id	sid	tid	token	lemma	pos
ejpam-7064	1	1	european	european	PROPN
ejpam-7064	1	2	journal	journal	PROPN
ejpam-7064	1	3	of	of	ADP
ejpam-7064	1	4	pure	pure	ADJ
ejpam-7064	1	5	and	and	CCONJ
ejpam-7064	1	6	applied	applied	ADJ
ejpam-7064	1	7	mathematics	mathematic	NOUN
ejpam-7064	1	8	2025	2025	NUM
ejpam-7064	1	9	,	,	PUNCT
ejpam-7064	1	10	vol	vol	NOUN
ejpam-7064	1	11	.	.	PROPN
ejpam-7064	1	12	18	18	NUM
ejpam-7064	1	13	,	,	PUNCT
ejpam-7064	1	14	issue	issue	NOUN
ejpam-7064	1	15	4	4	NUM
ejpam-7064	1	16	,	,	PUNCT
ejpam-7064	1	17	article	article	NOUN
ejpam-7064	1	18	number	number	NOUN
ejpam-7064	1	19	7064	7064	NUM
ejpam-7064	1	20	issn	issn	VERB
ejpam-7064	1	21	1307	1307	NUM
ejpam-7064	1	22	-	-	SYM
ejpam-7064	1	23	5543	5543	NUM
ejpam-7064	1	24	–	–	PUNCT
ejpam-7064	1	25	ejpam.com	ejpam.com	X
ejpam-7064	1	26	published	publish	VERB
ejpam-7064	1	27	by	by	ADP
ejpam-7064	1	28	new	new	PROPN
ejpam-7064	1	29	york	york	PROPN
ejpam-7064	1	30	business	business	PROPN
ejpam-7064	1	31	global	global	ADJ
ejpam-7064	1	32	using	use	VERB
ejpam-7064	1	33	the	the	DET
ejpam-7064	1	34	multi	multi	ADJ
ejpam-7064	1	35	-	-	ADJ
ejpam-7064	1	36	domain	domain	ADJ
ejpam-7064	1	37	spectral	spectral	ADJ
ejpam-7064	1	38	relaxation	relaxation	NOUN
ejpam-7064	1	39	method	method	NOUN
ejpam-7064	1	40	through	through	ADP
ejpam-7064	1	41	a	a	DET
ejpam-7064	1	42	numerical	numerical	ADJ
ejpam-7064	1	43	simulation	simulation	NOUN
ejpam-7064	1	44	for	for	ADP
ejpam-7064	1	45	the	the	DET
ejpam-7064	1	46	brusselator	brusselator	NOUN
ejpam-7064	1	47	system	system	NOUN
ejpam-7064	1	48	m.	m.	PROPN
ejpam-7064	1	49	adel1,∗	adel1,∗	PROPN
ejpam-7064	1	50	,	,	PUNCT
ejpam-7064	1	51	m.	m.	NOUN
ejpam-7064	1	52	m.	m.	PROPN
ejpam-7064	1	53	khader2,3	khader2,3	PROPN
ejpam-7064	1	54	,	,	PUNCT
ejpam-7064	1	55	hijaz	hijaz	PROPN
ejpam-7064	1	56	ahmad4	ahmad4	PROPN
ejpam-7064	1	57	,	,	PUNCT
ejpam-7064	1	58	osama	osama	PROPN
ejpam-7064	1	59	oqilat5	oqilat5	NOUN
ejpam-7064	1	60	,	,	PUNCT
ejpam-7064	1	61	w.	w.	PROPN
ejpam-7064	1	62	m.	m.	NOUN
ejpam-7064	1	63	abdelfattah6,7	abdelfattah6,7	PROPN
ejpam-7064	1	64	1	1	NUM
ejpam-7064	1	65	department	department	NOUN
ejpam-7064	1	66	of	of	ADP
ejpam-7064	1	67	mathematics	mathematic	NOUN
ejpam-7064	1	68	,	,	PUNCT
ejpam-7064	1	69	faculty	faculty	NOUN
ejpam-7064	1	70	of	of	ADP
ejpam-7064	1	71	science	science	NOUN
ejpam-7064	1	72	,	,	PUNCT
ejpam-7064	1	73	islamic	islamic	PROPN
ejpam-7064	1	74	university	university	PROPN
ejpam-7064	1	75	of	of	ADP
ejpam-7064	1	76	madinah	madinah	PROPN
ejpam-7064	1	77	,	,	PUNCT
ejpam-7064	1	78	madinah	madinah	PROPN
ejpam-7064	1	79	,	,	PUNCT
ejpam-7064	1	80	42351	42351	NUM
ejpam-7064	1	81	,	,	PUNCT
ejpam-7064	1	82	saudi	saudi	PROPN
ejpam-7064	1	83	arabia	arabia	PROPN
ejpam-7064	1	84	2	2	NUM
ejpam-7064	1	85	department	department	NOUN
ejpam-7064	1	86	of	of	ADP
ejpam-7064	1	87	mathematics	mathematic	NOUN
ejpam-7064	1	88	and	and	CCONJ
ejpam-7064	1	89	statistics	statistic	NOUN
ejpam-7064	1	90	,	,	PUNCT
ejpam-7064	1	91	college	college	NOUN
ejpam-7064	1	92	of	of	ADP
ejpam-7064	1	93	science	science	NOUN
ejpam-7064	1	94	,	,	PUNCT
ejpam-7064	1	95	imam	imam	PROPN
ejpam-7064	1	96	mohammad	mohammad	PROPN
ejpam-7064	1	97	ibn	ibn	PROPN
ejpam-7064	1	98	saud	saud	PROPN
ejpam-7064	1	99	islamic	islamic	PROPN
ejpam-7064	1	100	university	university	PROPN
ejpam-7064	1	101	(	(	PUNCT
ejpam-7064	1	102	imsiu	imsiu	PROPN
ejpam-7064	1	103	)	)	PUNCT
ejpam-7064	1	104	,	,	PUNCT
ejpam-7064	1	105	riyadh	riyadh	PROPN
ejpam-7064	1	106	,	,	PUNCT
ejpam-7064	1	107	saudi	saudi	PROPN
ejpam-7064	1	108	arabia	arabia	PROPN
ejpam-7064	1	109	3	3	NUM
ejpam-7064	1	110	department	department	NOUN
ejpam-7064	1	111	of	of	ADP
ejpam-7064	1	112	mathematics	mathematic	NOUN
ejpam-7064	1	113	,	,	PUNCT
ejpam-7064	1	114	faculty	faculty	NOUN
ejpam-7064	1	115	of	of	ADP
ejpam-7064	1	116	science	science	NOUN
ejpam-7064	1	117	,	,	PUNCT
ejpam-7064	1	118	benha	benha	VERB
ejpam-7064	1	119	university	university	NOUN
ejpam-7064	1	120	,	,	PUNCT
ejpam-7064	1	121	benha	benha	NOUN
ejpam-7064	1	122	,	,	PUNCT
ejpam-7064	1	123	egypt	egypt	PROPN
ejpam-7064	1	124	4	4	NUM
ejpam-7064	1	125	operational	operational	ADJ
ejpam-7064	1	126	research	research	NOUN
ejpam-7064	1	127	center	center	NOUN
ejpam-7064	1	128	in	in	ADP
ejpam-7064	1	129	healthcare	healthcare	PROPN
ejpam-7064	1	130	,	,	PUNCT
ejpam-7064	1	131	near	near	ADP
ejpam-7064	1	132	east	east	PROPN
ejpam-7064	1	133	university	university	PROPN
ejpam-7064	1	134	,	,	PUNCT
ejpam-7064	1	135	nicosia	nicosia	PROPN
ejpam-7064	1	136	/	/	SYM
ejpam-7064	1	137	trnc	trnc	PROPN
ejpam-7064	1	138	,	,	PUNCT
ejpam-7064	1	139	99138	99138	NUM
ejpam-7064	1	140	mersin	mersin	PROPN
ejpam-7064	1	141	10	10	NUM
ejpam-7064	1	142	,	,	PUNCT
ejpam-7064	1	143	turkey	turkey	PROPN
ejpam-7064	1	144	5	5	NUM
ejpam-7064	1	145	department	department	NOUN
ejpam-7064	1	146	of	of	ADP
ejpam-7064	1	147	basic	basic	ADJ
ejpam-7064	1	148	sciences	science	NOUN
ejpam-7064	1	149	,	,	PUNCT
ejpam-7064	1	150	faculty	faculty	NOUN
ejpam-7064	1	151	of	of	ADP
ejpam-7064	1	152	arts	art	NOUN
ejpam-7064	1	153	and	and	CCONJ
ejpam-7064	1	154	science	science	NOUN
ejpam-7064	1	155	,	,	PUNCT
ejpam-7064	1	156	hourani	hourani	NOUN
ejpam-7064	1	157	center	center	NOUN
ejpam-7064	1	158	for	for	ADP
ejpam-7064	1	159	applied	apply	VERB
ejpam-7064	1	160	scientific	scientific	ADJ
ejpam-7064	1	161	research	research	NOUN
ejpam-7064	1	162	,	,	PUNCT
ejpam-7064	1	163	al	al	PROPN
ejpam-7064	1	164	-	-	PUNCT
ejpam-7064	1	165	ahliyya	ahliyya	PROPN
ejpam-7064	1	166	amman	amman	PROPN
ejpam-7064	1	167	university	university	PROPN
ejpam-7064	1	168	,	,	PUNCT
ejpam-7064	1	169	amman	amman	PROPN
ejpam-7064	1	170	,	,	PUNCT
ejpam-7064	1	171	jordan	jordan	PROPN
ejpam-7064	1	172	6	6	NUM
ejpam-7064	1	173	college	college	NOUN
ejpam-7064	1	174	of	of	ADP
ejpam-7064	1	175	engineering	engineering	NOUN
ejpam-7064	1	176	,	,	PUNCT
ejpam-7064	1	177	university	university	NOUN
ejpam-7064	1	178	of	of	ADP
ejpam-7064	1	179	business	business	NOUN
ejpam-7064	1	180	and	and	CCONJ
ejpam-7064	1	181	technology	technology	NOUN
ejpam-7064	1	182	,	,	PUNCT
ejpam-7064	1	183	jeddah	jeddah	PROPN
ejpam-7064	1	184	23435	23435	NUM
ejpam-7064	1	185	,	,	PUNCT
ejpam-7064	1	186	ksa	ksa	PROPN
ejpam-7064	1	187	7	7	NUM
ejpam-7064	1	188	department	department	NOUN
ejpam-7064	1	189	of	of	ADP
ejpam-7064	1	190	engineering	engineering	NOUN
ejpam-7064	1	191	mathematics	mathematic	NOUN
ejpam-7064	1	192	and	and	CCONJ
ejpam-7064	1	193	physics	physics	NOUN
ejpam-7064	1	194	,	,	PUNCT
ejpam-7064	1	195	faculty	faculty	NOUN
ejpam-7064	1	196	of	of	ADP
ejpam-7064	1	197	engineering	engineering	PROPN
ejpam-7064	1	198	,	,	PUNCT
ejpam-7064	1	199	zagazig	zagazig	PROPN
ejpam-7064	1	200	university	university	PROPN
ejpam-7064	1	201	,	,	PUNCT
ejpam-7064	1	202	p.o	p.o	PROPN
ejpam-7064	1	203	.	.	PROPN
ejpam-7064	1	204	44519	44519	NUM
ejpam-7064	1	205	,	,	PUNCT
ejpam-7064	1	206	egypt	egypt	PROPN
ejpam-7064	1	207	abstract	abstract	PROPN
ejpam-7064	1	208	.	.	PUNCT
ejpam-7064	2	1	we	we	PRON
ejpam-7064	2	2	introduce	introduce	VERB
ejpam-7064	2	3	the	the	DET
ejpam-7064	2	4	numerical	numerical	ADJ
ejpam-7064	2	5	solutions	solution	NOUN
ejpam-7064	2	6	of	of	ADP
ejpam-7064	2	7	the	the	DET
ejpam-7064	2	8	brusselator	brusselator	NOUN
ejpam-7064	2	9	system	system	NOUN
ejpam-7064	2	10	by	by	ADP
ejpam-7064	2	11	applying	apply	VERB
ejpam-7064	2	12	the	the	DET
ejpam-7064	2	13	multidomain	multidomain	ADJ
ejpam-7064	2	14	spectral	spectral	ADJ
ejpam-7064	2	15	relaxation	relaxation	NOUN
ejpam-7064	2	16	method	method	NOUN
ejpam-7064	2	17	(	(	PUNCT
ejpam-7064	2	18	msrm	msrm	PROPN
ejpam-7064	2	19	)	)	PUNCT
ejpam-7064	2	20	.	.	PUNCT
ejpam-7064	3	1	the	the	DET
ejpam-7064	3	2	proposed	propose	VERB
ejpam-7064	3	3	method	method	NOUN
ejpam-7064	3	4	is	be	AUX
ejpam-7064	3	5	a	a	DET
ejpam-7064	3	6	combination	combination	NOUN
ejpam-7064	3	7	of	of	ADP
ejpam-7064	3	8	the	the	DET
ejpam-7064	3	9	chebyshev	chebyshev	NOUN
ejpam-7064	3	10	pseudo	pseudo	NOUN
ejpam-7064	3	11	-	-	ADJ
ejpam-7064	3	12	spectral	spectral	ADJ
ejpam-7064	3	13	method	method	NOUN
ejpam-7064	3	14	and	and	CCONJ
ejpam-7064	3	15	the	the	DET
ejpam-7064	3	16	gauss	gauss	ADJ
ejpam-7064	3	17	-	-	PUNCT
ejpam-7064	3	18	seidel	seidel	PROPN
ejpam-7064	3	19	relaxation	relaxation	NOUN
ejpam-7064	3	20	approach	approach	NOUN
ejpam-7064	3	21	.	.	PUNCT
ejpam-7064	4	1	this	this	DET
ejpam-7064	4	2	method	method	NOUN
ejpam-7064	4	3	breaks	break	VERB
ejpam-7064	4	4	down	down	ADP
ejpam-7064	4	5	the	the	DET
ejpam-7064	4	6	main	main	ADJ
ejpam-7064	4	7	interval	interval	NOUN
ejpam-7064	4	8	into	into	ADP
ejpam-7064	4	9	several	several	ADJ
ejpam-7064	4	10	small	small	ADJ
ejpam-7064	4	11	subintervals	subinterval	NOUN
ejpam-7064	4	12	,	,	PUNCT
ejpam-7064	4	13	finding	find	VERB
ejpam-7064	4	14	solutions	solution	NOUN
ejpam-7064	4	15	within	within	ADP
ejpam-7064	4	16	each	each	DET
ejpam-7064	4	17	interval	interval	NOUN
ejpam-7064	4	18	.	.	PUNCT
ejpam-7064	5	1	this	this	DET
ejpam-7064	5	2	approach	approach	NOUN
ejpam-7064	5	3	also	also	ADV
ejpam-7064	5	4	transforms	transform	VERB
ejpam-7064	5	5	the	the	DET
ejpam-7064	5	6	model	model	NOUN
ejpam-7064	5	7	into	into	ADP
ejpam-7064	5	8	a	a	DET
ejpam-7064	5	9	set	set	NOUN
ejpam-7064	5	10	of	of	ADP
ejpam-7064	5	11	algebraic	algebraic	ADJ
ejpam-7064	5	12	equations	equation	NOUN
ejpam-7064	5	13	.	.	PUNCT
ejpam-7064	6	1	we	we	PRON
ejpam-7064	6	2	present	present	VERB
ejpam-7064	6	3	the	the	DET
ejpam-7064	6	4	error	error	NOUN
ejpam-7064	6	5	analysis	analysis	NOUN
ejpam-7064	6	6	and	and	CCONJ
ejpam-7064	6	7	the	the	DET
ejpam-7064	6	8	order	order	NOUN
ejpam-7064	6	9	of	of	ADP
ejpam-7064	6	10	convergence	convergence	NOUN
ejpam-7064	6	11	for	for	ADP
ejpam-7064	6	12	the	the	DET
ejpam-7064	6	13	proposed	propose	VERB
ejpam-7064	6	14	scheme	scheme	NOUN
ejpam-7064	6	15	.	.	PUNCT
ejpam-7064	7	1	we	we	PRON
ejpam-7064	7	2	validate	validate	VERB
ejpam-7064	7	3	the	the	DET
ejpam-7064	7	4	effectiveness	effectiveness	NOUN
ejpam-7064	7	5	and	and	CCONJ
ejpam-7064	7	6	precision	precision	NOUN
ejpam-7064	7	7	of	of	ADP
ejpam-7064	7	8	the	the	DET
ejpam-7064	7	9	given	give	VERB
ejpam-7064	7	10	procedure	procedure	NOUN
ejpam-7064	7	11	by	by	ADP
ejpam-7064	7	12	utilizing	utilize	VERB
ejpam-7064	7	13	the	the	DET
ejpam-7064	7	14	fourth	fourth	ADJ
ejpam-7064	7	15	-	-	PUNCT
ejpam-7064	7	16	order	order	NOUN
ejpam-7064	7	17	runge	runge	NOUN
ejpam-7064	7	18	-	-	PUNCT
ejpam-7064	7	19	kutta	kutta	NOUN
ejpam-7064	7	20	method	method	NOUN
ejpam-7064	7	21	(	(	PUNCT
ejpam-7064	7	22	rk4	rk4	NOUN
ejpam-7064	7	23	m	m	NOUN
ejpam-7064	7	24	)	)	PUNCT
ejpam-7064	7	25	,	,	PUNCT
ejpam-7064	7	26	and	and	CCONJ
ejpam-7064	7	27	the	the	DET
ejpam-7064	7	28	variational	variational	ADJ
ejpam-7064	7	29	iteration	iteration	NOUN
ejpam-7064	7	30	method	method	NOUN
ejpam-7064	7	31	.	.	PUNCT
ejpam-7064	8	1	the	the	DET
ejpam-7064	8	2	considered	consider	VERB
ejpam-7064	8	3	results	result	NOUN
ejpam-7064	8	4	are	be	AUX
ejpam-7064	8	5	tabularly	tabularly	ADV
ejpam-7064	8	6	and	and	CCONJ
ejpam-7064	8	7	graphically	graphically	ADV
ejpam-7064	8	8	demonstrated	demonstrate	VERB
ejpam-7064	8	9	with	with	ADP
ejpam-7064	8	10	different	different	ADJ
ejpam-7064	8	11	values	value	NOUN
ejpam-7064	8	12	of	of	ADP
ejpam-7064	8	13	the	the	DET
ejpam-7064	8	14	model	model	NOUN
ejpam-7064	8	15	’s	’s	PART
ejpam-7064	8	16	parameters	parameter	NOUN
ejpam-7064	8	17	.	.	PUNCT
ejpam-7064	9	1	from	from	ADP
ejpam-7064	9	2	a	a	DET
ejpam-7064	9	3	numerical	numerical	ADJ
ejpam-7064	9	4	viewpoint	viewpoint	NOUN
ejpam-7064	9	5	,	,	PUNCT
ejpam-7064	9	6	the	the	DET
ejpam-7064	9	7	given	give	VERB
ejpam-7064	9	8	simulations	simulation	NOUN
ejpam-7064	9	9	and	and	CCONJ
ejpam-7064	9	10	results	result	NOUN
ejpam-7064	9	11	indicate	indicate	VERB
ejpam-7064	9	12	that	that	SCONJ
ejpam-7064	9	13	the	the	DET
ejpam-7064	9	14	proposed	propose	VERB
ejpam-7064	9	15	algorithm	algorithm	NOUN
ejpam-7064	9	16	is	be	AUX
ejpam-7064	9	17	a	a	DET
ejpam-7064	9	18	straightforward	straightforward	ADJ
ejpam-7064	9	19	and	and	CCONJ
ejpam-7064	9	20	appropriate	appropriate	ADJ
ejpam-7064	9	21	tool	tool	NOUN
ejpam-7064	9	22	with	with	ADP
ejpam-7064	9	23	computational	computational	ADJ
ejpam-7064	9	24	efficiency	efficiency	NOUN
ejpam-7064	9	25	for	for	ADP
ejpam-7064	9	26	such	such	ADJ
ejpam-7064	9	27	models	model	NOUN
ejpam-7064	9	28	.	.	PUNCT
ejpam-7064	10	1	2020	2020	NUM
ejpam-7064	10	2	mathematics	mathematic	NOUN
ejpam-7064	10	3	subject	subject	NOUN
ejpam-7064	10	4	classifications	classification	NOUN
ejpam-7064	10	5	:	:	PUNCT
ejpam-7064	10	6	41a30	41a30	NUM
ejpam-7064	10	7	,	,	PUNCT
ejpam-7064	10	8	49m27	49m27	NUM
ejpam-7064	10	9	,	,	PUNCT
ejpam-7064	10	10	65n20	65n20	NUM
ejpam-7064	10	11	key	key	ADJ
ejpam-7064	10	12	words	word	NOUN
ejpam-7064	10	13	and	and	CCONJ
ejpam-7064	10	14	phrases	phrase	NOUN
ejpam-7064	10	15	:	:	PUNCT
ejpam-7064	10	16	brusselator	brusselator	NOUN
ejpam-7064	10	17	system	system	NOUN
ejpam-7064	10	18	,	,	PUNCT
ejpam-7064	10	19	msrm	msrm	PROPN
ejpam-7064	10	20	,	,	PUNCT
ejpam-7064	10	21	chebyshev	chebyshev	PROPN
ejpam-7064	10	22	pseudo	pseudo	NOUN
ejpam-7064	10	23	-	-	ADJ
ejpam-7064	10	24	spectral	spectral	ADJ
ejpam-7064	10	25	method	method	NOUN
ejpam-7064	10	26	,	,	PUNCT
ejpam-7064	10	27	gauss	gauss	ADJ
ejpam-7064	10	28	-	-	PUNCT
ejpam-7064	10	29	seidel	seidel	PROPN
ejpam-7064	10	30	relaxation	relaxation	NOUN
ejpam-7064	10	31	approach	approach	NOUN
ejpam-7064	10	32	,	,	PUNCT
ejpam-7064	10	33	convergence	convergence	NOUN
ejpam-7064	10	34	analysis	analysis	NOUN
ejpam-7064	10	35	,	,	PUNCT
ejpam-7064	10	36	rk4	rk4	NOUN
ejpam-7064	10	37	m	m	NOUN
ejpam-7064	10	38	∗corresponding	∗corresponde	VERB
ejpam-7064	10	39	author	author	NOUN
ejpam-7064	10	40	.	.	PUNCT
ejpam-7064	11	1	doi	doi	NOUN
ejpam-7064	11	2	:	:	PUNCT
ejpam-7064	11	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7064	https://doi.org/10.29020/nybg.ejpam.v18i4.7064	NUM
ejpam-7064	11	4	email	email	NOUN
ejpam-7064	11	5	addresses	address	VERB
ejpam-7064	11	6	:	:	PUNCT
ejpam-7064	11	7	adel@sci.cu.edu.eg	adel@sci.cu.edu.eg	PROPN
ejpam-7064	11	8	(	(	PUNCT
ejpam-7064	11	9	m.	m.	PROPN
ejpam-7064	11	10	adel	adel	PROPN
ejpam-7064	11	11	)	)	PUNCT
ejpam-7064	11	12	,	,	PUNCT
ejpam-7064	11	13	mmkhader@imamu.edu.sa	mmkhader@imamu.edu.sa	PROPN
ejpam-7064	11	14	(	(	PUNCT
ejpam-7064	11	15	m.	m.	NOUN
ejpam-7064	11	16	m.	m.	NOUN
ejpam-7064	11	17	khader	khader	PROPN
ejpam-7064	11	18	)	)	PUNCT
ejpam-7064	11	19	,	,	PUNCT
ejpam-7064	11	20	hijaz.ahmad@neu.edu.tr	hijaz.ahmad@neu.edu.tr	PROPN
ejpam-7064	11	21	(	(	PUNCT
ejpam-7064	11	22	h.	h.	PROPN
ejpam-7064	11	23	ahmad	ahmad	PROPN
ejpam-7064	11	24	)	)	PUNCT
ejpam-7064	11	25	,	,	PUNCT
ejpam-7064	11	26	o.oqilat@ammanu.edu.jo	o.oqilat@ammanu.edu.jo	NOUN
ejpam-7064	11	27	(	(	PUNCT
ejpam-7064	11	28	o.	o.	NOUN
ejpam-7064	11	29	oqilat	oqilat	NOUN
ejpam-7064	11	30	)	)	PUNCT
ejpam-7064	11	31	,	,	PUNCT
ejpam-7064	11	32	w.abdelfattah@ubt.edu.sa	w.abdelfattah@ubt.edu.sa	PROPN
ejpam-7064	11	33	(	(	PUNCT
ejpam-7064	11	34	w.	w.	PROPN
ejpam-7064	11	35	m.	m.	PROPN
ejpam-7064	11	36	abdelfattah	abdelfattah	PROPN
ejpam-7064	11	37	)	)	PUNCT
ejpam-7064	11	38	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7064	12	1	1	1	NUM
ejpam-7064	12	2	copyright	copyright	NOUN
ejpam-7064	12	3	:	:	PUNCT
ejpam-7064	12	4	©	©	PROPN
ejpam-7064	12	5	2025	2025	NUM
ejpam-7064	12	6	the	the	DET
ejpam-7064	12	7	author(s	author(s	NOUN
ejpam-7064	12	8	)	)	PUNCT
ejpam-7064	12	9	.	.	PUNCT
ejpam-7064	13	1	(	(	PUNCT
ejpam-7064	13	2	cc	cc	NOUN
ejpam-7064	13	3	by	by	ADP
ejpam-7064	13	4	-	-	PUNCT
ejpam-7064	13	5	nc	nc	PROPN
ejpam-7064	13	6	4.0	4.0	NUM
ejpam-7064	13	7	)	)	PUNCT
ejpam-7064	13	8	m.	m.	NOUN
ejpam-7064	13	9	adel	adel	PROPN
ejpam-7064	13	10	et	et	PROPN
ejpam-7064	13	11	al	al	PROPN
ejpam-7064	13	12	.	.	PUNCT
ejpam-7064	13	13	/	/	SYM
ejpam-7064	13	14	eur	eur	PROPN
ejpam-7064	13	15	.	.	PUNCT
ejpam-7064	14	1	j.	j.	PROPN
ejpam-7064	14	2	pure	pure	PROPN
ejpam-7064	14	3	appl	appl	PROPN
ejpam-7064	14	4	.	.	PROPN
ejpam-7064	14	5	math	math	PROPN
ejpam-7064	14	6	,	,	PUNCT
ejpam-7064	14	7	18	18	NUM
ejpam-7064	14	8	(	(	PUNCT
ejpam-7064	14	9	4	4	NUM
ejpam-7064	14	10	)	)	PUNCT
ejpam-7064	14	11	(	(	PUNCT
ejpam-7064	14	12	2025	2025	NUM
ejpam-7064	14	13	)	)	PUNCT
ejpam-7064	14	14	,	,	PUNCT
ejpam-7064	14	15	7064	7064	NUM
ejpam-7064	14	16	2	2	NUM
ejpam-7064	14	17	of	of	ADP
ejpam-7064	14	18	11	11	NUM
ejpam-7064	14	19	1	1	NUM
ejpam-7064	14	20	.	.	PUNCT
ejpam-7064	15	1	introduction	introduction	NOUN
ejpam-7064	15	2	while	while	SCONJ
ejpam-7064	15	3	spectral	spectral	ADJ
ejpam-7064	15	4	methods	method	NOUN
ejpam-7064	15	5	are	be	AUX
ejpam-7064	15	6	recognized	recognize	VERB
ejpam-7064	15	7	for	for	ADP
ejpam-7064	15	8	their	their	PRON
ejpam-7064	15	9	precision	precision	NOUN
ejpam-7064	15	10	,	,	PUNCT
ejpam-7064	15	11	their	their	PRON
ejpam-7064	15	12	accuracy	accuracy	NOUN
ejpam-7064	15	13	diminishes	diminish	VERB
ejpam-7064	15	14	for	for	ADP
ejpam-7064	15	15	non	non	ADJ
ejpam-7064	15	16	-	-	ADJ
ejpam-7064	15	17	smooth	smooth	ADJ
ejpam-7064	15	18	solutions	solution	NOUN
ejpam-7064	15	19	and	and	CCONJ
ejpam-7064	15	20	extensive	extensive	ADJ
ejpam-7064	15	21	domain	domain	NOUN
ejpam-7064	15	22	issues	issue	NOUN
ejpam-7064	15	23	,	,	PUNCT
ejpam-7064	15	24	even	even	ADV
ejpam-7064	15	25	when	when	SCONJ
ejpam-7064	15	26	more	more	ADJ
ejpam-7064	15	27	grid	grid	NOUN
ejpam-7064	15	28	points	point	NOUN
ejpam-7064	15	29	are	be	AUX
ejpam-7064	15	30	added	add	VERB
ejpam-7064	15	31	(	(	PUNCT
ejpam-7064	15	32	[	[	X
ejpam-7064	15	33	1	1	NUM
ejpam-7064	15	34	]	]	PUNCT
ejpam-7064	15	35	,	,	PUNCT
ejpam-7064	16	1	[	[	X
ejpam-7064	16	2	2	2	NUM
ejpam-7064	16	3	]	]	NUM
ejpam-7064	16	4	)	)	PUNCT
ejpam-7064	16	5	.	.	PUNCT
ejpam-7064	17	1	domain	domain	NOUN
ejpam-7064	17	2	decomposition	decomposition	NOUN
ejpam-7064	17	3	has	have	AUX
ejpam-7064	17	4	mainly	mainly	ADV
ejpam-7064	17	5	been	be	AUX
ejpam-7064	17	6	used	use	VERB
ejpam-7064	17	7	with	with	ADP
ejpam-7064	17	8	semi	semi	ADJ
ejpam-7064	17	9	-	-	ADJ
ejpam-7064	17	10	analytical	analytical	ADJ
ejpam-7064	17	11	techniques	technique	NOUN
ejpam-7064	17	12	to	to	PART
ejpam-7064	17	13	address	address	VERB
ejpam-7064	17	14	the	the	DET
ejpam-7064	17	15	numerical	numerical	ADJ
ejpam-7064	17	16	solutions	solution	NOUN
ejpam-7064	17	17	of	of	ADP
ejpam-7064	17	18	some	some	DET
ejpam-7064	17	19	systems	system	NOUN
ejpam-7064	17	20	.	.	PUNCT
ejpam-7064	18	1	such	such	ADJ
ejpam-7064	18	2	techniques	technique	NOUN
ejpam-7064	18	3	encompass	encompass	NOUN
ejpam-7064	18	4	methods	method	NOUN
ejpam-7064	18	5	like	like	ADP
ejpam-7064	18	6	the	the	DET
ejpam-7064	18	7	multistage	multistage	NOUN
ejpam-7064	18	8	adomian	adomian	NOUN
ejpam-7064	18	9	decomposition	decomposition	NOUN
ejpam-7064	18	10	method	method	NOUN
ejpam-7064	18	11	[	[	X
ejpam-7064	18	12	3	3	NUM
ejpam-7064	18	13	]	]	PUNCT
ejpam-7064	18	14	,	,	PUNCT
ejpam-7064	18	15	multistage	multistage	NOUN
ejpam-7064	18	16	variational	variational	ADJ
ejpam-7064	18	17	iteration	iteration	NOUN
ejpam-7064	18	18	method	method	NOUN
ejpam-7064	18	19	[	[	X
ejpam-7064	18	20	4	4	NUM
ejpam-7064	18	21	]	]	PUNCT
ejpam-7064	18	22	,	,	PUNCT
ejpam-7064	18	23	and	and	CCONJ
ejpam-7064	18	24	multistage	multistage	NOUN
ejpam-7064	18	25	homotopy	homotopy	NOUN
ejpam-7064	18	26	perturbation	perturbation	NOUN
ejpam-7064	18	27	method	method	NOUN
ejpam-7064	18	28	[	[	X
ejpam-7064	18	29	5	5	NUM
ejpam-7064	18	30	]	]	PUNCT
ejpam-7064	18	31	.	.	PUNCT
ejpam-7064	19	1	however	however	ADV
ejpam-7064	19	2	,	,	PUNCT
ejpam-7064	19	3	a	a	DET
ejpam-7064	19	4	challenge	challenge	NOUN
ejpam-7064	19	5	faced	face	VERB
ejpam-7064	19	6	by	by	ADP
ejpam-7064	19	7	multi	multi	ADJ
ejpam-7064	19	8	-	-	ADJ
ejpam-7064	19	9	domain	domain	ADJ
ejpam-7064	19	10	techniques	technique	NOUN
ejpam-7064	19	11	based	base	VERB
ejpam-7064	19	12	on	on	ADP
ejpam-7064	19	13	analytical	analytical	ADJ
ejpam-7064	19	14	approximations	approximation	NOUN
ejpam-7064	19	15	is	be	AUX
ejpam-7064	19	16	the	the	DET
ejpam-7064	19	17	long	long	ADJ
ejpam-7064	19	18	and	and	CCONJ
ejpam-7064	19	19	complex	complex	ADJ
ejpam-7064	19	20	process	process	NOUN
ejpam-7064	19	21	of	of	ADP
ejpam-7064	19	22	analytical	analytical	ADJ
ejpam-7064	19	23	integration	integration	NOUN
ejpam-7064	19	24	within	within	ADP
ejpam-7064	19	25	each	each	DET
ejpam-7064	19	26	sub	sub	NOUN
ejpam-7064	19	27	-	-	NOUN
ejpam-7064	19	28	domain	domain	NOUN
ejpam-7064	19	29	.	.	PUNCT
ejpam-7064	20	1	motsa	motsa	NOUN
ejpam-7064	20	2	and	and	CCONJ
ejpam-7064	20	3	colleagues	colleague	NOUN
ejpam-7064	20	4	(	(	PUNCT
ejpam-7064	20	5	[	[	X
ejpam-7064	20	6	6	6	NUM
ejpam-7064	20	7	]	]	PUNCT
ejpam-7064	20	8	,	,	PUNCT
ejpam-7064	20	9	[	[	X
ejpam-7064	20	10	7	7	NUM
ejpam-7064	20	11	]	]	PUNCT
ejpam-7064	20	12	)	)	PUNCT
ejpam-7064	20	13	introduced	introduce	VERB
ejpam-7064	20	14	a	a	DET
ejpam-7064	20	15	spectral	spectral	ADJ
ejpam-7064	20	16	method	method	NOUN
ejpam-7064	20	17	-	-	PUNCT
ejpam-7064	20	18	based	base	VERB
ejpam-7064	20	19	multi	multi	ADJ
ejpam-7064	20	20	-	-	ADJ
ejpam-7064	20	21	domain	domain	ADJ
ejpam-7064	20	22	numerical	numerical	ADJ
ejpam-7064	20	23	approach	approach	NOUN
ejpam-7064	20	24	,	,	PUNCT
ejpam-7064	20	25	setting	set	VERB
ejpam-7064	20	26	it	it	PRON
ejpam-7064	20	27	apart	apart	ADV
ejpam-7064	20	28	from	from	ADP
ejpam-7064	20	29	earlier	early	ADJ
ejpam-7064	20	30	multi	multi	ADJ
ejpam-7064	20	31	-	-	ADJ
ejpam-7064	20	32	domain	domain	ADJ
ejpam-7064	20	33	strategies	strategy	NOUN
ejpam-7064	20	34	by	by	ADP
ejpam-7064	20	35	being	be	AUX
ejpam-7064	20	36	entirely	entirely	ADV
ejpam-7064	20	37	numerical	numerical	ADJ
ejpam-7064	20	38	.	.	PUNCT
ejpam-7064	21	1	other	other	ADJ
ejpam-7064	21	2	numerical	numerical	ADJ
ejpam-7064	21	3	strategies	strategy	NOUN
ejpam-7064	21	4	that	that	PRON
ejpam-7064	21	5	have	have	AUX
ejpam-7064	21	6	employed	employ	VERB
ejpam-7064	21	7	domain	domain	NOUN
ejpam-7064	21	8	decomposition	decomposition	NOUN
ejpam-7064	21	9	for	for	ADP
ejpam-7064	21	10	chaotic	chaotic	ADJ
ejpam-7064	21	11	systems	system	NOUN
ejpam-7064	21	12	are	be	AUX
ejpam-7064	21	13	the	the	DET
ejpam-7064	21	14	time	time	NOUN
ejpam-7064	21	15	discretization	discretization	NOUN
ejpam-7064	21	16	[	[	X
ejpam-7064	21	17	8	8	NUM
ejpam-7064	21	18	]	]	PUNCT
ejpam-7064	21	19	,	,	PUNCT
ejpam-7064	21	20	piecewise	piecewise	VERB
ejpam-7064	21	21	successive	successive	ADJ
ejpam-7064	21	22	linearization	linearization	NOUN
ejpam-7064	21	23	[	[	X
ejpam-7064	21	24	9	9	NUM
ejpam-7064	21	25	]	]	PUNCT
ejpam-7064	21	26	,	,	PUNCT
ejpam-7064	21	27	piecewise	piecewise	PROPN
ejpam-7064	21	28	spectral	spectral	PROPN
ejpam-7064	21	29	homotopy	homotopy	VERB
ejpam-7064	21	30	analysis	analysis	NOUN
ejpam-7064	21	31	[	[	X
ejpam-7064	21	32	10	10	NUM
ejpam-7064	21	33	]	]	PUNCT
ejpam-7064	21	34	,	,	PUNCT
ejpam-7064	21	35	and	and	CCONJ
ejpam-7064	21	36	multi	multi	ADJ
ejpam-7064	21	37	-	-	ADJ
ejpam-7064	21	38	domain	domain	ADJ
ejpam-7064	21	39	compact	compact	ADJ
ejpam-7064	21	40	finite	finite	NOUN
ejpam-7064	21	41	difference	difference	NOUN
ejpam-7064	21	42	relaxation	relaxation	NOUN
ejpam-7064	21	43	(	(	PUNCT
ejpam-7064	21	44	[	[	X
ejpam-7064	21	45	11	11	NUM
ejpam-7064	21	46	]	]	PUNCT
ejpam-7064	21	47	,	,	PUNCT
ejpam-7064	21	48	[	[	X
ejpam-7064	21	49	12	12	NUM
ejpam-7064	21	50	]	]	PUNCT
ejpam-7064	21	51	)	)	PUNCT
ejpam-7064	21	52	.	.	PUNCT
ejpam-7064	22	1	also	also	ADV
ejpam-7064	22	2	,	,	PUNCT
ejpam-7064	22	3	there	there	PRON
ejpam-7064	22	4	are	be	VERB
ejpam-7064	22	5	numerical	numerical	ADJ
ejpam-7064	22	6	algorithms	algorithm	NOUN
ejpam-7064	22	7	can	can	AUX
ejpam-7064	22	8	be	be	AUX
ejpam-7064	22	9	applied	apply	VERB
ejpam-7064	22	10	in	in	ADP
ejpam-7064	22	11	many	many	ADJ
ejpam-7064	22	12	real	real	ADJ
ejpam-7064	22	13	life	life	NOUN
ejpam-7064	22	14	problems	problem	NOUN
ejpam-7064	22	15	as	as	ADP
ejpam-7064	22	16	in	in	ADP
ejpam-7064	22	17	the	the	DET
ejpam-7064	22	18	operation	operation	NOUN
ejpam-7064	22	19	research	research	NOUN
ejpam-7064	22	20	,	,	PUNCT
ejpam-7064	22	21	data	data	VERB
ejpam-7064	22	22	analysis	analysis	NOUN
ejpam-7064	22	23	and	and	CCONJ
ejpam-7064	22	24	the	the	DET
ejpam-7064	22	25	financial	financial	ADJ
ejpam-7064	22	26	mathematics	mathematic	NOUN
ejpam-7064	22	27	(	(	PUNCT
ejpam-7064	22	28	[	[	X
ejpam-7064	22	29	13	13	NUM
ejpam-7064	22	30	]	]	PUNCT
ejpam-7064	22	31	,	,	PUNCT
ejpam-7064	22	32	[	[	X
ejpam-7064	22	33	14	14	NUM
ejpam-7064	22	34	]	]	SYM
ejpam-7064	22	35	)	)	PUNCT
ejpam-7064	22	36	,	,	PUNCT
ejpam-7064	22	37	also	also	ADV
ejpam-7064	22	38	in	in	ADP
ejpam-7064	22	39	the	the	DET
ejpam-7064	22	40	simulations	simulation	NOUN
ejpam-7064	22	41	of	of	ADP
ejpam-7064	22	42	some	some	DET
ejpam-7064	22	43	biological	biological	ADJ
ejpam-7064	22	44	models	model	NOUN
ejpam-7064	22	45	as	as	ADP
ejpam-7064	22	46	in	in	ADP
ejpam-7064	22	47	(	(	PUNCT
ejpam-7064	22	48	[	[	X
ejpam-7064	22	49	15],[16	15],[16	PROPN
ejpam-7064	22	50	]	]	X
ejpam-7064	22	51	)	)	PUNCT
ejpam-7064	22	52	.	.	PUNCT
ejpam-7064	23	1	in	in	ADP
ejpam-7064	23	2	this	this	DET
ejpam-7064	23	3	work	work	NOUN
ejpam-7064	23	4	,	,	PUNCT
ejpam-7064	23	5	we	we	PRON
ejpam-7064	23	6	describe	describe	VERB
ejpam-7064	23	7	the	the	DET
ejpam-7064	23	8	brusselator	brusselator	NOUN
ejpam-7064	23	9	mathematical	mathematical	ADJ
ejpam-7064	23	10	model	model	NOUN
ejpam-7064	23	11	,	,	PUNCT
ejpam-7064	23	12	which	which	PRON
ejpam-7064	23	13	predicts	predict	VERB
ejpam-7064	23	14	the	the	DET
ejpam-7064	23	15	oscillations	oscillation	NOUN
ejpam-7064	23	16	in	in	ADP
ejpam-7064	23	17	chemical	chemical	ADJ
ejpam-7064	23	18	reactions	reaction	NOUN
ejpam-7064	23	19	.	.	PUNCT
ejpam-7064	24	1	we	we	PRON
ejpam-7064	24	2	present	present	VERB
ejpam-7064	24	3	an	an	DET
ejpam-7064	24	4	argument	argument	NOUN
ejpam-7064	24	5	for	for	ADP
ejpam-7064	24	6	why	why	SCONJ
ejpam-7064	24	7	modern	modern	ADJ
ejpam-7064	24	8	thermodynamics	thermodynamic	NOUN
ejpam-7064	24	9	is	be	AUX
ejpam-7064	24	10	important	important	ADJ
ejpam-7064	24	11	in	in	ADP
ejpam-7064	24	12	analyzing	analyze	VERB
ejpam-7064	24	13	a	a	DET
ejpam-7064	24	14	system	system	NOUN
ejpam-7064	24	15	that	that	PRON
ejpam-7064	24	16	constantly	constantly	ADV
ejpam-7064	24	17	interacts	interact	VERB
ejpam-7064	24	18	with	with	ADP
ejpam-7064	24	19	its	its	PRON
ejpam-7064	24	20	environment	environment	NOUN
ejpam-7064	24	21	,	,	PUNCT
ejpam-7064	24	22	and	and	CCONJ
ejpam-7064	24	23	which	which	PRON
ejpam-7064	24	24	operates	operate	VERB
ejpam-7064	24	25	far	far	ADV
ejpam-7064	24	26	from	from	ADP
ejpam-7064	24	27	thermodynamic	thermodynamic	ADJ
ejpam-7064	24	28	equilibrium	equilibrium	NOUN
ejpam-7064	24	29	.	.	PUNCT
ejpam-7064	25	1	the	the	DET
ejpam-7064	25	2	brusselator	brusselator	NOUN
ejpam-7064	25	3	model	model	NOUN
ejpam-7064	25	4	has	have	AUX
ejpam-7064	25	5	been	be	AUX
ejpam-7064	25	6	used	use	VERB
ejpam-7064	25	7	in	in	ADP
ejpam-7064	25	8	a	a	DET
ejpam-7064	25	9	wide	wide	ADJ
ejpam-7064	25	10	range	range	NOUN
ejpam-7064	25	11	of	of	ADP
ejpam-7064	25	12	applications	application	NOUN
ejpam-7064	25	13	in	in	ADP
ejpam-7064	25	14	chemical	chemical	ADJ
ejpam-7064	25	15	research	research	NOUN
ejpam-7064	25	16	,	,	PUNCT
ejpam-7064	25	17	where	where	SCONJ
ejpam-7064	25	18	it	it	PRON
ejpam-7064	25	19	has	have	AUX
ejpam-7064	25	20	been	be	AUX
ejpam-7064	25	21	used	use	VERB
ejpam-7064	25	22	to	to	PART
ejpam-7064	25	23	study	study	VERB
ejpam-7064	25	24	the	the	DET
ejpam-7064	25	25	formation	formation	NOUN
ejpam-7064	25	26	of	of	ADP
ejpam-7064	25	27	spatial	spatial	ADJ
ejpam-7064	25	28	patterns	pattern	NOUN
ejpam-7064	25	29	in	in	ADP
ejpam-7064	25	30	chemical	chemical	NOUN
ejpam-7064	25	31	systems	system	NOUN
ejpam-7064	25	32	,	,	PUNCT
ejpam-7064	25	33	such	such	ADJ
ejpam-7064	25	34	as	as	ADP
ejpam-7064	25	35	turing	ture	VERB
ejpam-7064	25	36	patterns	pattern	NOUN
ejpam-7064	25	37	and	and	CCONJ
ejpam-7064	25	38	spiral	spiral	ADJ
ejpam-7064	25	39	waves	wave	NOUN
ejpam-7064	25	40	.	.	PUNCT
ejpam-7064	26	1	it	it	PRON
ejpam-7064	26	2	is	be	AUX
ejpam-7064	26	3	considered	consider	VERB
ejpam-7064	26	4	a	a	DET
ejpam-7064	26	5	theoretical	theoretical	ADJ
ejpam-7064	26	6	model	model	NOUN
ejpam-7064	26	7	for	for	ADP
ejpam-7064	26	8	a	a	DET
ejpam-7064	26	9	type	type	NOUN
ejpam-7064	26	10	of	of	ADP
ejpam-7064	26	11	self	self	NOUN
ejpam-7064	26	12	-	-	PUNCT
ejpam-7064	26	13	catalytic	catalytic	ADJ
ejpam-7064	26	14	reaction	reaction	NOUN
ejpam-7064	26	15	[	[	X
ejpam-7064	26	16	17	17	NUM
ejpam-7064	26	17	]	]	PUNCT
ejpam-7064	26	18	.	.	PUNCT
ejpam-7064	27	1	it	it	PRON
ejpam-7064	27	2	is	be	AUX
ejpam-7064	27	3	also	also	ADV
ejpam-7064	27	4	considered	consider	VERB
ejpam-7064	27	5	an	an	DET
ejpam-7064	27	6	example	example	NOUN
ejpam-7064	27	7	of	of	ADP
ejpam-7064	27	8	an	an	DET
ejpam-7064	27	9	autocatalytic	autocatalytic	ADJ
ejpam-7064	27	10	,	,	PUNCT
ejpam-7064	27	11	oscillatory	oscillatory	ADJ
ejpam-7064	27	12	chemical	chemical	NOUN
ejpam-7064	27	13	reaction	reaction	NOUN
ejpam-7064	27	14	,	,	PUNCT
ejpam-7064	27	15	that	that	ADV
ejpam-7064	27	16	is	is	ADV
ejpam-7064	27	17	,	,	PUNCT
ejpam-7064	27	18	a	a	DET
ejpam-7064	27	19	reaction	reaction	NOUN
ejpam-7064	27	20	in	in	ADP
ejpam-7064	27	21	which	which	PRON
ejpam-7064	27	22	a	a	DET
ejpam-7064	27	23	species	species	NOUN
ejpam-7064	27	24	increases	increase	VERB
ejpam-7064	27	25	the	the	DET
ejpam-7064	27	26	rate	rate	NOUN
ejpam-7064	27	27	of	of	ADP
ejpam-7064	27	28	its	its	PRON
ejpam-7064	27	29	productive	productive	ADJ
ejpam-7064	27	30	reaction	reaction	NOUN
ejpam-7064	27	31	[	[	X
ejpam-7064	27	32	18	18	NUM
ejpam-7064	27	33	]	]	PUNCT
ejpam-7064	27	34	.	.	PUNCT
ejpam-7064	28	1	in	in	ADP
ejpam-7064	28	2	this	this	DET
ejpam-7064	28	3	paper	paper	NOUN
ejpam-7064	28	4	,	,	PUNCT
ejpam-7064	28	5	we	we	PRON
ejpam-7064	28	6	aim	aim	VERB
ejpam-7064	28	7	to	to	PART
ejpam-7064	28	8	determine	determine	VERB
ejpam-7064	28	9	and	and	CCONJ
ejpam-7064	28	10	provide	provide	VERB
ejpam-7064	28	11	the	the	DET
ejpam-7064	28	12	numerical	numerical	ADJ
ejpam-7064	28	13	solutions	solution	NOUN
ejpam-7064	28	14	to	to	ADP
ejpam-7064	28	15	the	the	DET
ejpam-7064	28	16	brusselator	brusselator	NOUN
ejpam-7064	28	17	system	system	NOUN
ejpam-7064	28	18	using	use	VERB
ejpam-7064	28	19	the	the	DET
ejpam-7064	28	20	msrm	msrm	NOUN
ejpam-7064	28	21	.	.	PUNCT
ejpam-7064	29	1	this	this	DET
ejpam-7064	29	2	technique	technique	NOUN
ejpam-7064	29	3	incorporates	incorporate	VERB
ejpam-7064	29	4	the	the	DET
ejpam-7064	29	5	chebyshev	chebyshev	PROPN
ejpam-7064	29	6	spectral	spectral	ADJ
ejpam-7064	29	7	method	method	NOUN
ejpam-7064	29	8	(	(	PUNCT
ejpam-7064	29	9	[	[	X
ejpam-7064	29	10	19	19	NUM
ejpam-7064	29	11	]	]	PUNCT
ejpam-7064	29	12	,	,	PUNCT
ejpam-7064	29	13	[	[	X
ejpam-7064	29	14	20	20	NUM
ejpam-7064	29	15	]	]	PUNCT
ejpam-7064	29	16	)	)	PUNCT
ejpam-7064	29	17	and	and	CCONJ
ejpam-7064	29	18	the	the	DET
ejpam-7064	29	19	gauss	gauss	PROPN
ejpam-7064	29	20	-	-	PUNCT
ejpam-7064	29	21	seidel	seidel	PROPN
ejpam-7064	29	22	method	method	NOUN
ejpam-7064	29	23	process	process	NOUN
ejpam-7064	29	24	to	to	PART
ejpam-7064	29	25	numerically	numerically	ADV
ejpam-7064	29	26	treat	treat	VERB
ejpam-7064	29	27	the	the	DET
ejpam-7064	29	28	system	system	NOUN
ejpam-7064	29	29	across	across	ADP
ejpam-7064	29	30	several	several	ADJ
ejpam-7064	29	31	sub	sub	NOUN
ejpam-7064	29	32	-	-	NOUN
ejpam-7064	29	33	domains	domain	NOUN
ejpam-7064	29	34	that	that	PRON
ejpam-7064	29	35	constitute	constitute	VERB
ejpam-7064	29	36	the	the	DET
ejpam-7064	29	37	entire	entire	ADJ
ejpam-7064	29	38	problem	problem	NOUN
ejpam-7064	29	39	domain	domain	NOUN
ejpam-7064	29	40	.	.	PUNCT
ejpam-7064	30	1	we	we	PRON
ejpam-7064	30	2	can	can	AUX
ejpam-7064	30	3	confidently	confidently	ADV
ejpam-7064	30	4	assess	assess	VERB
ejpam-7064	30	5	the	the	DET
ejpam-7064	30	6	effectiveness	effectiveness	NOUN
ejpam-7064	30	7	of	of	ADP
ejpam-7064	30	8	the	the	DET
ejpam-7064	30	9	given	give	VERB
ejpam-7064	30	10	numerical	numerical	ADJ
ejpam-7064	30	11	approach	approach	NOUN
ejpam-7064	30	12	for	for	ADP
ejpam-7064	30	13	the	the	DET
ejpam-7064	30	14	model	model	NOUN
ejpam-7064	30	15	under	under	ADP
ejpam-7064	30	16	study	study	NOUN
ejpam-7064	30	17	.	.	PUNCT
ejpam-7064	31	1	the	the	DET
ejpam-7064	31	2	numerical	numerical	ADJ
ejpam-7064	31	3	solutions	solution	NOUN
ejpam-7064	31	4	validate	validate	VERB
ejpam-7064	31	5	that	that	SCONJ
ejpam-7064	31	6	the	the	DET
ejpam-7064	31	7	proposed	propose	VERB
ejpam-7064	31	8	technique	technique	NOUN
ejpam-7064	31	9	may	may	AUX
ejpam-7064	31	10	effectively	effectively	ADV
ejpam-7064	31	11	tackle	tackle	VERB
ejpam-7064	31	12	the	the	DET
ejpam-7064	31	13	specified	specified	ADJ
ejpam-7064	31	14	model	model	NOUN
ejpam-7064	31	15	,	,	PUNCT
ejpam-7064	31	16	aligning	align	VERB
ejpam-7064	31	17	well	well	ADV
ejpam-7064	31	18	with	with	ADP
ejpam-7064	31	19	existing	exist	VERB
ejpam-7064	31	20	solutions	solution	NOUN
ejpam-7064	31	21	.	.	PUNCT
ejpam-7064	32	1	by	by	ADP
ejpam-7064	32	2	adding	add	VERB
ejpam-7064	32	3	terms	term	NOUN
ejpam-7064	32	4	from	from	ADP
ejpam-7064	32	5	the	the	DET
ejpam-7064	32	6	solution	solution	NOUN
ejpam-7064	32	7	series	series	NOUN
ejpam-7064	32	8	,	,	PUNCT
ejpam-7064	32	9	we	we	PRON
ejpam-7064	32	10	can	can	AUX
ejpam-7064	32	11	further	far	ADV
ejpam-7064	32	12	minimize	minimize	VERB
ejpam-7064	32	13	relative	relative	ADJ
ejpam-7064	32	14	errors	error	NOUN
ejpam-7064	32	15	.	.	PUNCT
ejpam-7064	33	1	we	we	PRON
ejpam-7064	33	2	highlight	highlight	VERB
ejpam-7064	33	3	the	the	DET
ejpam-7064	33	4	efficiency	efficiency	NOUN
ejpam-7064	33	5	and	and	CCONJ
ejpam-7064	33	6	vast	vast	ADJ
ejpam-7064	33	7	potential	potential	NOUN
ejpam-7064	33	8	of	of	ADP
ejpam-7064	33	9	our	our	PRON
ejpam-7064	33	10	proposed	propose	VERB
ejpam-7064	33	11	numerical	numerical	ADJ
ejpam-7064	33	12	method	method	NOUN
ejpam-7064	33	13	by	by	ADP
ejpam-7064	33	14	contrasting	contrast	VERB
ejpam-7064	33	15	the	the	DET
ejpam-7064	33	16	estimated	estimate	VERB
ejpam-7064	33	17	solutions	solution	NOUN
ejpam-7064	33	18	with	with	ADP
ejpam-7064	33	19	those	those	PRON
ejpam-7064	33	20	obtained	obtain	VERB
ejpam-7064	33	21	from	from	ADP
ejpam-7064	33	22	the	the	DET
ejpam-7064	33	23	rk4	rk4	NOUN
ejpam-7064	33	24	m.	m.	NOUN
ejpam-7064	33	25	we	we	PRON
ejpam-7064	33	26	also	also	ADV
ejpam-7064	33	27	illustrate	illustrate	VERB
ejpam-7064	33	28	that	that	SCONJ
ejpam-7064	33	29	the	the	DET
ejpam-7064	33	30	multi	multi	ADJ
ejpam-7064	33	31	-	-	ADJ
ejpam-7064	33	32	domain	domain	ADJ
ejpam-7064	33	33	strategy	strategy	NOUN
ejpam-7064	33	34	’s	’s	PART
ejpam-7064	33	35	strength	strength	NOUN
ejpam-7064	33	36	lies	lie	VERB
ejpam-7064	33	37	in	in	ADP
ejpam-7064	33	38	its	its	PRON
ejpam-7064	33	39	reduced	reduce	VERB
ejpam-7064	33	40	error	error	NOUN
ejpam-7064	33	41	accumulation	accumulation	NOUN
ejpam-7064	33	42	across	across	ADP
ejpam-7064	33	43	sub	sub	NOUN
ejpam-7064	33	44	-	-	NOUN
ejpam-7064	33	45	domains	domain	NOUN
ejpam-7064	33	46	compared	compare	VERB
ejpam-7064	33	47	to	to	ADP
ejpam-7064	33	48	considering	consider	VERB
ejpam-7064	33	49	a	a	DET
ejpam-7064	33	50	single	single	ADJ
ejpam-7064	33	51	domain	domain	NOUN
ejpam-7064	33	52	.	.	PUNCT
ejpam-7064	34	1	the	the	DET
ejpam-7064	34	2	proposed	propose	VERB
ejpam-7064	34	3	method	method	NOUN
ejpam-7064	34	4	is	be	AUX
ejpam-7064	34	5	a	a	DET
ejpam-7064	34	6	powerful	powerful	ADJ
ejpam-7064	34	7	technique	technique	NOUN
ejpam-7064	34	8	that	that	PRON
ejpam-7064	34	9	uses	use	VERB
ejpam-7064	34	10	an	an	DET
ejpam-7064	34	11	approach	approach	NOUN
ejpam-7064	34	12	of	of	ADP
ejpam-7064	34	13	linearization	linearization	NOUN
ejpam-7064	34	14	of	of	ADP
ejpam-7064	34	15	nonlinear	nonlinear	ADJ
ejpam-7064	34	16	equations	equation	NOUN
ejpam-7064	34	17	for	for	ADP
ejpam-7064	34	18	obtaining	obtain	VERB
ejpam-7064	34	19	a	a	DET
ejpam-7064	34	20	better	well	ADJ
ejpam-7064	34	21	series	series	NOUN
ejpam-7064	34	22	solution	solution	NOUN
ejpam-7064	34	23	,	,	PUNCT
ejpam-7064	34	24	which	which	PRON
ejpam-7064	34	25	provides	provide	VERB
ejpam-7064	34	26	efficient	efficient	ADJ
ejpam-7064	34	27	algorithms	algorithm	NOUN
ejpam-7064	34	28	for	for	ADP
ejpam-7064	34	29	approximate	approximate	ADJ
ejpam-7064	34	30	solutions	solution	NOUN
ejpam-7064	34	31	,	,	PUNCT
ejpam-7064	34	32	giving	give	VERB
ejpam-7064	34	33	effective	effective	ADJ
ejpam-7064	34	34	precision	precision	NOUN
ejpam-7064	34	35	and	and	CCONJ
ejpam-7064	34	36	convergence	convergence	NOUN
ejpam-7064	34	37	.	.	PUNCT
ejpam-7064	35	1	besides	besides	SCONJ
ejpam-7064	35	2	,	,	PUNCT
ejpam-7064	35	3	the	the	DET
ejpam-7064	35	4	solutions	solution	NOUN
ejpam-7064	35	5	converged	converge	VERB
ejpam-7064	35	6	in	in	ADP
ejpam-7064	35	7	a	a	DET
ejpam-7064	35	8	relatively	relatively	ADV
ejpam-7064	35	9	narrow	narrow	ADJ
ejpam-7064	35	10	region	region	NOUN
ejpam-7064	35	11	,	,	PUNCT
ejpam-7064	35	12	and	and	CCONJ
ejpam-7064	35	13	they	they	PRON
ejpam-7064	35	14	had	have	VERB
ejpam-7064	35	15	sluggish	sluggish	ADJ
ejpam-7064	35	16	convergence	convergence	NOUN
ejpam-7064	35	17	.	.	PUNCT
ejpam-7064	36	1	from	from	ADP
ejpam-7064	36	2	the	the	DET
ejpam-7064	36	3	novelty	novelty	NOUN
ejpam-7064	36	4	points	point	NOUN
ejpam-7064	36	5	,	,	PUNCT
ejpam-7064	36	6	the	the	DET
ejpam-7064	36	7	proposed	propose	VERB
ejpam-7064	36	8	method	method	NOUN
ejpam-7064	36	9	is	be	AUX
ejpam-7064	36	10	considered	consider	VERB
ejpam-7064	36	11	for	for	ADP
ejpam-7064	36	12	the	the	DET
ejpam-7064	36	13	first	first	ADJ
ejpam-7064	36	14	time	time	NOUN
ejpam-7064	36	15	for	for	ADP
ejpam-7064	36	16	solving	solve	VERB
ejpam-7064	36	17	m.	m.	NOUN
ejpam-7064	36	18	adel	adel	PROPN
ejpam-7064	36	19	et	et	PROPN
ejpam-7064	36	20	al	al	PROPN
ejpam-7064	36	21	.	.	PUNCT
ejpam-7064	36	22	/	/	SYM
ejpam-7064	36	23	eur	eur	PROPN
ejpam-7064	36	24	.	.	PUNCT
ejpam-7064	37	1	j.	j.	PROPN
ejpam-7064	37	2	pure	pure	PROPN
ejpam-7064	37	3	appl	appl	PROPN
ejpam-7064	37	4	.	.	PROPN
ejpam-7064	37	5	math	math	PROPN
ejpam-7064	37	6	,	,	PUNCT
ejpam-7064	37	7	18	18	NUM
ejpam-7064	37	8	(	(	PUNCT
ejpam-7064	37	9	4	4	NUM
ejpam-7064	37	10	)	)	PUNCT
ejpam-7064	37	11	(	(	PUNCT
ejpam-7064	37	12	2025	2025	NUM
ejpam-7064	37	13	)	)	PUNCT
ejpam-7064	37	14	,	,	PUNCT
ejpam-7064	37	15	7064	7064	NUM
ejpam-7064	37	16	3	3	NUM
ejpam-7064	37	17	of	of	ADP
ejpam-7064	37	18	11	11	NUM
ejpam-7064	37	19	the	the	DET
ejpam-7064	37	20	brusselator	brusselator	NOUN
ejpam-7064	37	21	system	system	NOUN
ejpam-7064	37	22	.	.	PUNCT
ejpam-7064	38	1	2	2	X
ejpam-7064	38	2	.	.	NUM
ejpam-7064	38	3	basic	basic	ADJ
ejpam-7064	38	4	concepts	concept	NOUN
ejpam-7064	38	5	2.1	2.1	NUM
ejpam-7064	38	6	.	.	PUNCT
ejpam-7064	38	7	mathematical	mathematical	ADJ
ejpam-7064	38	8	formulation	formulation	NOUN
ejpam-7064	38	9	here	here	ADV
ejpam-7064	38	10	,	,	PUNCT
ejpam-7064	38	11	we	we	PRON
ejpam-7064	38	12	focus	focus	VERB
ejpam-7064	38	13	on	on	ADP
ejpam-7064	38	14	the	the	DET
ejpam-7064	38	15	brusselator	brusselator	NOUN
ejpam-7064	38	16	system	system	NOUN
ejpam-7064	38	17	,	,	PUNCT
ejpam-7064	38	18	which	which	PRON
ejpam-7064	38	19	is	be	AUX
ejpam-7064	38	20	formulated	formulate	VERB
ejpam-7064	38	21	as	as	SCONJ
ejpam-7064	38	22	follows	follow	VERB
ejpam-7064	38	23	[	[	X
ejpam-7064	38	24	21	21	NUM
ejpam-7064	38	25	]	]	X
ejpam-7064	38	26	:	:	PUNCT
ejpam-7064	38	27	θ̇1(t	θ̇1(t	ADJ
ejpam-7064	38	28	)	)	PUNCT
ejpam-7064	39	1	=	=	PUNCT
ejpam-7064	39	2	δ	δ	X
ejpam-7064	39	3	−	−	PROPN
ejpam-7064	39	4	(	(	PUNCT
ejpam-7064	39	5	1	1	NUM
ejpam-7064	39	6	+	+	CCONJ
ejpam-7064	39	7	γ	γ	X
ejpam-7064	39	8	)	)	PUNCT
ejpam-7064	39	9	θ1(t	θ1(t	PROPN
ejpam-7064	39	10	)	)	PUNCT
ejpam-7064	39	11	+	+	CCONJ
ejpam-7064	39	12	(	(	PUNCT
ejpam-7064	39	13	θ1(t	θ1(t	PROPN
ejpam-7064	39	14	)	)	PUNCT
ejpam-7064	39	15	)	)	PUNCT
ejpam-7064	39	16	2	2	NUM
ejpam-7064	39	17	θ2(t	θ2(t	NOUN
ejpam-7064	39	18	)	)	PUNCT
ejpam-7064	39	19	,	,	PUNCT
ejpam-7064	39	20	(	(	PUNCT
ejpam-7064	39	21	1	1	X
ejpam-7064	39	22	)	)	PUNCT
ejpam-7064	39	23	θ̇2(t	θ̇2(t	PROPN
ejpam-7064	39	24	)	)	PUNCT
ejpam-7064	39	25	=	=	PUNCT
ejpam-7064	39	26	γ	γ	X
ejpam-7064	39	27	θ1(t)−	θ1(t)−	PROPN
ejpam-7064	39	28	(	(	PUNCT
ejpam-7064	39	29	θ1(t	θ1(t	PROPN
ejpam-7064	39	30	)	)	PUNCT
ejpam-7064	39	31	)	)	PUNCT
ejpam-7064	39	32	2	2	NUM
ejpam-7064	39	33	θ2(t	θ2(t	NOUN
ejpam-7064	39	34	)	)	PUNCT
ejpam-7064	39	35	,	,	PUNCT
ejpam-7064	39	36	(	(	PUNCT
ejpam-7064	39	37	2	2	X
ejpam-7064	39	38	)	)	PUNCT
ejpam-7064	39	39	with	with	ADP
ejpam-7064	39	40	the	the	DET
ejpam-7064	39	41	following	follow	VERB
ejpam-7064	39	42	initial	initial	ADJ
ejpam-7064	39	43	conditions	condition	NOUN
ejpam-7064	39	44	:	:	PUNCT
ejpam-7064	39	45	θ1(0	θ1(0	PROPN
ejpam-7064	39	46	)	)	PUNCT
ejpam-7064	39	47	=	=	SYM
ejpam-7064	39	48	θ01	θ01	NOUN
ejpam-7064	39	49	,	,	PUNCT
ejpam-7064	39	50	θ2(0	θ2(0	NOUN
ejpam-7064	39	51	)	)	PUNCT
ejpam-7064	39	52	=	=	SYM
ejpam-7064	39	53	θ02	θ02	NOUN
ejpam-7064	39	54	,	,	PUNCT
ejpam-7064	39	55	(	(	PUNCT
ejpam-7064	39	56	3	3	X
ejpam-7064	39	57	)	)	PUNCT
ejpam-7064	39	58	where	where	SCONJ
ejpam-7064	39	59	θ1	θ1	NOUN
ejpam-7064	39	60	and	and	CCONJ
ejpam-7064	39	61	θ2	θ2	PROPN
ejpam-7064	39	62	represent	represent	VERB
ejpam-7064	39	63	the	the	DET
ejpam-7064	39	64	concentration	concentration	NOUN
ejpam-7064	39	65	of	of	ADP
ejpam-7064	39	66	the	the	DET
ejpam-7064	39	67	reaction	reaction	NOUN
ejpam-7064	39	68	and	and	CCONJ
ejpam-7064	39	69	diffusion	diffusion	NOUN
ejpam-7064	39	70	processes	process	NOUN
ejpam-7064	39	71	,	,	PUNCT
ejpam-7064	39	72	respectively	respectively	ADV
ejpam-7064	39	73	,	,	PUNCT
ejpam-7064	39	74	the	the	DET
ejpam-7064	39	75	parameters	parameter	NOUN
ejpam-7064	39	76	δ	δ	PROPN
ejpam-7064	39	77	>	>	X
ejpam-7064	39	78	0	0	PROPN
ejpam-7064	39	79	,	,	PUNCT
ejpam-7064	39	80	γ	γ	X
ejpam-7064	39	81	>	>	X
ejpam-7064	39	82	0	0	NUM
ejpam-7064	39	83	,	,	PUNCT
ejpam-7064	39	84	and	and	CCONJ
ejpam-7064	39	85	θ01	θ01	NOUN
ejpam-7064	39	86	,	,	PUNCT
ejpam-7064	39	87	θ	θ	PROPN
ejpam-7064	39	88	0	0	NUM
ejpam-7064	39	89	2	2	NUM
ejpam-7064	39	90	are	be	AUX
ejpam-7064	39	91	constants	constant	NOUN
ejpam-7064	39	92	[	[	X
ejpam-7064	39	93	22	22	NUM
ejpam-7064	39	94	]	]	PUNCT
ejpam-7064	39	95	.	.	PUNCT
ejpam-7064	40	1	the	the	DET
ejpam-7064	40	2	system	system	NOUN
ejpam-7064	40	3	can	can	AUX
ejpam-7064	40	4	exhibit	exhibit	VERB
ejpam-7064	40	5	sustained	sustained	ADJ
ejpam-7064	40	6	oscillations	oscillation	NOUN
ejpam-7064	40	7	as	as	SCONJ
ejpam-7064	40	8	δ	δ	PROPN
ejpam-7064	40	9	increases	increase	VERB
ejpam-7064	40	10	beyond	beyond	ADP
ejpam-7064	40	11	this	this	DET
ejpam-7064	40	12	critical	critical	ADJ
ejpam-7064	40	13	value	value	NOUN
ejpam-7064	40	14	.	.	PUNCT
ejpam-7064	41	1	the	the	DET
ejpam-7064	41	2	parameter	parameter	NOUN
ejpam-7064	41	3	γ	γ	PROPN
ejpam-7064	41	4	controls	control	VERB
ejpam-7064	41	5	the	the	DET
ejpam-7064	41	6	balance	balance	NOUN
ejpam-7064	41	7	between	between	ADP
ejpam-7064	41	8	the	the	DET
ejpam-7064	41	9	reaction	reaction	NOUN
ejpam-7064	41	10	and	and	CCONJ
ejpam-7064	41	11	diffusion	diffusion	NOUN
ejpam-7064	41	12	processes	process	NOUN
ejpam-7064	41	13	.	.	PUNCT
ejpam-7064	42	1	the	the	DET
ejpam-7064	42	2	reaction	reaction	NOUN
ejpam-7064	42	3	dominates	dominate	VERB
ejpam-7064	42	4	at	at	ADP
ejpam-7064	42	5	low	low	ADJ
ejpam-7064	42	6	values	value	NOUN
ejpam-7064	42	7	of	of	ADP
ejpam-7064	42	8	γ	γ	NOUN
ejpam-7064	42	9	,	,	PUNCT
ejpam-7064	42	10	and	and	CCONJ
ejpam-7064	42	11	the	the	DET
ejpam-7064	42	12	system	system	NOUN
ejpam-7064	42	13	can	can	AUX
ejpam-7064	42	14	exhibit	exhibit	VERB
ejpam-7064	42	15	sustained	sustained	ADJ
ejpam-7064	42	16	oscillations	oscillation	NOUN
ejpam-7064	42	17	or	or	CCONJ
ejpam-7064	42	18	spiral	spiral	ADJ
ejpam-7064	42	19	waves	wave	NOUN
ejpam-7064	42	20	.	.	PUNCT
ejpam-7064	43	1	as	as	ADP
ejpam-7064	43	2	γ	γ	NOUN
ejpam-7064	43	3	increases	increase	NOUN
ejpam-7064	43	4	,	,	PUNCT
ejpam-7064	43	5	diffusion	diffusion	NOUN
ejpam-7064	43	6	becomes	become	VERB
ejpam-7064	43	7	more	more	ADV
ejpam-7064	43	8	important	important	ADJ
ejpam-7064	43	9	,	,	PUNCT
ejpam-7064	43	10	and	and	CCONJ
ejpam-7064	43	11	the	the	DET
ejpam-7064	43	12	system	system	NOUN
ejpam-7064	43	13	can	can	AUX
ejpam-7064	43	14	exhibit	exhibit	VERB
ejpam-7064	43	15	turing	ture	VERB
ejpam-7064	43	16	patterns	pattern	NOUN
ejpam-7064	43	17	.	.	PUNCT
ejpam-7064	44	1	2.2	2.2	NUM
ejpam-7064	44	2	.	.	PUNCT
ejpam-7064	45	1	the	the	DET
ejpam-7064	45	2	chebyshev	chebyshev	NOUN
ejpam-7064	45	3	-	-	PUNCT
ejpam-7064	45	4	lagrange	lagrange	NOUN
ejpam-7064	45	5	interpolation	interpolation	NOUN
ejpam-7064	45	6	the	the	DET
ejpam-7064	45	7	chebyshev	chebyshev	NOUN
ejpam-7064	45	8	polynomials	polynomial	NOUN
ejpam-7064	45	9	tk(y	tk(y	NOUN
ejpam-7064	45	10	)	)	PUNCT
ejpam-7064	45	11	of	of	ADP
ejpam-7064	45	12	order	order	NOUN
ejpam-7064	45	13	k	k	X
ejpam-7064	45	14	are	be	AUX
ejpam-7064	45	15	generated	generate	VERB
ejpam-7064	45	16	from	from	ADP
ejpam-7064	45	17	the	the	DET
ejpam-7064	45	18	following	follow	VERB
ejpam-7064	45	19	formula	formula	NOUN
ejpam-7064	45	20	:	:	PUNCT
ejpam-7064	45	21	tk(y	tk(y	X
ejpam-7064	45	22	)	)	PUNCT
ejpam-7064	46	1	=	=	SYM
ejpam-7064	46	2	cos	cos	PROPN
ejpam-7064	46	3	(	(	PUNCT
ejpam-7064	46	4	k	k	PROPN
ejpam-7064	46	5	arccos(y	arccos(y	NOUN
ejpam-7064	46	6	)	)	PUNCT
ejpam-7064	46	7	)	)	PUNCT
ejpam-7064	46	8	,	,	PUNCT
ejpam-7064	46	9	k	k	PROPN
ejpam-7064	46	10	∈	∈	PROPN
ejpam-7064	46	11	n.	n.	NOUN
ejpam-7064	46	12	(	(	PUNCT
ejpam-7064	46	13	4	4	NUM
ejpam-7064	46	14	)	)	PUNCT
ejpam-7064	46	15	the	the	DET
ejpam-7064	46	16	chebyshev	chebyshev	NOUN
ejpam-7064	46	17	-	-	PUNCT
ejpam-7064	46	18	lagrange	lagrange	NOUN
ejpam-7064	46	19	interpolation	interpolation	NOUN
ejpam-7064	46	20	of	of	ADP
ejpam-7064	46	21	the	the	DET
ejpam-7064	46	22	function	function	NOUN
ejpam-7064	46	23	ψ(y	ψ(y	NOUN
ejpam-7064	46	24	)	)	PUNCT
ejpam-7064	46	25	at	at	ADP
ejpam-7064	46	26	y	y	PROPN
ejpam-7064	46	27	=	=	SYM
ejpam-7064	46	28	yi	yi	PROPN
ejpam-7064	46	29	,	,	PUNCT
ejpam-7064	46	30	i	i	NOUN
ejpam-7064	46	31	=	=	NOUN
ejpam-7064	46	32	0	0	NUM
ejpam-7064	46	33	,	,	PUNCT
ejpam-7064	46	34	1	1	NUM
ejpam-7064	46	35	,	,	PUNCT
ejpam-7064	46	36	...	...	PUNCT
ejpam-7064	46	37	,	,	PUNCT
ejpam-7064	46	38	m	m	VERB
ejpam-7064	46	39	is	be	AUX
ejpam-7064	46	40	denoted	denote	VERB
ejpam-7064	46	41	by	by	ADP
ejpam-7064	46	42	ψm(y	ψm(y	NOUN
ejpam-7064	46	43	)	)	PUNCT
ejpam-7064	46	44	and	and	CCONJ
ejpam-7064	46	45	defined	define	VERB
ejpam-7064	46	46	as	as	SCONJ
ejpam-7064	46	47	follows	follow	VERB
ejpam-7064	46	48	:	:	PUNCT
ejpam-7064	46	49	ψm(y	ψm(y	X
ejpam-7064	46	50	)	)	PUNCT
ejpam-7064	46	51	=	=	PUNCT
ejpam-7064	46	52	m∑	m∑	CCONJ
ejpam-7064	46	53	i=0	i=0	ADJ
ejpam-7064	46	54	ψili(y	ψili(y	PROPN
ejpam-7064	46	55	)	)	PUNCT
ejpam-7064	46	56	,	,	PUNCT
ejpam-7064	46	57	(	(	PUNCT
ejpam-7064	46	58	5	5	X
ejpam-7064	46	59	)	)	PUNCT
ejpam-7064	46	60	where	where	SCONJ
ejpam-7064	46	61	li(y	li(y	NOUN
ejpam-7064	46	62	)	)	PUNCT
ejpam-7064	46	63	,	,	PUNCT
ejpam-7064	46	64	i	i	PRON
ejpam-7064	46	65	=	=	NOUN
ejpam-7064	46	66	0	0	NUM
ejpam-7064	46	67	,	,	PUNCT
ejpam-7064	46	68	1	1	NUM
ejpam-7064	46	69	,	,	PUNCT
ejpam-7064	46	70	...	...	PUNCT
ejpam-7064	46	71	,	,	PUNCT
ejpam-7064	46	72	m	m	PROPN
ejpam-7064	46	73	are	be	AUX
ejpam-7064	46	74	the	the	DET
ejpam-7064	46	75	lagrange	lagrange	NOUN
ejpam-7064	46	76	’s	’s	PART
ejpam-7064	46	77	polynomials	polynomial	NOUN
ejpam-7064	46	78	of	of	ADP
ejpam-7064	46	79	degree	degree	NOUN
ejpam-7064	46	80	i.	i.	NOUN
ejpam-7064	46	81	the	the	DET
ejpam-7064	46	82	extreme	extreme	ADJ
ejpam-7064	46	83	yi	yi	PROPN
ejpam-7064	46	84	of	of	ADP
ejpam-7064	46	85	tm(y	tm(y	PROPN
ejpam-7064	46	86	)	)	PUNCT
ejpam-7064	46	87	,	,	PUNCT
ejpam-7064	46	88	which	which	PRON
ejpam-7064	46	89	are	be	AUX
ejpam-7064	46	90	the	the	DET
ejpam-7064	46	91	chebyshev	chebyshev	PROPN
ejpam-7064	46	92	-	-	PUNCT
ejpam-7064	46	93	gauss	gaus	VERB
ejpam-7064	46	94	-	-	PUNCT
ejpam-7064	46	95	lobatto	lobatto	NOUN
ejpam-7064	46	96	points	point	NOUN
ejpam-7064	46	97	(	(	PUNCT
ejpam-7064	46	98	cglps	cglp	NOUN
ejpam-7064	46	99	)	)	PUNCT
ejpam-7064	46	100	,	,	PUNCT
ejpam-7064	46	101	are	be	AUX
ejpam-7064	46	102	chosen	choose	VERB
ejpam-7064	46	103	to	to	PART
ejpam-7064	46	104	be	be	AUX
ejpam-7064	46	105	the	the	DET
ejpam-7064	46	106	collocation	collocation	NOUN
ejpam-7064	46	107	points	point	NOUN
ejpam-7064	46	108	,	,	PUNCT
ejpam-7064	46	109	and	and	CCONJ
ejpam-7064	46	110	defined	define	VERB
ejpam-7064	46	111	by	by	ADP
ejpam-7064	46	112	:	:	PUNCT
ejpam-7064	46	113	{	{	PUNCT
ejpam-7064	46	114	yi}mi=0	yi}mi=0	PROPN
ejpam-7064	46	115	=	=	SYM
ejpam-7064	46	116	{	{	PUNCT
ejpam-7064	46	117	cos	cos	X
ejpam-7064	46	118	(	(	PUNCT
ejpam-7064	46	119	πi	πi	ADV
ejpam-7064	46	120	m	m	PROPN
ejpam-7064	46	121	)	)	PUNCT
ejpam-7064	46	122	}	}	PUNCT
ejpam-7064	46	123	m	m	VERB
ejpam-7064	46	124	i=0	i=0	ADJ
ejpam-7064	46	125	.	.	PUNCT
ejpam-7064	47	1	(	(	PUNCT
ejpam-7064	47	2	6	6	X
ejpam-7064	47	3	)	)	PUNCT
ejpam-7064	47	4	remark	remark	NOUN
ejpam-7064	47	5	1	1	NUM
ejpam-7064	47	6	.	.	PUNCT
ejpam-7064	48	1	this	this	DET
ejpam-7064	48	2	previous	previous	ADJ
ejpam-7064	48	3	choice	choice	NOUN
ejpam-7064	48	4	was	be	AUX
ejpam-7064	48	5	made	make	VERB
ejpam-7064	48	6	based	base	VERB
ejpam-7064	48	7	on	on	ADP
ejpam-7064	48	8	our	our	PRON
ejpam-7064	48	9	knowledge	knowledge	NOUN
ejpam-7064	48	10	that	that	SCONJ
ejpam-7064	48	11	the	the	DET
ejpam-7064	48	12	error	error	NOUN
ejpam-7064	48	13	in	in	ADP
ejpam-7064	48	14	lagrange	lagrange	NOUN
ejpam-7064	48	15	interpolation	interpolation	NOUN
ejpam-7064	48	16	is	be	AUX
ejpam-7064	48	17	minimized	minimize	VERB
ejpam-7064	48	18	if	if	SCONJ
ejpam-7064	48	19	the	the	DET
ejpam-7064	48	20	interpolation	interpolation	NOUN
ejpam-7064	48	21	points	point	NOUN
ejpam-7064	48	22	are	be	AUX
ejpam-7064	48	23	zeros	zero	NOUN
ejpam-7064	48	24	of	of	ADP
ejpam-7064	48	25	the	the	DET
ejpam-7064	48	26	polynomials	polynomial	NOUN
ejpam-7064	48	27	.	.	PUNCT
ejpam-7064	49	1	m.	m.	PROPN
ejpam-7064	49	2	adel	adel	PROPN
ejpam-7064	49	3	et	et	PROPN
ejpam-7064	49	4	al	al	PROPN
ejpam-7064	49	5	.	.	PUNCT
ejpam-7064	49	6	/	/	SYM
ejpam-7064	49	7	eur	eur	PROPN
ejpam-7064	49	8	.	.	PUNCT
ejpam-7064	50	1	j.	j.	PROPN
ejpam-7064	50	2	pure	pure	PROPN
ejpam-7064	50	3	appl	appl	PROPN
ejpam-7064	50	4	.	.	PROPN
ejpam-7064	50	5	math	math	PROPN
ejpam-7064	50	6	,	,	PUNCT
ejpam-7064	50	7	18	18	NUM
ejpam-7064	50	8	(	(	PUNCT
ejpam-7064	50	9	4	4	NUM
ejpam-7064	50	10	)	)	PUNCT
ejpam-7064	50	11	(	(	PUNCT
ejpam-7064	50	12	2025	2025	NUM
ejpam-7064	50	13	)	)	PUNCT
ejpam-7064	50	14	,	,	PUNCT
ejpam-7064	50	15	7064	7064	NUM
ejpam-7064	50	16	4	4	NUM
ejpam-7064	50	17	of	of	ADP
ejpam-7064	50	18	11	11	NUM
ejpam-7064	50	19	3	3	NUM
ejpam-7064	50	20	.	.	PUNCT
ejpam-7064	50	21	numerical	numerical	ADJ
ejpam-7064	50	22	implementation	implementation	NOUN
ejpam-7064	50	23	of	of	ADP
ejpam-7064	50	24	the	the	DET
ejpam-7064	50	25	msrm	msrm	PROPN
ejpam-7064	50	26	the	the	DET
ejpam-7064	50	27	suggested	suggest	VERB
ejpam-7064	50	28	approach	approach	NOUN
ejpam-7064	50	29	will	will	AUX
ejpam-7064	50	30	be	be	AUX
ejpam-7064	50	31	used	use	VERB
ejpam-7064	50	32	to	to	PART
ejpam-7064	50	33	obtain	obtain	VERB
ejpam-7064	50	34	the	the	DET
ejpam-7064	50	35	numerical	numerical	ADJ
ejpam-7064	50	36	solutions	solution	NOUN
ejpam-7064	50	37	of	of	ADP
ejpam-7064	50	38	the	the	DET
ejpam-7064	50	39	investigated	investigated	ADJ
ejpam-7064	50	40	model	model	NOUN
ejpam-7064	50	41	with	with	ADP
ejpam-7064	50	42	the	the	DET
ejpam-7064	50	43	help	help	NOUN
ejpam-7064	50	44	of	of	ADP
ejpam-7064	50	45	the	the	DET
ejpam-7064	50	46	following	follow	VERB
ejpam-7064	50	47	steps	step	NOUN
ejpam-7064	50	48	(	(	PUNCT
ejpam-7064	50	49	algorithm	algorithm	NOUN
ejpam-7064	50	50	):	):	PUNCT
ejpam-7064	50	51	(	(	PUNCT
ejpam-7064	50	52	i	i	NOUN
ejpam-7064	50	53	)	)	PUNCT
ejpam-7064	50	54	without	without	ADP
ejpam-7064	50	55	losing	lose	VERB
ejpam-7064	50	56	the	the	DET
ejpam-7064	50	57	system	system	NOUN
ejpam-7064	50	58	’s	’s	PART
ejpam-7064	50	59	generality	generality	NOUN
ejpam-7064	51	1	,	,	PUNCT
ejpam-7064	51	2	we	we	PRON
ejpam-7064	51	3	describe	describe	VERB
ejpam-7064	51	4	the	the	DET
ejpam-7064	51	5	system	system	NOUN
ejpam-7064	51	6	(	(	PUNCT
ejpam-7064	51	7	1)-(2	1)-(2	NUM
ejpam-7064	51	8	)	)	PUNCT
ejpam-7064	51	9	as	as	SCONJ
ejpam-7064	51	10	follows	follow	VERB
ejpam-7064	51	11	[	[	X
ejpam-7064	51	12	23	23	NUM
ejpam-7064	51	13	]	]	X
ejpam-7064	51	14	:	:	PUNCT
ejpam-7064	51	15	ξ̇	ξ̇	NOUN
ejpam-7064	51	16	+	+	X
ejpam-7064	51	17	c	c	X
ejpam-7064	51	18	ξ	ξ	X
ejpam-7064	51	19	+	+	NOUN
ejpam-7064	51	20	n(ξ	n(ξ	NOUN
ejpam-7064	51	21	)	)	PUNCT
ejpam-7064	51	22	=	=	SYM
ejpam-7064	51	23	0	0	NUM
ejpam-7064	51	24	,	,	PUNCT
ejpam-7064	51	25	(	(	PUNCT
ejpam-7064	51	26	7	7	X
ejpam-7064	51	27	)	)	PUNCT
ejpam-7064	51	28	where	where	SCONJ
ejpam-7064	51	29	ξ(t	ξ(t	NOUN
ejpam-7064	51	30	)	)	PUNCT
ejpam-7064	51	31	=	=	PUNCT
ejpam-7064	52	1	[	[	X
ejpam-7064	52	2	θ1(t	θ1(t	PROPN
ejpam-7064	52	3	)	)	PUNCT
ejpam-7064	52	4	,	,	PUNCT
ejpam-7064	52	5	θ2(t	θ2(t	PROPN
ejpam-7064	52	6	)	)	PUNCT
ejpam-7064	52	7	]	]	PUNCT
ejpam-7064	53	1	t	t	NOUN
ejpam-7064	53	2	;	;	PUNCT
ejpam-7064	53	3	c	c	X
ejpam-7064	53	4	is	be	AUX
ejpam-7064	53	5	an	an	DET
ejpam-7064	53	6	2	2	NUM
ejpam-7064	53	7	×	×	NOUN
ejpam-7064	53	8	2	2	NUM
ejpam-7064	53	9	matrix	matrix	NOUN
ejpam-7064	53	10	with	with	ADP
ejpam-7064	53	11	entries	entry	NOUN
ejpam-7064	53	12	ci	ci	PROPN
ejpam-7064	53	13	,	,	PUNCT
ejpam-7064	53	14	j	j	PROPN
ejpam-7064	53	15	,	,	PUNCT
ejpam-7064	53	16	i	i	PROPN
ejpam-7064	53	17	,	,	PUNCT
ejpam-7064	53	18	j	j	PROPN
ejpam-7064	53	19	=	=	SYM
ejpam-7064	53	20	1	1	NUM
ejpam-7064	53	21	,	,	PUNCT
ejpam-7064	53	22	2	2	NUM
ejpam-7064	53	23	and	and	CCONJ
ejpam-7064	53	24	is	be	AUX
ejpam-7064	53	25	defined	define	VERB
ejpam-7064	53	26	by	by	ADP
ejpam-7064	53	27	:	:	PUNCT
ejpam-7064	53	28	c	c	X
ejpam-7064	53	29	=	=	SYM
ejpam-7064	53	30	(	(	PUNCT
ejpam-7064	53	31	1	1	NUM
ejpam-7064	53	32	+	+	CCONJ
ejpam-7064	53	33	γ	γ	X
ejpam-7064	53	34	0	0	NUM
ejpam-7064	53	35	−γ	−γ	NOUN
ejpam-7064	53	36	0	0	NUM
ejpam-7064	53	37	)	)	PUNCT
ejpam-7064	53	38	,	,	PUNCT
ejpam-7064	53	39	here	here	ADV
ejpam-7064	53	40	the	the	DET
ejpam-7064	53	41	elements	element	NOUN
ejpam-7064	53	42	c1,2	c1,2	ADJ
ejpam-7064	53	43	and	and	CCONJ
ejpam-7064	53	44	c2,2	c2,2	NOUN
ejpam-7064	53	45	are	be	AUX
ejpam-7064	53	46	equal	equal	ADJ
ejpam-7064	53	47	zero	zero	NUM
ejpam-7064	53	48	,	,	PUNCT
ejpam-7064	53	49	because	because	SCONJ
ejpam-7064	53	50	the	the	DET
ejpam-7064	53	51	equations	equation	NOUN
ejpam-7064	53	52	(	(	PUNCT
ejpam-7064	53	53	1)-(2	1)-(2	NUM
ejpam-7064	53	54	)	)	PUNCT
ejpam-7064	53	55	do	do	AUX
ejpam-7064	53	56	not	not	PART
ejpam-7064	53	57	contain	contain	VERB
ejpam-7064	53	58	on	on	ADP
ejpam-7064	53	59	linear	linear	ADJ
ejpam-7064	53	60	terms	term	NOUN
ejpam-7064	53	61	of	of	ADP
ejpam-7064	53	62	θ2(t	θ2(t	PROPN
ejpam-7064	53	63	)	)	PUNCT
ejpam-7064	53	64	.	.	PUNCT
ejpam-7064	54	1	also	also	ADV
ejpam-7064	54	2	n(ξ	n(ξ	NOUN
ejpam-7064	54	3	)	)	PUNCT
ejpam-7064	54	4	is	be	AUX
ejpam-7064	54	5	a	a	DET
ejpam-7064	54	6	vector	vector	NOUN
ejpam-7064	54	7	of	of	ADP
ejpam-7064	54	8	nonlinear	nonlinear	ADJ
ejpam-7064	54	9	terms	term	NOUN
ejpam-7064	54	10	of	of	ADP
ejpam-7064	54	11	eq.(7	eq.(7	NOUN
ejpam-7064	54	12	)	)	PUNCT
ejpam-7064	54	13	and	and	CCONJ
ejpam-7064	54	14	is	be	AUX
ejpam-7064	54	15	defined	define	VERB
ejpam-7064	54	16	by	by	ADP
ejpam-7064	54	17	:	:	PUNCT
ejpam-7064	54	18	n(ξ	n(ξ	NUM
ejpam-7064	54	19	)	)	PUNCT
ejpam-7064	55	1	=	=	NOUN
ejpam-7064	55	2	(	(	PUNCT
ejpam-7064	55	3	−δ	−δ	ADJ
ejpam-7064	55	4	−	−	PROPN
ejpam-7064	55	5	(	(	PUNCT
ejpam-7064	55	6	θ1(t	θ1(t	PROPN
ejpam-7064	55	7	)	)	PUNCT
ejpam-7064	55	8	)	)	PUNCT
ejpam-7064	55	9	2	2	NUM
ejpam-7064	55	10	θ2(t	θ2(t	PROPN
ejpam-7064	55	11	)	)	PUNCT
ejpam-7064	55	12	(	(	PUNCT
ejpam-7064	55	13	θ1(t	θ1(t	PROPN
ejpam-7064	55	14	)	)	PUNCT
ejpam-7064	55	15	)	)	PUNCT
ejpam-7064	55	16	2	2	NUM
ejpam-7064	55	17	θ2(t	θ2(t	NOUN
ejpam-7064	55	18	)	)	PUNCT
ejpam-7064	55	19	)	)	PUNCT
ejpam-7064	55	20	.	.	PUNCT
ejpam-7064	56	1	(	(	PUNCT
ejpam-7064	56	2	ii	ii	X
ejpam-7064	56	3	)	)	PUNCT
ejpam-7064	56	4	we	we	PRON
ejpam-7064	56	5	define	define	VERB
ejpam-7064	56	6	the	the	DET
ejpam-7064	56	7	following	follow	VERB
ejpam-7064	56	8	set	set	NOUN
ejpam-7064	56	9	of	of	ADP
ejpam-7064	56	10	lagrange	lagrange	NOUN
ejpam-7064	56	11	polynomials	polynomial	NOUN
ejpam-7064	56	12	{	{	PUNCT
ejpam-7064	56	13	li(y)}mi=0	li(y)}mi=0	NOUN
ejpam-7064	56	14	of	of	ADP
ejpam-7064	56	15	order	order	NOUN
ejpam-7064	56	16	i	i	PRON
ejpam-7064	56	17	,	,	PUNCT
ejpam-7064	56	18	which	which	PRON
ejpam-7064	56	19	are	be	AUX
ejpam-7064	56	20	based	base	VERB
ejpam-7064	56	21	on	on	ADP
ejpam-7064	56	22	the	the	DET
ejpam-7064	56	23	cglps	cglp	NOUN
ejpam-7064	56	24	as	as	SCONJ
ejpam-7064	56	25	follows	follow	VERB
ejpam-7064	56	26	:	:	PUNCT
ejpam-7064	56	27	li(y	li(y	X
ejpam-7064	56	28	)	)	PUNCT
ejpam-7064	56	29	=	=	SYM
ejpam-7064	56	30	(	(	PUNCT
ejpam-7064	56	31	−1)i+1	−1)i+1	NOUN
ejpam-7064	56	32	(	(	PUNCT
ejpam-7064	56	33	1−	1−	NUM
ejpam-7064	56	34	y2	y2	PROPN
ejpam-7064	56	35	)	)	PUNCT
ejpam-7064	56	36	tm(y	tm(y	NUM
ejpam-7064	56	37	)	)	PUNCT
ejpam-7064	56	38	ℏim2	ℏim2	PROPN
ejpam-7064	56	39	(	(	PUNCT
ejpam-7064	56	40	y	y	PROPN
ejpam-7064	56	41	−	−	PROPN
ejpam-7064	56	42	yi	yi	PROPN
ejpam-7064	56	43	)	)	PUNCT
ejpam-7064	56	44	,	,	PUNCT
ejpam-7064	56	45	i	i	PRON
ejpam-7064	56	46	=	=	NOUN
ejpam-7064	56	47	0	0	NUM
ejpam-7064	56	48	,	,	PUNCT
ejpam-7064	56	49	1	1	NUM
ejpam-7064	56	50	,	,	PUNCT
ejpam-7064	56	51	.	.	PUNCT
ejpam-7064	56	52	.	.	PUNCT
ejpam-7064	56	53	.	.	PUNCT
ejpam-7064	57	1	,	,	PUNCT
ejpam-7064	57	2	m	m	PROPN
ejpam-7064	57	3	,	,	PUNCT
ejpam-7064	57	4	(	(	PUNCT
ejpam-7064	57	5	8)	8)	NUM
ejpam-7064	57	6	where	where	SCONJ
ejpam-7064	57	7	ℏ0	ℏ0	NOUN
ejpam-7064	57	8	=	=	SYM
ejpam-7064	57	9	ℏm	ℏm	PROPN
ejpam-7064	57	10	=	=	ADJ
ejpam-7064	57	11	2	2	NUM
ejpam-7064	57	12	,	,	PUNCT
ejpam-7064	57	13	ℏi	ℏi	NOUN
ejpam-7064	57	14	=	=	SYM
ejpam-7064	57	15	1	1	NUM
ejpam-7064	57	16	for	for	ADP
ejpam-7064	57	17	i	i	PRON
ejpam-7064	57	18	=	=	NOUN
ejpam-7064	57	19	1	1	NUM
ejpam-7064	57	20	,	,	PUNCT
ejpam-7064	57	21	2	2	NUM
ejpam-7064	57	22	,	,	PUNCT
ejpam-7064	57	23	.	.	PUNCT
ejpam-7064	57	24	.	.	PUNCT
ejpam-7064	58	1	.	.	PUNCT
ejpam-7064	59	1	,	,	PUNCT
ejpam-7064	59	2	m−	m−	PROPN
ejpam-7064	59	3	1	1	NUM
ejpam-7064	59	4	.	.	PUNCT
ejpam-7064	60	1	also	also	ADV
ejpam-7064	60	2	,	,	PUNCT
ejpam-7064	60	3	the	the	DET
ejpam-7064	60	4	chebyshev	chebyshev	NOUN
ejpam-7064	60	5	polynomial	polynomial	NOUN
ejpam-7064	60	6	tm(y	tm(y	PUNCT
ejpam-7064	60	7	)	)	PUNCT
ejpam-7064	60	8	,	,	PUNCT
ejpam-7064	60	9	and	and	CCONJ
ejpam-7064	60	10	the	the	DET
ejpam-7064	60	11	cglps	cglp	NOUN
ejpam-7064	60	12	yi	yi	NOUN
ejpam-7064	60	13	are	be	AUX
ejpam-7064	60	14	defined	define	VERB
ejpam-7064	60	15	in	in	ADP
ejpam-7064	60	16	(	(	PUNCT
ejpam-7064	60	17	5	5	NUM
ejpam-7064	60	18	)	)	PUNCT
ejpam-7064	60	19	and	and	CCONJ
ejpam-7064	60	20	(	(	PUNCT
ejpam-7064	60	21	6	6	NUM
ejpam-7064	60	22	)	)	PUNCT
ejpam-7064	60	23	,	,	PUNCT
ejpam-7064	60	24	respectively	respectively	ADV
ejpam-7064	60	25	.	.	PUNCT
ejpam-7064	61	1	(	(	PUNCT
ejpam-7064	61	2	iii	iii	X
ejpam-7064	61	3	)	)	PUNCT
ejpam-7064	61	4	we	we	PRON
ejpam-7064	61	5	use	use	VERB
ejpam-7064	61	6	the	the	DET
ejpam-7064	61	7	chebyshev	chebyshev	NOUN
ejpam-7064	61	8	-	-	PUNCT
ejpam-7064	61	9	lagrange	lagrange	NOUN
ejpam-7064	61	10	interpolation	interpolation	NOUN
ejpam-7064	61	11	of	of	ADP
ejpam-7064	61	12	the	the	DET
ejpam-7064	61	13	function	function	NOUN
ejpam-7064	61	14	v(y	v(y	NUM
ejpam-7064	61	15	)	)	PUNCT
ejpam-7064	61	16	at	at	ADP
ejpam-7064	61	17	y	y	PROPN
ejpam-7064	61	18	=	=	SYM
ejpam-7064	61	19	yi	yi	PROPN
ejpam-7064	61	20	,	,	PUNCT
ejpam-7064	61	21	i	i	NOUN
ejpam-7064	61	22	=	=	NOUN
ejpam-7064	61	23	0	0	NUM
ejpam-7064	61	24	,	,	PUNCT
ejpam-7064	61	25	1	1	NUM
ejpam-7064	61	26	,	,	PUNCT
ejpam-7064	61	27	...	...	PUNCT
ejpam-7064	61	28	,	,	PUNCT
ejpam-7064	61	29	m	m	PROPN
ejpam-7064	61	30	,	,	PUNCT
ejpam-7064	61	31	which	which	PRON
ejpam-7064	61	32	is	be	AUX
ejpam-7064	61	33	denoted	denote	VERB
ejpam-7064	61	34	by	by	ADP
ejpam-7064	61	35	vm(y	vm(y	NOUN
ejpam-7064	61	36	)	)	PUNCT
ejpam-7064	61	37	and	and	CCONJ
ejpam-7064	61	38	defined	define	VERB
ejpam-7064	61	39	as	as	SCONJ
ejpam-7064	61	40	follows	follow	VERB
ejpam-7064	61	41	:	:	PUNCT
ejpam-7064	61	42	vm(y	vm(y	X
ejpam-7064	61	43	)	)	PUNCT
ejpam-7064	61	44	=	=	PUNCT
ejpam-7064	61	45	m∑	m∑	CCONJ
ejpam-7064	61	46	i=0	i=0	PROPN
ejpam-7064	61	47	vili(y	vili(y	PROPN
ejpam-7064	61	48	)	)	PUNCT
ejpam-7064	61	49	,	,	PUNCT
ejpam-7064	61	50	(	(	PUNCT
ejpam-7064	61	51	9	9	X
ejpam-7064	61	52	)	)	PUNCT
ejpam-7064	61	53	where	where	SCONJ
ejpam-7064	61	54	the	the	DET
ejpam-7064	61	55	coefficients	coefficient	NOUN
ejpam-7064	61	56	vi	vi	NOUN
ejpam-7064	61	57	=	=	SYM
ejpam-7064	61	58	v(yi	v(yi	NUM
ejpam-7064	61	59	)	)	PUNCT
ejpam-7064	61	60	.	.	PUNCT
ejpam-7064	62	1	(	(	PUNCT
ejpam-7064	62	2	iv	iv	X
ejpam-7064	62	3	)	)	PUNCT
ejpam-7064	62	4	we	we	PRON
ejpam-7064	62	5	calculate	calculate	VERB
ejpam-7064	62	6	the	the	DET
ejpam-7064	62	7	first	first	ADJ
ejpam-7064	62	8	derivative	derivative	NOUN
ejpam-7064	62	9	of	of	ADP
ejpam-7064	62	10	the	the	DET
ejpam-7064	62	11	approximate	approximate	ADJ
ejpam-7064	62	12	solution	solution	NOUN
ejpam-7064	62	13	(	(	PUNCT
ejpam-7064	62	14	9	9	NUM
ejpam-7064	62	15	)	)	PUNCT
ejpam-7064	62	16	at	at	ADP
ejpam-7064	62	17	the	the	DET
ejpam-7064	62	18	collocation	collocation	NOUN
ejpam-7064	62	19	points	point	VERB
ejpam-7064	62	20	yi	yi	PROPN
ejpam-7064	62	21	as	as	SCONJ
ejpam-7064	62	22	follows	follow	VERB
ejpam-7064	62	23	:	:	PUNCT
ejpam-7064	63	1	dvm(y	dvm(y	NOUN
ejpam-7064	63	2	)	)	PUNCT
ejpam-7064	63	3	dy	dy	NOUN
ejpam-7064	63	4	=	=	SYM
ejpam-7064	63	5	m∑	m∑	PROPN
ejpam-7064	63	6	k=0	k=0	PROPN
ejpam-7064	63	7	v	v	PROPN
ejpam-7064	63	8	(	(	PUNCT
ejpam-7064	63	9	yk	yk	PROPN
ejpam-7064	63	10	)	)	PUNCT
ejpam-7064	63	11	dlk	dlk	PROPN
ejpam-7064	63	12	(	(	PUNCT
ejpam-7064	63	13	yi	yi	NOUN
ejpam-7064	63	14	)	)	PUNCT
ejpam-7064	63	15	dy	dy	NOUN
ejpam-7064	63	16	=	=	SYM
ejpam-7064	63	17	m∑	m∑	PROPN
ejpam-7064	63	18	k=0	k=0	PROPN
ejpam-7064	63	19	di	di	PROPN
ejpam-7064	63	20	k	k	PROPN
ejpam-7064	63	21	v	v	PROPN
ejpam-7064	63	22	(	(	PUNCT
ejpam-7064	63	23	yk	yk	PROPN
ejpam-7064	63	24	)	)	PUNCT
ejpam-7064	63	25	=	=	SYM
ejpam-7064	63	26	dvi	dvi	PROPN
ejpam-7064	63	27	,	,	PUNCT
ejpam-7064	63	28	i	i	NOUN
ejpam-7064	63	29	=	=	NOUN
ejpam-7064	63	30	0	0	NUM
ejpam-7064	63	31	,	,	PUNCT
ejpam-7064	63	32	1	1	NUM
ejpam-7064	63	33	,	,	PUNCT
ejpam-7064	63	34	.	.	PUNCT
ejpam-7064	63	35	.	.	PUNCT
ejpam-7064	63	36	.	.	PUNCT
ejpam-7064	64	1	,	,	PUNCT
ejpam-7064	64	2	m	m	PROPN
ejpam-7064	64	3	,	,	PUNCT
ejpam-7064	64	4	(	(	PUNCT
ejpam-7064	64	5	10	10	NUM
ejpam-7064	64	6	)	)	PUNCT
ejpam-7064	64	7	the	the	DET
ejpam-7064	64	8	elements	element	NOUN
ejpam-7064	64	9	of	of	ADP
ejpam-7064	64	10	the	the	DET
ejpam-7064	64	11	first	first	ADJ
ejpam-7064	64	12	-	-	PUNCT
ejpam-7064	64	13	order	order	NOUN
ejpam-7064	64	14	chebyshev	chebyshev	NOUN
ejpam-7064	64	15	differentiation	differentiation	NOUN
ejpam-7064	64	16	matrix	matrix	NOUN
ejpam-7064	64	17	dik	dik	NOUN
ejpam-7064	64	18	can	can	AUX
ejpam-7064	64	19	be	be	AUX
ejpam-7064	64	20	evaluated	evaluate	VERB
ejpam-7064	64	21	for	for	ADP
ejpam-7064	64	22	i	i	PRON
ejpam-7064	64	23	,	,	PUNCT
ejpam-7064	64	24	k	k	PROPN
ejpam-7064	64	25	=	=	SYM
ejpam-7064	64	26	0	0	NUM
ejpam-7064	64	27	,	,	PUNCT
ejpam-7064	64	28	1	1	NUM
ejpam-7064	64	29	,	,	PUNCT
ejpam-7064	64	30	.	.	PUNCT
ejpam-7064	64	31	.	.	PUNCT
ejpam-7064	65	1	.	.	PUNCT
ejpam-7064	66	1	,	,	PUNCT
ejpam-7064	66	2	m	m	VERB
ejpam-7064	66	3	at	at	ADP
ejpam-7064	66	4	the	the	DET
ejpam-7064	66	5	collocation	collocation	NOUN
ejpam-7064	66	6	points	point	VERB
ejpam-7064	66	7	yi	yi	PROPN
ejpam-7064	66	8	(	(	PUNCT
ejpam-7064	66	9	6	6	NUM
ejpam-7064	66	10	)	)	PUNCT
ejpam-7064	66	11	as	as	SCONJ
ejpam-7064	66	12	follows	follow	VERB
ejpam-7064	66	13	[	[	X
ejpam-7064	66	14	24	24	NUM
ejpam-7064	66	15	]	]	X
ejpam-7064	66	16	:	:	PUNCT
ejpam-7064	66	17	dik	dik	X
ejpam-7064	66	18	=	=	SYM
ejpam-7064	66	19	dlk	dlk	X
ejpam-7064	66	20	(	(	PUNCT
ejpam-7064	66	21	yi	yi	NOUN
ejpam-7064	66	22	)	)	PUNCT
ejpam-7064	66	23	dy	dy	NOUN
ejpam-7064	66	24	=	=	SYM
ejpam-7064	66	25			NUM
ejpam-7064	66	26	ℏi(−1)k+i	ℏi(−1)k+i	PROPN
ejpam-7064	66	27	ℏk(yk−yi	ℏk(yk−yi	NOUN
ejpam-7064	66	28	)	)	PUNCT
ejpam-7064	66	29	,	,	PUNCT
ejpam-7064	67	1	i	i	PRON
ejpam-7064	67	2	̸=	̸=	PROPN
ejpam-7064	67	3	k	k	NOUN
ejpam-7064	67	4	,	,	PUNCT
ejpam-7064	67	5	−	−	PROPN
ejpam-7064	67	6	yi	yi	PROPN
ejpam-7064	67	7	(	(	PUNCT
ejpam-7064	67	8	1−y2i	1−y2i	NUM
ejpam-7064	67	9	)	)	PUNCT
ejpam-7064	67	10	,	,	PUNCT
ejpam-7064	67	11	(	(	PUNCT
ejpam-7064	67	12	i	i	PRON
ejpam-7064	67	13	=	=	SYM
ejpam-7064	67	14	k	k	X
ejpam-7064	67	15	)	)	PUNCT
ejpam-7064	67	16	̸=	̸=	PROPN
ejpam-7064	67	17	0,m	0,m	NUM
ejpam-7064	67	18	,	,	PUNCT
ejpam-7064	67	19	2m2	2m2	NUM
ejpam-7064	67	20	+	+	SYM
ejpam-7064	67	21	1	1	NUM
ejpam-7064	67	22	6	6	NUM
ejpam-7064	67	23	,	,	PUNCT
ejpam-7064	67	24	i	i	PRON
ejpam-7064	67	25	,	,	PUNCT
ejpam-7064	67	26	k	k	PROPN
ejpam-7064	67	27	=	=	SYM
ejpam-7064	67	28	0	0	NUM
ejpam-7064	67	29	,	,	PUNCT
ejpam-7064	67	30	−2m2	−2m2	PUNCT
ejpam-7064	67	31	+	+	NOUN
ejpam-7064	67	32	1	1	NUM
ejpam-7064	67	33	6	6	NUM
ejpam-7064	67	34	,	,	PUNCT
ejpam-7064	67	35	i	i	PRON
ejpam-7064	67	36	,	,	PUNCT
ejpam-7064	67	37	k	k	PROPN
ejpam-7064	67	38	=	=	PUNCT
ejpam-7064	67	39	m.	m.	NOUN
ejpam-7064	67	40	(	(	PUNCT
ejpam-7064	67	41	11	11	NUM
ejpam-7064	67	42	)	)	PUNCT
ejpam-7064	67	43	m.	m.	NOUN
ejpam-7064	67	44	adel	adel	PROPN
ejpam-7064	67	45	et	et	PROPN
ejpam-7064	67	46	al	al	PROPN
ejpam-7064	67	47	.	.	PUNCT
ejpam-7064	67	48	/	/	SYM
ejpam-7064	67	49	eur	eur	PROPN
ejpam-7064	67	50	.	.	PUNCT
ejpam-7064	68	1	j.	j.	PROPN
ejpam-7064	68	2	pure	pure	PROPN
ejpam-7064	68	3	appl	appl	PROPN
ejpam-7064	68	4	.	.	PROPN
ejpam-7064	68	5	math	math	PROPN
ejpam-7064	68	6	,	,	PUNCT
ejpam-7064	68	7	18	18	NUM
ejpam-7064	68	8	(	(	PUNCT
ejpam-7064	68	9	4	4	NUM
ejpam-7064	68	10	)	)	PUNCT
ejpam-7064	68	11	(	(	PUNCT
ejpam-7064	68	12	2025	2025	NUM
ejpam-7064	68	13	)	)	PUNCT
ejpam-7064	68	14	,	,	PUNCT
ejpam-7064	68	15	7064	7064	NUM
ejpam-7064	68	16	5	5	NUM
ejpam-7064	68	17	of	of	ADP
ejpam-7064	68	18	11	11	NUM
ejpam-7064	68	19	(	(	PUNCT
ejpam-7064	68	20	v	v	NOUN
ejpam-7064	68	21	)	)	PUNCT
ejpam-7064	69	1	we	we	PRON
ejpam-7064	69	2	divide	divide	VERB
ejpam-7064	69	3	the	the	DET
ejpam-7064	69	4	interval	interval	NOUN
ejpam-7064	69	5	i	i	PRON
ejpam-7064	69	6	=	=	PUNCT
ejpam-7064	70	1	[	[	X
ejpam-7064	70	2	0	0	NUM
ejpam-7064	70	3	,	,	PUNCT
ejpam-7064	70	4	t	t	NOUN
ejpam-7064	70	5	]	]	PUNCT
ejpam-7064	70	6	into	into	ADP
ejpam-7064	70	7	n	n	ADP
ejpam-7064	70	8	subdomains	subdomain	NOUN
ejpam-7064	70	9	with	with	ADP
ejpam-7064	70	10	a	a	DET
ejpam-7064	70	11	uniform	uniform	ADJ
ejpam-7064	70	12	length	length	NOUN
ejpam-7064	70	13	t	t	PROPN
ejpam-7064	70	14	n	n	NOUN
ejpam-7064	70	15	=	=	SYM
ejpam-7064	70	16	tj	tj	PROPN
ejpam-7064	70	17	−	−	PROPN
ejpam-7064	70	18	tj−1	tj−1	NOUN
ejpam-7064	70	19	,	,	PUNCT
ejpam-7064	70	20	where	where	SCONJ
ejpam-7064	70	21	ij	ij	NOUN
ejpam-7064	71	1	=	=	PUNCT
ejpam-7064	72	1	[	[	X
ejpam-7064	72	2	tj−1	tj−1	PROPN
ejpam-7064	72	3	,	,	PUNCT
ejpam-7064	72	4	tj	tj	NOUN
ejpam-7064	72	5	]	]	PUNCT
ejpam-7064	72	6	has	have	VERB
ejpam-7064	72	7	the	the	DET
ejpam-7064	72	8	characteristic	characteristic	ADJ
ejpam-7064	72	9	that	that	SCONJ
ejpam-7064	72	10	:	:	PUNCT
ejpam-7064	72	11	n⋃	n⋃	X
ejpam-7064	72	12	j=1	j=1	PROPN
ejpam-7064	73	1	[	[	X
ejpam-7064	73	2	tj−1	tj−1	PROPN
ejpam-7064	73	3	,	,	PUNCT
ejpam-7064	73	4	tj	tj	X
ejpam-7064	73	5	]	]	PUNCT
ejpam-7064	73	6	=	=	PUNCT
ejpam-7064	74	1	[	[	X
ejpam-7064	74	2	0	0	NUM
ejpam-7064	74	3	,	,	PUNCT
ejpam-7064	74	4	t	t	X
ejpam-7064	74	5	]	]	PUNCT
ejpam-7064	74	6	.	.	PUNCT
ejpam-7064	75	1	(	(	PUNCT
ejpam-7064	75	2	12	12	NUM
ejpam-7064	75	3	)	)	PUNCT
ejpam-7064	75	4	now	now	ADV
ejpam-7064	75	5	,	,	PUNCT
ejpam-7064	75	6	by	by	ADP
ejpam-7064	75	7	using	use	VERB
ejpam-7064	75	8	the	the	DET
ejpam-7064	75	9	following	following	ADJ
ejpam-7064	75	10	linear	linear	ADJ
ejpam-7064	75	11	transformation	transformation	NOUN
ejpam-7064	75	12	,	,	PUNCT
ejpam-7064	75	13	we	we	PRON
ejpam-7064	75	14	can	can	AUX
ejpam-7064	75	15	convert	convert	VERB
ejpam-7064	75	16	each	each	DET
ejpam-7064	75	17	subdomain	subdomain	NOUN
ejpam-7064	75	18	of	of	ADP
ejpam-7064	75	19	the	the	DET
ejpam-7064	75	20	form	form	NOUN
ejpam-7064	75	21	[	[	X
ejpam-7064	75	22	tj−1	tj−1	NOUN
ejpam-7064	75	23	,	,	PUNCT
ejpam-7064	75	24	tj	tj	NOUN
ejpam-7064	75	25	]	]	PUNCT
ejpam-7064	75	26	to	to	ADP
ejpam-7064	75	27	the	the	DET
ejpam-7064	75	28	domain	domain	NOUN
ejpam-7064	75	29	of	of	ADP
ejpam-7064	75	30	the	the	DET
ejpam-7064	75	31	cglps	cglp	NOUN
ejpam-7064	75	32	[	[	X
ejpam-7064	75	33	−1	−1	NOUN
ejpam-7064	75	34	,	,	PUNCT
ejpam-7064	75	35	1	1	NUM
ejpam-7064	75	36	]	]	PUNCT
ejpam-7064	75	37	,	,	PUNCT
ejpam-7064	75	38	which	which	PRON
ejpam-7064	75	39	is	be	AUX
ejpam-7064	75	40	specified	specify	VERB
ejpam-7064	75	41	in	in	ADP
ejpam-7064	75	42	eq.(6	eq.(6	ADJ
ejpam-7064	75	43	):	):	PUNCT
ejpam-7064	75	44	t̂	t̂	X
ejpam-7064	76	1	=	=	SYM
ejpam-7064	76	2	0.5(tj	0.5(tj	NUM
ejpam-7064	77	1	−	−	NOUN
ejpam-7064	77	2	tj−1)y	tj−1)y	PUNCT
ejpam-7064	78	1	+	+	CCONJ
ejpam-7064	78	2	0.5(tj−1	0.5(tj−1	NOUN
ejpam-7064	78	3	+	+	CCONJ
ejpam-7064	78	4	tj	tj	NOUN
ejpam-7064	78	5	)	)	PUNCT
ejpam-7064	78	6	=	=	SYM
ejpam-7064	78	7	0.5(t	0.5(t	PROPN
ejpam-7064	78	8	/	/	SYM
ejpam-7064	78	9	n	n	CCONJ
ejpam-7064	78	10	)	)	PUNCT
ejpam-7064	78	11	y	y	PROPN
ejpam-7064	79	1	+	+	NUM
ejpam-7064	79	2	0.5(tj−1	0.5(tj−1	NOUN
ejpam-7064	79	3	+	+	CCONJ
ejpam-7064	79	4	tj	tj	NOUN
ejpam-7064	79	5	)	)	PUNCT
ejpam-7064	79	6	,	,	PUNCT
ejpam-7064	79	7	j	j	PROPN
ejpam-7064	79	8	=	=	SYM
ejpam-7064	79	9	1	1	NUM
ejpam-7064	79	10	,	,	PUNCT
ejpam-7064	79	11	2	2	NUM
ejpam-7064	79	12	,	,	PUNCT
ejpam-7064	79	13	.	.	PUNCT
ejpam-7064	79	14	.	.	PUNCT
ejpam-7064	79	15	.	.	PUNCT
ejpam-7064	80	1	,	,	PUNCT
ejpam-7064	80	2	n.	n.	PROPN
ejpam-7064	80	3	(	(	PUNCT
ejpam-7064	80	4	vi	vi	NOUN
ejpam-7064	80	5	)	)	PUNCT
ejpam-7064	80	6	we	we	PRON
ejpam-7064	80	7	estimate	estimate	VERB
ejpam-7064	80	8	the	the	DET
ejpam-7064	80	9	derivatives	derivative	NOUN
ejpam-7064	80	10	of	of	ADP
ejpam-7064	80	11	the	the	DET
ejpam-7064	80	12	first	first	ADJ
ejpam-7064	80	13	term	term	NOUN
ejpam-7064	80	14	in	in	ADP
ejpam-7064	80	15	the	the	DET
ejpam-7064	80	16	system	system	NOUN
ejpam-7064	80	17	of	of	ADP
ejpam-7064	80	18	odes	ode	NOUN
ejpam-7064	80	19	(	(	PUNCT
ejpam-7064	80	20	7	7	NUM
ejpam-7064	80	21	)	)	PUNCT
ejpam-7064	80	22	with	with	ADP
ejpam-7064	80	23	the	the	DET
ejpam-7064	80	24	help	help	NOUN
ejpam-7064	80	25	of	of	ADP
ejpam-7064	80	26	the	the	DET
ejpam-7064	80	27	chebyshev	chebyshev	NOUN
ejpam-7064	80	28	differentiation	differentiation	NOUN
ejpam-7064	80	29	matrix	matrix	NOUN
ejpam-7064	80	30	,	,	PUNCT
ejpam-7064	80	31	to	to	PART
ejpam-7064	80	32	reduce	reduce	VERB
ejpam-7064	80	33	it	it	PRON
ejpam-7064	80	34	to	to	ADP
ejpam-7064	80	35	a	a	DET
ejpam-7064	80	36	system	system	NOUN
ejpam-7064	80	37	of	of	ADP
ejpam-7064	80	38	algebraic	algebraic	ADJ
ejpam-7064	80	39	equations	equation	NOUN
ejpam-7064	80	40	.	.	PUNCT
ejpam-7064	81	1	we	we	PRON
ejpam-7064	81	2	use	use	VERB
ejpam-7064	81	3	θj	θj	NOUN
ejpam-7064	81	4	s	s	PART
ejpam-7064	81	5	=	=	PUNCT
ejpam-7064	81	6	[	[	PUNCT
ejpam-7064	81	7	θs	θs	X
ejpam-7064	81	8	(	(	PUNCT
ejpam-7064	81	9	yj0	yj0	PROPN
ejpam-7064	81	10	)	)	PUNCT
ejpam-7064	81	11	,	,	PUNCT
ejpam-7064	81	12	θs	θs	PRON
ejpam-7064	81	13	(	(	PUNCT
ejpam-7064	81	14	yj1	yj1	NOUN
ejpam-7064	81	15	)	)	PUNCT
ejpam-7064	81	16	,	,	PUNCT
ejpam-7064	81	17	·	·	PUNCT
ejpam-7064	81	18	·	·	PUNCT
ejpam-7064	81	19	·	·	PUNCT
ejpam-7064	81	20	,	,	PUNCT
ejpam-7064	81	21	θs	θs	PRON
ejpam-7064	81	22	(	(	PUNCT
ejpam-7064	81	23	yjm	yjm	PROPN
ejpam-7064	81	24	)	)	PUNCT
ejpam-7064	81	25	]	]	PUNCT
ejpam-7064	81	26	t	t	NOUN
ejpam-7064	81	27	,	,	PUNCT
ejpam-7064	81	28	and	and	CCONJ
ejpam-7064	81	29	yjk	yjk	NOUN
ejpam-7064	81	30	,	,	PUNCT
ejpam-7064	81	31	k	k	PROPN
ejpam-7064	81	32	=	=	SYM
ejpam-7064	81	33	0	0	NUM
ejpam-7064	81	34	,	,	PUNCT
ejpam-7064	81	35	1	1	NUM
ejpam-7064	81	36	,	,	PUNCT
ejpam-7064	81	37	...	...	PUNCT
ejpam-7064	81	38	,	,	PUNCT
ejpam-7064	81	39	m	m	VERB
ejpam-7064	81	40	to	to	PART
ejpam-7064	81	41	represent	represent	VERB
ejpam-7064	81	42	the	the	DET
ejpam-7064	81	43	approximate	approximate	ADJ
ejpam-7064	81	44	solution	solution	NOUN
ejpam-7064	81	45	and	and	CCONJ
ejpam-7064	81	46	the	the	DET
ejpam-7064	81	47	collocation	collocation	NOUN
ejpam-7064	81	48	points	point	VERB
ejpam-7064	81	49	in	in	ADP
ejpam-7064	81	50	each	each	DET
ejpam-7064	81	51	subdomain	subdomain	NOUN
ejpam-7064	81	52	,	,	PUNCT
ejpam-7064	81	53	respectively	respectively	ADV
ejpam-7064	81	54	.	.	PUNCT
ejpam-7064	82	1	these	these	DET
ejpam-7064	82	2	considerations	consideration	NOUN
ejpam-7064	82	3	lead	lead	VERB
ejpam-7064	82	4	us	we	PRON
ejpam-7064	82	5	to	to	ADP
ejpam-7064	82	6	the	the	DET
ejpam-7064	82	7	following	follow	VERB
ejpam-7064	82	8	matrix	matrix	NOUN
ejpam-7064	82	9	form	form	NOUN
ejpam-7064	82	10	system	system	NOUN
ejpam-7064	82	11	:(	:(	SYM
ejpam-7064	82	12	2n	2n	NUM
ejpam-7064	82	13	t	t	PROPN
ejpam-7064	82	14	d+	d+	PUNCT
ejpam-7064	82	15	cs	cs	PROPN
ejpam-7064	82	16	,	,	PUNCT
ejpam-7064	82	17	s	s	PART
ejpam-7064	82	18	i	i	NOUN
ejpam-7064	82	19	)	)	PUNCT
ejpam-7064	82	20	θj	θj	PROPN
ejpam-7064	83	1	s	s	PART
ejpam-7064	84	1	+	+	NUM
ejpam-7064	84	2	2∑	2∑	NUM
ejpam-7064	84	3	i=1	i=1	X
ejpam-7064	84	4	i̸=s	i̸=s	PROPN
ejpam-7064	84	5	cs	cs	NOUN
ejpam-7064	84	6	,	,	PUNCT
ejpam-7064	84	7	iθ	iθ	ADP
ejpam-7064	84	8	j	j	PROPN
ejpam-7064	84	9	i	i	PROPN
ejpam-7064	84	10	+	+	PROPN
ejpam-7064	84	11	nj	nj	PROPN
ejpam-7064	84	12	s(θ	s(θ	PROPN
ejpam-7064	84	13	)	)	PUNCT
ejpam-7064	85	1	=	=	SYM
ejpam-7064	85	2	0	0	NUM
ejpam-7064	85	3	,	,	PUNCT
ejpam-7064	85	4	s	s	PART
ejpam-7064	85	5	=	=	SYM
ejpam-7064	85	6	1	1	NUM
ejpam-7064	85	7	,	,	PUNCT
ejpam-7064	85	8	2	2	NUM
ejpam-7064	85	9	,	,	PUNCT
ejpam-7064	85	10	(	(	PUNCT
ejpam-7064	85	11	13	13	NUM
ejpam-7064	85	12	)	)	PUNCT
ejpam-7064	85	13	where	where	SCONJ
ejpam-7064	85	14	cs	cs	X
ejpam-7064	85	15	,	,	PUNCT
ejpam-7064	85	16	i	i	PRON
ejpam-7064	85	17	are	be	AUX
ejpam-7064	85	18	the	the	DET
ejpam-7064	85	19	elements	element	NOUN
ejpam-7064	85	20	of	of	ADP
ejpam-7064	85	21	the	the	DET
ejpam-7064	85	22	matrix	matrix	NOUN
ejpam-7064	85	23	c	c	NOUN
ejpam-7064	85	24	defined	define	VERB
ejpam-7064	85	25	in	in	ADP
ejpam-7064	85	26	(	(	PUNCT
ejpam-7064	85	27	7	7	NUM
ejpam-7064	85	28	)	)	PUNCT
ejpam-7064	85	29	,	,	PUNCT
ejpam-7064	85	30	and	and	CCONJ
ejpam-7064	85	31	:	:	PUNCT
ejpam-7064	85	32	θ	θ	X
ejpam-7064	85	33	=	=	PUNCT
ejpam-7064	86	1	[	[	X
ejpam-7064	86	2	θ1,θ2	θ1,θ2	PROPN
ejpam-7064	86	3	]	]	X
ejpam-7064	86	4	t	t	PROPN
ejpam-7064	86	5	,	,	PUNCT
ejpam-7064	86	6	ns(θ	ns(θ	ADV
ejpam-7064	86	7	)	)	PUNCT
ejpam-7064	86	8	=	=	PUNCT
ejpam-7064	87	1	[	[	X
ejpam-7064	87	2	ns	ns	INTJ
ejpam-7064	87	3	(	(	PUNCT
ejpam-7064	87	4	θ	θ	PROPN
ejpam-7064	87	5	(	(	PUNCT
ejpam-7064	87	6	y0	y0	NOUN
ejpam-7064	87	7	)	)	PUNCT
ejpam-7064	87	8	)	)	PUNCT
ejpam-7064	87	9	,	,	PUNCT
ejpam-7064	87	10	ns	ns	INTJ
ejpam-7064	87	11	(	(	PUNCT
ejpam-7064	87	12	θ	θ	PROPN
ejpam-7064	87	13	(	(	PUNCT
ejpam-7064	87	14	y1	y1	NOUN
ejpam-7064	87	15	)	)	PUNCT
ejpam-7064	87	16	)	)	PUNCT
ejpam-7064	87	17	,	,	PUNCT
ejpam-7064	87	18	.	.	PUNCT
ejpam-7064	87	19	.	.	PUNCT
ejpam-7064	88	1	.	.	PUNCT
ejpam-7064	89	1	,	,	PUNCT
ejpam-7064	89	2	ns	ns	INTJ
ejpam-7064	89	3	(	(	PUNCT
ejpam-7064	89	4	θ	θ	PROPN
ejpam-7064	89	5	(	(	PUNCT
ejpam-7064	89	6	ym))]t	ym))]t	PROPN
ejpam-7064	89	7	.	.	PUNCT
ejpam-7064	90	1	(	(	PUNCT
ejpam-7064	90	2	vii	vii	PROPN
ejpam-7064	90	3	)	)	PUNCT
ejpam-7064	90	4	by	by	ADP
ejpam-7064	90	5	using	use	VERB
ejpam-7064	90	6	the	the	DET
ejpam-7064	90	7	gauss	gauss	ADJ
ejpam-7064	90	8	-	-	PUNCT
ejpam-7064	90	9	seidel	seidel	PROPN
ejpam-7064	90	10	method	method	NOUN
ejpam-7064	90	11	to	to	PART
ejpam-7064	90	12	solve	solve	VERB
ejpam-7064	90	13	the	the	DET
ejpam-7064	90	14	algebraic	algebraic	ADJ
ejpam-7064	90	15	equations	equation	NOUN
ejpam-7064	90	16	(	(	PUNCT
ejpam-7064	90	17	13	13	NUM
ejpam-7064	90	18	)	)	PUNCT
ejpam-7064	90	19	in	in	ADP
ejpam-7064	90	20	each	each	DET
ejpam-7064	90	21	subdomain	subdomain	NOUN
ejpam-7064	90	22	ij	ij	NOUN
ejpam-7064	90	23	,	,	PUNCT
ejpam-7064	90	24	we	we	PRON
ejpam-7064	90	25	can	can	AUX
ejpam-7064	90	26	reduce	reduce	VERB
ejpam-7064	90	27	it	it	PRON
ejpam-7064	90	28	to	to	ADP
ejpam-7064	90	29	the	the	DET
ejpam-7064	90	30	following	follow	VERB
ejpam-7064	90	31	iteration	iteration	NOUN
ejpam-7064	90	32	formula	formula	NOUN
ejpam-7064	90	33	:(	:(	SYM
ejpam-7064	91	1	2n	2n	NUM
ejpam-7064	91	2	t	t	PROPN
ejpam-7064	91	3	d+	d+	PUNCT
ejpam-7064	91	4	cs	cs	PROPN
ejpam-7064	91	5	,	,	PUNCT
ejpam-7064	91	6	s	s	PART
ejpam-7064	91	7	i	i	NOUN
ejpam-7064	91	8	)	)	PUNCT
ejpam-7064	91	9	θj	θj	PROPN
ejpam-7064	92	1	s	s	PROPN
ejpam-7064	92	2	,	,	PUNCT
ejpam-7064	92	3	p+1	p+1	NOUN
ejpam-7064	92	4	=	=	PUNCT
ejpam-7064	93	1	−	−	PROPN
ejpam-7064	93	2	s−1∑	s−1∑	NUM
ejpam-7064	93	3	i=1	i=1	PROPN
ejpam-7064	93	4	cs	cs	PROPN
ejpam-7064	93	5	,	,	PUNCT
ejpam-7064	93	6	iθ	iθ	ADP
ejpam-7064	93	7	j	j	PROPN
ejpam-7064	93	8	i	i	PROPN
ejpam-7064	93	9	,	,	PUNCT
ejpam-7064	93	10	p	p	NOUN
ejpam-7064	93	11	−	−	PROPN
ejpam-7064	93	12	2∑	2∑	NUM
ejpam-7064	94	1	i	i	PRON
ejpam-7064	94	2	=	=	PROPN
ejpam-7064	94	3	s+1	s+1	PROPN
ejpam-7064	94	4	cs	cs	PROPN
ejpam-7064	94	5	,	,	PUNCT
ejpam-7064	94	6	iθ	iθ	ADP
ejpam-7064	94	7	j	j	PROPN
ejpam-7064	94	8	i	i	PROPN
ejpam-7064	94	9	,	,	PUNCT
ejpam-7064	94	10	p	p	PROPN
ejpam-7064	94	11	−nj	−nj	PROPN
ejpam-7064	94	12	s	s	PROPN
ejpam-7064	94	13	,	,	PUNCT
ejpam-7064	94	14	p	p	X
ejpam-7064	94	15	,	,	PUNCT
ejpam-7064	94	16	s	s	PART
ejpam-7064	94	17	=	=	SYM
ejpam-7064	94	18	1	1	NUM
ejpam-7064	94	19	,	,	PUNCT
ejpam-7064	94	20	2	2	NUM
ejpam-7064	94	21	,	,	PUNCT
ejpam-7064	94	22	(	(	PUNCT
ejpam-7064	94	23	14	14	NUM
ejpam-7064	94	24	)	)	PUNCT
ejpam-7064	94	25	where	where	SCONJ
ejpam-7064	94	26	θs	θ	NOUN
ejpam-7064	94	27	,	,	PUNCT
ejpam-7064	94	28	p+1	p+1	PROPN
ejpam-7064	94	29	is	be	AUX
ejpam-7064	94	30	the	the	DET
ejpam-7064	94	31	numerical	numerical	ADJ
ejpam-7064	94	32	estimation	estimation	NOUN
ejpam-7064	94	33	of	of	ADP
ejpam-7064	94	34	θs	θs	PRON
ejpam-7064	94	35	at	at	ADP
ejpam-7064	94	36	the	the	DET
ejpam-7064	94	37	(	(	PUNCT
ejpam-7064	94	38	p+1)th	p+1)th	NOUN
ejpam-7064	94	39	iteration	iteration	NOUN
ejpam-7064	94	40	,	,	PUNCT
ejpam-7064	94	41	and	and	CCONJ
ejpam-7064	94	42	nj	nj	PROPN
ejpam-7064	94	43	s	s	PROPN
ejpam-7064	94	44	,	,	PUNCT
ejpam-7064	94	45	p	p	X
ejpam-7064	94	46	=	=	SYM
ejpam-7064	94	47	ns	ns	PROPN
ejpam-7064	94	48	(	(	PUNCT
ejpam-7064	94	49	θj	θj	NOUN
ejpam-7064	94	50	1,p	1,p	PROPN
ejpam-7064	94	51	,	,	PUNCT
ejpam-7064	94	52	θ	θ	PROPN
ejpam-7064	94	53	j	j	PROPN
ejpam-7064	94	54	2,p	2,p	PROPN
ejpam-7064	94	55	,	,	PUNCT
ejpam-7064	94	56	.	.	PUNCT
ejpam-7064	94	57	.	.	PUNCT
ejpam-7064	94	58	.	.	PUNCT
ejpam-7064	95	1	,	,	PUNCT
ejpam-7064	95	2	θ	θ	PROPN
ejpam-7064	95	3	j	j	PROPN
ejpam-7064	95	4	s−1,p	s−1,p	PROPN
ejpam-7064	95	5	,	,	PUNCT
ejpam-7064	95	6	θ	θ	PROPN
ejpam-7064	95	7	j	j	PROPN
ejpam-7064	95	8	s	s	PROPN
ejpam-7064	95	9	,	,	PUNCT
ejpam-7064	95	10	p	p	NOUN
ejpam-7064	95	11	)	)	PUNCT
ejpam-7064	95	12	are	be	AUX
ejpam-7064	95	13	used	use	VERB
ejpam-7064	95	14	to	to	PART
ejpam-7064	95	15	evaluate	evaluate	VERB
ejpam-7064	95	16	the	the	DET
ejpam-7064	95	17	nonlinear	nonlinear	ADJ
ejpam-7064	95	18	terms	term	NOUN
ejpam-7064	95	19	.	.	PUNCT
ejpam-7064	96	1	(	(	PUNCT
ejpam-7064	96	2	viii	viii	NOUN
ejpam-7064	96	3	)	)	PUNCT
ejpam-7064	96	4	in	in	ADP
ejpam-7064	96	5	light	light	NOUN
ejpam-7064	96	6	of	of	ADP
ejpam-7064	96	7	the	the	DET
ejpam-7064	96	8	above	above	NOUN
ejpam-7064	96	9	,	,	PUNCT
ejpam-7064	96	10	the	the	DET
ejpam-7064	96	11	numerical	numerical	ADJ
ejpam-7064	96	12	solution	solution	NOUN
ejpam-7064	96	13	can	can	AUX
ejpam-7064	96	14	be	be	AUX
ejpam-7064	96	15	obtained	obtain	VERB
ejpam-7064	96	16	as	as	SCONJ
ejpam-7064	96	17	follows	follow	VERB
ejpam-7064	96	18	:	:	PUNCT
ejpam-7064	96	19	θj	θj	PROPN
ejpam-7064	96	20	s	s	PROPN
ejpam-7064	96	21	,	,	PUNCT
ejpam-7064	96	22	p+1	p+1	PROPN
ejpam-7064	96	23	=	=	PUNCT
ejpam-7064	97	1	a−1	a−1	PROPN
ejpam-7064	97	2	s	s	PRON
ejpam-7064	97	3	bj	bj	NOUN
ejpam-7064	97	4	s	s	PRON
ejpam-7064	97	5	,	,	PUNCT
ejpam-7064	97	6	(	(	PUNCT
ejpam-7064	97	7	15	15	NUM
ejpam-7064	97	8	)	)	PUNCT
ejpam-7064	97	9	where	where	SCONJ
ejpam-7064	97	10	as	as	SCONJ
ejpam-7064	97	11	=	=	PROPN
ejpam-7064	97	12	2n	2n	NUM
ejpam-7064	97	13	t	t	PROPN
ejpam-7064	97	14	d+	d+	PUNCT
ejpam-7064	97	15	cs	cs	PROPN
ejpam-7064	97	16	,	,	PUNCT
ejpam-7064	97	17	s	s	PART
ejpam-7064	97	18	i	i	PRON
ejpam-7064	97	19	,	,	PUNCT
ejpam-7064	97	20	bj	bj	ADP
ejpam-7064	97	21	s	s	NOUN
ejpam-7064	97	22	=	=	X
ejpam-7064	97	23	−	−	PROPN
ejpam-7064	97	24	s−1∑	s−1∑	NUM
ejpam-7064	97	25	i=1	i=1	PROPN
ejpam-7064	98	1	cs	cs	PROPN
ejpam-7064	98	2	,	,	PUNCT
ejpam-7064	98	3	iθ	iθ	ADP
ejpam-7064	98	4	j	j	PROPN
ejpam-7064	98	5	i	i	PROPN
ejpam-7064	98	6	,	,	PUNCT
ejpam-7064	98	7	p	p	NOUN
ejpam-7064	98	8	−	−	PROPN
ejpam-7064	98	9	2∑	2∑	NUM
ejpam-7064	99	1	i	i	PRON
ejpam-7064	99	2	=	=	PROPN
ejpam-7064	99	3	s+1	s+1	PROPN
ejpam-7064	99	4	cs	cs	PROPN
ejpam-7064	99	5	,	,	PUNCT
ejpam-7064	99	6	iθ	iθ	ADP
ejpam-7064	99	7	j	j	PROPN
ejpam-7064	99	8	i	i	PROPN
ejpam-7064	99	9	,	,	PUNCT
ejpam-7064	99	10	p	p	PROPN
ejpam-7064	99	11	−nj	−nj	PROPN
ejpam-7064	99	12	s	s	PROPN
ejpam-7064	99	13	,	,	PUNCT
ejpam-7064	99	14	p.	p.	NOUN
ejpam-7064	100	1	we	we	PRON
ejpam-7064	100	2	will	will	AUX
ejpam-7064	100	3	use	use	VERB
ejpam-7064	100	4	the	the	DET
ejpam-7064	100	5	initial	initial	ADJ
ejpam-7064	100	6	conditions	condition	NOUN
ejpam-7064	100	7	in	in	ADP
ejpam-7064	100	8	the	the	DET
ejpam-7064	100	9	first	first	ADJ
ejpam-7064	100	10	iteration	iteration	NOUN
ejpam-7064	100	11	at	at	ADP
ejpam-7064	100	12	p	p	NOUN
ejpam-7064	100	13	=	=	PROPN
ejpam-7064	100	14	0	0	NUM
ejpam-7064	100	15	,	,	PUNCT
ejpam-7064	100	16	of	of	ADP
ejpam-7064	100	17	the	the	DET
ejpam-7064	100	18	iteration	iteration	NOUN
ejpam-7064	100	19	matrix	matrix	NOUN
ejpam-7064	100	20	form	form	NOUN
ejpam-7064	100	21	(	(	PUNCT
ejpam-7064	100	22	15	15	NUM
ejpam-7064	100	23	)	)	PUNCT
ejpam-7064	100	24	.	.	PUNCT
ejpam-7064	101	1	the	the	DET
ejpam-7064	101	2	solution	solution	NOUN
ejpam-7064	101	3	of	of	ADP
ejpam-7064	101	4	the	the	DET
ejpam-7064	101	5	system	system	NOUN
ejpam-7064	101	6	(	(	PUNCT
ejpam-7064	101	7	7	7	X
ejpam-7064	101	8	)	)	PUNCT
ejpam-7064	101	9	is	be	AUX
ejpam-7064	101	10	then	then	ADV
ejpam-7064	101	11	given	give	VERB
ejpam-7064	101	12	by	by	ADP
ejpam-7064	101	13	[	[	X
ejpam-7064	101	14	25	25	NUM
ejpam-7064	101	15	]	]	X
ejpam-7064	101	16	:	:	PUNCT
ejpam-7064	101	17	θs	θ	NOUN
ejpam-7064	101	18	=	=	SYM
ejpam-7064	101	19	n⋃	n⋃	PROPN
ejpam-7064	102	1	j=1	j=1	NOUN
ejpam-7064	102	2	θj	θj	NOUN
ejpam-7064	102	3	s	s	PROPN
ejpam-7064	102	4	(	(	PUNCT
ejpam-7064	102	5	yj	yj	PROPN
ejpam-7064	102	6	)	)	PUNCT
ejpam-7064	102	7	.	.	PUNCT
ejpam-7064	103	1	(	(	PUNCT
ejpam-7064	103	2	16	16	X
ejpam-7064	103	3	)	)	PUNCT
ejpam-7064	103	4	m.	m.	NOUN
ejpam-7064	103	5	adel	adel	PROPN
ejpam-7064	103	6	et	et	PROPN
ejpam-7064	103	7	al	al	PROPN
ejpam-7064	103	8	.	.	PUNCT
ejpam-7064	103	9	/	/	SYM
ejpam-7064	103	10	eur	eur	PROPN
ejpam-7064	103	11	.	.	PUNCT
ejpam-7064	104	1	j.	j.	PROPN
ejpam-7064	104	2	pure	pure	PROPN
ejpam-7064	104	3	appl	appl	PROPN
ejpam-7064	104	4	.	.	PROPN
ejpam-7064	104	5	math	math	PROPN
ejpam-7064	104	6	,	,	PUNCT
ejpam-7064	104	7	18	18	NUM
ejpam-7064	104	8	(	(	PUNCT
ejpam-7064	104	9	4	4	NUM
ejpam-7064	104	10	)	)	PUNCT
ejpam-7064	104	11	(	(	PUNCT
ejpam-7064	104	12	2025	2025	NUM
ejpam-7064	104	13	)	)	PUNCT
ejpam-7064	104	14	,	,	PUNCT
ejpam-7064	104	15	7064	7064	NUM
ejpam-7064	104	16	6	6	NUM
ejpam-7064	104	17	of	of	ADP
ejpam-7064	104	18	11	11	NUM
ejpam-7064	104	19	4	4	NUM
ejpam-7064	104	20	.	.	PUNCT
ejpam-7064	104	21	convergence	convergence	NOUN
ejpam-7064	104	22	and	and	CCONJ
ejpam-7064	104	23	error	error	NOUN
ejpam-7064	104	24	analysis	analysis	NOUN
ejpam-7064	104	25	we	we	PRON
ejpam-7064	104	26	describe	describe	VERB
ejpam-7064	104	27	how	how	SCONJ
ejpam-7064	104	28	domain	domain	NOUN
ejpam-7064	104	29	decomposition	decomposition	NOUN
ejpam-7064	104	30	affects	affect	VERB
ejpam-7064	104	31	msrm	msrm	DET
ejpam-7064	104	32	convergence	convergence	NOUN
ejpam-7064	104	33	and	and	CCONJ
ejpam-7064	104	34	error	error	NOUN
ejpam-7064	104	35	estimates	estimate	NOUN
ejpam-7064	104	36	.	.	PUNCT
ejpam-7064	105	1	eq.(15	eq.(15	NOUN
ejpam-7064	105	2	)	)	PUNCT
ejpam-7064	105	3	can	can	AUX
ejpam-7064	105	4	be	be	AUX
ejpam-7064	105	5	expressed	express	VERB
ejpam-7064	105	6	as	as	ADP
ejpam-7064	105	7	a	a	DET
ejpam-7064	105	8	block	block	NOUN
ejpam-7064	105	9	matrix	matrix	NOUN
ejpam-7064	105	10	system	system	NOUN
ejpam-7064	105	11	as	as	SCONJ
ejpam-7064	105	12	follows	follow	VERB
ejpam-7064	105	13	:	:	PUNCT
ejpam-7064	106	1	aθ	aθ	NOUN
ejpam-7064	106	2	=	=	SYM
ejpam-7064	106	3	b	b	PROPN
ejpam-7064	106	4	,	,	PUNCT
ejpam-7064	106	5	(	(	PUNCT
ejpam-7064	106	6	17	17	NUM
ejpam-7064	106	7	)	)	PUNCT
ejpam-7064	106	8	where	where	SCONJ
ejpam-7064	106	9	a	a	DET
ejpam-7064	106	10	=	=	SYM
ejpam-7064	106	11	(	(	PUNCT
ejpam-7064	106	12	2n	2n	NUM
ejpam-7064	106	13	t	t	NOUN
ejpam-7064	106	14	d+	d+	PUNCT
ejpam-7064	107	1	c1,1	c1,1	NOUN
ejpam-7064	107	2	i	i	PRON
ejpam-7064	107	3	c1,2	c1,2	VERB
ejpam-7064	108	1	i	i	PRON
ejpam-7064	108	2	c2,1	c2,1	VERB
ejpam-7064	109	1	i	i	PRON
ejpam-7064	109	2	2n	2n	NUM
ejpam-7064	109	3	t	t	PROPN
ejpam-7064	109	4	d+	d+	PUNCT
ejpam-7064	109	5	c2,2	c2,2	PROPN
ejpam-7064	109	6	i	i	PROPN
ejpam-7064	109	7	)	)	PUNCT
ejpam-7064	109	8	,	,	PUNCT
ejpam-7064	109	9	θj	θj	NOUN
ejpam-7064	110	1	=	=	SYM
ejpam-7064	110	2	(	(	PUNCT
ejpam-7064	110	3	θj	θj	NOUN
ejpam-7064	110	4	1	1	NUM
ejpam-7064	110	5	θj	θj	NOUN
ejpam-7064	110	6	2	2	NUM
ejpam-7064	110	7	)	)	PUNCT
ejpam-7064	110	8	,	,	PUNCT
ejpam-7064	110	9	and	and	CCONJ
ejpam-7064	110	10	bj	bj	VERB
ejpam-7064	110	11	=	=	SYM
ejpam-7064	110	12	(	(	PUNCT
ejpam-7064	110	13	−nj	−nj	PROPN
ejpam-7064	110	14	1	1	NUM
ejpam-7064	110	15	−nj	−nj	PROPN
ejpam-7064	110	16	2	2	NUM
ejpam-7064	110	17	)	)	PUNCT
ejpam-7064	110	18	.	.	PUNCT
ejpam-7064	111	1	theorem	theorem	NOUN
ejpam-7064	111	2	1	1	NUM
ejpam-7064	111	3	.	.	PUNCT
ejpam-7064	112	1	the	the	DET
ejpam-7064	112	2	sequence	sequence	NOUN
ejpam-7064	112	3	of	of	ADP
ejpam-7064	112	4	solutions	solution	NOUN
ejpam-7064	112	5	{	{	PUNCT
ejpam-7064	112	6	θ(k	θ(k	ADJ
ejpam-7064	112	7	)	)	PUNCT
ejpam-7064	112	8	}	}	PUNCT
ejpam-7064	112	9	∞	∞	NUM
ejpam-7064	112	10	k=0	k=0	PROPN
ejpam-7064	112	11	,	,	PUNCT
ejpam-7064	112	12	which	which	PRON
ejpam-7064	112	13	is	be	AUX
ejpam-7064	112	14	generated	generate	VERB
ejpam-7064	112	15	from	from	ADP
ejpam-7064	112	16	(	(	PUNCT
ejpam-7064	112	17	15	15	NUM
ejpam-7064	112	18	)	)	PUNCT
ejpam-7064	112	19	by	by	ADP
ejpam-7064	112	20	θ	θ	PROPN
ejpam-7064	112	21	=	=	PRON
ejpam-7064	112	22	a−1b	a−1b	NOUN
ejpam-7064	112	23	with	with	ADP
ejpam-7064	112	24	any	any	DET
ejpam-7064	112	25	choice	choice	NOUN
ejpam-7064	112	26	of	of	ADP
ejpam-7064	112	27	θ(0	θ(0	PROPN
ejpam-7064	112	28	)	)	PUNCT
ejpam-7064	112	29	∈	∈	PROPN
ejpam-7064	112	30	rn̄	rn̄	NOUN
ejpam-7064	112	31	,	,	PUNCT
ejpam-7064	112	32	converges	converge	VERB
ejpam-7064	112	33	to	to	ADP
ejpam-7064	112	34	the	the	DET
ejpam-7064	112	35	unique	unique	ADJ
ejpam-7064	112	36	solution	solution	NOUN
ejpam-7064	112	37	θ̄	θ̄	ADJ
ejpam-7064	112	38	if	if	SCONJ
ejpam-7064	112	39	the	the	DET
ejpam-7064	112	40	matrix	matrix	NOUN
ejpam-7064	112	41	a	a	PRON
ejpam-7064	112	42	is	be	AUX
ejpam-7064	112	43	strictly	strictly	ADV
ejpam-7064	112	44	diagonally	diagonally	ADV
ejpam-7064	112	45	dominant	dominant	ADJ
ejpam-7064	112	46	.	.	PUNCT
ejpam-7064	113	1	proof	proof	NOUN
ejpam-7064	113	2	.	.	PUNCT
ejpam-7064	114	1	the	the	DET
ejpam-7064	114	2	details	detail	NOUN
ejpam-7064	114	3	of	of	ADP
ejpam-7064	114	4	the	the	DET
ejpam-7064	114	5	proof	proof	NOUN
ejpam-7064	114	6	of	of	ADP
ejpam-7064	114	7	this	this	DET
ejpam-7064	114	8	theorem	theorem	NOUN
ejpam-7064	114	9	can	can	AUX
ejpam-7064	114	10	be	be	AUX
ejpam-7064	114	11	found	find	VERB
ejpam-7064	114	12	in	in	ADP
ejpam-7064	114	13	[	[	X
ejpam-7064	114	14	26	26	NUM
ejpam-7064	114	15	]	]	PUNCT
ejpam-7064	114	16	.	.	PUNCT
ejpam-7064	115	1	theorem	theorem	NOUN
ejpam-7064	115	2	2	2	NUM
ejpam-7064	115	3	.	.	PUNCT
ejpam-7064	116	1	[	[	X
ejpam-7064	116	2	27	27	NUM
ejpam-7064	116	3	]	]	PUNCT
ejpam-7064	116	4	let	let	AUX
ejpam-7064	116	5	θs(t	θs(t	X
ejpam-7064	116	6	)	)	PUNCT
ejpam-7064	116	7	be	be	AUX
ejpam-7064	116	8	a	a	DET
ejpam-7064	116	9	polynomial	polynomial	NOUN
ejpam-7064	116	10	of	of	ADP
ejpam-7064	116	11	degree	degree	NOUN
ejpam-7064	116	12	≤	≤	X
ejpam-7064	116	13	m	m	VERB
ejpam-7064	116	14	that	that	PRON
ejpam-7064	116	15	interpolates	interpolate	VERB
ejpam-7064	116	16	the	the	DET
ejpam-7064	116	17	function	function	NOUN
ejpam-7064	116	18	θs(t	θs(t	NOUN
ejpam-7064	116	19	)	)	PUNCT
ejpam-7064	116	20	∈	∈	PROPN
ejpam-7064	116	21	cm+1[0	cm+1[0	PROPN
ejpam-7064	116	22	,	,	PUNCT
ejpam-7064	116	23	t	t	X
ejpam-7064	116	24	]	]	PUNCT
ejpam-7064	116	25	at	at	ADP
ejpam-7064	116	26	m+	m+	NUM
ejpam-7064	116	27	1	1	NUM
ejpam-7064	116	28	various	various	ADJ
ejpam-7064	116	29	points	point	NOUN
ejpam-7064	116	30	y0	y0	PROPN
ejpam-7064	116	31	,	,	PUNCT
ejpam-7064	116	32	y1	y1	NOUN
ejpam-7064	116	33	,	,	PUNCT
ejpam-7064	116	34	.	.	PUNCT
ejpam-7064	116	35	.	.	PUNCT
ejpam-7064	117	1	.	.	PUNCT
ejpam-7064	118	1	,	,	PUNCT
ejpam-7064	118	2	ym	ym	PROPN
ejpam-7064	118	3	∈	∈	PROPN
ejpam-7064	119	1	[	[	X
ejpam-7064	119	2	tj	tj	X
ejpam-7064	119	3	,	,	PUNCT
ejpam-7064	119	4	tj+1	tj+1	PROPN
ejpam-7064	119	5	]	]	PUNCT
ejpam-7064	119	6	,	,	PUNCT
ejpam-7064	119	7	with	with	ADP
ejpam-7064	119	8	the	the	DET
ejpam-7064	119	9	property	property	NOUN
ejpam-7064	119	10	(	(	PUNCT
ejpam-7064	119	11	12	12	NUM
ejpam-7064	119	12	)	)	PUNCT
ejpam-7064	119	13	.	.	PUNCT
ejpam-7064	120	1	according	accord	VERB
ejpam-7064	120	2	to	to	ADP
ejpam-7064	120	3	(	(	PUNCT
ejpam-7064	120	4	8)	8)	NUM
ejpam-7064	120	5	,	,	PUNCT
ejpam-7064	120	6	if	if	SCONJ
ejpam-7064	120	7	the	the	DET
ejpam-7064	120	8	nodes	node	NOUN
ejpam-7064	120	9	yi	yi	NOUN
ejpam-7064	120	10	are	be	AUX
ejpam-7064	120	11	used	use	VERB
ejpam-7064	120	12	as	as	ADP
ejpam-7064	120	13	the	the	DET
ejpam-7064	120	14	cglps	cglp	NOUN
ejpam-7064	120	15	,	,	PUNCT
ejpam-7064	120	16	the	the	DET
ejpam-7064	120	17	error	error	NOUN
ejpam-7064	120	18	term	term	NOUN
ejpam-7064	120	19	for	for	ADP
ejpam-7064	120	20	the	the	DET
ejpam-7064	120	21	polynomial	polynomial	ADJ
ejpam-7064	120	22	interpolation	interpolation	NOUN
ejpam-7064	120	23	in	in	ADP
ejpam-7064	120	24	[	[	X
ejpam-7064	120	25	0	0	NUM
ejpam-7064	120	26	,	,	PUNCT
ejpam-7064	120	27	t	t	X
ejpam-7064	120	28	]	]	PUNCT
ejpam-7064	120	29	using	use	VERB
ejpam-7064	120	30	the	the	DET
ejpam-7064	120	31	nodes	node	NOUN
ejpam-7064	120	32	yi	yi	NOUN
ejpam-7064	120	33	in	in	ADP
ejpam-7064	120	34	each	each	DET
ejpam-7064	120	35	sub	sub	NOUN
ejpam-7064	120	36	-	-	NOUN
ejpam-7064	120	37	domain	domain	NOUN
ejpam-7064	120	38	is	be	AUX
ejpam-7064	120	39	estimated	estimate	VERB
ejpam-7064	120	40	as	as	SCONJ
ejpam-7064	120	41	follows	follow	VERB
ejpam-7064	120	42	:	:	PUNCT
ejpam-7064	120	43	e(t	e(t	NOUN
ejpam-7064	120	44	)	)	PUNCT
ejpam-7064	120	45	=	=	PUNCT
ejpam-7064	120	46	|θs(t)−θs(t)|	|θs(t)−θs(t)|	NUM
ejpam-7064	120	47	≤	≤	X
ejpam-7064	120	48	λtm+1	λtm+1	X
ejpam-7064	120	49	(	(	PUNCT
ejpam-7064	120	50	4n)m(m+	4n)m(m+	NUM
ejpam-7064	120	51	1	1	NUM
ejpam-7064	120	52	)	)	PUNCT
ejpam-7064	120	53	!	!	PUNCT
ejpam-7064	120	54	,	,	PUNCT
ejpam-7064	121	1	λ	λ	X
ejpam-7064	121	2	̸=	̸=	PROPN
ejpam-7064	121	3	0	0	NUM
ejpam-7064	121	4	.	.	PUNCT
ejpam-7064	122	1	(	(	PUNCT
ejpam-7064	122	2	18	18	NUM
ejpam-7064	122	3	)	)	PUNCT
ejpam-7064	122	4	remark	remark	NOUN
ejpam-7064	122	5	2	2	NUM
ejpam-7064	122	6	.	.	PUNCT
ejpam-7064	123	1	it	it	PRON
ejpam-7064	123	2	can	can	AUX
ejpam-7064	123	3	be	be	AUX
ejpam-7064	123	4	shown	show	VERB
ejpam-7064	123	5	that	that	SCONJ
ejpam-7064	123	6	the	the	DET
ejpam-7064	123	7	error	error	NOUN
ejpam-7064	123	8	in	in	ADP
ejpam-7064	123	9	the	the	DET
ejpam-7064	123	10	multi	multi	ADJ
ejpam-7064	123	11	-	-	ADJ
ejpam-7064	123	12	domain	domain	ADJ
ejpam-7064	123	13	situation	situation	NOUN
ejpam-7064	123	14	is	be	AUX
ejpam-7064	123	15	significantly	significantly	ADV
ejpam-7064	123	16	smaller	small	ADJ
ejpam-7064	123	17	than	than	ADP
ejpam-7064	123	18	the	the	DET
ejpam-7064	123	19	single	single	ADJ
ejpam-7064	123	20	domain	domain	NOUN
ejpam-7064	123	21	example	example	NOUN
ejpam-7064	123	22	,	,	PUNCT
ejpam-7064	123	23	n	n	NOUN
ejpam-7064	123	24	=	=	SYM
ejpam-7064	123	25	1	1	NUM
ejpam-7064	123	26	,	,	PUNCT
ejpam-7064	123	27	due	due	ADP
ejpam-7064	123	28	to	to	ADP
ejpam-7064	123	29	the	the	DET
ejpam-7064	123	30	factor	factor	NOUN
ejpam-7064	123	31	(	(	PUNCT
ejpam-7064	123	32	1	1	NUM
ejpam-7064	123	33	n	n	NOUN
ejpam-7064	123	34	)	)	PUNCT
ejpam-7064	123	35	m	m	VERB
ejpam-7064	123	36	<	<	X
ejpam-7064	123	37	<	<	X
ejpam-7064	123	38	1	1	NUM
ejpam-7064	123	39	for	for	ADP
ejpam-7064	123	40	large	large	ADJ
ejpam-7064	123	41	n.	n.	NOUN
ejpam-7064	123	42	5	5	NUM
ejpam-7064	123	43	.	.	PUNCT
ejpam-7064	123	44	numerical	numerical	PROPN
ejpam-7064	123	45	simulation	simulation	PROPN
ejpam-7064	123	46	by	by	ADP
ejpam-7064	123	47	addressing	address	VERB
ejpam-7064	123	48	the	the	DET
ejpam-7064	123	49	system	system	NOUN
ejpam-7064	123	50	(	(	PUNCT
ejpam-7064	123	51	1)-(2	1)-(2	NUM
ejpam-7064	123	52	)	)	PUNCT
ejpam-7064	123	53	in	in	ADP
ejpam-7064	123	54	the	the	DET
ejpam-7064	123	55	range	range	NOUN
ejpam-7064	123	56	[	[	X
ejpam-7064	123	57	0	0	NUM
ejpam-7064	123	58	,	,	PUNCT
ejpam-7064	123	59	3	3	NUM
ejpam-7064	123	60	]	]	PUNCT
ejpam-7064	123	61	with	with	ADP
ejpam-7064	123	62	various	various	ADJ
ejpam-7064	123	63	values	value	NOUN
ejpam-7064	123	64	of	of	ADP
ejpam-7064	123	65	m	m	PROPN
ejpam-7064	123	66	,	,	PUNCT
ejpam-7064	123	67	δ	δ	PROPN
ejpam-7064	123	68	,	,	PUNCT
ejpam-7064	123	69	γ	γ	X
ejpam-7064	123	70	with	with	ADP
ejpam-7064	123	71	initial	initial	ADJ
ejpam-7064	123	72	conditions	condition	NOUN
ejpam-7064	123	73	θ01	θ01	NOUN
ejpam-7064	123	74	=	=	SYM
ejpam-7064	123	75	θ02	θ02	NOUN
ejpam-7064	123	76	=	=	SYM
ejpam-7064	123	77	1	1	NUM
ejpam-7064	123	78	,	,	PUNCT
ejpam-7064	123	79	we	we	PRON
ejpam-7064	123	80	will	will	AUX
ejpam-7064	123	81	show	show	VERB
ejpam-7064	123	82	a	a	DET
ejpam-7064	123	83	numerical	numerical	ADJ
ejpam-7064	123	84	simulation	simulation	NOUN
ejpam-7064	123	85	on	on	ADP
ejpam-7064	123	86	a	a	DET
ejpam-7064	123	87	test	test	NOUN
ejpam-7064	123	88	example	example	NOUN
ejpam-7064	123	89	to	to	PART
ejpam-7064	123	90	demonstrate	demonstrate	VERB
ejpam-7064	123	91	the	the	DET
ejpam-7064	123	92	accuracy	accuracy	NOUN
ejpam-7064	123	93	of	of	ADP
ejpam-7064	123	94	the	the	DET
ejpam-7064	123	95	provided	provide	VERB
ejpam-7064	123	96	numerical	numerical	ADJ
ejpam-7064	123	97	scheme	scheme	NOUN
ejpam-7064	123	98	.	.	PUNCT
ejpam-7064	124	1	figure	figure	NOUN
ejpam-7064	124	2	1	1	NUM
ejpam-7064	124	3	(	(	PUNCT
ejpam-7064	124	4	a	a	DET
ejpam-7064	124	5	,	,	PUNCT
ejpam-7064	124	6	b	b	NOUN
ejpam-7064	124	7	)	)	PUNCT
ejpam-7064	124	8	shows	show	VERB
ejpam-7064	124	9	the	the	DET
ejpam-7064	124	10	behavior	behavior	NOUN
ejpam-7064	124	11	of	of	ADP
ejpam-7064	124	12	the	the	DET
ejpam-7064	124	13	obtained	obtain	VERB
ejpam-7064	124	14	approximate	approximate	ADJ
ejpam-7064	124	15	solutions	solution	NOUN
ejpam-7064	124	16	using	use	VERB
ejpam-7064	124	17	different	different	ADJ
ejpam-7064	124	18	values	value	NOUN
ejpam-7064	124	19	of	of	ADP
ejpam-7064	124	20	the	the	DET
ejpam-7064	124	21	order	order	NOUN
ejpam-7064	124	22	of	of	ADP
ejpam-7064	124	23	the	the	DET
ejpam-7064	124	24	used	use	VERB
ejpam-7064	124	25	polynomials	polynomial	NOUN
ejpam-7064	124	26	,	,	PUNCT
ejpam-7064	124	27	m	m	VERB
ejpam-7064	124	28	=	=	NOUN
ejpam-7064	124	29	3	3	NUM
ejpam-7064	124	30	,	,	PUNCT
ejpam-7064	124	31	m	m	VERB
ejpam-7064	124	32	=	=	NOUN
ejpam-7064	124	33	7	7	NUM
ejpam-7064	124	34	,	,	PUNCT
ejpam-7064	124	35	at	at	ADP
ejpam-7064	124	36	δ	δ	NOUN
ejpam-7064	124	37	=	=	PUNCT
ejpam-7064	124	38	0.25	0.25	NUM
ejpam-7064	124	39	,	,	PUNCT
ejpam-7064	124	40	γ	γ	X
ejpam-7064	124	41	=	=	SYM
ejpam-7064	124	42	1	1	NUM
ejpam-7064	124	43	.	.	PUNCT
ejpam-7064	125	1	we	we	PRON
ejpam-7064	125	2	compared	compare	VERB
ejpam-7064	125	3	the	the	DET
ejpam-7064	125	4	results	result	NOUN
ejpam-7064	125	5	to	to	ADP
ejpam-7064	125	6	those	those	PRON
ejpam-7064	125	7	obtained	obtain	VERB
ejpam-7064	125	8	using	use	VERB
ejpam-7064	125	9	the	the	DET
ejpam-7064	125	10	rk4	rk4	NOUN
ejpam-7064	125	11	m	m	NOUN
ejpam-7064	125	12	(	(	PUNCT
ejpam-7064	125	13	as	as	ADP
ejpam-7064	125	14	a	a	DET
ejpam-7064	125	15	reference	reference	NOUN
ejpam-7064	125	16	solution	solution	NOUN
ejpam-7064	125	17	)	)	PUNCT
ejpam-7064	125	18	with	with	ADP
ejpam-7064	125	19	δ	δ	PROPN
ejpam-7064	125	20	=	=	SYM
ejpam-7064	125	21	0.0	0.0	NUM
ejpam-7064	125	22	,	,	PUNCT
ejpam-7064	125	23	and	and	CCONJ
ejpam-7064	125	24	γ	γ	X
ejpam-7064	125	25	=	=	SYM
ejpam-7064	125	26	1	1	NUM
ejpam-7064	125	27	in	in	ADP
ejpam-7064	125	28	figure	figure	NOUN
ejpam-7064	125	29	2	2	NUM
ejpam-7064	125	30	(	(	PUNCT
ejpam-7064	125	31	a	a	DET
ejpam-7064	125	32	,	,	PUNCT
ejpam-7064	125	33	b	b	NOUN
ejpam-7064	125	34	)	)	PUNCT
ejpam-7064	125	35	.	.	PUNCT
ejpam-7064	126	1	this	this	DET
ejpam-7064	126	2	comparison	comparison	NOUN
ejpam-7064	126	3	demonstrates	demonstrate	VERB
ejpam-7064	126	4	that	that	SCONJ
ejpam-7064	126	5	the	the	DET
ejpam-7064	126	6	proposed	propose	VERB
ejpam-7064	126	7	method	method	NOUN
ejpam-7064	126	8	is	be	AUX
ejpam-7064	126	9	appropriate	appropriate	ADJ
ejpam-7064	126	10	for	for	ADP
ejpam-7064	126	11	solving	solve	VERB
ejpam-7064	126	12	the	the	DET
ejpam-7064	126	13	suggested	suggest	VERB
ejpam-7064	126	14	model	model	NOUN
ejpam-7064	126	15	.	.	PUNCT
ejpam-7064	127	1	the	the	DET
ejpam-7064	127	2	behavior	behavior	NOUN
ejpam-7064	127	3	of	of	ADP
ejpam-7064	127	4	the	the	DET
ejpam-7064	127	5	approximate	approximate	ADJ
ejpam-7064	127	6	solution	solution	NOUN
ejpam-7064	127	7	via	via	ADP
ejpam-7064	127	8	distinct	distinct	ADJ
ejpam-7064	127	9	values	value	NOUN
ejpam-7064	127	10	of	of	ADP
ejpam-7064	127	11	γ	γ	X
ejpam-7064	127	12	=	=	SYM
ejpam-7064	127	13	0.5	0.5	NUM
ejpam-7064	127	14	,	,	PUNCT
ejpam-7064	127	15	1.0	1.0	NUM
ejpam-7064	127	16	,	,	PUNCT
ejpam-7064	127	17	1.5	1.5	NUM
ejpam-7064	127	18	with	with	ADP
ejpam-7064	127	19	m	m	PROPN
ejpam-7064	127	20	=	=	SYM
ejpam-7064	127	21	5	5	NUM
ejpam-7064	127	22	,	,	PUNCT
ejpam-7064	127	23	δ	δ	X
ejpam-7064	127	24	=	=	SYM
ejpam-7064	127	25	0	0	NUM
ejpam-7064	127	26	is	be	AUX
ejpam-7064	127	27	presented	present	VERB
ejpam-7064	127	28	in	in	ADP
ejpam-7064	127	29	figure	figure	NOUN
ejpam-7064	127	30	(	(	PUNCT
ejpam-7064	127	31	a	a	DET
ejpam-7064	127	32	,	,	PUNCT
ejpam-7064	127	33	b	b	NOUN
ejpam-7064	127	34	)	)	PUNCT
ejpam-7064	127	35	.	.	PUNCT
ejpam-7064	128	1	from	from	ADP
ejpam-7064	128	2	this	this	DET
ejpam-7064	128	3	figure	figure	NOUN
ejpam-7064	128	4	,	,	PUNCT
ejpam-7064	128	5	we	we	PRON
ejpam-7064	128	6	can	can	AUX
ejpam-7064	128	7	confirm	confirm	VERB
ejpam-7064	128	8	that	that	SCONJ
ejpam-7064	128	9	the	the	DET
ejpam-7064	128	10	parameter	parameter	NOUN
ejpam-7064	128	11	γ	γ	PROPN
ejpam-7064	128	12	controls	control	VERB
ejpam-7064	128	13	the	the	DET
ejpam-7064	128	14	balance	balance	NOUN
ejpam-7064	128	15	between	between	ADP
ejpam-7064	128	16	the	the	DET
ejpam-7064	128	17	reaction	reaction	NOUN
ejpam-7064	128	18	and	and	CCONJ
ejpam-7064	128	19	diffusion	diffusion	NOUN
ejpam-7064	128	20	processes	process	NOUN
ejpam-7064	128	21	.	.	PUNCT
ejpam-7064	129	1	figure	figure	NOUN
ejpam-7064	129	2	(	(	PUNCT
ejpam-7064	129	3	a	a	DET
ejpam-7064	129	4	,	,	PUNCT
ejpam-7064	129	5	b	b	NOUN
ejpam-7064	129	6	)	)	PUNCT
ejpam-7064	129	7	also	also	ADV
ejpam-7064	129	8	displays	display	VERB
ejpam-7064	129	9	the	the	DET
ejpam-7064	129	10	behavior	behavior	NOUN
ejpam-7064	129	11	of	of	ADP
ejpam-7064	129	12	the	the	DET
ejpam-7064	129	13	numerical	numerical	ADJ
ejpam-7064	129	14	solutions	solution	NOUN
ejpam-7064	129	15	with	with	ADP
ejpam-7064	129	16	various	various	ADJ
ejpam-7064	129	17	m.	m.	NOUN
ejpam-7064	129	18	adel	adel	PROPN
ejpam-7064	129	19	et	et	PROPN
ejpam-7064	129	20	al	al	PROPN
ejpam-7064	129	21	.	.	PUNCT
ejpam-7064	129	22	/	/	SYM
ejpam-7064	129	23	eur	eur	PROPN
ejpam-7064	129	24	.	.	PUNCT
ejpam-7064	130	1	j.	j.	PROPN
ejpam-7064	130	2	pure	pure	PROPN
ejpam-7064	130	3	appl	appl	PROPN
ejpam-7064	130	4	.	.	PROPN
ejpam-7064	130	5	math	math	PROPN
ejpam-7064	130	6	,	,	PUNCT
ejpam-7064	130	7	18	18	NUM
ejpam-7064	130	8	(	(	PUNCT
ejpam-7064	130	9	4	4	NUM
ejpam-7064	130	10	)	)	PUNCT
ejpam-7064	130	11	(	(	PUNCT
ejpam-7064	130	12	2025	2025	NUM
ejpam-7064	130	13	)	)	PUNCT
ejpam-7064	130	14	,	,	PUNCT
ejpam-7064	130	15	7064	7064	NUM
ejpam-7064	130	16	7	7	NUM
ejpam-7064	130	17	of	of	ADP
ejpam-7064	130	18	11	11	NUM
ejpam-7064	130	19	fig	fig	NOUN
ejpam-7064	130	20	.	.	PUNCT
ejpam-7064	131	1	1	1	NUM
ejpam-7064	131	2	:	:	PUNCT
ejpam-7064	131	3	the	the	DET
ejpam-7064	131	4	approximate	approximate	ADJ
ejpam-7064	131	5	solution	solution	NOUN
ejpam-7064	131	6	θ1(t	θ1(t	PROPN
ejpam-7064	131	7	)	)	PUNCT
ejpam-7064	131	8	,	,	PUNCT
ejpam-7064	131	9	θ2(t	θ2(t	PROPN
ejpam-7064	131	10	)	)	PUNCT
ejpam-7064	131	11	via	via	ADP
ejpam-7064	131	12	various	various	ADJ
ejpam-7064	131	13	values	value	NOUN
ejpam-7064	131	14	of	of	ADP
ejpam-7064	131	15	m.	m.	NOUN
ejpam-7064	131	16	fig	fig	NOUN
ejpam-7064	131	17	.	.	PUNCT
ejpam-7064	132	1	2	2	NUM
ejpam-7064	132	2	:	:	PUNCT
ejpam-7064	132	3	the	the	DET
ejpam-7064	132	4	solution	solution	NOUN
ejpam-7064	132	5	θ1(t	θ1(t	PROPN
ejpam-7064	132	6	)	)	PUNCT
ejpam-7064	132	7	,	,	PUNCT
ejpam-7064	132	8	θ2(t	θ2(t	PROPN
ejpam-7064	132	9	)	)	PUNCT
ejpam-7064	132	10	by	by	ADP
ejpam-7064	132	11	msrm	msrm	PROPN
ejpam-7064	132	12	and	and	CCONJ
ejpam-7064	132	13	rk4	rk4	NOUN
ejpam-7064	132	14	m.	m.	NOUN
ejpam-7064	132	15	values	value	NOUN
ejpam-7064	132	16	of	of	ADP
ejpam-7064	132	17	δ	δ	PROPN
ejpam-7064	132	18	=	=	PROPN
ejpam-7064	132	19	0.0	0.0	NUM
ejpam-7064	132	20	,	,	PUNCT
ejpam-7064	132	21	0.5	0.5	NUM
ejpam-7064	132	22	,	,	PUNCT
ejpam-7064	132	23	1.0	1.0	NUM
ejpam-7064	132	24	,	,	PUNCT
ejpam-7064	132	25	at	at	ADP
ejpam-7064	132	26	m	m	PROPN
ejpam-7064	132	27	=	=	SYM
ejpam-7064	132	28	5	5	NUM
ejpam-7064	132	29	,	,	PUNCT
ejpam-7064	132	30	γ	γ	X
ejpam-7064	132	31	=	=	SYM
ejpam-7064	132	32	0.75	0.75	NUM
ejpam-7064	132	33	.	.	PUNCT
ejpam-7064	133	1	from	from	ADP
ejpam-7064	133	2	this	this	DET
ejpam-7064	133	3	figure	figure	NOUN
ejpam-7064	133	4	,	,	PUNCT
ejpam-7064	133	5	we	we	PRON
ejpam-7064	133	6	can	can	AUX
ejpam-7064	133	7	confirm	confirm	VERB
ejpam-7064	133	8	that	that	SCONJ
ejpam-7064	133	9	the	the	DET
ejpam-7064	133	10	system	system	NOUN
ejpam-7064	133	11	can	can	AUX
ejpam-7064	133	12	exhibit	exhibit	VERB
ejpam-7064	133	13	sustained	sustained	ADJ
ejpam-7064	133	14	oscillations	oscillation	NOUN
ejpam-7064	133	15	as	as	SCONJ
ejpam-7064	133	16	δ	δ	PROPN
ejpam-7064	133	17	increases	increase	VERB
ejpam-7064	133	18	beyond	beyond	ADP
ejpam-7064	133	19	this	this	DET
ejpam-7064	133	20	critical	critical	ADJ
ejpam-7064	133	21	value	value	NOUN
ejpam-7064	133	22	.	.	PUNCT
ejpam-7064	134	1	through	through	ADP
ejpam-7064	134	2	the	the	DET
ejpam-7064	134	3	above	above	ADJ
ejpam-7064	134	4	results	result	NOUN
ejpam-7064	134	5	(	(	PUNCT
ejpam-7064	134	6	figures	figure	NOUN
ejpam-7064	134	7	1	1	NUM
ejpam-7064	134	8	-	-	SYM
ejpam-7064	134	9	4	4	NUM
ejpam-7064	134	10	)	)	PUNCT
ejpam-7064	134	11	,	,	PUNCT
ejpam-7064	134	12	we	we	PRON
ejpam-7064	134	13	can	can	AUX
ejpam-7064	134	14	see	see	VERB
ejpam-7064	134	15	how	how	SCONJ
ejpam-7064	134	16	the	the	DET
ejpam-7064	134	17	numerical	numerical	ADJ
ejpam-7064	134	18	solution	solution	NOUN
ejpam-7064	134	19	behaves	behave	VERB
ejpam-7064	134	20	when	when	SCONJ
ejpam-7064	134	21	the	the	DET
ejpam-7064	134	22	proposed	propose	VERB
ejpam-7064	134	23	approach	approach	NOUN
ejpam-7064	134	24	is	be	AUX
ejpam-7064	134	25	applied	apply	VERB
ejpam-7064	134	26	to	to	ADP
ejpam-7064	134	27	the	the	DET
ejpam-7064	134	28	values	value	NOUN
ejpam-7064	134	29	of	of	ADP
ejpam-7064	134	30	m	m	PROPN
ejpam-7064	134	31	,	,	PUNCT
ejpam-7064	134	32	γ	γ	PROPN
ejpam-7064	134	33	,	,	PUNCT
ejpam-7064	134	34	δ	δ	PROPN
ejpam-7064	134	35	.	.	PUNCT
ejpam-7064	135	1	from	from	ADP
ejpam-7064	135	2	figure	figure	NOUN
ejpam-7064	135	3	3	3	NUM
ejpam-7064	135	4	,	,	PUNCT
ejpam-7064	135	5	we	we	PRON
ejpam-7064	135	6	can	can	AUX
ejpam-7064	135	7	confirm	confirm	VERB
ejpam-7064	135	8	that	that	SCONJ
ejpam-7064	135	9	as	as	ADP
ejpam-7064	135	10	the	the	DET
ejpam-7064	135	11	value	value	NOUN
ejpam-7064	135	12	of	of	ADP
ejpam-7064	135	13	parameter	parameter	NOUN
ejpam-7064	135	14	γ	γ	PROPN
ejpam-7064	135	15	increases	increase	NOUN
ejpam-7064	135	16	,	,	PUNCT
ejpam-7064	135	17	the	the	DET
ejpam-7064	135	18	value	value	NOUN
ejpam-7064	135	19	of	of	ADP
ejpam-7064	135	20	θ1(t	θ1(t	PROPN
ejpam-7064	135	21	)	)	PUNCT
ejpam-7064	135	22	decreases	decrease	NOUN
ejpam-7064	135	23	,	,	PUNCT
ejpam-7064	135	24	and	and	CCONJ
ejpam-7064	135	25	the	the	DET
ejpam-7064	135	26	value	value	NOUN
ejpam-7064	135	27	of	of	ADP
ejpam-7064	135	28	θ2(t	θ2(t	NOUN
ejpam-7064	135	29	)	)	PUNCT
ejpam-7064	135	30	increases	increase	NOUN
ejpam-7064	135	31	,	,	PUNCT
ejpam-7064	135	32	and	and	CCONJ
ejpam-7064	135	33	this	this	PRON
ejpam-7064	135	34	is	be	AUX
ejpam-7064	135	35	consistent	consistent	ADJ
ejpam-7064	135	36	with	with	ADP
ejpam-7064	135	37	the	the	DET
ejpam-7064	135	38	nature	nature	NOUN
ejpam-7064	135	39	of	of	ADP
ejpam-7064	135	40	the	the	DET
ejpam-7064	135	41	effect	effect	NOUN
ejpam-7064	135	42	of	of	ADP
ejpam-7064	135	43	this	this	DET
ejpam-7064	135	44	parameter	parameter	NOUN
ejpam-7064	135	45	on	on	ADP
ejpam-7064	135	46	chemical	chemical	ADJ
ejpam-7064	135	47	reactions	reaction	NOUN
ejpam-7064	135	48	of	of	ADP
ejpam-7064	135	49	this	this	DET
ejpam-7064	135	50	type	type	NOUN
ejpam-7064	135	51	.	.	PUNCT
ejpam-7064	136	1	from	from	ADP
ejpam-7064	136	2	figure	figure	NOUN
ejpam-7064	136	3	4	4	NUM
ejpam-7064	136	4	,	,	PUNCT
ejpam-7064	136	5	we	we	PRON
ejpam-7064	136	6	find	find	VERB
ejpam-7064	136	7	that	that	SCONJ
ejpam-7064	136	8	as	as	ADP
ejpam-7064	136	9	the	the	DET
ejpam-7064	136	10	value	value	NOUN
ejpam-7064	136	11	of	of	ADP
ejpam-7064	136	12	δ	δ	PROPN
ejpam-7064	136	13	increases	increase	NOUN
ejpam-7064	136	14	,	,	PUNCT
ejpam-7064	136	15	the	the	DET
ejpam-7064	136	16	value	value	NOUN
ejpam-7064	136	17	of	of	ADP
ejpam-7064	136	18	θ1(t	θ1(t	SYM
ejpam-7064	136	19	)	)	PUNCT
ejpam-7064	136	20	increases	increase	NOUN
ejpam-7064	136	21	,	,	PUNCT
ejpam-7064	136	22	and	and	CCONJ
ejpam-7064	136	23	the	the	DET
ejpam-7064	136	24	value	value	NOUN
ejpam-7064	136	25	of	of	ADP
ejpam-7064	136	26	θ2(t	θ2(t	NOUN
ejpam-7064	136	27	)	)	PUNCT
ejpam-7064	136	28	decreases	decrease	VERB
ejpam-7064	136	29	,	,	PUNCT
ejpam-7064	136	30	and	and	CCONJ
ejpam-7064	136	31	this	this	PRON
ejpam-7064	136	32	is	be	AUX
ejpam-7064	136	33	consistent	consistent	ADJ
ejpam-7064	136	34	with	with	ADP
ejpam-7064	136	35	the	the	DET
ejpam-7064	136	36	nature	nature	NOUN
ejpam-7064	136	37	of	of	ADP
ejpam-7064	136	38	the	the	DET
ejpam-7064	136	39	effect	effect	NOUN
ejpam-7064	136	40	of	of	ADP
ejpam-7064	136	41	this	this	DET
ejpam-7064	136	42	parameter	parameter	NOUN
ejpam-7064	136	43	on	on	ADP
ejpam-7064	136	44	chemical	chemical	ADJ
ejpam-7064	136	45	reactions	reaction	NOUN
ejpam-7064	136	46	of	of	ADP
ejpam-7064	136	47	this	this	DET
ejpam-7064	136	48	type	type	NOUN
ejpam-7064	136	49	.	.	PUNCT
ejpam-7064	137	1	in	in	ADP
ejpam-7064	137	2	addition	addition	NOUN
ejpam-7064	137	3	,	,	PUNCT
ejpam-7064	137	4	to	to	PART
ejpam-7064	137	5	validate	validate	VERB
ejpam-7064	137	6	our	our	PRON
ejpam-7064	137	7	numerical	numerical	ADJ
ejpam-7064	137	8	solutions	solution	NOUN
ejpam-7064	137	9	,	,	PUNCT
ejpam-7064	137	10	we	we	PRON
ejpam-7064	137	11	present	present	VERB
ejpam-7064	137	12	a	a	DET
ejpam-7064	137	13	comparison	comparison	NOUN
ejpam-7064	137	14	of	of	ADP
ejpam-7064	137	15	the	the	DET
ejpam-7064	137	16	relative	relative	ADJ
ejpam-7064	137	17	error	error	NOUN
ejpam-7064	137	18	(	(	PUNCT
ejpam-7064	137	19	re	re	NOUN
ejpam-7064	137	20	)	)	PUNCT
ejpam-7064	137	21	in	in	ADP
ejpam-7064	137	22	table	table	NOUN
ejpam-7064	137	23	1	1	NUM
ejpam-7064	137	24	with	with	ADP
ejpam-7064	137	25	those	those	DET
ejpam-7064	137	26	solutions	solution	NOUN
ejpam-7064	137	27	obtained	obtain	VERB
ejpam-7064	137	28	by	by	ADP
ejpam-7064	137	29	the	the	DET
ejpam-7064	137	30	variational	variational	ADJ
ejpam-7064	137	31	iteration	iteration	NOUN
ejpam-7064	137	32	method	method	NOUN
ejpam-7064	137	33	(	(	PUNCT
ejpam-7064	137	34	vim	vim	NOUN
ejpam-7064	137	35	)	)	PUNCT
ejpam-7064	138	1	[	[	X
ejpam-7064	138	2	22	22	NUM
ejpam-7064	138	3	]	]	PUNCT
ejpam-7064	138	4	with	with	ADP
ejpam-7064	138	5	integer	integer	PROPN
ejpam-7064	138	6	derivative	derivative	ADJ
ejpam-7064	138	7	α	α	NOUN
ejpam-7064	138	8	=	=	SYM
ejpam-7064	138	9	1	1	X
ejpam-7064	138	10	.	.	PUNCT
ejpam-7064	139	1	we	we	PRON
ejpam-7064	139	2	considered	consider	VERB
ejpam-7064	139	3	the	the	DET
ejpam-7064	139	4	system	system	NOUN
ejpam-7064	139	5	(	(	PUNCT
ejpam-7064	139	6	1)-(2	1)-(2	NUM
ejpam-7064	139	7	)	)	PUNCT
ejpam-7064	139	8	in	in	ADP
ejpam-7064	139	9	the	the	DET
ejpam-7064	139	10	range	range	NOUN
ejpam-7064	139	11	[	[	X
ejpam-7064	139	12	0	0	NUM
ejpam-7064	139	13	,	,	PUNCT
ejpam-7064	139	14	2	2	NUM
ejpam-7064	139	15	]	]	PUNCT
ejpam-7064	139	16	with	with	ADP
ejpam-7064	139	17	initial	initial	ADJ
ejpam-7064	139	18	conditions	condition	NOUN
ejpam-7064	139	19	θ01	θ01	NOUN
ejpam-7064	139	20	=	=	SYM
ejpam-7064	139	21	θ02	θ02	NOUN
ejpam-7064	139	22	=	=	SYM
ejpam-7064	139	23	1	1	NUM
ejpam-7064	139	24	,	,	PUNCT
ejpam-7064	139	25	δ	δ	NOUN
ejpam-7064	139	26	=	=	PUNCT
ejpam-7064	139	27	0.25	0.25	NUM
ejpam-7064	139	28	,	,	PUNCT
ejpam-7064	139	29	γ	γ	X
ejpam-7064	139	30	=	=	SYM
ejpam-7064	139	31	1	1	NUM
ejpam-7064	139	32	,	,	PUNCT
ejpam-7064	139	33	and	and	CCONJ
ejpam-7064	139	34	m	m	NOUN
ejpam-7064	139	35	=	=	ADJ
ejpam-7064	139	36	5	5	X
ejpam-7064	139	37	.	.	PUNCT
ejpam-7064	140	1	here	here	ADV
ejpam-7064	140	2	,	,	PUNCT
ejpam-7064	140	3	to	to	PART
ejpam-7064	140	4	evaluate	evaluate	VERB
ejpam-7064	140	5	the	the	DET
ejpam-7064	140	6	re	re	NOUN
ejpam-7064	140	7	,	,	PUNCT
ejpam-7064	140	8	we	we	PRON
ejpam-7064	140	9	took	take	VERB
ejpam-7064	140	10	the	the	DET
ejpam-7064	140	11	numerical	numerical	ADJ
ejpam-7064	140	12	solutions	solution	NOUN
ejpam-7064	140	13	obtained	obtain	VERB
ejpam-7064	140	14	by	by	ADP
ejpam-7064	140	15	the	the	DET
ejpam-7064	140	16	rk4	rk4	PROPN
ejpam-7064	140	17	method	method	NOUN
ejpam-7064	140	18	as	as	ADP
ejpam-7064	140	19	reference	reference	NOUN
ejpam-7064	140	20	solutions	solution	NOUN
ejpam-7064	140	21	.	.	PUNCT
ejpam-7064	141	1	this	this	PRON
ejpam-7064	141	2	is	be	AUX
ejpam-7064	141	3	due	due	ADJ
ejpam-7064	141	4	to	to	ADP
ejpam-7064	141	5	the	the	DET
ejpam-7064	141	6	lack	lack	NOUN
ejpam-7064	141	7	of	of	ADP
ejpam-7064	141	8	knowledge	knowledge	NOUN
ejpam-7064	141	9	of	of	ADP
ejpam-7064	141	10	the	the	DET
ejpam-7064	141	11	exact	exact	ADJ
ejpam-7064	141	12	solutions	solution	NOUN
ejpam-7064	141	13	of	of	ADP
ejpam-7064	141	14	the	the	DET
ejpam-7064	141	15	proposed	propose	VERB
ejpam-7064	141	16	model	model	NOUN
ejpam-7064	141	17	.	.	PUNCT
ejpam-7064	142	1	this	this	DET
ejpam-7064	142	2	comparison	comparison	NOUN
ejpam-7064	142	3	shows	show	VERB
ejpam-7064	142	4	the	the	DET
ejpam-7064	142	5	thoroughness	thoroughness	NOUN
ejpam-7064	142	6	of	of	ADP
ejpam-7064	142	7	the	the	DET
ejpam-7064	142	8	proposed	propose	VERB
ejpam-7064	142	9	method	method	NOUN
ejpam-7064	142	10	and	and	CCONJ
ejpam-7064	142	11	has	have	VERB
ejpam-7064	142	12	the	the	DET
ejpam-7064	142	13	largest	large	ADJ
ejpam-7064	142	14	convergence	convergence	NOUN
ejpam-7064	142	15	interval	interval	NOUN
ejpam-7064	142	16	compared	compare	VERB
ejpam-7064	142	17	to	to	ADP
ejpam-7064	142	18	the	the	DET
ejpam-7064	142	19	vim	vim	NOUN
ejpam-7064	142	20	.	.	PUNCT
ejpam-7064	143	1	finally	finally	ADV
ejpam-7064	143	2	,	,	PUNCT
ejpam-7064	143	3	we	we	PRON
ejpam-7064	143	4	can	can	AUX
ejpam-7064	143	5	confirm	confirm	VERB
ejpam-7064	143	6	that	that	SCONJ
ejpam-7064	143	7	the	the	DET
ejpam-7064	143	8	proposed	propose	VERB
ejpam-7064	143	9	method	method	NOUN
ejpam-7064	143	10	in	in	ADP
ejpam-7064	143	11	this	this	DET
ejpam-7064	143	12	article	article	NOUN
ejpam-7064	143	13	addressed	address	VERB
ejpam-7064	143	14	and	and	CCONJ
ejpam-7064	143	15	overcame	overcome	VERB
ejpam-7064	143	16	the	the	DET
ejpam-7064	143	17	shortcomings	shortcoming	NOUN
ejpam-7064	143	18	of	of	ADP
ejpam-7064	143	19	the	the	DET
ejpam-7064	143	20	vim	vim	PROPN
ejpam-7064	143	21	method	method	NOUN
ejpam-7064	143	22	.	.	PUNCT
ejpam-7064	144	1	m.	m.	NOUN
ejpam-7064	144	2	adel	adel	PROPN
ejpam-7064	144	3	et	et	PROPN
ejpam-7064	144	4	al	al	PROPN
ejpam-7064	144	5	.	.	PUNCT
ejpam-7064	144	6	/	/	SYM
ejpam-7064	144	7	eur	eur	PROPN
ejpam-7064	144	8	.	.	PUNCT
ejpam-7064	145	1	j.	j.	PROPN
ejpam-7064	145	2	pure	pure	PROPN
ejpam-7064	145	3	appl	appl	PROPN
ejpam-7064	145	4	.	.	PROPN
ejpam-7064	145	5	math	math	PROPN
ejpam-7064	145	6	,	,	PUNCT
ejpam-7064	145	7	18	18	NUM
ejpam-7064	145	8	(	(	PUNCT
ejpam-7064	145	9	4	4	NUM
ejpam-7064	145	10	)	)	PUNCT
ejpam-7064	145	11	(	(	PUNCT
ejpam-7064	145	12	2025	2025	NUM
ejpam-7064	145	13	)	)	PUNCT
ejpam-7064	145	14	,	,	PUNCT
ejpam-7064	145	15	7064	7064	NUM
ejpam-7064	145	16	8	8	NUM
ejpam-7064	145	17	of	of	ADP
ejpam-7064	145	18	11	11	NUM
ejpam-7064	145	19	fig	fig	NOUN
ejpam-7064	145	20	.	.	PUNCT
ejpam-7064	146	1	3	3	NUM
ejpam-7064	146	2	:	:	PUNCT
ejpam-7064	146	3	the	the	DET
ejpam-7064	146	4	approximate	approximate	ADJ
ejpam-7064	146	5	solution	solution	NOUN
ejpam-7064	146	6	θ1(t	θ1(t	PROPN
ejpam-7064	146	7	)	)	PUNCT
ejpam-7064	146	8	,	,	PUNCT
ejpam-7064	146	9	θ2(t	θ2(t	PROPN
ejpam-7064	146	10	)	)	PUNCT
ejpam-7064	146	11	via	via	ADP
ejpam-7064	146	12	various	various	ADJ
ejpam-7064	146	13	values	value	NOUN
ejpam-7064	146	14	of	of	ADP
ejpam-7064	146	15	γ	γ	PROPN
ejpam-7064	146	16	.	.	PROPN
ejpam-7064	146	17	fig	fig	NOUN
ejpam-7064	146	18	.	.	PUNCT
ejpam-7064	147	1	4	4	NUM
ejpam-7064	147	2	:	:	PUNCT
ejpam-7064	147	3	the	the	DET
ejpam-7064	147	4	approximate	approximate	ADJ
ejpam-7064	147	5	solution	solution	NOUN
ejpam-7064	147	6	θ1(t	θ1(t	PROPN
ejpam-7064	147	7	)	)	PUNCT
ejpam-7064	147	8	,	,	PUNCT
ejpam-7064	147	9	θ2(t	θ2(t	PROPN
ejpam-7064	147	10	)	)	PUNCT
ejpam-7064	147	11	via	via	ADP
ejpam-7064	147	12	various	various	ADJ
ejpam-7064	147	13	values	value	NOUN
ejpam-7064	147	14	of	of	ADP
ejpam-7064	147	15	δ	δ	PROPN
ejpam-7064	147	16	.	.	PUNCT
ejpam-7064	147	17	table	table	NOUN
ejpam-7064	147	18	1	1	NUM
ejpam-7064	147	19	.	.	PUNCT
ejpam-7064	148	1	the	the	DET
ejpam-7064	148	2	relative	relative	ADJ
ejpam-7064	148	3	error	error	NOUN
ejpam-7064	148	4	for	for	ADP
ejpam-7064	148	5	numerical	numerical	ADJ
ejpam-7064	148	6	solutions	solution	NOUN
ejpam-7064	148	7	by	by	ADP
ejpam-7064	148	8	using	use	VERB
ejpam-7064	148	9	msrm	msrm	PROPN
ejpam-7064	148	10	and	and	CCONJ
ejpam-7064	148	11	vim	vim	NOUN
ejpam-7064	149	1	[	[	X
ejpam-7064	149	2	22	22	NUM
ejpam-7064	149	3	]	]	PUNCT
ejpam-7064	149	4	at	at	ADP
ejpam-7064	149	5	m	m	PROPN
ejpam-7064	149	6	=	=	SYM
ejpam-7064	149	7	5	5	NUM
ejpam-7064	149	8	.	.	NOUN
ejpam-7064	149	9	relative	relative	ADJ
ejpam-7064	149	10	error	error	NOUN
ejpam-7064	149	11	-	-	PUNCT
ejpam-7064	149	12	θ1(t	θ1(t	NOUN
ejpam-7064	149	13	)	)	PUNCT
ejpam-7064	149	14	at	at	ADP
ejpam-7064	149	15	m	m	PROPN
ejpam-7064	149	16	=	=	SYM
ejpam-7064	149	17	5	5	NUM
ejpam-7064	149	18	relative	relative	ADJ
ejpam-7064	149	19	error	error	NOUN
ejpam-7064	149	20	-	-	PUNCT
ejpam-7064	149	21	θ2(t	θ2(t	NOUN
ejpam-7064	149	22	)	)	PUNCT
ejpam-7064	149	23	at	at	ADP
ejpam-7064	149	24	m	m	NOUN
ejpam-7064	149	25	=	=	SYM
ejpam-7064	149	26	5	5	NUM
ejpam-7064	149	27	t	t	NOUN
ejpam-7064	149	28	msrm	msrm	NOUN
ejpam-7064	149	29	vim	vim	INTJ
ejpam-7064	149	30	msrm	msrm	PROPN
ejpam-7064	149	31	vim	vim	INTJ
ejpam-7064	149	32	0.00	0.00	NUM
ejpam-7064	149	33	0.25	0.25	NUM
ejpam-7064	149	34	0.50	0.50	NUM
ejpam-7064	149	35	0.75	0.75	NUM
ejpam-7064	149	36	1.00	1.00	NUM
ejpam-7064	149	37	1.25	1.25	NUM
ejpam-7064	149	38	1.50	1.50	NUM
ejpam-7064	149	39	1.75	1.75	NUM
ejpam-7064	149	40	2.00	2.00	NUM
ejpam-7064	149	41	5.15975e-06	5.15975e-06	NUM
ejpam-7064	149	42	2.75961e-06	2.75961e-06	NUM
ejpam-7064	149	43	0.18523e-05	0.18523e-05	NUM
ejpam-7064	149	44	7.13289e-06	7.13289e-06	NUM
ejpam-7064	149	45	6.28410e-06	6.28410e-06	NUM
ejpam-7064	149	46	2.63985e-06	2.63985e-06	NUM
ejpam-7064	149	47	8.02514e-05	8.02514e-05	NUM
ejpam-7064	149	48	7.01478e-05	7.01478e-05	NUM
ejpam-7064	149	49	6.52041e-05	6.52041e-05	NUM
ejpam-7064	149	50	2.15671e-04	2.15671e-04	NUM
ejpam-7064	149	51	6.32587e-04	6.32587e-04	NUM
ejpam-7064	149	52	3.25874e-04	3.25874e-04	NUM
ejpam-7064	149	53	2.32104e-03	2.32104e-03	NUM
ejpam-7064	150	1	4.01573e-03	4.01573e-03	NUM
ejpam-7064	150	2	7.25890e-02	7.25890e-02	NOUN
ejpam-7064	150	3	0.21546e-02	0.21546e-02	NOUN
ejpam-7064	150	4	0.21456e-01	0.21456e-01	NUM
ejpam-7064	150	5	0.25643e-00	0.25643e-00	NUM
ejpam-7064	150	6	8.00145e-06	8.00145e-06	NUM
ejpam-7064	150	7	3.25874e-06	3.25874e-06	NUM
ejpam-7064	150	8	6.65402e-05	6.65402e-05	NUM
ejpam-7064	150	9	0.01478e-06	0.01478e-06	NUM
ejpam-7064	150	10	2.01478e-07	2.01478e-07	NUM
ejpam-7064	150	11	3.25874e-06	3.25874e-06	NUM
ejpam-7064	150	12	0.25641e-05	0.25641e-05	NOUN
ejpam-7064	151	1	6.02587e-06	6.02587e-06	NUM
ejpam-7064	151	2	0.21478e-05	0.21478e-05	NUM
ejpam-7064	151	3	2.31456e-05	2.31456e-05	NUM
ejpam-7064	151	4	8.02145e-04	8.02145e-04	NUM
ejpam-7064	151	5	2.01597e-04	2.01597e-04	NUM
ejpam-7064	151	6	0.23145e-03	0.23145e-03	NUM
ejpam-7064	151	7	1.25489e-03	1.25489e-03	NUM
ejpam-7064	151	8	2.32014e-02	2.32014e-02	NUM
ejpam-7064	151	9	0.02546e-02	0.02546e-02	NUM
ejpam-7064	151	10	0.56479e-01	0.56479e-01	NUM
ejpam-7064	151	11	0.36547e-00	0.36547e-00	NUM
ejpam-7064	151	12	6	6	NUM
ejpam-7064	151	13	.	.	PUNCT
ejpam-7064	151	14	conclusions	conclusion	NOUN
ejpam-7064	151	15	through	through	ADP
ejpam-7064	151	16	this	this	DET
ejpam-7064	151	17	work	work	NOUN
ejpam-7064	151	18	,	,	PUNCT
ejpam-7064	151	19	the	the	DET
ejpam-7064	151	20	multi	multi	ADJ
ejpam-7064	151	21	-	-	ADJ
ejpam-7064	151	22	domain	domain	ADJ
ejpam-7064	151	23	approach	approach	NOUN
ejpam-7064	151	24	,	,	PUNCT
ejpam-7064	151	25	known	know	VERB
ejpam-7064	151	26	as	as	ADP
ejpam-7064	151	27	the	the	DET
ejpam-7064	151	28	msrm	msrm	NOUN
ejpam-7064	151	29	,	,	PUNCT
ejpam-7064	151	30	is	be	AUX
ejpam-7064	151	31	modified	modify	VERB
ejpam-7064	151	32	to	to	PART
ejpam-7064	151	33	solve	solve	VERB
ejpam-7064	151	34	the	the	DET
ejpam-7064	151	35	given	give	VERB
ejpam-7064	151	36	brusselator	brusselator	NOUN
ejpam-7064	151	37	system	system	NOUN
ejpam-7064	151	38	.	.	PUNCT
ejpam-7064	152	1	the	the	DET
ejpam-7064	152	2	numerical	numerical	PROPN
ejpam-7064	152	3	simulation	simulation	NOUN
ejpam-7064	152	4	of	of	ADP
ejpam-7064	152	5	the	the	DET
ejpam-7064	152	6	model	model	NOUN
ejpam-7064	152	7	under	under	ADP
ejpam-7064	152	8	study	study	NOUN
ejpam-7064	152	9	m.	m.	NOUN
ejpam-7064	152	10	adel	adel	PROPN
ejpam-7064	152	11	et	et	PROPN
ejpam-7064	152	12	al	al	PROPN
ejpam-7064	152	13	.	.	PUNCT
ejpam-7064	152	14	/	/	SYM
ejpam-7064	152	15	eur	eur	PROPN
ejpam-7064	152	16	.	.	PUNCT
ejpam-7064	153	1	j.	j.	PROPN
ejpam-7064	153	2	pure	pure	PROPN
ejpam-7064	153	3	appl	appl	PROPN
ejpam-7064	153	4	.	.	PROPN
ejpam-7064	153	5	math	math	PROPN
ejpam-7064	153	6	,	,	PUNCT
ejpam-7064	153	7	18	18	NUM
ejpam-7064	153	8	(	(	PUNCT
ejpam-7064	153	9	4	4	NUM
ejpam-7064	153	10	)	)	PUNCT
ejpam-7064	153	11	(	(	PUNCT
ejpam-7064	153	12	2025	2025	NUM
ejpam-7064	153	13	)	)	PUNCT
ejpam-7064	153	14	,	,	PUNCT
ejpam-7064	153	15	7064	7064	NUM
ejpam-7064	153	16	9	9	NUM
ejpam-7064	153	17	of	of	ADP
ejpam-7064	153	18	11	11	NUM
ejpam-7064	153	19	was	be	AUX
ejpam-7064	153	20	investigated	investigate	VERB
ejpam-7064	153	21	by	by	ADP
ejpam-7064	153	22	calculating	calculate	VERB
ejpam-7064	153	23	the	the	DET
ejpam-7064	153	24	relative	relative	ADJ
ejpam-7064	153	25	error	error	NOUN
ejpam-7064	153	26	with	with	ADP
ejpam-7064	153	27	various	various	ADJ
ejpam-7064	153	28	values	value	NOUN
ejpam-7064	153	29	of	of	ADP
ejpam-7064	153	30	the	the	DET
ejpam-7064	153	31	approximation	approximation	NOUN
ejpam-7064	153	32	orderm	orderm	NOUN
ejpam-7064	153	33	.	.	PUNCT
ejpam-7064	154	1	by	by	ADP
ejpam-7064	154	2	including	include	VERB
ejpam-7064	154	3	more	more	ADJ
ejpam-7064	154	4	terms	term	NOUN
ejpam-7064	154	5	from	from	ADP
ejpam-7064	154	6	the	the	DET
ejpam-7064	154	7	approximation	approximation	NOUN
ejpam-7064	154	8	solution	solution	NOUN
ejpam-7064	154	9	series	series	NOUN
ejpam-7064	154	10	,	,	PUNCT
ejpam-7064	154	11	or	or	CCONJ
ejpam-7064	154	12	by	by	ADP
ejpam-7064	154	13	raisingm	raisingm	VERB
ejpam-7064	154	14	,	,	PUNCT
ejpam-7064	154	15	we	we	PRON
ejpam-7064	154	16	may	may	AUX
ejpam-7064	154	17	also	also	ADV
ejpam-7064	154	18	regulate	regulate	VERB
ejpam-7064	154	19	the	the	DET
ejpam-7064	154	20	precision	precision	NOUN
ejpam-7064	154	21	of	of	ADP
ejpam-7064	154	22	the	the	DET
ejpam-7064	154	23	error	error	NOUN
ejpam-7064	154	24	and	and	CCONJ
ejpam-7064	154	25	lower	lower	VERB
ejpam-7064	154	26	it	it	PRON
ejpam-7064	154	27	.	.	PUNCT
ejpam-7064	155	1	by	by	ADP
ejpam-7064	155	2	assessing	assess	VERB
ejpam-7064	155	3	the	the	DET
ejpam-7064	155	4	relative	relative	ADJ
ejpam-7064	155	5	error	error	NOUN
ejpam-7064	155	6	,	,	PUNCT
ejpam-7064	155	7	we	we	PRON
ejpam-7064	155	8	can	can	AUX
ejpam-7064	155	9	ensure	ensure	VERB
ejpam-7064	155	10	that	that	SCONJ
ejpam-7064	155	11	the	the	DET
ejpam-7064	155	12	proposed	propose	VERB
ejpam-7064	155	13	technique	technique	NOUN
ejpam-7064	155	14	is	be	AUX
ejpam-7064	155	15	accurate	accurate	ADJ
ejpam-7064	155	16	and	and	CCONJ
ejpam-7064	155	17	efficient	efficient	ADJ
ejpam-7064	155	18	.	.	PUNCT
ejpam-7064	156	1	the	the	DET
ejpam-7064	156	2	proposed	propose	VERB
ejpam-7064	156	3	method	method	NOUN
ejpam-7064	156	4	shows	show	VERB
ejpam-7064	156	5	its	its	PRON
ejpam-7064	156	6	advantage	advantage	NOUN
ejpam-7064	156	7	in	in	ADP
ejpam-7064	156	8	that	that	DET
ejpam-7064	156	9	calculations	calculation	NOUN
ejpam-7064	156	10	are	be	AUX
ejpam-7064	156	11	relatively	relatively	ADV
ejpam-7064	156	12	easy	easy	ADJ
ejpam-7064	156	13	to	to	PART
ejpam-7064	156	14	follow	follow	VERB
ejpam-7064	156	15	and	and	CCONJ
ejpam-7064	156	16	understand	understand	VERB
ejpam-7064	156	17	.	.	PUNCT
ejpam-7064	157	1	the	the	DET
ejpam-7064	157	2	results	result	NOUN
ejpam-7064	157	3	obtained	obtain	VERB
ejpam-7064	157	4	by	by	ADP
ejpam-7064	157	5	the	the	DET
ejpam-7064	157	6	msrm	msrm	NOUN
ejpam-7064	157	7	are	be	AUX
ejpam-7064	157	8	accurate	accurate	ADJ
ejpam-7064	157	9	,	,	PUNCT
ejpam-7064	157	10	valid	valid	ADJ
ejpam-7064	157	11	for	for	ADP
ejpam-7064	157	12	a	a	DET
ejpam-7064	157	13	longer	long	ADJ
ejpam-7064	157	14	period	period	NOUN
ejpam-7064	157	15	,	,	PUNCT
ejpam-7064	157	16	and	and	CCONJ
ejpam-7064	157	17	highly	highly	ADV
ejpam-7064	157	18	compatible	compatible	ADJ
ejpam-7064	157	19	with	with	ADP
ejpam-7064	157	20	those	those	PRON
ejpam-7064	157	21	obtained	obtain	VERB
ejpam-7064	157	22	by	by	ADP
ejpam-7064	157	23	the	the	DET
ejpam-7064	157	24	rk4	rk4	NOUN
ejpam-7064	157	25	m	m	NOUN
ejpam-7064	157	26	and	and	CCONJ
ejpam-7064	157	27	the	the	DET
ejpam-7064	157	28	vim	vim	NOUN
ejpam-7064	157	29	(	(	PUNCT
ejpam-7064	157	30	but	but	CCONJ
ejpam-7064	157	31	in	in	ADP
ejpam-7064	157	32	small	small	ADJ
ejpam-7064	157	33	intervals	interval	NOUN
ejpam-7064	157	34	)	)	PUNCT
ejpam-7064	157	35	.	.	PUNCT
ejpam-7064	158	1	hence	hence	ADV
ejpam-7064	158	2	,	,	PUNCT
ejpam-7064	158	3	this	this	DET
ejpam-7064	158	4	technique	technique	NOUN
ejpam-7064	158	5	can	can	AUX
ejpam-7064	158	6	be	be	AUX
ejpam-7064	158	7	used	use	VERB
ejpam-7064	158	8	to	to	PART
ejpam-7064	158	9	solve	solve	VERB
ejpam-7064	158	10	many	many	ADJ
ejpam-7064	158	11	other	other	ADJ
ejpam-7064	158	12	nonlinear	nonlinear	ADJ
ejpam-7064	158	13	problems	problem	NOUN
ejpam-7064	158	14	that	that	PRON
ejpam-7064	158	15	appear	appear	VERB
ejpam-7064	158	16	in	in	ADP
ejpam-7064	158	17	the	the	DET
ejpam-7064	158	18	applied	apply	VERB
ejpam-7064	158	19	sciences	science	NOUN
ejpam-7064	158	20	and	and	CCONJ
ejpam-7064	158	21	engineering	engineering	NOUN
ejpam-7064	158	22	applications	application	NOUN
ejpam-7064	158	23	.	.	PUNCT
ejpam-7064	159	1	the	the	DET
ejpam-7064	159	2	outcomes	outcome	NOUN
ejpam-7064	159	3	additionally	additionally	ADV
ejpam-7064	159	4	demonstrate	demonstrate	VERB
ejpam-7064	159	5	the	the	DET
ejpam-7064	159	6	proposed	propose	VERB
ejpam-7064	159	7	msrm	msrm	PROPN
ejpam-7064	159	8	’s	’s	PART
ejpam-7064	159	9	accuracy	accuracy	NOUN
ejpam-7064	159	10	,	,	PUNCT
ejpam-7064	159	11	computational	computational	ADJ
ejpam-7064	159	12	effectiveness	effectiveness	NOUN
ejpam-7064	159	13	,	,	PUNCT
ejpam-7064	159	14	and	and	CCONJ
ejpam-7064	159	15	dependability	dependability	NOUN
ejpam-7064	159	16	as	as	ADP
ejpam-7064	159	17	a	a	DET
ejpam-7064	159	18	solution	solution	NOUN
ejpam-7064	159	19	for	for	ADP
ejpam-7064	159	20	solving	solve	VERB
ejpam-7064	159	21	this	this	DET
ejpam-7064	159	22	model	model	NOUN
ejpam-7064	159	23	.	.	PUNCT
ejpam-7064	160	1	all	all	DET
ejpam-7064	160	2	the	the	DET
ejpam-7064	160	3	numerical	numerical	ADJ
ejpam-7064	160	4	results	result	NOUN
ejpam-7064	160	5	were	be	AUX
ejpam-7064	160	6	obtained	obtain	VERB
ejpam-7064	160	7	with	with	ADP
ejpam-7064	160	8	the	the	DET
ejpam-7064	160	9	help	help	NOUN
ejpam-7064	160	10	of	of	ADP
ejpam-7064	160	11	the	the	DET
ejpam-7064	160	12	mathematica	mathematica	PROPN
ejpam-7064	160	13	software	software	PROPN
ejpam-7064	160	14	program	program	PROPN
ejpam-7064	160	15	.	.	PUNCT
ejpam-7064	161	1	as	as	ADP
ejpam-7064	161	2	future	future	ADJ
ejpam-7064	161	3	work	work	NOUN
ejpam-7064	161	4	and	and	CCONJ
ejpam-7064	161	5	an	an	DET
ejpam-7064	161	6	attempt	attempt	NOUN
ejpam-7064	161	7	to	to	PART
ejpam-7064	161	8	generalize	generalize	VERB
ejpam-7064	161	9	the	the	DET
ejpam-7064	161	10	results	result	NOUN
ejpam-7064	161	11	obtained	obtain	VERB
ejpam-7064	161	12	in	in	ADP
ejpam-7064	161	13	this	this	DET
ejpam-7064	161	14	paper	paper	NOUN
ejpam-7064	161	15	,	,	PUNCT
ejpam-7064	161	16	we	we	PRON
ejpam-7064	161	17	will	will	AUX
ejpam-7064	161	18	try	try	VERB
ejpam-7064	161	19	to	to	PART
ejpam-7064	161	20	treat	treat	VERB
ejpam-7064	161	21	one	one	NUM
ejpam-7064	161	22	or	or	CCONJ
ejpam-7064	161	23	all	all	PRON
ejpam-7064	161	24	of	of	ADP
ejpam-7064	161	25	the	the	DET
ejpam-7064	161	26	following	following	ADJ
ejpam-7064	161	27	suggestions	suggestion	NOUN
ejpam-7064	161	28	:	:	PUNCT
ejpam-7064	161	29	(	(	PUNCT
ejpam-7064	161	30	i	i	NOUN
ejpam-7064	161	31	)	)	PUNCT
ejpam-7064	161	32	we	we	PRON
ejpam-7064	161	33	deal	deal	VERB
ejpam-7064	161	34	with	with	ADP
ejpam-7064	161	35	the	the	DET
ejpam-7064	161	36	same	same	ADJ
ejpam-7064	161	37	problem	problem	NOUN
ejpam-7064	161	38	,	,	PUNCT
ejpam-7064	161	39	but	but	CCONJ
ejpam-7064	161	40	using	use	VERB
ejpam-7064	161	41	a	a	DET
ejpam-7064	161	42	different	different	ADJ
ejpam-7064	161	43	type	type	NOUN
ejpam-7064	161	44	of	of	ADP
ejpam-7064	161	45	polynomial	polynomial	ADJ
ejpam-7064	161	46	.	.	PUNCT
ejpam-7064	162	1	(	(	PUNCT
ejpam-7064	162	2	ii	ii	NOUN
ejpam-7064	162	3	)	)	PUNCT
ejpam-7064	162	4	we	we	PRON
ejpam-7064	162	5	consider	consider	VERB
ejpam-7064	162	6	the	the	DET
ejpam-7064	162	7	model	model	NOUN
ejpam-7064	162	8	in	in	ADP
ejpam-7064	162	9	its	its	PRON
ejpam-7064	162	10	fractional	fractional	ADJ
ejpam-7064	162	11	form	form	NOUN
ejpam-7064	162	12	and	and	CCONJ
ejpam-7064	162	13	solve	solve	VERB
ejpam-7064	162	14	it	it	PRON
ejpam-7064	162	15	numerically	numerically	ADV
ejpam-7064	162	16	with	with	ADP
ejpam-7064	162	17	the	the	DET
ejpam-7064	162	18	help	help	NOUN
ejpam-7064	162	19	of	of	ADP
ejpam-7064	162	20	a	a	DET
ejpam-7064	162	21	suitable	suitable	ADJ
ejpam-7064	162	22	numerical	numerical	ADJ
ejpam-7064	162	23	/	/	SYM
ejpam-7064	162	24	approximate	approximate	ADJ
ejpam-7064	162	25	method	method	NOUN
ejpam-7064	162	26	.	.	PUNCT
ejpam-7064	163	1	(	(	PUNCT
ejpam-7064	163	2	iii	iii	X
ejpam-7064	163	3	)	)	PUNCT
ejpam-7064	163	4	we	we	PRON
ejpam-7064	163	5	try	try	VERB
ejpam-7064	163	6	to	to	PART
ejpam-7064	163	7	modify	modify	VERB
ejpam-7064	163	8	the	the	DET
ejpam-7064	163	9	proposed	propose	VERB
ejpam-7064	163	10	method	method	NOUN
ejpam-7064	163	11	in	in	ADP
ejpam-7064	163	12	the	the	DET
ejpam-7064	163	13	current	current	ADJ
ejpam-7064	163	14	work	work	NOUN
ejpam-7064	163	15	to	to	PART
ejpam-7064	163	16	treat	treat	VERB
ejpam-7064	163	17	some	some	DET
ejpam-7064	163	18	weaknesses	weakness	NOUN
ejpam-7064	163	19	of	of	ADP
ejpam-7064	163	20	the	the	DET
ejpam-7064	163	21	method	method	NOUN
ejpam-7064	163	22	,	,	PUNCT
ejpam-7064	163	23	such	such	ADJ
ejpam-7064	163	24	as	as	ADP
ejpam-7064	163	25	the	the	DET
ejpam-7064	163	26	low	low	ADJ
ejpam-7064	163	27	accuracy	accuracy	NOUN
ejpam-7064	163	28	of	of	ADP
ejpam-7064	163	29	the	the	DET
ejpam-7064	163	30	resulting	result	VERB
ejpam-7064	163	31	solutions	solution	NOUN
ejpam-7064	163	32	compared	compare	VERB
ejpam-7064	163	33	to	to	ADP
ejpam-7064	163	34	other	other	ADJ
ejpam-7064	163	35	methods	method	NOUN
ejpam-7064	163	36	,	,	PUNCT
ejpam-7064	163	37	and	and	CCONJ
ejpam-7064	163	38	then	then	ADV
ejpam-7064	163	39	use	use	VERB
ejpam-7064	163	40	it	it	PRON
ejpam-7064	163	41	for	for	ADP
ejpam-7064	163	42	solving	solve	VERB
ejpam-7064	163	43	numerically	numerically	ADV
ejpam-7064	163	44	some	some	DET
ejpam-7064	163	45	other	other	ADJ
ejpam-7064	163	46	models	model	NOUN
ejpam-7064	163	47	.	.	PUNCT
ejpam-7064	164	1	competing	compete	VERB
ejpam-7064	164	2	interests	interest	NOUN
ejpam-7064	164	3	:	:	PUNCT
ejpam-7064	164	4	there	there	PRON
ejpam-7064	164	5	is	be	VERB
ejpam-7064	164	6	no	no	DET
ejpam-7064	164	7	conflict	conflict	NOUN
ejpam-7064	164	8	of	of	ADP
ejpam-7064	164	9	interest	interest	NOUN
ejpam-7064	164	10	.	.	PUNCT
ejpam-7064	165	1	authors	author	NOUN
ejpam-7064	165	2	’	'	PUNCT
ejpam-7064	165	3	contributions	contribution	NOUN
ejpam-7064	165	4	:	:	PUNCT
ejpam-7064	165	5	this	this	DET
ejpam-7064	165	6	study	study	NOUN
ejpam-7064	165	7	was	be	AUX
ejpam-7064	165	8	written	write	VERB
ejpam-7064	165	9	in	in	ADP
ejpam-7064	165	10	collaboration	collaboration	NOUN
ejpam-7064	165	11	the	the	DET
ejpam-7064	165	12	authors	author	NOUN
ejpam-7064	165	13	.	.	PUNCT
ejpam-7064	166	1	acknowledgements	acknowledgement	NOUN
ejpam-7064	166	2	the	the	DET
ejpam-7064	166	3	researchers	researcher	NOUN
ejpam-7064	166	4	wish	wish	VERB
ejpam-7064	166	5	to	to	PART
ejpam-7064	166	6	extend	extend	VERB
ejpam-7064	166	7	their	their	PRON
ejpam-7064	166	8	sincere	sincere	ADJ
ejpam-7064	166	9	gratitude	gratitude	NOUN
ejpam-7064	166	10	to	to	ADP
ejpam-7064	166	11	the	the	DET
ejpam-7064	166	12	deanship	deanship	NOUN
ejpam-7064	166	13	of	of	ADP
ejpam-7064	166	14	scientific	scientific	ADJ
ejpam-7064	166	15	research	research	NOUN
ejpam-7064	166	16	at	at	ADP
ejpam-7064	166	17	the	the	DET
ejpam-7064	166	18	islamic	islamic	PROPN
ejpam-7064	166	19	university	university	PROPN
ejpam-7064	166	20	of	of	ADP
ejpam-7064	166	21	madinah	madinah	PROPN
ejpam-7064	166	22	for	for	ADP
ejpam-7064	166	23	the	the	DET
ejpam-7064	166	24	support	support	NOUN
ejpam-7064	166	25	provided	provide	VERB
ejpam-7064	166	26	to	to	ADP
ejpam-7064	166	27	the	the	DET
ejpam-7064	166	28	postpublishing	postpublishe	VERB
ejpam-7064	166	29	program	program	NOUN
ejpam-7064	166	30	.	.	PUNCT
ejpam-7064	167	1	references	reference	NOUN
ejpam-7064	167	2	[	[	X
ejpam-7064	167	3	1	1	NUM
ejpam-7064	167	4	]	]	PUNCT
ejpam-7064	167	5	m.	m.	NOUN
ejpam-7064	167	6	m.	m.	NOUN
ejpam-7064	167	7	khader	khader	PROPN
ejpam-7064	167	8	.	.	PUNCT
ejpam-7064	168	1	on	on	ADP
ejpam-7064	168	2	the	the	DET
ejpam-7064	168	3	numerical	numerical	ADJ
ejpam-7064	168	4	solutions	solution	NOUN
ejpam-7064	168	5	for	for	ADP
ejpam-7064	168	6	the	the	DET
ejpam-7064	168	7	fractional	fractional	ADJ
ejpam-7064	168	8	diffusion	diffusion	NOUN
ejpam-7064	168	9	equation	equation	NOUN
ejpam-7064	168	10	.	.	PUNCT
ejpam-7064	169	1	communications	communication	NOUN
ejpam-7064	169	2	in	in	ADP
ejpam-7064	169	3	nonlinear	nonlinear	ADJ
ejpam-7064	169	4	science	science	NOUN
ejpam-7064	169	5	and	and	CCONJ
ejpam-7064	169	6	numerical	numerical	ADJ
ejpam-7064	169	7	simulations	simulation	NOUN
ejpam-7064	169	8	,	,	PUNCT
ejpam-7064	169	9	16:2535–2542	16:2535–2542	NUM
ejpam-7064	169	10	,	,	PUNCT
ejpam-7064	169	11	2011	2011	NUM
ejpam-7064	169	12	.	.	PUNCT
ejpam-7064	170	1	[	[	X
ejpam-7064	170	2	2	2	NUM
ejpam-7064	170	3	]	]	PUNCT
ejpam-7064	170	4	m.	m.	NOUN
ejpam-7064	170	5	m.	m.	NOUN
ejpam-7064	170	6	khader	khader	PROPN
ejpam-7064	170	7	and	and	CCONJ
ejpam-7064	170	8	m.	m.	PROPN
ejpam-7064	170	9	adel	adel	PROPN
ejpam-7064	170	10	.	.	PUNCT
ejpam-7064	171	1	chebyshev	chebyshev	PROPN
ejpam-7064	171	2	wavelet	wavelet	NOUN
ejpam-7064	171	3	procedure	procedure	NOUN
ejpam-7064	171	4	for	for	ADP
ejpam-7064	171	5	solving	solve	VERB
ejpam-7064	171	6	fldes	flde	NOUN
ejpam-7064	171	7	.	.	PUNCT
ejpam-7064	172	1	acta	acta	PROPN
ejpam-7064	172	2	applicandae	applicandae	PROPN
ejpam-7064	172	3	mathematicae	mathematicae	PROPN
ejpam-7064	172	4	,	,	PUNCT
ejpam-7064	172	5	158(1):1–10	158(1):1–10	NUM
ejpam-7064	172	6	,	,	PUNCT
ejpam-7064	172	7	2018	2018	NUM
ejpam-7064	172	8	.	.	PUNCT
ejpam-7064	173	1	[	[	X
ejpam-7064	173	2	3	3	X
ejpam-7064	173	3	]	]	X
ejpam-7064	173	4	o.	o.	PROPN
ejpam-7064	173	5	abdulaziz	abdulaziz	PROPN
ejpam-7064	173	6	,	,	PUNCT
ejpam-7064	173	7	n.	n.	PROPN
ejpam-7064	173	8	f.	f.	PROPN
ejpam-7064	173	9	m.	m.	PROPN
ejpam-7064	173	10	noor	noor	PROPN
ejpam-7064	173	11	,	,	PUNCT
ejpam-7064	173	12	i.	i.	PROPN
ejpam-7064	173	13	hashim	hashim	PROPN
ejpam-7064	173	14	,	,	PUNCT
ejpam-7064	173	15	and	and	CCONJ
ejpam-7064	173	16	m.	m.	PROPN
ejpam-7064	173	17	s.	s.	PROPN
ejpam-7064	173	18	m.	m.	PROPN
ejpam-7064	173	19	noorani	noorani	PROPN
ejpam-7064	173	20	.	.	PUNCT
ejpam-7064	174	1	further	further	ADJ
ejpam-7064	174	2	accuracy	accuracy	NOUN
ejpam-7064	174	3	tests	test	NOUN
ejpam-7064	174	4	on	on	ADP
ejpam-7064	174	5	the	the	DET
ejpam-7064	174	6	adomian	adomian	NOUN
ejpam-7064	174	7	decomposition	decomposition	NOUN
ejpam-7064	174	8	method	method	NOUN
ejpam-7064	174	9	for	for	ADP
ejpam-7064	174	10	chaotic	chaotic	ADJ
ejpam-7064	174	11	systems	system	NOUN
ejpam-7064	174	12	.	.	PUNCT
ejpam-7064	175	1	chaos	chaos	NOUN
ejpam-7064	175	2	solitons	soliton	NOUN
ejpam-7064	175	3	and	and	CCONJ
ejpam-7064	175	4	fractals	fractal	NOUN
ejpam-7064	175	5	,	,	PUNCT
ejpam-7064	175	6	36:1405–1411	36:1405–1411	NUM
ejpam-7064	175	7	,	,	PUNCT
ejpam-7064	175	8	2008	2008	NUM
ejpam-7064	175	9	.	.	PUNCT
ejpam-7064	176	1	[	[	X
ejpam-7064	176	2	4	4	X
ejpam-7064	176	3	]	]	PUNCT
ejpam-7064	176	4	b.	b.	PROPN
ejpam-7064	176	5	batiha	batiha	PROPN
ejpam-7064	176	6	,	,	PUNCT
ejpam-7064	176	7	m.	m.	NOUN
ejpam-7064	176	8	s.	s.	PROPN
ejpam-7064	176	9	m.	m.	PROPN
ejpam-7064	176	10	noorani	noorani	PROPN
ejpam-7064	176	11	,	,	PUNCT
ejpam-7064	176	12	i.	i.	PROPN
ejpam-7064	176	13	hashim	hashim	PROPN
ejpam-7064	176	14	,	,	PUNCT
ejpam-7064	176	15	and	and	CCONJ
ejpam-7064	176	16	e.	e.	PROPN
ejpam-7064	176	17	s.	s.	PROPN
ejpam-7064	176	18	ismail	ismail	PROPN
ejpam-7064	176	19	.	.	PUNCT
ejpam-7064	177	1	the	the	DET
ejpam-7064	177	2	multistage	multistage	NOUN
ejpam-7064	177	3	variational	variational	ADJ
ejpam-7064	177	4	iteration	iteration	NOUN
ejpam-7064	177	5	method	method	NOUN
ejpam-7064	177	6	for	for	ADP
ejpam-7064	177	7	a	a	DET
ejpam-7064	177	8	class	class	NOUN
ejpam-7064	177	9	of	of	ADP
ejpam-7064	177	10	nonlinear	nonlinear	ADJ
ejpam-7064	177	11	systems	system	NOUN
ejpam-7064	177	12	of	of	ADP
ejpam-7064	177	13	odes	ode	NOUN
ejpam-7064	177	14	.	.	PUNCT
ejpam-7064	178	1	physica	physica	PROPN
ejpam-7064	178	2	scripta	scripta	PROPN
ejpam-7064	178	3	,	,	PUNCT
ejpam-7064	178	4	76:388	76:388	NUM
ejpam-7064	178	5	–	–	PUNCT
ejpam-7064	178	6	392	392	NUM
ejpam-7064	178	7	,	,	PUNCT
ejpam-7064	178	8	2007	2007	NUM
ejpam-7064	178	9	.	.	PUNCT
ejpam-7064	179	1	m.	m.	NOUN
ejpam-7064	179	2	adel	adel	PROPN
ejpam-7064	179	3	et	et	PROPN
ejpam-7064	179	4	al	al	PROPN
ejpam-7064	179	5	.	.	PUNCT
ejpam-7064	179	6	/	/	SYM
ejpam-7064	179	7	eur	eur	PROPN
ejpam-7064	179	8	.	.	PUNCT
ejpam-7064	180	1	j.	j.	PROPN
ejpam-7064	180	2	pure	pure	PROPN
ejpam-7064	180	3	appl	appl	PROPN
ejpam-7064	180	4	.	.	PROPN
ejpam-7064	180	5	math	math	PROPN
ejpam-7064	180	6	,	,	PUNCT
ejpam-7064	180	7	18	18	NUM
ejpam-7064	180	8	(	(	PUNCT
ejpam-7064	180	9	4	4	NUM
ejpam-7064	180	10	)	)	PUNCT
ejpam-7064	180	11	(	(	PUNCT
ejpam-7064	180	12	2025	2025	NUM
ejpam-7064	180	13	)	)	PUNCT
ejpam-7064	180	14	,	,	PUNCT
ejpam-7064	180	15	7064	7064	NUM
ejpam-7064	180	16	10	10	NUM
ejpam-7064	180	17	of	of	ADP
ejpam-7064	180	18	11	11	NUM
ejpam-7064	180	19	[	[	SYM
ejpam-7064	180	20	5	5	NUM
ejpam-7064	180	21	]	]	PUNCT
ejpam-7064	180	22	m.	m.	NOUN
ejpam-7064	180	23	s.	s.	PROPN
ejpam-7064	180	24	h.	h.	PROPN
ejpam-7064	180	25	chowdhury	chowdhury	PROPN
ejpam-7064	180	26	,	,	PUNCT
ejpam-7064	180	27	i.	i.	PROPN
ejpam-7064	180	28	hashim	hashim	PROPN
ejpam-7064	180	29	,	,	PUNCT
ejpam-7064	180	30	and	and	CCONJ
ejpam-7064	180	31	s.	s.	PROPN
ejpam-7064	180	32	momani	momani	PROPN
ejpam-7064	180	33	.	.	PUNCT
ejpam-7064	181	1	the	the	DET
ejpam-7064	181	2	multistage	multistage	NOUN
ejpam-7064	181	3	homotopyperturbation	homotopyperturbation	NOUN
ejpam-7064	181	4	method	method	NOUN
ejpam-7064	181	5	:	:	PUNCT
ejpam-7064	181	6	a	a	DET
ejpam-7064	181	7	powerful	powerful	ADJ
ejpam-7064	181	8	scheme	scheme	NOUN
ejpam-7064	181	9	for	for	ADP
ejpam-7064	181	10	handling	handle	VERB
ejpam-7064	181	11	the	the	DET
ejpam-7064	181	12	lorenz	lorenz	PROPN
ejpam-7064	181	13	system	system	NOUN
ejpam-7064	181	14	.	.	PUNCT
ejpam-7064	182	1	chaos	chaos	NOUN
ejpam-7064	182	2	solitons	soliton	NOUN
ejpam-7064	182	3	and	and	CCONJ
ejpam-7064	182	4	fractals	fractal	NOUN
ejpam-7064	182	5	,	,	PUNCT
ejpam-7064	182	6	40:1929–1937	40:1929–1937	NUM
ejpam-7064	182	7	,	,	PUNCT
ejpam-7064	182	8	2009	2009	NUM
ejpam-7064	182	9	.	.	PUNCT
ejpam-7064	183	1	[	[	X
ejpam-7064	183	2	6	6	NUM
ejpam-7064	183	3	]	]	PUNCT
ejpam-7064	183	4	s.	s.	PROPN
ejpam-7064	183	5	s.	s.	PROPN
ejpam-7064	183	6	motsa	motsa	PROPN
ejpam-7064	183	7	,	,	PUNCT
ejpam-7064	183	8	p.	p.	PROPN
ejpam-7064	183	9	dlamini	dlamini	PROPN
ejpam-7064	183	10	,	,	PUNCT
ejpam-7064	183	11	and	and	CCONJ
ejpam-7064	183	12	m.	m.	NOUN
ejpam-7064	183	13	khumalo	khumalo	PROPN
ejpam-7064	183	14	.	.	PUNCT
ejpam-7064	184	1	a	a	DET
ejpam-7064	184	2	new	new	ADJ
ejpam-7064	184	3	multistage	multistage	NOUN
ejpam-7064	184	4	spectral	spectral	ADJ
ejpam-7064	184	5	relaxation	relaxation	NOUN
ejpam-7064	184	6	method	method	NOUN
ejpam-7064	184	7	for	for	ADP
ejpam-7064	184	8	solving	solve	VERB
ejpam-7064	184	9	chaotic	chaotic	ADJ
ejpam-7064	184	10	initial	initial	ADJ
ejpam-7064	184	11	value	value	NOUN
ejpam-7064	184	12	systems	system	NOUN
ejpam-7064	184	13	.	.	PUNCT
ejpam-7064	185	1	nonlinear	nonlinear	ADJ
ejpam-7064	185	2	dynamics	dynamic	NOUN
ejpam-7064	185	3	,	,	PUNCT
ejpam-7064	185	4	72:265–283	72:265–283	NUM
ejpam-7064	185	5	,	,	PUNCT
ejpam-7064	185	6	2013	2013	NUM
ejpam-7064	185	7	.	.	PUNCT
ejpam-7064	186	1	[	[	X
ejpam-7064	186	2	7	7	X
ejpam-7064	186	3	]	]	X
ejpam-7064	186	4	s.	s.	PROPN
ejpam-7064	186	5	s.	s.	PROPN
ejpam-7064	186	6	motsa	motsa	PROPN
ejpam-7064	186	7	,	,	PUNCT
ejpam-7064	186	8	p.	p.	PROPN
ejpam-7064	186	9	g.	g.	PROPN
ejpam-7064	186	10	dlamini	dlamini	PROPN
ejpam-7064	186	11	,	,	PUNCT
ejpam-7064	186	12	and	and	CCONJ
ejpam-7064	186	13	m.	m.	NOUN
ejpam-7064	186	14	khumalo	khumalo	PROPN
ejpam-7064	186	15	.	.	PUNCT
ejpam-7064	187	1	solving	solve	VERB
ejpam-7064	187	2	hyperchaotic	hyperchaotic	ADJ
ejpam-7064	187	3	systems	system	NOUN
ejpam-7064	187	4	using	use	VERB
ejpam-7064	187	5	the	the	DET
ejpam-7064	187	6	spectral	spectral	ADJ
ejpam-7064	187	7	relaxation	relaxation	NOUN
ejpam-7064	187	8	method	method	NOUN
ejpam-7064	187	9	.	.	PUNCT
ejpam-7064	188	1	abstract	abstract	ADJ
ejpam-7064	188	2	and	and	CCONJ
ejpam-7064	188	3	applied	apply	VERB
ejpam-7064	188	4	analysis	analysis	NOUN
ejpam-7064	188	5	,	,	PUNCT
ejpam-7064	188	6	pages	page	NOUN
ejpam-7064	188	7	1–18	1–18	NUM
ejpam-7064	188	8	,	,	PUNCT
ejpam-7064	188	9	2012	2012	NUM
ejpam-7064	188	10	.	.	PUNCT
ejpam-7064	189	1	[	[	X
ejpam-7064	189	2	8	8	NUM
ejpam-7064	189	3	]	]	PUNCT
ejpam-7064	189	4	m.	m.	NOUN
ejpam-7064	189	5	s.	s.	PROPN
ejpam-7064	189	6	khan	khan	PROPN
ejpam-7064	189	7	and	and	CCONJ
ejpam-7064	189	8	m.	m.	PROPN
ejpam-7064	189	9	i.	i.	PROPN
ejpam-7064	189	10	khan	khan	PROPN
ejpam-7064	189	11	.	.	PUNCT
ejpam-7064	190	1	a	a	DET
ejpam-7064	190	2	novel	novel	ADJ
ejpam-7064	190	3	numerical	numerical	ADJ
ejpam-7064	190	4	algorithm	algorithm	NOUN
ejpam-7064	190	5	based	base	VERB
ejpam-7064	190	6	on	on	ADP
ejpam-7064	190	7	galerkin	galerkin	ADJ
ejpam-7064	190	8	-	-	PUNCT
ejpam-7064	190	9	petrov	petrov	PROPN
ejpam-7064	190	10	time	time	NOUN
ejpam-7064	190	11	-	-	PUNCT
ejpam-7064	190	12	discretization	discretization	NOUN
ejpam-7064	190	13	method	method	NOUN
ejpam-7064	190	14	for	for	ADP
ejpam-7064	190	15	solving	solve	VERB
ejpam-7064	190	16	chaotic	chaotic	ADJ
ejpam-7064	190	17	nonlinear	nonlinear	ADJ
ejpam-7064	190	18	dynamical	dynamical	ADJ
ejpam-7064	190	19	systems	system	NOUN
ejpam-7064	190	20	.	.	PUNCT
ejpam-7064	191	1	nonlinear	nonlinear	ADJ
ejpam-7064	191	2	dynamics	dynamic	NOUN
ejpam-7064	191	3	,	,	PUNCT
ejpam-7064	191	4	91(3):1555–1569	91(3):1555–1569	NUM
ejpam-7064	191	5	,	,	PUNCT
ejpam-7064	191	6	2018	2018	NUM
ejpam-7064	191	7	.	.	PUNCT
ejpam-7064	192	1	[	[	X
ejpam-7064	192	2	9	9	NUM
ejpam-7064	192	3	]	]	PUNCT
ejpam-7064	192	4	s.	s.	PROPN
ejpam-7064	192	5	s.	s.	PROPN
ejpam-7064	192	6	motsa	motsa	PROPN
ejpam-7064	192	7	.	.	PUNCT
ejpam-7064	193	1	a	a	DET
ejpam-7064	193	2	new	new	ADJ
ejpam-7064	193	3	piecewise	piecewise	NOUN
ejpam-7064	193	4	-	-	PUNCT
ejpam-7064	193	5	quasilinearization	quasilinearization	NOUN
ejpam-7064	193	6	method	method	NOUN
ejpam-7064	193	7	for	for	ADP
ejpam-7064	193	8	solving	solve	VERB
ejpam-7064	193	9	chaotic	chaotic	ADJ
ejpam-7064	193	10	systems	system	NOUN
ejpam-7064	193	11	of	of	ADP
ejpam-7064	193	12	initial	initial	ADJ
ejpam-7064	193	13	value	value	NOUN
ejpam-7064	193	14	problems	problem	NOUN
ejpam-7064	193	15	.	.	PUNCT
ejpam-7064	194	1	central	central	ADJ
ejpam-7064	194	2	european	european	PROPN
ejpam-7064	194	3	journal	journal	PROPN
ejpam-7064	194	4	of	of	ADP
ejpam-7064	194	5	physics	physics	PROPN
ejpam-7064	194	6	,	,	PUNCT
ejpam-7064	194	7	10(4):936–946	10(4):936–946	PROPN
ejpam-7064	194	8	,	,	PUNCT
ejpam-7064	194	9	2012	2012	NUM
ejpam-7064	194	10	.	.	PUNCT
ejpam-7064	195	1	[	[	X
ejpam-7064	195	2	10	10	NUM
ejpam-7064	195	3	]	]	X
ejpam-7064	195	4	m.	m.	NOUN
ejpam-7064	195	5	karimi	karimi	PROPN
ejpam-7064	195	6	and	and	CCONJ
ejpam-7064	195	7	h.	h.	PROPN
ejpam-7064	195	8	s.	s.	PROPN
ejpam-7064	195	9	nik	nik	PROPN
ejpam-7064	195	10	.	.	PUNCT
ejpam-7064	195	11	a	a	DET
ejpam-7064	195	12	piecewise	piecewise	NOUN
ejpam-7064	195	13	spectral	spectral	ADJ
ejpam-7064	195	14	method	method	NOUN
ejpam-7064	195	15	for	for	ADP
ejpam-7064	195	16	solving	solve	VERB
ejpam-7064	195	17	the	the	DET
ejpam-7064	195	18	chaotic	chaotic	ADJ
ejpam-7064	195	19	control	control	NOUN
ejpam-7064	195	20	problems	problem	NOUN
ejpam-7064	195	21	of	of	ADP
ejpam-7064	195	22	the	the	DET
ejpam-7064	195	23	hyperchaotic	hyperchaotic	ADJ
ejpam-7064	195	24	finance	finance	NOUN
ejpam-7064	195	25	system	system	NOUN
ejpam-7064	195	26	.	.	PUNCT
ejpam-7064	196	1	international	international	ADJ
ejpam-7064	196	2	journal	journal	PROPN
ejpam-7064	196	3	of	of	ADP
ejpam-7064	196	4	numerical	numerical	PROPN
ejpam-7064	196	5	modelling	modelling	NOUN
ejpam-7064	196	6	:	:	PUNCT
ejpam-7064	196	7	electronic	electronic	ADJ
ejpam-7064	196	8	networks	network	NOUN
ejpam-7064	196	9	,	,	PUNCT
ejpam-7064	196	10	devices	device	NOUN
ejpam-7064	196	11	and	and	CCONJ
ejpam-7064	196	12	fields	field	NOUN
ejpam-7064	196	13	,	,	PUNCT
ejpam-7064	196	14	31(3):1–14	31(3):1–14	NUM
ejpam-7064	196	15	,	,	PUNCT
ejpam-7064	196	16	2018	2018	NUM
ejpam-7064	196	17	.	.	PUNCT
ejpam-7064	197	1	[	[	X
ejpam-7064	197	2	11	11	NUM
ejpam-7064	197	3	]	]	X
ejpam-7064	197	4	d.	d.	PROPN
ejpam-7064	197	5	mathale	mathale	PROPN
ejpam-7064	197	6	,	,	PUNCT
ejpam-7064	197	7	p.	p.	PROPN
ejpam-7064	197	8	g.	g.	PROPN
ejpam-7064	197	9	dlamini	dlamini	PROPN
ejpam-7064	197	10	,	,	PUNCT
ejpam-7064	197	11	and	and	CCONJ
ejpam-7064	197	12	m.	m.	NOUN
ejpam-7064	197	13	khumalo	khumalo	PROPN
ejpam-7064	197	14	.	.	PUNCT
ejpam-7064	198	1	compact	compact	ADJ
ejpam-7064	198	2	finite	finite	ADJ
ejpam-7064	198	3	difference	difference	NOUN
ejpam-7064	198	4	relaxation	relaxation	NOUN
ejpam-7064	198	5	method	method	NOUN
ejpam-7064	198	6	for	for	ADP
ejpam-7064	198	7	chaotic	chaotic	ADJ
ejpam-7064	198	8	and	and	CCONJ
ejpam-7064	198	9	hyperchaotic	hyperchaotic	ADJ
ejpam-7064	198	10	initial	initial	ADJ
ejpam-7064	198	11	value	value	NOUN
ejpam-7064	198	12	systems	system	NOUN
ejpam-7064	198	13	.	.	PUNCT
ejpam-7064	199	1	computational	computational	ADJ
ejpam-7064	199	2	and	and	CCONJ
ejpam-7064	199	3	applied	applied	ADJ
ejpam-7064	199	4	mathematics	mathematic	NOUN
ejpam-7064	199	5	,	,	PUNCT
ejpam-7064	199	6	37(4):5187–5202	37(4):5187–5202	NUM
ejpam-7064	199	7	,	,	PUNCT
ejpam-7064	199	8	2018	2018	NUM
ejpam-7064	199	9	.	.	PUNCT
ejpam-7064	200	1	[	[	X
ejpam-7064	200	2	12	12	NUM
ejpam-7064	200	3	]	]	PUNCT
ejpam-7064	200	4	m.	m.	NOUN
ejpam-7064	200	5	m.	m.	NOUN
ejpam-7064	200	6	khader	khader	PROPN
ejpam-7064	200	7	.	.	PUNCT
ejpam-7064	201	1	numerical	numerical	ADJ
ejpam-7064	201	2	solutions	solution	NOUN
ejpam-7064	201	3	for	for	ADP
ejpam-7064	201	4	the	the	DET
ejpam-7064	201	5	problem	problem	NOUN
ejpam-7064	201	6	of	of	ADP
ejpam-7064	201	7	the	the	DET
ejpam-7064	201	8	boundary	boundary	ADJ
ejpam-7064	201	9	layer	layer	NOUN
ejpam-7064	201	10	flow	flow	NOUN
ejpam-7064	201	11	of	of	ADP
ejpam-7064	201	12	a	a	DET
ejpam-7064	201	13	powell	powell	NOUN
ejpam-7064	201	14	-	-	PUNCT
ejpam-7064	201	15	eyring	eyre	VERB
ejpam-7064	201	16	fluid	fluid	NOUN
ejpam-7064	201	17	over	over	ADP
ejpam-7064	201	18	an	an	DET
ejpam-7064	201	19	exponential	exponential	ADJ
ejpam-7064	201	20	sheet	sheet	NOUN
ejpam-7064	201	21	using	use	VERB
ejpam-7064	201	22	the	the	DET
ejpam-7064	201	23	spectral	spectral	ADJ
ejpam-7064	201	24	relaxation	relaxation	NOUN
ejpam-7064	201	25	method	method	NOUN
ejpam-7064	201	26	.	.	PUNCT
ejpam-7064	202	1	indian	indian	PROPN
ejpam-7064	202	2	journal	journal	PROPN
ejpam-7064	202	3	of	of	ADP
ejpam-7064	202	4	physics	physics	PROPN
ejpam-7064	202	5	,	,	PUNCT
ejpam-7064	202	6	94(9):1369–1374	94(9):1369–1374	NUM
ejpam-7064	202	7	,	,	PUNCT
ejpam-7064	202	8	2020	2020	NUM
ejpam-7064	202	9	.	.	PUNCT
ejpam-7064	203	1	[	[	X
ejpam-7064	203	2	13	13	NUM
ejpam-7064	203	3	]	]	PUNCT
ejpam-7064	203	4	t.	t.	PROPN
ejpam-7064	203	5	omara	omara	PROPN
ejpam-7064	203	6	.	.	PUNCT
ejpam-7064	204	1	penalized	penalize	VERB
ejpam-7064	204	2	estimators	estimator	NOUN
ejpam-7064	204	3	for	for	ADP
ejpam-7064	204	4	modified	modify	VERB
ejpam-7064	204	5	log	log	NOUN
ejpam-7064	204	6	-	-	PUNCT
ejpam-7064	204	7	bilal	bilal	NOUN
ejpam-7064	204	8	regression	regression	NOUN
ejpam-7064	204	9	:	:	PUNCT
ejpam-7064	204	10	simulations	simulation	NOUN
ejpam-7064	204	11	and	and	CCONJ
ejpam-7064	204	12	applications	application	NOUN
ejpam-7064	204	13	.	.	PUNCT
ejpam-7064	205	1	statistics	statistic	NOUN
ejpam-7064	205	2	,	,	PUNCT
ejpam-7064	205	3	optimization	optimization	NOUN
ejpam-7064	205	4	&	&	CCONJ
ejpam-7064	205	5	information	information	NOUN
ejpam-7064	205	6	computing	computing	NOUN
ejpam-7064	205	7	,	,	PUNCT
ejpam-7064	205	8	14(3):1566–1583	14(3):1566–1583	NUM
ejpam-7064	205	9	,	,	PUNCT
ejpam-7064	205	10	2025	2025	NUM
ejpam-7064	205	11	.	.	PUNCT
ejpam-7064	206	1	[	[	X
ejpam-7064	206	2	14	14	NUM
ejpam-7064	206	3	]	]	PUNCT
ejpam-7064	206	4	t.	t.	PROPN
ejpam-7064	206	5	omara	omara	ADJ
ejpam-7064	206	6	.	.	PUNCT
ejpam-7064	207	1	robust	robust	ADJ
ejpam-7064	207	2	lasso	lasso	NOUN
ejpam-7064	207	3	estimator	estimator	NOUN
ejpam-7064	207	4	for	for	ADP
ejpam-7064	207	5	the	the	DET
ejpam-7064	207	6	liu	liu	PROPN
ejpam-7064	207	7	-	-	PUNCT
ejpam-7064	207	8	type	type	NOUN
ejpam-7064	207	9	regression	regression	NOUN
ejpam-7064	207	10	model	model	NOUN
ejpam-7064	207	11	and	and	CCONJ
ejpam-7064	207	12	its	its	PRON
ejpam-7064	207	13	applications	application	NOUN
ejpam-7064	207	14	.	.	PUNCT
ejpam-7064	208	1	statistics	statistic	NOUN
ejpam-7064	208	2	,	,	PUNCT
ejpam-7064	208	3	optimization	optimization	NOUN
ejpam-7064	208	4	&	&	CCONJ
ejpam-7064	208	5	information	information	PROPN
ejpam-7064	208	6	computing	computing	PROPN
ejpam-7064	208	7	,	,	PUNCT
ejpam-7064	208	8	13(5):1819–1831	13(5):1819–1831	NUM
ejpam-7064	208	9	,	,	PUNCT
ejpam-7064	208	10	2025	2025	NUM
ejpam-7064	208	11	.	.	PUNCT
ejpam-7064	209	1	[	[	X
ejpam-7064	209	2	15	15	NUM
ejpam-7064	209	3	]	]	X
ejpam-7064	209	4	n.	n.	PROPN
ejpam-7064	209	5	h.	h.	PROPN
ejpam-7064	209	6	sweilem	sweilem	PROPN
ejpam-7064	209	7	,	,	PUNCT
ejpam-7064	209	8	m.	m.	NOUN
ejpam-7064	209	9	m.	m.	NOUN
ejpam-7064	209	10	khader	khader	PROPN
ejpam-7064	209	11	,	,	PUNCT
ejpam-7064	209	12	and	and	CCONJ
ejpam-7064	209	13	m.	m.	PROPN
ejpam-7064	209	14	adel	adel	PROPN
ejpam-7064	209	15	.	.	PROPN
ejpam-7064	210	1	numerical	numerical	PROPN
ejpam-7064	210	2	simulation	simulation	PROPN
ejpam-7064	210	3	of	of	ADP
ejpam-7064	210	4	fractional	fractional	ADJ
ejpam-7064	210	5	cable	cable	NOUN
ejpam-7064	210	6	equation	equation	NOUN
ejpam-7064	210	7	of	of	ADP
ejpam-7064	210	8	spiny	spiny	ADJ
ejpam-7064	210	9	neuronal	neuronal	ADJ
ejpam-7064	210	10	dendrites	dendrite	NOUN
ejpam-7064	210	11	.	.	PUNCT
ejpam-7064	211	1	journal	journal	NOUN
ejpam-7064	211	2	of	of	ADP
ejpam-7064	211	3	advanced	advanced	ADJ
ejpam-7064	211	4	research	research	NOUN
ejpam-7064	211	5	,	,	PUNCT
ejpam-7064	211	6	5(2):253–259	5(2):253–259	NOUN
ejpam-7064	211	7	,	,	PUNCT
ejpam-7064	211	8	2014	2014	NUM
ejpam-7064	211	9	.	.	PUNCT
ejpam-7064	212	1	[	[	X
ejpam-7064	212	2	16	16	NUM
ejpam-7064	212	3	]	]	PUNCT
ejpam-7064	212	4	m.	m.	NOUN
ejpam-7064	212	5	m.	m.	NOUN
ejpam-7064	212	6	khader	khader	PROPN
ejpam-7064	212	7	,	,	PUNCT
ejpam-7064	212	8	n.	n.	PROPN
ejpam-7064	212	9	h.	h.	PROPN
ejpam-7064	212	10	sweilam	sweilam	PROPN
ejpam-7064	212	11	,	,	PUNCT
ejpam-7064	212	12	and	and	CCONJ
ejpam-7064	212	13	a.	a.	NOUN
ejpam-7064	212	14	m.	m.	PROPN
ejpam-7064	212	15	s.	s.	PROPN
ejpam-7064	212	16	mahdy	mahdy	PROPN
ejpam-7064	212	17	.	.	PUNCT
ejpam-7064	213	1	two	two	NUM
ejpam-7064	213	2	computational	computational	ADJ
ejpam-7064	213	3	algorithms	algorithm	NOUN
ejpam-7064	213	4	for	for	ADP
ejpam-7064	213	5	the	the	DET
ejpam-7064	213	6	numerical	numerical	ADJ
ejpam-7064	213	7	solution	solution	NOUN
ejpam-7064	213	8	for	for	ADP
ejpam-7064	213	9	systems	system	NOUN
ejpam-7064	213	10	of	of	ADP
ejpam-7064	213	11	fractional	fractional	ADJ
ejpam-7064	213	12	differential	differential	ADJ
ejpam-7064	213	13	equations	equation	NOUN
ejpam-7064	213	14	.	.	PUNCT
ejpam-7064	214	1	arab	arab	PROPN
ejpam-7064	214	2	journal	journal	PROPN
ejpam-7064	214	3	of	of	ADP
ejpam-7064	214	4	mathematical	mathematical	ADJ
ejpam-7064	214	5	sciences	science	NOUN
ejpam-7064	214	6	,	,	PUNCT
ejpam-7064	214	7	21(1):39–52	21(1):39–52	NUM
ejpam-7064	214	8	,	,	PUNCT
ejpam-7064	214	9	2015	2015	NUM
ejpam-7064	214	10	.	.	PUNCT
ejpam-7064	215	1	[	[	X
ejpam-7064	215	2	17	17	NUM
ejpam-7064	215	3	]	]	PUNCT
ejpam-7064	215	4	k.	k.	PROPN
ejpam-7064	215	5	s.	s.	PROPN
ejpam-7064	215	6	nisar	nisar	PROPN
ejpam-7064	215	7	,	,	PUNCT
ejpam-7064	215	8	r.	r.	PROPN
ejpam-7064	215	9	jagatheeshwari	jagatheeshwari	PROPN
ejpam-7064	215	10	,	,	PUNCT
ejpam-7064	215	11	c.	c.	PROPN
ejpam-7064	215	12	ravichandran	ravichandran	NOUN
ejpam-7064	215	13	,	,	PUNCT
ejpam-7064	215	14	and	and	CCONJ
ejpam-7064	215	15	p.	p.	PROPN
ejpam-7064	215	16	veeresha	veeresha	PROPN
ejpam-7064	215	17	.	.	PUNCT
ejpam-7064	216	1	an	an	DET
ejpam-7064	216	2	effective	effective	ADJ
ejpam-7064	216	3	analytical	analytical	ADJ
ejpam-7064	216	4	method	method	NOUN
ejpam-7064	216	5	for	for	ADP
ejpam-7064	216	6	the	the	DET
ejpam-7064	216	7	fractional	fractional	ADJ
ejpam-7064	216	8	brusselator	brusselator	NOUN
ejpam-7064	216	9	reaction	reaction	NOUN
ejpam-7064	216	10	-	-	PUNCT
ejpam-7064	216	11	diffusion	diffusion	NOUN
ejpam-7064	216	12	system	system	NOUN
ejpam-7064	216	13	.	.	PUNCT
ejpam-7064	217	1	mathematical	mathematical	ADJ
ejpam-7064	217	2	methods	method	NOUN
ejpam-7064	217	3	in	in	ADP
ejpam-7064	217	4	the	the	DET
ejpam-7064	217	5	applied	apply	VERB
ejpam-7064	217	6	sciences	science	NOUN
ejpam-7064	217	7	,	,	PUNCT
ejpam-7064	217	8	46(18):18749–18758	46(18):18749–18758	NUM
ejpam-7064	217	9	,	,	PUNCT
ejpam-7064	217	10	2023	2023	NUM
ejpam-7064	217	11	.	.	PUNCT
ejpam-7064	218	1	[	[	X
ejpam-7064	218	2	18	18	NUM
ejpam-7064	218	3	]	]	PUNCT
ejpam-7064	218	4	m.	m.	NOUN
ejpam-7064	218	5	m.	m.	NOUN
ejpam-7064	218	6	khader	khader	PROPN
ejpam-7064	218	7	,	,	PUNCT
ejpam-7064	218	8	j.	j.	PROPN
ejpam-7064	218	9	e.	e.	PROPN
ejpam-7064	218	10	m.	m.	PROPN
ejpam-7064	218	11	dı́az	dı́az	PROPN
ejpam-7064	218	12	,	,	PUNCT
ejpam-7064	218	13	k.	k.	PROPN
ejpam-7064	218	14	m.	m.	PROPN
ejpam-7064	218	15	saad	saad	PROPN
ejpam-7064	218	16	,	,	PUNCT
ejpam-7064	218	17	and	and	CCONJ
ejpam-7064	218	18	w.	w.	PROPN
ejpam-7064	218	19	m.	m.	PROPN
ejpam-7064	218	20	hamanah	hamanah	PROPN
ejpam-7064	218	21	.	.	PUNCT
ejpam-7064	219	1	vieta	vieta	PROPN
ejpam-7064	219	2	-	-	PUNCT
ejpam-7064	219	3	lucas	lucas	PROPN
ejpam-7064	219	4	polynomials	polynomial	NOUN
ejpam-7064	219	5	for	for	ADP
ejpam-7064	219	6	the	the	DET
ejpam-7064	219	7	brusselator	brusselator	NOUN
ejpam-7064	219	8	system	system	NOUN
ejpam-7064	219	9	with	with	ADP
ejpam-7064	219	10	the	the	DET
ejpam-7064	219	11	rabotnov	rabotnov	NOUN
ejpam-7064	219	12	fractional	fractional	ADJ
ejpam-7064	219	13	-	-	PUNCT
ejpam-7064	219	14	exponential	exponential	ADJ
ejpam-7064	219	15	kernel	kernel	NOUN
ejpam-7064	219	16	fractional	fractional	PROPN
ejpam-7064	219	17	derivative	derivative	PROPN
ejpam-7064	219	18	.	.	PUNCT
ejpam-7064	219	19	symmetry	symmetry	PROPN
ejpam-7064	219	20	,	,	PUNCT
ejpam-7064	219	21	15(9):1–10	15(9):1–10	NUM
ejpam-7064	219	22	,	,	PUNCT
ejpam-7064	219	23	2023	2023	NUM
ejpam-7064	219	24	.	.	PUNCT
ejpam-7064	220	1	[	[	X
ejpam-7064	220	2	19	19	NUM
ejpam-7064	220	3	]	]	PUNCT
ejpam-7064	220	4	m.	m.	NOUN
ejpam-7064	220	5	m.	m.	NOUN
ejpam-7064	220	6	khader	khader	PROPN
ejpam-7064	220	7	and	and	CCONJ
ejpam-7064	220	8	k.	k.	PROPN
ejpam-7064	220	9	m.	m.	PROPN
ejpam-7064	220	10	saad	saad	PROPN
ejpam-7064	220	11	.	.	PUNCT
ejpam-7064	221	1	a	a	DET
ejpam-7064	221	2	numerical	numerical	ADJ
ejpam-7064	221	3	study	study	NOUN
ejpam-7064	221	4	using	use	VERB
ejpam-7064	221	5	chebyshev	chebyshev	NOUN
ejpam-7064	221	6	collocation	collocation	NOUN
ejpam-7064	221	7	method	method	NOUN
ejpam-7064	221	8	for	for	ADP
ejpam-7064	221	9	a	a	DET
ejpam-7064	221	10	problem	problem	NOUN
ejpam-7064	221	11	of	of	ADP
ejpam-7064	221	12	biological	biological	ADJ
ejpam-7064	221	13	invasion	invasion	NOUN
ejpam-7064	221	14	:	:	PUNCT
ejpam-7064	221	15	fractional	fractional	ADJ
ejpam-7064	221	16	fisher	fisher	PROPN
ejpam-7064	221	17	equation	equation	NOUN
ejpam-7064	221	18	.	.	PUNCT
ejpam-7064	222	1	international	international	ADJ
ejpam-7064	222	2	journal	journal	NOUN
ejpam-7064	222	3	of	of	ADP
ejpam-7064	222	4	biomathematics	biomathematic	NOUN
ejpam-7064	222	5	,	,	PUNCT
ejpam-7064	222	6	11(8):1–15	11(8):1–15	NUM
ejpam-7064	222	7	,	,	PUNCT
ejpam-7064	222	8	2018	2018	NUM
ejpam-7064	222	9	.	.	PUNCT
ejpam-7064	223	1	[	[	X
ejpam-7064	223	2	20	20	NUM
ejpam-7064	223	3	]	]	PUNCT
ejpam-7064	223	4	k.	k.	PROPN
ejpam-7064	223	5	m.	m.	PROPN
ejpam-7064	223	6	saad	saad	PROPN
ejpam-7064	223	7	,	,	PUNCT
ejpam-7064	223	8	m.	m.	NOUN
ejpam-7064	223	9	m.	m.	PROPN
ejpam-7064	223	10	khader	khader	PROPN
ejpam-7064	223	11	,	,	PUNCT
ejpam-7064	223	12	j.	j.	PROPN
ejpam-7064	223	13	f.	f.	PROPN
ejpam-7064	223	14	gomez	gomez	PROPN
ejpam-7064	223	15	-	-	PUNCT
ejpam-7064	223	16	aguilar	aguilar	PROPN
ejpam-7064	223	17	,	,	PUNCT
ejpam-7064	223	18	and	and	CCONJ
ejpam-7064	223	19	d.	d.	PROPN
ejpam-7064	223	20	baleanu	baleanu	PROPN
ejpam-7064	223	21	.	.	PUNCT
ejpam-7064	224	1	numerical	numerical	PROPN
ejpam-7064	224	2	solutions	solutions	PROPN
ejpam-7064	224	3	m.	m.	PROPN
ejpam-7064	224	4	adel	adel	PROPN
ejpam-7064	224	5	et	et	PROPN
ejpam-7064	224	6	al	al	PROPN
ejpam-7064	224	7	.	.	PUNCT
ejpam-7064	224	8	/	/	SYM
ejpam-7064	224	9	eur	eur	PROPN
ejpam-7064	224	10	.	.	PUNCT
ejpam-7064	225	1	j.	j.	PROPN
ejpam-7064	225	2	pure	pure	PROPN
ejpam-7064	225	3	appl	appl	PROPN
ejpam-7064	225	4	.	.	PROPN
ejpam-7064	225	5	math	math	PROPN
ejpam-7064	225	6	,	,	PUNCT
ejpam-7064	225	7	18	18	NUM
ejpam-7064	225	8	(	(	PUNCT
ejpam-7064	225	9	4	4	NUM
ejpam-7064	225	10	)	)	PUNCT
ejpam-7064	225	11	(	(	PUNCT
ejpam-7064	225	12	2025	2025	NUM
ejpam-7064	225	13	)	)	PUNCT
ejpam-7064	225	14	,	,	PUNCT
ejpam-7064	225	15	7064	7064	NUM
ejpam-7064	225	16	11	11	NUM
ejpam-7064	225	17	of	of	ADP
ejpam-7064	225	18	11	11	NUM
ejpam-7064	225	19	of	of	ADP
ejpam-7064	225	20	the	the	DET
ejpam-7064	225	21	fractional	fractional	ADJ
ejpam-7064	225	22	fisher	fisher	PROPN
ejpam-7064	225	23	’s	’s	PART
ejpam-7064	225	24	type	type	NOUN
ejpam-7064	225	25	equations	equation	NOUN
ejpam-7064	225	26	with	with	ADP
ejpam-7064	225	27	atangana	atangana	PROPN
ejpam-7064	225	28	-	-	PUNCT
ejpam-7064	225	29	baleanu	baleanu	ADJ
ejpam-7064	225	30	fractional	fractional	ADJ
ejpam-7064	225	31	derivative	derivative	NOUN
ejpam-7064	225	32	by	by	ADP
ejpam-7064	225	33	using	use	VERB
ejpam-7064	225	34	spectral	spectral	ADJ
ejpam-7064	225	35	collocation	collocation	NOUN
ejpam-7064	225	36	methods	method	NOUN
ejpam-7064	225	37	.	.	PUNCT
ejpam-7064	226	1	chaos	chaos	NOUN
ejpam-7064	226	2	,	,	PUNCT
ejpam-7064	226	3	29:1–5	29:1–5	NUM
ejpam-7064	226	4	,	,	PUNCT
ejpam-7064	226	5	2019	2019	NUM
ejpam-7064	226	6	.	.	PUNCT
ejpam-7064	227	1	[	[	X
ejpam-7064	227	2	21	21	NUM
ejpam-7064	227	3	]	]	PUNCT
ejpam-7064	227	4	v.	v.	ADP
ejpam-7064	227	5	gafiychuk	gafiychuk	NOUN
ejpam-7064	227	6	and	and	CCONJ
ejpam-7064	227	7	b.	b.	PROPN
ejpam-7064	227	8	datsko	datsko	PROPN
ejpam-7064	227	9	.	.	PUNCT
ejpam-7064	228	1	stability	stability	NOUN
ejpam-7064	228	2	analysis	analysis	NOUN
ejpam-7064	228	3	and	and	CCONJ
ejpam-7064	228	4	limit	limit	VERB
ejpam-7064	228	5	cycle	cycle	NOUN
ejpam-7064	228	6	in	in	ADP
ejpam-7064	228	7	a	a	DET
ejpam-7064	228	8	fractional	fractional	ADJ
ejpam-7064	228	9	system	system	NOUN
ejpam-7064	228	10	with	with	ADP
ejpam-7064	228	11	brusselator	brusselator	NOUN
ejpam-7064	228	12	nonlinearities	nonlinearitie	NOUN
ejpam-7064	228	13	.	.	PUNCT
ejpam-7064	229	1	physics	physics	NOUN
ejpam-7064	229	2	letters	letter	NOUN
ejpam-7064	229	3	a	a	PRON
ejpam-7064	229	4	,	,	PUNCT
ejpam-7064	229	5	372(29):4902–4904	372(29):4902–4904	NUM
ejpam-7064	229	6	,	,	PUNCT
ejpam-7064	229	7	2008	2008	NUM
ejpam-7064	229	8	.	.	PUNCT
ejpam-7064	230	1	[	[	X
ejpam-7064	230	2	22	22	NUM
ejpam-7064	230	3	]	]	X
ejpam-7064	230	4	h.	h.	PROPN
ejpam-7064	230	5	jafari	jafari	PROPN
ejpam-7064	230	6	,	,	PUNCT
ejpam-7064	230	7	a.	a.	NOUN
ejpam-7064	230	8	kadem	kadem	PROPN
ejpam-7064	230	9	,	,	PUNCT
ejpam-7064	230	10	and	and	CCONJ
ejpam-7064	230	11	d.	d.	PROPN
ejpam-7064	230	12	baleanu	baleanu	PROPN
ejpam-7064	230	13	.	.	PUNCT
ejpam-7064	231	1	variational	variational	ADJ
ejpam-7064	231	2	iteration	iteration	NOUN
ejpam-7064	231	3	method	method	NOUN
ejpam-7064	231	4	for	for	ADP
ejpam-7064	231	5	a	a	DET
ejpam-7064	231	6	fractionalorder	fractionalorder	ADJ
ejpam-7064	231	7	brusselator	brusselator	NOUN
ejpam-7064	231	8	system	system	NOUN
ejpam-7064	231	9	.	.	PUNCT
ejpam-7064	232	1	abstract	abstract	ADJ
ejpam-7064	232	2	and	and	CCONJ
ejpam-7064	232	3	applied	apply	VERB
ejpam-7064	232	4	analysis	analysis	NOUN
ejpam-7064	232	5	,	,	PUNCT
ejpam-7064	232	6	page	page	NOUN
ejpam-7064	232	7	496323	496323	NUM
ejpam-7064	232	8	,	,	PUNCT
ejpam-7064	232	9	2014	2014	NUM
ejpam-7064	232	10	.	.	PUNCT
ejpam-7064	233	1	[	[	X
ejpam-7064	233	2	23	23	NUM
ejpam-7064	233	3	]	]	X
ejpam-7064	233	4	p.	p.	NOUN
ejpam-7064	233	5	reiterer	reiterer	PROPN
ejpam-7064	233	6	,	,	PUNCT
ejpam-7064	233	7	c.	c.	PROPN
ejpam-7064	233	8	lainscsek	lainscsek	PROPN
ejpam-7064	233	9	,	,	PUNCT
ejpam-7064	233	10	sch	sch	INTJ
ejpam-7064	233	11	,	,	PUNCT
ejpam-7064	233	12	and	and	CCONJ
ejpam-7064	233	13	j.	j.	PROPN
ejpam-7064	233	14	maquet	maquet	PROPN
ejpam-7064	233	15	.	.	PUNCT
ejpam-7064	234	1	a	a	DET
ejpam-7064	234	2	nine	nine	NUM
ejpam-7064	234	3	-	-	PUNCT
ejpam-7064	234	4	dimensional	dimensional	ADJ
ejpam-7064	234	5	lorenz	lorenz	NOUN
ejpam-7064	234	6	system	system	NOUN
ejpam-7064	234	7	to	to	PART
ejpam-7064	234	8	study	study	VERB
ejpam-7064	234	9	high	high	ADJ
ejpam-7064	234	10	-	-	PUNCT
ejpam-7064	234	11	dimensional	dimensional	ADJ
ejpam-7064	234	12	chaos	chaos	NOUN
ejpam-7064	234	13	.	.	PUNCT
ejpam-7064	235	1	journal	journal	PROPN
ejpam-7064	235	2	of	of	ADP
ejpam-7064	235	3	physics	physics	PROPN
ejpam-7064	235	4	a	a	DET
ejpam-7064	235	5	:	:	PUNCT
ejpam-7064	235	6	math	math	NOUN
ejpam-7064	235	7	.	.	PUNCT
ejpam-7064	236	1	gen	gen	PROPN
ejpam-7064	236	2	.	.	PROPN
ejpam-7064	236	3	,	,	PUNCT
ejpam-7064	236	4	31:7121–7139	31:7121–7139	PROPN
ejpam-7064	236	5	,	,	PUNCT
ejpam-7064	236	6	1998	1998	NUM
ejpam-7064	236	7	.	.	PUNCT
ejpam-7064	237	1	[	[	X
ejpam-7064	237	2	24	24	NUM
ejpam-7064	237	3	]	]	PUNCT
ejpam-7064	237	4	l.	l.	PROPN
ejpam-7064	237	5	n.	n.	PROPN
ejpam-7064	237	6	trefethen	trefethen	PROPN
ejpam-7064	237	7	.	.	PUNCT
ejpam-7064	238	1	spectral	spectral	ADJ
ejpam-7064	238	2	methods	method	NOUN
ejpam-7064	238	3	in	in	ADP
ejpam-7064	238	4	matlab	matlab	PROPN
ejpam-7064	238	5	.	.	PUNCT
ejpam-7064	239	1	siam	siam	PROPN
ejpam-7064	239	2	,	,	PUNCT
ejpam-7064	239	3	philadelphia	philadelphia	PROPN
ejpam-7064	239	4	,	,	PUNCT
ejpam-7064	239	5	pa	pa	PROPN
ejpam-7064	239	6	,	,	PUNCT
ejpam-7064	239	7	usa	usa	PROPN
ejpam-7064	239	8	,	,	PUNCT
ejpam-7064	239	9	2000	2000	NUM
ejpam-7064	239	10	.	.	PUNCT
ejpam-7064	240	1	[	[	X
ejpam-7064	240	2	25	25	NUM
ejpam-7064	240	3	]	]	PUNCT
ejpam-7064	240	4	j.	j.	PROPN
ejpam-7064	240	5	n.	n.	PROPN
ejpam-7064	240	6	kouagou	kouagou	PROPN
ejpam-7064	240	7	,	,	PUNCT
ejpam-7064	240	8	p.	p.	PROPN
ejpam-7064	240	9	g.	g.	PROPN
ejpam-7064	240	10	dlamini	dlamini	PROPN
ejpam-7064	240	11	,	,	PUNCT
ejpam-7064	240	12	and	and	CCONJ
ejpam-7064	240	13	s.	s.	PROPN
ejpam-7064	240	14	m.	m.	PROPN
ejpam-7064	240	15	simelane	simelane	PROPN
ejpam-7064	240	16	.	.	PUNCT
ejpam-7064	241	1	on	on	ADP
ejpam-7064	241	2	the	the	DET
ejpam-7064	241	3	multi	multi	ADJ
ejpam-7064	241	4	-	-	ADJ
ejpam-7064	241	5	domain	domain	ADJ
ejpam-7064	241	6	compact	compact	ADJ
ejpam-7064	241	7	finite	finite	ADJ
ejpam-7064	241	8	difference	difference	NOUN
ejpam-7064	241	9	relaxation	relaxation	NOUN
ejpam-7064	241	10	method	method	NOUN
ejpam-7064	241	11	for	for	ADP
ejpam-7064	241	12	high	high	ADJ
ejpam-7064	241	13	dimensional	dimensional	ADJ
ejpam-7064	241	14	chaos	chaos	NOUN
ejpam-7064	241	15	:	:	PUNCT
ejpam-7064	241	16	the	the	DET
ejpam-7064	241	17	nine	nine	NUM
ejpam-7064	241	18	-	-	PUNCT
ejpam-7064	241	19	dimensional	dimensional	ADJ
ejpam-7064	241	20	lorenz	lorenz	PROPN
ejpam-7064	241	21	system	system	NOUN
ejpam-7064	241	22	.	.	PUNCT
ejpam-7064	242	1	alexandria	alexandria	PROPN
ejpam-7064	242	2	engineering	engineering	PROPN
ejpam-7064	242	3	journal	journal	PROPN
ejpam-7064	242	4	,	,	PUNCT
ejpam-7064	242	5	59(4):2617–2625	59(4):2617–2625	NUM
ejpam-7064	242	6	,	,	PUNCT
ejpam-7064	242	7	2020	2020	NUM
ejpam-7064	242	8	.	.	PUNCT
ejpam-7064	243	1	[	[	X
ejpam-7064	243	2	26	26	NUM
ejpam-7064	243	3	]	]	PUNCT
ejpam-7064	243	4	m.	m.	NOUN
ejpam-7064	243	5	adel	adel	PROPN
ejpam-7064	243	6	,	,	PUNCT
ejpam-7064	243	7	m.	m.	NOUN
ejpam-7064	243	8	m.	m.	NOUN
ejpam-7064	243	9	khader	khader	PROPN
ejpam-7064	243	10	,	,	PUNCT
ejpam-7064	243	11	t.	t.	PROPN
ejpam-7064	243	12	a.	a.	NOUN
ejpam-7064	243	13	assiri	assiri	PROPN
ejpam-7064	243	14	,	,	PUNCT
ejpam-7064	243	15	and	and	CCONJ
ejpam-7064	243	16	w.	w.	PROPN
ejpam-7064	243	17	kallel	kallel	PROPN
ejpam-7064	243	18	.	.	PUNCT
ejpam-7064	244	1	simulating	simulate	VERB
ejpam-7064	244	2	covid-19	covid-19	PROPN
ejpam-7064	244	3	model	model	NOUN
ejpam-7064	244	4	research	research	NOUN
ejpam-7064	244	5	using	use	VERB
ejpam-7064	244	6	a	a	DET
ejpam-7064	244	7	multidomain	multidomain	ADJ
ejpam-7064	244	8	spectral	spectral	ADJ
ejpam-7064	244	9	relaxation	relaxation	NOUN
ejpam-7064	244	10	technique	technique	NOUN
ejpam-7064	244	11	.	.	PUNCT
ejpam-7064	245	1	symmetry	symmetry	NOUN
ejpam-7064	245	2	,	,	PUNCT
ejpam-7064	245	3	15:931	15:931	NUM
ejpam-7064	245	4	,	,	PUNCT
ejpam-7064	245	5	2023	2023	NUM
ejpam-7064	245	6	.	.	PUNCT
ejpam-7064	246	1	[	[	X
ejpam-7064	246	2	27	27	NUM
ejpam-7064	246	3	]	]	X
ejpam-7064	246	4	p.	p.	NOUN
ejpam-7064	246	5	dlamini	dlamini	PROPN
ejpam-7064	246	6	and	and	CCONJ
ejpam-7064	246	7	s.	s.	PROPN
ejpam-7064	246	8	simelane	simelane	PROPN
ejpam-7064	246	9	.	.	PUNCT
ejpam-7064	247	1	an	an	DET
ejpam-7064	247	2	efficient	efficient	ADJ
ejpam-7064	247	3	spectral	spectral	ADJ
ejpam-7064	247	4	method	method	NOUN
ejpam-7064	247	5	-	-	PUNCT
ejpam-7064	247	6	based	base	VERB
ejpam-7064	247	7	algorithm	algorithm	NOUN
ejpam-7064	247	8	for	for	ADP
ejpam-7064	247	9	solving	solve	VERB
ejpam-7064	247	10	a	a	DET
ejpam-7064	247	11	high	high	ADV
ejpam-7064	247	12	-	-	PUNCT
ejpam-7064	247	13	dimensional	dimensional	ADJ
ejpam-7064	247	14	chaotic	chaotic	ADJ
ejpam-7064	247	15	lorenz	lorenz	PROPN
ejpam-7064	247	16	system	system	NOUN
ejpam-7064	247	17	.	.	PUNCT
ejpam-7064	248	1	journal	journal	PROPN
ejpam-7064	248	2	of	of	ADP
ejpam-7064	248	3	applied	applied	ADJ
ejpam-7064	248	4	computational	computational	ADJ
ejpam-7064	248	5	mechanics	mechanic	NOUN
ejpam-7064	248	6	,	,	PUNCT
ejpam-7064	248	7	7(1):225–234	7(1):225–234	NUM
ejpam-7064	248	8	,	,	PUNCT
ejpam-7064	248	9	2021	2021	NUM
ejpam-7064	248	10	.	.	PUNCT