id	sid	tid	token	lemma	pos
ejpam-5703	1	1	european	european	PROPN
ejpam-5703	1	2	journal	journal	PROPN
ejpam-5703	1	3	of	of	ADP
ejpam-5703	1	4	pure	pure	ADJ
ejpam-5703	1	5	and	and	CCONJ
ejpam-5703	1	6	applied	applied	ADJ
ejpam-5703	1	7	mathematics	mathematic	NOUN
ejpam-5703	1	8	2025	2025	NUM
ejpam-5703	1	9	,	,	PUNCT
ejpam-5703	1	10	vol	vol	NOUN
ejpam-5703	1	11	.	.	PROPN
ejpam-5703	1	12	18	18	NUM
ejpam-5703	1	13	,	,	PUNCT
ejpam-5703	1	14	issue	issue	NOUN
ejpam-5703	1	15	2	2	NUM
ejpam-5703	1	16	,	,	PUNCT
ejpam-5703	1	17	article	article	NOUN
ejpam-5703	1	18	number	number	NOUN
ejpam-5703	1	19	5703	5703	NUM
ejpam-5703	1	20	issn	issn	VERB
ejpam-5703	1	21	1307	1307	NUM
ejpam-5703	1	22	-	-	SYM
ejpam-5703	1	23	5543	5543	NUM
ejpam-5703	1	24	–	–	PUNCT
ejpam-5703	1	25	ejpam.com	ejpam.com	X
ejpam-5703	1	26	published	publish	VERB
ejpam-5703	1	27	by	by	ADP
ejpam-5703	1	28	new	new	PROPN
ejpam-5703	1	29	york	york	PROPN
ejpam-5703	1	30	business	business	PROPN
ejpam-5703	1	31	global	global	PROPN
ejpam-5703	1	32	nonstandard	nonstandard	ADJ
ejpam-5703	1	33	finite	finite	ADJ
ejpam-5703	1	34	difference	difference	NOUN
ejpam-5703	1	35	predictor	predictor	NOUN
ejpam-5703	1	36	corrector	corrector	NOUN
ejpam-5703	1	37	method	method	NOUN
ejpam-5703	1	38	for	for	ADP
ejpam-5703	1	39	quadratic	quadratic	ADJ
ejpam-5703	1	40	riccati	riccati	NOUN
ejpam-5703	1	41	differential	differential	NOUN
ejpam-5703	1	42	equation	equation	NOUN
ejpam-5703	1	43	basit	basit	PROPN
ejpam-5703	1	44	rehman1,2	rehman1,2	PROPN
ejpam-5703	1	45	,	,	PUNCT
ejpam-5703	1	46	muhammad	muhammad	PROPN
ejpam-5703	1	47	abdaal	abdaal	PROPN
ejpam-5703	1	48	bin	bin	PROPN
ejpam-5703	1	49	iqbal3,∗	iqbal3,∗	VERB
ejpam-5703	1	50	,	,	PUNCT
ejpam-5703	1	51	aziz	aziz	PROPN
ejpam-5703	1	52	khan4	khan4	PROPN
ejpam-5703	1	53	,	,	PUNCT
ejpam-5703	2	1	d.	d.	PROPN
ejpam-5703	2	2	k.	k.	PROPN
ejpam-5703	3	1	almutairi5	almutairi5	PROPN
ejpam-5703	3	2	,	,	PUNCT
ejpam-5703	3	3	thabet	thabet	ADJ
ejpam-5703	3	4	abdeljawad4	abdeljawad4	NOUN
ejpam-5703	3	5	1	1	NUM
ejpam-5703	3	6	department	department	NOUN
ejpam-5703	3	7	of	of	ADP
ejpam-5703	3	8	mathematics	mathematic	NOUN
ejpam-5703	3	9	,	,	PUNCT
ejpam-5703	3	10	govt	govt	NOUN
ejpam-5703	3	11	.	.	PUNCT
ejpam-5703	4	1	municipal	municipal	ADJ
ejpam-5703	4	2	graduate	graduate	PROPN
ejpam-5703	4	3	college	college	PROPN
ejpam-5703	4	4	,	,	PUNCT
ejpam-5703	4	5	jaranwala	jaranwala	PROPN
ejpam-5703	4	6	road	road	PROPN
ejpam-5703	4	7	,	,	PUNCT
ejpam-5703	4	8	faisalabad	faisalabad	PROPN
ejpam-5703	4	9	37250	37250	NUM
ejpam-5703	4	10	,	,	PUNCT
ejpam-5703	4	11	pakistan	pakistan	PROPN
ejpam-5703	4	12	2	2	NUM
ejpam-5703	4	13	department	department	NOUN
ejpam-5703	4	14	of	of	ADP
ejpam-5703	4	15	mathematics	mathematic	NOUN
ejpam-5703	4	16	,	,	PUNCT
ejpam-5703	4	17	government	government	NOUN
ejpam-5703	4	18	college	college	PROPN
ejpam-5703	4	19	university	university	PROPN
ejpam-5703	4	20	,	,	PUNCT
ejpam-5703	4	21	faisalabad	faisalabad	PROPN
ejpam-5703	4	22	38000	38000	NUM
ejpam-5703	4	23	,	,	PUNCT
ejpam-5703	4	24	pakistan	pakistan	PROPN
ejpam-5703	4	25	3	3	NUM
ejpam-5703	4	26	department	department	NOUN
ejpam-5703	4	27	of	of	ADP
ejpam-5703	4	28	mathematics	mathematics	PROPN
ejpam-5703	4	29	,	,	PUNCT
ejpam-5703	4	30	university	university	NOUN
ejpam-5703	4	31	of	of	ADP
ejpam-5703	4	32	the	the	DET
ejpam-5703	4	33	punjab	punjab	PROPN
ejpam-5703	4	34	,	,	PUNCT
ejpam-5703	4	35	quaid	quaid	PROPN
ejpam-5703	4	36	-	-	PUNCT
ejpam-5703	4	37	e	e	PROPN
ejpam-5703	4	38	-	-	PROPN
ejpam-5703	4	39	azam	azam	PROPN
ejpam-5703	4	40	campus	campus	NOUN
ejpam-5703	4	41	,	,	PUNCT
ejpam-5703	4	42	lahore	lahore	NOUN
ejpam-5703	4	43	54590	54590	NUM
ejpam-5703	4	44	,	,	PUNCT
ejpam-5703	4	45	pakistan	pakistan	PROPN
ejpam-5703	4	46	4	4	NUM
ejpam-5703	4	47	department	department	NOUN
ejpam-5703	4	48	of	of	ADP
ejpam-5703	4	49	mathematics	mathematic	NOUN
ejpam-5703	4	50	and	and	CCONJ
ejpam-5703	4	51	sciences	science	NOUN
ejpam-5703	4	52	,	,	PUNCT
ejpam-5703	4	53	prince	prince	PROPN
ejpam-5703	4	54	sultan	sultan	PROPN
ejpam-5703	4	55	university	university	PROPN
ejpam-5703	4	56	,	,	PUNCT
ejpam-5703	4	57	p.o	p.o	PROPN
ejpam-5703	4	58	.	.	PROPN
ejpam-5703	4	59	box	box	PROPN
ejpam-5703	4	60	66833	66833	NUM
ejpam-5703	4	61	,	,	PUNCT
ejpam-5703	4	62	11586	11586	NUM
ejpam-5703	4	63	riyadh	riyadh	NOUN
ejpam-5703	4	64	,	,	PUNCT
ejpam-5703	4	65	saudi	saudi	PROPN
ejpam-5703	4	66	arabia	arabia	PROPN
ejpam-5703	4	67	5	5	NUM
ejpam-5703	4	68	department	department	NOUN
ejpam-5703	4	69	of	of	ADP
ejpam-5703	4	70	mathematics	mathematic	NOUN
ejpam-5703	4	71	,	,	PUNCT
ejpam-5703	4	72	college	college	NOUN
ejpam-5703	4	73	of	of	ADP
ejpam-5703	4	74	science	science	PROPN
ejpam-5703	4	75	al	al	PROPN
ejpam-5703	4	76	-	-	PUNCT
ejpam-5703	4	77	zulfi	zulfi	PROPN
ejpam-5703	4	78	,	,	PUNCT
ejpam-5703	4	79	majmaah	majmaah	PROPN
ejpam-5703	4	80	university	university	NOUN
ejpam-5703	4	81	,	,	PUNCT
ejpam-5703	4	82	11952	11952	NUM
ejpam-5703	4	83	al	al	PROPN
ejpam-5703	4	84	-	-	PUNCT
ejpam-5703	4	85	majmaah	majmaah	PROPN
ejpam-5703	4	86	,	,	PUNCT
ejpam-5703	4	87	saudi	saudi	PROPN
ejpam-5703	4	88	arabia	arabia	PROPN
ejpam-5703	4	89	abstract	abstract	NOUN
ejpam-5703	4	90	.	.	PUNCT
ejpam-5703	5	1	solving	solve	VERB
ejpam-5703	5	2	nonlinear	nonlinear	ADJ
ejpam-5703	5	3	differential	differential	ADJ
ejpam-5703	5	4	equations	equation	NOUN
ejpam-5703	5	5	reliably	reliably	ADV
ejpam-5703	5	6	and	and	CCONJ
ejpam-5703	5	7	effectively	effectively	ADV
ejpam-5703	5	8	is	be	AUX
ejpam-5703	5	9	critical	critical	ADJ
ejpam-5703	5	10	for	for	ADP
ejpam-5703	5	11	applications	application	NOUN
ejpam-5703	5	12	in	in	ADP
ejpam-5703	5	13	epidemiology	epidemiology	NOUN
ejpam-5703	5	14	,	,	PUNCT
ejpam-5703	5	15	ecology	ecology	NOUN
ejpam-5703	5	16	,	,	PUNCT
ejpam-5703	5	17	and	and	CCONJ
ejpam-5703	5	18	finance	finance	NOUN
ejpam-5703	5	19	.	.	PUNCT
ejpam-5703	6	1	traditional	traditional	ADJ
ejpam-5703	6	2	finite	finite	ADJ
ejpam-5703	6	3	difference	difference	NOUN
ejpam-5703	6	4	approaches	approach	NOUN
ejpam-5703	6	5	frequently	frequently	ADV
ejpam-5703	6	6	exhibit	exhibit	VERB
ejpam-5703	6	7	numerical	numerical	ADJ
ejpam-5703	6	8	instability	instability	NOUN
ejpam-5703	6	9	and	and	CCONJ
ejpam-5703	6	10	fail	fail	VERB
ejpam-5703	6	11	to	to	PART
ejpam-5703	6	12	maintain	maintain	VERB
ejpam-5703	6	13	crucial	crucial	ADJ
ejpam-5703	6	14	features	feature	NOUN
ejpam-5703	6	15	such	such	ADJ
ejpam-5703	6	16	as	as	ADP
ejpam-5703	6	17	positivity	positivity	NOUN
ejpam-5703	6	18	and	and	CCONJ
ejpam-5703	6	19	boundedness	boundedness	PROPN
ejpam-5703	6	20	.	.	PROPN
ejpam-5703	6	21	motivated	motivate	VERB
ejpam-5703	6	22	by	by	ADP
ejpam-5703	6	23	these	these	DET
ejpam-5703	6	24	restrictions	restriction	NOUN
ejpam-5703	6	25	,	,	PUNCT
ejpam-5703	6	26	we	we	PRON
ejpam-5703	6	27	provide	provide	VERB
ejpam-5703	6	28	an	an	DET
ejpam-5703	6	29	unconditionally	unconditionally	ADV
ejpam-5703	6	30	stable	stable	ADJ
ejpam-5703	6	31	nonstandard	nonstandard	ADJ
ejpam-5703	6	32	finite	finite	ADJ
ejpam-5703	6	33	difference	difference	NOUN
ejpam-5703	6	34	predictor	predictor	NOUN
ejpam-5703	6	35	-	-	PUNCT
ejpam-5703	6	36	corrector	corrector	NOUN
ejpam-5703	6	37	(	(	PUNCT
ejpam-5703	6	38	nsfd	nsfd	ADJ
ejpam-5703	6	39	-	-	PUNCT
ejpam-5703	6	40	pc	pc	NOUN
ejpam-5703	6	41	)	)	PUNCT
ejpam-5703	6	42	strategy	strategy	NOUN
ejpam-5703	6	43	for	for	ADP
ejpam-5703	6	44	solving	solve	VERB
ejpam-5703	6	45	nonlinear	nonlinear	ADJ
ejpam-5703	6	46	quadratic	quadratic	ADJ
ejpam-5703	6	47	riccati	riccati	NOUN
ejpam-5703	6	48	differential	differential	NOUN
ejpam-5703	6	49	equations	equation	NOUN
ejpam-5703	6	50	.	.	PUNCT
ejpam-5703	7	1	particularly	particularly	ADV
ejpam-5703	7	2	when	when	SCONJ
ejpam-5703	7	3	the	the	DET
ejpam-5703	7	4	step	step	NOUN
ejpam-5703	7	5	size	size	NOUN
ejpam-5703	7	6	h	h	NOUN
ejpam-5703	7	7	rises	rise	NOUN
ejpam-5703	7	8	,	,	PUNCT
ejpam-5703	7	9	nsfd	nsfd	ADJ
ejpam-5703	7	10	-	-	PUNCT
ejpam-5703	7	11	pc	pc	NOUN
ejpam-5703	7	12	typically	typically	ADV
ejpam-5703	7	13	yields	yield	VERB
ejpam-5703	7	14	the	the	DET
ejpam-5703	7	15	solution	solution	NOUN
ejpam-5703	7	16	that	that	PRON
ejpam-5703	7	17	is	be	AUX
ejpam-5703	7	18	closer	close	ADJ
ejpam-5703	7	19	to	to	ADP
ejpam-5703	7	20	the	the	DET
ejpam-5703	7	21	exact	exact	ADJ
ejpam-5703	7	22	solution	solution	NOUN
ejpam-5703	7	23	.	.	PUNCT
ejpam-5703	8	1	riccati	riccati	PROPN
ejpam-5703	8	2	differential	differential	NOUN
ejpam-5703	8	3	equation	equation	NOUN
ejpam-5703	8	4	is	be	AUX
ejpam-5703	8	5	1st	1st	ADJ
ejpam-5703	8	6	-	-	PUNCT
ejpam-5703	8	7	order	order	NOUN
ejpam-5703	8	8	quadratic	quadratic	ADJ
ejpam-5703	8	9	ode	ode	NOUN
ejpam-5703	8	10	with	with	ADP
ejpam-5703	8	11	several	several	ADJ
ejpam-5703	8	12	systems	system	NOUN
ejpam-5703	8	13	and	and	CCONJ
ejpam-5703	8	14	control	control	NOUN
ejpam-5703	8	15	theory	theory	NOUN
ejpam-5703	8	16	applications	application	NOUN
ejpam-5703	8	17	.	.	PUNCT
ejpam-5703	9	1	our	our	PRON
ejpam-5703	9	2	technique	technique	NOUN
ejpam-5703	9	3	achieves	achieve	VERB
ejpam-5703	9	4	first	first	ADJ
ejpam-5703	9	5	-	-	PUNCT
ejpam-5703	9	6	order	order	NOUN
ejpam-5703	9	7	temporal	temporal	ADJ
ejpam-5703	9	8	precision	precision	NOUN
ejpam-5703	9	9	while	while	SCONJ
ejpam-5703	9	10	keeping	keep	VERB
ejpam-5703	9	11	the	the	DET
ejpam-5703	9	12	continuous	continuous	ADJ
ejpam-5703	9	13	model	model	NOUN
ejpam-5703	9	14	’s	’s	PART
ejpam-5703	9	15	fundamental	fundamental	ADJ
ejpam-5703	9	16	qualitative	qualitative	ADJ
ejpam-5703	9	17	properties	property	NOUN
ejpam-5703	9	18	.	.	PUNCT
ejpam-5703	10	1	we	we	PRON
ejpam-5703	10	2	compare	compare	VERB
ejpam-5703	10	3	the	the	DET
ejpam-5703	10	4	proposed	propose	VERB
ejpam-5703	10	5	nsfd	nsfd	ADJ
ejpam-5703	10	6	-	-	PUNCT
ejpam-5703	10	7	pc	pc	NOUN
ejpam-5703	10	8	scheme	scheme	NOUN
ejpam-5703	10	9	to	to	ADP
ejpam-5703	10	10	the	the	DET
ejpam-5703	10	11	usual	usual	ADJ
ejpam-5703	10	12	euler	euler	NOUN
ejpam-5703	10	13	predictor	predictor	NOUN
ejpam-5703	10	14	-	-	PUNCT
ejpam-5703	10	15	corrector	corrector	NOUN
ejpam-5703	10	16	approach	approach	NOUN
ejpam-5703	10	17	and	and	CCONJ
ejpam-5703	10	18	find	find	VERB
ejpam-5703	10	19	that	that	SCONJ
ejpam-5703	10	20	it	it	PRON
ejpam-5703	10	21	performs	perform	VERB
ejpam-5703	10	22	much	much	ADV
ejpam-5703	10	23	better	well	ADV
ejpam-5703	10	24	in	in	ADP
ejpam-5703	10	25	accuracy	accuracy	NOUN
ejpam-5703	10	26	and	and	CCONJ
ejpam-5703	10	27	consistency	consistency	NOUN
ejpam-5703	10	28	with	with	ADP
ejpam-5703	10	29	exact	exact	ADJ
ejpam-5703	10	30	answers	answer	NOUN
ejpam-5703	10	31	.	.	PUNCT
ejpam-5703	11	1	the	the	DET
ejpam-5703	11	2	results	result	NOUN
ejpam-5703	11	3	show	show	VERB
ejpam-5703	11	4	that	that	SCONJ
ejpam-5703	11	5	our	our	PRON
ejpam-5703	11	6	method	method	NOUN
ejpam-5703	11	7	is	be	AUX
ejpam-5703	11	8	a	a	DET
ejpam-5703	11	9	superior	superior	ADJ
ejpam-5703	11	10	and	and	CCONJ
ejpam-5703	11	11	dependable	dependable	ADJ
ejpam-5703	11	12	option	option	NOUN
ejpam-5703	11	13	for	for	ADP
ejpam-5703	11	14	solving	solve	VERB
ejpam-5703	11	15	nonlinear	nonlinear	ADJ
ejpam-5703	11	16	differential	differential	ADJ
ejpam-5703	11	17	equations	equation	NOUN
ejpam-5703	11	18	,	,	PUNCT
ejpam-5703	11	19	making	make	VERB
ejpam-5703	11	20	it	it	PRON
ejpam-5703	11	21	extremely	extremely	ADV
ejpam-5703	11	22	useful	useful	ADJ
ejpam-5703	11	23	in	in	ADP
ejpam-5703	11	24	various	various	ADJ
ejpam-5703	11	25	applications	application	NOUN
ejpam-5703	11	26	.	.	PUNCT
ejpam-5703	12	1	2020	2020	NUM
ejpam-5703	12	2	mathematics	mathematic	NOUN
ejpam-5703	12	3	subject	subject	NOUN
ejpam-5703	12	4	classifications	classification	NOUN
ejpam-5703	12	5	:	:	PUNCT
ejpam-5703	12	6	65l05	65l05	NUM
ejpam-5703	12	7	,	,	PUNCT
ejpam-5703	12	8	65l20	65l20	NUM
ejpam-5703	12	9	,	,	PUNCT
ejpam-5703	12	10	34a34	34a34	NUM
ejpam-5703	12	11	,	,	PUNCT
ejpam-5703	12	12	93d05	93d05	NUM
ejpam-5703	12	13	key	key	ADJ
ejpam-5703	12	14	words	word	NOUN
ejpam-5703	12	15	and	and	CCONJ
ejpam-5703	12	16	phrases	phrase	NOUN
ejpam-5703	12	17	:	:	PUNCT
ejpam-5703	12	18	qualitative	qualitative	ADJ
ejpam-5703	12	19	theory	theory	NOUN
ejpam-5703	12	20	,	,	PUNCT
ejpam-5703	12	21	stability	stability	NOUN
ejpam-5703	12	22	,	,	PUNCT
ejpam-5703	12	23	numerical	numerical	ADJ
ejpam-5703	12	24	methods	method	NOUN
ejpam-5703	12	25	∗corresponding	∗corresponde	VERB
ejpam-5703	12	26	author	author	NOUN
ejpam-5703	12	27	.	.	PUNCT
ejpam-5703	13	1	doi	doi	NOUN
ejpam-5703	13	2	:	:	PUNCT
ejpam-5703	13	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5703	https://doi.org/10.29020/nybg.ejpam.v18i2.5703	PUNCT
ejpam-5703	13	4	email	email	NOUN
ejpam-5703	13	5	addresses	address	NOUN
ejpam-5703	13	6	:	:	PUNCT
ejpam-5703	13	7	basitmughal2012@gmail.com	basitmughal2012@gmail.com	X
ejpam-5703	13	8	(	(	PUNCT
ejpam-5703	13	9	b.	b.	PROPN
ejpam-5703	13	10	rehman	rehman	PROPN
ejpam-5703	13	11	)	)	PUNCT
ejpam-5703	13	12	,	,	PUNCT
ejpam-5703	13	13	shahidwani177@gmail.com	shahidwani177@gmail.com	X
ejpam-5703	13	14	(	(	PUNCT
ejpam-5703	13	15	m.	m.	NOUN
ejpam-5703	13	16	a.	a.	PROPN
ejpam-5703	13	17	b.	b.	PROPN
ejpam-5703	13	18	iqbal	iqbal	PROPN
ejpam-5703	13	19	)	)	PUNCT
ejpam-5703	13	20	,	,	PUNCT
ejpam-5703	13	21	akhan@psu.edu.sa	akhan@psu.edu.sa	PROPN
ejpam-5703	13	22	(	(	PUNCT
ejpam-5703	13	23	a.	a.	PROPN
ejpam-5703	13	24	khan	khan	PROPN
ejpam-5703	13	25	)	)	PUNCT
ejpam-5703	13	26	,	,	PUNCT
ejpam-5703	13	27	dk.almutairi@mu.edu.sa	dk.almutairi@mu.edu.sa	PROPN
ejpam-5703	13	28	(	(	PUNCT
ejpam-5703	13	29	d.	d.	PROPN
ejpam-5703	13	30	k.	k.	PROPN
ejpam-5703	13	31	almutairi	almutairi	PROPN
ejpam-5703	13	32	)	)	PUNCT
ejpam-5703	13	33	,	,	PUNCT
ejpam-5703	13	34	tabdeljawad@psu.edu.sa	tabdeljawad@psu.edu.sa	PROPN
ejpam-5703	13	35	(	(	PUNCT
ejpam-5703	13	36	t.	t.	NOUN
ejpam-5703	13	37	abdeljawad	abdeljawad	PROPN
ejpam-5703	13	38	)	)	PUNCT
ejpam-5703	13	39	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5703	13	40	1	1	NUM
ejpam-5703	13	41	copyright	copyright	NOUN
ejpam-5703	13	42	:	:	PUNCT
ejpam-5703	14	1	©	©	PROPN
ejpam-5703	14	2	2025	2025	NUM
ejpam-5703	14	3	the	the	DET
ejpam-5703	14	4	author(s	author(s	NOUN
ejpam-5703	14	5	)	)	PUNCT
ejpam-5703	14	6	.	.	PUNCT
ejpam-5703	15	1	(	(	PUNCT
ejpam-5703	15	2	cc	cc	NOUN
ejpam-5703	15	3	by	by	ADP
ejpam-5703	15	4	-	-	PUNCT
ejpam-5703	15	5	nc	nc	PROPN
ejpam-5703	15	6	4.0	4.0	NUM
ejpam-5703	15	7	)	)	PUNCT
ejpam-5703	15	8	b.	b.	PROPN
ejpam-5703	15	9	rehman	rehman	PROPN
ejpam-5703	15	10	et	et	PROPN
ejpam-5703	15	11	al	al	PROPN
ejpam-5703	15	12	.	.	PUNCT
ejpam-5703	15	13	/	/	SYM
ejpam-5703	15	14	eur	eur	PROPN
ejpam-5703	15	15	.	.	PUNCT
ejpam-5703	16	1	j.	j.	PROPN
ejpam-5703	16	2	pure	pure	PROPN
ejpam-5703	16	3	appl	appl	PROPN
ejpam-5703	16	4	.	.	PROPN
ejpam-5703	16	5	math	math	PROPN
ejpam-5703	16	6	,	,	PUNCT
ejpam-5703	16	7	18	18	NUM
ejpam-5703	16	8	(	(	PUNCT
ejpam-5703	16	9	2	2	NUM
ejpam-5703	16	10	)	)	PUNCT
ejpam-5703	16	11	(	(	PUNCT
ejpam-5703	16	12	2025	2025	NUM
ejpam-5703	16	13	)	)	PUNCT
ejpam-5703	16	14	,	,	PUNCT
ejpam-5703	16	15	5703	5703	NUM
ejpam-5703	16	16	2	2	NUM
ejpam-5703	16	17	of	of	ADP
ejpam-5703	16	18	16	16	NUM
ejpam-5703	16	19	1	1	NUM
ejpam-5703	16	20	.	.	PUNCT
ejpam-5703	17	1	introduction	introduction	NOUN
ejpam-5703	17	2	ronald	ronald	PROPN
ejpam-5703	17	3	mickens	mickens	PROPN
ejpam-5703	17	4	started	start	VERB
ejpam-5703	17	5	creating	create	VERB
ejpam-5703	17	6	numerical	numerical	ADJ
ejpam-5703	17	7	schemes	scheme	NOUN
ejpam-5703	17	8	for	for	ADP
ejpam-5703	17	9	addressing	address	VERB
ejpam-5703	17	10	physical	physical	ADJ
ejpam-5703	17	11	problems	problem	NOUN
ejpam-5703	17	12	that	that	PRON
ejpam-5703	17	13	preserve	preserve	VERB
ejpam-5703	17	14	the	the	DET
ejpam-5703	17	15	physical	physical	ADJ
ejpam-5703	17	16	aspects	aspect	NOUN
ejpam-5703	17	17	of	of	ADP
ejpam-5703	17	18	the	the	DET
ejpam-5703	17	19	original	original	ADJ
ejpam-5703	17	20	systems	system	NOUN
ejpam-5703	17	21	,	,	PUNCT
ejpam-5703	17	22	including	include	VERB
ejpam-5703	17	23	stability	stability	NOUN
ejpam-5703	17	24	properties	property	NOUN
ejpam-5703	17	25	,	,	PUNCT
ejpam-5703	17	26	utilizing	utilize	VERB
ejpam-5703	17	27	nsfd	nsfd	ADJ
ejpam-5703	17	28	schemes	scheme	NOUN
ejpam-5703	17	29	[	[	X
ejpam-5703	17	30	1	1	NUM
ejpam-5703	17	31	,	,	PUNCT
ejpam-5703	17	32	2	2	NUM
ejpam-5703	17	33	]	]	PUNCT
ejpam-5703	17	34	.	.	PUNCT
ejpam-5703	18	1	this	this	PRON
ejpam-5703	18	2	has	have	AUX
ejpam-5703	18	3	led	lead	VERB
ejpam-5703	18	4	to	to	ADP
ejpam-5703	18	5	the	the	DET
ejpam-5703	18	6	development	development	NOUN
ejpam-5703	18	7	of	of	ADP
ejpam-5703	18	8	numerous	numerous	ADJ
ejpam-5703	18	9	discretization	discretization	NOUN
ejpam-5703	18	10	of	of	ADP
ejpam-5703	18	11	nonlinear	nonlinear	ADJ
ejpam-5703	18	12	equations	equation	NOUN
ejpam-5703	18	13	in	in	ADP
ejpam-5703	18	14	various	various	ADJ
ejpam-5703	18	15	fields	field	NOUN
ejpam-5703	18	16	[	[	X
ejpam-5703	18	17	3	3	NUM
ejpam-5703	18	18	]	]	PUNCT
ejpam-5703	18	19	.	.	PUNCT
ejpam-5703	19	1	in	in	ADP
ejpam-5703	19	2	science	science	NOUN
ejpam-5703	19	3	and	and	CCONJ
ejpam-5703	19	4	engineering	engineering	NOUN
ejpam-5703	19	5	,	,	PUNCT
ejpam-5703	19	6	differential	differential	ADJ
ejpam-5703	19	7	equations	equation	NOUN
ejpam-5703	19	8	are	be	AUX
ejpam-5703	19	9	a	a	DET
ejpam-5703	19	10	frequently	frequently	ADV
ejpam-5703	19	11	used	use	VERB
ejpam-5703	19	12	tool	tool	NOUN
ejpam-5703	19	13	for	for	ADP
ejpam-5703	19	14	problem	problem	NOUN
ejpam-5703	19	15	solving	solving	NOUN
ejpam-5703	19	16	.	.	PUNCT
ejpam-5703	20	1	the	the	DET
ejpam-5703	20	2	differential	differential	ADJ
ejpam-5703	20	3	equation	equation	NOUN
ejpam-5703	20	4	’s	’s	PART
ejpam-5703	20	5	complexity	complexity	NOUN
ejpam-5703	20	6	and	and	CCONJ
ejpam-5703	20	7	nonlinearity	nonlinearity	NOUN
ejpam-5703	20	8	make	make	VERB
ejpam-5703	20	9	it	it	PRON
ejpam-5703	20	10	challenging	challenging	ADJ
ejpam-5703	20	11	to	to	PART
ejpam-5703	20	12	solve	solve	VERB
ejpam-5703	20	13	analytically	analytically	ADV
ejpam-5703	20	14	,	,	PUNCT
ejpam-5703	20	15	despite	despite	SCONJ
ejpam-5703	20	16	being	be	AUX
ejpam-5703	20	17	used	use	VERB
ejpam-5703	20	18	to	to	PART
ejpam-5703	20	19	mimic	mimic	VERB
ejpam-5703	20	20	a	a	DET
ejpam-5703	20	21	wide	wide	ADJ
ejpam-5703	20	22	range	range	NOUN
ejpam-5703	20	23	of	of	ADP
ejpam-5703	20	24	real	real	ADJ
ejpam-5703	20	25	-	-	PUNCT
ejpam-5703	20	26	world	world	NOUN
ejpam-5703	20	27	issues	issue	NOUN
ejpam-5703	20	28	.	.	PUNCT
ejpam-5703	21	1	numerical	numerical	ADJ
ejpam-5703	21	2	approaches	approach	NOUN
ejpam-5703	21	3	were	be	AUX
ejpam-5703	21	4	developed	develop	VERB
ejpam-5703	21	5	in	in	ADP
ejpam-5703	21	6	response	response	NOUN
ejpam-5703	21	7	to	to	ADP
ejpam-5703	21	8	the	the	DET
ejpam-5703	21	9	difficulties	difficulty	NOUN
ejpam-5703	21	10	in	in	ADP
ejpam-5703	21	11	obtaining	obtain	VERB
ejpam-5703	21	12	analytical	analytical	ADJ
ejpam-5703	21	13	solutions	solution	NOUN
ejpam-5703	21	14	for	for	ADP
ejpam-5703	21	15	real	real	ADJ
ejpam-5703	21	16	-	-	PUNCT
ejpam-5703	21	17	world	world	NOUN
ejpam-5703	21	18	issues	issue	NOUN
ejpam-5703	21	19	.	.	PUNCT
ejpam-5703	22	1	nlode	nlode	PROPN
ejpam-5703	22	2	is	be	AUX
ejpam-5703	22	3	essential	essential	ADJ
ejpam-5703	22	4	to	to	ADP
ejpam-5703	22	5	many	many	ADJ
ejpam-5703	22	6	branches	branch	NOUN
ejpam-5703	22	7	of	of	ADP
ejpam-5703	22	8	pure	pure	ADJ
ejpam-5703	22	9	and	and	CCONJ
ejpam-5703	22	10	applied	applied	ADJ
ejpam-5703	22	11	mathematics	mathematic	NOUN
ejpam-5703	23	1	[	[	X
ejpam-5703	23	2	4	4	NUM
ejpam-5703	23	3	]	]	PUNCT
ejpam-5703	23	4	,	,	PUNCT
ejpam-5703	23	5	including	include	VERB
ejpam-5703	23	6	biology	biology	NOUN
ejpam-5703	23	7	[	[	X
ejpam-5703	23	8	5	5	NUM
ejpam-5703	23	9	,	,	PUNCT
ejpam-5703	23	10	6	6	NUM
ejpam-5703	23	11	]	]	PUNCT
ejpam-5703	23	12	,	,	PUNCT
ejpam-5703	23	13	astronomy	astronomy	NOUN
ejpam-5703	23	14	,	,	PUNCT
ejpam-5703	23	15	engineering	engineering	NOUN
ejpam-5703	23	16	,	,	PUNCT
ejpam-5703	23	17	applied	apply	VERB
ejpam-5703	23	18	mechanics	mechanic	NOUN
ejpam-5703	23	19	[	[	X
ejpam-5703	23	20	7],and	7],and	NUM
ejpam-5703	23	21	quantum	quantum	PROPN
ejpam-5703	23	22	physics	physics	NOUN
ejpam-5703	23	23	.	.	PUNCT
ejpam-5703	24	1	numerical	numerical	PROPN
ejpam-5703	24	2	and	and	CCONJ
ejpam-5703	24	3	analytical	analytical	ADJ
ejpam-5703	24	4	solutions	solution	NOUN
ejpam-5703	24	5	to	to	PART
ejpam-5703	24	6	nlode	nlode	PROPN
ejpam-5703	24	7	have	have	AUX
ejpam-5703	24	8	drawn	draw	VERB
ejpam-5703	24	9	interest	interest	NOUN
ejpam-5703	24	10	in	in	ADP
ejpam-5703	24	11	numerous	numerous	ADJ
ejpam-5703	24	12	practical	practical	ADJ
ejpam-5703	24	13	scientific	scientific	ADJ
ejpam-5703	24	14	domains	domain	NOUN
ejpam-5703	24	15	[	[	X
ejpam-5703	24	16	8–10	8–10	NOUN
ejpam-5703	24	17	]	]	PUNCT
ejpam-5703	24	18	,	,	PUNCT
ejpam-5703	24	19	the	the	DET
ejpam-5703	24	20	riccati	riccati	PROPN
ejpam-5703	24	21	differential	differential	NOUN
ejpam-5703	24	22	equation	equation	NOUN
ejpam-5703	24	23	is	be	AUX
ejpam-5703	24	24	a	a	DET
ejpam-5703	24	25	type	type	NOUN
ejpam-5703	24	26	of	of	ADP
ejpam-5703	24	27	nonlinear	nonlinear	ADJ
ejpam-5703	24	28	differential	differential	ADJ
ejpam-5703	24	29	equation	equation	NOUN
ejpam-5703	24	30	that	that	PRON
ejpam-5703	24	31	has	have	VERB
ejpam-5703	24	32	great	great	ADJ
ejpam-5703	24	33	importance	importance	NOUN
ejpam-5703	24	34	.	.	PUNCT
ejpam-5703	25	1	for	for	ADP
ejpam-5703	25	2	example	example	NOUN
ejpam-5703	25	3	,	,	PUNCT
ejpam-5703	25	4	the	the	DET
ejpam-5703	25	5	riccati	riccati	PROPN
ejpam-5703	25	6	differential	differential	NOUN
ejpam-5703	25	7	equation	equation	NOUN
ejpam-5703	25	8	and	and	CCONJ
ejpam-5703	25	9	a	a	DET
ejpam-5703	25	10	1d	1d	NUM
ejpam-5703	25	11	static	static	ADJ
ejpam-5703	25	12	schrodinger	schrodinger	NOUN
ejpam-5703	25	13	equation	equation	NOUN
ejpam-5703	25	14	are	be	AUX
ejpam-5703	25	15	closely	closely	ADV
ejpam-5703	25	16	connected	connect	VERB
ejpam-5703	25	17	.	.	PUNCT
ejpam-5703	26	1	[	[	X
ejpam-5703	26	2	11	11	NUM
ejpam-5703	26	3	,	,	PUNCT
ejpam-5703	26	4	12	12	NUM
ejpam-5703	26	5	]	]	PUNCT
ejpam-5703	26	6	a	a	DET
ejpam-5703	26	7	well	well	ADV
ejpam-5703	26	8	-	-	PUNCT
ejpam-5703	26	9	known	know	VERB
ejpam-5703	26	10	nonlinear	nonlinear	ADJ
ejpam-5703	26	11	differential	differential	ADJ
ejpam-5703	26	12	equation	equation	NOUN
ejpam-5703	26	13	(	(	PUNCT
ejpam-5703	26	14	nlde	nlde	ADV
ejpam-5703	26	15	)	)	PUNCT
ejpam-5703	26	16	,	,	PUNCT
ejpam-5703	26	17	the	the	DET
ejpam-5703	26	18	riccati	riccati	PROPN
ejpam-5703	26	19	differential	differential	NOUN
ejpam-5703	26	20	equation	equation	NOUN
ejpam-5703	26	21	finds	find	VERB
ejpam-5703	26	22	use	use	NOUN
ejpam-5703	26	23	in	in	ADP
ejpam-5703	26	24	a	a	DET
ejpam-5703	26	25	variety	variety	NOUN
ejpam-5703	26	26	of	of	ADP
ejpam-5703	26	27	scientific	scientific	ADJ
ejpam-5703	26	28	and	and	CCONJ
ejpam-5703	26	29	technical	technical	ADJ
ejpam-5703	26	30	fields	field	NOUN
ejpam-5703	26	31	,	,	PUNCT
ejpam-5703	26	32	including	include	VERB
ejpam-5703	26	33	financial	financial	ADJ
ejpam-5703	26	34	mathematics	mathematic	NOUN
ejpam-5703	26	35	,	,	PUNCT
ejpam-5703	26	36	network	network	NOUN
ejpam-5703	26	37	synthesis	synthesis	NOUN
ejpam-5703	26	38	,	,	PUNCT
ejpam-5703	26	39	resilient	resilient	ADJ
ejpam-5703	26	40	stabilization	stabilization	NOUN
ejpam-5703	26	41	,	,	PUNCT
ejpam-5703	26	42	stochastic	stochastic	ADJ
ejpam-5703	26	43	realization	realization	NOUN
ejpam-5703	26	44	theory	theory	NOUN
ejpam-5703	26	45	,	,	PUNCT
ejpam-5703	26	46	and	and	CCONJ
ejpam-5703	26	47	optimal	optimal	ADJ
ejpam-5703	26	48	control	control	NOUN
ejpam-5703	26	49	.	.	PUNCT
ejpam-5703	27	1	for	for	ADP
ejpam-5703	27	2	simulating	simulate	VERB
ejpam-5703	27	3	a	a	DET
ejpam-5703	27	4	variety	variety	NOUN
ejpam-5703	27	5	of	of	ADP
ejpam-5703	27	6	physical	physical	ADJ
ejpam-5703	27	7	scenarios	scenario	NOUN
ejpam-5703	27	8	,	,	PUNCT
ejpam-5703	27	9	such	such	ADJ
ejpam-5703	27	10	as	as	ADP
ejpam-5703	27	11	spring	spring	NOUN
ejpam-5703	27	12	mass	mass	NOUN
ejpam-5703	27	13	systems	system	NOUN
ejpam-5703	27	14	,	,	PUNCT
ejpam-5703	27	15	beam	beam	NOUN
ejpam-5703	27	16	bending	bending	NOUN
ejpam-5703	27	17	,	,	PUNCT
ejpam-5703	27	18	resistor	resistor	NOUN
ejpam-5703	27	19	-	-	PUNCT
ejpam-5703	27	20	capacitor	capacitor	NOUN
ejpam-5703	27	21	-	-	PUNCT
ejpam-5703	27	22	induction	induction	NOUN
ejpam-5703	27	23	circuits	circuit	NOUN
ejpam-5703	27	24	,	,	PUNCT
ejpam-5703	27	25	chemical	chemical	ADJ
ejpam-5703	27	26	reactions	reaction	NOUN
ejpam-5703	27	27	[	[	X
ejpam-5703	27	28	13	13	NUM
ejpam-5703	27	29	]	]	PUNCT
ejpam-5703	27	30	,	,	PUNCT
ejpam-5703	27	31	pendulums	pendulum	NOUN
ejpam-5703	27	32	,	,	PUNCT
ejpam-5703	27	33	the	the	DET
ejpam-5703	27	34	motion	motion	NOUN
ejpam-5703	27	35	of	of	ADP
ejpam-5703	27	36	rotating	rotate	VERB
ejpam-5703	27	37	masses	masse	NOUN
ejpam-5703	27	38	around	around	ADP
ejpam-5703	27	39	bodies	body	NOUN
ejpam-5703	27	40	,	,	PUNCT
ejpam-5703	27	41	and	and	CCONJ
ejpam-5703	27	42	more	more	ADJ
ejpam-5703	27	43	,	,	PUNCT
ejpam-5703	27	44	nonlinear	nonlinear	ADJ
ejpam-5703	27	45	differential	differential	ADJ
ejpam-5703	27	46	equations	equation	NOUN
ejpam-5703	27	47	are	be	AUX
ejpam-5703	27	48	crucial	crucial	ADJ
ejpam-5703	27	49	tools	tool	NOUN
ejpam-5703	27	50	[	[	X
ejpam-5703	27	51	14	14	NUM
ejpam-5703	27	52	]	]	PUNCT
ejpam-5703	27	53	.	.	PUNCT
ejpam-5703	28	1	even	even	ADV
ejpam-5703	28	2	though	though	SCONJ
ejpam-5703	28	3	riccati	riccati	PROPN
ejpam-5703	28	4	equations	equation	NOUN
ejpam-5703	28	5	are	be	AUX
ejpam-5703	28	6	used	use	VERB
ejpam-5703	28	7	extensively	extensively	ADV
ejpam-5703	28	8	,	,	PUNCT
ejpam-5703	28	9	traditional	traditional	ADJ
ejpam-5703	28	10	numerical	numerical	ADJ
ejpam-5703	28	11	techniques	technique	NOUN
ejpam-5703	28	12	,	,	PUNCT
ejpam-5703	28	13	including	include	VERB
ejpam-5703	28	14	basic	basic	ADJ
ejpam-5703	28	15	finite	finite	ADJ
ejpam-5703	28	16	difference	difference	NOUN
ejpam-5703	28	17	approaches	approach	NOUN
ejpam-5703	28	18	,	,	PUNCT
ejpam-5703	28	19	usually	usually	ADV
ejpam-5703	28	20	experience	experience	VERB
ejpam-5703	28	21	numerical	numerical	ADJ
ejpam-5703	28	22	instability	instability	NOUN
ejpam-5703	28	23	,	,	PUNCT
ejpam-5703	28	24	especially	especially	ADV
ejpam-5703	28	25	when	when	SCONJ
ejpam-5703	28	26	step	step	NOUN
ejpam-5703	28	27	sizes	size	NOUN
ejpam-5703	28	28	are	be	AUX
ejpam-5703	28	29	larger	large	ADJ
ejpam-5703	28	30	.	.	PUNCT
ejpam-5703	29	1	important	important	ADJ
ejpam-5703	29	2	characteristics	characteristic	NOUN
ejpam-5703	29	3	like	like	ADP
ejpam-5703	29	4	positivity	positivity	NOUN
ejpam-5703	29	5	and	and	CCONJ
ejpam-5703	29	6	boundedness	boundedness	NOUN
ejpam-5703	29	7	,	,	PUNCT
ejpam-5703	29	8	which	which	PRON
ejpam-5703	29	9	are	be	AUX
ejpam-5703	29	10	essential	essential	ADJ
ejpam-5703	29	11	for	for	ADP
ejpam-5703	29	12	preserving	preserve	VERB
ejpam-5703	29	13	the	the	DET
ejpam-5703	29	14	physical	physical	ADJ
ejpam-5703	29	15	integrity	integrity	NOUN
ejpam-5703	29	16	of	of	ADP
ejpam-5703	29	17	solutions	solution	NOUN
ejpam-5703	29	18	,	,	PUNCT
ejpam-5703	29	19	are	be	AUX
ejpam-5703	29	20	frequently	frequently	ADV
ejpam-5703	29	21	lost	lose	VERB
ejpam-5703	29	22	in	in	ADP
ejpam-5703	29	23	these	these	DET
ejpam-5703	29	24	conventional	conventional	ADJ
ejpam-5703	29	25	approaches	approach	NOUN
ejpam-5703	29	26	.	.	PUNCT
ejpam-5703	30	1	as	as	ADP
ejpam-5703	30	2	a	a	DET
ejpam-5703	30	3	result	result	NOUN
ejpam-5703	30	4	,	,	PUNCT
ejpam-5703	30	5	there	there	PRON
ejpam-5703	30	6	is	be	VERB
ejpam-5703	30	7	an	an	DET
ejpam-5703	30	8	increasing	increase	VERB
ejpam-5703	30	9	demand	demand	NOUN
ejpam-5703	30	10	for	for	ADP
ejpam-5703	30	11	more	more	ADV
ejpam-5703	30	12	robust	robust	ADJ
ejpam-5703	30	13	and	and	CCONJ
ejpam-5703	30	14	precise	precise	ADJ
ejpam-5703	30	15	numerical	numerical	ADJ
ejpam-5703	30	16	systems	system	NOUN
ejpam-5703	30	17	that	that	PRON
ejpam-5703	30	18	may	may	AUX
ejpam-5703	30	19	overcome	overcome	VERB
ejpam-5703	30	20	these	these	DET
ejpam-5703	30	21	constraints	constraint	NOUN
ejpam-5703	30	22	[	[	X
ejpam-5703	30	23	15	15	NUM
ejpam-5703	30	24	,	,	PUNCT
ejpam-5703	30	25	16	16	NUM
ejpam-5703	30	26	]	]	PUNCT
ejpam-5703	30	27	.	.	PUNCT
ejpam-5703	31	1	numerical	numerical	ADJ
ejpam-5703	31	2	instability	instability	NOUN
ejpam-5703	31	3	and	and	CCONJ
ejpam-5703	31	4	bias	bias	NOUN
ejpam-5703	31	5	are	be	AUX
ejpam-5703	31	6	problems	problem	NOUN
ejpam-5703	31	7	with	with	ADP
ejpam-5703	31	8	standard	standard	ADJ
ejpam-5703	31	9	finite	finite	ADJ
ejpam-5703	31	10	difference	difference	NOUN
ejpam-5703	31	11	methods	method	NOUN
ejpam-5703	31	12	for	for	ADP
ejpam-5703	31	13	solving	solve	VERB
ejpam-5703	31	14	nonlinear	nonlinear	ADJ
ejpam-5703	31	15	differential	differential	ADJ
ejpam-5703	31	16	equations	equation	NOUN
ejpam-5703	31	17	that	that	PRON
ejpam-5703	31	18	model	model	VERB
ejpam-5703	31	19	real	real	ADJ
ejpam-5703	31	20	-	-	PUNCT
ejpam-5703	31	21	world	world	NOUN
ejpam-5703	31	22	phenomena	phenomenon	NOUN
ejpam-5703	31	23	.	.	PUNCT
ejpam-5703	32	1	if	if	SCONJ
ejpam-5703	32	2	large	large	ADJ
ejpam-5703	32	3	step	step	NOUN
ejpam-5703	32	4	sizes	size	NOUN
ejpam-5703	32	5	are	be	AUX
ejpam-5703	32	6	utilized	utilize	VERB
ejpam-5703	32	7	in	in	ADP
ejpam-5703	32	8	the	the	DET
ejpam-5703	32	9	numerical	numerical	PROPN
ejpam-5703	32	10	simulation	simulation	PROPN
ejpam-5703	32	11	,	,	PUNCT
ejpam-5703	32	12	this	this	DET
ejpam-5703	32	13	unwanted	unwanted	ADJ
ejpam-5703	32	14	behavior	behavior	NOUN
ejpam-5703	32	15	is	be	AUX
ejpam-5703	32	16	typical	typical	ADJ
ejpam-5703	32	17	.	.	PUNCT
ejpam-5703	33	1	the	the	DET
ejpam-5703	33	2	nsfd	nsfd	ADJ
ejpam-5703	33	3	-	-	PUNCT
ejpam-5703	33	4	pc	pc	NOUN
ejpam-5703	33	5	technique	technique	NOUN
ejpam-5703	33	6	,	,	PUNCT
ejpam-5703	33	7	which	which	PRON
ejpam-5703	33	8	was	be	AUX
ejpam-5703	33	9	suggested	suggest	VERB
ejpam-5703	33	10	and	and	CCONJ
ejpam-5703	33	11	made	make	VERB
ejpam-5703	33	12	famous	famous	ADJ
ejpam-5703	33	13	by	by	ADP
ejpam-5703	33	14	[	[	X
ejpam-5703	33	15	17	17	NUM
ejpam-5703	33	16	]	]	PUNCT
ejpam-5703	33	17	,	,	PUNCT
ejpam-5703	33	18	is	be	AUX
ejpam-5703	33	19	used	use	VERB
ejpam-5703	33	20	to	to	PART
ejpam-5703	33	21	address	address	VERB
ejpam-5703	33	22	these	these	DET
ejpam-5703	33	23	drawbacks	drawback	NOUN
ejpam-5703	33	24	.	.	PUNCT
ejpam-5703	34	1	some	some	DET
ejpam-5703	34	2	qualitative	qualitative	ADJ
ejpam-5703	34	3	aspects	aspect	NOUN
ejpam-5703	34	4	of	of	ADP
ejpam-5703	34	5	the	the	DET
ejpam-5703	34	6	continuous	continuous	ADJ
ejpam-5703	34	7	-	-	PUNCT
ejpam-5703	34	8	time	time	NOUN
ejpam-5703	34	9	model	model	NOUN
ejpam-5703	34	10	,	,	PUNCT
ejpam-5703	34	11	like	like	ADP
ejpam-5703	34	12	positivity	positivity	NOUN
ejpam-5703	34	13	and	and	CCONJ
ejpam-5703	34	14	boundedness	boundedness	NOUN
ejpam-5703	34	15	,	,	PUNCT
ejpam-5703	34	16	are	be	AUX
ejpam-5703	34	17	preserved	preserve	VERB
ejpam-5703	34	18	by	by	ADP
ejpam-5703	34	19	the	the	DET
ejpam-5703	34	20	nsfd	nsfd	ADJ
ejpam-5703	34	21	-	-	PUNCT
ejpam-5703	34	22	pc	pc	NOUN
ejpam-5703	34	23	approach	approach	NOUN
ejpam-5703	34	24	,	,	PUNCT
ejpam-5703	34	25	which	which	PRON
ejpam-5703	34	26	is	be	AUX
ejpam-5703	34	27	dynamically	dynamically	ADV
ejpam-5703	34	28	consistent	consistent	ADJ
ejpam-5703	34	29	due	due	ADP
ejpam-5703	34	30	to	to	ADP
ejpam-5703	34	31	its	its	PRON
ejpam-5703	34	32	well	well	ADV
ejpam-5703	34	33	-	-	PUNCT
ejpam-5703	34	34	crafted	craft	VERB
ejpam-5703	34	35	rules	rule	NOUN
ejpam-5703	34	36	.	.	PUNCT
ejpam-5703	35	1	an	an	DET
ejpam-5703	35	2	italian	italian	ADJ
ejpam-5703	35	3	nobel	nobel	PROPN
ejpam-5703	35	4	laureate	laureate	PROPN
ejpam-5703	35	5	,	,	PUNCT
ejpam-5703	35	6	the	the	DET
ejpam-5703	35	7	jacopo	jacopo	PROPN
ejpam-5703	35	8	francessco	francessco	PROPN
ejpam-5703	35	9	riccati	riccati	PROPN
ejpam-5703	35	10	introduces	introduce	VERB
ejpam-5703	35	11	a	a	DET
ejpam-5703	35	12	famous	famous	ADJ
ejpam-5703	35	13	differential	differential	NOUN
ejpam-5703	35	14	equation	equation	NOUN
ejpam-5703	35	15	titled	title	VERB
ejpam-5703	35	16	as	as	ADP
ejpam-5703	35	17	riccati	riccati	PROPN
ejpam-5703	35	18	differential	differential	NOUN
ejpam-5703	35	19	equation	equation	NOUN
ejpam-5703	35	20	.	.	PUNCT
ejpam-5703	36	1	it	it	PRON
ejpam-5703	36	2	is	be	AUX
ejpam-5703	36	3	1st	1st	ADJ
ejpam-5703	36	4	order	order	NOUN
ejpam-5703	36	5	non	non	ADJ
ejpam-5703	36	6	-	-	ADJ
ejpam-5703	36	7	linear	linear	ADJ
ejpam-5703	36	8	differential	differential	ADJ
ejpam-5703	36	9	equation	equation	NOUN
ejpam-5703	36	10	.	.	PUNCT
ejpam-5703	37	1	riccati	riccati	PROPN
ejpam-5703	37	2	differential	differential	NOUN
ejpam-5703	37	3	equation	equation	NOUN
ejpam-5703	37	4	has	have	VERB
ejpam-5703	37	5	many	many	ADJ
ejpam-5703	37	6	uses	use	NOUN
ejpam-5703	37	7	in	in	ADP
ejpam-5703	37	8	engineering	engineering	NOUN
ejpam-5703	37	9	[	[	X
ejpam-5703	37	10	18	18	NUM
ejpam-5703	37	11	,	,	PUNCT
ejpam-5703	37	12	19	19	NUM
ejpam-5703	37	13	]	]	PUNCT
ejpam-5703	37	14	.	.	PUNCT
ejpam-5703	38	1	non	non	ADJ
ejpam-5703	38	2	-	-	ADJ
ejpam-5703	38	3	linear	linear	ADJ
ejpam-5703	38	4	differential	differential	NOUN
ejpam-5703	38	5	equation	equation	NOUN
ejpam-5703	38	6	had	have	AUX
ejpam-5703	38	7	been	be	AUX
ejpam-5703	38	8	studied	study	VERB
ejpam-5703	38	9	by	by	ADP
ejpam-5703	38	10	many	many	ADJ
ejpam-5703	38	11	researchers	researcher	NOUN
ejpam-5703	38	12	using	use	VERB
ejpam-5703	38	13	different	different	ADJ
ejpam-5703	38	14	variational	variational	ADJ
ejpam-5703	38	15	and	and	CCONJ
ejpam-5703	38	16	perturbation	perturbation	NOUN
ejpam-5703	38	17	approaches	approach	NOUN
ejpam-5703	38	18	(	(	PUNCT
ejpam-5703	38	19	vapa	vapa	VERB
ejpam-5703	38	20	)	)	PUNCT
ejpam-5703	38	21	,	,	PUNCT
ejpam-5703	38	22	such	such	ADJ
ejpam-5703	38	23	as	as	ADP
ejpam-5703	38	24	variational	variational	ADJ
ejpam-5703	38	25	iterative	iterative	NOUN
ejpam-5703	38	26	methods	method	NOUN
ejpam-5703	38	27	,	,	PUNCT
ejpam-5703	38	28	homotopy	homotopy	VERB
ejpam-5703	38	29	perturbation	perturbation	NOUN
ejpam-5703	38	30	methods	method	NOUN
ejpam-5703	38	31	(	(	PUNCT
ejpam-5703	38	32	hpm	hpm	NOUN
ejpam-5703	38	33	)	)	PUNCT
ejpam-5703	38	34	and	and	CCONJ
ejpam-5703	38	35	adomian	adomian	NOUN
ejpam-5703	38	36	decomposition	decomposition	NOUN
ejpam-5703	38	37	method	method	NOUN
ejpam-5703	38	38	(	(	PUNCT
ejpam-5703	38	39	adm	adm	PROPN
ejpam-5703	38	40	)	)	PUNCT
ejpam-5703	39	1	[	[	X
ejpam-5703	39	2	20	20	NUM
ejpam-5703	39	3	,	,	PUNCT
ejpam-5703	39	4	21	21	NUM
ejpam-5703	39	5	]	]	PUNCT
ejpam-5703	39	6	.	.	PUNCT
ejpam-5703	40	1	notably	notably	ADV
ejpam-5703	40	2	,	,	PUNCT
ejpam-5703	40	3	a	a	DET
ejpam-5703	40	4	large	large	ADJ
ejpam-5703	40	5	number	number	NOUN
ejpam-5703	40	6	of	of	ADP
ejpam-5703	40	7	these	these	DET
ejpam-5703	40	8	studies	study	NOUN
ejpam-5703	40	9	outline	outline	VERB
ejpam-5703	40	10	the	the	DET
ejpam-5703	40	11	power	power	NOUN
ejpam-5703	40	12	series	series	NOUN
ejpam-5703	40	13	solution	solution	NOUN
ejpam-5703	40	14	for	for	ADP
ejpam-5703	40	15	these	these	DET
ejpam-5703	40	16	kinds	kind	NOUN
ejpam-5703	40	17	of	of	ADP
ejpam-5703	40	18	issues	issue	NOUN
ejpam-5703	40	19	.	.	PUNCT
ejpam-5703	41	1	[	[	X
ejpam-5703	41	2	18	18	NUM
ejpam-5703	41	3	]	]	PUNCT
ejpam-5703	41	4	.	.	PUNCT
ejpam-5703	42	1	sometimes	sometimes	ADV
ejpam-5703	42	2	,	,	PUNCT
ejpam-5703	42	3	for	for	ADP
ejpam-5703	42	4	certain	certain	ADJ
ejpam-5703	42	5	values	value	NOUN
ejpam-5703	42	6	of	of	ADP
ejpam-5703	42	7	step	step	NOUN
ejpam-5703	42	8	size	size	NOUN
ejpam-5703	42	9	,	,	PUNCT
ejpam-5703	42	10	positivity	positivity	NOUN
ejpam-5703	42	11	of	of	ADP
ejpam-5703	42	12	solutions	solution	NOUN
ejpam-5703	42	13	and	and	CCONJ
ejpam-5703	42	14	the	the	DET
ejpam-5703	42	15	boundedb	boundedb	NOUN
ejpam-5703	42	16	.	.	PUNCT
ejpam-5703	43	1	rehman	rehman	NOUN
ejpam-5703	43	2	et	et	PROPN
ejpam-5703	43	3	al	al	PROPN
ejpam-5703	43	4	.	.	PUNCT
ejpam-5703	43	5	/	/	SYM
ejpam-5703	43	6	eur	eur	PROPN
ejpam-5703	43	7	.	.	PUNCT
ejpam-5703	44	1	j.	j.	PROPN
ejpam-5703	44	2	pure	pure	PROPN
ejpam-5703	44	3	appl	appl	PROPN
ejpam-5703	44	4	.	.	PROPN
ejpam-5703	44	5	math	math	PROPN
ejpam-5703	44	6	,	,	PUNCT
ejpam-5703	44	7	18	18	NUM
ejpam-5703	44	8	(	(	PUNCT
ejpam-5703	44	9	2	2	NUM
ejpam-5703	44	10	)	)	PUNCT
ejpam-5703	44	11	(	(	PUNCT
ejpam-5703	44	12	2025	2025	NUM
ejpam-5703	44	13	)	)	PUNCT
ejpam-5703	44	14	,	,	PUNCT
ejpam-5703	44	15	5703	5703	NUM
ejpam-5703	44	16	3	3	NUM
ejpam-5703	44	17	of	of	ADP
ejpam-5703	44	18	16	16	NUM
ejpam-5703	44	19	ness	ness	NOUN
ejpam-5703	44	20	loses	lose	VERB
ejpam-5703	44	21	by	by	ADP
ejpam-5703	44	22	these	these	DET
ejpam-5703	44	23	methods	method	NOUN
ejpam-5703	44	24	.	.	PUNCT
ejpam-5703	45	1	in	in	ADP
ejpam-5703	45	2	[	[	X
ejpam-5703	45	3	22	22	NUM
ejpam-5703	45	4	]	]	X
ejpam-5703	45	5	f.	f.	PROPN
ejpam-5703	45	6	m.	m.	PROPN
ejpam-5703	45	7	fernndez	fernndez	PROPN
ejpam-5703	45	8	has	have	AUX
ejpam-5703	45	9	stated	state	VERB
ejpam-5703	45	10	that	that	SCONJ
ejpam-5703	45	11	for	for	ADP
ejpam-5703	45	12	the	the	DET
ejpam-5703	45	13	non	non	ADJ
ejpam-5703	45	14	-	-	ADJ
ejpam-5703	45	15	linear	linear	ADJ
ejpam-5703	45	16	differential	differential	ADJ
ejpam-5703	45	17	equations	equation	NOUN
ejpam-5703	45	18	(	(	PUNCT
ejpam-5703	45	19	vapa	vapa	ADJ
ejpam-5703	45	20	)	)	PUNCT
ejpam-5703	45	21	methods	method	NOUN
ejpam-5703	45	22	are	be	AUX
ejpam-5703	45	23	not	not	PART
ejpam-5703	45	24	suitable	suitable	ADJ
ejpam-5703	45	25	.	.	PUNCT
ejpam-5703	46	1	in	in	ADP
ejpam-5703	46	2	his	his	PRON
ejpam-5703	46	3	paper	paper	NOUN
ejpam-5703	46	4	,	,	PUNCT
ejpam-5703	46	5	he	he	PRON
ejpam-5703	46	6	stated	state	VERB
ejpam-5703	46	7	that	that	SCONJ
ejpam-5703	46	8	these	these	DET
ejpam-5703	46	9	methods	method	NOUN
ejpam-5703	46	10	converges	converge	VERB
ejpam-5703	46	11	conditionally	conditionally	ADV
ejpam-5703	46	12	that	that	PRON
ejpam-5703	46	13	depends	depend	VERB
ejpam-5703	46	14	upon	upon	SCONJ
ejpam-5703	46	15	the	the	DET
ejpam-5703	46	16	step	step	NOUN
ejpam-5703	46	17	sizes	size	NOUN
ejpam-5703	46	18	and	and	CCONJ
ejpam-5703	46	19	initial	initial	ADJ
ejpam-5703	46	20	conditions	condition	NOUN
ejpam-5703	46	21	.	.	PUNCT
ejpam-5703	47	1	samia	samia	PROPN
ejpam-5703	47	2	riaz	riaz	PROPN
ejpam-5703	47	3	et	et	PROPN
ejpam-5703	47	4	al	al	PROPN
ejpam-5703	47	5	in	in	ADP
ejpam-5703	47	6	[	[	X
ejpam-5703	47	7	23	23	NUM
ejpam-5703	47	8	]	]	PUNCT
ejpam-5703	47	9	has	have	AUX
ejpam-5703	47	10	mentioned	mention	VERB
ejpam-5703	47	11	that	that	SCONJ
ejpam-5703	47	12	nsfd	nsfd	ADJ
ejpam-5703	47	13	-	-	PUNCT
ejpam-5703	47	14	pc	pc	NOUN
ejpam-5703	47	15	scheme	scheme	NOUN
ejpam-5703	47	16	is	be	AUX
ejpam-5703	47	17	more	more	ADV
ejpam-5703	47	18	reliable	reliable	ADJ
ejpam-5703	47	19	and	and	CCONJ
ejpam-5703	47	20	accurate	accurate	ADJ
ejpam-5703	47	21	as	as	SCONJ
ejpam-5703	47	22	compared	compare	VERB
ejpam-5703	47	23	to	to	PART
ejpam-5703	47	24	euler	euler	VERB
ejpam-5703	47	25	method	method	NOUN
ejpam-5703	47	26	and	and	CCONJ
ejpam-5703	47	27	rk-4	rk-4	ADP
ejpam-5703	47	28	to	to	PART
ejpam-5703	47	29	solve	solve	VERB
ejpam-5703	47	30	nonlinear	nonlinear	ADJ
ejpam-5703	47	31	quadratic	quadratic	ADJ
ejpam-5703	47	32	differential	differential	NOUN
ejpam-5703	47	33	equation	equation	NOUN
ejpam-5703	47	34	.	.	PUNCT
ejpam-5703	48	1	to	to	PART
ejpam-5703	48	2	address	address	VERB
ejpam-5703	48	3	these	these	DET
ejpam-5703	48	4	shortcomings	shortcoming	NOUN
ejpam-5703	48	5	,	,	PUNCT
ejpam-5703	48	6	this	this	DET
ejpam-5703	48	7	work	work	NOUN
ejpam-5703	48	8	proposes	propose	VERB
ejpam-5703	48	9	a	a	DET
ejpam-5703	48	10	more	more	ADV
ejpam-5703	48	11	robust	robust	ADJ
ejpam-5703	48	12	alternative	alternative	NOUN
ejpam-5703	48	13	:	:	PUNCT
ejpam-5703	48	14	the	the	DET
ejpam-5703	48	15	nsfd	nsfd	ADJ
ejpam-5703	48	16	-	-	PUNCT
ejpam-5703	48	17	pc	pc	NOUN
ejpam-5703	48	18	technique	technique	NOUN
ejpam-5703	48	19	.	.	PUNCT
ejpam-5703	49	1	mickens	micken	NOUN
ejpam-5703	49	2	pioneered	pioneer	VERB
ejpam-5703	49	3	nsfd	nsfd	ADJ
ejpam-5703	49	4	-	-	PUNCT
ejpam-5703	49	5	pc	pc	NOUN
ejpam-5703	49	6	approaches	approach	NOUN
ejpam-5703	49	7	,	,	PUNCT
ejpam-5703	49	8	which	which	PRON
ejpam-5703	49	9	are	be	AUX
ejpam-5703	49	10	notable	notable	ADJ
ejpam-5703	49	11	for	for	ADP
ejpam-5703	49	12	preserving	preserve	VERB
ejpam-5703	49	13	important	important	ADJ
ejpam-5703	49	14	characteristics	characteristic	NOUN
ejpam-5703	49	15	of	of	ADP
ejpam-5703	49	16	the	the	DET
ejpam-5703	49	17	original	original	ADJ
ejpam-5703	49	18	differential	differential	ADJ
ejpam-5703	49	19	equations	equation	NOUN
ejpam-5703	49	20	.	.	PUNCT
ejpam-5703	50	1	our	our	PRON
ejpam-5703	50	2	technique	technique	NOUN
ejpam-5703	50	3	builds	build	VERB
ejpam-5703	50	4	on	on	ADP
ejpam-5703	50	5	this	this	DET
ejpam-5703	50	6	principle	principle	NOUN
ejpam-5703	50	7	by	by	ADP
ejpam-5703	50	8	creating	create	VERB
ejpam-5703	50	9	an	an	DET
ejpam-5703	50	10	unconditionally	unconditionally	ADV
ejpam-5703	50	11	stable	stable	ADJ
ejpam-5703	50	12	nsfd	nsfd	ADJ
ejpam-5703	50	13	-	-	PUNCT
ejpam-5703	50	14	pc	pc	NOUN
ejpam-5703	50	15	scheme	scheme	NOUN
ejpam-5703	50	16	for	for	ADP
ejpam-5703	50	17	nonlinear	nonlinear	ADJ
ejpam-5703	50	18	quadratic	quadratic	ADJ
ejpam-5703	50	19	riccati	riccati	NOUN
ejpam-5703	50	20	differential	differential	NOUN
ejpam-5703	50	21	equations	equation	NOUN
ejpam-5703	50	22	.	.	PUNCT
ejpam-5703	51	1	unlike	unlike	ADP
ejpam-5703	51	2	existing	exist	VERB
ejpam-5703	51	3	methods	method	NOUN
ejpam-5703	51	4	,	,	PUNCT
ejpam-5703	51	5	our	our	PRON
ejpam-5703	51	6	scheme	scheme	NOUN
ejpam-5703	51	7	assures	assure	VERB
ejpam-5703	51	8	first	first	ADJ
ejpam-5703	51	9	-	-	PUNCT
ejpam-5703	51	10	order	order	NOUN
ejpam-5703	51	11	temporal	temporal	ADJ
ejpam-5703	51	12	precision	precision	NOUN
ejpam-5703	51	13	,	,	PUNCT
ejpam-5703	51	14	preserves	preserve	VERB
ejpam-5703	51	15	crucial	crucial	ADJ
ejpam-5703	51	16	aspects	aspect	NOUN
ejpam-5703	51	17	of	of	ADP
ejpam-5703	51	18	the	the	DET
ejpam-5703	51	19	precise	precise	ADJ
ejpam-5703	51	20	solution	solution	NOUN
ejpam-5703	51	21	such	such	ADJ
ejpam-5703	51	22	as	as	ADP
ejpam-5703	51	23	positivity	positivity	NOUN
ejpam-5703	51	24	and	and	CCONJ
ejpam-5703	51	25	boundedness	boundedness	NOUN
ejpam-5703	51	26	,	,	PUNCT
ejpam-5703	51	27	and	and	CCONJ
ejpam-5703	51	28	is	be	AUX
ejpam-5703	51	29	stable	stable	ADJ
ejpam-5703	51	30	across	across	ADP
ejpam-5703	51	31	a	a	DET
ejpam-5703	51	32	wide	wide	ADJ
ejpam-5703	51	33	range	range	NOUN
ejpam-5703	51	34	of	of	ADP
ejpam-5703	51	35	step	step	NOUN
ejpam-5703	51	36	sizes	size	NOUN
ejpam-5703	51	37	.	.	PUNCT
ejpam-5703	52	1	it	it	PRON
ejpam-5703	52	2	convergences	convergence	VERB
ejpam-5703	52	3	accurately	accurately	ADV
ejpam-5703	52	4	and	and	CCONJ
ejpam-5703	52	5	for	for	ADP
ejpam-5703	52	6	the	the	DET
ejpam-5703	52	7	differential	differential	ADJ
ejpam-5703	52	8	equations	equation	NOUN
ejpam-5703	52	9	it	it	PRON
ejpam-5703	52	10	preserves	preserve	VERB
ejpam-5703	52	11	important	important	ADJ
ejpam-5703	52	12	properties	property	NOUN
ejpam-5703	52	13	of	of	ADP
ejpam-5703	52	14	exact	exact	ADJ
ejpam-5703	52	15	solutions	solution	NOUN
ejpam-5703	52	16	.	.	PUNCT
ejpam-5703	53	1	this	this	DET
ejpam-5703	53	2	method	method	NOUN
ejpam-5703	53	3	shows	show	VERB
ejpam-5703	53	4	the	the	DET
ejpam-5703	53	5	numerical	numerical	ADJ
ejpam-5703	53	6	stability	stability	NOUN
ejpam-5703	53	7	for	for	ADP
ejpam-5703	53	8	different	different	ADJ
ejpam-5703	53	9	step	step	NOUN
ejpam-5703	53	10	sizes	size	NOUN
ejpam-5703	53	11	,	,	PUNCT
ejpam-5703	53	12	whereas	whereas	SCONJ
ejpam-5703	53	13	for	for	ADP
ejpam-5703	53	14	larger	large	ADJ
ejpam-5703	53	15	step	step	NOUN
ejpam-5703	53	16	sizes	size	NOUN
ejpam-5703	53	17	other	other	ADJ
ejpam-5703	53	18	standard	standard	ADJ
ejpam-5703	53	19	techniques	technique	NOUN
ejpam-5703	53	20	lose	lose	VERB
ejpam-5703	53	21	stability	stability	NOUN
ejpam-5703	53	22	and	and	CCONJ
ejpam-5703	53	23	do	do	AUX
ejpam-5703	53	24	not	not	PART
ejpam-5703	53	25	converges	converge	VERB
ejpam-5703	53	26	to	to	ADP
ejpam-5703	53	27	right	right	ADJ
ejpam-5703	53	28	solution	solution	NOUN
ejpam-5703	53	29	.	.	PUNCT
ejpam-5703	54	1	this	this	PRON
ejpam-5703	54	2	is	be	AUX
ejpam-5703	54	3	the	the	DET
ejpam-5703	54	4	structure	structure	NOUN
ejpam-5703	54	5	of	of	ADP
ejpam-5703	54	6	the	the	DET
ejpam-5703	54	7	remainder	remainder	NOUN
ejpam-5703	54	8	of	of	ADP
ejpam-5703	54	9	the	the	DET
ejpam-5703	54	10	paper	paper	NOUN
ejpam-5703	54	11	:	:	PUNCT
ejpam-5703	54	12	in	in	ADP
ejpam-5703	54	13	section	section	NOUN
ejpam-5703	54	14	2	2	NUM
ejpam-5703	54	15	,	,	PUNCT
ejpam-5703	54	16	the	the	DET
ejpam-5703	54	17	theoretical	theoretical	ADJ
ejpam-5703	54	18	background	background	NOUN
ejpam-5703	54	19	of	of	ADP
ejpam-5703	54	20	the	the	DET
ejpam-5703	54	21	suggested	suggest	VERB
ejpam-5703	54	22	nsfd	nsfd	ADJ
ejpam-5703	54	23	-	-	PUNCT
ejpam-5703	54	24	pc	pc	NOUN
ejpam-5703	54	25	system	system	NOUN
ejpam-5703	54	26	is	be	AUX
ejpam-5703	54	27	explained	explain	VERB
ejpam-5703	54	28	,	,	PUNCT
ejpam-5703	54	29	along	along	ADP
ejpam-5703	54	30	with	with	ADP
ejpam-5703	54	31	the	the	DET
ejpam-5703	54	32	numerical	numerical	ADJ
ejpam-5703	54	33	method	method	NOUN
ejpam-5703	54	34	.	.	PUNCT
ejpam-5703	55	1	section	section	NOUN
ejpam-5703	55	2	3	3	NUM
ejpam-5703	55	3	digs	dig	VERB
ejpam-5703	55	4	into	into	ADP
ejpam-5703	55	5	the	the	DET
ejpam-5703	55	6	predictor	predictor	NOUN
ejpam-5703	55	7	component	component	NOUN
ejpam-5703	55	8	of	of	ADP
ejpam-5703	55	9	the	the	DET
ejpam-5703	55	10	nsfd	nsfd	ADJ
ejpam-5703	55	11	method	method	NOUN
ejpam-5703	55	12	,	,	PUNCT
ejpam-5703	55	13	outlining	outline	VERB
ejpam-5703	55	14	its	its	PRON
ejpam-5703	55	15	development	development	NOUN
ejpam-5703	55	16	and	and	CCONJ
ejpam-5703	55	17	execution	execution	NOUN
ejpam-5703	55	18	.	.	PUNCT
ejpam-5703	56	1	section	section	NOUN
ejpam-5703	56	2	4	4	NUM
ejpam-5703	56	3	delves	delf	NOUN
ejpam-5703	56	4	into	into	ADP
ejpam-5703	56	5	the	the	DET
ejpam-5703	56	6	riccati	riccati	PROPN
ejpam-5703	56	7	differential	differential	PROPN
ejpam-5703	56	8	equation	equation	NOUN
ejpam-5703	56	9	,	,	PUNCT
ejpam-5703	56	10	exploring	explore	VERB
ejpam-5703	56	11	its	its	PRON
ejpam-5703	56	12	significance	significance	NOUN
ejpam-5703	56	13	and	and	CCONJ
ejpam-5703	56	14	the	the	DET
ejpam-5703	56	15	difficulties	difficulty	NOUN
ejpam-5703	56	16	involved	involve	VERB
ejpam-5703	56	17	in	in	ADP
ejpam-5703	56	18	numerically	numerically	ADV
ejpam-5703	56	19	solving	solve	VERB
ejpam-5703	56	20	it	it	PRON
ejpam-5703	56	21	.	.	PUNCT
ejpam-5703	57	1	in	in	ADP
ejpam-5703	57	2	section	section	NOUN
ejpam-5703	57	3	5	5	NUM
ejpam-5703	57	4	,	,	PUNCT
ejpam-5703	57	5	we	we	PRON
ejpam-5703	57	6	apply	apply	VERB
ejpam-5703	57	7	the	the	DET
ejpam-5703	57	8	nsfd	nsfd	ADJ
ejpam-5703	57	9	-	-	PUNCT
ejpam-5703	57	10	pc	pc	NOUN
ejpam-5703	57	11	approach	approach	NOUN
ejpam-5703	57	12	to	to	ADP
ejpam-5703	57	13	the	the	DET
ejpam-5703	57	14	riccati	riccati	PROPN
ejpam-5703	57	15	equation	equation	NOUN
ejpam-5703	57	16	,	,	PUNCT
ejpam-5703	57	17	demonstrating	demonstrate	VERB
ejpam-5703	57	18	how	how	SCONJ
ejpam-5703	57	19	this	this	DET
ejpam-5703	57	20	method	method	NOUN
ejpam-5703	57	21	effectively	effectively	ADV
ejpam-5703	57	22	tackles	tackle	VERB
ejpam-5703	57	23	nonlinearity	nonlinearity	NOUN
ejpam-5703	57	24	.	.	PUNCT
ejpam-5703	58	1	section	section	NOUN
ejpam-5703	58	2	6	6	NUM
ejpam-5703	58	3	contains	contain	VERB
ejpam-5703	58	4	the	the	DET
ejpam-5703	58	5	results	result	NOUN
ejpam-5703	58	6	and	and	CCONJ
ejpam-5703	58	7	discussion	discussion	NOUN
ejpam-5703	58	8	,	,	PUNCT
ejpam-5703	58	9	which	which	PRON
ejpam-5703	58	10	compare	compare	VERB
ejpam-5703	58	11	the	the	DET
ejpam-5703	58	12	accuracy	accuracy	NOUN
ejpam-5703	58	13	and	and	CCONJ
ejpam-5703	58	14	stability	stability	NOUN
ejpam-5703	58	15	of	of	ADP
ejpam-5703	58	16	the	the	DET
ejpam-5703	58	17	proposed	propose	VERB
ejpam-5703	58	18	scheme	scheme	NOUN
ejpam-5703	58	19	to	to	ADP
ejpam-5703	58	20	traditional	traditional	ADJ
ejpam-5703	58	21	methods	method	NOUN
ejpam-5703	58	22	.	.	PUNCT
ejpam-5703	59	1	the	the	DET
ejpam-5703	59	2	concluding	concluding	NOUN
ejpam-5703	59	3	remarks	remark	NOUN
ejpam-5703	59	4	are	be	AUX
ejpam-5703	59	5	discuss	discus	VERB
ejpam-5703	59	6	in	in	ADP
ejpam-5703	59	7	section	section	NOUN
ejpam-5703	59	8	7	7	NUM
ejpam-5703	59	9	.	.	SYM
ejpam-5703	59	10	2	2	NUM
ejpam-5703	59	11	.	.	NOUN
ejpam-5703	59	12	numerical	numerical	PROPN
ejpam-5703	59	13	method	method	PROPN
ejpam-5703	59	14	ronald	ronald	PROPN
ejpam-5703	59	15	e.	e.	PROPN
ejpam-5703	59	16	mickens	mickens	PROPN
ejpam-5703	59	17	developed	develop	VERB
ejpam-5703	59	18	the	the	DET
ejpam-5703	59	19	nsfd	nsfd	ADJ
ejpam-5703	59	20	-	-	PUNCT
ejpam-5703	59	21	pc	pc	NOUN
ejpam-5703	59	22	method	method	NOUN
ejpam-5703	59	23	for	for	ADP
ejpam-5703	59	24	the	the	DET
ejpam-5703	59	25	numerical	numerical	ADJ
ejpam-5703	59	26	solution	solution	NOUN
ejpam-5703	59	27	of	of	ADP
ejpam-5703	59	28	differential	differential	ADJ
ejpam-5703	59	29	equations	equation	NOUN
ejpam-5703	60	1	[	[	X
ejpam-5703	60	2	18	18	NUM
ejpam-5703	60	3	]	]	PUNCT
ejpam-5703	60	4	.	.	PUNCT
ejpam-5703	61	1	other	other	ADJ
ejpam-5703	61	2	standard	standard	ADJ
ejpam-5703	61	3	numerical	numerical	ADJ
ejpam-5703	61	4	methods	method	NOUN
ejpam-5703	61	5	occasionally	occasionally	ADV
ejpam-5703	61	6	produce	produce	VERB
ejpam-5703	61	7	unsteadiness	unsteadiness	NOUN
ejpam-5703	61	8	for	for	ADP
ejpam-5703	61	9	larger	large	ADJ
ejpam-5703	61	10	step	step	NOUN
ejpam-5703	61	11	sizes	size	NOUN
ejpam-5703	61	12	,	,	PUNCT
ejpam-5703	61	13	such	such	ADJ
ejpam-5703	61	14	as	as	ADP
ejpam-5703	61	15	the	the	DET
ejpam-5703	61	16	euler	euler	PROPN
ejpam-5703	61	17	predictor	predictor	PROPN
ejpam-5703	61	18	corrector	corrector	NOUN
ejpam-5703	61	19	method	method	NOUN
ejpam-5703	61	20	[	[	X
ejpam-5703	61	21	24	24	NUM
ejpam-5703	61	22	]	]	PUNCT
ejpam-5703	61	23	.	.	PUNCT
ejpam-5703	62	1	the	the	DET
ejpam-5703	62	2	”	"	PUNCT
ejpam-5703	62	3	nsfd	nsfd	ADJ
ejpam-5703	62	4	-	-	PUNCT
ejpam-5703	62	5	pc	pc	NOUN
ejpam-5703	62	6	method	method	NOUN
ejpam-5703	62	7	”	"	PUNCT
ejpam-5703	62	8	is	be	AUX
ejpam-5703	62	9	a	a	DET
ejpam-5703	62	10	numerical	numerical	ADJ
ejpam-5703	62	11	system	system	NOUN
ejpam-5703	62	12	that	that	PRON
ejpam-5703	62	13	has	have	AUX
ejpam-5703	62	14	been	be	AUX
ejpam-5703	62	15	developed	develop	VERB
ejpam-5703	62	16	to	to	PART
ejpam-5703	62	17	prevent	prevent	VERB
ejpam-5703	62	18	these	these	DET
ejpam-5703	62	19	kinds	kind	NOUN
ejpam-5703	62	20	of	of	ADP
ejpam-5703	62	21	numerical	numerical	ADJ
ejpam-5703	62	22	instabilities	instability	NOUN
ejpam-5703	62	23	.	.	PUNCT
ejpam-5703	63	1	the	the	DET
ejpam-5703	63	2	nsfd	nsfd	ADJ
ejpam-5703	63	3	-	-	PUNCT
ejpam-5703	63	4	pc	pc	NOUN
ejpam-5703	63	5	scheme	scheme	NOUN
ejpam-5703	63	6	’s	’s	PART
ejpam-5703	63	7	structure	structure	NOUN
ejpam-5703	63	8	is	be	AUX
ejpam-5703	63	9	responsible	responsible	ADJ
ejpam-5703	63	10	for	for	ADP
ejpam-5703	63	11	its	its	PRON
ejpam-5703	63	12	stability	stability	NOUN
ejpam-5703	63	13	and	and	CCONJ
ejpam-5703	63	14	positively	positively	ADV
ejpam-5703	63	15	for	for	ADP
ejpam-5703	63	16	big	big	ADJ
ejpam-5703	63	17	step	step	NOUN
ejpam-5703	63	18	sizes	size	NOUN
ejpam-5703	63	19	.	.	PUNCT
ejpam-5703	64	1	the	the	DET
ejpam-5703	64	2	predictor	predictor	NOUN
ejpam-5703	64	3	and	and	CCONJ
ejpam-5703	64	4	corrector	corrector	NOUN
ejpam-5703	64	5	are	be	AUX
ejpam-5703	64	6	the	the	DET
ejpam-5703	64	7	two	two	NUM
ejpam-5703	64	8	main	main	ADJ
ejpam-5703	64	9	steps	step	NOUN
ejpam-5703	64	10	in	in	ADP
ejpam-5703	64	11	the	the	DET
ejpam-5703	64	12	nsfd	nsfd	ADJ
ejpam-5703	64	13	-	-	PUNCT
ejpam-5703	64	14	pc	pc	NOUN
ejpam-5703	64	15	technique	technique	NOUN
ejpam-5703	64	16	.	.	PUNCT
ejpam-5703	65	1	the	the	DET
ejpam-5703	65	2	predictor	predictor	NOUN
ejpam-5703	65	3	phase	phase	NOUN
ejpam-5703	65	4	gives	give	VERB
ejpam-5703	65	5	an	an	DET
ejpam-5703	65	6	initial	initial	ADJ
ejpam-5703	65	7	solution	solution	NOUN
ejpam-5703	65	8	estimate	estimate	NOUN
ejpam-5703	65	9	,	,	PUNCT
ejpam-5703	65	10	which	which	PRON
ejpam-5703	65	11	is	be	AUX
ejpam-5703	65	12	then	then	ADV
ejpam-5703	65	13	refined	refine	VERB
ejpam-5703	65	14	by	by	ADP
ejpam-5703	65	15	the	the	DET
ejpam-5703	65	16	corrector	corrector	NOUN
ejpam-5703	65	17	step	step	NOUN
ejpam-5703	65	18	,	,	PUNCT
ejpam-5703	65	19	which	which	PRON
ejpam-5703	65	20	includes	include	VERB
ejpam-5703	65	21	additional	additional	ADJ
ejpam-5703	65	22	terms	term	NOUN
ejpam-5703	65	23	to	to	PART
ejpam-5703	65	24	improve	improve	VERB
ejpam-5703	65	25	accuracy	accuracy	NOUN
ejpam-5703	65	26	and	and	CCONJ
ejpam-5703	65	27	stability	stability	NOUN
ejpam-5703	65	28	.	.	PUNCT
ejpam-5703	66	1	this	this	DET
ejpam-5703	66	2	two	two	NUM
ejpam-5703	66	3	-	-	PUNCT
ejpam-5703	66	4	stage	stage	NOUN
ejpam-5703	66	5	procedure	procedure	NOUN
ejpam-5703	66	6	enables	enable	VERB
ejpam-5703	66	7	the	the	DET
ejpam-5703	66	8	method	method	NOUN
ejpam-5703	66	9	to	to	PART
ejpam-5703	66	10	effectively	effectively	ADV
ejpam-5703	66	11	tackle	tackle	VERB
ejpam-5703	66	12	the	the	DET
ejpam-5703	66	13	complexities	complexity	NOUN
ejpam-5703	66	14	of	of	ADP
ejpam-5703	66	15	nonlinear	nonlinear	ADJ
ejpam-5703	66	16	differential	differential	ADJ
ejpam-5703	66	17	equations	equation	NOUN
ejpam-5703	66	18	,	,	PUNCT
ejpam-5703	66	19	including	include	VERB
ejpam-5703	66	20	bigger	big	ADJ
ejpam-5703	66	21	step	step	NOUN
ejpam-5703	66	22	sizes	size	NOUN
ejpam-5703	66	23	where	where	SCONJ
ejpam-5703	66	24	typical	typical	ADJ
ejpam-5703	66	25	methods	method	NOUN
ejpam-5703	66	26	fail	fail	VERB
ejpam-5703	66	27	.	.	PUNCT
ejpam-5703	67	1	when	when	SCONJ
ejpam-5703	67	2	developing	develop	VERB
ejpam-5703	67	3	the	the	DET
ejpam-5703	67	4	nsfd	nsfd	ADJ
ejpam-5703	67	5	-	-	PUNCT
ejpam-5703	67	6	pc	pc	NOUN
ejpam-5703	67	7	scheme	scheme	NOUN
ejpam-5703	67	8	,	,	PUNCT
ejpam-5703	67	9	we	we	PRON
ejpam-5703	67	10	assume	assume	VERB
ejpam-5703	67	11	the	the	DET
ejpam-5703	67	12	following	follow	VERB
ejpam-5703	67	13	:	:	PUNCT
ejpam-5703	67	14	•	•	ADP
ejpam-5703	67	15	the	the	DET
ejpam-5703	67	16	differential	differential	ADJ
ejpam-5703	67	17	equation	equation	NOUN
ejpam-5703	67	18	under	under	ADP
ejpam-5703	67	19	discussion	discussion	NOUN
ejpam-5703	67	20	is	be	AUX
ejpam-5703	67	21	first	first	ADJ
ejpam-5703	67	22	-	-	PUNCT
ejpam-5703	67	23	order	order	NOUN
ejpam-5703	67	24	and	and	CCONJ
ejpam-5703	67	25	nonlinear	nonlinear	ADJ
ejpam-5703	67	26	,	,	PUNCT
ejpam-5703	67	27	as	as	SCONJ
ejpam-5703	67	28	is	be	AUX
ejpam-5703	67	29	common	common	ADJ
ejpam-5703	67	30	for	for	ADP
ejpam-5703	67	31	riccati	riccati	NOUN
ejpam-5703	67	32	-	-	PUNCT
ejpam-5703	67	33	type	type	NOUN
ejpam-5703	67	34	problems	problem	NOUN
ejpam-5703	67	35	.	.	PUNCT
ejpam-5703	68	1	b.	b.	PROPN
ejpam-5703	68	2	rehman	rehman	PROPN
ejpam-5703	68	3	et	et	PROPN
ejpam-5703	68	4	al	al	PROPN
ejpam-5703	68	5	.	.	PUNCT
ejpam-5703	68	6	/	/	SYM
ejpam-5703	68	7	eur	eur	PROPN
ejpam-5703	68	8	.	.	PUNCT
ejpam-5703	69	1	j.	j.	PROPN
ejpam-5703	69	2	pure	pure	PROPN
ejpam-5703	69	3	appl	appl	PROPN
ejpam-5703	69	4	.	.	PROPN
ejpam-5703	69	5	math	math	PROPN
ejpam-5703	69	6	,	,	PUNCT
ejpam-5703	69	7	18	18	NUM
ejpam-5703	69	8	(	(	PUNCT
ejpam-5703	69	9	2	2	NUM
ejpam-5703	69	10	)	)	PUNCT
ejpam-5703	69	11	(	(	PUNCT
ejpam-5703	69	12	2025	2025	NUM
ejpam-5703	69	13	)	)	PUNCT
ejpam-5703	69	14	,	,	PUNCT
ejpam-5703	69	15	5703	5703	NUM
ejpam-5703	69	16	4	4	NUM
ejpam-5703	69	17	of	of	ADP
ejpam-5703	69	18	16	16	NUM
ejpam-5703	69	19	•	•	NOUN
ejpam-5703	69	20	the	the	DET
ejpam-5703	69	21	solution	solution	NOUN
ejpam-5703	69	22	remains	remain	VERB
ejpam-5703	69	23	bounded	bounded	ADJ
ejpam-5703	69	24	and	and	CCONJ
ejpam-5703	69	25	positive	positive	ADJ
ejpam-5703	69	26	,	,	PUNCT
ejpam-5703	69	27	which	which	PRON
ejpam-5703	69	28	are	be	AUX
ejpam-5703	69	29	characteristics	characteristic	NOUN
ejpam-5703	69	30	that	that	SCONJ
ejpam-5703	69	31	our	our	PRON
ejpam-5703	69	32	strategy	strategy	NOUN
ejpam-5703	69	33	is	be	AUX
ejpam-5703	69	34	intended	intend	VERB
ejpam-5703	69	35	to	to	PART
ejpam-5703	69	36	retain	retain	VERB
ejpam-5703	69	37	.	.	PUNCT
ejpam-5703	70	1	•	•	NUM
ejpam-5703	70	2	the	the	DET
ejpam-5703	70	3	method	method	NOUN
ejpam-5703	70	4	’s	’s	PART
ejpam-5703	70	5	step	step	NOUN
ejpam-5703	70	6	size	size	NOUN
ejpam-5703	70	7	h	h	NOUN
ejpam-5703	70	8	is	be	AUX
ejpam-5703	70	9	chosen	choose	VERB
ejpam-5703	70	10	to	to	PART
ejpam-5703	70	11	ensure	ensure	VERB
ejpam-5703	70	12	unconditional	unconditional	ADJ
ejpam-5703	70	13	stability	stability	NOUN
ejpam-5703	70	14	,	,	PUNCT
ejpam-5703	70	15	which	which	PRON
ejpam-5703	70	16	is	be	AUX
ejpam-5703	70	17	a	a	DET
ejpam-5703	70	18	substantial	substantial	ADJ
ejpam-5703	70	19	improvement	improvement	NOUN
ejpam-5703	70	20	over	over	ADP
ejpam-5703	70	21	traditional	traditional	ADJ
ejpam-5703	70	22	approaches	approach	NOUN
ejpam-5703	70	23	that	that	PRON
ejpam-5703	70	24	demand	demand	VERB
ejpam-5703	70	25	modest	modest	ADJ
ejpam-5703	70	26	step	step	NOUN
ejpam-5703	70	27	sizes	size	NOUN
ejpam-5703	70	28	for	for	ADP
ejpam-5703	70	29	stability	stability	NOUN
ejpam-5703	70	30	.	.	PUNCT
ejpam-5703	71	1	2.1	2.1	NUM
ejpam-5703	71	2	.	.	PUNCT
ejpam-5703	71	3	construction	construction	NOUN
ejpam-5703	71	4	of	of	ADP
ejpam-5703	71	5	the	the	DET
ejpam-5703	71	6	nsfd	nsfd	ADJ
ejpam-5703	71	7	-	-	PUNCT
ejpam-5703	71	8	pc	pc	NOUN
ejpam-5703	71	9	method	method	NOUN
ejpam-5703	71	10	the	the	DET
ejpam-5703	71	11	nsfd	nsfd	ADJ
ejpam-5703	71	12	-	-	PUNCT
ejpam-5703	71	13	pc	pc	NOUN
ejpam-5703	71	14	method	method	NOUN
ejpam-5703	71	15	is	be	AUX
ejpam-5703	71	16	built	build	VERB
ejpam-5703	71	17	on	on	ADP
ejpam-5703	71	18	carefully	carefully	ADV
ejpam-5703	71	19	developed	develop	VERB
ejpam-5703	71	20	principles	principle	NOUN
ejpam-5703	71	21	that	that	PRON
ejpam-5703	71	22	distinguish	distinguish	VERB
ejpam-5703	71	23	it	it	PRON
ejpam-5703	71	24	from	from	ADP
ejpam-5703	71	25	traditional	traditional	ADJ
ejpam-5703	71	26	finite	finite	ADJ
ejpam-5703	71	27	difference	difference	NOUN
ejpam-5703	71	28	systems	system	NOUN
ejpam-5703	71	29	.	.	PUNCT
ejpam-5703	72	1	the	the	DET
ejpam-5703	72	2	discrete	discrete	ADJ
ejpam-5703	72	3	model	model	NOUN
ejpam-5703	72	4	is	be	AUX
ejpam-5703	72	5	constructed	construct	VERB
ejpam-5703	72	6	as	as	SCONJ
ejpam-5703	72	7	follows	follow	VERB
ejpam-5703	72	8	:	:	PUNCT
ejpam-5703	72	9	•	•	NUM
ejpam-5703	72	10	predictor	predictor	NOUN
ejpam-5703	72	11	step	step	NOUN
ejpam-5703	72	12	:	:	PUNCT
ejpam-5703	72	13	at	at	ADP
ejpam-5703	72	14	this	this	DET
ejpam-5703	72	15	point	point	NOUN
ejpam-5703	72	16	,	,	PUNCT
ejpam-5703	72	17	we	we	PRON
ejpam-5703	72	18	generate	generate	VERB
ejpam-5703	72	19	an	an	DET
ejpam-5703	72	20	initial	initial	ADJ
ejpam-5703	72	21	approximation	approximation	NOUN
ejpam-5703	72	22	y	y	PROPN
ejpam-5703	72	23	(	(	PUNCT
ejpam-5703	72	24	p	p	X
ejpam-5703	72	25	)	)	PUNCT
ejpam-5703	72	26	n+1	n+1	PROPN
ejpam-5703	72	27	of	of	ADP
ejpam-5703	72	28	the	the	DET
ejpam-5703	72	29	solution	solution	NOUN
ejpam-5703	72	30	at	at	ADP
ejpam-5703	72	31	the	the	DET
ejpam-5703	72	32	following	following	ADJ
ejpam-5703	72	33	time	time	NOUN
ejpam-5703	72	34	step	step	NOUN
ejpam-5703	72	35	using	use	VERB
ejpam-5703	72	36	the	the	DET
ejpam-5703	72	37	conventional	conventional	ADJ
ejpam-5703	72	38	nsfd	nsfd	ADJ
ejpam-5703	72	39	scheme	scheme	NOUN
ejpam-5703	72	40	.	.	PUNCT
ejpam-5703	73	1	y	y	NOUN
ejpam-5703	73	2	(	(	PUNCT
ejpam-5703	73	3	p	p	X
ejpam-5703	73	4	)	)	PUNCT
ejpam-5703	73	5	n+1	n+1	PROPN
ejpam-5703	73	6	=	=	SYM
ejpam-5703	73	7	yn	yn	PROPN
ejpam-5703	73	8	+	+	SYM
ejpam-5703	73	9	hf(tn	hf(tn	PROPN
ejpam-5703	73	10	,	,	PUNCT
ejpam-5703	73	11	yn	yn	PROPN
ejpam-5703	73	12	)	)	PUNCT
ejpam-5703	73	13	,	,	PUNCT
ejpam-5703	73	14	where	where	SCONJ
ejpam-5703	73	15	f(tn	f(tn	PROPN
ejpam-5703	73	16	,	,	PUNCT
ejpam-5703	73	17	yn	yn	NOUN
ejpam-5703	73	18	)	)	PUNCT
ejpam-5703	73	19	represents	represent	VERB
ejpam-5703	73	20	the	the	DET
ejpam-5703	73	21	right	right	ADJ
ejpam-5703	73	22	-	-	PUNCT
ejpam-5703	73	23	hand	hand	NOUN
ejpam-5703	73	24	side	side	NOUN
ejpam-5703	73	25	of	of	ADP
ejpam-5703	73	26	the	the	DET
ejpam-5703	73	27	differential	differential	ADJ
ejpam-5703	73	28	equation	equation	NOUN
ejpam-5703	73	29	evaluated	evaluate	VERB
ejpam-5703	73	30	at	at	ADP
ejpam-5703	73	31	(	(	PUNCT
ejpam-5703	73	32	tn	tn	PROPN
ejpam-5703	73	33	,	,	PUNCT
ejpam-5703	73	34	yn	yn	PROPN
ejpam-5703	73	35	)	)	PUNCT
ejpam-5703	73	36	,	,	PUNCT
ejpam-5703	73	37	h	h	PROPN
ejpam-5703	73	38	is	be	AUX
ejpam-5703	73	39	the	the	DET
ejpam-5703	73	40	step	step	NOUN
ejpam-5703	73	41	size	size	NOUN
ejpam-5703	73	42	,	,	PUNCT
ejpam-5703	73	43	and	and	CCONJ
ejpam-5703	73	44	yn	yn	PROPN
ejpam-5703	73	45	is	be	AUX
ejpam-5703	73	46	the	the	DET
ejpam-5703	73	47	function	function	NOUN
ejpam-5703	73	48	value	value	NOUN
ejpam-5703	73	49	.	.	PUNCT
ejpam-5703	74	1	•	•	NUM
ejpam-5703	74	2	corrector	corrector	NOUN
ejpam-5703	74	3	step	step	NOUN
ejpam-5703	74	4	:	:	PUNCT
ejpam-5703	74	5	through	through	ADP
ejpam-5703	74	6	predictor	predictor	NOUN
ejpam-5703	74	7	value	value	NOUN
ejpam-5703	74	8	refinement	refinement	NOUN
ejpam-5703	74	9	,	,	PUNCT
ejpam-5703	74	10	the	the	DET
ejpam-5703	74	11	corrector	corrector	NOUN
ejpam-5703	74	12	step	step	NOUN
ejpam-5703	74	13	increases	increase	VERB
ejpam-5703	74	14	the	the	DET
ejpam-5703	74	15	correctness	correctness	NOUN
ejpam-5703	74	16	of	of	ADP
ejpam-5703	74	17	the	the	DET
ejpam-5703	74	18	answer	answer	NOUN
ejpam-5703	74	19	.	.	PUNCT
ejpam-5703	75	1	to	to	PART
ejpam-5703	75	2	guarantee	guarantee	VERB
ejpam-5703	75	3	stability	stability	NOUN
ejpam-5703	75	4	,	,	PUNCT
ejpam-5703	75	5	we	we	PRON
ejpam-5703	75	6	add	add	VERB
ejpam-5703	75	7	one	one	NUM
ejpam-5703	75	8	more	more	ADJ
ejpam-5703	75	9	term	term	NOUN
ejpam-5703	75	10	:	:	PUNCT
ejpam-5703	75	11	yn+1	yn+1	PROPN
ejpam-5703	75	12	=	=	PUNCT
ejpam-5703	75	13	yn	yn	PROPN
ejpam-5703	75	14	+	+	CCONJ
ejpam-5703	75	15	h	h	NOUN
ejpam-5703	75	16	2	2	NUM
ejpam-5703	75	17	[	[	PUNCT
ejpam-5703	75	18	f(tn	f(tn	PROPN
ejpam-5703	75	19	,	,	PUNCT
ejpam-5703	75	20	yn	yn	PROPN
ejpam-5703	75	21	)	)	PUNCT
ejpam-5703	76	1	+	+	CCONJ
ejpam-5703	77	1	ϵ−1	ϵ−1	PROPN
ejpam-5703	77	2	h	h	NOUN
ejpam-5703	77	3	y	y	PROPN
ejpam-5703	77	4	(	(	PUNCT
ejpam-5703	77	5	p	p	X
ejpam-5703	77	6	)	)	PUNCT
ejpam-5703	77	7	n+1	n+1	PROPN
ejpam-5703	77	8	]	]	PUNCT
ejpam-5703	77	9	,	,	PUNCT
ejpam-5703	77	10	where	where	SCONJ
ejpam-5703	77	11	ϵ	ϵ	PROPN
ejpam-5703	77	12	is	be	AUX
ejpam-5703	77	13	a	a	DET
ejpam-5703	77	14	small	small	ADJ
ejpam-5703	77	15	,	,	PUNCT
ejpam-5703	77	16	positive	positive	ADJ
ejpam-5703	77	17	parameter	parameter	NOUN
ejpam-5703	77	18	that	that	PRON
ejpam-5703	77	19	has	have	AUX
ejpam-5703	77	20	been	be	AUX
ejpam-5703	77	21	selected	select	VERB
ejpam-5703	77	22	to	to	PART
ejpam-5703	77	23	control	control	VERB
ejpam-5703	77	24	the	the	DET
ejpam-5703	77	25	corrector	corrector	NOUN
ejpam-5703	77	26	term	term	NOUN
ejpam-5703	77	27	’s	’s	PART
ejpam-5703	77	28	influence	influence	NOUN
ejpam-5703	77	29	.	.	PUNCT
ejpam-5703	78	1	this	this	DET
ejpam-5703	78	2	modification	modification	NOUN
ejpam-5703	78	3	aids	aid	NOUN
ejpam-5703	78	4	in	in	ADP
ejpam-5703	78	5	solution	solution	NOUN
ejpam-5703	78	6	stabilization	stabilization	NOUN
ejpam-5703	78	7	for	for	ADP
ejpam-5703	78	8	all	all	DET
ejpam-5703	78	9	step	step	NOUN
ejpam-5703	78	10	sizes	size	NOUN
ejpam-5703	78	11	.	.	PUNCT
ejpam-5703	79	1	the	the	DET
ejpam-5703	79	2	corrector	corrector	NOUN
ejpam-5703	79	3	step	step	NOUN
ejpam-5703	79	4	must	must	AUX
ejpam-5703	79	5	contain	contain	VERB
ejpam-5703	79	6	the	the	DET
ejpam-5703	79	7	term	term	NOUN
ejpam-5703	80	1	ϵ−1	ϵ−1	PROPN
ejpam-5703	80	2	h	h	NOUN
ejpam-5703	80	3	y	y	PROPN
ejpam-5703	80	4	(	(	PUNCT
ejpam-5703	80	5	p	p	X
ejpam-5703	80	6	)	)	PUNCT
ejpam-5703	80	7	n+1	n+1	PROPN
ejpam-5703	80	8	to	to	PART
ejpam-5703	80	9	guarantee	guarantee	VERB
ejpam-5703	80	10	that	that	SCONJ
ejpam-5703	80	11	the	the	DET
ejpam-5703	80	12	nsfd	nsfd	ADJ
ejpam-5703	80	13	-	-	PUNCT
ejpam-5703	80	14	pc	pc	NOUN
ejpam-5703	80	15	approach	approach	NOUN
ejpam-5703	80	16	retains	retain	VERB
ejpam-5703	80	17	positivity	positivity	NOUN
ejpam-5703	80	18	,	,	PUNCT
ejpam-5703	80	19	boundedness	boundedness	NOUN
ejpam-5703	80	20	,	,	PUNCT
ejpam-5703	80	21	and	and	CCONJ
ejpam-5703	80	22	stability	stability	NOUN
ejpam-5703	80	23	even	even	ADV
ejpam-5703	80	24	for	for	ADP
ejpam-5703	80	25	higher	high	ADJ
ejpam-5703	80	26	h.	h.	NOUN
ejpam-5703	80	27	compared	compare	VERB
ejpam-5703	80	28	to	to	ADP
ejpam-5703	80	29	traditional	traditional	ADJ
ejpam-5703	80	30	finite	finite	ADJ
ejpam-5703	80	31	difference	difference	NOUN
ejpam-5703	80	32	approaches	approach	NOUN
ejpam-5703	80	33	,	,	PUNCT
ejpam-5703	80	34	which	which	PRON
ejpam-5703	80	35	frequently	frequently	ADV
ejpam-5703	80	36	lose	lose	VERB
ejpam-5703	80	37	accuracy	accuracy	NOUN
ejpam-5703	80	38	and	and	CCONJ
ejpam-5703	80	39	stability	stability	NOUN
ejpam-5703	80	40	as	as	SCONJ
ejpam-5703	80	41	h	h	NOUN
ejpam-5703	80	42	grows	grow	VERB
ejpam-5703	80	43	,	,	PUNCT
ejpam-5703	80	44	this	this	DET
ejpam-5703	80	45	property	property	NOUN
ejpam-5703	80	46	is	be	AUX
ejpam-5703	80	47	a	a	DET
ejpam-5703	80	48	major	major	ADJ
ejpam-5703	80	49	advantage	advantage	NOUN
ejpam-5703	80	50	.	.	PUNCT
ejpam-5703	81	1	the	the	DET
ejpam-5703	81	2	nsfd	nsfd	ADJ
ejpam-5703	81	3	-	-	PUNCT
ejpam-5703	81	4	pc	pc	NOUN
ejpam-5703	81	5	method	method	NOUN
ejpam-5703	81	6	,	,	PUNCT
ejpam-5703	81	7	which	which	PRON
ejpam-5703	81	8	solves	solve	VERB
ejpam-5703	81	9	nonlinear	nonlinear	ADJ
ejpam-5703	81	10	differential	differential	ADJ
ejpam-5703	81	11	equations	equation	NOUN
ejpam-5703	81	12	like	like	ADP
ejpam-5703	81	13	the	the	DET
ejpam-5703	81	14	riccati	riccati	PROPN
ejpam-5703	81	15	equation	equation	NOUN
ejpam-5703	81	16	,	,	PUNCT
ejpam-5703	81	17	is	be	AUX
ejpam-5703	81	18	a	a	DET
ejpam-5703	81	19	potent	potent	ADJ
ejpam-5703	81	20	tool	tool	NOUN
ejpam-5703	81	21	because	because	SCONJ
ejpam-5703	81	22	it	it	PRON
ejpam-5703	81	23	adheres	adhere	VERB
ejpam-5703	81	24	to	to	ADP
ejpam-5703	81	25	a	a	DET
ejpam-5703	81	26	twostep	twostep	NOUN
ejpam-5703	81	27	predictor	predictor	NOUN
ejpam-5703	81	28	-	-	PUNCT
ejpam-5703	81	29	corrector	corrector	NOUN
ejpam-5703	81	30	approach	approach	NOUN
ejpam-5703	81	31	that	that	PRON
ejpam-5703	81	32	preserves	preserve	VERB
ejpam-5703	81	33	key	key	ADJ
ejpam-5703	81	34	elements	element	NOUN
ejpam-5703	81	35	of	of	ADP
ejpam-5703	81	36	the	the	DET
ejpam-5703	81	37	original	original	ADJ
ejpam-5703	81	38	differential	differential	NOUN
ejpam-5703	81	39	equation	equation	NOUN
ejpam-5703	81	40	while	while	SCONJ
ejpam-5703	81	41	increasing	increase	VERB
ejpam-5703	81	42	accuracy	accuracy	NOUN
ejpam-5703	81	43	.	.	PUNCT
ejpam-5703	82	1	3	3	X
ejpam-5703	82	2	.	.	X
ejpam-5703	82	3	predictor	predictor	NOUN
ejpam-5703	82	4	(	(	PUNCT
ejpam-5703	82	5	nsfd	nsfd	PROPN
ejpam-5703	82	6	)	)	PUNCT
ejpam-5703	82	7	the	the	DET
ejpam-5703	82	8	following	follow	VERB
ejpam-5703	82	9	guidelines	guideline	NOUN
ejpam-5703	82	10	govern	govern	VERB
ejpam-5703	82	11	a	a	DET
ejpam-5703	82	12	discrete	discrete	ADJ
ejpam-5703	82	13	representation	representation	NOUN
ejpam-5703	82	14	of	of	ADP
ejpam-5703	82	15	a	a	DET
ejpam-5703	82	16	system	system	NOUN
ejpam-5703	82	17	of	of	ADP
ejpam-5703	82	18	differential	differential	ADJ
ejpam-5703	82	19	equations	equation	NOUN
ejpam-5703	82	20	using	use	VERB
ejpam-5703	82	21	a	a	DET
ejpam-5703	82	22	non	non	ADJ
ejpam-5703	82	23	-	-	ADJ
ejpam-5703	82	24	standard	standard	ADJ
ejpam-5703	82	25	finite	finite	ADJ
ejpam-5703	82	26	difference	difference	NOUN
ejpam-5703	82	27	method	method	NOUN
ejpam-5703	82	28	:	:	PUNCT
ejpam-5703	82	29	1	1	X
ejpam-5703	82	30	.	.	X
ejpam-5703	83	1	in	in	ADP
ejpam-5703	83	2	the	the	DET
ejpam-5703	83	3	differential	differential	ADJ
ejpam-5703	83	4	equations	equation	NOUN
ejpam-5703	83	5	,	,	PUNCT
ejpam-5703	83	6	the	the	DET
ejpam-5703	83	7	orders	order	NOUN
ejpam-5703	83	8	of	of	ADP
ejpam-5703	83	9	the	the	DET
ejpam-5703	83	10	discrete	discrete	ADJ
ejpam-5703	83	11	derivatives	derivative	NOUN
ejpam-5703	83	12	and	and	CCONJ
ejpam-5703	83	13	their	their	PRON
ejpam-5703	83	14	corresponding	correspond	VERB
ejpam-5703	83	15	derivatives	derivative	NOUN
ejpam-5703	83	16	must	must	AUX
ejpam-5703	83	17	be	be	AUX
ejpam-5703	83	18	equal	equal	ADJ
ejpam-5703	83	19	.	.	PUNCT
ejpam-5703	84	1	2	2	X
ejpam-5703	84	2	.	.	NOUN
ejpam-5703	84	3	discrete	discrete	ADJ
ejpam-5703	84	4	representations	representation	NOUN
ejpam-5703	84	5	for	for	ADP
ejpam-5703	84	6	derivatives	derivative	NOUN
ejpam-5703	84	7	such	such	ADJ
ejpam-5703	84	8	that	that	PRON
ejpam-5703	84	9	ϕ(h	ϕ(h	PROPN
ejpam-5703	84	10	)	)	PUNCT
ejpam-5703	84	11	=	=	SYM
ejpam-5703	84	12	o(h2	o(h2	NOUN
ejpam-5703	84	13	)	)	PUNCT
ejpam-5703	84	14	can	can	AUX
ejpam-5703	84	15	be	be	AUX
ejpam-5703	84	16	obtained	obtain	VERB
ejpam-5703	84	17	using	use	VERB
ejpam-5703	84	18	a	a	DET
ejpam-5703	84	19	non	non	ADJ
ejpam-5703	84	20	-	-	ADJ
ejpam-5703	84	21	trivial	trivial	ADJ
ejpam-5703	84	22	denominator	denominator	NOUN
ejpam-5703	84	23	function	function	NOUN
ejpam-5703	84	24	,	,	PUNCT
ejpam-5703	84	25	provided	provide	VERB
ejpam-5703	84	26	that	that	DET
ejpam-5703	84	27	h	h	NOUN
ejpam-5703	84	28	→	→	SYM
ejpam-5703	84	29	0	0	NUM
ejpam-5703	84	30	,	,	PUNCT
ejpam-5703	84	31	ϕ(h	ϕ(h	PROPN
ejpam-5703	84	32	)	)	PUNCT
ejpam-5703	84	33	→	→	SYM
ejpam-5703	84	34	0	0	X
ejpam-5703	84	35	.	.	PUNCT
ejpam-5703	85	1	b.	b.	PROPN
ejpam-5703	85	2	rehman	rehman	PROPN
ejpam-5703	85	3	et	et	PROPN
ejpam-5703	85	4	al	al	PROPN
ejpam-5703	85	5	.	.	PUNCT
ejpam-5703	85	6	/	/	SYM
ejpam-5703	85	7	eur	eur	PROPN
ejpam-5703	85	8	.	.	PUNCT
ejpam-5703	86	1	j.	j.	PROPN
ejpam-5703	86	2	pure	pure	PROPN
ejpam-5703	86	3	appl	appl	PROPN
ejpam-5703	86	4	.	.	PROPN
ejpam-5703	86	5	math	math	PROPN
ejpam-5703	86	6	,	,	PUNCT
ejpam-5703	86	7	18	18	NUM
ejpam-5703	86	8	(	(	PUNCT
ejpam-5703	86	9	2	2	NUM
ejpam-5703	86	10	)	)	PUNCT
ejpam-5703	86	11	(	(	PUNCT
ejpam-5703	86	12	2025	2025	NUM
ejpam-5703	86	13	)	)	PUNCT
ejpam-5703	86	14	,	,	PUNCT
ejpam-5703	86	15	5703	5703	NUM
ejpam-5703	86	16	5	5	NUM
ejpam-5703	86	17	of	of	ADP
ejpam-5703	86	18	16	16	NUM
ejpam-5703	86	19	3	3	NUM
ejpam-5703	86	20	.	.	PUNCT
ejpam-5703	87	1	nonlinear	nonlinear	ADJ
ejpam-5703	87	2	terms	term	NOUN
ejpam-5703	87	3	should	should	AUX
ejpam-5703	87	4	generally	generally	ADV
ejpam-5703	87	5	be	be	AUX
ejpam-5703	87	6	represented	represent	VERB
ejpam-5703	87	7	by	by	ADP
ejpam-5703	87	8	a	a	DET
ejpam-5703	87	9	non	non	ADJ
ejpam-5703	87	10	-	-	ADJ
ejpam-5703	87	11	local	local	ADJ
ejpam-5703	87	12	discrete	discrete	ADJ
ejpam-5703	87	13	representation	representation	NOUN
ejpam-5703	87	14	.	.	PUNCT
ejpam-5703	88	1	4	4	X
ejpam-5703	88	2	.	.	X
ejpam-5703	88	3	the	the	DET
ejpam-5703	88	4	discretized	discretized	ADJ
ejpam-5703	88	5	model	model	NOUN
ejpam-5703	88	6	and	and	CCONJ
ejpam-5703	88	7	its	its	PRON
ejpam-5703	88	8	solutions	solution	NOUN
ejpam-5703	88	9	should	should	AUX
ejpam-5703	88	10	be	be	AUX
ejpam-5703	88	11	subject	subject	ADJ
ejpam-5703	88	12	to	to	ADP
ejpam-5703	88	13	the	the	DET
ejpam-5703	88	14	same	same	ADJ
ejpam-5703	88	15	special	special	ADJ
ejpam-5703	88	16	criteria	criterion	NOUN
ejpam-5703	88	17	that	that	PRON
ejpam-5703	88	18	apply	apply	VERB
ejpam-5703	88	19	to	to	ADP
ejpam-5703	88	20	the	the	DET
ejpam-5703	88	21	differential	differential	ADJ
ejpam-5703	88	22	equation	equation	NOUN
ejpam-5703	88	23	or	or	CCONJ
ejpam-5703	88	24	its	its	PRON
ejpam-5703	88	25	solutions	solution	NOUN
ejpam-5703	88	26	.	.	PUNCT
ejpam-5703	89	1	4	4	X
ejpam-5703	89	2	.	.	X
ejpam-5703	89	3	riccati	riccati	NOUN
ejpam-5703	89	4	equation	equation	NOUN
ejpam-5703	89	5	let	let	VERB
ejpam-5703	89	6	’s	’s	PRON
ejpam-5703	89	7	look	look	VERB
ejpam-5703	89	8	at	at	ADP
ejpam-5703	89	9	the	the	DET
ejpam-5703	89	10	re	re	NOUN
ejpam-5703	89	11	to	to	PART
ejpam-5703	89	12	demonstrate	demonstrate	VERB
ejpam-5703	89	13	the	the	DET
ejpam-5703	89	14	effectiveness	effectiveness	NOUN
ejpam-5703	89	15	of	of	ADP
ejpam-5703	89	16	our	our	PRON
ejpam-5703	89	17	suggested	suggest	VERB
ejpam-5703	89	18	nsfd	nsfd	ADJ
ejpam-5703	89	19	-	-	PUNCT
ejpam-5703	89	20	pc	pc	NOUN
ejpam-5703	89	21	system	system	NOUN
ejpam-5703	89	22	.	.	PUNCT
ejpam-5703	90	1	[	[	X
ejpam-5703	90	2	25	25	NUM
ejpam-5703	90	3	]	]	X
ejpam-5703	90	4	:	:	PUNCT
ejpam-5703	90	5	dy(t	dy(t	X
ejpam-5703	90	6	)	)	PUNCT
ejpam-5703	90	7	dt	dt	NOUN
ejpam-5703	91	1	=	=	SYM
ejpam-5703	91	2	1	1	NUM
ejpam-5703	91	3	+	+	NUM
ejpam-5703	91	4	2y(t)−	2y(t)−	NUM
ejpam-5703	91	5	y2(t	y2(t	PROPN
ejpam-5703	91	6	)	)	PUNCT
ejpam-5703	91	7	,	,	PUNCT
ejpam-5703	91	8	(	(	PUNCT
ejpam-5703	91	9	1	1	X
ejpam-5703	91	10	)	)	PUNCT
ejpam-5703	91	11	with	with	ADP
ejpam-5703	91	12	y(0	y(0	PROPN
ejpam-5703	91	13	)	)	PUNCT
ejpam-5703	91	14	=	=	SYM
ejpam-5703	91	15	0	0	PUNCT
ejpam-5703	92	1	as	as	ADP
ejpam-5703	92	2	the	the	DET
ejpam-5703	92	3	initial	initial	ADJ
ejpam-5703	92	4	condition	condition	NOUN
ejpam-5703	92	5	.	.	PUNCT
ejpam-5703	93	1	the	the	DET
ejpam-5703	93	2	following	following	NOUN
ejpam-5703	93	3	provides	provide	VERB
ejpam-5703	93	4	the	the	DET
ejpam-5703	93	5	exact	exact	ADJ
ejpam-5703	93	6	answer	answer	NOUN
ejpam-5703	93	7	to	to	ADP
ejpam-5703	93	8	eq	eq	PROPN
ejpam-5703	93	9	.	.	PUNCT
ejpam-5703	94	1	(	(	PUNCT
ejpam-5703	94	2	1	1	NUM
ejpam-5703	94	3	):	):	PUNCT
ejpam-5703	94	4	y	y	PROPN
ejpam-5703	94	5	=	=	SYM
ejpam-5703	94	6	1	1	NUM
ejpam-5703	94	7	+	+	CCONJ
ejpam-5703	94	8	√	√	NUM
ejpam-5703	94	9	2	2	NUM
ejpam-5703	94	10	tanh	tanh	NOUN
ejpam-5703	94	11	(	(	PUNCT
ejpam-5703	94	12	√	√	NUM
ejpam-5703	94	13	2t+	2t+	NUM
ejpam-5703	94	14	1	1	NUM
ejpam-5703	94	15	2	2	NUM
ejpam-5703	94	16	log	log	NOUN
ejpam-5703	94	17	(	(	PUNCT
ejpam-5703	94	18	√	√	NUM
ejpam-5703	94	19	2−	2−	NUM
ejpam-5703	94	20	1√	1√	PROPN
ejpam-5703	94	21	2	2	NUM
ejpam-5703	94	22	+	+	CCONJ
ejpam-5703	94	23	1	1	NUM
ejpam-5703	94	24	)	)	PUNCT
ejpam-5703	94	25	)	)	PUNCT
ejpam-5703	94	26	.	.	PUNCT
ejpam-5703	95	1	(	(	PUNCT
ejpam-5703	95	2	2	2	X
ejpam-5703	95	3	)	)	PUNCT
ejpam-5703	95	4	4.1	4.1	NUM
ejpam-5703	95	5	.	.	PUNCT
ejpam-5703	96	1	qualitative	qualitative	ADJ
ejpam-5703	96	2	analysis	analysis	NOUN
ejpam-5703	96	3	of	of	ADP
ejpam-5703	96	4	assumed	assumed	ADJ
ejpam-5703	96	5	model	model	PROPN
ejpam-5703	96	6	examine	examine	VERB
ejpam-5703	96	7	eq	eq	X
ejpam-5703	96	8	.	.	PUNCT
ejpam-5703	97	1	(	(	PUNCT
ejpam-5703	97	2	1	1	NUM
ejpam-5703	97	3	)	)	PUNCT
ejpam-5703	97	4	.	.	PUNCT
ejpam-5703	98	1	without	without	ADP
ejpam-5703	98	2	getting	get	VERB
ejpam-5703	98	3	explicit	explicit	ADJ
ejpam-5703	98	4	solutions	solution	NOUN
ejpam-5703	98	5	,	,	PUNCT
ejpam-5703	98	6	the	the	DET
ejpam-5703	98	7	qualitative	qualitative	ADJ
ejpam-5703	98	8	analysis	analysis	NOUN
ejpam-5703	98	9	is	be	AUX
ejpam-5703	98	10	carried	carry	VERB
ejpam-5703	98	11	out	out	ADP
ejpam-5703	98	12	to	to	PART
ejpam-5703	98	13	examine	examine	VERB
ejpam-5703	98	14	the	the	DET
ejpam-5703	98	15	equilibrium	equilibrium	NOUN
ejpam-5703	98	16	points	point	NOUN
ejpam-5703	98	17	,	,	PUNCT
ejpam-5703	98	18	their	their	PRON
ejpam-5703	98	19	stability	stability	NOUN
ejpam-5703	98	20	,	,	PUNCT
ejpam-5703	98	21	and	and	CCONJ
ejpam-5703	98	22	the	the	DET
ejpam-5703	98	23	system	system	NOUN
ejpam-5703	98	24	’s	’s	PART
ejpam-5703	98	25	overall	overall	ADJ
ejpam-5703	98	26	behavior	behavior	NOUN
ejpam-5703	98	27	.	.	PUNCT
ejpam-5703	99	1	4.1.1	4.1.1	X
ejpam-5703	99	2	.	.	PUNCT
ejpam-5703	100	1	equilibrium	equilibrium	NOUN
ejpam-5703	100	2	points	point	VERB
ejpam-5703	100	3	the	the	DET
ejpam-5703	100	4	equilibrium	equilibrium	NOUN
ejpam-5703	100	5	points	point	NOUN
ejpam-5703	100	6	y∗	y∗	ADV
ejpam-5703	100	7	are	be	AUX
ejpam-5703	100	8	obtained	obtain	VERB
ejpam-5703	100	9	by	by	ADP
ejpam-5703	100	10	setting	set	VERB
ejpam-5703	100	11	dy(t	dy(t	PUNCT
ejpam-5703	100	12	)	)	PUNCT
ejpam-5703	100	13	dt	dt	NOUN
ejpam-5703	101	1	=	=	PUNCT
ejpam-5703	101	2	0	0	NUM
ejpam-5703	101	3	:	:	SYM
ejpam-5703	101	4	1	1	NUM
ejpam-5703	101	5	+	+	NUM
ejpam-5703	101	6	2y	2y	NUM
ejpam-5703	101	7	−	−	NOUN
ejpam-5703	101	8	y2	y2	NOUN
ejpam-5703	101	9	=	=	NOUN
ejpam-5703	101	10	0	0	PROPN
ejpam-5703	101	11	.	.	PUNCT
ejpam-5703	102	1	(	(	PUNCT
ejpam-5703	102	2	3	3	X
ejpam-5703	102	3	)	)	PUNCT
ejpam-5703	102	4	after	after	ADP
ejpam-5703	102	5	solve	solve	VERB
ejpam-5703	102	6	the	the	DET
ejpam-5703	102	7	aforementioned	aforementioned	ADJ
ejpam-5703	102	8	equation	equation	NOUN
ejpam-5703	102	9	,	,	PUNCT
ejpam-5703	102	10	the	the	DET
ejpam-5703	102	11	equilibrium	equilibrium	NOUN
ejpam-5703	102	12	points	point	NOUN
ejpam-5703	102	13	are	be	AUX
ejpam-5703	102	14	y∗	y∗	ADV
ejpam-5703	102	15	=	=	NUM
ejpam-5703	102	16	1	1	NUM
ejpam-5703	102	17	+	+	CCONJ
ejpam-5703	102	18	√	√	NUM
ejpam-5703	102	19	2	2	NUM
ejpam-5703	102	20	and	and	CCONJ
ejpam-5703	102	21	y∗	y∗	NOUN
ejpam-5703	102	22	=	=	SYM
ejpam-5703	103	1	1−	1−	NUM
ejpam-5703	103	2	√	√	NUM
ejpam-5703	104	1	2	2	NUM
ejpam-5703	104	2	.	.	X
ejpam-5703	104	3	4.1.2	4.1.2	NUM
ejpam-5703	104	4	.	.	PUNCT
ejpam-5703	104	5	stability	stability	NOUN
ejpam-5703	104	6	analysis	analysis	NOUN
ejpam-5703	104	7	to	to	PART
ejpam-5703	104	8	assess	assess	VERB
ejpam-5703	104	9	the	the	DET
ejpam-5703	104	10	stability	stability	NOUN
ejpam-5703	104	11	of	of	ADP
ejpam-5703	104	12	the	the	DET
ejpam-5703	104	13	equilibrium	equilibrium	NOUN
ejpam-5703	104	14	points	point	NOUN
ejpam-5703	104	15	,	,	PUNCT
ejpam-5703	104	16	we	we	PRON
ejpam-5703	104	17	differentiate	differentiate	VERB
ejpam-5703	104	18	eq.(3	eq.(3	NOUN
ejpam-5703	104	19	)	)	PUNCT
ejpam-5703	104	20	with	with	ADP
ejpam-5703	104	21	respect	respect	NOUN
ejpam-5703	104	22	to	to	ADP
ejpam-5703	104	23	y	y	NOUN
ejpam-5703	104	24	:	:	PUNCT
ejpam-5703	104	25	evaluating	evaluate	VERB
ejpam-5703	104	26	f	f	PROPN
ejpam-5703	104	27	′(y	′(y	PROPN
ejpam-5703	104	28	)	)	PUNCT
ejpam-5703	104	29	at	at	ADP
ejpam-5703	104	30	the	the	DET
ejpam-5703	104	31	equilibrium	equilibrium	NOUN
ejpam-5703	104	32	points	point	NOUN
ejpam-5703	104	33	:	:	PUNCT
ejpam-5703	104	34	•	•	ADP
ejpam-5703	104	35	at	at	ADP
ejpam-5703	104	36	y∗	y∗	ADV
ejpam-5703	104	37	=	=	SYM
ejpam-5703	104	38	1	1	NUM
ejpam-5703	104	39	+	+	CCONJ
ejpam-5703	104	40	√	√	NUM
ejpam-5703	104	41	2	2	NUM
ejpam-5703	104	42	:	:	PUNCT
ejpam-5703	104	43	f	f	PROPN
ejpam-5703	104	44	′(1	′(1	PROPN
ejpam-5703	104	45	+	+	CCONJ
ejpam-5703	104	46	√	√	NUM
ejpam-5703	104	47	2	2	NUM
ejpam-5703	104	48	)	)	PUNCT
ejpam-5703	104	49	=	=	PUNCT
ejpam-5703	104	50	2−	2−	NUM
ejpam-5703	104	51	2(1	2(1	NUM
ejpam-5703	104	52	+	+	CCONJ
ejpam-5703	104	53	√	√	NUM
ejpam-5703	104	54	2	2	NUM
ejpam-5703	104	55	)	)	PUNCT
ejpam-5703	104	56	=	=	SYM
ejpam-5703	105	1	−2	−2	NOUN
ejpam-5703	105	2	√	√	ADV
ejpam-5703	105	3	2	2	NUM
ejpam-5703	105	4	<	<	X
ejpam-5703	105	5	0	0	NUM
ejpam-5703	105	6	,	,	PUNCT
ejpam-5703	105	7	indicating	indicate	VERB
ejpam-5703	105	8	that	that	SCONJ
ejpam-5703	105	9	y	y	PROPN
ejpam-5703	105	10	=	=	SYM
ejpam-5703	105	11	1	1	NUM
ejpam-5703	105	12	+	+	CCONJ
ejpam-5703	105	13	√	√	NUM
ejpam-5703	105	14	2	2	NUM
ejpam-5703	105	15	is	be	AUX
ejpam-5703	105	16	a	a	DET
ejpam-5703	105	17	stable	stable	ADJ
ejpam-5703	105	18	equilibrium	equilibrium	NOUN
ejpam-5703	105	19	point	point	NOUN
ejpam-5703	105	20	.	.	PUNCT
ejpam-5703	106	1	•	•	NOUN
ejpam-5703	106	2	at	at	ADP
ejpam-5703	106	3	y∗	y∗	PROPN
ejpam-5703	106	4	=	=	SYM
ejpam-5703	107	1	1−	1−	NUM
ejpam-5703	107	2	√	√	NUM
ejpam-5703	108	1	2	2	NUM
ejpam-5703	108	2	:	:	PUNCT
ejpam-5703	108	3	f	f	PROPN
ejpam-5703	108	4	′(1−	′(1−	ADJ
ejpam-5703	108	5	√	√	PROPN
ejpam-5703	108	6	2	2	NUM
ejpam-5703	108	7	)	)	PUNCT
ejpam-5703	108	8	=	=	PUNCT
ejpam-5703	108	9	2−	2−	NUM
ejpam-5703	108	10	2(1−	2(1−	NUM
ejpam-5703	108	11	√	√	NUM
ejpam-5703	108	12	2	2	NUM
ejpam-5703	108	13	)	)	PUNCT
ejpam-5703	108	14	=	=	SYM
ejpam-5703	108	15	2	2	NUM
ejpam-5703	108	16	√	√	NUM
ejpam-5703	108	17	2	2	NUM
ejpam-5703	108	18	>	>	X
ejpam-5703	108	19	0	0	NUM
ejpam-5703	108	20	,	,	PUNCT
ejpam-5703	108	21	which	which	PRON
ejpam-5703	108	22	implies	imply	VERB
ejpam-5703	108	23	that	that	SCONJ
ejpam-5703	108	24	y	y	PROPN
ejpam-5703	108	25	=	=	SYM
ejpam-5703	108	26	1−	1−	NUM
ejpam-5703	108	27	√	√	NUM
ejpam-5703	108	28	2	2	NUM
ejpam-5703	108	29	is	be	AUX
ejpam-5703	108	30	an	an	DET
ejpam-5703	108	31	unstable	unstable	ADJ
ejpam-5703	108	32	equilibrium	equilibrium	NOUN
ejpam-5703	108	33	point	point	NOUN
ejpam-5703	108	34	.	.	PUNCT
ejpam-5703	109	1	b.	b.	PROPN
ejpam-5703	109	2	rehman	rehman	PROPN
ejpam-5703	109	3	et	et	PROPN
ejpam-5703	109	4	al	al	PROPN
ejpam-5703	109	5	.	.	PUNCT
ejpam-5703	109	6	/	/	SYM
ejpam-5703	109	7	eur	eur	PROPN
ejpam-5703	109	8	.	.	PUNCT
ejpam-5703	110	1	j.	j.	PROPN
ejpam-5703	110	2	pure	pure	PROPN
ejpam-5703	110	3	appl	appl	PROPN
ejpam-5703	110	4	.	.	PROPN
ejpam-5703	110	5	math	math	PROPN
ejpam-5703	110	6	,	,	PUNCT
ejpam-5703	110	7	18	18	NUM
ejpam-5703	110	8	(	(	PUNCT
ejpam-5703	110	9	2	2	NUM
ejpam-5703	110	10	)	)	PUNCT
ejpam-5703	110	11	(	(	PUNCT
ejpam-5703	110	12	2025	2025	NUM
ejpam-5703	110	13	)	)	PUNCT
ejpam-5703	110	14	,	,	PUNCT
ejpam-5703	110	15	5703	5703	NUM
ejpam-5703	110	16	6	6	NUM
ejpam-5703	110	17	of	of	ADP
ejpam-5703	110	18	16	16	NUM
ejpam-5703	110	19	4.1.3	4.1.3	NUM
ejpam-5703	110	20	.	.	PUNCT
ejpam-5703	110	21	phase	phase	NOUN
ejpam-5703	110	22	line	line	NOUN
ejpam-5703	110	23	analysis	analysis	NOUN
ejpam-5703	110	24	the	the	DET
ejpam-5703	110	25	phase	phase	NOUN
ejpam-5703	110	26	line	line	NOUN
ejpam-5703	110	27	analysis	analysis	NOUN
ejpam-5703	110	28	provides	provide	VERB
ejpam-5703	110	29	insight	insight	NOUN
ejpam-5703	110	30	into	into	ADP
ejpam-5703	110	31	the	the	DET
ejpam-5703	110	32	directional	directional	ADJ
ejpam-5703	110	33	behavior	behavior	NOUN
ejpam-5703	110	34	of	of	ADP
ejpam-5703	110	35	the	the	DET
ejpam-5703	110	36	solutions	solution	NOUN
ejpam-5703	110	37	around	around	ADP
ejpam-5703	110	38	the	the	DET
ejpam-5703	110	39	equilibrium	equilibrium	NOUN
ejpam-5703	110	40	points	point	NOUN
ejpam-5703	110	41	:	:	PUNCT
ejpam-5703	110	42	•	•	NOUN
ejpam-5703	110	43	for	for	ADP
ejpam-5703	110	44	y	y	PROPN
ejpam-5703	110	45	<	<	X
ejpam-5703	110	46	1	1	NUM
ejpam-5703	110	47	−	−	NOUN
ejpam-5703	110	48	√	√	NUM
ejpam-5703	110	49	2	2	NUM
ejpam-5703	110	50	,	,	PUNCT
ejpam-5703	110	51	f(y	f(y	NOUN
ejpam-5703	110	52	)	)	PUNCT
ejpam-5703	110	53	=	=	SYM
ejpam-5703	111	1	1	1	NUM
ejpam-5703	111	2	+	+	NUM
ejpam-5703	111	3	2y	2y	PROPN
ejpam-5703	111	4	−	−	ADP
ejpam-5703	112	1	y2	y2	PROPN
ejpam-5703	112	2	>	>	X
ejpam-5703	112	3	0	0	PROPN
ejpam-5703	112	4	,	,	PUNCT
ejpam-5703	112	5	indicating	indicate	VERB
ejpam-5703	112	6	that	that	SCONJ
ejpam-5703	112	7	dy	dy	VERB
ejpam-5703	112	8	dt	dt	X
ejpam-5703	112	9	>	>	X
ejpam-5703	112	10	0	0	NUM
ejpam-5703	112	11	,	,	PUNCT
ejpam-5703	112	12	and	and	CCONJ
ejpam-5703	112	13	thus	thus	ADV
ejpam-5703	112	14	y(t	y(t	NUM
ejpam-5703	112	15	)	)	PUNCT
ejpam-5703	112	16	increases	increase	NOUN
ejpam-5703	112	17	.	.	PUNCT
ejpam-5703	113	1	•	•	NOUN
ejpam-5703	113	2	for	for	ADP
ejpam-5703	113	3	1−	1−	NUM
ejpam-5703	113	4	√	√	ADP
ejpam-5703	113	5	2	2	NUM
ejpam-5703	113	6	<	<	X
ejpam-5703	113	7	y	y	X
ejpam-5703	113	8	<	<	X
ejpam-5703	113	9	1	1	NUM
ejpam-5703	113	10	+	+	CCONJ
ejpam-5703	113	11	√	√	NUM
ejpam-5703	113	12	2	2	NUM
ejpam-5703	113	13	,	,	PUNCT
ejpam-5703	113	14	f(y	f(y	NOUN
ejpam-5703	113	15	)	)	PUNCT
ejpam-5703	113	16	<	<	X
ejpam-5703	113	17	0	0	NUM
ejpam-5703	113	18	,	,	PUNCT
ejpam-5703	113	19	meaning	mean	VERB
ejpam-5703	113	20	dy	dy	NOUN
ejpam-5703	113	21	dt	dt	X
ejpam-5703	113	22	<	<	X
ejpam-5703	113	23	0	0	PROPN
ejpam-5703	113	24	,	,	PUNCT
ejpam-5703	113	25	so	so	ADV
ejpam-5703	113	26	y(t	y(t	NUM
ejpam-5703	113	27	)	)	PUNCT
ejpam-5703	113	28	decreases	decrease	VERB
ejpam-5703	113	29	.	.	PUNCT
ejpam-5703	114	1	•	•	NOUN
ejpam-5703	114	2	for	for	ADP
ejpam-5703	114	3	y	y	PROPN
ejpam-5703	114	4	>	>	X
ejpam-5703	114	5	1	1	NUM
ejpam-5703	115	1	+	+	CCONJ
ejpam-5703	115	2	√	√	NUM
ejpam-5703	115	3	2	2	NUM
ejpam-5703	115	4	,	,	PUNCT
ejpam-5703	115	5	f(y	f(y	NOUN
ejpam-5703	115	6	)	)	PUNCT
ejpam-5703	115	7	>	>	X
ejpam-5703	116	1	0	0	NUM
ejpam-5703	116	2	,	,	PUNCT
ejpam-5703	116	3	which	which	PRON
ejpam-5703	116	4	results	result	VERB
ejpam-5703	116	5	in	in	ADP
ejpam-5703	116	6	dy	dy	X
ejpam-5703	116	7	dt	dt	X
ejpam-5703	116	8	>	>	X
ejpam-5703	116	9	0	0	NUM
ejpam-5703	116	10	,	,	PUNCT
ejpam-5703	116	11	and	and	CCONJ
ejpam-5703	116	12	y(t	y(t	NOUN
ejpam-5703	116	13	)	)	PUNCT
ejpam-5703	116	14	increases	increase	NOUN
ejpam-5703	116	15	.	.	PUNCT
ejpam-5703	117	1	this	this	DET
ejpam-5703	117	2	analysis	analysis	NOUN
ejpam-5703	117	3	indicates	indicate	VERB
ejpam-5703	117	4	that	that	SCONJ
ejpam-5703	117	5	y	y	NOUN
ejpam-5703	117	6	=	=	SYM
ejpam-5703	117	7	1	1	NUM
ejpam-5703	117	8	+	+	CCONJ
ejpam-5703	117	9	√	√	NUM
ejpam-5703	117	10	2	2	NUM
ejpam-5703	117	11	is	be	AUX
ejpam-5703	117	12	an	an	DET
ejpam-5703	117	13	attractor	attractor	NOUN
ejpam-5703	117	14	,	,	PUNCT
ejpam-5703	117	15	while	while	SCONJ
ejpam-5703	117	16	y	y	PROPN
ejpam-5703	117	17	=	=	PROPN
ejpam-5703	117	18	1	1	NUM
ejpam-5703	117	19	−	−	NOUN
ejpam-5703	117	20	√	√	NUM
ejpam-5703	117	21	2	2	NUM
ejpam-5703	117	22	serves	serve	VERB
ejpam-5703	117	23	as	as	ADP
ejpam-5703	117	24	a	a	DET
ejpam-5703	117	25	repeller	repeller	NOUN
ejpam-5703	117	26	.	.	PUNCT
ejpam-5703	118	1	figure	figure	NOUN
ejpam-5703	118	2	1	1	NUM
ejpam-5703	118	3	:	:	PUNCT
ejpam-5703	118	4	directional	directional	ADJ
ejpam-5703	118	5	field	field	NOUN
ejpam-5703	118	6	along	along	ADP
ejpam-5703	118	7	with	with	ADP
ejpam-5703	118	8	phase	phase	NOUN
ejpam-5703	118	9	portrait	portrait	NOUN
ejpam-5703	118	10	4.1.4	4.1.4	NUM
ejpam-5703	118	11	.	.	PUNCT
ejpam-5703	118	12	direction	direction	NOUN
ejpam-5703	118	13	field	field	NOUN
ejpam-5703	118	14	and	and	CCONJ
ejpam-5703	118	15	long	long	ADJ
ejpam-5703	118	16	term	term	NOUN
ejpam-5703	118	17	behavior	behavior	NOUN
ejpam-5703	118	18	the	the	DET
ejpam-5703	118	19	direction	direction	NOUN
ejpam-5703	118	20	field	field	NOUN
ejpam-5703	118	21	can	can	AUX
ejpam-5703	118	22	be	be	AUX
ejpam-5703	118	23	plotted	plot	VERB
ejpam-5703	118	24	to	to	PART
ejpam-5703	118	25	visualize	visualize	VERB
ejpam-5703	118	26	the	the	DET
ejpam-5703	118	27	trajectories	trajectory	NOUN
ejpam-5703	118	28	of	of	ADP
ejpam-5703	118	29	y(t	y(t	PROPN
ejpam-5703	118	30	)	)	PUNCT
ejpam-5703	118	31	over	over	ADP
ejpam-5703	118	32	time	time	NOUN
ejpam-5703	118	33	,	,	PUNCT
ejpam-5703	118	34	which	which	PRON
ejpam-5703	118	35	further	far	ADV
ejpam-5703	118	36	corroborates	corroborate	VERB
ejpam-5703	118	37	the	the	DET
ejpam-5703	118	38	stability	stability	NOUN
ejpam-5703	118	39	characteristics	characteristic	NOUN
ejpam-5703	118	40	identified	identify	VERB
ejpam-5703	118	41	.	.	PUNCT
ejpam-5703	119	1	the	the	DET
ejpam-5703	119	2	long	long	ADJ
ejpam-5703	119	3	-	-	PUNCT
ejpam-5703	119	4	term	term	NOUN
ejpam-5703	119	5	asymptotic	asymptotic	ADJ
ejpam-5703	119	6	behavior	behavior	NOUN
ejpam-5703	119	7	of	of	ADP
ejpam-5703	119	8	the	the	DET
ejpam-5703	119	9	solutions	solution	NOUN
ejpam-5703	119	10	reveals	reveal	VERB
ejpam-5703	119	11	that	that	SCONJ
ejpam-5703	119	12	as	as	ADP
ejpam-5703	119	13	t	t	PROPN
ejpam-5703	119	14	→	→	SYM
ejpam-5703	119	15	∞	∞	PROPN
ejpam-5703	119	16	,	,	PUNCT
ejpam-5703	119	17	any	any	DET
ejpam-5703	119	18	trajectory	trajectory	NOUN
ejpam-5703	119	19	that	that	PRON
ejpam-5703	119	20	starts	start	VERB
ejpam-5703	119	21	within	within	ADP
ejpam-5703	119	22	y	y	PROPN
ejpam-5703	119	23	>	>	X
ejpam-5703	119	24	1−	1−	NUM
ejpam-5703	119	25	√	√	NUM
ejpam-5703	119	26	2	2	NUM
ejpam-5703	119	27	will	will	AUX
ejpam-5703	119	28	converge	converge	VERB
ejpam-5703	119	29	to	to	ADP
ejpam-5703	119	30	the	the	DET
ejpam-5703	119	31	stable	stable	ADJ
ejpam-5703	119	32	equilibrium	equilibrium	NOUN
ejpam-5703	119	33	y	y	PROPN
ejpam-5703	119	34	=	=	SYM
ejpam-5703	119	35	1	1	NUM
ejpam-5703	119	36	+	+	CCONJ
ejpam-5703	119	37	√	√	NUM
ejpam-5703	119	38	2	2	NUM
ejpam-5703	119	39	.	.	PUNCT
ejpam-5703	120	1	conversely	conversely	ADV
ejpam-5703	120	2	,	,	PUNCT
ejpam-5703	120	3	initial	initial	ADJ
ejpam-5703	120	4	conditions	condition	NOUN
ejpam-5703	120	5	y(t0	y(t0	PROPN
ejpam-5703	120	6	)	)	PUNCT
ejpam-5703	120	7	<	<	X
ejpam-5703	121	1	1−	1−	NUM
ejpam-5703	121	2	√	√	NUM
ejpam-5703	121	3	2	2	NUM
ejpam-5703	121	4	will	will	AUX
ejpam-5703	121	5	diverge	diverge	VERB
ejpam-5703	121	6	away	away	ADV
ejpam-5703	121	7	from	from	ADP
ejpam-5703	121	8	this	this	DET
ejpam-5703	121	9	region	region	NOUN
ejpam-5703	121	10	.	.	PUNCT
ejpam-5703	122	1	5	5	X
ejpam-5703	122	2	.	.	X
ejpam-5703	122	3	application	application	NOUN
ejpam-5703	122	4	of	of	ADP
ejpam-5703	122	5	nsfd	nsfd	ADJ
ejpam-5703	122	6	-	-	PUNCT
ejpam-5703	122	7	pc	pc	NOUN
ejpam-5703	122	8	scheme	scheme	NOUN
ejpam-5703	122	9	for	for	ADP
ejpam-5703	122	10	the	the	DET
ejpam-5703	122	11	re	re	NOUN
ejpam-5703	122	12	,	,	PUNCT
ejpam-5703	122	13	the	the	DET
ejpam-5703	122	14	predictor	predictor	NOUN
ejpam-5703	122	15	step	step	NOUN
ejpam-5703	122	16	of	of	ADP
ejpam-5703	122	17	the	the	DET
ejpam-5703	122	18	nsfd	nsfd	ADJ
ejpam-5703	122	19	-	-	PUNCT
ejpam-5703	122	20	pc	pc	NOUN
ejpam-5703	122	21	method	method	NOUN
ejpam-5703	122	22	with	with	ADP
ejpam-5703	122	23	non	non	ADJ
ejpam-5703	122	24	-	-	ADJ
ejpam-5703	122	25	local	local	ADJ
ejpam-5703	122	26	approximation	approximation	NOUN
ejpam-5703	122	27	of	of	ADP
ejpam-5703	122	28	nonlinear	nonlinear	ADJ
ejpam-5703	122	29	terms	term	NOUN
ejpam-5703	122	30	can	can	AUX
ejpam-5703	122	31	be	be	AUX
ejpam-5703	122	32	built	build	VERB
ejpam-5703	122	33	as	as	SCONJ
ejpam-5703	122	34	follows	follow	VERB
ejpam-5703	122	35	:	:	PUNCT
ejpam-5703	123	1	yn+1	yn+1	PROPN
ejpam-5703	123	2	−	−	PROPN
ejpam-5703	124	1	yn	yn	INTJ
ejpam-5703	124	2	h	h	NOUN
ejpam-5703	124	3	=	=	NOUN
ejpam-5703	124	4	1	1	NUM
ejpam-5703	125	1	+	+	CCONJ
ejpam-5703	125	2	2yn	2yn	ADJ
ejpam-5703	125	3	−	−	PROPN
ejpam-5703	125	4	ynyn+1	ynyn+1	NOUN
ejpam-5703	125	5	,	,	PUNCT
ejpam-5703	125	6	(	(	PUNCT
ejpam-5703	125	7	4	4	X
ejpam-5703	125	8	)	)	PUNCT
ejpam-5703	125	9	b.	b.	PROPN
ejpam-5703	125	10	rehman	rehman	PROPN
ejpam-5703	125	11	et	et	PROPN
ejpam-5703	125	12	al	al	PROPN
ejpam-5703	125	13	.	.	PUNCT
ejpam-5703	125	14	/	/	SYM
ejpam-5703	125	15	eur	eur	PROPN
ejpam-5703	125	16	.	.	PUNCT
ejpam-5703	126	1	j.	j.	PROPN
ejpam-5703	126	2	pure	pure	PROPN
ejpam-5703	126	3	appl	appl	PROPN
ejpam-5703	126	4	.	.	PROPN
ejpam-5703	126	5	math	math	PROPN
ejpam-5703	126	6	,	,	PUNCT
ejpam-5703	126	7	18	18	NUM
ejpam-5703	126	8	(	(	PUNCT
ejpam-5703	126	9	2	2	NUM
ejpam-5703	126	10	)	)	PUNCT
ejpam-5703	126	11	(	(	PUNCT
ejpam-5703	126	12	2025	2025	NUM
ejpam-5703	126	13	)	)	PUNCT
ejpam-5703	126	14	,	,	PUNCT
ejpam-5703	126	15	5703	5703	NUM
ejpam-5703	126	16	7	7	NUM
ejpam-5703	126	17	of	of	ADP
ejpam-5703	126	18	16	16	NUM
ejpam-5703	126	19	figure	figure	NOUN
ejpam-5703	126	20	2	2	NUM
ejpam-5703	126	21	:	:	PUNCT
ejpam-5703	126	22	directional	directional	ADJ
ejpam-5703	126	23	field	field	NOUN
ejpam-5703	126	24	of	of	ADP
ejpam-5703	126	25	stable	stable	ADJ
ejpam-5703	126	26	and	and	CCONJ
ejpam-5703	126	27	unstable	unstable	ADJ
ejpam-5703	126	28	points	point	NOUN
ejpam-5703	126	29	figure	figure	NOUN
ejpam-5703	126	30	3	3	NUM
ejpam-5703	126	31	:	:	PUNCT
ejpam-5703	126	32	directional	directional	ADJ
ejpam-5703	126	33	field	field	NOUN
ejpam-5703	126	34	of	of	ADP
ejpam-5703	126	35	stable	stable	ADJ
ejpam-5703	126	36	and	and	CCONJ
ejpam-5703	126	37	unstable	unstable	ADJ
ejpam-5703	126	38	points	point	NOUN
ejpam-5703	126	39	with	with	ADP
ejpam-5703	126	40	curves	curve	NOUN
ejpam-5703	126	41	which	which	PRON
ejpam-5703	126	42	provides	provide	VERB
ejpam-5703	126	43	:	:	PUNCT
ejpam-5703	126	44	yn+1	yn+1	PROPN
ejpam-5703	126	45	=	=	SYM
ejpam-5703	126	46	yn	yn	PROPN
ejpam-5703	126	47	+	+	SYM
ejpam-5703	126	48	h+	h+	PROPN
ejpam-5703	126	49	2hyn	2hyn	NUM
ejpam-5703	126	50	1	1	NUM
ejpam-5703	126	51	+	+	NUM
ejpam-5703	126	52	hyn	hyn	PROPN
ejpam-5703	126	53	.	.	PUNCT
ejpam-5703	127	1	(	(	PUNCT
ejpam-5703	127	2	5	5	X
ejpam-5703	127	3	)	)	PUNCT
ejpam-5703	127	4	the	the	DET
ejpam-5703	127	5	non	non	ADJ
ejpam-5703	127	6	-	-	ADJ
ejpam-5703	127	7	standard	standard	ADJ
ejpam-5703	127	8	finite	finite	ADJ
ejpam-5703	127	9	difference	difference	NOUN
ejpam-5703	127	10	predictor	predictor	NOUN
ejpam-5703	127	11	formula	formula	NOUN
ejpam-5703	127	12	for	for	ADP
ejpam-5703	127	13	the	the	DET
ejpam-5703	127	14	given	give	VERB
ejpam-5703	127	15	differential	differential	ADJ
ejpam-5703	127	16	equation	equation	NOUN
ejpam-5703	127	17	from	from	ADP
ejpam-5703	127	18	eq.(5	eq.(5	NOUN
ejpam-5703	127	19	)	)	PUNCT
ejpam-5703	127	20	is	be	AUX
ejpam-5703	127	21	:	:	PUNCT
ejpam-5703	127	22	y	y	PROPN
ejpam-5703	127	23	(	(	PUNCT
ejpam-5703	127	24	p	p	X
ejpam-5703	127	25	)	)	PUNCT
ejpam-5703	127	26	n+1	n+1	PROPN
ejpam-5703	127	27	=	=	SYM
ejpam-5703	127	28	y	y	PROPN
ejpam-5703	127	29	(	(	PUNCT
ejpam-5703	127	30	p	p	NOUN
ejpam-5703	127	31	)	)	PUNCT
ejpam-5703	127	32	n	n	PROPN
ejpam-5703	127	33	+	+	CCONJ
ejpam-5703	127	34	h+	h+	X
ejpam-5703	127	35	2hy	2hy	X
ejpam-5703	127	36	(	(	PUNCT
ejpam-5703	127	37	p	p	NOUN
ejpam-5703	127	38	)	)	PUNCT
ejpam-5703	127	39	n	n	PRON
ejpam-5703	127	40	1	1	NUM
ejpam-5703	127	41	+	+	NUM
ejpam-5703	127	42	hy	hy	NOUN
ejpam-5703	127	43	(	(	PUNCT
ejpam-5703	127	44	p	p	NOUN
ejpam-5703	127	45	)	)	PUNCT
ejpam-5703	127	46	n	n	NOUN
ejpam-5703	127	47	.	.	PUNCT
ejpam-5703	128	1	(	(	PUNCT
ejpam-5703	128	2	6	6	NUM
ejpam-5703	128	3	)	)	PUNCT
ejpam-5703	128	4	b.	b.	PROPN
ejpam-5703	128	5	rehman	rehman	PROPN
ejpam-5703	128	6	et	et	PROPN
ejpam-5703	128	7	al	al	PROPN
ejpam-5703	128	8	.	.	PUNCT
ejpam-5703	128	9	/	/	SYM
ejpam-5703	128	10	eur	eur	PROPN
ejpam-5703	128	11	.	.	PUNCT
ejpam-5703	129	1	j.	j.	PROPN
ejpam-5703	129	2	pure	pure	PROPN
ejpam-5703	129	3	appl	appl	PROPN
ejpam-5703	129	4	.	.	PROPN
ejpam-5703	129	5	math	math	PROPN
ejpam-5703	129	6	,	,	PUNCT
ejpam-5703	129	7	18	18	NUM
ejpam-5703	129	8	(	(	PUNCT
ejpam-5703	129	9	2	2	NUM
ejpam-5703	129	10	)	)	PUNCT
ejpam-5703	129	11	(	(	PUNCT
ejpam-5703	129	12	2025	2025	NUM
ejpam-5703	129	13	)	)	PUNCT
ejpam-5703	129	14	,	,	PUNCT
ejpam-5703	129	15	5703	5703	NUM
ejpam-5703	129	16	8	8	NUM
ejpam-5703	129	17	of	of	ADP
ejpam-5703	129	18	16	16	NUM
ejpam-5703	129	19	figure	figure	NOUN
ejpam-5703	129	20	4	4	NUM
ejpam-5703	129	21	:	:	PUNCT
ejpam-5703	129	22	phase	phase	NOUN
ejpam-5703	129	23	portrait	portrait	NOUN
ejpam-5703	129	24	of	of	ADP
ejpam-5703	129	25	stable	stable	ADJ
ejpam-5703	129	26	and	and	CCONJ
ejpam-5703	129	27	unstable	unstable	ADJ
ejpam-5703	129	28	points	point	NOUN
ejpam-5703	129	29	figure	figure	NOUN
ejpam-5703	129	30	5	5	NUM
ejpam-5703	129	31	:	:	PUNCT
ejpam-5703	129	32	time	time	NOUN
ejpam-5703	129	33	series	series	PROPN
ejpam-5703	129	34	solution	solution	NOUN
ejpam-5703	129	35	the	the	DET
ejpam-5703	129	36	corrector	corrector	NOUN
ejpam-5703	129	37	step	step	NOUN
ejpam-5703	129	38	can	can	AUX
ejpam-5703	129	39	be	be	AUX
ejpam-5703	129	40	constructed	construct	VERB
ejpam-5703	129	41	by	by	ADP
ejpam-5703	129	42	adding	add	VERB
ejpam-5703	129	43	the	the	DET
ejpam-5703	129	44	term	term	NOUN
ejpam-5703	129	45	ϵ−1	ϵ−1	PROPN
ejpam-5703	129	46	h	h	NOUN
ejpam-5703	129	47	yn+1	yn+1	PROPN
ejpam-5703	129	48	in	in	ADP
ejpam-5703	129	49	the	the	DET
ejpam-5703	129	50	nsfd	nsfd	ADJ
ejpam-5703	129	51	scheme	scheme	NOUN
ejpam-5703	129	52	:	:	PUNCT
ejpam-5703	129	53	yn+1	yn+1	PROPN
ejpam-5703	129	54	−	−	PROPN
ejpam-5703	130	1	yn	yn	INTJ
ejpam-5703	130	2	h	h	NOUN
ejpam-5703	130	3	=	=	NOUN
ejpam-5703	130	4	1	1	NUM
ejpam-5703	131	1	+	+	CCONJ
ejpam-5703	131	2	2yn	2yn	ADJ
ejpam-5703	131	3	−	−	DET
ejpam-5703	131	4	ynyn+1	ynyn+1	PROPN
ejpam-5703	131	5	−	−	PROPN
ejpam-5703	131	6	ϵ−1	ϵ−1	PROPN
ejpam-5703	131	7	h	h	NOUN
ejpam-5703	131	8	yn+1	yn+1	PROPN
ejpam-5703	132	1	+	+	CCONJ
ejpam-5703	132	2	ϵ−1	ϵ−1	PROPN
ejpam-5703	132	3	h	h	NOUN
ejpam-5703	132	4	yn+1	yn+1	PROPN
ejpam-5703	132	5	,	,	PUNCT
ejpam-5703	132	6	(	(	PUNCT
ejpam-5703	132	7	7	7	X
ejpam-5703	132	8	)	)	PUNCT
ejpam-5703	132	9	which	which	PRON
ejpam-5703	132	10	gives	give	VERB
ejpam-5703	132	11	:	:	PUNCT
ejpam-5703	132	12	yn+1	yn+1	PROPN
ejpam-5703	132	13	=	=	SYM
ejpam-5703	132	14	h+	h+	X
ejpam-5703	132	15	yn	yn	PROPN
ejpam-5703	132	16	+	+	CCONJ
ejpam-5703	132	17	ϵ−1yn+1	ϵ−1yn+1	PROPN
ejpam-5703	133	1	+	+	CCONJ
ejpam-5703	133	2	2hyn	2hyn	NUM
ejpam-5703	133	3	1	1	NUM
ejpam-5703	133	4	+	+	NUM
ejpam-5703	133	5	hyn	hyn	PROPN
ejpam-5703	133	6	+	+	CCONJ
ejpam-5703	133	7	ϵ−1	ϵ−1	PROPN
ejpam-5703	133	8	.	.	PUNCT
ejpam-5703	134	1	(	(	PUNCT
ejpam-5703	134	2	8)	8)	NUM
ejpam-5703	134	3	b.	b.	PROPN
ejpam-5703	134	4	rehman	rehman	PROPN
ejpam-5703	134	5	et	et	PROPN
ejpam-5703	134	6	al	al	PROPN
ejpam-5703	134	7	.	.	PUNCT
ejpam-5703	134	8	/	/	SYM
ejpam-5703	134	9	eur	eur	PROPN
ejpam-5703	134	10	.	.	PUNCT
ejpam-5703	135	1	j.	j.	PROPN
ejpam-5703	135	2	pure	pure	PROPN
ejpam-5703	135	3	appl	appl	PROPN
ejpam-5703	135	4	.	.	PROPN
ejpam-5703	135	5	math	math	PROPN
ejpam-5703	135	6	,	,	PUNCT
ejpam-5703	135	7	18	18	NUM
ejpam-5703	135	8	(	(	PUNCT
ejpam-5703	135	9	2	2	NUM
ejpam-5703	135	10	)	)	PUNCT
ejpam-5703	135	11	(	(	PUNCT
ejpam-5703	135	12	2025	2025	NUM
ejpam-5703	135	13	)	)	PUNCT
ejpam-5703	135	14	,	,	PUNCT
ejpam-5703	135	15	5703	5703	NUM
ejpam-5703	135	16	9	9	NUM
ejpam-5703	135	17	of	of	ADP
ejpam-5703	135	18	16	16	NUM
ejpam-5703	135	19	the	the	DET
ejpam-5703	135	20	non	non	ADJ
ejpam-5703	135	21	-	-	ADJ
ejpam-5703	135	22	standard	standard	ADJ
ejpam-5703	135	23	finite	finite	ADJ
ejpam-5703	135	24	difference	difference	NOUN
ejpam-5703	135	25	corrector	corrector	NOUN
ejpam-5703	135	26	formula	formula	NOUN
ejpam-5703	135	27	is	be	AUX
ejpam-5703	135	28	:	:	PUNCT
ejpam-5703	135	29	y	y	PROPN
ejpam-5703	135	30	(	(	PUNCT
ejpam-5703	135	31	c	c	X
ejpam-5703	135	32	)	)	PUNCT
ejpam-5703	135	33	n+1	n+1	PROPN
ejpam-5703	135	34	=	=	SYM
ejpam-5703	135	35	h+	h+	X
ejpam-5703	135	36	y	y	PROPN
ejpam-5703	135	37	(	(	PUNCT
ejpam-5703	135	38	p	p	NOUN
ejpam-5703	135	39	)	)	PUNCT
ejpam-5703	135	40	n	n	NOUN
ejpam-5703	135	41	+	+	NUM
ejpam-5703	135	42	ϵ−1y	ϵ−1y	X
ejpam-5703	135	43	(	(	PUNCT
ejpam-5703	135	44	p	p	NOUN
ejpam-5703	135	45	)	)	PUNCT
ejpam-5703	135	46	n+1	n+1	PROPN
ejpam-5703	135	47	+	+	NUM
ejpam-5703	135	48	2hy	2hy	X
ejpam-5703	135	49	(	(	PUNCT
ejpam-5703	135	50	p	p	NOUN
ejpam-5703	135	51	)	)	PUNCT
ejpam-5703	135	52	n	n	PRON
ejpam-5703	135	53	1	1	NUM
ejpam-5703	135	54	+	+	NUM
ejpam-5703	135	55	hy	hy	NOUN
ejpam-5703	135	56	(	(	PUNCT
ejpam-5703	135	57	p	p	NOUN
ejpam-5703	135	58	)	)	PUNCT
ejpam-5703	135	59	n	n	PROPN
ejpam-5703	135	60	+	+	CCONJ
ejpam-5703	135	61	ϵ−1	ϵ−1	PROPN
ejpam-5703	135	62	.	.	PUNCT
ejpam-5703	136	1	(	(	PUNCT
ejpam-5703	136	2	9	9	X
ejpam-5703	136	3	)	)	PUNCT
ejpam-5703	136	4	where	where	SCONJ
ejpam-5703	136	5	yn+1	yn+1	PROPN
ejpam-5703	136	6	indicates	indicate	VERB
ejpam-5703	136	7	that	that	SCONJ
ejpam-5703	136	8	the	the	DET
ejpam-5703	136	9	value	value	NOUN
ejpam-5703	136	10	of	of	ADP
ejpam-5703	136	11	the	the	DET
ejpam-5703	136	12	solution	solution	NOUN
ejpam-5703	136	13	is	be	AUX
ejpam-5703	136	14	yn+1	yn+1	NUM
ejpam-5703	136	15	at	at	ADP
ejpam-5703	136	16	(	(	PUNCT
ejpam-5703	136	17	n	n	X
ejpam-5703	136	18	+	+	CCONJ
ejpam-5703	136	19	1)th	1)th	NUM
ejpam-5703	136	20	time	time	NOUN
ejpam-5703	136	21	step	step	NOUN
ejpam-5703	136	22	and	and	CCONJ
ejpam-5703	136	23	yn	yn	PRON
ejpam-5703	136	24	at	at	ADP
ejpam-5703	136	25	nth	nth	PROPN
ejpam-5703	136	26	time	time	NOUN
ejpam-5703	136	27	step	step	NOUN
ejpam-5703	136	28	,	,	PUNCT
ejpam-5703	136	29	where	where	SCONJ
ejpam-5703	136	30	h	h	NOUN
ejpam-5703	136	31	is	be	AUX
ejpam-5703	136	32	the	the	DET
ejpam-5703	136	33	time	time	NOUN
ejpam-5703	136	34	step	step	NOUN
ejpam-5703	136	35	.	.	PUNCT
ejpam-5703	137	1	only	only	ADV
ejpam-5703	137	2	the	the	DET
ejpam-5703	137	3	non	non	ADJ
ejpam-5703	137	4	-	-	ADJ
ejpam-5703	137	5	linear	linear	ADJ
ejpam-5703	137	6	term	term	NOUN
ejpam-5703	137	7	in	in	ADP
ejpam-5703	137	8	this	this	DET
ejpam-5703	137	9	formulation	formulation	NOUN
ejpam-5703	137	10	is	be	AUX
ejpam-5703	137	11	approximated	approximate	VERB
ejpam-5703	137	12	using	use	VERB
ejpam-5703	137	13	the	the	DET
ejpam-5703	137	14	non	non	ADJ
ejpam-5703	137	15	-	-	ADJ
ejpam-5703	137	16	local	local	ADJ
ejpam-5703	137	17	method	method	NOUN
ejpam-5703	137	18	;	;	PUNCT
ejpam-5703	137	19	the	the	DET
ejpam-5703	137	20	time	time	NOUN
ejpam-5703	137	21	step	step	NOUN
ejpam-5703	137	22	parameter	parameter	PROPN
ejpam-5703	137	23	h	h	PROPN
ejpam-5703	137	24	is	be	AUX
ejpam-5703	137	25	approximated	approximate	VERB
ejpam-5703	137	26	using	use	VERB
ejpam-5703	137	27	the	the	DET
ejpam-5703	137	28	conventional	conventional	ADJ
ejpam-5703	137	29	method	method	NOUN
ejpam-5703	137	30	,	,	PUNCT
ejpam-5703	137	31	as	as	ADP
ejpam-5703	137	32	in	in	ADP
ejpam-5703	137	33	a	a	DET
ejpam-5703	137	34	regular	regular	ADJ
ejpam-5703	137	35	finite	finite	ADJ
ejpam-5703	137	36	difference	difference	NOUN
ejpam-5703	137	37	scheme	scheme	NOUN
ejpam-5703	137	38	.	.	PUNCT
ejpam-5703	138	1	if	if	SCONJ
ejpam-5703	138	2	a	a	DET
ejpam-5703	138	3	non	non	ADJ
ejpam-5703	138	4	-	-	ADJ
ejpam-5703	138	5	trivial	trivial	ADJ
ejpam-5703	138	6	denominator	denominator	NOUN
ejpam-5703	138	7	function	function	NOUN
ejpam-5703	138	8	ϕ(h	ϕ(h	PROPN
ejpam-5703	138	9	)	)	PUNCT
ejpam-5703	138	10	is	be	AUX
ejpam-5703	138	11	used	use	VERB
ejpam-5703	138	12	,	,	PUNCT
ejpam-5703	138	13	such	such	ADJ
ejpam-5703	138	14	that	that	SCONJ
ejpam-5703	138	15	ϕ(h	ϕ(h	PROPN
ejpam-5703	138	16	)	)	PUNCT
ejpam-5703	138	17	→	→	SYM
ejpam-5703	138	18	0	0	PUNCT
ejpam-5703	138	19	as	as	ADP
ejpam-5703	138	20	h	h	NOUN
ejpam-5703	138	21	→	→	SYM
ejpam-5703	138	22	0	0	NUM
ejpam-5703	138	23	,	,	PUNCT
ejpam-5703	138	24	the	the	DET
ejpam-5703	138	25	scheme	scheme	NOUN
ejpam-5703	138	26	is	be	AUX
ejpam-5703	138	27	more	more	ADV
ejpam-5703	138	28	suitable	suitable	ADJ
ejpam-5703	138	29	for	for	ADP
ejpam-5703	138	30	large	large	ADJ
ejpam-5703	138	31	step	step	NOUN
ejpam-5703	138	32	sizes	size	NOUN
ejpam-5703	138	33	.	.	PUNCT
ejpam-5703	139	1	for	for	ADP
ejpam-5703	139	2	the	the	DET
ejpam-5703	139	3	riccati	riccati	PROPN
ejpam-5703	139	4	problem	problem	NOUN
ejpam-5703	139	5	,	,	PUNCT
ejpam-5703	139	6	the	the	DET
ejpam-5703	139	7	denominator	denominator	NOUN
ejpam-5703	139	8	can	can	AUX
ejpam-5703	139	9	be	be	AUX
ejpam-5703	139	10	approximated	approximate	VERB
ejpam-5703	139	11	as	as	ADP
ejpam-5703	139	12	:	:	PUNCT
ejpam-5703	139	13	φ(h	φ(h	NOUN
ejpam-5703	139	14	)	)	PUNCT
ejpam-5703	139	15	=	=	SYM
ejpam-5703	139	16	1−	1−	NUM
ejpam-5703	139	17	e−h	e−h	NOUN
ejpam-5703	139	18	.	.	PUNCT
ejpam-5703	140	1	(	(	PUNCT
ejpam-5703	140	2	10	10	NUM
ejpam-5703	140	3	)	)	PUNCT
ejpam-5703	140	4	this	this	DET
ejpam-5703	140	5	denominator	denominator	NOUN
ejpam-5703	140	6	turns	turn	VERB
ejpam-5703	140	7	our	our	PRON
ejpam-5703	140	8	approach	approach	NOUN
ejpam-5703	140	9	into	into	ADP
ejpam-5703	140	10	:	:	PUNCT
ejpam-5703	140	11	y	y	PROPN
ejpam-5703	140	12	(	(	PUNCT
ejpam-5703	140	13	p	p	NOUN
ejpam-5703	140	14	)	)	PUNCT
ejpam-5703	140	15	n+1	n+1	PROPN
ejpam-5703	140	16	=	=	SYM
ejpam-5703	140	17	y	y	PROPN
ejpam-5703	140	18	(	(	PUNCT
ejpam-5703	140	19	p	p	NOUN
ejpam-5703	140	20	)	)	PUNCT
ejpam-5703	140	21	n	n	PROPN
ejpam-5703	140	22	+	+	CCONJ
ejpam-5703	140	23	1−	1−	NUM
ejpam-5703	140	24	e−h	e−h	ADP
ejpam-5703	140	25	+	+	NOUN
ejpam-5703	140	26	2(1−	2(1−	NUM
ejpam-5703	140	27	e−h)y	e−h)y	PROPN
ejpam-5703	140	28	(	(	PUNCT
ejpam-5703	140	29	p	p	NOUN
ejpam-5703	140	30	)	)	PUNCT
ejpam-5703	140	31	n	n	PRON
ejpam-5703	140	32	1	1	NUM
ejpam-5703	140	33	+	+	CCONJ
ejpam-5703	140	34	(	(	PUNCT
ejpam-5703	140	35	1−	1−	NUM
ejpam-5703	140	36	e−h)y	e−h)y	PROPN
ejpam-5703	140	37	(	(	PUNCT
ejpam-5703	140	38	p	p	NOUN
ejpam-5703	140	39	)	)	PUNCT
ejpam-5703	140	40	n	n	NOUN
ejpam-5703	140	41	.	.	PUNCT
ejpam-5703	141	1	(	(	PUNCT
ejpam-5703	141	2	11	11	NUM
ejpam-5703	141	3	)	)	PUNCT
ejpam-5703	141	4	the	the	DET
ejpam-5703	141	5	corrector	corrector	NOUN
ejpam-5703	141	6	step	step	NOUN
ejpam-5703	141	7	is	be	AUX
ejpam-5703	141	8	:	:	PUNCT
ejpam-5703	141	9	y	y	PROPN
ejpam-5703	141	10	(	(	PUNCT
ejpam-5703	141	11	c	c	X
ejpam-5703	141	12	)	)	PUNCT
ejpam-5703	141	13	n+1	n+1	PROPN
ejpam-5703	141	14	=	=	SYM
ejpam-5703	141	15	1−	1−	NUM
ejpam-5703	141	16	e−h	e−h	ADP
ejpam-5703	141	17	+	+	NOUN
ejpam-5703	141	18	y	y	PROPN
ejpam-5703	141	19	(	(	PUNCT
ejpam-5703	141	20	p	p	NOUN
ejpam-5703	141	21	)	)	PUNCT
ejpam-5703	141	22	n	n	NOUN
ejpam-5703	141	23	+	+	NUM
ejpam-5703	141	24	ϵ−1y	ϵ−1y	X
ejpam-5703	141	25	(	(	PUNCT
ejpam-5703	141	26	p	p	NOUN
ejpam-5703	141	27	)	)	PUNCT
ejpam-5703	141	28	n+1	n+1	PROPN
ejpam-5703	141	29	+	+	NUM
ejpam-5703	141	30	2(1−	2(1−	NUM
ejpam-5703	141	31	e−h)y	e−h)y	PROPN
ejpam-5703	141	32	(	(	PUNCT
ejpam-5703	141	33	p	p	NOUN
ejpam-5703	141	34	)	)	PUNCT
ejpam-5703	141	35	n	n	PRON
ejpam-5703	141	36	1	1	NUM
ejpam-5703	141	37	+	+	CCONJ
ejpam-5703	141	38	(	(	PUNCT
ejpam-5703	141	39	1−	1−	NUM
ejpam-5703	141	40	e−h)y	e−h)y	PROPN
ejpam-5703	141	41	(	(	PUNCT
ejpam-5703	141	42	p	p	NOUN
ejpam-5703	141	43	)	)	PUNCT
ejpam-5703	141	44	n	n	PROPN
ejpam-5703	142	1	+	+	CCONJ
ejpam-5703	143	1	ϵ−1	ϵ−1	PROPN
ejpam-5703	143	2	.	.	PUNCT
ejpam-5703	144	1	(	(	PUNCT
ejpam-5703	144	2	12	12	NUM
ejpam-5703	144	3	)	)	PUNCT
ejpam-5703	144	4	we	we	PRON
ejpam-5703	144	5	may	may	AUX
ejpam-5703	144	6	assess	assess	VERB
ejpam-5703	144	7	how	how	SCONJ
ejpam-5703	144	8	the	the	DET
ejpam-5703	144	9	non	non	ADJ
ejpam-5703	144	10	trivial	trivial	ADJ
ejpam-5703	144	11	denominator	denominator	NOUN
ejpam-5703	144	12	overcomes	overcome	VERB
ejpam-5703	144	13	the	the	DET
ejpam-5703	144	14	nsfd	nsfd	ADJ
ejpam-5703	144	15	-	-	PUNCT
ejpam-5703	144	16	pc	pc	NOUN
ejpam-5703	144	17	scheme	scheme	NOUN
ejpam-5703	144	18	’s	’s	PART
ejpam-5703	144	19	unstable	unstable	ADJ
ejpam-5703	144	20	behavior	behavior	NOUN
ejpam-5703	144	21	in	in	ADP
ejpam-5703	144	22	the	the	DET
ejpam-5703	144	23	following	follow	VERB
ejpam-5703	144	24	section	section	NOUN
ejpam-5703	144	25	.	.	PUNCT
ejpam-5703	145	1	figure	figure	VERB
ejpam-5703	145	2	6	6	NUM
ejpam-5703	145	3	:	:	PUNCT
ejpam-5703	145	4	comparison	comparison	NOUN
ejpam-5703	145	5	of	of	ADP
ejpam-5703	145	6	nsfd	nsfd	ADJ
ejpam-5703	145	7	-	-	PUNCT
ejpam-5703	145	8	pc	pc	NOUN
ejpam-5703	145	9	scheme	scheme	NOUN
ejpam-5703	145	10	and	and	CCONJ
ejpam-5703	145	11	euler	euler	NOUN
ejpam-5703	145	12	-	-	PUNCT
ejpam-5703	145	13	pc	pc	NOUN
ejpam-5703	145	14	with	with	ADP
ejpam-5703	145	15	exact	exact	ADJ
ejpam-5703	145	16	solution	solution	NOUN
ejpam-5703	145	17	at	at	ADP
ejpam-5703	145	18	h=0.1	h=0.1	PROPN
ejpam-5703	145	19	b.	b.	PROPN
ejpam-5703	145	20	rehman	rehman	PROPN
ejpam-5703	145	21	et	et	PROPN
ejpam-5703	145	22	al	al	PROPN
ejpam-5703	145	23	.	.	PUNCT
ejpam-5703	145	24	/	/	SYM
ejpam-5703	145	25	eur	eur	PROPN
ejpam-5703	145	26	.	.	PUNCT
ejpam-5703	146	1	j.	j.	PROPN
ejpam-5703	146	2	pure	pure	PROPN
ejpam-5703	146	3	appl	appl	PROPN
ejpam-5703	146	4	.	.	PROPN
ejpam-5703	146	5	math	math	PROPN
ejpam-5703	146	6	,	,	PUNCT
ejpam-5703	146	7	18	18	NUM
ejpam-5703	146	8	(	(	PUNCT
ejpam-5703	146	9	2	2	NUM
ejpam-5703	146	10	)	)	PUNCT
ejpam-5703	146	11	(	(	PUNCT
ejpam-5703	146	12	2025	2025	NUM
ejpam-5703	146	13	)	)	PUNCT
ejpam-5703	146	14	,	,	PUNCT
ejpam-5703	146	15	5703	5703	NUM
ejpam-5703	146	16	10	10	NUM
ejpam-5703	146	17	of	of	ADP
ejpam-5703	146	18	16	16	NUM
ejpam-5703	146	19	figure	figure	NOUN
ejpam-5703	146	20	7	7	NUM
ejpam-5703	146	21	:	:	PUNCT
ejpam-5703	146	22	comparison	comparison	NOUN
ejpam-5703	146	23	of	of	ADP
ejpam-5703	146	24	nsfd	nsfd	ADJ
ejpam-5703	146	25	-	-	PUNCT
ejpam-5703	146	26	pc	pc	NOUN
ejpam-5703	146	27	scheme	scheme	NOUN
ejpam-5703	146	28	and	and	CCONJ
ejpam-5703	146	29	euler	euler	NOUN
ejpam-5703	146	30	-	-	PUNCT
ejpam-5703	146	31	pc	pc	NOUN
ejpam-5703	146	32	with	with	ADP
ejpam-5703	146	33	exact	exact	ADJ
ejpam-5703	146	34	solution	solution	NOUN
ejpam-5703	146	35	for	for	ADP
ejpam-5703	146	36	step	step	NOUN
ejpam-5703	146	37	size	size	NOUN
ejpam-5703	146	38	0.1	0.1	NUM
ejpam-5703	146	39	figure	figure	NOUN
ejpam-5703	146	40	8	8	NUM
ejpam-5703	146	41	:	:	PUNCT
ejpam-5703	146	42	comparison	comparison	NOUN
ejpam-5703	146	43	of	of	ADP
ejpam-5703	146	44	nsfd	nsfd	ADJ
ejpam-5703	146	45	-	-	PUNCT
ejpam-5703	146	46	pc	pc	NOUN
ejpam-5703	146	47	and	and	CCONJ
ejpam-5703	146	48	euler	euler	NOUN
ejpam-5703	146	49	-	-	PUNCT
ejpam-5703	146	50	pc	pc	NOUN
ejpam-5703	146	51	with	with	ADP
ejpam-5703	146	52	exact	exact	ADJ
ejpam-5703	146	53	solution	solution	NOUN
ejpam-5703	146	54	with	with	ADP
ejpam-5703	146	55	step	step	NOUN
ejpam-5703	146	56	size	size	NOUN
ejpam-5703	146	57	h=1	h=1	PROPN
ejpam-5703	146	58	6	6	NUM
ejpam-5703	146	59	.	.	PUNCT
ejpam-5703	146	60	results	result	NOUN
ejpam-5703	146	61	and	and	CCONJ
ejpam-5703	146	62	discussions	discussion	NOUN
ejpam-5703	146	63	in	in	ADP
ejpam-5703	146	64	this	this	DET
ejpam-5703	146	65	section	section	NOUN
ejpam-5703	146	66	,	,	PUNCT
ejpam-5703	146	67	we	we	PRON
ejpam-5703	146	68	apply	apply	VERB
ejpam-5703	146	69	the	the	DET
ejpam-5703	146	70	suggested	suggest	VERB
ejpam-5703	146	71	nsfd	nsfd	ADJ
ejpam-5703	146	72	-	-	PUNCT
ejpam-5703	146	73	pc	pc	NOUN
ejpam-5703	146	74	algorithms	algorithm	NOUN
ejpam-5703	146	75	to	to	ADP
ejpam-5703	146	76	the	the	DET
ejpam-5703	146	77	riccati	riccati	PROPN
ejpam-5703	146	78	problem	problem	NOUN
ejpam-5703	146	79	in	in	ADP
ejpam-5703	146	80	order	order	NOUN
ejpam-5703	146	81	to	to	PART
ejpam-5703	146	82	assess	assess	VERB
ejpam-5703	146	83	their	their	PRON
ejpam-5703	146	84	performance	performance	NOUN
ejpam-5703	146	85	.	.	PUNCT
ejpam-5703	147	1	we	we	PRON
ejpam-5703	147	2	compare	compare	VERB
ejpam-5703	147	3	the	the	DET
ejpam-5703	147	4	numerical	numerical	ADJ
ejpam-5703	147	5	results	result	NOUN
ejpam-5703	147	6	from	from	ADP
ejpam-5703	147	7	the	the	DET
ejpam-5703	147	8	nsfdpc	nsfdpc	PROPN
ejpam-5703	147	9	schemes	scheme	NOUN
ejpam-5703	147	10	,	,	PUNCT
ejpam-5703	147	11	as	as	SCONJ
ejpam-5703	147	12	defined	define	VERB
ejpam-5703	147	13	in	in	ADP
ejpam-5703	147	14	eq	eq	ADP
ejpam-5703	147	15	.	.	PUNCT
ejpam-5703	148	1	(	(	PUNCT
ejpam-5703	148	2	1	1	NUM
ejpam-5703	148	3	)	)	PUNCT
ejpam-5703	148	4	,	,	PUNCT
ejpam-5703	148	5	with	with	ADP
ejpam-5703	148	6	the	the	DET
ejpam-5703	148	7	precise	precise	ADJ
ejpam-5703	148	8	solution	solution	NOUN
ejpam-5703	148	9	in	in	ADP
ejpam-5703	148	10	order	order	NOUN
ejpam-5703	148	11	to	to	PART
ejpam-5703	148	12	evaluate	evaluate	VERB
ejpam-5703	148	13	the	the	DET
ejpam-5703	148	14	method	method	NOUN
ejpam-5703	148	15	’s	’s	PART
ejpam-5703	148	16	accuracy	accuracy	NOUN
ejpam-5703	148	17	.	.	PUNCT
ejpam-5703	149	1	initially	initially	ADV
ejpam-5703	149	2	,	,	PUNCT
ejpam-5703	149	3	we	we	PRON
ejpam-5703	149	4	observe	observe	VERB
ejpam-5703	149	5	that	that	SCONJ
ejpam-5703	149	6	for	for	ADP
ejpam-5703	149	7	small	small	ADJ
ejpam-5703	149	8	step	step	NOUN
ejpam-5703	149	9	sizes	size	NOUN
ejpam-5703	149	10	h	h	NOUN
ejpam-5703	149	11	=	=	NOUN
ejpam-5703	149	12	0.1	0.1	NUM
ejpam-5703	149	13	,	,	PUNCT
ejpam-5703	149	14	h	h	NOUN
ejpam-5703	149	15	=	=	SYM
ejpam-5703	149	16	1	1	NUM
ejpam-5703	149	17	,	,	PUNCT
ejpam-5703	149	18	1.1	1.1	NUM
ejpam-5703	149	19	,	,	PUNCT
ejpam-5703	149	20	1.8	1.8	NUM
ejpam-5703	149	21	,	,	PUNCT
ejpam-5703	149	22	the	the	DET
ejpam-5703	149	23	nsfd	nsfd	ADJ
ejpam-5703	149	24	-	-	PUNCT
ejpam-5703	149	25	pc	pc	NOUN
ejpam-5703	149	26	scheme	scheme	NOUN
ejpam-5703	149	27	shows	show	VERB
ejpam-5703	149	28	excellent	excellent	ADJ
ejpam-5703	149	29	consistency	consistency	NOUN
ejpam-5703	149	30	with	with	ADP
ejpam-5703	149	31	the	the	DET
ejpam-5703	149	32	exact	exact	ADJ
ejpam-5703	149	33	solution	solution	NOUN
ejpam-5703	149	34	,	,	PUNCT
ejpam-5703	149	35	as	as	SCONJ
ejpam-5703	149	36	illustrated	illustrate	VERB
ejpam-5703	149	37	in	in	ADP
ejpam-5703	149	38	figures	figure	NOUN
ejpam-5703	149	39	7	7	NUM
ejpam-5703	149	40	,	,	PUNCT
ejpam-5703	149	41	8	8	NUM
ejpam-5703	149	42	,	,	PUNCT
ejpam-5703	149	43	9	9	NUM
ejpam-5703	149	44	and	and	CCONJ
ejpam-5703	149	45	10	10	NUM
ejpam-5703	149	46	.	.	PUNCT
ejpam-5703	150	1	this	this	PRON
ejpam-5703	150	2	illustrates	illustrate	VERB
ejpam-5703	150	3	the	the	DET
ejpam-5703	150	4	accuracy	accuracy	NOUN
ejpam-5703	150	5	and	and	CCONJ
ejpam-5703	150	6	consistency	consistency	NOUN
ejpam-5703	150	7	of	of	ADP
ejpam-5703	150	8	the	the	DET
ejpam-5703	150	9	approach	approach	NOUN
ejpam-5703	150	10	under	under	ADP
ejpam-5703	150	11	more	more	ADV
ejpam-5703	150	12	precise	precise	ADJ
ejpam-5703	150	13	discretization	discretization	NOUN
ejpam-5703	150	14	.	.	PUNCT
ejpam-5703	151	1	nevertheless	nevertheless	ADV
ejpam-5703	151	2	,	,	PUNCT
ejpam-5703	151	3	the	the	DET
ejpam-5703	151	4	nsfd	nsfd	ADJ
ejpam-5703	151	5	-	-	PUNCT
ejpam-5703	151	6	pc	pc	NOUN
ejpam-5703	151	7	technique	technique	NOUN
ejpam-5703	151	8	with	with	ADP
ejpam-5703	151	9	a	a	DET
ejpam-5703	151	10	trivial	trivial	ADJ
ejpam-5703	151	11	denominator	denominator	NOUN
ejpam-5703	151	12	starts	start	VERB
ejpam-5703	151	13	to	to	PART
ejpam-5703	151	14	show	show	VERB
ejpam-5703	151	15	non	non	ADJ
ejpam-5703	151	16	-	-	ADJ
ejpam-5703	151	17	physical	physical	ADJ
ejpam-5703	151	18	oscillations	oscillation	NOUN
ejpam-5703	151	19	when	when	SCONJ
ejpam-5703	151	20	the	the	DET
ejpam-5703	151	21	step	step	NOUN
ejpam-5703	151	22	size	size	NOUN
ejpam-5703	151	23	is	be	AUX
ejpam-5703	151	24	raised	raise	VERB
ejpam-5703	151	25	to	to	ADP
ejpam-5703	151	26	h	h	PROPN
ejpam-5703	151	27	b.	b.	PROPN
ejpam-5703	151	28	rehman	rehman	PROPN
ejpam-5703	151	29	et	et	PROPN
ejpam-5703	151	30	al	al	PROPN
ejpam-5703	151	31	.	.	PUNCT
ejpam-5703	151	32	/	/	SYM
ejpam-5703	151	33	eur	eur	PROPN
ejpam-5703	151	34	.	.	PUNCT
ejpam-5703	152	1	j.	j.	PROPN
ejpam-5703	152	2	pure	pure	PROPN
ejpam-5703	152	3	appl	appl	PROPN
ejpam-5703	152	4	.	.	PROPN
ejpam-5703	152	5	math	math	PROPN
ejpam-5703	152	6	,	,	PUNCT
ejpam-5703	152	7	18	18	NUM
ejpam-5703	152	8	(	(	PUNCT
ejpam-5703	152	9	2	2	NUM
ejpam-5703	152	10	)	)	PUNCT
ejpam-5703	152	11	(	(	PUNCT
ejpam-5703	152	12	2025	2025	NUM
ejpam-5703	152	13	)	)	PUNCT
ejpam-5703	152	14	,	,	PUNCT
ejpam-5703	152	15	5703	5703	NUM
ejpam-5703	152	16	11	11	NUM
ejpam-5703	152	17	of	of	ADP
ejpam-5703	152	18	16	16	NUM
ejpam-5703	152	19	figure	figure	NOUN
ejpam-5703	152	20	9	9	NUM
ejpam-5703	152	21	:	:	PUNCT
ejpam-5703	152	22	comparison	comparison	NOUN
ejpam-5703	152	23	of	of	ADP
ejpam-5703	152	24	nsfd	nsfd	ADJ
ejpam-5703	152	25	-	-	PUNCT
ejpam-5703	152	26	pc	pc	NOUN
ejpam-5703	152	27	scheme	scheme	NOUN
ejpam-5703	152	28	and	and	CCONJ
ejpam-5703	152	29	euler	euler	NOUN
ejpam-5703	152	30	-	-	PUNCT
ejpam-5703	152	31	pc	pc	NOUN
ejpam-5703	152	32	with	with	ADP
ejpam-5703	152	33	exact	exact	ADJ
ejpam-5703	152	34	solution	solution	NOUN
ejpam-5703	152	35	for	for	ADP
ejpam-5703	152	36	h=1.1	h=1.1	NOUN
ejpam-5703	152	37	=	=	SYM
ejpam-5703	152	38	5	5	X
ejpam-5703	152	39	.	.	PUNCT
ejpam-5703	153	1	although	although	SCONJ
ejpam-5703	153	2	these	these	DET
ejpam-5703	153	3	oscillations	oscillation	NOUN
ejpam-5703	153	4	are	be	AUX
ejpam-5703	153	5	prominent	prominent	ADJ
ejpam-5703	153	6	,	,	PUNCT
ejpam-5703	153	7	the	the	DET
ejpam-5703	153	8	solution	solution	NOUN
ejpam-5703	153	9	tends	tend	VERB
ejpam-5703	153	10	to	to	PART
ejpam-5703	153	11	align	align	VERB
ejpam-5703	153	12	with	with	ADP
ejpam-5703	153	13	the	the	DET
ejpam-5703	153	14	exact	exact	ADJ
ejpam-5703	153	15	solution	solution	NOUN
ejpam-5703	153	16	after	after	ADP
ejpam-5703	153	17	some	some	DET
ejpam-5703	153	18	time	time	NOUN
ejpam-5703	153	19	,	,	PUNCT
ejpam-5703	153	20	suggesting	suggest	VERB
ejpam-5703	153	21	that	that	SCONJ
ejpam-5703	153	22	the	the	DET
ejpam-5703	153	23	method	method	NOUN
ejpam-5703	153	24	still	still	ADV
ejpam-5703	153	25	maintains	maintain	VERB
ejpam-5703	153	26	a	a	DET
ejpam-5703	153	27	degree	degree	NOUN
ejpam-5703	153	28	of	of	ADP
ejpam-5703	153	29	accuracy	accuracy	NOUN
ejpam-5703	153	30	over	over	ADP
ejpam-5703	153	31	extended	extended	ADJ
ejpam-5703	153	32	periods	period	NOUN
ejpam-5703	153	33	.	.	PUNCT
ejpam-5703	154	1	when	when	SCONJ
ejpam-5703	154	2	the	the	DET
ejpam-5703	154	3	step	step	NOUN
ejpam-5703	154	4	size	size	NOUN
ejpam-5703	154	5	is	be	AUX
ejpam-5703	154	6	further	far	ADV
ejpam-5703	154	7	increased	increase	VERB
ejpam-5703	154	8	to	to	ADP
ejpam-5703	154	9	h	h	NOUN
ejpam-5703	154	10	=	=	NOUN
ejpam-5703	154	11	100	100	NUM
ejpam-5703	154	12	and	and	CCONJ
ejpam-5703	154	13	even	even	ADV
ejpam-5703	154	14	h	h	NOUN
ejpam-5703	154	15	=	=	NUM
ejpam-5703	154	16	200	200	NUM
ejpam-5703	154	17	,	,	PUNCT
ejpam-5703	154	18	the	the	DET
ejpam-5703	154	19	euler	euler	NOUN
ejpam-5703	154	20	scheme	scheme	NOUN
ejpam-5703	154	21	exhibits	exhibit	VERB
ejpam-5703	154	22	increasingly	increasingly	ADV
ejpam-5703	154	23	large	large	ADJ
ejpam-5703	154	24	oscillations	oscillation	NOUN
ejpam-5703	154	25	.	.	PUNCT
ejpam-5703	155	1	these	these	DET
ejpam-5703	155	2	oscillations	oscillation	NOUN
ejpam-5703	155	3	indicate	indicate	VERB
ejpam-5703	155	4	a	a	DET
ejpam-5703	155	5	divergence	divergence	NOUN
ejpam-5703	155	6	from	from	ADP
ejpam-5703	155	7	the	the	DET
ejpam-5703	155	8	exact	exact	ADJ
ejpam-5703	155	9	solution	solution	NOUN
ejpam-5703	155	10	,	,	PUNCT
ejpam-5703	155	11	demonstrating	demonstrate	VERB
ejpam-5703	155	12	the	the	DET
ejpam-5703	155	13	limitations	limitation	NOUN
ejpam-5703	155	14	of	of	ADP
ejpam-5703	155	15	the	the	DET
ejpam-5703	155	16	method	method	NOUN
ejpam-5703	155	17	when	when	SCONJ
ejpam-5703	155	18	a	a	DET
ejpam-5703	155	19	trivial	trivial	ADJ
ejpam-5703	155	20	denominator	denominator	NOUN
ejpam-5703	155	21	is	be	AUX
ejpam-5703	155	22	used	use	VERB
ejpam-5703	155	23	at	at	ADP
ejpam-5703	155	24	large	large	ADJ
ejpam-5703	155	25	step	step	NOUN
ejpam-5703	155	26	sizes	size	NOUN
ejpam-5703	155	27	.	.	PUNCT
ejpam-5703	156	1	despite	despite	SCONJ
ejpam-5703	156	2	this	this	PRON
ejpam-5703	156	3	,	,	PUNCT
ejpam-5703	156	4	the	the	DET
ejpam-5703	156	5	nsfd	nsfd	ADJ
ejpam-5703	156	6	-	-	PUNCT
ejpam-5703	156	7	pc	pc	NOUN
ejpam-5703	156	8	scheme	scheme	NOUN
ejpam-5703	156	9	overcomes	overcome	VERB
ejpam-5703	156	10	this	this	DET
ejpam-5703	156	11	issue	issue	NOUN
ejpam-5703	156	12	.	.	PUNCT
ejpam-5703	157	1	for	for	ADP
ejpam-5703	157	2	large	large	ADJ
ejpam-5703	157	3	step	step	NOUN
ejpam-5703	157	4	sizes	size	NOUN
ejpam-5703	157	5	,	,	PUNCT
ejpam-5703	157	6	including	include	VERB
ejpam-5703	157	7	h	h	NOUN
ejpam-5703	157	8	=	=	NOUN
ejpam-5703	157	9	1.8	1.8	NUM
ejpam-5703	157	10	,	,	PUNCT
ejpam-5703	157	11	h	h	NOUN
ejpam-5703	157	12	=	=	SYM
ejpam-5703	157	13	5	5	NUM
ejpam-5703	157	14	,	,	PUNCT
ejpam-5703	157	15	and	and	CCONJ
ejpam-5703	157	16	beyond	beyond	ADP
ejpam-5703	157	17	,	,	PUNCT
ejpam-5703	157	18	the	the	DET
ejpam-5703	157	19	nsfdpc	nsfdpc	PROPN
ejpam-5703	157	20	method	method	NOUN
ejpam-5703	157	21	with	with	ADP
ejpam-5703	157	22	a	a	DET
ejpam-5703	157	23	non	non	ADJ
ejpam-5703	157	24	-	-	ADJ
ejpam-5703	157	25	trivial	trivial	ADJ
ejpam-5703	157	26	denominator	denominator	NOUN
ejpam-5703	157	27	remains	remain	VERB
ejpam-5703	157	28	consistent	consistent	ADJ
ejpam-5703	157	29	with	with	ADP
ejpam-5703	157	30	the	the	DET
ejpam-5703	157	31	exact	exact	ADJ
ejpam-5703	157	32	solution	solution	NOUN
ejpam-5703	157	33	across	across	ADP
ejpam-5703	157	34	all	all	DET
ejpam-5703	157	35	time	time	NOUN
ejpam-5703	157	36	intervals	interval	NOUN
ejpam-5703	157	37	,	,	PUNCT
ejpam-5703	157	38	highlighting	highlight	VERB
ejpam-5703	157	39	its	its	PRON
ejpam-5703	157	40	robustness	robustness	NOUN
ejpam-5703	157	41	.	.	PUNCT
ejpam-5703	158	1	the	the	DET
ejpam-5703	158	2	ability	ability	NOUN
ejpam-5703	158	3	of	of	ADP
ejpam-5703	158	4	the	the	DET
ejpam-5703	158	5	nsfd	nsfd	ADJ
ejpam-5703	158	6	-	-	PUNCT
ejpam-5703	158	7	pc	pc	NOUN
ejpam-5703	158	8	method	method	NOUN
ejpam-5703	158	9	with	with	ADP
ejpam-5703	158	10	a	a	DET
ejpam-5703	158	11	non	non	ADJ
ejpam-5703	158	12	-	-	ADJ
ejpam-5703	158	13	trivial	trivial	ADJ
ejpam-5703	158	14	denominator	denominator	NOUN
ejpam-5703	158	15	to	to	PART
ejpam-5703	158	16	handle	handle	VERB
ejpam-5703	158	17	large	large	ADJ
ejpam-5703	158	18	step	step	NOUN
ejpam-5703	158	19	sizes	size	NOUN
ejpam-5703	158	20	is	be	AUX
ejpam-5703	158	21	a	a	DET
ejpam-5703	158	22	significant	significant	ADJ
ejpam-5703	158	23	improvement	improvement	NOUN
ejpam-5703	158	24	,	,	PUNCT
ejpam-5703	158	25	as	as	SCONJ
ejpam-5703	158	26	it	it	PRON
ejpam-5703	158	27	allows	allow	VERB
ejpam-5703	158	28	for	for	ADP
ejpam-5703	158	29	accurate	accurate	ADJ
ejpam-5703	158	30	results	result	NOUN
ejpam-5703	158	31	even	even	ADV
ejpam-5703	158	32	with	with	ADP
ejpam-5703	158	33	discretizations	discretization	NOUN
ejpam-5703	158	34	,	,	PUNCT
ejpam-5703	158	35	reducing	reduce	VERB
ejpam-5703	158	36	computational	computational	ADJ
ejpam-5703	158	37	cost	cost	NOUN
ejpam-5703	158	38	.	.	PUNCT
ejpam-5703	159	1	this	this	DET
ejpam-5703	159	2	adjustment	adjustment	NOUN
ejpam-5703	159	3	effectively	effectively	ADV
ejpam-5703	159	4	mitigates	mitigate	VERB
ejpam-5703	159	5	the	the	DET
ejpam-5703	159	6	oscillatory	oscillatory	ADJ
ejpam-5703	159	7	behavior	behavior	NOUN
ejpam-5703	159	8	observed	observe	VERB
ejpam-5703	159	9	with	with	ADP
ejpam-5703	159	10	the	the	DET
ejpam-5703	159	11	trivial	trivial	ADJ
ejpam-5703	159	12	denominator	denominator	NOUN
ejpam-5703	159	13	and	and	CCONJ
ejpam-5703	159	14	makes	make	VERB
ejpam-5703	159	15	the	the	DET
ejpam-5703	159	16	method	method	NOUN
ejpam-5703	159	17	reliable	reliable	ADJ
ejpam-5703	159	18	for	for	ADP
ejpam-5703	159	19	a	a	DET
ejpam-5703	159	20	wider	wide	ADJ
ejpam-5703	159	21	range	range	NOUN
ejpam-5703	159	22	of	of	ADP
ejpam-5703	159	23	step	step	NOUN
ejpam-5703	159	24	sizes	size	NOUN
ejpam-5703	159	25	.	.	PUNCT
ejpam-5703	160	1	in	in	ADP
ejpam-5703	160	2	contrast	contrast	NOUN
ejpam-5703	160	3	,	,	PUNCT
ejpam-5703	160	4	the	the	DET
ejpam-5703	160	5	euler	euler	ADJ
ejpam-5703	160	6	-	-	PUNCT
ejpam-5703	160	7	pc	pc	NOUN
ejpam-5703	160	8	method	method	NOUN
ejpam-5703	160	9	,	,	PUNCT
ejpam-5703	160	10	which	which	PRON
ejpam-5703	160	11	was	be	AUX
ejpam-5703	160	12	also	also	ADV
ejpam-5703	160	13	applied	apply	VERB
ejpam-5703	160	14	to	to	ADP
ejpam-5703	160	15	the	the	DET
ejpam-5703	160	16	riccati	riccati	PROPN
ejpam-5703	160	17	equation	equation	NOUN
ejpam-5703	160	18	for	for	ADP
ejpam-5703	160	19	comparison	comparison	NOUN
ejpam-5703	160	20	,	,	PUNCT
ejpam-5703	160	21	becomes	become	VERB
ejpam-5703	160	22	unstable	unstable	ADJ
ejpam-5703	160	23	when	when	SCONJ
ejpam-5703	160	24	the	the	DET
ejpam-5703	160	25	step	step	NOUN
ejpam-5703	160	26	size	size	NOUN
ejpam-5703	160	27	is	be	AUX
ejpam-5703	160	28	increased	increase	VERB
ejpam-5703	160	29	to	to	ADP
ejpam-5703	160	30	h	h	NOUN
ejpam-5703	160	31	=	=	NOUN
ejpam-5703	160	32	1.8	1.8	NUM
ejpam-5703	160	33	,	,	PUNCT
ejpam-5703	160	34	h	h	NOUN
ejpam-5703	160	35	=	=	SYM
ejpam-5703	160	36	5	5	NUM
ejpam-5703	160	37	,	,	PUNCT
ejpam-5703	160	38	h=100	h=100	PROPN
ejpam-5703	160	39	,	,	PUNCT
ejpam-5703	160	40	h=200	h=200	PROPN
ejpam-5703	160	41	as	as	SCONJ
ejpam-5703	160	42	shown	show	VERB
ejpam-5703	160	43	in	in	ADP
ejpam-5703	160	44	figures	figure	NOUN
ejpam-5703	160	45	10	10	NUM
ejpam-5703	160	46	,	,	PUNCT
ejpam-5703	160	47	11	11	NUM
ejpam-5703	160	48	,	,	PUNCT
ejpam-5703	160	49	12	12	NUM
ejpam-5703	160	50	,	,	PUNCT
ejpam-5703	160	51	13	13	NUM
ejpam-5703	160	52	and	and	CCONJ
ejpam-5703	160	53	14	14	NUM
ejpam-5703	160	54	,	,	PUNCT
ejpam-5703	160	55	the	the	DET
ejpam-5703	160	56	euler	euler	ADJ
ejpam-5703	160	57	-	-	PUNCT
ejpam-5703	160	58	pc	pc	NOUN
ejpam-5703	160	59	method	method	NOUN
ejpam-5703	160	60	exhibits	exhibit	VERB
ejpam-5703	160	61	non	non	ADJ
ejpam-5703	160	62	-	-	ADJ
ejpam-5703	160	63	physical	physical	ADJ
ejpam-5703	160	64	oscillations	oscillation	NOUN
ejpam-5703	160	65	and	and	CCONJ
ejpam-5703	160	66	eventually	eventually	ADV
ejpam-5703	160	67	becomes	become	VERB
ejpam-5703	160	68	unbounded	unbounded	ADJ
ejpam-5703	160	69	over	over	ADP
ejpam-5703	160	70	a	a	DET
ejpam-5703	160	71	longer	long	ADJ
ejpam-5703	160	72	time	time	NOUN
ejpam-5703	160	73	interval	interval	NOUN
ejpam-5703	160	74	,	,	PUNCT
ejpam-5703	160	75	indicating	indicate	VERB
ejpam-5703	160	76	a	a	DET
ejpam-5703	160	77	significant	significant	ADJ
ejpam-5703	160	78	loss	loss	NOUN
ejpam-5703	160	79	of	of	ADP
ejpam-5703	160	80	accuracy	accuracy	NOUN
ejpam-5703	160	81	.	.	PUNCT
ejpam-5703	161	1	the	the	DET
ejpam-5703	161	2	instability	instability	NOUN
ejpam-5703	161	3	of	of	ADP
ejpam-5703	161	4	the	the	DET
ejpam-5703	161	5	euler	euler	VERB
ejpam-5703	161	6	-	-	PUNCT
ejpam-5703	161	7	pc	pc	NOUN
ejpam-5703	161	8	method	method	NOUN
ejpam-5703	161	9	for	for	ADP
ejpam-5703	161	10	larger	large	ADJ
ejpam-5703	161	11	step	step	NOUN
ejpam-5703	161	12	sizes	size	NOUN
ejpam-5703	161	13	further	far	ADV
ejpam-5703	161	14	emphasizes	emphasize	VERB
ejpam-5703	161	15	the	the	DET
ejpam-5703	161	16	superiority	superiority	NOUN
ejpam-5703	161	17	of	of	ADP
ejpam-5703	161	18	the	the	DET
ejpam-5703	161	19	nsfd	nsfd	ADJ
ejpam-5703	161	20	-	-	PUNCT
ejpam-5703	161	21	pc	pc	NOUN
ejpam-5703	161	22	method	method	NOUN
ejpam-5703	161	23	,	,	PUNCT
ejpam-5703	161	24	especially	especially	ADV
ejpam-5703	161	25	when	when	SCONJ
ejpam-5703	161	26	using	use	VERB
ejpam-5703	161	27	a	a	DET
ejpam-5703	161	28	non	non	ADJ
ejpam-5703	161	29	-	-	ADJ
ejpam-5703	161	30	trivial	trivial	ADJ
ejpam-5703	161	31	denominator	denominator	NOUN
ejpam-5703	161	32	.	.	PUNCT
ejpam-5703	162	1	time	time	PROPN
ejpam-5703	162	2	series	series	PROPN
ejpam-5703	162	3	solution	solution	NOUN
ejpam-5703	162	4	of	of	ADP
ejpam-5703	162	5	the	the	DET
ejpam-5703	162	6	nsfd	nsfd	ADJ
ejpam-5703	162	7	-	-	PUNCT
ejpam-5703	162	8	pc	pc	NOUN
ejpam-5703	162	9	and	and	CCONJ
ejpam-5703	162	10	euler	euler	NOUN
ejpam-5703	162	11	-	-	PUNCT
ejpam-5703	162	12	pc	pc	NOUN
ejpam-5703	162	13	methods	method	NOUN
ejpam-5703	162	14	are	be	AUX
ejpam-5703	162	15	presented	present	VERB
ejpam-5703	162	16	in	in	ADP
ejpam-5703	162	17	figure	figure	NOUN
ejpam-5703	162	18	5	5	NUM
ejpam-5703	162	19	,	,	PUNCT
ejpam-5703	162	20	where	where	SCONJ
ejpam-5703	162	21	it	it	PRON
ejpam-5703	162	22	becomes	become	VERB
ejpam-5703	162	23	evident	evident	ADJ
ejpam-5703	162	24	that	that	SCONJ
ejpam-5703	162	25	the	the	DET
ejpam-5703	162	26	nsfd	nsfd	ADJ
ejpam-5703	162	27	-	-	PUNCT
ejpam-5703	162	28	pc	pc	NOUN
ejpam-5703	162	29	method	method	NOUN
ejpam-5703	162	30	significantly	significantly	ADV
ejpam-5703	162	31	outperforms	outperform	VERB
ejpam-5703	162	32	the	the	DET
ejpam-5703	162	33	eulerpc	eulerpc	NOUN
ejpam-5703	162	34	method	method	NOUN
ejpam-5703	162	35	in	in	ADP
ejpam-5703	162	36	terms	term	NOUN
ejpam-5703	162	37	of	of	ADP
ejpam-5703	162	38	minimizing	minimize	VERB
ejpam-5703	162	39	numerical	numerical	ADJ
ejpam-5703	162	40	error	error	NOUN
ejpam-5703	162	41	.	.	PUNCT
ejpam-5703	163	1	the	the	DET
ejpam-5703	163	2	results	result	NOUN
ejpam-5703	163	3	highlight	highlight	VERB
ejpam-5703	163	4	the	the	DET
ejpam-5703	163	5	reliability	reliability	NOUN
ejpam-5703	163	6	and	and	CCONJ
ejpam-5703	163	7	accuracy	accuracy	NOUN
ejpam-5703	163	8	of	of	ADP
ejpam-5703	163	9	the	the	DET
ejpam-5703	163	10	nsfd	nsfd	ADJ
ejpam-5703	163	11	-	-	PUNCT
ejpam-5703	163	12	pc	pc	NOUN
ejpam-5703	163	13	method	method	NOUN
ejpam-5703	163	14	,	,	PUNCT
ejpam-5703	163	15	especially	especially	ADV
ejpam-5703	163	16	for	for	ADP
ejpam-5703	163	17	large	large	ADJ
ejpam-5703	163	18	step	step	NOUN
ejpam-5703	163	19	sizes	size	NOUN
ejpam-5703	163	20	,	,	PUNCT
ejpam-5703	163	21	and	and	CCONJ
ejpam-5703	163	22	suggest	suggest	VERB
ejpam-5703	163	23	its	its	PRON
ejpam-5703	163	24	applicability	applicability	NOUN
ejpam-5703	163	25	in	in	ADP
ejpam-5703	163	26	solving	solve	VERB
ejpam-5703	163	27	nonlinear	nonlinear	ADJ
ejpam-5703	163	28	differential	differential	ADJ
ejpam-5703	163	29	equations	equation	NOUN
ejpam-5703	163	30	like	like	ADP
ejpam-5703	163	31	the	the	DET
ejpam-5703	163	32	riccati	riccati	PROPN
ejpam-5703	163	33	equation	equation	NOUN
ejpam-5703	163	34	across	across	ADP
ejpam-5703	163	35	varying	vary	VERB
ejpam-5703	163	36	time	time	NOUN
ejpam-5703	163	37	intervals	interval	NOUN
ejpam-5703	163	38	and	and	CCONJ
ejpam-5703	163	39	step	step	NOUN
ejpam-5703	163	40	sizes	size	NOUN
ejpam-5703	163	41	.	.	PUNCT
ejpam-5703	164	1	finally	finally	ADV
ejpam-5703	164	2	the	the	DET
ejpam-5703	164	3	systems	system	NOUN
ejpam-5703	164	4	stability	stability	NOUN
ejpam-5703	164	5	,	,	PUNCT
ejpam-5703	164	6	phase	phase	NOUN
ejpam-5703	164	7	line	line	NOUN
ejpam-5703	164	8	analysis	analysis	NOUN
ejpam-5703	164	9	and	and	CCONJ
ejpam-5703	164	10	directional	directional	ADJ
ejpam-5703	164	11	fields	field	NOUN
ejpam-5703	164	12	are	be	AUX
ejpam-5703	164	13	shown	show	VERB
ejpam-5703	164	14	in	in	ADP
ejpam-5703	164	15	figures	figure	NOUN
ejpam-5703	164	16	1	1	NUM
ejpam-5703	164	17	,	,	PUNCT
ejpam-5703	164	18	2	2	NUM
ejpam-5703	164	19	,	,	PUNCT
ejpam-5703	164	20	3	3	NUM
ejpam-5703	164	21	,	,	PUNCT
ejpam-5703	164	22	and	and	CCONJ
ejpam-5703	164	23	4	4	X
ejpam-5703	164	24	.	.	X
ejpam-5703	165	1	the	the	DET
ejpam-5703	165	2	system	system	NOUN
ejpam-5703	165	3	’s	’s	PART
ejpam-5703	165	4	asymptotic	asymptotic	ADJ
ejpam-5703	165	5	stability	stability	NOUN
ejpam-5703	165	6	b.	b.	PROPN
ejpam-5703	165	7	rehman	rehman	PROPN
ejpam-5703	165	8	et	et	PROPN
ejpam-5703	165	9	al	al	PROPN
ejpam-5703	165	10	.	.	PUNCT
ejpam-5703	165	11	/	/	SYM
ejpam-5703	165	12	eur	eur	PROPN
ejpam-5703	165	13	.	.	PUNCT
ejpam-5703	166	1	j.	j.	PROPN
ejpam-5703	166	2	pure	pure	PROPN
ejpam-5703	166	3	appl	appl	PROPN
ejpam-5703	166	4	.	.	PROPN
ejpam-5703	166	5	math	math	PROPN
ejpam-5703	166	6	,	,	PUNCT
ejpam-5703	166	7	18	18	NUM
ejpam-5703	166	8	(	(	PUNCT
ejpam-5703	166	9	2	2	NUM
ejpam-5703	166	10	)	)	PUNCT
ejpam-5703	166	11	(	(	PUNCT
ejpam-5703	166	12	2025	2025	NUM
ejpam-5703	166	13	)	)	PUNCT
ejpam-5703	166	14	,	,	PUNCT
ejpam-5703	166	15	5703	5703	NUM
ejpam-5703	166	16	12	12	NUM
ejpam-5703	166	17	of	of	ADP
ejpam-5703	166	18	16	16	NUM
ejpam-5703	166	19	figure	figure	NOUN
ejpam-5703	166	20	10	10	NUM
ejpam-5703	166	21	:	:	PUNCT
ejpam-5703	166	22	comparison	comparison	NOUN
ejpam-5703	166	23	of	of	ADP
ejpam-5703	166	24	nsfd	nsfd	ADJ
ejpam-5703	166	25	-	-	PUNCT
ejpam-5703	166	26	pc	pc	NOUN
ejpam-5703	166	27	scheme	scheme	NOUN
ejpam-5703	166	28	and	and	CCONJ
ejpam-5703	166	29	euler	euler	NOUN
ejpam-5703	166	30	-	-	PUNCT
ejpam-5703	166	31	pc	pc	NOUN
ejpam-5703	166	32	with	with	ADP
ejpam-5703	166	33	exact	exact	ADJ
ejpam-5703	166	34	solution	solution	NOUN
ejpam-5703	166	35	for	for	ADP
ejpam-5703	166	36	h=1.8	h=1.8	NOUN
ejpam-5703	166	37	figure	figure	NOUN
ejpam-5703	166	38	11	11	NUM
ejpam-5703	166	39	:	:	PUNCT
ejpam-5703	166	40	comparison	comparison	NOUN
ejpam-5703	166	41	of	of	ADP
ejpam-5703	166	42	nsfd	nsfd	ADJ
ejpam-5703	166	43	-	-	PUNCT
ejpam-5703	166	44	pc	pc	NOUN
ejpam-5703	166	45	scheme	scheme	NOUN
ejpam-5703	166	46	and	and	CCONJ
ejpam-5703	166	47	euler	euler	NOUN
ejpam-5703	166	48	-	-	PUNCT
ejpam-5703	166	49	pc	pc	NOUN
ejpam-5703	166	50	with	with	ADP
ejpam-5703	166	51	exact	exact	ADJ
ejpam-5703	166	52	solution	solution	NOUN
ejpam-5703	166	53	for	for	ADP
ejpam-5703	166	54	h=5	h=5	PROPN
ejpam-5703	166	55	toward	toward	ADP
ejpam-5703	166	56	the	the	DET
ejpam-5703	166	57	positive	positive	ADJ
ejpam-5703	166	58	equilibrium	equilibrium	NOUN
ejpam-5703	166	59	is	be	AUX
ejpam-5703	166	60	highlighted	highlight	VERB
ejpam-5703	166	61	by	by	ADP
ejpam-5703	166	62	this	this	DET
ejpam-5703	166	63	analysis	analysis	NOUN
ejpam-5703	166	64	.	.	PUNCT
ejpam-5703	167	1	7	7	X
ejpam-5703	167	2	.	.	X
ejpam-5703	167	3	conclusion	conclusion	NOUN
ejpam-5703	167	4	in	in	ADP
ejpam-5703	167	5	this	this	DET
ejpam-5703	167	6	work	work	NOUN
ejpam-5703	167	7	,	,	PUNCT
ejpam-5703	167	8	we	we	PRON
ejpam-5703	167	9	propose	propose	VERB
ejpam-5703	167	10	an	an	DET
ejpam-5703	167	11	nsfd	nsfd	ADJ
ejpam-5703	167	12	-	-	PUNCT
ejpam-5703	167	13	pc	pc	NOUN
ejpam-5703	167	14	method	method	NOUN
ejpam-5703	167	15	for	for	ADP
ejpam-5703	167	16	solving	solve	VERB
ejpam-5703	167	17	the	the	DET
ejpam-5703	167	18	nonlinear	nonlinear	ADJ
ejpam-5703	167	19	quadratic	quadratic	ADJ
ejpam-5703	167	20	riccati	riccati	NOUN
ejpam-5703	167	21	differential	differential	NOUN
ejpam-5703	167	22	equation	equation	NOUN
ejpam-5703	167	23	that	that	PRON
ejpam-5703	167	24	is	be	AUX
ejpam-5703	167	25	unconditionally	unconditionally	ADV
ejpam-5703	167	26	stable	stable	ADJ
ejpam-5703	167	27	.	.	PUNCT
ejpam-5703	168	1	even	even	ADV
ejpam-5703	168	2	with	with	ADP
ejpam-5703	168	3	larger	large	ADJ
ejpam-5703	168	4	step	step	NOUN
ejpam-5703	168	5	sizes	size	NOUN
ejpam-5703	168	6	,	,	PUNCT
ejpam-5703	168	7	the	the	DET
ejpam-5703	168	8	nsfd	nsfd	ADJ
ejpam-5703	168	9	-	-	PUNCT
ejpam-5703	168	10	pc	pc	NOUN
ejpam-5703	168	11	method	method	NOUN
ejpam-5703	168	12	,	,	PUNCT
ejpam-5703	168	13	which	which	PRON
ejpam-5703	168	14	incorporates	incorporate	VERB
ejpam-5703	168	15	a	a	DET
ejpam-5703	168	16	non	non	ADJ
ejpam-5703	168	17	-	-	ADJ
ejpam-5703	168	18	trivial	trivial	ADJ
ejpam-5703	168	19	denominator	denominator	NOUN
ejpam-5703	168	20	,	,	PUNCT
ejpam-5703	168	21	has	have	AUX
ejpam-5703	168	22	demonstrated	demonstrate	VERB
ejpam-5703	168	23	significant	significant	ADJ
ejpam-5703	168	24	benefits	benefit	NOUN
ejpam-5703	168	25	,	,	PUNCT
ejpam-5703	168	26	especially	especially	ADV
ejpam-5703	168	27	in	in	ADP
ejpam-5703	168	28	terms	term	NOUN
ejpam-5703	168	29	of	of	ADP
ejpam-5703	168	30	stability	stability	NOUN
ejpam-5703	168	31	.	.	PUNCT
ejpam-5703	169	1	a	a	DET
ejpam-5703	169	2	comprehensive	comprehensive	ADJ
ejpam-5703	169	3	examination	examination	NOUN
ejpam-5703	169	4	revealed	reveal	VERB
ejpam-5703	169	5	that	that	SCONJ
ejpam-5703	169	6	the	the	DET
ejpam-5703	169	7	euler	euler	VERB
ejpam-5703	169	8	-	-	PUNCT
ejpam-5703	169	9	pc	pc	NOUN
ejpam-5703	169	10	method	method	NOUN
ejpam-5703	169	11	exhibits	exhibit	VERB
ejpam-5703	169	12	needless	needless	ADJ
ejpam-5703	169	13	oscillations	oscillation	NOUN
ejpam-5703	169	14	or	or	CCONJ
ejpam-5703	169	15	even	even	ADV
ejpam-5703	169	16	diverges	diverge	VERB
ejpam-5703	169	17	when	when	SCONJ
ejpam-5703	169	18	the	the	DET
ejpam-5703	169	19	step	step	NOUN
ejpam-5703	169	20	size	size	NOUN
ejpam-5703	169	21	grows	grow	VERB
ejpam-5703	169	22	.	.	PUNCT
ejpam-5703	170	1	in	in	ADP
ejpam-5703	170	2	contrast	contrast	NOUN
ejpam-5703	170	3	,	,	PUNCT
ejpam-5703	170	4	the	the	DET
ejpam-5703	170	5	nsfd	nsfd	ADJ
ejpam-5703	170	6	-	-	PUNCT
ejpam-5703	170	7	pc	pc	NOUN
ejpam-5703	170	8	approach	approach	NOUN
ejpam-5703	170	9	is	be	AUX
ejpam-5703	170	10	stable	stable	ADJ
ejpam-5703	170	11	and	and	CCONJ
ejpam-5703	170	12	consistent	consistent	ADJ
ejpam-5703	170	13	with	with	ADP
ejpam-5703	170	14	the	the	DET
ejpam-5703	170	15	exact	exact	PROPN
ejpam-5703	170	16	b.	b.	PROPN
ejpam-5703	170	17	rehman	rehman	PROPN
ejpam-5703	170	18	et	et	PROPN
ejpam-5703	170	19	al	al	PROPN
ejpam-5703	170	20	.	.	PUNCT
ejpam-5703	170	21	/	/	SYM
ejpam-5703	170	22	eur	eur	PROPN
ejpam-5703	170	23	.	.	PUNCT
ejpam-5703	171	1	j.	j.	PROPN
ejpam-5703	171	2	pure	pure	PROPN
ejpam-5703	171	3	appl	appl	PROPN
ejpam-5703	171	4	.	.	PROPN
ejpam-5703	171	5	math	math	PROPN
ejpam-5703	171	6	,	,	PUNCT
ejpam-5703	171	7	18	18	NUM
ejpam-5703	171	8	(	(	PUNCT
ejpam-5703	171	9	2	2	NUM
ejpam-5703	171	10	)	)	PUNCT
ejpam-5703	171	11	(	(	PUNCT
ejpam-5703	171	12	2025	2025	NUM
ejpam-5703	171	13	)	)	PUNCT
ejpam-5703	171	14	,	,	PUNCT
ejpam-5703	171	15	5703	5703	NUM
ejpam-5703	171	16	13	13	NUM
ejpam-5703	171	17	of	of	ADP
ejpam-5703	171	18	16	16	NUM
ejpam-5703	171	19	figure	figure	NOUN
ejpam-5703	171	20	12	12	NUM
ejpam-5703	171	21	:	:	PUNCT
ejpam-5703	171	22	comparison	comparison	NOUN
ejpam-5703	171	23	of	of	ADP
ejpam-5703	171	24	nsfd	nsfd	ADJ
ejpam-5703	171	25	-	-	PUNCT
ejpam-5703	171	26	pc	pc	NOUN
ejpam-5703	171	27	scheme	scheme	NOUN
ejpam-5703	171	28	and	and	CCONJ
ejpam-5703	171	29	euler	euler	NOUN
ejpam-5703	171	30	-	-	PUNCT
ejpam-5703	171	31	pc	pc	NOUN
ejpam-5703	171	32	with	with	ADP
ejpam-5703	171	33	exact	exact	ADJ
ejpam-5703	171	34	solution	solution	NOUN
ejpam-5703	171	35	for	for	ADP
ejpam-5703	171	36	h=5	h=5	PROPN
ejpam-5703	171	37	solution	solution	NOUN
ejpam-5703	171	38	regardless	regardless	ADV
ejpam-5703	171	39	of	of	ADP
ejpam-5703	171	40	step	step	NOUN
ejpam-5703	171	41	size	size	NOUN
ejpam-5703	171	42	.	.	PUNCT
ejpam-5703	172	1	this	this	DET
ejpam-5703	172	2	durability	durability	NOUN
ejpam-5703	172	3	makes	make	VERB
ejpam-5703	172	4	it	it	PRON
ejpam-5703	172	5	a	a	DET
ejpam-5703	172	6	great	great	ADJ
ejpam-5703	172	7	candidate	candidate	NOUN
ejpam-5703	172	8	for	for	ADP
ejpam-5703	172	9	solving	solve	VERB
ejpam-5703	172	10	nonlinear	nonlinear	ADJ
ejpam-5703	172	11	and	and	CCONJ
ejpam-5703	172	12	stiff	stiff	ADJ
ejpam-5703	172	13	differential	differential	ADJ
ejpam-5703	172	14	equations	equation	NOUN
ejpam-5703	172	15	.	.	PUNCT
ejpam-5703	173	1	the	the	DET
ejpam-5703	173	2	comparison	comparison	NOUN
ejpam-5703	173	3	clearly	clearly	ADV
ejpam-5703	173	4	demonstrates	demonstrate	VERB
ejpam-5703	173	5	the	the	DET
ejpam-5703	173	6	advantages	advantage	NOUN
ejpam-5703	173	7	of	of	ADP
ejpam-5703	173	8	the	the	DET
ejpam-5703	173	9	nsfd	nsfd	ADJ
ejpam-5703	173	10	-	-	PUNCT
ejpam-5703	173	11	pc	pc	NOUN
ejpam-5703	173	12	method	method	NOUN
ejpam-5703	173	13	over	over	ADP
ejpam-5703	173	14	the	the	DET
ejpam-5703	173	15	euler	euler	ADJ
ejpam-5703	173	16	-	-	PUNCT
ejpam-5703	173	17	pc	pc	NOUN
ejpam-5703	173	18	method	method	NOUN
ejpam-5703	173	19	.	.	PUNCT
ejpam-5703	174	1	the	the	DET
ejpam-5703	174	2	nsfd	nsfd	ADJ
ejpam-5703	174	3	-	-	PUNCT
ejpam-5703	174	4	pc	pc	NOUN
ejpam-5703	174	5	method	method	NOUN
ejpam-5703	174	6	not	not	PART
ejpam-5703	174	7	only	only	ADV
ejpam-5703	174	8	improves	improve	VERB
ejpam-5703	174	9	accuracy	accuracy	NOUN
ejpam-5703	174	10	but	but	CCONJ
ejpam-5703	174	11	also	also	ADV
ejpam-5703	174	12	increases	increase	VERB
ejpam-5703	174	13	stability	stability	NOUN
ejpam-5703	174	14	while	while	SCONJ
ejpam-5703	174	15	solving	solve	VERB
ejpam-5703	174	16	complex	complex	ADJ
ejpam-5703	174	17	differential	differential	ADJ
ejpam-5703	174	18	equations	equation	NOUN
ejpam-5703	174	19	.	.	PUNCT
ejpam-5703	175	1	these	these	DET
ejpam-5703	175	2	characteristics	characteristic	NOUN
ejpam-5703	175	3	are	be	AUX
ejpam-5703	175	4	especially	especially	ADV
ejpam-5703	175	5	significant	significant	ADJ
ejpam-5703	175	6	when	when	SCONJ
ejpam-5703	175	7	dealing	deal	VERB
ejpam-5703	175	8	with	with	ADP
ejpam-5703	175	9	stiff	stiff	ADJ
ejpam-5703	175	10	systems	system	NOUN
ejpam-5703	175	11	,	,	PUNCT
ejpam-5703	175	12	where	where	SCONJ
ejpam-5703	175	13	small	small	ADJ
ejpam-5703	175	14	step	step	NOUN
ejpam-5703	175	15	sizes	size	NOUN
ejpam-5703	175	16	are	be	AUX
ejpam-5703	175	17	typically	typically	ADV
ejpam-5703	175	18	necessary	necessary	ADJ
ejpam-5703	175	19	to	to	PART
ejpam-5703	175	20	maintain	maintain	VERB
ejpam-5703	175	21	stability	stability	NOUN
ejpam-5703	175	22	using	use	VERB
ejpam-5703	175	23	traditional	traditional	ADJ
ejpam-5703	175	24	methods	method	NOUN
ejpam-5703	175	25	.	.	PUNCT
ejpam-5703	176	1	the	the	DET
ejpam-5703	176	2	nsfd	nsfd	ADJ
ejpam-5703	176	3	-	-	PUNCT
ejpam-5703	176	4	pc	pc	NOUN
ejpam-5703	176	5	method	method	NOUN
ejpam-5703	176	6	minimizes	minimize	VERB
ejpam-5703	176	7	the	the	DET
ejpam-5703	176	8	overall	overall	ADJ
ejpam-5703	176	9	computational	computational	ADJ
ejpam-5703	176	10	cost	cost	NOUN
ejpam-5703	176	11	for	for	ADP
ejpam-5703	176	12	long	long	ADJ
ejpam-5703	176	13	-	-	PUNCT
ejpam-5703	176	14	term	term	NOUN
ejpam-5703	176	15	simulations	simulation	NOUN
ejpam-5703	176	16	by	by	ADP
ejpam-5703	176	17	permitting	permit	VERB
ejpam-5703	176	18	bigger	big	ADJ
ejpam-5703	176	19	step	step	NOUN
ejpam-5703	176	20	sizes	size	NOUN
ejpam-5703	176	21	while	while	SCONJ
ejpam-5703	176	22	maintaining	maintain	VERB
ejpam-5703	176	23	accuracy	accuracy	NOUN
ejpam-5703	176	24	,	,	PUNCT
ejpam-5703	176	25	making	make	VERB
ejpam-5703	176	26	it	it	PRON
ejpam-5703	176	27	an	an	DET
ejpam-5703	176	28	efficient	efficient	ADJ
ejpam-5703	176	29	alternative	alternative	NOUN
ejpam-5703	176	30	for	for	ADP
ejpam-5703	176	31	a	a	DET
ejpam-5703	176	32	wide	wide	ADJ
ejpam-5703	176	33	range	range	NOUN
ejpam-5703	176	34	of	of	ADP
ejpam-5703	176	35	applications	application	NOUN
ejpam-5703	176	36	.	.	PUNCT
ejpam-5703	177	1	while	while	SCONJ
ejpam-5703	177	2	it	it	PRON
ejpam-5703	177	3	is	be	AUX
ejpam-5703	177	4	true	true	ADJ
ejpam-5703	177	5	that	that	SCONJ
ejpam-5703	177	6	the	the	DET
ejpam-5703	177	7	nsfd	nsfd	ADJ
ejpam-5703	177	8	-	-	PUNCT
ejpam-5703	177	9	pc	pc	NOUN
ejpam-5703	177	10	technique	technique	NOUN
ejpam-5703	177	11	requires	require	VERB
ejpam-5703	177	12	slightly	slightly	ADV
ejpam-5703	177	13	more	more	ADJ
ejpam-5703	177	14	computing	computing	NOUN
ejpam-5703	177	15	power	power	NOUN
ejpam-5703	177	16	due	due	ADP
ejpam-5703	177	17	to	to	ADP
ejpam-5703	177	18	its	its	PRON
ejpam-5703	177	19	non	non	ADJ
ejpam-5703	177	20	-	-	ADJ
ejpam-5703	177	21	trivial	trivial	ADJ
ejpam-5703	177	22	structure	structure	NOUN
ejpam-5703	177	23	,	,	PUNCT
ejpam-5703	177	24	the	the	DET
ejpam-5703	177	25	trade	trade	NOUN
ejpam-5703	177	26	-	-	PUNCT
ejpam-5703	177	27	off	off	NOUN
ejpam-5703	177	28	is	be	AUX
ejpam-5703	177	29	negligible	negligible	ADJ
ejpam-5703	177	30	when	when	SCONJ
ejpam-5703	177	31	compared	compare	VERB
ejpam-5703	177	32	to	to	ADP
ejpam-5703	177	33	the	the	DET
ejpam-5703	177	34	significant	significant	ADJ
ejpam-5703	177	35	improvements	improvement	NOUN
ejpam-5703	177	36	in	in	ADP
ejpam-5703	177	37	accuracy	accuracy	NOUN
ejpam-5703	177	38	and	and	CCONJ
ejpam-5703	177	39	stability	stability	NOUN
ejpam-5703	177	40	.	.	PUNCT
ejpam-5703	178	1	its	its	PRON
ejpam-5703	178	2	ability	ability	NOUN
ejpam-5703	178	3	to	to	PART
ejpam-5703	178	4	create	create	VERB
ejpam-5703	178	5	solutions	solution	NOUN
ejpam-5703	178	6	that	that	PRON
ejpam-5703	178	7	closely	closely	ADV
ejpam-5703	178	8	resemble	resemble	VERB
ejpam-5703	178	9	exact	exact	ADJ
ejpam-5703	178	10	solutions	solution	NOUN
ejpam-5703	178	11	while	while	SCONJ
ejpam-5703	178	12	remaining	remain	VERB
ejpam-5703	178	13	stable	stable	ADJ
ejpam-5703	178	14	across	across	ADP
ejpam-5703	178	15	a	a	DET
ejpam-5703	178	16	wide	wide	ADJ
ejpam-5703	178	17	range	range	NOUN
ejpam-5703	178	18	of	of	ADP
ejpam-5703	178	19	step	step	NOUN
ejpam-5703	178	20	sizes	size	NOUN
ejpam-5703	178	21	makes	make	VERB
ejpam-5703	178	22	it	it	PRON
ejpam-5703	178	23	the	the	DET
ejpam-5703	178	24	favored	favor	VERB
ejpam-5703	178	25	method	method	NOUN
ejpam-5703	178	26	for	for	ADP
ejpam-5703	178	27	numerical	numerical	ADJ
ejpam-5703	178	28	analysis	analysis	NOUN
ejpam-5703	178	29	.	.	PUNCT
ejpam-5703	179	1	overall	overall	ADV
ejpam-5703	179	2	,	,	PUNCT
ejpam-5703	179	3	the	the	DET
ejpam-5703	179	4	nsfd	nsfd	ADJ
ejpam-5703	179	5	-	-	PUNCT
ejpam-5703	179	6	pc	pc	NOUN
ejpam-5703	179	7	approach	approach	NOUN
ejpam-5703	179	8	stands	stand	VERB
ejpam-5703	179	9	out	out	ADP
ejpam-5703	179	10	as	as	ADP
ejpam-5703	179	11	a	a	DET
ejpam-5703	179	12	dependable	dependable	ADJ
ejpam-5703	179	13	,	,	PUNCT
ejpam-5703	179	14	precise	precise	ADJ
ejpam-5703	179	15	,	,	PUNCT
ejpam-5703	179	16	and	and	CCONJ
ejpam-5703	179	17	computationally	computationally	ADV
ejpam-5703	179	18	efficient	efficient	ADJ
ejpam-5703	179	19	tool	tool	NOUN
ejpam-5703	179	20	for	for	ADP
ejpam-5703	179	21	solving	solve	VERB
ejpam-5703	179	22	complex	complex	ADJ
ejpam-5703	179	23	,	,	PUNCT
ejpam-5703	179	24	nonlinear	nonlinear	ADJ
ejpam-5703	179	25	,	,	PUNCT
ejpam-5703	179	26	and	and	CCONJ
ejpam-5703	179	27	stiff	stiff	ADJ
ejpam-5703	179	28	differential	differential	ADJ
ejpam-5703	179	29	equations	equation	NOUN
ejpam-5703	179	30	,	,	PUNCT
ejpam-5703	179	31	highlighting	highlight	VERB
ejpam-5703	179	32	its	its	PRON
ejpam-5703	179	33	importance	importance	NOUN
ejpam-5703	179	34	in	in	ADP
ejpam-5703	179	35	applied	applied	ADJ
ejpam-5703	179	36	mathematics	mathematic	NOUN
ejpam-5703	179	37	and	and	CCONJ
ejpam-5703	179	38	computer	computer	NOUN
ejpam-5703	179	39	research	research	NOUN
ejpam-5703	179	40	.	.	PUNCT
ejpam-5703	180	1	authors	author	NOUN
ejpam-5703	180	2	’	’	PART
ejpam-5703	180	3	contributions	contribution	NOUN
ejpam-5703	180	4	br	br	PROPN
ejpam-5703	180	5	participated	participate	VERB
ejpam-5703	180	6	in	in	ADP
ejpam-5703	180	7	the	the	DET
ejpam-5703	180	8	conceptualization	conceptualization	NOUN
ejpam-5703	180	9	,	,	PUNCT
ejpam-5703	180	10	investigation	investigation	NOUN
ejpam-5703	180	11	,	,	PUNCT
ejpam-5703	180	12	validation	validation	NOUN
ejpam-5703	180	13	,	,	PUNCT
ejpam-5703	180	14	visualization	visualization	NOUN
ejpam-5703	180	15	and	and	CCONJ
ejpam-5703	180	16	writing	write	VERB
ejpam-5703	180	17	the	the	DET
ejpam-5703	180	18	original	original	ADJ
ejpam-5703	180	19	draft	draft	NOUN
ejpam-5703	180	20	.	.	PUNCT
ejpam-5703	181	1	mab	mab	PROPN
ejpam-5703	181	2	participated	participate	VERB
ejpam-5703	181	3	in	in	ADP
ejpam-5703	181	4	the	the	DET
ejpam-5703	181	5	formal	formal	ADJ
ejpam-5703	181	6	analysis	analysis	NOUN
ejpam-5703	181	7	,	,	PUNCT
ejpam-5703	181	8	data	data	NOUN
ejpam-5703	181	9	curation	curation	NOUN
ejpam-5703	181	10	,	,	PUNCT
ejpam-5703	181	11	investigation	investigation	NOUN
ejpam-5703	181	12	,	,	PUNCT
ejpam-5703	181	13	supervision	supervision	NOUN
ejpam-5703	181	14	,	,	PUNCT
ejpam-5703	181	15	review	review	NOUN
ejpam-5703	181	16	and	and	CCONJ
ejpam-5703	181	17	editing	editing	NOUN
ejpam-5703	181	18	of	of	ADP
ejpam-5703	181	19	the	the	DET
ejpam-5703	181	20	manuscript	manuscript	NOUN
ejpam-5703	181	21	.	.	PUNCT
ejpam-5703	182	1	ak	ak	PROPN
ejpam-5703	182	2	participated	participate	VERB
ejpam-5703	182	3	in	in	ADP
ejpam-5703	182	4	the	the	DET
ejpam-5703	182	5	conceptualization	conceptualization	NOUN
ejpam-5703	182	6	,	,	PUNCT
ejpam-5703	182	7	administration	administration	NOUN
ejpam-5703	182	8	,	,	PUNCT
ejpam-5703	182	9	validation	validation	NOUN
ejpam-5703	182	10	,	,	PUNCT
ejpam-5703	182	11	visualization	visualization	NOUN
ejpam-5703	182	12	and	and	CCONJ
ejpam-5703	182	13	writing	writing	NOUN
ejpam-5703	182	14	of	of	ADP
ejpam-5703	182	15	the	the	DET
ejpam-5703	182	16	manuscript	manuscript	NOUN
ejpam-5703	182	17	.	.	PUNCT
ejpam-5703	183	1	dka	dka	PROPN
ejpam-5703	183	2	participated	participate	VERB
ejpam-5703	183	3	in	in	ADP
ejpam-5703	183	4	the	the	DET
ejpam-5703	183	5	review	review	NOUN
ejpam-5703	183	6	and	and	CCONJ
ejpam-5703	183	7	editing	editing	NOUN
ejpam-5703	183	8	of	of	ADP
ejpam-5703	183	9	the	the	DET
ejpam-5703	183	10	manuscript	manuscript	NOUN
ejpam-5703	183	11	.	.	PUNCT
ejpam-5703	184	1	ta	ta	PROPN
ejpam-5703	184	2	participated	participate	VERB
ejpam-5703	184	3	in	in	ADP
ejpam-5703	184	4	the	the	DET
ejpam-5703	184	5	administration	administration	NOUN
ejpam-5703	184	6	,	,	PUNCT
ejpam-5703	184	7	validation	validation	NOUN
ejpam-5703	184	8	,	,	PUNCT
ejpam-5703	184	9	visualization	visualization	NOUN
ejpam-5703	184	10	,	,	PUNCT
ejpam-5703	184	11	review	review	NOUN
ejpam-5703	184	12	and	and	CCONJ
ejpam-5703	184	13	editing	editing	NOUN
ejpam-5703	184	14	of	of	ADP
ejpam-5703	184	15	the	the	DET
ejpam-5703	184	16	manuscript	manuscript	NOUN
ejpam-5703	184	17	.	.	PUNCT
ejpam-5703	185	1	all	all	DET
ejpam-5703	185	2	authors	author	NOUN
ejpam-5703	185	3	read	read	VERB
ejpam-5703	185	4	and	and	CCONJ
ejpam-5703	185	5	approved	approve	VERB
ejpam-5703	185	6	the	the	DET
ejpam-5703	185	7	final	final	ADJ
ejpam-5703	185	8	manuscript	manuscript	NOUN
ejpam-5703	185	9	.	.	PUNCT
ejpam-5703	186	1	b.	b.	PROPN
ejpam-5703	186	2	rehman	rehman	PROPN
ejpam-5703	186	3	et	et	PROPN
ejpam-5703	186	4	al	al	PROPN
ejpam-5703	186	5	.	.	PUNCT
ejpam-5703	186	6	/	/	SYM
ejpam-5703	186	7	eur	eur	PROPN
ejpam-5703	186	8	.	.	PUNCT
ejpam-5703	187	1	j.	j.	PROPN
ejpam-5703	187	2	pure	pure	PROPN
ejpam-5703	187	3	appl	appl	PROPN
ejpam-5703	187	4	.	.	PROPN
ejpam-5703	187	5	math	math	PROPN
ejpam-5703	187	6	,	,	PUNCT
ejpam-5703	187	7	18	18	NUM
ejpam-5703	187	8	(	(	PUNCT
ejpam-5703	187	9	2	2	NUM
ejpam-5703	187	10	)	)	PUNCT
ejpam-5703	187	11	(	(	PUNCT
ejpam-5703	187	12	2025	2025	NUM
ejpam-5703	187	13	)	)	PUNCT
ejpam-5703	187	14	,	,	PUNCT
ejpam-5703	187	15	5703	5703	NUM
ejpam-5703	187	16	14	14	NUM
ejpam-5703	187	17	of	of	ADP
ejpam-5703	187	18	16	16	NUM
ejpam-5703	187	19	figure	figure	NOUN
ejpam-5703	187	20	13	13	NUM
ejpam-5703	187	21	:	:	PUNCT
ejpam-5703	187	22	comparison	comparison	NOUN
ejpam-5703	187	23	of	of	ADP
ejpam-5703	187	24	nsfd	nsfd	ADJ
ejpam-5703	187	25	-	-	PUNCT
ejpam-5703	187	26	pc	pc	NOUN
ejpam-5703	187	27	scheme	scheme	NOUN
ejpam-5703	187	28	and	and	CCONJ
ejpam-5703	187	29	euler	euler	NOUN
ejpam-5703	187	30	-	-	PUNCT
ejpam-5703	187	31	pc	pc	NOUN
ejpam-5703	187	32	with	with	ADP
ejpam-5703	187	33	exact	exact	ADJ
ejpam-5703	187	34	solution	solution	NOUN
ejpam-5703	187	35	for	for	ADP
ejpam-5703	187	36	h=100	h=100	PROPN
ejpam-5703	187	37	figure	figure	NOUN
ejpam-5703	187	38	14	14	NUM
ejpam-5703	187	39	:	:	PUNCT
ejpam-5703	187	40	comparison	comparison	NOUN
ejpam-5703	187	41	of	of	ADP
ejpam-5703	187	42	nsfd	nsfd	ADJ
ejpam-5703	187	43	-	-	PUNCT
ejpam-5703	187	44	pc	pc	NOUN
ejpam-5703	187	45	scheme	scheme	NOUN
ejpam-5703	187	46	and	and	CCONJ
ejpam-5703	187	47	euler	euler	NOUN
ejpam-5703	187	48	-	-	PUNCT
ejpam-5703	187	49	pc	pc	NOUN
ejpam-5703	187	50	with	with	ADP
ejpam-5703	187	51	exact	exact	ADJ
ejpam-5703	187	52	solution	solution	NOUN
ejpam-5703	187	53	for	for	ADP
ejpam-5703	187	54	h=200	h=200	NOUN
ejpam-5703	187	55	acknowledgements	acknowledgement	NOUN
ejpam-5703	187	56	d.k.a	d.k.a	PROPN
ejpam-5703	187	57	.	.	PROPN
ejpam-5703	187	58	extends	extend	VERB
ejpam-5703	187	59	the	the	DET
ejpam-5703	187	60	appreciation	appreciation	NOUN
ejpam-5703	187	61	to	to	ADP
ejpam-5703	187	62	the	the	DET
ejpam-5703	187	63	deanship	deanship	NOUN
ejpam-5703	187	64	of	of	ADP
ejpam-5703	187	65	postgraduate	postgraduate	NOUN
ejpam-5703	187	66	studies	study	NOUN
ejpam-5703	187	67	and	and	CCONJ
ejpam-5703	187	68	scientific	scientific	ADJ
ejpam-5703	187	69	research	research	NOUN
ejpam-5703	187	70	at	at	ADP
ejpam-5703	187	71	majmaah	majmaah	PROPN
ejpam-5703	187	72	university	university	PROPN
ejpam-5703	187	73	for	for	ADP
ejpam-5703	187	74	funding	fund	VERB
ejpam-5703	187	75	this	this	DET
ejpam-5703	187	76	research	research	NOUN
ejpam-5703	187	77	work	work	NOUN
ejpam-5703	187	78	.	.	PUNCT
ejpam-5703	188	1	a.k	a.k	PROPN
ejpam-5703	188	2	and	and	CCONJ
ejpam-5703	188	3	t.a	t.a	PROPN
ejpam-5703	188	4	would	would	AUX
ejpam-5703	188	5	like	like	VERB
ejpam-5703	188	6	to	to	PART
ejpam-5703	188	7	thank	thank	VERB
ejpam-5703	188	8	prince	prince	PROPN
ejpam-5703	188	9	sultan	sultan	PROPN
ejpam-5703	188	10	university	university	PROPN
ejpam-5703	188	11	for	for	ADP
ejpam-5703	188	12	paying	pay	VERB
ejpam-5703	188	13	the	the	DET
ejpam-5703	188	14	apc	apc	NOUN
ejpam-5703	188	15	and	and	CCONJ
ejpam-5703	188	16	the	the	DET
ejpam-5703	188	17	support	support	NOUN
ejpam-5703	188	18	through	through	ADP
ejpam-5703	188	19	tas	tas	PROPN
ejpam-5703	188	20	research	research	NOUN
ejpam-5703	188	21	lab	lab	NOUN
ejpam-5703	188	22	.	.	PUNCT
ejpam-5703	189	1	b.	b.	PROPN
ejpam-5703	189	2	rehman	rehman	PROPN
ejpam-5703	189	3	et	et	PROPN
ejpam-5703	189	4	al	al	PROPN
ejpam-5703	189	5	.	.	PUNCT
ejpam-5703	189	6	/	/	SYM
ejpam-5703	189	7	eur	eur	PROPN
ejpam-5703	189	8	.	.	PUNCT
ejpam-5703	190	1	j.	j.	PROPN
ejpam-5703	190	2	pure	pure	PROPN
ejpam-5703	190	3	appl	appl	PROPN
ejpam-5703	190	4	.	.	PROPN
ejpam-5703	190	5	math	math	PROPN
ejpam-5703	190	6	,	,	PUNCT
ejpam-5703	190	7	18	18	NUM
ejpam-5703	190	8	(	(	PUNCT
ejpam-5703	190	9	2	2	NUM
ejpam-5703	190	10	)	)	PUNCT
ejpam-5703	190	11	(	(	PUNCT
ejpam-5703	190	12	2025	2025	NUM
ejpam-5703	190	13	)	)	PUNCT
ejpam-5703	190	14	,	,	PUNCT
ejpam-5703	190	15	5703	5703	NUM
ejpam-5703	190	16	15	15	NUM
ejpam-5703	190	17	of	of	ADP
ejpam-5703	190	18	16	16	NUM
ejpam-5703	190	19	availability	availability	NOUN
ejpam-5703	190	20	of	of	ADP
ejpam-5703	190	21	data	datum	NOUN
ejpam-5703	190	22	and	and	CCONJ
ejpam-5703	190	23	materials	material	NOUN
ejpam-5703	190	24	all	all	DET
ejpam-5703	190	25	data	datum	NOUN
ejpam-5703	190	26	that	that	PRON
ejpam-5703	190	27	support	support	VERB
ejpam-5703	190	28	the	the	DET
ejpam-5703	190	29	findings	finding	NOUN
ejpam-5703	190	30	of	of	ADP
ejpam-5703	190	31	this	this	DET
ejpam-5703	190	32	study	study	NOUN
ejpam-5703	190	33	are	be	AUX
ejpam-5703	190	34	included	include	VERB
ejpam-5703	190	35	in	in	ADP
ejpam-5703	190	36	the	the	DET
ejpam-5703	190	37	article	article	NOUN
ejpam-5703	190	38	.	.	PUNCT
ejpam-5703	191	1	competing	compete	VERB
ejpam-5703	191	2	interests	interest	NOUN
ejpam-5703	191	3	:	:	PUNCT
ejpam-5703	191	4	the	the	DET
ejpam-5703	191	5	authors	author	NOUN
ejpam-5703	191	6	declare	declare	VERB
ejpam-5703	191	7	that	that	SCONJ
ejpam-5703	191	8	they	they	PRON
ejpam-5703	191	9	have	have	VERB
ejpam-5703	191	10	no	no	DET
ejpam-5703	191	11	competing	compete	VERB
ejpam-5703	191	12	interests	interest	NOUN
ejpam-5703	191	13	.	.	PUNCT
ejpam-5703	192	1	references	reference	NOUN
ejpam-5703	192	2	[	[	X
ejpam-5703	192	3	1	1	NUM
ejpam-5703	192	4	]	]	PUNCT
ejpam-5703	192	5	r.	r.	PROPN
ejpam-5703	192	6	e.	e.	PROPN
ejpam-5703	192	7	mickens	mickens	PROPN
ejpam-5703	192	8	.	.	PUNCT
ejpam-5703	193	1	numerical	numerical	ADJ
ejpam-5703	193	2	integration	integration	NOUN
ejpam-5703	193	3	of	of	ADP
ejpam-5703	193	4	population	population	NOUN
ejpam-5703	193	5	models	model	NOUN
ejpam-5703	193	6	satisfying	satisfy	VERB
ejpam-5703	193	7	conservation	conservation	NOUN
ejpam-5703	193	8	laws	law	NOUN
ejpam-5703	193	9	:	:	PUNCT
ejpam-5703	193	10	nsfd	nsfd	ADJ
ejpam-5703	193	11	methods	method	NOUN
ejpam-5703	193	12	.	.	PUNCT
ejpam-5703	194	1	journal	journal	NOUN
ejpam-5703	194	2	of	of	ADP
ejpam-5703	194	3	biological	biological	ADJ
ejpam-5703	194	4	dynamics	dynamic	NOUN
ejpam-5703	194	5	,	,	PUNCT
ejpam-5703	194	6	1(4):427–436	1(4):427–436	NUM
ejpam-5703	194	7	,	,	PUNCT
ejpam-5703	194	8	2007	2007	NUM
ejpam-5703	194	9	.	.	PUNCT
ejpam-5703	195	1	[	[	X
ejpam-5703	195	2	2	2	NUM
ejpam-5703	195	3	]	]	PUNCT
ejpam-5703	195	4	r.	r.	PROPN
ejpam-5703	195	5	e.	e.	PROPN
ejpam-5703	195	6	mickens	mickens	PROPN
ejpam-5703	195	7	.	.	PUNCT
ejpam-5703	196	1	dynamic	dynamic	ADJ
ejpam-5703	196	2	consistency	consistency	NOUN
ejpam-5703	196	3	:	:	PUNCT
ejpam-5703	196	4	a	a	DET
ejpam-5703	196	5	fundamental	fundamental	ADJ
ejpam-5703	196	6	principle	principle	NOUN
ejpam-5703	196	7	for	for	ADP
ejpam-5703	196	8	constructing	construct	VERB
ejpam-5703	196	9	nonstandard	nonstandard	ADJ
ejpam-5703	196	10	finite	finite	ADJ
ejpam-5703	196	11	difference	difference	NOUN
ejpam-5703	196	12	schemes	scheme	NOUN
ejpam-5703	196	13	for	for	ADP
ejpam-5703	196	14	differential	differential	ADJ
ejpam-5703	196	15	equations	equation	NOUN
ejpam-5703	196	16	.	.	PUNCT
ejpam-5703	197	1	journal	journal	NOUN
ejpam-5703	197	2	of	of	ADP
ejpam-5703	197	3	difference	difference	NOUN
ejpam-5703	197	4	equations	equation	NOUN
ejpam-5703	197	5	and	and	CCONJ
ejpam-5703	197	6	applications	application	NOUN
ejpam-5703	197	7	,	,	PUNCT
ejpam-5703	197	8	11(7):645–653	11(7):645–653	PROPN
ejpam-5703	197	9	,	,	PUNCT
ejpam-5703	197	10	2005	2005	NUM
ejpam-5703	197	11	.	.	PUNCT
ejpam-5703	198	1	[	[	X
ejpam-5703	198	2	3	3	X
ejpam-5703	198	3	]	]	X
ejpam-5703	198	4	d.	d.	PROPN
ejpam-5703	198	5	t.	t.	PROPN
ejpam-5703	198	6	dimitrov	dimitrov	PROPN
ejpam-5703	198	7	and	and	CCONJ
ejpam-5703	198	8	h.	h.	PROPN
ejpam-5703	198	9	v.	v.	PROPN
ejpam-5703	198	10	kojouharov	kojouharov	PROPN
ejpam-5703	198	11	.	.	PUNCT
ejpam-5703	199	1	positive	positive	ADJ
ejpam-5703	199	2	and	and	CCONJ
ejpam-5703	199	3	elementary	elementary	ADJ
ejpam-5703	199	4	stable	stable	ADJ
ejpam-5703	199	5	nonstandard	nonstandard	ADJ
ejpam-5703	199	6	numerical	numerical	ADJ
ejpam-5703	199	7	methods	method	NOUN
ejpam-5703	199	8	with	with	ADP
ejpam-5703	199	9	applications	application	NOUN
ejpam-5703	199	10	to	to	ADP
ejpam-5703	199	11	predator	predator	NOUN
ejpam-5703	199	12	-	-	PUNCT
ejpam-5703	199	13	prey	prey	NOUN
ejpam-5703	199	14	models	model	NOUN
ejpam-5703	199	15	.	.	PUNCT
ejpam-5703	200	1	journal	journal	NOUN
ejpam-5703	200	2	of	of	ADP
ejpam-5703	200	3	computational	computational	ADJ
ejpam-5703	200	4	and	and	CCONJ
ejpam-5703	200	5	applied	applied	ADJ
ejpam-5703	200	6	mathematics	mathematic	NOUN
ejpam-5703	200	7	,	,	PUNCT
ejpam-5703	200	8	11(1–2):98–108	11(1–2):98–108	NUM
ejpam-5703	200	9	,	,	PUNCT
ejpam-5703	200	10	2006	2006	NUM
ejpam-5703	200	11	.	.	PUNCT
ejpam-5703	201	1	[	[	X
ejpam-5703	201	2	4	4	X
ejpam-5703	201	3	]	]	PUNCT
ejpam-5703	201	4	s.	s.	PROPN
ejpam-5703	201	5	k.	k.	PROPN
ejpam-5703	201	6	sharma	sharma	PROPN
ejpam-5703	201	7	,	,	PUNCT
ejpam-5703	201	8	r.	r.	PROPN
ejpam-5703	201	9	alghamdi	alghamdi	PROPN
ejpam-5703	201	10	,	,	PUNCT
ejpam-5703	201	11	s.	s.	PROPN
ejpam-5703	201	12	alasmari	alasmari	PROPN
ejpam-5703	201	13	,	,	PUNCT
ejpam-5703	201	14	n.	n.	PROPN
ejpam-5703	201	15	k.	k.	PROPN
ejpam-5703	201	16	sharma	sharma	PROPN
ejpam-5703	201	17	,	,	PUNCT
ejpam-5703	201	18	h.	h.	PROPN
ejpam-5703	201	19	khan	khan	PROPN
ejpam-5703	201	20	,	,	PUNCT
ejpam-5703	201	21	and	and	CCONJ
ejpam-5703	201	22	f.	f.	PROPN
ejpam-5703	201	23	ahmad	ahmad	PROPN
ejpam-5703	201	24	.	.	PUNCT
ejpam-5703	202	1	fractional	fractional	ADJ
ejpam-5703	202	2	order	order	NOUN
ejpam-5703	202	3	pid	pid	NOUN
ejpam-5703	202	4	controllers	controller	NOUN
ejpam-5703	202	5	for	for	ADP
ejpam-5703	202	6	collaborative	collaborative	ADJ
ejpam-5703	202	7	energy	energy	NOUN
ejpam-5703	202	8	management	management	NOUN
ejpam-5703	202	9	in	in	ADP
ejpam-5703	202	10	iot	iot	ADJ
ejpam-5703	202	11	-	-	PUNCT
ejpam-5703	202	12	smart	smart	ADJ
ejpam-5703	202	13	cities	city	NOUN
ejpam-5703	202	14	:	:	PUNCT
ejpam-5703	202	15	hybrid	hybrid	ADJ
ejpam-5703	202	16	optimization	optimization	NOUN
ejpam-5703	202	17	algorithms	algorithm	NOUN
ejpam-5703	202	18	for	for	ADP
ejpam-5703	202	19	demand	demand	NOUN
ejpam-5703	202	20	.	.	PUNCT
ejpam-5703	203	1	energy	energy	NOUN
ejpam-5703	203	2	reports	report	NOUN
ejpam-5703	203	3	,	,	PUNCT
ejpam-5703	203	4	12:5551–5566	12:5551–5566	NUM
ejpam-5703	203	5	,	,	PUNCT
ejpam-5703	203	6	2024	2024	NUM
ejpam-5703	203	7	.	.	PUNCT
ejpam-5703	204	1	[	[	X
ejpam-5703	204	2	5	5	NUM
ejpam-5703	204	3	]	]	PUNCT
ejpam-5703	204	4	a.	a.	NOUN
ejpam-5703	204	5	alkhazzan	alkhazzan	PROPN
ejpam-5703	204	6	,	,	PUNCT
ejpam-5703	204	7	j.	j.	PROPN
ejpam-5703	204	8	wang	wang	PROPN
ejpam-5703	204	9	,	,	PUNCT
ejpam-5703	204	10	y.	y.	PROPN
ejpam-5703	204	11	nie	nie	PROPN
ejpam-5703	204	12	,	,	PUNCT
ejpam-5703	204	13	h.	h.	PROPN
ejpam-5703	204	14	khan	khan	PROPN
ejpam-5703	204	15	,	,	PUNCT
ejpam-5703	204	16	and	and	CCONJ
ejpam-5703	204	17	j.	j.	PROPN
ejpam-5703	204	18	alzabut	alzabut	PROPN
ejpam-5703	204	19	.	.	PUNCT
ejpam-5703	205	1	a	a	DET
ejpam-5703	205	2	novel	novel	NOUN
ejpam-5703	205	3	svir	svir	NOUN
ejpam-5703	205	4	epidemic	epidemic	NOUN
ejpam-5703	205	5	model	model	NOUN
ejpam-5703	205	6	with	with	ADP
ejpam-5703	205	7	jumps	jump	NOUN
ejpam-5703	205	8	for	for	ADP
ejpam-5703	205	9	understanding	understand	VERB
ejpam-5703	205	10	the	the	DET
ejpam-5703	205	11	dynamics	dynamic	NOUN
ejpam-5703	205	12	of	of	ADP
ejpam-5703	205	13	the	the	DET
ejpam-5703	205	14	spread	spread	NOUN
ejpam-5703	205	15	of	of	ADP
ejpam-5703	205	16	dual	dual	ADJ
ejpam-5703	205	17	diseases	disease	NOUN
ejpam-5703	205	18	.	.	PUNCT
ejpam-5703	206	1	chaos	chaos	NOUN
ejpam-5703	206	2	:	:	PUNCT
ejpam-5703	206	3	an	an	DET
ejpam-5703	206	4	interdisciplinary	interdisciplinary	ADJ
ejpam-5703	206	5	journal	journal	NOUN
ejpam-5703	206	6	of	of	ADP
ejpam-5703	206	7	nonlinear	nonlinear	ADJ
ejpam-5703	206	8	science	science	NOUN
ejpam-5703	206	9	,	,	PUNCT
ejpam-5703	206	10	34(9	34(9	NUM
ejpam-5703	206	11	)	)	PUNCT
ejpam-5703	206	12	,	,	PUNCT
ejpam-5703	206	13	2024	2024	NUM
ejpam-5703	206	14	.	.	PUNCT
ejpam-5703	207	1	[	[	X
ejpam-5703	207	2	6	6	NUM
ejpam-5703	207	3	]	]	X
ejpam-5703	207	4	h.	h.	PROPN
ejpam-5703	207	5	khan	khan	PROPN
ejpam-5703	207	6	,	,	PUNCT
ejpam-5703	207	7	j.	j.	PROPN
ejpam-5703	207	8	alzabut	alzabut	PROPN
ejpam-5703	207	9	,	,	PUNCT
ejpam-5703	207	10	d.	d.	PROPN
ejpam-5703	207	11	k.	k.	PROPN
ejpam-5703	207	12	almutairi	almutairi	PROPN
ejpam-5703	207	13	,	,	PUNCT
ejpam-5703	207	14	and	and	CCONJ
ejpam-5703	207	15	w.	w.	PROPN
ejpam-5703	207	16	k.	k.	PROPN
ejpam-5703	207	17	alqurashi	alqurashi	PROPN
ejpam-5703	207	18	.	.	PUNCT
ejpam-5703	208	1	the	the	DET
ejpam-5703	208	2	use	use	NOUN
ejpam-5703	208	3	of	of	ADP
ejpam-5703	208	4	artificial	artificial	ADJ
ejpam-5703	208	5	intelligence	intelligence	NOUN
ejpam-5703	208	6	in	in	ADP
ejpam-5703	208	7	data	datum	NOUN
ejpam-5703	208	8	analysis	analysis	NOUN
ejpam-5703	208	9	with	with	ADP
ejpam-5703	208	10	error	error	NOUN
ejpam-5703	208	11	recognitions	recognition	NOUN
ejpam-5703	208	12	in	in	ADP
ejpam-5703	208	13	liver	liver	NOUN
ejpam-5703	208	14	transplantation	transplantation	NOUN
ejpam-5703	208	15	in	in	ADP
ejpam-5703	208	16	hiv	hiv	PROPN
ejpam-5703	208	17	-	-	PUNCT
ejpam-5703	208	18	aids	aid	NOUN
ejpam-5703	208	19	patients	patient	NOUN
ejpam-5703	208	20	using	use	VERB
ejpam-5703	208	21	modified	modify	VERB
ejpam-5703	208	22	abc	abc	PROPN
ejpam-5703	208	23	fractional	fractional	ADJ
ejpam-5703	208	24	order	order	NOUN
ejpam-5703	208	25	operators	operator	NOUN
ejpam-5703	208	26	.	.	PUNCT
ejpam-5703	209	1	fractal	fractal	ADJ
ejpam-5703	209	2	and	and	CCONJ
ejpam-5703	209	3	fractional	fractional	ADJ
ejpam-5703	209	4	,	,	PUNCT
ejpam-5703	209	5	9:16	9:16	NUM
ejpam-5703	209	6	,	,	PUNCT
ejpam-5703	209	7	2025	2025	NUM
ejpam-5703	209	8	.	.	PUNCT
ejpam-5703	210	1	[	[	X
ejpam-5703	210	2	7	7	X
ejpam-5703	210	3	]	]	X
ejpam-5703	210	4	h.	h.	PROPN
ejpam-5703	210	5	khan	khan	PROPN
ejpam-5703	210	6	,	,	PUNCT
ejpam-5703	210	7	j.	j.	PROPN
ejpam-5703	210	8	alzabut	alzabut	PROPN
ejpam-5703	210	9	,	,	PUNCT
ejpam-5703	210	10	and	and	CCONJ
ejpam-5703	210	11	a.	a.	NOUN
ejpam-5703	210	12	alkhazzan	alkhazzan	PROPN
ejpam-5703	210	13	.	.	PUNCT
ejpam-5703	211	1	qualitative	qualitative	ADJ
ejpam-5703	211	2	dynamical	dynamical	ADJ
ejpam-5703	211	3	study	study	NOUN
ejpam-5703	211	4	of	of	ADP
ejpam-5703	211	5	hybrid	hybrid	ADJ
ejpam-5703	211	6	system	system	NOUN
ejpam-5703	211	7	of	of	ADP
ejpam-5703	211	8	pantograph	pantograph	NOUN
ejpam-5703	211	9	equations	equation	NOUN
ejpam-5703	211	10	with	with	ADP
ejpam-5703	211	11	nonlinear	nonlinear	ADJ
ejpam-5703	211	12	p	p	PROPN
ejpam-5703	211	13	-	-	PUNCT
ejpam-5703	211	14	laplacian	laplacian	ADJ
ejpam-5703	211	15	operator	operator	NOUN
ejpam-5703	211	16	in	in	ADP
ejpam-5703	211	17	banach	banach	NOUN
ejpam-5703	211	18	’s	’s	PART
ejpam-5703	211	19	space	space	NOUN
ejpam-5703	211	20	.	.	PUNCT
ejpam-5703	212	1	results	result	NOUN
ejpam-5703	212	2	in	in	ADP
ejpam-5703	212	3	control	control	NOUN
ejpam-5703	212	4	and	and	CCONJ
ejpam-5703	212	5	optimization	optimization	NOUN
ejpam-5703	212	6	,	,	PUNCT
ejpam-5703	212	7	15(100416	15(100416	NUM
ejpam-5703	212	8	)	)	PUNCT
ejpam-5703	212	9	,	,	PUNCT
ejpam-5703	212	10	2024	2024	NUM
ejpam-5703	212	11	.	.	PUNCT
ejpam-5703	213	1	[	[	X
ejpam-5703	213	2	8	8	NUM
ejpam-5703	213	3	]	]	PUNCT
ejpam-5703	213	4	a.	a.	NOUN
ejpam-5703	213	5	alkhazzan	alkhazzan	PROPN
ejpam-5703	213	6	,	,	PUNCT
ejpam-5703	213	7	j.	j.	PROPN
ejpam-5703	213	8	wang	wang	PROPN
ejpam-5703	213	9	,	,	PUNCT
ejpam-5703	213	10	y.	y.	PROPN
ejpam-5703	213	11	nie	nie	PROPN
ejpam-5703	213	12	,	,	PUNCT
ejpam-5703	213	13	s.	s.	PROPN
ejpam-5703	213	14	m.	m.	PROPN
ejpam-5703	213	15	a.	a.	PROPN
ejpam-5703	213	16	shah	shah	PROPN
ejpam-5703	213	17	,	,	PUNCT
ejpam-5703	213	18	d.	d.	PROPN
ejpam-5703	213	19	k.	k.	PROPN
ejpam-5703	213	20	almutairi	almutairi	PROPN
ejpam-5703	213	21	,	,	PUNCT
ejpam-5703	213	22	h.	h.	PROPN
ejpam-5703	213	23	khan	khan	PROPN
ejpam-5703	213	24	,	,	PUNCT
ejpam-5703	213	25	and	and	CCONJ
ejpam-5703	213	26	j.	j.	PROPN
ejpam-5703	213	27	alzabut	alzabut	PROPN
ejpam-5703	213	28	.	.	PUNCT
ejpam-5703	214	1	lyapunov	lyapunov	NOUN
ejpam-5703	214	2	-	-	PUNCT
ejpam-5703	214	3	based	base	VERB
ejpam-5703	214	4	analysis	analysis	NOUN
ejpam-5703	214	5	and	and	CCONJ
ejpam-5703	214	6	worm	worm	NOUN
ejpam-5703	214	7	extinction	extinction	NOUN
ejpam-5703	214	8	in	in	ADP
ejpam-5703	214	9	wireless	wireless	ADJ
ejpam-5703	214	10	networks	network	NOUN
ejpam-5703	214	11	using	use	VERB
ejpam-5703	214	12	stochastic	stochastic	ADJ
ejpam-5703	214	13	sveir	sveir	ADJ
ejpam-5703	214	14	model	model	NOUN
ejpam-5703	214	15	.	.	PUNCT
ejpam-5703	215	1	alexandria	alexandria	PROPN
ejpam-5703	215	2	engineering	engineering	PROPN
ejpam-5703	215	3	journal	journal	PROPN
ejpam-5703	215	4	,	,	PUNCT
ejpam-5703	215	5	118:337–353	118:337–353	NUM
ejpam-5703	215	6	,	,	PUNCT
ejpam-5703	215	7	2025	2025	NUM
ejpam-5703	215	8	.	.	PUNCT
ejpam-5703	216	1	[	[	X
ejpam-5703	216	2	9	9	NUM
ejpam-5703	216	3	]	]	PUNCT
ejpam-5703	216	4	m.	m.	NOUN
ejpam-5703	216	5	m.	m.	NOUN
ejpam-5703	216	6	belhamiti	belhamiti	PROPN
ejpam-5703	216	7	,	,	PUNCT
ejpam-5703	216	8	z.	z.	PROPN
ejpam-5703	216	9	dahmani	dahmani	PROPN
ejpam-5703	216	10	,	,	PUNCT
ejpam-5703	216	11	j.	j.	PROPN
ejpam-5703	216	12	alzabut	alzabut	PROPN
ejpam-5703	216	13	,	,	PUNCT
ejpam-5703	216	14	d.	d.	PROPN
ejpam-5703	216	15	k.	k.	PROPN
ejpam-5703	216	16	almutairi	almutairi	PROPN
ejpam-5703	216	17	,	,	PUNCT
ejpam-5703	216	18	and	and	CCONJ
ejpam-5703	216	19	h.	h.	PROPN
ejpam-5703	216	20	khan	khan	PROPN
ejpam-5703	216	21	.	.	PUNCT
ejpam-5703	217	1	analyzing	analyze	VERB
ejpam-5703	217	2	chaotic	chaotic	ADJ
ejpam-5703	217	3	systems	system	NOUN
ejpam-5703	217	4	with	with	ADP
ejpam-5703	217	5	multi	multi	ADJ
ejpam-5703	217	6	-	-	ADJ
ejpam-5703	217	7	step	step	ADJ
ejpam-5703	217	8	methods	method	NOUN
ejpam-5703	217	9	:	:	PUNCT
ejpam-5703	217	10	theory	theory	NOUN
ejpam-5703	217	11	and	and	CCONJ
ejpam-5703	217	12	simulations	simulation	NOUN
ejpam-5703	217	13	.	.	PUNCT
ejpam-5703	218	1	alexandria	alexandria	PROPN
ejpam-5703	218	2	engineering	engineering	PROPN
ejpam-5703	218	3	journal	journal	PROPN
ejpam-5703	218	4	,	,	PUNCT
ejpam-5703	218	5	113:516–534	113:516–534	NUM
ejpam-5703	218	6	,	,	PUNCT
ejpam-5703	218	7	2025	2025	NUM
ejpam-5703	218	8	.	.	PUNCT
ejpam-5703	219	1	[	[	X
ejpam-5703	219	2	10	10	NUM
ejpam-5703	219	3	]	]	X
ejpam-5703	219	4	i.	i.	PROPN
ejpam-5703	219	5	ullah	ullah	PROPN
ejpam-5703	219	6	,	,	PUNCT
ejpam-5703	219	7	m.	m.	NOUN
ejpam-5703	219	8	bilal	bilal	PROPN
ejpam-5703	219	9	,	,	PUNCT
ejpam-5703	219	10	d.	d.	PROPN
ejpam-5703	219	11	shah	shah	PROPN
ejpam-5703	219	12	,	,	PUNCT
ejpam-5703	219	13	h.	h.	PROPN
ejpam-5703	219	14	khanh	khanh	PROPN
ejpam-5703	219	15	,	,	PUNCT
ejpam-5703	219	16	j.	j.	PROPN
ejpam-5703	219	17	alzabut	alzabut	PROPN
ejpam-5703	219	18	,	,	PUNCT
ejpam-5703	219	19	and	and	CCONJ
ejpam-5703	219	20	h.	h.	PROPN
ejpam-5703	219	21	m.	m.	PROPN
ejpam-5703	219	22	alkhawar	alkhawar	PROPN
ejpam-5703	219	23	.	.	PUNCT
ejpam-5703	220	1	study	study	NOUN
ejpam-5703	220	2	of	of	ADP
ejpam-5703	220	3	nonlinear	nonlinear	ADJ
ejpam-5703	220	4	wave	wave	NOUN
ejpam-5703	220	5	equation	equation	NOUN
ejpam-5703	220	6	of	of	ADP
ejpam-5703	220	7	optical	optical	ADJ
ejpam-5703	220	8	field	field	NOUN
ejpam-5703	220	9	for	for	ADP
ejpam-5703	220	10	solotonic	solotonic	ADJ
ejpam-5703	220	11	type	type	NOUN
ejpam-5703	220	12	results	result	NOUN
ejpam-5703	220	13	.	.	PUNCT
ejpam-5703	221	1	partial	partial	ADJ
ejpam-5703	221	2	differential	differential	ADJ
ejpam-5703	221	3	equations	equation	NOUN
ejpam-5703	221	4	in	in	ADP
ejpam-5703	221	5	applied	applied	ADJ
ejpam-5703	221	6	mathematics	mathematic	NOUN
ejpam-5703	221	7	,	,	PUNCT
ejpam-5703	221	8	page	page	NOUN
ejpam-5703	221	9	101048	101048	NUM
ejpam-5703	221	10	,	,	PUNCT
ejpam-5703	221	11	2025	2025	NUM
ejpam-5703	221	12	.	.	PUNCT
ejpam-5703	222	1	[	[	X
ejpam-5703	222	2	11	11	NUM
ejpam-5703	222	3	]	]	PUNCT
ejpam-5703	222	4	w.	w.	PROPN
ejpam-5703	222	5	s.	s.	PROPN
ejpam-5703	222	6	yirga	yirga	PROPN
ejpam-5703	222	7	,	,	PUNCT
ejpam-5703	222	8	f.	f.	PROPN
ejpam-5703	222	9	w.	w.	PROPN
ejpam-5703	222	10	gelu	gelu	PROPN
ejpam-5703	222	11	,	,	PUNCT
ejpam-5703	222	12	w.	w.	PROPN
ejpam-5703	222	13	g.	g.	PROPN
ejpam-5703	222	14	melesse	melesse	PROPN
ejpam-5703	222	15	,	,	PUNCT
ejpam-5703	222	16	and	and	CCONJ
ejpam-5703	222	17	g.	g.	PROPN
ejpam-5703	222	18	s.	s.	PROPN
ejpam-5703	222	19	duressa	duressa	PROPN
ejpam-5703	222	20	.	.	PUNCT
ejpam-5703	223	1	efficient	efficient	ADJ
ejpam-5703	223	2	numerical	numerical	ADJ
ejpam-5703	223	3	method	method	NOUN
ejpam-5703	223	4	for	for	ADP
ejpam-5703	223	5	solving	solve	VERB
ejpam-5703	223	6	a	a	DET
ejpam-5703	223	7	quadratic	quadratic	ADJ
ejpam-5703	223	8	riccati	riccati	NOUN
ejpam-5703	223	9	differential	differential	NOUN
ejpam-5703	223	10	equation	equation	NOUN
ejpam-5703	223	11	.	.	PUNCT
ejpam-5703	224	1	abstract	abstract	ADJ
ejpam-5703	224	2	and	and	CCONJ
ejpam-5703	224	3	applied	apply	VERB
ejpam-5703	224	4	analysis	analysis	NOUN
ejpam-5703	224	5	,	,	PUNCT
ejpam-5703	224	6	1(1433858	1(1433858	NUM
ejpam-5703	224	7	)	)	PUNCT
ejpam-5703	224	8	,	,	PUNCT
ejpam-5703	224	9	2024	2024	NUM
ejpam-5703	224	10	.	.	PUNCT
ejpam-5703	225	1	[	[	X
ejpam-5703	225	2	12	12	NUM
ejpam-5703	225	3	]	]	X
ejpam-5703	225	4	r.	r.	PROPN
ejpam-5703	225	5	v.	v.	PROPN
ejpam-5703	225	6	segura	segura	PROPN
ejpam-5703	225	7	,	,	PUNCT
ejpam-5703	225	8	f.	f.	PROPN
ejpam-5703	225	9	m.	m.	PROPN
ejpam-5703	225	10	dorantes	dorantes	PROPN
ejpam-5703	225	11	,	,	PUNCT
ejpam-5703	225	12	l.	l.	PROPN
ejpam-5703	225	13	v.	v.	PROPN
ejpam-5703	225	14	hernández	hernández	PROPN
ejpam-5703	225	15	,	,	PUNCT
ejpam-5703	225	16	and	and	CCONJ
ejpam-5703	225	17	b.	b.	PROPN
ejpam-5703	225	18	a.	a.	PROPN
ejpam-5703	225	19	hernández	hernández	PROPN
ejpam-5703	225	20	.	.	PUNCT
ejpam-5703	226	1	tuning	tune	VERB
ejpam-5703	226	2	b.	b.	PROPN
ejpam-5703	226	3	rehman	rehman	PROPN
ejpam-5703	226	4	et	et	PROPN
ejpam-5703	226	5	al	al	PROPN
ejpam-5703	226	6	.	.	PUNCT
ejpam-5703	226	7	/	/	SYM
ejpam-5703	226	8	eur	eur	PROPN
ejpam-5703	226	9	.	.	PUNCT
ejpam-5703	227	1	j.	j.	PROPN
ejpam-5703	227	2	pure	pure	PROPN
ejpam-5703	227	3	appl	appl	PROPN
ejpam-5703	227	4	.	.	PROPN
ejpam-5703	227	5	math	math	PROPN
ejpam-5703	227	6	,	,	PUNCT
ejpam-5703	227	7	18	18	NUM
ejpam-5703	227	8	(	(	PUNCT
ejpam-5703	227	9	2	2	NUM
ejpam-5703	227	10	)	)	PUNCT
ejpam-5703	227	11	(	(	PUNCT
ejpam-5703	227	12	2025	2025	NUM
ejpam-5703	227	13	)	)	PUNCT
ejpam-5703	227	14	,	,	PUNCT
ejpam-5703	227	15	5703	5703	NUM
ejpam-5703	227	16	16	16	NUM
ejpam-5703	227	17	of	of	ADP
ejpam-5703	227	18	16	16	NUM
ejpam-5703	227	19	of	of	ADP
ejpam-5703	227	20	a	a	DET
ejpam-5703	227	21	time	time	NOUN
ejpam-5703	227	22	-	-	PUNCT
ejpam-5703	227	23	delayed	delay	VERB
ejpam-5703	227	24	controller	controller	NOUN
ejpam-5703	227	25	for	for	ADP
ejpam-5703	227	26	a	a	DET
ejpam-5703	227	27	general	general	ADJ
ejpam-5703	227	28	class	class	NOUN
ejpam-5703	227	29	of	of	ADP
ejpam-5703	227	30	second	second	ADJ
ejpam-5703	227	31	-	-	PUNCT
ejpam-5703	227	32	order	order	NOUN
ejpam-5703	227	33	linear	linear	ADJ
ejpam-5703	227	34	time	time	NOUN
ejpam-5703	227	35	invariant	invariant	ADJ
ejpam-5703	227	36	systems	system	NOUN
ejpam-5703	227	37	with	with	ADP
ejpam-5703	227	38	dead	dead	ADJ
ejpam-5703	227	39	-	-	PUNCT
ejpam-5703	227	40	time	time	NOUN
ejpam-5703	227	41	.	.	PUNCT
ejpam-5703	228	1	iet	iet	PROPN
ejpam-5703	228	2	control	control	PROPN
ejpam-5703	228	3	theory	theory	NOUN
ejpam-5703	228	4	and	and	CCONJ
ejpam-5703	228	5	applications	application	NOUN
ejpam-5703	228	6	,	,	PUNCT
ejpam-5703	228	7	13:451–457	13:451–457	NUM
ejpam-5703	228	8	,	,	PUNCT
ejpam-5703	228	9	2018	2018	NUM
ejpam-5703	228	10	.	.	PUNCT
ejpam-5703	229	1	[	[	X
ejpam-5703	229	2	13	13	NUM
ejpam-5703	229	3	]	]	PUNCT
ejpam-5703	229	4	m.	m.	NOUN
ejpam-5703	229	5	sivashankar	sivashankar	PROPN
ejpam-5703	229	6	,	,	PUNCT
ejpam-5703	229	7	s.	s.	PROPN
ejpam-5703	229	8	sabarinathan	sabarinathan	PROPN
ejpam-5703	229	9	,	,	PUNCT
ejpam-5703	229	10	h.	h.	PROPN
ejpam-5703	229	11	khan	khan	PROPN
ejpam-5703	229	12	,	,	PUNCT
ejpam-5703	229	13	j.	j.	PROPN
ejpam-5703	229	14	alzabut	alzabut	PROPN
ejpam-5703	229	15	,	,	PUNCT
ejpam-5703	229	16	and	and	CCONJ
ejpam-5703	229	17	j.	j.	PROPN
ejpam-5703	229	18	f.	f.	PROPN
ejpam-5703	229	19	gómez	gómez	PROPN
ejpam-5703	229	20	-	-	PUNCT
ejpam-5703	229	21	aguilar	aguilar	PROPN
ejpam-5703	229	22	.	.	PUNCT
ejpam-5703	230	1	stability	stability	NOUN
ejpam-5703	230	2	and	and	CCONJ
ejpam-5703	230	3	computational	computational	ADJ
ejpam-5703	230	4	results	result	NOUN
ejpam-5703	230	5	for	for	ADP
ejpam-5703	230	6	chemical	chemical	ADJ
ejpam-5703	230	7	kinetics	kinetic	NOUN
ejpam-5703	230	8	reactions	reaction	NOUN
ejpam-5703	230	9	in	in	ADP
ejpam-5703	230	10	enzyme	enzyme	NOUN
ejpam-5703	230	11	.	.	PUNCT
ejpam-5703	231	1	journal	journal	PROPN
ejpam-5703	231	2	of	of	ADP
ejpam-5703	231	3	mathematical	mathematical	ADJ
ejpam-5703	231	4	chemistry	chemistry	NOUN
ejpam-5703	231	5	,	,	PUNCT
ejpam-5703	231	6	62(9):2346–2367	62(9):2346–2367	NUM
ejpam-5703	231	7	,	,	PUNCT
ejpam-5703	231	8	2024	2024	NUM
ejpam-5703	231	9	.	.	PUNCT
ejpam-5703	232	1	[	[	X
ejpam-5703	232	2	14	14	NUM
ejpam-5703	232	3	]	]	X
ejpam-5703	232	4	g.	g.	NOUN
ejpam-5703	232	5	file	file	NOUN
ejpam-5703	232	6	and	and	CCONJ
ejpam-5703	232	7	t.	t.	PROPN
ejpam-5703	232	8	aga	aga	PROPN
ejpam-5703	232	9	.	.	PUNCT
ejpam-5703	233	1	numerical	numerical	ADJ
ejpam-5703	233	2	solution	solution	NOUN
ejpam-5703	233	3	of	of	ADP
ejpam-5703	233	4	quadratic	quadratic	ADJ
ejpam-5703	233	5	riccati	riccati	PROPN
ejpam-5703	233	6	differential	differential	NOUN
ejpam-5703	233	7	equations	equation	NOUN
ejpam-5703	233	8	.	.	PUNCT
ejpam-5703	234	1	egyptian	egyptian	ADJ
ejpam-5703	234	2	journal	journal	PROPN
ejpam-5703	234	3	of	of	ADP
ejpam-5703	234	4	basic	basic	ADJ
ejpam-5703	234	5	and	and	CCONJ
ejpam-5703	234	6	applied	applied	ADJ
ejpam-5703	234	7	sciences	science	NOUN
ejpam-5703	234	8	,	,	PUNCT
ejpam-5703	234	9	3(4):392–397	3(4):392–397	NUM
ejpam-5703	234	10	,	,	PUNCT
ejpam-5703	234	11	2016	2016	NUM
ejpam-5703	234	12	.	.	PUNCT
ejpam-5703	235	1	[	[	X
ejpam-5703	235	2	15	15	NUM
ejpam-5703	235	3	]	]	X
ejpam-5703	235	4	g.	g.	NOUN
ejpam-5703	235	5	file	file	NOUN
ejpam-5703	235	6	and	and	CCONJ
ejpam-5703	235	7	t.	t.	PROPN
ejpam-5703	235	8	aga	aga	PROPN
ejpam-5703	235	9	.	.	PUNCT
ejpam-5703	236	1	numerical	numerical	ADJ
ejpam-5703	236	2	solution	solution	NOUN
ejpam-5703	236	3	of	of	ADP
ejpam-5703	236	4	quadratic	quadratic	ADJ
ejpam-5703	236	5	riccati	riccati	PROPN
ejpam-5703	236	6	differential	differential	NOUN
ejpam-5703	236	7	equations	equation	NOUN
ejpam-5703	236	8	.	.	PUNCT
ejpam-5703	237	1	egyptian	egyptian	ADJ
ejpam-5703	237	2	journal	journal	PROPN
ejpam-5703	237	3	of	of	ADP
ejpam-5703	237	4	basic	basic	ADJ
ejpam-5703	237	5	and	and	CCONJ
ejpam-5703	237	6	applied	applied	ADJ
ejpam-5703	237	7	sciences	science	NOUN
ejpam-5703	237	8	,	,	PUNCT
ejpam-5703	237	9	3(4):392–397	3(4):392–397	NUM
ejpam-5703	237	10	,	,	PUNCT
ejpam-5703	237	11	2016	2016	NUM
ejpam-5703	237	12	.	.	PUNCT
ejpam-5703	238	1	[	[	X
ejpam-5703	238	2	16	16	NUM
ejpam-5703	238	3	]	]	X
ejpam-5703	238	4	o.	o.	PROPN
ejpam-5703	238	5	ala’yed	ala’yed	PROPN
ejpam-5703	238	6	,	,	PUNCT
ejpam-5703	238	7	b.	b.	PROPN
ejpam-5703	238	8	batiha	batiha	PROPN
ejpam-5703	238	9	,	,	PUNCT
ejpam-5703	238	10	d.	d.	PROPN
ejpam-5703	238	11	alghazo	alghazo	NOUN
ejpam-5703	238	12	,	,	PUNCT
ejpam-5703	238	13	and	and	CCONJ
ejpam-5703	238	14	f.	f.	PROPN
ejpam-5703	238	15	ghanim	ghanim	PROPN
ejpam-5703	238	16	.	.	PUNCT
ejpam-5703	239	1	cubic	cubic	PROPN
ejpam-5703	239	2	b	b	X
ejpam-5703	239	3	-	-	PUNCT
ejpam-5703	239	4	spline	spline	NOUN
ejpam-5703	239	5	method	method	NOUN
ejpam-5703	239	6	for	for	ADP
ejpam-5703	239	7	the	the	DET
ejpam-5703	239	8	solution	solution	NOUN
ejpam-5703	239	9	of	of	ADP
ejpam-5703	239	10	the	the	DET
ejpam-5703	239	11	quadratic	quadratic	ADJ
ejpam-5703	239	12	riccati	riccati	PROPN
ejpam-5703	239	13	differential	differential	NOUN
ejpam-5703	239	14	equation	equation	NOUN
ejpam-5703	239	15	.	.	PUNCT
ejpam-5703	240	1	aims	aim	VERB
ejpam-5703	240	2	mathematics	mathematic	NOUN
ejpam-5703	240	3	,	,	PUNCT
ejpam-5703	240	4	8(4):9576	8(4):9576	NUM
ejpam-5703	240	5	–	–	PUNCT
ejpam-5703	240	6	9584	9584	NUM
ejpam-5703	240	7	,	,	PUNCT
ejpam-5703	240	8	2023	2023	NUM
ejpam-5703	240	9	.	.	PUNCT
ejpam-5703	241	1	[	[	X
ejpam-5703	241	2	17	17	NUM
ejpam-5703	241	3	]	]	X
ejpam-5703	241	4	d.	d.	PROPN
ejpam-5703	241	5	t.	t.	PROPN
ejpam-5703	241	6	dimitrov	dimitrov	PROPN
ejpam-5703	241	7	and	and	CCONJ
ejpam-5703	241	8	h.	h.	PROPN
ejpam-5703	241	9	v.	v.	PROPN
ejpam-5703	241	10	kojouharov	kojouharov	PROPN
ejpam-5703	241	11	.	.	PUNCT
ejpam-5703	242	1	nonstandard	nonstandard	ADJ
ejpam-5703	242	2	finite	finite	ADJ
ejpam-5703	242	3	-	-	PUNCT
ejpam-5703	242	4	difference	difference	NOUN
ejpam-5703	242	5	methods	method	NOUN
ejpam-5703	242	6	for	for	ADP
ejpam-5703	242	7	predator	predator	NOUN
ejpam-5703	242	8	-	-	PUNCT
ejpam-5703	242	9	prey	prey	NOUN
ejpam-5703	242	10	models	model	NOUN
ejpam-5703	242	11	with	with	ADP
ejpam-5703	242	12	general	general	ADJ
ejpam-5703	242	13	functional	functional	ADJ
ejpam-5703	242	14	response	response	NOUN
ejpam-5703	242	15	.	.	PUNCT
ejpam-5703	243	1	mathematics	mathematic	NOUN
ejpam-5703	243	2	and	and	CCONJ
ejpam-5703	243	3	computers	computer	NOUN
ejpam-5703	243	4	in	in	ADP
ejpam-5703	243	5	simulation	simulation	NOUN
ejpam-5703	243	6	,	,	PUNCT
ejpam-5703	243	7	78(1):1–11	78(1):1–11	NUM
ejpam-5703	243	8	,	,	PUNCT
ejpam-5703	243	9	2008	2008	NUM
ejpam-5703	243	10	.	.	PUNCT
ejpam-5703	244	1	[	[	X
ejpam-5703	244	2	18	18	NUM
ejpam-5703	244	3	]	]	X
ejpam-5703	244	4	r.	r.	PROPN
ejpam-5703	244	5	e.	e.	PROPN
ejpam-5703	244	6	mickens	mickens	PROPN
ejpam-5703	244	7	.	.	PUNCT
ejpam-5703	245	1	nonstandard	nonstandard	ADJ
ejpam-5703	245	2	finite	finite	ADJ
ejpam-5703	245	3	difference	difference	NOUN
ejpam-5703	245	4	models	model	NOUN
ejpam-5703	245	5	of	of	ADP
ejpam-5703	245	6	differential	differential	ADJ
ejpam-5703	245	7	equations	equation	NOUN
ejpam-5703	245	8	.	.	PUNCT
ejpam-5703	246	1	world	world	PROPN
ejpam-5703	246	2	scientific	scientific	PROPN
ejpam-5703	246	3	,	,	PUNCT
ejpam-5703	246	4	london	london	PROPN
ejpam-5703	246	5	,	,	PUNCT
ejpam-5703	246	6	1993	1993	NUM
ejpam-5703	246	7	.	.	PUNCT
ejpam-5703	247	1	[	[	X
ejpam-5703	247	2	19	19	NUM
ejpam-5703	247	3	]	]	PUNCT
ejpam-5703	247	4	s.	s.	PROPN
ejpam-5703	247	5	abbasbandy	abbasbandy	PROPN
ejpam-5703	247	6	.	.	PUNCT
ejpam-5703	248	1	a	a	DET
ejpam-5703	248	2	new	new	ADJ
ejpam-5703	248	3	application	application	NOUN
ejpam-5703	248	4	of	of	ADP
ejpam-5703	248	5	he	he	PRON
ejpam-5703	248	6	’s	’	VERB
ejpam-5703	248	7	variational	variational	ADJ
ejpam-5703	248	8	iteration	iteration	NOUN
ejpam-5703	248	9	method	method	NOUN
ejpam-5703	248	10	for	for	ADP
ejpam-5703	248	11	quadratic	quadratic	ADJ
ejpam-5703	248	12	riccati	riccati	NOUN
ejpam-5703	248	13	differential	differential	NOUN
ejpam-5703	248	14	equation	equation	NOUN
ejpam-5703	248	15	by	by	ADP
ejpam-5703	248	16	using	use	VERB
ejpam-5703	248	17	adomian	adomian	NOUN
ejpam-5703	248	18	’s	’s	PART
ejpam-5703	248	19	polynomials	polynomial	NOUN
ejpam-5703	248	20	.	.	PUNCT
ejpam-5703	249	1	journal	journal	NOUN
ejpam-5703	249	2	of	of	ADP
ejpam-5703	249	3	computational	computational	ADJ
ejpam-5703	249	4	and	and	CCONJ
ejpam-5703	249	5	applied	applied	ADJ
ejpam-5703	249	6	mathematics	mathematic	NOUN
ejpam-5703	249	7	,	,	PUNCT
ejpam-5703	249	8	207(1):59–63	207(1):59–63	NUM
ejpam-5703	249	9	,	,	PUNCT
ejpam-5703	249	10	2007	2007	NUM
ejpam-5703	249	11	.	.	PUNCT
ejpam-5703	250	1	[	[	X
ejpam-5703	250	2	20	20	NUM
ejpam-5703	250	3	]	]	X
ejpam-5703	250	4	f.	f.	PROPN
ejpam-5703	250	5	ayaz	ayaz	PROPN
ejpam-5703	250	6	.	.	PUNCT
ejpam-5703	251	1	applications	application	NOUN
ejpam-5703	251	2	of	of	ADP
ejpam-5703	251	3	differential	differential	ADJ
ejpam-5703	251	4	transform	transform	NOUN
ejpam-5703	251	5	method	method	NOUN
ejpam-5703	251	6	to	to	ADP
ejpam-5703	251	7	differential	differential	VERB
ejpam-5703	251	8	-	-	PUNCT
ejpam-5703	251	9	algebraic	algebraic	ADJ
ejpam-5703	251	10	equations	equation	NOUN
ejpam-5703	251	11	.	.	PUNCT
ejpam-5703	252	1	applied	apply	VERB
ejpam-5703	252	2	mathematics	mathematic	NOUN
ejpam-5703	252	3	and	and	CCONJ
ejpam-5703	252	4	computation	computation	NOUN
ejpam-5703	252	5	,	,	PUNCT
ejpam-5703	252	6	152(3):649–657	152(3):649–657	NUM
ejpam-5703	252	7	,	,	PUNCT
ejpam-5703	252	8	2004	2004	NUM
ejpam-5703	252	9	.	.	PUNCT
ejpam-5703	253	1	[	[	X
ejpam-5703	253	2	21	21	NUM
ejpam-5703	253	3	]	]	PUNCT
ejpam-5703	253	4	m.	m.	NOUN
ejpam-5703	253	5	a.	a.	PROPN
ejpam-5703	253	6	el	el	PROPN
ejpam-5703	253	7	-	-	PUNCT
ejpam-5703	253	8	tawil	tawil	PROPN
ejpam-5703	253	9	,	,	PUNCT
ejpam-5703	253	10	a.	a.	NOUN
ejpam-5703	253	11	a.	a.	NOUN
ejpam-5703	253	12	bahnasawi	bahnasawi	PROPN
ejpam-5703	253	13	,	,	PUNCT
ejpam-5703	253	14	and	and	CCONJ
ejpam-5703	253	15	a.	a.	NOUN
ejpam-5703	253	16	a.	a.	PROPN
ejpam-5703	253	17	naby	naby	PROPN
ejpam-5703	253	18	.	.	PUNCT
ejpam-5703	254	1	solving	solve	VERB
ejpam-5703	254	2	riccati	riccati	PROPN
ejpam-5703	254	3	differential	differential	NOUN
ejpam-5703	254	4	equation	equation	NOUN
ejpam-5703	254	5	using	use	VERB
ejpam-5703	254	6	adomian	adomian	NOUN
ejpam-5703	254	7	’s	’s	PART
ejpam-5703	254	8	decomposition	decomposition	NOUN
ejpam-5703	254	9	method	method	NOUN
ejpam-5703	254	10	.	.	PUNCT
ejpam-5703	255	1	applied	apply	VERB
ejpam-5703	255	2	mathematics	mathematic	NOUN
ejpam-5703	255	3	and	and	CCONJ
ejpam-5703	255	4	computation	computation	NOUN
ejpam-5703	255	5	,	,	PUNCT
ejpam-5703	255	6	157(2):503–514	157(2):503–514	PROPN
ejpam-5703	255	7	,	,	PUNCT
ejpam-5703	255	8	2004	2004	NUM
ejpam-5703	255	9	.	.	PUNCT
ejpam-5703	256	1	[	[	X
ejpam-5703	256	2	22	22	NUM
ejpam-5703	256	3	]	]	X
ejpam-5703	256	4	f.	f.	PROPN
ejpam-5703	256	5	m.	m.	PROPN
ejpam-5703	256	6	fernández	fernández	PROPN
ejpam-5703	256	7	.	.	PUNCT
ejpam-5703	257	1	on	on	ADP
ejpam-5703	257	2	some	some	DET
ejpam-5703	257	3	approximate	approximate	ADJ
ejpam-5703	257	4	methods	method	NOUN
ejpam-5703	257	5	for	for	ADP
ejpam-5703	257	6	nonlinear	nonlinear	ADJ
ejpam-5703	257	7	models	model	NOUN
ejpam-5703	257	8	.	.	PUNCT
ejpam-5703	258	1	applied	apply	VERB
ejpam-5703	258	2	mathematics	mathematic	NOUN
ejpam-5703	258	3	and	and	CCONJ
ejpam-5703	258	4	computation	computation	NOUN
ejpam-5703	258	5	,	,	PUNCT
ejpam-5703	258	6	215(1):168–174	215(1):168–174	NUM
ejpam-5703	258	7	,	,	PUNCT
ejpam-5703	258	8	2009	2009	NUM
ejpam-5703	258	9	.	.	PUNCT
ejpam-5703	259	1	[	[	X
ejpam-5703	259	2	23	23	NUM
ejpam-5703	259	3	]	]	PUNCT
ejpam-5703	259	4	s.	s.	PROPN
ejpam-5703	259	5	riaz	riaz	PROPN
ejpam-5703	259	6	,	,	PUNCT
ejpam-5703	259	7	m.	m.	PROPN
ejpam-5703	259	8	rafiq	rafiq	PROPN
ejpam-5703	259	9	,	,	PUNCT
ejpam-5703	259	10	and	and	CCONJ
ejpam-5703	259	11	o.	o.	PROPN
ejpam-5703	259	12	ahmad	ahmad	PROPN
ejpam-5703	259	13	.	.	PUNCT
ejpam-5703	260	1	non	non	PROPN
ejpam-5703	260	2	standard	standard	ADJ
ejpam-5703	260	3	finite	finite	ADJ
ejpam-5703	260	4	difference	difference	NOUN
ejpam-5703	260	5	method	method	NOUN
ejpam-5703	260	6	for	for	ADP
ejpam-5703	260	7	quadratic	quadratic	ADJ
ejpam-5703	260	8	riccati	riccati	NOUN
ejpam-5703	260	9	differential	differential	NOUN
ejpam-5703	260	10	equation	equation	NOUN
ejpam-5703	260	11	.	.	PUNCT
ejpam-5703	261	1	punjab	punjab	PROPN
ejpam-5703	261	2	university	university	PROPN
ejpam-5703	261	3	journal	journal	NOUN
ejpam-5703	261	4	of	of	ADP
ejpam-5703	261	5	mathematics	mathematic	NOUN
ejpam-5703	261	6	,	,	PUNCT
ejpam-5703	261	7	47(2):49–55	47(2):49–55	NUM
ejpam-5703	261	8	,	,	PUNCT
ejpam-5703	261	9	2015	2015	NUM
ejpam-5703	261	10	.	.	PUNCT
ejpam-5703	262	1	[	[	X
ejpam-5703	262	2	24	24	NUM
ejpam-5703	262	3	]	]	PUNCT
ejpam-5703	262	4	a.	a.	NOUN
ejpam-5703	262	5	arikoglu	arikoglu	PROPN
ejpam-5703	262	6	and	and	CCONJ
ejpam-5703	262	7	i.	i.	PROPN
ejpam-5703	262	8	ozkol	ozkol	PROPN
ejpam-5703	262	9	.	.	PUNCT
ejpam-5703	263	1	solution	solution	NOUN
ejpam-5703	263	2	of	of	ADP
ejpam-5703	263	3	fractional	fractional	ADJ
ejpam-5703	263	4	differential	differential	ADJ
ejpam-5703	263	5	equations	equation	NOUN
ejpam-5703	263	6	by	by	ADP
ejpam-5703	263	7	using	use	VERB
ejpam-5703	263	8	differential	differential	ADJ
ejpam-5703	263	9	transform	transform	NOUN
ejpam-5703	263	10	method	method	NOUN
ejpam-5703	263	11	.	.	PUNCT
ejpam-5703	264	1	chaos	chaos	NOUN
ejpam-5703	264	2	,	,	PUNCT
ejpam-5703	264	3	solitons	soliton	NOUN
ejpam-5703	264	4	and	and	CCONJ
ejpam-5703	264	5	fractals	fractal	NOUN
ejpam-5703	264	6	,	,	PUNCT
ejpam-5703	264	7	34(5):1473–1481	34(5):1473–1481	NUM
ejpam-5703	264	8	,	,	PUNCT
ejpam-5703	264	9	2007	2007	NUM
ejpam-5703	264	10	.	.	PUNCT
ejpam-5703	265	1	[	[	X
ejpam-5703	265	2	25	25	NUM
ejpam-5703	265	3	]	]	X
ejpam-5703	265	4	y.	y.	PROPN
ejpam-5703	265	5	tan	tan	PROPN
ejpam-5703	265	6	and	and	CCONJ
ejpam-5703	265	7	s.	s.	PROPN
ejpam-5703	265	8	abbasbandy	abbasbandy	PROPN
ejpam-5703	265	9	.	.	PUNCT
ejpam-5703	266	1	homotopy	homotopy	VERB
ejpam-5703	266	2	analysis	analysis	NOUN
ejpam-5703	266	3	method	method	NOUN
ejpam-5703	266	4	for	for	ADP
ejpam-5703	266	5	quadratic	quadratic	ADJ
ejpam-5703	266	6	riccati	riccati	NOUN
ejpam-5703	266	7	differential	differential	NOUN
ejpam-5703	266	8	equation	equation	NOUN
ejpam-5703	266	9	.	.	PUNCT
ejpam-5703	267	1	communications	communication	NOUN
ejpam-5703	267	2	in	in	ADP
ejpam-5703	267	3	nonlinear	nonlinear	ADJ
ejpam-5703	267	4	science	science	NOUN
ejpam-5703	267	5	and	and	CCONJ
ejpam-5703	267	6	numerical	numerical	PROPN
ejpam-5703	267	7	simulation	simulation	PROPN
ejpam-5703	267	8	,	,	PUNCT
ejpam-5703	267	9	13(3):539–546	13(3):539–546	NUM
ejpam-5703	267	10	,	,	PUNCT
ejpam-5703	267	11	2008	2008	NUM
ejpam-5703	267	12	.	.	PUNCT