id	sid	tid	token	lemma	pos
ejpam-310	1	1	8_kurulay.dvi	8_kurulay.dvi	NUM
ejpam-310	1	2	european	european	ADJ
ejpam-310	1	3	journal	journal	PROPN
ejpam-310	1	4	of	of	ADP
ejpam-310	1	5	pure	pure	ADJ
ejpam-310	1	6	and	and	CCONJ
ejpam-310	1	7	applied	apply	VERB
ejpam-310	1	8	mathematics	mathematic	NOUN
ejpam-310	1	9	vol	vol	NOUN
ejpam-310	1	10	.	.	PROPN
ejpam-310	2	1	2	2	NUM
ejpam-310	2	2	,	,	PUNCT
ejpam-310	2	3	no	no	INTJ
ejpam-310	2	4	.	.	NOUN
ejpam-310	2	5	2	2	NUM
ejpam-310	2	6	,	,	PUNCT
ejpam-310	2	7	2009	2009	NUM
ejpam-310	2	8	,	,	PUNCT
ejpam-310	2	9	(	(	PUNCT
ejpam-310	2	10	268	268	NUM
ejpam-310	2	11	-	-	SYM
ejpam-310	2	12	277	277	NUM
ejpam-310	2	13	)	)	PUNCT
ejpam-310	2	14	issn	issn	PROPN
ejpam-310	2	15	1307	1307	NUM
ejpam-310	2	16	-	-	SYM
ejpam-310	2	17	5543	5543	NUM
ejpam-310	2	18	–	–	PUNCT
ejpam-310	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-310	2	20	a	a	DET
ejpam-310	2	21	novel	novel	ADJ
ejpam-310	2	22	power	power	NOUN
ejpam-310	2	23	series	series	NOUN
ejpam-310	2	24	method	method	NOUN
ejpam-310	2	25	for	for	ADP
ejpam-310	2	26	solving	solve	VERB
ejpam-310	2	27	second	second	ADJ
ejpam-310	2	28	order	order	NOUN
ejpam-310	2	29	partial	partial	ADJ
ejpam-310	2	30	differential	differential	NOUN
ejpam-310	2	31	equations	equation	NOUN
ejpam-310	2	32	muhammet	muhammet	VERB
ejpam-310	2	33	kurulay1	kurulay1	NOUN
ejpam-310	2	34	and	and	CCONJ
ejpam-310	2	35	mustafa	mustafa	PROPN
ejpam-310	2	36	bayram2∗	bayram2∗	PROPN
ejpam-310	2	37	1	1	NUM
ejpam-310	2	38	yildiz	yildiz	PROPN
ejpam-310	2	39	technical	technical	PROPN
ejpam-310	2	40	university	university	PROPN
ejpam-310	2	41	,	,	PUNCT
ejpam-310	2	42	faculty	faculty	NOUN
ejpam-310	2	43	of	of	ADP
ejpam-310	2	44	art	art	NOUN
ejpam-310	2	45	and	and	CCONJ
ejpam-310	2	46	sciences	science	NOUN
ejpam-310	2	47	,	,	PUNCT
ejpam-310	2	48	department	department	NOUN
ejpam-310	2	49	of	of	ADP
ejpam-310	2	50	mathematics	mathematic	NOUN
ejpam-310	2	51	,	,	PUNCT
ejpam-310	2	52	34210	34210	NUM
ejpam-310	2	53	-	-	SYM
ejpam-310	2	54	davutpasa-̇istanbul	davutpasa-̇istanbul	PROPN
ejpam-310	2	55	2	2	NUM
ejpam-310	2	56	fatih	fatih	PROPN
ejpam-310	2	57	university	university	NOUN
ejpam-310	2	58	,	,	PUNCT
ejpam-310	2	59	faculty	faculty	NOUN
ejpam-310	2	60	of	of	ADP
ejpam-310	2	61	art	art	NOUN
ejpam-310	2	62	and	and	CCONJ
ejpam-310	2	63	sciences	science	NOUN
ejpam-310	2	64	,	,	PUNCT
ejpam-310	2	65	department	department	NOUN
ejpam-310	2	66	of	of	ADP
ejpam-310	2	67	mathematics	mathematic	NOUN
ejpam-310	2	68	,	,	PUNCT
ejpam-310	2	69	34500	34500	NUM
ejpam-310	2	70	-	-	SYM
ejpam-310	2	71	buyukcekmece-̇istanbul	buyukcekmece-̇istanbul	PROPN
ejpam-310	2	72	/	/	SYM
ejpam-310	2	73	turkey	turkey	NOUN
ejpam-310	2	74	abstract	abstract	NOUN
ejpam-310	2	75	.	.	PUNCT
ejpam-310	3	1	in	in	ADP
ejpam-310	3	2	this	this	DET
ejpam-310	3	3	article	article	NOUN
ejpam-310	3	4	,	,	PUNCT
ejpam-310	3	5	a	a	DET
ejpam-310	3	6	new	new	ADJ
ejpam-310	3	7	approach	approach	NOUN
ejpam-310	3	8	is	be	AUX
ejpam-310	3	9	proposed	propose	VERB
ejpam-310	3	10	to	to	PART
ejpam-310	3	11	solve	solve	VERB
ejpam-310	3	12	partial	partial	ADJ
ejpam-310	3	13	differential	differential	NOUN
ejpam-310	3	14	equation	equation	NOUN
ejpam-310	3	15	.	.	PUNCT
ejpam-310	4	1	this	this	DET
ejpam-310	4	2	method	method	NOUN
ejpam-310	4	3	is	be	AUX
ejpam-310	4	4	based	base	VERB
ejpam-310	4	5	on	on	ADP
ejpam-310	4	6	generalized	generalized	ADJ
ejpam-310	4	7	taylor	taylor	PROPN
ejpam-310	4	8	’s	’s	PART
ejpam-310	4	9	formula	formula	NOUN
ejpam-310	4	10	.	.	PUNCT
ejpam-310	5	1	the	the	DET
ejpam-310	5	2	solution	solution	NOUN
ejpam-310	5	3	of	of	ADP
ejpam-310	5	4	partial	partial	ADJ
ejpam-310	5	5	differential	differential	NOUN
ejpam-310	5	6	equations	equation	NOUN
ejpam-310	5	7	can	can	AUX
ejpam-310	5	8	be	be	AUX
ejpam-310	5	9	expanded	expand	VERB
ejpam-310	5	10	using	use	VERB
ejpam-310	5	11	maple	maple	NOUN
ejpam-310	5	12	.	.	PUNCT
ejpam-310	6	1	doing	do	VERB
ejpam-310	6	2	some	some	DET
ejpam-310	6	3	simple	simple	ADJ
ejpam-310	6	4	mathematical	mathematical	ADJ
ejpam-310	6	5	operations	operation	NOUN
ejpam-310	6	6	on	on	ADP
ejpam-310	6	7	these	these	DET
ejpam-310	6	8	equations	equation	NOUN
ejpam-310	6	9	,	,	PUNCT
ejpam-310	6	10	we	we	PRON
ejpam-310	6	11	can	can	AUX
ejpam-310	6	12	get	get	VERB
ejpam-310	6	13	a	a	DET
ejpam-310	6	14	closed	closed	ADJ
ejpam-310	6	15	form	form	NOUN
ejpam-310	6	16	series	series	NOUN
ejpam-310	6	17	solution	solution	NOUN
ejpam-310	6	18	or	or	CCONJ
ejpam-310	6	19	approximate	approximate	ADJ
ejpam-310	6	20	solution	solution	NOUN
ejpam-310	6	21	quickly	quickly	ADV
ejpam-310	6	22	.	.	PUNCT
ejpam-310	7	1	pde	pde	NOUN
ejpam-310	7	2	problems	problem	NOUN
ejpam-310	7	3	with	with	ADP
ejpam-310	7	4	constant	constant	ADJ
ejpam-310	7	5	and	and	CCONJ
ejpam-310	7	6	variable	variable	ADJ
ejpam-310	7	7	coefficients	coefficient	NOUN
ejpam-310	7	8	are	be	AUX
ejpam-310	7	9	solved	solve	VERB
ejpam-310	7	10	by	by	ADP
ejpam-310	7	11	the	the	DET
ejpam-310	7	12	present	present	ADJ
ejpam-310	7	13	method	method	NOUN
ejpam-310	7	14	.	.	PUNCT
ejpam-310	8	1	with	with	ADP
ejpam-310	8	2	this	this	DET
ejpam-310	8	3	method	method	NOUN
ejpam-310	8	4	,	,	PUNCT
ejpam-310	8	5	we	we	PRON
ejpam-310	8	6	can	can	AUX
ejpam-310	8	7	reach	reach	VERB
ejpam-310	8	8	same	same	ADJ
ejpam-310	8	9	results	result	NOUN
ejpam-310	8	10	simpler	simple	ADJ
ejpam-310	8	11	way	way	NOUN
ejpam-310	8	12	than	than	ADP
ejpam-310	8	13	other	other	ADJ
ejpam-310	8	14	analytical	analytical	ADJ
ejpam-310	8	15	or	or	CCONJ
ejpam-310	8	16	approximate	approximate	ADJ
ejpam-310	8	17	methods	method	NOUN
ejpam-310	8	18	.	.	PUNCT
ejpam-310	9	1	key	key	ADJ
ejpam-310	9	2	words	word	NOUN
ejpam-310	9	3	:	:	PUNCT
ejpam-310	9	4	second	second	ADJ
ejpam-310	9	5	order	order	NOUN
ejpam-310	9	6	partial	partial	ADJ
ejpam-310	9	7	differential	differential	NOUN
ejpam-310	9	8	equations	equation	NOUN
ejpam-310	9	9	;	;	PUNCT
ejpam-310	9	10	power	power	NOUN
ejpam-310	9	11	series	series	NOUN
ejpam-310	9	12	.	.	PUNCT
ejpam-310	10	1	∗corresponding	∗corresponde	VERB
ejpam-310	10	2	author	author	NOUN
ejpam-310	10	3	.	.	PUNCT
ejpam-310	11	1	email	email	NOUN
ejpam-310	11	2	addresses	address	NOUN
ejpam-310	11	3	:	:	PUNCT
ejpam-310	11	4	muhammetkurulay	muhammetkurulay	PROPN
ejpam-310	11	5	�	�	PROPN
ejpam-310	11	6	yahoo	yahoo	PROPN
ejpam-310	11	7	.	.	PUNCT
ejpam-310	12	1	om	om	PROPN
ejpam-310	12	2	(	(	PUNCT
ejpam-310	12	3	m.	m.	NOUN
ejpam-310	12	4	kurulay	kurulay	PROPN
ejpam-310	12	5	)	)	PUNCT
ejpam-310	12	6	,	,	PUNCT
ejpam-310	12	7	mbayram�fatih.edu.tr	mbayram�fatih.edu.tr	PROPN
ejpam-310	12	8	(	(	PUNCT
ejpam-310	12	9	m.	m.	PROPN
ejpam-310	12	10	bayram	bayram	PROPN
ejpam-310	12	11	)	)	PUNCT
ejpam-310	12	12	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-310	13	1	268	268	NUM
ejpam-310	13	2	c	c	NOUN
ejpam-310	13	3	©	©	PROPN
ejpam-310	13	4	2009	2009	NUM
ejpam-310	13	5	ejpam	ejpam	NOUN
ejpam-310	13	6	all	all	DET
ejpam-310	13	7	rights	right	NOUN
ejpam-310	13	8	reserved	reserve	VERB
ejpam-310	13	9	.	.	PUNCT
ejpam-310	14	1	m.	m.	NOUN
ejpam-310	14	2	kurulay	kurulay	PROPN
ejpam-310	14	3	and	and	CCONJ
ejpam-310	14	4	m.	m.	PROPN
ejpam-310	14	5	bayram	bayram	PROPN
ejpam-310	14	6	/	/	SYM
ejpam-310	14	7	eur	eur	PROPN
ejpam-310	14	8	.	.	PUNCT
ejpam-310	15	1	j.	j.	PROPN
ejpam-310	15	2	pure	pure	PROPN
ejpam-310	15	3	appl	appl	PROPN
ejpam-310	15	4	.	.	PROPN
ejpam-310	15	5	math	math	PROPN
ejpam-310	15	6	,	,	PUNCT
ejpam-310	15	7	2	2	NUM
ejpam-310	15	8	(	(	PUNCT
ejpam-310	15	9	2009	2009	NUM
ejpam-310	15	10	)	)	PUNCT
ejpam-310	15	11	,	,	PUNCT
ejpam-310	15	12	(	(	PUNCT
ejpam-310	15	13	268	268	NUM
ejpam-310	15	14	-	-	SYM
ejpam-310	15	15	277	277	NUM
ejpam-310	15	16	)	)	PUNCT
ejpam-310	15	17	269	269	NUM
ejpam-310	15	18	1	1	NUM
ejpam-310	15	19	.	.	PUNCT
ejpam-310	16	1	introduction	introduction	NOUN
ejpam-310	16	2	study	study	NOUN
ejpam-310	16	3	about	about	ADP
ejpam-310	16	4	partial	partial	ADJ
ejpam-310	16	5	differential	differential	NOUN
ejpam-310	16	6	algebraic	algebraic	ADJ
ejpam-310	16	7	equation	equation	NOUN
ejpam-310	16	8	were	be	AUX
ejpam-310	16	9	done	do	VERB
ejpam-310	16	10	by	by	ADP
ejpam-310	16	11	marszalek	marszalek	NOUN
ejpam-310	16	12	.	.	PUNCT
ejpam-310	17	1	marszalek	marszalek	PROPN
ejpam-310	17	2	studied	study	VERB
ejpam-310	17	3	analysis	analysis	NOUN
ejpam-310	17	4	of	of	ADP
ejpam-310	17	5	the	the	DET
ejpam-310	17	6	partial	partial	ADJ
ejpam-310	17	7	differential	differential	NOUN
ejpam-310	17	8	algebraic	algebraic	ADJ
ejpam-310	17	9	equations	equation	NOUN
ejpam-310	18	1	[	[	X
ejpam-310	18	2	1	1	NUM
ejpam-310	18	3	]	]	PUNCT
ejpam-310	18	4	.	.	PUNCT
ejpam-310	19	1	lucht	lucht	PROPN
ejpam-310	19	2	ve	ve	AUX
ejpam-310	19	3	strehmel	strehmel	VERB
ejpam-310	19	4	[	[	X
ejpam-310	19	5	2	2	NUM
ejpam-310	19	6	,	,	PUNCT
ejpam-310	19	7	3	3	NUM
ejpam-310	19	8	]	]	PUNCT
ejpam-310	19	9	studied	study	VERB
ejpam-310	19	10	numerical	numerical	ADJ
ejpam-310	19	11	solution	solution	NOUN
ejpam-310	19	12	and	and	CCONJ
ejpam-310	19	13	indexes	index	NOUN
ejpam-310	19	14	of	of	ADP
ejpam-310	19	15	the	the	DET
ejpam-310	19	16	linear	linear	ADJ
ejpam-310	19	17	partial	partial	ADJ
ejpam-310	19	18	differential	differential	NOUN
ejpam-310	19	19	equations	equation	NOUN
ejpam-310	19	20	with	with	ADP
ejpam-310	19	21	constant	constant	ADJ
ejpam-310	19	22	coefficients	coefficient	NOUN
ejpam-310	19	23	.	.	PUNCT
ejpam-310	20	1	a	a	DET
ejpam-310	20	2	study	study	NOUN
ejpam-310	20	3	about	about	ADP
ejpam-310	20	4	characteristics	characteristic	NOUN
ejpam-310	20	5	analysis	analysis	NOUN
ejpam-310	20	6	and	and	CCONJ
ejpam-310	20	7	differential	differential	ADJ
ejpam-310	20	8	index	index	NOUN
ejpam-310	20	9	of	of	ADP
ejpam-310	20	10	the	the	DET
ejpam-310	20	11	partial	partial	ADJ
ejpam-310	20	12	differential	differential	NOUN
ejpam-310	20	13	algebraic	algebraic	ADJ
ejpam-310	20	14	equations	equation	NOUN
ejpam-310	20	15	were	be	AUX
ejpam-310	20	16	given	give	VERB
ejpam-310	20	17	by	by	ADP
ejpam-310	20	18	martinson	martinson	NOUN
ejpam-310	20	19	and	and	CCONJ
ejpam-310	20	20	barton	barton	PROPN
ejpam-310	21	1	[	[	X
ejpam-310	21	2	5	5	NUM
ejpam-310	21	3	,	,	PUNCT
ejpam-310	21	4	6	6	NUM
ejpam-310	21	5	]	]	PUNCT
ejpam-310	21	6	.	.	PUNCT
ejpam-310	22	1	debrabant	debrabant	PROPN
ejpam-310	22	2	and	and	CCONJ
ejpam-310	22	3	strehmel	strehmel	ADJ
ejpam-310	22	4	investigated	investigate	VERB
ejpam-310	22	5	convergence	convergence	NOUN
ejpam-310	22	6	of	of	ADP
ejpam-310	22	7	the	the	DET
ejpam-310	22	8	runge	runge	NOUN
ejpam-310	22	9	-	-	PUNCT
ejpam-310	22	10	kutta	kutta	NOUN
ejpam-310	22	11	method	method	NOUN
ejpam-310	22	12	for	for	ADP
ejpam-310	22	13	linear	linear	ADJ
ejpam-310	22	14	partial	partial	ADJ
ejpam-310	22	15	differential	differential	NOUN
ejpam-310	22	16	algebnraic	algebnraic	PROPN
ejpam-310	22	17	equations	equation	NOUN
ejpam-310	23	1	[	[	X
ejpam-310	23	2	4	4	NUM
ejpam-310	23	3	]	]	PUNCT
ejpam-310	23	4	.	.	PUNCT
ejpam-310	24	1	chen	chen	PROPN
ejpam-310	24	2	and	and	CCONJ
ejpam-310	24	3	ho	ho	X
ejpam-310	25	1	[	[	X
ejpam-310	25	2	7	7	NUM
ejpam-310	25	3	]	]	PUNCT
ejpam-310	25	4	proposed	propose	VERB
ejpam-310	25	5	methods	method	NOUN
ejpam-310	25	6	to	to	ADP
ejpam-310	25	7	solving	solve	VERB
ejpam-310	25	8	partial	partial	ADJ
ejpam-310	25	9	differential	differential	ADJ
ejpam-310	25	10	equations	equation	NOUN
ejpam-310	25	11	by	by	ADP
ejpam-310	25	12	two	two	NUM
ejpam-310	25	13	-	-	PUNCT
ejpam-310	25	14	dimensional	dimensional	ADJ
ejpam-310	25	15	differential	differential	ADJ
ejpam-310	25	16	transform	transform	NOUN
ejpam-310	25	17	method	method	NOUN
ejpam-310	25	18	.	.	PUNCT
ejpam-310	26	1	the	the	DET
ejpam-310	26	2	method	method	NOUN
ejpam-310	26	3	was	be	AUX
ejpam-310	26	4	applied	apply	VERB
ejpam-310	26	5	to	to	ADP
ejpam-310	26	6	the	the	DET
ejpam-310	26	7	partial	partial	ADJ
ejpam-310	26	8	differential	differential	NOUN
ejpam-310	26	9	equation	equation	NOUN
ejpam-310	26	10	[	[	X
ejpam-310	26	11	8–10].second	8–10].second	NUM
ejpam-310	26	12	-	-	PUNCT
ejpam-310	26	13	order	order	NOUN
ejpam-310	26	14	linear	linear	ADJ
ejpam-310	26	15	partial	partial	ADJ
ejpam-310	26	16	differential	differential	NOUN
ejpam-310	26	17	equations	equation	NOUN
ejpam-310	26	18	problems	problem	NOUN
ejpam-310	26	19	were	be	AUX
ejpam-310	26	20	solved	solve	VERB
ejpam-310	26	21	by	by	ADP
ejpam-310	26	22	yang	yang	PROPN
ejpam-310	26	23	,	,	PUNCT
ejpam-310	26	24	liu	liu	PROPN
ejpam-310	26	25	and	and	CCONJ
ejpam-310	26	26	bai	bai	PROPN
ejpam-310	27	1	[	[	X
ejpam-310	27	2	11	11	NUM
ejpam-310	27	3	]	]	PUNCT
ejpam-310	27	4	.	.	PUNCT
ejpam-310	28	1	chebyshev	chebyshev	PROPN
ejpam-310	28	2	polynomial	polynomial	ADJ
ejpam-310	28	3	solutions	solution	NOUN
ejpam-310	28	4	of	of	ADP
ejpam-310	28	5	second	second	ADJ
ejpam-310	28	6	-	-	PUNCT
ejpam-310	28	7	order	order	NOUN
ejpam-310	28	8	linear	linear	ADJ
ejpam-310	28	9	partial	partial	ADJ
ejpam-310	28	10	differential	differential	NOUN
ejpam-310	28	11	equations	equation	NOUN
ejpam-310	28	12	[	[	X
ejpam-310	28	13	12	12	NUM
ejpam-310	28	14	]	]	PUNCT
ejpam-310	28	15	.	.	PUNCT
ejpam-310	29	1	in	in	ADP
ejpam-310	29	2	this	this	DET
ejpam-310	29	3	paper	paper	NOUN
ejpam-310	29	4	,	,	PUNCT
ejpam-310	29	5	we	we	PRON
ejpam-310	29	6	propose	propose	VERB
ejpam-310	29	7	,	,	PUNCT
ejpam-310	29	8	by	by	ADP
ejpam-310	29	9	making	make	VERB
ejpam-310	29	10	full	full	ADJ
ejpam-310	29	11	use	use	NOUN
ejpam-310	29	12	of	of	ADP
ejpam-310	29	13	the	the	DET
ejpam-310	29	14	properties	property	NOUN
ejpam-310	29	15	of	of	ADP
ejpam-310	29	16	power	power	NOUN
ejpam-310	29	17	series	series	NOUN
ejpam-310	29	18	,	,	PUNCT
ejpam-310	29	19	a	a	DET
ejpam-310	29	20	generral	generral	ADJ
ejpam-310	29	21	scheme	scheme	NOUN
ejpam-310	29	22	for	for	ADP
ejpam-310	29	23	solving	solve	VERB
ejpam-310	29	24	the	the	DET
ejpam-310	29	25	second	second	ADJ
ejpam-310	29	26	-	-	PUNCT
ejpam-310	29	27	order	order	NOUN
ejpam-310	29	28	partial	partial	ADJ
ejpam-310	29	29	differential	differential	NOUN
ejpam-310	29	30	equation	equation	NOUN
ejpam-310	29	31	a(x	a(x	NOUN
ejpam-310	29	32	,	,	PUNCT
ejpam-310	29	33	y	y	PROPN
ejpam-310	29	34	)	)	PUNCT
ejpam-310	29	35	∂	∂	NOUN
ejpam-310	29	36	2u	2u	PROPN
ejpam-310	29	37	∂	∂	NOUN
ejpam-310	29	38	x2	x2	PROPN
ejpam-310	29	39	+	+	CCONJ
ejpam-310	29	40	b(x	b(x	PROPN
ejpam-310	29	41	,	,	PUNCT
ejpam-310	29	42	y	y	PROPN
ejpam-310	29	43	)	)	PUNCT
ejpam-310	29	44	∂	∂	NOUN
ejpam-310	29	45	2u	2u	PROPN
ejpam-310	29	46	∂	∂	NOUN
ejpam-310	30	1	x∂	x∂	PROPN
ejpam-310	30	2	y	y	PROPN
ejpam-310	30	3	+	+	PROPN
ejpam-310	30	4	c(x	c(x	PROPN
ejpam-310	30	5	,	,	PUNCT
ejpam-310	30	6	y	y	PROPN
ejpam-310	30	7	)	)	PUNCT
ejpam-310	30	8	∂	∂	NOUN
ejpam-310	30	9	2u	2u	NOUN
ejpam-310	30	10	∂	∂	NOUN
ejpam-310	30	11	y2	y2	NOUN
ejpam-310	31	1	+	+	CCONJ
ejpam-310	31	2	d(x	d(x	PROPN
ejpam-310	31	3	,	,	PUNCT
ejpam-310	31	4	y	y	PROPN
ejpam-310	31	5	)	)	PUNCT
ejpam-310	31	6	∂	∂	NUM
ejpam-310	31	7	u	u	NOUN
ejpam-310	31	8	∂	∂	NOUN
ejpam-310	31	9	x	x	NOUN
ejpam-310	32	1	+	+	NOUN
ejpam-310	32	2	e(x	e(x	NUM
ejpam-310	32	3	,	,	PUNCT
ejpam-310	32	4	y	y	NOUN
ejpam-310	32	5	)	)	PUNCT
ejpam-310	32	6	∂	∂	NUM
ejpam-310	32	7	u	u	NOUN
ejpam-310	32	8	∂	∂	NOUN
ejpam-310	32	9	y	y	PROPN
ejpam-310	32	10	+	+	NUM
ejpam-310	32	11	f	f	X
ejpam-310	32	12	(	(	PUNCT
ejpam-310	32	13	x	x	INTJ
ejpam-310	32	14	,	,	PUNCT
ejpam-310	32	15	y)u+	y)u+	NUM
ejpam-310	32	16	g(x	g(x	PROPN
ejpam-310	32	17	,	,	PUNCT
ejpam-310	32	18	y	y	PROPN
ejpam-310	32	19	)	)	PUNCT
ejpam-310	32	20	=	=	SYM
ejpam-310	32	21	0	0	PUNCT
ejpam-310	32	22	(	(	PUNCT
ejpam-310	32	23	1.1	1.1	NUM
ejpam-310	32	24	)	)	PUNCT
ejpam-310	32	25	with	with	ADP
ejpam-310	32	26	the	the	DET
ejpam-310	32	27	initial	initial	ADJ
ejpam-310	32	28	conditions	condition	NOUN
ejpam-310	32	29	u(x	u(x	NOUN
ejpam-310	32	30	,	,	PUNCT
ejpam-310	32	31	0	0	NUM
ejpam-310	32	32	)	)	PUNCT
ejpam-310	32	33	=	=	SYM
ejpam-310	32	34	p(x	p(x	PROPN
ejpam-310	32	35	)	)	PUNCT
ejpam-310	32	36	,	,	PUNCT
ejpam-310	32	37	∂	∂	NUM
ejpam-310	32	38	∂	∂	NOUN
ejpam-310	32	39	y	y	PROPN
ejpam-310	32	40	u(x	u(x	PROPN
ejpam-310	32	41	,	,	PUNCT
ejpam-310	32	42	0	0	NUM
ejpam-310	32	43	)	)	PUNCT
ejpam-310	32	44	=	=	SYM
ejpam-310	32	45	q(xπ	q(xπ	X
ejpam-310	32	46	)	)	PUNCT
ejpam-310	32	47	(	(	PUNCT
ejpam-310	32	48	1.2	1.2	NUM
ejpam-310	32	49	)	)	PUNCT
ejpam-310	32	50	finally	finally	ADV
ejpam-310	32	51	,	,	PUNCT
ejpam-310	32	52	three	three	NUM
ejpam-310	32	53	pde	pde	NOUN
ejpam-310	32	54	problems	problem	NOUN
ejpam-310	32	55	are	be	AUX
ejpam-310	32	56	solved	solve	VERB
ejpam-310	32	57	by	by	ADP
ejpam-310	32	58	the	the	DET
ejpam-310	32	59	present	present	ADJ
ejpam-310	32	60	method	method	NOUN
ejpam-310	32	61	,	,	PUNCT
ejpam-310	32	62	and	and	CCONJ
ejpam-310	32	63	the	the	DET
ejpam-310	32	64	calculated	calculate	VERB
ejpam-310	32	65	results	result	NOUN
ejpam-310	32	66	are	be	AUX
ejpam-310	32	67	compared	compare	VERB
ejpam-310	32	68	very	very	ADV
ejpam-310	32	69	well	well	ADV
ejpam-310	32	70	with	with	ADP
ejpam-310	32	71	those	those	PRON
ejpam-310	32	72	obtained	obtain	VERB
ejpam-310	32	73	by	by	ADP
ejpam-310	32	74	other	other	ADJ
ejpam-310	32	75	analytical	analytical	ADJ
ejpam-310	32	76	or	or	CCONJ
ejpam-310	32	77	approximate	approximate	ADJ
ejpam-310	32	78	methods	method	NOUN
ejpam-310	32	79	.	.	PUNCT
ejpam-310	33	1	m.	m.	NOUN
ejpam-310	33	2	kurulay	kurulay	PROPN
ejpam-310	33	3	and	and	CCONJ
ejpam-310	33	4	m.	m.	PROPN
ejpam-310	33	5	bayram	bayram	PROPN
ejpam-310	33	6	/	/	SYM
ejpam-310	33	7	eur	eur	PROPN
ejpam-310	33	8	.	.	PUNCT
ejpam-310	34	1	j.	j.	PROPN
ejpam-310	34	2	pure	pure	PROPN
ejpam-310	34	3	appl	appl	PROPN
ejpam-310	34	4	.	.	PROPN
ejpam-310	34	5	math	math	PROPN
ejpam-310	34	6	,	,	PUNCT
ejpam-310	34	7	2	2	NUM
ejpam-310	34	8	(	(	PUNCT
ejpam-310	34	9	2009	2009	NUM
ejpam-310	34	10	)	)	PUNCT
ejpam-310	34	11	,	,	PUNCT
ejpam-310	34	12	(	(	PUNCT
ejpam-310	34	13	268	268	NUM
ejpam-310	34	14	-	-	SYM
ejpam-310	34	15	277	277	NUM
ejpam-310	34	16	)	)	PUNCT
ejpam-310	34	17	270	270	NUM
ejpam-310	34	18	2	2	NUM
ejpam-310	34	19	.	.	PUNCT
ejpam-310	34	20	preliminary	preliminary	ADJ
ejpam-310	34	21	knowledge	knowledge	NOUN
ejpam-310	34	22	the	the	DET
ejpam-310	34	23	basic	basic	ADJ
ejpam-310	34	24	theory	theory	NOUN
ejpam-310	34	25	of	of	ADP
ejpam-310	34	26	power	power	NOUN
ejpam-310	34	27	series	series	NOUN
ejpam-310	34	28	is	be	AUX
ejpam-310	34	29	stated	state	VERB
ejpam-310	34	30	below	below	ADV
ejpam-310	34	31	.	.	PUNCT
ejpam-310	35	1	in	in	ADP
ejpam-310	35	2	what	what	PRON
ejpam-310	35	3	follows	follow	VERB
ejpam-310	35	4	,	,	PUNCT
ejpam-310	35	5	we	we	PRON
ejpam-310	35	6	assume	assume	VERB
ejpam-310	35	7	that	that	SCONJ
ejpam-310	35	8	for	for	ADP
ejpam-310	35	9	each	each	DET
ejpam-310	35	10	function	function	NOUN
ejpam-310	35	11	involved	involve	VERB
ejpam-310	35	12	in	in	ADP
ejpam-310	35	13	our	our	PRON
ejpam-310	35	14	study	study	NOUN
ejpam-310	35	15	,	,	PUNCT
ejpam-310	35	16	all	all	PRON
ejpam-310	35	17	its	its	PRON
ejpam-310	35	18	derivatives	derivative	NOUN
ejpam-310	35	19	are	be	AUX
ejpam-310	35	20	existent	existent	ADJ
ejpam-310	35	21	and	and	CCONJ
ejpam-310	35	22	continuous	continuous	ADJ
ejpam-310	35	23	in	in	ADP
ejpam-310	35	24	the	the	DET
ejpam-310	35	25	region	region	NOUN
ejpam-310	35	26	of	of	ADP
ejpam-310	35	27	interest	interest	NOUN
ejpam-310	35	28	.	.	PUNCT
ejpam-310	36	1	the	the	DET
ejpam-310	36	2	taylor	taylor	PROPN
ejpam-310	36	3	series	series	PROPN
ejpam-310	36	4	may	may	AUX
ejpam-310	36	5	also	also	ADV
ejpam-310	36	6	be	be	AUX
ejpam-310	36	7	generalized	generalize	VERB
ejpam-310	36	8	to	to	ADP
ejpam-310	36	9	functions	function	NOUN
ejpam-310	36	10	of	of	ADP
ejpam-310	36	11	more	more	ADJ
ejpam-310	36	12	than	than	ADP
ejpam-310	36	13	one	one	NUM
ejpam-310	36	14	variable	variable	NOUN
ejpam-310	36	15	with	with	ADP
ejpam-310	36	16	t	t	PROPN
ejpam-310	36	17	(	(	PUNCT
ejpam-310	36	18	x1	x1	PROPN
ejpam-310	36	19	,	,	PUNCT
ejpam-310	36	20	...	...	PUNCT
ejpam-310	36	21	,	,	PUNCT
ejpam-310	36	22	xd	xd	ADP
ejpam-310	36	23	)	)	PUNCT
ejpam-310	37	1	=	=	SYM
ejpam-310	38	1	∞	∞	NUM
ejpam-310	38	2	∑	∑	PROPN
ejpam-310	38	3	n1=0	n1=0	PROPN
ejpam-310	38	4	...	...	PUNCT
ejpam-310	39	1	∞	∞	NUM
ejpam-310	39	2	∑	∑	PROPN
ejpam-310	39	3	nd=0	nd=0	PROPN
ejpam-310	39	4	∂	∂	NUM
ejpam-310	39	5	n	n	PRON
ejpam-310	39	6	∂	∂	NUM
ejpam-310	39	7	x	x	NOUN
ejpam-310	39	8	n1	n1	PROPN
ejpam-310	39	9	d	d	NOUN
ejpam-310	39	10	...	...	PUNCT
ejpam-310	39	11	∂	∂	NUM
ejpam-310	39	12	nd	nd	NOUN
ejpam-310	39	13	∂	∂	NOUN
ejpam-310	39	14	x	x	INTJ
ejpam-310	39	15	nd	nd	ADP
ejpam-310	39	16	d	d	PROPN
ejpam-310	39	17	f	f	PROPN
ejpam-310	39	18	(	(	PUNCT
ejpam-310	39	19	a1	a1	PROPN
ejpam-310	39	20	,	,	PUNCT
ejpam-310	39	21	...	...	PUNCT
ejpam-310	39	22	,	,	PUNCT
ejpam-310	39	23	ad	ad	NOUN
ejpam-310	39	24	)	)	PUNCT
ejpam-310	39	25	n1,	n1,	NOUN
ejpam-310	39	26	...	...	NOUN
ejpam-310	39	27	,nd	,nd	PUNCT
ejpam-310	39	28	(	(	PUNCT
ejpam-310	39	29	x1−	x1−	PROPN
ejpam-310	39	30	a1	a1	PROPN
ejpam-310	39	31	)	)	PUNCT
ejpam-310	39	32	n1	n1	NOUN
ejpam-310	39	33	...	...	PUNCT
ejpam-310	39	34	(	(	PUNCT
ejpam-310	39	35	xd	xd	INTJ
ejpam-310	39	36	−	−	NOUN
ejpam-310	40	1	ad	ad	NOUN
ejpam-310	40	2	)	)	PUNCT
ejpam-310	40	3	nd	nd	ADP
ejpam-310	40	4	(	(	PUNCT
ejpam-310	40	5	2.1	2.1	NUM
ejpam-310	40	6	)	)	PUNCT
ejpam-310	40	7	for	for	ADP
ejpam-310	40	8	example	example	NOUN
ejpam-310	40	9	,	,	PUNCT
ejpam-310	40	10	for	for	ADP
ejpam-310	40	11	a	a	DET
ejpam-310	40	12	function	function	NOUN
ejpam-310	40	13	that	that	PRON
ejpam-310	40	14	depends	depend	VERB
ejpam-310	40	15	on	on	ADP
ejpam-310	40	16	two	two	NUM
ejpam-310	40	17	variables	variable	NOUN
ejpam-310	40	18	,	,	PUNCT
ejpam-310	40	19	x	x	PUNCT
ejpam-310	40	20	and	and	CCONJ
ejpam-310	40	21	y	y	PROPN
ejpam-310	40	22	,	,	PUNCT
ejpam-310	40	23	the	the	DET
ejpam-310	40	24	taylor	taylor	PROPN
ejpam-310	40	25	series	series	NOUN
ejpam-310	40	26	to	to	ADP
ejpam-310	40	27	second	second	ADJ
ejpam-310	40	28	order	order	NOUN
ejpam-310	40	29	about	about	ADP
ejpam-310	40	30	the	the	DET
ejpam-310	40	31	point	point	NOUN
ejpam-310	40	32	(	(	PUNCT
ejpam-310	40	33	a	a	DET
ejpam-310	40	34	,	,	PUNCT
ejpam-310	40	35	b	b	NOUN
ejpam-310	40	36	)	)	PUNCT
ejpam-310	40	37	is	be	AUX
ejpam-310	40	38	:	:	PUNCT
ejpam-310	40	39	f	f	X
ejpam-310	40	40	(	(	PUNCT
ejpam-310	40	41	x	x	INTJ
ejpam-310	40	42	,	,	PUNCT
ejpam-310	40	43	y	y	PROPN
ejpam-310	40	44	)	)	PUNCT
ejpam-310	41	1	=	=	SYM
ejpam-310	41	2	f	f	X
ejpam-310	41	3	(	(	PUNCT
ejpam-310	41	4	a	a	DET
ejpam-310	41	5	,	,	PUNCT
ejpam-310	41	6	b	b	NOUN
ejpam-310	41	7	)	)	PUNCT
ejpam-310	41	8	+	+	CCONJ
ejpam-310	41	9	fx(a	fx(a	NOUN
ejpam-310	41	10	,	,	PUNCT
ejpam-310	41	11	b)(x	b)(x	NOUN
ejpam-310	41	12	−	−	PROPN
ejpam-310	41	13	a	a	X
ejpam-310	41	14	)	)	PUNCT
ejpam-310	41	15	+	+	NUM
ejpam-310	41	16	f	f	PROPN
ejpam-310	41	17	y(a	y(a	PROPN
ejpam-310	41	18	,	,	PUNCT
ejpam-310	41	19	b)(y	b)(y	PUNCT
ejpam-310	41	20	−	−	PROPN
ejpam-310	41	21	b	b	X
ejpam-310	41	22	)	)	PUNCT
ejpam-310	41	23	=	=	SYM
ejpam-310	41	24	1	1	NUM
ejpam-310	41	25	2	2	NUM
ejpam-310	41	26	!	!	PUNCT
ejpam-310	41	27	�	�	PROPN
ejpam-310	41	28	fx	fx	PROPN
ejpam-310	41	29	x(a	x(a	NOUN
ejpam-310	41	30	,	,	PUNCT
ejpam-310	41	31	b)(x	b)(x	NOUN
ejpam-310	41	32	−	−	PROPN
ejpam-310	41	33	a)2	a)2	NOUN
ejpam-310	41	34	+	+	CCONJ
ejpam-310	41	35	2	2	NUM
ejpam-310	41	36	fx	fx	NOUN
ejpam-310	41	37	y(a	y(a	NOUN
ejpam-310	41	38	,	,	PUNCT
ejpam-310	41	39	b)(x	b)(x	NOUN
ejpam-310	41	40	−	−	PROPN
ejpam-310	41	41	a)(y	a)(y	PROPN
ejpam-310	41	42	−	−	PROPN
ejpam-310	41	43	b	b	NOUN
ejpam-310	41	44	)	)	PUNCT
ejpam-310	42	1	+	+	CCONJ
ejpam-310	42	2	f	f	PROPN
ejpam-310	42	3	y	y	PROPN
ejpam-310	42	4	y(a	y(a	PROPN
ejpam-310	42	5	,	,	PUNCT
ejpam-310	42	6	b)(y	b)(y	PUNCT
ejpam-310	42	7	−	−	NUM
ejpam-310	42	8	b)2	b)2	PROPN
ejpam-310	42	9	�	�	PROPN
ejpam-310	42	10	+	+	CCONJ
ejpam-310	42	11	.	.	PUNCT
ejpam-310	42	12	.	.	PUNCT
ejpam-310	42	13	.	.	PUNCT
ejpam-310	43	1	(	(	PUNCT
ejpam-310	43	2	2.2	2.2	NUM
ejpam-310	43	3	)	)	PUNCT
ejpam-310	43	4	where	where	SCONJ
ejpam-310	43	5	the	the	DET
ejpam-310	43	6	subscripts	subscript	NOUN
ejpam-310	43	7	denote	denote	VERB
ejpam-310	43	8	the	the	DET
ejpam-310	43	9	respective	respective	ADJ
ejpam-310	43	10	partial	partial	ADJ
ejpam-310	43	11	derivatives	derivative	NOUN
ejpam-310	43	12	.	.	PUNCT
ejpam-310	44	1	definition	definition	NOUN
ejpam-310	44	2	1	1	NUM
ejpam-310	44	3	.	.	PUNCT
ejpam-310	45	1	the	the	DET
ejpam-310	45	2	coefficient	coefficient	NOUN
ejpam-310	45	3	of	of	ADP
ejpam-310	45	4	variables	variable	NOUN
ejpam-310	45	5	of	of	ADP
ejpam-310	45	6	a	a	DET
ejpam-310	45	7	function	function	NOUN
ejpam-310	45	8	w(x	w(x	PROPN
ejpam-310	45	9	,	,	PUNCT
ejpam-310	45	10	y	y	PROPN
ejpam-310	45	11	)	)	PUNCT
ejpam-310	45	12	is	be	AUX
ejpam-310	45	13	defined	define	VERB
ejpam-310	45	14	as	as	ADP
ejpam-310	45	15	w	w	PROPN
ejpam-310	45	16	(	(	PUNCT
ejpam-310	45	17	k	k	NOUN
ejpam-310	45	18	,	,	PUNCT
ejpam-310	45	19	h	h	NOUN
ejpam-310	45	20	)	)	PUNCT
ejpam-310	45	21	=	=	SYM
ejpam-310	46	1	1	1	NUM
ejpam-310	46	2	k!h	k!h	PROPN
ejpam-310	46	3	!	!	PUNCT
ejpam-310	46	4	�	�	PROPN
ejpam-310	46	5	∂	∂	NUM
ejpam-310	46	6	k+hw(x	k+hw(x	PROPN
ejpam-310	46	7	,	,	PUNCT
ejpam-310	46	8	y	y	PROPN
ejpam-310	46	9	)	)	PUNCT
ejpam-310	46	10	∂	∂	NUM
ejpam-310	46	11	x	x	SYM
ejpam-310	46	12	k∂	k∂	PROPN
ejpam-310	46	13	yh	yh	PROPN
ejpam-310	46	14	�	�	PROPN
ejpam-310	46	15	x=0	x=0	NUM
ejpam-310	46	16	y=0	y=0	NOUN
ejpam-310	46	17	,	,	PUNCT
ejpam-310	46	18	(	(	PUNCT
ejpam-310	46	19	2.3	2.3	NUM
ejpam-310	46	20	)	)	PUNCT
ejpam-310	46	21	where	where	SCONJ
ejpam-310	46	22	it	it	PRON
ejpam-310	46	23	is	be	AUX
ejpam-310	46	24	be	be	AUX
ejpam-310	46	25	noted	note	VERB
ejpam-310	46	26	that	that	SCONJ
ejpam-310	46	27	upper	upper	ADJ
ejpam-310	46	28	case	case	NOUN
ejpam-310	46	29	symbol	symbol	NOUN
ejpam-310	46	30	w	w	PROPN
ejpam-310	46	31	(	(	PUNCT
ejpam-310	46	32	k	k	NOUN
ejpam-310	46	33	,	,	PUNCT
ejpam-310	46	34	h	h	NOUN
ejpam-310	46	35	)	)	PUNCT
ejpam-310	46	36	is	be	AUX
ejpam-310	46	37	used	use	VERB
ejpam-310	46	38	to	to	PART
ejpam-310	46	39	denote	denote	VERB
ejpam-310	46	40	the	the	DET
ejpam-310	46	41	coefficients	coefficient	NOUN
ejpam-310	46	42	of	of	ADP
ejpam-310	46	43	variables	variable	NOUN
ejpam-310	46	44	in	in	ADP
ejpam-310	46	45	(	(	PUNCT
ejpam-310	46	46	2.2	2.2	NUM
ejpam-310	46	47	)	)	PUNCT
ejpam-310	46	48	which	which	PRON
ejpam-310	46	49	represented	represent	VERB
ejpam-310	46	50	by	by	ADP
ejpam-310	46	51	a	a	DET
ejpam-310	46	52	corresponding	correspond	VERB
ejpam-310	46	53	lower	low	ADJ
ejpam-310	46	54	case	case	NOUN
ejpam-310	46	55	symbol	symbol	NOUN
ejpam-310	46	56	w(x	w(x	PROPN
ejpam-310	46	57	,	,	PUNCT
ejpam-310	46	58	y	y	PROPN
ejpam-310	46	59	)	)	PUNCT
ejpam-310	46	60	.	.	PUNCT
ejpam-310	47	1	definition	definition	NOUN
ejpam-310	47	2	2	2	NUM
ejpam-310	47	3	.	.	PUNCT
ejpam-310	48	1	the	the	DET
ejpam-310	48	2	inverse	inverse	NOUN
ejpam-310	48	3	of	of	ADP
ejpam-310	48	4	w	w	PROPN
ejpam-310	48	5	(	(	PUNCT
ejpam-310	48	6	k	k	NOUN
ejpam-310	48	7	,	,	PUNCT
ejpam-310	48	8	h	h	NOUN
ejpam-310	48	9	)	)	PUNCT
ejpam-310	48	10	is	be	AUX
ejpam-310	48	11	defined	define	VERB
ejpam-310	48	12	as	as	ADP
ejpam-310	48	13	w(x	w(x	PROPN
ejpam-310	48	14	,	,	PUNCT
ejpam-310	48	15	y	y	NOUN
ejpam-310	48	16	)	)	PUNCT
ejpam-310	49	1	=	=	SYM
ejpam-310	49	2	∞	∞	NUM
ejpam-310	49	3	∑	∑	PUNCT
ejpam-310	49	4	k=0	k=0	PROPN
ejpam-310	49	5	∞	∞	PROPN
ejpam-310	49	6	∑	∑	PROPN
ejpam-310	49	7	h=0	h=0	PROPN
ejpam-310	49	8	w	w	PROPN
ejpam-310	49	9	(	(	PUNCT
ejpam-310	49	10	k	k	NOUN
ejpam-310	49	11	,	,	PUNCT
ejpam-310	49	12	h)x	h)x	X
ejpam-310	49	13	k	k	PROPN
ejpam-310	50	1	yh	yh	PROPN
ejpam-310	50	2	.	.	PROPN
ejpam-310	50	3	(	(	PUNCT
ejpam-310	50	4	2.4	2.4	NUM
ejpam-310	50	5	)	)	PUNCT
ejpam-310	50	6	from	from	ADP
ejpam-310	50	7	equations	equation	NOUN
ejpam-310	50	8	(	(	PUNCT
ejpam-310	50	9	2.3	2.3	NUM
ejpam-310	50	10	)	)	PUNCT
ejpam-310	50	11	and	and	CCONJ
ejpam-310	50	12	(	(	PUNCT
ejpam-310	50	13	2.4	2.4	NUM
ejpam-310	50	14	)	)	PUNCT
ejpam-310	50	15	,	,	PUNCT
ejpam-310	50	16	we	we	PRON
ejpam-310	50	17	obtain	obtain	VERB
ejpam-310	50	18	m.	m.	NOUN
ejpam-310	50	19	kurulay	kurulay	NOUN
ejpam-310	50	20	and	and	CCONJ
ejpam-310	50	21	m.	m.	PROPN
ejpam-310	50	22	bayram	bayram	PROPN
ejpam-310	50	23	/	/	SYM
ejpam-310	50	24	eur	eur	PROPN
ejpam-310	50	25	.	.	PUNCT
ejpam-310	51	1	j.	j.	PROPN
ejpam-310	51	2	pure	pure	PROPN
ejpam-310	51	3	appl	appl	PROPN
ejpam-310	51	4	.	.	PROPN
ejpam-310	51	5	math	math	PROPN
ejpam-310	51	6	,	,	PUNCT
ejpam-310	51	7	2	2	NUM
ejpam-310	51	8	(	(	PUNCT
ejpam-310	51	9	2009	2009	NUM
ejpam-310	51	10	)	)	PUNCT
ejpam-310	51	11	,	,	PUNCT
ejpam-310	51	12	(	(	PUNCT
ejpam-310	51	13	268	268	NUM
ejpam-310	51	14	-	-	SYM
ejpam-310	51	15	277	277	NUM
ejpam-310	51	16	)	)	PUNCT
ejpam-310	51	17	271	271	NUM
ejpam-310	51	18	w(x	w(x	PROPN
ejpam-310	51	19	,	,	PUNCT
ejpam-310	51	20	y	y	NOUN
ejpam-310	51	21	)	)	PUNCT
ejpam-310	51	22	=	=	SYM
ejpam-310	52	1	∞	∞	NUM
ejpam-310	52	2	∑	∑	PUNCT
ejpam-310	52	3	k=0	k=0	PROPN
ejpam-310	52	4	∞	∞	PROPN
ejpam-310	52	5	∑	∑	PUNCT
ejpam-310	52	6	h=0	h=0	PROPN
ejpam-310	52	7	x	x	PUNCT
ejpam-310	53	1	k	k	NOUN
ejpam-310	53	2	yh	yh	PROPN
ejpam-310	53	3	k!h	k!h	PROPN
ejpam-310	53	4	!	!	PUNCT
ejpam-310	53	5	�	�	PROPN
ejpam-310	53	6	∂	∂	NUM
ejpam-310	53	7	k+hw(x	k+hw(x	PROPN
ejpam-310	53	8	,	,	PUNCT
ejpam-310	53	9	y	y	PROPN
ejpam-310	53	10	)	)	PUNCT
ejpam-310	53	11	∂	∂	NUM
ejpam-310	53	12	x	x	SYM
ejpam-310	53	13	k∂	k∂	PROPN
ejpam-310	53	14	yh	yh	PROPN
ejpam-310	53	15	�	�	PROPN
ejpam-310	53	16	x=0	x=0	PUNCT
ejpam-310	53	17	y=0	y=0	NOUN
ejpam-310	53	18	(	(	PUNCT
ejpam-310	53	19	2.5	2.5	NUM
ejpam-310	53	20	)	)	PUNCT
ejpam-310	53	21	theorem	theorem	NOUN
ejpam-310	53	22	1	1	NUM
ejpam-310	53	23	.	.	PUNCT
ejpam-310	54	1	if	if	SCONJ
ejpam-310	54	2	w(x	w(x	NUM
ejpam-310	54	3	,	,	PUNCT
ejpam-310	54	4	y	y	PROPN
ejpam-310	54	5	)	)	PUNCT
ejpam-310	55	1	=	=	SYM
ejpam-310	55	2	u(x	u(x	NOUN
ejpam-310	55	3	,	,	PUNCT
ejpam-310	55	4	y)±	y)±	ADJ
ejpam-310	55	5	v(x	v(x	NOUN
ejpam-310	55	6	,	,	PUNCT
ejpam-310	55	7	y	y	PROPN
ejpam-310	55	8	)	)	PUNCT
ejpam-310	55	9	,	,	PUNCT
ejpam-310	55	10	then	then	ADV
ejpam-310	55	11	w	w	PROPN
ejpam-310	55	12	(	(	PUNCT
ejpam-310	55	13	k	k	NOUN
ejpam-310	55	14	,	,	PUNCT
ejpam-310	55	15	h	h	NOUN
ejpam-310	55	16	)	)	PUNCT
ejpam-310	55	17	=	=	SYM
ejpam-310	55	18	u(k	u(k	PROPN
ejpam-310	55	19	,	,	PUNCT
ejpam-310	55	20	h)±	h)±	PROPN
ejpam-310	55	21	v	v	NOUN
ejpam-310	55	22	(	(	PUNCT
ejpam-310	55	23	k	k	NOUN
ejpam-310	55	24	,	,	PUNCT
ejpam-310	55	25	h	h	NOUN
ejpam-310	55	26	)	)	PUNCT
ejpam-310	55	27	.	.	PUNCT
ejpam-310	56	1	proof	proof	NOUN
ejpam-310	56	2	.	.	PUNCT
ejpam-310	57	1	by	by	ADP
ejpam-310	57	2	definition	definition	NOUN
ejpam-310	57	3	1	1	NUM
ejpam-310	57	4	we	we	PRON
ejpam-310	57	5	have	have	VERB
ejpam-310	57	6	u(k	u(k	PROPN
ejpam-310	57	7	,	,	PUNCT
ejpam-310	57	8	h	h	NOUN
ejpam-310	57	9	)	)	PUNCT
ejpam-310	57	10	=	=	SYM
ejpam-310	58	1	1	1	NUM
ejpam-310	58	2	k!h	k!h	PROPN
ejpam-310	58	3	!	!	PUNCT
ejpam-310	58	4	�	�	PROPN
ejpam-310	58	5	∂	∂	NUM
ejpam-310	58	6	k+h	k+h	X
ejpam-310	58	7	∂	∂	NUM
ejpam-310	58	8	x	x	SYM
ejpam-310	58	9	k∂	k∂	PROPN
ejpam-310	58	10	yh	yh	PROPN
ejpam-310	58	11	u(x	u(x	PROPN
ejpam-310	58	12	,	,	PUNCT
ejpam-310	58	13	y	y	X
ejpam-310	58	14	)	)	PUNCT
ejpam-310	58	15	�	�	PROPN
ejpam-310	58	16	x=0	x=0	NUM
ejpam-310	58	17	y=0	y=0	NOUN
ejpam-310	58	18	(	(	PUNCT
ejpam-310	58	19	2.6	2.6	NUM
ejpam-310	58	20	)	)	PUNCT
ejpam-310	58	21	v	v	NOUN
ejpam-310	58	22	(	(	PUNCT
ejpam-310	58	23	k	k	NOUN
ejpam-310	58	24	,	,	PUNCT
ejpam-310	58	25	h	h	NOUN
ejpam-310	58	26	)	)	PUNCT
ejpam-310	58	27	=	=	SYM
ejpam-310	58	28	1	1	NUM
ejpam-310	58	29	k!h	k!h	PROPN
ejpam-310	58	30	!	!	PUNCT
ejpam-310	58	31	�	�	PROPN
ejpam-310	58	32	∂	∂	NUM
ejpam-310	58	33	k+h	k+h	X
ejpam-310	58	34	∂	∂	NUM
ejpam-310	58	35	x	x	SYM
ejpam-310	58	36	k∂	k∂	PROPN
ejpam-310	58	37	yh	yh	NOUN
ejpam-310	58	38	v(x	v(x	PROPN
ejpam-310	58	39	,	,	PUNCT
ejpam-310	58	40	y	y	PROPN
ejpam-310	58	41	)	)	PUNCT
ejpam-310	58	42	�	�	PROPN
ejpam-310	58	43	x=0	x=0	NUM
ejpam-310	58	44	y=0	y=0	X
ejpam-310	58	45	(	(	PUNCT
ejpam-310	58	46	2.7	2.7	NUM
ejpam-310	58	47	)	)	PUNCT
ejpam-310	58	48	w	w	NOUN
ejpam-310	59	1	(	(	PUNCT
ejpam-310	59	2	k	k	NOUN
ejpam-310	59	3	,	,	PUNCT
ejpam-310	59	4	h	h	NOUN
ejpam-310	59	5	)	)	PUNCT
ejpam-310	59	6	=	=	SYM
ejpam-310	60	1	1	1	NUM
ejpam-310	60	2	k!h	k!h	PROPN
ejpam-310	60	3	!	!	PUNCT
ejpam-310	60	4	�	�	PROPN
ejpam-310	60	5	∂	∂	NUM
ejpam-310	60	6	k+h	k+h	X
ejpam-310	60	7	∂	∂	NUM
ejpam-310	60	8	x	x	SYM
ejpam-310	60	9	k∂	k∂	PROPN
ejpam-310	60	10	yh	yh	PROPN
ejpam-310	60	11	u(x	u(x	PROPN
ejpam-310	60	12	,	,	PUNCT
ejpam-310	60	13	y)±	y)±	ADJ
ejpam-310	60	14	v(x	v(x	NOUN
ejpam-310	60	15	,	,	PUNCT
ejpam-310	60	16	y	y	PROPN
ejpam-310	60	17	)	)	PUNCT
ejpam-310	60	18	�	�	PROPN
ejpam-310	60	19	x=0	x=0	NUM
ejpam-310	60	20	y=0	y=0	X
ejpam-310	60	21	(	(	PUNCT
ejpam-310	60	22	2.8	2.8	NUM
ejpam-310	60	23	)	)	PUNCT
ejpam-310	60	24	using	use	VERB
ejpam-310	60	25	equations	equation	NOUN
ejpam-310	60	26	(	(	PUNCT
ejpam-310	60	27	2.6)-(2.8	2.6)-(2.8	NUM
ejpam-310	60	28	)	)	PUNCT
ejpam-310	60	29	,	,	PUNCT
ejpam-310	60	30	we	we	PRON
ejpam-310	60	31	have	have	VERB
ejpam-310	60	32	w	w	PROPN
ejpam-310	60	33	(	(	PUNCT
ejpam-310	60	34	k	k	NOUN
ejpam-310	60	35	,	,	PUNCT
ejpam-310	60	36	h	h	NOUN
ejpam-310	60	37	)	)	PUNCT
ejpam-310	60	38	=	=	SYM
ejpam-310	60	39	u(k	u(k	PROPN
ejpam-310	60	40	,	,	PUNCT
ejpam-310	60	41	h)±	h)±	PROPN
ejpam-310	60	42	v	v	NOUN
ejpam-310	60	43	(	(	PUNCT
ejpam-310	60	44	k	k	NOUN
ejpam-310	60	45	,	,	PUNCT
ejpam-310	60	46	h	h	NOUN
ejpam-310	60	47	)	)	PUNCT
ejpam-310	60	48	(	(	PUNCT
ejpam-310	60	49	2.9	2.9	NUM
ejpam-310	60	50	)	)	PUNCT
ejpam-310	60	51	theorem	theorem	NOUN
ejpam-310	60	52	2	2	NUM
ejpam-310	60	53	.	.	PUNCT
ejpam-310	61	1	if	if	SCONJ
ejpam-310	61	2	w(x	w(x	NUM
ejpam-310	61	3	,	,	PUNCT
ejpam-310	61	4	y	y	PROPN
ejpam-310	61	5	)	)	PUNCT
ejpam-310	61	6	=	=	NOUN
ejpam-310	61	7	λu(x	λu(x	NOUN
ejpam-310	61	8	,	,	PUNCT
ejpam-310	61	9	y	y	PROPN
ejpam-310	61	10	)	)	PUNCT
ejpam-310	61	11	,	,	PUNCT
ejpam-310	61	12	then	then	ADV
ejpam-310	61	13	w	w	PROPN
ejpam-310	61	14	(	(	PUNCT
ejpam-310	61	15	k	k	NOUN
ejpam-310	61	16	,	,	PUNCT
ejpam-310	61	17	h	h	NOUN
ejpam-310	61	18	)	)	PUNCT
ejpam-310	61	19	=	=	PUNCT
ejpam-310	62	1	λu(k	λu(k	ADJ
ejpam-310	62	2	,	,	PUNCT
ejpam-310	62	3	h	h	NOUN
ejpam-310	62	4	)	)	PUNCT
ejpam-310	62	5	.	.	PUNCT
ejpam-310	63	1	proof	proof	NOUN
ejpam-310	63	2	.	.	PUNCT
ejpam-310	64	1	by	by	ADP
ejpam-310	64	2	definition	definition	NOUN
ejpam-310	64	3	1	1	NUM
ejpam-310	64	4	we	we	PRON
ejpam-310	64	5	have	have	VERB
ejpam-310	64	6	u(k	u(k	PROPN
ejpam-310	64	7	,	,	PUNCT
ejpam-310	64	8	h	h	NOUN
ejpam-310	64	9	)	)	PUNCT
ejpam-310	64	10	=	=	SYM
ejpam-310	65	1	1	1	NUM
ejpam-310	65	2	k!h	k!h	PROPN
ejpam-310	65	3	!	!	PUNCT
ejpam-310	65	4	�	�	PROPN
ejpam-310	65	5	∂	∂	NUM
ejpam-310	65	6	k+h	k+h	X
ejpam-310	65	7	∂	∂	NUM
ejpam-310	65	8	x	x	SYM
ejpam-310	65	9	k∂	k∂	PROPN
ejpam-310	65	10	yh	yh	PROPN
ejpam-310	65	11	u(x	u(x	PROPN
ejpam-310	65	12	,	,	PUNCT
ejpam-310	65	13	y	y	X
ejpam-310	65	14	)	)	PUNCT
ejpam-310	65	15	�	�	PROPN
ejpam-310	65	16	x=0	x=0	NUM
ejpam-310	65	17	y=0	y=0	NOUN
ejpam-310	65	18	(	(	PUNCT
ejpam-310	65	19	2.10	2.10	NUM
ejpam-310	65	20	)	)	PUNCT
ejpam-310	65	21	w	w	NOUN
ejpam-310	65	22	(	(	PUNCT
ejpam-310	65	23	k	k	NOUN
ejpam-310	65	24	,	,	PUNCT
ejpam-310	65	25	h	h	NOUN
ejpam-310	65	26	)	)	PUNCT
ejpam-310	65	27	=	=	SYM
ejpam-310	65	28	1	1	NUM
ejpam-310	65	29	k!h	k!h	PROPN
ejpam-310	65	30	!	!	PUNCT
ejpam-310	65	31	�	�	PROPN
ejpam-310	65	32	∂	∂	NUM
ejpam-310	65	33	k+h	k+h	X
ejpam-310	65	34	∂	∂	NUM
ejpam-310	65	35	x	x	SYM
ejpam-310	65	36	k∂	k∂	PROPN
ejpam-310	65	37	yh	yh	PROPN
ejpam-310	65	38	λw(x	λw(x	X
ejpam-310	65	39	,	,	PUNCT
ejpam-310	65	40	y	y	PROPN
ejpam-310	65	41	)	)	PUNCT
ejpam-310	65	42	�	�	PROPN
ejpam-310	65	43	x=0	x=0	NUM
ejpam-310	65	44	y=0	y=0	NOUN
ejpam-310	65	45	(	(	PUNCT
ejpam-310	65	46	2.11	2.11	NUM
ejpam-310	65	47	)	)	PUNCT
ejpam-310	65	48	using	use	VERB
ejpam-310	65	49	equations	equation	NOUN
ejpam-310	65	50	(	(	PUNCT
ejpam-310	65	51	2.10)-(2.11	2.10)-(2.11	NUM
ejpam-310	65	52	)	)	PUNCT
ejpam-310	65	53	,	,	PUNCT
ejpam-310	65	54	we	we	PRON
ejpam-310	65	55	have	have	VERB
ejpam-310	65	56	w	w	PROPN
ejpam-310	65	57	(	(	PUNCT
ejpam-310	65	58	k	k	NOUN
ejpam-310	65	59	,	,	PUNCT
ejpam-310	65	60	h	h	NOUN
ejpam-310	65	61	)	)	PUNCT
ejpam-310	65	62	=	=	PUNCT
ejpam-310	66	1	λu(k	λu(k	ADJ
ejpam-310	66	2	,	,	PUNCT
ejpam-310	66	3	h	h	NOUN
ejpam-310	66	4	)	)	PUNCT
ejpam-310	66	5	.	.	PUNCT
ejpam-310	67	1	(	(	PUNCT
ejpam-310	67	2	2.12	2.12	NUM
ejpam-310	67	3	)	)	PUNCT
ejpam-310	67	4	m.	m.	NOUN
ejpam-310	67	5	kurulay	kurulay	NOUN
ejpam-310	67	6	and	and	CCONJ
ejpam-310	67	7	m.	m.	PROPN
ejpam-310	67	8	bayram	bayram	PROPN
ejpam-310	67	9	/	/	SYM
ejpam-310	67	10	eur	eur	PROPN
ejpam-310	67	11	.	.	PUNCT
ejpam-310	68	1	j.	j.	PROPN
ejpam-310	68	2	pure	pure	PROPN
ejpam-310	68	3	appl	appl	PROPN
ejpam-310	68	4	.	.	PROPN
ejpam-310	68	5	math	math	PROPN
ejpam-310	68	6	,	,	PUNCT
ejpam-310	68	7	2	2	NUM
ejpam-310	68	8	(	(	PUNCT
ejpam-310	68	9	2009	2009	NUM
ejpam-310	68	10	)	)	PUNCT
ejpam-310	68	11	,	,	PUNCT
ejpam-310	68	12	(	(	PUNCT
ejpam-310	68	13	268	268	NUM
ejpam-310	68	14	-	-	SYM
ejpam-310	68	15	277	277	NUM
ejpam-310	68	16	)	)	PUNCT
ejpam-310	68	17	272	272	NUM
ejpam-310	68	18	3	3	NUM
ejpam-310	68	19	.	.	PUNCT
ejpam-310	68	20	numerical	numerical	ADJ
ejpam-310	68	21	solution	solution	NOUN
ejpam-310	68	22	of	of	ADP
ejpam-310	68	23	second	second	ADJ
ejpam-310	68	24	-	-	PUNCT
ejpam-310	68	25	order	order	NOUN
ejpam-310	68	26	partial	partial	ADJ
ejpam-310	68	27	differential	differential	NOUN
ejpam-310	68	28	equations	equation	NOUN
ejpam-310	68	29	this	this	DET
ejpam-310	68	30	section	section	NOUN
ejpam-310	68	31	aim	aim	VERB
ejpam-310	68	32	at	at	ADP
ejpam-310	68	33	describing	describe	VERB
ejpam-310	68	34	a	a	DET
ejpam-310	68	35	numerical	numerical	ADJ
ejpam-310	68	36	solution	solution	NOUN
ejpam-310	68	37	of	of	ADP
ejpam-310	68	38	partial	partial	ADJ
ejpam-310	68	39	differential	differential	ADJ
ejpam-310	68	40	equations	equation	NOUN
ejpam-310	68	41	by	by	ADP
ejpam-310	68	42	power	power	NOUN
ejpam-310	68	43	series	series	NOUN
ejpam-310	68	44	.	.	PUNCT
ejpam-310	69	1	we	we	PRON
ejpam-310	69	2	write	write	VERB
ejpam-310	69	3	power	power	NOUN
ejpam-310	69	4	series	series	NOUN
ejpam-310	69	5	in	in	ADP
ejpam-310	69	6	the	the	DET
ejpam-310	69	7	form	form	NOUN
ejpam-310	69	8	w(x	w(x	PROPN
ejpam-310	69	9	,	,	PUNCT
ejpam-310	69	10	y	y	NOUN
ejpam-310	69	11	)	)	PUNCT
ejpam-310	70	1	=	=	NOUN
ejpam-310	70	2	w	w	X
ejpam-310	70	3	(	(	PUNCT
ejpam-310	70	4	0	0	NUM
ejpam-310	70	5	,	,	PUNCT
ejpam-310	70	6	0	0	NUM
ejpam-310	70	7	)	)	PUNCT
ejpam-310	70	8	+	+	NOUN
ejpam-310	70	9	w	w	NOUN
ejpam-310	70	10	(	(	PUNCT
ejpam-310	70	11	1	1	NUM
ejpam-310	70	12	,	,	PUNCT
ejpam-310	70	13	0)x	0)x	NOUN
ejpam-310	71	1	+	+	ADJ
ejpam-310	71	2	w	w	ADJ
ejpam-310	71	3	(	(	PUNCT
ejpam-310	71	4	0	0	NUM
ejpam-310	71	5	,	,	PUNCT
ejpam-310	71	6	1)y	1)y	NUM
ejpam-310	71	7	+	+	PROPN
ejpam-310	71	8	w	w	PROPN
ejpam-310	71	9	(	(	PUNCT
ejpam-310	71	10	1	1	NUM
ejpam-310	71	11	,	,	PUNCT
ejpam-310	71	12	1)x	1)x	NUM
ejpam-310	71	13	y	y	NOUN
ejpam-310	71	14	+	+	NUM
ejpam-310	71	15	...	...	PUNCT
ejpam-310	72	1	+	+	CCONJ
ejpam-310	72	2	ax	ax	NOUN
ejpam-310	72	3	m	m	VERB
ejpam-310	72	4	yn	yn	X
ejpam-310	72	5	(	(	PUNCT
ejpam-310	72	6	3.1	3.1	NUM
ejpam-310	72	7	)	)	PUNCT
ejpam-310	72	8	where	where	SCONJ
ejpam-310	72	9	w	w	PROPN
ejpam-310	72	10	(	(	PUNCT
ejpam-310	72	11	0	0	NUM
ejpam-310	72	12	,	,	PUNCT
ejpam-310	72	13	0	0	NUM
ejpam-310	72	14	)	)	PUNCT
ejpam-310	72	15	,	,	PUNCT
ejpam-310	72	16	w	w	PROPN
ejpam-310	72	17	(	(	PUNCT
ejpam-310	72	18	1	1	NUM
ejpam-310	72	19	,	,	PUNCT
ejpam-310	72	20	0	0	NUM
ejpam-310	72	21	)	)	PUNCT
ejpam-310	72	22	,	,	PUNCT
ejpam-310	72	23	w	w	PROPN
ejpam-310	72	24	(	(	PUNCT
ejpam-310	72	25	0	0	NUM
ejpam-310	72	26	,	,	PUNCT
ejpam-310	72	27	1	1	NUM
ejpam-310	72	28	)	)	PUNCT
ejpam-310	72	29	,	,	PUNCT
ejpam-310	72	30	w	w	PROPN
ejpam-310	72	31	(	(	PUNCT
ejpam-310	72	32	1	1	NUM
ejpam-310	72	33	,	,	PUNCT
ejpam-310	72	34	1	1	NUM
ejpam-310	72	35	)	)	PUNCT
ejpam-310	72	36	...	...	PUNCT
ejpam-310	72	37	are	be	AUX
ejpam-310	72	38	known	know	VERB
ejpam-310	72	39	constants	constant	NOUN
ejpam-310	72	40	but	but	CCONJ
ejpam-310	72	41	is	be	AUX
ejpam-310	72	42	unknown	unknown	ADJ
ejpam-310	72	43	constant	constant	ADJ
ejpam-310	72	44	.	.	PUNCT
ejpam-310	73	1	substituting	substitute	VERB
ejpam-310	73	2	(	(	PUNCT
ejpam-310	73	3	3.1	3.1	NUM
ejpam-310	73	4	)	)	PUNCT
ejpam-310	73	5	into	into	ADP
ejpam-310	73	6	(	(	PUNCT
ejpam-310	73	7	1.1	1.1	NUM
ejpam-310	73	8	)	)	PUNCT
ejpam-310	73	9	,	,	PUNCT
ejpam-310	73	10	we	we	PRON
ejpam-310	73	11	can	can	AUX
ejpam-310	73	12	get	get	VERB
ejpam-310	73	13	the	the	DET
ejpam-310	73	14	following	following	NOUN
ejpam-310	73	15	:	:	PUNCT
ejpam-310	74	1	w	w	X
ejpam-310	74	2	(	(	PUNCT
ejpam-310	74	3	m	m	PROPN
ejpam-310	74	4	,	,	PUNCT
ejpam-310	74	5	n	n	CCONJ
ejpam-310	74	6	)	)	PUNCT
ejpam-310	74	7	=	=	PUNCT
ejpam-310	74	8	(	(	PUNCT
ejpam-310	74	9	µa+λ)x	µa+λ)x	NOUN
ejpam-310	74	10	m	m	NOUN
ejpam-310	74	11	yn−i	yn−i	NOUN
ejpam-310	74	12	=	=	SYM
ejpam-310	74	13	0	0	NUM
ejpam-310	74	14	(	(	PUNCT
ejpam-310	74	15	3.2	3.2	NUM
ejpam-310	74	16	)	)	PUNCT
ejpam-310	74	17	where	where	SCONJ
ejpam-310	74	18	µ	µ	NOUN
ejpam-310	74	19	and	and	CCONJ
ejpam-310	74	20	λ	λ	NOUN
ejpam-310	74	21	are	be	AUX
ejpam-310	74	22	constant	constant	ADJ
ejpam-310	74	23	and	and	CCONJ
ejpam-310	74	24	is	be	AUX
ejpam-310	74	25	order	order	NOUN
ejpam-310	74	26	of	of	ADP
ejpam-310	74	27	partial	partial	ADJ
ejpam-310	74	28	differential	differential	NOUN
ejpam-310	74	29	equation	equation	NOUN
ejpam-310	74	30	.	.	PUNCT
ejpam-310	75	1	from	from	ADP
ejpam-310	75	2	(	(	PUNCT
ejpam-310	75	3	3.2	3.2	NUM
ejpam-310	75	4	)	)	PUNCT
ejpam-310	75	5	,	,	PUNCT
ejpam-310	75	6	we	we	PRON
ejpam-310	75	7	have	have	VERB
ejpam-310	75	8	a	a	DET
ejpam-310	75	9	constant	constant	ADJ
ejpam-310	75	10	.	.	PUNCT
ejpam-310	76	1	substituting	substitute	VERB
ejpam-310	76	2	(	(	PUNCT
ejpam-310	76	3	3.2	3.2	NUM
ejpam-310	76	4	)	)	PUNCT
ejpam-310	76	5	into	into	ADP
ejpam-310	76	6	(	(	PUNCT
ejpam-310	76	7	3.1	3.1	NUM
ejpam-310	76	8	)	)	PUNCT
ejpam-310	76	9	,	,	PUNCT
ejpam-310	76	10	we	we	PRON
ejpam-310	76	11	get	get	VERB
ejpam-310	76	12	solution	solution	NOUN
ejpam-310	76	13	arbitrary	arbitrary	ADJ
ejpam-310	76	14	order	order	NOUN
ejpam-310	76	15	of	of	ADP
ejpam-310	76	16	partial	partial	ADJ
ejpam-310	76	17	differential	differential	NOUN
ejpam-310	76	18	equation	equation	NOUN
ejpam-310	76	19	.	.	PUNCT
ejpam-310	77	1	repeating	repeat	VERB
ejpam-310	77	2	this	this	DET
ejpam-310	77	3	procedure	procedure	NOUN
ejpam-310	77	4	we	we	PRON
ejpam-310	77	5	can	can	AUX
ejpam-310	77	6	get	get	VERB
ejpam-310	77	7	the	the	DET
ejpam-310	77	8	arbitrary	arbitrary	ADJ
ejpam-310	77	9	order	order	NOUN
ejpam-310	77	10	power	power	NOUN
ejpam-310	77	11	series	series	NOUN
ejpam-310	77	12	of	of	ADP
ejpam-310	77	13	the	the	DET
ejpam-310	77	14	solution	solution	NOUN
ejpam-310	77	15	for	for	ADP
ejpam-310	77	16	pdes	pde	NOUN
ejpam-310	77	17	in	in	ADP
ejpam-310	77	18	(	(	PUNCT
ejpam-310	77	19	1.1	1.1	NUM
ejpam-310	77	20	)	)	PUNCT
ejpam-310	77	21	.	.	PUNCT
ejpam-310	78	1	4	4	X
ejpam-310	78	2	.	.	X
ejpam-310	78	3	applications	application	NOUN
ejpam-310	78	4	example	example	NOUN
ejpam-310	78	5	1	1	X
ejpam-310	78	6	.	.	PUNCT
ejpam-310	79	1	the	the	DET
ejpam-310	79	2	test	test	NOUN
ejpam-310	79	3	problem	problem	NOUN
ejpam-310	79	4	consider	consider	VERB
ejpam-310	79	5	the	the	DET
ejpam-310	79	6	fallowing	fallowe	VERB
ejpam-310	79	7	partial	partial	ADJ
ejpam-310	79	8	differential	differential	NOUN
ejpam-310	79	9	equation	equation	NOUN
ejpam-310	79	10	[	[	X
ejpam-310	79	11	7	7	NUM
ejpam-310	79	12	]	]	PUNCT
ejpam-310	79	13	,	,	PUNCT
ejpam-310	79	14	∂	∂	NUM
ejpam-310	79	15	2u(x	2u(x	NUM
ejpam-310	79	16	.t	.t	NOUN
ejpam-310	79	17	)	)	PUNCT
ejpam-310	79	18	∂	∂	NUM
ejpam-310	80	1	t2	t2	PROPN
ejpam-310	80	2	−	−	PROPN
ejpam-310	80	3	c2	c2	PROPN
ejpam-310	80	4	∂	∂	NUM
ejpam-310	80	5	2u(x	2u(x	NUM
ejpam-310	80	6	.t	.t	NOUN
ejpam-310	80	7	)	)	PUNCT
ejpam-310	80	8	∂	∂	PUNCT
ejpam-310	81	1	x2	x2	NOUN
ejpam-310	81	2	=	=	SYM
ejpam-310	81	3	0	0	NUM
ejpam-310	81	4	(	(	PUNCT
ejpam-310	81	5	4.1	4.1	NUM
ejpam-310	81	6	)	)	PUNCT
ejpam-310	81	7	with	with	ADP
ejpam-310	81	8	initial	initial	ADJ
ejpam-310	81	9	condition	condition	NOUN
ejpam-310	81	10	u(x	u(x	NOUN
ejpam-310	81	11	,	,	PUNCT
ejpam-310	81	12	0	0	NUM
ejpam-310	81	13	)	)	PUNCT
ejpam-310	81	14	=	=	SYM
ejpam-310	82	1	x3	x3	ADJ
ejpam-310	82	2	(	(	PUNCT
ejpam-310	82	3	4.2	4.2	NUM
ejpam-310	82	4	)	)	PUNCT
ejpam-310	82	5	∂	∂	NOUN
ejpam-310	82	6	u(x	u(x	PROPN
ejpam-310	82	7	,	,	PUNCT
ejpam-310	82	8	t	t	PROPN
ejpam-310	82	9	)	)	PUNCT
ejpam-310	82	10	∂	∂	NOUN
ejpam-310	82	11	t	t	NOUN
ejpam-310	83	1	=	=	SYM
ejpam-310	84	1	x	x	PROPN
ejpam-310	84	2	.	.	PUNCT
ejpam-310	85	1	(	(	PUNCT
ejpam-310	85	2	4.3	4.3	NUM
ejpam-310	85	3	)	)	PUNCT
ejpam-310	85	4	m.	m.	NOUN
ejpam-310	85	5	kurulay	kurulay	NOUN
ejpam-310	85	6	and	and	CCONJ
ejpam-310	85	7	m.	m.	PROPN
ejpam-310	85	8	bayram	bayram	PROPN
ejpam-310	85	9	/	/	SYM
ejpam-310	85	10	eur	eur	PROPN
ejpam-310	85	11	.	.	PUNCT
ejpam-310	86	1	j.	j.	PROPN
ejpam-310	86	2	pure	pure	PROPN
ejpam-310	86	3	appl	appl	PROPN
ejpam-310	86	4	.	.	PROPN
ejpam-310	86	5	math	math	PROPN
ejpam-310	86	6	,	,	PUNCT
ejpam-310	86	7	2	2	NUM
ejpam-310	86	8	(	(	PUNCT
ejpam-310	86	9	2009	2009	NUM
ejpam-310	86	10	)	)	PUNCT
ejpam-310	86	11	,	,	PUNCT
ejpam-310	86	12	(	(	PUNCT
ejpam-310	86	13	268	268	NUM
ejpam-310	86	14	-	-	SYM
ejpam-310	86	15	277	277	NUM
ejpam-310	86	16	)	)	PUNCT
ejpam-310	86	17	273	273	NUM
ejpam-310	86	18	using	use	VERB
ejpam-310	86	19	equation	equation	NOUN
ejpam-310	86	20	(	(	PUNCT
ejpam-310	86	21	2.4	2.4	NUM
ejpam-310	86	22	)	)	PUNCT
ejpam-310	86	23	,	,	PUNCT
ejpam-310	86	24	and	and	CCONJ
ejpam-310	86	25	initial	initial	ADJ
ejpam-310	86	26	condition	condition	NOUN
ejpam-310	86	27	equation	equation	NOUN
ejpam-310	86	28	(	(	PUNCT
ejpam-310	86	29	4.2),we	4.2),we	PRON
ejpam-310	86	30	obtain	obtain	VERB
ejpam-310	86	31	u(i	u(i	NOUN
ejpam-310	86	32	,	,	PUNCT
ejpam-310	86	33	0	0	NUM
ejpam-310	86	34	)	)	PUNCT
ejpam-310	86	35	=	=	SYM
ejpam-310	86	36	0	0	NUM
ejpam-310	86	37	,	,	PUNCT
ejpam-310	86	38	i	i	PRON
ejpam-310	86	39	=	=	NOUN
ejpam-310	86	40	0	0	NUM
ejpam-310	86	41	,	,	PUNCT
ejpam-310	86	42	1	1	NUM
ejpam-310	86	43	,	,	PUNCT
ejpam-310	86	44	2	2	NUM
ejpam-310	86	45	,	,	PUNCT
ejpam-310	86	46	4	4	NUM
ejpam-310	86	47	,	,	PUNCT
ejpam-310	86	48	...	...	PUNCT
ejpam-310	86	49	,	,	PUNCT
ejpam-310	86	50	m	m	PROPN
ejpam-310	86	51	,	,	PUNCT
ejpam-310	86	52	u(3	u(3	PROPN
ejpam-310	86	53	,	,	PUNCT
ejpam-310	86	54	0	0	NUM
ejpam-310	86	55	)	)	PUNCT
ejpam-310	86	56	=	=	SYM
ejpam-310	86	57	1	1	X
ejpam-310	86	58	.	.	PUNCT
ejpam-310	87	1	(	(	PUNCT
ejpam-310	87	2	4.4	4.4	NUM
ejpam-310	87	3	)	)	PUNCT
ejpam-310	87	4	using	use	VERB
ejpam-310	87	5	equation	equation	NOUN
ejpam-310	87	6	(	(	PUNCT
ejpam-310	87	7	2.4	2.4	NUM
ejpam-310	87	8	)	)	PUNCT
ejpam-310	87	9	,	,	PUNCT
ejpam-310	87	10	and	and	CCONJ
ejpam-310	87	11	initial	initial	ADJ
ejpam-310	87	12	condition	condition	NOUN
ejpam-310	87	13	equation	equation	NOUN
ejpam-310	87	14	(	(	PUNCT
ejpam-310	87	15	4.3),we	4.3),we	NUM
ejpam-310	87	16	obtain	obtain	VERB
ejpam-310	87	17	u(i	u(i	NOUN
ejpam-310	87	18	,	,	PUNCT
ejpam-310	87	19	1	1	NUM
ejpam-310	87	20	)	)	PUNCT
ejpam-310	87	21	=	=	SYM
ejpam-310	87	22	0	0	NUM
ejpam-310	87	23	,	,	PUNCT
ejpam-310	87	24	i	i	PRON
ejpam-310	87	25	=	=	NOUN
ejpam-310	87	26	0	0	NUM
ejpam-310	87	27	,	,	PUNCT
ejpam-310	87	28	2	2	NUM
ejpam-310	87	29	,	,	PUNCT
ejpam-310	87	30	...	...	PUNCT
ejpam-310	87	31	,	,	PUNCT
ejpam-310	87	32	n	n	CCONJ
ejpam-310	87	33	,	,	PUNCT
ejpam-310	87	34	u(1	u(1	PROPN
ejpam-310	87	35	,	,	PUNCT
ejpam-310	87	36	1	1	NUM
ejpam-310	87	37	)	)	PUNCT
ejpam-310	87	38	=	=	SYM
ejpam-310	87	39	1	1	X
ejpam-310	87	40	.	.	PUNCT
ejpam-310	87	41	(	(	PUNCT
ejpam-310	87	42	4.5	4.5	NUM
ejpam-310	87	43	)	)	PUNCT
ejpam-310	87	44	substituting	substitute	VERB
ejpam-310	87	45	equations	equation	NOUN
ejpam-310	87	46	(	(	PUNCT
ejpam-310	87	47	4.4)-(4.5	4.4)-(4.5	NUM
ejpam-310	87	48	)	)	PUNCT
ejpam-310	87	49	into	into	ADP
ejpam-310	87	50	equations	equation	NOUN
ejpam-310	87	51	(	(	PUNCT
ejpam-310	87	52	2.4	2.4	NUM
ejpam-310	87	53	)	)	PUNCT
ejpam-310	87	54	,	,	PUNCT
ejpam-310	87	55	we	we	PRON
ejpam-310	87	56	have	have	VERB
ejpam-310	87	57	u1(x	u1(x	PROPN
ejpam-310	87	58	,	,	PUNCT
ejpam-310	87	59	t	t	PROPN
ejpam-310	87	60	)	)	PUNCT
ejpam-310	87	61	=	=	PUNCT
ejpam-310	88	1	x	x	SYM
ejpam-310	88	2	t	t	NOUN
ejpam-310	88	3	+	+	CCONJ
ejpam-310	88	4	x3	x3	ADJ
ejpam-310	88	5	+	+	CCONJ
ejpam-310	88	6	ax	ax	NOUN
ejpam-310	88	7	t2	t2	NOUN
ejpam-310	88	8	(	(	PUNCT
ejpam-310	88	9	4.6	4.6	NUM
ejpam-310	88	10	)	)	PUNCT
ejpam-310	88	11	substituting	substitute	VERB
ejpam-310	88	12	equations	equation	NOUN
ejpam-310	88	13	(	(	PUNCT
ejpam-310	88	14	4.6	4.6	NUM
ejpam-310	88	15	)	)	PUNCT
ejpam-310	88	16	into	into	ADP
ejpam-310	88	17	equations	equation	NOUN
ejpam-310	88	18	(	(	PUNCT
ejpam-310	88	19	4.1	4.1	NUM
ejpam-310	88	20	)	)	PUNCT
ejpam-310	88	21	,	,	PUNCT
ejpam-310	88	22	and	and	CCONJ
ejpam-310	88	23	by	by	ADP
ejpam-310	88	24	recursive	recursive	ADJ
ejpam-310	88	25	method	method	NOUN
ejpam-310	88	26	,	,	PUNCT
ejpam-310	88	27	the	the	DET
ejpam-310	88	28	results	result	NOUN
ejpam-310	88	29	corresponding	correspond	VERB
ejpam-310	88	30	to	to	ADP
ejpam-310	88	31	m→∞	m→∞	NUM
ejpam-310	88	32	,	,	PUNCT
ejpam-310	88	33	n→∞	n→∞	NUM
ejpam-310	88	34	are	be	AUX
ejpam-310	88	35	listed	list	VERB
ejpam-310	88	36	as	as	SCONJ
ejpam-310	88	37	follows	follow	VERB
ejpam-310	88	38	u(1	u(1	PROPN
ejpam-310	88	39	,	,	PUNCT
ejpam-310	88	40	2	2	NUM
ejpam-310	88	41	)	)	PUNCT
ejpam-310	88	42	=	=	SYM
ejpam-310	88	43	3c2	3c2	NUM
ejpam-310	88	44	(	(	PUNCT
ejpam-310	88	45	4.7	4.7	NUM
ejpam-310	88	46	)	)	PUNCT
ejpam-310	88	47	and	and	CCONJ
ejpam-310	88	48	the	the	DET
ejpam-310	88	49	others	other	NOUN
ejpam-310	88	50	are	be	AUX
ejpam-310	88	51	zero	zero	NUM
ejpam-310	88	52	.	.	PUNCT
ejpam-310	89	1	we	we	PRON
ejpam-310	89	2	obtain	obtain	VERB
ejpam-310	89	3	the	the	DET
ejpam-310	89	4	closed	close	VERB
ejpam-310	89	5	form	form	NOUN
ejpam-310	89	6	series	series	NOUN
ejpam-310	89	7	solution	solution	NOUN
ejpam-310	89	8	as	as	SCONJ
ejpam-310	89	9	follows	follow	VERB
ejpam-310	89	10	.	.	PUNCT
ejpam-310	90	1	u(x	u(x	PROPN
ejpam-310	90	2	,	,	PUNCT
ejpam-310	90	3	t	t	NOUN
ejpam-310	90	4	)	)	PUNCT
ejpam-310	90	5	=	=	PUNCT
ejpam-310	91	1	x	x	SYM
ejpam-310	91	2	t	t	NOUN
ejpam-310	91	3	+	+	CCONJ
ejpam-310	91	4	x3	x3	ADJ
ejpam-310	91	5	+	+	CCONJ
ejpam-310	91	6	3c2	3c2	NUM
ejpam-310	91	7	x	x	SYM
ejpam-310	91	8	t2	t2	NOUN
ejpam-310	91	9	(	(	PUNCT
ejpam-310	91	10	4.8	4.8	NUM
ejpam-310	91	11	)	)	PUNCT
ejpam-310	91	12	by	by	ADP
ejpam-310	91	13	analitik	analitik	NOUN
ejpam-310	91	14	method	method	NOUN
ejpam-310	91	15	[	[	X
ejpam-310	91	16	7	7	NUM
ejpam-310	91	17	]	]	PUNCT
ejpam-310	91	18	,	,	PUNCT
ejpam-310	91	19	a	a	DET
ejpam-310	91	20	closed	closed	ADJ
ejpam-310	91	21	form	form	NOUN
ejpam-310	91	22	solution	solution	NOUN
ejpam-310	91	23	is	be	AUX
ejpam-310	91	24	obtained	obtain	VERB
ejpam-310	91	25	as	as	ADP
ejpam-310	91	26	follows	follow	NOUN
ejpam-310	91	27	.	.	PUNCT
ejpam-310	92	1	uˆ(x	uˆ(x	PUNCT
ejpam-310	92	2	,	,	PUNCT
ejpam-310	92	3	t	t	X
ejpam-310	92	4	)	)	PUNCT
ejpam-310	92	5	=	=	PUNCT
ejpam-310	93	1	x	x	SYM
ejpam-310	93	2	t	t	NOUN
ejpam-310	93	3	+	+	CCONJ
ejpam-310	93	4	x3	x3	ADJ
ejpam-310	93	5	+	+	CCONJ
ejpam-310	93	6	3c2	3c2	NUM
ejpam-310	93	7	x	x	SYM
ejpam-310	93	8	t2	t2	NOUN
ejpam-310	93	9	(	(	PUNCT
ejpam-310	93	10	4.9	4.9	NUM
ejpam-310	93	11	)	)	PUNCT
ejpam-310	93	12	from	from	ADP
ejpam-310	93	13	last	last	ADJ
ejpam-310	93	14	two	two	NUM
ejpam-310	93	15	equations	equation	NOUN
ejpam-310	93	16	,	,	PUNCT
ejpam-310	93	17	we	we	PRON
ejpam-310	93	18	have	have	VERB
ejpam-310	93	19	u(x	u(x	NOUN
ejpam-310	93	20	,	,	PUNCT
ejpam-310	93	21	t	t	PROPN
ejpam-310	93	22	)	)	PUNCT
ejpam-310	93	23	=	=	PUNCT
ejpam-310	93	24	uˆ(x	uˆ(x	NUM
ejpam-310	93	25	,	,	PUNCT
ejpam-310	93	26	t	t	PROPN
ejpam-310	93	27	)	)	PUNCT
ejpam-310	93	28	.	.	PUNCT
ejpam-310	94	1	example	example	NOUN
ejpam-310	95	1	2	2	NUM
ejpam-310	95	2	.	.	X
ejpam-310	95	3	we	we	PRON
ejpam-310	95	4	now	now	ADV
ejpam-310	95	5	consider	consider	VERB
ejpam-310	95	6	the	the	DET
ejpam-310	95	7	problem	problem	NOUN
ejpam-310	95	8	[	[	X
ejpam-310	95	9	12	12	NUM
ejpam-310	95	10	]	]	PUNCT
ejpam-310	95	11	m.	m.	NOUN
ejpam-310	95	12	kurulay	kurulay	NOUN
ejpam-310	95	13	and	and	CCONJ
ejpam-310	95	14	m.	m.	PROPN
ejpam-310	95	15	bayram	bayram	PROPN
ejpam-310	95	16	/	/	SYM
ejpam-310	95	17	eur	eur	PROPN
ejpam-310	95	18	.	.	PUNCT
ejpam-310	96	1	j.	j.	PROPN
ejpam-310	96	2	pure	pure	PROPN
ejpam-310	96	3	appl	appl	PROPN
ejpam-310	96	4	.	.	PROPN
ejpam-310	96	5	math	math	PROPN
ejpam-310	96	6	,	,	PUNCT
ejpam-310	96	7	2	2	NUM
ejpam-310	96	8	(	(	PUNCT
ejpam-310	96	9	2009	2009	NUM
ejpam-310	96	10	)	)	PUNCT
ejpam-310	96	11	,	,	PUNCT
ejpam-310	96	12	(	(	PUNCT
ejpam-310	96	13	268	268	NUM
ejpam-310	96	14	-	-	SYM
ejpam-310	96	15	277	277	NUM
ejpam-310	96	16	)	)	PUNCT
ejpam-310	96	17	274	274	NUM
ejpam-310	96	18	ut	ut	NOUN
ejpam-310	96	19	t	t	PROPN
ejpam-310	96	20	=	=	PUNCT
ejpam-310	96	21	ux	ux	PROPN
ejpam-310	96	22	x	x	SYM
ejpam-310	97	1	+	+	NUM
ejpam-310	97	2	6	6	NUM
ejpam-310	97	3	(	(	PUNCT
ejpam-310	97	4	4.10	4.10	NUM
ejpam-310	97	5	)	)	PUNCT
ejpam-310	97	6	with	with	ADP
ejpam-310	97	7	initial	initial	ADJ
ejpam-310	97	8	condition	condition	NOUN
ejpam-310	97	9	u(x	u(x	NOUN
ejpam-310	97	10	,	,	PUNCT
ejpam-310	97	11	0	0	NUM
ejpam-310	97	12	)	)	PUNCT
ejpam-310	97	13	=	=	SYM
ejpam-310	97	14	x2	x2	PROPN
ejpam-310	97	15	,	,	PUNCT
ejpam-310	97	16	ut(x	ut(x	PUNCT
ejpam-310	97	17	,	,	PUNCT
ejpam-310	97	18	0	0	NUM
ejpam-310	97	19	)	)	PUNCT
ejpam-310	97	20	=	=	SYM
ejpam-310	97	21	4x	4x	NOUN
ejpam-310	97	22	.	.	PUNCT
ejpam-310	98	1	(	(	PUNCT
ejpam-310	98	2	4.11	4.11	NUM
ejpam-310	98	3	)	)	PUNCT
ejpam-310	98	4	using	use	VERB
ejpam-310	98	5	equation	equation	NOUN
ejpam-310	98	6	(	(	PUNCT
ejpam-310	98	7	2.4	2.4	NUM
ejpam-310	98	8	)	)	PUNCT
ejpam-310	98	9	,	,	PUNCT
ejpam-310	98	10	and	and	CCONJ
ejpam-310	98	11	initial	initial	ADJ
ejpam-310	98	12	condition	condition	NOUN
ejpam-310	98	13	equation	equation	NOUN
ejpam-310	98	14	(	(	PUNCT
ejpam-310	98	15	4.11),we	4.11),we	NOUN
ejpam-310	98	16	obtain	obtain	VERB
ejpam-310	98	17	u(i	u(i	NOUN
ejpam-310	98	18	,	,	PUNCT
ejpam-310	98	19	0	0	NUM
ejpam-310	98	20	)	)	PUNCT
ejpam-310	98	21	=	=	SYM
ejpam-310	98	22	0	0	NUM
ejpam-310	98	23	,	,	PUNCT
ejpam-310	98	24	i	i	PRON
ejpam-310	98	25	=	=	NOUN
ejpam-310	98	26	0	0	NUM
ejpam-310	98	27	,	,	PUNCT
ejpam-310	98	28	1	1	NUM
ejpam-310	98	29	,	,	PUNCT
ejpam-310	98	30	3	3	NUM
ejpam-310	98	31	,	,	PUNCT
ejpam-310	98	32	4	4	NUM
ejpam-310	98	33	,	,	PUNCT
ejpam-310	98	34	...	...	PUNCT
ejpam-310	98	35	,	,	PUNCT
ejpam-310	98	36	m	m	PROPN
ejpam-310	98	37	,	,	PUNCT
ejpam-310	98	38	u(2	u(2	ADJ
ejpam-310	98	39	,	,	PUNCT
ejpam-310	98	40	0	0	NUM
ejpam-310	98	41	)	)	PUNCT
ejpam-310	98	42	=	=	SYM
ejpam-310	98	43	1	1	NUM
ejpam-310	98	44	(	(	PUNCT
ejpam-310	98	45	4.12	4.12	NUM
ejpam-310	98	46	)	)	PUNCT
ejpam-310	98	47	using	use	VERB
ejpam-310	98	48	equation	equation	NOUN
ejpam-310	98	49	(	(	PUNCT
ejpam-310	98	50	2.4	2.4	NUM
ejpam-310	98	51	)	)	PUNCT
ejpam-310	98	52	,	,	PUNCT
ejpam-310	98	53	and	and	CCONJ
ejpam-310	98	54	initial	initial	ADJ
ejpam-310	98	55	condition	condition	NOUN
ejpam-310	98	56	equation	equation	NOUN
ejpam-310	98	57	(	(	PUNCT
ejpam-310	98	58	4.12),we	4.12),we	NOUN
ejpam-310	98	59	obtain	obtain	VERB
ejpam-310	98	60	u(i	u(i	NOUN
ejpam-310	98	61	,	,	PUNCT
ejpam-310	98	62	1	1	NUM
ejpam-310	98	63	)	)	PUNCT
ejpam-310	98	64	=	=	SYM
ejpam-310	98	65	0	0	NUM
ejpam-310	98	66	,	,	PUNCT
ejpam-310	98	67	i	i	PRON
ejpam-310	98	68	=	=	NOUN
ejpam-310	98	69	0	0	NUM
ejpam-310	98	70	,	,	PUNCT
ejpam-310	98	71	2	2	NUM
ejpam-310	98	72	,	,	PUNCT
ejpam-310	98	73	...	...	PUNCT
ejpam-310	98	74	,	,	PUNCT
ejpam-310	98	75	n	n	CCONJ
ejpam-310	98	76	,	,	PUNCT
ejpam-310	98	77	u(1	u(1	PROPN
ejpam-310	98	78	,	,	PUNCT
ejpam-310	98	79	1	1	NUM
ejpam-310	98	80	)	)	PUNCT
ejpam-310	98	81	=	=	SYM
ejpam-310	98	82	4	4	NUM
ejpam-310	98	83	(	(	PUNCT
ejpam-310	98	84	4.13	4.13	NUM
ejpam-310	98	85	)	)	PUNCT
ejpam-310	98	86	substituting	substitute	VERB
ejpam-310	98	87	equations	equation	NOUN
ejpam-310	98	88	(	(	PUNCT
ejpam-310	98	89	4.12)-(4.13	4.12)-(4.13	NUM
ejpam-310	98	90	)	)	PUNCT
ejpam-310	98	91	into	into	ADP
ejpam-310	98	92	equations	equation	NOUN
ejpam-310	98	93	(	(	PUNCT
ejpam-310	98	94	2.4	2.4	NUM
ejpam-310	98	95	)	)	PUNCT
ejpam-310	98	96	,	,	PUNCT
ejpam-310	98	97	we	we	PRON
ejpam-310	98	98	have	have	VERB
ejpam-310	98	99	u1(x	u1(x	PROPN
ejpam-310	98	100	,	,	PUNCT
ejpam-310	98	101	t	t	PROPN
ejpam-310	98	102	)	)	PUNCT
ejpam-310	98	103	=	=	PROPN
ejpam-310	99	1	4x	4x	NUM
ejpam-310	99	2	t	t	NOUN
ejpam-310	99	3	+	+	CCONJ
ejpam-310	99	4	x2	x2	PROPN
ejpam-310	99	5	+	+	CCONJ
ejpam-310	99	6	at2	at2	PROPN
ejpam-310	99	7	(	(	PUNCT
ejpam-310	99	8	4.14	4.14	NUM
ejpam-310	99	9	)	)	PUNCT
ejpam-310	99	10	substituting	substitute	VERB
ejpam-310	99	11	equations(4.14	equations(4.14	NOUN
ejpam-310	99	12	)	)	PUNCT
ejpam-310	99	13	into	into	ADP
ejpam-310	99	14	equations	equation	NOUN
ejpam-310	99	15	(	(	PUNCT
ejpam-310	99	16	4.10	4.10	NUM
ejpam-310	99	17	)	)	PUNCT
ejpam-310	99	18	,	,	PUNCT
ejpam-310	99	19	we	we	PRON
ejpam-310	99	20	get	get	VERB
ejpam-310	99	21	the	the	DET
ejpam-310	99	22	results	result	NOUN
ejpam-310	99	23	corresponding	correspond	VERB
ejpam-310	99	24	to	to	ADP
ejpam-310	99	25	m→∞	m→∞	NUM
ejpam-310	99	26	,	,	PUNCT
ejpam-310	99	27	n→∞	n→∞	NUM
ejpam-310	99	28	are	be	AUX
ejpam-310	99	29	listed	list	VERB
ejpam-310	99	30	as	as	SCONJ
ejpam-310	99	31	follows	follow	VERB
ejpam-310	99	32	u(0	u(0	PROPN
ejpam-310	99	33	,	,	PUNCT
ejpam-310	99	34	2	2	NUM
ejpam-310	99	35	)	)	PUNCT
ejpam-310	99	36	=	=	SYM
ejpam-310	99	37	4	4	NUM
ejpam-310	99	38	(	(	PUNCT
ejpam-310	99	39	4.15	4.15	NUM
ejpam-310	99	40	)	)	PUNCT
ejpam-310	99	41	and	and	CCONJ
ejpam-310	99	42	the	the	DET
ejpam-310	99	43	others	other	NOUN
ejpam-310	99	44	are	be	AUX
ejpam-310	99	45	zero	zero	NUM
ejpam-310	99	46	.	.	PUNCT
ejpam-310	100	1	m.	m.	NOUN
ejpam-310	100	2	kurulay	kurulay	PROPN
ejpam-310	100	3	and	and	CCONJ
ejpam-310	100	4	m.	m.	PROPN
ejpam-310	100	5	bayram	bayram	PROPN
ejpam-310	100	6	/	/	SYM
ejpam-310	100	7	eur	eur	PROPN
ejpam-310	100	8	.	.	PUNCT
ejpam-310	101	1	j.	j.	PROPN
ejpam-310	101	2	pure	pure	PROPN
ejpam-310	101	3	appl	appl	PROPN
ejpam-310	101	4	.	.	PROPN
ejpam-310	101	5	math	math	PROPN
ejpam-310	101	6	,	,	PUNCT
ejpam-310	101	7	2	2	NUM
ejpam-310	101	8	(	(	PUNCT
ejpam-310	101	9	2009	2009	NUM
ejpam-310	101	10	)	)	PUNCT
ejpam-310	101	11	,	,	PUNCT
ejpam-310	101	12	(	(	PUNCT
ejpam-310	101	13	268	268	NUM
ejpam-310	101	14	-	-	SYM
ejpam-310	101	15	277	277	NUM
ejpam-310	101	16	)	)	PUNCT
ejpam-310	101	17	275	275	NUM
ejpam-310	101	18	substituting	substitute	VERB
ejpam-310	101	19	all	all	DET
ejpam-310	101	20	u(k	u(k	PROPN
ejpam-310	101	21	,	,	PUNCT
ejpam-310	101	22	h	h	NOUN
ejpam-310	101	23	)	)	PUNCT
ejpam-310	101	24	into	into	ADP
ejpam-310	101	25	equation	equation	NOUN
ejpam-310	101	26	(	(	PUNCT
ejpam-310	101	27	2.4),we	2.4),we	NUM
ejpam-310	101	28	obtain	obtain	VERB
ejpam-310	101	29	the	the	DET
ejpam-310	101	30	closed	close	VERB
ejpam-310	101	31	form	form	NOUN
ejpam-310	101	32	series	series	NOUN
ejpam-310	101	33	solution	solution	NOUN
ejpam-310	101	34	as	as	SCONJ
ejpam-310	101	35	follows	follow	VERB
ejpam-310	101	36	.	.	PUNCT
ejpam-310	102	1	u(x	u(x	PROPN
ejpam-310	102	2	,	,	PUNCT
ejpam-310	102	3	t	t	X
ejpam-310	102	4	)	)	PUNCT
ejpam-310	102	5	=	=	PROPN
ejpam-310	103	1	4x	4x	NUM
ejpam-310	103	2	t	t	NOUN
ejpam-310	103	3	+	+	CCONJ
ejpam-310	103	4	x2	x2	PROPN
ejpam-310	103	5	+	+	NUM
ejpam-310	103	6	4t2	4t2	NUM
ejpam-310	103	7	(	(	PUNCT
ejpam-310	103	8	4.16	4.16	NUM
ejpam-310	103	9	)	)	PUNCT
ejpam-310	103	10	again	again	ADV
ejpam-310	103	11	,	,	PUNCT
ejpam-310	103	12	we	we	PRON
ejpam-310	103	13	have	have	AUX
ejpam-310	103	14	obtained	obtain	VERB
ejpam-310	103	15	the	the	DET
ejpam-310	103	16	exact	exact	ADJ
ejpam-310	103	17	solution	solution	NOUN
ejpam-310	103	18	of	of	ADP
ejpam-310	103	19	the	the	DET
ejpam-310	103	20	initial	initial	ADJ
ejpam-310	103	21	value	value	NOUN
ejpam-310	103	22	problem	problem	NOUN
ejpam-310	103	23	stated	state	VERB
ejpam-310	103	24	previously	previously	ADV
ejpam-310	103	25	.	.	PUNCT
ejpam-310	104	1	example	example	NOUN
ejpam-310	105	1	3	3	NUM
ejpam-310	105	2	.	.	PUNCT
ejpam-310	106	1	[	[	X
ejpam-310	106	2	7	7	NUM
ejpam-310	106	3	]	]	SYM
ejpam-310	106	4	∂	∂	NUM
ejpam-310	106	5	2u(x	2u(x	NUM
ejpam-310	106	6	.t	.t	NOUN
ejpam-310	106	7	)	)	PUNCT
ejpam-310	106	8	∂	∂	NUM
ejpam-310	106	9	t2	t2	PROPN
ejpam-310	106	10	−	−	PROPN
ejpam-310	106	11	∂	∂	NOUN
ejpam-310	106	12	2u(x	2u(x	NUM
ejpam-310	106	13	.t	.t	NOUN
ejpam-310	106	14	)	)	PUNCT
ejpam-310	106	15	∂	∂	PUNCT
ejpam-310	107	1	x2	x2	INTJ
ejpam-310	107	2	−	−	PROPN
ejpam-310	108	1	x2u(x	x2u(x	PROPN
ejpam-310	108	2	,	,	PUNCT
ejpam-310	108	3	t	t	PROPN
ejpam-310	108	4	)	)	PUNCT
ejpam-310	108	5	=	=	SYM
ejpam-310	108	6	x	x	X
ejpam-310	108	7	(	(	PUNCT
ejpam-310	108	8	4.17	4.17	NUM
ejpam-310	108	9	)	)	PUNCT
ejpam-310	108	10	with	with	ADP
ejpam-310	108	11	initial	initial	ADJ
ejpam-310	108	12	condition	condition	NOUN
ejpam-310	108	13	u(x	u(x	NOUN
ejpam-310	108	14	,	,	PUNCT
ejpam-310	108	15	0	0	NUM
ejpam-310	108	16	)	)	PUNCT
ejpam-310	108	17	=	=	SYM
ejpam-310	108	18	0	0	NUM
ejpam-310	108	19	,	,	PUNCT
ejpam-310	108	20	∂	∂	NUM
ejpam-310	108	21	u(x	u(x	NOUN
ejpam-310	108	22	,	,	PUNCT
ejpam-310	108	23	0	0	NUM
ejpam-310	108	24	)	)	PUNCT
ejpam-310	108	25	∂	∂	NOUN
ejpam-310	108	26	t	t	NOUN
ejpam-310	108	27	=	=	SYM
ejpam-310	108	28	0	0	PROPN
ejpam-310	108	29	.	.	PUNCT
ejpam-310	108	30	(	(	PUNCT
ejpam-310	108	31	4.18	4.18	NUM
ejpam-310	108	32	)	)	PUNCT
ejpam-310	108	33	using	use	VERB
ejpam-310	108	34	equation	equation	NOUN
ejpam-310	108	35	(	(	PUNCT
ejpam-310	108	36	2.4	2.4	NUM
ejpam-310	108	37	)	)	PUNCT
ejpam-310	108	38	and	and	CCONJ
ejpam-310	108	39	initial	initial	ADJ
ejpam-310	108	40	conditions(4.18	conditions(4.18	NUM
ejpam-310	108	41	)	)	PUNCT
ejpam-310	108	42	,	,	PUNCT
ejpam-310	108	43	we	we	PRON
ejpam-310	108	44	have	have	VERB
ejpam-310	108	45	u(i	u(i	NOUN
ejpam-310	108	46	,	,	PUNCT
ejpam-310	108	47	0	0	NUM
ejpam-310	108	48	)	)	PUNCT
ejpam-310	108	49	=	=	SYM
ejpam-310	109	1	0	0	NUM
ejpam-310	109	2	,	,	PUNCT
ejpam-310	109	3	i	i	PRON
ejpam-310	109	4	=	=	NOUN
ejpam-310	109	5	0	0	NUM
ejpam-310	109	6	,	,	PUNCT
ejpam-310	109	7	1	1	NUM
ejpam-310	109	8	,	,	PUNCT
ejpam-310	109	9	2	2	NUM
ejpam-310	109	10	,	,	PUNCT
ejpam-310	109	11	...	...	PUNCT
ejpam-310	109	12	,	,	PUNCT
ejpam-310	109	13	m.	m.	NOUN
ejpam-310	109	14	(	(	PUNCT
ejpam-310	109	15	4.19	4.19	NUM
ejpam-310	109	16	)	)	PUNCT
ejpam-310	109	17	u(i	u(i	NOUN
ejpam-310	109	18	,	,	PUNCT
ejpam-310	109	19	1	1	NUM
ejpam-310	109	20	)	)	PUNCT
ejpam-310	109	21	=	=	SYM
ejpam-310	109	22	0	0	NUM
ejpam-310	109	23	,	,	PUNCT
ejpam-310	109	24	i	i	PRON
ejpam-310	109	25	=	=	NOUN
ejpam-310	109	26	0	0	NUM
ejpam-310	109	27	,	,	PUNCT
ejpam-310	109	28	1	1	NUM
ejpam-310	109	29	,	,	PUNCT
ejpam-310	109	30	2	2	NUM
ejpam-310	109	31	,	,	PUNCT
ejpam-310	109	32	...	...	PUNCT
ejpam-310	109	33	,	,	PUNCT
ejpam-310	109	34	n.	n.	PROPN
ejpam-310	109	35	(	(	PUNCT
ejpam-310	109	36	4.20	4.20	NUM
ejpam-310	109	37	)	)	PUNCT
ejpam-310	109	38	the	the	DET
ejpam-310	109	39	results	result	NOUN
ejpam-310	109	40	corresponding	correspond	VERB
ejpam-310	109	41	to	to	ADP
ejpam-310	109	42	m→∞	m→∞	NUM
ejpam-310	109	43	,	,	PUNCT
ejpam-310	109	44	n→∞	n→∞	NUM
ejpam-310	109	45	are	be	AUX
ejpam-310	109	46	listed	list	VERB
ejpam-310	109	47	as	as	SCONJ
ejpam-310	109	48	follows	follow	VERB
ejpam-310	109	49	u(1	u(1	PROPN
ejpam-310	109	50	,	,	PUNCT
ejpam-310	109	51	2	2	NUM
ejpam-310	109	52	)	)	PUNCT
ejpam-310	109	53	=	=	SYM
ejpam-310	109	54	1	1	NUM
ejpam-310	109	55	2	2	NUM
ejpam-310	109	56	,	,	PUNCT
ejpam-310	109	57	u(3	u(3	PROPN
ejpam-310	109	58	,	,	PUNCT
ejpam-310	109	59	4	4	NUM
ejpam-310	109	60	)	)	PUNCT
ejpam-310	109	61	=	=	SYM
ejpam-310	109	62	1	1	NUM
ejpam-310	109	63	24	24	NUM
ejpam-310	109	64	,	,	PUNCT
ejpam-310	109	65	u(1	u(1	PROPN
ejpam-310	109	66	,	,	PUNCT
ejpam-310	109	67	6	6	NUM
ejpam-310	109	68	)	)	PUNCT
ejpam-310	109	69	=	=	SYM
ejpam-310	109	70	1	1	NUM
ejpam-310	109	71	120	120	NUM
ejpam-310	109	72	and	and	CCONJ
ejpam-310	109	73	the	the	DET
ejpam-310	109	74	others	other	NOUN
ejpam-310	109	75	are	be	AUX
ejpam-310	109	76	zero	zero	NUM
ejpam-310	109	77	.	.	PUNCT
ejpam-310	110	1	references	reference	NOUN
ejpam-310	110	2	276	276	NUM
ejpam-310	110	3	substituting	substitute	VERB
ejpam-310	110	4	all	all	DET
ejpam-310	110	5	u(k	u(k	PROPN
ejpam-310	110	6	,	,	PUNCT
ejpam-310	110	7	h	h	NOUN
ejpam-310	110	8	)	)	PUNCT
ejpam-310	110	9	into	into	ADP
ejpam-310	110	10	equation(2.4	equation(2.4	NOUN
ejpam-310	110	11	)	)	PUNCT
ejpam-310	110	12	,	,	PUNCT
ejpam-310	110	13	we	we	PRON
ejpam-310	110	14	obtain	obtain	VERB
ejpam-310	110	15	u(x	u(x	NOUN
ejpam-310	110	16	,	,	PUNCT
ejpam-310	110	17	t	t	NOUN
ejpam-310	110	18	)	)	PUNCT
ejpam-310	110	19	=	=	PUNCT
ejpam-310	111	1	x	x	SYM
ejpam-310	111	2	t2	t2	NOUN
ejpam-310	111	3	2	2	NUM
ejpam-310	111	4	+	+	CCONJ
ejpam-310	111	5	x3	x3	ADJ
ejpam-310	111	6	t4	t4	PROPN
ejpam-310	111	7	24	24	NUM
ejpam-310	112	1	+	+	CCONJ
ejpam-310	112	2	x	x	PROPN
ejpam-310	112	3	t6	t6	PROPN
ejpam-310	112	4	120	120	NUM
ejpam-310	112	5	.	.	PUNCT
ejpam-310	113	1	(	(	PUNCT
ejpam-310	113	2	4.21	4.21	NUM
ejpam-310	113	3	)	)	PUNCT
ejpam-310	113	4	in	in	ADP
ejpam-310	113	5	this	this	DET
ejpam-310	113	6	case	case	NOUN
ejpam-310	113	7	,	,	PUNCT
ejpam-310	113	8	we	we	PRON
ejpam-310	113	9	have	have	AUX
ejpam-310	113	10	obtained	obtain	VERB
ejpam-310	113	11	the	the	DET
ejpam-310	113	12	exact	exact	ADJ
ejpam-310	113	13	solution	solution	NOUN
ejpam-310	113	14	of	of	ADP
ejpam-310	113	15	the	the	DET
ejpam-310	113	16	targeted	target	VERB
ejpam-310	113	17	equation	equation	NOUN
ejpam-310	113	18	with	with	ADP
ejpam-310	113	19	the	the	DET
ejpam-310	113	20	specified	specified	ADJ
ejpam-310	113	21	initial	initial	ADJ
ejpam-310	113	22	conditions	condition	NOUN
ejpam-310	113	23	5	5	NUM
ejpam-310	113	24	.	.	X
ejpam-310	114	1	conclusion	conclusion	NOUN
ejpam-310	114	2	analytic	analytic	ADJ
ejpam-310	114	3	solutions	solution	NOUN
ejpam-310	114	4	of	of	ADP
ejpam-310	114	5	the	the	DET
ejpam-310	114	6	second	second	ADJ
ejpam-310	114	7	-	-	PUNCT
ejpam-310	114	8	order	order	NOUN
ejpam-310	114	9	linear	linear	ADJ
ejpam-310	114	10	partial	partial	ADJ
ejpam-310	114	11	differential	differential	NOUN
ejpam-310	114	12	equations	equation	NOUN
ejpam-310	114	13	with	with	ADP
ejpam-310	114	14	variable	variable	ADJ
ejpam-310	114	15	coefficients	coefficient	NOUN
ejpam-310	114	16	are	be	AUX
ejpam-310	114	17	usually	usually	ADV
ejpam-310	114	18	difficult	difficult	ADJ
ejpam-310	114	19	.	.	PUNCT
ejpam-310	115	1	in	in	ADP
ejpam-310	115	2	many	many	ADJ
ejpam-310	115	3	cases	case	NOUN
ejpam-310	115	4	,	,	PUNCT
ejpam-310	115	5	it	it	PRON
ejpam-310	115	6	is	be	AUX
ejpam-310	115	7	required	require	VERB
ejpam-310	115	8	toapproximate	toapproximate	ADJ
ejpam-310	115	9	solutions	solution	NOUN
ejpam-310	115	10	.	.	PUNCT
ejpam-310	116	1	for	for	ADP
ejpam-310	116	2	this	this	DET
ejpam-310	116	3	purpose	purpose	NOUN
ejpam-310	116	4	,	,	PUNCT
ejpam-310	116	5	power	power	NOUN
ejpam-310	116	6	series	series	NOUN
ejpam-310	116	7	method	method	NOUN
ejpam-310	116	8	can	can	AUX
ejpam-310	116	9	be	be	AUX
ejpam-310	116	10	proposed.in	proposed.in	PRON
ejpam-310	116	11	this	this	DET
ejpam-310	116	12	study	study	NOUN
ejpam-310	116	13	,	,	PUNCT
ejpam-310	116	14	the	the	DET
ejpam-310	116	15	usefulness	usefulness	NOUN
ejpam-310	116	16	power	power	NOUN
ejpam-310	116	17	series	series	PROPN
ejpam-310	116	18	method	method	PROPN
ejpam-310	116	19	presented	present	VERB
ejpam-310	116	20	for	for	ADP
ejpam-310	116	21	the	the	DET
ejpam-310	116	22	approximate	approximate	ADJ
ejpam-310	116	23	solution	solution	NOUN
ejpam-310	116	24	of	of	ADP
ejpam-310	116	25	the	the	DET
ejpam-310	116	26	second	second	ADJ
ejpam-310	116	27	-	-	PUNCT
ejpam-310	116	28	order	order	NOUN
ejpam-310	116	29	linear	linear	ADJ
ejpam-310	116	30	partial	partial	ADJ
ejpam-310	116	31	differential	differential	NOUN
ejpam-310	116	32	equations	equation	NOUN
ejpam-310	116	33	is	be	AUX
ejpam-310	116	34	discussed	discuss	VERB
ejpam-310	116	35	.	.	PUNCT
ejpam-310	117	1	also	also	ADV
ejpam-310	117	2	,	,	PUNCT
ejpam-310	117	3	the	the	DET
ejpam-310	117	4	method	method	NOUN
ejpam-310	117	5	can	can	AUX
ejpam-310	117	6	be	be	AUX
ejpam-310	117	7	applied	apply	VERB
ejpam-310	117	8	to	to	ADP
ejpam-310	117	9	the	the	DET
ejpam-310	117	10	non	non	ADJ
ejpam-310	117	11	-	-	ADJ
ejpam-310	117	12	homogeneous	homogeneous	ADJ
ejpam-310	117	13	(	(	PUNCT
ejpam-310	117	14	example	example	NOUN
ejpam-310	117	15	2	2	NUM
ejpam-310	117	16	)	)	PUNCT
ejpam-310	117	17	and	and	CCONJ
ejpam-310	117	18	homogeneous	homogeneous	ADJ
ejpam-310	117	19	(	(	PUNCT
ejpam-310	117	20	examples	example	NOUN
ejpam-310	117	21	1	1	NUM
ejpam-310	117	22	)	)	PUNCT
ejpam-310	117	23	cases	case	NOUN
ejpam-310	117	24	.	.	PUNCT
ejpam-310	118	1	this	this	DET
ejpam-310	118	2	method	method	NOUN
ejpam-310	118	3	is	be	AUX
ejpam-310	118	4	very	very	ADV
ejpam-310	118	5	simple	simple	ADJ
ejpam-310	118	6	an	an	DET
ejpam-310	118	7	effective	effective	ADJ
ejpam-310	118	8	for	for	ADP
ejpam-310	118	9	most	most	ADJ
ejpam-310	118	10	of	of	ADP
ejpam-310	118	11	linear	linear	ADJ
ejpam-310	118	12	partial	partial	ADJ
ejpam-310	118	13	differential	differential	NOUN
ejpam-310	118	14	equations	equation	NOUN
ejpam-310	118	15	.	.	PUNCT
ejpam-310	119	1	references	reference	NOUN
ejpam-310	119	2	[	[	X
ejpam-310	119	3	1	1	NUM
ejpam-310	119	4	]	]	X
ejpam-310	119	5	marszalek	marszalek	NOUN
ejpam-310	119	6	,	,	PUNCT
ejpam-310	119	7	w.	w.	NOUN
ejpam-310	119	8	(	(	PUNCT
ejpam-310	119	9	1997	1997	NUM
ejpam-310	119	10	)	)	PUNCT
ejpam-310	119	11	,	,	PUNCT
ejpam-310	119	12	analysis	analysis	NOUN
ejpam-310	119	13	of	of	ADP
ejpam-310	119	14	partial	partial	ADJ
ejpam-310	119	15	differential	differential	NOUN
ejpam-310	119	16	algebraic	algebraic	ADJ
ejpam-310	119	17	equations	equation	NOUN
ejpam-310	119	18	,	,	PUNCT
ejpam-310	119	19	ph.d	ph.d	PROPN
ejpam-310	119	20	.	.	PUNCT
ejpam-310	120	1	thesis	thesis	NOUN
ejpam-310	120	2	,	,	PUNCT
ejpam-310	120	3	north	north	PROPN
ejpam-310	120	4	carolina	carolina	PROPN
ejpam-310	120	5	state	state	PROPN
ejpam-310	120	6	university	university	PROPN
ejpam-310	120	7	,	,	PUNCT
ejpam-310	120	8	raleigh	raleigh	PROPN
ejpam-310	120	9	.	.	PUNCT
ejpam-310	121	1	[	[	X
ejpam-310	121	2	2	2	NUM
ejpam-310	121	3	]	]	PUNCT
ejpam-310	121	4	lucht	lucht	NOUN
ejpam-310	121	5	,	,	PUNCT
ejpam-310	121	6	w.	w.	PROPN
ejpam-310	121	7	,	,	PUNCT
ejpam-310	121	8	strehmel	strehmel	PROPN
ejpam-310	121	9	,	,	PUNCT
ejpam-310	121	10	k.	k.	PROPN
ejpam-310	121	11	,	,	PUNCT
ejpam-310	121	12	eichler	eichler	NOUN
ejpam-310	121	13	-	-	PUNCT
ejpam-310	121	14	liebenow	liebenow	PROPN
ejpam-310	121	15	,	,	PUNCT
ejpam-310	121	16	c.	c.	PROPN
ejpam-310	121	17	(	(	PUNCT
ejpam-310	121	18	1997a	1997a	NUM
ejpam-310	121	19	)	)	PUNCT
ejpam-310	121	20	,	,	PUNCT
ejpam-310	121	21	“	"	PUNCT
ejpam-310	121	22	linear	linear	ADJ
ejpam-310	121	23	partial	partial	ADJ
ejpam-310	121	24	differential	differential	NOUN
ejpam-310	121	25	algebraic	algebraic	ADJ
ejpam-310	121	26	equations	equation	NOUN
ejpam-310	121	27	,	,	PUNCT
ejpam-310	121	28	part	part	NOUN
ejpam-310	121	29	i	i	PRON
ejpam-310	121	30	:	:	PUNCT
ejpam-310	121	31	indexes	index	NOUN
ejpam-310	121	32	,	,	PUNCT
ejpam-310	121	33	consistent	consistent	ADJ
ejpam-310	121	34	boundary	boundary	ADJ
ejpam-310	121	35	/	/	SYM
ejpam-310	121	36	initial	initial	ADJ
ejpam-310	121	37	conditions	condition	NOUN
ejpam-310	121	38	”	"	PUNCT
ejpam-310	121	39	,	,	PUNCT
ejpam-310	121	40	report	report	VERB
ejpam-310	121	41	17	17	NUM
ejpam-310	121	42	,	,	PUNCT
ejpam-310	121	43	fachbereich	fachbereich	PROPN
ejpam-310	121	44	mathematik	mathematik	PROPN
ejpam-310	121	45	und	und	PROPN
ejpam-310	121	46	informatik	informatik	PROPN
ejpam-310	121	47	,	,	PUNCT
ejpam-310	121	48	martin	martin	PROPN
ejpam-310	121	49	-	-	PUNCT
ejpam-310	121	50	luther	luther	PROPN
ejpam-310	121	51	-	-	PUNCT
ejpam-310	121	52	universitat	universitat	PROPN
ejpam-310	121	53	halle	halle	NOUN
ejpam-310	121	54	.	.	PUNCT
ejpam-310	122	1	[	[	X
ejpam-310	122	2	3	3	X
ejpam-310	122	3	]	]	X
ejpam-310	122	4	lucht	lucht	NOUN
ejpam-310	122	5	,	,	PUNCT
ejpam-310	122	6	w.	w.	PROPN
ejpam-310	122	7	,	,	PUNCT
ejpam-310	122	8	strehmel	strehmel	PROPN
ejpam-310	122	9	,	,	PUNCT
ejpam-310	122	10	k.	k.	PROPN
ejpam-310	122	11	,	,	PUNCT
ejpam-310	122	12	eichler	eichler	NOUN
ejpam-310	122	13	-	-	PUNCT
ejpam-310	122	14	liebenow	liebenow	PROPN
ejpam-310	122	15	,	,	PUNCT
ejpam-310	122	16	c.	c.	PROPN
ejpam-310	122	17	(	(	PUNCT
ejpam-310	122	18	1997b	1997b	NUM
ejpam-310	122	19	)	)	PUNCT
ejpam-310	122	20	,	,	PUNCT
ejpam-310	122	21	“	"	PUNCT
ejpam-310	122	22	linear	linear	ADJ
ejpam-310	122	23	partial	partial	ADJ
ejpam-310	122	24	differential	differential	NOUN
ejpam-310	122	25	algebraic	algebraic	ADJ
ejpam-310	122	26	equations	equation	NOUN
ejpam-310	122	27	,	,	PUNCT
ejpam-310	122	28	part	part	PROPN
ejpam-310	122	29	ii	ii	PROPN
ejpam-310	122	30	:	:	PUNCT
ejpam-310	122	31	numerical	numerical	ADJ
ejpam-310	122	32	solution	solution	NOUN
ejpam-310	122	33	”	"	PUNCT
ejpam-310	122	34	,	,	PUNCT
ejpam-310	122	35	report	report	NOUN
ejpam-310	122	36	18	18	NUM
ejpam-310	122	37	,	,	PUNCT
ejpam-310	122	38	fachbereich	fachbereich	PROPN
ejpam-310	122	39	mathematik	mathematik	PROPN
ejpam-310	122	40	und	und	PROPN
ejpam-310	122	41	informatik	informatik	PROPN
ejpam-310	122	42	,	,	PUNCT
ejpam-310	122	43	martin	martin	PROPN
ejpam-310	122	44	-	-	PUNCT
ejpam-310	122	45	luther	luther	PROPN
ejpam-310	122	46	-	-	PUNCT
ejpam-310	122	47	universitat	universitat	PROPN
ejpam-310	122	48	halle	halle	NOUN
ejpam-310	122	49	.	.	PUNCT
ejpam-310	123	1	references	reference	NOUN
ejpam-310	123	2	277	277	NUM
ejpam-310	123	3	[	[	X
ejpam-310	123	4	4	4	NUM
ejpam-310	123	5	]	]	X
ejpam-310	123	6	debrabant	debrabant	PROPN
ejpam-310	123	7	,	,	PUNCT
ejpam-310	123	8	k.	k.	PROPN
ejpam-310	123	9	ve	ve	PROPN
ejpam-310	123	10	strehmel	strehmel	PROPN
ejpam-310	123	11	k.	k.	PROPN
ejpam-310	123	12	(	(	PUNCT
ejpam-310	123	13	2005	2005	NUM
ejpam-310	123	14	)	)	PUNCT
ejpam-310	123	15	,	,	PUNCT
ejpam-310	123	16	“	"	PUNCT
ejpam-310	123	17	convergence	convergence	NOUN
ejpam-310	123	18	of	of	ADP
ejpam-310	123	19	runge	runge	NOUN
ejpam-310	123	20	-	-	PUNCT
ejpam-310	123	21	kutta	kutta	NOUN
ejpam-310	123	22	methods	method	NOUN
ejpam-310	123	23	applied	apply	VERB
ejpam-310	123	24	to	to	AUX
ejpam-310	123	25	linear	linear	VERB
ejpam-310	123	26	partial	partial	ADJ
ejpam-310	123	27	differential	differential	ADJ
ejpam-310	123	28	-	-	PUNCT
ejpam-310	123	29	algebraic	algebraic	ADJ
ejpam-310	123	30	equations	equation	NOUN
ejpam-310	123	31	”	"	PUNCT
ejpam-310	123	32	,	,	PUNCT
ejpam-310	123	33	applied	apply	VERB
ejpam-310	123	34	numerical	numerical	ADJ
ejpam-310	123	35	mathematics	mathematic	NOUN
ejpam-310	123	36	,	,	PUNCT
ejpam-310	123	37	53:213	53:213	NUM
ejpam-310	123	38	-	-	SYM
ejpam-310	123	39	229	229	NUM
ejpam-310	123	40	.	.	PUNCT
ejpam-310	124	1	[	[	X
ejpam-310	124	2	5	5	NUM
ejpam-310	124	3	]	]	X
ejpam-310	124	4	martinson	martinson	NOUN
ejpam-310	124	5	,	,	PUNCT
ejpam-310	124	6	w.	w.	PROPN
ejpam-310	124	7	,	,	PUNCT
ejpam-310	124	8	barton	barton	PROPN
ejpam-310	124	9	,	,	PUNCT
ejpam-310	124	10	p.	p.	NOUN
ejpam-310	124	11	(	(	PUNCT
ejpam-310	124	12	2000	2000	NUM
ejpam-310	124	13	)	)	PUNCT
ejpam-310	124	14	,	,	PUNCT
ejpam-310	124	15	“	"	PUNCT
ejpam-310	124	16	a	a	DET
ejpam-310	124	17	differentiation	differentiation	NOUN
ejpam-310	124	18	index	index	NOUN
ejpam-310	124	19	for	for	ADP
ejpam-310	124	20	partial	partial	ADJ
ejpam-310	124	21	differentialalgebraic	differentialalgebraic	ADJ
ejpam-310	124	22	equations	equation	NOUN
ejpam-310	124	23	”	"	PUNCT
ejpam-310	124	24	,	,	PUNCT
ejpam-310	124	25	siam	siam	PROPN
ejpam-310	124	26	j.	j.	PROPN
ejpam-310	124	27	sci	sci	PROPN
ejpam-310	124	28	.	.	PUNCT
ejpam-310	125	1	comput	comput	PROPN
ejpam-310	125	2	.	.	PUNCT
ejpam-310	125	3	,	,	PUNCT
ejpam-310	125	4	vol	vol	NOUN
ejpam-310	125	5	.	.	PROPN
ejpam-310	125	6	21	21	NUM
ejpam-310	125	7	,	,	PUNCT
ejpam-310	125	8	6:2295	6:2295	NOUN
ejpam-310	125	9	-	-	SYM
ejpam-310	125	10	2315	2315	NUM
ejpam-310	125	11	.	.	PUNCT
ejpam-310	126	1	[	[	X
ejpam-310	126	2	6	6	NUM
ejpam-310	126	3	]	]	X
ejpam-310	126	4	martinson	martinson	NOUN
ejpam-310	126	5	,	,	PUNCT
ejpam-310	126	6	w.	w.	PROPN
ejpam-310	126	7	,	,	PUNCT
ejpam-310	126	8	barton	barton	PROPN
ejpam-310	126	9	,	,	PUNCT
ejpam-310	126	10	p.	p.	PROPN
ejpam-310	126	11	(	(	PUNCT
ejpam-310	126	12	2002	2002	NUM
ejpam-310	126	13	)	)	PUNCT
ejpam-310	126	14	,	,	PUNCT
ejpam-310	126	15	“	"	PUNCT
ejpam-310	126	16	index	index	NOUN
ejpam-310	126	17	and	and	CCONJ
ejpam-310	126	18	characteristic	characteristic	ADJ
ejpam-310	126	19	analysis	analysis	NOUN
ejpam-310	126	20	of	of	ADP
ejpam-310	126	21	linear	linear	ADJ
ejpam-310	126	22	pdae	pdae	NOUN
ejpam-310	126	23	systems	system	NOUN
ejpam-310	126	24	”	"	PUNCT
ejpam-310	126	25	,	,	PUNCT
ejpam-310	126	26	siam	siam	PROPN
ejpam-310	126	27	j.	j.	PROPN
ejpam-310	126	28	sci	sci	PROPN
ejpam-310	126	29	.	.	PUNCT
ejpam-310	126	30	comput	comput	PROPN
ejpam-310	126	31	.	.	PUNCT
ejpam-310	126	32	,	,	PUNCT
ejpam-310	126	33	vol	vol	NOUN
ejpam-310	126	34	.	.	PROPN
ejpam-310	126	35	24	24	NUM
ejpam-310	126	36	,	,	PUNCT
ejpam-310	126	37	3:905	3:905	NUM
ejpam-310	126	38	-	-	SYM
ejpam-310	126	39	923	923	NUM
ejpam-310	126	40	.	.	PUNCT
ejpam-310	127	1	[	[	X
ejpam-310	127	2	7	7	NUM
ejpam-310	127	3	]	]	X
ejpam-310	127	4	chen	chen	PROPN
ejpam-310	127	5	,	,	PUNCT
ejpam-310	127	6	c.k	c.k	PROPN
ejpam-310	127	7	.	.	PROPN
ejpam-310	127	8	,	,	PUNCT
ejpam-310	127	9	ho	ho	PROPN
ejpam-310	127	10	,	,	PUNCT
ejpam-310	127	11	s.h	s.h	PROPN
ejpam-310	127	12	.	.	PROPN
ejpam-310	127	13	(	(	PUNCT
ejpam-310	127	14	1999	1999	NUM
ejpam-310	127	15	)	)	PUNCT
ejpam-310	127	16	,	,	PUNCT
ejpam-310	127	17	“	"	PUNCT
ejpam-310	127	18	solving	solve	VERB
ejpam-310	127	19	partial	partial	ADJ
ejpam-310	127	20	differential	differential	NOUN
ejpam-310	127	21	equations	equation	NOUN
ejpam-310	127	22	by	by	ADP
ejpam-310	127	23	two	two	NUM
ejpam-310	127	24	-	-	PUNCT
ejpam-310	127	25	dimensional	dimensional	ADJ
ejpam-310	127	26	differential	differential	ADJ
ejpam-310	127	27	transform	transform	NOUN
ejpam-310	127	28	method	method	NOUN
ejpam-310	127	29	”	"	PUNCT
ejpam-310	127	30	,	,	PUNCT
ejpam-310	127	31	applied	apply	VERB
ejpam-310	127	32	mathematics	mathematic	NOUN
ejpam-310	127	33	and	and	CCONJ
ejpam-310	127	34	computation,106:171	computation,106:171	NOUN
ejpam-310	127	35	-	-	PUNCT
ejpam-310	127	36	179	179	NUM
ejpam-310	127	37	.	.	PUNCT
ejpam-310	128	1	[	[	X
ejpam-310	128	2	8	8	NUM
ejpam-310	128	3	]	]	X
ejpam-310	128	4	hassan	hassan	PROPN
ejpam-310	128	5	,	,	PUNCT
ejpam-310	128	6	i.h	i.h	PROPN
ejpam-310	128	7	.	.	PUNCT
ejpam-310	128	8	(	(	PUNCT
ejpam-310	128	9	2002	2002	NUM
ejpam-310	128	10	)	)	PUNCT
ejpam-310	128	11	,	,	PUNCT
ejpam-310	128	12	“	"	PUNCT
ejpam-310	128	13	on	on	ADP
ejpam-310	128	14	solving	solve	VERB
ejpam-310	128	15	some	some	DET
ejpam-310	128	16	eigenvalue	eigenvalue	ADJ
ejpam-310	128	17	problems	problem	NOUN
ejpam-310	128	18	by	by	ADP
ejpam-310	128	19	using	use	VERB
ejpam-310	128	20	a	a	DET
ejpam-310	128	21	differential	differential	ADJ
ejpam-310	128	22	transformation	transformation	NOUN
ejpam-310	128	23	”	"	PUNCT
ejpam-310	128	24	,	,	PUNCT
ejpam-310	128	25	applied	apply	VERB
ejpam-310	128	26	mathematics	mathematic	NOUN
ejpam-310	128	27	and	and	CCONJ
ejpam-310	128	28	computation	computation	NOUN
ejpam-310	128	29	,	,	PUNCT
ejpam-310	128	30	127:1	127:1	NUM
ejpam-310	128	31	-	-	SYM
ejpam-310	128	32	22	22	NUM
ejpam-310	128	33	.	.	PUNCT
ejpam-310	129	1	[	[	X
ejpam-310	129	2	9	9	NUM
ejpam-310	129	3	]	]	X
ejpam-310	129	4	jang	jang	PROPN
ejpam-310	129	5	,	,	PUNCT
ejpam-310	129	6	m.j	m.j	PROPN
ejpam-310	129	7	.	.	PROPN
ejpam-310	129	8	,	,	PUNCT
ejpam-310	129	9	chen	chen	PROPN
ejpam-310	129	10	,	,	PUNCT
ejpam-310	129	11	c.l	c.l	PROPN
ejpam-310	129	12	.	.	PROPN
ejpam-310	129	13	,	,	PUNCT
ejpam-310	129	14	liy	liy	PROPN
ejpam-310	129	15	,	,	PUNCT
ejpam-310	129	16	l.c	l.c	PROPN
ejpam-310	129	17	.	.	PROPN
ejpam-310	129	18	(	(	PUNCT
ejpam-310	129	19	2000	2000	NUM
ejpam-310	129	20	)	)	PUNCT
ejpam-310	129	21	,	,	PUNCT
ejpam-310	129	22	“	"	PUNCT
ejpam-310	129	23	on	on	ADP
ejpam-310	129	24	solving	solve	VERB
ejpam-310	129	25	the	the	DET
ejpam-310	129	26	initial	initial	ADJ
ejpam-310	129	27	-	-	PUNCT
ejpam-310	129	28	value	value	NOUN
ejpam-310	129	29	problems	problem	NOUN
ejpam-310	129	30	using	use	VERB
ejpam-310	129	31	the	the	DET
ejpam-310	129	32	differential	differential	ADJ
ejpam-310	129	33	transformation	transformation	NOUN
ejpam-310	129	34	method	method	NOUN
ejpam-310	129	35	”	"	PUNCT
ejpam-310	129	36	,	,	PUNCT
ejpam-310	129	37	applied	apply	VERB
ejpam-310	129	38	mathematics	mathematic	NOUN
ejpam-310	129	39	and	and	CCONJ
ejpam-310	129	40	computation	computation	NOUN
ejpam-310	129	41	,	,	PUNCT
ejpam-310	129	42	115:145160	115:145160	NUM
ejpam-310	129	43	.	.	PUNCT
ejpam-310	130	1	[	[	X
ejpam-310	130	2	10	10	NUM
ejpam-310	130	3	]	]	X
ejpam-310	130	4	liu	liu	PROPN
ejpam-310	130	5	,	,	PUNCT
ejpam-310	130	6	h.	h.	PROPN
ejpam-310	130	7	and	and	CCONJ
ejpam-310	130	8	song	song	PROPN
ejpam-310	130	9	,	,	PUNCT
ejpam-310	130	10	y.	y.	PROPN
ejpam-310	130	11	(	(	PUNCT
ejpam-310	130	12	2007	2007	NUM
ejpam-310	130	13	)	)	PUNCT
ejpam-310	130	14	,	,	PUNCT
ejpam-310	130	15	“	"	PUNCT
ejpam-310	130	16	differential	differential	ADJ
ejpam-310	130	17	transform	transform	NOUN
ejpam-310	130	18	method	method	NOUN
ejpam-310	130	19	applied	apply	VERB
ejpam-310	130	20	to	to	ADP
ejpam-310	130	21	high	high	ADJ
ejpam-310	130	22	index	index	NOUN
ejpam-310	130	23	differential	differential	ADJ
ejpam-310	130	24	-	-	PUNCT
ejpam-310	130	25	algebraic	algebraic	ADJ
ejpam-310	130	26	equations	equation	NOUN
ejpam-310	130	27	”	"	PUNCT
ejpam-310	130	28	,	,	PUNCT
ejpam-310	130	29	applied	apply	VERB
ejpam-310	130	30	mathematics	mathematic	NOUN
ejpam-310	130	31	and	and	CCONJ
ejpam-310	130	32	computation	computation	NOUN
ejpam-310	130	33	,	,	PUNCT
ejpam-310	130	34	184:748	184:748	NOUN
ejpam-310	130	35	-	-	PUNCT
ejpam-310	130	36	753	753	NUM
ejpam-310	130	37	.	.	PUNCT
ejpam-310	131	1	[	[	X
ejpam-310	131	2	11	11	NUM
ejpam-310	131	3	]	]	SYM
ejpam-310	131	4	x	x	PROPN
ejpam-310	131	5	yang	yang	PROPN
ejpam-310	131	6	,	,	PUNCT
ejpam-310	131	7	y.	y.	PROPN
ejpam-310	131	8	liu	liu	PROPN
ejpam-310	131	9	,	,	PUNCT
ejpam-310	131	10	s.	s.	PROPN
ejpam-310	131	11	bai	bai	PROPN
ejpam-310	131	12	,	,	PUNCT
ejpam-310	131	13	(	(	PUNCT
ejpam-310	131	14	2006	2006	NUM
ejpam-310	131	15	)	)	PUNCT
ejpam-310	131	16	.	.	PUNCT
ejpam-310	132	1	“	"	PUNCT
ejpam-310	132	2	a	a	DET
ejpam-310	132	3	numerical	numerical	ADJ
ejpam-310	132	4	solution	solution	NOUN
ejpam-310	132	5	of	of	ADP
ejpam-310	132	6	second	second	ADJ
ejpam-310	132	7	-	-	PUNCT
ejpam-310	132	8	order	order	NOUN
ejpam-310	132	9	linear	linear	ADJ
ejpam-310	132	10	partial	partial	ADJ
ejpam-310	132	11	differential	differential	NOUN
ejpam-310	132	12	equations	equation	NOUN
ejpam-310	132	13	by	by	ADP
ejpam-310	132	14	differential	differential	ADJ
ejpam-310	132	15	transform	transform	NOUN
ejpam-310	132	16	”	"	PUNCT
ejpam-310	132	17	,	,	PUNCT
ejpam-310	132	18	applied	apply	VERB
ejpam-310	132	19	mathematics	mathematic	NOUN
ejpam-310	132	20	and	and	CCONJ
ejpam-310	132	21	computation	computation	NOUN
ejpam-310	132	22	173	173	NUM
ejpam-310	132	23	;	;	PUNCT
ejpam-310	132	24	792	792	NUM
ejpam-310	132	25	-	-	SYM
ejpam-310	132	26	802	802	NUM
ejpam-310	132	27	.	.	PUNCT
ejpam-310	133	1	[	[	X
ejpam-310	133	2	12	12	NUM
ejpam-310	133	3	]	]	X
ejpam-310	133	4	c.kesan	c.kesan	NUM
ejpam-310	133	5	,	,	PUNCT
ejpam-310	133	6	(	(	PUNCT
ejpam-310	133	7	2003	2003	NUM
ejpam-310	133	8	)	)	PUNCT
ejpam-310	133	9	,	,	PUNCT
ejpam-310	133	10	“	"	PUNCT
ejpam-310	133	11	chebyshev	chebyshev	PROPN
ejpam-310	133	12	polynomial	polynomial	ADJ
ejpam-310	133	13	solutions	solution	NOUN
ejpam-310	133	14	of	of	ADP
ejpam-310	133	15	second	second	ADJ
ejpam-310	133	16	-	-	PUNCT
ejpam-310	133	17	order	order	NOUN
ejpam-310	133	18	linear	linear	ADJ
ejpam-310	133	19	partial	partial	ADJ
ejpam-310	133	20	differential	differential	NOUN
ejpam-310	133	21	equations	equation	NOUN
ejpam-310	133	22	”	"	PUNCT
ejpam-310	133	23	,	,	PUNCT
ejpam-310	133	24	applied	apply	VERB
ejpam-310	133	25	mathematics	mathematic	NOUN
ejpam-310	133	26	and	and	CCONJ
ejpam-310	133	27	computation	computation	NOUN
ejpam-310	133	28	134	134	NUM
ejpam-310	133	29	;	;	PUNCT
ejpam-310	133	30	109–124	109–124	NUM
ejpam-310	133	31	.	.	PUNCT
ejpam-310	134	1	[	[	X
ejpam-310	134	2	13	13	NUM
ejpam-310	134	3	]	]	X
ejpam-310	134	4	bayram	bayram	PROPN
ejpam-310	134	5	,	,	PUNCT
ejpam-310	134	6	m.	m.	NOUN
ejpam-310	134	7	,	,	PUNCT
ejpam-310	134	8	çelik	çelik	PROPN
ejpam-310	134	9	,	,	PUNCT
ejpam-310	134	10	e.	e.	PROPN
ejpam-310	134	11	,	,	PUNCT
ejpam-310	134	12	(	(	PUNCT
ejpam-310	134	13	2003	2003	NUM
ejpam-310	134	14	)	)	PUNCT
ejpam-310	134	15	,	,	PUNCT
ejpam-310	134	16	“	"	PUNCT
ejpam-310	134	17	arbitrary	arbitrary	ADJ
ejpam-310	134	18	order	order	NOUN
ejpam-310	134	19	numerical	numerical	ADJ
ejpam-310	134	20	method	method	NOUN
ejpam-310	134	21	for	for	ADP
ejpam-310	134	22	solving	solve	VERB
ejpam-310	134	23	differentialalgebraic	differentialalgebraic	ADJ
ejpam-310	134	24	equations	equation	NOUN
ejpam-310	134	25	by	by	ADP
ejpam-310	134	26	padé	padé	PROPN
ejpam-310	134	27	series	series	PROPN
ejpam-310	134	28	”	"	PUNCT
ejpam-310	134	29	,	,	PUNCT
ejpam-310	134	30	applied	apply	VERB
ejpam-310	134	31	mathematics	mathematic	NOUN
ejpam-310	134	32	and	and	CCONJ
ejpam-310	134	33	computation	computation	NOUN
ejpam-310	134	34	.	.	PUNCT
ejpam-310	135	1	137;57	137;57	NUM
ejpam-310	135	2	-	-	SYM
ejpam-310	135	3	65	65	NUM
ejpam-310	135	4	.	.	PUNCT