id	sid	tid	token	lemma	pos
cana-5406	1	1	communications	communication	NOUN
cana-5406	1	2	on	on	ADP
cana-5406	1	3	applied	apply	VERB
cana-5406	1	4	nonlinear	nonlinear	ADJ
cana-5406	1	5	analysis	analysis	NOUN
cana-5406	1	6	issn	issn	NOUN
cana-5406	1	7	:	:	PUNCT
cana-5406	1	8	1074	1074	NUM
cana-5406	1	9	-	-	PUNCT
cana-5406	1	10	133x	133x	NUM
cana-5406	1	11	vol	vol	VERB
cana-5406	1	12	32	32	NUM
cana-5406	1	13	no	no	NOUN
cana-5406	1	14	.	.	PUNCT
cana-5406	2	1	10s	10	NOUN
cana-5406	2	2	(	(	PUNCT
cana-5406	2	3	2025	2025	NUM
cana-5406	2	4	)	)	PUNCT
cana-5406	2	5	2162	2162	NUM
cana-5406	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5406	3	1	the	the	DET
cana-5406	3	2	numerical	numerical	ADJ
cana-5406	3	3	solutions	solution	NOUN
cana-5406	3	4	of	of	ADP
cana-5406	3	5	partial	partial	ADJ
cana-5406	3	6	differential	differential	ADJ
cana-5406	3	7	equations	equation	NOUN
cana-5406	3	8	using	use	VERB
cana-5406	3	9	twothree	twothree	NOUN
cana-5406	3	10	-	-	PUNCT
cana-5406	3	11	dimensions	dimension	NOUN
cana-5406	3	12	differential	differential	NOUN
cana-5406	3	13	transform	transform	NOUN
cana-5406	3	14	method	method	NOUN
cana-5406	3	15	rohit	rohit	PROPN
cana-5406	3	16	nagargoje1	nagargoje1	PROPN
cana-5406	3	17	,	,	PUNCT
cana-5406	3	18	avinash	avinash	PROPN
cana-5406	3	19	khambayat2	khambayat2	PROPN
cana-5406	3	20	1	1	NUM
cana-5406	3	21	.	.	PUNCT
cana-5406	3	22	research	research	NOUN
cana-5406	3	23	scholar	scholar	NOUN
cana-5406	3	24	,	,	PUNCT
cana-5406	3	25	department	department	NOUN
cana-5406	3	26	of	of	ADP
cana-5406	3	27	mathematics	mathematic	NOUN
cana-5406	3	28	,	,	PUNCT
cana-5406	3	29	school	school	NOUN
cana-5406	3	30	of	of	ADP
cana-5406	3	31	science	science	NOUN
cana-5406	3	32	,	,	PUNCT
cana-5406	3	33	sandip	sandip	PROPN
cana-5406	3	34	university	university	PROPN
cana-5406	3	35	nasik	nasik	PROPN
cana-5406	3	36	,	,	PUNCT
cana-5406	3	37	maharashtra	maharashtra	PROPN
cana-5406	3	38	email	email	NOUN
cana-5406	3	39	:	:	PUNCT
cana-5406	3	40	rnagargoje92@gmail.com	rnagargoje92@gmail.com	X
cana-5406	3	41	2	2	NUM
cana-5406	3	42	.	.	PUNCT
cana-5406	3	43	professor	professor	NOUN
cana-5406	3	44	,	,	PUNCT
cana-5406	3	45	department	department	NOUN
cana-5406	3	46	of	of	ADP
cana-5406	3	47	mathematics	mathematic	NOUN
cana-5406	3	48	,	,	PUNCT
cana-5406	3	49	school	school	NOUN
cana-5406	3	50	of	of	ADP
cana-5406	3	51	science	science	NOUN
cana-5406	3	52	,	,	PUNCT
cana-5406	3	53	sandip	sandip	PROPN
cana-5406	3	54	university	university	PROPN
cana-5406	3	55	nasik	nasik	PROPN
cana-5406	3	56	,	,	PUNCT
cana-5406	3	57	maharashtra	maharashtra	PROPN
cana-5406	3	58	email	email	NOUN
cana-5406	3	59	:	:	PUNCT
cana-5406	3	60	avinash.khambayat@sandipuniversity.edu.in	avinash.khambayat@sandipuniversity.edu.in	ADV
cana-5406	3	61	article	article	NOUN
cana-5406	3	62	history	history	NOUN
cana-5406	3	63	:	:	PUNCT
cana-5406	3	64	received	receive	VERB
cana-5406	3	65	:	:	PUNCT
cana-5406	3	66	12	12	NUM
cana-5406	3	67	-	-	SYM
cana-5406	3	68	01	01	NUM
cana-5406	3	69	-	-	PUNCT
cana-5406	3	70	2025	2025	NUM
cana-5406	3	71	revised	revise	VERB
cana-5406	3	72	:	:	PUNCT
cana-5406	3	73	15	15	NUM
cana-5406	3	74	-	-	NUM
cana-5406	3	75	02	02	NUM
cana-5406	3	76	-	-	PUNCT
cana-5406	3	77	2025	2025	NUM
cana-5406	3	78	accepted	accept	VERB
cana-5406	3	79	:	:	PUNCT
cana-5406	3	80	01	01	NUM
cana-5406	3	81	-	-	SYM
cana-5406	3	82	03	03	NUM
cana-5406	3	83	-	-	PUNCT
cana-5406	3	84	2025	2025	NUM
cana-5406	3	85	abstract	abstract	NOUN
cana-5406	3	86	:	:	PUNCT
cana-5406	3	87	differential	differential	ADJ
cana-5406	3	88	transform	transform	NOUN
cana-5406	3	89	method	method	NOUN
cana-5406	3	90	is	be	AUX
cana-5406	3	91	the	the	DET
cana-5406	3	92	one	one	NUM
cana-5406	3	93	of	of	ADP
cana-5406	3	94	the	the	DET
cana-5406	3	95	novel	novel	ADJ
cana-5406	3	96	and	and	CCONJ
cana-5406	3	97	unique	unique	ADJ
cana-5406	3	98	methods	method	NOUN
cana-5406	3	99	which	which	PRON
cana-5406	3	100	provides	provide	VERB
cana-5406	3	101	series	series	NOUN
cana-5406	3	102	solution	solution	NOUN
cana-5406	3	103	.	.	PUNCT
cana-5406	4	1	the	the	DET
cana-5406	4	2	approach	approach	NOUN
cana-5406	4	3	mainly	mainly	ADV
cana-5406	4	4	rests	rest	VERB
cana-5406	4	5	on	on	ADP
cana-5406	4	6	the	the	DET
cana-5406	4	7	differential	differential	ADJ
cana-5406	4	8	transform	transform	NOUN
cana-5406	4	9	method	method	NOUN
cana-5406	4	10	(	(	PUNCT
cana-5406	4	11	dtm	dtm	PROPN
cana-5406	4	12	)	)	PUNCT
cana-5406	4	13	which	which	PRON
cana-5406	4	14	is	be	AUX
cana-5406	4	15	one	one	NUM
cana-5406	4	16	of	of	ADP
cana-5406	4	17	the	the	DET
cana-5406	4	18	approximate	approximate	ADJ
cana-5406	4	19	methods	method	NOUN
cana-5406	4	20	to	to	PART
cana-5406	4	21	achieved	achieved	VERB
cana-5406	4	22	exact	exact	ADJ
cana-5406	4	23	solution	solution	NOUN
cana-5406	4	24	of	of	ADP
cana-5406	4	25	one	one	NUM
cana-5406	4	26	dimensional	dimensional	ADJ
cana-5406	4	27	up	up	ADP
cana-5406	4	28	to	to	ADP
cana-5406	4	29	multidimensional	multidimensional	ADJ
cana-5406	4	30	.	.	PUNCT
cana-5406	5	1	the	the	DET
cana-5406	5	2	method	method	NOUN
cana-5406	5	3	can	can	AUX
cana-5406	5	4	easily	easily	ADV
cana-5406	5	5	be	be	AUX
cana-5406	5	6	applied	apply	VERB
cana-5406	5	7	on	on	ADP
cana-5406	5	8	many	many	ADJ
cana-5406	5	9	problems	problem	NOUN
cana-5406	5	10	in	in	ADP
cana-5406	5	11	the	the	DET
cana-5406	5	12	field	field	NOUN
cana-5406	5	13	of	of	ADP
cana-5406	5	14	differential	differential	ADJ
cana-5406	5	15	equations	equation	NOUN
cana-5406	5	16	and	and	CCONJ
cana-5406	5	17	partial	partial	ADJ
cana-5406	5	18	differential	differential	ADJ
cana-5406	5	19	equations	equation	NOUN
cana-5406	5	20	(	(	PUNCT
cana-5406	5	21	pde	pde	NOUN
cana-5406	5	22	)	)	PUNCT
cana-5406	5	23	.	.	PUNCT
cana-5406	6	1	dtm	dtm	PROPN
cana-5406	6	2	is	be	AUX
cana-5406	6	3	used	use	VERB
cana-5406	6	4	to	to	PART
cana-5406	6	5	reduces	reduce	VERB
cana-5406	6	6	the	the	DET
cana-5406	6	7	size	size	NOUN
cana-5406	6	8	of	of	ADP
cana-5406	6	9	calculus	calculus	NOUN
cana-5406	6	10	work	work	NOUN
cana-5406	6	11	and	and	CCONJ
cana-5406	6	12	gives	give	VERB
cana-5406	6	13	the	the	DET
cana-5406	6	14	solution	solution	NOUN
cana-5406	6	15	of	of	ADP
cana-5406	6	16	higher	high	ADJ
cana-5406	6	17	order	order	NOUN
cana-5406	6	18	two	two	NUM
cana-5406	6	19	-	-	PUNCT
cana-5406	6	20	dimensional	dimensional	ADJ
cana-5406	6	21	,	,	PUNCT
cana-5406	6	22	three	three	NUM
cana-5406	6	23	-	-	PUNCT
cana-5406	6	24	dimensional	dimensional	ADJ
cana-5406	6	25	,	,	PUNCT
cana-5406	6	26	multi	multi	ADJ
cana-5406	6	27	-	-	ADJ
cana-5406	6	28	dimensional	dimensional	ADJ
cana-5406	6	29	differential	differential	ADJ
cana-5406	6	30	equation	equation	NOUN
cana-5406	6	31	.	.	PUNCT
cana-5406	7	1	keywords	keyword	NOUN
cana-5406	7	2	:	:	PUNCT
cana-5406	7	3	differential	differential	NOUN
cana-5406	7	4	transformed	transform	VERB
cana-5406	7	5	method	method	NOUN
cana-5406	7	6	,	,	PUNCT
cana-5406	7	7	two	two	NUM
cana-5406	7	8	-	-	PUNCT
cana-5406	7	9	dimensional	dimensional	ADJ
cana-5406	7	10	,	,	PUNCT
cana-5406	7	11	three	three	NUM
cana-5406	7	12	-	-	PUNCT
cana-5406	7	13	dimensional	dimensional	ADJ
cana-5406	7	14	,	,	PUNCT
cana-5406	7	15	multidimensional	multidimensional	ADJ
cana-5406	7	16	partial	partial	ADJ
cana-5406	7	17	differential	differential	NOUN
cana-5406	7	18	equation	equation	NOUN
cana-5406	7	19	.	.	PUNCT
cana-5406	8	1	1	1	X
cana-5406	8	2	.	.	X
cana-5406	8	3	introduction	introduction	NOUN
cana-5406	8	4	the	the	DET
cana-5406	8	5	analytical	analytical	ADJ
cana-5406	8	6	approaches	approach	NOUN
cana-5406	8	7	of	of	ADP
cana-5406	8	8	the	the	DET
cana-5406	8	9	differential	differential	ADJ
cana-5406	8	10	transform	transform	NOUN
cana-5406	8	11	method	method	NOUN
cana-5406	8	12	have	have	AUX
cana-5406	8	13	been	be	AUX
cana-5406	8	14	succeeded	succeed	VERB
cana-5406	8	15	to	to	PART
cana-5406	8	16	solve	solve	VERB
cana-5406	8	17	differential	differential	ADJ
cana-5406	8	18	equations	equation	NOUN
cana-5406	8	19	and	and	CCONJ
cana-5406	8	20	integral	integral	ADJ
cana-5406	8	21	equations	equation	NOUN
cana-5406	8	22	in	in	ADP
cana-5406	8	23	many	many	ADJ
cana-5406	8	24	fields	field	NOUN
cana-5406	8	25	.	.	PUNCT
cana-5406	9	1	the	the	DET
cana-5406	9	2	basic	basic	ADJ
cana-5406	9	3	concept	concept	NOUN
cana-5406	9	4	of	of	ADP
cana-5406	9	5	the	the	DET
cana-5406	9	6	differential	differential	ADJ
cana-5406	9	7	transform	transform	NOUN
cana-5406	9	8	method	method	NOUN
cana-5406	9	9	is	be	AUX
cana-5406	9	10	based	base	VERB
cana-5406	9	11	on	on	ADP
cana-5406	9	12	the	the	DET
cana-5406	9	13	taylor	taylor	PROPN
cana-5406	9	14	series	series	PROPN
cana-5406	9	15	.	.	PUNCT
cana-5406	10	1	the	the	DET
cana-5406	10	2	differential	differential	ADJ
cana-5406	10	3	transform	transform	NOUN
cana-5406	10	4	method	method	NOUN
cana-5406	10	5	was	be	AUX
cana-5406	10	6	first	first	ADV
cana-5406	10	7	introduced	introduce	VERB
cana-5406	10	8	by	by	ADP
cana-5406	10	9	j.k	j.k	PROPN
cana-5406	10	10	.	.	PROPN
cana-5406	10	11	zhou	zhou	PROPN
cana-5406	10	12	in	in	ADP
cana-5406	10	13	a	a	DET
cana-5406	10	14	study	study	NOUN
cana-5406	10	15	about	about	ADP
cana-5406	10	16	electrical	electrical	ADJ
cana-5406	10	17	circuits	circuit	NOUN
cana-5406	10	18	.	.	PUNCT
cana-5406	11	1	the	the	DET
cana-5406	11	2	differential	differential	ADJ
cana-5406	11	3	transform	transform	NOUN
cana-5406	11	4	method	method	NOUN
cana-5406	11	5	obtains	obtain	VERB
cana-5406	11	6	an	an	DET
cana-5406	11	7	analytical	analytical	ADJ
cana-5406	11	8	solution	solution	NOUN
cana-5406	11	9	in	in	ADP
cana-5406	11	10	the	the	DET
cana-5406	11	11	form	form	NOUN
cana-5406	11	12	of	of	ADP
cana-5406	11	13	a	a	DET
cana-5406	11	14	polynomial	polynomial	ADJ
cana-5406	11	15	equations	equation	NOUN
cana-5406	11	16	[	[	X
cana-5406	11	17	1	1	NUM
cana-5406	11	18	]	]	PUNCT
cana-5406	11	19	.	.	PUNCT
cana-5406	12	1	furthermore	furthermore	ADV
cana-5406	12	2	,	,	PUNCT
cana-5406	12	3	a	a	DET
cana-5406	12	4	variety	variety	NOUN
cana-5406	12	5	of	of	ADP
cana-5406	12	6	methods	method	NOUN
cana-5406	12	7	,	,	PUNCT
cana-5406	12	8	exact	exact	ADJ
cana-5406	12	9	approximate	approximate	ADJ
cana-5406	12	10	and	and	CCONJ
cana-5406	12	11	purely	purely	ADV
cana-5406	12	12	numerical	numerical	ADJ
cana-5406	12	13	are	be	AUX
cana-5406	12	14	available	available	ADJ
cana-5406	12	15	for	for	ADP
cana-5406	12	16	the	the	DET
cana-5406	12	17	solution	solution	NOUN
cana-5406	12	18	of	of	ADP
cana-5406	12	19	differential	differential	ADJ
cana-5406	12	20	equations	equation	NOUN
cana-5406	12	21	.	.	PUNCT
cana-5406	13	1	most	most	ADJ
cana-5406	13	2	of	of	ADP
cana-5406	13	3	these	these	DET
cana-5406	13	4	methods	method	NOUN
cana-5406	13	5	are	be	AUX
cana-5406	13	6	computationally	computationally	ADV
cana-5406	13	7	intensive	intensive	ADJ
cana-5406	13	8	because	because	SCONJ
cana-5406	13	9	they	they	PRON
cana-5406	13	10	are	be	AUX
cana-5406	13	11	trial	trial	NOUN
cana-5406	13	12	-	-	PUNCT
cana-5406	13	13	and	and	CCONJ
cana-5406	13	14	error	error	NOUN
cana-5406	13	15	in	in	ADP
cana-5406	13	16	nature	nature	NOUN
cana-5406	13	17	,	,	PUNCT
cana-5406	13	18	or	or	CCONJ
cana-5406	13	19	need	need	VERB
cana-5406	13	20	complicated	complicated	ADJ
cana-5406	13	21	symbolic	symbolic	ADJ
cana-5406	13	22	computations	computation	NOUN
cana-5406	13	23	.	.	PUNCT
cana-5406	14	1	furthermore	furthermore	ADV
cana-5406	14	2	,	,	PUNCT
cana-5406	14	3	the	the	DET
cana-5406	14	4	differential	differential	ADJ
cana-5406	14	5	transformation	transformation	NOUN
cana-5406	14	6	technique	technique	NOUN
cana-5406	14	7	is	be	AUX
cana-5406	14	8	one	one	NUM
cana-5406	14	9	of	of	ADP
cana-5406	14	10	the	the	DET
cana-5406	14	11	numerical	numerical	ADJ
cana-5406	14	12	methods	method	NOUN
cana-5406	14	13	for	for	ADP
cana-5406	14	14	ordinary	ordinary	ADJ
cana-5406	14	15	differential	differential	ADJ
cana-5406	14	16	equations	equation	NOUN
cana-5406	14	17	.	.	PUNCT
cana-5406	15	1	the	the	DET
cana-5406	15	2	concept	concept	NOUN
cana-5406	15	3	of	of	ADP
cana-5406	15	4	differential	differential	ADJ
cana-5406	15	5	transformation	transformation	NOUN
cana-5406	15	6	was	be	AUX
cana-5406	15	7	first	first	ADV
cana-5406	15	8	proposed	propose	VERB
cana-5406	15	9	by	by	ADP
cana-5406	15	10	zhou	zhou	PROPN
cana-5406	16	1	[	[	X
cana-5406	16	2	2	2	NUM
cana-5406	16	3	]	]	PUNCT
cana-5406	16	4	.	.	PUNCT
cana-5406	17	1	it	it	PRON
cana-5406	17	2	is	be	AUX
cana-5406	17	3	different	different	ADJ
cana-5406	17	4	from	from	ADP
cana-5406	17	5	the	the	DET
cana-5406	17	6	traditional	traditional	ADJ
cana-5406	17	7	high	high	ADJ
cana-5406	17	8	order	order	NOUN
cana-5406	17	9	taylor	taylor	PROPN
cana-5406	17	10	’s	’s	PART
cana-5406	17	11	series	series	PROPN
cana-5406	17	12	method	method	NOUN
cana-5406	17	13	,	,	PUNCT
cana-5406	17	14	which	which	PRON
cana-5406	17	15	requires	require	VERB
cana-5406	17	16	symbolic	symbolic	ADJ
cana-5406	17	17	competition	competition	NOUN
cana-5406	17	18	of	of	ADP
cana-5406	17	19	the	the	DET
cana-5406	17	20	necessary	necessary	ADJ
cana-5406	17	21	derivatives	derivative	NOUN
cana-5406	17	22	of	of	ADP
cana-5406	17	23	the	the	DET
cana-5406	17	24	data	data	NOUN
cana-5406	17	25	functions	function	NOUN
cana-5406	17	26	.	.	PUNCT
cana-5406	18	1	the	the	DET
cana-5406	18	2	taylor	taylor	PROPN
cana-5406	18	3	series	series	PROPN
cana-5406	18	4	method	method	NOUN
cana-5406	18	5	has	have	AUX
cana-5406	18	6	computationally	computationally	ADV
cana-5406	18	7	taken	take	VERB
cana-5406	18	8	a	a	DET
cana-5406	18	9	long	long	ADJ
cana-5406	18	10	time	time	NOUN
cana-5406	18	11	for	for	ADP
cana-5406	18	12	big	big	ADJ
cana-5406	18	13	orders	order	NOUN
cana-5406	18	14	;	;	PUNCT
cana-5406	18	15	by	by	ADP
cana-5406	18	16	using	use	VERB
cana-5406	18	17	this	this	DET
cana-5406	18	18	method	method	NOUN
cana-5406	18	19	,	,	PUNCT
cana-5406	18	20	it	it	PRON
cana-5406	18	21	is	be	AUX
cana-5406	18	22	possible	possible	ADJ
cana-5406	18	23	to	to	PART
cana-5406	18	24	obtain	obtain	VERB
cana-5406	18	25	highly	highly	ADV
cana-5406	18	26	accurate	accurate	ADJ
cana-5406	18	27	results	result	NOUN
cana-5406	18	28	(	(	PUNCT
cana-5406	18	29	up	up	ADP
cana-5406	18	30	to	to	ADP
cana-5406	18	31	3th	3th	ADJ
cana-5406	18	32	order	order	NOUN
cana-5406	18	33	)	)	PUNCT
cana-5406	18	34	or	or	CCONJ
cana-5406	18	35	exact	exact	ADJ
cana-5406	18	36	solutions	solution	NOUN
cana-5406	18	37	for	for	ADP
cana-5406	18	38	differential	differential	ADJ
cana-5406	18	39	equations	equation	NOUN
cana-5406	18	40	[	[	X
cana-5406	18	41	3	3	NUM
cana-5406	18	42	]	]	PUNCT
cana-5406	18	43	.	.	PUNCT
cana-5406	19	1	with	with	ADP
cana-5406	19	2	this	this	DET
cana-5406	19	3	technique	technique	NOUN
cana-5406	19	4	the	the	DET
cana-5406	19	5	given	give	VERB
cana-5406	19	6	partial	partial	ADJ
cana-5406	19	7	differential	differential	NOUN
cana-5406	19	8	equation	equation	NOUN
cana-5406	19	9	and	and	CCONJ
cana-5406	19	10	related	relate	VERB
cana-5406	19	11	initial	initial	ADJ
cana-5406	19	12	conditions	condition	NOUN
cana-5406	19	13	are	be	AUX
cana-5406	19	14	transformed	transform	VERB
cana-5406	19	15	into	into	ADP
cana-5406	19	16	a	a	DET
cana-5406	19	17	recurrence	recurrence	NOUN
cana-5406	19	18	equation	equation	NOUN
cana-5406	19	19	that	that	PRON
cana-5406	19	20	finally	finally	ADV
cana-5406	19	21	leads	lead	VERB
cana-5406	19	22	to	to	ADP
cana-5406	19	23	the	the	DET
cana-5406	19	24	solution	solution	NOUN
cana-5406	19	25	of	of	ADP
cana-5406	19	26	a	a	DET
cana-5406	19	27	system	system	NOUN
cana-5406	19	28	of	of	ADP
cana-5406	19	29	algebraic	algebraic	ADJ
cana-5406	19	30	equations	equation	NOUN
cana-5406	19	31	as	as	ADP
cana-5406	19	32	coefficients	coefficient	NOUN
cana-5406	19	33	of	of	ADP
cana-5406	19	34	a	a	DET
cana-5406	19	35	power	power	NOUN
cana-5406	19	36	series	series	NOUN
cana-5406	19	37	solution	solution	NOUN
cana-5406	19	38	[	[	X
cana-5406	19	39	4	4	NUM
cana-5406	19	40	]	]	PUNCT
cana-5406	19	41	.	.	PUNCT
cana-5406	20	1	this	this	DET
cana-5406	20	2	method	method	NOUN
cana-5406	20	3	is	be	AUX
cana-5406	20	4	useful	useful	ADJ
cana-5406	20	5	for	for	ADP
cana-5406	20	6	obtaining	obtain	VERB
cana-5406	20	7	exact	exact	ADJ
cana-5406	20	8	and	and	CCONJ
cana-5406	20	9	approximate	approximate	ADJ
cana-5406	20	10	solutions	solution	NOUN
cana-5406	20	11	of	of	ADP
cana-5406	20	12	linear	linear	PROPN
cana-5406	20	13	and	and	CCONJ
cana-5406	20	14	nonlinear	nonlinear	ADJ
cana-5406	20	15	ordinary	ordinary	ADJ
cana-5406	20	16	and	and	CCONJ
cana-5406	20	17	partial	partial	ADJ
cana-5406	20	18	differential	differential	ADJ
cana-5406	20	19	equations	equation	NOUN
cana-5406	21	1	[	[	X
cana-5406	21	2	5	5	NUM
cana-5406	21	3	-	-	SYM
cana-5406	21	4	6	6	NUM
cana-5406	21	5	]	]	PUNCT
cana-5406	21	6	.	.	PUNCT
cana-5406	22	1	in	in	ADP
cana-5406	22	2	this	this	DET
cana-5406	22	3	method	method	NOUN
cana-5406	22	4	there	there	PRON
cana-5406	22	5	is	be	VERB
cana-5406	22	6	no	no	DET
cana-5406	22	7	need	need	NOUN
cana-5406	22	8	for	for	ADP
cana-5406	22	9	linearization	linearization	NOUN
cana-5406	22	10	or	or	CCONJ
cana-5406	22	11	perturbations	perturbation	NOUN
cana-5406	22	12	,	,	PUNCT
cana-5406	22	13	large	large	ADJ
cana-5406	22	14	computational	computational	ADJ
cana-5406	22	15	work	work	NOUN
cana-5406	22	16	and	and	CCONJ
cana-5406	22	17	round	round	ADJ
cana-5406	22	18	-	-	PUNCT
cana-5406	22	19	off	off	ADP
cana-5406	22	20	errors	error	NOUN
cana-5406	22	21	are	be	AUX
cana-5406	22	22	avoided	avoid	VERB
cana-5406	22	23	.	.	PUNCT
cana-5406	23	1	it	it	PRON
cana-5406	23	2	has	have	VERB
cana-5406	23	3	mailto:rnagargoje92@gmail.com	mailto:rnagargoje92@gmail.com	PROPN
cana-5406	23	4	mailto:avinash.khambayat@sandipuniversity.edu.in	mailto:avinash.khambayat@sandipuniversity.edu.in	PROPN
cana-5406	23	5	communications	communication	NOUN
cana-5406	23	6	on	on	ADP
cana-5406	23	7	applied	apply	VERB
cana-5406	23	8	nonlinear	nonlinear	ADJ
cana-5406	23	9	analysis	analysis	NOUN
cana-5406	23	10	issn	issn	NOUN
cana-5406	23	11	:	:	PUNCT
cana-5406	23	12	1074	1074	NUM
cana-5406	23	13	-	-	PUNCT
cana-5406	23	14	133x	133x	NUM
cana-5406	23	15	vol	vol	VERB
cana-5406	23	16	32	32	NUM
cana-5406	23	17	no	no	NOUN
cana-5406	23	18	.	.	PUNCT
cana-5406	24	1	10s	10	NOUN
cana-5406	24	2	(	(	PUNCT
cana-5406	24	3	2025	2025	NUM
cana-5406	24	4	)	)	PUNCT
cana-5406	24	5	2163	2163	NUM
cana-5406	24	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5406	24	7	been	be	AUX
cana-5406	24	8	used	use	VERB
cana-5406	24	9	to	to	PART
cana-5406	24	10	solve	solve	VERB
cana-5406	24	11	effectively	effectively	ADV
cana-5406	24	12	,	,	PUNCT
cana-5406	24	13	easily	easily	ADV
cana-5406	24	14	and	and	CCONJ
cana-5406	24	15	accurately	accurately	ADV
cana-5406	24	16	a	a	DET
cana-5406	24	17	large	large	ADJ
cana-5406	24	18	class	class	NOUN
cana-5406	24	19	of	of	ADP
cana-5406	24	20	linear	linear	PROPN
cana-5406	24	21	and	and	CCONJ
cana-5406	24	22	nonlinear	nonlinear	ADJ
cana-5406	24	23	problems	problem	NOUN
cana-5406	24	24	with	with	ADP
cana-5406	24	25	approximations	approximation	NOUN
cana-5406	24	26	.	.	PUNCT
cana-5406	25	1	it	it	PRON
cana-5406	25	2	is	be	AUX
cana-5406	25	3	possible	possible	ADJ
cana-5406	25	4	to	to	PART
cana-5406	25	5	solve	solve	VERB
cana-5406	25	6	system	system	NOUN
cana-5406	25	7	of	of	ADP
cana-5406	25	8	differential	differential	ADJ
cana-5406	25	9	equations	equation	NOUN
cana-5406	25	10	,	,	PUNCT
cana-5406	25	11	differential	differential	ADJ
cana-5406	25	12	algebraic	algebraic	ADJ
cana-5406	25	13	equations	equation	NOUN
cana-5406	25	14	,	,	PUNCT
cana-5406	25	15	difference	difference	NOUN
cana-5406	25	16	equations	equation	NOUN
cana-5406	25	17	,	,	PUNCT
cana-5406	25	18	differential	differential	ADJ
cana-5406	25	19	difference	difference	NOUN
cana-5406	25	20	equations	equation	NOUN
cana-5406	25	21	,	,	PUNCT
cana-5406	25	22	partial	partial	ADJ
cana-5406	25	23	differential	differential	ADJ
cana-5406	25	24	equations	equation	NOUN
cana-5406	25	25	[	[	X
cana-5406	25	26	7	7	NUM
cana-5406	25	27	]	]	PUNCT
cana-5406	25	28	.	.	PUNCT
cana-5406	26	1	moreover	moreover	ADV
cana-5406	26	2	,	,	PUNCT
cana-5406	26	3	the	the	DET
cana-5406	26	4	applying	applying	NOUN
cana-5406	26	5	of	of	ADP
cana-5406	26	6	dtm	dtm	PROPN
cana-5406	26	7	is	be	AUX
cana-5406	26	8	effective	effective	ADJ
cana-5406	26	9	for	for	ADP
cana-5406	26	10	solving	solve	VERB
cana-5406	26	11	two	two	NUM
cana-5406	26	12	-	-	PUNCT
cana-5406	26	13	dimensional	dimensional	ADJ
cana-5406	26	14	and	and	CCONJ
cana-5406	26	15	three	three	NUM
cana-5406	26	16	-	-	PUNCT
cana-5406	26	17	dimensional	dimensional	ADJ
cana-5406	26	18	pdes	pde	NOUN
cana-5406	26	19	with	with	ADP
cana-5406	26	20	initial	initial	ADJ
cana-5406	26	21	value	value	NOUN
cana-5406	26	22	problems	problem	NOUN
cana-5406	26	23	[	[	X
cana-5406	26	24	8	8	NUM
cana-5406	26	25	-	-	SYM
cana-5406	26	26	10	10	NUM
cana-5406	26	27	]	]	PUNCT
cana-5406	26	28	.	.	PUNCT
cana-5406	27	1	it	it	PRON
cana-5406	27	2	causes	cause	VERB
cana-5406	27	3	scientific	scientific	ADJ
cana-5406	27	4	findings	finding	NOUN
cana-5406	27	5	in	in	ADP
cana-5406	27	6	the	the	PRON
cana-5406	27	7	for	for	ADP
cana-5406	27	8	mentioned	mention	VERB
cana-5406	27	9	study	study	NOUN
cana-5406	27	10	fields	field	NOUN
cana-5406	27	11	.	.	PUNCT
cana-5406	28	1	it	it	PRON
cana-5406	28	2	is	be	AUX
cana-5406	28	3	critical	critical	ADJ
cana-5406	28	4	to	to	PART
cana-5406	28	5	investigate	investigate	VERB
cana-5406	28	6	different	different	ADJ
cana-5406	28	7	techniques	technique	NOUN
cana-5406	28	8	for	for	ADP
cana-5406	28	9	integrating	integrate	VERB
cana-5406	28	10	these	these	DET
cana-5406	28	11	pdes	pde	NOUN
cana-5406	28	12	.	.	PUNCT
cana-5406	29	1	the	the	DET
cana-5406	29	2	dtm	dtm	PROPN
cana-5406	29	3	is	be	AUX
cana-5406	29	4	a	a	DET
cana-5406	29	5	highly	highly	ADV
cana-5406	29	6	successful	successful	ADJ
cana-5406	29	7	and	and	CCONJ
cana-5406	29	8	efficient	efficient	ADJ
cana-5406	29	9	instrument	instrument	NOUN
cana-5406	29	10	for	for	ADP
cana-5406	29	11	addressing	address	VERB
cana-5406	29	12	both	both	DET
cana-5406	29	13	one	one	NUM
cana-5406	29	14	-	-	PUNCT
cana-5406	29	15	dimensional	dimensional	ADJ
cana-5406	29	16	and	and	CCONJ
cana-5406	29	17	multidimensional	multidimensional	ADJ
cana-5406	29	18	problems	problem	NOUN
cana-5406	29	19	[	[	X
cana-5406	29	20	11	11	NUM
cana-5406	29	21	]	]	PUNCT
cana-5406	29	22	.	.	PUNCT
cana-5406	30	1	this	this	DET
cana-5406	30	2	method	method	NOUN
cana-5406	30	3	uses	use	VERB
cana-5406	30	4	a	a	DET
cana-5406	30	5	sequential	sequential	ADJ
cana-5406	30	6	method	method	NOUN
cana-5406	30	7	to	to	PART
cana-5406	30	8	create	create	VERB
cana-5406	30	9	analytical	analytical	ADJ
cana-5406	30	10	solutions	solution	NOUN
cana-5406	30	11	in	in	ADP
cana-5406	30	12	the	the	DET
cana-5406	30	13	form	form	NOUN
cana-5406	30	14	of	of	ADP
cana-5406	30	15	polynomials	polynomial	NOUN
cana-5406	30	16	,	,	PUNCT
cana-5406	30	17	which	which	PRON
cana-5406	30	18	is	be	AUX
cana-5406	30	19	based	base	VERB
cana-5406	30	20	on	on	ADP
cana-5406	30	21	the	the	DET
cana-5406	30	22	taylor	taylor	PROPN
cana-5406	30	23	series	series	PROPN
cana-5406	30	24	expansion	expansion	NOUN
cana-5406	31	1	[	[	X
cana-5406	31	2	12	12	NUM
cana-5406	31	3	]	]	PUNCT
cana-5406	31	4	.	.	PUNCT
cana-5406	32	1	the	the	DET
cana-5406	32	2	dtm	dtm	PROPN
cana-5406	32	3	has	have	AUX
cana-5406	32	4	been	be	AUX
cana-5406	32	5	used	use	VERB
cana-5406	32	6	to	to	ADP
cana-5406	32	7	solving	solve	VERB
cana-5406	32	8	both	both	CCONJ
cana-5406	32	9	linear	linear	ADJ
cana-5406	32	10	and	and	CCONJ
cana-5406	32	11	nonlinear	nonlinear	ADJ
cana-5406	32	12	differential	differential	ADJ
cana-5406	32	13	equations	equation	NOUN
cana-5406	32	14	,	,	PUNCT
cana-5406	32	15	including	include	VERB
cana-5406	32	16	the	the	DET
cana-5406	32	17	kdv	kdv	NOUN
cana-5406	32	18	and	and	CCONJ
cana-5406	32	19	mkdv	mkdv	ADJ
cana-5406	32	20	equations	equation	NOUN
cana-5406	32	21	given	give	VERB
cana-5406	32	22	by	by	ADP
cana-5406	32	23	angalgil	angalgil	PROPN
cana-5406	32	24	&	&	CCONJ
cana-5406	32	25	ayaz	ayaz	PROPN
cana-5406	32	26	,	,	PUNCT
cana-5406	32	27	2009	2009	NUM
cana-5406	32	28	in	in	ADP
cana-5406	32	29	[	[	X
cana-5406	32	30	13	13	NUM
cana-5406	32	31	]	]	PUNCT
cana-5406	32	32	.	.	PUNCT
cana-5406	33	1	the	the	DET
cana-5406	33	2	two	two	NUM
cana-5406	33	3	-	-	PUNCT
cana-5406	33	4	point	point	NOUN
cana-5406	33	5	boundary	boundary	ADJ
cana-5406	33	6	value	value	NOUN
cana-5406	33	7	problem	problem	NOUN
cana-5406	33	8	[	[	X
cana-5406	33	9	14	14	NUM
cana-5406	33	10	]	]	PUNCT
cana-5406	33	11	.	.	PUNCT
cana-5406	34	1	(	(	PUNCT
cana-5406	34	2	chenand	chenand	PROPN
cana-5406	34	3	&	&	CCONJ
cana-5406	34	4	liu	liu	PROPN
cana-5406	34	5	,	,	PUNCT
cana-5406	34	6	1998	1998	NUM
cana-5406	34	7	)	)	PUNCT
cana-5406	34	8	,	,	PUNCT
cana-5406	34	9	the	the	DET
cana-5406	34	10	linear	linear	ADJ
cana-5406	34	11	parabolichyperbolic	parabolichyperbolic	ADJ
cana-5406	34	12	partial	partial	ADJ
cana-5406	34	13	differential	differential	NOUN
cana-5406	34	14	equations	equation	NOUN
cana-5406	34	15	[	[	X
cana-5406	34	16	15	15	NUM
cana-5406	34	17	]	]	PUNCT
cana-5406	34	18	.	.	PUNCT
cana-5406	35	1	(	(	PUNCT
cana-5406	35	2	biazar	biazar	NOUN
cana-5406	35	3	et	et	PROPN
cana-5406	35	4	al	al	PROPN
cana-5406	35	5	.	.	PROPN
cana-5406	35	6	,	,	PUNCT
cana-5406	35	7	2010	2010	NUM
cana-5406	35	8	)	)	PUNCT
cana-5406	35	9	,	,	PUNCT
cana-5406	35	10	the	the	DET
cana-5406	35	11	two	two	NUM
cana-5406	35	12	-	-	PUNCT
cana-5406	35	13	dimensional	dimensional	ADJ
cana-5406	35	14	nonlinear	nonlinear	ADJ
cana-5406	35	15	gas	gas	NOUN
cana-5406	35	16	dynamic	dynamic	NOUN
cana-5406	35	17	,	,	PUNCT
cana-5406	35	18	and	and	CCONJ
cana-5406	35	19	the	the	DET
cana-5406	35	20	klien	klien	PROPN
cana-5406	35	21	-	-	PUNCT
cana-5406	35	22	gordon	gordon	PROPN
cana-5406	35	23	equations	equation	NOUN
cana-5406	35	24	[	[	X
cana-5406	35	25	16	16	NUM
cana-5406	35	26	]	]	PUNCT
cana-5406	35	27	.	.	PUNCT
cana-5406	36	1	the	the	DET
cana-5406	36	2	differential	differential	ADJ
cana-5406	36	3	transform	transform	NOUN
cana-5406	36	4	approach	approach	NOUN
cana-5406	36	5	is	be	AUX
cana-5406	36	6	also	also	ADV
cana-5406	36	7	taken	take	VERB
cana-5406	36	8	into	into	ADP
cana-5406	36	9	consideration	consideration	NOUN
cana-5406	36	10	for	for	ADP
cana-5406	36	11	solving	solve	VERB
cana-5406	36	12	the	the	DET
cana-5406	36	13	three	three	NUM
cana-5406	36	14	-	-	PUNCT
cana-5406	36	15	dimensional	dimensional	ADJ
cana-5406	36	16	linear	linear	ADJ
cana-5406	36	17	helmholtz	helmholtz	NOUN
cana-5406	36	18	problem	problem	NOUN
cana-5406	36	19	in	in	ADP
cana-5406	36	20	the	the	DET
cana-5406	36	21	following	follow	VERB
cana-5406	36	22	form	form	NOUN
cana-5406	36	23	:	:	PUNCT
cana-5406	36	24	𝑙	𝑙	X
cana-5406	36	25	𝜕𝑧2	𝜕𝑧2	NOUN
cana-5406	36	26	𝜕𝑝2	𝜕𝑝2	ADV
cana-5406	37	1	+	+	ADP
cana-5406	37	2	𝑚	𝑚	X
cana-5406	37	3	𝜕𝑧2	𝜕𝑧2	NOUN
cana-5406	37	4	𝜕𝑞2	𝜕𝑞2	NOUN
cana-5406	37	5	+	+	PUNCT
cana-5406	37	6	𝑛	𝑛	DET
cana-5406	37	7	𝜕𝑧2	𝜕𝑧2	ADJ
cana-5406	37	8	𝜕𝑟2	𝜕𝑟2	NOUN
cana-5406	37	9	+	+	X
cana-5406	37	10	𝜆𝑧	𝜆𝑧	X
cana-5406	37	11	=	=	SYM
cana-5406	37	12	𝐺(𝑝	𝐺(𝑝	NUM
cana-5406	37	13	,	,	PUNCT
cana-5406	37	14	𝑞	𝑞	X
cana-5406	37	15	,	,	PUNCT
cana-5406	37	16	𝑟	𝑟	NOUN
cana-5406	37	17	)	)	PUNCT
cana-5406	37	18	with	with	ADP
cana-5406	37	19	the	the	DET
cana-5406	37	20	initial	initial	ADJ
cana-5406	37	21	conditions	condition	NOUN
cana-5406	37	22	:	:	PUNCT
cana-5406	37	23	𝑧(𝑜	𝑧(𝑜	ADJ
cana-5406	37	24	,	,	PUNCT
cana-5406	37	25	𝑞	𝑞	X
cana-5406	37	26	,	,	PUNCT
cana-5406	37	27	𝑟	𝑟	X
cana-5406	37	28	)	)	PUNCT
cana-5406	37	29	=	=	SYM
cana-5406	37	30	𝑔1(𝑞	𝑔1(𝑞	PROPN
cana-5406	37	31	,	,	PUNCT
cana-5406	37	32	𝑟	𝑟	NOUN
cana-5406	37	33	)	)	PUNCT
cana-5406	37	34	=	=	SYM
cana-5406	37	35	𝑧𝑝(𝑜	𝑧𝑝(𝑜	NOUN
cana-5406	37	36	,	,	PUNCT
cana-5406	37	37	𝑞	𝑞	X
cana-5406	37	38	,	,	PUNCT
cana-5406	37	39	𝑟	𝑟	X
cana-5406	37	40	)	)	PUNCT
cana-5406	37	41	=	=	SYM
cana-5406	38	1	𝑔2(𝑞	𝑔2(𝑞	X
cana-5406	38	2	,	,	PUNCT
cana-5406	38	3	𝑟	𝑟	NOUN
cana-5406	38	4	)	)	PUNCT
cana-5406	38	5	𝑧(𝑝	𝑧(𝑝	PROPN
cana-5406	38	6	,	,	PUNCT
cana-5406	38	7	𝑜	𝑜	PROPN
cana-5406	38	8	,	,	PUNCT
cana-5406	38	9	𝑟	𝑟	X
cana-5406	38	10	)	)	PUNCT
cana-5406	38	11	=	=	SYM
cana-5406	38	12	𝑔3(𝑝	𝑔3(𝑝	PROPN
cana-5406	38	13	,	,	PUNCT
cana-5406	38	14	𝑟	𝑟	NOUN
cana-5406	38	15	)	)	PUNCT
cana-5406	38	16	=	=	SYM
cana-5406	38	17	𝑧𝑞(𝑝	𝑧𝑞(𝑝	PROPN
cana-5406	38	18	,	,	PUNCT
cana-5406	38	19	𝑜	𝑜	NOUN
cana-5406	38	20	,	,	PUNCT
cana-5406	38	21	𝑟	𝑟	X
cana-5406	38	22	)	)	PUNCT
cana-5406	38	23	=	=	SYM
cana-5406	38	24	𝑔4(𝑝	𝑔4(𝑝	PROPN
cana-5406	38	25	,	,	PUNCT
cana-5406	38	26	𝑟	𝑟	NOUN
cana-5406	38	27	)	)	PUNCT
cana-5406	38	28	𝑧(𝑝	𝑧(𝑝	PROPN
cana-5406	38	29	,	,	PUNCT
cana-5406	38	30	𝑞	𝑞	PROPN
cana-5406	38	31	,	,	PUNCT
cana-5406	38	32	𝑜	𝑜	NOUN
cana-5406	38	33	)	)	PUNCT
cana-5406	38	34	=	=	SYM
cana-5406	39	1	𝑔5(𝑝	𝑔5(𝑝	PROPN
cana-5406	39	2	,	,	PUNCT
cana-5406	39	3	𝑞	𝑞	NOUN
cana-5406	39	4	)	)	PUNCT
cana-5406	39	5	=	=	SYM
cana-5406	39	6	𝑧𝑟(𝑝	𝑧𝑟(𝑝	NOUN
cana-5406	39	7	,	,	PUNCT
cana-5406	39	8	𝑞	𝑞	NOUN
cana-5406	39	9	,	,	PUNCT
cana-5406	39	10	𝑜	𝑜	NOUN
cana-5406	39	11	)	)	PUNCT
cana-5406	39	12	=	=	SYM
cana-5406	40	1	𝑔6(𝑝	𝑔6(𝑝	PROPN
cana-5406	40	2	,	,	PUNCT
cana-5406	40	3	𝑞	𝑞	NOUN
cana-5406	40	4	)	)	PUNCT
cana-5406	40	5	where	where	SCONJ
cana-5406	40	6	𝑔1(𝑞	𝑔1(𝑞	PROPN
cana-5406	40	7	,	,	PUNCT
cana-5406	40	8	𝑟	𝑟	NOUN
cana-5406	40	9	)	)	PUNCT
cana-5406	40	10	,	,	PUNCT
cana-5406	40	11	𝑔2(𝑞	𝑔2(𝑞	PROPN
cana-5406	40	12	,	,	PUNCT
cana-5406	40	13	𝑟	𝑟	NOUN
cana-5406	40	14	)	)	PUNCT
cana-5406	40	15	,	,	PUNCT
cana-5406	40	16	𝑔3(𝑝	𝑔3(𝑝	PROPN
cana-5406	40	17	,	,	PUNCT
cana-5406	40	18	𝑟	𝑟	NOUN
cana-5406	40	19	)	)	PUNCT
cana-5406	40	20	,	,	PUNCT
cana-5406	40	21	𝑔4(𝑝	𝑔4(𝑝	PROPN
cana-5406	40	22	,	,	PUNCT
cana-5406	40	23	𝑟	𝑟	NOUN
cana-5406	40	24	)	)	PUNCT
cana-5406	40	25	,	,	PUNCT
cana-5406	40	26	𝑔5(𝑝	𝑔5(𝑝	PROPN
cana-5406	40	27	,	,	PUNCT
cana-5406	40	28	𝑞	𝑞	NOUN
cana-5406	40	29	)	)	PUNCT
cana-5406	40	30	,	,	PUNCT
cana-5406	40	31	𝑔6(𝑝	𝑔6(𝑝	PROPN
cana-5406	40	32	,	,	PUNCT
cana-5406	40	33	𝑞	𝑞	NOUN
cana-5406	40	34	)	)	PUNCT
cana-5406	40	35	and	and	CCONJ
cana-5406	40	36	𝑙,𝑚	𝑙,𝑚	PROPN
cana-5406	40	37	,	,	PUNCT
cana-5406	40	38	𝑛	𝑛	PROPN
cana-5406	40	39	,	,	PUNCT
cana-5406	40	40	𝜆	𝜆	PRON
cana-5406	40	41	are	be	AUX
cana-5406	40	42	given	give	VERB
cana-5406	40	43	function	function	NOUN
cana-5406	40	44	and	and	CCONJ
cana-5406	40	45	constant	constant	ADJ
cana-5406	40	46	respective	respective	ADJ
cana-5406	41	1	[	[	X
cana-5406	41	2	17	17	NUM
cana-5406	41	3	]	]	PUNCT
cana-5406	41	4	.	.	PUNCT
cana-5406	42	1	this	this	DET
cana-5406	42	2	equation	equation	NOUN
cana-5406	42	3	has	have	VERB
cana-5406	42	4	wide	wide	ADJ
cana-5406	42	5	applications	application	NOUN
cana-5406	42	6	in	in	ADP
cana-5406	42	7	various	various	ADJ
cana-5406	42	8	filed	file	VERB
cana-5406	42	9	such	such	ADJ
cana-5406	42	10	as	as	ADP
cana-5406	42	11	electrical	electrical	ADJ
cana-5406	42	12	and	and	CCONJ
cana-5406	42	13	mechanical	mechanical	ADJ
cana-5406	42	14	engineering	engineering	NOUN
cana-5406	42	15	and	and	CCONJ
cana-5406	42	16	physics	physics	NOUN
cana-5406	42	17	.	.	PUNCT
cana-5406	43	1	these	these	DET
cana-5406	43	2	equations	equation	NOUN
cana-5406	43	3	the	the	DET
cana-5406	43	4	reader	reader	NOUN
cana-5406	43	5	is	be	AUX
cana-5406	43	6	referred	refer	VERB
cana-5406	43	7	to	to	ADP
cana-5406	43	8	(	(	PUNCT
cana-5406	43	9	zwilinger	zwilinger	X
cana-5406	43	10	,	,	PUNCT
cana-5406	43	11	1992	1992	NUM
cana-5406	43	12	burdenand	burdenand	NOUN
cana-5406	43	13	and	and	CCONJ
cana-5406	43	14	faires	faire	NOUN
cana-5406	43	15	,	,	PUNCT
cana-5406	43	16	1993	1993	NUM
cana-5406	43	17	)	)	PUNCT
cana-5406	44	1	[	[	X
cana-5406	44	2	18	18	NUM
cana-5406	44	3	]	]	PUNCT
cana-5406	44	4	.	.	PUNCT
cana-5406	45	1	jafari	jafari	PROPN
cana-5406	45	2	and	and	CCONJ
cana-5406	45	3	zabini	zabini	PROPN
cana-5406	45	4	solved	solve	VERB
cana-5406	45	5	the	the	DET
cana-5406	45	6	above	above	ADJ
cana-5406	45	7	equations	equation	NOUN
cana-5406	45	8	by	by	ADP
cana-5406	45	9	homotope	homotope	NOUN
cana-5406	45	10	perturbation	perturbation	NOUN
cana-5406	45	11	method	method	NOUN
cana-5406	45	12	and	and	CCONJ
cana-5406	45	13	homotop	homotop	VERB
cana-5406	45	14	analysis	analysis	NOUN
cana-5406	45	15	method	method	NOUN
cana-5406	45	16	respectively	respectively	ADV
cana-5406	45	17	[	[	X
cana-5406	45	18	19	19	NUM
cana-5406	45	19	]	]	PUNCT
cana-5406	45	20	.	.	PUNCT
cana-5406	46	1	(	(	PUNCT
cana-5406	46	2	jafari.et.al.2010b	jafari.et.al.2010b	PROPN
cana-5406	46	3	and	and	CCONJ
cana-5406	46	4	2010c	2010c	NUM
cana-5406	46	5	)	)	PUNCT
cana-5406	46	6	.	.	PUNCT
cana-5406	47	1	in	in	ADP
cana-5406	47	2	this	this	DET
cana-5406	47	3	paper	paper	NOUN
cana-5406	47	4	we	we	PRON
cana-5406	47	5	apply	apply	VERB
cana-5406	47	6	dtm	dtm	PROPN
cana-5406	47	7	for	for	ADP
cana-5406	47	8	helmholtz	helmholtz	NOUN
cana-5406	47	9	equation	equation	NOUN
cana-5406	47	10	and	and	CCONJ
cana-5406	47	11	schrodinger	schrodinger	PROPN
cana-5406	47	12	equations	equation	NOUN
cana-5406	47	13	,	,	PUNCT
cana-5406	47	14	partial	partial	ADJ
cana-5406	47	15	differential	differential	NOUN
cana-5406	47	16	equation	equation	NOUN
cana-5406	47	17	[	[	X
cana-5406	47	18	20	20	NUM
cana-5406	47	19	-	-	SYM
cana-5406	47	20	21	21	NUM
cana-5406	47	21	]	]	PUNCT
cana-5406	47	22	.	.	PUNCT
cana-5406	48	1	2	2	X
cana-5406	48	2	.	.	X
cana-5406	48	3	methods	method	NOUN
cana-5406	48	4	in	in	ADP
cana-5406	48	5	this	this	DET
cana-5406	48	6	research	research	NOUN
cana-5406	48	7	article	article	NOUN
cana-5406	48	8	we	we	PRON
cana-5406	48	9	proposed	propose	VERB
cana-5406	48	10	,	,	PUNCT
cana-5406	48	11	the	the	DET
cana-5406	48	12	differential	differential	ADJ
cana-5406	48	13	transformation	transformation	NOUN
cana-5406	48	14	method	method	NOUN
cana-5406	48	15	(	(	PUNCT
cana-5406	48	16	dtm	dtm	PROPN
cana-5406	48	17	)	)	PUNCT
cana-5406	48	18	has	have	AUX
cana-5406	48	19	been	be	AUX
cana-5406	48	20	successfully	successfully	ADV
cana-5406	48	21	applied	apply	VERB
cana-5406	48	22	to	to	PART
cana-5406	48	23	find	find	VERB
cana-5406	48	24	exact	exact	ADJ
cana-5406	48	25	and	and	CCONJ
cana-5406	48	26	approximate	approximate	ADJ
cana-5406	48	27	solution	solution	NOUN
cana-5406	48	28	of	of	ADP
cana-5406	48	29	the	the	DET
cana-5406	48	30	second	second	ADJ
cana-5406	48	31	order	order	NOUN
cana-5406	48	32	differential	differential	NOUN
cana-5406	48	33	equations	equation	NOUN
cana-5406	48	34	.	.	PUNCT
cana-5406	49	1	the	the	DET
cana-5406	49	2	method	method	NOUN
cana-5406	49	3	was	be	AUX
cana-5406	49	4	used	use	VERB
cana-5406	49	5	in	in	ADP
cana-5406	49	6	a	a	DET
cana-5406	49	7	direct	direct	ADJ
cana-5406	49	8	way	way	NOUN
cana-5406	49	9	without	without	ADP
cana-5406	49	10	using	use	VERB
cana-5406	49	11	linearization	linearization	NOUN
cana-5406	49	12	,	,	PUNCT
cana-5406	49	13	perturbation	perturbation	NOUN
cana-5406	49	14	or	or	CCONJ
cana-5406	49	15	restrictive	restrictive	ADJ
cana-5406	49	16	assumptions	assumption	NOUN
cana-5406	49	17	.	.	PUNCT
cana-5406	50	1	and	and	CCONJ
cana-5406	50	2	solving	solve	VERB
cana-5406	50	3	partial	partial	ADJ
cana-5406	50	4	differential	differential	ADJ
cana-5406	50	5	equations	equation	NOUN
cana-5406	50	6	in	in	ADP
cana-5406	50	7	two	two	NUM
cana-5406	50	8	,	,	PUNCT
cana-5406	50	9	three	three	NUM
cana-5406	50	10	-	-	PUNCT
cana-5406	50	11	dimensional	dimensional	ADJ
cana-5406	50	12	linear	linear	NOUN
cana-5406	50	13	and	and	CCONJ
cana-5406	50	14	nonlinear	nonlinear	ADJ
cana-5406	50	15	,	,	PUNCT
cana-5406	50	16	have	have	AUX
cana-5406	50	17	been	be	AUX
cana-5406	50	18	solved	solve	VERB
cana-5406	50	19	effectively	effectively	ADV
cana-5406	50	20	using	use	VERB
cana-5406	50	21	the	the	DET
cana-5406	50	22	differential	differential	ADJ
cana-5406	50	23	transform	transform	NOUN
cana-5406	50	24	method	method	NOUN
cana-5406	50	25	.	.	PUNCT
cana-5406	51	1	therefore	therefore	ADV
cana-5406	51	2	,	,	PUNCT
cana-5406	51	3	it	it	PRON
cana-5406	51	4	is	be	AUX
cana-5406	51	5	not	not	PART
cana-5406	51	6	affected	affect	VERB
cana-5406	51	7	by	by	ADP
cana-5406	51	8	computation	computation	NOUN
cana-5406	51	9	round	round	NOUN
cana-5406	51	10	off	off	ADP
cana-5406	51	11	errors	error	NOUN
cana-5406	51	12	and	and	CCONJ
cana-5406	51	13	one	one	NOUN
cana-5406	51	14	is	be	AUX
cana-5406	51	15	not	not	PART
cana-5406	51	16	faced	face	VERB
cana-5406	51	17	with	with	ADP
cana-5406	51	18	the	the	DET
cana-5406	51	19	necessities	necessity	NOUN
cana-5406	51	20	of	of	ADP
cana-5406	51	21	large	large	ADJ
cana-5406	51	22	computer	computer	NOUN
cana-5406	51	23	memory	memory	NOUN
cana-5406	51	24	and	and	CCONJ
cana-5406	51	25	time	time	NOUN
cana-5406	51	26	.	.	PUNCT
cana-5406	52	1	communications	communication	NOUN
cana-5406	52	2	on	on	ADP
cana-5406	52	3	applied	apply	VERB
cana-5406	52	4	nonlinear	nonlinear	ADJ
cana-5406	52	5	analysis	analysis	NOUN
cana-5406	52	6	issn	issn	NOUN
cana-5406	52	7	:	:	PUNCT
cana-5406	52	8	1074	1074	NUM
cana-5406	52	9	-	-	PUNCT
cana-5406	52	10	133x	133x	NUM
cana-5406	52	11	vol	vol	VERB
cana-5406	52	12	32	32	NUM
cana-5406	52	13	no	no	NOUN
cana-5406	52	14	.	.	PUNCT
cana-5406	53	1	10s	10	NOUN
cana-5406	53	2	(	(	PUNCT
cana-5406	53	3	2025	2025	NUM
cana-5406	53	4	)	)	PUNCT
cana-5406	53	5	2164	2164	NUM
cana-5406	53	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5406	53	7	definitions	definition	NOUN
cana-5406	53	8	of	of	ADP
cana-5406	53	9	multi	multi	ADJ
cana-5406	53	10	-	-	ADJ
cana-5406	53	11	dimensional	dimensional	ADJ
cana-5406	53	12	dtm	dtm	NOUN
cana-5406	53	13	:	:	PUNCT
cana-5406	53	14	we	we	PRON
cana-5406	53	15	define	define	VERB
cana-5406	53	16	dimensional	dimensional	ADJ
cana-5406	53	17	differential	differential	ADJ
cana-5406	53	18	transform	transform	NOUN
cana-5406	53	19	and	and	CCONJ
cana-5406	53	20	fundamental	fundamental	ADJ
cana-5406	53	21	operation	operation	NOUN
cana-5406	53	22	of	of	ADP
cana-5406	53	23	the	the	DET
cana-5406	53	24	function	function	NOUN
cana-5406	53	25	)	)	PUNCT
cana-5406	53	26	,	,	PUNCT
cana-5406	53	27	...	...	PUNCT
cana-5406	53	28	,	,	PUNCT
cana-5406	53	29	(	(	PUNCT
cana-5406	53	30	21	21	NUM
cana-5406	53	31	mxxxz	mxxxz	NOUN
cana-5406	53	32	as	as	ADP
cana-5406	53	33	,	,	PUNCT
cana-5406	53	34	)	)	PUNCT
cana-5406	53	35	0	0	NUM
cana-5406	53	36	.....	.....	SYM
cana-5406	53	37	0,0	0,0	NOUN
cana-5406	53	38	(	(	PUNCT
cana-5406	53	39	2	2	NUM
cana-5406	53	40	21	21	NUM
cana-5406	53	41	21	21	NUM
cana-5406	53	42	...	...	PUNCT
cana-5406	53	43	21	21	NUM
cana-5406	53	44	21	21	NUM
cana-5406	53	45	,	,	PUNCT
cana-5406	53	46	...	...	PUNCT
cana-5406	53	47	,	,	PUNCT
cana-5406	53	48	)	)	PUNCT
cana-5406	53	49	,	,	PUNCT
cana-5406	53	50	...	...	PUNCT
cana-5406	53	51	,	,	PUNCT
cana-5406	53	52	,	,	PUNCT
cana-5406	53	53	(	(	PUNCT
cana-5406	53	54	!	!	PUNCT
cana-5406	53	55	!	!	PUNCT
cana-5406	53	56	...	...	PUNCT
cana-5406	54	1	!	!	X
cana-5406	55	1	1	1	NUM
cana-5406	55	2	)	)	PUNCT
cana-5406	55	3	,	,	PUNCT
cana-5406	55	4	...	...	PUNCT
cana-5406	55	5	,	,	PUNCT
cana-5406	55	6	(	(	PUNCT
cana-5406	55	7	1	1	NUM
cana-5406	55	8	21	21	NUM
cana-5406	55	9			PROPN
cana-5406	55	10			PROPN
cana-5406	55	11			NOUN
cana-5406	55	12			NOUN
cana-5406	55	13			NOUN
cana-5406	55	14			PROPN
cana-5406	55	15			NOUN
cana-5406	55	16			NOUN
cana-5406	55	17	=	=	PUNCT
cana-5406	56	1	+	+	PROPN
cana-5406	56	2	+	+	PROPN
cana-5406	56	3	+	+	NOUN
cana-5406	56	4	m	m	VERB
cana-5406	56	5	m	m	VERB
cana-5406	56	6	k	k	X
cana-5406	56	7	m	m	VERB
cana-5406	56	8	kk	kk	PROPN
cana-5406	56	9	m	m	PROPN
cana-5406	56	10	kkk	kkk	PROPN
cana-5406	56	11	m	m	VERB
cana-5406	56	12	m	m	VERB
cana-5406	56	13	xxx	xxx	PROPN
cana-5406	56	14	xxxz	xxxz	PROPN
cana-5406	56	15	kkk	kkk	PROPN
cana-5406	56	16	kkkz	kkkz	PROPN
cana-5406	56	17	(	(	PUNCT
cana-5406	56	18	1	1	NUM
cana-5406	56	19	)	)	PUNCT
cana-5406	56	20	where	where	SCONJ
cana-5406	56	21	)	)	PUNCT
cana-5406	56	22	,	,	PUNCT
cana-5406	56	23	...	...	PUNCT
cana-5406	56	24	,	,	PUNCT
cana-5406	56	25	(	(	PUNCT
cana-5406	56	26	21	21	NUM
cana-5406	56	27	mxxxz	mxxxz	NOUN
cana-5406	56	28	is	be	AUX
cana-5406	56	29	original	original	ADJ
cana-5406	56	30	function	function	NOUN
cana-5406	56	31	and	and	CCONJ
cana-5406	56	32	)	)	PUNCT
cana-5406	56	33	,	,	PUNCT
cana-5406	56	34	...	...	PUNCT
cana-5406	56	35	,	,	PUNCT
cana-5406	56	36	(	(	PUNCT
cana-5406	56	37	21	21	NUM
cana-5406	56	38	mkkkz	mkkkz	NOUN
cana-5406	56	39	is	be	AUX
cana-5406	56	40	transformed	transform	VERB
cana-5406	56	41	function	function	NOUN
cana-5406	56	42	.	.	PUNCT
cana-5406	57	1	the	the	DET
cana-5406	57	2	differential	differential	ADJ
cana-5406	57	3	inverse	inverse	NOUN
cana-5406	57	4	transform	transform	NOUN
cana-5406	57	5	of	of	ADP
cana-5406	57	6	)	)	PUNCT
cana-5406	57	7	,	,	PUNCT
cana-5406	57	8	...	...	PUNCT
cana-5406	57	9	,	,	PUNCT
cana-5406	57	10	(	(	PUNCT
cana-5406	57	11	21	21	NUM
cana-5406	57	12	mxxxz	mxxxz	NOUN
cana-5406	57	13	is	be	AUX
cana-5406	57	14	defined	define	VERB
cana-5406	57	15	as	as	SCONJ
cana-5406	57	16	follows	follow	VERB
cana-5406	57	17	m	m	VERB
cana-5406	57	18	m	m	VERB
cana-5406	57	19	k	k	X
cana-5406	57	20	m	m	VERB
cana-5406	57	21	k	k	X
cana-5406	58	1	k	k	PROPN
cana-5406	58	2	k	k	PROPN
cana-5406	59	1	k	k	PROPN
cana-5406	59	2	k	k	PROPN
cana-5406	59	3	mm	mm	INTJ
cana-5406	59	4	xxxkkkzxxxz	xxxkkkzxxxz	NOUN
cana-5406	59	5	...	...	PUNCT
cana-5406	59	6	)	)	PUNCT
cana-5406	59	7	,	,	PUNCT
cana-5406	59	8	...	...	PUNCT
cana-5406	59	9	,	,	PUNCT
cana-5406	59	10	(	(	PUNCT
cana-5406	59	11	...	...	PUNCT
cana-5406	59	12	)	)	PUNCT
cana-5406	59	13	,	,	PUNCT
cana-5406	59	14	...	...	PUNCT
cana-5406	59	15	,	,	PUNCT
cana-5406	59	16	(	(	PUNCT
cana-5406	59	17	2	2	NUM
cana-5406	59	18	1	1	NUM
cana-5406	59	19	2	2	NUM
cana-5406	59	20	1	1	NUM
cana-5406	59	21	2	2	NUM
cana-5406	59	22	0	0	NUM
cana-5406	59	23	0	0	NUM
cana-5406	59	24	0	0	NUM
cana-5406	59	25	12121	12121	NUM
cana-5406	59	26			PART
cana-5406	59	27			X
cana-5406	59	28			VERB
cana-5406	59	29	=	=	SYM
cana-5406	59	30			X
cana-5406	59	31	=	=	SYM
cana-5406	59	32			NOUN
cana-5406	59	33	=	=	PUNCT
cana-5406	59	34	=	=	SYM
cana-5406	59	35	(	(	PUNCT
cana-5406	59	36	2	2	NUM
cana-5406	59	37	)	)	PUNCT
cana-5406	59	38	and	and	CCONJ
cana-5406	59	39	from	from	ADP
cana-5406	59	40	equation	equation	NOUN
cana-5406	59	41	(	(	PUNCT
cana-5406	59	42	1	1	NUM
cana-5406	59	43	)	)	PUNCT
cana-5406	59	44	and	and	CCONJ
cana-5406	59	45	(	(	PUNCT
cana-5406	59	46	2	2	X
cana-5406	59	47	)	)	PUNCT
cana-5406	59	48	we	we	PRON
cana-5406	59	49	can	can	AUX
cana-5406	59	50	conclude	conclude	VERB
cana-5406	59	51	m	m	VERB
cana-5406	59	52	m	m	VERB
cana-5406	59	53	m	m	VERB
cana-5406	59	54	m	m	VERB
cana-5406	59	55	k	k	X
cana-5406	59	56	m	m	VERB
cana-5406	59	57	k	k	X
cana-5406	60	1	k	k	PROPN
cana-5406	60	2	k	k	PROPN
cana-5406	61	1	k	k	PROPN
cana-5406	61	2	k	k	PROPN
cana-5406	62	1	k	k	PROPN
cana-5406	62	2	m	m	VERB
cana-5406	62	3	kk	kk	PROPN
cana-5406	62	4	m	m	PROPN
cana-5406	62	5	kkk	kkk	PROPN
cana-5406	62	6	m	m	VERB
cana-5406	62	7	m	m	VERB
cana-5406	62	8	xxx	xxx	ADJ
cana-5406	62	9	xxx	xxx	NOUN
cana-5406	63	1	xxxz	xxxz	PROPN
cana-5406	63	2	kkk	kkk	PROPN
cana-5406	63	3	xxxz	xxxz	PROPN
cana-5406	63	4	...	...	PUNCT
cana-5406	63	5	,	,	PUNCT
cana-5406	63	6	...	...	PUNCT
cana-5406	63	7	,	,	PUNCT
cana-5406	63	8	)	)	PUNCT
cana-5406	63	9	,	,	PUNCT
cana-5406	63	10	...	...	PUNCT
cana-5406	63	11	,	,	PUNCT
cana-5406	63	12	(	(	PUNCT
cana-5406	63	13	!	!	PUNCT
cana-5406	63	14	!	!	PUNCT
cana-5406	63	15	...	...	PUNCT
cana-5406	63	16	!	!	PUNCT
cana-5406	64	1	1	1	NUM
cana-5406	64	2	...	...	PUNCT
cana-5406	64	3	)	)	PUNCT
cana-5406	64	4	,	,	PUNCT
cana-5406	64	5	...	...	PUNCT
cana-5406	64	6	,	,	PUNCT
cana-5406	64	7	(	(	PUNCT
cana-5406	64	8	2	2	NUM
cana-5406	64	9	1	1	NUM
cana-5406	64	10	2	2	NUM
cana-5406	64	11	1	1	NUM
cana-5406	64	12	1	1	NUM
cana-5406	64	13	21	21	NUM
cana-5406	64	14	2	2	NUM
cana-5406	64	15	0	0	NUM
cana-5406	64	16	0	0	NUM
cana-5406	64	17	0	0	NUM
cana-5406	64	18	1	1	NUM
cana-5406	64	19	)	)	PUNCT
cana-5406	64	20	0	0	NUM
cana-5406	64	21	.....	.....	SYM
cana-5406	64	22	0,0	0,0	NOUN
cana-5406	64	23	(	(	PUNCT
cana-5406	64	24	2	2	NUM
cana-5406	64	25	21	21	NUM
cana-5406	64	26	21	21	NUM
cana-5406	64	27	...	...	PUNCT
cana-5406	64	28	21	21	NUM
cana-5406	64	29	21	21	NUM
cana-5406	64	30			ADV
cana-5406	64	31			X
cana-5406	64	32			VERB
cana-5406	64	33	=	=	SYM
cana-5406	64	34			X
cana-5406	64	35	=	=	SYM
cana-5406	64	36			X
cana-5406	64	37	=	=	PUNCT
cana-5406	65	1	+	+	ADJ
cana-5406	65	2	+	+	ADJ
cana-5406	65	3	+	+	ADJ
cana-5406	65	4			ADJ
cana-5406	65	5			PROPN
cana-5406	65	6			X
cana-5406	65	7			NOUN
cana-5406	65	8			NOUN
cana-5406	65	9			PROPN
cana-5406	65	10			NOUN
cana-5406	65	11			NOUN
cana-5406	65	12	=	=	SYM
cana-5406	65	13	(	(	PUNCT
cana-5406	65	14	3	3	X
cana-5406	65	15	)	)	PUNCT
cana-5406	65	16	theorem	theorem	NOUN
cana-5406	65	17	1	1	NUM
cana-5406	65	18	:	:	PUNCT
cana-5406	65	19	if	if	SCONJ
cana-5406	65	20	𝑧(𝑝1	𝑧(𝑝1	NOUN
cana-5406	65	21	,	,	PUNCT
cana-5406	65	22	𝑝2	𝑝2	NOUN
cana-5406	65	23	…	…	PUNCT
cana-5406	65	24	,	,	PUNCT
cana-5406	65	25	𝑝𝑚	𝑝𝑚	NOUN
cana-5406	65	26	)	)	PUNCT
cana-5406	65	27	=	=	PRON
cana-5406	65	28	𝜆𝑓	𝜆𝑓	PROPN
cana-5406	65	29	(	(	PUNCT
cana-5406	65	30	𝑝1	𝑝1	NOUN
cana-5406	65	31	,	,	PUNCT
cana-5406	65	32	𝑝2	𝑝2	NOUN
cana-5406	65	33	…	…	PUNCT
cana-5406	65	34	,	,	PUNCT
cana-5406	65	35	𝑝𝑚	𝑝𝑚	NOUN
cana-5406	65	36	)	)	PUNCT
cana-5406	65	37	then	then	ADV
cana-5406	65	38	,	,	PUNCT
cana-5406	65	39	𝑍(𝑘1	𝑍(𝑘1	PROPN
cana-5406	65	40	,	,	PUNCT
cana-5406	65	41	𝑘2	𝑘2	PROPN
cana-5406	65	42	…	…	PUNCT
cana-5406	65	43	,	,	PUNCT
cana-5406	65	44	𝑘𝑚	𝑘𝑚	INTJ
cana-5406	65	45	)	)	PUNCT
cana-5406	65	46	=	=	SYM
cana-5406	65	47	𝜆𝑓	𝜆𝑓	PROPN
cana-5406	65	48	(	(	PUNCT
cana-5406	65	49	𝑘1	𝑘1	PROPN
cana-5406	65	50	,	,	PUNCT
cana-5406	65	51	𝑘2	𝑘2	PROPN
cana-5406	65	52	,	,	PUNCT
cana-5406	65	53	…	…	PUNCT
cana-5406	65	54	,	,	PUNCT
cana-5406	65	55	𝑘𝑚	𝑘𝑚	INTJ
cana-5406	65	56	)	)	PUNCT
cana-5406	65	57	theorem	theorem	NOUN
cana-5406	65	58	2	2	NUM
cana-5406	65	59	:	:	PUNCT
cana-5406	65	60	if	if	SCONJ
cana-5406	65	61	𝑧(𝑝1	𝑧(𝑝1	NOUN
cana-5406	65	62	,	,	PUNCT
cana-5406	65	63	𝑝2	𝑝2	NOUN
cana-5406	65	64	…	…	PUNCT
cana-5406	65	65	,	,	PUNCT
cana-5406	65	66	𝑝𝑚	𝑝𝑚	NOUN
cana-5406	65	67	)	)	PUNCT
cana-5406	65	68	=	=	SYM
cana-5406	65	69	𝜕𝑓(𝑝1,𝑝2,	𝜕𝑓(𝑝1,𝑝2,	NOUN
cana-5406	65	70	…	…	X
cana-5406	65	71	,𝑝𝑚	,𝑝𝑚	PUNCT
cana-5406	65	72	)	)	PUNCT
cana-5406	65	73	𝜕𝑝1	𝜕𝑝1	PROPN
cana-5406	65	74	then	then	ADV
cana-5406	65	75	,	,	PUNCT
cana-5406	65	76	𝑍(𝑘1	𝑍(𝑘1	PROPN
cana-5406	65	77	,	,	PUNCT
cana-5406	65	78	𝑘2	𝑘2	PROPN
cana-5406	65	79	…	…	PUNCT
cana-5406	65	80	,	,	PUNCT
cana-5406	65	81	𝑘𝑚	𝑘𝑚	INTJ
cana-5406	65	82	)	)	PUNCT
cana-5406	65	83	=	=	SYM
cana-5406	65	84	(	(	PUNCT
cana-5406	65	85	𝑘𝑖	𝑘𝑖	ADP
cana-5406	65	86	+	+	NUM
cana-5406	65	87	1)𝐹	1)𝐹	PROPN
cana-5406	65	88	(	(	PUNCT
cana-5406	65	89	𝑘1	𝑘1	PROPN
cana-5406	65	90	,	,	PUNCT
cana-5406	65	91	𝑘2	𝑘2	PROPN
cana-5406	65	92	,	,	PUNCT
cana-5406	65	93	…	…	PUNCT
cana-5406	65	94	,	,	PUNCT
cana-5406	65	95	(	(	PUNCT
cana-5406	65	96	𝑘𝑖	𝑘𝑖	NOUN
cana-5406	66	1	+	+	NOUN
cana-5406	66	2	1	1	NUM
cana-5406	66	3	)	)	PUNCT
cana-5406	66	4	,	,	PUNCT
cana-5406	66	5	…	…	PUNCT
cana-5406	66	6	,	,	PUNCT
cana-5406	66	7	𝑘𝑚	𝑘𝑚	INTJ
cana-5406	66	8	)	)	PUNCT
cana-5406	66	9	theorem	theorem	VERB
cana-5406	66	10	3	3	NUM
cana-5406	66	11	:	:	PUNCT
cana-5406	66	12	if	if	SCONJ
cana-5406	66	13	𝑧(𝑝1	𝑧(𝑝1	NOUN
cana-5406	66	14	,	,	PUNCT
cana-5406	66	15	𝑝2	𝑝2	NOUN
cana-5406	66	16	…	…	PUNCT
cana-5406	66	17	,	,	PUNCT
cana-5406	66	18	𝑝𝑚	𝑝𝑚	NOUN
cana-5406	66	19	)	)	PUNCT
cana-5406	67	1	=	=	SYM
cana-5406	67	2	𝑝1	𝑝1	NOUN
cana-5406	67	3	ℎ1	ℎ1	PROPN
cana-5406	67	4	,	,	PUNCT
cana-5406	67	5	𝑝2	𝑝2	NOUN
cana-5406	67	6	ℎ2	ℎ2	NOUN
cana-5406	67	7	…	…	SYM
cana-5406	67	8	𝑝𝑚	𝑝𝑚	ADP
cana-5406	67	9	ℎ𝑚	ℎ𝑚	NOUN
cana-5406	67	10	then	then	ADV
cana-5406	67	11	,	,	PUNCT
cana-5406	67	12	𝑍(𝑘1	𝑍(𝑘1	PROPN
cana-5406	67	13	,	,	PUNCT
cana-5406	67	14	𝑘2	𝑘2	PROPN
cana-5406	67	15	…	…	PUNCT
cana-5406	67	16	,	,	PUNCT
cana-5406	67	17	𝑘𝑚	𝑘𝑚	INTJ
cana-5406	67	18	)	)	PUNCT
cana-5406	67	19	=	=	SYM
cana-5406	67	20	𝛿(𝑘1	𝛿(𝑘1	NOUN
cana-5406	68	1	−	−	PROPN
cana-5406	68	2	ℎ1)𝛿(𝑘2	ℎ1)𝛿(𝑘2	VERB
cana-5406	68	3	−	−	PRON
cana-5406	68	4	ℎ2)	ℎ2)	NOUN
cana-5406	68	5	…	…	SYM
cana-5406	68	6	𝛿(𝑘𝑚	𝛿(𝑘𝑚	NOUN
cana-5406	68	7	−	−	NOUN
cana-5406	68	8	ℎ𝑚	ℎ𝑚	NOUN
cana-5406	68	9	)	)	PUNCT
cana-5406	68	10	where	where	SCONJ
cana-5406	68	11	,	,	PUNCT
cana-5406	68	12	𝛿(𝑘𝑖	𝛿(𝑘𝑖	PROPN
cana-5406	68	13	−	−	PROPN
cana-5406	68	14	ℎ𝑖	ℎ𝑖	NOUN
cana-5406	68	15	)	)	PUNCT
cana-5406	68	16	=	=	PRON
cana-5406	68	17	{	{	PUNCT
cana-5406	68	18	1	1	NUM
cana-5406	68	19	0	0	NUM
cana-5406	68	20	𝑘𝑖	𝑘𝑖	NOUN
cana-5406	68	21	=	=	SYM
cana-5406	68	22	ℎ𝑖	ℎ𝑖	NOUN
cana-5406	68	23	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	NOUN
cana-5406	68	24	theorem	theorem	VERB
cana-5406	68	25	4	4	NUM
cana-5406	68	26	:	:	PUNCT
cana-5406	68	27	if	if	SCONJ
cana-5406	68	28	𝑧(𝑝1	𝑧(𝑝1	NOUN
cana-5406	68	29	,	,	PUNCT
cana-5406	68	30	𝑝2	𝑝2	NOUN
cana-5406	68	31	…	…	PUNCT
cana-5406	68	32	,	,	PUNCT
cana-5406	68	33	𝑝𝑚	𝑝𝑚	NOUN
cana-5406	68	34	)	)	PUNCT
cana-5406	69	1	=	=	SYM
cana-5406	69	2	𝑝1	𝑝1	NOUN
cana-5406	69	3	ℎ1	ℎ1	PROPN
cana-5406	69	4	,	,	PUNCT
cana-5406	69	5	𝑝2	𝑝2	NOUN
cana-5406	69	6	ℎ2	ℎ2	NOUN
cana-5406	69	7	…	…	SYM
cana-5406	69	8	sin(𝑎𝑥𝑖	sin(𝑎𝑥𝑖	NOUN
cana-5406	69	9	+	+	NUM
cana-5406	69	10	𝑏)	𝑏)	PROPN
cana-5406	69	11	…	…	PUNCT
cana-5406	69	12	𝑝𝑚	𝑝𝑚	PRON
cana-5406	69	13	ℎ𝑚	ℎ𝑚	NOUN
cana-5406	69	14	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	NOUN
cana-5406	69	15	𝑍(𝑘1	𝑍(𝑘1	PROPN
cana-5406	69	16	,	,	PUNCT
cana-5406	69	17	𝑘2	𝑘2	PROPN
cana-5406	69	18	…	…	PUNCT
cana-5406	69	19	,	,	PUNCT
cana-5406	69	20	𝑘𝑚	𝑘𝑚	INTJ
cana-5406	69	21	)	)	PUNCT
cana-5406	69	22	=	=	SYM
cana-5406	69	23	𝛿(𝑘1	𝛿(𝑘1	NOUN
cana-5406	70	1	−	−	PROPN
cana-5406	70	2	𝑘2	𝑘2	PROPN
cana-5406	70	3	)	)	PUNCT
cana-5406	70	4	…	…	PUNCT
cana-5406	71	1	𝑎𝑘𝑖	𝑎𝑘𝑖	NOUN
cana-5406	71	2	𝑘𝑖	𝑘𝑖	NOUN
cana-5406	71	3	!	!	PUNCT
cana-5406	71	4	sin	sin	NOUN
cana-5406	71	5	(	(	PUNCT
cana-5406	71	6	𝑘𝑖𝜋	𝑘𝑖𝜋	NOUN
cana-5406	71	7	2	2	NUM
cana-5406	71	8	+	+	NUM
cana-5406	71	9	𝑏)	𝑏)	PROPN
cana-5406	71	10	…	…	PROPN
cana-5406	71	11	𝛿(𝑘𝑚	𝛿(𝑘𝑚	PROPN
cana-5406	71	12	−	−	ADP
cana-5406	71	13	ℎ𝑚	ℎ𝑚	NOUN
cana-5406	71	14	)	)	PUNCT
cana-5406	71	15	theorem	theorem	VERB
cana-5406	71	16	5	5	NUM
cana-5406	71	17	:	:	PUNCT
cana-5406	71	18	if	if	SCONJ
cana-5406	71	19	𝑧(𝑝1	𝑧(𝑝1	NOUN
cana-5406	71	20	,	,	PUNCT
cana-5406	71	21	𝑝2	𝑝2	NOUN
cana-5406	71	22	…	…	PUNCT
cana-5406	71	23	,	,	PUNCT
cana-5406	71	24	𝑝𝑚	𝑝𝑚	NOUN
cana-5406	71	25	)	)	PUNCT
cana-5406	72	1	=	=	SYM
cana-5406	72	2	𝑝1	𝑝1	NOUN
cana-5406	72	3	ℎ1	ℎ1	PROPN
cana-5406	72	4	,	,	PUNCT
cana-5406	72	5	𝑝2	𝑝2	NOUN
cana-5406	72	6	ℎ2	ℎ2	NOUN
cana-5406	72	7	…	…	SYM
cana-5406	72	8	cos(𝑎𝑥𝑖	cos(𝑎𝑥𝑖	NOUN
cana-5406	72	9	+	+	NUM
cana-5406	72	10	𝑏)	𝑏)	PROPN
cana-5406	72	11	…	…	PUNCT
cana-5406	72	12	𝑝𝑚	𝑝𝑚	PRON
cana-5406	72	13	ℎ𝑚	ℎ𝑚	NOUN
cana-5406	72	14	𝑡ℎ𝑒𝑛	𝑡ℎ𝑒𝑛	NOUN
cana-5406	72	15	𝑍(𝑘1	𝑍(𝑘1	PROPN
cana-5406	72	16	,	,	PUNCT
cana-5406	72	17	𝑘2	𝑘2	PROPN
cana-5406	72	18	…	…	PUNCT
cana-5406	72	19	,	,	PUNCT
cana-5406	72	20	𝑘𝑚	𝑘𝑚	INTJ
cana-5406	72	21	)	)	PUNCT
cana-5406	72	22	=	=	SYM
cana-5406	72	23	𝛿(𝑘1	𝛿(𝑘1	NOUN
cana-5406	73	1	−	−	PROPN
cana-5406	73	2	𝑘2	𝑘2	PROPN
cana-5406	73	3	)	)	PUNCT
cana-5406	73	4	…	…	PUNCT
cana-5406	73	5	𝑎𝑘𝑖	𝑎𝑘𝑖	NOUN
cana-5406	73	6	𝑘𝑖	𝑘𝑖	NOUN
cana-5406	73	7	!	!	PUNCT
cana-5406	73	8	cos	cos	PROPN
cana-5406	74	1	(	(	PUNCT
cana-5406	74	2	𝑘𝑖𝜋	𝑘𝑖𝜋	NOUN
cana-5406	74	3	2	2	NUM
cana-5406	74	4	+	+	NUM
cana-5406	74	5	𝑏)	𝑏)	PROPN
cana-5406	74	6	…	…	PROPN
cana-5406	74	7	𝛿(𝑘𝑚	𝛿(𝑘𝑚	PROPN
cana-5406	74	8	−	−	ADP
cana-5406	74	9	ℎ𝑚	ℎ𝑚	NOUN
cana-5406	74	10	)	)	PUNCT
cana-5406	74	11	communications	communication	NOUN
cana-5406	74	12	on	on	ADP
cana-5406	74	13	applied	apply	VERB
cana-5406	74	14	nonlinear	nonlinear	ADJ
cana-5406	74	15	analysis	analysis	NOUN
cana-5406	74	16	issn	issn	NOUN
cana-5406	74	17	:	:	PUNCT
cana-5406	74	18	1074	1074	NUM
cana-5406	74	19	-	-	PUNCT
cana-5406	74	20	133x	133x	NUM
cana-5406	74	21	vol	vol	VERB
cana-5406	74	22	32	32	NUM
cana-5406	74	23	no	no	NOUN
cana-5406	74	24	.	.	PUNCT
cana-5406	75	1	10s	10	NOUN
cana-5406	75	2	(	(	PUNCT
cana-5406	75	3	2025	2025	NUM
cana-5406	75	4	)	)	PUNCT
cana-5406	75	5	2165	2165	NUM
cana-5406	75	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5406	75	7	3	3	X
cana-5406	75	8	.	.	NOUN
cana-5406	75	9	results	result	NOUN
cana-5406	75	10	solving	solve	VERB
cana-5406	75	11	two	two	NUM
cana-5406	75	12	numerical	numerical	ADJ
cana-5406	75	13	using	use	VERB
cana-5406	75	14	dtm	dtm	PROPN
cana-5406	75	15	:	:	PUNCT
cana-5406	75	16	example	example	NOUN
cana-5406	76	1	[	[	X
cana-5406	76	2	1	1	X
cana-5406	76	3	]	]	PUNCT
cana-5406	76	4	consider	consider	VERB
cana-5406	76	5	the	the	DET
cana-5406	76	6	following	follow	VERB
cana-5406	76	7	two	two	NUM
cana-5406	76	8	-	-	PUNCT
cana-5406	76	9	dimensional	dimensional	ADJ
cana-5406	76	10	schrodinger	schrodinger	NOUN
cana-5406	76	11	equations	equation	NOUN
cana-5406	76	12	:	:	PUNCT
cana-5406	76	13	𝜕2𝑧	𝜕2𝑧	PROPN
cana-5406	76	14	𝜕𝑝2	𝜕𝑝2	PROPN
cana-5406	76	15	+	+	CCONJ
cana-5406	76	16	𝜕2𝑧	𝜕2𝑧	PROPN
cana-5406	76	17	𝜕𝑞2	𝜕𝑞2	NOUN
cana-5406	76	18	−	−	PROPN
cana-5406	76	19	4𝑧	4𝑧	NOUN
cana-5406	76	20	=	=	PUNCT
cana-5406	76	21	(	(	PUNCT
cana-5406	76	22	24𝑝2	24𝑝2	NUM
cana-5406	76	23	−	−	NOUN
cana-5406	76	24	5𝑝4	5𝑝4	NUM
cana-5406	76	25	)	)	PUNCT
cana-5406	76	26	cos(q	cos(q	PROPN
cana-5406	76	27	)	)	PUNCT
cana-5406	76	28	(	(	PUNCT
cana-5406	76	29	4	4	X
cana-5406	76	30	)	)	PUNCT
cana-5406	76	31	with	with	ADP
cana-5406	76	32	the	the	DET
cana-5406	76	33	initial	initial	ADJ
cana-5406	76	34	condition	condition	NOUN
cana-5406	76	35	𝑧(0	𝑧(0	PROPN
cana-5406	76	36	,	,	PUNCT
cana-5406	76	37	𝑞	𝑞	X
cana-5406	76	38	)	)	PUNCT
cana-5406	76	39	=	=	SYM
cana-5406	76	40	0	0	NUM
cana-5406	76	41	,	,	PUNCT
cana-5406	76	42	𝑧𝑝(0	𝑧𝑝(0	PROPN
cana-5406	76	43	,	,	PUNCT
cana-5406	76	44	𝑞	𝑞	NOUN
cana-5406	76	45	)	)	PUNCT
cana-5406	76	46	=	=	SYM
cana-5406	76	47	0	0	PUNCT
cana-5406	77	1	(	(	PUNCT
cana-5406	77	2	5	5	NUM
cana-5406	77	3	)	)	PUNCT
cana-5406	77	4	the	the	DET
cana-5406	77	5	exact	exact	ADJ
cana-5406	77	6	solution	solution	NOUN
cana-5406	77	7	can	can	AUX
cana-5406	77	8	be	be	AUX
cana-5406	77	9	expressed	express	VERB
cana-5406	77	10	as	as	ADP
cana-5406	77	11	𝑧(𝑝	𝑧(𝑝	PROPN
cana-5406	77	12	,	,	PUNCT
cana-5406	77	13	𝑡	𝑡	X
cana-5406	77	14	)	)	PUNCT
cana-5406	77	15	=	=	SYM
cana-5406	77	16	𝑝4cos	𝑝4cos	PROPN
cana-5406	77	17	(	(	PUNCT
cana-5406	77	18	q	q	X
cana-5406	77	19	)	)	PUNCT
cana-5406	77	20	taking	take	VERB
cana-5406	77	21	the	the	DET
cana-5406	77	22	differential	differential	ADJ
cana-5406	77	23	transform	transform	NOUN
cana-5406	77	24	of	of	ADP
cana-5406	77	25	(	(	PUNCT
cana-5406	77	26	4	4	NUM
cana-5406	77	27	)	)	PUNCT
cana-5406	77	28	(	(	PUNCT
cana-5406	77	29	𝑘1	𝑘1	NOUN
cana-5406	77	30	+	+	CCONJ
cana-5406	77	31	2	2	NUM
cana-5406	77	32	)	)	PUNCT
cana-5406	77	33	(	(	PUNCT
cana-5406	77	34	𝑘1	𝑘1	NOUN
cana-5406	77	35	+	+	CCONJ
cana-5406	77	36	1	1	NUM
cana-5406	77	37	)	)	PUNCT
cana-5406	77	38	𝑍	𝑍	PROPN
cana-5406	77	39	(	(	PUNCT
cana-5406	77	40	𝑘1	𝑘1	PROPN
cana-5406	77	41	+	+	CCONJ
cana-5406	77	42	2𝑘2	2𝑘2	NUM
cana-5406	77	43	)	)	PUNCT
cana-5406	78	1	+	+	CCONJ
cana-5406	78	2	(	(	PUNCT
cana-5406	78	3	𝑘2	𝑘2	PROPN
cana-5406	78	4	+	+	CCONJ
cana-5406	78	5	2	2	NUM
cana-5406	78	6	)	)	PUNCT
cana-5406	78	7	(	(	PUNCT
cana-5406	78	8	𝑘2	𝑘2	PROPN
cana-5406	78	9	+	+	CCONJ
cana-5406	78	10	1	1	X
cana-5406	78	11	)	)	PUNCT
cana-5406	78	12	𝑍	𝑍	PROPN
cana-5406	78	13	(	(	PUNCT
cana-5406	78	14	𝑘1	𝑘1	NOUN
cana-5406	78	15	,	,	PUNCT
cana-5406	78	16	𝑘2	𝑘2	PROPN
cana-5406	78	17	+	+	CCONJ
cana-5406	78	18	2	2	X
cana-5406	78	19	)	)	PUNCT
cana-5406	78	20	−	−	PROPN
cana-5406	78	21	4𝑍	4𝑍	NOUN
cana-5406	78	22	(	(	PUNCT
cana-5406	78	23	𝑘1	𝑘1	PROPN
cana-5406	78	24	,	,	PUNCT
cana-5406	78	25	𝑘2	𝑘2	PROPN
cana-5406	78	26	)	)	PUNCT
cana-5406	78	27	=	=	SYM
cana-5406	78	28	24	24	NUM
cana-5406	78	29	𝛿(𝑘1	𝛿(𝑘1	NOUN
cana-5406	78	30	−	−	PROPN
cana-5406	78	31	2	2	NUM
cana-5406	78	32	)	)	PUNCT
cana-5406	78	33	1	1	NUM
cana-5406	78	34	𝑘2	𝑘2	NOUN
cana-5406	78	35	!	!	PUNCT
cana-5406	79	1	cos	cos	PROPN
cana-5406	79	2	(	(	PUNCT
cana-5406	79	3	𝑘2𝜋	𝑘2𝜋	PROPN
cana-5406	79	4	2	2	NUM
cana-5406	79	5	)	)	PUNCT
cana-5406	79	6	−	−	NOUN
cana-5406	79	7	5𝛿(𝑘1	5𝛿(𝑘1	NUM
cana-5406	79	8	−	−	NOUN
cana-5406	79	9	4	4	NUM
cana-5406	79	10	)	)	PUNCT
cana-5406	79	11	1	1	NUM
cana-5406	79	12	𝑘2	𝑘2	NOUN
cana-5406	79	13	!	!	PUNCT
cana-5406	80	1	cos	cos	PROPN
cana-5406	80	2	(	(	PUNCT
cana-5406	80	3	𝑘2𝜋	𝑘2𝜋	PROPN
cana-5406	80	4	2	2	NUM
cana-5406	80	5	)	)	PUNCT
cana-5406	80	6	(	(	PUNCT
cana-5406	80	7	6	6	NUM
cana-5406	80	8	)	)	PUNCT
cana-5406	80	9	from	from	ADP
cana-5406	80	10	the	the	DET
cana-5406	80	11	initial	initial	ADJ
cana-5406	80	12	condition	condition	NOUN
cana-5406	80	13	given	give	VERB
cana-5406	80	14	by	by	ADP
cana-5406	80	15	equation	equation	NOUN
cana-5406	80	16	(	(	PUNCT
cana-5406	80	17	5	5	NUM
cana-5406	80	18	)	)	PUNCT
cana-5406	80	19	𝑍(0	𝑍(0	PROPN
cana-5406	80	20	,	,	PUNCT
cana-5406	80	21	𝑘2	𝑘2	PROPN
cana-5406	80	22	,	,	PUNCT
cana-5406	80	23	)	)	PUNCT
cana-5406	80	24	=	=	SYM
cana-5406	80	25	0	0	PUNCT
cana-5406	80	26	𝑍(1	𝑍(1	NOUN
cana-5406	80	27	,	,	PUNCT
cana-5406	80	28	𝑘2	𝑘2	PROPN
cana-5406	80	29	)	)	PUNCT
cana-5406	81	1	=	=	PUNCT
cana-5406	81	2	0	0	NUM
cana-5406	82	1	𝑘2	𝑘2	NOUN
cana-5406	82	2	=	=	PUNCT
cana-5406	82	3	0,1,2	0,1,2	NUM
cana-5406	82	4	,	,	PUNCT
cana-5406	82	5	…	…	PUNCT
cana-5406	82	6	(	(	PUNCT
cana-5406	82	7	7	7	X
cana-5406	82	8	)	)	PUNCT
cana-5406	82	9	substituting	substitute	VERB
cana-5406	82	10	equation	equation	NOUN
cana-5406	82	11	(	(	PUNCT
cana-5406	82	12	6	6	NUM
cana-5406	82	13	)	)	PUNCT
cana-5406	82	14	into	into	ADP
cana-5406	82	15	equation	equation	NOUN
cana-5406	82	16	(	(	PUNCT
cana-5406	82	17	7	7	NUM
cana-5406	82	18	)	)	PUNCT
cana-5406	82	19	by	by	ADP
cana-5406	82	20	means	mean	NOUN
cana-5406	82	21	of	of	ADP
cana-5406	82	22	recursive	recursive	ADJ
cana-5406	82	23	method	method	NOUN
cana-5406	82	24	,	,	PUNCT
cana-5406	82	25	the	the	DET
cana-5406	82	26	results	result	NOUN
cana-5406	82	27	are	be	AUX
cana-5406	82	28	𝑍(𝑘1,𝑘2	𝑍(𝑘1,𝑘2	NOUN
cana-5406	82	29	,	,	PUNCT
cana-5406	82	30	)	)	PUNCT
cana-5406	83	1	=	=	SYM
cana-5406	83	2	{	{	PUNCT
cana-5406	83	3	1	1	NUM
cana-5406	83	4	𝑘2	𝑘2	PROPN
cana-5406	83	5	!	!	PUNCT
cana-5406	84	1	cos	cos	PROPN
cana-5406	84	2	(	(	PUNCT
cana-5406	84	3	𝑘2𝜋	𝑘2𝜋	PROPN
cana-5406	84	4	2	2	NUM
cana-5406	84	5	)	)	PUNCT
cana-5406	84	6	,	,	PUNCT
cana-5406	84	7	𝑖𝑓	𝑖𝑓	CCONJ
cana-5406	84	8	𝑘1	𝑘1	PROPN
cana-5406	84	9	=	=	NOUN
cana-5406	84	10	4	4	NUM
cana-5406	84	11	0	0	NUM
cana-5406	84	12	,	,	PUNCT
cana-5406	84	13	𝑜.	𝑜.	NOUN
cana-5406	84	14	𝑤.	𝑤.	NOUN
cana-5406	84	15	we	we	PRON
cana-5406	84	16	obtained	obtain	VERB
cana-5406	84	17	the	the	DET
cana-5406	84	18	series	series	NOUN
cana-5406	84	19	solution	solution	NOUN
cana-5406	84	20	as	as	ADP
cana-5406	84	21	𝑍(𝑝	𝑍(𝑝	X
cana-5406	84	22	,	,	PUNCT
cana-5406	84	23	𝑞	𝑞	X
cana-5406	84	24	)	)	PUNCT
cana-5406	84	25	=	=	SYM
cana-5406	84	26	∑	∑	PROPN
cana-5406	84	27	∑	∑	PROPN
cana-5406	84	28	𝑍(𝑘1	𝑍(𝑘1	PROPN
cana-5406	84	29	,	,	PUNCT
cana-5406	84	30	𝑘2)𝑝	𝑘2)𝑝	NOUN
cana-5406	84	31	𝑘1𝑞𝑘2	𝑘1𝑞𝑘2	PROPN
cana-5406	84	32	=	=	SYM
cana-5406	84	33	∞	∞	PROPN
cana-5406	84	34	𝑘2=0	𝑘2=0	PROPN
cana-5406	84	35	∞	∞	NUM
cana-5406	84	36	𝑘1=0	𝑘1=0	PROPN
cana-5406	84	37	𝑝4	𝑝4	NOUN
cana-5406	84	38	cos(q	cos(q	PROPN
cana-5406	84	39	)	)	PUNCT
cana-5406	84	40	which	which	PRON
cana-5406	84	41	is	be	AUX
cana-5406	84	42	exact	exact	ADJ
cana-5406	84	43	solution	solution	NOUN
cana-5406	84	44	.	.	PUNCT
cana-5406	85	1	example	example	NOUN
cana-5406	86	1	[	[	X
cana-5406	86	2	2	2	X
cana-5406	86	3	]	]	PUNCT
cana-5406	86	4	consider	consider	VERB
cana-5406	86	5	the	the	DET
cana-5406	86	6	following	follow	VERB
cana-5406	86	7	three	three	NUM
cana-5406	86	8	-	-	PUNCT
cana-5406	86	9	dimensional	dimensional	ADJ
cana-5406	86	10	helmholtz	helmholtz	NOUN
cana-5406	86	11	equations	equation	NOUN
cana-5406	86	12	:	:	PUNCT
cana-5406	87	1	𝜕2𝑧	𝜕2𝑧	PROPN
cana-5406	87	2	𝜕𝑝2	𝜕𝑝2	PROPN
cana-5406	87	3	+	+	CCONJ
cana-5406	87	4	𝜕2𝑧	𝜕2𝑧	PROPN
cana-5406	87	5	𝜕𝑞2	𝜕𝑞2	NOUN
cana-5406	87	6	−	−	PROPN
cana-5406	87	7	𝜕2𝑧	𝜕2𝑧	NOUN
cana-5406	87	8	𝜕𝑟2	𝜕𝑟2	NOUN
cana-5406	87	9	−	−	NOUN
cana-5406	87	10	8𝑧	8𝑧	NUM
cana-5406	87	11	=	=	SYM
cana-5406	87	12	(	(	PUNCT
cana-5406	87	13	24𝑝2	24𝑝2	NUM
cana-5406	87	14	−	−	NOUN
cana-5406	87	15	8𝑝4	8𝑝4	NUM
cana-5406	87	16	)	)	PUNCT
cana-5406	87	17	cos	cos	PROPN
cana-5406	87	18	(	(	PUNCT
cana-5406	87	19	q)sin	q)sin	PROPN
cana-5406	87	20	(	(	PUNCT
cana-5406	87	21	𝑟	𝑟	NOUN
cana-5406	87	22	)	)	PUNCT
cana-5406	87	23	(	(	PUNCT
cana-5406	87	24	8)	8)	NUM
cana-5406	87	25	with	with	ADP
cana-5406	87	26	the	the	DET
cana-5406	87	27	initial	initial	ADJ
cana-5406	87	28	condition	condition	NOUN
cana-5406	87	29	𝑧(0	𝑧(0	PROPN
cana-5406	87	30	,	,	PUNCT
cana-5406	87	31	𝑞	𝑞	X
cana-5406	87	32	,	,	PUNCT
cana-5406	87	33	𝑟	𝑟	NOUN
cana-5406	87	34	)	)	PUNCT
cana-5406	87	35	=	=	SYM
cana-5406	87	36	0	0	NUM
cana-5406	87	37	,	,	PUNCT
cana-5406	87	38	𝑧𝑝(0	𝑧𝑝(0	PROPN
cana-5406	87	39	,	,	PUNCT
cana-5406	87	40	𝑞	𝑞	X
cana-5406	87	41	,	,	PUNCT
cana-5406	87	42	𝑟	𝑟	NOUN
cana-5406	87	43	)	)	PUNCT
cana-5406	87	44	=	=	SYM
cana-5406	87	45	0	0	PUNCT
cana-5406	88	1	(	(	PUNCT
cana-5406	88	2	9	9	NUM
cana-5406	88	3	)	)	PUNCT
cana-5406	88	4	the	the	DET
cana-5406	88	5	exact	exact	ADJ
cana-5406	88	6	solution	solution	NOUN
cana-5406	88	7	can	can	AUX
cana-5406	88	8	be	be	AUX
cana-5406	88	9	expressed	express	VERB
cana-5406	88	10	as	as	ADP
cana-5406	88	11	𝑧(𝑝	𝑧(𝑝	PROPN
cana-5406	88	12	,	,	PUNCT
cana-5406	88	13	𝑡	𝑡	X
cana-5406	88	14	)	)	PUNCT
cana-5406	88	15	=	=	SYM
cana-5406	88	16	𝑝4cos	𝑝4cos	PROPN
cana-5406	88	17	(	(	PUNCT
cana-5406	88	18	q)sin	q)sin	PROPN
cana-5406	88	19	(	(	PUNCT
cana-5406	88	20	𝑟	𝑟	NOUN
cana-5406	88	21	)	)	PUNCT
cana-5406	88	22	taking	take	VERB
cana-5406	88	23	the	the	DET
cana-5406	88	24	differential	differential	ADJ
cana-5406	88	25	transform	transform	NOUN
cana-5406	88	26	of	of	ADP
cana-5406	88	27	(	(	PUNCT
cana-5406	88	28	8)	8)	NUM
cana-5406	88	29	(	(	PUNCT
cana-5406	88	30	k1	k1	NOUN
cana-5406	88	31	+	+	NOUN
cana-5406	88	32	2	2	NUM
cana-5406	88	33	)	)	PUNCT
cana-5406	88	34	(	(	PUNCT
cana-5406	88	35	k1	k1	X
cana-5406	88	36	+	+	NOUN
cana-5406	88	37	1	1	NUM
cana-5406	88	38	)	)	PUNCT
cana-5406	88	39	z	z	NOUN
cana-5406	88	40	(	(	PUNCT
cana-5406	88	41	k1	k1	X
cana-5406	88	42	+	+	PROPN
cana-5406	88	43	2	2	NUM
cana-5406	88	44	,	,	PUNCT
cana-5406	88	45	k2	k2	ADJ
cana-5406	88	46	,	,	PUNCT
cana-5406	88	47	k3	k3	VERB
cana-5406	88	48	)	)	PUNCT
cana-5406	88	49	+	+	CCONJ
cana-5406	88	50	(	(	PUNCT
cana-5406	88	51	k2	k2	ADJ
cana-5406	88	52	+	+	PROPN
cana-5406	88	53	2	2	NUM
cana-5406	88	54	)	)	PUNCT
cana-5406	88	55	(	(	PUNCT
cana-5406	88	56	k2	k2	X
cana-5406	88	57	+	+	PROPN
cana-5406	88	58	1	1	NUM
cana-5406	88	59	)	)	PUNCT
cana-5406	88	60	z	z	NOUN
cana-5406	88	61	(	(	PUNCT
cana-5406	88	62	k1	k1	NOUN
cana-5406	88	63	,	,	PUNCT
cana-5406	88	64	k2	k2	NOUN
cana-5406	88	65	+	+	PROPN
cana-5406	88	66	2	2	NUM
cana-5406	88	67	,	,	PUNCT
cana-5406	88	68	k3)(k3	k3)(k3	PUNCT
cana-5406	88	69	+	+	PROPN
cana-5406	88	70	2	2	NUM
cana-5406	88	71	)	)	PUNCT
cana-5406	88	72	(	(	PUNCT
cana-5406	88	73	k3	k3	VERB
cana-5406	88	74	+	+	NOUN
cana-5406	88	75	1	1	NUM
cana-5406	88	76	)	)	PUNCT
cana-5406	88	77	z	z	NOUN
cana-5406	88	78	(	(	PUNCT
cana-5406	88	79	k1	k1	PROPN
cana-5406	88	80	,	,	PUNCT
cana-5406	88	81	k2	k2	NOUN
cana-5406	88	82	,	,	PUNCT
cana-5406	88	83	k3	k3	VERB
cana-5406	88	84	+	+	NOUN
cana-5406	88	85	2	2	NUM
cana-5406	88	86	)	)	PUNCT
cana-5406	88	87	8z	8z	NUM
cana-5406	88	88	(	(	PUNCT
cana-5406	88	89	k1	k1	PROPN
cana-5406	88	90	,	,	PUNCT
cana-5406	88	91	k2	k2	NOUN
cana-5406	88	92	,	,	PUNCT
cana-5406	88	93	k3	k3	ADJ
cana-5406	88	94	)	)	PUNCT
cana-5406	88	95	communications	communication	NOUN
cana-5406	88	96	on	on	ADP
cana-5406	88	97	applied	apply	VERB
cana-5406	88	98	nonlinear	nonlinear	ADJ
cana-5406	88	99	analysis	analysis	NOUN
cana-5406	88	100	issn	issn	NOUN
cana-5406	88	101	:	:	PUNCT
cana-5406	88	102	1074	1074	NUM
cana-5406	88	103	-	-	PUNCT
cana-5406	88	104	133x	133x	NUM
cana-5406	88	105	vol	vol	VERB
cana-5406	88	106	32	32	NUM
cana-5406	88	107	no	no	NOUN
cana-5406	88	108	.	.	PUNCT
cana-5406	89	1	10s	10	NOUN
cana-5406	89	2	(	(	PUNCT
cana-5406	89	3	2025	2025	NUM
cana-5406	89	4	)	)	PUNCT
cana-5406	89	5	2166	2166	NUM
cana-5406	89	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5406	90	1	=	=	SYM
cana-5406	90	2	24𝛿(𝑘1	24𝛿(𝑘1	NUM
cana-5406	90	3	−	−	NUM
cana-5406	90	4	2	2	NUM
cana-5406	90	5	)	)	PUNCT
cana-5406	90	6	1	1	NUM
cana-5406	90	7	𝑘2	𝑘2	NOUN
cana-5406	90	8	!	!	PUNCT
cana-5406	91	1	cos	cos	PROPN
cana-5406	91	2	(	(	PUNCT
cana-5406	91	3	𝑘2𝜋	𝑘2𝜋	PROPN
cana-5406	91	4	2	2	NUM
cana-5406	91	5	)	)	PUNCT
cana-5406	91	6	1	1	NUM
cana-5406	91	7	𝑘3	𝑘3	PROPN
cana-5406	91	8	!	!	PUNCT
cana-5406	92	1	sin	sin	NOUN
cana-5406	92	2	(	(	PUNCT
cana-5406	92	3	𝑘3𝜋	𝑘3𝜋	DET
cana-5406	92	4	2	2	NUM
cana-5406	92	5	)	)	PUNCT
cana-5406	92	6	−	−	NOUN
cana-5406	92	7	8𝛿(𝑘1	8𝛿(𝑘1	NUM
cana-5406	92	8	−	−	PROPN
cana-5406	92	9	4	4	NUM
cana-5406	92	10	)	)	SYM
cana-5406	92	11	1	1	NUM
cana-5406	92	12	𝑘2	𝑘2	NOUN
cana-5406	92	13	!	!	PUNCT
cana-5406	93	1	cos	cos	PROPN
cana-5406	93	2	(	(	PUNCT
cana-5406	93	3	𝑘2𝜋	𝑘2𝜋	PROPN
cana-5406	93	4	2	2	NUM
cana-5406	93	5	)	)	PUNCT
cana-5406	93	6	1	1	NUM
cana-5406	93	7	𝑘3	𝑘3	PROPN
cana-5406	93	8	!	!	PUNCT
cana-5406	94	1	sin	sin	NOUN
cana-5406	94	2	(	(	PUNCT
cana-5406	94	3	𝑘3𝜋	𝑘3𝜋	DET
cana-5406	94	4	2	2	NUM
cana-5406	94	5	)	)	PUNCT
cana-5406	94	6	(	(	PUNCT
cana-5406	94	7	10	10	NUM
cana-5406	94	8	)	)	PUNCT
cana-5406	94	9	from	from	ADP
cana-5406	94	10	the	the	DET
cana-5406	94	11	initial	initial	ADJ
cana-5406	94	12	condition	condition	NOUN
cana-5406	94	13	given	give	VERB
cana-5406	94	14	by	by	ADP
cana-5406	94	15	equation	equation	NOUN
cana-5406	94	16	(	(	PUNCT
cana-5406	94	17	9	9	NUM
cana-5406	94	18	)	)	PUNCT
cana-5406	94	19	𝑍(0	𝑍(0	PROPN
cana-5406	94	20	,	,	PUNCT
cana-5406	94	21	𝑘2	𝑘2	PROPN
cana-5406	94	22	,	,	PUNCT
cana-5406	94	23	𝑘3	𝑘3	PROPN
cana-5406	94	24	)	)	PUNCT
cana-5406	94	25	=	=	SYM
cana-5406	94	26	0	0	PUNCT
cana-5406	94	27	𝑍(1	𝑍(1	NOUN
cana-5406	94	28	,	,	PUNCT
cana-5406	94	29	𝑘2	𝑘2	PROPN
cana-5406	94	30	,	,	PUNCT
cana-5406	94	31	𝑘3	𝑘3	PROPN
cana-5406	94	32	)	)	PUNCT
cana-5406	94	33	=	=	PUNCT
cana-5406	94	34	0	0	NUM
cana-5406	95	1	𝑘2,𝑘3	𝑘2,𝑘3	PROPN
cana-5406	95	2	=	=	SYM
cana-5406	95	3	0,1,2	0,1,2	NUM
cana-5406	95	4	,	,	PUNCT
cana-5406	95	5	…	…	PUNCT
cana-5406	95	6	(	(	PUNCT
cana-5406	95	7	11	11	X
cana-5406	95	8	)	)	PUNCT
cana-5406	95	9	substituting	substitute	VERB
cana-5406	95	10	equation	equation	NOUN
cana-5406	95	11	(	(	PUNCT
cana-5406	95	12	11	11	NUM
cana-5406	95	13	)	)	PUNCT
cana-5406	95	14	into	into	ADP
cana-5406	95	15	equation	equation	NOUN
cana-5406	95	16	(	(	PUNCT
cana-5406	95	17	10	10	NUM
cana-5406	95	18	)	)	PUNCT
cana-5406	95	19	by	by	ADP
cana-5406	95	20	means	mean	NOUN
cana-5406	95	21	of	of	ADP
cana-5406	95	22	recursive	recursive	ADJ
cana-5406	95	23	method	method	NOUN
cana-5406	95	24	,	,	PUNCT
cana-5406	95	25	the	the	DET
cana-5406	95	26	results	result	NOUN
cana-5406	95	27	are	be	AUX
cana-5406	95	28	z(𝑘1,𝑘2,𝑘3	z(𝑘1,𝑘2,𝑘3	NOUN
cana-5406	95	29	,	,	PUNCT
cana-5406	95	30	)	)	PUNCT
cana-5406	96	1	=	=	SYM
cana-5406	96	2	0	0	PUNCT
cana-5406	97	1	𝑖𝑓	𝑖𝑓	NUM
cana-5406	97	2	𝑘1	𝑘1	ADJ
cana-5406	97	3	≠	≠	PROPN
cana-5406	97	4	8	8	NUM
cana-5406	97	5	&	&	CCONJ
cana-5406	97	6	𝑘2,𝑘3	𝑘2,𝑘3	PROPN
cana-5406	97	7	,	,	PUNCT
cana-5406	97	8	=	=	PUNCT
cana-5406	98	1	0,1,2	0,1,2	NUM
cana-5406	98	2	,	,	PUNCT
cana-5406	98	3	…	…	PUNCT
cana-5406	98	4	𝑍(8	𝑍(8	PUNCT
cana-5406	98	5	𝑘2,𝑘3	𝑘2,𝑘3	NOUN
cana-5406	98	6	=	=	SYM
cana-5406	98	7	1	1	NUM
cana-5406	98	8	𝑘2	𝑘2	NOUN
cana-5406	98	9	!	!	PUNCT
cana-5406	99	1	cos	cos	PROPN
cana-5406	99	2	(	(	PUNCT
cana-5406	99	3	𝑘2𝜋	𝑘2𝜋	PROPN
cana-5406	99	4	2	2	NUM
cana-5406	99	5	)	)	PUNCT
cana-5406	99	6	1	1	NUM
cana-5406	99	7	𝑘3	𝑘3	PROPN
cana-5406	99	8	!	!	PUNCT
cana-5406	100	1	sin	sin	NOUN
cana-5406	100	2	(	(	PUNCT
cana-5406	100	3	𝑘3𝜋	𝑘3𝜋	DET
cana-5406	100	4	2	2	NUM
cana-5406	100	5	)	)	PUNCT
cana-5406	100	6	𝑖𝑓	𝑖𝑓	ADP
cana-5406	101	1	𝑘2,𝑘3	𝑘2,𝑘3	PROPN
cana-5406	101	2	,	,	PUNCT
cana-5406	101	3	=	=	PUNCT
cana-5406	101	4	0,1,2	0,1,2	NUM
cana-5406	101	5	,	,	PUNCT
cana-5406	101	6	…	…	PUNCT
cana-5406	101	7	we	we	PRON
cana-5406	101	8	obtained	obtain	VERB
cana-5406	101	9	the	the	DET
cana-5406	101	10	series	series	NOUN
cana-5406	101	11	solution	solution	NOUN
cana-5406	101	12	as	as	ADP
cana-5406	101	13	𝑍(𝑝	𝑍(𝑝	X
cana-5406	101	14	,	,	PUNCT
cana-5406	101	15	𝑞	𝑞	PROPN
cana-5406	101	16	,	,	PUNCT
cana-5406	101	17	𝑟	𝑟	NOUN
cana-5406	101	18	)	)	PUNCT
cana-5406	101	19	=	=	PUNCT
cana-5406	101	20	∑	∑	PUNCT
cana-5406	101	21	∑	∑	PROPN
cana-5406	101	22	∑	∑	PROPN
cana-5406	101	23	𝑍(𝑘1𝑘2	𝑍(𝑘1𝑘2	ADP
cana-5406	101	24	,	,	PUNCT
cana-5406	101	25	𝑘3	𝑘3	PROPN
cana-5406	101	26	)	)	PUNCT
cana-5406	101	27	∞	∞	PROPN
cana-5406	102	1	𝑘3=0	𝑘3=0	PROPN
cana-5406	102	2	𝑝𝑘1𝑞𝑘2𝑟𝑘3	𝑝𝑘1𝑞𝑘2𝑟𝑘3	ADJ
cana-5406	102	3	=	=	SYM
cana-5406	102	4	∞	∞	PROPN
cana-5406	102	5	𝑘2=0	𝑘2=0	PROPN
cana-5406	103	1	∞	∞	NUM
cana-5406	103	2	𝑘1=0	𝑘1=0	PROPN
cana-5406	103	3	𝑝4	𝑝4	NOUN
cana-5406	103	4	cos(q	cos(q	PROPN
cana-5406	103	5	)	)	PUNCT
cana-5406	103	6	sin(𝑟	sin(𝑟	NOUN
cana-5406	103	7	)	)	PUNCT
cana-5406	103	8	which	which	PRON
cana-5406	103	9	is	be	AUX
cana-5406	103	10	exact	exact	ADJ
cana-5406	103	11	solution	solution	NOUN
cana-5406	103	12	.	.	PUNCT
cana-5406	104	1	example	example	NOUN
cana-5406	105	1	[	[	X
cana-5406	105	2	3	3	X
cana-5406	105	3	]	]	PUNCT
cana-5406	105	4	consider	consider	VERB
cana-5406	105	5	pide	pide	ADJ
cana-5406	105	6	,	,	PUNCT
cana-5406	105	7	𝑥𝑢𝑥	𝑥𝑢𝑥	NOUN
cana-5406	105	8	=	=	PUNCT
cana-5406	105	9	𝑢𝑡𝑡	𝑢𝑡𝑡	PROPN
cana-5406	105	10	+	+	CCONJ
cana-5406	105	11	𝑥𝑠𝑖𝑛𝑡	𝑥𝑠𝑖𝑛𝑡	PROPN
cana-5406	105	12	−	−	PROPN
cana-5406	105	13	∫	∫	PROPN
cana-5406	106	1	𝑠𝑖𝑛(𝑡	𝑠𝑖𝑛(𝑡	PROPN
cana-5406	106	2	−	−	PROPN
cana-5406	106	3	𝑧	𝑧	NOUN
cana-5406	106	4	)	)	PUNCT
cana-5406	106	5	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5406	106	6	,	,	PUNCT
cana-5406	106	7	𝑧	𝑧	NOUN
cana-5406	106	8	)	)	PUNCT
cana-5406	106	9	𝑑𝑧	𝑑𝑧	NOUN
cana-5406	106	10	𝑡	𝑡	PROPN
cana-5406	106	11	0	0	NUM
cana-5406	106	12	with	with	ADP
cana-5406	106	13	initial	initial	ADJ
cana-5406	106	14	conditions	condition	NOUN
cana-5406	106	15	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5406	106	16	,	,	PUNCT
cana-5406	106	17	0	0	NUM
cana-5406	106	18	)	)	PUNCT
cana-5406	106	19	=	=	SYM
cana-5406	106	20	0	0	NUM
cana-5406	106	21	,	,	PUNCT
cana-5406	106	22	𝑢𝑡(𝑥	𝑢𝑡(𝑥	ADV
cana-5406	106	23	,	,	PUNCT
cana-5406	106	24	0	0	NUM
cana-5406	106	25	)	)	PUNCT
cana-5406	106	26	=	=	SYM
cana-5406	106	27	𝑥	𝑥	NOUN
cana-5406	106	28	and	and	CCONJ
cana-5406	106	29	boundary	boundary	ADJ
cana-5406	106	30	condition	condition	NOUN
cana-5406	106	31	𝑢(1	𝑢(1	PROPN
cana-5406	106	32	,	,	PUNCT
cana-5406	106	33	𝑡	𝑡	X
cana-5406	106	34	)	)	PUNCT
cana-5406	106	35	=	=	SYM
cana-5406	107	1	𝑡	𝑡	NOUN
cana-5406	107	2	solution	solution	NOUN
cana-5406	107	3	:	:	PUNCT
cana-5406	107	4	given	give	VERB
cana-5406	107	5	,	,	PUNCT
cana-5406	107	6	𝑥𝑢𝑥	𝑥𝑢𝑥	NOUN
cana-5406	107	7	=	=	PUNCT
cana-5406	107	8	𝑢𝑡𝑡	𝑢𝑡𝑡	PROPN
cana-5406	107	9	+	+	CCONJ
cana-5406	107	10	𝑥𝑠𝑖𝑛𝑡	𝑥𝑠𝑖𝑛𝑡	PROPN
cana-5406	107	11	−	−	PROPN
cana-5406	107	12	∫	∫	PROPN
cana-5406	108	1	𝑠𝑖𝑛(𝑡	𝑠𝑖𝑛(𝑡	PROPN
cana-5406	108	2	−	−	PROPN
cana-5406	108	3	𝑧)𝑢(𝑥	𝑧)𝑢(𝑥	PROPN
cana-5406	108	4	,	,	PUNCT
cana-5406	108	5	𝑧)𝑑𝑧	𝑧)𝑑𝑧	PROPN
cana-5406	108	6	𝑡	𝑡	PROPN
cana-5406	108	7	0	0	NUM
cana-5406	108	8	𝑢𝑡𝑡	𝑢𝑡𝑡	NOUN
cana-5406	108	9	=	=	NOUN
cana-5406	108	10	𝑥𝑢𝑥	𝑥𝑢𝑥	NOUN
cana-5406	108	11	−	−	PROPN
cana-5406	108	12	𝑥𝑠𝑖𝑛𝑡	𝑥𝑠𝑖𝑛𝑡	PROPN
cana-5406	108	13	−	−	PROPN
cana-5406	108	14	𝑠𝑖𝑛𝑡	𝑠𝑖𝑛𝑡	NOUN
cana-5406	108	15	∫	∫	PROPN
cana-5406	108	16	𝑐𝑜𝑠𝑧𝑢(𝑥	𝑐𝑜𝑠𝑧𝑢(𝑥	PROPN
cana-5406	108	17	,	,	PUNCT
cana-5406	108	18	𝑧)𝑑𝑧	𝑧)𝑑𝑧	PROPN
cana-5406	108	19	+	+	NUM
cana-5406	108	20	𝑐𝑜𝑠𝑡∫	𝑐𝑜𝑠𝑡∫	PROPN
cana-5406	108	21	𝑠𝑖𝑛𝑧𝑢(𝑥	𝑠𝑖𝑛𝑧𝑢(𝑥	VERB
cana-5406	108	22	,	,	PUNCT
cana-5406	108	23	𝑧)𝑑𝑧	𝑧)𝑑𝑧	PROPN
cana-5406	108	24	𝑡	𝑡	PROPN
cana-5406	108	25	0	0	NUM
cana-5406	108	26	𝑡	𝑡	NOUN
cana-5406	108	27	0	0	NUM
cana-5406	108	28	(	(	PUNCT
cana-5406	108	29	12	12	NUM
cana-5406	108	30	)	)	PUNCT
cana-5406	108	31	with	with	ADP
cana-5406	108	32	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5406	108	33	,	,	PUNCT
cana-5406	108	34	0	0	NUM
cana-5406	108	35	)	)	PUNCT
cana-5406	108	36	=	=	SYM
cana-5406	108	37	0	0	NUM
cana-5406	108	38	,	,	PUNCT
cana-5406	108	39	𝑢𝑡(𝑥	𝑢𝑡(𝑥	ADV
cana-5406	108	40	,	,	PUNCT
cana-5406	108	41	0	0	NUM
cana-5406	108	42	)	)	PUNCT
cana-5406	108	43	=	=	SYM
cana-5406	109	1	𝑥	𝑥	PROPN
cana-5406	109	2	(	(	PUNCT
cana-5406	109	3	13	13	NUM
cana-5406	109	4	)	)	PUNCT
cana-5406	109	5	and	and	CCONJ
cana-5406	109	6	𝑢(1	𝑢(1	PROPN
cana-5406	109	7	,	,	PUNCT
cana-5406	109	8	𝑡	𝑡	X
cana-5406	109	9	)	)	PUNCT
cana-5406	109	10	=	=	SYM
cana-5406	109	11	𝑡	𝑡	PROPN
cana-5406	109	12	(	(	PUNCT
cana-5406	109	13	14	14	NUM
cana-5406	109	14	)	)	PUNCT
cana-5406	109	15	appling	apple	VERB
cana-5406	109	16	two	two	NUM
cana-5406	109	17	dimensional	dimensional	ADJ
cana-5406	109	18	dtm	dtm	NOUN
cana-5406	109	19	on	on	ADP
cana-5406	109	20	both	both	DET
cana-5406	109	21	sides	side	NOUN
cana-5406	109	22	of	of	ADP
cana-5406	109	23	equations	equation	NOUN
cana-5406	109	24	(	(	PUNCT
cana-5406	109	25	12	12	NUM
cana-5406	109	26	)	)	PUNCT
cana-5406	109	27	,	,	PUNCT
cana-5406	109	28	communications	communication	NOUN
cana-5406	109	29	on	on	ADP
cana-5406	109	30	applied	apply	VERB
cana-5406	109	31	nonlinear	nonlinear	ADJ
cana-5406	109	32	analysis	analysis	NOUN
cana-5406	109	33	issn	issn	NOUN
cana-5406	109	34	:	:	PUNCT
cana-5406	109	35	1074	1074	NUM
cana-5406	109	36	-	-	PUNCT
cana-5406	109	37	133x	133x	NUM
cana-5406	109	38	vol	vol	VERB
cana-5406	109	39	32	32	NUM
cana-5406	109	40	no	no	NOUN
cana-5406	109	41	.	.	PUNCT
cana-5406	110	1	10s	10	NOUN
cana-5406	110	2	(	(	PUNCT
cana-5406	110	3	2025	2025	NUM
cana-5406	110	4	)	)	PUNCT
cana-5406	110	5	2167	2167	NUM
cana-5406	110	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5406	110	7	∴	∴	PROPN
cana-5406	110	8	𝑈(𝑘	𝑈(𝑘	PROPN
cana-5406	110	9	,	,	PUNCT
cana-5406	110	10	ℎ	ℎ	X
cana-5406	110	11	+	+	NOUN
cana-5406	110	12	2	2	NUM
cana-5406	110	13	)	)	PUNCT
cana-5406	110	14	=	=	SYM
cana-5406	110	15	1	1	NUM
cana-5406	110	16	(	(	PUNCT
cana-5406	110	17	ℎ	ℎ	X
cana-5406	110	18	+	+	NOUN
cana-5406	110	19	1)(ℎ	1)(ℎ	NUM
cana-5406	110	20	+	+	CCONJ
cana-5406	110	21	2	2	NUM
cana-5406	110	22	)	)	PUNCT
cana-5406	110	23	{	{	PUNCT
cana-5406	110	24	∑	∑	PUNCT
cana-5406	110	25	𝛿(𝛼	𝛿(𝛼	PROPN
cana-5406	110	26	−	−	PROPN
cana-5406	110	27	1)(𝑘	1)(𝑘	NUM
cana-5406	110	28	−	−	PROPN
cana-5406	110	29	𝛼	𝛼	PRON
cana-5406	110	30	+	+	NOUN
cana-5406	110	31	1)𝑈(𝑘	1)𝑈(𝑘	NUM
cana-5406	110	32	−	−	NOUN
cana-5406	110	33	𝛼	𝛼	PRON
cana-5406	110	34	+	+	NOUN
cana-5406	110	35	1	1	NUM
cana-5406	110	36	,	,	PUNCT
cana-5406	110	37	ℎ	ℎ	PROPN
cana-5406	110	38	)	)	PUNCT
cana-5406	110	39	𝑘	𝑘	ADP
cana-5406	110	40	𝛼=0	𝛼=0	PROPN
cana-5406	110	41	−	−	PROPN
cana-5406	110	42	𝛿(𝑘	𝛿(𝑘	PROPN
cana-5406	110	43	−	−	ADP
cana-5406	110	44	1	1	X
cana-5406	110	45	)	)	PUNCT
cana-5406	110	46	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
cana-5406	110	47	(	(	PUNCT
cana-5406	110	48	ℎ𝜋	ℎ𝜋	PROPN
cana-5406	110	49	2	2	NUM
cana-5406	110	50	)	)	PUNCT
cana-5406	110	51	ℎ	ℎ	PROPN
cana-5406	110	52	!	!	PUNCT
cana-5406	110	53	−∑∑	−∑∑	PROPN
cana-5406	110	54	(	(	PUNCT
cana-5406	110	55	1	1	NUM
cana-5406	110	56	𝛽	𝛽	NOUN
cana-5406	110	57	)	)	PUNCT
cana-5406	110	58	(	(	PUNCT
cana-5406	110	59	𝑠𝑖𝑛	𝑠𝑖𝑛	X
cana-5406	110	60	(	(	PUNCT
cana-5406	110	61	(	(	PUNCT
cana-5406	110	62	ℎ	ℎ	PROPN
cana-5406	110	63	−	−	PROPN
cana-5406	110	64	𝛽)𝜋	𝛽)𝜋	X
cana-5406	110	65	2	2	NUM
cana-5406	110	66	)	)	PUNCT
cana-5406	110	67	(	(	PUNCT
cana-5406	110	68	ℎ	ℎ	X
cana-5406	110	69	−	−	PROPN
cana-5406	110	70	𝛽	𝛽	NOUN
cana-5406	110	71	)	)	PUNCT
cana-5406	110	72	!	!	PUNCT
cana-5406	110	73	)	)	PUNCT
cana-5406	111	1	(	(	PUNCT
cana-5406	111	2	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
cana-5406	111	3	(	(	PUNCT
cana-5406	111	4	𝑠𝜋	𝑠𝜋	NOUN
cana-5406	111	5	2	2	NUM
cana-5406	111	6	)	)	PUNCT
cana-5406	111	7	𝑠	𝑠	NOUN
cana-5406	111	8	!	!	PUNCT
cana-5406	111	9	)	)	PUNCT
cana-5406	112	1	𝑈(𝑘	𝑈(𝑘	X
cana-5406	112	2	,	,	PUNCT
cana-5406	112	3	𝛽	𝛽	NOUN
cana-5406	112	4	−	−	NOUN
cana-5406	112	5	𝑠	𝑠	INTJ
cana-5406	112	6	−	−	PROPN
cana-5406	112	7	1	1	NUM
cana-5406	112	8	)	)	PUNCT
cana-5406	112	9	𝛽−1	𝛽−1	PROPN
cana-5406	112	10	𝑠=0	𝑠=0	PUNCT
cana-5406	112	11	ℎ	ℎ	PART
cana-5406	112	12	𝛽=1	𝛽=1	PROPN
cana-5406	112	13	+	+	NOUN
cana-5406	112	14	∑∑	∑∑	NOUN
cana-5406	112	15	(	(	PUNCT
cana-5406	112	16	1	1	NUM
cana-5406	112	17	𝛽	𝛽	NOUN
cana-5406	112	18	)	)	PUNCT
cana-5406	112	19	(	(	PUNCT
cana-5406	112	20	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
cana-5406	112	21	(	(	PUNCT
cana-5406	112	22	(	(	PUNCT
cana-5406	112	23	ℎ	ℎ	PROPN
cana-5406	112	24	−	−	PROPN
cana-5406	112	25	𝛽)𝜋	𝛽)𝜋	X
cana-5406	112	26	2	2	NUM
cana-5406	112	27	)	)	PUNCT
cana-5406	112	28	(	(	PUNCT
cana-5406	112	29	ℎ	ℎ	X
cana-5406	112	30	−	−	PROPN
cana-5406	112	31	𝛽	𝛽	NOUN
cana-5406	112	32	)	)	PUNCT
cana-5406	112	33	!	!	PUNCT
cana-5406	112	34	)	)	PUNCT
cana-5406	113	1	(	(	PUNCT
cana-5406	113	2	𝑠𝑖𝑛	𝑠𝑖𝑛	X
cana-5406	113	3	(	(	PUNCT
cana-5406	113	4	𝑠𝜋	𝑠𝜋	NOUN
cana-5406	113	5	2	2	NUM
cana-5406	113	6	)	)	PUNCT
cana-5406	113	7	𝑠	𝑠	NOUN
cana-5406	113	8	!	!	PUNCT
cana-5406	113	9	)	)	PUNCT
cana-5406	113	10	𝑈(𝑘	𝑈(𝑘	X
cana-5406	113	11	,	,	PUNCT
cana-5406	113	12	𝛽	𝛽	NOUN
cana-5406	113	13	−	−	NOUN
cana-5406	113	14	𝑠	𝑠	INTJ
cana-5406	113	15	−	−	PROPN
cana-5406	113	16	1	1	NUM
cana-5406	113	17	)	)	PUNCT
cana-5406	113	18	𝛽−1	𝛽−1	PROPN
cana-5406	113	19	𝑠=0	𝑠=0	PUNCT
cana-5406	113	20	ℎ	ℎ	PROPN
cana-5406	113	21	𝛽=0	𝛽=0	PROPN
cana-5406	113	22	}	}	PUNCT
cana-5406	113	23	∵	∵	NOUN
cana-5406	113	24	using	use	VERB
cana-5406	113	25	trigonometric	trigonometric	ADJ
cana-5406	113	26	identity	identity	NOUN
cana-5406	113	27	,	,	PUNCT
cana-5406	113	28	𝑠𝑖𝑛𝐴.	𝑠𝑖𝑛𝐴.	PUNCT
cana-5406	113	29	𝑐𝑜𝑠𝐵	𝑐𝑜𝑠𝐵	ADV
cana-5406	113	30	−	−	ADP
cana-5406	113	31	𝑐𝑜𝑠𝐴.	𝑐𝑜𝑠𝐴.	PROPN
cana-5406	114	1	𝑠𝑖𝑛𝐵	𝑠𝑖𝑛𝐵	NOUN
cana-5406	114	2	=	=	X
cana-5406	114	3	sin	sin	NOUN
cana-5406	114	4	(	(	PUNCT
cana-5406	114	5	𝐴	𝐴	PROPN
cana-5406	114	6	−	−	PROPN
cana-5406	114	7	𝐵	𝐵	PROPN
cana-5406	114	8	)	)	PUNCT
cana-5406	114	9	we	we	PRON
cana-5406	114	10	get	get	VERB
cana-5406	114	11	,	,	PUNCT
cana-5406	114	12	𝑈(𝑘	𝑈(𝑘	SYM
cana-5406	114	13	,	,	PUNCT
cana-5406	114	14	ℎ	ℎ	X
cana-5406	114	15	+	+	NOUN
cana-5406	114	16	2	2	NUM
cana-5406	114	17	)	)	PUNCT
cana-5406	114	18	=	=	SYM
cana-5406	114	19	1	1	NUM
cana-5406	114	20	(	(	PUNCT
cana-5406	114	21	ℎ	ℎ	X
cana-5406	114	22	+	+	NOUN
cana-5406	114	23	1)(ℎ	1)(ℎ	NUM
cana-5406	114	24	+	+	CCONJ
cana-5406	114	25	2	2	NUM
cana-5406	114	26	)	)	PUNCT
cana-5406	114	27	{	{	PUNCT
cana-5406	114	28	∑𝛿(𝛼	∑𝛿(𝛼	ADV
cana-5406	115	1	−	−	PROPN
cana-5406	115	2	1)(𝑘	1)(𝑘	NUM
cana-5406	115	3	−	−	PROPN
cana-5406	115	4	𝛼	𝛼	PRON
cana-5406	115	5	+	+	NOUN
cana-5406	115	6	1)𝑈(𝑘	1)𝑈(𝑘	NUM
cana-5406	115	7	−	−	NOUN
cana-5406	115	8	𝛼	𝛼	PRON
cana-5406	115	9	+	+	NOUN
cana-5406	115	10	1	1	NUM
cana-5406	115	11	,	,	PUNCT
cana-5406	115	12	ℎ	ℎ	PROPN
cana-5406	115	13	)	)	PUNCT
cana-5406	115	14	−	−	ADP
cana-5406	116	1	𝑘	𝑘	DET
cana-5406	116	2	𝛼=0	𝛼=0	PROPN
cana-5406	116	3	𝛿(𝑘	𝛿(𝑘	PROPN
cana-5406	116	4	−	−	ADP
cana-5406	116	5	1	1	X
cana-5406	116	6	)	)	PUNCT
cana-5406	116	7	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
cana-5406	116	8	(	(	PUNCT
cana-5406	116	9	ℎ𝜋	ℎ𝜋	PROPN
cana-5406	116	10	2	2	NUM
cana-5406	116	11	)	)	PUNCT
cana-5406	116	12	ℎ	ℎ	PROPN
cana-5406	116	13	!	!	PUNCT
cana-5406	117	1	−∑∑	−∑∑	PROPN
cana-5406	117	2	(	(	PUNCT
cana-5406	117	3	1	1	NUM
cana-5406	117	4	𝛽	𝛽	NOUN
cana-5406	117	5	)	)	PUNCT
cana-5406	117	6	(	(	PUNCT
cana-5406	117	7	𝑠𝑖𝑛	𝑠𝑖𝑛	X
cana-5406	117	8	(	(	PUNCT
cana-5406	117	9	(	(	PUNCT
cana-5406	117	10	ℎ	ℎ	PROPN
cana-5406	117	11	−	−	PROPN
cana-5406	117	12	𝛽	𝛽	NOUN
cana-5406	117	13	−	−	PROPN
cana-5406	117	14	𝑠)𝜋	𝑠)𝜋	NOUN
cana-5406	117	15	2	2	X
cana-5406	117	16	)	)	PUNCT
cana-5406	117	17	(	(	PUNCT
cana-5406	117	18	ℎ	ℎ	X
cana-5406	117	19	−	−	PROPN
cana-5406	117	20	𝛽	𝛽	NOUN
cana-5406	117	21	)	)	PUNCT
cana-5406	117	22	!	!	PUNCT
cana-5406	118	1	𝑠	𝑠	X
cana-5406	118	2	!	!	PUNCT
cana-5406	118	3	)	)	PUNCT
cana-5406	119	1	𝑈(𝑘	𝑈(𝑘	X
cana-5406	119	2	,	,	PUNCT
cana-5406	119	3	𝛽	𝛽	NOUN
cana-5406	119	4	−	−	NOUN
cana-5406	119	5	𝑠	𝑠	INTJ
cana-5406	119	6	−	−	PROPN
cana-5406	119	7	1	1	NUM
cana-5406	119	8	)	)	PUNCT
cana-5406	119	9	𝛽−1	𝛽−1	PROPN
cana-5406	119	10	𝑠=0	𝑠=0	PUNCT
cana-5406	119	11	ℎ	ℎ	PART
cana-5406	119	12	𝛽=1	𝛽=1	PROPN
cana-5406	119	13	}	}	PUNCT
cana-5406	119	14	(	(	PUNCT
cana-5406	119	15	15	15	NUM
cana-5406	119	16	)	)	PUNCT
cana-5406	119	17	now	now	ADV
cana-5406	119	18	applying	apply	VERB
cana-5406	119	19	two	two	NUM
cana-5406	119	20	-	-	PUNCT
cana-5406	119	21	dimensional	dimensional	ADJ
cana-5406	119	22	dtm	dtm	NOUN
cana-5406	119	23	on	on	ADP
cana-5406	119	24	initial	initial	ADJ
cana-5406	119	25	conditions	condition	NOUN
cana-5406	119	26	(	(	PUNCT
cana-5406	119	27	13	13	NUM
cana-5406	119	28	)	)	PUNCT
cana-5406	119	29	and	and	CCONJ
cana-5406	119	30	boundary	boundary	ADJ
cana-5406	119	31	conditions	condition	NOUN
cana-5406	119	32	(	(	PUNCT
cana-5406	119	33	14	14	NUM
cana-5406	119	34	)	)	PUNCT
cana-5406	119	35	we	we	PRON
cana-5406	119	36	get	get	VERB
cana-5406	119	37	,	,	PUNCT
cana-5406	119	38	𝑈(𝑘	𝑈(𝑘	SYM
cana-5406	119	39	,	,	PUNCT
cana-5406	119	40	0	0	NUM
cana-5406	119	41	)	)	PUNCT
cana-5406	119	42	=	=	SYM
cana-5406	119	43	0	0	NUM
cana-5406	119	44	;	;	PUNCT
cana-5406	119	45	∀𝑘	∀𝑘	NOUN
cana-5406	119	46	,	,	PUNCT
cana-5406	119	47	(	(	PUNCT
cana-5406	119	48	16	16	X
cana-5406	119	49	)	)	PUNCT
cana-5406	119	50	∴	∴	PROPN
cana-5406	119	51	𝑈(0,0	𝑈(0,0	NOUN
cana-5406	119	52	)	)	PUNCT
cana-5406	119	53	=	=	SYM
cana-5406	119	54	𝑈(1,0	𝑈(1,0	X
cana-5406	119	55	)	)	PUNCT
cana-5406	119	56	=	=	SYM
cana-5406	119	57	𝑈(2,0	𝑈(2,0	PROPN
cana-5406	119	58	)	)	PUNCT
cana-5406	119	59	=	=	SYM
cana-5406	119	60	𝑈(3,0	𝑈(3,0	NUM
cana-5406	119	61	)	)	PUNCT
cana-5406	119	62	=	=	SYM
cana-5406	119	63	⋯	⋯	PROPN
cana-5406	119	64	.	.	PUNCT
cana-5406	120	1	.=	.=	VERB
cana-5406	120	2	0	0	NUM
cana-5406	121	1	𝑈(𝑘	𝑈(𝑘	NUM
cana-5406	121	2	,	,	PUNCT
cana-5406	121	3	1	1	NUM
cana-5406	121	4	)	)	PUNCT
cana-5406	121	5	=	=	PUNCT
cana-5406	122	1	𝛿(𝑘	𝛿(𝑘	NOUN
cana-5406	122	2	−	−	NOUN
cana-5406	122	3	1	1	X
cana-5406	122	4	)	)	PUNCT
cana-5406	122	5	=	=	NOUN
cana-5406	122	6	{	{	PUNCT
cana-5406	122	7	1	1	NUM
cana-5406	122	8	;	;	PUNCT
cana-5406	122	9	𝑘	𝑘	X
cana-5406	122	10	=	=	NOUN
cana-5406	122	11	1	1	NUM
cana-5406	122	12	0	0	NUM
cana-5406	122	13	;	;	PUNCT
cana-5406	122	14	𝑘	𝑘	DET
cana-5406	122	15	≠	≠	PROPN
cana-5406	122	16	1	1	NUM
cana-5406	122	17	(	(	PUNCT
cana-5406	122	18	17	17	NUM
cana-5406	122	19	)	)	PUNCT
cana-5406	122	20	∴	∴	NOUN
cana-5406	122	21	𝑈(0,1	𝑈(0,1	NOUN
cana-5406	122	22	)	)	PUNCT
cana-5406	122	23	=	=	SYM
cana-5406	122	24	0	0	NUM
cana-5406	122	25	,	,	PUNCT
cana-5406	122	26	𝑈(1,1	𝑈(1,1	NOUN
cana-5406	122	27	)	)	PUNCT
cana-5406	122	28	=	=	SYM
cana-5406	122	29	1	1	NUM
cana-5406	122	30	,	,	PUNCT
cana-5406	122	31	𝑈(2,1	𝑈(2,1	NUM
cana-5406	122	32	)	)	PUNCT
cana-5406	122	33	=	=	SYM
cana-5406	122	34	𝑈(3,1	𝑈(3,1	ADJ
cana-5406	122	35	)	)	PUNCT
cana-5406	122	36	=	=	SYM
cana-5406	122	37	𝑈(4,1	𝑈(4,1	NOUN
cana-5406	122	38	)	)	PUNCT
cana-5406	122	39	=	=	SYM
cana-5406	122	40	⋯	⋯	PROPN
cana-5406	122	41	.	.	PUNCT
cana-5406	123	1	.0	.0	NUM
cana-5406	123	2	𝑈(1	𝑈(1	X
cana-5406	123	3	,	,	PUNCT
cana-5406	123	4	ℎ	ℎ	ADJ
cana-5406	123	5	)	)	PUNCT
cana-5406	123	6	=	=	PUNCT
cana-5406	124	1	𝛿(ℎ	𝛿(ℎ	ADJ
cana-5406	124	2	−	−	NOUN
cana-5406	124	3	1	1	NUM
cana-5406	124	4	)	)	PUNCT
cana-5406	124	5	=	=	PRON
cana-5406	124	6	{	{	PUNCT
cana-5406	124	7	1	1	NUM
cana-5406	124	8	;	;	PUNCT
cana-5406	124	9	ℎ	ℎ	X
cana-5406	124	10	=	=	SYM
cana-5406	124	11	1	1	NUM
cana-5406	124	12	0	0	NUM
cana-5406	124	13	;	;	PUNCT
cana-5406	124	14	ℎ	ℎ	PROPN
cana-5406	124	15	≠	≠	PROPN
cana-5406	124	16	1	1	NUM
cana-5406	124	17	(	(	PUNCT
cana-5406	124	18	18	18	NUM
cana-5406	124	19	)	)	PUNCT
cana-5406	124	20	∴	∴	NOUN
cana-5406	124	21	𝑈(1,0	𝑈(1,0	PROPN
cana-5406	124	22	)	)	PUNCT
cana-5406	124	23	=	=	SYM
cana-5406	124	24	0	0	NUM
cana-5406	124	25	,	,	PUNCT
cana-5406	124	26	𝑈(1,1	𝑈(1,1	NOUN
cana-5406	124	27	)	)	PUNCT
cana-5406	124	28	=	=	SYM
cana-5406	124	29	1	1	NUM
cana-5406	124	30	,	,	PUNCT
cana-5406	124	31	𝑈(1,2	𝑈(1,2	ADJ
cana-5406	124	32	)	)	PUNCT
cana-5406	124	33	=	=	SYM
cana-5406	124	34	𝑈(1,3	𝑈(1,3	PROPN
cana-5406	124	35	)	)	PUNCT
cana-5406	124	36	=	=	PUNCT
cana-5406	124	37	𝑈(1,4	𝑈(1,4	ADV
cana-5406	124	38	)	)	PUNCT
cana-5406	124	39	=	=	SYM
cana-5406	124	40	⋯	⋯	PROPN
cana-5406	124	41	.	.	PUNCT
cana-5406	125	1	.0	.0	NUM
cana-5406	125	2	put	put	VERB
cana-5406	125	3	ℎ	ℎ	NOUN
cana-5406	125	4	=	=	NOUN
cana-5406	125	5	0,1,2,3,4	0,1,2,3,4	NUM
cana-5406	125	6	,	,	PUNCT
cana-5406	125	7	…	…	PUNCT
cana-5406	125	8	.	.	PUNCT
cana-5406	126	1	in	in	ADP
cana-5406	126	2	equation	equation	NOUN
cana-5406	126	3	(	(	PUNCT
cana-5406	126	4	15	15	NUM
cana-5406	126	5	)	)	PUNCT
cana-5406	126	6	and	and	CCONJ
cana-5406	126	7	using	use	VERB
cana-5406	126	8	equations	equation	NOUN
cana-5406	126	9	(	(	PUNCT
cana-5406	126	10	16	16	NUM
cana-5406	126	11	)	)	PUNCT
cana-5406	126	12	to	to	ADP
cana-5406	126	13	(	(	PUNCT
cana-5406	126	14	18	18	NUM
cana-5406	126	15	)	)	PUNCT
cana-5406	126	16	,	,	PUNCT
cana-5406	126	17	if	if	SCONJ
cana-5406	126	18	ℎ	ℎ	PROPN
cana-5406	126	19	=	=	SYM
cana-5406	126	20	0	0	NUM
cana-5406	126	21	,	,	PUNCT
cana-5406	126	22	𝑈(𝑘	𝑈(𝑘	X
cana-5406	126	23	,	,	PUNCT
cana-5406	126	24	2	2	NUM
cana-5406	126	25	)	)	PUNCT
cana-5406	126	26	=	=	SYM
cana-5406	126	27	1	1	NUM
cana-5406	126	28	2	2	NUM
cana-5406	126	29	{	{	PUNCT
cana-5406	126	30	∑𝛿(𝛼	∑𝛿(𝛼	ADP
cana-5406	126	31	−	−	PROPN
cana-5406	126	32	1)(𝑘	1)(𝑘	NUM
cana-5406	126	33	−	−	NOUN
cana-5406	126	34	𝛼	𝛼	NOUN
cana-5406	126	35	+	+	NOUN
cana-5406	126	36	1	1	NUM
cana-5406	126	37	)	)	PUNCT
cana-5406	126	38	𝑈(𝑘	𝑈(𝑘	X
cana-5406	126	39	−	−	NOUN
cana-5406	126	40	𝛼	𝛼	NOUN
cana-5406	126	41	+	+	NOUN
cana-5406	126	42	1	1	NUM
cana-5406	126	43	,	,	PUNCT
cana-5406	126	44	0	0	NUM
cana-5406	126	45	)	)	PUNCT
cana-5406	126	46	𝑘	𝑘	PRON
cana-5406	126	47	𝛼=0	𝛼=0	PROPN
cana-5406	126	48	−	−	PROPN
cana-5406	126	49	𝛿(𝑘	𝛿(𝑘	PROPN
cana-5406	126	50	−	−	PROPN
cana-5406	126	51	1	1	X
cana-5406	126	52	)	)	PUNCT
cana-5406	126	53	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
cana-5406	126	54	0	0	NUM
cana-5406	126	55	ℎ	ℎ	PROPN
cana-5406	126	56	!	!	PUNCT
cana-5406	127	1	−	−	NOUN
cana-5406	127	2	0	0	NUM
cana-5406	127	3	}	}	PUNCT
cana-5406	127	4	communications	communication	NOUN
cana-5406	127	5	on	on	ADP
cana-5406	127	6	applied	apply	VERB
cana-5406	127	7	nonlinear	nonlinear	ADJ
cana-5406	127	8	analysis	analysis	NOUN
cana-5406	127	9	issn	issn	NOUN
cana-5406	127	10	:	:	PUNCT
cana-5406	127	11	1074	1074	NUM
cana-5406	127	12	-	-	PUNCT
cana-5406	127	13	133x	133x	NUM
cana-5406	127	14	vol	vol	VERB
cana-5406	127	15	32	32	NUM
cana-5406	127	16	no	no	NOUN
cana-5406	127	17	.	.	PUNCT
cana-5406	128	1	10s	10	NOUN
cana-5406	128	2	(	(	PUNCT
cana-5406	128	3	2025	2025	NUM
cana-5406	128	4	)	)	PUNCT
cana-5406	128	5	2168	2168	NUM
cana-5406	128	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5406	128	7	∴	∴	PROPN
cana-5406	128	8	𝑈(𝑘	𝑈(𝑘	SYM
cana-5406	128	9	,	,	PUNCT
cana-5406	128	10	2	2	NUM
cana-5406	128	11	)	)	PUNCT
cana-5406	128	12	=	=	SYM
cana-5406	128	13	1	1	NUM
cana-5406	128	14	2	2	NUM
cana-5406	128	15	{	{	PUNCT
cana-5406	128	16	∑	∑	PUNCT
cana-5406	128	17	𝛿(𝛼	𝛿(𝛼	PROPN
cana-5406	128	18	−	−	PROPN
cana-5406	128	19	1)(𝑘	1)(𝑘	NUM
cana-5406	128	20	−	−	NOUN
cana-5406	128	21	𝛼	𝛼	NOUN
cana-5406	128	22	+	+	NOUN
cana-5406	128	23	1	1	NUM
cana-5406	128	24	)	)	PUNCT
cana-5406	128	25	𝑈(𝑘	𝑈(𝑘	X
cana-5406	128	26	−	−	NOUN
cana-5406	128	27	𝛼	𝛼	PRON
cana-5406	128	28	+	+	NOUN
cana-5406	128	29	1,0	1,0	NUM
cana-5406	128	30	)	)	PUNCT
cana-5406	128	31	−	−	NOUN
cana-5406	128	32	0	0	NUM
cana-5406	129	1	−	−	NOUN
cana-5406	129	2	0	0	NUM
cana-5406	130	1	𝑘	𝑘	DET
cana-5406	130	2	𝛼=0	𝛼=0	PROPN
cana-5406	130	3	}	}	PUNCT
cana-5406	130	4	as	as	ADP
cana-5406	130	5	𝑈(𝑘	𝑈(𝑘	X
cana-5406	130	6	,	,	PUNCT
cana-5406	130	7	0	0	NUM
cana-5406	130	8	)	)	PUNCT
cana-5406	130	9	=	=	SYM
cana-5406	130	10	0	0	NUM
cana-5406	130	11	;	;	PUNCT
cana-5406	130	12	∀𝑘	∀𝑘	NOUN
cana-5406	130	13	,	,	PUNCT
cana-5406	130	14	∴	∴	NOUN
cana-5406	130	15	𝑈(𝑘	𝑈(𝑘	PUNCT
cana-5406	130	16	−	−	NOUN
cana-5406	130	17	𝛼	𝛼	NOUN
cana-5406	130	18	+	+	NOUN
cana-5406	130	19	1	1	NUM
cana-5406	130	20	,	,	PUNCT
cana-5406	130	21	0	0	NUM
cana-5406	130	22	)	)	PUNCT
cana-5406	130	23	=	=	SYM
cana-5406	130	24	0	0	NUM
cana-5406	131	1	∴	∴	NOUN
cana-5406	131	2	𝑈(𝑘	𝑈(𝑘	PROPN
cana-5406	131	3	,	,	PUNCT
cana-5406	131	4	2	2	NUM
cana-5406	131	5	)	)	PUNCT
cana-5406	131	6	=	=	SYM
cana-5406	131	7	0	0	NUM
cana-5406	131	8	,	,	PUNCT
cana-5406	131	9	∀𝑘	∀𝑘	X
cana-5406	131	10	⟹𝑈(0,2	⟹𝑈(0,2	PROPN
cana-5406	131	11	)	)	PUNCT
cana-5406	131	12	=	=	SYM
cana-5406	131	13	0	0	NUM
cana-5406	131	14	,	,	PUNCT
cana-5406	131	15	𝑈(1,2	𝑈(1,2	ADJ
cana-5406	131	16	)	)	PUNCT
cana-5406	131	17	=	=	SYM
cana-5406	131	18	0	0	NUM
cana-5406	131	19	,	,	PUNCT
cana-5406	131	20	𝑈(2,2	𝑈(2,2	NOUN
cana-5406	131	21	)	)	PUNCT
cana-5406	131	22	=	=	SYM
cana-5406	131	23	0	0	NUM
cana-5406	131	24	,	,	PUNCT
cana-5406	131	25	𝑈(3,2	𝑈(3,2	NOUN
cana-5406	131	26	)	)	PUNCT
cana-5406	131	27	=	=	SYM
cana-5406	131	28	0	0	NUM
cana-5406	131	29	,	,	PUNCT
cana-5406	131	30	𝑈(4,2	𝑈(4,2	PROPN
cana-5406	131	31	)	)	PUNCT
cana-5406	131	32	=	=	SYM
cana-5406	131	33	0	0	NUM
cana-5406	131	34	,	,	PUNCT
cana-5406	131	35	…	…	PUNCT
cana-5406	131	36	..	..	PUNCT
cana-5406	131	37	(	(	PUNCT
cana-5406	131	38	19	19	NUM
cana-5406	131	39	)	)	PUNCT
cana-5406	131	40	if	if	SCONJ
cana-5406	131	41	ℎ	ℎ	PROPN
cana-5406	131	42	=	=	SYM
cana-5406	131	43	1	1	NUM
cana-5406	131	44	,	,	PUNCT
cana-5406	131	45	𝑈(𝑘	𝑈(𝑘	SYM
cana-5406	131	46	,	,	PUNCT
cana-5406	131	47	3	3	NUM
cana-5406	131	48	)	)	PUNCT
cana-5406	131	49	=	=	SYM
cana-5406	131	50	1	1	NUM
cana-5406	131	51	6	6	NUM
cana-5406	131	52	{	{	PUNCT
cana-5406	131	53	∑𝛿(𝛼	∑𝛿(𝛼	PROPN
cana-5406	131	54	−	−	PROPN
cana-5406	131	55	1)(𝑘	1)(𝑘	NUM
cana-5406	131	56	−	−	NOUN
cana-5406	131	57	𝛼	𝛼	NOUN
cana-5406	131	58	+	+	NOUN
cana-5406	131	59	1	1	NUM
cana-5406	131	60	)	)	PUNCT
cana-5406	131	61	𝑈(𝑘	𝑈(𝑘	X
cana-5406	131	62	−	−	NOUN
cana-5406	131	63	𝛼	𝛼	PRON
cana-5406	131	64	+	+	NOUN
cana-5406	131	65	1	1	NUM
cana-5406	131	66	,	,	PUNCT
cana-5406	131	67	1	1	NUM
cana-5406	131	68	)	)	PUNCT
cana-5406	131	69	𝑘	𝑘	DET
cana-5406	131	70	𝛼=0	𝛼=0	PROPN
cana-5406	131	71	−	−	PROPN
cana-5406	131	72	𝛿(𝑘	𝛿(𝑘	PROPN
cana-5406	131	73	−	−	ADP
cana-5406	131	74	1	1	X
cana-5406	131	75	)	)	PUNCT
cana-5406	131	76	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
cana-5406	131	77	(	(	PUNCT
cana-5406	131	78	𝜋	𝜋	NOUN
cana-5406	131	79	2	2	NUM
cana-5406	131	80	)	)	PUNCT
cana-5406	131	81	1	1	NUM
cana-5406	131	82	!	!	PUNCT
cana-5406	132	1	−∑∑	−∑∑	PROPN
cana-5406	132	2	(	(	PUNCT
cana-5406	132	3	1	1	NUM
cana-5406	132	4	𝛽	𝛽	NOUN
cana-5406	132	5	)	)	PUNCT
cana-5406	132	6	(	(	PUNCT
cana-5406	132	7	𝑠𝑖𝑛	𝑠𝑖𝑛	X
cana-5406	132	8	(	(	PUNCT
cana-5406	132	9	(	(	PUNCT
cana-5406	132	10	1	1	NUM
cana-5406	132	11	−	−	PROPN
cana-5406	132	12	𝛽	𝛽	NOUN
cana-5406	132	13	−	−	PROPN
cana-5406	132	14	𝑠	𝑠	NOUN
cana-5406	132	15	)	)	PUNCT
cana-5406	132	16	𝜋	𝜋	PRON
cana-5406	132	17	2	2	NUM
cana-5406	132	18	)	)	PUNCT
cana-5406	132	19	(	(	PUNCT
cana-5406	132	20	1	1	NUM
cana-5406	132	21	−	−	PROPN
cana-5406	132	22	𝛽	𝛽	NOUN
cana-5406	132	23	)	)	PUNCT
cana-5406	132	24	!	!	PUNCT
cana-5406	133	1	𝑠	𝑠	X
cana-5406	133	2	!	!	PUNCT
cana-5406	133	3	)	)	PUNCT
cana-5406	134	1	𝑈(𝑘	𝑈(𝑘	X
cana-5406	134	2	,	,	PUNCT
cana-5406	134	3	𝛽	𝛽	NOUN
cana-5406	134	4	−	−	NOUN
cana-5406	134	5	𝑠	𝑠	INTJ
cana-5406	134	6	−	−	PROPN
cana-5406	134	7	1	1	NUM
cana-5406	134	8	)	)	PUNCT
cana-5406	134	9	𝛽−1	𝛽−1	PROPN
cana-5406	134	10	𝑠=0	𝑠=0	SYM
cana-5406	134	11	1	1	NUM
cana-5406	134	12	𝛽=1	𝛽=1	PROPN
cana-5406	134	13	}	}	PUNCT
cana-5406	134	14	if	if	SCONJ
cana-5406	134	15	𝑘	𝑘	X
cana-5406	134	16	=	=	SYM
cana-5406	134	17	0	0	NUM
cana-5406	134	18	∴	∴	PROPN
cana-5406	134	19	𝑈(0,3	𝑈(0,3	PROPN
cana-5406	134	20	)	)	PUNCT
cana-5406	134	21	=	=	SYM
cana-5406	135	1	1	1	NUM
cana-5406	135	2	6	6	NUM
cana-5406	135	3	{	{	PUNCT
cana-5406	135	4	0	0	NUM
cana-5406	135	5	−	−	NOUN
cana-5406	135	6	0	0	NUM
cana-5406	136	1	−	−	NOUN
cana-5406	136	2	0	0	NUM
cana-5406	136	3	}	}	PUNCT
cana-5406	136	4	=	=	SYM
cana-5406	136	5	0	0	PUNCT
cana-5406	137	1	if	if	SCONJ
cana-5406	137	2	𝑘	𝑘	X
cana-5406	137	3	=	=	SYM
cana-5406	137	4	1	1	NUM
cana-5406	137	5	∴	∴	PROPN
cana-5406	137	6	𝑈(1,3	𝑈(1,3	PROPN
cana-5406	137	7	)	)	PUNCT
cana-5406	138	1	=	=	SYM
cana-5406	138	2	1	1	NUM
cana-5406	138	3	6	6	NUM
cana-5406	138	4	{	{	PUNCT
cana-5406	138	5	∑	∑	PUNCT
cana-5406	138	6	𝛿(𝛼	𝛿(𝛼	PROPN
cana-5406	138	7	−	−	PROPN
cana-5406	138	8	1)(2	1)(2	NUM
cana-5406	138	9	−	−	NOUN
cana-5406	138	10	𝛼	𝛼	NOUN
cana-5406	138	11	)	)	PUNCT
cana-5406	138	12	𝑈(2	𝑈(2	NUM
cana-5406	138	13	−	−	PROPN
cana-5406	138	14	𝛼	𝛼	NOUN
cana-5406	138	15	,	,	PUNCT
cana-5406	138	16	1	1	NUM
cana-5406	138	17	)	)	PUNCT
cana-5406	138	18	−	−	PROPN
cana-5406	139	1	𝛿(1	𝛿(1	PROPN
cana-5406	139	2	−	−	PROPN
cana-5406	139	3	1	1	NUM
cana-5406	139	4	)	)	PUNCT
cana-5406	139	5	1	1	NUM
cana-5406	139	6	𝛼=0	𝛼=0	PROPN
cana-5406	139	7	}	}	PUNCT
cana-5406	139	8	=	=	SYM
cana-5406	140	1	1	1	NUM
cana-5406	140	2	6	6	NUM
cana-5406	140	3	{	{	PUNCT
cana-5406	140	4	0	0	NUM
cana-5406	140	5	+	+	CCONJ
cana-5406	140	6	(	(	PUNCT
cana-5406	140	7	1)(1	1)(1	NUM
cana-5406	140	8	)	)	PUNCT
cana-5406	140	9	𝑈(1,1	𝑈(1,1	NOUN
cana-5406	140	10	)	)	PUNCT
cana-5406	141	1	−	−	ADP
cana-5406	141	2	1	1	NUM
cana-5406	141	3	}	}	PUNCT
cana-5406	141	4	=	=	SYM
cana-5406	141	5	0	0	NUM
cana-5406	141	6	∵	∵	ADJ
cana-5406	141	7	𝑈(1,1	𝑈(1,1	NOUN
cana-5406	141	8	)	)	PUNCT
cana-5406	141	9	=	=	SYM
cana-5406	142	1	1	1	NUM
cana-5406	142	2	if	if	SCONJ
cana-5406	142	3	𝑘	𝑘	X
cana-5406	142	4	=	=	SYM
cana-5406	142	5	2	2	NUM
cana-5406	142	6	∴	∴	NOUN
cana-5406	142	7	𝑈(2,3	𝑈(2,3	NOUN
cana-5406	142	8	)	)	PUNCT
cana-5406	142	9	=	=	SYM
cana-5406	142	10	1	1	NUM
cana-5406	142	11	6	6	NUM
cana-5406	142	12	{	{	PUNCT
cana-5406	142	13	∑	∑	PUNCT
cana-5406	142	14	𝛿(𝛼	𝛿(𝛼	PROPN
cana-5406	142	15	−	−	PROPN
cana-5406	142	16	1)(3	1)(3	NUM
cana-5406	142	17	−	−	ADP
cana-5406	142	18	𝛼	𝛼	NOUN
cana-5406	142	19	)	)	PUNCT
cana-5406	142	20	𝑈(3	𝑈(3	NOUN
cana-5406	142	21	−	−	PROPN
cana-5406	142	22	𝛼	𝛼	NOUN
cana-5406	142	23	,	,	PUNCT
cana-5406	142	24	1	1	NUM
cana-5406	142	25	)	)	PUNCT
cana-5406	142	26	−	−	PROPN
cana-5406	143	1	𝛿(2	𝛿(2	NOUN
cana-5406	143	2	−	−	PROPN
cana-5406	143	3	1	1	NUM
cana-5406	143	4	)	)	PUNCT
cana-5406	143	5	2	2	NUM
cana-5406	143	6	𝛼=0	𝛼=0	PROPN
cana-5406	143	7	}	}	PUNCT
cana-5406	143	8	=	=	SYM
cana-5406	143	9	1	1	NUM
cana-5406	143	10	6	6	NUM
cana-5406	143	11	{	{	PUNCT
cana-5406	143	12	0	0	NUM
cana-5406	143	13	+	+	CCONJ
cana-5406	143	14	(	(	PUNCT
cana-5406	143	15	1)(2	1)(2	NUM
cana-5406	143	16	)	)	PUNCT
cana-5406	143	17	𝑈(2,1	𝑈(2,1	NUM
cana-5406	143	18	)	)	PUNCT
cana-5406	144	1	+	+	CCONJ
cana-5406	144	2	0	0	NUM
cana-5406	145	1	−	−	NOUN
cana-5406	145	2	0	0	NUM
cana-5406	145	3	}	}	PUNCT
cana-5406	145	4	=	=	SYM
cana-5406	145	5	0	0	NUM
cana-5406	145	6	∵	∵	NOUN
cana-5406	145	7	𝑈(2,1	𝑈(2,1	NUM
cana-5406	145	8	)	)	PUNCT
cana-5406	145	9	=	=	SYM
cana-5406	145	10	0	0	NUM
cana-5406	146	1	∴	∴	NOUN
cana-5406	146	2	𝑈(𝑘	𝑈(𝑘	PROPN
cana-5406	146	3	,	,	PUNCT
cana-5406	146	4	3	3	NUM
cana-5406	146	5	)	)	PUNCT
cana-5406	146	6	=	=	SYM
cana-5406	146	7	0	0	NUM
cana-5406	146	8	,	,	PUNCT
cana-5406	146	9	∀𝑘	∀𝑘	PUNCT
cana-5406	146	10	⟹𝑈(0,3	⟹𝑈(0,3	NUM
cana-5406	146	11	)	)	PUNCT
cana-5406	146	12	=	=	SYM
cana-5406	146	13	0	0	NUM
cana-5406	146	14	,	,	PUNCT
cana-5406	146	15	𝑈(1,3	𝑈(1,3	PROPN
cana-5406	146	16	)	)	PUNCT
cana-5406	146	17	=	=	SYM
cana-5406	146	18	0	0	NUM
cana-5406	146	19	,	,	PUNCT
cana-5406	146	20	𝑈(2,3	𝑈(2,3	ADJ
cana-5406	146	21	)	)	PUNCT
cana-5406	146	22	=	=	SYM
cana-5406	146	23	0	0	NUM
cana-5406	146	24	,	,	PUNCT
cana-5406	146	25	𝑈(3,3	𝑈(3,3	PROPN
cana-5406	146	26	)	)	PUNCT
cana-5406	146	27	=	=	SYM
cana-5406	146	28	0	0	NUM
cana-5406	146	29	,	,	PUNCT
cana-5406	146	30	𝑈(4,3	𝑈(4,3	NOUN
cana-5406	146	31	)	)	PUNCT
cana-5406	146	32	=	=	SYM
cana-5406	146	33	0	0	NUM
cana-5406	146	34	,	,	PUNCT
cana-5406	146	35	…	…	PUNCT
cana-5406	146	36	.	.	PUNCT
cana-5406	146	37	.	.	PUNCT
cana-5406	147	1	(	(	PUNCT
cana-5406	147	2	20	20	NUM
cana-5406	147	3	)	)	PUNCT
cana-5406	147	4	if	if	SCONJ
cana-5406	147	5	ℎ	ℎ	PROPN
cana-5406	147	6	=	=	SYM
cana-5406	147	7	2	2	NUM
cana-5406	147	8	,	,	PUNCT
cana-5406	147	9	𝑈(𝑘	𝑈(𝑘	X
cana-5406	147	10	,	,	PUNCT
cana-5406	147	11	4	4	NUM
cana-5406	147	12	)	)	PUNCT
cana-5406	147	13	=	=	SYM
cana-5406	147	14	1	1	NUM
cana-5406	147	15	12	12	NUM
cana-5406	147	16	{	{	PUNCT
cana-5406	147	17	∑	∑	PUNCT
cana-5406	147	18	𝛿(𝛼	𝛿(𝛼	PROPN
cana-5406	147	19	−	−	PROPN
cana-5406	147	20	1)(𝑘	1)(𝑘	NUM
cana-5406	147	21	−	−	PROPN
cana-5406	147	22	𝛼	𝛼	PRON
cana-5406	147	23	+	+	NOUN
cana-5406	147	24	1)𝑈(𝑘	1)𝑈(𝑘	NUM
cana-5406	147	25	−	−	NOUN
cana-5406	147	26	𝛼	𝛼	PRON
cana-5406	147	27	+	+	NOUN
cana-5406	147	28	1,2	1,2	NUM
cana-5406	147	29	)	)	PUNCT
cana-5406	147	30	𝑘	𝑘	DET
cana-5406	147	31	𝛼=0	𝛼=0	PROPN
cana-5406	147	32	−	−	PROPN
cana-5406	147	33	𝛿(𝑘	𝛿(𝑘	PROPN
cana-5406	147	34	−	−	PROPN
cana-5406	147	35	1	1	NUM
cana-5406	147	36	)	)	PUNCT
cana-5406	147	37	𝑠𝑖𝑛(𝜋	𝑠𝑖𝑛(𝜋	NOUN
cana-5406	147	38	)	)	PUNCT
cana-5406	147	39	2	2	NUM
cana-5406	147	40	!	!	PUNCT
cana-5406	148	1	−	−	NOUN
cana-5406	148	2	∑∑	∑∑	NOUN
cana-5406	148	3	(	(	PUNCT
cana-5406	148	4	1	1	NUM
cana-5406	148	5	𝛽	𝛽	NOUN
cana-5406	148	6	)	)	PUNCT
cana-5406	148	7	(	(	PUNCT
cana-5406	148	8	𝑠𝑖𝑛	𝑠𝑖𝑛	X
cana-5406	148	9	(	(	PUNCT
cana-5406	148	10	(	(	PUNCT
cana-5406	148	11	2	2	NUM
cana-5406	148	12	−	−	NOUN
cana-5406	148	13	𝛽	𝛽	NOUN
cana-5406	148	14	−	−	PROPN
cana-5406	148	15	𝑠)𝜋	𝑠)𝜋	NOUN
cana-5406	148	16	2	2	X
cana-5406	148	17	)	)	PUNCT
cana-5406	148	18	(	(	PUNCT
cana-5406	148	19	2	2	NUM
cana-5406	148	20	−	−	PROPN
cana-5406	148	21	𝛽	𝛽	NOUN
cana-5406	148	22	)	)	PUNCT
cana-5406	148	23	!	!	PUNCT
cana-5406	149	1	𝑠	𝑠	X
cana-5406	149	2	!	!	PUNCT
cana-5406	149	3	)	)	PUNCT
cana-5406	150	1	𝑈(𝑘	𝑈(𝑘	X
cana-5406	150	2	,	,	PUNCT
cana-5406	150	3	𝛽	𝛽	NOUN
cana-5406	150	4	−	−	NOUN
cana-5406	150	5	𝑠	𝑠	INTJ
cana-5406	150	6	−	−	PROPN
cana-5406	150	7	1	1	NUM
cana-5406	150	8	)	)	PUNCT
cana-5406	150	9	𝛽−1	𝛽−1	PROPN
cana-5406	150	10	𝑠=0	𝑠=0	SYM
cana-5406	150	11	2	2	NUM
cana-5406	150	12	𝛽=1	𝛽=1	NOUN
cana-5406	150	13	}	}	PUNCT
cana-5406	150	14	communications	communication	NOUN
cana-5406	150	15	on	on	ADP
cana-5406	150	16	applied	apply	VERB
cana-5406	150	17	nonlinear	nonlinear	ADJ
cana-5406	150	18	analysis	analysis	NOUN
cana-5406	150	19	issn	issn	NOUN
cana-5406	150	20	:	:	PUNCT
cana-5406	150	21	1074	1074	NUM
cana-5406	150	22	-	-	PUNCT
cana-5406	150	23	133x	133x	NUM
cana-5406	150	24	vol	vol	VERB
cana-5406	150	25	32	32	NUM
cana-5406	150	26	no	no	NOUN
cana-5406	150	27	.	.	PUNCT
cana-5406	151	1	10s	10	NOUN
cana-5406	151	2	(	(	PUNCT
cana-5406	151	3	2025	2025	NUM
cana-5406	151	4	)	)	PUNCT
cana-5406	151	5	2169	2169	NUM
cana-5406	151	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5406	151	7	∴	∴	PROPN
cana-5406	151	8	𝑈(𝑘	𝑈(𝑘	PROPN
cana-5406	151	9	,	,	PUNCT
cana-5406	151	10	4	4	NUM
cana-5406	151	11	)	)	PUNCT
cana-5406	151	12	=	=	SYM
cana-5406	151	13	1	1	NUM
cana-5406	151	14	12	12	NUM
cana-5406	151	15	{	{	PUNCT
cana-5406	151	16	∑𝛿(𝛼	∑𝛿(𝛼	PROPN
cana-5406	151	17	−	−	PROPN
cana-5406	152	1	1)(𝑘	1)(𝑘	NUM
cana-5406	152	2	−	−	PROPN
cana-5406	152	3	𝛼	𝛼	PRON
cana-5406	152	4	+	+	NOUN
cana-5406	152	5	1)𝑈(𝑘	1)𝑈(𝑘	NUM
cana-5406	152	6	−	−	NOUN
cana-5406	152	7	𝛼	𝛼	PRON
cana-5406	152	8	+	+	NOUN
cana-5406	152	9	1,2	1,2	NUM
cana-5406	152	10	)	)	PUNCT
cana-5406	153	1	+	+	CCONJ
cana-5406	153	2	𝛿(𝑘	𝛿(𝑘	PROPN
cana-5406	153	3	−	−	PROPN
cana-5406	153	4	1)𝑠𝑖𝑛𝜋	1)𝑠𝑖𝑛𝜋	NUM
cana-5406	153	5	2	2	NUM
cana-5406	153	6	𝑘	𝑘	DET
cana-5406	153	7	𝛼=0	𝛼=0	PROPN
cana-5406	153	8	−∑	−∑	PROPN
cana-5406	153	9	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
cana-5406	153	10	(	(	PUNCT
cana-5406	153	11	(	(	PUNCT
cana-5406	153	12	1	1	NUM
cana-5406	153	13	−	−	NOUN
cana-5406	153	14	𝑠)𝜋	𝑠)𝜋	NOUN
cana-5406	153	15	2	2	NUM
cana-5406	153	16	)	)	PUNCT
cana-5406	153	17	1	1	NUM
cana-5406	153	18	!	!	PUNCT
cana-5406	153	19	𝑠	𝑠	X
cana-5406	153	20	!	!	PUNCT
cana-5406	153	21	𝑈(𝑘,−𝑠	𝑈(𝑘,−𝑠	NUM
cana-5406	153	22	)	)	PUNCT
cana-5406	153	23	0	0	NUM
cana-5406	154	1	𝑠=0	𝑠=0	PROPN
cana-5406	154	2	−∑	−∑	PROPN
cana-5406	154	3	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
cana-5406	154	4	(	(	PUNCT
cana-5406	154	5	−𝑠𝜋	−𝑠𝜋	NOUN
cana-5406	154	6	2	2	NUM
cana-5406	154	7	)	)	PUNCT
cana-5406	154	8	0	0	NUM
cana-5406	154	9	!	!	PUNCT
cana-5406	155	1	𝑠	𝑠	X
cana-5406	155	2	!	!	PROPN
cana-5406	155	3	1	1	NUM
cana-5406	155	4	𝑠=0	𝑠=0	SYM
cana-5406	155	5	𝑈(𝑘	𝑈(𝑘	X
cana-5406	155	6	,	,	PUNCT
cana-5406	155	7	1	1	NUM
cana-5406	155	8	−	−	PROPN
cana-5406	155	9	𝑠	𝑠	NOUN
cana-5406	155	10	)	)	PUNCT
cana-5406	155	11	}	}	PUNCT
cana-5406	155	12	∴	∴	PROPN
cana-5406	155	13	𝑈(𝑘	𝑈(𝑘	PROPN
cana-5406	155	14	,	,	PUNCT
cana-5406	155	15	4	4	NUM
cana-5406	155	16	)	)	PUNCT
cana-5406	155	17	=	=	SYM
cana-5406	155	18	1	1	NUM
cana-5406	155	19	12	12	NUM
cana-5406	155	20	{	{	PUNCT
cana-5406	155	21	0	0	NUM
cana-5406	156	1	+	+	CCONJ
cana-5406	156	2	0	0	NUM
cana-5406	156	3	−	−	NOUN
cana-5406	156	4	𝑈(𝑘	𝑈(𝑘	NOUN
cana-5406	156	5	,	,	PUNCT
cana-5406	156	6	0	0	NUM
cana-5406	156	7	)	)	PUNCT
cana-5406	156	8	−	−	NOUN
cana-5406	156	9	0	0	NUM
cana-5406	157	1	+	+	CCONJ
cana-5406	157	2	𝑈(𝑘	𝑈(𝑘	NOUN
cana-5406	157	3	,	,	PUNCT
cana-5406	157	4	0	0	NUM
cana-5406	157	5	)	)	PUNCT
cana-5406	157	6	}	}	PUNCT
cana-5406	157	7	∴	∴	NOUN
cana-5406	157	8	𝑈(𝑘	𝑈(𝑘	PROPN
cana-5406	157	9	,	,	PUNCT
cana-5406	157	10	4	4	NUM
cana-5406	157	11	)	)	PUNCT
cana-5406	157	12	=	=	SYM
cana-5406	157	13	0	0	NUM
cana-5406	157	14	,	,	PUNCT
cana-5406	157	15	∀𝑘	∀𝑘	X
cana-5406	157	16	∵	∵	NOUN
cana-5406	157	17	𝑈(𝑘	𝑈(𝑘	NOUN
cana-5406	157	18	,	,	PUNCT
cana-5406	157	19	0	0	NUM
cana-5406	157	20	)	)	PUNCT
cana-5406	157	21	=	=	SYM
cana-5406	157	22	0	0	NUM
cana-5406	157	23	⟹𝑈(0,4	⟹𝑈(0,4	NOUN
cana-5406	157	24	)	)	PUNCT
cana-5406	157	25	=	=	SYM
cana-5406	157	26	0,𝑈(1,4	0,𝑈(1,4	NUM
cana-5406	157	27	)	)	PUNCT
cana-5406	157	28	=	=	SYM
cana-5406	157	29	0,𝑈(2,4	0,𝑈(2,4	NUM
cana-5406	157	30	)	)	PUNCT
cana-5406	157	31	=	=	SYM
cana-5406	158	1	0	0	NUM
cana-5406	158	2	,	,	PUNCT
cana-5406	158	3	𝑈(3,4	𝑈(3,4	ADJ
cana-5406	158	4	)	)	PUNCT
cana-5406	158	5	=	=	SYM
cana-5406	158	6	0,𝑈(4,4	0,𝑈(4,4	X
cana-5406	158	7	)	)	PUNCT
cana-5406	158	8	=	=	SYM
cana-5406	158	9	0	0	NUM
cana-5406	158	10	(	(	PUNCT
cana-5406	158	11	21	21	NUM
cana-5406	158	12	)	)	PUNCT
cana-5406	158	13	similarly	similarly	ADV
cana-5406	158	14	,	,	PUNCT
cana-5406	158	15	we	we	PRON
cana-5406	158	16	get	get	VERB
cana-5406	158	17	,	,	PUNCT
cana-5406	158	18	𝑈(𝑘	𝑈(𝑘	SYM
cana-5406	158	19	,	,	PUNCT
cana-5406	158	20	4	4	NUM
cana-5406	158	21	)	)	PUNCT
cana-5406	158	22	=	=	SYM
cana-5406	159	1	𝑈(𝑘	𝑈(𝑘	X
cana-5406	159	2	,	,	PUNCT
cana-5406	159	3	5	5	NUM
cana-5406	159	4	)	)	PUNCT
cana-5406	159	5	=	=	SYM
cana-5406	159	6	0	0	NUM
cana-5406	159	7	𝑈(𝑘	𝑈(𝑘	NOUN
cana-5406	159	8	,	,	PUNCT
cana-5406	159	9	6	6	NUM
cana-5406	159	10	)	)	PUNCT
cana-5406	159	11	=	=	SYM
cana-5406	159	12	𝑈(𝑘	𝑈(𝑘	X
cana-5406	159	13	,	,	PUNCT
cana-5406	159	14	7	7	NUM
cana-5406	159	15	)	)	PUNCT
cana-5406	159	16	=	=	SYM
cana-5406	159	17	⋯	⋯	PROPN
cana-5406	159	18	.	.	PUNCT
cana-5406	160	1	.=	.=	PROPN
cana-5406	160	2	0	0	NUM
cana-5406	160	3	,	,	PUNCT
cana-5406	160	4	∀𝑘	∀𝑘	NOUN
cana-5406	160	5	we	we	PRON
cana-5406	160	6	know	know	VERB
cana-5406	160	7	that	that	SCONJ
cana-5406	160	8	,	,	PUNCT
cana-5406	160	9	𝑢(𝑥	𝑢(𝑥	PROPN
cana-5406	160	10	,	,	PUNCT
cana-5406	160	11	𝑡	𝑡	NOUN
cana-5406	160	12	)	)	PUNCT
cana-5406	160	13	=	=	SYM
cana-5406	160	14	∑∑𝑈(𝑘	∑∑𝑈(𝑘	NOUN
cana-5406	160	15	,	,	PUNCT
cana-5406	160	16	ℎ)𝑥𝑘𝑡ℎ	ℎ)𝑥𝑘𝑡ℎ	VERB
cana-5406	160	17	∞	∞	NUM
cana-5406	160	18	ℎ=0	ℎ=0	NOUN
cana-5406	160	19	∞	∞	NUM
cana-5406	160	20	𝑘=0	𝑘=0	PROPN
cana-5406	160	21	=	=	PUNCT
cana-5406	160	22	{	{	PUNCT
cana-5406	160	23	𝑈(0,0	𝑈(0,0	NOUN
cana-5406	160	24	)	)	PUNCT
cana-5406	160	25	+	+	NUM
cana-5406	160	26	𝑈(1,0)𝑥	𝑈(1,0)𝑥	NOUN
cana-5406	160	27	+	+	CCONJ
cana-5406	160	28	𝑈(2,0)𝑥2	𝑈(2,0)𝑥2	PROPN
cana-5406	161	1	+	+	CCONJ
cana-5406	161	2	𝑈(3,0)𝑥3	𝑈(3,0)𝑥3	PROPN
cana-5406	162	1	+	+	NOUN
cana-5406	162	2	⋯	⋯	PROPN
cana-5406	162	3	.	.	PUNCT
cana-5406	162	4	}	}	PUNCT
cana-5406	163	1	+	+	CCONJ
cana-5406	163	2	{	{	PUNCT
cana-5406	163	3	𝑈(0,1)𝑡	𝑈(0,1)𝑡	NOUN
cana-5406	163	4	+	+	SYM
cana-5406	163	5	𝑈(1,1)𝑥𝑡	𝑈(1,1)𝑥𝑡	NOUN
cana-5406	163	6	+	+	CCONJ
cana-5406	163	7	𝑈(2,1)𝑥2𝑡	𝑈(2,1)𝑥2𝑡	PROPN
cana-5406	163	8	+	+	X
cana-5406	163	9	⋯	⋯	NOUN
cana-5406	163	10	.	.	PUNCT
cana-5406	163	11	}	}	PUNCT
cana-5406	164	1	+	+	CCONJ
cana-5406	164	2	{	{	PUNCT
cana-5406	164	3	𝑈(0,2)𝑡2	𝑈(0,2)𝑡2	PART
cana-5406	164	4	+	+	CCONJ
cana-5406	164	5	𝑈(1,2)𝑥𝑡2	𝑈(1,2)𝑥𝑡2	X
cana-5406	164	6	+	+	CCONJ
cana-5406	164	7	𝑈(2,2)𝑥2𝑡2	𝑈(2,2)𝑥2𝑡2	NOUN
cana-5406	164	8	+	+	NOUN
cana-5406	164	9	⋯	⋯	NOUN
cana-5406	164	10	}	}	PUNCT
cana-5406	164	11	+	+	CCONJ
cana-5406	164	12	⋯.	⋯.	PROPN
cana-5406	164	13	∴	∴	PROPN
cana-5406	164	14	𝒖(𝒙	𝒖(𝒙	PROPN
cana-5406	164	15	,	,	PUNCT
cana-5406	164	16	𝒕	𝒕	X
cana-5406	164	17	)	)	PUNCT
cana-5406	164	18	=	=	SYM
cana-5406	164	19	𝒙𝒕	𝒙𝒕	PROPN
cana-5406	164	20	(	(	PUNCT
cana-5406	164	21	fig	fig	NOUN
cana-5406	164	22	.	.	PUNCT
cana-5406	165	1	1.3	1.3	NUM
cana-5406	165	2	:	:	PUNCT
cana-5406	165	3	graph	graph	NOUN
cana-5406	165	4	of	of	ADP
cana-5406	165	5	𝒖(𝒙	𝒖(𝒙	NOUN
cana-5406	165	6	,	,	PUNCT
cana-5406	165	7	𝒕	𝒕	X
cana-5406	165	8	)	)	PUNCT
cana-5406	165	9	=	=	SYM
cana-5406	165	10	𝒙𝒕	𝒙𝒕	PROPN
cana-5406	165	11	for	for	ADP
cana-5406	165	12	−𝟐𝟎	−𝟐𝟎	VERB
cana-5406	165	13	≤	≤	NUM
cana-5406	165	14	𝒖	𝒖	X
cana-5406	165	15	≤	≤	NOUN
cana-5406	165	16	𝟐𝟎	𝟐𝟎	NUM
cana-5406	165	17	;	;	PUNCT
cana-5406	165	18	−𝟓	−𝟓	SYM
cana-5406	165	19	≤	≤	NUM
cana-5406	166	1	𝒙	𝒙	PROPN
cana-5406	166	2	≤	≤	NUM
cana-5406	166	3	𝟓	𝟓	NUM
cana-5406	166	4	;	;	PUNCT
cana-5406	166	5	𝟎	𝟎	NUM
cana-5406	166	6	≤	≤	NUM
cana-5406	166	7	𝒕	𝒕	PRON
cana-5406	166	8	≤	≤	NUM
cana-5406	166	9	𝟒	𝟒	NUM
cana-5406	166	10	)	)	PUNCT
cana-5406	166	11	-5	-5	NOUN
cana-5406	166	12	0	0	NUM
cana-5406	166	13	5	5	NUM
cana-5406	166	14	0	0	NUM
cana-5406	166	15	1	1	NUM
cana-5406	166	16	2	2	NUM
cana-5406	166	17	3	3	NUM
cana-5406	166	18	4	4	NUM
cana-5406	166	19	5	5	NUM
cana-5406	166	20	-20	-20	NUM
cana-5406	166	21	-10	-10	PUNCT
cana-5406	166	22	0	0	NUM
cana-5406	166	23	10	10	NUM
cana-5406	166	24	20	20	NUM
cana-5406	166	25	x	x	SYM
cana-5406	166	26	t	t	NOUN
cana-5406	166	27	u	u	PROPN
cana-5406	166	28	(	(	PUNCT
cana-5406	166	29	x	x	PROPN
cana-5406	166	30	,	,	PUNCT
cana-5406	166	31	t	t	PROPN
cana-5406	166	32	)	)	PUNCT
cana-5406	166	33	-20	-20	PUNCT
cana-5406	166	34	-10	-10	PUNCT
cana-5406	166	35	0	0	NUM
cana-5406	166	36	10	10	NUM
cana-5406	166	37	20	20	NUM
cana-5406	166	38	communications	communication	NOUN
cana-5406	166	39	on	on	ADP
cana-5406	166	40	applied	apply	VERB
cana-5406	166	41	nonlinear	nonlinear	ADJ
cana-5406	166	42	analysis	analysis	NOUN
cana-5406	166	43	issn	issn	NOUN
cana-5406	166	44	:	:	PUNCT
cana-5406	166	45	1074	1074	NUM
cana-5406	166	46	-	-	PUNCT
cana-5406	166	47	133x	133x	NUM
cana-5406	166	48	vol	vol	VERB
cana-5406	166	49	32	32	NUM
cana-5406	166	50	no	no	NOUN
cana-5406	166	51	.	.	PUNCT
cana-5406	167	1	10s	10	NOUN
cana-5406	167	2	(	(	PUNCT
cana-5406	167	3	2025	2025	NUM
cana-5406	167	4	)	)	PUNCT
cana-5406	167	5	2170	2170	NUM
cana-5406	167	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5406	167	7	4	4	X
cana-5406	167	8	.	.	PUNCT
cana-5406	167	9	conclusion	conclusion	NOUN
cana-5406	167	10	in	in	ADP
cana-5406	167	11	this	this	DET
cana-5406	167	12	paper	paper	NOUN
cana-5406	167	13	,	,	PUNCT
cana-5406	167	14	we	we	PRON
cana-5406	167	15	proposed	propose	VERB
cana-5406	167	16	the	the	DET
cana-5406	167	17	differential	differential	ADJ
cana-5406	167	18	transformation	transformation	NOUN
cana-5406	167	19	method	method	NOUN
cana-5406	167	20	(	(	PUNCT
cana-5406	167	21	dtm	dtm	PROPN
cana-5406	167	22	)	)	PUNCT
cana-5406	167	23	has	have	AUX
cana-5406	167	24	been	be	AUX
cana-5406	167	25	successfully	successfully	ADV
cana-5406	167	26	applied	apply	VERB
cana-5406	167	27	to	to	PART
cana-5406	167	28	find	find	VERB
cana-5406	167	29	exact	exact	ADJ
cana-5406	167	30	and	and	CCONJ
cana-5406	167	31	approximate	approximate	ADJ
cana-5406	167	32	solution	solution	NOUN
cana-5406	167	33	of	of	ADP
cana-5406	167	34	the	the	DET
cana-5406	167	35	second	second	ADJ
cana-5406	167	36	order	order	NOUN
cana-5406	167	37	differential	differential	NOUN
cana-5406	167	38	equations	equation	NOUN
cana-5406	167	39	.	.	PUNCT
cana-5406	168	1	the	the	DET
cana-5406	168	2	method	method	NOUN
cana-5406	168	3	was	be	AUX
cana-5406	168	4	used	use	VERB
cana-5406	168	5	in	in	ADP
cana-5406	168	6	a	a	DET
cana-5406	168	7	direct	direct	ADJ
cana-5406	168	8	way	way	NOUN
cana-5406	168	9	without	without	ADP
cana-5406	168	10	using	use	VERB
cana-5406	168	11	linearization	linearization	NOUN
cana-5406	168	12	,	,	PUNCT
cana-5406	168	13	perturbation	perturbation	NOUN
cana-5406	168	14	or	or	CCONJ
cana-5406	168	15	restrictive	restrictive	ADJ
cana-5406	168	16	assumptions	assumption	NOUN
cana-5406	168	17	.	.	PUNCT
cana-5406	169	1	while	while	SCONJ
cana-5406	169	2	,	,	PUNCT
cana-5406	169	3	this	this	DET
cana-5406	169	4	equation	equation	NOUN
cana-5406	169	5	solving	solve	VERB
cana-5406	169	6	partial	partial	ADJ
cana-5406	169	7	differential	differential	ADJ
cana-5406	169	8	equations	equation	NOUN
cana-5406	169	9	in	in	ADP
cana-5406	169	10	two	two	NUM
cana-5406	169	11	,	,	PUNCT
cana-5406	169	12	three	three	NUM
cana-5406	169	13	-	-	PUNCT
cana-5406	169	14	dimensional	dimensional	ADJ
cana-5406	169	15	linear	linear	NOUN
cana-5406	169	16	and	and	CCONJ
cana-5406	169	17	nonlinear	nonlinear	ADJ
cana-5406	169	18	,	,	PUNCT
cana-5406	169	19	have	have	AUX
cana-5406	169	20	been	be	AUX
cana-5406	169	21	solved	solve	VERB
cana-5406	169	22	effectively	effectively	ADV
cana-5406	169	23	using	use	VERB
cana-5406	169	24	the	the	DET
cana-5406	169	25	differential	differential	ADJ
cana-5406	169	26	transform	transform	NOUN
cana-5406	169	27	method	method	NOUN
cana-5406	169	28	.	.	PUNCT
cana-5406	170	1	therefore	therefore	ADV
cana-5406	170	2	,	,	PUNCT
cana-5406	170	3	it	it	PRON
cana-5406	170	4	is	be	AUX
cana-5406	170	5	not	not	PART
cana-5406	170	6	affected	affect	VERB
cana-5406	170	7	by	by	ADP
cana-5406	170	8	computation	computation	NOUN
cana-5406	170	9	round	round	NOUN
cana-5406	170	10	off	off	ADP
cana-5406	170	11	errors	error	NOUN
cana-5406	170	12	and	and	CCONJ
cana-5406	170	13	one	one	NOUN
cana-5406	170	14	is	be	AUX
cana-5406	170	15	not	not	PART
cana-5406	170	16	faced	face	VERB
cana-5406	170	17	with	with	ADP
cana-5406	170	18	the	the	DET
cana-5406	170	19	necessities	necessity	NOUN
cana-5406	170	20	of	of	ADP
cana-5406	170	21	large	large	ADJ
cana-5406	170	22	computer	computer	NOUN
cana-5406	170	23	memory	memory	NOUN
cana-5406	170	24	and	and	CCONJ
cana-5406	170	25	time	time	NOUN
cana-5406	170	26	.	.	PUNCT
cana-5406	171	1	moreover	moreover	ADV
cana-5406	171	2	,	,	PUNCT
cana-5406	171	3	this	this	DET
cana-5406	171	4	method	method	NOUN
cana-5406	171	5	provides	provide	VERB
cana-5406	171	6	a	a	DET
cana-5406	171	7	closed	closed	ADJ
cana-5406	171	8	-	-	PUNCT
cana-5406	171	9	series	series	NOUN
cana-5406	171	10	form	form	NOUN
cana-5406	171	11	solutions	solution	NOUN
cana-5406	171	12	with	with	ADP
cana-5406	171	13	the	the	DET
cana-5406	171	14	convergence	convergence	NOUN
cana-5406	171	15	region	region	NOUN
cana-5406	171	16	a	a	DET
cana-5406	171	17	specific	specific	ADJ
cana-5406	171	18	advantage	advantage	NOUN
cana-5406	171	19	of	of	ADP
cana-5406	171	20	this	this	DET
cana-5406	171	21	method	method	NOUN
cana-5406	171	22	is	be	AUX
cana-5406	171	23	provided	provide	VERB
cana-5406	171	24	to	to	PART
cana-5406	171	25	exact	exact	VERB
cana-5406	171	26	and	and	CCONJ
cana-5406	171	27	accurate	accurate	ADJ
cana-5406	171	28	solutions	solution	NOUN
cana-5406	171	29	up	up	ADP
cana-5406	171	30	to	to	ADP
cana-5406	171	31	the	the	DET
cana-5406	171	32	3rd	3rd	ADJ
cana-5406	171	33	dimensional	dimensional	ADJ
cana-5406	171	34	dtm	dtm	NOUN
cana-5406	171	35	over	over	ADP
cana-5406	171	36	any	any	DET
cana-5406	171	37	purely	purely	ADV
cana-5406	171	38	numerical	numerical	ADJ
cana-5406	171	39	method	method	NOUN
cana-5406	171	40	.	.	PUNCT
cana-5406	172	1	it	it	PRON
cana-5406	172	2	may	may	AUX
cana-5406	172	3	be	be	AUX
cana-5406	172	4	concluded	conclude	VERB
cana-5406	172	5	that	that	SCONJ
cana-5406	172	6	dtm	dtm	PROPN
cana-5406	172	7	is	be	AUX
cana-5406	172	8	very	very	ADV
cana-5406	172	9	powerful	powerful	ADJ
cana-5406	172	10	and	and	CCONJ
cana-5406	172	11	efficient	efficient	ADJ
cana-5406	172	12	in	in	ADP
cana-5406	172	13	finding	find	VERB
cana-5406	172	14	analytical	analytical	ADJ
cana-5406	172	15	as	as	ADV
cana-5406	172	16	well	well	ADV
cana-5406	172	17	as	as	ADP
cana-5406	172	18	numerical	numerical	ADJ
cana-5406	172	19	solutions	solution	NOUN
cana-5406	172	20	for	for	ADP
cana-5406	172	21	wide	wide	ADJ
cana-5406	172	22	classes	class	NOUN
cana-5406	172	23	of	of	ADP
cana-5406	172	24	differential	differential	ADJ
cana-5406	172	25	equations	equation	NOUN
cana-5406	172	26	.	.	PUNCT
cana-5406	173	1	references	reference	NOUN
cana-5406	173	2	[	[	X
cana-5406	173	3	1	1	NUM
cana-5406	173	4	]	]	X
cana-5406	173	5	zhou	zhou	PROPN
cana-5406	173	6	jk	jk	PROPN
cana-5406	173	7	.	.	PROPN
cana-5406	173	8	differential	differential	ADJ
cana-5406	173	9	transformation	transformation	NOUN
cana-5406	173	10	and	and	CCONJ
cana-5406	173	11	its	its	PRON
cana-5406	173	12	applications	application	NOUN
cana-5406	173	13	for	for	ADP
cana-5406	173	14	electrical	electrical	ADJ
cana-5406	173	15	circuits	circuit	NOUN
cana-5406	173	16	.	.	PUNCT
cana-5406	174	1	huazhong	huazhong	PROPN
cana-5406	174	2	university	university	PROPN
cana-5406	174	3	press	press	NOUN
cana-5406	174	4	,	,	PUNCT
cana-5406	174	5	wuhan	wuhan	PROPN
cana-5406	174	6	china	china	PROPN
cana-5406	174	7	(	(	PUNCT
cana-5406	174	8	in	in	ADP
cana-5406	174	9	chinese	chinese	ADJ
cana-5406	174	10	)	)	PUNCT
cana-5406	174	11	google	google	PROPN
cana-5406	174	12	schola	schola	PROPN
cana-5406	174	13	.	.	PUNCT
cana-5406	174	14	1986	1986	NUM
cana-5406	174	15	;	;	PUNCT
cana-5406	174	16	2:413	2:413	NUM
cana-5406	174	17	-	-	SYM
cana-5406	174	18	20	20	NUM
cana-5406	174	19	.	.	PUNCT
cana-5406	175	1	[	[	X
cana-5406	175	2	2	2	NUM
cana-5406	175	3	]	]	PUNCT
cana-5406	175	4	zou	zou	PROPN
cana-5406	175	5	l	l	PROPN
cana-5406	175	6	,	,	PUNCT
cana-5406	175	7	wang	wang	PROPN
cana-5406	175	8	z	z	PROPN
cana-5406	175	9	,	,	PUNCT
cana-5406	175	10	zong	zong	PROPN
cana-5406	175	11	z.	z.	PROPN
cana-5406	175	12	generalized	generalize	VERB
cana-5406	175	13	differential	differential	ADJ
cana-5406	175	14	transform	transform	NOUN
cana-5406	175	15	method	method	NOUN
cana-5406	175	16	to	to	ADP
cana-5406	175	17	differential	differential	ADJ
cana-5406	175	18	-	-	PUNCT
cana-5406	175	19	difference	difference	NOUN
cana-5406	175	20	equation	equation	NOUN
cana-5406	175	21	.	.	PUNCT
cana-5406	176	1	physics	physics	NOUN
cana-5406	176	2	letters	letter	NOUN
cana-5406	176	3	a.	a.	PROPN
cana-5406	176	4	2009	2009	NUM
cana-5406	176	5	nov	nov	PROPN
cana-5406	176	6	2;373(45):4142	2;373(45):4142	PROPN
cana-5406	176	7	-	-	PROPN
cana-5406	176	8	51	51	NUM
cana-5406	176	9	.	.	PUNCT
cana-5406	177	1	[	[	X
cana-5406	177	2	3	3	X
cana-5406	177	3	]	]	X
cana-5406	177	4	barton	barton	PROPN
cana-5406	177	5	d.	d.	PROPN
cana-5406	177	6	taylor	taylor	PROPN
cana-5406	177	7	series	series	PROPN
cana-5406	177	8	methods	method	NOUN
cana-5406	177	9	for	for	ADP
cana-5406	177	10	ordinary	ordinary	ADJ
cana-5406	177	11	differential	differential	ADJ
cana-5406	177	12	equations	equation	NOUN
cana-5406	177	13	:	:	PUNCT
cana-5406	177	14	an	an	DET
cana-5406	177	15	evaluation	evaluation	NOUN
cana-5406	177	16	.	.	PUNCT
cana-5406	178	1	mathematical	mathematical	ADJ
cana-5406	178	2	software	software	NOUN
cana-5406	178	3	.	.	PUNCT
cana-5406	179	1	1971:369	1971:369	NUM
cana-5406	179	2	-	-	SYM
cana-5406	179	3	90	90	NUM
cana-5406	179	4	.	.	PUNCT
cana-5406	180	1	[	[	X
cana-5406	180	2	4	4	X
cana-5406	180	3	]	]	X
cana-5406	180	4	denef	denef	PROPN
cana-5406	180	5	j	j	PROPN
cana-5406	180	6	,	,	PUNCT
cana-5406	180	7	lipshitz	lipshitz	PROPN
cana-5406	180	8	l.	l.	PROPN
cana-5406	180	9	power	power	PROPN
cana-5406	180	10	series	series	PROPN
cana-5406	180	11	solutions	solution	NOUN
cana-5406	180	12	of	of	ADP
cana-5406	180	13	algebraic	algebraic	PROPN
cana-5406	180	14	differential	differential	NOUN
cana-5406	180	15	equations	equation	NOUN
cana-5406	180	16	.	.	PUNCT
cana-5406	181	1	mathematische	mathematische	PROPN
cana-5406	181	2	annalen	annalen	PROPN
cana-5406	181	3	.	.	PUNCT
cana-5406	182	1	1984	1984	NUM
cana-5406	182	2	jun	jun	PROPN
cana-5406	182	3	;	;	PUNCT
cana-5406	182	4	267:213	267:213	NOUN
cana-5406	182	5	-	-	SYM
cana-5406	182	6	38	38	NUM
cana-5406	182	7	.	.	PUNCT
cana-5406	183	1	[	[	X
cana-5406	183	2	5	5	NUM
cana-5406	183	3	]	]	X
cana-5406	183	4	kanth	kanth	PROPN
cana-5406	183	5	ar	ar	PROPN
cana-5406	183	6	,	,	PUNCT
cana-5406	183	7	aruna	aruna	PROPN
cana-5406	183	8	k.	k.	PROPN
cana-5406	183	9	differential	differential	PROPN
cana-5406	183	10	transform	transform	VERB
cana-5406	183	11	method	method	NOUN
cana-5406	183	12	for	for	ADP
cana-5406	183	13	solving	solve	VERB
cana-5406	183	14	linear	linear	ADJ
cana-5406	183	15	and	and	CCONJ
cana-5406	183	16	non	non	ADJ
cana-5406	183	17	-	-	ADJ
cana-5406	183	18	linear	linear	ADJ
cana-5406	183	19	systems	system	NOUN
cana-5406	183	20	of	of	ADP
cana-5406	183	21	partial	partial	ADJ
cana-5406	183	22	differential	differential	ADJ
cana-5406	183	23	equations	equation	NOUN
cana-5406	183	24	.	.	PUNCT
cana-5406	184	1	physics	physics	NOUN
cana-5406	184	2	letters	letter	NOUN
cana-5406	184	3	a.	a.	PROPN
cana-5406	184	4	2008	2008	NUM
cana-5406	184	5	nov	nov	NOUN
cana-5406	184	6	17;372(46):6896	17;372(46):6896	PROPN
cana-5406	184	7	-	-	PUNCT
cana-5406	184	8	8	8	NUM
cana-5406	184	9	.	.	PUNCT
cana-5406	185	1	[	[	X
cana-5406	185	2	6	6	NUM
cana-5406	185	3	]	]	X
cana-5406	185	4	patil	patil	PROPN
cana-5406	185	5	n	n	CCONJ
cana-5406	185	6	,	,	PUNCT
cana-5406	185	7	khambayat	khambayat	PROPN
cana-5406	185	8	a.	a.	PROPN
cana-5406	185	9	differential	differential	PROPN
cana-5406	185	10	transform	transform	NOUN
cana-5406	185	11	method	method	NOUN
cana-5406	185	12	for	for	ADP
cana-5406	185	13	system	system	NOUN
cana-5406	185	14	of	of	ADP
cana-5406	185	15	linear	linear	PROPN
cana-5406	185	16	differential	differential	ADJ
cana-5406	185	17	equations	equation	NOUN
cana-5406	185	18	.	.	PUNCT
cana-5406	186	1	research	research	NOUN
cana-5406	186	2	journal	journal	PROPN
cana-5406	186	3	of	of	ADP
cana-5406	186	4	mathematical	mathematical	ADJ
cana-5406	186	5	and	and	CCONJ
cana-5406	186	6	statistical	statistical	ADJ
cana-5406	186	7	sciences	science	NOUN
cana-5406	186	8	issn	issn	PROPN
cana-5406	186	9	.	.	PROPN
cana-5406	187	1	2014	2014	NUM
cana-5406	187	2	mar	mar	PROPN
cana-5406	187	3	;	;	PUNCT
cana-5406	187	4	2320:6047	2320:6047	NUM
cana-5406	187	5	.	.	PUNCT
cana-5406	188	1	[	[	X
cana-5406	188	2	7	7	NUM
cana-5406	188	3	]	]	X
cana-5406	188	4	sewell	sewell	NOUN
cana-5406	188	5	g.	g.	PROPN
cana-5406	188	6	the	the	DET
cana-5406	188	7	numerical	numerical	ADJ
cana-5406	188	8	solution	solution	NOUN
cana-5406	188	9	of	of	ADP
cana-5406	188	10	ordinary	ordinary	ADJ
cana-5406	188	11	and	and	CCONJ
cana-5406	188	12	partial	partial	ADJ
cana-5406	188	13	differential	differential	ADJ
cana-5406	188	14	equations	equation	NOUN
cana-5406	188	15	.	.	PUNCT
cana-5406	189	1	john	john	PROPN
cana-5406	189	2	wiley	wiley	PROPN
cana-5406	189	3	&	&	CCONJ
cana-5406	189	4	sons	son	NOUN
cana-5406	189	5	;	;	PUNCT
cana-5406	189	6	2005	2005	NUM
cana-5406	189	7	jul	jul	NOUN
cana-5406	189	8	25	25	NUM
cana-5406	189	9	.	.	PUNCT
cana-5406	190	1	[	[	X
cana-5406	190	2	8	8	NUM
cana-5406	190	3	]	]	X
cana-5406	190	4	chen	chen	PROPN
cana-5406	190	5	co	co	PROPN
cana-5406	190	6	,	,	PUNCT
cana-5406	190	7	ho	ho	PROPN
cana-5406	190	8	sh	sh	PROPN
cana-5406	190	9	.	.	PUNCT
cana-5406	190	10	solving	solve	VERB
cana-5406	190	11	partial	partial	ADJ
cana-5406	190	12	differential	differential	NOUN
cana-5406	190	13	equations	equation	NOUN
cana-5406	190	14	by	by	ADP
cana-5406	190	15	two	two	NUM
cana-5406	190	16	-	-	PUNCT
cana-5406	190	17	dimensional	dimensional	ADJ
cana-5406	190	18	differential	differential	ADJ
cana-5406	190	19	transform	transform	NOUN
cana-5406	190	20	method	method	NOUN
cana-5406	190	21	.	.	PUNCT
cana-5406	191	1	applied	apply	VERB
cana-5406	191	2	mathematics	mathematic	NOUN
cana-5406	191	3	and	and	CCONJ
cana-5406	191	4	computation	computation	NOUN
cana-5406	191	5	.	.	PUNCT
cana-5406	192	1	1999	1999	NUM
cana-5406	192	2	dec	dec	PROPN
cana-5406	192	3	1;106(2	1;106(2	NUM
cana-5406	192	4	-	-	PUNCT
cana-5406	192	5	3):171	3):171	NUM
cana-5406	192	6	-	-	PUNCT
cana-5406	192	7	9	9	NUM
cana-5406	192	8	.	.	PUNCT
cana-5406	193	1	[	[	X
cana-5406	193	2	9	9	NUM
cana-5406	193	3	]	]	X
cana-5406	193	4	ayaz	ayaz	PROPN
cana-5406	193	5	f.	f.	PROPN
cana-5406	193	6	on	on	ADP
cana-5406	193	7	the	the	DET
cana-5406	193	8	two	two	NUM
cana-5406	193	9	-	-	PUNCT
cana-5406	193	10	dimensional	dimensional	ADJ
cana-5406	193	11	differential	differential	ADJ
cana-5406	193	12	transform	transform	NOUN
cana-5406	193	13	method	method	NOUN
cana-5406	193	14	.	.	PUNCT
cana-5406	194	1	applied	apply	VERB
cana-5406	194	2	mathematics	mathematic	NOUN
cana-5406	194	3	and	and	CCONJ
cana-5406	194	4	computation	computation	NOUN
cana-5406	194	5	.	.	PUNCT
cana-5406	195	1	2003	2003	NUM
cana-5406	195	2	nov	nov	NOUN
cana-5406	195	3	10;143(2	10;143(2	NUM
cana-5406	195	4	-	-	PUNCT
cana-5406	195	5	3):361	3):361	NUM
cana-5406	195	6	-	-	SYM
cana-5406	195	7	74	74	NUM
cana-5406	195	8	.	.	PUNCT
cana-5406	196	1	[	[	X
cana-5406	196	2	10	10	NUM
cana-5406	196	3	]	]	X
cana-5406	196	4	richardson	richardson	PROPN
cana-5406	196	5	sm	sm	PROPN
cana-5406	196	6	,	,	PUNCT
cana-5406	196	7	cornish	cornish	PROPN
cana-5406	196	8	ar	ar	PROPN
cana-5406	196	9	.	.	PROPN
cana-5406	196	10	solution	solution	NOUN
cana-5406	196	11	of	of	ADP
cana-5406	196	12	three	three	NUM
cana-5406	196	13	-	-	PUNCT
cana-5406	196	14	dimensional	dimensional	ADJ
cana-5406	196	15	incompressible	incompressible	ADJ
cana-5406	196	16	flow	flow	NOUN
cana-5406	196	17	problems	problem	NOUN
cana-5406	196	18	.	.	PUNCT
cana-5406	197	1	journal	journal	NOUN
cana-5406	197	2	of	of	ADP
cana-5406	197	3	fluid	fluid	ADJ
cana-5406	197	4	mechanics	mechanic	NOUN
cana-5406	197	5	.	.	PUNCT
cana-5406	198	1	1977	1977	NUM
cana-5406	198	2	sep;82(2):309	sep;82(2):309	NOUN
cana-5406	198	3	-	-	PUNCT
cana-5406	198	4	19	19	NUM
cana-5406	198	5	.	.	PUNCT
cana-5406	199	1	[	[	X
cana-5406	199	2	11	11	NUM
cana-5406	199	3	]	]	X
cana-5406	199	4	gregor	gregor	PROPN
cana-5406	199	5	j.	j.	PROPN
cana-5406	199	6	the	the	DET
cana-5406	199	7	multidimensional	multidimensional	ADJ
cana-5406	199	8	$	$	SYM
cana-5406	199	9	z	z	NOUN
cana-5406	199	10	$	$	SYM
cana-5406	199	11	-transform	-transform	NOUN
cana-5406	199	12	and	and	CCONJ
cana-5406	199	13	its	its	PRON
cana-5406	199	14	use	use	NOUN
cana-5406	199	15	in	in	ADP
cana-5406	199	16	solution	solution	NOUN
cana-5406	199	17	of	of	ADP
cana-5406	199	18	partial	partial	ADJ
cana-5406	199	19	difference	difference	NOUN
cana-5406	199	20	equations	equation	NOUN
cana-5406	199	21	.	.	PUNCT
cana-5406	200	1	kybernetika	kybernetika	PROPN
cana-5406	200	2	.	.	PUNCT
cana-5406	201	1	1988;24(7):1	1988;24(7):1	NUM
cana-5406	201	2	-	-	PUNCT
cana-5406	201	3	3	3	NUM
cana-5406	201	4	.	.	PUNCT
cana-5406	202	1	[	[	X
cana-5406	202	2	12	12	NUM
cana-5406	202	3	]	]	X
cana-5406	202	4	eda	eda	PROPN
cana-5406	202	5	yülüklü	yülüklü	NOUN
cana-5406	202	6	,	,	PUNCT
cana-5406	202	7	ahmet	ahmet	PROPN
cana-5406	202	8	and	and	CCONJ
cana-5406	202	9	yasir	yasir	PROPN
cana-5406	202	10	khan	khan	PROPN
cana-5406	202	11	,	,	PUNCT
cana-5406	202	12	“	"	PUNCT
cana-5406	202	13	a	a	DET
cana-5406	202	14	taylor	taylor	PROPN
cana-5406	202	15	series	series	NOUN
cana-5406	202	16	based	base	VERB
cana-5406	202	17	method	method	NOUN
cana-5406	202	18	for	for	ADP
cana-5406	202	19	solving	solve	VERB
cana-5406	202	20	nonlinear	nonlinear	ADJ
cana-5406	202	21	sine	sine	NOUN
cana-5406	202	22	-	-	PUNCT
cana-5406	202	23	gordon	gordon	PROPN
cana-5406	202	24	and	and	CCONJ
cana-5406	202	25	klein	klein	PROPN
cana-5406	202	26	-	-	PUNCT
cana-5406	202	27	gordon	gordon	PROPN
cana-5406	202	28	equations	equation	NOUN
cana-5406	202	29	”	"	PUNCT
cana-5406	202	30	,	,	PUNCT
cana-5406	202	31	world	world	NOUN
cana-5406	202	32	applied	apply	VERB
cana-5406	202	33	sciences	science	NOUN
cana-5406	202	34	journal	journal	NOUN
cana-5406	202	35	,	,	PUNCT
cana-5406	202	36	12	12	NUM
cana-5406	202	37	(	(	PUNCT
cana-5406	202	38	1	1	NUM
cana-5406	202	39	):	):	PUNCT
cana-5406	202	40	21	21	NUM
cana-5406	202	41	-	-	SYM
cana-5406	202	42	27	27	NUM
cana-5406	202	43	,	,	PUNCT
cana-5406	202	44	2011	2011	NUM
cana-5406	202	45	,	,	PUNCT
cana-5406	202	46	issn	issn	PROPN
cana-5406	202	47	1818	1818	NUM
cana-5406	202	48	-	-	SYM
cana-5406	202	49	4952	4952	NUM
cana-5406	202	50	.	.	PUNCT
cana-5406	203	1	[	[	X
cana-5406	203	2	13	13	NUM
cana-5406	203	3	]	]	X
cana-5406	203	4	kangalgil	kangalgil	NOUN
cana-5406	203	5	f	f	PROPN
cana-5406	203	6	,	,	PUNCT
cana-5406	203	7	ayaz	ayaz	PROPN
cana-5406	203	8	f.	f.	PROPN
cana-5406	203	9	solitary	solitary	PROPN
cana-5406	203	10	wave	wave	NOUN
cana-5406	203	11	solutions	solution	NOUN
cana-5406	203	12	for	for	ADP
cana-5406	203	13	the	the	DET
cana-5406	203	14	kdv	kdv	NOUN
cana-5406	203	15	and	and	CCONJ
cana-5406	203	16	mkdv	mkdv	ADJ
cana-5406	203	17	equations	equation	NOUN
cana-5406	203	18	by	by	ADP
cana-5406	203	19	differential	differential	ADJ
cana-5406	203	20	transform	transform	NOUN
cana-5406	203	21	method	method	NOUN
cana-5406	203	22	.	.	PUNCT
cana-5406	204	1	chaos	chaos	NOUN
cana-5406	204	2	,	,	PUNCT
cana-5406	204	3	solitons	soliton	NOUN
cana-5406	204	4	&	&	CCONJ
cana-5406	204	5	fractals	fractal	NOUN
cana-5406	204	6	.	.	PUNCT
cana-5406	205	1	2009	2009	NUM
cana-5406	205	2	jul	jul	PROPN
cana-5406	205	3	15;41(1):464	15;41(1):464	NUM
cana-5406	205	4	-	-	SYM
cana-5406	205	5	72	72	NUM
cana-5406	205	6	.	.	PUNCT
cana-5406	206	1	communications	communication	NOUN
cana-5406	206	2	on	on	ADP
cana-5406	206	3	applied	apply	VERB
cana-5406	206	4	nonlinear	nonlinear	ADJ
cana-5406	206	5	analysis	analysis	NOUN
cana-5406	206	6	issn	issn	NOUN
cana-5406	206	7	:	:	PUNCT
cana-5406	206	8	1074	1074	NUM
cana-5406	206	9	-	-	PUNCT
cana-5406	206	10	133x	133x	NUM
cana-5406	206	11	vol	vol	VERB
cana-5406	206	12	32	32	NUM
cana-5406	206	13	no	no	NOUN
cana-5406	206	14	.	.	PUNCT
cana-5406	207	1	10s	10	NOUN
cana-5406	207	2	(	(	PUNCT
cana-5406	207	3	2025	2025	NUM
cana-5406	207	4	)	)	PUNCT
cana-5406	207	5	2171	2171	NUM
cana-5406	207	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5406	208	1	[	[	X
cana-5406	208	2	14	14	NUM
cana-5406	208	3	]	]	X
cana-5406	208	4	jafari	jafari	PROPN
cana-5406	208	5	h	h	NOUN
cana-5406	208	6	,	,	PUNCT
cana-5406	208	7	sadeghi	sadeghi	PROPN
cana-5406	208	8	s	s	PART
cana-5406	208	9	,	,	PUNCT
cana-5406	208	10	biswas	biswas	PROPN
cana-5406	208	11	a.	a.	PROPN
cana-5406	209	1	the	the	DET
cana-5406	209	2	differential	differential	ADJ
cana-5406	209	3	transform	transform	NOUN
cana-5406	209	4	method	method	NOUN
cana-5406	209	5	for	for	ADP
cana-5406	209	6	solving	solve	VERB
cana-5406	209	7	multidimensional	multidimensional	ADJ
cana-5406	209	8	partial	partial	ADJ
cana-5406	209	9	differential	differential	NOUN
cana-5406	209	10	equations	equation	NOUN
cana-5406	209	11	.	.	PUNCT
cana-5406	210	1	indian	indian	PROPN
cana-5406	210	2	journal	journal	PROPN
cana-5406	210	3	of	of	ADP
cana-5406	210	4	science	science	NOUN
cana-5406	210	5	and	and	CCONJ
cana-5406	210	6	technology	technology	NOUN
cana-5406	210	7	.	.	PUNCT
cana-5406	211	1	2012	2012	NUM
cana-5406	211	2	feb;5(2):200912	feb;5(2):200912	NUM
cana-5406	211	3	.	.	PUNCT
cana-5406	212	1	[	[	X
cana-5406	212	2	15	15	NUM
cana-5406	212	3	]	]	X
cana-5406	212	4	li	li	PROPN
cana-5406	212	5	j	j	PROPN
cana-5406	212	6	,	,	PUNCT
cana-5406	212	7	chen	chen	PROPN
cana-5406	212	8	yt	yt	PROPN
cana-5406	212	9	.	.	PUNCT
cana-5406	212	10	computational	computational	ADJ
cana-5406	212	11	partial	partial	ADJ
cana-5406	212	12	differential	differential	NOUN
cana-5406	212	13	equations	equation	NOUN
cana-5406	212	14	using	use	VERB
cana-5406	212	15	matlab	matlab	PROPN
cana-5406	212	16	®	®	PROPN
cana-5406	212	17	.	.	PUNCT
cana-5406	213	1	crc	crc	PROPN
cana-5406	213	2	press	press	PROPN
cana-5406	213	3	;	;	PUNCT
cana-5406	213	4	2019	2019	NUM
cana-5406	213	5	sep	sep	NOUN
cana-5406	213	6	26	26	NUM
cana-5406	213	7	.	.	PUNCT
cana-5406	214	1	[	[	X
cana-5406	214	2	16	16	NUM
cana-5406	214	3	]	]	X
cana-5406	214	4	jafari	jafari	PROPN
cana-5406	214	5	h	h	NOUN
cana-5406	214	6	,	,	PUNCT
cana-5406	214	7	sadeghi	sadeghi	PROPN
cana-5406	214	8	s	s	PART
cana-5406	214	9	,	,	PUNCT
cana-5406	214	10	biswas	biswas	PROPN
cana-5406	214	11	a.	a.	PROPN
cana-5406	214	12	the	the	DET
cana-5406	214	13	differential	differential	ADJ
cana-5406	214	14	transform	transform	NOUN
cana-5406	214	15	method	method	NOUN
cana-5406	214	16	for	for	ADP
cana-5406	214	17	solving	solve	VERB
cana-5406	214	18	multidimensional	multidimensional	ADJ
cana-5406	214	19	partial	partial	ADJ
cana-5406	214	20	differential	differential	NOUN
cana-5406	214	21	equations	equation	NOUN
cana-5406	214	22	.	.	PUNCT
cana-5406	215	1	indian	indian	PROPN
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cana-5406	215	3	of	of	ADP
cana-5406	215	4	science	science	NOUN
cana-5406	215	5	and	and	CCONJ
cana-5406	215	6	technology	technology	NOUN
cana-5406	215	7	.	.	PUNCT
cana-5406	216	1	2012	2012	NUM
cana-5406	216	2	feb;5(2):200912	feb;5(2):200912	NUM
cana-5406	216	3	.	.	PUNCT
cana-5406	217	1	[	[	X
cana-5406	217	2	17	17	NUM
cana-5406	217	3	]	]	X
cana-5406	217	4	maponi	maponi	NOUN
cana-5406	217	5	p	p	NOUN
cana-5406	217	6	,	,	PUNCT
cana-5406	217	7	misici	misici	PROPN
cana-5406	217	8	l	l	NOUN
cana-5406	217	9	,	,	PUNCT
cana-5406	217	10	zirilli	zirilli	PROPN
cana-5406	217	11	f.	f.	PROPN
cana-5406	218	1	an	an	DET
cana-5406	218	2	inverse	inverse	NOUN
cana-5406	218	3	problem	problem	NOUN
cana-5406	218	4	for	for	ADP
cana-5406	218	5	the	the	DET
cana-5406	218	6	three	three	NUM
cana-5406	218	7	-	-	PUNCT
cana-5406	218	8	dimensional	dimensional	ADJ
cana-5406	218	9	vector	vector	NOUN
cana-5406	218	10	helmholtz	helmholtz	NOUN
cana-5406	218	11	equation	equation	NOUN
cana-5406	218	12	for	for	ADP
cana-5406	218	13	a	a	DET
cana-5406	218	14	perfectly	perfectly	ADV
cana-5406	218	15	conducting	conduct	VERB
cana-5406	218	16	obstacle	obstacle	NOUN
cana-5406	218	17	.	.	PUNCT
cana-5406	219	1	computers	computer	NOUN
cana-5406	219	2	&	&	CCONJ
cana-5406	219	3	mathematics	mathematics	PROPN
cana-5406	219	4	with	with	ADP
cana-5406	219	5	applications	application	NOUN
cana-5406	219	6	.	.	PUNCT
cana-5406	220	1	1991	1991	NUM
cana-5406	220	2	jan	jan	PROPN
cana-5406	220	3	1;22(4	1;22(4	PROPN
cana-5406	220	4	-	-	PUNCT
cana-5406	220	5	5):137	5):137	NUM
cana-5406	220	6	-	-	SYM
cana-5406	220	7	46	46	NUM
cana-5406	220	8	.	.	PUNCT
cana-5406	221	1	[	[	X
cana-5406	221	2	18	18	NUM
cana-5406	221	3	]	]	X
cana-5406	221	4	jafari	jafari	PROPN
cana-5406	221	5	h	h	NOUN
cana-5406	221	6	,	,	PUNCT
cana-5406	221	7	sadeghi	sadeghi	PROPN
cana-5406	221	8	s	s	PART
cana-5406	221	9	,	,	PUNCT
cana-5406	221	10	biswas	biswas	PROPN
cana-5406	221	11	a.	a.	PROPN
cana-5406	222	1	the	the	DET
cana-5406	222	2	differential	differential	ADJ
cana-5406	222	3	transform	transform	NOUN
cana-5406	222	4	method	method	NOUN
cana-5406	222	5	for	for	ADP
cana-5406	222	6	solving	solve	VERB
cana-5406	222	7	multidimensional	multidimensional	ADJ
cana-5406	222	8	partial	partial	ADJ
cana-5406	222	9	differential	differential	NOUN
cana-5406	222	10	equations	equation	NOUN
cana-5406	222	11	.	.	PUNCT
cana-5406	223	1	indian	indian	PROPN
cana-5406	223	2	journal	journal	PROPN
cana-5406	223	3	of	of	ADP
cana-5406	223	4	science	science	NOUN
cana-5406	223	5	and	and	CCONJ
cana-5406	223	6	technology	technology	NOUN
cana-5406	223	7	.	.	PUNCT
cana-5406	224	1	2012	2012	NUM
cana-5406	224	2	feb;5(2):200912	feb;5(2):200912	NUM
cana-5406	224	3	.	.	PUNCT
cana-5406	225	1	[	[	X
cana-5406	225	2	19	19	NUM
cana-5406	225	3	]	]	X
cana-5406	225	4	jafari	jafari	PROPN
cana-5406	225	5	h	h	NOUN
cana-5406	225	6	,	,	PUNCT
cana-5406	225	7	ghorbani	ghorbani	PROPN
cana-5406	225	8	m	m	PROPN
cana-5406	225	9	,	,	PUNCT
cana-5406	225	10	ghasempour	ghasempour	VERB
cana-5406	225	11	s.	s.	PROPN
cana-5406	225	12	a	a	DET
cana-5406	225	13	note	note	NOUN
cana-5406	225	14	on	on	ADP
cana-5406	225	15	exact	exact	ADJ
cana-5406	225	16	solutions	solution	NOUN
cana-5406	225	17	for	for	ADP
cana-5406	225	18	nonlinear	nonlinear	ADJ
cana-5406	225	19	integral	integral	ADJ
cana-5406	225	20	equations	equation	NOUN
cana-5406	225	21	by	by	ADP
cana-5406	225	22	a	a	DET
cana-5406	225	23	modified	modify	VERB
cana-5406	225	24	homotopy	homotopy	NOUN
cana-5406	225	25	perturbation	perturbation	NOUN
cana-5406	225	26	method	method	NOUN
cana-5406	225	27	.	.	PUNCT
cana-5406	226	1	new	new	ADJ
cana-5406	226	2	trends	trend	NOUN
cana-5406	226	3	in	in	ADP
cana-5406	226	4	mathematical	mathematical	ADJ
cana-5406	226	5	sciences	science	NOUN
cana-5406	226	6	.	.	PUNCT
cana-5406	227	1	2013;1(2):22	2013;1(2):22	NUM
cana-5406	227	2	-	-	SYM
cana-5406	227	3	6	6	NUM
cana-5406	227	4	.	.	PUNCT
cana-5406	228	1	[	[	X
cana-5406	228	2	20	20	NUM
cana-5406	228	3	]	]	X
cana-5406	228	4	alshammari	alshammari	PROPN
cana-5406	228	5	s	s	PROPN
cana-5406	228	6	,	,	PUNCT
cana-5406	228	7	abuasad	abuasad	PROPN
cana-5406	228	8	s.	s.	PROPN
cana-5406	228	9	exact	exact	ADJ
cana-5406	228	10	solutions	solution	NOUN
cana-5406	228	11	of	of	ADP
cana-5406	228	12	the	the	DET
cana-5406	228	13	3d	3d	PROPN
cana-5406	228	14	fractional	fractional	ADJ
cana-5406	228	15	helmholtz	helmholtz	NOUN
cana-5406	228	16	equation	equation	NOUN
cana-5406	228	17	by	by	ADP
cana-5406	228	18	fractional	fractional	ADJ
cana-5406	228	19	differential	differential	ADJ
cana-5406	228	20	transform	transform	NOUN
cana-5406	228	21	method	method	NOUN
cana-5406	228	22	.	.	PUNCT
cana-5406	229	1	journal	journal	NOUN
cana-5406	229	2	of	of	ADP
cana-5406	229	3	function	function	NOUN
cana-5406	229	4	spaces	space	NOUN
cana-5406	229	5	.	.	PUNCT
cana-5406	230	1	2022;2022(1):7374751	2022;2022(1):7374751	ADJ
cana-5406	230	2	.	.	PUNCT
cana-5406	231	1	[	[	X
cana-5406	231	2	21	21	NUM
cana-5406	231	3	]	]	PUNCT
cana-5406	231	4	borhanifar	borhanifar	ADV
cana-5406	231	5	a	a	X
cana-5406	231	6	,	,	PUNCT
cana-5406	231	7	abazari	abazari	ADJ
cana-5406	231	8	r.	r.	PROPN
cana-5406	231	9	numerical	numerical	PROPN
cana-5406	231	10	study	study	PROPN
cana-5406	231	11	of	of	ADP
cana-5406	231	12	nonlinear	nonlinear	ADJ
cana-5406	231	13	schrödinger	schrödinger	NOUN
cana-5406	231	14	and	and	CCONJ
cana-5406	231	15	coupled	couple	VERB
cana-5406	231	16	schrödinger	schrödinger	ADJ
cana-5406	231	17	equations	equation	NOUN
cana-5406	231	18	by	by	ADP
cana-5406	231	19	differential	differential	ADJ
cana-5406	231	20	transformation	transformation	NOUN
cana-5406	231	21	method	method	NOUN
cana-5406	231	22	.	.	PUNCT
cana-5406	232	1	optics	optic	NOUN
cana-5406	232	2	communications	communication	NOUN
cana-5406	232	3	.	.	PUNCT
cana-5406	233	1	2010	2010	NUM
cana-5406	233	2	may	may	AUX
cana-5406	233	3	15;283(10):2026	15;283(10):2026	NUM
cana-5406	233	4	-	-	SYM
cana-5406	233	5	31	31	NUM
cana-5406	233	6	.	.	PUNCT