id	sid	tid	token	lemma	pos
ejpam-4679	1	1	european	european	PROPN
ejpam-4679	1	2	journal	journal	PROPN
ejpam-4679	1	3	of	of	ADP
ejpam-4679	1	4	pure	pure	ADJ
ejpam-4679	1	5	and	and	CCONJ
ejpam-4679	1	6	applied	apply	VERB
ejpam-4679	1	7	mathematics	mathematic	NOUN
ejpam-4679	1	8	vol	vol	NOUN
ejpam-4679	1	9	.	.	PUNCT
ejpam-4679	2	1	16	16	NUM
ejpam-4679	2	2	,	,	PUNCT
ejpam-4679	2	3	no	no	INTJ
ejpam-4679	2	4	.	.	NOUN
ejpam-4679	2	5	1	1	NUM
ejpam-4679	2	6	,	,	PUNCT
ejpam-4679	2	7	2023	2023	NUM
ejpam-4679	2	8	,	,	PUNCT
ejpam-4679	2	9	491	491	NUM
ejpam-4679	2	10	-	-	SYM
ejpam-4679	2	11	502	502	NUM
ejpam-4679	2	12	issn	issn	PROPN
ejpam-4679	2	13	1307	1307	NUM
ejpam-4679	2	14	-	-	SYM
ejpam-4679	2	15	5543	5543	NUM
ejpam-4679	2	16	–	–	PUNCT
ejpam-4679	3	1	ejpam.com	ejpam.com	X
ejpam-4679	3	2	published	publish	VERB
ejpam-4679	3	3	by	by	ADP
ejpam-4679	3	4	new	new	PROPN
ejpam-4679	3	5	york	york	PROPN
ejpam-4679	3	6	business	business	PROPN
ejpam-4679	3	7	global	global	PROPN
ejpam-4679	3	8	an	an	DET
ejpam-4679	3	9	iterative	iterative	NOUN
ejpam-4679	3	10	approach	approach	NOUN
ejpam-4679	3	11	for	for	ADP
ejpam-4679	3	12	numerical	numerical	ADJ
ejpam-4679	3	13	solution	solution	NOUN
ejpam-4679	3	14	to	to	ADP
ejpam-4679	3	15	the	the	DET
ejpam-4679	3	16	time	time	NOUN
ejpam-4679	3	17	-	-	PUNCT
ejpam-4679	3	18	fractional	fractional	ADJ
ejpam-4679	3	19	richards	richard	NOUN
ejpam-4679	3	20	equation	equation	NOUN
ejpam-4679	3	21	with	with	ADP
ejpam-4679	3	22	implicit	implicit	ADJ
ejpam-4679	3	23	neumann	neumann	PROPN
ejpam-4679	3	24	boundary	boundary	ADJ
ejpam-4679	3	25	conditions	condition	NOUN
ejpam-4679	3	26	mustafa	mustafa	PROPN
ejpam-4679	3	27	zeki1,∗	zeki1,∗	PROPN
ejpam-4679	3	28	,	,	PUNCT
ejpam-4679	3	29	salih	salih	PROPN
ejpam-4679	3	30	tatar2	tatar2	PROPN
ejpam-4679	3	31	1	1	NUM
ejpam-4679	3	32	college	college	NOUN
ejpam-4679	3	33	of	of	ADP
ejpam-4679	3	34	engineering	engineering	NOUN
ejpam-4679	3	35	and	and	CCONJ
ejpam-4679	3	36	technology	technology	NOUN
ejpam-4679	3	37	,	,	PUNCT
ejpam-4679	3	38	american	american	PROPN
ejpam-4679	3	39	university	university	PROPN
ejpam-4679	3	40	of	of	ADP
ejpam-4679	3	41	the	the	DET
ejpam-4679	3	42	middle	middle	PROPN
ejpam-4679	3	43	east	east	PROPN
ejpam-4679	3	44	,	,	PUNCT
ejpam-4679	3	45	kuwait	kuwait	PROPN
ejpam-4679	3	46	2	2	NUM
ejpam-4679	3	47	department	department	NOUN
ejpam-4679	3	48	of	of	ADP
ejpam-4679	3	49	mathematics	mathematic	NOUN
ejpam-4679	3	50	and	and	CCONJ
ejpam-4679	3	51	computer	computer	NOUN
ejpam-4679	3	52	science	science	NOUN
ejpam-4679	3	53	,	,	PUNCT
ejpam-4679	3	54	college	college	NOUN
ejpam-4679	3	55	of	of	ADP
ejpam-4679	3	56	science	science	NOUN
ejpam-4679	3	57	and	and	CCONJ
ejpam-4679	3	58	general	general	ADJ
ejpam-4679	3	59	studies	study	NOUN
ejpam-4679	3	60	,	,	PUNCT
ejpam-4679	3	61	alfaisal	alfaisal	NOUN
ejpam-4679	3	62	university	university	NOUN
ejpam-4679	3	63	,	,	PUNCT
ejpam-4679	3	64	riyadh	riyadh	PROPN
ejpam-4679	3	65	,	,	PUNCT
ejpam-4679	3	66	ksa	ksa	PROPN
ejpam-4679	3	67	abstract	abstract	NOUN
ejpam-4679	3	68	.	.	PUNCT
ejpam-4679	4	1	in	in	ADP
ejpam-4679	4	2	this	this	DET
ejpam-4679	4	3	paper	paper	NOUN
ejpam-4679	4	4	,	,	PUNCT
ejpam-4679	4	5	we	we	PRON
ejpam-4679	4	6	develop	develop	VERB
ejpam-4679	4	7	an	an	DET
ejpam-4679	4	8	iterative	iterative	NOUN
ejpam-4679	4	9	method	method	NOUN
ejpam-4679	4	10	of	of	ADP
ejpam-4679	4	11	lines	line	NOUN
ejpam-4679	4	12	scheme	scheme	VERB
ejpam-4679	4	13	for	for	ADP
ejpam-4679	4	14	the	the	DET
ejpam-4679	4	15	numerical	numerical	ADJ
ejpam-4679	4	16	solution	solution	NOUN
ejpam-4679	4	17	to	to	ADP
ejpam-4679	4	18	the	the	DET
ejpam-4679	4	19	time	time	NOUN
ejpam-4679	4	20	fractional	fractional	PROPN
ejpam-4679	4	21	richards	richard	NOUN
ejpam-4679	4	22	equation	equation	NOUN
ejpam-4679	4	23	with	with	ADP
ejpam-4679	4	24	implicit	implicit	ADJ
ejpam-4679	4	25	neumann	neumann	PROPN
ejpam-4679	4	26	boundary	boundary	ADJ
ejpam-4679	4	27	conditions	condition	NOUN
ejpam-4679	4	28	,	,	PUNCT
ejpam-4679	4	29	which	which	PRON
ejpam-4679	4	30	is	be	AUX
ejpam-4679	4	31	an	an	DET
ejpam-4679	4	32	effective	effective	ADJ
ejpam-4679	4	33	tool	tool	NOUN
ejpam-4679	4	34	for	for	ADP
ejpam-4679	4	35	describing	describe	VERB
ejpam-4679	4	36	a	a	DET
ejpam-4679	4	37	process	process	NOUN
ejpam-4679	4	38	of	of	ADP
ejpam-4679	4	39	flow	flow	NOUN
ejpam-4679	4	40	through	through	ADP
ejpam-4679	4	41	unsaturated	unsaturated	ADJ
ejpam-4679	4	42	media	medium	NOUN
ejpam-4679	4	43	.	.	PUNCT
ejpam-4679	5	1	a	a	DET
ejpam-4679	5	2	numerical	numerical	ADJ
ejpam-4679	5	3	example	example	NOUN
ejpam-4679	5	4	is	be	AUX
ejpam-4679	5	5	provided	provide	VERB
ejpam-4679	5	6	to	to	PART
ejpam-4679	5	7	show	show	VERB
ejpam-4679	5	8	the	the	DET
ejpam-4679	5	9	effectiveness	effectiveness	NOUN
ejpam-4679	5	10	of	of	ADP
ejpam-4679	5	11	the	the	DET
ejpam-4679	5	12	presented	present	VERB
ejpam-4679	5	13	method	method	NOUN
ejpam-4679	5	14	for	for	ADP
ejpam-4679	5	15	different	different	ADJ
ejpam-4679	5	16	model	model	NOUN
ejpam-4679	5	17	parameters	parameter	NOUN
ejpam-4679	5	18	and	and	CCONJ
ejpam-4679	5	19	inputs	input	NOUN
ejpam-4679	5	20	.	.	PUNCT
ejpam-4679	6	1	the	the	DET
ejpam-4679	6	2	method	method	NOUN
ejpam-4679	6	3	illustrated	illustrate	VERB
ejpam-4679	6	4	here	here	ADV
ejpam-4679	6	5	can	can	AUX
ejpam-4679	6	6	be	be	AUX
ejpam-4679	6	7	applied	apply	VERB
ejpam-4679	6	8	to	to	ADP
ejpam-4679	6	9	other	other	ADJ
ejpam-4679	6	10	types	type	NOUN
ejpam-4679	6	11	richards	richard	NOUN
ejpam-4679	6	12	equation	equation	NOUN
ejpam-4679	6	13	with	with	ADP
ejpam-4679	6	14	various	various	ADJ
ejpam-4679	6	15	input	input	NOUN
ejpam-4679	6	16	functions	function	NOUN
ejpam-4679	6	17	and	and	CCONJ
ejpam-4679	6	18	dirichlet	dirichlet	PROPN
ejpam-4679	6	19	boundary	boundary	ADJ
ejpam-4679	6	20	conditions	condition	NOUN
ejpam-4679	6	21	.	.	PUNCT
ejpam-4679	7	1	2020	2020	NUM
ejpam-4679	7	2	mathematics	mathematic	NOUN
ejpam-4679	7	3	subject	subject	NOUN
ejpam-4679	7	4	classifications	classification	NOUN
ejpam-4679	7	5	:	:	PUNCT
ejpam-4679	7	6	35r11	35r11	NUM
ejpam-4679	7	7	,	,	PUNCT
ejpam-4679	7	8	65m20	65m20	NUM
ejpam-4679	7	9	,	,	PUNCT
ejpam-4679	7	10	65n40	65n40	NUM
ejpam-4679	7	11	key	key	ADJ
ejpam-4679	7	12	words	word	NOUN
ejpam-4679	7	13	and	and	CCONJ
ejpam-4679	7	14	phrases	phrase	NOUN
ejpam-4679	7	15	:	:	PUNCT
ejpam-4679	7	16	fractional	fractional	ADJ
ejpam-4679	7	17	richards	richard	NOUN
ejpam-4679	7	18	equation	equation	NOUN
ejpam-4679	7	19	,	,	PUNCT
ejpam-4679	7	20	caputo	caputo	PROPN
ejpam-4679	7	21	fractional	fractional	PROPN
ejpam-4679	7	22	derivative	derivative	NOUN
ejpam-4679	7	23	,	,	PUNCT
ejpam-4679	7	24	method	method	NOUN
ejpam-4679	7	25	of	of	ADP
ejpam-4679	7	26	lines	line	NOUN
ejpam-4679	7	27	1	1	NUM
ejpam-4679	7	28	.	.	PUNCT
ejpam-4679	8	1	introduction	introduction	NOUN
ejpam-4679	8	2	richards	richard	NOUN
ejpam-4679	8	3	equation	equation	NOUN
ejpam-4679	8	4	is	be	AUX
ejpam-4679	8	5	the	the	DET
ejpam-4679	8	6	fundamental	fundamental	ADJ
ejpam-4679	8	7	model	model	NOUN
ejpam-4679	8	8	for	for	ADP
ejpam-4679	8	9	describing	describe	VERB
ejpam-4679	8	10	flow	flow	NOUN
ejpam-4679	8	11	through	through	ADP
ejpam-4679	8	12	unsaturated	unsaturated	ADJ
ejpam-4679	8	13	media	medium	NOUN
ejpam-4679	8	14	.	.	PUNCT
ejpam-4679	9	1	richards	richard	NOUN
ejpam-4679	9	2	equation	equation	NOUN
ejpam-4679	9	3	takes	take	VERB
ejpam-4679	9	4	the	the	DET
ejpam-4679	9	5	following	follow	VERB
ejpam-4679	9	6	form	form	NOUN
ejpam-4679	9	7	when	when	SCONJ
ejpam-4679	9	8	water	water	NOUN
ejpam-4679	9	9	flows	flow	VERB
ejpam-4679	9	10	through	through	ADP
ejpam-4679	9	11	one	one	NUM
ejpam-4679	9	12	-	-	PUNCT
ejpam-4679	9	13	dimensional	dimensional	ADJ
ejpam-4679	9	14	horizontal	horizontal	ADJ
ejpam-4679	9	15	soils	soil	NOUN
ejpam-4679	9	16	:	:	PUNCT
ejpam-4679	9	17	∂u	∂u	PROPN
ejpam-4679	9	18	∂t	∂t	PROPN
ejpam-4679	9	19	=	=	SYM
ejpam-4679	9	20	∂	∂	NUM
ejpam-4679	9	21	∂x	∂x	PROPN
ejpam-4679	9	22	(	(	PUNCT
ejpam-4679	9	23	d(u	d(u	PROPN
ejpam-4679	9	24	)	)	PUNCT
ejpam-4679	9	25	∂u	∂u	PROPN
ejpam-4679	9	26	∂x	∂x	PROPN
ejpam-4679	9	27	)	)	PUNCT
ejpam-4679	9	28	,	,	PUNCT
ejpam-4679	9	29	(	(	PUNCT
ejpam-4679	9	30	1	1	X
ejpam-4679	9	31	)	)	PUNCT
ejpam-4679	9	32	where	where	SCONJ
ejpam-4679	9	33	u	u	NOUN
ejpam-4679	9	34	=	=	SYM
ejpam-4679	9	35	u(t	u(t	NOUN
ejpam-4679	9	36	,	,	PUNCT
ejpam-4679	9	37	x	x	X
ejpam-4679	9	38	)	)	PUNCT
ejpam-4679	9	39	is	be	AUX
ejpam-4679	9	40	the	the	DET
ejpam-4679	9	41	volumetric	volumetric	ADJ
ejpam-4679	9	42	water	water	NOUN
ejpam-4679	9	43	content	content	NOUN
ejpam-4679	9	44	,	,	PUNCT
ejpam-4679	9	45	d(u	d(u	PROPN
ejpam-4679	9	46	)	)	PUNCT
ejpam-4679	9	47	is	be	AUX
ejpam-4679	9	48	the	the	DET
ejpam-4679	9	49	water	water	NOUN
ejpam-4679	9	50	diffusivity	diffusivity	NOUN
ejpam-4679	9	51	,	,	PUNCT
ejpam-4679	9	52	t	t	PROPN
ejpam-4679	9	53	is	be	AUX
ejpam-4679	9	54	the	the	DET
ejpam-4679	9	55	time	time	NOUN
ejpam-4679	9	56	and	and	CCONJ
ejpam-4679	9	57	x	x	NOUN
ejpam-4679	9	58	is	be	AUX
ejpam-4679	9	59	the	the	DET
ejpam-4679	9	60	distance	distance	NOUN
ejpam-4679	9	61	from	from	ADP
ejpam-4679	9	62	the	the	DET
ejpam-4679	9	63	inlet	inlet	NOUN
ejpam-4679	9	64	of	of	ADP
ejpam-4679	9	65	the	the	DET
ejpam-4679	9	66	horizontal	horizontal	ADJ
ejpam-4679	9	67	medium	medium	NOUN
ejpam-4679	9	68	column	column	NOUN
ejpam-4679	9	69	.	.	PUNCT
ejpam-4679	10	1	the	the	DET
ejpam-4679	10	2	equation	equation	NOUN
ejpam-4679	10	3	(	(	PUNCT
ejpam-4679	10	4	1	1	X
ejpam-4679	10	5	)	)	PUNCT
ejpam-4679	10	6	takes	take	VERB
ejpam-4679	10	7	the	the	DET
ejpam-4679	10	8	following	follow	VERB
ejpam-4679	10	9	form	form	NOUN
ejpam-4679	10	10	after	after	SCONJ
ejpam-4679	10	11	the	the	DET
ejpam-4679	10	12	boltzmann	boltzmann	PROPN
ejpam-4679	10	13	scaling	scale	VERB
ejpam-4679	10	14	x	x	PUNCT
ejpam-4679	10	15	=	=	SYM
ejpam-4679	10	16	λt1/2	λt1/2	PROPN
ejpam-4679	10	17	:	:	PUNCT
ejpam-4679	10	18	−λ	−λ	NOUN
ejpam-4679	10	19	2	2	NUM
ejpam-4679	10	20	∂u	∂u	PROPN
ejpam-4679	10	21	∂λ	∂λ	PROPN
ejpam-4679	10	22	=	=	SYM
ejpam-4679	10	23	∂	∂	NUM
ejpam-4679	10	24	∂λ	∂λ	PROPN
ejpam-4679	10	25	(	(	PUNCT
ejpam-4679	10	26	d(u	d(u	PROPN
ejpam-4679	10	27	)	)	PUNCT
ejpam-4679	10	28	∂u	∂u	PROPN
ejpam-4679	10	29	∂λ	∂λ	PROPN
ejpam-4679	10	30	)	)	PUNCT
ejpam-4679	10	31	.	.	PUNCT
ejpam-4679	11	1	∗corresponding	∗corresponde	VERB
ejpam-4679	11	2	author	author	NOUN
ejpam-4679	11	3	.	.	PUNCT
ejpam-4679	12	1	doi	doi	NOUN
ejpam-4679	12	2	:	:	PUNCT
ejpam-4679	12	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4679	https://doi.org/10.29020/nybg.ejpam.v16i1.4679	NOUN
ejpam-4679	12	4	email	email	NOUN
ejpam-4679	12	5	addresses	address	NOUN
ejpam-4679	12	6	:	:	PUNCT
ejpam-4679	12	7	mustafa.zeki@aum.edu.kw	mustafa.zeki@aum.edu.kw	ADJ
ejpam-4679	12	8	(	(	PUNCT
ejpam-4679	12	9	m.	m.	NOUN
ejpam-4679	12	10	zeki	zeki	PROPN
ejpam-4679	12	11	)	)	PUNCT
ejpam-4679	12	12	,	,	PUNCT
ejpam-4679	12	13	statar@alfaisal.edu	statar@alfaisal.edu	PROPN
ejpam-4679	12	14	(	(	PUNCT
ejpam-4679	12	15	s.	s.	PROPN
ejpam-4679	12	16	tatar	tatar	PROPN
ejpam-4679	12	17	)	)	PUNCT
ejpam-4679	12	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4679	12	19	491	491	NUM
ejpam-4679	13	1	©	©	PROPN
ejpam-4679	13	2	2023	2023	NUM
ejpam-4679	13	3	ejpam	ejpam	NOUN
ejpam-4679	13	4	all	all	DET
ejpam-4679	13	5	rights	right	NOUN
ejpam-4679	13	6	reserved	reserve	VERB
ejpam-4679	13	7	.	.	PUNCT
ejpam-4679	14	1	m.	m.	PROPN
ejpam-4679	14	2	zeki	zeki	PROPN
ejpam-4679	14	3	,	,	PUNCT
ejpam-4679	14	4	s.	s.	PROPN
ejpam-4679	14	5	tatar	tatar	PROPN
ejpam-4679	14	6	/	/	SYM
ejpam-4679	14	7	eur	eur	PROPN
ejpam-4679	14	8	.	.	PUNCT
ejpam-4679	15	1	j.	j.	PROPN
ejpam-4679	15	2	pure	pure	PROPN
ejpam-4679	15	3	appl	appl	PROPN
ejpam-4679	15	4	.	.	PROPN
ejpam-4679	15	5	math	math	PROPN
ejpam-4679	15	6	,	,	PUNCT
ejpam-4679	15	7	16	16	NUM
ejpam-4679	15	8	(	(	PUNCT
ejpam-4679	15	9	1	1	NUM
ejpam-4679	15	10	)	)	PUNCT
ejpam-4679	15	11	(	(	PUNCT
ejpam-4679	15	12	2023	2023	NUM
ejpam-4679	15	13	)	)	PUNCT
ejpam-4679	15	14	,	,	PUNCT
ejpam-4679	15	15	491	491	NUM
ejpam-4679	15	16	-	-	SYM
ejpam-4679	15	17	502	502	NUM
ejpam-4679	15	18	492	492	NUM
ejpam-4679	15	19	however	however	ADV
ejpam-4679	15	20	many	many	ADJ
ejpam-4679	15	21	experiments	experiment	NOUN
ejpam-4679	15	22	show	show	VERB
ejpam-4679	15	23	that	that	SCONJ
ejpam-4679	15	24	the	the	DET
ejpam-4679	15	25	evolution	evolution	NOUN
ejpam-4679	15	26	of	of	ADP
ejpam-4679	15	27	a	a	DET
ejpam-4679	15	28	horizontal	horizontal	ADJ
ejpam-4679	15	29	wetting	wet	VERB
ejpam-4679	15	30	front	front	NOUN
ejpam-4679	15	31	deviates	deviate	VERB
ejpam-4679	15	32	significanlty	significanlty	NOUN
ejpam-4679	15	33	form	form	NOUN
ejpam-4679	15	34	boltzmann	boltzmann	NOUN
ejpam-4679	15	35	scaling	scaling	NOUN
ejpam-4679	15	36	.	.	PUNCT
ejpam-4679	16	1	these	these	DET
ejpam-4679	16	2	experiments	experiment	NOUN
ejpam-4679	16	3	reflect	reflect	VERB
ejpam-4679	16	4	anomalous	anomalous	ADJ
ejpam-4679	16	5	boltzmann	boltzmann	NOUN
ejpam-4679	16	6	scaling	scale	VERB
ejpam-4679	16	7	x	x	PUNCT
ejpam-4679	16	8	=	=	PUNCT
ejpam-4679	16	9	λ(u)tβ/2	λ(u)tβ/2	NUM
ejpam-4679	16	10	,	,	PUNCT
ejpam-4679	16	11	where	where	SCONJ
ejpam-4679	16	12	β	β	PROPN
ejpam-4679	16	13	is	be	AUX
ejpam-4679	16	14	the	the	DET
ejpam-4679	16	15	dimensionless	dimensionless	NOUN
ejpam-4679	16	16	exponent	exponent	NOUN
ejpam-4679	16	17	and	and	CCONJ
ejpam-4679	16	18	0	0	NUM
ejpam-4679	16	19	<	<	X
ejpam-4679	16	20	β	β	X
ejpam-4679	16	21	<	<	X
ejpam-4679	16	22	2	2	NUM
ejpam-4679	16	23	.	.	PUNCT
ejpam-4679	16	24	different	different	ADJ
ejpam-4679	16	25	models	model	NOUN
ejpam-4679	16	26	are	be	AUX
ejpam-4679	16	27	proposed	propose	VERB
ejpam-4679	16	28	to	to	PART
ejpam-4679	16	29	capture	capture	VERB
ejpam-4679	16	30	non	non	ADJ
ejpam-4679	16	31	-	-	ADJ
ejpam-4679	16	32	boltzman	boltzman	ADJ
ejpam-4679	16	33	scaling	scaling	NOUN
ejpam-4679	16	34	,	,	PUNCT
ejpam-4679	16	35	for	for	ADP
ejpam-4679	16	36	example	example	NOUN
ejpam-4679	16	37	see	see	VERB
ejpam-4679	16	38	[	[	X
ejpam-4679	16	39	4	4	X
ejpam-4679	16	40	]	]	X
ejpam-4679	16	41	[	[	X
ejpam-4679	16	42	13	13	NUM
ejpam-4679	16	43	]	]	PUNCT
ejpam-4679	16	44	.	.	PUNCT
ejpam-4679	17	1	in	in	ADP
ejpam-4679	17	2	[	[	X
ejpam-4679	17	3	4	4	NUM
ejpam-4679	17	4	]	]	PUNCT
ejpam-4679	17	5	and	and	CCONJ
ejpam-4679	17	6	[	[	X
ejpam-4679	17	7	9	9	NUM
ejpam-4679	17	8	]	]	PUNCT
ejpam-4679	17	9	,	,	PUNCT
ejpam-4679	17	10	the	the	DET
ejpam-4679	17	11	authors	author	NOUN
ejpam-4679	17	12	allow	allow	VERB
ejpam-4679	17	13	the	the	DET
ejpam-4679	17	14	water	water	NOUN
ejpam-4679	17	15	diffusivity	diffusivity	NOUN
ejpam-4679	17	16	d	d	NOUN
ejpam-4679	17	17	varies	vary	VERB
ejpam-4679	17	18	as	as	ADP
ejpam-4679	17	19	a	a	DET
ejpam-4679	17	20	function	function	NOUN
ejpam-4679	17	21	of	of	ADP
ejpam-4679	17	22	both	both	DET
ejpam-4679	17	23	water	water	NOUN
ejpam-4679	17	24	content	content	NOUN
ejpam-4679	17	25	and	and	CCONJ
ejpam-4679	17	26	time	time	NOUN
ejpam-4679	17	27	,	,	PUNCT
ejpam-4679	17	28	i.e.	i.e.	X
ejpam-4679	17	29	,	,	PUNCT
ejpam-4679	17	30	d	d	X
ejpam-4679	17	31	=	=	SYM
ejpam-4679	17	32	d(t	d(t	PROPN
ejpam-4679	17	33	,	,	PUNCT
ejpam-4679	17	34	u	u	NOUN
ejpam-4679	17	35	)	)	PUNCT
ejpam-4679	17	36	.	.	PUNCT
ejpam-4679	18	1	in	in	ADP
ejpam-4679	18	2	[	[	X
ejpam-4679	18	3	13	13	NUM
ejpam-4679	18	4	]	]	PUNCT
ejpam-4679	18	5	,	,	PUNCT
ejpam-4679	18	6	the	the	DET
ejpam-4679	18	7	authors	author	NOUN
ejpam-4679	18	8	propose	propose	VERB
ejpam-4679	18	9	the	the	DET
ejpam-4679	18	10	following	following	ADJ
ejpam-4679	18	11	time	time	NOUN
ejpam-4679	18	12	-	-	PUNCT
ejpam-4679	18	13	fractional	fractional	ADJ
ejpam-4679	18	14	richards	richard	NOUN
ejpam-4679	18	15	equation	equation	NOUN
ejpam-4679	18	16	:	:	PUNCT
ejpam-4679	18	17	∂βu	∂βu	PROPN
ejpam-4679	18	18	∂tβ	∂tβ	PROPN
ejpam-4679	18	19	=	=	SYM
ejpam-4679	18	20	∂	∂	NUM
ejpam-4679	18	21	∂x	∂x	PROPN
ejpam-4679	18	22	(	(	PUNCT
ejpam-4679	18	23	d(u	d(u	PROPN
ejpam-4679	18	24	)	)	PUNCT
ejpam-4679	18	25	∂u	∂u	PROPN
ejpam-4679	18	26	∂x	∂x	PROPN
ejpam-4679	18	27	)	)	PUNCT
ejpam-4679	18	28	,	,	PUNCT
ejpam-4679	18	29	(	(	PUNCT
ejpam-4679	18	30	2	2	X
ejpam-4679	18	31	)	)	PUNCT
ejpam-4679	18	32	where	where	SCONJ
ejpam-4679	18	33	0	0	PUNCT
ejpam-4679	18	34	<	<	X
ejpam-4679	18	35	β	β	X
ejpam-4679	18	36	<	<	X
ejpam-4679	18	37	1	1	NUM
ejpam-4679	18	38	is	be	AUX
ejpam-4679	18	39	the	the	DET
ejpam-4679	18	40	order	order	NOUN
ejpam-4679	18	41	of	of	ADP
ejpam-4679	18	42	the	the	DET
ejpam-4679	18	43	time	time	NOUN
ejpam-4679	18	44	-	-	PUNCT
ejpam-4679	18	45	fractional	fractional	ADJ
ejpam-4679	18	46	derivative	derivative	NOUN
ejpam-4679	18	47	,	,	PUNCT
ejpam-4679	18	48	0	0	PUNCT
ejpam-4679	18	49	<	<	X
ejpam-4679	18	50	β	β	X
ejpam-4679	18	51	<	<	X
ejpam-4679	18	52	1	1	NUM
ejpam-4679	18	53	,	,	PUNCT
ejpam-4679	18	54	∂βu	∂βu	PROPN
ejpam-4679	18	55	∂tβ	∂tβ	PROPN
ejpam-4679	18	56	is	be	AUX
ejpam-4679	18	57	the	the	DET
ejpam-4679	18	58	time	time	NOUN
ejpam-4679	18	59	-	-	PUNCT
ejpam-4679	18	60	fractional	fractional	ADJ
ejpam-4679	18	61	caputo	caputo	PROPN
ejpam-4679	18	62	fractional	fractional	PROPN
ejpam-4679	18	63	derivative	derivative	PROPN
ejpam-4679	18	64	and	and	CCONJ
ejpam-4679	18	65	defined	define	VERB
ejpam-4679	18	66	as	as	SCONJ
ejpam-4679	18	67	follows	follow	VERB
ejpam-4679	18	68	:	:	PUNCT
ejpam-4679	18	69	∂βu	∂βu	PROPN
ejpam-4679	18	70	∂tβ	∂tβ	PROPN
ejpam-4679	18	71	=	=	SYM
ejpam-4679	18	72	∫	∫	PROPN
ejpam-4679	18	73	t	t	PROPN
ejpam-4679	18	74	0	0	NUM
ejpam-4679	19	1	(	(	PUNCT
ejpam-4679	19	2	t−	t−	PROPN
ejpam-4679	19	3	ξ)−β	ξ)−β	PROPN
ejpam-4679	19	4	γ(1	γ(1	PROPN
ejpam-4679	19	5	−	−	PROPN
ejpam-4679	19	6	β	β	X
ejpam-4679	19	7	)	)	PUNCT
ejpam-4679	19	8	∂u(x	∂u(x	PROPN
ejpam-4679	19	9	,	,	PUNCT
ejpam-4679	19	10	ξ	ξ	X
ejpam-4679	19	11	)	)	PUNCT
ejpam-4679	19	12	∂ξ	∂ξ	NOUN
ejpam-4679	20	1	dξ	dξ	PROPN
ejpam-4679	20	2	,	,	PUNCT
ejpam-4679	20	3	where	where	SCONJ
ejpam-4679	20	4	γ	γ	X
ejpam-4679	20	5	(	(	PUNCT
ejpam-4679	20	6	.	.	PUNCT
ejpam-4679	20	7	)	)	PUNCT
ejpam-4679	20	8	is	be	AUX
ejpam-4679	20	9	the	the	DET
ejpam-4679	20	10	gamma	gamma	PROPN
ejpam-4679	20	11	function	function	NOUN
ejpam-4679	20	12	.	.	PUNCT
ejpam-4679	21	1	we	we	PRON
ejpam-4679	21	2	note	note	VERB
ejpam-4679	21	3	that	that	SCONJ
ejpam-4679	21	4	there	there	PRON
ejpam-4679	21	5	is	be	VERB
ejpam-4679	21	6	another	another	DET
ejpam-4679	21	7	kind	kind	NOUN
ejpam-4679	21	8	of	of	ADP
ejpam-4679	21	9	fractional	fractional	ADJ
ejpam-4679	21	10	derivative	derivative	NOUN
ejpam-4679	21	11	used	use	VERB
ejpam-4679	21	12	frequently	frequently	ADV
ejpam-4679	21	13	called	call	VERB
ejpam-4679	21	14	riemann	riemann	PROPN
ejpam-4679	21	15	-	-	PUNCT
ejpam-4679	21	16	lioville	lioville	ADJ
ejpam-4679	21	17	fractional	fractional	ADJ
ejpam-4679	21	18	derivative	derivative	NOUN
ejpam-4679	21	19	defined	define	VERB
ejpam-4679	21	20	by	by	ADP
ejpam-4679	21	21	r∂β	r∂β	NOUN
ejpam-4679	21	22	t	t	PROPN
ejpam-4679	21	23	u(x	u(x	PROPN
ejpam-4679	21	24	,	,	PUNCT
ejpam-4679	21	25	t	t	PROPN
ejpam-4679	21	26	)	)	PUNCT
ejpam-4679	21	27	=	=	SYM
ejpam-4679	21	28	∂	∂	NUM
ejpam-4679	22	1	∂t	∂t	PROPN
ejpam-4679	22	2	∫	∫	PROPN
ejpam-4679	22	3	t	t	PROPN
ejpam-4679	22	4	0	0	NUM
ejpam-4679	22	5	(	(	PUNCT
ejpam-4679	22	6	t−	t−	PROPN
ejpam-4679	22	7	ξ)−β	ξ)−β	PROPN
ejpam-4679	22	8	γ(1	γ(1	PROPN
ejpam-4679	22	9	−	−	NUM
ejpam-4679	22	10	β	β	NOUN
ejpam-4679	22	11	)	)	PUNCT
ejpam-4679	22	12	u(x	u(x	PROPN
ejpam-4679	22	13	,	,	PUNCT
ejpam-4679	22	14	ξ)dξ	ξ)dξ	PROPN
ejpam-4679	22	15	.	.	PUNCT
ejpam-4679	23	1	these	these	DET
ejpam-4679	23	2	two	two	NUM
ejpam-4679	23	3	fractional	fractional	ADJ
ejpam-4679	23	4	derivatives	derivative	NOUN
ejpam-4679	23	5	agree	agree	VERB
ejpam-4679	23	6	when	when	SCONJ
ejpam-4679	23	7	the	the	DET
ejpam-4679	23	8	initial	initial	ADJ
ejpam-4679	23	9	condition	condition	NOUN
ejpam-4679	23	10	is	be	AUX
ejpam-4679	23	11	zero	zero	NUM
ejpam-4679	23	12	.	.	PUNCT
ejpam-4679	24	1	kilbas	kilbas	PROPN
ejpam-4679	24	2	et	et	PROPN
ejpam-4679	24	3	al	al	PROPN
ejpam-4679	25	1	[	[	X
ejpam-4679	25	2	11	11	NUM
ejpam-4679	25	3	]	]	PUNCT
ejpam-4679	25	4	and	and	CCONJ
ejpam-4679	25	5	podlubny	podlubny	NOUN
ejpam-4679	25	6	[	[	X
ejpam-4679	25	7	17	17	NUM
ejpam-4679	25	8	]	]	PUNCT
ejpam-4679	25	9	can	can	AUX
ejpam-4679	25	10	be	be	AUX
ejpam-4679	25	11	referred	refer	VERB
ejpam-4679	25	12	for	for	ADP
ejpam-4679	25	13	further	further	ADJ
ejpam-4679	25	14	properties	property	NOUN
ejpam-4679	25	15	of	of	ADP
ejpam-4679	25	16	the	the	DET
ejpam-4679	25	17	caputo	caputo	PROPN
ejpam-4679	25	18	and	and	CCONJ
ejpam-4679	25	19	riemannlioville	riemannlioville	VERB
ejpam-4679	25	20	fractional	fractional	ADJ
ejpam-4679	25	21	derivatives	derivative	NOUN
ejpam-4679	25	22	.	.	PUNCT
ejpam-4679	26	1	since	since	SCONJ
ejpam-4679	26	2	the	the	DET
ejpam-4679	26	3	initial	initial	ADJ
ejpam-4679	26	4	condition	condition	NOUN
ejpam-4679	26	5	is	be	AUX
ejpam-4679	26	6	zero	zero	NUM
ejpam-4679	26	7	in	in	ADP
ejpam-4679	26	8	our	our	PRON
ejpam-4679	26	9	problem	problem	NOUN
ejpam-4679	26	10	,	,	PUNCT
ejpam-4679	26	11	any	any	DET
ejpam-4679	26	12	result	result	NOUN
ejpam-4679	26	13	found	find	VERB
ejpam-4679	26	14	in	in	ADP
ejpam-4679	26	15	the	the	DET
ejpam-4679	26	16	literature	literature	NOUN
ejpam-4679	26	17	for	for	ADP
ejpam-4679	26	18	one	one	NUM
ejpam-4679	26	19	of	of	ADP
ejpam-4679	26	20	these	these	DET
ejpam-4679	26	21	hold	hold	NOUN
ejpam-4679	26	22	for	for	ADP
ejpam-4679	26	23	the	the	DET
ejpam-4679	26	24	other	other	ADJ
ejpam-4679	26	25	one	one	NUM
ejpam-4679	26	26	.	.	PUNCT
ejpam-4679	27	1	for	for	ADP
ejpam-4679	27	2	the	the	DET
ejpam-4679	27	3	convenience	convenience	NOUN
ejpam-4679	27	4	of	of	ADP
ejpam-4679	27	5	the	the	DET
ejpam-4679	27	6	reader	reader	NOUN
ejpam-4679	27	7	,	,	PUNCT
ejpam-4679	27	8	we	we	PRON
ejpam-4679	27	9	present	present	VERB
ejpam-4679	27	10	the	the	DET
ejpam-4679	27	11	main	main	ADJ
ejpam-4679	27	12	steps	step	NOUN
ejpam-4679	27	13	of	of	ADP
ejpam-4679	27	14	the	the	DET
ejpam-4679	27	15	derivation	derivation	NOUN
ejpam-4679	27	16	of	of	ADP
ejpam-4679	27	17	the	the	DET
ejpam-4679	27	18	governing	govern	VERB
ejpam-4679	27	19	equation	equation	NOUN
ejpam-4679	27	20	by	by	ADP
ejpam-4679	27	21	following	follow	VERB
ejpam-4679	27	22	[	[	X
ejpam-4679	27	23	16	16	NUM
ejpam-4679	27	24	]	]	PUNCT
ejpam-4679	27	25	.	.	PUNCT
ejpam-4679	28	1	if	if	SCONJ
ejpam-4679	28	2	the	the	DET
ejpam-4679	28	3	fluid	fluid	ADJ
ejpam-4679	28	4	particles	particle	NOUN
ejpam-4679	28	5	are	be	AUX
ejpam-4679	28	6	trapped	trap	VERB
ejpam-4679	28	7	in	in	ADP
ejpam-4679	28	8	some	some	DET
ejpam-4679	28	9	regions	region	NOUN
ejpam-4679	28	10	for	for	ADP
ejpam-4679	28	11	several	several	ADJ
ejpam-4679	28	12	periods	period	NOUN
ejpam-4679	28	13	of	of	ADP
ejpam-4679	28	14	time	time	NOUN
ejpam-4679	28	15	s1	s1	NOUN
ejpam-4679	28	16	,	,	PUNCT
ejpam-4679	28	17	·	·	PUNCT
ejpam-4679	28	18	·	·	PUNCT
ejpam-4679	28	19	·	·	PUNCT
ejpam-4679	28	20	,	,	PUNCT
ejpam-4679	28	21	sn	sn	PROPN
ejpam-4679	28	22	then	then	ADV
ejpam-4679	28	23	the	the	DET
ejpam-4679	28	24	continuity	continuity	NOUN
ejpam-4679	28	25	equation	equation	NOUN
ejpam-4679	28	26	becomes	become	VERB
ejpam-4679	28	27	ut	ut	PROPN
ejpam-4679	28	28	=	=	PRON
ejpam-4679	29	1	−	−	PROPN
ejpam-4679	29	2	n∑	n∑	PROPN
ejpam-4679	29	3	i=1	i=1	PROPN
ejpam-4679	29	4	wi∇	wi∇	PUNCT
ejpam-4679	29	5	·	·	PUNCT
ejpam-4679	30	1	q(x	q(x	NOUN
ejpam-4679	30	2	,	,	PUNCT
ejpam-4679	30	3	t−	t−	PROPN
ejpam-4679	30	4	si	si	NOUN
ejpam-4679	30	5	)	)	PUNCT
ejpam-4679	30	6	,	,	PUNCT
ejpam-4679	30	7	(	(	PUNCT
ejpam-4679	30	8	3	3	X
ejpam-4679	30	9	)	)	PUNCT
ejpam-4679	30	10	where	where	SCONJ
ejpam-4679	30	11	wi	wi	PROPN
ejpam-4679	30	12	are	be	AUX
ejpam-4679	30	13	some	some	DET
ejpam-4679	30	14	weights	weight	NOUN
ejpam-4679	30	15	.	.	PUNCT
ejpam-4679	31	1	if	if	SCONJ
ejpam-4679	31	2	we	we	PRON
ejpam-4679	31	3	take	take	VERB
ejpam-4679	31	4	wi	wi	PROPN
ejpam-4679	31	5	=	=	SYM
ejpam-4679	31	6	w(si)∆si	w(si)∆si	PROPN
ejpam-4679	31	7	with	with	ADP
ejpam-4679	31	8	∆si	∆si	NOUN
ejpam-4679	31	9	=	=	PUNCT
ejpam-4679	31	10	si−si−1	si−si−1	NOUN
ejpam-4679	31	11	for	for	ADP
ejpam-4679	31	12	some	some	DET
ejpam-4679	31	13	weight	weight	NOUN
ejpam-4679	31	14	density	density	NOUN
ejpam-4679	31	15	w	w	PROPN
ejpam-4679	31	16	=	=	SYM
ejpam-4679	31	17	w(s	w(s	PROPN
ejpam-4679	31	18	)	)	PUNCT
ejpam-4679	31	19	,	,	PUNCT
ejpam-4679	31	20	and	and	CCONJ
ejpam-4679	31	21	take	take	VERB
ejpam-4679	31	22	limit	limit	NOUN
ejpam-4679	31	23	as	as	SCONJ
ejpam-4679	31	24	n	n	PRON
ejpam-4679	31	25	goes	go	VERB
ejpam-4679	31	26	to	to	ADP
ejpam-4679	31	27	∞	∞	PROPN
ejpam-4679	31	28	,	,	PUNCT
ejpam-4679	31	29	(	(	PUNCT
ejpam-4679	31	30	3	3	X
ejpam-4679	31	31	)	)	PUNCT
ejpam-4679	31	32	becomes	become	VERB
ejpam-4679	31	33	ut	ut	PROPN
ejpam-4679	31	34	=	=	PRON
ejpam-4679	32	1	−	−	PROPN
ejpam-4679	32	2	∫	∫	PROPN
ejpam-4679	32	3	t	t	PROPN
ejpam-4679	32	4	0	0	NUM
ejpam-4679	33	1	w(t−	w(t−	PROPN
ejpam-4679	33	2	s)∇	s)∇	PROPN
ejpam-4679	33	3	·	·	PUNCT
ejpam-4679	33	4	q(x	q(x	PROPN
ejpam-4679	33	5	,	,	PUNCT
ejpam-4679	33	6	s	s	X
ejpam-4679	33	7	)	)	PUNCT
ejpam-4679	33	8	ds	ds	NOUN
ejpam-4679	33	9	.	.	PUNCT
ejpam-4679	34	1	(	(	PUNCT
ejpam-4679	34	2	4	4	X
ejpam-4679	34	3	)	)	PUNCT
ejpam-4679	34	4	equation	equation	NOUN
ejpam-4679	34	5	(	(	PUNCT
ejpam-4679	34	6	4	4	X
ejpam-4679	34	7	)	)	PUNCT
ejpam-4679	34	8	accounts	account	NOUN
ejpam-4679	34	9	for	for	ADP
ejpam-4679	34	10	the	the	DET
ejpam-4679	34	11	fluid	fluid	ADJ
ejpam-4679	34	12	particles	particle	NOUN
ejpam-4679	34	13	that	that	PRON
ejpam-4679	34	14	can	can	AUX
ejpam-4679	34	15	be	be	AUX
ejpam-4679	34	16	trapped	trap	VERB
ejpam-4679	34	17	for	for	ADP
ejpam-4679	34	18	any	any	DET
ejpam-4679	34	19	period	period	NOUN
ejpam-4679	34	20	of	of	ADP
ejpam-4679	34	21	time	time	NOUN
ejpam-4679	34	22	.	.	PUNCT
ejpam-4679	35	1	the	the	DET
ejpam-4679	35	2	amount	amount	NOUN
ejpam-4679	35	3	of	of	ADP
ejpam-4679	35	4	flux	flux	NOUN
ejpam-4679	35	5	of	of	ADP
ejpam-4679	35	6	the	the	DET
ejpam-4679	35	7	particles	particle	NOUN
ejpam-4679	35	8	that	that	PRON
ejpam-4679	35	9	wait	wait	VERB
ejpam-4679	35	10	for	for	ADP
ejpam-4679	35	11	the	the	DET
ejpam-4679	35	12	time	time	NOUN
ejpam-4679	35	13	s	s	NOUN
ejpam-4679	35	14	equals	equal	VERB
ejpam-4679	35	15	w(s	w(s	PROPN
ejpam-4679	35	16	)	)	PUNCT
ejpam-4679	35	17	.	.	PUNCT
ejpam-4679	36	1	using	use	VERB
ejpam-4679	36	2	the	the	DET
ejpam-4679	36	3	choice	choice	NOUN
ejpam-4679	36	4	of	of	ADP
ejpam-4679	36	5	[	[	X
ejpam-4679	36	6	16	16	NUM
ejpam-4679	36	7	]	]	PUNCT
ejpam-4679	36	8	for	for	ADP
ejpam-4679	36	9	w	w	NOUN
ejpam-4679	36	10	we	we	PRON
ejpam-4679	36	11	arrive	arrive	VERB
ejpam-4679	36	12	at	at	ADP
ejpam-4679	36	13	:	:	PUNCT
ejpam-4679	36	14	m.	m.	NOUN
ejpam-4679	36	15	zeki	zeki	PROPN
ejpam-4679	36	16	,	,	PUNCT
ejpam-4679	36	17	s.	s.	PROPN
ejpam-4679	36	18	tatar	tatar	PROPN
ejpam-4679	36	19	/	/	SYM
ejpam-4679	36	20	eur	eur	PROPN
ejpam-4679	36	21	.	.	PUNCT
ejpam-4679	37	1	j.	j.	PROPN
ejpam-4679	37	2	pure	pure	PROPN
ejpam-4679	37	3	appl	appl	PROPN
ejpam-4679	37	4	.	.	PROPN
ejpam-4679	37	5	math	math	PROPN
ejpam-4679	37	6	,	,	PUNCT
ejpam-4679	37	7	16	16	NUM
ejpam-4679	37	8	(	(	PUNCT
ejpam-4679	37	9	1	1	NUM
ejpam-4679	37	10	)	)	PUNCT
ejpam-4679	37	11	(	(	PUNCT
ejpam-4679	37	12	2023	2023	NUM
ejpam-4679	37	13	)	)	PUNCT
ejpam-4679	37	14	,	,	PUNCT
ejpam-4679	37	15	491	491	NUM
ejpam-4679	37	16	-	-	SYM
ejpam-4679	37	17	502	502	NUM
ejpam-4679	37	18	493	493	NUM
ejpam-4679	37	19	ut	ut	NOUN
ejpam-4679	38	1	=	=	PRON
ejpam-4679	39	1	−	−	PROPN
ejpam-4679	39	2	1	1	NUM
ejpam-4679	39	3	γ(β	γ(β	PROPN
ejpam-4679	39	4	)	)	PUNCT
ejpam-4679	39	5	∂	∂	NOUN
ejpam-4679	40	1	∂t	∂t	PROPN
ejpam-4679	40	2	∫	∫	PROPN
ejpam-4679	40	3	t	t	PROPN
ejpam-4679	40	4	0	0	NUM
ejpam-4679	40	5	(	(	PUNCT
ejpam-4679	40	6	t−	t−	X
ejpam-4679	40	7	s)β−1∇	s)β−1∇	X
ejpam-4679	40	8	·	·	PUNCT
ejpam-4679	40	9	q(x	q(x	PROPN
ejpam-4679	40	10	,	,	PUNCT
ejpam-4679	40	11	s	s	X
ejpam-4679	40	12	)	)	PUNCT
ejpam-4679	40	13	ds	ds	ADJ
ejpam-4679	40	14	=	=	PUNCT
ejpam-4679	40	15	−r∂1−β	−r∂1−β	NOUN
ejpam-4679	40	16	t	t	PROPN
ejpam-4679	40	17	∇	∇	X
ejpam-4679	40	18	·	·	PUNCT
ejpam-4679	40	19	q	q	X
ejpam-4679	40	20	,	,	PUNCT
ejpam-4679	40	21	(	(	PUNCT
ejpam-4679	40	22	5	5	NUM
ejpam-4679	40	23	)	)	PUNCT
ejpam-4679	40	24	where	where	SCONJ
ejpam-4679	40	25	r∂1−β	r∂1−β	PROPN
ejpam-4679	40	26	t	t	PROPN
ejpam-4679	40	27	denotes	denote	VERB
ejpam-4679	40	28	the	the	DET
ejpam-4679	40	29	riemann	riemann	PROPN
ejpam-4679	40	30	-	-	PUNCT
ejpam-4679	40	31	liouville	liouville	VERB
ejpam-4679	40	32	fractional	fractional	ADJ
ejpam-4679	40	33	derivative	derivative	NOUN
ejpam-4679	40	34	of	of	ADP
ejpam-4679	40	35	order	order	NOUN
ejpam-4679	40	36	1	1	NUM
ejpam-4679	40	37	−	−	NOUN
ejpam-4679	41	1	β	β	X
ejpam-4679	41	2	.	.	PUNCT
ejpam-4679	42	1	if	if	SCONJ
ejpam-4679	42	2	we	we	PRON
ejpam-4679	42	3	apply	apply	VERB
ejpam-4679	42	4	the	the	DET
ejpam-4679	42	5	riemann	riemann	PROPN
ejpam-4679	42	6	-	-	PUNCT
ejpam-4679	42	7	lioville	lioville	ADJ
ejpam-4679	42	8	fractional	fractional	ADJ
ejpam-4679	42	9	operator	operator	NOUN
ejpam-4679	42	10	i1−β	i1−β	PROPN
ejpam-4679	42	11	t	t	PROPN
ejpam-4679	42	12	,	,	PUNCT
ejpam-4679	42	13	defined	define	VERB
ejpam-4679	42	14	by	by	ADP
ejpam-4679	42	15	i1−β	i1−β	PROPN
ejpam-4679	42	16	t	t	PROPN
ejpam-4679	42	17	u(x	u(x	NOUN
ejpam-4679	42	18	,	,	PUNCT
ejpam-4679	42	19	t	t	PROPN
ejpam-4679	42	20	)	)	PUNCT
ejpam-4679	42	21	:	:	PUNCT
ejpam-4679	43	1	=	=	SYM
ejpam-4679	43	2	1	1	X
ejpam-4679	44	1	γ(1	γ(1	NOUN
ejpam-4679	44	2	−	−	PROPN
ejpam-4679	44	3	β	β	NOUN
ejpam-4679	44	4	)	)	PUNCT
ejpam-4679	44	5	∫	∫	PROPN
ejpam-4679	44	6	t	t	PROPN
ejpam-4679	44	7	0	0	NUM
ejpam-4679	44	8	(	(	PUNCT
ejpam-4679	44	9	t−	t−	PROPN
ejpam-4679	44	10	s)−βu(x	s)−βu(x	PROPN
ejpam-4679	44	11	,	,	PUNCT
ejpam-4679	44	12	s	s	X
ejpam-4679	44	13	)	)	PUNCT
ejpam-4679	44	14	ds	ds	NOUN
ejpam-4679	44	15	to	to	ADP
ejpam-4679	44	16	both	both	DET
ejpam-4679	44	17	sides	side	NOUN
ejpam-4679	44	18	of	of	ADP
ejpam-4679	44	19	(	(	PUNCT
ejpam-4679	44	20	5	5	NUM
ejpam-4679	44	21	)	)	PUNCT
ejpam-4679	44	22	and	and	CCONJ
ejpam-4679	44	23	take	take	VERB
ejpam-4679	44	24	into	into	ADP
ejpam-4679	44	25	account	account	NOUN
ejpam-4679	44	26	the	the	DET
ejpam-4679	44	27	composition	composition	NOUN
ejpam-4679	44	28	formula	formula	NOUN
ejpam-4679	44	29	for	for	ADP
ejpam-4679	44	30	the	the	DET
ejpam-4679	44	31	functions	function	NOUN
ejpam-4679	44	32	with	with	ADP
ejpam-4679	44	33	vanishing	vanish	VERB
ejpam-4679	44	34	initial	initial	ADJ
ejpam-4679	44	35	conditions	condition	NOUN
ejpam-4679	44	36	we	we	PRON
ejpam-4679	44	37	have	have	VERB
ejpam-4679	44	38	:	:	PUNCT
ejpam-4679	44	39	∂β	∂β	PROPN
ejpam-4679	44	40	∂tβ	∂tβ	PROPN
ejpam-4679	44	41	u	u	NOUN
ejpam-4679	44	42	=	=	X
ejpam-4679	44	43	∇	∇	X
ejpam-4679	44	44	·	·	PUNCT
ejpam-4679	44	45	(	(	PUNCT
ejpam-4679	44	46	d(u)∇u	d(u)∇u	PROPN
ejpam-4679	44	47	)	)	PUNCT
ejpam-4679	44	48	.	.	PUNCT
ejpam-4679	45	1	(	(	PUNCT
ejpam-4679	45	2	6	6	NUM
ejpam-4679	45	3	)	)	PUNCT
ejpam-4679	45	4	equation	equation	NOUN
ejpam-4679	45	5	(	(	PUNCT
ejpam-4679	45	6	6	6	NUM
ejpam-4679	45	7	)	)	PUNCT
ejpam-4679	45	8	is	be	AUX
ejpam-4679	45	9	also	also	ADV
ejpam-4679	45	10	called	call	VERB
ejpam-4679	45	11	generalized	generalized	ADJ
ejpam-4679	45	12	richards	richard	NOUN
ejpam-4679	45	13	equation	equation	NOUN
ejpam-4679	45	14	can	can	AUX
ejpam-4679	45	15	be	be	AUX
ejpam-4679	45	16	found	find	VERB
ejpam-4679	45	17	in	in	ADP
ejpam-4679	45	18	many	many	ADJ
ejpam-4679	45	19	papers	paper	NOUN
ejpam-4679	45	20	.	.	PUNCT
ejpam-4679	46	1	note	note	VERB
ejpam-4679	46	2	that	that	SCONJ
ejpam-4679	46	3	in	in	ADP
ejpam-4679	46	4	the	the	DET
ejpam-4679	46	5	one	one	NUM
ejpam-4679	46	6	-	-	PUNCT
ejpam-4679	46	7	dimensional	dimensional	ADJ
ejpam-4679	46	8	case	case	NOUN
ejpam-4679	46	9	,	,	PUNCT
ejpam-4679	46	10	the	the	DET
ejpam-4679	46	11	equation	equation	NOUN
ejpam-4679	46	12	(	(	PUNCT
ejpam-4679	46	13	6	6	NUM
ejpam-4679	46	14	)	)	PUNCT
ejpam-4679	46	15	is	be	AUX
ejpam-4679	46	16	the	the	DET
ejpam-4679	46	17	same	same	ADJ
ejpam-4679	46	18	as	as	ADP
ejpam-4679	46	19	(	(	PUNCT
ejpam-4679	46	20	2	2	NUM
ejpam-4679	46	21	)	)	PUNCT
ejpam-4679	46	22	.	.	PUNCT
ejpam-4679	47	1	to	to	ADP
ejpam-4679	47	2	the	the	DET
ejpam-4679	47	3	best	good	ADJ
ejpam-4679	47	4	of	of	ADP
ejpam-4679	47	5	authors	author	NOUN
ejpam-4679	47	6	knowledge	knowledge	NOUN
ejpam-4679	47	7	,	,	PUNCT
ejpam-4679	47	8	there	there	PRON
ejpam-4679	47	9	are	be	VERB
ejpam-4679	47	10	only	only	ADV
ejpam-4679	47	11	a	a	DET
ejpam-4679	47	12	few	few	ADJ
ejpam-4679	47	13	studies	study	NOUN
ejpam-4679	47	14	for	for	ADP
ejpam-4679	47	15	the	the	DET
ejpam-4679	47	16	numerical	numerical	ADJ
ejpam-4679	47	17	solution	solution	NOUN
ejpam-4679	47	18	of	of	ADP
ejpam-4679	47	19	the	the	DET
ejpam-4679	47	20	nonlinear	nonlinear	ADJ
ejpam-4679	47	21	nonlocal	nonlocal	ADJ
ejpam-4679	47	22	partial	partial	ADJ
ejpam-4679	47	23	differential	differential	NOUN
ejpam-4679	47	24	equations	equation	NOUN
ejpam-4679	47	25	.	.	PUNCT
ejpam-4679	48	1	in	in	ADP
ejpam-4679	48	2	[	[	X
ejpam-4679	48	3	14	14	NUM
ejpam-4679	48	4	]	]	PUNCT
ejpam-4679	48	5	,	,	PUNCT
ejpam-4679	48	6	the	the	DET
ejpam-4679	48	7	fractional	fractional	ADJ
ejpam-4679	48	8	richards	richard	NOUN
ejpam-4679	48	9	equation	equation	NOUN
ejpam-4679	48	10	is	be	AUX
ejpam-4679	48	11	solved	solve	VERB
ejpam-4679	48	12	numerically	numerically	ADV
ejpam-4679	48	13	by	by	ADP
ejpam-4679	48	14	using	use	VERB
ejpam-4679	48	15	an	an	DET
ejpam-4679	48	16	implicit	implicit	ADJ
ejpam-4679	48	17	finite	finite	ADJ
ejpam-4679	48	18	difference	difference	NOUN
ejpam-4679	48	19	approximation	approximation	NOUN
ejpam-4679	48	20	.	.	PUNCT
ejpam-4679	49	1	they	they	PRON
ejpam-4679	49	2	convert	convert	VERB
ejpam-4679	49	3	the	the	DET
ejpam-4679	49	4	resulting	result	VERB
ejpam-4679	49	5	system	system	NOUN
ejpam-4679	49	6	of	of	ADP
ejpam-4679	49	7	equations	equation	NOUN
ejpam-4679	49	8	into	into	ADP
ejpam-4679	49	9	a	a	DET
ejpam-4679	49	10	tridiagonal	tridiagonal	ADJ
ejpam-4679	49	11	system	system	NOUN
ejpam-4679	49	12	of	of	ADP
ejpam-4679	49	13	non	non	ADJ
ejpam-4679	49	14	-	-	ADJ
ejpam-4679	49	15	linear	linear	ADJ
ejpam-4679	49	16	equations	equation	NOUN
ejpam-4679	49	17	.	.	PUNCT
ejpam-4679	50	1	then	then	ADV
ejpam-4679	50	2	they	they	PRON
ejpam-4679	50	3	solve	solve	VERB
ejpam-4679	50	4	the	the	DET
ejpam-4679	50	5	nonlinear	nonlinear	ADJ
ejpam-4679	50	6	system	system	NOUN
ejpam-4679	50	7	by	by	ADP
ejpam-4679	50	8	gauss	gauss	ADJ
ejpam-4679	50	9	elimination	elimination	NOUN
ejpam-4679	50	10	.	.	PUNCT
ejpam-4679	51	1	in	in	ADP
ejpam-4679	51	2	[	[	X
ejpam-4679	51	3	8	8	NUM
ejpam-4679	51	4	]	]	PUNCT
ejpam-4679	51	5	,	,	PUNCT
ejpam-4679	51	6	after	after	SCONJ
ejpam-4679	51	7	the	the	DET
ejpam-4679	51	8	authors	author	NOUN
ejpam-4679	51	9	state	state	VERB
ejpam-4679	51	10	the	the	DET
ejpam-4679	51	11	fractional	fractional	PROPN
ejpam-4679	51	12	richards	richard	NOUN
ejpam-4679	51	13	equation	equation	NOUN
ejpam-4679	51	14	as	as	ADP
ejpam-4679	51	15	an	an	DET
ejpam-4679	51	16	integral	integral	ADJ
ejpam-4679	51	17	equation	equation	NOUN
ejpam-4679	51	18	,	,	PUNCT
ejpam-4679	51	19	they	they	PRON
ejpam-4679	51	20	adopt	adopt	VERB
ejpam-4679	51	21	adams	adams	PROPN
ejpam-4679	51	22	-	-	PUNCT
ejpam-4679	51	23	bashforth	bashforth	PROPN
ejpam-4679	51	24	-	-	PUNCT
ejpam-4679	51	25	moulton	moulton	PROPN
ejpam-4679	51	26	algorithm	algorithm	NOUN
ejpam-4679	51	27	for	for	ADP
ejpam-4679	51	28	the	the	DET
ejpam-4679	51	29	nonlinear	nonlinear	ADJ
ejpam-4679	51	30	case	case	NOUN
ejpam-4679	51	31	.	.	PUNCT
ejpam-4679	52	1	they	they	PRON
ejpam-4679	52	2	test	test	VERB
ejpam-4679	52	3	their	their	PRON
ejpam-4679	52	4	numerical	numerical	ADJ
ejpam-4679	52	5	code	code	NOUN
ejpam-4679	52	6	by	by	ADP
ejpam-4679	52	7	comparing	compare	VERB
ejpam-4679	52	8	with	with	ADP
ejpam-4679	52	9	analytical	analytical	ADJ
ejpam-4679	52	10	results	result	NOUN
ejpam-4679	52	11	for	for	ADP
ejpam-4679	52	12	both	both	PRON
ejpam-4679	52	13	β	β	X
ejpam-4679	52	14	=	=	SYM
ejpam-4679	52	15	1	1	NUM
ejpam-4679	52	16	and	and	CCONJ
ejpam-4679	52	17	β	β	X
ejpam-4679	52	18	<	<	X
ejpam-4679	52	19	1	1	NUM
ejpam-4679	52	20	of	of	ADP
ejpam-4679	52	21	the	the	DET
ejpam-4679	52	22	linear	linear	ADJ
ejpam-4679	52	23	classical	classical	ADJ
ejpam-4679	52	24	and	and	CCONJ
ejpam-4679	52	25	fractional	fractional	ADJ
ejpam-4679	52	26	equations	equation	NOUN
ejpam-4679	52	27	.	.	PUNCT
ejpam-4679	53	1	in	in	ADP
ejpam-4679	53	2	[	[	X
ejpam-4679	53	3	7	7	NUM
ejpam-4679	53	4	]	]	PUNCT
ejpam-4679	53	5	,	,	PUNCT
ejpam-4679	53	6	the	the	DET
ejpam-4679	53	7	authors	author	NOUN
ejpam-4679	53	8	show	show	VERB
ejpam-4679	53	9	that	that	SCONJ
ejpam-4679	53	10	the	the	DET
ejpam-4679	53	11	fractional	fractional	ADJ
ejpam-4679	53	12	richards	richard	NOUN
ejpam-4679	53	13	equation	equation	NOUN
ejpam-4679	53	14	has	have	VERB
ejpam-4679	53	15	a	a	DET
ejpam-4679	53	16	form	form	NOUN
ejpam-4679	53	17	that	that	PRON
ejpam-4679	53	18	is	be	AUX
ejpam-4679	53	19	suitable	suitable	ADJ
ejpam-4679	53	20	for	for	ADP
ejpam-4679	53	21	a	a	DET
ejpam-4679	53	22	self	self	NOUN
ejpam-4679	53	23	-	-	PUNCT
ejpam-4679	53	24	similar	similar	ADJ
ejpam-4679	53	25	solution	solution	NOUN
ejpam-4679	53	26	using	use	VERB
ejpam-4679	53	27	the	the	DET
ejpam-4679	53	28	variable	variable	NOUN
ejpam-4679	53	29	ξ	ξ	NOUN
ejpam-4679	53	30	=	=	SYM
ejpam-4679	53	31	x	x	NOUN
ejpam-4679	53	32	/	/	SYM
ejpam-4679	53	33	tβ/2	tβ/2	NOUN
ejpam-4679	53	34	and	and	CCONJ
ejpam-4679	53	35	represent	represent	VERB
ejpam-4679	53	36	in	in	ADP
ejpam-4679	53	37	a	a	DET
ejpam-4679	53	38	form	form	NOUN
ejpam-4679	53	39	that	that	PRON
ejpam-4679	53	40	is	be	AUX
ejpam-4679	53	41	suitable	suitable	ADJ
ejpam-4679	53	42	for	for	ADP
ejpam-4679	53	43	finding	find	VERB
ejpam-4679	53	44	the	the	DET
ejpam-4679	53	45	self	self	NOUN
ejpam-4679	53	46	-	-	PUNCT
ejpam-4679	53	47	similar	similar	ADJ
ejpam-4679	53	48	solution	solution	NOUN
ejpam-4679	53	49	.	.	PUNCT
ejpam-4679	54	1	the	the	DET
ejpam-4679	54	2	self	self	NOUN
ejpam-4679	54	3	-	-	PUNCT
ejpam-4679	54	4	similar	similar	ADJ
ejpam-4679	54	5	solution	solution	NOUN
ejpam-4679	54	6	is	be	AUX
ejpam-4679	54	7	obtained	obtain	VERB
ejpam-4679	54	8	only	only	ADV
ejpam-4679	54	9	in	in	ADP
ejpam-4679	54	10	cases	case	NOUN
ejpam-4679	54	11	of	of	ADP
ejpam-4679	54	12	certain	certain	ADJ
ejpam-4679	54	13	initial	initial	ADJ
ejpam-4679	54	14	and	and	CCONJ
ejpam-4679	54	15	boundary	boundary	ADJ
ejpam-4679	54	16	conditions	condition	NOUN
ejpam-4679	54	17	:	:	PUNCT
ejpam-4679	54	18	u(t	u(t	NOUN
ejpam-4679	54	19	,	,	PUNCT
ejpam-4679	54	20	0	0	NUM
ejpam-4679	54	21	)	)	PUNCT
ejpam-4679	54	22	=	=	SYM
ejpam-4679	54	23	1	1	NUM
ejpam-4679	54	24	,	,	PUNCT
ejpam-4679	54	25	u(t,∞	u(t,∞	PROPN
ejpam-4679	54	26	)	)	PUNCT
ejpam-4679	55	1	=	=	SYM
ejpam-4679	55	2	0	0	NUM
ejpam-4679	55	3	,	,	PUNCT
ejpam-4679	55	4	u(0	u(0	PROPN
ejpam-4679	55	5	,	,	PUNCT
ejpam-4679	55	6	x	x	NOUN
ejpam-4679	55	7	)	)	PUNCT
ejpam-4679	55	8	=	=	SYM
ejpam-4679	55	9	0	0	X
ejpam-4679	55	10	.	.	PUNCT
ejpam-4679	56	1	the	the	DET
ejpam-4679	56	2	authors	author	NOUN
ejpam-4679	56	3	develop	develop	VERB
ejpam-4679	56	4	an	an	DET
ejpam-4679	56	5	implicit	implicit	ADJ
ejpam-4679	56	6	numerical	numerical	ADJ
ejpam-4679	56	7	approach	approach	NOUN
ejpam-4679	56	8	for	for	ADP
ejpam-4679	56	9	numerical	numerical	ADJ
ejpam-4679	56	10	simulation	simulation	PROPN
ejpam-4679	56	11	of	of	ADP
ejpam-4679	56	12	nonlinear	nonlinear	ADJ
ejpam-4679	56	13	variable	variable	ADJ
ejpam-4679	56	14	order	order	NOUN
ejpam-4679	56	15	time	time	NOUN
ejpam-4679	56	16	-	-	PUNCT
ejpam-4679	56	17	fractional	fractional	ADJ
ejpam-4679	56	18	diffusion	diffusion	NOUN
ejpam-4679	56	19	/	/	SYM
ejpam-4679	56	20	wave	wave	NOUN
ejpam-4679	56	21	-	-	PUNCT
ejpam-4679	56	22	diffusion	diffusion	NOUN
ejpam-4679	56	23	equations	equation	NOUN
ejpam-4679	56	24	in	in	ADP
ejpam-4679	56	25	[	[	X
ejpam-4679	56	26	20	20	NUM
ejpam-4679	56	27	]	]	PUNCT
ejpam-4679	56	28	.	.	PUNCT
ejpam-4679	57	1	these	these	DET
ejpam-4679	57	2	equations	equation	NOUN
ejpam-4679	57	3	are	be	AUX
ejpam-4679	57	4	useful	useful	ADJ
ejpam-4679	57	5	to	to	PART
ejpam-4679	57	6	describe	describe	VERB
ejpam-4679	57	7	liquid	liquid	ADJ
ejpam-4679	57	8	infiltration	infiltration	NOUN
ejpam-4679	57	9	for	for	ADP
ejpam-4679	57	10	both	both	DET
ejpam-4679	57	11	subdiffusion	subdiffusion	NOUN
ejpam-4679	57	12	and	and	CCONJ
ejpam-4679	57	13	superdiffusion	superdiffusion	NOUN
ejpam-4679	57	14	in	in	ADP
ejpam-4679	57	15	porous	porous	ADJ
ejpam-4679	57	16	media	medium	NOUN
ejpam-4679	57	17	.	.	PUNCT
ejpam-4679	58	1	as	as	ADP
ejpam-4679	58	2	a	a	DET
ejpam-4679	58	3	special	special	ADJ
ejpam-4679	58	4	case	case	NOUN
ejpam-4679	58	5	,	,	PUNCT
ejpam-4679	58	6	a	a	DET
ejpam-4679	58	7	time	time	NOUN
ejpam-4679	58	8	-	-	PUNCT
ejpam-4679	58	9	fractional	fractional	ADJ
ejpam-4679	58	10	boussinesq	boussinesq	ADJ
ejpam-4679	58	11	equation	equation	NOUN
ejpam-4679	58	12	is	be	AUX
ejpam-4679	58	13	considered	consider	VERB
ejpam-4679	58	14	.	.	PUNCT
ejpam-4679	59	1	in	in	ADP
ejpam-4679	59	2	the	the	DET
ejpam-4679	59	3	mentioned	mention	VERB
ejpam-4679	59	4	papers	paper	NOUN
ejpam-4679	59	5	above	above	ADV
ejpam-4679	59	6	,	,	PUNCT
ejpam-4679	59	7	either	either	CCONJ
ejpam-4679	59	8	a	a	DET
ejpam-4679	59	9	numerical	numerical	ADJ
ejpam-4679	59	10	method	method	NOUN
ejpam-4679	59	11	based	base	VERB
ejpam-4679	59	12	on	on	ADP
ejpam-4679	59	13	finite	finite	ADJ
ejpam-4679	59	14	difference	difference	NOUN
ejpam-4679	59	15	approximation	approximation	NOUN
ejpam-4679	59	16	or	or	CCONJ
ejpam-4679	59	17	a	a	DET
ejpam-4679	59	18	self	self	NOUN
ejpam-4679	59	19	-	-	PUNCT
ejpam-4679	59	20	similar	similar	ADJ
ejpam-4679	59	21	solution	solution	NOUN
ejpam-4679	59	22	method	method	NOUN
ejpam-4679	59	23	is	be	AUX
ejpam-4679	59	24	used	use	VERB
ejpam-4679	59	25	.	.	PUNCT
ejpam-4679	60	1	while	while	SCONJ
ejpam-4679	60	2	the	the	DET
ejpam-4679	60	3	self	self	NOUN
ejpam-4679	60	4	-	-	PUNCT
ejpam-4679	60	5	similar	similar	ADJ
ejpam-4679	60	6	solution	solution	NOUN
ejpam-4679	60	7	method	method	NOUN
ejpam-4679	60	8	has	have	VERB
ejpam-4679	60	9	a	a	DET
ejpam-4679	60	10	restriction	restriction	NOUN
ejpam-4679	60	11	on	on	ADP
ejpam-4679	60	12	the	the	DET
ejpam-4679	60	13	initial	initial	ADJ
ejpam-4679	60	14	and	and	CCONJ
ejpam-4679	60	15	boundary	boundary	ADJ
ejpam-4679	60	16	conditions	condition	NOUN
ejpam-4679	60	17	,	,	PUNCT
ejpam-4679	60	18	numerical	numerical	ADJ
ejpam-4679	60	19	methods	method	NOUN
ejpam-4679	60	20	based	base	VERB
ejpam-4679	60	21	on	on	ADP
ejpam-4679	60	22	finite	finite	ADJ
ejpam-4679	60	23	difference	difference	NOUN
ejpam-4679	60	24	approximation	approximation	NOUN
ejpam-4679	60	25	require	require	NOUN
ejpam-4679	60	26	solving	solve	VERB
ejpam-4679	60	27	a	a	DET
ejpam-4679	60	28	system	system	NOUN
ejpam-4679	60	29	of	of	ADP
ejpam-4679	60	30	nonlinear	nonlinear	ADJ
ejpam-4679	60	31	algebraic	algebraic	ADJ
ejpam-4679	60	32	equations	equation	NOUN
ejpam-4679	60	33	which	which	PRON
ejpam-4679	60	34	is	be	AUX
ejpam-4679	60	35	very	very	ADV
ejpam-4679	60	36	diffucult	diffucult	NOUN
ejpam-4679	60	37	to	to	PART
ejpam-4679	60	38	solve	solve	VERB
ejpam-4679	60	39	because	because	SCONJ
ejpam-4679	60	40	solving	solve	VERB
ejpam-4679	60	41	such	such	ADJ
ejpam-4679	60	42	systems	system	NOUN
ejpam-4679	60	43	requires	require	VERB
ejpam-4679	60	44	a	a	DET
ejpam-4679	60	45	good	good	ADJ
ejpam-4679	60	46	initial	initial	ADJ
ejpam-4679	60	47	guess	guess	NOUN
ejpam-4679	60	48	for	for	ADP
ejpam-4679	60	49	the	the	DET
ejpam-4679	60	50	solution	solution	NOUN
ejpam-4679	60	51	.	.	PUNCT
ejpam-4679	61	1	the	the	DET
ejpam-4679	61	2	method	method	NOUN
ejpam-4679	61	3	that	that	PRON
ejpam-4679	61	4	we	we	PRON
ejpam-4679	61	5	introduce	introduce	VERB
ejpam-4679	61	6	in	in	ADP
ejpam-4679	61	7	this	this	DET
ejpam-4679	61	8	paper	paper	NOUN
ejpam-4679	61	9	is	be	AUX
ejpam-4679	61	10	memory	memory	NOUN
ejpam-4679	61	11	efficient	efficient	ADJ
ejpam-4679	61	12	compared	compare	VERB
ejpam-4679	61	13	to	to	ADP
ejpam-4679	61	14	the	the	DET
ejpam-4679	61	15	methods	method	NOUN
ejpam-4679	61	16	that	that	PRON
ejpam-4679	61	17	use	use	VERB
ejpam-4679	61	18	solving	solve	VERB
ejpam-4679	61	19	system	system	NOUN
ejpam-4679	61	20	of	of	ADP
ejpam-4679	61	21	nonlinear	nonlinear	ADJ
ejpam-4679	61	22	algebraic	algebraic	ADJ
ejpam-4679	61	23	equations	equation	NOUN
ejpam-4679	61	24	.	.	PUNCT
ejpam-4679	62	1	in	in	ADP
ejpam-4679	62	2	addition	addition	NOUN
ejpam-4679	62	3	,	,	PUNCT
ejpam-4679	62	4	usage	usage	NOUN
ejpam-4679	62	5	of	of	ADP
ejpam-4679	62	6	nonlinear	nonlinear	ADJ
ejpam-4679	62	7	algebraic	algebraic	ADJ
ejpam-4679	62	8	equations	equation	NOUN
ejpam-4679	62	9	involves	involve	VERB
ejpam-4679	62	10	matrices	matrix	NOUN
ejpam-4679	62	11	of	of	ADP
ejpam-4679	62	12	dimension	dimension	NOUN
ejpam-4679	62	13	m	m	VERB
ejpam-4679	62	14	×n	×n	X
ejpam-4679	62	15	×k	×k	NOUN
ejpam-4679	62	16	,	,	PUNCT
ejpam-4679	62	17	where	where	SCONJ
ejpam-4679	62	18	m	m	NOUN
ejpam-4679	62	19	,	,	PUNCT
ejpam-4679	62	20	n	n	CCONJ
ejpam-4679	62	21	,	,	PUNCT
ejpam-4679	62	22	k	k	PROPN
ejpam-4679	62	23	are	be	AUX
ejpam-4679	62	24	number	number	NOUN
ejpam-4679	62	25	of	of	ADP
ejpam-4679	62	26	mesh	mesh	NOUN
ejpam-4679	62	27	points	point	NOUN
ejpam-4679	62	28	in	in	ADP
ejpam-4679	62	29	x	x	NOUN
ejpam-4679	62	30	,	,	PUNCT
ejpam-4679	62	31	y	y	PROPN
ejpam-4679	62	32	and	and	CCONJ
ejpam-4679	62	33	t	t	PROPN
ejpam-4679	62	34	directions	direction	NOUN
ejpam-4679	62	35	respectively	respectively	ADV
ejpam-4679	62	36	.	.	PUNCT
ejpam-4679	63	1	whereas	whereas	SCONJ
ejpam-4679	63	2	,	,	PUNCT
ejpam-4679	63	3	our	our	PRON
ejpam-4679	63	4	method	method	NOUN
ejpam-4679	63	5	uses	use	VERB
ejpam-4679	63	6	matrices	matrix	NOUN
ejpam-4679	63	7	only	only	ADV
ejpam-4679	63	8	as	as	ADV
ejpam-4679	63	9	big	big	ADJ
ejpam-4679	63	10	as	as	ADP
ejpam-4679	63	11	m	m	PROPN
ejpam-4679	63	12	×	×	NOUN
ejpam-4679	63	13	n	n	NOUN
ejpam-4679	63	14	in	in	ADP
ejpam-4679	63	15	solution	solution	NOUN
ejpam-4679	63	16	steps	step	NOUN
ejpam-4679	63	17	and	and	CCONJ
ejpam-4679	63	18	finally	finally	ADV
ejpam-4679	63	19	piles	pile	VERB
ejpam-4679	63	20	them	they	PRON
ejpam-4679	63	21	up	up	ADP
ejpam-4679	63	22	which	which	PRON
ejpam-4679	63	23	makes	make	VERB
ejpam-4679	63	24	our	our	PRON
ejpam-4679	63	25	method	method	NOUN
ejpam-4679	63	26	memory	memory	NOUN
ejpam-4679	63	27	efficient	efficient	ADJ
ejpam-4679	63	28	and	and	CCONJ
ejpam-4679	63	29	fast	fast	ADJ
ejpam-4679	63	30	,	,	PUNCT
ejpam-4679	63	31	see	see	VERB
ejpam-4679	63	32	section	section	NOUN
ejpam-4679	63	33	3	3	NUM
ejpam-4679	63	34	for	for	ADP
ejpam-4679	63	35	further	further	ADJ
ejpam-4679	63	36	details	detail	NOUN
ejpam-4679	63	37	and	and	CCONJ
ejpam-4679	63	38	discussions	discussion	NOUN
ejpam-4679	63	39	.	.	PUNCT
ejpam-4679	64	1	m.	m.	NOUN
ejpam-4679	64	2	zeki	zeki	PROPN
ejpam-4679	64	3	,	,	PUNCT
ejpam-4679	64	4	s.	s.	PROPN
ejpam-4679	64	5	tatar	tatar	PROPN
ejpam-4679	64	6	/	/	SYM
ejpam-4679	64	7	eur	eur	PROPN
ejpam-4679	64	8	.	.	PUNCT
ejpam-4679	65	1	j.	j.	PROPN
ejpam-4679	65	2	pure	pure	PROPN
ejpam-4679	65	3	appl	appl	PROPN
ejpam-4679	65	4	.	.	PROPN
ejpam-4679	65	5	math	math	PROPN
ejpam-4679	65	6	,	,	PUNCT
ejpam-4679	65	7	16	16	NUM
ejpam-4679	65	8	(	(	PUNCT
ejpam-4679	65	9	1	1	NUM
ejpam-4679	65	10	)	)	PUNCT
ejpam-4679	65	11	(	(	PUNCT
ejpam-4679	65	12	2023	2023	NUM
ejpam-4679	65	13	)	)	PUNCT
ejpam-4679	65	14	,	,	PUNCT
ejpam-4679	65	15	491	491	NUM
ejpam-4679	65	16	-	-	SYM
ejpam-4679	65	17	502	502	NUM
ejpam-4679	65	18	494	494	NUM
ejpam-4679	65	19	this	this	DET
ejpam-4679	65	20	paper	paper	NOUN
ejpam-4679	65	21	is	be	AUX
ejpam-4679	65	22	organized	organize	VERB
ejpam-4679	65	23	as	as	SCONJ
ejpam-4679	65	24	follows	follow	VERB
ejpam-4679	65	25	:	:	PUNCT
ejpam-4679	65	26	in	in	ADP
ejpam-4679	65	27	the	the	DET
ejpam-4679	65	28	next	next	ADJ
ejpam-4679	65	29	section	section	NOUN
ejpam-4679	65	30	,	,	PUNCT
ejpam-4679	65	31	we	we	PRON
ejpam-4679	65	32	formulate	formulate	VERB
ejpam-4679	65	33	and	and	CCONJ
ejpam-4679	65	34	linearize	linearize	VERB
ejpam-4679	65	35	the	the	DET
ejpam-4679	65	36	problem	problem	NOUN
ejpam-4679	65	37	and	and	CCONJ
ejpam-4679	65	38	provide	provide	VERB
ejpam-4679	65	39	its	its	PRON
ejpam-4679	65	40	analysis	analysis	NOUN
ejpam-4679	65	41	.	.	PUNCT
ejpam-4679	66	1	in	in	ADP
ejpam-4679	66	2	section	section	NOUN
ejpam-4679	66	3	3	3	NUM
ejpam-4679	66	4	,	,	PUNCT
ejpam-4679	66	5	we	we	PRON
ejpam-4679	66	6	present	present	VERB
ejpam-4679	66	7	the	the	DET
ejpam-4679	66	8	numerical	numerical	ADJ
ejpam-4679	66	9	method	method	NOUN
ejpam-4679	66	10	.	.	PUNCT
ejpam-4679	67	1	in	in	ADP
ejpam-4679	67	2	particular	particular	ADJ
ejpam-4679	67	3	,	,	PUNCT
ejpam-4679	67	4	by	by	ADP
ejpam-4679	67	5	introducing	introduce	VERB
ejpam-4679	67	6	an	an	DET
ejpam-4679	67	7	iterative	iterative	NOUN
ejpam-4679	67	8	approach	approach	NOUN
ejpam-4679	67	9	,	,	PUNCT
ejpam-4679	67	10	we	we	PRON
ejpam-4679	67	11	convert	convert	VERB
ejpam-4679	67	12	the	the	DET
ejpam-4679	67	13	fractional	fractional	ADJ
ejpam-4679	67	14	pde	pde	NOUN
ejpam-4679	67	15	with	with	ADP
ejpam-4679	67	16	implicit	implicit	ADJ
ejpam-4679	67	17	boundary	boundary	ADJ
ejpam-4679	67	18	conditions	condition	NOUN
ejpam-4679	67	19	into	into	ADP
ejpam-4679	67	20	a	a	DET
ejpam-4679	67	21	linear	linear	ADJ
ejpam-4679	67	22	one	one	NOUN
ejpam-4679	67	23	with	with	ADP
ejpam-4679	67	24	explicit	explicit	ADJ
ejpam-4679	67	25	boundary	boundary	ADJ
ejpam-4679	67	26	conditions	condition	NOUN
ejpam-4679	67	27	.	.	PUNCT
ejpam-4679	68	1	we	we	PRON
ejpam-4679	68	2	showed	show	VERB
ejpam-4679	68	3	that	that	SCONJ
ejpam-4679	68	4	,	,	PUNCT
ejpam-4679	68	5	the	the	DET
ejpam-4679	68	6	resulting	result	VERB
ejpam-4679	68	7	equations	equation	NOUN
ejpam-4679	68	8	can	can	AUX
ejpam-4679	68	9	be	be	AUX
ejpam-4679	68	10	reduced	reduce	VERB
ejpam-4679	68	11	to	to	PART
ejpam-4679	68	12	system	system	VERB
ejpam-4679	68	13	fractional	fractional	ADJ
ejpam-4679	68	14	odes	ode	NOUN
ejpam-4679	68	15	.	.	PUNCT
ejpam-4679	69	1	we	we	PRON
ejpam-4679	69	2	tested	test	VERB
ejpam-4679	69	3	the	the	DET
ejpam-4679	69	4	numerical	numerical	ADJ
ejpam-4679	69	5	method	method	NOUN
ejpam-4679	69	6	with	with	ADP
ejpam-4679	69	7	an	an	DET
ejpam-4679	69	8	example	example	NOUN
ejpam-4679	69	9	for	for	ADP
ejpam-4679	69	10	the	the	DET
ejpam-4679	69	11	critical	critical	ADJ
ejpam-4679	69	12	parameters	parameter	NOUN
ejpam-4679	69	13	of	of	ADP
ejpam-4679	69	14	the	the	DET
ejpam-4679	69	15	method	method	NOUN
ejpam-4679	69	16	.	.	PUNCT
ejpam-4679	70	1	in	in	ADP
ejpam-4679	70	2	particular	particular	ADJ
ejpam-4679	70	3	,	,	PUNCT
ejpam-4679	70	4	we	we	PRON
ejpam-4679	70	5	obtained	obtain	VERB
ejpam-4679	70	6	the	the	DET
ejpam-4679	70	7	dependency	dependency	NOUN
ejpam-4679	70	8	of	of	ADP
ejpam-4679	70	9	error	error	NOUN
ejpam-4679	70	10	,	,	PUNCT
ejpam-4679	70	11	cpu	cpu	NOUN
ejpam-4679	70	12	time	time	NOUN
ejpam-4679	70	13	and	and	CCONJ
ejpam-4679	70	14	other	other	ADJ
ejpam-4679	70	15	important	important	ADJ
ejpam-4679	70	16	numeric	numeric	ADJ
ejpam-4679	70	17	outcomes	outcome	NOUN
ejpam-4679	70	18	on	on	ADP
ejpam-4679	70	19	the	the	DET
ejpam-4679	70	20	method	method	NOUN
ejpam-4679	70	21	parameters	parameter	NOUN
ejpam-4679	70	22	.	.	PUNCT
ejpam-4679	71	1	2	2	X
ejpam-4679	71	2	.	.	X
ejpam-4679	71	3	formulation	formulation	NOUN
ejpam-4679	71	4	and	and	CCONJ
ejpam-4679	71	5	analysis	analysis	NOUN
ejpam-4679	71	6	of	of	ADP
ejpam-4679	71	7	the	the	DET
ejpam-4679	71	8	problem	problem	NOUN
ejpam-4679	71	9	in	in	ADP
ejpam-4679	71	10	this	this	DET
ejpam-4679	71	11	section	section	NOUN
ejpam-4679	71	12	,	,	PUNCT
ejpam-4679	71	13	we	we	PRON
ejpam-4679	71	14	formulate	formulate	VERB
ejpam-4679	71	15	and	and	CCONJ
ejpam-4679	71	16	linearize	linearize	VERB
ejpam-4679	71	17	the	the	DET
ejpam-4679	71	18	problem	problem	NOUN
ejpam-4679	71	19	under	under	ADP
ejpam-4679	71	20	consideration	consideration	NOUN
ejpam-4679	71	21	and	and	CCONJ
ejpam-4679	71	22	provide	provide	VERB
ejpam-4679	71	23	its	its	PRON
ejpam-4679	71	24	analysis	analysis	NOUN
ejpam-4679	71	25	.	.	PUNCT
ejpam-4679	72	1	we	we	PRON
ejpam-4679	72	2	consider	consider	VERB
ejpam-4679	72	3	the	the	DET
ejpam-4679	72	4	following	follow	VERB
ejpam-4679	72	5	problem:	problem:	PROPN
ejpam-4679	72	6	∂β	∂β	PROPN
ejpam-4679	72	7	∂tβ	∂tβ	PROPN
ejpam-4679	72	8	u	u	PROPN
ejpam-4679	72	9	=	=	PUNCT
ejpam-4679	72	10	(	(	PUNCT
ejpam-4679	72	11	d(u)ux)x	d(u)ux)x	INTJ
ejpam-4679	72	12	+	+	CCONJ
ejpam-4679	72	13	(	(	PUNCT
ejpam-4679	72	14	d(u)uy)y	d(u)uy)y	PROPN
ejpam-4679	72	15	+	+	CCONJ
ejpam-4679	72	16	f(t	f(t	NOUN
ejpam-4679	72	17	,	,	PUNCT
ejpam-4679	72	18	x	x	NOUN
ejpam-4679	72	19	,	,	PUNCT
ejpam-4679	72	20	y	y	PROPN
ejpam-4679	72	21	)	)	PUNCT
ejpam-4679	72	22	,	,	PUNCT
ejpam-4679	72	23	(	(	PUNCT
ejpam-4679	72	24	t	t	PROPN
ejpam-4679	72	25	,	,	PUNCT
ejpam-4679	72	26	x	x	NOUN
ejpam-4679	72	27	,	,	PUNCT
ejpam-4679	72	28	y	y	NOUN
ejpam-4679	72	29	)	)	PUNCT
ejpam-4679	72	30	∈	∈	PROPN
ejpam-4679	72	31	ωt	ωt	PROPN
ejpam-4679	72	32	,	,	PUNCT
ejpam-4679	72	33	u(0	u(0	PROPN
ejpam-4679	72	34	,	,	PUNCT
ejpam-4679	72	35	x	x	NOUN
ejpam-4679	72	36	,	,	PUNCT
ejpam-4679	72	37	y	y	PROPN
ejpam-4679	72	38	)	)	PUNCT
ejpam-4679	72	39	=	=	SYM
ejpam-4679	72	40	0	0	NUM
ejpam-4679	72	41	,	,	PUNCT
ejpam-4679	72	42	(	(	PUNCT
ejpam-4679	72	43	x	x	X
ejpam-4679	72	44	,	,	PUNCT
ejpam-4679	72	45	y	y	NOUN
ejpam-4679	72	46	)	)	PUNCT
ejpam-4679	72	47	∈	∈	PROPN
ejpam-4679	72	48	ω	ω	PROPN
ejpam-4679	72	49	,	,	PUNCT
ejpam-4679	72	50	d(u)ux(t	d(u)ux(t	PROPN
ejpam-4679	72	51	,	,	PUNCT
ejpam-4679	72	52	x	x	NOUN
ejpam-4679	72	53	,	,	PUNCT
ejpam-4679	72	54	y	y	NOUN
ejpam-4679	72	55	)	)	PUNCT
ejpam-4679	72	56	=	=	SYM
ejpam-4679	73	1	g2(t	g2(t	PROPN
ejpam-4679	73	2	,	,	PUNCT
ejpam-4679	73	3	y	y	PROPN
ejpam-4679	73	4	)	)	PUNCT
ejpam-4679	73	5	,	,	PUNCT
ejpam-4679	73	6	(	(	PUNCT
ejpam-4679	73	7	t	t	PROPN
ejpam-4679	73	8	,	,	PUNCT
ejpam-4679	73	9	x	x	NOUN
ejpam-4679	73	10	,	,	PUNCT
ejpam-4679	73	11	y	y	PROPN
ejpam-4679	73	12	)	)	PUNCT
ejpam-4679	73	13	∈	∈	PROPN
ejpam-4679	73	14	γ2	γ2	PROPN
ejpam-4679	73	15	t	t	PROPN
ejpam-4679	73	16	,	,	PUNCT
ejpam-4679	73	17	d(u)uy(t	d(u)uy(t	NOUN
ejpam-4679	73	18	,	,	PUNCT
ejpam-4679	73	19	x	x	NOUN
ejpam-4679	73	20	,	,	PUNCT
ejpam-4679	73	21	y	y	NOUN
ejpam-4679	73	22	)	)	PUNCT
ejpam-4679	73	23	=	=	SYM
ejpam-4679	74	1	g1(t	g1(t	PROPN
ejpam-4679	74	2	,	,	PUNCT
ejpam-4679	74	3	x	x	NOUN
ejpam-4679	74	4	)	)	PUNCT
ejpam-4679	74	5	,	,	PUNCT
ejpam-4679	74	6	(	(	PUNCT
ejpam-4679	74	7	t	t	PROPN
ejpam-4679	74	8	,	,	PUNCT
ejpam-4679	74	9	x	x	NOUN
ejpam-4679	74	10	,	,	PUNCT
ejpam-4679	74	11	y	y	NOUN
ejpam-4679	74	12	)	)	PUNCT
ejpam-4679	74	13	∈	∈	PROPN
ejpam-4679	74	14	γ1	γ1	PROPN
ejpam-4679	74	15	t	t	PROPN
ejpam-4679	74	16	,	,	PUNCT
ejpam-4679	74	17	u(t	u(t	PROPN
ejpam-4679	74	18	,	,	PUNCT
ejpam-4679	74	19	x	x	NOUN
ejpam-4679	74	20	,	,	PUNCT
ejpam-4679	74	21	y	y	NOUN
ejpam-4679	74	22	)	)	PUNCT
ejpam-4679	74	23	=	=	SYM
ejpam-4679	74	24	0	0	NUM
ejpam-4679	74	25	,	,	PUNCT
ejpam-4679	74	26	(	(	PUNCT
ejpam-4679	74	27	t	t	PROPN
ejpam-4679	74	28	,	,	PUNCT
ejpam-4679	74	29	x	x	NOUN
ejpam-4679	74	30	,	,	PUNCT
ejpam-4679	74	31	y	y	NOUN
ejpam-4679	74	32	)	)	PUNCT
ejpam-4679	74	33	∈	∈	PROPN
ejpam-4679	74	34	γ3	γ3	NOUN
ejpam-4679	74	35	t	t	PROPN
ejpam-4679	74	36	∪	∪	PROPN
ejpam-4679	74	37	∈	∈	PROPN
ejpam-4679	74	38	γ4	γ4	NOUN
ejpam-4679	74	39	t	t	NOUN
ejpam-4679	74	40	,	,	PUNCT
ejpam-4679	74	41	(	(	PUNCT
ejpam-4679	74	42	7	7	X
ejpam-4679	74	43	)	)	PUNCT
ejpam-4679	74	44	where	where	SCONJ
ejpam-4679	74	45	β	β	X
ejpam-4679	74	46	∈	∈	PROPN
ejpam-4679	74	47	(	(	PUNCT
ejpam-4679	74	48	0	0	NUM
ejpam-4679	74	49	,	,	PUNCT
ejpam-4679	74	50	1	1	NUM
ejpam-4679	74	51	)	)	PUNCT
ejpam-4679	74	52	is	be	AUX
ejpam-4679	74	53	the	the	DET
ejpam-4679	74	54	order	order	NOUN
ejpam-4679	74	55	of	of	ADP
ejpam-4679	74	56	the	the	DET
ejpam-4679	74	57	caputo	caputo	PROPN
ejpam-4679	74	58	fractional	fractional	PROPN
ejpam-4679	74	59	time	time	PROPN
ejpam-4679	74	60	derivative	derivative	PROPN
ejpam-4679	74	61	,	,	PUNCT
ejpam-4679	74	62	ω	ω	NOUN
ejpam-4679	74	63	:	:	PUNCT
ejpam-4679	74	64	=	=	SYM
ejpam-4679	74	65	(	(	PUNCT
ejpam-4679	74	66	0	0	NUM
ejpam-4679	74	67	,	,	PUNCT
ejpam-4679	74	68	1	1	NUM
ejpam-4679	74	69	)	)	PUNCT
ejpam-4679	74	70	×	×	NOUN
ejpam-4679	74	71	(	(	PUNCT
ejpam-4679	74	72	0	0	NUM
ejpam-4679	74	73	,	,	PUNCT
ejpam-4679	74	74	1	1	NUM
ejpam-4679	74	75	)	)	PUNCT
ejpam-4679	74	76	,	,	PUNCT
ejpam-4679	74	77	ωt	ωt	ADP
ejpam-4679	74	78	:	:	PUNCT
ejpam-4679	74	79	=	=	SYM
ejpam-4679	74	80	(	(	PUNCT
ejpam-4679	74	81	0	0	NUM
ejpam-4679	74	82	,	,	PUNCT
ejpam-4679	74	83	t	t	NOUN
ejpam-4679	74	84	)	)	PUNCT
ejpam-4679	74	85	×ω	×ω	ADV
ejpam-4679	74	86	,	,	PUNCT
ejpam-4679	74	87	γit	γit	AUX
ejpam-4679	74	88	:	:	PUNCT
ejpam-4679	74	89	=	=	SYM
ejpam-4679	74	90	(	(	PUNCT
ejpam-4679	74	91	0	0	NUM
ejpam-4679	74	92	,	,	PUNCT
ejpam-4679	74	93	t	t	NOUN
ejpam-4679	74	94	)	)	PUNCT
ejpam-4679	74	95	×γi	×γi	NOUN
ejpam-4679	74	96	,	,	PUNCT
ejpam-4679	74	97	i	i	PRON
ejpam-4679	74	98	=	=	NOUN
ejpam-4679	74	99	1	1	NUM
ejpam-4679	74	100	,	,	PUNCT
ejpam-4679	74	101	2	2	NUM
ejpam-4679	74	102	,	,	PUNCT
ejpam-4679	74	103	3	3	NUM
ejpam-4679	74	104	,	,	PUNCT
ejpam-4679	74	105	4	4	NUM
ejpam-4679	74	106	,	,	PUNCT
ejpam-4679	74	107	γ1	γ1	NOUN
ejpam-4679	74	108	:	:	PUNCT
ejpam-4679	74	109	=	=	SYM
ejpam-4679	74	110	(	(	PUNCT
ejpam-4679	74	111	0	0	NUM
ejpam-4679	74	112	,	,	PUNCT
ejpam-4679	74	113	1)×{1	1)×{1	NUM
ejpam-4679	74	114	}	}	PUNCT
ejpam-4679	74	115	,	,	PUNCT
ejpam-4679	74	116	γ2	γ2	NOUN
ejpam-4679	74	117	:	:	PUNCT
ejpam-4679	74	118	=	=	SYM
ejpam-4679	74	119	{	{	PUNCT
ejpam-4679	74	120	1}×(0	1}×(0	NUM
ejpam-4679	74	121	,	,	PUNCT
ejpam-4679	74	122	1),γ3	1),γ3	NUM
ejpam-4679	74	123	:	:	PUNCT
ejpam-4679	74	124	=	=	SYM
ejpam-4679	74	125	(	(	PUNCT
ejpam-4679	74	126	0	0	NUM
ejpam-4679	74	127	,	,	PUNCT
ejpam-4679	74	128	1	1	X
ejpam-4679	74	129	)	)	PUNCT
ejpam-4679	74	130	×	×	NOUN
ejpam-4679	74	131	{	{	PUNCT
ejpam-4679	74	132	0	0	NUM
ejpam-4679	74	133	}	}	PUNCT
ejpam-4679	74	134	,	,	PUNCT
ejpam-4679	74	135	γ4	γ4	NOUN
ejpam-4679	74	136	:	:	PUNCT
ejpam-4679	74	137	=	=	SYM
ejpam-4679	74	138	{	{	PUNCT
ejpam-4679	74	139	0	0	NUM
ejpam-4679	74	140	}	}	SYM
ejpam-4679	74	141	×	×	NOUN
ejpam-4679	74	142	(	(	PUNCT
ejpam-4679	74	143	0	0	NUM
ejpam-4679	74	144	,	,	PUNCT
ejpam-4679	74	145	1	1	NUM
ejpam-4679	74	146	)	)	PUNCT
ejpam-4679	74	147	and	and	CCONJ
ejpam-4679	74	148	t	t	X
ejpam-4679	74	149	>	>	X
ejpam-4679	74	150	0	0	PUNCT
ejpam-4679	74	151	is	be	AUX
ejpam-4679	74	152	a	a	DET
ejpam-4679	74	153	final	final	ADJ
ejpam-4679	74	154	time	time	NOUN
ejpam-4679	74	155	.	.	PUNCT
ejpam-4679	75	1	we	we	PRON
ejpam-4679	75	2	assume	assume	VERB
ejpam-4679	75	3	that	that	SCONJ
ejpam-4679	75	4	ω	ω	PROPN
ejpam-4679	75	5	is	be	AUX
ejpam-4679	75	6	a	a	DET
ejpam-4679	75	7	bounded	bounded	ADJ
ejpam-4679	75	8	simply	simply	ADV
ejpam-4679	75	9	connected	connected	ADJ
ejpam-4679	75	10	domain	domain	NOUN
ejpam-4679	75	11	with	with	ADP
ejpam-4679	75	12	a	a	DET
ejpam-4679	75	13	piece	piece	NOUN
ejpam-4679	75	14	-	-	PUNCT
ejpam-4679	75	15	wise	wise	ADJ
ejpam-4679	75	16	smooth	smooth	ADJ
ejpam-4679	75	17	boundary	boundary	ADJ
ejpam-4679	75	18	∂ω	∂ω	PROPN
ejpam-4679	75	19	=	=	SYM
ejpam-4679	75	20	γ1	γ1	PROPN
ejpam-4679	75	21	∪	∪	ADP
ejpam-4679	75	22	γ2	γ2	PROPN
ejpam-4679	75	23	∪	∪	PROPN
ejpam-4679	75	24	γ3	γ3	NOUN
ejpam-4679	75	25	∪	∪	NOUN
ejpam-4679	75	26	γ4	γ4	NOUN
ejpam-4679	75	27	,	,	PUNCT
ejpam-4679	75	28	γi	γi	X
ejpam-4679	75	29	∩	∩	ADJ
ejpam-4679	75	30	γj	γj	ADP
ejpam-4679	75	31	=	=	SYM
ejpam-4679	75	32	∅	∅	NOUN
ejpam-4679	75	33	,	,	PUNCT
ejpam-4679	75	34	i	i	PROPN
ejpam-4679	75	35	̸=	̸=	PROPN
ejpam-4679	75	36	j.	j.	PROPN
ejpam-4679	75	37	definition	definition	NOUN
ejpam-4679	75	38	1	1	NUM
ejpam-4679	75	39	.	.	PUNCT
ejpam-4679	76	1	let	let	VERB
ejpam-4679	76	2	l	l	NOUN
ejpam-4679	76	3	be	be	AUX
ejpam-4679	76	4	a	a	DET
ejpam-4679	76	5	closed	closed	ADJ
ejpam-4679	76	6	interval	interval	NOUN
ejpam-4679	76	7	.	.	PUNCT
ejpam-4679	77	1	a	a	DET
ejpam-4679	77	2	set	set	NOUN
ejpam-4679	77	3	d	d	ADP
ejpam-4679	77	4	satisfying	satisfy	VERB
ejpam-4679	77	5	the	the	DET
ejpam-4679	77	6	following	follow	VERB
ejpam-4679	77	7	conditions	condition	NOUN
ejpam-4679	77	8	is	be	AUX
ejpam-4679	77	9	called	call	VERB
ejpam-4679	77	10	the	the	DET
ejpam-4679	77	11	class	class	NOUN
ejpam-4679	77	12	of	of	ADP
ejpam-4679	77	13	admissible	admissible	ADJ
ejpam-4679	77	14	coefficients	coefficient	NOUN
ejpam-4679	77	15	for	for	ADP
ejpam-4679	77	16	the	the	DET
ejpam-4679	77	17	problem	problem	NOUN
ejpam-4679	77	18	(	(	PUNCT
ejpam-4679	77	19	7	7	NUM
ejpam-4679	77	20	)	)	PUNCT
ejpam-4679	77	21	:	:	PUNCT
ejpam-4679	78	1	d	d	X
ejpam-4679	78	2	∈	∈	PROPN
ejpam-4679	78	3	c(l	c(l	PROPN
ejpam-4679	78	4	)	)	PUNCT
ejpam-4679	78	5	,	,	PUNCT
ejpam-4679	78	6	c0	c0	PROPN
ejpam-4679	78	7	≤	≤	PROPN
ejpam-4679	78	8	d(s	d(s	PROPN
ejpam-4679	78	9	)	)	PUNCT
ejpam-4679	78	10	≤	≤	PROPN
ejpam-4679	78	11	c1	c1	NOUN
ejpam-4679	78	12	,	,	PUNCT
ejpam-4679	78	13	∀	∀	PUNCT
ejpam-4679	78	14	s	s	NOUN
ejpam-4679	78	15	∈	∈	PROPN
ejpam-4679	78	16	l	l	NOUN
ejpam-4679	78	17	,	,	PUNCT
ejpam-4679	78	18	(	(	PUNCT
ejpam-4679	78	19	8)	8)	X
ejpam-4679	78	20	(	(	PUNCT
ejpam-4679	78	21	d(u1)∇u1	d(u1)∇u1	PROPN
ejpam-4679	78	22	−	−	PROPN
ejpam-4679	78	23	d(u2)∇u2	d(u2)∇u2	PROPN
ejpam-4679	78	24	)	)	PUNCT
ejpam-4679	78	25	·	·	PUNCT
ejpam-4679	79	1	∇(u1	∇(u1	NOUN
ejpam-4679	79	2	−	−	PROPN
ejpam-4679	79	3	u2	u2	PROPN
ejpam-4679	79	4	)	)	PUNCT
ejpam-4679	79	5	≥	≥	NOUN
ejpam-4679	79	6	c2||∇(u1	c2||∇(u1	AUX
ejpam-4679	79	7	−	−	PROPN
ejpam-4679	79	8	u2)||2	u2)||2	NOUN
ejpam-4679	79	9	,	,	PUNCT
ejpam-4679	79	10	∀u1	∀u1	ADP
ejpam-4679	79	11	,	,	PUNCT
ejpam-4679	79	12	u2	u2	PROPN
ejpam-4679	79	13	∈	∈	PROPN
ejpam-4679	79	14	h1	h1	NOUN
ejpam-4679	79	15	0	0	NUM
ejpam-4679	79	16	(	(	PUNCT
ejpam-4679	79	17	ω	ω	NOUN
ejpam-4679	79	18	)	)	PUNCT
ejpam-4679	79	19	,	,	PUNCT
ejpam-4679	79	20	(	(	PUNCT
ejpam-4679	79	21	9	9	X
ejpam-4679	79	22	)	)	PUNCT
ejpam-4679	79	23	where	where	SCONJ
ejpam-4679	79	24	c0	c0	PROPN
ejpam-4679	79	25	,	,	PUNCT
ejpam-4679	79	26	c1	c1	PROPN
ejpam-4679	79	27	,	,	PUNCT
ejpam-4679	79	28	c2	c2	PROPN
ejpam-4679	79	29	are	be	AUX
ejpam-4679	79	30	positive	positive	ADJ
ejpam-4679	79	31	constants	constant	NOUN
ejpam-4679	79	32	.	.	PUNCT
ejpam-4679	80	1	definition	definition	NOUN
ejpam-4679	80	2	2	2	NUM
ejpam-4679	80	3	.	.	PUNCT
ejpam-4679	80	4	a	a	DET
ejpam-4679	80	5	weak	weak	ADJ
ejpam-4679	80	6	solution	solution	NOUN
ejpam-4679	80	7	of	of	ADP
ejpam-4679	80	8	the	the	DET
ejpam-4679	80	9	problem	problem	NOUN
ejpam-4679	80	10	(	(	PUNCT
ejpam-4679	80	11	7	7	X
ejpam-4679	80	12	)	)	PUNCT
ejpam-4679	80	13	is	be	AUX
ejpam-4679	80	14	a	a	DET
ejpam-4679	80	15	function	function	NOUN
ejpam-4679	80	16	u	u	NOUN
ejpam-4679	80	17	∈	∈	PROPN
ejpam-4679	80	18	sβ(ωt	sβ(ωt	NOUN
ejpam-4679	80	19	)	)	PUNCT
ejpam-4679	81	1	:	:	PUNCT
ejpam-4679	81	2	=	=	SYM
ejpam-4679	81	3	l2	l2	NOUN
ejpam-4679	81	4	(	(	PUNCT
ejpam-4679	81	5	0	0	NUM
ejpam-4679	81	6	,	,	PUNCT
ejpam-4679	81	7	t	t	NOUN
ejpam-4679	81	8	;	;	PUNCT
ejpam-4679	81	9	h1	h1	PROPN
ejpam-4679	81	10	0	0	NUM
ejpam-4679	81	11	(	(	PUNCT
ejpam-4679	81	12	ω	ω	NOUN
ejpam-4679	81	13	)	)	PUNCT
ejpam-4679	81	14	)	)	PUNCT
ejpam-4679	81	15	∩	∩	PROPN
ejpam-4679	81	16	w	w	ADP
ejpam-4679	81	17	β	β	X
ejpam-4679	81	18	2	2	NUM
ejpam-4679	81	19	(	(	PUNCT
ejpam-4679	81	20	0	0	NUM
ejpam-4679	81	21	,	,	PUNCT
ejpam-4679	81	22	t	t	NOUN
ejpam-4679	81	23	;	;	PUNCT
ejpam-4679	81	24	l2(ω	l2(ω	X
ejpam-4679	81	25	)	)	PUNCT
ejpam-4679	81	26	)	)	PUNCT
ejpam-4679	81	27	such	such	ADJ
ejpam-4679	81	28	that	that	SCONJ
ejpam-4679	81	29	the	the	DET
ejpam-4679	81	30	following	follow	VERB
ejpam-4679	81	31	integral	integral	ADJ
ejpam-4679	81	32	identity	identity	NOUN
ejpam-4679	81	33	holds	hold	VERB
ejpam-4679	81	34	for	for	ADP
ejpam-4679	81	35	a.e	a.e	PROPN
ejpam-4679	81	36	.	.	PROPN
ejpam-4679	81	37	t	t	PROPN
ejpam-4679	81	38	∈	∈	PROPN
ejpam-4679	82	1	[	[	X
ejpam-4679	82	2	0	0	NUM
ejpam-4679	82	3	,	,	PUNCT
ejpam-4679	82	4	t	t	X
ejpam-4679	82	5	]	]	PUNCT
ejpam-4679	82	6	:	:	PUNCT
ejpam-4679	82	7	∫	∫	PROPN
ejpam-4679	82	8	ω	ω	NUM
ejpam-4679	82	9	∂βu	∂βu	PROPN
ejpam-4679	82	10	∂tβ	∂tβ	PROPN
ejpam-4679	82	11	v	v	ADP
ejpam-4679	82	12	dx	dx	PROPN
ejpam-4679	82	13	dy	dy	PROPN
ejpam-4679	82	14	+	+	CCONJ
ejpam-4679	82	15	∫	∫	PROPN
ejpam-4679	82	16	ω	ω	PROPN
ejpam-4679	82	17	d	d	PROPN
ejpam-4679	82	18	(	(	PUNCT
ejpam-4679	82	19	u)∇u	u)∇u	PROPN
ejpam-4679	82	20	·	·	PUNCT
ejpam-4679	82	21	∇v	∇v	ADJ
ejpam-4679	82	22	dx	dx	PROPN
ejpam-4679	82	23	dy	dy	X
ejpam-4679	82	24	=	=	SYM
ejpam-4679	83	1	∫	∫	PROPN
ejpam-4679	83	2	ω	ω	PROPN
ejpam-4679	83	3	f	f	PROPN
ejpam-4679	83	4	v	v	NUM
ejpam-4679	83	5	dx	dx	PROPN
ejpam-4679	83	6	dy	dy	PROPN
ejpam-4679	83	7	+	+	CCONJ
ejpam-4679	83	8	∫	∫	PROPN
ejpam-4679	83	9	γ1	γ1	PROPN
ejpam-4679	83	10	t	t	PROPN
ejpam-4679	83	11	g1	g1	PROPN
ejpam-4679	83	12	v	v	ADP
ejpam-4679	83	13	dx	dx	PROPN
ejpam-4679	83	14	dy	dy	PROPN
ejpam-4679	83	15	+	+	CCONJ
ejpam-4679	83	16	∫	∫	PROPN
ejpam-4679	83	17	γ2	γ2	PROPN
ejpam-4679	83	18	t	t	PROPN
ejpam-4679	83	19	g2	g2	PROPN
ejpam-4679	83	20	v	v	ADP
ejpam-4679	83	21	dx	dx	PROPN
ejpam-4679	83	22	dy	dy	PROPN
ejpam-4679	83	23	,	,	PUNCT
ejpam-4679	83	24	(	(	PUNCT
ejpam-4679	83	25	10	10	NUM
ejpam-4679	83	26	)	)	PUNCT
ejpam-4679	83	27	m.	m.	NOUN
ejpam-4679	83	28	zeki	zeki	PROPN
ejpam-4679	83	29	,	,	PUNCT
ejpam-4679	83	30	s.	s.	PROPN
ejpam-4679	83	31	tatar	tatar	PROPN
ejpam-4679	83	32	/	/	SYM
ejpam-4679	83	33	eur	eur	PROPN
ejpam-4679	83	34	.	.	PUNCT
ejpam-4679	84	1	j.	j.	PROPN
ejpam-4679	84	2	pure	pure	PROPN
ejpam-4679	84	3	appl	appl	PROPN
ejpam-4679	84	4	.	.	PROPN
ejpam-4679	84	5	math	math	PROPN
ejpam-4679	84	6	,	,	PUNCT
ejpam-4679	84	7	16	16	NUM
ejpam-4679	84	8	(	(	PUNCT
ejpam-4679	84	9	1	1	NUM
ejpam-4679	84	10	)	)	PUNCT
ejpam-4679	84	11	(	(	PUNCT
ejpam-4679	84	12	2023	2023	NUM
ejpam-4679	84	13	)	)	PUNCT
ejpam-4679	84	14	,	,	PUNCT
ejpam-4679	84	15	491	491	NUM
ejpam-4679	84	16	-	-	SYM
ejpam-4679	84	17	502	502	NUM
ejpam-4679	84	18	495	495	NUM
ejpam-4679	84	19	for	for	ADP
ejpam-4679	84	20	each	each	DET
ejpam-4679	84	21	v	v	X
ejpam-4679	84	22	∈	∈	NOUN
ejpam-4679	84	23	sβ(ωt	sβ(ωt	NOUN
ejpam-4679	84	24	)	)	PUNCT
ejpam-4679	84	25	,	,	PUNCT
ejpam-4679	84	26	where	where	SCONJ
ejpam-4679	84	27	w	w	NOUN
ejpam-4679	84	28	β	β	X
ejpam-4679	84	29	2	2	NUM
ejpam-4679	84	30	(	(	PUNCT
ejpam-4679	84	31	0	0	NUM
ejpam-4679	84	32	,	,	PUNCT
ejpam-4679	84	33	t	t	NOUN
ejpam-4679	84	34	)	)	PUNCT
ejpam-4679	84	35	:	:	PUNCT
ejpam-4679	84	36	=	=	SYM
ejpam-4679	84	37	{	{	PUNCT
ejpam-4679	84	38	u	u	PROPN
ejpam-4679	84	39	∈	∈	PROPN
ejpam-4679	84	40	l2[0	l2[0	PROPN
ejpam-4679	84	41	,	,	PUNCT
ejpam-4679	84	42	t	t	X
ejpam-4679	84	43	]	]	PUNCT
ejpam-4679	84	44	:	:	PUNCT
ejpam-4679	85	1	∂βu	∂βu	PROPN
ejpam-4679	85	2	∂tβ	∂tβ	PROPN
ejpam-4679	85	3	∈	∈	PROPN
ejpam-4679	85	4	l2[0	l2[0	PROPN
ejpam-4679	85	5	,	,	PUNCT
ejpam-4679	85	6	t	t	X
ejpam-4679	85	7	]	]	PUNCT
ejpam-4679	85	8	andu(0	andu(0	PROPN
ejpam-4679	85	9	,	,	PUNCT
ejpam-4679	85	10	.	.	PUNCT
ejpam-4679	85	11	)	)	PUNCT
ejpam-4679	86	1	=	=	SYM
ejpam-4679	86	2	0	0	PUNCT
ejpam-4679	86	3	}	}	PUNCT
ejpam-4679	86	4	,	,	PUNCT
ejpam-4679	86	5	is	be	AUX
ejpam-4679	86	6	the	the	DET
ejpam-4679	86	7	fractional	fractional	ADJ
ejpam-4679	86	8	sobolev	sobolev	NOUN
ejpam-4679	86	9	space	space	NOUN
ejpam-4679	86	10	of	of	ADP
ejpam-4679	86	11	order	order	NOUN
ejpam-4679	86	12	β	β	X
ejpam-4679	86	13	.	.	PUNCT
ejpam-4679	87	1	we	we	PRON
ejpam-4679	87	2	note	note	VERB
ejpam-4679	87	3	that	that	SCONJ
ejpam-4679	87	4	sβ(ωt	sβ(ωt	NOUN
ejpam-4679	87	5	)	)	PUNCT
ejpam-4679	87	6	is	be	AUX
ejpam-4679	87	7	a	a	DET
ejpam-4679	87	8	banach	banach	NOUN
ejpam-4679	87	9	space	space	NOUN
ejpam-4679	87	10	with	with	ADP
ejpam-4679	87	11	the	the	DET
ejpam-4679	87	12	norm	norm	NOUN
ejpam-4679	87	13	:	:	PUNCT
ejpam-4679	87	14	∥u∥sβ(ωt	∥u∥sβ(ωt	ADJ
ejpam-4679	87	15	)	)	PUNCT
ejpam-4679	88	1	=	=	PUNCT
ejpam-4679	88	2	(	(	PUNCT
ejpam-4679	88	3	∥u∥2	∥u∥2	NOUN
ejpam-4679	88	4	wβ	wβ	ADP
ejpam-4679	88	5	2	2	NUM
ejpam-4679	88	6	(	(	PUNCT
ejpam-4679	88	7	0,t	0,t	NOUN
ejpam-4679	88	8	;	;	PUNCT
ejpam-4679	88	9	l2(ω	l2(ω	NUM
ejpam-4679	88	10	)	)	PUNCT
ejpam-4679	88	11	)	)	PUNCT
ejpam-4679	89	1	+	+	CCONJ
ejpam-4679	89	2	∥u∥2	∥u∥2	NOUN
ejpam-4679	89	3	l2(0,t	l2(0,t	NOUN
ejpam-4679	89	4	;	;	PUNCT
ejpam-4679	89	5	h1	h1	PROPN
ejpam-4679	89	6	0	0	NUM
ejpam-4679	89	7	(	(	PUNCT
ejpam-4679	89	8	ω	ω	NOUN
ejpam-4679	89	9	)	)	PUNCT
ejpam-4679	89	10	)	)	PUNCT
ejpam-4679	89	11	)	)	PUNCT
ejpam-4679	89	12	1	1	NUM
ejpam-4679	89	13	2	2	NUM
ejpam-4679	89	14	.	.	PUNCT
ejpam-4679	89	15	theorem	theorem	NOUN
ejpam-4679	89	16	1	1	NUM
ejpam-4679	89	17	.	.	PUNCT
ejpam-4679	90	1	[	[	X
ejpam-4679	90	2	22	22	NUM
ejpam-4679	90	3	]	]	PUNCT
ejpam-4679	90	4	let	let	VERB
ejpam-4679	90	5	d	d	X
ejpam-4679	90	6	∈	∈	PROPN
ejpam-4679	90	7	d.	d.	PROPN
ejpam-4679	90	8	then	then	ADV
ejpam-4679	90	9	the	the	DET
ejpam-4679	90	10	direct	direct	ADJ
ejpam-4679	90	11	problem	problem	NOUN
ejpam-4679	90	12	(	(	PUNCT
ejpam-4679	90	13	7	7	X
ejpam-4679	90	14	)	)	PUNCT
ejpam-4679	90	15	has	have	VERB
ejpam-4679	90	16	a	a	DET
ejpam-4679	90	17	unique	unique	ADJ
ejpam-4679	90	18	weak	weak	ADJ
ejpam-4679	90	19	solution	solution	NOUN
ejpam-4679	90	20	u	u	NOUN
ejpam-4679	90	21	∈	∈	PROPN
ejpam-4679	90	22	sβ(ωt	sβ(ωt	NOUN
ejpam-4679	90	23	)	)	PUNCT
ejpam-4679	90	24	.	.	PUNCT
ejpam-4679	91	1	moreover	moreover	ADV
ejpam-4679	91	2	,	,	PUNCT
ejpam-4679	91	3	for	for	ADP
ejpam-4679	91	4	a.e	a.e	PROPN
ejpam-4679	91	5	t	t	PROPN
ejpam-4679	91	6	∈	∈	PROPN
ejpam-4679	92	1	[	[	X
ejpam-4679	92	2	0	0	NUM
ejpam-4679	92	3	,	,	PUNCT
ejpam-4679	92	4	t	t	X
ejpam-4679	92	5	]	]	PUNCT
ejpam-4679	92	6	there	there	PRON
ejpam-4679	92	7	exist	exist	VERB
ejpam-4679	92	8	some	some	DET
ejpam-4679	92	9	constants	constant	NOUN
ejpam-4679	92	10	c	c	NOUN
ejpam-4679	92	11	,	,	PUNCT
ejpam-4679	92	12	c	c	X
ejpam-4679	92	13	>	>	X
ejpam-4679	92	14	0	0	NUM
ejpam-4679	92	15	such	such	ADJ
ejpam-4679	92	16	that	that	SCONJ
ejpam-4679	92	17	∂β∥u∥2	∂β∥u∥2	VERB
ejpam-4679	92	18	∂tβ	∂tβ	PROPN
ejpam-4679	92	19	+	+	PROPN
ejpam-4679	92	20	c	c	PROPN
ejpam-4679	92	21	∥u∥2h1	∥u∥2h1	NUM
ejpam-4679	92	22	0	0	NUM
ejpam-4679	92	23	(	(	PUNCT
ejpam-4679	92	24	ω	ω	NOUN
ejpam-4679	92	25	)	)	PUNCT
ejpam-4679	92	26	≤	≤	PUNCT
ejpam-4679	93	1	c	c	X
ejpam-4679	93	2	[	[	PUNCT
ejpam-4679	93	3	∥f∥2	∥f∥2	NOUN
ejpam-4679	93	4	+	+	CCONJ
ejpam-4679	93	5	∥g1∥2l2(γ1	∥g1∥2l2(γ1	NOUN
ejpam-4679	93	6	)	)	PUNCT
ejpam-4679	93	7	+	+	CCONJ
ejpam-4679	93	8	∥g2∥2l2(γ2	∥g2∥2l2(γ2	NOUN
ejpam-4679	93	9	)	)	PUNCT
ejpam-4679	93	10	]	]	PUNCT
ejpam-4679	93	11	.	.	PUNCT
ejpam-4679	94	1	we	we	PRON
ejpam-4679	94	2	note	note	VERB
ejpam-4679	94	3	that	that	SCONJ
ejpam-4679	94	4	the	the	DET
ejpam-4679	94	5	conditions	condition	NOUN
ejpam-4679	94	6	(	(	PUNCT
ejpam-4679	94	7	8)	8)	NUM
ejpam-4679	94	8	and	and	CCONJ
ejpam-4679	94	9	(	(	PUNCT
ejpam-4679	94	10	9	9	X
ejpam-4679	94	11	)	)	PUNCT
ejpam-4679	94	12	arise	arise	NOUN
ejpam-4679	94	13	in	in	ADP
ejpam-4679	94	14	the	the	DET
ejpam-4679	94	15	solvability	solvability	NOUN
ejpam-4679	94	16	of	of	ADP
ejpam-4679	94	17	the	the	DET
ejpam-4679	94	18	direct	direct	ADJ
ejpam-4679	94	19	problem	problem	NOUN
ejpam-4679	94	20	(	(	PUNCT
ejpam-4679	94	21	7	7	NUM
ejpam-4679	94	22	)	)	PUNCT
ejpam-4679	94	23	and	and	CCONJ
ejpam-4679	94	24	can	can	AUX
ejpam-4679	94	25	be	be	AUX
ejpam-4679	94	26	found	find	VERB
ejpam-4679	94	27	in	in	ADP
ejpam-4679	94	28	some	some	DET
ejpam-4679	94	29	papers	paper	NOUN
ejpam-4679	94	30	,	,	PUNCT
ejpam-4679	94	31	for	for	ADP
ejpam-4679	94	32	example	example	NOUN
ejpam-4679	94	33	see	see	VERB
ejpam-4679	94	34	the	the	DET
ejpam-4679	94	35	condition	condition	NOUN
ejpam-4679	94	36	h3	h3	NOUN
ejpam-4679	94	37	in	in	ADP
ejpam-4679	94	38	[	[	X
ejpam-4679	94	39	12	12	NUM
ejpam-4679	94	40	]	]	PUNCT
ejpam-4679	94	41	.	.	PUNCT
ejpam-4679	95	1	the	the	DET
ejpam-4679	95	2	main	main	ADJ
ejpam-4679	95	3	difficulty	difficulty	NOUN
ejpam-4679	95	4	in	in	ADP
ejpam-4679	95	5	solving	solve	VERB
ejpam-4679	95	6	the	the	DET
ejpam-4679	95	7	problem	problem	NOUN
ejpam-4679	95	8	(	(	PUNCT
ejpam-4679	95	9	7	7	X
ejpam-4679	95	10	)	)	PUNCT
ejpam-4679	95	11	numerically	numerically	ADV
ejpam-4679	95	12	comes	come	VERB
ejpam-4679	95	13	from	from	ADP
ejpam-4679	95	14	the	the	DET
ejpam-4679	95	15	fact	fact	NOUN
ejpam-4679	95	16	that	that	SCONJ
ejpam-4679	95	17	the	the	DET
ejpam-4679	95	18	boundary	boundary	ADJ
ejpam-4679	95	19	conditions	condition	NOUN
ejpam-4679	95	20	are	be	AUX
ejpam-4679	95	21	given	give	VERB
ejpam-4679	95	22	implicitly	implicitly	ADV
ejpam-4679	95	23	.	.	PUNCT
ejpam-4679	96	1	that	that	PRON
ejpam-4679	96	2	is	be	AUX
ejpam-4679	96	3	,	,	PUNCT
ejpam-4679	96	4	boundary	boundary	ADJ
ejpam-4679	96	5	conditions	condition	NOUN
ejpam-4679	96	6	depends	depend	VERB
ejpam-4679	96	7	on	on	ADP
ejpam-4679	96	8	the	the	DET
ejpam-4679	96	9	solution	solution	NOUN
ejpam-4679	96	10	itself	itself	PRON
ejpam-4679	96	11	.	.	PUNCT
ejpam-4679	97	1	without	without	ADP
ejpam-4679	97	2	knowing	know	VERB
ejpam-4679	97	3	the	the	DET
ejpam-4679	97	4	values	value	NOUN
ejpam-4679	97	5	of	of	ADP
ejpam-4679	97	6	the	the	DET
ejpam-4679	97	7	solution	solution	NOUN
ejpam-4679	97	8	at	at	ADP
ejpam-4679	97	9	the	the	DET
ejpam-4679	97	10	boundary	boundary	NOUN
ejpam-4679	97	11	,	,	PUNCT
ejpam-4679	97	12	the	the	DET
ejpam-4679	97	13	explicit	explicit	ADJ
ejpam-4679	97	14	numeric	numeric	ADJ
ejpam-4679	97	15	approximation	approximation	NOUN
ejpam-4679	97	16	at	at	ADP
ejpam-4679	97	17	the	the	DET
ejpam-4679	97	18	interior	interior	ADJ
ejpam-4679	97	19	points	point	NOUN
ejpam-4679	97	20	is	be	AUX
ejpam-4679	97	21	not	not	PART
ejpam-4679	97	22	possible	possible	ADJ
ejpam-4679	97	23	.	.	PUNCT
ejpam-4679	98	1	to	to	PART
ejpam-4679	98	2	overcome	overcome	VERB
ejpam-4679	98	3	this	this	DET
ejpam-4679	98	4	difficulty	difficulty	NOUN
ejpam-4679	98	5	,	,	PUNCT
ejpam-4679	98	6	we	we	PRON
ejpam-4679	98	7	approximate	approximate	VERB
ejpam-4679	98	8	the	the	DET
ejpam-4679	98	9	solution	solution	NOUN
ejpam-4679	98	10	using	use	VERB
ejpam-4679	98	11	the	the	DET
ejpam-4679	98	12	following	follow	VERB
ejpam-4679	98	13	recurrent	recurrent	ADJ
ejpam-4679	98	14	approximation	approximation	NOUN
ejpam-4679	98	15	scheme:	scheme:	NOUN
ejpam-4679	98	16	∂β	∂β	PROPN
ejpam-4679	98	17	∂tβ	∂tβ	PROPN
ejpam-4679	98	18	un	un	PROPN
ejpam-4679	99	1	=	=	PRON
ejpam-4679	99	2	(	(	PUNCT
ejpam-4679	99	3	d(un−1)unx)x	d(un−1)unx)x	VERB
ejpam-4679	99	4	+	+	CCONJ
ejpam-4679	99	5	(	(	PUNCT
ejpam-4679	99	6	d(un−1)uny	d(un−1)uny	X
ejpam-4679	99	7	)	)	PUNCT
ejpam-4679	99	8	y	y	PROPN
ejpam-4679	99	9	+	+	ADJ
ejpam-4679	99	10	f(t	f(t	PROPN
ejpam-4679	99	11	,	,	PUNCT
ejpam-4679	99	12	x	x	NOUN
ejpam-4679	99	13	,	,	PUNCT
ejpam-4679	99	14	y	y	PROPN
ejpam-4679	99	15	)	)	PUNCT
ejpam-4679	99	16	,	,	PUNCT
ejpam-4679	99	17	(	(	PUNCT
ejpam-4679	99	18	t	t	PROPN
ejpam-4679	99	19	,	,	PUNCT
ejpam-4679	99	20	x	x	NOUN
ejpam-4679	99	21	,	,	PUNCT
ejpam-4679	99	22	y	y	NOUN
ejpam-4679	99	23	)	)	PUNCT
ejpam-4679	99	24	∈	∈	PROPN
ejpam-4679	99	25	ωt	ωt	PROPN
ejpam-4679	99	26	,	,	PUNCT
ejpam-4679	99	27	un(0	un(0	PROPN
ejpam-4679	99	28	,	,	PUNCT
ejpam-4679	99	29	x	x	NOUN
ejpam-4679	99	30	,	,	PUNCT
ejpam-4679	99	31	y	y	NOUN
ejpam-4679	99	32	)	)	PUNCT
ejpam-4679	99	33	=	=	SYM
ejpam-4679	99	34	0	0	NUM
ejpam-4679	99	35	,	,	PUNCT
ejpam-4679	99	36	(	(	PUNCT
ejpam-4679	99	37	x	x	X
ejpam-4679	99	38	,	,	PUNCT
ejpam-4679	99	39	y	y	NOUN
ejpam-4679	99	40	)	)	PUNCT
ejpam-4679	99	41	∈	∈	PROPN
ejpam-4679	99	42	ω	ω	NOUN
ejpam-4679	99	43	,	,	PUNCT
ejpam-4679	99	44	d(un−1)unx(t	d(un−1)unx(t	PROPN
ejpam-4679	99	45	,	,	PUNCT
ejpam-4679	99	46	x	x	NOUN
ejpam-4679	99	47	,	,	PUNCT
ejpam-4679	99	48	y	y	NOUN
ejpam-4679	99	49	)	)	PUNCT
ejpam-4679	99	50	=	=	SYM
ejpam-4679	100	1	g2(y	g2(y	PROPN
ejpam-4679	100	2	,	,	PUNCT
ejpam-4679	100	3	t	t	PROPN
ejpam-4679	100	4	)	)	PUNCT
ejpam-4679	100	5	,	,	PUNCT
ejpam-4679	100	6	(	(	PUNCT
ejpam-4679	100	7	t	t	PROPN
ejpam-4679	100	8	,	,	PUNCT
ejpam-4679	100	9	x	x	NOUN
ejpam-4679	100	10	,	,	PUNCT
ejpam-4679	100	11	y	y	PROPN
ejpam-4679	100	12	)	)	PUNCT
ejpam-4679	100	13	∈	∈	PROPN
ejpam-4679	100	14	γ2	γ2	PROPN
ejpam-4679	100	15	t	t	PROPN
ejpam-4679	100	16	,	,	PUNCT
ejpam-4679	100	17	d(un−1)uny	d(un−1)uny	PROPN
ejpam-4679	100	18	(	(	PUNCT
ejpam-4679	100	19	t	t	PROPN
ejpam-4679	100	20	,	,	PUNCT
ejpam-4679	100	21	x	x	NOUN
ejpam-4679	100	22	,	,	PUNCT
ejpam-4679	100	23	y	y	NOUN
ejpam-4679	100	24	)	)	PUNCT
ejpam-4679	100	25	=	=	SYM
ejpam-4679	101	1	g1(x	g1(x	PROPN
ejpam-4679	101	2	,	,	PUNCT
ejpam-4679	101	3	t	t	PROPN
ejpam-4679	101	4	)	)	PUNCT
ejpam-4679	101	5	,	,	PUNCT
ejpam-4679	101	6	(	(	PUNCT
ejpam-4679	101	7	t	t	PROPN
ejpam-4679	101	8	,	,	PUNCT
ejpam-4679	101	9	x	x	NOUN
ejpam-4679	101	10	,	,	PUNCT
ejpam-4679	101	11	y	y	NOUN
ejpam-4679	101	12	)	)	PUNCT
ejpam-4679	101	13	∈	∈	PROPN
ejpam-4679	101	14	γ1	γ1	PROPN
ejpam-4679	101	15	t	t	PROPN
ejpam-4679	101	16	,	,	PUNCT
ejpam-4679	101	17	un(t	un(t	NUM
ejpam-4679	101	18	,	,	PUNCT
ejpam-4679	101	19	x	x	X
ejpam-4679	101	20	,	,	PUNCT
ejpam-4679	101	21	y	y	PROPN
ejpam-4679	101	22	)	)	PUNCT
ejpam-4679	101	23	=	=	SYM
ejpam-4679	101	24	0	0	NUM
ejpam-4679	101	25	,	,	PUNCT
ejpam-4679	101	26	(	(	PUNCT
ejpam-4679	101	27	t	t	PROPN
ejpam-4679	101	28	,	,	PUNCT
ejpam-4679	101	29	x	x	NOUN
ejpam-4679	101	30	,	,	PUNCT
ejpam-4679	101	31	y	y	NOUN
ejpam-4679	101	32	)	)	PUNCT
ejpam-4679	101	33	∈	∈	PROPN
ejpam-4679	101	34	γ3	γ3	NOUN
ejpam-4679	101	35	t	t	PROPN
ejpam-4679	101	36	∪	∪	NOUN
ejpam-4679	101	37	∈	∈	PROPN
ejpam-4679	101	38	γ4	γ4	NOUN
ejpam-4679	101	39	t	t	NOUN
ejpam-4679	101	40	.	.	PUNCT
ejpam-4679	102	1	(	(	PUNCT
ejpam-4679	102	2	11	11	NUM
ejpam-4679	102	3	)	)	PUNCT
ejpam-4679	102	4	here	here	ADV
ejpam-4679	102	5	,	,	PUNCT
ejpam-4679	102	6	the	the	DET
ejpam-4679	102	7	first	first	ADJ
ejpam-4679	102	8	approximation	approximation	NOUN
ejpam-4679	102	9	u(0)(t	u(0)(t	ADJ
ejpam-4679	102	10	,	,	PUNCT
ejpam-4679	102	11	x	x	NOUN
ejpam-4679	102	12	,	,	PUNCT
ejpam-4679	102	13	y	y	NOUN
ejpam-4679	102	14	)	)	PUNCT
ejpam-4679	102	15	is	be	AUX
ejpam-4679	102	16	given	give	VERB
ejpam-4679	102	17	and	and	CCONJ
ejpam-4679	102	18	u(n)(t	u(n)(t	PRON
ejpam-4679	102	19	,	,	PUNCT
ejpam-4679	102	20	x	x	NOUN
ejpam-4679	102	21	,	,	PUNCT
ejpam-4679	102	22	y	y	NOUN
ejpam-4679	102	23	)	)	PUNCT
ejpam-4679	102	24	are	be	AUX
ejpam-4679	102	25	the	the	DET
ejpam-4679	102	26	nth	nth	ADJ
ejpam-4679	102	27	iteration	iteration	NOUN
ejpam-4679	102	28	for	for	ADP
ejpam-4679	102	29	n	n	NOUN
ejpam-4679	102	30	=	=	SYM
ejpam-4679	102	31	1	1	NUM
ejpam-4679	102	32	,	,	PUNCT
ejpam-4679	102	33	2	2	NUM
ejpam-4679	102	34	,	,	PUNCT
ejpam-4679	102	35	·	·	PUNCT
ejpam-4679	102	36	·	·	PUNCT
ejpam-4679	102	37	·	·	PUNCT
ejpam-4679	102	38	.	.	PUNCT
ejpam-4679	103	1	in	in	ADP
ejpam-4679	103	2	this	this	DET
ejpam-4679	103	3	way	way	NOUN
ejpam-4679	103	4	,	,	PUNCT
ejpam-4679	103	5	the	the	DET
ejpam-4679	103	6	problem	problem	NOUN
ejpam-4679	103	7	becomes	become	VERB
ejpam-4679	103	8	linear	linear	ADJ
ejpam-4679	103	9	.	.	PUNCT
ejpam-4679	104	1	but	but	CCONJ
ejpam-4679	104	2	,	,	PUNCT
ejpam-4679	104	3	more	more	ADV
ejpam-4679	104	4	importantly	importantly	ADV
ejpam-4679	104	5	,	,	PUNCT
ejpam-4679	104	6	the	the	DET
ejpam-4679	104	7	boundary	boundary	ADJ
ejpam-4679	104	8	conditions	condition	NOUN
ejpam-4679	104	9	for	for	ADP
ejpam-4679	104	10	the	the	DET
ejpam-4679	104	11	solution	solution	NOUN
ejpam-4679	104	12	are	be	AUX
ejpam-4679	104	13	now	now	ADV
ejpam-4679	104	14	known	know	VERB
ejpam-4679	104	15	.	.	PUNCT
ejpam-4679	105	1	in	in	ADP
ejpam-4679	105	2	[	[	X
ejpam-4679	105	3	15	15	NUM
ejpam-4679	105	4	]	]	PUNCT
ejpam-4679	105	5	,	,	PUNCT
ejpam-4679	105	6	the	the	DET
ejpam-4679	105	7	authors	author	NOUN
ejpam-4679	105	8	linearized	linearize	VERB
ejpam-4679	105	9	a	a	DET
ejpam-4679	105	10	problem	problem	NOUN
ejpam-4679	105	11	for	for	ADP
ejpam-4679	105	12	the	the	DET
ejpam-4679	105	13	following	follow	VERB
ejpam-4679	105	14	nonlinear	nonlinear	ADJ
ejpam-4679	105	15	equation	equation	NOUN
ejpam-4679	105	16	:	:	PUNCT
ejpam-4679	105	17	∂	∂	NUM
ejpam-4679	105	18	∂t	∂t	PROPN
ejpam-4679	105	19	u(t	u(t	PROPN
ejpam-4679	105	20	,	,	PUNCT
ejpam-4679	105	21	x	x	NOUN
ejpam-4679	105	22	,	,	PUNCT
ejpam-4679	105	23	y	y	PROPN
ejpam-4679	105	24	)	)	PUNCT
ejpam-4679	105	25	−∇.	−∇.	PROPN
ejpam-4679	105	26	(	(	PUNCT
ejpam-4679	105	27	f(t	f(t	PROPN
ejpam-4679	105	28	2)∇u	2)∇u	NUM
ejpam-4679	105	29	)	)	PUNCT
ejpam-4679	105	30	=	=	SYM
ejpam-4679	106	1	f(t	f(t	NOUN
ejpam-4679	106	2	,	,	PUNCT
ejpam-4679	106	3	x	x	NOUN
ejpam-4679	106	4	,	,	PUNCT
ejpam-4679	106	5	y	y	PROPN
ejpam-4679	106	6	)	)	PUNCT
ejpam-4679	106	7	,	,	PUNCT
ejpam-4679	106	8	(	(	PUNCT
ejpam-4679	106	9	12	12	NUM
ejpam-4679	106	10	)	)	PUNCT
ejpam-4679	106	11	where	where	SCONJ
ejpam-4679	106	12	t	t	PROPN
ejpam-4679	106	13	2	2	NUM
ejpam-4679	106	14	=	=	SYM
ejpam-4679	106	15	|∇u|2	|∇u|2	NOUN
ejpam-4679	106	16	.	.	PUNCT
ejpam-4679	107	1	they	they	PRON
ejpam-4679	107	2	proved	prove	VERB
ejpam-4679	107	3	that	that	SCONJ
ejpam-4679	107	4	the	the	DET
ejpam-4679	107	5	solution	solution	NOUN
ejpam-4679	107	6	of	of	ADP
ejpam-4679	107	7	the	the	DET
ejpam-4679	107	8	linearized	linearize	VERB
ejpam-4679	107	9	problem	problem	NOUN
ejpam-4679	107	10	converges	converge	VERB
ejpam-4679	107	11	to	to	ADP
ejpam-4679	107	12	the	the	DET
ejpam-4679	107	13	solution	solution	NOUN
ejpam-4679	107	14	of	of	ADP
ejpam-4679	107	15	the	the	DET
ejpam-4679	107	16	associated	associated	ADJ
ejpam-4679	107	17	nonlinear	nonlinear	ADJ
ejpam-4679	107	18	problem	problem	NOUN
ejpam-4679	107	19	.	.	PUNCT
ejpam-4679	108	1	by	by	ADP
ejpam-4679	108	2	modifying	modify	VERB
ejpam-4679	108	3	the	the	DET
ejpam-4679	108	4	method	method	NOUN
ejpam-4679	108	5	used	use	VERB
ejpam-4679	108	6	in	in	ADP
ejpam-4679	108	7	[	[	X
ejpam-4679	108	8	15	15	NUM
ejpam-4679	108	9	]	]	PUNCT
ejpam-4679	108	10	for	for	ADP
ejpam-4679	108	11	the	the	DET
ejpam-4679	108	12	problem	problem	NOUN
ejpam-4679	108	13	(	(	PUNCT
ejpam-4679	108	14	7	7	NUM
ejpam-4679	108	15	)	)	PUNCT
ejpam-4679	108	16	,	,	PUNCT
ejpam-4679	108	17	it	it	PRON
ejpam-4679	108	18	can	can	AUX
ejpam-4679	108	19	be	be	AUX
ejpam-4679	108	20	proved	prove	VERB
ejpam-4679	108	21	that	that	SCONJ
ejpam-4679	108	22	the	the	DET
ejpam-4679	108	23	solution	solution	NOUN
ejpam-4679	108	24	to	to	ADP
ejpam-4679	108	25	the	the	DET
ejpam-4679	108	26	linearized	linearize	VERB
ejpam-4679	108	27	problem	problem	NOUN
ejpam-4679	108	28	(	(	PUNCT
ejpam-4679	108	29	11	11	NUM
ejpam-4679	108	30	)	)	PUNCT
ejpam-4679	108	31	converges	converge	NOUN
ejpam-4679	108	32	to	to	ADP
ejpam-4679	108	33	the	the	DET
ejpam-4679	108	34	solution	solution	NOUN
ejpam-4679	108	35	to	to	ADP
ejpam-4679	108	36	the	the	DET
ejpam-4679	108	37	problem	problem	NOUN
ejpam-4679	108	38	(	(	PUNCT
ejpam-4679	108	39	7	7	NUM
ejpam-4679	108	40	)	)	PUNCT
ejpam-4679	108	41	under	under	ADP
ejpam-4679	108	42	the	the	DET
ejpam-4679	108	43	conditions	condition	NOUN
ejpam-4679	109	1	d	d	X
ejpam-4679	109	2	∈	∈	PROPN
ejpam-4679	109	3	d	d	PROPN
ejpam-4679	109	4	,	,	PUNCT
ejpam-4679	109	5	f	f	PROPN
ejpam-4679	109	6	(	(	PUNCT
ejpam-4679	109	7	t	t	PROPN
ejpam-4679	109	8	,	,	PUNCT
ejpam-4679	109	9	x	x	NOUN
ejpam-4679	109	10	,	,	PUNCT
ejpam-4679	109	11	y	y	NOUN
ejpam-4679	109	12	)	)	PUNCT
ejpam-4679	109	13	∈	∈	PROPN
ejpam-4679	109	14	l2(ωt	l2(ωt	PROPN
ejpam-4679	109	15	)	)	PUNCT
ejpam-4679	109	16	,	,	PUNCT
ejpam-4679	109	17	g	g	NOUN
ejpam-4679	109	18	:	:	PUNCT
ejpam-4679	109	19	=	=	SYM
ejpam-4679	109	20	(	(	PUNCT
ejpam-4679	109	21	g1(t	g1(t	X
ejpam-4679	109	22	,	,	PUNCT
ejpam-4679	109	23	x	x	NOUN
ejpam-4679	109	24	)	)	PUNCT
ejpam-4679	109	25	,	,	PUNCT
ejpam-4679	109	26	g2(t	g2(t	PROPN
ejpam-4679	109	27	,	,	PUNCT
ejpam-4679	109	28	y	y	NOUN
ejpam-4679	109	29	)	)	PUNCT
ejpam-4679	109	30	)	)	PUNCT
ejpam-4679	110	1	∈	∈	PROPN
ejpam-4679	110	2	l2(γ1	l2(γ1	VERB
ejpam-4679	110	3	t	t	NOUN
ejpam-4679	110	4	)	)	PUNCT
ejpam-4679	110	5	×	×	PROPN
ejpam-4679	110	6	l2(γ2	l2(γ2	PROPN
ejpam-4679	110	7	t	t	NOUN
ejpam-4679	110	8	)	)	PUNCT
ejpam-4679	110	9	.	.	PUNCT
ejpam-4679	111	1	m.	m.	PROPN
ejpam-4679	111	2	zeki	zeki	PROPN
ejpam-4679	111	3	,	,	PUNCT
ejpam-4679	111	4	s.	s.	PROPN
ejpam-4679	111	5	tatar	tatar	PROPN
ejpam-4679	111	6	/	/	SYM
ejpam-4679	111	7	eur	eur	PROPN
ejpam-4679	111	8	.	.	PUNCT
ejpam-4679	112	1	j.	j.	PROPN
ejpam-4679	112	2	pure	pure	PROPN
ejpam-4679	112	3	appl	appl	PROPN
ejpam-4679	112	4	.	.	PROPN
ejpam-4679	112	5	math	math	PROPN
ejpam-4679	112	6	,	,	PUNCT
ejpam-4679	112	7	16	16	NUM
ejpam-4679	112	8	(	(	PUNCT
ejpam-4679	112	9	1	1	NUM
ejpam-4679	112	10	)	)	PUNCT
ejpam-4679	112	11	(	(	PUNCT
ejpam-4679	112	12	2023	2023	NUM
ejpam-4679	112	13	)	)	PUNCT
ejpam-4679	112	14	,	,	PUNCT
ejpam-4679	112	15	491	491	NUM
ejpam-4679	112	16	-	-	SYM
ejpam-4679	112	17	502	502	NUM
ejpam-4679	112	18	496	496	NUM
ejpam-4679	112	19	3	3	NUM
ejpam-4679	112	20	.	.	PUNCT
ejpam-4679	112	21	numerical	numerical	ADJ
ejpam-4679	112	22	solution	solution	NOUN
ejpam-4679	112	23	to	to	ADP
ejpam-4679	112	24	the	the	DET
ejpam-4679	112	25	fractional	fractional	ADJ
ejpam-4679	112	26	richards	richard	NOUN
ejpam-4679	112	27	equation	equation	NOUN
ejpam-4679	112	28	this	this	DET
ejpam-4679	112	29	section	section	NOUN
ejpam-4679	112	30	is	be	AUX
ejpam-4679	112	31	devoted	devote	VERB
ejpam-4679	112	32	to	to	ADP
ejpam-4679	112	33	numerical	numerical	ADJ
ejpam-4679	112	34	solution	solution	NOUN
ejpam-4679	112	35	to	to	ADP
ejpam-4679	112	36	the	the	DET
ejpam-4679	112	37	problem	problem	NOUN
ejpam-4679	112	38	(	(	PUNCT
ejpam-4679	112	39	7	7	NUM
ejpam-4679	112	40	)	)	PUNCT
ejpam-4679	112	41	.	.	PUNCT
ejpam-4679	113	1	we	we	PRON
ejpam-4679	113	2	first	first	ADV
ejpam-4679	113	3	illustrate	illustrate	VERB
ejpam-4679	113	4	the	the	DET
ejpam-4679	113	5	methodology	methodology	NOUN
ejpam-4679	113	6	on	on	ADP
ejpam-4679	113	7	a	a	DET
ejpam-4679	113	8	simple	simple	ADJ
ejpam-4679	113	9	equation	equation	NOUN
ejpam-4679	113	10	and	and	CCONJ
ejpam-4679	113	11	then	then	ADV
ejpam-4679	113	12	apply	apply	VERB
ejpam-4679	113	13	the	the	DET
ejpam-4679	113	14	idea	idea	NOUN
ejpam-4679	113	15	for	for	ADP
ejpam-4679	113	16	the	the	DET
ejpam-4679	113	17	problem	problem	NOUN
ejpam-4679	113	18	(	(	PUNCT
ejpam-4679	113	19	7	7	NUM
ejpam-4679	113	20	)	)	PUNCT
ejpam-4679	113	21	[	[	PUNCT
ejpam-4679	113	22	e.g.	e.g.	ADV
ejpam-4679	113	23	see	see	VERB
ejpam-4679	113	24	21	21	NUM
ejpam-4679	113	25	]	]	PUNCT
ejpam-4679	113	26	.	.	PUNCT
ejpam-4679	114	1	the	the	DET
ejpam-4679	114	2	main	main	ADJ
ejpam-4679	114	3	idea	idea	NOUN
ejpam-4679	114	4	was	be	AUX
ejpam-4679	114	5	to	to	PART
ejpam-4679	114	6	convert	convert	VERB
ejpam-4679	114	7	the	the	DET
ejpam-4679	114	8	equation	equation	NOUN
ejpam-4679	114	9	to	to	ADP
ejpam-4679	114	10	a	a	DET
ejpam-4679	114	11	system	system	NOUN
ejpam-4679	114	12	of	of	ADP
ejpam-4679	114	13	ordinary	ordinary	ADJ
ejpam-4679	114	14	differential	differential	ADJ
ejpam-4679	114	15	equations	equation	NOUN
ejpam-4679	114	16	(	(	PUNCT
ejpam-4679	114	17	odes	ode	NOUN
ejpam-4679	114	18	)	)	PUNCT
ejpam-4679	114	19	using	use	VERB
ejpam-4679	114	20	method	method	NOUN
ejpam-4679	114	21	of	of	ADP
ejpam-4679	114	22	lines	line	NOUN
ejpam-4679	114	23	and	and	CCONJ
ejpam-4679	114	24	vectorization	vectorization	NOUN
ejpam-4679	114	25	,	,	PUNCT
ejpam-4679	114	26	and	and	CCONJ
ejpam-4679	114	27	solve	solve	VERB
ejpam-4679	114	28	the	the	DET
ejpam-4679	114	29	resulting	result	VERB
ejpam-4679	114	30	system	system	NOUN
ejpam-4679	114	31	of	of	ADP
ejpam-4679	114	32	fractional	fractional	ADJ
ejpam-4679	114	33	odes	ode	NOUN
ejpam-4679	114	34	.	.	PUNCT
ejpam-4679	115	1	in	in	ADP
ejpam-4679	115	2	addition	addition	NOUN
ejpam-4679	115	3	to	to	ADP
ejpam-4679	115	4	using	use	VERB
ejpam-4679	115	5	the	the	DET
ejpam-4679	115	6	classical	classical	ADJ
ejpam-4679	115	7	method	method	NOUN
ejpam-4679	115	8	of	of	ADP
ejpam-4679	115	9	lines	line	NOUN
ejpam-4679	115	10	,	,	PUNCT
ejpam-4679	115	11	we	we	PRON
ejpam-4679	115	12	adopt	adopt	VERB
ejpam-4679	115	13	operator	operator	NOUN
ejpam-4679	115	14	approach	approach	NOUN
ejpam-4679	115	15	to	to	ADP
ejpam-4679	115	16	approximate	approximate	ADJ
ejpam-4679	115	17	derivatives	derivative	NOUN
ejpam-4679	115	18	which	which	PRON
ejpam-4679	115	19	reduces	reduce	VERB
ejpam-4679	115	20	computational	computational	ADJ
ejpam-4679	115	21	and	and	CCONJ
ejpam-4679	115	22	memory	memory	NOUN
ejpam-4679	115	23	demand	demand	NOUN
ejpam-4679	115	24	of	of	ADP
ejpam-4679	115	25	the	the	DET
ejpam-4679	115	26	algorithm	algorithm	NOUN
ejpam-4679	115	27	.	.	PUNCT
ejpam-4679	116	1	for	for	ADP
ejpam-4679	116	2	this	this	DET
ejpam-4679	116	3	purpose	purpose	NOUN
ejpam-4679	116	4	,	,	PUNCT
ejpam-4679	116	5	we	we	PRON
ejpam-4679	116	6	consider	consider	VERB
ejpam-4679	116	7	the	the	DET
ejpam-4679	116	8	discretization	discretization	NOUN
ejpam-4679	116	9	of	of	ADP
ejpam-4679	116	10	the	the	DET
ejpam-4679	116	11	following	follow	VERB
ejpam-4679	116	12	equation	equation	NOUN
ejpam-4679	116	13	:	:	PUNCT
ejpam-4679	116	14	∂u	∂u	PROPN
ejpam-4679	116	15	∂t	∂t	PROPN
ejpam-4679	116	16	=	=	PUNCT
ejpam-4679	116	17	∂2u	∂2u	PROPN
ejpam-4679	116	18	∂x2	∂x2	PROPN
ejpam-4679	116	19	+	+	CCONJ
ejpam-4679	116	20	∂2u	∂2u	ADJ
ejpam-4679	116	21	∂y2	∂y2	NOUN
ejpam-4679	116	22	+	+	CCONJ
ejpam-4679	116	23	f(t	f(t	NOUN
ejpam-4679	116	24	,	,	PUNCT
ejpam-4679	116	25	x	x	NOUN
ejpam-4679	116	26	,	,	PUNCT
ejpam-4679	116	27	y	y	PROPN
ejpam-4679	116	28	)	)	PUNCT
ejpam-4679	116	29	,	,	PUNCT
ejpam-4679	116	30	(	(	PUNCT
ejpam-4679	116	31	t	t	PROPN
ejpam-4679	116	32	,	,	PUNCT
ejpam-4679	116	33	x	x	NOUN
ejpam-4679	116	34	,	,	PUNCT
ejpam-4679	116	35	y	y	NOUN
ejpam-4679	116	36	)	)	PUNCT
ejpam-4679	116	37	∈	∈	PROPN
ejpam-4679	116	38	ωt	ωt	PROPN
ejpam-4679	116	39	.	.	PUNCT
ejpam-4679	117	1	(	(	PUNCT
ejpam-4679	117	2	13	13	NUM
ejpam-4679	117	3	)	)	PUNCT
ejpam-4679	117	4	let	let	VERB
ejpam-4679	117	5	xi	xi	X
ejpam-4679	118	1	=	=	PUNCT
ejpam-4679	118	2	0	0	PUNCT
ejpam-4679	119	1	+	+	CCONJ
ejpam-4679	119	2	i∆x	i∆x	NOUN
ejpam-4679	119	3	,	,	PUNCT
ejpam-4679	119	4	i	i	NOUN
ejpam-4679	119	5	=	=	NOUN
ejpam-4679	119	6	0	0	NUM
ejpam-4679	119	7	,	,	PUNCT
ejpam-4679	119	8	·	·	PUNCT
ejpam-4679	119	9	·	·	PUNCT
ejpam-4679	119	10	·	·	PUNCT
ejpam-4679	119	11	,	,	PUNCT
ejpam-4679	119	12	m	m	PROPN
ejpam-4679	119	13	and	and	CCONJ
ejpam-4679	119	14	yj	yj	PROPN
ejpam-4679	119	15	=	=	SYM
ejpam-4679	119	16	0	0	PUNCT
ejpam-4679	120	1	+	+	CCONJ
ejpam-4679	120	2	j∆y	j∆y	NOUN
ejpam-4679	120	3	,	,	PUNCT
ejpam-4679	120	4	j	j	PROPN
ejpam-4679	120	5	=	=	SYM
ejpam-4679	120	6	0	0	PROPN
ejpam-4679	120	7	,	,	PUNCT
ejpam-4679	120	8	·	·	PUNCT
ejpam-4679	120	9	·	·	PUNCT
ejpam-4679	120	10	·	·	PUNCT
ejpam-4679	120	11	,	,	PUNCT
ejpam-4679	120	12	n	n	CCONJ
ejpam-4679	120	13	with	with	ADP
ejpam-4679	120	14	∆x	∆x	PROPN
ejpam-4679	120	15	=	=	SYM
ejpam-4679	120	16	1	1	NUM
ejpam-4679	120	17	/	/	SYM
ejpam-4679	120	18	m	m	PROPN
ejpam-4679	120	19	and	and	CCONJ
ejpam-4679	120	20	∆y	∆y	X
ejpam-4679	120	21	=	=	NOUN
ejpam-4679	120	22	1	1	NUM
ejpam-4679	120	23	/	/	SYM
ejpam-4679	120	24	n	n	NOUN
ejpam-4679	120	25	.	.	PUNCT
ejpam-4679	121	1	also	also	ADV
ejpam-4679	121	2	,	,	PUNCT
ejpam-4679	121	3	let	let	VERB
ejpam-4679	121	4	uij(t	uij(t	X
ejpam-4679	121	5	)	)	PUNCT
ejpam-4679	121	6	represent	represent	VERB
ejpam-4679	121	7	the	the	DET
ejpam-4679	121	8	solution	solution	NOUN
ejpam-4679	121	9	at	at	ADP
ejpam-4679	121	10	point	point	NOUN
ejpam-4679	121	11	(	(	PUNCT
ejpam-4679	121	12	xi	xi	PROPN
ejpam-4679	121	13	,	,	PUNCT
ejpam-4679	121	14	yj	yj	PROPN
ejpam-4679	121	15	)	)	PUNCT
ejpam-4679	121	16	at	at	ADP
ejpam-4679	121	17	a	a	DET
ejpam-4679	121	18	time	time	NOUN
ejpam-4679	121	19	t	t	X
ejpam-4679	121	20	>	>	X
ejpam-4679	121	21	0	0	X
ejpam-4679	121	22	.	.	PUNCT
ejpam-4679	122	1	then	then	ADV
ejpam-4679	122	2	,	,	PUNCT
ejpam-4679	122	3	the	the	DET
ejpam-4679	122	4	centered	center	VERB
ejpam-4679	122	5	difference	difference	NOUN
ejpam-4679	122	6	approximation	approximation	NOUN
ejpam-4679	122	7	of	of	ADP
ejpam-4679	122	8	the	the	DET
ejpam-4679	122	9	time	time	NOUN
ejpam-4679	122	10	derivative	derivative	NOUN
ejpam-4679	122	11	at	at	ADP
ejpam-4679	122	12	point	point	NOUN
ejpam-4679	122	13	(	(	PUNCT
ejpam-4679	122	14	xi	xi	PROPN
ejpam-4679	122	15	,	,	PUNCT
ejpam-4679	122	16	yj	yj	PROPN
ejpam-4679	122	17	)	)	PUNCT
ejpam-4679	122	18	is	be	AUX
ejpam-4679	122	19	uij	uij	PRON
ejpam-4679	122	20	dt	dt	NOUN
ejpam-4679	122	21	=	=	PUNCT
ejpam-4679	122	22	ui+1j	ui+1j	PROPN
ejpam-4679	122	23	−	−	PROPN
ejpam-4679	122	24	2uij	2uij	NUM
ejpam-4679	123	1	+	+	CCONJ
ejpam-4679	123	2	ui−1j	ui−1j	ADJ
ejpam-4679	123	3	∆x2	∆x2	PRON
ejpam-4679	123	4	+	+	NUM
ejpam-4679	123	5	uij+1	uij+1	NOUN
ejpam-4679	123	6	−	−	NOUN
ejpam-4679	123	7	2uij	2uij	NOUN
ejpam-4679	124	1	+	+	CCONJ
ejpam-4679	124	2	uij−1	uij−1	PROPN
ejpam-4679	124	3	∆y2	∆y2	PROPN
ejpam-4679	124	4	+	+	CCONJ
ejpam-4679	124	5	f(t	f(t	PROPN
ejpam-4679	124	6	,	,	PUNCT
ejpam-4679	124	7	xi	xi	PROPN
ejpam-4679	124	8	,	,	PUNCT
ejpam-4679	124	9	yj	yj	PROPN
ejpam-4679	124	10	)	)	PUNCT
ejpam-4679	124	11	,	,	PUNCT
ejpam-4679	124	12	with	with	ADP
ejpam-4679	124	13	i	i	PROPN
ejpam-4679	124	14	=	=	SYM
ejpam-4679	124	15	1	1	NUM
ejpam-4679	124	16	,	,	PUNCT
ejpam-4679	124	17	·	·	PUNCT
ejpam-4679	124	18	·	·	PUNCT
ejpam-4679	124	19	·	·	PUNCT
ejpam-4679	124	20	,	,	PUNCT
ejpam-4679	124	21	n	n	CCONJ
ejpam-4679	124	22	−1	−1	NOUN
ejpam-4679	124	23	and	and	CCONJ
ejpam-4679	124	24	j	j	PROPN
ejpam-4679	124	25	=	=	SYM
ejpam-4679	124	26	1	1	NUM
ejpam-4679	124	27	,	,	PUNCT
ejpam-4679	124	28	·	·	PUNCT
ejpam-4679	124	29	·	·	PUNCT
ejpam-4679	124	30	·	·	PUNCT
ejpam-4679	124	31	,	,	PUNCT
ejpam-4679	124	32	m	m	VERB
ejpam-4679	124	33	−1	−1	NOUN
ejpam-4679	124	34	.	.	PUNCT
ejpam-4679	125	1	this	this	DET
ejpam-4679	125	2	approximation	approximation	NOUN
ejpam-4679	125	3	can	can	AUX
ejpam-4679	125	4	be	be	AUX
ejpam-4679	125	5	vectorized	vectorize	VERB
ejpam-4679	125	6	by	by	ADP
ejpam-4679	125	7	first	first	ADV
ejpam-4679	125	8	defining	define	VERB
ejpam-4679	125	9	the	the	DET
ejpam-4679	125	10	solution	solution	NOUN
ejpam-4679	125	11	matrix	matrix	NOUN
ejpam-4679	125	12	at	at	ADP
ejpam-4679	125	13	the	the	DET
ejpam-4679	125	14	interior	interior	ADJ
ejpam-4679	125	15	points	point	NOUN
ejpam-4679	125	16	[	[	X
ejpam-4679	125	17	uij	uij	X
ejpam-4679	125	18	]	]	X
ejpam-4679	125	19	=	=	SYM
ejpam-4679	125	20	u(xi	u(xi	X
ejpam-4679	125	21	,	,	PUNCT
ejpam-4679	125	22	yj	yj	PROPN
ejpam-4679	125	23	)	)	PUNCT
ejpam-4679	125	24	with	with	ADP
ejpam-4679	125	25	i	i	PROPN
ejpam-4679	125	26	=	=	NOUN
ejpam-4679	125	27	1	1	NUM
ejpam-4679	125	28	,	,	PUNCT
ejpam-4679	125	29	·	·	PUNCT
ejpam-4679	125	30	·	·	PUNCT
ejpam-4679	125	31	·	·	PUNCT
ejpam-4679	125	32	,	,	PUNCT
ejpam-4679	125	33	n	n	CCONJ
ejpam-4679	125	34	−	−	PROPN
ejpam-4679	125	35	1	1	NUM
ejpam-4679	125	36	and	and	CCONJ
ejpam-4679	125	37	j	j	NOUN
ejpam-4679	125	38	=	=	SYM
ejpam-4679	125	39	1	1	NUM
ejpam-4679	125	40	,	,	PUNCT
ejpam-4679	125	41	·	·	PUNCT
ejpam-4679	125	42	·	·	PUNCT
ejpam-4679	125	43	·	·	PUNCT
ejpam-4679	125	44	,	,	PUNCT
ejpam-4679	125	45	m	m	VERB
ejpam-4679	125	46	−	−	NOUN
ejpam-4679	126	1	1	1	X
ejpam-4679	126	2	.	.	PUNCT
ejpam-4679	127	1	we	we	PRON
ejpam-4679	127	2	define	define	VERB
ejpam-4679	127	3	the	the	DET
ejpam-4679	127	4	left	left	ADJ
ejpam-4679	127	5	and	and	CCONJ
ejpam-4679	127	6	right	right	ADJ
ejpam-4679	127	7	shift	shift	NOUN
ejpam-4679	127	8	operators	operator	NOUN
ejpam-4679	127	9	on	on	ADP
ejpam-4679	127	10	the	the	DET
ejpam-4679	127	11	matrix	matrix	NOUN
ejpam-4679	127	12	[	[	X
ejpam-4679	127	13	uij	uij	X
ejpam-4679	127	14	]	]	PUNCT
ejpam-4679	127	15	of	of	ADP
ejpam-4679	127	16	solution	solution	NOUN
ejpam-4679	127	17	approximations	approximation	NOUN
ejpam-4679	127	18	at	at	ADP
ejpam-4679	127	19	the	the	DET
ejpam-4679	127	20	interior	interior	ADJ
ejpam-4679	127	21	points	point	NOUN
ejpam-4679	127	22	as	as	SCONJ
ejpam-4679	127	23	follows	follow	VERB
ejpam-4679	127	24	:	:	PUNCT
ejpam-4679	127	25	ls([uij	ls([uij	PROPN
ejpam-4679	127	26	]	]	PUNCT
ejpam-4679	127	27	)	)	PUNCT
ejpam-4679	127	28	=	=	PUNCT
ejpam-4679	128	1	[	[	X
ejpam-4679	128	2	ui+1j	ui+1j	X
ejpam-4679	128	3	]	]	PUNCT
ejpam-4679	128	4	and	and	CCONJ
ejpam-4679	128	5	rs([uij	rs([uij	PROPN
ejpam-4679	128	6	]	]	PUNCT
ejpam-4679	128	7	)	)	PUNCT
ejpam-4679	128	8	=	=	PUNCT
ejpam-4679	129	1	[	[	X
ejpam-4679	129	2	ui−1j	ui−1j	X
ejpam-4679	129	3	]	]	X
ejpam-4679	129	4	,	,	PUNCT
ejpam-4679	129	5	(	(	PUNCT
ejpam-4679	129	6	14	14	NUM
ejpam-4679	129	7	)	)	PUNCT
ejpam-4679	129	8	with	with	ADP
ejpam-4679	129	9	i	i	PROPN
ejpam-4679	129	10	=	=	NOUN
ejpam-4679	129	11	1	1	NUM
ejpam-4679	129	12	,	,	PUNCT
ejpam-4679	129	13	·	·	PUNCT
ejpam-4679	129	14	·	·	PUNCT
ejpam-4679	129	15	·	·	PUNCT
ejpam-4679	129	16	,	,	PUNCT
ejpam-4679	129	17	n	n	CCONJ
ejpam-4679	129	18	−	−	PROPN
ejpam-4679	129	19	1	1	NUM
ejpam-4679	129	20	and	and	CCONJ
ejpam-4679	129	21	j	j	NOUN
ejpam-4679	129	22	=	=	SYM
ejpam-4679	129	23	1	1	NUM
ejpam-4679	129	24	,	,	PUNCT
ejpam-4679	129	25	·	·	PUNCT
ejpam-4679	129	26	·	·	PUNCT
ejpam-4679	129	27	·	·	PUNCT
ejpam-4679	129	28	,	,	PUNCT
ejpam-4679	129	29	m	m	VERB
ejpam-4679	129	30	−	−	NOUN
ejpam-4679	130	1	1	1	NUM
ejpam-4679	130	2	.	.	PUNCT
ejpam-4679	131	1	then	then	ADV
ejpam-4679	131	2	,	,	PUNCT
ejpam-4679	131	3	by	by	ADP
ejpam-4679	131	4	using	use	VERB
ejpam-4679	131	5	(	(	PUNCT
ejpam-4679	131	6	14	14	NUM
ejpam-4679	131	7	)	)	PUNCT
ejpam-4679	131	8	,	,	PUNCT
ejpam-4679	131	9	(	(	PUNCT
ejpam-4679	131	10	13	13	NUM
ejpam-4679	131	11	)	)	PUNCT
ejpam-4679	131	12	can	can	AUX
ejpam-4679	131	13	be	be	AUX
ejpam-4679	131	14	expressed	express	VERB
ejpam-4679	131	15	in	in	ADP
ejpam-4679	131	16	matrix	matrix	NOUN
ejpam-4679	131	17	form	form	NOUN
ejpam-4679	131	18	using	use	VERB
ejpam-4679	131	19	the	the	DET
ejpam-4679	131	20	left	left	ADJ
ejpam-4679	131	21	and	and	CCONJ
ejpam-4679	131	22	right	right	ADJ
ejpam-4679	131	23	shift	shift	NOUN
ejpam-4679	131	24	operators	operator	NOUN
ejpam-4679	131	25	in	in	ADP
ejpam-4679	131	26	the	the	DET
ejpam-4679	131	27	following	following	ADJ
ejpam-4679	131	28	way	way	NOUN
ejpam-4679	131	29	:	:	PUNCT
ejpam-4679	131	30	[	[	PUNCT
ejpam-4679	131	31	duij	duij	X
ejpam-4679	131	32	dt	dt	X
ejpam-4679	131	33	]	]	PUNCT
ejpam-4679	131	34	=	=	PUNCT
ejpam-4679	132	1	[	[	X
ejpam-4679	132	2	ls([uij	ls([uij	PROPN
ejpam-4679	132	3	]	]	X
ejpam-4679	132	4	)	)	PUNCT
ejpam-4679	133	1	−	−	PROPN
ejpam-4679	133	2	2[uij	2[uij	NUM
ejpam-4679	133	3	]	]	PUNCT
ejpam-4679	134	1	+	+	NUM
ejpam-4679	134	2	rs([uij	rs([uij	X
ejpam-4679	134	3	]	]	PUNCT
ejpam-4679	134	4	)	)	PUNCT
ejpam-4679	134	5	]	]	PUNCT
ejpam-4679	135	1	∆x2	∆x2	PRON
ejpam-4679	135	2	+	+	PUNCT
ejpam-4679	136	1	[	[	X
ejpam-4679	136	2	ls([uij	ls([uij	X
ejpam-4679	136	3	]	]	PUNCT
ejpam-4679	136	4	′	′	NUM
ejpam-4679	136	5	)	)	PUNCT
ejpam-4679	136	6	−	−	PROPN
ejpam-4679	137	1	2[uij	2[uij	NUM
ejpam-4679	137	2	]	]	PUNCT
ejpam-4679	137	3	−rs([uij	−rs([uij	X
ejpam-4679	137	4	]	]	PUNCT
ejpam-4679	137	5	′))]′	′))]′	PROPN
ejpam-4679	138	1	∆y2	∆y2	PROPN
ejpam-4679	138	2	+	+	CCONJ
ejpam-4679	138	3	f(t	f(t	PROPN
ejpam-4679	138	4	,	,	PUNCT
ejpam-4679	138	5	[	[	X
ejpam-4679	138	6	x	x	X
ejpam-4679	138	7	]	]	X
ejpam-4679	138	8	,	,	PUNCT
ejpam-4679	138	9	[	[	X
ejpam-4679	138	10	y	y	X
ejpam-4679	138	11	]	]	X
ejpam-4679	138	12	)	)	PUNCT
ejpam-4679	138	13	,	,	PUNCT
ejpam-4679	138	14	where	where	SCONJ
ejpam-4679	138	15	[	[	X
ejpam-4679	138	16	aij	aij	X
ejpam-4679	138	17	]	]	PUNCT
ejpam-4679	138	18	′	′	NUM
ejpam-4679	138	19	denotes	denote	NOUN
ejpam-4679	138	20	the	the	DET
ejpam-4679	138	21	transpose	transpose	NOUN
ejpam-4679	138	22	of	of	ADP
ejpam-4679	138	23	the	the	DET
ejpam-4679	138	24	matrix	matrix	NOUN
ejpam-4679	138	25	[	[	X
ejpam-4679	138	26	aij	aij	X
ejpam-4679	138	27	]	]	PUNCT
ejpam-4679	138	28	and	and	CCONJ
ejpam-4679	138	29	[	[	X
ejpam-4679	138	30	x	x	X
ejpam-4679	138	31	]	]	X
ejpam-4679	138	32	and	and	CCONJ
ejpam-4679	138	33	[	[	X
ejpam-4679	138	34	y	y	X
ejpam-4679	138	35	]	]	PUNCT
ejpam-4679	138	36	represent	represent	VERB
ejpam-4679	138	37	the	the	DET
ejpam-4679	138	38	matrices	matrix	NOUN
ejpam-4679	138	39	with	with	ADP
ejpam-4679	138	40	(	(	PUNCT
ejpam-4679	138	41	i	i	NOUN
ejpam-4679	138	42	,	,	PUNCT
ejpam-4679	138	43	j)th	j)th	ADJ
ejpam-4679	138	44	entries	entry	NOUN
ejpam-4679	138	45	given	give	VERB
ejpam-4679	138	46	as	as	ADP
ejpam-4679	138	47	x(i	x(i	PROPN
ejpam-4679	138	48	,	,	PUNCT
ejpam-4679	138	49	j	j	NOUN
ejpam-4679	138	50	)	)	PUNCT
ejpam-4679	138	51	=	=	PUNCT
ejpam-4679	139	1	xi	xi	PROPN
ejpam-4679	139	2	and	and	CCONJ
ejpam-4679	139	3	y	y	PROPN
ejpam-4679	139	4	(	(	PUNCT
ejpam-4679	139	5	i	i	PROPN
ejpam-4679	139	6	,	,	PUNCT
ejpam-4679	139	7	j	j	PROPN
ejpam-4679	139	8	)	)	PUNCT
ejpam-4679	140	1	=	=	SYM
ejpam-4679	140	2	yj	yj	PROPN
ejpam-4679	140	3	for	for	ADP
ejpam-4679	140	4	i	i	PROPN
ejpam-4679	140	5	=	=	NOUN
ejpam-4679	140	6	1	1	NUM
ejpam-4679	140	7	,	,	PUNCT
ejpam-4679	140	8	...	...	PUNCT
ejpam-4679	140	9	,	,	PUNCT
ejpam-4679	140	10	m	m	VERB
ejpam-4679	140	11	−	−	NOUN
ejpam-4679	140	12	1	1	NUM
ejpam-4679	140	13	and	and	CCONJ
ejpam-4679	140	14	j	j	NOUN
ejpam-4679	140	15	=	=	SYM
ejpam-4679	140	16	1	1	NUM
ejpam-4679	140	17	,	,	PUNCT
ejpam-4679	140	18	...	...	PUNCT
ejpam-4679	140	19	,	,	PUNCT
ejpam-4679	140	20	n	n	CCONJ
ejpam-4679	140	21	−	−	PROPN
ejpam-4679	141	1	1	1	NUM
ejpam-4679	141	2	.	.	PUNCT
ejpam-4679	142	1	next	next	ADV
ejpam-4679	142	2	we	we	PRON
ejpam-4679	142	3	consider	consider	VERB
ejpam-4679	142	4	the	the	DET
ejpam-4679	142	5	vectorization	vectorization	NOUN
ejpam-4679	142	6	of	of	ADP
ejpam-4679	142	7	the	the	DET
ejpam-4679	142	8	problem	problem	NOUN
ejpam-4679	142	9	(	(	PUNCT
ejpam-4679	142	10	11	11	NUM
ejpam-4679	142	11	)	)	PUNCT
ejpam-4679	142	12	.	.	PUNCT
ejpam-4679	143	1	for	for	ADP
ejpam-4679	143	2	n	n	NOUN
ejpam-4679	143	3	=	=	SYM
ejpam-4679	143	4	1	1	NUM
ejpam-4679	143	5	,	,	PUNCT
ejpam-4679	143	6	and	and	CCONJ
ejpam-4679	143	7	u(0)(t	u(0)(t	ADJ
ejpam-4679	143	8	,	,	PUNCT
ejpam-4679	143	9	x	x	NOUN
ejpam-4679	143	10	,	,	PUNCT
ejpam-4679	143	11	y	y	NOUN
ejpam-4679	143	12	)	)	PUNCT
ejpam-4679	143	13	=	=	SYM
ejpam-4679	143	14	0	0	NUM
ejpam-4679	143	15	,	,	PUNCT
ejpam-4679	143	16	we	we	PRON
ejpam-4679	143	17	have	have	VERB
ejpam-4679	143	18	to	to	PART
ejpam-4679	143	19	solve	solve	VERB
ejpam-4679	143	20	the	the	DET
ejpam-4679	143	21	following	following	ADJ
ejpam-4679	143	22	linear	linear	ADJ
ejpam-4679	143	23	problem	problem	NOUN
ejpam-4679	143	24	to	to	PART
ejpam-4679	143	25	get	get	VERB
ejpam-4679	143	26	the	the	DET
ejpam-4679	143	27	solution	solution	NOUN
ejpam-4679	143	28	u(1)(t	u(1)(t	NOUN
ejpam-4679	143	29	,	,	PUNCT
ejpam-4679	143	30	x	x	X
ejpam-4679	143	31	,	,	PUNCT
ejpam-4679	143	32	y):	y):	PROPN
ejpam-4679	144	1	∂β	∂β	PROPN
ejpam-4679	144	2	∂tβ	∂tβ	PROPN
ejpam-4679	144	3	u(1	u(1	PROPN
ejpam-4679	144	4	)	)	PUNCT
ejpam-4679	145	1	=	=	PRON
ejpam-4679	145	2	(	(	PUNCT
ejpam-4679	145	3	d(0)u	d(0)u	X
ejpam-4679	145	4	(	(	PUNCT
ejpam-4679	145	5	1	1	NUM
ejpam-4679	145	6	)	)	PUNCT
ejpam-4679	145	7	x	x	SYM
ejpam-4679	145	8	)	)	PUNCT
ejpam-4679	145	9	x	x	X
ejpam-4679	146	1	+	+	PUNCT
ejpam-4679	146	2	(	(	PUNCT
ejpam-4679	146	3	d(0)u	d(0)u	X
ejpam-4679	146	4	(	(	PUNCT
ejpam-4679	146	5	1	1	NUM
ejpam-4679	146	6	)	)	PUNCT
ejpam-4679	146	7	y	y	NOUN
ejpam-4679	146	8	)	)	PUNCT
ejpam-4679	146	9	y	y	PROPN
ejpam-4679	146	10	+	+	ADJ
ejpam-4679	146	11	f(t	f(t	PROPN
ejpam-4679	146	12	,	,	PUNCT
ejpam-4679	146	13	x	x	NOUN
ejpam-4679	146	14	,	,	PUNCT
ejpam-4679	146	15	y	y	PROPN
ejpam-4679	146	16	)	)	PUNCT
ejpam-4679	146	17	,	,	PUNCT
ejpam-4679	146	18	(	(	PUNCT
ejpam-4679	146	19	t	t	PROPN
ejpam-4679	146	20	,	,	PUNCT
ejpam-4679	146	21	x	x	NOUN
ejpam-4679	146	22	,	,	PUNCT
ejpam-4679	146	23	y	y	NOUN
ejpam-4679	146	24	)	)	PUNCT
ejpam-4679	146	25	∈	∈	PROPN
ejpam-4679	146	26	ωt	ωt	PROPN
ejpam-4679	146	27	,	,	PUNCT
ejpam-4679	146	28	u(1)(0	u(1)(0	ADV
ejpam-4679	146	29	,	,	PUNCT
ejpam-4679	146	30	x	x	NOUN
ejpam-4679	146	31	,	,	PUNCT
ejpam-4679	146	32	y	y	NOUN
ejpam-4679	146	33	)	)	PUNCT
ejpam-4679	146	34	=	=	SYM
ejpam-4679	146	35	0	0	NUM
ejpam-4679	146	36	,	,	PUNCT
ejpam-4679	146	37	(	(	PUNCT
ejpam-4679	146	38	x	x	X
ejpam-4679	146	39	,	,	PUNCT
ejpam-4679	146	40	y	y	NOUN
ejpam-4679	146	41	)	)	PUNCT
ejpam-4679	146	42	∈	∈	PROPN
ejpam-4679	146	43	ω	ω	PROPN
ejpam-4679	146	44	,	,	PUNCT
ejpam-4679	146	45	−d(0)u	−d(0)u	PROPN
ejpam-4679	146	46	(	(	PUNCT
ejpam-4679	146	47	1	1	NUM
ejpam-4679	146	48	)	)	PUNCT
ejpam-4679	146	49	x	x	NOUN
ejpam-4679	146	50	(	(	PUNCT
ejpam-4679	146	51	t	t	PROPN
ejpam-4679	146	52	,	,	PUNCT
ejpam-4679	146	53	1	1	NUM
ejpam-4679	146	54	,	,	PUNCT
ejpam-4679	146	55	y	y	NOUN
ejpam-4679	146	56	)	)	PUNCT
ejpam-4679	146	57	=	=	SYM
ejpam-4679	146	58	g1(t	g1(t	PROPN
ejpam-4679	146	59	,	,	PUNCT
ejpam-4679	146	60	y	y	PROPN
ejpam-4679	146	61	)	)	PUNCT
ejpam-4679	146	62	,	,	PUNCT
ejpam-4679	146	63	y	y	PROPN
ejpam-4679	146	64	∈	∈	PROPN
ejpam-4679	146	65	(	(	PUNCT
ejpam-4679	146	66	0	0	NUM
ejpam-4679	146	67	,	,	PUNCT
ejpam-4679	146	68	1	1	NUM
ejpam-4679	146	69	)	)	PUNCT
ejpam-4679	146	70	,	,	PUNCT
ejpam-4679	146	71	t	t	PROPN
ejpam-4679	146	72	∈	∈	PROPN
ejpam-4679	146	73	(	(	PUNCT
ejpam-4679	146	74	0	0	NUM
ejpam-4679	146	75	,	,	PUNCT
ejpam-4679	146	76	t	t	NOUN
ejpam-4679	146	77	)	)	PUNCT
ejpam-4679	146	78	,	,	PUNCT
ejpam-4679	146	79	−d(0)u	−d(0)u	PROPN
ejpam-4679	146	80	(	(	PUNCT
ejpam-4679	146	81	1	1	X
ejpam-4679	146	82	)	)	PUNCT
ejpam-4679	146	83	y	y	PROPN
ejpam-4679	146	84	(	(	PUNCT
ejpam-4679	146	85	t	t	PROPN
ejpam-4679	146	86	,	,	PUNCT
ejpam-4679	146	87	x	x	X
ejpam-4679	146	88	,	,	PUNCT
ejpam-4679	146	89	1	1	NUM
ejpam-4679	146	90	)	)	PUNCT
ejpam-4679	146	91	=	=	SYM
ejpam-4679	147	1	g2(t	g2(t	PROPN
ejpam-4679	147	2	,	,	PUNCT
ejpam-4679	147	3	x	x	NOUN
ejpam-4679	147	4	)	)	PUNCT
ejpam-4679	147	5	,	,	PUNCT
ejpam-4679	147	6	y	y	PROPN
ejpam-4679	147	7	∈	∈	PROPN
ejpam-4679	147	8	(	(	PUNCT
ejpam-4679	147	9	0	0	NUM
ejpam-4679	147	10	,	,	PUNCT
ejpam-4679	147	11	1	1	NUM
ejpam-4679	147	12	)	)	PUNCT
ejpam-4679	147	13	,	,	PUNCT
ejpam-4679	147	14	t	t	PROPN
ejpam-4679	147	15	∈	∈	PROPN
ejpam-4679	147	16	(	(	PUNCT
ejpam-4679	147	17	0	0	NUM
ejpam-4679	147	18	,	,	PUNCT
ejpam-4679	147	19	t	t	NOUN
ejpam-4679	147	20	)	)	PUNCT
ejpam-4679	147	21	,	,	PUNCT
ejpam-4679	147	22	u(1)(t	u(1)(t	ADJ
ejpam-4679	147	23	,	,	PUNCT
ejpam-4679	147	24	0	0	NUM
ejpam-4679	147	25	,	,	PUNCT
ejpam-4679	147	26	y	y	NOUN
ejpam-4679	147	27	)	)	PUNCT
ejpam-4679	147	28	=	=	SYM
ejpam-4679	147	29	0	0	NUM
ejpam-4679	147	30	,	,	PUNCT
ejpam-4679	147	31	x	x	SYM
ejpam-4679	147	32	∈	∈	PROPN
ejpam-4679	147	33	(	(	PUNCT
ejpam-4679	147	34	0	0	NUM
ejpam-4679	147	35	,	,	PUNCT
ejpam-4679	147	36	1	1	NUM
ejpam-4679	147	37	)	)	PUNCT
ejpam-4679	147	38	,	,	PUNCT
ejpam-4679	147	39	t	t	PROPN
ejpam-4679	147	40	∈	∈	PROPN
ejpam-4679	147	41	(	(	PUNCT
ejpam-4679	147	42	0	0	NUM
ejpam-4679	147	43	,	,	PUNCT
ejpam-4679	147	44	t	t	NOUN
ejpam-4679	147	45	)	)	PUNCT
ejpam-4679	147	46	,	,	PUNCT
ejpam-4679	147	47	u(1)(t	u(1)(t	ADJ
ejpam-4679	147	48	,	,	PUNCT
ejpam-4679	147	49	x	x	X
ejpam-4679	147	50	,	,	PUNCT
ejpam-4679	147	51	0	0	NUM
ejpam-4679	147	52	)	)	PUNCT
ejpam-4679	147	53	=	=	SYM
ejpam-4679	147	54	0	0	NUM
ejpam-4679	147	55	,	,	PUNCT
ejpam-4679	147	56	x	x	SYM
ejpam-4679	147	57	∈	∈	PROPN
ejpam-4679	147	58	(	(	PUNCT
ejpam-4679	147	59	0	0	NUM
ejpam-4679	147	60	,	,	PUNCT
ejpam-4679	147	61	1	1	NUM
ejpam-4679	147	62	)	)	PUNCT
ejpam-4679	147	63	,	,	PUNCT
ejpam-4679	147	64	t	t	PROPN
ejpam-4679	147	65	∈	∈	PROPN
ejpam-4679	147	66	(	(	PUNCT
ejpam-4679	147	67	0	0	NUM
ejpam-4679	147	68	,	,	PUNCT
ejpam-4679	147	69	t	t	NOUN
ejpam-4679	147	70	)	)	PUNCT
ejpam-4679	147	71	.	.	PUNCT
ejpam-4679	148	1	(	(	PUNCT
ejpam-4679	148	2	15	15	NUM
ejpam-4679	148	3	)	)	PUNCT
ejpam-4679	148	4	m.	m.	NOUN
ejpam-4679	148	5	zeki	zeki	PROPN
ejpam-4679	148	6	,	,	PUNCT
ejpam-4679	148	7	s.	s.	PROPN
ejpam-4679	148	8	tatar	tatar	PROPN
ejpam-4679	148	9	/	/	SYM
ejpam-4679	148	10	eur	eur	PROPN
ejpam-4679	148	11	.	.	PUNCT
ejpam-4679	149	1	j.	j.	PROPN
ejpam-4679	149	2	pure	pure	PROPN
ejpam-4679	149	3	appl	appl	PROPN
ejpam-4679	149	4	.	.	PROPN
ejpam-4679	149	5	math	math	PROPN
ejpam-4679	149	6	,	,	PUNCT
ejpam-4679	149	7	16	16	NUM
ejpam-4679	149	8	(	(	PUNCT
ejpam-4679	149	9	1	1	NUM
ejpam-4679	149	10	)	)	PUNCT
ejpam-4679	149	11	(	(	PUNCT
ejpam-4679	149	12	2023	2023	NUM
ejpam-4679	149	13	)	)	PUNCT
ejpam-4679	149	14	,	,	PUNCT
ejpam-4679	149	15	491	491	NUM
ejpam-4679	149	16	-	-	SYM
ejpam-4679	149	17	502	502	NUM
ejpam-4679	149	18	497	497	NUM
ejpam-4679	149	19	the	the	DET
ejpam-4679	149	20	problem	problem	NOUN
ejpam-4679	149	21	(	(	PUNCT
ejpam-4679	149	22	15	15	NUM
ejpam-4679	149	23	)	)	PUNCT
ejpam-4679	149	24	is	be	AUX
ejpam-4679	149	25	a	a	DET
ejpam-4679	149	26	fractional	fractional	ADJ
ejpam-4679	149	27	order	order	NOUN
ejpam-4679	149	28	and	and	CCONJ
ejpam-4679	149	29	a	a	DET
ejpam-4679	149	30	linear	linear	ADJ
ejpam-4679	149	31	problem	problem	NOUN
ejpam-4679	149	32	on	on	ADP
ejpam-4679	149	33	the	the	DET
ejpam-4679	149	34	given	give	VERB
ejpam-4679	149	35	domain	domain	NOUN
ejpam-4679	149	36	.	.	PUNCT
ejpam-4679	150	1	then	then	ADV
ejpam-4679	150	2	,	,	PUNCT
ejpam-4679	150	3	vectorized	vectorize	VERB
ejpam-4679	150	4	method	method	NOUN
ejpam-4679	150	5	of	of	ADP
ejpam-4679	150	6	line	line	NOUN
ejpam-4679	150	7	approach	approach	NOUN
ejpam-4679	150	8	described	describe	VERB
ejpam-4679	150	9	in	in	ADP
ejpam-4679	150	10	(	(	PUNCT
ejpam-4679	150	11	15	15	NUM
ejpam-4679	150	12	)	)	PUNCT
ejpam-4679	150	13	results	result	NOUN
ejpam-4679	150	14	in	in	ADP
ejpam-4679	150	15	the	the	DET
ejpam-4679	150	16	following	follow	VERB
ejpam-4679	150	17	difference	difference	NOUN
ejpam-4679	150	18	approximation	approximation	NOUN
ejpam-4679	150	19	:	:	PUNCT
ejpam-4679	150	20			PRON
ejpam-4679	150	21	[	[	PUNCT
ejpam-4679	150	22	dβu	dβu	ADJ
ejpam-4679	150	23	(	(	PUNCT
ejpam-4679	150	24	1	1	NUM
ejpam-4679	150	25	)	)	PUNCT
ejpam-4679	150	26	ij	ij	NOUN
ejpam-4679	151	1	dt	dt	X
ejpam-4679	151	2	]	]	X
ejpam-4679	151	3	=	=	SYM
ejpam-4679	151	4	d(0	d(0	NOUN
ejpam-4679	151	5	)	)	PUNCT
ejpam-4679	152	1	[	[	PUNCT
ejpam-4679	152	2	u	u	NOUN
ejpam-4679	152	3	(	(	PUNCT
ejpam-4679	152	4	1	1	NUM
ejpam-4679	152	5	)	)	PUNCT
ejpam-4679	152	6	xxij	xxij	NOUN
ejpam-4679	152	7	]	]	PUNCT
ejpam-4679	153	1	+	+	PUNCT
ejpam-4679	153	2	d(0	d(0	NOUN
ejpam-4679	153	3	)	)	PUNCT
ejpam-4679	153	4	[	[	PUNCT
ejpam-4679	153	5	u	u	NOUN
ejpam-4679	153	6	(	(	PUNCT
ejpam-4679	153	7	1	1	NUM
ejpam-4679	153	8	)	)	PUNCT
ejpam-4679	153	9	yyij	yyij	NOUN
ejpam-4679	153	10	]	]	PUNCT
ejpam-4679	153	11	+	+	CCONJ
ejpam-4679	153	12	f(t	f(t	NOUN
ejpam-4679	153	13	,	,	PUNCT
ejpam-4679	153	14	x	x	NOUN
ejpam-4679	153	15	,	,	PUNCT
ejpam-4679	153	16	y	y	PROPN
ejpam-4679	153	17	)	)	PUNCT
ejpam-4679	153	18	,	,	PUNCT
ejpam-4679	153	19	[	[	PUNCT
ejpam-4679	153	20	u	u	X
ejpam-4679	153	21	(	(	PUNCT
ejpam-4679	153	22	1	1	NUM
ejpam-4679	153	23	)	)	PUNCT
ejpam-4679	153	24	ij	ij	NOUN
ejpam-4679	153	25	(	(	PUNCT
ejpam-4679	153	26	0	0	NUM
ejpam-4679	153	27	)	)	PUNCT
ejpam-4679	153	28	]	]	PUNCT
ejpam-4679	153	29	=	=	PUNCT
ejpam-4679	154	1	[	[	X
ejpam-4679	154	2	h(x	h(x	PROPN
ejpam-4679	154	3	,	,	PUNCT
ejpam-4679	154	4	y	y	PROPN
ejpam-4679	154	5	)	)	PUNCT
ejpam-4679	154	6	]	]	PUNCT
ejpam-4679	154	7	.	.	PUNCT
ejpam-4679	155	1	this	this	PRON
ejpam-4679	155	2	is	be	AUX
ejpam-4679	155	3	a	a	DET
ejpam-4679	155	4	system	system	NOUN
ejpam-4679	155	5	of	of	ADP
ejpam-4679	155	6	linear	linear	ADJ
ejpam-4679	155	7	fractional	fractional	ADJ
ejpam-4679	155	8	odes	ode	NOUN
ejpam-4679	155	9	which	which	PRON
ejpam-4679	155	10	we	we	PRON
ejpam-4679	155	11	solve	solve	VERB
ejpam-4679	155	12	using	use	VERB
ejpam-4679	155	13	a	a	DET
ejpam-4679	155	14	matlab	matlab	NOUN
ejpam-4679	155	15	implementation	implementation	NOUN
ejpam-4679	155	16	of	of	ADP
ejpam-4679	155	17	the	the	DET
ejpam-4679	155	18	adam	adam	PROPN
ejpam-4679	155	19	-	-	PUNCT
ejpam-4679	155	20	bashfort	bashfort	NOUN
ejpam-4679	155	21	-	-	PUNCT
ejpam-4679	155	22	moulton	moulton	PROPN
ejpam-4679	155	23	(	(	PUNCT
ejpam-4679	155	24	abm	abm	PROPN
ejpam-4679	155	25	)	)	PUNCT
ejpam-4679	155	26	type	type	NOUN
ejpam-4679	155	27	predictor	predictor	NOUN
ejpam-4679	155	28	-	-	PUNCT
ejpam-4679	155	29	corrector	corrector	NOUN
ejpam-4679	155	30	pece	pece	PROPN
ejpam-4679	155	31	method	method	NOUN
ejpam-4679	155	32	given	give	VERB
ejpam-4679	155	33	in	in	ADP
ejpam-4679	155	34	[	[	X
ejpam-4679	155	35	1	1	NUM
ejpam-4679	155	36	]	]	PUNCT
ejpam-4679	155	37	.	.	PUNCT
ejpam-4679	156	1	the	the	DET
ejpam-4679	156	2	abm	abm	PROPN
ejpam-4679	156	3	is	be	AUX
ejpam-4679	156	4	a	a	DET
ejpam-4679	156	5	pece	pece	NOUN
ejpam-4679	156	6	(	(	PUNCT
ejpam-4679	156	7	predict	predict	VERB
ejpam-4679	156	8	-	-	PUNCT
ejpam-4679	156	9	evaluate	evaluate	VERB
ejpam-4679	156	10	-	-	PUNCT
ejpam-4679	156	11	correct	correct	ADJ
ejpam-4679	156	12	-	-	PUNCT
ejpam-4679	156	13	evaluate	evaluate	NOUN
ejpam-4679	156	14	)	)	PUNCT
ejpam-4679	156	15	type	type	NOUN
ejpam-4679	156	16	method	method	NOUN
ejpam-4679	156	17	;	;	PUNCT
ejpam-4679	156	18	that	that	PRON
ejpam-4679	156	19	is	is	ADV
ejpam-4679	156	20	,	,	PUNCT
ejpam-4679	156	21	for	for	ADP
ejpam-4679	156	22	the	the	DET
ejpam-4679	156	23	approximation	approximation	NOUN
ejpam-4679	156	24	of	of	ADP
ejpam-4679	156	25	a	a	DET
ejpam-4679	156	26	first	first	ADJ
ejpam-4679	156	27	order	order	NOUN
ejpam-4679	156	28	ode	ode	NOUN
ejpam-4679	156	29	of	of	ADP
ejpam-4679	156	30	the	the	DET
ejpam-4679	156	31	form	form	NOUN
ejpam-4679	156	32	{	{	PUNCT
ejpam-4679	156	33	y′	y′	NOUN
ejpam-4679	156	34	=	=	SYM
ejpam-4679	156	35	f(t	f(t	NOUN
ejpam-4679	156	36	,	,	PUNCT
ejpam-4679	156	37	y(t	y(t	NOUN
ejpam-4679	156	38	)	)	PUNCT
ejpam-4679	156	39	)	)	PUNCT
ejpam-4679	156	40	,	,	PUNCT
ejpam-4679	156	41	y(0	y(0	PROPN
ejpam-4679	156	42	)	)	PUNCT
ejpam-4679	156	43	=	=	SYM
ejpam-4679	156	44	y0	y0	NOUN
ejpam-4679	156	45	,	,	PUNCT
ejpam-4679	156	46	(	(	PUNCT
ejpam-4679	156	47	16	16	NUM
ejpam-4679	156	48	)	)	PUNCT
ejpam-4679	156	49	with	with	ADP
ejpam-4679	156	50	time	time	NOUN
ejpam-4679	156	51	approximation	approximation	NOUN
ejpam-4679	156	52	nodes	node	NOUN
ejpam-4679	156	53	tj	tj	NOUN
ejpam-4679	156	54	,	,	PUNCT
ejpam-4679	156	55	and	and	CCONJ
ejpam-4679	156	56	corresponding	corresponding	ADJ
ejpam-4679	156	57	approximations	approximation	NOUN
ejpam-4679	156	58	,	,	PUNCT
ejpam-4679	156	59	yj	yj	PROPN
ejpam-4679	156	60	∼=	∼=	PROPN
ejpam-4679	156	61	y(tj	y(tj	NOUN
ejpam-4679	156	62	)	)	PUNCT
ejpam-4679	156	63	at	at	ADP
ejpam-4679	156	64	each	each	DET
ejpam-4679	156	65	jth	jth	PROPN
ejpam-4679	156	66	step	step	NOUN
ejpam-4679	156	67	,	,	PUNCT
ejpam-4679	156	68	there	there	PRON
ejpam-4679	156	69	are	be	VERB
ejpam-4679	156	70	two	two	NUM
ejpam-4679	156	71	approximations	approximation	NOUN
ejpam-4679	156	72	computed	compute	VERB
ejpam-4679	156	73	for	for	ADP
ejpam-4679	156	74	the	the	DET
ejpam-4679	156	75	next	next	ADJ
ejpam-4679	156	76	node	node	NOUN
ejpam-4679	156	77	,	,	PUNCT
ejpam-4679	156	78	namely	namely	ADV
ejpam-4679	156	79	,	,	PUNCT
ejpam-4679	156	80	predictor	predictor	NOUN
ejpam-4679	156	81	,	,	PUNCT
ejpam-4679	156	82	yp(tj+1	yp(tj+1	PROPN
ejpam-4679	156	83	)	)	PUNCT
ejpam-4679	156	84	,	,	PUNCT
ejpam-4679	156	85	and	and	CCONJ
ejpam-4679	156	86	using	use	VERB
ejpam-4679	156	87	the	the	DET
ejpam-4679	156	88	predictor	predictor	NOUN
ejpam-4679	156	89	,	,	PUNCT
ejpam-4679	156	90	the	the	DET
ejpam-4679	156	91	corrector	corrector	NOUN
ejpam-4679	156	92	approximation	approximation	NOUN
ejpam-4679	156	93	yc(tj+1	yc(tj+1	NOUN
ejpam-4679	156	94	)	)	PUNCT
ejpam-4679	156	95	is	be	AUX
ejpam-4679	156	96	obtained	obtain	VERB
ejpam-4679	156	97	and	and	CCONJ
ejpam-4679	156	98	used	use	VERB
ejpam-4679	156	99	in	in	ADP
ejpam-4679	156	100	the	the	DET
ejpam-4679	156	101	calculation	calculation	NOUN
ejpam-4679	156	102	.	.	PUNCT
ejpam-4679	157	1	the	the	DET
ejpam-4679	157	2	error	error	NOUN
ejpam-4679	157	3	is	be	AUX
ejpam-4679	157	4	obtained	obtain	VERB
ejpam-4679	157	5	by	by	ADP
ejpam-4679	157	6	finding	find	VERB
ejpam-4679	157	7	the	the	DET
ejpam-4679	157	8	difference	difference	NOUN
ejpam-4679	157	9	of	of	ADP
ejpam-4679	157	10	predictor	predictor	NOUN
ejpam-4679	157	11	and	and	CCONJ
ejpam-4679	157	12	corrector	corrector	NOUN
ejpam-4679	157	13	approximations	approximation	NOUN
ejpam-4679	157	14	.	.	PUNCT
ejpam-4679	158	1	there	there	PRON
ejpam-4679	158	2	are	be	VERB
ejpam-4679	158	3	two	two	NUM
ejpam-4679	158	4	main	main	ADJ
ejpam-4679	158	5	advantages	advantage	NOUN
ejpam-4679	158	6	of	of	ADP
ejpam-4679	158	7	using	use	VERB
ejpam-4679	158	8	pece	pece	PROPN
ejpam-4679	158	9	type	type	NOUN
ejpam-4679	158	10	compared	compare	VERB
ejpam-4679	158	11	to	to	ADP
ejpam-4679	158	12	the	the	DET
ejpam-4679	158	13	classical	classical	ADJ
ejpam-4679	158	14	equivalent	equivalent	ADJ
ejpam-4679	158	15	-	-	PUNCT
ejpam-4679	158	16	order	order	NOUN
ejpam-4679	158	17	range	range	NOUN
ejpam-4679	158	18	-	-	PUNCT
ejpam-4679	158	19	kutta	kutta	NOUN
ejpam-4679	158	20	methods	method	NOUN
ejpam-4679	158	21	.	.	PUNCT
ejpam-4679	159	1	the	the	DET
ejpam-4679	159	2	first	first	ADJ
ejpam-4679	159	3	of	of	ADP
ejpam-4679	159	4	is	be	AUX
ejpam-4679	159	5	the	the	DET
ejpam-4679	159	6	increased	increase	VERB
ejpam-4679	159	7	accuracy	accuracy	NOUN
ejpam-4679	159	8	and	and	CCONJ
ejpam-4679	159	9	stability	stability	NOUN
ejpam-4679	159	10	,	,	PUNCT
ejpam-4679	159	11	see	see	VERB
ejpam-4679	159	12	[	[	X
ejpam-4679	159	13	10	10	NUM
ejpam-4679	159	14	]	]	PUNCT
ejpam-4679	159	15	,	,	PUNCT
ejpam-4679	159	16	[	[	X
ejpam-4679	159	17	5	5	NUM
ejpam-4679	159	18	,	,	PUNCT
ejpam-4679	159	19	ch	ch	NOUN
ejpam-4679	159	20	.	.	PROPN
ejpam-4679	159	21	6	6	NUM
ejpam-4679	159	22	]	]	PUNCT
ejpam-4679	159	23	.	.	PUNCT
ejpam-4679	160	1	for	for	ADP
ejpam-4679	160	2	the	the	DET
ejpam-4679	160	3	odes	ode	NOUN
ejpam-4679	160	4	with	with	ADP
ejpam-4679	160	5	fractional	fractional	ADJ
ejpam-4679	160	6	derivatives	derivative	NOUN
ejpam-4679	160	7	,	,	PUNCT
ejpam-4679	160	8	it	it	PRON
ejpam-4679	160	9	was	be	AUX
ejpam-4679	160	10	shown	show	VERB
ejpam-4679	160	11	that	that	SCONJ
ejpam-4679	160	12	the	the	DET
ejpam-4679	160	13	stability	stability	NOUN
ejpam-4679	160	14	and	and	CCONJ
ejpam-4679	160	15	accuracy	accuracy	NOUN
ejpam-4679	160	16	remains	remain	VERB
ejpam-4679	160	17	high	high	ADJ
ejpam-4679	160	18	compared	compare	VERB
ejpam-4679	160	19	to	to	ADP
ejpam-4679	160	20	equivalent	equivalent	ADJ
ejpam-4679	160	21	-	-	PUNCT
ejpam-4679	160	22	order	order	NOUN
ejpam-4679	160	23	numerical	numerical	ADJ
ejpam-4679	160	24	methods	method	NOUN
ejpam-4679	160	25	[	[	X
ejpam-4679	160	26	2	2	NUM
ejpam-4679	160	27	,	,	PUNCT
ejpam-4679	160	28	3	3	NUM
ejpam-4679	160	29	,	,	PUNCT
ejpam-4679	160	30	6	6	NUM
ejpam-4679	160	31	]	]	PUNCT
ejpam-4679	160	32	.	.	PUNCT
ejpam-4679	161	1	on	on	ADP
ejpam-4679	161	2	the	the	DET
ejpam-4679	161	3	other	other	ADJ
ejpam-4679	161	4	hand	hand	NOUN
ejpam-4679	161	5	,	,	PUNCT
ejpam-4679	161	6	it	it	PRON
ejpam-4679	161	7	is	be	AUX
ejpam-4679	161	8	proven	prove	VERB
ejpam-4679	161	9	in	in	ADP
ejpam-4679	161	10	[	[	X
ejpam-4679	161	11	2	2	X
ejpam-4679	161	12	]	]	PUNCT
ejpam-4679	161	13	that	that	PRON
ejpam-4679	161	14	,	,	PUNCT
ejpam-4679	161	15	under	under	ADP
ejpam-4679	161	16	the	the	DET
ejpam-4679	161	17	assumption	assumption	NOUN
ejpam-4679	161	18	that	that	SCONJ
ejpam-4679	161	19	the	the	DET
ejpam-4679	161	20	right	right	ADJ
ejpam-4679	161	21	-	-	PUNCT
ejpam-4679	161	22	hand	hand	NOUN
ejpam-4679	161	23	side	side	NOUN
ejpam-4679	161	24	in	in	ADP
ejpam-4679	161	25	the	the	DET
ejpam-4679	161	26	equation	equation	NOUN
ejpam-4679	161	27	(	(	PUNCT
ejpam-4679	161	28	17	17	NUM
ejpam-4679	161	29	)	)	PUNCT
ejpam-4679	161	30	are	be	AUX
ejpam-4679	161	31	from	from	ADP
ejpam-4679	161	32	c2[0	c2[0	PROPN
ejpam-4679	161	33	,	,	PUNCT
ejpam-4679	161	34	t	t	X
ejpam-4679	161	35	]	]	PUNCT
ejpam-4679	161	36	for	for	ADP
ejpam-4679	161	37	some	some	DET
ejpam-4679	161	38	t	t	PROPN
ejpam-4679	161	39	>	>	X
ejpam-4679	161	40	0	0	PROPN
ejpam-4679	161	41	,	,	PUNCT
ejpam-4679	161	42	then	then	ADV
ejpam-4679	161	43	the	the	DET
ejpam-4679	161	44	error	error	NOUN
ejpam-4679	161	45	is	be	AUX
ejpam-4679	161	46	of	of	ADP
ejpam-4679	161	47	order	order	NOUN
ejpam-4679	161	48	o(h1+β	o(h1+β	NUM
ejpam-4679	161	49	)	)	PUNCT
ejpam-4679	161	50	for	for	ADP
ejpam-4679	161	51	β	β	X
ejpam-4679	161	52	<	<	X
ejpam-4679	161	53	1	1	NUM
ejpam-4679	161	54	,	,	PUNCT
ejpam-4679	161	55	and	and	CCONJ
ejpam-4679	161	56	o(h2	o(h2	NOUN
ejpam-4679	161	57	)	)	PUNCT
ejpam-4679	161	58	for	for	ADP
ejpam-4679	161	59	β	β	X
ejpam-4679	161	60	>	>	X
ejpam-4679	161	61	1	1	NUM
ejpam-4679	161	62	,	,	PUNCT
ejpam-4679	161	63	respectively	respectively	ADV
ejpam-4679	161	64	.	.	PUNCT
ejpam-4679	162	1	the	the	DET
ejpam-4679	162	2	second	second	ADJ
ejpam-4679	162	3	advantage	advantage	NOUN
ejpam-4679	162	4	of	of	ADP
ejpam-4679	162	5	using	use	VERB
ejpam-4679	162	6	the	the	DET
ejpam-4679	162	7	pece	pece	PROPN
ejpam-4679	162	8	type	type	PROPN
ejpam-4679	162	9	numerical	numerical	PROPN
ejpam-4679	162	10	approximation	approximation	NOUN
ejpam-4679	162	11	is	be	AUX
ejpam-4679	162	12	the	the	DET
ejpam-4679	162	13	fact	fact	NOUN
ejpam-4679	162	14	that	that	SCONJ
ejpam-4679	162	15	,	,	PUNCT
ejpam-4679	162	16	this	this	DET
ejpam-4679	162	17	method	method	NOUN
ejpam-4679	162	18	can	can	AUX
ejpam-4679	162	19	assume	assume	VERB
ejpam-4679	162	20	variable	variable	ADJ
ejpam-4679	162	21	time	time	NOUN
ejpam-4679	162	22	steps	step	NOUN
ejpam-4679	162	23	that	that	PRON
ejpam-4679	162	24	reduces	reduce	VERB
ejpam-4679	162	25	the	the	DET
ejpam-4679	162	26	computational	computational	ADJ
ejpam-4679	162	27	cost	cost	NOUN
ejpam-4679	162	28	of	of	ADP
ejpam-4679	162	29	the	the	DET
ejpam-4679	162	30	approximation	approximation	NOUN
ejpam-4679	162	31	.	.	PUNCT
ejpam-4679	163	1	the	the	DET
ejpam-4679	163	2	method	method	NOUN
ejpam-4679	163	3	can	can	AUX
ejpam-4679	163	4	control	control	VERB
ejpam-4679	163	5	the	the	DET
ejpam-4679	163	6	time	time	NOUN
ejpam-4679	163	7	steps	step	NOUN
ejpam-4679	163	8	by	by	ADP
ejpam-4679	163	9	using	use	VERB
ejpam-4679	163	10	the	the	DET
ejpam-4679	163	11	difference	difference	NOUN
ejpam-4679	163	12	between	between	ADP
ejpam-4679	163	13	the	the	DET
ejpam-4679	163	14	corrector	corrector	NOUN
ejpam-4679	163	15	and	and	CCONJ
ejpam-4679	163	16	the	the	DET
ejpam-4679	163	17	predictor	predictor	NOUN
ejpam-4679	163	18	approximations	approximation	NOUN
ejpam-4679	163	19	.	.	PUNCT
ejpam-4679	164	1	when	when	SCONJ
ejpam-4679	164	2	the	the	DET
ejpam-4679	164	3	difference	difference	NOUN
ejpam-4679	164	4	is	be	AUX
ejpam-4679	164	5	smaller	small	ADJ
ejpam-4679	164	6	than	than	ADP
ejpam-4679	164	7	the	the	DET
ejpam-4679	164	8	desired	desire	VERB
ejpam-4679	164	9	level	level	NOUN
ejpam-4679	164	10	of	of	ADP
ejpam-4679	164	11	accuracy	accuracy	NOUN
ejpam-4679	164	12	with	with	ADP
ejpam-4679	164	13	the	the	DET
ejpam-4679	164	14	current	current	ADJ
ejpam-4679	164	15	time	time	NOUN
ejpam-4679	164	16	step	step	NOUN
ejpam-4679	164	17	,	,	PUNCT
ejpam-4679	164	18	this	this	PRON
ejpam-4679	164	19	is	be	AUX
ejpam-4679	164	20	used	use	VERB
ejpam-4679	164	21	as	as	ADP
ejpam-4679	164	22	an	an	DET
ejpam-4679	164	23	indication	indication	NOUN
ejpam-4679	164	24	that	that	SCONJ
ejpam-4679	164	25	the	the	DET
ejpam-4679	164	26	solver	solver	NOUN
ejpam-4679	164	27	is	be	AUX
ejpam-4679	164	28	in	in	ADP
ejpam-4679	164	29	a	a	DET
ejpam-4679	164	30	non	non	ADJ
ejpam-4679	164	31	-	-	ADJ
ejpam-4679	164	32	stiff	stiff	ADJ
ejpam-4679	164	33	area	area	NOUN
ejpam-4679	164	34	,	,	PUNCT
ejpam-4679	164	35	and	and	CCONJ
ejpam-4679	164	36	time	time	NOUN
ejpam-4679	164	37	steps	step	NOUN
ejpam-4679	164	38	are	be	AUX
ejpam-4679	164	39	increased	increase	VERB
ejpam-4679	164	40	in	in	ADP
ejpam-4679	164	41	an	an	DET
ejpam-4679	164	42	adaptive	adaptive	ADJ
ejpam-4679	164	43	manner	manner	NOUN
ejpam-4679	164	44	.	.	PUNCT
ejpam-4679	165	1	the	the	DET
ejpam-4679	165	2	idea	idea	NOUN
ejpam-4679	165	3	of	of	ADP
ejpam-4679	165	4	combining	combine	VERB
ejpam-4679	165	5	the	the	DET
ejpam-4679	165	6	method	method	NOUN
ejpam-4679	165	7	of	of	ADP
ejpam-4679	165	8	lines	line	NOUN
ejpam-4679	165	9	approach	approach	VERB
ejpam-4679	165	10	to	to	PART
ejpam-4679	165	11	reduce	reduce	VERB
ejpam-4679	165	12	the	the	DET
ejpam-4679	165	13	given	give	VERB
ejpam-4679	165	14	pde	pde	NOUN
ejpam-4679	165	15	to	to	ADP
ejpam-4679	165	16	a	a	DET
ejpam-4679	165	17	system	system	NOUN
ejpam-4679	165	18	of	of	ADP
ejpam-4679	165	19	odes	ode	NOUN
ejpam-4679	165	20	and	and	CCONJ
ejpam-4679	165	21	using	use	VERB
ejpam-4679	165	22	shift	shift	NOUN
ejpam-4679	165	23	operators	operator	NOUN
ejpam-4679	165	24	in	in	ADP
ejpam-4679	165	25	the	the	DET
ejpam-4679	165	26	evaluation	evaluation	NOUN
ejpam-4679	165	27	of	of	ADP
ejpam-4679	165	28	the	the	DET
ejpam-4679	165	29	rhs	rhs	PROPN
ejpam-4679	165	30	of	of	ADP
ejpam-4679	165	31	the	the	DET
ejpam-4679	165	32	pde	pde	NOUN
ejpam-4679	165	33	has	have	VERB
ejpam-4679	165	34	a	a	DET
ejpam-4679	165	35	two	two	NUM
ejpam-4679	165	36	major	major	ADJ
ejpam-4679	165	37	advantages	advantage	NOUN
ejpam-4679	165	38	compared	compare	VERB
ejpam-4679	165	39	to	to	ADP
ejpam-4679	165	40	similar	similar	ADJ
ejpam-4679	165	41	operator	operator	NOUN
ejpam-4679	165	42	approaches	approach	NOUN
ejpam-4679	165	43	such	such	ADJ
ejpam-4679	165	44	as	as	ADP
ejpam-4679	165	45	that	that	PRON
ejpam-4679	165	46	of	of	ADP
ejpam-4679	165	47	podlubny	podlubny	PROPN
ejpam-4679	165	48	’s	’s	PART
ejpam-4679	165	49	matrix	matrix	NOUN
ejpam-4679	165	50	operator	operator	NOUN
ejpam-4679	165	51	approach	approach	NOUN
ejpam-4679	165	52	[	[	X
ejpam-4679	165	53	18	18	NUM
ejpam-4679	165	54	,	,	PUNCT
ejpam-4679	165	55	19	19	NUM
ejpam-4679	165	56	]	]	PUNCT
ejpam-4679	165	57	.	.	PUNCT
ejpam-4679	166	1	the	the	DET
ejpam-4679	166	2	first	first	ADJ
ejpam-4679	166	3	major	major	ADJ
ejpam-4679	166	4	advantage	advantage	NOUN
ejpam-4679	166	5	comes	come	VERB
ejpam-4679	166	6	from	from	ADP
ejpam-4679	166	7	the	the	DET
ejpam-4679	166	8	amount	amount	NOUN
ejpam-4679	166	9	of	of	ADP
ejpam-4679	166	10	the	the	DET
ejpam-4679	166	11	memory	memory	NOUN
ejpam-4679	166	12	required	require	VERB
ejpam-4679	166	13	to	to	PART
ejpam-4679	166	14	solve	solve	VERB
ejpam-4679	166	15	the	the	DET
ejpam-4679	166	16	system	system	NOUN
ejpam-4679	166	17	.	.	PUNCT
ejpam-4679	167	1	matrices	matrix	NOUN
ejpam-4679	167	2	required	require	VERB
ejpam-4679	167	3	to	to	PART
ejpam-4679	167	4	compute	compute	VERB
ejpam-4679	167	5	the	the	DET
ejpam-4679	167	6	rhs	rhs	PROPN
ejpam-4679	167	7	function	function	NOUN
ejpam-4679	167	8	are	be	AUX
ejpam-4679	167	9	of	of	ADP
ejpam-4679	167	10	dimension	dimension	NOUN
ejpam-4679	167	11	m	m	NOUN
ejpam-4679	167	12	−	−	PROPN
ejpam-4679	167	13	1	1	NUM
ejpam-4679	167	14	×	×	NOUN
ejpam-4679	167	15	n	n	CCONJ
ejpam-4679	167	16	−	−	PROPN
ejpam-4679	167	17	1	1	NUM
ejpam-4679	167	18	.	.	PUNCT
ejpam-4679	168	1	whereas	whereas	SCONJ
ejpam-4679	168	2	,	,	PUNCT
ejpam-4679	168	3	in	in	ADP
ejpam-4679	168	4	matrix	matrix	NOUN
ejpam-4679	168	5	operator	operator	NOUN
ejpam-4679	168	6	approach	approach	NOUN
ejpam-4679	168	7	of	of	ADP
ejpam-4679	168	8	the	the	DET
ejpam-4679	168	9	podlubny	podlubny	NOUN
ejpam-4679	168	10	,	,	PUNCT
ejpam-4679	168	11	the	the	DET
ejpam-4679	168	12	three	three	NUM
ejpam-4679	168	13	-	-	PUNCT
ejpam-4679	168	14	diagonal	diagonal	ADJ
ejpam-4679	168	15	matrices	matrix	NOUN
ejpam-4679	168	16	used	use	VERB
ejpam-4679	168	17	for	for	ADP
ejpam-4679	168	18	difference	difference	NOUN
ejpam-4679	168	19	approximations	approximation	NOUN
ejpam-4679	168	20	are	be	AUX
ejpam-4679	168	21	of	of	ADP
ejpam-4679	168	22	dimension	dimension	NOUN
ejpam-4679	168	23	m	m	VERB
ejpam-4679	168	24	×n	×n	PROPN
ejpam-4679	168	25	×k	×k	NOUN
ejpam-4679	168	26	.	.	PUNCT
ejpam-4679	169	1	the	the	DET
ejpam-4679	169	2	second	second	ADJ
ejpam-4679	169	3	major	major	ADJ
ejpam-4679	169	4	advantage	advantage	NOUN
ejpam-4679	169	5	of	of	ADP
ejpam-4679	169	6	the	the	DET
ejpam-4679	169	7	method	method	NOUN
ejpam-4679	169	8	applied	apply	VERB
ejpam-4679	169	9	here	here	ADV
ejpam-4679	169	10	is	be	AUX
ejpam-4679	169	11	that	that	SCONJ
ejpam-4679	169	12	,	,	PUNCT
ejpam-4679	169	13	the	the	DET
ejpam-4679	169	14	ease	ease	NOUN
ejpam-4679	169	15	of	of	ADP
ejpam-4679	169	16	usage	usage	NOUN
ejpam-4679	169	17	in	in	ADP
ejpam-4679	169	18	solving	solve	VERB
ejpam-4679	169	19	linear	linear	ADJ
ejpam-4679	169	20	fractional	fractional	ADJ
ejpam-4679	169	21	pde	pde	NOUN
ejpam-4679	169	22	.	.	PUNCT
ejpam-4679	170	1	this	this	PRON
ejpam-4679	170	2	is	be	AUX
ejpam-4679	170	3	because	because	SCONJ
ejpam-4679	170	4	,	,	PUNCT
ejpam-4679	170	5	even	even	ADV
ejpam-4679	170	6	though	though	SCONJ
ejpam-4679	170	7	the	the	DET
ejpam-4679	170	8	matrix	matrix	NOUN
ejpam-4679	170	9	operator	operator	NOUN
ejpam-4679	170	10	approach	approach	NOUN
ejpam-4679	170	11	of	of	ADP
ejpam-4679	170	12	the	the	DET
ejpam-4679	170	13	podlubny	podlubny	PROPN
ejpam-4679	170	14	’s	’s	PART
ejpam-4679	170	15	method	method	NOUN
ejpam-4679	170	16	is	be	AUX
ejpam-4679	170	17	very	very	ADV
ejpam-4679	170	18	natural	natural	ADJ
ejpam-4679	170	19	in	in	ADP
ejpam-4679	170	20	dealing	deal	VERB
ejpam-4679	170	21	with	with	ADP
ejpam-4679	170	22	the	the	DET
ejpam-4679	170	23	linear	linear	PROPN
ejpam-4679	170	24	m.	m.	NOUN
ejpam-4679	170	25	zeki	zeki	PROPN
ejpam-4679	170	26	,	,	PUNCT
ejpam-4679	170	27	s.	s.	PROPN
ejpam-4679	170	28	tatar	tatar	PROPN
ejpam-4679	170	29	/	/	SYM
ejpam-4679	170	30	eur	eur	PROPN
ejpam-4679	170	31	.	.	PUNCT
ejpam-4679	171	1	j.	j.	PROPN
ejpam-4679	171	2	pure	pure	PROPN
ejpam-4679	171	3	appl	appl	PROPN
ejpam-4679	171	4	.	.	PROPN
ejpam-4679	171	5	math	math	PROPN
ejpam-4679	171	6	,	,	PUNCT
ejpam-4679	171	7	16	16	NUM
ejpam-4679	171	8	(	(	PUNCT
ejpam-4679	171	9	1	1	NUM
ejpam-4679	171	10	)	)	PUNCT
ejpam-4679	171	11	(	(	PUNCT
ejpam-4679	171	12	2023	2023	NUM
ejpam-4679	171	13	)	)	PUNCT
ejpam-4679	171	14	,	,	PUNCT
ejpam-4679	171	15	491	491	NUM
ejpam-4679	171	16	-	-	SYM
ejpam-4679	171	17	502	502	NUM
ejpam-4679	171	18	498	498	NUM
ejpam-4679	171	19	pdes	pde	NOUN
ejpam-4679	171	20	,	,	PUNCT
ejpam-4679	171	21	solving	solve	VERB
ejpam-4679	171	22	multi	multi	ADJ
ejpam-4679	171	23	-	-	ADJ
ejpam-4679	171	24	variable	variable	ADJ
ejpam-4679	171	25	ones	one	NOUN
ejpam-4679	171	26	requires	require	VERB
ejpam-4679	171	27	one	one	NUM
ejpam-4679	171	28	to	to	PART
ejpam-4679	171	29	solve	solve	VERB
ejpam-4679	171	30	algebraic	algebraic	ADJ
ejpam-4679	171	31	equation	equation	NOUN
ejpam-4679	171	32	of	of	ADP
ejpam-4679	171	33	very	very	ADV
ejpam-4679	171	34	high	high	ADJ
ejpam-4679	171	35	dimensions	dimension	NOUN
ejpam-4679	171	36	.	.	PUNCT
ejpam-4679	172	1	this	this	PRON
ejpam-4679	172	2	is	be	AUX
ejpam-4679	172	3	another	another	DET
ejpam-4679	172	4	challenge	challenge	NOUN
ejpam-4679	172	5	that	that	PRON
ejpam-4679	172	6	may	may	AUX
ejpam-4679	172	7	require	require	VERB
ejpam-4679	172	8	different	different	ADJ
ejpam-4679	172	9	approach	approach	NOUN
ejpam-4679	172	10	depending	depend	VERB
ejpam-4679	172	11	on	on	ADP
ejpam-4679	172	12	the	the	DET
ejpam-4679	172	13	memory	memory	NOUN
ejpam-4679	172	14	demand	demand	NOUN
ejpam-4679	172	15	involved	involve	VERB
ejpam-4679	172	16	in	in	ADP
ejpam-4679	172	17	solving	solve	VERB
ejpam-4679	172	18	the	the	DET
ejpam-4679	172	19	given	give	VERB
ejpam-4679	172	20	pde	pde	NOUN
ejpam-4679	172	21	.	.	PUNCT
ejpam-4679	173	1	in	in	ADP
ejpam-4679	173	2	addition	addition	NOUN
ejpam-4679	173	3	,	,	PUNCT
ejpam-4679	173	4	the	the	DET
ejpam-4679	173	5	introduced	introduce	VERB
ejpam-4679	173	6	shift	shift	NOUN
ejpam-4679	173	7	approach	approach	NOUN
ejpam-4679	173	8	provides	provide	VERB
ejpam-4679	173	9	gains	gain	NOUN
ejpam-4679	173	10	in	in	ADP
ejpam-4679	173	11	calculations	calculation	NOUN
ejpam-4679	173	12	in	in	ADP
ejpam-4679	173	13	terms	term	NOUN
ejpam-4679	173	14	of	of	ADP
ejpam-4679	173	15	speed	speed	NOUN
ejpam-4679	173	16	and	and	CCONJ
ejpam-4679	173	17	memory	memory	NOUN
ejpam-4679	173	18	compared	compare	VERB
ejpam-4679	173	19	to	to	ADP
ejpam-4679	173	20	other	other	ADJ
ejpam-4679	173	21	difference	difference	NOUN
ejpam-4679	173	22	calculations	calculation	NOUN
ejpam-4679	173	23	with	with	ADP
ejpam-4679	173	24	loops	loop	NOUN
ejpam-4679	173	25	and	and	CCONJ
ejpam-4679	173	26	diagonal	diagonal	ADJ
ejpam-4679	173	27	matrices	matrix	NOUN
ejpam-4679	173	28	.	.	PUNCT
ejpam-4679	174	1	figure	figure	NOUN
ejpam-4679	174	2	1	1	NUM
ejpam-4679	174	3	:	:	PUNCT
ejpam-4679	174	4	approximate	approximate	ADJ
ejpam-4679	174	5	solution	solution	NOUN
ejpam-4679	174	6	:	:	PUNCT
ejpam-4679	174	7	the	the	DET
ejpam-4679	174	8	numerical	numerical	ADJ
ejpam-4679	174	9	solution	solution	NOUN
ejpam-4679	174	10	and	and	CCONJ
ejpam-4679	174	11	the	the	DET
ejpam-4679	174	12	error	error	NOUN
ejpam-4679	174	13	distribution	distribution	NOUN
ejpam-4679	174	14	is	be	AUX
ejpam-4679	174	15	plotted	plot	VERB
ejpam-4679	174	16	at	at	ADP
ejpam-4679	174	17	t=1	t=1	ADV
ejpam-4679	174	18	for	for	ADP
ejpam-4679	174	19	∆t	∆t	PROPN
ejpam-4679	174	20	=	=	SYM
ejpam-4679	174	21	10−4	10−4	PROPN
ejpam-4679	174	22	,	,	PUNCT
ejpam-4679	174	23	α	α	NOUN
ejpam-4679	174	24	=	=	ADJ
ejpam-4679	174	25	0.8	0.8	NUM
ejpam-4679	174	26	and	and	CCONJ
ejpam-4679	174	27	the	the	DET
ejpam-4679	174	28	relative	relative	ADJ
ejpam-4679	174	29	error	error	NOUN
ejpam-4679	174	30	parameter	parameter	NOUN
ejpam-4679	174	31	ϵ	ϵ	X
ejpam-4679	174	32	=	=	SYM
ejpam-4679	174	33	10−6	10−6	NUM
ejpam-4679	174	34	.	.	PUNCT
ejpam-4679	175	1	the	the	DET
ejpam-4679	175	2	relative	relative	ADJ
ejpam-4679	175	3	error	error	NOUN
ejpam-4679	175	4	level	level	NOUN
ejpam-4679	175	5	,	,	PUNCT
ejpam-4679	175	6	ϵ	ϵ	X
ejpam-4679	175	7	=	=	SYM
ejpam-4679	175	8	10−6	10−6	PROPN
ejpam-4679	175	9	could	could	AUX
ejpam-4679	175	10	be	be	AUX
ejpam-4679	175	11	achieved	achieve	VERB
ejpam-4679	175	12	after	after	ADP
ejpam-4679	175	13	7	7	NUM
ejpam-4679	175	14	iterations	iteration	NOUN
ejpam-4679	175	15	.	.	PUNCT
ejpam-4679	176	1	example	example	NOUN
ejpam-4679	176	2	.	.	PUNCT
ejpam-4679	177	1	in	in	ADP
ejpam-4679	177	2	this	this	DET
ejpam-4679	177	3	example	example	NOUN
ejpam-4679	177	4	,	,	PUNCT
ejpam-4679	177	5	we	we	PRON
ejpam-4679	177	6	solve	solve	VERB
ejpam-4679	177	7	the	the	DET
ejpam-4679	177	8	problem	problem	NOUN
ejpam-4679	177	9	(	(	PUNCT
ejpam-4679	177	10	7	7	NUM
ejpam-4679	177	11	)	)	PUNCT
ejpam-4679	177	12	for	for	ADP
ejpam-4679	177	13	the	the	DET
ejpam-4679	177	14	water	water	NOUN
ejpam-4679	177	15	diffusivity	diffusivity	PROPN
ejpam-4679	177	16	d(u	d(u	PROPN
ejpam-4679	177	17	)	)	PUNCT
ejpam-4679	178	1	=	=	SYM
ejpam-4679	179	1	1/	1/	NUM
ejpam-4679	179	2	√	√	NUM
ejpam-4679	179	3	1	1	NUM
ejpam-4679	179	4	+	+	SYM
ejpam-4679	179	5	u	u	NOUN
ejpam-4679	179	6	,	,	PUNCT
ejpam-4679	179	7	where	where	SCONJ
ejpam-4679	179	8	u(t	u(t	NOUN
ejpam-4679	179	9	,	,	PUNCT
ejpam-4679	179	10	x	x	NOUN
ejpam-4679	179	11	,	,	PUNCT
ejpam-4679	179	12	y	y	NOUN
ejpam-4679	179	13	)	)	PUNCT
ejpam-4679	179	14	=	=	SYM
ejpam-4679	180	1	tx2y2	tx2y2	PROPN
ejpam-4679	180	2	.	.	PUNCT
ejpam-4679	181	1	the	the	DET
ejpam-4679	181	2	function	function	NOUN
ejpam-4679	181	3	f(t	f(t	PROPN
ejpam-4679	181	4	,	,	PUNCT
ejpam-4679	181	5	x	x	PRON
ejpam-4679	181	6	,	,	PUNCT
ejpam-4679	181	7	y	y	PROPN
ejpam-4679	181	8	)	)	PUNCT
ejpam-4679	181	9	is	be	AUX
ejpam-4679	181	10	obtained	obtain	VERB
ejpam-4679	181	11	by	by	ADP
ejpam-4679	181	12	the	the	DET
ejpam-4679	181	13	substitution	substitution	NOUN
ejpam-4679	181	14	of	of	ADP
ejpam-4679	181	15	the	the	DET
ejpam-4679	181	16	analytical	analytical	ADJ
ejpam-4679	181	17	solution	solution	NOUN
ejpam-4679	181	18	to	to	ADP
ejpam-4679	181	19	the	the	DET
ejpam-4679	181	20	equation	equation	NOUN
ejpam-4679	181	21	.	.	PUNCT
ejpam-4679	182	1	the	the	DET
ejpam-4679	182	2	dirichlet	dirichlet	PROPN
ejpam-4679	182	3	type	type	NOUN
ejpam-4679	182	4	boundary	boundary	ADJ
ejpam-4679	182	5	conditions	condition	NOUN
ejpam-4679	182	6	at	at	ADP
ejpam-4679	182	7	x	x	X
ejpam-4679	182	8	=	=	SYM
ejpam-4679	182	9	0	0	NUM
ejpam-4679	182	10	and	and	CCONJ
ejpam-4679	182	11	y	y	PROPN
ejpam-4679	182	12	=	=	SYM
ejpam-4679	182	13	0	0	NUM
ejpam-4679	182	14	are	be	AUX
ejpam-4679	182	15	obtained	obtain	VERB
ejpam-4679	182	16	by	by	ADP
ejpam-4679	182	17	the	the	DET
ejpam-4679	182	18	substitution	substitution	NOUN
ejpam-4679	182	19	of	of	ADP
ejpam-4679	182	20	the	the	DET
ejpam-4679	182	21	corresponding	corresponding	ADJ
ejpam-4679	182	22	values	value	NOUN
ejpam-4679	182	23	to	to	ADP
ejpam-4679	182	24	the	the	DET
ejpam-4679	182	25	analytic	analytic	ADJ
ejpam-4679	182	26	solution	solution	NOUN
ejpam-4679	182	27	as	as	ADP
ejpam-4679	182	28	u(t	u(t	NOUN
ejpam-4679	182	29	,	,	PUNCT
ejpam-4679	182	30	0	0	NUM
ejpam-4679	182	31	,	,	PUNCT
ejpam-4679	182	32	y	y	NOUN
ejpam-4679	182	33	)	)	PUNCT
ejpam-4679	182	34	=	=	SYM
ejpam-4679	182	35	0	0	NUM
ejpam-4679	182	36	and	and	CCONJ
ejpam-4679	182	37	u(t	u(t	NOUN
ejpam-4679	182	38	,	,	PUNCT
ejpam-4679	182	39	x	x	NOUN
ejpam-4679	182	40	,	,	PUNCT
ejpam-4679	182	41	0	0	NUM
ejpam-4679	182	42	)	)	PUNCT
ejpam-4679	182	43	=	=	SYM
ejpam-4679	183	1	0	0	X
ejpam-4679	183	2	.	.	PUNCT
ejpam-4679	184	1	the	the	DET
ejpam-4679	184	2	neumann	neumann	PROPN
ejpam-4679	184	3	type	type	NOUN
ejpam-4679	184	4	boundary	boundary	ADJ
ejpam-4679	184	5	conditions	condition	NOUN
ejpam-4679	184	6	at	at	ADP
ejpam-4679	184	7	x	x	X
ejpam-4679	184	8	=	=	SYM
ejpam-4679	184	9	1	1	NUM
ejpam-4679	184	10	and	and	CCONJ
ejpam-4679	184	11	y	y	NOUN
ejpam-4679	184	12	=	=	SYM
ejpam-4679	184	13	1	1	NUM
ejpam-4679	184	14	are	be	AUX
ejpam-4679	184	15	obtained	obtain	VERB
ejpam-4679	184	16	from	from	ADP
ejpam-4679	184	17	the	the	DET
ejpam-4679	184	18	equations	equation	NOUN
ejpam-4679	184	19	:	:	PUNCT
ejpam-4679	184	20			SYM
ejpam-4679	184	21	−d(u)ux(t	−d(u)ux(t	PROPN
ejpam-4679	184	22	,	,	PUNCT
ejpam-4679	184	23	1	1	NUM
ejpam-4679	184	24	,	,	PUNCT
ejpam-4679	184	25	y	y	NOUN
ejpam-4679	184	26	)	)	PUNCT
ejpam-4679	184	27	=	=	PUNCT
ejpam-4679	185	1	−	−	PROPN
ejpam-4679	185	2	2ty2√	2ty2√	NUM
ejpam-4679	185	3	1+tx2y2	1+tx2y2	NUM
ejpam-4679	185	4	,	,	PUNCT
ejpam-4679	185	5	−d(u)uy(t	−d(u)uy(t	PROPN
ejpam-4679	185	6	,	,	PUNCT
ejpam-4679	185	7	x	x	NOUN
ejpam-4679	185	8	,	,	PUNCT
ejpam-4679	185	9	1	1	NUM
ejpam-4679	185	10	)	)	PUNCT
ejpam-4679	185	11	=	=	SYM
ejpam-4679	186	1	−	−	PROPN
ejpam-4679	186	2	2tx2√	2tx2√	NUM
ejpam-4679	186	3	1+tx2y2	1+tx2y2	NUM
ejpam-4679	186	4	.	.	PUNCT
ejpam-4679	187	1	(	(	PUNCT
ejpam-4679	187	2	17	17	NUM
ejpam-4679	187	3	)	)	PUNCT
ejpam-4679	187	4	unless	unless	SCONJ
ejpam-4679	187	5	otherwise	otherwise	ADV
ejpam-4679	187	6	stated	state	VERB
ejpam-4679	187	7	,	,	PUNCT
ejpam-4679	187	8	the	the	DET
ejpam-4679	187	9	parameters	parameter	NOUN
ejpam-4679	187	10	used	use	VERB
ejpam-4679	187	11	for	for	ADP
ejpam-4679	187	12	the	the	DET
ejpam-4679	187	13	numerical	numerical	ADJ
ejpam-4679	187	14	simulations	simulation	NOUN
ejpam-4679	187	15	are	be	AUX
ejpam-4679	187	16	taken	take	VERB
ejpam-4679	187	17	as	as	ADP
ejpam-4679	187	18	∆x	∆x	PROPN
ejpam-4679	187	19	=	=	SYM
ejpam-4679	187	20	0.1	0.1	NUM
ejpam-4679	187	21	(	(	PUNCT
ejpam-4679	187	22	m	m	NOUN
ejpam-4679	187	23	=	=	NOUN
ejpam-4679	187	24	10	10	NUM
ejpam-4679	187	25	)	)	PUNCT
ejpam-4679	187	26	,	,	PUNCT
ejpam-4679	187	27	∆y	∆y	NOUN
ejpam-4679	187	28	=	=	NOUN
ejpam-4679	187	29	0.1(n	0.1(n	PUNCT
ejpam-4679	187	30	=	=	SYM
ejpam-4679	187	31	10	10	NUM
ejpam-4679	187	32	)	)	PUNCT
ejpam-4679	187	33	,	,	PUNCT
ejpam-4679	187	34	∆t	∆t	PROPN
ejpam-4679	187	35	=	=	SYM
ejpam-4679	187	36	10−6	10−6	NUM
ejpam-4679	187	37	and	and	CCONJ
ejpam-4679	187	38	β	β	X
ejpam-4679	187	39	=	=	ADJ
ejpam-4679	187	40	0.6	0.6	NUM
ejpam-4679	187	41	.	.	PUNCT
ejpam-4679	188	1	the	the	DET
ejpam-4679	188	2	initial	initial	ADJ
ejpam-4679	188	3	approximation	approximation	NOUN
ejpam-4679	188	4	function	function	NOUN
ejpam-4679	188	5	,	,	PUNCT
ejpam-4679	188	6	u0(t	u0(t	PROPN
ejpam-4679	188	7	,	,	PUNCT
ejpam-4679	188	8	x	x	NOUN
ejpam-4679	188	9	,	,	PUNCT
ejpam-4679	188	10	y	y	PROPN
ejpam-4679	188	11	)	)	PUNCT
ejpam-4679	188	12	,	,	PUNCT
ejpam-4679	188	13	is	be	AUX
ejpam-4679	188	14	taken	take	VERB
ejpam-4679	188	15	to	to	PART
ejpam-4679	188	16	be	be	AUX
ejpam-4679	188	17	zero	zero	NUM
ejpam-4679	188	18	.	.	PUNCT
ejpam-4679	189	1	the	the	DET
ejpam-4679	189	2	absolute	absolute	ADJ
ejpam-4679	189	3	error	error	NOUN
ejpam-4679	189	4	estimations	estimation	NOUN
ejpam-4679	189	5	at	at	ADP
ejpam-4679	189	6	nth	nth	PROPN
ejpam-4679	189	7	iteration	iteration	NOUN
ejpam-4679	189	8	are	be	AUX
ejpam-4679	189	9	defined	define	VERB
ejpam-4679	189	10	as	as	ADP
ejpam-4679	189	11	the	the	DET
ejpam-4679	189	12	maximum	maximum	NOUN
ejpam-4679	189	13	of	of	ADP
ejpam-4679	189	14	the	the	DET
ejpam-4679	189	15	difference	difference	NOUN
ejpam-4679	189	16	between	between	ADP
ejpam-4679	189	17	the	the	DET
ejpam-4679	189	18	approximating	approximate	VERB
ejpam-4679	189	19	numerical	numerical	ADJ
ejpam-4679	189	20	solution	solution	NOUN
ejpam-4679	189	21	and	and	CCONJ
ejpam-4679	189	22	the	the	DET
ejpam-4679	189	23	analytic	analytic	ADJ
ejpam-4679	189	24	solution	solution	NOUN
ejpam-4679	189	25	at	at	ADP
ejpam-4679	189	26	time	time	NOUN
ejpam-4679	189	27	t	t	NOUN
ejpam-4679	189	28	=	=	SYM
ejpam-4679	189	29	1	1	NUM
ejpam-4679	189	30	on	on	ADP
ejpam-4679	189	31	the	the	DET
ejpam-4679	189	32	approximation	approximation	NOUN
ejpam-4679	189	33	points	point	NOUN
ejpam-4679	189	34	on	on	ADP
ejpam-4679	189	35	ω	ω	NUM
ejpam-4679	189	36	.	.	PUNCT
ejpam-4679	190	1	namely	namely	ADV
ejpam-4679	190	2	,	,	PUNCT
ejpam-4679	190	3	error	error	NOUN
ejpam-4679	190	4	=	=	SYM
ejpam-4679	190	5	maxi	maxi	NOUN
ejpam-4679	190	6	,	,	PUNCT
ejpam-4679	190	7	j	j	PROPN
ejpam-4679	190	8	|uki	|uki	PROPN
ejpam-4679	190	9	,	,	PUNCT
ejpam-4679	190	10	j(1	j(1	NOUN
ejpam-4679	190	11	)	)	PUNCT
ejpam-4679	190	12	−	−	PROPN
ejpam-4679	191	1	u(1	u(1	PROPN
ejpam-4679	191	2	,	,	PUNCT
ejpam-4679	191	3	xi	xi	PROPN
ejpam-4679	191	4	,	,	PUNCT
ejpam-4679	191	5	yj)|	yj)|	NOUN
ejpam-4679	191	6	for	for	ADP
ejpam-4679	191	7	i	i	PRON
ejpam-4679	191	8	=	=	SYM
ejpam-4679	191	9	0	0	NUM
ejpam-4679	191	10	,	,	PUNCT
ejpam-4679	191	11	1	1	NUM
ejpam-4679	191	12	,	,	PUNCT
ejpam-4679	191	13	.	.	PUNCT
ejpam-4679	191	14	.	.	PUNCT
ejpam-4679	192	1	.m	.m	PROPN
ejpam-4679	193	1	and	and	CCONJ
ejpam-4679	193	2	j	j	PROPN
ejpam-4679	193	3	=	=	SYM
ejpam-4679	193	4	0	0	PROPN
ejpam-4679	193	5	,	,	PUNCT
ejpam-4679	193	6	1	1	NUM
ejpam-4679	193	7	,	,	PUNCT
ejpam-4679	193	8	.	.	PUNCT
ejpam-4679	193	9	.	.	PUNCT
ejpam-4679	193	10	.	.	PUNCT
ejpam-4679	194	1	n	n	PROPN
ejpam-4679	194	2	with	with	ADP
ejpam-4679	194	3	uki	uki	PROPN
ejpam-4679	194	4	,	,	PUNCT
ejpam-4679	194	5	j(t	j(t	PROPN
ejpam-4679	194	6	)	)	PUNCT
ejpam-4679	194	7	representing	represent	VERB
ejpam-4679	194	8	the	the	DET
ejpam-4679	194	9	numerical	numerical	ADJ
ejpam-4679	194	10	approximation	approximation	NOUN
ejpam-4679	194	11	to	to	ADP
ejpam-4679	194	12	the	the	DET
ejpam-4679	194	13	solution	solution	NOUN
ejpam-4679	194	14	at	at	ADP
ejpam-4679	194	15	the	the	DET
ejpam-4679	194	16	kth	kth	PROPN
ejpam-4679	194	17	iteration	iteration	NOUN
ejpam-4679	194	18	at	at	ADP
ejpam-4679	194	19	time	time	NOUN
ejpam-4679	194	20	t.	t.	PROPN
ejpam-4679	194	21	the	the	DET
ejpam-4679	194	22	relative	relative	ADJ
ejpam-4679	194	23	error	error	NOUN
ejpam-4679	194	24	,	,	PUNCT
ejpam-4679	194	25	relerror	relerror	NOUN
ejpam-4679	194	26	,	,	PUNCT
ejpam-4679	194	27	is	be	AUX
ejpam-4679	194	28	defined	define	VERB
ejpam-4679	194	29	as	as	ADP
ejpam-4679	194	30	the	the	DET
ejpam-4679	194	31	maximum	maximum	NOUN
ejpam-4679	194	32	of	of	ADP
ejpam-4679	194	33	the	the	DET
ejpam-4679	194	34	difference	difference	NOUN
ejpam-4679	194	35	between	between	ADP
ejpam-4679	194	36	the	the	DET
ejpam-4679	194	37	consecutive	consecutive	ADJ
ejpam-4679	194	38	iterations	iteration	NOUN
ejpam-4679	194	39	of	of	ADP
ejpam-4679	194	40	the	the	DET
ejpam-4679	194	41	numerical	numerical	ADJ
ejpam-4679	194	42	solutions	solution	NOUN
ejpam-4679	194	43	at	at	ADP
ejpam-4679	194	44	time	time	NOUN
ejpam-4679	195	1	t	t	NOUN
ejpam-4679	195	2	=	=	SYM
ejpam-4679	195	3	1	1	X
ejpam-4679	195	4	.	.	X
ejpam-4679	195	5	that	that	PRON
ejpam-4679	195	6	is	be	AUX
ejpam-4679	195	7	,	,	PUNCT
ejpam-4679	195	8	m.	m.	NOUN
ejpam-4679	195	9	zeki	zeki	PROPN
ejpam-4679	195	10	,	,	PUNCT
ejpam-4679	195	11	s.	s.	PROPN
ejpam-4679	195	12	tatar	tatar	PROPN
ejpam-4679	195	13	/	/	SYM
ejpam-4679	195	14	eur	eur	PROPN
ejpam-4679	195	15	.	.	PUNCT
ejpam-4679	196	1	j.	j.	PROPN
ejpam-4679	196	2	pure	pure	PROPN
ejpam-4679	196	3	appl	appl	PROPN
ejpam-4679	196	4	.	.	PROPN
ejpam-4679	196	5	math	math	PROPN
ejpam-4679	196	6	,	,	PUNCT
ejpam-4679	196	7	16	16	NUM
ejpam-4679	196	8	(	(	PUNCT
ejpam-4679	196	9	1	1	NUM
ejpam-4679	196	10	)	)	PUNCT
ejpam-4679	196	11	(	(	PUNCT
ejpam-4679	196	12	2023	2023	NUM
ejpam-4679	196	13	)	)	PUNCT
ejpam-4679	196	14	,	,	PUNCT
ejpam-4679	196	15	491	491	NUM
ejpam-4679	196	16	-	-	SYM
ejpam-4679	196	17	502	502	NUM
ejpam-4679	196	18	499	499	NUM
ejpam-4679	196	19	relerror	relerror	NOUN
ejpam-4679	196	20	=	=	SYM
ejpam-4679	196	21	maxi	maxi	ADJ
ejpam-4679	196	22	,	,	PUNCT
ejpam-4679	196	23	j	j	PROPN
ejpam-4679	196	24	|uki	|uki	PROPN
ejpam-4679	196	25	,	,	PUNCT
ejpam-4679	196	26	j(1	j(1	NOUN
ejpam-4679	196	27	)	)	PUNCT
ejpam-4679	196	28	−	−	PROPN
ejpam-4679	197	1	uk−1	uk−1	PROPN
ejpam-4679	197	2	i	i	PROPN
ejpam-4679	197	3	,	,	PUNCT
ejpam-4679	197	4	j	j	PROPN
ejpam-4679	197	5	(	(	PUNCT
ejpam-4679	197	6	1)|	1)|	NUM
ejpam-4679	197	7	for	for	ADP
ejpam-4679	197	8	k	k	PROPN
ejpam-4679	197	9	=	=	SYM
ejpam-4679	197	10	1	1	NUM
ejpam-4679	197	11	,	,	PUNCT
ejpam-4679	197	12	2	2	NUM
ejpam-4679	197	13	,	,	PUNCT
ejpam-4679	197	14	.	.	PUNCT
ejpam-4679	197	15	.	.	PUNCT
ejpam-4679	198	1	.	.	PUNCT
ejpam-4679	199	1	and	and	CCONJ
ejpam-4679	199	2	u0i	u0i	PROPN
ejpam-4679	199	3	,	,	PUNCT
ejpam-4679	199	4	j	j	PROPN
ejpam-4679	199	5	being	be	AUX
ejpam-4679	199	6	the	the	DET
ejpam-4679	199	7	value	value	NOUN
ejpam-4679	199	8	of	of	ADP
ejpam-4679	199	9	the	the	DET
ejpam-4679	199	10	initial	initial	ADJ
ejpam-4679	199	11	approximation	approximation	NOUN
ejpam-4679	199	12	function	function	NOUN
ejpam-4679	199	13	at	at	ADP
ejpam-4679	199	14	(	(	PUNCT
ejpam-4679	199	15	xi	xi	PROPN
ejpam-4679	199	16	,	,	PUNCT
ejpam-4679	199	17	yj	yj	PROPN
ejpam-4679	199	18	)	)	PUNCT
ejpam-4679	199	19	.	.	PUNCT
ejpam-4679	200	1	importantly	importantly	ADV
ejpam-4679	200	2	,	,	PUNCT
ejpam-4679	200	3	the	the	DET
ejpam-4679	200	4	iteration	iteration	NOUN
ejpam-4679	200	5	process	process	NOUN
ejpam-4679	200	6	stops	stop	VERB
ejpam-4679	200	7	when	when	SCONJ
ejpam-4679	200	8	the	the	DET
ejpam-4679	200	9	relative	relative	ADJ
ejpam-4679	200	10	error	error	NOUN
ejpam-4679	200	11	is	be	AUX
ejpam-4679	200	12	less	less	ADJ
ejpam-4679	200	13	than	than	ADP
ejpam-4679	200	14	the	the	DET
ejpam-4679	200	15	provided	provide	VERB
ejpam-4679	200	16	ϵ.	ϵ.	NOUN
ejpam-4679	200	17	we	we	PRON
ejpam-4679	200	18	note	note	VERB
ejpam-4679	200	19	that	that	SCONJ
ejpam-4679	200	20	,	,	PUNCT
ejpam-4679	200	21	we	we	PRON
ejpam-4679	200	22	did	do	VERB
ejpam-4679	200	23	simulations	simulation	NOUN
ejpam-4679	200	24	with	with	ADP
ejpam-4679	200	25	n	n	NOUN
ejpam-4679	200	26	=	=	SYM
ejpam-4679	200	27	20	20	NUM
ejpam-4679	200	28	,	,	PUNCT
ejpam-4679	200	29	m	m	VERB
ejpam-4679	200	30	=	=	NOUN
ejpam-4679	200	31	20	20	NUM
ejpam-4679	200	32	,	,	PUNCT
ejpam-4679	200	33	but	but	CCONJ
ejpam-4679	200	34	the	the	DET
ejpam-4679	200	35	simulation	simulation	NOUN
ejpam-4679	200	36	results	result	NOUN
ejpam-4679	200	37	did	do	AUX
ejpam-4679	200	38	not	not	PART
ejpam-4679	200	39	improve	improve	VERB
ejpam-4679	200	40	at	at	ADV
ejpam-4679	200	41	all	all	ADV
ejpam-4679	200	42	.	.	PUNCT
ejpam-4679	201	1	however	however	ADV
ejpam-4679	201	2	,	,	PUNCT
ejpam-4679	201	3	the	the	DET
ejpam-4679	201	4	cpu	cpu	ADJ
ejpam-4679	201	5	time	time	NOUN
ejpam-4679	201	6	increased	increase	VERB
ejpam-4679	201	7	substantially	substantially	ADV
ejpam-4679	201	8	.	.	PUNCT
ejpam-4679	202	1	in	in	ADP
ejpam-4679	202	2	addition	addition	NOUN
ejpam-4679	202	3	,	,	PUNCT
ejpam-4679	202	4	the	the	DET
ejpam-4679	202	5	simulations	simulation	NOUN
ejpam-4679	202	6	run	run	VERB
ejpam-4679	202	7	with	with	ADP
ejpam-4679	202	8	different	different	ADJ
ejpam-4679	202	9	initial	initial	ADJ
ejpam-4679	202	10	approximation	approximation	NOUN
ejpam-4679	202	11	function	function	NOUN
ejpam-4679	202	12	u0(t	u0(t	PROPN
ejpam-4679	202	13	,	,	PUNCT
ejpam-4679	202	14	x	x	NOUN
ejpam-4679	202	15	,	,	PUNCT
ejpam-4679	202	16	y	y	NOUN
ejpam-4679	202	17	)	)	PUNCT
ejpam-4679	202	18	other	other	ADJ
ejpam-4679	202	19	than	than	ADP
ejpam-4679	202	20	zero	zero	NUM
ejpam-4679	202	21	also	also	ADV
ejpam-4679	202	22	did	do	AUX
ejpam-4679	202	23	not	not	PART
ejpam-4679	202	24	lead	lead	VERB
ejpam-4679	202	25	to	to	ADP
ejpam-4679	202	26	any	any	DET
ejpam-4679	202	27	substantial	substantial	ADJ
ejpam-4679	202	28	improvements	improvement	NOUN
ejpam-4679	202	29	in	in	ADP
ejpam-4679	202	30	the	the	DET
ejpam-4679	202	31	results	result	NOUN
ejpam-4679	202	32	.	.	PUNCT
ejpam-4679	203	1	hence	hence	ADV
ejpam-4679	203	2	,	,	PUNCT
ejpam-4679	203	3	throughout	throughout	ADP
ejpam-4679	203	4	all	all	DET
ejpam-4679	203	5	simulations	simulation	NOUN
ejpam-4679	203	6	we	we	PRON
ejpam-4679	203	7	only	only	ADV
ejpam-4679	203	8	consider	consider	VERB
ejpam-4679	203	9	n	n	NOUN
ejpam-4679	203	10	=	=	SYM
ejpam-4679	203	11	m	m	NOUN
ejpam-4679	203	12	=	=	NOUN
ejpam-4679	203	13	10	10	NUM
ejpam-4679	203	14	and	and	CCONJ
ejpam-4679	203	15	u0(t	u0(t	ADJ
ejpam-4679	203	16	,	,	PUNCT
ejpam-4679	203	17	x	x	NOUN
ejpam-4679	203	18	,	,	PUNCT
ejpam-4679	203	19	y	y	PROPN
ejpam-4679	203	20	)	)	PUNCT
ejpam-4679	203	21	=	=	SYM
ejpam-4679	204	1	0	0	X
ejpam-4679	204	2	.	.	PUNCT
ejpam-4679	205	1	in	in	ADP
ejpam-4679	205	2	figure	figure	NOUN
ejpam-4679	205	3	1	1	NUM
ejpam-4679	205	4	,	,	PUNCT
ejpam-4679	205	5	we	we	PRON
ejpam-4679	205	6	simulated	simulate	VERB
ejpam-4679	205	7	the	the	DET
ejpam-4679	205	8	model	model	NOUN
ejpam-4679	205	9	with	with	ADP
ejpam-4679	205	10	ϵ	ϵ	PROPN
ejpam-4679	205	11	=	=	SYM
ejpam-4679	205	12	0.0001	0.0001	NUM
ejpam-4679	205	13	to	to	PART
ejpam-4679	205	14	obtain	obtain	VERB
ejpam-4679	205	15	the	the	DET
ejpam-4679	205	16	approximate	approximate	ADJ
ejpam-4679	205	17	solution	solution	NOUN
ejpam-4679	205	18	.	.	PUNCT
ejpam-4679	206	1	it	it	PRON
ejpam-4679	206	2	took	take	VERB
ejpam-4679	206	3	5	5	NUM
ejpam-4679	206	4	steps	step	NOUN
ejpam-4679	206	5	to	to	PART
ejpam-4679	206	6	achieve	achieve	VERB
ejpam-4679	206	7	the	the	DET
ejpam-4679	206	8	relative	relative	ADJ
ejpam-4679	206	9	error	error	NOUN
ejpam-4679	206	10	of	of	ADP
ejpam-4679	206	11	the	the	DET
ejpam-4679	206	12	differences	difference	NOUN
ejpam-4679	206	13	to	to	PART
ejpam-4679	206	14	be	be	AUX
ejpam-4679	206	15	less	less	ADJ
ejpam-4679	206	16	than	than	ADP
ejpam-4679	206	17	the	the	DET
ejpam-4679	206	18	given	give	VERB
ejpam-4679	206	19	ϵ.	ϵ.	NOUN
ejpam-4679	206	20	the	the	DET
ejpam-4679	206	21	error	error	NOUN
ejpam-4679	206	22	distribution	distribution	NOUN
ejpam-4679	206	23	at	at	ADP
ejpam-4679	206	24	time	time	NOUN
ejpam-4679	206	25	t	t	NOUN
ejpam-4679	206	26	=	=	SYM
ejpam-4679	206	27	1	1	NUM
ejpam-4679	206	28	is	be	AUX
ejpam-4679	206	29	given	give	VERB
ejpam-4679	206	30	with	with	ADP
ejpam-4679	206	31	the	the	DET
ejpam-4679	206	32	approximate	approximate	ADJ
ejpam-4679	206	33	solution	solution	NOUN
ejpam-4679	206	34	.	.	PUNCT
ejpam-4679	207	1	as	as	SCONJ
ejpam-4679	207	2	seen	see	VERB
ejpam-4679	207	3	from	from	ADP
ejpam-4679	207	4	the	the	DET
ejpam-4679	207	5	figure	figure	NOUN
ejpam-4679	207	6	1	1	NUM
ejpam-4679	207	7	left	left	ADJ
ejpam-4679	207	8	panel	panel	NOUN
ejpam-4679	207	9	,	,	PUNCT
ejpam-4679	207	10	the	the	DET
ejpam-4679	207	11	error	error	NOUN
ejpam-4679	207	12	distribution	distribution	NOUN
ejpam-4679	207	13	closely	closely	ADV
ejpam-4679	207	14	traces	trace	VERB
ejpam-4679	207	15	the	the	DET
ejpam-4679	207	16	approximate	approximate	ADJ
ejpam-4679	207	17	solution	solution	NOUN
ejpam-4679	207	18	in	in	ADP
ejpam-4679	207	19	terms	term	NOUN
ejpam-4679	207	20	of	of	ADP
ejpam-4679	207	21	the	the	DET
ejpam-4679	207	22	magnitude	magnitude	NOUN
ejpam-4679	207	23	.	.	PUNCT
ejpam-4679	208	1	that	that	PRON
ejpam-4679	208	2	is	is	ADV
ejpam-4679	208	3	,	,	PUNCT
ejpam-4679	208	4	error	error	NOUN
ejpam-4679	208	5	is	be	AUX
ejpam-4679	208	6	large	large	ADJ
ejpam-4679	208	7	at	at	ADP
ejpam-4679	208	8	the	the	DET
ejpam-4679	208	9	points	point	NOUN
ejpam-4679	208	10	where	where	SCONJ
ejpam-4679	208	11	the	the	DET
ejpam-4679	208	12	solution	solution	NOUN
ejpam-4679	208	13	is	be	AUX
ejpam-4679	208	14	large	large	ADJ
ejpam-4679	208	15	.	.	PUNCT
ejpam-4679	209	1	figure	figure	NOUN
ejpam-4679	209	2	2	2	NUM
ejpam-4679	209	3	:	:	PUNCT
ejpam-4679	209	4	absolute	absolute	ADJ
ejpam-4679	209	5	and	and	CCONJ
ejpam-4679	209	6	relative	relative	ADJ
ejpam-4679	209	7	error	error	NOUN
ejpam-4679	209	8	dependence	dependence	NOUN
ejpam-4679	209	9	to	to	ADP
ejpam-4679	209	10	the	the	DET
ejpam-4679	209	11	iteration	iteration	NOUN
ejpam-4679	209	12	number	number	NOUN
ejpam-4679	209	13	.	.	PUNCT
ejpam-4679	210	1	both	both	DET
ejpam-4679	210	2	type	type	NOUN
ejpam-4679	210	3	of	of	ADP
ejpam-4679	210	4	errors	error	NOUN
ejpam-4679	210	5	decay	decay	VERB
ejpam-4679	210	6	linearly	linearly	ADV
ejpam-4679	210	7	in	in	ADP
ejpam-4679	210	8	logarithm	logarithm	NOUN
ejpam-4679	210	9	depending	depend	VERB
ejpam-4679	210	10	on	on	ADP
ejpam-4679	210	11	the	the	DET
ejpam-4679	210	12	iteration	iteration	NOUN
ejpam-4679	210	13	number	number	NOUN
ejpam-4679	210	14	.	.	PUNCT
ejpam-4679	211	1	to	to	PART
ejpam-4679	211	2	observe	observe	VERB
ejpam-4679	211	3	the	the	DET
ejpam-4679	211	4	improvement	improvement	NOUN
ejpam-4679	211	5	in	in	ADP
ejpam-4679	211	6	the	the	DET
ejpam-4679	211	7	error	error	NOUN
ejpam-4679	211	8	with	with	ADP
ejpam-4679	211	9	respect	respect	NOUN
ejpam-4679	211	10	to	to	ADP
ejpam-4679	211	11	the	the	DET
ejpam-4679	211	12	iteration	iteration	NOUN
ejpam-4679	211	13	number	number	NOUN
ejpam-4679	211	14	,	,	PUNCT
ejpam-4679	211	15	we	we	PRON
ejpam-4679	211	16	next	next	ADV
ejpam-4679	211	17	simulated	simulate	VERB
ejpam-4679	211	18	the	the	DET
ejpam-4679	211	19	model	model	NOUN
ejpam-4679	211	20	and	and	CCONJ
ejpam-4679	211	21	evaluated	evaluate	VERB
ejpam-4679	211	22	both	both	CCONJ
ejpam-4679	211	23	absolute	absolute	ADJ
ejpam-4679	211	24	and	and	CCONJ
ejpam-4679	211	25	relative	relative	ADJ
ejpam-4679	211	26	errors	error	NOUN
ejpam-4679	211	27	in	in	ADP
ejpam-4679	211	28	logarithmic	logarithmic	ADJ
ejpam-4679	211	29	function	function	NOUN
ejpam-4679	211	30	.	.	PUNCT
ejpam-4679	212	1	the	the	DET
ejpam-4679	212	2	results	result	NOUN
ejpam-4679	212	3	are	be	AUX
ejpam-4679	212	4	shown	show	VERB
ejpam-4679	212	5	in	in	ADP
ejpam-4679	212	6	figure	figure	NOUN
ejpam-4679	212	7	2	2	NUM
ejpam-4679	212	8	.	.	PUNCT
ejpam-4679	213	1	it	it	PRON
ejpam-4679	213	2	appears	appear	VERB
ejpam-4679	213	3	that	that	SCONJ
ejpam-4679	213	4	,	,	PUNCT
ejpam-4679	213	5	when	when	SCONJ
ejpam-4679	213	6	the	the	DET
ejpam-4679	213	7	initial	initial	ADJ
ejpam-4679	213	8	approximation	approximation	NOUN
ejpam-4679	213	9	function	function	NOUN
ejpam-4679	213	10	for	for	ADP
ejpam-4679	213	11	the	the	DET
ejpam-4679	213	12	iteration	iteration	NOUN
ejpam-4679	213	13	is	be	AUX
ejpam-4679	213	14	chosen	choose	VERB
ejpam-4679	213	15	as	as	ADP
ejpam-4679	213	16	zero	zero	NUM
ejpam-4679	213	17	,	,	PUNCT
ejpam-4679	213	18	both	both	DET
ejpam-4679	213	19	absolute	absolute	ADJ
ejpam-4679	213	20	and	and	CCONJ
ejpam-4679	213	21	relative	relative	ADJ
ejpam-4679	213	22	errors	error	NOUN
ejpam-4679	213	23	progress	progress	VERB
ejpam-4679	213	24	linearly	linearly	ADV
ejpam-4679	213	25	with	with	ADP
ejpam-4679	213	26	respect	respect	NOUN
ejpam-4679	213	27	to	to	ADP
ejpam-4679	213	28	the	the	DET
ejpam-4679	213	29	iteration	iteration	NOUN
ejpam-4679	213	30	number	number	NOUN
ejpam-4679	213	31	.	.	PUNCT
ejpam-4679	214	1	this	this	PRON
ejpam-4679	214	2	is	be	AUX
ejpam-4679	214	3	important	important	ADJ
ejpam-4679	214	4	in	in	ADP
ejpam-4679	214	5	the	the	DET
ejpam-4679	214	6	following	following	ADJ
ejpam-4679	214	7	way	way	NOUN
ejpam-4679	214	8	;	;	PUNCT
ejpam-4679	214	9	instead	instead	ADV
ejpam-4679	214	10	of	of	ADP
ejpam-4679	214	11	using	use	VERB
ejpam-4679	214	12	refined	refined	ADJ
ejpam-4679	214	13	step	step	NOUN
ejpam-4679	214	14	size	size	NOUN
ejpam-4679	214	15	to	to	PART
ejpam-4679	214	16	improve	improve	VERB
ejpam-4679	214	17	the	the	DET
ejpam-4679	214	18	error	error	NOUN
ejpam-4679	214	19	,	,	PUNCT
ejpam-4679	214	20	we	we	PRON
ejpam-4679	214	21	can	can	AUX
ejpam-4679	214	22	increase	increase	VERB
ejpam-4679	214	23	and	and	CCONJ
ejpam-4679	214	24	obtain	obtain	VERB
ejpam-4679	214	25	much	much	ADV
ejpam-4679	214	26	faster	fast	ADJ
ejpam-4679	214	27	results	result	NOUN
ejpam-4679	214	28	with	with	ADP
ejpam-4679	214	29	less	less	ADJ
ejpam-4679	214	30	error	error	NOUN
ejpam-4679	214	31	.	.	PUNCT
ejpam-4679	215	1	this	this	PRON
ejpam-4679	215	2	is	be	AUX
ejpam-4679	215	3	analyzed	analyze	VERB
ejpam-4679	215	4	in	in	ADP
ejpam-4679	215	5	figure	figure	NOUN
ejpam-4679	215	6	3	3	NUM
ejpam-4679	215	7	in	in	ADP
ejpam-4679	215	8	which	which	PRON
ejpam-4679	215	9	we	we	PRON
ejpam-4679	215	10	consider	consider	VERB
ejpam-4679	215	11	the	the	DET
ejpam-4679	215	12	dependency	dependency	NOUN
ejpam-4679	215	13	of	of	ADP
ejpam-4679	215	14	the	the	DET
ejpam-4679	215	15	results	result	NOUN
ejpam-4679	215	16	on	on	ADP
ejpam-4679	215	17	both	both	CCONJ
ejpam-4679	215	18	the	the	DET
ejpam-4679	215	19	time	time	NOUN
ejpam-4679	215	20	step	step	NOUN
ejpam-4679	215	21	and	and	CCONJ
ejpam-4679	215	22	ϵ.	ϵ.	NOUN
ejpam-4679	215	23	importantly	importantly	ADV
ejpam-4679	215	24	,	,	PUNCT
ejpam-4679	215	25	the	the	DET
ejpam-4679	215	26	improvement	improvement	NOUN
ejpam-4679	215	27	in	in	ADP
ejpam-4679	215	28	the	the	DET
ejpam-4679	215	29	error	error	NOUN
ejpam-4679	215	30	with	with	ADP
ejpam-4679	215	31	the	the	DET
ejpam-4679	215	32	refinement	refinement	NOUN
ejpam-4679	215	33	of	of	ADP
ejpam-4679	215	34	time	time	NOUN
ejpam-4679	215	35	step	step	NOUN
ejpam-4679	215	36	size	size	NOUN
ejpam-4679	215	37	is	be	AUX
ejpam-4679	215	38	very	very	ADV
ejpam-4679	215	39	subtle	subtle	ADJ
ejpam-4679	215	40	compared	compare	VERB
ejpam-4679	215	41	to	to	ADP
ejpam-4679	215	42	the	the	DET
ejpam-4679	215	43	improvement	improvement	NOUN
ejpam-4679	215	44	in	in	ADP
ejpam-4679	215	45	error	error	NOUN
ejpam-4679	215	46	with	with	ADP
ejpam-4679	215	47	ϵ.	ϵ.	NOUN
ejpam-4679	215	48	however	however	ADV
ejpam-4679	215	49	,	,	PUNCT
ejpam-4679	215	50	the	the	DET
ejpam-4679	215	51	computational	computational	ADJ
ejpam-4679	215	52	cost	cost	NOUN
ejpam-4679	215	53	of	of	ADP
ejpam-4679	215	54	the	the	DET
ejpam-4679	215	55	refinement	refinement	NOUN
ejpam-4679	215	56	of	of	ADP
ejpam-4679	215	57	the	the	DET
ejpam-4679	215	58	time	time	NOUN
ejpam-4679	215	59	step	step	NOUN
ejpam-4679	215	60	size	size	NOUN
ejpam-4679	215	61	is	be	AUX
ejpam-4679	215	62	enormous	enormous	ADJ
ejpam-4679	215	63	.	.	PUNCT
ejpam-4679	216	1	finally	finally	ADV
ejpam-4679	216	2	,	,	PUNCT
ejpam-4679	216	3	we	we	PRON
ejpam-4679	216	4	considered	consider	VERB
ejpam-4679	216	5	the	the	DET
ejpam-4679	216	6	dependence	dependence	NOUN
ejpam-4679	216	7	of	of	ADP
ejpam-4679	216	8	the	the	DET
ejpam-4679	216	9	error	error	NOUN
ejpam-4679	216	10	,	,	PUNCT
ejpam-4679	216	11	cpu	cpu	NOUN
ejpam-4679	216	12	time	time	NOUN
ejpam-4679	216	13	and	and	CCONJ
ejpam-4679	216	14	iteration	iteration	NOUN
ejpam-4679	216	15	number	number	NOUN
ejpam-4679	216	16	to	to	ADP
ejpam-4679	216	17	the	the	DET
ejpam-4679	216	18	fractional	fractional	ADJ
ejpam-4679	216	19	derivative	derivative	ADJ
ejpam-4679	216	20	order	order	NOUN
ejpam-4679	216	21	alpha	alpha	NOUN
ejpam-4679	216	22	for	for	ADP
ejpam-4679	216	23	the	the	DET
ejpam-4679	216	24	given	give	VERB
ejpam-4679	216	25	ϵ	ϵ	PROPN
ejpam-4679	216	26	=	=	SYM
ejpam-4679	216	27	0.0001	0.0001	NUM
ejpam-4679	216	28	,	,	PUNCT
ejpam-4679	216	29	see	see	VERB
ejpam-4679	216	30	figure	figure	NOUN
ejpam-4679	216	31	4	4	NUM
ejpam-4679	216	32	.	.	PUNCT
ejpam-4679	217	1	it	it	PRON
ejpam-4679	217	2	appears	appear	VERB
ejpam-4679	217	3	that	that	SCONJ
ejpam-4679	217	4	,	,	PUNCT
ejpam-4679	217	5	the	the	DET
ejpam-4679	217	6	change	change	NOUN
ejpam-4679	217	7	in	in	ADP
ejpam-4679	217	8	the	the	DET
ejpam-4679	217	9	error	error	NOUN
ejpam-4679	217	10	with	with	ADP
ejpam-4679	217	11	decreasing	decrease	VERB
ejpam-4679	217	12	alpha	alpha	NOUN
ejpam-4679	217	13	is	be	AUX
ejpam-4679	217	14	subtle	subtle	ADJ
ejpam-4679	217	15	;	;	PUNCT
ejpam-4679	217	16	whereas	whereas	SCONJ
ejpam-4679	217	17	the	the	DET
ejpam-4679	217	18	computational	computational	ADJ
ejpam-4679	217	19	cost	cost	NOUN
ejpam-4679	217	20	m.	m.	NOUN
ejpam-4679	217	21	zeki	zeki	PROPN
ejpam-4679	217	22	,	,	PUNCT
ejpam-4679	217	23	s.	s.	PROPN
ejpam-4679	217	24	tatar	tatar	PROPN
ejpam-4679	217	25	/	/	SYM
ejpam-4679	217	26	eur	eur	PROPN
ejpam-4679	217	27	.	.	PUNCT
ejpam-4679	218	1	j.	j.	PROPN
ejpam-4679	218	2	pure	pure	PROPN
ejpam-4679	218	3	appl	appl	PROPN
ejpam-4679	218	4	.	.	PROPN
ejpam-4679	218	5	math	math	PROPN
ejpam-4679	218	6	,	,	PUNCT
ejpam-4679	218	7	16	16	NUM
ejpam-4679	218	8	(	(	PUNCT
ejpam-4679	218	9	1	1	NUM
ejpam-4679	218	10	)	)	PUNCT
ejpam-4679	218	11	(	(	PUNCT
ejpam-4679	218	12	2023	2023	NUM
ejpam-4679	218	13	)	)	PUNCT
ejpam-4679	218	14	,	,	PUNCT
ejpam-4679	218	15	491	491	NUM
ejpam-4679	218	16	-	-	SYM
ejpam-4679	218	17	502	502	NUM
ejpam-4679	218	18	500	500	NUM
ejpam-4679	218	19	increases	increase	NOUN
ejpam-4679	218	20	with	with	ADP
ejpam-4679	218	21	reduction	reduction	NOUN
ejpam-4679	218	22	in	in	ADP
ejpam-4679	218	23	alpha	alpha	NOUN
ejpam-4679	218	24	.	.	PUNCT
ejpam-4679	219	1	interestingly	interestingly	ADV
ejpam-4679	219	2	,	,	PUNCT
ejpam-4679	219	3	number	number	NOUN
ejpam-4679	219	4	of	of	ADP
ejpam-4679	219	5	iterations	iteration	NOUN
ejpam-4679	219	6	necessary	necessary	ADJ
ejpam-4679	219	7	to	to	PART
ejpam-4679	219	8	achieve	achieve	VERB
ejpam-4679	219	9	the	the	DET
ejpam-4679	219	10	given	give	VERB
ejpam-4679	219	11	relative	relative	ADJ
ejpam-4679	219	12	error	error	NOUN
ejpam-4679	219	13	remains	remain	VERB
ejpam-4679	219	14	intact	intact	ADJ
ejpam-4679	219	15	.	.	PUNCT
ejpam-4679	220	1	figure	figure	NOUN
ejpam-4679	220	2	3	3	NUM
ejpam-4679	220	3	:	:	PUNCT
ejpam-4679	220	4	absolute	absolute	ADJ
ejpam-4679	220	5	error	error	NOUN
ejpam-4679	220	6	,	,	PUNCT
ejpam-4679	220	7	cpu	cpu	NOUN
ejpam-4679	220	8	time	time	NOUN
ejpam-4679	220	9	and	and	CCONJ
ejpam-4679	220	10	iteration	iteration	NOUN
ejpam-4679	220	11	number	number	NOUN
ejpam-4679	220	12	dependence	dependence	NOUN
ejpam-4679	220	13	to	to	ADP
ejpam-4679	220	14	both	both	DET
ejpam-4679	220	15	time	time	NOUN
ejpam-4679	220	16	step	step	NOUN
ejpam-4679	220	17	size	size	NOUN
ejpam-4679	220	18	and	and	CCONJ
ejpam-4679	220	19	relative	relative	ADJ
ejpam-4679	220	20	error	error	NOUN
ejpam-4679	220	21	bound	bind	VERB
ejpam-4679	220	22	ϵ	ϵ	PART
ejpam-4679	220	23	figure	figure	NOUN
ejpam-4679	220	24	4	4	NUM
ejpam-4679	220	25	:	:	PUNCT
ejpam-4679	220	26	absolute	absolute	ADJ
ejpam-4679	220	27	error	error	NOUN
ejpam-4679	220	28	,	,	PUNCT
ejpam-4679	220	29	cpu	cpu	NOUN
ejpam-4679	220	30	time	time	NOUN
ejpam-4679	220	31	and	and	CCONJ
ejpam-4679	220	32	iteration	iteration	NOUN
ejpam-4679	220	33	number	number	NOUN
ejpam-4679	220	34	dependence	dependence	NOUN
ejpam-4679	220	35	to	to	ADP
ejpam-4679	220	36	the	the	DET
ejpam-4679	220	37	fractional	fractional	ADJ
ejpam-4679	220	38	derivative	derivative	ADJ
ejpam-4679	220	39	order	order	NOUN
ejpam-4679	220	40	β	β	NOUN
ejpam-4679	220	41	references	reference	NOUN
ejpam-4679	220	42	501	501	NUM
ejpam-4679	220	43	references	reference	NOUN
ejpam-4679	220	44	[	[	X
ejpam-4679	220	45	1	1	NUM
ejpam-4679	220	46	]	]	PUNCT
ejpam-4679	220	47	kendall	kendall	PROPN
ejpam-4679	220	48	atkinson	atkinson	PROPN
ejpam-4679	220	49	.	.	PUNCT
ejpam-4679	221	1	an	an	DET
ejpam-4679	221	2	introduction	introduction	NOUN
ejpam-4679	221	3	to	to	ADP
ejpam-4679	221	4	numerical	numerical	ADJ
ejpam-4679	221	5	analysis	analysis	NOUN
ejpam-4679	221	6	.	.	PUNCT
ejpam-4679	222	1	john	john	PROPN
ejpam-4679	222	2	wiley	wiley	PROPN
ejpam-4679	222	3	&	&	CCONJ
ejpam-4679	222	4	sons	son	NOUN
ejpam-4679	222	5	,	,	PUNCT
ejpam-4679	222	6	1991	1991	NUM
ejpam-4679	222	7	.	.	PUNCT
ejpam-4679	223	1	[	[	X
ejpam-4679	223	2	2	2	NUM
ejpam-4679	223	3	]	]	X
ejpam-4679	223	4	kai	kai	PROPN
ejpam-4679	223	5	diethelm	diethelm	PROPN
ejpam-4679	223	6	,	,	PUNCT
ejpam-4679	223	7	neville	neville	PROPN
ejpam-4679	223	8	j	j	PROPN
ejpam-4679	223	9	ford	ford	PROPN
ejpam-4679	223	10	,	,	PUNCT
ejpam-4679	223	11	and	and	CCONJ
ejpam-4679	223	12	alan	alan	PROPN
ejpam-4679	223	13	d	d	PROPN
ejpam-4679	223	14	freed	free	VERB
ejpam-4679	223	15	.	.	PUNCT
ejpam-4679	224	1	detailed	detailed	ADJ
ejpam-4679	224	2	error	error	NOUN
ejpam-4679	224	3	analysis	analysis	NOUN
ejpam-4679	224	4	for	for	ADP
ejpam-4679	224	5	a	a	DET
ejpam-4679	224	6	fractional	fractional	ADJ
ejpam-4679	224	7	adams	adams	PROPN
ejpam-4679	224	8	method	method	PROPN
ejpam-4679	224	9	.	.	PUNCT
ejpam-4679	225	1	numerical	numerical	ADJ
ejpam-4679	225	2	algorithms	algorithms	PROPN
ejpam-4679	225	3	,	,	PUNCT
ejpam-4679	225	4	36(1):31–52	36(1):31–52	NUM
ejpam-4679	225	5	,	,	PUNCT
ejpam-4679	225	6	2004	2004	NUM
ejpam-4679	225	7	.	.	PUNCT
ejpam-4679	226	1	[	[	X
ejpam-4679	226	2	3	3	NUM
ejpam-4679	226	3	]	]	X
ejpam-4679	226	4	kai	kai	PROPN
ejpam-4679	226	5	diethelm	diethelm	PROPN
ejpam-4679	226	6	and	and	CCONJ
ejpam-4679	226	7	alan	alan	PROPN
ejpam-4679	226	8	d	d	PROPN
ejpam-4679	226	9	freed	free	VERB
ejpam-4679	226	10	.	.	PUNCT
ejpam-4679	227	1	the	the	DET
ejpam-4679	227	2	fracpece	fracpece	NOUN
ejpam-4679	227	3	subroutine	subroutine	NOUN
ejpam-4679	227	4	for	for	ADP
ejpam-4679	227	5	the	the	DET
ejpam-4679	227	6	numerical	numerical	ADJ
ejpam-4679	227	7	solution	solution	NOUN
ejpam-4679	227	8	of	of	ADP
ejpam-4679	227	9	differential	differential	ADJ
ejpam-4679	227	10	equations	equation	NOUN
ejpam-4679	227	11	of	of	ADP
ejpam-4679	227	12	fractional	fractional	ADJ
ejpam-4679	227	13	order	order	NOUN
ejpam-4679	227	14	.	.	PUNCT
ejpam-4679	228	1	forschung	forschung	PROPN
ejpam-4679	228	2	und	und	PROPN
ejpam-4679	228	3	wissenschaftliches	wissenschaftliche	NOUN
ejpam-4679	228	4	rechnen	rechnen	PROPN
ejpam-4679	228	5	,	,	PUNCT
ejpam-4679	228	6	1999:57–71	1999:57–71	PROPN
ejpam-4679	228	7	,	,	PUNCT
ejpam-4679	228	8	1998	1998	NUM
ejpam-4679	228	9	.	.	PUNCT
ejpam-4679	229	1	[	[	X
ejpam-4679	229	2	4	4	NUM
ejpam-4679	229	3	]	]	X
ejpam-4679	229	4	abd	abd	PROPN
ejpam-4679	229	5	el	el	PROPN
ejpam-4679	229	6	-	-	PROPN
ejpam-4679	229	7	ghany	ghany	NOUN
ejpam-4679	229	8	el	el	PROPN
ejpam-4679	229	9	abd	abd	PROPN
ejpam-4679	229	10	and	and	CCONJ
ejpam-4679	229	11	jacek	jacek	PROPN
ejpam-4679	229	12	j	j	PROPN
ejpam-4679	229	13	milczarek	milczarek	PROPN
ejpam-4679	229	14	.	.	PUNCT
ejpam-4679	230	1	neutron	neutron	PROPN
ejpam-4679	230	2	radiography	radiography	NOUN
ejpam-4679	230	3	study	study	NOUN
ejpam-4679	230	4	of	of	ADP
ejpam-4679	230	5	water	water	NOUN
ejpam-4679	230	6	absorption	absorption	NOUN
ejpam-4679	230	7	in	in	ADP
ejpam-4679	230	8	porous	porous	ADJ
ejpam-4679	230	9	building	building	NOUN
ejpam-4679	230	10	materials	material	NOUN
ejpam-4679	230	11	:	:	PUNCT
ejpam-4679	230	12	anomalous	anomalous	ADJ
ejpam-4679	230	13	diffusion	diffusion	NOUN
ejpam-4679	230	14	analysis	analysis	NOUN
ejpam-4679	230	15	.	.	PUNCT
ejpam-4679	231	1	journal	journal	PROPN
ejpam-4679	231	2	of	of	ADP
ejpam-4679	231	3	physics	physics	PROPN
ejpam-4679	232	1	d	d	PROPN
ejpam-4679	232	2	:	:	PUNCT
ejpam-4679	232	3	applied	applied	ADJ
ejpam-4679	232	4	physics	physic	NOUN
ejpam-4679	232	5	,	,	PUNCT
ejpam-4679	232	6	37(16):2305	37(16):2305	NUM
ejpam-4679	232	7	,	,	PUNCT
ejpam-4679	232	8	2004	2004	NUM
ejpam-4679	232	9	.	.	PUNCT
ejpam-4679	233	1	[	[	X
ejpam-4679	233	2	5	5	NUM
ejpam-4679	233	3	]	]	PUNCT
ejpam-4679	233	4	hairer	hairer	NOUN
ejpam-4679	233	5	ernst	ernst	PROPN
ejpam-4679	233	6	and	and	CCONJ
ejpam-4679	233	7	wanner	wanner	PROPN
ejpam-4679	233	8	gerhard	gerhard	PROPN
ejpam-4679	233	9	.	.	PUNCT
ejpam-4679	234	1	solving	solve	VERB
ejpam-4679	234	2	ordinary	ordinary	ADJ
ejpam-4679	234	3	differential	differential	ADJ
ejpam-4679	234	4	equations	equation	NOUN
ejpam-4679	234	5	ii	ii	PROPN
ejpam-4679	234	6	:	:	PUNCT
ejpam-4679	234	7	stiff	stiff	ADJ
ejpam-4679	234	8	and	and	CCONJ
ejpam-4679	234	9	differentialalgebraic	differentialalgebraic	ADJ
ejpam-4679	234	10	problems	problem	NOUN
ejpam-4679	234	11	,	,	PUNCT
ejpam-4679	234	12	1996	1996	NUM
ejpam-4679	234	13	.	.	PUNCT
ejpam-4679	235	1	[	[	X
ejpam-4679	235	2	6	6	NUM
ejpam-4679	235	3	]	]	PUNCT
ejpam-4679	235	4	roberto	roberto	PROPN
ejpam-4679	235	5	garrappa	garrappa	NOUN
ejpam-4679	235	6	.	.	PUNCT
ejpam-4679	236	1	on	on	ADP
ejpam-4679	236	2	linear	linear	ADJ
ejpam-4679	236	3	stability	stability	NOUN
ejpam-4679	236	4	of	of	ADP
ejpam-4679	236	5	predictor	predictor	NOUN
ejpam-4679	236	6	–	–	PUNCT
ejpam-4679	236	7	corrector	corrector	NOUN
ejpam-4679	236	8	algorithms	algorithm	NOUN
ejpam-4679	236	9	for	for	ADP
ejpam-4679	236	10	fractional	fractional	ADJ
ejpam-4679	236	11	differential	differential	ADJ
ejpam-4679	236	12	equations	equation	NOUN
ejpam-4679	236	13	.	.	PUNCT
ejpam-4679	237	1	international	international	ADJ
ejpam-4679	237	2	journal	journal	PROPN
ejpam-4679	237	3	of	of	ADP
ejpam-4679	237	4	computer	computer	NOUN
ejpam-4679	237	5	mathematics	mathematic	NOUN
ejpam-4679	237	6	,	,	PUNCT
ejpam-4679	237	7	87(10):2281	87(10):2281	NUM
ejpam-4679	237	8	–	–	PUNCT
ejpam-4679	237	9	2290	2290	NUM
ejpam-4679	237	10	,	,	PUNCT
ejpam-4679	237	11	2010	2010	NUM
ejpam-4679	237	12	.	.	PUNCT
ejpam-4679	238	1	[	[	X
ejpam-4679	238	2	7	7	X
ejpam-4679	238	3	]	]	X
ejpam-4679	238	4	dn	dn	NOUN
ejpam-4679	238	5	gerasimov	gerasimov	VERB
ejpam-4679	238	6	,	,	PUNCT
ejpam-4679	238	7	va	va	PROPN
ejpam-4679	238	8	kondratieva	kondratieva	PROPN
ejpam-4679	238	9	,	,	PUNCT
ejpam-4679	238	10	and	and	CCONJ
ejpam-4679	238	11	oa	oa	PROPN
ejpam-4679	238	12	sinkevich	sinkevich	NOUN
ejpam-4679	238	13	.	.	PUNCT
ejpam-4679	239	1	an	an	DET
ejpam-4679	239	2	anomalous	anomalous	ADJ
ejpam-4679	239	3	non	non	ADJ
ejpam-4679	239	4	-	-	ADJ
ejpam-4679	239	5	self	self	NOUN
ejpam-4679	239	6	-	-	PUNCT
ejpam-4679	239	7	similar	similar	ADJ
ejpam-4679	239	8	infiltration	infiltration	NOUN
ejpam-4679	239	9	and	and	CCONJ
ejpam-4679	239	10	fractional	fractional	ADJ
ejpam-4679	239	11	diffusion	diffusion	NOUN
ejpam-4679	239	12	equation	equation	NOUN
ejpam-4679	239	13	.	.	PUNCT
ejpam-4679	240	1	physica	physica	NOUN
ejpam-4679	240	2	d	d	NOUN
ejpam-4679	240	3	:	:	PUNCT
ejpam-4679	240	4	nonlinear	nonlinear	ADJ
ejpam-4679	240	5	phenomena	phenomenon	NOUN
ejpam-4679	240	6	,	,	PUNCT
ejpam-4679	240	7	239(16):1593–1597	239(16):1593–1597	NUM
ejpam-4679	240	8	,	,	PUNCT
ejpam-4679	240	9	2010	2010	NUM
ejpam-4679	240	10	.	.	PUNCT
ejpam-4679	241	1	[	[	X
ejpam-4679	241	2	8	8	NUM
ejpam-4679	241	3	]	]	X
ejpam-4679	241	4	e	e	NOUN
ejpam-4679	241	5	gerolymatou	gerolymatou	NOUN
ejpam-4679	241	6	,	,	PUNCT
ejpam-4679	241	7	i	i	PRON
ejpam-4679	241	8	vardoulakis	vardoulaki	VERB
ejpam-4679	241	9	,	,	PUNCT
ejpam-4679	241	10	and	and	CCONJ
ejpam-4679	241	11	r	r	NOUN
ejpam-4679	241	12	hilfer	hilfer	NOUN
ejpam-4679	241	13	.	.	PUNCT
ejpam-4679	242	1	modelling	model	VERB
ejpam-4679	242	2	infiltration	infiltration	NOUN
ejpam-4679	242	3	by	by	ADP
ejpam-4679	242	4	means	mean	NOUN
ejpam-4679	242	5	of	of	ADP
ejpam-4679	242	6	a	a	DET
ejpam-4679	242	7	nonlinear	nonlinear	ADJ
ejpam-4679	242	8	fractional	fractional	ADJ
ejpam-4679	242	9	diffusion	diffusion	NOUN
ejpam-4679	242	10	model	model	NOUN
ejpam-4679	242	11	.	.	PUNCT
ejpam-4679	243	1	journal	journal	PROPN
ejpam-4679	243	2	of	of	ADP
ejpam-4679	243	3	physics	physics	PROPN
ejpam-4679	244	1	d	d	PROPN
ejpam-4679	244	2	:	:	PUNCT
ejpam-4679	244	3	applied	applied	ADJ
ejpam-4679	244	4	physics	physic	NOUN
ejpam-4679	244	5	,	,	PUNCT
ejpam-4679	244	6	39(18):4104	39(18):4104	NUM
ejpam-4679	244	7	,	,	PUNCT
ejpam-4679	244	8	2006	2006	NUM
ejpam-4679	244	9	.	.	PUNCT
ejpam-4679	245	1	[	[	X
ejpam-4679	245	2	9	9	NUM
ejpam-4679	245	3	]	]	X
ejpam-4679	245	4	ivan	ivan	PROPN
ejpam-4679	245	5	a	a	DET
ejpam-4679	245	6	guerrini	guerrini	NOUN
ejpam-4679	245	7	and	and	CCONJ
ejpam-4679	245	8	d	d	NOUN
ejpam-4679	245	9	swartzendruber	swartzendruber	NOUN
ejpam-4679	245	10	.	.	PUNCT
ejpam-4679	246	1	soil	soil	NOUN
ejpam-4679	246	2	water	water	NOUN
ejpam-4679	246	3	diffusivity	diffusivity	NOUN
ejpam-4679	246	4	as	as	ADP
ejpam-4679	246	5	explicitly	explicitly	ADV
ejpam-4679	246	6	dependent	dependent	ADJ
ejpam-4679	246	7	on	on	ADP
ejpam-4679	246	8	both	both	DET
ejpam-4679	246	9	time	time	NOUN
ejpam-4679	246	10	and	and	CCONJ
ejpam-4679	246	11	water	water	NOUN
ejpam-4679	246	12	content	content	NOUN
ejpam-4679	246	13	.	.	PUNCT
ejpam-4679	247	1	soil	soil	NOUN
ejpam-4679	247	2	science	science	PROPN
ejpam-4679	247	3	society	society	PROPN
ejpam-4679	247	4	of	of	ADP
ejpam-4679	247	5	america	america	PROPN
ejpam-4679	247	6	journal	journal	PROPN
ejpam-4679	247	7	,	,	PUNCT
ejpam-4679	247	8	56(2):335	56(2):335	PROPN
ejpam-4679	247	9	–	–	PUNCT
ejpam-4679	247	10	340	340	NUM
ejpam-4679	247	11	,	,	PUNCT
ejpam-4679	247	12	1992	1992	NUM
ejpam-4679	247	13	.	.	PUNCT
ejpam-4679	248	1	[	[	X
ejpam-4679	248	2	10	10	NUM
ejpam-4679	248	3	]	]	PUNCT
ejpam-4679	248	4	arieh	arieh	ADJ
ejpam-4679	248	5	iserles	iserle	NOUN
ejpam-4679	248	6	.	.	PUNCT
ejpam-4679	249	1	a	a	DET
ejpam-4679	249	2	first	first	ADJ
ejpam-4679	249	3	course	course	NOUN
ejpam-4679	249	4	in	in	ADP
ejpam-4679	249	5	the	the	DET
ejpam-4679	249	6	numerical	numerical	ADJ
ejpam-4679	249	7	analysis	analysis	NOUN
ejpam-4679	249	8	of	of	ADP
ejpam-4679	249	9	differential	differential	ADJ
ejpam-4679	249	10	equations	equation	NOUN
ejpam-4679	249	11	.	.	PUNCT
ejpam-4679	250	1	number	number	NOUN
ejpam-4679	250	2	44	44	NUM
ejpam-4679	250	3	.	.	PUNCT
ejpam-4679	251	1	cambridge	cambridge	PROPN
ejpam-4679	251	2	university	university	PROPN
ejpam-4679	251	3	press	press	NOUN
ejpam-4679	251	4	,	,	PUNCT
ejpam-4679	251	5	2009	2009	NUM
ejpam-4679	251	6	.	.	PUNCT
ejpam-4679	252	1	[	[	X
ejpam-4679	252	2	11	11	NUM
ejpam-4679	252	3	]	]	PUNCT
ejpam-4679	252	4	anatolĭı	anatolĭı	PROPN
ejpam-4679	252	5	aleksandrovich	aleksandrovich	PROPN
ejpam-4679	252	6	kilbas	kilbas	PROPN
ejpam-4679	252	7	,	,	PUNCT
ejpam-4679	252	8	hari	hari	PROPN
ejpam-4679	252	9	m	m	PROPN
ejpam-4679	252	10	srivastava	srivastava	PROPN
ejpam-4679	252	11	,	,	PUNCT
ejpam-4679	252	12	and	and	CCONJ
ejpam-4679	252	13	juan	juan	PROPN
ejpam-4679	252	14	j	j	PROPN
ejpam-4679	252	15	trujillo	trujillo	PROPN
ejpam-4679	252	16	.	.	PUNCT
ejpam-4679	252	17	theory	theory	NOUN
ejpam-4679	252	18	and	and	CCONJ
ejpam-4679	252	19	applications	application	NOUN
ejpam-4679	252	20	of	of	ADP
ejpam-4679	252	21	fractional	fractional	ADJ
ejpam-4679	252	22	differential	differential	ADJ
ejpam-4679	252	23	equations	equation	NOUN
ejpam-4679	252	24	,	,	PUNCT
ejpam-4679	252	25	volume	volume	NOUN
ejpam-4679	252	26	204	204	NUM
ejpam-4679	252	27	.	.	PUNCT
ejpam-4679	253	1	elsevier	elsevier	NOUN
ejpam-4679	253	2	,	,	PUNCT
ejpam-4679	253	3	2006	2006	NUM
ejpam-4679	253	4	.	.	PUNCT
ejpam-4679	254	1	[	[	X
ejpam-4679	254	2	12	12	NUM
ejpam-4679	254	3	]	]	X
ejpam-4679	254	4	j	j	PROPN
ejpam-4679	254	5	manimaran	manimaran	PROPN
ejpam-4679	254	6	,	,	PUNCT
ejpam-4679	254	7	l	l	PROPN
ejpam-4679	254	8	shangerganesh	shangerganesh	NOUN
ejpam-4679	254	9	,	,	PUNCT
ejpam-4679	254	10	a	a	DET
ejpam-4679	254	11	debbouche	debbouche	NOUN
ejpam-4679	254	12	,	,	PUNCT
ejpam-4679	254	13	and	and	CCONJ
ejpam-4679	254	14	j	j	PROPN
ejpam-4679	254	15	-	-	PROPN
ejpam-4679	254	16	c	c	PROPN
ejpam-4679	254	17	cortés	cortés	PROPN
ejpam-4679	254	18	.	.	PUNCT
ejpam-4679	255	1	a	a	DET
ejpam-4679	255	2	time	time	NOUN
ejpam-4679	255	3	-	-	PUNCT
ejpam-4679	255	4	fractional	fractional	ADJ
ejpam-4679	255	5	hiv	hiv	PROPN
ejpam-4679	255	6	infection	infection	NOUN
ejpam-4679	255	7	model	model	NOUN
ejpam-4679	255	8	with	with	ADP
ejpam-4679	255	9	nonlinear	nonlinear	ADJ
ejpam-4679	255	10	diffusion	diffusion	NOUN
ejpam-4679	255	11	.	.	PUNCT
ejpam-4679	256	1	results	result	NOUN
ejpam-4679	256	2	in	in	ADP
ejpam-4679	256	3	physics	physics	NOUN
ejpam-4679	256	4	,	,	PUNCT
ejpam-4679	256	5	25:104293	25:104293	NOUN
ejpam-4679	256	6	,	,	PUNCT
ejpam-4679	256	7	2021	2021	NUM
ejpam-4679	256	8	.	.	PUNCT
ejpam-4679	257	1	[	[	X
ejpam-4679	257	2	13	13	NUM
ejpam-4679	257	3	]	]	SYM
ejpam-4679	257	4	yakov	yakov	PROPN
ejpam-4679	257	5	pachepsky	pachepsky	PROPN
ejpam-4679	257	6	,	,	PUNCT
ejpam-4679	257	7	dennis	dennis	PROPN
ejpam-4679	257	8	timlin	timlin	PROPN
ejpam-4679	257	9	,	,	PUNCT
ejpam-4679	257	10	and	and	CCONJ
ejpam-4679	257	11	walter	walter	PROPN
ejpam-4679	257	12	rawls	rawl	VERB
ejpam-4679	257	13	.	.	PUNCT
ejpam-4679	258	1	generalized	generalized	ADJ
ejpam-4679	258	2	richards	richard	NOUN
ejpam-4679	258	3	’	'	PUNCT
ejpam-4679	258	4	equation	equation	NOUN
ejpam-4679	258	5	to	to	PART
ejpam-4679	258	6	simulate	simulate	VERB
ejpam-4679	258	7	water	water	NOUN
ejpam-4679	258	8	transport	transport	NOUN
ejpam-4679	258	9	in	in	ADP
ejpam-4679	258	10	unsaturated	unsaturated	ADJ
ejpam-4679	258	11	soils	soil	NOUN
ejpam-4679	258	12	.	.	PUNCT
ejpam-4679	259	1	journal	journal	NOUN
ejpam-4679	259	2	of	of	ADP
ejpam-4679	259	3	hydrology	hydrology	NOUN
ejpam-4679	259	4	,	,	PUNCT
ejpam-4679	259	5	272(1	272(1	NUM
ejpam-4679	259	6	-	-	SYM
ejpam-4679	259	7	4):3–13	4):3–13	NUM
ejpam-4679	259	8	,	,	PUNCT
ejpam-4679	259	9	2003	2003	NUM
ejpam-4679	259	10	.	.	PUNCT
ejpam-4679	260	1	references	reference	NOUN
ejpam-4679	260	2	502	502	NUM
ejpam-4679	261	1	[	[	X
ejpam-4679	261	2	14	14	NUM
ejpam-4679	261	3	]	]	SYM
ejpam-4679	261	4	yakov	yakov	PROPN
ejpam-4679	261	5	pachepsky	pachepsky	PROPN
ejpam-4679	261	6	,	,	PUNCT
ejpam-4679	261	7	dennis	dennis	PROPN
ejpam-4679	261	8	timlin	timlin	PROPN
ejpam-4679	261	9	,	,	PUNCT
ejpam-4679	261	10	and	and	CCONJ
ejpam-4679	261	11	walter	walter	PROPN
ejpam-4679	261	12	rawls	rawl	VERB
ejpam-4679	261	13	.	.	PUNCT
ejpam-4679	262	1	generalized	generalized	ADJ
ejpam-4679	262	2	richards	richard	NOUN
ejpam-4679	262	3	’	'	PUNCT
ejpam-4679	262	4	equation	equation	NOUN
ejpam-4679	262	5	to	to	PART
ejpam-4679	262	6	simulate	simulate	VERB
ejpam-4679	262	7	water	water	NOUN
ejpam-4679	262	8	transport	transport	NOUN
ejpam-4679	262	9	in	in	ADP
ejpam-4679	262	10	unsaturated	unsaturated	ADJ
ejpam-4679	262	11	soils	soil	NOUN
ejpam-4679	262	12	.	.	PUNCT
ejpam-4679	263	1	journal	journal	NOUN
ejpam-4679	263	2	of	of	ADP
ejpam-4679	263	3	hydrology	hydrology	NOUN
ejpam-4679	263	4	,	,	PUNCT
ejpam-4679	263	5	272(1	272(1	NUM
ejpam-4679	263	6	-	-	SYM
ejpam-4679	263	7	4):3–13	4):3–13	NUM
ejpam-4679	263	8	,	,	PUNCT
ejpam-4679	263	9	2003	2003	NUM
ejpam-4679	263	10	.	.	PUNCT
ejpam-4679	264	1	[	[	X
ejpam-4679	264	2	15	15	NUM
ejpam-4679	264	3	]	]	X
ejpam-4679	264	4	burhan	burhan	PROPN
ejpam-4679	264	5	pektaş	pektaş	PROPN
ejpam-4679	264	6	and	and	CCONJ
ejpam-4679	264	7	ege	ege	PROPN
ejpam-4679	264	8	tamci	tamci	NOUN
ejpam-4679	264	9	.	.	PUNCT
ejpam-4679	265	1	the	the	DET
ejpam-4679	265	2	heat	heat	NOUN
ejpam-4679	265	3	flux	flux	NOUN
ejpam-4679	265	4	identification	identification	NOUN
ejpam-4679	265	5	problem	problem	NOUN
ejpam-4679	265	6	for	for	ADP
ejpam-4679	265	7	a	a	DET
ejpam-4679	265	8	nonlinear	nonlinear	ADJ
ejpam-4679	265	9	parabolic	parabolic	ADJ
ejpam-4679	265	10	equation	equation	NOUN
ejpam-4679	265	11	in	in	ADP
ejpam-4679	265	12	2d	2d	NOUN
ejpam-4679	265	13	.	.	PUNCT
ejpam-4679	266	1	journal	journal	NOUN
ejpam-4679	266	2	of	of	ADP
ejpam-4679	266	3	computational	computational	ADJ
ejpam-4679	266	4	and	and	CCONJ
ejpam-4679	266	5	applied	applied	ADJ
ejpam-4679	266	6	mathematics	mathematic	NOUN
ejpam-4679	266	7	,	,	PUNCT
ejpam-4679	266	8	312:134–142	312:134–142	NUM
ejpam-4679	266	9	,	,	PUNCT
ejpam-4679	266	10	2017	2017	NUM
ejpam-4679	266	11	.	.	PUNCT
ejpam-4679	267	1	[	[	X
ejpam-4679	267	2	16	16	NUM
ejpam-4679	267	3	]	]	X
ejpam-4679	267	4	lukasz	lukasz	PROPN
ejpam-4679	267	5	p	p	PROPN
ejpam-4679	267	6	lociniczak	lociniczak	NOUN
ejpam-4679	267	7	.	.	PUNCT
ejpam-4679	268	1	analytical	analytical	ADJ
ejpam-4679	268	2	studies	study	NOUN
ejpam-4679	268	3	of	of	ADP
ejpam-4679	268	4	a	a	DET
ejpam-4679	268	5	time	time	NOUN
ejpam-4679	268	6	-	-	PUNCT
ejpam-4679	268	7	fractional	fractional	ADJ
ejpam-4679	268	8	porous	porous	ADJ
ejpam-4679	268	9	medium	medium	NOUN
ejpam-4679	268	10	equation	equation	NOUN
ejpam-4679	268	11	.	.	PUNCT
ejpam-4679	269	1	derivation	derivation	NOUN
ejpam-4679	269	2	,	,	PUNCT
ejpam-4679	269	3	approximation	approximation	NOUN
ejpam-4679	269	4	and	and	CCONJ
ejpam-4679	269	5	applications	application	NOUN
ejpam-4679	269	6	.	.	PUNCT
ejpam-4679	270	1	communications	communication	NOUN
ejpam-4679	270	2	in	in	ADP
ejpam-4679	270	3	nonlinear	nonlinear	ADJ
ejpam-4679	270	4	science	science	NOUN
ejpam-4679	270	5	and	and	CCONJ
ejpam-4679	270	6	numerical	numerical	PROPN
ejpam-4679	270	7	simulation	simulation	PROPN
ejpam-4679	270	8	,	,	PUNCT
ejpam-4679	270	9	24(1	24(1	NUM
ejpam-4679	270	10	-	-	SYM
ejpam-4679	270	11	3):169–183	3):169–183	NUM
ejpam-4679	270	12	,	,	PUNCT
ejpam-4679	270	13	2015	2015	NUM
ejpam-4679	270	14	.	.	PUNCT
ejpam-4679	271	1	[	[	X
ejpam-4679	271	2	17	17	NUM
ejpam-4679	271	3	]	]	X
ejpam-4679	271	4	i	i	PRON
ejpam-4679	271	5	podlubnv	podlubnv	PROPN
ejpam-4679	271	6	.	.	PUNCT
ejpam-4679	272	1	fractional	fractional	ADJ
ejpam-4679	272	2	differential	differential	ADJ
ejpam-4679	272	3	equations	equation	NOUN
ejpam-4679	272	4	academic	academic	ADJ
ejpam-4679	272	5	press	press	NOUN
ejpam-4679	272	6	.	.	PUNCT
ejpam-4679	273	1	san	san	PROPN
ejpam-4679	273	2	diego	diego	PROPN
ejpam-4679	273	3	,	,	PUNCT
ejpam-4679	273	4	boston	boston	PROPN
ejpam-4679	273	5	,	,	PUNCT
ejpam-4679	273	6	6	6	NUM
ejpam-4679	273	7	,	,	PUNCT
ejpam-4679	273	8	1999	1999	NUM
ejpam-4679	273	9	.	.	PUNCT
ejpam-4679	274	1	[	[	X
ejpam-4679	274	2	18	18	NUM
ejpam-4679	274	3	]	]	PUNCT
ejpam-4679	274	4	igor	igor	NOUN
ejpam-4679	274	5	podlubny	podlubny	PROPN
ejpam-4679	274	6	.	.	PUNCT
ejpam-4679	274	7	matrix	matrix	NOUN
ejpam-4679	274	8	approach	approach	NOUN
ejpam-4679	274	9	to	to	PART
ejpam-4679	274	10	discrete	discrete	VERB
ejpam-4679	274	11	fractional	fractional	ADJ
ejpam-4679	274	12	calculus	calculus	NOUN
ejpam-4679	274	13	.	.	PUNCT
ejpam-4679	275	1	fractional	fractional	ADJ
ejpam-4679	275	2	calculus	calculus	NOUN
ejpam-4679	275	3	and	and	CCONJ
ejpam-4679	275	4	applied	apply	VERB
ejpam-4679	275	5	analysis	analysis	NOUN
ejpam-4679	275	6	,	,	PUNCT
ejpam-4679	275	7	3(4):359–386	3(4):359–386	NUM
ejpam-4679	275	8	,	,	PUNCT
ejpam-4679	275	9	2000	2000	NUM
ejpam-4679	275	10	.	.	PUNCT
ejpam-4679	276	1	[	[	X
ejpam-4679	276	2	19	19	NUM
ejpam-4679	276	3	]	]	X
ejpam-4679	276	4	igor	igor	NOUN
ejpam-4679	276	5	podlubny	podlubny	PROPN
ejpam-4679	276	6	,	,	PUNCT
ejpam-4679	276	7	aleksei	aleksei	ADJ
ejpam-4679	276	8	chechkin	chechkin	NOUN
ejpam-4679	276	9	,	,	PUNCT
ejpam-4679	276	10	tomas	toma	NOUN
ejpam-4679	276	11	skovranek	skovranek	VERB
ejpam-4679	276	12	,	,	PUNCT
ejpam-4679	276	13	yangquan	yangquan	PROPN
ejpam-4679	276	14	chen	chen	PROPN
ejpam-4679	276	15	,	,	PUNCT
ejpam-4679	276	16	and	and	CCONJ
ejpam-4679	276	17	blas	blas	PROPN
ejpam-4679	276	18	m	m	PROPN
ejpam-4679	276	19	vinagre	vinagre	PROPN
ejpam-4679	276	20	jara	jara	PROPN
ejpam-4679	276	21	.	.	PUNCT
ejpam-4679	276	22	matrix	matrix	NOUN
ejpam-4679	276	23	approach	approach	NOUN
ejpam-4679	276	24	to	to	PART
ejpam-4679	276	25	discrete	discrete	VERB
ejpam-4679	276	26	fractional	fractional	ADJ
ejpam-4679	276	27	calculus	calculus	NOUN
ejpam-4679	276	28	ii	ii	PROPN
ejpam-4679	276	29	:	:	PUNCT
ejpam-4679	276	30	partial	partial	ADJ
ejpam-4679	276	31	fractional	fractional	ADJ
ejpam-4679	276	32	differential	differential	ADJ
ejpam-4679	276	33	equations	equation	NOUN
ejpam-4679	276	34	.	.	PUNCT
ejpam-4679	277	1	journal	journal	NOUN
ejpam-4679	277	2	of	of	ADP
ejpam-4679	277	3	computational	computational	ADJ
ejpam-4679	277	4	physics	physic	NOUN
ejpam-4679	277	5	,	,	PUNCT
ejpam-4679	277	6	228(8):3137–3153	228(8):3137–3153	NUM
ejpam-4679	277	7	,	,	PUNCT
ejpam-4679	277	8	2009	2009	NUM
ejpam-4679	277	9	.	.	PUNCT
ejpam-4679	278	1	[	[	X
ejpam-4679	278	2	20	20	NUM
ejpam-4679	278	3	]	]	SYM
ejpam-4679	278	4	shujun	shujun	PROPN
ejpam-4679	278	5	shen	shen	PROPN
ejpam-4679	278	6	,	,	PUNCT
ejpam-4679	278	7	fawang	fawang	PROPN
ejpam-4679	278	8	liu	liu	PROPN
ejpam-4679	278	9	,	,	PUNCT
ejpam-4679	278	10	q	q	PROPN
ejpam-4679	278	11	liu	liu	PROPN
ejpam-4679	278	12	,	,	PUNCT
ejpam-4679	278	13	and	and	CCONJ
ejpam-4679	278	14	vo	vo	PROPN
ejpam-4679	278	15	anh	anh	PROPN
ejpam-4679	278	16	.	.	PUNCT
ejpam-4679	279	1	numerical	numerical	PROPN
ejpam-4679	279	2	simulation	simulation	PROPN
ejpam-4679	279	3	of	of	ADP
ejpam-4679	279	4	anomalous	anomalous	ADJ
ejpam-4679	279	5	infiltration	infiltration	NOUN
ejpam-4679	279	6	in	in	ADP
ejpam-4679	279	7	porous	porous	ADJ
ejpam-4679	279	8	media	medium	NOUN
ejpam-4679	279	9	.	.	PUNCT
ejpam-4679	280	1	numerical	numerical	ADJ
ejpam-4679	280	2	algorithms	algorithms	PROPN
ejpam-4679	280	3	,	,	PUNCT
ejpam-4679	280	4	68(3):443–454	68(3):443–454	NOUN
ejpam-4679	280	5	,	,	PUNCT
ejpam-4679	280	6	2015	2015	NUM
ejpam-4679	280	7	.	.	PUNCT
ejpam-4679	281	1	[	[	X
ejpam-4679	281	2	21	21	NUM
ejpam-4679	281	3	]	]	X
ejpam-4679	281	4	salih	salih	PROPN
ejpam-4679	281	5	tatar	tatar	PROPN
ejpam-4679	281	6	,	,	PUNCT
ejpam-4679	281	7	ramazan	ramazan	PROPN
ejpam-4679	281	8	tnaztepe	tnaztepe	VERB
ejpam-4679	281	9	,	,	PUNCT
ejpam-4679	281	10	and	and	CCONJ
ejpam-4679	281	11	mustafa	mustafa	PROPN
ejpam-4679	281	12	zeki	zeki	PROPN
ejpam-4679	281	13	.	.	PUNCT
ejpam-4679	282	1	numerical	numerical	ADJ
ejpam-4679	282	2	solutions	solution	NOUN
ejpam-4679	282	3	of	of	ADP
ejpam-4679	282	4	direct	direct	ADJ
ejpam-4679	282	5	and	and	CCONJ
ejpam-4679	282	6	inverse	inverse	NOUN
ejpam-4679	282	7	problems	problem	NOUN
ejpam-4679	282	8	for	for	ADP
ejpam-4679	282	9	a	a	DET
ejpam-4679	282	10	time	time	NOUN
ejpam-4679	282	11	fractional	fractional	ADJ
ejpam-4679	282	12	viscoelastoplastic	viscoelastoplastic	ADJ
ejpam-4679	282	13	equation	equation	NOUN
ejpam-4679	282	14	.	.	PUNCT
ejpam-4679	283	1	journal	journal	NOUN
ejpam-4679	283	2	of	of	ADP
ejpam-4679	283	3	engineering	engineering	NOUN
ejpam-4679	283	4	mechanics	mechanic	NOUN
ejpam-4679	283	5	,	,	PUNCT
ejpam-4679	283	6	143(7):04017035	143(7):04017035	NUM
ejpam-4679	283	7	,	,	PUNCT
ejpam-4679	283	8	2017	2017	NUM
ejpam-4679	283	9	.	.	PUNCT
ejpam-4679	284	1	[	[	X
ejpam-4679	284	2	22	22	NUM
ejpam-4679	284	3	]	]	X
ejpam-4679	284	4	salih	salih	PROPN
ejpam-4679	284	5	tatar	tatar	PROPN
ejpam-4679	284	6	and	and	CCONJ
ejpam-4679	284	7	süleyman	süleyman	ADJ
ejpam-4679	284	8	ulusoy	ulusoy	NOUN
ejpam-4679	284	9	.	.	PUNCT
ejpam-4679	285	1	an	an	DET
ejpam-4679	285	2	inverse	inverse	ADJ
ejpam-4679	285	3	problem	problem	NOUN
ejpam-4679	285	4	for	for	ADP
ejpam-4679	285	5	a	a	DET
ejpam-4679	285	6	nonlinear	nonlinear	ADJ
ejpam-4679	285	7	diffusion	diffusion	NOUN
ejpam-4679	285	8	equation	equation	NOUN
ejpam-4679	285	9	with	with	ADP
ejpam-4679	285	10	time	time	NOUN
ejpam-4679	285	11	-	-	PUNCT
ejpam-4679	285	12	fractional	fractional	ADJ
ejpam-4679	285	13	derivative	derivative	NOUN
ejpam-4679	285	14	.	.	PUNCT
ejpam-4679	286	1	journal	journal	PROPN
ejpam-4679	286	2	of	of	ADP
ejpam-4679	286	3	inverse	inverse	NOUN
ejpam-4679	286	4	and	and	CCONJ
ejpam-4679	286	5	ill	ill	ADV
ejpam-4679	286	6	-	-	PUNCT
ejpam-4679	286	7	posed	pose	VERB
ejpam-4679	286	8	problems	problem	NOUN
ejpam-4679	286	9	,	,	PUNCT
ejpam-4679	286	10	25(2):185–193	25(2):185–193	NUM
ejpam-4679	286	11	,	,	PUNCT
ejpam-4679	286	12	2017	2017	NUM
ejpam-4679	286	13	.	.	PUNCT