id	sid	tid	token	lemma	pos
ejpam-5427	1	1	european	european	PROPN
ejpam-5427	1	2	journal	journal	PROPN
ejpam-5427	1	3	of	of	ADP
ejpam-5427	1	4	pure	pure	ADJ
ejpam-5427	1	5	and	and	CCONJ
ejpam-5427	1	6	applied	apply	VERB
ejpam-5427	1	7	mathematics	mathematic	NOUN
ejpam-5427	1	8	vol	vol	NOUN
ejpam-5427	1	9	.	.	PROPN
ejpam-5427	2	1	17	17	NUM
ejpam-5427	2	2	,	,	PUNCT
ejpam-5427	2	3	no	no	INTJ
ejpam-5427	2	4	.	.	NOUN
ejpam-5427	2	5	4	4	NUM
ejpam-5427	2	6	,	,	PUNCT
ejpam-5427	2	7	2024	2024	NUM
ejpam-5427	2	8	,	,	PUNCT
ejpam-5427	2	9	3622	3622	NUM
ejpam-5427	2	10	-	-	SYM
ejpam-5427	2	11	3641	3641	NUM
ejpam-5427	2	12	issn	issn	PROPN
ejpam-5427	2	13	1307	1307	NUM
ejpam-5427	2	14	-	-	SYM
ejpam-5427	2	15	5543	5543	NUM
ejpam-5427	2	16	–	–	PUNCT
ejpam-5427	3	1	ejpam.com	ejpam.com	X
ejpam-5427	3	2	published	publish	VERB
ejpam-5427	3	3	by	by	ADP
ejpam-5427	3	4	new	new	PROPN
ejpam-5427	3	5	york	york	PROPN
ejpam-5427	3	6	business	business	PROPN
ejpam-5427	3	7	global	global	PROPN
ejpam-5427	3	8	a	a	DET
ejpam-5427	3	9	novel	novel	ADJ
ejpam-5427	3	10	analytical	analytical	ADJ
ejpam-5427	3	11	approximate	approximate	ADJ
ejpam-5427	3	12	solution	solution	NOUN
ejpam-5427	3	13	for	for	ADP
ejpam-5427	3	14	strongly	strongly	ADV
ejpam-5427	3	15	nonlinear	nonlinear	ADJ
ejpam-5427	3	16	third	third	ADJ
ejpam-5427	3	17	-	-	PUNCT
ejpam-5427	3	18	order	order	NOUN
ejpam-5427	3	19	jerk	jerk	NOUN
ejpam-5427	3	20	equations	equation	NOUN
ejpam-5427	3	21	using	use	VERB
ejpam-5427	3	22	a	a	DET
ejpam-5427	3	23	modified	modify	VERB
ejpam-5427	3	24	iteration	iteration	NOUN
ejpam-5427	3	25	method	method	NOUN
ejpam-5427	3	26	gamal	gamal	PROPN
ejpam-5427	3	27	m.	m.	PROPN
ejpam-5427	3	28	ismail1,2,∗	ismail1,2,∗	PROPN
ejpam-5427	3	29	,	,	PUNCT
ejpam-5427	3	30	mohammed	mohammed	PROPN
ejpam-5427	3	31	i.	i.	PROPN
ejpam-5427	3	32	yamani1	yamani1	PROPN
ejpam-5427	3	33	1	1	NUM
ejpam-5427	3	34	department	department	NOUN
ejpam-5427	3	35	of	of	ADP
ejpam-5427	3	36	mathematics	mathematic	NOUN
ejpam-5427	3	37	,	,	PUNCT
ejpam-5427	3	38	faculty	faculty	NOUN
ejpam-5427	3	39	of	of	ADP
ejpam-5427	3	40	science	science	NOUN
ejpam-5427	3	41	,	,	PUNCT
ejpam-5427	3	42	islamic	islamic	PROPN
ejpam-5427	3	43	university	university	PROPN
ejpam-5427	3	44	of	of	ADP
ejpam-5427	3	45	madinah	madinah	PROPN
ejpam-5427	3	46	,	,	PUNCT
ejpam-5427	3	47	madinah	madinah	PROPN
ejpam-5427	3	48	,	,	PUNCT
ejpam-5427	3	49	42351	42351	NUM
ejpam-5427	3	50	,	,	PUNCT
ejpam-5427	3	51	saudi	saudi	PROPN
ejpam-5427	3	52	arabia	arabia	PROPN
ejpam-5427	3	53	2	2	NUM
ejpam-5427	3	54	department	department	NOUN
ejpam-5427	3	55	of	of	ADP
ejpam-5427	3	56	mathematics	mathematic	NOUN
ejpam-5427	3	57	,	,	PUNCT
ejpam-5427	3	58	faculty	faculty	NOUN
ejpam-5427	3	59	of	of	ADP
ejpam-5427	3	60	science	science	NOUN
ejpam-5427	3	61	,	,	PUNCT
ejpam-5427	3	62	sohag	sohag	NOUN
ejpam-5427	3	63	university	university	NOUN
ejpam-5427	3	64	,	,	PUNCT
ejpam-5427	3	65	sohag	sohag	NOUN
ejpam-5427	3	66	82524	82524	NUM
ejpam-5427	3	67	,	,	PUNCT
ejpam-5427	3	68	egypt	egypt	PROPN
ejpam-5427	3	69	abstract	abstract	PROPN
ejpam-5427	3	70	.	.	PUNCT
ejpam-5427	4	1	nonlinear	nonlinear	ADJ
ejpam-5427	4	2	jerk	jerk	PROPN
ejpam-5427	4	3	equations	equation	NOUN
ejpam-5427	4	4	,	,	PUNCT
ejpam-5427	4	5	characterized	characterize	VERB
ejpam-5427	4	6	by	by	ADP
ejpam-5427	4	7	a	a	DET
ejpam-5427	4	8	third	third	ADJ
ejpam-5427	4	9	-	-	PUNCT
ejpam-5427	4	10	order	order	NOUN
ejpam-5427	4	11	time	time	NOUN
ejpam-5427	4	12	derivative	derivative	NOUN
ejpam-5427	4	13	,	,	PUNCT
ejpam-5427	4	14	play	play	VERB
ejpam-5427	4	15	a	a	DET
ejpam-5427	4	16	crucial	crucial	ADJ
ejpam-5427	4	17	role	role	NOUN
ejpam-5427	4	18	in	in	ADP
ejpam-5427	4	19	modeling	model	VERB
ejpam-5427	4	20	various	various	ADJ
ejpam-5427	4	21	physical	physical	ADJ
ejpam-5427	4	22	phenomena	phenomenon	NOUN
ejpam-5427	4	23	across	across	ADP
ejpam-5427	4	24	disciplines	discipline	NOUN
ejpam-5427	4	25	like	like	ADP
ejpam-5427	4	26	mechanics	mechanic	NOUN
ejpam-5427	4	27	,	,	PUNCT
ejpam-5427	4	28	circuits	circuit	NOUN
ejpam-5427	4	29	,	,	PUNCT
ejpam-5427	4	30	and	and	CCONJ
ejpam-5427	4	31	biology	biology	NOUN
ejpam-5427	4	32	.	.	PUNCT
ejpam-5427	5	1	accurately	accurately	ADV
ejpam-5427	5	2	solving	solve	VERB
ejpam-5427	5	3	these	these	DET
ejpam-5427	5	4	equations	equation	NOUN
ejpam-5427	5	5	is	be	AUX
ejpam-5427	5	6	essential	essential	ADJ
ejpam-5427	5	7	for	for	ADP
ejpam-5427	5	8	understanding	understanding	NOUN
ejpam-5427	5	9	and	and	CCONJ
ejpam-5427	5	10	predicting	predict	VERB
ejpam-5427	5	11	the	the	DET
ejpam-5427	5	12	behavior	behavior	NOUN
ejpam-5427	5	13	of	of	ADP
ejpam-5427	5	14	such	such	ADJ
ejpam-5427	5	15	systems	system	NOUN
ejpam-5427	5	16	.	.	PUNCT
ejpam-5427	6	1	however	however	ADV
ejpam-5427	6	2	,	,	PUNCT
ejpam-5427	6	3	obtaining	obtain	VERB
ejpam-5427	6	4	analytical	analytical	ADJ
ejpam-5427	6	5	solutions	solution	NOUN
ejpam-5427	6	6	for	for	ADP
ejpam-5427	6	7	nonlinear	nonlinear	ADJ
ejpam-5427	6	8	jerk	jerk	PROPN
ejpam-5427	6	9	equations	equation	NOUN
ejpam-5427	6	10	can	can	AUX
ejpam-5427	6	11	be	be	AUX
ejpam-5427	6	12	challenging	challenge	VERB
ejpam-5427	6	13	,	,	PUNCT
ejpam-5427	6	14	necessitating	necessitate	VERB
ejpam-5427	6	15	the	the	DET
ejpam-5427	6	16	development	development	NOUN
ejpam-5427	6	17	of	of	ADP
ejpam-5427	6	18	robust	robust	ADJ
ejpam-5427	6	19	and	and	CCONJ
ejpam-5427	6	20	accurate	accurate	ADJ
ejpam-5427	6	21	approximation	approximation	NOUN
ejpam-5427	6	22	methods	method	NOUN
ejpam-5427	6	23	.	.	PUNCT
ejpam-5427	7	1	this	this	DET
ejpam-5427	7	2	work	work	NOUN
ejpam-5427	7	3	explores	explore	NOUN
ejpam-5427	7	4	,	,	PUNCT
ejpam-5427	7	5	for	for	ADP
ejpam-5427	7	6	the	the	DET
ejpam-5427	7	7	first	first	ADJ
ejpam-5427	7	8	time	time	NOUN
ejpam-5427	7	9	,	,	PUNCT
ejpam-5427	7	10	the	the	DET
ejpam-5427	7	11	application	application	NOUN
ejpam-5427	7	12	of	of	ADP
ejpam-5427	7	13	the	the	DET
ejpam-5427	7	14	modified	modify	VERB
ejpam-5427	7	15	iteration	iteration	NOUN
ejpam-5427	7	16	approach	approach	NOUN
ejpam-5427	7	17	to	to	PART
ejpam-5427	7	18	solve	solve	VERB
ejpam-5427	7	19	third	third	ADJ
ejpam-5427	7	20	-	-	PUNCT
ejpam-5427	7	21	order	order	NOUN
ejpam-5427	7	22	jerk	jerk	NOUN
ejpam-5427	7	23	equations	equation	NOUN
ejpam-5427	7	24	.	.	PUNCT
ejpam-5427	8	1	by	by	ADP
ejpam-5427	8	2	comparing	compare	VERB
ejpam-5427	8	3	the	the	DET
ejpam-5427	8	4	obtained	obtain	VERB
ejpam-5427	8	5	approximate	approximate	ADJ
ejpam-5427	8	6	solutions	solution	NOUN
ejpam-5427	8	7	with	with	ADP
ejpam-5427	8	8	both	both	CCONJ
ejpam-5427	8	9	exact	exact	ADJ
ejpam-5427	8	10	and	and	CCONJ
ejpam-5427	8	11	existing	exist	VERB
ejpam-5427	8	12	analytical	analytical	ADJ
ejpam-5427	8	13	solutions	solution	NOUN
ejpam-5427	8	14	for	for	ADP
ejpam-5427	8	15	established	establish	VERB
ejpam-5427	8	16	engineering	engineering	NOUN
ejpam-5427	8	17	problems	problem	NOUN
ejpam-5427	8	18	,	,	PUNCT
ejpam-5427	8	19	we	we	PRON
ejpam-5427	8	20	demonstrate	demonstrate	VERB
ejpam-5427	8	21	the	the	DET
ejpam-5427	8	22	superior	superior	ADJ
ejpam-5427	8	23	accuracy	accuracy	NOUN
ejpam-5427	8	24	and	and	CCONJ
ejpam-5427	8	25	rapid	rapid	ADJ
ejpam-5427	8	26	convergence	convergence	NOUN
ejpam-5427	8	27	of	of	ADP
ejpam-5427	8	28	the	the	DET
ejpam-5427	8	29	proposed	propose	VERB
ejpam-5427	8	30	method	method	NOUN
ejpam-5427	8	31	.	.	PUNCT
ejpam-5427	9	1	the	the	DET
ejpam-5427	9	2	significantly	significantly	ADV
ejpam-5427	9	3	reduced	reduce	VERB
ejpam-5427	9	4	error	error	NOUN
ejpam-5427	9	5	percentages	percentage	NOUN
ejpam-5427	9	6	highlight	highlight	VERB
ejpam-5427	9	7	the	the	DET
ejpam-5427	9	8	effectiveness	effectiveness	NOUN
ejpam-5427	9	9	of	of	ADP
ejpam-5427	9	10	the	the	DET
ejpam-5427	9	11	modified	modify	VERB
ejpam-5427	9	12	iteration	iteration	NOUN
ejpam-5427	9	13	approach	approach	NOUN
ejpam-5427	9	14	in	in	ADP
ejpam-5427	9	15	providing	provide	VERB
ejpam-5427	9	16	precise	precise	ADJ
ejpam-5427	9	17	solutions	solution	NOUN
ejpam-5427	9	18	for	for	ADP
ejpam-5427	9	19	nonlinear	nonlinear	ADJ
ejpam-5427	9	20	jerk	jerk	PROPN
ejpam-5427	9	21	equations	equation	NOUN
ejpam-5427	9	22	,	,	PUNCT
ejpam-5427	9	23	paving	pave	VERB
ejpam-5427	9	24	the	the	DET
ejpam-5427	9	25	way	way	NOUN
ejpam-5427	9	26	for	for	ADP
ejpam-5427	9	27	its	its	PRON
ejpam-5427	9	28	application	application	NOUN
ejpam-5427	9	29	in	in	ADP
ejpam-5427	9	30	a	a	DET
ejpam-5427	9	31	wide	wide	ADJ
ejpam-5427	9	32	range	range	NOUN
ejpam-5427	9	33	of	of	ADP
ejpam-5427	9	34	oscillation	oscillation	NOUN
ejpam-5427	9	35	problems	problem	NOUN
ejpam-5427	9	36	within	within	ADP
ejpam-5427	9	37	nonlinear	nonlinear	ADJ
ejpam-5427	9	38	sciences	science	NOUN
ejpam-5427	9	39	and	and	CCONJ
ejpam-5427	9	40	engineering	engineering	NOUN
ejpam-5427	9	41	.	.	PUNCT
ejpam-5427	10	1	2020	2020	NUM
ejpam-5427	10	2	mathematics	mathematic	NOUN
ejpam-5427	10	3	subject	subject	NOUN
ejpam-5427	10	4	classifications	classification	NOUN
ejpam-5427	10	5	:	:	PUNCT
ejpam-5427	10	6	34a34	34a34	NUM
ejpam-5427	10	7	,	,	PUNCT
ejpam-5427	10	8	34c15	34c15	NUM
ejpam-5427	10	9	,	,	PUNCT
ejpam-5427	10	10	34c25	34c25	NUM
ejpam-5427	10	11	,	,	PUNCT
ejpam-5427	10	12	35l65	35l65	NUM
ejpam-5427	10	13	,	,	PUNCT
ejpam-5427	10	14	37n30	37n30	NUM
ejpam-5427	10	15	key	key	ADJ
ejpam-5427	10	16	words	word	NOUN
ejpam-5427	10	17	and	and	CCONJ
ejpam-5427	10	18	phrases	phrase	NOUN
ejpam-5427	10	19	:	:	PUNCT
ejpam-5427	10	20	modified	modify	VERB
ejpam-5427	10	21	iteration	iteration	NOUN
ejpam-5427	10	22	method	method	NOUN
ejpam-5427	10	23	,	,	PUNCT
ejpam-5427	10	24	third	third	ADJ
ejpam-5427	10	25	-	-	PUNCT
ejpam-5427	10	26	order	order	NOUN
ejpam-5427	10	27	jerk	jerk	NOUN
ejpam-5427	10	28	equations	equation	NOUN
ejpam-5427	10	29	,	,	PUNCT
ejpam-5427	10	30	analytical	analytical	ADJ
ejpam-5427	10	31	solutions	solution	NOUN
ejpam-5427	10	32	,	,	PUNCT
ejpam-5427	10	33	nonlinear	nonlinear	ADJ
ejpam-5427	10	34	oscillator	oscillator	NOUN
ejpam-5427	10	35	,	,	PUNCT
ejpam-5427	10	36	exact	exact	ADJ
ejpam-5427	10	37	solution	solution	NOUN
ejpam-5427	10	38	1	1	NUM
ejpam-5427	10	39	.	.	PUNCT
ejpam-5427	11	1	introduction	introduction	NOUN
ejpam-5427	11	2	differential	differential	NOUN
ejpam-5427	11	3	equations	equation	NOUN
ejpam-5427	11	4	are	be	AUX
ejpam-5427	11	5	widely	widely	ADV
ejpam-5427	11	6	employed	employ	VERB
ejpam-5427	11	7	to	to	PART
ejpam-5427	11	8	describe	describe	VERB
ejpam-5427	11	9	the	the	DET
ejpam-5427	11	10	evolution	evolution	NOUN
ejpam-5427	11	11	of	of	ADP
ejpam-5427	11	12	complex	complex	ADJ
ejpam-5427	11	13	systems	system	NOUN
ejpam-5427	11	14	in	in	ADP
ejpam-5427	11	15	many	many	ADJ
ejpam-5427	11	16	fields	field	NOUN
ejpam-5427	11	17	,	,	PUNCT
ejpam-5427	11	18	including	include	VERB
ejpam-5427	11	19	physics	physics	NOUN
ejpam-5427	11	20	and	and	CCONJ
ejpam-5427	11	21	engineering	engineering	NOUN
ejpam-5427	11	22	.	.	PUNCT
ejpam-5427	12	1	nonlinear	nonlinear	ADJ
ejpam-5427	12	2	differential	differential	ADJ
ejpam-5427	12	3	equations	equation	NOUN
ejpam-5427	12	4	play	play	VERB
ejpam-5427	12	5	a	a	DET
ejpam-5427	12	6	crucial	crucial	ADJ
ejpam-5427	12	7	role	role	NOUN
ejpam-5427	12	8	in	in	ADP
ejpam-5427	12	9	modeling	model	VERB
ejpam-5427	12	10	various	various	ADJ
ejpam-5427	12	11	scientific	scientific	ADJ
ejpam-5427	12	12	phenomena	phenomenon	NOUN
ejpam-5427	12	13	and	and	CCONJ
ejpam-5427	12	14	have	have	VERB
ejpam-5427	12	15	many	many	ADJ
ejpam-5427	12	16	applications	application	NOUN
ejpam-5427	12	17	in	in	ADP
ejpam-5427	12	18	various	various	ADJ
ejpam-5427	12	19	branches	branch	NOUN
ejpam-5427	12	20	of	of	ADP
ejpam-5427	12	21	science	science	NOUN
ejpam-5427	12	22	.	.	PUNCT
ejpam-5427	13	1	researchers	researcher	NOUN
ejpam-5427	13	2	seek	seek	VERB
ejpam-5427	13	3	effective	effective	ADJ
ejpam-5427	13	4	solutions	solution	NOUN
ejpam-5427	13	5	to	to	ADP
ejpam-5427	13	6	such	such	ADJ
ejpam-5427	13	7	problems	problem	NOUN
ejpam-5427	13	8	using	use	VERB
ejpam-5427	13	9	analytical	analytical	ADJ
ejpam-5427	13	10	or	or	CCONJ
ejpam-5427	13	11	numerical	numerical	ADJ
ejpam-5427	13	12	approaches	approach	NOUN
ejpam-5427	13	13	.	.	PUNCT
ejpam-5427	14	1	recently	recently	ADV
ejpam-5427	14	2	,	,	PUNCT
ejpam-5427	14	3	there	there	PRON
ejpam-5427	14	4	has	have	AUX
ejpam-5427	14	5	been	be	AUX
ejpam-5427	14	6	an	an	DET
ejpam-5427	14	7	increasing	increase	VERB
ejpam-5427	14	8	interest	interest	NOUN
ejpam-5427	14	9	in	in	ADP
ejpam-5427	14	10	analytical	analytical	ADJ
ejpam-5427	14	11	solutions	solution	NOUN
ejpam-5427	14	12	for	for	ADP
ejpam-5427	14	13	nonlinear	nonlinear	ADJ
ejpam-5427	14	14	differential	differential	ADJ
ejpam-5427	14	15	equations	equation	NOUN
ejpam-5427	14	16	.	.	PUNCT
ejpam-5427	15	1	the	the	DET
ejpam-5427	15	2	key	key	ADJ
ejpam-5427	15	3	issue	issue	NOUN
ejpam-5427	15	4	in	in	ADP
ejpam-5427	15	5	studying	study	VERB
ejpam-5427	15	6	nonlinear	nonlinear	ADJ
ejpam-5427	15	7	differential	differential	ADJ
ejpam-5427	15	8	equations	equation	NOUN
ejpam-5427	15	9	is	be	AUX
ejpam-5427	15	10	finding	find	VERB
ejpam-5427	15	11	∗corresponding	∗corresponde	VERB
ejpam-5427	15	12	author	author	NOUN
ejpam-5427	15	13	.	.	PUNCT
ejpam-5427	16	1	doi	doi	NOUN
ejpam-5427	16	2	:	:	PUNCT
ejpam-5427	16	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5427	https://doi.org/10.29020/nybg.ejpam.v17i4.5427	ADJ
ejpam-5427	16	4	email	email	NOUN
ejpam-5427	16	5	addresses	address	NOUN
ejpam-5427	16	6	:	:	PUNCT
ejpam-5427	16	7	gamalm2010@yahoo.com	gamalm2010@yahoo.com	X
ejpam-5427	16	8	(	(	PUNCT
ejpam-5427	16	9	g.	g.	PROPN
ejpam-5427	16	10	m.	m.	PROPN
ejpam-5427	16	11	ismail	ismail	PROPN
ejpam-5427	16	12	)	)	PUNCT
ejpam-5427	16	13	,	,	PUNCT
ejpam-5427	16	14	shingl6600@gmail.com	shingl6600@gmail.com	X
ejpam-5427	17	1	(	(	PUNCT
ejpam-5427	17	2	m.	m.	NOUN
ejpam-5427	17	3	i.	i.	PROPN
ejpam-5427	17	4	yamani	yamani	PROPN
ejpam-5427	17	5	)	)	PUNCT
ejpam-5427	17	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5427	17	7	3622	3622	NUM
ejpam-5427	18	1	copyright	copyright	NOUN
ejpam-5427	18	2	:	:	PUNCT
ejpam-5427	18	3	©	©	PROPN
ejpam-5427	18	4	2024	2024	NUM
ejpam-5427	18	5	the	the	DET
ejpam-5427	18	6	author(s	author(s	NOUN
ejpam-5427	18	7	)	)	PUNCT
ejpam-5427	18	8	.	.	PUNCT
ejpam-5427	19	1	(	(	PUNCT
ejpam-5427	19	2	cc	cc	NOUN
ejpam-5427	19	3	by	by	ADP
ejpam-5427	19	4	-	-	PUNCT
ejpam-5427	19	5	nc	nc	PROPN
ejpam-5427	19	6	4.0	4.0	NUM
ejpam-5427	19	7	)	)	PUNCT
ejpam-5427	19	8	g.	g.	PROPN
ejpam-5427	19	9	m.	m.	PROPN
ejpam-5427	19	10	ismail	ismail	PROPN
ejpam-5427	19	11	,	,	PUNCT
ejpam-5427	19	12	m.	m.	NOUN
ejpam-5427	19	13	i.	i.	PROPN
ejpam-5427	19	14	yamani	yamani	PROPN
ejpam-5427	19	15	/	/	SYM
ejpam-5427	19	16	eur	eur	PROPN
ejpam-5427	19	17	.	.	PUNCT
ejpam-5427	20	1	j.	j.	PROPN
ejpam-5427	20	2	pure	pure	PROPN
ejpam-5427	20	3	appl	appl	PROPN
ejpam-5427	20	4	.	.	PROPN
ejpam-5427	20	5	math	math	PROPN
ejpam-5427	20	6	,	,	PUNCT
ejpam-5427	20	7	17	17	NUM
ejpam-5427	20	8	(	(	PUNCT
ejpam-5427	20	9	4	4	NUM
ejpam-5427	20	10	)	)	PUNCT
ejpam-5427	20	11	(	(	PUNCT
ejpam-5427	20	12	2024	2024	NUM
ejpam-5427	20	13	)	)	PUNCT
ejpam-5427	20	14	,	,	PUNCT
ejpam-5427	20	15	3622	3622	NUM
ejpam-5427	20	16	-	-	SYM
ejpam-5427	20	17	3641	3641	NUM
ejpam-5427	20	18	3623	3623	NUM
ejpam-5427	20	19	the	the	DET
ejpam-5427	20	20	exact	exact	ADJ
ejpam-5427	20	21	solutions	solution	NOUN
ejpam-5427	20	22	.	.	PUNCT
ejpam-5427	21	1	on	on	ADP
ejpam-5427	21	2	the	the	DET
ejpam-5427	21	3	other	other	ADJ
ejpam-5427	21	4	hand	hand	NOUN
ejpam-5427	21	5	,	,	PUNCT
ejpam-5427	21	6	computing	compute	VERB
ejpam-5427	21	7	the	the	DET
ejpam-5427	21	8	exact	exact	ADJ
ejpam-5427	21	9	results	result	NOUN
ejpam-5427	21	10	can	can	AUX
ejpam-5427	21	11	be	be	AUX
ejpam-5427	21	12	challenging	challenge	VERB
ejpam-5427	21	13	,	,	PUNCT
ejpam-5427	21	14	especially	especially	ADV
ejpam-5427	21	15	in	in	ADP
ejpam-5427	21	16	equations	equation	NOUN
ejpam-5427	21	17	with	with	ADP
ejpam-5427	21	18	a	a	DET
ejpam-5427	21	19	high	high	ADJ
ejpam-5427	21	20	degree	degree	NOUN
ejpam-5427	21	21	of	of	ADP
ejpam-5427	21	22	nonlinearity	nonlinearity	NOUN
ejpam-5427	21	23	,	,	PUNCT
ejpam-5427	21	24	mainly	mainly	ADV
ejpam-5427	21	25	using	use	VERB
ejpam-5427	21	26	traditional	traditional	ADJ
ejpam-5427	21	27	analytical	analytical	ADJ
ejpam-5427	21	28	techniques	technique	NOUN
ejpam-5427	21	29	.	.	PUNCT
ejpam-5427	22	1	to	to	PART
ejpam-5427	22	2	overcome	overcome	VERB
ejpam-5427	22	3	this	this	DET
ejpam-5427	22	4	problem	problem	NOUN
ejpam-5427	22	5	,	,	PUNCT
ejpam-5427	22	6	many	many	ADJ
ejpam-5427	22	7	novel	novel	ADJ
ejpam-5427	22	8	approaches	approach	NOUN
ejpam-5427	22	9	are	be	AUX
ejpam-5427	22	10	presented	present	VERB
ejpam-5427	22	11	to	to	PART
ejpam-5427	22	12	deal	deal	VERB
ejpam-5427	22	13	with	with	ADP
ejpam-5427	22	14	this	this	DET
ejpam-5427	22	15	shortage	shortage	NOUN
ejpam-5427	22	16	.	.	PUNCT
ejpam-5427	23	1	for	for	ADP
ejpam-5427	23	2	example	example	NOUN
ejpam-5427	23	3	,	,	PUNCT
ejpam-5427	23	4	harmonic	harmonic	ADJ
ejpam-5427	23	5	balance	balance	NOUN
ejpam-5427	23	6	method	method	NOUN
ejpam-5427	23	7	[	[	X
ejpam-5427	23	8	1–3	1–3	NOUN
ejpam-5427	23	9	]	]	X
ejpam-5427	23	10	,	,	PUNCT
ejpam-5427	23	11	variational	variational	ADJ
ejpam-5427	23	12	iteration	iteration	NOUN
ejpam-5427	23	13	method	method	NOUN
ejpam-5427	23	14	[	[	X
ejpam-5427	23	15	4	4	NUM
ejpam-5427	23	16	,	,	PUNCT
ejpam-5427	23	17	5	5	NUM
ejpam-5427	23	18	]	]	PUNCT
ejpam-5427	23	19	,	,	PUNCT
ejpam-5427	23	20	hamiltonian	hamiltonian	ADJ
ejpam-5427	23	21	approach	approach	NOUN
ejpam-5427	23	22	[	[	X
ejpam-5427	23	23	6	6	NUM
ejpam-5427	23	24	,	,	PUNCT
ejpam-5427	23	25	7	7	NUM
ejpam-5427	23	26	]	]	PUNCT
ejpam-5427	23	27	,	,	PUNCT
ejpam-5427	23	28	modified	modify	VERB
ejpam-5427	23	29	algebraic	algebraic	ADJ
ejpam-5427	23	30	method	method	NOUN
ejpam-5427	23	31	[	[	X
ejpam-5427	23	32	8	8	NUM
ejpam-5427	23	33	,	,	PUNCT
ejpam-5427	23	34	9	9	NUM
ejpam-5427	23	35	]	]	PUNCT
ejpam-5427	23	36	,	,	PUNCT
ejpam-5427	23	37	global	global	ADJ
ejpam-5427	23	38	residue	residue	NOUN
ejpam-5427	23	39	harmonic	harmonic	ADJ
ejpam-5427	23	40	balance	balance	NOUN
ejpam-5427	23	41	method	method	NOUN
ejpam-5427	23	42	[	[	X
ejpam-5427	23	43	10	10	NUM
ejpam-5427	23	44	,	,	PUNCT
ejpam-5427	23	45	11	11	NUM
ejpam-5427	23	46	]	]	PUNCT
ejpam-5427	23	47	,	,	PUNCT
ejpam-5427	23	48	energy	energy	NOUN
ejpam-5427	23	49	balance	balance	NOUN
ejpam-5427	23	50	method	method	NOUN
ejpam-5427	23	51	[	[	X
ejpam-5427	23	52	12–14	12–14	NUM
ejpam-5427	23	53	]	]	X
ejpam-5427	23	54	.	.	PUNCT
ejpam-5427	24	1	linearizing	linearize	VERB
ejpam-5427	24	2	method	method	NOUN
ejpam-5427	24	3	[	[	X
ejpam-5427	24	4	15	15	NUM
ejpam-5427	24	5	]	]	PUNCT
ejpam-5427	24	6	,	,	PUNCT
ejpam-5427	24	7	multiple	multiple	ADJ
ejpam-5427	24	8	scales	scale	NOUN
ejpam-5427	24	9	method	method	NOUN
ejpam-5427	24	10	[	[	X
ejpam-5427	24	11	16	16	NUM
ejpam-5427	24	12	]	]	PUNCT
ejpam-5427	24	13	,	,	PUNCT
ejpam-5427	24	14	non	non	ADJ
ejpam-5427	24	15	-	-	ADJ
ejpam-5427	24	16	perturbative	perturbative	ADJ
ejpam-5427	24	17	approach	approach	NOUN
ejpam-5427	24	18	[	[	X
ejpam-5427	24	19	17	17	NUM
ejpam-5427	24	20	,	,	PUNCT
ejpam-5427	24	21	18	18	NUM
ejpam-5427	24	22	]	]	PUNCT
ejpam-5427	24	23	,	,	PUNCT
ejpam-5427	24	24	adomian	adomian	NOUN
ejpam-5427	24	25	decomposition	decomposition	NOUN
ejpam-5427	24	26	method	method	NOUN
ejpam-5427	24	27	[	[	X
ejpam-5427	24	28	19	19	NUM
ejpam-5427	24	29	]	]	PUNCT
ejpam-5427	24	30	,	,	PUNCT
ejpam-5427	24	31	optimal	optimal	ADJ
ejpam-5427	24	32	variational	variational	ADJ
ejpam-5427	24	33	iteration	iteration	NOUN
ejpam-5427	24	34	method	method	NOUN
ejpam-5427	24	35	[	[	X
ejpam-5427	24	36	20	20	NUM
ejpam-5427	24	37	]	]	PUNCT
ejpam-5427	24	38	and	and	CCONJ
ejpam-5427	24	39	galerkin	galerkin	PROPN
ejpam-5427	24	40	method	method	NOUN
ejpam-5427	24	41	[	[	X
ejpam-5427	24	42	21	21	NUM
ejpam-5427	24	43	]	]	PUNCT
ejpam-5427	24	44	.	.	PUNCT
ejpam-5427	25	1	these	these	DET
ejpam-5427	25	2	analytical	analytical	ADJ
ejpam-5427	25	3	approaches	approach	NOUN
ejpam-5427	25	4	have	have	AUX
ejpam-5427	25	5	been	be	AUX
ejpam-5427	25	6	extensively	extensively	ADV
ejpam-5427	25	7	utilized	utilize	VERB
ejpam-5427	25	8	to	to	PART
ejpam-5427	25	9	examine	examine	VERB
ejpam-5427	25	10	the	the	DET
ejpam-5427	25	11	frequency	frequency	NOUN
ejpam-5427	25	12	and	and	CCONJ
ejpam-5427	25	13	periodic	periodic	ADJ
ejpam-5427	25	14	solutions	solution	NOUN
ejpam-5427	25	15	of	of	ADP
ejpam-5427	25	16	nonlinear	nonlinear	ADJ
ejpam-5427	25	17	oscillators	oscillator	NOUN
ejpam-5427	25	18	.	.	PUNCT
ejpam-5427	26	1	nonlinear	nonlinear	ADJ
ejpam-5427	26	2	third	third	ADJ
ejpam-5427	26	3	-	-	PUNCT
ejpam-5427	26	4	order	order	NOUN
ejpam-5427	26	5	jerk	jerk	NOUN
ejpam-5427	26	6	equations	equation	NOUN
ejpam-5427	26	7	are	be	AUX
ejpam-5427	26	8	useful	useful	ADJ
ejpam-5427	26	9	for	for	ADP
ejpam-5427	26	10	analyzing	analyze	VERB
ejpam-5427	26	11	structures	structure	NOUN
ejpam-5427	26	12	with	with	ADP
ejpam-5427	26	13	rotating	rotate	VERB
ejpam-5427	26	14	and	and	CCONJ
ejpam-5427	26	15	translating	translate	VERB
ejpam-5427	26	16	movements	movement	NOUN
ejpam-5427	26	17	,	,	PUNCT
ejpam-5427	26	18	such	such	ADJ
ejpam-5427	26	19	as	as	ADP
ejpam-5427	26	20	machine	machine	NOUN
ejpam-5427	26	21	tools	tool	NOUN
ejpam-5427	26	22	or	or	CCONJ
ejpam-5427	26	23	robots	robot	NOUN
ejpam-5427	26	24	[	[	X
ejpam-5427	26	25	22	22	NUM
ejpam-5427	26	26	]	]	PUNCT
ejpam-5427	26	27	.	.	PUNCT
ejpam-5427	27	1	nonlinear	nonlinear	ADJ
ejpam-5427	27	2	third	third	ADJ
ejpam-5427	27	3	-	-	PUNCT
ejpam-5427	27	4	order	order	NOUN
ejpam-5427	27	5	jerk	jerk	NOUN
ejpam-5427	27	6	equations	equation	NOUN
ejpam-5427	27	7	are	be	AUX
ejpam-5427	27	8	differential	differential	ADJ
ejpam-5427	27	9	equations	equation	NOUN
ejpam-5427	27	10	that	that	PRON
ejpam-5427	27	11	describe	describe	VERB
ejpam-5427	27	12	the	the	DET
ejpam-5427	27	13	evolution	evolution	NOUN
ejpam-5427	27	14	of	of	ADP
ejpam-5427	27	15	a	a	DET
ejpam-5427	27	16	system	system	NOUN
ejpam-5427	27	17	’s	’s	PART
ejpam-5427	27	18	jerk	jerk	NOUN
ejpam-5427	27	19	,	,	PUNCT
ejpam-5427	27	20	which	which	PRON
ejpam-5427	27	21	is	be	AUX
ejpam-5427	27	22	the	the	DET
ejpam-5427	27	23	rate	rate	NOUN
ejpam-5427	27	24	of	of	ADP
ejpam-5427	27	25	change	change	NOUN
ejpam-5427	27	26	of	of	ADP
ejpam-5427	27	27	acceleration	acceleration	NOUN
ejpam-5427	27	28	.	.	PUNCT
ejpam-5427	28	1	in	in	ADP
ejpam-5427	28	2	simpler	simple	ADJ
ejpam-5427	28	3	terms	term	NOUN
ejpam-5427	28	4	,	,	PUNCT
ejpam-5427	28	5	it	it	PRON
ejpam-5427	28	6	represents	represent	VERB
ejpam-5427	28	7	the	the	DET
ejpam-5427	28	8	”	"	PUNCT
ejpam-5427	28	9	snap	snap	NOUN
ejpam-5427	28	10	”	"	PUNCT
ejpam-5427	28	11	or	or	CCONJ
ejpam-5427	28	12	”	"	PUNCT
ejpam-5427	28	13	jolt	jolt	NOUN
ejpam-5427	28	14	”	"	PUNCT
ejpam-5427	28	15	felt	feel	VERB
ejpam-5427	28	16	when	when	SCONJ
ejpam-5427	28	17	acceleration	acceleration	NOUN
ejpam-5427	28	18	changes	change	VERB
ejpam-5427	28	19	abruptly	abruptly	ADV
ejpam-5427	28	20	.	.	PUNCT
ejpam-5427	29	1	jerk	jerk	NOUN
ejpam-5427	29	2	equations	equation	NOUN
ejpam-5427	29	3	are	be	AUX
ejpam-5427	29	4	powerful	powerful	ADJ
ejpam-5427	29	5	tools	tool	NOUN
ejpam-5427	29	6	for	for	ADP
ejpam-5427	29	7	modeling	model	VERB
ejpam-5427	29	8	complex	complex	ADJ
ejpam-5427	29	9	dynamical	dynamical	ADJ
ejpam-5427	29	10	systems	system	NOUN
ejpam-5427	29	11	exhibiting	exhibit	VERB
ejpam-5427	29	12	rich	rich	ADJ
ejpam-5427	29	13	and	and	CCONJ
ejpam-5427	29	14	often	often	ADV
ejpam-5427	29	15	unpredictable	unpredictable	ADJ
ejpam-5427	29	16	behavior	behavior	NOUN
ejpam-5427	29	17	.	.	PUNCT
ejpam-5427	30	1	understanding	understand	VERB
ejpam-5427	30	2	their	their	PRON
ejpam-5427	30	3	properties	property	NOUN
ejpam-5427	30	4	and	and	CCONJ
ejpam-5427	30	5	developing	develop	VERB
ejpam-5427	30	6	effective	effective	ADJ
ejpam-5427	30	7	methods	method	NOUN
ejpam-5427	30	8	for	for	ADP
ejpam-5427	30	9	their	their	PRON
ejpam-5427	30	10	analysis	analysis	NOUN
ejpam-5427	30	11	is	be	AUX
ejpam-5427	30	12	crucial	crucial	ADJ
ejpam-5427	30	13	for	for	ADP
ejpam-5427	30	14	advancing	advance	VERB
ejpam-5427	30	15	our	our	PRON
ejpam-5427	30	16	knowledge	knowledge	NOUN
ejpam-5427	30	17	in	in	ADP
ejpam-5427	30	18	various	various	ADJ
ejpam-5427	30	19	scientific	scientific	ADJ
ejpam-5427	30	20	and	and	CCONJ
ejpam-5427	30	21	engineering	engineering	NOUN
ejpam-5427	30	22	disciplines	discipline	NOUN
ejpam-5427	30	23	.	.	PUNCT
ejpam-5427	31	1	nonlinear	nonlinear	ADJ
ejpam-5427	31	2	third	third	ADJ
ejpam-5427	31	3	-	-	PUNCT
ejpam-5427	31	4	order	order	NOUN
ejpam-5427	31	5	jerk	jerk	NOUN
ejpam-5427	31	6	equations	equation	NOUN
ejpam-5427	31	7	may	may	AUX
ejpam-5427	31	8	explain	explain	VERB
ejpam-5427	31	9	a	a	DET
ejpam-5427	31	10	variety	variety	NOUN
ejpam-5427	31	11	of	of	ADP
ejpam-5427	31	12	physical	physical	ADJ
ejpam-5427	31	13	issues	issue	NOUN
ejpam-5427	31	14	,	,	PUNCT
ejpam-5427	31	15	including	include	VERB
ejpam-5427	31	16	third	third	ADJ
ejpam-5427	31	17	-	-	PUNCT
ejpam-5427	31	18	order	order	NOUN
ejpam-5427	31	19	mechanical	mechanical	ADJ
ejpam-5427	31	20	oscillators	oscillator	NOUN
ejpam-5427	31	21	[	[	X
ejpam-5427	31	22	23	23	NUM
ejpam-5427	31	23	]	]	PUNCT
ejpam-5427	31	24	.	.	PUNCT
ejpam-5427	32	1	nowadays	nowadays	ADV
ejpam-5427	32	2	,	,	PUNCT
ejpam-5427	32	3	due	due	ADP
ejpam-5427	32	4	to	to	ADP
ejpam-5427	32	5	the	the	DET
ejpam-5427	32	6	need	need	NOUN
ejpam-5427	32	7	of	of	ADP
ejpam-5427	32	8	knowing	know	VERB
ejpam-5427	32	9	the	the	DET
ejpam-5427	32	10	analytical	analytical	ADJ
ejpam-5427	32	11	solutions	solution	NOUN
ejpam-5427	32	12	of	of	ADP
ejpam-5427	32	13	the	the	DET
ejpam-5427	32	14	nonlinear	nonlinear	ADJ
ejpam-5427	32	15	jerk	jerk	PROPN
ejpam-5427	32	16	equations	equation	NOUN
ejpam-5427	32	17	.	.	PUNCT
ejpam-5427	33	1	several	several	ADJ
ejpam-5427	33	2	diverse	diverse	ADJ
ejpam-5427	33	3	techniques	technique	NOUN
ejpam-5427	33	4	have	have	AUX
ejpam-5427	33	5	been	be	AUX
ejpam-5427	33	6	proposed	propose	VERB
ejpam-5427	33	7	to	to	PART
ejpam-5427	33	8	find	find	VERB
ejpam-5427	33	9	the	the	DET
ejpam-5427	33	10	analytical	analytical	ADJ
ejpam-5427	33	11	solutions	solution	NOUN
ejpam-5427	33	12	of	of	ADP
ejpam-5427	33	13	like	like	ADP
ejpam-5427	33	14	these	these	DET
ejpam-5427	33	15	problems	problem	NOUN
ejpam-5427	33	16	such	such	ADJ
ejpam-5427	33	17	as	as	ADP
ejpam-5427	33	18	block	block	NOUN
ejpam-5427	33	19	method	method	NOUN
ejpam-5427	33	20	[	[	X
ejpam-5427	33	21	24	24	NUM
ejpam-5427	33	22	]	]	PUNCT
ejpam-5427	33	23	,	,	PUNCT
ejpam-5427	33	24	harmonic	harmonic	ADJ
ejpam-5427	33	25	balance	balance	NOUN
ejpam-5427	33	26	method	method	NOUN
ejpam-5427	33	27	[	[	X
ejpam-5427	33	28	25	25	NUM
ejpam-5427	33	29	,	,	PUNCT
ejpam-5427	33	30	26	26	NUM
ejpam-5427	33	31	]	]	PUNCT
ejpam-5427	33	32	,	,	PUNCT
ejpam-5427	33	33	homotopy	homotopy	VERB
ejpam-5427	33	34	perturbation	perturbation	NOUN
ejpam-5427	33	35	method	method	NOUN
ejpam-5427	33	36	[	[	X
ejpam-5427	33	37	27	27	NUM
ejpam-5427	33	38	]	]	PUNCT
ejpam-5427	33	39	,	,	PUNCT
ejpam-5427	33	40	parameter	parameter	NOUN
ejpam-5427	33	41	perturbation	perturbation	NOUN
ejpam-5427	33	42	method	method	NOUN
ejpam-5427	33	43	[	[	X
ejpam-5427	33	44	28	28	NUM
ejpam-5427	33	45	]	]	PUNCT
ejpam-5427	33	46	,	,	PUNCT
ejpam-5427	33	47	mickens	micken	VERB
ejpam-5427	33	48	iteration	iteration	NOUN
ejpam-5427	33	49	method	method	NOUN
ejpam-5427	33	50	[	[	X
ejpam-5427	33	51	29	29	NUM
ejpam-5427	33	52	]	]	X
ejpam-5427	33	53	,	,	PUNCT
ejpam-5427	33	54	linstedt	linstedt	ADJ
ejpam-5427	33	55	-	-	PUNCT
ejpam-5427	33	56	poincare	poincare	PROPN
ejpam-5427	33	57	methods	method	NOUN
ejpam-5427	33	58	[	[	X
ejpam-5427	33	59	30	30	NUM
ejpam-5427	33	60	]	]	PUNCT
ejpam-5427	33	61	,	,	PUNCT
ejpam-5427	33	62	residue	residue	NOUN
ejpam-5427	33	63	harmonic	harmonic	ADJ
ejpam-5427	33	64	balance	balance	NOUN
ejpam-5427	33	65	method	method	NOUN
ejpam-5427	33	66	[	[	X
ejpam-5427	33	67	31	31	NUM
ejpam-5427	33	68	]	]	PUNCT
ejpam-5427	33	69	,	,	PUNCT
ejpam-5427	33	70	multiple	multiple	ADJ
ejpam-5427	33	71	scales	scale	NOUN
ejpam-5427	33	72	lindstedt	lindstedt	PROPN
ejpam-5427	33	73	-	-	PUNCT
ejpam-5427	33	74	poincare	poincare	PROPN
ejpam-5427	33	75	method	method	NOUN
ejpam-5427	33	76	[	[	X
ejpam-5427	33	77	32	32	NUM
ejpam-5427	33	78	]	]	PUNCT
ejpam-5427	33	79	,	,	PUNCT
ejpam-5427	33	80	differential	differential	ADJ
ejpam-5427	33	81	transform	transform	NOUN
ejpam-5427	33	82	method	method	NOUN
ejpam-5427	33	83	[	[	X
ejpam-5427	33	84	33	33	NUM
ejpam-5427	33	85	]	]	PUNCT
ejpam-5427	33	86	,	,	PUNCT
ejpam-5427	33	87	modified	modify	VERB
ejpam-5427	33	88	harmonic	harmonic	ADJ
ejpam-5427	33	89	balance	balance	NOUN
ejpam-5427	33	90	method	method	NOUN
ejpam-5427	33	91	[	[	X
ejpam-5427	33	92	34	34	NUM
ejpam-5427	33	93	]	]	PUNCT
ejpam-5427	33	94	,	,	PUNCT
ejpam-5427	33	95	variational	variational	ADJ
ejpam-5427	33	96	iteration	iteration	NOUN
ejpam-5427	33	97	method	method	NOUN
ejpam-5427	33	98	[	[	X
ejpam-5427	33	99	35	35	NUM
ejpam-5427	33	100	]	]	PUNCT
ejpam-5427	33	101	and	and	CCONJ
ejpam-5427	33	102	homotopy	homotopy	VERB
ejpam-5427	33	103	asymptotic	asymptotic	ADJ
ejpam-5427	33	104	method	method	NOUN
ejpam-5427	33	105	[	[	X
ejpam-5427	33	106	36	36	NUM
ejpam-5427	33	107	]	]	PUNCT
ejpam-5427	33	108	to	to	PART
ejpam-5427	33	109	solve	solve	VERB
ejpam-5427	33	110	the	the	DET
ejpam-5427	33	111	present	present	ADJ
ejpam-5427	33	112	problems	problem	NOUN
ejpam-5427	33	113	.	.	PUNCT
ejpam-5427	34	1	recently	recently	ADV
ejpam-5427	34	2	,	,	PUNCT
ejpam-5427	34	3	ismail	ismail	PROPN
ejpam-5427	34	4	and	and	CCONJ
ejpam-5427	34	5	abu	abu	PROPN
ejpam-5427	34	6	-	-	PUNCT
ejpam-5427	34	7	zinadah	zinadah	PROPN
ejpam-5427	34	8	[	[	X
ejpam-5427	34	9	37	37	NUM
ejpam-5427	34	10	]	]	PUNCT
ejpam-5427	34	11	used	use	VERB
ejpam-5427	34	12	the	the	DET
ejpam-5427	34	13	global	global	ADJ
ejpam-5427	34	14	error	error	NOUN
ejpam-5427	34	15	minimization	minimization	NOUN
ejpam-5427	34	16	method	method	NOUN
ejpam-5427	34	17	for	for	ADP
ejpam-5427	34	18	solving	solve	VERB
ejpam-5427	34	19	the	the	DET
ejpam-5427	34	20	current	current	ADJ
ejpam-5427	34	21	problems	problem	NOUN
ejpam-5427	34	22	.	.	PUNCT
ejpam-5427	35	1	in	in	ADP
ejpam-5427	35	2	this	this	DET
ejpam-5427	35	3	study	study	NOUN
ejpam-5427	35	4	,	,	PUNCT
ejpam-5427	35	5	we	we	PRON
ejpam-5427	35	6	apply	apply	VERB
ejpam-5427	35	7	the	the	DET
ejpam-5427	35	8	modified	modify	VERB
ejpam-5427	35	9	iteration	iteration	NOUN
ejpam-5427	35	10	technique	technique	NOUN
ejpam-5427	35	11	,	,	PUNCT
ejpam-5427	35	12	a	a	DET
ejpam-5427	35	13	powerful	powerful	ADJ
ejpam-5427	35	14	analytical	analytical	ADJ
ejpam-5427	35	15	method	method	NOUN
ejpam-5427	35	16	with	with	ADP
ejpam-5427	35	17	high	high	ADJ
ejpam-5427	35	18	accuracy	accuracy	NOUN
ejpam-5427	35	19	and	and	CCONJ
ejpam-5427	35	20	efficiency	efficiency	NOUN
ejpam-5427	35	21	,	,	PUNCT
ejpam-5427	35	22	to	to	PART
ejpam-5427	35	23	obtain	obtain	VERB
ejpam-5427	35	24	higher	high	ADJ
ejpam-5427	35	25	-	-	PUNCT
ejpam-5427	35	26	order	order	NOUN
ejpam-5427	35	27	analytic	analytic	ADJ
ejpam-5427	35	28	approximations	approximation	NOUN
ejpam-5427	35	29	for	for	ADP
ejpam-5427	35	30	nonlinear	nonlinear	ADJ
ejpam-5427	35	31	jerk	jerk	PROPN
ejpam-5427	35	32	equations	equation	NOUN
ejpam-5427	35	33	.	.	PUNCT
ejpam-5427	36	1	the	the	DET
ejpam-5427	36	2	primary	primary	ADJ
ejpam-5427	36	3	advantage	advantage	NOUN
ejpam-5427	36	4	of	of	ADP
ejpam-5427	36	5	this	this	DET
ejpam-5427	36	6	method	method	NOUN
ejpam-5427	36	7	lies	lie	VERB
ejpam-5427	36	8	in	in	ADP
ejpam-5427	36	9	its	its	PRON
ejpam-5427	36	10	ability	ability	NOUN
ejpam-5427	36	11	to	to	PART
ejpam-5427	36	12	provide	provide	VERB
ejpam-5427	36	13	both	both	DET
ejpam-5427	36	14	simplicity	simplicity	NOUN
ejpam-5427	36	15	and	and	CCONJ
ejpam-5427	36	16	accuracy	accuracy	NOUN
ejpam-5427	36	17	when	when	SCONJ
ejpam-5427	36	18	solving	solve	VERB
ejpam-5427	36	19	higher	high	ADJ
ejpam-5427	36	20	-	-	PUNCT
ejpam-5427	36	21	order	order	NOUN
ejpam-5427	36	22	differential	differential	ADJ
ejpam-5427	36	23	equations	equation	NOUN
ejpam-5427	36	24	.	.	PUNCT
ejpam-5427	37	1	the	the	DET
ejpam-5427	37	2	numerical	numerical	ADJ
ejpam-5427	37	3	solution	solution	NOUN
ejpam-5427	37	4	is	be	AUX
ejpam-5427	37	5	obtained	obtain	VERB
ejpam-5427	37	6	using	use	VERB
ejpam-5427	37	7	the	the	DET
ejpam-5427	37	8	fourth	fourth	ADJ
ejpam-5427	37	9	-	-	PUNCT
ejpam-5427	37	10	order	order	NOUN
ejpam-5427	37	11	runge	runge	NOUN
ejpam-5427	37	12	-	-	PUNCT
ejpam-5427	37	13	kutta	kutta	NOUN
ejpam-5427	37	14	method	method	NOUN
ejpam-5427	37	15	.	.	PUNCT
ejpam-5427	38	1	a	a	DET
ejpam-5427	38	2	comparison	comparison	NOUN
ejpam-5427	38	3	between	between	ADP
ejpam-5427	38	4	the	the	DET
ejpam-5427	38	5	analytical	analytical	ADJ
ejpam-5427	38	6	and	and	CCONJ
ejpam-5427	38	7	numerical	numerical	ADJ
ejpam-5427	38	8	solutions	solution	NOUN
ejpam-5427	38	9	,	,	PUNCT
ejpam-5427	38	10	presented	present	VERB
ejpam-5427	38	11	through	through	ADP
ejpam-5427	38	12	tables	table	NOUN
ejpam-5427	38	13	and	and	CCONJ
ejpam-5427	38	14	corresponding	corresponding	ADJ
ejpam-5427	38	15	figures	figure	NOUN
ejpam-5427	38	16	,	,	PUNCT
ejpam-5427	38	17	emphasizes	emphasize	VERB
ejpam-5427	38	18	the	the	DET
ejpam-5427	38	19	accuracy	accuracy	NOUN
ejpam-5427	38	20	of	of	ADP
ejpam-5427	38	21	the	the	DET
ejpam-5427	38	22	modified	modify	VERB
ejpam-5427	38	23	iteration	iteration	NOUN
ejpam-5427	38	24	technique	technique	NOUN
ejpam-5427	38	25	.	.	PUNCT
ejpam-5427	39	1	2	2	X
ejpam-5427	39	2	.	.	X
ejpam-5427	39	3	the	the	DET
ejpam-5427	39	4	iteration	iteration	NOUN
ejpam-5427	39	5	procedure	procedure	NOUN
ejpam-5427	39	6	consider	consider	VERB
ejpam-5427	39	7	a	a	DET
ejpam-5427	39	8	non	non	ADJ
ejpam-5427	39	9	-	-	ADJ
ejpam-5427	39	10	linear	linear	ADJ
ejpam-5427	39	11	equation	equation	NOUN
ejpam-5427	39	12	ẍ+	ẍ+	PROPN
ejpam-5427	39	13	f(x	f(x	PROPN
ejpam-5427	39	14	,	,	PUNCT
ejpam-5427	39	15	ẋ	ẋ	PROPN
ejpam-5427	39	16	,	,	PUNCT
ejpam-5427	39	17	ẍ	ẍ	X
ejpam-5427	39	18	)	)	PUNCT
ejpam-5427	40	1	=	=	SYM
ejpam-5427	40	2	0	0	NUM
ejpam-5427	40	3	,	,	PUNCT
ejpam-5427	40	4	x(0	x(0	PROPN
ejpam-5427	40	5	)	)	PUNCT
ejpam-5427	40	6	=	=	SYM
ejpam-5427	41	1	a	a	PRON
ejpam-5427	41	2	,	,	PUNCT
ejpam-5427	41	3	ẋ(0	ẋ(0	X
ejpam-5427	41	4	)	)	PUNCT
ejpam-5427	41	5	=	=	SYM
ejpam-5427	42	1	0	0	X
ejpam-5427	42	2	.	.	PUNCT
ejpam-5427	43	1	(	(	PUNCT
ejpam-5427	43	2	1	1	X
ejpam-5427	43	3	)	)	PUNCT
ejpam-5427	43	4	g.	g.	PROPN
ejpam-5427	43	5	m.	m.	PROPN
ejpam-5427	43	6	ismail	ismail	PROPN
ejpam-5427	43	7	,	,	PUNCT
ejpam-5427	43	8	m.	m.	NOUN
ejpam-5427	43	9	i.	i.	PROPN
ejpam-5427	43	10	yamani	yamani	PROPN
ejpam-5427	43	11	/	/	SYM
ejpam-5427	43	12	eur	eur	PROPN
ejpam-5427	43	13	.	.	PUNCT
ejpam-5427	44	1	j.	j.	PROPN
ejpam-5427	44	2	pure	pure	PROPN
ejpam-5427	44	3	appl	appl	PROPN
ejpam-5427	44	4	.	.	PROPN
ejpam-5427	44	5	math	math	PROPN
ejpam-5427	44	6	,	,	PUNCT
ejpam-5427	44	7	17	17	NUM
ejpam-5427	44	8	(	(	PUNCT
ejpam-5427	44	9	4	4	NUM
ejpam-5427	44	10	)	)	PUNCT
ejpam-5427	44	11	(	(	PUNCT
ejpam-5427	44	12	2024	2024	NUM
ejpam-5427	44	13	)	)	PUNCT
ejpam-5427	44	14	,	,	PUNCT
ejpam-5427	44	15	3622	3622	NUM
ejpam-5427	44	16	-	-	SYM
ejpam-5427	44	17	3641	3641	NUM
ejpam-5427	44	18	3624	3624	NUM
ejpam-5427	44	19	rewrite	rewrite	VERB
ejpam-5427	44	20	eq	eq	ADP
ejpam-5427	44	21	.	.	PUNCT
ejpam-5427	45	1	(	(	PUNCT
ejpam-5427	45	2	1	1	X
ejpam-5427	45	3	)	)	PUNCT
ejpam-5427	45	4	to	to	PART
ejpam-5427	45	5	be	be	AUX
ejpam-5427	45	6	in	in	ADP
ejpam-5427	45	7	the	the	DET
ejpam-5427	45	8	form	form	NOUN
ejpam-5427	45	9	:	:	PUNCT
ejpam-5427	45	10	ẍ+	ẍ+	PUNCT
ejpam-5427	45	11	ω2x	ω2x	SYM
ejpam-5427	45	12	=	=	SYM
ejpam-5427	45	13	ω2x−	ω2x−	PROPN
ejpam-5427	45	14	f(x	f(x	PROPN
ejpam-5427	45	15	,	,	PUNCT
ejpam-5427	45	16	ẋ	ẋ	PROPN
ejpam-5427	45	17	,	,	PUNCT
ejpam-5427	45	18	ẍ	ẍ	X
ejpam-5427	45	19	)	)	PUNCT
ejpam-5427	46	1	≊	≊	PRON
ejpam-5427	47	1	f	f	PROPN
ejpam-5427	47	2	(	(	PUNCT
ejpam-5427	47	3	xk	xk	PROPN
ejpam-5427	47	4	,	,	PUNCT
ejpam-5427	47	5	ẋk	ẋk	PROPN
ejpam-5427	47	6	,	,	PUNCT
ejpam-5427	47	7	ẍk	ẍk	PROPN
ejpam-5427	47	8	)	)	PUNCT
ejpam-5427	47	9	,	,	PUNCT
ejpam-5427	47	10	(	(	PUNCT
ejpam-5427	47	11	2	2	X
ejpam-5427	47	12	)	)	PUNCT
ejpam-5427	47	13	where	where	SCONJ
ejpam-5427	47	14	ẋ	ẋ	PROPN
ejpam-5427	47	15	and	and	CCONJ
ejpam-5427	47	16	ẍ	ẍ	PROPN
ejpam-5427	47	17	represent	represent	VERB
ejpam-5427	47	18	the	the	DET
ejpam-5427	47	19	first	first	ADJ
ejpam-5427	47	20	and	and	CCONJ
ejpam-5427	47	21	second	second	ADJ
ejpam-5427	47	22	derivatives	derivative	NOUN
ejpam-5427	47	23	with	with	ADP
ejpam-5427	47	24	respect	respect	NOUN
ejpam-5427	47	25	to	to	ADP
ejpam-5427	47	26	time	time	NOUN
ejpam-5427	47	27	,	,	PUNCT
ejpam-5427	47	28	respectively	respectively	ADV
ejpam-5427	47	29	,	,	PUNCT
ejpam-5427	47	30	and	and	CCONJ
ejpam-5427	47	31	ω	ω	PROPN
ejpam-5427	47	32	is	be	AUX
ejpam-5427	47	33	an	an	DET
ejpam-5427	47	34	unknown	unknown	ADJ
ejpam-5427	47	35	constant	constant	NOUN
ejpam-5427	47	36	.	.	PUNCT
ejpam-5427	48	1	according	accord	VERB
ejpam-5427	48	2	to	to	ADP
ejpam-5427	48	3	ref	ref	NOUN
ejpam-5427	48	4	[	[	X
ejpam-5427	48	5	38	38	NUM
ejpam-5427	48	6	]	]	PUNCT
ejpam-5427	48	7	,	,	PUNCT
ejpam-5427	48	8	eq	eq	NOUN
ejpam-5427	48	9	.	.	PUNCT
ejpam-5427	49	1	(	(	PUNCT
ejpam-5427	49	2	2	2	X
ejpam-5427	49	3	)	)	PUNCT
ejpam-5427	49	4	can	can	AUX
ejpam-5427	49	5	be	be	AUX
ejpam-5427	49	6	rewritten	rewrite	VERB
ejpam-5427	49	7	as	as	ADP
ejpam-5427	49	8	ẍk+1	ẍk+1	NOUN
ejpam-5427	49	9	+	+	CCONJ
ejpam-5427	49	10	ω2	ω2	ADJ
ejpam-5427	49	11	kxk+1	kxk+1	X
ejpam-5427	49	12	=	=	SYM
ejpam-5427	49	13	f	f	X
ejpam-5427	49	14	(	(	PUNCT
ejpam-5427	49	15	xk	xk	PROPN
ejpam-5427	49	16	,	,	PUNCT
ejpam-5427	49	17	ẋk	ẋk	PROPN
ejpam-5427	49	18	,	,	PUNCT
ejpam-5427	49	19	ẍk	ẍk	PROPN
ejpam-5427	49	20	)	)	PUNCT
ejpam-5427	49	21	,	,	PUNCT
ejpam-5427	49	22	k	k	X
ejpam-5427	49	23	=	=	SYM
ejpam-5427	49	24	0	0	NUM
ejpam-5427	49	25	,	,	PUNCT
ejpam-5427	49	26	1	1	NUM
ejpam-5427	49	27	,	,	PUNCT
ejpam-5427	49	28	2	2	NUM
ejpam-5427	49	29	,	,	PUNCT
ejpam-5427	49	30	...	...	PUNCT
ejpam-5427	49	31	,	,	PUNCT
ejpam-5427	49	32	(	(	PUNCT
ejpam-5427	49	33	3	3	X
ejpam-5427	49	34	)	)	PUNCT
ejpam-5427	49	35	and	and	CCONJ
ejpam-5427	49	36	the	the	DET
ejpam-5427	49	37	imputes	impute	NOUN
ejpam-5427	49	38	of	of	ADP
ejpam-5427	49	39	starting	start	VERB
ejpam-5427	49	40	functions	function	NOUN
ejpam-5427	49	41	are	be	AUX
ejpam-5427	49	42	x0(t	x0(t	NUM
ejpam-5427	49	43	)	)	PUNCT
ejpam-5427	49	44	=	=	PUNCT
ejpam-5427	49	45	a	a	DET
ejpam-5427	49	46	cosω0	cosω0	NOUN
ejpam-5427	49	47	t.	t.	NOUN
ejpam-5427	49	48	(	(	PUNCT
ejpam-5427	49	49	4	4	X
ejpam-5427	49	50	)	)	PUNCT
ejpam-5427	49	51	it	it	PRON
ejpam-5427	49	52	is	be	AUX
ejpam-5427	49	53	further	far	ADV
ejpam-5427	49	54	required	require	VERB
ejpam-5427	49	55	that	that	SCONJ
ejpam-5427	49	56	for	for	ADP
ejpam-5427	49	57	each	each	DET
ejpam-5427	49	58	k	k	NOUN
ejpam-5427	49	59	,	,	PUNCT
ejpam-5427	49	60	the	the	DET
ejpam-5427	49	61	solution	solution	NOUN
ejpam-5427	49	62	to	to	ADP
ejpam-5427	49	63	eq	eq	PROPN
ejpam-5427	49	64	.	.	PUNCT
ejpam-5427	50	1	(	(	PUNCT
ejpam-5427	50	2	3	3	NUM
ejpam-5427	50	3	)	)	PUNCT
ejpam-5427	50	4	,	,	PUNCT
ejpam-5427	50	5	is	be	AUX
ejpam-5427	50	6	to	to	PART
ejpam-5427	50	7	satisfy	satisfy	VERB
ejpam-5427	50	8	initial	initial	ADJ
ejpam-5427	50	9	conditions	condition	NOUN
ejpam-5427	50	10	xk+1(0	xk+1(0	PUNCT
ejpam-5427	50	11	)	)	PUNCT
ejpam-5427	51	1	=	=	SYM
ejpam-5427	51	2	a	a	PRON
ejpam-5427	51	3	,	,	PUNCT
ejpam-5427	51	4	ẋk+1(0	ẋk+1(0	PROPN
ejpam-5427	51	5	)	)	PUNCT
ejpam-5427	51	6	=	=	SYM
ejpam-5427	52	1	0	0	X
ejpam-5427	52	2	.	.	PUNCT
ejpam-5427	53	1	(	(	PUNCT
ejpam-5427	53	2	5	5	NUM
ejpam-5427	53	3	)	)	PUNCT
ejpam-5427	53	4	3	3	NUM
ejpam-5427	53	5	.	.	PUNCT
ejpam-5427	53	6	applications	application	NOUN
ejpam-5427	53	7	in	in	ADP
ejpam-5427	53	8	this	this	DET
ejpam-5427	53	9	section	section	NOUN
ejpam-5427	53	10	,	,	PUNCT
ejpam-5427	53	11	we	we	PRON
ejpam-5427	53	12	illustrate	illustrate	VERB
ejpam-5427	53	13	the	the	DET
ejpam-5427	53	14	fundamental	fundamental	ADJ
ejpam-5427	53	15	concept	concept	NOUN
ejpam-5427	53	16	of	of	ADP
ejpam-5427	53	17	the	the	DET
ejpam-5427	53	18	modified	modify	VERB
ejpam-5427	53	19	iteration	iteration	NOUN
ejpam-5427	53	20	approach	approach	NOUN
ejpam-5427	53	21	by	by	ADP
ejpam-5427	53	22	considering	consider	VERB
ejpam-5427	53	23	the	the	DET
ejpam-5427	53	24	following	follow	VERB
ejpam-5427	53	25	non	non	ADJ
ejpam-5427	53	26	-	-	ADJ
ejpam-5427	53	27	linear	linear	ADJ
ejpam-5427	53	28	differential	differential	ADJ
ejpam-5427	53	29	equation	equation	NOUN
ejpam-5427	53	30	:	:	PUNCT
ejpam-5427	53	31	...	...	PUNCT
ejpam-5427	54	1	x	x	X
ejpam-5427	55	1	+	+	NUM
ejpam-5427	55	2	f	f	X
ejpam-5427	55	3	(	(	PUNCT
ejpam-5427	55	4	x	x	NOUN
ejpam-5427	55	5	,	,	PUNCT
ejpam-5427	55	6	ẋ	ẋ	PROPN
ejpam-5427	55	7	,	,	PUNCT
ejpam-5427	55	8	ẍ	ẍ	X
ejpam-5427	55	9	)	)	PUNCT
ejpam-5427	55	10	,	,	PUNCT
ejpam-5427	55	11	x(0	x(0	PROPN
ejpam-5427	55	12	)	)	PUNCT
ejpam-5427	55	13	=	=	SYM
ejpam-5427	55	14	0	0	NUM
ejpam-5427	55	15	,	,	PUNCT
ejpam-5427	55	16	ẋ(0	ẋ(0	X
ejpam-5427	55	17	)	)	PUNCT
ejpam-5427	55	18	=	=	SYM
ejpam-5427	55	19	a	a	PRON
ejpam-5427	55	20	,	,	PUNCT
ejpam-5427	55	21	ẍ(0	ẍ(0	PROPN
ejpam-5427	55	22	)	)	PUNCT
ejpam-5427	55	23	=	=	SYM
ejpam-5427	56	1	0	0	X
ejpam-5427	56	2	.	.	PUNCT
ejpam-5427	57	1	(	(	PUNCT
ejpam-5427	57	2	6	6	NUM
ejpam-5427	57	3	)	)	PUNCT
ejpam-5427	57	4	following	follow	VERB
ejpam-5427	57	5	[	[	X
ejpam-5427	57	6	3	3	NUM
ejpam-5427	57	7	]	]	PUNCT
ejpam-5427	57	8	,	,	PUNCT
ejpam-5427	57	9	the	the	DET
ejpam-5427	57	10	general	general	ADJ
ejpam-5427	57	11	non	non	ADJ
ejpam-5427	57	12	-	-	ADJ
ejpam-5427	57	13	linear	linear	ADJ
ejpam-5427	57	14	third	third	ADJ
ejpam-5427	57	15	order	order	NOUN
ejpam-5427	57	16	jerk	jerk	NOUN
ejpam-5427	57	17	equation	equation	NOUN
ejpam-5427	57	18	has	have	VERB
ejpam-5427	57	19	the	the	DET
ejpam-5427	57	20	form	form	NOUN
ejpam-5427	57	21	...	...	PUNCT
ejpam-5427	58	1	x	x	SYM
ejpam-5427	58	2	=	=	PRON
ejpam-5427	58	3	−γ	−γ	NOUN
ejpam-5427	58	4	ẋ−	ẋ−	NOUN
ejpam-5427	58	5	αẋ3	αẋ3	NUM
ejpam-5427	58	6	−	−	NOUN
ejpam-5427	58	7	βx2ẋ+	βx2ẋ+	NOUN
ejpam-5427	58	8	δxẋẍ−	δxẋẍ−	X
ejpam-5427	58	9	εẋ	εẋ	ADJ
ejpam-5427	58	10	ẍ2	ẍ2	NOUN
ejpam-5427	58	11	,	,	PUNCT
ejpam-5427	58	12	(	(	PUNCT
ejpam-5427	58	13	7	7	X
ejpam-5427	58	14	)	)	PUNCT
ejpam-5427	58	15	with	with	ADP
ejpam-5427	58	16	x(0	x(0	PROPN
ejpam-5427	58	17	)	)	PUNCT
ejpam-5427	58	18	=	=	SYM
ejpam-5427	58	19	0	0	NUM
ejpam-5427	58	20	,	,	PUNCT
ejpam-5427	58	21	ẋ(0	ẋ(0	X
ejpam-5427	58	22	)	)	PUNCT
ejpam-5427	58	23	=	=	SYM
ejpam-5427	58	24	a	a	PRON
ejpam-5427	58	25	,	,	PUNCT
ejpam-5427	58	26	ẍ(0	ẍ(0	PROPN
ejpam-5427	58	27	)	)	PUNCT
ejpam-5427	59	1	=	=	SYM
ejpam-5427	59	2	0	0	X
ejpam-5427	59	3	.	.	PUNCT
ejpam-5427	60	1	(	(	PUNCT
ejpam-5427	60	2	8)	8)	NUM
ejpam-5427	60	3	where	where	SCONJ
ejpam-5427	60	4	the	the	DET
ejpam-5427	60	5	parameters	parameter	NOUN
ejpam-5427	60	6	α	α	PRON
ejpam-5427	60	7	,	,	PUNCT
ejpam-5427	60	8	β	β	X
ejpam-5427	60	9	,	,	PUNCT
ejpam-5427	60	10	γ	γ	PROPN
ejpam-5427	60	11	,	,	PUNCT
ejpam-5427	60	12	δ	δ	PROPN
ejpam-5427	60	13	and	and	CCONJ
ejpam-5427	60	14	ε	ε	PROPN
ejpam-5427	60	15	are	be	AUX
ejpam-5427	60	16	constants	constant	NOUN
ejpam-5427	60	17	.	.	PUNCT
ejpam-5427	61	1	3.1	3.1	NUM
ejpam-5427	61	2	.	.	PUNCT
ejpam-5427	62	1	jerk	jerk	NOUN
ejpam-5427	62	2	function	function	NOUN
ejpam-5427	62	3	containing	contain	VERB
ejpam-5427	62	4	time	time	NOUN
ejpam-5427	62	5	’s	’s	PART
ejpam-5427	62	6	velocity	velocity	NOUN
ejpam-5427	62	7	times	time	NOUN
ejpam-5427	62	8	acceleration	acceleration	NOUN
ejpam-5427	62	9	and	and	CCONJ
ejpam-5427	62	10	velocity	velocity	NOUN
ejpam-5427	62	11	in	in	ADP
ejpam-5427	62	12	this	this	DET
ejpam-5427	62	13	case	case	NOUN
ejpam-5427	62	14	at	at	ADP
ejpam-5427	62	15	γ	γ	PROPN
ejpam-5427	62	16	=	=	SYM
ejpam-5427	62	17	δ	δ	PROPN
ejpam-5427	62	18	=	=	SYM
ejpam-5427	62	19	1	1	NUM
ejpam-5427	62	20	,	,	PUNCT
ejpam-5427	62	21	α	α	NOUN
ejpam-5427	62	22	=	=	PUNCT
ejpam-5427	62	23	β	β	X
ejpam-5427	62	24	=	=	PUNCT
ejpam-5427	62	25	ε	ε	PROPN
ejpam-5427	62	26	=	=	SYM
ejpam-5427	62	27	0	0	PROPN
ejpam-5427	62	28	,	,	PUNCT
ejpam-5427	62	29	in	in	ADP
ejpam-5427	62	30	eq	eq	ADP
ejpam-5427	62	31	.	.	PUNCT
ejpam-5427	63	1	(	(	PUNCT
ejpam-5427	63	2	7	7	NUM
ejpam-5427	63	3	)	)	PUNCT
ejpam-5427	63	4	,	,	PUNCT
ejpam-5427	63	5	the	the	DET
ejpam-5427	63	6	non	non	ADJ
ejpam-5427	63	7	-	-	ADJ
ejpam-5427	63	8	linear	linear	ADJ
ejpam-5427	63	9	equation	equation	NOUN
ejpam-5427	63	10	is	be	AUX
ejpam-5427	63	11	in	in	ADP
ejpam-5427	63	12	the	the	DET
ejpam-5427	63	13	following	following	NOUN
ejpam-5427	63	14	[	[	X
ejpam-5427	63	15	1	1	NUM
ejpam-5427	63	16	]	]	PUNCT
ejpam-5427	63	17	:	:	PUNCT
ejpam-5427	63	18	...	...	PUNCT
ejpam-5427	64	1	x	x	X
ejpam-5427	65	1	+	+	CCONJ
ejpam-5427	65	2	ẋ−	ẋ−	PROPN
ejpam-5427	65	3	xẋẍ	xẋẍ	PROPN
ejpam-5427	65	4	=	=	SYM
ejpam-5427	65	5	0	0	PROPN
ejpam-5427	65	6	,	,	PUNCT
ejpam-5427	65	7	x(0	x(0	PROPN
ejpam-5427	65	8	)	)	PUNCT
ejpam-5427	65	9	=	=	SYM
ejpam-5427	65	10	0	0	NUM
ejpam-5427	65	11	,	,	PUNCT
ejpam-5427	65	12	ẋ(0	ẋ(0	X
ejpam-5427	65	13	)	)	PUNCT
ejpam-5427	65	14	=	=	SYM
ejpam-5427	65	15	a	a	PRON
ejpam-5427	65	16	,	,	PUNCT
ejpam-5427	65	17	ẍ(0	ẍ(0	PROPN
ejpam-5427	65	18	)	)	PUNCT
ejpam-5427	65	19	=	=	SYM
ejpam-5427	66	1	0	0	X
ejpam-5427	66	2	.	.	PUNCT
ejpam-5427	67	1	(	(	PUNCT
ejpam-5427	67	2	9	9	NUM
ejpam-5427	67	3	)	)	PUNCT
ejpam-5427	67	4	eq	eq	NOUN
ejpam-5427	67	5	.	.	PUNCT
ejpam-5427	68	1	(	(	PUNCT
ejpam-5427	68	2	9	9	X
ejpam-5427	68	3	)	)	PUNCT
ejpam-5427	68	4	can	can	AUX
ejpam-5427	68	5	be	be	AUX
ejpam-5427	68	6	rewritten	rewrite	VERB
ejpam-5427	68	7	in	in	ADP
ejpam-5427	68	8	the	the	DET
ejpam-5427	68	9	form	form	NOUN
ejpam-5427	68	10	ẋ	ẋ	PUNCT
ejpam-5427	69	1	=	=	SYM
ejpam-5427	69	2	y	y	PROPN
ejpam-5427	69	3	,	,	PUNCT
ejpam-5427	69	4	ẏ	ẏ	PROPN
ejpam-5427	69	5	=	=	SYM
ejpam-5427	69	6	ẍ	ẍ	PROPN
ejpam-5427	69	7	,	,	PUNCT
ejpam-5427	69	8	(	(	PUNCT
ejpam-5427	69	9	10	10	NUM
ejpam-5427	69	10	)	)	PUNCT
ejpam-5427	69	11	g.	g.	PROPN
ejpam-5427	69	12	m.	m.	PROPN
ejpam-5427	69	13	ismail	ismail	PROPN
ejpam-5427	69	14	,	,	PUNCT
ejpam-5427	69	15	m.	m.	NOUN
ejpam-5427	69	16	i.	i.	PROPN
ejpam-5427	69	17	yamani	yamani	PROPN
ejpam-5427	69	18	/	/	SYM
ejpam-5427	69	19	eur	eur	PROPN
ejpam-5427	69	20	.	.	PUNCT
ejpam-5427	70	1	j.	j.	PROPN
ejpam-5427	70	2	pure	pure	PROPN
ejpam-5427	70	3	appl	appl	PROPN
ejpam-5427	70	4	.	.	PROPN
ejpam-5427	70	5	math	math	PROPN
ejpam-5427	70	6	,	,	PUNCT
ejpam-5427	70	7	17	17	NUM
ejpam-5427	70	8	(	(	PUNCT
ejpam-5427	70	9	4	4	NUM
ejpam-5427	70	10	)	)	PUNCT
ejpam-5427	70	11	(	(	PUNCT
ejpam-5427	70	12	2024	2024	NUM
ejpam-5427	70	13	)	)	PUNCT
ejpam-5427	70	14	,	,	PUNCT
ejpam-5427	70	15	3622	3622	NUM
ejpam-5427	70	16	-	-	SYM
ejpam-5427	70	17	3641	3641	NUM
ejpam-5427	70	18	3625	3625	NUM
ejpam-5427	70	19	then	then	ADV
ejpam-5427	70	20	eq	eq	ADP
ejpam-5427	70	21	.	.	PUNCT
ejpam-5427	71	1	(	(	PUNCT
ejpam-5427	71	2	10	10	NUM
ejpam-5427	71	3	)	)	PUNCT
ejpam-5427	71	4	becomes	become	VERB
ejpam-5427	71	5	ÿ	ÿ	PROPN
ejpam-5427	71	6	+	+	CCONJ
ejpam-5427	72	1	y	y	PROPN
ejpam-5427	72	2	−	−	PROPN
ejpam-5427	72	3	ȳyẏ	ȳyẏ	NOUN
ejpam-5427	72	4	=	=	SYM
ejpam-5427	72	5	0	0	NUM
ejpam-5427	72	6	,	,	PUNCT
ejpam-5427	72	7	y(0	y(0	PROPN
ejpam-5427	72	8	)	)	PUNCT
ejpam-5427	72	9	=	=	SYM
ejpam-5427	72	10	a	a	PROPN
ejpam-5427	72	11	,	,	PUNCT
ejpam-5427	72	12	ẏ(0	ẏ(0	NUM
ejpam-5427	72	13	)	)	PUNCT
ejpam-5427	72	14	=	=	SYM
ejpam-5427	73	1	0	0	X
ejpam-5427	73	2	.	.	PUNCT
ejpam-5427	74	1	(	(	PUNCT
ejpam-5427	74	2	11	11	NUM
ejpam-5427	74	3	)	)	PUNCT
ejpam-5427	74	4	where	where	SCONJ
ejpam-5427	74	5	ȳ	ȳ	PROPN
ejpam-5427	74	6	is	be	AUX
ejpam-5427	74	7	the	the	DET
ejpam-5427	74	8	integration	integration	NOUN
ejpam-5427	74	9	of	of	ADP
ejpam-5427	74	10	x	x	SYM
ejpam-5427	74	11	ÿ	ÿ	PROPN
ejpam-5427	74	12	+	+	NUM
ejpam-5427	74	13	ω2y	ω2y	X
ejpam-5427	74	14	=	=	PUNCT
ejpam-5427	74	15	ω2y	ω2y	PUNCT
ejpam-5427	74	16	−	−	PROPN
ejpam-5427	75	1	y	y	PROPN
ejpam-5427	75	2	+	+	PROPN
ejpam-5427	75	3	ȳyẏ.	ȳyẏ.	PROPN
ejpam-5427	75	4	(	(	PUNCT
ejpam-5427	75	5	12	12	NUM
ejpam-5427	75	6	)	)	PUNCT
ejpam-5427	75	7	the	the	DET
ejpam-5427	75	8	iteration	iteration	NOUN
ejpam-5427	75	9	technique	technique	NOUN
ejpam-5427	75	10	according	accord	VERB
ejpam-5427	75	11	to	to	ADP
ejpam-5427	75	12	eq	eq	PROPN
ejpam-5427	75	13	.	.	PUNCT
ejpam-5427	76	1	(	(	PUNCT
ejpam-5427	76	2	3	3	X
ejpam-5427	76	3	)	)	PUNCT
ejpam-5427	76	4	is	be	AUX
ejpam-5427	76	5	ÿk+1	ÿk+1	NOUN
ejpam-5427	77	1	+	+	CCONJ
ejpam-5427	77	2	ω2	ω2	ADJ
ejpam-5427	77	3	kyk+1	kyk+1	PROPN
ejpam-5427	77	4	=	=	SYM
ejpam-5427	77	5	ω2	ω2	ADJ
ejpam-5427	77	6	kyk	kyk	PROPN
ejpam-5427	77	7	−	−	PROPN
ejpam-5427	77	8	yk	yk	PROPN
ejpam-5427	77	9	+	+	CCONJ
ejpam-5427	77	10	ȳkykẏk	ȳkykẏk	PROPN
ejpam-5427	77	11	.	.	PUNCT
ejpam-5427	77	12	(	(	PUNCT
ejpam-5427	77	13	13	13	NUM
ejpam-5427	77	14	)	)	PUNCT
ejpam-5427	77	15	3.1.1	3.1.1	NUM
ejpam-5427	77	16	.	.	PUNCT
ejpam-5427	78	1	first	first	ADJ
ejpam-5427	78	2	iteration	iteration	NOUN
ejpam-5427	78	3	solution	solution	NOUN
ejpam-5427	78	4	for	for	ADP
ejpam-5427	78	5	the	the	DET
ejpam-5427	78	6	first	first	ADJ
ejpam-5427	78	7	iteration	iteration	NOUN
ejpam-5427	78	8	,	,	PUNCT
ejpam-5427	78	9	at	at	ADP
ejpam-5427	78	10	k	k	PROPN
ejpam-5427	78	11	=	=	SYM
ejpam-5427	78	12	0	0	PROPN
ejpam-5427	78	13	,	,	PUNCT
ejpam-5427	78	14	we	we	PRON
ejpam-5427	78	15	get	get	VERB
ejpam-5427	78	16	ÿ1	ÿ1	ADJ
ejpam-5427	78	17	+	+	CCONJ
ejpam-5427	79	1	ω2	ω2	ADJ
ejpam-5427	79	2	0y1	0y1	NUM
ejpam-5427	80	1	=	=	SYM
ejpam-5427	80	2	ω2	ω2	NUM
ejpam-5427	80	3	0y0	0y0	NUM
ejpam-5427	81	1	−	−	PROPN
ejpam-5427	81	2	y0	y0	PROPN
ejpam-5427	81	3	+	+	PROPN
ejpam-5427	81	4	ȳ0y0ẏ0	ȳ0y0ẏ0	PROPN
ejpam-5427	81	5	.	.	PUNCT
ejpam-5427	82	1	(	(	PUNCT
ejpam-5427	82	2	14	14	NUM
ejpam-5427	82	3	)	)	PUNCT
ejpam-5427	82	4	according	accord	VERB
ejpam-5427	82	5	to	to	ADP
ejpam-5427	82	6	eq	eq	PROPN
ejpam-5427	82	7	.	.	PUNCT
ejpam-5427	83	1	(	(	PUNCT
ejpam-5427	83	2	4	4	NUM
ejpam-5427	83	3	)	)	PUNCT
ejpam-5427	83	4	,	,	PUNCT
ejpam-5427	83	5	we	we	PRON
ejpam-5427	83	6	have	have	VERB
ejpam-5427	83	7	y0(t	y0(t	VERB
ejpam-5427	83	8	)	)	PUNCT
ejpam-5427	83	9	=	=	PUNCT
ejpam-5427	83	10	a	a	DET
ejpam-5427	83	11	cosω0	cosω0	NOUN
ejpam-5427	83	12	t.	t.	NOUN
ejpam-5427	83	13	(	(	PUNCT
ejpam-5427	83	14	15	15	NUM
ejpam-5427	83	15	)	)	PUNCT
ejpam-5427	83	16	inserting	insert	VERB
ejpam-5427	83	17	eq	eq	X
ejpam-5427	83	18	.	.	PUNCT
ejpam-5427	84	1	(	(	PUNCT
ejpam-5427	84	2	15	15	NUM
ejpam-5427	84	3	)	)	PUNCT
ejpam-5427	84	4	into	into	ADP
ejpam-5427	84	5	eq	eq	NOUN
ejpam-5427	84	6	.	.	PUNCT
ejpam-5427	85	1	(	(	PUNCT
ejpam-5427	85	2	14	14	NUM
ejpam-5427	85	3	)	)	PUNCT
ejpam-5427	85	4	,	,	PUNCT
ejpam-5427	85	5	to	to	PART
ejpam-5427	85	6	obtain	obtain	VERB
ejpam-5427	85	7	ÿ1	ÿ1	NOUN
ejpam-5427	85	8	+	+	CCONJ
ejpam-5427	85	9	ω2	ω2	ADJ
ejpam-5427	85	10	0y1	0y1	NUM
ejpam-5427	85	11	=	=	SYM
ejpam-5427	85	12	1	1	NUM
ejpam-5427	85	13	4	4	NUM
ejpam-5427	85	14	(	(	PUNCT
ejpam-5427	85	15	−4a−a3	−4a−a3	NOUN
ejpam-5427	85	16	+	+	NUM
ejpam-5427	85	17	4aω2	4aω2	NUM
ejpam-5427	85	18	0	0	NUM
ejpam-5427	85	19	)	)	PUNCT
ejpam-5427	85	20	cos(ω0t)−	cos(ω0t)−	PROPN
ejpam-5427	85	21	a3	a3	VERB
ejpam-5427	85	22	4	4	NUM
ejpam-5427	85	23	cos(3ω0	cos(3ω0	NOUN
ejpam-5427	85	24	t	t	NOUN
ejpam-5427	85	25	)	)	PUNCT
ejpam-5427	85	26	.	.	PUNCT
ejpam-5427	86	1	(	(	PUNCT
ejpam-5427	86	2	16	16	NUM
ejpam-5427	86	3	)	)	PUNCT
ejpam-5427	86	4	a	a	DET
ejpam-5427	86	5	secular	secular	ADJ
ejpam-5427	86	6	term	term	NOUN
ejpam-5427	86	7	is	be	AUX
ejpam-5427	86	8	a	a	DET
ejpam-5427	86	9	term	term	NOUN
ejpam-5427	86	10	in	in	ADP
ejpam-5427	86	11	the	the	DET
ejpam-5427	86	12	solution	solution	NOUN
ejpam-5427	86	13	that	that	PRON
ejpam-5427	86	14	grows	grow	VERB
ejpam-5427	86	15	linearly	linearly	ADV
ejpam-5427	86	16	or	or	CCONJ
ejpam-5427	86	17	polynomially	polynomially	ADV
ejpam-5427	86	18	with	with	ADP
ejpam-5427	86	19	time	time	NOUN
ejpam-5427	86	20	.	.	PUNCT
ejpam-5427	87	1	secular	secular	ADJ
ejpam-5427	87	2	terms	term	NOUN
ejpam-5427	87	3	often	often	ADV
ejpam-5427	87	4	arise	arise	VERB
ejpam-5427	87	5	when	when	SCONJ
ejpam-5427	87	6	using	use	VERB
ejpam-5427	87	7	naive	naive	ADJ
ejpam-5427	87	8	perturbation	perturbation	NOUN
ejpam-5427	87	9	methods	method	NOUN
ejpam-5427	87	10	on	on	ADP
ejpam-5427	87	11	systems	system	NOUN
ejpam-5427	87	12	with	with	ADP
ejpam-5427	87	13	natural	natural	ADJ
ejpam-5427	87	14	frequencies	frequency	NOUN
ejpam-5427	87	15	that	that	PRON
ejpam-5427	87	16	are	be	AUX
ejpam-5427	87	17	close	close	ADJ
ejpam-5427	87	18	to	to	ADP
ejpam-5427	87	19	being	be	AUX
ejpam-5427	87	20	resonant	resonant	ADJ
ejpam-5427	87	21	with	with	ADP
ejpam-5427	87	22	the	the	DET
ejpam-5427	87	23	perturbation	perturbation	NOUN
ejpam-5427	87	24	frequency	frequency	NOUN
ejpam-5427	87	25	.	.	PUNCT
ejpam-5427	88	1	secular	secular	ADJ
ejpam-5427	88	2	terms	term	NOUN
ejpam-5427	88	3	are	be	AUX
ejpam-5427	88	4	undesirable	undesirable	ADJ
ejpam-5427	88	5	for	for	ADP
ejpam-5427	88	6	several	several	ADJ
ejpam-5427	88	7	reasons	reason	NOUN
ejpam-5427	88	8	,	,	PUNCT
ejpam-5427	88	9	for	for	ADP
ejpam-5427	88	10	example	example	NOUN
ejpam-5427	88	11	,	,	PUNCT
ejpam-5427	88	12	breakdown	breakdown	NOUN
ejpam-5427	88	13	of	of	ADP
ejpam-5427	88	14	perturbation	perturbation	NOUN
ejpam-5427	88	15	theory	theory	NOUN
ejpam-5427	88	16	and	and	CCONJ
ejpam-5427	88	17	loss	loss	NOUN
ejpam-5427	88	18	of	of	ADP
ejpam-5427	88	19	periodicity	periodicity	NOUN
ejpam-5427	88	20	:	:	PUNCT
ejpam-5427	88	21	to	to	PART
ejpam-5427	88	22	avoid	avoid	VERB
ejpam-5427	88	23	secular	secular	ADJ
ejpam-5427	88	24	term	term	NOUN
ejpam-5427	88	25	from	from	ADP
ejpam-5427	88	26	equation	equation	NOUN
ejpam-5427	88	27	(	(	PUNCT
ejpam-5427	88	28	16	16	NUM
ejpam-5427	88	29	)	)	PUNCT
ejpam-5427	88	30	,	,	PUNCT
ejpam-5427	88	31	we	we	PRON
ejpam-5427	88	32	obtain	obtain	VERB
ejpam-5427	88	33	ω0	ω0	ADV
ejpam-5427	88	34	=	=	SYM
ejpam-5427	88	35	1	1	NUM
ejpam-5427	88	36	2	2	NUM
ejpam-5427	88	37	√	√	NUM
ejpam-5427	88	38	4	4	NUM
ejpam-5427	88	39	+	+	NOUN
ejpam-5427	88	40	a2	a2	PROPN
ejpam-5427	88	41	.	.	PUNCT
ejpam-5427	89	1	(	(	PUNCT
ejpam-5427	89	2	17	17	NUM
ejpam-5427	89	3	)	)	PUNCT
ejpam-5427	89	4	solving	solve	VERB
ejpam-5427	89	5	eq	eq	NOUN
ejpam-5427	89	6	.	.	PUNCT
ejpam-5427	90	1	(	(	PUNCT
ejpam-5427	90	2	16	16	NUM
ejpam-5427	90	3	)	)	PUNCT
ejpam-5427	90	4	with	with	ADP
ejpam-5427	90	5	initial	initial	ADJ
ejpam-5427	90	6	conditions	condition	NOUN
ejpam-5427	90	7	(	(	PUNCT
ejpam-5427	90	8	5	5	NUM
ejpam-5427	90	9	)	)	PUNCT
ejpam-5427	90	10	,	,	PUNCT
ejpam-5427	90	11	the	the	DET
ejpam-5427	90	12	first	first	ADJ
ejpam-5427	90	13	approximate	approximate	ADJ
ejpam-5427	90	14	solution	solution	NOUN
ejpam-5427	90	15	y1	y1	NOUN
ejpam-5427	90	16	of	of	ADP
ejpam-5427	90	17	is	be	AUX
ejpam-5427	90	18	obtained	obtain	VERB
ejpam-5427	90	19	as	as	ADP
ejpam-5427	90	20	y1	y1	NOUN
ejpam-5427	90	21	=	=	SYM
ejpam-5427	90	22	(	(	PUNCT
ejpam-5427	90	23	a+	a+	PUNCT
ejpam-5427	90	24	a3	a3	NOUN
ejpam-5427	90	25	32ω2	32ω2	NUM
ejpam-5427	90	26	0	0	NUM
ejpam-5427	90	27	)	)	PUNCT
ejpam-5427	90	28	cos(ω1t)−	cos(ω1t)−	PROPN
ejpam-5427	90	29	a3	a3	VERB
ejpam-5427	90	30	32ω2	32ω2	NUM
ejpam-5427	90	31	0	0	NUM
ejpam-5427	90	32	cos(3ω1	cos(3ω1	PROPN
ejpam-5427	90	33	t	t	PROPN
ejpam-5427	90	34	)	)	PUNCT
ejpam-5427	90	35	.	.	PUNCT
ejpam-5427	91	1	(	(	PUNCT
ejpam-5427	91	2	18	18	NUM
ejpam-5427	91	3	)	)	PUNCT
ejpam-5427	91	4	3.1.2	3.1.2	NUM
ejpam-5427	91	5	.	.	PUNCT
ejpam-5427	92	1	second	second	ADJ
ejpam-5427	92	2	iteration	iteration	NOUN
ejpam-5427	92	3	solution	solution	NOUN
ejpam-5427	92	4	for	for	ADP
ejpam-5427	92	5	the	the	DET
ejpam-5427	92	6	second	second	ADJ
ejpam-5427	92	7	level	level	NOUN
ejpam-5427	92	8	of	of	ADP
ejpam-5427	92	9	iteration	iteration	NOUN
ejpam-5427	92	10	continuing	continue	VERB
ejpam-5427	92	11	to	to	ADP
ejpam-5427	92	12	k	k	PROPN
ejpam-5427	92	13	=	=	PUNCT
ejpam-5427	92	14	1	1	X
ejpam-5427	92	15	.	.	X
ejpam-5427	93	1	substituting	substitute	VERB
ejpam-5427	93	2	eq	eq	ADP
ejpam-5427	93	3	.	.	PUNCT
ejpam-5427	94	1	(	(	PUNCT
ejpam-5427	94	2	18	18	NUM
ejpam-5427	94	3	)	)	PUNCT
ejpam-5427	94	4	into	into	ADP
ejpam-5427	94	5	eq	eq	NOUN
ejpam-5427	94	6	.	.	PUNCT
ejpam-5427	95	1	(	(	PUNCT
ejpam-5427	95	2	13	13	NUM
ejpam-5427	95	3	)	)	PUNCT
ejpam-5427	95	4	,	,	PUNCT
ejpam-5427	95	5	to	to	PART
ejpam-5427	95	6	obtain	obtain	VERB
ejpam-5427	95	7	ÿ2	ÿ2	NOUN
ejpam-5427	95	8	+	+	CCONJ
ejpam-5427	95	9	ω2	ω2	ADJ
ejpam-5427	95	10	1y2	1y2	NUM
ejpam-5427	96	1	=	=	SYM
ejpam-5427	96	2	−	−	PROPN
ejpam-5427	96	3	(	(	PUNCT
ejpam-5427	96	4	a(32	a(32	PROPN
ejpam-5427	96	5	+	+	NOUN
ejpam-5427	96	6	9a2)(6144	9a2)(6144	NUM
ejpam-5427	96	7	+	+	ADJ
ejpam-5427	96	8	4608a2	4608a2	NOUN
ejpam-5427	96	9	+	+	NOUN
ejpam-5427	96	10	1136a4	1136a4	NOUN
ejpam-5427	96	11	+	+	ADJ
ejpam-5427	96	12	93a6−384(4+a2)2ω2	93a6−384(4+a2)2ω2	NOUN
ejpam-5427	96	13	1	1	NUM
ejpam-5427	96	14	3072(4+a2)3	3072(4+a2)3	NUM
ejpam-5427	96	15	)	)	PUNCT
ejpam-5427	96	16	cos(ω1	cos(ω1	PROPN
ejpam-5427	96	17	t	t	PROPN
ejpam-5427	96	18	)	)	PUNCT
ejpam-5427	97	1	+	+	CCONJ
ejpam-5427	97	2	(	(	PUNCT
ejpam-5427	97	3	a3(9216	a3(9216	ADJ
ejpam-5427	97	4	+	+	PROPN
ejpam-5427	97	5	7936a2	7936a2	NOUN
ejpam-5427	97	6	+	+	NOUN
ejpam-5427	97	7	2296a4	2296a4	NOUN
ejpam-5427	97	8	+	+	ADJ
ejpam-5427	97	9	223a6−64(4+a2)2ω2	223a6−64(4+a2)2ω2	NUM
ejpam-5427	97	10	1	1	NUM
ejpam-5427	97	11	)	)	PUNCT
ejpam-5427	97	12	512(4+a2)3	512(4+a2)3	NUM
ejpam-5427	97	13	)	)	PUNCT
ejpam-5427	97	14	cos(3ω1	cos(3ω1	PROPN
ejpam-5427	97	15	t	t	PROPN
ejpam-5427	97	16	)	)	PUNCT
ejpam-5427	97	17	+	+	CCONJ
ejpam-5427	97	18	(	(	PUNCT
ejpam-5427	97	19	a5(3328	a5(3328	ADP
ejpam-5427	97	20	+	+	NOUN
ejpam-5427	97	21	1928a2	1928a2	NOUN
ejpam-5427	97	22	+	+	ADJ
ejpam-5427	97	23	279a4	279a4	NUM
ejpam-5427	97	24	)	)	PUNCT
ejpam-5427	97	25	1536(4+a2)3	1536(4+a2)3	NUM
ejpam-5427	97	26	)	)	PUNCT
ejpam-5427	97	27	cos(5ω1	cos(5ω1	PROPN
ejpam-5427	97	28	t	t	PROPN
ejpam-5427	97	29	)	)	PUNCT
ejpam-5427	97	30	+	+	CCONJ
ejpam-5427	97	31	(	(	PUNCT
ejpam-5427	97	32	13a7(32	13a7(32	ADJ
ejpam-5427	97	33	+	+	NOUN
ejpam-5427	97	34	9a2	9a2	NUM
ejpam-5427	97	35	)	)	PUNCT
ejpam-5427	97	36	6144(4+a2)3	6144(4+a2)3	NUM
ejpam-5427	97	37	)	)	PUNCT
ejpam-5427	97	38	cos(7ω1	cos(7ω1	PROPN
ejpam-5427	97	39	t	t	NOUN
ejpam-5427	97	40	)	)	PUNCT
ejpam-5427	97	41	−	−	PROPN
ejpam-5427	97	42	(	(	PUNCT
ejpam-5427	97	43	a9	a9	PROPN
ejpam-5427	97	44	2048(4+a2)3	2048(4+a2)3	NUM
ejpam-5427	97	45	)	)	PUNCT
ejpam-5427	97	46	cos(9ω1	cos(9ω1	PROPN
ejpam-5427	97	47	t	t	NOUN
ejpam-5427	97	48	)	)	PUNCT
ejpam-5427	97	49	.	.	PUNCT
ejpam-5427	97	50	.	.	PUNCT
ejpam-5427	98	1	(	(	PUNCT
ejpam-5427	98	2	19	19	NUM
ejpam-5427	98	3	)	)	PUNCT
ejpam-5427	98	4	g.	g.	PROPN
ejpam-5427	98	5	m.	m.	PROPN
ejpam-5427	98	6	ismail	ismail	PROPN
ejpam-5427	98	7	,	,	PUNCT
ejpam-5427	98	8	m.	m.	NOUN
ejpam-5427	98	9	i.	i.	PROPN
ejpam-5427	98	10	yamani	yamani	PROPN
ejpam-5427	98	11	/	/	SYM
ejpam-5427	98	12	eur	eur	PROPN
ejpam-5427	98	13	.	.	PUNCT
ejpam-5427	99	1	j.	j.	PROPN
ejpam-5427	99	2	pure	pure	PROPN
ejpam-5427	99	3	appl	appl	PROPN
ejpam-5427	99	4	.	.	PROPN
ejpam-5427	99	5	math	math	PROPN
ejpam-5427	99	6	,	,	PUNCT
ejpam-5427	99	7	17	17	NUM
ejpam-5427	99	8	(	(	PUNCT
ejpam-5427	99	9	4	4	NUM
ejpam-5427	99	10	)	)	PUNCT
ejpam-5427	99	11	(	(	PUNCT
ejpam-5427	99	12	2024	2024	NUM
ejpam-5427	99	13	)	)	PUNCT
ejpam-5427	99	14	,	,	PUNCT
ejpam-5427	99	15	3622	3622	NUM
ejpam-5427	99	16	-	-	SYM
ejpam-5427	99	17	3641	3641	NUM
ejpam-5427	99	18	3626	3626	NUM
ejpam-5427	99	19	to	to	PART
ejpam-5427	99	20	avoid	avoid	VERB
ejpam-5427	99	21	dominating	dominating	NOUN
ejpam-5427	99	22	terms	term	NOUN
ejpam-5427	99	23	,	,	PUNCT
ejpam-5427	99	24	we	we	PRON
ejpam-5427	99	25	obtain	obtain	VERB
ejpam-5427	99	26	ω1	ω1	PROPN
ejpam-5427	99	27	=	=	PUNCT
ejpam-5427	100	1	√	√	NUM
ejpam-5427	100	2	6144	6144	NUM
ejpam-5427	100	3	+	+	CCONJ
ejpam-5427	100	4	4608a2	4608a2	NOUN
ejpam-5427	101	1	+	+	PUNCT
ejpam-5427	101	2	1136a4	1136a4	NUM
ejpam-5427	101	3	+	+	CCONJ
ejpam-5427	101	4	93a6	93a6	NUM
ejpam-5427	101	5	6144	6144	NUM
ejpam-5427	102	1	+	+	CCONJ
ejpam-5427	102	2	3072a2	3072a2	NUM
ejpam-5427	102	3	+	+	CCONJ
ejpam-5427	102	4	384a4	384a4	NUM
ejpam-5427	102	5	.	.	PUNCT
ejpam-5427	103	1	(	(	PUNCT
ejpam-5427	103	2	20	20	NUM
ejpam-5427	103	3	)	)	PUNCT
ejpam-5427	103	4	after	after	ADP
ejpam-5427	103	5	solving	solve	VERB
ejpam-5427	103	6	eq	eq	ADP
ejpam-5427	103	7	.	.	PUNCT
ejpam-5427	104	1	(	(	PUNCT
ejpam-5427	104	2	19	19	NUM
ejpam-5427	104	3	)	)	PUNCT
ejpam-5427	104	4	with	with	ADP
ejpam-5427	104	5	the	the	DET
ejpam-5427	104	6	initial	initial	ADJ
ejpam-5427	104	7	conditions	condition	NOUN
ejpam-5427	104	8	,	,	PUNCT
ejpam-5427	104	9	we	we	PRON
ejpam-5427	104	10	have	have	VERB
ejpam-5427	104	11	the	the	DET
ejpam-5427	104	12	second	second	ADJ
ejpam-5427	104	13	approximate	approximate	ADJ
ejpam-5427	104	14	solution	solution	NOUN
ejpam-5427	104	15	.	.	PUNCT
ejpam-5427	105	1	y2	y2	NOUN
ejpam-5427	106	1	=	=	SYM
ejpam-5427	107	1	(	(	PUNCT
ejpam-5427	107	2	a3(103680	a3(103680	ADV
ejpam-5427	107	3	+	+	ADJ
ejpam-5427	107	4	85120a2	85120a2	NOUN
ejpam-5427	107	5	+	+	NOUN
ejpam-5427	107	6	23485a4	23485a4	PROPN
ejpam-5427	107	7	+	+	ADJ
ejpam-5427	107	8	2178a6)+720a(4+a2)2(256	2178a6)+720a(4+a2)2(256	PROPN
ejpam-5427	107	9	+	+	ADJ
ejpam-5427	107	10	63a2)ω2	63a2)ω2	PROPN
ejpam-5427	107	11	1	1	NUM
ejpam-5427	107	12	46080(4+a2)33ω2	46080(4+a2)33ω2	NUM
ejpam-5427	107	13	1	1	NUM
ejpam-5427	107	14	)	)	PUNCT
ejpam-5427	107	15	cos(ω2	cos(ω2	NOUN
ejpam-5427	107	16	t	t	PROPN
ejpam-5427	107	17	)	)	PUNCT
ejpam-5427	107	18	+	+	CCONJ
ejpam-5427	107	19	(	(	PUNCT
ejpam-5427	107	20	a3(103680	a3(103680	ADV
ejpam-5427	107	21	+	+	ADJ
ejpam-5427	107	22	85120a2	85120a2	NOUN
ejpam-5427	107	23	+	+	NOUN
ejpam-5427	107	24	23485a4	23485a4	PROPN
ejpam-5427	107	25	+	+	ADJ
ejpam-5427	107	26	2178a6)+720a(4+a2)2(256	2178a6)+720a(4+a2)2(256	PROPN
ejpam-5427	107	27	+	+	ADJ
ejpam-5427	107	28	63a2)ω2	63a2)ω2	PROPN
ejpam-5427	107	29	1	1	NUM
ejpam-5427	107	30	4096(4+a2)3ω2	4096(4+a2)3ω2	NUM
ejpam-5427	107	31	1	1	NUM
ejpam-5427	107	32	)	)	PUNCT
ejpam-5427	107	33	cos(3ω2	cos(3ω2	PROPN
ejpam-5427	107	34	t	t	PROPN
ejpam-5427	107	35	)	)	PUNCT
ejpam-5427	107	36	+	+	CCONJ
ejpam-5427	107	37	(	(	PUNCT
ejpam-5427	107	38	a5(3328	a5(3328	ADP
ejpam-5427	107	39	+	+	NOUN
ejpam-5427	107	40	1928a2	1928a2	NOUN
ejpam-5427	107	41	+	+	NOUN
ejpam-5427	107	42	279a4	279a4	NUM
ejpam-5427	107	43	)	)	PUNCT
ejpam-5427	107	44	36864(4+a2)3ω2	36864(4+a2)3ω2	NUM
ejpam-5427	107	45	1	1	NUM
ejpam-5427	107	46	)	)	PUNCT
ejpam-5427	107	47	cos(5ω2	cos(5ω2	PROPN
ejpam-5427	107	48	t	t	PROPN
ejpam-5427	107	49	)	)	PUNCT
ejpam-5427	107	50	+	+	CCONJ
ejpam-5427	108	1	(	(	PUNCT
ejpam-5427	108	2	13a7(32	13a7(32	ADJ
ejpam-5427	108	3	+	+	NOUN
ejpam-5427	108	4	9a2	9a2	NUM
ejpam-5427	108	5	)	)	PUNCT
ejpam-5427	109	1	294912(4+a2)3ω2	294912(4+a2)3ω2	NUM
ejpam-5427	109	2	1	1	NUM
ejpam-5427	109	3	)	)	PUNCT
ejpam-5427	109	4	cos(7ω2	cos(7ω2	NOUN
ejpam-5427	109	5	t	t	PROPN
ejpam-5427	109	6	)	)	PUNCT
ejpam-5427	109	7	+	+	CCONJ
ejpam-5427	109	8	(	(	PUNCT
ejpam-5427	109	9	a9	a9	PROPN
ejpam-5427	109	10	163840(4+a2)3ω2	163840(4+a2)3ω2	NUM
ejpam-5427	109	11	1	1	NUM
ejpam-5427	109	12	)	)	PUNCT
ejpam-5427	109	13	cos(9ω2	cos(9ω2	PROPN
ejpam-5427	109	14	t	t	PROPN
ejpam-5427	109	15	)	)	PUNCT
ejpam-5427	109	16	.	.	PUNCT
ejpam-5427	110	1	(	(	PUNCT
ejpam-5427	110	2	21	21	NUM
ejpam-5427	110	3	)	)	PUNCT
ejpam-5427	110	4	3.1.3	3.1.3	NUM
ejpam-5427	110	5	.	.	PUNCT
ejpam-5427	110	6	third	third	ADJ
ejpam-5427	110	7	iteration	iteration	NOUN
ejpam-5427	110	8	solution	solution	NOUN
ejpam-5427	110	9	for	for	ADP
ejpam-5427	110	10	the	the	DET
ejpam-5427	110	11	third	third	ADJ
ejpam-5427	110	12	level	level	NOUN
ejpam-5427	110	13	of	of	ADP
ejpam-5427	110	14	iteration	iteration	NOUN
ejpam-5427	110	15	,	,	PUNCT
ejpam-5427	110	16	continuing	continue	VERB
ejpam-5427	110	17	to	to	ADP
ejpam-5427	110	18	k	k	X
ejpam-5427	110	19	=	=	SYM
ejpam-5427	110	20	2	2	NUM
ejpam-5427	110	21	,	,	PUNCT
ejpam-5427	110	22	we	we	PRON
ejpam-5427	110	23	substituting	substitute	VERB
ejpam-5427	110	24	y2	y2	PROPN
ejpam-5427	110	25	from	from	ADP
ejpam-5427	110	26	eq	eq	PROPN
ejpam-5427	110	27	.	.	PUNCT
ejpam-5427	111	1	(	(	PUNCT
ejpam-5427	111	2	21	21	NUM
ejpam-5427	111	3	)	)	PUNCT
ejpam-5427	111	4	into	into	ADP
ejpam-5427	111	5	the	the	DET
ejpam-5427	111	6	right	right	ADJ
ejpam-5427	111	7	-	-	PUNCT
ejpam-5427	111	8	hand	hand	NOUN
ejpam-5427	111	9	side	side	NOUN
ejpam-5427	111	10	of	of	ADP
ejpam-5427	111	11	eq	eq	PROPN
ejpam-5427	111	12	.	.	PUNCT
ejpam-5427	112	1	(	(	PUNCT
ejpam-5427	112	2	13	13	NUM
ejpam-5427	112	3	)	)	PUNCT
ejpam-5427	112	4	,	,	PUNCT
ejpam-5427	112	5	we	we	PRON
ejpam-5427	112	6	have	have	VERB
ejpam-5427	112	7	.	.	PUNCT
ejpam-5427	113	1	ÿ3	ÿ3	PROPN
ejpam-5427	113	2	+	+	CCONJ
ejpam-5427	113	3	ω2	ω2	ADJ
ejpam-5427	113	4	2y3	2y3	NUM
ejpam-5427	113	5	=	=	SYM
ejpam-5427	113	6	ω2	ω2	ADJ
ejpam-5427	113	7	2y2	2y2	NUM
ejpam-5427	113	8	−	−	PROPN
ejpam-5427	114	1	y2	y2	INTJ
ejpam-5427	114	2	+	+	CCONJ
ejpam-5427	114	3	ȳ2y2ẏ2	ȳ2y2ẏ2	NOUN
ejpam-5427	114	4	.	.	PUNCT
ejpam-5427	115	1	(	(	PUNCT
ejpam-5427	115	2	22	22	X
ejpam-5427	115	3	)	)	PUNCT
ejpam-5427	115	4	solving	solve	VERB
ejpam-5427	115	5	equation	equation	NOUN
ejpam-5427	115	6	(	(	PUNCT
ejpam-5427	115	7	22	22	NUM
ejpam-5427	115	8	)	)	PUNCT
ejpam-5427	115	9	,	,	PUNCT
ejpam-5427	115	10	and	and	CCONJ
ejpam-5427	115	11	avoiding	avoid	VERB
ejpam-5427	115	12	secular	secular	ADJ
ejpam-5427	115	13	terms	term	NOUN
ejpam-5427	115	14	,	,	PUNCT
ejpam-5427	115	15	we	we	PRON
ejpam-5427	115	16	can	can	AUX
ejpam-5427	115	17	obtain	obtain	VERB
ejpam-5427	115	18	ω2	ω2	ADJ
ejpam-5427	115	19	by	by	ADP
ejpam-5427	115	20	using	use	VERB
ejpam-5427	115	21	mathematica	mathematica	PROPN
ejpam-5427	115	22	command	command	PROPN
ejpam-5427	115	23	software	software	PROPN
ejpam-5427	115	24	program	program	PROPN
ejpam-5427	115	25	.	.	PUNCT
ejpam-5427	116	1	the	the	DET
ejpam-5427	116	2	findings	finding	NOUN
ejpam-5427	116	3	found	find	VERB
ejpam-5427	116	4	for	for	ADP
ejpam-5427	116	5	y3	y3	NOUN
ejpam-5427	116	6	,	,	PUNCT
ejpam-5427	116	7	need	need	VERB
ejpam-5427	116	8	too	too	ADV
ejpam-5427	116	9	much	much	ADJ
ejpam-5427	116	10	space	space	NOUN
ejpam-5427	116	11	and	and	CCONJ
ejpam-5427	116	12	can	can	AUX
ejpam-5427	116	13	not	not	PART
ejpam-5427	116	14	be	be	AUX
ejpam-5427	116	15	shown	show	VERB
ejpam-5427	116	16	here	here	ADV
ejpam-5427	116	17	.	.	PUNCT
ejpam-5427	117	1	however	however	ADV
ejpam-5427	117	2	,	,	PUNCT
ejpam-5427	117	3	the	the	DET
ejpam-5427	117	4	numerical	numerical	ADJ
ejpam-5427	117	5	values	value	NOUN
ejpam-5427	117	6	will	will	AUX
ejpam-5427	117	7	be	be	AUX
ejpam-5427	117	8	shown	show	VERB
ejpam-5427	117	9	in	in	ADP
ejpam-5427	117	10	the	the	DET
ejpam-5427	117	11	findings	finding	NOUN
ejpam-5427	117	12	and	and	CCONJ
ejpam-5427	117	13	discussion	discussion	NOUN
ejpam-5427	117	14	part	part	NOUN
ejpam-5427	117	15	.	.	PUNCT
ejpam-5427	118	1	ω2	ω2	ADV
ejpam-5427	118	2	=	=	SYM
ejpam-5427	118	3	(	(	PUNCT
ejpam-5427	118	4	√	√	NUM
ejpam-5427	118	5	(	(	PUNCT
ejpam-5427	118	6	1/(4	1/(4	NUM
ejpam-5427	118	7	+	+	NOUN
ejpam-5427	118	8	a2)9a(1470839609502185029632000	a2)9a(1470839609502185029632000	NOUN
ejpam-5427	118	9	+	+	CCONJ
ejpam-5427	118	10	4826192468679044628480000a2	4826192468679044628480000a2	NOUN
ejpam-5427	119	1	+7296583778952951103488000a4	+7296583778952951103488000a4	NOUN
ejpam-5427	119	2	+	+	CCONJ
ejpam-5427	119	3	6729655286686996758528000a6	6729655286686996758528000a6	NUM
ejpam-5427	119	4	+4224062453812034745139200a8	+4224062453812034745139200a8	NOUN
ejpam-5427	120	1	+	+	CCONJ
ejpam-5427	120	2	1905190794429295126118400a10	1905190794429295126118400a10	NUM
ejpam-5427	120	3	+635148579378340823040000a12	+635148579378340823040000a12	NOUN
ejpam-5427	121	1	+	+	CCONJ
ejpam-5427	122	1	158430275820381536256000a14	158430275820381536256000a14	NUM
ejpam-5427	122	2	+29559820082388423147520a16	+29559820082388423147520a16	X
ejpam-5427	123	1	+	+	CCONJ
ejpam-5427	123	2	4072969446127757557760a18	4072969446127757557760a18	NOUN
ejpam-5427	123	3	+402650199557972162560a20	+402650199557972162560a20	NOUN
ejpam-5427	124	1	+	+	CCONJ
ejpam-5427	124	2	27028701991773424000a22	27028701991773424000a22	NUM
ejpam-5427	124	3	+1103351520402981540a24	+1103351520402981540a24	NOUN
ejpam-5427	124	4	+	+	CCONJ
ejpam-5427	124	5	20664999056050911a26	20664999056050911a26	NUM
ejpam-5427	124	6	)	)	PUNCT
ejpam-5427	124	7	)	)	PUNCT
ejpam-5427	124	8	)	)	PUNCT
ejpam-5427	125	1	/(3840	/(3840	PUNCT
ejpam-5427	126	1	√	√	NUM
ejpam-5427	126	2	7	7	NUM
ejpam-5427	126	3	√	√	PROPN
ejpam-5427	126	4	(	(	PUNCT
ejpam-5427	126	5	1	1	NUM
ejpam-5427	126	6	(	(	PUNCT
ejpam-5427	126	7	4+a2)7	4+a2)7	PROPN
ejpam-5427	126	8	a(6144	a(6144	PROPN
ejpam-5427	126	9	+	+	CCONJ
ejpam-5427	126	10	4608a2	4608a2	NOUN
ejpam-5427	127	1	+	+	NUM
ejpam-5427	127	2	1136a4	1136a4	NUM
ejpam-5427	127	3	+	+	CCONJ
ejpam-5427	127	4	93a6)2(23592960	93a6)2(23592960	NUM
ejpam-5427	127	5	+24330240a2	+24330240a2	NOUN
ejpam-5427	127	6	+	+	CCONJ
ejpam-5427	127	7	9397760a4	9397760a4	NUM
ejpam-5427	127	8	+	+	CCONJ
ejpam-5427	127	9	1618520a6	1618520a6	NUM
ejpam-5427	127	10	+	+	NUM
ejpam-5427	127	11	105309a8	105309a8	NUM
ejpam-5427	127	12	)	)	PUNCT
ejpam-5427	127	13	)	)	PUNCT
ejpam-5427	127	14	)	)	PUNCT
ejpam-5427	127	15	.	.	PUNCT
ejpam-5427	128	1	(	(	PUNCT
ejpam-5427	128	2	23	23	X
ejpam-5427	128	3	)	)	PUNCT
ejpam-5427	128	4	integrating	integrate	VERB
ejpam-5427	128	5	eq	eq	PROPN
ejpam-5427	128	6	.	.	PUNCT
ejpam-5427	129	1	(	(	PUNCT
ejpam-5427	129	2	21	21	NUM
ejpam-5427	129	3	)	)	PUNCT
ejpam-5427	129	4	,	,	PUNCT
ejpam-5427	129	5	we	we	PRON
ejpam-5427	129	6	obtain	obtain	VERB
ejpam-5427	129	7	the	the	DET
ejpam-5427	129	8	analytical	analytical	ADJ
ejpam-5427	129	9	solution	solution	NOUN
ejpam-5427	129	10	of	of	ADP
ejpam-5427	129	11	eq	eq	PROPN
ejpam-5427	129	12	.	.	PUNCT
ejpam-5427	130	1	(	(	PUNCT
ejpam-5427	130	2	9	9	NUM
ejpam-5427	130	3	)	)	PUNCT
ejpam-5427	130	4	in	in	ADP
ejpam-5427	130	5	the	the	DET
ejpam-5427	130	6	form	form	NOUN
ejpam-5427	130	7	:	:	PUNCT
ejpam-5427	130	8	x	x	SYM
ejpam-5427	130	9	=	=	SYM
ejpam-5427	130	10	(	(	PUNCT
ejpam-5427	130	11	(	(	PUNCT
ejpam-5427	130	12	4a(23592960	4a(23592960	NUM
ejpam-5427	130	13	+	+	NOUN
ejpam-5427	130	14	24330240a2	24330240a2	ADJ
ejpam-5427	130	15	+	+	NOUN
ejpam-5427	130	16	9397760a4	9397760a4	ADJ
ejpam-5427	130	17	+	+	ADJ
ejpam-5427	130	18	1618520a6	1618520a6	NUM
ejpam-5427	130	19	+	+	NOUN
ejpam-5427	130	20	105309a8	105309a8	NUM
ejpam-5427	130	21	)	)	PUNCT
ejpam-5427	130	22	ω2	ω2	ADJ
ejpam-5427	130	23	)	)	PUNCT
ejpam-5427	130	24	sin(ω2	sin(ω2	PROPN
ejpam-5427	130	25	t	t	PROPN
ejpam-5427	130	26	)	)	PUNCT
ejpam-5427	130	27	−	−	PROPN
ejpam-5427	130	28	(	(	PUNCT
ejpam-5427	130	29	20a3(49152	20a3(49152	NUM
ejpam-5427	130	30	+	+	NOUN
ejpam-5427	130	31	43008a2	43008a2	ADJ
ejpam-5427	130	32	+	+	NOUN
ejpam-5427	130	33	12640a4	12640a4	ADJ
ejpam-5427	130	34	+	+	NOUN
ejpam-5427	130	35	1245a6	1245a6	NUM
ejpam-5427	130	36	)	)	PUNCT
ejpam-5427	130	37	ω2	ω2	ADJ
ejpam-5427	130	38	)	)	PUNCT
ejpam-5427	130	39	sin(3ω2	sin(3ω2	PROPN
ejpam-5427	130	40	t	t	PROPN
ejpam-5427	130	41	)	)	PUNCT
ejpam-5427	131	1	+	+	CCONJ
ejpam-5427	131	2	(	(	PUNCT
ejpam-5427	131	3	26624a5	26624a5	NUM
ejpam-5427	131	4	+	+	ADJ
ejpam-5427	131	5	15424a7	15424a7	PROPN
ejpam-5427	131	6	+	+	ADJ
ejpam-5427	131	7	2232a9	2232a9	NUM
ejpam-5427	131	8	ω2	ω2	ADJ
ejpam-5427	131	9	)	)	PUNCT
ejpam-5427	131	10	sin(5ω2t)−	sin(5ω2t)−	PROPN
ejpam-5427	131	11	(	(	PUNCT
ejpam-5427	131	12	2080a7	2080a7	NUM
ejpam-5427	131	13	+	+	PROPN
ejpam-5427	131	14	585a9	585a9	NUM
ejpam-5427	131	15	7ω2	7ω2	NUM
ejpam-5427	131	16	)	)	PUNCT
ejpam-5427	131	17	sin(7ω2	sin(7ω2	NOUN
ejpam-5427	131	18	t	t	PROPN
ejpam-5427	131	19	)	)	PUNCT
ejpam-5427	131	20	+	+	CCONJ
ejpam-5427	131	21	(	(	PUNCT
ejpam-5427	131	22	a9	a9	PROPN
ejpam-5427	131	23	ω2	ω2	ADJ
ejpam-5427	131	24	)	)	PUNCT
ejpam-5427	131	25	sin(9ω2	sin(9ω2	PROPN
ejpam-5427	131	26	t	t	PROPN
ejpam-5427	131	27	)	)	PUNCT
ejpam-5427	131	28	)	)	PUNCT
ejpam-5427	131	29	/	/	PUNCT
ejpam-5427	131	30	(	(	PUNCT
ejpam-5427	131	31	3840(4	3840(4	NUM
ejpam-5427	131	32	+	+	ADJ
ejpam-5427	131	33	a2)(6144	a2)(6144	NOUN
ejpam-5427	131	34	+	+	X
ejpam-5427	131	35	4608a2	4608a2	NOUN
ejpam-5427	131	36	+	+	NUM
ejpam-5427	131	37	1136a4	1136a4	NUM
ejpam-5427	131	38	+	+	CCONJ
ejpam-5427	131	39	93a6	93a6	NUM
ejpam-5427	131	40	)	)	PUNCT
ejpam-5427	131	41	)	)	PUNCT
ejpam-5427	131	42	(	(	PUNCT
ejpam-5427	131	43	24	24	NUM
ejpam-5427	131	44	)	)	PUNCT
ejpam-5427	131	45	g.	g.	PROPN
ejpam-5427	131	46	m.	m.	PROPN
ejpam-5427	131	47	ismail	ismail	PROPN
ejpam-5427	131	48	,	,	PUNCT
ejpam-5427	131	49	m.	m.	NOUN
ejpam-5427	131	50	i.	i.	PROPN
ejpam-5427	131	51	yamani	yamani	PROPN
ejpam-5427	131	52	/	/	SYM
ejpam-5427	131	53	eur	eur	PROPN
ejpam-5427	131	54	.	.	PUNCT
ejpam-5427	132	1	j.	j.	PROPN
ejpam-5427	132	2	pure	pure	PROPN
ejpam-5427	132	3	appl	appl	PROPN
ejpam-5427	132	4	.	.	PROPN
ejpam-5427	132	5	math	math	PROPN
ejpam-5427	132	6	,	,	PUNCT
ejpam-5427	132	7	17	17	NUM
ejpam-5427	132	8	(	(	PUNCT
ejpam-5427	132	9	4	4	NUM
ejpam-5427	132	10	)	)	PUNCT
ejpam-5427	132	11	(	(	PUNCT
ejpam-5427	132	12	2024	2024	NUM
ejpam-5427	132	13	)	)	PUNCT
ejpam-5427	132	14	,	,	PUNCT
ejpam-5427	132	15	3622	3622	NUM
ejpam-5427	132	16	-	-	SYM
ejpam-5427	132	17	3641	3641	NUM
ejpam-5427	132	18	3627	3627	NUM
ejpam-5427	132	19	3.2	3.2	NUM
ejpam-5427	132	20	.	.	PUNCT
ejpam-5427	133	1	jerk	jerk	NOUN
ejpam-5427	133	2	function	function	NOUN
ejpam-5427	133	3	containing	contain	VERB
ejpam-5427	133	4	velocity	velocity	NOUN
ejpam-5427	133	5	times	time	NOUN
ejpam-5427	133	6	acceleration	acceleration	NOUN
ejpam-5427	133	7	-	-	PUNCT
ejpam-5427	133	8	squared	square	VERB
ejpam-5427	133	9	,	,	PUNCT
ejpam-5427	133	10	and	and	CCONJ
ejpam-5427	133	11	velocity	velocity	VERB
ejpam-5427	133	12	another	another	DET
ejpam-5427	133	13	case	case	NOUN
ejpam-5427	133	14	of	of	ADP
ejpam-5427	133	15	the	the	DET
ejpam-5427	133	16	jerk	jerk	NOUN
ejpam-5427	133	17	equation	equation	NOUN
ejpam-5427	133	18	is	be	AUX
ejpam-5427	133	19	considered	consider	VERB
ejpam-5427	133	20	by	by	ADP
ejpam-5427	133	21	putting	put	VERB
ejpam-5427	133	22	γ	γ	NOUN
ejpam-5427	133	23	=	=	SYM
ejpam-5427	133	24	ε	ε	PROPN
ejpam-5427	133	25	=	=	SYM
ejpam-5427	133	26	1	1	NUM
ejpam-5427	133	27	,	,	PUNCT
ejpam-5427	133	28	α	α	NOUN
ejpam-5427	133	29	=	=	X
ejpam-5427	134	1	β	β	X
ejpam-5427	134	2	=	=	PUNCT
ejpam-5427	134	3	δ	δ	X
ejpam-5427	134	4	=	=	SYM
ejpam-5427	134	5	0	0	PROPN
ejpam-5427	134	6	,	,	PUNCT
ejpam-5427	134	7	in	in	ADP
ejpam-5427	134	8	eq	eq	ADP
ejpam-5427	134	9	.	.	PUNCT
ejpam-5427	135	1	(	(	PUNCT
ejpam-5427	135	2	7	7	NUM
ejpam-5427	135	3	)	)	PUNCT
ejpam-5427	135	4	to	to	PART
ejpam-5427	135	5	obtain	obtain	VERB
ejpam-5427	135	6	[	[	X
ejpam-5427	135	7	1	1	NUM
ejpam-5427	135	8	]	]	PUNCT
ejpam-5427	135	9	:	:	PUNCT
ejpam-5427	135	10	...	...	PUNCT
ejpam-5427	136	1	x	x	X
ejpam-5427	137	1	+	+	PUNCT
ejpam-5427	137	2	ẋ+	ẋ+	ADJ
ejpam-5427	137	3	ẋẍ2	ẋẍ2	PUNCT
ejpam-5427	137	4	=	=	SYM
ejpam-5427	137	5	0	0	PROPN
ejpam-5427	137	6	,	,	PUNCT
ejpam-5427	137	7	x(0	x(0	PROPN
ejpam-5427	137	8	)	)	PUNCT
ejpam-5427	138	1	=	=	SYM
ejpam-5427	138	2	0	0	NUM
ejpam-5427	138	3	,	,	PUNCT
ejpam-5427	138	4	ẋ(0	ẋ(0	X
ejpam-5427	138	5	)	)	PUNCT
ejpam-5427	138	6	=	=	SYM
ejpam-5427	139	1	a	a	PRON
ejpam-5427	139	2	,	,	PUNCT
ejpam-5427	139	3	ẍ(0	ẍ(0	PROPN
ejpam-5427	139	4	)	)	PUNCT
ejpam-5427	140	1	=	=	SYM
ejpam-5427	140	2	0	0	X
ejpam-5427	140	3	.	.	PUNCT
ejpam-5427	141	1	(	(	PUNCT
ejpam-5427	141	2	25	25	NUM
ejpam-5427	141	3	)	)	PUNCT
ejpam-5427	141	4	similar	similar	ADJ
ejpam-5427	141	5	to	to	ADP
ejpam-5427	141	6	application	application	NOUN
ejpam-5427	141	7	(	(	PUNCT
ejpam-5427	141	8	1	1	NUM
ejpam-5427	141	9	)	)	PUNCT
ejpam-5427	141	10	,	,	PUNCT
ejpam-5427	141	11	eq	eq	NOUN
ejpam-5427	141	12	.	.	PUNCT
ejpam-5427	142	1	(	(	PUNCT
ejpam-5427	142	2	25	25	NUM
ejpam-5427	142	3	)	)	PUNCT
ejpam-5427	142	4	can	can	AUX
ejpam-5427	142	5	be	be	AUX
ejpam-5427	142	6	rewritten	rewrite	VERB
ejpam-5427	142	7	in	in	ADP
ejpam-5427	142	8	the	the	DET
ejpam-5427	142	9	form	form	NOUN
ejpam-5427	142	10	ÿ	ÿ	PROPN
ejpam-5427	142	11	+	+	CCONJ
ejpam-5427	142	12	y	y	PROPN
ejpam-5427	142	13	+	+	CCONJ
ejpam-5427	142	14	yẏ2	yẏ2	ADJ
ejpam-5427	142	15	=	=	SYM
ejpam-5427	142	16	0	0	X
ejpam-5427	142	17	y(0	y(0	PROPN
ejpam-5427	142	18	)	)	PUNCT
ejpam-5427	142	19	=	=	SYM
ejpam-5427	143	1	a	a	PROPN
ejpam-5427	143	2	,	,	PUNCT
ejpam-5427	143	3	ẏ(0	ẏ(0	NUM
ejpam-5427	143	4	)	)	PUNCT
ejpam-5427	143	5	=	=	SYM
ejpam-5427	144	1	0	0	X
ejpam-5427	144	2	.	.	PUNCT
ejpam-5427	145	1	(	(	PUNCT
ejpam-5427	145	2	26	26	NUM
ejpam-5427	145	3	)	)	PUNCT
ejpam-5427	145	4	following	follow	VERB
ejpam-5427	145	5	the	the	DET
ejpam-5427	145	6	iteration	iteration	NOUN
ejpam-5427	145	7	scheme	scheme	NOUN
ejpam-5427	145	8	(	(	PUNCT
ejpam-5427	145	9	3	3	NUM
ejpam-5427	145	10	)	)	PUNCT
ejpam-5427	145	11	,	,	PUNCT
ejpam-5427	145	12	we	we	PRON
ejpam-5427	145	13	have	have	VERB
ejpam-5427	145	14	ÿk+1	ÿk+1	VERB
ejpam-5427	145	15	+	+	CCONJ
ejpam-5427	145	16	ω2	ω2	ADJ
ejpam-5427	145	17	k+1yk+1	k+1yk+1	PROPN
ejpam-5427	145	18	=	=	SYM
ejpam-5427	145	19	ω2	ω2	ADJ
ejpam-5427	145	20	kyk	kyk	PROPN
ejpam-5427	145	21	−	−	PROPN
ejpam-5427	145	22	yk	yk	PROPN
ejpam-5427	146	1	−	−	PROPN
ejpam-5427	146	2	ykẏ	ykẏ	PROPN
ejpam-5427	146	3	2	2	NUM
ejpam-5427	146	4	k.	k.	NOUN
ejpam-5427	146	5	(	(	PUNCT
ejpam-5427	146	6	27	27	NUM
ejpam-5427	146	7	)	)	PUNCT
ejpam-5427	146	8	3.2.1	3.2.1	NUM
ejpam-5427	146	9	.	.	PUNCT
ejpam-5427	147	1	first	first	ADJ
ejpam-5427	147	2	iteration	iteration	NOUN
ejpam-5427	147	3	solution	solution	NOUN
ejpam-5427	147	4	for	for	ADP
ejpam-5427	147	5	first	first	ADJ
ejpam-5427	147	6	iteration	iteration	NOUN
ejpam-5427	147	7	at	at	ADP
ejpam-5427	147	8	k	k	PROPN
ejpam-5427	147	9	=	=	SYM
ejpam-5427	147	10	0	0	PROPN
ejpam-5427	147	11	,	,	PUNCT
ejpam-5427	147	12	we	we	PRON
ejpam-5427	147	13	get	get	VERB
ejpam-5427	147	14	ÿ1	ÿ1	ADJ
ejpam-5427	147	15	+	+	CCONJ
ejpam-5427	147	16	ω2	ω2	ADJ
ejpam-5427	147	17	0y1	0y1	NUM
ejpam-5427	148	1	=	=	SYM
ejpam-5427	148	2	1	1	NUM
ejpam-5427	148	3	4	4	NUM
ejpam-5427	148	4	(	(	PUNCT
ejpam-5427	148	5	−4ẏ	−4ẏ	PROPN
ejpam-5427	148	6	+	+	CCONJ
ejpam-5427	148	7	4ẏω2	4ẏω2	NUM
ejpam-5427	148	8	0	0	NUM
ejpam-5427	149	1	−a3ω2	−a3ω2	PROPN
ejpam-5427	149	2	0	0	NUM
ejpam-5427	149	3	)	)	PUNCT
ejpam-5427	150	1	cos(ω0	cos(ω0	PROPN
ejpam-5427	150	2	t	t	PROPN
ejpam-5427	150	3	)	)	PUNCT
ejpam-5427	151	1	+	+	CCONJ
ejpam-5427	151	2	a3ω2	a3ω2	NUM
ejpam-5427	151	3	0	0	NUM
ejpam-5427	151	4	4	4	NUM
ejpam-5427	151	5	cos(3ω0	cos(3ω0	NOUN
ejpam-5427	151	6	t	t	NOUN
ejpam-5427	151	7	)	)	PUNCT
ejpam-5427	151	8	.	.	PUNCT
ejpam-5427	152	1	(	(	PUNCT
ejpam-5427	152	2	28	28	NUM
ejpam-5427	152	3	)	)	PUNCT
ejpam-5427	152	4	to	to	PART
ejpam-5427	152	5	avoid	avoid	VERB
ejpam-5427	152	6	secular	secular	ADJ
ejpam-5427	152	7	term	term	NOUN
ejpam-5427	152	8	from	from	ADP
ejpam-5427	152	9	equation	equation	NOUN
ejpam-5427	152	10	(	(	PUNCT
ejpam-5427	152	11	28	28	NUM
ejpam-5427	152	12	)	)	PUNCT
ejpam-5427	152	13	,	,	PUNCT
ejpam-5427	152	14	we	we	PRON
ejpam-5427	152	15	obtain	obtain	VERB
ejpam-5427	152	16	ω0	ω0	NOUN
ejpam-5427	152	17	=	=	SYM
ejpam-5427	152	18	2√	2√	PROPN
ejpam-5427	152	19	4−a2	4−a2	NUM
ejpam-5427	152	20	.	.	PUNCT
ejpam-5427	153	1	(	(	PUNCT
ejpam-5427	153	2	29	29	NUM
ejpam-5427	153	3	)	)	PUNCT
ejpam-5427	153	4	solving	solve	VERB
ejpam-5427	153	5	eq	eq	NOUN
ejpam-5427	153	6	.	.	PUNCT
ejpam-5427	154	1	(	(	PUNCT
ejpam-5427	154	2	28	28	NUM
ejpam-5427	154	3	)	)	PUNCT
ejpam-5427	154	4	with	with	ADP
ejpam-5427	154	5	initial	initial	ADJ
ejpam-5427	154	6	conditions	condition	NOUN
ejpam-5427	154	7	(	(	PUNCT
ejpam-5427	154	8	5	5	NUM
ejpam-5427	154	9	)	)	PUNCT
ejpam-5427	154	10	,	,	PUNCT
ejpam-5427	154	11	the	the	DET
ejpam-5427	154	12	first	first	ADJ
ejpam-5427	154	13	approximate	approximate	ADJ
ejpam-5427	154	14	solution	solution	NOUN
ejpam-5427	154	15	y1	y1	NOUN
ejpam-5427	154	16	is	be	AUX
ejpam-5427	154	17	obtained	obtain	VERB
ejpam-5427	154	18	as	as	ADP
ejpam-5427	154	19	y1	y1	NOUN
ejpam-5427	154	20	=	=	SYM
ejpam-5427	154	21	(	(	PUNCT
ejpam-5427	154	22	a+	a+	X
ejpam-5427	154	23	a3	a3	NOUN
ejpam-5427	154	24	32	32	NUM
ejpam-5427	154	25	)	)	PUNCT
ejpam-5427	154	26	cos(ω1t)−	cos(ω1t)−	PROPN
ejpam-5427	154	27	a3	a3	VERB
ejpam-5427	154	28	32	32	NUM
ejpam-5427	154	29	cos(3ω1	cos(3ω1	PROPN
ejpam-5427	154	30	t	t	PROPN
ejpam-5427	154	31	)	)	PUNCT
ejpam-5427	154	32	.	.	PUNCT
ejpam-5427	155	1	(	(	PUNCT
ejpam-5427	155	2	30	30	NUM
ejpam-5427	155	3	)	)	PUNCT
ejpam-5427	155	4	3.2.2	3.2.2	NUM
ejpam-5427	155	5	.	.	PUNCT
ejpam-5427	155	6	second	second	ADJ
ejpam-5427	155	7	iteration	iteration	NOUN
ejpam-5427	155	8	solution	solution	NOUN
ejpam-5427	155	9	for	for	ADP
ejpam-5427	155	10	the	the	DET
ejpam-5427	155	11	second	second	ADJ
ejpam-5427	155	12	level	level	NOUN
ejpam-5427	155	13	of	of	ADP
ejpam-5427	155	14	iteration	iteration	NOUN
ejpam-5427	155	15	continuing	continue	VERB
ejpam-5427	155	16	to	to	ADP
ejpam-5427	155	17	k	k	X
ejpam-5427	155	18	=	=	SYM
ejpam-5427	155	19	1	1	NUM
ejpam-5427	155	20	gives	give	NOUN
ejpam-5427	155	21	,	,	PUNCT
ejpam-5427	155	22	ÿ2	ÿ2	NOUN
ejpam-5427	155	23	+	+	CCONJ
ejpam-5427	155	24	ω2	ω2	ADJ
ejpam-5427	155	25	1y2	1y2	NUM
ejpam-5427	155	26	=	=	SYM
ejpam-5427	155	27	(	(	PUNCT
ejpam-5427	155	28	−a(32+a2)(2048+(−2048	−a(32+a2)(2048+(−2048	PUNCT
ejpam-5427	155	29	+	+	NOUN
ejpam-5427	155	30	512a2−48a4	512a2−48a4	NUM
ejpam-5427	155	31	+	+	NOUN
ejpam-5427	155	32	7a6)ω2	7a6)ω2	NUM
ejpam-5427	155	33	1	1	NUM
ejpam-5427	155	34	)	)	PUNCT
ejpam-5427	155	35	65536	65536	NUM
ejpam-5427	155	36	)	)	PUNCT
ejpam-5427	156	1	cos(ω1	cos(ω1	PROPN
ejpam-5427	156	2	t	t	PROPN
ejpam-5427	156	3	)	)	PUNCT
ejpam-5427	157	1	+	+	CCONJ
ejpam-5427	157	2	(	(	PUNCT
ejpam-5427	157	3	a3(1024+(7168	a3(1024+(7168	ADP
ejpam-5427	157	4	+	+	NOUN
ejpam-5427	157	5	1280a2	1280a2	NOUN
ejpam-5427	157	6	+	+	NOUN
ejpam-5427	157	7	56a4	56a4	NUM
ejpam-5427	157	8	+	+	SYM
ejpam-5427	157	9	3a6)ω2	3a6)ω2	NUM
ejpam-5427	157	10	1	1	NUM
ejpam-5427	157	11	)	)	PUNCT
ejpam-5427	157	12	32768	32768	NUM
ejpam-5427	157	13	)	)	PUNCT
ejpam-5427	158	1	cos(3ω1	cos(3ω1	PROPN
ejpam-5427	158	2	t	t	PROPN
ejpam-5427	158	3	)	)	PUNCT
ejpam-5427	159	1	−.	−.	NOUN
ejpam-5427	159	2	(	(	PUNCT
ejpam-5427	159	3	a5(1792	a5(1792	ADP
ejpam-5427	159	4	+	+	SYM
ejpam-5427	159	5	88a2+a4)ω2	88a2+a4)ω2	NUM
ejpam-5427	159	6	1	1	NUM
ejpam-5427	159	7	32768	32768	NUM
ejpam-5427	159	8	)	)	PUNCT
ejpam-5427	160	1	cos(5ω1	cos(5ω1	PROPN
ejpam-5427	160	2	t	t	PROPN
ejpam-5427	160	3	)	)	PUNCT
ejpam-5427	161	1	+	+	CCONJ
ejpam-5427	161	2	(	(	PUNCT
ejpam-5427	161	3	15a7(32+a2)ω2	15a7(32+a2)ω2	NUM
ejpam-5427	161	4	1	1	NUM
ejpam-5427	161	5	131072	131072	NUM
ejpam-5427	161	6	)	)	PUNCT
ejpam-5427	161	7	cos(7ω1	cos(7ω1	PROPN
ejpam-5427	161	8	t	t	PROPN
ejpam-5427	161	9	)	)	PUNCT
ejpam-5427	161	10	−	−	PROPN
ejpam-5427	161	11	(	(	PUNCT
ejpam-5427	161	12	9a9ω2	9a9ω2	NOUN
ejpam-5427	161	13	1	1	NUM
ejpam-5427	161	14	)	)	PUNCT
ejpam-5427	161	15	131072	131072	NUM
ejpam-5427	161	16	)	)	PUNCT
ejpam-5427	161	17	cos(9ω1	cos(9ω1	PROPN
ejpam-5427	161	18	t	t	NOUN
ejpam-5427	161	19	)	)	PUNCT
ejpam-5427	161	20	.	.	PUNCT
ejpam-5427	161	21	.	.	PUNCT
ejpam-5427	162	1	(	(	PUNCT
ejpam-5427	162	2	31	31	NUM
ejpam-5427	162	3	)	)	PUNCT
ejpam-5427	162	4	to	to	PART
ejpam-5427	162	5	avoid	avoid	VERB
ejpam-5427	162	6	dominating	dominate	VERB
ejpam-5427	162	7	terms	term	NOUN
ejpam-5427	162	8	in	in	ADP
ejpam-5427	162	9	eq	eq	NOUN
ejpam-5427	162	10	(	(	PUNCT
ejpam-5427	162	11	31	31	NUM
ejpam-5427	162	12	)	)	PUNCT
ejpam-5427	162	13	,	,	PUNCT
ejpam-5427	162	14	we	we	PRON
ejpam-5427	162	15	obtain	obtain	VERB
ejpam-5427	162	16	ω1	ω1	NOUN
ejpam-5427	162	17	=	=	PUNCT
ejpam-5427	162	18	32	32	NUM
ejpam-5427	162	19	√	√	NUM
ejpam-5427	162	20	2	2	NUM
ejpam-5427	162	21	√	√	NUM
ejpam-5427	162	22	32	32	NUM
ejpam-5427	162	23	+	+	SYM
ejpam-5427	162	24	a2	a2	PROPN
ejpam-5427	162	25	√	√	ADP
ejpam-5427	162	26	65536−	65536−	NUM
ejpam-5427	162	27	14336a2	14336a2	NOUN
ejpam-5427	162	28	+	+	CCONJ
ejpam-5427	162	29	1024a4	1024a4	NUM
ejpam-5427	162	30	−	−	NOUN
ejpam-5427	162	31	176a6	176a6	NUM
ejpam-5427	162	32	−	−	NOUN
ejpam-5427	162	33	7a8	7a8	NUM
ejpam-5427	162	34	,	,	PUNCT
ejpam-5427	162	35	(	(	PUNCT
ejpam-5427	162	36	32	32	NUM
ejpam-5427	162	37	)	)	PUNCT
ejpam-5427	162	38	g.	g.	PROPN
ejpam-5427	162	39	m.	m.	PROPN
ejpam-5427	162	40	ismail	ismail	PROPN
ejpam-5427	162	41	,	,	PUNCT
ejpam-5427	162	42	m.	m.	NOUN
ejpam-5427	162	43	i.	i.	PROPN
ejpam-5427	162	44	yamani	yamani	PROPN
ejpam-5427	162	45	/	/	SYM
ejpam-5427	162	46	eur	eur	PROPN
ejpam-5427	162	47	.	.	PUNCT
ejpam-5427	163	1	j.	j.	PROPN
ejpam-5427	163	2	pure	pure	PROPN
ejpam-5427	163	3	appl	appl	PROPN
ejpam-5427	163	4	.	.	PROPN
ejpam-5427	163	5	math	math	PROPN
ejpam-5427	163	6	,	,	PUNCT
ejpam-5427	163	7	17	17	NUM
ejpam-5427	163	8	(	(	PUNCT
ejpam-5427	163	9	4	4	NUM
ejpam-5427	163	10	)	)	PUNCT
ejpam-5427	163	11	(	(	PUNCT
ejpam-5427	163	12	2024	2024	NUM
ejpam-5427	163	13	)	)	PUNCT
ejpam-5427	163	14	,	,	PUNCT
ejpam-5427	163	15	3622	3622	NUM
ejpam-5427	163	16	-	-	SYM
ejpam-5427	163	17	3641	3641	NUM
ejpam-5427	163	18	3628	3628	NUM
ejpam-5427	163	19	after	after	ADP
ejpam-5427	163	20	solving	solve	VERB
ejpam-5427	163	21	eq	eq	ADP
ejpam-5427	163	22	.	.	PUNCT
ejpam-5427	164	1	(	(	PUNCT
ejpam-5427	164	2	31	31	NUM
ejpam-5427	164	3	)	)	PUNCT
ejpam-5427	164	4	with	with	ADP
ejpam-5427	164	5	the	the	DET
ejpam-5427	164	6	initial	initial	ADJ
ejpam-5427	164	7	conditions	condition	NOUN
ejpam-5427	164	8	,	,	PUNCT
ejpam-5427	164	9	we	we	PRON
ejpam-5427	164	10	have	have	VERB
ejpam-5427	164	11	the	the	DET
ejpam-5427	164	12	second	second	ADJ
ejpam-5427	164	13	approximate	approximate	ADJ
ejpam-5427	164	14	solution	solution	NOUN
ejpam-5427	164	15	.	.	PUNCT
ejpam-5427	165	1	y2	y2	NOUN
ejpam-5427	166	1	=	=	PRON
ejpam-5427	167	1	(	(	PUNCT
ejpam-5427	167	2	a+	a+	PUNCT
ejpam-5427	167	3	7a3	7a3	NUM
ejpam-5427	167	4	256	256	NUM
ejpam-5427	167	5	+	+	CCONJ
ejpam-5427	167	6	a5	a5	PROPN
ejpam-5427	167	7	384	384	NUM
ejpam-5427	167	8	+	+	CCONJ
ejpam-5427	167	9	35a7	35a7	NUM
ejpam-5427	167	10	196608	196608	NUM
ejpam-5427	167	11	+	+	CCONJ
ejpam-5427	167	12	23a9	23a9	NUM
ejpam-5427	167	13	1966080	1966080	NUM
ejpam-5427	167	14	+	+	CCONJ
ejpam-5427	167	15	a3	a3	VERB
ejpam-5427	167	16	256ω2	256ω2	NUM
ejpam-5427	167	17	1	1	NUM
ejpam-5427	167	18	)	)	PUNCT
ejpam-5427	167	19	cos(ω2	cos(ω2	NOUN
ejpam-5427	167	20	t	t	NOUN
ejpam-5427	167	21	)	)	PUNCT
ejpam-5427	167	22	−	−	PROPN
ejpam-5427	168	1	(	(	PUNCT
ejpam-5427	168	2	a3(1024+(7168	a3(1024+(7168	ADP
ejpam-5427	168	3	+	+	NOUN
ejpam-5427	168	4	1280a2	1280a2	NOUN
ejpam-5427	168	5	+	+	NOUN
ejpam-5427	168	6	56a4	56a4	NUM
ejpam-5427	168	7	+	+	SYM
ejpam-5427	168	8	3a6)ω2	3a6)ω2	NUM
ejpam-5427	168	9	1	1	NUM
ejpam-5427	168	10	)	)	PUNCT
ejpam-5427	168	11	262144ω2	262144ω2	NOUN
ejpam-5427	168	12	1	1	NUM
ejpam-5427	168	13	)	)	PUNCT
ejpam-5427	168	14	cos(3ω2	cos(3ω2	PROPN
ejpam-5427	168	15	t	t	PROPN
ejpam-5427	168	16	)	)	PUNCT
ejpam-5427	168	17	+	+	CCONJ
ejpam-5427	169	1	(	(	PUNCT
ejpam-5427	169	2	a5(1792	a5(1792	ADV
ejpam-5427	169	3	+	+	NOUN
ejpam-5427	169	4	88a2+a4	88a2+a4	NUM
ejpam-5427	169	5	)	)	PUNCT
ejpam-5427	169	6	786432	786432	NUM
ejpam-5427	169	7	)	)	PUNCT
ejpam-5427	170	1	cos(5ω2t)−	cos(5ω2t)−	PROPN
ejpam-5427	170	2	(	(	PUNCT
ejpam-5427	170	3	5a7(32+a2	5a7(32+a2	PROPN
ejpam-5427	170	4	)	)	PUNCT
ejpam-5427	170	5	2097152	2097152	NUM
ejpam-5427	170	6	)	)	PUNCT
ejpam-5427	170	7	cos(7ω2	cos(7ω2	NOUN
ejpam-5427	170	8	t	t	PROPN
ejpam-5427	170	9	)	)	PUNCT
ejpam-5427	170	10	+	+	CCONJ
ejpam-5427	170	11	(	(	PUNCT
ejpam-5427	170	12	9a9	9a9	NUM
ejpam-5427	170	13	10485760	10485760	NUM
ejpam-5427	170	14	)	)	PUNCT
ejpam-5427	170	15	cos(9ω2	cos(9ω2	PROPN
ejpam-5427	170	16	t	t	PROPN
ejpam-5427	170	17	)	)	PUNCT
ejpam-5427	170	18	.	.	PUNCT
ejpam-5427	171	1	(	(	PUNCT
ejpam-5427	171	2	33	33	NUM
ejpam-5427	171	3	)	)	PUNCT
ejpam-5427	171	4	3.2.3	3.2.3	NUM
ejpam-5427	171	5	.	.	PUNCT
ejpam-5427	171	6	third	third	ADJ
ejpam-5427	171	7	iteration	iteration	NOUN
ejpam-5427	171	8	solution	solution	NOUN
ejpam-5427	171	9	for	for	ADP
ejpam-5427	171	10	the	the	DET
ejpam-5427	171	11	third	third	ADJ
ejpam-5427	171	12	level	level	NOUN
ejpam-5427	171	13	of	of	ADP
ejpam-5427	171	14	iteration	iteration	NOUN
ejpam-5427	171	15	continuing	continue	VERB
ejpam-5427	171	16	to	to	ADP
ejpam-5427	171	17	k	k	PROPN
ejpam-5427	171	18	=	=	SYM
ejpam-5427	171	19	2	2	X
ejpam-5427	171	20	.	.	PUNCT
ejpam-5427	171	21	substituting	substitute	VERB
ejpam-5427	171	22	y2	y2	PROPN
ejpam-5427	171	23	from	from	ADP
ejpam-5427	171	24	eq	eq	PROPN
ejpam-5427	171	25	.	.	PUNCT
ejpam-5427	172	1	(	(	PUNCT
ejpam-5427	172	2	32	32	NUM
ejpam-5427	172	3	)	)	PUNCT
ejpam-5427	172	4	into	into	ADP
ejpam-5427	172	5	the	the	DET
ejpam-5427	172	6	right	right	ADJ
ejpam-5427	172	7	hand	hand	NOUN
ejpam-5427	172	8	side	side	NOUN
ejpam-5427	172	9	of	of	ADP
ejpam-5427	172	10	eq	eq	PROPN
ejpam-5427	172	11	.	.	PUNCT
ejpam-5427	173	1	(	(	PUNCT
ejpam-5427	173	2	13	13	NUM
ejpam-5427	173	3	)	)	PUNCT
ejpam-5427	173	4	,	,	PUNCT
ejpam-5427	173	5	we	we	PRON
ejpam-5427	173	6	have	have	VERB
ejpam-5427	173	7	ÿ3	ÿ3	PROPN
ejpam-5427	173	8	+	+	CCONJ
ejpam-5427	173	9	ω2	ω2	ADJ
ejpam-5427	173	10	2y3	2y3	NUM
ejpam-5427	174	1	=	=	SYM
ejpam-5427	174	2	ω2	ω2	ADJ
ejpam-5427	174	3	2y2	2y2	NUM
ejpam-5427	174	4	−	−	PROPN
ejpam-5427	175	1	y2	y2	PROPN
ejpam-5427	175	2	−	−	PROPN
ejpam-5427	175	3	y2ẏ	y2ẏ	ADJ
ejpam-5427	175	4	2	2	NUM
ejpam-5427	175	5	2	2	NUM
ejpam-5427	175	6	.	.	PUNCT
ejpam-5427	176	1	(	(	PUNCT
ejpam-5427	176	2	34	34	NUM
ejpam-5427	176	3	)	)	PUNCT
ejpam-5427	176	4	solving	solve	VERB
ejpam-5427	176	5	eq	eq	NOUN
ejpam-5427	176	6	.	.	PUNCT
ejpam-5427	177	1	(	(	PUNCT
ejpam-5427	177	2	34	34	NUM
ejpam-5427	177	3	)	)	PUNCT
ejpam-5427	177	4	,	,	PUNCT
ejpam-5427	177	5	and	and	CCONJ
ejpam-5427	177	6	avoiding	avoid	VERB
ejpam-5427	177	7	secular	secular	ADJ
ejpam-5427	177	8	terms	term	NOUN
ejpam-5427	177	9	,	,	PUNCT
ejpam-5427	177	10	we	we	PRON
ejpam-5427	177	11	can	can	AUX
ejpam-5427	177	12	obtain	obtain	VERB
ejpam-5427	177	13	ω2	ω2	ADV
ejpam-5427	177	14	in	in	ADP
ejpam-5427	177	15	the	the	DET
ejpam-5427	177	16	same	same	ADJ
ejpam-5427	177	17	manner	manner	NOUN
ejpam-5427	177	18	as	as	ADP
ejpam-5427	177	19	application	application	NOUN
ejpam-5427	177	20	(	(	PUNCT
ejpam-5427	177	21	1	1	NUM
ejpam-5427	177	22	)	)	PUNCT
ejpam-5427	177	23	.	.	PUNCT
ejpam-5427	178	1	the	the	DET
ejpam-5427	178	2	numerical	numerical	PROPN
ejpam-5427	178	3	data	data	PROPN
ejpam-5427	178	4	will	will	AUX
ejpam-5427	178	5	be	be	AUX
ejpam-5427	178	6	presented	present	VERB
ejpam-5427	178	7	in	in	ADP
ejpam-5427	178	8	the	the	DET
ejpam-5427	178	9	findings	finding	NOUN
ejpam-5427	178	10	and	and	CCONJ
ejpam-5427	178	11	discussion	discussion	NOUN
ejpam-5427	178	12	section	section	NOUN
ejpam-5427	178	13	.	.	PUNCT
ejpam-5427	179	1	ω2	ω2	NOUN
ejpam-5427	179	2	=	=	SYM
ejpam-5427	179	3	(	(	PUNCT
ejpam-5427	179	4	10485760	10485760	NUM
ejpam-5427	179	5	√	√	NUM
ejpam-5427	179	6	23592960a+737280a3	23592960a+737280a3	NUM
ejpam-5427	180	1	+	+	NUM
ejpam-5427	181	1	38400a5	38400a5	PROPN
ejpam-5427	181	2	+	+	ADJ
ejpam-5427	181	3	6360a7−39a9	6360a7−39a9	PROPN
ejpam-5427	181	4	2048−512a2	2048−512a2	NOUN
ejpam-5427	181	5	+	+	NOUN
ejpam-5427	181	6	48a4−7a6	48a4−7a6	PROPN
ejpam-5427	181	7	)	)	PUNCT
ejpam-5427	181	8	/(√	/(√	PUNCT
ejpam-5427	182	1	(	(	PUNCT
ejpam-5427	182	2	(	(	PUNCT
ejpam-5427	182	3	−2594073385365405696000a+	−2594073385365405696000a+	X
ejpam-5427	182	4	567453553048682496000a3	567453553048682496000a3	PROPN
ejpam-5427	182	5	−44754521296994304000a5	−44754521296994304000a5	PUNCT
ejpam-5427	182	6	−	−	PROPN
ejpam-5427	182	7	3232564185661440000a7	3232564185661440000a7	NUM
ejpam-5427	183	1	+172513374398054400a9	+172513374398054400a9	NOUN
ejpam-5427	184	1	+	+	CCONJ
ejpam-5427	184	2	248228493865779200a11	248228493865779200a11	NUM
ejpam-5427	184	3	+19274524734259200a13	+19274524734259200a13	NOUN
ejpam-5427	184	4	+	+	X
ejpam-5427	184	5	2109308770713600a15	2109308770713600a15	NUM
ejpam-5427	184	6	+185788373401600a17	+185788373401600a17	NOUN
ejpam-5427	185	1	+	+	CCONJ
ejpam-5427	185	2	8293138432000a19	8293138432000a19	PROPN
ejpam-5427	185	3	+	+	CCONJ
ejpam-5427	185	4	200006092800a21	200006092800a21	NUM
ejpam-5427	185	5	+2252995200a23	+2252995200a23	NOUN
ejpam-5427	186	1	+	+	X
ejpam-5427	187	1	174151100a25	174151100a25	NUM
ejpam-5427	187	2	−	−	NOUN
ejpam-5427	187	3	997773a27)/(−2048	997773a27)/(−2048	NUM
ejpam-5427	188	1	+	+	CCONJ
ejpam-5427	188	2	512a2	512a2	NUM
ejpam-5427	188	3	−48a4	−48a4	NUM
ejpam-5427	188	4	+	+	NOUN
ejpam-5427	188	5	7a6	7a6	NUM
ejpam-5427	188	6	)	)	PUNCT
ejpam-5427	188	7	)	)	PUNCT
ejpam-5427	188	8	)	)	PUNCT
ejpam-5427	188	9	.	.	PUNCT
ejpam-5427	189	1	(	(	PUNCT
ejpam-5427	189	2	35	35	NUM
ejpam-5427	189	3	)	)	PUNCT
ejpam-5427	189	4	integrating	integrate	VERB
ejpam-5427	189	5	eq	eq	NOUN
ejpam-5427	189	6	.	.	PUNCT
ejpam-5427	190	1	(	(	PUNCT
ejpam-5427	190	2	33	33	NUM
ejpam-5427	190	3	)	)	PUNCT
ejpam-5427	190	4	,	,	PUNCT
ejpam-5427	190	5	we	we	PRON
ejpam-5427	190	6	obtain	obtain	VERB
ejpam-5427	190	7	the	the	DET
ejpam-5427	190	8	analytical	analytical	ADJ
ejpam-5427	190	9	solution	solution	NOUN
ejpam-5427	190	10	of	of	ADP
ejpam-5427	190	11	eq	eq	PROPN
ejpam-5427	190	12	.	.	PUNCT
ejpam-5427	191	1	(	(	PUNCT
ejpam-5427	191	2	25	25	NUM
ejpam-5427	191	3	)	)	PUNCT
ejpam-5427	191	4	in	in	ADP
ejpam-5427	191	5	the	the	DET
ejpam-5427	191	6	form	form	NOUN
ejpam-5427	191	7	:	:	PUNCT
ejpam-5427	191	8	x	x	SYM
ejpam-5427	191	9	=	=	SYM
ejpam-5427	191	10	1	1	NUM
ejpam-5427	191	11	220200960	220200960	NUM
ejpam-5427	191	12	ω2	ω2	ADV
ejpam-5427	191	13	(	(	PUNCT
ejpam-5427	191	14	−28a	−28a	PROPN
ejpam-5427	191	15	(	(	PUNCT
ejpam-5427	191	16	−7864320−	−7864320−	PROPN
ejpam-5427	191	17	245760a2	245760a2	NOUN
ejpam-5427	192	1	−	−	NOUN
ejpam-5427	192	2	12800a4	12800a4	NUM
ejpam-5427	193	1	−	−	NOUN
ejpam-5427	193	2	2120a6	2120a6	NUM
ejpam-5427	194	1	+	+	CCONJ
ejpam-5427	194	2	13a8	13a8	NUM
ejpam-5427	194	3	)	)	PUNCT
ejpam-5427	194	4	sin(ω2	sin(ω2	PROPN
ejpam-5427	194	5	t	t	PROPN
ejpam-5427	194	6	)	)	PUNCT
ejpam-5427	194	7	+140a3	+140a3	NOUN
ejpam-5427	194	8	(	(	PUNCT
ejpam-5427	194	9	−16384−	−16384−	PROPN
ejpam-5427	194	10	2048a2	2048a2	PROPN
ejpam-5427	195	1	−	−	ADP
ejpam-5427	195	2	160a4	160a4	NUM
ejpam-5427	196	1	+	+	SYM
ejpam-5427	196	2	a6	a6	NOUN
ejpam-5427	196	3	)	)	PUNCT
ejpam-5427	196	4	sin(3ω2	sin(3ω2	PROPN
ejpam-5427	196	5	t	t	PROPN
ejpam-5427	196	6	)	)	PUNCT
ejpam-5427	197	1	+	+	PROPN
ejpam-5427	197	2	(	(	PUNCT
ejpam-5427	197	3	100352a5	100352a5	PROPN
ejpam-5427	197	4	+	+	NUM
ejpam-5427	197	5	4928a7	4928a7	NUM
ejpam-5427	197	6	+	+	CCONJ
ejpam-5427	197	7	56a9	56a9	NUM
ejpam-5427	197	8	)	)	PUNCT
ejpam-5427	197	9	sin(5ω2	sin(5ω2	PROPN
ejpam-5427	197	10	t	t	NOUN
ejpam-5427	197	11	)	)	PUNCT
ejpam-5427	197	12	−	−	PROPN
ejpam-5427	198	1	(	(	PUNCT
ejpam-5427	198	2	2400a7	2400a7	NUM
ejpam-5427	198	3	+	+	NUM
ejpam-5427	198	4	75a9	75a9	NUM
ejpam-5427	198	5	)	)	PUNCT
ejpam-5427	198	6	sin(7ω2	sin(7ω2	NOUN
ejpam-5427	198	7	t	t	PROPN
ejpam-5427	198	8	)	)	PUNCT
ejpam-5427	198	9	+	+	CCONJ
ejpam-5427	199	1	21a9	21a9	NUM
ejpam-5427	199	2	sin(9ω2	sin(9ω2	PROPN
ejpam-5427	199	3	t	t	PROPN
ejpam-5427	199	4	)	)	PUNCT
ejpam-5427	199	5	)	)	PUNCT
ejpam-5427	199	6	.	.	PUNCT
ejpam-5427	199	7	.	.	PUNCT
ejpam-5427	200	1	(	(	PUNCT
ejpam-5427	200	2	36	36	NUM
ejpam-5427	200	3	)	)	PUNCT
ejpam-5427	200	4	4	4	NUM
ejpam-5427	200	5	.	.	PUNCT
ejpam-5427	201	1	discussions	discussion	NOUN
ejpam-5427	201	2	in	in	ADP
ejpam-5427	201	3	this	this	DET
ejpam-5427	201	4	section	section	NOUN
ejpam-5427	201	5	,	,	PUNCT
ejpam-5427	201	6	the	the	DET
ejpam-5427	201	7	approximate	approximate	ADJ
ejpam-5427	201	8	analytical	analytical	ADJ
ejpam-5427	201	9	solutions	solution	NOUN
ejpam-5427	201	10	of	of	ADP
ejpam-5427	201	11	eqs	eqs	PROPN
ejpam-5427	201	12	.	.	PUNCT
ejpam-5427	202	1	(	(	PUNCT
ejpam-5427	202	2	9	9	NUM
ejpam-5427	202	3	)	)	PUNCT
ejpam-5427	202	4	and	and	CCONJ
ejpam-5427	202	5	(	(	PUNCT
ejpam-5427	202	6	25	25	NUM
ejpam-5427	202	7	)	)	PUNCT
ejpam-5427	202	8	,	,	PUNCT
ejpam-5427	202	9	obtained	obtain	VERB
ejpam-5427	202	10	using	use	VERB
ejpam-5427	202	11	the	the	DET
ejpam-5427	202	12	modified	modify	VERB
ejpam-5427	202	13	iteration	iteration	NOUN
ejpam-5427	202	14	approach	approach	NOUN
ejpam-5427	202	15	as	as	SCONJ
ejpam-5427	202	16	shown	show	VERB
ejpam-5427	202	17	in	in	ADP
ejpam-5427	202	18	eqs	eqs	PROPN
ejpam-5427	202	19	.	.	PUNCT
ejpam-5427	203	1	(	(	PUNCT
ejpam-5427	203	2	24	24	NUM
ejpam-5427	203	3	)	)	PUNCT
ejpam-5427	203	4	and	and	CCONJ
ejpam-5427	203	5	(	(	PUNCT
ejpam-5427	203	6	36	36	NUM
ejpam-5427	203	7	)	)	PUNCT
ejpam-5427	203	8	,	,	PUNCT
ejpam-5427	203	9	are	be	AUX
ejpam-5427	203	10	compared	compare	VERB
ejpam-5427	203	11	with	with	ADP
ejpam-5427	203	12	those	those	PRON
ejpam-5427	203	13	obtained	obtain	VERB
ejpam-5427	203	14	from	from	ADP
ejpam-5427	203	15	fourth	fourth	ADJ
ejpam-5427	203	16	-	-	PUNCT
ejpam-5427	203	17	order	order	NOUN
ejpam-5427	203	18	runge	runge	NOUN
ejpam-5427	203	19	-	-	PUNCT
ejpam-5427	203	20	kutta	kutta	NOUN
ejpam-5427	203	21	numerical	numerical	ADJ
ejpam-5427	203	22	solutions	solution	NOUN
ejpam-5427	203	23	and	and	CCONJ
ejpam-5427	203	24	other	other	ADJ
ejpam-5427	203	25	known	know	VERB
ejpam-5427	203	26	analytical	analytical	ADJ
ejpam-5427	203	27	methods	method	NOUN
ejpam-5427	203	28	from	from	ADP
ejpam-5427	203	29	the	the	DET
ejpam-5427	203	30	literature	literature	NOUN
ejpam-5427	203	31	.	.	PUNCT
ejpam-5427	204	1	this	this	DET
ejpam-5427	204	2	comparison	comparison	NOUN
ejpam-5427	204	3	is	be	AUX
ejpam-5427	204	4	presented	present	VERB
ejpam-5427	204	5	in	in	ADP
ejpam-5427	204	6	figures	figure	NOUN
ejpam-5427	204	7	1	1	NUM
ejpam-5427	204	8	−	−	PROPN
ejpam-5427	204	9	4	4	NUM
ejpam-5427	204	10	g.	g.	PROPN
ejpam-5427	204	11	m.	m.	PROPN
ejpam-5427	204	12	ismail	ismail	PROPN
ejpam-5427	204	13	,	,	PUNCT
ejpam-5427	204	14	m.	m.	NOUN
ejpam-5427	204	15	i.	i.	PROPN
ejpam-5427	204	16	yamani	yamani	PROPN
ejpam-5427	204	17	/	/	SYM
ejpam-5427	204	18	eur	eur	PROPN
ejpam-5427	204	19	.	.	PUNCT
ejpam-5427	205	1	j.	j.	PROPN
ejpam-5427	205	2	pure	pure	PROPN
ejpam-5427	205	3	appl	appl	PROPN
ejpam-5427	205	4	.	.	PROPN
ejpam-5427	205	5	math	math	PROPN
ejpam-5427	205	6	,	,	PUNCT
ejpam-5427	205	7	17	17	NUM
ejpam-5427	205	8	(	(	PUNCT
ejpam-5427	205	9	4	4	NUM
ejpam-5427	205	10	)	)	PUNCT
ejpam-5427	205	11	(	(	PUNCT
ejpam-5427	205	12	2024	2024	NUM
ejpam-5427	205	13	)	)	PUNCT
ejpam-5427	205	14	,	,	PUNCT
ejpam-5427	205	15	3622	3622	NUM
ejpam-5427	205	16	-	-	SYM
ejpam-5427	205	17	3641	3641	NUM
ejpam-5427	205	18	3629	3629	NUM
ejpam-5427	205	19	and	and	CCONJ
ejpam-5427	205	20	tables	table	NOUN
ejpam-5427	205	21	1−	1−	NUM
ejpam-5427	205	22	6	6	NUM
ejpam-5427	205	23	.	.	PUNCT
ejpam-5427	206	1	the	the	DET
ejpam-5427	206	2	graphical	graphical	ADJ
ejpam-5427	206	3	representations	representation	NOUN
ejpam-5427	206	4	clearly	clearly	ADV
ejpam-5427	206	5	demonstrate	demonstrate	VERB
ejpam-5427	206	6	that	that	SCONJ
ejpam-5427	206	7	the	the	DET
ejpam-5427	206	8	results	result	NOUN
ejpam-5427	206	9	obtained	obtain	VERB
ejpam-5427	206	10	from	from	ADP
ejpam-5427	206	11	the	the	DET
ejpam-5427	206	12	present	present	ADJ
ejpam-5427	206	13	approach	approach	NOUN
ejpam-5427	206	14	are	be	AUX
ejpam-5427	206	15	in	in	ADP
ejpam-5427	206	16	excellent	excellent	ADJ
ejpam-5427	206	17	agreement	agreement	NOUN
ejpam-5427	206	18	with	with	ADP
ejpam-5427	206	19	those	those	PRON
ejpam-5427	206	20	obtained	obtain	VERB
ejpam-5427	206	21	using	use	VERB
ejpam-5427	206	22	the	the	DET
ejpam-5427	206	23	fourth	fourth	ADJ
ejpam-5427	206	24	-	-	PUNCT
ejpam-5427	206	25	order	order	NOUN
ejpam-5427	206	26	runge	runge	NOUN
ejpam-5427	206	27	-	-	PUNCT
ejpam-5427	206	28	kutta	kutta	NOUN
ejpam-5427	206	29	method	method	NOUN
ejpam-5427	206	30	.	.	PUNCT
ejpam-5427	207	1	moreover	moreover	ADV
ejpam-5427	207	2	,	,	PUNCT
ejpam-5427	207	3	the	the	DET
ejpam-5427	207	4	present	present	ADJ
ejpam-5427	207	5	approach	approach	NOUN
ejpam-5427	207	6	accurately	accurately	ADV
ejpam-5427	207	7	predicts	predict	VERB
ejpam-5427	207	8	the	the	DET
ejpam-5427	207	9	periodic	periodic	ADJ
ejpam-5427	207	10	behavior	behavior	NOUN
ejpam-5427	207	11	of	of	ADP
ejpam-5427	207	12	the	the	DET
ejpam-5427	207	13	equations	equation	NOUN
ejpam-5427	207	14	over	over	ADP
ejpam-5427	207	15	a	a	DET
ejpam-5427	207	16	wide	wide	ADJ
ejpam-5427	207	17	range	range	NOUN
ejpam-5427	207	18	.	.	PUNCT
ejpam-5427	208	1	to	to	PART
ejpam-5427	208	2	demonstrate	demonstrate	VERB
ejpam-5427	208	3	the	the	DET
ejpam-5427	208	4	exceptional	exceptional	ADJ
ejpam-5427	208	5	accuracy	accuracy	NOUN
ejpam-5427	208	6	of	of	ADP
ejpam-5427	208	7	the	the	DET
ejpam-5427	208	8	modified	modify	VERB
ejpam-5427	208	9	iteration	iteration	NOUN
ejpam-5427	208	10	technique	technique	NOUN
ejpam-5427	208	11	,	,	PUNCT
ejpam-5427	208	12	we	we	PRON
ejpam-5427	208	13	examine	examine	VERB
ejpam-5427	208	14	two	two	NUM
ejpam-5427	208	15	cases	case	NOUN
ejpam-5427	208	16	of	of	ADP
ejpam-5427	208	17	non	non	ADJ
ejpam-5427	208	18	-	-	ADJ
ejpam-5427	208	19	linear	linear	ADJ
ejpam-5427	208	20	third	third	ADJ
ejpam-5427	208	21	-	-	PUNCT
ejpam-5427	208	22	order	order	NOUN
ejpam-5427	208	23	jerk	jerk	NOUN
ejpam-5427	208	24	equations	equation	NOUN
ejpam-5427	208	25	.	.	PUNCT
ejpam-5427	209	1	we	we	PRON
ejpam-5427	209	2	compare	compare	VERB
ejpam-5427	209	3	the	the	DET
ejpam-5427	209	4	approximate	approximate	ADJ
ejpam-5427	209	5	results	result	NOUN
ejpam-5427	209	6	obtained	obtain	VERB
ejpam-5427	209	7	using	use	VERB
ejpam-5427	209	8	this	this	DET
ejpam-5427	209	9	technique	technique	NOUN
ejpam-5427	209	10	with	with	ADP
ejpam-5427	209	11	existing	exist	VERB
ejpam-5427	209	12	analytical	analytical	ADJ
ejpam-5427	209	13	solutions	solution	NOUN
ejpam-5427	209	14	from	from	ADP
ejpam-5427	209	15	the	the	DET
ejpam-5427	209	16	literature	literature	NOUN
ejpam-5427	209	17	and	and	CCONJ
ejpam-5427	209	18	with	with	ADP
ejpam-5427	209	19	numerical	numerical	ADJ
ejpam-5427	209	20	integration	integration	NOUN
ejpam-5427	209	21	results	result	NOUN
ejpam-5427	209	22	to	to	PART
ejpam-5427	209	23	validate	validate	VERB
ejpam-5427	209	24	the	the	DET
ejpam-5427	209	25	accuracy	accuracy	NOUN
ejpam-5427	209	26	of	of	ADP
ejpam-5427	209	27	the	the	DET
ejpam-5427	209	28	solutions	solution	NOUN
ejpam-5427	209	29	derived	derive	VERB
ejpam-5427	209	30	.	.	PUNCT
ejpam-5427	210	1	for	for	ADP
ejpam-5427	210	2	the	the	DET
ejpam-5427	210	3	same	same	ADJ
ejpam-5427	210	4	cases	case	NOUN
ejpam-5427	210	5	discussed	discuss	VERB
ejpam-5427	210	6	using	use	VERB
ejpam-5427	210	7	the	the	DET
ejpam-5427	210	8	block	block	NOUN
ejpam-5427	210	9	method	method	NOUN
ejpam-5427	210	10	[	[	X
ejpam-5427	210	11	24	24	NUM
ejpam-5427	210	12	]	]	PUNCT
ejpam-5427	210	13	,	,	PUNCT
ejpam-5427	210	14	harmonic	harmonic	ADJ
ejpam-5427	210	15	balance	balance	NOUN
ejpam-5427	210	16	method	method	NOUN
ejpam-5427	210	17	[	[	X
ejpam-5427	210	18	25	25	NUM
ejpam-5427	210	19	]	]	PUNCT
ejpam-5427	210	20	,	,	PUNCT
ejpam-5427	210	21	homotopy	homotopy	VERB
ejpam-5427	210	22	perturbation	perturbation	NOUN
ejpam-5427	210	23	method	method	NOUN
ejpam-5427	210	24	[	[	X
ejpam-5427	210	25	27	27	NUM
ejpam-5427	210	26	]	]	X
ejpam-5427	210	27	,	,	PUNCT
ejpam-5427	210	28	linstedt	linstedt	ADJ
ejpam-5427	210	29	-	-	PUNCT
ejpam-5427	210	30	poincare	poincare	PROPN
ejpam-5427	210	31	methods	method	NOUN
ejpam-5427	210	32	[	[	X
ejpam-5427	210	33	30	30	NUM
ejpam-5427	210	34	]	]	PUNCT
ejpam-5427	210	35	,	,	PUNCT
ejpam-5427	210	36	residue	residue	NOUN
ejpam-5427	210	37	harmonic	harmonic	ADJ
ejpam-5427	210	38	balance	balance	NOUN
ejpam-5427	210	39	method	method	NOUN
ejpam-5427	210	40	[	[	X
ejpam-5427	210	41	31	31	NUM
ejpam-5427	210	42	]	]	PUNCT
ejpam-5427	210	43	,	,	PUNCT
ejpam-5427	210	44	multiple	multiple	ADJ
ejpam-5427	210	45	scales	scale	NOUN
ejpam-5427	210	46	lindstedt	lindstedt	PROPN
ejpam-5427	210	47	-	-	PUNCT
ejpam-5427	210	48	poincare	poincare	PROPN
ejpam-5427	211	1	[	[	X
ejpam-5427	211	2	32	32	NUM
ejpam-5427	211	3	]	]	PUNCT
ejpam-5427	211	4	,	,	PUNCT
ejpam-5427	211	5	modified	modify	VERB
ejpam-5427	211	6	harmonic	harmonic	ADJ
ejpam-5427	211	7	balance	balance	NOUN
ejpam-5427	211	8	method	method	NOUN
ejpam-5427	211	9	[	[	X
ejpam-5427	211	10	34	34	NUM
ejpam-5427	211	11	]	]	PUNCT
ejpam-5427	211	12	,	,	PUNCT
ejpam-5427	211	13	differential	differential	ADJ
ejpam-5427	211	14	transform	transform	NOUN
ejpam-5427	211	15	method	method	NOUN
ejpam-5427	211	16	[	[	X
ejpam-5427	211	17	33	33	NUM
ejpam-5427	211	18	]	]	PUNCT
ejpam-5427	211	19	,	,	PUNCT
ejpam-5427	211	20	and	and	CCONJ
ejpam-5427	211	21	global	global	ADJ
ejpam-5427	211	22	error	error	NOUN
ejpam-5427	211	23	minimization	minimization	NOUN
ejpam-5427	211	24	method	method	NOUN
ejpam-5427	211	25	[	[	X
ejpam-5427	211	26	37	37	NUM
ejpam-5427	211	27	]	]	PUNCT
ejpam-5427	211	28	,	,	PUNCT
ejpam-5427	211	29	the	the	DET
ejpam-5427	211	30	present	present	ADJ
ejpam-5427	211	31	results	result	NOUN
ejpam-5427	211	32	were	be	AUX
ejpam-5427	211	33	compared	compare	VERB
ejpam-5427	211	34	with	with	ADP
ejpam-5427	211	35	those	those	PRON
ejpam-5427	211	36	obtained	obtain	VERB
ejpam-5427	211	37	by	by	ADP
ejpam-5427	211	38	the	the	DET
ejpam-5427	211	39	modified	modify	VERB
ejpam-5427	211	40	iteration	iteration	NOUN
ejpam-5427	211	41	technique	technique	NOUN
ejpam-5427	211	42	,	,	PUNCT
ejpam-5427	211	43	as	as	SCONJ
ejpam-5427	211	44	shown	show	VERB
ejpam-5427	211	45	in	in	ADP
ejpam-5427	211	46	tables	table	NOUN
ejpam-5427	211	47	1−	1−	NUM
ejpam-5427	211	48	6	6	NUM
ejpam-5427	211	49	.	.	PUNCT
ejpam-5427	212	1	the	the	DET
ejpam-5427	212	2	numerical	numerical	ADJ
ejpam-5427	212	3	results	result	NOUN
ejpam-5427	212	4	show	show	VERB
ejpam-5427	212	5	excellent	excellent	ADJ
ejpam-5427	212	6	agreement	agreement	NOUN
ejpam-5427	212	7	with	with	ADP
ejpam-5427	212	8	the	the	DET
ejpam-5427	212	9	third	third	ADJ
ejpam-5427	212	10	-	-	PUNCT
ejpam-5427	212	11	order	order	NOUN
ejpam-5427	212	12	approximate	approximate	ADJ
ejpam-5427	212	13	analytical	analytical	ADJ
ejpam-5427	212	14	solutions	solution	NOUN
ejpam-5427	212	15	obtained	obtain	VERB
ejpam-5427	212	16	in	in	ADP
ejpam-5427	212	17	this	this	DET
ejpam-5427	212	18	study	study	NOUN
ejpam-5427	212	19	using	use	VERB
ejpam-5427	212	20	the	the	DET
ejpam-5427	212	21	modified	modify	VERB
ejpam-5427	212	22	iteration	iteration	NOUN
ejpam-5427	212	23	technique	technique	NOUN
ejpam-5427	212	24	.	.	PUNCT
ejpam-5427	213	1	a	a	DET
ejpam-5427	213	2	comparison	comparison	NOUN
ejpam-5427	213	3	between	between	ADP
ejpam-5427	213	4	the	the	DET
ejpam-5427	213	5	higher	high	ADJ
ejpam-5427	213	6	-	-	PUNCT
ejpam-5427	213	7	order	order	NOUN
ejpam-5427	213	8	approximate	approximate	ADJ
ejpam-5427	213	9	solution	solution	NOUN
ejpam-5427	213	10	,	,	PUNCT
ejpam-5427	213	11	the	the	DET
ejpam-5427	213	12	differential	differential	ADJ
ejpam-5427	213	13	transform	transform	NOUN
ejpam-5427	213	14	method	method	NOUN
ejpam-5427	213	15	[	[	X
ejpam-5427	213	16	33	33	NUM
ejpam-5427	213	17	]	]	PUNCT
ejpam-5427	213	18	,	,	PUNCT
ejpam-5427	213	19	and	and	CCONJ
ejpam-5427	213	20	the	the	DET
ejpam-5427	213	21	modified	modify	VERB
ejpam-5427	213	22	global	global	ADJ
ejpam-5427	213	23	error	error	NOUN
ejpam-5427	213	24	minimization	minimization	NOUN
ejpam-5427	213	25	method	method	NOUN
ejpam-5427	213	26	[	[	X
ejpam-5427	213	27	37	37	NUM
ejpam-5427	213	28	]	]	PUNCT
ejpam-5427	213	29	with	with	ADP
ejpam-5427	213	30	the	the	DET
ejpam-5427	213	31	corresponding	corresponding	ADJ
ejpam-5427	213	32	numerical	numerical	ADJ
ejpam-5427	213	33	solution	solution	NOUN
ejpam-5427	213	34	is	be	AUX
ejpam-5427	213	35	presented	present	VERB
ejpam-5427	213	36	in	in	ADP
ejpam-5427	213	37	figures	figure	NOUN
ejpam-5427	213	38	1	1	NUM
ejpam-5427	213	39	−	−	NOUN
ejpam-5427	213	40	4	4	NUM
ejpam-5427	213	41	for	for	ADP
ejpam-5427	213	42	a	a	DET
ejpam-5427	213	43	=	=	SYM
ejpam-5427	213	44	0.3	0.3	NUM
ejpam-5427	213	45	and	and	CCONJ
ejpam-5427	213	46	a	a	DET
ejpam-5427	213	47	=	=	NOUN
ejpam-5427	213	48	1	1	X
ejpam-5427	213	49	.	.	PUNCT
ejpam-5427	214	1	it	it	PRON
ejpam-5427	214	2	is	be	AUX
ejpam-5427	214	3	clear	clear	ADJ
ejpam-5427	214	4	that	that	SCONJ
ejpam-5427	214	5	the	the	DET
ejpam-5427	214	6	approximation	approximation	NOUN
ejpam-5427	214	7	of	of	ADP
ejpam-5427	214	8	the	the	DET
ejpam-5427	214	9	solution	solution	NOUN
ejpam-5427	214	10	using	use	VERB
ejpam-5427	214	11	the	the	DET
ejpam-5427	214	12	modified	modify	VERB
ejpam-5427	214	13	iteration	iteration	NOUN
ejpam-5427	214	14	technique	technique	NOUN
ejpam-5427	214	15	agrees	agree	VERB
ejpam-5427	214	16	with	with	ADP
ejpam-5427	214	17	the	the	DET
ejpam-5427	214	18	differential	differential	ADJ
ejpam-5427	214	19	transform	transform	NOUN
ejpam-5427	214	20	method	method	NOUN
ejpam-5427	214	21	,	,	PUNCT
ejpam-5427	214	22	the	the	DET
ejpam-5427	214	23	modified	modify	VERB
ejpam-5427	214	24	global	global	ADJ
ejpam-5427	214	25	error	error	NOUN
ejpam-5427	214	26	minimization	minimization	NOUN
ejpam-5427	214	27	method	method	NOUN
ejpam-5427	214	28	,	,	PUNCT
ejpam-5427	214	29	and	and	CCONJ
ejpam-5427	214	30	the	the	DET
ejpam-5427	214	31	numerical	numerical	ADJ
ejpam-5427	214	32	solution	solution	NOUN
ejpam-5427	214	33	.	.	PUNCT
ejpam-5427	215	1	furthermore	furthermore	ADV
ejpam-5427	215	2	,	,	PUNCT
ejpam-5427	215	3	the	the	DET
ejpam-5427	215	4	approximate	approximate	ADJ
ejpam-5427	215	5	frequencies	frequency	NOUN
ejpam-5427	215	6	agree	agree	VERB
ejpam-5427	215	7	well	well	ADV
ejpam-5427	215	8	with	with	ADP
ejpam-5427	215	9	the	the	DET
ejpam-5427	215	10	corresponding	corresponding	ADJ
ejpam-5427	215	11	exact	exact	ADJ
ejpam-5427	215	12	solutions	solution	NOUN
ejpam-5427	215	13	,	,	PUNCT
ejpam-5427	215	14	implying	imply	VERB
ejpam-5427	215	15	that	that	SCONJ
ejpam-5427	215	16	using	use	VERB
ejpam-5427	215	17	the	the	DET
ejpam-5427	215	18	modified	modify	VERB
ejpam-5427	215	19	iteration	iteration	NOUN
ejpam-5427	215	20	technique	technique	NOUN
ejpam-5427	215	21	with	with	ADP
ejpam-5427	215	22	higher	high	ADJ
ejpam-5427	215	23	orders	order	NOUN
ejpam-5427	215	24	produces	produce	VERB
ejpam-5427	215	25	realistic	realistic	ADJ
ejpam-5427	215	26	results	result	NOUN
ejpam-5427	215	27	.	.	PUNCT
ejpam-5427	216	1	we	we	PRON
ejpam-5427	216	2	looked	look	VERB
ejpam-5427	216	3	at	at	ADP
ejpam-5427	216	4	the	the	DET
ejpam-5427	216	5	percentage	percentage	NOUN
ejpam-5427	216	6	error	error	NOUN
ejpam-5427	216	7	(	(	PUNCT
ejpam-5427	216	8	%	%	INTJ
ejpam-5427	216	9	)	)	PUNCT
ejpam-5427	216	10	by	by	ADP
ejpam-5427	216	11	the	the	DET
ejpam-5427	216	12	definition	definition	NOUN
ejpam-5427	216	13	to	to	PART
ejpam-5427	216	14	confirm	confirm	VERB
ejpam-5427	216	15	the	the	DET
ejpam-5427	216	16	accuracy	accuracy	NOUN
ejpam-5427	216	17	.	.	PUNCT
ejpam-5427	217	1	error	error	NOUN
ejpam-5427	217	2	=	=	SYM
ejpam-5427	217	3	∣∣∣∣te	∣∣∣∣te	NOUN
ejpam-5427	217	4	−	−	PROPN
ejpam-5427	217	5	tapp	tapp	PROPN
ejpam-5427	217	6	te	te	PROPN
ejpam-5427	217	7	∣∣∣∣×	∣∣∣∣×	PROPN
ejpam-5427	217	8	100	100	NUM
ejpam-5427	217	9	%	%	NOUN
ejpam-5427	217	10	.	.	PUNCT
ejpam-5427	218	1	where	where	SCONJ
ejpam-5427	218	2	the	the	DET
ejpam-5427	218	3	various	various	ADJ
ejpam-5427	218	4	approximate	approximate	ADJ
ejpam-5427	218	5	periods	period	NOUN
ejpam-5427	218	6	obtained	obtain	VERB
ejpam-5427	218	7	by	by	ADP
ejpam-5427	218	8	tapp	tapp	PROPN
ejpam-5427	218	9	and	and	CCONJ
ejpam-5427	218	10	te	te	PROPN
ejpam-5427	218	11	represents	represent	VERB
ejpam-5427	218	12	the	the	DET
ejpam-5427	218	13	corresponding	corresponding	ADJ
ejpam-5427	218	14	exact	exact	ADJ
ejpam-5427	218	15	period	period	NOUN
ejpam-5427	218	16	of	of	ADP
ejpam-5427	218	17	the	the	DET
ejpam-5427	218	18	oscillator	oscillator	NOUN
ejpam-5427	218	19	.	.	PUNCT
ejpam-5427	219	1	g.	g.	PROPN
ejpam-5427	219	2	m.	m.	PROPN
ejpam-5427	219	3	ismail	ismail	PROPN
ejpam-5427	219	4	,	,	PUNCT
ejpam-5427	219	5	m.	m.	NOUN
ejpam-5427	219	6	i.	i.	PROPN
ejpam-5427	219	7	yamani	yamani	PROPN
ejpam-5427	219	8	/	/	SYM
ejpam-5427	219	9	eur	eur	PROPN
ejpam-5427	219	10	.	.	PUNCT
ejpam-5427	220	1	j.	j.	PROPN
ejpam-5427	220	2	pure	pure	PROPN
ejpam-5427	220	3	appl	appl	PROPN
ejpam-5427	220	4	.	.	PROPN
ejpam-5427	220	5	math	math	PROPN
ejpam-5427	220	6	,	,	PUNCT
ejpam-5427	220	7	17	17	NUM
ejpam-5427	220	8	(	(	PUNCT
ejpam-5427	220	9	4	4	NUM
ejpam-5427	220	10	)	)	PUNCT
ejpam-5427	220	11	(	(	PUNCT
ejpam-5427	220	12	2024	2024	NUM
ejpam-5427	220	13	)	)	PUNCT
ejpam-5427	220	14	,	,	PUNCT
ejpam-5427	220	15	3622	3622	NUM
ejpam-5427	220	16	-	-	SYM
ejpam-5427	220	17	3641	3641	NUM
ejpam-5427	220	18	3630	3630	NUM
ejpam-5427	220	19	table	table	NOUN
ejpam-5427	220	20	1	1	NUM
ejpam-5427	220	21	:	:	PUNCT
ejpam-5427	220	22	comparison	comparison	NOUN
ejpam-5427	220	23	of	of	ADP
ejpam-5427	220	24	the	the	DET
ejpam-5427	220	25	approximate	approximate	ADJ
ejpam-5427	220	26	and	and	CCONJ
ejpam-5427	220	27	exact	exact	ADJ
ejpam-5427	220	28	solutions	solution	NOUN
ejpam-5427	220	29	for	for	ADP
ejpam-5427	220	30	eq	eq	PROPN
ejpam-5427	220	31	.	.	PUNCT
ejpam-5427	221	1	(	(	PUNCT
ejpam-5427	221	2	9	9	NUM
ejpam-5427	221	3	)	)	PUNCT
ejpam-5427	221	4	.	.	PUNCT
ejpam-5427	222	1	a	a	DET
ejpam-5427	222	2	te	te	PROPN
ejpam-5427	222	3	t3current	t3current	NOUN
ejpam-5427	222	4	t3	t3	NOUN
ejpam-5427	223	1	[	[	X
ejpam-5427	223	2	37	37	NUM
ejpam-5427	223	3	]	]	PUNCT
ejpam-5427	223	4	t3	t3	NOUN
ejpam-5427	224	1	[	[	X
ejpam-5427	224	2	32	32	NUM
ejpam-5427	224	3	]	]	PUNCT
ejpam-5427	224	4	t3	t3	NOUN
ejpam-5427	225	1	[	[	X
ejpam-5427	225	2	31	31	NUM
ejpam-5427	225	3	]	]	PUNCT
ejpam-5427	225	4	t3	t3	PROPN
ejpam-5427	226	1	[	[	X
ejpam-5427	226	2	27	27	NUM
ejpam-5427	226	3	]	]	X
ejpam-5427	226	4	t3	t3	PROPN
ejpam-5427	227	1	[	[	X
ejpam-5427	227	2	30	30	NUM
ejpam-5427	227	3	]	]	X
ejpam-5427	227	4	t3	t3	NOUN
ejpam-5427	228	1	[	[	X
ejpam-5427	228	2	25	25	NUM
ejpam-5427	228	3	]	]	PUNCT
ejpam-5427	228	4	t3	t3	PROPN
ejpam-5427	229	1	[	[	X
ejpam-5427	229	2	34	34	NUM
ejpam-5427	229	3	]	]	SYM
ejpam-5427	229	4	0.1	0.1	NUM
ejpam-5427	229	5	6.275347	6.275347	NUM
ejpam-5427	229	6	6.275347	6.275347	NUM
ejpam-5427	229	7	6.275347	6.275347	NUM
ejpam-5427	229	8	6.2753468	6.2753468	NUM
ejpam-5427	229	9	6.275346837	6.275346837	NUM
ejpam-5427	229	10	6.27534684	6.27534684	NUM
ejpam-5427	229	11	6.275348	6.275348	NUM
ejpam-5427	229	12	6.275346	6.275346	NUM
ejpam-5427	229	13	6.275346837	6.275346837	NUM
ejpam-5427	229	14	0	0	NUM
ejpam-5427	229	15	0	0	NUM
ejpam-5427	229	16	3.19e	3.19e	NUM
ejpam-5427	229	17	−6	−6	NOUN
ejpam-5427	229	18	2.59e	2.59e	NUM
ejpam-5427	229	19	−6	−6	NOUN
ejpam-5427	229	20	2.55e	2.55e	NUM
ejpam-5427	229	21	−6	−6	NOUN
ejpam-5427	229	22	1.59e	1.59e	NUM
ejpam-5427	229	23	−5	−5	NOUN
ejpam-5427	229	24	1.59e	1.59e	NUM
ejpam-5427	229	25	−5	−5	NOUN
ejpam-5427	229	26	2.59e	2.59e	NUM
ejpam-5427	229	27	−6	−6	NOUN
ejpam-5427	229	28	0.2	0.2	NUM
ejpam-5427	229	29	6.252016	6.252016	NUM
ejpam-5427	229	30	6.252016	6.252016	NUM
ejpam-5427	229	31	6.252016	6.252016	NUM
ejpam-5427	229	32	6.2520158	6.2520158	NUM
ejpam-5427	229	33	6.25201599	6.25201599	NUM
ejpam-5427	229	34	6.25201599	6.25201599	NUM
ejpam-5427	229	35	6.252028	6.252028	NUM
ejpam-5427	229	36	6.252003	6.252003	NUM
ejpam-5427	229	37	6.25201599	6.25201599	NUM
ejpam-5427	229	38	0	0	NUM
ejpam-5427	229	39	0	0	NUM
ejpam-5427	229	40	3.19e	3.19e	NUM
ejpam-5427	229	41	−6	−6	NOUN
ejpam-5427	229	42	1.59e	1.59e	NUM
ejpam-5427	229	43	−7	−7	ADP
ejpam-5427	229	44	1.59e	1.59e	NUM
ejpam-5427	229	45	−7	−7	ADP
ejpam-5427	229	46	1.92e	1.92e	NUM
ejpam-5427	229	47	−4	−4	X
ejpam-5427	230	1	2.08e	2.08e	NUM
ejpam-5427	230	2	−4	−4	X
ejpam-5427	230	3	1.59e	1.59e	NUM
ejpam-5427	230	4	−7	−7	NOUN
ejpam-5427	230	5	0.5	0.5	NUM
ejpam-5427	230	6	6.096061	6.096061	NUM
ejpam-5427	230	7	6.096061	6.096061	NUM
ejpam-5427	230	8	6.096061	6.096061	NUM
ejpam-5427	230	9	6.0960246	6.0960246	NUM
ejpam-5427	230	10	6.09606050	6.09606050	NUM
ejpam-5427	230	11	6.09605904	6.09605904	NUM
ejpam-5427	231	1	6.096491	6.096491	NUM
ejpam-5427	231	2	6.095585	6.095585	NUM
ejpam-5427	231	3	6.096060516	6.096060516	NUM
ejpam-5427	231	4	0	0	NUM
ejpam-5427	231	5	0	0	NUM
ejpam-5427	232	1	5.97e	5.97e	NUM
ejpam-5427	232	2	−4	−4	NOUN
ejpam-5427	232	3	8.20e	8.20e	NUM
ejpam-5427	232	4	−6	−6	NOUN
ejpam-5427	232	5	3.12e	3.12e	NUM
ejpam-5427	232	6	−5	−5	NOUN
ejpam-5427	232	7	0.00706	0.00706	NUM
ejpam-5427	232	8	0.00781	0.00781	NUM
ejpam-5427	232	9	7.93e	7.93e	NUM
ejpam-5427	232	10	−7	−7	NOUN
ejpam-5427	232	11	1	1	NUM
ejpam-5427	232	12	5.626007	5.626007	NUM
ejpam-5427	232	13	5.62587	5.62587	NUM
ejpam-5427	232	14	5.62602	5.62602	NUM
ejpam-5427	232	15	5.6245487	5.6245487	NUM
ejpam-5427	232	16	5.62599289	5.62599289	NUM
ejpam-5427	232	17	5.62579479	5.62579479	NUM
ejpam-5427	232	18	5.630343	5.630343	NUM
ejpam-5427	232	19	5.619852	5.619852	NUM
ejpam-5427	232	20	5.62599937	5.62599937	NUM
ejpam-5427	232	21	2.43e	2.43e	NUM
ejpam-5427	232	22	−5	−5	ADP
ejpam-5427	232	23	2.31e	2.31e	NUM
ejpam-5427	232	24	−4	−4	NOUN
ejpam-5427	232	25	0.02592	0.02592	NUM
ejpam-5427	232	26	2.51e	2.51e	NUM
ejpam-5427	232	27	−4	−4	NUM
ejpam-5427	232	28	0.00377	0.00377	NUM
ejpam-5427	232	29	0.07707	0.07707	NUM
ejpam-5427	232	30	0.10940	0.10940	NUM
ejpam-5427	232	31	1.36e	1.36e	NUM
ejpam-5427	232	32	−4	−4	NOUN
ejpam-5427	232	33	2	2	NUM
ejpam-5427	232	34	4.491214	4.491214	NUM
ejpam-5427	232	35	4.48492	4.48492	NUM
ejpam-5427	232	36	4.47661	4.47661	NUM
ejpam-5427	232	37	4.4664554	4.4664554	NUM
ejpam-5427	232	38	4.49012538	4.49012538	NUM
ejpam-5427	232	39	4.48208113	4.48208113	NUM
ejpam-5427	232	40	4.509311	4.509311	NUM
ejpam-5427	232	41	4.442883	4.442883	NUM
ejpam-5427	232	42	4.49112308	4.49112308	NUM
ejpam-5427	232	43	0.14014	0.14014	NUM
ejpam-5427	232	44	0.47234	0.47234	NUM
ejpam-5427	232	45	0.55127	0.55127	NUM
ejpam-5427	232	46	0.02424	0.02424	NUM
ejpam-5427	232	47	0.20335	0.20335	NUM
ejpam-5427	232	48	0.40294	0.40294	NUM
ejpam-5427	232	49	1.07612	1.07612	NUM
ejpam-5427	232	50	0.00202	0.00202	NUM
ejpam-5427	232	51	table	table	NOUN
ejpam-5427	232	52	2	2	NUM
ejpam-5427	232	53	:	:	PUNCT
ejpam-5427	232	54	comparison	comparison	NOUN
ejpam-5427	232	55	between	between	ADP
ejpam-5427	232	56	the	the	DET
ejpam-5427	232	57	numerical	numerical	ADJ
ejpam-5427	232	58	solution	solution	NOUN
ejpam-5427	232	59	and	and	CCONJ
ejpam-5427	232	60	analytical	analytical	ADJ
ejpam-5427	232	61	solutions	solution	NOUN
ejpam-5427	232	62	at	at	ADP
ejpam-5427	232	63	a	a	DET
ejpam-5427	232	64	=	=	SYM
ejpam-5427	232	65	0.2	0.2	NUM
ejpam-5427	232	66	for	for	ADP
ejpam-5427	232	67	eq	eq	PROPN
ejpam-5427	232	68	.	.	PUNCT
ejpam-5427	233	1	(	(	PUNCT
ejpam-5427	233	2	9	9	X
ejpam-5427	233	3	)	)	PUNCT
ejpam-5427	233	4	t	t	NOUN
ejpam-5427	233	5	block	block	NOUN
ejpam-5427	233	6	method	method	NOUN
ejpam-5427	233	7	mdtm	mdtm	VERB
ejpam-5427	233	8	[	[	X
ejpam-5427	233	9	4/4	4/4	NUM
ejpam-5427	233	10	]	]	PUNCT
ejpam-5427	233	11	and	and	CCONJ
ejpam-5427	233	12	present	present	ADJ
ejpam-5427	233	13	solution	solution	NOUN
ejpam-5427	233	14	numerical	numerical	ADJ
ejpam-5427	233	15	solution	solution	NOUN
ejpam-5427	233	16	[	[	X
ejpam-5427	233	17	24	24	NUM
ejpam-5427	233	18	]	]	X
ejpam-5427	234	1	[	[	X
ejpam-5427	234	2	5/5	5/5	NUM
ejpam-5427	234	3	]	]	PUNCT
ejpam-5427	235	1	[	[	X
ejpam-5427	235	2	33	33	NUM
ejpam-5427	235	3	]	]	SYM
ejpam-5427	235	4	0	0	NUM
ejpam-5427	235	5	0	0	NUM
ejpam-5427	235	6	0	0	NUM
ejpam-5427	235	7	0	0	NUM
ejpam-5427	235	8	0	0	NUM
ejpam-5427	235	9	0.125	0.125	NUM
ejpam-5427	235	10	0.024934	0.024934	NUM
ejpam-5427	235	11	0.024951214	0.024951214	NUM
ejpam-5427	235	12	0.024934943	0.024934943	NUM
ejpam-5427	235	13	0.024935034	0.024935034	NUM
ejpam-5427	235	14	0.25	0.25	NUM
ejpam-5427	235	15	0.049480	0.049480	NUM
ejpam-5427	235	16	0.049511005	0.049511005	NUM
ejpam-5427	235	17	0.049480664	0.049480664	NUM
ejpam-5427	235	18	0.049480891	0.049480891	NUM
ejpam-5427	235	19	0.375	0.375	NUM
ejpam-5427	235	20	0.073253	0.073253	NUM
ejpam-5427	235	21	0.073293861	0.073293861	NUM
ejpam-5427	235	22	0.073253553	0.073253553	NUM
ejpam-5427	235	23	0.073253560	0.073253560	NUM
ejpam-5427	235	24	0.5	0.5	NUM
ejpam-5427	235	25	0.095881	0.095881	NUM
ejpam-5427	235	26	0.095926024	0.095926024	NUM
ejpam-5427	235	27	0.095881202	0.095881202	NUM
ejpam-5427	235	28	0.095881465	0.095881465	NUM
ejpam-5427	235	29	0.625	0.625	NUM
ejpam-5427	235	30	0.117008	0.117008	NUM
ejpam-5427	236	1	0.117051228	0.117051228	NUM
ejpam-5427	236	2	0.117007962	0.117007962	NOUN
ejpam-5427	236	3	0.117008021	0.117008021	NUM
ejpam-5427	236	4	0.75	0.75	NUM
ejpam-5427	236	5	0.1363	0.1363	NUM
ejpam-5427	236	6	0.136336241	0.136336241	NUM
ejpam-5427	236	7	0.136300404	0.136300404	NUM
ejpam-5427	236	8	0.136300551	0.136300551	NUM
ejpam-5427	236	9	0.875	0.875	NUM
ejpam-5427	236	10	0.153453	0.153453	NUM
ejpam-5427	236	11	0.153476143	0.153476143	NUM
ejpam-5427	236	12	0.153452636	0.153452636	NUM
ejpam-5427	236	13	0.153452785	0.153452785	NUM
ejpam-5427	236	14	1	1	NUM
ejpam-5427	236	15	0.168191	0.168191	NUM
ejpam-5427	236	16	0.168199251	0.168199251	NUM
ejpam-5427	236	17	0.168191377	0.168191377	NUM
ejpam-5427	236	18	0.168191348	0.168191348	NUM
ejpam-5427	236	19	1.125	1.125	NUM
ejpam-5427	236	20	0.180281	0.180281	NUM
ejpam-5427	236	21	0.180271603	0.180271603	NUM
ejpam-5427	236	22	0.180280677	0.180280677	NUM
ejpam-5427	236	23	0.180280833	0.180280833	NUM
ejpam-5427	236	24	1.25	1.25	NUM
ejpam-5427	236	25	0.180281	0.180281	NUM
ejpam-5427	236	26	0.180271603	0.180271603	NUM
ejpam-5427	236	27	0.180280677	0.180280677	NUM
ejpam-5427	236	28	0.180280833	0.180280833	NUM
ejpam-5427	236	29	1.375	1.375	NUM
ejpam-5427	236	30	0.195778	0.195778	NUM
ejpam-5427	236	31	0.195739784	0.195739784	NUM
ejpam-5427	236	32	0.195778569	0.195778569	NUM
ejpam-5427	236	33	0.195778587	0.195778587	NUM
ejpam-5427	236	34	1.5	1.5	NUM
ejpam-5427	236	35	0.198937	0.198937	NUM
ejpam-5427	236	36	0.198888450	0.198888450	NUM
ejpam-5427	236	37	0.198936744	0.198936744	NUM
ejpam-5427	236	38	0.198936684	0.198936684	NUM
ejpam-5427	236	39	1.625	1.625	NUM
ejpam-5427	236	40	0.198949	0.198949	NUM
ejpam-5427	237	1	0.198896377	0.198896377	NUM
ejpam-5427	237	2	0.198949462	0.198949462	NUM
ejpam-5427	237	3	0.198949302	0.198949302	NUM
ejpam-5427	237	4	1.75	1.75	NUM
ejpam-5427	237	5	0.195816	0.195816	NUM
ejpam-5427	237	6	0.195763266	0.195763266	NUM
ejpam-5427	237	7	0.195816515	0.195816515	NUM
ejpam-5427	237	8	0.195816396	0.195816396	NUM
ejpam-5427	237	9	1.875	1.875	NUM
ejpam-5427	237	10	0.189589	0.189589	NUM
ejpam-5427	237	11	0.189539059	0.189539059	NUM
ejpam-5427	237	12	0.189588706	0.189588706	NUM
ejpam-5427	237	13	0.189588464	0.189588464	NUM
ejpam-5427	237	14	2	2	NUM
ejpam-5427	237	15	0.180367	0.180367	NUM
ejpam-5427	237	16	0.180323081	0.180323081	NUM
ejpam-5427	237	17	0.180366838	0.180366838	NUM
ejpam-5427	237	18	0.180366565	0.180366565	NUM
ejpam-5427	237	19	g.	g.	PROPN
ejpam-5427	237	20	m.	m.	PROPN
ejpam-5427	237	21	ismail	ismail	PROPN
ejpam-5427	237	22	,	,	PUNCT
ejpam-5427	237	23	m.	m.	NOUN
ejpam-5427	237	24	i.	i.	PROPN
ejpam-5427	237	25	yamani	yamani	PROPN
ejpam-5427	237	26	/	/	SYM
ejpam-5427	237	27	eur	eur	PROPN
ejpam-5427	237	28	.	.	PUNCT
ejpam-5427	238	1	j.	j.	PROPN
ejpam-5427	238	2	pure	pure	PROPN
ejpam-5427	238	3	appl	appl	PROPN
ejpam-5427	238	4	.	.	PROPN
ejpam-5427	238	5	math	math	PROPN
ejpam-5427	238	6	,	,	PUNCT
ejpam-5427	238	7	17	17	NUM
ejpam-5427	238	8	(	(	PUNCT
ejpam-5427	238	9	4	4	NUM
ejpam-5427	238	10	)	)	PUNCT
ejpam-5427	238	11	(	(	PUNCT
ejpam-5427	238	12	2024	2024	NUM
ejpam-5427	238	13	)	)	PUNCT
ejpam-5427	238	14	,	,	PUNCT
ejpam-5427	238	15	3622	3622	NUM
ejpam-5427	238	16	-	-	SYM
ejpam-5427	238	17	3641	3641	NUM
ejpam-5427	238	18	3631	3631	NUM
ejpam-5427	238	19	table	table	NOUN
ejpam-5427	238	20	3	3	NUM
ejpam-5427	238	21	:	:	PUNCT
ejpam-5427	238	22	comparison	comparison	NOUN
ejpam-5427	238	23	between	between	ADP
ejpam-5427	238	24	the	the	DET
ejpam-5427	238	25	numerical	numerical	ADJ
ejpam-5427	238	26	solution	solution	NOUN
ejpam-5427	238	27	and	and	CCONJ
ejpam-5427	238	28	analytical	analytical	ADJ
ejpam-5427	238	29	solutions	solution	NOUN
ejpam-5427	238	30	at	at	ADP
ejpam-5427	238	31	a	a	DET
ejpam-5427	238	32	=	=	SYM
ejpam-5427	238	33	0.4	0.4	NUM
ejpam-5427	238	34	for	for	ADP
ejpam-5427	238	35	eq	eq	PROPN
ejpam-5427	238	36	.	.	PUNCT
ejpam-5427	239	1	(	(	PUNCT
ejpam-5427	239	2	9	9	X
ejpam-5427	239	3	)	)	PUNCT
ejpam-5427	239	4	t	t	NOUN
ejpam-5427	239	5	block	block	NOUN
ejpam-5427	239	6	method	method	NOUN
ejpam-5427	239	7	mdtm	mdtm	VERB
ejpam-5427	239	8	[	[	X
ejpam-5427	239	9	4/4	4/4	NUM
ejpam-5427	239	10	]	]	PUNCT
ejpam-5427	239	11	and	and	CCONJ
ejpam-5427	239	12	present	present	ADJ
ejpam-5427	239	13	solution	solution	NOUN
ejpam-5427	239	14	numerical	numerical	ADJ
ejpam-5427	239	15	solution	solution	NOUN
ejpam-5427	239	16	[	[	X
ejpam-5427	239	17	24	24	NUM
ejpam-5427	239	18	]	]	X
ejpam-5427	240	1	[	[	X
ejpam-5427	240	2	5/5	5/5	NUM
ejpam-5427	240	3	]	]	PUNCT
ejpam-5427	241	1	[	[	X
ejpam-5427	241	2	33	33	NUM
ejpam-5427	241	3	]	]	SYM
ejpam-5427	241	4	0	0	NUM
ejpam-5427	241	5	0	0	NUM
ejpam-5427	241	6	0	0	NUM
ejpam-5427	241	7	0	0	NUM
ejpam-5427	241	8	0	0	NUM
ejpam-5427	241	9	0.125	0.125	NUM
ejpam-5427	241	10	0.049869	0.049869	NUM
ejpam-5427	241	11	0.049869861	0.049869861	NUM
ejpam-5427	241	12	0.049869861	0.049869861	NUM
ejpam-5427	241	13	0.049870029	0.049870029	NUM
ejpam-5427	241	14	0.25	0.25	NUM
ejpam-5427	241	15	0.098960	0.098960	NUM
ejpam-5427	241	16	0.098960562	0.098960562	NUM
ejpam-5427	241	17	0.098960558	0.098960558	NUM
ejpam-5427	241	18	0.098961002	0.098961002	NUM
ejpam-5427	241	19	0.375	0.375	NUM
ejpam-5427	241	20	0.146501	0.146501	NUM
ejpam-5427	241	21	0.146501385	0.146501385	NUM
ejpam-5427	241	22	0.146501379	0.146501379	NUM
ejpam-5427	241	23	0.146501402	0.146501402	NUM
ejpam-5427	241	24	0.5	0.5	NUM
ejpam-5427	241	25	0.191739	0.191739	NUM
ejpam-5427	241	26	0.191738916	0.191738916	NUM
ejpam-5427	241	27	0.191738937	0.191738937	NUM
ejpam-5427	241	28	0.191739420	0.191739420	NUM
ejpam-5427	241	29	0.625	0.625	NUM
ejpam-5427	241	30	0.233947	0.233947	NUM
ejpam-5427	241	31	0.233946661	0.233946661	NUM
ejpam-5427	241	32	0.233946816	0.233946816	NUM
ejpam-5427	241	33	0.233946758	0.233946758	NUM
ejpam-5427	241	34	0.75	0.75	NUM
ejpam-5427	241	35	0.272436	0.272436	NUM
ejpam-5427	241	36	0.272435646	0.272435646	NUM
ejpam-5427	241	37	0.272436179	0.272436179	NUM
ejpam-5427	241	38	0.272435964	0.272435964	NUM
ejpam-5427	241	39	0.875	0.875	NUM
ejpam-5427	241	40	0.306566	0.306566	NUM
ejpam-5427	241	41	0.306566039	0.306566039	NUM
ejpam-5427	241	42	0.306567314	0.306567314	NUM
ejpam-5427	241	43	0.306566352	0.306566352	NUM
ejpam-5427	241	44	1	1	NUM
ejpam-5427	241	45	0.33576	0.33576	NUM
ejpam-5427	241	46	0.335759596	0.335759596	NUM
ejpam-5427	241	47	0.335761911	0.335761911	NUM
ejpam-5427	241	48	0.335759593	0.335759593	NUM
ejpam-5427	241	49	1.125	1.125	NUM
ejpam-5427	241	50	0.359513	0.359513	NUM
ejpam-5427	241	51	0.359512477	0.359512477	NUM
ejpam-5427	241	52	0.359515583	0.359515583	NUM
ejpam-5427	241	53	0.359513002	0.359513002	NUM
ejpam-5427	241	54	1.25	1.25	NUM
ejpam-5427	241	55	0.377408	0.377408	NUM
ejpam-5427	241	56	0.377407791	0.377407791	NUM
ejpam-5427	241	57	0.377410047	0.377410047	NUM
ejpam-5427	241	58	0.377407810	0.377407810	NUM
ejpam-5427	241	59	1.375	1.375	NUM
ejpam-5427	241	60	0.389127	0.389127	NUM
ejpam-5427	241	61	0.389126999	0.389126999	NUM
ejpam-5427	241	62	0.389124206	0.389124206	NUM
ejpam-5427	241	63	0.389127373	0.389127373	NUM
ejpam-5427	241	64	1.5	1.5	NUM
ejpam-5427	241	65	0.39446	0.39446	NUM
ejpam-5427	241	66	0.394459308	0.394459308	NUM
ejpam-5427	241	67	0.394443406	0.394443406	NUM
ejpam-5427	241	68	0.394459515	0.394459515	NUM
ejpam-5427	241	69	1.625	1.625	NUM
ejpam-5427	241	70	0.393308	0.393308	NUM
ejpam-5427	241	71	0.393308207	0.393308207	NUM
ejpam-5427	241	72	0.393266152	0.393266152	NUM
ejpam-5427	241	73	0.393308138	0.393308138	NUM
ejpam-5427	242	1	1.75	1.75	NUM
ejpam-5427	242	2	0.385695	0.385695	NUM
ejpam-5427	242	3	0.385694562	0.385694562	NUM
ejpam-5427	242	4	0.385607769	0.385607769	NUM
ejpam-5427	242	5	0.385694560	0.385694560	NUM
ejpam-5427	242	6	1.875	1.875	NUM
ejpam-5427	242	7	0.371756	0.371756	NUM
ejpam-5427	242	8	0.371755941	0.371755941	NUM
ejpam-5427	242	9	0.371755564	0.371755564	NUM
ejpam-5427	242	10	0.371600658	0.371600658	NUM
ejpam-5427	242	11	2	2	NUM
ejpam-5427	242	12	0.351742	0.351742	NUM
ejpam-5427	242	13	0.351742248	0.351742248	NUM
ejpam-5427	242	14	0.351491092	0.351491092	NUM
ejpam-5427	242	15	0.351741644	0.351741644	NUM
ejpam-5427	242	16	g.	g.	PROPN
ejpam-5427	242	17	m.	m.	PROPN
ejpam-5427	242	18	ismail	ismail	PROPN
ejpam-5427	242	19	,	,	PUNCT
ejpam-5427	242	20	m.	m.	NOUN
ejpam-5427	242	21	i.	i.	PROPN
ejpam-5427	242	22	yamani	yamani	PROPN
ejpam-5427	242	23	/	/	SYM
ejpam-5427	242	24	eur	eur	PROPN
ejpam-5427	242	25	.	.	PUNCT
ejpam-5427	243	1	j.	j.	PROPN
ejpam-5427	243	2	pure	pure	PROPN
ejpam-5427	243	3	appl	appl	PROPN
ejpam-5427	243	4	.	.	PROPN
ejpam-5427	243	5	math	math	PROPN
ejpam-5427	243	6	,	,	PUNCT
ejpam-5427	243	7	17	17	NUM
ejpam-5427	243	8	(	(	PUNCT
ejpam-5427	243	9	4	4	NUM
ejpam-5427	243	10	)	)	PUNCT
ejpam-5427	243	11	(	(	PUNCT
ejpam-5427	243	12	2024	2024	NUM
ejpam-5427	243	13	)	)	PUNCT
ejpam-5427	243	14	,	,	PUNCT
ejpam-5427	243	15	3622	3622	NUM
ejpam-5427	243	16	-	-	SYM
ejpam-5427	243	17	3641	3641	NUM
ejpam-5427	243	18	3632	3632	NUM
ejpam-5427	243	19	figure	figure	NOUN
ejpam-5427	243	20	1	1	NUM
ejpam-5427	243	21	:	:	PUNCT
ejpam-5427	243	22	comparison	comparison	NOUN
ejpam-5427	243	23	between	between	ADP
ejpam-5427	243	24	higher	high	ADJ
ejpam-5427	243	25	order	order	NOUN
ejpam-5427	243	26	analytical	analytical	ADJ
ejpam-5427	243	27	solution	solution	NOUN
ejpam-5427	243	28	(	(	PUNCT
ejpam-5427	243	29	black	black	ADJ
ejpam-5427	243	30	line	line	NOUN
ejpam-5427	243	31	)	)	PUNCT
ejpam-5427	243	32	,	,	PUNCT
ejpam-5427	243	33	mgemm	mgemm	NOUN
ejpam-5427	244	1	[	[	X
ejpam-5427	244	2	37	37	NUM
ejpam-5427	244	3	]	]	X
ejpam-5427	244	4	(	(	PUNCT
ejpam-5427	244	5	red	red	ADJ
ejpam-5427	244	6	line	line	NOUN
ejpam-5427	244	7	)	)	PUNCT
ejpam-5427	244	8	,	,	PUNCT
ejpam-5427	244	9	and	and	CCONJ
ejpam-5427	244	10	the	the	DET
ejpam-5427	244	11	numerical	numerical	ADJ
ejpam-5427	244	12	solution	solution	NOUN
ejpam-5427	244	13	(	(	PUNCT
ejpam-5427	244	14	blue	blue	ADJ
ejpam-5427	244	15	line	line	NOUN
ejpam-5427	244	16	)	)	PUNCT
ejpam-5427	244	17	at	at	ADP
ejpam-5427	244	18	a	a	DET
ejpam-5427	244	19	=	=	SYM
ejpam-5427	244	20	1	1	NUM
ejpam-5427	244	21	,	,	PUNCT
ejpam-5427	244	22	for	for	ADP
ejpam-5427	244	23	eq	eq	NOUN
ejpam-5427	244	24	.	.	PUNCT
ejpam-5427	244	25	(	(	PUNCT
ejpam-5427	244	26	9	9	NUM
ejpam-5427	244	27	)	)	PUNCT
ejpam-5427	244	28	.	.	PUNCT
ejpam-5427	245	1	g.	g.	PROPN
ejpam-5427	245	2	m.	m.	PROPN
ejpam-5427	245	3	ismail	ismail	PROPN
ejpam-5427	245	4	,	,	PUNCT
ejpam-5427	245	5	m.	m.	NOUN
ejpam-5427	245	6	i.	i.	PROPN
ejpam-5427	245	7	yamani	yamani	PROPN
ejpam-5427	245	8	/	/	SYM
ejpam-5427	245	9	eur	eur	PROPN
ejpam-5427	245	10	.	.	PUNCT
ejpam-5427	246	1	j.	j.	PROPN
ejpam-5427	246	2	pure	pure	PROPN
ejpam-5427	246	3	appl	appl	PROPN
ejpam-5427	246	4	.	.	PROPN
ejpam-5427	246	5	math	math	PROPN
ejpam-5427	246	6	,	,	PUNCT
ejpam-5427	246	7	17	17	NUM
ejpam-5427	246	8	(	(	PUNCT
ejpam-5427	246	9	4	4	NUM
ejpam-5427	246	10	)	)	PUNCT
ejpam-5427	246	11	(	(	PUNCT
ejpam-5427	246	12	2024	2024	NUM
ejpam-5427	246	13	)	)	PUNCT
ejpam-5427	246	14	,	,	PUNCT
ejpam-5427	246	15	3622	3622	NUM
ejpam-5427	246	16	-	-	SYM
ejpam-5427	246	17	3641	3641	NUM
ejpam-5427	246	18	3633	3633	NUM
ejpam-5427	246	19	figure	figure	NOUN
ejpam-5427	246	20	2	2	NUM
ejpam-5427	246	21	:	:	PUNCT
ejpam-5427	246	22	comparison	comparison	NOUN
ejpam-5427	246	23	between	between	ADP
ejpam-5427	246	24	higher	high	ADJ
ejpam-5427	246	25	order	order	NOUN
ejpam-5427	246	26	analytical	analytical	ADJ
ejpam-5427	246	27	solution	solution	NOUN
ejpam-5427	246	28	(	(	PUNCT
ejpam-5427	246	29	black	black	ADJ
ejpam-5427	246	30	line	line	NOUN
ejpam-5427	246	31	)	)	PUNCT
ejpam-5427	246	32	,	,	PUNCT
ejpam-5427	246	33	mdtm	mdtm	VERB
ejpam-5427	246	34	[	[	X
ejpam-5427	246	35	33	33	NUM
ejpam-5427	246	36	]	]	X
ejpam-5427	246	37	(	(	PUNCT
ejpam-5427	246	38	red	red	ADJ
ejpam-5427	246	39	line	line	NOUN
ejpam-5427	246	40	)	)	PUNCT
ejpam-5427	246	41	,	,	PUNCT
ejpam-5427	246	42	and	and	CCONJ
ejpam-5427	246	43	the	the	DET
ejpam-5427	246	44	numerical	numerical	ADJ
ejpam-5427	246	45	solution	solution	NOUN
ejpam-5427	246	46	(	(	PUNCT
ejpam-5427	246	47	blue	blue	ADJ
ejpam-5427	246	48	line	line	NOUN
ejpam-5427	246	49	)	)	PUNCT
ejpam-5427	246	50	at	at	ADP
ejpam-5427	246	51	a	a	DET
ejpam-5427	246	52	=	=	SYM
ejpam-5427	246	53	0.3	0.3	NUM
ejpam-5427	246	54	,	,	PUNCT
ejpam-5427	246	55	for	for	ADP
ejpam-5427	246	56	eq	eq	NOUN
ejpam-5427	246	57	.	.	PUNCT
ejpam-5427	247	1	(	(	PUNCT
ejpam-5427	247	2	9	9	NUM
ejpam-5427	247	3	)	)	PUNCT
ejpam-5427	247	4	.	.	PUNCT
ejpam-5427	248	1	g.	g.	PROPN
ejpam-5427	248	2	m.	m.	PROPN
ejpam-5427	248	3	ismail	ismail	PROPN
ejpam-5427	248	4	,	,	PUNCT
ejpam-5427	248	5	m.	m.	NOUN
ejpam-5427	248	6	i.	i.	PROPN
ejpam-5427	248	7	yamani	yamani	PROPN
ejpam-5427	248	8	/	/	SYM
ejpam-5427	248	9	eur	eur	PROPN
ejpam-5427	248	10	.	.	PUNCT
ejpam-5427	249	1	j.	j.	PROPN
ejpam-5427	249	2	pure	pure	PROPN
ejpam-5427	249	3	appl	appl	PROPN
ejpam-5427	249	4	.	.	PROPN
ejpam-5427	249	5	math	math	PROPN
ejpam-5427	249	6	,	,	PUNCT
ejpam-5427	249	7	17	17	NUM
ejpam-5427	249	8	(	(	PUNCT
ejpam-5427	249	9	4	4	NUM
ejpam-5427	249	10	)	)	PUNCT
ejpam-5427	249	11	(	(	PUNCT
ejpam-5427	249	12	2024	2024	NUM
ejpam-5427	249	13	)	)	PUNCT
ejpam-5427	249	14	,	,	PUNCT
ejpam-5427	249	15	3622	3622	NUM
ejpam-5427	249	16	-	-	SYM
ejpam-5427	249	17	3641	3641	NUM
ejpam-5427	249	18	3634	3634	NUM
ejpam-5427	249	19	table	table	NOUN
ejpam-5427	249	20	4	4	NUM
ejpam-5427	249	21	:	:	PUNCT
ejpam-5427	249	22	comparison	comparison	NOUN
ejpam-5427	249	23	of	of	ADP
ejpam-5427	249	24	the	the	DET
ejpam-5427	249	25	approximate	approximate	ADJ
ejpam-5427	249	26	and	and	CCONJ
ejpam-5427	249	27	exact	exact	ADJ
ejpam-5427	249	28	solutions	solution	NOUN
ejpam-5427	249	29	for	for	ADP
ejpam-5427	249	30	eq	eq	PROPN
ejpam-5427	249	31	.	.	PUNCT
ejpam-5427	250	1	(	(	PUNCT
ejpam-5427	250	2	25	25	NUM
ejpam-5427	250	3	)	)	PUNCT
ejpam-5427	250	4	.	.	PUNCT
ejpam-5427	251	1	a	a	DET
ejpam-5427	251	2	te	te	PROPN
ejpam-5427	251	3	t3current	t3current	NOUN
ejpam-5427	251	4	t3	t3	NOUN
ejpam-5427	252	1	[	[	X
ejpam-5427	252	2	37	37	NUM
ejpam-5427	252	3	]	]	PUNCT
ejpam-5427	252	4	t3	t3	NOUN
ejpam-5427	253	1	[	[	X
ejpam-5427	253	2	32	32	NUM
ejpam-5427	253	3	]	]	PUNCT
ejpam-5427	253	4	t3	t3	NOUN
ejpam-5427	254	1	[	[	X
ejpam-5427	254	2	31	31	NUM
ejpam-5427	254	3	]	]	PUNCT
ejpam-5427	254	4	t3	t3	PROPN
ejpam-5427	255	1	[	[	X
ejpam-5427	255	2	27	27	NUM
ejpam-5427	255	3	]	]	X
ejpam-5427	255	4	t3	t3	PROPN
ejpam-5427	256	1	[	[	X
ejpam-5427	256	2	30	30	NUM
ejpam-5427	256	3	]	]	X
ejpam-5427	256	4	t3	t3	NOUN
ejpam-5427	257	1	[	[	X
ejpam-5427	257	2	25	25	NUM
ejpam-5427	257	3	]	]	PUNCT
ejpam-5427	257	4	t3	t3	PROPN
ejpam-5427	258	1	[	[	X
ejpam-5427	258	2	34	34	NUM
ejpam-5427	258	3	]	]	SYM
ejpam-5427	258	4	0.1	0.1	NUM
ejpam-5427	258	5	6.27533378	6.27533378	NUM
ejpam-5427	258	6	6.27533378	6.27533378	NUM
ejpam-5427	258	7	6.27533378	6.27533378	NUM
ejpam-5427	258	8	6.27533378	6.27533378	NUM
ejpam-5427	258	9	6.2753338	6.2753338	NUM
ejpam-5427	258	10	6.27533378	6.27533378	NUM
ejpam-5427	258	11	6.275329	6.275329	NUM
ejpam-5427	258	12	6.2753264	6.2753264	NUM
ejpam-5427	258	13	6.27533378	6.27533378	NUM
ejpam-5427	258	14	0	0	NUM
ejpam-5427	258	15	0	0	NUM
ejpam-5427	258	16	0	0	NUM
ejpam-5427	258	17	0	0	NUM
ejpam-5427	258	18	0	0	NUM
ejpam-5427	258	19	7.61e	7.61e	NUM
ejpam-5427	258	20	−5	−5	NOUN
ejpam-5427	259	1	1.18e	1.18e	NUM
ejpam-5427	259	2	−4	−4	NOUN
ejpam-5427	259	3	0	0	NUM
ejpam-5427	259	4	0.2	0.2	NUM
ejpam-5427	259	5	6.251809	6.251809	NUM
ejpam-5427	260	1	6.25180898	6.25180898	NUM
ejpam-5427	260	2	6.25180898	6.25180898	NUM
ejpam-5427	260	3	6.25180884	6.25180884	NUM
ejpam-5427	260	4	6.25180911	6.25180911	NUM
ejpam-5427	260	5	6.25182078	6.25182078	NUM
ejpam-5427	260	6	6.251740	6.251740	NUM
ejpam-5427	261	1	6.251690	6.251690	NUM
ejpam-5427	261	2	6.2518089	6.2518089	NUM
ejpam-5427	261	3	3.19e	3.19e	NUM
ejpam-5427	261	4	−7	−7	NOUN
ejpam-5427	261	5	3.19e	3.19e	NUM
ejpam-5427	261	6	−7	−7	NOUN
ejpam-5427	261	7	2.56e	2.56e	NUM
ejpam-5427	261	8	−6	−6	NOUN
ejpam-5427	262	1	1.76e	1.76e	NUM
ejpam-5427	262	2	−6	−6	NOUN
ejpam-5427	262	3	1.88e	1.88e	NUM
ejpam-5427	262	4	−4	−4	NUM
ejpam-5427	263	1	0.00110	0.00110	NUM
ejpam-5427	263	2	0.00190	0.00190	NUM
ejpam-5427	263	3	1.59e	1.59e	NUM
ejpam-5427	263	4	−6	−6	NOUN
ejpam-5427	263	5	0.5	0.5	NUM
ejpam-5427	263	6	6.088449	6.088449	NUM
ejpam-5427	263	7	6.08845097	6.08845097	NUM
ejpam-5427	263	8	6.08845017	6.08845017	NUM
ejpam-5427	263	9	6.08841902	6.08841902	NUM
ejpam-5427	263	10	6.08848374	6.08848374	NUM
ejpam-5427	263	11	6.08815979	6.08815979	NUM
ejpam-5427	263	12	6.085649	6.085649	NUM
ejpam-5427	263	13	6.083668	6.083668	NUM
ejpam-5427	263	14	6.088450	6.088450	NUM
ejpam-5427	263	15	3.24e	3.24e	NUM
ejpam-5427	263	16	−5	−5	ADP
ejpam-5427	263	17	1.92e	1.92e	NUM
ejpam-5427	263	18	−5	−5	NOUN
ejpam-5427	263	19	4.92e	4.92e	NUM
ejpam-5427	263	20	−4	−4	NOUN
ejpam-5427	264	1	5.71e	5.71e	NUM
ejpam-5427	264	2	−4	−4	NOUN
ejpam-5427	264	3	0.00475	0.00475	NUM
ejpam-5427	264	4	0.04599	0.04599	NUM
ejpam-5427	264	5	0.07853	0.07853	NUM
ejpam-5427	265	1	1.64e	1.64e	NUM
ejpam-5427	265	2	−5	−5	ADV
ejpam-5427	266	1	1	1	NUM
ejpam-5427	266	2	5.527200	5.527200	NUM
ejpam-5427	266	3	5.527510790	5.527510790	NUM
ejpam-5427	266	4	5.527656919	5.527656919	NUM
ejpam-5427	266	5	5.52576588	5.52576588	NUM
ejpam-5427	266	6	5.52994105	5.52994105	NUM
ejpam-5427	266	7	5.50818960	5.50818960	NUM
ejpam-5427	266	8	5.477174	5.477174	NUM
ejpam-5427	266	9	5.441398	5.441398	NUM
ejpam-5427	266	10	5.527497	5.527497	NUM
ejpam-5427	266	11	0.00562	0.00562	NUM
ejpam-5427	266	12	0.00827	0.00827	NUM
ejpam-5427	266	13	2.59e	2.59e	NUM
ejpam-5427	266	14	−4	−4	X
ejpam-5427	266	15	0.04959	0.04959	NUM
ejpam-5427	266	16	0.343943	0.343943	NUM
ejpam-5427	266	17	0.90509	0.90509	NUM
ejpam-5427	266	18	1.55236	1.55236	NUM
ejpam-5427	266	19	0.00537	0.00537	NUM
ejpam-5427	266	20	2	2	NUM
ejpam-5427	266	21	4.690247	4.690247	NUM
ejpam-5427	266	22	4.6831871	4.6831871	NUM
ejpam-5427	266	23	4.7771790	4.7771790	NUM
ejpam-5427	266	24	4.68572454	4.68572454	NUM
ejpam-5427	266	25	4.72603111	4.72603111	NUM
ejpam-5427	266	26	4.44735707	4.44735707	NUM
ejpam-5427	266	27	4.412733	4.412733	NUM
ejpam-5427	266	28	4.155936	4.155936	NUM
ejpam-5427	266	29	4.683269	4.683269	NUM
ejpam-5427	266	30	0.15052	0.15052	NUM
ejpam-5427	266	31	1.85346	1.85346	NUM
ejpam-5427	266	32	0.09642	0.09642	NUM
ejpam-5427	266	33	0.76295	0.76295	NUM
ejpam-5427	266	34	5.17847	5.17847	NUM
ejpam-5427	266	35	5.91683	5.91683	NUM
ejpam-5427	266	36	11.39196	11.39196	NUM
ejpam-5427	266	37	0.14878	0.14878	NUM
ejpam-5427	266	38	table	table	NOUN
ejpam-5427	266	39	5	5	NUM
ejpam-5427	266	40	:	:	PUNCT
ejpam-5427	266	41	comparison	comparison	NOUN
ejpam-5427	266	42	between	between	ADP
ejpam-5427	266	43	the	the	DET
ejpam-5427	266	44	numerical	numerical	ADJ
ejpam-5427	266	45	solution	solution	NOUN
ejpam-5427	266	46	and	and	CCONJ
ejpam-5427	266	47	analytical	analytical	ADJ
ejpam-5427	266	48	solutions	solution	NOUN
ejpam-5427	266	49	at	at	ADP
ejpam-5427	266	50	a	a	DET
ejpam-5427	266	51	=	=	SYM
ejpam-5427	266	52	0.2	0.2	NUM
ejpam-5427	266	53	for	for	ADP
ejpam-5427	266	54	eq	eq	PROPN
ejpam-5427	266	55	.	.	PUNCT
ejpam-5427	267	1	(	(	PUNCT
ejpam-5427	267	2	25	25	NUM
ejpam-5427	267	3	)	)	PUNCT
ejpam-5427	267	4	t	t	NOUN
ejpam-5427	267	5	block	block	NOUN
ejpam-5427	267	6	method	method	NOUN
ejpam-5427	267	7	mdtm	mdtm	VERB
ejpam-5427	267	8	[	[	X
ejpam-5427	267	9	4/4	4/4	NUM
ejpam-5427	267	10	]	]	PUNCT
ejpam-5427	267	11	and	and	CCONJ
ejpam-5427	267	12	present	present	ADJ
ejpam-5427	267	13	solution	solution	NOUN
ejpam-5427	267	14	numerical	numerical	ADJ
ejpam-5427	267	15	solution	solution	NOUN
ejpam-5427	267	16	[	[	X
ejpam-5427	267	17	24	24	NUM
ejpam-5427	267	18	]	]	X
ejpam-5427	268	1	[	[	X
ejpam-5427	268	2	5/5	5/5	NUM
ejpam-5427	268	3	]	]	PUNCT
ejpam-5427	269	1	[	[	X
ejpam-5427	269	2	33	33	NUM
ejpam-5427	269	3	]	]	SYM
ejpam-5427	269	4	0	0	NUM
ejpam-5427	269	5	0	0	NUM
ejpam-5427	269	6	0	0	NUM
ejpam-5427	269	7	0	0	NUM
ejpam-5427	269	8	0	0	NUM
ejpam-5427	269	9	0.125	0.125	NUM
ejpam-5427	269	10	0.024934	0.024934	NUM
ejpam-5427	269	11	0.024934942	0.024934942	NUM
ejpam-5427	269	12	0.024934943	0.024934943	NUM
ejpam-5427	269	13	0.024935034	0.024935034	NUM
ejpam-5427	269	14	0.25	0.25	NUM
ejpam-5427	269	15	0.049480	0.049480	NUM
ejpam-5427	269	16	0.049480663	0.049480663	NUM
ejpam-5427	269	17	0.049480664	0.049480664	NUM
ejpam-5427	269	18	0.049480891	0.049480891	NUM
ejpam-5427	269	19	0.375	0.375	NUM
ejpam-5427	269	20	0.073253	0.073253	NUM
ejpam-5427	269	21	0.073253551	0.073253551	NUM
ejpam-5427	269	22	0.073253552	0.073253552	NUM
ejpam-5427	269	23	0.073253560	0.073253560	NUM
ejpam-5427	269	24	0.5	0.5	NUM
ejpam-5427	269	25	0.095881	0.095881	NUM
ejpam-5427	269	26	0.095881197	0.095881197	NUM
ejpam-5427	269	27	0.095881199	0.095881199	NUM
ejpam-5427	269	28	0.095881461	0.095881461	NUM
ejpam-5427	269	29	0.625	0.625	NUM
ejpam-5427	269	30	0.117008	0.117008	NUM
ejpam-5427	269	31	0.117007942	0.117007942	NUM
ejpam-5427	269	32	0.117007949	0.117007949	NUM
ejpam-5427	269	33	0.117008005	0.117008005	NUM
ejpam-5427	269	34	0.75	0.75	NUM
ejpam-5427	269	35	0.1363	0.1363	NUM
ejpam-5427	269	36	0.136300334	0.136300334	NUM
ejpam-5427	269	37	0.136300356	0.136300356	NUM
ejpam-5427	269	38	0.136300499	0.136300499	NUM
ejpam-5427	269	39	0.875	0.875	NUM
ejpam-5427	269	40	0.153452	0.153452	NUM
ejpam-5427	270	1	0.153452432	0.153452432	NUM
ejpam-5427	270	2	0.153452503	0.153452503	NUM
ejpam-5427	270	3	0.153452647	0.153452647	NUM
ejpam-5427	270	4	1	1	NUM
ejpam-5427	270	5	0.168191	0.168191	NUM
ejpam-5427	270	6	0.168190868	0.168190868	NUM
ejpam-5427	270	7	0.168191071	0.168191071	NUM
ejpam-5427	270	8	0.168191036	0.168191036	NUM
ejpam-5427	270	9	1.125	1.125	NUM
ejpam-5427	270	10	0.18028	0.18028	NUM
ejpam-5427	270	11	0.180279542	0.180279542	NUM
ejpam-5427	270	12	0.180280059	0.180280059	NUM
ejpam-5427	270	13	0.180280209	0.180280209	NUM
ejpam-5427	270	14	1.25	1.25	NUM
ejpam-5427	270	15	0.189525	0.189525	NUM
ejpam-5427	270	16	0.189523851	0.189523851	NUM
ejpam-5427	270	17	0.189525026	0.189525026	NUM
ejpam-5427	270	18	0.189524937	0.189524937	NUM
ejpam-5427	270	19	1.375	1.375	NUM
ejpam-5427	270	20	0.195777	0.195777	NUM
ejpam-5427	271	1	0.195774284	0.195774284	NUM
ejpam-5427	271	2	0.195776702	0.195776702	NUM
ejpam-5427	271	3	0.195776711	0.195776711	NUM
ejpam-5427	271	4	1.5	1.5	NUM
ejpam-5427	271	5	0.198934	0.198934	NUM
ejpam-5427	271	6	0.198929290	0.198929290	NUM
ejpam-5427	271	7	0.198933855	0.198933855	NUM
ejpam-5427	271	8	0.198933786	0.198933786	NUM
ejpam-5427	271	9	1.625	1.625	NUM
ejpam-5427	271	10	0.198945	0.198945	NUM
ejpam-5427	271	11	0.198937278	0.198937278	NUM
ejpam-5427	271	12	0.198945268	0.198945268	NUM
ejpam-5427	271	13	0.198945100	0.198945100	NUM
ejpam-5427	271	14	1.75	1.75	NUM
ejpam-5427	271	15	0.195811	0.195811	NUM
ejpam-5427	271	16	0.195797675	0.195797675	NUM
ejpam-5427	271	17	0.195810754	0.195810754	NUM
ejpam-5427	271	18	0.195810626	0.195810626	NUM
ejpam-5427	271	19	1.875	1.875	NUM
ejpam-5427	271	20	0.189581	0.189581	NUM
ejpam-5427	271	21	0.189560997	0.189560997	NUM
ejpam-5427	272	1	0.189581165	0.189581165	NUM
ejpam-5427	272	2	0.189580915	0.189580915	NUM
ejpam-5427	272	3	2	2	NUM
ejpam-5427	272	4	0.180357	0.180357	NUM
ejpam-5427	272	5	0.180327919	0.180327919	NUM
ejpam-5427	272	6	0.180357378	0.180357378	NUM
ejpam-5427	272	7	0.180357098	0.180357098	NUM
ejpam-5427	272	8	g.	g.	NOUN
ejpam-5427	272	9	m.	m.	PROPN
ejpam-5427	272	10	ismail	ismail	PROPN
ejpam-5427	272	11	,	,	PUNCT
ejpam-5427	272	12	m.	m.	NOUN
ejpam-5427	272	13	i.	i.	PROPN
ejpam-5427	272	14	yamani	yamani	PROPN
ejpam-5427	272	15	/	/	SYM
ejpam-5427	272	16	eur	eur	PROPN
ejpam-5427	272	17	.	.	PUNCT
ejpam-5427	273	1	j.	j.	PROPN
ejpam-5427	273	2	pure	pure	PROPN
ejpam-5427	273	3	appl	appl	PROPN
ejpam-5427	273	4	.	.	PROPN
ejpam-5427	273	5	math	math	PROPN
ejpam-5427	273	6	,	,	PUNCT
ejpam-5427	273	7	17	17	NUM
ejpam-5427	273	8	(	(	PUNCT
ejpam-5427	273	9	4	4	NUM
ejpam-5427	273	10	)	)	PUNCT
ejpam-5427	273	11	(	(	PUNCT
ejpam-5427	273	12	2024	2024	NUM
ejpam-5427	273	13	)	)	PUNCT
ejpam-5427	273	14	,	,	PUNCT
ejpam-5427	273	15	3622	3622	NUM
ejpam-5427	273	16	-	-	SYM
ejpam-5427	273	17	3641	3641	NUM
ejpam-5427	273	18	3635	3635	NUM
ejpam-5427	273	19	table	table	NOUN
ejpam-5427	273	20	6	6	NUM
ejpam-5427	273	21	:	:	PUNCT
ejpam-5427	273	22	comparison	comparison	NOUN
ejpam-5427	273	23	between	between	ADP
ejpam-5427	273	24	the	the	DET
ejpam-5427	273	25	numerical	numerical	ADJ
ejpam-5427	273	26	solution	solution	NOUN
ejpam-5427	273	27	and	and	CCONJ
ejpam-5427	273	28	analytical	analytical	ADJ
ejpam-5427	273	29	solutions	solution	NOUN
ejpam-5427	273	30	at	at	ADP
ejpam-5427	273	31	a	a	DET
ejpam-5427	273	32	=	=	SYM
ejpam-5427	273	33	0.4	0.4	NUM
ejpam-5427	273	34	for	for	ADP
ejpam-5427	273	35	eq	eq	PROPN
ejpam-5427	273	36	.	.	PUNCT
ejpam-5427	274	1	(	(	PUNCT
ejpam-5427	274	2	25	25	NUM
ejpam-5427	274	3	)	)	PUNCT
ejpam-5427	274	4	t	t	NOUN
ejpam-5427	274	5	block	block	NOUN
ejpam-5427	274	6	method	method	NOUN
ejpam-5427	274	7	mdtm	mdtm	VERB
ejpam-5427	274	8	[	[	X
ejpam-5427	274	9	4/4	4/4	NUM
ejpam-5427	274	10	]	]	PUNCT
ejpam-5427	274	11	and	and	CCONJ
ejpam-5427	274	12	present	present	ADJ
ejpam-5427	274	13	solution	solution	NOUN
ejpam-5427	274	14	numerical	numerical	ADJ
ejpam-5427	274	15	solution	solution	NOUN
ejpam-5427	274	16	[	[	X
ejpam-5427	274	17	24	24	NUM
ejpam-5427	274	18	]	]	X
ejpam-5427	275	1	[	[	X
ejpam-5427	275	2	5/5	5/5	NUM
ejpam-5427	275	3	]	]	PUNCT
ejpam-5427	276	1	[	[	X
ejpam-5427	276	2	33	33	NUM
ejpam-5427	276	3	]	]	SYM
ejpam-5427	276	4	0	0	NUM
ejpam-5427	276	5	0	0	NUM
ejpam-5427	276	6	0	0	NUM
ejpam-5427	276	7	0	0	NUM
ejpam-5427	276	8	0	0	NUM
ejpam-5427	276	9	0.125	0.125	NUM
ejpam-5427	276	10	0.049869	0.049869	NUM
ejpam-5427	276	11	0.049869861	0.049869861	NUM
ejpam-5427	276	12	0.049869863	0.049869863	NUM
ejpam-5427	276	13	0.049870029	0.049870029	NUM
ejpam-5427	276	14	0.25	0.25	NUM
ejpam-5427	276	15	0.098960	0.098960	NUM
ejpam-5427	276	16	0.098960556	0.098960556	NUM
ejpam-5427	276	17	0.098960576	0.098960576	NUM
ejpam-5427	276	18	0.098961001	0.098961001	NUM
ejpam-5427	276	19	0.375	0.375	NUM
ejpam-5427	276	20	0.146501	0.146501	NUM
ejpam-5427	276	21	0.146501354	0.146501354	NUM
ejpam-5427	276	22	0.146501423	0.146501423	NUM
ejpam-5427	276	23	0.146501386	0.146501386	NUM
ejpam-5427	276	24	0.5	0.5	NUM
ejpam-5427	276	25	0.191739	0.191739	NUM
ejpam-5427	276	26	0.191738758	0.191738758	NUM
ejpam-5427	276	27	0.191738937	0.191738937	NUM
ejpam-5427	276	28	0.191739302	0.191739302	NUM
ejpam-5427	276	29	0.625	0.625	NUM
ejpam-5427	276	30	0.233946	0.233946	NUM
ejpam-5427	276	31	0.233945991	0.233945991	NUM
ejpam-5427	276	32	0.233946416	0.233946416	NUM
ejpam-5427	276	33	0.233946249	0.233946249	NUM
ejpam-5427	276	34	0.75	0.75	NUM
ejpam-5427	276	35	0.272434	0.272434	NUM
ejpam-5427	276	36	0.272433351	0.272433351	NUM
ejpam-5427	276	37	0.272434399	0.272434399	NUM
ejpam-5427	276	38	0.272434276	0.272434276	NUM
ejpam-5427	276	39	0.875	0.875	NUM
ejpam-5427	276	40	0.306562	0.306562	NUM
ejpam-5427	276	41	0.306559422	0.306559422	NUM
ejpam-5427	276	42	0.306562164	0.306562164	NUM
ejpam-5427	276	43	0.306561832	0.306561832	NUM
ejpam-5427	276	44	1	1	NUM
ejpam-5427	276	45	0.335749	0.335749	NUM
ejpam-5427	276	46	0.335743004	0.335743004	NUM
ejpam-5427	276	47	0.33575013	0.33575013	NUM
ejpam-5427	276	48	0.335749291	0.335749291	NUM
ejpam-5427	276	49	1.125	1.125	NUM
ejpam-5427	276	50	0.359492	0.359492	NUM
ejpam-5427	276	51	0.359475362	0.359475362	NUM
ejpam-5427	276	52	0.359492741	0.359492741	NUM
ejpam-5427	276	53	0.359492282	0.359492282	NUM
ejpam-5427	276	54	1.25	1.25	NUM
ejpam-5427	276	55	0.37737	0.37737	NUM
ejpam-5427	276	56	0.377332285	0.377332285	NUM
ejpam-5427	276	57	0.377371297	0.377371297	NUM
ejpam-5427	276	58	0.377370224	0.377370224	NUM
ejpam-5427	276	59	1.375	1.375	NUM
ejpam-5427	276	60	0.389065	0.389065	NUM
ejpam-5427	276	61	0.388985315	0.388985315	NUM
ejpam-5427	276	62	0.389065644	0.389065644	NUM
ejpam-5427	276	63	0.389064877	0.389064877	NUM
ejpam-5427	276	64	1.5	1.5	NUM
ejpam-5427	276	65	0.394363	0.394363	NUM
ejpam-5427	276	66	0.394211444	0.394211444	NUM
ejpam-5427	276	67	0.394363972	0.394363972	NUM
ejpam-5427	276	68	0.394363009	0.394363009	NUM
ejpam-5427	276	69	1.625	1.625	NUM
ejpam-5427	276	70	0.393169	0.393169	NUM
ejpam-5427	276	71	0.392900613	0.392900613	NUM
ejpam-5427	276	72	0.393169669	0.393169669	NUM
ejpam-5427	276	73	0.393168420	0.393168420	NUM
ejpam-5427	276	74	1.75	1.75	NUM
ejpam-5427	276	75	0.385503	0.385503	NUM
ejpam-5427	276	76	0.385060429	0.385060429	NUM
ejpam-5427	276	77	0.385504547	0.385504547	NUM
ejpam-5427	276	78	0.385503391	0.385503391	NUM
ejpam-5427	276	79	1.875	1.875	NUM
ejpam-5427	276	80	0.371507	0.371507	NUM
ejpam-5427	276	81	0.370817684	0.370817684	NUM
ejpam-5427	277	1	0.371508112	0.371508112	NUM
ejpam-5427	277	2	0.371506638	0.371506638	NUM
ejpam-5427	277	3	2	2	NUM
ejpam-5427	277	4	0.351432	0.351432	NUM
ejpam-5427	277	5	0.350416451	0.350416451	NUM
ejpam-5427	277	6	0.351432939	0.351432939	NUM
ejpam-5427	277	7	0.351431339	0.351431339	NUM
ejpam-5427	277	8	g.	g.	PROPN
ejpam-5427	277	9	m.	m.	PROPN
ejpam-5427	277	10	ismail	ismail	PROPN
ejpam-5427	277	11	,	,	PUNCT
ejpam-5427	277	12	m.	m.	NOUN
ejpam-5427	277	13	i.	i.	PROPN
ejpam-5427	277	14	yamani	yamani	PROPN
ejpam-5427	277	15	/	/	SYM
ejpam-5427	277	16	eur	eur	PROPN
ejpam-5427	277	17	.	.	PUNCT
ejpam-5427	278	1	j.	j.	PROPN
ejpam-5427	278	2	pure	pure	PROPN
ejpam-5427	278	3	appl	appl	PROPN
ejpam-5427	278	4	.	.	PROPN
ejpam-5427	278	5	math	math	PROPN
ejpam-5427	278	6	,	,	PUNCT
ejpam-5427	278	7	17	17	NUM
ejpam-5427	278	8	(	(	PUNCT
ejpam-5427	278	9	4	4	NUM
ejpam-5427	278	10	)	)	PUNCT
ejpam-5427	278	11	(	(	PUNCT
ejpam-5427	278	12	2024	2024	NUM
ejpam-5427	278	13	)	)	PUNCT
ejpam-5427	278	14	,	,	PUNCT
ejpam-5427	278	15	3622	3622	NUM
ejpam-5427	278	16	-	-	SYM
ejpam-5427	278	17	3641	3641	NUM
ejpam-5427	278	18	3636	3636	NUM
ejpam-5427	278	19	figure	figure	NOUN
ejpam-5427	278	20	3	3	NUM
ejpam-5427	278	21	:	:	PUNCT
ejpam-5427	278	22	comparison	comparison	NOUN
ejpam-5427	278	23	between	between	ADP
ejpam-5427	278	24	higher	high	ADJ
ejpam-5427	278	25	order	order	NOUN
ejpam-5427	278	26	analytical	analytical	ADJ
ejpam-5427	278	27	solution	solution	NOUN
ejpam-5427	278	28	(	(	PUNCT
ejpam-5427	278	29	black	black	ADJ
ejpam-5427	278	30	line	line	NOUN
ejpam-5427	278	31	)	)	PUNCT
ejpam-5427	278	32	,	,	PUNCT
ejpam-5427	278	33	mgemm	mgemm	NOUN
ejpam-5427	279	1	[	[	X
ejpam-5427	279	2	37	37	NUM
ejpam-5427	279	3	]	]	X
ejpam-5427	279	4	(	(	PUNCT
ejpam-5427	279	5	red	red	ADJ
ejpam-5427	279	6	line	line	NOUN
ejpam-5427	279	7	)	)	PUNCT
ejpam-5427	279	8	,	,	PUNCT
ejpam-5427	279	9	and	and	CCONJ
ejpam-5427	279	10	the	the	DET
ejpam-5427	279	11	numerical	numerical	ADJ
ejpam-5427	279	12	solution	solution	NOUN
ejpam-5427	279	13	(	(	PUNCT
ejpam-5427	279	14	blue	blue	ADJ
ejpam-5427	279	15	line	line	NOUN
ejpam-5427	279	16	)	)	PUNCT
ejpam-5427	279	17	at	at	ADP
ejpam-5427	279	18	a	a	DET
ejpam-5427	279	19	=	=	SYM
ejpam-5427	279	20	1	1	NUM
ejpam-5427	279	21	,	,	PUNCT
ejpam-5427	279	22	for	for	ADP
ejpam-5427	279	23	eq	eq	NOUN
ejpam-5427	279	24	.	.	PUNCT
ejpam-5427	279	25	(	(	PUNCT
ejpam-5427	279	26	25	25	NUM
ejpam-5427	279	27	)	)	PUNCT
ejpam-5427	279	28	.	.	PUNCT
ejpam-5427	280	1	g.	g.	PROPN
ejpam-5427	280	2	m.	m.	PROPN
ejpam-5427	280	3	ismail	ismail	PROPN
ejpam-5427	280	4	,	,	PUNCT
ejpam-5427	280	5	m.	m.	NOUN
ejpam-5427	280	6	i.	i.	PROPN
ejpam-5427	280	7	yamani	yamani	PROPN
ejpam-5427	280	8	/	/	SYM
ejpam-5427	280	9	eur	eur	PROPN
ejpam-5427	280	10	.	.	PUNCT
ejpam-5427	281	1	j.	j.	PROPN
ejpam-5427	281	2	pure	pure	PROPN
ejpam-5427	281	3	appl	appl	PROPN
ejpam-5427	281	4	.	.	PROPN
ejpam-5427	281	5	math	math	PROPN
ejpam-5427	281	6	,	,	PUNCT
ejpam-5427	281	7	17	17	NUM
ejpam-5427	281	8	(	(	PUNCT
ejpam-5427	281	9	4	4	NUM
ejpam-5427	281	10	)	)	PUNCT
ejpam-5427	281	11	(	(	PUNCT
ejpam-5427	281	12	2024	2024	NUM
ejpam-5427	281	13	)	)	PUNCT
ejpam-5427	281	14	,	,	PUNCT
ejpam-5427	281	15	3622	3622	NUM
ejpam-5427	281	16	-	-	SYM
ejpam-5427	281	17	3641	3641	NUM
ejpam-5427	281	18	3637	3637	NUM
ejpam-5427	281	19	figure	figure	NOUN
ejpam-5427	281	20	4	4	NUM
ejpam-5427	281	21	:	:	PUNCT
ejpam-5427	281	22	comparison	comparison	NOUN
ejpam-5427	281	23	between	between	ADP
ejpam-5427	281	24	higher	high	ADJ
ejpam-5427	281	25	order	order	NOUN
ejpam-5427	281	26	analytical	analytical	ADJ
ejpam-5427	281	27	solution	solution	NOUN
ejpam-5427	281	28	(	(	PUNCT
ejpam-5427	281	29	black	black	ADJ
ejpam-5427	281	30	line	line	NOUN
ejpam-5427	281	31	)	)	PUNCT
ejpam-5427	281	32	,	,	PUNCT
ejpam-5427	281	33	mdtm	mdtm	VERB
ejpam-5427	281	34	[	[	X
ejpam-5427	281	35	33	33	NUM
ejpam-5427	281	36	]	]	X
ejpam-5427	281	37	(	(	PUNCT
ejpam-5427	281	38	red	red	ADJ
ejpam-5427	281	39	line	line	NOUN
ejpam-5427	281	40	)	)	PUNCT
ejpam-5427	281	41	,	,	PUNCT
ejpam-5427	281	42	and	and	CCONJ
ejpam-5427	281	43	the	the	DET
ejpam-5427	281	44	numerical	numerical	ADJ
ejpam-5427	281	45	solution	solution	NOUN
ejpam-5427	281	46	(	(	PUNCT
ejpam-5427	281	47	blue	blue	ADJ
ejpam-5427	281	48	line	line	NOUN
ejpam-5427	281	49	)	)	PUNCT
ejpam-5427	281	50	at	at	ADP
ejpam-5427	281	51	a	a	DET
ejpam-5427	281	52	=	=	SYM
ejpam-5427	281	53	0.3	0.3	NUM
ejpam-5427	281	54	,	,	PUNCT
ejpam-5427	281	55	for	for	ADP
ejpam-5427	281	56	eq	eq	NOUN
ejpam-5427	281	57	.	.	PUNCT
ejpam-5427	282	1	(	(	PUNCT
ejpam-5427	282	2	25	25	NUM
ejpam-5427	282	3	)	)	PUNCT
ejpam-5427	282	4	.	.	PUNCT
ejpam-5427	283	1	references	reference	NOUN
ejpam-5427	283	2	3638	3638	NUM
ejpam-5427	283	3	5	5	NUM
ejpam-5427	283	4	.	.	PUNCT
ejpam-5427	283	5	conclusion	conclusion	NOUN
ejpam-5427	283	6	in	in	ADP
ejpam-5427	283	7	this	this	DET
ejpam-5427	283	8	study	study	NOUN
ejpam-5427	283	9	,	,	PUNCT
ejpam-5427	283	10	a	a	DET
ejpam-5427	283	11	modified	modify	VERB
ejpam-5427	283	12	iteration	iteration	NOUN
ejpam-5427	283	13	approach	approach	NOUN
ejpam-5427	283	14	was	be	AUX
ejpam-5427	283	15	developed	develop	VERB
ejpam-5427	283	16	and	and	CCONJ
ejpam-5427	283	17	employed	employ	VERB
ejpam-5427	283	18	to	to	PART
ejpam-5427	283	19	solve	solve	VERB
ejpam-5427	283	20	two	two	NUM
ejpam-5427	283	21	nonlinear	nonlinear	ADJ
ejpam-5427	283	22	third	third	ADJ
ejpam-5427	283	23	-	-	PUNCT
ejpam-5427	283	24	order	order	NOUN
ejpam-5427	283	25	jerk	jerk	NOUN
ejpam-5427	283	26	equations	equation	NOUN
ejpam-5427	283	27	with	with	ADP
ejpam-5427	283	28	broad	broad	ADJ
ejpam-5427	283	29	engineering	engineering	NOUN
ejpam-5427	283	30	applications	application	NOUN
ejpam-5427	283	31	.	.	PUNCT
ejpam-5427	284	1	the	the	DET
ejpam-5427	284	2	modified	modify	VERB
ejpam-5427	284	3	approach	approach	NOUN
ejpam-5427	284	4	successfully	successfully	ADV
ejpam-5427	284	5	determined	determine	VERB
ejpam-5427	284	6	approximate	approximate	ADJ
ejpam-5427	284	7	analytical	analytical	ADJ
ejpam-5427	284	8	solutions	solution	NOUN
ejpam-5427	284	9	for	for	ADP
ejpam-5427	284	10	these	these	DET
ejpam-5427	284	11	equations	equation	NOUN
ejpam-5427	284	12	.	.	PUNCT
ejpam-5427	285	1	a	a	DET
ejpam-5427	285	2	comparison	comparison	NOUN
ejpam-5427	285	3	of	of	ADP
ejpam-5427	285	4	the	the	DET
ejpam-5427	285	5	obtained	obtain	VERB
ejpam-5427	285	6	results	result	NOUN
ejpam-5427	285	7	with	with	ADP
ejpam-5427	285	8	numerical	numerical	ADJ
ejpam-5427	285	9	solutions	solution	NOUN
ejpam-5427	285	10	demonstrated	demonstrate	VERB
ejpam-5427	285	11	the	the	DET
ejpam-5427	285	12	excellent	excellent	ADJ
ejpam-5427	285	13	accuracy	accuracy	NOUN
ejpam-5427	285	14	of	of	ADP
ejpam-5427	285	15	the	the	DET
ejpam-5427	285	16	proposed	propose	VERB
ejpam-5427	285	17	method	method	NOUN
ejpam-5427	285	18	.	.	PUNCT
ejpam-5427	286	1	the	the	DET
ejpam-5427	286	2	present	present	ADJ
ejpam-5427	286	3	approach	approach	NOUN
ejpam-5427	286	4	offers	offer	VERB
ejpam-5427	286	5	solutions	solution	NOUN
ejpam-5427	286	6	in	in	ADP
ejpam-5427	286	7	a	a	DET
ejpam-5427	286	8	readily	readily	ADV
ejpam-5427	286	9	usable	usable	ADJ
ejpam-5427	286	10	analytical	analytical	ADJ
ejpam-5427	286	11	form	form	NOUN
ejpam-5427	286	12	,	,	PUNCT
ejpam-5427	286	13	exhibiting	exhibit	VERB
ejpam-5427	286	14	superior	superior	ADJ
ejpam-5427	286	15	accuracy	accuracy	NOUN
ejpam-5427	286	16	and	and	CCONJ
ejpam-5427	286	17	a	a	DET
ejpam-5427	286	18	wider	wide	ADJ
ejpam-5427	286	19	range	range	NOUN
ejpam-5427	286	20	of	of	ADP
ejpam-5427	286	21	applicability	applicability	NOUN
ejpam-5427	286	22	compared	compare	VERB
ejpam-5427	286	23	to	to	ADP
ejpam-5427	286	24	other	other	ADJ
ejpam-5427	286	25	established	establish	VERB
ejpam-5427	286	26	analytical	analytical	ADJ
ejpam-5427	286	27	methods	method	NOUN
ejpam-5427	286	28	found	find	VERB
ejpam-5427	286	29	in	in	ADP
ejpam-5427	286	30	the	the	DET
ejpam-5427	286	31	literature	literature	NOUN
ejpam-5427	286	32	.	.	PUNCT
ejpam-5427	287	1	this	this	DET
ejpam-5427	287	2	technique	technique	NOUN
ejpam-5427	287	3	proves	prove	VERB
ejpam-5427	287	4	to	to	PART
ejpam-5427	287	5	be	be	AUX
ejpam-5427	287	6	a	a	DET
ejpam-5427	287	7	powerful	powerful	ADJ
ejpam-5427	287	8	and	and	CCONJ
ejpam-5427	287	9	effective	effective	ADJ
ejpam-5427	287	10	mathematical	mathematical	ADJ
ejpam-5427	287	11	tool	tool	NOUN
ejpam-5427	287	12	for	for	ADP
ejpam-5427	287	13	solving	solve	VERB
ejpam-5427	287	14	highly	highly	ADV
ejpam-5427	287	15	nonlinear	nonlinear	ADJ
ejpam-5427	287	16	third	third	ADJ
ejpam-5427	287	17	-	-	PUNCT
ejpam-5427	287	18	order	order	NOUN
ejpam-5427	287	19	differential	differential	ADJ
ejpam-5427	287	20	equations	equation	NOUN
ejpam-5427	287	21	arising	arise	VERB
ejpam-5427	287	22	in	in	ADP
ejpam-5427	287	23	mathematical	mathematical	ADJ
ejpam-5427	287	24	physics	physics	NOUN
ejpam-5427	287	25	,	,	PUNCT
ejpam-5427	287	26	applied	apply	VERB
ejpam-5427	287	27	mathematics	mathematic	NOUN
ejpam-5427	287	28	,	,	PUNCT
ejpam-5427	287	29	and	and	CCONJ
ejpam-5427	287	30	engineering	engineering	NOUN
ejpam-5427	287	31	.	.	PUNCT
ejpam-5427	288	1	furthermore	furthermore	ADV
ejpam-5427	288	2	,	,	PUNCT
ejpam-5427	288	3	the	the	DET
ejpam-5427	288	4	iterative	iterative	ADJ
ejpam-5427	288	5	nature	nature	NOUN
ejpam-5427	288	6	of	of	ADP
ejpam-5427	288	7	the	the	DET
ejpam-5427	288	8	method	method	NOUN
ejpam-5427	288	9	allows	allow	VERB
ejpam-5427	288	10	for	for	SCONJ
ejpam-5427	288	11	the	the	DET
ejpam-5427	288	12	computation	computation	NOUN
ejpam-5427	288	13	of	of	ADP
ejpam-5427	288	14	higher	high	ADJ
ejpam-5427	288	15	-	-	PUNCT
ejpam-5427	288	16	order	order	NOUN
ejpam-5427	288	17	approximations	approximation	NOUN
ejpam-5427	288	18	to	to	PART
ejpam-5427	288	19	achieve	achieve	VERB
ejpam-5427	288	20	even	even	ADV
ejpam-5427	288	21	greater	great	ADJ
ejpam-5427	288	22	accuracy	accuracy	NOUN
ejpam-5427	288	23	if	if	SCONJ
ejpam-5427	288	24	desired	desire	VERB
ejpam-5427	288	25	.	.	PUNCT
ejpam-5427	289	1	the	the	DET
ejpam-5427	289	2	modified	modify	VERB
ejpam-5427	289	3	iteration	iteration	NOUN
ejpam-5427	289	4	technique	technique	NOUN
ejpam-5427	289	5	facilitates	facilitate	VERB
ejpam-5427	289	6	the	the	DET
ejpam-5427	289	7	straightforward	straightforward	ADJ
ejpam-5427	289	8	calculation	calculation	NOUN
ejpam-5427	289	9	of	of	ADP
ejpam-5427	289	10	these	these	DET
ejpam-5427	289	11	higher	high	ADJ
ejpam-5427	289	12	-	-	PUNCT
ejpam-5427	289	13	order	order	NOUN
ejpam-5427	289	14	terms	term	NOUN
ejpam-5427	289	15	,	,	PUNCT
ejpam-5427	289	16	leading	lead	VERB
ejpam-5427	289	17	to	to	ADP
ejpam-5427	289	18	solutions	solution	NOUN
ejpam-5427	289	19	that	that	SCONJ
ejpam-5427	289	20	closely	closely	ADV
ejpam-5427	289	21	approximate	approximate	VERB
ejpam-5427	289	22	the	the	DET
ejpam-5427	289	23	exact	exact	ADJ
ejpam-5427	289	24	solutions	solution	NOUN
ejpam-5427	289	25	.	.	PUNCT
ejpam-5427	290	1	consequently	consequently	ADV
ejpam-5427	290	2	,	,	PUNCT
ejpam-5427	290	3	the	the	DET
ejpam-5427	290	4	present	present	ADJ
ejpam-5427	290	5	method	method	NOUN
ejpam-5427	290	6	demonstrates	demonstrate	VERB
ejpam-5427	290	7	consistent	consistent	ADJ
ejpam-5427	290	8	and	and	CCONJ
ejpam-5427	290	9	reliable	reliable	ADJ
ejpam-5427	290	10	performance	performance	NOUN
ejpam-5427	290	11	,	,	PUNCT
ejpam-5427	290	12	offering	offer	VERB
ejpam-5427	290	13	a	a	DET
ejpam-5427	290	14	simple	simple	ADJ
ejpam-5427	290	15	yet	yet	CCONJ
ejpam-5427	290	16	effective	effective	ADJ
ejpam-5427	290	17	approach	approach	NOUN
ejpam-5427	290	18	for	for	ADP
ejpam-5427	290	19	obtaining	obtain	VERB
ejpam-5427	290	20	novel	novel	ADJ
ejpam-5427	290	21	solutions	solution	NOUN
ejpam-5427	290	22	to	to	ADP
ejpam-5427	290	23	a	a	DET
ejpam-5427	290	24	variety	variety	NOUN
ejpam-5427	290	25	of	of	ADP
ejpam-5427	290	26	nonlinear	nonlinear	ADJ
ejpam-5427	290	27	problems	problem	NOUN
ejpam-5427	290	28	.	.	PUNCT
ejpam-5427	291	1	future	future	ADJ
ejpam-5427	291	2	research	research	NOUN
ejpam-5427	291	3	can	can	AUX
ejpam-5427	291	4	focus	focus	VERB
ejpam-5427	291	5	on	on	ADP
ejpam-5427	291	6	a	a	DET
ejpam-5427	291	7	deeper	deep	ADJ
ejpam-5427	291	8	qualitative	qualitative	ADJ
ejpam-5427	291	9	analysis	analysis	NOUN
ejpam-5427	291	10	of	of	ADP
ejpam-5427	291	11	third	third	ADJ
ejpam-5427	291	12	-	-	PUNCT
ejpam-5427	291	13	order	order	NOUN
ejpam-5427	291	14	systems	system	NOUN
ejpam-5427	291	15	,	,	PUNCT
ejpam-5427	291	16	exploring	explore	VERB
ejpam-5427	291	17	the	the	DET
ejpam-5427	291	18	existence	existence	NOUN
ejpam-5427	291	19	and	and	CCONJ
ejpam-5427	291	20	uniqueness	uniqueness	NOUN
ejpam-5427	291	21	of	of	ADP
ejpam-5427	291	22	solutions	solution	NOUN
ejpam-5427	291	23	,	,	PUNCT
ejpam-5427	291	24	stability	stability	NOUN
ejpam-5427	291	25	analysis	analysis	NOUN
ejpam-5427	291	26	,	,	PUNCT
ejpam-5427	291	27	and	and	CCONJ
ejpam-5427	291	28	bifurcation	bifurcation	NOUN
ejpam-5427	291	29	behavior	behavior	NOUN
ejpam-5427	291	30	[	[	X
ejpam-5427	291	31	39	39	NUM
ejpam-5427	291	32	,	,	PUNCT
ejpam-5427	291	33	40	40	NUM
ejpam-5427	291	34	]	]	PUNCT
ejpam-5427	291	35	.	.	PUNCT
ejpam-5427	292	1	because	because	SCONJ
ejpam-5427	292	2	of	of	ADP
ejpam-5427	292	3	the	the	DET
ejpam-5427	292	4	great	great	ADJ
ejpam-5427	292	5	importance	importance	NOUN
ejpam-5427	292	6	of	of	ADP
ejpam-5427	292	7	applications	application	NOUN
ejpam-5427	292	8	of	of	ADP
ejpam-5427	292	9	nonlinear	nonlinear	ADJ
ejpam-5427	292	10	third	third	ADJ
ejpam-5427	292	11	-	-	PUNCT
ejpam-5427	292	12	order	order	NOUN
ejpam-5427	292	13	jerk	jerk	NOUN
ejpam-5427	292	14	equations	equation	NOUN
ejpam-5427	292	15	,	,	PUNCT
ejpam-5427	292	16	more	more	ADV
ejpam-5427	292	17	analytical	analytical	ADJ
ejpam-5427	292	18	and	and	CCONJ
ejpam-5427	292	19	numerical	numerical	ADJ
ejpam-5427	292	20	methods	method	NOUN
ejpam-5427	292	21	will	will	AUX
ejpam-5427	292	22	be	be	AUX
ejpam-5427	292	23	developed	develop	VERB
ejpam-5427	292	24	to	to	PART
ejpam-5427	292	25	solve	solve	VERB
ejpam-5427	292	26	such	such	ADJ
ejpam-5427	292	27	problems	problem	NOUN
ejpam-5427	292	28	in	in	ADP
ejpam-5427	292	29	future	future	ADJ
ejpam-5427	292	30	work	work	NOUN
ejpam-5427	292	31	.	.	PUNCT
ejpam-5427	293	1	references	reference	NOUN
ejpam-5427	293	2	[	[	X
ejpam-5427	293	3	1	1	NUM
ejpam-5427	293	4	]	]	PUNCT
ejpam-5427	293	5	l.	l.	PROPN
ejpam-5427	293	6	cveticanin	cveticanin	PROPN
ejpam-5427	293	7	and	and	CCONJ
ejpam-5427	293	8	g.m	g.m	PROPN
ejpam-5427	293	9	.	.	PROPN
ejpam-5427	293	10	ismail	ismail	PROPN
ejpam-5427	293	11	,	,	PUNCT
ejpam-5427	293	12	higher	high	ADJ
ejpam-5427	293	13	order	order	NOUN
ejpam-5427	293	14	approximate	approximate	ADJ
ejpam-5427	293	15	periodic	periodic	ADJ
ejpam-5427	293	16	solutions	solution	NOUN
ejpam-5427	293	17	for	for	ADP
ejpam-5427	293	18	the	the	DET
ejpam-5427	293	19	oscillator	oscillator	NOUN
ejpam-5427	293	20	with	with	ADP
ejpam-5427	293	21	strong	strong	ADJ
ejpam-5427	293	22	nonlinearity	nonlinearity	NOUN
ejpam-5427	293	23	of	of	ADP
ejpam-5427	293	24	polynomial	polynomial	ADJ
ejpam-5427	293	25	type	type	NOUN
ejpam-5427	293	26	,	,	PUNCT
ejpam-5427	293	27	european	european	PROPN
ejpam-5427	293	28	physical	physical	PROPN
ejpam-5427	293	29	journal	journal	PROPN
ejpam-5427	293	30	plus	plus	CCONJ
ejpam-5427	293	31	.	.	PROPN
ejpam-5427	293	32	134	134	NUM
ejpam-5427	293	33	,	,	PUNCT
ejpam-5427	293	34	(	(	PUNCT
ejpam-5427	293	35	2019	2019	NUM
ejpam-5427	293	36	)	)	PUNCT
ejpam-5427	293	37	266	266	NUM
ejpam-5427	293	38	.	.	PUNCT
ejpam-5427	294	1	[	[	X
ejpam-5427	294	2	2	2	X
ejpam-5427	294	3	]	]	PUNCT
ejpam-5427	294	4	h.	h.	PROPN
ejpam-5427	294	5	hu	hu	PROPN
ejpam-5427	294	6	and	and	CCONJ
ejpam-5427	294	7	j.h	j.h	PROPN
ejpam-5427	294	8	.	.	PROPN
ejpam-5427	294	9	tang	tang	PROPN
ejpam-5427	294	10	,	,	PUNCT
ejpam-5427	294	11	solution	solution	NOUN
ejpam-5427	294	12	of	of	ADP
ejpam-5427	294	13	a	a	DET
ejpam-5427	294	14	duffing	duffing	NOUN
ejpam-5427	294	15	-	-	PUNCT
ejpam-5427	294	16	harmonic	harmonic	ADJ
ejpam-5427	294	17	oscillator	oscillator	NOUN
ejpam-5427	294	18	by	by	ADP
ejpam-5427	294	19	the	the	DET
ejpam-5427	294	20	method	method	NOUN
ejpam-5427	294	21	of	of	ADP
ejpam-5427	294	22	harmonic	harmonic	ADJ
ejpam-5427	294	23	balance	balance	NOUN
ejpam-5427	294	24	,	,	PUNCT
ejpam-5427	294	25	journal	journal	NOUN
ejpam-5427	294	26	of	of	ADP
ejpam-5427	294	27	sound	sound	NOUN
ejpam-5427	294	28	and	and	CCONJ
ejpam-5427	294	29	vibration	vibration	NOUN
ejpam-5427	294	30	.	.	PUNCT
ejpam-5427	295	1	294	294	NUM
ejpam-5427	295	2	,	,	PUNCT
ejpam-5427	295	3	(	(	PUNCT
ejpam-5427	295	4	2006	2006	NUM
ejpam-5427	295	5	)	)	PUNCT
ejpam-5427	295	6	637	637	NUM
ejpam-5427	295	7	-	-	SYM
ejpam-5427	295	8	639	639	NUM
ejpam-5427	295	9	.	.	PUNCT
ejpam-5427	296	1	[	[	X
ejpam-5427	296	2	3	3	X
ejpam-5427	296	3	]	]	X
ejpam-5427	296	4	s.	s.	PROPN
ejpam-5427	296	5	wang	wang	PROPN
ejpam-5427	296	6	,	,	PUNCT
ejpam-5427	296	7	y.	y.	PROPN
ejpam-5427	296	8	zhang	zhang	PROPN
ejpam-5427	296	9	,	,	PUNCT
ejpam-5427	296	10	w.	w.	PROPN
ejpam-5427	296	11	guo	guo	PROPN
ejpam-5427	296	12	,	,	PUNCT
ejpam-5427	296	13	t.	t.	NOUN
ejpam-5427	296	14	pi	pi	PROPN
ejpam-5427	296	15	and	and	CCONJ
ejpam-5427	296	16	x.	x.	PROPN
ejpam-5427	296	17	li	li	PROPN
ejpam-5427	296	18	,	,	PUNCT
ejpam-5427	296	19	vibration	vibration	VERB
ejpam-5427	296	20	analysis	analysis	NOUN
ejpam-5427	296	21	of	of	ADP
ejpam-5427	296	22	nonlinear	nonlinear	ADJ
ejpam-5427	296	23	damping	damp	VERB
ejpam-5427	296	24	systems	system	NOUN
ejpam-5427	296	25	by	by	ADP
ejpam-5427	296	26	the	the	DET
ejpam-5427	296	27	discrete	discrete	ADJ
ejpam-5427	296	28	incremental	incremental	ADJ
ejpam-5427	296	29	harmonic	harmonic	ADJ
ejpam-5427	296	30	balance	balance	NOUN
ejpam-5427	296	31	method	method	NOUN
ejpam-5427	296	32	,	,	PUNCT
ejpam-5427	296	33	nonlinear	nonlinear	ADJ
ejpam-5427	296	34	dynamics	dynamic	NOUN
ejpam-5427	296	35	.	.	PUNCT
ejpam-5427	297	1	111	111	NUM
ejpam-5427	297	2	(	(	PUNCT
ejpam-5427	297	3	2023	2023	NUM
ejpam-5427	297	4	)	)	PUNCT
ejpam-5427	297	5	2009	2009	NUM
ejpam-5427	297	6	-	-	SYM
ejpam-5427	297	7	2028	2028	NUM
ejpam-5427	297	8	.	.	PUNCT
ejpam-5427	298	1	[	[	X
ejpam-5427	298	2	4	4	X
ejpam-5427	298	3	]	]	X
ejpam-5427	298	4	w.	w.	PROPN
ejpam-5427	298	5	tang	tang	PROPN
ejpam-5427	298	6	,	,	PUNCT
ejpam-5427	298	7	n.	n.	PROPN
ejpam-5427	298	8	anjum	anjum	PROPN
ejpam-5427	298	9	and	and	CCONJ
ejpam-5427	298	10	j.h	j.h	PROPN
ejpam-5427	298	11	.	.	PUNCT
ejpam-5427	299	1	he	he	PRON
ejpam-5427	299	2	,	,	PUNCT
ejpam-5427	299	3	variational	variational	ADJ
ejpam-5427	299	4	iteration	iteration	NOUN
ejpam-5427	299	5	method	method	NOUN
ejpam-5427	299	6	for	for	ADP
ejpam-5427	299	7	the	the	DET
ejpam-5427	299	8	nanobeamsbased	nanobeamsbase	VERB
ejpam-5427	299	9	n	n	CCONJ
ejpam-5427	299	10	/	/	SYM
ejpam-5427	299	11	mems	mem	NOUN
ejpam-5427	299	12	system	system	NOUN
ejpam-5427	299	13	,	,	PUNCT
ejpam-5427	299	14	methodsx	methodsx	NOUN
ejpam-5427	299	15	.	.	PUNCT
ejpam-5427	299	16	11	11	NUM
ejpam-5427	299	17	,	,	PUNCT
ejpam-5427	299	18	(	(	PUNCT
ejpam-5427	299	19	2023	2023	NUM
ejpam-5427	299	20	)	)	PUNCT
ejpam-5427	299	21	102465	102465	NUM
ejpam-5427	299	22	.	.	PUNCT
ejpam-5427	300	1	[	[	X
ejpam-5427	300	2	5	5	X
ejpam-5427	300	3	]	]	PUNCT
ejpam-5427	300	4	s.	s.	PROPN
ejpam-5427	300	5	rehman	rehman	PROPN
ejpam-5427	300	6	,	,	PUNCT
ejpam-5427	300	7	a.	a.	PROPN
ejpam-5427	300	8	hussain	hussain	PROPN
ejpam-5427	300	9	,	,	PUNCT
ejpam-5427	300	10	j.u	j.u	PROPN
ejpam-5427	300	11	.	.	PROPN
ejpam-5427	300	12	rahman	rahman	PROPN
ejpam-5427	300	13	,	,	PUNCT
ejpam-5427	300	14	n.	n.	PROPN
ejpam-5427	300	15	anjum	anjum	PROPN
ejpam-5427	300	16	,	,	PUNCT
ejpam-5427	300	17	t.	t.	PROPN
ejpam-5427	300	18	munir	munir	PROPN
ejpam-5427	300	19	,	,	PUNCT
ejpam-5427	300	20	modified	modify	VERB
ejpam-5427	300	21	laplace	laplace	NOUN
ejpam-5427	300	22	based	base	VERB
ejpam-5427	300	23	variational	variational	ADJ
ejpam-5427	300	24	iteration	iteration	NOUN
ejpam-5427	300	25	method	method	NOUN
ejpam-5427	300	26	for	for	ADP
ejpam-5427	300	27	the	the	DET
ejpam-5427	300	28	mechanical	mechanical	ADJ
ejpam-5427	300	29	vibrations	vibration	NOUN
ejpam-5427	300	30	and	and	CCONJ
ejpam-5427	300	31	its	its	PRON
ejpam-5427	300	32	applications	application	NOUN
ejpam-5427	300	33	,	,	PUNCT
ejpam-5427	300	34	acta	acta	PROPN
ejpam-5427	300	35	mechanica	mechanica	PROPN
ejpam-5427	300	36	et	et	PROPN
ejpam-5427	300	37	automatica	automatica	PROPN
ejpam-5427	300	38	.	.	PROPN
ejpam-5427	300	39	16	16	NUM
ejpam-5427	300	40	,	,	PUNCT
ejpam-5427	300	41	(	(	PUNCT
ejpam-5427	300	42	2022	2022	NUM
ejpam-5427	300	43	)	)	PUNCT
ejpam-5427	300	44	98	98	NUM
ejpam-5427	300	45	-	-	SYM
ejpam-5427	300	46	102	102	NUM
ejpam-5427	300	47	.	.	PUNCT
ejpam-5427	300	48	references	reference	NOUN
ejpam-5427	300	49	3639	3639	NUM
ejpam-5427	301	1	[	[	X
ejpam-5427	301	2	6	6	NUM
ejpam-5427	301	3	]	]	PUNCT
ejpam-5427	301	4	j.	j.	PROPN
ejpam-5427	301	5	h.	h.	PROPN
ejpam-5427	301	6	he	he	PRON
ejpam-5427	301	7	,	,	PUNCT
ejpam-5427	301	8	hamiltonian	hamiltonian	ADJ
ejpam-5427	301	9	approach	approach	NOUN
ejpam-5427	301	10	to	to	ADP
ejpam-5427	301	11	nonlinear	nonlinear	ADJ
ejpam-5427	301	12	oscillators	oscillator	NOUN
ejpam-5427	301	13	,	,	PUNCT
ejpam-5427	301	14	physics	physics	NOUN
ejpam-5427	301	15	letter	letter	NOUN
ejpam-5427	301	16	a.	a.	PROPN
ejpam-5427	301	17	374	374	NUM
ejpam-5427	301	18	,	,	PUNCT
ejpam-5427	301	19	(	(	PUNCT
ejpam-5427	301	20	2010	2010	NUM
ejpam-5427	301	21	)	)	PUNCT
ejpam-5427	301	22	2312	2312	NUM
ejpam-5427	301	23	-	-	SYM
ejpam-5427	301	24	2314	2314	NUM
ejpam-5427	301	25	.	.	PUNCT
ejpam-5427	302	1	[	[	X
ejpam-5427	302	2	7	7	NUM
ejpam-5427	302	3	]	]	X
ejpam-5427	302	4	g.m	g.m	PROPN
ejpam-5427	302	5	.	.	PUNCT
ejpam-5427	302	6	ismail	ismail	PROPN
ejpam-5427	302	7	and	and	CCONJ
ejpam-5427	302	8	l.	l.	PROPN
ejpam-5427	302	9	cveticanin	cveticanin	PROPN
ejpam-5427	302	10	,	,	PUNCT
ejpam-5427	302	11	higher	high	ADJ
ejpam-5427	302	12	order	order	NOUN
ejpam-5427	302	13	hamiltonian	hamiltonian	ADJ
ejpam-5427	302	14	approach	approach	NOUN
ejpam-5427	302	15	for	for	ADP
ejpam-5427	302	16	solving	solve	VERB
ejpam-5427	302	17	doubly	doubly	ADV
ejpam-5427	302	18	clamped	clamp	VERB
ejpam-5427	302	19	beam	beam	NOUN
ejpam-5427	302	20	type	type	NOUN
ejpam-5427	302	21	n	n	CCONJ
ejpam-5427	302	22	/	/	SYM
ejpam-5427	302	23	mems	mem	NOUN
ejpam-5427	302	24	subjected	subject	VERB
ejpam-5427	302	25	to	to	ADP
ejpam-5427	302	26	the	the	DET
ejpam-5427	302	27	van	van	PROPN
ejpam-5427	302	28	der	der	NOUN
ejpam-5427	302	29	waals	waal	NOUN
ejpam-5427	302	30	attraction	attraction	NOUN
ejpam-5427	302	31	,	,	PUNCT
ejpam-5427	302	32	chinese	chinese	ADJ
ejpam-5427	302	33	journal	journal	PROPN
ejpam-5427	302	34	of	of	ADP
ejpam-5427	302	35	physics	physics	PROPN
ejpam-5427	302	36	.	.	PUNCT
ejpam-5427	303	1	72	72	NUM
ejpam-5427	303	2	,	,	PUNCT
ejpam-5427	303	3	(	(	PUNCT
ejpam-5427	303	4	2021	2021	NUM
ejpam-5427	303	5	)	)	PUNCT
ejpam-5427	303	6	69	69	NUM
ejpam-5427	303	7	-	-	SYM
ejpam-5427	303	8	77	77	NUM
ejpam-5427	303	9	.	.	PUNCT
ejpam-5427	304	1	[	[	X
ejpam-5427	304	2	8	8	NUM
ejpam-5427	304	3	]	]	X
ejpam-5427	304	4	g.	g.	PROPN
ejpam-5427	304	5	m.	m.	PROPN
ejpam-5427	304	6	ismail	ismail	PROPN
ejpam-5427	304	7	,	,	PUNCT
ejpam-5427	304	8	a.	a.	PROPN
ejpam-5427	304	9	kamel	kamel	PROPN
ejpam-5427	304	10	and	and	CCONJ
ejpam-5427	304	11	a.	a.	PROPN
ejpam-5427	304	12	alsarrania	alsarrania	PROPN
ejpam-5427	304	13	,	,	PUNCT
ejpam-5427	304	14	approximate	approximate	ADJ
ejpam-5427	304	15	analytical	analytical	ADJ
ejpam-5427	304	16	solutions	solution	NOUN
ejpam-5427	304	17	to	to	ADP
ejpam-5427	304	18	nonlinear	nonlinear	ADJ
ejpam-5427	304	19	oscillations	oscillation	NOUN
ejpam-5427	304	20	via	via	ADP
ejpam-5427	304	21	semi	semi	ADJ
ejpam-5427	304	22	-	-	ADJ
ejpam-5427	304	23	analytical	analytical	ADJ
ejpam-5427	304	24	method	method	NOUN
ejpam-5427	304	25	,	,	PUNCT
ejpam-5427	304	26	alexandria	alexandria	PROPN
ejpam-5427	304	27	engineering	engineering	PROPN
ejpam-5427	304	28	journal	journal	PROPN
ejpam-5427	304	29	.	.	PUNCT
ejpam-5427	305	1	98	98	NUM
ejpam-5427	305	2	,	,	PUNCT
ejpam-5427	305	3	(	(	PUNCT
ejpam-5427	305	4	2024	2024	NUM
ejpam-5427	305	5	)	)	PUNCT
ejpam-5427	305	6	97	97	NUM
ejpam-5427	305	7	-	-	SYM
ejpam-5427	305	8	102	102	NUM
ejpam-5427	305	9	.	.	PUNCT
ejpam-5427	306	1	[	[	X
ejpam-5427	306	2	9	9	NUM
ejpam-5427	306	3	]	]	PUNCT
ejpam-5427	306	4	m.	m.	NOUN
ejpam-5427	306	5	mohammadian	mohammadian	NOUN
ejpam-5427	306	6	,	,	PUNCT
ejpam-5427	306	7	approximate	approximate	ADJ
ejpam-5427	306	8	analytical	analytical	ADJ
ejpam-5427	306	9	solutions	solution	NOUN
ejpam-5427	306	10	to	to	PART
ejpam-5427	306	11	nonlinear	nonlinear	VERB
ejpam-5427	306	12	damped	damp	VERB
ejpam-5427	306	13	oscillatory	oscillatory	ADJ
ejpam-5427	306	14	systems	system	NOUN
ejpam-5427	306	15	using	use	VERB
ejpam-5427	306	16	a	a	DET
ejpam-5427	306	17	modified	modify	VERB
ejpam-5427	306	18	algebraic	algebraic	ADJ
ejpam-5427	306	19	methods	method	NOUN
ejpam-5427	306	20	,	,	PUNCT
ejpam-5427	306	21	journal	journal	NOUN
ejpam-5427	306	22	of	of	ADP
ejpam-5427	306	23	applied	apply	VERB
ejpam-5427	306	24	mechanics	mechanic	NOUN
ejpam-5427	306	25	and	and	CCONJ
ejpam-5427	306	26	technical	technical	ADJ
ejpam-5427	306	27	physics	physic	NOUN
ejpam-5427	306	28	.	.	PUNCT
ejpam-5427	307	1	62	62	NUM
ejpam-5427	307	2	,	,	PUNCT
ejpam-5427	307	3	(	(	PUNCT
ejpam-5427	307	4	2021	2021	NUM
ejpam-5427	307	5	)	)	PUNCT
ejpam-5427	307	6	70	70	NUM
ejpam-5427	307	7	-	-	SYM
ejpam-5427	307	8	78	78	NUM
ejpam-5427	307	9	.	.	PUNCT
ejpam-5427	308	1	[	[	X
ejpam-5427	308	2	10	10	NUM
ejpam-5427	308	3	]	]	X
ejpam-5427	308	4	g.m	g.m	PROPN
ejpam-5427	308	5	.	.	PROPN
ejpam-5427	308	6	ismail	ismail	PROPN
ejpam-5427	308	7	,	,	PUNCT
ejpam-5427	308	8	m.a	m.a	PROPN
ejpam-5427	308	9	.	.	PROPN
ejpam-5427	308	10	hosen	hosen	PROPN
ejpam-5427	308	11	,	,	PUNCT
ejpam-5427	308	12	m.	m.	NOUN
ejpam-5427	308	13	mohammadian	mohammadian	NOUN
ejpam-5427	308	14	,	,	PUNCT
ejpam-5427	308	15	m.	m.	NOUN
ejpam-5427	308	16	bayat	bayat	PROPN
ejpam-5427	308	17	and	and	CCONJ
ejpam-5427	308	18	m.	m.	PROPN
ejpam-5427	308	19	el	el	PROPN
ejpam-5427	308	20	-	-	PUNCT
ejpam-5427	308	21	moshneb	moshneb	ADJ
ejpam-5427	308	22	,	,	PUNCT
ejpam-5427	308	23	nonlinear	nonlinear	ADJ
ejpam-5427	308	24	vibration	vibration	NOUN
ejpam-5427	308	25	of	of	ADP
ejpam-5427	308	26	electrostatically	electrostatically	ADV
ejpam-5427	308	27	actuated	actuate	VERB
ejpam-5427	308	28	microbeam	microbeam	NOUN
ejpam-5427	308	29	,	,	PUNCT
ejpam-5427	308	30	mathematics	mathematic	NOUN
ejpam-5427	308	31	.	.	PUNCT
ejpam-5427	309	1	10	10	NUM
ejpam-5427	309	2	,	,	PUNCT
ejpam-5427	309	3	(	(	PUNCT
ejpam-5427	309	4	2022	2022	NUM
ejpam-5427	309	5	)	)	PUNCT
ejpam-5427	309	6	4762	4762	NUM
ejpam-5427	309	7	.	.	PUNCT
ejpam-5427	310	1	[	[	X
ejpam-5427	310	2	11	11	NUM
ejpam-5427	310	3	]	]	PUNCT
ejpam-5427	310	4	m.	m.	NOUN
ejpam-5427	310	5	mohammadian	mohammadian	NOUN
ejpam-5427	310	6	and	and	CCONJ
ejpam-5427	310	7	m.	m.	NOUN
ejpam-5427	310	8	akbarzade	akbarzade	PROPN
ejpam-5427	310	9	,	,	PUNCT
ejpam-5427	310	10	higher	high	ADJ
ejpam-5427	310	11	-	-	PUNCT
ejpam-5427	310	12	order	order	NOUN
ejpam-5427	310	13	approximate	approximate	ADJ
ejpam-5427	310	14	analytical	analytical	ADJ
ejpam-5427	310	15	solutions	solution	NOUN
ejpam-5427	310	16	to	to	PART
ejpam-5427	310	17	nonlinear	nonlinear	VERB
ejpam-5427	310	18	oscillatory	oscillatory	ADJ
ejpam-5427	310	19	systems	system	NOUN
ejpam-5427	310	20	arising	arise	VERB
ejpam-5427	310	21	in	in	ADP
ejpam-5427	310	22	engineering	engineering	NOUN
ejpam-5427	310	23	problems	problem	NOUN
ejpam-5427	310	24	.	.	PUNCT
ejpam-5427	311	1	archive	archive	NOUN
ejpam-5427	311	2	of	of	ADP
ejpam-5427	311	3	applied	apply	VERB
ejpam-5427	311	4	mechanics	mechanic	NOUN
ejpam-5427	311	5	87	87	NUM
ejpam-5427	311	6	,	,	PUNCT
ejpam-5427	311	7	(	(	PUNCT
ejpam-5427	311	8	2017	2017	NUM
ejpam-5427	311	9	)	)	PUNCT
ejpam-5427	311	10	1317	1317	NUM
ejpam-5427	311	11	-	-	SYM
ejpam-5427	311	12	1332	1332	NUM
ejpam-5427	311	13	.	.	PUNCT
ejpam-5427	312	1	[	[	X
ejpam-5427	312	2	12	12	NUM
ejpam-5427	312	3	]	]	X
ejpam-5427	312	4	md	md	PROPN
ejpam-5427	312	5	.	.	PROPN
ejpam-5427	312	6	alal	alal	PROPN
ejpam-5427	312	7	hosen	hosen	PROPN
ejpam-5427	312	8	,	,	PUNCT
ejpam-5427	312	9	g.m	g.m	PROPN
ejpam-5427	312	10	.	.	PROPN
ejpam-5427	312	11	ismail	ismail	PROPN
ejpam-5427	312	12	,	,	PUNCT
ejpam-5427	312	13	a.	a.	PROPN
ejpam-5427	312	14	yildirim	yildirim	PROPN
ejpam-5427	312	15	and	and	CCONJ
ejpam-5427	312	16	m.a.s	m.a.s	PROPN
ejpam-5427	312	17	.	.	PROPN
ejpam-5427	312	18	kamal	kamal	PROPN
ejpam-5427	312	19	,	,	PUNCT
ejpam-5427	312	20	a	a	DET
ejpam-5427	312	21	modified	modify	VERB
ejpam-5427	312	22	energy	energy	NOUN
ejpam-5427	312	23	balance	balance	NOUN
ejpam-5427	312	24	method	method	NOUN
ejpam-5427	312	25	to	to	PART
ejpam-5427	312	26	obtain	obtain	VERB
ejpam-5427	312	27	higher	high	ADJ
ejpam-5427	312	28	-	-	PUNCT
ejpam-5427	312	29	order	order	NOUN
ejpam-5427	312	30	analytical	analytical	ADJ
ejpam-5427	312	31	approximations	approximation	NOUN
ejpam-5427	312	32	to	to	ADP
ejpam-5427	312	33	the	the	DET
ejpam-5427	312	34	oscillators	oscillator	NOUN
ejpam-5427	312	35	with	with	ADP
ejpam-5427	312	36	cubic	cubic	ADJ
ejpam-5427	312	37	and	and	CCONJ
ejpam-5427	312	38	harmonic	harmonic	ADJ
ejpam-5427	312	39	restoring	restore	VERB
ejpam-5427	312	40	force	force	NOUN
ejpam-5427	312	41	.	.	PUNCT
ejpam-5427	313	1	journal	journal	NOUN
ejpam-5427	313	2	of	of	ADP
ejpam-5427	313	3	applied	applied	ADJ
ejpam-5427	313	4	and	and	CCONJ
ejpam-5427	313	5	computational	computational	ADJ
ejpam-5427	313	6	mechanics	mechanic	NOUN
ejpam-5427	313	7	.	.	PUNCT
ejpam-5427	314	1	6	6	NUM
ejpam-5427	314	2	,	,	PUNCT
ejpam-5427	314	3	(	(	PUNCT
ejpam-5427	314	4	2020	2020	NUM
ejpam-5427	314	5	)	)	PUNCT
ejpam-5427	314	6	320	320	NUM
ejpam-5427	314	7	-	-	SYM
ejpam-5427	314	8	331	331	NUM
ejpam-5427	314	9	.	.	PUNCT
ejpam-5427	315	1	[	[	X
ejpam-5427	315	2	13	13	NUM
ejpam-5427	315	3	]	]	X
ejpam-5427	315	4	j.h	j.h	PROPN
ejpam-5427	315	5	.	.	PUNCT
ejpam-5427	316	1	he	he	PRON
ejpam-5427	316	2	,	,	PUNCT
ejpam-5427	316	3	preliminary	preliminary	ADJ
ejpam-5427	316	4	report	report	NOUN
ejpam-5427	316	5	on	on	ADP
ejpam-5427	316	6	the	the	DET
ejpam-5427	316	7	energy	energy	NOUN
ejpam-5427	316	8	balance	balance	NOUN
ejpam-5427	316	9	for	for	ADP
ejpam-5427	316	10	nonlinear	nonlinear	ADJ
ejpam-5427	316	11	oscillations	oscillation	NOUN
ejpam-5427	316	12	,	,	PUNCT
ejpam-5427	316	13	mechanics	mechanic	NOUN
ejpam-5427	316	14	research	research	NOUN
ejpam-5427	316	15	communications	communication	NOUN
ejpam-5427	316	16	.	.	PUNCT
ejpam-5427	317	1	29	29	NUM
ejpam-5427	317	2	,	,	PUNCT
ejpam-5427	317	3	(	(	PUNCT
ejpam-5427	317	4	2002	2002	NUM
ejpam-5427	317	5	)	)	PUNCT
ejpam-5427	317	6	107	107	NUM
ejpam-5427	317	7	-	-	SYM
ejpam-5427	317	8	111	111	NUM
ejpam-5427	317	9	.	.	PUNCT
ejpam-5427	318	1	[	[	X
ejpam-5427	318	2	14	14	NUM
ejpam-5427	318	3	]	]	X
ejpam-5427	318	4	m.	m.	NOUN
ejpam-5427	318	5	molla	molla	PROPN
ejpam-5427	318	6	and	and	CCONJ
ejpam-5427	318	7	n.	n.	PROPN
ejpam-5427	318	8	sharif	sharif	PROPN
ejpam-5427	318	9	,	,	PUNCT
ejpam-5427	318	10	energy	energy	NOUN
ejpam-5427	318	11	balance	balance	NOUN
ejpam-5427	318	12	method	method	NOUN
ejpam-5427	318	13	for	for	ADP
ejpam-5427	318	14	solving	solve	VERB
ejpam-5427	318	15	nonlinear	nonlinear	ADJ
ejpam-5427	318	16	oscillators	oscillator	NOUN
ejpam-5427	318	17	with	with	ADP
ejpam-5427	318	18	non	non	ADJ
ejpam-5427	318	19	-	-	ADJ
ejpam-5427	318	20	rational	rational	ADJ
ejpam-5427	318	21	restoring	restore	VERB
ejpam-5427	318	22	force	force	NOUN
ejpam-5427	318	23	,	,	PUNCT
ejpam-5427	318	24	applied	apply	VERB
ejpam-5427	318	25	mathematical	mathematical	ADJ
ejpam-5427	318	26	sciences	science	NOUN
ejpam-5427	318	27	.	.	PUNCT
ejpam-5427	319	1	17	17	NUM
ejpam-5427	319	2	,	,	PUNCT
ejpam-5427	319	3	(	(	PUNCT
ejpam-5427	319	4	2023	2023	NUM
ejpam-5427	319	5	)	)	PUNCT
ejpam-5427	319	6	689700	689700	NUM
ejpam-5427	319	7	.	.	PUNCT
ejpam-5427	320	1	[	[	X
ejpam-5427	320	2	15	15	NUM
ejpam-5427	320	3	]	]	X
ejpam-5427	320	4	y.	y.	PROPN
ejpam-5427	320	5	o.	o.	PROPN
ejpam-5427	321	1	el	el	PROPN
ejpam-5427	321	2	-	-	PROPN
ejpam-5427	321	3	dib	dib	PROPN
ejpam-5427	321	4	,	,	PUNCT
ejpam-5427	321	5	an	an	DET
ejpam-5427	321	6	efficient	efficient	ADJ
ejpam-5427	321	7	approach	approach	NOUN
ejpam-5427	321	8	to	to	ADP
ejpam-5427	321	9	solving	solve	VERB
ejpam-5427	321	10	fractional	fractional	ADJ
ejpam-5427	321	11	van	van	PROPN
ejpam-5427	321	12	der	der	PROPN
ejpam-5427	321	13	pol	pol	PROPN
ejpam-5427	321	14	-	-	PUNCT
ejpam-5427	321	15	duffing	duffe	VERB
ejpam-5427	321	16	jerk	jerk	PROPN
ejpam-5427	321	17	oscillator	oscillator	NOUN
ejpam-5427	321	18	.	.	PUNCT
ejpam-5427	322	1	communications	communication	NOUN
ejpam-5427	322	2	in	in	ADP
ejpam-5427	322	3	theoretical	theoretical	ADJ
ejpam-5427	322	4	physics	physics	NOUN
ejpam-5427	322	5	,	,	PUNCT
ejpam-5427	322	6	74	74	NUM
ejpam-5427	322	7	,	,	PUNCT
ejpam-5427	322	8	(	(	PUNCT
ejpam-5427	322	9	2022	2022	NUM
ejpam-5427	322	10	)	)	PUNCT
ejpam-5427	322	11	105006	105006	NUM
ejpam-5427	322	12	[	[	X
ejpam-5427	322	13	16	16	NUM
ejpam-5427	322	14	]	]	X
ejpam-5427	322	15	w.	w.	PROPN
ejpam-5427	322	16	alhejaili	alhejaili	PROPN
ejpam-5427	322	17	,	,	PUNCT
ejpam-5427	322	18	a.h	a.h	PROPN
ejpam-5427	322	19	.	.	PROPN
ejpam-5427	322	20	salas	salas	PROPN
ejpam-5427	322	21	,	,	PUNCT
ejpam-5427	322	22	e.	e.	PROPN
ejpam-5427	322	23	tag	tag	PROPN
ejpam-5427	322	24	-	-	PUNCT
ejpam-5427	322	25	eldin	eldin	PROPN
ejpam-5427	322	26	and	and	CCONJ
ejpam-5427	322	27	s.a	s.a	PROPN
ejpam-5427	322	28	.	.	PROPN
ejpam-5427	323	1	el	el	PROPN
ejpam-5427	323	2	-	-	PUNCT
ejpam-5427	323	3	tantawy	tantawy	ADJ
ejpam-5427	323	4	,	,	PUNCT
ejpam-5427	323	5	on	on	ADP
ejpam-5427	323	6	perturbative	perturbative	ADJ
ejpam-5427	323	7	methods	method	NOUN
ejpam-5427	323	8	for	for	ADP
ejpam-5427	323	9	analyzing	analyze	VERB
ejpam-5427	323	10	third	third	ADJ
ejpam-5427	323	11	-	-	PUNCT
ejpam-5427	323	12	order	order	NOUN
ejpam-5427	323	13	forced	force	VERB
ejpam-5427	323	14	van	van	PROPN
ejpam-5427	323	15	-	-	PUNCT
ejpam-5427	323	16	der	der	ADJ
ejpam-5427	323	17	pol	pol	PROPN
ejpam-5427	323	18	oscillators	oscillator	NOUN
ejpam-5427	323	19	,	,	PUNCT
ejpam-5427	323	20	symmetry	symmetry	NOUN
ejpam-5427	323	21	.	.	PUNCT
ejpam-5427	324	1	15	15	NUM
ejpam-5427	324	2	,	,	PUNCT
ejpam-5427	324	3	(	(	PUNCT
ejpam-5427	324	4	2023	2023	NUM
ejpam-5427	324	5	)	)	PUNCT
ejpam-5427	324	6	,	,	PUNCT
ejpam-5427	324	7	15	15	NUM
ejpam-5427	324	8	,	,	PUNCT
ejpam-5427	324	9	89	89	NUM
ejpam-5427	324	10	.	.	PUNCT
ejpam-5427	325	1	[	[	X
ejpam-5427	325	2	17	17	NUM
ejpam-5427	325	3	]	]	X
ejpam-5427	325	4	y.	y.	PROPN
ejpam-5427	325	5	o.	o.	PROPN
ejpam-5427	325	6	el	el	PROPN
ejpam-5427	325	7	-	-	PROPN
ejpam-5427	325	8	dib	dib	PROPN
ejpam-5427	325	9	,	,	PUNCT
ejpam-5427	325	10	the	the	DET
ejpam-5427	325	11	simplest	simple	ADJ
ejpam-5427	325	12	approach	approach	NOUN
ejpam-5427	325	13	to	to	ADP
ejpam-5427	325	14	solving	solve	VERB
ejpam-5427	325	15	the	the	DET
ejpam-5427	325	16	cubic	cubic	ADJ
ejpam-5427	325	17	nonlinear	nonlinear	PROPN
ejpam-5427	325	18	jerk	jerk	PROPN
ejpam-5427	325	19	oscillator	oscillator	NOUN
ejpam-5427	325	20	with	with	ADP
ejpam-5427	325	21	the	the	DET
ejpam-5427	325	22	non	non	ADJ
ejpam-5427	325	23	-	-	ADJ
ejpam-5427	325	24	perturbative	perturbative	ADJ
ejpam-5427	325	25	method	method	NOUN
ejpam-5427	325	26	,	,	PUNCT
ejpam-5427	325	27	mathematical	mathematical	ADJ
ejpam-5427	325	28	methods	method	NOUN
ejpam-5427	325	29	in	in	ADP
ejpam-5427	325	30	the	the	DET
ejpam-5427	325	31	applied	apply	VERB
ejpam-5427	325	32	sciences	science	NOUN
ejpam-5427	325	33	.	.	PUNCT
ejpam-5427	326	1	45	45	NUM
ejpam-5427	326	2	,	,	PUNCT
ejpam-5427	326	3	(	(	PUNCT
ejpam-5427	326	4	2022	2022	NUM
ejpam-5427	326	5	)	)	PUNCT
ejpam-5427	326	6	5165	5165	NUM
ejpam-5427	326	7	-	-	SYM
ejpam-5427	326	8	5183	5183	NUM
ejpam-5427	326	9	.	.	PUNCT
ejpam-5427	327	1	[	[	X
ejpam-5427	327	2	18	18	NUM
ejpam-5427	327	3	]	]	X
ejpam-5427	327	4	g.m	g.m	PROPN
ejpam-5427	327	5	.	.	PROPN
ejpam-5427	327	6	ismail	ismail	PROPN
ejpam-5427	327	7	,	,	PUNCT
ejpam-5427	327	8	g.m	g.m	PROPN
ejpam-5427	327	9	.	.	PROPN
ejpam-5427	327	10	moatimid	moatimid	PROPN
ejpam-5427	327	11	and	and	CCONJ
ejpam-5427	327	12	m.i	m.i	PROPN
ejpam-5427	327	13	.	.	PROPN
ejpam-5427	327	14	yamani	yamani	PROPN
ejpam-5427	327	15	,	,	PUNCT
ejpam-5427	327	16	periodic	periodic	ADJ
ejpam-5427	327	17	solutions	solution	NOUN
ejpam-5427	327	18	of	of	ADP
ejpam-5427	327	19	strongly	strongly	ADV
ejpam-5427	327	20	nonlinear	nonlinear	ADJ
ejpam-5427	327	21	oscillators	oscillator	NOUN
ejpam-5427	327	22	using	use	VERB
ejpam-5427	327	23	he	he	PRON
ejpam-5427	327	24	’s	’s	PART
ejpam-5427	327	25	frequency	frequency	NOUN
ejpam-5427	327	26	formulation	formulation	NOUN
ejpam-5427	327	27	,	,	PUNCT
ejpam-5427	327	28	european	european	ADJ
ejpam-5427	327	29	journal	journal	NOUN
ejpam-5427	327	30	of	of	ADP
ejpam-5427	327	31	pure	pure	ADJ
ejpam-5427	327	32	and	and	CCONJ
ejpam-5427	327	33	applied	applied	ADJ
ejpam-5427	327	34	mathematics	mathematic	NOUN
ejpam-5427	327	35	,	,	PUNCT
ejpam-5427	327	36	17	17	NUM
ejpam-5427	327	37	(	(	PUNCT
ejpam-5427	327	38	2024	2024	NUM
ejpam-5427	327	39	)	)	PUNCT
ejpam-5427	327	40	2155	2155	NUM
ejpam-5427	327	41	-	-	SYM
ejpam-5427	327	42	2172	2172	NUM
ejpam-5427	327	43	.	.	PUNCT
ejpam-5427	328	1	references	reference	NOUN
ejpam-5427	328	2	3640	3640	NUM
ejpam-5427	328	3	[	[	X
ejpam-5427	328	4	19	19	NUM
ejpam-5427	328	5	]	]	PUNCT
ejpam-5427	328	6	m.	m.	NOUN
ejpam-5427	328	7	turkyilmazoglu	turkyilmazoglu	NOUN
ejpam-5427	328	8	,	,	PUNCT
ejpam-5427	328	9	nonlinear	nonlinear	ADJ
ejpam-5427	328	10	problems	problem	NOUN
ejpam-5427	328	11	via	via	ADP
ejpam-5427	328	12	a	a	DET
ejpam-5427	328	13	convergence	convergence	NOUN
ejpam-5427	328	14	accelerated	accelerate	VERB
ejpam-5427	328	15	decomposition	decomposition	NOUN
ejpam-5427	328	16	method	method	NOUN
ejpam-5427	328	17	of	of	ADP
ejpam-5427	328	18	adomian	adomian	NOUN
ejpam-5427	328	19	.	.	PUNCT
ejpam-5427	329	1	computer	computer	NOUN
ejpam-5427	329	2	modeling	modeling	NOUN
ejpam-5427	329	3	in	in	ADP
ejpam-5427	329	4	engineering	engineering	NOUN
ejpam-5427	329	5	and	and	CCONJ
ejpam-5427	329	6	sciences	science	NOUN
ejpam-5427	329	7	.	.	PUNCT
ejpam-5427	330	1	127	127	NUM
ejpam-5427	330	2	,	,	PUNCT
ejpam-5427	330	3	(	(	PUNCT
ejpam-5427	330	4	2021	2021	NUM
ejpam-5427	330	5	)	)	PUNCT
ejpam-5427	330	6	1	1	NUM
ejpam-5427	330	7	-	-	SYM
ejpam-5427	330	8	22	22	NUM
ejpam-5427	330	9	.	.	PUNCT
ejpam-5427	331	1	[	[	X
ejpam-5427	331	2	20	20	NUM
ejpam-5427	331	3	]	]	X
ejpam-5427	331	4	g.h	g.h	PROPN
ejpam-5427	331	5	.	.	PROPN
ejpam-5427	331	6	ibraheem	ibraheem	PROPN
ejpam-5427	331	7	,	,	PUNCT
ejpam-5427	331	8	m.	m.	NOUN
ejpam-5427	331	9	turkyilmazoglu	turkyilmazoglu	NOUN
ejpam-5427	331	10	and	and	CCONJ
ejpam-5427	331	11	m.a	m.a	PROPN
ejpam-5427	331	12	.	.	PROPN
ejpam-5427	331	13	al	al	PROPN
ejpam-5427	331	14	-	-	PUNCT
ejpam-5427	331	15	jawary	jawary	ADJ
ejpam-5427	331	16	,	,	PUNCT
ejpam-5427	331	17	novel	novel	ADJ
ejpam-5427	331	18	approximate	approximate	ADJ
ejpam-5427	331	19	solution	solution	NOUN
ejpam-5427	331	20	for	for	ADP
ejpam-5427	331	21	fractional	fractional	ADJ
ejpam-5427	331	22	differential	differential	ADJ
ejpam-5427	331	23	equations	equation	NOUN
ejpam-5427	331	24	by	by	ADP
ejpam-5427	331	25	the	the	DET
ejpam-5427	331	26	optimal	optimal	ADJ
ejpam-5427	331	27	variational	variational	ADJ
ejpam-5427	331	28	iteration	iteration	NOUN
ejpam-5427	331	29	method	method	NOUN
ejpam-5427	331	30	,	,	PUNCT
ejpam-5427	331	31	journal	journal	NOUN
ejpam-5427	331	32	of	of	ADP
ejpam-5427	331	33	computational	computational	ADJ
ejpam-5427	331	34	science	science	NOUN
ejpam-5427	331	35	.	.	PUNCT
ejpam-5427	332	1	64	64	NUM
ejpam-5427	332	2	,	,	PUNCT
ejpam-5427	332	3	(	(	PUNCT
ejpam-5427	332	4	2022	2022	NUM
ejpam-5427	332	5	)	)	PUNCT
ejpam-5427	332	6	101841	101841	NUM
ejpam-5427	332	7	.	.	PUNCT
ejpam-5427	333	1	[	[	X
ejpam-5427	333	2	21	21	NUM
ejpam-5427	333	3	]	]	X
ejpam-5427	333	4	c.	c.	PROPN
ejpam-5427	333	5	wei	wei	PROPN
ejpam-5427	333	6	,	,	PUNCT
ejpam-5427	333	7	h.	h.	PROPN
ejpam-5427	333	8	jing	jing	PROPN
ejpam-5427	333	9	,	,	PUNCT
ejpam-5427	333	10	a.	a.	PROPN
ejpam-5427	333	11	zhang	zhang	PROPN
ejpam-5427	333	12	,	,	PUNCT
ejpam-5427	333	13	b.	b.	PROPN
ejpam-5427	333	14	huang	huang	PROPN
ejpam-5427	333	15	,	,	PUNCT
ejpam-5427	333	16	g.m	g.m	PROPN
ejpam-5427	333	17	.	.	PROPN
ejpam-5427	333	18	ismail	ismail	PROPN
ejpam-5427	333	19	and	and	CCONJ
ejpam-5427	333	20	j.	j.	PROPN
ejpam-5427	333	21	wang	wang	PROPN
ejpam-5427	333	22	,	,	PUNCT
ejpam-5427	333	23	the	the	DET
ejpam-5427	333	24	analysis	analysis	NOUN
ejpam-5427	333	25	of	of	ADP
ejpam-5427	333	26	bending	bending	NOUN
ejpam-5427	333	27	of	of	ADP
ejpam-5427	333	28	an	an	DET
ejpam-5427	333	29	elastic	elastic	ADJ
ejpam-5427	333	30	beam	beam	NOUN
ejpam-5427	333	31	resting	rest	VERB
ejpam-5427	333	32	on	on	ADP
ejpam-5427	333	33	a	a	DET
ejpam-5427	333	34	nonlinear	nonlinear	ADJ
ejpam-5427	333	35	winkler	winkler	NOUN
ejpam-5427	333	36	foundation	foundation	NOUN
ejpam-5427	333	37	with	with	ADP
ejpam-5427	333	38	the	the	DET
ejpam-5427	333	39	galerkin	galerkin	ADJ
ejpam-5427	333	40	method	method	NOUN
ejpam-5427	333	41	,	,	PUNCT
ejpam-5427	333	42	acta	acta	PROPN
ejpam-5427	333	43	mechanica	mechanica	PROPN
ejpam-5427	333	44	solida	solida	PROPN
ejpam-5427	333	45	sinica	sinica	PROPN
ejpam-5427	333	46	.	.	PUNCT
ejpam-5427	333	47	37	37	NUM
ejpam-5427	333	48	,	,	PUNCT
ejpam-5427	333	49	(	(	PUNCT
ejpam-5427	333	50	2024	2024	NUM
ejpam-5427	333	51	)	)	PUNCT
ejpam-5427	333	52	https://doi.org/10.1007/s10338024-00515-2	https://doi.org/10.1007/s10338024-00515-2	PROPN
ejpam-5427	333	53	[	[	X
ejpam-5427	333	54	22	22	NUM
ejpam-5427	333	55	]	]	X
ejpam-5427	333	56	n.	n.	NOUN
ejpam-5427	333	57	herişanu	herişanu	NOUN
ejpam-5427	333	58	and	and	CCONJ
ejpam-5427	333	59	v.	v.	ADP
ejpam-5427	333	60	marinca	marinca	NOUN
ejpam-5427	333	61	,	,	PUNCT
ejpam-5427	333	62	approximate	approximate	ADJ
ejpam-5427	333	63	analytical	analytical	ADJ
ejpam-5427	333	64	solutions	solution	NOUN
ejpam-5427	333	65	to	to	ADP
ejpam-5427	333	66	jerk	jerk	PROPN
ejpam-5427	333	67	equations	equation	NOUN
ejpam-5427	333	68	.	.	PUNCT
ejpam-5427	334	1	dynamical	dynamical	ADJ
ejpam-5427	334	2	systems	system	NOUN
ejpam-5427	334	3	:	:	PUNCT
ejpam-5427	334	4	theoretical	theoretical	ADJ
ejpam-5427	334	5	and	and	CCONJ
ejpam-5427	334	6	experimental	experimental	ADJ
ejpam-5427	334	7	analysis	analysis	NOUN
ejpam-5427	334	8	.	.	PUNCT
ejpam-5427	334	9	182	182	NUM
ejpam-5427	334	10	,	,	PUNCT
ejpam-5427	334	11	(	(	PUNCT
ejpam-5427	334	12	2016	2016	NUM
ejpam-5427	334	13	)	)	PUNCT
ejpam-5427	334	14	169	169	NUM
ejpam-5427	334	15	-	-	SYM
ejpam-5427	334	16	176	176	NUM
ejpam-5427	334	17	.	.	PUNCT
ejpam-5427	335	1	[	[	X
ejpam-5427	335	2	23	23	NUM
ejpam-5427	335	3	]	]	X
ejpam-5427	335	4	e.	e.	PROPN
ejpam-5427	335	5	momoniat	momoniat	PROPN
ejpam-5427	335	6	and	and	CCONJ
ejpam-5427	335	7	f.	f.	PROPN
ejpam-5427	335	8	mahomed	mahomed	PROPN
ejpam-5427	335	9	,	,	PUNCT
ejpam-5427	335	10	symmetry	symmetry	NOUN
ejpam-5427	335	11	reduction	reduction	NOUN
ejpam-5427	335	12	and	and	CCONJ
ejpam-5427	335	13	numerical	numerical	ADJ
ejpam-5427	335	14	solution	solution	NOUN
ejpam-5427	335	15	of	of	ADP
ejpam-5427	335	16	a	a	DET
ejpam-5427	335	17	third	third	ADJ
ejpam-5427	335	18	-	-	PUNCT
ejpam-5427	335	19	order	order	NOUN
ejpam-5427	335	20	ode	ode	NOUN
ejpam-5427	335	21	from	from	ADP
ejpam-5427	335	22	thin	thin	ADJ
ejpam-5427	335	23	film	film	NOUN
ejpam-5427	335	24	flow	flow	NOUN
ejpam-5427	335	25	.	.	PUNCT
ejpam-5427	336	1	mathematical	mathematical	ADJ
ejpam-5427	336	2	and	and	CCONJ
ejpam-5427	336	3	computational	computational	ADJ
ejpam-5427	336	4	applications	application	NOUN
ejpam-5427	336	5	.	.	PUNCT
ejpam-5427	337	1	15	15	NUM
ejpam-5427	337	2	,	,	PUNCT
ejpam-5427	337	3	(	(	PUNCT
ejpam-5427	337	4	2010	2010	NUM
ejpam-5427	337	5	)	)	PUNCT
ejpam-5427	338	1	709	709	NUM
ejpam-5427	338	2	-	-	SYM
ejpam-5427	338	3	719	719	NUM
ejpam-5427	338	4	.	.	PUNCT
ejpam-5427	339	1	[	[	X
ejpam-5427	339	2	24	24	NUM
ejpam-5427	339	3	]	]	X
ejpam-5427	339	4	b.s	b.s	PROPN
ejpam-5427	339	5	.	.	PUNCT
ejpam-5427	339	6	h.	h.	PROPN
ejpam-5427	339	7	kashkari	kashkari	PROPN
ejpam-5427	339	8	and	and	CCONJ
ejpam-5427	339	9	s.	s.	PROPN
ejpam-5427	339	10	alqarni	alqarni	PROPN
ejpam-5427	339	11	,	,	PUNCT
ejpam-5427	339	12	two	two	NUM
ejpam-5427	339	13	-	-	PUNCT
ejpam-5427	339	14	step	step	NOUN
ejpam-5427	339	15	hybrid	hybrid	ADJ
ejpam-5427	339	16	block	block	NOUN
ejpam-5427	339	17	method	method	NOUN
ejpam-5427	339	18	for	for	ADP
ejpam-5427	339	19	solving	solve	VERB
ejpam-5427	339	20	nonlinear	nonlinear	ADJ
ejpam-5427	339	21	jerk	jerk	PROPN
ejpam-5427	339	22	equations	equation	NOUN
ejpam-5427	339	23	.	.	PUNCT
ejpam-5427	340	1	journal	journal	PROPN
ejpam-5427	340	2	of	of	ADP
ejpam-5427	340	3	applied	apply	VERB
ejpam-5427	340	4	mathematics	mathematic	NOUN
ejpam-5427	340	5	and	and	CCONJ
ejpam-5427	340	6	physics	physics	NOUN
ejpam-5427	340	7	,	,	PUNCT
ejpam-5427	340	8	7	7	NUM
ejpam-5427	340	9	(	(	PUNCT
ejpam-5427	340	10	2019	2019	NUM
ejpam-5427	340	11	)	)	PUNCT
ejpam-5427	340	12	1893	1893	NUM
ejpam-5427	340	13	-	-	SYM
ejpam-5427	340	14	1910	1910	NUM
ejpam-5427	340	15	.	.	PUNCT
ejpam-5427	341	1	[	[	X
ejpam-5427	341	2	25	25	NUM
ejpam-5427	341	3	]	]	X
ejpam-5427	341	4	h.p.w	h.p.w	NOUN
ejpam-5427	341	5	.	.	PUNCT
ejpam-5427	342	1	gottlieb	gottlieb	PROPN
ejpam-5427	342	2	,	,	PUNCT
ejpam-5427	342	3	harmonic	harmonic	ADJ
ejpam-5427	342	4	balance	balance	NOUN
ejpam-5427	342	5	approach	approach	NOUN
ejpam-5427	342	6	to	to	ADP
ejpam-5427	342	7	periodic	periodic	ADJ
ejpam-5427	342	8	solution	solution	NOUN
ejpam-5427	342	9	of	of	ADP
ejpam-5427	342	10	nonlinear	nonlinear	ADJ
ejpam-5427	342	11	jerk	jerk	PROPN
ejpam-5427	342	12	equation	equation	NOUN
ejpam-5427	342	13	,	,	PUNCT
ejpam-5427	342	14	journal	journal	NOUN
ejpam-5427	342	15	of	of	ADP
ejpam-5427	342	16	sound	sound	NOUN
ejpam-5427	342	17	and	and	CCONJ
ejpam-5427	342	18	vibration	vibration	NOUN
ejpam-5427	342	19	.	.	PUNCT
ejpam-5427	343	1	271	271	NUM
ejpam-5427	343	2	,	,	PUNCT
ejpam-5427	343	3	(	(	PUNCT
ejpam-5427	343	4	2004	2004	NUM
ejpam-5427	343	5	)	)	PUNCT
ejpam-5427	343	6	671	671	NUM
ejpam-5427	343	7	-	-	SYM
ejpam-5427	343	8	83	83	NUM
ejpam-5427	343	9	.	.	PUNCT
ejpam-5427	344	1	[	[	X
ejpam-5427	344	2	26	26	NUM
ejpam-5427	344	3	]	]	X
ejpam-5427	344	4	b.s	b.s	PROPN
ejpam-5427	344	5	.	.	PROPN
ejpam-5427	344	6	wu	wu	PROPN
ejpam-5427	344	7	,	,	PUNCT
ejpam-5427	344	8	c.w	c.w	PROPN
ejpam-5427	344	9	.	.	PROPN
ejpam-5427	344	10	lim	lim	PROPN
ejpam-5427	344	11	and	and	CCONJ
ejpam-5427	344	12	w.p	w.p	PROPN
ejpam-5427	344	13	.	.	PROPN
ejpam-5427	344	14	sun	sun	PROPN
ejpam-5427	344	15	,	,	PUNCT
ejpam-5427	344	16	improved	improve	VERB
ejpam-5427	344	17	harmonic	harmonic	ADJ
ejpam-5427	344	18	balance	balance	NOUN
ejpam-5427	344	19	approach	approach	NOUN
ejpam-5427	344	20	to	to	ADP
ejpam-5427	344	21	periodic	periodic	ADJ
ejpam-5427	344	22	solutions	solution	NOUN
ejpam-5427	344	23	of	of	ADP
ejpam-5427	344	24	non	non	ADJ
ejpam-5427	344	25	-	-	ADJ
ejpam-5427	344	26	linear	linear	ADJ
ejpam-5427	344	27	jerk	jerk	NOUN
ejpam-5427	344	28	equations	equation	NOUN
ejpam-5427	344	29	,	,	PUNCT
ejpam-5427	344	30	physics	physics	NOUN
ejpam-5427	344	31	letters	letter	NOUN
ejpam-5427	344	32	a.	a.	PROPN
ejpam-5427	344	33	354	354	NUM
ejpam-5427	344	34	,	,	PUNCT
ejpam-5427	344	35	(	(	PUNCT
ejpam-5427	344	36	2006	2006	NUM
ejpam-5427	344	37	)	)	PUNCT
ejpam-5427	344	38	95	95	NUM
ejpam-5427	344	39	-	-	SYM
ejpam-5427	344	40	100	100	NUM
ejpam-5427	344	41	.	.	PUNCT
ejpam-5427	345	1	[	[	X
ejpam-5427	345	2	27	27	NUM
ejpam-5427	345	3	]	]	X
ejpam-5427	345	4	x.y	x.y	PROPN
ejpam-5427	345	5	.	.	PROPN
ejpam-5427	345	6	ma	ma	PROPN
ejpam-5427	345	7	,	,	PUNCT
ejpam-5427	345	8	l.p	l.p	PROPN
ejpam-5427	345	9	.	.	PROPN
ejpam-5427	345	10	wei	wei	PROPN
ejpam-5427	345	11	and	and	CCONJ
ejpam-5427	345	12	z.j	z.j	PROPN
ejpam-5427	345	13	.	.	PROPN
ejpam-5427	345	14	guo	guo	PROPN
ejpam-5427	345	15	,	,	PUNCT
ejpam-5427	345	16	he	he	PRON
ejpam-5427	345	17	’s	’	VERB
ejpam-5427	345	18	homotopy	homotopy	PROPN
ejpam-5427	345	19	perturbation	perturbation	NOUN
ejpam-5427	345	20	method	method	NOUN
ejpam-5427	345	21	to	to	ADP
ejpam-5427	345	22	periodic	periodic	ADJ
ejpam-5427	345	23	solutions	solution	NOUN
ejpam-5427	345	24	of	of	ADP
ejpam-5427	345	25	nonlinear	nonlinear	ADJ
ejpam-5427	345	26	jerk	jerk	PROPN
ejpam-5427	345	27	equations	equation	NOUN
ejpam-5427	345	28	,	,	PUNCT
ejpam-5427	345	29	journal	journal	NOUN
ejpam-5427	345	30	of	of	ADP
ejpam-5427	345	31	sound	sound	NOUN
ejpam-5427	345	32	and	and	CCONJ
ejpam-5427	345	33	vibration	vibration	NOUN
ejpam-5427	345	34	.	.	PUNCT
ejpam-5427	346	1	314	314	NUM
ejpam-5427	346	2	,	,	PUNCT
ejpam-5427	346	3	(	(	PUNCT
ejpam-5427	346	4	2008	2008	NUM
ejpam-5427	346	5	)	)	PUNCT
ejpam-5427	346	6	217	217	NUM
ejpam-5427	346	7	-	-	SYM
ejpam-5427	346	8	27	27	NUM
ejpam-5427	346	9	.	.	PUNCT
ejpam-5427	347	1	[	[	X
ejpam-5427	347	2	28	28	NUM
ejpam-5427	347	3	]	]	X
ejpam-5427	347	4	h.	h.	PROPN
ejpam-5427	347	5	hu	hu	PROPN
ejpam-5427	347	6	,	,	PUNCT
ejpam-5427	347	7	perturbation	perturbation	NOUN
ejpam-5427	347	8	method	method	NOUN
ejpam-5427	347	9	for	for	ADP
ejpam-5427	347	10	periodic	periodic	ADJ
ejpam-5427	347	11	solutions	solution	NOUN
ejpam-5427	347	12	of	of	ADP
ejpam-5427	347	13	nonlinear	nonlinear	ADJ
ejpam-5427	347	14	jerk	jerk	PROPN
ejpam-5427	347	15	equations	equation	NOUN
ejpam-5427	347	16	,	,	PUNCT
ejpam-5427	347	17	physics	physics	NOUN
ejpam-5427	347	18	letters	letter	NOUN
ejpam-5427	347	19	a.	a.	PROPN
ejpam-5427	347	20	372	372	NUM
ejpam-5427	347	21	,	,	PUNCT
ejpam-5427	347	22	(	(	PUNCT
ejpam-5427	347	23	2008	2008	NUM
ejpam-5427	347	24	)	)	PUNCT
ejpam-5427	347	25	4205	4205	NUM
ejpam-5427	347	26	-	-	SYM
ejpam-5427	347	27	4209	4209	NUM
ejpam-5427	347	28	.	.	PUNCT
ejpam-5427	348	1	[	[	X
ejpam-5427	348	2	29	29	NUM
ejpam-5427	348	3	]	]	X
ejpam-5427	348	4	h.hu	h.hu	PROPN
ejpam-5427	348	5	,	,	PUNCT
ejpam-5427	348	6	m.y	m.y	PROPN
ejpam-5427	348	7	.	.	PROPN
ejpam-5427	348	8	zheng	zheng	PROPN
ejpam-5427	348	9	,	,	PUNCT
ejpam-5427	348	10	and	and	CCONJ
ejpam-5427	348	11	yj	yj	PROPN
ejpam-5427	348	12	.	.	PROPN
ejpam-5427	348	13	guo	guo	PROPN
ejpam-5427	348	14	,	,	PUNCT
ejpam-5427	348	15	iteration	iteration	NOUN
ejpam-5427	348	16	calculations	calculation	NOUN
ejpam-5427	348	17	of	of	ADP
ejpam-5427	348	18	periodic	periodic	ADJ
ejpam-5427	348	19	solutions	solution	NOUN
ejpam-5427	348	20	to	to	ADP
ejpam-5427	348	21	nonlinear	nonlinear	ADJ
ejpam-5427	348	22	jerk	jerk	PROPN
ejpam-5427	348	23	equations	equation	NOUN
ejpam-5427	348	24	,	,	PUNCT
ejpam-5427	348	25	acta	acta	PROPN
ejpam-5427	348	26	mechanica	mechanica	PROPN
ejpam-5427	348	27	.	.	PUNCT
ejpam-5427	349	1	209	209	NUM
ejpam-5427	349	2	,	,	PUNCT
ejpam-5427	349	3	(	(	PUNCT
ejpam-5427	349	4	2010	2010	NUM
ejpam-5427	349	5	)	)	PUNCT
ejpam-5427	349	6	269	269	NUM
ejpam-5427	349	7	-	-	SYM
ejpam-5427	349	8	274	274	NUM
ejpam-5427	349	9	.	.	PUNCT
ejpam-5427	350	1	[	[	X
ejpam-5427	350	2	30	30	NUM
ejpam-5427	350	3	]	]	X
ejpam-5427	350	4	j.i	j.i	PROPN
ejpam-5427	350	5	.	.	PROPN
ejpam-5427	350	6	ramos	ramos	PROPN
ejpam-5427	350	7	,	,	PUNCT
ejpam-5427	350	8	approximate	approximate	ADJ
ejpam-5427	350	9	methods	method	NOUN
ejpam-5427	350	10	based	base	VERB
ejpam-5427	350	11	on	on	ADP
ejpam-5427	350	12	order	order	NOUN
ejpam-5427	350	13	reduction	reduction	NOUN
ejpam-5427	350	14	for	for	ADP
ejpam-5427	350	15	the	the	DET
ejpam-5427	350	16	periodic	periodic	ADJ
ejpam-5427	350	17	solutions	solution	NOUN
ejpam-5427	350	18	of	of	ADP
ejpam-5427	350	19	nonlinear	nonlinear	ADJ
ejpam-5427	350	20	third	third	ADJ
ejpam-5427	350	21	-	-	PUNCT
ejpam-5427	350	22	order	order	NOUN
ejpam-5427	350	23	ordinary	ordinary	ADJ
ejpam-5427	350	24	differential	differential	ADJ
ejpam-5427	350	25	equations	equation	NOUN
ejpam-5427	350	26	,	,	PUNCT
ejpam-5427	350	27	applied	apply	VERB
ejpam-5427	350	28	mathematics	mathematic	NOUN
ejpam-5427	350	29	and	and	CCONJ
ejpam-5427	350	30	computation	computation	NOUN
ejpam-5427	350	31	.	.	PUNCT
ejpam-5427	351	1	215	215	NUM
ejpam-5427	351	2	,	,	PUNCT
ejpam-5427	351	3	(	(	PUNCT
ejpam-5427	351	4	2010	2010	NUM
ejpam-5427	351	5	)	)	PUNCT
ejpam-5427	351	6	4304	4304	NUM
ejpam-5427	351	7	-	-	SYM
ejpam-5427	351	8	4319	4319	NUM
ejpam-5427	351	9	.	.	PUNCT
ejpam-5427	352	1	[	[	X
ejpam-5427	352	2	31	31	NUM
ejpam-5427	352	3	]	]	X
ejpam-5427	352	4	a.y.t	a.y.t	PROPN
ejpam-5427	352	5	leung	leung	PROPN
ejpam-5427	352	6	amd	amd	PROPN
ejpam-5427	352	7	z.j	z.j	PROPN
ejpam-5427	352	8	guo	guo	PROPN
ejpam-5427	352	9	,	,	PUNCT
ejpam-5427	352	10	residue	residue	NOUN
ejpam-5427	352	11	harmonic	harmonic	ADJ
ejpam-5427	352	12	balance	balance	NOUN
ejpam-5427	352	13	approach	approach	NOUN
ejpam-5427	352	14	to	to	PART
ejpam-5427	352	15	limit	limit	VERB
ejpam-5427	352	16	cycles	cycle	NOUN
ejpam-5427	352	17	of	of	ADP
ejpam-5427	352	18	nonlinear	nonlinear	ADJ
ejpam-5427	352	19	jerk	jerk	PROPN
ejpam-5427	352	20	equations	equation	NOUN
ejpam-5427	352	21	,	,	PUNCT
ejpam-5427	352	22	international	international	ADJ
ejpam-5427	352	23	journal	journal	PROPN
ejpam-5427	352	24	non	non	ADJ
ejpam-5427	352	25	-	-	ADJ
ejpam-5427	352	26	linear	linear	ADJ
ejpam-5427	352	27	mechanics	mechanic	NOUN
ejpam-5427	352	28	.	.	PUNCT
ejpam-5427	353	1	46	46	NUM
ejpam-5427	353	2	,	,	PUNCT
ejpam-5427	353	3	(	(	PUNCT
ejpam-5427	353	4	2011	2011	NUM
ejpam-5427	353	5	)	)	PUNCT
ejpam-5427	353	6	898906	898906	NUM
ejpam-5427	353	7	.	.	PUNCT
ejpam-5427	354	1	references	reference	NOUN
ejpam-5427	354	2	3641	3641	NUM
ejpam-5427	354	3	[	[	X
ejpam-5427	354	4	32	32	NUM
ejpam-5427	354	5	]	]	PUNCT
ejpam-5427	354	6	m.m.f	m.m.f	ADJ
ejpam-5427	354	7	karahan	karahan	PROPN
ejpam-5427	354	8	,	,	PUNCT
ejpam-5427	354	9	approximate	approximate	ADJ
ejpam-5427	354	10	solutions	solution	NOUN
ejpam-5427	354	11	for	for	ADP
ejpam-5427	354	12	the	the	DET
ejpam-5427	354	13	nonlinear	nonlinear	ADJ
ejpam-5427	354	14	third	third	ADJ
ejpam-5427	354	15	-	-	PUNCT
ejpam-5427	354	16	order	order	NOUN
ejpam-5427	354	17	ordinary	ordinary	ADJ
ejpam-5427	354	18	differential	differential	ADJ
ejpam-5427	354	19	equations	equation	NOUN
ejpam-5427	354	20	,	,	PUNCT
ejpam-5427	354	21	zeitschrift	zeitschrift	NOUN
ejpam-5427	354	22	für	für	NOUN
ejpam-5427	354	23	naturforschung	naturforschung	PROPN
ejpam-5427	354	24	a.	a.	NOUN
ejpam-5427	354	25	(	(	PUNCT
ejpam-5427	354	26	2017	2017	NUM
ejpam-5427	354	27	)	)	PUNCT
ejpam-5427	354	28	.	.	PUNCT
ejpam-5427	355	1	doi	doi	NOUN
ejpam-5427	355	2	:	:	PUNCT
ejpam-5427	355	3	10.1515	10.1515	NUM
ejpam-5427	355	4	/	/	SYM
ejpam-5427	355	5	zna-20160502	zna-20160502	NOUN
ejpam-5427	355	6	.	.	PUNCT
ejpam-5427	356	1	[	[	X
ejpam-5427	356	2	33	33	NUM
ejpam-5427	356	3	]	]	PUNCT
ejpam-5427	356	4	a.	a.	NOUN
ejpam-5427	356	5	mirzabeigy	mirzabeigy	NOUN
ejpam-5427	356	6	and	and	CCONJ
ejpam-5427	356	7	a.	a.	PROPN
ejpam-5427	356	8	yildirim	yildirim	PROPN
ejpam-5427	356	9	,	,	PUNCT
ejpam-5427	356	10	a.approximate	a.approximate	ADJ
ejpam-5427	356	11	periodic	periodic	ADJ
ejpam-5427	356	12	solution	solution	NOUN
ejpam-5427	356	13	for	for	ADP
ejpam-5427	356	14	nonlinear	nonlinear	ADJ
ejpam-5427	356	15	jerk	jerk	NOUN
ejpam-5427	356	16	equation	equation	NOUN
ejpam-5427	356	17	as	as	ADP
ejpam-5427	356	18	a	a	DET
ejpam-5427	356	19	third	third	ADJ
ejpam-5427	356	20	-	-	PUNCT
ejpam-5427	356	21	order	order	NOUN
ejpam-5427	356	22	nonlinear	nonlinear	ADJ
ejpam-5427	356	23	equation	equation	NOUN
ejpam-5427	356	24	via	via	ADP
ejpam-5427	356	25	modified	modify	VERB
ejpam-5427	356	26	differential	differential	ADJ
ejpam-5427	356	27	transform	transform	NOUN
ejpam-5427	356	28	method	method	NOUN
ejpam-5427	356	29	,	,	PUNCT
ejpam-5427	356	30	engineering	engineering	NOUN
ejpam-5427	356	31	computations	computation	NOUN
ejpam-5427	356	32	,	,	PUNCT
ejpam-5427	356	33	31	31	NUM
ejpam-5427	356	34	,	,	PUNCT
ejpam-5427	356	35	(	(	PUNCT
ejpam-5427	356	36	2014	2014	NUM
ejpam-5427	356	37	)	)	PUNCT
ejpam-5427	356	38	622	622	NUM
ejpam-5427	356	39	-	-	SYM
ejpam-5427	356	40	633	633	NUM
ejpam-5427	356	41	.	.	PUNCT
ejpam-5427	357	1	[	[	X
ejpam-5427	357	2	34	34	NUM
ejpam-5427	357	3	]	]	X
ejpam-5427	357	4	m.s	m.s	PROPN
ejpam-5427	357	5	.	.	PROPN
ejpam-5427	357	6	rahman	rahman	PROPN
ejpam-5427	357	7	and	and	CCONJ
ejpam-5427	357	8	a.s.m.z	a.s.m.z	PROPN
ejpam-5427	357	9	hasan	hasan	PROPN
ejpam-5427	357	10	,	,	PUNCT
ejpam-5427	357	11	modified	modify	VERB
ejpam-5427	357	12	harmonic	harmonic	ADJ
ejpam-5427	357	13	balance	balance	NOUN
ejpam-5427	357	14	method	method	NOUN
ejpam-5427	357	15	for	for	ADP
ejpam-5427	357	16	the	the	DET
ejpam-5427	357	17	solution	solution	NOUN
ejpam-5427	357	18	of	of	ADP
ejpam-5427	357	19	nonlinear	nonlinear	ADJ
ejpam-5427	357	20	jerk	jerk	PROPN
ejpam-5427	357	21	equations	equation	NOUN
ejpam-5427	357	22	,	,	PUNCT
ejpam-5427	357	23	results	result	NOUN
ejpam-5427	357	24	in	in	ADP
ejpam-5427	357	25	physics	physics	NOUN
ejpam-5427	357	26	.	.	PUNCT
ejpam-5427	358	1	8	8	NUM
ejpam-5427	358	2	,	,	PUNCT
ejpam-5427	358	3	(	(	PUNCT
ejpam-5427	358	4	2018	2018	NUM
ejpam-5427	358	5	)	)	PUNCT
ejpam-5427	358	6	893	893	NUM
ejpam-5427	358	7	-	-	SYM
ejpam-5427	358	8	897	897	NUM
ejpam-5427	358	9	.	.	PUNCT
ejpam-5427	359	1	[	[	X
ejpam-5427	359	2	35	35	NUM
ejpam-5427	359	3	]	]	X
ejpam-5427	359	4	b.	b.	PROPN
ejpam-5427	359	5	raftari	raftari	PROPN
ejpam-5427	359	6	,	,	PUNCT
ejpam-5427	359	7	he	he	PRON
ejpam-5427	359	8	’s	’	VERB
ejpam-5427	359	9	variational	variational	ADJ
ejpam-5427	359	10	iteration	iteration	NOUN
ejpam-5427	359	11	method	method	NOUN
ejpam-5427	359	12	for	for	ADP
ejpam-5427	359	13	nonlinear	nonlinear	ADJ
ejpam-5427	359	14	jerk	jerk	PROPN
ejpam-5427	359	15	equations	equation	NOUN
ejpam-5427	359	16	:	:	PUNCT
ejpam-5427	359	17	simple	simple	ADJ
ejpam-5427	359	18	but	but	CCONJ
ejpam-5427	359	19	effective	effective	ADJ
ejpam-5427	359	20	behrouz	behrouz	NOUN
ejpam-5427	359	21	raftari	raftari	NOUN
ejpam-5427	359	22	,	,	PUNCT
ejpam-5427	359	23	shock	shock	NOUN
ejpam-5427	359	24	and	and	CCONJ
ejpam-5427	359	25	vibration	vibration	NOUN
ejpam-5427	359	26	20	20	NUM
ejpam-5427	359	27	,	,	PUNCT
ejpam-5427	359	28	(	(	PUNCT
ejpam-5427	359	29	2013	2013	NUM
ejpam-5427	359	30	)	)	PUNCT
ejpam-5427	359	31	351	351	NUM
ejpam-5427	359	32	-	-	SYM
ejpam-5427	359	33	356	356	NUM
ejpam-5427	359	34	[	[	X
ejpam-5427	359	35	36	36	NUM
ejpam-5427	359	36	]	]	PUNCT
ejpam-5427	359	37	v.	v.	CCONJ
ejpam-5427	359	38	marinca	marinca	NOUN
ejpam-5427	359	39	and	and	CCONJ
ejpam-5427	359	40	n.	n.	PROPN
ejpam-5427	359	41	herisanu	herisanu	PROPN
ejpam-5427	359	42	,	,	PUNCT
ejpam-5427	359	43	nonlinear	nonlinear	ADJ
ejpam-5427	359	44	dynamical	dynamical	ADJ
ejpam-5427	359	45	systems	system	NOUN
ejpam-5427	359	46	in	in	ADP
ejpam-5427	359	47	engineering	engineering	NOUN
ejpam-5427	359	48	.	.	PUNCT
ejpam-5427	360	1	some	some	DET
ejpam-5427	360	2	approximate	approximate	ADJ
ejpam-5427	360	3	approaches	approach	NOUN
ejpam-5427	360	4	,	,	PUNCT
ejpam-5427	360	5	springer	springer	NOUN
ejpam-5427	360	6	verlag	verlag	PROPN
ejpam-5427	360	7	,	,	PUNCT
ejpam-5427	360	8	berlin	berlin	PROPN
ejpam-5427	360	9	.	.	PUNCT
ejpam-5427	360	10	(	(	PUNCT
ejpam-5427	360	11	2011	2011	NUM
ejpam-5427	360	12	)	)	PUNCT
ejpam-5427	360	13	.	.	PUNCT
ejpam-5427	361	1	[	[	X
ejpam-5427	361	2	37	37	NUM
ejpam-5427	361	3	]	]	X
ejpam-5427	361	4	g.m	g.m	PROPN
ejpam-5427	361	5	.	.	PUNCT
ejpam-5427	361	6	ismail	ismail	PROPN
ejpam-5427	361	7	and	and	CCONJ
ejpam-5427	361	8	h.abu	h.abu	PROPN
ejpam-5427	361	9	-	-	PUNCT
ejpam-5427	361	10	zinadah	zinadah	ADJ
ejpam-5427	361	11	,	,	PUNCT
ejpam-5427	361	12	analytic	analytic	ADJ
ejpam-5427	361	13	approximations	approximation	NOUN
ejpam-5427	361	14	to	to	ADP
ejpam-5427	361	15	non	non	ADJ
ejpam-5427	361	16	-	-	ADJ
ejpam-5427	361	17	linear	linear	ADJ
ejpam-5427	361	18	third	third	ADJ
ejpam-5427	361	19	order	order	NOUN
ejpam-5427	361	20	jerk	jerk	NOUN
ejpam-5427	361	21	equations	equation	NOUN
ejpam-5427	361	22	via	via	ADP
ejpam-5427	361	23	modified	modify	VERB
ejpam-5427	361	24	global	global	ADJ
ejpam-5427	361	25	error	error	NOUN
ejpam-5427	361	26	minimization	minimization	NOUN
ejpam-5427	361	27	method	method	NOUN
ejpam-5427	361	28	,	,	PUNCT
ejpam-5427	361	29	journal	journal	NOUN
ejpam-5427	361	30	of	of	ADP
ejpam-5427	361	31	king	king	PROPN
ejpam-5427	361	32	saud	saud	PROPN
ejpam-5427	361	33	university	university	PROPN
ejpam-5427	361	34	-	-	PUNCT
ejpam-5427	361	35	science	science	NOUN
ejpam-5427	361	36	.	.	PUNCT
ejpam-5427	362	1	33	33	NUM
ejpam-5427	362	2	,	,	PUNCT
ejpam-5427	362	3	(	(	PUNCT
ejpam-5427	362	4	2021	2021	NUM
ejpam-5427	362	5	)	)	PUNCT
ejpam-5427	362	6	101219	101219	NUM
ejpam-5427	362	7	.	.	PUNCT
ejpam-5427	363	1	[	[	X
ejpam-5427	363	2	38	38	NUM
ejpam-5427	363	3	]	]	X
ejpam-5427	363	4	r.e	r.e	PROPN
ejpam-5427	363	5	.	.	PROPN
ejpam-5427	363	6	mickens	mickens	PROPN
ejpam-5427	363	7	,	,	PUNCT
ejpam-5427	363	8	iteration	iteration	NOUN
ejpam-5427	363	9	procedure	procedure	NOUN
ejpam-5427	363	10	for	for	ADP
ejpam-5427	363	11	determining	determine	VERB
ejpam-5427	363	12	approximate	approximate	ADJ
ejpam-5427	363	13	solutions	solution	NOUN
ejpam-5427	363	14	to	to	ADP
ejpam-5427	363	15	nonlinear	nonlinear	ADJ
ejpam-5427	363	16	oscillator	oscillator	NOUN
ejpam-5427	363	17	equation	equation	NOUN
ejpam-5427	363	18	,	,	PUNCT
ejpam-5427	363	19	journal	journal	NOUN
ejpam-5427	363	20	of	of	ADP
ejpam-5427	363	21	sound	sound	NOUN
ejpam-5427	363	22	and	and	CCONJ
ejpam-5427	363	23	vibration	vibration	NOUN
ejpam-5427	363	24	.	.	PUNCT
ejpam-5427	364	1	116	116	NUM
ejpam-5427	364	2	,	,	PUNCT
ejpam-5427	364	3	(	(	PUNCT
ejpam-5427	364	4	1987	1987	NUM
ejpam-5427	364	5	)	)	PUNCT
ejpam-5427	364	6	185	185	NUM
ejpam-5427	364	7	-	-	SYM
ejpam-5427	364	8	188	188	NUM
ejpam-5427	364	9	.	.	PUNCT
ejpam-5427	365	1	[	[	X
ejpam-5427	365	2	39	39	NUM
ejpam-5427	365	3	]	]	PUNCT
ejpam-5427	365	4	p.	p.	PROPN
ejpam-5427	365	5	gautam	gautam	PROPN
ejpam-5427	365	6	,	,	PUNCT
ejpam-5427	365	7	a.	a.	NOUN
ejpam-5427	365	8	shukla	shukla	NOUN
ejpam-5427	365	9	,	,	PUNCT
ejpam-5427	365	10	m.	m.	NOUN
ejpam-5427	365	11	johnson	johnson	PROPN
ejpam-5427	365	12	and	and	CCONJ
ejpam-5427	365	13	v.	v.	PROPN
ejpam-5427	365	14	vijayakumar	vijayakumar	PROPN
ejpam-5427	365	15	,	,	PUNCT
ejpam-5427	365	16	approximate	approximate	ADJ
ejpam-5427	365	17	controllability	controllability	NOUN
ejpam-5427	365	18	of	of	ADP
ejpam-5427	365	19	third	third	ADJ
ejpam-5427	365	20	order	order	NOUN
ejpam-5427	365	21	dispersion	dispersion	NOUN
ejpam-5427	365	22	systems	system	NOUN
ejpam-5427	365	23	,	,	PUNCT
ejpam-5427	365	24	bulletin	bulletin	PROPN
ejpam-5427	365	25	des	des	PROPN
ejpam-5427	365	26	sciences	sciences	PROPN
ejpam-5427	365	27	mathématiques	mathématiques	PROPN
ejpam-5427	365	28	.	.	PROPN
ejpam-5427	365	29	191	191	NUM
ejpam-5427	365	30	,	,	PUNCT
ejpam-5427	365	31	(	(	PUNCT
ejpam-5427	365	32	2024	2024	NUM
ejpam-5427	365	33	)	)	PUNCT
ejpam-5427	365	34	103394	103394	NUM
ejpam-5427	365	35	.	.	PUNCT
ejpam-5427	366	1	[	[	X
ejpam-5427	366	2	40	40	NUM
ejpam-5427	366	3	]	]	PUNCT
ejpam-5427	366	4	c.	c.	PROPN
ejpam-5427	366	5	dineshkumar	dineshkumar	PROPN
ejpam-5427	366	6	,	,	PUNCT
ejpam-5427	366	7	r.	r.	PROPN
ejpam-5427	366	8	udhayakumar	udhayakumar	PROPN
ejpam-5427	366	9	,	,	PUNCT
ejpam-5427	366	10	v.	v.	PROPN
ejpam-5427	366	11	vijayakumar	vijayakumar	PROPN
ejpam-5427	366	12	,	,	PUNCT
ejpam-5427	366	13	a.	a.	NOUN
ejpam-5427	366	14	shukla	shukla	NOUN
ejpam-5427	366	15	and	and	CCONJ
ejpam-5427	366	16	k.s	k.s	PROPN
ejpam-5427	366	17	.	.	PROPN
ejpam-5427	366	18	nisar	nisar	PROPN
ejpam-5427	366	19	,	,	PUNCT
ejpam-5427	366	20	new	new	ADJ
ejpam-5427	366	21	discussion	discussion	NOUN
ejpam-5427	366	22	regarding	regard	VERB
ejpam-5427	366	23	approximate	approximate	ADJ
ejpam-5427	366	24	controllability	controllability	NOUN
ejpam-5427	366	25	for	for	ADP
ejpam-5427	366	26	sobolev	sobolev	NOUN
ejpam-5427	366	27	-	-	PUNCT
ejpam-5427	366	28	type	type	NOUN
ejpam-5427	366	29	fractional	fractional	ADJ
ejpam-5427	366	30	stochastic	stochastic	ADJ
ejpam-5427	366	31	hemivariational	hemivariational	ADJ
ejpam-5427	366	32	inequalities	inequality	NOUN
ejpam-5427	366	33	of	of	ADP
ejpam-5427	366	34	order	order	NOUN
ejpam-5427	366	35	r	r	NOUN
ejpam-5427	366	36	∈	∈	PROPN
ejpam-5427	366	37	(	(	PUNCT
ejpam-5427	366	38	1	1	NUM
ejpam-5427	366	39	,	,	PUNCT
ejpam-5427	366	40	2	2	NUM
ejpam-5427	366	41	)	)	PUNCT
ejpam-5427	366	42	,	,	PUNCT
ejpam-5427	366	43	communications	communication	NOUN
ejpam-5427	366	44	in	in	ADP
ejpam-5427	366	45	nonlinear	nonlinear	ADJ
ejpam-5427	366	46	science	science	NOUN
ejpam-5427	366	47	and	and	CCONJ
ejpam-5427	366	48	numerical	numerical	PROPN
ejpam-5427	366	49	simulation	simulation	PROPN
ejpam-5427	366	50	.	.	PUNCT
ejpam-5427	367	1	116	116	NUM
ejpam-5427	367	2	,	,	PUNCT
ejpam-5427	367	3	(	(	PUNCT
ejpam-5427	367	4	2023	2023	NUM
ejpam-5427	367	5	)	)	PUNCT
ejpam-5427	367	6	106891	106891	NUM
ejpam-5427	367	7	.	.	PUNCT