id	sid	tid	token	lemma	pos
ejpam-5232	1	1	european	european	PROPN
ejpam-5232	1	2	journal	journal	PROPN
ejpam-5232	1	3	of	of	ADP
ejpam-5232	1	4	pure	pure	ADJ
ejpam-5232	1	5	and	and	CCONJ
ejpam-5232	1	6	applied	apply	VERB
ejpam-5232	1	7	mathematics	mathematic	NOUN
ejpam-5232	1	8	vol	vol	NOUN
ejpam-5232	1	9	.	.	PROPN
ejpam-5232	2	1	17	17	NUM
ejpam-5232	2	2	,	,	PUNCT
ejpam-5232	2	3	no	no	INTJ
ejpam-5232	2	4	.	.	NOUN
ejpam-5232	2	5	3	3	NUM
ejpam-5232	2	6	,	,	PUNCT
ejpam-5232	2	7	2024	2024	NUM
ejpam-5232	2	8	,	,	PUNCT
ejpam-5232	2	9	1497	1497	NUM
ejpam-5232	2	10	-	-	SYM
ejpam-5232	2	11	1515	1515	NUM
ejpam-5232	2	12	issn	issn	PROPN
ejpam-5232	2	13	1307	1307	NUM
ejpam-5232	2	14	-	-	SYM
ejpam-5232	2	15	5543	5543	NUM
ejpam-5232	2	16	–	–	PUNCT
ejpam-5232	3	1	ejpam.com	ejpam.com	X
ejpam-5232	3	2	published	publish	VERB
ejpam-5232	3	3	by	by	ADP
ejpam-5232	3	4	new	new	PROPN
ejpam-5232	3	5	york	york	PROPN
ejpam-5232	3	6	business	business	PROPN
ejpam-5232	3	7	global	global	PROPN
ejpam-5232	3	8	an	an	DET
ejpam-5232	3	9	efficient	efficient	ADJ
ejpam-5232	3	10	numerical	numerical	ADJ
ejpam-5232	3	11	approach	approach	NOUN
ejpam-5232	3	12	based	base	VERB
ejpam-5232	3	13	on	on	ADP
ejpam-5232	3	14	the	the	DET
ejpam-5232	3	15	adomian	adomian	NOUN
ejpam-5232	3	16	chebyshev	chebyshev	NOUN
ejpam-5232	3	17	decomposition	decomposition	NOUN
ejpam-5232	3	18	method	method	NOUN
ejpam-5232	3	19	for	for	ADP
ejpam-5232	3	20	two	two	NUM
ejpam-5232	3	21	-	-	PUNCT
ejpam-5232	3	22	point	point	NOUN
ejpam-5232	3	23	boundary	boundary	ADJ
ejpam-5232	3	24	value	value	NOUN
ejpam-5232	3	25	problems	problem	NOUN
ejpam-5232	3	26	amani	amani	VERB
ejpam-5232	3	27	al	al	PROPN
ejpam-5232	3	28	-	-	PUNCT
ejpam-5232	3	29	refaidi2	refaidi2	PROPN
ejpam-5232	3	30	,	,	PUNCT
ejpam-5232	3	31	nawal	nawal	PROPN
ejpam-5232	3	32	alzaid1	alzaid1	PROPN
ejpam-5232	3	33	,	,	PUNCT
ejpam-5232	3	34	huda	huda	PROPN
ejpam-5232	3	35	bakodah1,∗	bakodah1,∗	PROPN
ejpam-5232	3	36	,	,	PUNCT
ejpam-5232	3	37	mariam	mariam	PROPN
ejpam-5232	3	38	al	al	PROPN
ejpam-5232	3	39	-	-	PUNCT
ejpam-5232	3	40	mazmumy1	mazmumy1	PROPN
ejpam-5232	3	41	1	1	NUM
ejpam-5232	3	42	department	department	NOUN
ejpam-5232	3	43	of	of	ADP
ejpam-5232	3	44	mathematics	mathematic	NOUN
ejpam-5232	3	45	and	and	CCONJ
ejpam-5232	3	46	statistics	statistic	NOUN
ejpam-5232	3	47	,	,	PUNCT
ejpam-5232	3	48	faculty	faculty	NOUN
ejpam-5232	3	49	of	of	ADP
ejpam-5232	3	50	science	science	NOUN
ejpam-5232	3	51	,	,	PUNCT
ejpam-5232	3	52	university	university	NOUN
ejpam-5232	3	53	of	of	ADP
ejpam-5232	3	54	jeddah	jeddah	PROPN
ejpam-5232	3	55	,	,	PUNCT
ejpam-5232	3	56	p.o	p.o	PROPN
ejpam-5232	3	57	.	.	PROPN
ejpam-5232	3	58	box	box	PROPN
ejpam-5232	3	59	80327	80327	NUM
ejpam-5232	3	60	,	,	PUNCT
ejpam-5232	3	61	jeddah	jeddah	PROPN
ejpam-5232	3	62	,	,	PUNCT
ejpam-5232	3	63	saudi	saudi	PROPN
ejpam-5232	3	64	arabia	arabia	PROPN
ejpam-5232	3	65	.	.	PUNCT
ejpam-5232	4	1	2	2	NUM
ejpam-5232	4	2	department	department	NOUN
ejpam-5232	4	3	of	of	ADP
ejpam-5232	4	4	mathematics	mathematics	PROPN
ejpam-5232	4	5	,	,	PUNCT
ejpam-5232	4	6	al	al	PROPN
ejpam-5232	4	7	-	-	PUNCT
ejpam-5232	4	8	qunfudhah	qunfudhah	PROPN
ejpam-5232	4	9	university	university	NOUN
ejpam-5232	4	10	college	college	NOUN
ejpam-5232	4	11	,	,	PUNCT
ejpam-5232	4	12	umm	umm	INTJ
ejpam-5232	4	13	al	al	PROPN
ejpam-5232	4	14	-	-	PUNCT
ejpam-5232	4	15	qura	qura	PROPN
ejpam-5232	4	16	university	university	PROPN
ejpam-5232	4	17	,	,	PUNCT
ejpam-5232	4	18	makkah	makkah	PROPN
ejpam-5232	4	19	,	,	PUNCT
ejpam-5232	4	20	saudi	saudi	PROPN
ejpam-5232	4	21	arabia	arabia	PROPN
ejpam-5232	4	22	.	.	PUNCT
ejpam-5232	5	1	abstract	abstract	PROPN
ejpam-5232	5	2	.	.	PUNCT
ejpam-5232	6	1	the	the	DET
ejpam-5232	6	2	current	current	ADJ
ejpam-5232	6	3	manuscript	manuscript	NOUN
ejpam-5232	6	4	devises	devise	VERB
ejpam-5232	6	5	an	an	DET
ejpam-5232	6	6	efficient	efficient	ADJ
ejpam-5232	6	7	numerical	numerical	ADJ
ejpam-5232	6	8	method	method	NOUN
ejpam-5232	6	9	for	for	ADP
ejpam-5232	6	10	solving	solve	VERB
ejpam-5232	6	11	two	two	NUM
ejpam-5232	6	12	-	-	PUNCT
ejpam-5232	6	13	point	point	NOUN
ejpam-5232	6	14	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	6	15	boundary	boundary	ADJ
ejpam-5232	6	16	value	value	NOUN
ejpam-5232	6	17	problems	problem	NOUN
ejpam-5232	6	18	(	(	PUNCT
ejpam-5232	6	19	bvps	bvps	NOUN
ejpam-5232	6	20	)	)	PUNCT
ejpam-5232	6	21	with	with	ADP
ejpam-5232	6	22	dirichlet	dirichlet	PROPN
ejpam-5232	6	23	conditions	condition	NOUN
ejpam-5232	6	24	.	.	PUNCT
ejpam-5232	7	1	the	the	DET
ejpam-5232	7	2	method	method	NOUN
ejpam-5232	7	3	is	be	AUX
ejpam-5232	7	4	based	base	VERB
ejpam-5232	7	5	on	on	ADP
ejpam-5232	7	6	the	the	DET
ejpam-5232	7	7	application	application	NOUN
ejpam-5232	7	8	of	of	ADP
ejpam-5232	7	9	the	the	DET
ejpam-5232	7	10	celebrated	celebrate	VERB
ejpam-5232	7	11	adomian	adomian	NOUN
ejpam-5232	7	12	decomposition	decomposition	NOUN
ejpam-5232	7	13	method	method	NOUN
ejpam-5232	7	14	(	(	PUNCT
ejpam-5232	7	15	adm	adm	PROPN
ejpam-5232	7	16	)	)	PUNCT
ejpam-5232	7	17	and	and	CCONJ
ejpam-5232	7	18	,	,	PUNCT
ejpam-5232	7	19	the	the	DET
ejpam-5232	7	20	chebyshev	chebyshev	NOUN
ejpam-5232	7	21	polynomials	polynomial	NOUN
ejpam-5232	7	22	.	.	PUNCT
ejpam-5232	8	1	this	this	DET
ejpam-5232	8	2	method	method	NOUN
ejpam-5232	8	3	which	which	PRON
ejpam-5232	8	4	refers	refer	VERB
ejpam-5232	8	5	to	to	ADP
ejpam-5232	8	6	”	"	PUNCT
ejpam-5232	8	7	adomian	adomian	NOUN
ejpam-5232	8	8	chebyshev	chebyshev	NOUN
ejpam-5232	8	9	decomposition	decomposition	NOUN
ejpam-5232	8	10	method	method	NOUN
ejpam-5232	8	11	”	"	PUNCT
ejpam-5232	8	12	(	(	PUNCT
ejpam-5232	8	13	acdm	acdm	ADV
ejpam-5232	8	14	)	)	PUNCT
ejpam-5232	8	15	is	be	AUX
ejpam-5232	8	16	further	far	ADV
ejpam-5232	8	17	proved	prove	VERB
ejpam-5232	8	18	to	to	PART
ejpam-5232	8	19	be	be	AUX
ejpam-5232	8	20	a	a	DET
ejpam-5232	8	21	robust	robust	ADJ
ejpam-5232	8	22	numerical	numerical	ADJ
ejpam-5232	8	23	method	method	NOUN
ejpam-5232	8	24	as	as	SCONJ
ejpam-5232	8	25	the	the	DET
ejpam-5232	8	26	associated	associated	ADJ
ejpam-5232	8	27	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	8	28	terms	term	NOUN
ejpam-5232	8	29	are	be	AUX
ejpam-5232	8	30	successfully	successfully	ADV
ejpam-5232	8	31	reinstated	reinstate	VERB
ejpam-5232	8	32	with	with	ADP
ejpam-5232	8	33	a	a	DET
ejpam-5232	8	34	reliable	reliable	ADJ
ejpam-5232	8	35	chebyshev	chebyshev	NOUN
ejpam-5232	8	36	series	series	NOUN
ejpam-5232	8	37	.	.	PUNCT
ejpam-5232	9	1	lastly	lastly	ADV
ejpam-5232	9	2	,	,	PUNCT
ejpam-5232	9	3	a	a	DET
ejpam-5232	9	4	comparative	comparative	ADJ
ejpam-5232	9	5	study	study	NOUN
ejpam-5232	9	6	between	between	ADP
ejpam-5232	9	7	the	the	DET
ejpam-5232	9	8	acquired	acquire	VERB
ejpam-5232	9	9	numerical	numerical	ADJ
ejpam-5232	9	10	results	result	NOUN
ejpam-5232	9	11	and	and	CCONJ
ejpam-5232	9	12	the	the	DET
ejpam-5232	9	13	existing	exist	VERB
ejpam-5232	9	14	exact	exact	ADJ
ejpam-5232	9	15	solutions	solution	NOUN
ejpam-5232	9	16	of	of	ADP
ejpam-5232	9	17	the	the	DET
ejpam-5232	9	18	test	test	NOUN
ejpam-5232	9	19	problems	problem	NOUN
ejpam-5232	9	20	has	have	AUX
ejpam-5232	9	21	been	be	AUX
ejpam-5232	9	22	established	establish	VERB
ejpam-5232	9	23	to	to	PART
ejpam-5232	9	24	demonstrate	demonstrate	VERB
ejpam-5232	9	25	the	the	DET
ejpam-5232	9	26	salient	salient	NOUN
ejpam-5232	9	27	features	feature	NOUN
ejpam-5232	9	28	of	of	ADP
ejpam-5232	9	29	the	the	DET
ejpam-5232	9	30	devised	devise	VERB
ejpam-5232	9	31	method	method	NOUN
ejpam-5232	9	32	.	.	PUNCT
ejpam-5232	10	1	2020	2020	NUM
ejpam-5232	10	2	mathematics	mathematic	NOUN
ejpam-5232	10	3	subject	subject	NOUN
ejpam-5232	10	4	classifications	classification	NOUN
ejpam-5232	10	5	:	:	PUNCT
ejpam-5232	10	6	34a30,34a34,34b15	34a30,34a34,34b15	NUM
ejpam-5232	10	7	key	key	ADJ
ejpam-5232	10	8	words	word	NOUN
ejpam-5232	10	9	and	and	CCONJ
ejpam-5232	10	10	phrases	phrase	NOUN
ejpam-5232	10	11	:	:	PUNCT
ejpam-5232	10	12	boundary	boundary	ADJ
ejpam-5232	10	13	value	value	NOUN
ejpam-5232	10	14	problems	problem	NOUN
ejpam-5232	10	15	(	(	PUNCT
ejpam-5232	10	16	bvps	bvps	NOUN
ejpam-5232	10	17	)	)	PUNCT
ejpam-5232	10	18	,	,	PUNCT
ejpam-5232	10	19	adomian	adomian	NOUN
ejpam-5232	10	20	decomposition	decomposition	NOUN
ejpam-5232	10	21	method	method	NOUN
ejpam-5232	10	22	(	(	PUNCT
ejpam-5232	10	23	adm	adm	PROPN
ejpam-5232	10	24	)	)	PUNCT
ejpam-5232	10	25	,	,	PUNCT
ejpam-5232	10	26	chebyshev	chebyshev	NOUN
ejpam-5232	10	27	polynomials	polynomial	NOUN
ejpam-5232	10	28	,	,	PUNCT
ejpam-5232	10	29	adomian	adomian	NOUN
ejpam-5232	10	30	chebyshev	chebyshev	NOUN
ejpam-5232	10	31	decomposition	decomposition	NOUN
ejpam-5232	10	32	method	method	NOUN
ejpam-5232	10	33	(	(	PUNCT
ejpam-5232	10	34	acdm	acdm	ADJ
ejpam-5232	10	35	)	)	PUNCT
ejpam-5232	10	36	,	,	PUNCT
ejpam-5232	10	37	dirichlet	dirichlet	PROPN
ejpam-5232	10	38	conditions	condition	NOUN
ejpam-5232	10	39	1	1	NUM
ejpam-5232	10	40	.	.	PUNCT
ejpam-5232	10	41	introduction	introduction	NOUN
ejpam-5232	10	42	the	the	DET
ejpam-5232	10	43	celebrated	celebrated	ADJ
ejpam-5232	10	44	adomian	adomian	NOUN
ejpam-5232	10	45	decomposition	decomposition	NOUN
ejpam-5232	10	46	method	method	NOUN
ejpam-5232	10	47	(	(	PUNCT
ejpam-5232	10	48	adm	adm	PROPN
ejpam-5232	10	49	)	)	PUNCT
ejpam-5232	10	50	is	be	AUX
ejpam-5232	10	51	a	a	DET
ejpam-5232	10	52	well	well	ADV
ejpam-5232	10	53	-	-	PUNCT
ejpam-5232	10	54	known	know	VERB
ejpam-5232	10	55	semi	semi	ADJ
ejpam-5232	10	56	-	-	ADJ
ejpam-5232	10	57	analytical	analytical	ADJ
ejpam-5232	10	58	method	method	NOUN
ejpam-5232	10	59	that	that	PRON
ejpam-5232	10	60	has	have	AUX
ejpam-5232	10	61	been	be	AUX
ejpam-5232	10	62	attested	attest	VERB
ejpam-5232	10	63	by	by	ADP
ejpam-5232	10	64	many	many	ADJ
ejpam-5232	10	65	researchers	researcher	NOUN
ejpam-5232	10	66	to	to	PART
ejpam-5232	10	67	be	be	AUX
ejpam-5232	10	68	an	an	DET
ejpam-5232	10	69	effective	effective	ADJ
ejpam-5232	10	70	approach	approach	NOUN
ejpam-5232	10	71	for	for	ADP
ejpam-5232	10	72	solving	solve	VERB
ejpam-5232	10	73	wide	wide	ADJ
ejpam-5232	10	74	classes	class	NOUN
ejpam-5232	10	75	of	of	ADP
ejpam-5232	10	76	differential	differential	ADJ
ejpam-5232	10	77	,	,	PUNCT
ejpam-5232	10	78	integral	integral	ADJ
ejpam-5232	10	79	and	and	CCONJ
ejpam-5232	10	80	,	,	PUNCT
ejpam-5232	10	81	integro	integro	ADJ
ejpam-5232	10	82	-	-	PUNCT
ejpam-5232	10	83	differential	differential	NOUN
ejpam-5232	10	84	equations	equation	NOUN
ejpam-5232	10	85	.	.	PUNCT
ejpam-5232	11	1	the	the	DET
ejpam-5232	11	2	method	method	NOUN
ejpam-5232	11	3	reveals	reveal	VERB
ejpam-5232	11	4	the	the	DET
ejpam-5232	11	5	solution	solution	NOUN
ejpam-5232	11	6	as	as	ADP
ejpam-5232	11	7	a	a	DET
ejpam-5232	11	8	rapidly	rapidly	ADV
ejpam-5232	11	9	convergent	convergent	ADJ
ejpam-5232	11	10	series	series	NOUN
ejpam-5232	11	11	that	that	PRON
ejpam-5232	11	12	tends	tend	VERB
ejpam-5232	11	13	to	to	PART
ejpam-5232	11	14	accurately	accurately	ADV
ejpam-5232	11	15	converge	converge	VERB
ejpam-5232	11	16	to	to	ADP
ejpam-5232	11	17	the	the	DET
ejpam-5232	11	18	exact	exact	ADJ
ejpam-5232	11	19	analytical	analytical	ADJ
ejpam-5232	11	20	solution	solution	NOUN
ejpam-5232	11	21	[	[	X
ejpam-5232	11	22	2	2	NUM
ejpam-5232	11	23	,	,	PUNCT
ejpam-5232	11	24	3	3	NUM
ejpam-5232	11	25	,	,	PUNCT
ejpam-5232	11	26	7	7	NUM
ejpam-5232	11	27	,	,	PUNCT
ejpam-5232	11	28	8	8	NUM
ejpam-5232	11	29	,	,	PUNCT
ejpam-5232	11	30	11	11	NUM
ejpam-5232	11	31	,	,	PUNCT
ejpam-5232	11	32	24	24	NUM
ejpam-5232	11	33	]	]	PUNCT
ejpam-5232	11	34	.	.	PUNCT
ejpam-5232	12	1	additionally	additionally	ADV
ejpam-5232	12	2	,	,	PUNCT
ejpam-5232	12	3	the	the	DET
ejpam-5232	12	4	method	method	NOUN
ejpam-5232	12	5	is	be	AUX
ejpam-5232	12	6	so	so	ADV
ejpam-5232	12	7	flexible	flexible	ADJ
ejpam-5232	12	8	to	to	PART
ejpam-5232	12	9	be	be	AUX
ejpam-5232	12	10	applied	apply	VERB
ejpam-5232	12	11	to	to	ADP
ejpam-5232	12	12	the	the	DET
ejpam-5232	12	13	governing	govern	VERB
ejpam-5232	12	14	functional	functional	ADJ
ejpam-5232	12	15	equations	equation	NOUN
ejpam-5232	12	16	directly	directly	ADV
ejpam-5232	12	17	without	without	ADP
ejpam-5232	12	18	the	the	DET
ejpam-5232	12	19	need	need	NOUN
ejpam-5232	12	20	of	of	ADP
ejpam-5232	12	21	either	either	PRON
ejpam-5232	12	22	∗corresponding	∗corresponde	VERB
ejpam-5232	12	23	author	author	NOUN
ejpam-5232	12	24	.	.	PUNCT
ejpam-5232	13	1	doi	doi	NOUN
ejpam-5232	13	2	:	:	PUNCT
ejpam-5232	13	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5232	https://doi.org/10.29020/nybg.ejpam.v17i3.5232	PROPN
ejpam-5232	13	4	email	email	NOUN
ejpam-5232	13	5	addresses	address	VERB
ejpam-5232	13	6	:	:	PUNCT
ejpam-5232	13	7	ahrfede@uqu.edu.sa	ahrfede@uqu.edu.sa	PROPN
ejpam-5232	13	8	(	(	PUNCT
ejpam-5232	13	9	a.	a.	PROPN
ejpam-5232	13	10	al	al	PROPN
ejpam-5232	13	11	-	-	PUNCT
ejpam-5232	13	12	refaidi	refaidi	PROPN
ejpam-5232	13	13	)	)	PUNCT
ejpam-5232	13	14	,	,	PUNCT
ejpam-5232	13	15	naalzaid@uj.edu.sa	naalzaid@uj.edu.sa	PROPN
ejpam-5232	13	16	(	(	PUNCT
ejpam-5232	13	17	n.	n.	PROPN
ejpam-5232	13	18	al	al	PROPN
ejpam-5232	13	19	-	-	PUNCT
ejpam-5232	13	20	zaid	zaid	PROPN
ejpam-5232	13	21	)	)	PUNCT
ejpam-5232	13	22	,	,	PUNCT
ejpam-5232	13	23	hobakodah@uj.edu.sa	hobakodah@uj.edu.sa	PROPN
ejpam-5232	13	24	(	(	PUNCT
ejpam-5232	13	25	h.	h.	NOUN
ejpam-5232	13	26	bakodah	bakodah	PROPN
ejpam-5232	13	27	)	)	PUNCT
ejpam-5232	13	28	,	,	PUNCT
ejpam-5232	13	29	mhalmazmumy@uj.edu.sa	mhalmazmumy@uj.edu.sa	PROPN
ejpam-5232	13	30	(	(	PUNCT
ejpam-5232	13	31	m.	m.	PROPN
ejpam-5232	13	32	al	al	PROPN
ejpam-5232	13	33	-	-	PUNCT
ejpam-5232	13	34	mazmumy	mazmumy	PROPN
ejpam-5232	13	35	)	)	PUNCT
ejpam-5232	13	36	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5232	13	37	1497	1497	NUM
ejpam-5232	14	1	©	©	PROPN
ejpam-5232	14	2	2024	2024	NUM
ejpam-5232	14	3	ejpam	ejpam	NOUN
ejpam-5232	14	4	all	all	DET
ejpam-5232	14	5	rights	right	NOUN
ejpam-5232	14	6	reserved	reserve	VERB
ejpam-5232	14	7	.	.	PUNCT
ejpam-5232	15	1	h.	h.	PROPN
ejpam-5232	15	2	bakodah	bakodah	PROPN
ejpam-5232	15	3	et	et	PROPN
ejpam-5232	15	4	al	al	PROPN
ejpam-5232	15	5	.	.	PUNCT
ejpam-5232	15	6	/	/	SYM
ejpam-5232	15	7	eur	eur	PROPN
ejpam-5232	15	8	.	.	PUNCT
ejpam-5232	16	1	j.	j.	PROPN
ejpam-5232	16	2	pure	pure	PROPN
ejpam-5232	16	3	appl	appl	PROPN
ejpam-5232	16	4	.	.	PROPN
ejpam-5232	16	5	math	math	PROPN
ejpam-5232	16	6	,	,	PUNCT
ejpam-5232	16	7	17	17	NUM
ejpam-5232	16	8	(	(	PUNCT
ejpam-5232	16	9	3	3	NUM
ejpam-5232	16	10	)	)	PUNCT
ejpam-5232	16	11	(	(	PUNCT
ejpam-5232	16	12	2024	2024	NUM
ejpam-5232	16	13	)	)	PUNCT
ejpam-5232	16	14	,	,	PUNCT
ejpam-5232	16	15	1497	1497	NUM
ejpam-5232	16	16	-	-	SYM
ejpam-5232	16	17	1515	1515	NUM
ejpam-5232	16	18	1498	1498	NUM
ejpam-5232	16	19	restricting	restrict	VERB
ejpam-5232	16	20	the	the	DET
ejpam-5232	16	21	method	method	NOUN
ejpam-5232	16	22	/	/	SYM
ejpam-5232	16	23	solution	solution	NOUN
ejpam-5232	16	24	to	to	ADP
ejpam-5232	16	25	a	a	DET
ejpam-5232	16	26	particular	particular	ADJ
ejpam-5232	16	27	domain	domain	NOUN
ejpam-5232	16	28	,	,	PUNCT
ejpam-5232	16	29	or	or	CCONJ
ejpam-5232	16	30	by	by	ADP
ejpam-5232	16	31	making	make	VERB
ejpam-5232	16	32	use	use	NOUN
ejpam-5232	16	33	of	of	ADP
ejpam-5232	16	34	certain	certain	ADJ
ejpam-5232	16	35	simplifications	simplification	NOUN
ejpam-5232	16	36	like	like	ADP
ejpam-5232	16	37	perturbation	perturbation	NOUN
ejpam-5232	16	38	,	,	PUNCT
ejpam-5232	16	39	discretization	discretization	NOUN
ejpam-5232	16	40	,	,	PUNCT
ejpam-5232	16	41	or	or	CCONJ
ejpam-5232	16	42	linearization	linearization	NOUN
ejpam-5232	16	43	[	[	X
ejpam-5232	16	44	23	23	NUM
ejpam-5232	16	45	]	]	PUNCT
ejpam-5232	16	46	.	.	PUNCT
ejpam-5232	17	1	furthermore	furthermore	ADV
ejpam-5232	17	2	,	,	PUNCT
ejpam-5232	17	3	like	like	ADP
ejpam-5232	17	4	any	any	DET
ejpam-5232	17	5	other	other	ADJ
ejpam-5232	17	6	mathematical	mathematical	ADJ
ejpam-5232	17	7	method	method	NOUN
ejpam-5232	17	8	in	in	ADP
ejpam-5232	17	9	the	the	DET
ejpam-5232	17	10	literature	literature	NOUN
ejpam-5232	17	11	,	,	PUNCT
ejpam-5232	17	12	various	various	ADJ
ejpam-5232	17	13	researchers	researcher	NOUN
ejpam-5232	17	14	have	have	AUX
ejpam-5232	17	15	equally	equally	ADV
ejpam-5232	17	16	proposed	propose	VERB
ejpam-5232	17	17	different	different	ADJ
ejpam-5232	17	18	extensions	extension	NOUN
ejpam-5232	17	19	and	and	CCONJ
ejpam-5232	17	20	modifications	modification	NOUN
ejpam-5232	17	21	to	to	ADP
ejpam-5232	17	22	the	the	DET
ejpam-5232	17	23	adm	adm	NOUN
ejpam-5232	17	24	,	,	PUNCT
ejpam-5232	17	25	thereby	thereby	ADV
ejpam-5232	17	26	improving	improve	VERB
ejpam-5232	17	27	the	the	DET
ejpam-5232	17	28	convergence	convergence	NOUN
ejpam-5232	17	29	rate	rate	NOUN
ejpam-5232	17	30	of	of	ADP
ejpam-5232	17	31	the	the	DET
ejpam-5232	17	32	method	method	NOUN
ejpam-5232	17	33	and	and	CCONJ
ejpam-5232	17	34	,	,	PUNCT
ejpam-5232	17	35	also	also	ADV
ejpam-5232	17	36	,	,	PUNCT
ejpam-5232	17	37	extending	extend	VERB
ejpam-5232	17	38	its	its	PRON
ejpam-5232	17	39	applicability	applicability	NOUN
ejpam-5232	17	40	,	,	PUNCT
ejpam-5232	17	41	[	[	X
ejpam-5232	17	42	6	6	NUM
ejpam-5232	17	43	,	,	PUNCT
ejpam-5232	17	44	10	10	NUM
ejpam-5232	17	45	,	,	PUNCT
ejpam-5232	17	46	12	12	NUM
ejpam-5232	17	47	,	,	PUNCT
ejpam-5232	17	48	13	13	NUM
ejpam-5232	17	49	,	,	PUNCT
ejpam-5232	17	50	20	20	NUM
ejpam-5232	17	51	]	]	PUNCT
ejpam-5232	17	52	.	.	PUNCT
ejpam-5232	18	1	in	in	ADP
ejpam-5232	18	2	addition	addition	NOUN
ejpam-5232	18	3	,	,	PUNCT
ejpam-5232	18	4	the	the	DET
ejpam-5232	18	5	utilization	utilization	NOUN
ejpam-5232	18	6	of	of	ADP
ejpam-5232	18	7	green	green	PROPN
ejpam-5232	18	8	’s	’s	PART
ejpam-5232	18	9	function	function	NOUN
ejpam-5232	18	10	approach	approach	NOUN
ejpam-5232	18	11	on	on	ADP
ejpam-5232	18	12	the	the	DET
ejpam-5232	18	13	bvps	bvps	NOUN
ejpam-5232	18	14	for	for	ADP
ejpam-5232	18	15	treating	treat	VERB
ejpam-5232	18	16	ordinary	ordinary	ADJ
ejpam-5232	18	17	differential	differential	ADJ
ejpam-5232	18	18	equations	equation	NOUN
ejpam-5232	18	19	(	(	PUNCT
ejpam-5232	18	20	odes	ode	NOUN
ejpam-5232	18	21	)	)	PUNCT
ejpam-5232	18	22	has	have	AUX
ejpam-5232	18	23	been	be	AUX
ejpam-5232	18	24	overcome	overcome	VERB
ejpam-5232	18	25	with	with	ADP
ejpam-5232	18	26	the	the	DET
ejpam-5232	18	27	invention	invention	NOUN
ejpam-5232	18	28	of	of	ADP
ejpam-5232	18	29	the	the	DET
ejpam-5232	18	30	adm[5	adm[5	NOUN
ejpam-5232	18	31	,	,	PUNCT
ejpam-5232	18	32	21	21	NUM
ejpam-5232	18	33	]	]	PUNCT
ejpam-5232	18	34	;	;	PUNCT
ejpam-5232	18	35	as	as	SCONJ
ejpam-5232	18	36	the	the	DET
ejpam-5232	18	37	acquisition	acquisition	NOUN
ejpam-5232	18	38	of	of	ADP
ejpam-5232	18	39	approximate	approximate	ADJ
ejpam-5232	18	40	analytic	analytic	ADJ
ejpam-5232	18	41	solutions	solution	NOUN
ejpam-5232	18	42	are	be	AUX
ejpam-5232	18	43	attained	attain	VERB
ejpam-5232	18	44	and	and	CCONJ
ejpam-5232	18	45	greatly	greatly	ADV
ejpam-5232	18	46	facilitated	facilitate	VERB
ejpam-5232	18	47	.	.	PUNCT
ejpam-5232	19	1	there	there	PRON
ejpam-5232	19	2	are	be	VERB
ejpam-5232	19	3	numerous	numerous	ADJ
ejpam-5232	19	4	efficient	efficient	ADJ
ejpam-5232	19	5	methods	method	NOUN
ejpam-5232	19	6	based	base	VERB
ejpam-5232	19	7	on	on	ADP
ejpam-5232	19	8	the	the	DET
ejpam-5232	19	9	adm	adm	NOUN
ejpam-5232	19	10	for	for	ADP
ejpam-5232	19	11	solving	solve	VERB
ejpam-5232	19	12	bvps	bvps	NOUN
ejpam-5232	19	13	of	of	ADP
ejpam-5232	19	14	odes	ode	NOUN
ejpam-5232	19	15	such	such	ADJ
ejpam-5232	19	16	as	as	ADP
ejpam-5232	19	17	the	the	DET
ejpam-5232	19	18	double	double	ADJ
ejpam-5232	19	19	decomposition	decomposition	NOUN
ejpam-5232	19	20	method	method	NOUN
ejpam-5232	19	21	[	[	X
ejpam-5232	19	22	3	3	NUM
ejpam-5232	19	23	,	,	PUNCT
ejpam-5232	19	24	4	4	NUM
ejpam-5232	19	25	]	]	PUNCT
ejpam-5232	19	26	and	and	CCONJ
ejpam-5232	19	27	,	,	PUNCT
ejpam-5232	19	28	the	the	DET
ejpam-5232	19	29	duan	duan	PROPN
ejpam-5232	19	30	-	-	PUNCT
ejpam-5232	19	31	rach	rach	PROPN
ejpam-5232	19	32	modified	modify	VERB
ejpam-5232	19	33	decomposition	decomposition	NOUN
ejpam-5232	19	34	method	method	NOUN
ejpam-5232	19	35	[	[	X
ejpam-5232	19	36	16	16	NUM
ejpam-5232	19	37	]	]	PUNCT
ejpam-5232	19	38	to	to	PART
ejpam-5232	19	39	mention	mention	VERB
ejpam-5232	19	40	a	a	DET
ejpam-5232	19	41	few	few	ADJ
ejpam-5232	19	42	.	.	PUNCT
ejpam-5232	20	1	however	however	ADV
ejpam-5232	20	2	,	,	PUNCT
ejpam-5232	20	3	in	in	ADP
ejpam-5232	20	4	the	the	DET
ejpam-5232	20	5	current	current	ADJ
ejpam-5232	20	6	manuscript	manuscript	NOUN
ejpam-5232	20	7	,	,	PUNCT
ejpam-5232	20	8	we	we	PRON
ejpam-5232	20	9	shall	shall	AUX
ejpam-5232	20	10	devise	devise	VERB
ejpam-5232	20	11	an	an	DET
ejpam-5232	20	12	efficient	efficient	ADJ
ejpam-5232	20	13	numerical	numerical	ADJ
ejpam-5232	20	14	method	method	NOUN
ejpam-5232	20	15	based	base	VERB
ejpam-5232	20	16	on	on	ADP
ejpam-5232	20	17	the	the	DET
ejpam-5232	20	18	application	application	NOUN
ejpam-5232	20	19	of	of	ADP
ejpam-5232	20	20	the	the	DET
ejpam-5232	20	21	adm	adm	PROPN
ejpam-5232	20	22	and	and	CCONJ
ejpam-5232	20	23	,	,	PUNCT
ejpam-5232	20	24	chebyshev	chebyshev	NOUN
ejpam-5232	20	25	polynomials	polynomial	NOUN
ejpam-5232	20	26	to	to	PART
ejpam-5232	20	27	solve	solve	VERB
ejpam-5232	20	28	a	a	DET
ejpam-5232	20	29	class	class	NOUN
ejpam-5232	20	30	of	of	ADP
ejpam-5232	20	31	two	two	NUM
ejpam-5232	20	32	-	-	PUNCT
ejpam-5232	20	33	point	point	NOUN
ejpam-5232	20	34	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	20	35	bvps	bvps	NOUN
ejpam-5232	20	36	with	with	ADP
ejpam-5232	20	37	dirichlet	dirichlet	PROPN
ejpam-5232	20	38	boundary	boundary	PROPN
ejpam-5232	20	39	conditions	condition	NOUN
ejpam-5232	20	40	.	.	PUNCT
ejpam-5232	21	1	this	this	DET
ejpam-5232	21	2	method	method	NOUN
ejpam-5232	21	3	that	that	PRON
ejpam-5232	21	4	called	call	VERB
ejpam-5232	21	5	acdm	acdm	ADP
ejpam-5232	21	6	makes	make	VERB
ejpam-5232	21	7	use	use	NOUN
ejpam-5232	21	8	of	of	ADP
ejpam-5232	21	9	the	the	DET
ejpam-5232	21	10	traditional	traditional	ADJ
ejpam-5232	21	11	adm	adm	PROPN
ejpam-5232	21	12	together	together	ADV
ejpam-5232	21	13	with	with	ADP
ejpam-5232	21	14	the	the	DET
ejpam-5232	21	15	chebyshev	chebyshev	PROPN
ejpam-5232	21	16	orthogonal	orthogonal	ADJ
ejpam-5232	21	17	polynomials	polynomial	NOUN
ejpam-5232	21	18	to	to	PART
ejpam-5232	21	19	solve	solve	VERB
ejpam-5232	21	20	bvps	bvps	NOUN
ejpam-5232	21	21	.	.	PUNCT
ejpam-5232	22	1	more	more	ADJ
ejpam-5232	22	2	,	,	PUNCT
ejpam-5232	22	3	the	the	DET
ejpam-5232	22	4	method	method	NOUN
ejpam-5232	22	5	first	first	ADV
ejpam-5232	22	6	appeared	appear	VERB
ejpam-5232	22	7	in	in	ADP
ejpam-5232	22	8	[	[	X
ejpam-5232	22	9	19	19	NUM
ejpam-5232	22	10	]	]	PUNCT
ejpam-5232	22	11	to	to	PART
ejpam-5232	22	12	solve	solve	VERB
ejpam-5232	22	13	only	only	ADV
ejpam-5232	22	14	certain	certain	ADJ
ejpam-5232	22	15	initial	initial	ADJ
ejpam-5232	22	16	value	value	NOUN
ejpam-5232	22	17	problems	problem	NOUN
ejpam-5232	22	18	and	and	CCONJ
ejpam-5232	22	19	;	;	PUNCT
ejpam-5232	22	20	thus	thus	ADV
ejpam-5232	22	21	,	,	PUNCT
ejpam-5232	22	22	the	the	DET
ejpam-5232	22	23	method	method	NOUN
ejpam-5232	22	24	is	be	AUX
ejpam-5232	22	25	extended	extend	VERB
ejpam-5232	22	26	in	in	ADP
ejpam-5232	22	27	the	the	DET
ejpam-5232	22	28	present	present	ADJ
ejpam-5232	22	29	study	study	NOUN
ejpam-5232	22	30	in	in	ADP
ejpam-5232	22	31	order	order	NOUN
ejpam-5232	22	32	to	to	PART
ejpam-5232	22	33	be	be	AUX
ejpam-5232	22	34	able	able	ADJ
ejpam-5232	22	35	to	to	PART
ejpam-5232	22	36	cover	cover	VERB
ejpam-5232	22	37	a	a	DET
ejpam-5232	22	38	wide	wide	ADJ
ejpam-5232	22	39	range	range	NOUN
ejpam-5232	22	40	of	of	ADP
ejpam-5232	22	41	applications	application	NOUN
ejpam-5232	22	42	.	.	PUNCT
ejpam-5232	23	1	additionally	additionally	ADV
ejpam-5232	23	2	,	,	PUNCT
ejpam-5232	23	3	a	a	DET
ejpam-5232	23	4	comparative	comparative	ADJ
ejpam-5232	23	5	study	study	NOUN
ejpam-5232	23	6	between	between	ADP
ejpam-5232	23	7	the	the	DET
ejpam-5232	23	8	acquired	acquire	VERB
ejpam-5232	23	9	numerical	numerical	ADJ
ejpam-5232	23	10	results	result	NOUN
ejpam-5232	23	11	by	by	ADP
ejpam-5232	23	12	the	the	DET
ejpam-5232	23	13	devised	devise	VERB
ejpam-5232	23	14	method	method	NOUN
ejpam-5232	23	15	and	and	CCONJ
ejpam-5232	23	16	the	the	DET
ejpam-5232	23	17	existing	exist	VERB
ejpam-5232	23	18	exact	exact	ADJ
ejpam-5232	23	19	solutions	solution	NOUN
ejpam-5232	23	20	of	of	ADP
ejpam-5232	23	21	the	the	DET
ejpam-5232	23	22	test	test	NOUN
ejpam-5232	23	23	problems	problem	NOUN
ejpam-5232	23	24	will	will	AUX
ejpam-5232	23	25	be	be	AUX
ejpam-5232	23	26	established	establish	VERB
ejpam-5232	23	27	to	to	PART
ejpam-5232	23	28	demonstrate	demonstrate	VERB
ejpam-5232	23	29	certain	certain	ADJ
ejpam-5232	23	30	salient	salient	NOUN
ejpam-5232	23	31	features	feature	NOUN
ejpam-5232	23	32	of	of	ADP
ejpam-5232	23	33	the	the	DET
ejpam-5232	23	34	devised	devise	VERB
ejpam-5232	23	35	method	method	NOUN
ejpam-5232	23	36	.	.	PUNCT
ejpam-5232	24	1	lastly	lastly	ADV
ejpam-5232	24	2	,	,	PUNCT
ejpam-5232	24	3	we	we	PRON
ejpam-5232	24	4	arrange	arrange	VERB
ejpam-5232	24	5	the	the	DET
ejpam-5232	24	6	manuscript	manuscript	NOUN
ejpam-5232	24	7	in	in	ADP
ejpam-5232	24	8	the	the	DET
ejpam-5232	24	9	following	following	ADJ
ejpam-5232	24	10	way	way	NOUN
ejpam-5232	24	11	:	:	PUNCT
ejpam-5232	24	12	in	in	ADP
ejpam-5232	24	13	sections	section	NOUN
ejpam-5232	24	14	2	2	NUM
ejpam-5232	24	15	and	and	CCONJ
ejpam-5232	24	16	3	3	NUM
ejpam-5232	24	17	,	,	PUNCT
ejpam-5232	24	18	we	we	PRON
ejpam-5232	24	19	present	present	VERB
ejpam-5232	24	20	the	the	DET
ejpam-5232	24	21	methods	method	NOUN
ejpam-5232	24	22	based	base	VERB
ejpam-5232	24	23	on	on	ADP
ejpam-5232	24	24	the	the	DET
ejpam-5232	24	25	traditional	traditional	ADJ
ejpam-5232	24	26	adm	adm	PROPN
ejpam-5232	24	27	and	and	CCONJ
ejpam-5232	24	28	acdm	acdm	ADJ
ejpam-5232	24	29	for	for	ADP
ejpam-5232	24	30	solving	solve	VERB
ejpam-5232	24	31	bvps	bvps	NOUN
ejpam-5232	24	32	with	with	ADP
ejpam-5232	24	33	dirichlet	dirichlet	PROPN
ejpam-5232	24	34	boundary	boundary	PROPN
ejpam-5232	24	35	conditions	condition	NOUN
ejpam-5232	24	36	,	,	PUNCT
ejpam-5232	24	37	respectively	respectively	ADV
ejpam-5232	24	38	.	.	PUNCT
ejpam-5232	25	1	section	section	NOUN
ejpam-5232	25	2	4	4	NUM
ejpam-5232	25	3	gives	give	VERB
ejpam-5232	25	4	the	the	DET
ejpam-5232	25	5	numerical	numerical	ADJ
ejpam-5232	25	6	application	application	NOUN
ejpam-5232	25	7	of	of	ADP
ejpam-5232	25	8	the	the	DET
ejpam-5232	25	9	devised	devise	VERB
ejpam-5232	25	10	method	method	NOUN
ejpam-5232	25	11	in	in	ADP
ejpam-5232	25	12	section	section	NOUN
ejpam-5232	25	13	3	3	NUM
ejpam-5232	25	14	;	;	PUNCT
ejpam-5232	25	15	while	while	SCONJ
ejpam-5232	25	16	section	section	NOUN
ejpam-5232	25	17	5	5	NUM
ejpam-5232	25	18	gives	give	VERB
ejpam-5232	25	19	some	some	DET
ejpam-5232	25	20	concluding	concluding	NOUN
ejpam-5232	25	21	notes	note	NOUN
ejpam-5232	25	22	.	.	PUNCT
ejpam-5232	26	1	2	2	X
ejpam-5232	26	2	.	.	X
ejpam-5232	26	3	adomian	adomian	NOUN
ejpam-5232	26	4	decomposition	decomposition	NOUN
ejpam-5232	26	5	method	method	NOUN
ejpam-5232	26	6	(	(	PUNCT
ejpam-5232	26	7	adm	adm	PROPN
ejpam-5232	26	8	)	)	PUNCT
ejpam-5232	26	9	for	for	ADP
ejpam-5232	26	10	bvps	bvps	NOUN
ejpam-5232	26	11	let	let	VERB
ejpam-5232	26	12	us	we	PRON
ejpam-5232	26	13	consider	consider	VERB
ejpam-5232	26	14	the	the	DET
ejpam-5232	26	15	generalized	generalized	ADJ
ejpam-5232	26	16	second	second	ADJ
ejpam-5232	26	17	-	-	PUNCT
ejpam-5232	26	18	order	order	NOUN
ejpam-5232	26	19	nonlinear	nonlinear	ADJ
ejpam-5232	26	20	version	version	NOUN
ejpam-5232	26	21	of	of	ADP
ejpam-5232	26	22	the	the	DET
ejpam-5232	26	23	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	26	24	ode	ode	NOUN
ejpam-5232	26	25	expressed	express	VERB
ejpam-5232	26	26	in	in	ADP
ejpam-5232	26	27	operator	operator	NOUN
ejpam-5232	26	28	form	form	NOUN
ejpam-5232	26	29	as	as	SCONJ
ejpam-5232	26	30	follows	follow	VERB
ejpam-5232	26	31	lu(x	lu(x	NOUN
ejpam-5232	26	32	)	)	PUNCT
ejpam-5232	27	1	+	+	SYM
ejpam-5232	27	2	ru(x	ru(x	NOUN
ejpam-5232	27	3	)	)	PUNCT
ejpam-5232	27	4	+	+	NOUN
ejpam-5232	27	5	nu(x	nu(x	NOUN
ejpam-5232	27	6	)	)	PUNCT
ejpam-5232	27	7	=	=	SYM
ejpam-5232	27	8	g(x	g(x	NOUN
ejpam-5232	27	9	)	)	PUNCT
ejpam-5232	27	10	,	,	PUNCT
ejpam-5232	27	11	(	(	PUNCT
ejpam-5232	27	12	1	1	X
ejpam-5232	27	13	)	)	PUNCT
ejpam-5232	27	14	together	together	ADV
ejpam-5232	27	15	with	with	ADP
ejpam-5232	27	16	the	the	DET
ejpam-5232	27	17	following	follow	VERB
ejpam-5232	27	18	dirichlet	dirichlet	PROPN
ejpam-5232	27	19	boundary	boundary	PROPN
ejpam-5232	27	20	conditions	condition	NOUN
ejpam-5232	27	21	u	u	PROPN
ejpam-5232	27	22	(	(	PUNCT
ejpam-5232	27	23	α1	α1	PROPN
ejpam-5232	27	24	)	)	PUNCT
ejpam-5232	27	25	=	=	SYM
ejpam-5232	27	26	β1	β1	PROPN
ejpam-5232	27	27	and	and	CCONJ
ejpam-5232	27	28	u	u	NOUN
ejpam-5232	27	29	(	(	PUNCT
ejpam-5232	27	30	α2	α2	PROPN
ejpam-5232	27	31	)	)	PUNCT
ejpam-5232	28	1	=	=	SYM
ejpam-5232	28	2	β2	β2	VERB
ejpam-5232	28	3	,	,	PUNCT
ejpam-5232	28	4	(	(	PUNCT
ejpam-5232	28	5	2	2	X
ejpam-5232	28	6	)	)	PUNCT
ejpam-5232	28	7	where	where	SCONJ
ejpam-5232	28	8	β1	β1	PROPN
ejpam-5232	28	9	and	and	CCONJ
ejpam-5232	28	10	β2	β2	NOUN
ejpam-5232	28	11	are	be	AUX
ejpam-5232	28	12	real	real	ADJ
ejpam-5232	28	13	constants	constant	NOUN
ejpam-5232	28	14	,	,	PUNCT
ejpam-5232	28	15	l	l	NOUN
ejpam-5232	28	16	is	be	AUX
ejpam-5232	28	17	the	the	DET
ejpam-5232	28	18	highest	high	ADJ
ejpam-5232	28	19	linear	linear	ADJ
ejpam-5232	28	20	operator	operator	NOUN
ejpam-5232	28	21	and	and	CCONJ
ejpam-5232	28	22	,	,	PUNCT
ejpam-5232	28	23	r	r	NOUN
ejpam-5232	28	24	is	be	AUX
ejpam-5232	28	25	an	an	DET
ejpam-5232	28	26	operator	operator	NOUN
ejpam-5232	28	27	with	with	ADP
ejpam-5232	28	28	degree	degree	NOUN
ejpam-5232	28	29	less	less	ADJ
ejpam-5232	28	30	than	than	ADP
ejpam-5232	28	31	of	of	ADP
ejpam-5232	28	32	l;n	l;n	PROPN
ejpam-5232	28	33	is	be	AUX
ejpam-5232	28	34	the	the	DET
ejpam-5232	28	35	nonlinear	nonlinear	ADJ
ejpam-5232	28	36	operator	operator	NOUN
ejpam-5232	28	37	,	,	PUNCT
ejpam-5232	28	38	while	while	SCONJ
ejpam-5232	28	39	the	the	DET
ejpam-5232	28	40	function	function	NOUN
ejpam-5232	28	41	g(x	g(x	NOUN
ejpam-5232	28	42	)	)	PUNCT
ejpam-5232	28	43	on	on	ADP
ejpam-5232	28	44	the	the	DET
ejpam-5232	28	45	other	other	ADJ
ejpam-5232	28	46	side	side	NOUN
ejpam-5232	28	47	of	of	ADP
ejpam-5232	28	48	the	the	DET
ejpam-5232	28	49	above	above	ADJ
ejpam-5232	28	50	equation	equation	NOUN
ejpam-5232	28	51	is	be	AUX
ejpam-5232	28	52	a	a	DET
ejpam-5232	28	53	prescribed	prescribed	ADJ
ejpam-5232	28	54	source	source	NOUN
ejpam-5232	28	55	term	term	NOUN
ejpam-5232	28	56	,	,	PUNCT
ejpam-5232	28	57	which	which	PRON
ejpam-5232	28	58	is	be	AUX
ejpam-5232	28	59	a	a	DET
ejpam-5232	28	60	given	give	VERB
ejpam-5232	28	61	continuous	continuous	ADJ
ejpam-5232	28	62	function	function	NOUN
ejpam-5232	28	63	.	.	PUNCT
ejpam-5232	29	1	what	what	PRON
ejpam-5232	29	2	’s	’	VERB
ejpam-5232	29	3	more	more	ADJ
ejpam-5232	29	4	,	,	PUNCT
ejpam-5232	29	5	if	if	SCONJ
ejpam-5232	29	6	the	the	DET
ejpam-5232	29	7	operator	operator	NOUN
ejpam-5232	29	8	l	l	NOUN
ejpam-5232	29	9	is	be	AUX
ejpam-5232	29	10	assumed	assume	VERB
ejpam-5232	29	11	to	to	PART
ejpam-5232	29	12	be	be	AUX
ejpam-5232	29	13	invertible	invertible	ADJ
ejpam-5232	29	14	and	and	CCONJ
ejpam-5232	29	15	,	,	PUNCT
ejpam-5232	29	16	further	far	ADV
ejpam-5232	29	17	apply	apply	VERB
ejpam-5232	29	18	its	its	PRON
ejpam-5232	29	19	corresponding	corresponding	ADJ
ejpam-5232	29	20	inverse	inverse	NOUN
ejpam-5232	29	21	operator	operator	NOUN
ejpam-5232	29	22	l−1	l−1	PROPN
ejpam-5232	29	23	to	to	ADP
ejpam-5232	29	24	all	all	DET
ejpam-5232	29	25	the	the	DET
ejpam-5232	29	26	parts	part	NOUN
ejpam-5232	29	27	of	of	ADP
ejpam-5232	29	28	eq	eq	PROPN
ejpam-5232	29	29	.	.	PUNCT
ejpam-5232	30	1	(	(	PUNCT
ejpam-5232	30	2	1	1	NUM
ejpam-5232	30	3	)	)	PUNCT
ejpam-5232	30	4	,	,	PUNCT
ejpam-5232	30	5	we	we	PRON
ejpam-5232	30	6	get	get	VERB
ejpam-5232	30	7	after	after	ADP
ejpam-5232	30	8	solving	solve	VERB
ejpam-5232	30	9	for	for	ADP
ejpam-5232	30	10	lu(x	lu(x	NOUN
ejpam-5232	30	11	)	)	PUNCT
ejpam-5232	30	12	the	the	DET
ejpam-5232	30	13	following	follow	VERB
ejpam-5232	30	14	expression	expression	NOUN
ejpam-5232	30	15	for	for	ADP
ejpam-5232	30	16	u(x	u(x	NOUN
ejpam-5232	30	17	)	)	PUNCT
ejpam-5232	30	18	u(x	u(x	NOUN
ejpam-5232	30	19	)	)	PUNCT
ejpam-5232	30	20	=	=	SYM
ejpam-5232	31	1	φ(x	φ(x	NOUN
ejpam-5232	31	2	)	)	PUNCT
ejpam-5232	32	1	+	+	CCONJ
ejpam-5232	32	2	l−1(g(x))−	l−1(g(x))−	ADJ
ejpam-5232	32	3	l−1(ru(x))−	l−1(ru(x))−	NOUN
ejpam-5232	32	4	l−1(nu(x	l−1(nu(x	PROPN
ejpam-5232	32	5	)	)	PUNCT
ejpam-5232	32	6	)	)	PUNCT
ejpam-5232	32	7	,	,	PUNCT
ejpam-5232	32	8	(	(	PUNCT
ejpam-5232	32	9	3	3	X
ejpam-5232	32	10	)	)	PUNCT
ejpam-5232	32	11	h.	h.	NOUN
ejpam-5232	32	12	bakodah	bakodah	PROPN
ejpam-5232	32	13	et	et	PROPN
ejpam-5232	32	14	al	al	PROPN
ejpam-5232	32	15	.	.	PUNCT
ejpam-5232	32	16	/	/	SYM
ejpam-5232	32	17	eur	eur	PROPN
ejpam-5232	32	18	.	.	PUNCT
ejpam-5232	33	1	j.	j.	PROPN
ejpam-5232	33	2	pure	pure	PROPN
ejpam-5232	33	3	appl	appl	PROPN
ejpam-5232	33	4	.	.	PROPN
ejpam-5232	33	5	math	math	PROPN
ejpam-5232	33	6	,	,	PUNCT
ejpam-5232	33	7	17	17	NUM
ejpam-5232	33	8	(	(	PUNCT
ejpam-5232	33	9	3	3	NUM
ejpam-5232	33	10	)	)	PUNCT
ejpam-5232	33	11	(	(	PUNCT
ejpam-5232	33	12	2024	2024	NUM
ejpam-5232	33	13	)	)	PUNCT
ejpam-5232	33	14	,	,	PUNCT
ejpam-5232	33	15	1497	1497	NUM
ejpam-5232	33	16	-	-	SYM
ejpam-5232	33	17	1515	1515	NUM
ejpam-5232	33	18	1499	1499	NUM
ejpam-5232	33	19	where	where	SCONJ
ejpam-5232	33	20	φ(x	φ(x	NOUN
ejpam-5232	33	21	)	)	PUNCT
ejpam-5232	33	22	satisfies	satisfie	NOUN
ejpam-5232	33	23	lφ(x	lφ(x	NOUN
ejpam-5232	33	24	)	)	PUNCT
ejpam-5232	33	25	=	=	SYM
ejpam-5232	34	1	0	0	X
ejpam-5232	34	2	.	.	PUNCT
ejpam-5232	35	1	in	in	ADP
ejpam-5232	35	2	particular	particular	ADJ
ejpam-5232	35	3	,	,	PUNCT
ejpam-5232	35	4	since	since	SCONJ
ejpam-5232	35	5	we	we	PRON
ejpam-5232	35	6	are	be	AUX
ejpam-5232	35	7	considering	consider	VERB
ejpam-5232	35	8	a	a	DET
ejpam-5232	35	9	generalized	generalized	ADJ
ejpam-5232	35	10	second	second	ADJ
ejpam-5232	35	11	-	-	PUNCT
ejpam-5232	35	12	order	order	NOUN
ejpam-5232	35	13	nonlinear	nonlinear	ADJ
ejpam-5232	35	14	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	35	15	ode	ode	NOUN
ejpam-5232	35	16	,	,	PUNCT
ejpam-5232	35	17	let	let	VERB
ejpam-5232	35	18	us	we	PRON
ejpam-5232	35	19	consider	consider	VERB
ejpam-5232	35	20	the	the	DET
ejpam-5232	35	21	inverse	inverse	NOUN
ejpam-5232	35	22	operator	operator	NOUN
ejpam-5232	35	23	of	of	ADP
ejpam-5232	35	24	l	l	NOUN
ejpam-5232	35	25	to	to	PART
ejpam-5232	35	26	be	be	AUX
ejpam-5232	35	27	a	a	DET
ejpam-5232	35	28	two	two	NUM
ejpam-5232	35	29	-	-	PUNCT
ejpam-5232	35	30	fold	fold	ADJ
ejpam-5232	35	31	definite	definite	ADJ
ejpam-5232	35	32	integration	integration	NOUN
ejpam-5232	35	33	of	of	ADP
ejpam-5232	35	34	the	the	DET
ejpam-5232	35	35	form	form	NOUN
ejpam-5232	35	36	l−1	l−1	PROPN
ejpam-5232	35	37	(	(	PUNCT
ejpam-5232	35	38	.	.	PUNCT
ejpam-5232	35	39	)	)	PUNCT
ejpam-5232	36	1	=	=	SYM
ejpam-5232	37	1	∫	∫	PROPN
ejpam-5232	37	2	x	x	SYM
ejpam-5232	37	3	α1	α1	PROPN
ejpam-5232	37	4	∫	∫	PROPN
ejpam-5232	37	5	x	x	SYM
ejpam-5232	37	6	α1	α1	PROPN
ejpam-5232	37	7	(	(	PUNCT
ejpam-5232	37	8	.)dxdx	.)dxdx	NOUN
ejpam-5232	37	9	.	.	PUNCT
ejpam-5232	38	1	(	(	PUNCT
ejpam-5232	38	2	4	4	X
ejpam-5232	38	3	)	)	PUNCT
ejpam-5232	38	4	appling	appling	NOUN
ejpam-5232	38	5	l−1	l−1	PROPN
ejpam-5232	38	6	defined	define	VERB
ejpam-5232	38	7	above	above	ADV
ejpam-5232	38	8	to	to	ADP
ejpam-5232	38	9	all	all	DET
ejpam-5232	38	10	the	the	DET
ejpam-5232	38	11	parts	part	NOUN
ejpam-5232	38	12	of	of	ADP
ejpam-5232	38	13	eq	eq	PROPN
ejpam-5232	38	14	.	.	PUNCT
ejpam-5232	39	1	(	(	PUNCT
ejpam-5232	39	2	1	1	NUM
ejpam-5232	39	3	)	)	PUNCT
ejpam-5232	39	4	and	and	CCONJ
ejpam-5232	39	5	using	use	VERB
ejpam-5232	39	6	the	the	DET
ejpam-5232	39	7	boundary	boundary	ADJ
ejpam-5232	39	8	condition	condition	NOUN
ejpam-5232	39	9	u	u	PROPN
ejpam-5232	39	10	(	(	PUNCT
ejpam-5232	39	11	α1	α1	PROPN
ejpam-5232	39	12	)	)	PUNCT
ejpam-5232	39	13	=	=	SYM
ejpam-5232	39	14	β1	β1	PROPN
ejpam-5232	39	15	yields	yield	VERB
ejpam-5232	39	16	u(x	u(x	NOUN
ejpam-5232	39	17	)	)	PUNCT
ejpam-5232	39	18	=	=	SYM
ejpam-5232	39	19	u	u	SYM
ejpam-5232	39	20	(	(	PUNCT
ejpam-5232	39	21	α1	α1	PROPN
ejpam-5232	39	22	)	)	PUNCT
ejpam-5232	40	1	+	+	NUM
ejpam-5232	40	2	z	z	NOUN
ejpam-5232	40	3	(	(	PUNCT
ejpam-5232	40	4	x−	x−	PROPN
ejpam-5232	40	5	α1	α1	PROPN
ejpam-5232	40	6	)	)	PUNCT
ejpam-5232	40	7	+	+	CCONJ
ejpam-5232	40	8	l−1g(x)−	l−1g(x)−	PROPN
ejpam-5232	40	9	l−1ru−	l−1ru−	PROPN
ejpam-5232	40	10	l−1nu	l−1nu	NOUN
ejpam-5232	40	11	,	,	PUNCT
ejpam-5232	40	12	(	(	PUNCT
ejpam-5232	40	13	5	5	NUM
ejpam-5232	40	14	)	)	PUNCT
ejpam-5232	40	15	where	where	SCONJ
ejpam-5232	40	16	z	z	NOUN
ejpam-5232	40	17	=	=	SYM
ejpam-5232	40	18	u′	u′	PROPN
ejpam-5232	40	19	(	(	PUNCT
ejpam-5232	40	20	α1	α1	PROPN
ejpam-5232	40	21	)	)	PUNCT
ejpam-5232	40	22	.	.	PUNCT
ejpam-5232	41	1	next	next	ADV
ejpam-5232	41	2	,	,	PUNCT
ejpam-5232	41	3	by	by	ADP
ejpam-5232	41	4	decomposing	decompose	VERB
ejpam-5232	41	5	the	the	DET
ejpam-5232	41	6	solution	solution	NOUN
ejpam-5232	41	7	u	u	NOUN
ejpam-5232	41	8	and	and	CCONJ
ejpam-5232	41	9	the	the	DET
ejpam-5232	41	10	nonlinear	nonlinear	ADJ
ejpam-5232	41	11	term	term	NOUN
ejpam-5232	41	12	nu	nu	PROPN
ejpam-5232	41	13	to	to	ADP
ejpam-5232	41	14	series	series	NOUN
ejpam-5232	41	15	forms	form	NOUN
ejpam-5232	41	16	,	,	PUNCT
ejpam-5232	41	17	say	say	VERB
ejpam-5232	41	18	u	u	NOUN
ejpam-5232	41	19	=	=	PUNCT
ejpam-5232	41	20	∑∞	∑∞	X
ejpam-5232	41	21	n=0	n=0	NUM
ejpam-5232	41	22	un	un	NOUN
ejpam-5232	41	23	and	and	CCONJ
ejpam-5232	41	24	,	,	PUNCT
ejpam-5232	41	25	nu	nu	PROPN
ejpam-5232	41	26	=	=	PUNCT
ejpam-5232	41	27	∑∞	∑∞	NOUN
ejpam-5232	41	28	n=0an	n=0an	ADP
ejpam-5232	41	29	,	,	PUNCT
ejpam-5232	41	30	where	where	SCONJ
ejpam-5232	41	31	the	the	DET
ejpam-5232	41	32	components	component	NOUN
ejpam-5232	41	33	un(x	un(x	NOUN
ejpam-5232	41	34	)	)	PUNCT
ejpam-5232	41	35	,	,	PUNCT
ejpam-5232	41	36	n	n	PRON
ejpam-5232	41	37	≥	≥	NOUN
ejpam-5232	41	38	0	0	NUM
ejpam-5232	41	39	,	,	PUNCT
ejpam-5232	41	40	are	be	AUX
ejpam-5232	41	41	to	to	PART
ejpam-5232	41	42	be	be	AUX
ejpam-5232	41	43	determined	determine	VERB
ejpam-5232	41	44	in	in	ADP
ejpam-5232	41	45	a	a	DET
ejpam-5232	41	46	recursive	recursive	ADJ
ejpam-5232	41	47	manner	manner	NOUN
ejpam-5232	41	48	,	,	PUNCT
ejpam-5232	41	49	and	and	CCONJ
ejpam-5232	41	50	an	an	DET
ejpam-5232	41	51	’s	’s	NOUN
ejpam-5232	41	52	are	be	AUX
ejpam-5232	41	53	the	the	DET
ejpam-5232	41	54	adomian	adomian	NOUN
ejpam-5232	41	55	polynomials	polynomial	NOUN
ejpam-5232	41	56	that	that	PRON
ejpam-5232	41	57	take	take	VERB
ejpam-5232	41	58	care	care	NOUN
ejpam-5232	41	59	of	of	ADP
ejpam-5232	41	60	the	the	DET
ejpam-5232	41	61	nonlinear	nonlinear	ADJ
ejpam-5232	41	62	terms	term	NOUN
ejpam-5232	41	63	and	and	CCONJ
ejpam-5232	41	64	,	,	PUNCT
ejpam-5232	41	65	recurrently	recurrently	ADV
ejpam-5232	41	66	determined	determine	VERB
ejpam-5232	41	67	via	via	ADP
ejpam-5232	41	68	the	the	DET
ejpam-5232	41	69	following	follow	VERB
ejpam-5232	41	70	formula	formula	NOUN
ejpam-5232	41	71	[	[	X
ejpam-5232	41	72	2	2	NUM
ejpam-5232	41	73	,	,	PUNCT
ejpam-5232	41	74	3	3	NUM
ejpam-5232	41	75	,	,	PUNCT
ejpam-5232	41	76	7	7	NUM
ejpam-5232	41	77	,	,	PUNCT
ejpam-5232	41	78	8	8	NUM
ejpam-5232	41	79	,	,	PUNCT
ejpam-5232	41	80	11	11	NUM
ejpam-5232	41	81	,	,	PUNCT
ejpam-5232	41	82	24	24	NUM
ejpam-5232	41	83	]	]	PUNCT
ejpam-5232	41	84	an	an	DET
ejpam-5232	41	85	=	=	SYM
ejpam-5232	41	86	1	1	NUM
ejpam-5232	41	87	n	n	NOUN
ejpam-5232	41	88	!	!	PUNCT
ejpam-5232	42	1	dn	dn	PROPN
ejpam-5232	42	2	dλn	dλn	PROPN
ejpam-5232	43	1	[	[	PUNCT
ejpam-5232	43	2	n	n	PROPN
ejpam-5232	43	3	(	(	PUNCT
ejpam-5232	43	4	n∑	n∑	PROPN
ejpam-5232	43	5	i=0	i=0	PROPN
ejpam-5232	43	6	λiui	λiui	X
ejpam-5232	43	7	)	)	PUNCT
ejpam-5232	43	8	]	]	PUNCT
ejpam-5232	44	1	λ=0	λ=0	X
ejpam-5232	44	2	,	,	PUNCT
ejpam-5232	44	3	n	n	PROPN
ejpam-5232	44	4	=	=	SYM
ejpam-5232	44	5	0	0	NUM
ejpam-5232	44	6	,	,	PUNCT
ejpam-5232	44	7	1	1	NUM
ejpam-5232	44	8	,	,	PUNCT
ejpam-5232	44	9	2	2	NUM
ejpam-5232	44	10	,	,	PUNCT
ejpam-5232	44	11	.	.	PUNCT
ejpam-5232	44	12	.	.	PUNCT
ejpam-5232	44	13	.	.	PUNCT
ejpam-5232	45	1	(	(	PUNCT
ejpam-5232	45	2	6	6	NUM
ejpam-5232	45	3	)	)	PUNCT
ejpam-5232	45	4	and	and	CCONJ
ejpam-5232	45	5	thereafter	thereafter	ADV
ejpam-5232	45	6	substitute	substitute	VERB
ejpam-5232	45	7	them	they	PRON
ejpam-5232	45	8	into	into	ADP
ejpam-5232	45	9	the	the	DET
ejpam-5232	45	10	above	above	ADJ
ejpam-5232	45	11	equation	equation	NOUN
ejpam-5232	45	12	yields	yield	VERB
ejpam-5232	45	13	the	the	DET
ejpam-5232	45	14	following	follow	VERB
ejpam-5232	45	15	∞∑	∞∑	PROPN
ejpam-5232	45	16	n=0	n=0	NUM
ejpam-5232	45	17	un	un	NOUN
ejpam-5232	45	18	=	=	SYM
ejpam-5232	45	19	u	u	PROPN
ejpam-5232	45	20	(	(	PUNCT
ejpam-5232	45	21	α1	α1	PROPN
ejpam-5232	45	22	)	)	PUNCT
ejpam-5232	46	1	+	+	NUM
ejpam-5232	46	2	z	z	NOUN
ejpam-5232	46	3	(	(	PUNCT
ejpam-5232	46	4	x−	x−	PROPN
ejpam-5232	46	5	α1	α1	PROPN
ejpam-5232	46	6	)	)	PUNCT
ejpam-5232	46	7	+	+	CCONJ
ejpam-5232	46	8	l−1g(x)−	l−1g(x)−	PROPN
ejpam-5232	46	9	l−1r	l−1r	PROPN
ejpam-5232	46	10	(	(	PUNCT
ejpam-5232	46	11	∞∑	∞∑	PROPN
ejpam-5232	46	12	n=0	n=0	NUM
ejpam-5232	46	13	un	un	NOUN
ejpam-5232	46	14	)	)	PUNCT
ejpam-5232	47	1	−	−	PROPN
ejpam-5232	47	2	l−1	l−1	PROPN
ejpam-5232	47	3	(	(	PUNCT
ejpam-5232	47	4	∞∑	∞∑	PROPN
ejpam-5232	47	5	n=0	n=0	PROPN
ejpam-5232	47	6	an	an	PRON
ejpam-5232	47	7	)	)	PUNCT
ejpam-5232	47	8	,	,	PUNCT
ejpam-5232	47	9	(	(	PUNCT
ejpam-5232	47	10	7	7	X
ejpam-5232	47	11	)	)	PUNCT
ejpam-5232	47	12	more	more	ADV
ejpam-5232	47	13	so	so	ADV
ejpam-5232	47	14	,	,	PUNCT
ejpam-5232	47	15	the	the	DET
ejpam-5232	47	16	adm	adm	PROPN
ejpam-5232	47	17	identifies	identify	VERB
ejpam-5232	47	18	the	the	DET
ejpam-5232	47	19	zeroth	zeroth	PROPN
ejpam-5232	47	20	component	component	NOUN
ejpam-5232	47	21	u0(x	u0(x	NOUN
ejpam-5232	47	22	)	)	PUNCT
ejpam-5232	47	23	with	with	ADP
ejpam-5232	47	24	the	the	DET
ejpam-5232	47	25	terms	term	NOUN
ejpam-5232	47	26	emanating	emanate	VERB
ejpam-5232	47	27	from	from	ADP
ejpam-5232	47	28	the	the	DET
ejpam-5232	47	29	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	47	30	term	term	NOUN
ejpam-5232	47	31	and	and	CCONJ
ejpam-5232	47	32	boundary	boundary	ADJ
ejpam-5232	47	33	conditions	condition	NOUN
ejpam-5232	47	34	,	,	PUNCT
ejpam-5232	47	35	and	and	CCONJ
ejpam-5232	47	36	the	the	DET
ejpam-5232	47	37	rest	rest	NOUN
ejpam-5232	47	38	follows	follow	VERB
ejpam-5232	47	39	recurrently	recurrently	ADV
ejpam-5232	47	40	as	as	SCONJ
ejpam-5232	47	41	given	give	VERB
ejpam-5232	47	42	in	in	ADP
ejpam-5232	47	43	the	the	DET
ejpam-5232	47	44	following	follow	VERB
ejpam-5232	47	45	recurrence	recurrence	NOUN
ejpam-5232	47	46	relation	relation	PROPN
ejpam-5232	47	47	{	{	PUNCT
ejpam-5232	47	48	u0(x	u0(x	NOUN
ejpam-5232	47	49	)	)	PUNCT
ejpam-5232	47	50	=	=	SYM
ejpam-5232	47	51	u	u	SYM
ejpam-5232	47	52	(	(	PUNCT
ejpam-5232	47	53	α1	α1	PROPN
ejpam-5232	47	54	)	)	PUNCT
ejpam-5232	48	1	+	+	NUM
ejpam-5232	48	2	z	z	NOUN
ejpam-5232	48	3	(	(	PUNCT
ejpam-5232	48	4	x−	x−	PROPN
ejpam-5232	48	5	α1	α1	PROPN
ejpam-5232	48	6	)	)	PUNCT
ejpam-5232	48	7	+	+	CCONJ
ejpam-5232	48	8	l−1g(x	l−1g(x	ADJ
ejpam-5232	48	9	)	)	PUNCT
ejpam-5232	48	10	,	,	PUNCT
ejpam-5232	48	11	un+1(x	un+1(x	PROPN
ejpam-5232	48	12	)	)	PUNCT
ejpam-5232	48	13	=	=	PRON
ejpam-5232	48	14	−l−1run	−l−1run	VERB
ejpam-5232	48	15	−	−	NOUN
ejpam-5232	48	16	l−1an	l−1an	NOUN
ejpam-5232	48	17	,	,	PUNCT
ejpam-5232	48	18	n	n	X
ejpam-5232	48	19	≥	≥	NOUN
ejpam-5232	48	20	0	0	NUM
ejpam-5232	48	21	.	.	PUNCT
ejpam-5232	49	1	(	(	PUNCT
ejpam-5232	49	2	8)	8)	NUM
ejpam-5232	49	3	the	the	DET
ejpam-5232	49	4	recurrence	recurrence	NOUN
ejpam-5232	49	5	relation	relation	NOUN
ejpam-5232	49	6	or	or	CCONJ
ejpam-5232	49	7	procedure	procedure	NOUN
ejpam-5232	49	8	could	could	AUX
ejpam-5232	49	9	be	be	AUX
ejpam-5232	49	10	carried	carry	VERB
ejpam-5232	49	11	out	out	ADP
ejpam-5232	49	12	to	to	PART
ejpam-5232	49	13	calculate	calculate	VERB
ejpam-5232	49	14	as	as	ADV
ejpam-5232	49	15	many	many	ADJ
ejpam-5232	49	16	components	component	NOUN
ejpam-5232	49	17	as	as	SCONJ
ejpam-5232	49	18	we	we	PRON
ejpam-5232	49	19	like	like	VERB
ejpam-5232	49	20	.	.	PUNCT
ejpam-5232	50	1	furthermore	furthermore	ADV
ejpam-5232	50	2	,	,	PUNCT
ejpam-5232	50	3	using	use	VERB
ejpam-5232	50	4	the	the	DET
ejpam-5232	50	5	second	second	ADJ
ejpam-5232	50	6	boundary	boundary	ADJ
ejpam-5232	50	7	condition	condition	NOUN
ejpam-5232	50	8	u	u	NOUN
ejpam-5232	50	9	(	(	PUNCT
ejpam-5232	50	10	α2	α2	PROPN
ejpam-5232	50	11	)	)	PUNCT
ejpam-5232	50	12	=	=	VERB
ejpam-5232	51	1	β2	β2	VERB
ejpam-5232	51	2	in	in	ADP
ejpam-5232	51	3	the	the	DET
ejpam-5232	51	4	obtained	obtain	VERB
ejpam-5232	51	5	series	series	NOUN
ejpam-5232	51	6	solution	solution	NOUN
ejpam-5232	51	7	and	and	CCONJ
ejpam-5232	51	8	comparing	compare	VERB
ejpam-5232	51	9	coefficients	coefficient	NOUN
ejpam-5232	51	10	of	of	ADP
ejpam-5232	51	11	like	like	ADP
ejpam-5232	51	12	powers	power	NOUN
ejpam-5232	51	13	of	of	ADP
ejpam-5232	51	14	x	x	PRON
ejpam-5232	51	15	leads	lead	VERB
ejpam-5232	51	16	to	to	ADP
ejpam-5232	51	17	the	the	DET
ejpam-5232	51	18	determination	determination	NOUN
ejpam-5232	51	19	of	of	ADP
ejpam-5232	51	20	z.	z.	PROPN
ejpam-5232	51	21	moreover	moreover	ADV
ejpam-5232	51	22	,	,	PUNCT
ejpam-5232	51	23	in	in	ADP
ejpam-5232	51	24	many	many	ADJ
ejpam-5232	51	25	bvps	bvps	NOUN
ejpam-5232	51	26	of	of	ADP
ejpam-5232	51	27	exact	exact	ADJ
ejpam-5232	51	28	solutions	solution	NOUN
ejpam-5232	51	29	,	,	PUNCT
ejpam-5232	51	30	the	the	DET
ejpam-5232	51	31	obtained	obtain	VERB
ejpam-5232	51	32	series	series	NOUN
ejpam-5232	51	33	provides	provide	VERB
ejpam-5232	51	34	the	the	DET
ejpam-5232	51	35	solution	solution	NOUN
ejpam-5232	51	36	in	in	ADP
ejpam-5232	51	37	a	a	DET
ejpam-5232	51	38	closed	closed	ADJ
ejpam-5232	51	39	-	-	PUNCT
ejpam-5232	51	40	form	form	NOUN
ejpam-5232	51	41	.	.	PUNCT
ejpam-5232	52	1	3	3	X
ejpam-5232	52	2	.	.	X
ejpam-5232	52	3	adomian	adomian	NOUN
ejpam-5232	52	4	chebyshev	chebyshev	NOUN
ejpam-5232	52	5	decomposition	decomposition	NOUN
ejpam-5232	52	6	method	method	NOUN
ejpam-5232	52	7	(	(	PUNCT
ejpam-5232	52	8	acdm	acdm	ADJ
ejpam-5232	52	9	)	)	PUNCT
ejpam-5232	52	10	for	for	ADP
ejpam-5232	52	11	bvps	bvps	NOUN
ejpam-5232	52	12	here	here	ADV
ejpam-5232	52	13	,	,	PUNCT
ejpam-5232	52	14	we	we	PRON
ejpam-5232	52	15	present	present	VERB
ejpam-5232	52	16	the	the	DET
ejpam-5232	52	17	methodology	methodology	NOUN
ejpam-5232	52	18	as	as	ADP
ejpam-5232	52	19	the	the	DET
ejpam-5232	52	20	mixture	mixture	NOUN
ejpam-5232	52	21	of	of	ADP
ejpam-5232	52	22	the	the	DET
ejpam-5232	52	23	adm	adm	PROPN
ejpam-5232	52	24	and	and	CCONJ
ejpam-5232	52	25	,	,	PUNCT
ejpam-5232	52	26	the	the	DET
ejpam-5232	52	27	chebyshev	chebyshev	NOUN
ejpam-5232	52	28	polynomials	polynomial	NOUN
ejpam-5232	52	29	.	.	PUNCT
ejpam-5232	53	1	in	in	ADP
ejpam-5232	53	2	numerical	numerical	ADJ
ejpam-5232	53	3	analysis	analysis	NOUN
ejpam-5232	53	4	,	,	PUNCT
ejpam-5232	53	5	it	it	PRON
ejpam-5232	53	6	is	be	AUX
ejpam-5232	53	7	often	often	ADV
ejpam-5232	53	8	important	important	ADJ
ejpam-5232	53	9	to	to	PART
ejpam-5232	53	10	find	find	VERB
ejpam-5232	53	11	the	the	DET
ejpam-5232	53	12	polynomials	polynomial	NOUN
ejpam-5232	53	13	pn	pn	VERB
ejpam-5232	53	14	,	,	PUNCT
ejpam-5232	53	15	of	of	ADP
ejpam-5232	53	16	specified	specify	VERB
ejpam-5232	53	17	h.	h.	PROPN
ejpam-5232	53	18	bakodah	bakodah	PROPN
ejpam-5232	53	19	et	et	PROPN
ejpam-5232	53	20	al	al	PROPN
ejpam-5232	53	21	.	.	PUNCT
ejpam-5232	53	22	/	/	SYM
ejpam-5232	53	23	eur	eur	PROPN
ejpam-5232	53	24	.	.	PUNCT
ejpam-5232	54	1	j.	j.	PROPN
ejpam-5232	54	2	pure	pure	PROPN
ejpam-5232	54	3	appl	appl	PROPN
ejpam-5232	54	4	.	.	PROPN
ejpam-5232	54	5	math	math	PROPN
ejpam-5232	54	6	,	,	PUNCT
ejpam-5232	54	7	17	17	NUM
ejpam-5232	54	8	(	(	PUNCT
ejpam-5232	54	9	3	3	NUM
ejpam-5232	54	10	)	)	PUNCT
ejpam-5232	54	11	(	(	PUNCT
ejpam-5232	54	12	2024	2024	NUM
ejpam-5232	54	13	)	)	PUNCT
ejpam-5232	54	14	,	,	PUNCT
ejpam-5232	54	15	1497	1497	NUM
ejpam-5232	54	16	-	-	SYM
ejpam-5232	54	17	1515	1515	NUM
ejpam-5232	54	18	1500	1500	NUM
ejpam-5232	54	19	maximum	maximum	NOUN
ejpam-5232	54	20	degree	degree	NOUN
ejpam-5232	54	21	n	n	CCONJ
ejpam-5232	54	22	,	,	PUNCT
ejpam-5232	54	23	such	such	ADJ
ejpam-5232	54	24	that	that	SCONJ
ejpam-5232	54	25	,	,	PUNCT
ejpam-5232	54	26	for	for	ADP
ejpam-5232	54	27	a	a	DET
ejpam-5232	54	28	function	function	NOUN
ejpam-5232	54	29	f(x	f(x	PROPN
ejpam-5232	54	30	)	)	PUNCT
ejpam-5232	54	31	on	on	ADP
ejpam-5232	54	32	the	the	DET
ejpam-5232	54	33	interval	interval	NOUN
ejpam-5232	54	34	[	[	X
ejpam-5232	54	35	a	a	X
ejpam-5232	54	36	,	,	PUNCT
ejpam-5232	54	37	b	b	NOUN
ejpam-5232	54	38	]	]	X
ejpam-5232	54	39	,	,	PUNCT
ejpam-5232	54	40	|f(x)−	|f(x)−	NOUN
ejpam-5232	54	41	pn(x)|	pn(x)|	NOUN
ejpam-5232	54	42	has	have	VERB
ejpam-5232	54	43	as	as	ADV
ejpam-5232	54	44	small	small	ADJ
ejpam-5232	54	45	maximum	maximum	ADJ
ejpam-5232	54	46	value	value	NOUN
ejpam-5232	54	47	over	over	ADP
ejpam-5232	54	48	[	[	X
ejpam-5232	54	49	a	a	DET
ejpam-5232	54	50	,	,	PUNCT
ejpam-5232	54	51	b	b	NOUN
ejpam-5232	54	52	]	]	PUNCT
ejpam-5232	54	53	as	as	ADP
ejpam-5232	54	54	possible	possible	ADJ
ejpam-5232	54	55	.	.	PUNCT
ejpam-5232	55	1	usually	usually	ADV
ejpam-5232	55	2	,	,	PUNCT
ejpam-5232	55	3	this	this	DET
ejpam-5232	55	4	polynomials	polynomial	NOUN
ejpam-5232	55	5	pn	pn	NOUN
ejpam-5232	55	6	is	be	AUX
ejpam-5232	55	7	rather	rather	ADV
ejpam-5232	55	8	difficult	difficult	ADJ
ejpam-5232	55	9	to	to	PART
ejpam-5232	55	10	find	find	VERB
ejpam-5232	55	11	,	,	PUNCT
ejpam-5232	55	12	but	but	CCONJ
ejpam-5232	55	13	a	a	DET
ejpam-5232	55	14	very	very	ADV
ejpam-5232	55	15	good	good	ADJ
ejpam-5232	55	16	approximation	approximation	NOUN
ejpam-5232	55	17	to	to	ADP
ejpam-5232	55	18	pn	pn	PROPN
ejpam-5232	55	19	can	can	AUX
ejpam-5232	55	20	be	be	AUX
ejpam-5232	55	21	found	find	VERB
ejpam-5232	55	22	with	with	ADP
ejpam-5232	55	23	relative	relative	ADJ
ejpam-5232	55	24	easily	easily	ADV
ejpam-5232	55	25	.	.	PUNCT
ejpam-5232	56	1	this	this	DET
ejpam-5232	56	2	approximation	approximation	NOUN
ejpam-5232	56	3	takes	take	VERB
ejpam-5232	56	4	the	the	DET
ejpam-5232	56	5	form	form	NOUN
ejpam-5232	56	6	of	of	ADP
ejpam-5232	56	7	a	a	DET
ejpam-5232	56	8	linear	linear	ADJ
ejpam-5232	56	9	combination	combination	NOUN
ejpam-5232	56	10	of	of	ADP
ejpam-5232	56	11	a	a	DET
ejpam-5232	56	12	special	special	ADJ
ejpam-5232	56	13	group	group	NOUN
ejpam-5232	56	14	of	of	ADP
ejpam-5232	56	15	polynomials	polynomial	NOUN
ejpam-5232	56	16	that	that	PRON
ejpam-5232	56	17	are	be	AUX
ejpam-5232	56	18	named	name	VERB
ejpam-5232	56	19	after	after	ADP
ejpam-5232	56	20	the	the	DET
ejpam-5232	56	21	prolific	prolific	ADJ
ejpam-5232	56	22	mathematician	mathematician	PROPN
ejpam-5232	56	23	pafnuty	pafnuty	PROPN
ejpam-5232	56	24	lvovich	lvovich	PROPN
ejpam-5232	56	25	chebyshev	chebyshev	PROPN
ejpam-5232	56	26	(	(	PUNCT
ejpam-5232	56	27	1821	1821	NUM
ejpam-5232	56	28	-	-	SYM
ejpam-5232	56	29	1894	1894	NUM
ejpam-5232	56	30	)	)	PUNCT
ejpam-5232	56	31	.	.	PUNCT
ejpam-5232	57	1	definition	definition	NOUN
ejpam-5232	57	2	1	1	NUM
ejpam-5232	57	3	.	.	PUNCT
ejpam-5232	58	1	[	[	X
ejpam-5232	58	2	14	14	NUM
ejpam-5232	58	3	]	]	X
ejpam-5232	58	4	(	(	PUNCT
ejpam-5232	58	5	1	1	NUM
ejpam-5232	58	6	)	)	PUNCT
ejpam-5232	58	7	.	.	PUNCT
ejpam-5232	59	1	the	the	DET
ejpam-5232	59	2	chebyshev	chebyshev	NOUN
ejpam-5232	59	3	polynomials	polynomial	NOUN
ejpam-5232	59	4	of	of	ADP
ejpam-5232	59	5	the	the	DET
ejpam-5232	59	6	first	first	ADJ
ejpam-5232	59	7	kind	kind	NOUN
ejpam-5232	59	8	are	be	AUX
ejpam-5232	59	9	defined	define	VERB
ejpam-5232	59	10	as	as	ADP
ejpam-5232	59	11	tn(x	tn(x	PUNCT
ejpam-5232	59	12	)	)	PUNCT
ejpam-5232	59	13	=	=	SYM
ejpam-5232	59	14	cosnθ	cosnθ	PROPN
ejpam-5232	59	15	,	,	PUNCT
ejpam-5232	59	16	x	x	PROPN
ejpam-5232	59	17	=	=	PUNCT
ejpam-5232	59	18	cos	cos	PROPN
ejpam-5232	59	19	θ	θ	PROPN
ejpam-5232	59	20	,	,	PUNCT
ejpam-5232	59	21	−1	−1	NOUN
ejpam-5232	59	22	≤	≤	NUM
ejpam-5232	59	23	x	x	PUNCT
ejpam-5232	59	24	≤	≤	NUM
ejpam-5232	59	25	1	1	NUM
ejpam-5232	59	26	,	,	PUNCT
ejpam-5232	59	27	n	n	NOUN
ejpam-5232	59	28	=	=	SYM
ejpam-5232	59	29	0	0	NUM
ejpam-5232	59	30	,	,	PUNCT
ejpam-5232	59	31	1	1	NUM
ejpam-5232	59	32	,	,	PUNCT
ejpam-5232	59	33	2	2	NUM
ejpam-5232	59	34	,	,	PUNCT
ejpam-5232	59	35	.	.	PUNCT
ejpam-5232	59	36	.	.	PUNCT
ejpam-5232	59	37	.	.	PUNCT
ejpam-5232	60	1	(	(	PUNCT
ejpam-5232	60	2	9	9	NUM
ejpam-5232	60	3	)	)	PUNCT
ejpam-5232	60	4	(	(	PUNCT
ejpam-5232	60	5	2	2	NUM
ejpam-5232	60	6	)	)	PUNCT
ejpam-5232	60	7	.	.	PUNCT
ejpam-5232	61	1	the	the	DET
ejpam-5232	61	2	chebyshev	chebyshev	NOUN
ejpam-5232	61	3	polynomials	polynomial	NOUN
ejpam-5232	61	4	of	of	ADP
ejpam-5232	61	5	the	the	DET
ejpam-5232	61	6	second	second	ADJ
ejpam-5232	61	7	kind	kind	NOUN
ejpam-5232	61	8	are	be	AUX
ejpam-5232	61	9	defined	define	VERB
ejpam-5232	61	10	as	as	ADP
ejpam-5232	61	11	un(x	un(x	NOUN
ejpam-5232	61	12	)	)	PUNCT
ejpam-5232	61	13	=	=	SYM
ejpam-5232	61	14	sin[(n+	sin[(n+	PROPN
ejpam-5232	61	15	1)θ	1)θ	NUM
ejpam-5232	61	16	]	]	X
ejpam-5232	61	17	sin	sin	NOUN
ejpam-5232	61	18	θ	θ	PROPN
ejpam-5232	61	19	,	,	PUNCT
ejpam-5232	61	20	x	x	PROPN
ejpam-5232	61	21	=	=	PUNCT
ejpam-5232	61	22	cos	cos	PROPN
ejpam-5232	61	23	θ	θ	PROPN
ejpam-5232	61	24	,	,	PUNCT
ejpam-5232	61	25	−1	−1	NOUN
ejpam-5232	61	26	≤	≤	NUM
ejpam-5232	61	27	x	x	PUNCT
ejpam-5232	61	28	≤	≤	NUM
ejpam-5232	61	29	1	1	NUM
ejpam-5232	61	30	,	,	PUNCT
ejpam-5232	61	31	n	n	NOUN
ejpam-5232	61	32	=	=	SYM
ejpam-5232	61	33	0	0	NUM
ejpam-5232	61	34	,	,	PUNCT
ejpam-5232	61	35	1	1	NUM
ejpam-5232	61	36	,	,	PUNCT
ejpam-5232	61	37	2	2	NUM
ejpam-5232	61	38	,	,	PUNCT
ejpam-5232	61	39	.	.	PUNCT
ejpam-5232	61	40	.	.	PUNCT
ejpam-5232	61	41	.	.	PUNCT
ejpam-5232	62	1	(	(	PUNCT
ejpam-5232	62	2	10	10	NUM
ejpam-5232	62	3	)	)	PUNCT
ejpam-5232	62	4	it	it	PRON
ejpam-5232	62	5	may	may	AUX
ejpam-5232	62	6	be	be	AUX
ejpam-5232	62	7	instantly	instantly	ADV
ejpam-5232	62	8	obvious	obvious	ADJ
ejpam-5232	62	9	from	from	ADP
ejpam-5232	62	10	the	the	DET
ejpam-5232	62	11	above	above	ADJ
ejpam-5232	62	12	definitions	definition	NOUN
ejpam-5232	62	13	that	that	PRON
ejpam-5232	62	14	chebyshev	chebyshev	PROPN
ejpam-5232	62	15	polynomials	polynomial	NOUN
ejpam-5232	62	16	are	be	AUX
ejpam-5232	62	17	indeed	indeed	ADV
ejpam-5232	62	18	polynomials	polynomial	NOUN
ejpam-5232	62	19	.	.	PUNCT
ejpam-5232	63	1	therefore	therefore	ADV
ejpam-5232	63	2	,	,	PUNCT
ejpam-5232	63	3	note	note	VERB
ejpam-5232	63	4	that	that	SCONJ
ejpam-5232	63	5	the	the	DET
ejpam-5232	63	6	trigonometric	trigonometric	ADJ
ejpam-5232	63	7	identity	identity	NOUN
ejpam-5232	63	8	,	,	PUNCT
ejpam-5232	63	9	cos[(n+	cos[(n+	NOUN
ejpam-5232	63	10	1)θ	1)θ	NUM
ejpam-5232	63	11	]	]	X
ejpam-5232	63	12	+	+	CCONJ
ejpam-5232	63	13	cos[(n−	cos[(n−	VERB
ejpam-5232	63	14	1)θ	1)θ	NUM
ejpam-5232	63	15	]	]	X
ejpam-5232	63	16	=	=	SYM
ejpam-5232	63	17	2	2	NUM
ejpam-5232	63	18	cos	cos	PROPN
ejpam-5232	63	19	θ	θ	PROPN
ejpam-5232	63	20	cosnθ	cosnθ	NOUN
ejpam-5232	63	21	,	,	PUNCT
ejpam-5232	63	22	(	(	PUNCT
ejpam-5232	63	23	11	11	NUM
ejpam-5232	63	24	)	)	PUNCT
ejpam-5232	63	25	supplies	supply	VERB
ejpam-5232	63	26	a	a	DET
ejpam-5232	63	27	recurrence	recurrence	NOUN
ejpam-5232	63	28	relation	relation	NOUN
ejpam-5232	63	29	for	for	ADP
ejpam-5232	63	30	the	the	DET
ejpam-5232	63	31	functions	function	NOUN
ejpam-5232	63	32	as	as	ADP
ejpam-5232	63	33	,	,	PUNCT
ejpam-5232	63	34	tn(x	tn(x	PUNCT
ejpam-5232	63	35	)	)	PUNCT
ejpam-5232	63	36	=	=	SYM
ejpam-5232	63	37	cosnθ	cosnθ	PROPN
ejpam-5232	63	38	,	,	PUNCT
ejpam-5232	63	39	(	(	PUNCT
ejpam-5232	63	40	12	12	NUM
ejpam-5232	63	41	)	)	PUNCT
ejpam-5232	63	42	tn+1(x	tn+1(x	NUM
ejpam-5232	63	43	)	)	PUNCT
ejpam-5232	64	1	+	+	CCONJ
ejpam-5232	64	2	tn−1(x	tn−1(x	NOUN
ejpam-5232	64	3	)	)	PUNCT
ejpam-5232	64	4	=	=	SYM
ejpam-5232	65	1	2xtn(x	2xtn(x	NUM
ejpam-5232	65	2	)	)	PUNCT
ejpam-5232	65	3	,	,	PUNCT
ejpam-5232	65	4	(	(	PUNCT
ejpam-5232	65	5	13	13	NUM
ejpam-5232	65	6	)	)	PUNCT
ejpam-5232	65	7	or	or	CCONJ
ejpam-5232	65	8	equally	equally	ADV
ejpam-5232	65	9	expressed	express	VERB
ejpam-5232	65	10	as	as	ADP
ejpam-5232	65	11	tn+1(x	tn+1(x	NUM
ejpam-5232	65	12	)	)	PUNCT
ejpam-5232	65	13	=	=	SYM
ejpam-5232	66	1	2xtn(x)−	2xtn(x)−	NUM
ejpam-5232	66	2	tn−1(x	tn−1(x	NOUN
ejpam-5232	66	3	)	)	PUNCT
ejpam-5232	66	4	.	.	PUNCT
ejpam-5232	67	1	(	(	PUNCT
ejpam-5232	67	2	14	14	NUM
ejpam-5232	67	3	)	)	PUNCT
ejpam-5232	67	4	since	since	SCONJ
ejpam-5232	67	5	t0(x	t0(x	NOUN
ejpam-5232	67	6	)	)	PUNCT
ejpam-5232	67	7	=	=	SYM
ejpam-5232	67	8	cos	cos	ADP
ejpam-5232	67	9	0	0	NUM
ejpam-5232	67	10	=	=	SYM
ejpam-5232	67	11	1	1	NUM
ejpam-5232	67	12	and	and	CCONJ
ejpam-5232	67	13	t1(x	t1(x	NOUN
ejpam-5232	67	14	)	)	PUNCT
ejpam-5232	68	1	=	=	PUNCT
ejpam-5232	68	2	cos	co	NOUN
ejpam-5232	68	3	θ	θ	PROPN
ejpam-5232	68	4	=	=	SYM
ejpam-5232	68	5	x	x	X
ejpam-5232	68	6	,	,	PUNCT
ejpam-5232	68	7	eq	eq	NOUN
ejpam-5232	68	8	.	.	PUNCT
ejpam-5232	69	1	(	(	PUNCT
ejpam-5232	69	2	14	14	NUM
ejpam-5232	69	3	)	)	PUNCT
ejpam-5232	69	4	can	can	AUX
ejpam-5232	69	5	be	be	AUX
ejpam-5232	69	6	used	use	VERB
ejpam-5232	69	7	to	to	PART
ejpam-5232	69	8	generate	generate	VERB
ejpam-5232	69	9	any	any	DET
ejpam-5232	69	10	number	number	NOUN
ejpam-5232	69	11	of	of	ADP
ejpam-5232	69	12	the	the	DET
ejpam-5232	69	13	tn(x	tn(x	NOUN
ejpam-5232	69	14	)	)	PUNCT
ejpam-5232	69	15	in	in	ADP
ejpam-5232	69	16	their	their	PRON
ejpam-5232	69	17	specific	specific	ADJ
ejpam-5232	69	18	polynomial	polynomial	ADJ
ejpam-5232	69	19	forms	form	NOUN
ejpam-5232	69	20	as	as	ADP
ejpam-5232	69	21	t2(x	t2(x	NOUN
ejpam-5232	69	22	)	)	PUNCT
ejpam-5232	69	23	=	=	SYM
ejpam-5232	70	1	2x2	2x2	NUM
ejpam-5232	70	2	−	−	NUM
ejpam-5232	70	3	1	1	NUM
ejpam-5232	70	4	,	,	PUNCT
ejpam-5232	70	5	t3(x	t3(x	PROPN
ejpam-5232	70	6	)	)	PUNCT
ejpam-5232	70	7	=	=	SYM
ejpam-5232	70	8	4x3	4x3	NUM
ejpam-5232	70	9	−	−	NUM
ejpam-5232	70	10	3x	3x	NUM
ejpam-5232	70	11	,	,	PUNCT
ejpam-5232	70	12	t4(x	t4(x	NUM
ejpam-5232	70	13	)	)	PUNCT
ejpam-5232	70	14	=	=	SYM
ejpam-5232	70	15	8x4	8x4	NUM
ejpam-5232	71	1	−	−	NOUN
ejpam-5232	71	2	8x2	8x2	NUM
ejpam-5232	71	3	+	+	CCONJ
ejpam-5232	71	4	1	1	NUM
ejpam-5232	71	5	,	,	PUNCT
ejpam-5232	71	6	t5(x	t5(x	NUM
ejpam-5232	71	7	)	)	PUNCT
ejpam-5232	71	8	=	=	PUNCT
ejpam-5232	72	1	16x5	16x5	NUM
ejpam-5232	72	2	−	−	NUM
ejpam-5232	72	3	20x3	20x3	NUM
ejpam-5232	72	4	+	+	CCONJ
ejpam-5232	72	5	5x	5x	NUM
ejpam-5232	72	6	,	,	PUNCT
ejpam-5232	72	7	...	...	PUNCT
ejpam-5232	72	8	(	(	PUNCT
ejpam-5232	72	9	15	15	NUM
ejpam-5232	72	10	)	)	PUNCT
ejpam-5232	72	11	besides	besides	SCONJ
ejpam-5232	72	12	,	,	PUNCT
ejpam-5232	72	13	many	many	ADJ
ejpam-5232	72	14	mathematical	mathematical	ADJ
ejpam-5232	72	15	techniques	technique	NOUN
ejpam-5232	72	16	have	have	AUX
ejpam-5232	72	17	been	be	AUX
ejpam-5232	72	18	devised	devise	VERB
ejpam-5232	72	19	based	base	VERB
ejpam-5232	72	20	on	on	ADP
ejpam-5232	72	21	the	the	DET
ejpam-5232	72	22	chebyshev	chebyshev	NOUN
ejpam-5232	72	23	polynomials	polynomial	NOUN
ejpam-5232	72	24	to	to	PART
ejpam-5232	72	25	treat	treat	VERB
ejpam-5232	72	26	different	different	ADJ
ejpam-5232	72	27	types	type	NOUN
ejpam-5232	72	28	of	of	ADP
ejpam-5232	72	29	functional	functional	ADJ
ejpam-5232	72	30	equations	equation	NOUN
ejpam-5232	72	31	;	;	PUNCT
ejpam-5232	72	32	more	more	ADV
ejpam-5232	72	33	especially	especially	ADV
ejpam-5232	72	34	,	,	PUNCT
ejpam-5232	72	35	with	with	ADP
ejpam-5232	72	36	regards	regard	NOUN
ejpam-5232	72	37	to	to	ADP
ejpam-5232	72	38	its	its	PRON
ejpam-5232	72	39	discrete	discrete	ADJ
ejpam-5232	72	40	orthogonality	orthogonality	NOUN
ejpam-5232	72	41	relations	relation	NOUN
ejpam-5232	72	42	which	which	PRON
ejpam-5232	72	43	were	be	AUX
ejpam-5232	72	44	found	find	VERB
ejpam-5232	72	45	to	to	PART
ejpam-5232	72	46	have	have	VERB
ejpam-5232	72	47	considerable	considerable	ADJ
ejpam-5232	72	48	advantages	advantage	NOUN
ejpam-5232	72	49	.	.	PUNCT
ejpam-5232	73	1	for	for	ADP
ejpam-5232	73	2	instance	instance	NOUN
ejpam-5232	73	3	,	,	PUNCT
ejpam-5232	73	4	hoseini	hoseini	NOUN
ejpam-5232	73	5	[	[	X
ejpam-5232	73	6	19	19	NUM
ejpam-5232	73	7	]	]	PUNCT
ejpam-5232	73	8	presented	present	VERB
ejpam-5232	73	9	a	a	DET
ejpam-5232	73	10	promising	promising	ADJ
ejpam-5232	73	11	modification	modification	NOUN
ejpam-5232	73	12	of	of	ADP
ejpam-5232	73	13	the	the	DET
ejpam-5232	73	14	adm	adm	NOUN
ejpam-5232	73	15	through	through	ADP
ejpam-5232	73	16	the	the	DET
ejpam-5232	73	17	application	application	NOUN
ejpam-5232	73	18	of	of	ADP
ejpam-5232	73	19	the	the	DET
ejpam-5232	73	20	chebyshev	chebyshev	NOUN
ejpam-5232	73	21	polynomials	polynomial	NOUN
ejpam-5232	73	22	to	to	PART
ejpam-5232	73	23	solve	solve	VERB
ejpam-5232	73	24	initial	initial	ADJ
ejpam-5232	73	25	value	value	NOUN
ejpam-5232	73	26	problems	problem	NOUN
ejpam-5232	73	27	.	.	PUNCT
ejpam-5232	74	1	moreover	moreover	ADV
ejpam-5232	74	2	,	,	PUNCT
ejpam-5232	74	3	we	we	PRON
ejpam-5232	74	4	shall	shall	AUX
ejpam-5232	74	5	expand	expand	VERB
ejpam-5232	74	6	the	the	DET
ejpam-5232	74	7	work	work	NOUN
ejpam-5232	74	8	done	do	VERB
ejpam-5232	74	9	in	in	ADP
ejpam-5232	74	10	[	[	X
ejpam-5232	74	11	19	19	NUM
ejpam-5232	74	12	]	]	PUNCT
ejpam-5232	74	13	by	by	ADP
ejpam-5232	74	14	performing	perform	VERB
ejpam-5232	74	15	approximations	approximation	NOUN
ejpam-5232	74	16	using	use	VERB
ejpam-5232	74	17	chebyshev	chebyshev	NOUN
ejpam-5232	74	18	polynomials	polynomial	NOUN
ejpam-5232	74	19	with	with	ADP
ejpam-5232	74	20	fractional	fractional	ADJ
ejpam-5232	74	21	function	function	NOUN
ejpam-5232	74	22	as	as	ADP
ejpam-5232	74	23	in	in	ADP
ejpam-5232	74	24	the	the	DET
ejpam-5232	74	25	padé	padé	ADJ
ejpam-5232	74	26	method	method	NOUN
ejpam-5232	74	27	[	[	X
ejpam-5232	74	28	9	9	NUM
ejpam-5232	74	29	]	]	PUNCT
ejpam-5232	74	30	,	,	PUNCT
ejpam-5232	74	31	but	but	CCONJ
ejpam-5232	74	32	except	except	SCONJ
ejpam-5232	74	33	by	by	ADP
ejpam-5232	74	34	replacing	replace	VERB
ejpam-5232	74	35	each	each	DET
ejpam-5232	74	36	term	term	NOUN
ejpam-5232	74	37	of	of	ADP
ejpam-5232	74	38	h.	h.	PROPN
ejpam-5232	74	39	bakodah	bakodah	PROPN
ejpam-5232	74	40	et	et	PROPN
ejpam-5232	74	41	al	al	PROPN
ejpam-5232	74	42	.	.	PUNCT
ejpam-5232	74	43	/	/	SYM
ejpam-5232	74	44	eur	eur	PROPN
ejpam-5232	74	45	.	.	PUNCT
ejpam-5232	75	1	j.	j.	PROPN
ejpam-5232	75	2	pure	pure	PROPN
ejpam-5232	75	3	appl	appl	PROPN
ejpam-5232	75	4	.	.	PROPN
ejpam-5232	75	5	math	math	PROPN
ejpam-5232	75	6	,	,	PUNCT
ejpam-5232	75	7	17	17	NUM
ejpam-5232	75	8	(	(	PUNCT
ejpam-5232	75	9	3	3	NUM
ejpam-5232	75	10	)	)	PUNCT
ejpam-5232	75	11	(	(	PUNCT
ejpam-5232	75	12	2024	2024	NUM
ejpam-5232	75	13	)	)	PUNCT
ejpam-5232	75	14	,	,	PUNCT
ejpam-5232	75	15	1497	1497	NUM
ejpam-5232	75	16	-	-	SYM
ejpam-5232	75	17	1515	1515	NUM
ejpam-5232	75	18	1501	1501	NUM
ejpam-5232	75	19	x	x	PUNCT
ejpam-5232	75	20	in	in	ADP
ejpam-5232	75	21	padé	padé	ADJ
ejpam-5232	75	22	approximation	approximation	NOUN
ejpam-5232	75	23	with	with	ADP
ejpam-5232	75	24	the	the	DET
ejpam-5232	75	25	chebyshev	chebyshev	NOUN
ejpam-5232	75	26	polynomials	polynomial	NOUN
ejpam-5232	75	27	of	of	ADP
ejpam-5232	75	28	degree	degree	NOUN
ejpam-5232	75	29	k.	k.	PROPN
ejpam-5232	76	1	furthermore	furthermore	ADV
ejpam-5232	76	2	,	,	PUNCT
ejpam-5232	76	3	to	to	PART
ejpam-5232	76	4	derive	derive	VERB
ejpam-5232	76	5	the	the	DET
ejpam-5232	76	6	acdm	acdm	ADV
ejpam-5232	76	7	based	base	VERB
ejpam-5232	76	8	on	on	ADP
ejpam-5232	76	9	the	the	DET
ejpam-5232	76	10	adm	adm	PROPN
ejpam-5232	76	11	and	and	CCONJ
ejpam-5232	76	12	chebyshev	chebyshev	NOUN
ejpam-5232	76	13	polynomials	polynomial	NOUN
ejpam-5232	76	14	,	,	PUNCT
ejpam-5232	76	15	we	we	PRON
ejpam-5232	76	16	first	first	ADV
ejpam-5232	76	17	rewrite	rewrite	VERB
ejpam-5232	76	18	the	the	DET
ejpam-5232	76	19	function	function	NOUN
ejpam-5232	76	20	g(x	g(x	NOUN
ejpam-5232	76	21	)	)	PUNCT
ejpam-5232	76	22	in	in	ADP
ejpam-5232	76	23	eq	eq	ADP
ejpam-5232	76	24	.	.	PUNCT
ejpam-5232	77	1	(	(	PUNCT
ejpam-5232	77	2	8)	8)	NUM
ejpam-5232	77	3	in	in	ADP
ejpam-5232	77	4	terms	term	NOUN
ejpam-5232	77	5	of	of	ADP
ejpam-5232	77	6	the	the	DET
ejpam-5232	77	7	chebyshev	chebyshev	PROPN
ejpam-5232	77	8	series	series	NOUN
ejpam-5232	77	9	as	as	SCONJ
ejpam-5232	77	10	follows	follow	VERB
ejpam-5232	77	11	g(x	g(x	NOUN
ejpam-5232	77	12	)	)	PUNCT
ejpam-5232	78	1	=	=	PUNCT
ejpam-5232	78	2	m∑	m∑	CCONJ
ejpam-5232	78	3	i=0	i=0	PROPN
ejpam-5232	78	4	aiti(x	aiti(x	PROPN
ejpam-5232	78	5	)	)	PUNCT
ejpam-5232	78	6	,	,	PUNCT
ejpam-5232	78	7	(	(	PUNCT
ejpam-5232	78	8	16	16	NUM
ejpam-5232	78	9	)	)	PUNCT
ejpam-5232	78	10	where	where	SCONJ
ejpam-5232	78	11	ti(x	ti(x	NUM
ejpam-5232	78	12	)	)	PUNCT
ejpam-5232	78	13	are	be	AUX
ejpam-5232	78	14	the	the	DET
ejpam-5232	78	15	first	first	ADJ
ejpam-5232	78	16	kind	kind	NOUN
ejpam-5232	78	17	of	of	ADP
ejpam-5232	78	18	orthogonal	orthogonal	ADJ
ejpam-5232	78	19	chebyshev	chebyshev	NOUN
ejpam-5232	78	20	polynomials	polynomial	NOUN
ejpam-5232	78	21	,	,	PUNCT
ejpam-5232	78	22	and	and	CCONJ
ejpam-5232	78	23	the	the	DET
ejpam-5232	78	24	coefficients	coefficient	NOUN
ejpam-5232	78	25	ak	ak	PROPN
ejpam-5232	78	26	are	be	AUX
ejpam-5232	78	27	determined	determine	VERB
ejpam-5232	78	28	from	from	ADP
ejpam-5232	78	29	the	the	DET
ejpam-5232	78	30	orthogonal	orthogonal	ADJ
ejpam-5232	78	31	polynomials	polynomial	NOUN
ejpam-5232	78	32	as	as	SCONJ
ejpam-5232	78	33	follows	follow	VERB
ejpam-5232	78	34	{	{	PUNCT
ejpam-5232	78	35	a0	a0	NOUN
ejpam-5232	78	36	=	=	SYM
ejpam-5232	78	37	1	1	NUM
ejpam-5232	78	38	π	π	NOUN
ejpam-5232	78	39	∫	∫	PROPN
ejpam-5232	78	40	1	1	NUM
ejpam-5232	78	41	−1	−1	NOUN
ejpam-5232	78	42	f(x)t0√	f(x)t0√	NOUN
ejpam-5232	78	43	1−x2	1−x2	NUM
ejpam-5232	78	44	dx	dx	PROPN
ejpam-5232	78	45	,	,	PUNCT
ejpam-5232	78	46	ak	ak	PROPN
ejpam-5232	78	47	=	=	SYM
ejpam-5232	78	48	2	2	NUM
ejpam-5232	78	49	π	π	NOUN
ejpam-5232	78	50	∫	∫	PROPN
ejpam-5232	78	51	1	1	NUM
ejpam-5232	78	52	−1	−1	NOUN
ejpam-5232	78	53	f(x)tk(x)√	f(x)tk(x)√	PROPN
ejpam-5232	78	54	1−x2	1−x2	NUM
ejpam-5232	78	55	dx	dx	NOUN
ejpam-5232	78	56	,	,	PUNCT
ejpam-5232	78	57	k	k	PROPN
ejpam-5232	78	58	≥	≥	NUM
ejpam-5232	78	59	1	1	NUM
ejpam-5232	78	60	.	.	PUNCT
ejpam-5232	79	1	(	(	PUNCT
ejpam-5232	79	2	17	17	NUM
ejpam-5232	79	3	)	)	PUNCT
ejpam-5232	79	4	therefore	therefore	ADV
ejpam-5232	79	5	,	,	PUNCT
ejpam-5232	79	6	from	from	ADP
ejpam-5232	79	7	eq	eq	ADP
ejpam-5232	79	8	.	.	PUNCT
ejpam-5232	80	1	(	(	PUNCT
ejpam-5232	80	2	8)	8)	NUM
ejpam-5232	80	3	,	,	PUNCT
ejpam-5232	80	4	we	we	PRON
ejpam-5232	80	5	,	,	PUNCT
ejpam-5232	80	6	thus	thus	ADV
ejpam-5232	80	7	obtain	obtain	VERB
ejpam-5232	80	8	the	the	DET
ejpam-5232	80	9	following	following	NOUN
ejpam-5232	80	10	acdm	acdm	ADP
ejpam-5232	80	11	recurrent	recurrent	ADJ
ejpam-5232	80	12	relation	relation	NOUN
ejpam-5232	80	13	as	as	SCONJ
ejpam-5232	80	14	follows	follow	VERB
ejpam-5232	80	15	{	{	PUNCT
ejpam-5232	80	16	u0(x	u0(x	NOUN
ejpam-5232	80	17	)	)	PUNCT
ejpam-5232	80	18	=	=	SYM
ejpam-5232	80	19	u	u	SYM
ejpam-5232	80	20	(	(	PUNCT
ejpam-5232	80	21	α1	α1	PROPN
ejpam-5232	80	22	)	)	PUNCT
ejpam-5232	81	1	+	+	NUM
ejpam-5232	81	2	z	z	NOUN
ejpam-5232	81	3	(	(	PUNCT
ejpam-5232	81	4	x−	x−	PROPN
ejpam-5232	81	5	α1	α1	PROPN
ejpam-5232	81	6	)	)	PUNCT
ejpam-5232	82	1	+	+	CCONJ
ejpam-5232	82	2	l−1	l−1	PROPN
ejpam-5232	82	3	(	(	PUNCT
ejpam-5232	82	4	a0t0(x	a0t0(x	NOUN
ejpam-5232	82	5	)	)	PUNCT
ejpam-5232	82	6	+	+	NOUN
ejpam-5232	82	7	a1t1(x	a1t1(x	X
ejpam-5232	82	8	)	)	PUNCT
ejpam-5232	82	9	+	+	CCONJ
ejpam-5232	82	10	·	·	PUNCT
ejpam-5232	82	11	·	·	PUNCT
ejpam-5232	82	12	·	·	PUNCT
ejpam-5232	82	13	+	+	NUM
ejpam-5232	82	14	amtm(x	amtm(x	NOUN
ejpam-5232	82	15	)	)	PUNCT
ejpam-5232	82	16	)	)	PUNCT
ejpam-5232	82	17	,	,	PUNCT
ejpam-5232	82	18	un+1(x	un+1(x	PROPN
ejpam-5232	82	19	)	)	PUNCT
ejpam-5232	82	20	=	=	PRON
ejpam-5232	82	21	−l−1run	−l−1run	VERB
ejpam-5232	82	22	−	−	NOUN
ejpam-5232	82	23	l−1an	l−1an	NOUN
ejpam-5232	82	24	,	,	PUNCT
ejpam-5232	82	25	n	n	X
ejpam-5232	82	26	≥	≥	NOUN
ejpam-5232	82	27	0	0	NUM
ejpam-5232	82	28	.	.	PUNCT
ejpam-5232	83	1	(	(	PUNCT
ejpam-5232	83	2	18	18	NUM
ejpam-5232	83	3	)	)	PUNCT
ejpam-5232	83	4	finally	finally	ADV
ejpam-5232	83	5	,	,	PUNCT
ejpam-5232	83	6	in	in	ADP
ejpam-5232	83	7	what	what	PRON
ejpam-5232	83	8	follows	follow	VERB
ejpam-5232	83	9	,	,	PUNCT
ejpam-5232	83	10	we	we	PRON
ejpam-5232	83	11	will	will	AUX
ejpam-5232	83	12	be	be	AUX
ejpam-5232	83	13	demonstrating	demonstrate	VERB
ejpam-5232	83	14	the	the	DET
ejpam-5232	83	15	devised	devise	VERB
ejpam-5232	83	16	acdm	acdm	ADJ
ejpam-5232	83	17	scheme	scheme	NOUN
ejpam-5232	83	18	given	give	VERB
ejpam-5232	83	19	in	in	ADP
ejpam-5232	83	20	eq	eq	ADP
ejpam-5232	83	21	.	.	PUNCT
ejpam-5232	84	1	(	(	PUNCT
ejpam-5232	84	2	18	18	NUM
ejpam-5232	84	3	)	)	PUNCT
ejpam-5232	84	4	to	to	PART
ejpam-5232	84	5	obtain	obtain	VERB
ejpam-5232	84	6	an	an	DET
ejpam-5232	84	7	approximate	approximate	ADJ
ejpam-5232	84	8	solution	solution	NOUN
ejpam-5232	84	9	via	via	ADP
ejpam-5232	84	10	φn	φn	ADP
ejpam-5232	84	11	=	=	PUNCT
ejpam-5232	84	12	∑n−1	∑n−1	ADJ
ejpam-5232	84	13	n=0	n=0	PROPN
ejpam-5232	84	14	un	un	PROPN
ejpam-5232	84	15	.	.	PROPN
ejpam-5232	84	16	remark	remark	PROPN
ejpam-5232	84	17	1	1	NUM
ejpam-5232	84	18	.	.	PUNCT
ejpam-5232	85	1	[	[	X
ejpam-5232	85	2	14	14	NUM
ejpam-5232	85	3	]	]	PUNCT
ejpam-5232	85	4	the	the	DET
ejpam-5232	85	5	technique	technique	NOUN
ejpam-5232	85	6	for	for	ADP
ejpam-5232	85	7	using	use	VERB
ejpam-5232	85	8	the	the	DET
ejpam-5232	85	9	chebyshev	chebyshev	NOUN
ejpam-5232	85	10	polynomial	polynomial	NOUN
ejpam-5232	85	11	is	be	AUX
ejpam-5232	85	12	extended	extend	VERB
ejpam-5232	85	13	to	to	ADP
ejpam-5232	85	14	a	a	DET
ejpam-5232	85	15	general	general	ADJ
ejpam-5232	85	16	closed	closed	ADJ
ejpam-5232	85	17	interval	interval	NOUN
ejpam-5232	85	18	[	[	X
ejpam-5232	85	19	a	a	X
ejpam-5232	85	20	,	,	PUNCT
ejpam-5232	85	21	b	b	NOUN
ejpam-5232	85	22	]	]	X
ejpam-5232	85	23	through	through	ADP
ejpam-5232	85	24	the	the	DET
ejpam-5232	85	25	change	change	NOUN
ejpam-5232	85	26	of	of	ADP
ejpam-5232	85	27	the	the	DET
ejpam-5232	85	28	following	follow	VERB
ejpam-5232	85	29	variables	variable	NOUN
ejpam-5232	85	30	t	t	PROPN
ejpam-5232	86	1	=	=	SYM
ejpam-5232	86	2	1	1	NUM
ejpam-5232	86	3	2	2	NUM
ejpam-5232	87	1	[	[	X
ejpam-5232	87	2	(	(	PUNCT
ejpam-5232	87	3	b−	b−	PROPN
ejpam-5232	87	4	a)x+	a)x+	PROPN
ejpam-5232	87	5	a+	a+	PUNCT
ejpam-5232	87	6	b	b	NOUN
ejpam-5232	87	7	]	]	X
ejpam-5232	87	8	.	.	PUNCT
ejpam-5232	88	1	(	(	PUNCT
ejpam-5232	88	2	19	19	NUM
ejpam-5232	88	3	)	)	SYM
ejpam-5232	88	4	4	4	NUM
ejpam-5232	88	5	.	.	PUNCT
ejpam-5232	88	6	numerical	numerical	ADJ
ejpam-5232	88	7	applications	application	NOUN
ejpam-5232	88	8	in	in	ADP
ejpam-5232	88	9	this	this	DET
ejpam-5232	88	10	section	section	NOUN
ejpam-5232	88	11	,	,	PUNCT
ejpam-5232	88	12	certain	certain	ADJ
ejpam-5232	88	13	bvps	bvps	NOUN
ejpam-5232	88	14	have	have	AUX
ejpam-5232	88	15	been	be	AUX
ejpam-5232	88	16	are	be	AUX
ejpam-5232	88	17	considered	consider	VERB
ejpam-5232	88	18	as	as	ADP
ejpam-5232	88	19	test	test	NOUN
ejpam-5232	88	20	problems	problem	NOUN
ejpam-5232	88	21	to	to	PART
ejpam-5232	88	22	demonstrate	demonstrate	VERB
ejpam-5232	88	23	the	the	DET
ejpam-5232	88	24	efficiency	efficiency	NOUN
ejpam-5232	88	25	of	of	ADP
ejpam-5232	88	26	the	the	DET
ejpam-5232	88	27	devised	devise	VERB
ejpam-5232	88	28	acdm	acdm	ADJ
ejpam-5232	88	29	methodology	methodology	NOUN
ejpam-5232	88	30	.	.	PUNCT
ejpam-5232	89	1	it	it	PRON
ejpam-5232	89	2	is	be	AUX
ejpam-5232	89	3	worthy	worthy	ADJ
ejpam-5232	89	4	to	to	PART
ejpam-5232	89	5	mention	mention	VERB
ejpam-5232	89	6	that	that	SCONJ
ejpam-5232	89	7	all	all	DET
ejpam-5232	89	8	computations	computation	NOUN
ejpam-5232	89	9	are	be	AUX
ejpam-5232	89	10	performed	perform	VERB
ejpam-5232	89	11	by	by	ADP
ejpam-5232	89	12	using	use	VERB
ejpam-5232	89	13	maple	maple	NOUN
ejpam-5232	89	14	18	18	NUM
ejpam-5232	89	15	version	version	NOUN
ejpam-5232	89	16	.	.	PUNCT
ejpam-5232	90	1	example	example	NOUN
ejpam-5232	91	1	1	1	NUM
ejpam-5232	91	2	.	.	X
ejpam-5232	91	3	consider	consider	VERB
ejpam-5232	91	4	the	the	DET
ejpam-5232	91	5	linear	linear	ADJ
ejpam-5232	91	6	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	91	7	bvp	bvp	NOUN
ejpam-5232	92	1	[	[	X
ejpam-5232	92	2	22	22	NUM
ejpam-5232	92	3	]	]	X
ejpam-5232	92	4	u′′	u′′	PROPN
ejpam-5232	92	5	=	=	X
ejpam-5232	92	6	u+	u+	NUM
ejpam-5232	92	7	2ex	2ex	NOUN
ejpam-5232	92	8	,	,	PUNCT
ejpam-5232	92	9	u(0	u(0	PROPN
ejpam-5232	92	10	)	)	PUNCT
ejpam-5232	92	11	=	=	SYM
ejpam-5232	92	12	0	0	NUM
ejpam-5232	92	13	,	,	PUNCT
ejpam-5232	92	14	u(1	u(1	PROPN
ejpam-5232	92	15	)	)	PUNCT
ejpam-5232	92	16	=	=	SYM
ejpam-5232	93	1	e	e	NOUN
ejpam-5232	93	2	,	,	PUNCT
ejpam-5232	93	3	(	(	PUNCT
ejpam-5232	93	4	20	20	NUM
ejpam-5232	93	5	)	)	PUNCT
ejpam-5232	93	6	that	that	PRON
ejpam-5232	93	7	admits	admit	VERB
ejpam-5232	93	8	the	the	DET
ejpam-5232	93	9	following	following	ADJ
ejpam-5232	93	10	exact	exact	ADJ
ejpam-5232	93	11	analytical	analytical	ADJ
ejpam-5232	93	12	solution	solution	NOUN
ejpam-5232	93	13	u(x	u(x	NOUN
ejpam-5232	93	14	)	)	PUNCT
ejpam-5232	93	15	=	=	SYM
ejpam-5232	93	16	xex	xex	PROPN
ejpam-5232	93	17	.	.	PUNCT
ejpam-5232	94	1	thus	thus	ADV
ejpam-5232	94	2	,	,	PUNCT
ejpam-5232	94	3	according	accord	VERB
ejpam-5232	94	4	to	to	ADP
ejpam-5232	94	5	the	the	DET
ejpam-5232	94	6	adm	adm	PROPN
ejpam-5232	94	7	,	,	PUNCT
ejpam-5232	94	8	the	the	DET
ejpam-5232	94	9	bvp	bvp	PROPN
ejpam-5232	94	10	admits	admit	VERB
ejpam-5232	94	11	the	the	DET
ejpam-5232	94	12	following	follow	VERB
ejpam-5232	94	13	{	{	PUNCT
ejpam-5232	94	14	u0(x	u0(x	NOUN
ejpam-5232	94	15	)	)	PUNCT
ejpam-5232	94	16	=	=	SYM
ejpam-5232	94	17	u(0	u(0	NOUN
ejpam-5232	94	18	)	)	PUNCT
ejpam-5232	94	19	+	+	CCONJ
ejpam-5232	94	20	zx+	zx+	NOUN
ejpam-5232	94	21	l−1g(x	l−1g(x	X
ejpam-5232	94	22	)	)	PUNCT
ejpam-5232	94	23	,	,	PUNCT
ejpam-5232	94	24	un+1(x	un+1(x	NOUN
ejpam-5232	94	25	)	)	PUNCT
ejpam-5232	94	26	=	=	NOUN
ejpam-5232	94	27	l−1un	l−1un	NOUN
ejpam-5232	94	28	,	,	PUNCT
ejpam-5232	94	29	n	n	PRON
ejpam-5232	94	30	≥	≥	NOUN
ejpam-5232	94	31	0	0	NUM
ejpam-5232	94	32	.	.	PUNCT
ejpam-5232	95	1	h.	h.	PROPN
ejpam-5232	95	2	bakodah	bakodah	PROPN
ejpam-5232	95	3	et	et	PROPN
ejpam-5232	95	4	al	al	PROPN
ejpam-5232	95	5	.	.	PUNCT
ejpam-5232	95	6	/	/	SYM
ejpam-5232	95	7	eur	eur	PROPN
ejpam-5232	95	8	.	.	PUNCT
ejpam-5232	96	1	j.	j.	PROPN
ejpam-5232	96	2	pure	pure	PROPN
ejpam-5232	96	3	appl	appl	PROPN
ejpam-5232	96	4	.	.	PROPN
ejpam-5232	96	5	math	math	PROPN
ejpam-5232	96	6	,	,	PUNCT
ejpam-5232	96	7	17	17	NUM
ejpam-5232	96	8	(	(	PUNCT
ejpam-5232	96	9	3	3	NUM
ejpam-5232	96	10	)	)	PUNCT
ejpam-5232	96	11	(	(	PUNCT
ejpam-5232	96	12	2024	2024	NUM
ejpam-5232	96	13	)	)	PUNCT
ejpam-5232	96	14	,	,	PUNCT
ejpam-5232	96	15	1497	1497	NUM
ejpam-5232	96	16	-	-	SYM
ejpam-5232	96	17	1515	1515	NUM
ejpam-5232	96	18	1502	1502	NUM
ejpam-5232	96	19	where	where	SCONJ
ejpam-5232	96	20	l	l	NOUN
ejpam-5232	96	21	(	(	PUNCT
ejpam-5232	96	22	.	.	PUNCT
ejpam-5232	96	23	)	)	PUNCT
ejpam-5232	97	1	=	=	PUNCT
ejpam-5232	97	2	d2	d2	PROPN
ejpam-5232	97	3	dx2	dx2	PROPN
ejpam-5232	97	4	(	(	PUNCT
ejpam-5232	97	5	.	.	PUNCT
ejpam-5232	97	6	)	)	PUNCT
ejpam-5232	97	7	,	,	PUNCT
ejpam-5232	97	8	l	l	NOUN
ejpam-5232	97	9	−1	−1	NOUN
ejpam-5232	97	10	(	(	PUNCT
ejpam-5232	97	11	.	.	PUNCT
ejpam-5232	97	12	)	)	PUNCT
ejpam-5232	98	1	=	=	PUNCT
ejpam-5232	99	1	∫	∫	PUNCT
ejpam-5232	99	2	x	x	SYM
ejpam-5232	99	3	0	0	NUM
ejpam-5232	99	4	∫	∫	PROPN
ejpam-5232	99	5	x	x	X
ejpam-5232	99	6	0	0	PUNCT
ejpam-5232	99	7	(	(	PUNCT
ejpam-5232	99	8	.)dxdx	.)dxdx	NOUN
ejpam-5232	99	9	,	,	PUNCT
ejpam-5232	99	10	and	and	CCONJ
ejpam-5232	99	11	,	,	PUNCT
ejpam-5232	99	12	g(x	g(x	NOUN
ejpam-5232	99	13	)	)	PUNCT
ejpam-5232	100	1	=	=	PUNCT
ejpam-5232	100	2	2ex	2ex	NOUN
ejpam-5232	100	3	.	.	PUNCT
ejpam-5232	101	1	we	we	PRON
ejpam-5232	101	2	now	now	ADV
ejpam-5232	101	3	make	make	VERB
ejpam-5232	101	4	use	use	NOUN
ejpam-5232	101	5	of	of	ADP
ejpam-5232	101	6	the	the	DET
ejpam-5232	101	7	chebyshev	chebyshev	NOUN
ejpam-5232	101	8	expansion	expansion	NOUN
ejpam-5232	101	9	for	for	ADP
ejpam-5232	101	10	the	the	DET
ejpam-5232	101	11	function	function	NOUN
ejpam-5232	101	12	g(x	g(x	NOUN
ejpam-5232	101	13	)	)	PUNCT
ejpam-5232	101	14	from	from	ADP
ejpam-5232	101	15	eq	eq	ADP
ejpam-5232	101	16	.	.	PUNCT
ejpam-5232	102	1	(	(	PUNCT
ejpam-5232	102	2	16	16	NUM
ejpam-5232	102	3	)	)	PUNCT
ejpam-5232	102	4	say	say	VERB
ejpam-5232	102	5	,	,	PUNCT
ejpam-5232	102	6	g(x	g(x	NOUN
ejpam-5232	102	7	)	)	PUNCT
ejpam-5232	102	8	∼=	∼=	PROPN
ejpam-5232	102	9	∑10	∑10	PUNCT
ejpam-5232	102	10	i=0	i=0	PROPN
ejpam-5232	103	1	aiti(2x	aiti(2x	VERB
ejpam-5232	103	2	−	−	NOUN
ejpam-5232	103	3	1	1	NUM
ejpam-5232	103	4	)	)	PUNCT
ejpam-5232	103	5	,	,	PUNCT
ejpam-5232	103	6	where	where	SCONJ
ejpam-5232	103	7	the	the	DET
ejpam-5232	103	8	coefficients	coefficient	NOUN
ejpam-5232	103	9	a0	a0	PROPN
ejpam-5232	103	10	and	and	CCONJ
ejpam-5232	103	11	ai	ai	PROPN
ejpam-5232	103	12	are	be	AUX
ejpam-5232	103	13	computed	compute	VERB
ejpam-5232	103	14	from	from	ADP
ejpam-5232	103	15	eq	eq	PROPN
ejpam-5232	103	16	.	.	PUNCT
ejpam-5232	104	1	(	(	PUNCT
ejpam-5232	104	2	17	17	NUM
ejpam-5232	104	3	)	)	PUNCT
ejpam-5232	104	4	as	as	ADP
ejpam-5232	104	5	a0	a0	NOUN
ejpam-5232	104	6	=	=	SYM
ejpam-5232	104	7	1	1	NUM
ejpam-5232	104	8	π	π	NOUN
ejpam-5232	104	9	∫	∫	PROPN
ejpam-5232	104	10	1	1	NUM
ejpam-5232	104	11	−1	−1	NOUN
ejpam-5232	104	12	g(0.5	g(0.5	VERB
ejpam-5232	104	13	+	+	CCONJ
ejpam-5232	104	14	0.5x)t0(x)√	0.5x)t0(x)√	NUM
ejpam-5232	104	15	1−	1−	NUM
ejpam-5232	104	16	x2	x2	NUM
ejpam-5232	104	17	dx	dx	PROPN
ejpam-5232	104	18	,	,	PUNCT
ejpam-5232	104	19	ai	ai	VERB
ejpam-5232	104	20	=	=	NOUN
ejpam-5232	104	21	2	2	NUM
ejpam-5232	104	22	π	π	NOUN
ejpam-5232	104	23	∫	∫	PROPN
ejpam-5232	104	24	1	1	NUM
ejpam-5232	104	25	−1	−1	NOUN
ejpam-5232	104	26	g(0.5	g(0.5	PROPN
ejpam-5232	104	27	+	+	CCONJ
ejpam-5232	104	28	0.5x)ti(x)√	0.5x)ti(x)√	PROPN
ejpam-5232	104	29	1−	1−	NUM
ejpam-5232	104	30	x2	x2	NUM
ejpam-5232	104	31	dx	dx	PROPN
ejpam-5232	104	32	,	,	PUNCT
ejpam-5232	104	33	i	i	PRON
ejpam-5232	104	34	=	=	NOUN
ejpam-5232	104	35	1	1	NUM
ejpam-5232	104	36	,	,	PUNCT
ejpam-5232	104	37	2	2	NUM
ejpam-5232	104	38	,	,	PUNCT
ejpam-5232	104	39	.	.	PUNCT
ejpam-5232	104	40	.	.	PUNCT
ejpam-5232	104	41	.	.	PUNCT
ejpam-5232	105	1	10	10	NUM
ejpam-5232	105	2	.	.	PUNCT
ejpam-5232	106	1	thus	thus	ADV
ejpam-5232	106	2	,	,	PUNCT
ejpam-5232	106	3	g(x	g(x	NOUN
ejpam-5232	106	4	)	)	PUNCT
ejpam-5232	106	5	becomes	become	VERB
ejpam-5232	106	6	g(x	g(x	NOUN
ejpam-5232	106	7	)	)	PUNCT
ejpam-5232	107	1	∼=	∼=	VERB
ejpam-5232	107	2	2.0000000000000387	2.0000000000000387	NUM
ejpam-5232	107	3	+	+	NUM
ejpam-5232	107	4	1.99999999999064x+	1.99999999999064x+	NUM
ejpam-5232	108	1	1.0000000003722x2	1.0000000003722x2	NUM
ejpam-5232	108	2	+0.3333333275x3	+0.3333333275x3	NOUN
ejpam-5232	108	3	+	+	SYM
ejpam-5232	108	4	0.0833333792x4	0.0833333792x4	NUM
ejpam-5232	108	5	+	+	NUM
ejpam-5232	108	6	0.01666645453x5	0.01666645453x5	NUM
ejpam-5232	108	7	+	+	NUM
ejpam-5232	108	8	·	·	PUNCT
ejpam-5232	108	9	·	·	PUNCT
ejpam-5232	108	10	·	·	PUNCT
ejpam-5232	108	11	therefore	therefore	ADV
ejpam-5232	108	12	,	,	PUNCT
ejpam-5232	108	13	having	having	AUX
ejpam-5232	108	14	determined	determine	VERB
ejpam-5232	108	15	g(x	g(x	NOUN
ejpam-5232	108	16	)	)	PUNCT
ejpam-5232	108	17	,	,	PUNCT
ejpam-5232	108	18	the	the	DET
ejpam-5232	108	19	acdm	acdm	ADJ
ejpam-5232	108	20	solution	solution	NOUN
ejpam-5232	108	21	is	be	AUX
ejpam-5232	108	22	recurrently	recurrently	ADV
ejpam-5232	108	23	given	give	VERB
ejpam-5232	108	24	from	from	ADP
ejpam-5232	108	25	eq	eq	ADP
ejpam-5232	108	26	.	.	PUNCT
ejpam-5232	109	1	(	(	PUNCT
ejpam-5232	109	2	18	18	NUM
ejpam-5232	109	3	)	)	PUNCT
ejpam-5232	109	4	as	as	ADP
ejpam-5232	109	5	u0	u0	ADJ
ejpam-5232	109	6	=	=	PROPN
ejpam-5232	109	7	zx+	zx+	NOUN
ejpam-5232	109	8	1.0000000000000193x2	1.0000000000000193x2	NUM
ejpam-5232	109	9	+	+	NUM
ejpam-5232	109	10	0.33333333333177x3	0.33333333333177x3	NUM
ejpam-5232	109	11	+	+	CCONJ
ejpam-5232	109	12	0.083333333643x4	0.083333333643x4	NUM
ejpam-5232	110	1	+	+	CCONJ
ejpam-5232	110	2	0.016666666377x5	0.016666666377x5	NUM
ejpam-5232	110	3	+	+	X
ejpam-5232	110	4	·	·	PUNCT
ejpam-5232	110	5	·	·	PUNCT
ejpam-5232	110	6	·	·	PUNCT
ejpam-5232	110	7	,	,	PUNCT
ejpam-5232	110	8	u1	u1	NOUN
ejpam-5232	110	9	=	=	SYM
ejpam-5232	110	10	0.166666667zx3	0.166666667zx3	NOUN
ejpam-5232	111	1	+	+	CCONJ
ejpam-5232	112	1	0.0833333333x4	0.0833333333x4	NUM
ejpam-5232	112	2	+	+	CCONJ
ejpam-5232	112	3	0.0166666666x5	0.0166666666x5	NUM
ejpam-5232	112	4	+	+	CCONJ
ejpam-5232	112	5	0.0027777777x6	0.0027777777x6	NUM
ejpam-5232	112	6	+	+	NUM
ejpam-5232	112	7	0.0003968253899x7	0.0003968253899x7	NUM
ejpam-5232	112	8	+	+	CCONJ
ejpam-5232	112	9	·	·	PUNCT
ejpam-5232	112	10	·	·	PUNCT
ejpam-5232	112	11	·	·	PUNCT
ejpam-5232	112	12	,	,	PUNCT
ejpam-5232	112	13	...	...	PUNCT
ejpam-5232	112	14	in	in	ADP
ejpam-5232	112	15	the	the	DET
ejpam-5232	112	16	same	same	ADJ
ejpam-5232	112	17	way	way	NOUN
ejpam-5232	112	18	,	,	PUNCT
ejpam-5232	112	19	we	we	PRON
ejpam-5232	112	20	compute	compute	VERB
ejpam-5232	112	21	u2	u2	NOUN
ejpam-5232	112	22	,	,	PUNCT
ejpam-5232	112	23	u3	u3	NOUN
ejpam-5232	112	24	and	and	CCONJ
ejpam-5232	112	25	u4	u4	PROPN
ejpam-5232	112	26	,	,	PUNCT
ejpam-5232	112	27	then	then	ADV
ejpam-5232	112	28	we	we	PRON
ejpam-5232	112	29	have	have	VERB
ejpam-5232	112	30	φ5	φ5	ADJ
ejpam-5232	112	31	=	=	PUNCT
ejpam-5232	113	1	∑4	∑4	PROPN
ejpam-5232	113	2	i=0	i=0	PROPN
ejpam-5232	113	3	ui	ui	PROPN
ejpam-5232	113	4	.	.	PUNCT
ejpam-5232	114	1	now	now	ADV
ejpam-5232	114	2	,	,	PUNCT
ejpam-5232	114	3	to	to	PART
ejpam-5232	114	4	determine	determine	VERB
ejpam-5232	114	5	z	z	PROPN
ejpam-5232	114	6	,	,	PUNCT
ejpam-5232	114	7	we	we	PRON
ejpam-5232	114	8	substitute	substitute	VERB
ejpam-5232	114	9	the	the	DET
ejpam-5232	114	10	boundary	boundary	ADJ
ejpam-5232	114	11	condition	condition	NOUN
ejpam-5232	114	12	at	at	ADP
ejpam-5232	114	13	x	x	X
ejpam-5232	114	14	=	=	SYM
ejpam-5232	114	15	1	1	NUM
ejpam-5232	114	16	in	in	ADP
ejpam-5232	114	17	φ5	φ5	PROPN
ejpam-5232	114	18	to	to	PART
ejpam-5232	114	19	get	get	VERB
ejpam-5232	114	20	φ5	φ5	ADJ
ejpam-5232	114	21	=	=	SYM
ejpam-5232	114	22	1.543080630	1.543080630	NUM
ejpam-5232	114	23	+	+	CCONJ
ejpam-5232	114	24	1.175201168z	1.175201168z	NOUN
ejpam-5232	114	25	.	.	PUNCT
ejpam-5232	115	1	more	more	ADJ
ejpam-5232	115	2	,	,	PUNCT
ejpam-5232	115	3	φ5	φ5	PROPN
ejpam-5232	115	4	requires	require	VERB
ejpam-5232	115	5	the	the	DET
ejpam-5232	115	6	boundary	boundary	ADJ
ejpam-5232	115	7	condition	condition	NOUN
ejpam-5232	115	8	φ5(1	φ5(1	NOUN
ejpam-5232	115	9	)	)	PUNCT
ejpam-5232	116	1	=	=	SYM
ejpam-5232	116	2	e	e	NOUN
ejpam-5232	116	3	,	,	PUNCT
ejpam-5232	116	4	such	such	ADJ
ejpam-5232	116	5	after	after	ADP
ejpam-5232	116	6	solving	solve	VERB
ejpam-5232	116	7	this	this	DET
ejpam-5232	116	8	relation	relation	NOUN
ejpam-5232	116	9	gives	give	VERB
ejpam-5232	116	10	z	z	NOUN
ejpam-5232	116	11	=	=	SYM
ejpam-5232	116	12	1.0000000253	1.0000000253	NUM
ejpam-5232	116	13	.	.	PUNCT
ejpam-5232	117	1	thus	thus	ADV
ejpam-5232	117	2	,	,	PUNCT
ejpam-5232	117	3	since	since	SCONJ
ejpam-5232	117	4	the	the	DET
ejpam-5232	117	5	constant	constant	ADJ
ejpam-5232	117	6	z	z	NOUN
ejpam-5232	117	7	is	be	AUX
ejpam-5232	117	8	determined	determine	VERB
ejpam-5232	117	9	,	,	PUNCT
ejpam-5232	117	10	the	the	DET
ejpam-5232	117	11	solution	solution	NOUN
ejpam-5232	117	12	in	in	ADP
ejpam-5232	117	13	a	a	DET
ejpam-5232	117	14	series	series	NOUN
ejpam-5232	117	15	form	form	NOUN
ejpam-5232	117	16	follows	follow	VERB
ejpam-5232	117	17	instantly	instantly	ADV
ejpam-5232	117	18	.	.	PUNCT
ejpam-5232	118	1	the	the	DET
ejpam-5232	118	2	matching	matching	NOUN
ejpam-5232	118	3	of	of	ADP
ejpam-5232	118	4	φ5	φ5	PROPN
ejpam-5232	118	5	with	with	ADP
ejpam-5232	118	6	the	the	DET
ejpam-5232	118	7	exact	exact	ADJ
ejpam-5232	118	8	solution	solution	NOUN
ejpam-5232	118	9	is	be	AUX
ejpam-5232	118	10	accurate	accurate	ADJ
ejpam-5232	118	11	as	as	SCONJ
ejpam-5232	118	12	demonstrated	demonstrate	VERB
ejpam-5232	118	13	in	in	ADP
ejpam-5232	118	14	table	table	NOUN
ejpam-5232	118	15	1	1	NUM
ejpam-5232	118	16	.	.	PUNCT
ejpam-5232	119	1	in	in	ADP
ejpam-5232	119	2	figure	figure	NOUN
ejpam-5232	119	3	1	1	NUM
ejpam-5232	119	4	,	,	PUNCT
ejpam-5232	119	5	we	we	PRON
ejpam-5232	119	6	depict	depict	VERB
ejpam-5232	119	7	the	the	DET
ejpam-5232	119	8	curves	curve	NOUN
ejpam-5232	119	9	of	of	ADP
ejpam-5232	119	10	φ5	φ5	ADJ
ejpam-5232	119	11	and	and	CCONJ
ejpam-5232	119	12	the	the	DET
ejpam-5232	119	13	exact	exact	ADJ
ejpam-5232	119	14	analytical	analytical	ADJ
ejpam-5232	119	15	solution	solution	NOUN
ejpam-5232	119	16	u(x	u(x	NOUN
ejpam-5232	119	17	)	)	PUNCT
ejpam-5232	119	18	=	=	SYM
ejpam-5232	119	19	xex	xex	PROPN
ejpam-5232	119	20	in	in	ADP
ejpam-5232	119	21	the	the	DET
ejpam-5232	119	22	approximate	approximate	ADJ
ejpam-5232	119	23	region	region	NOUN
ejpam-5232	119	24	0	0	NUM
ejpam-5232	119	25	≤	≤	NUM
ejpam-5232	119	26	x	x	SYM
ejpam-5232	119	27	≤	≤	NUM
ejpam-5232	119	28	1	1	NUM
ejpam-5232	119	29	.	.	PUNCT
ejpam-5232	120	1	h.	h.	PROPN
ejpam-5232	120	2	bakodah	bakodah	PROPN
ejpam-5232	120	3	et	et	PROPN
ejpam-5232	120	4	al	al	PROPN
ejpam-5232	120	5	.	.	PUNCT
ejpam-5232	120	6	/	/	SYM
ejpam-5232	120	7	eur	eur	PROPN
ejpam-5232	120	8	.	.	PUNCT
ejpam-5232	121	1	j.	j.	PROPN
ejpam-5232	121	2	pure	pure	PROPN
ejpam-5232	121	3	appl	appl	PROPN
ejpam-5232	121	4	.	.	PROPN
ejpam-5232	121	5	math	math	PROPN
ejpam-5232	121	6	,	,	PUNCT
ejpam-5232	121	7	17	17	NUM
ejpam-5232	121	8	(	(	PUNCT
ejpam-5232	121	9	3	3	NUM
ejpam-5232	121	10	)	)	PUNCT
ejpam-5232	121	11	(	(	PUNCT
ejpam-5232	121	12	2024	2024	NUM
ejpam-5232	121	13	)	)	PUNCT
ejpam-5232	121	14	,	,	PUNCT
ejpam-5232	121	15	1497	1497	NUM
ejpam-5232	121	16	-	-	SYM
ejpam-5232	121	17	1515	1515	NUM
ejpam-5232	121	18	1503	1503	NUM
ejpam-5232	121	19	table	table	NOUN
ejpam-5232	121	20	1	1	NUM
ejpam-5232	121	21	:	:	PUNCT
ejpam-5232	121	22	absolute	absolute	ADJ
ejpam-5232	121	23	error	error	NOUN
ejpam-5232	121	24	between	between	ADP
ejpam-5232	121	25	the	the	DET
ejpam-5232	121	26	exact	exact	ADJ
ejpam-5232	121	27	and	and	CCONJ
ejpam-5232	121	28	acdm	acdm	ADJ
ejpam-5232	121	29	solutions	solution	NOUN
ejpam-5232	121	30	in	in	ADP
ejpam-5232	121	31	example	example	NOUN
ejpam-5232	121	32	1	1	NUM
ejpam-5232	121	33	.	.	X
ejpam-5232	122	1	x	x	PUNCT
ejpam-5232	122	2	exact	exact	ADJ
ejpam-5232	122	3	solution	solution	NOUN
ejpam-5232	122	4	acdm	acdm	ADP
ejpam-5232	122	5	solution	solution	NOUN
ejpam-5232	122	6	absolute	absolute	ADJ
ejpam-5232	122	7	error	error	NOUN
ejpam-5232	122	8	0.0	0.0	NUM
ejpam-5232	122	9	0	0	NUM
ejpam-5232	122	10	0	0	NUM
ejpam-5232	122	11	0	0	NUM
ejpam-5232	122	12	0.1	0.1	NUM
ejpam-5232	122	13	1.10517092×	1.10517092×	NUM
ejpam-5232	122	14	10−1	10−1	NUM
ejpam-5232	122	15	1.10517094×	1.10517094×	NUM
ejpam-5232	122	16	10−1	10−1	PROPN
ejpam-5232	122	17	2.53649074×	2.53649074×	NUM
ejpam-5232	122	18	10−9	10−9	NUM
ejpam-5232	122	19	0.2	0.2	NUM
ejpam-5232	122	20	2.44280552×	2.44280552×	NUM
ejpam-5232	122	21	10−1	10−1	NUM
ejpam-5232	122	22	2.44280557×	2.44280557×	NUM
ejpam-5232	122	23	10−1	10−1	NUM
ejpam-5232	122	24	5.09836706×	5.09836706×	NUM
ejpam-5232	122	25	10−9	10−9	NUM
ejpam-5232	122	26	0.3	0.3	NUM
ejpam-5232	122	27	4.04957642×	4.04957642×	NUM
ejpam-5232	122	28	10−1	10−1	NUM
ejpam-5232	122	29	4.04957650×	4.04957650×	NOUN
ejpam-5232	122	30	10−1	10−1	NUM
ejpam-5232	122	31	7.71122380×	7.71122380×	NOUN
ejpam-5232	122	32	10−9	10−9	NUM
ejpam-5232	122	33	0.4	0.4	NUM
ejpam-5232	122	34	5.96729879×	5.96729879×	NUM
ejpam-5232	122	35	10−1	10−1	NUM
ejpam-5232	122	36	5.96729889×	5.96729889×	NUM
ejpam-5232	122	37	10−1	10−1	PROPN
ejpam-5232	122	38	1.04002264×	1.04002264×	NUM
ejpam-5232	122	39	10−8	10−8	NUM
ejpam-5232	122	40	0.5	0.5	NUM
ejpam-5232	122	41	8.24360635×	8.24360635×	X
ejpam-5232	122	42	10−1	10−1	PROPN
ejpam-5232	122	43	8.24360649×	8.24360649×	PROPN
ejpam-5232	122	44	10−1	10−1	NUM
ejpam-5232	122	45	1.31822171×	1.31822171×	NUM
ejpam-5232	122	46	10−8	10−8	NUM
ejpam-5232	122	47	0.6	0.6	NUM
ejpam-5232	122	48	1.09327128	1.09327128	NUM
ejpam-5232	122	49	1.09327130	1.09327130	NUM
ejpam-5232	122	50	1.60211319×	1.60211319×	NOUN
ejpam-5232	122	51	10−8	10−8	NUM
ejpam-5232	122	52	0.7	0.7	NUM
ejpam-5232	122	53	1.40962690	1.40962690	NUM
ejpam-5232	122	54	1.4096269	1.4096269	NUM
ejpam-5232	122	55	1.86512214×	1.86512214×	NUM
ejpam-5232	122	56	10−8	10−8	NUM
ejpam-5232	122	57	0.8	0.8	NUM
ejpam-5232	122	58	1.78043274	1.78043274	NUM
ejpam-5232	122	59	1.78043276	1.78043276	NUM
ejpam-5232	122	60	2.00216909×	2.00216909×	NUM
ejpam-5232	122	61	10−8	10−8	NUM
ejpam-5232	122	62	0.9	0.9	NUM
ejpam-5232	122	63	2.21364280	2.21364280	NUM
ejpam-5232	122	64	2.21364282	2.21364282	NUM
ejpam-5232	122	65	1.68194966×	1.68194966×	NUM
ejpam-5232	122	66	10−8	10−8	NUM
ejpam-5232	122	67	1.0	1.0	NUM
ejpam-5232	122	68	2.71828183	2.71828183	NUM
ejpam-5232	122	69	2.71828183	2.71828183	NUM
ejpam-5232	122	70	1.×	1.×	PROPN
ejpam-5232	122	71	10−29	10−29	NOUN
ejpam-5232	122	72	figure	figure	NOUN
ejpam-5232	122	73	1	1	NUM
ejpam-5232	122	74	:	:	PUNCT
ejpam-5232	122	75	comparison	comparison	NOUN
ejpam-5232	122	76	between	between	ADP
ejpam-5232	122	77	the	the	DET
ejpam-5232	122	78	exact	exact	ADJ
ejpam-5232	122	79	and	and	CCONJ
ejpam-5232	122	80	acdm	acdm	ADJ
ejpam-5232	122	81	solutions	solution	NOUN
ejpam-5232	122	82	in	in	ADP
ejpam-5232	122	83	example	example	NOUN
ejpam-5232	122	84	1	1	NUM
ejpam-5232	122	85	.	.	PUNCT
ejpam-5232	122	86	example	example	NOUN
ejpam-5232	122	87	2	2	NUM
ejpam-5232	122	88	.	.	X
ejpam-5232	122	89	consider	consider	VERB
ejpam-5232	122	90	the	the	DET
ejpam-5232	122	91	nonlinear	nonlinear	ADJ
ejpam-5232	122	92	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	122	93	bvp	bvp	NOUN
ejpam-5232	122	94	[	[	X
ejpam-5232	122	95	17	17	NUM
ejpam-5232	122	96	]	]	X
ejpam-5232	122	97	u′′	u′′	PROPN
ejpam-5232	122	98	=	=	PROPN
ejpam-5232	122	99	u2	u2	PROPN
ejpam-5232	122	100	+	+	CCONJ
ejpam-5232	122	101	2π2	2π2	NUM
ejpam-5232	123	1	cos	co	NOUN
ejpam-5232	123	2	2πx−	2πx−	ADV
ejpam-5232	123	3	sin4	sin4	PROPN
ejpam-5232	123	4	πx	πx	NOUN
ejpam-5232	123	5	,	,	PUNCT
ejpam-5232	123	6	u(0	u(0	PROPN
ejpam-5232	123	7	)	)	PUNCT
ejpam-5232	123	8	=	=	SYM
ejpam-5232	123	9	u(1	u(1	PROPN
ejpam-5232	123	10	)	)	PUNCT
ejpam-5232	123	11	=	=	SYM
ejpam-5232	123	12	0	0	NUM
ejpam-5232	123	13	,	,	PUNCT
ejpam-5232	123	14	(	(	PUNCT
ejpam-5232	123	15	21	21	NUM
ejpam-5232	123	16	)	)	PUNCT
ejpam-5232	123	17	having	have	VERB
ejpam-5232	123	18	the	the	DET
ejpam-5232	123	19	following	follow	VERB
ejpam-5232	123	20	exact	exact	ADJ
ejpam-5232	123	21	analytical	analytical	ADJ
ejpam-5232	123	22	solution	solution	NOUN
ejpam-5232	123	23	u(x	u(x	NOUN
ejpam-5232	123	24	)	)	PUNCT
ejpam-5232	123	25	=	=	SYM
ejpam-5232	123	26	sin2	sin2	NOUN
ejpam-5232	123	27	πx	πx	VERB
ejpam-5232	123	28	.	.	X
ejpam-5232	123	29	again	again	ADV
ejpam-5232	123	30	,	,	PUNCT
ejpam-5232	123	31	based	base	VERB
ejpam-5232	123	32	on	on	ADP
ejpam-5232	123	33	the	the	DET
ejpam-5232	123	34	adm	adm	PROPN
ejpam-5232	123	35	,	,	PUNCT
ejpam-5232	123	36	the	the	DET
ejpam-5232	123	37	bvp	bvp	NOUN
ejpam-5232	123	38	have	have	VERB
ejpam-5232	123	39	the	the	DET
ejpam-5232	123	40	following	follow	VERB
ejpam-5232	123	41	{	{	PUNCT
ejpam-5232	123	42	u0(x	u0(x	NOUN
ejpam-5232	123	43	)	)	PUNCT
ejpam-5232	123	44	=	=	SYM
ejpam-5232	123	45	u(0	u(0	NOUN
ejpam-5232	123	46	)	)	PUNCT
ejpam-5232	123	47	+	+	CCONJ
ejpam-5232	123	48	zx+	zx+	NOUN
ejpam-5232	123	49	l−1g(x	l−1g(x	X
ejpam-5232	123	50	)	)	PUNCT
ejpam-5232	123	51	,	,	PUNCT
ejpam-5232	123	52	un+1(x	un+1(x	NOUN
ejpam-5232	123	53	)	)	PUNCT
ejpam-5232	123	54	=	=	SYM
ejpam-5232	123	55	l−1an	l−1an	NOUN
ejpam-5232	123	56	,	,	PUNCT
ejpam-5232	123	57	n	n	X
ejpam-5232	123	58	≥	≥	NOUN
ejpam-5232	123	59	0	0	NUM
ejpam-5232	123	60	.	.	PUNCT
ejpam-5232	124	1	where	where	SCONJ
ejpam-5232	124	2	adomian	adomian	NOUN
ejpam-5232	124	3	polynomials	polynomial	VERB
ejpam-5232	124	4	an	an	PRON
ejpam-5232	124	5	of	of	ADP
ejpam-5232	124	6	a	a	DET
ejpam-5232	124	7	nonlinear	nonlinear	ADJ
ejpam-5232	124	8	term	term	NOUN
ejpam-5232	124	9	u2	u2	NOUN
ejpam-5232	124	10	are	be	AUX
ejpam-5232	124	11	determined	determine	VERB
ejpam-5232	124	12	from	from	ADP
ejpam-5232	124	13	eq	eq	PROPN
ejpam-5232	124	14	.	.	PUNCT
ejpam-5232	125	1	(	(	PUNCT
ejpam-5232	125	2	6	6	NUM
ejpam-5232	125	3	)	)	PUNCT
ejpam-5232	125	4	as	as	ADP
ejpam-5232	125	5	h.	h.	PROPN
ejpam-5232	125	6	bakodah	bakodah	PROPN
ejpam-5232	125	7	et	et	PROPN
ejpam-5232	125	8	al	al	PROPN
ejpam-5232	125	9	.	.	PUNCT
ejpam-5232	125	10	/	/	SYM
ejpam-5232	125	11	eur	eur	PROPN
ejpam-5232	125	12	.	.	PUNCT
ejpam-5232	126	1	j.	j.	PROPN
ejpam-5232	126	2	pure	pure	PROPN
ejpam-5232	126	3	appl	appl	PROPN
ejpam-5232	126	4	.	.	PROPN
ejpam-5232	126	5	math	math	PROPN
ejpam-5232	126	6	,	,	PUNCT
ejpam-5232	126	7	17	17	NUM
ejpam-5232	126	8	(	(	PUNCT
ejpam-5232	126	9	3	3	NUM
ejpam-5232	126	10	)	)	PUNCT
ejpam-5232	126	11	(	(	PUNCT
ejpam-5232	126	12	2024	2024	NUM
ejpam-5232	126	13	)	)	PUNCT
ejpam-5232	126	14	,	,	PUNCT
ejpam-5232	126	15	1497	1497	NUM
ejpam-5232	126	16	-	-	SYM
ejpam-5232	126	17	1515	1515	NUM
ejpam-5232	126	18	1504	1504	NUM
ejpam-5232	126	19	follows	follow	VERB
ejpam-5232	126	20	:	:	PUNCT
ejpam-5232	126	21	a0	a0	PROPN
ejpam-5232	126	22	=	=	SYM
ejpam-5232	126	23	u20	u20	PROPN
ejpam-5232	126	24	,	,	PUNCT
ejpam-5232	126	25	a1	a1	NOUN
ejpam-5232	126	26	=	=	SYM
ejpam-5232	126	27	2u0u1	2u0u1	NUM
ejpam-5232	126	28	,	,	PUNCT
ejpam-5232	126	29	a2	a2	PROPN
ejpam-5232	126	30	=	=	SYM
ejpam-5232	126	31	2u0u2	2u0u2	PUNCT
ejpam-5232	127	1	+	+	CCONJ
ejpam-5232	127	2	u21	u21	NOUN
ejpam-5232	127	3	,	,	PUNCT
ejpam-5232	127	4	a3	a3	NOUN
ejpam-5232	127	5	=	=	SYM
ejpam-5232	127	6	2u0u3	2u0u3	NUM
ejpam-5232	127	7	+	+	CCONJ
ejpam-5232	127	8	2u1u2	2u1u2	NUM
ejpam-5232	127	9	,	,	PUNCT
ejpam-5232	127	10	...	...	PUNCT
ejpam-5232	127	11	in	in	ADP
ejpam-5232	127	12	similar	similar	ADJ
ejpam-5232	127	13	manner	manner	NOUN
ejpam-5232	127	14	,	,	PUNCT
ejpam-5232	127	15	g(x	g(x	NOUN
ejpam-5232	127	16	)	)	PUNCT
ejpam-5232	127	17	becomes	become	VERB
ejpam-5232	127	18	g(x	g(x	NOUN
ejpam-5232	127	19	)	)	PUNCT
ejpam-5232	128	1	∼=	∼=	PROPN
ejpam-5232	128	2	19.739432398−	19.739432398−	NUM
ejpam-5232	128	3	0.063110987x−	0.063110987x−	NUM
ejpam-5232	128	4	386.709633571x2	386.709633571x2	NUM
ejpam-5232	129	1	−	−	PROPN
ejpam-5232	130	1	52.590635088x3	52.590635088x3	NUM
ejpam-5232	130	2	+1664.947764846x4	+1664.947764846x4	NOUN
ejpam-5232	130	3	−	−	PROPN
ejpam-5232	131	1	2526.987198109x5	2526.987198109x5	NUM
ejpam-5232	131	2	+	+	NUM
ejpam-5232	131	3	·	·	PUNCT
ejpam-5232	131	4	·	·	PUNCT
ejpam-5232	131	5	·	·	PUNCT
ejpam-5232	131	6	therefore	therefore	ADV
ejpam-5232	131	7	,	,	PUNCT
ejpam-5232	131	8	having	having	AUX
ejpam-5232	131	9	determined	determine	VERB
ejpam-5232	131	10	g(x	g(x	NOUN
ejpam-5232	131	11	)	)	PUNCT
ejpam-5232	131	12	above	above	ADV
ejpam-5232	131	13	,	,	PUNCT
ejpam-5232	131	14	the	the	DET
ejpam-5232	131	15	acdm	acdm	ADJ
ejpam-5232	131	16	solution	solution	NOUN
ejpam-5232	131	17	is	be	AUX
ejpam-5232	131	18	recurrently	recurrently	ADV
ejpam-5232	131	19	given	give	VERB
ejpam-5232	131	20	from	from	ADP
ejpam-5232	131	21	eq	eq	ADP
ejpam-5232	131	22	.	.	PUNCT
ejpam-5232	132	1	(	(	PUNCT
ejpam-5232	132	2	18	18	NUM
ejpam-5232	132	3	)	)	PUNCT
ejpam-5232	132	4	,	,	PUNCT
ejpam-5232	132	5	thus	thus	ADV
ejpam-5232	132	6	obtain	obtain	VERB
ejpam-5232	132	7	φ5	φ5	ADJ
ejpam-5232	132	8	=	=	SYM
ejpam-5232	132	9	∑4	∑4	PROPN
ejpam-5232	132	10	i=0	i=0	PROPN
ejpam-5232	132	11	ui	ui	PROPN
ejpam-5232	132	12	,	,	PUNCT
ejpam-5232	132	13	then	then	ADV
ejpam-5232	132	14	we	we	PRON
ejpam-5232	132	15	find	find	VERB
ejpam-5232	132	16	z	z	NOUN
ejpam-5232	132	17	=	=	SYM
ejpam-5232	132	18	4.213845191×	4.213845191×	NUM
ejpam-5232	132	19	10−6	10−6	NUM
ejpam-5232	132	20	.	.	PUNCT
ejpam-5232	133	1	therefore	therefore	ADV
ejpam-5232	133	2	,	,	PUNCT
ejpam-5232	133	3	since	since	SCONJ
ejpam-5232	133	4	the	the	DET
ejpam-5232	133	5	constant	constant	ADJ
ejpam-5232	133	6	value	value	NOUN
ejpam-5232	133	7	of	of	ADP
ejpam-5232	133	8	z	z	PROPN
ejpam-5232	133	9	is	be	AUX
ejpam-5232	133	10	determined	determine	VERB
ejpam-5232	133	11	,	,	PUNCT
ejpam-5232	133	12	the	the	DET
ejpam-5232	133	13	series	series	NOUN
ejpam-5232	133	14	solution	solution	NOUN
ejpam-5232	133	15	of	of	ADP
ejpam-5232	133	16	the	the	DET
ejpam-5232	133	17	problem	problem	NOUN
ejpam-5232	133	18	follows	follow	VERB
ejpam-5232	133	19	instantly	instantly	ADV
ejpam-5232	133	20	.	.	PUNCT
ejpam-5232	134	1	the	the	DET
ejpam-5232	134	2	matching	matching	NOUN
ejpam-5232	134	3	of	of	ADP
ejpam-5232	134	4	φ5	φ5	PROPN
ejpam-5232	134	5	with	with	ADP
ejpam-5232	134	6	the	the	DET
ejpam-5232	134	7	exact	exact	ADJ
ejpam-5232	134	8	solution	solution	NOUN
ejpam-5232	134	9	is	be	AUX
ejpam-5232	134	10	accurate	accurate	ADJ
ejpam-5232	134	11	as	as	SCONJ
ejpam-5232	134	12	demonstrated	demonstrate	VERB
ejpam-5232	134	13	in	in	ADP
ejpam-5232	134	14	table	table	NOUN
ejpam-5232	134	15	2	2	NUM
ejpam-5232	134	16	.	.	PUNCT
ejpam-5232	135	1	in	in	ADP
ejpam-5232	135	2	figure	figure	NOUN
ejpam-5232	135	3	2	2	NUM
ejpam-5232	135	4	,	,	PUNCT
ejpam-5232	135	5	we	we	PRON
ejpam-5232	135	6	depict	depict	VERB
ejpam-5232	135	7	the	the	DET
ejpam-5232	135	8	curves	curve	NOUN
ejpam-5232	135	9	of	of	ADP
ejpam-5232	135	10	φ5	φ5	ADJ
ejpam-5232	135	11	and	and	CCONJ
ejpam-5232	135	12	the	the	DET
ejpam-5232	135	13	exact	exact	ADJ
ejpam-5232	135	14	analytical	analytical	ADJ
ejpam-5232	135	15	solution	solution	NOUN
ejpam-5232	135	16	u(x	u(x	NOUN
ejpam-5232	135	17	)	)	PUNCT
ejpam-5232	135	18	=	=	SYM
ejpam-5232	135	19	sin2	sin2	NOUN
ejpam-5232	135	20	πx	πx	NOUN
ejpam-5232	135	21	in	in	ADP
ejpam-5232	135	22	the	the	DET
ejpam-5232	135	23	approximate	approximate	ADJ
ejpam-5232	135	24	region	region	NOUN
ejpam-5232	135	25	0	0	NUM
ejpam-5232	135	26	≤	≤	NUM
ejpam-5232	135	27	x	x	SYM
ejpam-5232	135	28	≤	≤	NUM
ejpam-5232	135	29	1	1	NUM
ejpam-5232	135	30	.	.	PUNCT
ejpam-5232	135	31	table	table	NOUN
ejpam-5232	135	32	2	2	NUM
ejpam-5232	135	33	:	:	PUNCT
ejpam-5232	135	34	absolute	absolute	ADJ
ejpam-5232	135	35	error	error	NOUN
ejpam-5232	135	36	between	between	ADP
ejpam-5232	135	37	the	the	DET
ejpam-5232	135	38	exact	exact	ADJ
ejpam-5232	135	39	and	and	CCONJ
ejpam-5232	135	40	acdm	acdm	ADJ
ejpam-5232	135	41	solutions	solution	NOUN
ejpam-5232	135	42	in	in	ADP
ejpam-5232	135	43	example	example	NOUN
ejpam-5232	135	44	2	2	NUM
ejpam-5232	135	45	x	x	SYM
ejpam-5232	135	46	exact	exact	ADJ
ejpam-5232	135	47	solution	solution	NOUN
ejpam-5232	135	48	acdm	acdm	ADP
ejpam-5232	135	49	solution	solution	NOUN
ejpam-5232	135	50	absolute	absolute	ADJ
ejpam-5232	135	51	error	error	NOUN
ejpam-5232	135	52	0.0	0.0	NUM
ejpam-5232	135	53	0	0	NUM
ejpam-5232	135	54	0	0	NUM
ejpam-5232	135	55	0	0	NUM
ejpam-5232	135	56	0.1	0.1	NUM
ejpam-5232	135	57	9.54915028×	9.54915028×	NUM
ejpam-5232	135	58	10−2	10−2	NUM
ejpam-5232	135	59	9.54918613×	9.54918613×	NOUN
ejpam-5232	135	60	10−2	10−2	NUM
ejpam-5232	135	61	3.58489171×	3.58489171×	NUM
ejpam-5232	135	62	10−7	10−7	NUM
ejpam-5232	135	63	0.2	0.2	NUM
ejpam-5232	135	64	3.45491503×	3.45491503×	NUM
ejpam-5232	135	65	10−1	10−1	PROPN
ejpam-5232	135	66	3.45492103×	3.45492103×	NUM
ejpam-5232	135	67	10−1	10−1	NUM
ejpam-5232	135	68	6.00678252×	6.00678252×	NOUN
ejpam-5232	135	69	10−7	10−7	NUM
ejpam-5232	135	70	0.3	0.3	NUM
ejpam-5232	135	71	6.54508497×	6.54508497×	NUM
ejpam-5232	135	72	10−1	10−1	NUM
ejpam-5232	135	73	6.54509467×	6.54509467×	NUM
ejpam-5232	135	74	10−1	10−1	NUM
ejpam-5232	135	75	9.70293389×	9.70293389×	NUM
ejpam-5232	135	76	10−7	10−7	NUM
ejpam-5232	135	77	0.4	0.4	NUM
ejpam-5232	135	78	9.04508497×	9.04508497×	NUM
ejpam-5232	135	79	10−1	10−1	NUM
ejpam-5232	135	80	9.04510189×	9.04510189×	NOUN
ejpam-5232	135	81	10−1	10−1	NUM
ejpam-5232	135	82	1.69139683×	1.69139683×	NUM
ejpam-5232	135	83	10−6	10−6	NUM
ejpam-5232	135	84	0.5	0.5	NUM
ejpam-5232	135	85	1.00000000	1.00000000	NUM
ejpam-5232	135	86	1.00000133	1.00000133	NUM
ejpam-5232	135	87	1.33401846×	1.33401846×	NUM
ejpam-5232	135	88	10−6	10−6	NUM
ejpam-5232	135	89	0.6	0.6	NUM
ejpam-5232	135	90	9.04508497×	9.04508497×	NUM
ejpam-5232	135	91	10−1	10−1	NUM
ejpam-5232	135	92	9.04510994×	9.04510994×	NOUN
ejpam-5232	135	93	10−1	10−1	NUM
ejpam-5232	136	1	2.49639628×	2.49639628×	NUM
ejpam-5232	137	1	10−6	10−6	NUM
ejpam-5232	138	1	0.7	0.7	NUM
ejpam-5232	138	2	6.54508497×	6.54508497×	NUM
ejpam-5232	138	3	10−1	10−1	NUM
ejpam-5232	138	4	6.54511059×	6.54511059×	NUM
ejpam-5232	138	5	10−1	10−1	NUM
ejpam-5232	138	6	2.56152588×	2.56152588×	NUM
ejpam-5232	138	7	10−6	10−6	NUM
ejpam-5232	138	8	0.8	0.8	NUM
ejpam-5232	138	9	3.45491503×	3.45491503×	NUM
ejpam-5232	138	10	10−1	10−1	NUM
ejpam-5232	138	11	3.45494307×	3.45494307×	NUM
ejpam-5232	138	12	10−1	10−1	PROPN
ejpam-5232	138	13	2.80459804×	2.80459804×	NUM
ejpam-5232	138	14	10−6	10−6	NUM
ejpam-5232	138	15	0.9	0.9	NUM
ejpam-5232	138	16	9.54915028×	9.54915028×	NUM
ejpam-5232	138	17	10−2	10−2	NUM
ejpam-5232	138	18	9.54939626×	9.54939626×	NUM
ejpam-5232	138	19	10−2	10−2	NUM
ejpam-5232	138	20	2.45981055×	2.45981055×	NUM
ejpam-5232	138	21	10−6	10−6	NUM
ejpam-5232	138	22	1.0	1.0	NUM
ejpam-5232	138	23	−1.30000000×	−1.30000000×	NOUN
ejpam-5232	138	24	10−26	10−26	NUM
ejpam-5232	138	25	2.47124121×	2.47124121×	NUM
ejpam-5232	138	26	10−61	10−61	NOUN
ejpam-5232	138	27	1.30000000×	1.30000000×	NUM
ejpam-5232	138	28	10−26	10−26	NUM
ejpam-5232	138	29	h.	h.	NOUN
ejpam-5232	138	30	bakodah	bakodah	PROPN
ejpam-5232	138	31	et	et	PROPN
ejpam-5232	138	32	al	al	PROPN
ejpam-5232	138	33	.	.	PUNCT
ejpam-5232	138	34	/	/	SYM
ejpam-5232	138	35	eur	eur	PROPN
ejpam-5232	138	36	.	.	PUNCT
ejpam-5232	139	1	j.	j.	PROPN
ejpam-5232	139	2	pure	pure	PROPN
ejpam-5232	139	3	appl	appl	PROPN
ejpam-5232	139	4	.	.	PROPN
ejpam-5232	139	5	math	math	PROPN
ejpam-5232	139	6	,	,	PUNCT
ejpam-5232	139	7	17	17	NUM
ejpam-5232	139	8	(	(	PUNCT
ejpam-5232	139	9	3	3	NUM
ejpam-5232	139	10	)	)	PUNCT
ejpam-5232	139	11	(	(	PUNCT
ejpam-5232	139	12	2024	2024	NUM
ejpam-5232	139	13	)	)	PUNCT
ejpam-5232	139	14	,	,	PUNCT
ejpam-5232	139	15	1497	1497	NUM
ejpam-5232	139	16	-	-	SYM
ejpam-5232	139	17	1515	1515	NUM
ejpam-5232	139	18	1505	1505	NUM
ejpam-5232	139	19	figure	figure	NOUN
ejpam-5232	139	20	2	2	NUM
ejpam-5232	139	21	:	:	PUNCT
ejpam-5232	139	22	comparison	comparison	NOUN
ejpam-5232	139	23	between	between	ADP
ejpam-5232	139	24	the	the	DET
ejpam-5232	139	25	exact	exact	ADJ
ejpam-5232	139	26	and	and	CCONJ
ejpam-5232	139	27	acdm	acdm	ADJ
ejpam-5232	139	28	solutions	solution	NOUN
ejpam-5232	139	29	in	in	ADP
ejpam-5232	139	30	example	example	NOUN
ejpam-5232	139	31	2	2	NUM
ejpam-5232	139	32	example	example	NOUN
ejpam-5232	139	33	3	3	NUM
ejpam-5232	139	34	.	.	PUNCT
ejpam-5232	139	35	consider	consider	VERB
ejpam-5232	139	36	the	the	DET
ejpam-5232	139	37	following	follow	VERB
ejpam-5232	139	38	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	139	39	bvp	bvp	NOUN
ejpam-5232	139	40	[	[	X
ejpam-5232	139	41	18	18	NUM
ejpam-5232	139	42	]	]	SYM
ejpam-5232	139	43	u′′′(x	u′′′(x	PROPN
ejpam-5232	139	44	)	)	PUNCT
ejpam-5232	139	45	=	=	SYM
ejpam-5232	140	1	u(x)−	u(x)−	PROPN
ejpam-5232	140	2	3ex	3ex	NOUN
ejpam-5232	140	3	,	,	PUNCT
ejpam-5232	140	4	u(0	u(0	NOUN
ejpam-5232	140	5	)	)	PUNCT
ejpam-5232	140	6	=	=	SYM
ejpam-5232	140	7	1	1	X
ejpam-5232	140	8	,	,	PUNCT
ejpam-5232	140	9	u(1	u(1	PROPN
ejpam-5232	140	10	)	)	PUNCT
ejpam-5232	140	11	=	=	SYM
ejpam-5232	140	12	u′(0	u′(0	PROPN
ejpam-5232	140	13	)	)	PUNCT
ejpam-5232	140	14	=	=	SYM
ejpam-5232	140	15	0	0	NUM
ejpam-5232	140	16	,	,	PUNCT
ejpam-5232	140	17	(	(	PUNCT
ejpam-5232	140	18	22	22	NUM
ejpam-5232	140	19	)	)	PUNCT
ejpam-5232	140	20	that	that	PRON
ejpam-5232	140	21	admits	admit	VERB
ejpam-5232	140	22	the	the	DET
ejpam-5232	140	23	following	following	ADJ
ejpam-5232	140	24	exact	exact	ADJ
ejpam-5232	140	25	analytical	analytical	ADJ
ejpam-5232	140	26	solution	solution	NOUN
ejpam-5232	140	27	u(x	u(x	NOUN
ejpam-5232	140	28	)	)	PUNCT
ejpam-5232	140	29	=	=	SYM
ejpam-5232	140	30	(	(	PUNCT
ejpam-5232	140	31	1−	1−	NUM
ejpam-5232	140	32	x)ex	x)ex	PROPN
ejpam-5232	140	33	.	.	PUNCT
ejpam-5232	141	1	therefore	therefore	ADV
ejpam-5232	141	2	,	,	PUNCT
ejpam-5232	141	3	the	the	DET
ejpam-5232	141	4	adm	adm	NOUN
ejpam-5232	141	5	of	of	ADP
ejpam-5232	141	6	the	the	DET
ejpam-5232	141	7	bvp	bvp	NOUN
ejpam-5232	141	8	is	be	AUX
ejpam-5232	141	9	recurrently	recurrently	ADV
ejpam-5232	141	10	given	give	VERB
ejpam-5232	141	11	as	as	ADP
ejpam-5232	141	12	followsu0(x	followsu0(x	NOUN
ejpam-5232	141	13	)	)	PUNCT
ejpam-5232	141	14	=	=	SYM
ejpam-5232	141	15	u(0	u(0	NOUN
ejpam-5232	141	16	)	)	PUNCT
ejpam-5232	142	1	+	+	CCONJ
ejpam-5232	142	2	xu′(0	xu′(0	NOUN
ejpam-5232	142	3	)	)	PUNCT
ejpam-5232	143	1	+	+	CCONJ
ejpam-5232	143	2	tx2	tx2	NOUN
ejpam-5232	143	3	2	2	NUM
ejpam-5232	143	4	+	+	CCONJ
ejpam-5232	143	5	l−1g(x	l−1g(x	ADJ
ejpam-5232	143	6	)	)	PUNCT
ejpam-5232	143	7	,	,	PUNCT
ejpam-5232	143	8	un+1(x	un+1(x	NOUN
ejpam-5232	143	9	)	)	PUNCT
ejpam-5232	143	10	=	=	NOUN
ejpam-5232	143	11	l−1un	l−1un	NOUN
ejpam-5232	143	12	,	,	PUNCT
ejpam-5232	143	13	n	n	PRON
ejpam-5232	143	14	≥	≥	NOUN
ejpam-5232	143	15	0	0	NUM
ejpam-5232	143	16	,	,	PUNCT
ejpam-5232	143	17	where	where	SCONJ
ejpam-5232	143	18	l	l	NOUN
ejpam-5232	143	19	(	(	PUNCT
ejpam-5232	143	20	.	.	PUNCT
ejpam-5232	143	21	)	)	PUNCT
ejpam-5232	144	1	=	=	PRON
ejpam-5232	144	2	d3	d3	PROPN
ejpam-5232	144	3	(	(	PUNCT
ejpam-5232	144	4	.	.	PUNCT
ejpam-5232	144	5	)	)	PUNCT
ejpam-5232	145	1	dxx	dxx	NOUN
ejpam-5232	145	2	,	,	PUNCT
ejpam-5232	145	3	g(x	g(x	NOUN
ejpam-5232	145	4	)	)	PUNCT
ejpam-5232	145	5	=	=	SYM
ejpam-5232	145	6	−3ex	−3ex	PROPN
ejpam-5232	145	7	and	and	CCONJ
ejpam-5232	145	8	,	,	PUNCT
ejpam-5232	145	9	l−1	l−1	PROPN
ejpam-5232	145	10	(	(	PUNCT
ejpam-5232	145	11	.	.	PUNCT
ejpam-5232	145	12	)	)	PUNCT
ejpam-5232	146	1	=	=	PUNCT
ejpam-5232	147	1	∫	∫	PUNCT
ejpam-5232	147	2	x	x	SYM
ejpam-5232	147	3	0	0	NUM
ejpam-5232	147	4	∫	∫	PROPN
ejpam-5232	147	5	x	x	SYM
ejpam-5232	147	6	0	0	NUM
ejpam-5232	147	7	∫	∫	PROPN
ejpam-5232	147	8	x	x	SYM
ejpam-5232	147	9	0	0	PROPN
ejpam-5232	147	10	(	(	PUNCT
ejpam-5232	147	11	.)dxdxdx	.)dxdxdx	ADJ
ejpam-5232	147	12	.	.	PUNCT
ejpam-5232	148	1	as	as	ADP
ejpam-5232	148	2	proceeding	proceed	VERB
ejpam-5232	148	3	before	before	ADV
ejpam-5232	148	4	,	,	PUNCT
ejpam-5232	148	5	we	we	PRON
ejpam-5232	148	6	determine	determine	VERB
ejpam-5232	148	7	g(x	g(x	NOUN
ejpam-5232	148	8	)	)	PUNCT
ejpam-5232	148	9	as	as	SCONJ
ejpam-5232	148	10	follows	follow	VERB
ejpam-5232	148	11	g(x	g(x	NOUN
ejpam-5232	148	12	)	)	PUNCT
ejpam-5232	149	1	∼=	∼=	PROPN
ejpam-5232	149	2	−3.0000000000000581−	−3.0000000000000581−	PROPN
ejpam-5232	149	3	2.99999999998x−	2.99999999998x−	NUM
ejpam-5232	149	4	1.500000000558x2−	1.500000000558x2−	NUM
ejpam-5232	149	5	0.49999999133x3	0.49999999133x3	NUM
ejpam-5232	149	6	+	+	CCONJ
ejpam-5232	149	7	·	·	PUNCT
ejpam-5232	149	8	·	·	PUNCT
ejpam-5232	149	9	·	·	PUNCT
ejpam-5232	150	1	in	in	ADP
ejpam-5232	150	2	similar	similar	ADJ
ejpam-5232	150	3	manner	manner	NOUN
ejpam-5232	150	4	,	,	PUNCT
ejpam-5232	150	5	we	we	PRON
ejpam-5232	150	6	get	get	VERB
ejpam-5232	150	7	t	t	NOUN
ejpam-5232	150	8	=	=	SYM
ejpam-5232	150	9	−0.9999999999985	−0.9999999999985	PROPN
ejpam-5232	150	10	.	.	PUNCT
ejpam-5232	151	1	therefore	therefore	ADV
ejpam-5232	151	2	,	,	PUNCT
ejpam-5232	151	3	since	since	SCONJ
ejpam-5232	151	4	the	the	DET
ejpam-5232	151	5	constant	constant	ADJ
ejpam-5232	151	6	value	value	NOUN
ejpam-5232	151	7	of	of	ADP
ejpam-5232	151	8	t	t	PROPN
ejpam-5232	151	9	is	be	AUX
ejpam-5232	151	10	determined	determine	VERB
ejpam-5232	151	11	,	,	PUNCT
ejpam-5232	151	12	the	the	DET
ejpam-5232	151	13	series	series	NOUN
ejpam-5232	151	14	solution	solution	NOUN
ejpam-5232	151	15	of	of	ADP
ejpam-5232	151	16	the	the	DET
ejpam-5232	151	17	problem	problem	NOUN
ejpam-5232	151	18	follows	follow	VERB
ejpam-5232	151	19	instantly	instantly	ADV
ejpam-5232	151	20	.	.	PUNCT
ejpam-5232	152	1	the	the	DET
ejpam-5232	152	2	matching	matching	NOUN
ejpam-5232	152	3	of	of	ADP
ejpam-5232	152	4	φ5	φ5	PROPN
ejpam-5232	152	5	with	with	ADP
ejpam-5232	152	6	the	the	DET
ejpam-5232	152	7	exact	exact	ADJ
ejpam-5232	152	8	solution	solution	NOUN
ejpam-5232	152	9	is	be	AUX
ejpam-5232	152	10	remarkable	remarkable	ADJ
ejpam-5232	152	11	as	as	SCONJ
ejpam-5232	152	12	reported	report	VERB
ejpam-5232	152	13	in	in	ADP
ejpam-5232	152	14	table	table	NOUN
ejpam-5232	152	15	3	3	NUM
ejpam-5232	152	16	.	.	PUNCT
ejpam-5232	153	1	in	in	ADP
ejpam-5232	153	2	figure	figure	NOUN
ejpam-5232	153	3	3	3	NUM
ejpam-5232	153	4	,	,	PUNCT
ejpam-5232	153	5	we	we	PRON
ejpam-5232	153	6	depict	depict	VERB
ejpam-5232	153	7	the	the	DET
ejpam-5232	153	8	curves	curve	NOUN
ejpam-5232	153	9	of	of	ADP
ejpam-5232	153	10	φ5	φ5	ADJ
ejpam-5232	153	11	and	and	CCONJ
ejpam-5232	153	12	the	the	DET
ejpam-5232	153	13	exact	exact	ADJ
ejpam-5232	153	14	analytical	analytical	ADJ
ejpam-5232	153	15	solution	solution	NOUN
ejpam-5232	153	16	u(x	u(x	NOUN
ejpam-5232	153	17	)	)	PUNCT
ejpam-5232	153	18	=	=	SYM
ejpam-5232	153	19	(	(	PUNCT
ejpam-5232	153	20	1−	1−	NUM
ejpam-5232	153	21	x)ex	x)ex	PROPN
ejpam-5232	153	22	in	in	ADP
ejpam-5232	153	23	the	the	DET
ejpam-5232	153	24	approximate	approximate	ADJ
ejpam-5232	153	25	region	region	NOUN
ejpam-5232	154	1	0	0	NUM
ejpam-5232	154	2	≤	≤	NUM
ejpam-5232	154	3	x	x	SYM
ejpam-5232	154	4	≤	≤	NUM
ejpam-5232	154	5	1	1	NUM
ejpam-5232	154	6	.	.	PUNCT
ejpam-5232	154	7	h.	h.	PROPN
ejpam-5232	154	8	bakodah	bakodah	PROPN
ejpam-5232	154	9	et	et	PROPN
ejpam-5232	154	10	al	al	PROPN
ejpam-5232	154	11	.	.	PUNCT
ejpam-5232	154	12	/	/	SYM
ejpam-5232	154	13	eur	eur	PROPN
ejpam-5232	154	14	.	.	PUNCT
ejpam-5232	155	1	j.	j.	PROPN
ejpam-5232	155	2	pure	pure	PROPN
ejpam-5232	155	3	appl	appl	PROPN
ejpam-5232	155	4	.	.	PROPN
ejpam-5232	155	5	math	math	PROPN
ejpam-5232	155	6	,	,	PUNCT
ejpam-5232	155	7	17	17	NUM
ejpam-5232	155	8	(	(	PUNCT
ejpam-5232	155	9	3	3	NUM
ejpam-5232	155	10	)	)	PUNCT
ejpam-5232	155	11	(	(	PUNCT
ejpam-5232	155	12	2024	2024	NUM
ejpam-5232	155	13	)	)	PUNCT
ejpam-5232	155	14	,	,	PUNCT
ejpam-5232	155	15	1497	1497	NUM
ejpam-5232	155	16	-	-	SYM
ejpam-5232	155	17	1515	1515	NUM
ejpam-5232	155	18	1506	1506	NUM
ejpam-5232	155	19	table	table	NOUN
ejpam-5232	155	20	3	3	NUM
ejpam-5232	155	21	:	:	PUNCT
ejpam-5232	155	22	absolute	absolute	ADJ
ejpam-5232	155	23	error	error	NOUN
ejpam-5232	155	24	between	between	ADP
ejpam-5232	155	25	the	the	DET
ejpam-5232	155	26	exact	exact	ADJ
ejpam-5232	155	27	and	and	CCONJ
ejpam-5232	155	28	acdm	acdm	ADJ
ejpam-5232	155	29	solutions	solution	NOUN
ejpam-5232	155	30	in	in	ADP
ejpam-5232	155	31	example	example	NOUN
ejpam-5232	155	32	3	3	NUM
ejpam-5232	155	33	x	x	NOUN
ejpam-5232	155	34	exact	exact	ADJ
ejpam-5232	155	35	solution	solution	NOUN
ejpam-5232	155	36	acdm	acdm	ADP
ejpam-5232	155	37	solution	solution	NOUN
ejpam-5232	155	38	absolute	absolute	ADJ
ejpam-5232	155	39	error	error	NOUN
ejpam-5232	155	40	0.0	0.0	NUM
ejpam-5232	155	41	1	1	NUM
ejpam-5232	155	42	1	1	NUM
ejpam-5232	155	43	0	0	NUM
ejpam-5232	155	44	0.1	0.1	NUM
ejpam-5232	155	45	9.94653826×	9.94653826×	NUM
ejpam-5232	155	46	10−1	10−1	NUM
ejpam-5232	155	47	9.94653826×	9.94653826×	NUM
ejpam-5232	155	48	10−1	10−1	NUM
ejpam-5232	155	49	7.49228630×	7.49228630×	NUM
ejpam-5232	155	50	10−15	10−15	NUM
ejpam-5232	155	51	0.2	0.2	NUM
ejpam-5232	155	52	9.77122207×	9.77122207×	NUM
ejpam-5232	155	53	10−1	10−1	NUM
ejpam-5232	155	54	9.77122207×	9.77122207×	NUM
ejpam-5232	155	55	10−1	10−1	NUM
ejpam-5232	155	56	2.99634613×	2.99634613×	NOUN
ejpam-5232	155	57	10−14	10−14	NUM
ejpam-5232	155	58	0.3	0.3	NUM
ejpam-5232	155	59	9.44901165×	9.44901165×	NOUN
ejpam-5232	155	60	10−1	10−1	NUM
ejpam-5232	155	61	9.44901165×	9.44901165×	NUM
ejpam-5232	155	62	10−1	10−1	PROPN
ejpam-5232	155	63	6.74469668×	6.74469668×	NUM
ejpam-5232	155	64	10−14	10−14	NUM
ejpam-5232	155	65	0.4	0.4	NUM
ejpam-5232	155	66	8.95094819×	8.95094819×	NOUN
ejpam-5232	155	67	10−1	10−1	PROPN
ejpam-5232	155	68	8.95094819×	8.95094819×	ADP
ejpam-5232	155	69	10−1	10−1	NUM
ejpam-5232	155	70	1.19977986×	1.19977986×	NUM
ejpam-5232	155	71	10−13	10−13	NUM
ejpam-5232	155	72	0.5	0.5	NUM
ejpam-5232	155	73	8.24360635×	8.24360635×	NUM
ejpam-5232	155	74	10−1	10−1	PROPN
ejpam-5232	155	75	8.24360635×	8.24360635×	NUM
ejpam-5232	155	76	10−1	10−1	PROPN
ejpam-5232	155	77	1.87622933×	1.87622933×	NUM
ejpam-5232	155	78	10−13	10−13	PROPN
ejpam-5232	155	79	0.6	0.6	NUM
ejpam-5232	155	80	7.28847520×	7.28847520×	NUM
ejpam-5232	155	81	10−1	10−1	NUM
ejpam-5232	155	82	7.2887520×	7.2887520×	NUM
ejpam-5232	155	83	10−1	10−1	NUM
ejpam-5232	155	84	2.70272115×	2.70272115×	NOUN
ejpam-5232	155	85	10−13	10−13	PROPN
ejpam-5232	155	86	0.7	0.7	NUM
ejpam-5232	155	87	6.04125812×	6.04125812×	NUM
ejpam-5232	155	88	10−1	10−1	PROPN
ejpam-5232	155	89	6.04125812×	6.04125812×	NUM
ejpam-5232	155	90	10−1	10−1	NUM
ejpam-5232	155	91	3.65511599×	3.65511599×	NUM
ejpam-5232	155	92	10−13	10−13	NUM
ejpam-5232	155	93	0.8	0.8	NUM
ejpam-5232	155	94	4.45108186×	4.45108186×	NUM
ejpam-5232	155	95	10−1	10−1	NUM
ejpam-5232	155	96	4.45108186×	4.45108186×	NUM
ejpam-5232	155	97	10−1	10−1	NUM
ejpam-5232	155	98	4.56646544×	4.56646544×	NUM
ejpam-5232	155	99	10−13	10−13	PROPN
ejpam-5232	155	100	0.9	0.9	NUM
ejpam-5232	155	101	2.45960311×	2.45960311×	NUM
ejpam-5232	155	102	10−1	10−1	NUM
ejpam-5232	155	103	2.45960311×	2.45960311×	NUM
ejpam-5232	155	104	10−1	10−1	NUM
ejpam-5232	155	105	4.57186783×	4.57186783×	NOUN
ejpam-5232	155	106	10−13	10−13	PROPN
ejpam-5232	155	107	1.0	1.0	NUM
ejpam-5232	155	108	0	0	NUM
ejpam-5232	155	109	1×	1×	NUM
ejpam-5232	155	110	10−30	10−30	PROPN
ejpam-5232	155	111	1×	1×	NUM
ejpam-5232	155	112	10−30	10−30	PROPN
ejpam-5232	155	113	figure	figure	NOUN
ejpam-5232	155	114	3	3	NUM
ejpam-5232	155	115	:	:	PUNCT
ejpam-5232	155	116	comparison	comparison	NOUN
ejpam-5232	155	117	between	between	ADP
ejpam-5232	155	118	the	the	DET
ejpam-5232	155	119	exact	exact	ADJ
ejpam-5232	155	120	and	and	CCONJ
ejpam-5232	155	121	acdm	acdm	ADJ
ejpam-5232	155	122	solutions	solution	NOUN
ejpam-5232	155	123	in	in	ADP
ejpam-5232	155	124	example	example	NOUN
ejpam-5232	155	125	3	3	NUM
ejpam-5232	155	126	example	example	NOUN
ejpam-5232	155	127	4	4	NUM
ejpam-5232	155	128	.	.	PUNCT
ejpam-5232	155	129	consider	consider	VERB
ejpam-5232	155	130	the	the	DET
ejpam-5232	155	131	following	follow	VERB
ejpam-5232	155	132	nonlinear	nonlinear	ADJ
ejpam-5232	155	133	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	155	134	bvp	bvp	NOUN
ejpam-5232	155	135	[	[	X
ejpam-5232	155	136	1	1	NUM
ejpam-5232	155	137	]	]	PUNCT
ejpam-5232	155	138	u(iv)(x	u(iv)(x	NOUN
ejpam-5232	155	139	)	)	PUNCT
ejpam-5232	156	1	=	=	PUNCT
ejpam-5232	157	1	u2(x)−	u2(x)−	X
ejpam-5232	157	2	x10	x10	NOUN
ejpam-5232	157	3	+	+	NOUN
ejpam-5232	157	4	4x9	4x9	NUM
ejpam-5232	157	5	−	−	NUM
ejpam-5232	157	6	4x8	4x8	NUM
ejpam-5232	157	7	−	−	NUM
ejpam-5232	157	8	4x7	4x7	NUM
ejpam-5232	158	1	+	+	CCONJ
ejpam-5232	158	2	8x6	8x6	NUM
ejpam-5232	158	3	−	−	NUM
ejpam-5232	158	4	4x4	4x4	NUM
ejpam-5232	159	1	+	+	CCONJ
ejpam-5232	159	2	120x−	120x−	NUM
ejpam-5232	159	3	48	48	NUM
ejpam-5232	159	4	,	,	PUNCT
ejpam-5232	159	5	u(0	u(0	NOUN
ejpam-5232	159	6	)	)	PUNCT
ejpam-5232	159	7	=	=	SYM
ejpam-5232	159	8	u′(0	u′(0	PROPN
ejpam-5232	159	9	)	)	PUNCT
ejpam-5232	159	10	=	=	SYM
ejpam-5232	159	11	0	0	NUM
ejpam-5232	159	12	,	,	PUNCT
ejpam-5232	159	13	u(1	u(1	PROPN
ejpam-5232	159	14	)	)	PUNCT
ejpam-5232	159	15	=	=	SYM
ejpam-5232	159	16	u′(1	u′(1	NOUN
ejpam-5232	159	17	)	)	PUNCT
ejpam-5232	159	18	=	=	SYM
ejpam-5232	159	19	1	1	NUM
ejpam-5232	159	20	,	,	PUNCT
ejpam-5232	159	21	(	(	PUNCT
ejpam-5232	159	22	23	23	NUM
ejpam-5232	159	23	)	)	PUNCT
ejpam-5232	159	24	having	have	VERB
ejpam-5232	159	25	the	the	DET
ejpam-5232	159	26	following	follow	VERB
ejpam-5232	159	27	exact	exact	ADJ
ejpam-5232	159	28	analytical	analytical	ADJ
ejpam-5232	159	29	solution	solution	NOUN
ejpam-5232	159	30	u(x	u(x	NOUN
ejpam-5232	159	31	)	)	PUNCT
ejpam-5232	159	32	=	=	SYM
ejpam-5232	159	33	x5	x5	NOUN
ejpam-5232	159	34	−	−	NUM
ejpam-5232	159	35	2x4	2x4	NUM
ejpam-5232	159	36	+	+	SYM
ejpam-5232	159	37	2x2	2x2	NUM
ejpam-5232	159	38	.	.	PUNCT
ejpam-5232	160	1	h.	h.	PROPN
ejpam-5232	160	2	bakodah	bakodah	PROPN
ejpam-5232	160	3	et	et	PROPN
ejpam-5232	160	4	al	al	PROPN
ejpam-5232	160	5	.	.	PUNCT
ejpam-5232	160	6	/	/	SYM
ejpam-5232	160	7	eur	eur	PROPN
ejpam-5232	160	8	.	.	PUNCT
ejpam-5232	161	1	j.	j.	PROPN
ejpam-5232	161	2	pure	pure	PROPN
ejpam-5232	161	3	appl	appl	PROPN
ejpam-5232	161	4	.	.	PROPN
ejpam-5232	161	5	math	math	PROPN
ejpam-5232	161	6	,	,	PUNCT
ejpam-5232	161	7	17	17	NUM
ejpam-5232	161	8	(	(	PUNCT
ejpam-5232	161	9	3	3	NUM
ejpam-5232	161	10	)	)	PUNCT
ejpam-5232	161	11	(	(	PUNCT
ejpam-5232	161	12	2024	2024	NUM
ejpam-5232	161	13	)	)	PUNCT
ejpam-5232	161	14	,	,	PUNCT
ejpam-5232	161	15	1497	1497	NUM
ejpam-5232	161	16	-	-	SYM
ejpam-5232	161	17	1515	1515	NUM
ejpam-5232	161	18	1507	1507	NUM
ejpam-5232	161	19	accordingly	accordingly	ADV
ejpam-5232	162	1	,	,	PUNCT
ejpam-5232	162	2	the	the	DET
ejpam-5232	162	3	adm	adm	NOUN
ejpam-5232	162	4	gives	give	VERB
ejpam-5232	162	5	the	the	DET
ejpam-5232	162	6	following	follow	VERB
ejpam-5232	162	7	recurrent	recurrent	ADJ
ejpam-5232	162	8	relation	relation	NOUN
ejpam-5232	162	9	to	to	ADP
ejpam-5232	162	10	the	the	DET
ejpam-5232	162	11	bvp	bvp	X
ejpam-5232	162	12	u0(x	u0(x	NOUN
ejpam-5232	162	13	)	)	PUNCT
ejpam-5232	162	14	=	=	SYM
ejpam-5232	162	15	u(0	u(0	NOUN
ejpam-5232	162	16	)	)	PUNCT
ejpam-5232	163	1	+	+	CCONJ
ejpam-5232	163	2	xu′(0	xu′(0	NOUN
ejpam-5232	163	3	)	)	PUNCT
ejpam-5232	164	1	+	+	CCONJ
ejpam-5232	164	2	tx2	tx2	NOUN
ejpam-5232	164	3	2	2	NUM
ejpam-5232	164	4	!	!	PUNCT
ejpam-5232	165	1	+	+	CCONJ
ejpam-5232	165	2	kx3	kx3	NOUN
ejpam-5232	165	3	3	3	NUM
ejpam-5232	165	4	!	!	PUNCT
ejpam-5232	166	1	+	+	CCONJ
ejpam-5232	166	2	l−1g(x	l−1g(x	ADJ
ejpam-5232	166	3	)	)	PUNCT
ejpam-5232	166	4	,	,	PUNCT
ejpam-5232	166	5	un+1(x	un+1(x	NOUN
ejpam-5232	166	6	)	)	PUNCT
ejpam-5232	166	7	=	=	SYM
ejpam-5232	166	8	l−1an	l−1an	NOUN
ejpam-5232	166	9	,	,	PUNCT
ejpam-5232	166	10	n	n	X
ejpam-5232	166	11	≥	≥	NOUN
ejpam-5232	166	12	0	0	NUM
ejpam-5232	166	13	.	.	PUNCT
ejpam-5232	167	1	where	where	SCONJ
ejpam-5232	167	2	l	l	NOUN
ejpam-5232	167	3	(	(	PUNCT
ejpam-5232	167	4	.	.	PUNCT
ejpam-5232	167	5	)	)	PUNCT
ejpam-5232	167	6	=	=	PUNCT
ejpam-5232	167	7	d4	d4	PROPN
ejpam-5232	167	8	(	(	PUNCT
ejpam-5232	167	9	.	.	PUNCT
ejpam-5232	167	10	)	)	PUNCT
ejpam-5232	168	1	dx4	dx4	INTJ
ejpam-5232	168	2	,	,	PUNCT
ejpam-5232	168	3	g(x	g(x	NOUN
ejpam-5232	168	4	)	)	PUNCT
ejpam-5232	169	1	=	=	PUNCT
ejpam-5232	170	1	−x10	−x10	PROPN
ejpam-5232	170	2	+	+	NOUN
ejpam-5232	170	3	4x9	4x9	NUM
ejpam-5232	170	4	−	−	NUM
ejpam-5232	170	5	4x8	4x8	NUM
ejpam-5232	170	6	−	−	NUM
ejpam-5232	170	7	4x7	4x7	NUM
ejpam-5232	171	1	+	+	CCONJ
ejpam-5232	171	2	8x6	8x6	NUM
ejpam-5232	171	3	−	−	NUM
ejpam-5232	171	4	4x4	4x4	NUM
ejpam-5232	172	1	+	+	SYM
ejpam-5232	172	2	120x−	120x−	NUM
ejpam-5232	172	3	48	48	NUM
ejpam-5232	172	4	and	and	CCONJ
ejpam-5232	172	5	l−1	l−1	PROPN
ejpam-5232	172	6	(	(	PUNCT
ejpam-5232	172	7	.	.	PUNCT
ejpam-5232	172	8	)	)	PUNCT
ejpam-5232	173	1	=	=	NOUN
ejpam-5232	173	2	∫	∫	NOUN
ejpam-5232	173	3	x	x	SYM
ejpam-5232	173	4	0	0	NUM
ejpam-5232	173	5	∫	∫	PROPN
ejpam-5232	173	6	x	x	SYM
ejpam-5232	173	7	0	0	NUM
ejpam-5232	173	8	∫	∫	PROPN
ejpam-5232	173	9	x	x	SYM
ejpam-5232	173	10	0	0	NUM
ejpam-5232	173	11	∫	∫	PROPN
ejpam-5232	173	12	x	x	SYM
ejpam-5232	173	13	0	0	NUM
ejpam-5232	173	14	(	(	PUNCT
ejpam-5232	173	15	.)dxdxdxdx	.)dxdxdxdx	NOUN
ejpam-5232	173	16	.	.	PUNCT
ejpam-5232	174	1	in	in	ADP
ejpam-5232	174	2	similar	similar	ADJ
ejpam-5232	174	3	manner	manner	NOUN
ejpam-5232	174	4	,	,	PUNCT
ejpam-5232	174	5	g(x	g(x	NOUN
ejpam-5232	174	6	)	)	PUNCT
ejpam-5232	174	7	becomes	become	VERB
ejpam-5232	174	8	g(x	g(x	NOUN
ejpam-5232	174	9	)	)	PUNCT
ejpam-5232	174	10	∼=	∼=	PROPN
ejpam-5232	174	11	−48	−48	PRON
ejpam-5232	175	1	+	+	NUM
ejpam-5232	175	2	120x−	120x−	NUM
ejpam-5232	175	3	1×	1×	NUM
ejpam-5232	175	4	10−29x2	10−29x2	CCONJ
ejpam-5232	176	1	−	−	PROPN
ejpam-5232	176	2	4x4	4x4	NUM
ejpam-5232	177	1	+	+	NUM
ejpam-5232	177	2	8x6	8x6	NUM
ejpam-5232	177	3	−	−	NUM
ejpam-5232	177	4	4x7	4x7	NUM
ejpam-5232	178	1	+	+	CCONJ
ejpam-5232	178	2	·	·	PUNCT
ejpam-5232	178	3	·	·	PUNCT
ejpam-5232	179	1	·	·	PUNCT
ejpam-5232	179	2	.	.	PUNCT
ejpam-5232	180	1	now	now	ADV
ejpam-5232	180	2	,	,	PUNCT
ejpam-5232	180	3	we	we	PRON
ejpam-5232	180	4	determine	determine	VERB
ejpam-5232	180	5	t	t	NOUN
ejpam-5232	180	6	=	=	SYM
ejpam-5232	180	7	3.9999999999	3.9999999999	NUM
ejpam-5232	180	8	,	,	PUNCT
ejpam-5232	180	9	and	and	CCONJ
ejpam-5232	180	10	k	k	PROPN
ejpam-5232	180	11	=	=	SYM
ejpam-5232	180	12	3.319466361×	3.319466361×	NUM
ejpam-5232	180	13	10−17	10−17	NUM
ejpam-5232	180	14	.	.	PUNCT
ejpam-5232	181	1	therefore	therefore	ADV
ejpam-5232	181	2	,	,	PUNCT
ejpam-5232	181	3	since	since	SCONJ
ejpam-5232	181	4	the	the	DET
ejpam-5232	181	5	constant	constant	ADJ
ejpam-5232	181	6	values	value	NOUN
ejpam-5232	181	7	of	of	ADP
ejpam-5232	181	8	t	t	PROPN
ejpam-5232	181	9	and	and	CCONJ
ejpam-5232	181	10	k	k	PROPN
ejpam-5232	181	11	are	be	AUX
ejpam-5232	181	12	determined	determine	VERB
ejpam-5232	181	13	,	,	PUNCT
ejpam-5232	181	14	the	the	DET
ejpam-5232	181	15	series	series	NOUN
ejpam-5232	181	16	solution	solution	NOUN
ejpam-5232	181	17	of	of	ADP
ejpam-5232	181	18	the	the	DET
ejpam-5232	181	19	problem	problem	NOUN
ejpam-5232	181	20	follows	follow	VERB
ejpam-5232	181	21	instantly	instantly	ADV
ejpam-5232	181	22	.	.	PUNCT
ejpam-5232	182	1	the	the	DET
ejpam-5232	182	2	matching	matching	NOUN
ejpam-5232	182	3	of	of	ADP
ejpam-5232	182	4	φ5	φ5	PROPN
ejpam-5232	182	5	with	with	ADP
ejpam-5232	182	6	the	the	DET
ejpam-5232	182	7	exact	exact	ADJ
ejpam-5232	182	8	solution	solution	NOUN
ejpam-5232	182	9	is	be	AUX
ejpam-5232	182	10	amazing	amazing	ADJ
ejpam-5232	182	11	as	as	SCONJ
ejpam-5232	182	12	reported	report	VERB
ejpam-5232	182	13	in	in	ADP
ejpam-5232	182	14	table	table	NOUN
ejpam-5232	182	15	4	4	NUM
ejpam-5232	182	16	.	.	PUNCT
ejpam-5232	183	1	in	in	ADP
ejpam-5232	183	2	figure	figure	NOUN
ejpam-5232	183	3	4	4	NUM
ejpam-5232	183	4	,	,	PUNCT
ejpam-5232	183	5	we	we	PRON
ejpam-5232	183	6	depict	depict	VERB
ejpam-5232	183	7	the	the	DET
ejpam-5232	183	8	curves	curve	NOUN
ejpam-5232	183	9	of	of	ADP
ejpam-5232	183	10	φ5	φ5	ADJ
ejpam-5232	183	11	and	and	CCONJ
ejpam-5232	183	12	that	that	PRON
ejpam-5232	183	13	of	of	ADP
ejpam-5232	183	14	the	the	DET
ejpam-5232	183	15	exact	exact	ADJ
ejpam-5232	183	16	analytical	analytical	ADJ
ejpam-5232	183	17	solution	solution	NOUN
ejpam-5232	183	18	u(x	u(x	NOUN
ejpam-5232	183	19	)	)	PUNCT
ejpam-5232	183	20	=	=	SYM
ejpam-5232	183	21	x5	x5	NOUN
ejpam-5232	183	22	−	−	NUM
ejpam-5232	183	23	2x4	2x4	NUM
ejpam-5232	184	1	+	+	CCONJ
ejpam-5232	184	2	2x2	2x2	NUM
ejpam-5232	184	3	in	in	ADP
ejpam-5232	184	4	the	the	DET
ejpam-5232	184	5	approximate	approximate	ADJ
ejpam-5232	184	6	region	region	NOUN
ejpam-5232	184	7	0	0	NUM
ejpam-5232	184	8	≤	≤	NUM
ejpam-5232	184	9	x	x	SYM
ejpam-5232	184	10	≤	≤	NUM
ejpam-5232	184	11	1	1	NUM
ejpam-5232	184	12	.	.	PUNCT
ejpam-5232	184	13	table	table	NOUN
ejpam-5232	184	14	4	4	NUM
ejpam-5232	184	15	:	:	PUNCT
ejpam-5232	184	16	absolute	absolute	ADJ
ejpam-5232	184	17	error	error	NOUN
ejpam-5232	184	18	between	between	ADP
ejpam-5232	184	19	the	the	DET
ejpam-5232	184	20	exact	exact	ADJ
ejpam-5232	184	21	and	and	CCONJ
ejpam-5232	184	22	acdm	acdm	ADJ
ejpam-5232	184	23	solutions	solution	NOUN
ejpam-5232	184	24	in	in	ADP
ejpam-5232	184	25	example	example	NOUN
ejpam-5232	184	26	1	1	NUM
ejpam-5232	184	27	x	x	SYM
ejpam-5232	184	28	exact	exact	ADJ
ejpam-5232	184	29	solution	solution	NOUN
ejpam-5232	184	30	acdm	acdm	ADP
ejpam-5232	184	31	solution	solution	NOUN
ejpam-5232	184	32	absolute	absolute	ADJ
ejpam-5232	184	33	error	error	NOUN
ejpam-5232	184	34	0.0	0.0	NUM
ejpam-5232	184	35	0	0	NUM
ejpam-5232	184	36	0	0	NUM
ejpam-5232	184	37	0	0	NUM
ejpam-5232	184	38	0.1	0.1	NUM
ejpam-5232	184	39	1.98100000×	1.98100000×	NUM
ejpam-5232	184	40	10−2	10−2	NUM
ejpam-5232	184	41	1.9810000×	1.9810000×	NUM
ejpam-5232	184	42	10−2	10−2	NUM
ejpam-5232	184	43	4.77923286×	4.77923286×	NUM
ejpam-5232	184	44	10−20	10−20	NOUN
ejpam-5232	184	45	0.2	0.2	NUM
ejpam-5232	184	46	7.71200000×	7.71200000×	NUM
ejpam-5232	184	47	10−2	10−2	NUM
ejpam-5232	184	48	7.71200000×	7.71200000×	NUM
ejpam-5232	184	49	10−2	10−2	NUM
ejpam-5232	184	50	1.69039567×	1.69039567×	NUM
ejpam-5232	184	51	10−19	10−19	NOUN
ejpam-5232	184	52	0.3	0.3	NUM
ejpam-5232	184	53	1.66230000×	1.66230000×	NUM
ejpam-5232	184	54	10−1	10−1	NUM
ejpam-5232	184	55	1.66230000×	1.66230000×	NUM
ejpam-5232	184	56	10−1	10−1	NUM
ejpam-5232	184	57	3.30547636×	3.30547636×	NUM
ejpam-5232	184	58	10−19	10−19	NOUN
ejpam-5232	184	59	0.4	0.4	NUM
ejpam-5232	184	60	2.79040000×	2.79040000×	NUM
ejpam-5232	184	61	10−1	10−1	NUM
ejpam-5232	184	62	2.79040000×	2.79040000×	NUM
ejpam-5232	184	63	10−1	10−1	NUM
ejpam-5232	184	64	4.99126063×	4.99126063×	NUM
ejpam-5232	184	65	10−19	10−19	NOUN
ejpam-5232	184	66	0.5	0.5	NUM
ejpam-5232	184	67	4.06250000×	4.06250000×	NOUN
ejpam-5232	184	68	10−1	10−1	NUM
ejpam-5232	184	69	4.06250000×	4.06250000×	NOUN
ejpam-5232	184	70	10−1	10−1	NUM
ejpam-5232	184	71	6.41596782×	6.41596782×	NOUN
ejpam-5232	184	72	10−19	10−19	NOUN
ejpam-5232	184	73	0.6	0.6	NUM
ejpam-5232	184	74	5.38560000×	5.38560000×	NUM
ejpam-5232	184	75	10−1	10−1	NUM
ejpam-5232	184	76	5.38560000×	5.38560000×	NUM
ejpam-5232	184	77	10−1	10−1	NUM
ejpam-5232	184	78	7.24810853×	7.24810853×	ADJ
ejpam-5232	184	79	10−19	10−19	ADJ
ejpam-5232	184	80	0.7	0.7	NUM
ejpam-5232	184	81	6.67870000×	6.67870000×	NUM
ejpam-5232	184	82	10−1	10−1	NUM
ejpam-5232	184	83	6.67870000×	6.67870000×	NUM
ejpam-5232	184	84	10−1	10−1	NUM
ejpam-5232	184	85	7.15675166×	7.15675166×	NUM
ejpam-5232	184	86	10−19	10−19	NUM
ejpam-5232	184	87	0.8	0.8	NUM
ejpam-5232	184	88	7.88480000×	7.88480000×	NUM
ejpam-5232	184	89	10−1	10−1	NUM
ejpam-5232	184	90	7.88480000×	7.88480000×	NUM
ejpam-5232	184	91	10−1	10−1	PROPN
ejpam-5232	184	92	5.81377176×	5.81377176×	NUM
ejpam-5232	184	93	10−19	10−19	ADJ
ejpam-5232	184	94	0.9	0.9	NUM
ejpam-5232	184	95	8.98290000×	8.98290000×	NUM
ejpam-5232	184	96	10−1	10−1	NUM
ejpam-5232	184	97	8.98290000×	8.98290000×	PROPN
ejpam-5232	184	98	10−1	10−1	NUM
ejpam-5232	184	99	2.96356361×	2.96356361×	NUM
ejpam-5232	184	100	10−19	10−19	NUM
ejpam-5232	184	101	1.0	1.0	NUM
ejpam-5232	184	102	1	1	NUM
ejpam-5232	184	103	1	1	NUM
ejpam-5232	184	104	2.00000000×	2.00000000×	NUM
ejpam-5232	184	105	10−29	10−29	PROPN
ejpam-5232	184	106	h.	h.	NOUN
ejpam-5232	184	107	bakodah	bakodah	PROPN
ejpam-5232	184	108	et	et	PROPN
ejpam-5232	184	109	al	al	PROPN
ejpam-5232	184	110	.	.	PUNCT
ejpam-5232	184	111	/	/	SYM
ejpam-5232	184	112	eur	eur	PROPN
ejpam-5232	184	113	.	.	PUNCT
ejpam-5232	185	1	j.	j.	PROPN
ejpam-5232	185	2	pure	pure	PROPN
ejpam-5232	185	3	appl	appl	PROPN
ejpam-5232	185	4	.	.	PROPN
ejpam-5232	185	5	math	math	PROPN
ejpam-5232	185	6	,	,	PUNCT
ejpam-5232	185	7	17	17	NUM
ejpam-5232	185	8	(	(	PUNCT
ejpam-5232	185	9	3	3	NUM
ejpam-5232	185	10	)	)	PUNCT
ejpam-5232	185	11	(	(	PUNCT
ejpam-5232	185	12	2024	2024	NUM
ejpam-5232	185	13	)	)	PUNCT
ejpam-5232	185	14	,	,	PUNCT
ejpam-5232	185	15	1497	1497	NUM
ejpam-5232	185	16	-	-	SYM
ejpam-5232	185	17	1515	1515	NUM
ejpam-5232	185	18	1508	1508	NUM
ejpam-5232	185	19	figure	figure	NOUN
ejpam-5232	185	20	4	4	NUM
ejpam-5232	185	21	:	:	PUNCT
ejpam-5232	185	22	comparison	comparison	NOUN
ejpam-5232	185	23	between	between	ADP
ejpam-5232	185	24	the	the	DET
ejpam-5232	185	25	exact	exact	ADJ
ejpam-5232	185	26	and	and	CCONJ
ejpam-5232	185	27	acdm	acdm	ADJ
ejpam-5232	185	28	solutions	solution	NOUN
ejpam-5232	185	29	in	in	ADP
ejpam-5232	185	30	example	example	NOUN
ejpam-5232	185	31	4	4	NUM
ejpam-5232	185	32	example	example	NOUN
ejpam-5232	185	33	5	5	NUM
ejpam-5232	185	34	.	.	X
ejpam-5232	185	35	consider	consider	VERB
ejpam-5232	185	36	the	the	DET
ejpam-5232	185	37	linear	linear	ADJ
ejpam-5232	185	38	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	185	39	system	system	NOUN
ejpam-5232	185	40	of	of	ADP
ejpam-5232	185	41	second	second	ADJ
ejpam-5232	185	42	-	-	PUNCT
ejpam-5232	185	43	order	order	NOUN
ejpam-5232	185	44	bvps	bvps	NOUN
ejpam-5232	186	1	[	[	X
ejpam-5232	186	2	15	15	NUM
ejpam-5232	186	3	]	]	X
ejpam-5232	186	4	{	{	PUNCT
ejpam-5232	186	5	u′′(x	u′′(x	NOUN
ejpam-5232	186	6	)	)	PUNCT
ejpam-5232	186	7	+	+	CCONJ
ejpam-5232	186	8	(	(	PUNCT
ejpam-5232	186	9	2x−	2x−	NUM
ejpam-5232	186	10	1)u′(x	1)u′(x	NUM
ejpam-5232	186	11	)	)	PUNCT
ejpam-5232	186	12	+	+	NUM
ejpam-5232	186	13	cos(πx)v′(x	cos(πx)v′(x	NOUN
ejpam-5232	186	14	)	)	PUNCT
ejpam-5232	186	15	=	=	SYM
ejpam-5232	186	16	g1(x	g1(x	NOUN
ejpam-5232	186	17	)	)	PUNCT
ejpam-5232	186	18	,	,	PUNCT
ejpam-5232	186	19	u(0	u(0	PROPN
ejpam-5232	186	20	)	)	PUNCT
ejpam-5232	186	21	=	=	SYM
ejpam-5232	186	22	u(1	u(1	PROPN
ejpam-5232	186	23	)	)	PUNCT
ejpam-5232	186	24	=	=	SYM
ejpam-5232	186	25	0	0	NUM
ejpam-5232	186	26	,	,	PUNCT
ejpam-5232	186	27	0	0	NUM
ejpam-5232	186	28	≤	≤	NUM
ejpam-5232	186	29	x	x	SYM
ejpam-5232	186	30	≤	≤	NUM
ejpam-5232	186	31	1	1	NUM
ejpam-5232	186	32	,	,	PUNCT
ejpam-5232	186	33	v′′(x	v′′(x	NOUN
ejpam-5232	186	34	)	)	PUNCT
ejpam-5232	186	35	+	+	NUM
ejpam-5232	186	36	xu(x	xu(x	NOUN
ejpam-5232	186	37	)	)	PUNCT
ejpam-5232	186	38	=	=	SYM
ejpam-5232	187	1	g2(x	g2(x	PROPN
ejpam-5232	187	2	)	)	PUNCT
ejpam-5232	187	3	,	,	PUNCT
ejpam-5232	187	4	v(0	v(0	PROPN
ejpam-5232	187	5	)	)	PUNCT
ejpam-5232	187	6	=	=	SYM
ejpam-5232	188	1	v(1	v(1	ADJ
ejpam-5232	188	2	)	)	PUNCT
ejpam-5232	188	3	=	=	SYM
ejpam-5232	188	4	0	0	NUM
ejpam-5232	188	5	,	,	PUNCT
ejpam-5232	188	6	0	0	NUM
ejpam-5232	188	7	≤	≤	NUM
ejpam-5232	188	8	x	x	SYM
ejpam-5232	188	9	≤	≤	NUM
ejpam-5232	188	10	1	1	NUM
ejpam-5232	188	11	,	,	PUNCT
ejpam-5232	188	12	(	(	PUNCT
ejpam-5232	188	13	24	24	NUM
ejpam-5232	188	14	)	)	PUNCT
ejpam-5232	188	15	where	where	SCONJ
ejpam-5232	188	16	g1(x	g1(x	NOUN
ejpam-5232	188	17	)	)	PUNCT
ejpam-5232	188	18	and	and	CCONJ
ejpam-5232	188	19	g2(x	g2(x	NOUN
ejpam-5232	188	20	)	)	PUNCT
ejpam-5232	188	21	are	be	AUX
ejpam-5232	188	22	given	give	VERB
ejpam-5232	188	23	by	by	ADP
ejpam-5232	188	24	g1(x	g1(x	NOUN
ejpam-5232	188	25	)	)	PUNCT
ejpam-5232	188	26	=	=	NOUN
ejpam-5232	188	27	−π2	−π2	NOUN
ejpam-5232	188	28	sin(πx	sin(πx	NOUN
ejpam-5232	188	29	)	)	PUNCT
ejpam-5232	188	30	+	+	CCONJ
ejpam-5232	188	31	(	(	PUNCT
ejpam-5232	188	32	2x	2x	NUM
ejpam-5232	188	33	−	−	PROPN
ejpam-5232	188	34	1)π	1)π	NUM
ejpam-5232	188	35	cos(πx	cos(πx	NOUN
ejpam-5232	188	36	)	)	PUNCT
ejpam-5232	189	1	+	+	CCONJ
ejpam-5232	189	2	(	(	PUNCT
ejpam-5232	189	3	2x−	2x−	NUM
ejpam-5232	189	4	1	1	NUM
ejpam-5232	189	5	)	)	PUNCT
ejpam-5232	189	6	cos(πx	cos(πx	NOUN
ejpam-5232	189	7	)	)	PUNCT
ejpam-5232	189	8	,	,	PUNCT
ejpam-5232	189	9	and	and	CCONJ
ejpam-5232	189	10	g2(x	g2(x	PROPN
ejpam-5232	189	11	)	)	PUNCT
ejpam-5232	189	12	=	=	SYM
ejpam-5232	190	1	2	2	NUM
ejpam-5232	190	2	+	+	CCONJ
ejpam-5232	190	3	x	x	NOUN
ejpam-5232	190	4	sin(πx	sin(πx	NOUN
ejpam-5232	190	5	)	)	PUNCT
ejpam-5232	190	6	.	.	PUNCT
ejpam-5232	191	1	in	in	ADP
ejpam-5232	191	2	addition	addition	NOUN
ejpam-5232	191	3	,	,	PUNCT
ejpam-5232	191	4	the	the	DET
ejpam-5232	191	5	following	follow	VERB
ejpam-5232	191	6	exact	exact	ADJ
ejpam-5232	191	7	analytical	analytical	ADJ
ejpam-5232	191	8	solution	solution	NOUN
ejpam-5232	191	9	set	set	VERB
ejpam-5232	191	10	satisfies	satisfy	VERB
ejpam-5232	191	11	the	the	DET
ejpam-5232	191	12	system	system	NOUN
ejpam-5232	191	13	u(x	u(x	VERB
ejpam-5232	191	14	)	)	PUNCT
ejpam-5232	191	15	=	=	SYM
ejpam-5232	191	16	sin(πx	sin(πx	NOUN
ejpam-5232	191	17	)	)	PUNCT
ejpam-5232	191	18	and	and	CCONJ
ejpam-5232	191	19	,	,	PUNCT
ejpam-5232	191	20	v(x	v(x	PROPN
ejpam-5232	191	21	)	)	PUNCT
ejpam-5232	192	1	=	=	SYM
ejpam-5232	193	1	x2	x2	PROPN
ejpam-5232	193	2	−	−	PROPN
ejpam-5232	193	3	x.	x.	NOUN
ejpam-5232	193	4	consequently	consequently	ADV
ejpam-5232	193	5	,	,	PUNCT
ejpam-5232	193	6	the	the	DET
ejpam-5232	193	7	adm	adm	PROPN
ejpam-5232	193	8	recurrent	recurrent	NOUN
ejpam-5232	193	9	relation	relation	NOUN
ejpam-5232	193	10	for	for	ADP
ejpam-5232	193	11	the	the	DET
ejpam-5232	193	12	system	system	NOUN
ejpam-5232	193	13	is	be	AUX
ejpam-5232	193	14	given	give	VERB
ejpam-5232	193	15	by	by	PROPN
ejpam-5232	193	16	u0(x	u0(x	PART
ejpam-5232	193	17	)	)	PUNCT
ejpam-5232	193	18	=	=	SYM
ejpam-5232	193	19	u(0	u(0	NOUN
ejpam-5232	193	20	)	)	PUNCT
ejpam-5232	193	21	+	+	NUM
ejpam-5232	193	22	z1x+	z1x+	NUM
ejpam-5232	193	23	l−1g1(x	l−1g1(x	NOUN
ejpam-5232	193	24	)	)	PUNCT
ejpam-5232	193	25	,	,	PUNCT
ejpam-5232	193	26	v0(x	v0(x	X
ejpam-5232	193	27	)	)	PUNCT
ejpam-5232	193	28	=	=	SYM
ejpam-5232	193	29	v(0	v(0	NOUN
ejpam-5232	193	30	)	)	PUNCT
ejpam-5232	194	1	+	+	CCONJ
ejpam-5232	194	2	z2x+	z2x+	PROPN
ejpam-5232	194	3	l−1g2(x	l−1g2(x	PROPN
ejpam-5232	194	4	)	)	PUNCT
ejpam-5232	194	5	,	,	PUNCT
ejpam-5232	194	6	un+1(x	un+1(x	PROPN
ejpam-5232	194	7	)	)	PUNCT
ejpam-5232	194	8	=	=	SYM
ejpam-5232	194	9	−l−1	−l−1	NOUN
ejpam-5232	194	10	(	(	PUNCT
ejpam-5232	194	11	(	(	PUNCT
ejpam-5232	194	12	2x−	2x−	NUM
ejpam-5232	194	13	1)u′n)−	1)u′n)−	NUM
ejpam-5232	194	14	l−1	l−1	PROPN
ejpam-5232	194	15	(	(	PUNCT
ejpam-5232	194	16	cos(πx)v′n	cos(πx)v′n	PROPN
ejpam-5232	194	17	)	)	PUNCT
ejpam-5232	194	18	,	,	PUNCT
ejpam-5232	194	19	n	n	X
ejpam-5232	194	20	≥	≥	NOUN
ejpam-5232	194	21	0	0	NUM
ejpam-5232	194	22	,	,	PUNCT
ejpam-5232	194	23	vn+1(x	vn+1(x	NOUN
ejpam-5232	194	24	)	)	PUNCT
ejpam-5232	194	25	=	=	PUNCT
ejpam-5232	195	1	−l−1	−l−1	NOUN
ejpam-5232	195	2	(	(	PUNCT
ejpam-5232	195	3	xun	xun	PROPN
ejpam-5232	195	4	)	)	PUNCT
ejpam-5232	195	5	,	,	PUNCT
ejpam-5232	195	6	n	n	X
ejpam-5232	195	7	≥	≥	NOUN
ejpam-5232	195	8	0	0	NUM
ejpam-5232	195	9	.	.	PUNCT
ejpam-5232	196	1	we	we	PRON
ejpam-5232	196	2	use	use	VERB
ejpam-5232	196	3	the	the	DET
ejpam-5232	196	4	chebyshev	chebyshev	NOUN
ejpam-5232	196	5	expansion	expansion	NOUN
ejpam-5232	196	6	to	to	PART
ejpam-5232	196	7	determine	determine	VERB
ejpam-5232	196	8	the	the	DET
ejpam-5232	196	9	series	series	NOUN
ejpam-5232	196	10	forms	form	NOUN
ejpam-5232	196	11	of	of	ADP
ejpam-5232	196	12	g1(x	g1(x	NOUN
ejpam-5232	196	13	)	)	PUNCT
ejpam-5232	196	14	and	and	CCONJ
ejpam-5232	196	15	g2(x	g2(x	PROPN
ejpam-5232	196	16	)	)	PUNCT
ejpam-5232	196	17	from	from	ADP
ejpam-5232	196	18	eq	eq	ADP
ejpam-5232	196	19	.	.	PUNCT
ejpam-5232	197	1	(	(	PUNCT
ejpam-5232	197	2	16	16	NUM
ejpam-5232	197	3	)	)	PUNCT
ejpam-5232	197	4	say	say	VERB
ejpam-5232	197	5	,	,	PUNCT
ejpam-5232	197	6	g1(x	g1(x	NOUN
ejpam-5232	197	7	)	)	PUNCT
ejpam-5232	197	8	∼=	∼=	PROPN
ejpam-5232	197	9	∑10	∑10	PUNCT
ejpam-5232	197	10	i=0	i=0	PROPN
ejpam-5232	197	11	aiti(2x	aiti(2x	VERB
ejpam-5232	197	12	−	−	NOUN
ejpam-5232	197	13	1	1	NUM
ejpam-5232	197	14	)	)	PUNCT
ejpam-5232	197	15	,	,	PUNCT
ejpam-5232	197	16	and	and	CCONJ
ejpam-5232	197	17	g2(x	g2(x	PROPN
ejpam-5232	197	18	)	)	PUNCT
ejpam-5232	197	19	∼=	∼=	PROPN
ejpam-5232	197	20	∑10	∑10	PUNCT
ejpam-5232	197	21	i=0	i=0	PROPN
ejpam-5232	197	22	biti(2x	biti(2x	NOUN
ejpam-5232	197	23	−	−	NOUN
ejpam-5232	197	24	1	1	NUM
ejpam-5232	197	25	)	)	PUNCT
ejpam-5232	197	26	,	,	PUNCT
ejpam-5232	197	27	where	where	SCONJ
ejpam-5232	197	28	the	the	DET
ejpam-5232	197	29	coefficients	coefficient	NOUN
ejpam-5232	197	30	a0	a0	PROPN
ejpam-5232	197	31	,	,	PUNCT
ejpam-5232	197	32	b0	b0	NOUN
ejpam-5232	197	33	,	,	PUNCT
ejpam-5232	197	34	ai	ai	VERB
ejpam-5232	197	35	and	and	CCONJ
ejpam-5232	197	36	bi	bi	NOUN
ejpam-5232	197	37	are	be	AUX
ejpam-5232	197	38	computed	compute	VERB
ejpam-5232	197	39	from	from	ADP
ejpam-5232	197	40	eq	eq	PROPN
ejpam-5232	197	41	.	.	PUNCT
ejpam-5232	198	1	(	(	PUNCT
ejpam-5232	198	2	17	17	NUM
ejpam-5232	198	3	)	)	PUNCT
ejpam-5232	198	4	as	as	ADP
ejpam-5232	198	5	a0	a0	NOUN
ejpam-5232	198	6	=	=	SYM
ejpam-5232	198	7	1	1	NUM
ejpam-5232	198	8	π	π	NOUN
ejpam-5232	198	9	∫	∫	PROPN
ejpam-5232	198	10	1	1	NUM
ejpam-5232	198	11	−1	−1	NOUN
ejpam-5232	198	12	g1(0.5	g1(0.5	NOUN
ejpam-5232	198	13	+	+	NOUN
ejpam-5232	198	14	0.5x)t0(x)√	0.5x)t0(x)√	NUM
ejpam-5232	198	15	1−	1−	NUM
ejpam-5232	198	16	x2	x2	NUM
ejpam-5232	198	17	dx	dx	PROPN
ejpam-5232	198	18	,	,	PUNCT
ejpam-5232	198	19	b0	b0	NOUN
ejpam-5232	198	20	=	=	SYM
ejpam-5232	198	21	1	1	NUM
ejpam-5232	198	22	π	π	NOUN
ejpam-5232	198	23	∫	∫	PROPN
ejpam-5232	198	24	1	1	NUM
ejpam-5232	198	25	−1	−1	NOUN
ejpam-5232	198	26	g2(0.5	g2(0.5	PROPN
ejpam-5232	198	27	+	+	NOUN
ejpam-5232	198	28	0.5x)t0(x)√	0.5x)t0(x)√	NUM
ejpam-5232	198	29	1−	1−	NUM
ejpam-5232	199	1	x2	x2	NOUN
ejpam-5232	199	2	dx	dx	PROPN
ejpam-5232	199	3	ai	ai	VERB
ejpam-5232	199	4	=	=	SYM
ejpam-5232	199	5	2	2	NUM
ejpam-5232	199	6	π	π	NOUN
ejpam-5232	199	7	∫	∫	NOUN
ejpam-5232	199	8	1	1	NUM
ejpam-5232	199	9	−1	−1	NOUN
ejpam-5232	199	10	g1(0.5	g1(0.5	NOUN
ejpam-5232	199	11	+	+	CCONJ
ejpam-5232	199	12	0.5x)ti(x)√	0.5x)ti(x)√	PROPN
ejpam-5232	199	13	1−	1−	NUM
ejpam-5232	199	14	x2	x2	NUM
ejpam-5232	199	15	dx	dx	PROPN
ejpam-5232	199	16	,	,	PUNCT
ejpam-5232	199	17	bi	bi	NOUN
ejpam-5232	199	18	=	=	VERB
ejpam-5232	199	19	2	2	NUM
ejpam-5232	199	20	π	π	NOUN
ejpam-5232	199	21	∫	∫	PROPN
ejpam-5232	199	22	1	1	NUM
ejpam-5232	199	23	−1	−1	NOUN
ejpam-5232	199	24	g2(0.5	g2(0.5	PROPN
ejpam-5232	199	25	+	+	CCONJ
ejpam-5232	199	26	0.5x)ti(x)√	0.5x)ti(x)√	PROPN
ejpam-5232	199	27	1−	1−	NUM
ejpam-5232	200	1	x2	x2	NOUN
ejpam-5232	200	2	dx	dx	PROPN
ejpam-5232	200	3	i	i	NOUN
ejpam-5232	200	4	=	=	NOUN
ejpam-5232	200	5	1	1	NUM
ejpam-5232	200	6	,	,	PUNCT
ejpam-5232	200	7	2	2	NUM
ejpam-5232	200	8	,	,	PUNCT
ejpam-5232	200	9	.	.	PUNCT
ejpam-5232	200	10	.	.	PUNCT
ejpam-5232	200	11	.	.	PUNCT
ejpam-5232	201	1	10	10	NUM
ejpam-5232	201	2	.	.	PUNCT
ejpam-5232	202	1	h.	h.	NOUN
ejpam-5232	202	2	bakodah	bakodah	PROPN
ejpam-5232	202	3	et	et	PROPN
ejpam-5232	202	4	al	al	PROPN
ejpam-5232	202	5	.	.	PUNCT
ejpam-5232	202	6	/	/	SYM
ejpam-5232	202	7	eur	eur	PROPN
ejpam-5232	202	8	.	.	PUNCT
ejpam-5232	203	1	j.	j.	PROPN
ejpam-5232	203	2	pure	pure	PROPN
ejpam-5232	203	3	appl	appl	PROPN
ejpam-5232	203	4	.	.	PROPN
ejpam-5232	203	5	math	math	PROPN
ejpam-5232	203	6	,	,	PUNCT
ejpam-5232	203	7	17	17	NUM
ejpam-5232	203	8	(	(	PUNCT
ejpam-5232	203	9	3	3	NUM
ejpam-5232	203	10	)	)	PUNCT
ejpam-5232	203	11	(	(	PUNCT
ejpam-5232	203	12	2024	2024	NUM
ejpam-5232	203	13	)	)	PUNCT
ejpam-5232	203	14	,	,	PUNCT
ejpam-5232	203	15	1497	1497	NUM
ejpam-5232	203	16	-	-	SYM
ejpam-5232	203	17	1515	1515	NUM
ejpam-5232	203	18	1509	1509	NUM
ejpam-5232	203	19	additionally	additionally	ADV
ejpam-5232	203	20	,	,	PUNCT
ejpam-5232	203	21	g1(x	g1(x	NOUN
ejpam-5232	203	22	)	)	PUNCT
ejpam-5232	203	23	and	and	CCONJ
ejpam-5232	203	24	g2(x	g2(x	NOUN
ejpam-5232	203	25	)	)	PUNCT
ejpam-5232	203	26	are	be	AUX
ejpam-5232	203	27	explicitly	explicitly	ADV
ejpam-5232	203	28	found	find	VERB
ejpam-5232	203	29	from	from	ADP
ejpam-5232	203	30	eq	eq	PROPN
ejpam-5232	203	31	.	.	PUNCT
ejpam-5232	204	1	(	(	PUNCT
ejpam-5232	204	2	16	16	NUM
ejpam-5232	204	3	)	)	PUNCT
ejpam-5232	204	4	as	as	ADP
ejpam-5232	204	5	g1(x	g1(x	NOUN
ejpam-5232	204	6	)	)	PUNCT
ejpam-5232	204	7	∼=	∼=	NOUN
ejpam-5232	204	8	−4.141592658−	−4.141592658−	NOUN
ejpam-5232	204	9	22.723090021x+	22.723090021x+	NUM
ejpam-5232	205	1	20.437876252x2	20.437876252x2	NUM
ejpam-5232	205	2	+	+	CCONJ
ejpam-5232	205	3	10.12859625x3	10.12859625x3	NUM
ejpam-5232	205	4	+	+	NUM
ejpam-5232	205	5	·	·	PUNCT
ejpam-5232	205	6	·	·	PUNCT
ejpam-5232	205	7	·	·	PUNCT
ejpam-5232	205	8	g2(x	g2(x	X
ejpam-5232	205	9	)	)	PUNCT
ejpam-5232	205	10	∼=	∼=	PROPN
ejpam-5232	205	11	1.999999988	1.999999988	NUM
ejpam-5232	206	1	+	+	NUM
ejpam-5232	206	2	0.000002814x+	0.000002814x+	NUM
ejpam-5232	206	3	3.141480108x2	3.141480108x2	NUM
ejpam-5232	207	1	+	+	SYM
ejpam-5232	207	2	0.001753695x3	0.001753695x3	NUM
ejpam-5232	207	3	+	+	CCONJ
ejpam-5232	207	4	·	·	PUNCT
ejpam-5232	207	5	·	·	PUNCT
ejpam-5232	207	6	·	·	PUNCT
ejpam-5232	207	7	now	now	ADV
ejpam-5232	207	8	,	,	PUNCT
ejpam-5232	207	9	we	we	PRON
ejpam-5232	207	10	determine	determine	VERB
ejpam-5232	207	11	z1	z1	NOUN
ejpam-5232	207	12	=	=	SYM
ejpam-5232	207	13	3.141584852	3.141584852	NUM
ejpam-5232	207	14	,	,	PUNCT
ejpam-5232	207	15	and	and	CCONJ
ejpam-5232	207	16	z2	z2	PROPN
ejpam-5232	207	17	=	=	SYM
ejpam-5232	207	18	−1.0000214289	−1.0000214289	PROPN
ejpam-5232	207	19	.	.	PUNCT
ejpam-5232	208	1	therefore	therefore	ADV
ejpam-5232	208	2	,	,	PUNCT
ejpam-5232	208	3	since	since	SCONJ
ejpam-5232	208	4	the	the	DET
ejpam-5232	208	5	constant	constant	ADJ
ejpam-5232	208	6	values	value	NOUN
ejpam-5232	208	7	of	of	ADP
ejpam-5232	208	8	z1	z1	PROPN
ejpam-5232	208	9	and	and	CCONJ
ejpam-5232	208	10	z2	z2	NOUN
ejpam-5232	208	11	are	be	AUX
ejpam-5232	208	12	determined	determine	VERB
ejpam-5232	208	13	above	above	ADV
ejpam-5232	208	14	,	,	PUNCT
ejpam-5232	208	15	the	the	DET
ejpam-5232	208	16	series	series	NOUN
ejpam-5232	208	17	solution	solution	NOUN
ejpam-5232	208	18	of	of	ADP
ejpam-5232	208	19	the	the	DET
ejpam-5232	208	20	problem	problem	NOUN
ejpam-5232	208	21	follows	follow	VERB
ejpam-5232	208	22	instantly	instantly	ADV
ejpam-5232	208	23	.	.	PUNCT
ejpam-5232	209	1	the	the	DET
ejpam-5232	209	2	matching	matching	NOUN
ejpam-5232	209	3	of	of	ADP
ejpam-5232	209	4	ψ5	ψ5	PROPN
ejpam-5232	209	5	=	=	SYM
ejpam-5232	209	6	∑4	∑4	PROPN
ejpam-5232	209	7	i=0	i=0	PROPN
ejpam-5232	209	8	vi	vi	PROPN
ejpam-5232	209	9	with	with	ADP
ejpam-5232	209	10	the	the	DET
ejpam-5232	209	11	exact	exact	ADJ
ejpam-5232	209	12	solution	solution	NOUN
ejpam-5232	209	13	is	be	AUX
ejpam-5232	209	14	commendable	commendable	ADJ
ejpam-5232	209	15	as	as	SCONJ
ejpam-5232	209	16	reported	report	VERB
ejpam-5232	209	17	in	in	ADP
ejpam-5232	209	18	table	table	NOUN
ejpam-5232	209	19	5	5	NUM
ejpam-5232	209	20	.	.	PUNCT
ejpam-5232	210	1	in	in	ADP
ejpam-5232	210	2	figure	figure	NOUN
ejpam-5232	210	3	5	5	NUM
ejpam-5232	210	4	,	,	PUNCT
ejpam-5232	210	5	we	we	PRON
ejpam-5232	210	6	depict	depict	VERB
ejpam-5232	210	7	the	the	DET
ejpam-5232	210	8	curves	curve	NOUN
ejpam-5232	210	9	of	of	ADP
ejpam-5232	210	10	ψ5	ψ5	NOUN
ejpam-5232	210	11	and	and	CCONJ
ejpam-5232	210	12	the	the	DET
ejpam-5232	210	13	exact	exact	ADJ
ejpam-5232	210	14	analytical	analytical	ADJ
ejpam-5232	210	15	solution	solution	NOUN
ejpam-5232	210	16	v(x	v(x	NUM
ejpam-5232	210	17	)	)	PUNCT
ejpam-5232	211	1	=	=	SYM
ejpam-5232	212	1	x2	x2	NUM
ejpam-5232	213	1	−	−	NOUN
ejpam-5232	213	2	x	x	PUNCT
ejpam-5232	213	3	in	in	ADP
ejpam-5232	213	4	the	the	DET
ejpam-5232	213	5	approximate	approximate	ADJ
ejpam-5232	213	6	region	region	NOUN
ejpam-5232	213	7	0	0	NUM
ejpam-5232	213	8	≤	≤	NUM
ejpam-5232	213	9	x	x	SYM
ejpam-5232	213	10	≤	≤	NUM
ejpam-5232	213	11	1	1	NUM
ejpam-5232	213	12	.	.	PUNCT
ejpam-5232	213	13	table	table	NOUN
ejpam-5232	213	14	5	5	NUM
ejpam-5232	213	15	:	:	PUNCT
ejpam-5232	213	16	absolute	absolute	ADJ
ejpam-5232	213	17	error	error	NOUN
ejpam-5232	213	18	between	between	ADP
ejpam-5232	213	19	the	the	DET
ejpam-5232	213	20	exact	exact	ADJ
ejpam-5232	213	21	and	and	CCONJ
ejpam-5232	213	22	acdm	acdm	ADJ
ejpam-5232	213	23	solutions	solution	NOUN
ejpam-5232	213	24	v(x	v(x	PROPN
ejpam-5232	213	25	)	)	PUNCT
ejpam-5232	213	26	in	in	ADP
ejpam-5232	213	27	example	example	NOUN
ejpam-5232	213	28	5	5	NUM
ejpam-5232	213	29	x	x	NOUN
ejpam-5232	213	30	acdm	acdm	ADV
ejpam-5232	213	31	solution	solution	NOUN
ejpam-5232	213	32	ψ5(x	ψ5(x	NOUN
ejpam-5232	213	33	)	)	PUNCT
ejpam-5232	213	34	exact	exact	ADJ
ejpam-5232	213	35	solution	solution	NOUN
ejpam-5232	213	36	v(x	v(x	NOUN
ejpam-5232	213	37	)	)	PUNCT
ejpam-5232	213	38	absolute	absolute	ADJ
ejpam-5232	213	39	error	error	NOUN
ejpam-5232	213	40	0.0	0.0	NUM
ejpam-5232	213	41	0	0	NUM
ejpam-5232	213	42	0	0	NUM
ejpam-5232	213	43	0	0	NUM
ejpam-5232	213	44	0.1	0.1	NUM
ejpam-5232	213	45	−9.00021428×	−9.00021428×	NUM
ejpam-5232	213	46	10−2	10−2	NUM
ejpam-5232	213	47	−9.00000000×	−9.00000000×	CCONJ
ejpam-5232	213	48	10−2	10−2	NUM
ejpam-5232	213	49	2.14282294×	2.14282294×	NUM
ejpam-5232	214	1	10−6	10−6	NUM
ejpam-5232	214	2	0.2	0.2	NUM
ejpam-5232	214	3	−1.60004284×	−1.60004284×	NUM
ejpam-5232	214	4	10−1	10−1	PROPN
ejpam-5232	214	5	−1.60000000×	−1.60000000×	CCONJ
ejpam-5232	214	6	10−1	10−1	NUM
ejpam-5232	214	7	4.28395716×	4.28395716×	NUM
ejpam-5232	214	8	10−6	10−6	NUM
ejpam-5232	214	9	0.3	0.3	NUM
ejpam-5232	214	10	−2.10006407×	−2.10006407×	NUM
ejpam-5232	214	11	10−1	10−1	PROPN
ejpam-5232	214	12	−2.10000000×	−2.10000000×	NOUN
ejpam-5232	214	13	10−1	10−1	PROPN
ejpam-5232	214	14	6.40680363×	6.40680363×	ADP
ejpam-5232	214	15	10−6	10−6	NUM
ejpam-5232	214	16	0.4	0.4	NUM
ejpam-5232	214	17	−2.40008430×	−2.40008430×	NUM
ejpam-5232	214	18	10−1	10−1	NUM
ejpam-5232	214	19	−2.40000000×	−2.40000000×	SYM
ejpam-5232	214	20	10−1	10−1	NUM
ejpam-5232	214	21	8.43004588×	8.43004588×	NUM
ejpam-5232	214	22	10−6	10−6	NUM
ejpam-5232	214	23	0.5	0.5	NUM
ejpam-5232	214	24	−2.50010128×	−2.50010128×	NOUN
ejpam-5232	214	25	10−1	10−1	PROPN
ejpam-5232	214	26	−2.50000000×	−2.50000000×	SYM
ejpam-5232	214	27	10−1	10−1	PROPN
ejpam-5232	214	28	1.01279366×	1.01279366×	NUM
ejpam-5232	214	29	10−5	10−5	NUM
ejpam-5232	214	30	0.6	0.6	NUM
ejpam-5232	214	31	−2.40011187×	−2.40011187×	NUM
ejpam-5232	214	32	10−1	10−1	PROPN
ejpam-5232	214	33	−2.4000000×	−2.4000000×	ADP
ejpam-5232	214	34	10−1	10−1	PROPN
ejpam-5232	214	35	1.10872057×	1.10872057×	NUM
ejpam-5232	214	36	10−5	10−5	NUM
ejpam-5232	214	37	0.7	0.7	NUM
ejpam-5232	214	38	−2.10010776×	−2.10010776×	NOUN
ejpam-5232	214	39	10−1	10−1	PROPN
ejpam-5232	214	40	−2.10000000×	−2.10000000×	PROPN
ejpam-5232	214	41	10−1	10−1	PROPN
ejpam-5232	214	42	1.07759673×	1.07759673×	NUM
ejpam-5232	214	43	10−5	10−5	NUM
ejpam-5232	214	44	0.8	0.8	NUM
ejpam-5232	214	45	−1.60008755×	−1.60008755×	NOUN
ejpam-5232	214	46	10−1	10−1	PROPN
ejpam-5232	214	47	−1.60000000×	−1.60000000×	ADP
ejpam-5232	214	48	10−1	10−1	PROPN
ejpam-5232	214	49	8.75509042×	8.75509042×	NUM
ejpam-5232	214	50	10−6	10−6	NUM
ejpam-5232	214	51	0.9	0.9	NUM
ejpam-5232	214	52	−9.00049736×	−9.00049736×	CCONJ
ejpam-5232	214	53	10−2	10−2	NUM
ejpam-5232	214	54	−9.00000000×	−9.00000000×	CCONJ
ejpam-5232	214	55	10−2	10−2	NUM
ejpam-5232	214	56	4.97362094×	4.97362094×	NOUN
ejpam-5232	214	57	10−6	10−6	NUM
ejpam-5232	214	58	1.0	1.0	NUM
ejpam-5232	214	59	−3.45366895×	−3.45366895×	NOUN
ejpam-5232	214	60	10−28	10−28	NOUN
ejpam-5232	214	61	0	0	NUM
ejpam-5232	214	62	3.45366895×	3.45366895×	NUM
ejpam-5232	214	63	10−28	10−28	NUM
ejpam-5232	214	64	figure	figure	NOUN
ejpam-5232	214	65	5	5	NUM
ejpam-5232	214	66	:	:	PUNCT
ejpam-5232	214	67	comparison	comparison	NOUN
ejpam-5232	214	68	between	between	ADP
ejpam-5232	214	69	the	the	DET
ejpam-5232	214	70	exact	exact	ADJ
ejpam-5232	214	71	and	and	CCONJ
ejpam-5232	214	72	acdm	acdm	ADJ
ejpam-5232	214	73	solutions	solution	NOUN
ejpam-5232	214	74	in	in	ADP
ejpam-5232	214	75	example	example	NOUN
ejpam-5232	214	76	5	5	NUM
ejpam-5232	214	77	for	for	ADP
ejpam-5232	214	78	v(x	v(x	PROPN
ejpam-5232	214	79	)	)	PUNCT
ejpam-5232	214	80	h.	h.	NOUN
ejpam-5232	214	81	bakodah	bakodah	PROPN
ejpam-5232	214	82	et	et	PROPN
ejpam-5232	214	83	al	al	PROPN
ejpam-5232	214	84	.	.	PUNCT
ejpam-5232	214	85	/	/	SYM
ejpam-5232	214	86	eur	eur	PROPN
ejpam-5232	214	87	.	.	PUNCT
ejpam-5232	215	1	j.	j.	PROPN
ejpam-5232	215	2	pure	pure	PROPN
ejpam-5232	215	3	appl	appl	PROPN
ejpam-5232	215	4	.	.	PROPN
ejpam-5232	215	5	math	math	PROPN
ejpam-5232	215	6	,	,	PUNCT
ejpam-5232	215	7	17	17	NUM
ejpam-5232	215	8	(	(	PUNCT
ejpam-5232	215	9	3	3	NUM
ejpam-5232	215	10	)	)	PUNCT
ejpam-5232	215	11	(	(	PUNCT
ejpam-5232	215	12	2024	2024	NUM
ejpam-5232	215	13	)	)	PUNCT
ejpam-5232	215	14	,	,	PUNCT
ejpam-5232	215	15	1497	1497	NUM
ejpam-5232	215	16	-	-	SYM
ejpam-5232	215	17	1515	1515	NUM
ejpam-5232	215	18	1510	1510	NUM
ejpam-5232	215	19	the	the	DET
ejpam-5232	215	20	matching	matching	NOUN
ejpam-5232	215	21	of	of	ADP
ejpam-5232	215	22	φ5	φ5	NOUN
ejpam-5232	215	23	=	=	SYM
ejpam-5232	216	1	∑4	∑4	PROPN
ejpam-5232	217	1	i=1	i=1	PROPN
ejpam-5232	218	1	ui	ui	PROPN
ejpam-5232	219	1	with	with	ADP
ejpam-5232	219	2	the	the	DET
ejpam-5232	219	3	exact	exact	ADJ
ejpam-5232	219	4	solution	solution	NOUN
ejpam-5232	219	5	is	be	AUX
ejpam-5232	219	6	commendable	commendable	ADJ
ejpam-5232	219	7	as	as	SCONJ
ejpam-5232	219	8	reported	report	VERB
ejpam-5232	219	9	in	in	ADP
ejpam-5232	219	10	table	table	NOUN
ejpam-5232	219	11	6	6	NUM
ejpam-5232	219	12	.	.	PUNCT
ejpam-5232	220	1	in	in	ADP
ejpam-5232	220	2	figure	figure	NOUN
ejpam-5232	220	3	6	6	NUM
ejpam-5232	220	4	,	,	PUNCT
ejpam-5232	220	5	we	we	PRON
ejpam-5232	220	6	depict	depict	VERB
ejpam-5232	220	7	the	the	DET
ejpam-5232	220	8	curves	curve	NOUN
ejpam-5232	220	9	of	of	ADP
ejpam-5232	220	10	φ5	φ5	ADJ
ejpam-5232	220	11	and	and	CCONJ
ejpam-5232	220	12	the	the	DET
ejpam-5232	220	13	exact	exact	ADJ
ejpam-5232	220	14	analytical	analytical	ADJ
ejpam-5232	220	15	solution	solution	NOUN
ejpam-5232	220	16	u(x	u(x	NOUN
ejpam-5232	220	17	)	)	PUNCT
ejpam-5232	220	18	=	=	SYM
ejpam-5232	220	19	sin(πx	sin(πx	NOUN
ejpam-5232	220	20	)	)	PUNCT
ejpam-5232	220	21	in	in	ADP
ejpam-5232	220	22	the	the	DET
ejpam-5232	220	23	approximate	approximate	ADJ
ejpam-5232	220	24	region	region	NOUN
ejpam-5232	220	25	0	0	NUM
ejpam-5232	220	26	≤	≤	NUM
ejpam-5232	220	27	x	x	SYM
ejpam-5232	220	28	≤	≤	NUM
ejpam-5232	220	29	1	1	NUM
ejpam-5232	220	30	.	.	PUNCT
ejpam-5232	220	31	table	table	NOUN
ejpam-5232	220	32	6	6	NUM
ejpam-5232	220	33	:	:	PUNCT
ejpam-5232	220	34	absolute	absolute	ADJ
ejpam-5232	220	35	error	error	NOUN
ejpam-5232	220	36	between	between	ADP
ejpam-5232	220	37	the	the	DET
ejpam-5232	220	38	exact	exact	ADJ
ejpam-5232	220	39	and	and	CCONJ
ejpam-5232	220	40	acdm	acdm	ADJ
ejpam-5232	220	41	solutions	solution	NOUN
ejpam-5232	220	42	u(x	u(x	NOUN
ejpam-5232	220	43	)	)	PUNCT
ejpam-5232	220	44	in	in	ADP
ejpam-5232	220	45	example	example	NOUN
ejpam-5232	220	46	5	5	NUM
ejpam-5232	220	47	x	x	NOUN
ejpam-5232	220	48	acdm	acdm	ADJ
ejpam-5232	220	49	solution	solution	NOUN
ejpam-5232	220	50	φ5(x	φ5(x	NOUN
ejpam-5232	220	51	)	)	PUNCT
ejpam-5232	220	52	exact	exact	ADJ
ejpam-5232	220	53	solution	solution	NOUN
ejpam-5232	220	54	u(x	u(x	NOUN
ejpam-5232	220	55	)	)	PUNCT
ejpam-5232	220	56	absolute	absolute	ADJ
ejpam-5232	220	57	error	error	NOUN
ejpam-5232	220	58	0.0	0.0	NUM
ejpam-5232	220	59	1.00000000×	1.00000000×	NUM
ejpam-5232	220	60	10−27	10−27	NUM
ejpam-5232	220	61	0	0	NUM
ejpam-5232	220	62	1.00000000×	1.00000000×	NUM
ejpam-5232	220	63	10−27	10−27	PROPN
ejpam-5232	220	64	0.1	0.1	NUM
ejpam-5232	220	65	3.09016283×	3.09016283×	NUM
ejpam-5232	220	66	10−1	10−1	NUM
ejpam-5232	220	67	3.09016994×	3.09016994×	NUM
ejpam-5232	220	68	10−1	10−1	NUM
ejpam-5232	220	69	7.11807212×	7.11807212×	NUM
ejpam-5232	220	70	10−7	10−7	NUM
ejpam-5232	220	71	0.2	0.2	NUM
ejpam-5232	220	72	5.87783841×	5.87783841×	NOUN
ejpam-5232	220	73	10−1	10−1	NUM
ejpam-5232	220	74	5.87785252×	5.87785252×	NUM
ejpam-5232	220	75	10−1	10−1	NUM
ejpam-5232	220	76	1.41152139×	1.41152139×	NUM
ejpam-5232	220	77	10−6	10−6	NUM
ejpam-5232	220	78	0.3	0.3	NUM
ejpam-5232	220	79	8.09014318×	8.09014318×	NUM
ejpam-5232	220	80	10−1	10−1	NUM
ejpam-5232	220	81	8.09016994×	8.09016994×	NOUN
ejpam-5232	220	82	10−1	10−1	NUM
ejpam-5232	221	1	2.67611588×	2.67611588×	NUM
ejpam-5232	221	2	10−6	10−6	NUM
ejpam-5232	221	3	0.4	0.4	NUM
ejpam-5232	221	4	9.51051322×	9.51051322×	X
ejpam-5232	221	5	10−1	10−1	PROPN
ejpam-5232	221	6	9.51056516×	9.51056516×	NUM
ejpam-5232	221	7	10−1	10−1	NUM
ejpam-5232	221	8	5.19434595×	5.19434595×	NUM
ejpam-5232	221	9	10−6	10−6	NUM
ejpam-5232	221	10	0.5	0.5	NUM
ejpam-5232	221	11	9.99991110×	9.99991110×	NUM
ejpam-5232	221	12	10−1	10−1	NUM
ejpam-5232	221	13	1	1	NUM
ejpam-5232	221	14	8.89040303×	8.89040303×	NUM
ejpam-5232	221	15	10−6	10−6	NUM
ejpam-5232	221	16	0.6	0.6	NUM
ejpam-5232	221	17	9.51043993×	9.51043993×	NUM
ejpam-5232	221	18	10−1	10−1	NUM
ejpam-5232	221	19	9.51056516×	9.51056516×	NUM
ejpam-5232	221	20	10−1	10−1	PROPN
ejpam-5232	221	21	1.2523000×	1.2523000×	NUM
ejpam-5232	221	22	10−5	10−5	NUM
ejpam-5232	221	23	0.7	0.7	NUM
ejpam-5232	221	24	8.09002815×	8.09002815×	NOUN
ejpam-5232	221	25	10−1	10−1	NUM
ejpam-5232	221	26	8.09016994×	8.09016994×	NOUN
ejpam-5232	221	27	10−1	10−1	NUM
ejpam-5232	221	28	1.41795077×	1.41795077×	NUM
ejpam-5232	221	29	10−5	10−5	NUM
ejpam-5232	221	30	0.8	0.8	NUM
ejpam-5232	221	31	5.87772869×	5.87772869×	NUM
ejpam-5232	221	32	10−1	10−1	NUM
ejpam-5232	221	33	5.87785252×	5.87785252×	NUM
ejpam-5232	221	34	10−1	10−1	NUM
ejpam-5232	221	35	1.23837067×	1.23837067×	NUM
ejpam-5232	221	36	10−5	10−5	NUM
ejpam-5232	221	37	0.9	0.9	NUM
ejpam-5232	221	38	3.09009889×	3.09009889×	NUM
ejpam-5232	221	39	10−1	10−1	NUM
ejpam-5232	221	40	3.09016994×	3.09016994×	NUM
ejpam-5232	221	41	10−1	10−1	NUM
ejpam-5232	221	42	7.10572450×	7.10572450×	NUM
ejpam-5232	221	43	10−6	10−6	NUM
ejpam-5232	221	44	1.0	1.0	NUM
ejpam-5232	221	45	−3.03006339×	−3.03006339×	NUM
ejpam-5232	221	46	10−27	10−27	NUM
ejpam-5232	221	47	−4.97115803×	−4.97115803×	X
ejpam-5232	221	48	10−31	10−31	PROPN
ejpam-5232	221	49	3.02956627×	3.02956627×	NUM
ejpam-5232	221	50	10−27	10−27	NUM
ejpam-5232	221	51	figure	figure	NOUN
ejpam-5232	221	52	6	6	NUM
ejpam-5232	221	53	:	:	PUNCT
ejpam-5232	221	54	comparison	comparison	NOUN
ejpam-5232	221	55	between	between	ADP
ejpam-5232	221	56	the	the	DET
ejpam-5232	221	57	exact	exact	ADJ
ejpam-5232	221	58	and	and	CCONJ
ejpam-5232	221	59	acdm	acdm	ADJ
ejpam-5232	221	60	solutions	solution	NOUN
ejpam-5232	221	61	in	in	ADP
ejpam-5232	221	62	example	example	NOUN
ejpam-5232	221	63	5	5	NUM
ejpam-5232	221	64	for	for	ADP
ejpam-5232	221	65	u(x	u(x	NOUN
ejpam-5232	221	66	)	)	PUNCT
ejpam-5232	221	67	example	example	NOUN
ejpam-5232	221	68	6	6	NUM
ejpam-5232	221	69	.	.	PUNCT
ejpam-5232	222	1	consider	consider	VERB
ejpam-5232	222	2	the	the	DET
ejpam-5232	222	3	nonlinear	nonlinear	ADJ
ejpam-5232	222	4	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	222	5	system	system	NOUN
ejpam-5232	222	6	of	of	ADP
ejpam-5232	222	7	second	second	ADJ
ejpam-5232	222	8	-	-	PUNCT
ejpam-5232	222	9	order	order	NOUN
ejpam-5232	222	10	bvps	bvps	NOUN
ejpam-5232	223	1	[	[	X
ejpam-5232	223	2	15	15	NUM
ejpam-5232	223	3	]	]	X
ejpam-5232	223	4	{	{	PUNCT
ejpam-5232	223	5	u′′(x	u′′(x	NOUN
ejpam-5232	223	6	)	)	PUNCT
ejpam-5232	223	7	+	+	NUM
ejpam-5232	223	8	xu′(x	xu′(x	PROPN
ejpam-5232	223	9	)	)	PUNCT
ejpam-5232	224	1	+	+	NUM
ejpam-5232	224	2	cos(πx)v′(x	cos(πx)v′(x	NOUN
ejpam-5232	224	3	)	)	PUNCT
ejpam-5232	224	4	=	=	SYM
ejpam-5232	224	5	g1(x	g1(x	NOUN
ejpam-5232	224	6	)	)	PUNCT
ejpam-5232	224	7	,	,	PUNCT
ejpam-5232	224	8	u(0	u(0	PROPN
ejpam-5232	224	9	)	)	PUNCT
ejpam-5232	224	10	=	=	SYM
ejpam-5232	224	11	u(1	u(1	PROPN
ejpam-5232	224	12	)	)	PUNCT
ejpam-5232	224	13	=	=	SYM
ejpam-5232	224	14	0	0	NUM
ejpam-5232	224	15	,	,	PUNCT
ejpam-5232	224	16	0	0	NUM
ejpam-5232	224	17	≤	≤	NUM
ejpam-5232	224	18	x	x	SYM
ejpam-5232	224	19	≤	≤	NUM
ejpam-5232	224	20	1	1	NUM
ejpam-5232	224	21	,	,	PUNCT
ejpam-5232	224	22	v′′(x	v′′(x	NOUN
ejpam-5232	224	23	)	)	PUNCT
ejpam-5232	224	24	+	+	NUM
ejpam-5232	224	25	xu′(x	xu′(x	X
ejpam-5232	224	26	)	)	PUNCT
ejpam-5232	225	1	+	+	CCONJ
ejpam-5232	225	2	x	x	SYM
ejpam-5232	225	3	(	(	PUNCT
ejpam-5232	225	4	v′(x	v′(x	NOUN
ejpam-5232	225	5	)	)	PUNCT
ejpam-5232	225	6	)	)	PUNCT
ejpam-5232	225	7	2	2	X
ejpam-5232	225	8	=	=	SYM
ejpam-5232	225	9	g2(x	g2(x	PROPN
ejpam-5232	225	10	)	)	PUNCT
ejpam-5232	225	11	,	,	PUNCT
ejpam-5232	225	12	v(0	v(0	PROPN
ejpam-5232	225	13	)	)	PUNCT
ejpam-5232	225	14	=	=	SYM
ejpam-5232	226	1	v(1	v(1	ADJ
ejpam-5232	226	2	)	)	PUNCT
ejpam-5232	226	3	=	=	SYM
ejpam-5232	226	4	0	0	NUM
ejpam-5232	226	5	,	,	PUNCT
ejpam-5232	226	6	0	0	NUM
ejpam-5232	226	7	≤	≤	NUM
ejpam-5232	226	8	x	x	SYM
ejpam-5232	226	9	≤	≤	NUM
ejpam-5232	226	10	1	1	NUM
ejpam-5232	226	11	,	,	PUNCT
ejpam-5232	226	12	(	(	PUNCT
ejpam-5232	226	13	25	25	NUM
ejpam-5232	226	14	)	)	PUNCT
ejpam-5232	226	15	h.	h.	NOUN
ejpam-5232	226	16	bakodah	bakodah	PROPN
ejpam-5232	226	17	et	et	PROPN
ejpam-5232	226	18	al	al	PROPN
ejpam-5232	226	19	.	.	PUNCT
ejpam-5232	226	20	/	/	SYM
ejpam-5232	226	21	eur	eur	PROPN
ejpam-5232	226	22	.	.	PUNCT
ejpam-5232	227	1	j.	j.	PROPN
ejpam-5232	227	2	pure	pure	PROPN
ejpam-5232	227	3	appl	appl	PROPN
ejpam-5232	227	4	.	.	PROPN
ejpam-5232	227	5	math	math	PROPN
ejpam-5232	227	6	,	,	PUNCT
ejpam-5232	227	7	17	17	NUM
ejpam-5232	227	8	(	(	PUNCT
ejpam-5232	227	9	3	3	NUM
ejpam-5232	227	10	)	)	PUNCT
ejpam-5232	227	11	(	(	PUNCT
ejpam-5232	227	12	2024	2024	NUM
ejpam-5232	227	13	)	)	PUNCT
ejpam-5232	227	14	,	,	PUNCT
ejpam-5232	227	15	1497	1497	NUM
ejpam-5232	227	16	-	-	SYM
ejpam-5232	227	17	1515	1515	NUM
ejpam-5232	227	18	1511	1511	NUM
ejpam-5232	227	19	where	where	SCONJ
ejpam-5232	227	20	g1(x	g1(x	NOUN
ejpam-5232	227	21	)	)	PUNCT
ejpam-5232	227	22	and	and	CCONJ
ejpam-5232	227	23	g2(x	g2(x	NOUN
ejpam-5232	227	24	)	)	PUNCT
ejpam-5232	227	25	are	be	AUX
ejpam-5232	227	26	given	give	VERB
ejpam-5232	227	27	by	by	ADP
ejpam-5232	227	28	g1(x	g1(x	NOUN
ejpam-5232	227	29	)	)	PUNCT
ejpam-5232	227	30	=	=	SYM
ejpam-5232	227	31	sin(x)+	sin(x)+	PROPN
ejpam-5232	227	32	(	(	PUNCT
ejpam-5232	227	33	x2	x2	NOUN
ejpam-5232	228	1	−	−	PROPN
ejpam-5232	228	2	x+	x+	SYM
ejpam-5232	228	3	2	2	NUM
ejpam-5232	228	4	)	)	PUNCT
ejpam-5232	228	5	cos(x)+(1−	cos(x)+(1−	X
ejpam-5232	228	6	2x	2x	NUM
ejpam-5232	228	7	)	)	PUNCT
ejpam-5232	228	8	cos(πx	cos(πx	NOUN
ejpam-5232	228	9	)	)	PUNCT
ejpam-5232	228	10	,	,	PUNCT
ejpam-5232	228	11	g2(x	g2(x	X
ejpam-5232	228	12	)	)	PUNCT
ejpam-5232	229	1	=	=	PUNCT
ejpam-5232	229	2	−2	−2	NOUN
ejpam-5232	229	3	+	+	NUM
ejpam-5232	229	4	x	x	NOUN
ejpam-5232	229	5	sin(πx	sin(πx	NOUN
ejpam-5232	229	6	)	)	PUNCT
ejpam-5232	229	7	+	+	CCONJ
ejpam-5232	229	8	(	(	PUNCT
ejpam-5232	229	9	x2	x2	INTJ
ejpam-5232	229	10	−	−	PROPN
ejpam-5232	229	11	x	x	SYM
ejpam-5232	229	12	)	)	PUNCT
ejpam-5232	229	13	cos(x	cos(x	PROPN
ejpam-5232	229	14	)	)	PUNCT
ejpam-5232	230	1	+	+	CCONJ
ejpam-5232	230	2	x(1−	x(1−	PROPN
ejpam-5232	230	3	2x)2	2x)2	NUM
ejpam-5232	230	4	.	.	PUNCT
ejpam-5232	231	1	additionally	additionally	ADV
ejpam-5232	231	2	,	,	PUNCT
ejpam-5232	231	3	the	the	DET
ejpam-5232	231	4	above	above	ADJ
ejpam-5232	231	5	system	system	NOUN
ejpam-5232	231	6	admits	admit	VERB
ejpam-5232	231	7	the	the	DET
ejpam-5232	231	8	following	following	ADJ
ejpam-5232	231	9	exact	exact	ADJ
ejpam-5232	231	10	analytical	analytical	ADJ
ejpam-5232	231	11	solution	solution	NOUN
ejpam-5232	231	12	u(x	u(x	NOUN
ejpam-5232	231	13	)	)	PUNCT
ejpam-5232	231	14	=	=	SYM
ejpam-5232	231	15	(	(	PUNCT
ejpam-5232	231	16	x−	x−	PROPN
ejpam-5232	231	17	1	1	NUM
ejpam-5232	231	18	)	)	PUNCT
ejpam-5232	231	19	sin(x	sin(x	PROPN
ejpam-5232	231	20	)	)	PUNCT
ejpam-5232	231	21	and	and	CCONJ
ejpam-5232	231	22	v(x	v(x	NUM
ejpam-5232	231	23	)	)	PUNCT
ejpam-5232	232	1	=	=	SYM
ejpam-5232	232	2	x−	x−	PROPN
ejpam-5232	232	3	x2	x2	PROPN
ejpam-5232	232	4	.	.	PUNCT
ejpam-5232	233	1	as	as	SCONJ
ejpam-5232	233	2	preceded	precede	VERB
ejpam-5232	233	3	,	,	PUNCT
ejpam-5232	233	4	the	the	DET
ejpam-5232	233	5	recurrent	recurrent	ADJ
ejpam-5232	233	6	relation	relation	NOUN
ejpam-5232	233	7	via	via	ADP
ejpam-5232	233	8	the	the	DET
ejpam-5232	233	9	adm	adm	NOUN
ejpam-5232	233	10	takes	take	VERB
ejpam-5232	233	11	the	the	DET
ejpam-5232	233	12	following	follow	VERB
ejpam-5232	233	13	form	form	PROPN
ejpam-5232	233	14	u0(x	u0(x	PRON
ejpam-5232	233	15	)	)	PUNCT
ejpam-5232	233	16	=	=	SYM
ejpam-5232	233	17	u(0	u(0	NOUN
ejpam-5232	233	18	)	)	PUNCT
ejpam-5232	234	1	+	+	NUM
ejpam-5232	234	2	z1x+	z1x+	NUM
ejpam-5232	234	3	l−1g1(x	l−1g1(x	NOUN
ejpam-5232	234	4	)	)	PUNCT
ejpam-5232	234	5	,	,	PUNCT
ejpam-5232	234	6	v0(x	v0(x	X
ejpam-5232	234	7	)	)	PUNCT
ejpam-5232	234	8	=	=	SYM
ejpam-5232	234	9	v(0	v(0	NOUN
ejpam-5232	234	10	)	)	PUNCT
ejpam-5232	235	1	+	+	CCONJ
ejpam-5232	235	2	z2x+	z2x+	PROPN
ejpam-5232	235	3	l−1g2(x	l−1g2(x	PROPN
ejpam-5232	235	4	)	)	PUNCT
ejpam-5232	235	5	,	,	PUNCT
ejpam-5232	235	6	un+1(x	un+1(x	NOUN
ejpam-5232	235	7	)	)	PUNCT
ejpam-5232	235	8	=	=	SYM
ejpam-5232	236	1	−l−1xu′n	−l−1xu′n	NOUN
ejpam-5232	236	2	−	−	PROPN
ejpam-5232	236	3	l−1	l−1	PROPN
ejpam-5232	236	4	cos(πx)v′n	cos(πx)v′n	NOUN
ejpam-5232	236	5	,	,	PUNCT
ejpam-5232	236	6	n	n	X
ejpam-5232	236	7	≥	≥	NOUN
ejpam-5232	236	8	0	0	NUM
ejpam-5232	236	9	,	,	PUNCT
ejpam-5232	236	10	vn+1(x	vn+1(x	NOUN
ejpam-5232	236	11	)	)	PUNCT
ejpam-5232	236	12	=	=	SYM
ejpam-5232	237	1	−l−1xu′n	−l−1xu′n	NOUN
ejpam-5232	237	2	−	−	PROPN
ejpam-5232	238	1	l−1xan	l−1xan	PROPN
ejpam-5232	238	2	,	,	PUNCT
ejpam-5232	238	3	n	n	CCONJ
ejpam-5232	238	4	≥	≥	NOUN
ejpam-5232	238	5	0	0	NUM
ejpam-5232	238	6	,	,	PUNCT
ejpam-5232	238	7	from	from	ADP
ejpam-5232	238	8	eq	eq	ADP
ejpam-5232	238	9	.	.	PUNCT
ejpam-5232	239	1	(	(	PUNCT
ejpam-5232	239	2	6	6	NUM
ejpam-5232	239	3	)	)	PUNCT
ejpam-5232	239	4	,	,	PUNCT
ejpam-5232	239	5	the	the	DET
ejpam-5232	239	6	nonlinear	nonlinear	ADJ
ejpam-5232	239	7	term	term	NOUN
ejpam-5232	239	8	nv	nv	PROPN
ejpam-5232	239	9	=	=	PUNCT
ejpam-5232	240	1	(	(	PUNCT
ejpam-5232	240	2	v′)2	v′)2	NOUN
ejpam-5232	240	3	is	be	AUX
ejpam-5232	240	4	also	also	ADV
ejpam-5232	240	5	expressed	express	VERB
ejpam-5232	240	6	through	through	ADP
ejpam-5232	240	7	the	the	DET
ejpam-5232	240	8	following	follow	VERB
ejpam-5232	240	9	adomian	adomian	NOUN
ejpam-5232	240	10	polynomials	polynomial	VERB
ejpam-5232	240	11	an	an	PRON
ejpam-5232	240	12	are	be	AUX
ejpam-5232	240	13	given	give	VERB
ejpam-5232	240	14	as	as	ADP
ejpam-5232	240	15	a0	a0	NOUN
ejpam-5232	240	16	=	=	SYM
ejpam-5232	240	17	(	(	PUNCT
ejpam-5232	240	18	v′0	v′0	NOUN
ejpam-5232	240	19	)	)	PUNCT
ejpam-5232	240	20	2	2	NUM
ejpam-5232	240	21	,	,	PUNCT
ejpam-5232	240	22	a1	a1	NOUN
ejpam-5232	240	23	=	=	SYM
ejpam-5232	240	24	2(v′0)(v	2(v′0)(v	NUM
ejpam-5232	240	25	′	′	NOUN
ejpam-5232	240	26	1	1	NUM
ejpam-5232	240	27	)	)	PUNCT
ejpam-5232	240	28	,	,	PUNCT
ejpam-5232	240	29	a2	a2	PROPN
ejpam-5232	240	30	=	=	SYM
ejpam-5232	241	1	2(v′0)(v	2(v′0)(v	NOUN
ejpam-5232	241	2	′	′	NOUN
ejpam-5232	241	3	2	2	NUM
ejpam-5232	241	4	)	)	PUNCT
ejpam-5232	241	5	+	+	CCONJ
ejpam-5232	241	6	(	(	PUNCT
ejpam-5232	241	7	v′1	v′1	ADJ
ejpam-5232	241	8	)	)	PUNCT
ejpam-5232	241	9	2	2	NUM
ejpam-5232	241	10	,	,	PUNCT
ejpam-5232	241	11	a3	a3	NOUN
ejpam-5232	241	12	=	=	SYM
ejpam-5232	241	13	2(v′0)(v	2(v′0)(v	NUM
ejpam-5232	241	14	′	′	NOUN
ejpam-5232	241	15	3	3	NUM
ejpam-5232	241	16	)	)	PUNCT
ejpam-5232	242	1	+	+	CCONJ
ejpam-5232	242	2	2(v′1)(v	2(v′1)(v	NUM
ejpam-5232	242	3	′	′	NUM
ejpam-5232	242	4	2	2	NUM
ejpam-5232	242	5	)	)	PUNCT
ejpam-5232	242	6	,	,	PUNCT
ejpam-5232	242	7	...	...	PUNCT
ejpam-5232	242	8	in	in	ADP
ejpam-5232	242	9	similar	similar	ADJ
ejpam-5232	242	10	manner	manner	NOUN
ejpam-5232	242	11	,	,	PUNCT
ejpam-5232	242	12	using	use	VERB
ejpam-5232	242	13	the	the	DET
ejpam-5232	242	14	relation	relation	NOUN
ejpam-5232	242	15	given	give	VERB
ejpam-5232	242	16	in	in	ADP
ejpam-5232	242	17	eq	eq	ADP
ejpam-5232	242	18	.	.	PUNCT
ejpam-5232	243	1	(	(	PUNCT
ejpam-5232	243	2	16	16	NUM
ejpam-5232	243	3	)	)	PUNCT
ejpam-5232	243	4	,	,	PUNCT
ejpam-5232	243	5	we	we	PRON
ejpam-5232	243	6	equally	equally	ADV
ejpam-5232	243	7	obtain	obtain	VERB
ejpam-5232	243	8	g1(x	g1(x	NOUN
ejpam-5232	243	9	)	)	PUNCT
ejpam-5232	243	10	∼=	∼=	PROPN
ejpam-5232	243	11	3.000000001−	3.000000001−	NUM
ejpam-5232	243	12	2.000000476x−	2.000000476x−	NOUN
ejpam-5232	243	13	4.934779553x2	4.934779553x2	NUM
ejpam-5232	244	1	+	+	CCONJ
ejpam-5232	244	2	10.20251612x3	10.20251612x3	NUM
ejpam-5232	244	3	+	+	NUM
ejpam-5232	244	4	·	·	PUNCT
ejpam-5232	244	5	·	·	PUNCT
ejpam-5232	244	6	·	·	PUNCT
ejpam-5232	244	7	,	,	PUNCT
ejpam-5232	244	8	g2(x	g2(x	NOUN
ejpam-5232	244	9	)	)	PUNCT
ejpam-5232	244	10	∼=	∼=	PROPN
ejpam-5232	244	11	−2.0−	−2.0−	ADJ
ejpam-5232	244	12	1.5896928×	1.5896928×	NUM
ejpam-5232	244	13	10−10x−	10−10x−	ADJ
ejpam-5232	244	14	2.0x2	2.0x2	NUM
ejpam-5232	244	15	+	+	CCONJ
ejpam-5232	244	16	4.500000096x3	4.500000096x3	NUM
ejpam-5232	244	17	+	+	NUM
ejpam-5232	244	18	·	·	PUNCT
ejpam-5232	244	19	·	·	PUNCT
ejpam-5232	244	20	·	·	PUNCT
ejpam-5232	245	1	so	so	ADV
ejpam-5232	245	2	,	,	PUNCT
ejpam-5232	245	3	we	we	PRON
ejpam-5232	245	4	find	find	VERB
ejpam-5232	245	5	z1	z1	NOUN
ejpam-5232	245	6	=	=	SYM
ejpam-5232	245	7	−1.000001152	−1.000001152	PROPN
ejpam-5232	245	8	,	,	PUNCT
ejpam-5232	245	9	z2	z2	PROPN
ejpam-5232	245	10	=	=	SYM
ejpam-5232	245	11	0.999830865	0.999830865	NUM
ejpam-5232	245	12	.	.	PUNCT
ejpam-5232	246	1	therefore	therefore	ADV
ejpam-5232	246	2	,	,	PUNCT
ejpam-5232	246	3	since	since	SCONJ
ejpam-5232	246	4	the	the	DET
ejpam-5232	246	5	constant	constant	ADJ
ejpam-5232	246	6	values	value	NOUN
ejpam-5232	246	7	of	of	ADP
ejpam-5232	246	8	z1	z1	PROPN
ejpam-5232	246	9	and	and	CCONJ
ejpam-5232	246	10	z2	z2	PROPN
ejpam-5232	246	11	are	be	AUX
ejpam-5232	246	12	determined	determine	VERB
ejpam-5232	246	13	,	,	PUNCT
ejpam-5232	246	14	the	the	DET
ejpam-5232	246	15	series	series	NOUN
ejpam-5232	246	16	solution	solution	NOUN
ejpam-5232	246	17	of	of	ADP
ejpam-5232	246	18	the	the	DET
ejpam-5232	246	19	problem	problem	NOUN
ejpam-5232	246	20	follows	follow	VERB
ejpam-5232	246	21	instantly	instantly	ADV
ejpam-5232	246	22	.	.	PUNCT
ejpam-5232	247	1	the	the	DET
ejpam-5232	247	2	matching	matching	NOUN
ejpam-5232	247	3	of	of	ADP
ejpam-5232	247	4	ψ5	ψ5	PROPN
ejpam-5232	247	5	=	=	SYM
ejpam-5232	247	6	∑4	∑4	PROPN
ejpam-5232	247	7	i=0	i=0	PROPN
ejpam-5232	247	8	vi	vi	PROPN
ejpam-5232	247	9	with	with	ADP
ejpam-5232	247	10	the	the	DET
ejpam-5232	247	11	exact	exact	ADJ
ejpam-5232	247	12	solution	solution	NOUN
ejpam-5232	247	13	is	be	AUX
ejpam-5232	247	14	demonstrated	demonstrate	VERB
ejpam-5232	247	15	in	in	ADP
ejpam-5232	247	16	table	table	NOUN
ejpam-5232	247	17	7	7	NUM
ejpam-5232	247	18	.	.	PUNCT
ejpam-5232	248	1	in	in	ADP
ejpam-5232	248	2	figure	figure	NOUN
ejpam-5232	248	3	7	7	NUM
ejpam-5232	248	4	we	we	PRON
ejpam-5232	248	5	depict	depict	VERB
ejpam-5232	248	6	the	the	DET
ejpam-5232	248	7	curves	curve	NOUN
ejpam-5232	248	8	of	of	ADP
ejpam-5232	248	9	ψ5	ψ5	NOUN
ejpam-5232	248	10	and	and	CCONJ
ejpam-5232	248	11	the	the	DET
ejpam-5232	248	12	exact	exact	ADJ
ejpam-5232	248	13	analytical	analytical	ADJ
ejpam-5232	248	14	solution	solution	NOUN
ejpam-5232	248	15	v(x	v(x	NUM
ejpam-5232	248	16	)	)	PUNCT
ejpam-5232	249	1	=	=	PUNCT
ejpam-5232	250	1	x	x	PUNCT
ejpam-5232	250	2	−	−	NOUN
ejpam-5232	250	3	x2	x2	PROPN
ejpam-5232	250	4	in	in	ADP
ejpam-5232	250	5	the	the	DET
ejpam-5232	250	6	approximate	approximate	ADJ
ejpam-5232	250	7	region	region	NOUN
ejpam-5232	250	8	0	0	NUM
ejpam-5232	250	9	≤	≤	NUM
ejpam-5232	250	10	x	x	SYM
ejpam-5232	250	11	≤	≤	NUM
ejpam-5232	250	12	1	1	NUM
ejpam-5232	250	13	.	.	PUNCT
ejpam-5232	250	14	table	table	NOUN
ejpam-5232	250	15	7	7	NUM
ejpam-5232	250	16	:	:	PUNCT
ejpam-5232	250	17	absolute	absolute	ADJ
ejpam-5232	250	18	error	error	NOUN
ejpam-5232	250	19	between	between	ADP
ejpam-5232	250	20	the	the	DET
ejpam-5232	250	21	exact	exact	ADJ
ejpam-5232	250	22	and	and	CCONJ
ejpam-5232	250	23	acdm	acdm	ADJ
ejpam-5232	250	24	solutions	solution	NOUN
ejpam-5232	250	25	v(x	v(x	PROPN
ejpam-5232	250	26	)	)	PUNCT
ejpam-5232	250	27	in	in	ADP
ejpam-5232	250	28	example	example	NOUN
ejpam-5232	250	29	6	6	NUM
ejpam-5232	251	1	.	.	X
ejpam-5232	251	2	x	x	SYM
ejpam-5232	251	3	acdm	acdm	ADP
ejpam-5232	251	4	solution	solution	NOUN
ejpam-5232	251	5	ψ5(x	ψ5(x	NOUN
ejpam-5232	251	6	)	)	PUNCT
ejpam-5232	251	7	exact	exact	ADJ
ejpam-5232	251	8	solution	solution	NOUN
ejpam-5232	251	9	v(x	v(x	NOUN
ejpam-5232	251	10	)	)	PUNCT
ejpam-5232	251	11	absolute	absolute	ADJ
ejpam-5232	251	12	error	error	NOUN
ejpam-5232	251	13	0.0	0.0	NUM
ejpam-5232	251	14	1.24003340×	1.24003340×	NUM
ejpam-5232	251	15	10−22	10−22	NUM
ejpam-5232	251	16	0	0	NUM
ejpam-5232	251	17	1.24003340×	1.24003340×	NUM
ejpam-5232	251	18	10−22	10−22	NUM
ejpam-5232	251	19	0.1	0.1	NUM
ejpam-5232	251	20	8.99831359×	8.99831359×	NOUN
ejpam-5232	251	21	10−2	10−2	NUM
ejpam-5232	251	22	9.00000000×	9.00000000×	NOUN
ejpam-5232	251	23	10−2	10−2	NUM
ejpam-5232	251	24	1.68640966×	1.68640966×	NOUN
ejpam-5232	251	25	10−5	10−5	NUM
ejpam-5232	251	26	0.2	0.2	NUM
ejpam-5232	251	27	1.59966511×	1.59966511×	NUM
ejpam-5232	251	28	10−1	10−1	NUM
ejpam-5232	251	29	1.6000000×	1.6000000×	NUM
ejpam-5232	251	30	10−1	10−1	NUM
ejpam-5232	251	31	3.34886510×	3.34886510×	NUM
ejpam-5232	251	32	10−5	10−5	NUM
ejpam-5232	251	33	0.3	0.3	NUM
ejpam-5232	251	34	2.09950234×	2.09950234×	NUM
ejpam-5232	251	35	10−1	10−1	NUM
ejpam-5232	251	36	2.1000000×	2.1000000×	NUM
ejpam-5232	251	37	10−1	10−1	NUM
ejpam-5232	251	38	4.97663491×	4.97663491×	NUM
ejpam-5232	251	39	10−5	10−5	NUM
ejpam-5232	251	40	0.4	0.4	NUM
ejpam-5232	251	41	2.39934409×	2.39934409×	NUM
ejpam-5232	251	42	10−1	10−1	NUM
ejpam-5232	251	43	2.4000000×	2.4000000×	NUM
ejpam-5232	251	44	10−1	10−1	NUM
ejpam-5232	251	45	6.55905833×	6.55905833×	ADP
ejpam-5232	251	46	10−5	10−5	NUM
ejpam-5232	251	47	0.5	0.5	NUM
ejpam-5232	251	48	2.49919498×	2.49919498×	NUM
ejpam-5232	251	49	10−1	10−1	PROPN
ejpam-5232	251	50	2.5000000×	2.5000000×	NUM
ejpam-5232	251	51	10−1	10−1	NUM
ejpam-5232	251	52	8.05024359×	8.05024359×	NUM
ejpam-5232	251	53	10−5	10−5	NUM
ejpam-5232	251	54	0.6	0.6	NUM
ejpam-5232	251	55	2.39906904×	2.39906904×	NUM
ejpam-5232	251	56	10−1	10−1	NUM
ejpam-5232	251	57	2.4000000×	2.4000000×	NUM
ejpam-5232	251	58	10−1	10−1	NUM
ejpam-5232	251	59	9.30960974×	9.30960974×	NOUN
ejpam-5232	251	60	10−5	10−5	NUM
ejpam-5232	251	61	0.7	0.7	NUM
ejpam-5232	251	62	2.09900091×	2.09900091×	NUM
ejpam-5232	251	63	10−1	10−1	NUM
ejpam-5232	251	64	2.1000000×	2.1000000×	NUM
ejpam-5232	251	65	10−1	10−1	NUM
ejpam-5232	251	66	9.99091708×	9.99091708×	NUM
ejpam-5232	251	67	10−5	10−5	NUM
ejpam-5232	251	68	0.8	0.8	NUM
ejpam-5232	251	69	1.59906373×	1.59906373×	NUM
ejpam-5232	251	70	10−1	10−1	NUM
ejpam-5232	251	71	1.6000000×	1.6000000×	NUM
ejpam-5232	251	72	10−1	10−1	NUM
ejpam-5232	251	73	9.36273128×	9.36273128×	NUM
ejpam-5232	251	74	10−5	10−5	NUM
ejpam-5232	251	75	0.9	0.9	NUM
ejpam-5232	251	76	8.99368847×	8.99368847×	NUM
ejpam-5232	251	77	10−2	10−2	NUM
ejpam-5232	251	78	9.000000×	9.000000×	NUM
ejpam-5232	251	79	10−2	10−2	NUM
ejpam-5232	251	80	6.31153078×	6.31153078×	NUM
ejpam-5232	251	81	10−5	10−5	NUM
ejpam-5232	251	82	1.0	1.0	NUM
ejpam-5232	251	83	1.29287648×	1.29287648×	NUM
ejpam-5232	251	84	10−21	10−21	NUM
ejpam-5232	251	85	0	0	NUM
ejpam-5232	251	86	1.29287648×	1.29287648×	NUM
ejpam-5232	251	87	10−21	10−21	PROPN
ejpam-5232	251	88	h.	h.	PROPN
ejpam-5232	251	89	bakodah	bakodah	PROPN
ejpam-5232	251	90	et	et	PROPN
ejpam-5232	251	91	al	al	PROPN
ejpam-5232	251	92	.	.	PUNCT
ejpam-5232	251	93	/	/	SYM
ejpam-5232	251	94	eur	eur	PROPN
ejpam-5232	251	95	.	.	PUNCT
ejpam-5232	252	1	j.	j.	PROPN
ejpam-5232	252	2	pure	pure	PROPN
ejpam-5232	252	3	appl	appl	PROPN
ejpam-5232	252	4	.	.	PROPN
ejpam-5232	252	5	math	math	PROPN
ejpam-5232	252	6	,	,	PUNCT
ejpam-5232	252	7	17	17	NUM
ejpam-5232	252	8	(	(	PUNCT
ejpam-5232	252	9	3	3	NUM
ejpam-5232	252	10	)	)	PUNCT
ejpam-5232	252	11	(	(	PUNCT
ejpam-5232	252	12	2024	2024	NUM
ejpam-5232	252	13	)	)	PUNCT
ejpam-5232	252	14	,	,	PUNCT
ejpam-5232	252	15	1497	1497	NUM
ejpam-5232	252	16	-	-	SYM
ejpam-5232	252	17	1515	1515	NUM
ejpam-5232	252	18	1512	1512	NUM
ejpam-5232	252	19	figure	figure	NOUN
ejpam-5232	252	20	7	7	NUM
ejpam-5232	252	21	:	:	PUNCT
ejpam-5232	252	22	comparison	comparison	NOUN
ejpam-5232	252	23	between	between	ADP
ejpam-5232	252	24	the	the	DET
ejpam-5232	252	25	exact	exact	ADJ
ejpam-5232	252	26	and	and	CCONJ
ejpam-5232	252	27	acdm	acdm	ADJ
ejpam-5232	252	28	solutions	solution	NOUN
ejpam-5232	252	29	in	in	ADP
ejpam-5232	252	30	example	example	NOUN
ejpam-5232	252	31	6	6	NUM
ejpam-5232	252	32	for	for	ADP
ejpam-5232	252	33	v(x	v(x	NOUN
ejpam-5232	252	34	)	)	PUNCT
ejpam-5232	252	35	the	the	DET
ejpam-5232	252	36	matching	matching	NOUN
ejpam-5232	252	37	of	of	ADP
ejpam-5232	252	38	φ5	φ5	PROPN
ejpam-5232	252	39	with	with	ADP
ejpam-5232	252	40	the	the	DET
ejpam-5232	252	41	exact	exact	ADJ
ejpam-5232	252	42	solution	solution	NOUN
ejpam-5232	252	43	is	be	AUX
ejpam-5232	252	44	commendable	commendable	ADJ
ejpam-5232	252	45	as	as	SCONJ
ejpam-5232	252	46	reported	report	VERB
ejpam-5232	252	47	in	in	ADP
ejpam-5232	252	48	table	table	NOUN
ejpam-5232	252	49	8	8	NUM
ejpam-5232	252	50	.	.	PUNCT
ejpam-5232	253	1	in	in	ADP
ejpam-5232	253	2	figure	figure	NOUN
ejpam-5232	253	3	8	8	NUM
ejpam-5232	253	4	,	,	PUNCT
ejpam-5232	253	5	we	we	PRON
ejpam-5232	253	6	depict	depict	VERB
ejpam-5232	253	7	the	the	DET
ejpam-5232	253	8	curves	curve	NOUN
ejpam-5232	253	9	of	of	ADP
ejpam-5232	253	10	φ5	φ5	ADJ
ejpam-5232	253	11	=	=	SYM
ejpam-5232	253	12	∑4	∑4	PROPN
ejpam-5232	253	13	i=0	i=0	PROPN
ejpam-5232	253	14	ui	ui	PROPN
ejpam-5232	253	15	and	and	CCONJ
ejpam-5232	253	16	the	the	DET
ejpam-5232	253	17	exact	exact	ADJ
ejpam-5232	253	18	analytical	analytical	ADJ
ejpam-5232	253	19	solution	solution	NOUN
ejpam-5232	253	20	u(x	u(x	NOUN
ejpam-5232	253	21	)	)	PUNCT
ejpam-5232	253	22	=	=	SYM
ejpam-5232	253	23	(	(	PUNCT
ejpam-5232	253	24	x−	x−	PROPN
ejpam-5232	253	25	1	1	NUM
ejpam-5232	253	26	)	)	PUNCT
ejpam-5232	253	27	sin(x	sin(x	PROPN
ejpam-5232	253	28	)	)	PUNCT
ejpam-5232	253	29	in	in	ADP
ejpam-5232	253	30	the	the	DET
ejpam-5232	253	31	approximate	approximate	ADJ
ejpam-5232	253	32	region	region	NOUN
ejpam-5232	254	1	0	0	NUM
ejpam-5232	254	2	≤	≤	NUM
ejpam-5232	254	3	x	x	SYM
ejpam-5232	254	4	≤	≤	NUM
ejpam-5232	254	5	1	1	NUM
ejpam-5232	254	6	.	.	PUNCT
ejpam-5232	254	7	table	table	NOUN
ejpam-5232	254	8	8	8	NUM
ejpam-5232	254	9	:	:	PUNCT
ejpam-5232	254	10	absolute	absolute	ADJ
ejpam-5232	254	11	error	error	NOUN
ejpam-5232	254	12	between	between	ADP
ejpam-5232	254	13	the	the	DET
ejpam-5232	254	14	exact	exact	ADJ
ejpam-5232	254	15	and	and	CCONJ
ejpam-5232	254	16	acdm	acdm	ADJ
ejpam-5232	254	17	solutions	solution	NOUN
ejpam-5232	254	18	u(x	u(x	NOUN
ejpam-5232	254	19	)	)	PUNCT
ejpam-5232	254	20	in	in	ADP
ejpam-5232	254	21	example	example	NOUN
ejpam-5232	254	22	6	6	NUM
ejpam-5232	254	23	.	.	X
ejpam-5232	255	1	x	x	PUNCT
ejpam-5232	255	2	acdm	acdm	ADP
ejpam-5232	255	3	solution	solution	NOUN
ejpam-5232	255	4	φ5(x	φ5(x	NOUN
ejpam-5232	255	5	)	)	PUNCT
ejpam-5232	255	6	exact	exact	ADJ
ejpam-5232	255	7	solution	solution	NOUN
ejpam-5232	255	8	u(x	u(x	NOUN
ejpam-5232	255	9	)	)	PUNCT
ejpam-5232	255	10	absolute	absolute	ADJ
ejpam-5232	255	11	error	error	NOUN
ejpam-5232	255	12	0.0	0.0	NUM
ejpam-5232	255	13	−2.15883226×	−2.15883226×	NUM
ejpam-5232	255	14	10−15	10−15	NOUN
ejpam-5232	255	15	0	0	NUM
ejpam-5232	255	16	2.15883226×	2.15883226×	NUM
ejpam-5232	255	17	10−15	10−15	NUM
ejpam-5232	255	18	0.1	0.1	NUM
ejpam-5232	255	19	−8.98493539×	−8.98493539×	NUM
ejpam-5232	255	20	10−2	10−2	NUM
ejpam-5232	255	21	−8.98500750×	−8.98500750×	NOUN
ejpam-5232	255	22	10−2	10−2	NUM
ejpam-5232	255	23	7.21035532×	7.21035532×	NUM
ejpam-5232	255	24	10−7	10−7	NUM
ejpam-5232	255	25	0.2	0.2	NUM
ejpam-5232	255	26	−1.58932458×	−1.58932458×	NOUN
ejpam-5232	255	27	10−1	10−1	NUM
ejpam-5232	255	28	−1.558935465×	−1.558935465×	ADP
ejpam-5232	255	29	10−1	10−1	NUM
ejpam-5232	255	30	3.00633437×	3.00633437×	NOUN
ejpam-5232	255	31	10−6	10−6	NUM
ejpam-5232	255	32	0.3	0.3	NUM
ejpam-5232	255	33	−2.06857574×	−2.06857574×	NUM
ejpam-5232	255	34	10−1	10−1	PROPN
ejpam-5232	255	35	−2.06864145×	−2.06864145×	VERB
ejpam-5232	255	36	10−1	10−1	PROPN
ejpam-5232	255	37	6.57114337×	6.57114337×	NOUN
ejpam-5232	255	38	10−6	10−6	NUM
ejpam-5232	255	39	0.4	0.4	NUM
ejpam-5232	255	40	−2.33639930×	−2.33639930×	SYM
ejpam-5232	255	41	10−1	10−1	PROPN
ejpam-5232	255	42	−2.3365100×	−2.3365100×	PROPN
ejpam-5232	255	43	10−1	10−1	NUM
ejpam-5232	255	44	1.10754214×	1.10754214×	PROPN
ejpam-5232	255	45	10−5	10−5	NUM
ejpam-5232	255	46	0.5	0.5	NUM
ejpam-5232	255	47	−2.39696515×	−2.39696515×	NUM
ejpam-5232	255	48	10−1	10−1	PROPN
ejpam-5232	255	49	−2.39712769×	−2.39712769×	NUM
ejpam-5232	255	50	10−1	10−1	PROPN
ejpam-5232	255	51	1.62538649×	1.62538649×	PROPN
ejpam-5232	255	52	10−5	10−5	NUM
ejpam-5232	255	53	0.6	0.6	NUM
ejpam-5232	255	54	−2.25835101×	−2.25835101×	NUM
ejpam-5232	255	55	10−1	10−1	NUM
ejpam-5232	255	56	−2.25856989×	−2.25856989×	VERB
ejpam-5232	255	57	10−1	10−1	NUM
ejpam-5232	255	58	2.18878914×	2.18878914×	NUM
ejpam-5232	255	59	10−5	10−5	NUM
ejpam-5232	255	60	0.7	0.7	NUM
ejpam-5232	255	61	−1.93237792×	−1.93237792×	NUM
ejpam-5232	255	62	10−1	10−1	PROPN
ejpam-5232	255	63	−1.93265306×	−1.93265306×	NUM
ejpam-5232	255	64	10−1	10−1	PROPN
ejpam-5232	256	1	2.7514182910−5	2.7514182910−5	NUM
ejpam-5232	256	2	0.8	0.8	NUM
ejpam-5232	256	3	−1.43439660×	−1.43439660×	NOUN
ejpam-5232	256	4	10−1	10−1	PROPN
ejpam-5232	256	5	−1.43471218×	−1.43471218×	NUM
ejpam-5232	256	6	10−1	10−1	PROPN
ejpam-5232	256	7	3.15577978×	3.15577978×	NUM
ejpam-5232	256	8	10−5	10−5	NUM
ejpam-5232	256	9	0.9	0.9	NUM
ejpam-5232	256	10	−7.83043755×	−7.83043755×	NOUN
ejpam-5232	256	11	10−2	10−2	NUM
ejpam-5232	256	12	−7.83326910×	−7.83326910×	NOUN
ejpam-5232	256	13	10−2	10−2	NUM
ejpam-5232	256	14	2.83154484×	2.83154484×	NUM
ejpam-5232	256	15	10−5	10−5	NUM
ejpam-5232	256	16	1.0	1.0	NUM
ejpam-5232	256	17	−1.48468813×	−1.48468813×	NOUN
ejpam-5232	256	18	10−14	10−14	NUM
ejpam-5232	256	19	0	0	NUM
ejpam-5232	256	20	1.48468813×	1.48468813×	NUM
ejpam-5232	256	21	10−14	10−14	NUM
ejpam-5232	256	22	references	reference	NOUN
ejpam-5232	256	23	1513	1513	NUM
ejpam-5232	256	24	figure	figure	NOUN
ejpam-5232	256	25	8	8	NUM
ejpam-5232	256	26	:	:	PUNCT
ejpam-5232	256	27	comparison	comparison	NOUN
ejpam-5232	256	28	between	between	ADP
ejpam-5232	256	29	the	the	DET
ejpam-5232	256	30	exact	exact	ADJ
ejpam-5232	256	31	and	and	CCONJ
ejpam-5232	256	32	acdm	acdm	ADJ
ejpam-5232	256	33	solutions	solution	NOUN
ejpam-5232	256	34	in	in	ADP
ejpam-5232	256	35	example	example	NOUN
ejpam-5232	256	36	6	6	NUM
ejpam-5232	256	37	for	for	ADP
ejpam-5232	256	38	u(x	u(x	NOUN
ejpam-5232	256	39	)	)	PUNCT
ejpam-5232	256	40	.	.	PUNCT
ejpam-5232	257	1	5	5	X
ejpam-5232	257	2	.	.	X
ejpam-5232	257	3	conclusion	conclusion	NOUN
ejpam-5232	257	4	in	in	ADP
ejpam-5232	257	5	conclusion	conclusion	NOUN
ejpam-5232	257	6	,	,	PUNCT
ejpam-5232	257	7	the	the	DET
ejpam-5232	257	8	current	current	ADJ
ejpam-5232	257	9	manuscript	manuscript	NOUN
ejpam-5232	257	10	devised	devise	VERB
ejpam-5232	257	11	an	an	DET
ejpam-5232	257	12	efficient	efficient	ADJ
ejpam-5232	257	13	numerical	numerical	ADJ
ejpam-5232	257	14	method	method	NOUN
ejpam-5232	257	15	based	base	VERB
ejpam-5232	257	16	on	on	ADP
ejpam-5232	257	17	the	the	DET
ejpam-5232	257	18	application	application	NOUN
ejpam-5232	257	19	of	of	ADP
ejpam-5232	257	20	the	the	DET
ejpam-5232	257	21	celebrated	celebrated	ADJ
ejpam-5232	257	22	adm	adm	PROPN
ejpam-5232	257	23	and	and	CCONJ
ejpam-5232	257	24	,	,	PUNCT
ejpam-5232	257	25	chebyshev	chebyshev	NOUN
ejpam-5232	257	26	polynomials	polynomial	NOUN
ejpam-5232	257	27	for	for	ADP
ejpam-5232	257	28	solving	solve	VERB
ejpam-5232	257	29	two	two	NUM
ejpam-5232	257	30	-	-	PUNCT
ejpam-5232	257	31	point	point	NOUN
ejpam-5232	257	32	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5232	257	33	bvps	bvps	NOUN
ejpam-5232	257	34	with	with	ADP
ejpam-5232	257	35	dirichlet	dirichlet	PROPN
ejpam-5232	257	36	boundary	boundary	PROPN
ejpam-5232	257	37	conditions	condition	NOUN
ejpam-5232	257	38	.	.	PUNCT
ejpam-5232	258	1	the	the	DET
ejpam-5232	258	2	devised	devise	VERB
ejpam-5232	258	3	method	method	NOUN
ejpam-5232	258	4	that	that	PRON
ejpam-5232	258	5	is	be	AUX
ejpam-5232	258	6	called	call	VERB
ejpam-5232	258	7	the	the	DET
ejpam-5232	258	8	acdm	acdm	ADJ
ejpam-5232	258	9	was	be	AUX
ejpam-5232	258	10	further	far	ADV
ejpam-5232	258	11	successfully	successfully	ADV
ejpam-5232	258	12	applied	apply	VERB
ejpam-5232	258	13	to	to	ADP
ejpam-5232	258	14	some	some	DET
ejpam-5232	258	15	test	test	NOUN
ejpam-5232	258	16	problems	problem	NOUN
ejpam-5232	258	17	comprising	comprise	VERB
ejpam-5232	258	18	of	of	ADP
ejpam-5232	258	19	both	both	CCONJ
ejpam-5232	258	20	linear	linear	ADJ
ejpam-5232	258	21	and	and	CCONJ
ejpam-5232	258	22	nonlinear	nonlinear	ADJ
ejpam-5232	258	23	problems	problem	NOUN
ejpam-5232	258	24	,	,	PUNCT
ejpam-5232	258	25	including	include	VERB
ejpam-5232	258	26	coupled	couple	VERB
ejpam-5232	258	27	nonlinear	nonlinear	ADJ
ejpam-5232	258	28	systems	system	NOUN
ejpam-5232	258	29	.	.	PUNCT
ejpam-5232	259	1	additionally	additionally	ADV
ejpam-5232	259	2	,	,	PUNCT
ejpam-5232	259	3	a	a	DET
ejpam-5232	259	4	comparative	comparative	ADJ
ejpam-5232	259	5	study	study	NOUN
ejpam-5232	259	6	between	between	ADP
ejpam-5232	259	7	the	the	DET
ejpam-5232	259	8	acquired	acquire	VERB
ejpam-5232	259	9	numerical	numerical	ADJ
ejpam-5232	259	10	results	result	NOUN
ejpam-5232	259	11	and	and	CCONJ
ejpam-5232	259	12	the	the	DET
ejpam-5232	259	13	existing	exist	VERB
ejpam-5232	259	14	exact	exact	ADJ
ejpam-5232	259	15	solutions	solution	NOUN
ejpam-5232	259	16	of	of	ADP
ejpam-5232	259	17	the	the	DET
ejpam-5232	259	18	test	test	NOUN
ejpam-5232	259	19	problems	problem	NOUN
ejpam-5232	259	20	was	be	AUX
ejpam-5232	259	21	established	establish	VERB
ejpam-5232	259	22	to	to	PART
ejpam-5232	259	23	demonstrate	demonstrate	VERB
ejpam-5232	259	24	certain	certain	ADJ
ejpam-5232	259	25	salient	salient	NOUN
ejpam-5232	259	26	features	feature	NOUN
ejpam-5232	259	27	of	of	ADP
ejpam-5232	259	28	the	the	DET
ejpam-5232	259	29	devised	devise	VERB
ejpam-5232	259	30	method	method	NOUN
ejpam-5232	259	31	.	.	PUNCT
ejpam-5232	260	1	lastly	lastly	ADV
ejpam-5232	260	2	,	,	PUNCT
ejpam-5232	260	3	the	the	DET
ejpam-5232	260	4	devised	devise	VERB
ejpam-5232	260	5	method	method	NOUN
ejpam-5232	260	6	is	be	AUX
ejpam-5232	260	7	proved	prove	VERB
ejpam-5232	260	8	to	to	PART
ejpam-5232	260	9	be	be	AUX
ejpam-5232	260	10	a	a	DET
ejpam-5232	260	11	robust	robust	ADJ
ejpam-5232	260	12	numerical	numerical	ADJ
ejpam-5232	260	13	method	method	NOUN
ejpam-5232	260	14	for	for	ADP
ejpam-5232	260	15	solving	solve	VERB
ejpam-5232	260	16	various	various	ADJ
ejpam-5232	260	17	classes	class	NOUN
ejpam-5232	260	18	of	of	ADP
ejpam-5232	260	19	functional	functional	ADJ
ejpam-5232	260	20	equations	equation	NOUN
ejpam-5232	260	21	and	and	CCONJ
ejpam-5232	260	22	,	,	PUNCT
ejpam-5232	260	23	can	can	AUX
ejpam-5232	260	24	be	be	AUX
ejpam-5232	260	25	broadened	broaden	VERB
ejpam-5232	260	26	to	to	PART
ejpam-5232	260	27	tackle	tackle	VERB
ejpam-5232	260	28	other	other	ADJ
ejpam-5232	260	29	problems	problem	NOUN
ejpam-5232	260	30	with	with	ADP
ejpam-5232	260	31	different	different	ADJ
ejpam-5232	260	32	types	type	NOUN
ejpam-5232	260	33	of	of	ADP
ejpam-5232	260	34	conditions	condition	NOUN
ejpam-5232	260	35	.	.	PUNCT
ejpam-5232	261	1	references	reference	NOUN
ejpam-5232	261	2	[	[	X
ejpam-5232	261	3	1	1	X
ejpam-5232	261	4	]	]	X
ejpam-5232	261	5	o.	o.	PROPN
ejpam-5232	261	6	adeyeye	adeyeye	PROPN
ejpam-5232	261	7	and	and	CCONJ
ejpam-5232	261	8	z.	z.	PROPN
ejpam-5232	261	9	omar	omar	PROPN
ejpam-5232	261	10	.	.	PUNCT
ejpam-5232	262	1	solving	solve	VERB
ejpam-5232	262	2	nonlinear	nonlinear	ADJ
ejpam-5232	262	3	fourth	fourth	ADJ
ejpam-5232	262	4	-	-	PUNCT
ejpam-5232	262	5	order	order	NOUN
ejpam-5232	262	6	boundary	boundary	ADJ
ejpam-5232	262	7	value	value	NOUN
ejpam-5232	262	8	problems	problem	NOUN
ejpam-5232	262	9	using	use	VERB
ejpam-5232	262	10	a	a	DET
ejpam-5232	262	11	numerical	numerical	ADJ
ejpam-5232	262	12	approach	approach	NOUN
ejpam-5232	262	13	:	:	PUNCT
ejpam-5232	262	14	(	(	PUNCT
ejpam-5232	262	15	m+	m+	NUM
ejpam-5232	262	16	1)th	1)th	NOUN
ejpam-5232	262	17	-	-	PUNCT
ejpam-5232	262	18	step	step	NOUN
ejpam-5232	262	19	block	block	NOUN
ejpam-5232	262	20	method	method	NOUN
ejpam-5232	262	21	.	.	PUNCT
ejpam-5232	263	1	international	international	ADJ
ejpam-5232	263	2	journal	journal	PROPN
ejpam-5232	263	3	of	of	ADP
ejpam-5232	263	4	differential	differential	ADJ
ejpam-5232	263	5	equations	equation	NOUN
ejpam-5232	263	6	,	,	PUNCT
ejpam-5232	263	7	pages	page	NOUN
ejpam-5232	263	8	1–9	1–9	NUM
ejpam-5232	263	9	,	,	PUNCT
ejpam-5232	263	10	2017	2017	NUM
ejpam-5232	263	11	.	.	PUNCT
ejpam-5232	264	1	[	[	X
ejpam-5232	264	2	2	2	NUM
ejpam-5232	264	3	]	]	X
ejpam-5232	264	4	g.	g.	NOUN
ejpam-5232	264	5	adomian	adomian	PROPN
ejpam-5232	264	6	.	.	PUNCT
ejpam-5232	265	1	solving	solve	VERB
ejpam-5232	265	2	frontier	frontier	NOUN
ejpam-5232	265	3	problems	problem	NOUN
ejpam-5232	265	4	of	of	ADP
ejpam-5232	265	5	physics	physics	NOUN
ejpam-5232	265	6	:	:	PUNCT
ejpam-5232	265	7	the	the	DET
ejpam-5232	265	8	decomposition	decomposition	NOUN
ejpam-5232	265	9	method	method	NOUN
ejpam-5232	265	10	.	.	PUNCT
ejpam-5232	266	1	kluwer	kluwer	NOUN
ejpam-5232	266	2	,	,	PUNCT
ejpam-5232	266	3	1994	1994	NUM
ejpam-5232	266	4	.	.	PUNCT
ejpam-5232	267	1	[	[	X
ejpam-5232	267	2	3	3	X
ejpam-5232	267	3	]	]	SYM
ejpam-5232	267	4	g	g	NOUN
ejpam-5232	267	5	adomian	adomian	NOUN
ejpam-5232	267	6	and	and	CCONJ
ejpam-5232	267	7	r	r	NOUN
ejpam-5232	267	8	rach	rach	NOUN
ejpam-5232	267	9	.	.	PUNCT
ejpam-5232	268	1	analytic	analytic	ADJ
ejpam-5232	268	2	solution	solution	NOUN
ejpam-5232	268	3	of	of	ADP
ejpam-5232	268	4	nonlinear	nonlinear	ADJ
ejpam-5232	268	5	boundary	boundary	ADJ
ejpam-5232	268	6	-	-	PUNCT
ejpam-5232	268	7	value	value	NOUN
ejpam-5232	268	8	problems	problem	NOUN
ejpam-5232	268	9	in	in	ADP
ejpam-5232	268	10	several	several	ADJ
ejpam-5232	268	11	dimensions	dimension	NOUN
ejpam-5232	268	12	by	by	ADP
ejpam-5232	268	13	decomposition	decomposition	NOUN
ejpam-5232	268	14	.	.	PUNCT
ejpam-5232	269	1	journal	journal	NOUN
ejpam-5232	269	2	of	of	ADP
ejpam-5232	269	3	mathematical	mathematical	ADJ
ejpam-5232	269	4	analysis	analysis	NOUN
ejpam-5232	269	5	and	and	CCONJ
ejpam-5232	269	6	applications	application	NOUN
ejpam-5232	269	7	,	,	PUNCT
ejpam-5232	269	8	174:118–137	174:118–137	NUM
ejpam-5232	269	9	,	,	PUNCT
ejpam-5232	269	10	1993	1993	NUM
ejpam-5232	269	11	.	.	PUNCT
ejpam-5232	270	1	references	reference	NOUN
ejpam-5232	270	2	1514	1514	NUM
ejpam-5232	270	3	[	[	X
ejpam-5232	270	4	4	4	NUM
ejpam-5232	270	5	]	]	SYM
ejpam-5232	270	6	g	g	NOUN
ejpam-5232	270	7	adomian	adomian	NOUN
ejpam-5232	270	8	and	and	CCONJ
ejpam-5232	270	9	r	r	NOUN
ejpam-5232	270	10	rach	rach	NOUN
ejpam-5232	270	11	.	.	PUNCT
ejpam-5232	271	1	a	a	DET
ejpam-5232	271	2	new	new	ADJ
ejpam-5232	271	3	algorithm	algorithm	NOUN
ejpam-5232	271	4	for	for	ADP
ejpam-5232	271	5	matching	match	VERB
ejpam-5232	271	6	boundary	boundary	ADJ
ejpam-5232	271	7	conditions	condition	NOUN
ejpam-5232	271	8	in	in	ADP
ejpam-5232	271	9	decomposition	decomposition	NOUN
ejpam-5232	271	10	solutions	solution	NOUN
ejpam-5232	271	11	.	.	PUNCT
ejpam-5232	272	1	applied	apply	VERB
ejpam-5232	272	2	mathematics	mathematic	NOUN
ejpam-5232	272	3	and	and	CCONJ
ejpam-5232	272	4	computation	computation	NOUN
ejpam-5232	272	5	,	,	PUNCT
ejpam-5232	272	6	57(1):61–68	57(1):61–68	NUM
ejpam-5232	272	7	,	,	PUNCT
ejpam-5232	272	8	1993	1993	NUM
ejpam-5232	272	9	.	.	PUNCT
ejpam-5232	273	1	[	[	X
ejpam-5232	273	2	5	5	X
ejpam-5232	273	3	]	]	X
ejpam-5232	273	4	waleed	waleed	PROPN
ejpam-5232	273	5	al	al	PROPN
ejpam-5232	273	6	-	-	PUNCT
ejpam-5232	273	7	hayani	hayani	PROPN
ejpam-5232	273	8	.	.	PUNCT
ejpam-5232	274	1	adomian	adomian	NOUN
ejpam-5232	274	2	decomposition	decomposition	NOUN
ejpam-5232	274	3	method	method	NOUN
ejpam-5232	274	4	with	with	ADP
ejpam-5232	274	5	green	green	PROPN
ejpam-5232	274	6	’s	’s	PART
ejpam-5232	274	7	function	function	NOUN
ejpam-5232	274	8	for	for	ADP
ejpam-5232	274	9	sixthorder	sixthorder	NOUN
ejpam-5232	274	10	boundary	boundary	ADJ
ejpam-5232	274	11	value	value	NOUN
ejpam-5232	274	12	problems	problem	NOUN
ejpam-5232	274	13	.	.	PUNCT
ejpam-5232	275	1	computers	computer	NOUN
ejpam-5232	275	2	&	&	CCONJ
ejpam-5232	275	3	mathematics	mathematics	PROPN
ejpam-5232	275	4	with	with	ADP
ejpam-5232	275	5	applications	application	NOUN
ejpam-5232	275	6	,	,	PUNCT
ejpam-5232	275	7	61(6):1567–1575	61(6):1567–1575	NUM
ejpam-5232	275	8	,	,	PUNCT
ejpam-5232	275	9	2011	2011	NUM
ejpam-5232	275	10	.	.	PUNCT
ejpam-5232	276	1	[	[	X
ejpam-5232	276	2	6	6	NUM
ejpam-5232	276	3	]	]	PUNCT
ejpam-5232	276	4	m.	m.	NOUN
ejpam-5232	276	5	h.	h.	PROPN
ejpam-5232	276	6	al	al	PROPN
ejpam-5232	276	7	-	-	PUNCT
ejpam-5232	276	8	mazmumy	mazmumy	PROPN
ejpam-5232	276	9	,	,	PUNCT
ejpam-5232	276	10	f.	f.	PROPN
ejpam-5232	276	11	a.	a.	PROPN
ejpam-5232	276	12	hendi	hendi	PROPN
ejpam-5232	276	13	,	,	PUNCT
ejpam-5232	276	14	h.	h.	PROPN
ejpam-5232	276	15	o.	o.	PROPN
ejpam-5232	276	16	bakodah	bakodah	PROPN
ejpam-5232	276	17	,	,	PUNCT
ejpam-5232	276	18	and	and	CCONJ
ejpam-5232	276	19	h.	h.	PROPN
ejpam-5232	276	20	alzumi	alzumi	PROPN
ejpam-5232	276	21	.	.	PUNCT
ejpam-5232	277	1	recent	recent	ADJ
ejpam-5232	277	2	modifications	modification	NOUN
ejpam-5232	277	3	of	of	ADP
ejpam-5232	277	4	adomian	adomian	ADJ
ejpam-5232	277	5	decomposition	decomposition	NOUN
ejpam-5232	277	6	method	method	NOUN
ejpam-5232	277	7	for	for	ADP
ejpam-5232	277	8	initial	initial	ADJ
ejpam-5232	277	9	value	value	NOUN
ejpam-5232	277	10	problem	problem	NOUN
ejpam-5232	277	11	in	in	ADP
ejpam-5232	277	12	ordinary	ordinary	ADJ
ejpam-5232	277	13	differential	differential	ADJ
ejpam-5232	277	14	equations	equation	NOUN
ejpam-5232	277	15	.	.	PUNCT
ejpam-5232	278	1	american	american	PROPN
ejpam-5232	278	2	journal	journal	PROPN
ejpam-5232	278	3	of	of	ADP
ejpam-5232	278	4	computational	computational	ADJ
ejpam-5232	278	5	mathematics	mathematic	NOUN
ejpam-5232	278	6	,	,	PUNCT
ejpam-5232	278	7	2:228–234	2:228–234	NUM
ejpam-5232	278	8	,	,	PUNCT
ejpam-5232	278	9	2012	2012	NUM
ejpam-5232	278	10	.	.	PUNCT
ejpam-5232	279	1	[	[	X
ejpam-5232	279	2	7	7	X
ejpam-5232	279	3	]	]	PUNCT
ejpam-5232	279	4	m.	m.	NOUN
ejpam-5232	279	5	h.	h.	PROPN
ejpam-5232	279	6	almazmumy	almazmumy	PROPN
ejpam-5232	279	7	,	,	PUNCT
ejpam-5232	279	8	h.	h.	PROPN
ejpam-5232	279	9	o.	o.	PROPN
ejpam-5232	279	10	bakodah	bakodah	PROPN
ejpam-5232	279	11	,	,	PUNCT
ejpam-5232	279	12	n.	n.	PROPN
ejpam-5232	279	13	a.	a.	PROPN
ejpam-5232	279	14	al	al	PROPN
ejpam-5232	279	15	-	-	PUNCT
ejpam-5232	279	16	zaid	zaid	PROPN
ejpam-5232	279	17	,	,	PUNCT
ejpam-5232	279	18	a.	a.	NOUN
ejpam-5232	279	19	ebaid	ebaid	PROPN
ejpam-5232	279	20	,	,	PUNCT
ejpam-5232	279	21	and	and	CCONJ
ejpam-5232	279	22	r.	r.	PROPN
ejpam-5232	279	23	rach	rach	PROPN
ejpam-5232	279	24	.	.	PUNCT
ejpam-5232	280	1	approximate	approximate	ADJ
ejpam-5232	280	2	analytical	analytical	ADJ
ejpam-5232	280	3	solution	solution	NOUN
ejpam-5232	280	4	for	for	ADP
ejpam-5232	280	5	1	1	NUM
ejpam-5232	280	6	-	-	PUNCT
ejpam-5232	280	7	d	d	NOUN
ejpam-5232	280	8	problems	problem	NOUN
ejpam-5232	280	9	of	of	ADP
ejpam-5232	280	10	thermoelasticity	thermoelasticity	NOUN
ejpam-5232	280	11	with	with	ADP
ejpam-5232	280	12	dirichlet	dirichlet	PROPN
ejpam-5232	280	13	condition	condition	NOUN
ejpam-5232	280	14	.	.	PUNCT
ejpam-5232	281	1	thermal	thermal	ADJ
ejpam-5232	281	2	science	science	NOUN
ejpam-5232	281	3	,	,	PUNCT
ejpam-5232	281	4	23(1):255–269	23(1):255–269	PROPN
ejpam-5232	281	5	,	,	PUNCT
ejpam-5232	281	6	2019	2019	NUM
ejpam-5232	281	7	.	.	PUNCT
ejpam-5232	282	1	[	[	X
ejpam-5232	282	2	8	8	NUM
ejpam-5232	282	3	]	]	X
ejpam-5232	282	4	n.	n.	NOUN
ejpam-5232	282	5	a	a	DET
ejpam-5232	282	6	alzaid	alzaid	NOUN
ejpam-5232	282	7	and	and	CCONJ
ejpam-5232	282	8	h.	h.	PROPN
ejpam-5232	282	9	o.	o.	PROPN
ejpam-5232	282	10	bakodah	bakodah	PROPN
ejpam-5232	282	11	.	.	PUNCT
ejpam-5232	283	1	numerical	numerical	ADJ
ejpam-5232	283	2	treatment	treatment	NOUN
ejpam-5232	283	3	of	of	ADP
ejpam-5232	283	4	initial	initial	ADJ
ejpam-5232	283	5	-	-	PUNCT
ejpam-5232	283	6	boundary	boundary	NOUN
ejpam-5232	283	7	value	value	NOUN
ejpam-5232	283	8	problems	problem	NOUN
ejpam-5232	283	9	with	with	ADP
ejpam-5232	283	10	mixed	mixed	ADJ
ejpam-5232	283	11	boundary	boundary	ADJ
ejpam-5232	283	12	conditions	condition	NOUN
ejpam-5232	283	13	.	.	PUNCT
ejpam-5232	284	1	american	american	ADJ
ejpam-5232	284	2	journal	journal	PROPN
ejpam-5232	284	3	of	of	ADP
ejpam-5232	284	4	computational	computational	ADJ
ejpam-5232	284	5	mathematics	mathematic	NOUN
ejpam-5232	284	6	,	,	PUNCT
ejpam-5232	284	7	8(02):153	8(02):153	NUM
ejpam-5232	284	8	,	,	PUNCT
ejpam-5232	284	9	2018	2018	NUM
ejpam-5232	284	10	.	.	PUNCT
ejpam-5232	285	1	[	[	X
ejpam-5232	285	2	9	9	NUM
ejpam-5232	285	3	]	]	X
ejpam-5232	285	4	g.	g.	PROPN
ejpam-5232	285	5	a.	a.	PROPN
ejpam-5232	285	6	baker	baker	PROPN
ejpam-5232	285	7	and	and	CCONJ
ejpam-5232	285	8	p.	p.	PROPN
ejpam-5232	285	9	graves	grave	NOUN
ejpam-5232	285	10	-	-	PUNCT
ejpam-5232	285	11	morris	morris	NOUN
ejpam-5232	285	12	.	.	PUNCT
ejpam-5232	286	1	padé	padé	ADJ
ejpam-5232	286	2	approximants	approximant	NOUN
ejpam-5232	286	3	:	:	PUNCT
ejpam-5232	286	4	encyclopedia	encyclopedia	NOUN
ejpam-5232	286	5	of	of	ADP
ejpam-5232	286	6	mathematics	mathematic	NOUN
ejpam-5232	286	7	and	and	CCONJ
ejpam-5232	286	8	it	it	PRON
ejpam-5232	286	9	’s	’	VERB
ejpam-5232	286	10	applications	application	NOUN
ejpam-5232	286	11	.	.	PUNCT
ejpam-5232	287	1	cambridge	cambridge	PROPN
ejpam-5232	287	2	university	university	PROPN
ejpam-5232	287	3	press	press	NOUN
ejpam-5232	287	4	;	;	PUNCT
ejpam-5232	287	5	2nd	2nd	PROPN
ejpam-5232	287	6	edition	edition	NOUN
ejpam-5232	287	7	,	,	PUNCT
ejpam-5232	287	8	1996	1996	NUM
ejpam-5232	287	9	.	.	PUNCT
ejpam-5232	288	1	[	[	X
ejpam-5232	288	2	10	10	NUM
ejpam-5232	288	3	]	]	X
ejpam-5232	288	4	h.	h.	PROPN
ejpam-5232	288	5	o.	o.	PROPN
ejpam-5232	288	6	bakodah	bakodah	PROPN
ejpam-5232	288	7	,	,	PUNCT
ejpam-5232	288	8	m.	m.	NOUN
ejpam-5232	288	9	h.	h.	PROPN
ejpam-5232	288	10	al	al	PROPN
ejpam-5232	288	11	-	-	PUNCT
ejpam-5232	288	12	mazmumy	mazmumy	PROPN
ejpam-5232	288	13	,	,	PUNCT
ejpam-5232	288	14	and	and	CCONJ
ejpam-5232	288	15	s.	s.	PROPN
ejpam-5232	288	16	o.	o.	PROPN
ejpam-5232	288	17	almuhalbedi	almuhalbedi	PROPN
ejpam-5232	288	18	.	.	PUNCT
ejpam-5232	289	1	an	an	DET
ejpam-5232	289	2	efficient	efficient	ADJ
ejpam-5232	289	3	modification	modification	NOUN
ejpam-5232	289	4	of	of	ADP
ejpam-5232	289	5	the	the	DET
ejpam-5232	289	6	adomian	adomian	NOUN
ejpam-5232	289	7	decomposition	decomposition	NOUN
ejpam-5232	289	8	method	method	NOUN
ejpam-5232	289	9	for	for	ADP
ejpam-5232	289	10	solving	solve	VERB
ejpam-5232	289	11	integro	integro	ADJ
ejpam-5232	289	12	-	-	PUNCT
ejpam-5232	289	13	differential	differential	NOUN
ejpam-5232	289	14	equations	equation	NOUN
ejpam-5232	289	15	.	.	PUNCT
ejpam-5232	290	1	math	math	NOUN
ejpam-5232	290	2	.	.	PUNCT
ejpam-5232	291	1	sci	sci	PROPN
ejpam-5232	291	2	.	.	PROPN
ejpam-5232	291	3	lett	lett	PROPN
ejpam-5232	291	4	,	,	PUNCT
ejpam-5232	291	5	21:15–21	21:15–21	PROPN
ejpam-5232	291	6	,	,	PUNCT
ejpam-5232	291	7	2017	2017	NUM
ejpam-5232	291	8	.	.	PUNCT
ejpam-5232	292	1	[	[	X
ejpam-5232	292	2	11	11	NUM
ejpam-5232	292	3	]	]	X
ejpam-5232	292	4	h.	h.	PROPN
ejpam-5232	292	5	o.	o.	PROPN
ejpam-5232	292	6	bakodah	bakodah	NOUN
ejpam-5232	292	7	and	and	CCONJ
ejpam-5232	292	8	n.	n.	PROPN
ejpam-5232	292	9	a.	a.	PROPN
ejpam-5232	292	10	al	al	PROPN
ejpam-5232	292	11	-	-	PUNCT
ejpam-5232	292	12	zaid	zaid	PROPN
ejpam-5232	292	13	.	.	PUNCT
ejpam-5232	293	1	computational	computational	ADJ
ejpam-5232	293	2	approaches	approach	NOUN
ejpam-5232	293	3	to	to	ADP
ejpam-5232	293	4	initial	initial	ADJ
ejpam-5232	293	5	-	-	PUNCT
ejpam-5232	293	6	boundary	boundary	NOUN
ejpam-5232	293	7	value	value	NOUN
ejpam-5232	293	8	problems	problem	NOUN
ejpam-5232	293	9	with	with	ADP
ejpam-5232	293	10	neumann	neumann	PROPN
ejpam-5232	293	11	boundary	boundary	ADJ
ejpam-5232	293	12	conditions	condition	NOUN
ejpam-5232	293	13	.	.	PUNCT
ejpam-5232	294	1	journal	journal	PROPN
ejpam-5232	294	2	of	of	ADP
ejpam-5232	294	3	taibah	taibah	PROPN
ejpam-5232	294	4	university	university	PROPN
ejpam-5232	294	5	for	for	ADP
ejpam-5232	294	6	science	science	NOUN
ejpam-5232	294	7	,	,	PUNCT
ejpam-5232	294	8	12(5):612–619	12(5):612–619	NUM
ejpam-5232	294	9	,	,	PUNCT
ejpam-5232	294	10	2018	2018	NUM
ejpam-5232	294	11	.	.	PUNCT
ejpam-5232	295	1	[	[	X
ejpam-5232	295	2	12	12	NUM
ejpam-5232	295	3	]	]	X
ejpam-5232	295	4	h.	h.	PROPN
ejpam-5232	295	5	o.	o.	PROPN
ejpam-5232	295	6	bakodah	bakodah	PROPN
ejpam-5232	295	7	,	,	PUNCT
ejpam-5232	295	8	m.	m.	NOUN
ejpam-5232	295	9	a.	a.	PROPN
ejpam-5232	295	10	banaja	banaja	PROPN
ejpam-5232	295	11	,	,	PUNCT
ejpam-5232	295	12	b.	b.	PROPN
ejpam-5232	295	13	a.	a.	PROPN
ejpam-5232	295	14	alrigi	alrigi	PROPN
ejpam-5232	295	15	,	,	PUNCT
ejpam-5232	295	16	a.	a.	PROPN
ejpam-5232	295	17	ebaid	ebaid	PROPN
ejpam-5232	295	18	,	,	PUNCT
ejpam-5232	295	19	and	and	CCONJ
ejpam-5232	295	20	r.	r.	PROPN
ejpam-5232	295	21	rach	rach	PROPN
ejpam-5232	295	22	.	.	PUNCT
ejpam-5232	296	1	an	an	DET
ejpam-5232	296	2	efficient	efficient	ADJ
ejpam-5232	296	3	modification	modification	NOUN
ejpam-5232	296	4	of	of	ADP
ejpam-5232	296	5	the	the	DET
ejpam-5232	296	6	decomposition	decomposition	NOUN
ejpam-5232	296	7	method	method	NOUN
ejpam-5232	296	8	with	with	ADP
ejpam-5232	296	9	a	a	DET
ejpam-5232	296	10	convergence	convergence	NOUN
ejpam-5232	296	11	parameter	parameter	NOUN
ejpam-5232	296	12	for	for	ADP
ejpam-5232	296	13	solving	solve	VERB
ejpam-5232	296	14	korteweg	korteweg	PROPN
ejpam-5232	296	15	de	de	PROPN
ejpam-5232	296	16	vries	vries	PROPN
ejpam-5232	296	17	equations	equation	NOUN
ejpam-5232	296	18	.	.	PUNCT
ejpam-5232	297	1	journal	journal	PROPN
ejpam-5232	297	2	of	of	ADP
ejpam-5232	297	3	king	king	PROPN
ejpam-5232	297	4	saud	saud	PROPN
ejpam-5232	297	5	university	university	PROPN
ejpam-5232	297	6	-	-	PUNCT
ejpam-5232	297	7	science	science	NOUN
ejpam-5232	297	8	,	,	PUNCT
ejpam-5232	297	9	31(4):1424	31(4):1424	NUM
ejpam-5232	297	10	–	–	PUNCT
ejpam-5232	297	11	1430	1430	NUM
ejpam-5232	297	12	,	,	PUNCT
ejpam-5232	297	13	2019	2019	NUM
ejpam-5232	297	14	.	.	PUNCT
ejpam-5232	298	1	[	[	X
ejpam-5232	298	2	13	13	NUM
ejpam-5232	298	3	]	]	X
ejpam-5232	298	4	h.	h.	PROPN
ejpam-5232	298	5	o.	o.	PROPN
ejpam-5232	298	6	bakodah	bakodah	PROPN
ejpam-5232	298	7	,	,	PUNCT
ejpam-5232	298	8	f.	f.	PROPN
ejpam-5232	298	9	a.	a.	PROPN
ejpam-5232	298	10	hendi	hendi	PROPN
ejpam-5232	298	11	,	,	PUNCT
ejpam-5232	298	12	and	and	CCONJ
ejpam-5232	298	13	n.	n.	PROPN
ejpam-5232	298	14	a.	a.	PROPN
ejpam-5232	298	15	al	al	PROPN
ejpam-5232	298	16	-	-	PUNCT
ejpam-5232	298	17	zaid	zaid	PROPN
ejpam-5232	298	18	.	.	PUNCT
ejpam-5232	299	1	application	application	NOUN
ejpam-5232	299	2	of	of	ADP
ejpam-5232	299	3	the	the	DET
ejpam-5232	299	4	new	new	ADJ
ejpam-5232	299	5	modified	modify	VERB
ejpam-5232	299	6	decomposition	decomposition	NOUN
ejpam-5232	299	7	method	method	NOUN
ejpam-5232	299	8	to	to	ADP
ejpam-5232	299	9	the	the	DET
ejpam-5232	299	10	regularized	regularize	VERB
ejpam-5232	299	11	long	long	ADJ
ejpam-5232	299	12	-	-	PUNCT
ejpam-5232	299	13	wave	wave	NOUN
ejpam-5232	299	14	equation	equation	NOUN
ejpam-5232	299	15	.	.	PUNCT
ejpam-5232	300	1	life	life	NOUN
ejpam-5232	300	2	science	science	PROPN
ejpam-5232	300	3	journal	journal	PROPN
ejpam-5232	300	4	,	,	PUNCT
ejpam-5232	300	5	9(4):5862–5866	9(4):5862–5866	PROPN
ejpam-5232	300	6	,	,	PUNCT
ejpam-5232	300	7	2012	2012	NUM
ejpam-5232	300	8	.	.	PUNCT
ejpam-5232	301	1	[	[	X
ejpam-5232	301	2	14	14	NUM
ejpam-5232	301	3	]	]	X
ejpam-5232	301	4	r.	r.	PROPN
ejpam-5232	301	5	burden	burden	PROPN
ejpam-5232	301	6	and	and	CCONJ
ejpam-5232	301	7	j.	j.	PROPN
ejpam-5232	301	8	fairies	fairies	PROPN
ejpam-5232	301	9	.	.	PUNCT
ejpam-5232	302	1	numerical	numerical	ADJ
ejpam-5232	302	2	analysis	analysis	NOUN
ejpam-5232	302	3	.	.	PUNCT
ejpam-5232	303	1	brooks	brooks	PROPN
ejpam-5232	303	2	/	/	SYM
ejpam-5232	303	3	cole	cole	PROPN
ejpam-5232	303	4	,	,	PUNCT
ejpam-5232	303	5	thomson	thomson	NOUN
ejpam-5232	303	6	learning	learning	NOUN
ejpam-5232	303	7	(	(	PUNCT
ejpam-5232	303	8	9th	9th	ADJ
ejpam-5232	303	9	eds	ed	NOUN
ejpam-5232	303	10	.	.	PUNCT
ejpam-5232	303	11	)	)	PUNCT
ejpam-5232	303	12	,	,	PUNCT
ejpam-5232	303	13	2010	2010	NUM
ejpam-5232	303	14	.	.	PUNCT
ejpam-5232	304	1	[	[	X
ejpam-5232	304	2	15	15	NUM
ejpam-5232	304	3	]	]	X
ejpam-5232	304	4	m.	m.	NOUN
ejpam-5232	304	5	dehghan	dehghan	PROPN
ejpam-5232	304	6	and	and	CCONJ
ejpam-5232	304	7	a.	a.	PROPN
ejpam-5232	304	8	nikpour	nikpour	PROPN
ejpam-5232	304	9	.	.	PUNCT
ejpam-5232	305	1	numerical	numerical	ADJ
ejpam-5232	305	2	solution	solution	NOUN
ejpam-5232	305	3	of	of	ADP
ejpam-5232	305	4	the	the	DET
ejpam-5232	305	5	system	system	NOUN
ejpam-5232	305	6	of	of	ADP
ejpam-5232	305	7	second	second	ADJ
ejpam-5232	305	8	-	-	PUNCT
ejpam-5232	305	9	order	order	NOUN
ejpam-5232	305	10	boundary	boundary	ADJ
ejpam-5232	305	11	value	value	NOUN
ejpam-5232	305	12	problems	problem	NOUN
ejpam-5232	305	13	using	use	VERB
ejpam-5232	305	14	the	the	DET
ejpam-5232	305	15	local	local	ADJ
ejpam-5232	305	16	radial	radial	ADJ
ejpam-5232	305	17	basis	basis	NOUN
ejpam-5232	305	18	functions	function	NOUN
ejpam-5232	305	19	based	base	VERB
ejpam-5232	305	20	differential	differential	ADJ
ejpam-5232	305	21	quadrature	quadrature	NOUN
ejpam-5232	305	22	collocation	collocation	NOUN
ejpam-5232	305	23	method	method	NOUN
ejpam-5232	305	24	.	.	PUNCT
ejpam-5232	306	1	applied	apply	VERB
ejpam-5232	306	2	mathematical	mathematical	ADJ
ejpam-5232	306	3	modelling	modelling	NOUN
ejpam-5232	306	4	,	,	PUNCT
ejpam-5232	306	5	37(18	37(18	PROPN
ejpam-5232	306	6	-	-	SYM
ejpam-5232	306	7	19):8578–8599	19):8578–8599	ADV
ejpam-5232	306	8	,	,	PUNCT
ejpam-5232	306	9	2013	2013	NUM
ejpam-5232	306	10	.	.	PUNCT
ejpam-5232	307	1	references	reference	NOUN
ejpam-5232	307	2	1515	1515	NUM
ejpam-5232	307	3	[	[	X
ejpam-5232	307	4	16	16	NUM
ejpam-5232	307	5	]	]	PUNCT
ejpam-5232	307	6	j.	j.	PROPN
ejpam-5232	307	7	s.	s.	PROPN
ejpam-5232	307	8	duan	duan	PROPN
ejpam-5232	307	9	and	and	CCONJ
ejpam-5232	307	10	r.	r.	PROPN
ejpam-5232	307	11	rach	rach	PROPN
ejpam-5232	307	12	.	.	PUNCT
ejpam-5232	308	1	a	a	DET
ejpam-5232	308	2	new	new	ADJ
ejpam-5232	308	3	modification	modification	NOUN
ejpam-5232	308	4	of	of	ADP
ejpam-5232	308	5	the	the	DET
ejpam-5232	308	6	adomian	adomian	NOUN
ejpam-5232	308	7	decomposition	decomposition	NOUN
ejpam-5232	308	8	method	method	NOUN
ejpam-5232	308	9	for	for	ADP
ejpam-5232	308	10	solving	solve	VERB
ejpam-5232	308	11	boundary	boundary	ADJ
ejpam-5232	308	12	value	value	NOUN
ejpam-5232	308	13	problems	problem	NOUN
ejpam-5232	308	14	for	for	ADP
ejpam-5232	308	15	higher	high	ADJ
ejpam-5232	308	16	order	order	NOUN
ejpam-5232	308	17	nonlinear	nonlinear	ADJ
ejpam-5232	308	18	differential	differential	ADJ
ejpam-5232	308	19	equations	equation	NOUN
ejpam-5232	308	20	.	.	PUNCT
ejpam-5232	309	1	applied	apply	VERB
ejpam-5232	309	2	mathematics	mathematic	NOUN
ejpam-5232	309	3	and	and	CCONJ
ejpam-5232	309	4	computation	computation	NOUN
ejpam-5232	309	5	,	,	PUNCT
ejpam-5232	309	6	218(8):4090–4118	218(8):4090–4118	NUM
ejpam-5232	309	7	,	,	PUNCT
ejpam-5232	309	8	2011	2011	NUM
ejpam-5232	309	9	.	.	PUNCT
ejpam-5232	310	1	[	[	X
ejpam-5232	310	2	17	17	NUM
ejpam-5232	310	3	]	]	X
ejpam-5232	310	4	i.	i.	PROPN
ejpam-5232	310	5	el	el	PROPN
ejpam-5232	310	6	-	-	PUNCT
ejpam-5232	310	7	kalla	kalla	PROPN
ejpam-5232	310	8	,	,	PUNCT
ejpam-5232	310	9	a.	a.	PROPN
ejpam-5232	310	10	el	el	PROPN
ejpam-5232	310	11	mhlawy	mhlawy	PROPN
ejpam-5232	310	12	,	,	PUNCT
ejpam-5232	310	13	and	and	CCONJ
ejpam-5232	310	14	m.	m.	NOUN
ejpam-5232	310	15	botros	botro	NOUN
ejpam-5232	310	16	.	.	PUNCT
ejpam-5232	311	1	a	a	DET
ejpam-5232	311	2	continuous	continuous	ADJ
ejpam-5232	311	3	solution	solution	NOUN
ejpam-5232	311	4	of	of	ADP
ejpam-5232	311	5	solving	solve	VERB
ejpam-5232	311	6	a	a	DET
ejpam-5232	311	7	class	class	NOUN
ejpam-5232	311	8	of	of	ADP
ejpam-5232	311	9	nonlineartwo	nonlineartwo	NOUN
ejpam-5232	311	10	point	point	NOUN
ejpam-5232	311	11	boundary	boundary	ADJ
ejpam-5232	311	12	value	value	NOUN
ejpam-5232	311	13	problem	problem	NOUN
ejpam-5232	311	14	using	use	VERB
ejpam-5232	311	15	adomian	adomian	NOUN
ejpam-5232	311	16	decomposition	decomposition	NOUN
ejpam-5232	311	17	method	method	NOUN
ejpam-5232	311	18	.	.	PUNCT
ejpam-5232	312	1	ain	ain	PROPN
ejpam-5232	312	2	shams	sham	NOUN
ejpam-5232	312	3	engineering	engineering	NOUN
ejpam-5232	312	4	journal	journal	PROPN
ejpam-5232	312	5	,	,	PUNCT
ejpam-5232	312	6	10(1):211–216	10(1):211–216	NUM
ejpam-5232	312	7	,	,	PUNCT
ejpam-5232	312	8	2019	2019	NUM
ejpam-5232	312	9	.	.	PUNCT
ejpam-5232	313	1	[	[	X
ejpam-5232	313	2	18	18	NUM
ejpam-5232	313	3	]	]	X
ejpam-5232	313	4	y.	y.	PROPN
ejpam-5232	313	5	q.	q.	PROPN
ejpam-5232	313	6	hasan	hasan	PROPN
ejpam-5232	313	7	.	.	PUNCT
ejpam-5232	314	1	the	the	DET
ejpam-5232	314	2	numerical	numerical	ADJ
ejpam-5232	314	3	solution	solution	NOUN
ejpam-5232	314	4	of	of	ADP
ejpam-5232	314	5	third	third	ADJ
ejpam-5232	314	6	-	-	PUNCT
ejpam-5232	314	7	order	order	NOUN
ejpam-5232	314	8	boundary	boundary	ADJ
ejpam-5232	314	9	value	value	NOUN
ejpam-5232	314	10	problems	problem	NOUN
ejpam-5232	314	11	by	by	ADP
ejpam-5232	314	12	the	the	DET
ejpam-5232	314	13	modified	modify	VERB
ejpam-5232	314	14	decomposition	decomposition	NOUN
ejpam-5232	314	15	method	method	NOUN
ejpam-5232	314	16	.	.	PUNCT
ejpam-5232	315	1	advances	advance	NOUN
ejpam-5232	315	2	in	in	ADP
ejpam-5232	315	3	intelligent	intelligent	ADJ
ejpam-5232	315	4	transportation	transportation	NOUN
ejpam-5232	315	5	systems	system	NOUN
ejpam-5232	315	6	,	,	PUNCT
ejpam-5232	315	7	1(3):71–74	1(3):71–74	NUM
ejpam-5232	315	8	,	,	PUNCT
ejpam-5232	315	9	2012	2012	NUM
ejpam-5232	315	10	.	.	PUNCT
ejpam-5232	316	1	[	[	X
ejpam-5232	316	2	19	19	NUM
ejpam-5232	316	3	]	]	PUNCT
ejpam-5232	316	4	m.	m.	NOUN
ejpam-5232	316	5	m.	m.	PROPN
ejpam-5232	316	6	hosseini	hosseini	PROPN
ejpam-5232	316	7	.	.	PROPN
ejpam-5232	316	8	adomian	adomian	PROPN
ejpam-5232	316	9	decomposition	decomposition	NOUN
ejpam-5232	316	10	method	method	NOUN
ejpam-5232	316	11	with	with	ADP
ejpam-5232	316	12	chebyshev	chebyshev	NOUN
ejpam-5232	316	13	polynomials	polynomial	NOUN
ejpam-5232	316	14	.	.	PUNCT
ejpam-5232	317	1	applied	apply	VERB
ejpam-5232	317	2	mathematics	mathematic	NOUN
ejpam-5232	317	3	and	and	CCONJ
ejpam-5232	317	4	computation	computation	NOUN
ejpam-5232	317	5	,	,	PUNCT
ejpam-5232	317	6	175(2):1685–1693	175(2):1685–1693	NUM
ejpam-5232	317	7	,	,	PUNCT
ejpam-5232	317	8	2006	2006	NUM
ejpam-5232	317	9	.	.	PUNCT
ejpam-5232	318	1	[	[	X
ejpam-5232	318	2	20	20	NUM
ejpam-5232	318	3	]	]	PUNCT
ejpam-5232	318	4	b.	b.	PROPN
ejpam-5232	318	5	s.	s.	PROPN
ejpam-5232	318	6	kashkari	kashkari	PROPN
ejpam-5232	318	7	and	and	CCONJ
ejpam-5232	318	8	h.	h.	PROPN
ejpam-5232	318	9	o.	o.	PROPN
ejpam-5232	318	10	bakodah	bakodah	PROPN
ejpam-5232	318	11	.	.	PUNCT
ejpam-5232	319	1	new	new	ADJ
ejpam-5232	319	2	modification	modification	NOUN
ejpam-5232	319	3	of	of	ADP
ejpam-5232	319	4	laplace	laplace	NOUN
ejpam-5232	319	5	decomposition	decomposition	NOUN
ejpam-5232	319	6	method	method	NOUN
ejpam-5232	319	7	for	for	ADP
ejpam-5232	319	8	seventh	seventh	ADJ
ejpam-5232	319	9	order	order	NOUN
ejpam-5232	319	10	kdv	kdv	NOUN
ejpam-5232	319	11	equation	equation	NOUN
ejpam-5232	319	12	.	.	PUNCT
ejpam-5232	320	1	applied	apply	VERB
ejpam-5232	320	2	mathematics	mathematics	PROPN
ejpam-5232	320	3	&	&	CCONJ
ejpam-5232	320	4	information	information	NOUN
ejpam-5232	320	5	sciences	sciences	PROPN
ejpam-5232	320	6	,	,	PUNCT
ejpam-5232	320	7	9(5):2507	9(5):2507	NUM
ejpam-5232	320	8	,	,	PUNCT
ejpam-5232	320	9	2015	2015	NUM
ejpam-5232	320	10	.	.	PUNCT
ejpam-5232	321	1	[	[	X
ejpam-5232	321	2	21	21	NUM
ejpam-5232	321	3	]	]	X
ejpam-5232	321	4	afrah	afrah	PROPN
ejpam-5232	321	5	saad	saad	PROPN
ejpam-5232	321	6	mahmood	mahmood	PROPN
ejpam-5232	321	7	,	,	PUNCT
ejpam-5232	321	8	luis	luis	PROPN
ejpam-5232	321	9	casasús	casasús	PROPN
ejpam-5232	321	10	,	,	PUNCT
ejpam-5232	321	11	and	and	CCONJ
ejpam-5232	321	12	waleed	waleed	PROPN
ejpam-5232	321	13	al	al	PROPN
ejpam-5232	321	14	-	-	PUNCT
ejpam-5232	321	15	hayani	hayani	PROPN
ejpam-5232	321	16	.	.	PUNCT
ejpam-5232	322	1	analysis	analysis	NOUN
ejpam-5232	322	2	of	of	ADP
ejpam-5232	322	3	resonant	resonant	ADJ
ejpam-5232	322	4	oscillators	oscillator	NOUN
ejpam-5232	322	5	with	with	ADP
ejpam-5232	322	6	the	the	DET
ejpam-5232	322	7	adomian	adomian	NOUN
ejpam-5232	322	8	decomposition	decomposition	NOUN
ejpam-5232	322	9	method	method	NOUN
ejpam-5232	322	10	.	.	PUNCT
ejpam-5232	323	1	physics	physics	NOUN
ejpam-5232	323	2	letters	letter	NOUN
ejpam-5232	323	3	a	a	PRON
ejpam-5232	323	4	,	,	PUNCT
ejpam-5232	323	5	357(4	357(4	NUM
ejpam-5232	323	6	-	-	SYM
ejpam-5232	323	7	5):306	5):306	NUM
ejpam-5232	323	8	–	–	PUNCT
ejpam-5232	323	9	313	313	NUM
ejpam-5232	323	10	,	,	PUNCT
ejpam-5232	323	11	2006	2006	NUM
ejpam-5232	323	12	.	.	PUNCT
ejpam-5232	324	1	[	[	X
ejpam-5232	324	2	22	22	NUM
ejpam-5232	324	3	]	]	PUNCT
ejpam-5232	324	4	t.	t.	PROPN
ejpam-5232	324	5	sauer	sauer	PROPN
ejpam-5232	324	6	.	.	PUNCT
ejpam-5232	325	1	numerical	numerical	ADJ
ejpam-5232	325	2	analysis	analysis	PROPN
ejpam-5232	325	3	.	.	PUNCT
ejpam-5232	326	1	addison	addison	PROPN
ejpam-5232	326	2	-	-	PUNCT
ejpam-5232	326	3	wesley	wesley	PROPN
ejpam-5232	326	4	publishing	publishing	PROPN
ejpam-5232	326	5	company	company	NOUN
ejpam-5232	326	6	,	,	PUNCT
ejpam-5232	326	7	2011	2011	NUM
ejpam-5232	326	8	.	.	PUNCT
ejpam-5232	327	1	[	[	X
ejpam-5232	327	2	23	23	NUM
ejpam-5232	327	3	]	]	PUNCT
ejpam-5232	327	4	a.	a.	NOUN
ejpam-5232	327	5	m.	m.	NOUN
ejpam-5232	327	6	wazwaz	wazwaz	PROPN
ejpam-5232	327	7	.	.	PUNCT
ejpam-5232	328	1	a	a	DET
ejpam-5232	328	2	reliable	reliable	ADJ
ejpam-5232	328	3	algorithm	algorithm	NOUN
ejpam-5232	328	4	for	for	ADP
ejpam-5232	328	5	obtaining	obtain	VERB
ejpam-5232	328	6	positive	positive	ADJ
ejpam-5232	328	7	solutions	solution	NOUN
ejpam-5232	328	8	for	for	ADP
ejpam-5232	328	9	nonlinear	nonlinear	ADJ
ejpam-5232	328	10	boundary	boundary	ADJ
ejpam-5232	328	11	value	value	NOUN
ejpam-5232	328	12	problems	problem	NOUN
ejpam-5232	328	13	.	.	PUNCT
ejpam-5232	329	1	computers	computer	NOUN
ejpam-5232	329	2	&	&	CCONJ
ejpam-5232	329	3	mathematics	mathematics	PROPN
ejpam-5232	329	4	with	with	ADP
ejpam-5232	329	5	applications	application	NOUN
ejpam-5232	329	6	,	,	PUNCT
ejpam-5232	329	7	41(1011):1237–1244	41(1011):1237–1244	PROPN
ejpam-5232	329	8	,	,	PUNCT
ejpam-5232	329	9	2001	2001	NUM
ejpam-5232	329	10	.	.	PUNCT
ejpam-5232	330	1	[	[	X
ejpam-5232	330	2	24	24	NUM
ejpam-5232	330	3	]	]	PUNCT
ejpam-5232	330	4	a.	a.	NOUN
ejpam-5232	330	5	m.	m.	NOUN
ejpam-5232	330	6	wazwaz	wazwaz	PROPN
ejpam-5232	330	7	.	.	PUNCT
ejpam-5232	331	1	the	the	DET
ejpam-5232	331	2	modified	modify	VERB
ejpam-5232	331	3	decomposition	decomposition	NOUN
ejpam-5232	331	4	method	method	NOUN
ejpam-5232	331	5	and	and	CCONJ
ejpam-5232	331	6	padé	padé	ADJ
ejpam-5232	331	7	approximants	approximant	NOUN
ejpam-5232	331	8	for	for	ADP
ejpam-5232	331	9	a	a	DET
ejpam-5232	331	10	boundary	boundary	ADJ
ejpam-5232	331	11	layer	layer	NOUN
ejpam-5232	331	12	equation	equation	NOUN
ejpam-5232	331	13	in	in	ADP
ejpam-5232	331	14	unbounded	unbounded	ADJ
ejpam-5232	331	15	domain	domain	NOUN
ejpam-5232	331	16	.	.	PUNCT
ejpam-5232	332	1	applied	apply	VERB
ejpam-5232	332	2	mathematics	mathematic	NOUN
ejpam-5232	332	3	and	and	CCONJ
ejpam-5232	332	4	computation	computation	NOUN
ejpam-5232	332	5	,	,	PUNCT
ejpam-5232	332	6	177(2):737–744	177(2):737–744	NUM
ejpam-5232	332	7	,	,	PUNCT
ejpam-5232	332	8	2006	2006	NUM
ejpam-5232	332	9	.	.	PUNCT