id	sid	tid	token	lemma	pos
cana-5476	1	1	communications	communication	NOUN
cana-5476	1	2	on	on	ADP
cana-5476	1	3	applied	apply	VERB
cana-5476	1	4	nonlinear	nonlinear	ADJ
cana-5476	1	5	analysis	analysis	NOUN
cana-5476	1	6	issn	issn	NOUN
cana-5476	1	7	:	:	PUNCT
cana-5476	1	8	1074	1074	NUM
cana-5476	1	9	-	-	PUNCT
cana-5476	1	10	133x	133x	NUM
cana-5476	1	11	vol	vol	NOUN
cana-5476	1	12	32	32	NUM
cana-5476	1	13	no	no	NOUN
cana-5476	1	14	.	.	PUNCT
cana-5476	2	1	1s	1s	NUM
cana-5476	2	2	(	(	PUNCT
cana-5476	2	3	2025	2025	NUM
cana-5476	2	4	)	)	PUNCT
cana-5476	2	5	665	665	NUM
cana-5476	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5476	2	7	applying	apply	VERB
cana-5476	2	8	differential	differential	ADJ
cana-5476	2	9	transform	transform	NOUN
cana-5476	2	10	method	method	NOUN
cana-5476	2	11	(	(	PUNCT
cana-5476	2	12	dtm	dtm	PROPN
cana-5476	2	13	)	)	PUNCT
cana-5476	2	14	to	to	PART
cana-5476	2	15	get	get	VERB
cana-5476	2	16	series	series	NOUN
cana-5476	2	17	solution	solution	NOUN
cana-5476	2	18	of	of	ADP
cana-5476	2	19	sixth	sixth	ADJ
cana-5476	2	20	order	order	NOUN
cana-5476	2	21	boundary	boundary	ADJ
cana-5476	2	22	value	value	NOUN
cana-5476	2	23	problems	problem	NOUN
cana-5476	2	24	dnyaneshwar	dnyaneshwar	PROPN
cana-5476	2	25	kadam1	kadam1	PROPN
cana-5476	2	26	,	,	PUNCT
cana-5476	2	27	avinash	avinash	PROPN
cana-5476	2	28	khambayat2	khambayat2	PROPN
cana-5476	2	29	1research	1research	NUM
cana-5476	2	30	scholar	scholar	NOUN
cana-5476	2	31	,	,	PUNCT
cana-5476	2	32	department	department	NOUN
cana-5476	2	33	of	of	ADP
cana-5476	2	34	mathematics	mathematic	NOUN
cana-5476	2	35	,	,	PUNCT
cana-5476	2	36	school	school	NOUN
cana-5476	2	37	of	of	ADP
cana-5476	2	38	science	science	NOUN
cana-5476	2	39	,	,	PUNCT
cana-5476	2	40	sandip	sandip	PROPN
cana-5476	2	41	university	university	PROPN
cana-5476	2	42	,	,	PUNCT
cana-5476	2	43	nasik	nasik	PROPN
cana-5476	2	44	,	,	PUNCT
cana-5476	2	45	maharashtra	maharashtra	PROPN
cana-5476	2	46	,	,	PUNCT
cana-5476	2	47	india	india	PROPN
cana-5476	2	48	1assistant	1assistant	PROPN
cana-5476	2	49	professor	professor	NOUN
cana-5476	2	50	,	,	PUNCT
cana-5476	2	51	xavier	xavier	PROPN
cana-5476	2	52	institute	institute	PROPN
cana-5476	2	53	of	of	ADP
cana-5476	2	54	engineering	engineering	PROPN
cana-5476	2	55	,	,	PUNCT
cana-5476	2	56	mumbai	mumbai	PROPN
cana-5476	2	57	,	,	PUNCT
cana-5476	2	58	maharashtra	maharashtra	PROPN
cana-5476	2	59	,	,	PUNCT
cana-5476	2	60	india	india	PROPN
cana-5476	2	61	2professor	2professor	PROPN
cana-5476	2	62	,	,	PUNCT
cana-5476	2	63	department	department	NOUN
cana-5476	2	64	of	of	ADP
cana-5476	2	65	mathematics	mathematic	NOUN
cana-5476	2	66	,	,	PUNCT
cana-5476	2	67	school	school	NOUN
cana-5476	2	68	of	of	ADP
cana-5476	2	69	science	science	NOUN
cana-5476	2	70	,	,	PUNCT
cana-5476	2	71	sandip	sandip	PROPN
cana-5476	2	72	university	university	PROPN
cana-5476	2	73	,	,	PUNCT
cana-5476	2	74	nasik	nasik	PROPN
cana-5476	2	75	,	,	PUNCT
cana-5476	2	76	maharashtra	maharashtra	PROPN
cana-5476	2	77	,	,	PUNCT
cana-5476	2	78	india	india	PROPN
cana-5476	2	79	1dskadam7@gmail.com	1dskadam7@gmail.com	NUM
cana-5476	2	80	,	,	PUNCT
cana-5476	2	81	2avinash.khambayat@sandipuniversity.edu.in	2avinash.khambayat@sandipuniversity.edu.in	NUM
cana-5476	2	82	article	article	NOUN
cana-5476	2	83	history	history	NOUN
cana-5476	2	84	:	:	PUNCT
cana-5476	2	85	received	receive	VERB
cana-5476	2	86	:	:	PUNCT
cana-5476	2	87	12	12	NUM
cana-5476	2	88	-	-	SYM
cana-5476	2	89	11	11	NUM
cana-5476	2	90	-	-	PUNCT
cana-5476	2	91	2024	2024	NUM
cana-5476	2	92	revised	revise	VERB
cana-5476	2	93	:	:	PUNCT
cana-5476	2	94	15	15	NUM
cana-5476	2	95	-	-	SYM
cana-5476	2	96	12	12	NUM
cana-5476	2	97	-	-	PUNCT
cana-5476	2	98	2024	2024	NUM
cana-5476	2	99	accepted	accept	VERB
cana-5476	2	100	:	:	PUNCT
cana-5476	2	101	18	18	NUM
cana-5476	2	102	-	-	SYM
cana-5476	2	103	01	01	NUM
cana-5476	2	104	-	-	PUNCT
cana-5476	2	105	2025	2025	NUM
cana-5476	2	106	abstract	abstract	NOUN
cana-5476	2	107	:	:	PUNCT
cana-5476	2	108	the	the	DET
cana-5476	2	109	differential	differential	ADJ
cana-5476	2	110	transform	transform	NOUN
cana-5476	2	111	method	method	NOUN
cana-5476	2	112	(	(	PUNCT
cana-5476	2	113	dtm	dtm	PROPN
cana-5476	2	114	)	)	PUNCT
cana-5476	2	115	is	be	AUX
cana-5476	2	116	an	an	DET
cana-5476	2	117	efficient	efficient	ADJ
cana-5476	2	118	and	and	CCONJ
cana-5476	2	119	versatile	versatile	ADJ
cana-5476	2	120	analytical	analytical	ADJ
cana-5476	2	121	technique	technique	NOUN
cana-5476	2	122	for	for	ADP
cana-5476	2	123	obtaining	obtain	VERB
cana-5476	2	124	series	series	NOUN
cana-5476	2	125	solutions	solution	NOUN
cana-5476	2	126	to	to	ADP
cana-5476	2	127	various	various	ADJ
cana-5476	2	128	differential	differential	NOUN
cana-5476	2	129	and	and	CCONJ
cana-5476	2	130	integral	integral	ADJ
cana-5476	2	131	equations	equation	NOUN
cana-5476	2	132	.	.	PUNCT
cana-5476	3	1	by	by	ADP
cana-5476	3	2	significantly	significantly	ADV
cana-5476	3	3	reducing	reduce	VERB
cana-5476	3	4	computational	computational	ADJ
cana-5476	3	5	effort	effort	NOUN
cana-5476	3	6	while	while	SCONJ
cana-5476	3	7	preserving	preserve	VERB
cana-5476	3	8	accuracy	accuracy	NOUN
cana-5476	3	9	,	,	PUNCT
cana-5476	3	10	the	the	DET
cana-5476	3	11	dtm	dtm	PROPN
cana-5476	3	12	offers	offer	VERB
cana-5476	3	13	an	an	DET
cana-5476	3	14	attractive	attractive	ADJ
cana-5476	3	15	alternative	alternative	NOUN
cana-5476	3	16	to	to	ADP
cana-5476	3	17	conventional	conventional	ADJ
cana-5476	3	18	methods	method	NOUN
cana-5476	3	19	.	.	PUNCT
cana-5476	4	1	this	this	DET
cana-5476	4	2	paper	paper	NOUN
cana-5476	4	3	demonstrates	demonstrate	VERB
cana-5476	4	4	the	the	DET
cana-5476	4	5	efficacy	efficacy	NOUN
cana-5476	4	6	and	and	CCONJ
cana-5476	4	7	simplicity	simplicity	NOUN
cana-5476	4	8	of	of	ADP
cana-5476	4	9	the	the	DET
cana-5476	4	10	dtm	dtm	NOUN
cana-5476	4	11	through	through	ADP
cana-5476	4	12	illustrative	illustrative	ADJ
cana-5476	4	13	examples	example	NOUN
cana-5476	4	14	,	,	PUNCT
cana-5476	4	15	focusing	focus	VERB
cana-5476	4	16	on	on	ADP
cana-5476	4	17	higher	high	ADJ
cana-5476	4	18	-	-	PUNCT
cana-5476	4	19	order	order	NOUN
cana-5476	4	20	differential	differential	ADJ
cana-5476	4	21	equations	equation	NOUN
cana-5476	4	22	with	with	ADP
cana-5476	4	23	boundary	boundary	ADJ
cana-5476	4	24	value	value	NOUN
cana-5476	4	25	problems	problem	NOUN
cana-5476	4	26	to	to	PART
cana-5476	4	27	derive	derive	VERB
cana-5476	4	28	precise	precise	ADJ
cana-5476	4	29	series	series	NOUN
cana-5476	4	30	solutions	solution	NOUN
cana-5476	4	31	.	.	PUNCT
cana-5476	5	1	furthermore	furthermore	ADV
cana-5476	5	2	,	,	PUNCT
cana-5476	5	3	the	the	DET
cana-5476	5	4	dtm	dtm	PROPN
cana-5476	5	5	's	's	PART
cana-5476	5	6	adaptability	adaptability	NOUN
cana-5476	5	7	and	and	CCONJ
cana-5476	5	8	ease	ease	NOUN
cana-5476	5	9	of	of	ADP
cana-5476	5	10	implementation	implementation	NOUN
cana-5476	5	11	make	make	VERB
cana-5476	5	12	it	it	PRON
cana-5476	5	13	particularly	particularly	ADV
cana-5476	5	14	suited	suit	VERB
cana-5476	5	15	for	for	ADP
cana-5476	5	16	solving	solve	VERB
cana-5476	5	17	complex	complex	ADJ
cana-5476	5	18	mathematical	mathematical	ADJ
cana-5476	5	19	models	model	NOUN
cana-5476	5	20	.	.	PUNCT
cana-5476	6	1	its	its	PRON
cana-5476	6	2	applications	application	NOUN
cana-5476	6	3	span	span	VERB
cana-5476	6	4	diverse	diverse	ADJ
cana-5476	6	5	fields	field	NOUN
cana-5476	6	6	,	,	PUNCT
cana-5476	6	7	including	include	VERB
cana-5476	6	8	engineering	engineering	NOUN
cana-5476	6	9	,	,	PUNCT
cana-5476	6	10	physics	physics	NOUN
cana-5476	6	11	,	,	PUNCT
cana-5476	6	12	and	and	CCONJ
cana-5476	6	13	applied	applied	ADJ
cana-5476	6	14	sciences	science	NOUN
cana-5476	6	15	,	,	PUNCT
cana-5476	6	16	where	where	SCONJ
cana-5476	6	17	it	it	PRON
cana-5476	6	18	has	have	AUX
cana-5476	6	19	been	be	AUX
cana-5476	6	20	effectively	effectively	ADV
cana-5476	6	21	utilized	utilize	VERB
cana-5476	6	22	for	for	ADP
cana-5476	6	23	analysing	analyse	VERB
cana-5476	6	24	heat	heat	NOUN
cana-5476	6	25	transfer	transfer	NOUN
cana-5476	6	26	,	,	PUNCT
cana-5476	6	27	fluid	fluid	ADJ
cana-5476	6	28	dynamics	dynamic	NOUN
cana-5476	6	29	,	,	PUNCT
cana-5476	6	30	wave	wave	NOUN
cana-5476	6	31	propagation	propagation	NOUN
cana-5476	6	32	,	,	PUNCT
cana-5476	6	33	and	and	CCONJ
cana-5476	6	34	electrical	electrical	ADJ
cana-5476	6	35	circuit	circuit	NOUN
cana-5476	6	36	problems	problem	NOUN
cana-5476	6	37	.	.	PUNCT
cana-5476	7	1	the	the	DET
cana-5476	7	2	findings	finding	NOUN
cana-5476	7	3	underscore	underscore	VERB
cana-5476	7	4	the	the	DET
cana-5476	7	5	potential	potential	NOUN
cana-5476	7	6	of	of	ADP
cana-5476	7	7	the	the	DET
cana-5476	7	8	dtm	dtm	PROPN
cana-5476	7	9	as	as	ADP
cana-5476	7	10	a	a	DET
cana-5476	7	11	powerful	powerful	ADJ
cana-5476	7	12	tool	tool	NOUN
cana-5476	7	13	for	for	ADP
cana-5476	7	14	tackling	tackle	VERB
cana-5476	7	15	challenging	challenging	ADJ
cana-5476	7	16	problems	problem	NOUN
cana-5476	7	17	in	in	ADP
cana-5476	7	18	theoretical	theoretical	ADJ
cana-5476	7	19	and	and	CCONJ
cana-5476	7	20	applied	applied	ADJ
cana-5476	7	21	mathematics	mathematic	NOUN
cana-5476	7	22	.	.	PUNCT
cana-5476	8	1	keywords	keyword	NOUN
cana-5476	8	2	:	:	PUNCT
cana-5476	8	3	differential	differential	NOUN
cana-5476	8	4	transform	transform	NOUN
cana-5476	8	5	method(dtm	method(dtm	PROPN
cana-5476	8	6	)	)	PUNCT
cana-5476	8	7	,	,	PUNCT
cana-5476	8	8	higher	high	ADJ
cana-5476	8	9	order	order	NOUN
cana-5476	8	10	boundary	boundary	ADJ
cana-5476	8	11	value	value	NOUN
cana-5476	8	12	problems	problem	NOUN
cana-5476	8	13	1	1	NUM
cana-5476	8	14	.	.	PUNCT
cana-5476	9	1	introduction	introduction	NOUN
cana-5476	9	2	the	the	DET
cana-5476	9	3	differential	differential	ADJ
cana-5476	9	4	transform	transform	NOUN
cana-5476	9	5	method	method	NOUN
cana-5476	9	6	(	(	PUNCT
cana-5476	9	7	dtm	dtm	PROPN
cana-5476	9	8	)	)	PUNCT
cana-5476	9	9	,	,	PUNCT
cana-5476	9	10	first	first	ADV
cana-5476	9	11	introduced	introduce	VERB
cana-5476	9	12	by	by	ADP
cana-5476	9	13	j.	j.	PROPN
cana-5476	9	14	k.	k.	PROPN
cana-5476	9	15	zhou	zhou	PROPN
cana-5476	9	16	in	in	ADP
cana-5476	9	17	1986	1986	NUM
cana-5476	9	18	for	for	ADP
cana-5476	9	19	solving	solve	VERB
cana-5476	9	20	problems	problem	NOUN
cana-5476	9	21	in	in	ADP
cana-5476	9	22	electric	electric	ADJ
cana-5476	9	23	circuits	circuit	NOUN
cana-5476	9	24	,	,	PUNCT
cana-5476	9	25	has	have	AUX
cana-5476	9	26	since	since	SCONJ
cana-5476	9	27	evolved	evolve	VERB
cana-5476	9	28	into	into	ADP
cana-5476	9	29	a	a	DET
cana-5476	9	30	versatile	versatile	ADJ
cana-5476	9	31	analytical	analytical	ADJ
cana-5476	9	32	tool	tool	NOUN
cana-5476	9	33	for	for	ADP
cana-5476	9	34	addressing	address	VERB
cana-5476	9	35	a	a	DET
cana-5476	9	36	wide	wide	ADJ
cana-5476	9	37	range	range	NOUN
cana-5476	9	38	of	of	ADP
cana-5476	9	39	mathematical	mathematical	ADJ
cana-5476	9	40	problems	problem	NOUN
cana-5476	9	41	[	[	X
cana-5476	9	42	2	2	NUM
cana-5476	9	43	]	]	PUNCT
cana-5476	9	44	.	.	PUNCT
cana-5476	10	1	farshid	farshid	PROPN
cana-5476	10	2	mirzaee	mirzaee	PROPN
cana-5476	10	3	extended	extend	VERB
cana-5476	10	4	its	its	PRON
cana-5476	10	5	application	application	NOUN
cana-5476	10	6	to	to	ADP
cana-5476	10	7	ordinary	ordinary	ADJ
cana-5476	10	8	linear	linear	ADJ
cana-5476	10	9	and	and	CCONJ
cana-5476	10	10	nonlinear	nonlinear	ADJ
cana-5476	10	11	differential	differential	ADJ
cana-5476	10	12	equations	equation	NOUN
cana-5476	10	13	[	[	X
cana-5476	10	14	1	1	NUM
cana-5476	10	15	]	]	PUNCT
cana-5476	10	16	,	,	PUNCT
cana-5476	10	17	while	while	SCONJ
cana-5476	10	18	narhari	narhari	PROPN
cana-5476	10	19	patil	patil	PROPN
cana-5476	10	20	and	and	CCONJ
cana-5476	10	21	avinash	avinash	PROPN
cana-5476	10	22	khambayat	khambayat	PROPN
cana-5476	10	23	utilized	utilize	VERB
cana-5476	10	24	it	it	PRON
cana-5476	10	25	for	for	ADP
cana-5476	10	26	solving	solve	VERB
cana-5476	10	27	linear	linear	PROPN
cana-5476	10	28	differential	differential	ADJ
cana-5476	10	29	equations	equation	NOUN
cana-5476	11	1	[	[	X
cana-5476	11	2	3	3	NUM
cana-5476	11	3	]	]	PUNCT
cana-5476	11	4	.	.	PUNCT
cana-5476	12	1	shawagfeh	shawagfeh	PROPN
cana-5476	12	2	n.	n.	PROPN
cana-5476	12	3	and	and	CCONJ
cana-5476	12	4	kaya	kaya	PROPN
cana-5476	12	5	d	d	PROPN
cana-5476	12	6	used	use	VERB
cana-5476	12	7	dtm	dtm	PROPN
cana-5476	12	8	for	for	ADP
cana-5476	12	9	solving	solve	VERB
cana-5476	12	10	the	the	DET
cana-5476	12	11	euler	euler	NOUN
cana-5476	12	12	equidimensional	equidimensional	ADJ
cana-5476	12	13	equation.[4	equation.[4	NOUN
cana-5476	12	14	]	]	PUNCT
cana-5476	12	15	.	.	PUNCT
cana-5476	13	1	y.	y.	PROPN
cana-5476	13	2	keskin	keskin	PROPN
cana-5476	13	3	and	and	CCONJ
cana-5476	13	4	g.	g.	PROPN
cana-5476	13	5	oturance	oturance	PROPN
cana-5476	13	6	further	far	ADV
cana-5476	13	7	advanced	advance	VERB
cana-5476	13	8	the	the	DET
cana-5476	13	9	method	method	NOUN
cana-5476	13	10	by	by	ADP
cana-5476	13	11	employing	employ	VERB
cana-5476	13	12	the	the	DET
cana-5476	13	13	reduced	reduce	VERB
cana-5476	13	14	differential	differential	ADJ
cana-5476	13	15	transform	transform	NOUN
cana-5476	13	16	method	method	NOUN
cana-5476	13	17	(	(	PUNCT
cana-5476	13	18	rdtm	rdtm	VERB
cana-5476	13	19	)	)	PUNCT
cana-5476	13	20	to	to	PART
cana-5476	13	21	tackle	tackle	VERB
cana-5476	13	22	partial	partial	ADJ
cana-5476	13	23	differential	differential	NOUN
cana-5476	13	24	equations	equation	NOUN
cana-5476	13	25	[	[	X
cana-5476	13	26	5	5	NUM
cana-5476	13	27	]	]	PUNCT
cana-5476	13	28	.	.	PUNCT
cana-5476	14	1	in	in	ADP
cana-5476	14	2	recent	recent	ADJ
cana-5476	14	3	years	year	NOUN
cana-5476	14	4	,	,	PUNCT
cana-5476	14	5	dtm	dtm	PROPN
cana-5476	14	6	has	have	AUX
cana-5476	14	7	gained	gain	VERB
cana-5476	14	8	significant	significant	ADJ
cana-5476	14	9	attention	attention	NOUN
cana-5476	14	10	for	for	ADP
cana-5476	14	11	its	its	PRON
cana-5476	14	12	ability	ability	NOUN
cana-5476	14	13	to	to	PART
cana-5476	14	14	solve	solve	VERB
cana-5476	14	15	fractional	fractional	ADJ
cana-5476	14	16	differential	differential	NOUN
cana-5476	14	17	equations	equation	NOUN
cana-5476	14	18	,	,	PUNCT
cana-5476	14	19	as	as	SCONJ
cana-5476	14	20	highlighted	highlight	VERB
cana-5476	14	21	in	in	ADP
cana-5476	14	22	studies	study	NOUN
cana-5476	14	23	focusing	focus	VERB
cana-5476	14	24	on	on	ADP
cana-5476	14	25	its	its	PRON
cana-5476	14	26	application	application	NOUN
cana-5476	14	27	to	to	ADP
cana-5476	14	28	boundary	boundary	ADJ
cana-5476	14	29	value	value	NOUN
cana-5476	14	30	problems	problem	NOUN
cana-5476	14	31	,	,	PUNCT
cana-5476	14	32	optimal	optimal	ADJ
cana-5476	14	33	control	control	NOUN
cana-5476	14	34	,	,	PUNCT
cana-5476	14	35	and	and	CCONJ
cana-5476	14	36	calculus	calculus	NOUN
cana-5476	14	37	of	of	ADP
cana-5476	14	38	variations	variation	NOUN
cana-5476	14	39	[	[	X
cana-5476	14	40	2	2	NUM
cana-5476	14	41	]	]	PUNCT
cana-5476	14	42	.	.	PUNCT
cana-5476	15	1	additionally	additionally	ADV
cana-5476	15	2	,	,	PUNCT
cana-5476	15	3	advancements	advancement	NOUN
cana-5476	15	4	in	in	ADP
cana-5476	15	5	fractional	fractional	ADJ
cana-5476	15	6	dtm	dtm	PROPN
cana-5476	15	7	have	have	AUX
cana-5476	15	8	opened	open	VERB
cana-5476	15	9	new	new	ADJ
cana-5476	15	10	avenues	avenue	NOUN
cana-5476	15	11	for	for	ADP
cana-5476	15	12	addressing	address	VERB
cana-5476	15	13	problems	problem	NOUN
cana-5476	15	14	in	in	ADP
cana-5476	15	15	engineering	engineering	NOUN
cana-5476	15	16	and	and	CCONJ
cana-5476	15	17	applied	apply	VERB
cana-5476	15	18	sciences	science	NOUN
cana-5476	15	19	,	,	PUNCT
cana-5476	15	20	further	far	ADV
cana-5476	15	21	solidifying	solidify	VERB
cana-5476	15	22	its	its	PRON
cana-5476	15	23	role	role	NOUN
cana-5476	15	24	as	as	ADP
cana-5476	15	25	a	a	DET
cana-5476	15	26	powerful	powerful	ADJ
cana-5476	15	27	semi	semi	ADJ
cana-5476	15	28	-	-	ADJ
cana-5476	15	29	analytical	analytical	ADJ
cana-5476	15	30	method	method	NOUN
cana-5476	15	31	[	[	X
cana-5476	15	32	1	1	NUM
cana-5476	15	33	]	]	PUNCT
cana-5476	15	34	.	.	PUNCT
cana-5476	16	1	dtm	dtm	PROPN
cana-5476	16	2	's	's	PART
cana-5476	16	3	adaptability	adaptability	NOUN
cana-5476	16	4	and	and	CCONJ
cana-5476	16	5	computational	computational	ADJ
cana-5476	16	6	efficiency	efficiency	NOUN
cana-5476	16	7	make	make	VERB
cana-5476	16	8	it	it	PRON
cana-5476	16	9	a	a	DET
cana-5476	16	10	valuable	valuable	ADJ
cana-5476	16	11	tool	tool	NOUN
cana-5476	16	12	for	for	ADP
cana-5476	16	13	solving	solve	VERB
cana-5476	16	14	both	both	CCONJ
cana-5476	16	15	linear	linear	ADJ
cana-5476	16	16	and	and	CCONJ
cana-5476	16	17	nonlinear	nonlinear	ADJ
cana-5476	16	18	ordinary	ordinary	ADJ
cana-5476	16	19	and	and	CCONJ
cana-5476	16	20	partial	partial	ADJ
cana-5476	16	21	differential	differential	NOUN
cana-5476	16	22	equations	equation	NOUN
cana-5476	16	23	,	,	PUNCT
cana-5476	16	24	offering	offer	VERB
cana-5476	16	25	precise	precise	ADJ
cana-5476	16	26	solutions	solution	NOUN
cana-5476	16	27	with	with	ADP
cana-5476	16	28	reduced	reduce	VERB
cana-5476	16	29	effort	effort	NOUN
cana-5476	16	30	compared	compare	VERB
cana-5476	16	31	to	to	ADP
cana-5476	16	32	traditional	traditional	ADJ
cana-5476	16	33	numerical	numerical	ADJ
cana-5476	16	34	methods	method	NOUN
cana-5476	16	35	.	.	PUNCT
cana-5476	17	1	communications	communication	NOUN
cana-5476	17	2	on	on	ADP
cana-5476	17	3	applied	apply	VERB
cana-5476	17	4	nonlinear	nonlinear	ADJ
cana-5476	17	5	analysis	analysis	NOUN
cana-5476	17	6	issn	issn	NOUN
cana-5476	17	7	:	:	PUNCT
cana-5476	17	8	1074	1074	NUM
cana-5476	17	9	-	-	PUNCT
cana-5476	17	10	133x	133x	NUM
cana-5476	17	11	vol	vol	NOUN
cana-5476	17	12	32	32	NUM
cana-5476	17	13	no	no	NOUN
cana-5476	17	14	.	.	PUNCT
cana-5476	18	1	1s	1s	NUM
cana-5476	18	2	(	(	PUNCT
cana-5476	18	3	2025	2025	NUM
cana-5476	18	4	)	)	PUNCT
cana-5476	18	5	666	666	NUM
cana-5476	19	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5476	19	2	2	2	X
cana-5476	19	3	.	.	X
cana-5476	19	4	objectives	objective	NOUN
cana-5476	19	5	this	this	DET
cana-5476	19	6	study	study	NOUN
cana-5476	19	7	aims	aim	VERB
cana-5476	19	8	to	to	PART
cana-5476	19	9	explore	explore	VERB
cana-5476	19	10	the	the	DET
cana-5476	19	11	efficiency	efficiency	NOUN
cana-5476	19	12	and	and	CCONJ
cana-5476	19	13	applicability	applicability	NOUN
cana-5476	19	14	of	of	ADP
cana-5476	19	15	the	the	DET
cana-5476	19	16	differential	differential	ADJ
cana-5476	19	17	transform	transform	NOUN
cana-5476	19	18	method	method	NOUN
cana-5476	19	19	(	(	PUNCT
cana-5476	19	20	dtm	dtm	PROPN
cana-5476	19	21	)	)	PUNCT
cana-5476	19	22	in	in	ADP
cana-5476	19	23	deriving	derive	VERB
cana-5476	19	24	series	series	NOUN
cana-5476	19	25	solutions	solution	NOUN
cana-5476	19	26	for	for	ADP
cana-5476	19	27	sixth	sixth	ADJ
cana-5476	19	28	-	-	PUNCT
cana-5476	19	29	order	order	NOUN
cana-5476	19	30	boundary	boundary	ADJ
cana-5476	19	31	value	value	NOUN
cana-5476	19	32	problems	problem	NOUN
cana-5476	19	33	.	.	PUNCT
cana-5476	20	1	by	by	ADP
cana-5476	20	2	systematically	systematically	ADV
cana-5476	20	3	analysing	analyse	VERB
cana-5476	20	4	its	its	PRON
cana-5476	20	5	computational	computational	ADJ
cana-5476	20	6	advantages	advantage	NOUN
cana-5476	20	7	,	,	PUNCT
cana-5476	20	8	the	the	DET
cana-5476	20	9	research	research	NOUN
cana-5476	20	10	seeks	seek	VERB
cana-5476	20	11	to	to	PART
cana-5476	20	12	establish	establish	VERB
cana-5476	20	13	dtm	dtm	PROPN
cana-5476	20	14	as	as	ADP
cana-5476	20	15	a	a	DET
cana-5476	20	16	reliable	reliable	ADJ
cana-5476	20	17	approach	approach	NOUN
cana-5476	20	18	for	for	ADP
cana-5476	20	19	tackling	tackle	VERB
cana-5476	20	20	complex	complex	ADJ
cana-5476	20	21	differential	differential	ADJ
cana-5476	20	22	equations	equation	NOUN
cana-5476	20	23	with	with	ADP
cana-5476	20	24	boundary	boundary	ADJ
cana-5476	20	25	constraints	constraint	NOUN
cana-5476	20	26	.	.	PUNCT
cana-5476	21	1	the	the	DET
cana-5476	21	2	study	study	NOUN
cana-5476	21	3	will	will	AUX
cana-5476	21	4	demonstrate	demonstrate	VERB
cana-5476	21	5	the	the	DET
cana-5476	21	6	effectiveness	effectiveness	NOUN
cana-5476	21	7	of	of	ADP
cana-5476	21	8	dtm	dtm	PROPN
cana-5476	21	9	through	through	ADP
cana-5476	21	10	practical	practical	ADJ
cana-5476	21	11	examples	example	NOUN
cana-5476	21	12	,	,	PUNCT
cana-5476	21	13	highlighting	highlight	VERB
cana-5476	21	14	its	its	PRON
cana-5476	21	15	role	role	NOUN
cana-5476	21	16	in	in	ADP
cana-5476	21	17	simplifying	simplify	VERB
cana-5476	21	18	problem	problem	NOUN
cana-5476	21	19	-	-	PUNCT
cana-5476	21	20	solving	solving	NOUN
cana-5476	21	21	while	while	SCONJ
cana-5476	21	22	maintaining	maintain	VERB
cana-5476	21	23	precision	precision	NOUN
cana-5476	21	24	.	.	PUNCT
cana-5476	22	1	additionally	additionally	ADV
cana-5476	22	2	,	,	PUNCT
cana-5476	22	3	the	the	DET
cana-5476	22	4	research	research	NOUN
cana-5476	22	5	intends	intend	VERB
cana-5476	22	6	to	to	PART
cana-5476	22	7	investigate	investigate	VERB
cana-5476	22	8	the	the	DET
cana-5476	22	9	adaptability	adaptability	NOUN
cana-5476	22	10	of	of	ADP
cana-5476	22	11	dtm	dtm	PROPN
cana-5476	22	12	across	across	ADP
cana-5476	22	13	various	various	ADJ
cana-5476	22	14	scientific	scientific	ADJ
cana-5476	22	15	fields	field	NOUN
cana-5476	22	16	,	,	PUNCT
cana-5476	22	17	including	include	VERB
cana-5476	22	18	engineering	engineering	NOUN
cana-5476	22	19	and	and	CCONJ
cana-5476	22	20	physics	physics	NOUN
cana-5476	22	21	,	,	PUNCT
cana-5476	22	22	reinforcing	reinforce	VERB
cana-5476	22	23	its	its	PRON
cana-5476	22	24	potential	potential	NOUN
cana-5476	22	25	as	as	ADP
cana-5476	22	26	a	a	DET
cana-5476	22	27	valuable	valuable	ADJ
cana-5476	22	28	analytical	analytical	ADJ
cana-5476	22	29	tool	tool	NOUN
cana-5476	22	30	for	for	ADP
cana-5476	22	31	mathematical	mathematical	ADJ
cana-5476	22	32	modelling	modelling	NOUN
cana-5476	22	33	.	.	PUNCT
cana-5476	23	1	3	3	X
cana-5476	23	2	.	.	X
cana-5476	23	3	methods	method	NOUN
cana-5476	23	4	the	the	DET
cana-5476	23	5	differential	differential	ADJ
cana-5476	23	6	transform	transform	NOUN
cana-5476	23	7	method	method	NOUN
cana-5476	23	8	:	:	PUNCT
cana-5476	23	9	the	the	DET
cana-5476	23	10	𝑟th	𝑟th	ADJ
cana-5476	23	11	derivative	derivative	NOUN
cana-5476	23	12	of	of	ADP
cana-5476	23	13	a	a	DET
cana-5476	23	14	function	function	NOUN
cana-5476	23	15	is	be	AUX
cana-5476	23	16	transformed	transform	VERB
cana-5476	23	17	as	as	SCONJ
cana-5476	23	18	described	describe	VERB
cana-5476	23	19	below	below	ADV
cana-5476	23	20	.	.	PUNCT
cana-5476	24	1	𝑈(𝑟	𝑈(𝑟	X
cana-5476	24	2	)	)	PUNCT
cana-5476	24	3	=	=	SYM
cana-5476	24	4	1	1	NUM
cana-5476	24	5	𝑟	𝑟	NOUN
cana-5476	24	6	!	!	PUNCT
cana-5476	25	1	(	(	PUNCT
cana-5476	25	2	𝑑𝑟𝑢(𝑥	𝑑𝑟𝑢(𝑥	PROPN
cana-5476	25	3	)	)	PUNCT
cana-5476	25	4	𝑑𝑥𝑟	𝑑𝑥𝑟	NOUN
cana-5476	25	5	)	)	PUNCT
cana-5476	26	1	𝑎𝑡	𝑎𝑡	ADP
cana-5476	26	2	𝑥	𝑥	PRON
cana-5476	26	3	=	=	SYM
cana-5476	26	4	𝑥0	𝑥0	NOUN
cana-5476	26	5	…	…	PUNCT
cana-5476	26	6	(	(	PUNCT
cana-5476	26	7	1	1	X
cana-5476	26	8	)	)	PUNCT
cana-5476	26	9	let	let	VERB
cana-5476	26	10	u(x	u(x	NOUN
cana-5476	26	11	)	)	PUNCT
cana-5476	26	12	represent	represent	VERB
cana-5476	26	13	the	the	DET
cana-5476	26	14	original	original	ADJ
cana-5476	26	15	function	function	NOUN
cana-5476	26	16	and	and	CCONJ
cana-5476	26	17	u(r	u(r	NOUN
cana-5476	26	18	)	)	PUNCT
cana-5476	27	1	denote	denote	VERB
cana-5476	27	2	the	the	DET
cana-5476	27	3	transformed	transform	VERB
cana-5476	27	4	function	function	NOUN
cana-5476	27	5	.	.	PUNCT
cana-5476	28	1	the	the	DET
cana-5476	28	2	inverse	inverse	ADJ
cana-5476	28	3	differential	differential	NOUN
cana-5476	28	4	transformation	transformation	NOUN
cana-5476	28	5	of	of	ADP
cana-5476	28	6	u(r	u(r	NOUN
cana-5476	28	7	)	)	PUNCT
cana-5476	28	8	is	be	AUX
cana-5476	28	9	defined	define	VERB
cana-5476	28	10	as	as	SCONJ
cana-5476	28	11	follows	follow	VERB
cana-5476	28	12	:	:	PUNCT
cana-5476	28	13	𝑢(𝑥	𝑢(𝑥	NUM
cana-5476	28	14	)	)	PUNCT
cana-5476	28	15	=	=	PUNCT
cana-5476	29	1	∑	∑	PUNCT
cana-5476	29	2	𝑈(𝑟)(𝑥	𝑈(𝑟)(𝑥	ADP
cana-5476	29	3	−	−	NOUN
cana-5476	29	4	𝑥0)𝑟	𝑥0)𝑟	VERB
cana-5476	29	5	∞	∞	PROPN
cana-5476	29	6	𝑟=0	𝑟=0	PUNCT
cana-5476	29	7	…	…	PUNCT
cana-5476	29	8	(	(	PUNCT
cana-5476	29	9	2	2	NUM
cana-5476	29	10	)	)	PUNCT
cana-5476	29	11	if	if	SCONJ
cana-5476	29	12	𝑥0	𝑥0	NOUN
cana-5476	29	13	=	=	SYM
cana-5476	29	14	0	0	NUM
cana-5476	29	15	,	,	PUNCT
cana-5476	29	16	the	the	DET
cana-5476	29	17	function	function	NOUN
cana-5476	29	18	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	29	19	)	)	PUNCT
cana-5476	29	20	in	in	ADP
cana-5476	29	21	(	(	PUNCT
cana-5476	29	22	2	2	X
cana-5476	29	23	)	)	PUNCT
cana-5476	29	24	is	be	AUX
cana-5476	29	25	expressed	express	VERB
cana-5476	29	26	as	as	ADP
cana-5476	29	27	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	29	28	)	)	PUNCT
cana-5476	29	29	=	=	PUNCT
cana-5476	30	1	∑	∑	PUNCT
cana-5476	30	2	𝑈(𝑟	𝑈(𝑟	X
cana-5476	30	3	)	)	PUNCT
cana-5476	30	4	∞	∞	NUM
cana-5476	30	5	𝑟=0	𝑟=0	PUNCT
cana-5476	30	6	𝑥𝑟	𝑥𝑟	NOUN
cana-5476	30	7	…	…	PUNCT
cana-5476	30	8	(	(	PUNCT
cana-5476	30	9	3	3	X
cana-5476	30	10	)	)	PUNCT
cana-5476	30	11	we	we	PRON
cana-5476	30	12	utilize	utilize	VERB
cana-5476	30	13	the	the	DET
cana-5476	30	14	following	follow	VERB
cana-5476	30	15	core	core	ADJ
cana-5476	30	16	theorems	theorem	NOUN
cana-5476	30	17	of	of	ADP
cana-5476	30	18	the	the	DET
cana-5476	30	19	differential	differential	ADJ
cana-5476	30	20	transform	transform	NOUN
cana-5476	30	21	method	method	NOUN
cana-5476	30	22	given	give	VERB
cana-5476	30	23	by	by	ADP
cana-5476	30	24	j.	j.	PROPN
cana-5476	30	25	k.	k.	PROPN
cana-5476	30	26	zhou	zhou	PROPN
cana-5476	31	1	[	[	X
cana-5476	31	2	1	1	NUM
cana-5476	31	3	]	]	PUNCT
cana-5476	31	4	:	:	PUNCT
cana-5476	31	5	theorem	theorem	NOUN
cana-5476	31	6	1	1	NUM
cana-5476	31	7	]	]	PUNCT
cana-5476	31	8	if	if	SCONJ
cana-5476	31	9	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	31	10	)	)	PUNCT
cana-5476	31	11	=	=	SYM
cana-5476	31	12	𝛼𝑔(𝑥	𝛼𝑔(𝑥	PROPN
cana-5476	31	13	)	)	PUNCT
cana-5476	31	14	±	±	NOUN
cana-5476	31	15	𝛽ℎ(𝑥	𝛽ℎ(𝑥	NUM
cana-5476	31	16	)	)	PUNCT
cana-5476	31	17	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	VERB
cana-5476	31	18	𝑈(𝑟	𝑈(𝑟	NOUN
cana-5476	31	19	)	)	PUNCT
cana-5476	31	20	=	=	SYM
cana-5476	31	21	𝛼𝐺(𝑟	𝛼𝐺(𝑟	PROPN
cana-5476	31	22	)	)	PUNCT
cana-5476	31	23	±	±	PROPN
cana-5476	31	24	𝛽𝐻(𝑟	𝛽𝐻(𝑟	PROPN
cana-5476	31	25	)	)	PUNCT
cana-5476	31	26	theorem	theorem	VERB
cana-5476	31	27	2	2	NUM
cana-5476	31	28	]	]	PUNCT
cana-5476	31	29	if	if	SCONJ
cana-5476	31	30	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	31	31	)	)	PUNCT
cana-5476	31	32	=	=	NOUN
cana-5476	32	1	𝑥𝑚	𝑥𝑚	NOUN
cana-5476	32	2	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	VERB
cana-5476	32	3	𝑈	𝑈	PROPN
cana-5476	32	4	(	(	PUNCT
cana-5476	32	5	𝑟	𝑟	NOUN
cana-5476	32	6	)	)	PUNCT
cana-5476	32	7	=	=	SYM
cana-5476	32	8	𝛿(𝑟	𝛿(𝑟	PROPN
cana-5476	32	9	−	−	PROPN
cana-5476	32	10	𝑚	𝑚	NOUN
cana-5476	32	11	)	)	PUNCT
cana-5476	32	12	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	ADJ
cana-5476	32	13	𝛿(𝑟	𝛿(𝑟	PROPN
cana-5476	32	14	−	−	PROPN
cana-5476	32	15	𝑚	𝑚	NOUN
cana-5476	32	16	)	)	PUNCT
cana-5476	32	17	=	=	NOUN
cana-5476	32	18	{	{	PUNCT
cana-5476	32	19	1	1	NUM
cana-5476	32	20	,	,	PUNCT
cana-5476	32	21	𝑖𝑓	𝑖𝑓	NOUN
cana-5476	32	22	𝑟	𝑟	NOUN
cana-5476	32	23	=	=	SYM
cana-5476	32	24	𝑚	𝑚	PROPN
cana-5476	32	25	0	0	NUM
cana-5476	32	26	,	,	PUNCT
cana-5476	32	27	𝑖𝑓	𝑖𝑓	ADP
cana-5476	32	28	𝑟	𝑟	NOUN
cana-5476	32	29	≠	≠	PROPN
cana-5476	32	30	𝑚	𝑚	PROPN
cana-5476	32	31	theorem	theorem	NOUN
cana-5476	32	32	3	3	NUM
cana-5476	32	33	]	]	PUNCT
cana-5476	32	34	if	if	SCONJ
cana-5476	32	35	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	32	36	)	)	PUNCT
cana-5476	32	37	=	=	NOUN
cana-5476	32	38	𝑒𝑥	𝑒𝑥	NOUN
cana-5476	32	39	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	VERB
cana-5476	32	40	𝑈(𝑟	𝑈(𝑟	NOUN
cana-5476	32	41	)	)	PUNCT
cana-5476	32	42	=	=	SYM
cana-5476	32	43	1	1	NUM
cana-5476	32	44	𝑟	𝑟	NOUN
cana-5476	32	45	!	!	PUNCT
cana-5476	32	46	theorem	theorem	VERB
cana-5476	32	47	4	4	NUM
cana-5476	32	48	]	]	PUNCT
cana-5476	32	49	if	if	SCONJ
cana-5476	32	50	𝑢	𝑢	X
cana-5476	32	51	(	(	PUNCT
cana-5476	32	52	𝑥	𝑥	NOUN
cana-5476	32	53	)	)	PUNCT
cana-5476	32	54	=	=	SYM
cana-5476	32	55	𝑔	𝑔	PROPN
cana-5476	32	56	(	(	PUNCT
cana-5476	32	57	𝑥	𝑥	NOUN
cana-5476	32	58	)	)	PUNCT
cana-5476	32	59	ℎ	ℎ	PROPN
cana-5476	32	60	(	(	PUNCT
cana-5476	32	61	𝑥	𝑥	NOUN
cana-5476	32	62	)	)	PUNCT
cana-5476	32	63	then	then	ADV
cana-5476	32	64	𝑈(𝑟	𝑈(𝑟	ADP
cana-5476	32	65	)	)	PUNCT
cana-5476	32	66	=	=	PUNCT
cana-5476	32	67	∑	∑	PUNCT
cana-5476	32	68	𝐺(𝑙)𝐻(𝑟	𝐺(𝑙)𝐻(𝑟	PROPN
cana-5476	32	69	−	−	PROPN
cana-5476	32	70	𝑙)𝑟	𝑙)𝑟	X
cana-5476	32	71	𝑙=0	𝑙=0	PROPN
cana-5476	32	72	theorem	theorem	VERB
cana-5476	32	73	5	5	NUM
cana-5476	32	74	]	]	PUNCT
cana-5476	32	75	if	if	SCONJ
cana-5476	32	76	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	32	77	)	)	PUNCT
cana-5476	32	78	=	=	SYM
cana-5476	32	79	𝑢1(𝑥	𝑢1(𝑥	NUM
cana-5476	32	80	)	)	PUNCT
cana-5476	32	81	𝑢2(𝑥	𝑢2(𝑥	PROPN
cana-5476	32	82	)	)	PUNCT
cana-5476	32	83	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	VERB
cana-5476	32	84	𝑈(𝑟	𝑈(𝑟	NOUN
cana-5476	32	85	)	)	PUNCT
cana-5476	32	86	=	=	SYM
cana-5476	32	87	∑	∑	PUNCT
cana-5476	32	88	𝑈1(𝑟1	𝑈1(𝑟1	PROPN
cana-5476	32	89	)	)	PUNCT
cana-5476	32	90	𝑈2(𝑟	𝑈2(𝑟	VERB
cana-5476	32	91	−	−	NOUN
cana-5476	32	92	𝑟1)𝑟	𝑟1)𝑟	NOUN
cana-5476	32	93	𝑟1=0	𝑟1=0	ADJ
cana-5476	32	94	communications	communication	NOUN
cana-5476	32	95	on	on	ADP
cana-5476	32	96	applied	apply	VERB
cana-5476	32	97	nonlinear	nonlinear	ADJ
cana-5476	32	98	analysis	analysis	NOUN
cana-5476	32	99	issn	issn	NOUN
cana-5476	32	100	:	:	PUNCT
cana-5476	32	101	1074	1074	NUM
cana-5476	32	102	-	-	PUNCT
cana-5476	32	103	133x	133x	NUM
cana-5476	32	104	vol	vol	NOUN
cana-5476	32	105	32	32	NUM
cana-5476	32	106	no	no	NOUN
cana-5476	32	107	.	.	PUNCT
cana-5476	33	1	1s	1s	NUM
cana-5476	33	2	(	(	PUNCT
cana-5476	33	3	2025	2025	NUM
cana-5476	33	4	)	)	PUNCT
cana-5476	33	5	667	667	NUM
cana-5476	33	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5476	33	7	theorem	theorem	VERB
cana-5476	33	8	6	6	NUM
cana-5476	33	9	]	]	PUNCT
cana-5476	33	10	if	if	SCONJ
cana-5476	33	11	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	33	12	)	)	PUNCT
cana-5476	33	13	=	=	PUNCT
cana-5476	33	14	𝑑𝑛𝑢1(𝑥	𝑑𝑛𝑢1(𝑥	X
cana-5476	33	15	)	)	PUNCT
cana-5476	33	16	𝑑𝑥𝑛	𝑑𝑥𝑛	VERB
cana-5476	33	17	,	,	PUNCT
cana-5476	33	18	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	NOUN
cana-5476	33	19	𝑈(𝑟	𝑈(𝑟	NOUN
cana-5476	33	20	)	)	PUNCT
cana-5476	33	21	=	=	SYM
cana-5476	33	22	(	(	PUNCT
cana-5476	33	23	𝑟+𝑛	𝑟+𝑛	PROPN
cana-5476	33	24	)	)	PUNCT
cana-5476	33	25	!	!	PUNCT
cana-5476	34	1	𝑟	𝑟	X
cana-5476	34	2	!	!	X
cana-5476	34	3	𝑈1(𝑟	𝑈1(𝑟	PROPN
cana-5476	34	4	+	+	CCONJ
cana-5476	34	5	𝑛	𝑛	X
cana-5476	34	6	)	)	PUNCT
cana-5476	34	7	theorem	theorem	VERB
cana-5476	34	8	7	7	NUM
cana-5476	34	9	]	]	PUNCT
cana-5476	34	10	if	if	SCONJ
cana-5476	34	11	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	34	12	)	)	PUNCT
cana-5476	35	1	=	=	PUNCT
cana-5476	35	2	𝑒𝜆𝑥	𝑒𝜆𝑥	NOUN
cana-5476	35	3	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	VERB
cana-5476	35	4	𝑈(𝑟	𝑈(𝑟	NOUN
cana-5476	35	5	)	)	PUNCT
cana-5476	35	6	=	=	PRON
cana-5476	35	7	𝜆𝑟	𝜆𝑟	ADJ
cana-5476	35	8	𝑟	𝑟	NOUN
cana-5476	35	9	!	!	NOUN
cana-5476	35	10	,	,	PUNCT
cana-5476	35	11	𝜆	𝜆	PRON
cana-5476	35	12	𝑖𝑠	𝑖𝑠	NOUN
cana-5476	35	13	𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡	𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡	NOUN
cana-5476	35	14	theorem	theorem	VERB
cana-5476	35	15	8	8	NUM
cana-5476	35	16	]	]	PUNCT
cana-5476	35	17	if	if	SCONJ
cana-5476	35	18	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	35	19	)	)	PUNCT
cana-5476	35	20	=	=	NOUN
cana-5476	35	21	𝑠𝑖𝑛(𝑤𝑥	𝑠𝑖𝑛(𝑤𝑥	NOUN
cana-5476	35	22	+	+	SYM
cana-5476	35	23	𝛼	𝛼	X
cana-5476	35	24	)	)	PUNCT
cana-5476	35	25	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	NOUN
cana-5476	35	26	𝑈(𝑟	𝑈(𝑟	NOUN
cana-5476	35	27	)	)	PUNCT
cana-5476	35	28	=	=	SYM
cana-5476	35	29	𝑤𝑟	𝑤𝑟	PROPN
cana-5476	35	30	𝑟	𝑟	X
cana-5476	35	31	!	!	PUNCT
cana-5476	35	32	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
cana-5476	35	33	(	(	PUNCT
cana-5476	35	34	𝑟	𝑟	NOUN
cana-5476	35	35	𝜋	𝜋	SYM
cana-5476	35	36	2	2	NUM
cana-5476	35	37	+	+	NUM
cana-5476	35	38	𝛼	𝛼	NOUN
cana-5476	35	39	)	)	PUNCT
cana-5476	35	40	,	,	PUNCT
cana-5476	35	41	where	where	SCONJ
cana-5476	35	42	𝛼	𝛼	X
cana-5476	35	43	,	,	PUNCT
cana-5476	35	44	𝑤	𝑤	VERB
cana-5476	35	45	are	be	AUX
cana-5476	35	46	constants	constant	NOUN
cana-5476	35	47	.	.	PUNCT
cana-5476	36	1	theorem	theorem	VERB
cana-5476	36	2	9	9	NUM
cana-5476	36	3	]	]	PUNCT
cana-5476	36	4	if	if	SCONJ
cana-5476	36	5	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	36	6	)	)	PUNCT
cana-5476	36	7	=	=	PUNCT
cana-5476	37	1	=	=	PUNCT
cana-5476	37	2	𝑐𝑜𝑠(𝑤𝑥	𝑐𝑜𝑠(𝑤𝑥	NOUN
cana-5476	37	3	+	+	CCONJ
cana-5476	37	4	𝛼	𝛼	X
cana-5476	37	5	)	)	PUNCT
cana-5476	37	6	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	VERB
cana-5476	37	7	𝑈	𝑈	PROPN
cana-5476	37	8	(	(	PUNCT
cana-5476	37	9	𝑟	𝑟	NOUN
cana-5476	37	10	)	)	PUNCT
cana-5476	38	1	=	=	SYM
cana-5476	38	2	𝑤𝑟	𝑤𝑟	PROPN
cana-5476	38	3	𝑟	𝑟	X
cana-5476	38	4	!	!	PUNCT
cana-5476	38	5	𝑐𝑜𝑠	𝑐𝑜𝑠	PROPN
cana-5476	38	6	(	(	PUNCT
cana-5476	38	7	𝑟	𝑟	X
cana-5476	38	8	𝜋	𝜋	ADP
cana-5476	38	9	2	2	NUM
cana-5476	38	10	+	+	NUM
cana-5476	38	11	𝛼	𝛼	NOUN
cana-5476	38	12	)	)	PUNCT
cana-5476	38	13	,	,	PUNCT
cana-5476	38	14	where	where	SCONJ
cana-5476	38	15	𝛼	𝛼	X
cana-5476	38	16	,	,	PUNCT
cana-5476	38	17	𝑤	𝑤	VERB
cana-5476	38	18	are	be	AUX
cana-5476	38	19	constants	constant	NOUN
cana-5476	38	20	.	.	PUNCT
cana-5476	39	1	4	4	X
cana-5476	39	2	.	.	NOUN
cana-5476	39	3	results	result	NOUN
cana-5476	39	4	example	example	NOUN
cana-5476	39	5	1	1	NUM
cana-5476	39	6	:	:	PUNCT
cana-5476	39	7	consider	consider	VERB
cana-5476	39	8	the	the	DET
cana-5476	39	9	following	follow	VERB
cana-5476	39	10	equation	equation	NOUN
cana-5476	39	11	5	5	NUM
cana-5476	39	12	.	.	PUNCT
cana-5476	39	13	𝑢6(𝑥	𝑢6(𝑥	NUM
cana-5476	39	14	)	)	PUNCT
cana-5476	40	1	=	=	NOUN
cana-5476	40	2	𝑒−𝑥	𝑒−𝑥	NOUN
cana-5476	40	3	+	+	CCONJ
cana-5476	40	4	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	40	5	)	)	PUNCT
cana-5476	40	6	,	,	PUNCT
cana-5476	40	7	0	0	PUNCT
cana-5476	40	8	<	<	X
cana-5476	40	9	x	x	X
cana-5476	40	10	<	<	X
cana-5476	40	11	1	1	NUM
cana-5476	40	12	…	…	PUNCT
cana-5476	40	13	(	(	PUNCT
cana-5476	40	14	4	4	NUM
cana-5476	40	15	)	)	PUNCT
cana-5476	40	16	subjected	subject	VERB
cana-5476	40	17	to	to	ADP
cana-5476	40	18	the	the	DET
cana-5476	40	19	conditions	condition	NOUN
cana-5476	40	20	,	,	PUNCT
cana-5476	40	21	𝑢(0	𝑢(0	PROPN
cana-5476	40	22	)	)	PUNCT
cana-5476	40	23	=	=	PUNCT
cana-5476	40	24	𝑢′(0	𝑢′(0	NOUN
cana-5476	40	25	)	)	PUNCT
cana-5476	40	26	=	=	SYM
cana-5476	40	27	𝑢′′(0	𝑢′′(0	NOUN
cana-5476	40	28	)	)	PUNCT
cana-5476	41	1	=	=	SYM
cana-5476	41	2	1	1	NUM
cana-5476	41	3	,	,	PUNCT
cana-5476	41	4	𝑢(1	𝑢(1	NOUN
cana-5476	41	5	)	)	PUNCT
cana-5476	41	6	=	=	SYM
cana-5476	41	7	𝑢′(1	𝑢′(1	ADJ
cana-5476	41	8	)	)	PUNCT
cana-5476	41	9	=	=	SYM
cana-5476	41	10	2	2	NUM
cana-5476	41	11	…	…	PUNCT
cana-5476	41	12	(	(	PUNCT
cana-5476	41	13	5	5	NUM
cana-5476	41	14	)	)	PUNCT
cana-5476	41	15	now	now	ADV
cana-5476	41	16	we	we	PRON
cana-5476	41	17	apply	apply	VERB
cana-5476	41	18	dtm	dtm	PROPN
cana-5476	41	19	on	on	ADP
cana-5476	41	20	example	example	NOUN
cana-5476	41	21	1	1	NUM
cana-5476	41	22	,	,	PUNCT
cana-5476	41	23	using	use	VERB
cana-5476	41	24	above	above	ADP
cana-5476	41	25	theorems	theorem	NOUN
cana-5476	41	26	we	we	PRON
cana-5476	41	27	get	get	VERB
cana-5476	41	28	,	,	PUNCT
cana-5476	41	29	𝑟6𝑈(𝑟	𝑟6𝑈(𝑟	NOUN
cana-5476	41	30	)	)	PUNCT
cana-5476	41	31	=	=	SYM
cana-5476	41	32	1	1	NUM
cana-5476	41	33	𝑟	𝑟	NOUN
cana-5476	41	34	+	+	CCONJ
cana-5476	41	35	1	1	NUM
cana-5476	41	36	+	+	CCONJ
cana-5476	41	37	𝑈(𝑟	𝑈(𝑟	X
cana-5476	41	38	)	)	PUNCT
cana-5476	41	39	rearrange	rearrange	VERB
cana-5476	41	40	the	the	DET
cana-5476	41	41	equation	equation	NOUN
cana-5476	41	42	to	to	PART
cana-5476	41	43	solve	solve	VERB
cana-5476	41	44	for	for	ADP
cana-5476	41	45	u(r),𝑈(𝑟	u(r),𝑈(𝑟	NOUN
cana-5476	41	46	)	)	PUNCT
cana-5476	41	47	=	=	SYM
cana-5476	42	1	1	1	NUM
cana-5476	42	2	(	(	PUNCT
cana-5476	42	3	𝑟+1)(𝑟6−1	𝑟+1)(𝑟6−1	PROPN
cana-5476	42	4	)	)	PUNCT
cana-5476	42	5	with	with	ADP
cana-5476	42	6	the	the	DET
cana-5476	42	7	boundary	boundary	ADJ
cana-5476	42	8	conditions	condition	NOUN
cana-5476	42	9	u(0	u(0	NOUN
cana-5476	42	10	)	)	PUNCT
cana-5476	42	11	=	=	SYM
cana-5476	43	1	u(1	u(1	PROPN
cana-5476	43	2	)	)	PUNCT
cana-5476	43	3	=	=	SYM
cana-5476	43	4	u(2	u(2	PROPN
cana-5476	43	5	)	)	PUNCT
cana-5476	43	6	=	=	SYM
cana-5476	43	7	1	1	NUM
cana-5476	43	8	by	by	ADP
cana-5476	43	9	applying	apply	VERB
cana-5476	43	10	inverse	inverse	NOUN
cana-5476	43	11	differential	differential	NOUN
cana-5476	43	12	transform	transform	NOUN
cana-5476	43	13	,	,	PUNCT
cana-5476	43	14	we	we	PRON
cana-5476	43	15	obtain	obtain	VERB
cana-5476	43	16	the	the	DET
cana-5476	43	17	series	series	NOUN
cana-5476	43	18	solutions	solution	NOUN
cana-5476	43	19	,	,	PUNCT
cana-5476	43	20	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	43	21	)	)	PUNCT
cana-5476	43	22	=	=	PUNCT
cana-5476	44	1	∑	∑	PUNCT
cana-5476	44	2	1	1	NUM
cana-5476	44	3	(	(	PUNCT
cana-5476	44	4	𝑟	𝑟	NOUN
cana-5476	44	5	+	+	CCONJ
cana-5476	44	6	1)(𝑟6	1)(𝑟6	NUM
cana-5476	44	7	−	−	NOUN
cana-5476	44	8	1	1	NUM
cana-5476	44	9	)	)	PUNCT
cana-5476	44	10	𝑥𝑟	𝑥𝑟	PRON
cana-5476	44	11	𝑟	𝑟	NOUN
cana-5476	44	12	!	!	PUNCT
cana-5476	44	13	∞	∞	PROPN
cana-5476	44	14	𝑟=0	𝑟=0	PUNCT
cana-5476	44	15	since	since	SCONJ
cana-5476	44	16	u(1	u(1	PROPN
cana-5476	44	17	)	)	PUNCT
cana-5476	44	18	is	be	AUX
cana-5476	44	19	undefined	undefined	ADJ
cana-5476	44	20	,	,	PUNCT
cana-5476	44	21	the	the	DET
cana-5476	44	22	series	series	NOUN
cana-5476	44	23	representation	representation	NOUN
cana-5476	44	24	would	would	AUX
cana-5476	44	25	be	be	AUX
cana-5476	44	26	,	,	PUNCT
cana-5476	44	27	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	44	28	)	)	PUNCT
cana-5476	44	29	=	=	SYM
cana-5476	45	1	−1	−1	NOUN
cana-5476	45	2	+	+	NUM
cana-5476	45	3	𝑥2	𝑥2	NOUN
cana-5476	45	4	189	189	NUM
cana-5476	45	5	.	.	NOUN
cana-5476	45	6	2	2	NUM
cana-5476	45	7	!	!	PUNCT
cana-5476	46	1	+	+	CCONJ
cana-5476	46	2	𝑥3	𝑥3	ADJ
cana-5476	46	3	2912	2912	NUM
cana-5476	46	4	.	.	PUNCT
cana-5476	47	1	3	3	X
cana-5476	47	2	!	!	X
cana-5476	47	3	+	+	NUM
cana-5476	47	4	𝑥4	𝑥4	PROPN
cana-5476	47	5	20475	20475	NUM
cana-5476	47	6	.	.	PUNCT
cana-5476	48	1	4	4	X
cana-5476	48	2	!	!	PUNCT
cana-5476	49	1	+	+	CCONJ
cana-5476	49	2	𝑥5	𝑥5	PROPN
cana-5476	49	3	93744	93744	NUM
cana-5476	49	4	.	.	PUNCT
cana-5476	50	1	5	5	NUM
cana-5476	50	2	!	!	PUNCT
cana-5476	50	3	+	+	NUM
cana-5476	50	4	𝑥6	𝑥6	PROPN
cana-5476	50	5	326585	326585	NUM
cana-5476	50	6	.	.	PUNCT
cana-5476	51	1	6	6	NUM
cana-5476	51	2	!	!	PUNCT
cana-5476	51	3	+	+	CCONJ
cana-5476	51	4	𝑥7	𝑥7	VERB
cana-5476	51	5	941184	941184	NUM
cana-5476	51	6	.	.	PUNCT
cana-5476	52	1	7	7	X
cana-5476	52	2	!	!	X
cana-5476	52	3	+	+	NUM
cana-5476	52	4	𝑥8	𝑥8	NOUN
cana-5476	52	5	2359287	2359287	NUM
cana-5476	52	6	.	.	PUNCT
cana-5476	53	1	8	8	X
cana-5476	53	2	!	!	PUNCT
cana-5476	54	1	+	+	CCONJ
cana-5476	54	2	𝑥9	𝑥9	PROPN
cana-5476	54	3	5314400	5314400	NUM
cana-5476	54	4	.	.	PUNCT
cana-5476	55	1	9	9	X
cana-5476	55	2	!	!	X
cana-5476	55	3	the	the	DET
cana-5476	55	4	exact	exact	ADJ
cana-5476	55	5	solution	solution	NOUN
cana-5476	55	6	for	for	ADP
cana-5476	55	7	this	this	DET
cana-5476	55	8	example	example	NOUN
cana-5476	55	9	is	be	AUX
cana-5476	55	10	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	55	11	)	)	PUNCT
cana-5476	56	1	=	=	PUNCT
cana-5476	57	1	−𝑒−𝑥	−𝑒−𝑥	NOUN
cana-5476	57	2	is	be	AUX
cana-5476	57	3	maple	maple	NOUN
cana-5476	57	4	output	output	NOUN
cana-5476	57	5	graph	graph	NOUN
cana-5476	57	6	is	be	AUX
cana-5476	57	7	shown	show	VERB
cana-5476	57	8	in	in	ADP
cana-5476	57	9	the	the	DET
cana-5476	57	10	figure	figure	NOUN
cana-5476	57	11	(	(	PUNCT
cana-5476	57	12	1	1	NUM
cana-5476	57	13	)	)	PUNCT
cana-5476	57	14	below	below	ADV
cana-5476	57	15	:	:	PUNCT
cana-5476	57	16	communications	communication	NOUN
cana-5476	57	17	on	on	ADP
cana-5476	57	18	applied	apply	VERB
cana-5476	57	19	nonlinear	nonlinear	ADJ
cana-5476	57	20	analysis	analysis	NOUN
cana-5476	57	21	issn	issn	NOUN
cana-5476	57	22	:	:	PUNCT
cana-5476	57	23	1074	1074	NUM
cana-5476	57	24	-	-	PUNCT
cana-5476	57	25	133x	133x	NUM
cana-5476	57	26	vol	vol	NOUN
cana-5476	57	27	32	32	NUM
cana-5476	57	28	no	no	NOUN
cana-5476	57	29	.	.	PUNCT
cana-5476	58	1	1s	1s	NUM
cana-5476	58	2	(	(	PUNCT
cana-5476	58	3	2025	2025	NUM
cana-5476	58	4	)	)	PUNCT
cana-5476	58	5	668	668	NUM
cana-5476	58	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5476	58	7	figure	figure	NOUN
cana-5476	58	8	1	1	NUM
cana-5476	58	9	:	:	PUNCT
cana-5476	58	10	maple	maple	NOUN
cana-5476	58	11	output	output	NOUN
cana-5476	58	12	graph	graph	NOUN
cana-5476	58	13	example	example	NOUN
cana-5476	58	14	2	2	NUM
cana-5476	58	15	:	:	PUNCT
cana-5476	58	16	consider	consider	VERB
cana-5476	58	17	the	the	DET
cana-5476	58	18	following	follow	VERB
cana-5476	58	19	equation	equation	NOUN
cana-5476	58	20	6	6	NUM
cana-5476	58	21	.	.	PUNCT
cana-5476	58	22	𝑢6(𝑥	𝑢6(𝑥	NUM
cana-5476	58	23	)	)	PUNCT
cana-5476	59	1	+	+	SYM
cana-5476	59	2	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	59	3	)	)	PUNCT
cana-5476	60	1	=	=	NOUN
cana-5476	60	2	𝑒−𝑥	𝑒−𝑥	NOUN
cana-5476	60	3	,	,	PUNCT
cana-5476	60	4	0	0	PUNCT
cana-5476	60	5	<	<	X
cana-5476	60	6	x	x	X
cana-5476	60	7	<	<	X
cana-5476	60	8	1	1	NUM
cana-5476	60	9	…	…	PUNCT
cana-5476	60	10	(	(	PUNCT
cana-5476	60	11	6	6	NUM
cana-5476	60	12	)	)	PUNCT
cana-5476	60	13	subjected	subject	VERB
cana-5476	60	14	to	to	ADP
cana-5476	60	15	the	the	DET
cana-5476	60	16	conditions	condition	NOUN
cana-5476	60	17	,	,	PUNCT
cana-5476	60	18	𝑢(0	𝑢(0	PROPN
cana-5476	60	19	)	)	PUNCT
cana-5476	60	20	=	=	PUNCT
cana-5476	60	21	𝑢′(0	𝑢′(0	NOUN
cana-5476	60	22	)	)	PUNCT
cana-5476	60	23	=	=	SYM
cana-5476	60	24	𝑢′′(0	𝑢′′(0	NOUN
cana-5476	60	25	)	)	PUNCT
cana-5476	61	1	=	=	SYM
cana-5476	61	2	1	1	NUM
cana-5476	61	3	,	,	PUNCT
cana-5476	61	4	𝑢(1	𝑢(1	NOUN
cana-5476	61	5	)	)	PUNCT
cana-5476	61	6	=	=	SYM
cana-5476	61	7	𝑢′(1	𝑢′(1	ADJ
cana-5476	61	8	)	)	PUNCT
cana-5476	61	9	=	=	SYM
cana-5476	61	10	2	2	NUM
cana-5476	61	11	…	…	PUNCT
cana-5476	61	12	(	(	PUNCT
cana-5476	61	13	7	7	NUM
cana-5476	61	14	)	)	PUNCT
cana-5476	61	15	now	now	ADV
cana-5476	61	16	we	we	PRON
cana-5476	61	17	apply	apply	VERB
cana-5476	61	18	dtm	dtm	PROPN
cana-5476	61	19	on	on	ADP
cana-5476	61	20	example	example	NOUN
cana-5476	61	21	1	1	NUM
cana-5476	61	22	,	,	PUNCT
cana-5476	61	23	using	use	VERB
cana-5476	61	24	above	above	ADP
cana-5476	61	25	theorems	theorem	NOUN
cana-5476	61	26	we	we	PRON
cana-5476	61	27	get	get	VERB
cana-5476	61	28	,	,	PUNCT
cana-5476	61	29	𝑟6𝑈(𝑟	𝑟6𝑈(𝑟	NOUN
cana-5476	61	30	)	)	PUNCT
cana-5476	61	31	+	+	CCONJ
cana-5476	61	32	𝑈(𝑟	𝑈(𝑟	X
cana-5476	61	33	)	)	PUNCT
cana-5476	61	34	=	=	SYM
cana-5476	61	35	1	1	NUM
cana-5476	61	36	𝑟	𝑟	NOUN
cana-5476	61	37	+	+	SYM
cana-5476	61	38	1	1	NUM
cana-5476	61	39	rearrange	rearrange	VERB
cana-5476	61	40	the	the	DET
cana-5476	61	41	equation	equation	NOUN
cana-5476	61	42	to	to	PART
cana-5476	61	43	solve	solve	VERB
cana-5476	61	44	for	for	ADP
cana-5476	61	45	u(r	u(r	NOUN
cana-5476	61	46	)	)	PUNCT
cana-5476	61	47	,	,	PUNCT
cana-5476	61	48	𝑈(𝑟	𝑈(𝑟	ADP
cana-5476	61	49	)	)	PUNCT
cana-5476	61	50	=	=	SYM
cana-5476	61	51	1	1	NUM
cana-5476	61	52	(	(	PUNCT
cana-5476	61	53	𝑟	𝑟	NOUN
cana-5476	61	54	+	+	SYM
cana-5476	61	55	1)(𝑟6	1)(𝑟6	NUM
cana-5476	61	56	+	+	CCONJ
cana-5476	61	57	1	1	NUM
cana-5476	61	58	)	)	PUNCT
cana-5476	61	59	by	by	ADP
cana-5476	61	60	applying	apply	VERB
cana-5476	61	61	inverse	inverse	NOUN
cana-5476	61	62	differential	differential	NOUN
cana-5476	61	63	transform	transform	NOUN
cana-5476	61	64	,	,	PUNCT
cana-5476	61	65	we	we	PRON
cana-5476	61	66	obtain	obtain	VERB
cana-5476	61	67	the	the	DET
cana-5476	61	68	series	series	NOUN
cana-5476	61	69	solutions	solution	NOUN
cana-5476	61	70	,	,	PUNCT
cana-5476	61	71	𝑢(𝑟	𝑢(𝑟	NOUN
cana-5476	61	72	)	)	PUNCT
cana-5476	61	73	=	=	PUNCT
cana-5476	62	1	∑	∑	PUNCT
cana-5476	62	2	1	1	NUM
cana-5476	62	3	(	(	PUNCT
cana-5476	62	4	𝑟	𝑟	NOUN
cana-5476	62	5	+	+	SYM
cana-5476	62	6	1)(𝑟6	1)(𝑟6	NUM
cana-5476	62	7	+	+	CCONJ
cana-5476	62	8	1	1	X
cana-5476	62	9	)	)	PUNCT
cana-5476	62	10	𝑥𝑟	𝑥𝑟	PRON
cana-5476	62	11	𝑟	𝑟	NOUN
cana-5476	62	12	!	!	PUNCT
cana-5476	63	1	∞	∞	NUM
cana-5476	63	2	𝑟=0	𝑟=0	X
cana-5476	63	3	the	the	DET
cana-5476	63	4	series	series	NOUN
cana-5476	63	5	representation	representation	NOUN
cana-5476	63	6	would	would	AUX
cana-5476	63	7	be	be	AUX
cana-5476	63	8	,	,	PUNCT
cana-5476	63	9	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	63	10	)	)	PUNCT
cana-5476	63	11	=	=	NOUN
cana-5476	64	1	1	1	NUM
cana-5476	64	2	+	+	CCONJ
cana-5476	64	3	𝑥	𝑥	PROPN
cana-5476	64	4	4	4	NUM
cana-5476	64	5	.	.	NOUN
cana-5476	64	6	1	1	NUM
cana-5476	64	7	!	!	PUNCT
cana-5476	65	1	+	+	NUM
cana-5476	65	2	𝑥2	𝑥2	NOUN
cana-5476	65	3	195	195	NUM
cana-5476	65	4	.	.	NOUN
cana-5476	65	5	2	2	NUM
cana-5476	65	6	!	!	PUNCT
cana-5476	66	1	+	+	NUM
cana-5476	66	2	𝑥3	𝑥3	ADJ
cana-5476	66	3	2920	2920	NUM
cana-5476	66	4	.	.	PUNCT
cana-5476	67	1	3	3	X
cana-5476	67	2	!	!	X
cana-5476	67	3	+	+	NUM
cana-5476	67	4	𝑥4	𝑥4	PROPN
cana-5476	67	5	20485	20485	NUM
cana-5476	67	6	.	.	PUNCT
cana-5476	68	1	4	4	X
cana-5476	68	2	!	!	PUNCT
cana-5476	69	1	+	+	CCONJ
cana-5476	69	2	𝑥5	𝑥5	PROPN
cana-5476	69	3	93756	93756	NUM
cana-5476	69	4	.	.	PUNCT
cana-5476	70	1	5	5	NUM
cana-5476	70	2	!	!	PUNCT
cana-5476	70	3	+	+	NUM
cana-5476	70	4	𝑥6	𝑥6	PROPN
cana-5476	70	5	326599	326599	NUM
cana-5476	70	6	.	.	PUNCT
cana-5476	71	1	6	6	NUM
cana-5476	71	2	!	!	PUNCT
cana-5476	71	3	+	+	CCONJ
cana-5476	71	4	𝑥7	𝑥7	VERB
cana-5476	71	5	941192	941192	NUM
cana-5476	71	6	.	.	PUNCT
cana-5476	72	1	7	7	X
cana-5476	72	2	!	!	X
cana-5476	72	3	+	+	PUNCT
cana-5476	72	4	𝑥8	𝑥8	NOUN
cana-5476	72	5	2359350	2359350	NUM
cana-5476	72	6	.	.	PUNCT
cana-5476	73	1	8	8	NUM
cana-5476	73	2	!	!	PUNCT
cana-5476	74	1	+	+	CCONJ
cana-5476	74	2	𝑥9	𝑥9	PROPN
cana-5476	74	3	5314410	5314410	NUM
cana-5476	74	4	.	.	PUNCT
cana-5476	75	1	9	9	X
cana-5476	75	2	!	!	X
cana-5476	75	3	communications	communication	NOUN
cana-5476	75	4	on	on	ADP
cana-5476	75	5	applied	apply	VERB
cana-5476	75	6	nonlinear	nonlinear	ADJ
cana-5476	75	7	analysis	analysis	NOUN
cana-5476	75	8	issn	issn	NOUN
cana-5476	75	9	:	:	PUNCT
cana-5476	75	10	1074	1074	NUM
cana-5476	75	11	-	-	PUNCT
cana-5476	75	12	133x	133x	NUM
cana-5476	75	13	vol	vol	NOUN
cana-5476	75	14	32	32	NUM
cana-5476	75	15	no	no	NOUN
cana-5476	75	16	.	.	PUNCT
cana-5476	76	1	1s	1s	NUM
cana-5476	76	2	(	(	PUNCT
cana-5476	76	3	2025	2025	NUM
cana-5476	76	4	)	)	PUNCT
cana-5476	76	5	669	669	NUM
cana-5476	76	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5476	76	7	the	the	DET
cana-5476	76	8	exact	exact	ADJ
cana-5476	76	9	solution	solution	NOUN
cana-5476	76	10	for	for	ADP
cana-5476	76	11	this	this	DET
cana-5476	76	12	example	example	NOUN
cana-5476	76	13	is	be	AUX
cana-5476	76	14	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5476	76	15	)	)	PUNCT
cana-5476	76	16	=	=	NOUN
cana-5476	76	17	1	1	NUM
cana-5476	76	18	2	2	NUM
cana-5476	76	19	𝑒−𝑥	𝑒−𝑥	NOUN
cana-5476	76	20	is	be	AUX
cana-5476	76	21	maple	maple	NOUN
cana-5476	76	22	output	output	NOUN
cana-5476	76	23	graph	graph	NOUN
cana-5476	76	24	is	be	AUX
cana-5476	76	25	shown	show	VERB
cana-5476	76	26	in	in	ADP
cana-5476	76	27	the	the	DET
cana-5476	76	28	figure	figure	NOUN
cana-5476	76	29	(	(	PUNCT
cana-5476	76	30	2	2	NUM
cana-5476	76	31	)	)	PUNCT
cana-5476	76	32	below	below	ADV
cana-5476	76	33	:	:	PUNCT
cana-5476	76	34	figure	figure	NOUN
cana-5476	76	35	2	2	NUM
cana-5476	76	36	:	:	PUNCT
cana-5476	76	37	maple	maple	NOUN
cana-5476	76	38	output	output	NOUN
cana-5476	76	39	graph	graph	NOUN
cana-5476	76	40	5	5	NUM
cana-5476	76	41	.	.	PUNCT
cana-5476	76	42	discussion	discussion	NOUN
cana-5476	76	43	in	in	ADP
cana-5476	76	44	this	this	DET
cana-5476	76	45	study	study	NOUN
cana-5476	76	46	,	,	PUNCT
cana-5476	76	47	we	we	PRON
cana-5476	76	48	effectively	effectively	ADV
cana-5476	76	49	use	use	VERB
cana-5476	76	50	dtm	dtm	PROPN
cana-5476	76	51	to	to	PART
cana-5476	76	52	solve	solve	VERB
cana-5476	76	53	differential	differential	ADJ
cana-5476	76	54	equations	equation	NOUN
cana-5476	76	55	with	with	ADP
cana-5476	76	56	boundary	boundary	ADJ
cana-5476	76	57	conditions	condition	NOUN
cana-5476	76	58	.	.	PUNCT
cana-5476	77	1	dtm	dtm	PROPN
cana-5476	77	2	proves	prove	VERB
cana-5476	77	3	to	to	PART
cana-5476	77	4	be	be	AUX
cana-5476	77	5	a	a	DET
cana-5476	77	6	reliable	reliable	ADJ
cana-5476	77	7	and	and	CCONJ
cana-5476	77	8	efficient	efficient	ADJ
cana-5476	77	9	technique	technique	NOUN
cana-5476	77	10	for	for	ADP
cana-5476	77	11	addressing	address	VERB
cana-5476	77	12	boundary	boundary	ADJ
cana-5476	77	13	value	value	NOUN
cana-5476	77	14	problems	problem	NOUN
cana-5476	77	15	.	.	PUNCT
cana-5476	78	1	the	the	DET
cana-5476	78	2	precision	precision	NOUN
cana-5476	78	3	of	of	ADP
cana-5476	78	4	the	the	DET
cana-5476	78	5	results	result	NOUN
cana-5476	78	6	can	can	AUX
cana-5476	78	7	be	be	AUX
cana-5476	78	8	improved	improve	VERB
cana-5476	78	9	by	by	ADP
cana-5476	78	10	incorporating	incorporate	VERB
cana-5476	78	11	additional	additional	ADJ
cana-5476	78	12	terms	term	NOUN
cana-5476	78	13	into	into	ADP
cana-5476	78	14	the	the	DET
cana-5476	78	15	series	series	NOUN
cana-5476	78	16	.	.	PUNCT
cana-5476	79	1	this	this	DET
cana-5476	79	2	approach	approach	NOUN
cana-5476	79	3	is	be	AUX
cana-5476	79	4	highly	highly	ADV
cana-5476	79	5	effective	effective	ADJ
cana-5476	79	6	for	for	ADP
cana-5476	79	7	tackling	tackle	VERB
cana-5476	79	8	differential	differential	ADJ
cana-5476	79	9	equations	equation	NOUN
cana-5476	79	10	involving	involve	VERB
cana-5476	79	11	boundary	boundary	ADJ
cana-5476	79	12	conditions	condition	NOUN
cana-5476	79	13	.	.	PUNCT
cana-5476	80	1	refrences	refrence	VERB
cana-5476	81	1	[	[	X
cana-5476	81	2	1	1	X
cana-5476	81	3	]	]	PUNCT
cana-5476	81	4	farshid	farshid	NOUN
cana-5476	81	5	mirzaee	mirzaee	PROPN
cana-5476	81	6	,	,	PUNCT
cana-5476	81	7	“	"	PUNCT
cana-5476	81	8	differential	differential	ADJ
cana-5476	81	9	transform	transform	NOUN
cana-5476	81	10	method	method	NOUN
cana-5476	81	11	for	for	ADP
cana-5476	81	12	solving	solve	VERB
cana-5476	81	13	linear	linear	ADJ
cana-5476	81	14	and	and	CCONJ
cana-5476	81	15	nonlinear	nonlinear	ADJ
cana-5476	81	16	system	system	NOUN
cana-5476	81	17	of	of	ADP
cana-5476	81	18	ordinary	ordinary	ADJ
cana-5476	81	19	differential	differential	ADJ
cana-5476	81	20	equation	equation	NOUN
cana-5476	81	21	”	"	PUNCT
cana-5476	81	22	,	,	PUNCT
cana-5476	81	23	appl.math.vol.5.2011	appl.math.vol.5.2011	PROPN
cana-5476	81	24	.	.	PUNCT
cana-5476	82	1	[	[	X
cana-5476	82	2	2	2	X
cana-5476	82	3	]	]	PUNCT
cana-5476	82	4	j.	j.	PROPN
cana-5476	82	5	k.	k.	PROPN
cana-5476	82	6	zhou	zhou	PROPN
cana-5476	82	7	,	,	PUNCT
cana-5476	82	8	"	"	PUNCT
cana-5476	82	9	differential	differential	ADJ
cana-5476	82	10	transformation	transformation	NOUN
cana-5476	82	11	and	and	CCONJ
cana-5476	82	12	its	its	PRON
cana-5476	82	13	applications	application	NOUN
cana-5476	82	14	for	for	ADP
cana-5476	82	15	electrical	electrical	ADJ
cana-5476	82	16	circuits	circuit	NOUN
cana-5476	82	17	,	,	PUNCT
cana-5476	82	18	"	"	PUNCT
cana-5476	82	19	huazhong	huazhong	PROPN
cana-5476	82	20	university	university	PROPN
cana-5476	82	21	press	press	NOUN
cana-5476	82	22	,	,	PUNCT
cana-5476	82	23	wuhan	wuhan	PROPN
cana-5476	82	24	,	,	PUNCT
cana-5476	82	25	china	china	PROPN
cana-5476	82	26	,	,	PUNCT
cana-5476	82	27	1986	1986	NUM
cana-5476	82	28	.	.	PUNCT
cana-5476	83	1	[	[	X
cana-5476	83	2	3	3	X
cana-5476	83	3	]	]	X
cana-5476	83	4	narhari	narhari	ADJ
cana-5476	83	5	patil	patil	NOUN
cana-5476	83	6	and	and	CCONJ
cana-5476	83	7	avinash	avinash	PROPN
cana-5476	83	8	khambayat	khambayat	PROPN
cana-5476	83	9	,	,	PUNCT
cana-5476	83	10	"	"	PUNCT
cana-5476	83	11	differential	differential	ADJ
cana-5476	83	12	transform	transform	NOUN
cana-5476	83	13	method	method	NOUN
cana-5476	83	14	for	for	ADP
cana-5476	83	15	system	system	NOUN
cana-5476	83	16	of	of	ADP
cana-5476	83	17	linear	linear	PROPN
cana-5476	83	18	differential	differential	ADJ
cana-5476	83	19	equations	equation	NOUN
cana-5476	83	20	,	,	PUNCT
cana-5476	83	21	"	"	PUNCT
cana-5476	83	22	research	research	NOUN
cana-5476	83	23	journal	journal	NOUN
cana-5476	83	24	of	of	ADP
cana-5476	83	25	mathematical	mathematical	ADJ
cana-5476	83	26	and	and	CCONJ
cana-5476	83	27	statistical	statistical	ADJ
cana-5476	83	28	sciences	science	NOUN
cana-5476	83	29	,	,	PUNCT
cana-5476	83	30	vol	vol	NOUN
cana-5476	83	31	.	.	PUNCT
cana-5476	83	32	2(3	2(3	NUM
cana-5476	83	33	)	)	PUNCT
cana-5476	83	34	,	,	PUNCT
cana-5476	83	35	46	46	NUM
cana-5476	83	36	,	,	PUNCT
cana-5476	83	37	march	march	PROPN
cana-5476	83	38	(	(	PUNCT
cana-5476	83	39	2014	2014	NUM
cana-5476	83	40	)	)	PUNCT
cana-5476	83	41	.	.	PUNCT
cana-5476	84	1	[	[	X
cana-5476	84	2	4	4	NUM
cana-5476	84	3	]	]	X
cana-5476	84	4	shawagfeh	shawagfeh	X
cana-5476	84	5	n.	n.	PROPN
cana-5476	84	6	and	and	CCONJ
cana-5476	84	7	kaya	kaya	PROPN
cana-5476	84	8	d.	d.	PROPN
cana-5476	84	9	,	,	PUNCT
cana-5476	84	10	“	"	PUNCT
cana-5476	84	11	comparing	compare	VERB
cana-5476	84	12	numerical	numerical	ADJ
cana-5476	84	13	methods	method	NOUN
cana-5476	84	14	for	for	ADP
cana-5476	84	15	solution	solution	NOUN
cana-5476	84	16	of	of	ADP
cana-5476	84	17	ordinary	ordinary	ADJ
cana-5476	84	18	differential	differential	ADJ
cana-5476	84	19	equation	equation	NOUN
cana-5476	84	20	”	"	PUNCT
cana-5476	84	21	,	,	PUNCT
cana-5476	84	22	appl.math.lett	appl.math.lett	NOUN
cana-5476	84	23	.	.	PUNCT
cana-5476	84	24	,17(2004)323	,17(2004)323	PROPN
cana-5476	84	25	-	-	PUNCT
cana-5476	84	26	328	328	NUM
cana-5476	84	27	.	.	PUNCT
cana-5476	85	1	[	[	X
cana-5476	85	2	5	5	NUM
cana-5476	85	3	]	]	PUNCT
cana-5476	85	4	y.keskin	y.keskin	PROPN
cana-5476	85	5	,	,	PUNCT
cana-5476	85	6	g.	g.	PROPN
cana-5476	85	7	oturance	oturance	NOUN
cana-5476	85	8	,	,	PUNCT
cana-5476	85	9	“	"	PUNCT
cana-5476	85	10	reduced	reduce	VERB
cana-5476	85	11	differential	differential	ADJ
cana-5476	85	12	transform	transform	NOUN
cana-5476	85	13	method	method	NOUN
cana-5476	85	14	for	for	ADP
cana-5476	85	15	partial	partial	ADJ
cana-5476	85	16	differential	differential	ADJ
cana-5476	85	17	equations	equation	NOUN
cana-5476	85	18	”	"	PUNCT
cana-5476	85	19	,	,	PUNCT
cana-5476	85	20	international	international	ADJ
cana-5476	85	21	journal	journal	NOUN
cana-5476	85	22	of	of	ADP
cana-5476	85	23	nonlinear	nonlinear	PROPN
cana-5476	85	24	sciences	sciences	PROPN
cana-5476	85	25	and	and	CCONJ
cana-5476	85	26	numerical	numerical	ADJ
cana-5476	85	27	simulation,2009,10(6),741	simulation,2009,10(6),741	NOUN
cana-5476	85	28	-	-	PUNCT
cana-5476	85	29	749	749	NUM
cana-5476	85	30	.	.	PUNCT