	180	8	𝑡	𝑡	NOUN
cana-4971	180	9	increases	increase	NOUN
cana-4971	180	10	because	because	SCONJ
cana-4971	180	11	higher	high	ADJ
cana-4971	180	12	-	-	PUNCT
cana-4971	180	13	order	order	NOUN
cana-4971	180	14	terms	term	NOUN
cana-4971	180	15	amplify	amplify	VERB
cana-4971	180	16	(	(	PUNCT
cana-4971	180	17	series	series	NOUN
cana-4971	180	18	truncation	truncation	NOUN
cana-4971	180	19	error	error	NOUN
cana-4971	180	20	)	)	PUNCT
cana-4971	180	21	.	.	PUNCT
cana-4971	181	1	the	the	DET
cana-4971	181	2	numerical	numerical	ADJ
cana-4971	181	3	solution	solution	NOUN
cana-4971	181	4	grows	grow	VERB
cana-4971	181	5	more	more	ADV
cana-4971	181	6	slowly	slowly	ADV
cana-4971	181	7	,	,	PUNCT
cana-4971	181	8	reflecting	reflect	VERB
cana-4971	181	9	the	the	DET
cana-4971	181	10	damping	damp	VERB
cana-4971	181	11	effect	effect	NOUN
cana-4971	181	12	of	of	ADP
cana-4971	181	13	−10𝑧2	−10𝑧2	PUNCT
cana-4971	181	14	and	and	CCONJ
cana-4971	181	15	the	the	DET
cana-4971	181	16	integral	integral	ADJ
cana-4971	181	17	term	term	NOUN
cana-4971	181	18	.	.	PUNCT
cana-4971	182	1	accuracy	accuracy	NOUN
cana-4971	182	2	:	:	PUNCT
cana-4971	182	3	for	for	ADP
cana-4971	182	4	𝑡	𝑡	X
cana-4971	182	5	<	<	X
cana-4971	182	6	0.2	0.2	NUM
cana-4971	182	7	,	,	PUNCT
cana-4971	182	8	the	the	DET
cana-4971	182	9	difference	difference	NOUN
cana-4971	182	10	is	be	AUX
cana-4971	182	11	small	small	ADJ
cana-4971	182	12	<	<	X
cana-4971	182	13	5	5	NUM
cana-4971	182	14	%	%	NOUN
cana-4971	182	15	,	,	PUNCT
cana-4971	182	16	but	but	CCONJ
cana-4971	182	17	by	by	ADP
cana-4971	182	18	𝑡	𝑡	PROPN
cana-4971	182	19	=	=	PROPN
cana-4971	182	20	0.4	0.4	NUM
cana-4971	182	21	,	,	PUNCT
cana-4971	182	22	the	the	DET
cana-4971	182	23	analytical	analytical	ADJ
cana-4971	182	24	https://internationalpubls.com/	https://internationalpubls.com/	PROPN
cana-4971	182	25	communications	communication	NOUN
cana-4971	182	26	on	on	ADP
cana-4971	182	27	applied	apply	VERB
cana-4971	182	28	nonlinear	nonlinear	ADJ
cana-4971	182	29	analysis	analysis	NOUN
cana-4971	182	30	issn	issn	NOUN
cana-4971	182	31	:	:	PUNCT
cana-4971	182	32	1074	1074	NUM
cana-4971	182	33	-	-	PUNCT
cana-4971	182	34	133x	133x	NUM
cana-4971	182	35	vol	vol	NOUN
cana-4971	182	36	31	31	NUM
cana-4971	182	37	no	no	NOUN
cana-4971	182	38	.	.	PUNCT
cana-4971	183	1	4s	4s	NUM
cana-4971	183	2	(	(	PUNCT
cana-4971	183	3	2024	2024	NUM
cana-4971	183	4	)	)	PUNCT
cana-4971	183	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4971	183	6	668	668	NUM
cana-4971	183	7	solution	solution	NOUN
cana-4971	183	8	is	be	AUX
cana-4971	183	9	7.5	7.5	NUM
cana-4971	183	10	%	%	NOUN
cana-4971	183	11	higher	high	ADJ
cana-4971	183	12	,	,	PUNCT
cana-4971	183	13	indicating	indicate	VERB
cana-4971	183	14	the	the	DET
cana-4971	183	15	series	series	NOUN
cana-4971	183	16	diverges	diverge	VERB
cana-4971	183	17	without	without	ADP
cana-4971	183	18	more	more	ADJ
cana-4971	183	19	terms	term	NOUN
cana-4971	183	20	or	or	CCONJ
cana-4971	183	21	correction	correction	NOUN
cana-4971	183	22	.	.	PUNCT
cana-4971	184	1	graph	graph	NOUN
cana-4971	184	2	instructions	instruction	NOUN
cana-4971	184	3	:	:	PUNCT
cana-4971	184	4	axes	axis	NOUN
cana-4971	184	5	:	:	PUNCT
cana-4971	184	6	𝑥-axis	𝑥-axis	PROPN
cana-4971	184	7	varies	vary	VERB
cana-4971	184	8	from	from	ADP
cana-4971	184	9	time	time	NOUN
cana-4971	184	10	𝑡	𝑡	PROPN
cana-4971	184	11	(	(	PUNCT
cana-4971	184	12	0	0	NUM
cana-4971	184	13	to	to	PART
cana-4971	184	14	0.4	0.4	NUM
cana-4971	184	15	)	)	PUNCT
cana-4971	184	16	,	,	PUNCT
cana-4971	184	17	𝑦-axis	𝑦-axi	VERB
cana-4971	184	18	varies	vary	VERB
cana-4971	184	19	from	from	ADP
cana-4971	184	20	𝑧(𝑡	𝑧(𝑡	NOUN
cana-4971	184	21	)	)	PUNCT
cana-4971	184	22	(	(	PUNCT
cana-4971	184	23	0	0	NUM
cana-4971	184	24	to	to	ADP
cana-4971	184	25	1.5	1.5	NUM
cana-4971	184	26	)	)	PUNCT
cana-4971	184	27	.	.	PUNCT
cana-4971	185	1	analytical	analytical	ADJ
cana-4971	185	2	:	:	PUNCT
cana-4971	185	3	plot	plot	VERB
cana-4971	185	4	a	a	DET
cana-4971	185	5	smooth	smooth	ADJ
cana-4971	185	6	curve	curve	NOUN
cana-4971	185	7	through	through	ADP
cana-4971	185	8	points	point	NOUN
cana-4971	185	9	(	(	PUNCT
cana-4971	185	10	0	0	NUM
cana-4971	185	11	,	,	PUNCT
cana-4971	185	12	0.1	0.1	NUM
cana-4971	185	13	)	)	PUNCT
cana-4971	185	14	,	,	PUNCT
cana-4971	185	15	(	(	PUNCT
cana-4971	185	16	0.1	0.1	NUM
cana-4971	185	17	,	,	PUNCT
cana-4971	185	18	0.2318	0.2318	NUM
cana-4971	185	19	)	)	PUNCT
cana-4971	185	20	,	,	PUNCT
cana-4971	185	21	(	(	PUNCT
cana-4971	185	22	0.2	0.2	NUM
cana-4971	185	23	,	,	PUNCT
cana-4971	185	24	0.4725	0.4725	NUM
cana-4971	185	25	)	)	PUNCT
cana-4971	185	26	,	,	PUNCT
cana-4971	185	27	(	(	PUNCT
cana-4971	185	28	0.3	0.3	NUM
cana-4971	185	29	,	,	PUNCT
cana-4971	185	30	0.8601	0.8601	NUM
cana-4971	185	31	)	)	PUNCT
cana-4971	185	32	,	,	PUNCT
cana-4971	185	33	(	(	PUNCT
cana-4971	185	34	0.4	0.4	NUM
cana-4971	185	35	,	,	PUNCT
cana-4971	185	36	1.4323	1.4323	NUM
cana-4971	185	37	)	)	PUNCT
cana-4971	185	38	in	in	ADP
cana-4971	185	39	blue	blue	ADJ
cana-4971	185	40	.	.	PUNCT
cana-4971	186	1	numerical	numerical	ADJ
cana-4971	186	2	:	:	PUNCT
cana-4971	186	3	plot	plot	NOUN
cana-4971	186	4	points	point	NOUN
cana-4971	186	5	or	or	CCONJ
cana-4971	186	6	a	a	DET
cana-4971	186	7	curve	curve	NOUN
cana-4971	186	8	through	through	ADP
cana-4971	186	9	(	(	PUNCT
cana-4971	186	10	0	0	NUM
cana-4971	186	11	,	,	PUNCT
cana-4971	186	12	0.1	0.1	NUM
cana-4971	186	13	)	)	PUNCT
cana-4971	186	14	,	,	PUNCT
cana-4971	186	15	(	(	PUNCT
cana-4971	186	16	0.1	0.1	NUM
cana-4971	186	17	,	,	PUNCT
cana-4971	186	18	0.2286	0.2286	NUM
cana-4971	186	19	)	)	PUNCT
cana-4971	186	20	,	,	PUNCT
cana-4971	186	21	(	(	PUNCT
cana-4971	186	22	0.2	0.2	NUM
cana-4971	186	23	,	,	PUNCT
cana-4971	186	24	0.4597	0.4597	NUM
cana-4971	186	25	)	)	PUNCT
cana-4971	186	26	,	,	PUNCT
cana-4971	186	27	(	(	PUNCT
cana-4971	186	28	0.3	0.3	NUM
cana-4971	186	29	,	,	PUNCT
cana-4971	186	30	0.8227	0.8227	NUM
cana-4971	186	31	)	)	PUNCT
cana-4971	186	32	,	,	PUNCT
cana-4971	186	33	(	(	PUNCT
cana-4971	186	34	0.4	0.4	NUM
cana-4971	186	35	,	,	PUNCT
cana-4971	186	36	1.3317	1.3317	NUM
cana-4971	186	37	)	)	PUNCT
cana-4971	186	38	in	in	ADP
cana-4971	186	39	red	red	PROPN
cana-4971	186	40	.	.	PUNCT
cana-4971	186	41	appearance	appearance	NOUN
cana-4971	186	42	:	:	PUNCT
cana-4971	186	43	both	both	DET
cana-4971	186	44	curves	curve	NOUN
cana-4971	186	45	rise	rise	VERB
cana-4971	186	46	steeply	steeply	ADV
cana-4971	186	47	,	,	PUNCT
cana-4971	186	48	but	but	CCONJ
cana-4971	186	49	the	the	DET
cana-4971	186	50	red	red	ADJ
cana-4971	186	51	(	(	PUNCT
cana-4971	186	52	numerical	numerical	PROPN
cana-4971	186	53	)	)	PUNCT
cana-4971	186	54	curve	curve	NOUN
cana-4971	186	55	lies	lie	VERB
cana-4971	186	56	slightly	slightly	ADV
cana-4971	186	57	below	below	ADP
cana-4971	186	58	the	the	DET
cana-4971	186	59	blue	blue	ADJ
cana-4971	186	60	(	(	PUNCT
cana-4971	186	61	analytical	analytical	ADJ
cana-4971	186	62	)	)	PUNCT
cana-4971	186	63	curve	curve	NOUN
cana-4971	186	64	,	,	PUNCT
cana-4971	186	65	with	with	ADP
cana-4971	186	66	the	the	DET
cana-4971	186	67	gap	gap	NOUN
cana-4971	186	68	widening	widen	VERB
cana-4971	186	69	as	as	ADP
cana-4971	186	70	𝑡	𝑡	PROPN
cana-4971	186	71	increases	increase	NOUN
cana-4971	186	72	.	.	PUNCT
cana-4971	187	1	2.3	2.3	NUM
cana-4971	187	2	matlab	matlab	NOUN
cana-4971	187	3	implementation	implementation	NOUN
cana-4971	187	4	the	the	DET
cana-4971	187	5	following	follow	VERB
cana-4971	187	6	matlab	matlab	PROPN
cana-4971	187	7	script	script	NOUN
cana-4971	187	8	computes	compute	NOUN
cana-4971	187	9	and	and	CCONJ
cana-4971	187	10	plots	plot	VERB
cana-4971	187	11	the	the	DET
cana-4971	187	12	series	series	NOUN
cana-4971	187	13	and	and	CCONJ
cana-4971	187	14	numerical	numerical	ADJ
cana-4971	187	15	solutions	solution	NOUN
cana-4971	187	16	:	:	PUNCT
cana-4971	188	1	[	[	X
cana-4971	188	2	language	language	NOUN
cana-4971	188	3	=	=	SYM
cana-4971	188	4	matlab	matlab	NOUN
cana-4971	188	5	]	]	X
cana-4971	188	6	clear	clear	ADJ
cana-4971	188	7	all	all	PRON
cana-4971	188	8	;	;	PUNCT
cana-4971	188	9	close	close	ADV
cana-4971	188	10	all	all	PRON
cana-4971	188	11	;	;	PUNCT
cana-4971	188	12	clc	clc	PROPN
cana-4971	188	13	;	;	PUNCT
cana-4971	188	14	%	%	NOUN
cana-4971	188	15	time	time	NOUN
cana-4971	188	16	span	span	VERB
cana-4971	188	17	tspan	tspan	PROPN
cana-4971	188	18	=	=	PUNCT
cana-4971	189	1	[	[	X
cana-4971	189	2	0	0	NUM
cana-4971	189	3	0.5	0.5	NUM
cana-4971	189	4	]	]	PUNCT
cana-4971	189	5	;	;	PUNCT
cana-4971	189	6	%	%	NOUN
cana-4971	189	7	series	series	PROPN
cana-4971	189	8	solution	solution	NOUN
cana-4971	189	9	a0	a0	PROPN
cana-4971	189	10	=	=	SYM
cana-4971	189	11	0.1	0.1	NUM
cana-4971	189	12	;	;	PUNCT
cana-4971	189	13	a1	a1	NOUN
cana-4971	189	14	=	=	SYM
cana-4971	189	15	0.9	0.9	NUM
cana-4971	189	16	;	;	PUNCT
cana-4971	189	17	a2	a2	PROPN
cana-4971	189	18	=	=	SYM
cana-4971	189	19	3.55	3.55	NUM
cana-4971	189	20	;	;	PUNCT
cana-4971	189	21	a3	a3	NOUN
cana-4971	189	22	=	=	SYM
cana-4971	189	23	6.3167	6.3167	NUM
cana-4971	189	24	;	;	PUNCT
cana-4971	189	25	series_solution	series_solution	NOUN
cana-4971	189	26	=	=	SYM
cana-4971	189	27	@(t	@(t	PROPN
cana-4971	189	28	)	)	PUNCT
cana-4971	189	29	a0	a0	NOUN
cana-4971	189	30	+	+	CCONJ
cana-4971	189	31	a1*t	a1*t	NOUN
cana-4971	189	32	+	+	CCONJ
cana-4971	189	33	a2*t.^2	a2*t.^2	PROPN
cana-4971	189	34	+	+	CCONJ
cana-4971	189	35	a3*t.^3	a3*t.^3	NOUN
cana-4971	189	36	;	;	PUNCT
cana-4971	189	37	%	%	PROPN
cana-4971	189	38	numerical	numerical	PROPN
cana-4971	189	39	solution	solution	NOUN
cana-4971	189	40	odefun	odefun	NOUN
cana-4971	189	41	=	=	PUNCT
cana-4971	189	42	@(t	@(t	PROPN
cana-4971	189	43	,	,	PUNCT
cana-4971	189	44	y	y	NOUN
cana-4971	189	45	)	)	PUNCT
cana-4971	190	1	[	[	X
cana-4971	190	2	10*y(1	10*y(1	X
cana-4971	190	3	)	)	PUNCT
cana-4971	190	4	10*y(1)^2	10*y(1)^2	NUM
cana-4971	190	5	10*y(1)*y(2	10*y(1)*y(2	NUM
cana-4971	190	6	)	)	PUNCT
cana-4971	190	7	;	;	PUNCT
cana-4971	190	8	y(1	y(1	PROPN
cana-4971	190	9	)	)	PUNCT
cana-4971	190	10	]	]	X
cana-4971	190	11	;	;	PUNCT
cana-4971	190	12	initial_conditions	initial_condition	NOUN
cana-4971	191	1	=	=	PUNCT
cana-4971	192	1	[	[	X
cana-4971	192	2	0.1	0.1	NUM
cana-4971	192	3	;	;	PUNCT
cana-4971	192	4	0	0	NUM
cana-4971	192	5	]	]	PUNCT
cana-4971	192	6	;	;	PUNCT
cana-4971	193	1	[	[	X
cana-4971	193	2	t_num	t_num	PROPN
cana-4971	193	3	,	,	PUNCT
cana-4971	193	4	y_num	y_num	X
cana-4971	193	5	]	]	X
cana-4971	193	6	=	=	SYM
cana-4971	193	7	ode45(odefun	ode45(odefun	NOUN
cana-4971	193	8	,	,	PUNCT
cana-4971	193	9	tspan	tspan	PROPN
cana-4971	193	10	,	,	PUNCT
cana-4971	193	11	initial_conditions	initial_condition	NOUN
cana-4971	193	12	)	)	PUNCT
cana-4971	193	13	;	;	PUNCT
cana-4971	193	14	%	%	NOUN
cana-4971	193	15	evaluate	evaluate	VERB
cana-4971	193	16	series	series	NOUN
cana-4971	193	17	solution	solution	NOUN
cana-4971	193	18	u_series	u_series	X
cana-4971	193	19	=	=	SYM
cana-4971	193	20	series_solution(t_num	series_solution(t_num	PROPN
cana-4971	193	21	)	)	PUNCT
cana-4971	193	22	;	;	PUNCT
cana-4971	193	23	%	%	NOUN
cana-4971	193	24	plot	plot	NOUN
cana-4971	193	25	figure	figure	NOUN
cana-4971	193	26	;	;	PUNCT
cana-4971	193	27	plot(t_num	plot(t_num	PRON
cana-4971	193	28	,	,	PUNCT
cana-4971	193	29	u_series	u_serie	NOUN
cana-4971	193	30	,	,	PUNCT
cana-4971	193	31	'	'	PUNCT
cana-4971	193	32	b-	b-	X
cana-4971	193	33	'	'	PUNCT
cana-4971	193	34	,	,	PUNCT
cana-4971	193	35	'	'	PUNCT
cana-4971	193	36	linewidth	linewidth	NOUN
cana-4971	193	37	'	'	PUNCT
cana-4971	193	38	,	,	PUNCT
cana-4971	193	39	2	2	NUM
cana-4971	193	40	,	,	PUNCT
cana-4971	193	41	'	'	PUNCT
cana-4971	193	42	displayname	displayname	PROPN
cana-4971	193	43	'	'	PUNCT
cana-4971	193	44	,	,	PUNCT
cana-4971	193	45	'	'	PUNCT
cana-4971	193	46	series	series	NOUN
cana-4971	193	47	solution	solution	NOUN
cana-4971	193	48	'	'	PUNCT
cana-4971	193	49	)	)	PUNCT
cana-4971	193	50	;	;	PUNCT
cana-4971	193	51	hold	hold	VERB
cana-4971	193	52	on	on	ADP
cana-4971	193	53	;	;	PUNCT
cana-4971	193	54	plot(t_num	plot(t_num	ADJ
cana-4971	193	55	,	,	PUNCT
cana-4971	193	56	y_num(:,1	y_num(:,1	NOUN
cana-4971	193	57	)	)	PUNCT
cana-4971	193	58	,	,	PUNCT
cana-4971	193	59	'	'	PUNCT
cana-4971	193	60	r--	r--	NOUN
cana-4971	193	61	'	'	PUNCT
cana-4971	193	62	,	,	PUNCT
cana-4971	193	63	'	'	PUNCT
cana-4971	193	64	linewidth	linewidth	NOUN
cana-4971	193	65	'	'	PUNCT
cana-4971	193	66	,	,	PUNCT
cana-4971	193	67	2	2	NUM
cana-4971	193	68	,	,	PUNCT
cana-4971	193	69	'	'	PUNCT
cana-4971	193	70	displayname	displayname	PROPN
cana-4971	193	71	'	'	PUNCT
cana-4971	193	72	,	,	PUNCT
cana-4971	193	73	'	'	PUNCT
cana-4971	193	74	numerical	numerical	ADJ
cana-4971	193	75	solution	solution	NOUN
cana-4971	193	76	'	'	PUNCT
cana-4971	193	77	)	)	PUNCT
cana-4971	193	78	;	;	PUNCT
cana-4971	193	79	grid	grid	VERB
cana-4971	193	80	on	on	ADP
cana-4971	193	81	;	;	PUNCT
cana-4971	193	82	xlabel('time	xlabel('time	PROPN
cana-4971	193	83	(	(	PUNCT
cana-4971	193	84	t	t	NOUN
cana-4971	193	85	)	)	PUNCT
cana-4971	193	86	'	'	PUNCT
cana-4971	193	87	)	)	PUNCT
cana-4971	193	88	;	;	PUNCT
cana-4971	193	89	ylabel('u(t	ylabel('u(t	NOUN
cana-4971	193	90	)	)	PUNCT
cana-4971	193	91	'	'	PUNCT
cana-4971	193	92	)	)	PUNCT
cana-4971	193	93	;	;	PUNCT
cana-4971	193	94	title('series	title('serie	NOUN
cana-4971	193	95	vs.	vs.	ADP
cana-4971	193	96	numerical	numerical	ADJ
cana-4971	193	97	solutions	solution	NOUN
cana-4971	193	98	'	'	PUNCT
cana-4971	193	99	)	)	PUNCT
cana-4971	193	100	;	;	PUNCT
cana-4971	193	101	legend	legend	NOUN
cana-4971	193	102	;	;	PUNCT
cana-4971	193	103	hold	hold	VERB
cana-4971	193	104	off	off	ADP
cana-4971	193	105	;	;	PUNCT
cana-4971	193	106	%	%	NOUN
cana-4971	193	107	error	error	NOUN
cana-4971	193	108	calculation	calculation	NOUN
cana-4971	193	109	error	error	NOUN
cana-4971	193	110	=	=	PUNCT
cana-4971	193	111	abs(u_series	abs(u_serie	NOUN
cana-4971	193	112	y_num(:,1	y_num(:,1	NOUN
cana-4971	193	113	)	)	PUNCT
cana-4971	193	114	)	)	PUNCT
cana-4971	193	115	;	;	PUNCT
cana-4971	193	116	figure	figure	NOUN
cana-4971	193	117	;	;	PUNCT
cana-4971	193	118	plot(t_num	plot(t_num	NOUN
cana-4971	193	119	,	,	PUNCT
cana-4971	193	120	error	error	NOUN
cana-4971	193	121	,	,	PUNCT
cana-4971	193	122	'	'	PUNCT
cana-4971	193	123	k-	k-	X
cana-4971	193	124	'	'	PUNCT
cana-4971	193	125	,	,	PUNCT
cana-4971	193	126	'	'	PUNCT
cana-4971	193	127	linewidth	linewidth	NOUN
cana-4971	193	128	'	'	PUNCT
cana-4971	193	129	,	,	PUNCT
cana-4971	193	130	2	2	NUM
cana-4971	193	131	)	)	PUNCT
cana-4971	193	132	;	;	PUNCT
cana-4971	193	133	grid	grid	VERB
cana-4971	193	134	on	on	ADP
cana-4971	193	135	;	;	PUNCT
cana-4971	193	136	xlabel('time	xlabel('time	PROPN
cana-4971	193	137	(	(	PUNCT
cana-4971	193	138	t	t	NOUN
cana-4971	193	139	)	)	PUNCT
cana-4971	193	140	'	'	PUNCT
cana-4971	193	141	)	)	PUNCT
cana-4971	193	142	;	;	PUNCT
cana-4971	193	143	ylabel('absolute	ylabel('absolute	NOUN
cana-4971	193	144	error	error	NOUN
cana-4971	193	145	'	'	PUNCT
cana-4971	193	146	)	)	PUNCT
cana-4971	193	147	;	;	PUNCT
cana-4971	193	148	https://internationalpubls.com/	https://internationalpubls.com/	PROPN
cana-4971	193	149	communications	communication	NOUN
cana-4971	193	150	on	on	ADP
cana-4971	193	151	applied	apply	VERB
cana-4971	193	152	nonlinear	nonlinear	ADJ
cana-4971	193	153	analysis	analysis	NOUN
cana-4971	193	154	issn	issn	NOUN
cana-4971	193	155	:	:	PUNCT
cana-4971	193	156	1074	1074	NUM
cana-4971	193	157	-	-	PUNCT
cana-4971	193	158	133x	133x	NUM
cana-4971	193	159	vol	vol	NOUN
cana-4971	193	160	31	31	NUM
cana-4971	193	161	no	no	NOUN
cana-4971	193	162	.	.	PUNCT
cana-4971	194	1	4s	4s	NUM
cana-4971	194	2	(	(	PUNCT
cana-4971	194	3	2024	2024	NUM
cana-4971	194	4	)	)	PUNCT
cana-4971	194	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4971	194	6	669	669	NUM
cana-4971	194	7	title('error	title('error	NOUN
cana-4971	194	8	between	between	ADP
cana-4971	194	9	series	series	PROPN
cana-4971	194	10	and	and	CCONJ
cana-4971	194	11	numerical	numerical	ADJ
cana-4971	194	12	solutions	solution	NOUN
cana-4971	194	13	'	'	PUNCT
cana-4971	194	14	)	)	PUNCT
cana-4971	194	15	;	;	PUNCT
cana-4971	194	16	%	%	NOUN
cana-4971	194	17	display	display	VERB
cana-4971	194	18	some	some	DET
cana-4971	194	19	solution	solution	NOUN
cana-4971	194	20	values	value	NOUN
cana-4971	194	21	disp('time	disp('time	PROPN
cana-4971	194	22	series	series	PROPN
cana-4971	194	23	solution	solution	NOUN
cana-4971	194	24	numerical	numerical	PROPN
cana-4971	194	25	solution	solution	NOUN
cana-4971	194	26	'	'	PUNCT
cana-4971	194	27	)	)	PUNCT
cana-4971	194	28	;	;	PUNCT
cana-4971	194	29	disp([t_num(1:10	disp([t_num(1:10	PROPN
cana-4971	194	30	:	:	PUNCT
cana-4971	194	31	end	end	NOUN
cana-4971	194	32	)	)	PUNCT
cana-4971	194	33	,	,	PUNCT
cana-4971	194	34	u_series(1:10	u_series(1:10	PROPN
cana-4971	194	35	:	:	PUNCT
cana-4971	194	36	end	end	NOUN
cana-4971	194	37	)	)	PUNCT
cana-4971	194	38	,	,	PUNCT
cana-4971	194	39	y_num(1:10	y_num(1:10	NOUN
cana-4971	194	40	:	:	PUNCT
cana-4971	194	41	end,1	end,1	PROPN
cana-4971	194	42	)	)	PUNCT
cana-4971	194	43	]	]	PUNCT
cana-4971	194	44	)	)	PUNCT
cana-4971	194	45	;	;	PUNCT
cana-4971	194	46	3	3	X
cana-4971	194	47	.	.	NOUN
cana-4971	194	48	results	result	VERB
cana-4971	194	49	3.1	3.1	NUM
cana-4971	194	50	analytical	analytical	ADJ
cana-4971	194	51	solutions	solution	NOUN
cana-4971	194	52	both	both	CCONJ
cana-4971	194	53	the	the	DET
cana-4971	194	54	series	series	NOUN
cana-4971	194	55	and	and	CCONJ
cana-4971	194	56	hybrid	hybrid	ADJ
cana-4971	194	57	methods	method	NOUN
cana-4971	194	58	yield	yield	NOUN
cana-4971	194	59	:	:	PUNCT
cana-4971	194	60	𝑧(𝑡	𝑧(𝑡	PROPN
cana-4971	194	61	)	)	PUNCT
cana-4971	195	1	≈	≈	PROPN
cana-4971	195	2	0.1	0.1	NUM
cana-4971	196	1	+	+	CCONJ
cana-4971	196	2	0.9𝑡	0.9𝑡	NUM
cana-4971	197	1	+	+	CCONJ
cana-4971	197	2	3.55𝑡2	3.55𝑡2	NUM
cana-4971	197	3	+	+	SYM
cana-4971	197	4	6.3167𝑡3	6.3167𝑡3	NUM
cana-4971	197	5	the	the	DET
cana-4971	197	6	hybrid	hybrid	ADJ
cana-4971	197	7	method	method	NOUN
cana-4971	197	8	confirms	confirm	VERB
cana-4971	197	9	the	the	DET
cana-4971	197	10	series	series	NOUN
cana-4971	197	11	solution	solution	NOUN
cana-4971	197	12	,	,	PUNCT
cana-4971	197	13	as	as	SCONJ
cana-4971	197	14	both	both	PRON
cana-4971	197	15	rely	rely	VERB
cana-4971	197	16	on	on	ADP
cana-4971	197	17	coefficient	coefficient	NOUN
cana-4971	197	18	matching	matching	NOUN
cana-4971	197	19	,	,	PUNCT
cana-4971	197	20	but	but	CCONJ
cana-4971	197	21	the	the	DET
cana-4971	197	22	laplace	laplace	NOUN
cana-4971	197	23	approach	approach	NOUN
cana-4971	197	24	offers	offer	VERB
cana-4971	197	25	potential	potential	NOUN
cana-4971	197	26	for	for	ADP
cana-4971	197	27	handling	handle	VERB
cana-4971	197	28	more	more	ADV
cana-4971	197	29	complex	complex	ADJ
cana-4971	197	30	integral	integral	ADJ
cana-4971	197	31	terms	term	NOUN
cana-4971	197	32	in	in	ADP
cana-4971	197	33	future	future	ADJ
cana-4971	197	34	extensions	extension	NOUN
cana-4971	197	35	.	.	PUNCT
cana-4971	198	1	figure	figure	NOUN
cana-4971	198	2	1	1	NUM
cana-4971	198	3	:	:	PUNCT
cana-4971	198	4	graph	graph	NOUN
cana-4971	198	5	of	of	ADP
cana-4971	198	6	analytical	analytical	ADJ
cana-4971	198	7	vs	vs	ADP
cana-4971	198	8	numerical	numerical	ADJ
cana-4971	198	9	solution	solution	NOUN
cana-4971	198	10	3.2	3.2	NUM
cana-4971	198	11	numerical	numerical	ADJ
cana-4971	198	12	solution	solution	NOUN
cana-4971	198	13	the	the	DET
cana-4971	198	14	numerical	numerical	ADJ
cana-4971	198	15	solution	solution	NOUN
cana-4971	198	16	,	,	PUNCT
cana-4971	198	17	computed	compute	VERB
cana-4971	198	18	via	via	ADP
cana-4971	198	19	ode45	ode45	NOUN
cana-4971	198	20	,	,	PUNCT
cana-4971	198	21	provides	provide	VERB
cana-4971	198	22	a	a	DET
cana-4971	198	23	reference	reference	NOUN
cana-4971	198	24	trajectory	trajectory	NOUN
cana-4971	198	25	.	.	PUNCT
cana-4971	199	1	figure	figure	NOUN
cana-4971	199	2	1	1	NUM
cana-4971	199	3	(	(	PUNCT
cana-4971	199	4	generated	generate	VERB
cana-4971	199	5	by	by	ADP
cana-4971	199	6	the	the	DET
cana-4971	199	7	matlab	matlab	PROPN
cana-4971	199	8	script	script	NOUN
cana-4971	199	9	)	)	PUNCT
cana-4971	199	10	shows	show	VERB
cana-4971	199	11	the	the	DET
cana-4971	199	12	series	series	NOUN
cana-4971	199	13	solution	solution	NOUN
cana-4971	199	14	(	(	PUNCT
cana-4971	199	15	blue	blue	ADJ
cana-4971	199	16	solid	solid	ADJ
cana-4971	199	17	line	line	NOUN
cana-4971	199	18	)	)	PUNCT
cana-4971	199	19	closely	closely	ADV
cana-4971	199	20	matching	match	VERB
cana-4971	199	21	the	the	DET
cana-4971	199	22	numerical	numerical	ADJ
cana-4971	199	23	solution	solution	NOUN
cana-4971	199	24	(	(	PUNCT
cana-4971	199	25	red	red	ADJ
cana-4971	199	26	dashed	dash	VERB
cana-4971	199	27	line	line	NOUN
cana-4971	199	28	)	)	PUNCT
cana-4971	199	29	for	for	ADP
cana-4971	199	30	𝑡	𝑡	PROPN
cana-4971	199	31	∈	∈	PROPN
cana-4971	200	1	[	[	X
cana-4971	200	2	0,0.5	0,0.5	NUM
cana-4971	200	3	]	]	X
cana-4971	200	4	.	.	PUNCT
cana-4971	201	1	3.3	3.3	NUM
cana-4971	201	2	error	error	NOUN
cana-4971	201	3	analysis	analysis	NOUN
cana-4971	201	4	figure	figure	NOUN
cana-4971	201	5	2	2	NUM
cana-4971	201	6	plots	plot	NOUN
cana-4971	201	7	the	the	DET
cana-4971	201	8	absolute	absolute	ADJ
cana-4971	201	9	error	error	NOUN
cana-4971	201	10	|𝑧series(𝑡	|𝑧series(𝑡	NOUN
cana-4971	201	11	)	)	PUNCT
cana-4971	201	12	−	−	PROPN
cana-4971	201	13	𝑧numerical(𝑡)|	𝑧numerical(𝑡)|	PROPN
cana-4971	201	14	.	.	PUNCT
cana-4971	202	1	the	the	DET
cana-4971	202	2	error	error	NOUN
cana-4971	202	3	remains	remain	VERB
cana-4971	202	4	small	small	ADJ
cana-4971	202	5	(	(	PUNCT
cana-4971	202	6	on	on	ADP
cana-4971	202	7	the	the	DET
cana-4971	202	8	order	order	NOUN
cana-4971	202	9	of	of	ADP
cana-4971	202	10	10−3	10−3	NUM
cana-4971	202	11	)	)	PUNCT
cana-4971	202	12	for	for	ADP
cana-4971	202	13	𝑡	𝑡	X
cana-4971	202	14	<	<	X
cana-4971	202	15	0.3	0.3	NUM
cana-4971	202	16	,	,	PUNCT
cana-4971	202	17	but	but	CCONJ
cana-4971	202	18	increases	increase	NOUN
cana-4971	202	19	for	for	ADP
cana-4971	202	20	larger	large	ADJ
cana-4971	202	21	𝑡	𝑡	NOUN
cana-4971	202	22	,	,	PUNCT
cana-4971	202	23	indicating	indicate	VERB
cana-4971	202	24	the	the	DET
cana-4971	202	25	series	series	PROPN
cana-4971	202	26	truncation	truncation	NOUN
cana-4971	202	27	limits	limit	NOUN
cana-4971	202	28	accuracy	accuracy	NOUN
cana-4971	202	29	.	.	PUNCT
cana-4971	203	1	https://internationalpubls.com/	https://internationalpubls.com/	ADJ
cana-4971	203	2	communications	communication	NOUN
cana-4971	203	3	on	on	ADP
cana-4971	203	4	applied	apply	VERB
cana-4971	203	5	nonlinear	nonlinear	ADJ
cana-4971	203	6	analysis	analysis	NOUN
cana-4971	203	7	issn	issn	NOUN
cana-4971	203	8	:	:	PUNCT
cana-4971	203	9	1074	1074	NUM
cana-4971	203	10	-	-	PUNCT
cana-4971	203	11	133x	133x	NUM
cana-4971	203	12	vol	vol	NOUN
cana-4971	203	13	31	31	NUM
cana-4971	203	14	no	no	NOUN
cana-4971	203	15	.	.	PUNCT
cana-4971	204	1	4s	4s	NUM
cana-4971	204	2	(	(	PUNCT
cana-4971	204	3	2024	2024	NUM
cana-4971	204	4	)	)	PUNCT
cana-4971	204	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4971	204	6	670	670	NUM
cana-4971	204	7	4	4	NUM
cana-4971	204	8	.	.	PUNCT
cana-4971	204	9	discussion	discussion	NOUN
cana-4971	204	10	accuracy	accuracy	NOUN
cana-4971	204	11	:	:	PUNCT
cana-4971	204	12	•	•	ADP
cana-4971	204	13	the	the	DET
cana-4971	204	14	series	series	NOUN
cana-4971	204	15	solution	solution	NOUN
cana-4971	204	16	is	be	AUX
cana-4971	204	17	highly	highly	ADV
cana-4971	204	18	accurate	accurate	ADJ
cana-4971	204	19	for	for	ADP
cana-4971	204	20	small	small	ADJ
cana-4971	204	21	𝑡	𝑡	NOUN
cana-4971	204	22	,	,	PUNCT
cana-4971	204	23	as	as	SCONJ
cana-4971	204	24	it	it	PRON
cana-4971	204	25	captures	capture	VERB
cana-4971	204	26	the	the	DET
cana-4971	204	27	local	local	ADJ
cana-4971	204	28	behavior	behavior	NOUN
cana-4971	204	29	near	near	ADP
cana-4971	204	30	𝑡	𝑡	PROPN
cana-4971	204	31	=	=	NOUN
cana-4971	204	32	0	0	X
cana-4971	204	33	.	.	PUNCT
cana-4971	205	1	however	however	ADV
cana-4971	205	2	,	,	PUNCT
cana-4971	205	3	truncation	truncation	NOUN
cana-4971	205	4	to	to	ADP
cana-4971	205	5	four	four	NUM
cana-4971	205	6	terms	term	NOUN
cana-4971	205	7	limits	limit	VERB
cana-4971	205	8	its	its	PRON
cana-4971	205	9	validity	validity	NOUN
cana-4971	205	10	for	for	ADP
cana-4971	205	11	𝑡	𝑡	X
cana-4971	205	12	>	>	X
cana-4971	205	13	0.3	0.3	NUM
cana-4971	205	14	.	.	PUNCT
cana-4971	206	1	•	•	NUM
cana-4971	206	2	the	the	DET
cana-4971	206	3	hybrid	hybrid	NOUN
cana-4971	206	4	method	method	NOUN
cana-4971	206	5	produces	produce	VERB
cana-4971	206	6	identical	identical	ADJ
cana-4971	206	7	results	result	NOUN
cana-4971	206	8	,	,	PUNCT
cana-4971	206	9	suggesting	suggest	VERB
cana-4971	206	10	that	that	SCONJ
cana-4971	206	11	the	the	DET
cana-4971	206	12	laplace	laplace	NOUN
cana-4971	206	13	transform	transform	NOUN
cana-4971	206	14	,	,	PUNCT
cana-4971	206	15	in	in	ADP
cana-4971	206	16	this	this	DET
cana-4971	206	17	case	case	NOUN
cana-4971	206	18	,	,	PUNCT
cana-4971	206	19	serves	serve	VERB
cana-4971	206	20	as	as	ADP
cana-4971	206	21	a	a	DET
cana-4971	206	22	verification	verification	NOUN
cana-4971	206	23	tool	tool	NOUN
cana-4971	206	24	rather	rather	ADV
cana-4971	206	25	than	than	ADP
cana-4971	206	26	an	an	DET
cana-4971	206	27	enhancement	enhancement	NOUN
cana-4971	206	28	for	for	ADP
cana-4971	206	29	this	this	DET
cana-4971	206	30	specific	specific	ADJ
cana-4971	206	31	equation	equation	NOUN
cana-4971	206	32	.	.	PUNCT
cana-4971	207	1	•	•	NUM
cana-4971	207	2	the	the	DET
cana-4971	207	3	numerical	numerical	ADJ
cana-4971	207	4	solution	solution	NOUN
cana-4971	207	5	is	be	AUX
cana-4971	207	6	robust	robust	ADJ
cana-4971	207	7	across	across	ADP
cana-4971	207	8	the	the	DET
cana-4971	207	9	entire	entire	ADJ
cana-4971	207	10	interval	interval	NOUN
cana-4971	207	11	,	,	PUNCT
cana-4971	207	12	as	as	SCONJ
cana-4971	207	13	ode45	ode45	NOUN
cana-4971	207	14	adapts	adapt	VERB
cana-4971	207	15	step	step	NOUN
cana-4971	207	16	sizes	size	NOUN
cana-4971	207	17	to	to	PART
cana-4971	207	18	maintain	maintain	VERB
cana-4971	207	19	accuracy	accuracy	NOUN
cana-4971	207	20	.	.	PUNCT
cana-4971	208	1	computational	computational	ADJ
cana-4971	208	2	efficiency	efficiency	NOUN
cana-4971	208	3	:	:	PUNCT
cana-4971	208	4	•	•	ADP
cana-4971	208	5	the	the	DET
cana-4971	208	6	series	series	NOUN
cana-4971	208	7	method	method	NOUN
cana-4971	208	8	requires	require	VERB
cana-4971	208	9	manual	manual	ADJ
cana-4971	208	10	derivation	derivation	NOUN
cana-4971	208	11	of	of	ADP
cana-4971	208	12	coefficients	coefficient	NOUN
cana-4971	208	13	,	,	PUNCT
cana-4971	208	14	which	which	PRON
cana-4971	208	15	is	be	AUX
cana-4971	208	16	labor	labor	NOUN
cana-4971	208	17	-	-	PUNCT
cana-4971	208	18	intensive	intensive	ADJ
cana-4971	208	19	for	for	ADP
cana-4971	208	20	higher	high	ADJ
cana-4971	208	21	terms	term	NOUN
cana-4971	208	22	.	.	PUNCT
cana-4971	209	1	computational	computational	ADJ
cana-4971	209	2	automation	automation	NOUN
cana-4971	209	3	could	could	AUX
cana-4971	209	4	improve	improve	VERB
cana-4971	209	5	efficiency	efficiency	NOUN
cana-4971	209	6	.	.	PUNCT
cana-4971	210	1	•	•	NUM
cana-4971	210	2	the	the	DET
cana-4971	210	3	hybrid	hybrid	NOUN
cana-4971	210	4	method	method	NOUN
cana-4971	210	5	involves	involve	VERB
cana-4971	210	6	complex	complex	ADJ
cana-4971	210	7	convolution	convolution	NOUN
cana-4971	210	8	terms	term	NOUN
cana-4971	210	9	,	,	PUNCT
cana-4971	210	10	making	make	VERB
cana-4971	210	11	it	it	PRON
cana-4971	210	12	computationally	computationally	ADV
cana-4971	210	13	intensive	intensive	ADJ
cana-4971	210	14	unless	unless	SCONJ
cana-4971	210	15	approximated	approximate	VERB
cana-4971	210	16	.	.	PUNCT
cana-4971	211	1	•	•	NUM
cana-4971	211	2	the	the	DET
cana-4971	211	3	numerical	numerical	ADJ
cana-4971	211	4	method	method	NOUN
cana-4971	211	5	is	be	AUX
cana-4971	211	6	efficient	efficient	ADJ
cana-4971	211	7	,	,	PUNCT
cana-4971	211	8	leveraging	leverage	VERB
cana-4971	211	9	matlab	matlab	PROPN
cana-4971	211	10	’s	’s	PART
cana-4971	211	11	optimized	optimize	VERB
cana-4971	211	12	solvers	solver	NOUN
cana-4971	211	13	,	,	PUNCT
cana-4971	211	14	with	with	ADP
cana-4971	211	15	a	a	DET
cana-4971	211	16	runtime	runtime	NOUN
cana-4971	211	17	of	of	ADP
cana-4971	211	18	milliseconds	millisecond	NOUN
cana-4971	211	19	for	for	ADP
cana-4971	211	20	𝑡	𝑡	PROPN
cana-4971	211	21	∈	∈	PROPN
cana-4971	211	22	[	[	X
cana-4971	211	23	0,0.5	0,0.5	NUM
cana-4971	211	24	]	]	PUNCT
cana-4971	211	25	.	.	PUNCT
cana-4971	212	1	convergence	convergence	NOUN
cana-4971	212	2	:	:	PUNCT
cana-4971	212	3	•	•	ADP
cana-4971	212	4	the	the	DET
cana-4971	212	5	series	series	NOUN
cana-4971	212	6	solution	solution	NOUN
cana-4971	212	7	’s	’s	PART
cana-4971	212	8	radius	radius	NOUN
cana-4971	212	9	of	of	ADP
cana-4971	212	10	convergence	convergence	NOUN
cana-4971	212	11	depends	depend	VERB
cana-4971	212	12	on	on	ADP
cana-4971	212	13	the	the	DET
cana-4971	212	14	equation	equation	NOUN
cana-4971	212	15	’s	’s	PART
cana-4971	212	16	nonlinearities	nonlinearitie	NOUN
cana-4971	212	17	.	.	PUNCT
cana-4971	213	1	for	for	ADP
cana-4971	213	2	larger	large	ADJ
cana-4971	213	3	𝑡	𝑡	NOUN
cana-4971	213	4	,	,	PUNCT
cana-4971	213	5	additional	additional	ADJ
cana-4971	213	6	terms	term	NOUN
cana-4971	213	7	or	or	CCONJ
cana-4971	213	8	alternative	alternative	ADJ
cana-4971	213	9	methods	method	NOUN
cana-4971	213	10	(	(	PUNCT
cana-4971	213	11	e.g.	e.g.	ADV
cana-4971	213	12	,	,	PUNCT
cana-4971	213	13	padé	padé	NOUN
cana-4971	213	14	approximants	approximant	NOUN
cana-4971	213	15	)	)	PUNCT
cana-4971	213	16	are	be	AUX
cana-4971	213	17	needed	need	VERB
cana-4971	213	18	.	.	PUNCT
cana-4971	214	1	•	•	NUM
cana-4971	214	2	the	the	DET
cana-4971	214	3	numerical	numerical	ADJ
cana-4971	214	4	solution	solution	NOUN
cana-4971	214	5	avoids	avoid	VERB
cana-4971	214	6	convergence	convergence	NOUN
cana-4971	214	7	issues	issue	NOUN
cana-4971	214	8	,	,	PUNCT
cana-4971	214	9	provided	provide	VERB
cana-4971	214	10	the	the	DET
cana-4971	214	11	system	system	NOUN
cana-4971	214	12	is	be	AUX
cana-4971	214	13	well	well	ADV
cana-4971	214	14	-	-	PUNCT
cana-4971	214	15	posed	pose	VERB
cana-4971	214	16	.	.	PUNCT
cana-4971	215	1	novelty	novelty	NOUN
cana-4971	215	2	:	:	PUNCT
cana-4971	215	3	•	•	ADP
cana-4971	215	4	the	the	DET
cana-4971	215	5	hybrid	hybrid	ADJ
cana-4971	215	6	laplace	laplace	NOUN
cana-4971	215	7	-	-	PUNCT
cana-4971	215	8	series	series	NOUN
cana-4971	215	9	method	method	NOUN
cana-4971	215	10	is	be	AUX
cana-4971	215	11	novel	novel	ADJ
cana-4971	215	12	in	in	ADP
cana-4971	215	13	its	its	PRON
cana-4971	215	14	attempt	attempt	NOUN
cana-4971	215	15	to	to	PART
cana-4971	215	16	combine	combine	AUX
cana-4971	215	17	transform	transform	VERB
cana-4971	215	18	techniques	technique	NOUN
cana-4971	215	19	with	with	ADP
cana-4971	215	20	series	series	NOUN
cana-4971	215	21	expansions	expansion	NOUN
cana-4971	215	22	for	for	ADP
cana-4971	215	23	nonlinear	nonlinear	ADJ
cana-4971	215	24	integro	integro	ADJ
cana-4971	215	25	-	-	PUNCT
cana-4971	215	26	differential	differential	NOUN
cana-4971	215	27	equations	equation	NOUN
cana-4971	215	28	.	.	PUNCT
cana-4971	216	1	while	while	SCONJ
cana-4971	216	2	it	it	PRON
cana-4971	216	3	yields	yield	VERB
cana-4971	216	4	the	the	DET
cana-4971	216	5	same	same	ADJ
cana-4971	216	6	result	result	NOUN
cana-4971	216	7	here	here	ADV
cana-4971	216	8	,	,	PUNCT
cana-4971	216	9	it	it	PRON
cana-4971	216	10	offers	offer	VERB
cana-4971	216	11	a	a	DET
cana-4971	216	12	framework	framework	NOUN
cana-4971	216	13	for	for	ADP
cana-4971	216	14	equations	equation	NOUN
cana-4971	216	15	where	where	SCONJ
cana-4971	216	16	direct	direct	ADJ
cana-4971	216	17	series	series	NOUN
cana-4971	216	18	methods	method	NOUN
cana-4971	216	19	are	be	AUX
cana-4971	216	20	intractable	intractable	ADJ
cana-4971	216	21	.	.	PUNCT
cana-4971	217	1	limitations	limitation	NOUN
cana-4971	217	2	:	:	PUNCT
cana-4971	217	3	•	•	ADP
cana-4971	217	4	the	the	DET
cana-4971	217	5	series	series	NOUN
cana-4971	217	6	solution	solution	NOUN
cana-4971	217	7	diverges	diverge	VERB
cana-4971	217	8	for	for	ADP
cana-4971	217	9	large	large	ADJ
cana-4971	217	10	𝑡	𝑡	NOUN
cana-4971	217	11	,	,	PUNCT
cana-4971	217	12	necessitating	necessitate	VERB
cana-4971	217	13	higher	high	ADJ
cana-4971	217	14	-	-	PUNCT
cana-4971	217	15	order	order	NOUN
cana-4971	217	16	terms	term	NOUN
cana-4971	217	17	or	or	CCONJ
cana-4971	217	18	alternative	alternative	ADJ
cana-4971	217	19	approximations	approximation	NOUN
cana-4971	217	20	.	.	PUNCT
cana-4971	218	1	•	•	NUM
cana-4971	218	2	the	the	DET
cana-4971	218	3	numerical	numerical	ADJ
cana-4971	218	4	method	method	NOUN
cana-4971	218	5	requires	require	VERB
cana-4971	218	6	reformulating	reformulate	VERB
cana-4971	218	7	the	the	DET
cana-4971	218	8	equation	equation	NOUN
cana-4971	218	9	as	as	ADP
cana-4971	218	10	a	a	DET
cana-4971	218	11	system	system	NOUN
cana-4971	218	12	,	,	PUNCT
cana-4971	218	13	which	which	PRON
cana-4971	218	14	may	may	AUX
cana-4971	218	15	not	not	PART
cana-4971	218	16	always	always	ADV
cana-4971	218	17	be	be	AUX
cana-4971	218	18	straightforward	straightforward	ADJ
cana-4971	218	19	for	for	ADP
cana-4971	218	20	complex	complex	ADJ
cana-4971	218	21	integrals	integral	NOUN
cana-4971	218	22	.	.	PUNCT
cana-4971	219	1	•	•	NUM
cana-4971	219	2	the	the	DET
cana-4971	219	3	hybrid	hybrid	NOUN
cana-4971	219	4	method	method	NOUN
cana-4971	219	5	’s	’s	PART
cana-4971	219	6	full	full	ADJ
cana-4971	219	7	potential	potential	NOUN
cana-4971	219	8	is	be	AUX
cana-4971	219	9	unrealized	unrealize	VERB
cana-4971	219	10	in	in	ADP
cana-4971	219	11	this	this	DET
cana-4971	219	12	case	case	NOUN
cana-4971	219	13	due	due	ADP
cana-4971	219	14	to	to	ADP
cana-4971	219	15	the	the	DET
cana-4971	219	16	equation	equation	NOUN
cana-4971	219	17	’s	’s	PART
cana-4971	219	18	structure	structure	NOUN
cana-4971	219	19	but	but	CCONJ
cana-4971	219	20	could	could	AUX
cana-4971	219	21	be	be	AUX
cana-4971	219	22	advantageous	advantageous	ADJ
cana-4971	219	23	for	for	ADP
cana-4971	219	24	equations	equation	NOUN
cana-4971	219	25	with	with	ADP
cana-4971	219	26	non	non	ADJ
cana-4971	219	27	-	-	ADJ
cana-4971	219	28	standard	standard	ADJ
cana-4971	219	29	integral	integral	ADJ
cana-4971	219	30	kernels	kernel	NOUN
cana-4971	219	31	.	.	PUNCT
cana-4971	220	1	5	5	NUM
cana-4971	220	2	.	.	X
cana-4971	220	3	conclusion	conclusion	NOUN
cana-4971	220	4	this	this	DET
cana-4971	220	5	study	study	NOUN
cana-4971	220	6	demonstrates	demonstrate	VERB
cana-4971	220	7	the	the	DET
cana-4971	220	8	efficacy	efficacy	NOUN
cana-4971	220	9	of	of	ADP
cana-4971	220	10	series	series	PROPN
cana-4971	220	11	,	,	PUNCT
cana-4971	220	12	hybrid	hybrid	ADJ
cana-4971	220	13	laplace	laplace	NOUN
cana-4971	220	14	-	-	PUNCT
cana-4971	220	15	series	series	NOUN
cana-4971	220	16	,	,	PUNCT
cana-4971	220	17	and	and	CCONJ
cana-4971	220	18	numerical	numerical	ADJ
cana-4971	220	19	methods	method	NOUN
cana-4971	220	20	for	for	ADP
cana-4971	220	21	solving	solve	VERB
cana-4971	220	22	a	a	DET
cana-4971	220	23	nonlinear	nonlinear	ADJ
cana-4971	220	24	volterra	volterra	NOUN
cana-4971	220	25	integro	integro	PROPN
cana-4971	220	26	-	-	PUNCT
cana-4971	220	27	differential	differential	NOUN
cana-4971	220	28	equation	equation	NOUN
cana-4971	220	29	.	.	PUNCT
cana-4971	221	1	the	the	DET
cana-4971	221	2	series	series	NOUN
cana-4971	221	3	and	and	CCONJ
cana-4971	221	4	hybrid	hybrid	ADJ
cana-4971	221	5	methods	method	NOUN
cana-4971	221	6	provide	provide	VERB
cana-4971	221	7	identical	identical	ADJ
cana-4971	221	8	analytical	analytical	ADJ
cana-4971	221	9	approximations	approximation	NOUN
cana-4971	221	10	,	,	PUNCT
cana-4971	221	11	accurate	accurate	ADJ
cana-4971	221	12	for	for	ADP
cana-4971	221	13	small	small	ADJ
cana-4971	221	14	time	time	NOUN
cana-4971	221	15	intervals	interval	NOUN
cana-4971	221	16	,	,	PUNCT
cana-4971	221	17	while	while	SCONJ
cana-4971	221	18	the	the	DET
cana-4971	221	19	numerical	numerical	ADJ
cana-4971	221	20	method	method	NOUN
cana-4971	221	21	offers	offer	VERB
cana-4971	221	22	a	a	DET
cana-4971	221	23	robust	robust	ADJ
cana-4971	221	24	solution	solution	NOUN
cana-4971	221	25	over	over	ADP
cana-4971	221	26	larger	large	ADJ
cana-4971	221	27	domains	domain	NOUN
cana-4971	221	28	.	.	PUNCT
cana-4971	222	1	the	the	DET
cana-4971	222	2	matlab	matlab	PROPN
cana-4971	222	3	implementation	implementation	NOUN
cana-4971	222	4	facilitates	facilitate	VERB
cana-4971	222	5	visualization	visualization	NOUN
cana-4971	222	6	and	and	CCONJ
cana-4971	222	7	error	error	NOUN
cana-4971	222	8	analysis	analysis	NOUN
cana-4971	222	9	[	[	X
cana-4971	222	10	8	8	NUM
cana-4971	222	11	]	]	PUNCT
cana-4971	222	12	,	,	PUNCT
cana-4971	222	13	confirming	confirm	VERB
cana-4971	222	14	the	the	DET
cana-4971	222	15	series	series	NOUN
cana-4971	222	16	solution	solution	NOUN
cana-4971	222	17	’s	’s	PART
cana-4971	222	18	accuracy	accuracy	NOUN
cana-4971	222	19	for	for	ADP
cana-4971	222	20	𝑡	𝑡	X
cana-4971	222	21	<	<	X
cana-4971	222	22	0.3	0.3	NUM
cana-4971	222	23	.	.	PUNCT
cana-4971	223	1	future	future	ADJ
cana-4971	223	2	work	work	NOUN
cana-4971	223	3	could	could	AUX
cana-4971	223	4	explore	explore	VERB
cana-4971	223	5	extending	extend	VERB
cana-4971	223	6	the	the	DET
cana-4971	223	7	hybrid	hybrid	ADJ
cana-4971	223	8	method	method	NOUN
cana-4971	223	9	to	to	ADP
cana-4971	223	10	equations	equation	NOUN
cana-4971	223	11	with	with	ADP
cana-4971	223	12	variable	variable	ADJ
cana-4971	223	13	coefficients	coefficient	NOUN
cana-4971	223	14	or	or	CCONJ
cana-4971	223	15	developing	develop	VERB
cana-4971	223	16	automated	automate	VERB
cana-4971	223	17	coefficient	coefficient	NOUN
cana-4971	223	18	computation	computation	NOUN
cana-4971	223	19	for	for	ADP
cana-4971	223	20	series	series	NOUN
cana-4971	223	21	solutions	solution	NOUN
cana-4971	223	22	.	.	PUNCT
cana-4971	224	1	https://internationalpubls.com/	https://internationalpubls.com/	ADJ
cana-4971	224	2	communications	communication	NOUN
cana-4971	224	3	on	on	ADP
cana-4971	224	4	applied	apply	VERB
cana-4971	224	5	nonlinear	nonlinear	ADJ
cana-4971	224	6	analysis	analysis	NOUN
cana-4971	224	7	issn	issn	NOUN
cana-4971	224	8	:	:	PUNCT
cana-4971	224	9	1074	1074	NUM
cana-4971	224	10	-	-	PUNCT
cana-4971	224	11	133x	133x	NUM
cana-4971	224	12	vol	vol	NOUN
cana-4971	224	13	31	31	NUM
cana-4971	224	14	no	no	NOUN
cana-4971	224	15	.	.	PUNCT
cana-4971	225	1	4s	4s	NUM
cana-4971	225	2	(	(	PUNCT
cana-4971	225	3	2024	2024	NUM
cana-4971	225	4	)	)	PUNCT
cana-4971	226	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4971	226	2	671	671	NUM
cana-4971	226	3	6	6	NUM
cana-4971	226	4	.	.	PUNCT
cana-4971	227	1	references	reference	NOUN
cana-4971	227	2	[	[	X
cana-4971	227	3	1	1	NUM
cana-4971	227	4	]	]	PUNCT
cana-4971	227	5	a.-k	a.-k	NOUN
cana-4971	227	6	.	.	PUNCT
cana-4971	228	1	alomari	alomari	PROPN
cana-4971	228	2	,	,	PUNCT
cana-4971	228	3	m.	m.	PROPN
cana-4971	228	4	alaroud	alaroud	PROPN
cana-4971	228	5	,	,	PUNCT
cana-4971	228	6	a.	a.	NOUN
cana-4971	228	7	almalki	almalki	ADV
cana-4971	228	8	,	,	PUNCT
cana-4971	228	9	and	and	CCONJ
cana-4971	228	10	n.	n.	PROPN
cana-4971	228	11	tahat	tahat	PROPN
cana-4971	228	12	,	,	PUNCT
cana-4971	228	13	“	"	PUNCT
cana-4971	228	14	extended	extended	ADJ
cana-4971	228	15	laplace	laplace	NOUN
cana-4971	228	16	power	power	NOUN
cana-4971	228	17	series	series	NOUN
cana-4971	228	18	method	method	NOUN
cana-4971	228	19	for	for	ADP
cana-4971	228	20	solving	solve	VERB
cana-4971	228	21	nonlinear	nonlinear	ADJ
cana-4971	228	22	caputo	caputo	PROPN
cana-4971	228	23	fractional	fractional	PROPN
cana-4971	228	24	volterra	volterra	PROPN
cana-4971	228	25	integro	integro	PROPN
cana-4971	228	26	-	-	PUNCT
cana-4971	228	27	differential	differential	NOUN
cana-4971	228	28	equations	equation	NOUN
cana-4971	228	29	,	,	PUNCT
cana-4971	228	30	”	"	PUNCT
cana-4971	228	31	symmetry	symmetry	NOUN
cana-4971	228	32	,	,	PUNCT
cana-4971	228	33	vol	vol	NOUN
cana-4971	228	34	.	.	PROPN
cana-4971	228	35	15	15	NUM
cana-4971	228	36	,	,	PUNCT
cana-4971	228	37	no	no	INTJ
cana-4971	228	38	.	.	NOUN
cana-4971	228	39	7	7	NUM
cana-4971	228	40	,	,	PUNCT
cana-4971	228	41	p.	p.	NOUN
cana-4971	228	42	1296	1296	NUM
cana-4971	228	43	,	,	PUNCT
cana-4971	228	44	jun	jun	PROPN
cana-4971	228	45	.	.	PROPN
cana-4971	228	46	2023	2023	NUM
cana-4971	228	47	,	,	PUNCT
cana-4971	228	48	doi	doi	NOUN
cana-4971	228	49	:	:	PUNCT
cana-4971	228	50	10.3390	10.3390	NUM
cana-4971	228	51	/	/	SYM
cana-4971	228	52	sym15071296	sym15071296	NOUN
cana-4971	228	53	.	.	PUNCT
cana-4971	229	1	[	[	X
cana-4971	229	2	2	2	NUM
cana-4971	229	3	]	]	PUNCT
cana-4971	229	4	a.	a.	PROPN
cana-4971	229	5	el	el	PROPN
cana-4971	229	6	-	-	PUNCT
cana-4971	229	7	ajou	ajou	ADJ
cana-4971	229	8	,	,	PUNCT
cana-4971	229	9	“	"	PUNCT
cana-4971	229	10	adapting	adapt	VERB
cana-4971	229	11	the	the	DET
cana-4971	229	12	laplace	laplace	NOUN
cana-4971	229	13	transform	transform	NOUN
cana-4971	229	14	to	to	PART
cana-4971	229	15	create	create	VERB
cana-4971	229	16	solitary	solitary	ADJ
cana-4971	229	17	solutions	solution	NOUN
cana-4971	229	18	for	for	ADP
cana-4971	229	19	the	the	DET
cana-4971	229	20	nonlinear	nonlinear	ADJ
cana-4971	229	21	time	time	NOUN
cana-4971	229	22	-	-	PUNCT
cana-4971	229	23	fractional	fractional	ADJ
cana-4971	229	24	dispersive	dispersive	ADJ
cana-4971	229	25	pdes	pde	NOUN
cana-4971	229	26	via	via	ADP
cana-4971	229	27	a	a	DET
cana-4971	229	28	new	new	ADJ
cana-4971	229	29	approach	approach	NOUN
cana-4971	229	30	,	,	PUNCT
cana-4971	229	31	”	"	PUNCT
cana-4971	229	32	the	the	DET
cana-4971	229	33	european	european	PROPN
cana-4971	229	34	physical	physical	PROPN
cana-4971	229	35	journal	journal	PROPN
cana-4971	229	36	plus	plus	CCONJ
cana-4971	229	37	,	,	PUNCT
cana-4971	229	38	vol	vol	NOUN
cana-4971	229	39	.	.	PROPN
cana-4971	229	40	136	136	NUM
cana-4971	229	41	,	,	PUNCT
cana-4971	229	42	no	no	INTJ
cana-4971	229	43	.	.	NOUN
cana-4971	229	44	2	2	NUM
cana-4971	229	45	,	,	PUNCT
cana-4971	229	46	feb	feb	PROPN
cana-4971	229	47	.	.	PROPN
cana-4971	229	48	2021	2021	NUM
cana-4971	229	49	,	,	PUNCT
cana-4971	229	50	doi	doi	NOUN
cana-4971	229	51	:	:	PUNCT
cana-4971	229	52	10.1140	10.1140	NUM
cana-4971	229	53	/	/	SYM
cana-4971	229	54	epjp	epjp	NOUN
cana-4971	229	55	/	/	SYM
cana-4971	229	56	s13360	s13360	NOUN
cana-4971	229	57	-	-	PUNCT
cana-4971	229	58	020	020	NUM
cana-4971	229	59	-	-	PUNCT
cana-4971	229	60	01061	01061	NUM
cana-4971	229	61	-	-	SYM
cana-4971	229	62	9	9	NUM
cana-4971	229	63	.	.	PUNCT
cana-4971	230	1	[	[	X
cana-4971	230	2	3	3	NUM
cana-4971	230	3	]	]	PUNCT
cana-4971	230	4	m.	m.	NOUN
cana-4971	230	5	alaroud	alaroud	PROPN
cana-4971	230	6	,	,	PUNCT
cana-4971	230	7	a.-k	a.-k	PROPN
cana-4971	230	8	.	.	PUNCT
cana-4971	231	1	alomari	alomari	PROPN
cana-4971	231	2	,	,	PUNCT
cana-4971	231	3	n.	n.	PROPN
cana-4971	231	4	tahat	tahat	PROPN
cana-4971	231	5	,	,	PUNCT
cana-4971	231	6	s.	s.	PROPN
cana-4971	231	7	al	al	PROPN
cana-4971	231	8	-	-	PUNCT
cana-4971	231	9	omari	omari	PROPN
cana-4971	231	10	,	,	PUNCT
cana-4971	231	11	and	and	CCONJ
cana-4971	231	12	a.	a.	NOUN
cana-4971	231	13	ishak	ishak	PROPN
cana-4971	231	14	,	,	PUNCT
cana-4971	231	15	“	"	PUNCT
cana-4971	231	16	a	a	DET
cana-4971	231	17	novel	novel	ADJ
cana-4971	231	18	solution	solution	NOUN
cana-4971	231	19	approach	approach	NOUN
cana-4971	231	20	for	for	ADP
cana-4971	231	21	time	time	NOUN
cana-4971	231	22	-	-	PUNCT
cana-4971	231	23	fractional	fractional	ADJ
cana-4971	231	24	hyperbolic	hyperbolic	ADJ
cana-4971	231	25	telegraph	telegraph	NOUN
cana-4971	231	26	differential	differential	NOUN
cana-4971	231	27	equation	equation	NOUN
cana-4971	231	28	with	with	ADP
cana-4971	231	29	caputo	caputo	PROPN
cana-4971	231	30	time	time	PROPN
cana-4971	231	31	differentiation	differentiation	NOUN
cana-4971	231	32	,	,	PUNCT
cana-4971	231	33	”	"	PUNCT
cana-4971	231	34	mathematics	mathematic	NOUN
cana-4971	231	35	,	,	PUNCT
cana-4971	231	36	vol	vol	NOUN
cana-4971	231	37	.	.	PROPN
cana-4971	231	38	11	11	NUM
cana-4971	231	39	,	,	PUNCT
cana-4971	231	40	no	no	INTJ
cana-4971	231	41	.	.	NOUN
cana-4971	231	42	9	9	NUM
cana-4971	231	43	,	,	PUNCT
cana-4971	231	44	p.	p.	NOUN
cana-4971	231	45	2181	2181	NUM
cana-4971	231	46	,	,	PUNCT
cana-4971	231	47	may	may	AUX
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cana-4971	232	5	.	.	PUNCT
cana-4971	233	1	siraj	siraj	PROPN
cana-4971	233	2	-	-	PUNCT
cana-4971	233	3	ul	ul	PROPN
cana-4971	233	4	-	-	PUNCT
cana-4971	233	5	islam	islam	PROPN
cana-4971	233	6	,	,	PUNCT
cana-4971	233	7	i.	i.	PROPN
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cana-4971	237	32	brusselator	brusselator	NOUN
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cana-4971	237	39	,	,	PUNCT
cana-4971	237	40	”	"	PUNCT
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cana-4971	237	42	,	,	PUNCT
cana-4971	237	43	vol	vol	NOUN
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cana-4971	238	41	”	"	PUNCT
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cana-4971	240	6	:	:	PUNCT
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