id	sid	tid	token	lemma	pos
cana-5705	1	1	communications	communication	NOUN
cana-5705	1	2	on	on	ADP
cana-5705	1	3	applied	apply	VERB
cana-5705	1	4	nonlinear	nonlinear	ADJ
cana-5705	1	5	analysis	analysis	NOUN
cana-5705	1	6	issn	issn	NOUN
cana-5705	1	7	:	:	PUNCT
cana-5705	1	8	1074	1074	NUM
cana-5705	1	9	-	-	PUNCT
cana-5705	1	10	133x	133x	NUM
cana-5705	1	11	vol	vol	VERB
cana-5705	1	12	32	32	NUM
cana-5705	1	13	no	no	NOUN
cana-5705	1	14	.	.	PUNCT
cana-5705	2	1	10s	10	NOUN
cana-5705	2	2	(	(	PUNCT
cana-5705	2	3	2025	2025	NUM
cana-5705	2	4	)	)	PUNCT
cana-5705	2	5	2653	2653	NUM
cana-5705	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5705	2	7	solving	solve	VERB
cana-5705	2	8	nonlinear	nonlinear	ADJ
cana-5705	2	9	diffusion	diffusion	NOUN
cana-5705	2	10	equation	equation	NOUN
cana-5705	2	11	of	of	ADP
cana-5705	2	12	porous	porous	ADJ
cana-5705	2	13	medium	medium	NOUN
cana-5705	2	14	with	with	ADP
cana-5705	2	15	linear	linear	ADJ
cana-5705	2	16	pressure	pressure	NOUN
cana-5705	2	17	profile	profile	NOUN
cana-5705	2	18	by	by	ADP
cana-5705	2	19	homotopy	homotopy	NOUN
cana-5705	2	20	perturbation	perturbation	NOUN
cana-5705	2	21	transform	transform	NOUN
cana-5705	2	22	method	method	NOUN
cana-5705	2	23	and	and	CCONJ
cana-5705	2	24	he	he	PRON
cana-5705	2	25	’s	’	VERB
cana-5705	2	26	polynomials	polynomial	NOUN
cana-5705	2	27	.	.	PUNCT
cana-5705	3	1	ramaa	ramaa	ADJ
cana-5705	3	2	sandu	sandu	NOUN
cana-5705	3	3	,	,	PUNCT
cana-5705	3	4	dr.b.b	dr.b.b	NOUN
cana-5705	3	5	.	.	PUNCT
cana-5705	4	1	waphare	waphare	PROPN
cana-5705	4	2	*	*	PROPN
cana-5705	4	3	department	department	PROPN
cana-5705	4	4	of	of	ADP
cana-5705	4	5	mathematics	mathematic	NOUN
cana-5705	4	6	and	and	CCONJ
cana-5705	4	7	statistics	statistic	NOUN
cana-5705	4	8	,	,	PUNCT
cana-5705	4	9	dr	dr	PROPN
cana-5705	4	10	.	.	PROPN
cana-5705	4	11	vishwanath	vishwanath	PROPN
cana-5705	4	12	karad	karad	PROPN
cana-5705	4	13	mit	mit	PROPN
cana-5705	4	14	world	world	PROPN
cana-5705	4	15	peace	peace	NOUN
cana-5705	4	16	university	university	PROPN
cana-5705	4	17	,	,	PUNCT
cana-5705	4	18	pune-38	pune-38	PROPN
cana-5705	4	19	e	e	PROPN
cana-5705	4	20	-	-	NOUN
cana-5705	4	21	mail	mail	NOUN
cana-5705	4	22	:	:	PUNCT
cana-5705	4	23	ramaa.sandu@mitwpu.edu.in	ramaa.sandu@mitwpu.edu.in	VERB
cana-5705	4	24	*	*	PROPN
cana-5705	4	25	department	department	NOUN
cana-5705	4	26	of	of	ADP
cana-5705	4	27	mathematics	mathematic	NOUN
cana-5705	4	28	,	,	PUNCT
cana-5705	4	29	mit	mit	NOUN
cana-5705	4	30	arts	art	NOUN
cana-5705	4	31	,	,	PUNCT
cana-5705	4	32	commerce	commerce	NOUN
cana-5705	4	33	and	and	CCONJ
cana-5705	4	34	science	science	PROPN
cana-5705	4	35	college	college	PROPN
cana-5705	4	36	,	,	PUNCT
cana-5705	4	37	alandi	alandi	NOUN
cana-5705	4	38	,	,	PUNCT
cana-5705	4	39	pune	pune	NOUN
cana-5705	4	40	.	.	PUNCT
cana-5705	5	1	e	e	X
cana-5705	5	2	-	-	NOUN
cana-5705	5	3	mail	mail	NOUN
cana-5705	5	4	:	:	PUNCT
cana-5705	6	1	balasahebwaphare@gmail.com	balasahebwaphare@gmail.com	X
cana-5705	6	2	article	article	NOUN
cana-5705	6	3	history	history	NOUN
cana-5705	6	4	:	:	PUNCT
cana-5705	6	5	received	receive	VERB
cana-5705	6	6	:	:	PUNCT
cana-5705	6	7	12	12	NUM
cana-5705	6	8	-	-	SYM
cana-5705	6	9	01	01	NUM
cana-5705	6	10	-	-	PUNCT
cana-5705	6	11	2025	2025	NUM
cana-5705	6	12	revised	revise	VERB
cana-5705	6	13	:	:	PUNCT
cana-5705	6	14	15	15	NUM
cana-5705	6	15	-	-	NUM
cana-5705	6	16	02	02	NUM
cana-5705	6	17	-	-	PUNCT
cana-5705	6	18	2025	2025	NUM
cana-5705	6	19	accepted	accept	VERB
cana-5705	6	20	:	:	PUNCT
cana-5705	6	21	01	01	NUM
cana-5705	6	22	-	-	SYM
cana-5705	6	23	03	03	NUM
cana-5705	6	24	-	-	PUNCT
cana-5705	6	25	2025	2025	NUM
cana-5705	6	26	abstract	abstract	NOUN
cana-5705	6	27	:	:	PUNCT
cana-5705	6	28	most	most	ADJ
cana-5705	6	29	physical	physical	ADJ
cana-5705	6	30	phenomenon	phenomenon	NOUN
cana-5705	6	31	and	and	CCONJ
cana-5705	6	32	processes	process	NOUN
cana-5705	6	33	in	in	ADP
cana-5705	6	34	the	the	DET
cana-5705	6	35	field	field	NOUN
cana-5705	6	36	of	of	ADP
cana-5705	6	37	fluid	fluid	ADJ
cana-5705	6	38	mechanics	mechanic	NOUN
cana-5705	6	39	are	be	AUX
cana-5705	6	40	governed	govern	VERB
cana-5705	6	41	by	by	ADP
cana-5705	6	42	partial	partial	ADJ
cana-5705	6	43	differential	differential	ADJ
cana-5705	6	44	equations	equation	NOUN
cana-5705	6	45	.	.	PUNCT
cana-5705	7	1	many	many	ADJ
cana-5705	7	2	nonlinear	nonlinear	ADJ
cana-5705	7	3	partial	partial	ADJ
cana-5705	7	4	differential	differential	NOUN
cana-5705	7	5	equations	equation	NOUN
cana-5705	7	6	do	do	AUX
cana-5705	7	7	not	not	PART
cana-5705	7	8	possess	possess	VERB
cana-5705	7	9	analytical	analytical	ADJ
cana-5705	7	10	solution	solution	NOUN
cana-5705	7	11	,	,	PUNCT
cana-5705	7	12	so	so	CCONJ
cana-5705	7	13	numerical	numerical	ADJ
cana-5705	7	14	methods	method	NOUN
cana-5705	7	15	are	be	AUX
cana-5705	7	16	commonly	commonly	ADV
cana-5705	7	17	used	use	VERB
cana-5705	7	18	to	to	PART
cana-5705	7	19	solve	solve	VERB
cana-5705	7	20	these	these	DET
cana-5705	7	21	equations	equation	NOUN
cana-5705	7	22	.	.	PUNCT
cana-5705	8	1	in	in	ADP
cana-5705	8	2	this	this	DET
cana-5705	8	3	paper	paper	NOUN
cana-5705	8	4	we	we	PRON
cana-5705	8	5	have	have	AUX
cana-5705	8	6	discussed	discuss	VERB
cana-5705	8	7	an	an	DET
cana-5705	8	8	analytical	analytical	ADJ
cana-5705	8	9	method	method	NOUN
cana-5705	8	10	,	,	PUNCT
cana-5705	8	11	which	which	PRON
cana-5705	8	12	is	be	AUX
cana-5705	8	13	a	a	DET
cana-5705	8	14	combination	combination	NOUN
cana-5705	8	15	of	of	ADP
cana-5705	8	16	laplace	laplace	NOUN
cana-5705	8	17	transforms	transform	VERB
cana-5705	8	18	and	and	CCONJ
cana-5705	8	19	homotopy	homotopy	VERB
cana-5705	8	20	perturbation	perturbation	NOUN
cana-5705	8	21	method	method	NOUN
cana-5705	8	22	called	call	VERB
cana-5705	8	23	as	as	ADP
cana-5705	8	24	homotopy	homotopy	NOUN
cana-5705	8	25	perturbation	perturbation	NOUN
cana-5705	8	26	transform	transform	NOUN
cana-5705	8	27	method	method	NOUN
cana-5705	8	28	(	(	PUNCT
cana-5705	8	29	hptm	hptm	NOUN
cana-5705	8	30	)	)	PUNCT
cana-5705	8	31	.	.	PUNCT
cana-5705	9	1	our	our	PRON
cana-5705	9	2	aim	aim	NOUN
cana-5705	9	3	is	be	AUX
cana-5705	9	4	to	to	PART
cana-5705	9	5	reduce	reduce	VERB
cana-5705	9	6	the	the	DET
cana-5705	9	7	volume	volume	NOUN
cana-5705	9	8	of	of	ADP
cana-5705	9	9	computational	computational	ADJ
cana-5705	9	10	work	work	NOUN
cana-5705	9	11	in	in	ADP
cana-5705	9	12	finding	find	VERB
cana-5705	9	13	the	the	DET
cana-5705	9	14	exact	exact	ADJ
cana-5705	9	15	solution	solution	NOUN
cana-5705	9	16	of	of	ADP
cana-5705	9	17	nonlinear	nonlinear	ADJ
cana-5705	9	18	partial	partial	ADJ
cana-5705	9	19	differential	differential	NOUN
cana-5705	9	20	equation	equation	NOUN
cana-5705	9	21	as	as	ADP
cana-5705	9	22	compared	compare	VERB
cana-5705	9	23	to	to	ADP
cana-5705	9	24	the	the	DET
cana-5705	9	25	classical	classical	ADJ
cana-5705	9	26	methods	method	NOUN
cana-5705	9	27	while	while	SCONJ
cana-5705	9	28	still	still	ADV
cana-5705	9	29	maintaining	maintain	VERB
cana-5705	9	30	the	the	DET
cana-5705	9	31	high	high	ADJ
cana-5705	9	32	accuracy	accuracy	NOUN
cana-5705	9	33	of	of	ADP
cana-5705	9	34	the	the	DET
cana-5705	9	35	numerical	numerical	ADJ
cana-5705	9	36	solution	solution	NOUN
cana-5705	9	37	.	.	PUNCT
cana-5705	10	1	one	one	NUM
cana-5705	10	2	such	such	ADJ
cana-5705	10	3	nonlinear	nonlinear	ADJ
cana-5705	10	4	diffusion	diffusion	NOUN
cana-5705	10	5	equation	equation	NOUN
cana-5705	10	6	of	of	ADP
cana-5705	10	7	porous	porous	ADJ
cana-5705	10	8	medium	medium	NOUN
cana-5705	10	9	with	with	ADP
cana-5705	10	10	linear	linear	ADJ
cana-5705	10	11	pressure	pressure	NOUN
cana-5705	10	12	profile	profile	NOUN
cana-5705	10	13	is	be	AUX
cana-5705	10	14	considered	consider	VERB
cana-5705	10	15	here	here	ADV
cana-5705	10	16	with	with	ADP
cana-5705	10	17	different	different	ADJ
cana-5705	10	18	initial	initial	ADJ
cana-5705	10	19	conditions	condition	NOUN
cana-5705	10	20	.	.	PUNCT
cana-5705	11	1	laplace	laplace	NOUN
cana-5705	11	2	transform	transform	NOUN
cana-5705	11	3	alone	alone	ADV
cana-5705	11	4	is	be	AUX
cana-5705	11	5	incapable	incapable	ADJ
cana-5705	11	6	of	of	ADP
cana-5705	11	7	handling	handle	VERB
cana-5705	11	8	nonlinear	nonlinear	ADJ
cana-5705	11	9	terms	term	NOUN
cana-5705	11	10	,	,	PUNCT
cana-5705	11	11	so	so	ADV
cana-5705	11	12	he	he	PRON
cana-5705	11	13	’s	’	VERB
cana-5705	11	14	polynomials	polynomial	NOUN
cana-5705	11	15	are	be	AUX
cana-5705	11	16	used	use	VERB
cana-5705	11	17	to	to	PART
cana-5705	11	18	simplify	simplify	VERB
cana-5705	11	19	the	the	DET
cana-5705	11	20	nonlinear	nonlinear	ADJ
cana-5705	11	21	terms	term	NOUN
cana-5705	11	22	appearing	appear	VERB
cana-5705	11	23	in	in	ADP
cana-5705	11	24	the	the	DET
cana-5705	11	25	equation	equation	NOUN
cana-5705	11	26	.	.	PUNCT
cana-5705	12	1	many	many	ADJ
cana-5705	12	2	researchers	researcher	NOUN
cana-5705	12	3	have	have	AUX
cana-5705	12	4	used	use	VERB
cana-5705	12	5	adomian	adomian	NOUN
cana-5705	12	6	polynomials	polynomial	NOUN
cana-5705	12	7	to	to	PART
cana-5705	12	8	decompose	decompose	VERB
cana-5705	12	9	the	the	DET
cana-5705	12	10	nonlinear	nonlinear	ADJ
cana-5705	12	11	terms	term	NOUN
cana-5705	12	12	of	of	ADP
cana-5705	12	13	the	the	DET
cana-5705	12	14	partial	partial	ADJ
cana-5705	12	15	differential	differential	NOUN
cana-5705	12	16	equations	equation	NOUN
cana-5705	12	17	arising	arise	VERB
cana-5705	12	18	in	in	ADP
cana-5705	12	19	fluid	fluid	ADJ
cana-5705	12	20	mechanics	mechanic	NOUN
cana-5705	12	21	.	.	PUNCT
cana-5705	13	1	but	but	CCONJ
cana-5705	13	2	the	the	DET
cana-5705	13	3	complexity	complexity	NOUN
cana-5705	13	4	and	and	CCONJ
cana-5705	13	5	calculation	calculation	NOUN
cana-5705	13	6	process	process	NOUN
cana-5705	13	7	are	be	AUX
cana-5705	13	8	much	much	ADV
cana-5705	13	9	easier	easy	ADJ
cana-5705	13	10	in	in	ADP
cana-5705	13	11	hptm	hptm	NOUN
cana-5705	13	12	compared	compare	VERB
cana-5705	13	13	to	to	ADP
cana-5705	13	14	adomian	adomian	NOUN
cana-5705	13	15	polynomials	polynomial	NOUN
cana-5705	13	16	.	.	PUNCT
cana-5705	14	1	keywords	keyword	NOUN
cana-5705	14	2	:	:	PUNCT
cana-5705	14	3	computational	computational	ADJ
cana-5705	14	4	mathematics	mathematic	NOUN
cana-5705	14	5	,	,	PUNCT
cana-5705	14	6	laplace	laplace	NOUN
cana-5705	14	7	transform	transform	NOUN
cana-5705	14	8	,	,	PUNCT
cana-5705	14	9	homotopy	homotopy	VERB
cana-5705	14	10	perturbation	perturbation	NOUN
cana-5705	14	11	method	method	NOUN
cana-5705	14	12	,	,	PUNCT
cana-5705	14	13	porous	porous	ADJ
cana-5705	14	14	medium	medium	ADJ
cana-5705	14	15	,	,	PUNCT
cana-5705	14	16	nonlinear	nonlinear	ADJ
cana-5705	14	17	equations	equation	NOUN
cana-5705	14	18	.	.	PUNCT
cana-5705	15	1	1	1	X
cana-5705	15	2	.	.	X
cana-5705	15	3	introduction	introduction	NOUN
cana-5705	15	4	the	the	DET
cana-5705	15	5	nonlinear	nonlinear	ADJ
cana-5705	15	6	diffusion	diffusion	NOUN
cana-5705	15	7	equation	equation	NOUN
cana-5705	15	8	is	be	AUX
cana-5705	15	9	a	a	DET
cana-5705	15	10	prominent	prominent	ADJ
cana-5705	15	11	example	example	NOUN
cana-5705	15	12	of	of	ADP
cana-5705	15	13	porous	porous	ADJ
cana-5705	15	14	medium	medium	ADJ
cana-5705	15	15	equation	equation	NOUN
cana-5705	15	16	.	.	PUNCT
cana-5705	16	1	most	most	ADJ
cana-5705	16	2	phenomena	phenomenon	NOUN
cana-5705	16	3	described	describe	VERB
cana-5705	16	4	by	by	ADP
cana-5705	16	5	nonlinear	nonlinear	ADJ
cana-5705	16	6	equations	equation	NOUN
cana-5705	16	7	are	be	AUX
cana-5705	16	8	still	still	ADV
cana-5705	16	9	difficult	difficult	ADJ
cana-5705	16	10	to	to	PART
cana-5705	16	11	understand	understand	VERB
cana-5705	16	12	analytically	analytically	ADV
cana-5705	16	13	hence	hence	ADV
cana-5705	16	14	approximate	approximate	ADJ
cana-5705	16	15	numerical	numerical	PROPN
cana-5705	16	16	method	method	PROPN
cana-5705	16	17	remains	remain	VERB
cana-5705	16	18	the	the	DET
cana-5705	16	19	only	only	ADJ
cana-5705	16	20	option	option	NOUN
cana-5705	16	21	.	.	PUNCT
cana-5705	17	1	analytic	analytic	ADJ
cana-5705	17	2	techniques	technique	NOUN
cana-5705	17	3	like	like	ADP
cana-5705	17	4	adomian	adomian	NOUN
cana-5705	17	5	decomposition	decomposition	NOUN
cana-5705	17	6	,	,	PUNCT
cana-5705	17	7	the	the	DET
cana-5705	17	8	variational	variational	ADJ
cana-5705	17	9	iteration	iteration	NOUN
cana-5705	17	10	methods	method	NOUN
cana-5705	17	11	etc	etc	X
cana-5705	17	12	.	.	X
cana-5705	17	13	are	be	AUX
cana-5705	17	14	approximate	approximate	ADJ
cana-5705	17	15	in	in	ADP
cana-5705	17	16	nature	nature	NOUN
cana-5705	17	17	.	.	PUNCT
cana-5705	18	1	these	these	DET
cana-5705	18	2	methods	method	NOUN
cana-5705	18	3	have	have	VERB
cana-5705	18	4	their	their	PRON
cana-5705	18	5	limitations	limitation	NOUN
cana-5705	18	6	to	to	PART
cana-5705	18	7	calculate	calculate	VERB
cana-5705	18	8	complex	complex	ADJ
cana-5705	18	9	adomian	adomian	NOUN
cana-5705	18	10	polynomials	polynomial	NOUN
cana-5705	18	11	,	,	PUNCT
cana-5705	18	12	lagrange	lagrange	PROPN
cana-5705	18	13	’s	’s	PART
cana-5705	18	14	multipliers	multiplier	NOUN
cana-5705	18	15	etc	etc	X
cana-5705	18	16	.	.	X
cana-5705	18	17	simpler	simple	ADJ
cana-5705	18	18	analytic	analytic	ADJ
cana-5705	18	19	method	method	NOUN
cana-5705	18	20	is	be	AUX
cana-5705	18	21	discussed	discuss	VERB
cana-5705	18	22	in	in	ADP
cana-5705	18	23	the	the	DET
cana-5705	18	24	present	present	ADJ
cana-5705	18	25	paper	paper	NOUN
cana-5705	18	26	.	.	PUNCT
cana-5705	19	1	homotopy	homotopy	NOUN
cana-5705	19	2	perturbation	perturbation	NOUN
cana-5705	19	3	transform	transform	NOUN
cana-5705	19	4	method	method	NOUN
cana-5705	19	5	(	(	PUNCT
cana-5705	19	6	hptm	hptm	NOUN
cana-5705	19	7	):	):	PUNCT
cana-5705	19	8	it	it	PRON
cana-5705	19	9	is	be	AUX
cana-5705	19	10	good	good	ADJ
cana-5705	19	11	old	old	ADJ
cana-5705	19	12	homotopy	homotopy	NOUN
cana-5705	19	13	perturbation	perturbation	NOUN
cana-5705	19	14	method	method	NOUN
cana-5705	19	15	combined	combine	VERB
cana-5705	19	16	with	with	ADP
cana-5705	19	17	laplace	laplace	NOUN
cana-5705	19	18	transform	transform	NOUN
cana-5705	19	19	method	method	NOUN
cana-5705	19	20	named	name	VERB
cana-5705	19	21	as	as	ADP
cana-5705	19	22	homotopy	homotopy	NOUN
cana-5705	19	23	perturbation	perturbation	NOUN
cana-5705	19	24	transform	transform	NOUN
cana-5705	19	25	method	method	NOUN
cana-5705	19	26	(	(	PUNCT
cana-5705	19	27	hptm	hptm	NOUN
cana-5705	19	28	)	)	PUNCT
cana-5705	19	29	.	.	PUNCT
cana-5705	20	1	this	this	DET
cana-5705	20	2	method	method	NOUN
cana-5705	20	3	has	have	AUX
cana-5705	20	4	proved	prove	VERB
cana-5705	20	5	to	to	PART
cana-5705	20	6	be	be	AUX
cana-5705	20	7	quite	quite	ADV
cana-5705	20	8	promising	promising	ADJ
cana-5705	20	9	in	in	ADP
cana-5705	20	10	solving	solve	VERB
cana-5705	20	11	linear	linear	NOUN
cana-5705	20	12	as	as	ADV
cana-5705	20	13	well	well	ADV
cana-5705	20	14	as	as	ADP
cana-5705	20	15	nonlinear	nonlinear	ADJ
cana-5705	20	16	problems	problem	NOUN
cana-5705	20	17	arising	arise	VERB
cana-5705	20	18	in	in	ADP
cana-5705	20	19	different	different	ADJ
cana-5705	20	20	fields	field	NOUN
cana-5705	20	21	of	of	ADP
cana-5705	20	22	science	science	NOUN
cana-5705	20	23	in	in	ADP
cana-5705	20	24	general	general	ADJ
cana-5705	20	25	and	and	CCONJ
cana-5705	20	26	fluid	fluid	ADJ
cana-5705	20	27	dynamics	dynamic	NOUN
cana-5705	20	28	in	in	ADP
cana-5705	20	29	particular	particular	ADJ
cana-5705	20	30	.	.	PUNCT
cana-5705	21	1	initially	initially	ADV
cana-5705	21	2	j.	j.	PROPN
cana-5705	21	3	h.	h.	PROPN
cana-5705	21	4	he	he	PRON
cana-5705	21	5	(	(	PUNCT
cana-5705	21	6	1999	1999	NUM
cana-5705	21	7	)	)	PUNCT
cana-5705	22	1	[	[	X
cana-5705	22	2	1	1	X
cana-5705	22	3	]	]	PUNCT
cana-5705	22	4	described	describe	VERB
cana-5705	22	5	the	the	DET
cana-5705	22	6	fundamentals	fundamental	NOUN
cana-5705	22	7	of	of	ADP
cana-5705	22	8	homotopy	homotopy	NOUN
cana-5705	22	9	perturbation	perturbation	NOUN
cana-5705	22	10	method	method	NOUN
cana-5705	22	11	.	.	PUNCT
cana-5705	23	1	he	he	PRON
cana-5705	23	2	had	have	AUX
cana-5705	23	3	showed	show	VERB
cana-5705	23	4	by	by	ADP
cana-5705	23	5	taking	take	VERB
cana-5705	23	6	some	some	DET
cana-5705	23	7	examples	example	NOUN
cana-5705	23	8	that	that	SCONJ
cana-5705	23	9	the	the	DET
cana-5705	23	10	homotopy	homotopy	NOUN
cana-5705	23	11	perturbation	perturbation	NOUN
cana-5705	23	12	technique	technique	NOUN
cana-5705	23	13	does	do	AUX
cana-5705	23	14	not	not	PART
cana-5705	23	15	depend	depend	VERB
cana-5705	23	16	upon	upon	SCONJ
cana-5705	23	17	a	a	DET
cana-5705	23	18	small	small	ADJ
cana-5705	23	19	parameter	parameter	NOUN
cana-5705	23	20	in	in	ADP
cana-5705	23	21	the	the	DET
cana-5705	23	22	equation	equation	NOUN
cana-5705	23	23	.	.	PUNCT
cana-5705	24	1	in	in	ADP
cana-5705	24	2	topology	topology	NOUN
cana-5705	24	3	,	,	PUNCT
cana-5705	24	4	a	a	DET
cana-5705	24	5	homotopy	homotopy	NOUN
cana-5705	24	6	is	be	AUX
cana-5705	24	7	constructed	construct	VERB
cana-5705	24	8	with	with	ADP
cana-5705	24	9	an	an	DET
cana-5705	24	10	embedding	embed	VERB
cana-5705	24	11	parameter	parameter	NOUN
cana-5705	24	12	communications	communication	NOUN
cana-5705	24	13	on	on	ADP
cana-5705	24	14	applied	apply	VERB
cana-5705	24	15	nonlinear	nonlinear	ADJ
cana-5705	24	16	analysis	analysis	NOUN
cana-5705	24	17	issn	issn	NOUN
cana-5705	24	18	:	:	PUNCT
cana-5705	24	19	1074	1074	NUM
cana-5705	24	20	-	-	PUNCT
cana-5705	24	21	133x	133x	NUM
cana-5705	24	22	vol	vol	VERB
cana-5705	24	23	32	32	NUM
cana-5705	24	24	no	no	NOUN
cana-5705	24	25	.	.	PUNCT
cana-5705	25	1	10s	10	NOUN
cana-5705	25	2	(	(	PUNCT
cana-5705	25	3	2025	2025	NUM
cana-5705	25	4	)	)	PUNCT
cana-5705	25	5	2654	2654	NUM
cana-5705	25	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5705	25	7	q∈	q∈	PROPN
cana-5705	26	1	[	[	X
cana-5705	26	2	0,1	0,1	NUM
cana-5705	26	3	]	]	PUNCT
cana-5705	26	4	which	which	PRON
cana-5705	26	5	is	be	AUX
cana-5705	26	6	considered	consider	VERB
cana-5705	26	7	as	as	ADP
cana-5705	26	8	a	a	DET
cana-5705	26	9	“	"	PUNCT
cana-5705	26	10	small	small	ADJ
cana-5705	26	11	parameter	parameter	NOUN
cana-5705	26	12	”	"	PUNCT
cana-5705	26	13	.	.	PUNCT
cana-5705	27	1	it	it	PRON
cana-5705	27	2	was	be	AUX
cana-5705	27	3	demonstrated	demonstrate	VERB
cana-5705	27	4	through	through	ADP
cana-5705	27	5	his	his	PRON
cana-5705	27	6	method	method	NOUN
cana-5705	27	7	that	that	SCONJ
cana-5705	27	8	the	the	DET
cana-5705	27	9	approximate	approximate	ADJ
cana-5705	27	10	solutions	solution	NOUN
cana-5705	27	11	obtained	obtain	VERB
cana-5705	27	12	by	by	ADP
cana-5705	27	13	the	the	DET
cana-5705	27	14	proposed	propose	VERB
cana-5705	27	15	method	method	NOUN
cana-5705	27	16	are	be	AUX
cana-5705	27	17	uniformly	uniformly	ADV
cana-5705	27	18	valid	valid	ADJ
cana-5705	27	19	for	for	ADP
cana-5705	27	20	both	both	CCONJ
cana-5705	27	21	small	small	ADJ
cana-5705	27	22	and	and	CCONJ
cana-5705	27	23	large	large	ADJ
cana-5705	27	24	parameters	parameter	NOUN
cana-5705	27	25	.	.	PUNCT
cana-5705	28	1	it	it	PRON
cana-5705	28	2	is	be	AUX
cana-5705	28	3	considered	consider	VERB
cana-5705	28	4	as	as	ADP
cana-5705	28	5	a	a	DET
cana-5705	28	6	promising	promising	ADJ
cana-5705	28	7	and	and	CCONJ
cana-5705	28	8	evolving	evolve	VERB
cana-5705	28	9	method	method	NOUN
cana-5705	28	10	.	.	PUNCT
cana-5705	29	1	not	not	PART
cana-5705	29	2	only	only	ADV
cana-5705	29	3	it	it	PRON
cana-5705	29	4	has	have	VERB
cana-5705	29	5	importance	importance	NOUN
cana-5705	29	6	in	in	ADP
cana-5705	29	7	solving	solve	VERB
cana-5705	29	8	mathematical	mathematical	ADJ
cana-5705	29	9	equations	equation	NOUN
cana-5705	29	10	,	,	PUNCT
cana-5705	29	11	it	it	PRON
cana-5705	29	12	can	can	AUX
cana-5705	29	13	be	be	AUX
cana-5705	29	14	applied	apply	VERB
cana-5705	29	15	to	to	ADP
cana-5705	29	16	other	other	ADJ
cana-5705	29	17	branches	branch	NOUN
cana-5705	29	18	of	of	ADP
cana-5705	29	19	modern	modern	ADJ
cana-5705	29	20	sciences	science	NOUN
cana-5705	29	21	.	.	PUNCT
cana-5705	30	1	lan	lan	PROPN
cana-5705	30	2	xu	xu	PROPN
cana-5705	31	1	(	(	PUNCT
cana-5705	31	2	2007	2007	NUM
cana-5705	31	3	)	)	PUNCT
cana-5705	32	1	[	[	X
cana-5705	32	2	2	2	X
cana-5705	32	3	]	]	PUNCT
cana-5705	32	4	had	have	AUX
cana-5705	32	5	applied	apply	VERB
cana-5705	32	6	the	the	DET
cana-5705	32	7	technique	technique	NOUN
cana-5705	32	8	to	to	PART
cana-5705	32	9	find	find	VERB
cana-5705	32	10	approximate	approximate	ADJ
cana-5705	32	11	solution	solution	NOUN
cana-5705	32	12	of	of	ADP
cana-5705	32	13	nonlinear	nonlinear	ADJ
cana-5705	32	14	boundary	boundary	ADJ
cana-5705	32	15	layer	layer	NOUN
cana-5705	32	16	equations	equation	NOUN
cana-5705	32	17	in	in	ADP
cana-5705	32	18	unbounded	unbounded	ADJ
cana-5705	32	19	domain	domain	NOUN
cana-5705	32	20	.	.	PUNCT
cana-5705	33	1	the	the	DET
cana-5705	33	2	results	result	NOUN
cana-5705	33	3	are	be	AUX
cana-5705	33	4	compared	compare	VERB
cana-5705	33	5	with	with	ADP
cana-5705	33	6	the	the	DET
cana-5705	33	7	results	result	NOUN
cana-5705	33	8	in	in	ADP
cana-5705	33	9	available	available	ADJ
cana-5705	33	10	literature	literature	NOUN
cana-5705	33	11	.	.	PUNCT
cana-5705	34	1	it	it	PRON
cana-5705	34	2	is	be	AUX
cana-5705	34	3	verified	verify	VERB
cana-5705	34	4	that	that	SCONJ
cana-5705	34	5	the	the	DET
cana-5705	34	6	method	method	NOUN
cana-5705	34	7	is	be	AUX
cana-5705	34	8	simple	simple	ADJ
cana-5705	34	9	and	and	CCONJ
cana-5705	34	10	useful	useful	ADJ
cana-5705	34	11	.	.	PUNCT
cana-5705	35	1	ghorbani	ghorbani	NOUN
cana-5705	35	2	(	(	PUNCT
cana-5705	35	3	2009	2009	NUM
cana-5705	35	4	)	)	PUNCT
cana-5705	36	1	[	[	X
cana-5705	36	2	3	3	X
cana-5705	36	3	]	]	PUNCT
cana-5705	36	4	used	use	VERB
cana-5705	36	5	he	he	PRON
cana-5705	36	6	’s	’	VERB
cana-5705	36	7	polynomials	polynomial	NOUN
cana-5705	36	8	over	over	ADP
cana-5705	36	9	adomian	adomian	NOUN
cana-5705	36	10	polynomials	polynomial	NOUN
cana-5705	36	11	,	,	PUNCT
cana-5705	36	12	to	to	PART
cana-5705	36	13	obtain	obtain	VERB
cana-5705	36	14	chaos	chaos	NOUN
cana-5705	36	15	solutions	solution	NOUN
cana-5705	36	16	fractals	fractal	NOUN
cana-5705	36	17	.	.	PUNCT
cana-5705	37	1	sari	sari	NOUN
cana-5705	37	2	(	(	PUNCT
cana-5705	37	3	2009	2009	NUM
cana-5705	37	4	)	)	PUNCT
cana-5705	38	1	[	[	X
cana-5705	38	2	4	4	X
cana-5705	38	3	]	]	PUNCT
cana-5705	38	4	demonstrated	demonstrate	VERB
cana-5705	38	5	compact	compact	ADJ
cana-5705	38	6	finite	finite	ADJ
cana-5705	38	7	difference	difference	NOUN
cana-5705	38	8	method	method	NOUN
cana-5705	38	9	in	in	ADP
cana-5705	38	10	space	space	NOUN
cana-5705	38	11	and	and	CCONJ
cana-5705	38	12	a	a	DET
cana-5705	38	13	low	low	ADJ
cana-5705	38	14	-	-	PUNCT
cana-5705	38	15	storage	storage	NOUN
cana-5705	38	16	total	total	ADJ
cana-5705	38	17	variation	variation	NOUN
cana-5705	38	18	diminishing	diminish	VERB
cana-5705	38	19	third	third	ADJ
cana-5705	38	20	-	-	PUNCT
cana-5705	38	21	order	order	NOUN
cana-5705	38	22	runge	runge	NOUN
cana-5705	38	23	-	-	PUNCT
cana-5705	38	24	kutta	kutta	NOUN
cana-5705	38	25	scheme	scheme	NOUN
cana-5705	38	26	in	in	ADP
cana-5705	38	27	time	time	NOUN
cana-5705	38	28	to	to	PART
cana-5705	38	29	find	find	VERB
cana-5705	38	30	the	the	DET
cana-5705	38	31	solutions	solution	NOUN
cana-5705	38	32	of	of	ADP
cana-5705	38	33	the	the	DET
cana-5705	38	34	porous	porous	ADJ
cana-5705	38	35	media	medium	NOUN
cana-5705	38	36	equation	equation	NOUN
cana-5705	38	37	in	in	ADP
cana-5705	38	38	nonlinear	nonlinear	ADJ
cana-5705	38	39	problems	problem	NOUN
cana-5705	38	40	of	of	ADP
cana-5705	38	41	heat	heat	NOUN
cana-5705	38	42	and	and	CCONJ
cana-5705	38	43	mass	mass	NOUN
cana-5705	38	44	transfer	transfer	NOUN
cana-5705	38	45	and	and	CCONJ
cana-5705	38	46	in	in	ADP
cana-5705	38	47	biological	biological	ADJ
cana-5705	38	48	systems	system	NOUN
cana-5705	38	49	.	.	PUNCT
cana-5705	39	1	in	in	ADP
cana-5705	39	2	the	the	DET
cana-5705	39	3	calculation	calculation	NOUN
cana-5705	39	4	of	of	ADP
cana-5705	39	5	the	the	DET
cana-5705	39	6	numerical	numerical	ADJ
cana-5705	39	7	derivatives	derivative	NOUN
cana-5705	39	8	,	,	PUNCT
cana-5705	39	9	a	a	DET
cana-5705	39	10	tridiagonal	tridiagonal	ADJ
cana-5705	39	11	band	band	NOUN
cana-5705	39	12	matrix	matrix	NOUN
cana-5705	39	13	algorithm	algorithm	NOUN
cana-5705	39	14	was	be	AUX
cana-5705	39	15	used	use	VERB
cana-5705	39	16	in	in	ADP
cana-5705	39	17	the	the	DET
cana-5705	39	18	calculation	calculation	NOUN
cana-5705	39	19	of	of	ADP
cana-5705	39	20	the	the	DET
cana-5705	39	21	numerical	numerical	PROPN
cana-5705	39	22	derivative	derivative	NOUN
cana-5705	39	23	.	.	PUNCT
cana-5705	40	1	however	however	ADV
cana-5705	40	2	,	,	PUNCT
cana-5705	40	3	the	the	DET
cana-5705	40	4	method	method	NOUN
cana-5705	40	5	used	use	VERB
cana-5705	40	6	is	be	AUX
cana-5705	40	7	not	not	PART
cana-5705	40	8	containing	contain	VERB
cana-5705	40	9	much	much	ADJ
cana-5705	40	10	numerical	numerical	ADJ
cana-5705	40	11	errors	error	NOUN
cana-5705	40	12	and	and	CCONJ
cana-5705	40	13	storage	storage	NOUN
cana-5705	40	14	capacity	capacity	NOUN
cana-5705	40	15	is	be	AUX
cana-5705	40	16	also	also	ADV
cana-5705	40	17	small	small	ADJ
cana-5705	40	18	.	.	PUNCT
cana-5705	41	1	the	the	DET
cana-5705	41	2	solution	solution	NOUN
cana-5705	41	3	obtained	obtain	VERB
cana-5705	41	4	by	by	ADP
cana-5705	41	5	this	this	DET
cana-5705	41	6	method	method	NOUN
cana-5705	41	7	is	be	AUX
cana-5705	41	8	compared	compare	VERB
cana-5705	41	9	with	with	ADP
cana-5705	41	10	the	the	DET
cana-5705	41	11	exact	exact	ADJ
cana-5705	41	12	solutions	solution	NOUN
cana-5705	41	13	to	to	PART
cana-5705	41	14	show	show	VERB
cana-5705	41	15	the	the	DET
cana-5705	41	16	accuracy	accuracy	NOUN
cana-5705	41	17	of	of	ADP
cana-5705	41	18	the	the	DET
cana-5705	41	19	method	method	NOUN
cana-5705	41	20	.	.	PUNCT
cana-5705	42	1	the	the	DET
cana-5705	42	2	approximate	approximate	ADJ
cana-5705	42	3	solutions	solution	NOUN
cana-5705	42	4	of	of	ADP
cana-5705	42	5	the	the	DET
cana-5705	42	6	equation	equation	NOUN
cana-5705	42	7	have	have	AUX
cana-5705	42	8	been	be	AUX
cana-5705	42	9	computed	compute	VERB
cana-5705	42	10	.	.	PUNCT
cana-5705	43	1	numerical	numerical	ADJ
cana-5705	43	2	solution	solution	NOUN
cana-5705	43	3	is	be	AUX
cana-5705	43	4	compared	compare	VERB
cana-5705	43	5	with	with	ADP
cana-5705	43	6	exact	exact	ADJ
cana-5705	43	7	solution	solution	NOUN
cana-5705	43	8	and	and	CCONJ
cana-5705	43	9	it	it	PRON
cana-5705	43	10	is	be	AUX
cana-5705	43	11	found	find	VERB
cana-5705	43	12	that	that	SCONJ
cana-5705	43	13	they	they	PRON
cana-5705	43	14	are	be	AUX
cana-5705	43	15	almost	almost	ADV
cana-5705	43	16	same	same	ADJ
cana-5705	43	17	.	.	PUNCT
cana-5705	44	1	so	so	ADV
cana-5705	44	2	the	the	DET
cana-5705	44	3	method	method	NOUN
cana-5705	44	4	was	be	AUX
cana-5705	44	5	proved	prove	VERB
cana-5705	44	6	to	to	PART
cana-5705	44	7	be	be	AUX
cana-5705	44	8	a	a	DET
cana-5705	44	9	very	very	ADV
cana-5705	44	10	good	good	ADJ
cana-5705	44	11	alternative	alternative	ADJ
cana-5705	44	12	method	method	NOUN
cana-5705	44	13	to	to	ADP
cana-5705	44	14	some	some	DET
cana-5705	44	15	available	available	ADJ
cana-5705	44	16	techniques	technique	NOUN
cana-5705	44	17	in	in	ADP
cana-5705	44	18	various	various	ADJ
cana-5705	44	19	realistic	realistic	ADJ
cana-5705	44	20	problems	problem	NOUN
cana-5705	44	21	.	.	PUNCT
cana-5705	45	1	in	in	ADP
cana-5705	45	2	hptm	hptm	NOUN
cana-5705	45	3	,	,	PUNCT
cana-5705	45	4	the	the	DET
cana-5705	45	5	nonlinear	nonlinear	ADJ
cana-5705	45	6	terms	term	NOUN
cana-5705	45	7	can	can	AUX
cana-5705	45	8	be	be	AUX
cana-5705	45	9	easily	easily	ADV
cana-5705	45	10	simplified	simplify	VERB
cana-5705	45	11	by	by	ADP
cana-5705	45	12	the	the	DET
cana-5705	45	13	use	use	NOUN
cana-5705	45	14	of	of	ADP
cana-5705	45	15	he	he	PRON
cana-5705	45	16	’s	’	VERB
cana-5705	45	17	polynomials	polynomial	NOUN
cana-5705	45	18	is	be	AUX
cana-5705	45	19	shown	show	VERB
cana-5705	45	20	by	by	ADP
cana-5705	45	21	khan	khan	PROPN
cana-5705	45	22	and	and	CCONJ
cana-5705	45	23	wu	wu	PROPN
cana-5705	45	24	(	(	PUNCT
cana-5705	45	25	2010	2010	NUM
cana-5705	45	26	)	)	PUNCT
cana-5705	46	1	[	[	X
cana-5705	46	2	5	5	NUM
cana-5705	46	3	]	]	PUNCT
cana-5705	46	4	.	.	PUNCT
cana-5705	47	1	gupta	gupta	PROPN
cana-5705	47	2	and	and	CCONJ
cana-5705	47	3	gupta	gupta	PROPN
cana-5705	47	4	(	(	PUNCT
cana-5705	47	5	2011	2011	NUM
cana-5705	47	6	)	)	PUNCT
cana-5705	48	1	[	[	X
cana-5705	48	2	6	6	NUM
cana-5705	48	3	]	]	PUNCT
cana-5705	48	4	had	have	AUX
cana-5705	48	5	showed	show	VERB
cana-5705	48	6	applications	application	NOUN
cana-5705	48	7	of	of	ADP
cana-5705	48	8	homotopy	homotopy	NOUN
cana-5705	48	9	perturbation	perturbation	NOUN
cana-5705	48	10	transform	transform	NOUN
cana-5705	48	11	method	method	NOUN
cana-5705	48	12	for	for	ADP
cana-5705	48	13	solving	solve	VERB
cana-5705	48	14	initial	initial	ADJ
cana-5705	48	15	boundary	boundary	ADJ
cana-5705	48	16	value	value	NOUN
cana-5705	48	17	problem	problem	NOUN
cana-5705	48	18	of	of	ADP
cana-5705	48	19	variable	variable	ADJ
cana-5705	48	20	coefficients	coefficient	NOUN
cana-5705	48	21	.	.	PUNCT
cana-5705	49	1	madani	madani	PROPN
cana-5705	49	2	et	et	PROPN
cana-5705	49	3	al	al	PROPN
cana-5705	49	4	(	(	PUNCT
cana-5705	49	5	2011	2011	NUM
cana-5705	49	6	)	)	PUNCT
cana-5705	50	1	[	[	X
cana-5705	50	2	7	7	X
cana-5705	50	3	]	]	PUNCT
cana-5705	50	4	applied	apply	VERB
cana-5705	50	5	the	the	DET
cana-5705	50	6	technique	technique	NOUN
cana-5705	50	7	in	in	ADP
cana-5705	50	8	mathematical	mathematical	ADJ
cana-5705	50	9	modelling	modelling	NOUN
cana-5705	50	10	.	.	PUNCT
cana-5705	51	1	by	by	ADP
cana-5705	51	2	using	use	VERB
cana-5705	51	3	this	this	DET
cana-5705	51	4	new	new	ADJ
cana-5705	51	5	method	method	NOUN
cana-5705	51	6	,	,	PUNCT
cana-5705	51	7	a	a	DET
cana-5705	51	8	combination	combination	NOUN
cana-5705	51	9	of	of	ADP
cana-5705	51	10	the	the	DET
cana-5705	51	11	laplace	laplace	NOUN
cana-5705	51	12	transforms	transform	VERB
cana-5705	51	13	and	and	CCONJ
cana-5705	51	14	homotopy	homotopy	VERB
cana-5705	51	15	perturbation	perturbation	NOUN
cana-5705	51	16	method	method	NOUN
cana-5705	51	17	(	(	PUNCT
cana-5705	51	18	lhpm	lhpm	NOUN
cana-5705	51	19	)	)	PUNCT
cana-5705	51	20	,	,	PUNCT
cana-5705	51	21	all	all	DET
cana-5705	51	22	conditions	condition	NOUN
cana-5705	51	23	could	could	AUX
cana-5705	51	24	be	be	AUX
cana-5705	51	25	satisfied	satisfied	ADJ
cana-5705	51	26	.	.	PUNCT
cana-5705	52	1	also	also	ADV
cana-5705	52	2	,	,	PUNCT
cana-5705	52	3	very	very	ADV
cana-5705	52	4	accurate	accurate	ADJ
cana-5705	52	5	results	result	NOUN
cana-5705	52	6	were	be	AUX
cana-5705	52	7	obtained	obtain	VERB
cana-5705	52	8	in	in	ADP
cana-5705	52	9	a	a	DET
cana-5705	52	10	wide	wide	ADJ
cana-5705	52	11	range	range	NOUN
cana-5705	52	12	via	via	ADP
cana-5705	52	13	one	one	NUM
cana-5705	52	14	or	or	CCONJ
cana-5705	52	15	two	two	NUM
cana-5705	52	16	iteration	iteration	NOUN
cana-5705	52	17	steps	step	NOUN
cana-5705	52	18	.	.	PUNCT
cana-5705	53	1	second	second	ADJ
cana-5705	53	2	order	order	NOUN
cana-5705	53	3	equation	equation	NOUN
cana-5705	53	4	with	with	ADP
cana-5705	53	5	respect	respect	NOUN
cana-5705	53	6	to	to	ADP
cana-5705	53	7	t	t	PROPN
cana-5705	53	8	is	be	AUX
cana-5705	53	9	also	also	ADV
cana-5705	53	10	giving	give	VERB
cana-5705	53	11	exact	exact	ADJ
cana-5705	53	12	solution	solution	NOUN
cana-5705	53	13	with	with	ADP
cana-5705	53	14	this	this	DET
cana-5705	53	15	method	method	NOUN
cana-5705	53	16	.	.	PUNCT
cana-5705	54	1	it	it	PRON
cana-5705	54	2	was	be	AUX
cana-5705	54	3	proposed	propose	VERB
cana-5705	54	4	that	that	SCONJ
cana-5705	54	5	laplace	laplace	NOUN
cana-5705	54	6	transform	transform	VERB
cana-5705	54	7	homotopy	homotopy	NOUN
cana-5705	54	8	perturbation	perturbation	NOUN
cana-5705	54	9	method	method	NOUN
cana-5705	54	10	(	(	PUNCT
cana-5705	54	11	lhpm	lhpm	NOUN
cana-5705	54	12	)	)	PUNCT
cana-5705	54	13	to	to	PART
cana-5705	54	14	be	be	AUX
cana-5705	54	15	used	use	VERB
cana-5705	54	16	to	to	PART
cana-5705	54	17	handle	handle	VERB
cana-5705	54	18	the	the	DET
cana-5705	54	19	time	time	NOUN
cana-5705	54	20	dependent	dependent	ADJ
cana-5705	54	21	non	non	ADJ
cana-5705	54	22	-	-	ADJ
cana-5705	54	23	homogeneous	homogeneous	ADJ
cana-5705	54	24	partial	partial	ADJ
cana-5705	54	25	differential	differential	NOUN
cana-5705	54	26	equations	equation	NOUN
cana-5705	54	27	.	.	PUNCT
cana-5705	55	1	furthermore	furthermore	ADV
cana-5705	55	2	,	,	PUNCT
cana-5705	55	3	comparisons	comparison	NOUN
cana-5705	55	4	were	be	AUX
cana-5705	55	5	made	make	VERB
cana-5705	55	6	between	between	ADP
cana-5705	55	7	the	the	DET
cana-5705	55	8	present	present	ADJ
cana-5705	55	9	method	method	NOUN
cana-5705	55	10	and	and	CCONJ
cana-5705	55	11	the	the	DET
cana-5705	55	12	hpm	hpm	NOUN
cana-5705	55	13	,	,	PUNCT
cana-5705	55	14	in	in	ADP
cana-5705	55	15	order	order	NOUN
cana-5705	55	16	to	to	PART
cana-5705	55	17	verify	verify	VERB
cana-5705	55	18	the	the	DET
cana-5705	55	19	efficiency	efficiency	NOUN
cana-5705	55	20	of	of	ADP
cana-5705	55	21	the	the	DET
cana-5705	55	22	present	present	ADJ
cana-5705	55	23	method	method	NOUN
cana-5705	55	24	for	for	ADP
cana-5705	55	25	its	its	PRON
cana-5705	55	26	application	application	NOUN
cana-5705	55	27	on	on	ADP
cana-5705	55	28	wider	wide	ADJ
cana-5705	55	29	range	range	NOUN
cana-5705	55	30	.	.	PUNCT
cana-5705	56	1	majid	majid	PROPN
cana-5705	56	2	khan	khan	PROPN
cana-5705	56	3	et	et	PROPN
cana-5705	56	4	al	al	PROPN
cana-5705	56	5	(	(	PUNCT
cana-5705	56	6	2012	2012	NUM
cana-5705	56	7	)	)	PUNCT
cana-5705	57	1	[	[	X
cana-5705	57	2	8	8	NUM
cana-5705	57	3	]	]	PUNCT
cana-5705	57	4	had	have	AUX
cana-5705	57	5	given	give	VERB
cana-5705	57	6	the	the	DET
cana-5705	57	7	approximate	approximate	ADJ
cana-5705	57	8	solution	solution	NOUN
cana-5705	57	9	of	of	ADP
cana-5705	57	10	nonlinear	nonlinear	ADJ
cana-5705	57	11	blasius	blasius	NOUN
cana-5705	57	12	flow	flow	NOUN
cana-5705	57	13	equations	equation	NOUN
cana-5705	57	14	by	by	ADP
cana-5705	57	15	using	use	VERB
cana-5705	57	16	homotopy	homotopy	NOUN
cana-5705	57	17	analysis	analysis	NOUN
cana-5705	57	18	transform	transform	NOUN
cana-5705	57	19	method	method	NOUN
cana-5705	57	20	(	(	PUNCT
cana-5705	57	21	hatm	hatm	ADJ
cana-5705	57	22	)	)	PUNCT
cana-5705	57	23	and	and	CCONJ
cana-5705	57	24	hptm	hptm	NOUN
cana-5705	57	25	.	.	PUNCT
cana-5705	58	1	the	the	DET
cana-5705	58	2	nonlinear	nonlinear	ADJ
cana-5705	58	3	terms	term	NOUN
cana-5705	58	4	are	be	AUX
cana-5705	58	5	simplified	simplify	VERB
cana-5705	58	6	with	with	ADP
cana-5705	58	7	the	the	DET
cana-5705	58	8	help	help	NOUN
cana-5705	58	9	of	of	ADP
cana-5705	58	10	he	he	PRON
cana-5705	58	11	’s	’	VERB
cana-5705	58	12	polynomials	polynomial	NOUN
cana-5705	58	13	.	.	PUNCT
cana-5705	59	1	the	the	DET
cana-5705	59	2	solution	solution	NOUN
cana-5705	59	3	obtained	obtain	VERB
cana-5705	59	4	with	with	ADP
cana-5705	59	5	hatm	hatm	PROPN
cana-5705	59	6	is	be	AUX
cana-5705	59	7	compared	compare	VERB
cana-5705	59	8	with	with	ADP
cana-5705	59	9	hptm	hptm	NOUN
cana-5705	59	10	and	and	CCONJ
cana-5705	59	11	other	other	ADJ
cana-5705	59	12	iterative	iterative	NOUN
cana-5705	59	13	methods	method	NOUN
cana-5705	59	14	.	.	PUNCT
cana-5705	60	1	jagdev	jagdev	PROPN
cana-5705	60	2	singh	singh	PROPN
cana-5705	60	3	et	et	PROPN
cana-5705	60	4	al	al	PROPN
cana-5705	60	5	(	(	PUNCT
cana-5705	60	6	2012	2012	NUM
cana-5705	60	7	)	)	PUNCT
cana-5705	61	1	[	[	X
cana-5705	61	2	9	9	NUM
cana-5705	61	3	]	]	PUNCT
cana-5705	61	4	have	have	AUX
cana-5705	61	5	applied	apply	VERB
cana-5705	61	6	hptm	hptm	NOUN
cana-5705	61	7	for	for	ADP
cana-5705	61	8	linear	linear	PROPN
cana-5705	61	9	and	and	CCONJ
cana-5705	61	10	non	non	ADJ
cana-5705	61	11	-	-	ADJ
cana-5705	61	12	linear	linear	ADJ
cana-5705	61	13	klein	klein	PROPN
cana-5705	61	14	-	-	PUNCT
cana-5705	61	15	gordon	gordon	PROPN
cana-5705	61	16	equations	equation	NOUN
cana-5705	61	17	.	.	PUNCT
cana-5705	62	1	devendra	devendra	PROPN
cana-5705	62	2	kumar	kumar	PROPN
cana-5705	62	3	et	et	PROPN
cana-5705	62	4	al	al	PROPN
cana-5705	62	5	(	(	PUNCT
cana-5705	62	6	2013	2013	NUM
cana-5705	62	7	)	)	PUNCT
cana-5705	63	1	[	[	X
cana-5705	63	2	10	10	NUM
cana-5705	63	3	]	]	PUNCT
cana-5705	63	4	have	have	AUX
cana-5705	63	5	applied	apply	VERB
cana-5705	63	6	the	the	DET
cana-5705	63	7	homotopy	homotopy	NOUN
cana-5705	63	8	perturbation	perturbation	NOUN
cana-5705	63	9	transform	transform	NOUN
cana-5705	63	10	method	method	NOUN
cana-5705	63	11	(	(	PUNCT
cana-5705	63	12	hptm	hptm	NOUN
cana-5705	63	13	)	)	PUNCT
cana-5705	63	14	to	to	PART
cana-5705	63	15	obtain	obtain	VERB
cana-5705	63	16	the	the	DET
cana-5705	63	17	solution	solution	NOUN
cana-5705	63	18	of	of	ADP
cana-5705	63	19	linear	linear	PROPN
cana-5705	63	20	and	and	CCONJ
cana-5705	63	21	nonlinear	nonlinear	ADJ
cana-5705	63	22	schrodinger	schrodinger	PROPN
cana-5705	63	23	equations	equation	NOUN
cana-5705	63	24	.	.	PUNCT
cana-5705	64	1	the	the	DET
cana-5705	64	2	main	main	ADJ
cana-5705	64	3	feature	feature	NOUN
cana-5705	64	4	of	of	ADP
cana-5705	64	5	this	this	DET
cana-5705	64	6	method	method	NOUN
cana-5705	64	7	is	be	AUX
cana-5705	64	8	to	to	PART
cana-5705	64	9	find	find	VERB
cana-5705	64	10	the	the	DET
cana-5705	64	11	solution	solution	NOUN
cana-5705	64	12	without	without	ADP
cana-5705	64	13	any	any	DET
cana-5705	64	14	discretization	discretization	NOUN
cana-5705	64	15	or	or	CCONJ
cana-5705	64	16	restrictive	restrictive	ADJ
cana-5705	64	17	assumptions	assumption	NOUN
cana-5705	64	18	and	and	CCONJ
cana-5705	64	19	avoids	avoid	VERB
cana-5705	64	20	the	the	DET
cana-5705	64	21	round	round	VERB
cana-5705	64	22	-	-	PUNCT
cana-5705	64	23	off	off	ADP
cana-5705	64	24	errors	error	NOUN
cana-5705	64	25	.	.	PUNCT
cana-5705	65	1	the	the	DET
cana-5705	65	2	fact	fact	NOUN
cana-5705	65	3	that	that	SCONJ
cana-5705	65	4	this	this	DET
cana-5705	65	5	technique	technique	NOUN
cana-5705	65	6	solves	solve	VERB
cana-5705	65	7	nonlinear	nonlinear	ADJ
cana-5705	65	8	problems	problem	NOUN
cana-5705	65	9	without	without	ADP
cana-5705	65	10	using	use	VERB
cana-5705	65	11	adomian	adomian	NOUN
cana-5705	65	12	polynomials	polynomial	NOUN
cana-5705	65	13	can	can	AUX
cana-5705	65	14	be	be	AUX
cana-5705	65	15	considered	consider	VERB
cana-5705	65	16	as	as	ADP
cana-5705	65	17	a	a	DET
cana-5705	65	18	clear	clear	ADJ
cana-5705	65	19	advantage	advantage	NOUN
cana-5705	65	20	of	of	ADP
cana-5705	65	21	this	this	DET
cana-5705	65	22	algorithm	algorithm	NOUN
cana-5705	65	23	over	over	ADP
cana-5705	65	24	the	the	DET
cana-5705	65	25	adomian	adomian	NOUN
cana-5705	65	26	decomposition	decomposition	NOUN
cana-5705	65	27	method	method	NOUN
cana-5705	65	28	(	(	PUNCT
cana-5705	65	29	adm	adm	PROPN
cana-5705	65	30	)	)	PUNCT
cana-5705	65	31	.	.	PUNCT
cana-5705	66	1	u.	u.	PROPN
cana-5705	66	2	filobello	filobello	PROPN
cana-5705	66	3	-	-	PUNCT
cana-5705	66	4	nino	nino	PROPN
cana-5705	66	5	et	et	PROPN
cana-5705	66	6	al	al	PROPN
cana-5705	66	7	(	(	PUNCT
cana-5705	66	8	2013	2013	NUM
cana-5705	66	9	)	)	PUNCT
cana-5705	67	1	[	[	X
cana-5705	67	2	11	11	NUM
cana-5705	67	3	]	]	PUNCT
cana-5705	67	4	have	have	AUX
cana-5705	67	5	proposed	propose	VERB
cana-5705	67	6	this	this	DET
cana-5705	67	7	method	method	NOUN
cana-5705	67	8	to	to	PART
cana-5705	67	9	solve	solve	VERB
cana-5705	67	10	nonlinear	nonlinear	ADJ
cana-5705	67	11	differential	differential	ADJ
cana-5705	67	12	equation	equation	NOUN
cana-5705	67	13	with	with	ADP
cana-5705	67	14	dirichlet	dirichlet	PROPN
cana-5705	67	15	,	,	PUNCT
cana-5705	67	16	neumann	neumann	PROPN
cana-5705	67	17	and	and	CCONJ
cana-5705	67	18	mixed	mixed	ADJ
cana-5705	67	19	boundary	boundary	ADJ
cana-5705	67	20	conditions	condition	NOUN
cana-5705	67	21	.	.	PUNCT
cana-5705	68	1	comparison	comparison	NOUN
cana-5705	68	2	is	be	AUX
cana-5705	68	3	made	make	VERB
cana-5705	68	4	between	between	ADP
cana-5705	68	5	the	the	DET
cana-5705	68	6	figures	figure	NOUN
cana-5705	68	7	of	of	ADP
cana-5705	68	8	exact	exact	ADJ
cana-5705	68	9	and	and	CCONJ
cana-5705	68	10	approximate	approximate	ADJ
cana-5705	68	11	solutions	solution	NOUN
cana-5705	68	12	,	,	PUNCT
cana-5705	68	13	and	and	CCONJ
cana-5705	68	14	it	it	PRON
cana-5705	68	15	is	be	AUX
cana-5705	68	16	seen	see	VERB
cana-5705	68	17	that	that	SCONJ
cana-5705	68	18	they	they	PRON
cana-5705	68	19	are	be	AUX
cana-5705	68	20	of	of	ADP
cana-5705	68	21	high	high	ADJ
cana-5705	68	22	accuracy	accuracy	NOUN
cana-5705	68	23	.	.	PUNCT
cana-5705	69	1	another	another	DET
cana-5705	69	2	advantage	advantage	NOUN
cana-5705	69	3	of	of	ADP
cana-5705	69	4	this	this	DET
cana-5705	69	5	method	method	NOUN
cana-5705	69	6	is	be	AUX
cana-5705	69	7	that	that	SCONJ
cana-5705	69	8	,	,	PUNCT
cana-5705	69	9	we	we	PRON
cana-5705	69	10	need	need	AUX
cana-5705	69	11	not	not	PART
cana-5705	69	12	have	have	VERB
cana-5705	69	13	to	to	PART
cana-5705	69	14	solve	solve	VERB
cana-5705	69	15	several	several	ADJ
cana-5705	69	16	recurrence	recurrence	NOUN
cana-5705	69	17	differential	differential	ADJ
cana-5705	69	18	equations	equation	NOUN
cana-5705	69	19	.	.	PUNCT
cana-5705	70	1	communications	communication	NOUN
cana-5705	70	2	on	on	ADP
cana-5705	70	3	applied	apply	VERB
cana-5705	70	4	nonlinear	nonlinear	ADJ
cana-5705	70	5	analysis	analysis	NOUN
cana-5705	70	6	issn	issn	NOUN
cana-5705	70	7	:	:	PUNCT
cana-5705	70	8	1074	1074	NUM
cana-5705	70	9	-	-	PUNCT
cana-5705	70	10	133x	133x	NUM
cana-5705	70	11	vol	vol	VERB
cana-5705	70	12	32	32	NUM
cana-5705	70	13	no	no	NOUN
cana-5705	70	14	.	.	PUNCT
cana-5705	71	1	10s	10	NOUN
cana-5705	71	2	(	(	PUNCT
cana-5705	71	3	2025	2025	NUM
cana-5705	71	4	)	)	PUNCT
cana-5705	71	5	2655	2655	NUM
cana-5705	71	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5705	72	1	saleem	saleem	PROPN
cana-5705	72	2	et	et	PROPN
cana-5705	72	3	al	al	PROPN
cana-5705	72	4	(	(	PUNCT
cana-5705	72	5	2017	2017	NUM
cana-5705	72	6	)	)	PUNCT
cana-5705	73	1	[	[	X
cana-5705	73	2	12	12	NUM
cana-5705	73	3	]	]	PUNCT
cana-5705	73	4	demonstrated	demonstrate	VERB
cana-5705	73	5	that	that	SCONJ
cana-5705	73	6	,	,	PUNCT
cana-5705	73	7	for	for	ADP
cana-5705	73	8	solving	solve	VERB
cana-5705	73	9	nonlinear	nonlinear	ADJ
cana-5705	73	10	equations	equation	NOUN
cana-5705	73	11	,	,	PUNCT
cana-5705	73	12	a	a	DET
cana-5705	73	13	combination	combination	NOUN
cana-5705	73	14	form	form	NOUN
cana-5705	73	15	of	of	ADP
cana-5705	73	16	the	the	DET
cana-5705	73	17	laplace	laplace	NOUN
cana-5705	73	18	transform	transform	NOUN
cana-5705	73	19	method	method	NOUN
cana-5705	73	20	along	along	ADP
cana-5705	73	21	with	with	ADP
cana-5705	73	22	the	the	DET
cana-5705	73	23	homotopy	homotopy	NOUN
cana-5705	73	24	perturbation	perturbation	NOUN
cana-5705	73	25	method	method	NOUN
cana-5705	73	26	was	be	AUX
cana-5705	73	27	used	use	VERB
cana-5705	73	28	.	.	PUNCT
cana-5705	74	1	proposed	propose	VERB
cana-5705	74	2	method	method	NOUN
cana-5705	74	3	solves	solve	VERB
cana-5705	74	4	nonlinear	nonlinear	ADJ
cana-5705	74	5	problems	problem	NOUN
cana-5705	74	6	without	without	ADP
cana-5705	74	7	using	use	VERB
cana-5705	74	8	adomian	adomian	NOUN
cana-5705	74	9	polynomials	polynomial	NOUN
cana-5705	74	10	can	can	AUX
cana-5705	74	11	be	be	AUX
cana-5705	74	12	thought	think	VERB
cana-5705	74	13	as	as	ADP
cana-5705	74	14	a	a	DET
cana-5705	74	15	vibrant	vibrant	ADJ
cana-5705	74	16	advantage	advantage	NOUN
cana-5705	74	17	of	of	ADP
cana-5705	74	18	this	this	DET
cana-5705	74	19	algorithm	algorithm	NOUN
cana-5705	74	20	over	over	ADP
cana-5705	74	21	the	the	DET
cana-5705	74	22	adomian	adomian	NOUN
cana-5705	74	23	decomposition	decomposition	NOUN
cana-5705	74	24	method	method	NOUN
cana-5705	74	25	.	.	PUNCT
cana-5705	75	1	swielam	swielam	PROPN
cana-5705	75	2	and	and	CCONJ
cana-5705	75	3	khadar	khadar	PROPN
cana-5705	75	4	(	(	PUNCT
cana-5705	75	5	2018	2018	NUM
cana-5705	75	6	)	)	PUNCT
cana-5705	76	1	[	[	X
cana-5705	76	2	13	13	NUM
cana-5705	76	3	]	]	PUNCT
cana-5705	76	4	obtained	obtain	VERB
cana-5705	76	5	exact	exact	ADJ
cana-5705	76	6	solution	solution	NOUN
cana-5705	76	7	of	of	ADP
cana-5705	76	8	some	some	DET
cana-5705	76	9	coupled	couple	VERB
cana-5705	76	10	non	non	ADJ
cana-5705	76	11	-	-	ADJ
cana-5705	76	12	linear	linear	ADJ
cana-5705	76	13	differential	differential	ADJ
cana-5705	76	14	equations	equation	NOUN
cana-5705	76	15	using	use	VERB
cana-5705	76	16	homotopy	homotopy	NOUN
cana-5705	76	17	perturbation	perturbation	NOUN
cana-5705	76	18	method	method	NOUN
cana-5705	76	19	using	use	VERB
cana-5705	76	20	laplace	laplace	NOUN
cana-5705	76	21	transform	transform	NOUN
cana-5705	76	22	and	and	CCONJ
cana-5705	76	23	pade	pade	NOUN
cana-5705	76	24	approximation	approximation	NOUN
cana-5705	76	25	.	.	PUNCT
cana-5705	77	1	the	the	DET
cana-5705	77	2	examples	example	NOUN
cana-5705	77	3	are	be	AUX
cana-5705	77	4	considered	consider	VERB
cana-5705	77	5	on	on	ADP
cana-5705	77	6	the	the	DET
cana-5705	77	7	coupled	couple	VERB
cana-5705	77	8	nonlinear	nonlinear	ADJ
cana-5705	77	9	system	system	NOUN
cana-5705	77	10	of	of	ADP
cana-5705	77	11	burger	burger	NOUN
cana-5705	77	12	equations	equation	NOUN
cana-5705	77	13	and	and	CCONJ
cana-5705	77	14	the	the	DET
cana-5705	77	15	coupled	couple	VERB
cana-5705	77	16	nonlinear	nonlinear	ADJ
cana-5705	77	17	system	system	NOUN
cana-5705	77	18	in	in	ADP
cana-5705	77	19	one	one	NUM
cana-5705	77	20	dimensional	dimensional	ADJ
cana-5705	77	21	thermoelasticity	thermoelasticity	NOUN
cana-5705	77	22	.	.	PUNCT
cana-5705	78	1	the	the	DET
cana-5705	78	2	results	result	NOUN
cana-5705	78	3	obtained	obtain	VERB
cana-5705	78	4	are	be	AUX
cana-5705	78	5	verified	verify	VERB
cana-5705	78	6	with	with	ADP
cana-5705	78	7	exact	exact	ADJ
cana-5705	78	8	solutions	solution	NOUN
cana-5705	78	9	.	.	PUNCT
cana-5705	79	1	so	so	ADV
cana-5705	79	2	the	the	DET
cana-5705	79	3	method	method	NOUN
cana-5705	79	4	is	be	AUX
cana-5705	79	5	strongly	strongly	ADV
cana-5705	79	6	applicable	applicable	ADJ
cana-5705	79	7	in	in	ADP
cana-5705	79	8	solving	solve	VERB
cana-5705	79	9	large	large	ADJ
cana-5705	79	10	number	number	NOUN
cana-5705	79	11	of	of	ADP
cana-5705	79	12	nonlinear	nonlinear	ADJ
cana-5705	79	13	differential	differential	ADJ
cana-5705	79	14	equations	equation	NOUN
cana-5705	79	15	.	.	PUNCT
cana-5705	80	1	comparison	comparison	NOUN
cana-5705	80	2	of	of	ADP
cana-5705	80	3	homotopy	homotopy	NOUN
cana-5705	80	4	perturbation	perturbation	NOUN
cana-5705	80	5	method	method	NOUN
cana-5705	80	6	(	(	PUNCT
cana-5705	80	7	hpm	hpm	NOUN
cana-5705	80	8	)	)	PUNCT
cana-5705	80	9	and	and	CCONJ
cana-5705	80	10	homotopy	homotopy	VERB
cana-5705	80	11	perturbation	perturbation	NOUN
cana-5705	80	12	transform	transform	NOUN
cana-5705	80	13	method	method	NOUN
cana-5705	80	14	(	(	PUNCT
cana-5705	80	15	hptm	hptm	NOUN
cana-5705	80	16	)	)	PUNCT
cana-5705	80	17	is	be	AUX
cana-5705	80	18	effectively	effectively	ADV
cana-5705	80	19	shown	show	VERB
cana-5705	80	20	by	by	ADP
cana-5705	80	21	mohammad	mohammad	PROPN
cana-5705	80	22	elbadri	elbadri	PROPN
cana-5705	80	23	(	(	PUNCT
cana-5705	80	24	2018	2018	NUM
cana-5705	80	25	)	)	PUNCT
cana-5705	81	1	[	[	X
cana-5705	81	2	14	14	NUM
cana-5705	81	3	]	]	PUNCT
cana-5705	81	4	.	.	PUNCT
cana-5705	82	1	authors	author	NOUN
cana-5705	82	2	have	have	AUX
cana-5705	82	3	claimed	claim	VERB
cana-5705	82	4	that	that	SCONJ
cana-5705	82	5	homotopy	homotopy	NOUN
cana-5705	82	6	perturbation	perturbation	NOUN
cana-5705	82	7	transform	transform	NOUN
cana-5705	82	8	method	method	NOUN
cana-5705	82	9	is	be	AUX
cana-5705	82	10	very	very	ADV
cana-5705	82	11	fast	fast	ADJ
cana-5705	82	12	convergent	convergent	NOUN
cana-5705	82	13	to	to	ADP
cana-5705	82	14	the	the	DET
cana-5705	82	15	solution	solution	NOUN
cana-5705	82	16	of	of	ADP
cana-5705	82	17	the	the	DET
cana-5705	82	18	partial	partial	ADJ
cana-5705	82	19	differential	differential	NOUN
cana-5705	82	20	equation	equation	NOUN
cana-5705	82	21	.	.	PUNCT
cana-5705	83	1	for	for	ADP
cana-5705	83	2	illustration	illustration	NOUN
cana-5705	83	3	and	and	CCONJ
cana-5705	83	4	more	more	ADJ
cana-5705	83	5	explanation	explanation	NOUN
cana-5705	83	6	of	of	ADP
cana-5705	83	7	the	the	DET
cana-5705	83	8	idea	idea	NOUN
cana-5705	83	9	,	,	PUNCT
cana-5705	83	10	some	some	DET
cana-5705	83	11	examples	example	NOUN
cana-5705	83	12	are	be	AUX
cana-5705	83	13	provided	provide	VERB
cana-5705	83	14	through	through	ADP
cana-5705	83	15	which	which	PRON
cana-5705	83	16	it	it	PRON
cana-5705	83	17	is	be	AUX
cana-5705	83	18	shown	show	VERB
cana-5705	83	19	that	that	SCONJ
cana-5705	83	20	most	most	ADJ
cana-5705	83	21	of	of	ADP
cana-5705	83	22	the	the	DET
cana-5705	83	23	inhomogeneous	inhomogeneous	ADJ
cana-5705	83	24	problems	problem	NOUN
cana-5705	83	25	give	give	VERB
cana-5705	83	26	exact	exact	ADJ
cana-5705	83	27	solution	solution	NOUN
cana-5705	83	28	by	by	ADP
cana-5705	83	29	hptm	hptm	NOUN
cana-5705	83	30	whereas	whereas	SCONJ
cana-5705	83	31	hpm	hpm	NOUN
cana-5705	83	32	gives	give	VERB
cana-5705	83	33	an	an	DET
cana-5705	83	34	approximate	approximate	ADJ
cana-5705	83	35	solution	solution	NOUN
cana-5705	83	36	to	to	ADP
cana-5705	83	37	these	these	DET
cana-5705	83	38	problems	problem	NOUN
cana-5705	83	39	.	.	PUNCT
cana-5705	84	1	mohamed	mohamed	PROPN
cana-5705	84	2	jleli	jleli	PROPN
cana-5705	84	3	et	et	PROPN
cana-5705	84	4	al	al	PROPN
cana-5705	84	5	(	(	PUNCT
cana-5705	84	6	2020	2020	NUM
cana-5705	84	7	)	)	PUNCT
cana-5705	85	1	[	[	X
cana-5705	85	2	15	15	NUM
cana-5705	85	3	]	]	PUNCT
cana-5705	85	4	have	have	AUX
cana-5705	85	5	successfully	successfully	ADV
cana-5705	85	6	applied	apply	VERB
cana-5705	85	7	hptm	hptm	NOUN
cana-5705	85	8	for	for	ADP
cana-5705	85	9	solving	solve	VERB
cana-5705	85	10	multidimensional	multidimensional	ADJ
cana-5705	85	11	time	time	NOUN
cana-5705	85	12	fractional	fractional	ADJ
cana-5705	85	13	partial	partial	ADJ
cana-5705	85	14	differential	differential	NOUN
cana-5705	85	15	equations	equation	NOUN
cana-5705	85	16	involving	involve	VERB
cana-5705	85	17	the	the	DET
cana-5705	85	18	recent	recent	ADJ
cana-5705	85	19	introduced	introduce	VERB
cana-5705	85	20	yang	yang	PROPN
cana-5705	85	21	-	-	PUNCT
cana-5705	85	22	abdel	abdel	PROPN
cana-5705	85	23	-	-	PUNCT
cana-5705	85	24	atycattani	atycattani	NOUN
cana-5705	85	25	fractional	fractional	ADJ
cana-5705	85	26	derivative	derivative	NOUN
cana-5705	85	27	.	.	PUNCT
cana-5705	86	1	the	the	DET
cana-5705	86	2	presented	present	VERB
cana-5705	86	3	examples	example	NOUN
cana-5705	86	4	show	show	VERB
cana-5705	86	5	that	that	SCONJ
cana-5705	86	6	this	this	DET
cana-5705	86	7	approach	approach	NOUN
cana-5705	86	8	is	be	AUX
cana-5705	86	9	very	very	ADV
cana-5705	86	10	powerful	powerful	ADJ
cana-5705	86	11	and	and	CCONJ
cana-5705	86	12	efficient	efficient	ADJ
cana-5705	86	13	for	for	ADP
cana-5705	86	14	finding	find	VERB
cana-5705	86	15	approximate	approximate	ADJ
cana-5705	86	16	solutions	solution	NOUN
cana-5705	86	17	for	for	ADP
cana-5705	86	18	wide	wide	ADJ
cana-5705	86	19	classes	class	NOUN
cana-5705	86	20	of	of	ADP
cana-5705	86	21	problems	problem	NOUN
cana-5705	86	22	arising	arise	VERB
cana-5705	86	23	in	in	ADP
cana-5705	86	24	science	science	NOUN
cana-5705	86	25	and	and	CCONJ
cana-5705	86	26	technology	technology	NOUN
cana-5705	86	27	.	.	PUNCT
cana-5705	87	1	2	2	X
cana-5705	87	2	.	.	X
cana-5705	87	3	objectives	objective	NOUN
cana-5705	87	4	since	since	SCONJ
cana-5705	87	5	last	last	ADJ
cana-5705	87	6	two	two	NUM
cana-5705	87	7	decades	decade	NOUN
cana-5705	87	8	,	,	PUNCT
cana-5705	87	9	there	there	PRON
cana-5705	87	10	is	be	VERB
cana-5705	87	11	a	a	DET
cana-5705	87	12	rapid	rapid	ADJ
cana-5705	87	13	development	development	NOUN
cana-5705	87	14	in	in	ADP
cana-5705	87	15	nonlinear	nonlinear	ADJ
cana-5705	87	16	science	science	NOUN
cana-5705	87	17	.	.	PUNCT
cana-5705	88	1	many	many	ADJ
cana-5705	88	2	researchers	researcher	NOUN
cana-5705	88	3	have	have	AUX
cana-5705	88	4	used	use	VERB
cana-5705	88	5	numerical	numerical	ADJ
cana-5705	88	6	and	and	CCONJ
cana-5705	88	7	analytical	analytical	ADJ
cana-5705	88	8	technique	technique	NOUN
cana-5705	88	9	to	to	PART
cana-5705	88	10	solve	solve	VERB
cana-5705	88	11	the	the	DET
cana-5705	88	12	nonlinear	nonlinear	ADJ
cana-5705	88	13	differential	differential	ADJ
cana-5705	88	14	equations	equation	NOUN
cana-5705	88	15	.	.	PUNCT
cana-5705	89	1	diffusion	diffusion	NOUN
cana-5705	89	2	equation	equation	NOUN
cana-5705	89	3	is	be	AUX
cana-5705	89	4	one	one	NUM
cana-5705	89	5	of	of	ADP
cana-5705	89	6	these	these	DET
cana-5705	89	7	differential	differential	ADJ
cana-5705	89	8	equations	equation	NOUN
cana-5705	89	9	in	in	ADP
cana-5705	89	10	the	the	DET
cana-5705	89	11	areas	area	NOUN
cana-5705	89	12	of	of	ADP
cana-5705	89	13	heat	heat	NOUN
cana-5705	89	14	and	and	CCONJ
cana-5705	89	15	mass	mass	NOUN
cana-5705	89	16	transfer	transfer	NOUN
cana-5705	89	17	,	,	PUNCT
cana-5705	89	18	biological	biological	ADJ
cana-5705	89	19	systems	system	NOUN
cana-5705	89	20	and	and	CCONJ
cana-5705	89	21	the	the	DET
cana-5705	89	22	processes	process	NOUN
cana-5705	89	23	involving	involve	VERB
cana-5705	89	24	fluid	fluid	ADJ
cana-5705	89	25	flow	flow	NOUN
cana-5705	89	26	.	.	PUNCT
cana-5705	90	1	to	to	PART
cana-5705	90	2	solve	solve	VERB
cana-5705	90	3	these	these	DET
cana-5705	90	4	differential	differential	ADJ
cana-5705	90	5	equations	equation	NOUN
cana-5705	90	6	analytically	analytically	ADV
cana-5705	90	7	and	and	CCONJ
cana-5705	90	8	to	to	PART
cana-5705	90	9	obtain	obtain	VERB
cana-5705	90	10	formal	formal	ADJ
cana-5705	90	11	and	and	CCONJ
cana-5705	90	12	approximate	approximate	ADJ
cana-5705	90	13	solutions	solution	NOUN
cana-5705	90	14	in	in	ADP
cana-5705	90	15	the	the	DET
cana-5705	90	16	series	series	NOUN
cana-5705	90	17	form	form	NOUN
cana-5705	90	18	is	be	AUX
cana-5705	90	19	the	the	DET
cana-5705	90	20	main	main	ADJ
cana-5705	90	21	objective	objective	NOUN
cana-5705	90	22	here	here	ADV
cana-5705	90	23	.	.	PUNCT
cana-5705	91	1	in	in	ADP
cana-5705	91	2	this	this	DET
cana-5705	91	3	paper	paper	NOUN
cana-5705	91	4	,	,	PUNCT
cana-5705	91	5	homotopy	homotopy	VERB
cana-5705	91	6	perturbation	perturbation	NOUN
cana-5705	91	7	transform	transform	NOUN
cana-5705	91	8	method	method	NOUN
cana-5705	91	9	is	be	AUX
cana-5705	91	10	applied	apply	VERB
cana-5705	91	11	to	to	PART
cana-5705	91	12	solve	solve	VERB
cana-5705	91	13	these	these	DET
cana-5705	91	14	nonlinear	nonlinear	ADJ
cana-5705	91	15	diffusion	diffusion	NOUN
cana-5705	91	16	equations	equation	NOUN
cana-5705	91	17	with	with	ADP
cana-5705	91	18	various	various	ADJ
cana-5705	91	19	boundary	boundary	ADJ
cana-5705	91	20	conditions	condition	NOUN
cana-5705	91	21	.	.	PUNCT
cana-5705	92	1	3	3	X
cana-5705	92	2	.	.	X
cana-5705	92	3	methods	method	NOUN
cana-5705	92	4	the	the	DET
cana-5705	92	5	proposed	propose	VERB
cana-5705	92	6	algorithm	algorithm	NOUN
cana-5705	92	7	provides	provide	VERB
cana-5705	92	8	the	the	DET
cana-5705	92	9	solution	solution	NOUN
cana-5705	92	10	in	in	ADP
cana-5705	92	11	a	a	DET
cana-5705	92	12	rapid	rapid	ADJ
cana-5705	92	13	convergent	convergent	NOUN
cana-5705	92	14	series	series	NOUN
cana-5705	92	15	which	which	PRON
cana-5705	92	16	may	may	AUX
cana-5705	92	17	lead	lead	VERB
cana-5705	92	18	to	to	ADP
cana-5705	92	19	the	the	DET
cana-5705	92	20	solution	solution	NOUN
cana-5705	92	21	in	in	ADP
cana-5705	92	22	a	a	DET
cana-5705	92	23	closed	closed	ADJ
cana-5705	92	24	form	form	NOUN
cana-5705	92	25	.	.	PUNCT
cana-5705	93	1	the	the	DET
cana-5705	93	2	advantage	advantage	NOUN
cana-5705	93	3	of	of	ADP
cana-5705	93	4	this	this	DET
cana-5705	93	5	method	method	NOUN
cana-5705	93	6	is	be	AUX
cana-5705	93	7	its	its	PRON
cana-5705	93	8	capability	capability	NOUN
cana-5705	93	9	of	of	ADP
cana-5705	93	10	combining	combine	VERB
cana-5705	93	11	two	two	NUM
cana-5705	93	12	powerful	powerful	ADJ
cana-5705	93	13	methods	method	NOUN
cana-5705	93	14	for	for	ADP
cana-5705	93	15	obtaining	obtain	VERB
cana-5705	93	16	exact	exact	ADJ
cana-5705	93	17	or	or	CCONJ
cana-5705	93	18	approximate	approximate	ADJ
cana-5705	93	19	solution	solution	NOUN
cana-5705	93	20	for	for	ADP
cana-5705	93	21	non	non	ADJ
cana-5705	93	22	-	-	ADJ
cana-5705	93	23	linear	linear	ADJ
cana-5705	93	24	equations	equation	NOUN
cana-5705	93	25	.	.	PUNCT
cana-5705	94	1	to	to	PART
cana-5705	94	2	illustrate	illustrate	VERB
cana-5705	94	3	the	the	DET
cana-5705	94	4	basic	basic	ADJ
cana-5705	94	5	idea	idea	NOUN
cana-5705	94	6	for	for	ADP
cana-5705	94	7	hptm	hptm	NOUN
cana-5705	94	8	,	,	PUNCT
cana-5705	94	9	we	we	PRON
cana-5705	94	10	consider	consider	VERB
cana-5705	94	11	a	a	DET
cana-5705	94	12	general	general	ADJ
cana-5705	94	13	non	non	ADJ
cana-5705	94	14	-	-	ADJ
cana-5705	94	15	linear	linear	ADJ
cana-5705	94	16	partial	partial	ADJ
cana-5705	94	17	differential	differential	NOUN
cana-5705	94	18	equation	equation	NOUN
cana-5705	94	19	with	with	ADP
cana-5705	94	20	the	the	DET
cana-5705	94	21	initial	initial	ADJ
cana-5705	94	22	conditions	condition	NOUN
cana-5705	94	23	of	of	ADP
cana-5705	94	24	the	the	DET
cana-5705	94	25	form	form	NOUN
cana-5705	94	26	𝐷𝜃(𝑥	𝐷𝜃(𝑥	NOUN
cana-5705	94	27	,	,	PUNCT
cana-5705	94	28	𝑡	𝑡	NOUN
cana-5705	94	29	)	)	PUNCT
cana-5705	94	30	+	+	CCONJ
cana-5705	94	31	𝑅𝜃(𝑥	𝑅𝜃(𝑥	PROPN
cana-5705	94	32	,	,	PUNCT
cana-5705	94	33	𝑡	𝑡	X
cana-5705	94	34	)	)	PUNCT
cana-5705	94	35	+	+	NUM
cana-5705	94	36	𝑁𝜃(𝑥	𝑁𝜃(𝑥	PROPN
cana-5705	94	37	,	,	PUNCT
cana-5705	94	38	𝑡	𝑡	NOUN
cana-5705	94	39	)	)	PUNCT
cana-5705	94	40	=	=	SYM
cana-5705	94	41	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5705	94	42	,	,	PUNCT
cana-5705	94	43	𝑡	𝑡	NOUN
cana-5705	94	44	)	)	PUNCT
cana-5705	94	45	(	(	PUNCT
cana-5705	94	46	1	1	NUM
cana-5705	94	47	)	)	PUNCT
cana-5705	94	48	with	with	ADP
cana-5705	94	49	initial	initial	ADJ
cana-5705	94	50	condition	condition	NOUN
cana-5705	94	51	𝜃(𝑥	𝜃(𝑥	NOUN
cana-5705	94	52	,	,	PUNCT
cana-5705	94	53	0	0	NUM
cana-5705	94	54	)	)	PUNCT
cana-5705	94	55	=	=	X
cana-5705	94	56	ℎ(𝑥	ℎ(𝑥	NOUN
cana-5705	94	57	)	)	PUNCT
cana-5705	94	58	and	and	CCONJ
cana-5705	95	1	𝜃𝑡	𝜃𝑡	ADV
cana-5705	95	2	(	(	PUNCT
cana-5705	95	3	𝑥	𝑥	NOUN
cana-5705	95	4	,	,	PUNCT
cana-5705	95	5	0	0	NUM
cana-5705	95	6	)	)	PUNCT
cana-5705	95	7	=	=	SYM
cana-5705	95	8	𝑔(𝑥	𝑔(𝑥	NOUN
cana-5705	95	9	)	)	PUNCT
cana-5705	95	10	where	where	SCONJ
cana-5705	95	11	d	d	NOUN
cana-5705	95	12	=	=	SYM
cana-5705	95	13	𝜕2	𝜕2	NOUN
cana-5705	95	14	𝜕𝑡2	𝜕𝑡2	NOUN
cana-5705	95	15	,	,	PUNCT
cana-5705	95	16	r	r	NOUN
cana-5705	95	17	is	be	AUX
cana-5705	95	18	the	the	DET
cana-5705	95	19	linear	linear	ADJ
cana-5705	95	20	differential	differential	NOUN
cana-5705	95	21	operator	operator	NOUN
cana-5705	95	22	of	of	ADP
cana-5705	95	23	less	less	ADJ
cana-5705	95	24	order	order	NOUN
cana-5705	95	25	than	than	ADP
cana-5705	95	26	d	d	PROPN
cana-5705	95	27	,	,	PUNCT
cana-5705	95	28	n	n	PRON
cana-5705	95	29	represents	represent	VERB
cana-5705	95	30	the	the	DET
cana-5705	95	31	general	general	ADJ
cana-5705	95	32	nonlinear	nonlinear	ADJ
cana-5705	95	33	differential	differential	NOUN
cana-5705	95	34	operator	operator	NOUN
cana-5705	95	35	and	and	CCONJ
cana-5705	95	36	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5705	95	37	,	,	PUNCT
cana-5705	95	38	𝑡	𝑡	NOUN
cana-5705	95	39	)	)	PUNCT
cana-5705	95	40	is	be	AUX
cana-5705	95	41	the	the	DET
cana-5705	95	42	source	source	NOUN
cana-5705	95	43	term	term	NOUN
cana-5705	95	44	.	.	PUNCT
cana-5705	96	1	taking	take	VERB
cana-5705	96	2	laplace	laplace	NOUN
cana-5705	96	3	transform	transform	NOUN
cana-5705	96	4	of	of	ADP
cana-5705	96	5	both	both	DET
cana-5705	96	6	sides	side	NOUN
cana-5705	96	7	of	of	ADP
cana-5705	96	8	eq	eq	PROPN
cana-5705	96	9	.	.	PUNCT
cana-5705	97	1	(	(	PUNCT
cana-5705	97	2	1	1	X
cana-5705	97	3	)	)	PUNCT
cana-5705	97	4	𝐿[𝐷𝜃(𝑥	𝐿[𝐷𝜃(𝑥	NOUN
cana-5705	97	5	,	,	PUNCT
cana-5705	97	6	𝑡	𝑡	NOUN
cana-5705	97	7	)	)	PUNCT
cana-5705	97	8	]	]	PUNCT
cana-5705	98	1	+	+	CCONJ
cana-5705	98	2	𝐿[𝑅𝜃(𝑥	𝐿[𝑅𝜃(𝑥	ADV
cana-5705	98	3	,	,	PUNCT
cana-5705	98	4	𝑡	𝑡	NOUN
cana-5705	98	5	)	)	PUNCT
cana-5705	98	6	]	]	PUNCT
cana-5705	99	1	+	+	CCONJ
cana-5705	99	2	𝐿[𝑁𝜃(𝑥	𝐿[𝑁𝜃(𝑥	PROPN
cana-5705	99	3	,	,	PUNCT
cana-5705	99	4	𝑡	𝑡	X
cana-5705	99	5	)	)	PUNCT
cana-5705	99	6	]	]	PUNCT
cana-5705	100	1	=	=	PUNCT
cana-5705	100	2	𝐿[𝑓(𝑥	𝐿[𝑓(𝑥	NOUN
cana-5705	100	3	,	,	PUNCT
cana-5705	100	4	𝑡	𝑡	NOUN
cana-5705	100	5	)	)	PUNCT
cana-5705	100	6	]	]	PUNCT
cana-5705	100	7	(	(	PUNCT
cana-5705	100	8	2	2	X
cana-5705	100	9	)	)	PUNCT
cana-5705	100	10	communications	communication	NOUN
cana-5705	100	11	on	on	ADP
cana-5705	100	12	applied	apply	VERB
cana-5705	100	13	nonlinear	nonlinear	ADJ
cana-5705	100	14	analysis	analysis	NOUN
cana-5705	100	15	issn	issn	NOUN
cana-5705	100	16	:	:	PUNCT
cana-5705	100	17	1074	1074	NUM
cana-5705	100	18	-	-	PUNCT
cana-5705	100	19	133x	133x	NUM
cana-5705	100	20	vol	vol	VERB
cana-5705	100	21	32	32	NUM
cana-5705	100	22	no	no	NOUN
cana-5705	100	23	.	.	PUNCT
cana-5705	101	1	10s	10	NOUN
cana-5705	101	2	(	(	PUNCT
cana-5705	101	3	2025	2025	NUM
cana-5705	101	4	)	)	PUNCT
cana-5705	101	5	2656	2656	NUM
cana-5705	101	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5705	101	7	using	use	VERB
cana-5705	101	8	differentiation	differentiation	NOUN
cana-5705	101	9	property	property	NOUN
cana-5705	101	10	of	of	ADP
cana-5705	101	11	laplace	laplace	NOUN
cana-5705	101	12	transform	transform	NOUN
cana-5705	101	13	𝐿[𝜃(𝑥	𝐿[𝜃(𝑥	NOUN
cana-5705	101	14	,	,	PUNCT
cana-5705	101	15	𝑡	𝑡	NOUN
cana-5705	101	16	)	)	PUNCT
cana-5705	101	17	]	]	PUNCT
cana-5705	101	18	=	=	PUNCT
cana-5705	101	19	ℎ(𝑥	ℎ(𝑥	NUM
cana-5705	101	20	)	)	PUNCT
cana-5705	101	21	𝑠	𝑠	NOUN
cana-5705	102	1	+	+	NUM
cana-5705	102	2	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5705	102	3	)	)	PUNCT
cana-5705	102	4	𝑠2	𝑠2	NOUN
cana-5705	102	5	−	−	PROPN
cana-5705	102	6	1	1	NUM
cana-5705	102	7	𝑠2	𝑠2	NOUN
cana-5705	102	8	𝐿[𝑅𝜃(𝑥	𝐿[𝑅𝜃(𝑥	NUM
cana-5705	102	9	,	,	PUNCT
cana-5705	102	10	𝑡	𝑡	PROPN
cana-5705	102	11	)	)	PUNCT
cana-5705	102	12	]	]	PUNCT
cana-5705	103	1	+	+	CCONJ
cana-5705	103	2	1	1	NUM
cana-5705	103	3	𝑠2	𝑠2	NOUN
cana-5705	103	4	𝐿[𝑓(𝑥	𝐿[𝑓(𝑥	NOUN
cana-5705	103	5	,	,	PUNCT
cana-5705	103	6	𝑡	𝑡	NOUN
cana-5705	103	7	)	)	PUNCT
cana-5705	103	8	]	]	PUNCT
cana-5705	104	1	−	−	PROPN
cana-5705	104	2	1	1	NUM
cana-5705	104	3	𝑠2	𝑠2	PROPN
cana-5705	104	4	𝐿[𝑁𝜃(𝑥	𝐿[𝑁𝜃(𝑥	PROPN
cana-5705	104	5	,	,	PUNCT
cana-5705	104	6	𝑡	𝑡	X
cana-5705	104	7	)	)	PUNCT
cana-5705	104	8	]	]	PUNCT
cana-5705	104	9	(	(	PUNCT
cana-5705	104	10	3	3	X
cana-5705	104	11	)	)	PUNCT
cana-5705	104	12	taking	take	VERB
cana-5705	104	13	laplace	laplace	NOUN
cana-5705	104	14	inverse	inverse	NOUN
cana-5705	104	15	on	on	ADP
cana-5705	104	16	both	both	DET
cana-5705	104	17	sides	side	NOUN
cana-5705	104	18	of	of	ADP
cana-5705	104	19	eq	eq	PROPN
cana-5705	104	20	.	.	PUNCT
cana-5705	105	1	(	(	PUNCT
cana-5705	105	2	3	3	X
cana-5705	105	3	)	)	PUNCT
cana-5705	105	4	𝜃(𝑥	𝜃(𝑥	NOUN
cana-5705	105	5	,	,	PUNCT
cana-5705	105	6	𝑡	𝑡	X
cana-5705	105	7	)	)	PUNCT
cana-5705	105	8	=	=	SYM
cana-5705	106	1	𝐹(𝑥	𝐹(𝑥	PROPN
cana-5705	106	2	,	,	PUNCT
cana-5705	106	3	𝑡	𝑡	NOUN
cana-5705	106	4	)	)	PUNCT
cana-5705	106	5	−	−	PROPN
cana-5705	107	1	𝐿−1	𝐿−1	NOUN
cana-5705	107	2	[	[	PUNCT
cana-5705	107	3	1	1	NUM
cana-5705	107	4	𝑠2	𝑠2	NOUN
cana-5705	107	5	𝐿(𝑅𝜃(𝑥	𝐿(𝑅𝜃(𝑥	PROPN
cana-5705	107	6	,	,	PUNCT
cana-5705	107	7	𝑡	𝑡	X
cana-5705	107	8	)	)	PUNCT
cana-5705	107	9	+	+	NUM
cana-5705	107	10	𝑁𝜃(𝑥	𝑁𝜃(𝑥	PROPN
cana-5705	107	11	,	,	PUNCT
cana-5705	107	12	𝑡	𝑡	NOUN
cana-5705	107	13	)	)	PUNCT
cana-5705	107	14	)	)	PUNCT
cana-5705	107	15	]	]	PUNCT
cana-5705	107	16	(	(	PUNCT
cana-5705	107	17	4	4	X
cana-5705	107	18	)	)	PUNCT
cana-5705	107	19	where	where	SCONJ
cana-5705	107	20	𝐹(𝑥	𝐹(𝑥	X
cana-5705	107	21	,	,	PUNCT
cana-5705	107	22	𝑡	𝑡	NOUN
cana-5705	107	23	)	)	PUNCT
cana-5705	107	24	represents	represent	VERB
cana-5705	107	25	the	the	DET
cana-5705	107	26	term	term	NOUN
cana-5705	107	27	arising	arise	VERB
cana-5705	107	28	from	from	ADP
cana-5705	107	29	the	the	DET
cana-5705	107	30	source	source	NOUN
cana-5705	107	31	term	term	NOUN
cana-5705	107	32	with	with	ADP
cana-5705	107	33	prescribed	prescribe	VERB
cana-5705	107	34	intial	intial	ADJ
cana-5705	107	35	conditions	condition	NOUN
cana-5705	107	36	now	now	ADV
cana-5705	107	37	by	by	ADP
cana-5705	107	38	applying	apply	VERB
cana-5705	107	39	homotopy	homotopy	NOUN
cana-5705	107	40	perturbation	perturbation	NOUN
cana-5705	107	41	method	method	NOUN
cana-5705	107	42	𝜃(𝑥	𝜃(𝑥	NOUN
cana-5705	107	43	,	,	PUNCT
cana-5705	107	44	𝑡	𝑡	NOUN
cana-5705	107	45	)	)	PUNCT
cana-5705	107	46	=	=	SYM
cana-5705	107	47	∑	∑	PUNCT
cana-5705	107	48	𝑞𝑛𝜃𝑛(𝑥	𝑞𝑛𝜃𝑛(𝑥	PROPN
cana-5705	107	49	,	,	PUNCT
cana-5705	107	50	𝑡)∞	𝑡)∞	NOUN
cana-5705	107	51	𝑛=0	𝑛=0	NOUN
cana-5705	107	52	(	(	PUNCT
cana-5705	107	53	5	5	NUM
cana-5705	107	54	)	)	PUNCT
cana-5705	107	55	where	where	SCONJ
cana-5705	107	56	q	q	NOUN
cana-5705	107	57	is	be	AUX
cana-5705	107	58	the	the	DET
cana-5705	107	59	embedding	embed	VERB
cana-5705	107	60	parameter	parameter	NOUN
cana-5705	107	61	&	&	CCONJ
cana-5705	107	62	q∈	q∈	PROPN
cana-5705	108	1	[	[	X
cana-5705	108	2	0,1	0,1	NUM
cana-5705	108	3	]	]	PUNCT
cana-5705	108	4	the	the	DET
cana-5705	108	5	non	non	ADJ
cana-5705	108	6	-	-	ADJ
cana-5705	108	7	linear	linear	ADJ
cana-5705	108	8	term	term	NOUN
cana-5705	108	9	can	can	AUX
cana-5705	108	10	be	be	AUX
cana-5705	108	11	decomposed	decompose	VERB
cana-5705	108	12	as	as	ADP
cana-5705	108	13	𝑁𝜃(𝑥	𝑁𝜃(𝑥	PROPN
cana-5705	108	14	,	,	PUNCT
cana-5705	108	15	𝑡	𝑡	X
cana-5705	108	16	)	)	PUNCT
cana-5705	108	17	=	=	PUNCT
cana-5705	109	1	∑	∑	PUNCT
cana-5705	109	2	𝑞𝑛𝐻𝑛(𝜃)∞	𝑞𝑛𝐻𝑛(𝜃)∞	PROPN
cana-5705	109	3	𝑛=0	𝑛=0	PROPN
cana-5705	109	4	(	(	PUNCT
cana-5705	109	5	6	6	NUM
cana-5705	109	6	)	)	PUNCT
cana-5705	109	7	for	for	ADP
cana-5705	109	8	some	some	DET
cana-5705	109	9	he	he	PRON
cana-5705	109	10	’s	’	VERB
cana-5705	109	11	polynomials	polynomial	VERB
cana-5705	109	12	𝐻𝑛(𝜃	𝐻𝑛(𝜃	PROPN
cana-5705	109	13	)	)	PUNCT
cana-5705	109	14	that	that	PRON
cana-5705	109	15	are	be	AUX
cana-5705	109	16	given	give	VERB
cana-5705	109	17	by	by	ADP
cana-5705	109	18	𝐻𝑛(𝜃0	𝐻𝑛(𝜃0	NOUN
cana-5705	109	19	,	,	PUNCT
cana-5705	109	20	𝜃1	𝜃1	VERB
cana-5705	109	21	,	,	PUNCT
cana-5705	109	22	𝜃2	𝜃2	NOUN
cana-5705	109	23	…	…	PUNCT
cana-5705	109	24	𝜃𝑛	𝜃𝑛	SYM
cana-5705	109	25	)	)	PUNCT
cana-5705	109	26	=	=	SYM
cana-5705	109	27	1	1	NUM
cana-5705	109	28	𝑛	𝑛	NOUN
cana-5705	109	29	!	!	PUNCT
cana-5705	109	30	𝜕𝑛	𝜕𝑛	NOUN
cana-5705	109	31	𝜕𝑞𝑛	𝜕𝑞𝑛	PUNCT
cana-5705	110	1	[	[	X
cana-5705	110	2	𝑁	𝑁	PROPN
cana-5705	110	3	∑	∑	PROPN
cana-5705	110	4	𝑞𝑖𝜃𝑖	𝑞𝑖𝜃𝑖	PROPN
cana-5705	110	5	∞	∞	PROPN
cana-5705	110	6	𝑖=0	𝑖=0	PROPN
cana-5705	110	7	]	]	PUNCT
cana-5705	111	1	𝑞=0	𝑞=0	PUNCT
cana-5705	111	2	𝑛	𝑛	NOUN
cana-5705	111	3	=	=	SYM
cana-5705	111	4	0	0	NUM
cana-5705	111	5	,	,	PUNCT
cana-5705	111	6	1	1	NUM
cana-5705	111	7	,	,	PUNCT
cana-5705	111	8	2	2	NUM
cana-5705	111	9	,	,	PUNCT
cana-5705	111	10	…	…	PUNCT
cana-5705	111	11	substituting	substitute	VERB
cana-5705	111	12	equations	equation	NOUN
cana-5705	111	13	(	(	PUNCT
cana-5705	111	14	5	5	NUM
cana-5705	111	15	)	)	PUNCT
cana-5705	111	16	and	and	CCONJ
cana-5705	111	17	(	(	PUNCT
cana-5705	111	18	6	6	NUM
cana-5705	111	19	)	)	PUNCT
cana-5705	111	20	in	in	ADP
cana-5705	111	21	eq	eq	ADP
cana-5705	111	22	.	.	PUNCT
cana-5705	112	1	(	(	PUNCT
cana-5705	112	2	4	4	X
cana-5705	112	3	)	)	PUNCT
cana-5705	112	4	we	we	PRON
cana-5705	112	5	get	get	VERB
cana-5705	112	6	∑	∑	ADV
cana-5705	112	7	𝑞𝑛𝜃𝑛(𝑥	𝑞𝑛𝜃𝑛(𝑥	PROPN
cana-5705	112	8	,	,	PUNCT
cana-5705	112	9	𝑡	𝑡	NOUN
cana-5705	112	10	)	)	PUNCT
cana-5705	112	11	=	=	SYM
cana-5705	112	12	𝐹(𝑥	𝐹(𝑥	PROPN
cana-5705	112	13	,	,	PUNCT
cana-5705	112	14	𝑡	𝑡	NOUN
cana-5705	112	15	)	)	PUNCT
cana-5705	112	16	−	−	PROPN
cana-5705	112	17	𝑞	𝑞	SYM
cana-5705	112	18	{	{	PUNCT
cana-5705	112	19	𝐿−1	𝐿−1	X
cana-5705	112	20	[	[	PUNCT
cana-5705	112	21	1	1	NUM
cana-5705	112	22	𝑠2	𝑠2	PROPN
cana-5705	112	23	𝐿	𝐿	PROPN
cana-5705	112	24	(	(	PUNCT
cana-5705	112	25	𝑅	𝑅	PROPN
cana-5705	112	26	∑	∑	PUNCT
cana-5705	112	27	𝑞𝑛𝜃𝑛(𝑥	𝑞𝑛𝜃𝑛(𝑥	PROPN
cana-5705	112	28	,	,	PUNCT
cana-5705	112	29	𝑡	𝑡	NOUN
cana-5705	112	30	)	)	PUNCT
cana-5705	112	31	∞	∞	NUM
cana-5705	112	32	𝑛=0	𝑛=0	PROPN
cana-5705	113	1	+	+	CCONJ
cana-5705	113	2	∑	∑	PUNCT
cana-5705	113	3	𝑞𝑛𝐻𝑛(𝜃	𝑞𝑛𝐻𝑛(𝜃	ADJ
cana-5705	113	4	)	)	PUNCT
cana-5705	113	5	)	)	PUNCT
cana-5705	114	1	]	]	PUNCT
cana-5705	114	2	}	}	PUNCT
cana-5705	114	3	∞	∞	NUM
cana-5705	114	4	𝑛=0	𝑛=0	NOUN
cana-5705	114	5	(	(	PUNCT
cana-5705	114	6	7	7	X
cana-5705	114	7	)	)	PUNCT
cana-5705	114	8	which	which	PRON
cana-5705	114	9	is	be	AUX
cana-5705	114	10	the	the	DET
cana-5705	114	11	coupling	coupling	NOUN
cana-5705	114	12	of	of	ADP
cana-5705	114	13	the	the	DET
cana-5705	114	14	laplace	laplace	NOUN
cana-5705	114	15	transform	transform	NOUN
cana-5705	114	16	and	and	CCONJ
cana-5705	114	17	the	the	DET
cana-5705	114	18	homotopy	homotopy	NOUN
cana-5705	114	19	perturbation	perturbation	NOUN
cana-5705	114	20	method	method	NOUN
cana-5705	114	21	using	use	VERB
cana-5705	114	22	he	he	PRON
cana-5705	114	23	’s	’s	PART
cana-5705	114	24	polynomials	polynomial	NOUN
cana-5705	114	25	.	.	PUNCT
cana-5705	115	1	comparing	compare	VERB
cana-5705	115	2	the	the	DET
cana-5705	115	3	co	co	NOUN
cana-5705	115	4	-	-	ADJ
cana-5705	115	5	efficient	efficient	ADJ
cana-5705	115	6	of	of	ADP
cana-5705	115	7	like	like	ADP
cana-5705	115	8	powers	power	NOUN
cana-5705	115	9	of	of	ADP
cana-5705	115	10	𝑞	𝑞	PROPN
cana-5705	115	11	,	,	PUNCT
cana-5705	115	12	the	the	DET
cana-5705	115	13	following	follow	VERB
cana-5705	115	14	approximations	approximation	NOUN
cana-5705	115	15	are	be	AUX
cana-5705	115	16	obtained	obtain	VERB
cana-5705	115	17	.	.	PUNCT
cana-5705	116	1	𝑞0	𝑞0	PROPN
cana-5705	116	2	∶	∶	PROPN
cana-5705	116	3	𝜃𝑜(𝑥	𝜃𝑜(𝑥	NOUN
cana-5705	116	4	,	,	PUNCT
cana-5705	116	5	𝑡	𝑡	X
cana-5705	116	6	)	)	PUNCT
cana-5705	116	7	=	=	SYM
cana-5705	116	8	𝐹(𝑥	𝐹(𝑥	PROPN
cana-5705	116	9	,	,	PUNCT
cana-5705	116	10	𝑡	𝑡	NOUN
cana-5705	116	11	)	)	PUNCT
cana-5705	116	12	𝑞1	𝑞1	PROPN
cana-5705	116	13	∶	∶	PROPN
cana-5705	116	14	𝜃1(𝑥	𝜃1(𝑥	NOUN
cana-5705	116	15	,	,	PUNCT
cana-5705	116	16	𝑡	𝑡	NOUN
cana-5705	116	17	)	)	PUNCT
cana-5705	116	18	=	=	SYM
cana-5705	116	19	−	−	PROPN
cana-5705	116	20	1	1	NUM
cana-5705	116	21	𝑠2	𝑠2	NOUN
cana-5705	116	22	𝐿[𝑅𝜃0(𝑥	𝐿[𝑅𝜃0(𝑥	PROPN
cana-5705	116	23	,	,	PUNCT
cana-5705	116	24	𝑡	𝑡	X
cana-5705	116	25	)	)	PUNCT
cana-5705	116	26	+	+	CCONJ
cana-5705	116	27	𝐻0(𝜃	𝐻0(𝜃	PROPN
cana-5705	116	28	)	)	PUNCT
cana-5705	116	29	]	]	PUNCT
cana-5705	116	30	𝑞2	𝑞2	VERB
cana-5705	116	31	∶	∶	PROPN
cana-5705	116	32	𝜃2(𝑥	𝜃2(𝑥	ADP
cana-5705	116	33	,	,	PUNCT
cana-5705	116	34	𝑡	𝑡	NOUN
cana-5705	116	35	)	)	PUNCT
cana-5705	116	36	=	=	SYM
cana-5705	116	37	−	−	PROPN
cana-5705	116	38	1	1	NUM
cana-5705	116	39	𝑠2	𝑠2	NOUN
cana-5705	116	40	𝐿[𝑅𝜃1(𝑥	𝐿[𝑅𝜃1(𝑥	PROPN
cana-5705	116	41	,	,	PUNCT
cana-5705	116	42	𝑡	𝑡	X
cana-5705	116	43	)	)	PUNCT
cana-5705	116	44	+	+	CCONJ
cana-5705	116	45	𝐻1(𝜃	𝐻1(𝜃	ADJ
cana-5705	116	46	)	)	PUNCT
cana-5705	116	47	]	]	PUNCT
cana-5705	117	1	𝑞3	𝑞3	PROPN
cana-5705	117	2	∶	∶	PROPN
cana-5705	117	3	𝜃3(𝑥	𝜃3(𝑥	SYM
cana-5705	117	4	,	,	PUNCT
cana-5705	117	5	𝑡	𝑡	X
cana-5705	117	6	)	)	PUNCT
cana-5705	117	7	=	=	SYM
cana-5705	117	8	−	−	PROPN
cana-5705	117	9	1	1	NUM
cana-5705	117	10	𝑠2	𝑠2	NOUN
cana-5705	117	11	𝐿[𝑅𝜃2(𝑥	𝐿[𝑅𝜃2(𝑥	PROPN
cana-5705	117	12	,	,	PUNCT
cana-5705	117	13	𝑡	𝑡	X
cana-5705	117	14	)	)	PUNCT
cana-5705	117	15	+	+	CCONJ
cana-5705	117	16	𝐻2(𝜃	𝐻2(𝜃	NUM
cana-5705	117	17	)	)	PUNCT
cana-5705	117	18	]	]	PUNCT
cana-5705	118	1	the	the	DET
cana-5705	118	2	best	good	ADJ
cana-5705	118	3	approximation	approximation	NOUN
cana-5705	118	4	for	for	ADP
cana-5705	118	5	the	the	DET
cana-5705	118	6	solution	solution	NOUN
cana-5705	118	7	is	be	AUX
cana-5705	118	8	𝜃	𝜃	NOUN
cana-5705	118	9	=	=	PUNCT
cana-5705	118	10	𝜃0	𝜃0	VERB
cana-5705	118	11	+	+	CCONJ
cana-5705	118	12	𝜃1	𝜃1	VERB
cana-5705	118	13	+	+	CCONJ
cana-5705	118	14	𝜃2	𝜃2	PROPN
cana-5705	118	15	+	+	X
cana-5705	118	16	…	…	PUNCT
cana-5705	118	17	…	…	PUNCT
cana-5705	118	18	.	.	PROPN
cana-5705	119	1	4	4	X
cana-5705	119	2	.	.	X
cana-5705	119	3	discussion	discussion	NOUN
cana-5705	119	4	and	and	CCONJ
cana-5705	119	5	results	result	NOUN
cana-5705	119	6	to	to	PART
cana-5705	119	7	evaluate	evaluate	VERB
cana-5705	119	8	the	the	DET
cana-5705	119	9	solution	solution	NOUN
cana-5705	119	10	procedure	procedure	NOUN
cana-5705	119	11	of	of	ADP
cana-5705	119	12	hptm	hptm	NOUN
cana-5705	119	13	,	,	PUNCT
cana-5705	119	14	we	we	PRON
cana-5705	119	15	discuss	discuss	VERB
cana-5705	119	16	the	the	DET
cana-5705	119	17	non	non	ADJ
cana-5705	119	18	-	-	ADJ
cana-5705	119	19	linear	linear	ADJ
cana-5705	119	20	diffusion	diffusion	NOUN
cana-5705	119	21	equation	equation	NOUN
cana-5705	119	22	of	of	ADP
cana-5705	119	23	porous	porous	ADJ
cana-5705	119	24	medium	medium	NOUN
cana-5705	119	25	with	with	ADP
cana-5705	119	26	linear	linear	ADJ
cana-5705	119	27	pressure	pressure	NOUN
cana-5705	119	28	profile	profile	NOUN
cana-5705	119	29	as	as	ADP
cana-5705	119	30	problem	problem	NOUN
cana-5705	119	31	i	i	PRON
cana-5705	119	32	𝜕𝑇	𝜕𝑇	VERB
cana-5705	119	33	𝜕𝑡	𝜕𝑡	NOUN
cana-5705	119	34	=	=	NOUN
cana-5705	119	35	𝜕	𝜕	NOUN
cana-5705	119	36	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	119	37	[	[	X
cana-5705	119	38	𝑇	𝑇	X
cana-5705	119	39	𝜕𝑇	𝜕𝑇	X
cana-5705	119	40	𝜕𝑥	𝜕𝑥	X
cana-5705	119	41	]	]	PUNCT
cana-5705	120	1	+	+	CCONJ
cana-5705	120	2	1	1	NUM
cana-5705	120	3	𝜌	𝜌	PART
cana-5705	120	4	𝜕𝑝	𝜕𝑝	NOUN
cana-5705	120	5	𝜕𝑥	𝜕𝑥	X
cana-5705	120	6	(	(	PUNCT
cana-5705	120	7	1	1	X
cana-5705	120	8	)	)	PUNCT
cana-5705	120	9	where	where	SCONJ
cana-5705	120	10	𝑝	𝑝	NOUN
cana-5705	120	11	=	=	PUNCT
cana-5705	120	12	linear	linear	ADJ
cana-5705	120	13	pressure	pressure	NOUN
cana-5705	120	14	=	=	PUNCT
cana-5705	120	15	𝑎𝑥	𝑎𝑥	NOUN
cana-5705	120	16	+	+	NUM
cana-5705	120	17	𝑏	𝑏	NOUN
cana-5705	120	18	,	,	PUNCT
cana-5705	120	19	with	with	ADP
cana-5705	120	20	𝑎	𝑎	ADJ
cana-5705	120	21	<	<	X
cana-5705	120	22	0	0	NUM
cana-5705	120	23	and	and	CCONJ
cana-5705	120	24	𝜌	𝜌	X
cana-5705	120	25	=	=	SYM
cana-5705	120	26	constant	constant	ADJ
cana-5705	120	27	density	density	NOUN
cana-5705	120	28	with	with	ADP
cana-5705	120	29	t(𝑥	t(𝑥	NOUN
cana-5705	120	30	,	,	PUNCT
cana-5705	120	31	0	0	NUM
cana-5705	120	32	)	)	PUNCT
cana-5705	120	33	=	=	NOUN
cana-5705	120	34	𝑒𝑥	𝑒𝑥	NOUN
cana-5705	121	1	so	so	ADV
cana-5705	121	2	,	,	PUNCT
cana-5705	121	3	eq	eq	NOUN
cana-5705	121	4	.	.	PUNCT
cana-5705	122	1	(	(	PUNCT
cana-5705	122	2	1	1	X
cana-5705	122	3	)	)	PUNCT
cana-5705	122	4	takes	take	VERB
cana-5705	122	5	the	the	DET
cana-5705	122	6	form	form	NOUN
cana-5705	122	7	communications	communication	NOUN
cana-5705	122	8	on	on	ADP
cana-5705	122	9	applied	apply	VERB
cana-5705	122	10	nonlinear	nonlinear	ADJ
cana-5705	122	11	analysis	analysis	NOUN
cana-5705	122	12	issn	issn	NOUN
cana-5705	122	13	:	:	PUNCT
cana-5705	122	14	1074	1074	NUM
cana-5705	122	15	-	-	PUNCT
cana-5705	122	16	133x	133x	NUM
cana-5705	122	17	vol	vol	VERB
cana-5705	122	18	32	32	NUM
cana-5705	122	19	no	no	NOUN
cana-5705	122	20	.	.	PUNCT
cana-5705	123	1	10s	10	NOUN
cana-5705	123	2	(	(	PUNCT
cana-5705	123	3	2025	2025	NUM
cana-5705	123	4	)	)	PUNCT
cana-5705	123	5	2657	2657	NUM
cana-5705	123	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5705	124	1	𝜕𝑇	𝜕𝑇	PUNCT
cana-5705	124	2	𝜕𝑡	𝜕𝑡	NOUN
cana-5705	124	3	=	=	NOUN
cana-5705	124	4	𝜕	𝜕	NOUN
cana-5705	124	5	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	125	1	[	[	X
cana-5705	125	2	𝑇	𝑇	X
cana-5705	125	3	𝜕𝑇	𝜕𝑇	X
cana-5705	125	4	𝜕𝑥	𝜕𝑥	X
cana-5705	125	5	]	]	PUNCT
cana-5705	126	1	+	+	CCONJ
cana-5705	126	2	1	1	NUM
cana-5705	126	3	𝜌	𝜌	X
cana-5705	126	4	(	(	PUNCT
cana-5705	126	5	𝑎	𝑎	NOUN
cana-5705	126	6	)	)	PUNCT
cana-5705	126	7	(	(	PUNCT
cana-5705	126	8	2	2	X
cana-5705	126	9	)	)	PUNCT
cana-5705	126	10	consider	consider	VERB
cana-5705	126	11	laplace	laplace	NOUN
cana-5705	126	12	transform	transform	NOUN
cana-5705	126	13	of	of	ADP
cana-5705	126	14	eq	eq	NOUN
cana-5705	126	15	.	.	PUNCT
cana-5705	127	1	(	(	PUNCT
cana-5705	127	2	2	2	X
cana-5705	127	3	)	)	PUNCT
cana-5705	127	4	𝐿	𝐿	PROPN
cana-5705	127	5	[	[	PUNCT
cana-5705	127	6	𝜕𝑇	𝜕𝑇	X
cana-5705	127	7	𝜕𝑡	𝜕𝑡	NOUN
cana-5705	127	8	]	]	X
cana-5705	127	9	=	=	PUNCT
cana-5705	127	10	𝐿	𝐿	PROPN
cana-5705	127	11	[	[	X
cana-5705	127	12	(	(	PUNCT
cana-5705	127	13	𝜕𝑇	𝜕𝑇	X
cana-5705	127	14	𝜕𝑥	𝜕𝑥	X
cana-5705	127	15	)	)	PUNCT
cana-5705	127	16	2	2	X
cana-5705	127	17	]	]	PUNCT
cana-5705	128	1	+	+	CCONJ
cana-5705	128	2	𝐿	𝐿	PROPN
cana-5705	128	3	[	[	X
cana-5705	128	4	𝑇	𝑇	PROPN
cana-5705	128	5	𝜕2𝑇	𝜕2𝑇	PROPN
cana-5705	128	6	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	128	7	]	]	PUNCT
cana-5705	129	1	+	+	CCONJ
cana-5705	129	2	𝐿	𝐿	PROPN
cana-5705	129	3	[	[	PUNCT
cana-5705	129	4	𝑎	𝑎	NOUN
cana-5705	129	5	𝜌	𝜌	X
cana-5705	129	6	]	]	PUNCT
cana-5705	129	7	using	use	VERB
cana-5705	129	8	the	the	DET
cana-5705	129	9	initial	initial	ADJ
cana-5705	129	10	condition	condition	NOUN
cana-5705	129	11	and	and	CCONJ
cana-5705	129	12	laplace	laplace	NOUN
cana-5705	129	13	transform	transform	NOUN
cana-5705	129	14	of	of	ADP
cana-5705	129	15	derivative	derivative	ADJ
cana-5705	129	16	𝑇(𝑥	𝑇(𝑥	PROPN
cana-5705	129	17	,	,	PUNCT
cana-5705	129	18	𝑠	𝑠	NOUN
cana-5705	129	19	)	)	PUNCT
cana-5705	129	20	=	=	SYM
cana-5705	130	1	𝑒𝑥	𝑒𝑥	NOUN
cana-5705	130	2	𝑠	𝑠	PROPN
cana-5705	131	1	+	+	CCONJ
cana-5705	131	2	1	1	NUM
cana-5705	131	3	𝑠	𝑠	X
cana-5705	131	4	𝐿	𝐿	PROPN
cana-5705	131	5	[	[	X
cana-5705	131	6	(	(	PUNCT
cana-5705	131	7	𝜕𝑇	𝜕𝑇	X
cana-5705	131	8	𝜕𝑥	𝜕𝑥	X
cana-5705	131	9	)	)	PUNCT
cana-5705	131	10	2	2	X
cana-5705	131	11	]	]	PUNCT
cana-5705	132	1	+	+	CCONJ
cana-5705	132	2	1	1	NUM
cana-5705	132	3	𝑠	𝑠	X
cana-5705	132	4	𝐿	𝐿	PROPN
cana-5705	132	5	[	[	X
cana-5705	132	6	𝑇	𝑇	PROPN
cana-5705	132	7	𝜕2𝑇	𝜕2𝑇	PROPN
cana-5705	132	8	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	132	9	]	]	X
cana-5705	132	10	(	(	PUNCT
cana-5705	132	11	3	3	X
cana-5705	132	12	)	)	PUNCT
cana-5705	132	13	taking	take	VERB
cana-5705	132	14	inverse	inverse	NOUN
cana-5705	132	15	transform	transform	NOUN
cana-5705	132	16	of	of	ADP
cana-5705	132	17	both	both	DET
cana-5705	132	18	sides	side	NOUN
cana-5705	132	19	of	of	ADP
cana-5705	132	20	eq	eq	PROPN
cana-5705	132	21	.	.	PUNCT
cana-5705	133	1	(	(	PUNCT
cana-5705	133	2	3	3	X
cana-5705	133	3	)	)	PUNCT
cana-5705	133	4	𝑇(𝑥	𝑇(𝑥	NOUN
cana-5705	133	5	,	,	PUNCT
cana-5705	133	6	𝑡	𝑡	NOUN
cana-5705	133	7	)	)	PUNCT
cana-5705	133	8	=	=	SYM
cana-5705	133	9	𝑒𝑥	𝑒𝑥	NOUN
cana-5705	134	1	+	+	CCONJ
cana-5705	134	2	𝑎	𝑎	X
cana-5705	134	3	𝜌	𝜌	X
cana-5705	134	4	𝑡	𝑡	X
cana-5705	134	5	+	+	X
cana-5705	135	1	𝐿−1	𝐿−1	NOUN
cana-5705	135	2	{	{	PUNCT
cana-5705	135	3	1	1	NUM
cana-5705	135	4	𝑠	𝑠	X
cana-5705	135	5	𝐿	𝐿	PROPN
cana-5705	135	6	[	[	X
cana-5705	135	7	(	(	PUNCT
cana-5705	135	8	𝜕𝑇	𝜕𝑇	X
cana-5705	135	9	𝜕𝑥	𝜕𝑥	X
cana-5705	135	10	)	)	PUNCT
cana-5705	135	11	2	2	NUM
cana-5705	135	12	+	+	CCONJ
cana-5705	135	13	𝑇	𝑇	PROPN
cana-5705	135	14	𝜕2𝑇	𝜕2𝑇	PROPN
cana-5705	135	15	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	135	16	]	]	PUNCT
cana-5705	135	17	}	}	PUNCT
cana-5705	135	18	(	(	PUNCT
cana-5705	135	19	4	4	X
cana-5705	135	20	)	)	PUNCT
cana-5705	135	21	by	by	ADP
cana-5705	135	22	homotopy	homotopy	NOUN
cana-5705	135	23	perturbation	perturbation	NOUN
cana-5705	135	24	method	method	NOUN
cana-5705	135	25	𝑇(𝑥	𝑇(𝑥	PROPN
cana-5705	135	26	,	,	PUNCT
cana-5705	135	27	𝑡	𝑡	PROPN
cana-5705	135	28	)	)	PUNCT
cana-5705	135	29	=	=	SYM
cana-5705	135	30	∑	∑	PUNCT
cana-5705	135	31	𝑞𝑛𝑇𝑛(𝑥	𝑞𝑛𝑇𝑛(𝑥	PROPN
cana-5705	135	32	,	,	PUNCT
cana-5705	135	33	𝑡)∞	𝑡)∞	NOUN
cana-5705	135	34	𝑛=0	𝑛=0	NOUN
cana-5705	135	35	(	(	PUNCT
cana-5705	135	36	5	5	NUM
cana-5705	135	37	)	)	PUNCT
cana-5705	135	38	substituting	substitute	VERB
cana-5705	135	39	eq	eq	ADP
cana-5705	135	40	.	.	PUNCT
cana-5705	135	41	(	(	PUNCT
cana-5705	135	42	5	5	NUM
cana-5705	135	43	)	)	PUNCT
cana-5705	135	44	in	in	ADP
cana-5705	135	45	eq	eq	ADP
cana-5705	135	46	.	.	PUNCT
cana-5705	135	47	(	(	PUNCT
cana-5705	135	48	4	4	NUM
cana-5705	135	49	)	)	PUNCT
cana-5705	135	50	and	and	CCONJ
cana-5705	135	51	using	use	VERB
cana-5705	135	52	he	he	PRON
cana-5705	135	53	’s	’s	NOUN
cana-5705	135	54	polynomials	polynomial	NOUN
cana-5705	135	55	∑	∑	ADV
cana-5705	135	56	𝑞𝑛𝑇𝑛(𝑥	𝑞𝑛𝑇𝑛(𝑥	PROPN
cana-5705	135	57	,	,	PUNCT
cana-5705	135	58	𝑡	𝑡	NOUN
cana-5705	135	59	)	)	PUNCT
cana-5705	135	60	∞	∞	NUM
cana-5705	135	61	𝑛=0	𝑛=0	PROPN
cana-5705	136	1	=	=	PUNCT
cana-5705	136	2	𝑒𝑥	𝑒𝑥	PROPN
cana-5705	136	3	+	+	CCONJ
cana-5705	136	4	𝑎	𝑎	X
cana-5705	136	5	𝜌	𝜌	X
cana-5705	136	6	𝑡	𝑡	NOUN
cana-5705	136	7	+	+	X
cana-5705	136	8	𝑞	𝑞	X
cana-5705	136	9	𝐿−1	𝐿−1	NOUN
cana-5705	136	10	{	{	PUNCT
cana-5705	136	11	1	1	NUM
cana-5705	136	12	𝑠	𝑠	PROPN
cana-5705	136	13	𝐿	𝐿	PROPN
cana-5705	136	14	(	(	PUNCT
cana-5705	136	15	∑	∑	ADV
cana-5705	136	16	𝑞𝑛𝐻𝑛	𝑞𝑛𝐻𝑛	PROPN
cana-5705	136	17	(	(	PUNCT
cana-5705	136	18	𝑇	𝑇	PROPN
cana-5705	136	19	)	)	PUNCT
cana-5705	136	20	)	)	PUNCT
cana-5705	136	21	}	}	PUNCT
cana-5705	136	22	where	where	SCONJ
cana-5705	136	23	𝐻0(𝑇	𝐻0(𝑇	NOUN
cana-5705	136	24	)	)	PUNCT
cana-5705	136	25	=	=	PRON
cana-5705	136	26	(	(	PUNCT
cana-5705	136	27	𝜕𝑇0	𝜕𝑇0	NOUN
cana-5705	136	28	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	136	29	)	)	PUNCT
cana-5705	136	30	2	2	NUM
cana-5705	136	31	+	+	CCONJ
cana-5705	136	32	𝑇𝑜	𝑇𝑜	PROPN
cana-5705	136	33	𝜕2𝑇0	𝜕2𝑇0	PROPN
cana-5705	136	34	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	136	35	𝐻1(𝑇	𝐻1(𝑇	PROPN
cana-5705	136	36	)	)	PUNCT
cana-5705	137	1	=	=	SYM
cana-5705	137	2	2	2	NUM
cana-5705	137	3	(	(	PUNCT
cana-5705	137	4	𝜕𝑇0	𝜕𝑇0	NOUN
cana-5705	137	5	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	137	6	)	)	PUNCT
cana-5705	137	7	(	(	PUNCT
cana-5705	137	8	𝜕𝑇1	𝜕𝑇1	PROPN
cana-5705	137	9	𝜕𝑥	𝜕𝑥	X
cana-5705	137	10	)	)	PUNCT
cana-5705	138	1	+	+	CCONJ
cana-5705	138	2	𝑇0	𝑇0	NOUN
cana-5705	138	3	𝜕2𝑇1	𝜕2𝑇1	ADJ
cana-5705	138	4	𝜕𝑥2	𝜕𝑥2	NOUN
cana-5705	138	5	+	+	CCONJ
cana-5705	138	6	𝑇1	𝑇1	PROPN
cana-5705	138	7	𝜕2𝑇0	𝜕2𝑇0	PROPN
cana-5705	138	8	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	138	9	comparing	compare	VERB
cana-5705	138	10	the	the	DET
cana-5705	138	11	co	co	NOUN
cana-5705	138	12	-	-	ADJ
cana-5705	138	13	efficient	efficient	ADJ
cana-5705	138	14	of	of	ADP
cana-5705	138	15	like	like	ADP
cana-5705	138	16	powers	power	NOUN
cana-5705	138	17	of	of	ADP
cana-5705	138	18	q	q	NOUN
cana-5705	138	19	,	,	PUNCT
cana-5705	138	20	the	the	DET
cana-5705	138	21	following	follow	VERB
cana-5705	138	22	approximations	approximation	NOUN
cana-5705	138	23	are	be	AUX
cana-5705	138	24	obtained	obtain	VERB
cana-5705	138	25	𝑞0	𝑞0	PROPN
cana-5705	138	26	∶	∶	PROPN
cana-5705	138	27	𝑇0(𝑥	𝑇0(𝑥	NUM
cana-5705	138	28	,	,	PUNCT
cana-5705	138	29	𝑡	𝑡	X
cana-5705	138	30	)	)	PUNCT
cana-5705	138	31	=	=	SYM
cana-5705	138	32	𝑒𝑥	𝑒𝑥	NOUN
cana-5705	139	1	+	+	CCONJ
cana-5705	139	2	𝑎	𝑎	X
cana-5705	139	3	𝜌	𝜌	X
cana-5705	139	4	𝑡	𝑡	X
cana-5705	139	5	𝑞1	𝑞1	PROPN
cana-5705	139	6	∶	∶	NOUN
cana-5705	139	7	𝑇1(𝑥	𝑇1(𝑥	NOUN
cana-5705	139	8	,	,	PUNCT
cana-5705	139	9	𝑡	𝑡	X
cana-5705	139	10	)	)	PUNCT
cana-5705	139	11	=	=	SYM
cana-5705	140	1	𝐿−1	𝐿−1	NOUN
cana-5705	140	2	[	[	PUNCT
cana-5705	140	3	1	1	NUM
cana-5705	140	4	𝑠	𝑠	X
cana-5705	140	5	𝐿	𝐿	PROPN
cana-5705	140	6	[	[	X
cana-5705	140	7	(	(	PUNCT
cana-5705	140	8	𝜕𝑇0	𝜕𝑇0	PROPN
cana-5705	140	9	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	140	10	)	)	PUNCT
cana-5705	140	11	2	2	NUM
cana-5705	141	1	+	+	NUM
cana-5705	141	2	𝑇0	𝑇0	NOUN
cana-5705	141	3	𝜕2𝑇0	𝜕2𝑇0	PROPN
cana-5705	141	4	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	141	5	]	]	X
cana-5705	141	6	]	]	X
cana-5705	142	1	=	=	PUNCT
cana-5705	142	2	𝐿−1	𝐿−1	NOUN
cana-5705	142	3	[	[	PUNCT
cana-5705	142	4	1	1	NUM
cana-5705	142	5	𝑠	𝑠	INTJ
cana-5705	142	6	(	(	PUNCT
cana-5705	142	7	2𝑒2𝑥	2𝑒2𝑥	NOUN
cana-5705	142	8	𝑠	𝑠	PROPN
cana-5705	142	9	+	+	CCONJ
cana-5705	142	10	𝑎	𝑎	PRON
cana-5705	142	11	𝜌	𝜌	PRON
cana-5705	142	12	𝑒𝑥	𝑒𝑥	NOUN
cana-5705	142	13	𝑠2	𝑠2	NOUN
cana-5705	142	14	)	)	PUNCT
cana-5705	142	15	]	]	PUNCT
cana-5705	142	16	𝑞1	𝑞1	PROPN
cana-5705	142	17	∶	∶	PROPN
cana-5705	142	18	𝑇1(𝑥	𝑇1(𝑥	NOUN
cana-5705	142	19	,	,	PUNCT
cana-5705	142	20	𝑡	𝑡	X
cana-5705	142	21	)	)	PUNCT
cana-5705	142	22	=	=	SYM
cana-5705	142	23	2𝑒2𝑥𝑡	2𝑒2𝑥𝑡	NUM
cana-5705	143	1	+	+	CCONJ
cana-5705	143	2	𝑎	𝑎	PROPN
cana-5705	143	3	𝜌	𝜌	NOUN
cana-5705	143	4	𝑒𝑥𝑡	𝑒𝑥𝑡	NOUN
cana-5705	143	5	𝑞2	𝑞2	PROPN
cana-5705	143	6	∶	∶	PROPN
cana-5705	143	7	𝑇2(𝑥	𝑇2(𝑥	PROPN
cana-5705	143	8	,	,	PUNCT
cana-5705	143	9	𝑡	𝑡	X
cana-5705	143	10	)	)	PUNCT
cana-5705	143	11	=	=	SYM
cana-5705	144	1	𝐿−1	𝐿−1	NOUN
cana-5705	144	2	[	[	PUNCT
cana-5705	144	3	1	1	NUM
cana-5705	144	4	𝑠	𝑠	PROPN
cana-5705	144	5	𝐿	𝐿	PROPN
cana-5705	144	6	{	{	PUNCT
cana-5705	144	7	2	2	NUM
cana-5705	144	8	(	(	PUNCT
cana-5705	144	9	𝜕𝑇0	𝜕𝑇0	PROPN
cana-5705	144	10	𝜕𝑥2	𝜕𝑥2	NOUN
cana-5705	144	11	)	)	PUNCT
cana-5705	144	12	(	(	PUNCT
cana-5705	144	13	𝜕𝑇1	𝜕𝑇1	PROPN
cana-5705	144	14	𝜕𝑥	𝜕𝑥	X
cana-5705	144	15	)	)	PUNCT
cana-5705	145	1	+	+	CCONJ
cana-5705	145	2	(	(	PUNCT
cana-5705	145	3	𝑇0	𝑇0	VERB
cana-5705	145	4	𝜕2𝑇1	𝜕2𝑇1	ADJ
cana-5705	145	5	𝜕𝑥2	𝜕𝑥2	NOUN
cana-5705	145	6	+	+	CCONJ
cana-5705	145	7	𝑇1	𝑇1	PROPN
cana-5705	145	8	𝜕2𝑇0	𝜕2𝑇0	PROPN
cana-5705	145	9	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	145	10	)	)	PUNCT
cana-5705	145	11	}	}	PUNCT
cana-5705	145	12	]	]	PUNCT
cana-5705	146	1	=	=	SYM
cana-5705	146	2	𝑡2	𝑡2	PROPN
cana-5705	146	3	[	[	X
cana-5705	146	4	9𝑒3𝑥	9𝑒3𝑥	NOUN
cana-5705	146	5	+	+	NUM
cana-5705	146	6	2𝑎	2𝑎	NUM
cana-5705	146	7	𝜌	𝜌	ADP
cana-5705	146	8	𝑒2𝑥	𝑒2𝑥	NOUN
cana-5705	146	9	]	]	X
cana-5705	146	10	+	+	CCONJ
cana-5705	146	11	𝑡3	𝑡3	PROPN
cana-5705	146	12	[	[	PUNCT
cana-5705	146	13	8𝑎𝑒2𝑥	8𝑎𝑒2𝑥	NUM
cana-5705	146	14	3𝜌	3𝜌	NUM
cana-5705	146	15	+	+	CCONJ
cana-5705	146	16	𝑎2𝑒𝑥	𝑎2𝑒𝑥	NOUN
cana-5705	146	17	3𝜌2	3𝜌2	NUM
cana-5705	146	18	]	]	PUNCT
cana-5705	146	19	…	…	PUNCT
cana-5705	146	20	…	…	PUNCT
cana-5705	146	21	…	…	PUNCT
cana-5705	146	22	..	..	PUNCT
cana-5705	147	1	∴	∴	PROPN
cana-5705	147	2	𝑇(𝑥	𝑇(𝑥	PROPN
cana-5705	147	3	,	,	PUNCT
cana-5705	147	4	𝑡	𝑡	PROPN
cana-5705	147	5	)	)	PUNCT
cana-5705	147	6	=	=	PUNCT
cana-5705	147	7	𝑇0	𝑇0	NOUN
cana-5705	148	1	+	+	CCONJ
cana-5705	148	2	𝑇1	𝑇1	NOUN
cana-5705	148	3	+	+	CCONJ
cana-5705	148	4	𝑇2	𝑇2	NOUN
cana-5705	148	5	+	+	CCONJ
cana-5705	148	6	⋯	⋯	NOUN
cana-5705	148	7	=	=	SYM
cana-5705	148	8	𝑒𝑥	𝑒𝑥	PROPN
cana-5705	148	9	+	+	NUM
cana-5705	148	10	𝑡	𝑡	X
cana-5705	148	11	[	[	PUNCT
cana-5705	148	12	𝑎	𝑎	NOUN
cana-5705	148	13	𝜌	𝜌	X
cana-5705	148	14	+	+	NOUN
cana-5705	148	15	2𝑒2𝑥	2𝑒2𝑥	NOUN
cana-5705	148	16	+	+	CCONJ
cana-5705	148	17	𝑎	𝑎	PRON
cana-5705	148	18	𝜌	𝜌	X
cana-5705	148	19	𝑒𝑥	𝑒𝑥	NOUN
cana-5705	148	20	]	]	PUNCT
cana-5705	149	1	+	+	CCONJ
cana-5705	150	1	𝑡2	𝑡2	ADJ
cana-5705	150	2	[	[	X
cana-5705	150	3	9𝑒3𝑥	9𝑒3𝑥	NOUN
cana-5705	150	4	+	+	NUM
cana-5705	150	5	2𝑎	2𝑎	NUM
cana-5705	150	6	𝜌	𝜌	ADP
cana-5705	150	7	𝑒2𝑥	𝑒2𝑥	NOUN
cana-5705	150	8	]	]	X
cana-5705	150	9	+	+	CCONJ
cana-5705	150	10	𝑡3	𝑡3	PROPN
cana-5705	150	11	[	[	PUNCT
cana-5705	150	12	8𝑎	8𝑎	NOUN
cana-5705	150	13	3𝜌	3𝜌	NUM
cana-5705	150	14	𝑒2𝑥	𝑒2𝑥	NOUN
cana-5705	150	15	+	+	CCONJ
cana-5705	150	16	𝑎2	𝑎2	PROPN
cana-5705	150	17	3𝜌2	3𝜌2	NUM
cana-5705	150	18	𝑒𝑥	𝑒𝑥	NOUN
cana-5705	150	19	]	]	X
cana-5705	150	20	+	+	NUM
cana-5705	150	21	⋯	⋯	NOUN
cana-5705	150	22	communications	communication	NOUN
cana-5705	150	23	on	on	ADP
cana-5705	150	24	applied	apply	VERB
cana-5705	150	25	nonlinear	nonlinear	ADJ
cana-5705	150	26	analysis	analysis	NOUN
cana-5705	150	27	issn	issn	NOUN
cana-5705	150	28	:	:	PUNCT
cana-5705	150	29	1074	1074	NUM
cana-5705	150	30	-	-	PUNCT
cana-5705	150	31	133x	133x	NUM
cana-5705	150	32	vol	vol	VERB
cana-5705	150	33	32	32	NUM
cana-5705	150	34	no	no	NOUN
cana-5705	150	35	.	.	PUNCT
cana-5705	151	1	10s	10	NOUN
cana-5705	151	2	(	(	PUNCT
cana-5705	151	3	2025	2025	NUM
cana-5705	151	4	)	)	PUNCT
cana-5705	151	5	2658	2658	NUM
cana-5705	151	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5705	151	7	as	as	ADP
cana-5705	151	8	an	an	DET
cana-5705	151	9	approximate	approximate	ADJ
cana-5705	151	10	solution	solution	NOUN
cana-5705	151	11	converges	converge	VERB
cana-5705	151	12	for	for	ADP
cana-5705	151	13	𝑡	𝑡	X
cana-5705	151	14	<	<	X
cana-5705	151	15	1	1	NUM
cana-5705	151	16	.	.	PUNCT
cana-5705	151	17	problem	problem	PROPN
cana-5705	151	18	ii	ii	PROPN
cana-5705	151	19	:	:	PUNCT
cana-5705	151	20	consider	consider	VERB
cana-5705	151	21	non	non	ADJ
cana-5705	151	22	-	-	ADJ
cana-5705	151	23	linear	linear	ADJ
cana-5705	151	24	diffusion	diffusion	NOUN
cana-5705	151	25	equation	equation	NOUN
cana-5705	151	26	of	of	ADP
cana-5705	151	27	porous	porous	ADJ
cana-5705	151	28	medium	medium	NOUN
cana-5705	151	29	with	with	ADP
cana-5705	151	30	pressure	pressure	NOUN
cana-5705	151	31	profile	profile	NOUN
cana-5705	151	32	is	be	AUX
cana-5705	151	33	𝜕𝑇	𝜕𝑇	PROPN
cana-5705	151	34	𝜕𝑡	𝜕𝑡	NOUN
cana-5705	151	35	=	=	SYM
cana-5705	151	36	𝜕	𝜕	NOUN
cana-5705	151	37	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	152	1	[	[	X
cana-5705	152	2	𝑇	𝑇	X
cana-5705	152	3	𝜕𝑇	𝜕𝑇	X
cana-5705	152	4	𝜕𝑥	𝜕𝑥	X
cana-5705	152	5	]	]	PUNCT
cana-5705	153	1	+	+	CCONJ
cana-5705	153	2	1	1	NUM
cana-5705	153	3	𝑝	𝑝	PROPN
cana-5705	153	4	𝜕𝑝	𝜕𝑝	NOUN
cana-5705	153	5	𝜕𝑥	𝜕𝑥	X
cana-5705	153	6	with	with	ADP
cana-5705	153	7	initial	initial	ADJ
cana-5705	153	8	condition	condition	NOUN
cana-5705	153	9	𝑇(𝑥	𝑇(𝑥	PROPN
cana-5705	153	10	,	,	PUNCT
cana-5705	153	11	0	0	NUM
cana-5705	153	12	)	)	PUNCT
cana-5705	153	13	=	=	NOUN
cana-5705	153	14	−𝑥	−𝑥	PUNCT
cana-5705	153	15	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5705	153	16	𝑝(𝑥	𝑝(𝑥	PROPN
cana-5705	153	17	)	)	PUNCT
cana-5705	153	18	=	=	PUNCT
cana-5705	153	19	𝑎𝑥	𝑎𝑥	NOUN
cana-5705	154	1	+	+	NUM
cana-5705	154	2	𝑏	𝑏	NOUN
cana-5705	154	3	,	,	PUNCT
cana-5705	154	4	𝑤𝑖𝑡ℎ	𝑤𝑖𝑡ℎ	NOUN
cana-5705	154	5	𝑎	𝑎	X
cana-5705	154	6	<	<	X
cana-5705	154	7	0	0	NUM
cana-5705	154	8	applying	apply	VERB
cana-5705	154	9	laplace	laplace	NOUN
cana-5705	154	10	transform	transform	NOUN
cana-5705	154	11	on	on	ADP
cana-5705	154	12	both	both	DET
cana-5705	154	13	sides	side	NOUN
cana-5705	154	14	𝐿	𝐿	PROPN
cana-5705	154	15	[	[	PUNCT
cana-5705	154	16	𝜕𝑇	𝜕𝑇	X
cana-5705	154	17	𝜕𝑥	𝜕𝑥	X
cana-5705	154	18	]	]	PUNCT
cana-5705	155	1	=	=	PUNCT
cana-5705	155	2	𝐿	𝐿	PROPN
cana-5705	155	3	[	[	X
cana-5705	155	4	(	(	PUNCT
cana-5705	155	5	𝜕𝑇	𝜕𝑇	X
cana-5705	155	6	𝜕𝑥	𝜕𝑥	X
cana-5705	155	7	)	)	PUNCT
cana-5705	155	8	2	2	X
cana-5705	155	9	]	]	PUNCT
cana-5705	156	1	+	+	CCONJ
cana-5705	156	2	𝐿	𝐿	PROPN
cana-5705	156	3	[	[	X
cana-5705	156	4	𝑇	𝑇	PROPN
cana-5705	156	5	𝜕2𝑇	𝜕2𝑇	PROPN
cana-5705	156	6	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	156	7	]	]	PUNCT
cana-5705	157	1	+	+	CCONJ
cana-5705	157	2	𝐿	𝐿	PROPN
cana-5705	157	3	[	[	PUNCT
cana-5705	157	4	1	1	NUM
cana-5705	157	5	𝜌	𝜌	PART
cana-5705	157	6	𝜕𝑝	𝜕𝑝	NOUN
cana-5705	157	7	𝜕𝑥	𝜕𝑥	X
cana-5705	157	8	]	]	PUNCT
cana-5705	157	9	(	(	PUNCT
cana-5705	157	10	1	1	X
cana-5705	157	11	)	)	PUNCT
cana-5705	157	12	using	use	VERB
cana-5705	157	13	initial	initial	ADJ
cana-5705	157	14	condition	condition	NOUN
cana-5705	157	15	⟹	⟹	ADP
cana-5705	157	16	𝑇(𝑥	𝑇(𝑥	NOUN
cana-5705	157	17	,	,	PUNCT
cana-5705	157	18	𝑠	𝑠	NOUN
cana-5705	157	19	)	)	PUNCT
cana-5705	157	20	=	=	NOUN
cana-5705	157	21	−𝑥	−𝑥	PUNCT
cana-5705	158	1	𝑠	𝑠	PROPN
cana-5705	158	2	+	+	NOUN
cana-5705	158	3	1	1	NUM
cana-5705	158	4	𝑠	𝑠	X
cana-5705	158	5	𝐿	𝐿	PROPN
cana-5705	158	6	[	[	X
cana-5705	158	7	(	(	PUNCT
cana-5705	158	8	𝜕𝑇	𝜕𝑇	X
cana-5705	158	9	𝜕𝑥	𝜕𝑥	X
cana-5705	158	10	)	)	PUNCT
cana-5705	158	11	2	2	NUM
cana-5705	159	1	+	+	CCONJ
cana-5705	159	2	𝑇	𝑇	PROPN
cana-5705	159	3	𝜕2𝑇	𝜕2𝑇	NOUN
cana-5705	159	4	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	159	5	]	]	PUNCT
cana-5705	160	1	+	+	CCONJ
cana-5705	160	2	𝑎	𝑎	X
cana-5705	160	3	𝜌𝑠2	𝜌𝑠2	NOUN
cana-5705	160	4	(	(	PUNCT
cana-5705	160	5	2	2	X
cana-5705	160	6	)	)	PUNCT
cana-5705	160	7	taking	take	VERB
cana-5705	160	8	inverse	inverse	NOUN
cana-5705	160	9	transform	transform	NOUN
cana-5705	160	10	of	of	ADP
cana-5705	160	11	eq	eq	NOUN
cana-5705	160	12	.	.	PUNCT
cana-5705	160	13	(	(	PUNCT
cana-5705	160	14	2	2	X
cana-5705	160	15	)	)	PUNCT
cana-5705	160	16	t(𝑥	t(𝑥	NOUN
cana-5705	160	17	,	,	PUNCT
cana-5705	160	18	𝑡	𝑡	NOUN
cana-5705	160	19	)	)	PUNCT
cana-5705	160	20	=	=	PUNCT
cana-5705	160	21	−𝑥	−𝑥	NOUN
cana-5705	160	22	+	+	CCONJ
cana-5705	160	23	𝑎	𝑎	PRON
cana-5705	160	24	𝜌	𝜌	X
cana-5705	160	25	𝑡	𝑡	X
cana-5705	160	26	+	+	X
cana-5705	160	27	𝐿−1	𝐿−1	NOUN
cana-5705	160	28	[	[	PUNCT
cana-5705	160	29	1	1	NUM
cana-5705	160	30	𝑠	𝑠	PROPN
cana-5705	160	31	𝐿	𝐿	PROPN
cana-5705	160	32	(	(	PUNCT
cana-5705	160	33	(	(	PUNCT
cana-5705	160	34	𝜕𝑇	𝜕𝑇	X
cana-5705	160	35	𝜕𝑥	𝜕𝑥	X
cana-5705	160	36	)	)	PUNCT
cana-5705	160	37	2	2	NUM
cana-5705	161	1	+	+	CCONJ
cana-5705	161	2	𝑇	𝑇	PROPN
cana-5705	161	3	𝜕2𝑇	𝜕2𝑇	PROPN
cana-5705	161	4	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	161	5	)	)	PUNCT
cana-5705	161	6	]	]	PUNCT
cana-5705	161	7	(	(	PUNCT
cana-5705	161	8	3	3	X
cana-5705	161	9	)	)	PUNCT
cana-5705	161	10	by	by	ADP
cana-5705	161	11	hpm	hpm	PROPN
cana-5705	161	12	𝑇(𝑥	𝑇(𝑥	PROPN
cana-5705	161	13	,	,	PUNCT
cana-5705	161	14	𝑡	𝑡	NOUN
cana-5705	161	15	)	)	PUNCT
cana-5705	161	16	=	=	SYM
cana-5705	161	17	∑	∑	PUNCT
cana-5705	161	18	𝑞𝑛𝑇𝑛(𝑥	𝑞𝑛𝑇𝑛(𝑥	PROPN
cana-5705	161	19	,	,	PUNCT
cana-5705	161	20	𝑡)∞	𝑡)∞	NOUN
cana-5705	161	21	𝑛=0	𝑛=0	NOUN
cana-5705	161	22	(	(	PUNCT
cana-5705	161	23	4	4	NUM
cana-5705	161	24	)	)	PUNCT
cana-5705	161	25	and	and	CCONJ
cana-5705	161	26	using	use	VERB
cana-5705	161	27	he	he	PRON
cana-5705	161	28	’s	’s	PART
cana-5705	161	29	polynomials	polynomial	NOUN
cana-5705	161	30	,	,	PUNCT
cana-5705	161	31	substituting	substitute	VERB
cana-5705	161	32	eq	eq	ADP
cana-5705	161	33	.	.	PUNCT
cana-5705	162	1	(	(	PUNCT
cana-5705	162	2	4	4	NUM
cana-5705	162	3	)	)	PUNCT
cana-5705	162	4	in	in	ADP
cana-5705	162	5	eq	eq	ADP
cana-5705	162	6	.	.	PUNCT
cana-5705	163	1	(	(	PUNCT
cana-5705	163	2	3	3	NUM
cana-5705	163	3	)	)	PUNCT
cana-5705	163	4	⟹	⟹	NUM
cana-5705	164	1	∑	∑	PUNCT
cana-5705	164	2	𝑞𝑛𝑇𝑛(𝑥	𝑞𝑛𝑇𝑛(𝑥	PROPN
cana-5705	164	3	,	,	PUNCT
cana-5705	164	4	𝑡	𝑡	NOUN
cana-5705	164	5	)	)	PUNCT
cana-5705	164	6	∞	∞	NUM
cana-5705	164	7	𝑛=0	𝑛=0	X
cana-5705	165	1	=	=	PUNCT
cana-5705	165	2	−𝑥	−𝑥	NOUN
cana-5705	165	3	+	+	CCONJ
cana-5705	165	4	𝑎	𝑎	PRON
cana-5705	165	5	𝜌	𝜌	X
cana-5705	165	6	𝑡	𝑡	NOUN
cana-5705	165	7	+	+	X
cana-5705	165	8	𝑞	𝑞	X
cana-5705	165	9	𝐿−1	𝐿−1	NOUN
cana-5705	165	10	{	{	PUNCT
cana-5705	165	11	1	1	NUM
cana-5705	165	12	𝑠	𝑠	PROPN
cana-5705	165	13	𝐿	𝐿	PROPN
cana-5705	165	14	(	(	PUNCT
cana-5705	165	15	∑	∑	ADV
cana-5705	165	16	𝑞𝑛𝐻𝑛	𝑞𝑛𝐻𝑛	PROPN
cana-5705	165	17	(	(	PUNCT
cana-5705	165	18	𝑇	𝑇	PROPN
cana-5705	165	19	)	)	PUNCT
cana-5705	165	20	)	)	PUNCT
cana-5705	165	21	}	}	PUNCT
cana-5705	165	22	where	where	SCONJ
cana-5705	165	23	𝐻0(𝑇	𝐻0(𝑇	NOUN
cana-5705	165	24	)	)	PUNCT
cana-5705	165	25	=	=	PRON
cana-5705	165	26	(	(	PUNCT
cana-5705	165	27	𝜕𝑇0	𝜕𝑇0	PROPN
cana-5705	165	28	ð𝑥	ð𝑥	NUM
cana-5705	165	29	)	)	PUNCT
cana-5705	165	30	2	2	NUM
cana-5705	165	31	+	+	CCONJ
cana-5705	165	32	𝑇0	𝑇0	PROPN
cana-5705	165	33	𝜕2𝑇0	𝜕2𝑇0	PROPN
cana-5705	165	34	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	165	35	𝐻1(𝑇	𝐻1(𝑇	PROPN
cana-5705	165	36	)	)	PUNCT
cana-5705	165	37	=	=	SYM
cana-5705	165	38	2	2	NUM
cana-5705	165	39	(	(	PUNCT
cana-5705	165	40	𝜕𝑇0	𝜕𝑇0	NOUN
cana-5705	165	41	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	165	42	)	)	PUNCT
cana-5705	165	43	(	(	PUNCT
cana-5705	165	44	𝜕𝑇1	𝜕𝑇1	PROPN
cana-5705	165	45	𝜕𝑥	𝜕𝑥	X
cana-5705	165	46	)	)	PUNCT
cana-5705	166	1	+	+	CCONJ
cana-5705	166	2	𝑇0	𝑇0	NOUN
cana-5705	166	3	𝜕2𝑇1	𝜕2𝑇1	ADJ
cana-5705	166	4	𝜕𝑥2	𝜕𝑥2	NOUN
cana-5705	166	5	+	+	CCONJ
cana-5705	166	6	𝑇1	𝑇1	PROPN
cana-5705	166	7	𝜕2𝑇0	𝜕2𝑇0	PROPN
cana-5705	166	8	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	166	9	comparing	compare	VERB
cana-5705	166	10	the	the	DET
cana-5705	166	11	co	co	NOUN
cana-5705	166	12	-	-	NOUN
cana-5705	166	13	eff	eff	PROPN
cana-5705	166	14	.	.	PUNCT
cana-5705	166	15	of	of	ADP
cana-5705	166	16	like	like	ADP
cana-5705	166	17	powers	power	NOUN
cana-5705	166	18	of	of	ADP
cana-5705	166	19	𝑞	𝑞	PRON
cana-5705	166	20	we	we	PRON
cana-5705	166	21	get	get	VERB
cana-5705	166	22	𝑞0	𝑞0	NOUN
cana-5705	166	23	∶	∶	PROPN
cana-5705	166	24	𝑇0(𝑥	𝑇0(𝑥	NUM
cana-5705	166	25	,	,	PUNCT
cana-5705	166	26	𝑡	𝑡	X
cana-5705	166	27	)	)	PUNCT
cana-5705	166	28	=	=	PUNCT
cana-5705	166	29	−𝑥	−𝑥	NOUN
cana-5705	167	1	+	+	CCONJ
cana-5705	167	2	𝑎	𝑎	PRON
cana-5705	167	3	𝜌	𝜌	X
cana-5705	167	4	𝑡	𝑡	X
cana-5705	167	5	𝑞1	𝑞1	PROPN
cana-5705	167	6	∶	∶	NOUN
cana-5705	167	7	𝑇1(𝑥	𝑇1(𝑥	NOUN
cana-5705	167	8	,	,	PUNCT
cana-5705	167	9	𝑡	𝑡	X
cana-5705	167	10	)	)	PUNCT
cana-5705	167	11	=	=	SYM
cana-5705	168	1	𝐿−1	𝐿−1	NOUN
cana-5705	168	2	{	{	PUNCT
cana-5705	168	3	1	1	NUM
cana-5705	168	4	𝑠	𝑠	X
cana-5705	168	5	𝐿	𝐿	PROPN
cana-5705	168	6	[	[	X
cana-5705	168	7	(	(	PUNCT
cana-5705	168	8	𝜕𝑇0	𝜕𝑇0	PROPN
cana-5705	168	9	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	168	10	)	)	PUNCT
cana-5705	168	11	2	2	NUM
cana-5705	169	1	+	+	NUM
cana-5705	169	2	𝑇0	𝑇0	NOUN
cana-5705	169	3	𝜕2𝑇0	𝜕2𝑇0	PROPN
cana-5705	169	4	𝜕𝑥2	𝜕𝑥2	NOUN
cana-5705	169	5	]	]	X
cana-5705	169	6	}	}	PUNCT
cana-5705	169	7	𝑇1(𝑥	𝑇1(𝑥	ADJ
cana-5705	169	8	,	,	PUNCT
cana-5705	169	9	𝑡	𝑡	X
cana-5705	169	10	)	)	PUNCT
cana-5705	169	11	=	=	SYM
cana-5705	170	1	𝐿−1	𝐿−1	NOUN
cana-5705	170	2	[	[	PUNCT
cana-5705	170	3	1	1	NUM
cana-5705	170	4	𝑠2	𝑠2	NOUN
cana-5705	170	5	]	]	PUNCT
cana-5705	170	6	=	=	SYM
cana-5705	170	7	𝑡	𝑡	PROPN
cana-5705	170	8	𝑞2	𝑞2	PROPN
cana-5705	170	9	∶	∶	PROPN
cana-5705	170	10	𝑇2(𝑥	𝑇2(𝑥	PROPN
cana-5705	170	11	,	,	PUNCT
cana-5705	170	12	𝑡	𝑡	X
cana-5705	170	13	)	)	PUNCT
cana-5705	170	14	=	=	SYM
cana-5705	171	1	𝐿−1	𝐿−1	NOUN
cana-5705	171	2	{	{	PUNCT
cana-5705	171	3	1	1	NUM
cana-5705	171	4	𝑠	𝑠	X
cana-5705	171	5	𝐿	𝐿	PROPN
cana-5705	171	6	[	[	X
cana-5705	171	7	2	2	NUM
cana-5705	171	8	(	(	PUNCT
cana-5705	171	9	𝜕𝑇0	𝜕𝑇0	NOUN
cana-5705	171	10	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	171	11	)	)	PUNCT
cana-5705	171	12	(	(	PUNCT
cana-5705	171	13	𝜕𝑇1	𝜕𝑇1	PROPN
cana-5705	171	14	𝜕𝑥	𝜕𝑥	X
cana-5705	171	15	)	)	PUNCT
cana-5705	172	1	+	+	CCONJ
cana-5705	172	2	(	(	PUNCT
cana-5705	172	3	𝑇0	𝑇0	VERB
cana-5705	172	4	𝜕2𝑇1	𝜕2𝑇1	ADJ
cana-5705	172	5	𝜕𝑥2	𝜕𝑥2	NOUN
cana-5705	172	6	+	+	CCONJ
cana-5705	172	7	𝑇1	𝑇1	PROPN
cana-5705	172	8	𝜕2𝑇0	𝜕2𝑇0	PROPN
cana-5705	172	9	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	172	10	)	)	PUNCT
cana-5705	172	11	]	]	PUNCT
cana-5705	172	12	}	}	PUNCT
cana-5705	172	13	communications	communication	NOUN
cana-5705	172	14	on	on	ADP
cana-5705	172	15	applied	apply	VERB
cana-5705	172	16	nonlinear	nonlinear	ADJ
cana-5705	172	17	analysis	analysis	NOUN
cana-5705	172	18	issn	issn	NOUN
cana-5705	172	19	:	:	PUNCT
cana-5705	172	20	1074	1074	NUM
cana-5705	172	21	-	-	PUNCT
cana-5705	172	22	133x	133x	NUM
cana-5705	172	23	vol	vol	VERB
cana-5705	172	24	32	32	NUM
cana-5705	172	25	no	no	NOUN
cana-5705	172	26	.	.	PUNCT
cana-5705	173	1	10s	10	NOUN
cana-5705	173	2	(	(	PUNCT
cana-5705	173	3	2025	2025	NUM
cana-5705	173	4	)	)	PUNCT
cana-5705	173	5	2659	2659	NUM
cana-5705	173	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5705	173	7	𝑇2(𝑥	𝑇2(𝑥	PROPN
cana-5705	173	8	,	,	PUNCT
cana-5705	173	9	𝑡	𝑡	X
cana-5705	173	10	)	)	PUNCT
cana-5705	173	11	=	=	SYM
cana-5705	173	12	0	0	NUM
cana-5705	173	13	∴	∴	PROPN
cana-5705	173	14	𝑇(𝑥	𝑇(𝑥	PROPN
cana-5705	173	15	,	,	PUNCT
cana-5705	173	16	𝑡	𝑡	PROPN
cana-5705	173	17	)	)	PUNCT
cana-5705	173	18	=	=	PUNCT
cana-5705	173	19	𝑇0	𝑇0	NOUN
cana-5705	173	20	+	+	CCONJ
cana-5705	173	21	𝑇1	𝑇1	NOUN
cana-5705	173	22	+	+	CCONJ
cana-5705	173	23	𝑇2	𝑇2	NOUN
cana-5705	173	24	+	+	CCONJ
cana-5705	173	25	⋯	⋯	NOUN
cana-5705	173	26	=	=	SYM
cana-5705	173	27	−𝑥	−𝑥	NOUN
cana-5705	173	28	(	(	PUNCT
cana-5705	173	29	𝑎	𝑎	NOUN
cana-5705	173	30	𝜌	𝜌	X
cana-5705	173	31	+	+	NOUN
cana-5705	173	32	1	1	NUM
cana-5705	173	33	)	)	PUNCT
cana-5705	173	34	𝑡	𝑡	PROPN
cana-5705	173	35	is	be	AUX
cana-5705	173	36	an	an	DET
cana-5705	173	37	exact	exact	ADJ
cana-5705	173	38	solution	solution	NOUN
cana-5705	173	39	.	.	PUNCT
cana-5705	174	1	problem	problem	NOUN
cana-5705	174	2	iii	iii	PROPN
cana-5705	174	3	consider	consider	VERB
cana-5705	174	4	the	the	DET
cana-5705	174	5	diffusion	diffusion	NOUN
cana-5705	174	6	equation	equation	NOUN
cana-5705	174	7	𝜕𝑇	𝜕𝑇	X
cana-5705	174	8	𝜕𝑡	𝜕𝑡	NOUN
cana-5705	174	9	=	=	SYM
cana-5705	174	10	𝜕	𝜕	NOUN
cana-5705	174	11	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	174	12	[	[	X
cana-5705	174	13	𝑇	𝑇	X
cana-5705	174	14	𝜕𝑇	𝜕𝑇	X
cana-5705	174	15	𝜕𝑥	𝜕𝑥	X
cana-5705	174	16	]	]	PUNCT
cana-5705	175	1	+	+	CCONJ
cana-5705	175	2	1	1	NUM
cana-5705	175	3	𝜌	𝜌	PART
cana-5705	175	4	𝜕𝑝	𝜕𝑝	NOUN
cana-5705	175	5	𝜕𝑥	𝜕𝑥	X
cana-5705	175	6	with	with	ADP
cana-5705	175	7	linear	linear	ADJ
cana-5705	175	8	pressure	pressure	NOUN
cana-5705	175	9	𝑝(𝑥	𝑝(𝑥	NOUN
cana-5705	175	10	)	)	PUNCT
cana-5705	176	1	=	=	PUNCT
cana-5705	176	2	𝑎𝑥	𝑎𝑥	NOUN
cana-5705	177	1	+	+	NUM
cana-5705	177	2	𝑏	𝑏	NOUN
cana-5705	177	3	,	,	PUNCT
cana-5705	177	4	𝑤𝑖𝑡ℎ	𝑤𝑖𝑡ℎ	NOUN
cana-5705	177	5	𝑎	𝑎	X
cana-5705	177	6	<	<	X
cana-5705	177	7	0	0	NUM
cana-5705	177	8	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5705	177	9	initial	initial	ADJ
cana-5705	177	10	condition	condition	NOUN
cana-5705	177	11	𝑇(𝑥	𝑇(𝑥	PROPN
cana-5705	177	12	,	,	PUNCT
cana-5705	177	13	0	0	NUM
cana-5705	177	14	)	)	PUNCT
cana-5705	177	15	=	=	SYM
cana-5705	177	16	𝑠𝑖𝑛𝑥	𝑠𝑖𝑛𝑥	NOUN
cana-5705	177	17	𝜕𝑇	𝜕𝑇	PUNCT
cana-5705	177	18	𝜕𝑡	𝜕𝑡	NOUN
cana-5705	177	19	=	=	SYM
cana-5705	177	20	𝜕	𝜕	NOUN
cana-5705	177	21	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	178	1	[	[	X
cana-5705	178	2	𝑇	𝑇	X
cana-5705	178	3	𝜕𝑇	𝜕𝑇	X
cana-5705	178	4	𝜕𝑥	𝜕𝑥	X
cana-5705	178	5	]	]	PUNCT
cana-5705	179	1	+	+	CCONJ
cana-5705	179	2	1	1	NUM
cana-5705	179	3	𝜌	𝜌	X
cana-5705	179	4	(	(	PUNCT
cana-5705	179	5	𝑎	𝑎	NOUN
cana-5705	179	6	)	)	PUNCT
cana-5705	179	7	(	(	PUNCT
cana-5705	179	8	1	1	X
cana-5705	179	9	)	)	PUNCT
cana-5705	179	10	consider	consider	VERB
cana-5705	179	11	laplace	laplace	NOUN
cana-5705	179	12	transform	transform	NOUN
cana-5705	179	13	of	of	ADP
cana-5705	179	14	eq	eq	NOUN
cana-5705	179	15	.	.	PUNCT
cana-5705	180	1	(	(	PUNCT
cana-5705	180	2	1	1	X
cana-5705	180	3	)	)	PUNCT
cana-5705	180	4	𝐿	𝐿	PROPN
cana-5705	180	5	[	[	PUNCT
cana-5705	180	6	𝜕𝑇	𝜕𝑇	X
cana-5705	180	7	𝜕𝑡	𝜕𝑡	NOUN
cana-5705	180	8	]	]	X
cana-5705	180	9	=	=	PUNCT
cana-5705	180	10	𝐿	𝐿	PROPN
cana-5705	180	11	[	[	X
cana-5705	180	12	(	(	PUNCT
cana-5705	180	13	𝜕𝑇	𝜕𝑇	X
cana-5705	180	14	𝜕𝑥	𝜕𝑥	X
cana-5705	180	15	)	)	PUNCT
cana-5705	180	16	2	2	X
cana-5705	180	17	]	]	PUNCT
cana-5705	181	1	+	+	CCONJ
cana-5705	181	2	𝐿	𝐿	PROPN
cana-5705	181	3	[	[	X
cana-5705	181	4	𝑇	𝑇	PROPN
cana-5705	181	5	𝜕2𝑇	𝜕2𝑇	PROPN
cana-5705	181	6	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	181	7	]	]	PUNCT
cana-5705	182	1	+	+	CCONJ
cana-5705	182	2	𝐿	𝐿	PROPN
cana-5705	182	3	[	[	PUNCT
cana-5705	182	4	𝑎	𝑎	NOUN
cana-5705	182	5	𝜌	𝜌	X
cana-5705	182	6	]	]	PUNCT
cana-5705	182	7	using	use	VERB
cana-5705	182	8	the	the	DET
cana-5705	182	9	initial	initial	ADJ
cana-5705	182	10	condition	condition	NOUN
cana-5705	182	11	and	and	CCONJ
cana-5705	182	12	laplace	laplace	NOUN
cana-5705	182	13	transform	transform	NOUN
cana-5705	182	14	of	of	ADP
cana-5705	182	15	derivative	derivative	ADJ
cana-5705	182	16	𝑇(𝑥	𝑇(𝑥	PROPN
cana-5705	182	17	,	,	PUNCT
cana-5705	182	18	𝑠	𝑠	NOUN
cana-5705	182	19	)	)	PUNCT
cana-5705	182	20	=	=	SYM
cana-5705	182	21	𝑠𝑖𝑛𝑥	𝑠𝑖𝑛𝑥	NOUN
cana-5705	182	22	𝑠	𝑠	PROPN
cana-5705	183	1	+	+	CCONJ
cana-5705	183	2	1	1	NUM
cana-5705	183	3	𝑠	𝑠	X
cana-5705	183	4	𝐿	𝐿	PROPN
cana-5705	183	5	[	[	X
cana-5705	183	6	(	(	PUNCT
cana-5705	183	7	𝜕𝑇	𝜕𝑇	X
cana-5705	183	8	𝜕𝑥	𝜕𝑥	X
cana-5705	183	9	)	)	PUNCT
cana-5705	183	10	2	2	NUM
cana-5705	184	1	+	+	CCONJ
cana-5705	184	2	𝑇	𝑇	PROPN
cana-5705	184	3	𝜕2𝑇	𝜕2𝑇	NOUN
cana-5705	184	4	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	184	5	]	]	PUNCT
cana-5705	185	1	+	+	CCONJ
cana-5705	185	2	𝑎	𝑎	X
cana-5705	185	3	𝜌𝑠2	𝜌𝑠2	NOUN
cana-5705	185	4	(	(	PUNCT
cana-5705	185	5	2	2	X
cana-5705	185	6	)	)	PUNCT
cana-5705	185	7	taking	take	VERB
cana-5705	185	8	inverse	inverse	NOUN
cana-5705	185	9	transform	transform	NOUN
cana-5705	185	10	of	of	ADP
cana-5705	185	11	both	both	DET
cana-5705	185	12	sides	side	NOUN
cana-5705	185	13	of	of	ADP
cana-5705	185	14	eq	eq	PROPN
cana-5705	185	15	.	.	PUNCT
cana-5705	185	16	(	(	PUNCT
cana-5705	185	17	2	2	X
cana-5705	185	18	)	)	PUNCT
cana-5705	185	19	𝑇(𝑥	𝑇(𝑥	NOUN
cana-5705	185	20	,	,	PUNCT
cana-5705	185	21	𝑡	𝑡	NOUN
cana-5705	185	22	)	)	PUNCT
cana-5705	185	23	=	=	SYM
cana-5705	185	24	𝑠𝑖𝑛𝑥	𝑠𝑖𝑛𝑥	NOUN
cana-5705	185	25	+	+	CCONJ
cana-5705	185	26	𝑎	𝑎	PRON
cana-5705	185	27	𝜌	𝜌	X
cana-5705	185	28	𝑡	𝑡	X
cana-5705	185	29	+	+	PROPN
cana-5705	185	30	𝐿−1	𝐿−1	NOUN
cana-5705	185	31	[	[	PUNCT
cana-5705	185	32	1	1	NUM
cana-5705	185	33	𝑠	𝑠	PROPN
cana-5705	185	34	𝐿	𝐿	PROPN
cana-5705	185	35	(	(	PUNCT
cana-5705	185	36	(	(	PUNCT
cana-5705	185	37	𝜕𝑇	𝜕𝑇	X
cana-5705	185	38	𝜕𝑥	𝜕𝑥	X
cana-5705	185	39	)	)	PUNCT
cana-5705	185	40	2	2	NUM
cana-5705	186	1	+	+	CCONJ
cana-5705	186	2	𝑇	𝑇	PROPN
cana-5705	186	3	𝜕2𝑇	𝜕2𝑇	PROPN
cana-5705	186	4	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	186	5	)	)	PUNCT
cana-5705	186	6	]	]	PUNCT
cana-5705	186	7	(	(	PUNCT
cana-5705	186	8	3	3	X
cana-5705	186	9	)	)	PUNCT
cana-5705	186	10	by	by	ADP
cana-5705	186	11	homotopy	homotopy	NOUN
cana-5705	186	12	perturbation	perturbation	NOUN
cana-5705	186	13	method	method	NOUN
cana-5705	186	14	𝑇(𝑥	𝑇(𝑥	PROPN
cana-5705	186	15	,	,	PUNCT
cana-5705	186	16	𝑡	𝑡	PROPN
cana-5705	186	17	)	)	PUNCT
cana-5705	186	18	=	=	SYM
cana-5705	186	19	∑	∑	PUNCT
cana-5705	186	20	𝑞𝑛𝑇𝑛(𝑥	𝑞𝑛𝑇𝑛(𝑥	PROPN
cana-5705	186	21	,	,	PUNCT
cana-5705	186	22	𝑡)∞	𝑡)∞	NOUN
cana-5705	186	23	𝑛=0	𝑛=0	NOUN
cana-5705	186	24	(	(	PUNCT
cana-5705	186	25	4	4	X
cana-5705	186	26	)	)	PUNCT
cana-5705	186	27	substituting	substitute	VERB
cana-5705	186	28	eq	eq	ADP
cana-5705	186	29	.	.	PUNCT
cana-5705	187	1	(	(	PUNCT
cana-5705	187	2	4	4	NUM
cana-5705	187	3	)	)	PUNCT
cana-5705	187	4	in	in	ADP
cana-5705	187	5	eq	eq	ADP
cana-5705	187	6	.	.	PUNCT
cana-5705	188	1	(	(	PUNCT
cana-5705	188	2	3	3	NUM
cana-5705	188	3	)	)	PUNCT
cana-5705	188	4	and	and	CCONJ
cana-5705	188	5	using	use	VERB
cana-5705	188	6	he	he	PRON
cana-5705	188	7	’s	’s	NOUN
cana-5705	188	8	polynomials	polynomial	NOUN
cana-5705	188	9	⟹	⟹	NUM
cana-5705	188	10	∑	∑	ADV
cana-5705	188	11	𝑞𝑛𝑇𝑛(𝑥	𝑞𝑛𝑇𝑛(𝑥	PROPN
cana-5705	188	12	,	,	PUNCT
cana-5705	188	13	𝑡	𝑡	NOUN
cana-5705	188	14	)	)	PUNCT
cana-5705	188	15	∞	∞	NUM
cana-5705	189	1	𝑛=0	𝑛=0	PROPN
cana-5705	189	2	=	=	PUNCT
cana-5705	189	3	𝑠𝑖𝑛𝑥	𝑠𝑖𝑛𝑥	NOUN
cana-5705	189	4	+	+	CCONJ
cana-5705	189	5	𝑎	𝑎	PRON
cana-5705	189	6	𝜌	𝜌	X
cana-5705	189	7	𝑡	𝑡	NOUN
cana-5705	189	8	+	+	X
cana-5705	189	9	𝑞	𝑞	X
cana-5705	189	10	𝐿−1	𝐿−1	NOUN
cana-5705	189	11	{	{	PUNCT
cana-5705	189	12	1	1	NUM
cana-5705	189	13	𝑠	𝑠	PROPN
cana-5705	189	14	𝐿	𝐿	PROPN
cana-5705	189	15	(	(	PUNCT
cana-5705	189	16	∑	∑	ADV
cana-5705	189	17	𝑞𝑛𝐻𝑛	𝑞𝑛𝐻𝑛	PROPN
cana-5705	189	18	(	(	PUNCT
cana-5705	189	19	𝑇	𝑇	PROPN
cana-5705	189	20	)	)	PUNCT
cana-5705	189	21	)	)	PUNCT
cana-5705	189	22	}	}	PUNCT
cana-5705	189	23	where	where	SCONJ
cana-5705	189	24	𝐻0(𝑇	𝐻0(𝑇	NOUN
cana-5705	189	25	)	)	PUNCT
cana-5705	189	26	=	=	PRON
cana-5705	189	27	(	(	PUNCT
cana-5705	189	28	𝜕𝑇0	𝜕𝑇0	PROPN
cana-5705	189	29	ð𝑥	ð𝑥	NUM
cana-5705	189	30	)	)	PUNCT
cana-5705	189	31	2	2	NUM
cana-5705	189	32	+	+	CCONJ
cana-5705	189	33	𝑇0	𝑇0	NOUN
cana-5705	189	34	𝜕2𝑇0	𝜕2𝑇0	PROPN
cana-5705	189	35	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	189	36	communications	communication	NOUN
cana-5705	189	37	on	on	ADP
cana-5705	189	38	applied	apply	VERB
cana-5705	189	39	nonlinear	nonlinear	ADJ
cana-5705	189	40	analysis	analysis	NOUN
cana-5705	189	41	issn	issn	NOUN
cana-5705	189	42	:	:	PUNCT
cana-5705	189	43	1074	1074	NUM
cana-5705	189	44	-	-	PUNCT
cana-5705	189	45	133x	133x	NUM
cana-5705	189	46	vol	vol	VERB
cana-5705	189	47	32	32	NUM
cana-5705	189	48	no	no	NOUN
cana-5705	189	49	.	.	PUNCT
cana-5705	190	1	10s	10	NOUN
cana-5705	190	2	(	(	PUNCT
cana-5705	190	3	2025	2025	NUM
cana-5705	190	4	)	)	PUNCT
cana-5705	190	5	2660	2660	NUM
cana-5705	190	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5705	190	7	𝐻1(𝑇	𝐻1(𝑇	PROPN
cana-5705	190	8	)	)	PUNCT
cana-5705	190	9	=	=	SYM
cana-5705	190	10	2	2	NUM
cana-5705	190	11	(	(	PUNCT
cana-5705	190	12	𝜕𝑇0	𝜕𝑇0	NOUN
cana-5705	190	13	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	190	14	)	)	PUNCT
cana-5705	190	15	(	(	PUNCT
cana-5705	190	16	𝜕𝑇1	𝜕𝑇1	PROPN
cana-5705	190	17	𝜕𝑥	𝜕𝑥	X
cana-5705	190	18	)	)	PUNCT
cana-5705	191	1	+	+	CCONJ
cana-5705	191	2	𝑇0	𝑇0	NOUN
cana-5705	191	3	𝜕2𝑇1	𝜕2𝑇1	ADJ
cana-5705	191	4	𝜕𝑥2	𝜕𝑥2	NOUN
cana-5705	191	5	+	+	CCONJ
cana-5705	191	6	𝑇1	𝑇1	PROPN
cana-5705	191	7	𝜕2𝑇0	𝜕2𝑇0	PROPN
cana-5705	191	8	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	191	9	comparing	compare	VERB
cana-5705	191	10	the	the	DET
cana-5705	191	11	co	co	NOUN
cana-5705	191	12	-	-	NOUN
cana-5705	191	13	eff	eff	PROPN
cana-5705	191	14	.	.	PUNCT
cana-5705	191	15	of	of	ADP
cana-5705	191	16	like	like	ADP
cana-5705	191	17	powers	power	NOUN
cana-5705	191	18	of	of	ADP
cana-5705	191	19	𝑞	𝑞	PRON
cana-5705	191	20	we	we	PRON
cana-5705	191	21	get	get	VERB
cana-5705	191	22	𝑞0	𝑞0	NOUN
cana-5705	191	23	∶	∶	PROPN
cana-5705	191	24	𝑇0(𝑥	𝑇0(𝑥	NUM
cana-5705	191	25	,	,	PUNCT
cana-5705	191	26	𝑡	𝑡	X
cana-5705	191	27	)	)	PUNCT
cana-5705	191	28	=	=	SYM
cana-5705	191	29	𝑠𝑖𝑛𝑥	𝑠𝑖𝑛𝑥	NOUN
cana-5705	191	30	+	+	CCONJ
cana-5705	191	31	𝑎	𝑎	PRON
cana-5705	191	32	𝜌	𝜌	X
cana-5705	191	33	𝑡	𝑡	X
cana-5705	191	34	𝑞1	𝑞1	PROPN
cana-5705	191	35	∶	∶	NOUN
cana-5705	191	36	𝑇1(𝑥	𝑇1(𝑥	NOUN
cana-5705	191	37	,	,	PUNCT
cana-5705	191	38	𝑡	𝑡	X
cana-5705	191	39	)	)	PUNCT
cana-5705	191	40	=	=	SYM
cana-5705	192	1	𝐿−1	𝐿−1	NOUN
cana-5705	192	2	{	{	PUNCT
cana-5705	192	3	1	1	NUM
cana-5705	192	4	𝑠	𝑠	X
cana-5705	192	5	𝐿	𝐿	PROPN
cana-5705	192	6	[	[	X
cana-5705	192	7	(	(	PUNCT
cana-5705	192	8	𝜕𝑇0	𝜕𝑇0	PROPN
cana-5705	192	9	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	192	10	)	)	PUNCT
cana-5705	192	11	2	2	NUM
cana-5705	193	1	+	+	NUM
cana-5705	193	2	𝑇0	𝑇0	NOUN
cana-5705	193	3	𝜕2𝑇0	𝜕2𝑇0	PROPN
cana-5705	193	4	𝜕𝑥2	𝜕𝑥2	NOUN
cana-5705	193	5	]	]	X
cana-5705	193	6	}	}	PUNCT
cana-5705	193	7	=	=	PUNCT
cana-5705	193	8	𝐿−1	𝐿−1	NOUN
cana-5705	193	9	[	[	PUNCT
cana-5705	193	10	1	1	NUM
cana-5705	193	11	𝑠	𝑠	PROPN
cana-5705	193	12	(	(	PUNCT
cana-5705	193	13	𝑐𝑜𝑠2𝑥	𝑐𝑜𝑠2𝑥	PROPN
cana-5705	193	14	𝑠	𝑠	PROPN
cana-5705	193	15	+	+	NUM
cana-5705	193	16	𝑠𝑖𝑛𝑥	𝑠𝑖𝑛𝑥	NOUN
cana-5705	194	1	𝑠	𝑠	PROPN
cana-5705	194	2	−	−	PROPN
cana-5705	194	3	𝑎	𝑎	PUNCT
cana-5705	194	4	𝜌	𝜌	X
cana-5705	194	5	𝑠𝑖𝑛𝑥	𝑠𝑖𝑛𝑥	NOUN
cana-5705	194	6	𝑠2	𝑠2	NOUN
cana-5705	194	7	)	)	PUNCT
cana-5705	194	8	]	]	PUNCT
cana-5705	195	1	𝑞1	𝑞1	PROPN
cana-5705	195	2	∶	∶	PROPN
cana-5705	195	3	𝑇1(𝑥	𝑇1(𝑥	NOUN
cana-5705	195	4	,	,	PUNCT
cana-5705	195	5	𝑡	𝑡	NOUN
cana-5705	195	6	)	)	PUNCT
cana-5705	195	7	=	=	SYM
cana-5705	195	8	𝑡𝑐𝑜𝑠2𝑥	𝑡𝑐𝑜𝑠2𝑥	NOUN
cana-5705	195	9	+	+	CCONJ
cana-5705	195	10	𝑡𝑠𝑖𝑛𝑥	𝑡𝑠𝑖𝑛𝑥	PROPN
cana-5705	196	1	−	−	PUNCT
cana-5705	196	2	𝑎	𝑎	DET
cana-5705	196	3	2𝜌	2𝜌	NOUN
cana-5705	196	4	𝑡2𝑠𝑖𝑛𝑥	𝑡2𝑠𝑖𝑛𝑥	NOUN
cana-5705	196	5	𝑞2	𝑞2	PROPN
cana-5705	196	6	∶	∶	PROPN
cana-5705	196	7	𝑇2(𝑥	𝑇2(𝑥	PROPN
cana-5705	196	8	,	,	PUNCT
cana-5705	196	9	𝑡	𝑡	X
cana-5705	196	10	)	)	PUNCT
cana-5705	196	11	=	=	SYM
cana-5705	197	1	𝐿−1	𝐿−1	NOUN
cana-5705	197	2	{	{	PUNCT
cana-5705	197	3	1	1	NUM
cana-5705	197	4	𝑠	𝑠	X
cana-5705	197	5	𝐿	𝐿	PROPN
cana-5705	197	6	[	[	X
cana-5705	197	7	2	2	NUM
cana-5705	197	8	(	(	PUNCT
cana-5705	197	9	𝜕𝑇0	𝜕𝑇0	NOUN
cana-5705	197	10	𝜕𝑥	𝜕𝑥	NOUN
cana-5705	197	11	)	)	PUNCT
cana-5705	197	12	(	(	PUNCT
cana-5705	197	13	𝜕𝑇1	𝜕𝑇1	PROPN
cana-5705	197	14	𝜕𝑥	𝜕𝑥	X
cana-5705	197	15	)	)	PUNCT
cana-5705	198	1	+	+	CCONJ
cana-5705	198	2	(	(	PUNCT
cana-5705	198	3	𝑇0	𝑇0	VERB
cana-5705	198	4	𝜕2𝑇1	𝜕2𝑇1	ADJ
cana-5705	198	5	𝜕𝑥2	𝜕𝑥2	NOUN
cana-5705	198	6	+	+	CCONJ
cana-5705	198	7	𝑇1	𝑇1	PROPN
cana-5705	198	8	𝜕2𝑇0	𝜕2𝑇0	PROPN
cana-5705	198	9	𝜕𝑥2	𝜕𝑥2	PROPN
cana-5705	198	10	)	)	PUNCT
cana-5705	198	11	]	]	PUNCT
cana-5705	198	12	}	}	PUNCT
cana-5705	198	13	=	=	SYM
cana-5705	198	14	𝑡4	𝑡4	NOUN
cana-5705	198	15	𝑎2𝑠𝑖𝑛𝑥	𝑎2𝑠𝑖𝑛𝑥	NOUN
cana-5705	198	16	8𝜌	8𝜌	NUM
cana-5705	198	17	−	−	PROPN
cana-5705	198	18	𝑡3	𝑡3	PROPN
cana-5705	198	19	𝑎(3𝑐𝑜𝑠2𝑥	𝑎(3𝑐𝑜𝑠2𝑥	NOUN
cana-5705	198	20	+	+	CCONJ
cana-5705	198	21	𝑠𝑖𝑛𝑥	𝑠𝑖𝑛𝑥	NOUN
cana-5705	198	22	)	)	PUNCT
cana-5705	198	23	3𝜌	3𝜌	NOUN
cana-5705	199	1	+	+	X
cana-5705	199	2	𝑡2	𝑡2	ADJ
cana-5705	199	3	(	(	PUNCT
cana-5705	199	4	2𝑐𝑜𝑠2𝑥	2𝑐𝑜𝑠2𝑥	NUM
cana-5705	199	5	−	−	PROPN
cana-5705	199	6	2𝑠𝑖𝑛𝑥𝑐𝑜𝑠2𝑥	2𝑠𝑖𝑛𝑥𝑐𝑜𝑠2𝑥	NUM
cana-5705	199	7	−	−	NOUN
cana-5705	199	8	5𝑠𝑖𝑛𝑥𝑐𝑜𝑠2𝑥	5𝑠𝑖𝑛𝑥𝑐𝑜𝑠2𝑥	NUM
cana-5705	199	9	2	2	NUM
cana-5705	199	10	∴	∴	PROPN
cana-5705	199	11	𝑇(𝑥	𝑇(𝑥	PROPN
cana-5705	199	12	,	,	PUNCT
cana-5705	199	13	𝑡	𝑡	PROPN
cana-5705	199	14	)	)	PUNCT
cana-5705	199	15	=	=	PUNCT
cana-5705	199	16	𝑇0	𝑇0	NOUN
cana-5705	200	1	+	+	CCONJ
cana-5705	200	2	𝑇1	𝑇1	NOUN
cana-5705	200	3	+	+	CCONJ
cana-5705	200	4	𝑇2	𝑇2	NOUN
cana-5705	200	5	+	+	CCONJ
cana-5705	200	6	⋯	⋯	NOUN
cana-5705	200	7	=	=	SYM
cana-5705	200	8	𝑠𝑖𝑛𝑥	𝑠𝑖𝑛𝑥	NOUN
cana-5705	200	9	+	+	CCONJ
cana-5705	200	10	𝑡	𝑡	X
cana-5705	200	11	[	[	PUNCT
cana-5705	200	12	𝑎	𝑎	NOUN
cana-5705	200	13	𝜌	𝜌	X
cana-5705	200	14	+	+	NOUN
cana-5705	200	15	𝑐𝑜𝑠2𝑥	𝑐𝑜𝑠2𝑥	X
cana-5705	200	16	+	+	NUM
cana-5705	200	17	𝑠𝑖𝑛𝑥	𝑠𝑖𝑛𝑥	NOUN
cana-5705	200	18	]	]	PUNCT
cana-5705	200	19	−	−	PROPN
cana-5705	200	20	𝑡2	𝑡2	PROPN
cana-5705	200	21	[	[	PUNCT
cana-5705	200	22	𝑎𝑠𝑖𝑛𝑥	𝑎𝑠𝑖𝑛𝑥	PROPN
cana-5705	200	23	2𝜌	2𝜌	NOUN
cana-5705	200	24	+	+	CCONJ
cana-5705	200	25	(	(	PUNCT
cana-5705	200	26	2𝑐𝑜𝑠2𝑥−2𝑠𝑖𝑛𝑥𝑐𝑜𝑠2𝑥−	2𝑐𝑜𝑠2𝑥−2𝑠𝑖𝑛𝑥𝑐𝑜𝑠2𝑥−	NUM
cana-5705	200	27	5𝑠𝑖𝑛𝑥𝑐𝑜𝑠2𝑥	5𝑠𝑖𝑛𝑥𝑐𝑜𝑠2𝑥	NUM
cana-5705	200	28	)	)	PUNCT
cana-5705	200	29	2	2	NUM
cana-5705	200	30	]	]	PUNCT
cana-5705	200	31	+	+	CCONJ
cana-5705	200	32	⋯.	⋯.	NOUN
cana-5705	200	33	as	as	ADP
cana-5705	200	34	an	an	DET
cana-5705	200	35	approximate	approximate	ADJ
cana-5705	200	36	solution	solution	NOUN
cana-5705	200	37	,	,	PUNCT
cana-5705	200	38	converges	converge	VERB
cana-5705	200	39	for	for	ADP
cana-5705	200	40	𝑡	𝑡	NOUN
cana-5705	200	41	<	<	X
cana-5705	200	42	1	1	NUM
cana-5705	200	43	.	.	NOUN
cana-5705	200	44	5	5	NUM
cana-5705	200	45	.	.	X
cana-5705	200	46	conclusion	conclusion	NOUN
cana-5705	200	47	in	in	ADP
cana-5705	200	48	this	this	DET
cana-5705	200	49	paper	paper	NOUN
cana-5705	200	50	,	,	PUNCT
cana-5705	200	51	a	a	DET
cana-5705	200	52	homotopy	homotopy	NOUN
cana-5705	200	53	perturbation	perturbation	NOUN
cana-5705	200	54	transform	transform	NOUN
cana-5705	200	55	method	method	NOUN
cana-5705	200	56	(	(	PUNCT
cana-5705	200	57	hptm	hptm	NOUN
cana-5705	200	58	)	)	PUNCT
cana-5705	200	59	is	be	AUX
cana-5705	200	60	discussed	discuss	VERB
cana-5705	200	61	for	for	ADP
cana-5705	200	62	solving	solve	VERB
cana-5705	200	63	non	non	ADJ
cana-5705	200	64	-	-	ADJ
cana-5705	200	65	linear	linear	ADJ
cana-5705	200	66	diffusion	diffusion	NOUN
cana-5705	200	67	equation	equation	NOUN
cana-5705	200	68	of	of	ADP
cana-5705	200	69	porous	porous	ADJ
cana-5705	200	70	medium	medium	NOUN
cana-5705	200	71	with	with	ADP
cana-5705	200	72	linear	linear	ADJ
cana-5705	200	73	pressure	pressure	NOUN
cana-5705	200	74	gradient	gradient	NOUN
cana-5705	200	75	under	under	ADP
cana-5705	200	76	different	different	ADJ
cana-5705	200	77	initial	initial	ADJ
cana-5705	200	78	conditions	condition	NOUN
cana-5705	200	79	.	.	PUNCT
cana-5705	201	1	from	from	ADP
cana-5705	201	2	this	this	DET
cana-5705	201	3	method	method	NOUN
cana-5705	201	4	we	we	PRON
cana-5705	201	5	can	can	AUX
cana-5705	201	6	conclude	conclude	VERB
cana-5705	201	7	that	that	SCONJ
cana-5705	201	8	the	the	DET
cana-5705	201	9	non	non	ADJ
cana-5705	201	10	-	-	ADJ
cana-5705	201	11	linear	linear	ADJ
cana-5705	201	12	problems	problem	NOUN
cana-5705	201	13	possess	possess	VERB
cana-5705	201	14	approximate	approximate	ADJ
cana-5705	201	15	or	or	CCONJ
cana-5705	201	16	exact	exact	ADJ
cana-5705	201	17	solution	solution	NOUN
cana-5705	201	18	by	by	ADP
cana-5705	201	19	analytical	analytical	ADJ
cana-5705	201	20	method	method	NOUN
cana-5705	201	21	.	.	PUNCT
cana-5705	202	1	this	this	DET
cana-5705	202	2	method	method	NOUN
cana-5705	202	3	is	be	AUX
cana-5705	202	4	capable	capable	ADJ
cana-5705	202	5	of	of	ADP
cana-5705	202	6	reducing	reduce	VERB
cana-5705	202	7	the	the	DET
cana-5705	202	8	volume	volume	NOUN
cana-5705	202	9	of	of	ADP
cana-5705	202	10	the	the	DET
cana-5705	202	11	computational	computational	ADJ
cana-5705	202	12	work	work	NOUN
cana-5705	202	13	as	as	SCONJ
cana-5705	202	14	compared	compare	VERB
cana-5705	202	15	to	to	ADP
cana-5705	202	16	the	the	DET
cana-5705	202	17	classical	classical	ADJ
cana-5705	202	18	methods	method	NOUN
cana-5705	202	19	while	while	SCONJ
cana-5705	202	20	still	still	ADV
cana-5705	202	21	maintaining	maintain	VERB
cana-5705	202	22	the	the	DET
cana-5705	202	23	high	high	ADJ
cana-5705	202	24	accuracy	accuracy	NOUN
cana-5705	202	25	of	of	ADP
cana-5705	202	26	the	the	DET
cana-5705	202	27	numerical	numerical	ADJ
cana-5705	202	28	result	result	NOUN
cana-5705	202	29	.	.	PUNCT
cana-5705	203	1	as	as	ADP
cana-5705	203	2	in	in	ADP
cana-5705	203	3	problem	problem	NOUN
cana-5705	203	4	i	i	PRON
cana-5705	203	5	,	,	PUNCT
cana-5705	203	6	with	with	ADP
cana-5705	203	7	initial	initial	ADJ
cana-5705	203	8	condition	condition	NOUN
cana-5705	203	9	as	as	ADP
cana-5705	203	10	an	an	DET
cana-5705	203	11	exponential	exponential	ADJ
cana-5705	203	12	term	term	NOUN
cana-5705	203	13	it	it	PRON
cana-5705	203	14	gives	give	VERB
cana-5705	203	15	approximate	approximate	ADJ
cana-5705	203	16	solution	solution	NOUN
cana-5705	203	17	with	with	ADP
cana-5705	203	18	the	the	DET
cana-5705	203	19	condition	condition	NOUN
cana-5705	203	20	𝑡	𝑡	X
cana-5705	203	21	<	<	X
cana-5705	203	22	1	1	NUM
cana-5705	203	23	.	.	PUNCT
cana-5705	203	24	where	where	SCONJ
cana-5705	203	25	as	as	ADP
cana-5705	203	26	in	in	ADP
cana-5705	203	27	problem	problem	PROPN
cana-5705	203	28	ii	ii	PROPN
cana-5705	203	29	,	,	PUNCT
cana-5705	203	30	with	with	ADP
cana-5705	203	31	initial	initial	ADJ
cana-5705	203	32	condition	condition	NOUN
cana-5705	203	33	as	as	ADP
cana-5705	203	34	a	a	DET
cana-5705	203	35	linear	linear	ADJ
cana-5705	203	36	term	term	NOUN
cana-5705	203	37	gives	give	VERB
cana-5705	203	38	exact	exact	ADJ
cana-5705	203	39	solution	solution	NOUN
cana-5705	203	40	for	for	ADP
cana-5705	203	41	any	any	DET
cana-5705	203	42	value	value	NOUN
cana-5705	203	43	of	of	ADP
cana-5705	203	44	t.	t.	PROPN
cana-5705	203	45	in	in	ADP
cana-5705	203	46	problem	problem	PROPN
cana-5705	203	47	iii	iii	PROPN
cana-5705	203	48	,	,	PUNCT
cana-5705	203	49	initial	initial	ADJ
cana-5705	203	50	condition	condition	NOUN
cana-5705	203	51	is	be	AUX
cana-5705	203	52	the	the	DET
cana-5705	203	53	sinusoidal	sinusoidal	ADJ
cana-5705	203	54	function	function	NOUN
cana-5705	203	55	,	,	PUNCT
cana-5705	203	56	which	which	PRON
cana-5705	203	57	gives	give	VERB
cana-5705	203	58	approximate	approximate	ADJ
cana-5705	203	59	solution	solution	NOUN
cana-5705	203	60	for	for	ADP
cana-5705	203	61	𝑡	𝑡	X
cana-5705	203	62	<	<	X
cana-5705	203	63	1	1	NUM
cana-5705	203	64	.	.	PUNCT
cana-5705	203	65	references	reference	NOUN
cana-5705	204	1	[	[	X
cana-5705	204	2	1	1	X
cana-5705	204	3	]	]	PUNCT
cana-5705	204	4	j.	j.	PROPN
cana-5705	204	5	h.	h.	PROPN
cana-5705	204	6	he	he	PRON
cana-5705	204	7	,	,	PUNCT
cana-5705	204	8	homotopy	homotopy	VERB
cana-5705	204	9	perturbation	perturbation	NOUN
cana-5705	204	10	technique	technique	NOUN
cana-5705	204	11	,	,	PUNCT
cana-5705	204	12	computer	computer	NOUN
cana-5705	204	13	methods	method	NOUN
cana-5705	204	14	in	in	ADP
cana-5705	204	15	applied	applied	ADJ
cana-5705	204	16	mechanics	mechanic	NOUN
cana-5705	204	17	and	and	CCONJ
cana-5705	204	18	engineering	engineering	NOUN
cana-5705	204	19	178(1999	178(1999	NUM
cana-5705	204	20	)	)	PUNCT
cana-5705	204	21	257	257	NUM
cana-5705	204	22	-	-	SYM
cana-5705	204	23	262	262	NUM
cana-5705	204	24	.	.	PUNCT
cana-5705	205	1	[	[	X
cana-5705	205	2	2	2	NUM
cana-5705	205	3	]	]	X
cana-5705	205	4	lan	lan	PROPN
cana-5705	205	5	xu	xu	PROPN
cana-5705	205	6	,	,	PUNCT
cana-5705	205	7	he	he	PRON
cana-5705	205	8	’s	’	VERB
cana-5705	205	9	homotopy	homotopy	NOUN
cana-5705	205	10	perturbation	perturbation	NOUN
cana-5705	205	11	method	method	NOUN
cana-5705	205	12	for	for	ADP
cana-5705	205	13	a	a	DET
cana-5705	205	14	boundary	boundary	ADJ
cana-5705	205	15	layer	layer	NOUN
cana-5705	205	16	equation	equation	NOUN
cana-5705	205	17	in	in	ADP
cana-5705	205	18	unbounded	unbounded	ADJ
cana-5705	205	19	domain	domain	NOUN
cana-5705	205	20	,	,	PUNCT
cana-5705	205	21	international	international	ADJ
cana-5705	205	22	journal	journal	NOUN
cana-5705	205	23	of	of	ADP
cana-5705	205	24	computer	computer	NOUN
cana-5705	205	25	and	and	CCONJ
cana-5705	205	26	mathematics	mathematic	NOUN
cana-5705	205	27	application	application	NOUN
cana-5705	205	28	.	.	PUNCT
cana-5705	206	1	elsevier-54(2007)10671070	elsevier-54(2007)10671070	NOUN
cana-5705	206	2	.	.	PUNCT
cana-5705	207	1	[	[	X
cana-5705	207	2	3	3	X
cana-5705	207	3	]	]	X
cana-5705	207	4	y.	y.	PROPN
cana-5705	207	5	khan	khan	PROPN
cana-5705	207	6	,	,	PUNCT
cana-5705	207	7	wu	wu	PROPN
cana-5705	207	8	q	q	PROPN
cana-5705	207	9	,	,	PUNCT
cana-5705	207	10	homotopy	homotopy	VERB
cana-5705	207	11	perturbation	perturbation	NOUN
cana-5705	207	12	transform	transform	NOUN
cana-5705	207	13	method	method	NOUN
cana-5705	207	14	for	for	ADP
cana-5705	207	15	non	non	ADJ
cana-5705	207	16	-	-	ADJ
cana-5705	207	17	linear	linear	ADJ
cana-5705	207	18	equations	equation	NOUN
cana-5705	207	19	using	use	VERB
cana-5705	207	20	he	he	PRON
cana-5705	207	21	’s	’s	PART
cana-5705	207	22	polynomials	polynomial	NOUN
cana-5705	207	23	,	,	PUNCT
cana-5705	207	24	journal	journal	NOUN
cana-5705	207	25	of	of	ADP
cana-5705	207	26	computers	computer	NOUN
cana-5705	207	27	and	and	CCONJ
cana-5705	207	28	mathematics	mathematic	NOUN
cana-5705	207	29	with	with	ADP
cana-5705	207	30	application	application	NOUN
cana-5705	207	31	,	,	PUNCT
cana-5705	207	32	elsevier	elsevier	NOUN
cana-5705	207	33	,	,	PUNCT
cana-5705	207	34	2010	2010	NUM
cana-5705	207	35	.	.	PUNCT
cana-5705	208	1	communications	communication	NOUN
cana-5705	208	2	on	on	ADP
cana-5705	208	3	applied	apply	VERB
cana-5705	208	4	nonlinear	nonlinear	ADJ
cana-5705	208	5	analysis	analysis	NOUN
cana-5705	208	6	issn	issn	NOUN
cana-5705	208	7	:	:	PUNCT
cana-5705	208	8	1074	1074	NUM
cana-5705	208	9	-	-	PUNCT
cana-5705	208	10	133x	133x	NUM
cana-5705	208	11	vol	vol	VERB
cana-5705	208	12	32	32	NUM
cana-5705	208	13	no	no	NOUN
cana-5705	208	14	.	.	PUNCT
cana-5705	209	1	10s	10	NOUN
cana-5705	209	2	(	(	PUNCT
cana-5705	209	3	2025	2025	NUM
cana-5705	209	4	)	)	PUNCT
cana-5705	209	5	2661	2661	NUM
cana-5705	209	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5705	210	1	[	[	X
cana-5705	210	2	4	4	X
cana-5705	210	3	]	]	X
cana-5705	210	4	asghar	asghar	PROPN
cana-5705	210	5	grorbani	grorbani	PROPN
cana-5705	210	6	,	,	PUNCT
cana-5705	210	7	beyond	beyond	ADP
cana-5705	210	8	adomian	adomian	NOUN
cana-5705	210	9	’s	’s	PART
cana-5705	210	10	polynomials	polynomial	NOUN
cana-5705	210	11	:	:	PUNCT
cana-5705	210	12	he	he	PRON
cana-5705	210	13	polynomials	polynomial	VERB
cana-5705	210	14	chaos	chaos	NOUN
cana-5705	210	15	solutions	solution	NOUN
cana-5705	210	16	fractals	fractal	NOUN
cana-5705	210	17	39(2009	39(2009	NUM
cana-5705	210	18	)	)	PUNCT
cana-5705	210	19	1486	1486	NUM
cana-5705	210	20	-	-	SYM
cana-5705	210	21	1492	1492	NUM
cana-5705	210	22	.	.	PUNCT
cana-5705	211	1	[	[	X
cana-5705	211	2	5	5	X
cana-5705	211	3	]	]	PUNCT
cana-5705	211	4	devendra	devendra	PROPN
cana-5705	211	5	kumar	kumar	PROPN
cana-5705	211	6	,	,	PUNCT
cana-5705	211	7	jagdar	jagdar	PROPN
cana-5705	211	8	singh	singh	PROPN
cana-5705	211	9	,	,	PUNCT
cana-5705	211	10	sushila	sushila	NOUN
cana-5705	211	11	,	,	PUNCT
cana-5705	211	12	application	application	NOUN
cana-5705	211	13	of	of	ADP
cana-5705	211	14	homotopy	homotopy	NOUN
cana-5705	211	15	perturbation	perturbation	NOUN
cana-5705	211	16	transform	transform	NOUN
cana-5705	211	17	method	method	NOUN
cana-5705	211	18	to	to	PART
cana-5705	211	19	linear	linear	VERB
cana-5705	211	20	and	and	CCONJ
cana-5705	211	21	nonlinear	nonlinear	PROPN
cana-5705	211	22	schrodinger	schrodinger	PROPN
cana-5705	211	23	’s	’s	PART
cana-5705	211	24	equations	equation	NOUN
cana-5705	211	25	,	,	PUNCT
cana-5705	211	26	international	international	ADJ
cana-5705	211	27	journal	journal	NOUN
cana-5705	211	28	of	of	ADP
cana-5705	211	29	non	non	ADJ
cana-5705	211	30	-	-	ADJ
cana-5705	211	31	linear	linear	ADJ
cana-5705	211	32	science	science	NOUN
cana-5705	211	33	vol,16	vol,16	NOUN
cana-5705	211	34	(	(	PUNCT
cana-5705	211	35	2013	2013	NUM
cana-5705	211	36	)	)	PUNCT
cana-5705	211	37	no.3	no.3	VERB
cana-5705	211	38	pp	pp	ADJ
cana-5705	211	39	203	203	NUM
cana-5705	211	40	-	-	SYM
cana-5705	211	41	209	209	NUM
cana-5705	211	42	.	.	PUNCT
cana-5705	212	1	[	[	X
cana-5705	212	2	6	6	NUM
cana-5705	212	3	]	]	X
cana-5705	212	4	gupta	gupta	PROPN
cana-5705	212	5	v.g	v.g	PROPN
cana-5705	212	6	.	.	PROPN
cana-5705	212	7	,	,	PUNCT
cana-5705	212	8	gupta	gupta	PROPN
cana-5705	212	9	s.	s.	PROPN
cana-5705	212	10	,	,	PUNCT
cana-5705	212	11	homotopy	homotopy	VERB
cana-5705	212	12	perturbation	perturbation	NOUN
cana-5705	212	13	transform	transform	NOUN
cana-5705	212	14	method	method	NOUN
cana-5705	212	15	for	for	ADP
cana-5705	212	16	solving	solve	VERB
cana-5705	212	17	initial	initial	ADJ
cana-5705	212	18	boundary	boundary	ADJ
cana-5705	212	19	value	value	NOUN
cana-5705	212	20	problem	problem	NOUN
cana-5705	212	21	of	of	ADP
cana-5705	212	22	variable	variable	ADJ
cana-5705	212	23	co	co	NOUN
cana-5705	212	24	-	-	ADJ
cana-5705	212	25	efficient	efficient	ADJ
cana-5705	212	26	;	;	PUNCT
cana-5705	212	27	international	international	ADJ
cana-5705	212	28	journal	journal	NOUN
cana-5705	212	29	of	of	ADP
cana-5705	212	30	non	non	ADJ
cana-5705	212	31	-	-	ADJ
cana-5705	212	32	linear	linear	ADJ
cana-5705	212	33	science	science	NOUN
cana-5705	212	34	,	,	PUNCT
cana-5705	212	35	vol.12(2011	vol.12(2011	ADJ
cana-5705	212	36	)	)	PUNCT
cana-5705	212	37	no.3	no.3	NOUN
cana-5705	212	38	pp270	pp270	PROPN
cana-5705	212	39	-	-	PUNCT
cana-5705	212	40	277	277	NUM
cana-5705	212	41	.	.	PUNCT
cana-5705	213	1	[	[	X
cana-5705	213	2	7	7	X
cana-5705	213	3	]	]	X
cana-5705	213	4	jagdev	jagdev	PROPN
cana-5705	213	5	singh	singh	PROPN
cana-5705	213	6	,	,	PUNCT
cana-5705	213	7	devendra	devendra	PROPN
cana-5705	213	8	kumar	kumar	PROPN
cana-5705	213	9	and	and	CCONJ
cana-5705	213	10	sushila	sushila	PROPN
cana-5705	213	11	rathore	rathore	PROPN
cana-5705	213	12	,	,	PUNCT
cana-5705	213	13	application	application	NOUN
cana-5705	213	14	of	of	ADP
cana-5705	213	15	homotopy	homotopy	NOUN
cana-5705	213	16	perturbation	perturbation	NOUN
cana-5705	213	17	transform	transform	NOUN
cana-5705	213	18	method	method	NOUN
cana-5705	213	19	for	for	ADP
cana-5705	213	20	solving	solve	VERB
cana-5705	213	21	linear	linear	ADJ
cana-5705	213	22	and	and	CCONJ
cana-5705	213	23	non	non	ADJ
cana-5705	213	24	-	-	ADJ
cana-5705	213	25	linear	linear	ADJ
cana-5705	213	26	klein	klein	PROPN
cana-5705	213	27	-	-	PUNCT
cana-5705	213	28	gordon	gordon	PROPN
cana-5705	213	29	equations	equation	NOUN
cana-5705	213	30	,	,	PUNCT
cana-5705	213	31	journal	journal	NOUN
cana-5705	213	32	of	of	ADP
cana-5705	213	33	information	information	NOUN
cana-5705	213	34	and	and	CCONJ
cana-5705	213	35	computing	computing	NOUN
cana-5705	213	36	science	science	NOUN
cana-5705	213	37	,	,	PUNCT
cana-5705	213	38	vol.7	vol.7	PROPN
cana-5705	213	39	,	,	PUNCT
cana-5705	213	40	no.2	no.2	PROPN
cana-5705	213	41	,	,	PUNCT
cana-5705	213	42	2012	2012	NUM
cana-5705	213	43	,	,	PUNCT
cana-5705	213	44	pp.131	pp.131	PROPN
cana-5705	213	45	-	-	SYM
cana-5705	213	46	139	139	NUM
cana-5705	213	47	.	.	PUNCT
cana-5705	214	1	[	[	X
cana-5705	214	2	8	8	NUM
cana-5705	214	3	]	]	X
cana-5705	214	4	mohammad	mohammad	PROPN
cana-5705	214	5	madani	madani	PROPN
cana-5705	214	6	,	,	PUNCT
cana-5705	214	7	mahdi	mahdi	PROPN
cana-5705	214	8	fathizadeh	fathizadeh	PROPN
cana-5705	214	9	,	,	PUNCT
cana-5705	214	10	yasir	yasir	PROPN
cana-5705	214	11	khan	khan	PROPN
cana-5705	214	12	,	,	PUNCT
cana-5705	214	13	ahmet	ahmet	PROPN
cana-5705	214	14	yildirim	yildirim	PROPN
cana-5705	214	15	,	,	PUNCT
cana-5705	214	16	mathematical	mathematical	ADJ
cana-5705	214	17	and	and	CCONJ
cana-5705	214	18	computer	computer	NOUN
cana-5705	214	19	modelling	model	VERB
cana-5705	214	20	53	53	NUM
cana-5705	214	21	(	(	PUNCT
cana-5705	214	22	2011	2011	NUM
cana-5705	214	23	)	)	PUNCT
cana-5705	214	24	elsevier	elsevier	NOUN
cana-5705	214	25	,	,	PUNCT
cana-5705	214	26	1937	1937	NUM
cana-5705	214	27	-	-	SYM
cana-5705	214	28	1945	1945	NUM
cana-5705	214	29	.	.	PUNCT
cana-5705	215	1	[	[	X
cana-5705	215	2	9	9	NUM
cana-5705	215	3	]	]	X
cana-5705	215	4	mubashra	mubashra	NOUN
cana-5705	215	5	saleem	saleem	PROPN
cana-5705	215	6	,	,	PUNCT
cana-5705	215	7	aqsa	aqsa	PROPN
cana-5705	215	8	mumtaz	mumtaz	PROPN
cana-5705	215	9	,	,	PUNCT
cana-5705	215	10	tahira	tahira	PROPN
cana-5705	215	11	amir	amir	PROPN
cana-5705	215	12	,	,	PUNCT
cana-5705	215	13	qazi	qazi	PROPN
cana-5705	215	14	muhmmad	muhmmad	PROPN
cana-5705	215	15	ul	ul	PROPN
cana-5705	215	16	hassan	hassan	PROPN
cana-5705	215	17	,	,	PUNCT
cana-5705	215	18	kamran	kamran	PROPN
cana-5705	215	19	ayub	ayub	PROPN
cana-5705	215	20	,	,	PUNCT
cana-5705	215	21	farhana	farhana	PROPN
cana-5705	215	22	kanwal	kanwal	PROPN
cana-5705	215	23	-	-	PUNCT
cana-5705	215	24	homotopy	homotopy	NOUN
cana-5705	215	25	perturbation	perturbation	NOUN
cana-5705	215	26	method	method	NOUN
cana-5705	215	27	using	use	VERB
cana-5705	215	28	he	he	PRON
cana-5705	215	29	’s	’s	PART
cana-5705	215	30	polynomial	polynomial	ADJ
cana-5705	215	31	for	for	ADP
cana-5705	215	32	solving	solve	VERB
cana-5705	215	33	nonlinear	nonlinear	ADJ
cana-5705	215	34	differential	differential	ADJ
cana-5705	215	35	equations	equation	NOUN
cana-5705	215	36	,	,	PUNCT
cana-5705	215	37	open	open	ADJ
cana-5705	215	38	science	science	NOUN
cana-5705	215	39	journal	journal	NOUN
cana-5705	215	40	of	of	ADP
cana-5705	215	41	mathematics	mathematic	NOUN
cana-5705	215	42	and	and	CCONJ
cana-5705	215	43	applications2017;5(2):8	applications2017;5(2):8	NOUN
cana-5705	215	44	-	-	SYM
cana-5705	215	45	11	11	NUM
cana-5705	215	46	.	.	PUNCT
cana-5705	216	1	[	[	X
cana-5705	216	2	10	10	NUM
cana-5705	216	3	]	]	X
cana-5705	216	4	sari	sari	NOUN
cana-5705	216	5	m	m	PROPN
cana-5705	216	6	,	,	PUNCT
cana-5705	216	7	solution	solution	NOUN
cana-5705	216	8	of	of	ADP
cana-5705	216	9	the	the	DET
cana-5705	216	10	porous	porous	ADJ
cana-5705	216	11	media	medium	NOUN
cana-5705	216	12	equation	equation	NOUN
cana-5705	216	13	by	by	ADP
cana-5705	216	14	a	a	DET
cana-5705	216	15	compact	compact	ADJ
cana-5705	216	16	finite	finite	NOUN
cana-5705	216	17	differential	differential	NOUN
cana-5705	216	18	method	method	NOUN
cana-5705	216	19	,	,	PUNCT
cana-5705	216	20	mathematical	mathematical	ADJ
cana-5705	216	21	problem	problem	NOUN
cana-5705	216	22	in	in	ADP
cana-5705	216	23	engineering	engineering	NOUN
cana-5705	216	24	,	,	PUNCT
cana-5705	216	25	hindwi	hindwi	CCONJ
cana-5705	216	26	publishing	publish	VERB
cana-5705	216	27	corporation	corporation	NOUN
cana-5705	216	28	,	,	PUNCT
cana-5705	216	29	2009	2009	NUM
cana-5705	216	30	.	.	PUNCT
cana-5705	217	1	[	[	X
cana-5705	217	2	11	11	NUM
cana-5705	217	3	]	]	X
cana-5705	217	4	n.	n.	PROPN
cana-5705	217	5	h.	h.	PROPN
cana-5705	217	6	sweilam	sweilam	PROPN
cana-5705	217	7	,	,	PUNCT
cana-5705	217	8	m.	m.	NOUN
cana-5705	217	9	m.	m.	NOUN
cana-5705	217	10	khader	khader	PROPN
cana-5705	217	11	,	,	PUNCT
cana-5705	217	12	exact	exact	ADJ
cana-5705	217	13	solution	solution	NOUN
cana-5705	217	14	of	of	ADP
cana-5705	217	15	some	some	DET
cana-5705	217	16	coupled	couple	VERB
cana-5705	217	17	non	non	ADJ
cana-5705	217	18	-	-	ADJ
cana-5705	217	19	linear	linear	ADJ
cana-5705	217	20	partial	partial	ADJ
cana-5705	217	21	differential	differential	NOUN
cana-5705	217	22	equations	equation	NOUN
cana-5705	217	23	using	use	VERB
cana-5705	217	24	the	the	DET
cana-5705	217	25	homotopy	homotopy	NOUN
cana-5705	217	26	perturbation	perturbation	NOUN
cana-5705	217	27	method	method	NOUN
cana-5705	217	28	,	,	PUNCT
cana-5705	217	29	computers	computer	NOUN
cana-5705	217	30	and	and	CCONJ
cana-5705	217	31	mathematics	mathematic	NOUN
cana-5705	217	32	with	with	ADP
cana-5705	217	33	application	application	NOUN
cana-5705	217	34	58	58	NUM
cana-5705	217	35	(	(	PUNCT
cana-5705	217	36	2009	2009	NUM
cana-5705	217	37	)	)	PUNCT
cana-5705	217	38	2134	2134	NUM
cana-5705	217	39	2141	2141	NUM
cana-5705	217	40	.	.	PUNCT
cana-5705	218	1	topological	topological	ADJ
cana-5705	218	2	methods	method	NOUN
cana-5705	218	3	in	in	ADP
cana-5705	218	4	non	non	ADJ
cana-5705	218	5	-	-	ADJ
cana-5705	218	6	linear	linear	ADJ
cana-5705	218	7	analysis	analysis	NOUN
cana-5705	218	8	31(2008	31(2008	NUM
cana-5705	218	9	)	)	PUNCT
cana-5705	218	10	205	205	NUM
cana-5705	218	11	-	-	SYM
cana-5705	218	12	209	209	NUM
cana-5705	218	13	.	.	PUNCT
cana-5705	219	1	[	[	X
cana-5705	219	2	12	12	NUM
cana-5705	219	3	]	]	X
cana-5705	219	4	majid	majid	PROPN
cana-5705	219	5	khan	khan	PROPN
cana-5705	219	6	,	,	PUNCT
cana-5705	219	7	muhammad	muhammad	PROPN
cana-5705	219	8	asif	asif	PROPN
cana-5705	219	9	gondal	gondal	PROPN
cana-5705	219	10	,	,	PUNCT
cana-5705	219	11	iqtadar	iqtadar	NOUN
cana-5705	219	12	hussain	hussain	PROPN
cana-5705	219	13	,	,	PUNCT
cana-5705	219	14	s.	s.	PROPN
cana-5705	219	15	karimi	karimi	PROPN
cana-5705	219	16	vanani	vanani	PROPN
cana-5705	219	17	,	,	PUNCT
cana-5705	219	18	a	a	DET
cana-5705	219	19	new	new	ADJ
cana-5705	219	20	comparative	comparative	ADJ
cana-5705	219	21	study	study	NOUN
cana-5705	219	22	between	between	ADP
cana-5705	219	23	homotopy	homotopy	NOUN
cana-5705	219	24	perturbation	perturbation	NOUN
cana-5705	219	25	transform	transform	NOUN
cana-5705	219	26	method	method	NOUN
cana-5705	219	27	on	on	ADP
cana-5705	219	28	a	a	DET
cana-5705	219	29	semi	semi	ADJ
cana-5705	219	30	-	-	ADJ
cana-5705	219	31	infinite	infinite	ADJ
cana-5705	219	32	domain	domain	NOUN
cana-5705	219	33	,	,	PUNCT
cana-5705	219	34	mathematical	mathematical	ADJ
cana-5705	219	35	and	and	CCONJ
cana-5705	219	36	computer	computer	NOUN
cana-5705	219	37	modelling	model	VERB
cana-5705	219	38	55(2012	55(2012	NUM
cana-5705	219	39	)	)	PUNCT
cana-5705	219	40	1143	1143	NUM
cana-5705	219	41	-	-	SYM
cana-5705	219	42	1150	1150	NUM
cana-5705	219	43	.	.	PUNCT
cana-5705	220	1	[	[	X
cana-5705	220	2	13	13	NUM
cana-5705	220	3	]	]	PUNCT
cana-5705	220	4	mohamed	mohamed	PROPN
cana-5705	220	5	elbadri	elbadri	PROPN
cana-5705	220	6	,	,	PUNCT
cana-5705	220	7	comparison	comparison	NOUN
cana-5705	220	8	between	between	ADP
cana-5705	220	9	the	the	DET
cana-5705	220	10	homotopy	homotopy	NOUN
cana-5705	220	11	perturbation	perturbation	NOUN
cana-5705	220	12	method	method	NOUN
cana-5705	220	13	and	and	CCONJ
cana-5705	220	14	homotopy	homotopy	VERB
cana-5705	220	15	perturbation	perturbation	NOUN
cana-5705	220	16	transform	transform	NOUN
cana-5705	220	17	method	method	NOUN
cana-5705	220	18	,	,	PUNCT
cana-5705	220	19	scientific	scientific	ADJ
cana-5705	220	20	research	research	NOUN
cana-5705	220	21	publishing	publishing	NOUN
cana-5705	220	22	-	-	PUNCT
cana-5705	220	23	applied	apply	VERB
cana-5705	220	24	mathematics	mathematic	NOUN
cana-5705	220	25	,	,	PUNCT
cana-5705	220	26	2018	2018	NUM
cana-5705	220	27	,	,	PUNCT
cana-5705	220	28	9	9	NUM
cana-5705	220	29	,	,	PUNCT
cana-5705	220	30	130	130	NUM
cana-5705	220	31	-	-	SYM
cana-5705	220	32	137	137	NUM
cana-5705	220	33	.	.	PUNCT
cana-5705	221	1	[	[	X
cana-5705	221	2	14	14	NUM
cana-5705	221	3	]	]	X
cana-5705	221	4	mohamed	mohamed	PROPN
cana-5705	221	5	jleli	jleli	PROPN
cana-5705	221	6	,	,	PUNCT
cana-5705	221	7	sunil	sunil	PROPN
cana-5705	221	8	kumar	kumar	PROPN
cana-5705	221	9	,	,	PUNCT
cana-5705	221	10	ranbir	ranbir	PROPN
cana-5705	221	11	kumar	kumar	PROPN
cana-5705	221	12	,	,	PUNCT
cana-5705	221	13	bessem	bessem	NOUN
cana-5705	221	14	samet	samet	NOUN
cana-5705	221	15	,	,	PUNCT
cana-5705	221	16	analytical	analytical	ADJ
cana-5705	221	17	approach	approach	NOUN
cana-5705	221	18	for	for	ADP
cana-5705	221	19	time	time	NOUN
cana-5705	221	20	fractional	fractional	ADJ
cana-5705	221	21	wave	wave	NOUN
cana-5705	221	22	equations	equation	NOUN
cana-5705	221	23	in	in	ADP
cana-5705	221	24	the	the	DET
cana-5705	221	25	sense	sense	NOUN
cana-5705	221	26	of	of	ADP
cana-5705	221	27	yang	yang	PROPN
cana-5705	221	28	-	-	PUNCT
cana-5705	221	29	abdel	abdel	PROPN
cana-5705	221	30	-	-	PUNCT
cana-5705	221	31	aty	aty	NOUN
cana-5705	221	32	-	-	NOUN
cana-5705	221	33	cattani	cattani	NOUN
cana-5705	221	34	via	via	ADP
cana-5705	221	35	the	the	DET
cana-5705	221	36	homotopy	homotopy	NOUN
cana-5705	221	37	perturbation	perturbation	NOUN
cana-5705	221	38	transform	transform	NOUN
cana-5705	221	39	method	method	NOUN
cana-5705	221	40	,	,	PUNCT
cana-5705	221	41	alexandria	alexandria	PROPN
cana-5705	221	42	engineering	engineering	PROPN
cana-5705	221	43	journal	journal	PROPN
cana-5705	221	44	(	(	PUNCT
cana-5705	221	45	2020)59	2020)59	NUM
cana-5705	221	46	,	,	PUNCT
cana-5705	221	47	2859	2859	NUM
cana-5705	221	48	-	-	SYM
cana-5705	221	49	2863	2863	NUM
cana-5705	221	50	.	.	PUNCT
cana-5705	222	1	[	[	X
cana-5705	222	2	15	15	NUM
cana-5705	222	3	]	]	X
cana-5705	222	4	u.	u.	NOUN
cana-5705	222	5	filobello	filobello	PROPN
cana-5705	222	6	-	-	PUNCT
cana-5705	222	7	nino	nino	PROPN
cana-5705	222	8	,	,	PUNCT
cana-5705	222	9	h.	h.	PROPN
cana-5705	222	10	vazquez	vazquez	PROPN
cana-5705	222	11	-leal	-leal	PROPN
cana-5705	222	12	,	,	PUNCT
cana-5705	222	13	y.	y.	PROPN
cana-5705	222	14	khan	khan	PROPN
cana-5705	222	15	,	,	PUNCT
cana-5705	222	16	a.	a.	PROPN
cana-5705	222	17	perez	perez	PROPN
cana-5705	222	18	-	-	PUNCT
cana-5705	222	19	sesma	sesma	PROPN
cana-5705	222	20	,	,	PUNCT
cana-5705	222	21	a.	a.	PROPN
cana-5705	222	22	diaz	diaz	PROPN
cana-5705	222	23	-	-	PUNCT
cana-5705	222	24	sanchez	sanchez	PROPN
cana-5705	222	25	,	,	PUNCT
cana-5705	222	26	v.	v.	ADP
cana-5705	222	27	m.	m.	NOUN
cana-5705	222	28	jimenezfernandez	jimenezfernandez	PROPN
cana-5705	222	29	,	,	PUNCT
cana-5705	222	30	a.	a.	PROPN
cana-5705	222	31	herrera	herrera	PROPN
cana-5705	222	32	-	-	PUNCT
cana-5705	222	33	may	may	PROPN
cana-5705	222	34	,	,	PUNCT
cana-5705	222	35	d.	d.	PROPN
cana-5705	222	36	pereyra	pereyra	PROPN
cana-5705	222	37	-	-	PUNCT
cana-5705	222	38	diaz	diaz	PROPN
cana-5705	222	39	,	,	PUNCT
cana-5705	222	40	j.	j.	PROPN
cana-5705	222	41	sanchez	sanchez	PROPN
cana-5705	222	42	-	-	PUNCT
cana-5705	222	43	orea	orea	PROPN
cana-5705	222	44	,	,	PUNCT
cana-5705	222	45	laplace	laplace	NOUN
cana-5705	222	46	transform	transform	VERB
cana-5705	222	47	homotopy	homotopy	NOUN
cana-5705	222	48	perturbation	perturbation	NOUN
cana-5705	222	49	method	method	NOUN
cana-5705	222	50	as	as	ADP
cana-5705	222	51	a	a	DET
cana-5705	222	52	powerful	powerful	ADJ
cana-5705	222	53	tool	tool	NOUN
cana-5705	222	54	to	to	PART
cana-5705	222	55	solve	solve	VERB
cana-5705	222	56	nonlinear	nonlinear	ADJ
cana-5705	222	57	problems	problem	NOUN
cana-5705	222	58	with	with	ADP
cana-5705	222	59	boundary	boundary	ADJ
cana-5705	222	60	conditions	condition	NOUN
cana-5705	222	61	defined	define	VERB
cana-5705	222	62	on	on	ADP
cana-5705	222	63	finite	finite	ADJ
cana-5705	222	64	intervals	interval	NOUN
cana-5705	222	65	,	,	PUNCT
cana-5705	222	66	comp	comp	PROPN
cana-5705	222	67	.	.	PUNCT
cana-5705	223	1	appl	appl	PROPN
cana-5705	223	2	.	.	PROPN
cana-5705	223	3	math	math	PROPN
cana-5705	223	4	.	.	PUNCT
cana-5705	224	1	,2013	,2013	PROPN
cana-5705	224	2	,	,	PUNCT
cana-5705	224	3	doi	doi	NOUN
cana-5705	224	4	10.1007	10.1007	NUM
cana-5705	224	5	/	/	SYM
cana-5705	224	6	s40314	s40314	NOUN
cana-5705	224	7	-	-	PUNCT
cana-5705	224	8	0130073	0130073	NUM
cana-5705	224	9	-	-	PUNCT
cana-5705	224	10	z.	z.	PROPN
cana-5705	224	11	nomenclature	nomenclature	PROPN
cana-5705	224	12	t	t	PROPN
cana-5705	224	13	temperature	temperature	NOUN
cana-5705	224	14	variable	variable	NOUN
cana-5705	224	15	in	in	ADP
cana-5705	224	16	problems	problem	NOUN
cana-5705	224	17	x	x	PUNCT
cana-5705	224	18	distance	distance	NOUN
cana-5705	224	19	variable	variable	NOUN
cana-5705	224	20	𝜃	𝜃	PRON
cana-5705	224	21	temperature	temperature	NOUN
cana-5705	224	22	variable	variable	NOUN
cana-5705	224	23	in	in	ADP
cana-5705	224	24	method	method	NOUN
cana-5705	224	25	t	t	PROPN
cana-5705	224	26	time	time	NOUN
cana-5705	224	27	variable	variable	ADJ
cana-5705	224	28	𝑝	𝑝	PROPN
cana-5705	224	29	pressure	pressure	NOUN
cana-5705	224	30	q	q	NOUN
cana-5705	224	31	embedding	embed	VERB
cana-5705	224	32	parameter	parameter	NOUN
cana-5705	224	33	𝜌	𝜌	ADP
cana-5705	224	34	density	density	NOUN
cana-5705	224	35	h	h	NOUN
cana-5705	225	1	he	he	PRON
cana-5705	225	2	’s	’	VERB
cana-5705	225	3	polynomial	polynomial	ADJ
cana-5705	225	4	term	term	NOUN
cana-5705	225	5	l	l	NOUN
cana-5705	225	6	laplace	laplace	NOUN
cana-5705	225	7	operator	operator	NOUN
cana-5705	225	8	𝜃𝑡	𝜃𝑡	CCONJ
cana-5705	225	9	velocity	velocity	NOUN
cana-5705	225	10	𝐿−1	𝐿−1	NOUN
cana-5705	225	11	inverse	inverse	ADJ
cana-5705	225	12	laplace	laplace	NOUN
cana-5705	225	13	operator	operator	NOUN
cana-5705	225	14	a	a	DET
cana-5705	225	15	constant	constant	ADJ
cana-5705	225	16	in	in	ADP
cana-5705	225	17	pressure	pressure	NOUN
cana-5705	225	18	term	term	NOUN