id	sid	tid	token	lemma	pos
iajs-881	1	1	ibn	ibn	PROPN
iajs-881	1	2	alhaitham	alhaitham	NOUN
iajs-881	1	3	j.	j.	PROPN
iajs-881	2	1	fo	fo	ADP
iajs-881	2	2	r	r	NOUN
iajs-881	2	3	pure	pure	ADJ
iajs-881	2	4	&	&	CCONJ
iajs-881	2	5	appl	appl	PROPN
iajs-881	2	6	.	.	PUNCT
iajs-881	3	1	sc	sc	PROPN
iajs-881	3	2	i.	i.	PROPN
iajs-881	3	3	vo	vo	PROPN
iajs-881	3	4	l.23	l.23	PROPN
iajs-881	3	5	(	(	PUNCT
iajs-881	3	6	3	3	NUM
iajs-881	3	7	)	)	PUNCT
iajs-881	3	8	2010	2010	NUM
iajs-881	3	9	finite	finite	ADJ
iajs-881	3	10	difference	difference	NOUN
iajs-881	3	11	method	method	NOUN
iajs-881	3	12	for	for	ADP
iajs-881	3	13	solving	solve	VERB
iajs-881	3	14	fractional	fractional	ADJ
iajs-881	3	15	hyperbolic	hyperbolic	ADJ
iajs-881	3	16	partial	partial	ADJ
iajs-881	3	17	differential	differential	NOUN
iajs-881	3	18	equations	equation	NOUN
iajs-881	3	19	g.	g.	PROPN
iajs-881	3	20	j.	j.	PROPN
iajs-881	3	21	mohammed	mohammed	PROPN
iajs-881	3	22	department	department	PROPN
iajs-881	3	23	of	of	ADP
iajs-881	3	24	mathematics	mathematics	PROPN
iajs-881	3	25	,	,	PUNCT
iajs-881	3	26	college	college	NOUN
iajs-881	3	27	of	of	ADP
iajs-881	3	28	education	education	NOUN
iajs-881	3	29	-ibn	-ibn	PUNCT
iajs-881	3	30	alhaitham	alhaitham	PROPN
iajs-881	3	31	,	,	PUNCT
iajs-881	3	32	baghdad	baghdad	PROPN
iajs-881	3	33	university	university	PROPN
iajs-881	3	34	.	.	PUNCT
iajs-881	4	1	abstract	abstract	ADJ
iajs-881	4	2	in	in	ADP
iajs-881	4	3	this	this	DET
iajs-881	4	4	paper	paper	NOUN
iajs-881	4	5	,	,	PUNCT
iajs-881	4	6	the	the	DET
iajs-881	4	7	finite	finite	ADJ
iajs-881	4	8	difference	difference	NOUN
iajs-881	4	9	method	method	NOUN
iajs-881	4	10	is	be	AUX
iajs-881	4	11	used	use	VERB
iajs-881	4	12	to	to	PART
iajs-881	4	13	solve	solve	VERB
iajs-881	4	14	fractional	fractional	ADJ
iajs-881	4	15	hyperbolic	hyperbolic	ADJ
iajs-881	4	16	partial	partial	ADJ
iajs-881	4	17	differential	differential	NOUN
iajs-881	4	18	equations	equation	NOUN
iajs-881	4	19	,	,	PUNCT
iajs-881	4	20	by	by	ADP
iajs-881	4	21	modifying	modify	VERB
iajs-881	4	22	the	the	DET
iajs-881	4	23	associated	associated	ADJ
iajs-881	4	24	explicit	explicit	ADJ
iajs-881	4	25	and	and	CCONJ
iajs-881	4	26	implicit	implicit	ADJ
iajs-881	4	27	difference	difference	NOUN
iajs-881	4	28	methods	method	NOUN
iajs-881	4	29	used	use	VERB
iajs-881	4	30	to	to	PART
iajs-881	4	31	solve	solve	VERB
iajs-881	4	32	fractional	fractional	ADJ
iajs-881	4	33	partial	partial	ADJ
iajs-881	4	34	differential	differential	NOUN
iajs-881	4	35	equation	equation	NOUN
iajs-881	4	36	.	.	PUNCT
iajs-881	5	1	a	a	DET
iajs-881	5	2	comparison	comparison	NOUN
iajs-881	5	3	with	with	ADP
iajs-881	5	4	the	the	DET
iajs-881	5	5	exact	exact	ADJ
iajs-881	5	6	solution	solution	NOUN
iajs-881	5	7	is	be	AUX
iajs-881	5	8	presented	present	VERB
iajs-881	5	9	and	and	CCONJ
iajs-881	5	10	the	the	DET
iajs-881	5	11	results	result	NOUN
iajs-881	5	12	are	be	AUX
iajs-881	5	13	given	give	VERB
iajs-881	5	14	in	in	ADP
iajs-881	5	15	tabulated	tabulate	VERB
iajs-881	5	16	form	form	NOUN
iajs-881	5	17	in	in	ADP
iajs-881	5	18	order	order	NOUN
iajs-881	5	19	to	to	PART
iajs-881	5	20	give	give	VERB
iajs-881	5	21	a	a	DET
iajs-881	5	22	good	good	ADJ
iajs-881	5	23	comparison	comparison	NOUN
iajs-881	5	24	with	with	ADP
iajs-881	5	25	the	the	DET
iajs-881	5	26	exact	exact	ADJ
iajs-881	5	27	solution	solution	NOUN
iajs-881	5	28	.	.	PUNCT
iajs-881	6	1	introduction	introduction	NOUN
iajs-881	6	2	an	an	DET
iajs-881	6	3	important	important	ADJ
iajs-881	6	4	type	type	NOUN
iajs-881	6	5	of	of	ADP
iajs-881	6	6	differential	differential	ADJ
iajs-881	6	7	equations	equation	NOUN
iajs-881	6	8	which	which	PRON
iajs-881	6	9	is	be	AUX
iajs-881	6	10	called	call	VERB
iajs-881	6	11	fractional	fractional	ADJ
iajs-881	6	12	differential	differential	ADJ
iajs-881	6	13	equations	equation	NOUN
iajs-881	6	14	in	in	ADP
iajs-881	6	15	which	which	PRON
iajs-881	6	16	the	the	DET
iajs-881	6	17	differintegration	differintegration	NOUN
iajs-881	6	18	is	be	AUX
iajs-881	6	19	of	of	ADP
iajs-881	6	20	non	non	ADJ
iajs-881	6	21	-	-	ADJ
iajs-881	6	22	integer	integer	ADJ
iajs-881	6	23	order	order	NOUN
iajs-881	7	1	[	[	X
iajs-881	7	2	1	1	NUM
iajs-881	7	3	]	]	PUNCT
iajs-881	7	4	.	.	PUNCT
iajs-881	8	1	real	real	ADJ
iajs-881	8	2	life	life	NOUN
iajs-881	8	3	problems	problem	NOUN
iajs-881	8	4	with	with	ADP
iajs-881	8	5	fractional	fractional	ADJ
iajs-881	8	6	differential	differential	ADJ
iajs-881	8	7	equations	equation	NOUN
iajs-881	8	8	are	be	AUX
iajs-881	8	9	of	of	ADP
iajs-881	8	10	great	great	ADJ
iajs-881	8	11	importance	importance	NOUN
iajs-881	8	12	,	,	PUNCT
iajs-881	8	13	since	since	SCONJ
iajs-881	8	14	fractional	fractional	ADJ
iajs-881	8	15	differential	differential	ADJ
iajs-881	8	16	equations	equation	NOUN
iajs-881	8	17	accumulate	accumulate	VERB
iajs-881	8	18	the	the	DET
iajs-881	8	19	whole	whole	ADJ
iajs-881	8	20	information	information	NOUN
iajs-881	8	21	of	of	ADP
iajs-881	8	22	the	the	DET
iajs-881	8	23	function	function	NOUN
iajs-881	8	24	in	in	ADP
iajs-881	8	25	a	a	DET
iajs-881	8	26	weighted	weight	VERB
iajs-881	8	27	form	form	NOUN
iajs-881	8	28	.	.	PUNCT
iajs-881	9	1	this	this	PRON
iajs-881	9	2	has	have	VERB
iajs-881	9	3	many	many	ADJ
iajs-881	9	4	applications	application	NOUN
iajs-881	9	5	in	in	ADP
iajs-881	9	6	physics	physics	NOUN
iajs-881	9	7	,	,	PUNCT
iajs-881	9	8	chemistry	chemistry	NOUN
iajs-881	9	9	,	,	PUNCT
iajs-881	9	10	engineering	engineering	NOUN
iajs-881	9	11	,	,	PUNCT
iajs-881	9	12	etc	etc	X
iajs-881	9	13	.	.	X
iajs-881	9	14	for	for	ADP
iajs-881	9	15	that	that	DET
iajs-881	9	16	reason	reason	NOUN
iajs-881	9	17	,	,	PUNCT
iajs-881	9	18	we	we	PRON
iajs-881	9	19	need	need	VERB
iajs-881	9	20	a	a	DET
iajs-881	9	21	method	method	NOUN
iajs-881	9	22	for	for	ADP
iajs-881	9	23	solving	solve	VERB
iajs-881	9	24	such	such	ADJ
iajs-881	9	25	equations	equation	NOUN
iajs-881	9	26	,	,	PUNCT
iajs-881	9	27	effectively	effectively	ADV
iajs-881	9	28	,	,	PUNCT
iajs-881	9	29	easy	easy	ADJ
iajs-881	9	30	use	use	NOUN
iajs-881	9	31	and	and	CCONJ
iajs-881	9	32	applied	apply	VERB
iajs-881	9	33	for	for	ADP
iajs-881	9	34	different	different	ADJ
iajs-881	9	35	p	p	NOUN
iajs-881	9	36	roblems[2	roblems[2	NOUN
iajs-881	9	37	]	]	PUNCT
iajs-881	9	38	.	.	PUNCT
iajs-881	10	1	consider	consider	VERB
iajs-881	10	2	the	the	DET
iajs-881	10	3	fractional	fractional	ADJ
iajs-881	10	4	order	order	NOUN
iajs-881	10	5	partial	partial	ADJ
iajs-881	10	6	differential	differential	NOUN
iajs-881	10	7	equation	equation	NOUN
iajs-881	11	1	[	[	X
iajs-881	11	2	3][4	3][4	NUM
iajs-881	11	3	]	]	X
iajs-881	11	4	:	:	PUNCT
iajs-881	11	5	2	2	NUM
iajs-881	11	6	2	2	NUM
iajs-881	11	7	u(x	u(x	NOUN
iajs-881	11	8	,	,	PUNCT
iajs-881	11	9	t	t	PROPN
iajs-881	11	10	)	)	PUNCT
iajs-881	11	11	t	t	PROPN
iajs-881	11	12			PROPN
iajs-881	11	13			PROPN
iajs-881	11	14	c(x	c(x	NOUN
iajs-881	11	15	,	,	PUNCT
iajs-881	11	16	t	t	PROPN
iajs-881	11	17	)	)	PUNCT
iajs-881	11	18	q	q	NOUN
iajs-881	11	19	q	q	X
iajs-881	11	20	u(x	u(x	PROPN
iajs-881	11	21	,	,	PUNCT
iajs-881	11	22	t	t	PROPN
iajs-881	11	23	)	)	PUNCT
iajs-881	11	24	x	x	SYM
iajs-881	11	25			ADJ
iajs-881	11	26			PROPN
iajs-881	11	27	+	+	SYM
iajs-881	11	28	s(x	s(x	PROPN
iajs-881	11	29	,	,	PUNCT
iajs-881	11	30	t	t	PROPN
iajs-881	11	31	)	)	PUNCT
iajs-881	11	32	,	,	PUNCT
iajs-881	11	33	l	l	NOUN
iajs-881	11	34			NUM
iajs-881	11	35	x	x	SYM
iajs-881	11	36			NUM
iajs-881	11	37	r	r	NOUN
iajs-881	11	38	,	,	PUNCT
iajs-881	11	39	0	0	NUM
iajs-881	11	40			NOUN
iajs-881	11	41	t	t	NOUN
iajs-881	11	42			NUM
iajs-881	11	43	t	t	NOUN
iajs-881	11	44	..............	..............	PUNCT
iajs-881	12	1	(	(	PUNCT
iajs-881	12	2	1	1	X
iajs-881	12	3	)	)	PUNCT
iajs-881	12	4	together	together	ADV
iajs-881	12	5	with	with	ADP
iajs-881	12	6	the	the	DET
iajs-881	12	7	initial	initial	ADJ
iajs-881	12	8	and	and	CCONJ
iajs-881	12	9	zero	zero	NUM
iajs-881	12	10	dirichlet	dirichlet	PROPN
iajs-881	12	11	boundary	boundary	ADJ
iajs-881	12	12	conditions	condition	NOUN
iajs-881	12	13	:	:	PUNCT
iajs-881	12	14	tu(x,0	tu(x,0	VERB
iajs-881	12	15	)	)	PUNCT
iajs-881	13	1	f	f	PROPN
iajs-881	13	2	(	(	PUNCT
iajs-881	13	3	x	x	X
iajs-881	13	4	)	)	PUNCT
iajs-881	13	5	,	,	PUNCT
iajs-881	13	6	u	u	PROPN
iajs-881	13	7	(	(	PUNCT
iajs-881	13	8	x,0)=h(x	x,0)=h(x	PROPN
iajs-881	13	9	)	)	PUNCT
iajs-881	13	10	,	,	PUNCT
iajs-881	14	1	l	l	NOUN
iajs-881	14	2	x	x	PUNCT
iajs-881	14	3	r	r	VERB
iajs-881	14	4	u(l	u(l	NOUN
iajs-881	14	5	,	,	PUNCT
iajs-881	14	6	t	t	PROPN
iajs-881	14	7	)	)	PUNCT
iajs-881	14	8	0	0	NUM
iajs-881	14	9	,	,	PUNCT
iajs-881	14	10	u(r	u(r	PROPN
iajs-881	14	11	,	,	PUNCT
iajs-881	14	12	t	t	PROPN
iajs-881	14	13	)	)	PUNCT
iajs-881	14	14	0	0	PUNCT
iajs-881	15	1	for	for	ADP
iajs-881	15	2	0	0	NUM
iajs-881	15	3	t	t	NOUN
iajs-881	15	4	t	t	PROPN
iajs-881	15	5			PROPN
iajs-881	15	6			NOUN
iajs-881	15	7			NOUN
iajs-881	16	1			X
iajs-881	16	2			INTJ
iajs-881	17	1			NUM
iajs-881	17	2			NUM
iajs-881	17	3			NUM
iajs-881	17	4			NUM
iajs-881	17	5			NUM
iajs-881	17	6	.	.	PUNCT
iajs-881	18	1	…	…	PUNCT
iajs-881	18	2	……	……	NOUN
iajs-881	18	3	.	.	PUNCT
iajs-881	19	1	(	(	PUNCT
iajs-881	19	2	2	2	X
iajs-881	19	3	)	)	PUNCT
iajs-881	19	4	where	where	SCONJ
iajs-881	19	5	q	q	PRON
iajs-881	19	6	q	q	X
iajs-881	19	7	u(x	u(x	PROPN
iajs-881	19	8	,	,	PUNCT
iajs-881	19	9	t	t	PROPN
iajs-881	19	10	)	)	PUNCT
iajs-881	19	11	x	x	SYM
iajs-881	19	12			ADJ
iajs-881	19	13			PROPN
iajs-881	19	14	denote	denote	VERB
iajs-881	19	15	the	the	DET
iajs-881	19	16	left	left	ADJ
iajs-881	19	17	-	-	PUNCT
iajs-881	19	18	hand	hand	NOUN
iajs-881	19	19	partial	partial	ADJ
iajs-881	19	20	fractional	fractional	ADJ
iajs-881	19	21	derivative	derivative	NOUN
iajs-881	19	22	of	of	ADP
iajs-881	19	23	order	order	NOUN
iajs-881	19	24	q	q	NOUN
iajs-881	19	25	of	of	ADP
iajs-881	19	26	the	the	DET
iajs-881	19	27	function	function	NOUN
iajs-881	19	28	u	u	NOUN
iajs-881	19	29	with	with	ADP
iajs-881	19	30	respect	respect	NOUN
iajs-881	19	31	to	to	ADP
iajs-881	19	32	x	x	PUNCT
iajs-881	19	33	and	and	CCONJ
iajs-881	19	34	1	1	NUM
iajs-881	19	35	<	<	X
iajs-881	19	36	q	q	PROPN
iajs-881	19	37			NUM
iajs-881	19	38	2	2	NUM
iajs-881	19	39	.	.	PUNCT
iajs-881	20	1	the	the	DET
iajs-881	20	2	left	left	ADV
iajs-881	20	3	-	-	PUNCT
iajs-881	20	4	handed	hand	VERB
iajs-881	20	5	shifted	shift	VERB
iajs-881	20	6	and	and	CCONJ
iajs-881	20	7	the	the	DET
iajs-881	20	8	right	right	ADV
iajs-881	20	9	-	-	PUNCT
iajs-881	20	10	handed	handed	ADJ
iajs-881	20	11	shifted	shift	VERB
iajs-881	20	12	grünwald	grünwald	NOUN
iajs-881	20	13	estimate	estimate	NOUN
iajs-881	20	14	to	to	ADP
iajs-881	20	15	the	the	DET
iajs-881	20	16	lefthanded	lefthanded	ADJ
iajs-881	20	17	and	and	CCONJ
iajs-881	20	18	right	right	ADV
iajs-881	20	19	-	-	PUNCT
iajs-881	20	20	handed	hand	VERB
iajs-881	20	21	derivatives	derivative	NOUN
iajs-881	20	22	,	,	PUNCT
iajs-881	20	23	are	be	AUX
iajs-881	20	24	given	give	VERB
iajs-881	20	25	by	by	ADP
iajs-881	20	26	[	[	X
iajs-881	20	27	1][5][6	1][5][6	NUM
iajs-881	20	28	]	]	X
iajs-881	20	29	:	:	PUNCT
iajs-881	20	30	q	q	PUNCT
iajs-881	20	31	q	q	X
iajs-881	21	1	d	d	X
iajs-881	21	2	f	f	X
iajs-881	21	3	(	(	PUNCT
iajs-881	21	4	x	x	NOUN
iajs-881	21	5	)	)	PUNCT
iajs-881	21	6	d	d	NOUN
iajs-881	21	7	x	x	NOUN
iajs-881	21	8			NOUN
iajs-881	21	9	q	q	NOUN
iajs-881	21	10	1	1	NUM
iajs-881	21	11	(	(	PUNCT
iajs-881	21	12	x)	x)	PROPN
iajs-881	21	13	n	n	X
iajs-881	21	14	k	k	X
iajs-881	21	15	0	0	X
iajs-881	21	16			X
iajs-881	21	17	gkf(x	gkf(x	PROPN
iajs-881	21	18			PROPN
iajs-881	21	19	(	(	PUNCT
iajs-881	21	20	k	k	PROPN
iajs-881	21	21			PROPN
iajs-881	21	22	1)x	1)x	NUM
iajs-881	21	23	)	)	PUNCT
iajs-881	21	24	ihjpas	ihjpa	VERB
iajs-881	21	25	ibn	ibn	PROPN
iajs-881	21	26	alhaitham	alhaitham	PROPN
iajs-881	22	1	j.	j.	PROPN
iajs-881	23	1	fo	fo	ADP
iajs-881	23	2	r	r	NOUN
iajs-881	23	3	pure	pure	ADJ
iajs-881	23	4	&	&	CCONJ
iajs-881	23	5	appl	appl	PROPN
iajs-881	23	6	.	.	PUNCT
iajs-881	24	1	sc	sc	PROPN
iajs-881	24	2	i.	i.	PROPN
iajs-881	24	3	vo	vo	PROPN
iajs-881	25	1	l.23	l.23	PROPN
iajs-881	25	2	(	(	PUNCT
iajs-881	25	3	3	3	NUM
iajs-881	25	4	)	)	PUNCT
iajs-881	25	5	2010	2010	NUM
iajs-881	25	6	q	q	NOUN
iajs-881	25	7	q	q	X
iajs-881	25	8	d	d	X
iajs-881	25	9	f	f	X
iajs-881	25	10	(	(	PUNCT
iajs-881	25	11	x	x	X
iajs-881	25	12	)	)	PUNCT
iajs-881	25	13	d	d	PROPN
iajs-881	25	14	x	x	PROPN
iajs-881	25	15			PROPN
iajs-881	25	16	q	q	PROPN
iajs-881	25	17	1	1	NUM
iajs-881	25	18	(	(	PUNCT
iajs-881	25	19	x)	x)	PROPN
iajs-881	25	20	n	n	X
iajs-881	25	21	k	k	X
iajs-881	25	22	0	0	X
iajs-881	25	23			X
iajs-881	25	24	gkf(x	gkf(x	NOUN
iajs-881	25	25	+	+	CCONJ
iajs-881	25	26	(	(	PUNCT
iajs-881	25	27	k	k	X
iajs-881	25	28			PROPN
iajs-881	25	29	1	1	NUM
iajs-881	25	30	)	)	PUNCT
iajs-881	25	31	x	x	ADJ
iajs-881	25	32	)	)	PUNCT
iajs-881	25	33	where	where	SCONJ
iajs-881	25	34	n	n	PRON
iajs-881	25	35	is	be	AUX
iajs-881	25	36	the	the	DET
iajs-881	25	37	number	number	NOUN
iajs-881	25	38	of	of	ADP
iajs-881	25	39	subdivisions	subdivision	NOUN
iajs-881	25	40	of	of	ADP
iajs-881	25	41	the	the	DET
iajs-881	25	42	interval	interval	NOUN
iajs-881	25	43	[	[	PUNCT
iajs-881	25	44	l	l	NOUN
iajs-881	25	45	,	,	PUNCT
iajs-881	25	46	r	r	NOUN
iajs-881	25	47	]	]	PUNCT
iajs-881	25	48	and	and	CCONJ
iajs-881	25	49	q	q	NOUN
iajs-881	25	50	is	be	AUX
iajs-881	25	51	a	a	DET
iajs-881	25	52	fractional	fractional	ADJ
iajs-881	25	53	number	number	NOUN
iajs-881	25	54	.	.	PUNCT
iajs-881	26	1	therefore	therefore	ADV
iajs-881	26	2	:	:	PUNCT
iajs-881	26	3	q	q	PUNCT
iajs-881	27	1	i	i	PRON
iajs-881	27	2	j	j	PROPN
iajs-881	27	3	q	q	X
iajs-881	27	4	u(x	u(x	PROPN
iajs-881	27	5	,	,	PUNCT
iajs-881	27	6	t	t	NOUN
iajs-881	27	7	)	)	PUNCT
iajs-881	27	8	x	x	PROPN
iajs-881	27	9			ADJ
iajs-881	27	10			ADJ
iajs-881	28	1			PROPN
iajs-881	28	2	q	q	NOUN
iajs-881	28	3	1	1	NUM
iajs-881	28	4	(	(	PUNCT
iajs-881	28	5	x)	x)	PROPN
iajs-881	28	6	i	i	PROPN
iajs-881	28	7	1	1	NUM
iajs-881	28	8	k	k	NOUN
iajs-881	28	9	0	0	NUM
iajs-881	28	10			ADV
iajs-881	28	11			NUM
iajs-881	28	12			NUM
iajs-881	28	13	gku(xi	gku(xi	ADJ
iajs-881	28	14			PROPN
iajs-881	28	15	(	(	PUNCT
iajs-881	28	16	k	k	PROPN
iajs-881	28	17			PROPN
iajs-881	28	18	1)x	1)x	NUM
iajs-881	28	19	,	,	PUNCT
iajs-881	28	20	tj	tj	NOUN
iajs-881	28	21	)	)	PUNCT
iajs-881	28	22			NOUN
iajs-881	28	23	q	q	NOUN
iajs-881	28	24	1	1	NUM
iajs-881	28	25	(	(	PUNCT
iajs-881	28	26	x)	x)	PROPN
iajs-881	28	27	i	i	PROPN
iajs-881	28	28	1	1	NUM
iajs-881	28	29	k	k	NOUN
iajs-881	28	30	0	0	NUM
iajs-881	28	31			ADV
iajs-881	28	32			NUM
iajs-881	28	33			X
iajs-881	28	34	gkuik+1	gkuik+1	NOUN
iajs-881	28	35	,	,	PUNCT
iajs-881	28	36	…	…	PUNCT
iajs-881	28	37	…	…	PUNCT
iajs-881	28	38	…	…	PUNCT
iajs-881	28	39	…	…	PUNCT
iajs-881	28	40	…	…	PUNCT
iajs-881	28	41	..	..	PUNCT
iajs-881	28	42	(	(	PUNCT
iajs-881	28	43	3	3	X
iajs-881	28	44	)	)	PUNCT
iajs-881	28	45	and	and	CCONJ
iajs-881	28	46	q	q	X
iajs-881	29	1	i	i	PRON
iajs-881	29	2	j	j	PROPN
iajs-881	29	3	q	q	X
iajs-881	29	4	u(x	u(x	PROPN
iajs-881	29	5	,	,	PUNCT
iajs-881	29	6	t	t	NOUN
iajs-881	29	7	)	)	PUNCT
iajs-881	29	8	x	x	PROPN
iajs-881	29	9			ADJ
iajs-881	29	10			PROPN
iajs-881	30	1			PROPN
iajs-881	30	2	q	q	NOUN
iajs-881	30	3	1	1	NUM
iajs-881	30	4	(	(	PUNCT
iajs-881	30	5	x)	x)	PROPN
iajs-881	30	6			X
iajs-881	30	7			VERB
iajs-881	30	8			NOUN
iajs-881	30	9	1	1	NUM
iajs-881	30	10	in	in	ADP
iajs-881	30	11	0k	0k	NOUN
iajs-881	30	12	gku(xi	gku(xi	VERB
iajs-881	31	1	+	+	CCONJ
iajs-881	32	1	(	(	PUNCT
iajs-881	32	2	k	k	X
iajs-881	32	3			PROPN
iajs-881	32	4	1	1	NUM
iajs-881	32	5	)	)	PUNCT
iajs-881	32	6	x	x	ADJ
iajs-881	32	7	,	,	PUNCT
iajs-881	32	8	tj	tj	NOUN
iajs-881	32	9	)	)	PUNCT
iajs-881	32	10			NOUN
iajs-881	32	11	q	q	NOUN
iajs-881	32	12	1	1	NUM
iajs-881	32	13	(	(	PUNCT
iajs-881	32	14	x)	x)	PROPN
iajs-881	32	15			X
iajs-881	32	16			VERB
iajs-881	32	17			NOUN
iajs-881	32	18	1	1	NUM
iajs-881	32	19	in	in	ADP
iajs-881	32	20	0k	0k	NOUN
iajs-881	32	21	gkui+k1,j	gkui+k1,j	NOUN
iajs-881	32	22	........................	........................	PUNCT
iajs-881	32	23	(	(	PUNCT
iajs-881	32	24	4	4	X
iajs-881	32	25	)	)	PUNCT
iajs-881	33	1	where	where	SCONJ
iajs-881	33	2	g0	g0	PROPN
iajs-881	33	3	1	1	NUM
iajs-881	33	4	and	and	CCONJ
iajs-881	33	5	gk	gk	PROPN
iajs-881	33	6			PROPN
iajs-881	33	7	(	(	PUNCT
iajs-881	33	8	1)k	1)k	PROPN
iajs-881	33	9	q(q	q(q	PROPN
iajs-881	33	10	1)	1)	NUM
iajs-881	33	11	...	...	PUNCT
iajs-881	33	12	(q	(q	PUNCT
iajs-881	33	13	k	k	NOUN
iajs-881	33	14	1	1	X
iajs-881	33	15	)	)	PUNCT
iajs-881	33	16	k	k	NOUN
iajs-881	33	17	!	!	PUNCT
iajs-881	33	18			PROPN
iajs-881	33	19			PROPN
iajs-881	33	20			ADV
iajs-881	33	21	,	,	PUNCT
iajs-881	33	22	k	k	PROPN
iajs-881	33	23			NUM
iajs-881	33	24	1,2	1,2	NUM
iajs-881	33	25	,	,	PUNCT
iajs-881	33	26	…	…	PUNCT
iajs-881	33	27	the	the	DET
iajs-881	33	28	explicit	explicit	ADJ
iajs-881	33	29	finite	finite	ADJ
iajs-881	33	30	difference	difference	NOUN
iajs-881	33	31	method	method	NOUN
iajs-881	33	32	for	for	ADP
iajs-881	33	33	solving	solve	VERB
iajs-881	33	34	fractional	fractional	ADJ
iajs-881	33	35	hyperbolic	hyperbolic	ADJ
iajs-881	33	36	partial	partial	ADJ
iajs-881	33	37	differential	differential	NOUN
iajs-881	33	38	equations	equation	NOUN
iajs-881	33	39	the	the	DET
iajs-881	33	40	explicit	explicit	ADJ
iajs-881	33	41	finite	finite	ADJ
iajs-881	33	42	difference	difference	NOUN
iajs-881	33	43	method	method	NOUN
iajs-881	33	44	is	be	AUX
iajs-881	33	45	improved	improve	VERB
iajs-881	33	46	to	to	PART
iajs-881	33	47	solve	solve	VERB
iajs-881	33	48	the	the	DET
iajs-881	33	49	initial	initial	ADJ
iajs-881	33	50	-	-	PUNCT
iajs-881	33	51	boundary	boundary	NOUN
iajs-881	33	52	value	value	NOUN
iajs-881	33	53	problem	problem	NOUN
iajs-881	33	54	(	(	PUNCT
iajs-881	33	55	1)-(2	1)-(2	NUM
iajs-881	33	56	)	)	PUNCT
iajs-881	33	57	.	.	PUNCT
iajs-881	34	1	to	to	PART
iajs-881	34	2	do	do	VERB
iajs-881	34	3	this	this	PRON
iajs-881	34	4	,	,	PUNCT
iajs-881	34	5	we	we	PRON
iajs-881	34	6	substitute	substitute	VERB
iajs-881	34	7	t	t	PROPN
iajs-881	34	8			NUM
iajs-881	34	9	tj	tj	NOUN
iajs-881	34	10	,	,	PUNCT
iajs-881	34	11	in	in	ADP
iajs-881	34	12	eq	eq	ADP
iajs-881	34	13	.	.	PUNCT
iajs-881	35	1	(	(	PUNCT
iajs-881	35	2	1	1	NUM
iajs-881	35	3	)	)	PUNCT
iajs-881	35	4	and	and	CCONJ
iajs-881	35	5	replace	replace	VERB
iajs-881	35	6	the	the	DET
iajs-881	35	7	partial	partial	ADJ
iajs-881	35	8	derivative	derivative	ADJ
iajs-881	35	9	2	2	NUM
iajs-881	35	10	2	2	NUM
iajs-881	35	11	u	u	NOUN
iajs-881	35	12	t	t	PROPN
iajs-881	35	13			PROPN
iajs-881	35	14			PROPN
iajs-881	35	15	with	with	ADP
iajs-881	35	16	its	its	PRON
iajs-881	35	17	central	central	ADJ
iajs-881	35	18	difference	difference	NOUN
iajs-881	35	19	approximation	approximation	NOUN
iajs-881	35	20	to	to	PART
iajs-881	35	21	get	get	VERB
iajs-881	35	22	:	:	PUNCT
iajs-881	35	23	q	q	PROPN
iajs-881	35	24	i	i	PRON
iajs-881	35	25	,	,	PUNCT
iajs-881	35	26	j	j	PROPN
iajs-881	35	27	1	1	NUM
iajs-881	35	28	i	i	PROPN
iajs-881	35	29	,	,	PUNCT
iajs-881	36	1	j	j	PROPN
iajs-881	36	2	i	i	PROPN
iajs-881	36	3	,	,	PUNCT
iajs-881	36	4	j	j	PROPN
iajs-881	36	5	1	1	NUM
iajs-881	36	6	i	i	PROPN
iajs-881	36	7	,	,	PUNCT
iajs-881	36	8	j	j	PROPN
iajs-881	36	9	i	i	PROPN
iajs-881	36	10	,	,	PUNCT
iajs-881	36	11	j	j	PROPN
iajs-881	36	12	i	i	PROPN
iajs-881	36	13	,	,	PUNCT
iajs-881	36	14	j2	j2	PROPN
iajs-881	36	15	q	q	PROPN
iajs-881	36	16	u	u	PROPN
iajs-881	36	17	2u	2u	VERB
iajs-881	36	18	u	u	NOUN
iajs-881	36	19	u	u	VERB
iajs-881	36	20	c	c	PROPN
iajs-881	36	21	s	s	X
iajs-881	36	22	(	(	PUNCT
iajs-881	36	23	t	t	PROPN
iajs-881	36	24	)	)	PUNCT
iajs-881	36	25	x	x	X
iajs-881	36	26			ADJ
iajs-881	36	27			NUM
iajs-881	36	28			ADV
iajs-881	36	29			PROPN
iajs-881	36	30			PROPN
iajs-881	36	31			PUNCT
iajs-881	36	32			PUNCT
iajs-881	36	33			ADJ
iajs-881	36	34	......................	......................	PUNCT
iajs-881	37	1	(	(	PUNCT
iajs-881	37	2	5	5	X
iajs-881	37	3	)	)	PUNCT
iajs-881	37	4	where	where	SCONJ
iajs-881	37	5	tjjt	tjjt	PROPN
iajs-881	37	6	,	,	PUNCT
iajs-881	37	7	j0,1,	j0,1,	NOUN
iajs-881	37	8	…	…	PUNCT
iajs-881	37	9	,m	,m	PUNCT
iajs-881	37	10	and	and	CCONJ
iajs-881	37	11	m	m	PROPN
iajs-881	37	12	is	be	AUX
iajs-881	37	13	the	the	DET
iajs-881	37	14	number	number	NOUN
iajs-881	37	15	of	of	ADP
iajs-881	37	16	subdivisions	subdivision	NOUN
iajs-881	37	17	of	of	ADP
iajs-881	37	18	the	the	DET
iajs-881	37	19	interval	interval	NOUN
iajs-881	38	1	[	[	X
iajs-881	38	2	0	0	NUM
iajs-881	38	3	,	,	PUNCT
iajs-881	38	4	t	t	PROPN
iajs-881	38	5	]	]	PUNCT
iajs-881	38	6	,	,	PUNCT
iajs-881	38	7	t	t	PROPN
iajs-881	38	8	r	r	PROPN
iajs-881	38	9	.	.	PUNCT
iajs-881	39	1	next	next	ADJ
iajs-881	39	2	,	,	PUNCT
iajs-881	39	3	substitute	substitute	ADJ
iajs-881	39	4	equation	equation	NOUN
iajs-881	39	5	(	(	PUNCT
iajs-881	39	6	3	3	NUM
iajs-881	39	7	)	)	PUNCT
iajs-881	39	8	in	in	ADP
iajs-881	39	9	equation	equation	NOUN
iajs-881	39	10	(	(	PUNCT
iajs-881	39	11	5	5	NUM
iajs-881	39	12	)	)	PUNCT
iajs-881	39	13	to	to	PART
iajs-881	39	14	obtain	obtain	VERB
iajs-881	39	15	:	:	PUNCT
iajs-881	39	16	i	i	PRON
iajs-881	39	17	1	1	NUM
iajs-881	39	18	i	i	PROPN
iajs-881	39	19	,	,	PUNCT
iajs-881	39	20	j	j	PROPN
iajs-881	39	21	1	1	NUM
iajs-881	39	22	i	i	PROPN
iajs-881	39	23	,	,	PUNCT
iajs-881	39	24	j	j	PROPN
iajs-881	40	1	i	i	PROPN
iajs-881	40	2	,	,	PUNCT
iajs-881	40	3	j	j	PROPN
iajs-881	40	4	1	1	NUM
iajs-881	40	5	i	i	PROPN
iajs-881	40	6	,	,	PUNCT
iajs-881	40	7	j	j	PROPN
iajs-881	41	1	k	k	PROPN
iajs-881	41	2	i	i	PRON
iajs-881	41	3	k	k	PROPN
iajs-881	41	4	1	1	NUM
iajs-881	41	5	,	,	PUNCT
iajs-881	41	6	j	j	PROPN
iajs-881	41	7	i	i	PROPN
iajs-881	41	8	,	,	PUNCT
iajs-881	41	9	j2	j2	PROPN
iajs-881	41	10	q	q	PROPN
iajs-881	41	11	k	k	PROPN
iajs-881	41	12	0	0	PUNCT
iajs-881	41	13	u	u	NOUN
iajs-881	41	14	2u	2u	NOUN
iajs-881	41	15	u	u	NOUN
iajs-881	41	16	c	c	PROPN
iajs-881	41	17	g	g	NOUN
iajs-881	41	18	u	u	PROPN
iajs-881	41	19	s	s	PART
iajs-881	41	20	,	,	PUNCT
iajs-881	41	21	i	i	PRON
iajs-881	41	22	1,2,	1,2,	NUM
iajs-881	41	23	...	...	PUNCT
iajs-881	41	24	,n	,n	PUNCT
iajs-881	41	25	1	1	NUM
iajs-881	41	26	;	;	PUNCT
iajs-881	41	27	j	j	PROPN
iajs-881	41	28	0,1	0,1	NUM
iajs-881	41	29	,	,	PUNCT
iajs-881	41	30	...	...	PUNCT
iajs-881	41	31	,	,	PUNCT
iajs-881	41	32	m	m	VERB
iajs-881	41	33	1	1	NUM
iajs-881	41	34	(	(	PUNCT
iajs-881	41	35	t	t	PROPN
iajs-881	41	36	)	)	PUNCT
iajs-881	41	37	(	(	PUNCT
iajs-881	41	38	x	x	X
iajs-881	41	39	)	)	PUNCT
iajs-881	41	40			ADV
iajs-881	41	41			PUNCT
iajs-881	41	42			PROPN
iajs-881	41	43			PROPN
iajs-881	41	44			PART
iajs-881	41	45			PROPN
iajs-881	41	46			PROPN
iajs-881	41	47			VERB
iajs-881	41	48			NUM
iajs-881	41	49			ADJ
iajs-881	41	50			NUM
iajs-881	41	51			PROPN
iajs-881	41	52			PROPN
iajs-881	41	53			PROPN
iajs-881	41	54			PUNCT
iajs-881	41	55			X
iajs-881	41	56			X
iajs-881	41	57	…	…	PUNCT
iajs-881	41	58	(	(	PUNCT
iajs-881	41	59	6	6	NUM
iajs-881	41	60	)	)	PUNCT
iajs-881	41	61	on	on	ADP
iajs-881	41	62	the	the	DET
iajs-881	41	63	other	other	ADJ
iajs-881	41	64	hand	hand	NOUN
iajs-881	41	65	,	,	PUNCT
iajs-881	41	66	the	the	DET
iajs-881	41	67	initial	initial	ADJ
iajs-881	41	68	and	and	CCONJ
iajs-881	41	69	boundary	boundary	ADJ
iajs-881	41	70	conditions	condition	NOUN
iajs-881	41	71	given	give	VERB
iajs-881	41	72	by	by	ADP
iajs-881	41	73	eq.(2	eq.(2	ADJ
iajs-881	41	74	)	)	PUNCT
iajs-881	41	75	becomes	become	VERB
iajs-881	41	76	:	:	PUNCT
iajs-881	41	77	i	i	PRON
iajs-881	41	78	i,0	i,0	X
iajs-881	42	1	i	i	PRON
iajs-881	43	1	i	i	PRON
iajs-881	43	2	0,j	0,j	VERB
iajs-881	43	3	j	j	PROPN
iajs-881	43	4	n	n	CCONJ
iajs-881	43	5	,	,	PUNCT
iajs-881	43	6	j	j	PROPN
iajs-881	43	7	u(x	u(x	PROPN
iajs-881	43	8	,	,	PUNCT
iajs-881	43	9	0	0	NUM
iajs-881	43	10	)	)	PUNCT
iajs-881	43	11	u	u	NOUN
iajs-881	43	12	u(x	u(x	NOUN
iajs-881	43	13	,	,	PUNCT
iajs-881	43	14	0	0	NUM
iajs-881	43	15	)	)	PUNCT
iajs-881	43	16	f	f	NOUN
iajs-881	43	17	(	(	PUNCT
iajs-881	43	18	x	x	PROPN
iajs-881	43	19	)	)	PUNCT
iajs-881	43	20	,	,	PUNCT
iajs-881	43	21	for	for	SCONJ
iajs-881	43	22	i	i	PRON
iajs-881	43	23	0,1,	0,1,	NOUN
iajs-881	43	24	...	...	PUNCT
iajs-881	43	25	,n	,n	PUNCT
iajs-881	43	26	t	t	PROPN
iajs-881	43	27	u	u	NOUN
iajs-881	43	28	u(l	u(l	PROPN
iajs-881	43	29	,	,	PUNCT
iajs-881	43	30	t	t	NOUN
iajs-881	43	31	)	)	PUNCT
iajs-881	43	32	0	0	NUM
iajs-881	43	33	,	,	PUNCT
iajs-881	43	34	u	u	PROPN
iajs-881	43	35	u(r	u(r	PROPN
iajs-881	43	36	,	,	PUNCT
iajs-881	43	37	t	t	PROPN
iajs-881	43	38	)	)	PUNCT
iajs-881	43	39	0	0	NUM
iajs-881	44	1	for	for	ADP
iajs-881	44	2	j	j	PROPN
iajs-881	44	3	0,1,	0,1,	NOUN
iajs-881	44	4	...	...	PUNCT
iajs-881	44	5	,m	,m	PUNCT
iajs-881	44	6			PROPN
iajs-881	45	1			PRON
iajs-881	46	1			NUM
iajs-881	47	1			PROPN
iajs-881	47	2			ADJ
iajs-881	47	3			PRON
iajs-881	48	1			NUM
iajs-881	49	1			NOUN
iajs-881	49	2			NOUN
iajs-881	50	1			NOUN
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iajs-881	52	6	3	3	NUM
iajs-881	52	7	)	)	PUNCT
iajs-881	52	8	2010	2010	NUM
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iajs-881	52	14	difference	difference	NOUN
iajs-881	52	15	approximation	approximation	NOUN
iajs-881	52	16	to	to	ADP
iajs-881	52	17	the	the	DET
iajs-881	52	18	initial	initial	ADJ
iajs-881	52	19	derivative	derivative	ADJ
iajs-881	52	20	conditions	condition	NOUN
iajs-881	52	21	,	,	PUNCT
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iajs-881	52	23	can	can	AUX
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iajs-881	52	39			NUM
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iajs-881	52	41			X
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iajs-881	52	44	…	…	PUNCT
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iajs-881	52	47	i	i	PRON
iajs-881	52	48	ih	ih	VERB
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iajs-881	52	50	)	)	PUNCT
iajs-881	52	51			PROPN
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iajs-881	52	59	n.	n.	PROPN
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iajs-881	52	62	i,1	i,1	NOUN
iajs-881	52	63	i	i	PRON
iajs-881	52	64	,	,	PUNCT
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iajs-881	52	67	u	u	NOUN
iajs-881	52	68	2	2	NUM
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iajs-881	52	70			PUNCT
iajs-881	52	71			NOUN
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iajs-881	52	74	,	,	PUNCT
iajs-881	52	75	…	…	PUNCT
iajs-881	52	76	,	,	PUNCT
iajs-881	52	77	n	n	CCONJ
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iajs-881	52	79	,	,	PUNCT
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iajs-881	52	81	(	(	PUNCT
iajs-881	52	82	6	6	NUM
iajs-881	52	83	)	)	PUNCT
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iajs-881	52	86	2	2	NUM
iajs-881	52	87	i	i	NOUN
iajs-881	52	88	1	1	X
iajs-881	53	1	i	i	PROPN
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iajs-881	53	4	2	2	NUM
iajs-881	53	5	i	i	PROPN
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iajs-881	53	8	1	1	NUM
iajs-881	53	9	i	i	PROPN
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iajs-881	53	11	j	j	PROPN
iajs-881	53	12	i	i	PROPN
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iajs-881	53	14	j	j	PROPN
iajs-881	54	1	1	1	NUM
iajs-881	54	2	k	k	NOUN
iajs-881	54	3	i	i	PRON
iajs-881	54	4	k	k	INTJ
iajs-881	54	5	1,j	1,j	VERB
iajs-881	54	6	i	i	PRON
iajs-881	54	7	,	,	PUNCT
iajs-881	54	8	jq	jq	PROPN
iajs-881	54	9	k	k	PROPN
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iajs-881	54	12	t	t	PROPN
iajs-881	54	13	)	)	PUNCT
iajs-881	54	14	c	c	PROPN
iajs-881	55	1	u	u	PROPN
iajs-881	55	2	2u	2u	VERB
iajs-881	55	3	u	u	NOUN
iajs-881	55	4	g	g	PROPN
iajs-881	55	5	u	u	X
iajs-881	55	6	s	s	X
iajs-881	55	7	(	(	PUNCT
iajs-881	55	8	t	t	PROPN
iajs-881	55	9	)	)	PUNCT
iajs-881	55	10	(	(	PUNCT
iajs-881	55	11	x	x	X
iajs-881	55	12	)	)	PUNCT
iajs-881	55	13			ADV
iajs-881	55	14			PUNCT
iajs-881	55	15			PROPN
iajs-881	55	16			PROPN
iajs-881	55	17			ADV
iajs-881	55	18			NUM
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iajs-881	55	20			NUM
iajs-881	55	21			PROPN
iajs-881	55	22			ADV
iajs-881	55	23			PUNCT
iajs-881	55	24			PUNCT
iajs-881	55	25			X
iajs-881	55	26			X
iajs-881	55	27	…	…	PUNCT
iajs-881	55	28	…	…	PUNCT
iajs-881	55	29	…	…	PUNCT
iajs-881	55	30	…	…	SYM
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iajs-881	55	32	…	…	PUNCT
iajs-881	55	33	.(7	.(7	NUM
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iajs-881	55	35	where	where	SCONJ
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iajs-881	55	37	…	…	SYM
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iajs-881	55	39	,	,	PUNCT
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iajs-881	55	42	,m1	,m1	PUNCT
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iajs-881	56	4	i	i	NOUN
iajs-881	56	5	1	1	NUM
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iajs-881	56	9	i,0	i,0	X
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iajs-881	59	4	c	c	PROPN
iajs-881	59	5	u	u	PROPN
iajs-881	59	6	2u	2u	VERB
iajs-881	59	7	u	u	NOUN
iajs-881	59	8	g	g	PROPN
iajs-881	59	9	u	u	X
iajs-881	59	10	s	s	X
iajs-881	59	11	(	(	PUNCT
iajs-881	59	12	t	t	PROPN
iajs-881	59	13	)	)	PUNCT
iajs-881	59	14	(	(	PUNCT
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iajs-881	59	16	)	)	PUNCT
iajs-881	59	17			PUNCT
iajs-881	59	18			PROPN
iajs-881	59	19			PROPN
iajs-881	59	20			ADV
iajs-881	59	21			NUM
iajs-881	59	22			NOUN
iajs-881	59	23			NUM
iajs-881	59	24			PROPN
iajs-881	59	25			ADV
iajs-881	59	26			PUNCT
iajs-881	59	27			PUNCT
iajs-881	59	28			X
iajs-881	59	29			X
iajs-881	59	30	…	…	PUNCT
iajs-881	59	31	…	…	PUNCT
iajs-881	59	32	..	..	PUNCT
iajs-881	59	33	…	…	PUNCT
iajs-881	59	34	…	…	PUNCT
iajs-881	59	35	…	…	PUNCT
iajs-881	59	36	(	(	PUNCT
iajs-881	59	37	8)	8)	NUM
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iajs-881	59	47	th	th	NUM
iajs-881	59	48			PROPN
iajs-881	59	49			NOUN
iajs-881	59	50			NOUN
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iajs-881	59	55	one	one	PRON
iajs-881	59	56	can	can	AUX
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iajs-881	59	58	that	that	SCONJ
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iajs-881	59	60	can	can	AUX
iajs-881	59	61	be	be	AUX
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iajs-881	59	63	from	from	ADP
iajs-881	59	64	the	the	DET
iajs-881	59	65	following	follow	VERB
iajs-881	59	66	equation	equation	NOUN
iajs-881	59	67	:	:	PUNCT
iajs-881	59	68	2	2	NUM
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iajs-881	59	70	1	1	NUM
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iajs-881	60	1	i	i	PRON
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iajs-881	61	2	k	k	PROPN
iajs-881	61	3	1	1	NUM
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iajs-881	61	12	(	(	PUNCT
iajs-881	61	13	t	t	PROPN
iajs-881	61	14	)	)	PUNCT
iajs-881	61	15	u	u	NOUN
iajs-881	61	16	f	f	PROPN
iajs-881	61	17	g	g	PROPN
iajs-881	62	1	f	f	PROPN
iajs-881	62	2	s	s	PROPN
iajs-881	62	3	tg	tg	PROPN
iajs-881	62	4	22	22	NUM
iajs-881	62	5	(	(	PUNCT
iajs-881	62	6	x	x	NOUN
iajs-881	62	7	)	)	PUNCT
iajs-881	62	8			VERB
iajs-881	62	9			PROPN
iajs-881	62	10			VERB
iajs-881	62	11			NUM
iajs-881	62	12			NOUN
iajs-881	62	13			X
iajs-881	63	1			PROPN
iajs-881	63	2			PROPN
iajs-881	63	3			ADV
iajs-881	63	4			PUNCT
iajs-881	63	5			PUNCT
iajs-881	63	6			X
iajs-881	63	7			X
iajs-881	63	8	,	,	PUNCT
iajs-881	63	9	i=0,1,	i=0,1,	PROPN
iajs-881	63	10	…	…	PUNCT
iajs-881	63	11	…	…	PUNCT
iajs-881	63	12	..	..	PUNCT
iajs-881	63	13	n	n	X
iajs-881	63	14	−1	−1	NOUN
iajs-881	63	15	where	where	SCONJ
iajs-881	63	16	i0	i0	PROPN
iajs-881	63	17	,	,	PUNCT
iajs-881	63	18	1	1	NUM
iajs-881	63	19	,	,	PUNCT
iajs-881	63	20	…	…	PUNCT
iajs-881	63	21	..	..	PUNCT
iajs-881	63	22	n1	n1	NOUN
iajs-881	63	23	.	.	PUNCT
iajs-881	64	1	by	by	ADP
iajs-881	64	2	evaluating	evaluate	VERB
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iajs-881	64	4	above	above	ADJ
iajs-881	64	5	equation	equation	NOUN
iajs-881	64	6	for	for	ADP
iajs-881	64	7	each	each	DET
iajs-881	64	8	i0,1,	i0,1,	NOUN
iajs-881	64	9	…	…	SYM
iajs-881	64	10	,n1	,n1	NOUN
iajs-881	64	11	,	,	PUNCT
iajs-881	64	12	one	one	PRON
iajs-881	64	13	can	can	AUX
iajs-881	64	14	get	get	VERB
iajs-881	64	15	the	the	DET
iajs-881	64	16	values	value	NOUN
iajs-881	64	17	of	of	ADP
iajs-881	64	18	i,1u	i,1u	PROPN
iajs-881	64	19	,	,	PUNCT
iajs-881	64	20	i	i	NOUN
iajs-881	64	21	1,2	1,2	NUM
iajs-881	64	22	,	,	PUNCT
iajs-881	64	23	...	...	PUNCT
iajs-881	64	24	,	,	PUNCT
iajs-881	64	25	n	n	PROPN
iajs-881	64	26	1	1	NUM
iajs-881	64	27			NOUN
iajs-881	64	28	.	.	PUNCT
iajs-881	65	1	then	then	ADV
iajs-881	65	2	by	by	ADP
iajs-881	65	3	evaluating	evaluate	VERB
iajs-881	65	4	equation	equation	NOUN
iajs-881	65	5	(	(	PUNCT
iajs-881	65	6	7	7	NUM
iajs-881	65	7	)	)	PUNCT
iajs-881	65	8	at	at	ADP
iajs-881	65	9	each	each	DET
iajs-881	65	10	i1,2,	i1,2,	NOUN
iajs-881	65	11	…	…	SYM
iajs-881	65	12	,n1	,n1	PUNCT
iajs-881	65	13	and	and	CCONJ
iajs-881	65	14	j2,3,	j2,3,	NOUN
iajs-881	65	15	…	…	PUNCT
iajs-881	65	16	,m1	,m1	PUNCT
iajs-881	65	17	one	one	PRON
iajs-881	65	18	can	can	AUX
iajs-881	65	19	get	get	VERB
iajs-881	65	20	the	the	DET
iajs-881	65	21	numerical	numerical	ADJ
iajs-881	65	22	solution	solution	NOUN
iajs-881	65	23	of	of	ADP
iajs-881	65	24	eq.(1	eq.(1	ADJ
iajs-881	65	25	)	)	PUNCT
iajs-881	65	26	.	.	PUNCT
iajs-881	66	1	then	then	ADV
iajs-881	66	2	the	the	DET
iajs-881	66	3	resulting	result	VERB
iajs-881	66	4	equation	equation	NOUN
iajs-881	66	5	can	can	AUX
iajs-881	66	6	be	be	AUX
iajs-881	66	7	explicitly	explicitly	ADV
iajs-881	66	8	solved	solve	VERB
iajs-881	66	9	to	to	PART
iajs-881	66	10	give	give	VERB
iajs-881	66	11	:	:	PUNCT
iajs-881	66	12	i	i	PROPN
iajs-881	66	13	1	1	NUM
iajs-881	66	14	i	i	PROPN
iajs-881	66	15	,	,	PUNCT
iajs-881	66	16	j	j	PROPN
iajs-881	66	17	1	1	NUM
iajs-881	66	18	i	i	PROPN
iajs-881	66	19	,	,	PUNCT
iajs-881	67	1	j	j	PROPN
iajs-881	67	2	i	i	PROPN
iajs-881	67	3	,	,	PUNCT
iajs-881	67	4	j	j	PROPN
iajs-881	67	5	1	1	NUM
iajs-881	67	6	w	w	NOUN
iajs-881	67	7	i	i	PRON
iajs-881	67	8	w	w	PROPN
iajs-881	67	9	1	1	NUM
iajs-881	67	10	,	,	PUNCT
iajs-881	67	11	j	j	PROPN
iajs-881	67	12	w	w	PROPN
iajs-881	67	13	0	0	NUM
iajs-881	67	14	u	u	NOUN
iajs-881	67	15	2u	2u	NOUN
iajs-881	67	16	u	u	NOUN
iajs-881	67	17	r	r	NOUN
iajs-881	67	18	g	g	PROPN
iajs-881	67	19	u	u	PROPN
iajs-881	67	20			ADV
iajs-881	67	21			PUNCT
iajs-881	67	22			PROPN
iajs-881	67	23			PROPN
iajs-881	67	24			PART
iajs-881	67	25			PROPN
iajs-881	67	26			PROPN
iajs-881	67	27			ADP
iajs-881	67	28			NUM
iajs-881	67	29			X
iajs-881	67	30	…	…	PUNCT
iajs-881	67	31	…	…	PUNCT
iajs-881	67	32	…	…	PUNCT
iajs-881	67	33	…	…	PUNCT
iajs-881	67	34	..	..	PUNCT
iajs-881	67	35	…	…	PUNCT
iajs-881	67	36	…	…	PUNCT
iajs-881	67	37	..	..	PUNCT
iajs-881	67	38	(	(	PUNCT
iajs-881	67	39	9	9	NUM
iajs-881	67	40	)	)	PUNCT
iajs-881	67	41	where	where	SCONJ
iajs-881	67	42	r	r	NOUN
iajs-881	67	43	=	=	SYM
iajs-881	67	44	2	2	NUM
iajs-881	67	45	qk	qk	NOUN
iajs-881	67	46	h	h	NOUN
iajs-881	67	47	.the	.the	PRON
iajs-881	67	48	resulting	result	VERB
iajs-881	67	49	difference	difference	NOUN
iajs-881	67	50	equation	equation	NOUN
iajs-881	67	51	is	be	AUX
iajs-881	67	52	stable	stable	ADJ
iajs-881	67	53	since	since	SCONJ
iajs-881	67	54	we	we	PRON
iajs-881	67	55	let	let	VERB
iajs-881	67	56	g0=1	g0=1	PROPN
iajs-881	67	57	and	and	CCONJ
iajs-881	67	58	gw	gw	PROPN
iajs-881	67	59	=	=	PUNCT
iajs-881	67	60	wq(q-1)k(q	wq(q-1)k(q	PROPN
iajs-881	67	61	-	-	PUNCT
iajs-881	67	62	w-1	w-1	NOUN
iajs-881	67	63	)	)	PUNCT
iajs-881	67	64	(	(	PUNCT
iajs-881	67	65	-1	-1	INTJ
iajs-881	67	66	)	)	PUNCT
iajs-881	67	67	w	w	NOUN
iajs-881	67	68	,	,	PUNCT
iajs-881	67	69	w	w	PROPN
iajs-881	67	70	=	=	SYM
iajs-881	67	71	1,2	1,2	NUM
iajs-881	67	72	,	,	PUNCT
iajs-881	67	73	…	…	PUNCT
iajs-881	67	74	..	..	PUNCT
iajs-881	67	75	1	1	NUM
iajs-881	67	76	≤	≤	NUM
iajs-881	67	77	q	q	PROPN
iajs-881	67	78	≤	≤	NUM
iajs-881	67	79	2	2	NUM
iajs-881	67	80	,	,	PUNCT
iajs-881	67	81	i≠1	i≠1	ADJ
iajs-881	67	82	,	,	PUNCT
iajs-881	67	83	hence	hence	ADV
iajs-881	67	84	gi	gi	VERB
iajs-881	67	85	≥	≥	NOUN
iajs-881	67	86	0	0	NUM
iajs-881	67	87	for	for	ADP
iajs-881	67	88	all	all	DET
iajs-881	67	89	value	value	NOUN
iajs-881	67	90	of	of	ADP
iajs-881	67	91	i.	i.	NOUN
iajs-881	67	92	therefore	therefore	ADV
iajs-881	67	93	:	:	PUNCT
iajs-881	67	94	i	i	PROPN
iajs-881	67	95	1	1	NUM
iajs-881	67	96	w	w	NOUN
iajs-881	67	97	w	w	PROPN
iajs-881	67	98	0	0	NUM
iajs-881	67	99	g	g	NOUN
iajs-881	67	100			ADV
iajs-881	67	101			NUM
iajs-881	67	102			ADJ
iajs-881	67	103			NOUN
iajs-881	67	104	g1	g1	ADV
iajs-881	67	105			PROPN
iajs-881	67	106	(q	(q	NOUN
iajs-881	67	107	)	)	PUNCT
iajs-881	67	108			NUM
iajs-881	67	109	q	q	X
iajs-881	67	110	…	…	PUNCT
iajs-881	67	111	…	…	PUNCT
iajs-881	67	112	…	…	PUNCT
iajs-881	67	113	…	…	PUNCT
iajs-881	67	114	…	…	PUNCT
iajs-881	67	115	…	…	PUNCT
iajs-881	67	116	(	(	PUNCT
iajs-881	67	117	10	10	NUM
iajs-881	67	118	)	)	PUNCT
iajs-881	67	119	the	the	DET
iajs-881	67	120	difference	difference	NOUN
iajs-881	67	121	between	between	ADP
iajs-881	67	122	the	the	DET
iajs-881	67	123	analytical	analytical	ADJ
iajs-881	67	124	and	and	CCONJ
iajs-881	67	125	numerical	numerical	ADJ
iajs-881	67	126	solutions	solution	NOUN
iajs-881	67	127	of	of	ADP
iajs-881	67	128	the	the	DET
iajs-881	67	129	difference	difference	NOUN
iajs-881	67	130	equation	equation	NOUN
iajs-881	67	131	remains	remain	VERB
iajs-881	67	132	bounded	bounded	ADJ
iajs-881	67	133	as	as	ADP
iajs-881	67	134	j	j	PROPN
iajs-881	67	135	increases	increase	NOUN
iajs-881	67	136	.	.	PUNCT
iajs-881	68	1	ihjpas	ihjpas	PROPN
iajs-881	68	2	ibn	ibn	PROPN
iajs-881	68	3	alhaitham	alhaitham	PROPN
iajs-881	68	4	j.	j.	PROPN
iajs-881	68	5	for	for	ADP
iajs-881	68	6	pure	pure	ADJ
iajs-881	68	7	&	&	CCONJ
iajs-881	68	8	appl	appl	PROPN
iajs-881	68	9	.	.	PUNCT
iajs-881	69	1	sci	sci	PROPN
iajs-881	69	2	.	.	PUNCT
iajs-881	70	1	vol.23	vol.23	PROPN
iajs-881	70	2	(	(	PUNCT
iajs-881	70	3	3	3	NUM
iajs-881	70	4	)	)	PUNCT
iajs-881	70	5	2010	2010	NUM
iajs-881	70	6	let	let	VERB
iajs-881	70	7	the	the	DET
iajs-881	70	8	error	error	NOUN
iajs-881	70	9	ei	ei	PROPN
iajs-881	70	10	,	,	PUNCT
iajs-881	70	11	j	j	PROPN
iajs-881	70	12	=	=	NOUN
iajs-881	70	13	u(hi	u(hi	PROPN
iajs-881	70	14	,	,	PUNCT
iajs-881	70	15	kj	kj	PROPN
iajs-881	70	16	)	)	PUNCT
iajs-881	70	17	ui	ui	PROPN
iajs-881	70	18	,	,	PUNCT
iajs-881	70	19	j	j	PROPN
iajs-881	70	20	then	then	ADV
iajs-881	70	21	the	the	DET
iajs-881	70	22	stability	stability	NOUN
iajs-881	70	23	condition	condition	NOUN
iajs-881	70	24	under	under	ADP
iajs-881	70	25	which	which	PRON
iajs-881	70	26	the	the	DET
iajs-881	70	27	finite	finite	ADJ
iajs-881	70	28	difference	difference	NOUN
iajs-881	70	29	eq	eq	ADP
iajs-881	70	30	.	.	PUNCT
iajs-881	71	1	(	(	PUNCT
iajs-881	71	2	9	9	X
iajs-881	71	3	)	)	PUNCT
iajs-881	71	4	is	be	AUX
iajs-881	71	5	stable	stable	ADJ
iajs-881	71	6	,	,	PUNCT
iajs-881	71	7	to	to	PART
iajs-881	71	8	find	find	VERB
iajs-881	71	9	the	the	DET
iajs-881	71	10	stability	stability	NOUN
iajs-881	71	11	conditions	condition	NOUN
iajs-881	71	12	under	under	ADP
iajs-881	71	13	which	which	PRON
iajs-881	71	14	the	the	DET
iajs-881	71	15	error	error	NOUN
iajs-881	71	16	ei	ei	NOUN
iajs-881	71	17	,	,	PUNCT
iajs-881	71	18	j	j	PROPN
iajs-881	71	19	is	be	AUX
iajs-881	71	20	bounded	bound	VERB
iajs-881	71	21	.	.	PUNCT
iajs-881	72	1	smith	smith	PROPN
iajs-881	73	1	[	[	X
iajs-881	73	2	7	7	X
iajs-881	73	3	]	]	PUNCT
iajs-881	73	4	shows	show	VERB
iajs-881	73	5	that	that	SCONJ
iajs-881	73	6	the	the	DET
iajs-881	73	7	error	error	NOUN
iajs-881	73	8	ei	ei	NOUN
iajs-881	73	9	,	,	PUNCT
iajs-881	73	10	j	j	PROPN
iajs-881	73	11	can	can	AUX
iajs-881	73	12	be	be	AUX
iajs-881	73	13	written	write	VERB
iajs-881	73	14	in	in	ADP
iajs-881	73	15	the	the	DET
iajs-881	73	16	form	form	NOUN
iajs-881	73	17	:	:	PUNCT
iajs-881	73	18	ei	ei	NOUN
iajs-881	73	19	,	,	PUNCT
iajs-881	73	20	j=	j=	VERB
iajs-881	73	21	ih	ih	PROPN
iajs-881	73	22	je	je	PROPN
iajs-881	73	23			NOUN
iajs-881	73	24	,	,	PUNCT
iajs-881	73	25	where	where	SCONJ
iajs-881	73	26	s=	s=	PROPN
iajs-881	73	27	ke	ke	NOUN
iajs-881	73	28	γ	γ	PROPN
iajs-881	73	29	=	=	SYM
iajs-881	73	30	1	1	NUM
iajs-881	73	31	…	…	PUNCT
iajs-881	73	32	…	…	PUNCT
iajs-881	73	33	…	…	PUNCT
iajs-881	73	34	…	…	PUNCT
iajs-881	73	35	…	…	PUNCT
iajs-881	73	36	…	…	PUNCT
iajs-881	73	37	…	…	PUNCT
iajs-881	73	38	.(11	.(11	NUM
iajs-881	73	39	)	)	PUNCT
iajs-881	73	40	where	where	SCONJ
iajs-881	73	41	α	α	NOUN
iajs-881	73	42	is	be	AUX
iajs-881	73	43	a	a	DET
iajs-881	73	44	complex	complex	ADJ
iajs-881	73	45	constant	constant	ADJ
iajs-881	73	46	,	,	PUNCT
iajs-881	73	47	one	one	PRON
iajs-881	73	48	can	can	AUX
iajs-881	73	49	substitute	substitute	VERB
iajs-881	73	50	eqs	eqs	PROPN
iajs-881	73	51	.(10	.(10	PROPN
iajs-881	73	52	)	)	PUNCT
iajs-881	73	53	,	,	PUNCT
iajs-881	73	54	(	(	PUNCT
iajs-881	73	55	11	11	NUM
iajs-881	73	56	)	)	PUNCT
iajs-881	73	57	into	into	ADP
iajs-881	73	58	(	(	PUNCT
iajs-881	73	59	9	9	NUM
iajs-881	73	60	)	)	PUNCT
iajs-881	73	61	,	,	PUNCT
iajs-881	73	62	to	to	PART
iajs-881	73	63	get	get	VERB
iajs-881	73	64	:	:	PUNCT
iajs-881	73	65	1	1	NUM
iajs-881	73	66	h(1	h(1	NOUN
iajs-881	73	67	w)2	w)2	VERB
iajs-881	73	68	rqe	rqe	NOUN
iajs-881	73	69	0	0	PROPN
iajs-881	73	70			VERB
iajs-881	73	71			ADJ
iajs-881	73	72			PROPN
iajs-881	73	73			PROPN
iajs-881	73	74			PROPN
iajs-881	73	75			NOUN
iajs-881	73	76			NOUN
iajs-881	73	77	assuming	assume	VERB
iajs-881	73	78	that	that	SCONJ
iajs-881	73	79	,	,	PUNCT
iajs-881	73	80	h(1	h(1	PROPN
iajs-881	73	81	w)	w)	VERB
iajs-881	73	82			PROPN
iajs-881	73	83			PROPN
iajs-881	73	84	,	,	PUNCT
iajs-881	73	85	then	then	ADV
iajs-881	73	86	it	it	PRON
iajs-881	73	87	is	be	AUX
iajs-881	73	88	easily	easily	ADV
iajs-881	73	89	known	know	VERB
iajs-881	73	90	that	that	SCONJ
iajs-881	73	91	the	the	DET
iajs-881	73	92	equation	equation	NOUN
iajs-881	73	93	for	for	ADP
iajs-881	73	94	r	r	NOUN
iajs-881	73	95	is	be	AUX
iajs-881	73	96	:	:	PUNCT
iajs-881	73	97	2	2	NUM
iajs-881	73	98	(	(	PUNCT
iajs-881	73	99	2	2	NUM
iajs-881	73	100	rqe	rqe	NOUN
iajs-881	73	101	)	)	PUNCT
iajs-881	73	102	1	1	NUM
iajs-881	73	103	0	0	NOUN
iajs-881	73	104			PROPN
iajs-881	73	105			PROPN
iajs-881	73	106			PROPN
iajs-881	73	107			ADV
iajs-881	73	108			ADV
iajs-881	73	109	let	let	VERB
iajs-881	73	110	a	a	DET
iajs-881	73	111	2	2	NUM
iajs-881	73	112	rqe	rqe	NOUN
iajs-881	73	113			PUNCT
iajs-881	73	114	,	,	PUNCT
iajs-881	73	115	where	where	SCONJ
iajs-881	73	116	e	e	PROPN
iajs-881	73	117	1	1	NUM
iajs-881	73	118			NOUN
iajs-881	73	119	hence	hence	ADV
iajs-881	73	120	the	the	DET
iajs-881	73	121	values	value	NOUN
iajs-881	73	122	of	of	ADP
iajs-881	73	123			PROPN
iajs-881	73	124	are	be	AUX
iajs-881	73	125	:	:	PUNCT
iajs-881	73	126	2	2	NUM
iajs-881	73	127	1	1	NUM
iajs-881	73	128	a	a	DET
iajs-881	73	129	a	a	DET
iajs-881	73	130	4	4	NUM
iajs-881	73	131	2	2	NUM
iajs-881	73	132			X
iajs-881	73	133			PROPN
iajs-881	73	134			PROPN
iajs-881	73	135			NUM
iajs-881	73	136	and	and	CCONJ
iajs-881	73	137	2	2	NUM
iajs-881	73	138	2	2	NUM
iajs-881	73	139	a	a	DET
iajs-881	73	140	a	a	DET
iajs-881	73	141	4	4	NUM
iajs-881	73	142	2	2	NUM
iajs-881	73	143			NOUN
iajs-881	73	144			ADV
iajs-881	73	145			PROPN
iajs-881	73	146			NUM
iajs-881	73	147	from	from	ADP
iajs-881	73	148	eq.(11	eq.(11	PROPN
iajs-881	73	149	)	)	PUNCT
iajs-881	73	150	,	,	PUNCT
iajs-881	73	151	the	the	DET
iajs-881	73	152	error	error	NOUN
iajs-881	73	153	will	will	AUX
iajs-881	73	154	not	not	PART
iajs-881	73	155	grow	grow	VERB
iajs-881	73	156	with	with	ADP
iajs-881	73	157	time	time	NOUN
iajs-881	73	158	if	if	SCONJ
iajs-881	73	159	1	1	NUM
iajs-881	73	160			NOUN
iajs-881	73	161	,	,	PUNCT
iajs-881	73	162	for	for	ADP
iajs-881	73	163	all	all	DET
iajs-881	73	164	real	real	ADJ
iajs-881	73	165	β	β	X
iajs-881	73	166	…	…	PUNCT
iajs-881	73	167	…	…	PUNCT
iajs-881	73	168	……	……	NOUN
iajs-881	73	169	……	……	NOUN
iajs-881	73	170	(	(	PUNCT
iajs-881	73	171	12	12	NUM
iajs-881	73	172	)	)	PUNCT
iajs-881	73	173	equation	equation	NOUN
iajs-881	73	174	(	(	PUNCT
iajs-881	73	175	12	12	NUM
iajs-881	73	176	)	)	PUNCT
iajs-881	73	177	is	be	AUX
iajs-881	73	178	called	call	VERB
iajs-881	73	179	the	the	DET
iajs-881	73	180	von	von	PROPN
iajs-881	73	181	-	-	PUNCT
iajs-881	73	182	neumann	neumann	PROPN
iajs-881	73	183	’s	’s	PART
iajs-881	73	184	condition	condition	NOUN
iajs-881	73	185	for	for	ADP
iajs-881	73	186	stability	stability	NOUN
iajs-881	73	187	.thus	.thus	INTJ
iajs-881	73	188	we	we	PRON
iajs-881	73	189	will	will	AUX
iajs-881	73	190	use	use	VERB
iajs-881	73	191	eq	eq	ADP
iajs-881	73	192	.	.	PUNCT
iajs-881	74	1	(	(	PUNCT
iajs-881	74	2	12	12	NUM
iajs-881	74	3	)	)	PUNCT
iajs-881	74	4	to	to	PART
iajs-881	74	5	find	find	VERB
iajs-881	74	6	the	the	DET
iajs-881	74	7	stability	stability	NOUN
iajs-881	74	8	condition	condition	NOUN
iajs-881	74	9	of	of	ADP
iajs-881	74	10	the	the	DET
iajs-881	74	11	finite	finite	ADJ
iajs-881	74	12	difference	difference	NOUN
iajs-881	74	13	equation	equation	NOUN
iajs-881	74	14	.	.	PUNCT
iajs-881	75	1	for	for	ADP
iajs-881	75	2	stability	stability	NOUN
iajs-881	75	3	;	;	PUNCT
iajs-881	75	4	as	as	SCONJ
iajs-881	75	5	r	r	NOUN
iajs-881	75	6	,	,	PUNCT
iajs-881	75	7	q	q	NOUN
iajs-881	75	8	and	and	CCONJ
iajs-881	75	9	β	β	X
iajs-881	75	10	are	be	AUX
iajs-881	75	11	real	real	ADJ
iajs-881	75	12	and	and	CCONJ
iajs-881	75	13	when	when	SCONJ
iajs-881	75	14	giving	give	VERB
iajs-881	75	15	stability	stability	NOUN
iajs-881	75	16	while	while	SCONJ
iajs-881	75	17	2	2	NUM
iajs-881	75	18	gives	give	VERB
iajs-881	75	19	instability	instability	NOUN
iajs-881	75	20	.	.	PUNCT
iajs-881	76	1	when	when	SCONJ
iajs-881	76	2	−1	−1	NOUN
iajs-881	76	3	≤	≤	VERB
iajs-881	76	4	a	a	DET
iajs-881	76	5	≤	≤	NUM
iajs-881	76	6	1	1	NUM
iajs-881	76	7	,	,	PUNCT
iajs-881	76	8	we	we	PRON
iajs-881	76	9	get	get	VERB
iajs-881	76	10	1	1	NUM
iajs-881	76	11	2and	2and	NUM
iajs-881	76	12			NOUN
iajs-881	76	13	are	be	AUX
iajs-881	76	14	complex	complex	ADJ
iajs-881	76	15	number	number	NOUN
iajs-881	76	16	,	,	PUNCT
iajs-881	76	17	hence	hence	ADV
iajs-881	76	18	:	:	PUNCT
iajs-881	76	19	2	2	NUM
iajs-881	76	20	1	1	NUM
iajs-881	76	21	a	a	DET
iajs-881	76	22	y	y	PROPN
iajs-881	76	23	4	4	NUM
iajs-881	76	24	a	a	DET
iajs-881	76	25	2	2	NUM
iajs-881	76	26			X
iajs-881	76	27			PROPN
iajs-881	76	28			PROPN
iajs-881	76	29			NUM
iajs-881	76	30	and	and	CCONJ
iajs-881	76	31	2	2	NUM
iajs-881	76	32	1	1	NUM
iajs-881	76	33	a	a	DET
iajs-881	76	34	y	y	PROPN
iajs-881	76	35	4	4	NUM
iajs-881	76	36	a	a	DET
iajs-881	76	37	2	2	NUM
iajs-881	76	38			NOUN
iajs-881	76	39			PROPN
iajs-881	76	40			PROPN
iajs-881	76	41			NUM
iajs-881	76	42	then	then	ADV
iajs-881	76	43	using	use	VERB
iajs-881	76	44	von	von	PROPN
iajs-881	76	45	-	-	PUNCT
iajs-881	76	46	neumann	neumann	PROPN
iajs-881	76	47	’s	’s	PART
iajs-881	76	48	condition	condition	NOUN
iajs-881	76	49	(	(	PUNCT
iajs-881	76	50	12	12	NUM
iajs-881	76	51	)	)	PUNCT
iajs-881	76	52	to	to	PART
iajs-881	76	53	prove	prove	VERB
iajs-881	76	54	that	that	SCONJ
iajs-881	76	55	eq.(9	eq.(9	ADJ
iajs-881	76	56	)	)	PUNCT
iajs-881	76	57	is	be	AUX
iajs-881	76	58	stable	stable	ADJ
iajs-881	76	59	for	for	ADP
iajs-881	76	60	1	1	NUM
iajs-881	76	61	a	a	DET
iajs-881	76	62	1	1	NUM
iajs-881	76	63			NOUN
iajs-881	76	64			NOUN
iajs-881	76	65	,	,	PUNCT
iajs-881	76	66	the	the	DET
iajs-881	76	67	only	only	ADJ
iajs-881	76	68	useful	useful	ADJ
iajs-881	76	69	inequality	inequality	NOUN
iajs-881	76	70	is	be	AUX
iajs-881	76	71	a	a	DET
iajs-881	76	72	1	1	NUM
iajs-881	76	73			NOUN
iajs-881	76	74	,	,	PUNCT
iajs-881	76	75	hence	hence	ADV
iajs-881	76	76	2	2	NUM
iajs-881	76	77	rqe	rqe	NOUN
iajs-881	76	78	1	1	PROPN
iajs-881	76	79			NOUN
iajs-881	76	80	,	,	PUNCT
iajs-881	76	81	where	where	SCONJ
iajs-881	76	82	e	e	PROPN
iajs-881	76	83	1	1	NUM
iajs-881	76	84			NOUN
iajs-881	76	85	.therefore	.therefore	ADP
iajs-881	76	86	;	;	PUNCT
iajs-881	76	87	1	1	NUM
iajs-881	76	88	r	r	NOUN
iajs-881	76	89	q	q	PUNCT
iajs-881	76	90			PROPN
iajs-881	76	91			NOUN
iajs-881	76	92	,	,	PUNCT
iajs-881	76	93	where	where	SCONJ
iajs-881	76	94	1	1	NUM
iajs-881	76	95	≤	≤	NOUN
iajs-881	76	96	q	q	PUNCT
iajs-881	76	97	≤	≤	NUM
iajs-881	76	98	2	2	NUM
iajs-881	76	99	.	.	PUNCT
iajs-881	77	1	hence	hence	ADV
iajs-881	77	2	,	,	PUNCT
iajs-881	77	3	1	1	NUM
iajs-881	77	4	r	r	NOUN
iajs-881	77	5	2	2	NUM
iajs-881	77	6			NOUN
iajs-881	77	7	,	,	PUNCT
iajs-881	77	8	which	which	PRON
iajs-881	77	9	is	be	AUX
iajs-881	77	10	the	the	DET
iajs-881	77	11	stability	stability	NOUN
iajs-881	77	12	condition	condition	NOUN
iajs-881	77	13	.	.	PUNCT
iajs-881	78	1	ibn	ibn	PROPN
iajs-881	78	2	alhaitham	alhaitham	PROPN
iajs-881	79	1	j.	j.	PROPN
iajs-881	80	1	fo	fo	ADP
iajs-881	80	2	r	r	NOUN
iajs-881	80	3	pure	pure	ADJ
iajs-881	80	4	&	&	CCONJ
iajs-881	80	5	appl	appl	PROPN
iajs-881	80	6	.	.	PUNCT
iajs-881	81	1	sc	sc	PROPN
iajs-881	81	2	i.	i.	PROPN
iajs-881	81	3	vo	vo	PROPN
iajs-881	81	4	l.23	l.23	PROPN
iajs-881	81	5	(	(	PUNCT
iajs-881	81	6	3	3	NUM
iajs-881	81	7	)	)	PUNCT
iajs-881	81	8	2010	2010	NUM
iajs-881	81	9	the	the	DET
iajs-881	81	10	implicit	implicit	ADJ
iajs-881	81	11	finite	finite	ADJ
iajs-881	81	12	difference	difference	NOUN
iajs-881	81	13	method	method	NOUN
iajs-881	81	14	for	for	ADP
iajs-881	81	15	solving	solve	VERB
iajs-881	81	16	fractional	fractional	ADJ
iajs-881	81	17	hyperbolic	hyperbolic	ADJ
iajs-881	81	18	partial	partial	ADJ
iajs-881	81	19	differential	differential	NOUN
iajs-881	81	20	equations	equation	NOUN
iajs-881	81	21	ihjpas	ihjpa	VERB
iajs-881	81	22	now	now	ADV
iajs-881	82	1	,	,	PUNCT
iajs-881	82	2	we	we	PRON
iajs-881	82	3	can	can	AUX
iajs-881	82	4	improve	improve	VERB
iajs-881	82	5	and	and	CCONJ
iajs-881	82	6	introduce	introduce	VERB
iajs-881	82	7	similar	similar	ADJ
iajs-881	82	8	approach	approach	NOUN
iajs-881	82	9	for	for	ADP
iajs-881	82	10	the	the	DET
iajs-881	82	11	implicit	implicit	ADJ
iajs-881	82	12	finite	finite	ADJ
iajs-881	82	13	difference	difference	NOUN
iajs-881	82	14	method	method	NOUN
iajs-881	82	15	to	to	PART
iajs-881	82	16	solved	solved	VERB
iajs-881	82	17	the	the	DET
iajs-881	82	18	one	one	NUM
iajs-881	82	19	–	–	PUNCT
iajs-881	82	20	sided	sided	ADJ
iajs-881	82	21	fractional	fractional	ADJ
iajs-881	82	22	hyperbolic	hyperbolic	ADJ
iajs-881	82	23	partial	partial	ADJ
iajs-881	82	24	differential	differential	NOUN
iajs-881	82	25	equations	equation	NOUN
iajs-881	82	26	.	.	PUNCT
iajs-881	83	1	the	the	DET
iajs-881	83	2	resulting	result	VERB
iajs-881	83	3	discretization	discretization	NOUN
iajs-881	83	4	takes	take	VERB
iajs-881	83	5	the	the	DET
iajs-881	83	6	following	follow	VERB
iajs-881	83	7	form	form	NOUN
iajs-881	83	8	:	:	PUNCT
iajs-881	83	9	i	i	PRON
iajs-881	83	10	1	1	NUM
iajs-881	84	1	i	i	PROPN
iajs-881	84	2	,	,	PUNCT
iajs-881	84	3	j	j	PROPN
iajs-881	84	4	1	1	NUM
iajs-881	84	5	i	i	PROPN
iajs-881	84	6	,	,	PUNCT
iajs-881	84	7	j	j	PROPN
iajs-881	84	8	i	i	PROPN
iajs-881	84	9	,	,	PUNCT
iajs-881	84	10	j	j	PROPN
iajs-881	84	11	1	1	NUM
iajs-881	84	12	i	i	PROPN
iajs-881	84	13	,	,	PUNCT
iajs-881	84	14	j	j	PROPN
iajs-881	84	15	w	w	VERB
iajs-881	84	16	i	i	NOUN
iajs-881	84	17	w	w	PROPN
iajs-881	84	18	1	1	NUM
iajs-881	84	19	,	,	PUNCT
iajs-881	84	20	j2	j2	PROPN
iajs-881	84	21	q	q	PROPN
iajs-881	84	22	w	w	PROPN
iajs-881	84	23	0	0	NUM
iajs-881	84	24	u	u	NOUN
iajs-881	84	25	2u	2u	NOUN
iajs-881	84	26	u	u	NOUN
iajs-881	84	27	c	c	PROPN
iajs-881	84	28	g	g	NOUN
iajs-881	84	29	u	u	PROPN
iajs-881	84	30	k	k	PROPN
iajs-881	84	31	h	h	PROPN
iajs-881	84	32			ADV
iajs-881	84	33			PUNCT
iajs-881	84	34			PROPN
iajs-881	84	35			PROPN
iajs-881	84	36			PART
iajs-881	84	37			PROPN
iajs-881	84	38			PROPN
iajs-881	84	39			ADP
iajs-881	84	40			NUM
iajs-881	84	41			X
iajs-881	84	42	where	where	SCONJ
iajs-881	84	43	i	i	PRON
iajs-881	84	44	1,2,	1,2,	VERB
iajs-881	84	45	...	...	PUNCT
iajs-881	84	46	,n	,n	PUNCT
iajs-881	84	47	1	1	NUM
iajs-881	84	48	;	;	PUNCT
iajs-881	84	49	j	j	PROPN
iajs-881	84	50	0,1,	0,1,	NOUN
iajs-881	84	51	...	...	PUNCT
iajs-881	84	52	,m	,m	PUNCT
iajs-881	84	53	1	1	NUM
iajs-881	84	54			PROPN
iajs-881	84	55			PROPN
iajs-881	84	56			PROPN
iajs-881	84	57	.	.	PUNCT
iajs-881	85	1	then	then	ADV
iajs-881	85	2	to	to	PART
iajs-881	85	3	get	get	VERB
iajs-881	85	4	i	i	PRON
iajs-881	85	5	1	1	NUM
iajs-881	85	6	i	i	PROPN
iajs-881	85	7	,	,	PUNCT
iajs-881	85	8	j	j	PROPN
iajs-881	85	9	1	1	NUM
iajs-881	85	10	i	i	PROPN
iajs-881	85	11	,	,	PUNCT
iajs-881	86	1	j	j	PROPN
iajs-881	86	2	i	i	PROPN
iajs-881	86	3	,	,	PUNCT
iajs-881	86	4	j	j	PROPN
iajs-881	86	5	1	1	NUM
iajs-881	86	6	w	w	NOUN
iajs-881	86	7	i	i	PRON
iajs-881	86	8	w	w	PROPN
iajs-881	86	9	1	1	NUM
iajs-881	86	10	,	,	PUNCT
iajs-881	86	11	j	j	PROPN
iajs-881	86	12	1	1	NUM
iajs-881	86	13	w	w	PROPN
iajs-881	86	14	0	0	NUM
iajs-881	86	15	u	u	NOUN
iajs-881	86	16	2u	2u	NOUN
iajs-881	86	17	u	u	NOUN
iajs-881	86	18	r	r	NOUN
iajs-881	86	19	g	g	PROPN
iajs-881	86	20	u	u	PROPN
iajs-881	86	21			ADV
iajs-881	86	22			PUNCT
iajs-881	86	23			PROPN
iajs-881	86	24			PROPN
iajs-881	86	25			VERB
iajs-881	86	26			PUNCT
iajs-881	86	27			PROPN
iajs-881	86	28			PROPN
iajs-881	86	29			ADP
iajs-881	86	30			NUM
iajs-881	86	31			X
iajs-881	86	32	…	…	PUNCT
iajs-881	86	33	…	…	PUNCT
iajs-881	86	34	…	…	PUNCT
iajs-881	86	35	…	…	PUNCT
iajs-881	86	36	…	…	PUNCT
iajs-881	86	37	…	…	PUNCT
iajs-881	86	38	…	…	PUNCT
iajs-881	86	39	..	..	PUNCT
iajs-881	86	40	(	(	PUNCT
iajs-881	86	41	13	13	NUM
iajs-881	86	42	)	)	PUNCT
iajs-881	86	43	in	in	ADP
iajs-881	86	44	the	the	DET
iajs-881	86	45	above	above	ADJ
iajs-881	86	46	equation	equation	NOUN
iajs-881	86	47	and	and	CCONJ
iajs-881	86	48	under	under	ADP
iajs-881	86	49	the	the	DET
iajs-881	86	50	same	same	ADJ
iajs-881	86	51	conditions	condition	NOUN
iajs-881	86	52	of	of	ADP
iajs-881	86	53	eq.(9	eq.(9	ADJ
iajs-881	86	54	)	)	PUNCT
iajs-881	86	55	and	and	CCONJ
iajs-881	86	56	substituting	substitute	VERB
iajs-881	86	57	eqs	eqs	PROPN
iajs-881	86	58	.	.	PUNCT
iajs-881	87	1	(	(	PUNCT
iajs-881	87	2	10	10	NUM
iajs-881	87	3	)	)	PUNCT
iajs-881	87	4	and	and	CCONJ
iajs-881	87	5	(	(	PUNCT
iajs-881	87	6	11	11	NUM
iajs-881	87	7	)	)	PUNCT
iajs-881	87	8	into	into	ADP
iajs-881	87	9	eq	eq	NOUN
iajs-881	87	10	.	.	PUNCT
iajs-881	88	1	(	(	PUNCT
iajs-881	88	2	13	13	NUM
iajs-881	88	3	)	)	PUNCT
iajs-881	88	4	,	,	PUNCT
iajs-881	88	5	one	one	PRON
iajs-881	88	6	can	can	AUX
iajs-881	88	7	get	get	VERB
iajs-881	88	8	:	:	PUNCT
iajs-881	88	9	12	12	NUM
iajs-881	88	10			ADJ
iajs-881	88	11			NOUN
iajs-881	88	12			VERB
iajs-881	88	13	<	<	X
iajs-881	88	14	rqe	rqe	PROPN
iajs-881	88	15	,	,	PUNCT
iajs-881	88	16	where	where	SCONJ
iajs-881	88	17	h(1	h(1	PROPN
iajs-881	88	18	w)	w)	NOUN
iajs-881	88	19			PROPN
iajs-881	88	20			PROPN
iajs-881	88	21	.	.	PUNCT
iajs-881	89	1	hence	hence	ADV
iajs-881	89	2	the	the	DET
iajs-881	89	3	values	value	NOUN
iajs-881	89	4	of	of	ADP
iajs-881	89	5			PROPN
iajs-881	89	6	are	be	AUX
iajs-881	89	7	:	:	PUNCT
iajs-881	89	8	1	1	NUM
iajs-881	89	9	2	2	NUM
iajs-881	89	10	1	1	NUM
iajs-881	89	11	1	1	NUM
iajs-881	89	12	(	(	PUNCT
iajs-881	89	13	1	1	NUM
iajs-881	89	14	a	a	NOUN
iajs-881	89	15	)	)	PUNCT
iajs-881	89	16	a	a	DET
iajs-881	89	17			ADJ
iajs-881	89	18			PROPN
iajs-881	89	19			PROPN
iajs-881	89	20			NUM
iajs-881	89	21	and	and	CCONJ
iajs-881	89	22	1	1	NUM
iajs-881	89	23	2	2	NUM
iajs-881	89	24	2	2	NUM
iajs-881	89	25	1	1	NUM
iajs-881	89	26	(	(	PUNCT
iajs-881	89	27	1	1	NUM
iajs-881	89	28	a	a	X
iajs-881	89	29	)	)	PUNCT
iajs-881	89	30	a	a	DET
iajs-881	89	31			PROPN
iajs-881	89	32			PROPN
iajs-881	89	33			PROPN
iajs-881	89	34			NUM
iajs-881	89	35	where	where	SCONJ
iajs-881	89	36	a	a	DET
iajs-881	89	37	1	1	NUM
iajs-881	89	38	rqe	rqe	NOUN
iajs-881	89	39			NOUN
iajs-881	89	40	.	.	PUNCT
iajs-881	90	1	to	to	PART
iajs-881	90	2	discuss	discuss	VERB
iajs-881	90	3	the	the	DET
iajs-881	90	4	stability	stability	NOUN
iajs-881	90	5	of	of	ADP
iajs-881	90	6	eq	eq	PROPN
iajs-881	90	7	.	.	PUNCT
iajs-881	91	1	(	(	PUNCT
iajs-881	91	2	13	13	NUM
iajs-881	91	3	)	)	PUNCT
iajs-881	91	4	;	;	PUNCT
iajs-881	91	5	by	by	ADP
iajs-881	91	6	using	use	VERB
iajs-881	91	7	von	von	PROPN
iajs-881	91	8	-	-	PUNCT
iajs-881	91	9	neumann	neumann	PROPN
iajs-881	91	10	’s	’s	PART
iajs-881	91	11	condition	condition	NOUN
iajs-881	91	12	(	(	PUNCT
iajs-881	91	13	12	12	NUM
iajs-881	91	14	)	)	PUNCT
iajs-881	91	15	.	.	PUNCT
iajs-881	92	1	when	when	SCONJ
iajs-881	92	2	a	a	DET
iajs-881	92	3	<	<	X
iajs-881	92	4	1	1	NUM
iajs-881	92	5	,	,	PUNCT
iajs-881	92	6	we	we	PRON
iajs-881	92	7	get	get	VERB
iajs-881	92	8	real	real	ADJ
iajs-881	92	9	the	the	DET
iajs-881	92	10	roots	root	NOUN
iajs-881	92	11	,	,	PUNCT
iajs-881	92	12	1	1	NUM
iajs-881	92	13	also	also	ADV
iajs-881	92	14	,	,	PUNCT
iajs-881	92	15	which	which	PRON
iajs-881	92	16	gives	give	VERB
iajs-881	92	17	instability	instability	NOUN
iajs-881	92	18	while	while	SCONJ
iajs-881	92	19	2	2	NUM
iajs-881	92	20	gives	give	VERB
iajs-881	92	21	stability	stability	NOUN
iajs-881	92	22	for	for	ADP
iajs-881	92	23	this	this	DET
iajs-881	92	24	problem	problem	NOUN
iajs-881	92	25	.	.	PUNCT
iajs-881	93	1	now	now	ADV
iajs-881	93	2	,	,	PUNCT
iajs-881	93	3	when	when	SCONJ
iajs-881	93	4	1	1	NUM
iajs-881	93	5	a	a	DET
iajs-881	93	6	1	1	NUM
iajs-881	93	7			NOUN
iajs-881	93	8			NOUN
iajs-881	93	9	,	,	PUNCT
iajs-881	93	10	we	we	PRON
iajs-881	93	11	get	get	VERB
iajs-881	93	12	complex	complex	ADJ
iajs-881	93	13	number	number	NOUN
iajs-881	93	14	,	,	PUNCT
iajs-881	93	15	which	which	PRON
iajs-881	93	16	are	be	AUX
iajs-881	93	17	1	1	NUM
iajs-881	93	18	2	2	NUM
iajs-881	93	19	1	1	NUM
iajs-881	93	20	1	1	NUM
iajs-881	93	21	(	(	PUNCT
iajs-881	93	22	1	1	NUM
iajs-881	93	23	a	a	X
iajs-881	93	24	)	)	PUNCT
iajs-881	93	25	a	a	DET
iajs-881	93	26			NOUN
iajs-881	93	27			NUM
iajs-881	93	28			PROPN
iajs-881	93	29			PROPN
iajs-881	93	30			NUM
iajs-881	93	31	and	and	CCONJ
iajs-881	94	1	1	1	NUM
iajs-881	94	2	2	2	NUM
iajs-881	94	3	1	1	NUM
iajs-881	94	4	1	1	NUM
iajs-881	94	5	(	(	PUNCT
iajs-881	94	6	1	1	NUM
iajs-881	94	7	a	a	NOUN
iajs-881	94	8	)	)	PUNCT
iajs-881	94	9	a	a	DET
iajs-881	94	10			X
iajs-881	94	11			NUM
iajs-881	94	12			PROPN
iajs-881	94	13			PROPN
iajs-881	94	14			NUM
iajs-881	94	15	.and	.and	PUNCT
iajs-881	95	1	the	the	DET
iajs-881	95	2	condition	condition	NOUN
iajs-881	95	3	of	of	ADP
iajs-881	95	4	the	the	DET
iajs-881	95	5	stability	stability	NOUN
iajs-881	95	6	leads	lead	VERB
iajs-881	95	7	to	to	ADP
iajs-881	95	8	r	r	PROPN
iajs-881	95	9	≥	≥	NUM
iajs-881	95	10	1	1	NUM
iajs-881	95	11	when	when	SCONJ
iajs-881	95	12	1	1	NUM
iajs-881	95	13	≤	≤	NOUN
iajs-881	95	14	q	q	ADJ
iajs-881	95	15	≤	≤	NUM
iajs-881	95	16	2	2	NUM
iajs-881	95	17	and	and	CCONJ
iajs-881	95	18	e	e	PROPN
iajs-881	95	19	1	1	PROPN
iajs-881	95	20			NOUN
iajs-881	95	21	therefore	therefore	ADV
iajs-881	95	22	;	;	PUNCT
iajs-881	95	23	the	the	DET
iajs-881	95	24	finite	finite	ADJ
iajs-881	95	25	difference	difference	NOUN
iajs-881	95	26	eq	eq	ADP
iajs-881	95	27	.	.	PUNCT
iajs-881	96	1	(	(	PUNCT
iajs-881	96	2	13	13	NUM
iajs-881	96	3	)	)	PUNCT
iajs-881	96	4	is	be	AUX
iajs-881	96	5	instable	instable	ADJ
iajs-881	96	6	for	for	ADP
iajs-881	96	7	r	r	NOUN
iajs-881	96	8	≤	≤	NUM
iajs-881	96	9	2	2	NUM
iajs-881	96	10	q	q	NOUN
iajs-881	96	11	,	,	PUNCT
iajs-881	96	12	1	1	NUM
iajs-881	96	13	≤	≤	NUM
iajs-881	96	14	q	q	PUNCT
iajs-881	96	15	≤	≤	NUM
iajs-881	96	16	2	2	NUM
iajs-881	96	17	.	.	PUNCT
iajs-881	96	18	illustrative	illustrative	ADJ
iajs-881	96	19	example	example	NOUN
iajs-881	96	20	to	to	PART
iajs-881	96	21	illustrate	illustrate	VERB
iajs-881	96	22	the	the	DET
iajs-881	96	23	methods	method	NOUN
iajs-881	96	24	of	of	ADP
iajs-881	96	25	the	the	DET
iajs-881	96	26	solution	solution	NOUN
iajs-881	96	27	,	,	PUNCT
iajs-881	96	28	an	an	DET
iajs-881	96	29	illustrative	illustrative	ADJ
iajs-881	96	30	numerical	numerical	ADJ
iajs-881	96	31	example	example	NOUN
iajs-881	96	32	is	be	AUX
iajs-881	96	33	considered	consider	VERB
iajs-881	96	34	:	:	PUNCT
iajs-881	96	35	example	example	NOUN
iajs-881	96	36	:	:	PUNCT
iajs-881	96	37	ibn	ibn	PROPN
iajs-881	96	38	alhaitham	alhaitham	NOUN
iajs-881	96	39	j.	j.	PROPN
iajs-881	96	40	for	for	ADP
iajs-881	96	41	pure	pure	ADJ
iajs-881	96	42	&	&	CCONJ
iajs-881	96	43	appl	appl	PROPN
iajs-881	96	44	.	.	PUNCT
iajs-881	97	1	sci	sci	PROPN
iajs-881	97	2	.	.	PUNCT
iajs-881	98	1	vol.23	vol.23	PROPN
iajs-881	98	2	(	(	PUNCT
iajs-881	98	3	3	3	NUM
iajs-881	98	4	)	)	PUNCT
iajs-881	98	5	2010	2010	NUM
iajs-881	98	6	consider	consider	VERB
iajs-881	98	7	the	the	DET
iajs-881	98	8	fractional	fractional	ADJ
iajs-881	98	9	order	order	NOUN
iajs-881	98	10	partial	partial	ADJ
iajs-881	98	11	differential	differential	NOUN
iajs-881	98	12	equation	equation	NOUN
iajs-881	98	13	:	:	PUNCT
iajs-881	98	14	ihjpas	ihjpa	VERB
iajs-881	98	15	1t0	1t0	NUM
iajs-881	98	16	,	,	PUNCT
iajs-881	98	17	2x0	2x0	NUM
iajs-881	98	18	,	,	PUNCT
iajs-881	98	19	xt546.2tx546.2x2x4	xt546.2tx546.2x2x4	NOUN
iajs-881	98	20	x	x	SYM
iajs-881	98	21	u	u	NOUN
iajs-881	98	22	x	x	PROPN
iajs-881	98	23	)	)	PUNCT
iajs-881	98	24	5.0	5.0	NUM
iajs-881	98	25	(	(	PUNCT
iajs-881	98	26	1	1	NUM
iajs-881	98	27	t	t	NOUN
iajs-881	98	28	u	u	NOUN
iajs-881	98	29	22232	22232	NUM
iajs-881	98	30	5.1	5.1	NUM
iajs-881	98	31	5.1	5.1	NUM
iajs-881	98	32	2	2	NUM
iajs-881	98	33	1	1	NUM
iajs-881	98	34	2	2	NUM
iajs-881	98	35	2	2	NUM
iajs-881	98	36			NOUN
iajs-881	98	37			ADJ
iajs-881	98	38			ADJ
iajs-881	98	39			VERB
iajs-881	98	40			NUM
iajs-881	98	41			ADJ
iajs-881	98	42			PROPN
iajs-881	98	43	together	together	ADV
iajs-881	98	44	with	with	ADP
iajs-881	98	45	initial	initial	ADJ
iajs-881	98	46	and	and	CCONJ
iajs-881	98	47	zero	zero	NUM
iajs-881	98	48	dirichlet	dirichlet	PROPN
iajs-881	98	49	boundary	boundary	ADJ
iajs-881	98	50	conditions	condition	NOUN
iajs-881	98	51	:	:	PUNCT
iajs-881	98	52	u(x	u(x	NOUN
iajs-881	98	53	,	,	PUNCT
iajs-881	98	54	0)=0	0)=0	NUM
iajs-881	98	55	,	,	PUNCT
iajs-881	98	56	u(x,0	u(x,0	PROPN
iajs-881	98	57	)	)	PUNCT
iajs-881	98	58	0	0	NUM
iajs-881	99	1	t	t	PROPN
iajs-881	99	2			PROPN
iajs-881	99	3			PROPN
iajs-881	99	4			PROPN
iajs-881	99	5	for	for	ADP
iajs-881	99	6	0	0	NUM
iajs-881	99	7	x	x	SYM
iajs-881	99	8	2	2	NUM
iajs-881	99	9			NOUN
iajs-881	99	10	..	..	PUNCT
iajs-881	100	1	u(0	u(0	NOUN
iajs-881	100	2	,	,	PUNCT
iajs-881	100	3	t)0	t)0	PROPN
iajs-881	100	4	,	,	PUNCT
iajs-881	100	5	u(1	u(1	PROPN
iajs-881	100	6	,	,	PUNCT
iajs-881	100	7	t)0	t)0	NOUN
iajs-881	100	8	for	for	ADP
iajs-881	100	9	0	0	NUM
iajs-881	100	10	t	t	NOUN
iajs-881	100	11	1	1	NUM
iajs-881	100	12			NOUN
iajs-881	100	13	.	.	PUNCT
iajs-881	101	1	this	this	DET
iajs-881	101	2	example	example	NOUN
iajs-881	101	3	has	have	VERB
iajs-881	101	4	the	the	DET
iajs-881	101	5	exact	exact	ADJ
iajs-881	101	6	solution	solution	NOUN
iajs-881	101	7	as	as	ADP
iajs-881	101	8	:	:	SYM
iajs-881	101	9	2	2	NUM
iajs-881	101	10	2u(x	2u(x	NOUN
iajs-881	101	11	,	,	PUNCT
iajs-881	101	12	t	t	PROPN
iajs-881	101	13	)	)	PUNCT
iajs-881	101	14	x	x	SYM
iajs-881	101	15	(	(	PUNCT
iajs-881	101	16	x	x	SYM
iajs-881	101	17	2)t	2)t	NUM
iajs-881	101	18	,	,	PUNCT
iajs-881	101	19			NUM
iajs-881	101	20			NOUN
iajs-881	101	21	[	[	NOUN
iajs-881	101	22	8	8	NUM
iajs-881	101	23	]	]	PUNCT
iajs-881	101	24	.	.	PUNCT
iajs-881	102	1	which	which	PRON
iajs-881	102	2	is	be	AUX
iajs-881	102	3	considered	consider	VERB
iajs-881	102	4	for	for	ADP
iajs-881	102	5	the	the	DET
iajs-881	102	6	comparison	comparison	NOUN
iajs-881	102	7	purpose	purpose	NOUN
iajs-881	102	8	.	.	PUNCT
iajs-881	103	1	here	here	ADV
iajs-881	103	2	;	;	PUNCT
iajs-881	103	3	we	we	PRON
iajs-881	103	4	use	use	VERB
iajs-881	103	5	the	the	DET
iajs-881	103	6	explicit	explicit	ADJ
iajs-881	103	7	and	and	CCONJ
iajs-881	103	8	implicit	implicit	ADJ
iajs-881	103	9	finite	finite	ADJ
iajs-881	103	10	difference	difference	NOUN
iajs-881	103	11	methods	method	NOUN
iajs-881	103	12	to	to	PART
iajs-881	103	13	solve	solve	VERB
iajs-881	103	14	this	this	DET
iajs-881	103	15	example	example	NOUN
iajs-881	103	16	numerically	numerically	ADV
iajs-881	103	17	.	.	PUNCT
iajs-881	104	1	to	to	PART
iajs-881	104	2	do	do	VERB
iajs-881	104	3	this	this	PRON
iajs-881	104	4	,	,	PUNCT
iajs-881	104	5	first	first	ADV
iajs-881	104	6	we	we	PRON
iajs-881	104	7	divide	divide	VERB
iajs-881	104	8	the	the	DET
iajs-881	104	9	x	x	NOUN
iajs-881	104	10	-	-	NOUN
iajs-881	104	11	interval	interval	NOUN
iajs-881	104	12	into	into	ADP
iajs-881	104	13	2	2	NUM
iajs-881	104	14	subintervals	subinterval	NOUN
iajs-881	104	15	such	such	ADJ
iajs-881	104	16	that	that	PRON
iajs-881	104	17	ix	ix	PROPN
iajs-881	104	18	i,	i,	X
iajs-881	105	1	i0,1,2	i0,1,2	PROPN
iajs-881	105	2	and	and	CCONJ
iajs-881	105	3	the	the	DET
iajs-881	105	4	t	t	NOUN
iajs-881	105	5	-	-	PUNCT
iajs-881	105	6	interval	interval	NOUN
iajs-881	105	7	into	into	ADP
iajs-881	105	8	2	2	NUM
iajs-881	105	9	subintervals	subinterval	NOUN
iajs-881	105	10	such	such	ADJ
iajs-881	105	11	that	that	SCONJ
iajs-881	105	12	j	j	PROPN
iajs-881	105	13	j	j	PROPN
iajs-881	105	14	t	t	PROPN
iajs-881	105	15	,	,	PUNCT
iajs-881	105	16	2	2	NUM
iajs-881	105	17			NUM
iajs-881	105	18	j0,1,2	j0,1,2	NOUN
iajs-881	105	19	.	.	PUNCT
iajs-881	106	1	thus	thus	ADV
iajs-881	106	2	,	,	PUNCT
iajs-881	106	3	the	the	DET
iajs-881	106	4	initial	initial	ADJ
iajs-881	106	5	and	and	CCONJ
iajs-881	106	6	zero	zero	NUM
iajs-881	106	7	dirichlet	dirichlet	PROPN
iajs-881	106	8	boundary	boundary	ADJ
iajs-881	106	9	conditions	condition	NOUN
iajs-881	106	10	become	become	VERB
iajs-881	106	11	:	:	PUNCT
iajs-881	106	12	iu(x	iu(x	NOUN
iajs-881	106	13	,	,	PUNCT
iajs-881	106	14	0	0	NUM
iajs-881	106	15	)	)	PUNCT
iajs-881	106	16	0	0	PROPN
iajs-881	106	17	for	for	ADP
iajs-881	106	18	i0,1,2	i0,1,2	PROPN
iajs-881	106	19	.	.	PROPN
iajs-881	106	20	iu(x	iu(x	NOUN
iajs-881	106	21	,	,	PUNCT
iajs-881	106	22	0	0	NUM
iajs-881	106	23	)	)	PUNCT
iajs-881	106	24	0	0	NUM
iajs-881	107	1	t	t	PROPN
iajs-881	107	2			PROPN
iajs-881	107	3			PROPN
iajs-881	107	4			PROPN
iajs-881	107	5	for	for	ADP
iajs-881	107	6	i0,1,2	i0,1,2	PROPN
iajs-881	107	7	.	.	PUNCT
iajs-881	108	1	ju(0,t	ju(0,t	ADJ
iajs-881	108	2	)	)	PUNCT
iajs-881	108	3	0	0	PROPN
iajs-881	108	4	for	for	ADP
iajs-881	108	5	j0,1,2	j0,1,2	PROPN
iajs-881	108	6	.	.	PUNCT
iajs-881	109	1	ju(1	ju(1	NOUN
iajs-881	109	2	,	,	PUNCT
iajs-881	109	3	t	t	PROPN
iajs-881	109	4	)	)	PUNCT
iajs-881	109	5	0	0	PROPN
iajs-881	109	6	for	for	ADP
iajs-881	109	7	j0,1,2	j0,1,2	PROPN
iajs-881	109	8	.	.	PUNCT
iajs-881	110	1	by	by	ADP
iajs-881	110	2	using	use	VERB
iajs-881	110	3	the	the	DET
iajs-881	110	4	central	central	ADJ
iajs-881	110	5	difference	difference	NOUN
iajs-881	110	6	approximation	approximation	NOUN
iajs-881	110	7	to	to	ADP
iajs-881	110	8	the	the	DET
iajs-881	110	9	initial	initial	ADJ
iajs-881	110	10	derivative	derivative	ADJ
iajs-881	110	11	condition	condition	NOUN
iajs-881	110	12	one	one	PRON
iajs-881	110	13	can	can	AUX
iajs-881	110	14	get	get	VERB
iajs-881	110	15	:	:	PUNCT
iajs-881	110	16	i,1	i,1	NOUN
iajs-881	110	17	i	i	PRON
iajs-881	110	18	,	,	PUNCT
iajs-881	110	19	1	1	NUM
iajs-881	110	20	1	1	NUM
iajs-881	110	21	(	(	PUNCT
iajs-881	110	22	u	u	NOUN
iajs-881	110	23	u	u	NOUN
iajs-881	110	24	)	)	PUNCT
iajs-881	110	25	0	0	NUM
iajs-881	110	26	2	2	NUM
iajs-881	110	27	t	t	NOUN
iajs-881	110	28			NUM
iajs-881	110	29			NUM
iajs-881	110	30			NOUN
iajs-881	110	31	;	;	PUNCT
iajs-881	110	32	hence	hence	ADV
iajs-881	110	33	i,1	i,1	VERB
iajs-881	110	34	i	i	PRON
iajs-881	110	35	,	,	PUNCT
iajs-881	110	36	1u	1u	PROPN
iajs-881	110	37	u	u	NOUN
iajs-881	110	38			PROPN
iajs-881	110	39	for	for	ADP
iajs-881	110	40	i0,1,2	i0,1,2	PROPN
iajs-881	110	41	.	.	PUNCT
iajs-881	111	1	moreover	moreover	ADV
iajs-881	111	2	,	,	PUNCT
iajs-881	111	3	equation	equation	NOUN
iajs-881	111	4	(	(	PUNCT
iajs-881	111	5	7	7	X
iajs-881	111	6	)	)	PUNCT
iajs-881	111	7	becomes	become	VERB
iajs-881	111	8	:	:	PUNCT
iajs-881	111	9	1	1	NUM
iajs-881	111	10	i	i	NOUN
iajs-881	111	11	1	1	NUM
iajs-881	111	12	2	2	NUM
iajs-881	111	13	i	i	NOUN
iajs-881	111	14	,	,	PUNCT
iajs-881	111	15	j	j	PROPN
iajs-881	111	16	1	1	NUM
iajs-881	111	17	i	i	PROPN
iajs-881	111	18	,	,	PUNCT
iajs-881	111	19	j	j	PROPN
iajs-881	112	1	i	i	PROPN
iajs-881	112	2	,	,	PUNCT
iajs-881	112	3	j	j	PROPN
iajs-881	112	4	1	1	NUM
iajs-881	113	1	i	i	NOUN
iajs-881	113	2	k	k	NOUN
iajs-881	114	1	i	i	PRON
iajs-881	114	2	k	k	PROPN
iajs-881	115	1	1,j	1,j	X
iajs-881	115	2	k	k	NOUN
iajs-881	115	3	0	0	PUNCT
iajs-881	115	4	u	u	NOUN
iajs-881	115	5	2u	2u	NOUN
iajs-881	115	6	u	u	NOUN
iajs-881	115	7	0.25x	0.25x	PROPN
iajs-881	115	8	g	g	PROPN
iajs-881	115	9	u	u	PROPN
iajs-881	115	10			ADV
iajs-881	115	11			PUNCT
iajs-881	115	12			PROPN
iajs-881	115	13			PROPN
iajs-881	115	14			ADP
iajs-881	115	15			PROPN
iajs-881	115	16			PROPN
iajs-881	115	17			PROPN
iajs-881	115	18			CCONJ
iajs-881	115	19			X
iajs-881	115	20	2	2	NUM
iajs-881	115	21	3	3	NUM
iajs-881	115	22	2	2	NUM
iajs-881	115	23	2	2	NUM
iajs-881	115	24	2	2	NUM
iajs-881	116	1	i	i	PRON
iajs-881	116	2	i	i	PRON
iajs-881	117	1	i	i	INTJ
iajs-881	117	2	j	j	VERB
iajs-881	118	1	i	i	PRON
iajs-881	118	2	j0	j0	PROPN
iajs-881	118	3	.2	.2	NUM
iajs-881	118	4	5	5	NUM
iajs-881	118	5	(	(	PUNCT
iajs-881	118	6	4	4	NUM
iajs-881	118	7	x	x	SYM
iajs-881	118	8	2	2	NUM
iajs-881	118	9	x	x	SYM
iajs-881	118	10	2	2	NUM
iajs-881	118	11	.5	.5	NUM
iajs-881	118	12	4	4	NUM
iajs-881	118	13	6	6	NUM
iajs-881	118	14	x	x	SYM
iajs-881	118	15	t	t	PROPN
iajs-881	118	16	2	2	NUM
iajs-881	118	17	.5	.5	NUM
iajs-881	118	18	4	4	NUM
iajs-881	118	19	6	6	NUM
iajs-881	118	20	x	x	SYM
iajs-881	118	21	t	t	PROPN
iajs-881	118	22	)	)	PUNCT
iajs-881	118	23			PUNCT
iajs-881	118	24			PROPN
iajs-881	118	25			VERB
iajs-881	118	26			PROPN
iajs-881	118	27			VERB
iajs-881	118	28	where	where	SCONJ
iajs-881	118	29	i1	i1	PROPN
iajs-881	118	30	and	and	CCONJ
iajs-881	118	31	j0	j0	PROPN
iajs-881	118	32	,	,	PUNCT
iajs-881	118	33	1	1	X
iajs-881	118	34	.	.	X
iajs-881	119	1	therefore	therefore	ADV
iajs-881	119	2	1	1	NUM
iajs-881	119	3	i	i	NOUN
iajs-881	119	4	1	1	NUM
iajs-881	119	5	2	2	NUM
iajs-881	119	6	i,1	i,1	NOUN
iajs-881	119	7	i,0	i,0	X
iajs-881	119	8	i	i	PRON
iajs-881	119	9	,	,	PUNCT
iajs-881	119	10	1	1	NUM
iajs-881	120	1	i	i	NOUN
iajs-881	120	2	k	k	VERB
iajs-881	121	1	i	i	PRON
iajs-881	121	2	k	k	PROPN
iajs-881	122	1	1,0	1,0	NUM
iajs-881	122	2	k	k	NOUN
iajs-881	122	3	0	0	PUNCT
iajs-881	122	4	u	u	NOUN
iajs-881	122	5	2u	2u	NOUN
iajs-881	122	6	u	u	NOUN
iajs-881	122	7	0.25x	0.25x	PROPN
iajs-881	122	8	g	g	PROPN
iajs-881	122	9	u	u	PROPN
iajs-881	122	10			X
iajs-881	122	11			PROPN
iajs-881	122	12			PROPN
iajs-881	122	13			ADP
iajs-881	122	14			PROPN
iajs-881	122	15			PROPN
iajs-881	122	16			PROPN
iajs-881	122	17			SYM
iajs-881	122	18			NOUN
iajs-881	122	19	2	2	NUM
iajs-881	122	20	3	3	NUM
iajs-881	122	21	2	2	NUM
iajs-881	122	22	2	2	NUM
iajs-881	122	23	2	2	NUM
iajs-881	123	1	i	i	PRON
iajs-881	123	2	i	i	PRON
iajs-881	123	3	i	i	VERB
iajs-881	123	4	0	0	NUM
iajs-881	123	5	00	00	NUM
iajs-881	123	6	.25	.25	NUM
iajs-881	123	7	(	(	PUNCT
iajs-881	123	8	4	4	NUM
iajs-881	123	9	x	x	SYM
iajs-881	123	10	2	2	NUM
iajs-881	123	11	x	x	SYM
iajs-881	123	12	2.54	2.54	NUM
iajs-881	123	13	6x	6x	NUM
iajs-881	123	14	t	t	PROPN
iajs-881	123	15	2.546	2.546	NUM
iajs-881	123	16	x	x	SYM
iajs-881	123	17	t	t	NOUN
iajs-881	123	18	)	)	PUNCT
iajs-881	123	19			PROPN
iajs-881	123	20			ADV
iajs-881	123	21			PROPN
iajs-881	123	22			NUM
iajs-881	123	23	ibn	ibn	PROPN
iajs-881	123	24	alhaitham	alhaitham	NOUN
iajs-881	123	25	j.	j.	PROPN
iajs-881	123	26	for	for	ADP
iajs-881	123	27	pure	pure	ADJ
iajs-881	123	28	&	&	CCONJ
iajs-881	123	29	appl	appl	PROPN
iajs-881	123	30	.	.	PUNCT
iajs-881	124	1	sci	sci	PROPN
iajs-881	124	2	.	.	PUNCT
iajs-881	125	1	vol.23	vol.23	PROPN
iajs-881	125	2	(	(	PUNCT
iajs-881	125	3	3	3	NUM
iajs-881	125	4	)	)	PUNCT
iajs-881	125	5	2010	2010	NUM
iajs-881	125	6	ihjpas	ihjpa	VERB
iajs-881	125	7	by	by	ADP
iajs-881	125	8	substituting	substitute	VERB
iajs-881	125	9	i	i	PRON
iajs-881	125	10	,	,	PUNCT
iajs-881	125	11	1	1	NUM
iajs-881	125	12	i,1u	i,1u	PROPN
iajs-881	125	13	u	u	NOUN
iajs-881	125	14			ADJ
iajs-881	125	15	in	in	ADP
iajs-881	125	16	the	the	DET
iajs-881	125	17	above	above	ADJ
iajs-881	125	18	equation	equation	NOUN
iajs-881	125	19	one	one	PRON
iajs-881	125	20	can	can	AUX
iajs-881	125	21	show	show	VERB
iajs-881	125	22	that	that	SCONJ
iajs-881	125	23	i,1u	i,1u	PROPN
iajs-881	125	24	can	can	AUX
iajs-881	125	25	be	be	AUX
iajs-881	125	26	calculated	calculate	VERB
iajs-881	125	27	from	from	ADP
iajs-881	125	28	the	the	DET
iajs-881	125	29	equation	equation	NOUN
iajs-881	125	30	1	1	NUM
iajs-881	125	31	i	i	NOUN
iajs-881	125	32	1	1	NUM
iajs-881	125	33	2	2	NUM
iajs-881	125	34	i,1	i,1	NOUN
iajs-881	125	35	i,0	i,0	NUM
iajs-881	126	1	i	i	NOUN
iajs-881	126	2	k	k	PROPN
iajs-881	127	1	i	i	PRON
iajs-881	127	2	k	k	PROPN
iajs-881	128	1	1,0	1,0	NUM
iajs-881	128	2	k	k	NOUN
iajs-881	128	3	0	0	PUNCT
iajs-881	128	4	u	u	NOUN
iajs-881	128	5	u	u	NOUN
iajs-881	128	6	0.125x	0.125x	PROPN
iajs-881	128	7	g	g	PROPN
iajs-881	128	8	u	u	PROPN
iajs-881	128	9			PROPN
iajs-881	128	10			PROPN
iajs-881	128	11			VERB
iajs-881	128	12			PROPN
iajs-881	128	13			PROPN
iajs-881	128	14			PUNCT
iajs-881	128	15			NOUN
iajs-881	128	16	2	2	NUM
iajs-881	128	17	3	3	NUM
iajs-881	128	18	2	2	NUM
iajs-881	128	19	2	2	NUM
iajs-881	128	20	2	2	NUM
iajs-881	128	21	i	i	PRON
iajs-881	128	22	i	i	PRON
iajs-881	128	23	i	i	VERB
iajs-881	128	24	0	0	NUM
iajs-881	128	25	00.125	00.125	NUM
iajs-881	128	26	(	(	PUNCT
iajs-881	128	27	4x	4x	NOUN
iajs-881	128	28	2x	2x	NUM
iajs-881	128	29	2.546x	2.546x	PROPN
iajs-881	128	30	t	t	PROPN
iajs-881	128	31	2.546xt	2.546xt	NUM
iajs-881	128	32	)	)	PUNCT
iajs-881	128	33			PROPN
iajs-881	128	34			ADV
iajs-881	128	35			PROPN
iajs-881	128	36			VERB
iajs-881	128	37	thus	thus	ADV
iajs-881	128	38	1,1u	1,1u	ADJ
iajs-881	128	39			NUM
iajs-881	128	40	2	2	NUM
iajs-881	128	41	3	3	NUM
iajs-881	128	42	1	1	NUM
iajs-881	128	43	10.125	10.125	NUM
iajs-881	128	44	(	(	PUNCT
iajs-881	128	45	4x	4x	NOUN
iajs-881	128	46	2x	2x	NOUN
iajs-881	128	47	)	)	PUNCT
iajs-881	128	48	0.25	0.25	PROPN
iajs-881	128	49			PROPN
iajs-881	128	50			PROPN
iajs-881	128	51	.	.	PUNCT
iajs-881	129	1	then	then	ADV
iajs-881	129	2	1	1	NUM
iajs-881	129	3	2	2	NUM
iajs-881	129	4	2	2	NUM
iajs-881	129	5	1,2	1,2	NUM
iajs-881	129	6	1,1	1,1	NUM
iajs-881	129	7	1,0	1,0	NUM
iajs-881	129	8	1	1	NUM
iajs-881	129	9	k	k	SYM
iajs-881	129	10	2	2	NUM
iajs-881	129	11	k,1	k,1	PROPN
iajs-881	129	12	k	k	PROPN
iajs-881	129	13	0	0	PUNCT
iajs-881	129	14	u	u	NOUN
iajs-881	129	15	2u	2u	NOUN
iajs-881	129	16	u	u	NOUN
iajs-881	129	17	0.25x	0.25x	PROPN
iajs-881	129	18	g	g	PROPN
iajs-881	129	19	u	u	PROPN
iajs-881	129	20			VERB
iajs-881	129	21			PROPN
iajs-881	129	22			PROPN
iajs-881	129	23			PROPN
iajs-881	129	24			SYM
iajs-881	129	25			NOUN
iajs-881	129	26	2	2	NUM
iajs-881	129	27	3	3	NUM
iajs-881	129	28	2	2	NUM
iajs-881	129	29	2	2	NUM
iajs-881	129	30	2	2	NUM
iajs-881	129	31	1	1	NUM
iajs-881	129	32	1	1	NUM
iajs-881	129	33	1	1	NUM
iajs-881	129	34	1	1	NUM
iajs-881	129	35	1	1	NUM
iajs-881	129	36	10	10	NUM
iajs-881	129	37	.2	.2	NUM
iajs-881	129	38	5	5	NUM
iajs-881	129	39	(	(	PUNCT
iajs-881	129	40	4	4	NUM
iajs-881	129	41	x	x	SYM
iajs-881	129	42	2	2	NUM
iajs-881	129	43	x	x	SYM
iajs-881	129	44	2	2	NUM
iajs-881	129	45	.5	.5	NUM
iajs-881	129	46	4	4	NUM
iajs-881	129	47	6	6	NUM
iajs-881	129	48	x	x	SYM
iajs-881	129	49	t	t	PROPN
iajs-881	129	50	2	2	NUM
iajs-881	129	51	.5	.5	NUM
iajs-881	129	52	4	4	NUM
iajs-881	129	53	6	6	NUM
iajs-881	129	54	x	x	SYM
iajs-881	129	55	t	t	NOUN
iajs-881	129	56	)	)	PUNCT
iajs-881	129	57			PROPN
iajs-881	129	58			ADV
iajs-881	129	59			PROPN
iajs-881	129	60			PART
iajs-881	129	61	0.947.	0.947.	NUM
iajs-881	129	62			NOUN
iajs-881	129	63	these	these	DET
iajs-881	129	64	values	value	NOUN
iajs-881	129	65	are	be	AUX
iajs-881	129	66	tabulated	tabulate	VERB
iajs-881	129	67	down	down	ADP
iajs-881	129	68	with	with	ADP
iajs-881	129	69	the	the	DET
iajs-881	129	70	comparison	comparison	NOUN
iajs-881	129	71	with	with	ADP
iajs-881	129	72	the	the	DET
iajs-881	129	73	exact	exact	ADJ
iajs-881	129	74	solution	solution	NOUN
iajs-881	129	75	.	.	PUNCT
iajs-881	130	1	see	see	VERB
iajs-881	130	2	table	table	NOUN
iajs-881	130	3	(	(	PUNCT
iajs-881	130	4	1	1	NUM
iajs-881	130	5	)	)	PUNCT
iajs-881	130	6	second	second	ADJ
iajs-881	130	7	,	,	PUNCT
iajs-881	130	8	we	we	PRON
iajs-881	130	9	divide	divide	VERB
iajs-881	130	10	the	the	DET
iajs-881	130	11	x	x	NOUN
iajs-881	130	12	-	-	NOUN
iajs-881	130	13	interval	interval	NOUN
iajs-881	130	14	into	into	ADP
iajs-881	130	15	10	10	NUM
iajs-881	130	16	and	and	CCONJ
iajs-881	130	17	the	the	DET
iajs-881	130	18	t	t	NOUN
iajs-881	130	19	-	-	PUNCT
iajs-881	130	20	interval	interval	NOUN
iajs-881	130	21	into	into	ADP
iajs-881	130	22	10	10	NUM
iajs-881	130	23	subinterval	subinterval	NOUN
iajs-881	130	24	.	.	PUNCT
iajs-881	131	1	thus	thus	ADV
iajs-881	131	2	,	,	PUNCT
iajs-881	131	3	the	the	DET
iajs-881	131	4	initial	initial	ADJ
iajs-881	131	5	and	and	CCONJ
iajs-881	131	6	zero	zero	NUM
iajs-881	131	7	dirichlet	dirichlet	PROPN
iajs-881	131	8	boundary	boundary	ADJ
iajs-881	131	9	conditions	condition	NOUN
iajs-881	131	10	become	become	VERB
iajs-881	131	11	:	:	PUNCT
iajs-881	131	12	iu(x	iu(x	NOUN
iajs-881	131	13	,	,	PUNCT
iajs-881	131	14	0	0	NUM
iajs-881	131	15	)	)	PUNCT
iajs-881	131	16	0	0	NUM
iajs-881	131	17	,	,	PUNCT
iajs-881	131	18	iu(x	iu(x	NOUN
iajs-881	131	19	,	,	PUNCT
iajs-881	131	20	0	0	NUM
iajs-881	131	21	)	)	PUNCT
iajs-881	131	22	0	0	NUM
iajs-881	132	1	t	t	PROPN
iajs-881	132	2			PROPN
iajs-881	132	3			PROPN
iajs-881	132	4			PROPN
iajs-881	132	5	for	for	ADP
iajs-881	132	6	i	i	PROPN
iajs-881	132	7			PROPN
iajs-881	132	8	0,1,	0,1,	NOUN
iajs-881	132	9	…	…	SYM
iajs-881	132	10	,10	,10	X
iajs-881	132	11	.	.	PUNCT
iajs-881	133	1	ju(0	ju(0	PROPN
iajs-881	133	2	,	,	PUNCT
iajs-881	133	3	t	t	PROPN
iajs-881	133	4	)	)	PUNCT
iajs-881	133	5	0	0	PROPN
iajs-881	133	6	,	,	PUNCT
iajs-881	133	7	ju(1	ju(1	NOUN
iajs-881	133	8	,	,	PUNCT
iajs-881	133	9	t	t	PROPN
iajs-881	133	10	)	)	PUNCT
iajs-881	133	11	0	0	PROPN
iajs-881	133	12	,	,	PUNCT
iajs-881	133	13	for	for	ADP
iajs-881	133	14	j	j	PROPN
iajs-881	133	15			PROPN
iajs-881	133	16	0,1,	0,1,	NOUN
iajs-881	133	17	…	…	SYM
iajs-881	133	18	,10	,10	X
iajs-881	133	19	.	.	PUNCT
iajs-881	134	1	the	the	DET
iajs-881	134	2	results	result	NOUN
iajs-881	134	3	are	be	AUX
iajs-881	134	4	presented	present	VERB
iajs-881	134	5	in	in	ADP
iajs-881	134	6	table	table	NOUN
iajs-881	134	7	(	(	PUNCT
iajs-881	134	8	2	2	NUM
iajs-881	134	9	)	)	PUNCT
iajs-881	134	10	.	.	PUNCT
iajs-881	135	1	conclusions	conclusion	NOUN
iajs-881	135	2	1	1	X
iajs-881	135	3	.	.	PUNCT
iajs-881	136	1	the	the	DET
iajs-881	136	2	finite	finite	ADJ
iajs-881	136	3	difference	difference	NOUN
iajs-881	136	4	method	method	NOUN
iajs-881	136	5	gave	give	VERB
iajs-881	136	6	the	the	DET
iajs-881	136	7	numerical	numerical	ADJ
iajs-881	136	8	solution	solution	NOUN
iajs-881	136	9	of	of	ADP
iajs-881	136	10	the	the	DET
iajs-881	136	11	fractional	fractional	ADJ
iajs-881	136	12	differential	differential	ADJ
iajs-881	136	13	equations	equation	NOUN
iajs-881	136	14	and	and	CCONJ
iajs-881	136	15	it	it	PRON
iajs-881	136	16	depended	depend	VERB
iajs-881	136	17	on	on	ADP
iajs-881	136	18	the	the	DET
iajs-881	136	19	grunwald	grunwald	NOUN
iajs-881	136	20	estimate	estimate	NOUN
iajs-881	136	21	for	for	ADP
iajs-881	136	22	the	the	DET
iajs-881	136	23	fractional	fractional	ADJ
iajs-881	136	24	derivatives	derivative	NOUN
iajs-881	136	25	.	.	PUNCT
iajs-881	137	1	2	2	X
iajs-881	137	2	.	.	X
iajs-881	137	3	the	the	DET
iajs-881	137	4	stability	stability	NOUN
iajs-881	137	5	results	result	VERB
iajs-881	137	6	in	in	ADP
iajs-881	137	7	the	the	DET
iajs-881	137	8	finite	finite	ADJ
iajs-881	137	9	partial	partial	ADJ
iajs-881	137	10	differential	differential	NOUN
iajs-881	137	11	equation	equation	NOUN
iajs-881	137	12	case	case	NOUN
iajs-881	137	13	as	as	ADP
iajs-881	137	14	generalization	generalization	NOUN
iajs-881	137	15	and	and	CCONJ
iajs-881	137	16	unification	unification	NOUN
iajs-881	137	17	for	for	ADP
iajs-881	137	18	the	the	DET
iajs-881	137	19	corresponding	corresponding	ADJ
iajs-881	137	20	result	result	NOUN
iajs-881	137	21	in	in	ADP
iajs-881	137	22	the	the	DET
iajs-881	137	23	classical	classical	ADJ
iajs-881	137	24	hyperbolic	hyperbolic	ADJ
iajs-881	137	25	partial	partial	ADJ
iajs-881	137	26	differential	differential	NOUN
iajs-881	137	27	equation	equation	NOUN
iajs-881	137	28	.	.	PUNCT
iajs-881	138	1	3	3	X
iajs-881	138	2	.	.	NOUN
iajs-881	138	3	similar	similar	ADJ
iajs-881	138	4	to	to	ADP
iajs-881	138	5	this	this	DET
iajs-881	138	6	work	work	NOUN
iajs-881	138	7	,	,	PUNCT
iajs-881	138	8	the	the	DET
iajs-881	138	9	explicit	explicit	ADJ
iajs-881	138	10	finite	finite	ADJ
iajs-881	138	11	difference	difference	NOUN
iajs-881	138	12	method	method	NOUN
iajs-881	138	13	can	can	AUX
iajs-881	138	14	be	be	AUX
iajs-881	138	15	also	also	ADV
iajs-881	138	16	used	use	VERB
iajs-881	138	17	to	to	PART
iajs-881	138	18	solve	solve	VERB
iajs-881	138	19	the	the	DET
iajs-881	138	20	initial	initial	ADJ
iajs-881	138	21	-	-	PUNCT
iajs-881	138	22	boundary	boundary	NOUN
iajs-881	138	23	value	value	NOUN
iajs-881	138	24	problems	problem	NOUN
iajs-881	138	25	of	of	ADP
iajs-881	138	26	the	the	DET
iajs-881	138	27	two	two	NUM
iajs-881	138	28	-	-	PUNCT
iajs-881	138	29	sided	sided	ADJ
iajs-881	138	30	fractional	fractional	ADJ
iajs-881	138	31	hyperbolic	hyperbolic	ADJ
iajs-881	138	32	partial	partial	ADJ
iajs-881	138	33	differential	differential	NOUN
iajs-881	138	34	equations	equation	NOUN
iajs-881	138	35	given	give	VERB
iajs-881	138	36	by	by	ADP
iajs-881	138	37	,	,	PUNCT
iajs-881	138	38	u(x	u(x	PROPN
iajs-881	138	39	,	,	PUNCT
iajs-881	138	40	t	t	PROPN
iajs-881	138	41	)	)	PUNCT
iajs-881	138	42	t	t	PROPN
iajs-881	138	43			PROPN
iajs-881	138	44			PROPN
iajs-881	138	45			PROPN
iajs-881	138	46	c(x	c(x	PROPN
iajs-881	138	47	,	,	PUNCT
iajs-881	138	48	t	t	PROPN
iajs-881	138	49	)	)	PUNCT
iajs-881	138	50	q	q	PRON
iajs-881	138	51	q	q	X
iajs-881	138	52	u(x	u(x	PROPN
iajs-881	138	53	,	,	PUNCT
iajs-881	138	54	t	t	NOUN
iajs-881	138	55	)	)	PUNCT
iajs-881	138	56	x	x	NOUN
iajs-881	138	57			ADJ
iajs-881	138	58			NOUN
iajs-881	138	59	+	+	CCONJ
iajs-881	138	60	d(x	d(x	PROPN
iajs-881	138	61	,	,	PUNCT
iajs-881	138	62	t	t	PROPN
iajs-881	138	63	)	)	PUNCT
iajs-881	138	64	q	q	NOUN
iajs-881	138	65	q	q	X
iajs-881	138	66	u(x	u(x	PROPN
iajs-881	138	67	,	,	PUNCT
iajs-881	138	68	t	t	PROPN
iajs-881	138	69	)	)	PUNCT
iajs-881	138	70	x	x	PROPN
iajs-881	138	71			ADJ
iajs-881	138	72			PROPN
iajs-881	138	73	+	+	CCONJ
iajs-881	138	74	s(x	s(x	PROPN
iajs-881	138	75	,	,	PUNCT
iajs-881	138	76	t	t	PROPN
iajs-881	138	77	)	)	PUNCT
iajs-881	138	78	together	together	ADV
iajs-881	138	79	with	with	ADP
iajs-881	138	80	the	the	DET
iajs-881	138	81	initial	initial	ADJ
iajs-881	138	82	and	and	CCONJ
iajs-881	138	83	zero	zero	NUM
iajs-881	138	84	dirichlet	dirichlet	PROPN
iajs-881	138	85	boundary	boundary	ADJ
iajs-881	138	86	conditions	condition	NOUN
iajs-881	138	87	:	:	PUNCT
iajs-881	138	88	u(x,0	u(x,0	X
iajs-881	138	89	)	)	PUNCT
iajs-881	138	90	f	f	PROPN
iajs-881	138	91	(	(	PUNCT
iajs-881	138	92	x	x	X
iajs-881	138	93	)	)	PUNCT
iajs-881	138	94	,	,	PUNCT
iajs-881	138	95	u(l	u(l	PROPN
iajs-881	138	96	,	,	PUNCT
iajs-881	138	97	t	t	PROPN
iajs-881	138	98	)	)	PUNCT
iajs-881	138	99	0,u(r	0,u(r	PROPN
iajs-881	138	100	,	,	PUNCT
iajs-881	138	101	t	t	PROPN
iajs-881	138	102	)	)	PUNCT
iajs-881	138	103	0	0	NUM
iajs-881	139	1	for	for	ADP
iajs-881	139	2	l	l	NOUN
iajs-881	139	3	x	x	PUNCT
iajs-881	139	4	r	r	VERB
iajs-881	139	5			NUM
iajs-881	139	6			PROPN
iajs-881	139	7			NUM
iajs-881	139	8			NOUN
iajs-881	139	9	where	where	SCONJ
iajs-881	139	10	l	l	NOUN
iajs-881	139	11			NUM
iajs-881	139	12	x	x	SYM
iajs-881	139	13			NUM
iajs-881	139	14	r	r	NOUN
iajs-881	139	15	,	,	PUNCT
iajs-881	139	16	0	0	NUM
iajs-881	139	17			NOUN
iajs-881	139	18	t	t	NOUN
iajs-881	139	19			NUM
iajs-881	139	20	t	t	PROPN
iajs-881	139	21	,	,	PUNCT
iajs-881	139	22	q	q	PRON
iajs-881	139	23	q	q	X
iajs-881	139	24	u(x	u(x	PROPN
iajs-881	139	25	,	,	PUNCT
iajs-881	139	26	t	t	NOUN
iajs-881	139	27	)	)	PUNCT
iajs-881	139	28	x	x	NOUN
iajs-881	139	29			ADJ
iajs-881	139	30			NOUN
iajs-881	139	31	and	and	CCONJ
iajs-881	139	32	q	q	ADJ
iajs-881	139	33	q	q	X
iajs-881	139	34	u(x	u(x	PROPN
iajs-881	139	35	,	,	PUNCT
iajs-881	139	36	t	t	PROPN
iajs-881	139	37	)	)	PUNCT
iajs-881	139	38	x	x	PROPN
iajs-881	139	39			PROPN
iajs-881	139	40			PROPN
iajs-881	139	41	denote	denote	VERB
iajs-881	139	42	the	the	DET
iajs-881	139	43	left	left	ADV
iajs-881	139	44	-	-	PUNCT
iajs-881	139	45	handed	hand	VERB
iajs-881	139	46	and	and	CCONJ
iajs-881	139	47	the	the	DET
iajs-881	139	48	righthanded	righthande	VERB
iajs-881	139	49	partial	partial	ADJ
iajs-881	139	50	fractional	fractional	ADJ
iajs-881	139	51	derivatives	derivative	NOUN
iajs-881	139	52	of	of	ADP
iajs-881	139	53	order	order	NOUN
iajs-881	139	54	q	q	NOUN
iajs-881	139	55	of	of	ADP
iajs-881	139	56	the	the	DET
iajs-881	139	57	function	function	NOUN
iajs-881	139	58	u	u	NOUN
iajs-881	139	59	with	with	ADP
iajs-881	139	60	respect	respect	NOUN
iajs-881	139	61	to	to	ADP
iajs-881	139	62	x	x	PUNCT
iajs-881	139	63	and	and	CCONJ
iajs-881	139	64	1	1	NUM
iajs-881	139	65	<	<	X
iajs-881	139	66	q	q	X
iajs-881	139	67			NUM
iajs-881	139	68	2	2	NUM
iajs-881	139	69	.	.	PUNCT
iajs-881	140	1	ibn	ibn	PROPN
iajs-881	140	2	alhaitham	alhaitham	NOUN
iajs-881	140	3	j.	j.	PROPN
iajs-881	141	1	fo	fo	ADP
iajs-881	141	2	r	r	NOUN
iajs-881	141	3	pure	pure	ADJ
iajs-881	141	4	&	&	CCONJ
iajs-881	141	5	appl	appl	PROPN
iajs-881	141	6	.	.	PUNCT
iajs-881	142	1	sc	sc	PROPN
iajs-881	142	2	i.	i.	PROPN
iajs-881	142	3	vo	vo	PROPN
iajs-881	142	4	l.23	l.23	PROPN
iajs-881	142	5	(	(	PUNCT
iajs-881	142	6	3	3	NUM
iajs-881	142	7	)	)	PUNCT
iajs-881	142	8	2010	2010	NUM
iajs-881	142	9	ihjpas	ihjpa	VERB
iajs-881	142	10	in	in	ADP
iajs-881	142	11	this	this	DET
iajs-881	142	12	case	case	NOUN
iajs-881	142	13	equation	equation	NOUN
iajs-881	142	14	(	(	PUNCT
iajs-881	142	15	4	4	NUM
iajs-881	142	16	)	)	PUNCT
iajs-881	142	17	becomes	become	VERB
iajs-881	142	18	i	i	PRON
iajs-881	142	19	1	1	NUM
iajs-881	142	20	n	n	NOUN
iajs-881	142	21	i	i	PRON
iajs-881	142	22	1	1	NUM
iajs-881	143	1	i	i	PROPN
iajs-881	143	2	,	,	PUNCT
iajs-881	143	3	j	j	PROPN
iajs-881	143	4	1	1	NUM
iajs-881	143	5	i	i	PROPN
iajs-881	143	6	,	,	PUNCT
iajs-881	143	7	j	j	PROPN
iajs-881	143	8	1	1	NUM
iajs-881	143	9	i	i	PROPN
iajs-881	143	10	,	,	PUNCT
iajs-881	143	11	j	j	PROPN
iajs-881	143	12	1	1	NUM
iajs-881	143	13	i	i	PROPN
iajs-881	143	14	,	,	PUNCT
iajs-881	143	15	j	j	PROPN
iajs-881	143	16	i	i	PROPN
iajs-881	143	17	,	,	PUNCT
iajs-881	143	18	j	j	PROPN
iajs-881	143	19	1	1	NUM
iajs-881	143	20	w	w	NOUN
iajs-881	143	21	i	i	PRON
iajs-881	143	22	w	w	PROPN
iajs-881	143	23	1	1	NUM
iajs-881	143	24	,	,	PUNCT
iajs-881	143	25	j	j	PROPN
iajs-881	143	26	w	w	NOUN
iajs-881	143	27	i	i	PROPN
iajs-881	143	28	w	w	PROPN
iajs-881	143	29	1	1	NUM
iajs-881	143	30	,	,	PUNCT
iajs-881	143	31	j	j	PROPN
iajs-881	143	32	i	i	PROPN
iajs-881	143	33	,	,	PUNCT
iajs-881	143	34	jq	jq	PROPN
iajs-881	143	35	q	q	PROPN
iajs-881	144	1	w	w	PROPN
iajs-881	144	2	0	0	NUM
iajs-881	145	1	w	w	NOUN
iajs-881	145	2	0	0	NUM
iajs-881	145	3	c	c	NOUN
iajs-881	145	4	d	d	X
iajs-881	145	5	u	u	PROPN
iajs-881	145	6	2u	2u	VERB
iajs-881	145	7	u	u	NOUN
iajs-881	145	8	g	g	PROPN
iajs-881	145	9	u	u	NOUN
iajs-881	145	10	g	g	PROPN
iajs-881	145	11	u	u	X
iajs-881	145	12	s	s	X
iajs-881	145	13	(	(	PUNCT
iajs-881	145	14	x	x	NOUN
iajs-881	145	15	)	)	PUNCT
iajs-881	145	16	(	(	PUNCT
iajs-881	145	17	x	x	X
iajs-881	145	18	)	)	PUNCT
iajs-881	145	19			PUNCT
iajs-881	145	20			PROPN
iajs-881	145	21			VERB
iajs-881	145	22			PROPN
iajs-881	145	23			PUNCT
iajs-881	145	24			PUNCT
iajs-881	145	25			PROPN
iajs-881	145	26			PROPN
iajs-881	145	27			ADV
iajs-881	145	28			VERB
iajs-881	145	29			PROPN
iajs-881	145	30			PROPN
iajs-881	145	31			PROPN
iajs-881	145	32			PROPN
iajs-881	145	33			PROPN
iajs-881	145	34			PROPN
iajs-881	145	35			ADV
iajs-881	145	36			PUNCT
iajs-881	145	37			PUNCT
iajs-881	145	38			X
iajs-881	145	39			X
iajs-881	145	40			X
iajs-881	145	41	4	4	NUM
iajs-881	145	42	.	.	PUNCT
iajs-881	146	1	in	in	ADP
iajs-881	146	2	a	a	DET
iajs-881	146	3	similar	similar	ADJ
iajs-881	146	4	manner	manner	NOUN
iajs-881	146	5	,	,	PUNCT
iajs-881	146	6	the	the	DET
iajs-881	146	7	implicit	implicit	ADJ
iajs-881	146	8	finite	finite	ADJ
iajs-881	146	9	difference	difference	NOUN
iajs-881	146	10	method	method	NOUN
iajs-881	146	11	can	can	AUX
iajs-881	146	12	be	be	AUX
iajs-881	146	13	also	also	ADV
iajs-881	146	14	used	use	VERB
iajs-881	146	15	to	to	PART
iajs-881	146	16	solve	solve	VERB
iajs-881	146	17	the	the	DET
iajs-881	146	18	initial	initial	ADJ
iajs-881	146	19	-	-	PUNCT
iajs-881	146	20	boundary	boundary	NOUN
iajs-881	146	21	value	value	NOUN
iajs-881	146	22	problems	problem	NOUN
iajs-881	146	23	of	of	ADP
iajs-881	146	24	the	the	DET
iajs-881	146	25	two	two	NUM
iajs-881	146	26	-	-	PUNCT
iajs-881	146	27	sided	sided	ADJ
iajs-881	146	28	fractional	fractional	ADJ
iajs-881	146	29	hyperbolic	hyperbolic	ADJ
iajs-881	146	30	partial	partial	ADJ
iajs-881	146	31	differential	differential	NOUN
iajs-881	146	32	equations	equation	NOUN
iajs-881	146	33	given	give	VERB
iajs-881	146	34	by	by	ADP
iajs-881	146	35	equations	equation	NOUN
iajs-881	146	36	:	:	PUNCT
iajs-881	146	37	u(x	u(x	PROPN
iajs-881	146	38	,	,	PUNCT
iajs-881	146	39	t	t	PROPN
iajs-881	146	40	)	)	PUNCT
iajs-881	146	41	t	t	PROPN
iajs-881	146	42			PROPN
iajs-881	146	43			PROPN
iajs-881	146	44			PROPN
iajs-881	146	45	c(x	c(x	PROPN
iajs-881	146	46	,	,	PUNCT
iajs-881	146	47	t	t	PROPN
iajs-881	146	48	)	)	PUNCT
iajs-881	146	49	q	q	PRON
iajs-881	146	50	q	q	X
iajs-881	146	51	u(x	u(x	PROPN
iajs-881	146	52	,	,	PUNCT
iajs-881	146	53	t	t	NOUN
iajs-881	146	54	)	)	PUNCT
iajs-881	146	55	x	x	NOUN
iajs-881	146	56			ADJ
iajs-881	146	57			NOUN
iajs-881	146	58	+	+	CCONJ
iajs-881	146	59	d(x	d(x	PROPN
iajs-881	146	60	,	,	PUNCT
iajs-881	146	61	t	t	PROPN
iajs-881	146	62	)	)	PUNCT
iajs-881	146	63	q	q	NOUN
iajs-881	146	64	q	q	X
iajs-881	146	65	u(x	u(x	PROPN
iajs-881	146	66	,	,	PUNCT
iajs-881	146	67	t	t	PROPN
iajs-881	146	68	)	)	PUNCT
iajs-881	146	69	x	x	PROPN
iajs-881	146	70			ADJ
iajs-881	146	71			PROPN
iajs-881	146	72	+	+	CCONJ
iajs-881	146	73	s(x	s(x	PROPN
iajs-881	146	74	,	,	PUNCT
iajs-881	146	75	t	t	PROPN
iajs-881	146	76	)	)	PUNCT
iajs-881	146	77	in	in	ADP
iajs-881	146	78	this	this	DET
iajs-881	146	79	case	case	NOUN
iajs-881	146	80	eq.(4)becomes	eq.(4)become	VERB
iajs-881	146	81	:	:	PUNCT
iajs-881	146	82	i	i	PROPN
iajs-881	146	83	1	1	NUM
iajs-881	146	84	n	n	NOUN
iajs-881	146	85	i	i	PRON
iajs-881	146	86	1	1	NUM
iajs-881	147	1	i	i	PROPN
iajs-881	147	2	,	,	PUNCT
iajs-881	147	3	j	j	PROPN
iajs-881	147	4	1	1	NUM
iajs-881	147	5	i	i	PROPN
iajs-881	147	6	,	,	PUNCT
iajs-881	147	7	j	j	PROPN
iajs-881	147	8	1	1	NUM
iajs-881	147	9	i	i	PROPN
iajs-881	147	10	,	,	PUNCT
iajs-881	147	11	j	j	PROPN
iajs-881	147	12	1	1	NUM
iajs-881	147	13	i	i	PROPN
iajs-881	147	14	,	,	PUNCT
iajs-881	147	15	j	j	PROPN
iajs-881	147	16	i	i	PROPN
iajs-881	147	17	,	,	PUNCT
iajs-881	147	18	j	j	PROPN
iajs-881	147	19	1	1	NUM
iajs-881	147	20	w	w	NOUN
iajs-881	147	21	i	i	PROPN
iajs-881	147	22	w	w	VERB
iajs-881	147	23	1,j	1,j	NUM
iajs-881	147	24	1	1	NUM
iajs-881	147	25	w	w	NOUN
iajs-881	147	26	i	i	PRON
iajs-881	147	27	w	w	VERB
iajs-881	147	28	1,j	1,j	NOUN
iajs-881	147	29	1	1	NUM
iajs-881	147	30	i	i	PROPN
iajs-881	147	31	,	,	PUNCT
iajs-881	147	32	j	j	PROPN
iajs-881	147	33	1q	1q	PROPN
iajs-881	147	34	q	q	PROPN
iajs-881	147	35	w	w	PROPN
iajs-881	147	36	0	0	NUM
iajs-881	148	1	w	w	NOUN
iajs-881	148	2	0	0	NUM
iajs-881	148	3	c	c	NOUN
iajs-881	148	4	d	d	X
iajs-881	148	5	u	u	PROPN
iajs-881	148	6	2u	2u	VERB
iajs-881	148	7	u	u	NOUN
iajs-881	148	8	g	g	PROPN
iajs-881	148	9	u	u	NOUN
iajs-881	148	10	g	g	PROPN
iajs-881	148	11	u	u	X
iajs-881	148	12	s	s	X
iajs-881	148	13	(	(	PUNCT
iajs-881	148	14	x	x	NOUN
iajs-881	148	15	)	)	PUNCT
iajs-881	148	16	(	(	PUNCT
iajs-881	148	17	x	x	X
iajs-881	148	18	)	)	PUNCT
iajs-881	148	19			PUNCT
iajs-881	148	20			PROPN
iajs-881	148	21			VERB
iajs-881	148	22			PROPN
iajs-881	148	23			PUNCT
iajs-881	148	24			PUNCT
iajs-881	148	25			PROPN
iajs-881	148	26			PROPN
iajs-881	148	27			PUNCT
iajs-881	148	28			CCONJ
iajs-881	148	29			PUNCT
iajs-881	148	30			PROPN
iajs-881	148	31			VERB
iajs-881	148	32			PUNCT
iajs-881	148	33			PROPN
iajs-881	148	34			PROPN
iajs-881	148	35			PROPN
iajs-881	148	36			PROPN
iajs-881	148	37			PROPN
iajs-881	148	38			ADV
iajs-881	148	39			PUNCT
iajs-881	148	40			PUNCT
iajs-881	148	41			X
iajs-881	148	42			X
iajs-881	148	43			X
iajs-881	148	44	where	where	SCONJ
iajs-881	148	45	i1,2	i1,2	ADP
iajs-881	148	46	,	,	PUNCT
iajs-881	148	47	…	…	PUNCT
iajs-881	148	48	,	,	PUNCT
iajs-881	148	49	n1	n1	NOUN
iajs-881	148	50	;	;	PUNCT
iajs-881	148	51	j0,1,	j0,1,	NOUN
iajs-881	148	52	…	…	PUNCT
iajs-881	148	53	,m1	,m1	NUM
iajs-881	148	54	.	.	PUNCT
iajs-881	149	1	references	reference	NOUN
iajs-881	149	2	1	1	NUM
iajs-881	149	3	.	.	PUNCT
iajs-881	149	4	nishimoto	nishimoto	PROPN
iajs-881	149	5	,	,	PUNCT
iajs-881	149	6	k.	k.	PROPN
iajs-881	149	7	(	(	PUNCT
iajs-881	149	8	1983	1983	NUM
iajs-881	149	9	)	)	PUNCT
iajs-881	149	10	,	,	PUNCT
iajs-881	149	11	"	"	PUNCT
iajs-881	149	12	fractional	fractional	ADJ
iajs-881	149	13	calculus	calculus	NOUN
iajs-881	149	14	:	:	PUNCT
iajs-881	149	15	integrations	integration	NOUN
iajs-881	149	16	and	and	CCONJ
iajs-881	149	17	differentiations	differentiation	NOUN
iajs-881	149	18	of	of	ADP
iajs-881	149	19	arbitrary	arbitrary	ADJ
iajs-881	149	20	order	order	NOUN
iajs-881	149	21	"	"	PUNCT
iajs-881	149	22	,	,	PUNCT
iajs-881	149	23	descartes	descartes	PROPN
iajs-881	149	24	press	press	NOUN
iajs-881	149	25	company	company	NOUN
iajs-881	149	26	koriyama	koriyama	PROPN
iajs-881	149	27	japan	japan	PROPN
iajs-881	149	28	.	.	PUNCT
iajs-881	150	1	2	2	X
iajs-881	150	2	.	.	X
iajs-881	150	3	al	al	NOUN
iajs-881	150	4	-	-	PUNCT
iajs-881	150	5	rahhal	rahhal	NOUN
iajs-881	150	6	,	,	PUNCT
iajs-881	150	7	d.	d.	PROPN
iajs-881	150	8	(	(	PUNCT
iajs-881	150	9	2005),"numerical	2005),"numerical	ADJ
iajs-881	150	10	solution	solution	NOUN
iajs-881	150	11	for	for	ADP
iajs-881	150	12	fractional	fractional	ADJ
iajs-881	150	13	integro	integro	ADJ
iajs-881	150	14	-	-	PUNCT
iajs-881	150	15	differential	differential	NOUN
iajs-881	150	16	equations	equation	NOUN
iajs-881	150	17	"	"	PUNCT
iajs-881	150	18	,	,	PUNCT
iajs-881	150	19	ph.d	ph.d	PROPN
iajs-881	150	20	.	.	PUNCT
iajs-881	151	1	thesis	thesis	PROPN
iajs-881	151	2	,	,	PUNCT
iajs-881	151	3	colle	colle	NOUN
iajs-881	151	4	ge	ge	PROPN
iajs-881	151	5	of	of	ADP
iajs-881	151	6	science	science	PROPN
iajs-881	151	7	,	,	PUNCT
iajs-881	151	8	university	university	NOUN
iajs-881	151	9	of	of	ADP
iajs-881	151	10	baghdad	baghdad	PROPN
iajs-881	151	11	.	.	PUNCT
iajs-881	152	1	3	3	X
iajs-881	152	2	.	.	X
iajs-881	152	3	diethelm	diethelm	PROPN
iajs-881	152	4	,	,	PUNCT
iajs-881	152	5	k.	k.	PROPN
iajs-881	152	6	(	(	PUNCT
iajs-881	152	7	1999	1999	NUM
iajs-881	152	8	)	)	PUNCT
iajs-881	152	9	"	"	PUNCT
iajs-881	152	10	anlysis	anlysis	NOUN
iajs-881	152	11	of	of	ADP
iajs-881	152	12	fractional	fractional	ADJ
iajs-881	152	13	differential	differential	ADJ
iajs-881	152	14	equations",department	equations",department	NOUN
iajs-881	152	15	of	of	ADP
iajs-881	152	16	mathematics	mathematic	NOUN
iajs-881	152	17	,	,	PUNCT
iajs-881	152	18	university	university	PROPN
iajs-881	152	19	of	of	ADP
iajs-881	152	20	manchester	manchester	PROPN
iajs-881	152	21	england	england	PROPN
iajs-881	152	22	.	.	PUNCT
iajs-881	153	1	4	4	X
iajs-881	153	2	.	.	X
iajs-881	153	3	meerschaert	meerschaert	NOUN
iajs-881	153	4	,	,	PUNCT
iajs-881	153	5	m.	m.	NOUN
iajs-881	153	6	and	and	CCONJ
iajs-881	153	7	tadjeran	tadjeran	NOUN
iajs-881	153	8	,	,	PUNCT
iajs-881	153	9	c.(2006	c.(2006	PROPN
iajs-881	153	10	)	)	PUNCT
iajs-881	153	11	”	"	PUNCT
iajs-881	153	12	finite	finite	ADJ
iajs-881	153	13	difference	difference	NOUN
iajs-881	153	14	approximation	approximation	NOUN
iajs-881	153	15	for	for	ADP
iajs-881	153	16	two	two	NUM
iajs-881	153	17	–	–	PUNCT
iajs-881	153	18	sided	sided	ADJ
iajs-881	153	19	space	space	NOUN
iajs-881	153	20	fractional	fractional	ADJ
iajs-881	153	21	partial	partial	ADJ
iajs-881	153	22	differential	differential	NOUN
iajs-881	153	23	equations	equation	NOUN
iajs-881	153	24	”	"	PUNCT
iajs-881	153	25	,	,	PUNCT
iajs-881	153	26	applied	apply	VERB
iajs-881	153	27	numerical	numerical	ADJ
iajs-881	153	28	mathematics	mathematic	NOUN
iajs-881	153	29	,	,	PUNCT
iajs-881	153	30	56	56	NUM
iajs-881	153	31	:	:	SYM
iajs-881	153	32	80	80	NUM
iajs-881	153	33	-	-	SYM
iajs-881	153	34	90	90	NUM
iajs-881	153	35	.	.	PUNCT
iajs-881	154	1	5	5	NUM
iajs-881	154	2	.	.	X
iajs-881	154	3	ames	ames	PROPN
iajs-881	154	4	,	,	PUNCT
iajs-881	154	5	w.	w.	PROPN
iajs-881	154	6	f.	f.	PROPN
iajs-881	154	7	(	(	PUNCT
iajs-881	154	8	1992	1992	NUM
iajs-881	154	9	)	)	PUNCT
iajs-881	154	10	"	"	PUNCT
iajs-881	154	11	numerical	numerical	ADJ
iajs-881	154	12	methods	method	NOUN
iajs-881	154	13	for	for	ADP
iajs-881	154	14	partial	partial	ADJ
iajs-881	154	15	differential	differential	ADJ
iajs-881	154	16	equations	equation	NOUN
iajs-881	154	17	"	"	PUNCT
iajs-881	154	18	,	,	PUNCT
iajs-881	154	19	3	3	NUM
iajs-881	154	20	rd	rd	NOUN
iajs-881	154	21	edition	edition	NOUN
iajs-881	154	22	,	,	PUNCT
iajs-881	154	23	academic	academic	ADJ
iajs-881	154	24	press	press	PROPN
iajs-881	154	25	,	,	PUNCT
iajs-881	154	26	inc	inc	PROPN
iajs-881	154	27	.	.	PROPN
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iajs-881	160	11	,	,	PUNCT
iajs-881	160	12	tj	tj	NOUN
iajs-881	160	13	)	)	PUNCT
iajs-881	160	14	explicit	explicit	ADJ
iajs-881	160	15	method	method	NOUN
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iajs-881	160	17	method	method	NOUN
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iajs-881	160	21	0.25	0.25	ADJ
iajs-881	160	22	0.25	0.25	NOUN
iajs-881	160	23	1	1	NUM
iajs-881	160	24	1	1	NUM
iajs-881	160	25	0.9472	0.9472	PROPN
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iajs-881	162	8	(	(	PUNCT
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iajs-881	162	13	numerical	numerical	ADJ
iajs-881	162	14	and	and	CCONJ
iajs-881	162	15	the	the	DET
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iajs-881	162	18	for	for	ADP
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iajs-881	162	22	.	.	PUNCT
iajs-881	163	1	xi	xi	X
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iajs-881	163	14	explicit	explicit	ADJ
iajs-881	163	15	method	method	NOUN
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iajs-881	163	17	method	method	NOUN
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iajs-881	163	19	0.5	0.5	NUM
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iajs-881	163	21	0.25	0.25	ADJ
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iajs-881	168	37	البحث	البحث	PROPN
iajs-881	168	38	،	،	PROPN
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iajs-881	168	40	طریق	طریق	PROPN
iajs-881	168	41	�	�	PROPN
iajs-881	168	42	ة	ة	PROPN
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iajs-881	168	44	�	�	PROPN
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iajs-881	168	47	�	�	PROPN
iajs-881	168	48	ة	ة	ADP
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iajs-881	168	53	�	�	PROPN
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iajs-881	168	56	�	�	PROPN
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iajs-881	168	59	�	�	PROPN
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iajs-881	168	61	القط	القط	PROPN
iajs-881	168	62	�	�	PROPN
iajs-881	168	63	ع	ع	PROPN
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iajs-881	168	65	�	�	PROPN
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iajs-881	168	68	�	�	PROPN
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iajs-881	168	72	�	�	PROPN
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iajs-881	168	75	�	�	PROPN
iajs-881	168	76	ة	ة	ADP
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iajs-881	168	88	،	،	PROPN
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iajs-881	168	90	طریقة	طریقة	ADJ
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iajs-881	169	3	النت	النت	VERB
iajs-881	169	4	�	�	PROPN
iajs-881	169	5	ائج	ائج	PROPN
iajs-881	169	6	ف	ف	PROPN
iajs-881	169	7	�	�	PROPN
iajs-881	169	8	ي	ي	SYM
iajs-881	169	9	ج	ج	PROPN
iajs-881	169	10	�	�	PROPN
iajs-881	169	11	داول	داول	PROPN
iajs-881	169	12	للحص	للحص	PROPN
iajs-881	169	13	�	�	PROPN
iajs-881	169	14	ول	ول	PROPN
iajs-881	169	15	عل	عل	PROPN
iajs-881	169	16	�	�	PROPN
iajs-881	169	17	ى	ى	PROPN
iajs-881	169	18	أفض	أفض	PROPN
iajs-881	169	19	�	�	PROPN
iajs-881	169	20	ل	ل	PROPN
iajs-881	169	21	مقارن	مقارن	PROPN
iajs-881	169	22	�	�	PROPN
iajs-881	169	23	ة	ة	PROPN
iajs-881	169	24	حیحالنتائج	حیحالنتائج	NOUN
iajs-881	169	25	العددیة	العددیة	VERB
iajs-881	170	1	مع	مع	INTJ
iajs-881	170	2	الحل	الحل	PROPN
iajs-881	170	3	الص	الص	PROPN
iajs-881	170	4	ورنتق	ورنتق	NOUN
iajs-881	170	5	.	.	PUNCT
iajs-881	171	1	حیحمع	حیحمع	NOUN
iajs-881	171	2	الحل	الحل	PROPN
iajs-881	171	3	الص	الص	PROPN
iajs-881	171	4	ihjpas	ihjpas	PROPN