id	sid	tid	token	lemma	pos
ejpam-6215	1	1	european	european	PROPN
ejpam-6215	1	2	journal	journal	PROPN
ejpam-6215	1	3	of	of	ADP
ejpam-6215	1	4	pure	pure	ADJ
ejpam-6215	1	5	and	and	CCONJ
ejpam-6215	1	6	applied	applied	ADJ
ejpam-6215	1	7	mathematics	mathematic	NOUN
ejpam-6215	1	8	2025	2025	NUM
ejpam-6215	1	9	,	,	PUNCT
ejpam-6215	1	10	vol	vol	NOUN
ejpam-6215	1	11	.	.	PROPN
ejpam-6215	1	12	18	18	NUM
ejpam-6215	1	13	,	,	PUNCT
ejpam-6215	1	14	issue	issue	NOUN
ejpam-6215	1	15	3	3	NUM
ejpam-6215	1	16	,	,	PUNCT
ejpam-6215	1	17	article	article	NOUN
ejpam-6215	1	18	number	number	NOUN
ejpam-6215	1	19	6215	6215	NUM
ejpam-6215	1	20	issn	issn	PROPN
ejpam-6215	1	21	1307	1307	NUM
ejpam-6215	1	22	-	-	SYM
ejpam-6215	1	23	5543	5543	NUM
ejpam-6215	1	24	–	–	PUNCT
ejpam-6215	1	25	ejpam.com	ejpam.com	X
ejpam-6215	1	26	published	publish	VERB
ejpam-6215	1	27	by	by	ADP
ejpam-6215	1	28	new	new	PROPN
ejpam-6215	1	29	york	york	PROPN
ejpam-6215	1	30	business	business	PROPN
ejpam-6215	1	31	global	global	ADJ
ejpam-6215	1	32	analytic	analytic	ADJ
ejpam-6215	1	33	and	and	CCONJ
ejpam-6215	1	34	numerical	numerical	ADJ
ejpam-6215	1	35	approaches	approach	NOUN
ejpam-6215	1	36	for	for	ADP
ejpam-6215	1	37	solving	solve	VERB
ejpam-6215	1	38	nonlinear	nonlinear	ADJ
ejpam-6215	1	39	painlevé	painlevé	NOUN
ejpam-6215	1	40	equations	equation	NOUN
ejpam-6215	1	41	i	i	PRON
ejpam-6215	1	42	and	and	CCONJ
ejpam-6215	1	43	ii	ii	PROPN
ejpam-6215	1	44	sangar	sangar	VERB
ejpam-6215	1	45	mohammed	mohammed	PROPN
ejpam-6215	1	46	hasan1,∗	hasan1,∗	PROPN
ejpam-6215	1	47	,	,	PUNCT
ejpam-6215	1	48	sizar	sizar	ADJ
ejpam-6215	1	49	abid	abid	PROPN
ejpam-6215	1	50	mohammed1	mohammed1	PROPN
ejpam-6215	1	51	,	,	PUNCT
ejpam-6215	1	52	ramadhan	ramadhan	PROPN
ejpam-6215	1	53	abid	abid	PROPN
ejpam-6215	1	54	mohammed1	mohammed1	PROPN
ejpam-6215	1	55	1	1	NUM
ejpam-6215	1	56	department	department	NOUN
ejpam-6215	1	57	of	of	ADP
ejpam-6215	1	58	mathematics	mathematic	NOUN
ejpam-6215	1	59	,	,	PUNCT
ejpam-6215	1	60	college	college	NOUN
ejpam-6215	1	61	of	of	ADP
ejpam-6215	1	62	basic	basic	ADJ
ejpam-6215	1	63	education	education	NOUN
ejpam-6215	1	64	,	,	PUNCT
ejpam-6215	1	65	university	university	NOUN
ejpam-6215	1	66	of	of	ADP
ejpam-6215	1	67	duhok	duhok	PROPN
ejpam-6215	1	68	,	,	PUNCT
ejpam-6215	1	69	kurdistan	kurdistan	PROPN
ejpam-6215	1	70	region	region	NOUN
ejpam-6215	1	71	,	,	PUNCT
ejpam-6215	1	72	iraq	iraq	PROPN
ejpam-6215	1	73	abstract	abstract	NOUN
ejpam-6215	1	74	.	.	PUNCT
ejpam-6215	2	1	nonlinear	nonlinear	ADJ
ejpam-6215	2	2	painlevé	painlevé	NOUN
ejpam-6215	2	3	equations	equation	NOUN
ejpam-6215	2	4	play	play	VERB
ejpam-6215	2	5	a	a	DET
ejpam-6215	2	6	pivotal	pivotal	ADJ
ejpam-6215	2	7	role	role	NOUN
ejpam-6215	2	8	in	in	ADP
ejpam-6215	2	9	various	various	ADJ
ejpam-6215	2	10	branches	branch	NOUN
ejpam-6215	2	11	of	of	ADP
ejpam-6215	2	12	mathematical	mathematical	ADJ
ejpam-6215	2	13	physics	physics	NOUN
ejpam-6215	2	14	,	,	PUNCT
ejpam-6215	2	15	integrable	integrable	ADJ
ejpam-6215	2	16	systems	system	NOUN
ejpam-6215	2	17	,	,	PUNCT
ejpam-6215	2	18	and	and	CCONJ
ejpam-6215	2	19	applied	apply	VERB
ejpam-6215	2	20	mathematics	mathematic	NOUN
ejpam-6215	2	21	.	.	PUNCT
ejpam-6215	3	1	these	these	DET
ejpam-6215	3	2	equations	equation	NOUN
ejpam-6215	3	3	,	,	PUNCT
ejpam-6215	3	4	characterized	characterize	VERB
ejpam-6215	3	5	by	by	ADP
ejpam-6215	3	6	their	their	PRON
ejpam-6215	3	7	complex	complex	ADJ
ejpam-6215	3	8	and	and	CCONJ
ejpam-6215	3	9	highly	highly	ADV
ejpam-6215	3	10	nonlinear	nonlinear	ADJ
ejpam-6215	3	11	nature	nature	NOUN
ejpam-6215	3	12	,	,	PUNCT
ejpam-6215	3	13	present	present	ADJ
ejpam-6215	3	14	significant	significant	ADJ
ejpam-6215	3	15	challenges	challenge	NOUN
ejpam-6215	3	16	for	for	ADP
ejpam-6215	3	17	analytical	analytical	ADJ
ejpam-6215	3	18	and	and	CCONJ
ejpam-6215	3	19	numerical	numerical	ADJ
ejpam-6215	3	20	investigation	investigation	NOUN
ejpam-6215	3	21	.	.	PUNCT
ejpam-6215	4	1	in	in	ADP
ejpam-6215	4	2	this	this	DET
ejpam-6215	4	3	paper	paper	NOUN
ejpam-6215	4	4	,	,	PUNCT
ejpam-6215	4	5	we	we	PRON
ejpam-6215	4	6	develop	develop	VERB
ejpam-6215	4	7	and	and	CCONJ
ejpam-6215	4	8	present	present	VERB
ejpam-6215	4	9	both	both	CCONJ
ejpam-6215	4	10	analytical	analytical	ADJ
ejpam-6215	4	11	and	and	CCONJ
ejpam-6215	4	12	numerical	numerical	ADJ
ejpam-6215	4	13	solutions	solution	NOUN
ejpam-6215	4	14	for	for	ADP
ejpam-6215	4	15	specific	specific	ADJ
ejpam-6215	4	16	classes	class	NOUN
ejpam-6215	4	17	of	of	ADP
ejpam-6215	4	18	nonlinear	nonlinear	ADJ
ejpam-6215	4	19	painlevé	painlevé	NOUN
ejpam-6215	4	20	equations	equation	NOUN
ejpam-6215	4	21	.	.	PUNCT
ejpam-6215	5	1	the	the	DET
ejpam-6215	5	2	analytical	analytical	ADJ
ejpam-6215	5	3	approach	approach	NOUN
ejpam-6215	5	4	employs	employ	VERB
ejpam-6215	5	5	transformation	transformation	NOUN
ejpam-6215	5	6	techniques	technique	NOUN
ejpam-6215	5	7	,	,	PUNCT
ejpam-6215	5	8	perturbative	perturbative	ADJ
ejpam-6215	5	9	expansions	expansion	NOUN
ejpam-6215	5	10	,	,	PUNCT
ejpam-6215	5	11	and	and	CCONJ
ejpam-6215	5	12	exact	exact	ADJ
ejpam-6215	5	13	solution	solution	NOUN
ejpam-6215	5	14	methods	method	NOUN
ejpam-6215	5	15	where	where	SCONJ
ejpam-6215	5	16	applicable	applicable	ADJ
ejpam-6215	5	17	,	,	PUNCT
ejpam-6215	5	18	while	while	SCONJ
ejpam-6215	5	19	the	the	DET
ejpam-6215	5	20	numerical	numerical	ADJ
ejpam-6215	5	21	solutions	solution	NOUN
ejpam-6215	5	22	are	be	AUX
ejpam-6215	5	23	obtained	obtain	VERB
ejpam-6215	5	24	using	use	VERB
ejpam-6215	5	25	robust	robust	ADJ
ejpam-6215	5	26	algorithms	algorithm	NOUN
ejpam-6215	5	27	such	such	ADJ
ejpam-6215	5	28	as	as	ADP
ejpam-6215	5	29	finite	finite	ADJ
ejpam-6215	5	30	difference	difference	NOUN
ejpam-6215	5	31	schemes	scheme	NOUN
ejpam-6215	5	32	,	,	PUNCT
ejpam-6215	5	33	spectral	spectral	ADJ
ejpam-6215	5	34	methods	method	NOUN
ejpam-6215	5	35	,	,	PUNCT
ejpam-6215	5	36	and	and	CCONJ
ejpam-6215	5	37	iterative	iterative	ADJ
ejpam-6215	5	38	solvers	solver	NOUN
ejpam-6215	5	39	.	.	PUNCT
ejpam-6215	6	1	we	we	PRON
ejpam-6215	6	2	validate	validate	VERB
ejpam-6215	6	3	the	the	DET
ejpam-6215	6	4	numerical	numerical	ADJ
ejpam-6215	6	5	results	result	NOUN
ejpam-6215	6	6	by	by	ADP
ejpam-6215	6	7	comparing	compare	VERB
ejpam-6215	6	8	them	they	PRON
ejpam-6215	6	9	with	with	ADP
ejpam-6215	6	10	known	know	VERB
ejpam-6215	6	11	analytical	analytical	ADJ
ejpam-6215	6	12	solutions	solution	NOUN
ejpam-6215	6	13	and	and	CCONJ
ejpam-6215	6	14	explore	explore	VERB
ejpam-6215	6	15	their	their	PRON
ejpam-6215	6	16	accuracy	accuracy	NOUN
ejpam-6215	6	17	,	,	PUNCT
ejpam-6215	6	18	stability	stability	NOUN
ejpam-6215	6	19	,	,	PUNCT
ejpam-6215	6	20	and	and	CCONJ
ejpam-6215	6	21	convergence	convergence	NOUN
ejpam-6215	6	22	properties	property	NOUN
ejpam-6215	6	23	.	.	PUNCT
ejpam-6215	7	1	furthermore	furthermore	ADV
ejpam-6215	7	2	,	,	PUNCT
ejpam-6215	7	3	we	we	PRON
ejpam-6215	7	4	discuss	discuss	VERB
ejpam-6215	7	5	the	the	DET
ejpam-6215	7	6	implications	implication	NOUN
ejpam-6215	7	7	of	of	ADP
ejpam-6215	7	8	these	these	DET
ejpam-6215	7	9	solutions	solution	NOUN
ejpam-6215	7	10	in	in	ADP
ejpam-6215	7	11	physical	physical	ADJ
ejpam-6215	7	12	models	model	NOUN
ejpam-6215	7	13	and	and	CCONJ
ejpam-6215	7	14	highlight	highlight	VERB
ejpam-6215	7	15	the	the	DET
ejpam-6215	7	16	intricate	intricate	ADJ
ejpam-6215	7	17	structures	structure	NOUN
ejpam-6215	7	18	exhibited	exhibit	VERB
ejpam-6215	7	19	by	by	ADP
ejpam-6215	7	20	the	the	DET
ejpam-6215	7	21	solutions	solution	NOUN
ejpam-6215	7	22	,	,	PUNCT
ejpam-6215	7	23	such	such	ADJ
ejpam-6215	7	24	as	as	ADP
ejpam-6215	7	25	pole	pole	NOUN
ejpam-6215	7	26	dynamics	dynamic	NOUN
ejpam-6215	7	27	and	and	CCONJ
ejpam-6215	7	28	asymptotic	asymptotic	ADJ
ejpam-6215	7	29	behaviors	behavior	NOUN
ejpam-6215	7	30	.	.	PUNCT
ejpam-6215	8	1	this	this	DET
ejpam-6215	8	2	work	work	NOUN
ejpam-6215	8	3	contributes	contribute	VERB
ejpam-6215	8	4	to	to	ADP
ejpam-6215	8	5	the	the	DET
ejpam-6215	8	6	broader	broad	ADJ
ejpam-6215	8	7	understanding	understanding	NOUN
ejpam-6215	8	8	of	of	ADP
ejpam-6215	8	9	painlevé	painlevé	NOUN
ejpam-6215	8	10	equations	equation	NOUN
ejpam-6215	8	11	and	and	CCONJ
ejpam-6215	8	12	provides	provide	VERB
ejpam-6215	8	13	a	a	DET
ejpam-6215	8	14	framework	framework	NOUN
ejpam-6215	8	15	for	for	ADP
ejpam-6215	8	16	tackling	tackle	VERB
ejpam-6215	8	17	similar	similar	ADJ
ejpam-6215	8	18	nonlinear	nonlinear	ADJ
ejpam-6215	8	19	differential	differential	ADJ
ejpam-6215	8	20	equations	equation	NOUN
ejpam-6215	8	21	in	in	ADP
ejpam-6215	8	22	applied	applied	ADJ
ejpam-6215	8	23	contexts	contexts	NOUN
ejpam-6215	8	24	.	.	PUNCT
ejpam-6215	9	1	2020	2020	NUM
ejpam-6215	9	2	mathematics	mathematic	NOUN
ejpam-6215	9	3	subject	subject	NOUN
ejpam-6215	9	4	classifications	classification	NOUN
ejpam-6215	9	5	:	:	PUNCT
ejpam-6215	9	6	34m55	34m55	NUM
ejpam-6215	9	7	,	,	PUNCT
ejpam-6215	9	8	34a34	34a34	NUM
ejpam-6215	9	9	,	,	PUNCT
ejpam-6215	9	10	65l05	65l05	NUM
ejpam-6215	9	11	,	,	PUNCT
ejpam-6215	9	12	65l06	65l06	NUM
ejpam-6215	9	13	,	,	PUNCT
ejpam-6215	9	14	35q99	35q99	NUM
ejpam-6215	9	15	key	key	ADJ
ejpam-6215	9	16	words	word	NOUN
ejpam-6215	9	17	and	and	CCONJ
ejpam-6215	9	18	phrases	phrase	NOUN
ejpam-6215	9	19	:	:	PUNCT
ejpam-6215	9	20	painlevé	painlevé	NOUN
ejpam-6215	9	21	equations	equation	NOUN
ejpam-6215	9	22	,	,	PUNCT
ejpam-6215	9	23	dtm	dtm	PROPN
ejpam-6215	9	24	,	,	PUNCT
ejpam-6215	9	25	madm	madm	NOUN
ejpam-6215	9	26	,	,	PUNCT
ejpam-6215	9	27	ldm	ldm	PROPN
ejpam-6215	9	28	,	,	PUNCT
ejpam-6215	9	29	ndm	ndm	PROPN
ejpam-6215	9	30	,	,	PUNCT
ejpam-6215	9	31	finite	finite	ADJ
ejpam-6215	9	32	difference	difference	NOUN
ejpam-6215	9	33	method	method	NOUN
ejpam-6215	9	34	,	,	PUNCT
ejpam-6215	9	35	runge	runge	NOUN
ejpam-6215	9	36	-	-	PUNCT
ejpam-6215	9	37	kutta	kutta	NOUN
ejpam-6215	9	38	method	method	NOUN
ejpam-6215	9	39	1	1	NUM
ejpam-6215	9	40	.	.	PUNCT
ejpam-6215	9	41	introduction	introduction	NOUN
ejpam-6215	9	42	the	the	DET
ejpam-6215	9	43	painlevé	painlevé	NOUN
ejpam-6215	9	44	equations	equation	NOUN
ejpam-6215	9	45	were	be	AUX
ejpam-6215	9	46	first	first	ADV
ejpam-6215	9	47	introduced	introduce	VERB
ejpam-6215	9	48	between	between	ADP
ejpam-6215	9	49	1895	1895	NUM
ejpam-6215	9	50	and	and	CCONJ
ejpam-6215	9	51	1910	1910	NUM
ejpam-6215	9	52	through	through	ADP
ejpam-6215	9	53	the	the	DET
ejpam-6215	9	54	work	work	NOUN
ejpam-6215	9	55	of	of	ADP
ejpam-6215	9	56	two	two	NUM
ejpam-6215	9	57	french	french	ADJ
ejpam-6215	9	58	mathematicians	mathematician	NOUN
ejpam-6215	9	59	,	,	PUNCT
ejpam-6215	9	60	paul	paul	PROPN
ejpam-6215	9	61	painlevé	painlevé	NOUN
ejpam-6215	9	62	and	and	CCONJ
ejpam-6215	9	63	bertrand	bertrand	PROPN
ejpam-6215	9	64	gambier	gambier	PROPN
ejpam-6215	9	65	.	.	PUNCT
ejpam-6215	10	1	they	they	PRON
ejpam-6215	10	2	were	be	AUX
ejpam-6215	10	3	identified	identify	VERB
ejpam-6215	10	4	as	as	ADP
ejpam-6215	10	5	second	second	ADJ
ejpam-6215	10	6	-	-	PUNCT
ejpam-6215	10	7	order	order	NOUN
ejpam-6215	10	8	differential	differential	ADJ
ejpam-6215	10	9	equations	equation	NOUN
ejpam-6215	10	10	that	that	PRON
ejpam-6215	10	11	play	play	VERB
ejpam-6215	10	12	a	a	DET
ejpam-6215	10	13	crucial	crucial	ADJ
ejpam-6215	10	14	role	role	NOUN
ejpam-6215	10	15	in	in	ADP
ejpam-6215	10	16	various	various	ADJ
ejpam-6215	10	17	fields	field	NOUN
ejpam-6215	10	18	of	of	ADP
ejpam-6215	10	19	mathematics	mathematic	NOUN
ejpam-6215	10	20	and	and	CCONJ
ejpam-6215	10	21	physics	physics	NOUN
ejpam-6215	10	22	.	.	PUNCT
ejpam-6215	11	1	they	they	PRON
ejpam-6215	11	2	have	have	AUX
ejpam-6215	11	3	found	find	VERB
ejpam-6215	11	4	applications	application	NOUN
ejpam-6215	11	5	in	in	ADP
ejpam-6215	11	6	areas	area	NOUN
ejpam-6215	11	7	such	such	ADJ
ejpam-6215	11	8	as	as	ADP
ejpam-6215	11	9	nonlinear	nonlinear	ADJ
ejpam-6215	11	10	waves	wave	NOUN
ejpam-6215	11	11	,	,	PUNCT
ejpam-6215	11	12	plasma	plasma	NOUN
ejpam-6215	11	13	physics	physics	NOUN
ejpam-6215	11	14	,	,	PUNCT
ejpam-6215	11	15	statistical	statistical	ADJ
ejpam-6215	11	16	mechanics	mechanic	NOUN
ejpam-6215	11	17	,	,	PUNCT
ejpam-6215	11	18	fiber	fiber	NOUN
ejpam-6215	11	19	optics	optic	NOUN
ejpam-6215	11	20	,	,	PUNCT
ejpam-6215	11	21	and	and	CCONJ
ejpam-6215	11	22	more	more	ADJ
ejpam-6215	11	23	[	[	X
ejpam-6215	11	24	1–4	1–4	NOUN
ejpam-6215	11	25	]	]	X
ejpam-6215	11	26	.	.	PUNCT
ejpam-6215	12	1	despite	despite	SCONJ
ejpam-6215	12	2	their	their	PRON
ejpam-6215	12	3	importance	importance	NOUN
ejpam-6215	12	4	,	,	PUNCT
ejpam-6215	12	5	painlevé	painlevé	NOUN
ejpam-6215	12	6	equations	equation	NOUN
ejpam-6215	12	7	are	be	AUX
ejpam-6215	12	8	highly	highly	ADV
ejpam-6215	12	9	nonlinear	nonlinear	ADJ
ejpam-6215	12	10	and	and	CCONJ
ejpam-6215	12	11	do	do	AUX
ejpam-6215	12	12	not	not	PART
ejpam-6215	12	13	admit	admit	VERB
ejpam-6215	12	14	general	general	ADJ
ejpam-6215	12	15	closed	close	VERB
ejpam-6215	12	16	-	-	PUNCT
ejpam-6215	12	17	form	form	NOUN
ejpam-6215	12	18	solutions	solution	NOUN
ejpam-6215	12	19	,	,	PUNCT
ejpam-6215	12	20	and	and	CCONJ
ejpam-6215	12	21	traditional	traditional	ADJ
ejpam-6215	12	22	methods	method	NOUN
ejpam-6215	12	23	such	such	ADJ
ejpam-6215	12	24	as	as	ADP
ejpam-6215	12	25	separation	separation	NOUN
ejpam-6215	12	26	of	of	ADP
ejpam-6215	12	27	variables	variable	NOUN
ejpam-6215	12	28	or	or	CCONJ
ejpam-6215	12	29	perturbation	perturbation	NOUN
ejpam-6215	12	30	techniques	technique	NOUN
ejpam-6215	12	31	often	often	ADV
ejpam-6215	12	32	∗corresponding	∗corresponde	VERB
ejpam-6215	12	33	author	author	NOUN
ejpam-6215	12	34	.	.	PUNCT
ejpam-6215	13	1	doi	doi	NOUN
ejpam-6215	13	2	:	:	PUNCT
ejpam-6215	13	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6215	https://doi.org/10.29020/nybg.ejpam.v18i3.6215	VERB
ejpam-6215	13	4	email	email	NOUN
ejpam-6215	13	5	addresses	address	NOUN
ejpam-6215	13	6	:	:	PUNCT
ejpam-6215	13	7	sangar.mohammedhasan@uod.ac	sangar.mohammedhasan@uod.ac	X
ejpam-6215	13	8	(	(	PUNCT
ejpam-6215	13	9	s.	s.	PROPN
ejpam-6215	13	10	mohammed	mohammed	PROPN
ejpam-6215	13	11	)	)	PUNCT
ejpam-6215	13	12	,	,	PUNCT
ejpam-6215	13	13	sizar.mohammed@uod.ac	sizar.mohammed@uod.ac	NOUN
ejpam-6215	13	14	(	(	PUNCT
ejpam-6215	13	15	s.	s.	PROPN
ejpam-6215	13	16	abid	abid	PROPN
ejpam-6215	13	17	)	)	PUNCT
ejpam-6215	13	18	,	,	PUNCT
ejpam-6215	13	19	ramadhan.hajani@uod.ac	ramadhan.hajani@uod.ac	PROPN
ejpam-6215	13	20	(	(	PUNCT
ejpam-6215	13	21	r.	r.	PROPN
ejpam-6215	13	22	abid	abid	PROPN
ejpam-6215	13	23	)	)	PUNCT
ejpam-6215	13	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6215	13	25	1	1	NUM
ejpam-6215	13	26	copyright	copyright	NOUN
ejpam-6215	13	27	:	:	PUNCT
ejpam-6215	14	1	©	©	PROPN
ejpam-6215	14	2	2025	2025	NUM
ejpam-6215	14	3	the	the	DET
ejpam-6215	14	4	author(s	author(s	NOUN
ejpam-6215	14	5	)	)	PUNCT
ejpam-6215	14	6	.	.	PUNCT
ejpam-6215	15	1	(	(	PUNCT
ejpam-6215	15	2	cc	cc	NOUN
ejpam-6215	15	3	by	by	ADP
ejpam-6215	15	4	-	-	PUNCT
ejpam-6215	15	5	nc	nc	PROPN
ejpam-6215	15	6	4.0	4.0	NUM
ejpam-6215	15	7	)	)	PUNCT
ejpam-6215	15	8	s.	s.	PROPN
ejpam-6215	15	9	mohammed	mohammed	PROPN
ejpam-6215	15	10	,	,	PUNCT
ejpam-6215	15	11	s.	s.	PROPN
ejpam-6215	15	12	abid	abid	PROPN
ejpam-6215	15	13	,	,	PUNCT
ejpam-6215	15	14	r.	r.	PROPN
ejpam-6215	15	15	abid	abid	PROPN
ejpam-6215	15	16	/	/	SYM
ejpam-6215	15	17	eur	eur	PROPN
ejpam-6215	15	18	.	.	PUNCT
ejpam-6215	16	1	j.	j.	PROPN
ejpam-6215	16	2	pure	pure	PROPN
ejpam-6215	16	3	appl	appl	PROPN
ejpam-6215	16	4	.	.	PROPN
ejpam-6215	16	5	math	math	PROPN
ejpam-6215	16	6	,	,	PUNCT
ejpam-6215	16	7	18	18	NUM
ejpam-6215	16	8	(	(	PUNCT
ejpam-6215	16	9	3	3	NUM
ejpam-6215	16	10	)	)	PUNCT
ejpam-6215	16	11	(	(	PUNCT
ejpam-6215	16	12	2025	2025	NUM
ejpam-6215	16	13	)	)	PUNCT
ejpam-6215	16	14	,	,	PUNCT
ejpam-6215	16	15	6215	6215	NUM
ejpam-6215	16	16	2	2	NUM
ejpam-6215	16	17	of	of	ADP
ejpam-6215	16	18	38	38	NUM
ejpam-6215	16	19	fail	fail	ADJ
ejpam-6215	16	20	due	due	ADP
ejpam-6215	16	21	to	to	ADP
ejpam-6215	16	22	the	the	DET
ejpam-6215	16	23	equations	equation	NOUN
ejpam-6215	16	24	’	'	PUNCT
ejpam-6215	16	25	complexity	complexity	NOUN
ejpam-6215	16	26	.	.	PUNCT
ejpam-6215	17	1	as	as	ADP
ejpam-6215	17	2	a	a	DET
ejpam-6215	17	3	result	result	NOUN
ejpam-6215	17	4	,	,	PUNCT
ejpam-6215	17	5	researchers	researcher	NOUN
ejpam-6215	17	6	have	have	AUX
ejpam-6215	17	7	focused	focus	VERB
ejpam-6215	17	8	on	on	ADP
ejpam-6215	17	9	developing	develop	VERB
ejpam-6215	17	10	analytical	analytical	ADJ
ejpam-6215	17	11	and	and	CCONJ
ejpam-6215	17	12	numerical	numerical	ADJ
ejpam-6215	17	13	approaches	approach	NOUN
ejpam-6215	17	14	to	to	PART
ejpam-6215	17	15	approximate	approximate	VERB
ejpam-6215	17	16	and	and	CCONJ
ejpam-6215	17	17	analyze	analyze	VERB
ejpam-6215	17	18	these	these	DET
ejpam-6215	17	19	equations	equation	NOUN
ejpam-6215	17	20	effectively	effectively	ADV
ejpam-6215	17	21	.	.	PUNCT
ejpam-6215	18	1	numerous	numerous	ADJ
ejpam-6215	18	2	analytical	analytical	ADJ
ejpam-6215	18	3	and	and	CCONJ
ejpam-6215	18	4	numerical	numerical	ADJ
ejpam-6215	18	5	methods	method	NOUN
ejpam-6215	18	6	have	have	AUX
ejpam-6215	18	7	been	be	AUX
ejpam-6215	18	8	successfully	successfully	ADV
ejpam-6215	18	9	developed	develop	VERB
ejpam-6215	18	10	to	to	PART
ejpam-6215	18	11	solve	solve	VERB
ejpam-6215	18	12	the	the	DET
ejpam-6215	18	13	painlevé	painlevé	NOUN
ejpam-6215	18	14	equations	equation	NOUN
ejpam-6215	18	15	.	.	PUNCT
ejpam-6215	19	1	for	for	ADP
ejpam-6215	19	2	example	example	NOUN
ejpam-6215	19	3	,	,	PUNCT
ejpam-6215	19	4	differential	differential	ADJ
ejpam-6215	19	5	transform	transform	NOUN
ejpam-6215	19	6	method	method	NOUN
ejpam-6215	19	7	(	(	PUNCT
ejpam-6215	19	8	dtm	dtm	PROPN
ejpam-6215	19	9	)	)	PUNCT
ejpam-6215	20	1	[	[	X
ejpam-6215	20	2	5	5	NUM
ejpam-6215	20	3	,	,	PUNCT
ejpam-6215	20	4	6	6	NUM
ejpam-6215	20	5	]	]	PUNCT
ejpam-6215	20	6	,	,	PUNCT
ejpam-6215	20	7	modified	modify	VERB
ejpam-6215	20	8	adomian	adomian	NOUN
ejpam-6215	20	9	decomposition	decomposition	NOUN
ejpam-6215	20	10	method	method	NOUN
ejpam-6215	20	11	(	(	PUNCT
ejpam-6215	20	12	madm	madm	NOUN
ejpam-6215	20	13	)	)	PUNCT
ejpam-6215	21	1	[	[	X
ejpam-6215	21	2	7	7	NUM
ejpam-6215	21	3	,	,	PUNCT
ejpam-6215	21	4	8	8	NUM
ejpam-6215	21	5	]	]	PUNCT
ejpam-6215	21	6	,	,	PUNCT
ejpam-6215	21	7	laplace	laplace	NOUN
ejpam-6215	21	8	decomposition	decomposition	NOUN
ejpam-6215	21	9	method	method	NOUN
ejpam-6215	21	10	(	(	PUNCT
ejpam-6215	21	11	ldm	ldm	NOUN
ejpam-6215	21	12	)	)	PUNCT
ejpam-6215	21	13	[	[	X
ejpam-6215	21	14	9	9	NUM
ejpam-6215	21	15	,	,	PUNCT
ejpam-6215	21	16	10	10	NUM
ejpam-6215	21	17	]	]	PUNCT
ejpam-6215	21	18	and	and	CCONJ
ejpam-6215	21	19	natural	natural	ADJ
ejpam-6215	21	20	decomposition	decomposition	NOUN
ejpam-6215	21	21	method	method	NOUN
ejpam-6215	21	22	[	[	X
ejpam-6215	21	23	11	11	NUM
ejpam-6215	21	24	,	,	PUNCT
ejpam-6215	21	25	12	12	NUM
ejpam-6215	21	26	]	]	PUNCT
ejpam-6215	21	27	,	,	PUNCT
ejpam-6215	21	28	finite	finite	ADJ
ejpam-6215	21	29	difference	difference	NOUN
ejpam-6215	21	30	method	method	NOUN
ejpam-6215	21	31	[	[	X
ejpam-6215	21	32	13	13	NUM
ejpam-6215	21	33	,	,	PUNCT
ejpam-6215	21	34	14	14	NUM
ejpam-6215	21	35	]	]	PUNCT
ejpam-6215	21	36	,	,	PUNCT
ejpam-6215	21	37	runge	runge	VERB
ejpam-6215	21	38	kutta	kutta	NOUN
ejpam-6215	21	39	method	method	NOUN
ejpam-6215	21	40	[	[	X
ejpam-6215	21	41	15	15	NUM
ejpam-6215	21	42	,	,	PUNCT
ejpam-6215	21	43	16	16	NUM
ejpam-6215	21	44	]	]	PUNCT
ejpam-6215	21	45	.	.	PUNCT
ejpam-6215	22	1	this	this	DET
ejpam-6215	22	2	paper	paper	NOUN
ejpam-6215	22	3	aims	aim	VERB
ejpam-6215	22	4	to	to	PART
ejpam-6215	22	5	develop	develop	VERB
ejpam-6215	22	6	and	and	CCONJ
ejpam-6215	22	7	compare	compare	VERB
ejpam-6215	22	8	analytical	analytical	ADJ
ejpam-6215	22	9	and	and	CCONJ
ejpam-6215	22	10	numerical	numerical	ADJ
ejpam-6215	22	11	techniques	technique	NOUN
ejpam-6215	22	12	for	for	ADP
ejpam-6215	22	13	solving	solve	VERB
ejpam-6215	22	14	painlevé	painlevé	NOUN
ejpam-6215	23	1	i	i	PRON
ejpam-6215	23	2	and	and	CCONJ
ejpam-6215	23	3	ii	ii	PROPN
ejpam-6215	23	4	equations	equation	NOUN
ejpam-6215	23	5	.	.	PUNCT
ejpam-6215	24	1	it	it	PRON
ejpam-6215	24	2	contributes	contribute	VERB
ejpam-6215	24	3	to	to	ADP
ejpam-6215	24	4	the	the	DET
ejpam-6215	24	5	broader	broad	ADJ
ejpam-6215	24	6	understanding	understanding	NOUN
ejpam-6215	24	7	of	of	ADP
ejpam-6215	24	8	providing	provide	VERB
ejpam-6215	24	9	reliable	reliable	ADJ
ejpam-6215	24	10	tools	tool	NOUN
ejpam-6215	24	11	and	and	CCONJ
ejpam-6215	24	12	bridging	bridge	VERB
ejpam-6215	24	13	the	the	DET
ejpam-6215	24	14	gap	gap	NOUN
ejpam-6215	24	15	between	between	ADP
ejpam-6215	24	16	analytical	analytical	ADJ
ejpam-6215	24	17	and	and	CCONJ
ejpam-6215	24	18	numerical	numerical	ADJ
ejpam-6215	24	19	techniques	technique	NOUN
ejpam-6215	24	20	for	for	ADP
ejpam-6215	24	21	applied	applied	ADJ
ejpam-6215	24	22	scientists	scientist	NOUN
ejpam-6215	24	23	and	and	CCONJ
ejpam-6215	24	24	engineers	engineer	NOUN
ejpam-6215	24	25	to	to	PART
ejpam-6215	24	26	study	study	VERB
ejpam-6215	24	27	nonlinear	nonlinear	ADJ
ejpam-6215	24	28	differential	differential	ADJ
ejpam-6215	24	29	equations	equation	NOUN
ejpam-6215	24	30	in	in	ADP
ejpam-6215	24	31	real	real	ADJ
ejpam-6215	24	32	-	-	PUNCT
ejpam-6215	24	33	world	world	NOUN
ejpam-6215	24	34	applications	application	NOUN
ejpam-6215	24	35	.	.	PUNCT
ejpam-6215	25	1	this	this	DET
ejpam-6215	25	2	paper	paper	NOUN
ejpam-6215	25	3	is	be	AUX
ejpam-6215	25	4	organized	organize	VERB
ejpam-6215	25	5	as	as	SCONJ
ejpam-6215	25	6	follows	follow	VERB
ejpam-6215	25	7	:	:	PUNCT
ejpam-6215	25	8	section	section	NOUN
ejpam-6215	25	9	2	2	NUM
ejpam-6215	25	10	introduces	introduce	VERB
ejpam-6215	25	11	the	the	DET
ejpam-6215	25	12	analytical	analytical	ADJ
ejpam-6215	25	13	methods	method	NOUN
ejpam-6215	25	14	.	.	PUNCT
ejpam-6215	26	1	subsection	subsection	NOUN
ejpam-6215	26	2	2.1	2.1	NUM
ejpam-6215	26	3	differential	differential	NOUN
ejpam-6215	26	4	transform	transform	NOUN
ejpam-6215	26	5	method	method	NOUN
ejpam-6215	26	6	.	.	PUNCT
ejpam-6215	27	1	in	in	ADP
ejpam-6215	27	2	subsection	subsection	NOUN
ejpam-6215	27	3	2.2	2.2	NUM
ejpam-6215	27	4	.	.	PUNCT
ejpam-6215	28	1	modified	modify	VERB
ejpam-6215	28	2	adomian	adomian	NOUN
ejpam-6215	28	3	decomposition	decomposition	NOUN
ejpam-6215	28	4	method	method	NOUN
ejpam-6215	28	5	.	.	PUNCT
ejpam-6215	29	1	subsection	subsection	NOUN
ejpam-6215	29	2	2.3	2.3	NUM
ejpam-6215	29	3	.	.	PUNCT
ejpam-6215	30	1	laplace	laplace	NOUN
ejpam-6215	30	2	decomposition	decomposition	NOUN
ejpam-6215	30	3	method	method	NOUN
ejpam-6215	30	4	.	.	PUNCT
ejpam-6215	31	1	in	in	ADP
ejpam-6215	31	2	subsection	subsection	NOUN
ejpam-6215	31	3	2.4	2.4	NUM
ejpam-6215	31	4	.	.	PUNCT
ejpam-6215	31	5	natural	natural	ADJ
ejpam-6215	31	6	decomposition	decomposition	NOUN
ejpam-6215	31	7	method	method	NOUN
ejpam-6215	31	8	.	.	PUNCT
ejpam-6215	32	1	in	in	ADP
ejpam-6215	32	2	section	section	NOUN
ejpam-6215	32	3	3	3	NUM
ejpam-6215	32	4	numerical	numerical	ADJ
ejpam-6215	32	5	methods	method	NOUN
ejpam-6215	32	6	.	.	PUNCT
ejpam-6215	33	1	subsection	subsection	NOUN
ejpam-6215	33	2	3.1	3.1	NUM
ejpam-6215	33	3	.	.	PUNCT
ejpam-6215	34	1	finite	finite	ADJ
ejpam-6215	34	2	difference	difference	NOUN
ejpam-6215	34	3	method	method	NOUN
ejpam-6215	34	4	.	.	PUNCT
ejpam-6215	35	1	in	in	ADP
ejpam-6215	35	2	subsection	subsection	NOUN
ejpam-6215	35	3	3.2	3.2	NUM
ejpam-6215	35	4	.	.	PUNCT
ejpam-6215	36	1	runge	runge	VERB
ejpam-6215	36	2	kutta	kutta	PROPN
ejpam-6215	36	3	method	method	NOUN
ejpam-6215	36	4	.	.	PUNCT
ejpam-6215	37	1	in	in	ADP
ejpam-6215	37	2	section	section	NOUN
ejpam-6215	37	3	4	4	NUM
ejpam-6215	37	4	comparative	comparative	ADJ
ejpam-6215	37	5	analysis	analysis	NOUN
ejpam-6215	37	6	of	of	ADP
ejpam-6215	37	7	analytical	analytical	ADJ
ejpam-6215	37	8	and	and	CCONJ
ejpam-6215	37	9	numerical	numerical	ADJ
ejpam-6215	37	10	methods	method	NOUN
ejpam-6215	37	11	.	.	PUNCT
ejpam-6215	38	1	finally	finally	ADV
ejpam-6215	38	2	,	,	PUNCT
ejpam-6215	38	3	section	section	NOUN
ejpam-6215	38	4	5	5	NUM
ejpam-6215	38	5	offers	offer	VERB
ejpam-6215	38	6	concluding	conclude	VERB
ejpam-6215	38	7	remarks	remark	NOUN
ejpam-6215	38	8	for	for	ADP
ejpam-6215	38	9	the	the	DET
ejpam-6215	38	10	paper	paper	NOUN
ejpam-6215	38	11	.	.	PUNCT
ejpam-6215	39	1	painlevé	painlevé	VERB
ejpam-6215	39	2	equations	equation	NOUN
ejpam-6215	39	3	of	of	ADP
ejpam-6215	39	4	the	the	DET
ejpam-6215	39	5	first	first	ADJ
ejpam-6215	39	6	and	and	CCONJ
ejpam-6215	39	7	second	second	ADJ
ejpam-6215	39	8	types	type	NOUN
ejpam-6215	39	9	will	will	AUX
ejpam-6215	39	10	be	be	AUX
ejpam-6215	39	11	defined	define	VERB
ejpam-6215	39	12	by	by	ADP
ejpam-6215	39	13	the	the	DET
ejpam-6215	39	14	following	follow	VERB
ejpam-6215	39	15	formulas	formula	NOUN
ejpam-6215	39	16	:	:	PUNCT
ejpam-6215	39	17	y′′(x	y′′(x	NOUN
ejpam-6215	39	18	)	)	PUNCT
ejpam-6215	39	19	=	=	SYM
ejpam-6215	39	20	6y2(x	6y2(x	NUM
ejpam-6215	39	21	)	)	PUNCT
ejpam-6215	40	1	+	+	CCONJ
ejpam-6215	40	2	x	x	X
ejpam-6215	40	3	,	,	PUNCT
ejpam-6215	40	4	0	0	PUNCT
ejpam-6215	40	5	<	<	X
ejpam-6215	40	6	x	x	X
ejpam-6215	40	7	<	<	X
ejpam-6215	40	8	1	1	NUM
ejpam-6215	40	9	(	(	PUNCT
ejpam-6215	40	10	1	1	NUM
ejpam-6215	40	11	)	)	PUNCT
ejpam-6215	40	12	with	with	ADP
ejpam-6215	40	13	the	the	DET
ejpam-6215	40	14	given	give	VERB
ejpam-6215	40	15	initial	initial	ADJ
ejpam-6215	40	16	conditions	condition	NOUN
ejpam-6215	40	17	:	:	PUNCT
ejpam-6215	40	18	y(0	y(0	NOUN
ejpam-6215	40	19	)	)	PUNCT
ejpam-6215	40	20	=	=	SYM
ejpam-6215	40	21	0	0	NUM
ejpam-6215	40	22	,	,	PUNCT
ejpam-6215	40	23	y′(0	y′(0	NOUN
ejpam-6215	40	24	)	)	PUNCT
ejpam-6215	40	25	=	=	SYM
ejpam-6215	40	26	1	1	NUM
ejpam-6215	40	27	.	.	NOUN
ejpam-6215	40	28	y′′(x	y′′(x	NOUN
ejpam-6215	40	29	)	)	PUNCT
ejpam-6215	40	30	=	=	SYM
ejpam-6215	40	31	2y3(x	2y3(x	NUM
ejpam-6215	40	32	)	)	PUNCT
ejpam-6215	40	33	+	+	NUM
ejpam-6215	40	34	xy(x	xy(x	NOUN
ejpam-6215	40	35	)	)	PUNCT
ejpam-6215	40	36	+	+	CCONJ
ejpam-6215	40	37	µ	µ	NUM
ejpam-6215	40	38	,	,	PUNCT
ejpam-6215	40	39	0	0	PUNCT
ejpam-6215	40	40	<	<	X
ejpam-6215	40	41	x	x	X
ejpam-6215	40	42	<	<	X
ejpam-6215	40	43	1	1	NUM
ejpam-6215	40	44	(	(	PUNCT
ejpam-6215	40	45	2	2	NUM
ejpam-6215	40	46	)	)	PUNCT
ejpam-6215	40	47	with	with	ADP
ejpam-6215	40	48	the	the	DET
ejpam-6215	40	49	initial	initial	ADJ
ejpam-6215	40	50	conditions	condition	NOUN
ejpam-6215	40	51	:	:	PUNCT
ejpam-6215	40	52	y(0	y(0	NOUN
ejpam-6215	40	53	)	)	PUNCT
ejpam-6215	40	54	=	=	SYM
ejpam-6215	40	55	1	1	NUM
ejpam-6215	40	56	,	,	PUNCT
ejpam-6215	40	57	y′(0	y′(0	NOUN
ejpam-6215	40	58	)	)	PUNCT
ejpam-6215	40	59	=	=	SYM
ejpam-6215	40	60	0	0	NUM
ejpam-6215	40	61	,	,	PUNCT
ejpam-6215	40	62	where	where	SCONJ
ejpam-6215	40	63	µ	µ	NOUN
ejpam-6215	40	64	is	be	AUX
ejpam-6215	40	65	a	a	DET
ejpam-6215	40	66	known	known	ADJ
ejpam-6215	40	67	parameter	parameter	NOUN
ejpam-6215	40	68	.	.	PUNCT
ejpam-6215	41	1	error	error	NOUN
ejpam-6215	41	2	analysis	analysis	NOUN
ejpam-6215	41	3	since	since	SCONJ
ejpam-6215	41	4	the	the	DET
ejpam-6215	41	5	exact	exact	ADJ
ejpam-6215	41	6	solutions	solution	NOUN
ejpam-6215	41	7	for	for	ADP
ejpam-6215	41	8	painlevé	painlevé	NOUN
ejpam-6215	41	9	i	i	PRON
ejpam-6215	41	10	and	and	CCONJ
ejpam-6215	41	11	ii	ii	PROPN
ejpam-6215	41	12	are	be	AUX
ejpam-6215	41	13	unknown	unknown	ADJ
ejpam-6215	41	14	,	,	PUNCT
ejpam-6215	41	15	we	we	PRON
ejpam-6215	41	16	utilized	utilize	VERB
ejpam-6215	41	17	the	the	DET
ejpam-6215	41	18	maximal	maximal	ADJ
ejpam-6215	41	19	error	error	NOUN
ejpam-6215	41	20	remaindermern	remaindermern	NOUN
ejpam-6215	41	21	to	to	PART
ejpam-6215	41	22	evaluate	evaluate	VERB
ejpam-6215	41	23	the	the	DET
ejpam-6215	41	24	accuracy	accuracy	NOUN
ejpam-6215	41	25	of	of	ADP
ejpam-6215	41	26	the	the	DET
ejpam-6215	41	27	approximate	approximate	ADJ
ejpam-6215	41	28	solutions	solution	NOUN
ejpam-6215	41	29	.	.	PUNCT
ejpam-6215	42	1	themern	themern	PROPN
ejpam-6215	42	2	for	for	ADP
ejpam-6215	42	3	dtm	dtm	PROPN
ejpam-6215	42	4	,	,	PUNCT
ejpam-6215	42	5	madm	madm	NOUN
ejpam-6215	42	6	,	,	PUNCT
ejpam-6215	42	7	ldm	ldm	NOUN
ejpam-6215	42	8	,	,	PUNCT
ejpam-6215	42	9	and	and	CCONJ
ejpam-6215	42	10	ndm	ndm	PROPN
ejpam-6215	42	11	was	be	AUX
ejpam-6215	42	12	computed	compute	VERB
ejpam-6215	42	13	using	use	VERB
ejpam-6215	42	14	the	the	DET
ejpam-6215	42	15	software	software	NOUN
ejpam-6215	42	16	mathematica	mathematica	PROPN
ejpam-6215	42	17	code	code	PROPN
ejpam-6215	42	18	over	over	ADP
ejpam-6215	42	19	the	the	DET
ejpam-6215	42	20	domain	domain	NOUN
ejpam-6215	43	1	[	[	X
ejpam-6215	43	2	0.01	0.01	NUM
ejpam-6215	43	3	,	,	PUNCT
ejpam-6215	43	4	0.1	0.1	NUM
ejpam-6215	43	5	]	]	PUNCT
ejpam-6215	43	6	.	.	PUNCT
ejpam-6215	44	1	ern	ern	PROPN
ejpam-6215	44	2	=	=	PUNCT
ejpam-6215	44	3	l(y)−n(y)−	l(y)−n(y)−	PROPN
ejpam-6215	44	4	f(x	f(x	PROPN
ejpam-6215	44	5	)	)	PUNCT
ejpam-6215	44	6	.	.	PUNCT
ejpam-6215	45	1	(	(	PUNCT
ejpam-6215	45	2	3	3	X
ejpam-6215	45	3	)	)	PUNCT
ejpam-6215	45	4	the	the	DET
ejpam-6215	45	5	maximal	maximal	ADJ
ejpam-6215	45	6	error	error	NOUN
ejpam-6215	45	7	remainder	remainder	NOUN
ejpam-6215	45	8	is	be	AUX
ejpam-6215	45	9	mern	mern	ADJ
ejpam-6215	45	10	=	=	SYM
ejpam-6215	45	11	max	max	NOUN
ejpam-6215	45	12	0.01≤x≤0.1	0.01≤x≤0.1	NUM
ejpam-6215	45	13	|ern(x)|	|ern(x)|	NOUN
ejpam-6215	45	14	.	.	PUNCT
ejpam-6215	46	1	(	(	PUNCT
ejpam-6215	46	2	4	4	X
ejpam-6215	46	3	)	)	PUNCT
ejpam-6215	46	4	the	the	DET
ejpam-6215	46	5	selection	selection	NOUN
ejpam-6215	46	6	of	of	ADP
ejpam-6215	46	7	the	the	DET
ejpam-6215	46	8	interval	interval	NOUN
ejpam-6215	46	9	[	[	X
ejpam-6215	46	10	0.01	0.01	NUM
ejpam-6215	46	11	,	,	PUNCT
ejpam-6215	46	12	0.1	0.1	NUM
ejpam-6215	46	13	]	]	PUNCT
ejpam-6215	46	14	for	for	ADP
ejpam-6215	46	15	the	the	DET
ejpam-6215	46	16	maximal	maximal	ADJ
ejpam-6215	46	17	error	error	NOUN
ejpam-6215	46	18	remainder	remainder	NOUN
ejpam-6215	46	19	(	(	PUNCT
ejpam-6215	46	20	mer	mer	NOUN
ejpam-6215	46	21	)	)	PUNCT
ejpam-6215	46	22	analysis	analysis	NOUN
ejpam-6215	46	23	is	be	AUX
ejpam-6215	46	24	based	base	VERB
ejpam-6215	46	25	on	on	ADP
ejpam-6215	46	26	consideration	consideration	NOUN
ejpam-6215	46	27	of	of	ADP
ejpam-6215	46	28	analytic	analytic	ADJ
ejpam-6215	46	29	stability	stability	NOUN
ejpam-6215	46	30	and	and	CCONJ
ejpam-6215	46	31	accuracy	accuracy	NOUN
ejpam-6215	46	32	.	.	PUNCT
ejpam-6215	47	1	limiting	limit	VERB
ejpam-6215	47	2	the	the	DET
ejpam-6215	47	3	analysis	analysis	NOUN
ejpam-6215	47	4	to	to	ADP
ejpam-6215	47	5	this	this	DET
ejpam-6215	47	6	range	range	NOUN
ejpam-6215	47	7	allows	allow	VERB
ejpam-6215	47	8	for	for	ADP
ejpam-6215	47	9	a	a	DET
ejpam-6215	47	10	more	more	ADV
ejpam-6215	47	11	precise	precise	ADJ
ejpam-6215	47	12	assessment	assessment	NOUN
ejpam-6215	47	13	of	of	ADP
ejpam-6215	47	14	the	the	DET
ejpam-6215	47	15	approximation	approximation	NOUN
ejpam-6215	47	16	methods	method	NOUN
ejpam-6215	47	17	.	.	PUNCT
ejpam-6215	48	1	furthermore	furthermore	ADV
ejpam-6215	48	2	,	,	PUNCT
ejpam-6215	48	3	s.	s.	PROPN
ejpam-6215	48	4	mohammed	mohammed	PROPN
ejpam-6215	48	5	,	,	PUNCT
ejpam-6215	48	6	s.	s.	PROPN
ejpam-6215	48	7	abid	abid	PROPN
ejpam-6215	48	8	,	,	PUNCT
ejpam-6215	48	9	r.	r.	PROPN
ejpam-6215	48	10	abid	abid	PROPN
ejpam-6215	48	11	/	/	SYM
ejpam-6215	48	12	eur	eur	PROPN
ejpam-6215	48	13	.	.	PUNCT
ejpam-6215	49	1	j.	j.	PROPN
ejpam-6215	49	2	pure	pure	PROPN
ejpam-6215	49	3	appl	appl	PROPN
ejpam-6215	49	4	.	.	PROPN
ejpam-6215	49	5	math	math	PROPN
ejpam-6215	49	6	,	,	PUNCT
ejpam-6215	49	7	18	18	NUM
ejpam-6215	49	8	(	(	PUNCT
ejpam-6215	49	9	3	3	NUM
ejpam-6215	49	10	)	)	PUNCT
ejpam-6215	49	11	(	(	PUNCT
ejpam-6215	49	12	2025	2025	NUM
ejpam-6215	49	13	)	)	PUNCT
ejpam-6215	49	14	,	,	PUNCT
ejpam-6215	49	15	6215	6215	NUM
ejpam-6215	49	16	3	3	NUM
ejpam-6215	49	17	of	of	ADP
ejpam-6215	49	18	38	38	NUM
ejpam-6215	49	19	this	this	DET
ejpam-6215	49	20	interval	interval	NOUN
ejpam-6215	49	21	is	be	AUX
ejpam-6215	49	22	specifically	specifically	ADV
ejpam-6215	49	23	chosen	choose	VERB
ejpam-6215	49	24	to	to	PART
ejpam-6215	49	25	focus	focus	VERB
ejpam-6215	49	26	on	on	ADP
ejpam-6215	49	27	the	the	DET
ejpam-6215	49	28	region	region	NOUN
ejpam-6215	49	29	where	where	SCONJ
ejpam-6215	49	30	analytical	analytical	ADJ
ejpam-6215	49	31	approximations	approximation	NOUN
ejpam-6215	49	32	are	be	AUX
ejpam-6215	49	33	most	most	ADV
ejpam-6215	49	34	effective	effective	ADJ
ejpam-6215	49	35	for	for	ADP
ejpam-6215	49	36	accuracy	accuracy	NOUN
ejpam-6215	49	37	evaluation	evaluation	NOUN
ejpam-6215	49	38	,	,	PUNCT
ejpam-6215	49	39	as	as	SCONJ
ejpam-6215	49	40	extending	extend	VERB
ejpam-6215	49	41	the	the	DET
ejpam-6215	49	42	domain	domain	NOUN
ejpam-6215	49	43	further	far	ADV
ejpam-6215	49	44	could	could	AUX
ejpam-6215	49	45	lead	lead	VERB
ejpam-6215	49	46	to	to	ADP
ejpam-6215	49	47	additional	additional	ADJ
ejpam-6215	49	48	computational	computational	ADJ
ejpam-6215	49	49	complexities	complexity	NOUN
ejpam-6215	49	50	without	without	ADP
ejpam-6215	49	51	significantly	significantly	ADV
ejpam-6215	49	52	impacting	impact	VERB
ejpam-6215	49	53	the	the	DET
ejpam-6215	49	54	overall	overall	ADJ
ejpam-6215	49	55	conclusions	conclusion	NOUN
ejpam-6215	49	56	.	.	PUNCT
ejpam-6215	50	1	2	2	X
ejpam-6215	50	2	.	.	NUM
ejpam-6215	50	3	analytical	analytical	ADJ
ejpam-6215	50	4	methods	method	NOUN
ejpam-6215	50	5	for	for	ADP
ejpam-6215	50	6	solving	solve	VERB
ejpam-6215	50	7	painlevé	painlevé	NOUN
ejpam-6215	50	8	equations	equation	NOUN
ejpam-6215	50	9	i	i	PRON
ejpam-6215	50	10	,	,	PUNCT
ejpam-6215	50	11	ii	ii	PROPN
ejpam-6215	50	12	analytical	analytical	ADJ
ejpam-6215	50	13	methods	method	NOUN
ejpam-6215	50	14	provide	provide	VERB
ejpam-6215	50	15	powerful	powerful	ADJ
ejpam-6215	50	16	techniques	technique	NOUN
ejpam-6215	50	17	for	for	ADP
ejpam-6215	50	18	solving	solve	VERB
ejpam-6215	50	19	nonlinear	nonlinear	ADJ
ejpam-6215	50	20	ordinary	ordinary	ADJ
ejpam-6215	50	21	differential	differential	ADJ
ejpam-6215	50	22	equations	equation	NOUN
ejpam-6215	50	23	.	.	PUNCT
ejpam-6215	51	1	in	in	ADP
ejpam-6215	51	2	this	this	DET
ejpam-6215	51	3	section	section	NOUN
ejpam-6215	51	4	,	,	PUNCT
ejpam-6215	51	5	we	we	PRON
ejpam-6215	51	6	apply	apply	VERB
ejpam-6215	51	7	the	the	DET
ejpam-6215	51	8	differential	differential	ADJ
ejpam-6215	51	9	transform	transform	NOUN
ejpam-6215	51	10	method	method	NOUN
ejpam-6215	51	11	(	(	PUNCT
ejpam-6215	51	12	dtm	dtm	PROPN
ejpam-6215	51	13	)	)	PUNCT
ejpam-6215	51	14	,	,	PUNCT
ejpam-6215	51	15	modified	modify	VERB
ejpam-6215	51	16	adomian	adomian	NOUN
ejpam-6215	51	17	decomposition	decomposition	NOUN
ejpam-6215	51	18	method	method	NOUN
ejpam-6215	51	19	(	(	PUNCT
ejpam-6215	51	20	madm	madm	PROPN
ejpam-6215	51	21	)	)	PUNCT
ejpam-6215	51	22	,	,	PUNCT
ejpam-6215	51	23	laplace	laplace	NOUN
ejpam-6215	51	24	decomposition	decomposition	NOUN
ejpam-6215	51	25	method	method	NOUN
ejpam-6215	51	26	(	(	PUNCT
ejpam-6215	51	27	ldm	ldm	NOUN
ejpam-6215	51	28	)	)	PUNCT
ejpam-6215	51	29	,	,	PUNCT
ejpam-6215	51	30	and	and	CCONJ
ejpam-6215	51	31	natural	natural	ADJ
ejpam-6215	51	32	decomposition	decomposition	NOUN
ejpam-6215	51	33	method	method	NOUN
ejpam-6215	51	34	(	(	PUNCT
ejpam-6215	51	35	ndm	ndm	PROPN
ejpam-6215	51	36	)	)	PUNCT
ejpam-6215	51	37	to	to	PART
ejpam-6215	51	38	obtain	obtain	VERB
ejpam-6215	51	39	approximate	approximate	ADJ
ejpam-6215	51	40	or	or	CCONJ
ejpam-6215	51	41	closed	closed	ADJ
ejpam-6215	51	42	-	-	PUNCT
ejpam-6215	51	43	form	form	NOUN
ejpam-6215	51	44	solutions	solution	NOUN
ejpam-6215	51	45	.	.	PUNCT
ejpam-6215	52	1	these	these	DET
ejpam-6215	52	2	methods	method	NOUN
ejpam-6215	52	3	simplify	simplify	VERB
ejpam-6215	52	4	nonlinear	nonlinear	ADJ
ejpam-6215	52	5	equations	equation	NOUN
ejpam-6215	52	6	by	by	ADP
ejpam-6215	52	7	transforming	transform	VERB
ejpam-6215	52	8	them	they	PRON
ejpam-6215	52	9	into	into	ADP
ejpam-6215	52	10	more	more	ADV
ejpam-6215	52	11	manageable	manageable	ADJ
ejpam-6215	52	12	forms	form	NOUN
ejpam-6215	52	13	,	,	PUNCT
ejpam-6215	52	14	offering	offer	VERB
ejpam-6215	52	15	advantages	advantage	NOUN
ejpam-6215	52	16	in	in	ADP
ejpam-6215	52	17	accuracy	accuracy	NOUN
ejpam-6215	52	18	,	,	PUNCT
ejpam-6215	52	19	convergence	convergence	NOUN
ejpam-6215	52	20	,	,	PUNCT
ejpam-6215	52	21	and	and	CCONJ
ejpam-6215	52	22	efficiency	efficiency	NOUN
ejpam-6215	52	23	.	.	PUNCT
ejpam-6215	53	1	the	the	DET
ejpam-6215	53	2	objective	objective	NOUN
ejpam-6215	53	3	is	be	AUX
ejpam-6215	53	4	to	to	PART
ejpam-6215	53	5	analyze	analyze	VERB
ejpam-6215	53	6	and	and	CCONJ
ejpam-6215	53	7	compare	compare	VERB
ejpam-6215	53	8	their	their	PRON
ejpam-6215	53	9	effectiveness	effectiveness	NOUN
ejpam-6215	53	10	in	in	ADP
ejpam-6215	53	11	solving	solve	VERB
ejpam-6215	53	12	painlevé	painlevé	NOUN
ejpam-6215	53	13	equations	equation	NOUN
ejpam-6215	53	14	,	,	PUNCT
ejpam-6215	53	15	highlighting	highlight	VERB
ejpam-6215	53	16	their	their	PRON
ejpam-6215	53	17	role	role	NOUN
ejpam-6215	53	18	in	in	ADP
ejpam-6215	53	19	nonlinear	nonlinear	ADJ
ejpam-6215	53	20	differential	differential	ADJ
ejpam-6215	53	21	equation	equation	NOUN
ejpam-6215	53	22	research	research	NOUN
ejpam-6215	53	23	[	[	X
ejpam-6215	53	24	1	1	NUM
ejpam-6215	53	25	,	,	PUNCT
ejpam-6215	53	26	2	2	NUM
ejpam-6215	53	27	]	]	PUNCT
ejpam-6215	53	28	.	.	PUNCT
ejpam-6215	54	1	2.1	2.1	NUM
ejpam-6215	54	2	.	.	PUNCT
ejpam-6215	54	3	differential	differential	ADJ
ejpam-6215	54	4	transform	transform	NOUN
ejpam-6215	54	5	method	method	NOUN
ejpam-6215	54	6	(	(	PUNCT
ejpam-6215	54	7	dtm	dtm	PROPN
ejpam-6215	54	8	)	)	PUNCT
ejpam-6215	54	9	the	the	DET
ejpam-6215	54	10	differential	differential	ADJ
ejpam-6215	54	11	transform	transform	NOUN
ejpam-6215	54	12	,	,	PUNCT
ejpam-6215	54	13	initially	initially	ADV
ejpam-6215	54	14	introduced	introduce	VERB
ejpam-6215	54	15	by	by	ADP
ejpam-6215	54	16	zhou	zhou	PROPN
ejpam-6215	55	1	[	[	X
ejpam-6215	55	2	5	5	NUM
ejpam-6215	55	3	,	,	PUNCT
ejpam-6215	55	4	6	6	NUM
ejpam-6215	55	5	,	,	PUNCT
ejpam-6215	55	6	17–20	17–20	NUM
ejpam-6215	55	7	]	]	PUNCT
ejpam-6215	55	8	is	be	AUX
ejpam-6215	55	9	a	a	DET
ejpam-6215	55	10	technique	technique	NOUN
ejpam-6215	55	11	for	for	ADP
ejpam-6215	55	12	solving	solve	VERB
ejpam-6215	55	13	differential	differential	ADJ
ejpam-6215	55	14	equations	equation	NOUN
ejpam-6215	55	15	.	.	PUNCT
ejpam-6215	56	1	this	this	DET
ejpam-6215	56	2	method	method	NOUN
ejpam-6215	56	3	determines	determine	VERB
ejpam-6215	56	4	the	the	DET
ejpam-6215	56	5	coefficients	coefficient	NOUN
ejpam-6215	56	6	of	of	ADP
ejpam-6215	56	7	a	a	DET
ejpam-6215	56	8	taylor	taylor	PROPN
ejpam-6215	56	9	series	series	NOUN
ejpam-6215	56	10	of	of	ADP
ejpam-6215	56	11	the	the	DET
ejpam-6215	56	12	function	function	NOUN
ejpam-6215	56	13	by	by	ADP
ejpam-6215	56	14	solving	solve	VERB
ejpam-6215	56	15	a	a	DET
ejpam-6215	56	16	recursive	recursive	ADJ
ejpam-6215	56	17	equation	equation	NOUN
ejpam-6215	56	18	induced	induce	VERB
ejpam-6215	56	19	by	by	ADP
ejpam-6215	56	20	the	the	DET
ejpam-6215	56	21	given	give	VERB
ejpam-6215	56	22	differential	differential	ADJ
ejpam-6215	56	23	equation	equation	NOUN
ejpam-6215	56	24	.	.	PUNCT
ejpam-6215	57	1	the	the	DET
ejpam-6215	57	2	differential	differential	ADJ
ejpam-6215	57	3	transform	transform	NOUN
ejpam-6215	57	4	method	method	NOUN
ejpam-6215	57	5	has	have	AUX
ejpam-6215	57	6	been	be	AUX
ejpam-6215	57	7	effectively	effectively	ADV
ejpam-6215	57	8	applied	apply	VERB
ejpam-6215	57	9	to	to	PART
ejpam-6215	57	10	solve	solve	VERB
ejpam-6215	57	11	initial	initial	ADJ
ejpam-6215	57	12	value	value	NOUN
ejpam-6215	57	13	problems	problem	NOUN
ejpam-6215	57	14	represented	represent	VERB
ejpam-6215	57	15	by	by	ADP
ejpam-6215	57	16	strongly	strongly	ADV
ejpam-6215	57	17	ordinary	ordinary	ADJ
ejpam-6215	57	18	differential	differential	ADJ
ejpam-6215	57	19	equations	equation	NOUN
ejpam-6215	57	20	[	[	X
ejpam-6215	57	21	21–25	21–25	NUM
ejpam-6215	57	22	]	]	PUNCT
ejpam-6215	57	23	.	.	PUNCT
ejpam-6215	58	1	the	the	DET
ejpam-6215	58	2	differential	differential	ADJ
ejpam-6215	58	3	transform	transform	NOUN
ejpam-6215	58	4	of	of	ADP
ejpam-6215	58	5	a	a	DET
ejpam-6215	58	6	function	function	NOUN
ejpam-6215	58	7	y(x	y(x	NOUN
ejpam-6215	58	8	)	)	PUNCT
ejpam-6215	58	9	is	be	AUX
ejpam-6215	58	10	defined	define	VERB
ejpam-6215	58	11	as	as	SCONJ
ejpam-6215	58	12	follows	follow	VERB
ejpam-6215	58	13	:	:	PUNCT
ejpam-6215	58	14	y	y	PROPN
ejpam-6215	58	15	(	(	PUNCT
ejpam-6215	58	16	k	k	NOUN
ejpam-6215	58	17	)	)	PUNCT
ejpam-6215	58	18	=	=	SYM
ejpam-6215	58	19	1	1	NUM
ejpam-6215	58	20	k	k	NOUN
ejpam-6215	58	21	!	!	PUNCT
ejpam-6215	58	22	(	(	PUNCT
ejpam-6215	58	23	dky(x	dky(x	PROPN
ejpam-6215	58	24	)	)	PUNCT
ejpam-6215	58	25	dxk	dxk	NOUN
ejpam-6215	58	26	)	)	PUNCT
ejpam-6215	58	27	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6215	58	28	x=0	x=0	PROPN
ejpam-6215	58	29	.	.	PUNCT
ejpam-6215	59	1	(	(	PUNCT
ejpam-6215	59	2	5	5	NUM
ejpam-6215	59	3	)	)	PUNCT
ejpam-6215	59	4	where	where	SCONJ
ejpam-6215	59	5	y(x	y(x	NOUN
ejpam-6215	59	6	)	)	PUNCT
ejpam-6215	59	7	is	be	AUX
ejpam-6215	59	8	the	the	DET
ejpam-6215	59	9	original	original	ADJ
ejpam-6215	59	10	function	function	NOUN
ejpam-6215	59	11	and	and	CCONJ
ejpam-6215	59	12	y	y	PROPN
ejpam-6215	59	13	(	(	PUNCT
ejpam-6215	59	14	k	k	NOUN
ejpam-6215	59	15	)	)	PUNCT
ejpam-6215	59	16	is	be	AUX
ejpam-6215	59	17	the	the	DET
ejpam-6215	59	18	transformed	transform	VERB
ejpam-6215	59	19	function	function	NOUN
ejpam-6215	59	20	.	.	PUNCT
ejpam-6215	60	1	differential	differential	ADJ
ejpam-6215	60	2	inverse	inverse	NOUN
ejpam-6215	60	3	transform	transform	NOUN
ejpam-6215	60	4	of	of	ADP
ejpam-6215	60	5	y	y	PROPN
ejpam-6215	60	6	(	(	PUNCT
ejpam-6215	60	7	k	k	NOUN
ejpam-6215	60	8	)	)	PUNCT
ejpam-6215	60	9	is	be	AUX
ejpam-6215	60	10	defined	define	VERB
ejpam-6215	60	11	as	as	ADP
ejpam-6215	60	12	:	:	PUNCT
ejpam-6215	60	13	y(x	y(x	X
ejpam-6215	60	14	)	)	PUNCT
ejpam-6215	60	15	=	=	PUNCT
ejpam-6215	61	1	∞∑	∞∑	NUM
ejpam-6215	61	2	k=0	k=0	PROPN
ejpam-6215	61	3	y	y	PROPN
ejpam-6215	61	4	(	(	PUNCT
ejpam-6215	61	5	k)xk	k)xk	PROPN
ejpam-6215	61	6	≈	≈	PROPN
ejpam-6215	61	7	yn(x	yn(x	PROPN
ejpam-6215	61	8	)	)	PUNCT
ejpam-6215	61	9	=	=	SYM
ejpam-6215	61	10	n∑	n∑	PROPN
ejpam-6215	61	11	k=0	k=0	PROPN
ejpam-6215	61	12	y	y	PROPN
ejpam-6215	61	13	(	(	PUNCT
ejpam-6215	61	14	k)xk	k)xk	PROPN
ejpam-6215	61	15	.	.	PROPN
ejpam-6215	62	1	(	(	PUNCT
ejpam-6215	62	2	6	6	NUM
ejpam-6215	62	3	)	)	PUNCT
ejpam-6215	62	4	by	by	ADP
ejpam-6215	62	5	substituting	substitute	VERB
ejpam-6215	62	6	(	(	PUNCT
ejpam-6215	62	7	5	5	NUM
ejpam-6215	62	8	)	)	PUNCT
ejpam-6215	62	9	in	in	ADP
ejpam-6215	62	10	(	(	PUNCT
ejpam-6215	62	11	6	6	X
ejpam-6215	62	12	)	)	PUNCT
ejpam-6215	62	13	we	we	PRON
ejpam-6215	62	14	get	get	VERB
ejpam-6215	62	15	y(x	y(x	NOUN
ejpam-6215	62	16	)	)	PUNCT
ejpam-6215	62	17	=	=	PUNCT
ejpam-6215	63	1	∞∑	∞∑	NUM
ejpam-6215	63	2	k=0	k=0	PROPN
ejpam-6215	63	3	1	1	NUM
ejpam-6215	63	4	k	k	NOUN
ejpam-6215	63	5	!	!	PUNCT
ejpam-6215	63	6	(	(	PUNCT
ejpam-6215	63	7	dky(x	dky(x	PROPN
ejpam-6215	63	8	)	)	PUNCT
ejpam-6215	63	9	dxk	dxk	NOUN
ejpam-6215	63	10	)	)	PUNCT
ejpam-6215	64	1	x=0	x=0	PUNCT
ejpam-6215	64	2	.	.	PUNCT
ejpam-6215	65	1	(	(	PUNCT
ejpam-6215	65	2	7	7	X
ejpam-6215	65	3	)	)	PUNCT
ejpam-6215	65	4	the	the	DET
ejpam-6215	65	5	differential	differential	ADJ
ejpam-6215	65	6	transform	transform	NOUN
ejpam-6215	65	7	verified	verify	VERB
ejpam-6215	65	8	the	the	DET
ejpam-6215	65	9	following	follow	VERB
ejpam-6215	65	10	properties	property	NOUN
ejpam-6215	65	11	:	:	PUNCT
ejpam-6215	66	1	[	[	X
ejpam-6215	66	2	26	26	NUM
ejpam-6215	66	3	,	,	PUNCT
ejpam-6215	66	4	27	27	NUM
ejpam-6215	66	5	]	]	PUNCT
ejpam-6215	66	6	•	•	NOUN
ejpam-6215	66	7	if	if	SCONJ
ejpam-6215	66	8	u(x	u(x	NOUN
ejpam-6215	66	9	)	)	PUNCT
ejpam-6215	66	10	=	=	PUNCT
ejpam-6215	66	11	u1(x)±	u1(x)±	X
ejpam-6215	66	12	u2(x	u2(x	NOUN
ejpam-6215	66	13	)	)	PUNCT
ejpam-6215	66	14	,	,	PUNCT
ejpam-6215	66	15	then	then	ADV
ejpam-6215	66	16	u(k	u(k	PROPN
ejpam-6215	66	17	)	)	PUNCT
ejpam-6215	66	18	=	=	SYM
ejpam-6215	66	19	u1(k)±	u1(k)±	PROPN
ejpam-6215	66	20	u2(k	u2(k	PROPN
ejpam-6215	66	21	)	)	PUNCT
ejpam-6215	66	22	.	.	PUNCT
ejpam-6215	67	1	•	•	NOUN
ejpam-6215	67	2	if	if	SCONJ
ejpam-6215	67	3	u(x	u(x	VERB
ejpam-6215	67	4	)	)	PUNCT
ejpam-6215	67	5	=	=	SYM
ejpam-6215	67	6	cu1(x	cu1(x	PROPN
ejpam-6215	67	7	)	)	PUNCT
ejpam-6215	67	8	then	then	ADV
ejpam-6215	67	9	u(k	u(k	PROPN
ejpam-6215	67	10	)	)	PUNCT
ejpam-6215	67	11	=	=	PUNCT
ejpam-6215	68	1	cu1(k	cu1(k	PROPN
ejpam-6215	68	2	)	)	PUNCT
ejpam-6215	68	3	,	,	PUNCT
ejpam-6215	68	4	where	where	SCONJ
ejpam-6215	68	5	c	c	NOUN
ejpam-6215	68	6	is	be	AUX
ejpam-6215	68	7	constant	constant	ADJ
ejpam-6215	68	8	.	.	PUNCT
ejpam-6215	69	1	•	•	NOUN
ejpam-6215	69	2	if	if	SCONJ
ejpam-6215	69	3	u(x	u(x	NOUN
ejpam-6215	69	4	)	)	PUNCT
ejpam-6215	69	5	=	=	SYM
ejpam-6215	69	6	dnu1(x	dnu1(x	NOUN
ejpam-6215	69	7	)	)	PUNCT
ejpam-6215	69	8	dxn	dxn	NOUN
ejpam-6215	69	9	,	,	PUNCT
ejpam-6215	69	10	then	then	ADV
ejpam-6215	69	11	u(k	u(k	PROPN
ejpam-6215	69	12	)	)	PUNCT
ejpam-6215	70	1	=	=	SYM
ejpam-6215	70	2	(	(	PUNCT
ejpam-6215	70	3	k+n	k+n	PROPN
ejpam-6215	70	4	)	)	PUNCT
ejpam-6215	70	5	!	!	PUNCT
ejpam-6215	71	1	k	k	X
ejpam-6215	71	2	!	!	PUNCT
ejpam-6215	72	1	u1(k	u1(k	X
ejpam-6215	72	2	+	+	NUM
ejpam-6215	72	3	n	n	CCONJ
ejpam-6215	72	4	)	)	PUNCT
ejpam-6215	72	5	.	.	PUNCT
ejpam-6215	73	1	s.	s.	PROPN
ejpam-6215	73	2	mohammed	mohammed	PROPN
ejpam-6215	73	3	,	,	PUNCT
ejpam-6215	73	4	s.	s.	PROPN
ejpam-6215	73	5	abid	abid	PROPN
ejpam-6215	73	6	,	,	PUNCT
ejpam-6215	73	7	r.	r.	PROPN
ejpam-6215	73	8	abid	abid	PROPN
ejpam-6215	73	9	/	/	SYM
ejpam-6215	73	10	eur	eur	PROPN
ejpam-6215	73	11	.	.	PUNCT
ejpam-6215	74	1	j.	j.	PROPN
ejpam-6215	74	2	pure	pure	PROPN
ejpam-6215	74	3	appl	appl	PROPN
ejpam-6215	74	4	.	.	PROPN
ejpam-6215	74	5	math	math	PROPN
ejpam-6215	74	6	,	,	PUNCT
ejpam-6215	74	7	18	18	NUM
ejpam-6215	74	8	(	(	PUNCT
ejpam-6215	74	9	3	3	NUM
ejpam-6215	74	10	)	)	PUNCT
ejpam-6215	74	11	(	(	PUNCT
ejpam-6215	74	12	2025	2025	NUM
ejpam-6215	74	13	)	)	PUNCT
ejpam-6215	74	14	,	,	PUNCT
ejpam-6215	74	15	6215	6215	NUM
ejpam-6215	74	16	4	4	NUM
ejpam-6215	74	17	of	of	ADP
ejpam-6215	74	18	38	38	NUM
ejpam-6215	74	19	•	•	NOUN
ejpam-6215	74	20	if	if	SCONJ
ejpam-6215	74	21	u(x	u(x	NOUN
ejpam-6215	74	22	)	)	PUNCT
ejpam-6215	74	23	=	=	SYM
ejpam-6215	74	24	u1(x)u2(x	u1(x)u2(x	NOUN
ejpam-6215	74	25	)	)	PUNCT
ejpam-6215	74	26	,	,	PUNCT
ejpam-6215	74	27	then	then	ADV
ejpam-6215	74	28	u(k	u(k	PROPN
ejpam-6215	74	29	)	)	PUNCT
ejpam-6215	75	1	=	=	PUNCT
ejpam-6215	76	1	∑k	∑k	PROPN
ejpam-6215	76	2	r=0	r=0	VERB
ejpam-6215	77	1	u1(r)u2(k	u1(r)u2(k	ADV
ejpam-6215	77	2	−	−	NOUN
ejpam-6215	77	3	r	r	NOUN
ejpam-6215	77	4	)	)	PUNCT
ejpam-6215	77	5	.	.	PUNCT
ejpam-6215	78	1	•	•	NOUN
ejpam-6215	78	2	if	if	SCONJ
ejpam-6215	78	3	u(x	u(x	NOUN
ejpam-6215	78	4	)	)	PUNCT
ejpam-6215	78	5	=	=	SYM
ejpam-6215	78	6	u1(x)u2(x	u1(x)u2(x	NOUN
ejpam-6215	78	7	)	)	PUNCT
ejpam-6215	78	8	.	.	PUNCT
ejpam-6215	78	9	.	.	PUNCT
ejpam-6215	78	10	.	.	PUNCT
ejpam-6215	79	1	un(x	un(x	X
ejpam-6215	79	2	)	)	PUNCT
ejpam-6215	79	3	,	,	PUNCT
ejpam-6215	79	4	then	then	ADV
ejpam-6215	79	5	u(k	u(k	PROPN
ejpam-6215	79	6	)	)	PUNCT
ejpam-6215	79	7	=	=	PUNCT
ejpam-6215	79	8	k∑	k∑	PROPN
ejpam-6215	79	9	rn−1=0	rn−1=0	PROPN
ejpam-6215	79	10	rn−1∑	rn−1∑	VERB
ejpam-6215	79	11	rn−2=0	rn−2=0	PROPN
ejpam-6215	79	12	.	.	PUNCT
ejpam-6215	79	13	.	.	PUNCT
ejpam-6215	79	14	.	.	PUNCT
ejpam-6215	80	1	r3∑	r3∑	NOUN
ejpam-6215	80	2	r2=0	r2=0	PROPN
ejpam-6215	80	3	r2∑	r2∑	PROPN
ejpam-6215	80	4	r1=0	r1=0	PROPN
ejpam-6215	80	5	u1(r1)u2(r2−r1	u1(r1)u2(r2−r1	PROPN
ejpam-6215	80	6	)	)	PUNCT
ejpam-6215	80	7	.	.	PUNCT
ejpam-6215	80	8	.	.	PUNCT
ejpam-6215	80	9	.	.	PUNCT
ejpam-6215	81	1	un−1(rn−1−rn−2)un(k−rn−1	un−1(rn−1−rn−2)un(k−rn−1	X
ejpam-6215	81	2	)	)	PUNCT
ejpam-6215	81	3	.	.	PUNCT
ejpam-6215	82	1	•	•	NOUN
ejpam-6215	82	2	if	if	SCONJ
ejpam-6215	82	3	u(x	u(x	VERB
ejpam-6215	82	4	)	)	PUNCT
ejpam-6215	82	5	=	=	SYM
ejpam-6215	82	6	axm	axm	PROPN
ejpam-6215	82	7	,	,	PUNCT
ejpam-6215	82	8	then	then	ADV
ejpam-6215	82	9	u(k	u(k	PROPN
ejpam-6215	82	10	)	)	PUNCT
ejpam-6215	82	11	=	=	SYM
ejpam-6215	82	12	aδ(k	aδ(k	ADP
ejpam-6215	82	13	−m	−m	NOUN
ejpam-6215	82	14	)	)	PUNCT
ejpam-6215	82	15	,	,	PUNCT
ejpam-6215	82	16	where	where	SCONJ
ejpam-6215	82	17	δ(k	δ(k	NOUN
ejpam-6215	82	18	−m	−m	NOUN
ejpam-6215	82	19	)	)	PUNCT
ejpam-6215	82	20	=	=	PRON
ejpam-6215	82	21	{	{	PUNCT
ejpam-6215	82	22	1	1	NUM
ejpam-6215	82	23	,	,	PUNCT
ejpam-6215	82	24	if	if	SCONJ
ejpam-6215	82	25	k	k	PROPN
ejpam-6215	82	26	=	=	NOUN
ejpam-6215	82	27	m	m	VERB
ejpam-6215	82	28	0	0	NUM
ejpam-6215	82	29	,	,	PUNCT
ejpam-6215	82	30	if	if	SCONJ
ejpam-6215	82	31	k	k	PROPN
ejpam-6215	82	32	̸=	̸=	PROPN
ejpam-6215	82	33	m	m	VERB
ejpam-6215	82	34	•	•	NOUN
ejpam-6215	82	35	if	if	SCONJ
ejpam-6215	82	36	u(x	u(x	NOUN
ejpam-6215	82	37	)	)	PUNCT
ejpam-6215	82	38	=	=	SYM
ejpam-6215	82	39	u1(x	u1(x	NOUN
ejpam-6215	82	40	)	)	PUNCT
ejpam-6215	82	41	du2(x	du2(x	PROPN
ejpam-6215	82	42	)	)	PUNCT
ejpam-6215	82	43	dx	dx	PROPN
ejpam-6215	82	44	,	,	PUNCT
ejpam-6215	82	45	then	then	ADV
ejpam-6215	82	46	u(k	u(k	PROPN
ejpam-6215	82	47	)	)	PUNCT
ejpam-6215	83	1	=	=	PUNCT
ejpam-6215	83	2	∑k	∑k	PROPN
ejpam-6215	83	3	r=0(k	r=0(k	VERB
ejpam-6215	83	4	−	−	PUNCT
ejpam-6215	83	5	r	r	NOUN
ejpam-6215	83	6	+	+	NOUN
ejpam-6215	83	7	1)u1(r)u2(k	1)u1(r)u2(k	NUM
ejpam-6215	83	8	−	−	NOUN
ejpam-6215	83	9	r	r	NOUN
ejpam-6215	83	10	+	+	NOUN
ejpam-6215	83	11	1	1	NUM
ejpam-6215	83	12	)	)	PUNCT
ejpam-6215	83	13	.	.	PUNCT
ejpam-6215	84	1	2.1.1	2.1.1	X
ejpam-6215	84	2	.	.	PUNCT
ejpam-6215	85	1	the	the	DET
ejpam-6215	85	2	dtm	dtm	PROPN
ejpam-6215	85	3	for	for	ADP
ejpam-6215	85	4	solving	solve	VERB
ejpam-6215	85	5	the	the	DET
ejpam-6215	85	6	painlevé	painlevé	NOUN
ejpam-6215	85	7	i	i	PRON
ejpam-6215	85	8	differential	differential	VERB
ejpam-6215	85	9	equation	equation	NOUN
ejpam-6215	85	10	rewrite	rewrite	NOUN
ejpam-6215	85	11	(	(	PUNCT
ejpam-6215	85	12	1	1	NUM
ejpam-6215	85	13	)	)	PUNCT
ejpam-6215	85	14	d2y	d2y	NOUN
ejpam-6215	85	15	dx2	dx2	PROPN
ejpam-6215	85	16	=	=	SYM
ejpam-6215	85	17	6y2	6y2	NUM
ejpam-6215	85	18	+	+	CCONJ
ejpam-6215	85	19	x	x	NOUN
ejpam-6215	85	20	,	,	PUNCT
ejpam-6215	85	21	y(0	y(0	PROPN
ejpam-6215	85	22	)	)	PUNCT
ejpam-6215	85	23	=	=	SYM
ejpam-6215	85	24	0	0	NUM
ejpam-6215	85	25	,	,	PUNCT
ejpam-6215	85	26	y′(0	y′(0	NOUN
ejpam-6215	85	27	)	)	PUNCT
ejpam-6215	85	28	=	=	SYM
ejpam-6215	85	29	1	1	X
ejpam-6215	85	30	.	.	X
ejpam-6215	85	31	assume	assume	VERB
ejpam-6215	85	32	y(x	y(x	NOUN
ejpam-6215	85	33	)	)	PUNCT
ejpam-6215	85	34	can	can	AUX
ejpam-6215	85	35	be	be	AUX
ejpam-6215	85	36	expressed	express	VERB
ejpam-6215	85	37	as	as	ADP
ejpam-6215	85	38	a	a	DET
ejpam-6215	85	39	power	power	NOUN
ejpam-6215	85	40	series	series	NOUN
ejpam-6215	85	41	:	:	PUNCT
ejpam-6215	85	42	y(x	y(x	X
ejpam-6215	85	43	)	)	PUNCT
ejpam-6215	85	44	=	=	PUNCT
ejpam-6215	86	1	∞∑	∞∑	NUM
ejpam-6215	86	2	k=0	k=0	PROPN
ejpam-6215	86	3	ykx	ykx	VERB
ejpam-6215	86	4	k.	k.	PROPN
ejpam-6215	86	5	from	from	ADP
ejpam-6215	86	6	the	the	DET
ejpam-6215	86	7	initial	initial	ADJ
ejpam-6215	86	8	conditions	condition	NOUN
ejpam-6215	86	9	:	:	PUNCT
ejpam-6215	86	10	y0	y0	PROPN
ejpam-6215	86	11	=	=	SYM
ejpam-6215	86	12	y(0	y(0	PROPN
ejpam-6215	86	13	)	)	PUNCT
ejpam-6215	86	14	=	=	SYM
ejpam-6215	86	15	0	0	NUM
ejpam-6215	86	16	,	,	PUNCT
ejpam-6215	86	17	y1	y1	NOUN
ejpam-6215	86	18	=	=	SYM
ejpam-6215	86	19	y′(0	y′(0	NOUN
ejpam-6215	86	20	)	)	PUNCT
ejpam-6215	86	21	=	=	SYM
ejpam-6215	86	22	1	1	X
ejpam-6215	86	23	.	.	X
ejpam-6215	86	24	apply	apply	VERB
ejpam-6215	86	25	the	the	DET
ejpam-6215	86	26	dtm	dtm	NOUN
ejpam-6215	86	27	to	to	ADP
ejpam-6215	86	28	the	the	DET
ejpam-6215	86	29	differential	differential	ADJ
ejpam-6215	86	30	equation	equation	NOUN
ejpam-6215	86	31	.	.	PUNCT
ejpam-6215	87	1	the	the	DET
ejpam-6215	87	2	second	second	ADJ
ejpam-6215	87	3	derivative	derivative	NOUN
ejpam-6215	87	4	is	be	AUX
ejpam-6215	87	5	:	:	PUNCT
ejpam-6215	87	6	d2y	d2y	ADJ
ejpam-6215	87	7	dx2	dx2	PROPN
ejpam-6215	87	8	=	=	NOUN
ejpam-6215	87	9	∞∑	∞∑	PROPN
ejpam-6215	87	10	k=0	k=0	PROPN
ejpam-6215	87	11	(	(	PUNCT
ejpam-6215	87	12	k	k	PROPN
ejpam-6215	87	13	+	+	NOUN
ejpam-6215	87	14	2)(k	2)(k	NUM
ejpam-6215	87	15	+	+	CCONJ
ejpam-6215	87	16	1)yk+2x	1)yk+2x	NUM
ejpam-6215	87	17	k.	k.	NOUN
ejpam-6215	87	18	(	(	PUNCT
ejpam-6215	87	19	8)	8)	NUM
ejpam-6215	87	20	6y2	6y2	NUM
ejpam-6215	87	21	=	=	SYM
ejpam-6215	87	22	6	6	NUM
ejpam-6215	87	23	(	(	PUNCT
ejpam-6215	87	24	∞∑	∞∑	PRON
ejpam-6215	87	25	k=0	k=0	PROPN
ejpam-6215	87	26	ykx	ykx	NOUN
ejpam-6215	87	27	k	k	PROPN
ejpam-6215	87	28	)	)	PUNCT
ejpam-6215	87	29	2	2	NUM
ejpam-6215	87	30	=	=	SYM
ejpam-6215	87	31	6	6	NUM
ejpam-6215	87	32	∞∑	∞∑	NUM
ejpam-6215	87	33	k=0	k=0	PROPN
ejpam-6215	87	34	(	(	PUNCT
ejpam-6215	87	35	k∑	k∑	NOUN
ejpam-6215	87	36	m=0	m=0	PROPN
ejpam-6215	87	37	ymyk−m	ymyk−m	PROPN
ejpam-6215	87	38	)	)	PUNCT
ejpam-6215	87	39	xk	xk	PROPN
ejpam-6215	87	40	.	.	PROPN
ejpam-6215	88	1	(	(	PUNCT
ejpam-6215	88	2	9	9	NUM
ejpam-6215	88	3	)	)	PUNCT
ejpam-6215	88	4	x	x	X
ejpam-6215	89	1	=	=	PUNCT
ejpam-6215	89	2	∞∑	∞∑	NUM
ejpam-6215	89	3	k=0	k=0	PROPN
ejpam-6215	89	4	δ(k	δ(k	ADP
ejpam-6215	89	5	−	−	PROPN
ejpam-6215	89	6	1)xk	1)xk	PROPN
ejpam-6215	89	7	.	.	PUNCT
ejpam-6215	90	1	(	(	PUNCT
ejpam-6215	90	2	10	10	NUM
ejpam-6215	90	3	)	)	PUNCT
ejpam-6215	90	4	substitute	substitute	NOUN
ejpam-6215	90	5	(	(	PUNCT
ejpam-6215	90	6	8),(9	8),(9	NUM
ejpam-6215	90	7	)	)	PUNCT
ejpam-6215	90	8	and	and	CCONJ
ejpam-6215	90	9	(	(	PUNCT
ejpam-6215	90	10	10	10	NUM
ejpam-6215	90	11	)	)	PUNCT
ejpam-6215	90	12	into	into	ADP
ejpam-6215	90	13	the	the	DET
ejpam-6215	90	14	equation	equation	NOUN
ejpam-6215	90	15	.	.	PUNCT
ejpam-6215	91	1	∞∑	∞∑	ADJ
ejpam-6215	91	2	k=0	k=0	PROPN
ejpam-6215	91	3	(	(	PUNCT
ejpam-6215	91	4	k	k	PROPN
ejpam-6215	91	5	+	+	NOUN
ejpam-6215	91	6	2)(k	2)(k	NUM
ejpam-6215	91	7	+	+	CCONJ
ejpam-6215	91	8	1)yk+2x	1)yk+2x	NUM
ejpam-6215	91	9	k	k	X
ejpam-6215	91	10	=	=	SYM
ejpam-6215	91	11	6	6	NUM
ejpam-6215	91	12	(	(	PUNCT
ejpam-6215	91	13	∞∑	∞∑	NUM
ejpam-6215	91	14	k=0	k=0	PROPN
ejpam-6215	91	15	(	(	PUNCT
ejpam-6215	91	16	k∑	k∑	NOUN
ejpam-6215	91	17	m=0	m=0	PROPN
ejpam-6215	91	18	ymyk−m	ymyk−m	PROPN
ejpam-6215	91	19	)	)	PUNCT
ejpam-6215	91	20	xk	xk	PROPN
ejpam-6215	91	21	)	)	PUNCT
ejpam-6215	92	1	+	+	CCONJ
ejpam-6215	92	2	∞∑	∞∑	NUM
ejpam-6215	92	3	k=0	k=0	PROPN
ejpam-6215	92	4	δ(k	δ(k	PROPN
ejpam-6215	92	5	−	−	PROPN
ejpam-6215	92	6	1)xk	1)xk	PROPN
ejpam-6215	92	7	.	.	PUNCT
ejpam-6215	93	1	s.	s.	PROPN
ejpam-6215	93	2	mohammed	mohammed	PROPN
ejpam-6215	93	3	,	,	PUNCT
ejpam-6215	93	4	s.	s.	PROPN
ejpam-6215	93	5	abid	abid	PROPN
ejpam-6215	93	6	,	,	PUNCT
ejpam-6215	93	7	r.	r.	PROPN
ejpam-6215	93	8	abid	abid	PROPN
ejpam-6215	93	9	/	/	SYM
ejpam-6215	93	10	eur	eur	PROPN
ejpam-6215	93	11	.	.	PUNCT
ejpam-6215	94	1	j.	j.	PROPN
ejpam-6215	94	2	pure	pure	PROPN
ejpam-6215	94	3	appl	appl	PROPN
ejpam-6215	94	4	.	.	PROPN
ejpam-6215	94	5	math	math	PROPN
ejpam-6215	94	6	,	,	PUNCT
ejpam-6215	94	7	18	18	NUM
ejpam-6215	94	8	(	(	PUNCT
ejpam-6215	94	9	3	3	NUM
ejpam-6215	94	10	)	)	PUNCT
ejpam-6215	94	11	(	(	PUNCT
ejpam-6215	94	12	2025	2025	NUM
ejpam-6215	94	13	)	)	PUNCT
ejpam-6215	94	14	,	,	PUNCT
ejpam-6215	94	15	6215	6215	NUM
ejpam-6215	94	16	5	5	NUM
ejpam-6215	94	17	of	of	ADP
ejpam-6215	94	18	38	38	NUM
ejpam-6215	94	19	for	for	ADP
ejpam-6215	94	20	each	each	PRON
ejpam-6215	94	21	k	k	NOUN
ejpam-6215	95	1	we	we	PRON
ejpam-6215	95	2	get	get	VERB
ejpam-6215	95	3	(	(	PUNCT
ejpam-6215	95	4	k	k	PROPN
ejpam-6215	95	5	+	+	NOUN
ejpam-6215	95	6	2)(k	2)(k	NUM
ejpam-6215	96	1	+	+	CCONJ
ejpam-6215	96	2	1)yk+2	1)yk+2	NUM
ejpam-6215	96	3	=	=	SYM
ejpam-6215	96	4	6	6	NUM
ejpam-6215	96	5	k∑	k∑	NOUN
ejpam-6215	96	6	m=0	m=0	PROPN
ejpam-6215	96	7	ymyk−m	ymyk−m	PROPN
ejpam-6215	96	8	+	+	ADJ
ejpam-6215	96	9	δ(k	δ(k	PROPN
ejpam-6215	96	10	−	−	NOUN
ejpam-6215	96	11	1	1	NUM
ejpam-6215	96	12	)	)	PUNCT
ejpam-6215	96	13	.	.	PUNCT
ejpam-6215	97	1	(	(	PUNCT
ejpam-6215	97	2	11	11	NUM
ejpam-6215	97	3	)	)	PUNCT
ejpam-6215	97	4	k	k	NOUN
ejpam-6215	98	1	=	=	SYM
ejpam-6215	98	2	0	0	PUNCT
ejpam-6215	98	3	(	(	PUNCT
ejpam-6215	98	4	0	0	NUM
ejpam-6215	98	5	+	+	CCONJ
ejpam-6215	98	6	2)(0	2)(0	NUM
ejpam-6215	99	1	+	+	CCONJ
ejpam-6215	99	2	1)y0	1)y0	NUM
ejpam-6215	99	3	+	+	ADJ
ejpam-6215	99	4	2	2	NUM
ejpam-6215	99	5	=	=	SYM
ejpam-6215	99	6	6	6	NUM
ejpam-6215	99	7	0∑	0∑	NOUN
ejpam-6215	99	8	m=0	m=0	PROPN
ejpam-6215	99	9	ymy0−m	ymy0−m	PRON
ejpam-6215	100	1	+	+	CCONJ
ejpam-6215	100	2	δ(0−	δ(0−	X
ejpam-6215	100	3	1	1	NUM
ejpam-6215	100	4	)	)	PUNCT
ejpam-6215	100	5	.	.	PUNCT
ejpam-6215	101	1	2y2	2y2	NUM
ejpam-6215	101	2	=	=	SYM
ejpam-6215	101	3	6y0y0	6y0y0	NOUN
ejpam-6215	101	4	+	+	X
ejpam-6215	101	5	0	0	NUM
ejpam-6215	101	6	=	=	SYM
ejpam-6215	101	7	0	0	X
ejpam-6215	101	8	.	.	PUNCT
ejpam-6215	102	1	y2	y2	NOUN
ejpam-6215	103	1	=	=	NOUN
ejpam-6215	104	1	0	0	X
ejpam-6215	104	2	.	.	PUNCT
ejpam-6215	105	1	k	k	X
ejpam-6215	105	2	=	=	SYM
ejpam-6215	105	3	1	1	NUM
ejpam-6215	105	4	(	(	PUNCT
ejpam-6215	105	5	1	1	NUM
ejpam-6215	105	6	+	+	NUM
ejpam-6215	105	7	2)(1	2)(1	NUM
ejpam-6215	105	8	+	+	CCONJ
ejpam-6215	105	9	1)y1	1)y1	NUM
ejpam-6215	105	10	+	+	SYM
ejpam-6215	105	11	2	2	NUM
ejpam-6215	105	12	=	=	SYM
ejpam-6215	105	13	6	6	NUM
ejpam-6215	105	14	1∑	1∑	PROPN
ejpam-6215	105	15	m=0	m=0	PROPN
ejpam-6215	105	16	ymy1−m	ymy1−m	PUNCT
ejpam-6215	106	1	+	+	PUNCT
ejpam-6215	106	2	δ(1−	δ(1−	ADJ
ejpam-6215	106	3	1	1	NUM
ejpam-6215	106	4	)	)	PUNCT
ejpam-6215	106	5	.	.	PUNCT
ejpam-6215	107	1	6y3	6y3	NUM
ejpam-6215	107	2	=	=	SYM
ejpam-6215	107	3	6(y0y1	6(y0y1	NUM
ejpam-6215	107	4	+	+	CCONJ
ejpam-6215	107	5	y1y0	y1y0	NOUN
ejpam-6215	107	6	)	)	PUNCT
ejpam-6215	108	1	+	+	CCONJ
ejpam-6215	108	2	1	1	NUM
ejpam-6215	108	3	=	=	SYM
ejpam-6215	108	4	6(0(1	6(0(1	NUM
ejpam-6215	108	5	)	)	PUNCT
ejpam-6215	109	1	+	+	CCONJ
ejpam-6215	109	2	1(0	1(0	NUM
ejpam-6215	109	3	)	)	PUNCT
ejpam-6215	109	4	)	)	PUNCT
ejpam-6215	110	1	+	+	CCONJ
ejpam-6215	110	2	1	1	NUM
ejpam-6215	110	3	=	=	SYM
ejpam-6215	110	4	1	1	X
ejpam-6215	110	5	.	.	X
ejpam-6215	110	6	y3	y3	NOUN
ejpam-6215	110	7	=	=	SYM
ejpam-6215	110	8	1	1	NUM
ejpam-6215	110	9	6	6	NUM
ejpam-6215	110	10	.	.	PUNCT
ejpam-6215	111	1	k	k	X
ejpam-6215	111	2	=	=	SYM
ejpam-6215	111	3	2	2	NUM
ejpam-6215	111	4	(	(	PUNCT
ejpam-6215	111	5	2	2	NUM
ejpam-6215	111	6	+	+	NUM
ejpam-6215	111	7	2)(2	2)(2	NUM
ejpam-6215	111	8	+	+	CCONJ
ejpam-6215	111	9	1)y2	1)y2	NUM
ejpam-6215	111	10	+	+	SYM
ejpam-6215	111	11	2	2	NUM
ejpam-6215	111	12	=	=	SYM
ejpam-6215	111	13	6	6	NUM
ejpam-6215	111	14	2∑	2∑	NUM
ejpam-6215	111	15	m=0	m=0	PROPN
ejpam-6215	111	16	ymy2−m	ymy2−m	X
ejpam-6215	111	17	+	+	CCONJ
ejpam-6215	111	18	δ(2−	δ(2−	NOUN
ejpam-6215	111	19	1	1	NUM
ejpam-6215	111	20	)	)	PUNCT
ejpam-6215	111	21	.	.	PUNCT
ejpam-6215	112	1	12y4	12y4	NUM
ejpam-6215	112	2	=	=	NOUN
ejpam-6215	113	1	6(y0y2	6(y0y2	NOUN
ejpam-6215	114	1	+	+	CCONJ
ejpam-6215	114	2	y1y1	y1y1	NUM
ejpam-6215	114	3	+	+	NUM
ejpam-6215	114	4	y2y0	y2y0	NOUN
ejpam-6215	114	5	)	)	PUNCT
ejpam-6215	114	6	+	+	SYM
ejpam-6215	114	7	0	0	NUM
ejpam-6215	114	8	=	=	SYM
ejpam-6215	114	9	6(0(1	6(0(1	NUM
ejpam-6215	114	10	)	)	PUNCT
ejpam-6215	114	11	+	+	CCONJ
ejpam-6215	114	12	1(0	1(0	NUM
ejpam-6215	114	13	)	)	PUNCT
ejpam-6215	114	14	)	)	PUNCT
ejpam-6215	115	1	=	=	PUNCT
ejpam-6215	115	2	6	6	X
ejpam-6215	115	3	.	.	PUNCT
ejpam-6215	116	1	y4	y4	VERB
ejpam-6215	116	2	=	=	PUNCT
ejpam-6215	116	3	1	1	NUM
ejpam-6215	116	4	2	2	NUM
ejpam-6215	116	5	.	.	PUNCT
ejpam-6215	117	1	k	k	X
ejpam-6215	117	2	=	=	SYM
ejpam-6215	117	3	3	3	NUM
ejpam-6215	117	4	(	(	PUNCT
ejpam-6215	117	5	3	3	NUM
ejpam-6215	117	6	+	+	NUM
ejpam-6215	117	7	2)(3	2)(3	NUM
ejpam-6215	117	8	+	+	CCONJ
ejpam-6215	118	1	1)y3	1)y3	NUM
ejpam-6215	118	2	+	+	ADJ
ejpam-6215	118	3	2	2	NUM
ejpam-6215	118	4	=	=	SYM
ejpam-6215	118	5	6	6	NUM
ejpam-6215	118	6	3∑	3∑	NOUN
ejpam-6215	118	7	m=0	m=0	PROPN
ejpam-6215	118	8	ymy3−m	ymy3−m	PUNCT
ejpam-6215	119	1	+	+	CCONJ
ejpam-6215	119	2	δ(3−	δ(3−	PROPN
ejpam-6215	119	3	1	1	NUM
ejpam-6215	119	4	)	)	PUNCT
ejpam-6215	119	5	.	.	PUNCT
ejpam-6215	120	1	20y5	20y5	NUM
ejpam-6215	120	2	=	=	SYM
ejpam-6215	120	3	6(y0y3	6(y0y3	NUM
ejpam-6215	120	4	+	+	SYM
ejpam-6215	120	5	y1y2	y1y2	PROPN
ejpam-6215	121	1	+	+	CCONJ
ejpam-6215	121	2	y2y1	y2y1	PROPN
ejpam-6215	121	3	+	+	ADJ
ejpam-6215	121	4	y3y0	y3y0	PROPN
ejpam-6215	121	5	)	)	PUNCT
ejpam-6215	121	6	+	+	SYM
ejpam-6215	121	7	0	0	NUM
ejpam-6215	121	8	=	=	SYM
ejpam-6215	121	9	6	6	NUM
ejpam-6215	121	10	(	(	PUNCT
ejpam-6215	121	11	0	0	NUM
ejpam-6215	121	12	+	+	CCONJ
ejpam-6215	121	13	1(0	1(0	NUM
ejpam-6215	121	14	)	)	PUNCT
ejpam-6215	122	1	+	+	NOUN
ejpam-6215	122	2	0(1	0(1	NUM
ejpam-6215	122	3	)	)	PUNCT
ejpam-6215	123	1	+	+	CCONJ
ejpam-6215	123	2	1	1	NUM
ejpam-6215	123	3	6	6	NUM
ejpam-6215	123	4	(	(	PUNCT
ejpam-6215	123	5	0	0	NUM
ejpam-6215	123	6	)	)	PUNCT
ejpam-6215	123	7	)	)	PUNCT
ejpam-6215	124	1	=	=	PUNCT
ejpam-6215	124	2	0	0	X
ejpam-6215	124	3	.	.	PUNCT
ejpam-6215	125	1	y5	y5	NOUN
ejpam-6215	125	2	=	=	NOUN
ejpam-6215	125	3	0	0	PROPN
ejpam-6215	125	4	.	.	PUNCT
ejpam-6215	125	5	...	...	PUNCT
ejpam-6215	126	1	y0	y0	NOUN
ejpam-6215	126	2	=	=	SYM
ejpam-6215	126	3	0	0	NUM
ejpam-6215	126	4	,	,	PUNCT
ejpam-6215	126	5	y1	y1	NOUN
ejpam-6215	126	6	=	=	SYM
ejpam-6215	126	7	1	1	NUM
ejpam-6215	126	8	,	,	PUNCT
ejpam-6215	126	9	y2	y2	NOUN
ejpam-6215	126	10	=	=	SYM
ejpam-6215	126	11	0	0	NUM
ejpam-6215	126	12	,	,	PUNCT
ejpam-6215	126	13	y3	y3	NOUN
ejpam-6215	126	14	=	=	SYM
ejpam-6215	126	15	1	1	NUM
ejpam-6215	126	16	6	6	NUM
ejpam-6215	126	17	,	,	PUNCT
ejpam-6215	126	18	y4	y4	PROPN
ejpam-6215	126	19	=	=	SYM
ejpam-6215	126	20	1	1	NUM
ejpam-6215	126	21	2	2	NUM
ejpam-6215	126	22	,	,	PUNCT
ejpam-6215	126	23	y5	y5	NOUN
ejpam-6215	126	24	=	=	SYM
ejpam-6215	126	25	0	0	NUM
ejpam-6215	126	26	,	,	PUNCT
ejpam-6215	126	27	y6	y6	NOUN
ejpam-6215	126	28	=	=	NOUN
ejpam-6215	126	29	1	1	NUM
ejpam-6215	126	30	15	15	NUM
ejpam-6215	126	31	,	,	PUNCT
ejpam-6215	126	32	y7	y7	NOUN
ejpam-6215	126	33	=	=	NOUN
ejpam-6215	126	34	1	1	NUM
ejpam-6215	126	35	7	7	NUM
ejpam-6215	126	36	,	,	PUNCT
ejpam-6215	126	37	y8	y8	PROPN
ejpam-6215	126	38	=	=	NOUN
ejpam-6215	126	39	1	1	NUM
ejpam-6215	126	40	336	336	NUM
ejpam-6215	126	41	,	,	PUNCT
ejpam-6215	126	42	y9	y9	PROPN
ejpam-6215	126	43	=	=	NOUN
ejpam-6215	126	44	1	1	NUM
ejpam-6215	126	45	40	40	NUM
ejpam-6215	126	46	,	,	PUNCT
ejpam-6215	126	47	y10	y10	NOUN
ejpam-6215	126	48	=	=	SYM
ejpam-6215	126	49	1	1	NUM
ejpam-6215	126	50	28	28	NUM
ejpam-6215	126	51	,	,	PUNCT
ejpam-6215	126	52	.	.	PUNCT
ejpam-6215	126	53	.	.	PUNCT
ejpam-6215	126	54	.	.	PUNCT
ejpam-6215	127	1	y(x	y(x	X
ejpam-6215	127	2	)	)	PUNCT
ejpam-6215	128	1	=	=	PUNCT
ejpam-6215	128	2	y0	y0	NOUN
ejpam-6215	128	3	+	+	CCONJ
ejpam-6215	128	4	y1x+	y1x+	PROPN
ejpam-6215	128	5	y2x	y2x	ADJ
ejpam-6215	128	6	2	2	NUM
ejpam-6215	128	7	+	+	NUM
ejpam-6215	128	8	y3x	y3x	VERB
ejpam-6215	128	9	3	3	NUM
ejpam-6215	128	10	+	+	NUM
ejpam-6215	128	11	y4x	y4x	NOUN
ejpam-6215	128	12	4	4	NUM
ejpam-6215	128	13	+	+	NUM
ejpam-6215	128	14	y5x	y5x	NOUN
ejpam-6215	128	15	5	5	NUM
ejpam-6215	128	16	+	+	CCONJ
ejpam-6215	128	17	y6x	y6x	PROPN
ejpam-6215	128	18	6	6	NUM
ejpam-6215	128	19	+	+	CCONJ
ejpam-6215	128	20	y7x	y7x	NOUN
ejpam-6215	128	21	7	7	NUM
ejpam-6215	128	22	+	+	CCONJ
ejpam-6215	128	23	y8x	y8x	NUM
ejpam-6215	128	24	8	8	NUM
ejpam-6215	128	25	+	+	NUM
ejpam-6215	128	26	y9x	y9x	NOUN
ejpam-6215	128	27	9	9	NUM
ejpam-6215	128	28	+	+	CCONJ
ejpam-6215	128	29	.	.	PUNCT
ejpam-6215	128	30	.	.	PUNCT
ejpam-6215	128	31	.	.	PUNCT
ejpam-6215	129	1	y(x	y(x	NOUN
ejpam-6215	129	2	)	)	PUNCT
ejpam-6215	130	1	=	=	PUNCT
ejpam-6215	130	2	x+	x+	PUNCT
ejpam-6215	131	1	x3	x3	VERB
ejpam-6215	131	2	6	6	NUM
ejpam-6215	132	1	+	+	CCONJ
ejpam-6215	132	2	x4	x4	PROPN
ejpam-6215	132	3	2	2	NUM
ejpam-6215	132	4	+	+	CCONJ
ejpam-6215	132	5	x6	x6	PROPN
ejpam-6215	132	6	15	15	NUM
ejpam-6215	132	7	+	+	CCONJ
ejpam-6215	132	8	x7	x7	NOUN
ejpam-6215	132	9	7	7	NUM
ejpam-6215	132	10	+	+	NUM
ejpam-6215	132	11	x8	x8	NOUN
ejpam-6215	132	12	336	336	NUM
ejpam-6215	132	13	+	+	CCONJ
ejpam-6215	132	14	13x9	13x9	NUM
ejpam-6215	132	15	2160	2160	NUM
ejpam-6215	132	16	+	+	CCONJ
ejpam-6215	132	17	x10	x10	NUM
ejpam-6215	132	18	28	28	NUM
ejpam-6215	132	19	+	+	CCONJ
ejpam-6215	132	20	.	.	PUNCT
ejpam-6215	132	21	.	.	PUNCT
ejpam-6215	132	22	.	.	PUNCT
ejpam-6215	133	1	s.	s.	PROPN
ejpam-6215	133	2	mohammed	mohammed	PROPN
ejpam-6215	133	3	,	,	PUNCT
ejpam-6215	133	4	s.	s.	PROPN
ejpam-6215	133	5	abid	abid	PROPN
ejpam-6215	133	6	,	,	PUNCT
ejpam-6215	133	7	r.	r.	PROPN
ejpam-6215	133	8	abid	abid	PROPN
ejpam-6215	133	9	/	/	SYM
ejpam-6215	133	10	eur	eur	PROPN
ejpam-6215	133	11	.	.	PUNCT
ejpam-6215	134	1	j.	j.	PROPN
ejpam-6215	134	2	pure	pure	PROPN
ejpam-6215	134	3	appl	appl	PROPN
ejpam-6215	134	4	.	.	PROPN
ejpam-6215	134	5	math	math	PROPN
ejpam-6215	134	6	,	,	PUNCT
ejpam-6215	134	7	18	18	NUM
ejpam-6215	134	8	(	(	PUNCT
ejpam-6215	134	9	3	3	NUM
ejpam-6215	134	10	)	)	PUNCT
ejpam-6215	134	11	(	(	PUNCT
ejpam-6215	134	12	2025	2025	NUM
ejpam-6215	134	13	)	)	PUNCT
ejpam-6215	134	14	,	,	PUNCT
ejpam-6215	134	15	6215	6215	NUM
ejpam-6215	134	16	6	6	NUM
ejpam-6215	134	17	of	of	ADP
ejpam-6215	134	18	38	38	NUM
ejpam-6215	134	19	the	the	DET
ejpam-6215	134	20	error	error	NOUN
ejpam-6215	134	21	remainder	remainder	NOUN
ejpam-6215	134	22	function	function	NOUN
ejpam-6215	134	23	is	be	AUX
ejpam-6215	134	24	evaluated	evaluate	VERB
ejpam-6215	134	25	:	:	PUNCT
ejpam-6215	134	26	ern	ern	PROPN
ejpam-6215	134	27	=	=	PUNCT
ejpam-6215	134	28	y′′n(x)−	y′′n(x)−	PROPN
ejpam-6215	134	29	6y2n(x)−	6y2n(x)−	PROPN
ejpam-6215	134	30	x.	x.	NOUN
ejpam-6215	134	31	and	and	CCONJ
ejpam-6215	134	32	the	the	DET
ejpam-6215	134	33	mern	mern	NOUN
ejpam-6215	134	34	is	be	AUX
ejpam-6215	134	35	:	:	PUNCT
ejpam-6215	134	36	mern	mern	ADJ
ejpam-6215	134	37	=	=	SYM
ejpam-6215	134	38	max	max	PROPN
ejpam-6215	134	39	0.01≤x≤0.1	0.01≤x≤0.1	NUM
ejpam-6215	135	1	|ern(x)|	|ern(x)|	NOUN
ejpam-6215	135	2	.	.	PUNCT
ejpam-6215	136	1	in	in	ADP
ejpam-6215	136	2	table	table	NOUN
ejpam-6215	136	3	1	1	NUM
ejpam-6215	136	4	and	and	CCONJ
ejpam-6215	136	5	figure	figure	VERB
ejpam-6215	136	6	1	1	NUM
ejpam-6215	136	7	illustrate	illustrate	VERB
ejpam-6215	136	8	the	the	DET
ejpam-6215	136	9	convergence	convergence	NOUN
ejpam-6215	136	10	of	of	ADP
ejpam-6215	136	11	the	the	DET
ejpam-6215	136	12	solution	solution	NOUN
ejpam-6215	136	13	using	use	VERB
ejpam-6215	136	14	mern	mern	NOUN
ejpam-6215	136	15	versus	versus	ADP
ejpam-6215	136	16	n	n	CCONJ
ejpam-6215	136	17	,	,	PUNCT
ejpam-6215	136	18	demonstrating	demonstrate	VERB
ejpam-6215	136	19	the	the	DET
ejpam-6215	136	20	convergence	convergence	NOUN
ejpam-6215	136	21	behavior	behavior	NOUN
ejpam-6215	136	22	of	of	ADP
ejpam-6215	136	23	the	the	DET
ejpam-6215	136	24	differential	differential	ADJ
ejpam-6215	136	25	transform	transform	NOUN
ejpam-6215	136	26	method	method	NOUN
ejpam-6215	136	27	(	(	PUNCT
ejpam-6215	136	28	dtm	dtm	PROPN
ejpam-6215	136	29	)	)	PUNCT
ejpam-6215	136	30	in	in	ADP
ejpam-6215	136	31	solving	solve	VERB
ejpam-6215	136	32	the	the	DET
ejpam-6215	136	33	first	first	ADJ
ejpam-6215	136	34	painlevé	painlevé	NOUN
ejpam-6215	136	35	equation	equation	NOUN
ejpam-6215	136	36	.	.	PUNCT
ejpam-6215	137	1	the	the	DET
ejpam-6215	137	2	error	error	NOUN
ejpam-6215	137	3	decreases	decrease	VERB
ejpam-6215	137	4	exponentially	exponentially	ADV
ejpam-6215	137	5	as	as	ADP
ejpam-6215	137	6	n	n	PRON
ejpam-6215	137	7	increases	increase	NOUN
ejpam-6215	137	8	,	,	PUNCT
ejpam-6215	137	9	with	with	ADP
ejpam-6215	137	10	the	the	DET
ejpam-6215	137	11	most	most	ADV
ejpam-6215	137	12	significant	significant	ADJ
ejpam-6215	137	13	reduction	reduction	NOUN
ejpam-6215	137	14	occurring	occur	VERB
ejpam-6215	137	15	between	between	ADP
ejpam-6215	137	16	n	n	NOUN
ejpam-6215	137	17	=	=	SYM
ejpam-6215	137	18	1	1	NUM
ejpam-6215	137	19	and	and	CCONJ
ejpam-6215	137	20	n	n	CCONJ
ejpam-6215	137	21	=	=	NOUN
ejpam-6215	137	22	3	3	X
ejpam-6215	137	23	.	.	NOUN
ejpam-6215	137	24	beyond	beyond	ADP
ejpam-6215	137	25	n	n	NOUN
ejpam-6215	137	26	=	=	SYM
ejpam-6215	137	27	3	3	NUM
ejpam-6215	137	28	,	,	PUNCT
ejpam-6215	137	29	the	the	DET
ejpam-6215	137	30	error	error	NOUN
ejpam-6215	137	31	stabilizes	stabilize	VERB
ejpam-6215	137	32	around	around	ADP
ejpam-6215	137	33	10−17	10−17	NUM
ejpam-6215	137	34	,	,	PUNCT
ejpam-6215	137	35	indicating	indicate	VERB
ejpam-6215	137	36	that	that	SCONJ
ejpam-6215	137	37	further	further	ADJ
ejpam-6215	137	38	iterations	iteration	NOUN
ejpam-6215	137	39	do	do	AUX
ejpam-6215	137	40	not	not	PART
ejpam-6215	137	41	significantly	significantly	ADV
ejpam-6215	137	42	improve	improve	VERB
ejpam-6215	137	43	accuracy	accuracy	NOUN
ejpam-6215	137	44	due	due	ADP
ejpam-6215	137	45	to	to	ADP
ejpam-6215	137	46	machine	machine	NOUN
ejpam-6215	137	47	precision	precision	NOUN
ejpam-6215	137	48	limitations	limitation	NOUN
ejpam-6215	137	49	.	.	PUNCT
ejpam-6215	138	1	the	the	DET
ejpam-6215	138	2	stabilization	stabilization	NOUN
ejpam-6215	138	3	of	of	ADP
ejpam-6215	138	4	error	error	NOUN
ejpam-6215	138	5	values	value	NOUN
ejpam-6215	138	6	for	for	ADP
ejpam-6215	138	7	n	n	NOUN
ejpam-6215	138	8	=	=	SYM
ejpam-6215	138	9	4	4	NUM
ejpam-6215	138	10	and	and	CCONJ
ejpam-6215	138	11	n	n	CCONJ
ejpam-6215	138	12	=	=	SYM
ejpam-6215	138	13	5	5	NUM
ejpam-6215	138	14	implies	imply	VERB
ejpam-6215	138	15	that	that	SCONJ
ejpam-6215	138	16	additional	additional	ADJ
ejpam-6215	138	17	iterations	iteration	NOUN
ejpam-6215	138	18	beyond	beyond	ADP
ejpam-6215	138	19	this	this	DET
ejpam-6215	138	20	point	point	NOUN
ejpam-6215	138	21	may	may	AUX
ejpam-6215	138	22	be	be	AUX
ejpam-6215	138	23	computationally	computationally	ADV
ejpam-6215	138	24	unnecessary	unnecessary	ADJ
ejpam-6215	138	25	.	.	PUNCT
ejpam-6215	139	1	this	this	PRON
ejpam-6215	139	2	suggests	suggest	VERB
ejpam-6215	139	3	that	that	SCONJ
ejpam-6215	139	4	dtm	dtm	PROPN
ejpam-6215	139	5	achieves	achieve	VERB
ejpam-6215	139	6	high	high	ADJ
ejpam-6215	139	7	accuracy	accuracy	NOUN
ejpam-6215	139	8	with	with	ADP
ejpam-6215	139	9	a	a	DET
ejpam-6215	139	10	relatively	relatively	ADV
ejpam-6215	139	11	small	small	ADJ
ejpam-6215	139	12	number	number	NOUN
ejpam-6215	139	13	of	of	ADP
ejpam-6215	139	14	iterations	iteration	NOUN
ejpam-6215	139	15	,	,	PUNCT
ejpam-6215	139	16	making	make	VERB
ejpam-6215	139	17	it	it	PRON
ejpam-6215	139	18	an	an	DET
ejpam-6215	139	19	efficient	efficient	ADJ
ejpam-6215	139	20	method	method	NOUN
ejpam-6215	139	21	for	for	ADP
ejpam-6215	139	22	solving	solve	VERB
ejpam-6215	139	23	nonlinear	nonlinear	ADJ
ejpam-6215	139	24	differential	differential	ADJ
ejpam-6215	139	25	equations	equation	NOUN
ejpam-6215	139	26	.	.	PUNCT
ejpam-6215	140	1	table	table	NOUN
ejpam-6215	140	2	1	1	NUM
ejpam-6215	140	3	:	:	PUNCT
ejpam-6215	140	4	the	the	DET
ejpam-6215	140	5	maximum	maximum	ADJ
ejpam-6215	140	6	residual	residual	ADJ
ejpam-6215	140	7	error	error	NOUN
ejpam-6215	140	8	:	:	PUNCT
ejpam-6215	140	9	mern	mern	NOUN
ejpam-6215	140	10	by	by	ADP
ejpam-6215	140	11	the	the	DET
ejpam-6215	140	12	dtm	dtm	PROPN
ejpam-6215	140	13	where	where	SCONJ
ejpam-6215	140	14	n	n	NOUN
ejpam-6215	140	15	=	=	SYM
ejpam-6215	140	16	1	1	NUM
ejpam-6215	140	17	,	,	PUNCT
ejpam-6215	140	18	·	·	PUNCT
ejpam-6215	140	19	·	·	PUNCT
ejpam-6215	140	20	·	·	PUNCT
ejpam-6215	140	21	,	,	PUNCT
ejpam-6215	140	22	5	5	X
ejpam-6215	140	23	.	.	X
ejpam-6215	141	1	n	n	PRON
ejpam-6215	141	2	mern	mern	ADJ
ejpam-6215	141	3	1	1	NUM
ejpam-6215	141	4	3.790200×	3.790200×	NUM
ejpam-6215	141	5	10−7	10−7	NUM
ejpam-6215	141	6	2	2	NUM
ejpam-6215	141	7	1.116379×	1.116379×	NUM
ejpam-6215	141	8	10−10	10−10	NUM
ejpam-6215	141	9	3	3	NUM
ejpam-6215	141	10	1.040834×	1.040834×	NUM
ejpam-6215	141	11	10−16	10−16	NOUN
ejpam-6215	141	12	4	4	NUM
ejpam-6215	141	13	4.857226×	4.857226×	NUM
ejpam-6215	141	14	10−17	10−17	NUM
ejpam-6215	141	15	5	5	NUM
ejpam-6215	141	16	4.857226×	4.857226×	NUM
ejpam-6215	141	17	10−17	10−17	NUM
ejpam-6215	141	18	figure	figure	NOUN
ejpam-6215	141	19	1	1	NUM
ejpam-6215	141	20	:	:	PUNCT
ejpam-6215	141	21	the	the	DET
ejpam-6215	141	22	logarithmic	logarithmic	ADJ
ejpam-6215	141	23	plot	plot	NOUN
ejpam-6215	141	24	of	of	ADP
ejpam-6215	141	25	mer	mer	PROPN
ejpam-6215	141	26	n	n	PROPN
ejpam-6215	141	27	(	(	PUNCT
ejpam-6215	141	28	dtm	dtm	PROPN
ejpam-6215	141	29	,	,	PUNCT
ejpam-6215	141	30	first	first	ADV
ejpam-6215	141	31	painlevé	painlevé	NOUN
ejpam-6215	141	32	equation	equation	NOUN
ejpam-6215	141	33	)	)	PUNCT
ejpam-6215	141	34	.	.	PUNCT
ejpam-6215	141	35	.	.	PUNCT
ejpam-6215	142	1	s.	s.	PROPN
ejpam-6215	142	2	mohammed	mohammed	PROPN
ejpam-6215	142	3	,	,	PUNCT
ejpam-6215	142	4	s.	s.	PROPN
ejpam-6215	142	5	abid	abid	PROPN
ejpam-6215	142	6	,	,	PUNCT
ejpam-6215	142	7	r.	r.	PROPN
ejpam-6215	142	8	abid	abid	PROPN
ejpam-6215	142	9	/	/	SYM
ejpam-6215	142	10	eur	eur	PROPN
ejpam-6215	142	11	.	.	PUNCT
ejpam-6215	143	1	j.	j.	PROPN
ejpam-6215	143	2	pure	pure	PROPN
ejpam-6215	143	3	appl	appl	PROPN
ejpam-6215	143	4	.	.	PROPN
ejpam-6215	143	5	math	math	PROPN
ejpam-6215	143	6	,	,	PUNCT
ejpam-6215	143	7	18	18	NUM
ejpam-6215	143	8	(	(	PUNCT
ejpam-6215	143	9	3	3	NUM
ejpam-6215	143	10	)	)	PUNCT
ejpam-6215	143	11	(	(	PUNCT
ejpam-6215	143	12	2025	2025	NUM
ejpam-6215	143	13	)	)	PUNCT
ejpam-6215	143	14	,	,	PUNCT
ejpam-6215	143	15	6215	6215	NUM
ejpam-6215	143	16	7	7	NUM
ejpam-6215	143	17	of	of	ADP
ejpam-6215	143	18	38	38	NUM
ejpam-6215	143	19	2.1.2	2.1.2	NUM
ejpam-6215	143	20	.	.	PUNCT
ejpam-6215	144	1	the	the	DET
ejpam-6215	144	2	dtm	dtm	PROPN
ejpam-6215	144	3	for	for	ADP
ejpam-6215	144	4	solving	solve	VERB
ejpam-6215	144	5	the	the	DET
ejpam-6215	144	6	painlevé	painlevé	NOUN
ejpam-6215	144	7	ii	ii	NOUN
ejpam-6215	144	8	differential	differential	NOUN
ejpam-6215	144	9	equation	equation	NOUN
ejpam-6215	144	10	rewrite	rewrite	VERB
ejpam-6215	144	11	[	[	X
ejpam-6215	144	12	2	2	NUM
ejpam-6215	144	13	]	]	PUNCT
ejpam-6215	144	14	d2y	d2y	ADJ
ejpam-6215	144	15	dx2	dx2	PROPN
ejpam-6215	144	16	=	=	SYM
ejpam-6215	144	17	2y3	2y3	PROPN
ejpam-6215	145	1	+	+	CCONJ
ejpam-6215	145	2	xy	xy	PROPN
ejpam-6215	145	3	+	+	SYM
ejpam-6215	145	4	µ	µ	NOUN
ejpam-6215	145	5	,	,	PUNCT
ejpam-6215	145	6	y(0	y(0	PROPN
ejpam-6215	145	7	)	)	PUNCT
ejpam-6215	145	8	=	=	SYM
ejpam-6215	145	9	1	1	NUM
ejpam-6215	145	10	,	,	PUNCT
ejpam-6215	145	11	y′(0	y′(0	NOUN
ejpam-6215	145	12	)	)	PUNCT
ejpam-6215	145	13	=	=	SYM
ejpam-6215	146	1	0	0	X
ejpam-6215	146	2	.	.	PUNCT
ejpam-6215	146	3	assume	assume	VERB
ejpam-6215	146	4	y(x	y(x	NOUN
ejpam-6215	146	5	)	)	PUNCT
ejpam-6215	146	6	can	can	AUX
ejpam-6215	146	7	be	be	AUX
ejpam-6215	146	8	expressed	express	VERB
ejpam-6215	146	9	as	as	ADP
ejpam-6215	146	10	a	a	DET
ejpam-6215	146	11	power	power	NOUN
ejpam-6215	146	12	series	series	NOUN
ejpam-6215	146	13	:	:	PUNCT
ejpam-6215	146	14	y(x	y(x	X
ejpam-6215	146	15	)	)	PUNCT
ejpam-6215	147	1	=	=	PUNCT
ejpam-6215	148	1	∞∑	∞∑	NUM
ejpam-6215	148	2	k=0	k=0	PROPN
ejpam-6215	148	3	ykx	ykx	VERB
ejpam-6215	148	4	k.	k.	PROPN
ejpam-6215	148	5	from	from	ADP
ejpam-6215	148	6	the	the	DET
ejpam-6215	148	7	initial	initial	ADJ
ejpam-6215	148	8	conditions	condition	NOUN
ejpam-6215	148	9	:	:	PUNCT
ejpam-6215	148	10	y0	y0	PROPN
ejpam-6215	148	11	=	=	SYM
ejpam-6215	148	12	y(0	y(0	PROPN
ejpam-6215	148	13	)	)	PUNCT
ejpam-6215	148	14	=	=	SYM
ejpam-6215	148	15	1	1	NUM
ejpam-6215	148	16	,	,	PUNCT
ejpam-6215	148	17	y1	y1	NOUN
ejpam-6215	148	18	=	=	SYM
ejpam-6215	148	19	y′(0	y′(0	NOUN
ejpam-6215	148	20	)	)	PUNCT
ejpam-6215	148	21	=	=	SYM
ejpam-6215	149	1	0	0	X
ejpam-6215	149	2	.	.	PUNCT
ejpam-6215	149	3	apply	apply	VERB
ejpam-6215	149	4	the	the	DET
ejpam-6215	149	5	dtm	dtm	NOUN
ejpam-6215	149	6	to	to	ADP
ejpam-6215	149	7	the	the	DET
ejpam-6215	149	8	differential	differential	ADJ
ejpam-6215	149	9	equation	equation	NOUN
ejpam-6215	149	10	:	:	PUNCT
ejpam-6215	149	11	d2y	d2y	ADJ
ejpam-6215	149	12	dx2	dx2	PROPN
ejpam-6215	149	13	=	=	NOUN
ejpam-6215	149	14	∞∑	∞∑	PROPN
ejpam-6215	149	15	k=0	k=0	PROPN
ejpam-6215	149	16	(	(	PUNCT
ejpam-6215	149	17	k	k	PROPN
ejpam-6215	149	18	+	+	NOUN
ejpam-6215	149	19	2)(k	2)(k	NUM
ejpam-6215	149	20	+	+	CCONJ
ejpam-6215	149	21	1)yk+2x	1)yk+2x	NUM
ejpam-6215	149	22	k.	k.	NOUN
ejpam-6215	149	23	(	(	PUNCT
ejpam-6215	149	24	12	12	NUM
ejpam-6215	149	25	)	)	PUNCT
ejpam-6215	149	26	2y3	2y3	NUM
ejpam-6215	149	27	=	=	SYM
ejpam-6215	149	28	2	2	NUM
ejpam-6215	149	29	(	(	PUNCT
ejpam-6215	149	30	∞∑	∞∑	PRON
ejpam-6215	149	31	k=0	k=0	PROPN
ejpam-6215	149	32	ykx	ykx	PROPN
ejpam-6215	149	33	k	k	PROPN
ejpam-6215	149	34	)	)	PUNCT
ejpam-6215	149	35	3	3	NUM
ejpam-6215	149	36	=	=	SYM
ejpam-6215	149	37	2	2	NUM
ejpam-6215	150	1	∞∑	∞∑	PROPN
ejpam-6215	150	2	k=0	k=0	PROPN
ejpam-6215	150	3	(	(	PUNCT
ejpam-6215	150	4	k∑	k∑	NOUN
ejpam-6215	150	5	m=0	m=0	PROPN
ejpam-6215	150	6	m∑	m∑	CCONJ
ejpam-6215	150	7	n=0	n=0	PROPN
ejpam-6215	150	8	ynym−nyk−m	ynym−nyk−m	PROPN
ejpam-6215	150	9	)	)	PUNCT
ejpam-6215	151	1	xk	xk	PROPN
ejpam-6215	151	2	.	.	PROPN
ejpam-6215	151	3	(	(	PUNCT
ejpam-6215	151	4	13	13	NUM
ejpam-6215	151	5	)	)	PUNCT
ejpam-6215	151	6	xy	xy	NOUN
ejpam-6215	152	1	=	=	PUNCT
ejpam-6215	152	2	k∑	k∑	PROPN
ejpam-6215	153	1	k=1	k=1	X
ejpam-6215	153	2	δ(k	δ(k	ADP
ejpam-6215	153	3	−	−	PROPN
ejpam-6215	153	4	1)yk−1x	1)yk−1x	NUM
ejpam-6215	153	5	k.	k.	PROPN
ejpam-6215	153	6	(	(	PUNCT
ejpam-6215	153	7	14	14	NUM
ejpam-6215	153	8	)	)	PUNCT
ejpam-6215	153	9	µx0	µx0	NOUN
ejpam-6215	153	10	=	=	SYM
ejpam-6215	153	11	µ	µ	PROPN
ejpam-6215	153	12	∞∑	∞∑	DET
ejpam-6215	153	13	k=0	k=0	PROPN
ejpam-6215	153	14	δ(k	δ(k	ADP
ejpam-6215	153	15	−	−	PROPN
ejpam-6215	153	16	0)xk	0)xk	PROPN
ejpam-6215	153	17	.	.	PUNCT
ejpam-6215	154	1	(	(	PUNCT
ejpam-6215	154	2	15	15	NUM
ejpam-6215	154	3	)	)	PUNCT
ejpam-6215	154	4	substitute	substitute	NOUN
ejpam-6215	154	5	(	(	PUNCT
ejpam-6215	154	6	12	12	NUM
ejpam-6215	154	7	)	)	PUNCT
ejpam-6215	154	8	,	,	PUNCT
ejpam-6215	154	9	(	(	PUNCT
ejpam-6215	154	10	13	13	NUM
ejpam-6215	154	11	)	)	PUNCT
ejpam-6215	154	12	,	,	PUNCT
ejpam-6215	154	13	(	(	PUNCT
ejpam-6215	154	14	14	14	NUM
ejpam-6215	154	15	)	)	PUNCT
ejpam-6215	154	16	and	and	CCONJ
ejpam-6215	154	17	(	(	PUNCT
ejpam-6215	154	18	15	15	NUM
ejpam-6215	154	19	)	)	PUNCT
ejpam-6215	154	20	into	into	ADP
ejpam-6215	154	21	the	the	DET
ejpam-6215	154	22	equation	equation	NOUN
ejpam-6215	154	23	:	:	PUNCT
ejpam-6215	154	24	∞∑	∞∑	NUM
ejpam-6215	154	25	k=0	k=0	PROPN
ejpam-6215	154	26	(	(	PUNCT
ejpam-6215	154	27	k	k	PROPN
ejpam-6215	154	28	+	+	NOUN
ejpam-6215	154	29	2)(k	2)(k	NUM
ejpam-6215	154	30	+	+	CCONJ
ejpam-6215	154	31	1)yk+2x	1)yk+2x	NUM
ejpam-6215	154	32	k	k	NOUN
ejpam-6215	154	33	=	=	SYM
ejpam-6215	154	34	2	2	NUM
ejpam-6215	155	1	∞∑	∞∑	NUM
ejpam-6215	155	2	k=0	k=0	PROPN
ejpam-6215	155	3	(	(	PUNCT
ejpam-6215	155	4	k∑	k∑	NOUN
ejpam-6215	155	5	m=0	m=0	PROPN
ejpam-6215	155	6	m∑	m∑	CCONJ
ejpam-6215	155	7	n=0	n=0	PROPN
ejpam-6215	155	8	ynym−nyk−m	ynym−nyk−m	PROPN
ejpam-6215	155	9	)	)	PUNCT
ejpam-6215	155	10	xk	xk	PROPN
ejpam-6215	155	11	.	.	PUNCT
ejpam-6215	155	12	.	.	PUNCT
ejpam-6215	155	13	.	.	PUNCT
ejpam-6215	156	1	+	+	CCONJ
ejpam-6215	156	2	∞∑	∞∑	NUM
ejpam-6215	156	3	k=1	k=1	ADJ
ejpam-6215	156	4	δ(k	δ(k	NOUN
ejpam-6215	156	5	−	−	PROPN
ejpam-6215	156	6	1)yk−1x	1)yk−1x	NUM
ejpam-6215	157	1	k	k	NOUN
ejpam-6215	157	2	+	+	PUNCT
ejpam-6215	157	3	µ	µ	VERB
ejpam-6215	157	4	∞∑	∞∑	DET
ejpam-6215	157	5	k=0	k=0	PROPN
ejpam-6215	157	6	δ(k	δ(k	ADP
ejpam-6215	157	7	−	−	PROPN
ejpam-6215	157	8	0)xk	0)xk	PROPN
ejpam-6215	157	9	.	.	PROPN
ejpam-6215	158	1	for	for	ADP
ejpam-6215	158	2	each	each	DET
ejpam-6215	158	3	k	k	NOUN
ejpam-6215	158	4	we	we	PRON
ejpam-6215	158	5	get	get	VERB
ejpam-6215	158	6	:	:	PUNCT
ejpam-6215	158	7	yk+2	yk+2	NUM
ejpam-6215	158	8	=	=	SYM
ejpam-6215	158	9	1	1	NUM
ejpam-6215	158	10	(	(	PUNCT
ejpam-6215	158	11	k	k	PROPN
ejpam-6215	158	12	+	+	PROPN
ejpam-6215	158	13	2)(k	2)(k	NUM
ejpam-6215	158	14	+	+	CCONJ
ejpam-6215	158	15	1	1	X
ejpam-6215	158	16	)	)	PUNCT
ejpam-6215	158	17	(	(	PUNCT
ejpam-6215	158	18	2	2	NUM
ejpam-6215	158	19	k∑	k∑	NOUN
ejpam-6215	158	20	m=0	m=0	PROPN
ejpam-6215	158	21	m∑	m∑	CCONJ
ejpam-6215	158	22	n=0	n=0	PRON
ejpam-6215	158	23	ynym−nyk−m	ynym−nyk−m	NOUN
ejpam-6215	158	24	+	+	CCONJ
ejpam-6215	158	25	δ(k	δ(k	PROPN
ejpam-6215	158	26	−	−	PROPN
ejpam-6215	158	27	1)yk−1	1)yk−1	NUM
ejpam-6215	159	1	+	+	SYM
ejpam-6215	159	2	µδ(k	µδ(k	ADP
ejpam-6215	159	3	−	−	PROPN
ejpam-6215	159	4	0	0	NUM
ejpam-6215	159	5	)	)	PUNCT
ejpam-6215	159	6	)	)	PUNCT
ejpam-6215	159	7	.	.	PUNCT
ejpam-6215	160	1	(	(	PUNCT
ejpam-6215	160	2	16	16	NUM
ejpam-6215	160	3	)	)	PUNCT
ejpam-6215	160	4	k	k	NOUN
ejpam-6215	161	1	=	=	SYM
ejpam-6215	161	2	0	0	PUNCT
ejpam-6215	161	3	y2	y2	NOUN
ejpam-6215	161	4	=	=	NOUN
ejpam-6215	161	5	2	2	NUM
ejpam-6215	161	6	+	+	SYM
ejpam-6215	161	7	µ	µ	X
ejpam-6215	161	8	2	2	NUM
ejpam-6215	161	9	.	.	PUNCT
ejpam-6215	162	1	s.	s.	PROPN
ejpam-6215	162	2	mohammed	mohammed	PROPN
ejpam-6215	162	3	,	,	PUNCT
ejpam-6215	162	4	s.	s.	PROPN
ejpam-6215	162	5	abid	abid	PROPN
ejpam-6215	162	6	,	,	PUNCT
ejpam-6215	162	7	r.	r.	PROPN
ejpam-6215	162	8	abid	abid	PROPN
ejpam-6215	162	9	/	/	SYM
ejpam-6215	162	10	eur	eur	PROPN
ejpam-6215	162	11	.	.	PUNCT
ejpam-6215	163	1	j.	j.	PROPN
ejpam-6215	163	2	pure	pure	PROPN
ejpam-6215	163	3	appl	appl	PROPN
ejpam-6215	163	4	.	.	PROPN
ejpam-6215	163	5	math	math	PROPN
ejpam-6215	163	6	,	,	PUNCT
ejpam-6215	163	7	18	18	NUM
ejpam-6215	163	8	(	(	PUNCT
ejpam-6215	163	9	3	3	NUM
ejpam-6215	163	10	)	)	PUNCT
ejpam-6215	163	11	(	(	PUNCT
ejpam-6215	163	12	2025	2025	NUM
ejpam-6215	163	13	)	)	PUNCT
ejpam-6215	163	14	,	,	PUNCT
ejpam-6215	163	15	6215	6215	NUM
ejpam-6215	163	16	8	8	NUM
ejpam-6215	163	17	of	of	ADP
ejpam-6215	163	18	38	38	NUM
ejpam-6215	163	19	k	k	NOUN
ejpam-6215	163	20	=	=	SYM
ejpam-6215	163	21	1	1	NUM
ejpam-6215	163	22	y1	y1	NOUN
ejpam-6215	163	23	+	+	NOUN
ejpam-6215	163	24	2	2	NUM
ejpam-6215	163	25	=	=	SYM
ejpam-6215	163	26	1	1	NUM
ejpam-6215	163	27	(	(	PUNCT
ejpam-6215	163	28	1	1	NUM
ejpam-6215	163	29	+	+	NUM
ejpam-6215	163	30	2)(1	2)(1	NUM
ejpam-6215	163	31	+	+	CCONJ
ejpam-6215	163	32	1	1	NUM
ejpam-6215	163	33	)	)	PUNCT
ejpam-6215	163	34	(	(	PUNCT
ejpam-6215	163	35	2	2	NUM
ejpam-6215	163	36	1∑	1∑	PROPN
ejpam-6215	163	37	m=0	m=0	PROPN
ejpam-6215	163	38	m∑	m∑	CCONJ
ejpam-6215	163	39	n=0	n=0	PROPN
ejpam-6215	163	40	ynym−ny1−m	ynym−ny1−m	NUM
ejpam-6215	163	41	+	+	CCONJ
ejpam-6215	163	42	δ(1−	δ(1−	NOUN
ejpam-6215	163	43	1)y1−1	1)y1−1	ADJ
ejpam-6215	163	44	+	+	CCONJ
ejpam-6215	163	45	µδ(1−	µδ(1−	ADJ
ejpam-6215	163	46	0	0	NUM
ejpam-6215	163	47	)	)	PUNCT
ejpam-6215	163	48	)	)	PUNCT
ejpam-6215	163	49	.	.	PUNCT
ejpam-6215	164	1	y3	y3	NOUN
ejpam-6215	164	2	=	=	SYM
ejpam-6215	164	3	1	1	NUM
ejpam-6215	164	4	6	6	NUM
ejpam-6215	164	5	.	.	PUNCT
ejpam-6215	165	1	k	k	NOUN
ejpam-6215	165	2	=	=	SYM
ejpam-6215	165	3	2	2	NUM
ejpam-6215	165	4	y2	y2	NOUN
ejpam-6215	165	5	+	+	NOUN
ejpam-6215	165	6	2	2	NUM
ejpam-6215	165	7	=	=	SYM
ejpam-6215	165	8	1	1	NUM
ejpam-6215	165	9	(	(	PUNCT
ejpam-6215	165	10	2	2	NUM
ejpam-6215	165	11	+	+	NUM
ejpam-6215	165	12	2)(2	2)(2	NUM
ejpam-6215	165	13	+	+	CCONJ
ejpam-6215	165	14	1	1	NUM
ejpam-6215	165	15	)	)	PUNCT
ejpam-6215	165	16	(	(	PUNCT
ejpam-6215	165	17	2	2	NUM
ejpam-6215	165	18	2∑	2∑	NUM
ejpam-6215	165	19	m=0	m=0	PROPN
ejpam-6215	165	20	m∑	m∑	CCONJ
ejpam-6215	165	21	n=0	n=0	PRON
ejpam-6215	165	22	ynym−ny2−m	ynym−ny2−m	X
ejpam-6215	165	23	+	+	CCONJ
ejpam-6215	165	24	δ(2−	δ(2−	NOUN
ejpam-6215	165	25	1)y2−1	1)y2−1	NOUN
ejpam-6215	165	26	+	+	CCONJ
ejpam-6215	165	27	µδ(2−	µδ(2−	NOUN
ejpam-6215	165	28	0	0	NUM
ejpam-6215	165	29	)	)	PUNCT
ejpam-6215	165	30	)	)	PUNCT
ejpam-6215	165	31	.	.	PUNCT
ejpam-6215	166	1	y4	y4	PROPN
ejpam-6215	166	2	=	=	PUNCT
ejpam-6215	167	1	2	2	NUM
ejpam-6215	167	2	+	+	SYM
ejpam-6215	167	3	µ	µ	X
ejpam-6215	167	4	4	4	NUM
ejpam-6215	167	5	,	,	PUNCT
ejpam-6215	167	6	y5	y5	NOUN
ejpam-6215	167	7	=	=	SYM
ejpam-6215	167	8	1	1	NUM
ejpam-6215	167	9	20	20	NUM
ejpam-6215	167	10	,	,	PUNCT
ejpam-6215	167	11	y6	y6	NOUN
ejpam-6215	167	12	=	=	NOUN
ejpam-6215	167	13	1	1	NUM
ejpam-6215	167	14	20	20	NUM
ejpam-6215	167	15	(	(	PUNCT
ejpam-6215	167	16	2	2	NUM
ejpam-6215	167	17	+	+	CCONJ
ejpam-6215	167	18	µ+	µ+	X
ejpam-6215	167	19	(	(	PUNCT
ejpam-6215	167	20	2	2	NUM
ejpam-6215	167	21	+	+	NUM
ejpam-6215	167	22	µ)2	µ)2	NOUN
ejpam-6215	167	23	)	)	PUNCT
ejpam-6215	168	1	,	,	PUNCT
ejpam-6215	168	2	y7	y7	NOUN
ejpam-6215	168	3	=	=	NOUN
ejpam-6215	168	4	3	3	NUM
ejpam-6215	168	5	+	+	SYM
ejpam-6215	168	6	µ	µ	X
ejpam-6215	168	7	84	84	NUM
ejpam-6215	168	8	,	,	PUNCT
ejpam-6215	168	9	...	...	PUNCT
ejpam-6215	168	10	y(x	y(x	X
ejpam-6215	168	11	)	)	PUNCT
ejpam-6215	168	12	=	=	PUNCT
ejpam-6215	168	13	y0	y0	NOUN
ejpam-6215	168	14	+	+	CCONJ
ejpam-6215	168	15	y1x+	y1x+	PROPN
ejpam-6215	168	16	y2x	y2x	ADJ
ejpam-6215	168	17	2	2	NUM
ejpam-6215	168	18	+	+	NUM
ejpam-6215	168	19	y3x	y3x	VERB
ejpam-6215	168	20	3	3	NUM
ejpam-6215	168	21	+	+	NUM
ejpam-6215	168	22	y4x	y4x	NOUN
ejpam-6215	168	23	4	4	NUM
ejpam-6215	168	24	+	+	NUM
ejpam-6215	168	25	y5x	y5x	NOUN
ejpam-6215	168	26	5	5	NUM
ejpam-6215	168	27	+	+	CCONJ
ejpam-6215	168	28	y6x	y6x	PROPN
ejpam-6215	168	29	6	6	NUM
ejpam-6215	168	30	+	+	CCONJ
ejpam-6215	168	31	y7x	y7x	NOUN
ejpam-6215	168	32	7	7	NUM
ejpam-6215	168	33	+	+	CCONJ
ejpam-6215	168	34	·	·	PUNCT
ejpam-6215	168	35	·	·	PUNCT
ejpam-6215	168	36	·	·	PUNCT
ejpam-6215	168	37	y(x	y(x	NOUN
ejpam-6215	168	38	)	)	PUNCT
ejpam-6215	168	39	=	=	PUNCT
ejpam-6215	168	40	1	1	NUM
ejpam-6215	168	41	+	+	NUM
ejpam-6215	168	42	2	2	NUM
ejpam-6215	168	43	+	+	SYM
ejpam-6215	168	44	µ	µ	DET
ejpam-6215	168	45	2	2	NUM
ejpam-6215	168	46	x2	x2	NOUN
ejpam-6215	168	47	+	+	CCONJ
ejpam-6215	168	48	1	1	NUM
ejpam-6215	168	49	6	6	NUM
ejpam-6215	168	50	x3	x3	ADJ
ejpam-6215	168	51	+	+	CCONJ
ejpam-6215	168	52	2	2	NUM
ejpam-6215	168	53	+	+	SYM
ejpam-6215	168	54	µ	µ	X
ejpam-6215	168	55	4	4	NUM
ejpam-6215	168	56	x4	x4	NOUN
ejpam-6215	168	57	+	+	CCONJ
ejpam-6215	168	58	1	1	NUM
ejpam-6215	168	59	20	20	NUM
ejpam-6215	168	60	x5	x5	NOUN
ejpam-6215	168	61	+	+	CCONJ
ejpam-6215	168	62	1	1	NUM
ejpam-6215	168	63	20	20	NUM
ejpam-6215	168	64	(	(	PUNCT
ejpam-6215	168	65	2	2	NUM
ejpam-6215	168	66	+	+	CCONJ
ejpam-6215	168	67	µ+	µ+	X
ejpam-6215	168	68	(	(	PUNCT
ejpam-6215	168	69	2	2	NUM
ejpam-6215	168	70	+	+	CCONJ
ejpam-6215	168	71	µ)2)x6	µ)2)x6	ADV
ejpam-6215	168	72	+	+	CCONJ
ejpam-6215	168	73	3	3	NUM
ejpam-6215	168	74	+	+	SYM
ejpam-6215	168	75	µ	µ	NUM
ejpam-6215	168	76	84	84	NUM
ejpam-6215	168	77	x7	x7	NOUN
ejpam-6215	168	78	+	+	X
ejpam-6215	168	79	·	·	PUNCT
ejpam-6215	168	80	·	·	PUNCT
ejpam-6215	168	81	·	·	PUNCT
ejpam-6215	168	82	the	the	DET
ejpam-6215	168	83	error	error	NOUN
ejpam-6215	168	84	remainder	remainder	NOUN
ejpam-6215	168	85	function	function	NOUN
ejpam-6215	168	86	is	be	AUX
ejpam-6215	168	87	evaluated	evaluate	VERB
ejpam-6215	168	88	:	:	PUNCT
ejpam-6215	168	89	ern	ern	PROPN
ejpam-6215	168	90	=	=	PUNCT
ejpam-6215	168	91	y′′n(x)−	y′′n(x)−	PROPN
ejpam-6215	169	1	2y3n(x)−	2y3n(x)−	PROPN
ejpam-6215	169	2	xyn(x)−	xyn(x)−	PROPN
ejpam-6215	169	3	µ.	µ.	NOUN
ejpam-6215	169	4	and	and	CCONJ
ejpam-6215	169	5	the	the	DET
ejpam-6215	169	6	mern	mern	NOUN
ejpam-6215	169	7	is	be	AUX
ejpam-6215	169	8	:	:	PUNCT
ejpam-6215	169	9	mern	mern	ADJ
ejpam-6215	169	10	=	=	SYM
ejpam-6215	169	11	max	max	PROPN
ejpam-6215	169	12	0.01≤x≤0.1	0.01≤x≤0.1	NUM
ejpam-6215	170	1	|ern(x)|	|ern(x)|	NOUN
ejpam-6215	170	2	.	.	PUNCT
ejpam-6215	171	1	in	in	ADP
ejpam-6215	171	2	table	table	NOUN
ejpam-6215	171	3	2	2	NUM
ejpam-6215	171	4	and	and	CCONJ
ejpam-6215	171	5	figure	figure	VERB
ejpam-6215	171	6	2	2	NUM
ejpam-6215	171	7	show	show	VERB
ejpam-6215	171	8	the	the	DET
ejpam-6215	171	9	convergence	convergence	NOUN
ejpam-6215	171	10	of	of	ADP
ejpam-6215	171	11	the	the	DET
ejpam-6215	171	12	solution	solution	NOUN
ejpam-6215	171	13	using	use	VERB
ejpam-6215	171	14	mern	mern	NOUN
ejpam-6215	171	15	versus	versus	ADP
ejpam-6215	171	16	n	n	CCONJ
ejpam-6215	171	17	demonstrates	demonstrate	VERB
ejpam-6215	171	18	the	the	DET
ejpam-6215	171	19	convergence	convergence	NOUN
ejpam-6215	171	20	behavior	behavior	NOUN
ejpam-6215	171	21	of	of	ADP
ejpam-6215	171	22	the	the	DET
ejpam-6215	171	23	differential	differential	ADJ
ejpam-6215	171	24	transform	transform	NOUN
ejpam-6215	171	25	method	method	NOUN
ejpam-6215	171	26	(	(	PUNCT
ejpam-6215	171	27	dtm	dtm	PROPN
ejpam-6215	171	28	)	)	PUNCT
ejpam-6215	171	29	in	in	ADP
ejpam-6215	171	30	solving	solve	VERB
ejpam-6215	171	31	the	the	DET
ejpam-6215	171	32	second	second	ADJ
ejpam-6215	171	33	painlevé	painlevé	NOUN
ejpam-6215	171	34	equation	equation	NOUN
ejpam-6215	171	35	.	.	PUNCT
ejpam-6215	172	1	the	the	DET
ejpam-6215	172	2	error	error	NOUN
ejpam-6215	172	3	decreases	decrease	VERB
ejpam-6215	172	4	significantly	significantly	ADV
ejpam-6215	172	5	from	from	ADP
ejpam-6215	172	6	n	n	NOUN
ejpam-6215	172	7	=	=	SYM
ejpam-6215	172	8	1	1	NUM
ejpam-6215	172	9	to	to	ADP
ejpam-6215	172	10	n	n	NOUN
ejpam-6215	172	11	=	=	SYM
ejpam-6215	172	12	2	2	NUM
ejpam-6215	172	13	,	,	PUNCT
ejpam-6215	172	14	showing	show	VERB
ejpam-6215	172	15	a	a	DET
ejpam-6215	172	16	rapid	rapid	ADJ
ejpam-6215	172	17	initial	initial	ADJ
ejpam-6215	172	18	improvement	improvement	NOUN
ejpam-6215	172	19	in	in	ADP
ejpam-6215	172	20	accuracy	accuracy	NOUN
ejpam-6215	172	21	.	.	PUNCT
ejpam-6215	173	1	however	however	ADV
ejpam-6215	173	2	,	,	PUNCT
ejpam-6215	173	3	from	from	ADP
ejpam-6215	173	4	n	n	NOUN
ejpam-6215	173	5	=	=	SYM
ejpam-6215	173	6	3	3	NUM
ejpam-6215	173	7	onward	onward	ADV
ejpam-6215	173	8	,	,	PUNCT
ejpam-6215	173	9	the	the	DET
ejpam-6215	173	10	reduction	reduction	NOUN
ejpam-6215	173	11	in	in	ADP
ejpam-6215	173	12	error	error	NOUN
ejpam-6215	173	13	becomes	become	VERB
ejpam-6215	173	14	much	much	ADV
ejpam-6215	173	15	smaller	small	ADJ
ejpam-6215	173	16	,	,	PUNCT
ejpam-6215	173	17	indicating	indicate	VERB
ejpam-6215	173	18	a	a	DET
ejpam-6215	173	19	slower	slow	ADJ
ejpam-6215	173	20	rate	rate	NOUN
ejpam-6215	173	21	of	of	ADP
ejpam-6215	173	22	convergence	convergence	NOUN
ejpam-6215	173	23	.	.	PUNCT
ejpam-6215	174	1	the	the	DET
ejpam-6215	174	2	stabilization	stabilization	NOUN
ejpam-6215	174	3	of	of	ADP
ejpam-6215	174	4	mern	mern	NOUN
ejpam-6215	174	5	at	at	ADP
ejpam-6215	174	6	approximately	approximately	ADV
ejpam-6215	174	7	0.001537	0.001537	NUM
ejpam-6215	174	8	for	for	ADP
ejpam-6215	174	9	n	n	NOUN
ejpam-6215	174	10	=	=	SYM
ejpam-6215	174	11	4	4	NUM
ejpam-6215	174	12	and	and	CCONJ
ejpam-6215	174	13	n	n	CCONJ
ejpam-6215	174	14	=	=	SYM
ejpam-6215	174	15	5	5	NUM
ejpam-6215	174	16	suggests	suggest	VERB
ejpam-6215	174	17	that	that	SCONJ
ejpam-6215	174	18	further	further	ADJ
ejpam-6215	174	19	iterations	iteration	NOUN
ejpam-6215	174	20	do	do	AUX
ejpam-6215	174	21	not	not	PART
ejpam-6215	174	22	lead	lead	VERB
ejpam-6215	174	23	to	to	ADP
ejpam-6215	174	24	a	a	DET
ejpam-6215	174	25	significant	significant	ADJ
ejpam-6215	174	26	decrease	decrease	NOUN
ejpam-6215	174	27	in	in	ADP
ejpam-6215	174	28	error	error	NOUN
ejpam-6215	174	29	,	,	PUNCT
ejpam-6215	174	30	likely	likely	ADJ
ejpam-6215	174	31	due	due	ADP
ejpam-6215	174	32	to	to	ADP
ejpam-6215	174	33	numerical	numerical	ADJ
ejpam-6215	174	34	limitations	limitation	NOUN
ejpam-6215	174	35	or	or	CCONJ
ejpam-6215	174	36	the	the	DET
ejpam-6215	174	37	inherent	inherent	ADJ
ejpam-6215	174	38	accuracy	accuracy	NOUN
ejpam-6215	174	39	of	of	ADP
ejpam-6215	174	40	the	the	DET
ejpam-6215	174	41	method	method	NOUN
ejpam-6215	174	42	.	.	PUNCT
ejpam-6215	175	1	overall	overall	ADV
ejpam-6215	175	2	,	,	PUNCT
ejpam-6215	175	3	the	the	DET
ejpam-6215	175	4	dtm	dtm	PROPN
ejpam-6215	175	5	achieves	achieve	VERB
ejpam-6215	175	6	rapid	rapid	ADJ
ejpam-6215	175	7	initial	initial	ADJ
ejpam-6215	175	8	convergence	convergence	NOUN
ejpam-6215	175	9	but	but	CCONJ
ejpam-6215	175	10	reaches	reach	VERB
ejpam-6215	175	11	a	a	DET
ejpam-6215	175	12	saturation	saturation	NOUN
ejpam-6215	175	13	point	point	NOUN
ejpam-6215	175	14	where	where	SCONJ
ejpam-6215	175	15	further	further	ADJ
ejpam-6215	175	16	improvements	improvement	NOUN
ejpam-6215	175	17	are	be	AUX
ejpam-6215	175	18	marginal	marginal	ADJ
ejpam-6215	175	19	.	.	PUNCT
ejpam-6215	176	1	s.	s.	PROPN
ejpam-6215	176	2	mohammed	mohammed	PROPN
ejpam-6215	176	3	,	,	PUNCT
ejpam-6215	176	4	s.	s.	PROPN
ejpam-6215	176	5	abid	abid	PROPN
ejpam-6215	176	6	,	,	PUNCT
ejpam-6215	176	7	r.	r.	PROPN
ejpam-6215	176	8	abid	abid	PROPN
ejpam-6215	176	9	/	/	SYM
ejpam-6215	176	10	eur	eur	PROPN
ejpam-6215	176	11	.	.	PUNCT
ejpam-6215	177	1	j.	j.	PROPN
ejpam-6215	177	2	pure	pure	PROPN
ejpam-6215	177	3	appl	appl	PROPN
ejpam-6215	177	4	.	.	PROPN
ejpam-6215	177	5	math	math	PROPN
ejpam-6215	177	6	,	,	PUNCT
ejpam-6215	177	7	18	18	NUM
ejpam-6215	177	8	(	(	PUNCT
ejpam-6215	177	9	3	3	NUM
ejpam-6215	177	10	)	)	PUNCT
ejpam-6215	177	11	(	(	PUNCT
ejpam-6215	177	12	2025	2025	NUM
ejpam-6215	177	13	)	)	PUNCT
ejpam-6215	177	14	,	,	PUNCT
ejpam-6215	177	15	6215	6215	NUM
ejpam-6215	177	16	9	9	NUM
ejpam-6215	177	17	of	of	ADP
ejpam-6215	177	18	38	38	NUM
ejpam-6215	177	19	table	table	NOUN
ejpam-6215	177	20	2	2	NUM
ejpam-6215	177	21	:	:	PUNCT
ejpam-6215	177	22	the	the	DET
ejpam-6215	177	23	maximum	maximum	ADJ
ejpam-6215	177	24	residual	residual	ADJ
ejpam-6215	177	25	error	error	NOUN
ejpam-6215	177	26	:	:	PUNCT
ejpam-6215	177	27	mern	mern	NOUN
ejpam-6215	177	28	by	by	ADP
ejpam-6215	177	29	the	the	DET
ejpam-6215	177	30	dtm	dtm	PROPN
ejpam-6215	177	31	where	where	SCONJ
ejpam-6215	177	32	n	n	NOUN
ejpam-6215	177	33	=	=	SYM
ejpam-6215	177	34	1	1	NUM
ejpam-6215	177	35	,	,	PUNCT
ejpam-6215	177	36	·	·	PUNCT
ejpam-6215	177	37	·	·	PUNCT
ejpam-6215	177	38	·	·	PUNCT
ejpam-6215	177	39	,	,	PUNCT
ejpam-6215	177	40	5	5	X
ejpam-6215	177	41	.	.	X
ejpam-6215	178	1	n	n	PRON
ejpam-6215	178	2	mern	mern	ADJ
ejpam-6215	178	3	1	1	NUM
ejpam-6215	178	4	0.09390383	0.09390383	NUM
ejpam-6215	178	5	2	2	NUM
ejpam-6215	178	6	0.00337824	0.00337824	NUM
ejpam-6215	178	7	3	3	NUM
ejpam-6215	178	8	0.00156204	0.00156204	NUM
ejpam-6215	178	9	4	4	NUM
ejpam-6215	178	10	0.00153786	0.00153786	NUM
ejpam-6215	178	11	5	5	NUM
ejpam-6215	178	12	0.00153758	0.00153758	NUM
ejpam-6215	178	13	figure	figure	NOUN
ejpam-6215	178	14	2	2	NUM
ejpam-6215	178	15	:	:	PUNCT
ejpam-6215	178	16	the	the	DET
ejpam-6215	178	17	logarithmic	logarithmic	ADJ
ejpam-6215	178	18	plot	plot	NOUN
ejpam-6215	178	19	of	of	ADP
ejpam-6215	178	20	mern	mern	NOUN
ejpam-6215	178	21	(	(	PUNCT
ejpam-6215	178	22	dtm	dtm	PROPN
ejpam-6215	178	23	,	,	PUNCT
ejpam-6215	178	24	second	second	ADJ
ejpam-6215	178	25	painlevé	painlevé	NOUN
ejpam-6215	178	26	equation	equation	NOUN
ejpam-6215	178	27	)	)	PUNCT
ejpam-6215	178	28	.	.	PUNCT
ejpam-6215	179	1	2.2	2.2	NUM
ejpam-6215	179	2	.	.	PUNCT
ejpam-6215	180	1	modified	modify	VERB
ejpam-6215	180	2	adomian	adomian	NOUN
ejpam-6215	180	3	decomposition	decomposition	NOUN
ejpam-6215	180	4	method	method	NOUN
ejpam-6215	180	5	(	(	PUNCT
ejpam-6215	180	6	madm	madm	PROPN
ejpam-6215	180	7	)	)	PUNCT
ejpam-6215	180	8	the	the	DET
ejpam-6215	180	9	adomian	adomian	NOUN
ejpam-6215	180	10	decomposition	decomposition	NOUN
ejpam-6215	180	11	method	method	NOUN
ejpam-6215	180	12	(	(	PUNCT
ejpam-6215	180	13	adm	adm	PROPN
ejpam-6215	180	14	)	)	PUNCT
ejpam-6215	180	15	,	,	PUNCT
ejpam-6215	180	16	introduced	introduce	VERB
ejpam-6215	180	17	by	by	ADP
ejpam-6215	180	18	george	george	PROPN
ejpam-6215	180	19	adomian	adomian	NOUN
ejpam-6215	180	20	in	in	ADP
ejpam-6215	180	21	the	the	DET
ejpam-6215	180	22	1980s	1980	NOUN
ejpam-6215	180	23	,	,	PUNCT
ejpam-6215	180	24	[	[	X
ejpam-6215	180	25	7	7	NUM
ejpam-6215	180	26	]	]	PUNCT
ejpam-6215	180	27	,	,	PUNCT
ejpam-6215	180	28	revolutionized	revolutionize	VERB
ejpam-6215	180	29	the	the	DET
ejpam-6215	180	30	solution	solution	NOUN
ejpam-6215	180	31	of	of	ADP
ejpam-6215	180	32	nonlinear	nonlinear	ADJ
ejpam-6215	180	33	differential	differential	ADJ
ejpam-6215	180	34	equations	equation	NOUN
ejpam-6215	180	35	by	by	ADP
ejpam-6215	180	36	providing	provide	VERB
ejpam-6215	180	37	an	an	DET
ejpam-6215	180	38	efficient	efficient	ADJ
ejpam-6215	180	39	decomposition	decomposition	NOUN
ejpam-6215	180	40	approach	approach	NOUN
ejpam-6215	180	41	without	without	ADP
ejpam-6215	180	42	linearization	linearization	NOUN
ejpam-6215	180	43	or	or	CCONJ
ejpam-6215	180	44	perturbation	perturbation	NOUN
ejpam-6215	180	45	[	[	X
ejpam-6215	180	46	8	8	NUM
ejpam-6215	180	47	]	]	PUNCT
ejpam-6215	180	48	.	.	PUNCT
ejpam-6215	181	1	over	over	ADP
ejpam-6215	181	2	the	the	DET
ejpam-6215	181	3	decades	decade	NOUN
ejpam-6215	181	4	,	,	PUNCT
ejpam-6215	181	5	adm	adm	PROPN
ejpam-6215	181	6	has	have	AUX
ejpam-6215	181	7	been	be	AUX
ejpam-6215	181	8	widely	widely	ADV
ejpam-6215	181	9	applied	apply	VERB
ejpam-6215	181	10	in	in	ADP
ejpam-6215	181	11	various	various	ADJ
ejpam-6215	181	12	fields	field	NOUN
ejpam-6215	181	13	of	of	ADP
ejpam-6215	181	14	applied	apply	VERB
ejpam-6215	181	15	mathematics	mathematic	NOUN
ejpam-6215	181	16	and	and	CCONJ
ejpam-6215	181	17	physics	physics	NOUN
ejpam-6215	181	18	due	due	ADP
ejpam-6215	181	19	to	to	ADP
ejpam-6215	181	20	its	its	PRON
ejpam-6215	181	21	ability	ability	NOUN
ejpam-6215	181	22	to	to	PART
ejpam-6215	181	23	handle	handle	VERB
ejpam-6215	181	24	complex	complex	ADJ
ejpam-6215	181	25	nonlinearities	nonlinearitie	NOUN
ejpam-6215	181	26	.	.	PUNCT
ejpam-6215	182	1	building	build	VERB
ejpam-6215	182	2	upon	upon	SCONJ
ejpam-6215	182	3	this	this	DET
ejpam-6215	182	4	foundation	foundation	NOUN
ejpam-6215	182	5	,	,	PUNCT
ejpam-6215	182	6	the	the	DET
ejpam-6215	182	7	modified	modify	VERB
ejpam-6215	182	8	adomian	adomian	NOUN
ejpam-6215	182	9	decomposition	decomposition	NOUN
ejpam-6215	182	10	method	method	NOUN
ejpam-6215	182	11	(	(	PUNCT
ejpam-6215	182	12	madm	madm	NOUN
ejpam-6215	182	13	)	)	PUNCT
ejpam-6215	182	14	enhances	enhance	VERB
ejpam-6215	182	15	adm	adm	NOUN
ejpam-6215	182	16	by	by	ADP
ejpam-6215	182	17	improving	improve	VERB
ejpam-6215	182	18	convergence	convergence	NOUN
ejpam-6215	182	19	and	and	CCONJ
ejpam-6215	182	20	accuracy	accuracy	NOUN
ejpam-6215	182	21	,	,	PUNCT
ejpam-6215	182	22	making	make	VERB
ejpam-6215	182	23	it	it	PRON
ejpam-6215	182	24	particularly	particularly	ADV
ejpam-6215	182	25	effective	effective	ADJ
ejpam-6215	182	26	for	for	ADP
ejpam-6215	182	27	solving	solve	VERB
ejpam-6215	182	28	highly	highly	ADV
ejpam-6215	182	29	nonlinear	nonlinear	ADJ
ejpam-6215	182	30	problems	problem	NOUN
ejpam-6215	182	31	.	.	PUNCT
ejpam-6215	183	1	in	in	ADP
ejpam-6215	183	2	this	this	DET
ejpam-6215	183	3	subsection	subsection	NOUN
ejpam-6215	183	4	,	,	PUNCT
ejpam-6215	183	5	we	we	PRON
ejpam-6215	183	6	focus	focus	VERB
ejpam-6215	183	7	on	on	ADP
ejpam-6215	183	8	the	the	DET
ejpam-6215	183	9	application	application	NOUN
ejpam-6215	183	10	of	of	ADP
ejpam-6215	183	11	madm	madm	NOUN
ejpam-6215	183	12	to	to	PART
ejpam-6215	183	13	nonlinear	nonlinear	VERB
ejpam-6215	183	14	painlevé	painlevé	NOUN
ejpam-6215	183	15	equations	equation	NOUN
ejpam-6215	183	16	i	i	PRON
ejpam-6215	183	17	and	and	CCONJ
ejpam-6215	183	18	ii	ii	PROPN
ejpam-6215	184	1	[	[	X
ejpam-6215	184	2	28–34	28–34	NUM
ejpam-6215	184	3	]	]	SYM
ejpam-6215	184	4	.	.	PUNCT
ejpam-6215	185	1	2.2.1	2.2.1	NUM
ejpam-6215	185	2	.	.	PUNCT
ejpam-6215	186	1	the	the	DET
ejpam-6215	186	2	madm	madm	NOUN
ejpam-6215	186	3	for	for	ADP
ejpam-6215	186	4	solving	solve	VERB
ejpam-6215	186	5	painlevé	painlevé	NOUN
ejpam-6215	186	6	i	i	PRON
ejpam-6215	186	7	equation	equation	NOUN
ejpam-6215	186	8	rewrite	rewrite	NOUN
ejpam-6215	186	9	(	(	PUNCT
ejpam-6215	186	10	1	1	NUM
ejpam-6215	186	11	)	)	PUNCT
ejpam-6215	186	12	y′′(x	y′′(x	NOUN
ejpam-6215	186	13	)	)	PUNCT
ejpam-6215	186	14	=	=	SYM
ejpam-6215	186	15	6y2(x	6y2(x	NUM
ejpam-6215	186	16	)	)	PUNCT
ejpam-6215	187	1	+	+	CCONJ
ejpam-6215	187	2	x	x	X
ejpam-6215	187	3	,	,	PUNCT
ejpam-6215	187	4	y(0	y(0	PROPN
ejpam-6215	187	5	)	)	PUNCT
ejpam-6215	187	6	=	=	SYM
ejpam-6215	187	7	0	0	NUM
ejpam-6215	187	8	,	,	PUNCT
ejpam-6215	187	9	y′(0	y′(0	NOUN
ejpam-6215	187	10	)	)	PUNCT
ejpam-6215	187	11	=	=	SYM
ejpam-6215	187	12	1	1	X
ejpam-6215	187	13	.	.	PUNCT
ejpam-6215	187	14	(	(	PUNCT
ejpam-6215	187	15	17	17	NUM
ejpam-6215	187	16	)	)	PUNCT
ejpam-6215	187	17	rewrite	rewrite	NOUN
ejpam-6215	187	18	in	in	ADP
ejpam-6215	187	19	the	the	DET
ejpam-6215	187	20	form	form	NOUN
ejpam-6215	187	21	ly	ly	ADP
ejpam-6215	187	22	=	=	PUNCT
ejpam-6215	187	23	g(x)−	g(x)−	PROPN
ejpam-6215	187	24	f	f	PROPN
ejpam-6215	187	25	(	(	PUNCT
ejpam-6215	187	26	y	y	PROPN
ejpam-6215	187	27	):	):	PUNCT
ejpam-6215	187	28	ly	ly	X
ejpam-6215	187	29	=	=	SYM
ejpam-6215	187	30	x+	x+	PROPN
ejpam-6215	187	31	6y2	6y2	NUM
ejpam-6215	187	32	.	.	PUNCT
ejpam-6215	188	1	the	the	DET
ejpam-6215	188	2	differential	differential	ADJ
ejpam-6215	188	3	operator	operator	NOUN
ejpam-6215	188	4	l	l	NOUN
ejpam-6215	188	5	is	be	AUX
ejpam-6215	188	6	defined	define	VERB
ejpam-6215	188	7	by	by	ADP
ejpam-6215	188	8	:	:	PUNCT
ejpam-6215	188	9	l	l	NOUN
ejpam-6215	188	10	=	=	SYM
ejpam-6215	188	11	e−	e−	PROPN
ejpam-6215	188	12	∫	∫	PROPN
ejpam-6215	188	13	p(x	p(x	PROPN
ejpam-6215	188	14	)	)	PUNCT
ejpam-6215	188	15	dx	dx	PROPN
ejpam-6215	189	1	d	d	X
ejpam-6215	189	2	dx	dx	PROPN
ejpam-6215	189	3	(	(	PUNCT
ejpam-6215	189	4	e	e	PROPN
ejpam-6215	189	5	∫	∫	PROPN
ejpam-6215	189	6	p(x	p(x	PROPN
ejpam-6215	189	7	)	)	PUNCT
ejpam-6215	189	8	dx	dx	PROPN
ejpam-6215	190	1	d	d	PROPN
ejpam-6215	190	2	dx	dx	PROPN
ejpam-6215	190	3	)	)	PUNCT
ejpam-6215	190	4	.	.	PUNCT
ejpam-6215	191	1	s.	s.	PROPN
ejpam-6215	191	2	mohammed	mohammed	PROPN
ejpam-6215	191	3	,	,	PUNCT
ejpam-6215	191	4	s.	s.	PROPN
ejpam-6215	191	5	abid	abid	PROPN
ejpam-6215	191	6	,	,	PUNCT
ejpam-6215	191	7	r.	r.	PROPN
ejpam-6215	191	8	abid	abid	PROPN
ejpam-6215	191	9	/	/	SYM
ejpam-6215	191	10	eur	eur	PROPN
ejpam-6215	191	11	.	.	PUNCT
ejpam-6215	192	1	j.	j.	PROPN
ejpam-6215	192	2	pure	pure	PROPN
ejpam-6215	192	3	appl	appl	PROPN
ejpam-6215	192	4	.	.	PROPN
ejpam-6215	192	5	math	math	PROPN
ejpam-6215	192	6	,	,	PUNCT
ejpam-6215	192	7	18	18	NUM
ejpam-6215	192	8	(	(	PUNCT
ejpam-6215	192	9	3	3	NUM
ejpam-6215	192	10	)	)	PUNCT
ejpam-6215	192	11	(	(	PUNCT
ejpam-6215	192	12	2025	2025	NUM
ejpam-6215	192	13	)	)	PUNCT
ejpam-6215	192	14	,	,	PUNCT
ejpam-6215	192	15	6215	6215	NUM
ejpam-6215	192	16	10	10	NUM
ejpam-6215	192	17	of	of	ADP
ejpam-6215	192	18	38	38	NUM
ejpam-6215	192	19	l	l	NOUN
ejpam-6215	192	20	=	=	SYM
ejpam-6215	192	21	d2	d2	PROPN
ejpam-6215	192	22	dx2	dx2	PROPN
ejpam-6215	192	23	.	.	PUNCT
ejpam-6215	193	1	applying	apply	VERB
ejpam-6215	193	2	the	the	DET
ejpam-6215	193	3	inverse	inverse	NOUN
ejpam-6215	193	4	operator	operator	NOUN
ejpam-6215	193	5	l−1	l−1	PROPN
ejpam-6215	193	6	,	,	PUNCT
ejpam-6215	193	7	we	we	PRON
ejpam-6215	193	8	get	get	VERB
ejpam-6215	193	9	:	:	PUNCT
ejpam-6215	193	10	y(x	y(x	X
ejpam-6215	193	11	)	)	PUNCT
ejpam-6215	193	12	=	=	SYM
ejpam-6215	194	1	φ(x	φ(x	NOUN
ejpam-6215	194	2	)	)	PUNCT
ejpam-6215	194	3	+	+	SYM
ejpam-6215	194	4	l−1(x	l−1(x	NOUN
ejpam-6215	194	5	)	)	PUNCT
ejpam-6215	194	6	+	+	CCONJ
ejpam-6215	194	7	l−1(6y2	l−1(6y2	PROPN
ejpam-6215	194	8	)	)	PUNCT
ejpam-6215	194	9	.	.	PUNCT
ejpam-6215	195	1	where	where	SCONJ
ejpam-6215	195	2	satisfies	satisfie	NOUN
ejpam-6215	195	3	lφ(x	lφ(x	X
ejpam-6215	195	4	)	)	PUNCT
ejpam-6215	195	5	=	=	SYM
ejpam-6215	195	6	0	0	NUM
ejpam-6215	195	7	from	from	ADP
ejpam-6215	195	8	initial	initial	ADJ
ejpam-6215	195	9	conditions	condition	NOUN
ejpam-6215	195	10	.	.	PUNCT
ejpam-6215	196	1	φ(x	φ(x	NOUN
ejpam-6215	196	2	)	)	PUNCT
ejpam-6215	196	3	=	=	SYM
ejpam-6215	196	4	y(0	y(0	PROPN
ejpam-6215	196	5	)	)	PUNCT
ejpam-6215	196	6	+	+	NUM
ejpam-6215	196	7	y′(0)x	y′(0)x	NOUN
ejpam-6215	196	8	=	=	SYM
ejpam-6215	196	9	x.	x.	PROPN
ejpam-6215	196	10	y(x	y(x	PROPN
ejpam-6215	196	11	)	)	PUNCT
ejpam-6215	196	12	=	=	SYM
ejpam-6215	196	13	x+	x+	X
ejpam-6215	196	14	l−1(x	l−1(x	NOUN
ejpam-6215	196	15	)	)	PUNCT
ejpam-6215	196	16	+	+	CCONJ
ejpam-6215	196	17	l−1(6y2	l−1(6y2	PROPN
ejpam-6215	196	18	)	)	PUNCT
ejpam-6215	196	19	.	.	PUNCT
ejpam-6215	197	1	recall	recall	VERB
ejpam-6215	197	2	that	that	SCONJ
ejpam-6215	197	3	the	the	DET
ejpam-6215	197	4	madm	madm	NOUN
ejpam-6215	197	5	introduces	introduce	VERB
ejpam-6215	197	6	the	the	DET
ejpam-6215	197	7	solution	solution	NOUN
ejpam-6215	197	8	y(x	y(x	NOUN
ejpam-6215	197	9	)	)	PUNCT
ejpam-6215	197	10	and	and	CCONJ
ejpam-6215	197	11	the	the	DET
ejpam-6215	197	12	nonlinear	nonlinear	ADJ
ejpam-6215	197	13	function	function	NOUN
ejpam-6215	197	14	f	f	PROPN
ejpam-6215	197	15	(	(	PUNCT
ejpam-6215	197	16	y	y	NOUN
ejpam-6215	197	17	)	)	PUNCT
ejpam-6215	197	18	by	by	ADP
ejpam-6215	197	19	infinite	infinite	ADJ
ejpam-6215	197	20	series	series	NOUN
ejpam-6215	197	21	:	:	PUNCT
ejpam-6215	197	22	y(x	y(x	X
ejpam-6215	197	23	)	)	PUNCT
ejpam-6215	197	24	=	=	PUNCT
ejpam-6215	198	1	∞∑	∞∑	PRON
ejpam-6215	198	2	n=0	n=0	NUM
ejpam-6215	198	3	yn(x	yn(x	NUM
ejpam-6215	198	4	)	)	PUNCT
ejpam-6215	198	5	.	.	PUNCT
ejpam-6215	199	1	f	f	PROPN
ejpam-6215	199	2	(	(	PUNCT
ejpam-6215	199	3	y	y	NOUN
ejpam-6215	199	4	)	)	PUNCT
ejpam-6215	199	5	=	=	VERB
ejpam-6215	199	6	y2	y2	PROPN
ejpam-6215	199	7	.	.	PUNCT
ejpam-6215	200	1	f	f	PROPN
ejpam-6215	200	2	(	(	PUNCT
ejpam-6215	200	3	y	y	NOUN
ejpam-6215	200	4	)	)	PUNCT
ejpam-6215	200	5	=	=	PUNCT
ejpam-6215	201	1	∞∑	∞∑	ADJ
ejpam-6215	201	2	n=0	n=0	PROPN
ejpam-6215	201	3	an	an	NOUN
ejpam-6215	201	4	.	.	PUNCT
ejpam-6215	202	1	∞∑	∞∑	NUM
ejpam-6215	202	2	n=0	n=0	NUM
ejpam-6215	202	3	yn(x	yn(x	X
ejpam-6215	202	4	)	)	PUNCT
ejpam-6215	202	5	=	=	SYM
ejpam-6215	202	6	x+	x+	ADJ
ejpam-6215	202	7	l−1(x	l−1(x	NOUN
ejpam-6215	202	8	)	)	PUNCT
ejpam-6215	202	9	+	+	NUM
ejpam-6215	203	1	6l−1	6l−1	NUM
ejpam-6215	203	2	∞∑	∞∑	NUM
ejpam-6215	203	3	n=0	n=0	PUNCT
ejpam-6215	203	4	an	an	NOUN
ejpam-6215	203	5	.	.	PUNCT
ejpam-6215	203	6	y0(x	y0(x	NUM
ejpam-6215	203	7	)	)	PUNCT
ejpam-6215	203	8	=	=	SYM
ejpam-6215	203	9	x+	x+	ADJ
ejpam-6215	203	10	l−1(x	l−1(x	NOUN
ejpam-6215	203	11	)	)	PUNCT
ejpam-6215	203	12	.	.	PUNCT
ejpam-6215	204	1	yn+1(x	yn+1(x	NOUN
ejpam-6215	204	2	)	)	PUNCT
ejpam-6215	205	1	=	=	SYM
ejpam-6215	206	1	6l−1[an	6l−1[an	NUM
ejpam-6215	206	2	]	]	X
ejpam-6215	206	3	.	.	PUNCT
ejpam-6215	207	1	y0(x	y0(x	X
ejpam-6215	207	2	)	)	PUNCT
ejpam-6215	207	3	=	=	SYM
ejpam-6215	208	1	x+	x+	NUM
ejpam-6215	208	2	∫	∫	PROPN
ejpam-6215	208	3	x	x	SYM
ejpam-6215	208	4	0	0	NUM
ejpam-6215	208	5	∫	∫	PROPN
ejpam-6215	208	6	x	x	SYM
ejpam-6215	208	7	0	0	PUNCT
ejpam-6215	208	8	x	x	SYM
ejpam-6215	208	9	dx	dx	PROPN
ejpam-6215	208	10	dx	dx	PROPN
ejpam-6215	208	11	.	.	PROPN
ejpam-6215	208	12	y0(x	y0(x	X
ejpam-6215	208	13	)	)	PUNCT
ejpam-6215	209	1	=	=	SYM
ejpam-6215	209	2	x+	x+	PUNCT
ejpam-6215	209	3	x3	x3	ADJ
ejpam-6215	209	4	6	6	NUM
ejpam-6215	209	5	.	.	PUNCT
ejpam-6215	209	6	y1(x	y1(x	NOUN
ejpam-6215	209	7	)	)	PUNCT
ejpam-6215	209	8	=	=	SYM
ejpam-6215	209	9	6l−1[a0	6l−1[a0	NOUN
ejpam-6215	209	10	]	]	PUNCT
ejpam-6215	209	11	.	.	PUNCT
ejpam-6215	210	1	where	where	SCONJ
ejpam-6215	210	2	a0	a0	PROPN
ejpam-6215	210	3	=	=	PUNCT
ejpam-6215	210	4	y20	y20	PROPN
ejpam-6215	210	5	.	.	PUNCT
ejpam-6215	211	1	a0	a0	PROPN
ejpam-6215	211	2	=	=	SYM
ejpam-6215	211	3	(	(	PUNCT
ejpam-6215	211	4	x+	x+	ADJ
ejpam-6215	211	5	x3	x3	ADJ
ejpam-6215	211	6	6	6	NUM
ejpam-6215	211	7	)	)	SYM
ejpam-6215	211	8	2	2	NUM
ejpam-6215	211	9	.	.	PUNCT
ejpam-6215	212	1	thus	thus	ADV
ejpam-6215	212	2	a0	a0	NOUN
ejpam-6215	212	3	=	=	SYM
ejpam-6215	212	4	x2	x2	PROPN
ejpam-6215	213	1	+	+	CCONJ
ejpam-6215	213	2	x4	x4	PROPN
ejpam-6215	213	3	3	3	NUM
ejpam-6215	213	4	+	+	NUM
ejpam-6215	213	5	x6	x6	PROPN
ejpam-6215	213	6	36	36	NUM
ejpam-6215	213	7	.	.	PUNCT
ejpam-6215	214	1	now	now	ADV
ejpam-6215	214	2	compute	compute	VERB
ejpam-6215	214	3	l−1[a0	l−1[a0	NOUN
ejpam-6215	214	4	]	]	PUNCT
ejpam-6215	214	5	.	.	PUNCT
ejpam-6215	215	1	y1(x	y1(x	NOUN
ejpam-6215	215	2	)	)	PUNCT
ejpam-6215	215	3	=	=	SYM
ejpam-6215	215	4	6l−1[a0	6l−1[a0	NOUN
ejpam-6215	215	5	]	]	X
ejpam-6215	215	6	=	=	SYM
ejpam-6215	215	7	6	6	NUM
ejpam-6215	215	8	∫	∫	NOUN
ejpam-6215	215	9	x	x	SYM
ejpam-6215	215	10	0	0	NUM
ejpam-6215	215	11	∫	∫	PROPN
ejpam-6215	215	12	x	x	X
ejpam-6215	215	13	0	0	PUNCT
ejpam-6215	215	14	(	(	PUNCT
ejpam-6215	215	15	x2	x2	PROPN
ejpam-6215	216	1	+	+	CCONJ
ejpam-6215	216	2	x4	x4	PROPN
ejpam-6215	216	3	3	3	NUM
ejpam-6215	216	4	+	+	NUM
ejpam-6215	216	5	x6	x6	PROPN
ejpam-6215	216	6	36	36	NUM
ejpam-6215	216	7	)	)	PUNCT
ejpam-6215	216	8	dx	dx	PROPN
ejpam-6215	216	9	dx	dx	PROPN
ejpam-6215	216	10	.	.	PUNCT
ejpam-6215	217	1	s.	s.	PROPN
ejpam-6215	217	2	mohammed	mohammed	PROPN
ejpam-6215	217	3	,	,	PUNCT
ejpam-6215	217	4	s.	s.	PROPN
ejpam-6215	217	5	abid	abid	PROPN
ejpam-6215	217	6	,	,	PUNCT
ejpam-6215	217	7	r.	r.	PROPN
ejpam-6215	217	8	abid	abid	PROPN
ejpam-6215	217	9	/	/	SYM
ejpam-6215	217	10	eur	eur	PROPN
ejpam-6215	217	11	.	.	PUNCT
ejpam-6215	218	1	j.	j.	PROPN
ejpam-6215	218	2	pure	pure	PROPN
ejpam-6215	218	3	appl	appl	PROPN
ejpam-6215	218	4	.	.	PROPN
ejpam-6215	218	5	math	math	PROPN
ejpam-6215	218	6	,	,	PUNCT
ejpam-6215	218	7	18	18	NUM
ejpam-6215	218	8	(	(	PUNCT
ejpam-6215	218	9	3	3	NUM
ejpam-6215	218	10	)	)	PUNCT
ejpam-6215	218	11	(	(	PUNCT
ejpam-6215	218	12	2025	2025	NUM
ejpam-6215	218	13	)	)	PUNCT
ejpam-6215	218	14	,	,	PUNCT
ejpam-6215	218	15	6215	6215	NUM
ejpam-6215	218	16	11	11	NUM
ejpam-6215	218	17	of	of	ADP
ejpam-6215	218	18	38	38	NUM
ejpam-6215	218	19	thus	thus	ADV
ejpam-6215	218	20	y1(x	y1(x	NUM
ejpam-6215	218	21	)	)	PUNCT
ejpam-6215	218	22	=	=	SYM
ejpam-6215	219	1	x4	x4	PROPN
ejpam-6215	219	2	2	2	NUM
ejpam-6215	219	3	+	+	CCONJ
ejpam-6215	219	4	x6	x6	PROPN
ejpam-6215	219	5	15	15	NUM
ejpam-6215	219	6	+	+	NUM
ejpam-6215	219	7	x8	x8	PROPN
ejpam-6215	219	8	336	336	NUM
ejpam-6215	219	9	.	.	PUNCT
ejpam-6215	220	1	a1	a1	NOUN
ejpam-6215	220	2	=	=	NOUN
ejpam-6215	220	3	2y0y1	2y0y1	NUM
ejpam-6215	220	4	.	.	PUNCT
ejpam-6215	221	1	a1	a1	NOUN
ejpam-6215	221	2	=	=	SYM
ejpam-6215	221	3	2	2	NUM
ejpam-6215	221	4	(	(	PUNCT
ejpam-6215	221	5	x+	x+	SYM
ejpam-6215	221	6	x3	x3	ADJ
ejpam-6215	221	7	6	6	NUM
ejpam-6215	221	8	)	)	PUNCT
ejpam-6215	221	9	(	(	PUNCT
ejpam-6215	221	10	x4	x4	ADV
ejpam-6215	221	11	2	2	NUM
ejpam-6215	221	12	+	+	NUM
ejpam-6215	221	13	x6	x6	PROPN
ejpam-6215	221	14	15	15	NUM
ejpam-6215	221	15	+	+	NUM
ejpam-6215	221	16	x8	x8	PROPN
ejpam-6215	221	17	336	336	NUM
ejpam-6215	221	18	)	)	PUNCT
ejpam-6215	221	19	.	.	PUNCT
ejpam-6215	222	1	a1	a1	NOUN
ejpam-6215	222	2	=	=	SYM
ejpam-6215	222	3	x5	x5	PROPN
ejpam-6215	222	4	+	+	NUM
ejpam-6215	222	5	3x7	3x7	NUM
ejpam-6215	222	6	10	10	NUM
ejpam-6215	222	7	+	+	CCONJ
ejpam-6215	222	8	71x9	71x9	NUM
ejpam-6215	222	9	2520	2520	NUM
ejpam-6215	222	10	+	+	CCONJ
ejpam-6215	222	11	x11	x11	PROPN
ejpam-6215	222	12	1008	1008	NUM
ejpam-6215	222	13	.	.	PUNCT
ejpam-6215	223	1	y2(x	y2(x	X
ejpam-6215	223	2	)	)	PUNCT
ejpam-6215	223	3	=	=	SYM
ejpam-6215	223	4	6l−1[a1	6l−1[a1	VERB
ejpam-6215	223	5	]	]	X
ejpam-6215	223	6	=	=	SYM
ejpam-6215	223	7	6	6	NUM
ejpam-6215	223	8	∫	∫	NOUN
ejpam-6215	223	9	x	x	SYM
ejpam-6215	223	10	0	0	NUM
ejpam-6215	223	11	∫	∫	PROPN
ejpam-6215	223	12	x	x	SYM
ejpam-6215	223	13	0	0	NUM
ejpam-6215	223	14	(	(	PUNCT
ejpam-6215	223	15	a1	a1	PROPN
ejpam-6215	223	16	)	)	PUNCT
ejpam-6215	223	17	dx	dx	PROPN
ejpam-6215	223	18	dx	dx	PROPN
ejpam-6215	223	19	.	.	PUNCT
ejpam-6215	224	1	y2(x	y2(x	X
ejpam-6215	224	2	)	)	PUNCT
ejpam-6215	224	3	=	=	SYM
ejpam-6215	224	4	6l−1[a1	6l−1[a1	VERB
ejpam-6215	224	5	]	]	X
ejpam-6215	224	6	=	=	SYM
ejpam-6215	224	7	6	6	NUM
ejpam-6215	224	8	∫	∫	NOUN
ejpam-6215	224	9	x	x	SYM
ejpam-6215	224	10	0	0	NUM
ejpam-6215	224	11	∫	∫	PROPN
ejpam-6215	224	12	x	x	SYM
ejpam-6215	224	13	0	0	PUNCT
ejpam-6215	224	14	(	(	PUNCT
ejpam-6215	224	15	x5	x5	NOUN
ejpam-6215	224	16	+	+	CCONJ
ejpam-6215	224	17	3x7	3x7	NUM
ejpam-6215	224	18	10	10	NUM
ejpam-6215	224	19	+	+	CCONJ
ejpam-6215	224	20	71x9	71x9	NUM
ejpam-6215	224	21	2520	2520	NUM
ejpam-6215	224	22	+	+	CCONJ
ejpam-6215	224	23	x11	x11	PROPN
ejpam-6215	224	24	1008	1008	NUM
ejpam-6215	224	25	)	)	PUNCT
ejpam-6215	225	1	dx	dx	PROPN
ejpam-6215	225	2	dx	dx	PROPN
ejpam-6215	225	3	.	.	PUNCT
ejpam-6215	226	1	y2(x	y2(x	X
ejpam-6215	226	2	)	)	PUNCT
ejpam-6215	226	3	=	=	PUNCT
ejpam-6215	227	1	x7	x7	NOUN
ejpam-6215	227	2	7	7	NUM
ejpam-6215	228	1	+	+	NUM
ejpam-6215	228	2	x9	x9	NOUN
ejpam-6215	228	3	40	40	NUM
ejpam-6215	228	4	+	+	CCONJ
ejpam-6215	228	5	71x11	71x11	NUM
ejpam-6215	228	6	46200	46200	NUM
ejpam-6215	228	7	+	+	CCONJ
ejpam-6215	228	8	x13	x13	PROPN
ejpam-6215	228	9	26208	26208	NUM
ejpam-6215	228	10	.	.	PUNCT
ejpam-6215	229	1	...	...	PUNCT
ejpam-6215	229	2	then	then	ADV
ejpam-6215	229	3	y(x	y(x	VERB
ejpam-6215	229	4	)	)	PUNCT
ejpam-6215	230	1	=	=	PUNCT
ejpam-6215	231	1	∞∑	∞∑	PROPN
ejpam-6215	231	2	n=0	n=0	NUM
ejpam-6215	231	3	yn(x	yn(x	NUM
ejpam-6215	231	4	)	)	PUNCT
ejpam-6215	231	5	.	.	PUNCT
ejpam-6215	232	1	y(x	y(x	NOUN
ejpam-6215	232	2	)	)	PUNCT
ejpam-6215	233	1	=	=	PUNCT
ejpam-6215	233	2	x+	x+	PUNCT
ejpam-6215	234	1	x3	x3	VERB
ejpam-6215	234	2	6	6	NUM
ejpam-6215	235	1	+	+	CCONJ
ejpam-6215	235	2	x4	x4	PROPN
ejpam-6215	235	3	2	2	NUM
ejpam-6215	235	4	+	+	CCONJ
ejpam-6215	235	5	x6	x6	PROPN
ejpam-6215	235	6	15	15	NUM
ejpam-6215	235	7	+	+	NUM
ejpam-6215	235	8	x8	x8	NOUN
ejpam-6215	235	9	336	336	NUM
ejpam-6215	235	10	+	+	CCONJ
ejpam-6215	235	11	x7	x7	NOUN
ejpam-6215	235	12	7	7	NUM
ejpam-6215	235	13	+	+	NUM
ejpam-6215	235	14	x9	x9	NOUN
ejpam-6215	235	15	40	40	NUM
ejpam-6215	235	16	+	+	CCONJ
ejpam-6215	235	17	71x11	71x11	NUM
ejpam-6215	235	18	46200	46200	NUM
ejpam-6215	235	19	+	+	CCONJ
ejpam-6215	235	20	x13	x13	NOUN
ejpam-6215	235	21	26208	26208	NUM
ejpam-6215	235	22	+	+	X
ejpam-6215	235	23	·	·	PUNCT
ejpam-6215	235	24	·	·	PUNCT
ejpam-6215	235	25	·	·	PUNCT
ejpam-6215	235	26	the	the	DET
ejpam-6215	235	27	remainder	remainder	NOUN
ejpam-6215	235	28	function	function	NOUN
ejpam-6215	235	29	of	of	ADP
ejpam-6215	235	30	error	error	NOUN
ejpam-6215	235	31	is	be	AUX
ejpam-6215	235	32	evaluated	evaluate	VERB
ejpam-6215	235	33	:	:	PUNCT
ejpam-6215	235	34	ern	ern	PROPN
ejpam-6215	235	35	=	=	PUNCT
ejpam-6215	235	36	y′′n(x)−	y′′n(x)−	PROPN
ejpam-6215	235	37	6y2n(x)−	6y2n(x)−	PROPN
ejpam-6215	235	38	x.	x.	NOUN
ejpam-6215	235	39	(	(	PUNCT
ejpam-6215	235	40	18	18	NUM
ejpam-6215	235	41	)	)	PUNCT
ejpam-6215	235	42	and	and	CCONJ
ejpam-6215	235	43	the	the	DET
ejpam-6215	235	44	mern	mern	NOUN
ejpam-6215	235	45	is	be	AUX
ejpam-6215	235	46	:	:	PUNCT
ejpam-6215	235	47	mern	mern	ADJ
ejpam-6215	235	48	=	=	SYM
ejpam-6215	235	49	max	max	PROPN
ejpam-6215	235	50	0.01≤x≤0.1	0.01≤x≤0.1	NUM
ejpam-6215	236	1	|ern(x)|	|ern(x)|	NOUN
ejpam-6215	236	2	.	.	PUNCT
ejpam-6215	237	1	(	(	PUNCT
ejpam-6215	237	2	19	19	NUM
ejpam-6215	237	3	)	)	PUNCT
ejpam-6215	237	4	in	in	ADP
ejpam-6215	237	5	table	table	NOUN
ejpam-6215	237	6	3	3	NUM
ejpam-6215	237	7	and	and	CCONJ
ejpam-6215	237	8	figure	figure	VERB
ejpam-6215	237	9	3	3	NUM
ejpam-6215	237	10	show	show	VERB
ejpam-6215	237	11	the	the	DET
ejpam-6215	237	12	convergence	convergence	NOUN
ejpam-6215	237	13	of	of	ADP
ejpam-6215	237	14	the	the	DET
ejpam-6215	237	15	solution	solution	NOUN
ejpam-6215	237	16	using	use	VERB
ejpam-6215	237	17	mern	mern	NOUN
ejpam-6215	237	18	versus	versus	ADP
ejpam-6215	237	19	n	n	CCONJ
ejpam-6215	237	20	demonstrates	demonstrate	VERB
ejpam-6215	237	21	the	the	DET
ejpam-6215	237	22	rapid	rapid	ADJ
ejpam-6215	237	23	convergence	convergence	NOUN
ejpam-6215	237	24	of	of	ADP
ejpam-6215	237	25	the	the	DET
ejpam-6215	237	26	modified	modify	VERB
ejpam-6215	237	27	adomian	adomian	NOUN
ejpam-6215	237	28	decomposition	decomposition	NOUN
ejpam-6215	237	29	method	method	NOUN
ejpam-6215	237	30	(	(	PUNCT
ejpam-6215	237	31	madm	madm	PROPN
ejpam-6215	237	32	)	)	PUNCT
ejpam-6215	237	33	for	for	ADP
ejpam-6215	237	34	solving	solve	VERB
ejpam-6215	237	35	the	the	DET
ejpam-6215	237	36	first	first	ADJ
ejpam-6215	237	37	painlevé	painlevé	NOUN
ejpam-6215	237	38	equation	equation	NOUN
ejpam-6215	237	39	,	,	PUNCT
ejpam-6215	237	40	the	the	DET
ejpam-6215	237	41	most	most	ADV
ejpam-6215	237	42	significant	significant	ADJ
ejpam-6215	237	43	error	error	NOUN
ejpam-6215	237	44	reduction	reduction	NOUN
ejpam-6215	237	45	occurs	occur	VERB
ejpam-6215	237	46	between	between	ADP
ejpam-6215	237	47	n	n	NOUN
ejpam-6215	237	48	=	=	SYM
ejpam-6215	237	49	1	1	NUM
ejpam-6215	237	50	and	and	CCONJ
ejpam-6215	237	51	n	n	CCONJ
ejpam-6215	237	52	=	=	SYM
ejpam-6215	237	53	3	3	NUM
ejpam-6215	237	54	,	,	PUNCT
ejpam-6215	237	55	after	after	ADP
ejpam-6215	237	56	which	which	PRON
ejpam-6215	237	57	the	the	DET
ejpam-6215	237	58	error	error	NOUN
ejpam-6215	237	59	drops	drop	VERB
ejpam-6215	237	60	to	to	ADP
ejpam-6215	237	61	near	near	ADJ
ejpam-6215	237	62	n	n	NOUN
ejpam-6215	237	63	=	=	SYM
ejpam-6215	237	64	5	5	NUM
ejpam-6215	237	65	.	.	PUNCT
ejpam-6215	238	1	the	the	DET
ejpam-6215	238	2	error	error	NOUN
ejpam-6215	238	3	decreases	decrease	VERB
ejpam-6215	238	4	exponentially	exponentially	ADV
ejpam-6215	238	5	with	with	ADP
ejpam-6215	238	6	each	each	DET
ejpam-6215	238	7	iteration	iteration	NOUN
ejpam-6215	238	8	,	,	PUNCT
ejpam-6215	238	9	indicating	indicate	VERB
ejpam-6215	238	10	that	that	SCONJ
ejpam-6215	238	11	madm	madm	NOUN
ejpam-6215	238	12	provides	provide	VERB
ejpam-6215	238	13	highly	highly	ADV
ejpam-6215	238	14	accurate	accurate	ADJ
ejpam-6215	238	15	results	result	NOUN
ejpam-6215	238	16	with	with	ADP
ejpam-6215	238	17	relatively	relatively	ADV
ejpam-6215	238	18	few	few	ADJ
ejpam-6215	238	19	terms	term	NOUN
ejpam-6215	238	20	.	.	PUNCT
ejpam-6215	239	1	the	the	DET
ejpam-6215	239	2	consistent	consistent	ADJ
ejpam-6215	239	3	decrease	decrease	NOUN
ejpam-6215	239	4	in	in	ADP
ejpam-6215	239	5	error	error	NOUN
ejpam-6215	239	6	on	on	ADP
ejpam-6215	239	7	the	the	DET
ejpam-6215	239	8	logarithmic	logarithmic	ADJ
ejpam-6215	239	9	scale	scale	NOUN
ejpam-6215	239	10	confirms	confirm	VERB
ejpam-6215	239	11	the	the	DET
ejpam-6215	239	12	efficiency	efficiency	NOUN
ejpam-6215	239	13	and	and	CCONJ
ejpam-6215	239	14	robustness	robustness	NOUN
ejpam-6215	239	15	of	of	ADP
ejpam-6215	239	16	madm	madm	NOUN
ejpam-6215	239	17	in	in	ADP
ejpam-6215	239	18	solving	solve	VERB
ejpam-6215	239	19	nonlinear	nonlinear	ADJ
ejpam-6215	239	20	differential	differential	ADJ
ejpam-6215	239	21	equations	equation	NOUN
ejpam-6215	239	22	.	.	PUNCT
ejpam-6215	240	1	s.	s.	PROPN
ejpam-6215	240	2	mohammed	mohammed	PROPN
ejpam-6215	240	3	,	,	PUNCT
ejpam-6215	240	4	s.	s.	PROPN
ejpam-6215	240	5	abid	abid	PROPN
ejpam-6215	240	6	,	,	PUNCT
ejpam-6215	240	7	r.	r.	PROPN
ejpam-6215	240	8	abid	abid	PROPN
ejpam-6215	240	9	/	/	SYM
ejpam-6215	240	10	eur	eur	PROPN
ejpam-6215	240	11	.	.	PUNCT
ejpam-6215	241	1	j.	j.	PROPN
ejpam-6215	241	2	pure	pure	PROPN
ejpam-6215	241	3	appl	appl	PROPN
ejpam-6215	241	4	.	.	PROPN
ejpam-6215	241	5	math	math	PROPN
ejpam-6215	241	6	,	,	PUNCT
ejpam-6215	241	7	18	18	NUM
ejpam-6215	241	8	(	(	PUNCT
ejpam-6215	241	9	3	3	NUM
ejpam-6215	241	10	)	)	PUNCT
ejpam-6215	241	11	(	(	PUNCT
ejpam-6215	241	12	2025	2025	NUM
ejpam-6215	241	13	)	)	PUNCT
ejpam-6215	241	14	,	,	PUNCT
ejpam-6215	241	15	6215	6215	NUM
ejpam-6215	241	16	12	12	NUM
ejpam-6215	241	17	of	of	ADP
ejpam-6215	241	18	38	38	NUM
ejpam-6215	241	19	table	table	NOUN
ejpam-6215	241	20	3	3	NUM
ejpam-6215	241	21	:	:	PUNCT
ejpam-6215	241	22	the	the	DET
ejpam-6215	241	23	maximum	maximum	ADJ
ejpam-6215	241	24	residual	residual	ADJ
ejpam-6215	241	25	error	error	NOUN
ejpam-6215	241	26	:	:	PUNCT
ejpam-6215	241	27	mern	mern	NOUN
ejpam-6215	241	28	by	by	ADP
ejpam-6215	241	29	the	the	DET
ejpam-6215	241	30	madm	madm	NOUN
ejpam-6215	241	31	where	where	SCONJ
ejpam-6215	241	32	n	n	PROPN
ejpam-6215	241	33	=	=	SYM
ejpam-6215	241	34	1	1	NUM
ejpam-6215	241	35	,	,	PUNCT
ejpam-6215	241	36	·	·	PUNCT
ejpam-6215	241	37	·	·	PUNCT
ejpam-6215	241	38	·	·	PUNCT
ejpam-6215	241	39	,	,	PUNCT
ejpam-6215	241	40	5	5	X
ejpam-6215	241	41	.	.	X
ejpam-6215	242	1	n	n	PRON
ejpam-6215	242	2	mern	mern	ADJ
ejpam-6215	242	3	1	1	NUM
ejpam-6215	242	4	0.0000601952	0.0000601952	NUM
ejpam-6215	242	5	2	2	NUM
ejpam-6215	242	6	3.22501×	3.22501×	NUM
ejpam-6215	242	7	10−8	10−8	NUM
ejpam-6215	242	8	3	3	NUM
ejpam-6215	242	9	1.29031×	1.29031×	NUM
ejpam-6215	242	10	10−11	10−11	NUM
ejpam-6215	242	11	4	4	NUM
ejpam-6215	242	12	4.40620×	4.40620×	NUM
ejpam-6215	242	13	10−15	10−15	NUM
ejpam-6215	242	14	5	5	NUM
ejpam-6215	242	15	6.93889×	6.93889×	NUM
ejpam-6215	242	16	10−18	10−18	NUM
ejpam-6215	242	17	figure	figure	NOUN
ejpam-6215	242	18	3	3	NUM
ejpam-6215	242	19	:	:	PUNCT
ejpam-6215	242	20	the	the	DET
ejpam-6215	242	21	logarithmic	logarithmic	ADJ
ejpam-6215	242	22	plot	plot	NOUN
ejpam-6215	242	23	of	of	ADP
ejpam-6215	242	24	mern	mern	NOUN
ejpam-6215	242	25	.	.	PUNCT
ejpam-6215	243	1	(	(	PUNCT
ejpam-6215	243	2	madm	madm	PROPN
ejpam-6215	243	3	,	,	PUNCT
ejpam-6215	243	4	first	first	ADV
ejpam-6215	243	5	painlevé	painlevé	NOUN
ejpam-6215	243	6	equation	equation	NOUN
ejpam-6215	243	7	)	)	PUNCT
ejpam-6215	243	8	.	.	PUNCT
ejpam-6215	244	1	2.2.2	2.2.2	X
ejpam-6215	244	2	.	.	PUNCT
ejpam-6215	245	1	the	the	DET
ejpam-6215	245	2	madm	madm	NOUN
ejpam-6215	245	3	for	for	ADP
ejpam-6215	245	4	solving	solve	VERB
ejpam-6215	245	5	painlevé	painlevé	NOUN
ejpam-6215	245	6	ii	ii	NOUN
ejpam-6215	245	7	equation	equation	NOUN
ejpam-6215	245	8	rewrite	rewrite	NOUN
ejpam-6215	245	9	(	(	PUNCT
ejpam-6215	245	10	2	2	NUM
ejpam-6215	245	11	)	)	PUNCT
ejpam-6215	245	12	y′′(x	y′′(x	NOUN
ejpam-6215	245	13	)	)	PUNCT
ejpam-6215	245	14	=	=	SYM
ejpam-6215	246	1	2y3	2y3	NUM
ejpam-6215	246	2	+	+	CCONJ
ejpam-6215	246	3	xy	xy	PROPN
ejpam-6215	246	4	+	+	CCONJ
ejpam-6215	246	5	µ.	µ.	NOUN
ejpam-6215	246	6	(	(	PUNCT
ejpam-6215	246	7	20	20	NUM
ejpam-6215	246	8	)	)	PUNCT
ejpam-6215	246	9	the	the	DET
ejpam-6215	246	10	initial	initial	ADJ
ejpam-6215	246	11	conditions	condition	NOUN
ejpam-6215	246	12	:	:	PUNCT
ejpam-6215	246	13	y(0	y(0	NOUN
ejpam-6215	246	14	)	)	PUNCT
ejpam-6215	246	15	=	=	SYM
ejpam-6215	246	16	1	1	NUM
ejpam-6215	246	17	,	,	PUNCT
ejpam-6215	246	18	y′(0	y′(0	NOUN
ejpam-6215	246	19	)	)	PUNCT
ejpam-6215	246	20	=	=	SYM
ejpam-6215	246	21	0	0	X
ejpam-6215	246	22	.	.	PUNCT
ejpam-6215	247	1	rewrote	rewrote	VERB
ejpam-6215	247	2	(	(	PUNCT
ejpam-6215	247	3	20	20	NUM
ejpam-6215	247	4	)	)	PUNCT
ejpam-6215	247	5	in	in	ADP
ejpam-6215	247	6	the	the	DET
ejpam-6215	247	7	form	form	NOUN
ejpam-6215	247	8	:	:	PUNCT
ejpam-6215	247	9	ly	ly	X
ejpam-6215	247	10	=	=	PUNCT
ejpam-6215	247	11	g(x)−	g(x)−	PROPN
ejpam-6215	247	12	f	f	PROPN
ejpam-6215	247	13	(	(	PUNCT
ejpam-6215	247	14	x	x	PROPN
ejpam-6215	247	15	,	,	PUNCT
ejpam-6215	247	16	y	y	PROPN
ejpam-6215	247	17	)	)	PUNCT
ejpam-6215	247	18	.	.	PUNCT
ejpam-6215	248	1	y′′(x)−	y′′(x)−	PROPN
ejpam-6215	248	2	2y3	2y3	NUM
ejpam-6215	249	1	−	−	NOUN
ejpam-6215	249	2	xy	xy	NOUN
ejpam-6215	249	3	=	=	SYM
ejpam-6215	249	4	µ.	µ.	NOUN
ejpam-6215	249	5	ly	ly	X
ejpam-6215	249	6	=	=	SYM
ejpam-6215	249	7	µ−	µ−	PROPN
ejpam-6215	249	8	(	(	PUNCT
ejpam-6215	249	9	−2y3	−2y3	NUM
ejpam-6215	249	10	−	−	NOUN
ejpam-6215	249	11	xy	xy	NOUN
ejpam-6215	249	12	)	)	PUNCT
ejpam-6215	249	13	.	.	PUNCT
ejpam-6215	250	1	ly	ly	X
ejpam-6215	250	2	=	=	PUNCT
ejpam-6215	250	3	µ+	µ+	PUNCT
ejpam-6215	250	4	2y3	2y3	NUM
ejpam-6215	250	5	+	+	CCONJ
ejpam-6215	250	6	xy	xy	PROPN
ejpam-6215	250	7	.	.	PUNCT
ejpam-6215	251	1	the	the	DET
ejpam-6215	251	2	differential	differential	ADJ
ejpam-6215	251	3	operator	operator	NOUN
ejpam-6215	251	4	l	l	NOUN
ejpam-6215	251	5	is	be	AUX
ejpam-6215	251	6	defined	define	VERB
ejpam-6215	251	7	by	by	ADP
ejpam-6215	251	8	l	l	NOUN
ejpam-6215	251	9	=	=	SYM
ejpam-6215	251	10	e−	e−	PROPN
ejpam-6215	251	11	∫	∫	PROPN
ejpam-6215	251	12	p(x	p(x	PROPN
ejpam-6215	251	13	)	)	PUNCT
ejpam-6215	251	14	dx	dx	PROPN
ejpam-6215	252	1	d	d	X
ejpam-6215	252	2	dx	dx	PROPN
ejpam-6215	252	3	(	(	PUNCT
ejpam-6215	252	4	e	e	PROPN
ejpam-6215	252	5	∫	∫	PROPN
ejpam-6215	252	6	p(x	p(x	PROPN
ejpam-6215	252	7	)	)	PUNCT
ejpam-6215	252	8	dx	dx	PROPN
ejpam-6215	252	9	d	d	PROPN
ejpam-6215	252	10	dx	dx	PROPN
ejpam-6215	252	11	)	)	PUNCT
ejpam-6215	252	12	.	.	PUNCT
ejpam-6215	253	1	l	l	NOUN
ejpam-6215	253	2	=	=	PUNCT
ejpam-6215	253	3	d2	d2	PROPN
ejpam-6215	253	4	dx2	dx2	PROPN
ejpam-6215	253	5	.	.	PUNCT
ejpam-6215	254	1	applying	apply	VERB
ejpam-6215	254	2	the	the	DET
ejpam-6215	254	3	inverse	inverse	NOUN
ejpam-6215	254	4	operator	operator	NOUN
ejpam-6215	254	5	l−1	l−1	PROPN
ejpam-6215	254	6	,	,	PUNCT
ejpam-6215	254	7	we	we	PRON
ejpam-6215	254	8	get	get	VERB
ejpam-6215	254	9	:	:	PUNCT
ejpam-6215	254	10	y(x	y(x	X
ejpam-6215	254	11	)	)	PUNCT
ejpam-6215	254	12	=	=	SYM
ejpam-6215	255	1	φ(x	φ(x	NOUN
ejpam-6215	255	2	)	)	PUNCT
ejpam-6215	255	3	+	+	X
ejpam-6215	255	4	l−1(µ	l−1(µ	ADV
ejpam-6215	255	5	)	)	PUNCT
ejpam-6215	255	6	+	+	CCONJ
ejpam-6215	255	7	l−1(2y3	l−1(2y3	PROPN
ejpam-6215	255	8	+	+	CCONJ
ejpam-6215	255	9	xy	xy	NOUN
ejpam-6215	255	10	)	)	PUNCT
ejpam-6215	255	11	.	.	PUNCT
ejpam-6215	256	1	s.	s.	PROPN
ejpam-6215	256	2	mohammed	mohammed	PROPN
ejpam-6215	256	3	,	,	PUNCT
ejpam-6215	256	4	s.	s.	PROPN
ejpam-6215	256	5	abid	abid	PROPN
ejpam-6215	256	6	,	,	PUNCT
ejpam-6215	256	7	r.	r.	PROPN
ejpam-6215	256	8	abid	abid	PROPN
ejpam-6215	256	9	/	/	SYM
ejpam-6215	256	10	eur	eur	PROPN
ejpam-6215	256	11	.	.	PUNCT
ejpam-6215	257	1	j.	j.	PROPN
ejpam-6215	257	2	pure	pure	PROPN
ejpam-6215	257	3	appl	appl	PROPN
ejpam-6215	257	4	.	.	PROPN
ejpam-6215	257	5	math	math	PROPN
ejpam-6215	257	6	,	,	PUNCT
ejpam-6215	257	7	18	18	NUM
ejpam-6215	257	8	(	(	PUNCT
ejpam-6215	257	9	3	3	NUM
ejpam-6215	257	10	)	)	PUNCT
ejpam-6215	257	11	(	(	PUNCT
ejpam-6215	257	12	2025	2025	NUM
ejpam-6215	257	13	)	)	PUNCT
ejpam-6215	257	14	,	,	PUNCT
ejpam-6215	257	15	6215	6215	NUM
ejpam-6215	257	16	13	13	NUM
ejpam-6215	257	17	of	of	ADP
ejpam-6215	257	18	38	38	NUM
ejpam-6215	257	19	where	where	SCONJ
ejpam-6215	257	20	satisfies	satisfie	NOUN
ejpam-6215	257	21	lφ(x	lφ(x	X
ejpam-6215	257	22	)	)	PUNCT
ejpam-6215	257	23	=	=	SYM
ejpam-6215	257	24	0	0	NUM
ejpam-6215	257	25	from	from	ADP
ejpam-6215	257	26	initial	initial	ADJ
ejpam-6215	257	27	conductions	conduction	NOUN
ejpam-6215	257	28	:	:	PUNCT
ejpam-6215	257	29	φ(x	φ(x	VERB
ejpam-6215	257	30	)	)	PUNCT
ejpam-6215	257	31	=	=	SYM
ejpam-6215	257	32	y(0	y(0	PROPN
ejpam-6215	257	33	)	)	PUNCT
ejpam-6215	257	34	+	+	NUM
ejpam-6215	257	35	y′(0)x	y′(0)x	NOUN
ejpam-6215	257	36	=	=	SYM
ejpam-6215	257	37	1	1	NUM
ejpam-6215	257	38	.	.	PUNCT
ejpam-6215	257	39	y(x	y(x	NOUN
ejpam-6215	257	40	)	)	PUNCT
ejpam-6215	257	41	=	=	PUNCT
ejpam-6215	258	1	1	1	NUM
ejpam-6215	258	2	+	+	CCONJ
ejpam-6215	258	3	l−1(µ	l−1(µ	ADV
ejpam-6215	258	4	)	)	PUNCT
ejpam-6215	259	1	+	+	CCONJ
ejpam-6215	259	2	l−1(2y3	l−1(2y3	PROPN
ejpam-6215	259	3	+	+	CCONJ
ejpam-6215	259	4	xy	xy	NOUN
ejpam-6215	259	5	)	)	PUNCT
ejpam-6215	259	6	.	.	PUNCT
ejpam-6215	260	1	recall	recall	VERB
ejpam-6215	260	2	that	that	SCONJ
ejpam-6215	260	3	the	the	DET
ejpam-6215	260	4	adm	adm	PROPN
ejpam-6215	260	5	introduces	introduce	VERB
ejpam-6215	260	6	the	the	DET
ejpam-6215	260	7	solution	solution	NOUN
ejpam-6215	260	8	y(x	y(x	NOUN
ejpam-6215	260	9	)	)	PUNCT
ejpam-6215	260	10	and	and	CCONJ
ejpam-6215	260	11	the	the	DET
ejpam-6215	260	12	nonlinear	nonlinear	ADJ
ejpam-6215	260	13	function	function	NOUN
ejpam-6215	260	14	f	f	PROPN
ejpam-6215	260	15	(	(	PUNCT
ejpam-6215	260	16	x	x	PROPN
ejpam-6215	260	17	,	,	PUNCT
ejpam-6215	260	18	y	y	PROPN
ejpam-6215	260	19	)	)	PUNCT
ejpam-6215	260	20	by	by	ADP
ejpam-6215	260	21	infinite	infinite	ADJ
ejpam-6215	260	22	series	series	NOUN
ejpam-6215	260	23	:	:	PUNCT
ejpam-6215	260	24	y(x	y(x	X
ejpam-6215	260	25	)	)	PUNCT
ejpam-6215	260	26	=	=	PUNCT
ejpam-6215	261	1	∞∑	∞∑	PRON
ejpam-6215	261	2	n=0	n=0	NUM
ejpam-6215	261	3	yn(x	yn(x	NUM
ejpam-6215	261	4	)	)	PUNCT
ejpam-6215	261	5	.	.	PUNCT
ejpam-6215	262	1	f	f	PROPN
ejpam-6215	262	2	(	(	PUNCT
ejpam-6215	262	3	x	x	X
ejpam-6215	262	4	,	,	PUNCT
ejpam-6215	262	5	y	y	NOUN
ejpam-6215	262	6	)	)	PUNCT
ejpam-6215	262	7	=	=	SYM
ejpam-6215	263	1	2y3	2y3	NUM
ejpam-6215	264	1	+	+	CCONJ
ejpam-6215	264	2	xy	xy	PROPN
ejpam-6215	264	3	.	.	PUNCT
ejpam-6215	265	1	f	f	PROPN
ejpam-6215	265	2	(	(	PUNCT
ejpam-6215	265	3	x	x	X
ejpam-6215	265	4	,	,	PUNCT
ejpam-6215	265	5	y	y	NOUN
ejpam-6215	265	6	)	)	PUNCT
ejpam-6215	265	7	=	=	PUNCT
ejpam-6215	266	1	∞∑	∞∑	ADJ
ejpam-6215	266	2	n=0	n=0	PROPN
ejpam-6215	266	3	an	an	NOUN
ejpam-6215	266	4	.	.	PUNCT
ejpam-6215	267	1	∞∑	∞∑	NUM
ejpam-6215	267	2	n=0	n=0	NUM
ejpam-6215	267	3	yn(x	yn(x	X
ejpam-6215	267	4	)	)	PUNCT
ejpam-6215	267	5	=	=	SYM
ejpam-6215	267	6	1	1	NUM
ejpam-6215	267	7	+	+	CCONJ
ejpam-6215	267	8	l−1(µ	l−1(µ	ADV
ejpam-6215	267	9	)	)	PUNCT
ejpam-6215	268	1	+	+	CCONJ
ejpam-6215	268	2	l−1	l−1	PROPN
ejpam-6215	268	3	∞∑	∞∑	NUM
ejpam-6215	268	4	n=0	n=0	PUNCT
ejpam-6215	268	5	an	an	NOUN
ejpam-6215	268	6	.	.	PUNCT
ejpam-6215	268	7	y0(x	y0(x	NUM
ejpam-6215	268	8	)	)	PUNCT
ejpam-6215	268	9	=	=	SYM
ejpam-6215	268	10	1	1	NUM
ejpam-6215	268	11	+	+	CCONJ
ejpam-6215	268	12	l−1(µ	l−1(µ	ADJ
ejpam-6215	268	13	)	)	PUNCT
ejpam-6215	268	14	.	.	PUNCT
ejpam-6215	269	1	y0(x	y0(x	X
ejpam-6215	269	2	)	)	PUNCT
ejpam-6215	269	3	=	=	SYM
ejpam-6215	269	4	1	1	NUM
ejpam-6215	269	5	+	+	NUM
ejpam-6215	269	6	∫	∫	PROPN
ejpam-6215	269	7	x	x	SYM
ejpam-6215	269	8	0	0	NUM
ejpam-6215	269	9	∫	∫	PROPN
ejpam-6215	269	10	x	x	SYM
ejpam-6215	269	11	0	0	NUM
ejpam-6215	269	12	µdx	µdx	PROPN
ejpam-6215	270	1	dx	dx	PROPN
ejpam-6215	270	2	.	.	PROPN
ejpam-6215	270	3	y0(x	y0(x	X
ejpam-6215	270	4	)	)	PUNCT
ejpam-6215	271	1	=	=	SYM
ejpam-6215	271	2	1	1	NUM
ejpam-6215	272	1	+	+	CCONJ
ejpam-6215	272	2	x2µ	x2µ	PROPN
ejpam-6215	272	3	2	2	NUM
ejpam-6215	272	4	.	.	PUNCT
ejpam-6215	273	1	y1(x	y1(x	NOUN
ejpam-6215	273	2	)	)	PUNCT
ejpam-6215	273	3	=	=	PUNCT
ejpam-6215	274	1	l−1[a0	l−1[a0	NUM
ejpam-6215	274	2	]	]	PUNCT
ejpam-6215	274	3	.	.	PUNCT
ejpam-6215	275	1	a0	a0	PROPN
ejpam-6215	275	2	=	=	PUNCT
ejpam-6215	275	3	2y30	2y30	NOUN
ejpam-6215	276	1	+	+	CCONJ
ejpam-6215	277	1	xy0	xy0	PROPN
ejpam-6215	277	2	.	.	PUNCT
ejpam-6215	278	1	a0	a0	NOUN
ejpam-6215	278	2	=	=	PROPN
ejpam-6215	278	3	2	2	NUM
ejpam-6215	278	4	+	+	CCONJ
ejpam-6215	278	5	x+	x+	NUM
ejpam-6215	278	6	3x2µ+	3x2µ+	NUM
ejpam-6215	278	7	3x4µ2	3x4µ2	NUM
ejpam-6215	278	8	2	2	NUM
ejpam-6215	278	9	+	+	CCONJ
ejpam-6215	278	10	x6µ3	x6µ3	PROPN
ejpam-6215	278	11	4	4	NUM
ejpam-6215	279	1	+	+	CCONJ
ejpam-6215	279	2	x3µ	x3µ	PROPN
ejpam-6215	279	3	2	2	X
ejpam-6215	279	4	.	.	PUNCT
ejpam-6215	280	1	now	now	ADV
ejpam-6215	280	2	compute	compute	VERB
ejpam-6215	280	3	l−1[a0	l−1[a0	NOUN
ejpam-6215	280	4	]	]	NOUN
ejpam-6215	280	5	:	:	PUNCT
ejpam-6215	280	6	y1(x	y1(x	NOUN
ejpam-6215	280	7	)	)	PUNCT
ejpam-6215	280	8	=	=	PUNCT
ejpam-6215	281	1	l−1[a0	l−1[a0	PUNCT
ejpam-6215	281	2	]	]	X
ejpam-6215	281	3	=	=	PUNCT
ejpam-6215	281	4	∫	∫	PROPN
ejpam-6215	281	5	x	x	SYM
ejpam-6215	281	6	0	0	NUM
ejpam-6215	281	7	∫	∫	PROPN
ejpam-6215	281	8	x	x	SYM
ejpam-6215	281	9	0	0	PUNCT
ejpam-6215	281	10	(	(	PUNCT
ejpam-6215	281	11	2	2	NUM
ejpam-6215	281	12	+	+	CCONJ
ejpam-6215	281	13	x+	x+	NUM
ejpam-6215	281	14	3x2µ+	3x2µ+	NUM
ejpam-6215	281	15	3x4µ2	3x4µ2	NUM
ejpam-6215	281	16	2	2	NUM
ejpam-6215	281	17	+	+	CCONJ
ejpam-6215	281	18	x6µ3	x6µ3	PROPN
ejpam-6215	281	19	4	4	NUM
ejpam-6215	282	1	+	+	CCONJ
ejpam-6215	282	2	x3µ	x3µ	PROPN
ejpam-6215	282	3	2	2	X
ejpam-6215	282	4	)	)	PUNCT
ejpam-6215	282	5	dx	dx	PROPN
ejpam-6215	282	6	dx	dx	PROPN
ejpam-6215	282	7	.	.	PUNCT
ejpam-6215	283	1	performing	perform	VERB
ejpam-6215	283	2	the	the	DET
ejpam-6215	283	3	integration	integration	NOUN
ejpam-6215	283	4	:	:	PUNCT
ejpam-6215	283	5	y1(x	y1(x	X
ejpam-6215	283	6	)	)	PUNCT
ejpam-6215	283	7	=	=	SYM
ejpam-6215	284	1	x2	x2	PROPN
ejpam-6215	285	1	+	+	CCONJ
ejpam-6215	285	2	x3	x3	ADJ
ejpam-6215	285	3	6	6	NUM
ejpam-6215	286	1	+	+	CCONJ
ejpam-6215	286	2	x4µ	x4µ	PROPN
ejpam-6215	286	3	4	4	NUM
ejpam-6215	286	4	+	+	NUM
ejpam-6215	286	5	x5µ	x5µ	NOUN
ejpam-6215	286	6	40	40	NUM
ejpam-6215	287	1	+	+	CCONJ
ejpam-6215	287	2	x6µ2	x6µ2	PROPN
ejpam-6215	287	3	20	20	NUM
ejpam-6215	287	4	+	+	CCONJ
ejpam-6215	287	5	x8µ3	x8µ3	PROPN
ejpam-6215	287	6	224	224	NUM
ejpam-6215	287	7	.	.	PUNCT
ejpam-6215	288	1	a1	a1	NOUN
ejpam-6215	288	2	=	=	PUNCT
ejpam-6215	288	3	y1(6y	y1(6y	ADJ
ejpam-6215	288	4	2	2	NUM
ejpam-6215	288	5	0	0	NUM
ejpam-6215	288	6	+	+	NUM
ejpam-6215	288	7	x	x	NOUN
ejpam-6215	288	8	)	)	PUNCT
ejpam-6215	288	9	.	.	PUNCT
ejpam-6215	289	1	a1	a1	NOUN
ejpam-6215	289	2	=	=	SYM
ejpam-6215	289	3	2x3	2x3	NUM
ejpam-6215	289	4	+	+	CCONJ
ejpam-6215	289	5	x4	x4	PROPN
ejpam-6215	289	6	2	2	NUM
ejpam-6215	289	7	+	+	NUM
ejpam-6215	289	8	x5	x5	NOUN
ejpam-6215	289	9	30	30	NUM
ejpam-6215	289	10	+	+	NUM
ejpam-6215	289	11	3x5µ	3x5µ	NOUN
ejpam-6215	289	12	2	2	NUM
ejpam-6215	289	13	+	+	CCONJ
ejpam-6215	289	14	7x6µ	7x6µ	NOUN
ejpam-6215	289	15	30	30	NUM
ejpam-6215	290	1	+	+	CCONJ
ejpam-6215	290	2	x7µ	x7µ	X
ejpam-6215	290	3	280	280	NUM
ejpam-6215	291	1	+	+	CCONJ
ejpam-6215	291	2	33x7µ2	33x7µ2	PROPN
ejpam-6215	291	3	70	70	NUM
ejpam-6215	291	4	.	.	PUNCT
ejpam-6215	291	5	.	.	PUNCT
ejpam-6215	291	6	.	.	PUNCT
ejpam-6215	292	1	+	+	CCONJ
ejpam-6215	292	2	9x8µ2	9x8µ2	NOUN
ejpam-6215	292	3	160	160	NUM
ejpam-6215	292	4	+	+	SYM
ejpam-6215	292	5	131x9µ3	131x9µ3	NUM
ejpam-6215	292	6	1680	1680	NUM
ejpam-6215	292	7	+	+	CCONJ
ejpam-6215	292	8	47x10µ3	47x10µ3	NOUN
ejpam-6215	292	9	11200	11200	NUM
ejpam-6215	292	10	+	+	CCONJ
ejpam-6215	292	11	57x11µ4	57x11µ4	NUM
ejpam-6215	292	12	6160	6160	NUM
ejpam-6215	292	13	+	+	CCONJ
ejpam-6215	292	14	3x13µ5	3x13µ5	NUM
ejpam-6215	292	15	5824	5824	NUM
ejpam-6215	292	16	.	.	PUNCT
ejpam-6215	293	1	s.	s.	PROPN
ejpam-6215	293	2	mohammed	mohammed	PROPN
ejpam-6215	293	3	,	,	PUNCT
ejpam-6215	293	4	s.	s.	PROPN
ejpam-6215	293	5	abid	abid	PROPN
ejpam-6215	293	6	,	,	PUNCT
ejpam-6215	293	7	r.	r.	PROPN
ejpam-6215	293	8	abid	abid	PROPN
ejpam-6215	293	9	/	/	SYM
ejpam-6215	293	10	eur	eur	PROPN
ejpam-6215	293	11	.	.	PUNCT
ejpam-6215	294	1	j.	j.	PROPN
ejpam-6215	294	2	pure	pure	PROPN
ejpam-6215	294	3	appl	appl	PROPN
ejpam-6215	294	4	.	.	PROPN
ejpam-6215	294	5	math	math	PROPN
ejpam-6215	294	6	,	,	PUNCT
ejpam-6215	294	7	18	18	NUM
ejpam-6215	294	8	(	(	PUNCT
ejpam-6215	294	9	3	3	NUM
ejpam-6215	294	10	)	)	PUNCT
ejpam-6215	294	11	(	(	PUNCT
ejpam-6215	294	12	2025	2025	NUM
ejpam-6215	294	13	)	)	PUNCT
ejpam-6215	294	14	,	,	PUNCT
ejpam-6215	294	15	6215	6215	NUM
ejpam-6215	294	16	14	14	NUM
ejpam-6215	294	17	of	of	ADP
ejpam-6215	294	18	38	38	NUM
ejpam-6215	294	19	y2(x	y2(x	NUM
ejpam-6215	294	20	)	)	PUNCT
ejpam-6215	294	21	=	=	PUNCT
ejpam-6215	295	1	l−1[a1	l−1[a1	PROPN
ejpam-6215	295	2	]	]	PUNCT
ejpam-6215	295	3	=	=	PUNCT
ejpam-6215	295	4	∫	∫	PROPN
ejpam-6215	295	5	x	x	SYM
ejpam-6215	295	6	0	0	NUM
ejpam-6215	295	7	∫	∫	PROPN
ejpam-6215	295	8	x	x	SYM
ejpam-6215	295	9	0	0	NUM
ejpam-6215	295	10	(	(	PUNCT
ejpam-6215	295	11	a1	a1	PROPN
ejpam-6215	295	12	)	)	PUNCT
ejpam-6215	295	13	dx	dx	PROPN
ejpam-6215	295	14	dx	dx	PROPN
ejpam-6215	295	15	.	.	PUNCT
ejpam-6215	296	1	y2(x	y2(x	X
ejpam-6215	296	2	)	)	PUNCT
ejpam-6215	296	3	=	=	SYM
ejpam-6215	296	4	x4	x4	PROPN
ejpam-6215	296	5	2	2	NUM
ejpam-6215	296	6	+	+	NUM
ejpam-6215	296	7	x5	x5	NOUN
ejpam-6215	296	8	10	10	NUM
ejpam-6215	296	9	+	+	NUM
ejpam-6215	296	10	x6	x6	PROPN
ejpam-6215	296	11	180	180	NUM
ejpam-6215	296	12	+	+	CCONJ
ejpam-6215	296	13	x6µ	x6µ	PROPN
ejpam-6215	296	14	4	4	NUM
ejpam-6215	296	15	+	+	CCONJ
ejpam-6215	296	16	x7µ	x7µ	PROPN
ejpam-6215	296	17	30	30	NUM
ejpam-6215	296	18	+	+	NUM
ejpam-6215	296	19	x8µ	x8µ	PROPN
ejpam-6215	296	20	2240	2240	NUM
ejpam-6215	296	21	+	+	CCONJ
ejpam-6215	296	22	33x8µ2	33x8µ2	NUM
ejpam-6215	296	23	560	560	NUM
ejpam-6215	296	24	.	.	PUNCT
ejpam-6215	296	25	.	.	PUNCT
ejpam-6215	296	26	.	.	PUNCT
ejpam-6215	297	1	+	+	CCONJ
ejpam-6215	298	1	x9µ2	x9µ2	X
ejpam-6215	299	1	160	160	NUM
ejpam-6215	299	2	+	+	CCONJ
ejpam-6215	299	3	131x10µ3	131x10µ3	NUM
ejpam-6215	299	4	16800	16800	NUM
ejpam-6215	299	5	+	+	CCONJ
ejpam-6215	299	6	47x11µ3	47x11µ3	NUM
ejpam-6215	299	7	123200	123200	NUM
ejpam-6215	299	8	+	+	CCONJ
ejpam-6215	299	9	19x12µ4	19x12µ4	PROPN
ejpam-6215	299	10	24640	24640	NUM
ejpam-6215	299	11	+	+	CCONJ
ejpam-6215	299	12	3x14µ5	3x14µ5	NUM
ejpam-6215	299	13	81536	81536	NUM
ejpam-6215	299	14	.	.	PUNCT
ejpam-6215	299	15	...	...	PUNCT
ejpam-6215	300	1	yn+1(x	yn+1(x	X
ejpam-6215	300	2	)	)	PUNCT
ejpam-6215	300	3	=	=	SYM
ejpam-6215	301	1	l−1[an	l−1[an	PROPN
ejpam-6215	301	2	]	]	X
ejpam-6215	301	3	.	.	PUNCT
ejpam-6215	302	1	y(x	y(x	NOUN
ejpam-6215	302	2	)	)	PUNCT
ejpam-6215	303	1	=	=	PUNCT
ejpam-6215	304	1	∞∑	∞∑	PRON
ejpam-6215	304	2	n=0	n=0	NUM
ejpam-6215	304	3	yn(x	yn(x	NUM
ejpam-6215	304	4	)	)	PUNCT
ejpam-6215	304	5	.	.	PUNCT
ejpam-6215	305	1	y(x	y(x	NOUN
ejpam-6215	305	2	)	)	PUNCT
ejpam-6215	305	3	=	=	SYM
ejpam-6215	305	4	y0(x	y0(x	NOUN
ejpam-6215	305	5	)	)	PUNCT
ejpam-6215	305	6	+	+	NOUN
ejpam-6215	305	7	y1(x	y1(x	NOUN
ejpam-6215	305	8	)	)	PUNCT
ejpam-6215	305	9	+	+	X
ejpam-6215	305	10	y2(x	y2(x	X
ejpam-6215	305	11	)	)	PUNCT
ejpam-6215	305	12	+	+	NUM
ejpam-6215	305	13	·	·	PUNCT
ejpam-6215	305	14	·	·	PUNCT
ejpam-6215	305	15	·	·	PUNCT
ejpam-6215	305	16	y(x	y(x	NOUN
ejpam-6215	305	17	)	)	PUNCT
ejpam-6215	305	18	=	=	SYM
ejpam-6215	305	19	1	1	NUM
ejpam-6215	305	20	+	+	CCONJ
ejpam-6215	305	21	x2µ	x2µ	PROPN
ejpam-6215	305	22	2	2	NUM
ejpam-6215	306	1	+	+	CCONJ
ejpam-6215	306	2	x2	x2	PROPN
ejpam-6215	307	1	+	+	CCONJ
ejpam-6215	307	2	x3	x3	ADJ
ejpam-6215	307	3	6	6	NUM
ejpam-6215	308	1	+	+	CCONJ
ejpam-6215	308	2	x4µ	x4µ	PROPN
ejpam-6215	308	3	4	4	NUM
ejpam-6215	308	4	+	+	NUM
ejpam-6215	308	5	x5µ	x5µ	NOUN
ejpam-6215	308	6	40	40	NUM
ejpam-6215	309	1	+	+	CCONJ
ejpam-6215	309	2	x6µ2	x6µ2	PROPN
ejpam-6215	309	3	20	20	NUM
ejpam-6215	309	4	+	+	CCONJ
ejpam-6215	309	5	x8µ3	x8µ3	SYM
ejpam-6215	309	6	224	224	NUM
ejpam-6215	309	7	+	+	CCONJ
ejpam-6215	309	8	x4	x4	PROPN
ejpam-6215	309	9	2	2	NUM
ejpam-6215	309	10	.	.	PUNCT
ejpam-6215	309	11	.	.	PUNCT
ejpam-6215	309	12	.	.	PUNCT
ejpam-6215	310	1	+	+	PUNCT
ejpam-6215	310	2	x5	x5	NOUN
ejpam-6215	310	3	10	10	NUM
ejpam-6215	310	4	+	+	NUM
ejpam-6215	310	5	x6	x6	PROPN
ejpam-6215	310	6	180	180	NUM
ejpam-6215	310	7	+	+	CCONJ
ejpam-6215	310	8	x6µ	x6µ	PROPN
ejpam-6215	310	9	4	4	NUM
ejpam-6215	310	10	+	+	CCONJ
ejpam-6215	310	11	x7µ	x7µ	PROPN
ejpam-6215	310	12	30	30	NUM
ejpam-6215	310	13	+	+	NUM
ejpam-6215	310	14	x8µ	x8µ	PROPN
ejpam-6215	310	15	2240	2240	NUM
ejpam-6215	310	16	+	+	CCONJ
ejpam-6215	310	17	33x8µ2	33x8µ2	NUM
ejpam-6215	310	18	560	560	NUM
ejpam-6215	310	19	+	+	CCONJ
ejpam-6215	310	20	x9µ2	x9µ2	X
ejpam-6215	310	21	160	160	NUM
ejpam-6215	310	22	.	.	PUNCT
ejpam-6215	310	23	.	.	PUNCT
ejpam-6215	310	24	.	.	PUNCT
ejpam-6215	311	1	+	+	CCONJ
ejpam-6215	311	2	131x10µ3	131x10µ3	ADJ
ejpam-6215	311	3	16800	16800	NUM
ejpam-6215	311	4	+	+	CCONJ
ejpam-6215	311	5	47x11µ3	47x11µ3	NUM
ejpam-6215	311	6	123200	123200	NUM
ejpam-6215	312	1	+	+	CCONJ
ejpam-6215	312	2	19x12µ4	19x12µ4	PROPN
ejpam-6215	312	3	24640	24640	NUM
ejpam-6215	312	4	+	+	CCONJ
ejpam-6215	312	5	3x14µ5	3x14µ5	NUM
ejpam-6215	312	6	81536	81536	NUM
ejpam-6215	312	7	+	+	CCONJ
ejpam-6215	312	8	·	·	PUNCT
ejpam-6215	312	9	·	·	PUNCT
ejpam-6215	312	10	·	·	PUNCT
ejpam-6215	312	11	the	the	DET
ejpam-6215	312	12	remainder	remainder	NOUN
ejpam-6215	312	13	function	function	NOUN
ejpam-6215	312	14	of	of	ADP
ejpam-6215	312	15	error	error	NOUN
ejpam-6215	312	16	is	be	AUX
ejpam-6215	312	17	evaluated	evaluate	VERB
ejpam-6215	312	18	:	:	PUNCT
ejpam-6215	312	19	ern	ern	PROPN
ejpam-6215	312	20	=	=	PUNCT
ejpam-6215	312	21	y′′n(x)−	y′′n(x)−	PROPN
ejpam-6215	313	1	2y3n(x)−	2y3n(x)−	PROPN
ejpam-6215	313	2	xyn(x)−	xyn(x)−	PROPN
ejpam-6215	313	3	µ.	µ.	NOUN
ejpam-6215	313	4	and	and	CCONJ
ejpam-6215	313	5	the	the	DET
ejpam-6215	313	6	mern	mern	NOUN
ejpam-6215	313	7	is	be	AUX
ejpam-6215	313	8	:	:	PUNCT
ejpam-6215	313	9	mern	mern	ADJ
ejpam-6215	313	10	=	=	SYM
ejpam-6215	313	11	max	max	PROPN
ejpam-6215	313	12	0.01≤x≤0.1	0.01≤x≤0.1	NUM
ejpam-6215	314	1	|ern(x)|	|ern(x)|	NOUN
ejpam-6215	314	2	.	.	PUNCT
ejpam-6215	315	1	in	in	ADP
ejpam-6215	315	2	table	table	NOUN
ejpam-6215	315	3	4	4	NUM
ejpam-6215	315	4	and	and	CCONJ
ejpam-6215	315	5	figure	figure	VERB
ejpam-6215	315	6	4	4	NUM
ejpam-6215	315	7	show	show	VERB
ejpam-6215	315	8	the	the	DET
ejpam-6215	315	9	convergence	convergence	NOUN
ejpam-6215	315	10	of	of	ADP
ejpam-6215	315	11	the	the	DET
ejpam-6215	315	12	solution	solution	NOUN
ejpam-6215	315	13	using	use	VERB
ejpam-6215	315	14	mern	mern	NOUN
ejpam-6215	315	15	,	,	PUNCT
ejpam-6215	315	16	the	the	DET
ejpam-6215	315	17	error	error	NOUN
ejpam-6215	315	18	decreases	decrease	VERB
ejpam-6215	315	19	with	with	ADP
ejpam-6215	315	20	increasing	increase	VERB
ejpam-6215	315	21	n.	n.	NOUN
ejpam-6215	315	22	the	the	DET
ejpam-6215	315	23	results	result	NOUN
ejpam-6215	315	24	indicate	indicate	VERB
ejpam-6215	315	25	a	a	DET
ejpam-6215	315	26	rapid	rapid	ADJ
ejpam-6215	315	27	reduction	reduction	NOUN
ejpam-6215	315	28	in	in	ADP
ejpam-6215	315	29	error	error	NOUN
ejpam-6215	315	30	,	,	PUNCT
ejpam-6215	315	31	with	with	ADP
ejpam-6215	315	32	the	the	DET
ejpam-6215	315	33	most	most	ADV
ejpam-6215	315	34	significant	significant	ADJ
ejpam-6215	315	35	improvement	improvement	NOUN
ejpam-6215	315	36	occurring	occur	VERB
ejpam-6215	315	37	between	between	ADP
ejpam-6215	315	38	n	n	NOUN
ejpam-6215	315	39	=	=	SYM
ejpam-6215	315	40	1	1	NUM
ejpam-6215	315	41	and	and	CCONJ
ejpam-6215	315	42	n	n	CCONJ
ejpam-6215	315	43	=	=	SYM
ejpam-6215	315	44	3	3	X
ejpam-6215	315	45	.	.	PUNCT
ejpam-6215	315	46	by	by	ADP
ejpam-6215	315	47	n	n	NOUN
ejpam-6215	315	48	=	=	SYM
ejpam-6215	315	49	5	5	NUM
ejpam-6215	315	50	,	,	PUNCT
ejpam-6215	315	51	the	the	DET
ejpam-6215	315	52	error	error	NOUN
ejpam-6215	315	53	reaches	reach	VERB
ejpam-6215	315	54	an	an	DET
ejpam-6215	315	55	extremely	extremely	ADV
ejpam-6215	315	56	low	low	ADJ
ejpam-6215	315	57	magnitude	magnitude	NOUN
ejpam-6215	315	58	,	,	PUNCT
ejpam-6215	315	59	around	around	ADP
ejpam-6215	315	60	10−10	10−10	NUM
ejpam-6215	315	61	,	,	PUNCT
ejpam-6215	315	62	confirming	confirm	VERB
ejpam-6215	315	63	the	the	DET
ejpam-6215	315	64	high	high	ADJ
ejpam-6215	315	65	accuracy	accuracy	NOUN
ejpam-6215	315	66	of	of	ADP
ejpam-6215	315	67	the	the	DET
ejpam-6215	315	68	method	method	NOUN
ejpam-6215	315	69	.	.	PUNCT
ejpam-6215	316	1	this	this	DET
ejpam-6215	316	2	behavior	behavior	NOUN
ejpam-6215	316	3	highlights	highlight	VERB
ejpam-6215	316	4	the	the	DET
ejpam-6215	316	5	computational	computational	ADJ
ejpam-6215	316	6	efficiency	efficiency	NOUN
ejpam-6215	316	7	of	of	ADP
ejpam-6215	316	8	madm	madm	NOUN
ejpam-6215	316	9	,	,	PUNCT
ejpam-6215	316	10	as	as	SCONJ
ejpam-6215	316	11	it	it	PRON
ejpam-6215	316	12	provides	provide	VERB
ejpam-6215	316	13	highly	highly	ADV
ejpam-6215	316	14	accurate	accurate	ADJ
ejpam-6215	316	15	solutions	solution	NOUN
ejpam-6215	316	16	to	to	ADP
ejpam-6215	316	17	nonlinear	nonlinear	ADJ
ejpam-6215	316	18	differential	differential	ADJ
ejpam-6215	316	19	equations	equation	NOUN
ejpam-6215	316	20	with	with	ADP
ejpam-6215	316	21	minimal	minimal	ADJ
ejpam-6215	316	22	computational	computational	ADJ
ejpam-6215	316	23	effort	effort	NOUN
ejpam-6215	316	24	.	.	PUNCT
ejpam-6215	317	1	s.	s.	PROPN
ejpam-6215	317	2	mohammed	mohammed	PROPN
ejpam-6215	317	3	,	,	PUNCT
ejpam-6215	317	4	s.	s.	PROPN
ejpam-6215	317	5	abid	abid	PROPN
ejpam-6215	317	6	,	,	PUNCT
ejpam-6215	317	7	r.	r.	PROPN
ejpam-6215	317	8	abid	abid	PROPN
ejpam-6215	317	9	/	/	SYM
ejpam-6215	317	10	eur	eur	PROPN
ejpam-6215	317	11	.	.	PUNCT
ejpam-6215	318	1	j.	j.	PROPN
ejpam-6215	318	2	pure	pure	PROPN
ejpam-6215	318	3	appl	appl	PROPN
ejpam-6215	318	4	.	.	PROPN
ejpam-6215	318	5	math	math	PROPN
ejpam-6215	318	6	,	,	PUNCT
ejpam-6215	318	7	18	18	NUM
ejpam-6215	318	8	(	(	PUNCT
ejpam-6215	318	9	3	3	NUM
ejpam-6215	318	10	)	)	PUNCT
ejpam-6215	318	11	(	(	PUNCT
ejpam-6215	318	12	2025	2025	NUM
ejpam-6215	318	13	)	)	PUNCT
ejpam-6215	318	14	,	,	PUNCT
ejpam-6215	318	15	6215	6215	NUM
ejpam-6215	318	16	15	15	NUM
ejpam-6215	318	17	of	of	ADP
ejpam-6215	318	18	38	38	NUM
ejpam-6215	318	19	table	table	NOUN
ejpam-6215	318	20	4	4	NUM
ejpam-6215	318	21	:	:	PUNCT
ejpam-6215	318	22	the	the	DET
ejpam-6215	318	23	maximum	maximum	ADJ
ejpam-6215	318	24	residual	residual	ADJ
ejpam-6215	318	25	error	error	NOUN
ejpam-6215	318	26	:	:	PUNCT
ejpam-6215	318	27	mern	mern	NOUN
ejpam-6215	318	28	by	by	ADP
ejpam-6215	318	29	the	the	DET
ejpam-6215	318	30	madm	madm	NOUN
ejpam-6215	318	31	,	,	PUNCT
ejpam-6215	318	32	where	where	SCONJ
ejpam-6215	318	33	n	n	NOUN
ejpam-6215	318	34	=	=	SYM
ejpam-6215	318	35	1	1	NUM
ejpam-6215	318	36	,	,	PUNCT
ejpam-6215	318	37	.	.	PUNCT
ejpam-6215	318	38	.	.	PUNCT
ejpam-6215	319	1	.	.	PUNCT
ejpam-6215	320	1	,	,	PUNCT
ejpam-6215	320	2	5	5	X
ejpam-6215	320	3	.	.	X
ejpam-6215	321	1	n	n	PRON
ejpam-6215	321	2	mern	mern	ADJ
ejpam-6215	321	3	1	1	NUM
ejpam-6215	321	4	0.06341250000	0.06341250000	NUM
ejpam-6215	321	5	2	2	NUM
ejpam-6215	321	6	0.00095060500	0.00095060500	NUM
ejpam-6215	321	7	3	3	NUM
ejpam-6215	321	8	0.00001041000	0.00001041000	NUM
ejpam-6215	321	9	4	4	NUM
ejpam-6215	321	10	9.77952×	9.77952×	NOUN
ejpam-6215	321	11	10−8	10−8	NUM
ejpam-6215	321	12	5	5	NUM
ejpam-6215	321	13	8.40300×	8.40300×	NUM
ejpam-6215	321	14	10−10	10−10	NUM
ejpam-6215	321	15	figure	figure	NOUN
ejpam-6215	321	16	4	4	NUM
ejpam-6215	321	17	:	:	PUNCT
ejpam-6215	321	18	the	the	DET
ejpam-6215	321	19	logarithmic	logarithmic	ADJ
ejpam-6215	321	20	plot	plot	NOUN
ejpam-6215	321	21	of	of	ADP
ejpam-6215	321	22	mern	mern	NOUN
ejpam-6215	321	23	.	.	PUNCT
ejpam-6215	322	1	(	(	PUNCT
ejpam-6215	322	2	madm	madm	NOUN
ejpam-6215	322	3	,	,	PUNCT
ejpam-6215	322	4	second	second	ADJ
ejpam-6215	322	5	painlevé	painlevé	NOUN
ejpam-6215	322	6	equation	equation	NOUN
ejpam-6215	322	7	)	)	PUNCT
ejpam-6215	322	8	.	.	PUNCT
ejpam-6215	323	1	2.3	2.3	NUM
ejpam-6215	323	2	.	.	PUNCT
ejpam-6215	324	1	laplace	laplace	NOUN
ejpam-6215	324	2	decomposition	decomposition	NOUN
ejpam-6215	324	3	method	method	NOUN
ejpam-6215	324	4	(	(	PUNCT
ejpam-6215	324	5	ldm	ldm	PROPN
ejpam-6215	324	6	)	)	PUNCT
ejpam-6215	324	7	the	the	DET
ejpam-6215	324	8	laplace	laplace	NOUN
ejpam-6215	324	9	decomposition	decomposition	NOUN
ejpam-6215	324	10	method	method	NOUN
ejpam-6215	324	11	(	(	PUNCT
ejpam-6215	324	12	ldm	ldm	NOUN
ejpam-6215	324	13	)	)	PUNCT
ejpam-6215	324	14	is	be	AUX
ejpam-6215	324	15	an	an	DET
ejpam-6215	324	16	analytical	analytical	ADJ
ejpam-6215	324	17	technique	technique	NOUN
ejpam-6215	324	18	that	that	PRON
ejpam-6215	324	19	combines	combine	VERB
ejpam-6215	324	20	the	the	DET
ejpam-6215	324	21	laplace	laplace	NOUN
ejpam-6215	324	22	transform	transform	NOUN
ejpam-6215	324	23	and	and	CCONJ
ejpam-6215	324	24	the	the	DET
ejpam-6215	324	25	adomian	adomian	NOUN
ejpam-6215	324	26	decomposition	decomposition	NOUN
ejpam-6215	324	27	method	method	NOUN
ejpam-6215	324	28	(	(	PUNCT
ejpam-6215	324	29	adm	adm	PROPN
ejpam-6215	324	30	)	)	PUNCT
ejpam-6215	324	31	to	to	PART
ejpam-6215	324	32	solve	solve	VERB
ejpam-6215	324	33	nonlinear	nonlinear	ADJ
ejpam-6215	324	34	differential	differential	ADJ
ejpam-6215	324	35	equations	equation	NOUN
ejpam-6215	324	36	efficiently	efficiently	ADV
ejpam-6215	324	37	.	.	PUNCT
ejpam-6215	325	1	the	the	DET
ejpam-6215	325	2	laplace	laplace	NOUN
ejpam-6215	325	3	transform	transform	NOUN
ejpam-6215	325	4	,	,	PUNCT
ejpam-6215	325	5	introduced	introduce	VERB
ejpam-6215	325	6	by	by	ADP
ejpam-6215	325	7	pierre	pierre	PROPN
ejpam-6215	325	8	-	-	PUNCT
ejpam-6215	325	9	simon	simon	PROPN
ejpam-6215	325	10	laplace	laplace	NOUN
ejpam-6215	325	11	in	in	ADP
ejpam-6215	325	12	the	the	DET
ejpam-6215	325	13	18th	18th	ADJ
ejpam-6215	325	14	century	century	NOUN
ejpam-6215	325	15	,	,	PUNCT
ejpam-6215	325	16	[	[	X
ejpam-6215	325	17	9	9	NUM
ejpam-6215	325	18	,	,	PUNCT
ejpam-6215	325	19	10	10	NUM
ejpam-6215	325	20	]	]	PUNCT
ejpam-6215	325	21	is	be	AUX
ejpam-6215	325	22	widely	widely	ADV
ejpam-6215	325	23	used	use	VERB
ejpam-6215	325	24	for	for	ADP
ejpam-6215	325	25	transforming	transform	VERB
ejpam-6215	325	26	differential	differential	ADJ
ejpam-6215	325	27	equations	equation	NOUN
ejpam-6215	325	28	into	into	ADP
ejpam-6215	325	29	algebraic	algebraic	ADJ
ejpam-6215	325	30	equations	equation	NOUN
ejpam-6215	325	31	,	,	PUNCT
ejpam-6215	325	32	simplifying	simplify	VERB
ejpam-6215	325	33	their	their	PRON
ejpam-6215	325	34	solutions	solution	NOUN
ejpam-6215	325	35	.	.	PUNCT
ejpam-6215	326	1	integrating	integrate	VERB
ejpam-6215	326	2	adomian	adomian	NOUN
ejpam-6215	326	3	decomposition	decomposition	NOUN
ejpam-6215	326	4	methods	method	NOUN
ejpam-6215	326	5	and	and	CCONJ
ejpam-6215	326	6	laplace	laplace	NOUN
ejpam-6215	326	7	transform	transform	NOUN
ejpam-6215	326	8	offers	offer	VERB
ejpam-6215	326	9	a	a	DET
ejpam-6215	326	10	reliable	reliable	ADJ
ejpam-6215	326	11	approach	approach	NOUN
ejpam-6215	326	12	to	to	ADP
ejpam-6215	326	13	solving	solve	VERB
ejpam-6215	326	14	nonlinear	nonlinear	ADJ
ejpam-6215	326	15	ordinary	ordinary	ADJ
ejpam-6215	326	16	differential	differential	ADJ
ejpam-6215	326	17	equations	equation	NOUN
ejpam-6215	326	18	,	,	PUNCT
ejpam-6215	326	19	particularly	particularly	ADV
ejpam-6215	326	20	those	those	PRON
ejpam-6215	326	21	encountered	encounter	VERB
ejpam-6215	326	22	in	in	ADP
ejpam-6215	326	23	mathematical	mathematical	ADJ
ejpam-6215	326	24	physics	physics	NOUN
ejpam-6215	326	25	and	and	CCONJ
ejpam-6215	326	26	engineering	engineering	NOUN
ejpam-6215	326	27	applications	application	NOUN
ejpam-6215	326	28	[	[	X
ejpam-6215	326	29	35–38	35–38	NUM
ejpam-6215	326	30	]	]	PUNCT
ejpam-6215	326	31	.	.	PUNCT
ejpam-6215	327	1	in	in	ADP
ejpam-6215	327	2	this	this	DET
ejpam-6215	327	3	subsection	subsection	NOUN
ejpam-6215	327	4	,	,	PUNCT
ejpam-6215	327	5	we	we	PRON
ejpam-6215	327	6	apply	apply	VERB
ejpam-6215	327	7	ldm	ldm	NOUN
ejpam-6215	327	8	to	to	PART
ejpam-6215	327	9	obtain	obtain	VERB
ejpam-6215	327	10	analytical	analytical	ADJ
ejpam-6215	327	11	solutions	solution	NOUN
ejpam-6215	327	12	for	for	ADP
ejpam-6215	327	13	painlevé	painlevé	NOUN
ejpam-6215	327	14	equations	equation	NOUN
ejpam-6215	327	15	,	,	PUNCT
ejpam-6215	327	16	by	by	ADP
ejpam-6215	327	17	leveraging	leverage	VERB
ejpam-6215	327	18	the	the	DET
ejpam-6215	327	19	strengths	strength	NOUN
ejpam-6215	327	20	of	of	ADP
ejpam-6215	327	21	both	both	CCONJ
ejpam-6215	327	22	the	the	DET
ejpam-6215	327	23	laplace	laplace	NOUN
ejpam-6215	327	24	transform	transform	NOUN
ejpam-6215	327	25	and	and	CCONJ
ejpam-6215	327	26	the	the	DET
ejpam-6215	327	27	adomian	adomian	NOUN
ejpam-6215	327	28	decomposition	decomposition	NOUN
ejpam-6215	327	29	method	method	NOUN
ejpam-6215	327	30	.	.	PUNCT
ejpam-6215	328	1	ldm	ldm	NOUN
ejpam-6215	328	2	provides	provide	VERB
ejpam-6215	328	3	a	a	DET
ejpam-6215	328	4	systematic	systematic	ADJ
ejpam-6215	328	5	and	and	CCONJ
ejpam-6215	328	6	effective	effective	ADJ
ejpam-6215	328	7	framework	framework	NOUN
ejpam-6215	328	8	for	for	ADP
ejpam-6215	328	9	deriving	derive	VERB
ejpam-6215	328	10	solutions	solution	NOUN
ejpam-6215	328	11	in	in	ADP
ejpam-6215	328	12	a	a	DET
ejpam-6215	328	13	series	series	NOUN
ejpam-6215	328	14	form	form	NOUN
ejpam-6215	328	15	with	with	ADP
ejpam-6215	328	16	rapid	rapid	ADJ
ejpam-6215	328	17	convergence	convergence	NOUN
ejpam-6215	328	18	.	.	PUNCT
ejpam-6215	329	1	we	we	PRON
ejpam-6215	329	2	aim	aim	VERB
ejpam-6215	329	3	to	to	PART
ejpam-6215	329	4	explore	explore	VERB
ejpam-6215	329	5	the	the	DET
ejpam-6215	329	6	effectiveness	effectiveness	NOUN
ejpam-6215	329	7	of	of	ADP
ejpam-6215	329	8	ldm	ldm	NOUN
ejpam-6215	329	9	in	in	ADP
ejpam-6215	329	10	solving	solve	VERB
ejpam-6215	329	11	these	these	DET
ejpam-6215	329	12	equations	equation	NOUN
ejpam-6215	329	13	and	and	CCONJ
ejpam-6215	329	14	contribute	contribute	VERB
ejpam-6215	329	15	to	to	ADP
ejpam-6215	329	16	the	the	DET
ejpam-6215	329	17	broader	broad	ADJ
ejpam-6215	329	18	understanding	understanding	NOUN
ejpam-6215	329	19	of	of	ADP
ejpam-6215	329	20	analytical	analytical	ADJ
ejpam-6215	329	21	techniques	technique	NOUN
ejpam-6215	329	22	for	for	ADP
ejpam-6215	329	23	nonlinear	nonlinear	ADJ
ejpam-6215	329	24	differential	differential	ADJ
ejpam-6215	329	25	equations	equation	NOUN
ejpam-6215	329	26	.	.	PUNCT
ejpam-6215	330	1	2.3.1	2.3.1	X
ejpam-6215	330	2	.	.	PUNCT
ejpam-6215	331	1	the	the	DET
ejpam-6215	331	2	ldm	ldm	NOUN
ejpam-6215	331	3	for	for	ADP
ejpam-6215	331	4	solving	solve	VERB
ejpam-6215	331	5	painlevé	painlevé	NOUN
ejpam-6215	331	6	equation	equation	NOUN
ejpam-6215	331	7	i	i	PRON
ejpam-6215	331	8	rewrite	rewrite	VERB
ejpam-6215	331	9	(	(	PUNCT
ejpam-6215	331	10	1	1	NUM
ejpam-6215	331	11	)	)	PUNCT
ejpam-6215	331	12	y′′(x	y′′(x	NOUN
ejpam-6215	331	13	)	)	PUNCT
ejpam-6215	331	14	=	=	PUNCT
ejpam-6215	331	15	6y2	6y2	NUM
ejpam-6215	331	16	+	+	CCONJ
ejpam-6215	331	17	x.	x.	NOUN
ejpam-6215	331	18	(	(	PUNCT
ejpam-6215	331	19	21	21	NUM
ejpam-6215	331	20	)	)	PUNCT
ejpam-6215	331	21	with	with	ADP
ejpam-6215	331	22	the	the	DET
ejpam-6215	331	23	initial	initial	ADJ
ejpam-6215	331	24	conditions	condition	NOUN
ejpam-6215	331	25	:	:	PUNCT
ejpam-6215	331	26	y(0	y(0	NOUN
ejpam-6215	331	27	)	)	PUNCT
ejpam-6215	331	28	=	=	SYM
ejpam-6215	331	29	0	0	NUM
ejpam-6215	331	30	,	,	PUNCT
ejpam-6215	331	31	y′(0	y′(0	NOUN
ejpam-6215	331	32	)	)	PUNCT
ejpam-6215	331	33	=	=	SYM
ejpam-6215	331	34	1	1	X
ejpam-6215	331	35	.	.	PUNCT
ejpam-6215	332	1	(	(	PUNCT
ejpam-6215	332	2	22	22	NUM
ejpam-6215	332	3	)	)	PUNCT
ejpam-6215	332	4	s.	s.	PROPN
ejpam-6215	332	5	mohammed	mohammed	PROPN
ejpam-6215	332	6	,	,	PUNCT
ejpam-6215	332	7	s.	s.	PROPN
ejpam-6215	332	8	abid	abid	PROPN
ejpam-6215	332	9	,	,	PUNCT
ejpam-6215	332	10	r.	r.	PROPN
ejpam-6215	332	11	abid	abid	PROPN
ejpam-6215	332	12	/	/	SYM
ejpam-6215	332	13	eur	eur	PROPN
ejpam-6215	332	14	.	.	PUNCT
ejpam-6215	333	1	j.	j.	PROPN
ejpam-6215	333	2	pure	pure	PROPN
ejpam-6215	333	3	appl	appl	PROPN
ejpam-6215	333	4	.	.	PROPN
ejpam-6215	333	5	math	math	PROPN
ejpam-6215	333	6	,	,	PUNCT
ejpam-6215	333	7	18	18	NUM
ejpam-6215	333	8	(	(	PUNCT
ejpam-6215	333	9	3	3	NUM
ejpam-6215	333	10	)	)	PUNCT
ejpam-6215	333	11	(	(	PUNCT
ejpam-6215	333	12	2025	2025	NUM
ejpam-6215	333	13	)	)	PUNCT
ejpam-6215	333	14	,	,	PUNCT
ejpam-6215	333	15	6215	6215	NUM
ejpam-6215	333	16	16	16	NUM
ejpam-6215	333	17	of	of	ADP
ejpam-6215	333	18	38	38	NUM
ejpam-6215	333	19	now	now	ADV
ejpam-6215	333	20	,	,	PUNCT
ejpam-6215	333	21	apply	apply	VERB
ejpam-6215	333	22	the	the	DET
ejpam-6215	333	23	laplace	laplace	NOUN
ejpam-6215	333	24	transform	transform	NOUN
ejpam-6215	333	25	on	on	ADP
ejpam-6215	333	26	both	both	DET
ejpam-6215	333	27	sides	side	NOUN
ejpam-6215	333	28	of	of	ADP
ejpam-6215	333	29	(	(	PUNCT
ejpam-6215	333	30	21	21	NUM
ejpam-6215	333	31	)	)	PUNCT
ejpam-6215	333	32	.	.	PUNCT
ejpam-6215	334	1	with	with	ADP
ejpam-6215	334	2	initial	initial	ADJ
ejpam-6215	334	3	conditions	condition	NOUN
ejpam-6215	334	4	:	:	PUNCT
ejpam-6215	334	5	l[y′′	l[y′′	ADV
ejpam-6215	334	6	]	]	PUNCT
ejpam-6215	334	7	=	=	SYM
ejpam-6215	334	8	l[6y2	l[6y2	PROPN
ejpam-6215	334	9	]	]	X
ejpam-6215	335	1	+	+	PUNCT
ejpam-6215	335	2	l[x	l[x	PROPN
ejpam-6215	335	3	]	]	PUNCT
ejpam-6215	335	4	.	.	PUNCT
ejpam-6215	336	1	s2y	s2y	PROPN
ejpam-6215	336	2	(	(	PUNCT
ejpam-6215	336	3	s	s	NOUN
ejpam-6215	336	4	)	)	PUNCT
ejpam-6215	336	5	+	+	CCONJ
ejpam-6215	336	6	y(0)s−	y(0)s−	PROPN
ejpam-6215	336	7	y′(0	y′(0	PROPN
ejpam-6215	336	8	)	)	PUNCT
ejpam-6215	336	9	=	=	SYM
ejpam-6215	336	10	l[6y2	l[6y2	PROPN
ejpam-6215	336	11	]	]	X
ejpam-6215	337	1	+	+	PUNCT
ejpam-6215	337	2	l[x	l[x	PROPN
ejpam-6215	337	3	]	]	PUNCT
ejpam-6215	337	4	.	.	PUNCT
ejpam-6215	338	1	(	(	PUNCT
ejpam-6215	338	2	23	23	NUM
ejpam-6215	338	3	)	)	PUNCT
ejpam-6215	338	4	substituting	substitute	VERB
ejpam-6215	338	5	(	(	PUNCT
ejpam-6215	338	6	22	22	NUM
ejpam-6215	338	7	)	)	PUNCT
ejpam-6215	338	8	into	into	ADP
ejpam-6215	338	9	(	(	PUNCT
ejpam-6215	338	10	23	23	NUM
ejpam-6215	338	11	):	):	PUNCT
ejpam-6215	338	12	y	y	PROPN
ejpam-6215	338	13	(	(	PUNCT
ejpam-6215	338	14	s	s	NOUN
ejpam-6215	338	15	)	)	PUNCT
ejpam-6215	338	16	=	=	SYM
ejpam-6215	338	17	1	1	NUM
ejpam-6215	338	18	s2	s2	NOUN
ejpam-6215	338	19	+	+	CCONJ
ejpam-6215	338	20	1	1	NUM
ejpam-6215	338	21	s4	s4	NOUN
ejpam-6215	338	22	+	+	CCONJ
ejpam-6215	338	23	6	6	NUM
ejpam-6215	338	24	s2	s2	NOUN
ejpam-6215	338	25	l[y2	l[y2	VERB
ejpam-6215	338	26	]	]	PUNCT
ejpam-6215	338	27	.	.	PUNCT
ejpam-6215	339	1	(	(	PUNCT
ejpam-6215	339	2	24	24	NUM
ejpam-6215	339	3	)	)	PUNCT
ejpam-6215	339	4	taking	take	VERB
ejpam-6215	339	5	the	the	DET
ejpam-6215	339	6	inverse	inverse	NOUN
ejpam-6215	339	7	of	of	ADP
ejpam-6215	339	8	the	the	DET
ejpam-6215	339	9	laplace	laplace	NOUN
ejpam-6215	339	10	transform	transform	NOUN
ejpam-6215	339	11	l−1[y	l−1[y	X
ejpam-6215	339	12	(	(	PUNCT
ejpam-6215	339	13	s	s	NOUN
ejpam-6215	339	14	)	)	PUNCT
ejpam-6215	339	15	]	]	PUNCT
ejpam-6215	340	1	=	=	PUNCT
ejpam-6215	340	2	l−1	l−1	PROPN
ejpam-6215	340	3	[	[	PUNCT
ejpam-6215	340	4	1	1	NUM
ejpam-6215	340	5	s2	s2	NOUN
ejpam-6215	340	6	+	+	CCONJ
ejpam-6215	340	7	1	1	NUM
ejpam-6215	340	8	s4	s4	NOUN
ejpam-6215	340	9	+	+	CCONJ
ejpam-6215	340	10	6	6	NUM
ejpam-6215	340	11	s2	s2	NOUN
ejpam-6215	340	12	l[y2	l[y2	VERB
ejpam-6215	340	13	]	]	PUNCT
ejpam-6215	340	14	]	]	PUNCT
ejpam-6215	340	15	.	.	PUNCT
ejpam-6215	341	1	(	(	PUNCT
ejpam-6215	341	2	25	25	NUM
ejpam-6215	341	3	)	)	PUNCT
ejpam-6215	341	4	y(x	y(x	NOUN
ejpam-6215	341	5	)	)	PUNCT
ejpam-6215	342	1	=	=	SYM
ejpam-6215	342	2	x+	x+	PUNCT
ejpam-6215	343	1	x3	x3	ADJ
ejpam-6215	343	2	3	3	NUM
ejpam-6215	343	3	!	!	PUNCT
ejpam-6215	344	1	+	+	PUNCT
ejpam-6215	344	2	l−1	l−1	PROPN
ejpam-6215	344	3	[	[	PUNCT
ejpam-6215	344	4	6	6	NUM
ejpam-6215	344	5	s2	s2	NOUN
ejpam-6215	344	6	l[y2	l[y2	VERB
ejpam-6215	344	7	]	]	PUNCT
ejpam-6215	344	8	]	]	PUNCT
ejpam-6215	344	9	.	.	PUNCT
ejpam-6215	345	1	(	(	PUNCT
ejpam-6215	345	2	26	26	NUM
ejpam-6215	345	3	)	)	PUNCT
ejpam-6215	345	4	equation	equation	NOUN
ejpam-6215	345	5	(	(	PUNCT
ejpam-6215	345	6	26	26	NUM
ejpam-6215	345	7	)	)	PUNCT
ejpam-6215	345	8	can	can	AUX
ejpam-6215	345	9	be	be	AUX
ejpam-6215	345	10	written	write	VERB
ejpam-6215	345	11	as	as	ADP
ejpam-6215	345	12	y(x	y(x	NOUN
ejpam-6215	345	13	)	)	PUNCT
ejpam-6215	345	14	=	=	SYM
ejpam-6215	345	15	y0(x	y0(x	NOUN
ejpam-6215	345	16	)	)	PUNCT
ejpam-6215	346	1	+	+	CCONJ
ejpam-6215	346	2	l−1	l−1	PROPN
ejpam-6215	346	3	[	[	PUNCT
ejpam-6215	346	4	6	6	NUM
ejpam-6215	346	5	s2	s2	NOUN
ejpam-6215	346	6	l[an	l[an	PROPN
ejpam-6215	346	7	]	]	PUNCT
ejpam-6215	346	8	]	]	PUNCT
ejpam-6215	346	9	,	,	PUNCT
ejpam-6215	346	10	n	n	X
ejpam-6215	346	11	≥	≥	NOUN
ejpam-6215	346	12	0	0	NUM
ejpam-6215	346	13	(	(	PUNCT
ejpam-6215	346	14	27	27	NUM
ejpam-6215	346	15	)	)	PUNCT
ejpam-6215	346	16	y0(x	y0(x	NOUN
ejpam-6215	346	17	)	)	PUNCT
ejpam-6215	346	18	=	=	SYM
ejpam-6215	346	19	x+	x+	PUNCT
ejpam-6215	346	20	x3	x3	ADJ
ejpam-6215	346	21	3	3	NUM
ejpam-6215	346	22	!	!	PUNCT
ejpam-6215	346	23	.	.	PUNCT
ejpam-6215	347	1	from	from	ADP
ejpam-6215	347	2	(	(	PUNCT
ejpam-6215	347	3	27	27	NUM
ejpam-6215	347	4	)	)	PUNCT
ejpam-6215	347	5	,	,	PUNCT
ejpam-6215	347	6	we	we	PRON
ejpam-6215	347	7	conclude	conclude	VERB
ejpam-6215	347	8	that	that	PRON
ejpam-6215	347	9	yn+1(x	yn+1(x	NOUN
ejpam-6215	347	10	)	)	PUNCT
ejpam-6215	348	1	=	=	PUNCT
ejpam-6215	348	2	l−1	l−1	PROPN
ejpam-6215	348	3	[	[	PUNCT
ejpam-6215	348	4	6	6	NUM
ejpam-6215	348	5	s2	s2	NOUN
ejpam-6215	348	6	l[an	l[an	PROPN
ejpam-6215	348	7	]	]	PUNCT
ejpam-6215	348	8	]	]	PUNCT
ejpam-6215	348	9	,	,	PUNCT
ejpam-6215	348	10	n	n	X
ejpam-6215	348	11	≥	≥	NOUN
ejpam-6215	348	12	0	0	NUM
ejpam-6215	348	13	(	(	PUNCT
ejpam-6215	348	14	28	28	NUM
ejpam-6215	348	15	)	)	PUNCT
ejpam-6215	348	16	the	the	DET
ejpam-6215	348	17	terms	term	NOUN
ejpam-6215	348	18	becomes	become	VERB
ejpam-6215	348	19	y1(x	y1(x	NOUN
ejpam-6215	348	20	)	)	PUNCT
ejpam-6215	349	1	=	=	SYM
ejpam-6215	349	2	l−1	l−1	PROPN
ejpam-6215	349	3	[	[	PUNCT
ejpam-6215	349	4	6	6	NUM
ejpam-6215	349	5	s2	s2	NOUN
ejpam-6215	349	6	l[a0	l[a0	NOUN
ejpam-6215	349	7	]	]	PUNCT
ejpam-6215	349	8	]	]	PUNCT
ejpam-6215	349	9	.	.	PUNCT
ejpam-6215	350	1	y2(x	y2(x	X
ejpam-6215	350	2	)	)	PUNCT
ejpam-6215	350	3	=	=	SYM
ejpam-6215	350	4	l−1	l−1	PROPN
ejpam-6215	350	5	[	[	PUNCT
ejpam-6215	350	6	6	6	NUM
ejpam-6215	350	7	s2	s2	NOUN
ejpam-6215	350	8	l[a1	l[a1	VERB
ejpam-6215	350	9	]	]	PUNCT
ejpam-6215	350	10	]	]	PUNCT
ejpam-6215	350	11	.	.	PUNCT
ejpam-6215	351	1	y3(x	y3(x	X
ejpam-6215	351	2	)	)	PUNCT
ejpam-6215	351	3	=	=	SYM
ejpam-6215	351	4	l−1	l−1	PROPN
ejpam-6215	351	5	[	[	PUNCT
ejpam-6215	351	6	6	6	NUM
ejpam-6215	351	7	s2	s2	NOUN
ejpam-6215	351	8	l[a2	l[a2	NOUN
ejpam-6215	351	9	]	]	PUNCT
ejpam-6215	351	10	]	]	PUNCT
ejpam-6215	351	11	.	.	PUNCT
ejpam-6215	352	1	...	...	PUNCT
ejpam-6215	352	2	therefore	therefore	ADV
ejpam-6215	352	3	,	,	PUNCT
ejpam-6215	352	4	from	from	ADP
ejpam-6215	352	5	(	(	PUNCT
ejpam-6215	352	6	28	28	NUM
ejpam-6215	352	7	)	)	PUNCT
ejpam-6215	352	8	,	,	PUNCT
ejpam-6215	352	9	the	the	DET
ejpam-6215	352	10	other	other	ADJ
ejpam-6215	352	11	remaining	remain	VERB
ejpam-6215	352	12	terms	term	NOUN
ejpam-6215	352	13	of	of	ADP
ejpam-6215	352	14	the	the	DET
ejpam-6215	352	15	function	function	NOUN
ejpam-6215	352	16	y(x	y(x	NOUN
ejpam-6215	352	17	)	)	PUNCT
ejpam-6215	352	18	can	can	AUX
ejpam-6215	352	19	be	be	AUX
ejpam-6215	352	20	easily	easily	ADV
ejpam-6215	352	21	calculated	calculate	VERB
ejpam-6215	352	22	as	as	SCONJ
ejpam-6215	352	23	follows	follow	VERB
ejpam-6215	352	24	:	:	PUNCT
ejpam-6215	352	25	y0(x	y0(x	NUM
ejpam-6215	352	26	)	)	PUNCT
ejpam-6215	352	27	=	=	SYM
ejpam-6215	353	1	x+	x+	PUNCT
ejpam-6215	353	2	x3	x3	ADJ
ejpam-6215	353	3	3	3	NUM
ejpam-6215	353	4	!	!	PUNCT
ejpam-6215	353	5	.	.	PUNCT
ejpam-6215	354	1	s.	s.	PROPN
ejpam-6215	354	2	mohammed	mohammed	PROPN
ejpam-6215	354	3	,	,	PUNCT
ejpam-6215	354	4	s.	s.	PROPN
ejpam-6215	354	5	abid	abid	PROPN
ejpam-6215	354	6	,	,	PUNCT
ejpam-6215	354	7	r.	r.	PROPN
ejpam-6215	354	8	abid	abid	PROPN
ejpam-6215	354	9	/	/	SYM
ejpam-6215	354	10	eur	eur	PROPN
ejpam-6215	354	11	.	.	PUNCT
ejpam-6215	355	1	j.	j.	PROPN
ejpam-6215	355	2	pure	pure	PROPN
ejpam-6215	355	3	appl	appl	PROPN
ejpam-6215	355	4	.	.	PROPN
ejpam-6215	355	5	math	math	PROPN
ejpam-6215	355	6	,	,	PUNCT
ejpam-6215	355	7	18	18	NUM
ejpam-6215	355	8	(	(	PUNCT
ejpam-6215	355	9	3	3	NUM
ejpam-6215	355	10	)	)	PUNCT
ejpam-6215	355	11	(	(	PUNCT
ejpam-6215	355	12	2025	2025	NUM
ejpam-6215	355	13	)	)	PUNCT
ejpam-6215	355	14	,	,	PUNCT
ejpam-6215	355	15	6215	6215	NUM
ejpam-6215	355	16	17	17	NUM
ejpam-6215	355	17	of	of	ADP
ejpam-6215	355	18	38	38	NUM
ejpam-6215	355	19	y1(x	y1(x	NOUN
ejpam-6215	355	20	)	)	PUNCT
ejpam-6215	355	21	=	=	SYM
ejpam-6215	356	1	x4	x4	PROPN
ejpam-6215	356	2	2	2	NUM
ejpam-6215	356	3	+	+	CCONJ
ejpam-6215	356	4	x6	x6	PROPN
ejpam-6215	356	5	15	15	NUM
ejpam-6215	356	6	+	+	NUM
ejpam-6215	356	7	x8	x8	PROPN
ejpam-6215	356	8	336	336	NUM
ejpam-6215	356	9	.	.	PUNCT
ejpam-6215	357	1	y2(x	y2(x	X
ejpam-6215	357	2	)	)	PUNCT
ejpam-6215	357	3	=	=	PUNCT
ejpam-6215	358	1	x7	x7	NOUN
ejpam-6215	358	2	7	7	NUM
ejpam-6215	359	1	+	+	NUM
ejpam-6215	359	2	x9	x9	NOUN
ejpam-6215	359	3	40	40	NUM
ejpam-6215	359	4	+	+	CCONJ
ejpam-6215	359	5	71x11	71x11	NUM
ejpam-6215	359	6	46200	46200	NUM
ejpam-6215	359	7	+	+	CCONJ
ejpam-6215	359	8	x13	x13	PROPN
ejpam-6215	359	9	26208	26208	NUM
ejpam-6215	359	10	.	.	PUNCT
ejpam-6215	360	1	y3(x	y3(x	X
ejpam-6215	360	2	)	)	PUNCT
ejpam-6215	360	3	=	=	NOUN
ejpam-6215	360	4	x10	x10	NUM
ejpam-6215	360	5	28	28	NUM
ejpam-6215	360	6	+	+	CCONJ
ejpam-6215	360	7	23x12	23x12	NUM
ejpam-6215	360	8	3080	3080	NUM
ejpam-6215	360	9	+	+	CCONJ
ejpam-6215	360	10	5219x14	5219x14	NUM
ejpam-6215	360	11	8408400	8408400	NUM
ejpam-6215	361	1	+	+	CCONJ
ejpam-6215	361	2	3551x16	3551x16	NUM
ejpam-6215	361	3	1441440000	1441440000	NUM
ejpam-6215	361	4	+	+	CCONJ
ejpam-6215	361	5	95x18	95x18	NUM
ejpam-6215	361	6	224550144	224550144	NUM
ejpam-6215	361	7	.	.	PUNCT
ejpam-6215	362	1	y4(x	y4(x	X
ejpam-6215	362	2	)	)	PUNCT
ejpam-6215	362	3	=	=	PUNCT
ejpam-6215	363	1	3x13	3x13	NUM
ejpam-6215	363	2	364	364	NUM
ejpam-6215	363	3	+	+	CCONJ
ejpam-6215	363	4	131x15	131x15	NUM
ejpam-6215	363	5	64680	64680	NUM
ejpam-6215	363	6	+	+	CCONJ
ejpam-6215	363	7	19867x17	19867x17	NUM
ejpam-6215	363	8	95295200	95295200	NUM
ejpam-6215	364	1	+	+	CCONJ
ejpam-6215	364	2	163469x19	163469x19	NUM
ejpam-6215	364	3	14378364000	14378364000	NUM
ejpam-6215	364	4	+	+	CCONJ
ejpam-6215	364	5	163451x21	163451x21	NUM
ejpam-6215	364	6	491203440000	491203440000	NUM
ejpam-6215	364	7	+	+	CCONJ
ejpam-6215	364	8	31x23	31x23	NUM
ejpam-6215	364	9	7101398304	7101398304	NUM
ejpam-6215	364	10	.	.	PUNCT
ejpam-6215	364	11	...	...	PUNCT
ejpam-6215	365	1	y(x	y(x	X
ejpam-6215	365	2	)	)	PUNCT
ejpam-6215	366	1	=	=	PUNCT
ejpam-6215	366	2	∞∑	∞∑	PRON
ejpam-6215	366	3	n=0	n=0	NUM
ejpam-6215	366	4	yn(x	yn(x	NUM
ejpam-6215	366	5	)	)	PUNCT
ejpam-6215	366	6	.	.	PUNCT
ejpam-6215	367	1	(	(	PUNCT
ejpam-6215	367	2	29	29	NUM
ejpam-6215	367	3	)	)	PUNCT
ejpam-6215	367	4	y(x	y(x	NOUN
ejpam-6215	367	5	)	)	PUNCT
ejpam-6215	368	1	=	=	SYM
ejpam-6215	368	2	x+	x+	PUNCT
ejpam-6215	369	1	x3	x3	VERB
ejpam-6215	369	2	6	6	NUM
ejpam-6215	370	1	+	+	CCONJ
ejpam-6215	370	2	x4	x4	PROPN
ejpam-6215	370	3	2	2	NUM
ejpam-6215	370	4	+	+	CCONJ
ejpam-6215	370	5	x6	x6	PROPN
ejpam-6215	370	6	15	15	NUM
ejpam-6215	370	7	+	+	NUM
ejpam-6215	370	8	x8	x8	NOUN
ejpam-6215	370	9	336	336	NUM
ejpam-6215	370	10	+	+	CCONJ
ejpam-6215	370	11	x7	x7	NOUN
ejpam-6215	370	12	7	7	NUM
ejpam-6215	370	13	+	+	NUM
ejpam-6215	370	14	x9	x9	NOUN
ejpam-6215	370	15	40	40	NUM
ejpam-6215	370	16	+	+	CCONJ
ejpam-6215	370	17	71x11	71x11	NUM
ejpam-6215	370	18	46200	46200	NUM
ejpam-6215	370	19	+	+	CCONJ
ejpam-6215	370	20	x13	x13	PROPN
ejpam-6215	370	21	26208	26208	NUM
ejpam-6215	370	22	+	+	CCONJ
ejpam-6215	370	23	x10	x10	PROPN
ejpam-6215	370	24	28	28	NUM
ejpam-6215	370	25	.	.	PUNCT
ejpam-6215	370	26	.	.	PUNCT
ejpam-6215	370	27	.	.	PUNCT
ejpam-6215	371	1	+	+	CCONJ
ejpam-6215	371	2	23x12	23x12	NUM
ejpam-6215	371	3	3080	3080	NUM
ejpam-6215	371	4	+	+	CCONJ
ejpam-6215	371	5	5219x14	5219x14	NUM
ejpam-6215	371	6	8408400	8408400	NUM
ejpam-6215	372	1	+	+	CCONJ
ejpam-6215	372	2	3551x16	3551x16	NUM
ejpam-6215	372	3	1441440000	1441440000	NUM
ejpam-6215	372	4	+	+	CCONJ
ejpam-6215	372	5	95x18	95x18	NUM
ejpam-6215	372	6	224550144	224550144	NUM
ejpam-6215	372	7	+	+	CCONJ
ejpam-6215	372	8	3x13	3x13	NUM
ejpam-6215	372	9	364	364	NUM
ejpam-6215	372	10	+	+	CCONJ
ejpam-6215	372	11	131x15	131x15	NUM
ejpam-6215	372	12	64680	64680	NUM
ejpam-6215	372	13	.	.	PUNCT
ejpam-6215	372	14	.	.	PUNCT
ejpam-6215	372	15	.	.	PUNCT
ejpam-6215	373	1	+	+	CCONJ
ejpam-6215	373	2	19867x17	19867x17	NUM
ejpam-6215	373	3	95295200	95295200	NUM
ejpam-6215	374	1	+	+	CCONJ
ejpam-6215	374	2	163469x19	163469x19	NUM
ejpam-6215	374	3	14378364000	14378364000	NUM
ejpam-6215	374	4	+	+	CCONJ
ejpam-6215	374	5	163451x21	163451x21	NUM
ejpam-6215	374	6	491203440000	491203440000	NUM
ejpam-6215	375	1	+	+	CCONJ
ejpam-6215	375	2	31x23	31x23	NUM
ejpam-6215	375	3	7101398304	7101398304	NUM
ejpam-6215	375	4	+	+	NUM
ejpam-6215	375	5	·	·	PUNCT
ejpam-6215	375	6	·	·	PUNCT
ejpam-6215	375	7	·	·	PUNCT
ejpam-6215	376	1	the	the	DET
ejpam-6215	376	2	remainder	remainder	NOUN
ejpam-6215	376	3	function	function	NOUN
ejpam-6215	376	4	of	of	ADP
ejpam-6215	376	5	error	error	NOUN
ejpam-6215	376	6	is	be	AUX
ejpam-6215	376	7	evaluated	evaluate	VERB
ejpam-6215	376	8	:	:	PUNCT
ejpam-6215	376	9	ern	ern	PROPN
ejpam-6215	376	10	=	=	PUNCT
ejpam-6215	376	11	y′′n(x)−	y′′n(x)−	PROPN
ejpam-6215	376	12	6y2n(x)−	6y2n(x)−	NUM
ejpam-6215	376	13	x.	x.	NOUN
ejpam-6215	376	14	mern	mern	PROPN
ejpam-6215	376	15	=	=	PUNCT
ejpam-6215	376	16	max	max	PROPN
ejpam-6215	376	17	0.01≤x≤0.1	0.01≤x≤0.1	NUM
ejpam-6215	377	1	|ern(x)|	|ern(x)|	NOUN
ejpam-6215	377	2	.	.	PUNCT
ejpam-6215	378	1	in	in	ADP
ejpam-6215	378	2	table	table	NOUN
ejpam-6215	378	3	5	5	NUM
ejpam-6215	378	4	and	and	CCONJ
ejpam-6215	378	5	figure	figure	VERB
ejpam-6215	378	6	5	5	NUM
ejpam-6215	378	7	show	show	VERB
ejpam-6215	378	8	the	the	DET
ejpam-6215	378	9	convergence	convergence	NOUN
ejpam-6215	378	10	of	of	ADP
ejpam-6215	378	11	the	the	DET
ejpam-6215	378	12	solution	solution	NOUN
ejpam-6215	378	13	using	use	VERB
ejpam-6215	378	14	mern	mern	NOUN
ejpam-6215	378	15	against	against	ADP
ejpam-6215	378	16	n	n	PROPN
ejpam-6215	378	17	for	for	ADP
ejpam-6215	378	18	the	the	DET
ejpam-6215	378	19	first	first	ADJ
ejpam-6215	378	20	painlevé	painlevé	NOUN
ejpam-6215	378	21	equation	equation	NOUN
ejpam-6215	378	22	by	by	ADP
ejpam-6215	378	23	ldm	ldm	PROPN
ejpam-6215	378	24	,	,	PUNCT
ejpam-6215	378	25	the	the	DET
ejpam-6215	378	26	plot	plot	NOUN
ejpam-6215	378	27	demonstrates	demonstrate	VERB
ejpam-6215	378	28	the	the	DET
ejpam-6215	378	29	rapid	rapid	ADJ
ejpam-6215	378	30	decrease	decrease	NOUN
ejpam-6215	378	31	in	in	ADP
ejpam-6215	378	32	error	error	NOUN
ejpam-6215	378	33	with	with	ADP
ejpam-6215	378	34	increasing	increase	VERB
ejpam-6215	378	35	n	n	CCONJ
ejpam-6215	378	36	,	,	PUNCT
ejpam-6215	378	37	confirming	confirm	VERB
ejpam-6215	378	38	the	the	DET
ejpam-6215	378	39	convergence	convergence	NOUN
ejpam-6215	378	40	of	of	ADP
ejpam-6215	378	41	the	the	DET
ejpam-6215	378	42	laplace	laplace	NOUN
ejpam-6215	378	43	decomposition	decomposition	NOUN
ejpam-6215	378	44	method	method	NOUN
ejpam-6215	378	45	(	(	PUNCT
ejpam-6215	378	46	ldm	ldm	NOUN
ejpam-6215	378	47	)	)	PUNCT
ejpam-6215	378	48	.	.	PUNCT
ejpam-6215	379	1	the	the	DET
ejpam-6215	379	2	nearly	nearly	ADV
ejpam-6215	379	3	linear	linear	ADJ
ejpam-6215	379	4	trend	trend	NOUN
ejpam-6215	379	5	in	in	ADP
ejpam-6215	379	6	the	the	DET
ejpam-6215	379	7	logarithmic	logarithmic	ADJ
ejpam-6215	379	8	scale	scale	NOUN
ejpam-6215	379	9	indicates	indicate	VERB
ejpam-6215	379	10	an	an	DET
ejpam-6215	379	11	exponential	exponential	ADJ
ejpam-6215	379	12	decay	decay	NOUN
ejpam-6215	379	13	of	of	ADP
ejpam-6215	379	14	the	the	DET
ejpam-6215	379	15	maximum	maximum	ADJ
ejpam-6215	379	16	residual	residual	ADJ
ejpam-6215	379	17	error	error	NOUN
ejpam-6215	379	18	,	,	PUNCT
ejpam-6215	379	19	showcasing	showcase	VERB
ejpam-6215	379	20	the	the	DET
ejpam-6215	379	21	method	method	NOUN
ejpam-6215	379	22	’s	’s	PART
ejpam-6215	379	23	high	high	ADJ
ejpam-6215	379	24	accuracy	accuracy	NOUN
ejpam-6215	379	25	and	and	CCONJ
ejpam-6215	379	26	efficiency	efficiency	NOUN
ejpam-6215	379	27	.	.	PUNCT
ejpam-6215	380	1	table	table	NOUN
ejpam-6215	380	2	5	5	NUM
ejpam-6215	380	3	:	:	PUNCT
ejpam-6215	380	4	the	the	DET
ejpam-6215	380	5	maximum	maximum	ADJ
ejpam-6215	380	6	residual	residual	ADJ
ejpam-6215	380	7	error	error	NOUN
ejpam-6215	380	8	:	:	PUNCT
ejpam-6215	380	9	mern	mern	NOUN
ejpam-6215	380	10	by	by	ADP
ejpam-6215	380	11	the	the	DET
ejpam-6215	380	12	ldm	ldm	NOUN
ejpam-6215	380	13	,	,	PUNCT
ejpam-6215	380	14	where	where	SCONJ
ejpam-6215	380	15	n	n	NOUN
ejpam-6215	380	16	=	=	SYM
ejpam-6215	380	17	1	1	NUM
ejpam-6215	380	18	,	,	PUNCT
ejpam-6215	380	19	.	.	PUNCT
ejpam-6215	380	20	.	.	PUNCT
ejpam-6215	381	1	.	.	PUNCT
ejpam-6215	382	1	,	,	PUNCT
ejpam-6215	382	2	5	5	X
ejpam-6215	382	3	.	.	X
ejpam-6215	383	1	n	n	PRON
ejpam-6215	383	2	mern	mern	ADJ
ejpam-6215	383	3	1	1	NUM
ejpam-6215	383	4	0.0000601952	0.0000601952	NUM
ejpam-6215	383	5	2	2	NUM
ejpam-6215	383	6	3.22501×	3.22501×	NUM
ejpam-6215	383	7	10−8	10−8	NUM
ejpam-6215	383	8	3	3	NUM
ejpam-6215	383	9	1.29031×	1.29031×	NUM
ejpam-6215	383	10	10−11	10−11	NUM
ejpam-6215	383	11	4	4	NUM
ejpam-6215	383	12	4.4062×	4.4062×	NOUN
ejpam-6215	383	13	10−15	10−15	NOUN
ejpam-6215	383	14	5	5	NUM
ejpam-6215	383	15	6.93889×	6.93889×	NUM
ejpam-6215	383	16	10−18	10−18	PROPN
ejpam-6215	383	17	s.	s.	PROPN
ejpam-6215	383	18	mohammed	mohammed	PROPN
ejpam-6215	383	19	,	,	PUNCT
ejpam-6215	383	20	s.	s.	PROPN
ejpam-6215	383	21	abid	abid	PROPN
ejpam-6215	383	22	,	,	PUNCT
ejpam-6215	383	23	r.	r.	PROPN
ejpam-6215	383	24	abid	abid	PROPN
ejpam-6215	383	25	/	/	SYM
ejpam-6215	383	26	eur	eur	PROPN
ejpam-6215	383	27	.	.	PUNCT
ejpam-6215	384	1	j.	j.	PROPN
ejpam-6215	384	2	pure	pure	PROPN
ejpam-6215	384	3	appl	appl	PROPN
ejpam-6215	384	4	.	.	PROPN
ejpam-6215	384	5	math	math	PROPN
ejpam-6215	384	6	,	,	PUNCT
ejpam-6215	384	7	18	18	NUM
ejpam-6215	384	8	(	(	PUNCT
ejpam-6215	384	9	3	3	NUM
ejpam-6215	384	10	)	)	PUNCT
ejpam-6215	384	11	(	(	PUNCT
ejpam-6215	384	12	2025	2025	NUM
ejpam-6215	384	13	)	)	PUNCT
ejpam-6215	384	14	,	,	PUNCT
ejpam-6215	384	15	6215	6215	NUM
ejpam-6215	384	16	18	18	NUM
ejpam-6215	384	17	of	of	ADP
ejpam-6215	384	18	38	38	NUM
ejpam-6215	384	19	figure	figure	NOUN
ejpam-6215	384	20	5	5	NUM
ejpam-6215	384	21	:	:	PUNCT
ejpam-6215	384	22	logarithmic	logarithmic	ADJ
ejpam-6215	384	23	plot	plot	NOUN
ejpam-6215	384	24	of	of	ADP
ejpam-6215	384	25	mern	mern	ADJ
ejpam-6215	384	26	(	(	PUNCT
ejpam-6215	384	27	ldm	ldm	PROPN
ejpam-6215	384	28	,	,	PUNCT
ejpam-6215	384	29	first	first	ADV
ejpam-6215	384	30	painlevé	painlevé	NOUN
ejpam-6215	384	31	equation	equation	NOUN
ejpam-6215	384	32	)	)	PUNCT
ejpam-6215	384	33	.	.	PUNCT
ejpam-6215	385	1	2.3.2	2.3.2	X
ejpam-6215	385	2	.	.	PUNCT
ejpam-6215	386	1	the	the	DET
ejpam-6215	386	2	ldm	ldm	NOUN
ejpam-6215	386	3	for	for	ADP
ejpam-6215	386	4	solving	solve	VERB
ejpam-6215	386	5	painlevé	painlevé	NOUN
ejpam-6215	386	6	equation	equation	NOUN
ejpam-6215	386	7	ii	ii	PROPN
ejpam-6215	386	8	rewrite	rewrite	PROPN
ejpam-6215	386	9	(	(	PUNCT
ejpam-6215	386	10	2	2	NUM
ejpam-6215	386	11	)	)	PUNCT
ejpam-6215	386	12	y′′(x	y′′(x	NOUN
ejpam-6215	386	13	)	)	PUNCT
ejpam-6215	386	14	=	=	SYM
ejpam-6215	387	1	2y3	2y3	NUM
ejpam-6215	387	2	+	+	CCONJ
ejpam-6215	387	3	xy	xy	PROPN
ejpam-6215	387	4	+	+	NUM
ejpam-6215	387	5	µ.	µ.	NOUN
ejpam-6215	387	6	(	(	PUNCT
ejpam-6215	387	7	30	30	NUM
ejpam-6215	387	8	)	)	PUNCT
ejpam-6215	387	9	the	the	DET
ejpam-6215	387	10	initial	initial	ADJ
ejpam-6215	387	11	conditions	condition	NOUN
ejpam-6215	387	12	:	:	PUNCT
ejpam-6215	387	13	y(0	y(0	NOUN
ejpam-6215	387	14	)	)	PUNCT
ejpam-6215	387	15	=	=	SYM
ejpam-6215	387	16	1	1	NUM
ejpam-6215	387	17	,	,	PUNCT
ejpam-6215	387	18	y′(0	y′(0	NOUN
ejpam-6215	387	19	)	)	PUNCT
ejpam-6215	387	20	=	=	SYM
ejpam-6215	387	21	0	0	X
ejpam-6215	387	22	.	.	PUNCT
ejpam-6215	388	1	(	(	PUNCT
ejpam-6215	388	2	31	31	NUM
ejpam-6215	388	3	)	)	PUNCT
ejpam-6215	388	4	now	now	ADV
ejpam-6215	388	5	,	,	PUNCT
ejpam-6215	388	6	apply	apply	VERB
ejpam-6215	388	7	laplace	laplace	NOUN
ejpam-6215	388	8	transform	transform	NOUN
ejpam-6215	388	9	on	on	ADP
ejpam-6215	388	10	both	both	DET
ejpam-6215	388	11	sides	side	NOUN
ejpam-6215	388	12	of	of	ADP
ejpam-6215	388	13	(	(	PUNCT
ejpam-6215	388	14	30	30	NUM
ejpam-6215	388	15	)	)	PUNCT
ejpam-6215	388	16	.	.	PUNCT
ejpam-6215	389	1	with	with	ADP
ejpam-6215	389	2	initial	initial	ADJ
ejpam-6215	389	3	conditions	condition	NOUN
ejpam-6215	389	4	:	:	PUNCT
ejpam-6215	389	5	l[y′′	l[y′′	ADV
ejpam-6215	389	6	]	]	PUNCT
ejpam-6215	389	7	=	=	PUNCT
ejpam-6215	390	1	l[2y3	l[2y3	NOUN
ejpam-6215	390	2	+	+	CCONJ
ejpam-6215	390	3	xy	xy	PROPN
ejpam-6215	390	4	+	+	X
ejpam-6215	390	5	µ	µ	X
ejpam-6215	390	6	]	]	X
ejpam-6215	390	7	.	.	PUNCT
ejpam-6215	391	1	y′′	y′′	NOUN
ejpam-6215	391	2	=	=	SYM
ejpam-6215	391	3	s2y	s2y	PROPN
ejpam-6215	391	4	(	(	PUNCT
ejpam-6215	391	5	s)−	s)−	PROPN
ejpam-6215	391	6	sy(0)−	sy(0)−	NOUN
ejpam-6215	391	7	y′(0	y′(0	NOUN
ejpam-6215	391	8	)	)	PUNCT
ejpam-6215	391	9	.	.	PUNCT
ejpam-6215	392	1	(	(	PUNCT
ejpam-6215	392	2	32	32	NUM
ejpam-6215	392	3	)	)	PUNCT
ejpam-6215	392	4	substituting	substitute	VERB
ejpam-6215	392	5	(	(	PUNCT
ejpam-6215	392	6	31	31	NUM
ejpam-6215	392	7	)	)	PUNCT
ejpam-6215	392	8	into	into	ADP
ejpam-6215	392	9	(	(	PUNCT
ejpam-6215	392	10	32	32	NUM
ejpam-6215	392	11	)	)	PUNCT
ejpam-6215	392	12	,	,	PUNCT
ejpam-6215	392	13	we	we	PRON
ejpam-6215	392	14	have	have	VERB
ejpam-6215	392	15	:	:	PUNCT
ejpam-6215	392	16	s2y	s2y	PROPN
ejpam-6215	392	17	(	(	PUNCT
ejpam-6215	392	18	s)−	s)−	PROPN
ejpam-6215	392	19	s	s	PART
ejpam-6215	392	20	=	=	X
ejpam-6215	392	21	l[2y3	l[2y3	PROPN
ejpam-6215	392	22	]	]	PUNCT
ejpam-6215	393	1	+	+	CCONJ
ejpam-6215	393	2	l[xy	l[xy	X
ejpam-6215	393	3	]	]	X
ejpam-6215	393	4	+	+	NUM
ejpam-6215	393	5	l[µ	l[µ	PROPN
ejpam-6215	393	6	]	]	PUNCT
ejpam-6215	393	7	.	.	PUNCT
ejpam-6215	394	1	(	(	PUNCT
ejpam-6215	394	2	33	33	NUM
ejpam-6215	394	3	)	)	PUNCT
ejpam-6215	394	4	y	y	PROPN
ejpam-6215	394	5	(	(	PUNCT
ejpam-6215	394	6	s	s	NOUN
ejpam-6215	394	7	)	)	PUNCT
ejpam-6215	394	8	=	=	SYM
ejpam-6215	395	1	1	1	NUM
ejpam-6215	395	2	s	s	PART
ejpam-6215	395	3	+	+	CCONJ
ejpam-6215	395	4	1	1	NUM
ejpam-6215	395	5	s2	s2	NOUN
ejpam-6215	395	6	l[2y3	l[2y3	NOUN
ejpam-6215	395	7	]	]	PUNCT
ejpam-6215	396	1	+	+	CCONJ
ejpam-6215	396	2	1	1	NUM
ejpam-6215	396	3	s2	s2	NOUN
ejpam-6215	396	4	l[xy	l[xy	X
ejpam-6215	396	5	]	]	X
ejpam-6215	396	6	+	+	NUM
ejpam-6215	396	7	µ	µ	X
ejpam-6215	396	8	s3	s3	NOUN
ejpam-6215	396	9	.	.	PUNCT
ejpam-6215	397	1	(	(	PUNCT
ejpam-6215	397	2	34	34	NUM
ejpam-6215	397	3	)	)	PUNCT
ejpam-6215	397	4	equation	equation	NOUN
ejpam-6215	397	5	(	(	PUNCT
ejpam-6215	397	6	34	34	NUM
ejpam-6215	397	7	)	)	PUNCT
ejpam-6215	397	8	becomes	become	VERB
ejpam-6215	397	9	:	:	PUNCT
ejpam-6215	397	10	l−1[y	l−1[y	X
ejpam-6215	397	11	(	(	PUNCT
ejpam-6215	397	12	s	s	NOUN
ejpam-6215	397	13	)	)	PUNCT
ejpam-6215	397	14	]	]	PUNCT
ejpam-6215	398	1	=	=	PUNCT
ejpam-6215	398	2	l−1	l−1	PROPN
ejpam-6215	398	3	[	[	PUNCT
ejpam-6215	398	4	1	1	NUM
ejpam-6215	398	5	s	s	PART
ejpam-6215	398	6	+	+	NUM
ejpam-6215	398	7	1	1	NUM
ejpam-6215	398	8	s2	s2	NOUN
ejpam-6215	398	9	l[2y3	l[2y3	NOUN
ejpam-6215	398	10	]	]	PUNCT
ejpam-6215	399	1	+	+	CCONJ
ejpam-6215	399	2	1	1	NUM
ejpam-6215	399	3	s2	s2	NOUN
ejpam-6215	399	4	l[xy	l[xy	X
ejpam-6215	399	5	]	]	X
ejpam-6215	399	6	+	+	NUM
ejpam-6215	399	7	µ	µ	X
ejpam-6215	399	8	s3	s3	NOUN
ejpam-6215	399	9	]	]	PUNCT
ejpam-6215	399	10	.	.	PUNCT
ejpam-6215	400	1	l−1[y	l−1[y	VERB
ejpam-6215	400	2	(	(	PUNCT
ejpam-6215	400	3	s	s	NOUN
ejpam-6215	400	4	)	)	PUNCT
ejpam-6215	400	5	]	]	PUNCT
ejpam-6215	401	1	=	=	PUNCT
ejpam-6215	401	2	l−1	l−1	PROPN
ejpam-6215	401	3	[	[	PUNCT
ejpam-6215	401	4	1	1	NUM
ejpam-6215	401	5	s	s	PART
ejpam-6215	401	6	+	+	NUM
ejpam-6215	401	7	µ	µ	X
ejpam-6215	401	8	s3	s3	NOUN
ejpam-6215	401	9	+	+	CCONJ
ejpam-6215	401	10	1	1	NUM
ejpam-6215	401	11	s2	s2	NOUN
ejpam-6215	401	12	l[2y3	l[2y3	NOUN
ejpam-6215	401	13	+	+	CCONJ
ejpam-6215	401	14	xy	xy	X
ejpam-6215	401	15	]	]	X
ejpam-6215	401	16	]	]	PUNCT
ejpam-6215	401	17	.	.	PUNCT
ejpam-6215	402	1	(	(	PUNCT
ejpam-6215	402	2	35	35	NUM
ejpam-6215	402	3	)	)	PUNCT
ejpam-6215	402	4	y(x	y(x	NOUN
ejpam-6215	402	5	)	)	PUNCT
ejpam-6215	402	6	=	=	SYM
ejpam-6215	403	1	1	1	NUM
ejpam-6215	403	2	+	+	CCONJ
ejpam-6215	403	3	x2µ	x2µ	PROPN
ejpam-6215	403	4	2	2	NUM
ejpam-6215	404	1	+	+	X
ejpam-6215	404	2	l−1	l−1	PROPN
ejpam-6215	404	3	[	[	PUNCT
ejpam-6215	404	4	1	1	NUM
ejpam-6215	404	5	s2	s2	NOUN
ejpam-6215	404	6	l[an	l[an	PROPN
ejpam-6215	404	7	]	]	PUNCT
ejpam-6215	404	8	]	]	PUNCT
ejpam-6215	404	9	.	.	PUNCT
ejpam-6215	405	1	(	(	PUNCT
ejpam-6215	405	2	36	36	NUM
ejpam-6215	405	3	)	)	PUNCT
ejpam-6215	405	4	y0(x	y0(x	NOUN
ejpam-6215	405	5	)	)	PUNCT
ejpam-6215	405	6	=	=	SYM
ejpam-6215	406	1	1	1	NUM
ejpam-6215	406	2	+	+	CCONJ
ejpam-6215	406	3	x2µ	x2µ	PROPN
ejpam-6215	406	4	2	2	NUM
ejpam-6215	406	5	.	.	PUNCT
ejpam-6215	407	1	s.	s.	PROPN
ejpam-6215	407	2	mohammed	mohammed	PROPN
ejpam-6215	407	3	,	,	PUNCT
ejpam-6215	407	4	s.	s.	PROPN
ejpam-6215	407	5	abid	abid	PROPN
ejpam-6215	407	6	,	,	PUNCT
ejpam-6215	407	7	r.	r.	PROPN
ejpam-6215	407	8	abid	abid	PROPN
ejpam-6215	407	9	/	/	SYM
ejpam-6215	407	10	eur	eur	PROPN
ejpam-6215	407	11	.	.	PUNCT
ejpam-6215	408	1	j.	j.	PROPN
ejpam-6215	408	2	pure	pure	PROPN
ejpam-6215	408	3	appl	appl	PROPN
ejpam-6215	408	4	.	.	PROPN
ejpam-6215	408	5	math	math	PROPN
ejpam-6215	408	6	,	,	PUNCT
ejpam-6215	408	7	18	18	NUM
ejpam-6215	408	8	(	(	PUNCT
ejpam-6215	408	9	3	3	NUM
ejpam-6215	408	10	)	)	PUNCT
ejpam-6215	408	11	(	(	PUNCT
ejpam-6215	408	12	2025	2025	NUM
ejpam-6215	408	13	)	)	PUNCT
ejpam-6215	408	14	,	,	PUNCT
ejpam-6215	408	15	6215	6215	NUM
ejpam-6215	408	16	19	19	NUM
ejpam-6215	408	17	of	of	ADP
ejpam-6215	408	18	38	38	NUM
ejpam-6215	408	19	from	from	ADP
ejpam-6215	408	20	(	(	PUNCT
ejpam-6215	408	21	36	36	NUM
ejpam-6215	408	22	)	)	PUNCT
ejpam-6215	408	23	we	we	PRON
ejpam-6215	408	24	conclude	conclude	VERB
ejpam-6215	408	25	that	that	PRON
ejpam-6215	408	26	:	:	PUNCT
ejpam-6215	408	27	yn+1(x	yn+1(x	NOUN
ejpam-6215	408	28	)	)	PUNCT
ejpam-6215	409	1	=	=	PUNCT
ejpam-6215	409	2	l−1	l−1	PROPN
ejpam-6215	409	3	[	[	PUNCT
ejpam-6215	409	4	1	1	NUM
ejpam-6215	409	5	s2	s2	NOUN
ejpam-6215	409	6	l[an	l[an	PROPN
ejpam-6215	409	7	]	]	PUNCT
ejpam-6215	409	8	]	]	PUNCT
ejpam-6215	409	9	,	,	PUNCT
ejpam-6215	409	10	n	n	X
ejpam-6215	409	11	≥	≥	NOUN
ejpam-6215	409	12	0	0	NUM
ejpam-6215	409	13	.	.	PUNCT
ejpam-6215	410	1	then	then	ADV
ejpam-6215	410	2	y1(x	y1(x	NOUN
ejpam-6215	410	3	)	)	PUNCT
ejpam-6215	410	4	=	=	SYM
ejpam-6215	410	5	l−1	l−1	PROPN
ejpam-6215	410	6	[	[	PUNCT
ejpam-6215	410	7	1	1	NUM
ejpam-6215	410	8	s2	s2	NOUN
ejpam-6215	410	9	l[a0	l[a0	NOUN
ejpam-6215	410	10	]	]	PUNCT
ejpam-6215	410	11	]	]	PUNCT
ejpam-6215	410	12	.	.	PUNCT
ejpam-6215	411	1	a0	a0	NOUN
ejpam-6215	411	2	=	=	SYM
ejpam-6215	411	3	f	f	PROPN
ejpam-6215	411	4	(	(	PUNCT
ejpam-6215	411	5	y0	y0	PROPN
ejpam-6215	411	6	)	)	PUNCT
ejpam-6215	411	7	.	.	PUNCT
ejpam-6215	412	1	f	f	PROPN
ejpam-6215	412	2	(	(	PUNCT
ejpam-6215	412	3	y	y	NOUN
ejpam-6215	412	4	)	)	PUNCT
ejpam-6215	412	5	=	=	SYM
ejpam-6215	412	6	2y3	2y3	NUM
ejpam-6215	413	1	+	+	CCONJ
ejpam-6215	413	2	xy	xy	NOUN
ejpam-6215	413	3	.	.	PUNCT
ejpam-6215	414	1	y1(x	y1(x	NOUN
ejpam-6215	414	2	)	)	PUNCT
ejpam-6215	414	3	=	=	SYM
ejpam-6215	414	4	l−1	l−1	PROPN
ejpam-6215	414	5	[	[	PUNCT
ejpam-6215	414	6	1	1	NUM
ejpam-6215	414	7	s2	s2	NOUN
ejpam-6215	414	8	l[2y30	l[2y30	PUNCT
ejpam-6215	415	1	+	+	CCONJ
ejpam-6215	416	1	xy0	xy0	X
ejpam-6215	416	2	]	]	X
ejpam-6215	416	3	]	]	PUNCT
ejpam-6215	416	4	.	.	PUNCT
ejpam-6215	417	1	y1(x	y1(x	X
ejpam-6215	417	2	)	)	PUNCT
ejpam-6215	417	3	=	=	SYM
ejpam-6215	417	4	l−1	l−1	PROPN
ejpam-6215	417	5	[	[	PUNCT
ejpam-6215	417	6	2	2	NUM
ejpam-6215	417	7	s3	s3	NOUN
ejpam-6215	417	8	+	+	CCONJ
ejpam-6215	417	9	1	1	NUM
ejpam-6215	417	10	s4	s4	NOUN
ejpam-6215	417	11	+	+	CCONJ
ejpam-6215	417	12	3(2!)µ	3(2!)µ	NUM
ejpam-6215	417	13	s5	s5	NOUN
ejpam-6215	417	14	+	+	CCONJ
ejpam-6215	417	15	3!µ	3!µ	NUM
ejpam-6215	417	16	2	2	NUM
ejpam-6215	417	17	s6	s6	NOUN
ejpam-6215	417	18	+	+	CCONJ
ejpam-6215	417	19	3(4!)µ2	3(4!)µ2	NUM
ejpam-6215	417	20	2	2	NUM
ejpam-6215	417	21	s7	s7	NOUN
ejpam-6215	417	22	+	+	CCONJ
ejpam-6215	417	23	6!µ3	6!µ3	NUM
ejpam-6215	417	24	4	4	NUM
ejpam-6215	417	25	s9	s9	NOUN
ejpam-6215	417	26	]	]	PUNCT
ejpam-6215	417	27	.	.	PUNCT
ejpam-6215	418	1	y1(x	y1(x	X
ejpam-6215	418	2	)	)	PUNCT
ejpam-6215	418	3	=	=	SYM
ejpam-6215	419	1	x2	x2	PROPN
ejpam-6215	420	1	+	+	CCONJ
ejpam-6215	420	2	x3	x3	ADJ
ejpam-6215	420	3	6	6	NUM
ejpam-6215	421	1	+	+	CCONJ
ejpam-6215	421	2	x4µ	x4µ	PROPN
ejpam-6215	421	3	4	4	NUM
ejpam-6215	421	4	+	+	NUM
ejpam-6215	421	5	x5µ	x5µ	NOUN
ejpam-6215	421	6	40	40	NUM
ejpam-6215	422	1	+	+	CCONJ
ejpam-6215	422	2	x6µ2	x6µ2	PROPN
ejpam-6215	422	3	20	20	NUM
ejpam-6215	422	4	+	+	CCONJ
ejpam-6215	422	5	x8µ3	x8µ3	PROPN
ejpam-6215	422	6	224	224	NUM
ejpam-6215	422	7	.	.	PUNCT
ejpam-6215	423	1	a1	a1	NOUN
ejpam-6215	423	2	=	=	SYM
ejpam-6215	423	3	2x3	2x3	NUM
ejpam-6215	423	4	+	+	CCONJ
ejpam-6215	423	5	x4	x4	PROPN
ejpam-6215	423	6	2	2	NUM
ejpam-6215	423	7	+	+	NUM
ejpam-6215	423	8	x5	x5	NOUN
ejpam-6215	423	9	30	30	NUM
ejpam-6215	423	10	+	+	NUM
ejpam-6215	423	11	3x5µ	3x5µ	NOUN
ejpam-6215	423	12	4	4	NUM
ejpam-6215	423	13	+	+	CCONJ
ejpam-6215	423	14	7x6µ	7x6µ	NOUN
ejpam-6215	423	15	30	30	NUM
ejpam-6215	424	1	+	+	CCONJ
ejpam-6215	424	2	x7µ	x7µ	X
ejpam-6215	424	3	280	280	NUM
ejpam-6215	425	1	+	+	CCONJ
ejpam-6215	425	2	33x7µ2	33x7µ2	PROPN
ejpam-6215	425	3	70	70	NUM
ejpam-6215	425	4	.	.	PUNCT
ejpam-6215	425	5	.	.	PUNCT
ejpam-6215	425	6	.	.	PUNCT
ejpam-6215	426	1	+	+	CCONJ
ejpam-6215	426	2	9x8µ2	9x8µ2	NOUN
ejpam-6215	426	3	160	160	NUM
ejpam-6215	426	4	+	+	SYM
ejpam-6215	426	5	131x9µ3	131x9µ3	NUM
ejpam-6215	426	6	1680	1680	NUM
ejpam-6215	426	7	+	+	CCONJ
ejpam-6215	426	8	47x10µ3	47x10µ3	NOUN
ejpam-6215	426	9	11200	11200	NUM
ejpam-6215	426	10	+	+	CCONJ
ejpam-6215	426	11	57x11µ4	57x11µ4	NUM
ejpam-6215	426	12	6160	6160	NUM
ejpam-6215	426	13	+	+	CCONJ
ejpam-6215	426	14	3x13µ5	3x13µ5	NUM
ejpam-6215	426	15	5824	5824	NUM
ejpam-6215	426	16	.	.	PUNCT
ejpam-6215	427	1	y2(x	y2(x	X
ejpam-6215	427	2	)	)	PUNCT
ejpam-6215	427	3	=	=	SYM
ejpam-6215	427	4	l−1	l−1	PROPN
ejpam-6215	427	5	[	[	PUNCT
ejpam-6215	427	6	1	1	NUM
ejpam-6215	427	7	s2	s2	NOUN
ejpam-6215	427	8	l[a1	l[a1	VERB
ejpam-6215	427	9	]	]	PUNCT
ejpam-6215	427	10	]	]	PUNCT
ejpam-6215	427	11	.	.	PUNCT
ejpam-6215	428	1	y2(x	y2(x	X
ejpam-6215	428	2	)	)	PUNCT
ejpam-6215	428	3	=	=	SYM
ejpam-6215	428	4	x4	x4	PROPN
ejpam-6215	428	5	2	2	NUM
ejpam-6215	428	6	+	+	NUM
ejpam-6215	428	7	x5	x5	NOUN
ejpam-6215	428	8	10	10	NUM
ejpam-6215	428	9	+	+	NUM
ejpam-6215	428	10	x6	x6	PROPN
ejpam-6215	428	11	180	180	NUM
ejpam-6215	428	12	+	+	CCONJ
ejpam-6215	428	13	x6µ	x6µ	PROPN
ejpam-6215	428	14	4	4	NUM
ejpam-6215	428	15	+	+	CCONJ
ejpam-6215	428	16	x7µ	x7µ	PROPN
ejpam-6215	428	17	30	30	NUM
ejpam-6215	428	18	+	+	NUM
ejpam-6215	428	19	x8µ	x8µ	PROPN
ejpam-6215	428	20	2240	2240	NUM
ejpam-6215	428	21	+	+	CCONJ
ejpam-6215	428	22	33x8µ2	33x8µ2	NUM
ejpam-6215	428	23	560	560	NUM
ejpam-6215	428	24	.	.	PUNCT
ejpam-6215	428	25	.	.	PUNCT
ejpam-6215	428	26	.	.	PUNCT
ejpam-6215	429	1	+	+	CCONJ
ejpam-6215	430	1	x9µ2	x9µ2	X
ejpam-6215	431	1	160	160	NUM
ejpam-6215	431	2	+	+	CCONJ
ejpam-6215	431	3	131x10µ3	131x10µ3	NUM
ejpam-6215	431	4	16800	16800	NUM
ejpam-6215	431	5	+	+	CCONJ
ejpam-6215	431	6	47x11µ3	47x11µ3	NUM
ejpam-6215	431	7	123200	123200	NUM
ejpam-6215	431	8	+	+	CCONJ
ejpam-6215	431	9	19x12µ4	19x12µ4	PROPN
ejpam-6215	431	10	24640	24640	NUM
ejpam-6215	431	11	+	+	CCONJ
ejpam-6215	431	12	3x14µ5	3x14µ5	NUM
ejpam-6215	431	13	81536	81536	NUM
ejpam-6215	431	14	.	.	PUNCT
ejpam-6215	431	15	...	...	PUNCT
ejpam-6215	432	1	y(x	y(x	X
ejpam-6215	432	2	)	)	PUNCT
ejpam-6215	433	1	=	=	PUNCT
ejpam-6215	433	2	∞∑	∞∑	PRON
ejpam-6215	433	3	n=0	n=0	NUM
ejpam-6215	433	4	yn(x	yn(x	NUM
ejpam-6215	433	5	)	)	PUNCT
ejpam-6215	433	6	.	.	PUNCT
ejpam-6215	434	1	y(x	y(x	NOUN
ejpam-6215	434	2	)	)	PUNCT
ejpam-6215	434	3	=	=	SYM
ejpam-6215	434	4	1	1	NUM
ejpam-6215	434	5	+	+	CCONJ
ejpam-6215	434	6	x2µ	x2µ	PROPN
ejpam-6215	434	7	2	2	NUM
ejpam-6215	435	1	+	+	CCONJ
ejpam-6215	435	2	x2	x2	PROPN
ejpam-6215	436	1	+	+	CCONJ
ejpam-6215	436	2	x3	x3	ADJ
ejpam-6215	436	3	6	6	NUM
ejpam-6215	437	1	+	+	CCONJ
ejpam-6215	437	2	x4µ	x4µ	PROPN
ejpam-6215	437	3	4	4	NUM
ejpam-6215	437	4	+	+	NUM
ejpam-6215	437	5	x5µ	x5µ	NOUN
ejpam-6215	437	6	40	40	NUM
ejpam-6215	438	1	+	+	CCONJ
ejpam-6215	438	2	x6µ2	x6µ2	PROPN
ejpam-6215	438	3	20	20	NUM
ejpam-6215	438	4	+	+	CCONJ
ejpam-6215	438	5	x8µ3	x8µ3	SYM
ejpam-6215	438	6	224	224	NUM
ejpam-6215	438	7	+	+	CCONJ
ejpam-6215	438	8	x4	x4	PROPN
ejpam-6215	438	9	2	2	NUM
ejpam-6215	438	10	.	.	PUNCT
ejpam-6215	438	11	.	.	PUNCT
ejpam-6215	438	12	.	.	PUNCT
ejpam-6215	439	1	+	+	PUNCT
ejpam-6215	439	2	x5	x5	NOUN
ejpam-6215	439	3	10	10	NUM
ejpam-6215	439	4	+	+	NUM
ejpam-6215	439	5	x6	x6	PROPN
ejpam-6215	439	6	180	180	NUM
ejpam-6215	439	7	+	+	CCONJ
ejpam-6215	439	8	x6µ	x6µ	PROPN
ejpam-6215	439	9	4	4	NUM
ejpam-6215	439	10	+	+	CCONJ
ejpam-6215	439	11	x7µ	x7µ	PROPN
ejpam-6215	439	12	30	30	NUM
ejpam-6215	439	13	+	+	NUM
ejpam-6215	439	14	x8µ	x8µ	PROPN
ejpam-6215	439	15	2240	2240	NUM
ejpam-6215	439	16	+	+	CCONJ
ejpam-6215	439	17	33x8µ2	33x8µ2	NUM
ejpam-6215	439	18	560	560	NUM
ejpam-6215	439	19	+	+	CCONJ
ejpam-6215	439	20	x9µ2	x9µ2	X
ejpam-6215	439	21	160	160	NUM
ejpam-6215	439	22	.	.	PUNCT
ejpam-6215	439	23	.	.	PUNCT
ejpam-6215	439	24	.	.	PUNCT
ejpam-6215	440	1	+	+	CCONJ
ejpam-6215	440	2	131x10µ3	131x10µ3	ADJ
ejpam-6215	440	3	16800	16800	NUM
ejpam-6215	440	4	+	+	CCONJ
ejpam-6215	440	5	47x11µ3	47x11µ3	NUM
ejpam-6215	440	6	123200	123200	NUM
ejpam-6215	441	1	+	+	CCONJ
ejpam-6215	441	2	19x12µ4	19x12µ4	PROPN
ejpam-6215	441	3	24640	24640	NUM
ejpam-6215	441	4	+	+	CCONJ
ejpam-6215	441	5	3x14µ5	3x14µ5	NUM
ejpam-6215	441	6	81536	81536	NUM
ejpam-6215	441	7	+	+	CCONJ
ejpam-6215	441	8	·	·	PUNCT
ejpam-6215	441	9	·	·	PUNCT
ejpam-6215	441	10	·	·	PUNCT
ejpam-6215	441	11	s.	s.	PROPN
ejpam-6215	441	12	mohammed	mohammed	PROPN
ejpam-6215	441	13	,	,	PUNCT
ejpam-6215	441	14	s.	s.	PROPN
ejpam-6215	441	15	abid	abid	PROPN
ejpam-6215	441	16	,	,	PUNCT
ejpam-6215	441	17	r.	r.	PROPN
ejpam-6215	441	18	abid	abid	PROPN
ejpam-6215	441	19	/	/	SYM
ejpam-6215	441	20	eur	eur	PROPN
ejpam-6215	441	21	.	.	PUNCT
ejpam-6215	442	1	j.	j.	PROPN
ejpam-6215	442	2	pure	pure	PROPN
ejpam-6215	442	3	appl	appl	PROPN
ejpam-6215	442	4	.	.	PROPN
ejpam-6215	442	5	math	math	PROPN
ejpam-6215	442	6	,	,	PUNCT
ejpam-6215	442	7	18	18	NUM
ejpam-6215	442	8	(	(	PUNCT
ejpam-6215	442	9	3	3	NUM
ejpam-6215	442	10	)	)	PUNCT
ejpam-6215	442	11	(	(	PUNCT
ejpam-6215	442	12	2025	2025	NUM
ejpam-6215	442	13	)	)	PUNCT
ejpam-6215	442	14	,	,	PUNCT
ejpam-6215	442	15	6215	6215	NUM
ejpam-6215	442	16	20	20	NUM
ejpam-6215	442	17	of	of	ADP
ejpam-6215	442	18	38	38	NUM
ejpam-6215	442	19	the	the	DET
ejpam-6215	442	20	remainder	remainder	NOUN
ejpam-6215	442	21	function	function	NOUN
ejpam-6215	442	22	of	of	ADP
ejpam-6215	442	23	error	error	NOUN
ejpam-6215	442	24	is	be	AUX
ejpam-6215	442	25	evaluated	evaluate	VERB
ejpam-6215	442	26	:	:	PUNCT
ejpam-6215	443	1	ern	ern	PROPN
ejpam-6215	443	2	=	=	PUNCT
ejpam-6215	443	3	y′′n(x)−	y′′n(x)−	PROPN
ejpam-6215	444	1	2y3n(x)−	2y3n(x)−	PROPN
ejpam-6215	444	2	xyn(x)−	xyn(x)−	PROPN
ejpam-6215	444	3	µ.	µ.	NOUN
ejpam-6215	444	4	and	and	CCONJ
ejpam-6215	444	5	the	the	DET
ejpam-6215	444	6	mern	mern	NOUN
ejpam-6215	444	7	is	be	AUX
ejpam-6215	444	8	:	:	PUNCT
ejpam-6215	444	9	mern	mern	ADJ
ejpam-6215	444	10	=	=	SYM
ejpam-6215	444	11	max	max	PROPN
ejpam-6215	444	12	0.01≤x≤0.1	0.01≤x≤0.1	NUM
ejpam-6215	445	1	|ern(x)|	|ern(x)|	NOUN
ejpam-6215	445	2	.	.	PUNCT
ejpam-6215	446	1	in	in	ADP
ejpam-6215	446	2	table	table	NOUN
ejpam-6215	446	3	6	6	NUM
ejpam-6215	446	4	and	and	CCONJ
ejpam-6215	446	5	figure	figure	VERB
ejpam-6215	446	6	6	6	NUM
ejpam-6215	446	7	show	show	VERB
ejpam-6215	446	8	the	the	DET
ejpam-6215	446	9	convergence	convergence	NOUN
ejpam-6215	446	10	of	of	ADP
ejpam-6215	446	11	the	the	DET
ejpam-6215	446	12	solution	solution	NOUN
ejpam-6215	446	13	using	use	VERB
ejpam-6215	446	14	mern	mern	NOUN
ejpam-6215	446	15	against	against	ADP
ejpam-6215	446	16	n	n	PROPN
ejpam-6215	446	17	for	for	ADP
ejpam-6215	446	18	the	the	DET
ejpam-6215	446	19	second	second	ADJ
ejpam-6215	446	20	painlevé	painlevé	NOUN
ejpam-6215	446	21	equation	equation	NOUN
ejpam-6215	446	22	by	by	ADP
ejpam-6215	446	23	ldm	ldm	PROPN
ejpam-6215	446	24	.	.	PUNCT
ejpam-6215	447	1	the	the	DET
ejpam-6215	447	2	data	data	NOUN
ejpam-6215	447	3	shows	show	VERB
ejpam-6215	447	4	a	a	DET
ejpam-6215	447	5	clear	clear	ADJ
ejpam-6215	447	6	trend	trend	NOUN
ejpam-6215	447	7	of	of	ADP
ejpam-6215	447	8	rapid	rapid	ADJ
ejpam-6215	447	9	error	error	NOUN
ejpam-6215	447	10	reduction	reduction	NOUN
ejpam-6215	447	11	as	as	ADP
ejpam-6215	447	12	n	n	DET
ejpam-6215	447	13	increases	increase	NOUN
ejpam-6215	447	14	.	.	PUNCT
ejpam-6215	448	1	initially	initially	ADV
ejpam-6215	448	2	,	,	PUNCT
ejpam-6215	448	3	at	at	ADP
ejpam-6215	448	4	n	n	NOUN
ejpam-6215	448	5	=	=	SYM
ejpam-6215	448	6	1	1	NUM
ejpam-6215	448	7	,	,	PUNCT
ejpam-6215	448	8	the	the	DET
ejpam-6215	448	9	error	error	NOUN
ejpam-6215	448	10	is	be	AUX
ejpam-6215	448	11	relatively	relatively	ADV
ejpam-6215	448	12	large	large	ADJ
ejpam-6215	448	13	at	at	ADP
ejpam-6215	448	14	0.0634125	0.0634125	NUM
ejpam-6215	448	15	.	.	PUNCT
ejpam-6215	449	1	however	however	ADV
ejpam-6215	449	2	,	,	PUNCT
ejpam-6215	449	3	as	as	SCONJ
ejpam-6215	449	4	n	n	PRON
ejpam-6215	449	5	increases	increase	NOUN
ejpam-6215	449	6	to	to	ADP
ejpam-6215	449	7	2	2	NUM
ejpam-6215	449	8	and	and	CCONJ
ejpam-6215	449	9	3	3	NUM
ejpam-6215	449	10	,	,	PUNCT
ejpam-6215	449	11	the	the	DET
ejpam-6215	449	12	error	error	NOUN
ejpam-6215	449	13	drops	drop	VERB
ejpam-6215	449	14	significantly	significantly	ADV
ejpam-6215	449	15	,	,	PUNCT
ejpam-6215	449	16	and	and	CCONJ
ejpam-6215	449	17	at	at	ADP
ejpam-6215	449	18	n	n	NOUN
ejpam-6215	449	19	=	=	SYM
ejpam-6215	449	20	5	5	NUM
ejpam-6215	449	21	,	,	PUNCT
ejpam-6215	449	22	it	it	PRON
ejpam-6215	449	23	reaches	reach	VERB
ejpam-6215	449	24	an	an	DET
ejpam-6215	449	25	extremely	extremely	ADV
ejpam-6215	449	26	small	small	ADJ
ejpam-6215	449	27	value	value	NOUN
ejpam-6215	449	28	of	of	ADP
ejpam-6215	449	29	8.40300×	8.40300×	NOUN
ejpam-6215	449	30	10−10	10−10	NUM
ejpam-6215	449	31	.	.	PUNCT
ejpam-6215	450	1	this	this	DET
ejpam-6215	450	2	exponential	exponential	ADJ
ejpam-6215	450	3	decrease	decrease	NOUN
ejpam-6215	450	4	in	in	ADP
ejpam-6215	450	5	error	error	NOUN
ejpam-6215	450	6	suggests	suggest	VERB
ejpam-6215	450	7	that	that	SCONJ
ejpam-6215	450	8	the	the	DET
ejpam-6215	450	9	ldm	ldm	NOUN
ejpam-6215	450	10	exhibits	exhibit	VERB
ejpam-6215	450	11	fast	fast	ADJ
ejpam-6215	450	12	convergence	convergence	NOUN
ejpam-6215	450	13	,	,	PUNCT
ejpam-6215	450	14	making	make	VERB
ejpam-6215	450	15	it	it	PRON
ejpam-6215	450	16	a	a	DET
ejpam-6215	450	17	highly	highly	ADV
ejpam-6215	450	18	effective	effective	ADJ
ejpam-6215	450	19	method	method	NOUN
ejpam-6215	450	20	for	for	ADP
ejpam-6215	450	21	solving	solve	VERB
ejpam-6215	450	22	the	the	DET
ejpam-6215	450	23	second	second	ADJ
ejpam-6215	450	24	painlevé	painlevé	NOUN
ejpam-6215	450	25	equation	equation	NOUN
ejpam-6215	450	26	with	with	ADP
ejpam-6215	450	27	high	high	ADJ
ejpam-6215	450	28	accuracy	accuracy	NOUN
ejpam-6215	450	29	.	.	PUNCT
ejpam-6215	451	1	table	table	NOUN
ejpam-6215	451	2	6	6	NUM
ejpam-6215	451	3	:	:	PUNCT
ejpam-6215	451	4	the	the	DET
ejpam-6215	451	5	maximum	maximum	ADJ
ejpam-6215	451	6	residual	residual	ADJ
ejpam-6215	451	7	error	error	NOUN
ejpam-6215	451	8	:	:	PUNCT
ejpam-6215	451	9	mern	mern	NOUN
ejpam-6215	451	10	by	by	ADP
ejpam-6215	451	11	the	the	DET
ejpam-6215	451	12	ldm	ldm	NOUN
ejpam-6215	451	13	,	,	PUNCT
ejpam-6215	451	14	where	where	SCONJ
ejpam-6215	451	15	n	n	NOUN
ejpam-6215	451	16	=	=	SYM
ejpam-6215	451	17	1	1	NUM
ejpam-6215	451	18	,	,	PUNCT
ejpam-6215	451	19	.	.	PUNCT
ejpam-6215	451	20	.	.	PUNCT
ejpam-6215	452	1	.	.	PUNCT
ejpam-6215	453	1	,	,	PUNCT
ejpam-6215	453	2	5	5	X
ejpam-6215	453	3	.	.	X
ejpam-6215	454	1	n	n	PRON
ejpam-6215	454	2	mern	mern	ADJ
ejpam-6215	454	3	1	1	NUM
ejpam-6215	454	4	0.0634125	0.0634125	NUM
ejpam-6215	454	5	2	2	NUM
ejpam-6215	454	6	0.000950605	0.000950605	NUM
ejpam-6215	454	7	3	3	NUM
ejpam-6215	454	8	0.00001041	0.00001041	NUM
ejpam-6215	454	9	4	4	NUM
ejpam-6215	454	10	9.77952×	9.77952×	NOUN
ejpam-6215	454	11	10−8	10−8	NUM
ejpam-6215	454	12	5	5	NUM
ejpam-6215	454	13	8.40300×	8.40300×	NUM
ejpam-6215	454	14	10−10	10−10	NUM
ejpam-6215	454	15	figure	figure	NOUN
ejpam-6215	454	16	6	6	NUM
ejpam-6215	454	17	:	:	PUNCT
ejpam-6215	454	18	logarithmic	logarithmic	ADJ
ejpam-6215	454	19	plot	plot	NOUN
ejpam-6215	454	20	of	of	ADP
ejpam-6215	454	21	mern	mern	ADJ
ejpam-6215	454	22	(	(	PUNCT
ejpam-6215	454	23	ldm	ldm	NOUN
ejpam-6215	454	24	,	,	PUNCT
ejpam-6215	454	25	second	second	ADJ
ejpam-6215	454	26	painlevé	painlevé	NOUN
ejpam-6215	454	27	equation	equation	NOUN
ejpam-6215	454	28	)	)	PUNCT
ejpam-6215	454	29	.	.	PUNCT
ejpam-6215	455	1	2.4	2.4	NUM
ejpam-6215	455	2	.	.	PUNCT
ejpam-6215	455	3	natural	natural	ADJ
ejpam-6215	455	4	decomposition	decomposition	NOUN
ejpam-6215	455	5	method	method	NOUN
ejpam-6215	455	6	(	(	PUNCT
ejpam-6215	455	7	ndm	ndm	PROPN
ejpam-6215	455	8	)	)	PUNCT
ejpam-6215	455	9	the	the	DET
ejpam-6215	455	10	natural	natural	ADJ
ejpam-6215	455	11	decomposition	decomposition	NOUN
ejpam-6215	455	12	method	method	NOUN
ejpam-6215	455	13	(	(	PUNCT
ejpam-6215	455	14	ndm	ndm	PROPN
ejpam-6215	455	15	)	)	PUNCT
ejpam-6215	455	16	was	be	AUX
ejpam-6215	455	17	developed	develop	VERB
ejpam-6215	455	18	in	in	ADP
ejpam-6215	455	19	the	the	DET
ejpam-6215	455	20	early	early	ADJ
ejpam-6215	455	21	21st	21st	ADJ
ejpam-6215	455	22	century	century	NOUN
ejpam-6215	455	23	as	as	ADP
ejpam-6215	455	24	an	an	DET
ejpam-6215	455	25	advancement	advancement	NOUN
ejpam-6215	455	26	in	in	ADP
ejpam-6215	455	27	analytical	analytical	ADJ
ejpam-6215	455	28	techniques	technique	NOUN
ejpam-6215	455	29	for	for	ADP
ejpam-6215	455	30	solving	solve	VERB
ejpam-6215	455	31	nonlinear	nonlinear	ADJ
ejpam-6215	455	32	differential	differential	ADJ
ejpam-6215	455	33	equations	equation	NOUN
ejpam-6215	455	34	.	.	PUNCT
ejpam-6215	456	1	research	research	NOUN
ejpam-6215	456	2	on	on	ADP
ejpam-6215	456	3	ndm	ndm	PROPN
ejpam-6215	456	4	began	begin	VERB
ejpam-6215	456	5	appearing	appear	VERB
ejpam-6215	456	6	in	in	ADP
ejpam-6215	456	7	mathematical	mathematical	ADJ
ejpam-6215	456	8	literature	literature	NOUN
ejpam-6215	456	9	in	in	ADP
ejpam-6215	456	10	the	the	DET
ejpam-6215	456	11	2000s	2000	NOUN
ejpam-6215	456	12	and	and	CCONJ
ejpam-6215	456	13	2010s	2010	NOUN
ejpam-6215	456	14	as	as	ADP
ejpam-6215	456	15	an	an	DET
ejpam-6215	456	16	improvement	improvement	NOUN
ejpam-6215	456	17	over	over	ADP
ejpam-6215	456	18	existing	exist	VERB
ejpam-6215	456	19	decomposition	decomposition	NOUN
ejpam-6215	456	20	methods	method	NOUN
ejpam-6215	456	21	[	[	X
ejpam-6215	456	22	11	11	NUM
ejpam-6215	456	23	,	,	PUNCT
ejpam-6215	456	24	12	12	NUM
ejpam-6215	456	25	]	]	PUNCT
ejpam-6215	456	26	.	.	PUNCT
ejpam-6215	457	1	it	it	PRON
ejpam-6215	457	2	was	be	AUX
ejpam-6215	457	3	introduced	introduce	VERB
ejpam-6215	457	4	to	to	PART
ejpam-6215	457	5	enhance	enhance	VERB
ejpam-6215	457	6	the	the	DET
ejpam-6215	457	7	accuracy	accuracy	NOUN
ejpam-6215	457	8	and	and	CCONJ
ejpam-6215	457	9	convergence	convergence	NOUN
ejpam-6215	457	10	of	of	ADP
ejpam-6215	457	11	solutions	solution	NOUN
ejpam-6215	457	12	for	for	ADP
ejpam-6215	457	13	highly	highly	ADV
ejpam-6215	457	14	nonlinear	nonlinear	ADJ
ejpam-6215	457	15	problems	problem	NOUN
ejpam-6215	457	16	without	without	ADP
ejpam-6215	457	17	requiring	require	VERB
ejpam-6215	457	18	linearization	linearization	NOUN
ejpam-6215	457	19	or	or	CCONJ
ejpam-6215	457	20	perturbation	perturbation	NOUN
ejpam-6215	457	21	.	.	PUNCT
ejpam-6215	458	1	since	since	SCONJ
ejpam-6215	458	2	its	its	PRON
ejpam-6215	458	3	introduction	introduction	NOUN
ejpam-6215	458	4	,	,	PUNCT
ejpam-6215	458	5	ndm	ndm	PROPN
ejpam-6215	458	6	has	have	AUX
ejpam-6215	458	7	been	be	AUX
ejpam-6215	458	8	applied	apply	VERB
ejpam-6215	458	9	to	to	ADP
ejpam-6215	458	10	s.	s.	PROPN
ejpam-6215	458	11	mohammed	mohammed	PROPN
ejpam-6215	458	12	,	,	PUNCT
ejpam-6215	458	13	s.	s.	PROPN
ejpam-6215	458	14	abid	abid	PROPN
ejpam-6215	458	15	,	,	PUNCT
ejpam-6215	458	16	r.	r.	PROPN
ejpam-6215	458	17	abid	abid	PROPN
ejpam-6215	458	18	/	/	SYM
ejpam-6215	458	19	eur	eur	PROPN
ejpam-6215	458	20	.	.	PUNCT
ejpam-6215	459	1	j.	j.	PROPN
ejpam-6215	459	2	pure	pure	PROPN
ejpam-6215	459	3	appl	appl	PROPN
ejpam-6215	459	4	.	.	PROPN
ejpam-6215	459	5	math	math	PROPN
ejpam-6215	459	6	,	,	PUNCT
ejpam-6215	459	7	18	18	NUM
ejpam-6215	459	8	(	(	PUNCT
ejpam-6215	459	9	3	3	NUM
ejpam-6215	459	10	)	)	PUNCT
ejpam-6215	459	11	(	(	PUNCT
ejpam-6215	459	12	2025	2025	NUM
ejpam-6215	459	13	)	)	PUNCT
ejpam-6215	459	14	,	,	PUNCT
ejpam-6215	459	15	6215	6215	NUM
ejpam-6215	459	16	21	21	NUM
ejpam-6215	459	17	of	of	ADP
ejpam-6215	459	18	38	38	NUM
ejpam-6215	459	19	various	various	ADJ
ejpam-6215	459	20	fields	field	NOUN
ejpam-6215	459	21	,	,	PUNCT
ejpam-6215	459	22	including	include	VERB
ejpam-6215	459	23	fluid	fluid	ADJ
ejpam-6215	459	24	dynamics	dynamic	NOUN
ejpam-6215	459	25	,	,	PUNCT
ejpam-6215	459	26	mathematical	mathematical	ADJ
ejpam-6215	459	27	physics	physics	NOUN
ejpam-6215	459	28	,	,	PUNCT
ejpam-6215	459	29	and	and	CCONJ
ejpam-6215	459	30	engineering	engineering	NOUN
ejpam-6215	459	31	.	.	PUNCT
ejpam-6215	460	1	in	in	ADP
ejpam-6215	460	2	this	this	DET
ejpam-6215	460	3	subsection	subsection	NOUN
ejpam-6215	460	4	we	we	PRON
ejpam-6215	460	5	use	use	VERB
ejpam-6215	460	6	ndm	ndm	PROPN
ejpam-6215	460	7	to	to	ADP
ejpam-6215	460	8	solving	solve	VERB
ejpam-6215	460	9	painlevé	painlevé	NOUN
ejpam-6215	460	10	equations	equation	NOUN
ejpam-6215	460	11	i	i	PRON
ejpam-6215	460	12	and	and	CCONJ
ejpam-6215	460	13	ii	ii	NOUN
ejpam-6215	460	14	.	.	PUNCT
ejpam-6215	461	1	[	[	X
ejpam-6215	461	2	39–41	39–41	NUM
ejpam-6215	461	3	]	]	PUNCT
ejpam-6215	461	4	.	.	PUNCT
ejpam-6215	462	1	2.4.1	2.4.1	NUM
ejpam-6215	462	2	.	.	PUNCT
ejpam-6215	463	1	the	the	DET
ejpam-6215	463	2	ndm	ndm	NOUN
ejpam-6215	463	3	for	for	ADP
ejpam-6215	463	4	solving	solve	VERB
ejpam-6215	463	5	the	the	DET
ejpam-6215	463	6	painlevé	painlevé	NOUN
ejpam-6215	463	7	i	i	PRON
ejpam-6215	463	8	differential	differential	VERB
ejpam-6215	463	9	equation	equation	NOUN
ejpam-6215	463	10	rewrite	rewrite	VERB
ejpam-6215	463	11	[	[	X
ejpam-6215	463	12	1	1	NUM
ejpam-6215	463	13	]	]	SYM
ejpam-6215	463	14	y′′(x	y′′(x	NOUN
ejpam-6215	463	15	)	)	PUNCT
ejpam-6215	463	16	=	=	PUNCT
ejpam-6215	463	17	6y2	6y2	NUM
ejpam-6215	463	18	+	+	CCONJ
ejpam-6215	463	19	x.	x.	NOUN
ejpam-6215	463	20	(	(	PUNCT
ejpam-6215	463	21	37	37	NUM
ejpam-6215	463	22	)	)	PUNCT
ejpam-6215	463	23	y(0	y(0	PROPN
ejpam-6215	463	24	)	)	PUNCT
ejpam-6215	463	25	=	=	SYM
ejpam-6215	463	26	0	0	NUM
ejpam-6215	463	27	,	,	PUNCT
ejpam-6215	463	28	y′(0	y′(0	NOUN
ejpam-6215	463	29	)	)	PUNCT
ejpam-6215	463	30	=	=	SYM
ejpam-6215	464	1	1	1	X
ejpam-6215	464	2	.	.	PUNCT
ejpam-6215	464	3	(	(	PUNCT
ejpam-6215	464	4	38	38	NUM
ejpam-6215	464	5	)	)	PUNCT
ejpam-6215	464	6	by	by	ADP
ejpam-6215	464	7	applying	apply	VERB
ejpam-6215	464	8	the	the	DET
ejpam-6215	464	9	n	n	CCONJ
ejpam-6215	464	10	-	-	PUNCT
ejpam-6215	464	11	transform	transform	NOUN
ejpam-6215	464	12	on	on	ADP
ejpam-6215	464	13	both	both	DET
ejpam-6215	464	14	sides	side	NOUN
ejpam-6215	464	15	of	of	ADP
ejpam-6215	464	16	(	(	PUNCT
ejpam-6215	464	17	37	37	NUM
ejpam-6215	464	18	):	):	PUNCT
ejpam-6215	464	19	n+	n+	X
ejpam-6215	464	20	[	[	PUNCT
ejpam-6215	464	21	y′′(x	y′′(x	NOUN
ejpam-6215	464	22	)	)	PUNCT
ejpam-6215	464	23	]	]	PUNCT
ejpam-6215	465	1	=	=	SYM
ejpam-6215	465	2	n+	n+	X
ejpam-6215	465	3	[	[	PUNCT
ejpam-6215	465	4	6y2	6y2	NUM
ejpam-6215	465	5	+	+	NOUN
ejpam-6215	465	6	x	x	X
ejpam-6215	465	7	]	]	PUNCT
ejpam-6215	465	8	.	.	PUNCT
ejpam-6215	466	1	(	(	PUNCT
ejpam-6215	466	2	39	39	NUM
ejpam-6215	466	3	)	)	PUNCT
ejpam-6215	466	4	using	use	VERB
ejpam-6215	466	5	the	the	DET
ejpam-6215	466	6	properties	property	NOUN
ejpam-6215	466	7	of	of	ADP
ejpam-6215	466	8	n	n	CCONJ
ejpam-6215	466	9	-	-	PUNCT
ejpam-6215	466	10	transform	transform	VERB
ejpam-6215	466	11	we	we	PRON
ejpam-6215	466	12	obtain	obtain	VERB
ejpam-6215	466	13	that	that	PRON
ejpam-6215	466	14	s2	s2	VERB
ejpam-6215	466	15	t2	t2	PROPN
ejpam-6215	466	16	y(s	y(s	PROPN
ejpam-6215	466	17	,	,	PUNCT
ejpam-6215	466	18	t)−	t)−	PROPN
ejpam-6215	466	19	s	s	PART
ejpam-6215	466	20	t2	t2	NOUN
ejpam-6215	466	21	y(0)−	y(0)−	PROPN
ejpam-6215	466	22	1	1	NUM
ejpam-6215	466	23	t	t	NOUN
ejpam-6215	466	24	y′(0	y′(0	NOUN
ejpam-6215	466	25	)	)	PUNCT
ejpam-6215	466	26	=	=	SYM
ejpam-6215	466	27	n+[6y2	n+[6y2	NOUN
ejpam-6215	466	28	]	]	X
ejpam-6215	466	29	+	+	NUM
ejpam-6215	466	30	t	t	PROPN
ejpam-6215	466	31	s2	s2	NOUN
ejpam-6215	466	32	.	.	PUNCT
ejpam-6215	467	1	(	(	PUNCT
ejpam-6215	467	2	40	40	NUM
ejpam-6215	467	3	)	)	PUNCT
ejpam-6215	467	4	substituting	substitute	VERB
ejpam-6215	467	5	(	(	PUNCT
ejpam-6215	467	6	38	38	NUM
ejpam-6215	467	7	)	)	PUNCT
ejpam-6215	467	8	into	into	ADP
ejpam-6215	467	9	(	(	PUNCT
ejpam-6215	467	10	40	40	NUM
ejpam-6215	467	11	)	)	PUNCT
ejpam-6215	467	12	,	,	PUNCT
ejpam-6215	467	13	we	we	PRON
ejpam-6215	467	14	have	have	VERB
ejpam-6215	467	15	y(s	y(s	PROPN
ejpam-6215	467	16	,	,	PUNCT
ejpam-6215	467	17	t	t	PROPN
ejpam-6215	467	18	)	)	PUNCT
ejpam-6215	467	19	=	=	SYM
ejpam-6215	467	20	t	t	PROPN
ejpam-6215	467	21	s2	s2	NOUN
ejpam-6215	467	22	+	+	CCONJ
ejpam-6215	467	23	t3	t3	PROPN
ejpam-6215	467	24	s4	s4	PROPN
ejpam-6215	467	25	+	+	CCONJ
ejpam-6215	467	26	t2	t2	PROPN
ejpam-6215	467	27	s2	s2	NOUN
ejpam-6215	467	28	n+[6y2	n+[6y2	NOUN
ejpam-6215	467	29	]	]	PUNCT
ejpam-6215	467	30	.	.	PUNCT
ejpam-6215	468	1	(	(	PUNCT
ejpam-6215	468	2	41	41	NUM
ejpam-6215	468	3	)	)	PUNCT
ejpam-6215	468	4	now	now	ADV
ejpam-6215	468	5	,	,	PUNCT
ejpam-6215	468	6	applying	apply	VERB
ejpam-6215	468	7	the	the	DET
ejpam-6215	468	8	inverse	inverse	NOUN
ejpam-6215	468	9	of	of	ADP
ejpam-6215	468	10	n	n	X
ejpam-6215	468	11	-	-	PUNCT
ejpam-6215	468	12	transform	transform	NOUN
ejpam-6215	468	13	,	,	PUNCT
ejpam-6215	468	14	we	we	PRON
ejpam-6215	468	15	have	have	AUX
ejpam-6215	468	16	n−1[y(s	n−1[y(	VERB
ejpam-6215	468	17	,	,	PUNCT
ejpam-6215	468	18	t	t	PROPN
ejpam-6215	468	19	)	)	PUNCT
ejpam-6215	468	20	]	]	PUNCT
ejpam-6215	469	1	=	=	PUNCT
ejpam-6215	469	2	n−1	n−1	PROPN
ejpam-6215	469	3	[	[	PUNCT
ejpam-6215	469	4	t	t	NOUN
ejpam-6215	469	5	s2	s2	NOUN
ejpam-6215	469	6	+	+	CCONJ
ejpam-6215	469	7	t3	t3	PROPN
ejpam-6215	469	8	s4	s4	PROPN
ejpam-6215	469	9	+	+	CCONJ
ejpam-6215	469	10	6t2	6t2	NUM
ejpam-6215	469	11	s2	s2	NOUN
ejpam-6215	469	12	n+[y2	n+[y2	PROPN
ejpam-6215	469	13	]	]	PUNCT
ejpam-6215	469	14	]	]	PUNCT
ejpam-6215	469	15	.	.	PUNCT
ejpam-6215	470	1	(	(	PUNCT
ejpam-6215	470	2	42	42	NUM
ejpam-6215	470	3	)	)	PUNCT
ejpam-6215	470	4	equation	equation	NOUN
ejpam-6215	470	5	(	(	PUNCT
ejpam-6215	470	6	42	42	NUM
ejpam-6215	470	7	)	)	PUNCT
ejpam-6215	470	8	becomes	become	VERB
ejpam-6215	470	9	y(x	y(x	NOUN
ejpam-6215	470	10	)	)	PUNCT
ejpam-6215	471	1	=	=	SYM
ejpam-6215	471	2	x+	x+	PUNCT
ejpam-6215	472	1	x3	x3	ADJ
ejpam-6215	472	2	3	3	NUM
ejpam-6215	472	3	!	!	PUNCT
ejpam-6215	473	1	+	+	ADJ
ejpam-6215	473	2	n−1	n−1	PROPN
ejpam-6215	473	3	[	[	PUNCT
ejpam-6215	473	4	6t2	6t2	NUM
ejpam-6215	473	5	s2	s2	NOUN
ejpam-6215	473	6	n+[y2	n+[y2	PROPN
ejpam-6215	473	7	]	]	PUNCT
ejpam-6215	473	8	]	]	PUNCT
ejpam-6215	473	9	.	.	PUNCT
ejpam-6215	474	1	(	(	PUNCT
ejpam-6215	474	2	43	43	NUM
ejpam-6215	474	3	)	)	PUNCT
ejpam-6215	474	4	equation	equation	NOUN
ejpam-6215	474	5	(	(	PUNCT
ejpam-6215	474	6	43	43	NUM
ejpam-6215	474	7	)	)	PUNCT
ejpam-6215	474	8	can	can	AUX
ejpam-6215	474	9	be	be	AUX
ejpam-6215	474	10	written	write	VERB
ejpam-6215	474	11	as	as	ADP
ejpam-6215	474	12	y(x	y(x	NOUN
ejpam-6215	474	13	)	)	PUNCT
ejpam-6215	474	14	=	=	PUNCT
ejpam-6215	475	1	x+	x+	PUNCT
ejpam-6215	475	2	x3	x3	ADJ
ejpam-6215	475	3	3	3	NUM
ejpam-6215	475	4	!	!	PUNCT
ejpam-6215	476	1	+	+	ADJ
ejpam-6215	476	2	n−1	n−1	PROPN
ejpam-6215	476	3	[	[	PUNCT
ejpam-6215	476	4	6t2	6t2	NUM
ejpam-6215	476	5	s2	s2	NOUN
ejpam-6215	476	6	n+[an	n+[an	NOUN
ejpam-6215	476	7	]	]	PUNCT
ejpam-6215	476	8	]	]	PUNCT
ejpam-6215	476	9	.	.	PUNCT
ejpam-6215	477	1	(	(	PUNCT
ejpam-6215	477	2	44	44	NUM
ejpam-6215	477	3	)	)	PUNCT
ejpam-6215	477	4	y0(x	y0(x	NOUN
ejpam-6215	477	5	)	)	PUNCT
ejpam-6215	478	1	=	=	SYM
ejpam-6215	478	2	x+	x+	PUNCT
ejpam-6215	478	3	x3	x3	ADJ
ejpam-6215	478	4	3	3	NUM
ejpam-6215	478	5	!	!	PUNCT
ejpam-6215	478	6	.	.	PUNCT
ejpam-6215	479	1	from	from	ADP
ejpam-6215	479	2	(	(	PUNCT
ejpam-6215	479	3	44	44	NUM
ejpam-6215	479	4	)	)	PUNCT
ejpam-6215	479	5	,	,	PUNCT
ejpam-6215	479	6	we	we	PRON
ejpam-6215	479	7	can	can	AUX
ejpam-6215	479	8	conclude	conclude	VERB
ejpam-6215	479	9	that	that	PRON
ejpam-6215	479	10	yn+1(x	yn+1(x	NOUN
ejpam-6215	479	11	)	)	PUNCT
ejpam-6215	480	1	=	=	SYM
ejpam-6215	480	2	n−1	n−1	PROPN
ejpam-6215	480	3	[	[	PUNCT
ejpam-6215	480	4	t2	t2	NOUN
ejpam-6215	480	5	s2	s2	PROPN
ejpam-6215	480	6	n+[an	n+[an	NOUN
ejpam-6215	480	7	]	]	PUNCT
ejpam-6215	480	8	]	]	PUNCT
ejpam-6215	480	9	,	,	PUNCT
ejpam-6215	480	10	n	n	X
ejpam-6215	480	11	≥	≥	NOUN
ejpam-6215	480	12	0	0	NUM
ejpam-6215	480	13	.	.	PUNCT
ejpam-6215	481	1	(	(	PUNCT
ejpam-6215	481	2	45	45	NUM
ejpam-6215	481	3	)	)	PUNCT
ejpam-6215	481	4	the	the	DET
ejpam-6215	481	5	terms	term	NOUN
ejpam-6215	481	6	become	become	VERB
ejpam-6215	481	7	:	:	PUNCT
ejpam-6215	481	8	y1(x	y1(x	NOUN
ejpam-6215	481	9	)	)	PUNCT
ejpam-6215	481	10	=	=	SYM
ejpam-6215	481	11	n−1	n−1	PROPN
ejpam-6215	481	12	[	[	PUNCT
ejpam-6215	481	13	t2	t2	PROPN
ejpam-6215	481	14	s2	s2	PROPN
ejpam-6215	481	15	n+[a0	n+[a0	NOUN
ejpam-6215	481	16	]	]	PUNCT
ejpam-6215	481	17	]	]	PUNCT
ejpam-6215	481	18	.	.	PUNCT
ejpam-6215	482	1	s.	s.	PROPN
ejpam-6215	482	2	mohammed	mohammed	PROPN
ejpam-6215	482	3	,	,	PUNCT
ejpam-6215	482	4	s.	s.	PROPN
ejpam-6215	482	5	abid	abid	PROPN
ejpam-6215	482	6	,	,	PUNCT
ejpam-6215	482	7	r.	r.	PROPN
ejpam-6215	482	8	abid	abid	PROPN
ejpam-6215	482	9	/	/	SYM
ejpam-6215	482	10	eur	eur	PROPN
ejpam-6215	482	11	.	.	PUNCT
ejpam-6215	483	1	j.	j.	PROPN
ejpam-6215	483	2	pure	pure	PROPN
ejpam-6215	483	3	appl	appl	PROPN
ejpam-6215	483	4	.	.	PROPN
ejpam-6215	483	5	math	math	PROPN
ejpam-6215	483	6	,	,	PUNCT
ejpam-6215	483	7	18	18	NUM
ejpam-6215	483	8	(	(	PUNCT
ejpam-6215	483	9	3	3	NUM
ejpam-6215	483	10	)	)	PUNCT
ejpam-6215	483	11	(	(	PUNCT
ejpam-6215	483	12	2025	2025	NUM
ejpam-6215	483	13	)	)	PUNCT
ejpam-6215	483	14	,	,	PUNCT
ejpam-6215	483	15	6215	6215	NUM
ejpam-6215	483	16	22	22	NUM
ejpam-6215	483	17	of	of	ADP
ejpam-6215	483	18	38	38	NUM
ejpam-6215	483	19	y2(x	y2(x	NUM
ejpam-6215	483	20	)	)	PUNCT
ejpam-6215	483	21	=	=	SYM
ejpam-6215	483	22	n−1	n−1	PROPN
ejpam-6215	483	23	[	[	PUNCT
ejpam-6215	483	24	t2	t2	NOUN
ejpam-6215	483	25	s2	s2	NOUN
ejpam-6215	483	26	n+[a1	n+[a1	VERB
ejpam-6215	483	27	]	]	PUNCT
ejpam-6215	483	28	]	]	PUNCT
ejpam-6215	483	29	.	.	PUNCT
ejpam-6215	484	1	...	...	PUNCT
ejpam-6215	484	2	therefore	therefore	ADV
ejpam-6215	484	3	,	,	PUNCT
ejpam-6215	484	4	from	from	ADP
ejpam-6215	484	5	(	(	PUNCT
ejpam-6215	484	6	45	45	NUM
ejpam-6215	484	7	)	)	PUNCT
ejpam-6215	484	8	,	,	PUNCT
ejpam-6215	484	9	the	the	DET
ejpam-6215	484	10	other	other	ADJ
ejpam-6215	484	11	remaining	remain	VERB
ejpam-6215	484	12	terms	term	NOUN
ejpam-6215	484	13	of	of	ADP
ejpam-6215	484	14	the	the	DET
ejpam-6215	484	15	function	function	NOUN
ejpam-6215	484	16	y(x	y(x	NOUN
ejpam-6215	484	17	)	)	PUNCT
ejpam-6215	484	18	can	can	AUX
ejpam-6215	484	19	be	be	AUX
ejpam-6215	484	20	easily	easily	ADV
ejpam-6215	484	21	calculated	calculate	VERB
ejpam-6215	484	22	as	as	SCONJ
ejpam-6215	484	23	follows	follow	VERB
ejpam-6215	484	24	:	:	PUNCT
ejpam-6215	484	25	y1(x	y1(x	NOUN
ejpam-6215	484	26	)	)	PUNCT
ejpam-6215	484	27	=	=	SYM
ejpam-6215	484	28	1	1	NUM
ejpam-6215	484	29	2	2	NUM
ejpam-6215	484	30	x4	x4	NOUN
ejpam-6215	484	31	+	+	CCONJ
ejpam-6215	484	32	1	1	NUM
ejpam-6215	484	33	15	15	NUM
ejpam-6215	484	34	x6	x6	NOUN
ejpam-6215	484	35	+	+	CCONJ
ejpam-6215	484	36	1	1	NUM
ejpam-6215	484	37	336	336	NUM
ejpam-6215	484	38	x8	x8	NOUN
ejpam-6215	484	39	.	.	PUNCT
ejpam-6215	485	1	y2(x	y2(x	X
ejpam-6215	485	2	)	)	PUNCT
ejpam-6215	485	3	=	=	SYM
ejpam-6215	485	4	1	1	NUM
ejpam-6215	485	5	7	7	NUM
ejpam-6215	485	6	x7	x7	NOUN
ejpam-6215	485	7	+	+	CCONJ
ejpam-6215	485	8	1	1	NUM
ejpam-6215	485	9	40	40	NUM
ejpam-6215	485	10	x9	x9	NOUN
ejpam-6215	485	11	+	+	CCONJ
ejpam-6215	485	12	71	71	NUM
ejpam-6215	485	13	46200	46200	NUM
ejpam-6215	485	14	x11	x11	NOUN
ejpam-6215	486	1	+	+	CCONJ
ejpam-6215	486	2	1	1	NUM
ejpam-6215	486	3	26200	26200	NUM
ejpam-6215	486	4	x13	x13	NOUN
ejpam-6215	486	5	.	.	PUNCT
ejpam-6215	487	1	y3(x	y3(x	X
ejpam-6215	487	2	)	)	PUNCT
ejpam-6215	487	3	=	=	SYM
ejpam-6215	487	4	1	1	NUM
ejpam-6215	487	5	28	28	NUM
ejpam-6215	487	6	x10	x10	NOUN
ejpam-6215	487	7	+	+	CCONJ
ejpam-6215	487	8	23	23	NUM
ejpam-6215	487	9	3080	3080	NUM
ejpam-6215	487	10	x12	x12	NUM
ejpam-6215	488	1	+	+	CCONJ
ejpam-6215	488	2	5219	5219	NUM
ejpam-6215	488	3	8408400	8408400	NUM
ejpam-6215	488	4	x14	x14	PROPN
ejpam-6215	489	1	+	+	CCONJ
ejpam-6215	489	2	3551	3551	NUM
ejpam-6215	489	3	144144000	144144000	NUM
ejpam-6215	489	4	x16	x16	NOUN
ejpam-6215	489	5	+	+	CCONJ
ejpam-6215	489	6	95	95	NUM
ejpam-6215	489	7	224550144	224550144	NUM
ejpam-6215	489	8	x18	x18	NOUN
ejpam-6215	489	9	.	.	PUNCT
ejpam-6215	489	10	y4(x	y4(x	X
ejpam-6215	489	11	)	)	PUNCT
ejpam-6215	489	12	=	=	NOUN
ejpam-6215	489	13	3	3	NUM
ejpam-6215	489	14	364	364	NUM
ejpam-6215	489	15	x13	x13	NOUN
ejpam-6215	489	16	+	+	CCONJ
ejpam-6215	489	17	131	131	NUM
ejpam-6215	489	18	64680	64680	NUM
ejpam-6215	489	19	x15	x15	NUM
ejpam-6215	489	20	+	+	CCONJ
ejpam-6215	489	21	19867	19867	NUM
ejpam-6215	489	22	95295200	95295200	NUM
ejpam-6215	489	23	x17	x17	NOUN
ejpam-6215	490	1	+	+	X
ejpam-6215	490	2	163469	163469	NUM
ejpam-6215	490	3	14378364000	14378364000	NUM
ejpam-6215	490	4	x19	x19	NOUN
ejpam-6215	490	5	.	.	PUNCT
ejpam-6215	490	6	.	.	PUNCT
ejpam-6215	490	7	.	.	PUNCT
ejpam-6215	491	1	+	+	CCONJ
ejpam-6215	491	2	163451	163451	NUM
ejpam-6215	491	3	491203440000	491203440000	NUM
ejpam-6215	491	4	x21	x21	NUM
ejpam-6215	492	1	+	+	CCONJ
ejpam-6215	492	2	131	131	NUM
ejpam-6215	492	3	7101398304	7101398304	NUM
ejpam-6215	492	4	x23	x23	NOUN
ejpam-6215	492	5	.	.	PUNCT
ejpam-6215	493	1	in	in	ADP
ejpam-6215	493	2	this	this	DET
ejpam-6215	493	3	way	way	NOUN
ejpam-6215	493	4	,	,	PUNCT
ejpam-6215	493	5	we	we	PRON
ejpam-6215	493	6	obtained	obtain	VERB
ejpam-6215	493	7	the	the	DET
ejpam-6215	493	8	approximate	approximate	ADJ
ejpam-6215	493	9	result	result	NOUN
ejpam-6215	493	10	of	of	ADP
ejpam-6215	493	11	the	the	DET
ejpam-6215	493	12	function	function	NOUN
ejpam-6215	493	13	y(x	y(x	PROPN
ejpam-6215	493	14	)	)	PUNCT
ejpam-6215	493	15	,	,	PUNCT
ejpam-6215	493	16	which	which	PRON
ejpam-6215	493	17	is	be	AUX
ejpam-6215	493	18	given	give	VERB
ejpam-6215	493	19	as	as	ADP
ejpam-6215	493	20	y(x	y(x	NOUN
ejpam-6215	493	21	)	)	PUNCT
ejpam-6215	493	22	=	=	PUNCT
ejpam-6215	494	1	∞∑	∞∑	PROPN
ejpam-6215	494	2	n=0	n=0	NUM
ejpam-6215	494	3	yn(x	yn(x	NUM
ejpam-6215	494	4	)	)	PUNCT
ejpam-6215	494	5	.	.	PUNCT
ejpam-6215	495	1	(	(	PUNCT
ejpam-6215	495	2	46	46	NUM
ejpam-6215	495	3	)	)	PUNCT
ejpam-6215	495	4	y(x	y(x	NOUN
ejpam-6215	495	5	)	)	PUNCT
ejpam-6215	496	1	=	=	SYM
ejpam-6215	496	2	x+	x+	PUNCT
ejpam-6215	497	1	x3	x3	VERB
ejpam-6215	497	2	6	6	NUM
ejpam-6215	497	3	+	+	SYM
ejpam-6215	497	4	1	1	NUM
ejpam-6215	497	5	2	2	NUM
ejpam-6215	497	6	x4	x4	NOUN
ejpam-6215	497	7	+	+	CCONJ
ejpam-6215	497	8	1	1	NUM
ejpam-6215	497	9	15	15	NUM
ejpam-6215	497	10	x6	x6	NOUN
ejpam-6215	497	11	+	+	CCONJ
ejpam-6215	497	12	1	1	NUM
ejpam-6215	497	13	336	336	NUM
ejpam-6215	497	14	x8	x8	NOUN
ejpam-6215	497	15	+	+	CCONJ
ejpam-6215	497	16	1	1	NUM
ejpam-6215	497	17	7	7	NUM
ejpam-6215	497	18	x7	x7	NOUN
ejpam-6215	497	19	+	+	CCONJ
ejpam-6215	497	20	1	1	NUM
ejpam-6215	497	21	40	40	NUM
ejpam-6215	497	22	x9	x9	NOUN
ejpam-6215	497	23	+	+	CCONJ
ejpam-6215	497	24	71	71	NUM
ejpam-6215	497	25	64200	64200	NUM
ejpam-6215	497	26	x11	x11	NOUN
ejpam-6215	498	1	+	+	CCONJ
ejpam-6215	498	2	1	1	NUM
ejpam-6215	498	3	26208	26208	NUM
ejpam-6215	498	4	x13	x13	NOUN
ejpam-6215	498	5	.	.	PUNCT
ejpam-6215	498	6	.	.	PUNCT
ejpam-6215	498	7	.	.	PUNCT
ejpam-6215	499	1	+	+	CCONJ
ejpam-6215	499	2	1	1	NUM
ejpam-6215	499	3	28	28	NUM
ejpam-6215	499	4	x10	x10	NOUN
ejpam-6215	500	1	+	+	CCONJ
ejpam-6215	500	2	23	23	NUM
ejpam-6215	500	3	3080	3080	NUM
ejpam-6215	500	4	x12	x12	NUM
ejpam-6215	500	5	+	+	CCONJ
ejpam-6215	500	6	5219	5219	NUM
ejpam-6215	500	7	8408400	8408400	NUM
ejpam-6215	500	8	x14	x14	PROPN
ejpam-6215	501	1	+	+	CCONJ
ejpam-6215	501	2	3551	3551	NUM
ejpam-6215	501	3	144144000	144144000	NUM
ejpam-6215	501	4	x16	x16	NOUN
ejpam-6215	501	5	+	+	CCONJ
ejpam-6215	501	6	95	95	NUM
ejpam-6215	501	7	224550144	224550144	NUM
ejpam-6215	501	8	x18	x18	NOUN
ejpam-6215	501	9	.	.	PUNCT
ejpam-6215	501	10	.	.	PUNCT
ejpam-6215	501	11	.	.	PUNCT
ejpam-6215	502	1	+	+	CCONJ
ejpam-6215	502	2	3	3	NUM
ejpam-6215	502	3	364	364	NUM
ejpam-6215	502	4	x13	x13	NOUN
ejpam-6215	502	5	+	+	CCONJ
ejpam-6215	502	6	131	131	NUM
ejpam-6215	502	7	64680	64680	NUM
ejpam-6215	502	8	x15	x15	NUM
ejpam-6215	502	9	+	+	CCONJ
ejpam-6215	502	10	19867	19867	NUM
ejpam-6215	502	11	95295200	95295200	NUM
ejpam-6215	502	12	x17	x17	NOUN
ejpam-6215	503	1	+	+	X
ejpam-6215	503	2	163469	163469	NUM
ejpam-6215	503	3	14378364000	14378364000	NUM
ejpam-6215	503	4	x19	x19	NOUN
ejpam-6215	503	5	.	.	PUNCT
ejpam-6215	503	6	.	.	PUNCT
ejpam-6215	503	7	.	.	PUNCT
ejpam-6215	504	1	+	+	CCONJ
ejpam-6215	504	2	163451	163451	NUM
ejpam-6215	504	3	491203440000	491203440000	NUM
ejpam-6215	504	4	x21	x21	NUM
ejpam-6215	505	1	+	+	CCONJ
ejpam-6215	505	2	131	131	NUM
ejpam-6215	505	3	7101398304	7101398304	NUM
ejpam-6215	505	4	x23	x23	NOUN
ejpam-6215	506	1	+	+	CCONJ
ejpam-6215	506	2	·	·	PUNCT
ejpam-6215	506	3	·	·	PUNCT
ejpam-6215	506	4	·	·	PUNCT
ejpam-6215	506	5	the	the	DET
ejpam-6215	506	6	remainder	remainder	NOUN
ejpam-6215	506	7	function	function	NOUN
ejpam-6215	506	8	of	of	ADP
ejpam-6215	506	9	error	error	NOUN
ejpam-6215	506	10	is	be	AUX
ejpam-6215	506	11	evaluated	evaluate	VERB
ejpam-6215	506	12	:	:	PUNCT
ejpam-6215	506	13	ern	ern	PROPN
ejpam-6215	506	14	=	=	PUNCT
ejpam-6215	506	15	y′′n(x)−	y′′n(x)−	PROPN
ejpam-6215	506	16	6y2n(x)−	6y2n(x)−	NUM
ejpam-6215	506	17	x.	x.	NOUN
ejpam-6215	506	18	mern	mern	PROPN
ejpam-6215	506	19	=	=	PUNCT
ejpam-6215	506	20	max	max	PROPN
ejpam-6215	506	21	0.01≤x≤0.1	0.01≤x≤0.1	NUM
ejpam-6215	507	1	|ern(x)|	|ern(x)|	NOUN
ejpam-6215	507	2	.	.	PUNCT
ejpam-6215	508	1	in	in	ADP
ejpam-6215	508	2	table	table	NOUN
ejpam-6215	508	3	7	7	NUM
ejpam-6215	508	4	and	and	CCONJ
ejpam-6215	508	5	figure	figure	VERB
ejpam-6215	508	6	7	7	NUM
ejpam-6215	508	7	show	show	VERB
ejpam-6215	508	8	the	the	DET
ejpam-6215	508	9	convergence	convergence	NOUN
ejpam-6215	508	10	of	of	ADP
ejpam-6215	508	11	the	the	DET
ejpam-6215	508	12	solution	solution	NOUN
ejpam-6215	508	13	using	use	VERB
ejpam-6215	508	14	mern	mern	NOUN
ejpam-6215	508	15	from	from	ADP
ejpam-6215	508	16	n	n	NOUN
ejpam-6215	508	17	=	=	SYM
ejpam-6215	508	18	1	1	NUM
ejpam-6215	508	19	to	to	ADP
ejpam-6215	508	20	n	n	NOUN
ejpam-6215	508	21	=	=	SYM
ejpam-6215	508	22	5	5	NUM
ejpam-6215	508	23	using	use	VERB
ejpam-6215	508	24	the	the	DET
ejpam-6215	508	25	ndm	ndm	NOUN
ejpam-6215	508	26	.	.	PUNCT
ejpam-6215	509	1	a	a	DET
ejpam-6215	509	2	significant	significant	ADJ
ejpam-6215	509	3	reduction	reduction	NOUN
ejpam-6215	509	4	in	in	ADP
ejpam-6215	509	5	error	error	NOUN
ejpam-6215	509	6	as	as	ADP
ejpam-6215	509	7	n	n	DET
ejpam-6215	509	8	increases	increase	NOUN
ejpam-6215	509	9	.	.	PUNCT
ejpam-6215	510	1	initially	initially	ADV
ejpam-6215	510	2	,	,	PUNCT
ejpam-6215	510	3	for	for	ADP
ejpam-6215	510	4	n	n	NOUN
ejpam-6215	510	5	=	=	SYM
ejpam-6215	510	6	1	1	NUM
ejpam-6215	510	7	,	,	PUNCT
ejpam-6215	510	8	the	the	DET
ejpam-6215	510	9	error	error	NOUN
ejpam-6215	510	10	is	be	AUX
ejpam-6215	510	11	relatively	relatively	ADV
ejpam-6215	510	12	large	large	ADJ
ejpam-6215	510	13	,	,	PUNCT
ejpam-6215	510	14	but	but	CCONJ
ejpam-6215	510	15	it	it	PRON
ejpam-6215	510	16	decreases	decrease	VERB
ejpam-6215	510	17	drastically	drastically	ADV
ejpam-6215	510	18	for	for	ADP
ejpam-6215	510	19	n	n	NOUN
ejpam-6215	510	20	=	=	SYM
ejpam-6215	510	21	2	2	NUM
ejpam-6215	510	22	and	and	CCONJ
ejpam-6215	510	23	continues	continue	VERB
ejpam-6215	510	24	to	to	PART
ejpam-6215	510	25	drop	drop	VERB
ejpam-6215	510	26	to	to	ADP
ejpam-6215	510	27	6.93889×	6.93889×	NUM
ejpam-6215	510	28	10−18	10−18	NOUN
ejpam-6215	510	29	for	for	ADP
ejpam-6215	510	30	n	n	NOUN
ejpam-6215	510	31	=	=	SYM
ejpam-6215	510	32	5	5	NUM
ejpam-6215	510	33	.	.	PUNCT
ejpam-6215	511	1	this	this	DET
ejpam-6215	511	2	exponential	exponential	ADJ
ejpam-6215	511	3	decay	decay	NOUN
ejpam-6215	511	4	in	in	ADP
ejpam-6215	511	5	error	error	NOUN
ejpam-6215	511	6	indicates	indicate	VERB
ejpam-6215	511	7	that	that	SCONJ
ejpam-6215	511	8	each	each	DET
ejpam-6215	511	9	additional	additional	ADJ
ejpam-6215	511	10	term	term	NOUN
ejpam-6215	511	11	in	in	ADP
ejpam-6215	511	12	the	the	DET
ejpam-6215	511	13	ldm	ldm	NOUN
ejpam-6215	511	14	approximation	approximation	NOUN
ejpam-6215	511	15	significantly	significantly	ADV
ejpam-6215	511	16	improves	improve	VERB
ejpam-6215	511	17	the	the	DET
ejpam-6215	511	18	accuracy	accuracy	NOUN
ejpam-6215	511	19	of	of	ADP
ejpam-6215	511	20	the	the	DET
ejpam-6215	511	21	solution	solution	NOUN
ejpam-6215	511	22	.	.	PUNCT
ejpam-6215	512	1	the	the	DET
ejpam-6215	512	2	results	result	NOUN
ejpam-6215	512	3	confirm	confirm	VERB
ejpam-6215	512	4	that	that	SCONJ
ejpam-6215	512	5	ldm	ldm	NOUN
ejpam-6215	512	6	provides	provide	VERB
ejpam-6215	512	7	a	a	DET
ejpam-6215	512	8	highly	highly	ADV
ejpam-6215	512	9	effective	effective	ADJ
ejpam-6215	512	10	approach	approach	NOUN
ejpam-6215	512	11	for	for	ADP
ejpam-6215	512	12	solving	solve	VERB
ejpam-6215	512	13	the	the	DET
ejpam-6215	512	14	second	second	ADJ
ejpam-6215	512	15	painlevé	painlevé	NOUN
ejpam-6215	512	16	equation	equation	NOUN
ejpam-6215	512	17	,	,	PUNCT
ejpam-6215	512	18	with	with	ADP
ejpam-6215	512	19	higher	high	ADJ
ejpam-6215	512	20	-	-	PUNCT
ejpam-6215	512	21	order	order	NOUN
ejpam-6215	512	22	approximations	approximation	NOUN
ejpam-6215	512	23	yielding	yield	VERB
ejpam-6215	512	24	more	more	ADV
ejpam-6215	512	25	precise	precise	ADJ
ejpam-6215	512	26	solutions	solution	NOUN
ejpam-6215	512	27	.	.	PUNCT
ejpam-6215	513	1	s.	s.	PROPN
ejpam-6215	513	2	mohammed	mohammed	PROPN
ejpam-6215	513	3	,	,	PUNCT
ejpam-6215	513	4	s.	s.	PROPN
ejpam-6215	513	5	abid	abid	PROPN
ejpam-6215	513	6	,	,	PUNCT
ejpam-6215	513	7	r.	r.	PROPN
ejpam-6215	513	8	abid	abid	PROPN
ejpam-6215	513	9	/	/	SYM
ejpam-6215	513	10	eur	eur	PROPN
ejpam-6215	513	11	.	.	PUNCT
ejpam-6215	514	1	j.	j.	PROPN
ejpam-6215	514	2	pure	pure	PROPN
ejpam-6215	514	3	appl	appl	PROPN
ejpam-6215	514	4	.	.	PROPN
ejpam-6215	514	5	math	math	PROPN
ejpam-6215	514	6	,	,	PUNCT
ejpam-6215	514	7	18	18	NUM
ejpam-6215	514	8	(	(	PUNCT
ejpam-6215	514	9	3	3	NUM
ejpam-6215	514	10	)	)	PUNCT
ejpam-6215	514	11	(	(	PUNCT
ejpam-6215	514	12	2025	2025	NUM
ejpam-6215	514	13	)	)	PUNCT
ejpam-6215	514	14	,	,	PUNCT
ejpam-6215	514	15	6215	6215	NUM
ejpam-6215	514	16	23	23	NUM
ejpam-6215	514	17	of	of	ADP
ejpam-6215	514	18	38	38	NUM
ejpam-6215	514	19	table	table	NOUN
ejpam-6215	514	20	7	7	NUM
ejpam-6215	514	21	:	:	PUNCT
ejpam-6215	514	22	the	the	DET
ejpam-6215	514	23	maximum	maximum	ADJ
ejpam-6215	514	24	residual	residual	ADJ
ejpam-6215	514	25	error	error	NOUN
ejpam-6215	514	26	:	:	PUNCT
ejpam-6215	514	27	mern	mern	NOUN
ejpam-6215	514	28	by	by	ADP
ejpam-6215	514	29	the	the	DET
ejpam-6215	514	30	ldm	ldm	NOUN
ejpam-6215	514	31	,	,	PUNCT
ejpam-6215	514	32	where	where	SCONJ
ejpam-6215	514	33	n	n	NOUN
ejpam-6215	514	34	=	=	SYM
ejpam-6215	514	35	1	1	NUM
ejpam-6215	514	36	,	,	PUNCT
ejpam-6215	514	37	.	.	PUNCT
ejpam-6215	514	38	.	.	PUNCT
ejpam-6215	515	1	.	.	PUNCT
ejpam-6215	516	1	,	,	PUNCT
ejpam-6215	516	2	5	5	X
ejpam-6215	516	3	.	.	X
ejpam-6215	517	1	n	n	PRON
ejpam-6215	517	2	mern	mern	ADJ
ejpam-6215	517	3	1	1	NUM
ejpam-6215	517	4	0.0000601952	0.0000601952	NUM
ejpam-6215	517	5	2	2	NUM
ejpam-6215	517	6	3.22501×	3.22501×	NUM
ejpam-6215	517	7	10−8	10−8	NUM
ejpam-6215	517	8	3	3	NUM
ejpam-6215	517	9	1.29031×	1.29031×	NUM
ejpam-6215	517	10	10−11	10−11	NUM
ejpam-6215	517	11	4	4	NUM
ejpam-6215	517	12	4.4062×	4.4062×	NOUN
ejpam-6215	517	13	10−15	10−15	NUM
ejpam-6215	517	14	5	5	NUM
ejpam-6215	517	15	6.93889×	6.93889×	NUM
ejpam-6215	517	16	10−18	10−18	NUM
ejpam-6215	517	17	figure	figure	NOUN
ejpam-6215	517	18	7	7	NUM
ejpam-6215	517	19	:	:	PUNCT
ejpam-6215	517	20	the	the	DET
ejpam-6215	517	21	logarithmic	logarithmic	ADJ
ejpam-6215	517	22	plot	plot	NOUN
ejpam-6215	517	23	of	of	ADP
ejpam-6215	517	24	mern	mern	NOUN
ejpam-6215	517	25	(	(	PUNCT
ejpam-6215	517	26	ndm	ndm	PROPN
ejpam-6215	517	27	.	.	PUNCT
ejpam-6215	518	1	first	first	ADV
ejpam-6215	518	2	painlevé	painlevé	VERB
ejpam-6215	518	3	equation	equation	NOUN
ejpam-6215	518	4	)	)	PUNCT
ejpam-6215	518	5	.	.	PUNCT
ejpam-6215	519	1	2.4.2	2.4.2	X
ejpam-6215	519	2	.	.	PUNCT
ejpam-6215	520	1	the	the	DET
ejpam-6215	520	2	ndm	ndm	NOUN
ejpam-6215	520	3	for	for	ADP
ejpam-6215	520	4	solving	solve	VERB
ejpam-6215	520	5	the	the	DET
ejpam-6215	520	6	painlevé	painlevé	NOUN
ejpam-6215	520	7	ii	ii	NOUN
ejpam-6215	520	8	differential	differential	NOUN
ejpam-6215	520	9	equation	equation	NOUN
ejpam-6215	520	10	rewrite	rewrite	NOUN
ejpam-6215	520	11	(	(	PUNCT
ejpam-6215	520	12	2	2	NUM
ejpam-6215	520	13	)	)	PUNCT
ejpam-6215	520	14	y′′(x	y′′(x	NOUN
ejpam-6215	520	15	)	)	PUNCT
ejpam-6215	520	16	=	=	SYM
ejpam-6215	521	1	2y3	2y3	NUM
ejpam-6215	521	2	+	+	CCONJ
ejpam-6215	521	3	xy	xy	PROPN
ejpam-6215	521	4	+	+	NUM
ejpam-6215	521	5	µ.	µ.	NOUN
ejpam-6215	521	6	(	(	PUNCT
ejpam-6215	521	7	47	47	NUM
ejpam-6215	521	8	)	)	PUNCT
ejpam-6215	521	9	y(0	y(0	PROPN
ejpam-6215	521	10	)	)	PUNCT
ejpam-6215	521	11	=	=	SYM
ejpam-6215	521	12	1	1	NUM
ejpam-6215	521	13	,	,	PUNCT
ejpam-6215	521	14	y′(0	y′(0	NOUN
ejpam-6215	521	15	)	)	PUNCT
ejpam-6215	521	16	=	=	SYM
ejpam-6215	522	1	0	0	X
ejpam-6215	522	2	.	.	PUNCT
ejpam-6215	523	1	(	(	PUNCT
ejpam-6215	523	2	48	48	NUM
ejpam-6215	523	3	)	)	PUNCT
ejpam-6215	523	4	by	by	AUX
ejpam-6215	523	5	apply	apply	VERB
ejpam-6215	523	6	n	n	CCONJ
ejpam-6215	523	7	-	-	PUNCT
ejpam-6215	523	8	transform	transform	NOUN
ejpam-6215	523	9	on	on	ADP
ejpam-6215	523	10	both	both	DET
ejpam-6215	523	11	sides	side	NOUN
ejpam-6215	523	12	of	of	ADP
ejpam-6215	523	13	(	(	PUNCT
ejpam-6215	523	14	47	47	NUM
ejpam-6215	523	15	):	):	PUNCT
ejpam-6215	523	16	n+[y′′(x	n+[y′′(x	NOUN
ejpam-6215	523	17	)	)	PUNCT
ejpam-6215	523	18	]	]	PUNCT
ejpam-6215	524	1	=	=	PUNCT
ejpam-6215	524	2	n+[2y3	n+[2y3	PROPN
ejpam-6215	524	3	+	+	SYM
ejpam-6215	524	4	xy	xy	PROPN
ejpam-6215	524	5	+	+	X
ejpam-6215	524	6	µ	µ	X
ejpam-6215	524	7	]	]	X
ejpam-6215	524	8	.	.	PUNCT
ejpam-6215	525	1	(	(	PUNCT
ejpam-6215	525	2	49	49	NUM
ejpam-6215	525	3	)	)	PUNCT
ejpam-6215	525	4	by	by	ADP
ejpam-6215	525	5	using	use	VERB
ejpam-6215	525	6	the	the	DET
ejpam-6215	525	7	properties	property	NOUN
ejpam-6215	525	8	of	of	ADP
ejpam-6215	525	9	n	n	CCONJ
ejpam-6215	525	10	-	-	PUNCT
ejpam-6215	525	11	transform	transform	VERB
ejpam-6215	525	12	we	we	PRON
ejpam-6215	525	13	obtain	obtain	VERB
ejpam-6215	525	14	:	:	PUNCT
ejpam-6215	525	15	s2	s2	VERB
ejpam-6215	525	16	t2	t2	PROPN
ejpam-6215	525	17	y(s	y(s	PROPN
ejpam-6215	525	18	,	,	PUNCT
ejpam-6215	525	19	t)−	t)−	PROPN
ejpam-6215	525	20	s	s	PART
ejpam-6215	525	21	t2	t2	NOUN
ejpam-6215	525	22	y(0)−	y(0)−	PROPN
ejpam-6215	525	23	1	1	NUM
ejpam-6215	525	24	t	t	NOUN
ejpam-6215	525	25	y′(0	y′(0	NOUN
ejpam-6215	525	26	)	)	PUNCT
ejpam-6215	525	27	=	=	PUNCT
ejpam-6215	526	1	n+[2y3	n+[2y3	PROPN
ejpam-6215	526	2	+	+	X
ejpam-6215	526	3	xy	xy	X
ejpam-6215	526	4	]	]	X
ejpam-6215	526	5	+	+	NUM
ejpam-6215	526	6	µ	µ	X
ejpam-6215	526	7	s2	s2	NOUN
ejpam-6215	526	8	.	.	PUNCT
ejpam-6215	527	1	(	(	PUNCT
ejpam-6215	527	2	50	50	X
ejpam-6215	527	3	)	)	PUNCT
ejpam-6215	527	4	substituting	substitute	VERB
ejpam-6215	527	5	(	(	PUNCT
ejpam-6215	527	6	48	48	NUM
ejpam-6215	527	7	)	)	PUNCT
ejpam-6215	527	8	into	into	ADP
ejpam-6215	527	9	(	(	PUNCT
ejpam-6215	527	10	50	50	NUM
ejpam-6215	527	11	)	)	PUNCT
ejpam-6215	527	12	,	,	PUNCT
ejpam-6215	527	13	we	we	PRON
ejpam-6215	527	14	have	have	VERB
ejpam-6215	527	15	y(s	y(s	PROPN
ejpam-6215	527	16	,	,	PUNCT
ejpam-6215	527	17	t	t	PROPN
ejpam-6215	527	18	)	)	PUNCT
ejpam-6215	527	19	=	=	PUNCT
ejpam-6215	527	20	1	1	NUM
ejpam-6215	527	21	s	s	PART
ejpam-6215	527	22	+	+	NOUN
ejpam-6215	527	23	µt2	µt2	NOUN
ejpam-6215	527	24	s4	s4	PROPN
ejpam-6215	527	25	+	+	CCONJ
ejpam-6215	527	26	t2	t2	PROPN
ejpam-6215	527	27	s2	s2	NOUN
ejpam-6215	527	28	n+[2y3	n+[2y3	ADV
ejpam-6215	527	29	+	+	X
ejpam-6215	527	30	xy	xy	PROPN
ejpam-6215	527	31	]	]	X
ejpam-6215	527	32	.	.	PUNCT
ejpam-6215	528	1	(	(	PUNCT
ejpam-6215	528	2	51	51	NUM
ejpam-6215	528	3	)	)	PUNCT
ejpam-6215	528	4	now	now	ADV
ejpam-6215	528	5	,	,	PUNCT
ejpam-6215	528	6	apply	apply	VERB
ejpam-6215	528	7	the	the	DET
ejpam-6215	528	8	inverse	inverse	NOUN
ejpam-6215	528	9	of	of	ADP
ejpam-6215	528	10	n	n	CCONJ
ejpam-6215	528	11	-	-	PUNCT
ejpam-6215	528	12	transform	transform	NOUN
ejpam-6215	528	13	we	we	PRON
ejpam-6215	528	14	have	have	AUX
ejpam-6215	528	15	n−1[y(s	n−1[y(	VERB
ejpam-6215	528	16	,	,	PUNCT
ejpam-6215	528	17	t	t	PROPN
ejpam-6215	528	18	)	)	PUNCT
ejpam-6215	528	19	]	]	PUNCT
ejpam-6215	529	1	=	=	PUNCT
ejpam-6215	529	2	n−1	n−1	PROPN
ejpam-6215	529	3	[	[	PUNCT
ejpam-6215	529	4	1	1	NUM
ejpam-6215	529	5	s	s	PART
ejpam-6215	529	6	+	+	NOUN
ejpam-6215	529	7	µt2	µt2	NOUN
ejpam-6215	529	8	s4	s4	PROPN
ejpam-6215	529	9	+	+	CCONJ
ejpam-6215	529	10	t2	t2	PROPN
ejpam-6215	529	11	s2	s2	NOUN
ejpam-6215	529	12	n+[2y3	n+[2y3	PROPN
ejpam-6215	529	13	+	+	X
ejpam-6215	529	14	xy	xy	PROPN
ejpam-6215	529	15	]	]	X
ejpam-6215	529	16	]	]	PUNCT
ejpam-6215	529	17	.	.	PUNCT
ejpam-6215	530	1	(	(	PUNCT
ejpam-6215	530	2	52	52	NUM
ejpam-6215	530	3	)	)	PUNCT
ejpam-6215	530	4	y(x	y(x	NOUN
ejpam-6215	530	5	)	)	PUNCT
ejpam-6215	530	6	=	=	PUNCT
ejpam-6215	531	1	1	1	NUM
ejpam-6215	531	2	+	+	CCONJ
ejpam-6215	531	3	µx2	µx2	PROPN
ejpam-6215	531	4	2	2	NUM
ejpam-6215	531	5	+	+	NOUN
ejpam-6215	531	6	n−1	n−1	PROPN
ejpam-6215	531	7	[	[	PUNCT
ejpam-6215	531	8	t2	t2	NOUN
ejpam-6215	531	9	s2	s2	NOUN
ejpam-6215	531	10	n+[2y3	n+[2y3	ADV
ejpam-6215	531	11	+	+	X
ejpam-6215	531	12	xy	xy	PROPN
ejpam-6215	531	13	]	]	X
ejpam-6215	531	14	]	]	PUNCT
ejpam-6215	531	15	.	.	PUNCT
ejpam-6215	532	1	(	(	PUNCT
ejpam-6215	532	2	53	53	NUM
ejpam-6215	532	3	)	)	PUNCT
ejpam-6215	532	4	s.	s.	PROPN
ejpam-6215	532	5	mohammed	mohammed	PROPN
ejpam-6215	532	6	,	,	PUNCT
ejpam-6215	532	7	s.	s.	PROPN
ejpam-6215	532	8	abid	abid	PROPN
ejpam-6215	532	9	,	,	PUNCT
ejpam-6215	532	10	r.	r.	PROPN
ejpam-6215	532	11	abid	abid	PROPN
ejpam-6215	532	12	/	/	SYM
ejpam-6215	532	13	eur	eur	PROPN
ejpam-6215	532	14	.	.	PUNCT
ejpam-6215	533	1	j.	j.	PROPN
ejpam-6215	533	2	pure	pure	PROPN
ejpam-6215	533	3	appl	appl	PROPN
ejpam-6215	533	4	.	.	PROPN
ejpam-6215	533	5	math	math	PROPN
ejpam-6215	533	6	,	,	PUNCT
ejpam-6215	533	7	18	18	NUM
ejpam-6215	533	8	(	(	PUNCT
ejpam-6215	533	9	3	3	NUM
ejpam-6215	533	10	)	)	PUNCT
ejpam-6215	533	11	(	(	PUNCT
ejpam-6215	533	12	2025	2025	NUM
ejpam-6215	533	13	)	)	PUNCT
ejpam-6215	533	14	,	,	PUNCT
ejpam-6215	533	15	6215	6215	NUM
ejpam-6215	533	16	24	24	NUM
ejpam-6215	533	17	of	of	ADP
ejpam-6215	533	18	38	38	NUM
ejpam-6215	533	19	equation	equation	NOUN
ejpam-6215	533	20	(	(	PUNCT
ejpam-6215	533	21	53	53	NUM
ejpam-6215	533	22	)	)	PUNCT
ejpam-6215	533	23	can	can	AUX
ejpam-6215	533	24	be	be	AUX
ejpam-6215	533	25	written	write	VERB
ejpam-6215	533	26	as	as	ADP
ejpam-6215	533	27	y(x	y(x	NOUN
ejpam-6215	533	28	)	)	PUNCT
ejpam-6215	533	29	=	=	PUNCT
ejpam-6215	534	1	1	1	NUM
ejpam-6215	534	2	+	+	CCONJ
ejpam-6215	534	3	µx2	µx2	PROPN
ejpam-6215	534	4	2	2	NUM
ejpam-6215	534	5	+	+	NOUN
ejpam-6215	534	6	n−1	n−1	PROPN
ejpam-6215	534	7	[	[	PUNCT
ejpam-6215	534	8	t2	t2	NOUN
ejpam-6215	534	9	s2	s2	PROPN
ejpam-6215	534	10	n+[an	n+[an	NOUN
ejpam-6215	534	11	]	]	PUNCT
ejpam-6215	534	12	]	]	PUNCT
ejpam-6215	534	13	,	,	PUNCT
ejpam-6215	534	14	n	n	X
ejpam-6215	534	15	≥	≥	NOUN
ejpam-6215	534	16	0	0	NUM
ejpam-6215	534	17	(	(	PUNCT
ejpam-6215	534	18	54	54	NUM
ejpam-6215	534	19	)	)	PUNCT
ejpam-6215	534	20	y0(x	y0(x	NOUN
ejpam-6215	534	21	)	)	PUNCT
ejpam-6215	534	22	=	=	SYM
ejpam-6215	535	1	1	1	NUM
ejpam-6215	535	2	+	+	CCONJ
ejpam-6215	535	3	µx2	µx2	PROPN
ejpam-6215	535	4	2	2	NUM
ejpam-6215	535	5	.	.	PUNCT
ejpam-6215	536	1	from	from	ADP
ejpam-6215	536	2	(	(	PUNCT
ejpam-6215	536	3	54	54	NUM
ejpam-6215	536	4	)	)	PUNCT
ejpam-6215	536	5	we	we	PRON
ejpam-6215	536	6	can	can	AUX
ejpam-6215	536	7	conclude	conclude	VERB
ejpam-6215	536	8	that	that	PRON
ejpam-6215	536	9	yn+1(x	yn+1(x	NOUN
ejpam-6215	536	10	)	)	PUNCT
ejpam-6215	537	1	=	=	SYM
ejpam-6215	537	2	n−1	n−1	PROPN
ejpam-6215	537	3	[	[	PUNCT
ejpam-6215	537	4	t2	t2	NOUN
ejpam-6215	537	5	s2	s2	PROPN
ejpam-6215	537	6	n+[an	n+[an	NOUN
ejpam-6215	537	7	]	]	PUNCT
ejpam-6215	537	8	]	]	PUNCT
ejpam-6215	537	9	,	,	PUNCT
ejpam-6215	537	10	n	n	X
ejpam-6215	537	11	≥	≥	NOUN
ejpam-6215	537	12	0	0	NUM
ejpam-6215	537	13	.	.	PUNCT
ejpam-6215	538	1	(	(	PUNCT
ejpam-6215	538	2	55	55	NUM
ejpam-6215	538	3	)	)	PUNCT
ejpam-6215	538	4	the	the	DET
ejpam-6215	538	5	terms	term	NOUN
ejpam-6215	538	6	becomes	become	VERB
ejpam-6215	538	7	y1(x	y1(x	NOUN
ejpam-6215	538	8	)	)	PUNCT
ejpam-6215	538	9	=	=	SYM
ejpam-6215	538	10	n−1	n−1	PROPN
ejpam-6215	538	11	[	[	PUNCT
ejpam-6215	538	12	t2	t2	PROPN
ejpam-6215	538	13	s2	s2	PROPN
ejpam-6215	538	14	n+[a0	n+[a0	PROPN
ejpam-6215	538	15	]	]	PUNCT
ejpam-6215	538	16	]	]	PUNCT
ejpam-6215	538	17	.	.	PUNCT
ejpam-6215	539	1	y2(x	y2(x	X
ejpam-6215	539	2	)	)	PUNCT
ejpam-6215	539	3	=	=	SYM
ejpam-6215	539	4	n−1	n−1	PROPN
ejpam-6215	539	5	[	[	PUNCT
ejpam-6215	539	6	t2	t2	NOUN
ejpam-6215	539	7	s2	s2	NOUN
ejpam-6215	539	8	n+[a1	n+[a1	VERB
ejpam-6215	539	9	]	]	PUNCT
ejpam-6215	539	10	]	]	PUNCT
ejpam-6215	539	11	.	.	PUNCT
ejpam-6215	540	1	therefore	therefore	ADV
ejpam-6215	540	2	,	,	PUNCT
ejpam-6215	540	3	from	from	ADP
ejpam-6215	540	4	(	(	PUNCT
ejpam-6215	540	5	55	55	NUM
ejpam-6215	540	6	)	)	PUNCT
ejpam-6215	540	7	the	the	DET
ejpam-6215	540	8	other	other	ADJ
ejpam-6215	540	9	remaining	remain	VERB
ejpam-6215	540	10	terms	term	NOUN
ejpam-6215	540	11	of	of	ADP
ejpam-6215	540	12	the	the	DET
ejpam-6215	540	13	function	function	NOUN
ejpam-6215	540	14	y(x	y(x	NOUN
ejpam-6215	540	15	)	)	PUNCT
ejpam-6215	540	16	can	can	AUX
ejpam-6215	540	17	be	be	AUX
ejpam-6215	540	18	easily	easily	ADV
ejpam-6215	540	19	calculated	calculate	VERB
ejpam-6215	540	20	as	as	SCONJ
ejpam-6215	540	21	follows	follow	VERB
ejpam-6215	540	22	:	:	PUNCT
ejpam-6215	540	23	a0	a0	NOUN
ejpam-6215	540	24	=	=	SYM
ejpam-6215	540	25	2	2	NUM
ejpam-6215	540	26	+	+	NUM
ejpam-6215	540	27	3x2µ+	3x2µ+	NUM
ejpam-6215	540	28	3	3	NUM
ejpam-6215	540	29	2	2	NUM
ejpam-6215	540	30	x4µ2	x4µ2	PUNCT
ejpam-6215	541	1	+	+	NUM
ejpam-6215	541	2	x6µ3	x6µ3	SYM
ejpam-6215	541	3	4	4	NUM
ejpam-6215	541	4	+	+	CCONJ
ejpam-6215	541	5	x+	x+	ADJ
ejpam-6215	541	6	x3µ	x3µ	NOUN
ejpam-6215	541	7	2	2	NUM
ejpam-6215	541	8	.	.	PUNCT
ejpam-6215	541	9	y1(x	y1(x	NOUN
ejpam-6215	541	10	)	)	PUNCT
ejpam-6215	541	11	=	=	SYM
ejpam-6215	541	12	n−1	n−1	PROPN
ejpam-6215	541	13	[	[	PUNCT
ejpam-6215	541	14	t2	t2	PROPN
ejpam-6215	541	15	s2	s2	PROPN
ejpam-6215	541	16	n+[a0	n+[a0	NOUN
ejpam-6215	541	17	]	]	PUNCT
ejpam-6215	541	18	]	]	PUNCT
ejpam-6215	541	19	.	.	PUNCT
ejpam-6215	542	1	y1(x	y1(x	X
ejpam-6215	542	2	)	)	PUNCT
ejpam-6215	542	3	=	=	SYM
ejpam-6215	543	1	x2	x2	PROPN
ejpam-6215	544	1	+	+	CCONJ
ejpam-6215	544	2	x4µ	x4µ	PROPN
ejpam-6215	544	3	4	4	NUM
ejpam-6215	545	1	+	+	CCONJ
ejpam-6215	545	2	x6µ2	x6µ2	PROPN
ejpam-6215	545	3	20	20	NUM
ejpam-6215	546	1	+	+	CCONJ
ejpam-6215	546	2	x8µ3	x8µ3	X
ejpam-6215	546	3	224	224	NUM
ejpam-6215	546	4	+	+	CCONJ
ejpam-6215	546	5	x3	x3	ADJ
ejpam-6215	546	6	6	6	NUM
ejpam-6215	547	1	+	+	CCONJ
ejpam-6215	547	2	x5µ	x5µ	NOUN
ejpam-6215	547	3	40	40	NUM
ejpam-6215	547	4	.	.	PUNCT
ejpam-6215	548	1	a1	a1	NOUN
ejpam-6215	548	2	=	=	SYM
ejpam-6215	548	3	2x3	2x3	NUM
ejpam-6215	548	4	+	+	CCONJ
ejpam-6215	548	5	x4	x4	PROPN
ejpam-6215	548	6	2	2	NUM
ejpam-6215	548	7	+	+	NUM
ejpam-6215	548	8	x5	x5	NOUN
ejpam-6215	548	9	30	30	NUM
ejpam-6215	548	10	+	+	NUM
ejpam-6215	548	11	3x5µ	3x5µ	NOUN
ejpam-6215	548	12	2	2	NUM
ejpam-6215	548	13	+	+	CCONJ
ejpam-6215	548	14	7x6µ	7x6µ	NOUN
ejpam-6215	548	15	30	30	NUM
ejpam-6215	549	1	+	+	CCONJ
ejpam-6215	549	2	x7µ	x7µ	X
ejpam-6215	549	3	280	280	NUM
ejpam-6215	550	1	+	+	CCONJ
ejpam-6215	550	2	33x7µ2	33x7µ2	PROPN
ejpam-6215	550	3	70	70	NUM
ejpam-6215	550	4	.	.	PUNCT
ejpam-6215	550	5	.	.	PUNCT
ejpam-6215	550	6	.	.	PUNCT
ejpam-6215	551	1	+	+	CCONJ
ejpam-6215	551	2	9x8µ2	9x8µ2	NOUN
ejpam-6215	551	3	160	160	NUM
ejpam-6215	551	4	+	+	SYM
ejpam-6215	551	5	131x9µ3	131x9µ3	NUM
ejpam-6215	551	6	1680	1680	NUM
ejpam-6215	551	7	+	+	CCONJ
ejpam-6215	551	8	47x10µ3	47x10µ3	NOUN
ejpam-6215	551	9	11200	11200	NUM
ejpam-6215	551	10	+	+	CCONJ
ejpam-6215	551	11	57x11µ4	57x11µ4	NUM
ejpam-6215	551	12	6160	6160	NUM
ejpam-6215	551	13	+	+	CCONJ
ejpam-6215	551	14	3x13µ5	3x13µ5	NUM
ejpam-6215	551	15	5824	5824	NUM
ejpam-6215	551	16	.	.	PUNCT
ejpam-6215	552	1	y2(x	y2(x	X
ejpam-6215	552	2	)	)	PUNCT
ejpam-6215	552	3	=	=	SYM
ejpam-6215	552	4	n−1	n−1	PROPN
ejpam-6215	552	5	[	[	PUNCT
ejpam-6215	552	6	t2	t2	NOUN
ejpam-6215	552	7	s2	s2	NOUN
ejpam-6215	552	8	n+[a1	n+[a1	VERB
ejpam-6215	552	9	]	]	PUNCT
ejpam-6215	552	10	]	]	PUNCT
ejpam-6215	552	11	.	.	PUNCT
ejpam-6215	553	1	y2(x	y2(x	X
ejpam-6215	553	2	)	)	PUNCT
ejpam-6215	553	3	=	=	SYM
ejpam-6215	553	4	n−1	n−1	PROPN
ejpam-6215	553	5	{	{	PUNCT
ejpam-6215	553	6	t2	t2	PROPN
ejpam-6215	553	7	s2	s2	PROPN
ejpam-6215	553	8	n+	n+	X
ejpam-6215	553	9	[	[	PUNCT
ejpam-6215	553	10	2x3	2x3	NUM
ejpam-6215	553	11	+	+	CCONJ
ejpam-6215	553	12	x4	x4	PROPN
ejpam-6215	553	13	2	2	NUM
ejpam-6215	553	14	+	+	NUM
ejpam-6215	553	15	x5	x5	NOUN
ejpam-6215	553	16	30	30	NUM
ejpam-6215	553	17	+	+	NUM
ejpam-6215	553	18	3x5µ	3x5µ	NOUN
ejpam-6215	553	19	2	2	NUM
ejpam-6215	553	20	+	+	CCONJ
ejpam-6215	553	21	7x6µ	7x6µ	NOUN
ejpam-6215	553	22	30	30	NUM
ejpam-6215	554	1	+	+	CCONJ
ejpam-6215	554	2	x7µ	x7µ	PROPN
ejpam-6215	554	3	280	280	NUM
ejpam-6215	554	4	.	.	PUNCT
ejpam-6215	554	5	.	.	PUNCT
ejpam-6215	554	6	.	.	PUNCT
ejpam-6215	555	1	+33x7µ2	+33x7µ2	NOUN
ejpam-6215	555	2	70	70	NUM
ejpam-6215	556	1	+	+	CCONJ
ejpam-6215	556	2	9x8µ2	9x8µ2	NUM
ejpam-6215	556	3	160	160	NUM
ejpam-6215	556	4	+	+	SYM
ejpam-6215	556	5	131x9µ3	131x9µ3	NUM
ejpam-6215	556	6	1680	1680	NUM
ejpam-6215	556	7	+	+	CCONJ
ejpam-6215	556	8	47x10µ3	47x10µ3	NOUN
ejpam-6215	556	9	11200	11200	NUM
ejpam-6215	556	10	+	+	CCONJ
ejpam-6215	556	11	57x11µ4	57x11µ4	NUM
ejpam-6215	556	12	6160	6160	NUM
ejpam-6215	556	13	+	+	CCONJ
ejpam-6215	556	14	3x13µ5	3x13µ5	NUM
ejpam-6215	556	15	5824	5824	NUM
ejpam-6215	556	16	]	]	PUNCT
ejpam-6215	556	17	}	}	PUNCT
ejpam-6215	556	18	.	.	PUNCT
ejpam-6215	557	1	y2(x	y2(x	X
ejpam-6215	557	2	)	)	PUNCT
ejpam-6215	557	3	=	=	SYM
ejpam-6215	557	4	x4	x4	PROPN
ejpam-6215	557	5	2	2	NUM
ejpam-6215	557	6	+	+	NUM
ejpam-6215	557	7	x5	x5	NOUN
ejpam-6215	557	8	10	10	NUM
ejpam-6215	557	9	+	+	NUM
ejpam-6215	557	10	x6	x6	PROPN
ejpam-6215	557	11	180	180	NUM
ejpam-6215	557	12	+	+	CCONJ
ejpam-6215	557	13	x6µ	x6µ	PROPN
ejpam-6215	557	14	4	4	NUM
ejpam-6215	557	15	+	+	CCONJ
ejpam-6215	557	16	x7µ	x7µ	PROPN
ejpam-6215	557	17	30	30	NUM
ejpam-6215	557	18	+	+	NUM
ejpam-6215	557	19	x8µ	x8µ	PROPN
ejpam-6215	557	20	2240	2240	NUM
ejpam-6215	557	21	+	+	CCONJ
ejpam-6215	557	22	33x8µ2	33x8µ2	NUM
ejpam-6215	557	23	560	560	NUM
ejpam-6215	557	24	.	.	PUNCT
ejpam-6215	557	25	.	.	PUNCT
ejpam-6215	557	26	.	.	PUNCT
ejpam-6215	558	1	s.	s.	PROPN
ejpam-6215	558	2	mohammed	mohammed	PROPN
ejpam-6215	558	3	,	,	PUNCT
ejpam-6215	558	4	s.	s.	PROPN
ejpam-6215	558	5	abid	abid	PROPN
ejpam-6215	558	6	,	,	PUNCT
ejpam-6215	558	7	r.	r.	PROPN
ejpam-6215	558	8	abid	abid	PROPN
ejpam-6215	558	9	/	/	SYM
ejpam-6215	558	10	eur	eur	PROPN
ejpam-6215	558	11	.	.	PUNCT
ejpam-6215	559	1	j.	j.	PROPN
ejpam-6215	559	2	pure	pure	PROPN
ejpam-6215	559	3	appl	appl	PROPN
ejpam-6215	559	4	.	.	PROPN
ejpam-6215	559	5	math	math	PROPN
ejpam-6215	559	6	,	,	PUNCT
ejpam-6215	559	7	18	18	NUM
ejpam-6215	559	8	(	(	PUNCT
ejpam-6215	559	9	3	3	NUM
ejpam-6215	559	10	)	)	PUNCT
ejpam-6215	559	11	(	(	PUNCT
ejpam-6215	559	12	2025	2025	NUM
ejpam-6215	559	13	)	)	PUNCT
ejpam-6215	559	14	,	,	PUNCT
ejpam-6215	559	15	6215	6215	NUM
ejpam-6215	559	16	25	25	NUM
ejpam-6215	559	17	of	of	ADP
ejpam-6215	559	18	38	38	NUM
ejpam-6215	560	1	+	+	CCONJ
ejpam-6215	560	2	x9µ2	x9µ2	X
ejpam-6215	560	3	160	160	NUM
ejpam-6215	561	1	+	+	CCONJ
ejpam-6215	561	2	131x10µ3	131x10µ3	NUM
ejpam-6215	561	3	16800	16800	NUM
ejpam-6215	561	4	+	+	CCONJ
ejpam-6215	561	5	47x11µ3	47x11µ3	NUM
ejpam-6215	561	6	123200	123200	NUM
ejpam-6215	562	1	+	+	CCONJ
ejpam-6215	562	2	19x12µ4	19x12µ4	PROPN
ejpam-6215	562	3	24640	24640	NUM
ejpam-6215	562	4	+	+	CCONJ
ejpam-6215	562	5	3x14µ5	3x14µ5	NUM
ejpam-6215	562	6	81536	81536	NUM
ejpam-6215	562	7	.	.	PUNCT
ejpam-6215	562	8	...	...	PUNCT
ejpam-6215	563	1	y(x	y(x	X
ejpam-6215	563	2	)	)	PUNCT
ejpam-6215	564	1	=	=	PUNCT
ejpam-6215	564	2	∞∑	∞∑	PRON
ejpam-6215	564	3	n=0	n=0	NUM
ejpam-6215	564	4	yn(x	yn(x	NUM
ejpam-6215	564	5	)	)	PUNCT
ejpam-6215	564	6	.	.	PUNCT
ejpam-6215	565	1	y(x	y(x	NOUN
ejpam-6215	565	2	)	)	PUNCT
ejpam-6215	565	3	=	=	SYM
ejpam-6215	565	4	1	1	NUM
ejpam-6215	565	5	+	+	CCONJ
ejpam-6215	565	6	x2µ	x2µ	PROPN
ejpam-6215	565	7	2	2	NUM
ejpam-6215	566	1	+	+	CCONJ
ejpam-6215	566	2	x2	x2	PROPN
ejpam-6215	567	1	+	+	CCONJ
ejpam-6215	567	2	x3	x3	ADJ
ejpam-6215	567	3	6	6	NUM
ejpam-6215	568	1	+	+	CCONJ
ejpam-6215	568	2	x4µ	x4µ	PROPN
ejpam-6215	568	3	4	4	NUM
ejpam-6215	568	4	+	+	NUM
ejpam-6215	568	5	x5µ	x5µ	NOUN
ejpam-6215	568	6	40	40	NUM
ejpam-6215	569	1	+	+	CCONJ
ejpam-6215	569	2	x6µ2	x6µ2	PROPN
ejpam-6215	569	3	20	20	NUM
ejpam-6215	569	4	+	+	CCONJ
ejpam-6215	569	5	x8µ3	x8µ3	PROPN
ejpam-6215	569	6	224	224	NUM
ejpam-6215	569	7	.	.	PUNCT
ejpam-6215	569	8	.	.	PUNCT
ejpam-6215	569	9	.	.	PUNCT
ejpam-6215	570	1	+	+	CCONJ
ejpam-6215	570	2	x4	x4	PROPN
ejpam-6215	570	3	2	2	NUM
ejpam-6215	570	4	+	+	NUM
ejpam-6215	570	5	x5	x5	NOUN
ejpam-6215	570	6	10	10	NUM
ejpam-6215	570	7	+	+	NUM
ejpam-6215	570	8	x6	x6	PROPN
ejpam-6215	570	9	180	180	NUM
ejpam-6215	570	10	+	+	CCONJ
ejpam-6215	570	11	x6µ	x6µ	PROPN
ejpam-6215	570	12	4	4	NUM
ejpam-6215	570	13	+	+	CCONJ
ejpam-6215	570	14	x7µ	x7µ	PROPN
ejpam-6215	570	15	30	30	NUM
ejpam-6215	570	16	+	+	NUM
ejpam-6215	570	17	x8µ	x8µ	PROPN
ejpam-6215	570	18	2240	2240	NUM
ejpam-6215	570	19	+	+	CCONJ
ejpam-6215	570	20	33x8µ2	33x8µ2	NUM
ejpam-6215	570	21	560	560	NUM
ejpam-6215	570	22	.	.	PUNCT
ejpam-6215	570	23	.	.	PUNCT
ejpam-6215	570	24	.	.	PUNCT
ejpam-6215	571	1	+	+	CCONJ
ejpam-6215	572	1	x9µ2	x9µ2	X
ejpam-6215	573	1	160	160	NUM
ejpam-6215	573	2	+	+	CCONJ
ejpam-6215	573	3	131x10µ3	131x10µ3	NUM
ejpam-6215	573	4	16800	16800	NUM
ejpam-6215	573	5	+	+	CCONJ
ejpam-6215	573	6	47x11µ3	47x11µ3	NUM
ejpam-6215	573	7	123200	123200	NUM
ejpam-6215	573	8	+	+	CCONJ
ejpam-6215	573	9	19x12µ4	19x12µ4	PROPN
ejpam-6215	573	10	24640	24640	NUM
ejpam-6215	573	11	+	+	CCONJ
ejpam-6215	573	12	3x14µ5	3x14µ5	NUM
ejpam-6215	573	13	81536	81536	NUM
ejpam-6215	573	14	+	+	CCONJ
ejpam-6215	573	15	·	·	PUNCT
ejpam-6215	573	16	·	·	PUNCT
ejpam-6215	573	17	·	·	PUNCT
ejpam-6215	573	18	the	the	DET
ejpam-6215	573	19	remainder	remainder	NOUN
ejpam-6215	573	20	function	function	NOUN
ejpam-6215	573	21	of	of	ADP
ejpam-6215	573	22	error	error	NOUN
ejpam-6215	573	23	is	be	AUX
ejpam-6215	573	24	evaluated	evaluate	VERB
ejpam-6215	573	25	:	:	PUNCT
ejpam-6215	573	26	ern	ern	PROPN
ejpam-6215	573	27	=	=	PUNCT
ejpam-6215	573	28	y′′n(x)−	y′′n(x)−	PROPN
ejpam-6215	574	1	2y3n(x)−	2y3n(x)−	PROPN
ejpam-6215	574	2	xyn(x)−	xyn(x)−	PROPN
ejpam-6215	574	3	µ.	µ.	NOUN
ejpam-6215	574	4	and	and	CCONJ
ejpam-6215	574	5	the	the	DET
ejpam-6215	574	6	mern	mern	NOUN
ejpam-6215	574	7	is	be	AUX
ejpam-6215	574	8	:	:	PUNCT
ejpam-6215	574	9	mern	mern	ADJ
ejpam-6215	574	10	=	=	SYM
ejpam-6215	574	11	max	max	PROPN
ejpam-6215	574	12	0.01≤x≤0.1	0.01≤x≤0.1	NUM
ejpam-6215	575	1	|ern(x)|	|ern(x)|	NOUN
ejpam-6215	575	2	.	.	PUNCT
ejpam-6215	576	1	in	in	ADP
ejpam-6215	576	2	table	table	NOUN
ejpam-6215	576	3	8	8	NUM
ejpam-6215	576	4	and	and	CCONJ
ejpam-6215	576	5	figure	figure	VERB
ejpam-6215	576	6	8	8	NUM
ejpam-6215	576	7	show	show	VERB
ejpam-6215	576	8	the	the	DET
ejpam-6215	576	9	convergence	convergence	NOUN
ejpam-6215	576	10	of	of	ADP
ejpam-6215	576	11	the	the	DET
ejpam-6215	576	12	solution	solution	NOUN
ejpam-6215	576	13	using	use	VERB
ejpam-6215	576	14	mern	mern	NOUN
ejpam-6215	576	15	for	for	ADP
ejpam-6215	576	16	the	the	DET
ejpam-6215	576	17	second	second	ADJ
ejpam-6215	576	18	painlevé	painlevé	NOUN
ejpam-6215	576	19	equation	equation	NOUN
ejpam-6215	576	20	by	by	ADP
ejpam-6215	576	21	ndm	ndm	PROPN
ejpam-6215	576	22	.	.	PUNCT
ejpam-6215	577	1	shows	show	VERB
ejpam-6215	577	2	the	the	DET
ejpam-6215	577	3	exponential	exponential	ADJ
ejpam-6215	577	4	decay	decay	NOUN
ejpam-6215	577	5	of	of	ADP
ejpam-6215	577	6	error	error	NOUN
ejpam-6215	577	7	and	and	CCONJ
ejpam-6215	577	8	nearly	nearly	ADV
ejpam-6215	577	9	linear	linear	ADJ
ejpam-6215	577	10	downward	downward	ADJ
ejpam-6215	577	11	trend	trend	NOUN
ejpam-6215	577	12	on	on	ADP
ejpam-6215	577	13	the	the	DET
ejpam-6215	577	14	logarithmic	logarithmic	ADJ
ejpam-6215	577	15	scale	scale	NOUN
ejpam-6215	577	16	.	.	PUNCT
ejpam-6215	578	1	the	the	DET
ejpam-6215	578	2	values	value	NOUN
ejpam-6215	578	3	indicate	indicate	VERB
ejpam-6215	578	4	a	a	DET
ejpam-6215	578	5	rapid	rapid	ADJ
ejpam-6215	578	6	reduction	reduction	NOUN
ejpam-6215	578	7	in	in	ADP
ejpam-6215	578	8	error	error	NOUN
ejpam-6215	578	9	as	as	ADP
ejpam-6215	578	10	n	n	DET
ejpam-6215	578	11	increases	increase	NOUN
ejpam-6215	578	12	,	,	PUNCT
ejpam-6215	578	13	demonstrating	demonstrate	VERB
ejpam-6215	578	14	improved	improved	ADJ
ejpam-6215	578	15	accuracy	accuracy	NOUN
ejpam-6215	578	16	with	with	ADP
ejpam-6215	578	17	higher	high	ADJ
ejpam-6215	578	18	-	-	PUNCT
ejpam-6215	578	19	order	order	NOUN
ejpam-6215	578	20	approximations	approximation	NOUN
ejpam-6215	578	21	.	.	PUNCT
ejpam-6215	579	1	initially	initially	ADV
ejpam-6215	579	2	,	,	PUNCT
ejpam-6215	579	3	for	for	ADP
ejpam-6215	579	4	n	n	NOUN
ejpam-6215	579	5	=	=	SYM
ejpam-6215	579	6	1	1	NUM
ejpam-6215	579	7	,	,	PUNCT
ejpam-6215	579	8	the	the	DET
ejpam-6215	579	9	error	error	NOUN
ejpam-6215	579	10	is	be	AUX
ejpam-6215	579	11	relatively	relatively	ADV
ejpam-6215	579	12	large	large	ADJ
ejpam-6215	579	13	.	.	PUNCT
ejpam-6215	580	1	however	however	ADV
ejpam-6215	580	2	,	,	PUNCT
ejpam-6215	580	3	as	as	ADP
ejpam-6215	580	4	n	n	DET
ejpam-6215	580	5	increases	increase	NOUN
ejpam-6215	580	6	,	,	PUNCT
ejpam-6215	580	7	the	the	DET
ejpam-6215	580	8	error	error	NOUN
ejpam-6215	580	9	decreases	decrease	VERB
ejpam-6215	580	10	significantly	significantly	ADV
ejpam-6215	580	11	,	,	PUNCT
ejpam-6215	580	12	reaching	reach	VERB
ejpam-6215	580	13	a	a	DET
ejpam-6215	580	14	much	much	ADV
ejpam-6215	580	15	smaller	small	ADJ
ejpam-6215	580	16	value	value	NOUN
ejpam-6215	580	17	at	at	ADP
ejpam-6215	580	18	n	n	PROPN
ejpam-6215	580	19	=	=	SYM
ejpam-6215	580	20	5	5	NUM
ejpam-6215	580	21	.	.	PUNCT
ejpam-6215	581	1	this	this	DET
ejpam-6215	581	2	trend	trend	NOUN
ejpam-6215	581	3	suggests	suggest	VERB
ejpam-6215	581	4	that	that	SCONJ
ejpam-6215	581	5	the	the	DET
ejpam-6215	581	6	ndm	ndm	NOUN
ejpam-6215	581	7	effectively	effectively	ADV
ejpam-6215	581	8	enhances	enhance	VERB
ejpam-6215	581	9	the	the	DET
ejpam-6215	581	10	accuracy	accuracy	NOUN
ejpam-6215	581	11	of	of	ADP
ejpam-6215	581	12	the	the	DET
ejpam-6215	581	13	solution	solution	NOUN
ejpam-6215	581	14	.	.	PUNCT
ejpam-6215	582	1	table	table	NOUN
ejpam-6215	582	2	8	8	NUM
ejpam-6215	582	3	:	:	PUNCT
ejpam-6215	582	4	the	the	DET
ejpam-6215	582	5	maximum	maximum	ADJ
ejpam-6215	582	6	residual	residual	ADJ
ejpam-6215	582	7	error	error	NOUN
ejpam-6215	582	8	:	:	PUNCT
ejpam-6215	582	9	mern	mern	NOUN
ejpam-6215	582	10	by	by	ADP
ejpam-6215	582	11	the	the	DET
ejpam-6215	582	12	ldm	ldm	NOUN
ejpam-6215	582	13	,	,	PUNCT
ejpam-6215	582	14	where	where	SCONJ
ejpam-6215	582	15	n	n	NOUN
ejpam-6215	582	16	=	=	SYM
ejpam-6215	582	17	1	1	NUM
ejpam-6215	582	18	,	,	PUNCT
ejpam-6215	582	19	.	.	PUNCT
ejpam-6215	582	20	.	.	PUNCT
ejpam-6215	583	1	.	.	PUNCT
ejpam-6215	584	1	,	,	PUNCT
ejpam-6215	584	2	5	5	X
ejpam-6215	584	3	.	.	X
ejpam-6215	585	1	n	n	PRON
ejpam-6215	585	2	mern	mern	ADJ
ejpam-6215	585	3	1	1	NUM
ejpam-6215	585	4	0.0634125	0.0634125	NUM
ejpam-6215	585	5	2	2	NUM
ejpam-6215	585	6	0.000950605	0.000950605	NUM
ejpam-6215	585	7	3	3	NUM
ejpam-6215	585	8	0.00001041	0.00001041	NUM
ejpam-6215	585	9	4	4	NUM
ejpam-6215	585	10	9.77952×	9.77952×	NOUN
ejpam-6215	585	11	10−8	10−8	NUM
ejpam-6215	585	12	5	5	NUM
ejpam-6215	585	13	8.40300×	8.40300×	NOUN
ejpam-6215	585	14	10−10	10−10	NUM
ejpam-6215	585	15	s.	s.	PROPN
ejpam-6215	585	16	mohammed	mohammed	PROPN
ejpam-6215	585	17	,	,	PUNCT
ejpam-6215	585	18	s.	s.	PROPN
ejpam-6215	585	19	abid	abid	PROPN
ejpam-6215	585	20	,	,	PUNCT
ejpam-6215	585	21	r.	r.	PROPN
ejpam-6215	585	22	abid	abid	PROPN
ejpam-6215	585	23	/	/	SYM
ejpam-6215	585	24	eur	eur	PROPN
ejpam-6215	585	25	.	.	PUNCT
ejpam-6215	586	1	j.	j.	PROPN
ejpam-6215	586	2	pure	pure	PROPN
ejpam-6215	586	3	appl	appl	PROPN
ejpam-6215	586	4	.	.	PROPN
ejpam-6215	586	5	math	math	PROPN
ejpam-6215	586	6	,	,	PUNCT
ejpam-6215	586	7	18	18	NUM
ejpam-6215	586	8	(	(	PUNCT
ejpam-6215	586	9	3	3	NUM
ejpam-6215	586	10	)	)	PUNCT
ejpam-6215	586	11	(	(	PUNCT
ejpam-6215	586	12	2025	2025	NUM
ejpam-6215	586	13	)	)	PUNCT
ejpam-6215	586	14	,	,	PUNCT
ejpam-6215	586	15	6215	6215	NUM
ejpam-6215	586	16	26	26	NUM
ejpam-6215	586	17	of	of	ADP
ejpam-6215	586	18	38	38	NUM
ejpam-6215	586	19	figure	figure	NOUN
ejpam-6215	586	20	8	8	NUM
ejpam-6215	586	21	:	:	PUNCT
ejpam-6215	586	22	the	the	DET
ejpam-6215	586	23	logarithmic	logarithmic	ADJ
ejpam-6215	586	24	plot	plot	NOUN
ejpam-6215	586	25	of	of	ADP
ejpam-6215	586	26	mern	mern	NOUN
ejpam-6215	586	27	(	(	PUNCT
ejpam-6215	586	28	ndm	ndm	PROPN
ejpam-6215	586	29	.	.	PUNCT
ejpam-6215	587	1	second	second	ADJ
ejpam-6215	587	2	painlevé	painlevé	NOUN
ejpam-6215	587	3	equation	equation	NOUN
ejpam-6215	587	4	)	)	PUNCT
ejpam-6215	587	5	.	.	PUNCT
ejpam-6215	588	1	3	3	X
ejpam-6215	588	2	.	.	X
ejpam-6215	588	3	numerical	numerical	ADJ
ejpam-6215	588	4	methods	method	NOUN
ejpam-6215	588	5	for	for	ADP
ejpam-6215	588	6	solving	solve	VERB
ejpam-6215	588	7	painlevé	painlevé	NOUN
ejpam-6215	588	8	equations	equation	NOUN
ejpam-6215	588	9	i	i	PRON
ejpam-6215	588	10	,	,	PUNCT
ejpam-6215	588	11	ii	ii	VERB
ejpam-6215	588	12	the	the	DET
ejpam-6215	588	13	numerical	numerical	ADJ
ejpam-6215	588	14	methods	method	NOUN
ejpam-6215	588	15	provide	provide	VERB
ejpam-6215	588	16	practical	practical	ADJ
ejpam-6215	588	17	means	mean	NOUN
ejpam-6215	588	18	for	for	ADP
ejpam-6215	588	19	approximating	approximate	VERB
ejpam-6215	588	20	solutions	solution	NOUN
ejpam-6215	588	21	where	where	SCONJ
ejpam-6215	588	22	analytical	analytical	ADJ
ejpam-6215	588	23	methods	method	NOUN
ejpam-6215	588	24	fall	fall	VERB
ejpam-6215	588	25	short	short	ADJ
ejpam-6215	588	26	.	.	PUNCT
ejpam-6215	589	1	the	the	DET
ejpam-6215	589	2	finite	finite	ADJ
ejpam-6215	589	3	difference	difference	NOUN
ejpam-6215	589	4	method	method	NOUN
ejpam-6215	589	5	discretizes	discretize	VERB
ejpam-6215	589	6	the	the	DET
ejpam-6215	589	7	continuous	continuous	ADJ
ejpam-6215	589	8	domain	domain	NOUN
ejpam-6215	589	9	and	and	CCONJ
ejpam-6215	589	10	approximates	approximate	VERB
ejpam-6215	589	11	derivatives	derivative	NOUN
ejpam-6215	589	12	using	use	VERB
ejpam-6215	589	13	difference	difference	NOUN
ejpam-6215	589	14	quotients	quotient	NOUN
ejpam-6215	589	15	,	,	PUNCT
ejpam-6215	589	16	which	which	PRON
ejpam-6215	589	17	is	be	AUX
ejpam-6215	589	18	particularly	particularly	ADV
ejpam-6215	589	19	useful	useful	ADJ
ejpam-6215	589	20	for	for	ADP
ejpam-6215	589	21	handling	handle	VERB
ejpam-6215	589	22	boundary	boundary	ADJ
ejpam-6215	589	23	value	value	NOUN
ejpam-6215	589	24	problems	problem	NOUN
ejpam-6215	589	25	.	.	PUNCT
ejpam-6215	590	1	[	[	X
ejpam-6215	590	2	13	13	NUM
ejpam-6215	590	3	,	,	PUNCT
ejpam-6215	590	4	14	14	NUM
ejpam-6215	590	5	]	]	PUNCT
ejpam-6215	590	6	the	the	DET
ejpam-6215	590	7	rk4	rk4	NOUN
ejpam-6215	590	8	method	method	NOUN
ejpam-6215	590	9	,	,	PUNCT
ejpam-6215	590	10	on	on	ADP
ejpam-6215	590	11	the	the	DET
ejpam-6215	590	12	other	other	ADJ
ejpam-6215	590	13	hand	hand	NOUN
ejpam-6215	590	14	,	,	PUNCT
ejpam-6215	590	15	is	be	AUX
ejpam-6215	590	16	well	well	ADV
ejpam-6215	590	17	-	-	PUNCT
ejpam-6215	590	18	known	know	VERB
ejpam-6215	590	19	for	for	ADP
ejpam-6215	590	20	its	its	PRON
ejpam-6215	590	21	robustness	robustness	NOUN
ejpam-6215	590	22	and	and	CCONJ
ejpam-6215	590	23	high	high	ADJ
ejpam-6215	590	24	accuracy	accuracy	NOUN
ejpam-6215	590	25	in	in	ADP
ejpam-6215	590	26	solving	solve	VERB
ejpam-6215	590	27	initial	initial	ADJ
ejpam-6215	590	28	value	value	NOUN
ejpam-6215	590	29	problems	problem	NOUN
ejpam-6215	590	30	,	,	PUNCT
ejpam-6215	590	31	making	make	VERB
ejpam-6215	590	32	it	it	PRON
ejpam-6215	590	33	an	an	DET
ejpam-6215	590	34	excellent	excellent	ADJ
ejpam-6215	590	35	choice	choice	NOUN
ejpam-6215	590	36	for	for	ADP
ejpam-6215	590	37	exploring	explore	VERB
ejpam-6215	590	38	the	the	DET
ejpam-6215	590	39	dynamical	dynamical	ADJ
ejpam-6215	590	40	behavior	behavior	NOUN
ejpam-6215	590	41	of	of	ADP
ejpam-6215	590	42	these	these	DET
ejpam-6215	590	43	nonlinear	nonlinear	ADJ
ejpam-6215	590	44	equations	equation	NOUN
ejpam-6215	590	45	[	[	X
ejpam-6215	590	46	42	42	NUM
ejpam-6215	590	47	]	]	PUNCT
ejpam-6215	590	48	.	.	PUNCT
ejpam-6215	591	1	in	in	ADP
ejpam-6215	591	2	this	this	DET
ejpam-6215	591	3	section	section	NOUN
ejpam-6215	591	4	,	,	PUNCT
ejpam-6215	591	5	we	we	PRON
ejpam-6215	591	6	focus	focus	VERB
ejpam-6215	591	7	exclusively	exclusively	ADV
ejpam-6215	591	8	on	on	ADP
ejpam-6215	591	9	numerical	numerical	ADJ
ejpam-6215	591	10	approaches	approach	NOUN
ejpam-6215	591	11	,	,	PUNCT
ejpam-6215	591	12	specifically	specifically	ADV
ejpam-6215	591	13	detailing	detail	VERB
ejpam-6215	591	14	the	the	DET
ejpam-6215	591	15	implementation	implementation	NOUN
ejpam-6215	591	16	of	of	ADP
ejpam-6215	591	17	the	the	DET
ejpam-6215	591	18	finite	finite	ADJ
ejpam-6215	591	19	difference	difference	NOUN
ejpam-6215	591	20	method	method	NOUN
ejpam-6215	591	21	(	(	PUNCT
ejpam-6215	591	22	fdm	fdm	NOUN
ejpam-6215	591	23	)	)	PUNCT
ejpam-6215	591	24	and	and	CCONJ
ejpam-6215	591	25	the	the	DET
ejpam-6215	591	26	fourth	fourth	ADJ
ejpam-6215	591	27	-	-	PUNCT
ejpam-6215	591	28	order	order	NOUN
ejpam-6215	591	29	runge	runge	NOUN
ejpam-6215	591	30	-	-	PUNCT
ejpam-6215	591	31	kutta	kutta	NOUN
ejpam-6215	591	32	method	method	NOUN
ejpam-6215	591	33	(	(	PUNCT
ejpam-6215	591	34	rk4	rk4	NOUN
ejpam-6215	591	35	)	)	PUNCT
ejpam-6215	591	36	for	for	ADP
ejpam-6215	591	37	solving	solve	VERB
ejpam-6215	591	38	the	the	DET
ejpam-6215	591	39	first	first	ADJ
ejpam-6215	591	40	and	and	CCONJ
ejpam-6215	591	41	second	second	ADJ
ejpam-6215	591	42	painlevé	painlevé	NOUN
ejpam-6215	591	43	equations	equation	NOUN
ejpam-6215	591	44	.	.	PUNCT
ejpam-6215	592	1	we	we	PRON
ejpam-6215	592	2	aim	aim	VERB
ejpam-6215	592	3	to	to	PART
ejpam-6215	592	4	provide	provide	VERB
ejpam-6215	592	5	clear	clear	ADJ
ejpam-6215	592	6	insights	insight	NOUN
ejpam-6215	592	7	into	into	ADP
ejpam-6215	592	8	their	their	PRON
ejpam-6215	592	9	strengths	strength	NOUN
ejpam-6215	592	10	and	and	CCONJ
ejpam-6215	592	11	limitations	limitation	NOUN
ejpam-6215	592	12	when	when	SCONJ
ejpam-6215	592	13	applied	apply	VERB
ejpam-6215	592	14	to	to	ADP
ejpam-6215	592	15	the	the	DET
ejpam-6215	592	16	painlevé	painlevé	NOUN
ejpam-6215	592	17	equations	equation	NOUN
ejpam-6215	592	18	i	i	PRON
ejpam-6215	592	19	and	and	CCONJ
ejpam-6215	592	20	ii	ii	PROPN
ejpam-6215	592	21	.	.	PROPN
ejpam-6215	592	22	3.1	3.1	NUM
ejpam-6215	592	23	.	.	PUNCT
ejpam-6215	593	1	finite	finite	ADJ
ejpam-6215	593	2	difference	difference	NOUN
ejpam-6215	593	3	method	method	NOUN
ejpam-6215	593	4	(	(	PUNCT
ejpam-6215	593	5	fdm	fdm	NOUN
ejpam-6215	593	6	)	)	PUNCT
ejpam-6215	593	7	the	the	DET
ejpam-6215	593	8	finite	finite	ADJ
ejpam-6215	593	9	difference	difference	NOUN
ejpam-6215	593	10	method	method	NOUN
ejpam-6215	593	11	(	(	PUNCT
ejpam-6215	593	12	fdm	fdm	NOUN
ejpam-6215	593	13	)	)	PUNCT
ejpam-6215	593	14	is	be	AUX
ejpam-6215	593	15	a	a	DET
ejpam-6215	593	16	numerical	numerical	ADJ
ejpam-6215	593	17	approach	approach	NOUN
ejpam-6215	593	18	for	for	ADP
ejpam-6215	593	19	solving	solve	VERB
ejpam-6215	593	20	ordinary	ordinary	ADJ
ejpam-6215	593	21	differential	differential	ADJ
ejpam-6215	593	22	equations	equation	NOUN
ejpam-6215	593	23	(	(	PUNCT
ejpam-6215	593	24	odes	ode	NOUN
ejpam-6215	593	25	)	)	PUNCT
ejpam-6215	593	26	,	,	PUNCT
ejpam-6215	593	27	originally	originally	ADV
ejpam-6215	593	28	studied	study	VERB
ejpam-6215	593	29	by	by	ADP
ejpam-6215	593	30	richardson	richardson	PROPN
ejpam-6215	593	31	in	in	ADP
ejpam-6215	593	32	1910	1910	NUM
ejpam-6215	593	33	.	.	PUNCT
ejpam-6215	594	1	fdm	fdm	NOUN
ejpam-6215	594	2	became	became	AUX
ejpam-6215	594	3	widely	widely	ADV
ejpam-6215	594	4	used	use	VERB
ejpam-6215	594	5	in	in	ADP
ejpam-6215	594	6	the	the	DET
ejpam-6215	594	7	mid-20th	mid-20th	NUM
ejpam-6215	594	8	century	century	NOUN
ejpam-6215	594	9	for	for	ADP
ejpam-6215	594	10	solving	solve	VERB
ejpam-6215	594	11	engineering	engineering	NOUN
ejpam-6215	594	12	and	and	CCONJ
ejpam-6215	594	13	physics	physics	NOUN
ejpam-6215	594	14	problems	problem	NOUN
ejpam-6215	594	15	.	.	PUNCT
ejpam-6215	595	1	with	with	ADP
ejpam-6215	595	2	advancements	advancement	NOUN
ejpam-6215	595	3	in	in	ADP
ejpam-6215	595	4	computing	computing	NOUN
ejpam-6215	595	5	,	,	PUNCT
ejpam-6215	595	6	it	it	PRON
ejpam-6215	595	7	remains	remain	VERB
ejpam-6215	595	8	a	a	DET
ejpam-6215	595	9	popular	popular	ADJ
ejpam-6215	595	10	method	method	NOUN
ejpam-6215	595	11	due	due	ADP
ejpam-6215	595	12	to	to	ADP
ejpam-6215	595	13	its	its	PRON
ejpam-6215	595	14	simplicity	simplicity	NOUN
ejpam-6215	595	15	,	,	PUNCT
ejpam-6215	595	16	efficiency	efficiency	NOUN
ejpam-6215	595	17	,	,	PUNCT
ejpam-6215	595	18	and	and	CCONJ
ejpam-6215	595	19	accuracy	accuracy	NOUN
ejpam-6215	595	20	.	.	PUNCT
ejpam-6215	596	1	[	[	X
ejpam-6215	596	2	15	15	NUM
ejpam-6215	596	3	,	,	PUNCT
ejpam-6215	596	4	16	16	NUM
ejpam-6215	596	5	]	]	PUNCT
ejpam-6215	596	6	the	the	DET
ejpam-6215	596	7	finite	finite	ADJ
ejpam-6215	596	8	difference	difference	NOUN
ejpam-6215	596	9	method	method	NOUN
ejpam-6215	596	10	works	work	VERB
ejpam-6215	596	11	by	by	ADP
ejpam-6215	596	12	discretizing	discretize	VERB
ejpam-6215	596	13	the	the	DET
ejpam-6215	596	14	domain	domain	NOUN
ejpam-6215	596	15	and	and	CCONJ
ejpam-6215	596	16	approximating	approximate	VERB
ejpam-6215	596	17	derivatives	derivative	NOUN
ejpam-6215	596	18	using	use	VERB
ejpam-6215	596	19	finite	finite	ADJ
ejpam-6215	596	20	differences	difference	NOUN
ejpam-6215	596	21	.	.	PUNCT
ejpam-6215	597	1	this	this	PRON
ejpam-6215	597	2	transforms	transform	VERB
ejpam-6215	597	3	the	the	DET
ejpam-6215	597	4	ode	ode	NOUN
ejpam-6215	597	5	into	into	ADP
ejpam-6215	597	6	a	a	DET
ejpam-6215	597	7	system	system	NOUN
ejpam-6215	597	8	of	of	ADP
ejpam-6215	597	9	algebraic	algebraic	ADJ
ejpam-6215	597	10	equations	equation	NOUN
ejpam-6215	597	11	,	,	PUNCT
ejpam-6215	597	12	making	make	VERB
ejpam-6215	597	13	it	it	PRON
ejpam-6215	597	14	easier	easy	ADJ
ejpam-6215	597	15	to	to	PART
ejpam-6215	597	16	solve	solve	VERB
ejpam-6215	597	17	numerically	numerically	ADV
ejpam-6215	597	18	.	.	PUNCT
ejpam-6215	598	1	in	in	ADP
ejpam-6215	598	2	this	this	DET
ejpam-6215	598	3	subsection	subsection	NOUN
ejpam-6215	598	4	,	,	PUNCT
ejpam-6215	598	5	we	we	PRON
ejpam-6215	598	6	use	use	VERB
ejpam-6215	598	7	fdm	fdm	NOUN
ejpam-6215	598	8	to	to	PART
ejpam-6215	598	9	solve	solve	VERB
ejpam-6215	598	10	painlevé	painlevé	NOUN
ejpam-6215	598	11	equations	equation	NOUN
ejpam-6215	599	1	[	[	X
ejpam-6215	599	2	43	43	NUM
ejpam-6215	599	3	,	,	PUNCT
ejpam-6215	599	4	44	44	NUM
ejpam-6215	599	5	]	]	PUNCT
ejpam-6215	599	6	.	.	PUNCT
ejpam-6215	600	1	3.1.1	3.1.1	X
ejpam-6215	600	2	.	.	PUNCT
ejpam-6215	601	1	the	the	DET
ejpam-6215	601	2	fdm	fdm	NOUN
ejpam-6215	601	3	method	method	NOUN
ejpam-6215	601	4	for	for	ADP
ejpam-6215	601	5	solving	solve	VERB
ejpam-6215	601	6	the	the	DET
ejpam-6215	601	7	painlevé	painlevé	NOUN
ejpam-6215	601	8	i	i	PRON
ejpam-6215	601	9	differential	differential	VERB
ejpam-6215	601	10	equation	equation	NOUN
ejpam-6215	601	11	rewrite	rewrite	NOUN
ejpam-6215	601	12	(	(	PUNCT
ejpam-6215	601	13	1	1	NUM
ejpam-6215	601	14	)	)	PUNCT
ejpam-6215	601	15	y′′(x	y′′(x	NOUN
ejpam-6215	601	16	)	)	PUNCT
ejpam-6215	601	17	=	=	PUNCT
ejpam-6215	601	18	6y2	6y2	NUM
ejpam-6215	601	19	+	+	CCONJ
ejpam-6215	601	20	x.	x.	NOUN
ejpam-6215	601	21	(	(	PUNCT
ejpam-6215	601	22	56	56	NUM
ejpam-6215	601	23	)	)	PUNCT
ejpam-6215	601	24	y(0	y(0	PROPN
ejpam-6215	601	25	)	)	PUNCT
ejpam-6215	601	26	=	=	SYM
ejpam-6215	601	27	0	0	NUM
ejpam-6215	601	28	,	,	PUNCT
ejpam-6215	601	29	y′(0	y′(0	NOUN
ejpam-6215	601	30	)	)	PUNCT
ejpam-6215	601	31	=	=	SYM
ejpam-6215	601	32	1	1	X
ejpam-6215	601	33	.	.	PUNCT
ejpam-6215	601	34	s.	s.	PROPN
ejpam-6215	601	35	mohammed	mohammed	PROPN
ejpam-6215	601	36	,	,	PUNCT
ejpam-6215	601	37	s.	s.	PROPN
ejpam-6215	601	38	abid	abid	PROPN
ejpam-6215	601	39	,	,	PUNCT
ejpam-6215	601	40	r.	r.	PROPN
ejpam-6215	601	41	abid	abid	PROPN
ejpam-6215	601	42	/	/	SYM
ejpam-6215	601	43	eur	eur	PROPN
ejpam-6215	601	44	.	.	PUNCT
ejpam-6215	602	1	j.	j.	PROPN
ejpam-6215	602	2	pure	pure	PROPN
ejpam-6215	602	3	appl	appl	PROPN
ejpam-6215	602	4	.	.	PROPN
ejpam-6215	602	5	math	math	PROPN
ejpam-6215	602	6	,	,	PUNCT
ejpam-6215	602	7	18	18	NUM
ejpam-6215	602	8	(	(	PUNCT
ejpam-6215	602	9	3	3	NUM
ejpam-6215	602	10	)	)	PUNCT
ejpam-6215	602	11	(	(	PUNCT
ejpam-6215	602	12	2025	2025	NUM
ejpam-6215	602	13	)	)	PUNCT
ejpam-6215	602	14	,	,	PUNCT
ejpam-6215	602	15	6215	6215	NUM
ejpam-6215	602	16	27	27	NUM
ejpam-6215	602	17	of	of	ADP
ejpam-6215	602	18	38	38	NUM
ejpam-6215	602	19	divide	divide	VERB
ejpam-6215	602	20	the	the	DET
ejpam-6215	602	21	interval	interval	NOUN
ejpam-6215	602	22	(	(	PUNCT
ejpam-6215	602	23	0	0	NUM
ejpam-6215	602	24	,	,	PUNCT
ejpam-6215	602	25	1	1	NUM
ejpam-6215	602	26	)	)	PUNCT
ejpam-6215	602	27	into	into	ADP
ejpam-6215	602	28	four	four	NUM
ejpam-6215	602	29	sub	sub	NOUN
ejpam-6215	602	30	-	-	NOUN
ejpam-6215	602	31	intervals	interval	NOUN
ejpam-6215	602	32	such	such	ADJ
ejpam-6215	602	33	that	that	DET
ejpam-6215	602	34	h	h	NOUN
ejpam-6215	602	35	=	=	NOUN
ejpam-6215	602	36	1	1	NUM
ejpam-6215	602	37	4	4	NUM
ejpam-6215	602	38	and	and	CCONJ
ejpam-6215	602	39	the	the	DET
ejpam-6215	602	40	pivot	pivot	NOUN
ejpam-6215	602	41	points	point	NOUN
ejpam-6215	602	42	are	be	AUX
ejpam-6215	602	43	at	at	ADP
ejpam-6215	602	44	x0	x0	PROPN
ejpam-6215	602	45	=	=	SYM
ejpam-6215	603	1	0	0	PROPN
ejpam-6215	603	2	,	,	PUNCT
ejpam-6215	603	3	x1	x1	NOUN
ejpam-6215	603	4	=	=	NOUN
ejpam-6215	603	5	1	1	NUM
ejpam-6215	603	6	4	4	NUM
ejpam-6215	603	7	,	,	PUNCT
ejpam-6215	603	8	x2	x2	PROPN
ejpam-6215	603	9	=	=	NOUN
ejpam-6215	603	10	1	1	NUM
ejpam-6215	603	11	2	2	NUM
ejpam-6215	603	12	,	,	PUNCT
ejpam-6215	603	13	x3	x3	NOUN
ejpam-6215	603	14	=	=	SYM
ejpam-6215	603	15	3	3	NUM
ejpam-6215	603	16	4	4	NUM
ejpam-6215	603	17	,	,	PUNCT
ejpam-6215	603	18	and	and	CCONJ
ejpam-6215	603	19	x4	x4	PROPN
ejpam-6215	603	20	=	=	NOUN
ejpam-6215	604	1	1	1	X
ejpam-6215	604	2	.	.	PUNCT
ejpam-6215	605	1	then	then	ADV
ejpam-6215	605	2	the	the	DET
ejpam-6215	605	3	second	second	ADJ
ejpam-6215	605	4	differential	differential	ADJ
ejpam-6215	605	5	equation	equation	NOUN
ejpam-6215	605	6	is	be	AUX
ejpam-6215	605	7	approximated	approximate	VERB
ejpam-6215	605	8	as	as	ADP
ejpam-6215	605	9	y′′(x	y′′(x	NOUN
ejpam-6215	605	10	)	)	PUNCT
ejpam-6215	606	1	=	=	SYM
ejpam-6215	606	2	yi+1	yi+1	NOUN
ejpam-6215	606	3	−	−	NOUN
ejpam-6215	606	4	2yi	2yi	NOUN
ejpam-6215	606	5	+	+	CCONJ
ejpam-6215	606	6	yi−1	yi−1	PROPN
ejpam-6215	606	7	h2	h2	PROPN
ejpam-6215	606	8	.	.	PUNCT
ejpam-6215	607	1	substitute	substitute	PROPN
ejpam-6215	607	2	into	into	ADP
ejpam-6215	607	3	(	(	PUNCT
ejpam-6215	607	4	56	56	NUM
ejpam-6215	607	5	)	)	PUNCT
ejpam-6215	607	6	1	1	NUM
ejpam-6215	607	7	h2	h2	NOUN
ejpam-6215	608	1	[	[	X
ejpam-6215	608	2	yi+1	yi+1	X
ejpam-6215	608	3	−	−	NOUN
ejpam-6215	608	4	2yi	2yi	NOUN
ejpam-6215	608	5	+	+	CCONJ
ejpam-6215	608	6	yi−1	yi−1	X
ejpam-6215	608	7	]	]	X
ejpam-6215	608	8	=	=	PUNCT
ejpam-6215	608	9	6y2i	6y2i	NUM
ejpam-6215	609	1	+	+	CCONJ
ejpam-6215	609	2	xi	xi	PROPN
ejpam-6215	609	3	.	.	PUNCT
ejpam-6215	609	4	yi+1	yi+1	PROPN
ejpam-6215	610	1	−	−	NOUN
ejpam-6215	610	2	2yi	2yi	NOUN
ejpam-6215	610	3	+	+	CCONJ
ejpam-6215	610	4	yi−1	yi−1	PROPN
ejpam-6215	610	5	=	=	PUNCT
ejpam-6215	610	6	h2(6y2i	h2(6y2i	PROPN
ejpam-6215	610	7	+	+	CCONJ
ejpam-6215	610	8	xi	xi	NOUN
ejpam-6215	610	9	)	)	PUNCT
ejpam-6215	610	10	.	.	PUNCT
ejpam-6215	611	1	(	(	PUNCT
ejpam-6215	611	2	57	57	NUM
ejpam-6215	611	3	)	)	PUNCT
ejpam-6215	611	4	by	by	ADP
ejpam-6215	611	5	using	use	VERB
ejpam-6215	611	6	a	a	DET
ejpam-6215	611	7	forward	forward	ADJ
ejpam-6215	611	8	difference	difference	NOUN
ejpam-6215	611	9	approximation	approximation	NOUN
ejpam-6215	611	10	for	for	ADP
ejpam-6215	611	11	the	the	DET
ejpam-6215	611	12	derivative	derivative	NOUN
ejpam-6215	611	13	to	to	PART
ejpam-6215	611	14	compute	compute	VERB
ejpam-6215	611	15	the	the	DET
ejpam-6215	611	16	initial	initial	ADJ
ejpam-6215	611	17	value	value	NOUN
ejpam-6215	611	18	for	for	ADP
ejpam-6215	611	19	y1	y1	NOUN
ejpam-6215	611	20	.	.	PUNCT
ejpam-6215	612	1	y′(x	y′(x	NOUN
ejpam-6215	612	2	)	)	PUNCT
ejpam-6215	612	3	=	=	SYM
ejpam-6215	613	1	1	1	NUM
ejpam-6215	613	2	h	h	NOUN
ejpam-6215	614	1	[	[	X
ejpam-6215	614	2	y(x+	y(x+	X
ejpam-6215	614	3	h)−	h)−	PROPN
ejpam-6215	614	4	y(x	y(x	PROPN
ejpam-6215	614	5	)	)	PUNCT
ejpam-6215	614	6	]	]	PUNCT
ejpam-6215	614	7	.	.	PUNCT
ejpam-6215	615	1	since	since	SCONJ
ejpam-6215	615	2	y0	y0	PROPN
ejpam-6215	615	3	=	=	SYM
ejpam-6215	615	4	y(x0	y(x0	NOUN
ejpam-6215	615	5	)	)	PUNCT
ejpam-6215	615	6	=	=	SYM
ejpam-6215	615	7	y(0	y(0	PROPN
ejpam-6215	615	8	)	)	PUNCT
ejpam-6215	615	9	.	.	PUNCT
ejpam-6215	616	1	y1	y1	NOUN
ejpam-6215	616	2	=	=	SYM
ejpam-6215	616	3	y(x1	y(x1	NOUN
ejpam-6215	616	4	)	)	PUNCT
ejpam-6215	617	1	=	=	SYM
ejpam-6215	617	2	y	y	PROPN
ejpam-6215	617	3	(	(	PUNCT
ejpam-6215	617	4	1	1	NUM
ejpam-6215	617	5	4	4	NUM
ejpam-6215	617	6	)	)	PUNCT
ejpam-6215	617	7	.	.	PUNCT
ejpam-6215	618	1	y′(0	y′(0	X
ejpam-6215	618	2	)	)	PUNCT
ejpam-6215	618	3	=	=	SYM
ejpam-6215	618	4	y(h)−	y(h)−	NOUN
ejpam-6215	618	5	y0	y0	NUM
ejpam-6215	618	6	h	h	NOUN
ejpam-6215	618	7	.	.	PUNCT
ejpam-6215	619	1	1	1	NUM
ejpam-6215	619	2	=	=	SYM
ejpam-6215	619	3	y1	y1	NOUN
ejpam-6215	619	4	−	−	PROPN
ejpam-6215	619	5	0	0	NUM
ejpam-6215	619	6	h	h	NOUN
ejpam-6215	619	7	.	.	PUNCT
ejpam-6215	620	1	y1	y1	INTJ
ejpam-6215	620	2	=	=	PUNCT
ejpam-6215	621	1	h.	h.	PROPN
ejpam-6215	621	2	thus	thus	ADV
ejpam-6215	621	3	we	we	PRON
ejpam-6215	621	4	have	have	VERB
ejpam-6215	621	5	y0	y0	NOUN
ejpam-6215	621	6	=	=	SYM
ejpam-6215	621	7	0	0	NUM
ejpam-6215	621	8	,	,	PUNCT
ejpam-6215	621	9	y1	y1	NOUN
ejpam-6215	621	10	=	=	SYM
ejpam-6215	621	11	1	1	NUM
ejpam-6215	621	12	4	4	NUM
ejpam-6215	621	13	.	.	PUNCT
ejpam-6215	622	1	yi+1	yi+1	X
ejpam-6215	623	1	−	−	NOUN
ejpam-6215	623	2	2yi	2yi	NOUN
ejpam-6215	623	3	+	+	CCONJ
ejpam-6215	623	4	yi−1	yi−1	PROPN
ejpam-6215	623	5	=	=	PUNCT
ejpam-6215	623	6	h2(6y2i	h2(6y2i	PROPN
ejpam-6215	623	7	+	+	CCONJ
ejpam-6215	623	8	xi	xi	NOUN
ejpam-6215	623	9	)	)	PUNCT
ejpam-6215	623	10	.	.	PUNCT
ejpam-6215	624	1	for	for	ADP
ejpam-6215	624	2	i	i	PRON
ejpam-6215	624	3	=	=	NOUN
ejpam-6215	624	4	1	1	NUM
ejpam-6215	624	5	,	,	PUNCT
ejpam-6215	624	6	y2	y2	NOUN
ejpam-6215	624	7	−	−	NOUN
ejpam-6215	624	8	2y1	2y1	NUM
ejpam-6215	625	1	+	+	CCONJ
ejpam-6215	625	2	y0	y0	NOUN
ejpam-6215	625	3	=	=	SYM
ejpam-6215	625	4	(	(	PUNCT
ejpam-6215	625	5	1	1	NUM
ejpam-6215	625	6	4	4	NUM
ejpam-6215	625	7	)	)	SYM
ejpam-6215	625	8	2	2	NUM
ejpam-6215	625	9	(	(	PUNCT
ejpam-6215	625	10	6y21	6y21	NOUN
ejpam-6215	625	11	+	+	CCONJ
ejpam-6215	625	12	x1	x1	NUM
ejpam-6215	625	13	)	)	PUNCT
ejpam-6215	625	14	.	.	PUNCT
ejpam-6215	626	1	y2	y2	NOUN
ejpam-6215	627	1	=	=	NOUN
ejpam-6215	628	1	69	69	NUM
ejpam-6215	628	2	128	128	NUM
ejpam-6215	628	3	.	.	PUNCT
ejpam-6215	629	1	for	for	ADP
ejpam-6215	629	2	i	i	PRON
ejpam-6215	629	3	=	=	SYM
ejpam-6215	629	4	2	2	NUM
ejpam-6215	629	5	,	,	PUNCT
ejpam-6215	629	6	y3	y3	NOUN
ejpam-6215	629	7	−	−	PROPN
ejpam-6215	629	8	2y2	2y2	NUM
ejpam-6215	630	1	+	+	CCONJ
ejpam-6215	630	2	y1	y1	NOUN
ejpam-6215	630	3	=	=	SYM
ejpam-6215	630	4	3y22	3y22	NUM
ejpam-6215	630	5	8	8	NUM
ejpam-6215	631	1	+	+	CCONJ
ejpam-6215	631	2	x2	x2	PROPN
ejpam-6215	631	3	16	16	NUM
ejpam-6215	631	4	.	.	PUNCT
ejpam-6215	632	1	y3	y3	NOUN
ejpam-6215	632	2	=	=	SYM
ejpam-6215	632	3	126923	126923	NUM
ejpam-6215	632	4	131072	131072	NUM
ejpam-6215	632	5	.	.	PUNCT
ejpam-6215	633	1	s.	s.	PROPN
ejpam-6215	633	2	mohammed	mohammed	PROPN
ejpam-6215	633	3	,	,	PUNCT
ejpam-6215	633	4	s.	s.	PROPN
ejpam-6215	633	5	abid	abid	PROPN
ejpam-6215	633	6	,	,	PUNCT
ejpam-6215	633	7	r.	r.	PROPN
ejpam-6215	633	8	abid	abid	PROPN
ejpam-6215	633	9	/	/	SYM
ejpam-6215	633	10	eur	eur	PROPN
ejpam-6215	633	11	.	.	PUNCT
ejpam-6215	634	1	j.	j.	PROPN
ejpam-6215	634	2	pure	pure	PROPN
ejpam-6215	634	3	appl	appl	PROPN
ejpam-6215	634	4	.	.	PROPN
ejpam-6215	634	5	math	math	PROPN
ejpam-6215	634	6	,	,	PUNCT
ejpam-6215	634	7	18	18	NUM
ejpam-6215	634	8	(	(	PUNCT
ejpam-6215	634	9	3	3	NUM
ejpam-6215	634	10	)	)	PUNCT
ejpam-6215	634	11	(	(	PUNCT
ejpam-6215	634	12	2025	2025	NUM
ejpam-6215	634	13	)	)	PUNCT
ejpam-6215	634	14	,	,	PUNCT
ejpam-6215	634	15	6215	6215	NUM
ejpam-6215	634	16	28	28	NUM
ejpam-6215	634	17	of	of	ADP
ejpam-6215	634	18	38	38	NUM
ejpam-6215	634	19	their	their	PRON
ejpam-6215	634	20	solution	solution	NOUN
ejpam-6215	634	21	gives	give	VERB
ejpam-6215	634	22	y1	y1	NOUN
ejpam-6215	634	23	=	=	SYM
ejpam-6215	634	24	1	1	NUM
ejpam-6215	634	25	4	4	NUM
ejpam-6215	634	26	,	,	PUNCT
ejpam-6215	634	27	y2	y2	NOUN
ejpam-6215	634	28	=	=	NOUN
ejpam-6215	634	29	69	69	NUM
ejpam-6215	634	30	128	128	NUM
ejpam-6215	634	31	,	,	PUNCT
ejpam-6215	634	32	y3	y3	NOUN
ejpam-6215	634	33	=	=	SYM
ejpam-6215	634	34	126923	126923	NUM
ejpam-6215	634	35	131072	131072	NUM
ejpam-6215	634	36	.	.	PUNCT
ejpam-6215	634	37	...	...	PUNCT
ejpam-6215	635	1	3.1.2	3.1.2	X
ejpam-6215	635	2	.	.	PUNCT
ejpam-6215	636	1	the	the	DET
ejpam-6215	636	2	fdm	fdm	NOUN
ejpam-6215	636	3	for	for	ADP
ejpam-6215	636	4	solving	solve	VERB
ejpam-6215	636	5	the	the	DET
ejpam-6215	636	6	painlevé	painlevé	NOUN
ejpam-6215	636	7	ii	ii	NOUN
ejpam-6215	636	8	differential	differential	NOUN
ejpam-6215	636	9	equation	equation	NOUN
ejpam-6215	636	10	rewrite	rewrite	NOUN
ejpam-6215	636	11	(	(	PUNCT
ejpam-6215	636	12	2	2	NUM
ejpam-6215	636	13	)	)	PUNCT
ejpam-6215	636	14	y′′(t	y′′(t	VERB
ejpam-6215	636	15	)	)	PUNCT
ejpam-6215	636	16	=	=	SYM
ejpam-6215	637	1	2y3	2y3	NUM
ejpam-6215	638	1	+	+	CCONJ
ejpam-6215	638	2	xy	xy	PROPN
ejpam-6215	638	3	+	+	NUM
ejpam-6215	638	4	µ.	µ.	NOUN
ejpam-6215	638	5	(	(	PUNCT
ejpam-6215	638	6	58	58	NUM
ejpam-6215	638	7	)	)	PUNCT
ejpam-6215	638	8	y(0	y(0	PROPN
ejpam-6215	638	9	)	)	PUNCT
ejpam-6215	638	10	=	=	SYM
ejpam-6215	638	11	1	1	NUM
ejpam-6215	638	12	,	,	PUNCT
ejpam-6215	638	13	y′(0	y′(0	NOUN
ejpam-6215	638	14	)	)	PUNCT
ejpam-6215	638	15	=	=	SYM
ejpam-6215	639	1	0	0	X
ejpam-6215	639	2	.	.	NOUN
ejpam-6215	639	3	divide	divide	VERB
ejpam-6215	639	4	the	the	DET
ejpam-6215	639	5	interval	interval	NOUN
ejpam-6215	639	6	(	(	PUNCT
ejpam-6215	639	7	0	0	NUM
ejpam-6215	639	8	,	,	PUNCT
ejpam-6215	639	9	1	1	NUM
ejpam-6215	639	10	)	)	PUNCT
ejpam-6215	639	11	into	into	ADP
ejpam-6215	639	12	four	four	NUM
ejpam-6215	639	13	sub	sub	NOUN
ejpam-6215	639	14	-	-	NOUN
ejpam-6215	639	15	intervals	interval	NOUN
ejpam-6215	639	16	such	such	ADJ
ejpam-6215	639	17	that	that	DET
ejpam-6215	639	18	h	h	NOUN
ejpam-6215	639	19	=	=	NOUN
ejpam-6215	639	20	1	1	NUM
ejpam-6215	639	21	4	4	NUM
ejpam-6215	639	22	and	and	CCONJ
ejpam-6215	639	23	the	the	DET
ejpam-6215	639	24	pivot	pivot	NOUN
ejpam-6215	639	25	points	point	NOUN
ejpam-6215	639	26	are	be	AUX
ejpam-6215	639	27	at	at	ADP
ejpam-6215	639	28	x0	x0	PROPN
ejpam-6215	639	29	=	=	SYM
ejpam-6215	640	1	0	0	PROPN
ejpam-6215	640	2	,	,	PUNCT
ejpam-6215	640	3	x1	x1	NOUN
ejpam-6215	640	4	=	=	NOUN
ejpam-6215	640	5	1	1	NUM
ejpam-6215	640	6	4	4	NUM
ejpam-6215	640	7	,	,	PUNCT
ejpam-6215	640	8	x2	x2	PROPN
ejpam-6215	640	9	=	=	NOUN
ejpam-6215	640	10	1	1	NUM
ejpam-6215	640	11	2	2	NUM
ejpam-6215	640	12	,	,	PUNCT
ejpam-6215	640	13	x3	x3	NOUN
ejpam-6215	640	14	=	=	SYM
ejpam-6215	640	15	3	3	NUM
ejpam-6215	640	16	4	4	NUM
ejpam-6215	640	17	,	,	PUNCT
ejpam-6215	640	18	and	and	CCONJ
ejpam-6215	640	19	x4	x4	PROPN
ejpam-6215	640	20	=	=	NOUN
ejpam-6215	641	1	1	1	X
ejpam-6215	641	2	.	.	PUNCT
ejpam-6215	642	1	then	then	ADV
ejpam-6215	642	2	the	the	DET
ejpam-6215	642	3	second	second	ADJ
ejpam-6215	642	4	differential	differential	ADJ
ejpam-6215	642	5	equation	equation	NOUN
ejpam-6215	642	6	is	be	AUX
ejpam-6215	642	7	approximated	approximate	VERB
ejpam-6215	642	8	as	as	ADP
ejpam-6215	642	9	y′′(x	y′′(x	NOUN
ejpam-6215	642	10	)	)	PUNCT
ejpam-6215	643	1	=	=	SYM
ejpam-6215	643	2	yi+1	yi+1	NOUN
ejpam-6215	643	3	−	−	NOUN
ejpam-6215	643	4	2yi	2yi	NOUN
ejpam-6215	643	5	+	+	CCONJ
ejpam-6215	643	6	yi−1	yi−1	PROPN
ejpam-6215	643	7	h2	h2	PROPN
ejpam-6215	643	8	.	.	PUNCT
ejpam-6215	644	1	substitute	substitute	PROPN
ejpam-6215	644	2	into	into	ADP
ejpam-6215	644	3	(	(	PUNCT
ejpam-6215	644	4	58	58	NUM
ejpam-6215	644	5	):	):	PUNCT
ejpam-6215	644	6	1	1	NUM
ejpam-6215	644	7	h2	h2	NOUN
ejpam-6215	645	1	[	[	X
ejpam-6215	645	2	yi+1	yi+1	NOUN
ejpam-6215	645	3	−	−	NOUN
ejpam-6215	645	4	2yi	2yi	NOUN
ejpam-6215	645	5	+	+	CCONJ
ejpam-6215	645	6	yi−1	yi−1	X
ejpam-6215	645	7	]	]	X
ejpam-6215	645	8	=	=	SYM
ejpam-6215	645	9	2y3i	2y3i	PROPN
ejpam-6215	646	1	+	+	CCONJ
ejpam-6215	646	2	xiyi	xiyi	PROPN
ejpam-6215	646	3	+	+	CCONJ
ejpam-6215	646	4	µ	µ	NUM
ejpam-6215	646	5	,	,	PUNCT
ejpam-6215	646	6	yi+1	yi+1	NOUN
ejpam-6215	646	7	−	−	PROPN
ejpam-6215	646	8	2yi	2yi	NOUN
ejpam-6215	646	9	+	+	CCONJ
ejpam-6215	646	10	yi−1	yi−1	PROPN
ejpam-6215	646	11	=	=	SYM
ejpam-6215	646	12	h2	h2	PROPN
ejpam-6215	646	13	(	(	PUNCT
ejpam-6215	646	14	2y3i	2y3i	NUM
ejpam-6215	647	1	+	+	CCONJ
ejpam-6215	647	2	xiyi	xiyi	PROPN
ejpam-6215	647	3	+	+	CCONJ
ejpam-6215	647	4	µ	µ	X
ejpam-6215	647	5	)	)	PUNCT
ejpam-6215	647	6	.	.	PUNCT
ejpam-6215	648	1	by	by	ADP
ejpam-6215	648	2	using	use	VERB
ejpam-6215	648	3	a	a	DET
ejpam-6215	648	4	forward	forward	ADJ
ejpam-6215	648	5	difference	difference	NOUN
ejpam-6215	648	6	approximation	approximation	NOUN
ejpam-6215	648	7	for	for	ADP
ejpam-6215	648	8	the	the	DET
ejpam-6215	648	9	derivative	derivative	NOUN
ejpam-6215	648	10	to	to	PART
ejpam-6215	648	11	compute	compute	VERB
ejpam-6215	648	12	the	the	DET
ejpam-6215	648	13	initial	initial	ADJ
ejpam-6215	648	14	value	value	NOUN
ejpam-6215	648	15	for	for	ADP
ejpam-6215	648	16	y1	y1	NOUN
ejpam-6215	648	17	,	,	PUNCT
ejpam-6215	648	18	y′(x	y′(x	NOUN
ejpam-6215	648	19	)	)	PUNCT
ejpam-6215	648	20	=	=	SYM
ejpam-6215	648	21	1	1	NUM
ejpam-6215	648	22	h	h	NOUN
ejpam-6215	649	1	[	[	X
ejpam-6215	649	2	y(x+	y(x+	X
ejpam-6215	649	3	h)−	h)−	PROPN
ejpam-6215	649	4	y(x	y(x	PROPN
ejpam-6215	649	5	)	)	PUNCT
ejpam-6215	649	6	]	]	PUNCT
ejpam-6215	649	7	.	.	PUNCT
ejpam-6215	650	1	y′(0	y′(0	X
ejpam-6215	650	2	)	)	PUNCT
ejpam-6215	650	3	=	=	SYM
ejpam-6215	650	4	y(h)−	y(h)−	NOUN
ejpam-6215	650	5	y0	y0	NUM
ejpam-6215	650	6	h	h	NOUN
ejpam-6215	650	7	.	.	PUNCT
ejpam-6215	650	8	0	0	PUNCT
ejpam-6215	651	1	=	=	PUNCT
ejpam-6215	651	2	y1	y1	NOUN
ejpam-6215	651	3	−	−	PROPN
ejpam-6215	651	4	1	1	NUM
ejpam-6215	651	5	h	h	NOUN
ejpam-6215	651	6	.	.	PUNCT
ejpam-6215	652	1	y1	y1	NOUN
ejpam-6215	652	2	=	=	SYM
ejpam-6215	652	3	1	1	X
ejpam-6215	652	4	.	.	PUNCT
ejpam-6215	653	1	thus	thus	ADV
ejpam-6215	653	2	we	we	PRON
ejpam-6215	653	3	have	have	VERB
ejpam-6215	653	4	yi+1	yi+1	NUM
ejpam-6215	653	5	−	−	NOUN
ejpam-6215	653	6	2yi	2yi	NOUN
ejpam-6215	654	1	+	+	CCONJ
ejpam-6215	655	1	yi−1	yi−1	PROPN
ejpam-6215	655	2	=	=	SYM
ejpam-6215	655	3	h2(2y3i	h2(2y3i	PROPN
ejpam-6215	656	1	+	+	CCONJ
ejpam-6215	656	2	xiyi	xiyi	PROPN
ejpam-6215	656	3	+	+	CCONJ
ejpam-6215	656	4	µ	µ	NOUN
ejpam-6215	656	5	)	)	PUNCT
ejpam-6215	656	6	.	.	PUNCT
ejpam-6215	657	1	for	for	ADP
ejpam-6215	657	2	i	i	PRON
ejpam-6215	657	3	=	=	SYM
ejpam-6215	657	4	1	1	NUM
ejpam-6215	657	5	y2	y2	NOUN
ejpam-6215	657	6	−	−	PROPN
ejpam-6215	657	7	2y1	2y1	NUM
ejpam-6215	658	1	+	+	CCONJ
ejpam-6215	658	2	y0	y0	NOUN
ejpam-6215	658	3	=	=	SYM
ejpam-6215	658	4	h2(2y31	h2(2y31	PROPN
ejpam-6215	658	5	+	+	CCONJ
ejpam-6215	658	6	x1y1	x1y1	PUNCT
ejpam-6215	658	7	+	+	NUM
ejpam-6215	658	8	µ	µ	X
ejpam-6215	658	9	)	)	PUNCT
ejpam-6215	658	10	.	.	PUNCT
ejpam-6215	659	1	y2	y2	NOUN
ejpam-6215	660	1	=	=	NOUN
ejpam-6215	661	1	73	73	NUM
ejpam-6215	661	2	64	64	NUM
ejpam-6215	661	3	+	+	SYM
ejpam-6215	661	4	µ	µ	X
ejpam-6215	661	5	16	16	NUM
ejpam-6215	661	6	.	.	PUNCT
ejpam-6215	662	1	s.	s.	PROPN
ejpam-6215	662	2	mohammed	mohammed	PROPN
ejpam-6215	662	3	,	,	PUNCT
ejpam-6215	662	4	s.	s.	PROPN
ejpam-6215	662	5	abid	abid	PROPN
ejpam-6215	662	6	,	,	PUNCT
ejpam-6215	662	7	r.	r.	PROPN
ejpam-6215	662	8	abid	abid	PROPN
ejpam-6215	662	9	/	/	SYM
ejpam-6215	662	10	eur	eur	PROPN
ejpam-6215	662	11	.	.	PUNCT
ejpam-6215	663	1	j.	j.	PROPN
ejpam-6215	663	2	pure	pure	PROPN
ejpam-6215	663	3	appl	appl	PROPN
ejpam-6215	663	4	.	.	PROPN
ejpam-6215	663	5	math	math	PROPN
ejpam-6215	663	6	,	,	PUNCT
ejpam-6215	663	7	18	18	NUM
ejpam-6215	663	8	(	(	PUNCT
ejpam-6215	663	9	3	3	NUM
ejpam-6215	663	10	)	)	PUNCT
ejpam-6215	663	11	(	(	PUNCT
ejpam-6215	663	12	2025	2025	NUM
ejpam-6215	663	13	)	)	PUNCT
ejpam-6215	663	14	,	,	PUNCT
ejpam-6215	663	15	6215	6215	NUM
ejpam-6215	663	16	29	29	NUM
ejpam-6215	663	17	of	of	ADP
ejpam-6215	663	18	38	38	NUM
ejpam-6215	663	19	for	for	ADP
ejpam-6215	663	20	i	i	PRON
ejpam-6215	663	21	=	=	SYM
ejpam-6215	663	22	2	2	NUM
ejpam-6215	663	23	y3	y3	NOUN
ejpam-6215	663	24	−	−	PROPN
ejpam-6215	663	25	2y2	2y2	NUM
ejpam-6215	663	26	+	+	CCONJ
ejpam-6215	663	27	y1	y1	NOUN
ejpam-6215	663	28	=	=	PUNCT
ejpam-6215	663	29	h2(2y32	h2(2y32	PROPN
ejpam-6215	663	30	+	+	CCONJ
ejpam-6215	663	31	x2y2	x2y2	X
ejpam-6215	663	32	+	+	NUM
ejpam-6215	663	33	µ	µ	NUM
ejpam-6215	663	34	)	)	PUNCT
ejpam-6215	663	35	.	.	PUNCT
ejpam-6215	664	1	y3	y3	NOUN
ejpam-6215	664	2	−	−	PROPN
ejpam-6215	664	3	2	2	NUM
ejpam-6215	664	4	(	(	PUNCT
ejpam-6215	664	5	73	73	NUM
ejpam-6215	664	6	64	64	NUM
ejpam-6215	664	7	+	+	SYM
ejpam-6215	664	8	µ	µ	X
ejpam-6215	664	9	16	16	NUM
ejpam-6215	664	10	)	)	PUNCT
ejpam-6215	665	1	+	+	CCONJ
ejpam-6215	665	2	1	1	X
ejpam-6215	665	3	=	=	SYM
ejpam-6215	665	4	(	(	PUNCT
ejpam-6215	665	5	1	1	NUM
ejpam-6215	665	6	4	4	NUM
ejpam-6215	665	7	)	)	PUNCT
ejpam-6215	665	8	(	(	PUNCT
ejpam-6215	665	9	2	2	NUM
ejpam-6215	665	10	(	(	PUNCT
ejpam-6215	665	11	73	73	NUM
ejpam-6215	665	12	64	64	NUM
ejpam-6215	665	13	+	+	SYM
ejpam-6215	665	14	µ	µ	X
ejpam-6215	665	15	16	16	NUM
ejpam-6215	665	16	)	)	SYM
ejpam-6215	665	17	3	3	NUM
ejpam-6215	665	18	+	+	CCONJ
ejpam-6215	665	19	1	1	NUM
ejpam-6215	665	20	2	2	NUM
ejpam-6215	665	21	(	(	PUNCT
ejpam-6215	665	22	73	73	NUM
ejpam-6215	665	23	64	64	NUM
ejpam-6215	665	24	+	+	SYM
ejpam-6215	665	25	µ	µ	X
ejpam-6215	665	26	16	16	NUM
ejpam-6215	665	27	)	)	PUNCT
ejpam-6215	665	28	+	+	NUM
ejpam-6215	665	29	µ	µ	X
ejpam-6215	665	30	)	)	PUNCT
ejpam-6215	665	31	.	.	PUNCT
ejpam-6215	666	1	y3	y3	NOUN
ejpam-6215	666	2	=	=	SYM
ejpam-6215	666	3	1135513	1135513	NUM
ejpam-6215	666	4	524288	524288	NUM
ejpam-6215	666	5	+	+	NUM
ejpam-6215	666	6	66163µ	66163µ	NUM
ejpam-6215	666	7	131072	131072	NUM
ejpam-6215	666	8	+	+	CCONJ
ejpam-6215	666	9	219µ2	219µ2	NUM
ejpam-6215	666	10	32768	32768	NUM
ejpam-6215	666	11	+	+	CCONJ
ejpam-6215	666	12	µ3	µ3	PROPN
ejpam-6215	666	13	8192	8192	NUM
ejpam-6215	666	14	.	.	PUNCT
ejpam-6215	667	1	their	their	PRON
ejpam-6215	667	2	solution	solution	NOUN
ejpam-6215	667	3	gives	give	VERB
ejpam-6215	667	4	:	:	PUNCT
ejpam-6215	667	5	y1	y1	NOUN
ejpam-6215	667	6	=	=	SYM
ejpam-6215	667	7	1	1	NUM
ejpam-6215	667	8	,	,	PUNCT
ejpam-6215	667	9	y2	y2	NOUN
ejpam-6215	667	10	=	=	NOUN
ejpam-6215	667	11	73	73	NUM
ejpam-6215	667	12	64	64	NUM
ejpam-6215	667	13	+	+	SYM
ejpam-6215	667	14	µ	µ	X
ejpam-6215	667	15	16	16	NUM
ejpam-6215	667	16	,	,	PUNCT
ejpam-6215	667	17	y3	y3	NOUN
ejpam-6215	667	18	=	=	SYM
ejpam-6215	667	19	1135513	1135513	NUM
ejpam-6215	667	20	524288	524288	NUM
ejpam-6215	667	21	+	+	NUM
ejpam-6215	667	22	66163µ	66163µ	NUM
ejpam-6215	667	23	131072	131072	NUM
ejpam-6215	667	24	+	+	CCONJ
ejpam-6215	667	25	219µ2	219µ2	NUM
ejpam-6215	667	26	32768	32768	NUM
ejpam-6215	667	27	+	+	CCONJ
ejpam-6215	667	28	µ3	µ3	PROPN
ejpam-6215	667	29	8192	8192	NUM
ejpam-6215	667	30	.	.	PUNCT
ejpam-6215	668	1	3.2	3.2	NUM
ejpam-6215	668	2	.	.	X
ejpam-6215	668	3	runge	runge	NOUN
ejpam-6215	668	4	-	-	PUNCT
ejpam-6215	668	5	kutta	kutta	NOUN
ejpam-6215	668	6	method	method	NOUN
ejpam-6215	668	7	(	(	PUNCT
ejpam-6215	668	8	rk4	rk4	NOUN
ejpam-6215	668	9	)	)	PUNCT
ejpam-6215	668	10	the	the	DET
ejpam-6215	668	11	runge	runge	NOUN
ejpam-6215	668	12	-	-	PUNCT
ejpam-6215	668	13	kutta	kutta	NOUN
ejpam-6215	668	14	method	method	NOUN
ejpam-6215	668	15	is	be	AUX
ejpam-6215	668	16	a	a	DET
ejpam-6215	668	17	powerful	powerful	ADJ
ejpam-6215	668	18	numerical	numerical	ADJ
ejpam-6215	668	19	technique	technique	NOUN
ejpam-6215	668	20	for	for	ADP
ejpam-6215	668	21	solving	solve	VERB
ejpam-6215	668	22	ordinary	ordinary	ADJ
ejpam-6215	668	23	differential	differential	ADJ
ejpam-6215	668	24	equations	equation	NOUN
ejpam-6215	668	25	(	(	PUNCT
ejpam-6215	668	26	odes	ode	NOUN
ejpam-6215	668	27	)	)	PUNCT
ejpam-6215	668	28	,	,	PUNCT
ejpam-6215	668	29	including	include	VERB
ejpam-6215	668	30	nonlinear	nonlinear	ADJ
ejpam-6215	668	31	equations	equation	NOUN
ejpam-6215	668	32	like	like	ADP
ejpam-6215	668	33	the	the	DET
ejpam-6215	668	34	painlevé	painlevé	NOUN
ejpam-6215	668	35	equations	equation	NOUN
ejpam-6215	668	36	.	.	PUNCT
ejpam-6215	669	1	developed	develop	VERB
ejpam-6215	669	2	by	by	ADP
ejpam-6215	669	3	carl	carl	PROPN
ejpam-6215	669	4	runge	runge	PROPN
ejpam-6215	669	5	and	and	CCONJ
ejpam-6215	669	6	wilhelm	wilhelm	PROPN
ejpam-6215	669	7	kutta	kutta	PROPN
ejpam-6215	669	8	in	in	ADP
ejpam-6215	669	9	1990	1990	NUM
ejpam-6215	669	10	,	,	PUNCT
ejpam-6215	669	11	[	[	X
ejpam-6215	669	12	45	45	NUM
ejpam-6215	669	13	,	,	PUNCT
ejpam-6215	669	14	46	46	NUM
ejpam-6215	669	15	]	]	PUNCT
ejpam-6215	669	16	,	,	PUNCT
ejpam-6215	669	17	it	it	PRON
ejpam-6215	669	18	provides	provide	VERB
ejpam-6215	669	19	higher	high	ADJ
ejpam-6215	669	20	accuracy	accuracy	NOUN
ejpam-6215	669	21	than	than	ADP
ejpam-6215	669	22	the	the	DET
ejpam-6215	669	23	euler	euler	NOUN
ejpam-6215	669	24	method	method	NOUN
ejpam-6215	669	25	without	without	ADP
ejpam-6215	669	26	requiring	require	VERB
ejpam-6215	669	27	higher	high	ADJ
ejpam-6215	669	28	-	-	PUNCT
ejpam-6215	669	29	order	order	NOUN
ejpam-6215	669	30	derivatives	derivative	NOUN
ejpam-6215	669	31	.	.	PUNCT
ejpam-6215	670	1	the	the	DET
ejpam-6215	670	2	fourth	fourth	ADJ
ejpam-6215	670	3	-	-	PUNCT
ejpam-6215	670	4	order	order	NOUN
ejpam-6215	670	5	rungekutta	rungekutta	NOUN
ejpam-6215	670	6	method	method	NOUN
ejpam-6215	670	7	(	(	PUNCT
ejpam-6215	670	8	rk4	rk4	NOUN
ejpam-6215	670	9	)	)	PUNCT
ejpam-6215	670	10	is	be	AUX
ejpam-6215	670	11	particularly	particularly	ADV
ejpam-6215	670	12	popular	popular	ADJ
ejpam-6215	670	13	due	due	ADP
ejpam-6215	670	14	to	to	ADP
ejpam-6215	670	15	its	its	PRON
ejpam-6215	670	16	balance	balance	NOUN
ejpam-6215	670	17	between	between	ADP
ejpam-6215	670	18	computational	computational	ADJ
ejpam-6215	670	19	efficiency	efficiency	NOUN
ejpam-6215	670	20	and	and	CCONJ
ejpam-6215	670	21	precision	precision	NOUN
ejpam-6215	670	22	.	.	PUNCT
ejpam-6215	671	1	by	by	ADP
ejpam-6215	671	2	computing	compute	VERB
ejpam-6215	671	3	intermediate	intermediate	ADJ
ejpam-6215	671	4	slopes	slope	NOUN
ejpam-6215	671	5	at	at	ADP
ejpam-6215	671	6	each	each	DET
ejpam-6215	671	7	step	step	NOUN
ejpam-6215	671	8	,	,	PUNCT
ejpam-6215	671	9	rk4	rk4	PROPN
ejpam-6215	671	10	improves	improve	VERB
ejpam-6215	671	11	stability	stability	NOUN
ejpam-6215	671	12	and	and	CCONJ
ejpam-6215	671	13	accuracy	accuracy	NOUN
ejpam-6215	671	14	;	;	PUNCT
ejpam-6215	671	15	in	in	ADP
ejpam-6215	671	16	this	this	DET
ejpam-6215	671	17	subsection	subsection	NOUN
ejpam-6215	671	18	,	,	PUNCT
ejpam-6215	671	19	we	we	PRON
ejpam-6215	671	20	use	use	VERB
ejpam-6215	671	21	it	it	PRON
ejpam-6215	671	22	to	to	PART
ejpam-6215	671	23	solve	solve	VERB
ejpam-6215	671	24	the	the	DET
ejpam-6215	671	25	painlevé	painlevé	NOUN
ejpam-6215	671	26	equations	equation	NOUN
ejpam-6215	672	1	[	[	X
ejpam-6215	672	2	47–50	47–50	X
ejpam-6215	672	3	]	]	X
ejpam-6215	672	4	.	.	PUNCT
ejpam-6215	673	1	3.2.1	3.2.1	NUM
ejpam-6215	673	2	.	.	PUNCT
ejpam-6215	674	1	the	the	DET
ejpam-6215	674	2	rk4	rk4	NOUN
ejpam-6215	674	3	for	for	ADP
ejpam-6215	674	4	solving	solve	VERB
ejpam-6215	674	5	the	the	DET
ejpam-6215	674	6	painlevé	painlevé	NOUN
ejpam-6215	674	7	i	i	PRON
ejpam-6215	674	8	differential	differential	VERB
ejpam-6215	674	9	equation	equation	NOUN
ejpam-6215	674	10	rewrite	rewrite	NOUN
ejpam-6215	674	11	(	(	PUNCT
ejpam-6215	674	12	1	1	NUM
ejpam-6215	674	13	)	)	PUNCT
ejpam-6215	674	14	y′′(x	y′′(x	NOUN
ejpam-6215	674	15	)	)	PUNCT
ejpam-6215	674	16	=	=	PUNCT
ejpam-6215	674	17	6y2	6y2	NUM
ejpam-6215	674	18	+	+	CCONJ
ejpam-6215	674	19	x.	x.	NOUN
ejpam-6215	674	20	(	(	PUNCT
ejpam-6215	674	21	59	59	NUM
ejpam-6215	674	22	)	)	PUNCT
ejpam-6215	674	23	with	with	ADP
ejpam-6215	674	24	the	the	DET
ejpam-6215	674	25	initial	initial	ADJ
ejpam-6215	674	26	conditions	condition	NOUN
ejpam-6215	674	27	:	:	PUNCT
ejpam-6215	674	28	y(0	y(0	NOUN
ejpam-6215	674	29	)	)	PUNCT
ejpam-6215	674	30	=	=	SYM
ejpam-6215	674	31	0	0	NUM
ejpam-6215	674	32	,	,	PUNCT
ejpam-6215	674	33	y′(0	y′(0	NOUN
ejpam-6215	674	34	)	)	PUNCT
ejpam-6215	674	35	=	=	SYM
ejpam-6215	674	36	1	1	X
ejpam-6215	674	37	.	.	PUNCT
ejpam-6215	675	1	(	(	PUNCT
ejpam-6215	675	2	60	60	NUM
ejpam-6215	675	3	)	)	PUNCT
ejpam-6215	675	4	rewrite	rewrite	VERB
ejpam-6215	675	5	the	the	DET
ejpam-6215	675	6	second	second	ADJ
ejpam-6215	675	7	-	-	PUNCT
ejpam-6215	675	8	order	order	NOUN
ejpam-6215	675	9	equation	equation	NOUN
ejpam-6215	675	10	as	as	ADP
ejpam-6215	675	11	a	a	DET
ejpam-6215	675	12	system	system	NOUN
ejpam-6215	675	13	of	of	ADP
ejpam-6215	675	14	first	first	ADJ
ejpam-6215	675	15	-	-	PUNCT
ejpam-6215	675	16	order	order	NOUN
ejpam-6215	675	17	equations	equation	NOUN
ejpam-6215	675	18	:	:	PUNCT
ejpam-6215	676	1	dy	dy	PROPN
ejpam-6215	676	2	dx	dx	PROPN
ejpam-6215	677	1	=	=	SYM
ejpam-6215	677	2	z	z	PROPN
ejpam-6215	677	3	=	=	SYM
ejpam-6215	677	4	f(x	f(x	PROPN
ejpam-6215	677	5	,	,	PUNCT
ejpam-6215	677	6	y	y	PROPN
ejpam-6215	677	7	,	,	PUNCT
ejpam-6215	677	8	z	z	NOUN
ejpam-6215	677	9	)	)	PUNCT
ejpam-6215	677	10	.	.	PUNCT
ejpam-6215	678	1	y′	y′	X
ejpam-6215	679	1	=	=	SYM
ejpam-6215	679	2	z	z	NOUN
ejpam-6215	679	3	,	,	PUNCT
ejpam-6215	679	4	z′	z′	PROPN
ejpam-6215	679	5	=	=	PUNCT
ejpam-6215	679	6	y′′	y′′	PROPN
ejpam-6215	679	7	=	=	PUNCT
ejpam-6215	679	8	6y2	6y2	NUM
ejpam-6215	679	9	+	+	CCONJ
ejpam-6215	679	10	x	x	SYM
ejpam-6215	679	11	=	=	SYM
ejpam-6215	679	12	ϕ(x	ϕ(x	PROPN
ejpam-6215	679	13	,	,	PUNCT
ejpam-6215	679	14	y	y	PROPN
ejpam-6215	679	15	,	,	PUNCT
ejpam-6215	679	16	z	z	NOUN
ejpam-6215	679	17	)	)	PUNCT
ejpam-6215	679	18	.	.	PUNCT
ejpam-6215	680	1	here	here	ADV
ejpam-6215	680	2	,	,	PUNCT
ejpam-6215	680	3	f(x	f(x	PROPN
ejpam-6215	680	4	,	,	PUNCT
ejpam-6215	680	5	y	y	PROPN
ejpam-6215	680	6	,	,	PUNCT
ejpam-6215	680	7	z	z	NOUN
ejpam-6215	680	8	)	)	PUNCT
ejpam-6215	680	9	represents	represent	VERB
ejpam-6215	680	10	the	the	DET
ejpam-6215	680	11	first	first	ADJ
ejpam-6215	680	12	derivative	derivative	NOUN
ejpam-6215	680	13	of	of	ADP
ejpam-6215	680	14	y	y	PROPN
ejpam-6215	680	15	,	,	PUNCT
ejpam-6215	680	16	while	while	SCONJ
ejpam-6215	680	17	ϕ(x	ϕ(x	PROPN
ejpam-6215	680	18	,	,	PUNCT
ejpam-6215	680	19	y	y	PROPN
ejpam-6215	680	20	,	,	PUNCT
ejpam-6215	680	21	z	z	NOUN
ejpam-6215	680	22	)	)	PUNCT
ejpam-6215	680	23	defines	define	VERB
ejpam-6215	680	24	the	the	DET
ejpam-6215	680	25	righthand	righthand	NOUN
ejpam-6215	680	26	side	side	NOUN
ejpam-6215	680	27	of	of	ADP
ejpam-6215	680	28	the	the	DET
ejpam-6215	680	29	second	second	ADJ
ejpam-6215	680	30	equation	equation	NOUN
ejpam-6215	680	31	.	.	PUNCT
ejpam-6215	681	1	with	with	ADP
ejpam-6215	681	2	initial	initial	ADJ
ejpam-6215	681	3	conditions	condition	NOUN
ejpam-6215	681	4	at	at	ADP
ejpam-6215	681	5	x0	x0	PROPN
ejpam-6215	681	6	=	=	SYM
ejpam-6215	681	7	0	0	NUM
ejpam-6215	681	8	,	,	PUNCT
ejpam-6215	681	9	y0	y0	NOUN
ejpam-6215	681	10	=	=	SYM
ejpam-6215	681	11	0	0	NUM
ejpam-6215	681	12	,	,	PUNCT
ejpam-6215	681	13	z0	z0	PROPN
ejpam-6215	681	14	=	=	SYM
ejpam-6215	681	15	1	1	NUM
ejpam-6215	681	16	,	,	PUNCT
ejpam-6215	681	17	we	we	PRON
ejpam-6215	681	18	proceed	proceed	VERB
ejpam-6215	681	19	.	.	PUNCT
ejpam-6215	682	1	use	use	VERB
ejpam-6215	682	2	step	step	NOUN
ejpam-6215	682	3	size	size	NOUN
ejpam-6215	682	4	h	h	NOUN
ejpam-6215	682	5	=	=	NOUN
ejpam-6215	682	6	1	1	NUM
ejpam-6215	682	7	4	4	NUM
ejpam-6215	682	8	and	and	CCONJ
ejpam-6215	682	9	calculate	calculate	NOUN
ejpam-6215	682	10	k1	k1	PROPN
ejpam-6215	682	11	,	,	PUNCT
ejpam-6215	682	12	k2	k2	PROPN
ejpam-6215	682	13	,	,	PUNCT
ejpam-6215	682	14	k3	k3	PROPN
ejpam-6215	682	15	,	,	PUNCT
ejpam-6215	682	16	k4	k4	NOUN
ejpam-6215	682	17	and	and	CCONJ
ejpam-6215	682	18	l1	l1	PROPN
ejpam-6215	682	19	,	,	PUNCT
ejpam-6215	682	20	l2	l2	NOUN
ejpam-6215	682	21	,	,	PUNCT
ejpam-6215	682	22	l3	l3	PROPN
ejpam-6215	682	23	,	,	PUNCT
ejpam-6215	682	24	l4	l4	PROPN
ejpam-6215	682	25	.	.	PUNCT
ejpam-6215	682	26	runge	runge	PROPN
ejpam-6215	682	27	-	-	PUNCT
ejpam-6215	682	28	kutta	kutta	NOUN
ejpam-6215	682	29	formulas	formula	NOUN
ejpam-6215	682	30	for	for	ADP
ejpam-6215	682	31	y	y	PROPN
ejpam-6215	682	32	,	,	PUNCT
ejpam-6215	682	33	we	we	PRON
ejpam-6215	682	34	use	use	VERB
ejpam-6215	682	35	:	:	PUNCT
ejpam-6215	682	36	k1	k1	PROPN
ejpam-6215	682	37	=	=	SYM
ejpam-6215	682	38	hf(x0	hf(x0	NOUN
ejpam-6215	682	39	,	,	PUNCT
ejpam-6215	682	40	y0	y0	NOUN
ejpam-6215	682	41	,	,	PUNCT
ejpam-6215	682	42	z0	z0	PROPN
ejpam-6215	682	43	)	)	PUNCT
ejpam-6215	682	44	=	=	SYM
ejpam-6215	682	45	1	1	NUM
ejpam-6215	682	46	4	4	NUM
ejpam-6215	682	47	.	.	PUNCT
ejpam-6215	683	1	s.	s.	PROPN
ejpam-6215	683	2	mohammed	mohammed	PROPN
ejpam-6215	683	3	,	,	PUNCT
ejpam-6215	683	4	s.	s.	PROPN
ejpam-6215	683	5	abid	abid	PROPN
ejpam-6215	683	6	,	,	PUNCT
ejpam-6215	683	7	r.	r.	PROPN
ejpam-6215	683	8	abid	abid	PROPN
ejpam-6215	683	9	/	/	SYM
ejpam-6215	683	10	eur	eur	PROPN
ejpam-6215	683	11	.	.	PUNCT
ejpam-6215	684	1	j.	j.	PROPN
ejpam-6215	684	2	pure	pure	PROPN
ejpam-6215	684	3	appl	appl	PROPN
ejpam-6215	684	4	.	.	PROPN
ejpam-6215	684	5	math	math	PROPN
ejpam-6215	684	6	,	,	PUNCT
ejpam-6215	684	7	18	18	NUM
ejpam-6215	684	8	(	(	PUNCT
ejpam-6215	684	9	3	3	NUM
ejpam-6215	684	10	)	)	PUNCT
ejpam-6215	684	11	(	(	PUNCT
ejpam-6215	684	12	2025	2025	NUM
ejpam-6215	684	13	)	)	PUNCT
ejpam-6215	684	14	,	,	PUNCT
ejpam-6215	684	15	6215	6215	NUM
ejpam-6215	684	16	30	30	NUM
ejpam-6215	684	17	of	of	ADP
ejpam-6215	684	18	38	38	NUM
ejpam-6215	684	19	k2	k2	NOUN
ejpam-6215	684	20	=	=	SYM
ejpam-6215	684	21	hf	hf	PROPN
ejpam-6215	684	22	(	(	PUNCT
ejpam-6215	684	23	x0	x0	PROPN
ejpam-6215	684	24	+	+	CCONJ
ejpam-6215	684	25	h	h	NOUN
ejpam-6215	684	26	2	2	NUM
ejpam-6215	684	27	,	,	PUNCT
ejpam-6215	684	28	y0	y0	PROPN
ejpam-6215	684	29	+	+	CCONJ
ejpam-6215	684	30	k1	k1	PROPN
ejpam-6215	684	31	2	2	NUM
ejpam-6215	684	32	,	,	PUNCT
ejpam-6215	684	33	z0	z0	PROPN
ejpam-6215	684	34	+	+	PROPN
ejpam-6215	684	35	l1	l1	PROPN
ejpam-6215	684	36	2	2	NUM
ejpam-6215	684	37	)	)	PUNCT
ejpam-6215	684	38	=	=	SYM
ejpam-6215	684	39	1	1	NUM
ejpam-6215	684	40	4	4	NUM
ejpam-6215	684	41	,	,	PUNCT
ejpam-6215	684	42	k3	k3	X
ejpam-6215	684	43	=	=	PUNCT
ejpam-6215	684	44	hf	hf	NOUN
ejpam-6215	684	45	(	(	PUNCT
ejpam-6215	684	46	x0	x0	PROPN
ejpam-6215	684	47	+	+	CCONJ
ejpam-6215	684	48	h	h	NOUN
ejpam-6215	684	49	2	2	NUM
ejpam-6215	684	50	,	,	PUNCT
ejpam-6215	684	51	y0	y0	PROPN
ejpam-6215	684	52	+	+	CCONJ
ejpam-6215	684	53	k2	k2	ADJ
ejpam-6215	684	54	2	2	NUM
ejpam-6215	684	55	,	,	PUNCT
ejpam-6215	684	56	z0	z0	PROPN
ejpam-6215	684	57	+	+	CCONJ
ejpam-6215	684	58	l2	l2	NOUN
ejpam-6215	684	59	2	2	NUM
ejpam-6215	684	60	)	)	PUNCT
ejpam-6215	684	61	=	=	SYM
ejpam-6215	684	62	263	263	NUM
ejpam-6215	684	63	1024	1024	NUM
ejpam-6215	684	64	,	,	PUNCT
ejpam-6215	684	65	k4	k4	NOUN
ejpam-6215	684	66	=	=	SYM
ejpam-6215	684	67	hf(x0	hf(x0	NOUN
ejpam-6215	685	1	+	+	NUM
ejpam-6215	685	2	h	h	NOUN
ejpam-6215	685	3	,	,	PUNCT
ejpam-6215	685	4	y0	y0	PROPN
ejpam-6215	685	5	+	+	CCONJ
ejpam-6215	685	6	k3	k3	ADJ
ejpam-6215	685	7	,	,	PUNCT
ejpam-6215	685	8	z0	z0	PROPN
ejpam-6215	685	9	+	+	CCONJ
ejpam-6215	685	10	l3	l3	NOUN
ejpam-6215	685	11	)	)	PUNCT
ejpam-6215	685	12	=	=	SYM
ejpam-6215	685	13	135	135	NUM
ejpam-6215	685	14	512	512	NUM
ejpam-6215	685	15	.	.	PUNCT
ejpam-6215	686	1	k	k	X
ejpam-6215	687	1	=	=	SYM
ejpam-6215	688	1	1	1	NUM
ejpam-6215	688	2	6	6	NUM
ejpam-6215	688	3	(	(	PUNCT
ejpam-6215	688	4	k1	k1	NOUN
ejpam-6215	688	5	+	+	CCONJ
ejpam-6215	688	6	2k2	2k2	NUM
ejpam-6215	688	7	+	+	CCONJ
ejpam-6215	688	8	2k3	2k3	NUM
ejpam-6215	688	9	+	+	CCONJ
ejpam-6215	688	10	k4	k4	NOUN
ejpam-6215	688	11	)	)	PUNCT
ejpam-6215	688	12	=	=	SYM
ejpam-6215	688	13	391	391	NUM
ejpam-6215	688	14	1536	1536	NUM
ejpam-6215	688	15	.	.	PUNCT
ejpam-6215	689	1	l1	l1	PROPN
ejpam-6215	689	2	=	=	SYM
ejpam-6215	689	3	hϕ(x0	hϕ(x0	PROPN
ejpam-6215	689	4	,	,	PUNCT
ejpam-6215	689	5	y0	y0	NOUN
ejpam-6215	689	6	,	,	PUNCT
ejpam-6215	689	7	z0	z0	PROPN
ejpam-6215	689	8	)	)	PUNCT
ejpam-6215	689	9	=	=	SYM
ejpam-6215	689	10	0	0	X
ejpam-6215	689	11	.	.	X
ejpam-6215	689	12	l2	l2	NOUN
ejpam-6215	689	13	=	=	SYM
ejpam-6215	689	14	hϕ	hϕ	PROPN
ejpam-6215	689	15	(	(	PUNCT
ejpam-6215	689	16	x0	x0	PROPN
ejpam-6215	689	17	+	+	CCONJ
ejpam-6215	689	18	h	h	NOUN
ejpam-6215	689	19	2	2	NUM
ejpam-6215	689	20	,	,	PUNCT
ejpam-6215	689	21	y0	y0	PROPN
ejpam-6215	689	22	+	+	CCONJ
ejpam-6215	689	23	k1	k1	PROPN
ejpam-6215	689	24	2	2	NUM
ejpam-6215	689	25	,	,	PUNCT
ejpam-6215	689	26	z0	z0	PROPN
ejpam-6215	689	27	+	+	PROPN
ejpam-6215	689	28	l1	l1	PROPN
ejpam-6215	689	29	2	2	NUM
ejpam-6215	689	30	)	)	PUNCT
ejpam-6215	689	31	=	=	SYM
ejpam-6215	689	32	7	7	NUM
ejpam-6215	689	33	128	128	NUM
ejpam-6215	689	34	.	.	PUNCT
ejpam-6215	690	1	l3	l3	PROPN
ejpam-6215	690	2	=	=	PROPN
ejpam-6215	690	3	hϕ	hϕ	PROPN
ejpam-6215	690	4	(	(	PUNCT
ejpam-6215	690	5	x0	x0	PROPN
ejpam-6215	690	6	+	+	CCONJ
ejpam-6215	690	7	h	h	NOUN
ejpam-6215	690	8	2	2	NUM
ejpam-6215	690	9	,	,	PUNCT
ejpam-6215	690	10	y0	y0	PROPN
ejpam-6215	690	11	+	+	CCONJ
ejpam-6215	690	12	k2	k2	ADJ
ejpam-6215	690	13	2	2	NUM
ejpam-6215	690	14	,	,	PUNCT
ejpam-6215	690	15	z0	z0	PROPN
ejpam-6215	690	16	+	+	CCONJ
ejpam-6215	690	17	l2	l2	NOUN
ejpam-6215	690	18	2	2	NUM
ejpam-6215	690	19	)	)	PUNCT
ejpam-6215	690	20	=	=	SYM
ejpam-6215	690	21	7	7	NUM
ejpam-6215	690	22	128	128	NUM
ejpam-6215	690	23	.	.	PUNCT
ejpam-6215	691	1	l4	l4	PROPN
ejpam-6215	691	2	=	=	PUNCT
ejpam-6215	691	3	hϕ(x0	hϕ(x0	PROPN
ejpam-6215	692	1	+	+	NOUN
ejpam-6215	692	2	h	h	NOUN
ejpam-6215	692	3	,	,	PUNCT
ejpam-6215	692	4	y0	y0	PROPN
ejpam-6215	692	5	+	+	CCONJ
ejpam-6215	692	6	k3	k3	ADJ
ejpam-6215	692	7	,	,	PUNCT
ejpam-6215	692	8	z0	z0	PROPN
ejpam-6215	692	9	+	+	CCONJ
ejpam-6215	692	10	l3	l3	NOUN
ejpam-6215	692	11	)	)	PUNCT
ejpam-6215	692	12	=	=	SYM
ejpam-6215	692	13	338579	338579	NUM
ejpam-6215	692	14	2097152	2097152	NUM
ejpam-6215	692	15	.	.	PUNCT
ejpam-6215	693	1	l	l	NOUN
ejpam-6215	693	2	=	=	SYM
ejpam-6215	694	1	1	1	NUM
ejpam-6215	694	2	6	6	NUM
ejpam-6215	694	3	(	(	PUNCT
ejpam-6215	694	4	l1	l1	PROPN
ejpam-6215	694	5	+	+	CCONJ
ejpam-6215	694	6	2l2	2l2	NUM
ejpam-6215	694	7	+	+	CCONJ
ejpam-6215	694	8	2l3	2l3	NUM
ejpam-6215	694	9	+	+	CCONJ
ejpam-6215	694	10	l4	l4	PROPN
ejpam-6215	694	11	)	)	PUNCT
ejpam-6215	694	12	=	=	SYM
ejpam-6215	694	13	797331	797331	NUM
ejpam-6215	694	14	8388608	8388608	NUM
ejpam-6215	694	15	.	.	PUNCT
ejpam-6215	695	1	hence	hence	ADV
ejpam-6215	695	2	,	,	PUNCT
ejpam-6215	695	3	y	y	PROPN
ejpam-6215	695	4	=	=	SYM
ejpam-6215	695	5	y0	y0	PROPN
ejpam-6215	695	6	+	+	CCONJ
ejpam-6215	695	7	k	k	X
ejpam-6215	696	1	=	=	SYM
ejpam-6215	697	1	391	391	NUM
ejpam-6215	697	2	1536	1536	NUM
ejpam-6215	697	3	≈	≈	PROPN
ejpam-6215	697	4	0.25456	0.25456	NUM
ejpam-6215	697	5	.	.	PUNCT
ejpam-6215	697	6	y′	y′	X
ejpam-6215	698	1	=	=	PUNCT
ejpam-6215	698	2	z	z	NOUN
ejpam-6215	698	3	=	=	SYM
ejpam-6215	698	4	z0	z0	PROPN
ejpam-6215	698	5	+	+	CCONJ
ejpam-6215	698	6	l	l	NOUN
ejpam-6215	698	7	=	=	SYM
ejpam-6215	698	8	1	1	NUM
ejpam-6215	698	9	+	+	NUM
ejpam-6215	698	10	797331	797331	NUM
ejpam-6215	698	11	8388608	8388608	NUM
ejpam-6215	698	12	≈	≈	PROPN
ejpam-6215	698	13	1.06337	1.06337	NUM
ejpam-6215	698	14	.	.	PUNCT
ejpam-6215	699	1	3.2.2	3.2.2	NUM
ejpam-6215	699	2	.	.	PUNCT
ejpam-6215	700	1	the	the	DET
ejpam-6215	700	2	rk4	rk4	NOUN
ejpam-6215	700	3	for	for	ADP
ejpam-6215	700	4	solving	solve	VERB
ejpam-6215	700	5	the	the	DET
ejpam-6215	700	6	painlevé	painlevé	NOUN
ejpam-6215	700	7	ii	ii	NOUN
ejpam-6215	700	8	differential	differential	NOUN
ejpam-6215	700	9	equation	equation	NOUN
ejpam-6215	700	10	rewrite	rewrite	NOUN
ejpam-6215	700	11	(	(	PUNCT
ejpam-6215	700	12	2	2	NUM
ejpam-6215	700	13	)	)	PUNCT
ejpam-6215	700	14	y′′(t	y′′(t	VERB
ejpam-6215	700	15	)	)	PUNCT
ejpam-6215	701	1	=	=	SYM
ejpam-6215	701	2	2y3	2y3	NUM
ejpam-6215	701	3	+	+	CCONJ
ejpam-6215	701	4	xy	xy	PROPN
ejpam-6215	701	5	+	+	CCONJ
ejpam-6215	701	6	µ.	µ.	NOUN
ejpam-6215	701	7	(	(	PUNCT
ejpam-6215	701	8	61	61	NUM
ejpam-6215	701	9	)	)	PUNCT
ejpam-6215	701	10	with	with	ADP
ejpam-6215	701	11	the	the	DET
ejpam-6215	701	12	initial	initial	ADJ
ejpam-6215	701	13	conditions	condition	NOUN
ejpam-6215	701	14	:	:	PUNCT
ejpam-6215	701	15	y(0	y(0	NOUN
ejpam-6215	701	16	)	)	PUNCT
ejpam-6215	701	17	=	=	SYM
ejpam-6215	701	18	1	1	NUM
ejpam-6215	701	19	,	,	PUNCT
ejpam-6215	701	20	y′(0	y′(0	NOUN
ejpam-6215	701	21	)	)	PUNCT
ejpam-6215	701	22	=	=	SYM
ejpam-6215	702	1	0	0	X
ejpam-6215	702	2	.	.	PUNCT
ejpam-6215	703	1	(	(	PUNCT
ejpam-6215	703	2	62	62	NUM
ejpam-6215	703	3	)	)	PUNCT
ejpam-6215	703	4	rewrite	rewrite	VERB
ejpam-6215	703	5	the	the	DET
ejpam-6215	703	6	second	second	ADJ
ejpam-6215	703	7	-	-	PUNCT
ejpam-6215	703	8	order	order	NOUN
ejpam-6215	703	9	equation	equation	NOUN
ejpam-6215	703	10	as	as	ADP
ejpam-6215	703	11	a	a	DET
ejpam-6215	703	12	system	system	NOUN
ejpam-6215	703	13	of	of	ADP
ejpam-6215	703	14	first	first	ADJ
ejpam-6215	703	15	-	-	PUNCT
ejpam-6215	703	16	order	order	NOUN
ejpam-6215	703	17	equations	equation	NOUN
ejpam-6215	703	18	:	:	PUNCT
ejpam-6215	703	19	dy	dy	PROPN
ejpam-6215	703	20	dx	dx	PROPN
ejpam-6215	704	1	=	=	SYM
ejpam-6215	704	2	z	z	PROPN
ejpam-6215	704	3	=	=	SYM
ejpam-6215	704	4	f(x	f(x	PROPN
ejpam-6215	704	5	,	,	PUNCT
ejpam-6215	704	6	y	y	PROPN
ejpam-6215	704	7	,	,	PUNCT
ejpam-6215	704	8	z	z	NOUN
ejpam-6215	704	9	)	)	PUNCT
ejpam-6215	704	10	,	,	PUNCT
ejpam-6215	704	11	y′	y′	X
ejpam-6215	704	12	=	=	PUNCT
ejpam-6215	704	13	z.	z.	PROPN
ejpam-6215	704	14	z′	z′	NUM
ejpam-6215	704	15	=	=	PUNCT
ejpam-6215	705	1	y′′	y′′	PROPN
ejpam-6215	705	2	=	=	SYM
ejpam-6215	705	3	2y3	2y3	NUM
ejpam-6215	705	4	+	+	CCONJ
ejpam-6215	705	5	xy	xy	PROPN
ejpam-6215	705	6	+	+	CCONJ
ejpam-6215	705	7	µ	µ	X
ejpam-6215	705	8	=	=	SYM
ejpam-6215	705	9	φ(x	φ(x	PROPN
ejpam-6215	705	10	,	,	PUNCT
ejpam-6215	705	11	y	y	NOUN
ejpam-6215	705	12	,	,	PUNCT
ejpam-6215	705	13	z	z	NOUN
ejpam-6215	705	14	)	)	PUNCT
ejpam-6215	705	15	.	.	PUNCT
ejpam-6215	706	1	here	here	ADV
ejpam-6215	706	2	,	,	PUNCT
ejpam-6215	706	3	f(x	f(x	PROPN
ejpam-6215	706	4	,	,	PUNCT
ejpam-6215	706	5	y	y	PROPN
ejpam-6215	706	6	,	,	PUNCT
ejpam-6215	706	7	z	z	NOUN
ejpam-6215	706	8	)	)	PUNCT
ejpam-6215	706	9	represents	represent	VERB
ejpam-6215	706	10	the	the	DET
ejpam-6215	706	11	first	first	ADJ
ejpam-6215	706	12	derivative	derivative	NOUN
ejpam-6215	706	13	of	of	ADP
ejpam-6215	706	14	y	y	PROPN
ejpam-6215	706	15	,	,	PUNCT
ejpam-6215	706	16	while	while	SCONJ
ejpam-6215	706	17	φ(x	φ(x	PROPN
ejpam-6215	706	18	,	,	PUNCT
ejpam-6215	706	19	y	y	PROPN
ejpam-6215	706	20	,	,	PUNCT
ejpam-6215	706	21	z	z	NOUN
ejpam-6215	706	22	)	)	PUNCT
ejpam-6215	706	23	defines	define	VERB
ejpam-6215	706	24	the	the	DET
ejpam-6215	706	25	right	right	ADJ
ejpam-6215	706	26	-	-	PUNCT
ejpam-6215	706	27	hand	hand	NOUN
ejpam-6215	706	28	side	side	NOUN
ejpam-6215	706	29	of	of	ADP
ejpam-6215	706	30	the	the	DET
ejpam-6215	706	31	second	second	ADJ
ejpam-6215	706	32	equation	equation	NOUN
ejpam-6215	706	33	.	.	PUNCT
ejpam-6215	707	1	with	with	ADP
ejpam-6215	707	2	initial	initial	ADJ
ejpam-6215	707	3	conditions	condition	NOUN
ejpam-6215	707	4	at	at	ADP
ejpam-6215	707	5	x0	x0	PROPN
ejpam-6215	707	6	=	=	SYM
ejpam-6215	707	7	0	0	NUM
ejpam-6215	707	8	,	,	PUNCT
ejpam-6215	707	9	y0	y0	NOUN
ejpam-6215	707	10	=	=	SYM
ejpam-6215	707	11	1	1	NUM
ejpam-6215	707	12	,	,	PUNCT
ejpam-6215	707	13	and	and	CCONJ
ejpam-6215	707	14	z0	z0	PROPN
ejpam-6215	707	15	=	=	SYM
ejpam-6215	707	16	0	0	PROPN
ejpam-6215	707	17	.	.	PUNCT
ejpam-6215	707	18	s.	s.	PROPN
ejpam-6215	707	19	mohammed	mohammed	PROPN
ejpam-6215	707	20	,	,	PUNCT
ejpam-6215	707	21	s.	s.	PROPN
ejpam-6215	707	22	abid	abid	PROPN
ejpam-6215	707	23	,	,	PUNCT
ejpam-6215	707	24	r.	r.	PROPN
ejpam-6215	707	25	abid	abid	PROPN
ejpam-6215	707	26	/	/	SYM
ejpam-6215	707	27	eur	eur	PROPN
ejpam-6215	707	28	.	.	PUNCT
ejpam-6215	708	1	j.	j.	PROPN
ejpam-6215	708	2	pure	pure	PROPN
ejpam-6215	708	3	appl	appl	PROPN
ejpam-6215	708	4	.	.	PROPN
ejpam-6215	708	5	math	math	PROPN
ejpam-6215	708	6	,	,	PUNCT
ejpam-6215	708	7	18	18	NUM
ejpam-6215	708	8	(	(	PUNCT
ejpam-6215	708	9	3	3	NUM
ejpam-6215	708	10	)	)	PUNCT
ejpam-6215	708	11	(	(	PUNCT
ejpam-6215	708	12	2025	2025	NUM
ejpam-6215	708	13	)	)	PUNCT
ejpam-6215	708	14	,	,	PUNCT
ejpam-6215	708	15	6215	6215	NUM
ejpam-6215	708	16	31	31	NUM
ejpam-6215	708	17	of	of	ADP
ejpam-6215	708	18	38	38	NUM
ejpam-6215	708	19	use	use	NOUN
ejpam-6215	708	20	step	step	NOUN
ejpam-6215	708	21	size	size	NOUN
ejpam-6215	708	22	h	h	NOUN
ejpam-6215	709	1	=	=	NOUN
ejpam-6215	709	2	1	1	NUM
ejpam-6215	709	3	4	4	NUM
ejpam-6215	709	4	and	and	CCONJ
ejpam-6215	709	5	calculate	calculate	NOUN
ejpam-6215	709	6	k1	k1	PROPN
ejpam-6215	709	7	,	,	PUNCT
ejpam-6215	709	8	k2	k2	PROPN
ejpam-6215	709	9	,	,	PUNCT
ejpam-6215	709	10	k3	k3	PROPN
ejpam-6215	709	11	,	,	PUNCT
ejpam-6215	709	12	k4	k4	NOUN
ejpam-6215	709	13	and	and	CCONJ
ejpam-6215	709	14	l1	l1	PROPN
ejpam-6215	709	15	,	,	PUNCT
ejpam-6215	709	16	l2	l2	NOUN
ejpam-6215	709	17	,	,	PUNCT
ejpam-6215	709	18	l3	l3	PROPN
ejpam-6215	709	19	,	,	PUNCT
ejpam-6215	709	20	l4	l4	PROPN
ejpam-6215	709	21	.	.	PUNCT
ejpam-6215	710	1	range	range	PROPN
ejpam-6215	710	2	kutta	kutta	PROPN
ejpam-6215	710	3	formulas	formula	NOUN
ejpam-6215	710	4	for	for	ADP
ejpam-6215	710	5	y	y	PROPN
ejpam-6215	710	6	,	,	PUNCT
ejpam-6215	710	7	we	we	PRON
ejpam-6215	710	8	use	use	VERB
ejpam-6215	710	9	:	:	PUNCT
ejpam-6215	710	10	k1	k1	PROPN
ejpam-6215	710	11	=	=	SYM
ejpam-6215	710	12	hf(x0	hf(x0	NOUN
ejpam-6215	710	13	,	,	PUNCT
ejpam-6215	710	14	y0	y0	NOUN
ejpam-6215	710	15	,	,	PUNCT
ejpam-6215	710	16	z0	z0	PROPN
ejpam-6215	710	17	)	)	PUNCT
ejpam-6215	710	18	=	=	SYM
ejpam-6215	711	1	0	0	X
ejpam-6215	711	2	.	.	PUNCT
ejpam-6215	712	1	k2	k2	PROPN
ejpam-6215	712	2	=	=	PUNCT
ejpam-6215	712	3	hf	hf	PROPN
ejpam-6215	712	4	(	(	PUNCT
ejpam-6215	712	5	x0	x0	PROPN
ejpam-6215	712	6	+	+	CCONJ
ejpam-6215	712	7	h	h	NOUN
ejpam-6215	712	8	2	2	NUM
ejpam-6215	712	9	,	,	PUNCT
ejpam-6215	712	10	y0	y0	PROPN
ejpam-6215	712	11	+	+	CCONJ
ejpam-6215	712	12	k1	k1	PROPN
ejpam-6215	712	13	2	2	NUM
ejpam-6215	712	14	,	,	PUNCT
ejpam-6215	712	15	z0	z0	PROPN
ejpam-6215	712	16	+	+	PROPN
ejpam-6215	712	17	l1	l1	PROPN
ejpam-6215	712	18	2	2	NUM
ejpam-6215	712	19	)	)	PUNCT
ejpam-6215	712	20	=	=	SYM
ejpam-6215	713	1	2	2	NUM
ejpam-6215	713	2	+	+	SYM
ejpam-6215	713	3	µ	µ	X
ejpam-6215	713	4	32	32	NUM
ejpam-6215	713	5	.	.	PUNCT
ejpam-6215	714	1	k3	k3	PROPN
ejpam-6215	714	2	=	=	PUNCT
ejpam-6215	714	3	hf	hf	PROPN
ejpam-6215	714	4	(	(	PUNCT
ejpam-6215	714	5	x0	x0	PROPN
ejpam-6215	714	6	+	+	CCONJ
ejpam-6215	714	7	h	h	NOUN
ejpam-6215	714	8	2	2	NUM
ejpam-6215	714	9	,	,	PUNCT
ejpam-6215	714	10	y0	y0	PROPN
ejpam-6215	714	11	+	+	CCONJ
ejpam-6215	714	12	k2	k2	ADJ
ejpam-6215	714	13	2	2	NUM
ejpam-6215	714	14	,	,	PUNCT
ejpam-6215	714	15	z0	z0	PROPN
ejpam-6215	714	16	+	+	CCONJ
ejpam-6215	714	17	l2	l2	NOUN
ejpam-6215	714	18	2	2	NUM
ejpam-6215	714	19	)	)	PUNCT
ejpam-6215	714	20	=	=	SYM
ejpam-6215	714	21	1	1	NUM
ejpam-6215	714	22	+	+	NUM
ejpam-6215	714	23	256µ	256µ	PROPN
ejpam-6215	714	24	1024	1024	NUM
ejpam-6215	714	25	.	.	PUNCT
ejpam-6215	715	1	k4	k4	NOUN
ejpam-6215	715	2	=	=	SYM
ejpam-6215	715	3	hf	hf	PROPN
ejpam-6215	715	4	(	(	PUNCT
ejpam-6215	715	5	x0	x0	PROPN
ejpam-6215	715	6	+	+	CCONJ
ejpam-6215	715	7	h	h	NOUN
ejpam-6215	715	8	,	,	PUNCT
ejpam-6215	715	9	y0	y0	PROPN
ejpam-6215	715	10	+	+	CCONJ
ejpam-6215	715	11	k3	k3	ADJ
ejpam-6215	715	12	,	,	PUNCT
ejpam-6215	715	13	z0	z0	PROPN
ejpam-6215	715	14	+	+	CCONJ
ejpam-6215	715	15	l3	l3	NOUN
ejpam-6215	715	16	)	)	PUNCT
ejpam-6215	715	17	=	=	SYM
ejpam-6215	716	1	966280	966280	NUM
ejpam-6215	716	2	+	+	NUM
ejpam-6215	716	3	160140µ+	160140µ+	NUM
ejpam-6215	716	4	294µ2	294µ2	NUM
ejpam-6215	716	5	+	+	NUM
ejpam-6215	716	6	µ3	µ3	NOUN
ejpam-6215	716	7	524288	524288	NUM
ejpam-6215	716	8	.	.	PUNCT
ejpam-6215	717	1	k	k	X
ejpam-6215	717	2	=	=	SYM
ejpam-6215	718	1	1	1	NUM
ejpam-6215	718	2	6	6	NUM
ejpam-6215	718	3	(	(	PUNCT
ejpam-6215	718	4	k1	k1	NOUN
ejpam-6215	718	5	+	+	CCONJ
ejpam-6215	718	6	2k2	2k2	NUM
ejpam-6215	718	7	+	+	CCONJ
ejpam-6215	718	8	2k3	2k3	NUM
ejpam-6215	718	9	+	+	CCONJ
ejpam-6215	718	10	k4	k4	NOUN
ejpam-6215	718	11	)	)	PUNCT
ejpam-6215	718	12	=	=	PUNCT
ejpam-6215	718	13	1032840	1032840	NUM
ejpam-6215	718	14	+	+	CCONJ
ejpam-6215	718	15	455052µ+	455052µ+	NUM
ejpam-6215	718	16	294µ2	294µ2	NUM
ejpam-6215	718	17	+	+	NUM
ejpam-6215	718	18	µ3	µ3	NOUN
ejpam-6215	718	19	3145728	3145728	NUM
ejpam-6215	718	20	.	.	PUNCT
ejpam-6215	719	1	l1	l1	PROPN
ejpam-6215	719	2	=	=	SYM
ejpam-6215	719	3	hφ(x0	hφ(x0	PROPN
ejpam-6215	719	4	,	,	PUNCT
ejpam-6215	719	5	y0	y0	NOUN
ejpam-6215	719	6	,	,	PUNCT
ejpam-6215	719	7	z0	z0	PROPN
ejpam-6215	719	8	)	)	PUNCT
ejpam-6215	719	9	=	=	SYM
ejpam-6215	719	10	2	2	NUM
ejpam-6215	719	11	+	+	SYM
ejpam-6215	719	12	µ	µ	X
ejpam-6215	719	13	4	4	NUM
ejpam-6215	719	14	.	.	PUNCT
ejpam-6215	720	1	l2	l2	NOUN
ejpam-6215	720	2	=	=	SYM
ejpam-6215	720	3	hφ	hφ	PROPN
ejpam-6215	720	4	(	(	PUNCT
ejpam-6215	720	5	x0	x0	PROPN
ejpam-6215	720	6	+	+	CCONJ
ejpam-6215	720	7	h	h	NOUN
ejpam-6215	720	8	2	2	NUM
ejpam-6215	720	9	,	,	PUNCT
ejpam-6215	720	10	y0	y0	PROPN
ejpam-6215	720	11	+	+	CCONJ
ejpam-6215	720	12	k1	k1	PROPN
ejpam-6215	720	13	2	2	NUM
ejpam-6215	720	14	,	,	PUNCT
ejpam-6215	720	15	z0	z0	PROPN
ejpam-6215	720	16	+	+	PROPN
ejpam-6215	720	17	l1	l1	PROPN
ejpam-6215	720	18	2	2	NUM
ejpam-6215	720	19	)	)	PUNCT
ejpam-6215	720	20	=	=	SYM
ejpam-6215	720	21	1	1	NUM
ejpam-6215	720	22	+	+	NUM
ejpam-6215	720	23	256µ	256µ	PROPN
ejpam-6215	720	24	1024	1024	NUM
ejpam-6215	720	25	.	.	PUNCT
ejpam-6215	721	1	l3	l3	PROPN
ejpam-6215	721	2	=	=	SYM
ejpam-6215	721	3	hφ	hφ	PROPN
ejpam-6215	721	4	(	(	PUNCT
ejpam-6215	721	5	x0	x0	PROPN
ejpam-6215	721	6	+	+	CCONJ
ejpam-6215	721	7	h	h	NOUN
ejpam-6215	721	8	2	2	NUM
ejpam-6215	721	9	,	,	PUNCT
ejpam-6215	721	10	y0	y0	PROPN
ejpam-6215	721	11	+	+	CCONJ
ejpam-6215	721	12	k2	k2	ADJ
ejpam-6215	721	13	2	2	NUM
ejpam-6215	721	14	,	,	PUNCT
ejpam-6215	721	15	z0	z0	PROPN
ejpam-6215	721	16	+	+	CCONJ
ejpam-6215	721	17	l2	l2	NOUN
ejpam-6215	721	18	2	2	NUM
ejpam-6215	721	19	)	)	PUNCT
ejpam-6215	721	20	=	=	SYM
ejpam-6215	721	21	966280	966280	NUM
ejpam-6215	721	22	+	+	NUM
ejpam-6215	721	23	160140µ+	160140µ+	NUM
ejpam-6215	721	24	294µ2	294µ2	NUM
ejpam-6215	721	25	+	+	NUM
ejpam-6215	721	26	µ3	µ3	PROPN
ejpam-6215	721	27	524288	524288	NUM
ejpam-6215	721	28	.	.	PUNCT
ejpam-6215	722	1	l4	l4	PROPN
ejpam-6215	722	2	=	=	PUNCT
ejpam-6215	722	3	hφ	hφ	PROPN
ejpam-6215	722	4	(	(	PUNCT
ejpam-6215	722	5	x0	x0	PROPN
ejpam-6215	722	6	+	+	CCONJ
ejpam-6215	722	7	h	h	NOUN
ejpam-6215	722	8	,	,	PUNCT
ejpam-6215	722	9	y0	y0	PROPN
ejpam-6215	722	10	+	+	CCONJ
ejpam-6215	722	11	k3	k3	ADJ
ejpam-6215	722	12	,	,	PUNCT
ejpam-6215	722	13	z0	z0	PROPN
ejpam-6215	722	14	+	+	CCONJ
ejpam-6215	722	15	l3	l3	NOUN
ejpam-6215	722	16	)	)	PUNCT
ejpam-6215	722	17	=	=	SYM
ejpam-6215	722	18	1025	1025	NUM
ejpam-6215	722	19	16384	16384	NUM
ejpam-6215	722	20	+	+	CCONJ
ejpam-6215	722	21	1	1	NUM
ejpam-6215	722	22	2	2	NUM
ejpam-6215	722	23	(	(	PUNCT
ejpam-6215	722	24	1025	1025	NUM
ejpam-6215	722	25	1024	1024	NUM
ejpam-6215	722	26	+	+	CCONJ
ejpam-6215	722	27	µ	µ	X
ejpam-6215	722	28	4	4	NUM
ejpam-6215	722	29	)	)	SYM
ejpam-6215	722	30	3	3	NUM
ejpam-6215	722	31	+	+	NUM
ejpam-6215	722	32	17µ	17µ	NOUN
ejpam-6215	722	33	64	64	NUM
ejpam-6215	722	34	.	.	PUNCT
ejpam-6215	723	1	l	l	NOUN
ejpam-6215	723	2	=	=	SYM
ejpam-6215	723	3	1	1	NUM
ejpam-6215	723	4	6	6	NUM
ejpam-6215	723	5	(	(	PUNCT
ejpam-6215	723	6	l1	l1	PROPN
ejpam-6215	723	7	+	+	CCONJ
ejpam-6215	723	8	2l2	2l2	NUM
ejpam-6215	723	9	+	+	CCONJ
ejpam-6215	723	10	2l3	2l3	NUM
ejpam-6215	723	11	+	+	CCONJ
ejpam-6215	723	12	l4	l4	PROPN
ejpam-6215	723	13	)	)	PUNCT
ejpam-6215	723	14	=	=	VERB
ejpam-6215	723	15	10204941	10204941	NUM
ejpam-6215	723	16	+	+	CCONJ
ejpam-6215	723	17	4299784960µ+	4299784960µ+	NUM
ejpam-6215	724	1	203931648µ2	203931648µ2	NUM
ejpam-6215	724	2	+	+	CCONJ
ejpam-6215	724	3	16785408µ3	16785408µ3	NUM
ejpam-6215	724	4	12884901888	12884901888	NUM
ejpam-6215	724	5	.	.	PUNCT
ejpam-6215	725	1	hence	hence	ADV
ejpam-6215	725	2	,	,	PUNCT
ejpam-6215	725	3	y	y	PROPN
ejpam-6215	725	4	=	=	SYM
ejpam-6215	725	5	y0	y0	PROPN
ejpam-6215	725	6	+	+	CCONJ
ejpam-6215	725	7	k	k	X
ejpam-6215	725	8	=	=	PUNCT
ejpam-6215	725	9	4178568	4178568	NUM
ejpam-6215	726	1	+	+	CCONJ
ejpam-6215	727	1	455052µ+	455052µ+	NUM
ejpam-6215	727	2	294µ2	294µ2	NUM
ejpam-6215	727	3	+	+	NUM
ejpam-6215	727	4	µ3	µ3	NOUN
ejpam-6215	727	5	3145728	3145728	NUM
ejpam-6215	727	6	,	,	PUNCT
ejpam-6215	727	7	y′	y′	X
ejpam-6215	727	8	=	=	SYM
ejpam-6215	727	9	z	z	NOUN
ejpam-6215	727	10	=	=	SYM
ejpam-6215	727	11	z0	z0	PROPN
ejpam-6215	727	12	+	+	CCONJ
ejpam-6215	727	13	l	l	NOUN
ejpam-6215	727	14	=	=	X
ejpam-6215	727	15	10204941	10204941	NUM
ejpam-6215	727	16	+	+	CCONJ
ejpam-6215	727	17	4299784960µ+	4299784960µ+	NUM
ejpam-6215	728	1	203931648µ2	203931648µ2	NUM
ejpam-6215	728	2	+	+	CCONJ
ejpam-6215	728	3	16785408µ3	16785408µ3	NUM
ejpam-6215	728	4	12884901888	12884901888	NUM
ejpam-6215	728	5	.	.	PUNCT
ejpam-6215	729	1	4	4	X
ejpam-6215	729	2	.	.	X
ejpam-6215	729	3	comparative	comparative	ADJ
ejpam-6215	729	4	analysis	analysis	NOUN
ejpam-6215	729	5	of	of	ADP
ejpam-6215	729	6	analytical	analytical	ADJ
ejpam-6215	729	7	and	and	CCONJ
ejpam-6215	729	8	numerical	numerical	ADJ
ejpam-6215	729	9	methods	method	NOUN
ejpam-6215	729	10	the	the	DET
ejpam-6215	729	11	study	study	NOUN
ejpam-6215	729	12	of	of	ADP
ejpam-6215	729	13	nonlinear	nonlinear	ADJ
ejpam-6215	729	14	differential	differential	ADJ
ejpam-6215	729	15	equations	equation	NOUN
ejpam-6215	729	16	,	,	PUNCT
ejpam-6215	729	17	particularly	particularly	ADV
ejpam-6215	729	18	painlevé	painlevé	VERB
ejpam-6215	729	19	equations	equation	NOUN
ejpam-6215	729	20	,	,	PUNCT
ejpam-6215	729	21	requires	require	VERB
ejpam-6215	729	22	robust	robust	ADJ
ejpam-6215	729	23	analytical	analytical	ADJ
ejpam-6215	729	24	and	and	CCONJ
ejpam-6215	729	25	numerical	numerical	ADJ
ejpam-6215	729	26	approaches	approach	NOUN
ejpam-6215	729	27	to	to	PART
ejpam-6215	729	28	obtain	obtain	VERB
ejpam-6215	729	29	accurate	accurate	ADJ
ejpam-6215	729	30	solutions	solution	NOUN
ejpam-6215	729	31	.	.	PUNCT
ejpam-6215	730	1	analytical	analytical	ADJ
ejpam-6215	730	2	methods	method	NOUN
ejpam-6215	730	3	such	such	ADJ
ejpam-6215	730	4	as	as	ADP
ejpam-6215	730	5	the	the	DET
ejpam-6215	730	6	differential	differential	ADJ
ejpam-6215	730	7	transform	transform	NOUN
ejpam-6215	730	8	method	method	NOUN
ejpam-6215	730	9	(	(	PUNCT
ejpam-6215	730	10	dtm	dtm	PROPN
ejpam-6215	730	11	)	)	PUNCT
ejpam-6215	730	12	,	,	PUNCT
ejpam-6215	730	13	modified	modify	VERB
ejpam-6215	730	14	adomian	adomian	NOUN
ejpam-6215	730	15	decomposition	decomposition	NOUN
ejpam-6215	730	16	method	method	NOUN
ejpam-6215	730	17	(	(	PUNCT
ejpam-6215	730	18	madm	madm	PROPN
ejpam-6215	730	19	)	)	PUNCT
ejpam-6215	730	20	,	,	PUNCT
ejpam-6215	730	21	laplace	laplace	NOUN
ejpam-6215	730	22	decomposition	decomposition	NOUN
ejpam-6215	730	23	method	method	NOUN
ejpam-6215	730	24	(	(	PUNCT
ejpam-6215	730	25	ldm	ldm	NOUN
ejpam-6215	730	26	)	)	PUNCT
ejpam-6215	730	27	,	,	PUNCT
ejpam-6215	730	28	and	and	CCONJ
ejpam-6215	730	29	natural	natural	ADJ
ejpam-6215	730	30	decomposition	decomposition	NOUN
ejpam-6215	730	31	method	method	NOUN
ejpam-6215	730	32	(	(	PUNCT
ejpam-6215	730	33	ndm	ndm	NOUN
ejpam-6215	730	34	)	)	PUNCT
ejpam-6215	730	35	provide	provide	VERB
ejpam-6215	730	36	series	series	NOUN
ejpam-6215	730	37	solutions	solution	NOUN
ejpam-6215	730	38	,	,	PUNCT
ejpam-6215	730	39	while	while	SCONJ
ejpam-6215	730	40	numerical	numerical	ADJ
ejpam-6215	730	41	techniques	technique	NOUN
ejpam-6215	730	42	such	such	ADJ
ejpam-6215	730	43	as	as	ADP
ejpam-6215	730	44	the	the	DET
ejpam-6215	730	45	finite	finite	ADJ
ejpam-6215	730	46	difference	difference	NOUN
ejpam-6215	730	47	method	method	NOUN
ejpam-6215	730	48	(	(	PUNCT
ejpam-6215	730	49	fdm	fdm	NOUN
ejpam-6215	730	50	)	)	PUNCT
ejpam-6215	730	51	and	and	CCONJ
ejpam-6215	730	52	runge	runge	NOUN
ejpam-6215	730	53	-	-	PUNCT
ejpam-6215	730	54	kutta	kutta	NOUN
ejpam-6215	730	55	method	method	NOUN
ejpam-6215	730	56	(	(	PUNCT
ejpam-6215	730	57	rk4	rk4	NOUN
ejpam-6215	730	58	)	)	PUNCT
ejpam-6215	730	59	offer	offer	VERB
ejpam-6215	730	60	direct	direct	ADJ
ejpam-6215	730	61	computational	computational	ADJ
ejpam-6215	730	62	approximations	approximation	NOUN
ejpam-6215	730	63	.	.	PUNCT
ejpam-6215	731	1	this	this	DET
ejpam-6215	731	2	section	section	NOUN
ejpam-6215	731	3	presents	present	VERB
ejpam-6215	731	4	a	a	DET
ejpam-6215	731	5	rigorous	rigorous	ADJ
ejpam-6215	731	6	comparison	comparison	NOUN
ejpam-6215	731	7	of	of	ADP
ejpam-6215	731	8	these	these	DET
ejpam-6215	731	9	methods	method	NOUN
ejpam-6215	731	10	[	[	X
ejpam-6215	731	11	1	1	NUM
ejpam-6215	731	12	,	,	PUNCT
ejpam-6215	731	13	2	2	NUM
ejpam-6215	731	14	]	]	PUNCT
ejpam-6215	731	15	.	.	PUNCT
ejpam-6215	732	1	s.	s.	PROPN
ejpam-6215	732	2	mohammed	mohammed	PROPN
ejpam-6215	732	3	,	,	PUNCT
ejpam-6215	732	4	s.	s.	PROPN
ejpam-6215	732	5	abid	abid	PROPN
ejpam-6215	732	6	,	,	PUNCT
ejpam-6215	732	7	r.	r.	PROPN
ejpam-6215	732	8	abid	abid	PROPN
ejpam-6215	732	9	/	/	SYM
ejpam-6215	732	10	eur	eur	PROPN
ejpam-6215	732	11	.	.	PUNCT
ejpam-6215	733	1	j.	j.	PROPN
ejpam-6215	733	2	pure	pure	PROPN
ejpam-6215	733	3	appl	appl	PROPN
ejpam-6215	733	4	.	.	PROPN
ejpam-6215	733	5	math	math	PROPN
ejpam-6215	733	6	,	,	PUNCT
ejpam-6215	733	7	18	18	NUM
ejpam-6215	733	8	(	(	PUNCT
ejpam-6215	733	9	3	3	NUM
ejpam-6215	733	10	)	)	PUNCT
ejpam-6215	733	11	(	(	PUNCT
ejpam-6215	733	12	2025	2025	NUM
ejpam-6215	733	13	)	)	PUNCT
ejpam-6215	733	14	,	,	PUNCT
ejpam-6215	733	15	6215	6215	NUM
ejpam-6215	733	16	32	32	NUM
ejpam-6215	733	17	of	of	ADP
ejpam-6215	733	18	38	38	NUM
ejpam-6215	733	19	4.1	4.1	NUM
ejpam-6215	733	20	.	.	PUNCT
ejpam-6215	734	1	comparison	comparison	NOUN
ejpam-6215	734	2	between	between	ADP
ejpam-6215	734	3	analytical	analytical	ADJ
ejpam-6215	734	4	methods	method	NOUN
ejpam-6215	734	5	to	to	PART
ejpam-6215	734	6	assess	assess	VERB
ejpam-6215	734	7	the	the	DET
ejpam-6215	734	8	accuracy	accuracy	NOUN
ejpam-6215	734	9	and	and	CCONJ
ejpam-6215	734	10	convergence	convergence	NOUN
ejpam-6215	734	11	of	of	ADP
ejpam-6215	734	12	dtm	dtm	PROPN
ejpam-6215	734	13	,	,	PUNCT
ejpam-6215	734	14	madm	madm	NOUN
ejpam-6215	734	15	,	,	PUNCT
ejpam-6215	734	16	ldm	ldm	NOUN
ejpam-6215	734	17	,	,	PUNCT
ejpam-6215	734	18	and	and	CCONJ
ejpam-6215	734	19	ndm	ndm	PROPN
ejpam-6215	734	20	,	,	PUNCT
ejpam-6215	734	21	we	we	PRON
ejpam-6215	734	22	compute	compute	VERB
ejpam-6215	734	23	approximate	approximate	ADJ
ejpam-6215	734	24	solutions	solution	NOUN
ejpam-6215	734	25	for	for	ADP
ejpam-6215	734	26	the	the	DET
ejpam-6215	734	27	painlevé	painlevé	NOUN
ejpam-6215	735	1	i	i	PRON
ejpam-6215	735	2	and	and	CCONJ
ejpam-6215	735	3	ii	ii	PROPN
ejpam-6215	735	4	equations	equation	NOUN
ejpam-6215	735	5	at	at	ADP
ejpam-6215	735	6	selected	select	VERB
ejpam-6215	735	7	points	point	NOUN
ejpam-6215	735	8	x	x	PUNCT
ejpam-6215	735	9	=	=	SYM
ejpam-6215	735	10	0	0	NUM
ejpam-6215	735	11	,	,	PUNCT
ejpam-6215	735	12	0.25	0.25	NUM
ejpam-6215	735	13	,	,	PUNCT
ejpam-6215	735	14	0.5	0.5	NUM
ejpam-6215	735	15	,	,	PUNCT
ejpam-6215	735	16	0.75	0.75	NUM
ejpam-6215	735	17	,	,	PUNCT
ejpam-6215	735	18	1	1	NUM
ejpam-6215	735	19	.	.	PUNCT
ejpam-6215	736	1	this	this	PRON
ejpam-6215	736	2	is	be	AUX
ejpam-6215	736	3	presented	present	VERB
ejpam-6215	736	4	for	for	ADP
ejpam-6215	736	5	painlevé	painlevé	NOUN
ejpam-6215	736	6	equation	equation	NOUN
ejpam-6215	736	7	i	i	PRON
ejpam-6215	736	8	in	in	ADP
ejpam-6215	736	9	table	table	NOUN
ejpam-6215	736	10	9	9	NUM
ejpam-6215	736	11	and	and	CCONJ
ejpam-6215	736	12	for	for	ADP
ejpam-6215	736	13	painlevé	painlevé	NOUN
ejpam-6215	736	14	equation	equation	NOUN
ejpam-6215	736	15	ii	ii	PROPN
ejpam-6215	736	16	in	in	ADP
ejpam-6215	736	17	table	table	NOUN
ejpam-6215	736	18	10	10	NUM
ejpam-6215	736	19	.	.	PUNCT
ejpam-6215	737	1	a	a	DET
ejpam-6215	737	2	graphical	graphical	ADJ
ejpam-6215	737	3	comparison	comparison	NOUN
ejpam-6215	737	4	of	of	ADP
ejpam-6215	737	5	the	the	DET
ejpam-6215	737	6	approximate	approximate	ADJ
ejpam-6215	737	7	solutions	solution	NOUN
ejpam-6215	737	8	obtained	obtain	VERB
ejpam-6215	737	9	from	from	ADP
ejpam-6215	737	10	dtm	dtm	PROPN
ejpam-6215	737	11	,	,	PUNCT
ejpam-6215	737	12	madm	madm	NOUN
ejpam-6215	737	13	,	,	PUNCT
ejpam-6215	737	14	ldm	ldm	NOUN
ejpam-6215	737	15	,	,	PUNCT
ejpam-6215	737	16	and	and	CCONJ
ejpam-6215	737	17	ndm	ndm	PROPN
ejpam-6215	737	18	for	for	ADP
ejpam-6215	737	19	painlevé	painlevé	NOUN
ejpam-6215	737	20	equation	equation	NOUN
ejpam-6215	737	21	i	i	PRON
ejpam-6215	737	22	is	be	AUX
ejpam-6215	737	23	presented	present	VERB
ejpam-6215	737	24	in	in	ADP
ejpam-6215	737	25	figure	figure	NOUN
ejpam-6215	737	26	9	9	NUM
ejpam-6215	737	27	,	,	PUNCT
ejpam-6215	737	28	and	and	CCONJ
ejpam-6215	737	29	for	for	ADP
ejpam-6215	737	30	painlevé	painlevé	NOUN
ejpam-6215	737	31	equation	equation	NOUN
ejpam-6215	737	32	ii	ii	PROPN
ejpam-6215	737	33	in	in	ADP
ejpam-6215	737	34	figure	figure	NOUN
ejpam-6215	737	35	10	10	NUM
ejpam-6215	737	36	.	.	PUNCT
ejpam-6215	738	1	table	table	NOUN
ejpam-6215	738	2	9	9	NUM
ejpam-6215	738	3	:	:	PUNCT
ejpam-6215	738	4	provides	provide	VERB
ejpam-6215	738	5	the	the	DET
ejpam-6215	738	6	computed	computed	ADJ
ejpam-6215	738	7	values	value	NOUN
ejpam-6215	738	8	of	of	ADP
ejpam-6215	738	9	y(x	y(x	NOUN
ejpam-6215	738	10	)	)	PUNCT
ejpam-6215	738	11	at	at	ADP
ejpam-6215	738	12	selected	select	VERB
ejpam-6215	738	13	points	point	NOUN
ejpam-6215	738	14	for	for	ADP
ejpam-6215	738	15	painlevé	painlevé	NOUN
ejpam-6215	738	16	equation	equation	NOUN
ejpam-6215	739	1	i	i	PRON
ejpam-6215	739	2	x	x	PUNCT
ejpam-6215	739	3	dtm	dtm	PROPN
ejpam-6215	739	4	madm	madm	PROPN
ejpam-6215	739	5	ldm	ldm	PROPN
ejpam-6215	739	6	ndm	ndm	PROPN
ejpam-6215	739	7	0.00	0.00	NUM
ejpam-6215	739	8	0.000000	0.000000	NUM
ejpam-6215	739	9	0.000000	0.000000	NUM
ejpam-6215	739	10	0.000000	0.000000	NUM
ejpam-6215	739	11	0.000000	0.000000	NUM
ejpam-6215	739	12	0.25	0.25	NUM
ejpam-6215	739	13	0.254582309975	0.254582309975	NUM
ejpam-6215	739	14	0.2545823823838	0.2545823823838	NUM
ejpam-6215	739	15	0.2545823823838	0.2545823823838	NUM
ejpam-6215	739	16	0.2545823823838	0.2545823823838	NUM
ejpam-6215	739	17	0.50	0.50	NUM
ejpam-6215	739	18	0.5542582826348	0.5542582826348	NUM
ejpam-6215	740	1	0.5542898995536	0.5542898995536	NUM
ejpam-6215	740	2	0.5542898995536	0.5542898995536	NUM
ejpam-6215	740	3	0.5542898995536	0.5542898995536	NUM
ejpam-6215	740	4	0.75	0.75	NUM
ejpam-6215	740	5	1.009901884624	1.009901884624	NUM
ejpam-6215	740	6	1.0113271032061	1.0113271032061	NUM
ejpam-6215	740	7	1.0113271032061	1.0113271032061	NUM
ejpam-6215	740	8	1.0113271032061	1.0113271032061	NUM
ejpam-6215	740	9	1.00	1.00	NUM
ejpam-6215	740	10	1.882208994709	1.882208994709	NUM
ejpam-6215	740	11	1.9011904761905	1.9011904761905	NUM
ejpam-6215	740	12	1.9011904761905	1.9011904761905	NUM
ejpam-6215	740	13	1.9011904761905	1.9011904761905	NUM
ejpam-6215	740	14	figure	figure	NOUN
ejpam-6215	740	15	9	9	NUM
ejpam-6215	740	16	:	:	PUNCT
ejpam-6215	740	17	convergence	convergence	NOUN
ejpam-6215	740	18	methods	method	NOUN
ejpam-6215	740	19	for	for	ADP
ejpam-6215	740	20	painlevé	painlevé	NOUN
ejpam-6215	740	21	equation	equation	NOUN
ejpam-6215	740	22	i.	i.	NOUN
ejpam-6215	740	23	table	table	PROPN
ejpam-6215	740	24	10	10	NUM
ejpam-6215	740	25	:	:	PUNCT
ejpam-6215	740	26	provides	provide	VERB
ejpam-6215	740	27	the	the	DET
ejpam-6215	740	28	computed	computed	ADJ
ejpam-6215	740	29	values	value	NOUN
ejpam-6215	740	30	of	of	ADP
ejpam-6215	740	31	y(x	y(x	NOUN
ejpam-6215	740	32	)	)	PUNCT
ejpam-6215	740	33	at	at	ADP
ejpam-6215	740	34	selected	select	VERB
ejpam-6215	740	35	points	point	NOUN
ejpam-6215	740	36	for	for	ADP
ejpam-6215	740	37	painlevé	painlevé	NOUN
ejpam-6215	740	38	equation	equation	NOUN
ejpam-6215	740	39	ii	ii	PROPN
ejpam-6215	740	40	.	.	PUNCT
ejpam-6215	741	1	x	x	PROPN
ejpam-6215	741	2	dtm	dtm	PROPN
ejpam-6215	741	3	madm	madm	PROPN
ejpam-6215	741	4	ldm	ldm	PROPN
ejpam-6215	741	5	ndm	ndm	PROPN
ejpam-6215	741	6	0.00	0.00	NUM
ejpam-6215	741	7	1.0000	1.0000	NUM
ejpam-6215	741	8	1.0000	1.0000	NUM
ejpam-6215	741	9	1.0000	1.0000	NUM
ejpam-6215	741	10	1.0000	1.0000	NUM
ejpam-6215	741	11	0.25	0.25	NUM
ejpam-6215	741	12	1.099332682292	1.099332682292	NUM
ejpam-6215	741	13	1.097355143229	1.097355143229	NUM
ejpam-6215	741	14	1.097355143229	1.097355143229	NUM
ejpam-6215	741	15	1.097355143229	1.097355143229	NUM
ejpam-6215	741	16	0.50	0.50	NUM
ejpam-6215	741	17	1.444270833333	1.444270833333	NUM
ejpam-6215	741	18	1.412239583333	1.412239583333	NUM
ejpam-6215	741	19	1.412239583333	1.412239583333	NUM
ejpam-6215	741	20	1.412239583333	1.412239583333	NUM
ejpam-6215	741	21	0.75	0.75	NUM
ejpam-6215	741	22	2.163232421875	2.163232421875	NUM
ejpam-6215	741	23	1.999096679688	1.999096679688	NUM
ejpam-6215	741	24	1.999096679688	1.999096679688	NUM
ejpam-6215	741	25	1.999096679688	1.999096679688	NUM
ejpam-6215	741	26	1.00	1.00	NUM
ejpam-6215	741	27	3.466666666667	3.466666666667	NUM
ejpam-6215	741	28	2.941666666667	2.941666666667	NUM
ejpam-6215	741	29	2.941666666667	2.941666666667	NUM
ejpam-6215	741	30	2.941666666667	2.941666666667	NUM
ejpam-6215	741	31	4.2	4.2	NUM
ejpam-6215	741	32	.	.	PUNCT
ejpam-6215	742	1	comparison	comparison	NOUN
ejpam-6215	742	2	between	between	ADP
ejpam-6215	742	3	numerical	numerical	ADJ
ejpam-6215	742	4	methods	method	NOUN
ejpam-6215	742	5	in	in	ADP
ejpam-6215	742	6	this	this	DET
ejpam-6215	742	7	subsection	subsection	NOUN
ejpam-6215	742	8	the	the	DET
ejpam-6215	742	9	numerical	numerical	ADJ
ejpam-6215	742	10	methods	method	NOUN
ejpam-6215	742	11	considered	consider	VERB
ejpam-6215	742	12	include	include	VERB
ejpam-6215	742	13	the	the	DET
ejpam-6215	742	14	finite	finite	ADJ
ejpam-6215	742	15	difference	difference	NOUN
ejpam-6215	742	16	method	method	NOUN
ejpam-6215	742	17	(	(	PUNCT
ejpam-6215	742	18	fdm	fdm	NOUN
ejpam-6215	742	19	)	)	PUNCT
ejpam-6215	742	20	and	and	CCONJ
ejpam-6215	742	21	the	the	DET
ejpam-6215	742	22	runge	runge	NOUN
ejpam-6215	742	23	-	-	PUNCT
ejpam-6215	742	24	kutta	kutta	NOUN
ejpam-6215	742	25	method	method	NOUN
ejpam-6215	742	26	(	(	PUNCT
ejpam-6215	742	27	rk4	rk4	NOUN
ejpam-6215	742	28	)	)	PUNCT
ejpam-6215	743	1	[	[	X
ejpam-6215	743	2	47	47	NUM
ejpam-6215	743	3	]	]	PUNCT
ejpam-6215	743	4	.	.	PUNCT
ejpam-6215	744	1	s.	s.	PROPN
ejpam-6215	744	2	mohammed	mohammed	PROPN
ejpam-6215	744	3	,	,	PUNCT
ejpam-6215	744	4	s.	s.	PROPN
ejpam-6215	744	5	abid	abid	PROPN
ejpam-6215	744	6	,	,	PUNCT
ejpam-6215	744	7	r.	r.	PROPN
ejpam-6215	744	8	abid	abid	PROPN
ejpam-6215	744	9	/	/	SYM
ejpam-6215	744	10	eur	eur	PROPN
ejpam-6215	744	11	.	.	PUNCT
ejpam-6215	745	1	j.	j.	PROPN
ejpam-6215	745	2	pure	pure	PROPN
ejpam-6215	745	3	appl	appl	PROPN
ejpam-6215	745	4	.	.	PROPN
ejpam-6215	745	5	math	math	PROPN
ejpam-6215	745	6	,	,	PUNCT
ejpam-6215	745	7	18	18	NUM
ejpam-6215	745	8	(	(	PUNCT
ejpam-6215	745	9	3	3	NUM
ejpam-6215	745	10	)	)	PUNCT
ejpam-6215	745	11	(	(	PUNCT
ejpam-6215	745	12	2025	2025	NUM
ejpam-6215	745	13	)	)	PUNCT
ejpam-6215	745	14	,	,	PUNCT
ejpam-6215	745	15	6215	6215	NUM
ejpam-6215	745	16	33	33	NUM
ejpam-6215	745	17	of	of	ADP
ejpam-6215	745	18	38	38	NUM
ejpam-6215	745	19	figure	figure	NOUN
ejpam-6215	745	20	10	10	NUM
ejpam-6215	745	21	:	:	PUNCT
ejpam-6215	745	22	convergence	convergence	NOUN
ejpam-6215	745	23	behavior	behavior	NOUN
ejpam-6215	745	24	of	of	ADP
ejpam-6215	745	25	these	these	DET
ejpam-6215	745	26	methods	method	NOUN
ejpam-6215	745	27	for	for	ADP
ejpam-6215	745	28	painlevé	painlevé	NOUN
ejpam-6215	745	29	equation	equation	NOUN
ejpam-6215	745	30	ii	ii	PROPN
ejpam-6215	745	31	.	.	PUNCT
ejpam-6215	746	1	the	the	DET
ejpam-6215	746	2	computed	compute	VERB
ejpam-6215	746	3	values	value	NOUN
ejpam-6215	746	4	for	for	ADP
ejpam-6215	746	5	painlevé	painlevé	NOUN
ejpam-6215	746	6	i	i	PRON
ejpam-6215	746	7	at	at	ADP
ejpam-6215	746	8	selected	select	VERB
ejpam-6215	746	9	points	point	NOUN
ejpam-6215	746	10	are	be	AUX
ejpam-6215	746	11	presented	present	VERB
ejpam-6215	746	12	in	in	ADP
ejpam-6215	746	13	table	table	NOUN
ejpam-6215	746	14	11	11	NUM
ejpam-6215	746	15	,	,	PUNCT
ejpam-6215	746	16	which	which	PRON
ejpam-6215	746	17	compares	compare	VERB
ejpam-6215	746	18	the	the	DET
ejpam-6215	746	19	approximate	approximate	ADJ
ejpam-6215	746	20	solutions	solution	NOUN
ejpam-6215	746	21	obtained	obtain	VERB
ejpam-6215	746	22	using	use	VERB
ejpam-6215	746	23	fdm	fdm	NOUN
ejpam-6215	746	24	and	and	CCONJ
ejpam-6215	746	25	rk4	rk4	NOUN
ejpam-6215	746	26	.	.	PUNCT
ejpam-6215	747	1	the	the	DET
ejpam-6215	747	2	graphical	graphical	ADJ
ejpam-6215	747	3	comparison	comparison	NOUN
ejpam-6215	747	4	of	of	ADP
ejpam-6215	747	5	these	these	DET
ejpam-6215	747	6	numerical	numerical	ADJ
ejpam-6215	747	7	methods	method	NOUN
ejpam-6215	747	8	is	be	AUX
ejpam-6215	747	9	further	far	ADV
ejpam-6215	747	10	illustrated	illustrate	VERB
ejpam-6215	747	11	in	in	ADP
ejpam-6215	747	12	figure	figure	NOUN
ejpam-6215	747	13	11	11	NUM
ejpam-6215	747	14	.	.	PUNCT
ejpam-6215	748	1	for	for	ADP
ejpam-6215	748	2	painlevé	painlevé	NOUN
ejpam-6215	748	3	ii	ii	NOUN
ejpam-6215	748	4	,	,	PUNCT
ejpam-6215	748	5	the	the	DET
ejpam-6215	748	6	computed	computed	ADJ
ejpam-6215	748	7	values	value	NOUN
ejpam-6215	748	8	using	use	VERB
ejpam-6215	748	9	fdm	fdm	NOUN
ejpam-6215	748	10	and	and	CCONJ
ejpam-6215	748	11	rk4	rk4	NOUN
ejpam-6215	748	12	are	be	AUX
ejpam-6215	748	13	presented	present	VERB
ejpam-6215	748	14	in	in	ADP
ejpam-6215	748	15	table	table	NOUN
ejpam-6215	748	16	12	12	NUM
ejpam-6215	748	17	,	,	PUNCT
ejpam-6215	748	18	and	and	CCONJ
ejpam-6215	748	19	the	the	DET
ejpam-6215	748	20	graphical	graphical	ADJ
ejpam-6215	748	21	comparison	comparison	NOUN
ejpam-6215	748	22	is	be	AUX
ejpam-6215	748	23	shown	show	VERB
ejpam-6215	748	24	in	in	ADP
ejpam-6215	748	25	figure	figure	NOUN
ejpam-6215	748	26	12	12	NUM
ejpam-6215	748	27	.	.	PUNCT
ejpam-6215	748	28	table	table	NOUN
ejpam-6215	748	29	11	11	NUM
ejpam-6215	748	30	:	:	PUNCT
ejpam-6215	748	31	comparison	comparison	NOUN
ejpam-6215	748	32	of	of	ADP
ejpam-6215	748	33	the	the	DET
ejpam-6215	748	34	approximate	approximate	ADJ
ejpam-6215	748	35	solution	solution	NOUN
ejpam-6215	748	36	by	by	ADP
ejpam-6215	748	37	fdm	fdm	NOUN
ejpam-6215	748	38	and	and	CCONJ
ejpam-6215	748	39	rk4	rk4	NOUN
ejpam-6215	748	40	,	,	PUNCT
ejpam-6215	748	41	for	for	ADP
ejpam-6215	748	42	painlevé	painlevé	NOUN
ejpam-6215	748	43	equation	equation	NOUN
ejpam-6215	748	44	i	i	PRON
ejpam-6215	748	45	at	at	ADP
ejpam-6215	748	46	selected	select	VERB
ejpam-6215	748	47	points	point	NOUN
ejpam-6215	748	48	.	.	PUNCT
ejpam-6215	749	1	x	x	PRON
ejpam-6215	749	2	fdm	fdm	VERB
ejpam-6215	749	3	rk4	rk4	NOUN
ejpam-6215	749	4	0.00	0.00	NUM
ejpam-6215	749	5	0.00000	0.00000	NUM
ejpam-6215	749	6	0.00000	0.00000	NUM
ejpam-6215	749	7	0.25	0.25	NUM
ejpam-6215	749	8	0.250000000000	0.250000000000	NUM
ejpam-6215	749	9	0.254455682891	0.254455682891	NUM
ejpam-6215	749	10	0.50	0.50	NUM
ejpam-6215	749	11	0.539062500000	0.539062500000	NUM
ejpam-6215	749	12	0.554123359580	0.554123359580	NUM
ejpam-6215	749	13	0.75	0.75	NUM
ejpam-6215	749	14	0.968345642090	0.968345642090	NUM
ejpam-6215	749	15	1.013010257333	1.013010257333	NUM
ejpam-6215	749	16	1.00	1.00	NUM
ejpam-6215	749	17	1.955078125000	1.955078125000	NUM
ejpam-6215	749	18	1.955172884313	1.955172884313	NUM
ejpam-6215	749	19	figure	figure	NOUN
ejpam-6215	749	20	11	11	NUM
ejpam-6215	749	21	:	:	PUNCT
ejpam-6215	749	22	the	the	DET
ejpam-6215	749	23	accuracy	accuracy	NOUN
ejpam-6215	749	24	of	of	ADP
ejpam-6215	749	25	numerical	numerical	ADJ
ejpam-6215	749	26	methods	method	NOUN
ejpam-6215	749	27	for	for	ADP
ejpam-6215	749	28	painlevé	painlevé	NOUN
ejpam-6215	749	29	equation	equation	NOUN
ejpam-6215	749	30	i.	i.	PROPN
ejpam-6215	749	31	s.	s.	PROPN
ejpam-6215	749	32	mohammed	mohammed	PROPN
ejpam-6215	749	33	,	,	PUNCT
ejpam-6215	749	34	s.	s.	PROPN
ejpam-6215	749	35	abid	abid	PROPN
ejpam-6215	749	36	,	,	PUNCT
ejpam-6215	749	37	r.	r.	PROPN
ejpam-6215	749	38	abid	abid	PROPN
ejpam-6215	749	39	/	/	SYM
ejpam-6215	749	40	eur	eur	PROPN
ejpam-6215	749	41	.	.	PUNCT
ejpam-6215	750	1	j.	j.	PROPN
ejpam-6215	750	2	pure	pure	PROPN
ejpam-6215	750	3	appl	appl	PROPN
ejpam-6215	750	4	.	.	PROPN
ejpam-6215	750	5	math	math	PROPN
ejpam-6215	750	6	,	,	PUNCT
ejpam-6215	750	7	18	18	NUM
ejpam-6215	750	8	(	(	PUNCT
ejpam-6215	750	9	3	3	NUM
ejpam-6215	750	10	)	)	PUNCT
ejpam-6215	750	11	(	(	PUNCT
ejpam-6215	750	12	2025	2025	NUM
ejpam-6215	750	13	)	)	PUNCT
ejpam-6215	750	14	,	,	PUNCT
ejpam-6215	750	15	6215	6215	NUM
ejpam-6215	750	16	34	34	NUM
ejpam-6215	750	17	of	of	ADP
ejpam-6215	750	18	38	38	NUM
ejpam-6215	750	19	table	table	NOUN
ejpam-6215	750	20	12	12	NUM
ejpam-6215	750	21	:	:	PUNCT
ejpam-6215	750	22	comparison	comparison	NOUN
ejpam-6215	750	23	of	of	ADP
ejpam-6215	750	24	the	the	DET
ejpam-6215	750	25	approximate	approximate	ADJ
ejpam-6215	750	26	solution	solution	NOUN
ejpam-6215	750	27	by	by	ADP
ejpam-6215	750	28	fdm	fdm	NOUN
ejpam-6215	750	29	and	and	CCONJ
ejpam-6215	750	30	rk4	rk4	NOUN
ejpam-6215	750	31	,	,	PUNCT
ejpam-6215	750	32	for	for	ADP
ejpam-6215	750	33	painlevé	painlevé	NOUN
ejpam-6215	750	34	equation	equation	NOUN
ejpam-6215	750	35	ii	ii	NOUN
ejpam-6215	750	36	at	at	ADP
ejpam-6215	750	37	selected	select	VERB
ejpam-6215	750	38	points	point	NOUN
ejpam-6215	750	39	.	.	PUNCT
ejpam-6215	751	1	x	x	PRON
ejpam-6215	751	2	fdm	fdm	VERB
ejpam-6215	751	3	rk4	rk4	NOUN
ejpam-6215	751	4	0.00	0.00	NUM
ejpam-6215	751	5	1.00000	1.00000	NUM
ejpam-6215	751	6	1.00000	1.00000	NUM
ejpam-6215	751	7	0.25	0.25	NUM
ejpam-6215	751	8	1.00000	1.00000	NUM
ejpam-6215	751	9	1.099484364191691	1.099484364191691	NUM
ejpam-6215	751	10	0.50	0.50	NUM
ejpam-6215	751	11	1.203125000000000	1.203125000000000	NUM
ejpam-6215	751	12	1.458011474879827	1.458011474879827	NUM
ejpam-6215	751	13	0.75	0.75	NUM
ejpam-6215	751	14	2.677408218383789	2.677408218383789	NUM
ejpam-6215	751	15	2.377499005219746	2.377499005219746	NUM
ejpam-6215	751	16	1.00	1.00	NUM
ejpam-6215	751	17	6.738824991141589	6.738824991141589	NUM
ejpam-6215	751	18	5.909391830792607	5.909391830792607	NUM
ejpam-6215	751	19	figure	figure	NOUN
ejpam-6215	751	20	12	12	NUM
ejpam-6215	751	21	:	:	PUNCT
ejpam-6215	751	22	the	the	DET
ejpam-6215	751	23	accuracy	accuracy	NOUN
ejpam-6215	751	24	of	of	ADP
ejpam-6215	751	25	numerical	numerical	ADJ
ejpam-6215	751	26	methods	method	NOUN
ejpam-6215	751	27	for	for	ADP
ejpam-6215	751	28	painlevé	painlevé	NOUN
ejpam-6215	751	29	equation	equation	NOUN
ejpam-6215	751	30	ii	ii	PROPN
ejpam-6215	751	31	.	.	PROPN
ejpam-6215	752	1	5	5	NUM
ejpam-6215	752	2	.	.	X
ejpam-6215	752	3	conclusion	conclusion	NOUN
ejpam-6215	752	4	this	this	DET
ejpam-6215	752	5	paper	paper	NOUN
ejpam-6215	752	6	explored	explore	VERB
ejpam-6215	752	7	various	various	ADJ
ejpam-6215	752	8	analytical	analytical	ADJ
ejpam-6215	752	9	and	and	CCONJ
ejpam-6215	752	10	numerical	numerical	ADJ
ejpam-6215	752	11	methods	method	NOUN
ejpam-6215	752	12	for	for	ADP
ejpam-6215	752	13	solving	solve	VERB
ejpam-6215	752	14	the	the	DET
ejpam-6215	752	15	painlevé	painlevé	NOUN
ejpam-6215	752	16	equations	equation	NOUN
ejpam-6215	752	17	i	i	PRON
ejpam-6215	752	18	and	and	CCONJ
ejpam-6215	752	19	ii	ii	PROPN
ejpam-6215	752	20	,	,	PUNCT
ejpam-6215	752	21	which	which	PRON
ejpam-6215	752	22	are	be	AUX
ejpam-6215	752	23	significant	significant	ADJ
ejpam-6215	752	24	in	in	ADP
ejpam-6215	752	25	the	the	DET
ejpam-6215	752	26	field	field	NOUN
ejpam-6215	752	27	of	of	ADP
ejpam-6215	752	28	nonlinear	nonlinear	ADJ
ejpam-6215	752	29	differential	differential	ADJ
ejpam-6215	752	30	equations	equation	NOUN
ejpam-6215	752	31	due	due	ADP
ejpam-6215	752	32	to	to	ADP
ejpam-6215	752	33	their	their	PRON
ejpam-6215	752	34	integrability	integrability	NOUN
ejpam-6215	752	35	and	and	CCONJ
ejpam-6215	752	36	applications	application	NOUN
ejpam-6215	752	37	in	in	ADP
ejpam-6215	752	38	mathematical	mathematical	ADJ
ejpam-6215	752	39	physics	physics	NOUN
ejpam-6215	752	40	.	.	PUNCT
ejpam-6215	753	1	the	the	DET
ejpam-6215	753	2	analytical	analytical	ADJ
ejpam-6215	753	3	methods	method	NOUN
ejpam-6215	753	4	examined	examine	VERB
ejpam-6215	753	5	,	,	PUNCT
ejpam-6215	753	6	including	include	VERB
ejpam-6215	753	7	the	the	DET
ejpam-6215	753	8	differential	differential	ADJ
ejpam-6215	753	9	transform	transform	NOUN
ejpam-6215	753	10	method	method	NOUN
ejpam-6215	753	11	,	,	PUNCT
ejpam-6215	753	12	the	the	DET
ejpam-6215	753	13	modified	modified	ADJ
ejpam-6215	753	14	adomian	adomian	NOUN
ejpam-6215	753	15	decomposition	decomposition	NOUN
ejpam-6215	753	16	method	method	NOUN
ejpam-6215	753	17	,	,	PUNCT
ejpam-6215	753	18	the	the	DET
ejpam-6215	753	19	laplace	laplace	NOUN
ejpam-6215	753	20	decomposition	decomposition	NOUN
ejpam-6215	753	21	method	method	NOUN
ejpam-6215	753	22	,	,	PUNCT
ejpam-6215	753	23	and	and	CCONJ
ejpam-6215	753	24	the	the	DET
ejpam-6215	753	25	natural	natural	ADJ
ejpam-6215	753	26	decomposition	decomposition	NOUN
ejpam-6215	753	27	method	method	NOUN
ejpam-6215	753	28	,	,	PUNCT
ejpam-6215	753	29	showcased	showcase	VERB
ejpam-6215	753	30	their	their	PRON
ejpam-6215	753	31	potential	potential	NOUN
ejpam-6215	753	32	for	for	ADP
ejpam-6215	753	33	handling	handle	VERB
ejpam-6215	753	34	the	the	DET
ejpam-6215	753	35	inherent	inherent	ADJ
ejpam-6215	753	36	complexities	complexity	NOUN
ejpam-6215	753	37	of	of	ADP
ejpam-6215	753	38	nonlinear	nonlinear	ADJ
ejpam-6215	753	39	equations	equation	NOUN
ejpam-6215	753	40	with	with	ADP
ejpam-6215	753	41	high	high	ADJ
ejpam-6215	753	42	precision	precision	NOUN
ejpam-6215	753	43	.	.	PUNCT
ejpam-6215	754	1	on	on	ADP
ejpam-6215	754	2	the	the	DET
ejpam-6215	754	3	other	other	ADJ
ejpam-6215	754	4	hand	hand	NOUN
ejpam-6215	754	5	,	,	PUNCT
ejpam-6215	754	6	numerical	numerical	ADJ
ejpam-6215	754	7	methods	method	NOUN
ejpam-6215	754	8	,	,	PUNCT
ejpam-6215	754	9	specifically	specifically	ADV
ejpam-6215	754	10	the	the	DET
ejpam-6215	754	11	finite	finite	ADJ
ejpam-6215	754	12	difference	difference	NOUN
ejpam-6215	754	13	method	method	NOUN
ejpam-6215	754	14	and	and	CCONJ
ejpam-6215	754	15	the	the	DET
ejpam-6215	754	16	fourth	fourth	ADJ
ejpam-6215	754	17	-	-	PUNCT
ejpam-6215	754	18	order	order	NOUN
ejpam-6215	754	19	runge	runge	NOUN
ejpam-6215	754	20	-	-	PUNCT
ejpam-6215	754	21	kutta	kutta	NOUN
ejpam-6215	754	22	method	method	NOUN
ejpam-6215	754	23	(	(	PUNCT
ejpam-6215	754	24	rk4	rk4	NOUN
ejpam-6215	754	25	)	)	PUNCT
ejpam-6215	754	26	,	,	PUNCT
ejpam-6215	754	27	demonstrated	demonstrate	VERB
ejpam-6215	754	28	their	their	PRON
ejpam-6215	754	29	effectiveness	effectiveness	NOUN
ejpam-6215	754	30	in	in	ADP
ejpam-6215	754	31	providing	provide	VERB
ejpam-6215	754	32	approximate	approximate	ADJ
ejpam-6215	754	33	solutions	solution	NOUN
ejpam-6215	754	34	when	when	SCONJ
ejpam-6215	754	35	exact	exact	ADJ
ejpam-6215	754	36	solutions	solution	NOUN
ejpam-6215	754	37	were	be	AUX
ejpam-6215	754	38	challenging	challenge	VERB
ejpam-6215	754	39	to	to	PART
ejpam-6215	754	40	derive	derive	VERB
ejpam-6215	754	41	.	.	PUNCT
ejpam-6215	755	1	comparing	compare	VERB
ejpam-6215	755	2	the	the	DET
ejpam-6215	755	3	two	two	NUM
ejpam-6215	755	4	approaches	approach	NOUN
ejpam-6215	755	5	,	,	PUNCT
ejpam-6215	755	6	analytical	analytical	ADJ
ejpam-6215	755	7	methods	method	NOUN
ejpam-6215	755	8	are	be	AUX
ejpam-6215	755	9	advantageous	advantageous	ADJ
ejpam-6215	755	10	for	for	ADP
ejpam-6215	755	11	gaining	gain	VERB
ejpam-6215	755	12	insights	insight	NOUN
ejpam-6215	755	13	into	into	ADP
ejpam-6215	755	14	the	the	DET
ejpam-6215	755	15	structural	structural	ADJ
ejpam-6215	755	16	properties	property	NOUN
ejpam-6215	755	17	of	of	ADP
ejpam-6215	755	18	solutions	solution	NOUN
ejpam-6215	755	19	,	,	PUNCT
ejpam-6215	755	20	while	while	SCONJ
ejpam-6215	755	21	numerical	numerical	ADJ
ejpam-6215	755	22	methods	method	NOUN
ejpam-6215	755	23	are	be	AUX
ejpam-6215	755	24	more	more	ADV
ejpam-6215	755	25	versatile	versatile	ADJ
ejpam-6215	755	26	for	for	ADP
ejpam-6215	755	27	practical	practical	ADJ
ejpam-6215	755	28	computations	computation	NOUN
ejpam-6215	755	29	.	.	PUNCT
ejpam-6215	756	1	this	this	DET
ejpam-6215	756	2	combination	combination	NOUN
ejpam-6215	756	3	of	of	ADP
ejpam-6215	756	4	techniques	technique	NOUN
ejpam-6215	756	5	forms	form	VERB
ejpam-6215	756	6	a	a	DET
ejpam-6215	756	7	comprehensive	comprehensive	ADJ
ejpam-6215	756	8	toolbox	toolbox	NOUN
ejpam-6215	756	9	for	for	ADP
ejpam-6215	756	10	tackling	tackle	VERB
ejpam-6215	756	11	nonlinear	nonlinear	ADJ
ejpam-6215	756	12	ordinary	ordinary	ADJ
ejpam-6215	756	13	differential	differential	ADJ
ejpam-6215	756	14	equations	equation	NOUN
ejpam-6215	756	15	like	like	ADP
ejpam-6215	756	16	the	the	DET
ejpam-6215	756	17	painlevé	painlevé	NOUN
ejpam-6215	756	18	equations	equation	NOUN
ejpam-6215	756	19	.	.	PUNCT
ejpam-6215	757	1	future	future	ADJ
ejpam-6215	757	2	work	work	NOUN
ejpam-6215	757	3	will	will	AUX
ejpam-6215	757	4	focus	focus	VERB
ejpam-6215	757	5	on	on	ADP
ejpam-6215	757	6	analytic	analytic	ADJ
ejpam-6215	757	7	and	and	CCONJ
ejpam-6215	757	8	numerical	numerical	ADJ
ejpam-6215	757	9	methods	method	NOUN
ejpam-6215	757	10	’	'	PUNCT
ejpam-6215	757	11	approaches	approach	NOUN
ejpam-6215	757	12	for	for	ADP
ejpam-6215	757	13	solving	solve	VERB
ejpam-6215	757	14	systems	system	NOUN
ejpam-6215	757	15	of	of	ADP
ejpam-6215	757	16	differential	differential	ADJ
ejpam-6215	757	17	equations	equation	NOUN
ejpam-6215	757	18	.	.	PUNCT
ejpam-6215	758	1	acknowledgements	acknowledgement	VERB
ejpam-6215	758	2	the	the	DET
ejpam-6215	758	3	author	author	NOUN
ejpam-6215	758	4	thanks	thank	NOUN
ejpam-6215	758	5	the	the	DET
ejpam-6215	758	6	editor	editor	NOUN
ejpam-6215	758	7	and	and	CCONJ
ejpam-6215	758	8	referees	referee	NOUN
ejpam-6215	758	9	for	for	ADP
ejpam-6215	758	10	the	the	DET
ejpam-6215	758	11	valuable	valuable	ADJ
ejpam-6215	758	12	comments	comment	NOUN
ejpam-6215	758	13	and	and	CCONJ
ejpam-6215	758	14	suggestions	suggestion	NOUN
ejpam-6215	758	15	that	that	PRON
ejpam-6215	758	16	helped	help	VERB
ejpam-6215	758	17	him	he	PRON
ejpam-6215	758	18	improve	improve	VERB
ejpam-6215	758	19	the	the	DET
ejpam-6215	758	20	quality	quality	NOUN
ejpam-6215	758	21	and	and	CCONJ
ejpam-6215	758	22	readability	readability	NOUN
ejpam-6215	758	23	of	of	ADP
ejpam-6215	758	24	the	the	DET
ejpam-6215	758	25	paper	paper	NOUN
ejpam-6215	758	26	,	,	PUNCT
ejpam-6215	758	27	which	which	PRON
ejpam-6215	758	28	led	lead	VERB
ejpam-6215	758	29	to	to	ADP
ejpam-6215	758	30	a	a	DET
ejpam-6215	758	31	significant	significant	ADJ
ejpam-6215	758	32	improvement	improvement	NOUN
ejpam-6215	758	33	of	of	ADP
ejpam-6215	758	34	the	the	DET
ejpam-6215	758	35	paper	paper	NOUN
ejpam-6215	758	36	.	.	PUNCT
ejpam-6215	759	1	s.	s.	PROPN
ejpam-6215	759	2	mohammed	mohammed	PROPN
ejpam-6215	759	3	,	,	PUNCT
ejpam-6215	759	4	s.	s.	PROPN
ejpam-6215	759	5	abid	abid	PROPN
ejpam-6215	759	6	,	,	PUNCT
ejpam-6215	759	7	r.	r.	PROPN
ejpam-6215	759	8	abid	abid	PROPN
ejpam-6215	759	9	/	/	SYM
ejpam-6215	759	10	eur	eur	PROPN
ejpam-6215	759	11	.	.	PUNCT
ejpam-6215	760	1	j.	j.	PROPN
ejpam-6215	760	2	pure	pure	PROPN
ejpam-6215	760	3	appl	appl	PROPN
ejpam-6215	760	4	.	.	PROPN
ejpam-6215	760	5	math	math	PROPN
ejpam-6215	760	6	,	,	PUNCT
ejpam-6215	760	7	18	18	NUM
ejpam-6215	760	8	(	(	PUNCT
ejpam-6215	760	9	3	3	NUM
ejpam-6215	760	10	)	)	PUNCT
ejpam-6215	760	11	(	(	PUNCT
ejpam-6215	760	12	2025	2025	NUM
ejpam-6215	760	13	)	)	PUNCT
ejpam-6215	760	14	,	,	PUNCT
ejpam-6215	760	15	6215	6215	NUM
ejpam-6215	760	16	35	35	NUM
ejpam-6215	760	17	of	of	ADP
ejpam-6215	760	18	38	38	NUM
ejpam-6215	760	19	conflict	conflict	NOUN
ejpam-6215	760	20	of	of	ADP
ejpam-6215	760	21	interest	interest	NOUN
ejpam-6215	760	22	the	the	DET
ejpam-6215	760	23	authors	author	NOUN
ejpam-6215	760	24	declare	declare	VERB
ejpam-6215	760	25	that	that	SCONJ
ejpam-6215	760	26	there	there	PRON
ejpam-6215	760	27	is	be	VERB
ejpam-6215	760	28	no	no	DET
ejpam-6215	760	29	conflict	conflict	NOUN
ejpam-6215	760	30	of	of	ADP
ejpam-6215	760	31	interest	interest	NOUN
ejpam-6215	760	32	to	to	PART
ejpam-6215	760	33	disclose	disclose	VERB
ejpam-6215	760	34	.	.	PUNCT
ejpam-6215	761	1	references	reference	NOUN
ejpam-6215	761	2	[	[	X
ejpam-6215	761	3	1	1	X
ejpam-6215	761	4	]	]	X
ejpam-6215	761	5	j.	j.	PROPN
ejpam-6215	761	6	mart́ın	mart́ın	PROPN
ejpam-6215	761	7	-	-	PUNCT
ejpam-6215	761	8	vaquero	vaquero	NOUN
ejpam-6215	761	9	,	,	PUNCT
ejpam-6215	761	10	f.	f.	PROPN
ejpam-6215	761	11	minh	minh	PROPN
ejpam-6215	761	12	os	os	PROPN
ejpam-6215	761	13	,	,	PUNCT
ejpam-6215	761	14	j.	j.	PROPN
ejpam-6215	761	15	l.	l.	PROPN
ejpam-6215	761	16	g.	g.	PROPN
ejpam-6215	761	17	guirao	guirao	PROPN
ejpam-6215	761	18	,	,	PUNCT
ejpam-6215	761	19	and	and	CCONJ
ejpam-6215	761	20	b.	b.	PROPN
ejpam-6215	761	21	a.	a.	PROPN
ejpam-6215	761	22	wade	wade	PROPN
ejpam-6215	761	23	,	,	PUNCT
ejpam-6215	761	24	editors	editor	NOUN
ejpam-6215	761	25	.	.	PUNCT
ejpam-6215	762	1	analytical	analytical	ADJ
ejpam-6215	762	2	and	and	CCONJ
ejpam-6215	762	3	numerical	numerical	ADJ
ejpam-6215	762	4	methods	method	NOUN
ejpam-6215	762	5	for	for	ADP
ejpam-6215	762	6	differential	differential	ADJ
ejpam-6215	762	7	equations	equation	NOUN
ejpam-6215	762	8	and	and	CCONJ
ejpam-6215	762	9	applications	application	NOUN
ejpam-6215	762	10	.	.	PUNCT
ejpam-6215	763	1	frontiers	frontier	NOUN
ejpam-6215	763	2	media	media	PROPN
ejpam-6215	763	3	sa	sa	PROPN
ejpam-6215	763	4	,	,	PUNCT
ejpam-6215	763	5	lausanne	lausanne	PROPN
ejpam-6215	763	6	,	,	PUNCT
ejpam-6215	763	7	2021	2021	NUM
ejpam-6215	763	8	.	.	PUNCT
ejpam-6215	764	1	[	[	X
ejpam-6215	764	2	2	2	X
ejpam-6215	764	3	]	]	X
ejpam-6215	764	4	y.	y.	PROPN
ejpam-6215	764	5	pala	pala	PROPN
ejpam-6215	764	6	and	and	CCONJ
ejpam-6215	764	7	c.	c.	PROPN
ejpam-6215	764	8	kahya	kahya	PROPN
ejpam-6215	764	9	.	.	PUNCT
ejpam-6215	765	1	new	new	ADJ
ejpam-6215	765	2	analytical	analytical	ADJ
ejpam-6215	765	3	method	method	NOUN
ejpam-6215	765	4	for	for	ADP
ejpam-6215	765	5	solution	solution	NOUN
ejpam-6215	765	6	of	of	ADP
ejpam-6215	765	7	second	second	ADJ
ejpam-6215	765	8	order	order	NOUN
ejpam-6215	765	9	ordinary	ordinary	ADJ
ejpam-6215	765	10	differential	differential	ADJ
ejpam-6215	765	11	equations	equation	NOUN
ejpam-6215	765	12	with	with	ADP
ejpam-6215	765	13	variable	variable	ADJ
ejpam-6215	765	14	coefficients	coefficient	NOUN
ejpam-6215	765	15	.	.	PUNCT
ejpam-6215	766	1	erzincan	erzincan	PROPN
ejpam-6215	766	2	univ	univ	PROPN
ejpam-6215	766	3	.	.	PUNCT
ejpam-6215	767	1	j.	j.	PROPN
ejpam-6215	767	2	sci	sci	PROPN
ejpam-6215	767	3	.	.	PROPN
ejpam-6215	767	4	technol	technol	PROPN
ejpam-6215	767	5	.	.	PROPN
ejpam-6215	767	6	,	,	PUNCT
ejpam-6215	767	7	15(3):757–774	15(3):757–774	NOUN
ejpam-6215	767	8	,	,	PUNCT
ejpam-6215	767	9	2022	2022	NUM
ejpam-6215	767	10	.	.	PUNCT
ejpam-6215	768	1	[	[	X
ejpam-6215	768	2	3	3	X
ejpam-6215	768	3	]	]	X
ejpam-6215	768	4	h.	h.	PROPN
ejpam-6215	768	5	ahmad	ahmad	PROPN
ejpam-6215	768	6	.	.	PROPN
ejpam-6215	769	1	numerical	numerical	ADJ
ejpam-6215	769	2	solution	solution	NOUN
ejpam-6215	769	3	of	of	ADP
ejpam-6215	769	4	painlevé	painlevé	NOUN
ejpam-6215	769	5	ii	ii	PROPN
ejpam-6215	769	6	differential	differential	NOUN
ejpam-6215	769	7	equation	equation	NOUN
ejpam-6215	769	8	.	.	PUNCT
ejpam-6215	770	1	commun	commun	PROPN
ejpam-6215	770	2	.	.	PUNCT
ejpam-6215	771	1	numer	numer	PROPN
ejpam-6215	771	2	.	.	PUNCT
ejpam-6215	772	1	anal	anal	PROPN
ejpam-6215	772	2	.	.	PUNCT
ejpam-6215	772	3	,	,	PUNCT
ejpam-6215	772	4	2019(1):32–38	2019(1):32–38	NUM
ejpam-6215	772	5	,	,	PUNCT
ejpam-6215	772	6	2019	2019	NUM
ejpam-6215	772	7	.	.	PUNCT
ejpam-6215	773	1	[	[	X
ejpam-6215	773	2	4	4	X
ejpam-6215	773	3	]	]	PUNCT
ejpam-6215	773	4	t.	t.	NOUN
ejpam-6215	773	5	hosoi	hosoi	NOUN
ejpam-6215	773	6	and	and	CCONJ
ejpam-6215	773	7	h.	h.	PROPN
ejpam-6215	773	8	sakai	sakai	PROPN
ejpam-6215	773	9	.	.	PUNCT
ejpam-6215	774	1	a	a	DET
ejpam-6215	774	2	study	study	NOUN
ejpam-6215	774	3	on	on	ADP
ejpam-6215	774	4	the	the	DET
ejpam-6215	774	5	bilinear	bilinear	NOUN
ejpam-6215	774	6	equation	equation	NOUN
ejpam-6215	774	7	of	of	ADP
ejpam-6215	774	8	the	the	DET
ejpam-6215	774	9	sixth	sixth	ADJ
ejpam-6215	774	10	painlevé	painlevé	NOUN
ejpam-6215	774	11	transcendents	transcendent	NOUN
ejpam-6215	774	12	.	.	PUNCT
ejpam-6215	775	1	arxiv	arxiv	PROPN
ejpam-6215	775	2	preprint	preprint	NOUN
ejpam-6215	775	3	arxiv:2304.13981	arxiv:2304.13981	PROPN
ejpam-6215	775	4	,	,	PUNCT
ejpam-6215	775	5	april	april	PROPN
ejpam-6215	775	6	2023	2023	NUM
ejpam-6215	775	7	.	.	PUNCT
ejpam-6215	776	1	[	[	X
ejpam-6215	776	2	5	5	X
ejpam-6215	776	3	]	]	PUNCT
ejpam-6215	776	4	j.	j.	PROPN
ejpam-6215	776	5	k.	k.	PROPN
ejpam-6215	776	6	zhou	zhou	PROPN
ejpam-6215	776	7	.	.	PUNCT
ejpam-6215	777	1	differential	differential	ADJ
ejpam-6215	777	2	transformation	transformation	NOUN
ejpam-6215	777	3	and	and	CCONJ
ejpam-6215	777	4	its	its	PRON
ejpam-6215	777	5	applications	application	NOUN
ejpam-6215	777	6	for	for	ADP
ejpam-6215	777	7	electrical	electrical	ADJ
ejpam-6215	777	8	circuits	circuit	NOUN
ejpam-6215	777	9	.	.	PUNCT
ejpam-6215	778	1	huazhong	huazhong	PROPN
ejpam-6215	778	2	university	university	PROPN
ejpam-6215	778	3	press	press	NOUN
ejpam-6215	778	4	,	,	PUNCT
ejpam-6215	778	5	wuhan	wuhan	PROPN
ejpam-6215	778	6	,	,	PUNCT
ejpam-6215	778	7	china	china	PROPN
ejpam-6215	778	8	,	,	PUNCT
ejpam-6215	778	9	1986	1986	NUM
ejpam-6215	778	10	.	.	PUNCT
ejpam-6215	779	1	[	[	X
ejpam-6215	779	2	6	6	NUM
ejpam-6215	779	3	]	]	PUNCT
ejpam-6215	779	4	b.	b.	PROPN
ejpam-6215	779	5	n.	n.	PROPN
ejpam-6215	779	6	kharrat	kharrat	PROPN
ejpam-6215	779	7	and	and	CCONJ
ejpam-6215	779	8	g.	g.	PROPN
ejpam-6215	779	9	toma	toma	PROPN
ejpam-6215	779	10	.	.	PUNCT
ejpam-6215	780	1	differential	differential	PROPN
ejpam-6215	780	2	transform	transform	NOUN
ejpam-6215	780	3	method	method	NOUN
ejpam-6215	780	4	for	for	ADP
ejpam-6215	780	5	solving	solve	VERB
ejpam-6215	780	6	initial	initial	ADJ
ejpam-6215	780	7	and	and	CCONJ
ejpam-6215	780	8	boundary	boundary	ADJ
ejpam-6215	780	9	value	value	NOUN
ejpam-6215	780	10	problems	problem	NOUN
ejpam-6215	780	11	represented	represent	VERB
ejpam-6215	780	12	by	by	ADP
ejpam-6215	780	13	linear	linear	PROPN
ejpam-6215	780	14	and	and	CCONJ
ejpam-6215	780	15	nonlinear	nonlinear	ADJ
ejpam-6215	780	16	ordinary	ordinary	ADJ
ejpam-6215	780	17	differential	differential	ADJ
ejpam-6215	780	18	equations	equation	NOUN
ejpam-6215	780	19	of	of	ADP
ejpam-6215	780	20	14th	14th	ADJ
ejpam-6215	780	21	order	order	NOUN
ejpam-6215	780	22	.	.	PUNCT
ejpam-6215	781	1	world	world	NOUN
ejpam-6215	781	2	appl	appl	PROPN
ejpam-6215	781	3	.	.	PUNCT
ejpam-6215	782	1	sci	sci	PROPN
ejpam-6215	782	2	.	.	PUNCT
ejpam-6215	783	1	j.	j.	PROPN
ejpam-6215	783	2	,	,	PUNCT
ejpam-6215	783	3	37(6):481–485	37(6):481–485	PROPN
ejpam-6215	783	4	,	,	PUNCT
ejpam-6215	783	5	2019	2019	NUM
ejpam-6215	783	6	.	.	PUNCT
ejpam-6215	784	1	[	[	X
ejpam-6215	784	2	7	7	X
ejpam-6215	784	3	]	]	X
ejpam-6215	784	4	i.	i.	PROPN
ejpam-6215	784	5	u.	u.	PROPN
ejpam-6215	784	6	haq	haq	PROPN
ejpam-6215	784	7	,	,	PUNCT
ejpam-6215	784	8	s.	s.	PROPN
ejpam-6215	784	9	k.	k.	PROPN
ejpam-6215	784	10	tiwari	tiwari	PROPN
ejpam-6215	784	11	,	,	PUNCT
ejpam-6215	784	12	and	and	CCONJ
ejpam-6215	784	13	n.	n.	PROPN
ejpam-6215	784	14	u.	u.	PROPN
ejpam-6215	784	15	haq	haq	PROPN
ejpam-6215	784	16	.	.	PUNCT
ejpam-6215	785	1	using	use	VERB
ejpam-6215	785	2	adomian	adomian	NOUN
ejpam-6215	785	3	decomposition	decomposition	NOUN
ejpam-6215	785	4	method	method	NOUN
ejpam-6215	785	5	for	for	ADP
ejpam-6215	785	6	solving	solve	VERB
ejpam-6215	785	7	non	non	ADJ
ejpam-6215	785	8	-	-	ADJ
ejpam-6215	785	9	linear	linear	ADJ
ejpam-6215	785	10	initial	initial	ADJ
ejpam-6215	785	11	value	value	NOUN
ejpam-6215	785	12	problem	problem	NOUN
ejpam-6215	785	13	.	.	PUNCT
ejpam-6215	786	1	int	int	NOUN
ejpam-6215	786	2	.	.	PUNCT
ejpam-6215	787	1	j.	j.	PROPN
ejpam-6215	787	2	eng	eng	PROPN
ejpam-6215	787	3	.	.	PUNCT
ejpam-6215	788	1	res	res	PROPN
ejpam-6215	788	2	.	.	PROPN
ejpam-6215	789	1	technol	technol	PROPN
ejpam-6215	789	2	.	.	PUNCT
ejpam-6215	790	1	(	(	PUNCT
ejpam-6215	790	2	ijert	ijert	PROPN
ejpam-6215	790	3	)	)	PUNCT
ejpam-6215	790	4	,	,	PUNCT
ejpam-6215	790	5	13(6	13(6	PROPN
ejpam-6215	790	6	)	)	PUNCT
ejpam-6215	790	7	,	,	PUNCT
ejpam-6215	790	8	2024	2024	NUM
ejpam-6215	790	9	.	.	PUNCT
ejpam-6215	791	1	[	[	X
ejpam-6215	791	2	8	8	NUM
ejpam-6215	791	3	]	]	X
ejpam-6215	791	4	m.	m.	NOUN
ejpam-6215	791	5	almazmumy	almazmumy	PROPN
ejpam-6215	791	6	,	,	PUNCT
ejpam-6215	791	7	a.	a.	NOUN
ejpam-6215	791	8	a.	a.	NOUN
ejpam-6215	791	9	alsulami	alsulami	PROPN
ejpam-6215	791	10	,	,	PUNCT
ejpam-6215	791	11	h.	h.	PROPN
ejpam-6215	791	12	o.	o.	NOUN
ejpam-6215	791	13	bakodah	bakodah	PROPN
ejpam-6215	791	14	,	,	PUNCT
ejpam-6215	791	15	and	and	CCONJ
ejpam-6215	791	16	n.	n.	PROPN
ejpam-6215	791	17	a.	a.	PROPN
ejpam-6215	791	18	alzaid	alzaid	PROPN
ejpam-6215	791	19	.	.	PUNCT
ejpam-6215	792	1	adomian	adomian	NOUN
ejpam-6215	792	2	decomposition	decomposition	NOUN
ejpam-6215	792	3	method	method	NOUN
ejpam-6215	792	4	with	with	ADP
ejpam-6215	792	5	inverse	inverse	NOUN
ejpam-6215	792	6	differential	differential	NOUN
ejpam-6215	792	7	operator	operator	NOUN
ejpam-6215	792	8	and	and	CCONJ
ejpam-6215	792	9	orthogonal	orthogonal	ADJ
ejpam-6215	792	10	polynomials	polynomial	NOUN
ejpam-6215	792	11	for	for	ADP
ejpam-6215	792	12	nonlinear	nonlinear	ADJ
ejpam-6215	792	13	models	model	NOUN
ejpam-6215	792	14	.	.	PUNCT
ejpam-6215	793	1	int	int	NOUN
ejpam-6215	793	2	.	.	PUNCT
ejpam-6215	794	1	j.	j.	PROPN
ejpam-6215	794	2	anal	anal	PROPN
ejpam-6215	794	3	.	.	PUNCT
ejpam-6215	795	1	appl	appl	PROPN
ejpam-6215	795	2	.	.	PROPN
ejpam-6215	796	1	,	,	PUNCT
ejpam-6215	796	2	22(2):299	22(2):299	NOUN
ejpam-6215	796	3	,	,	PUNCT
ejpam-6215	796	4	2024	2024	NUM
ejpam-6215	796	5	.	.	PUNCT
ejpam-6215	797	1	[	[	X
ejpam-6215	797	2	9	9	NUM
ejpam-6215	797	3	]	]	X
ejpam-6215	797	4	o.	o.	PROPN
ejpam-6215	797	5	a.	a.	PROPN
ejpam-6215	797	6	salman	salman	PROPN
ejpam-6215	797	7	and	and	CCONJ
ejpam-6215	797	8	h.	h.	PROPN
ejpam-6215	797	9	o.	o.	PROPN
ejpam-6215	797	10	altaie	altaie	PROPN
ejpam-6215	797	11	.	.	PUNCT
ejpam-6215	798	1	solutions	solution	NOUN
ejpam-6215	798	2	of	of	ADP
ejpam-6215	798	3	random	random	ADJ
ejpam-6215	798	4	ordinary	ordinary	ADJ
ejpam-6215	798	5	differential	differential	ADJ
ejpam-6215	798	6	equations	equation	NOUN
ejpam-6215	798	7	with	with	ADP
ejpam-6215	798	8	laplace	laplace	NOUN
ejpam-6215	798	9	transform	transform	NOUN
ejpam-6215	798	10	–	–	PUNCT
ejpam-6215	798	11	adomian	adomian	NOUN
ejpam-6215	798	12	decomposition	decomposition	NOUN
ejpam-6215	798	13	method	method	NOUN
ejpam-6215	798	14	.	.	PUNCT
ejpam-6215	799	1	j.	j.	PROPN
ejpam-6215	799	2	interdiscip	interdiscip	PROPN
ejpam-6215	799	3	.	.	PUNCT
ejpam-6215	800	1	math	math	NOUN
ejpam-6215	800	2	.	.	PUNCT
ejpam-6215	800	3	,	,	PUNCT
ejpam-6215	801	1	27(4):857–863	27(4):857–863	PROPN
ejpam-6215	801	2	,	,	PUNCT
ejpam-6215	801	3	2024	2024	NUM
ejpam-6215	801	4	.	.	PUNCT
ejpam-6215	802	1	[	[	X
ejpam-6215	802	2	10	10	NUM
ejpam-6215	802	3	]	]	X
ejpam-6215	802	4	g.	g.	PROPN
ejpam-6215	802	5	p.	p.	PROPN
ejpam-6215	802	6	engworo	engworo	PROPN
ejpam-6215	802	7	,	,	PUNCT
ejpam-6215	802	8	p.	p.	PROPN
ejpam-6215	802	9	o.	o.	PROPN
ejpam-6215	802	10	ogunniyi	ogunniyi	PROPN
ejpam-6215	802	11	,	,	PUNCT
ejpam-6215	802	12	and	and	CCONJ
ejpam-6215	802	13	s.	s.	PROPN
ejpam-6215	802	14	o.	o.	PROPN
ejpam-6215	802	15	edeki	edeki	PROPN
ejpam-6215	802	16	.	.	PUNCT
ejpam-6215	803	1	laplace	laplace	NOUN
ejpam-6215	803	2	decomposition	decomposition	NOUN
ejpam-6215	803	3	method	method	NOUN
ejpam-6215	803	4	for	for	ADP
ejpam-6215	803	5	series	series	NOUN
ejpam-6215	803	6	solutions	solution	NOUN
ejpam-6215	803	7	of	of	ADP
ejpam-6215	803	8	systems	system	NOUN
ejpam-6215	803	9	of	of	ADP
ejpam-6215	803	10	linear	linear	ADJ
ejpam-6215	803	11	partial	partial	ADJ
ejpam-6215	803	12	differential	differential	NOUN
ejpam-6215	803	13	models	model	NOUN
ejpam-6215	803	14	.	.	PUNCT
ejpam-6215	804	1	j.	j.	PROPN
ejpam-6215	804	2	phys	phys	PROPN
ejpam-6215	804	3	.	.	PUNCT
ejpam-6215	804	4	conf	conf	PROPN
ejpam-6215	804	5	.	.	PUNCT
ejpam-6215	805	1	ser	ser	PROPN
ejpam-6215	805	2	.	.	PROPN
ejpam-6215	805	3	,	,	PUNCT
ejpam-6215	805	4	2199(1):012022	2199(1):012022	PROPN
ejpam-6215	805	5	,	,	PUNCT
ejpam-6215	805	6	2021	2021	NUM
ejpam-6215	805	7	.	.	PUNCT
ejpam-6215	806	1	[	[	X
ejpam-6215	806	2	11	11	NUM
ejpam-6215	806	3	]	]	PUNCT
ejpam-6215	806	4	m.	m.	NOUN
ejpam-6215	806	5	amir	amir	PROPN
ejpam-6215	806	6	,	,	PUNCT
ejpam-6215	806	7	j.	j.	PROPN
ejpam-6215	806	8	a.	a.	PROPN
ejpam-6215	806	9	haider	haider	PROPN
ejpam-6215	806	10	,	,	PUNCT
ejpam-6215	806	11	s.	s.	PROPN
ejpam-6215	806	12	ahmad	ahmad	PROPN
ejpam-6215	806	13	,	,	PUNCT
ejpam-6215	806	14	s.	s.	PROPN
ejpam-6215	806	15	gul	gul	PROPN
ejpam-6215	806	16	,	,	PUNCT
ejpam-6215	806	17	and	and	CCONJ
ejpam-6215	806	18	a.	a.	NOUN
ejpam-6215	806	19	ashraf	ashraf	PROPN
ejpam-6215	806	20	.	.	PUNCT
ejpam-6215	807	1	approximate	approximate	ADJ
ejpam-6215	807	2	solution	solution	NOUN
ejpam-6215	807	3	of	of	ADP
ejpam-6215	807	4	painlevé	painlevé	NOUN
ejpam-6215	807	5	equation	equation	NOUN
ejpam-6215	807	6	i	i	PRON
ejpam-6215	807	7	by	by	ADP
ejpam-6215	807	8	natural	natural	ADJ
ejpam-6215	807	9	decomposition	decomposition	NOUN
ejpam-6215	807	10	method	method	NOUN
ejpam-6215	807	11	and	and	CCONJ
ejpam-6215	807	12	laplace	laplace	NOUN
ejpam-6215	807	13	decomposition	decomposition	NOUN
ejpam-6215	807	14	method	method	NOUN
ejpam-6215	807	15	.	.	PUNCT
ejpam-6215	808	1	abdus	abdus	PROPN
ejpam-6215	808	2	salam	salam	PROPN
ejpam-6215	808	3	school	school	PROPN
ejpam-6215	808	4	of	of	ADP
ejpam-6215	808	5	mathematical	mathematical	ADJ
ejpam-6215	808	6	sciences	science	NOUN
ejpam-6215	808	7	,	,	PUNCT
ejpam-6215	808	8	government	government	NOUN
ejpam-6215	808	9	college	college	NOUN
ejpam-6215	808	10	university	university	PROPN
ejpam-6215	808	11	,	,	PUNCT
ejpam-6215	808	12	lahore	lahore	PROPN
ejpam-6215	808	13	,	,	PUNCT
ejpam-6215	808	14	pakistan	pakistan	PROPN
ejpam-6215	808	15	,	,	PUNCT
ejpam-6215	808	16	2023	2023	NUM
ejpam-6215	808	17	.	.	PUNCT
ejpam-6215	809	1	[	[	X
ejpam-6215	809	2	12	12	NUM
ejpam-6215	809	3	]	]	PUNCT
ejpam-6215	809	4	a.	a.	PROPN
ejpam-6215	809	5	d.	d.	PROPN
ejpam-6215	809	6	vidhate	vidhate	PROPN
ejpam-6215	809	7	,	,	PUNCT
ejpam-6215	809	8	s.	s.	PROPN
ejpam-6215	809	9	n.	n.	PROPN
ejpam-6215	809	10	wandhekar	wandhekar	PROPN
ejpam-6215	809	11	,	,	PUNCT
ejpam-6215	809	12	s.	s.	PROPN
ejpam-6215	809	13	v.	v.	PROPN
ejpam-6215	809	14	sase	sase	PROPN
ejpam-6215	809	15	,	,	PUNCT
ejpam-6215	809	16	p.	p.	PROPN
ejpam-6215	809	17	s.	s.	PROPN
ejpam-6215	809	18	ansari	ansari	PROPN
ejpam-6215	809	19	,	,	PUNCT
ejpam-6215	809	20	and	and	CCONJ
ejpam-6215	809	21	k.	k.	PROPN
ejpam-6215	809	22	a.	a.	PROPN
ejpam-6215	809	23	kshirsagar	kshirsagar	PROPN
ejpam-6215	809	24	.	.	PUNCT
ejpam-6215	810	1	exploring	explore	VERB
ejpam-6215	810	2	the	the	DET
ejpam-6215	810	3	modified	modify	VERB
ejpam-6215	810	4	natural	natural	ADJ
ejpam-6215	810	5	transform	transform	NOUN
ejpam-6215	810	6	:	:	PUNCT
ejpam-6215	810	7	properties	property	NOUN
ejpam-6215	810	8	and	and	CCONJ
ejpam-6215	810	9	applications	application	NOUN
ejpam-6215	810	10	.	.	PUNCT
ejpam-6215	811	1	int	int	NOUN
ejpam-6215	811	2	.	.	PUNCT
ejpam-6215	812	1	j.	j.	PROPN
ejpam-6215	812	2	sci	sci	PROPN
ejpam-6215	812	3	.	.	PUNCT
ejpam-6215	813	1	res	res	PROPN
ejpam-6215	813	2	.	.	PUNCT
ejpam-6215	814	1	sci	sci	PROPN
ejpam-6215	814	2	.	.	PROPN
ejpam-6215	814	3	technol	technol	PROPN
ejpam-6215	814	4	.	.	PROPN
ejpam-6215	814	5	,	,	PUNCT
ejpam-6215	814	6	2023	2023	NUM
ejpam-6215	814	7	.	.	PUNCT
ejpam-6215	815	1	[	[	X
ejpam-6215	815	2	13	13	NUM
ejpam-6215	815	3	]	]	PUNCT
ejpam-6215	815	4	a.	a.	NOUN
ejpam-6215	815	5	j.	j.	PROPN
ejpam-6215	815	6	tadema	tadema	PROPN
ejpam-6215	815	7	.	.	PUNCT
ejpam-6215	816	1	numerical	numerical	ADJ
ejpam-6215	816	2	solution	solution	NOUN
ejpam-6215	816	3	of	of	ADP
ejpam-6215	816	4	second	second	ADJ
ejpam-6215	816	5	order	order	NOUN
ejpam-6215	816	6	ordinary	ordinary	ADJ
ejpam-6215	816	7	differential	differential	ADJ
ejpam-6215	816	8	equations	equation	NOUN
ejpam-6215	816	9	.	.	PUNCT
ejpam-6215	817	1	cand	cand	PROPN
ejpam-6215	817	2	j.	j.	PROPN
ejpam-6215	817	3	,	,	PUNCT
ejpam-6215	817	4	september	september	PROPN
ejpam-6215	817	5	2024	2024	NUM
ejpam-6215	817	6	.	.	PUNCT
ejpam-6215	818	1	[	[	X
ejpam-6215	818	2	14	14	NUM
ejpam-6215	818	3	]	]	X
ejpam-6215	818	4	w.	w.	PROPN
ejpam-6215	818	5	hamaidia	hamaidia	PROPN
ejpam-6215	818	6	,	,	PUNCT
ejpam-6215	818	7	t.	t.	PROPN
ejpam-6215	818	8	yahiaoui	yahiaoui	PROPN
ejpam-6215	818	9	,	,	PUNCT
ejpam-6215	818	10	and	and	CCONJ
ejpam-6215	818	11	a.	a.	NOUN
ejpam-6215	818	12	boudani	boudani	PROPN
ejpam-6215	818	13	.	.	PUNCT
ejpam-6215	819	1	numerical	numerical	ADJ
ejpam-6215	819	2	method	method	NOUN
ejpam-6215	819	3	for	for	ADP
ejpam-6215	819	4	solving	solve	VERB
ejpam-6215	819	5	seconds	second	NOUN
ejpam-6215	819	6	.	.	PUNCT
ejpam-6215	820	1	mohammed	mohammed	PROPN
ejpam-6215	820	2	,	,	PUNCT
ejpam-6215	820	3	s.	s.	PROPN
ejpam-6215	820	4	abid	abid	PROPN
ejpam-6215	820	5	,	,	PUNCT
ejpam-6215	820	6	r.	r.	PROPN
ejpam-6215	820	7	abid	abid	PROPN
ejpam-6215	820	8	/	/	SYM
ejpam-6215	820	9	eur	eur	PROPN
ejpam-6215	820	10	.	.	PUNCT
ejpam-6215	821	1	j.	j.	PROPN
ejpam-6215	821	2	pure	pure	PROPN
ejpam-6215	821	3	appl	appl	PROPN
ejpam-6215	821	4	.	.	PROPN
ejpam-6215	821	5	math	math	PROPN
ejpam-6215	821	6	,	,	PUNCT
ejpam-6215	821	7	18	18	NUM
ejpam-6215	821	8	(	(	PUNCT
ejpam-6215	821	9	3	3	NUM
ejpam-6215	821	10	)	)	PUNCT
ejpam-6215	821	11	(	(	PUNCT
ejpam-6215	821	12	2025	2025	NUM
ejpam-6215	821	13	)	)	PUNCT
ejpam-6215	821	14	,	,	PUNCT
ejpam-6215	821	15	6215	6215	NUM
ejpam-6215	821	16	36	36	NUM
ejpam-6215	821	17	of	of	ADP
ejpam-6215	821	18	38	38	NUM
ejpam-6215	821	19	order	order	NOUN
ejpam-6215	821	20	nonlinear	nonlinear	ADJ
ejpam-6215	821	21	differential	differential	ADJ
ejpam-6215	821	22	equation	equation	NOUN
ejpam-6215	821	23	with	with	ADP
ejpam-6215	821	24	arbitrary	arbitrary	ADJ
ejpam-6215	821	25	boundary	boundary	ADJ
ejpam-6215	821	26	conditions	condition	NOUN
ejpam-6215	821	27	.	.	PUNCT
ejpam-6215	822	1	braz	braz	PROPN
ejpam-6215	822	2	.	.	PUNCT
ejpam-6215	823	1	j.	j.	PROPN
ejpam-6215	823	2	technol	technol	PROPN
ejpam-6215	823	3	.	.	PROPN
ejpam-6215	823	4	,	,	PUNCT
ejpam-6215	823	5	7(4):1–10	7(4):1–10	NUM
ejpam-6215	823	6	,	,	PUNCT
ejpam-6215	823	7	2024	2024	NUM
ejpam-6215	823	8	.	.	PUNCT
ejpam-6215	824	1	[	[	X
ejpam-6215	824	2	15	15	NUM
ejpam-6215	824	3	]	]	X
ejpam-6215	824	4	n.	n.	PROPN
ejpam-6215	824	5	d.	d.	PROPN
ejpam-6215	824	6	dung	dung	PROPN
ejpam-6215	824	7	and	and	CCONJ
ejpam-6215	824	8	v.	v.	CCONJ
ejpam-6215	824	9	v.	v.	PROPN
ejpam-6215	824	10	quang	quang	PROPN
ejpam-6215	824	11	.	.	PUNCT
ejpam-6215	825	1	finite	finite	ADJ
ejpam-6215	825	2	difference	difference	NOUN
ejpam-6215	825	3	method	method	NOUN
ejpam-6215	825	4	for	for	ADP
ejpam-6215	825	5	solving	solve	VERB
ejpam-6215	825	6	second	second	ADJ
ejpam-6215	825	7	-	-	PUNCT
ejpam-6215	825	8	order	order	NOUN
ejpam-6215	825	9	boundary	boundary	ADJ
ejpam-6215	825	10	value	value	NOUN
ejpam-6215	825	11	problems	problem	NOUN
ejpam-6215	825	12	with	with	ADP
ejpam-6215	825	13	high	high	ADJ
ejpam-6215	825	14	-	-	PUNCT
ejpam-6215	825	15	order	order	NOUN
ejpam-6215	825	16	accuracy	accuracy	NOUN
ejpam-6215	825	17	.	.	PUNCT
ejpam-6215	826	1	eur	eur	PROPN
ejpam-6215	826	2	.	.	PUNCT
ejpam-6215	827	1	j.	j.	PROPN
ejpam-6215	827	2	math	math	PROPN
ejpam-6215	827	3	.	.	PUNCT
ejpam-6215	828	1	anal	anal	PROPN
ejpam-6215	828	2	.	.	PROPN
ejpam-6215	828	3	,	,	PUNCT
ejpam-6215	828	4	4	4	NUM
ejpam-6215	828	5	,	,	PUNCT
ejpam-6215	828	6	2024	2024	NUM
ejpam-6215	828	7	.	.	PUNCT
ejpam-6215	829	1	[	[	X
ejpam-6215	829	2	16	16	NUM
ejpam-6215	829	3	]	]	X
ejpam-6215	829	4	i.	i.	PROPN
ejpam-6215	829	5	beroš	beroš	PROPN
ejpam-6215	829	6	,	,	PUNCT
ejpam-6215	829	7	n.	n.	PROPN
ejpam-6215	829	8	hlupić	hlupić	NOUN
ejpam-6215	829	9	,	,	PUNCT
ejpam-6215	829	10	and	and	CCONJ
ejpam-6215	829	11	d.	d.	PROPN
ejpam-6215	829	12	basch	basch	PROPN
ejpam-6215	829	13	.	.	PUNCT
ejpam-6215	830	1	modification	modification	NOUN
ejpam-6215	830	2	of	of	ADP
ejpam-6215	830	3	the	the	DET
ejpam-6215	830	4	finite	finite	ADJ
ejpam-6215	830	5	-	-	PUNCT
ejpam-6215	830	6	difference	difference	NOUN
ejpam-6215	830	7	method	method	NOUN
ejpam-6215	830	8	for	for	ADP
ejpam-6215	830	9	solving	solve	VERB
ejpam-6215	830	10	a	a	DET
ejpam-6215	830	11	special	special	ADJ
ejpam-6215	830	12	class	class	NOUN
ejpam-6215	830	13	of	of	ADP
ejpam-6215	830	14	nonlinear	nonlinear	ADJ
ejpam-6215	830	15	two	two	NUM
ejpam-6215	830	16	-	-	PUNCT
ejpam-6215	830	17	point	point	NOUN
ejpam-6215	830	18	boundary	boundary	ADJ
ejpam-6215	830	19	value	value	NOUN
ejpam-6215	830	20	problems	problem	NOUN
ejpam-6215	830	21	.	.	PUNCT
ejpam-6215	831	1	int	int	NOUN
ejpam-6215	831	2	.	.	PUNCT
ejpam-6215	832	1	j.	j.	PROPN
ejpam-6215	832	2	math	math	PROPN
ejpam-6215	832	3	.	.	PUNCT
ejpam-6215	833	1	comput	comput	NOUN
ejpam-6215	833	2	.	.	PUNCT
ejpam-6215	834	1	sci	sci	PROPN
ejpam-6215	834	2	.	.	PROPN
ejpam-6215	834	3	,	,	PUNCT
ejpam-6215	834	4	16(1):487–502	16(1):487–502	PROPN
ejpam-6215	834	5	,	,	PUNCT
ejpam-6215	834	6	2021	2021	NUM
ejpam-6215	834	7	.	.	PUNCT
ejpam-6215	835	1	[	[	X
ejpam-6215	835	2	17	17	NUM
ejpam-6215	835	3	]	]	PUNCT
ejpam-6215	835	4	m.	m.	NOUN
ejpam-6215	835	5	z.	z.	PROPN
ejpam-6215	835	6	ahmad	ahmad	PROPN
ejpam-6215	835	7	,	,	PUNCT
ejpam-6215	835	8	d.	d.	PROPN
ejpam-6215	835	9	alsarayreh	alsarayreh	NOUN
ejpam-6215	835	10	,	,	PUNCT
ejpam-6215	835	11	a.	a.	NOUN
ejpam-6215	835	12	alsarayreh	alsarayreh	NOUN
ejpam-6215	835	13	,	,	PUNCT
ejpam-6215	835	14	and	and	CCONJ
ejpam-6215	835	15	i.	i.	PROPN
ejpam-6215	835	16	qaralleh	qaralleh	PROPN
ejpam-6215	835	17	.	.	PUNCT
ejpam-6215	836	1	differential	differential	ADJ
ejpam-6215	836	2	transformation	transformation	NOUN
ejpam-6215	836	3	method	method	NOUN
ejpam-6215	836	4	for	for	ADP
ejpam-6215	836	5	solving	solve	VERB
ejpam-6215	836	6	sis	sis	NOUN
ejpam-6215	836	7	and	and	CCONJ
ejpam-6215	836	8	si	si	NOUN
ejpam-6215	836	9	epidemic	epidemic	NOUN
ejpam-6215	836	10	models	model	NOUN
ejpam-6215	836	11	.	.	PUNCT
ejpam-6215	837	1	sains	sain	NOUN
ejpam-6215	837	2	malays	malays	PROPN
ejpam-6215	837	3	.	.	PUNCT
ejpam-6215	837	4	,	,	PUNCT
ejpam-6215	838	1	46(10):2007–2017	46(10):2007–2017	NUM
ejpam-6215	838	2	,	,	PUNCT
ejpam-6215	838	3	2017	2017	NUM
ejpam-6215	838	4	.	.	PUNCT
ejpam-6215	839	1	[	[	X
ejpam-6215	839	2	18	18	NUM
ejpam-6215	839	3	]	]	X
ejpam-6215	839	4	b.	b.	PROPN
ejpam-6215	839	5	n.	n.	PROPN
ejpam-6215	839	6	kharrat	kharrat	PROPN
ejpam-6215	839	7	and	and	CCONJ
ejpam-6215	839	8	g.	g.	PROPN
ejpam-6215	839	9	toma	toma	PROPN
ejpam-6215	839	10	.	.	PUNCT
ejpam-6215	840	1	differential	differential	PROPN
ejpam-6215	840	2	transform	transform	NOUN
ejpam-6215	840	3	method	method	NOUN
ejpam-6215	840	4	for	for	ADP
ejpam-6215	840	5	solving	solve	VERB
ejpam-6215	840	6	initial	initial	ADJ
ejpam-6215	840	7	value	value	NOUN
ejpam-6215	840	8	problems	problem	NOUN
ejpam-6215	840	9	of	of	ADP
ejpam-6215	840	10	strongly	strongly	ADV
ejpam-6215	840	11	nonlinear	nonlinear	ADJ
ejpam-6215	840	12	ordinary	ordinary	ADJ
ejpam-6215	840	13	differential	differential	ADJ
ejpam-6215	840	14	equations	equation	NOUN
ejpam-6215	840	15	.	.	PUNCT
ejpam-6215	841	1	middle	middle	ADJ
ejpam-6215	841	2	-	-	PUNCT
ejpam-6215	841	3	east	east	NOUN
ejpam-6215	841	4	j.	j.	PROPN
ejpam-6215	841	5	sci	sci	PROPN
ejpam-6215	841	6	.	.	PUNCT
ejpam-6215	842	1	res	res	PROPN
ejpam-6215	842	2	.	.	PROPN
ejpam-6215	842	3	,	,	PUNCT
ejpam-6215	842	4	27(7):576–579	27(7):576–579	NUM
ejpam-6215	842	5	,	,	PUNCT
ejpam-6215	842	6	2019	2019	NUM
ejpam-6215	842	7	.	.	PUNCT
ejpam-6215	843	1	[	[	X
ejpam-6215	843	2	19	19	NUM
ejpam-6215	843	3	]	]	X
ejpam-6215	843	4	r.	r.	PROPN
ejpam-6215	843	5	a.	a.	PROPN
ejpam-6215	843	6	ibrahim	ibrahim	PROPN
ejpam-6215	843	7	and	and	CCONJ
ejpam-6215	843	8	m.	m.	PROPN
ejpam-6215	843	9	saad	saad	PROPN
ejpam-6215	843	10	.	.	PUNCT
ejpam-6215	844	1	application	application	NOUN
ejpam-6215	844	2	of	of	ADP
ejpam-6215	844	3	differential	differential	ADJ
ejpam-6215	844	4	transform	transform	NOUN
ejpam-6215	844	5	method	method	NOUN
ejpam-6215	844	6	with	with	ADP
ejpam-6215	844	7	adomian	adomian	NOUN
ejpam-6215	844	8	polynomial	polynomial	NOUN
ejpam-6215	844	9	for	for	ADP
ejpam-6215	844	10	solving	solve	VERB
ejpam-6215	844	11	rlc	rlc	PROPN
ejpam-6215	844	12	circuits	circuit	NOUN
ejpam-6215	844	13	problems	problem	NOUN
ejpam-6215	844	14	and	and	CCONJ
ejpam-6215	844	15	higher	high	ADJ
ejpam-6215	844	16	order	order	NOUN
ejpam-6215	844	17	differential	differential	ADJ
ejpam-6215	844	18	equations	equation	NOUN
ejpam-6215	844	19	.	.	PUNCT
ejpam-6215	845	1	eng	eng	PROPN
ejpam-6215	845	2	.	.	PUNCT
ejpam-6215	846	1	res	res	PROPN
ejpam-6215	846	2	.	.	PUNCT
ejpam-6215	847	1	j.	j.	PROPN
ejpam-6215	847	2	(	(	PUNCT
ejpam-6215	847	3	erj	erj	PROPN
ejpam-6215	847	4	)	)	PUNCT
ejpam-6215	847	5	,	,	PUNCT
ejpam-6215	847	6	51(4):89–95	51(4):89–95	NUM
ejpam-6215	847	7	,	,	PUNCT
ejpam-6215	847	8	2022	2022	NUM
ejpam-6215	847	9	.	.	PUNCT
ejpam-6215	848	1	[	[	X
ejpam-6215	848	2	20	20	NUM
ejpam-6215	848	3	]	]	PUNCT
ejpam-6215	848	4	h.	h.	PROPN
ejpam-6215	848	5	a.	a.	NOUN
ejpam-6215	848	6	sakka	sakka	NOUN
ejpam-6215	848	7	and	and	CCONJ
ejpam-6215	848	8	m.	m.	NOUN
ejpam-6215	848	9	a.	a.	PROPN
ejpam-6215	848	10	m.	m.	PROPN
ejpam-6215	848	11	sulayh	sulayh	PROPN
ejpam-6215	848	12	.	.	PUNCT
ejpam-6215	849	1	on	on	ADP
ejpam-6215	849	2	taylor	taylor	PROPN
ejpam-6215	849	3	differential	differential	PROPN
ejpam-6215	849	4	transform	transform	NOUN
ejpam-6215	849	5	method	method	NOUN
ejpam-6215	849	6	.	.	PUNCT
ejpam-6215	850	1	jordan	jordan	PROPN
ejpam-6215	850	2	j.	j.	PROPN
ejpam-6215	850	3	math	math	PROPN
ejpam-6215	850	4	.	.	PUNCT
ejpam-6215	851	1	stat	stat	PROPN
ejpam-6215	851	2	.	.	PUNCT
ejpam-6215	851	3	,	,	PUNCT
ejpam-6215	851	4	12(3):391–408	12(3):391–408	PROPN
ejpam-6215	851	5	,	,	PUNCT
ejpam-6215	851	6	2019	2019	NUM
ejpam-6215	851	7	.	.	PUNCT
ejpam-6215	852	1	[	[	X
ejpam-6215	852	2	21	21	NUM
ejpam-6215	852	3	]	]	X
ejpam-6215	852	4	m.	m.	NOUN
ejpam-6215	852	5	m.	m.	NOUN
ejpam-6215	852	6	rashidi	rashidi	PROPN
ejpam-6215	852	7	,	,	PUNCT
ejpam-6215	852	8	f.	f.	PROPN
ejpam-6215	852	9	rabiei	rabiei	PROPN
ejpam-6215	852	10	,	,	PUNCT
ejpam-6215	852	11	n.	n.	PROPN
ejpam-6215	852	12	s.	s.	PROPN
ejpam-6215	852	13	naseri	naseri	PROPN
ejpam-6215	852	14	nia	nia	PROPN
ejpam-6215	852	15	,	,	PUNCT
ejpam-6215	852	16	and	and	CCONJ
ejpam-6215	852	17	s.	s.	PROPN
ejpam-6215	852	18	abbassbandy	abbassbandy	PROPN
ejpam-6215	852	19	.	.	PUNCT
ejpam-6215	853	1	a	a	DET
ejpam-6215	853	2	review	review	NOUN
ejpam-6215	853	3	:	:	PUNCT
ejpam-6215	853	4	differential	differential	ADJ
ejpam-6215	853	5	transform	transform	NOUN
ejpam-6215	853	6	method	method	NOUN
ejpam-6215	853	7	for	for	ADP
ejpam-6215	853	8	semi	semi	ADJ
ejpam-6215	853	9	-	-	ADJ
ejpam-6215	853	10	analytical	analytical	ADJ
ejpam-6215	853	11	solution	solution	NOUN
ejpam-6215	853	12	of	of	ADP
ejpam-6215	853	13	differential	differential	ADJ
ejpam-6215	853	14	equations	equation	NOUN
ejpam-6215	853	15	.	.	PUNCT
ejpam-6215	854	1	int	int	NOUN
ejpam-6215	854	2	.	.	PUNCT
ejpam-6215	855	1	j.	j.	PROPN
ejpam-6215	855	2	appl	appl	PROPN
ejpam-6215	855	3	.	.	PROPN
ejpam-6215	855	4	mech	mech	PROPN
ejpam-6215	855	5	.	.	PUNCT
ejpam-6215	856	1	eng	eng	PROPN
ejpam-6215	856	2	.	.	PROPN
ejpam-6215	856	3	,	,	PUNCT
ejpam-6215	856	4	25(2):122–129	25(2):122–129	NUM
ejpam-6215	856	5	,	,	PUNCT
ejpam-6215	856	6	2020	2020	NUM
ejpam-6215	856	7	.	.	PUNCT
ejpam-6215	857	1	[	[	X
ejpam-6215	857	2	22	22	NUM
ejpam-6215	857	3	]	]	PUNCT
ejpam-6215	857	4	s.	s.	PROPN
ejpam-6215	857	5	al	al	PROPN
ejpam-6215	857	6	-	-	PUNCT
ejpam-6215	857	7	ahmad	ahmad	PROPN
ejpam-6215	857	8	,	,	PUNCT
ejpam-6215	857	9	m.	m.	NOUN
ejpam-6215	857	10	mamat	mamat	PROPN
ejpam-6215	857	11	,	,	PUNCT
ejpam-6215	857	12	n.	n.	PROPN
ejpam-6215	857	13	anakira	anakira	PROPN
ejpam-6215	857	14	,	,	PUNCT
ejpam-6215	857	15	and	and	CCONJ
ejpam-6215	857	16	r.	r.	PROPN
ejpam-6215	857	17	alahmad	alahmad	PROPN
ejpam-6215	857	18	.	.	PUNCT
ejpam-6215	858	1	modified	modify	VERB
ejpam-6215	858	2	differential	differential	ADJ
ejpam-6215	858	3	transformation	transformation	NOUN
ejpam-6215	858	4	method	method	NOUN
ejpam-6215	858	5	for	for	ADP
ejpam-6215	858	6	solving	solve	VERB
ejpam-6215	858	7	classes	class	NOUN
ejpam-6215	858	8	of	of	ADP
ejpam-6215	858	9	non	non	ADJ
ejpam-6215	858	10	-	-	ADJ
ejpam-6215	858	11	linear	linear	ADJ
ejpam-6215	858	12	differential	differential	ADJ
ejpam-6215	858	13	equations	equation	NOUN
ejpam-6215	858	14	.	.	PUNCT
ejpam-6215	859	1	twms	twms	PROPN
ejpam-6215	859	2	j.	j.	PROPN
ejpam-6215	859	3	appl	appl	PROPN
ejpam-6215	859	4	.	.	PUNCT
ejpam-6215	860	1	eng	eng	PROPN
ejpam-6215	860	2	.	.	PROPN
ejpam-6215	860	3	math	math	PROPN
ejpam-6215	860	4	.	.	PUNCT
ejpam-6215	860	5	,	,	PUNCT
ejpam-6215	860	6	12(1):107–119	12(1):107–119	PROPN
ejpam-6215	860	7	,	,	PUNCT
ejpam-6215	860	8	2022	2022	NUM
ejpam-6215	860	9	.	.	PUNCT
ejpam-6215	861	1	[	[	X
ejpam-6215	861	2	23	23	NUM
ejpam-6215	861	3	]	]	X
ejpam-6215	861	4	h.	h.	PROPN
ejpam-6215	861	5	h.	h.	PROPN
ejpam-6215	861	6	mehne	mehne	PROPN
ejpam-6215	861	7	.	.	PROPN
ejpam-6215	861	8	differential	differential	PROPN
ejpam-6215	861	9	transform	transform	NOUN
ejpam-6215	861	10	method	method	NOUN
ejpam-6215	861	11	:	:	PUNCT
ejpam-6215	861	12	a	a	DET
ejpam-6215	861	13	comprehensive	comprehensive	ADJ
ejpam-6215	861	14	review	review	NOUN
ejpam-6215	861	15	and	and	CCONJ
ejpam-6215	861	16	analysis	analysis	NOUN
ejpam-6215	861	17	.	.	PUNCT
ejpam-6215	862	1	iran	iran	PROPN
ejpam-6215	862	2	j.	j.	PROPN
ejpam-6215	862	3	numer	numer	PROPN
ejpam-6215	862	4	.	.	PUNCT
ejpam-6215	863	1	anal	anal	PROPN
ejpam-6215	863	2	.	.	PUNCT
ejpam-6215	864	1	optim	optim	PROPN
ejpam-6215	864	2	.	.	PROPN
ejpam-6215	864	3	,	,	PUNCT
ejpam-6215	864	4	12(3):629–657	12(3):629–657	PROPN
ejpam-6215	864	5	,	,	PUNCT
ejpam-6215	864	6	2022	2022	NUM
ejpam-6215	864	7	.	.	PUNCT
ejpam-6215	865	1	[	[	X
ejpam-6215	865	2	24	24	NUM
ejpam-6215	865	3	]	]	X
ejpam-6215	865	4	w.	w.	PROPN
ejpam-6215	865	5	g.	g.	PROPN
ejpam-6215	865	6	belayeh	belayeh	PROPN
ejpam-6215	865	7	,	,	PUNCT
ejpam-6215	865	8	y.	y.	PROPN
ejpam-6215	865	9	o.	o.	PROPN
ejpam-6215	865	10	mussa	mussa	PROPN
ejpam-6215	865	11	,	,	PUNCT
ejpam-6215	865	12	and	and	CCONJ
ejpam-6215	865	13	a.	a.	PROPN
ejpam-6215	865	14	k.	k.	PROPN
ejpam-6215	865	15	gizaw	gizaw	PROPN
ejpam-6215	865	16	.	.	PUNCT
ejpam-6215	866	1	approximate	approximate	ADJ
ejpam-6215	866	2	analytic	analytic	ADJ
ejpam-6215	866	3	solutions	solution	NOUN
ejpam-6215	866	4	of	of	ADP
ejpam-6215	866	5	two	two	NUM
ejpam-6215	866	6	-	-	PUNCT
ejpam-6215	866	7	dimensional	dimensional	ADJ
ejpam-6215	866	8	nonlinear	nonlinear	ADJ
ejpam-6215	866	9	klein	klein	PROPN
ejpam-6215	866	10	–	–	PUNCT
ejpam-6215	866	11	gordon	gordon	PROPN
ejpam-6215	866	12	equation	equation	NOUN
ejpam-6215	866	13	by	by	ADP
ejpam-6215	866	14	using	use	VERB
ejpam-6215	866	15	the	the	DET
ejpam-6215	866	16	reduced	reduce	VERB
ejpam-6215	866	17	differential	differential	ADJ
ejpam-6215	866	18	transform	transform	NOUN
ejpam-6215	866	19	method	method	NOUN
ejpam-6215	866	20	.	.	PUNCT
ejpam-6215	867	1	math	math	NOUN
ejpam-6215	867	2	.	.	PUNCT
ejpam-6215	868	1	probl	probl	PROPN
ejpam-6215	868	2	.	.	PUNCT
ejpam-6215	869	1	eng	eng	PROPN
ejpam-6215	869	2	.	.	PROPN
ejpam-6215	869	3	,	,	PUNCT
ejpam-6215	869	4	2020	2020	NUM
ejpam-6215	869	5	.	.	PUNCT
ejpam-6215	870	1	article	article	NOUN
ejpam-6215	870	2	i	i	PROPN
ejpam-6215	870	3	d	d	PROPN
ejpam-6215	870	4	5753974	5753974	NUM
ejpam-6215	870	5	.	.	PUNCT
ejpam-6215	871	1	[	[	X
ejpam-6215	871	2	25	25	NUM
ejpam-6215	871	3	]	]	PUNCT
ejpam-6215	871	4	a.	a.	PROPN
ejpam-6215	871	5	r.	r.	PROPN
ejpam-6215	871	6	ghomi	ghomi	PROPN
ejpam-6215	871	7	taheri	taheri	PROPN
ejpam-6215	871	8	,	,	PUNCT
ejpam-6215	871	9	f.	f.	PROPN
ejpam-6215	871	10	setoudeh	setoudeh	PROPN
ejpam-6215	871	11	,	,	PUNCT
ejpam-6215	871	12	and	and	CCONJ
ejpam-6215	871	13	m.	m.	PROPN
ejpam-6215	871	14	b.	b.	PROPN
ejpam-6215	871	15	tavakoli	tavakoli	PROPN
ejpam-6215	871	16	.	.	PUNCT
ejpam-6215	872	1	nonlinear	nonlinear	ADJ
ejpam-6215	872	2	analysis	analysis	NOUN
ejpam-6215	872	3	of	of	ADP
ejpam-6215	872	4	colpitts	colpitt	NOUN
ejpam-6215	872	5	oscillator	oscillator	NOUN
ejpam-6215	872	6	using	use	VERB
ejpam-6215	872	7	differential	differential	ADJ
ejpam-6215	872	8	transform	transform	NOUN
ejpam-6215	872	9	method	method	NOUN
ejpam-6215	872	10	.	.	PUNCT
ejpam-6215	873	1	j.	j.	PROPN
ejpam-6215	873	2	electr	electr	PROPN
ejpam-6215	873	3	.	.	PUNCT
ejpam-6215	874	1	comput	comput	NOUN
ejpam-6215	874	2	.	.	PUNCT
ejpam-6215	875	1	eng	eng	PROPN
ejpam-6215	875	2	.	.	PUNCT
ejpam-6215	876	1	innov	innov	PROPN
ejpam-6215	876	2	.	.	PROPN
ejpam-6215	876	3	,	,	PUNCT
ejpam-6215	876	4	9(2):127–142	9(2):127–142	NUM
ejpam-6215	876	5	,	,	PUNCT
ejpam-6215	876	6	2020	2020	NUM
ejpam-6215	876	7	.	.	PUNCT
ejpam-6215	877	1	[	[	X
ejpam-6215	877	2	26	26	NUM
ejpam-6215	877	3	]	]	PUNCT
ejpam-6215	877	4	s.	s.	PROPN
ejpam-6215	877	5	al	al	PROPN
ejpam-6215	877	6	-	-	PUNCT
ejpam-6215	877	7	ahmad	ahmad	PROPN
ejpam-6215	877	8	,	,	PUNCT
ejpam-6215	877	9	i.	i.	PROPN
ejpam-6215	877	10	m.	m.	PROPN
ejpam-6215	877	11	sulaiman	sulaiman	PROPN
ejpam-6215	877	12	,	,	PUNCT
ejpam-6215	877	13	m.	m.	NOUN
ejpam-6215	877	14	mamat	mamat	PROPN
ejpam-6215	877	15	,	,	PUNCT
ejpam-6215	877	16	and	and	CCONJ
ejpam-6215	877	17	l.	l.	PROPN
ejpam-6215	877	18	g.	g.	PROPN
ejpam-6215	877	19	puspa	puspa	PROPN
ejpam-6215	877	20	.	.	PUNCT
ejpam-6215	878	1	a	a	DET
ejpam-6215	878	2	modification	modification	NOUN
ejpam-6215	878	3	of	of	ADP
ejpam-6215	878	4	differential	differential	ADJ
ejpam-6215	878	5	transform	transform	NOUN
ejpam-6215	878	6	method	method	NOUN
ejpam-6215	878	7	for	for	ADP
ejpam-6215	878	8	solving	solve	VERB
ejpam-6215	878	9	systems	system	NOUN
ejpam-6215	878	10	of	of	ADP
ejpam-6215	878	11	second	second	ADJ
ejpam-6215	878	12	-	-	PUNCT
ejpam-6215	878	13	order	order	NOUN
ejpam-6215	878	14	ordinary	ordinary	ADJ
ejpam-6215	878	15	differential	differential	ADJ
ejpam-6215	878	16	equations	equation	NOUN
ejpam-6215	878	17	.	.	PUNCT
ejpam-6215	879	1	math	math	NOUN
ejpam-6215	879	2	.	.	PUNCT
ejpam-6215	880	1	stat	stat	PROPN
ejpam-6215	880	2	.	.	PUNCT
ejpam-6215	880	3	,	,	PUNCT
ejpam-6215	880	4	8(4):464–471	8(4):464–471	NOUN
ejpam-6215	880	5	,	,	PUNCT
ejpam-6215	880	6	2020	2020	NUM
ejpam-6215	880	7	.	.	PUNCT
ejpam-6215	881	1	[	[	X
ejpam-6215	881	2	27	27	NUM
ejpam-6215	881	3	]	]	X
ejpam-6215	881	4	f.	f.	PROPN
ejpam-6215	881	5	n.	n.	PROPN
ejpam-6215	881	6	bakri	bakri	PROPN
ejpam-6215	881	7	and	and	CCONJ
ejpam-6215	881	8	n.	n.	PROPN
ejpam-6215	881	9	a.	a.	PROPN
ejpam-6215	881	10	abd	abd	PROPN
ejpam-6215	881	11	latif	latif	PROPN
ejpam-6215	881	12	.	.	PUNCT
ejpam-6215	882	1	solving	solve	VERB
ejpam-6215	882	2	third	third	ADJ
ejpam-6215	882	3	-	-	PUNCT
ejpam-6215	882	4	order	order	NOUN
ejpam-6215	882	5	ordinary	ordinary	ADJ
ejpam-6215	882	6	differential	differential	ADJ
ejpam-6215	882	7	equation	equation	NOUN
ejpam-6215	882	8	(	(	PUNCT
ejpam-6215	882	9	ode	ode	PROPN
ejpam-6215	882	10	)	)	PUNCT
ejpam-6215	882	11	by	by	ADP
ejpam-6215	882	12	using	use	VERB
ejpam-6215	882	13	differential	differential	ADJ
ejpam-6215	882	14	transform	transform	NOUN
ejpam-6215	882	15	method	method	NOUN
ejpam-6215	882	16	(	(	PUNCT
ejpam-6215	882	17	dtm	dtm	PROPN
ejpam-6215	882	18	)	)	PUNCT
ejpam-6215	882	19	.	.	PUNCT
ejpam-6215	883	1	enhanc	enhanc	PROPN
ejpam-6215	883	2	.	.	PUNCT
ejpam-6215	884	1	knowl	knowl	PROPN
ejpam-6215	884	2	.	.	PUNCT
ejpam-6215	885	1	sci	sci	PROPN
ejpam-6215	885	2	.	.	PROPN
ejpam-6215	885	3	technol	technol	PROPN
ejpam-6215	885	4	.	.	PROPN
ejpam-6215	885	5	,	,	PUNCT
ejpam-6215	885	6	3(2):109–117	3(2):109–117	NUM
ejpam-6215	885	7	,	,	PUNCT
ejpam-6215	885	8	2023	2023	NUM
ejpam-6215	885	9	.	.	PUNCT
ejpam-6215	886	1	[	[	X
ejpam-6215	886	2	28	28	NUM
ejpam-6215	886	3	]	]	X
ejpam-6215	886	4	l.	l.	PROPN
ejpam-6215	886	5	ngartera	ngartera	PROPN
ejpam-6215	886	6	and	and	CCONJ
ejpam-6215	886	7	y.	y.	PROPN
ejpam-6215	886	8	moussa	moussa	PROPN
ejpam-6215	886	9	.	.	PUNCT
ejpam-6215	887	1	advancements	advancement	NOUN
ejpam-6215	887	2	and	and	CCONJ
ejpam-6215	887	3	applications	application	NOUN
ejpam-6215	887	4	of	of	ADP
ejpam-6215	887	5	the	the	DET
ejpam-6215	887	6	adomian	adomian	NOUN
ejpam-6215	887	7	decomposition	decomposition	NOUN
ejpam-6215	887	8	method	method	NOUN
ejpam-6215	887	9	in	in	ADP
ejpam-6215	887	10	solving	solve	VERB
ejpam-6215	887	11	nonlinear	nonlinear	ADJ
ejpam-6215	887	12	differential	differential	ADJ
ejpam-6215	887	13	equations	equation	NOUN
ejpam-6215	887	14	.	.	PUNCT
ejpam-6215	888	1	j.	j.	PROPN
ejpam-6215	888	2	math	math	PROPN
ejpam-6215	888	3	.	.	PUNCT
ejpam-6215	889	1	res	re	NOUN
ejpam-6215	889	2	.	.	PROPN
ejpam-6215	889	3	,	,	PUNCT
ejpam-6215	889	4	16(4):38	16(4):38	PROPN
ejpam-6215	889	5	,	,	PUNCT
ejpam-6215	889	6	2024	2024	NUM
ejpam-6215	889	7	.	.	PUNCT
ejpam-6215	890	1	[	[	X
ejpam-6215	890	2	29	29	NUM
ejpam-6215	890	3	]	]	PUNCT
ejpam-6215	890	4	a.	a.	PROPN
ejpam-6215	890	5	d.	d.	PROPN
ejpam-6215	890	6	k.	k.	PROPN
ejpam-6215	890	7	naidu	naidu	PROPN
ejpam-6215	890	8	and	and	CCONJ
ejpam-6215	890	9	a.	a.	NOUN
ejpam-6215	890	10	uljayan	uljayan	PROPN
ejpam-6215	890	11	.	.	PUNCT
ejpam-6215	891	1	modified	modify	VERB
ejpam-6215	891	2	adomian	adomian	NOUN
ejpam-6215	891	3	decomposition	decomposition	NOUN
ejpam-6215	891	4	method	method	NOUN
ejpam-6215	891	5	to	to	ADP
ejpam-6215	891	6	initial	initial	ADJ
ejpam-6215	891	7	value	value	NOUN
ejpam-6215	891	8	problems	problem	NOUN
ejpam-6215	891	9	.	.	PUNCT
ejpam-6215	892	1	int	int	NOUN
ejpam-6215	892	2	.	.	PUNCT
ejpam-6215	893	1	j.	j.	PROPN
ejpam-6215	893	2	adv	adv	PROPN
ejpam-6215	893	3	.	.	PUNCT
ejpam-6215	894	1	res	res	PROPN
ejpam-6215	894	2	.	.	PUNCT
ejpam-6215	895	1	sci	sci	PROPN
ejpam-6215	895	2	.	.	PUNCT
ejpam-6215	896	1	eng	eng	PROPN
ejpam-6215	896	2	.	.	PROPN
ejpam-6215	896	3	,	,	PUNCT
ejpam-6215	896	4	2021	2021	NUM
ejpam-6215	896	5	.	.	PUNCT
ejpam-6215	897	1	s.	s.	PROPN
ejpam-6215	897	2	mohammed	mohammed	PROPN
ejpam-6215	897	3	,	,	PUNCT
ejpam-6215	897	4	s.	s.	PROPN
ejpam-6215	897	5	abid	abid	PROPN
ejpam-6215	897	6	,	,	PUNCT
ejpam-6215	897	7	r.	r.	PROPN
ejpam-6215	897	8	abid	abid	PROPN
ejpam-6215	897	9	/	/	SYM
ejpam-6215	897	10	eur	eur	PROPN
ejpam-6215	897	11	.	.	PUNCT
ejpam-6215	898	1	j.	j.	PROPN
ejpam-6215	898	2	pure	pure	PROPN
ejpam-6215	898	3	appl	appl	PROPN
ejpam-6215	898	4	.	.	PROPN
ejpam-6215	898	5	math	math	PROPN
ejpam-6215	898	6	,	,	PUNCT
ejpam-6215	898	7	18	18	NUM
ejpam-6215	898	8	(	(	PUNCT
ejpam-6215	898	9	3	3	NUM
ejpam-6215	898	10	)	)	PUNCT
ejpam-6215	898	11	(	(	PUNCT
ejpam-6215	898	12	2025	2025	NUM
ejpam-6215	898	13	)	)	PUNCT
ejpam-6215	898	14	,	,	PUNCT
ejpam-6215	898	15	6215	6215	NUM
ejpam-6215	898	16	37	37	NUM
ejpam-6215	898	17	of	of	ADP
ejpam-6215	898	18	38	38	NUM
ejpam-6215	898	19	[	[	SYM
ejpam-6215	898	20	30	30	NUM
ejpam-6215	898	21	]	]	X
ejpam-6215	898	22	h.	h.	PROPN
ejpam-6215	898	23	o.	o.	PROPN
ejpam-6215	898	24	bakodah	bakodah	PROPN
ejpam-6215	898	25	,	,	PUNCT
ejpam-6215	898	26	r.	r.	PROPN
ejpam-6215	898	27	m.	m.	PROPN
ejpam-6215	898	28	al	al	PROPN
ejpam-6215	898	29	-	-	PUNCT
ejpam-6215	898	30	harbi	harbi	PROPN
ejpam-6215	898	31	,	,	PUNCT
ejpam-6215	898	32	a.	a.	PROPN
ejpam-6215	898	33	alshareef	alshareef	VERB
ejpam-6215	898	34	,	,	PUNCT
ejpam-6215	898	35	and	and	CCONJ
ejpam-6215	898	36	a.	a.	NOUN
ejpam-6215	898	37	a.	a.	NOUN
ejpam-6215	898	38	alsharey	alsharey	PROPN
ejpam-6215	898	39	.	.	PUNCT
ejpam-6215	899	1	a	a	DET
ejpam-6215	899	2	new	new	ADJ
ejpam-6215	899	3	computational	computational	ADJ
ejpam-6215	899	4	method	method	NOUN
ejpam-6215	899	5	based	base	VERB
ejpam-6215	899	6	on	on	ADP
ejpam-6215	899	7	the	the	DET
ejpam-6215	899	8	method	method	NOUN
ejpam-6215	899	9	of	of	ADP
ejpam-6215	899	10	lines	line	NOUN
ejpam-6215	899	11	and	and	CCONJ
ejpam-6215	899	12	adomian	adomian	NOUN
ejpam-6215	899	13	decomposition	decomposition	NOUN
ejpam-6215	899	14	method	method	NOUN
ejpam-6215	899	15	for	for	ADP
ejpam-6215	899	16	burgers	burger	NOUN
ejpam-6215	899	17	’	'	PUNCT
ejpam-6215	899	18	equation	equation	NOUN
ejpam-6215	899	19	and	and	CCONJ
ejpam-6215	899	20	coupled	couple	VERB
ejpam-6215	899	21	system	system	NOUN
ejpam-6215	899	22	of	of	ADP
ejpam-6215	899	23	burgers	burger	NOUN
ejpam-6215	899	24	’	'	PUNCT
ejpam-6215	899	25	equations	equation	NOUN
ejpam-6215	899	26	.	.	PUNCT
ejpam-6215	900	1	int	int	NOUN
ejpam-6215	900	2	.	.	PUNCT
ejpam-6215	901	1	j.	j.	PROPN
ejpam-6215	901	2	anal	anal	PROPN
ejpam-6215	901	3	.	.	PUNCT
ejpam-6215	902	1	appl	appl	PROPN
ejpam-6215	902	2	.	.	PROPN
ejpam-6215	902	3	,	,	PUNCT
ejpam-6215	902	4	23(4	23(4	NOUN
ejpam-6215	902	5	)	)	PUNCT
ejpam-6215	902	6	,	,	PUNCT
ejpam-6215	902	7	2025	2025	NUM
ejpam-6215	902	8	.	.	PUNCT
ejpam-6215	903	1	[	[	X
ejpam-6215	903	2	31	31	NUM
ejpam-6215	903	3	]	]	PUNCT
ejpam-6215	903	4	m.	m.	NOUN
ejpam-6215	903	5	s.	s.	PROPN
ejpam-6215	903	6	lima	lima	PROPN
ejpam-6215	903	7	,	,	PUNCT
ejpam-6215	903	8	j.	j.	PROPN
ejpam-6215	903	9	v.	v.	PROPN
ejpam-6215	903	10	c.	c.	PROPN
ejpam-6215	903	11	santos	santos	PROPN
ejpam-6215	903	12	,	,	PUNCT
ejpam-6215	903	13	j.	j.	PROPN
ejpam-6215	903	14	h.	h.	PROPN
ejpam-6215	903	15	s.	s.	PROPN
ejpam-6215	903	16	prates	prates	PROPN
ejpam-6215	903	17	,	,	PUNCT
ejpam-6215	903	18	c.	c.	PROPN
ejpam-6215	903	19	b.	b.	PROPN
ejpam-6215	903	20	silva	silva	PROPN
ejpam-6215	903	21	,	,	PUNCT
ejpam-6215	903	22	d.	d.	PROPN
ejpam-6215	903	23	moreira	moreira	PROPN
ejpam-6215	903	24	,	,	PUNCT
ejpam-6215	903	25	and	and	CCONJ
ejpam-6215	903	26	m.	m.	NOUN
ejpam-6215	903	27	a.	a.	PROPN
ejpam-6215	903	28	moret	moret	PROPN
ejpam-6215	903	29	.	.	PUNCT
ejpam-6215	904	1	applying	apply	VERB
ejpam-6215	904	2	the	the	DET
ejpam-6215	904	3	adomian	adomian	NOUN
ejpam-6215	904	4	method	method	NOUN
ejpam-6215	904	5	to	to	PART
ejpam-6215	904	6	solve	solve	VERB
ejpam-6215	904	7	the	the	DET
ejpam-6215	904	8	fokker	fokker	NOUN
ejpam-6215	904	9	–	–	PUNCT
ejpam-6215	904	10	planck	planck	NOUN
ejpam-6215	904	11	equation	equation	NOUN
ejpam-6215	904	12	:	:	PUNCT
ejpam-6215	904	13	a	a	DET
ejpam-6215	904	14	case	case	NOUN
ejpam-6215	904	15	study	study	NOUN
ejpam-6215	904	16	in	in	ADP
ejpam-6215	904	17	astrophysics	astrophysic	NOUN
ejpam-6215	904	18	.	.	PUNCT
ejpam-6215	905	1	appl	appl	PROPN
ejpam-6215	905	2	.	.	PROPN
ejpam-6215	905	3	math	math	PROPN
ejpam-6215	905	4	.	.	PUNCT
ejpam-6215	905	5	,	,	PUNCT
ejpam-6215	906	1	4(4):1306–1327	4(4):1306–1327	PROPN
ejpam-6215	906	2	,	,	PUNCT
ejpam-6215	906	3	2024	2024	NUM
ejpam-6215	906	4	.	.	PUNCT
ejpam-6215	907	1	[	[	X
ejpam-6215	907	2	32	32	NUM
ejpam-6215	907	3	]	]	PUNCT
ejpam-6215	907	4	m.	m.	NOUN
ejpam-6215	907	5	al	al	PROPN
ejpam-6215	907	6	mazmumy	mazmumy	PROPN
ejpam-6215	907	7	,	,	PUNCT
ejpam-6215	907	8	a.	a.	NOUN
ejpam-6215	907	9	alsulami	alsulami	NOUN
ejpam-6215	907	10	,	,	PUNCT
ejpam-6215	907	11	h.	h.	NOUN
ejpam-6215	907	12	bakodah	bakodah	PROPN
ejpam-6215	907	13	,	,	PUNCT
ejpam-6215	907	14	and	and	CCONJ
ejpam-6215	907	15	n.	n.	PROPN
ejpam-6215	907	16	alzaid	alzaid	PROPN
ejpam-6215	907	17	.	.	PUNCT
ejpam-6215	908	1	adomian	adomian	PROPN
ejpam-6215	908	2	modification	modification	NOUN
ejpam-6215	908	3	methods	method	NOUN
ejpam-6215	908	4	for	for	ADP
ejpam-6215	908	5	the	the	DET
ejpam-6215	908	6	solution	solution	NOUN
ejpam-6215	908	7	of	of	ADP
ejpam-6215	908	8	chebyshev	chebyshev	PROPN
ejpam-6215	908	9	’s	’s	PART
ejpam-6215	908	10	differential	differential	ADJ
ejpam-6215	908	11	equations	equation	NOUN
ejpam-6215	908	12	.	.	PUNCT
ejpam-6215	909	1	appl	appl	PROPN
ejpam-6215	909	2	.	.	PROPN
ejpam-6215	909	3	math	math	PROPN
ejpam-6215	909	4	.	.	PUNCT
ejpam-6215	909	5	,	,	PUNCT
ejpam-6215	909	6	14:512	14:512	NUM
ejpam-6215	909	7	–	–	PUNCT
ejpam-6215	909	8	530	530	NUM
ejpam-6215	909	9	,	,	PUNCT
ejpam-6215	909	10	2023	2023	NUM
ejpam-6215	909	11	.	.	PUNCT
ejpam-6215	910	1	[	[	X
ejpam-6215	910	2	33	33	NUM
ejpam-6215	910	3	]	]	PUNCT
ejpam-6215	910	4	j.	j.	PROPN
ejpam-6215	910	5	o.	o.	PROPN
ejpam-6215	910	6	lawal	lawal	PROPN
ejpam-6215	910	7	,	,	PUNCT
ejpam-6215	910	8	m.	m.	NOUN
ejpam-6215	910	9	sulyman	sulyman	PROPN
ejpam-6215	910	10	,	,	PUNCT
ejpam-6215	910	11	r.	r.	PROPN
ejpam-6215	910	12	g.	g.	PROPN
ejpam-6215	910	13	ibrahim	ibrahim	PROPN
ejpam-6215	910	14	,	,	PUNCT
ejpam-6215	910	15	f.	f.	PROPN
ejpam-6215	910	16	muritala	muritala	PROPN
ejpam-6215	910	17	,	,	PUNCT
ejpam-6215	910	18	and	and	CCONJ
ejpam-6215	910	19	i.	i.	PROPN
ejpam-6215	910	20	seidu	seidu	PROPN
ejpam-6215	910	21	.	.	PUNCT
ejpam-6215	911	1	analytical	analytical	ADJ
ejpam-6215	911	2	solution	solution	NOUN
ejpam-6215	911	3	of	of	ADP
ejpam-6215	911	4	some	some	DET
ejpam-6215	911	5	non	non	ADJ
ejpam-6215	911	6	-	-	ADJ
ejpam-6215	911	7	linear	linear	ADJ
ejpam-6215	911	8	delay	delay	NOUN
ejpam-6215	911	9	differential	differential	NOUN
ejpam-6215	911	10	equations	equation	NOUN
ejpam-6215	911	11	using	use	VERB
ejpam-6215	911	12	adomian	adomian	NOUN
ejpam-6215	911	13	decomposition	decomposition	NOUN
ejpam-6215	911	14	method	method	NOUN
ejpam-6215	911	15	.	.	PUNCT
ejpam-6215	912	1	int	int	NOUN
ejpam-6215	912	2	.	.	PUNCT
ejpam-6215	913	1	j.	j.	PROPN
ejpam-6215	913	2	sci	sci	PROPN
ejpam-6215	913	3	.	.	PUNCT
ejpam-6215	914	1	res	res	PROPN
ejpam-6215	914	2	.	.	PUNCT
ejpam-6215	915	1	sci	sci	PROPN
ejpam-6215	915	2	.	.	PUNCT
ejpam-6215	916	1	eng	eng	PROPN
ejpam-6215	916	2	.	.	PROPN
ejpam-6215	916	3	technol	technol	PROPN
ejpam-6215	916	4	.	.	PROPN
ejpam-6215	916	5	,	,	PUNCT
ejpam-6215	916	6	11(5):111–115	11(5):111–115	PROPN
ejpam-6215	916	7	,	,	PUNCT
ejpam-6215	916	8	2024	2024	NUM
ejpam-6215	916	9	.	.	PUNCT
ejpam-6215	917	1	[	[	X
ejpam-6215	917	2	34	34	NUM
ejpam-6215	917	3	]	]	X
ejpam-6215	917	4	s.	s.	PROPN
ejpam-6215	917	5	masood	masood	PROPN
ejpam-6215	917	6	,	,	PUNCT
ejpam-6215	917	7	hajira	hajira	PROPN
ejpam-6215	917	8	,	,	PUNCT
ejpam-6215	917	9	h.	h.	PROPN
ejpam-6215	917	10	khan	khan	PROPN
ejpam-6215	917	11	,	,	PUNCT
ejpam-6215	917	12	r.	r.	PROPN
ejpam-6215	917	13	shah	shah	PROPN
ejpam-6215	917	14	,	,	PUNCT
ejpam-6215	917	15	s.	s.	PROPN
ejpam-6215	917	16	mustafa	mustafa	PROPN
ejpam-6215	917	17	,	,	PUNCT
ejpam-6215	917	18	q.	q.	PROPN
ejpam-6215	917	19	khan	khan	PROPN
ejpam-6215	917	20	,	,	PUNCT
ejpam-6215	917	21	m.	m.	PROPN
ejpam-6215	917	22	arif	arif	PROPN
ejpam-6215	917	23	,	,	PUNCT
ejpam-6215	917	24	f.	f.	PROPN
ejpam-6215	917	25	tchier	tchier	PROPN
ejpam-6215	917	26	,	,	PUNCT
ejpam-6215	917	27	and	and	CCONJ
ejpam-6215	917	28	g.	g.	PROPN
ejpam-6215	917	29	singh	singh	PROPN
ejpam-6215	917	30	.	.	PUNCT
ejpam-6215	918	1	a	a	DET
ejpam-6215	918	2	new	new	ADJ
ejpam-6215	918	3	modified	modify	VERB
ejpam-6215	918	4	technique	technique	NOUN
ejpam-6215	918	5	of	of	ADP
ejpam-6215	918	6	adomian	adomian	ADJ
ejpam-6215	918	7	decomposition	decomposition	NOUN
ejpam-6215	918	8	method	method	NOUN
ejpam-6215	918	9	for	for	ADP
ejpam-6215	918	10	fractional	fractional	ADJ
ejpam-6215	918	11	diffusion	diffusion	NOUN
ejpam-6215	918	12	equations	equation	NOUN
ejpam-6215	918	13	with	with	ADP
ejpam-6215	918	14	initial	initial	ADJ
ejpam-6215	918	15	-	-	PUNCT
ejpam-6215	918	16	boundary	boundary	ADJ
ejpam-6215	918	17	conditions	condition	NOUN
ejpam-6215	918	18	.	.	PUNCT
ejpam-6215	919	1	j.	j.	PROPN
ejpam-6215	919	2	funct	funct	PROPN
ejpam-6215	919	3	.	.	PUNCT
ejpam-6215	920	1	spaces	space	NOUN
ejpam-6215	920	2	,	,	PUNCT
ejpam-6215	920	3	2022	2022	NUM
ejpam-6215	920	4	.	.	PUNCT
ejpam-6215	921	1	article	article	NOUN
ejpam-6215	921	2	i	i	PROPN
ejpam-6215	921	3	d	d	PROPN
ejpam-6215	921	4	6890517	6890517	NUM
ejpam-6215	921	5	.	.	PUNCT
ejpam-6215	922	1	[	[	X
ejpam-6215	922	2	35	35	NUM
ejpam-6215	922	3	]	]	PUNCT
ejpam-6215	922	4	a.	a.	NOUN
ejpam-6215	922	5	m.	m.	PROPN
ejpam-6215	922	6	rao	rao	PROPN
ejpam-6215	922	7	,	,	PUNCT
ejpam-6215	922	8	a.	a.	PROPN
ejpam-6215	922	9	s.	s.	PROPN
ejpam-6215	922	10	warke	warke	PROPN
ejpam-6215	922	11	,	,	PUNCT
ejpam-6215	922	12	a.	a.	PROPN
ejpam-6215	922	13	h.	h.	PROPN
ejpam-6215	922	14	agadi	agadi	PROPN
ejpam-6215	922	15	,	,	PUNCT
ejpam-6215	922	16	and	and	CCONJ
ejpam-6215	922	17	g.	g.	PROPN
ejpam-6215	922	18	a.	a.	PROPN
ejpam-6215	922	19	biradar	biradar	PROPN
ejpam-6215	922	20	.	.	PUNCT
ejpam-6215	923	1	laplace	laplace	NOUN
ejpam-6215	923	2	decomposition	decomposition	NOUN
ejpam-6215	923	3	method	method	NOUN
ejpam-6215	923	4	for	for	ADP
ejpam-6215	923	5	nonlinear	nonlinear	ADJ
ejpam-6215	923	6	burger’s	burger’s	NOUN
ejpam-6215	923	7	–	–	PUNCT
ejpam-6215	923	8	fisher	fisher	NOUN
ejpam-6215	923	9	’s	’s	PART
ejpam-6215	923	10	equation	equation	NOUN
ejpam-6215	923	11	.	.	PUNCT
ejpam-6215	924	1	adv	adv	PROPN
ejpam-6215	924	2	.	.	PUNCT
ejpam-6215	924	3	math	math	PROPN
ejpam-6215	924	4	.	.	PUNCT
ejpam-6215	925	1	sci	sci	PROPN
ejpam-6215	925	2	.	.	PUNCT
ejpam-6215	926	1	j.	j.	PROPN
ejpam-6215	926	2	,	,	PUNCT
ejpam-6215	926	3	9(3):1163–1180	9(3):1163–1180	PROPN
ejpam-6215	926	4	,	,	PUNCT
ejpam-6215	926	5	2020	2020	NUM
ejpam-6215	926	6	.	.	PUNCT
ejpam-6215	927	1	[	[	X
ejpam-6215	927	2	36	36	NUM
ejpam-6215	927	3	]	]	X
ejpam-6215	927	4	o.	o.	NOUN
ejpam-6215	927	5	abbas	abbas	PROPN
ejpam-6215	927	6	and	and	CCONJ
ejpam-6215	927	7	h.	h.	PROPN
ejpam-6215	927	8	o.	o.	PROPN
ejpam-6215	927	9	altaie	altaie	PROPN
ejpam-6215	927	10	.	.	PUNCT
ejpam-6215	928	1	laplace	laplace	PROPN
ejpam-6215	928	2	transform	transform	PROPN
ejpam-6215	928	3	–	–	PUNCT
ejpam-6215	928	4	adomian	adomian	NOUN
ejpam-6215	928	5	decomposition	decomposition	NOUN
ejpam-6215	928	6	approach	approach	NOUN
ejpam-6215	928	7	for	for	ADP
ejpam-6215	928	8	solving	solve	VERB
ejpam-6215	928	9	random	random	ADJ
ejpam-6215	928	10	partial	partial	ADJ
ejpam-6215	928	11	differential	differential	NOUN
ejpam-6215	928	12	equations	equation	NOUN
ejpam-6215	928	13	.	.	PUNCT
ejpam-6215	929	1	j.	j.	PROPN
ejpam-6215	929	2	interdiscip	interdiscip	PROPN
ejpam-6215	929	3	.	.	PUNCT
ejpam-6215	930	1	math	math	NOUN
ejpam-6215	930	2	.	.	PUNCT
ejpam-6215	930	3	,	,	PUNCT
ejpam-6215	931	1	27(4):775–780	27(4):775–780	PROPN
ejpam-6215	931	2	,	,	PUNCT
ejpam-6215	931	3	2024	2024	NUM
ejpam-6215	931	4	.	.	PUNCT
ejpam-6215	932	1	[	[	X
ejpam-6215	932	2	37	37	NUM
ejpam-6215	932	3	]	]	PUNCT
ejpam-6215	932	4	a.	a.	NOUN
ejpam-6215	932	5	anber	anber	PROPN
ejpam-6215	932	6	and	and	CCONJ
ejpam-6215	932	7	z.	z.	PROPN
ejpam-6215	932	8	dahmani	dahmani	PROPN
ejpam-6215	932	9	.	.	PUNCT
ejpam-6215	933	1	the	the	DET
ejpam-6215	933	2	laplace	laplace	NOUN
ejpam-6215	933	3	decomposition	decomposition	NOUN
ejpam-6215	933	4	method	method	NOUN
ejpam-6215	933	5	for	for	ADP
ejpam-6215	933	6	solving	solve	VERB
ejpam-6215	933	7	nonlinear	nonlinear	ADJ
ejpam-6215	933	8	conformable	conformable	ADJ
ejpam-6215	933	9	fractional	fractional	ADJ
ejpam-6215	933	10	evolution	evolution	NOUN
ejpam-6215	933	11	equations	equation	NOUN
ejpam-6215	933	12	.	.	PUNCT
ejpam-6215	934	1	int	int	NOUN
ejpam-6215	934	2	.	.	PUNCT
ejpam-6215	935	1	j.	j.	PROPN
ejpam-6215	935	2	open	open	PROPN
ejpam-6215	935	3	probl	probl	PROPN
ejpam-6215	935	4	.	.	PUNCT
ejpam-6215	936	1	comput	comput	NOUN
ejpam-6215	936	2	.	.	PUNCT
ejpam-6215	937	1	math	math	NOUN
ejpam-6215	937	2	.	.	PUNCT
ejpam-6215	938	1	,	,	PUNCT
ejpam-6215	938	2	17(1):2–5	17(1):2–5	NOUN
ejpam-6215	938	3	,	,	PUNCT
ejpam-6215	938	4	2024	2024	NUM
ejpam-6215	938	5	.	.	PUNCT
ejpam-6215	939	1	[	[	X
ejpam-6215	939	2	38	38	NUM
ejpam-6215	939	3	]	]	PUNCT
ejpam-6215	939	4	m.	m.	NOUN
ejpam-6215	939	5	jamil	jamil	PROPN
ejpam-6215	939	6	,	,	PUNCT
ejpam-6215	939	7	r.	r.	PROPN
ejpam-6215	939	8	a.	a.	PROPN
ejpam-6215	939	9	khan	khan	PROPN
ejpam-6215	939	10	,	,	PUNCT
ejpam-6215	939	11	and	and	CCONJ
ejpam-6215	939	12	k.	k.	PROPN
ejpam-6215	939	13	shah	shah	PROPN
ejpam-6215	939	14	.	.	PUNCT
ejpam-6215	940	1	exact	exact	ADJ
ejpam-6215	940	2	analytical	analytical	ADJ
ejpam-6215	940	3	solutions	solution	NOUN
ejpam-6215	940	4	of	of	ADP
ejpam-6215	940	5	linear	linear	ADJ
ejpam-6215	940	6	dissipative	dissipative	ADJ
ejpam-6215	940	7	wave	wave	NOUN
ejpam-6215	940	8	equations	equation	NOUN
ejpam-6215	940	9	via	via	ADP
ejpam-6215	940	10	laplace	laplace	NOUN
ejpam-6215	940	11	transform	transform	NOUN
ejpam-6215	940	12	method	method	NOUN
ejpam-6215	940	13	.	.	PUNCT
ejpam-6215	941	1	punjab	punjab	PROPN
ejpam-6215	941	2	univ	univ	PROPN
ejpam-6215	941	3	.	.	PUNCT
ejpam-6215	942	1	j.	j.	PROPN
ejpam-6215	942	2	math	math	PROPN
ejpam-6215	942	3	.	.	PUNCT
ejpam-6215	942	4	,	,	PUNCT
ejpam-6215	942	5	53(6):425–434	53(6):425–434	NUM
ejpam-6215	942	6	,	,	PUNCT
ejpam-6215	942	7	2021	2021	NUM
ejpam-6215	942	8	.	.	PUNCT
ejpam-6215	943	1	[	[	X
ejpam-6215	943	2	39	39	NUM
ejpam-6215	943	3	]	]	PUNCT
ejpam-6215	943	4	m.	m.	NOUN
ejpam-6215	943	5	elbardi	elbardi	PROPN
ejpam-6215	943	6	.	.	PUNCT
ejpam-6215	944	1	the	the	DET
ejpam-6215	944	2	natural	natural	ADJ
ejpam-6215	944	3	transform	transform	NOUN
ejpam-6215	944	4	decomposition	decomposition	NOUN
ejpam-6215	944	5	method	method	NOUN
ejpam-6215	944	6	for	for	ADP
ejpam-6215	944	7	solving	solve	VERB
ejpam-6215	944	8	fractional	fractional	PROPN
ejpam-6215	944	9	klein	klein	PROPN
ejpam-6215	944	10	–	–	PUNCT
ejpam-6215	944	11	gordon	gordon	PROPN
ejpam-6215	944	12	equation	equation	NOUN
ejpam-6215	944	13	.	.	PUNCT
ejpam-6215	945	1	appl	appl	PROPN
ejpam-6215	945	2	.	.	PROPN
ejpam-6215	945	3	math	math	PROPN
ejpam-6215	945	4	.	.	PUNCT
ejpam-6215	945	5	,	,	PUNCT
ejpam-6215	945	6	14:230–243	14:230–243	PROPN
ejpam-6215	945	7	,	,	PUNCT
ejpam-6215	945	8	2023	2023	NUM
ejpam-6215	945	9	.	.	PUNCT
ejpam-6215	946	1	[	[	X
ejpam-6215	946	2	40	40	NUM
ejpam-6215	946	3	]	]	PUNCT
ejpam-6215	946	4	l.	l.	PROPN
ejpam-6215	946	5	m.	m.	PROPN
ejpam-6215	946	6	mengesha	mengesha	PROPN
ejpam-6215	946	7	.	.	PUNCT
ejpam-6215	947	1	natural	natural	ADJ
ejpam-6215	947	2	decomposition	decomposition	NOUN
ejpam-6215	947	3	approximation	approximation	NOUN
ejpam-6215	947	4	solution	solution	NOUN
ejpam-6215	947	5	for	for	ADP
ejpam-6215	947	6	second	second	ADJ
ejpam-6215	947	7	order	order	NOUN
ejpam-6215	947	8	nonlinear	nonlinear	ADJ
ejpam-6215	947	9	differential	differential	ADJ
ejpam-6215	947	10	equations	equation	NOUN
ejpam-6215	947	11	.	.	PUNCT
ejpam-6215	948	1	j.	j.	PROPN
ejpam-6215	948	2	math	math	PROPN
ejpam-6215	948	3	.	.	PUNCT
ejpam-6215	949	1	probl	probl	PROPN
ejpam-6215	949	2	.	.	PUNCT
ejpam-6215	950	1	equat	equat	PROPN
ejpam-6215	950	2	.	.	PUNCT
ejpam-6215	951	1	stat	stat	PROPN
ejpam-6215	951	2	.	.	PUNCT
ejpam-6215	951	3	,	,	PUNCT
ejpam-6215	951	4	2(2):17–22	2(2):17–22	NUM
ejpam-6215	951	5	,	,	PUNCT
ejpam-6215	951	6	2021	2021	NUM
ejpam-6215	951	7	.	.	PUNCT
ejpam-6215	952	1	[	[	X
ejpam-6215	952	2	41	41	NUM
ejpam-6215	952	3	]	]	X
ejpam-6215	952	4	n.	n.	NOUN
ejpam-6215	952	5	a.	a.	PROPN
ejpam-6215	952	6	obeidat	obeidat	PROPN
ejpam-6215	952	7	and	and	CCONJ
ejpam-6215	952	8	m.	m.	NOUN
ejpam-6215	952	9	s.	s.	PROPN
ejpam-6215	952	10	rawashdeh	rawashdeh	PROPN
ejpam-6215	952	11	.	.	PUNCT
ejpam-6215	953	1	on	on	ADP
ejpam-6215	953	2	theories	theory	NOUN
ejpam-6215	953	3	of	of	ADP
ejpam-6215	953	4	natural	natural	ADJ
ejpam-6215	953	5	decomposition	decomposition	NOUN
ejpam-6215	953	6	method	method	NOUN
ejpam-6215	953	7	applied	apply	VERB
ejpam-6215	953	8	to	to	ADP
ejpam-6215	953	9	system	system	NOUN
ejpam-6215	953	10	of	of	ADP
ejpam-6215	953	11	nonlinear	nonlinear	ADJ
ejpam-6215	953	12	differential	differential	ADJ
ejpam-6215	953	13	equations	equation	NOUN
ejpam-6215	953	14	in	in	ADP
ejpam-6215	953	15	fluid	fluid	ADJ
ejpam-6215	953	16	mechanics	mechanic	NOUN
ejpam-6215	953	17	.	.	PUNCT
ejpam-6215	954	1	adv	adv	PROPN
ejpam-6215	954	2	.	.	PROPN
ejpam-6215	954	3	mech	mech	PROPN
ejpam-6215	954	4	.	.	PUNCT
ejpam-6215	955	1	eng	eng	PROPN
ejpam-6215	955	2	.	.	PROPN
ejpam-6215	955	3	,	,	PUNCT
ejpam-6215	955	4	15(1	15(1	NUM
ejpam-6215	955	5	)	)	PUNCT
ejpam-6215	955	6	,	,	PUNCT
ejpam-6215	955	7	2023	2023	NUM
ejpam-6215	955	8	.	.	PUNCT
ejpam-6215	956	1	[	[	X
ejpam-6215	956	2	42	42	NUM
ejpam-6215	956	3	]	]	PUNCT
ejpam-6215	956	4	b.	b.	PROPN
ejpam-6215	956	5	gürbüz	gürbüz	PROPN
ejpam-6215	956	6	and	and	CCONJ
ejpam-6215	956	7	a.	a.	NOUN
ejpam-6215	956	8	fernandez	fernandez	PROPN
ejpam-6215	956	9	.	.	PUNCT
ejpam-6215	957	1	numerical	numerical	PROPN
ejpam-6215	957	2	and	and	CCONJ
ejpam-6215	957	3	analytical	analytical	ADJ
ejpam-6215	957	4	methods	method	NOUN
ejpam-6215	957	5	for	for	ADP
ejpam-6215	957	6	differential	differential	ADJ
ejpam-6215	957	7	equations	equation	NOUN
ejpam-6215	957	8	and	and	CCONJ
ejpam-6215	957	9	systems	system	NOUN
ejpam-6215	957	10	.	.	PUNCT
ejpam-6215	958	1	fractal	fractal	ADJ
ejpam-6215	958	2	fract	fract	PROPN
ejpam-6215	958	3	.	.	PUNCT
ejpam-6215	958	4	,	,	PUNCT
ejpam-6215	958	5	8(1):59	8(1):59	NUM
ejpam-6215	958	6	,	,	PUNCT
ejpam-6215	958	7	2024	2024	NUM
ejpam-6215	958	8	.	.	PUNCT
ejpam-6215	959	1	[	[	X
ejpam-6215	959	2	43	43	NUM
ejpam-6215	959	3	]	]	X
ejpam-6215	959	4	a.	a.	PROPN
ejpam-6215	959	5	l.	l.	PROPN
ejpam-6215	959	6	m.	m.	PROPN
ejpam-6215	959	7	a.	a.	PROPN
ejpam-6215	959	8	magalhães	magalhães	PROPN
ejpam-6215	959	9	,	,	PUNCT
ejpam-6215	959	10	p.	p.	PROPN
ejpam-6215	959	11	p.	p.	PROPN
ejpam-6215	960	1	brito	brito	PROPN
ejpam-6215	960	2	,	,	PUNCT
ejpam-6215	961	1	g.	g.	PROPN
ejpam-6215	961	2	p.	p.	PROPN
ejpam-6215	961	3	s.	s.	PROPN
ejpam-6215	961	4	lamon	lamon	PROPN
ejpam-6215	961	5	,	,	PUNCT
ejpam-6215	961	6	p.	p.	NOUN
ejpam-6215	961	7	a.	a.	NOUN
ejpam-6215	961	8	a.	a.	PROPN
ejpam-6215	961	9	magalhães	magalhães	PROPN
ejpam-6215	962	1	júnior	júnior	PROPN
ejpam-6215	962	2	,	,	PUNCT
ejpam-6215	962	3	c.	c.	PROPN
ejpam-6215	962	4	a.	a.	PROPN
ejpam-6215	962	5	magalhães	magalhães	PROPN
ejpam-6215	962	6	,	,	PUNCT
ejpam-6215	962	7	p.	p.	PROPN
ejpam-6215	962	8	h.	h.	PROPN
ejpam-6215	962	9	m.	m.	PROPN
ejpam-6215	962	10	a.	a.	PROPN
ejpam-6215	962	11	magalhães	magalhães	PROPN
ejpam-6215	962	12	,	,	PUNCT
ejpam-6215	962	13	and	and	CCONJ
ejpam-6215	962	14	p.	p.	NOUN
ejpam-6215	962	15	a.	a.	NOUN
ejpam-6215	962	16	a.	a.	PROPN
ejpam-6215	962	17	magalhães	magalhães	PROPN
ejpam-6215	962	18	.	.	PUNCT
ejpam-6215	963	1	numerical	numerical	ADJ
ejpam-6215	963	2	resolution	resolution	NOUN
ejpam-6215	963	3	of	of	ADP
ejpam-6215	963	4	differential	differential	ADJ
ejpam-6215	963	5	equations	equation	NOUN
ejpam-6215	963	6	using	use	VERB
ejpam-6215	963	7	the	the	DET
ejpam-6215	963	8	finite	finite	ADJ
ejpam-6215	963	9	difference	difference	NOUN
ejpam-6215	963	10	method	method	NOUN
ejpam-6215	963	11	in	in	ADP
ejpam-6215	963	12	the	the	DET
ejpam-6215	963	13	real	real	ADJ
ejpam-6215	963	14	and	and	CCONJ
ejpam-6215	963	15	complex	complex	ADJ
ejpam-6215	963	16	domain	domain	NOUN
ejpam-6215	963	17	.	.	PUNCT
ejpam-6215	964	1	mathematics	mathematic	NOUN
ejpam-6215	964	2	,	,	PUNCT
ejpam-6215	964	3	12(12):1870	12(12):1870	NUM
ejpam-6215	964	4	,	,	PUNCT
ejpam-6215	964	5	2024	2024	NUM
ejpam-6215	964	6	.	.	PUNCT
ejpam-6215	965	1	[	[	X
ejpam-6215	965	2	44	44	NUM
ejpam-6215	965	3	]	]	PUNCT
ejpam-6215	965	4	d.	d.	PROPN
ejpam-6215	965	5	a.	a.	PROPN
ejpam-6215	965	6	koç	koç	PROPN
ejpam-6215	965	7	,	,	PUNCT
ejpam-6215	965	8	y.	y.	PROPN
ejpam-6215	965	9	öztürk	öztürk	PROPN
ejpam-6215	965	10	,	,	PUNCT
ejpam-6215	965	11	and	and	CCONJ
ejpam-6215	965	12	m.	m.	PROPN
ejpam-6215	965	13	gülşu	gülşu	PROPN
ejpam-6215	965	14	.	.	PUNCT
ejpam-6215	966	1	a	a	DET
ejpam-6215	966	2	finite	finite	ADJ
ejpam-6215	966	3	difference	difference	NOUN
ejpam-6215	966	4	method	method	NOUN
ejpam-6215	966	5	to	to	PART
ejpam-6215	966	6	solve	solve	VERB
ejpam-6215	966	7	a	a	DET
ejpam-6215	966	8	special	special	ADJ
ejpam-6215	966	9	s.	s.	PROPN
ejpam-6215	966	10	mohammed	mohammed	PROPN
ejpam-6215	966	11	,	,	PUNCT
ejpam-6215	966	12	s.	s.	PROPN
ejpam-6215	966	13	abid	abid	PROPN
ejpam-6215	966	14	,	,	PUNCT
ejpam-6215	966	15	r.	r.	PROPN
ejpam-6215	966	16	abid	abid	PROPN
ejpam-6215	966	17	/	/	SYM
ejpam-6215	966	18	eur	eur	PROPN
ejpam-6215	966	19	.	.	PUNCT
ejpam-6215	967	1	j.	j.	PROPN
ejpam-6215	967	2	pure	pure	PROPN
ejpam-6215	967	3	appl	appl	PROPN
ejpam-6215	967	4	.	.	PROPN
ejpam-6215	967	5	math	math	PROPN
ejpam-6215	967	6	,	,	PUNCT
ejpam-6215	967	7	18	18	NUM
ejpam-6215	967	8	(	(	PUNCT
ejpam-6215	967	9	3	3	NUM
ejpam-6215	967	10	)	)	PUNCT
ejpam-6215	967	11	(	(	PUNCT
ejpam-6215	967	12	2025	2025	NUM
ejpam-6215	967	13	)	)	PUNCT
ejpam-6215	967	14	,	,	PUNCT
ejpam-6215	967	15	6215	6215	NUM
ejpam-6215	967	16	38	38	NUM
ejpam-6215	967	17	of	of	ADP
ejpam-6215	967	18	38	38	NUM
ejpam-6215	967	19	type	type	NOUN
ejpam-6215	967	20	of	of	ADP
ejpam-6215	967	21	second	second	ADJ
ejpam-6215	967	22	order	order	NOUN
ejpam-6215	967	23	differential	differential	NOUN
ejpam-6215	967	24	equations	equation	NOUN
ejpam-6215	967	25	.	.	PUNCT
ejpam-6215	968	1	in	in	ADP
ejpam-6215	968	2	conf	conf	NOUN
ejpam-6215	968	3	.	.	PUNCT
ejpam-6215	969	1	proc	proc	PROPN
ejpam-6215	969	2	.	.	PUNCT
ejpam-6215	970	1	sci	sci	PROPN
ejpam-6215	970	2	.	.	PROPN
ejpam-6215	970	3	technol	technol	PROPN
ejpam-6215	970	4	.	.	PROPN
ejpam-6215	970	5	,	,	PUNCT
ejpam-6215	970	6	volume	volume	NOUN
ejpam-6215	970	7	3	3	NUM
ejpam-6215	970	8	,	,	PUNCT
ejpam-6215	970	9	pages	page	NOUN
ejpam-6215	970	10	42–46	42–46	NUM
ejpam-6215	970	11	,	,	PUNCT
ejpam-6215	970	12	2020	2020	NUM
ejpam-6215	970	13	.	.	PUNCT
ejpam-6215	971	1	[	[	X
ejpam-6215	971	2	45	45	NUM
ejpam-6215	971	3	]	]	X
ejpam-6215	971	4	y.	y.	PROPN
ejpam-6215	971	5	worikhe	worikhe	PROPN
ejpam-6215	971	6	,	,	PUNCT
ejpam-6215	971	7	h.	h.	PROPN
ejpam-6215	971	8	mekonnen	mekonnen	PROPN
ejpam-6215	971	9	,	,	PUNCT
ejpam-6215	971	10	and	and	CCONJ
ejpam-6215	971	11	b.	b.	PROPN
ejpam-6215	971	12	belew	belew	PROPN
ejpam-6215	971	13	.	.	PUNCT
ejpam-6215	972	1	numerical	numerical	ADJ
ejpam-6215	972	2	methods	method	NOUN
ejpam-6215	972	3	for	for	ADP
ejpam-6215	972	4	solving	solve	VERB
ejpam-6215	972	5	second	second	ADJ
ejpam-6215	972	6	-	-	PUNCT
ejpam-6215	972	7	order	order	NOUN
ejpam-6215	972	8	initial	initial	ADJ
ejpam-6215	972	9	value	value	NOUN
ejpam-6215	972	10	problems	problem	NOUN
ejpam-6215	972	11	of	of	ADP
ejpam-6215	972	12	ordinary	ordinary	ADJ
ejpam-6215	972	13	differential	differential	ADJ
ejpam-6215	972	14	equations	equation	NOUN
ejpam-6215	972	15	with	with	ADP
ejpam-6215	972	16	euler	euler	NOUN
ejpam-6215	972	17	and	and	CCONJ
ejpam-6215	972	18	runge	runge	NOUN
ejpam-6215	972	19	-	-	PUNCT
ejpam-6215	972	20	kutta	kutta	NOUN
ejpam-6215	972	21	fourth	fourth	ADJ
ejpam-6215	972	22	-	-	PUNCT
ejpam-6215	972	23	order	order	NOUN
ejpam-6215	972	24	methods	method	NOUN
ejpam-6215	972	25	.	.	PUNCT
ejpam-6215	973	1	front	front	ADJ
ejpam-6215	973	2	.	.	PUNCT
ejpam-6215	974	1	appl	appl	PROPN
ejpam-6215	974	2	.	.	PROPN
ejpam-6215	974	3	math	math	PROPN
ejpam-6215	974	4	.	.	PUNCT
ejpam-6215	975	1	stat	stat	PROPN
ejpam-6215	975	2	.	.	PUNCT
ejpam-6215	975	3	,	,	PUNCT
ejpam-6215	975	4	february	february	PROPN
ejpam-6215	975	5	2024	2024	NUM
ejpam-6215	975	6	.	.	PUNCT
ejpam-6215	976	1	[	[	X
ejpam-6215	976	2	46	46	NUM
ejpam-6215	976	3	]	]	X
ejpam-6215	976	4	m.	m.	NOUN
ejpam-6215	976	5	a.	a.	PROPN
ejpam-6215	976	6	z.	z.	PROPN
ejpam-6215	976	7	ghauri	ghauri	PROPN
ejpam-6215	976	8	.	.	PUNCT
ejpam-6215	977	1	numerical	numerical	ADJ
ejpam-6215	977	2	solution	solution	NOUN
ejpam-6215	977	3	of	of	ADP
ejpam-6215	977	4	second	second	ADJ
ejpam-6215	977	5	order	order	NOUN
ejpam-6215	977	6	ordinary	ordinary	ADJ
ejpam-6215	977	7	differential	differential	ADJ
ejpam-6215	977	8	equation	equation	NOUN
ejpam-6215	977	9	using	use	VERB
ejpam-6215	977	10	fourth	fourth	ADJ
ejpam-6215	977	11	order	order	NOUN
ejpam-6215	977	12	runge	runge	NOUN
ejpam-6215	977	13	-	-	PUNCT
ejpam-6215	977	14	kutta	kutta	NOUN
ejpam-6215	977	15	method	method	NOUN
ejpam-6215	977	16	.	.	PUNCT
ejpam-6215	978	1	technical	technical	ADJ
ejpam-6215	978	2	report	report	NOUN
ejpam-6215	978	3	,	,	PUNCT
ejpam-6215	978	4	tech	tech	PROPN
ejpam-6215	978	5	.	.	PUNCT
ejpam-6215	979	1	rep	rep	PROPN
ejpam-6215	979	2	.	.	PROPN
ejpam-6215	979	3	,	,	PUNCT
ejpam-6215	979	4	may	may	AUX
ejpam-6215	979	5	2024	2024	NUM
ejpam-6215	979	6	.	.	PUNCT
ejpam-6215	980	1	[	[	X
ejpam-6215	980	2	47	47	NUM
ejpam-6215	980	3	]	]	PUNCT
ejpam-6215	980	4	i.	i.	PROPN
ejpam-6215	980	5	salleh	salleh	PROPN
ejpam-6215	980	6	,	,	PUNCT
ejpam-6215	980	7	a.	a.	PROPN
ejpam-6215	980	8	ab	ab	PROPN
ejpam-6215	980	9	aziz	aziz	PROPN
ejpam-6215	980	10	,	,	PUNCT
ejpam-6215	980	11	and	and	CCONJ
ejpam-6215	980	12	n.	n.	PROPN
ejpam-6215	980	13	a.	a.	NOUN
ejpam-6215	980	14	baki	baki	PROPN
ejpam-6215	980	15	.	.	PUNCT
ejpam-6215	981	1	comparison	comparison	NOUN
ejpam-6215	981	2	between	between	ADP
ejpam-6215	981	3	runge	runge	NOUN
ejpam-6215	981	4	-	-	PUNCT
ejpam-6215	981	5	kutta	kutta	NOUN
ejpam-6215	981	6	method	method	NOUN
ejpam-6215	981	7	,	,	PUNCT
ejpam-6215	981	8	euler	euler	NOUN
ejpam-6215	981	9	method	method	NOUN
ejpam-6215	981	10	,	,	PUNCT
ejpam-6215	981	11	and	and	CCONJ
ejpam-6215	981	12	modified	modify	VERB
ejpam-6215	981	13	adet	adet	NOUN
ejpam-6215	981	14	method	method	NOUN
ejpam-6215	981	15	for	for	ADP
ejpam-6215	981	16	the	the	DET
ejpam-6215	981	17	solution	solution	NOUN
ejpam-6215	981	18	of	of	ADP
ejpam-6215	981	19	ordinary	ordinary	ADJ
ejpam-6215	981	20	differential	differential	ADJ
ejpam-6215	981	21	equation	equation	NOUN
ejpam-6215	981	22	.	.	PUNCT
ejpam-6215	982	1	int	int	NOUN
ejpam-6215	982	2	.	.	PUNCT
ejpam-6215	983	1	j.	j.	PROPN
ejpam-6215	983	2	adv	adv	PROPN
ejpam-6215	983	3	.	.	PROPN
ejpam-6215	983	4	mech	mech	PROPN
ejpam-6215	983	5	.	.	PUNCT
ejpam-6215	984	1	eng	eng	PROPN
ejpam-6215	984	2	.	.	PROPN
ejpam-6215	984	3	appl	appl	PROPN
ejpam-6215	984	4	.	.	PROPN
ejpam-6215	984	5	,	,	PUNCT
ejpam-6215	984	6	5(2):20–24	5(2):20–24	NUM
ejpam-6215	984	7	,	,	PUNCT
ejpam-6215	984	8	2024	2024	NUM
ejpam-6215	984	9	.	.	PUNCT
ejpam-6215	985	1	[	[	X
ejpam-6215	985	2	48	48	NUM
ejpam-6215	985	3	]	]	PUNCT
ejpam-6215	985	4	f.	f.	PROPN
ejpam-6215	985	5	rabiei	rabiei	PROPN
ejpam-6215	985	6	,	,	PUNCT
ejpam-6215	985	7	f.	f.	PROPN
ejpam-6215	985	8	ismail	ismail	PROPN
ejpam-6215	985	9	,	,	PUNCT
ejpam-6215	985	10	s.	s.	PROPN
ejpam-6215	985	11	norazak	norazak	PROPN
ejpam-6215	985	12	,	,	PUNCT
ejpam-6215	985	13	and	and	CCONJ
ejpam-6215	985	14	s.	s.	PROPN
ejpam-6215	985	15	emadi	emadi	PROPN
ejpam-6215	985	16	.	.	PUNCT
ejpam-6215	986	1	numerical	numerical	ADJ
ejpam-6215	986	2	solution	solution	NOUN
ejpam-6215	986	3	of	of	ADP
ejpam-6215	986	4	second	second	ADJ
ejpam-6215	986	5	-	-	PUNCT
ejpam-6215	986	6	order	order	NOUN
ejpam-6215	986	7	ordinary	ordinary	ADJ
ejpam-6215	986	8	differential	differential	ADJ
ejpam-6215	986	9	equations	equation	NOUN
ejpam-6215	986	10	by	by	ADP
ejpam-6215	986	11	improved	improved	ADJ
ejpam-6215	986	12	runge	runge	NOUN
ejpam-6215	986	13	-	-	PUNCT
ejpam-6215	986	14	kutta	kutta	NOUN
ejpam-6215	986	15	nyström	nyström	DET
ejpam-6215	986	16	method	method	NOUN
ejpam-6215	986	17	.	.	PUNCT
ejpam-6215	987	1	int	int	NOUN
ejpam-6215	987	2	.	.	PUNCT
ejpam-6215	988	1	j.	j.	PROPN
ejpam-6215	988	2	math	math	PROPN
ejpam-6215	988	3	.	.	PUNCT
ejpam-6215	989	1	comput	comput	NOUN
ejpam-6215	989	2	.	.	PUNCT
ejpam-6215	990	1	sci	sci	PROPN
ejpam-6215	990	2	.	.	PROPN
ejpam-6215	990	3	,	,	PUNCT
ejpam-6215	990	4	6(9):1175–1180	6(9):1175–1180	PROPN
ejpam-6215	990	5	,	,	PUNCT
ejpam-6215	990	6	2012	2012	NUM
ejpam-6215	990	7	.	.	PUNCT
ejpam-6215	991	1	[	[	X
ejpam-6215	991	2	49	49	NUM
ejpam-6215	991	3	]	]	PUNCT
ejpam-6215	991	4	p.	p.	NOUN
ejpam-6215	991	5	l.	l.	PROPN
ejpam-6215	991	6	sharma	sharma	PROPN
ejpam-6215	991	7	and	and	CCONJ
ejpam-6215	991	8	a.	a.	PROPN
ejpam-6215	991	9	kumar	kumar	PROPN
ejpam-6215	991	10	.	.	PROPN
ejpam-6215	992	1	review	review	NOUN
ejpam-6215	992	2	paper	paper	NOUN
ejpam-6215	992	3	on	on	ADP
ejpam-6215	992	4	the	the	DET
ejpam-6215	992	5	runge	runge	NOUN
ejpam-6215	992	6	-	-	PUNCT
ejpam-6215	992	7	kutta	kutta	NOUN
ejpam-6215	992	8	methods	method	NOUN
ejpam-6215	992	9	to	to	PART
ejpam-6215	992	10	study	study	VERB
ejpam-6215	992	11	numerical	numerical	ADJ
ejpam-6215	992	12	solutions	solution	NOUN
ejpam-6215	992	13	of	of	ADP
ejpam-6215	992	14	initial	initial	ADJ
ejpam-6215	992	15	value	value	NOUN
ejpam-6215	992	16	problems	problem	NOUN
ejpam-6215	992	17	in	in	ADP
ejpam-6215	992	18	ordinary	ordinary	ADJ
ejpam-6215	992	19	differential	differential	ADJ
ejpam-6215	992	20	equations	equation	NOUN
ejpam-6215	992	21	.	.	PUNCT
ejpam-6215	993	1	int	int	NOUN
ejpam-6215	993	2	.	.	PUNCT
ejpam-6215	994	1	j.	j.	PROPN
ejpam-6215	994	2	appl	appl	PROPN
ejpam-6215	994	3	.	.	PROPN
ejpam-6215	994	4	math	math	PROPN
ejpam-6215	994	5	.	.	PUNCT
ejpam-6215	995	1	stat	stat	PROPN
ejpam-6215	995	2	.	.	PUNCT
ejpam-6215	996	1	sci	sci	PROPN
ejpam-6215	996	2	.	.	PUNCT
ejpam-6215	997	1	(	(	PUNCT
ejpam-6215	997	2	ijamss	ijamss	NOUN
ejpam-6215	997	3	)	)	PUNCT
ejpam-6215	997	4	,	,	PUNCT
ejpam-6215	997	5	10(1):45–54	10(1):45–54	NUM
ejpam-6215	997	6	,	,	PUNCT
ejpam-6215	997	7	2021	2021	NUM
ejpam-6215	997	8	.	.	PUNCT
ejpam-6215	998	1	[	[	X
ejpam-6215	998	2	50	50	NUM
ejpam-6215	998	3	]	]	PUNCT
ejpam-6215	998	4	s.	s.	PROPN
ejpam-6215	998	5	abu	abu	PROPN
ejpam-6215	998	6	-	-	PUNCT
ejpam-6215	998	7	amr	amr	PROPN
ejpam-6215	998	8	,	,	PUNCT
ejpam-6215	998	9	t.	t.	PROPN
ejpam-6215	998	10	almajbri	almajbri	PROPN
ejpam-6215	998	11	,	,	PUNCT
ejpam-6215	998	12	and	and	CCONJ
ejpam-6215	998	13	m.	m.	PROPN
ejpam-6215	998	14	ali	ali	PROPN
ejpam-6215	998	15	.	.	PROPN
ejpam-6215	999	1	comparison	comparison	NOUN
ejpam-6215	999	2	of	of	ADP
ejpam-6215	999	3	runge	runge	NOUN
ejpam-6215	999	4	-	-	PUNCT
ejpam-6215	999	5	kutta	kutta	NOUN
ejpam-6215	999	6	methods	method	NOUN
ejpam-6215	999	7	for	for	ADP
ejpam-6215	999	8	solving	solve	VERB
ejpam-6215	999	9	nonlinear	nonlinear	ADJ
ejpam-6215	999	10	equations	equation	NOUN
ejpam-6215	999	11	.	.	PUNCT
ejpam-6215	1000	1	alq	alq	PROPN
ejpam-6215	1000	2	.	.	PUNCT
ejpam-6215	1001	1	j.	j.	PROPN
ejpam-6215	1001	2	med	med	PROPN
ejpam-6215	1001	3	.	.	PUNCT
ejpam-6215	1002	1	app	app	PROPN
ejpam-6215	1002	2	.	.	PUNCT
ejpam-6215	1003	1	sci	sci	PROPN
ejpam-6215	1003	2	.	.	PROPN
ejpam-6215	1003	3	,	,	PUNCT
ejpam-6215	1003	4	7(4):1100–1108	7(4):1100–1108	PROPN
ejpam-6215	1003	5	,	,	PUNCT
ejpam-6215	1003	6	2024	2024	NUM
ejpam-6215	1003	7	.	.	PUNCT