id	sid	tid	token	lemma	pos
iajs-856	1	1	ibn	ibn	PROPN
iajs-856	1	2	alhaitham	alhaitham	NOUN
iajs-856	1	3	j.	j.	PROPN
iajs-856	2	1	fo	fo	ADP
iajs-856	2	2	r	r	NOUN
iajs-856	2	3	pure	pure	ADJ
iajs-856	2	4	&	&	CCONJ
iajs-856	2	5	appl	appl	PROPN
iajs-856	2	6	.	.	PUNCT
iajs-856	3	1	sc	sc	PROPN
iajs-856	3	2	i.	i.	PROPN
iajs-856	3	3	vo	vo	PROPN
iajs-856	4	1	l.24	l.24	PROPN
iajs-856	4	2	(	(	PUNCT
iajs-856	4	3	1	1	NUM
iajs-856	4	4	)	)	PUNCT
iajs-856	4	5	2011	2011	NUM
iajs-856	4	6	explicit	explicit	ADJ
iajs-856	4	7	finite	finite	ADJ
iajs-856	4	8	difference	difference	NOUN
iajs-856	4	9	approximation	approximation	NOUN
iajs-856	4	10	for	for	ADP
iajs-856	4	11	the	the	DET
iajs-856	4	12	twodimensional	twodimensional	ADJ
iajs-856	4	13	fractional	fractional	ADJ
iajs-856	4	14	dispersion	dispersion	NOUN
iajs-856	4	15	equation	equation	NOUN
iajs-856	4	16	i.	i.	PROPN
iajs-856	4	17	i.	i.	PROPN
iajs-856	4	18	gorial	gorial	PROPN
iajs-856	4	19	department	department	PROPN
iajs-856	4	20	of	of	ADP
iajs-856	4	21	mathematics	mathematic	NOUN
iajs-856	4	22	,	,	PUNCT
iajs-856	4	23	ibn	ibn	PROPN
iajs-856	4	24	al	al	PROPN
iajs-856	4	25	–	–	PROPN
iajs-856	4	26	haitham	haitham	PROPN
iajs-856	4	27	college	college	NOUN
iajs-856	4	28	education	education	NOUN
iajs-856	4	29	,	,	PUNCT
iajs-856	4	30	baghdad	baghdad	PROPN
iajs-856	4	31	university	university	PROPN
iajs-856	4	32	received	receive	VERB
iajs-856	4	33	in	in	ADP
iajs-856	4	34	feb,7,2010	feb,7,2010	PROPN
iajs-856	4	35	accepted	accept	VERB
iajs-856	4	36	in	in	ADP
iajs-856	4	37	may,13,2010	may,13,2010	PROPN
iajs-856	4	38	abstract	abstract	NOUN
iajs-856	4	39	in	in	ADP
iajs-856	4	40	this	this	DET
iajs-856	4	41	paper	paper	NOUN
iajs-856	4	42	,	,	PUNCT
iajs-856	4	43	we	we	PRON
iajs-856	4	44	introduce	introduce	VERB
iajs-856	4	45	and	and	CCONJ
iajs-856	4	46	discuss	discuss	VERB
iajs-856	4	47	an	an	DET
iajs-856	4	48	algorithm	algorithm	NOUN
iajs-856	4	49	for	for	ADP
iajs-856	4	50	the	the	DET
iajs-856	4	51	numerical	numerical	ADJ
iajs-856	4	52	solution	solution	NOUN
iajs-856	4	53	of	of	ADP
iajs-856	4	54	two	two	NUM
iajs-856	4	55	dimensional	dimensional	ADJ
iajs-856	4	56	fractional	fractional	ADJ
iajs-856	4	57	dispersion	dispersion	NOUN
iajs-856	4	58	equation	equation	NOUN
iajs-856	4	59	.	.	PUNCT
iajs-856	5	1	the	the	DET
iajs-856	5	2	algorithm	algorithm	NOUN
iajs-856	5	3	for	for	ADP
iajs-856	5	4	the	the	DET
iajs-856	5	5	numerical	numerical	ADJ
iajs-856	5	6	solution	solution	NOUN
iajs-856	5	7	of	of	ADP
iajs-856	5	8	this	this	DET
iajs-856	5	9	equation	equation	NOUN
iajs-856	5	10	is	be	AUX
iajs-856	5	11	based	base	VERB
iajs-856	5	12	on	on	ADP
iajs-856	5	13	explicit	explicit	ADJ
iajs-856	5	14	finite	finite	ADJ
iajs-856	5	15	difference	difference	NOUN
iajs-856	5	16	approximation	approximation	NOUN
iajs-856	5	17	.	.	PUNCT
iajs-856	6	1	consistency	consistency	NOUN
iajs-856	6	2	,	,	PUNCT
iajs-856	6	3	conditional	conditional	ADJ
iajs-856	6	4	stability	stability	NOUN
iajs-856	6	5	,	,	PUNCT
iajs-856	6	6	and	and	CCONJ
iajs-856	6	7	convergence	convergence	NOUN
iajs-856	6	8	of	of	ADP
iajs-856	6	9	this	this	DET
iajs-856	6	10	numerical	numerical	ADJ
iajs-856	6	11	method	method	NOUN
iajs-856	6	12	are	be	AUX
iajs-856	6	13	described	describe	VERB
iajs-856	6	14	.	.	PUNCT
iajs-856	7	1	finally	finally	ADV
iajs-856	7	2	,	,	PUNCT
iajs-856	7	3	numerical	numerical	ADJ
iajs-856	7	4	example	example	NOUN
iajs-856	7	5	is	be	AUX
iajs-856	7	6	presented	present	VERB
iajs-856	7	7	to	to	PART
iajs-856	7	8	show	show	VERB
iajs-856	7	9	the	the	DET
iajs-856	7	10	dispersion	dispersion	NOUN
iajs-856	7	11	behavior	behavior	NOUN
iajs-856	7	12	according	accord	VERB
iajs-856	7	13	to	to	ADP
iajs-856	7	14	the	the	DET
iajs-856	7	15	order	order	NOUN
iajs-856	7	16	of	of	ADP
iajs-856	7	17	the	the	DET
iajs-856	7	18	fractional	fractional	ADJ
iajs-856	7	19	derivative	derivative	NOUN
iajs-856	7	20	and	and	CCONJ
iajs-856	7	21	we	we	PRON
iajs-856	7	22	demonstrate	demonstrate	VERB
iajs-856	7	23	that	that	SCONJ
iajs-856	7	24	our	our	PRON
iajs-856	7	25	explicit	explicit	ADJ
iajs-856	7	26	finite	finite	ADJ
iajs-856	7	27	difference	difference	NOUN
iajs-856	7	28	approximation	approximation	NOUN
iajs-856	7	29	is	be	AUX
iajs-856	7	30	a	a	DET
iajs-856	7	31	computationally	computationally	ADV
iajs-856	7	32	efficient	efficient	ADJ
iajs-856	7	33	method	method	NOUN
iajs-856	7	34	for	for	ADP
iajs-856	7	35	solving	solve	VERB
iajs-856	7	36	two	two	NUM
iajs-856	7	37	-	-	PUNCT
iajs-856	7	38	dimensional	dimensional	ADJ
iajs-856	7	39	fractional	fractional	ADJ
iajs-856	7	40	dispersion	dispersion	NOUN
iajs-856	7	41	equation	equation	NOUN
iajs-856	7	42	.	.	PUNCT
iajs-856	8	1	key	key	ADJ
iajs-856	8	2	words	word	NOUN
iajs-856	8	3	:	:	PUNCT
iajs-856	8	4	fractional	fractional	ADJ
iajs-856	8	5	derivative	derivative	ADJ
iajs-856	8	6	,	,	PUNCT
iajs-856	8	7	two	two	NUM
iajs-856	8	8	-	-	PUNCT
iajs-856	8	9	dimensional	dimensional	ADJ
iajs-856	8	10	probem	probem	NOUN
iajs-856	8	11	,	,	PUNCT
iajs-856	8	12	explicit	explicit	ADJ
iajs-856	8	13	euler	euler	NOUN
iajs-856	8	14	method	method	NOUN
iajs-856	8	15	,	,	PUNCT
iajs-856	8	16	fractional	fractional	ADJ
iajs-856	8	17	dispersion	dispersion	NOUN
iajs-856	8	18	equation	equation	NOUN
iajs-856	8	19	,	,	PUNCT
iajs-856	8	20	s	s	PART
iajs-856	8	21	tability	tability	NOUN
iajs-856	8	22	,	,	PUNCT
iajs-856	8	23	convergence	convergence	NOUN
iajs-856	8	24	introduction	introduction	NOUN
iajs-856	8	25	the	the	DET
iajs-856	8	26	space	space	NOUN
iajs-856	8	27	fractional	fractional	ADJ
iajs-856	8	28	dispersion	dispersion	NOUN
iajs-856	8	29	equation	equation	NOUN
iajs-856	8	30	is	be	AUX
iajs-856	8	31	obtained	obtain	VERB
iajs-856	8	32	from	from	ADP
iajs-856	8	33	the	the	DET
iajs-856	8	34	classical	classical	ADJ
iajs-856	8	35	dispersion	dispersion	NOUN
iajs-856	8	36	equation	equation	NOUN
iajs-856	8	37	by	by	ADP
iajs-856	8	38	replacing	replace	VERB
iajs-856	8	39	the	the	DET
iajs-856	8	40	second	second	ADJ
iajs-856	8	41	space	space	NOUN
iajs-856	8	42	derivative	derivative	NOUN
iajs-856	8	43	by	by	ADP
iajs-856	8	44	a	a	DET
iajs-856	8	45	fractional	fractional	ADJ
iajs-856	8	46	derivative	derivative	NOUN
iajs-856	8	47	.	.	PUNCT
iajs-856	9	1	numerical	numerical	ADJ
iajs-856	9	2	methods	method	NOUN
iajs-856	9	3	associated	associate	VERB
iajs-856	9	4	with	with	ADP
iajs-856	9	5	integer	integer	NOUN
iajs-856	9	6	-	-	PUNCT
iajs-856	9	7	order	order	NOUN
iajs-856	9	8	differential	differential	ADJ
iajs-856	9	9	equations	equation	NOUN
iajs-856	9	10	have	have	AUX
iajs-856	9	11	been	be	AUX
iajs-856	9	12	treated	treat	VERB
iajs-856	9	13	extensively	extensively	ADV
iajs-856	9	14	in	in	ADP
iajs-856	9	15	the	the	DET
iajs-856	9	16	literature	literature	NOUN
iajs-856	9	17	.	.	PUNCT
iajs-856	10	1	on	on	ADP
iajs-856	10	2	other	other	ADJ
iajs-856	10	3	hand	hand	NOUN
iajs-856	10	4	,	,	PUNCT
iajs-856	10	5	studies	study	NOUN
iajs-856	10	6	of	of	ADP
iajs-856	10	7	the	the	DET
iajs-856	10	8	numerical	numerical	ADJ
iajs-856	10	9	methods	method	NOUN
iajs-856	10	10	and	and	CCONJ
iajs-856	10	11	error	error	NOUN
iajs-856	10	12	estimates	estimate	NOUN
iajs-856	10	13	of	of	ADP
iajs-856	10	14	fractional	fractional	ADJ
iajs-856	10	15	order	order	NOUN
iajs-856	10	16	differential	differential	ADJ
iajs-856	10	17	equations	equation	NOUN
iajs-856	10	18	are	be	AUX
iajs-856	10	19	quite	quite	ADV
iajs-856	10	20	limited	limited	ADJ
iajs-856	10	21	to	to	ADP
iajs-856	10	22	date	date	NOUN
iajs-856	10	23	[	[	X
iajs-856	10	24	1	1	NUM
iajs-856	10	25	,	,	PUNCT
iajs-856	10	26	2	2	NUM
iajs-856	10	27	,	,	PUNCT
iajs-856	10	28	3	3	NUM
iajs-856	10	29	]	]	PUNCT
iajs-856	10	30	.	.	PUNCT
iajs-856	11	1	many	many	ADJ
iajs-856	11	2	works	work	VERB
iajs-856	11	3	by	by	ADP
iajs-856	11	4	researchers	researcher	NOUN
iajs-856	11	5	from	from	ADP
iajs-856	11	6	various	various	ADJ
iajs-856	11	7	fields	field	NOUN
iajs-856	11	8	of	of	ADP
iajs-856	11	9	science	science	NOUN
iajs-856	11	10	and	and	CCONJ
iajs-856	11	11	engineering	engineering	NOUN
iajs-856	11	12	deal	deal	NOUN
iajs-856	11	13	with	with	ADP
iajs-856	11	14	dynamical	dynamical	ADJ
iajs-856	11	15	systems	system	NOUN
iajs-856	11	16	described	describe	VERB
iajs-856	11	17	by	by	ADP
iajs-856	11	18	fractional	fractional	ADJ
iajs-856	11	19	partial	partial	ADJ
iajs-856	11	20	differential	differential	NOUN
iajs-856	11	21	equations	equation	NOUN
iajs-856	11	22	,	,	PUNCT
iajs-856	11	23	which	which	PRON
iajs-856	11	24	have	have	AUX
iajs-856	11	25	been	be	AUX
iajs-856	11	26	used	use	VERB
iajs-856	11	27	to	to	PART
iajs-856	11	28	represent	represent	VERB
iajs-856	11	29	many	many	ADJ
iajs-856	11	30	natural	natural	ADJ
iajs-856	11	31	processes	process	NOUN
iajs-856	11	32	in	in	ADP
iajs-856	11	33	physics	physics	NOUN
iajs-856	11	34	[	[	X
iajs-856	11	35	4	4	NUM
iajs-856	11	36	]	]	PUNCT
iajs-856	11	37	,	,	PUNCT
iajs-856	11	38	finance	finance	NOUN
iajs-856	11	39	[	[	X
iajs-856	11	40	5,6	5,6	NUM
iajs-856	11	41	]	]	PUNCT
iajs-856	11	42	,	,	PUNCT
iajs-856	11	43	and	and	CCONJ
iajs-856	11	44	hydrology	hydrology	NOUN
iajs-856	12	1	[	[	X
iajs-856	12	2	7,8	7,8	NUM
iajs-856	12	3	]	]	PUNCT
iajs-856	12	4	.	.	PUNCT
iajs-856	13	1	in	in	ADP
iajs-856	13	2	this	this	DET
iajs-856	13	3	paper	paper	NOUN
iajs-856	13	4	,	,	PUNCT
iajs-856	13	5	we	we	PRON
iajs-856	13	6	find	find	VERB
iajs-856	13	7	the	the	DET
iajs-856	13	8	numerical	numerical	ADJ
iajs-856	13	9	solution	solution	NOUN
iajs-856	13	10	of	of	ADP
iajs-856	13	11	the	the	DET
iajs-856	13	12	two	two	NUM
iajs-856	13	13	-	-	PUNCT
iajs-856	13	14	dimensional	dimensional	ADJ
iajs-856	13	15	fractional	fractional	ADJ
iajs-856	13	16	dispersion	dispersion	NOUN
iajs-856	13	17	equation	equation	NOUN
iajs-856	13	18	of	of	ADP
iajs-856	13	19	the	the	DET
iajs-856	13	20	form	form	NOUN
iajs-856	13	21	:	:	PUNCT
iajs-856	13	22	)	)	PUNCT
iajs-856	13	23	,	,	PUNCT
iajs-856	13	24	,	,	PUNCT
iajs-856	13	25	(	(	PUNCT
iajs-856	13	26	)	)	PUNCT
iajs-856	13	27	,	,	PUNCT
iajs-856	13	28	,	,	PUNCT
iajs-856	13	29	(	(	PUNCT
iajs-856	13	30	)	)	PUNCT
iajs-856	13	31	,	,	PUNCT
iajs-856	13	32	(	(	PUNCT
iajs-856	13	33	)	)	PUNCT
iajs-856	13	34	,	,	PUNCT
iajs-856	13	35	,	,	PUNCT
iajs-856	13	36	(	(	PUNCT
iajs-856	13	37	)	)	PUNCT
iajs-856	13	38	,	,	PUNCT
iajs-856	13	39	(	(	PUNCT
iajs-856	13	40	)	)	PUNCT
iajs-856	13	41	,	,	PUNCT
iajs-856	13	42	,	,	PUNCT
iajs-856	13	43	(	(	PUNCT
iajs-856	13	44	tyxq	tyxq	NOUN
iajs-856	13	45	y	y	PROPN
iajs-856	13	46	tyxu	tyxu	PROPN
iajs-856	13	47	yxb	yxb	NOUN
iajs-856	13	48	x	x	PUNCT
iajs-856	13	49	tyxu	tyxu	PROPN
iajs-856	13	50	yxa	yxa	PROPN
iajs-856	13	51	t	t	PROPN
iajs-856	13	52	tyxu	tyxu	PROPN
iajs-856	13	53			PROPN
iajs-856	13	54			PROPN
iajs-856	13	55			PROPN
iajs-856	13	56			PROPN
iajs-856	13	57			PROPN
iajs-856	13	58			PROPN
iajs-856	13	59			PROPN
iajs-856	13	60			ADJ
iajs-856	13	61			PROPN
iajs-856	13	62			PROPN
iajs-856	13	63			PROPN
iajs-856	13	64			NUM
iajs-856	13	65			NUM
iajs-856	13	66	…	…	PUNCT
iajs-856	13	67	…	…	PUNCT
iajs-856	13	68	…	…	PUNCT
iajs-856	13	69	…	…	PUNCT
iajs-856	13	70	(	(	PUNCT
iajs-856	13	71	1	1	NUM
iajs-856	13	72	)	)	PUNCT
iajs-856	13	73	subject	subject	NOUN
iajs-856	13	74	to	to	ADP
iajs-856	13	75	the	the	DET
iajs-856	13	76	initial	initial	ADJ
iajs-856	13	77	condition	condition	NOUN
iajs-856	13	78	u	u	NOUN
iajs-856	13	79	(	(	PUNCT
iajs-856	13	80	x	x	X
iajs-856	13	81	,	,	PUNCT
iajs-856	13	82	y,0	y,0	NUM
iajs-856	13	83	)	)	PUNCT
iajs-856	14	1	=	=	SYM
iajs-856	14	2	f(x	f(x	PROPN
iajs-856	14	3	,	,	PUNCT
iajs-856	14	4	y	y	PROPN
iajs-856	14	5	)	)	PUNCT
iajs-856	14	6	,	,	PUNCT
iajs-856	14	7	for	for	ADP
iajs-856	14	8	x0	x0	PROPN
iajs-856	14	9			PROPN
iajs-856	14	10	x	x	INTJ
iajs-856	14	11			PROPN
iajs-856	14	12	xr	xr	PROPN
iajs-856	14	13	and	and	CCONJ
iajs-856	14	14	y0	y0	PROPN
iajs-856	14	15			PROPN
iajs-856	14	16	y	y	NUM
iajs-856	14	17	yr	yr	NOUN
iajs-856	14	18	…	…	PUNCT
iajs-856	14	19	…	…	PUNCT
iajs-856	14	20	…	…	PUNCT
iajs-856	14	21	…	…	PUNCT
iajs-856	14	22	…	…	PUNCT
iajs-856	14	23	…	…	PUNCT
iajs-856	14	24	…	…	PUNCT
iajs-856	14	25	(	(	PUNCT
iajs-856	14	26	2	2	NUM
iajs-856	14	27	)	)	PUNCT
iajs-856	14	28	and	and	CCONJ
iajs-856	14	29	the	the	DET
iajs-856	14	30	boundary	boundary	ADJ
iajs-856	14	31	conditions	condition	NOUN
iajs-856	14	32	u	u	NOUN
iajs-856	14	33	(	(	PUNCT
iajs-856	14	34	x0,y	x0,y	PROPN
iajs-856	14	35	,	,	PUNCT
iajs-856	14	36	t	t	PROPN
iajs-856	14	37	)	)	PUNCT
iajs-856	14	38	=	=	SYM
iajs-856	14	39	0	0	NUM
iajs-856	14	40	,	,	PUNCT
iajs-856	14	41	for	for	ADP
iajs-856	14	42	y0	y0	PROPN
iajs-856	14	43			PROPN
iajs-856	14	44	y	y	NUM
iajs-856	14	45	yr	yr	NOUN
iajs-856	14	46	and	and	CCONJ
iajs-856	14	47	0	0	NOUN
iajs-856	14	48	t	t	PROPN
iajs-856	14	49			NUM
iajs-856	14	50	τ	τ	X
iajs-856	14	51	u	u	NOUN
iajs-856	14	52	(	(	PUNCT
iajs-856	14	53	x	x	NOUN
iajs-856	14	54	,	,	PUNCT
iajs-856	14	55	y0,t	y0,t	NOUN
iajs-856	14	56	)	)	PUNCT
iajs-856	14	57	=	=	SYM
iajs-856	14	58	0	0	NUM
iajs-856	14	59	,	,	PUNCT
iajs-856	14	60	for	for	ADP
iajs-856	14	61	x0	x0	PROPN
iajs-856	14	62			PROPN
iajs-856	14	63	x	x	INTJ
iajs-856	15	1			PROPN
iajs-856	15	2	xr	xr	PROPN
iajs-856	15	3	and	and	CCONJ
iajs-856	15	4	0	0	PROPN
iajs-856	15	5	t	t	PROPN
iajs-856	15	6			NUM
iajs-856	15	7	τ	τ	X
iajs-856	15	8	…	…	SYM
iajs-856	15	9	…	…	PUNCT
iajs-856	15	10	…	…	PUNCT
iajs-856	15	11	…	…	PUNCT
iajs-856	15	12	(	(	PUNCT
iajs-856	15	13	3	3	X
iajs-856	15	14	)	)	PUNCT
iajs-856	15	15	u	u	NOUN
iajs-856	15	16	(	(	PUNCT
iajs-856	15	17	xr	xr	PROPN
iajs-856	15	18	,	,	PUNCT
iajs-856	15	19	y	y	PROPN
iajs-856	15	20	,	,	PUNCT
iajs-856	15	21	t	t	PROPN
iajs-856	15	22	)	)	PUNCT
iajs-856	15	23	=	=	SYM
iajs-856	16	1	g(y	g(y	PROPN
iajs-856	16	2	,	,	PUNCT
iajs-856	16	3	t	t	PROPN
iajs-856	16	4	)	)	PUNCT
iajs-856	16	5	,	,	PUNCT
iajs-856	16	6	for	for	ADP
iajs-856	16	7	y0	y0	PROPN
iajs-856	16	8			PROPN
iajs-856	16	9	y	y	NUM
iajs-856	16	10	yr	yr	NOUN
iajs-856	16	11	and	and	CCONJ
iajs-856	16	12	0	0	NOUN
iajs-856	16	13	t	t	PROPN
iajs-856	16	14			NUM
iajs-856	16	15	τ	τ	X
iajs-856	16	16	u	u	NOUN
iajs-856	16	17	(	(	PUNCT
iajs-856	16	18	x	x	NOUN
iajs-856	16	19	,	,	PUNCT
iajs-856	16	20	yr	yr	PROPN
iajs-856	16	21	,	,	PUNCT
iajs-856	16	22	t	t	PROPN
iajs-856	16	23	)	)	PUNCT
iajs-856	16	24	=	=	SYM
iajs-856	16	25	k(x	k(x	PROPN
iajs-856	16	26	,	,	PUNCT
iajs-856	16	27	t	t	PROPN
iajs-856	16	28	)	)	PUNCT
iajs-856	16	29	,	,	PUNCT
iajs-856	16	30	for	for	ADP
iajs-856	16	31	x0	x0	PROPN
iajs-856	16	32			PROPN
iajs-856	16	33	x	x	INTJ
iajs-856	16	34			PROPN
iajs-856	16	35	xr	xr	PROPN
iajs-856	16	36	and	and	CCONJ
iajs-856	16	37	0	0	PROPN
iajs-856	16	38	t	t	PROPN
iajs-856	16	39			NUM
iajs-856	16	40	τ	τ	PROPN
iajs-856	16	41	ibn	ibn	PROPN
iajs-856	16	42	alhaitham	alhaitham	NOUN
iajs-856	16	43	j.	j.	PROPN
iajs-856	17	1	fo	fo	ADP
iajs-856	17	2	r	r	NOUN
iajs-856	17	3	pure	pure	ADJ
iajs-856	17	4	&	&	CCONJ
iajs-856	17	5	appl	appl	PROPN
iajs-856	17	6	.	.	PUNCT
iajs-856	18	1	sc	sc	PROPN
iajs-856	18	2	i.	i.	PROPN
iajs-856	18	3	vo	vo	PROPN
iajs-856	18	4	l.24	l.24	PROPN
iajs-856	18	5	(	(	PUNCT
iajs-856	18	6	1	1	NUM
iajs-856	18	7	)	)	PUNCT
iajs-856	18	8	2011	2011	NUM
iajs-856	18	9	where	where	SCONJ
iajs-856	18	10	a	a	DET
iajs-856	18	11	,	,	PUNCT
iajs-856	18	12	b	b	NOUN
iajs-856	18	13	and	and	CCONJ
iajs-856	18	14	f	f	PROPN
iajs-856	18	15	are	be	AUX
iajs-856	18	16	known	know	VERB
iajs-856	18	17	functions	function	NOUN
iajs-856	18	18	of	of	ADP
iajs-856	18	19	x	x	X
iajs-856	18	20	and	and	CCONJ
iajs-856	18	21	y	y	PROPN
iajs-856	18	22	,	,	PUNCT
iajs-856	18	23	g	g	PROPN
iajs-856	18	24	is	be	AUX
iajs-856	18	25	a	a	DET
iajs-856	18	26	known	know	VERB
iajs-856	18	27	function	function	NOUN
iajs-856	18	28	of	of	ADP
iajs-856	18	29	y	y	PROPN
iajs-856	18	30	and	and	CCONJ
iajs-856	18	31	t	t	PROPN
iajs-856	18	32	,	,	PUNCT
iajs-856	18	33	k	k	PROPN
iajs-856	18	34	is	be	AUX
iajs-856	18	35	aknwon	aknwon	VERB
iajs-856	18	36	function	function	NOUN
iajs-856	18	37	of	of	ADP
iajs-856	18	38	x	x	PUNCT
iajs-856	18	39	and	and	CCONJ
iajs-856	18	40	t.	t.	PROPN
iajs-856	18	41			PROPN
iajs-856	18	42	and	and	CCONJ
iajs-856	18	43			PROPN
iajs-856	18	44	are	be	AUX
iajs-856	18	45	given	give	VERB
iajs-856	18	46	fractional	fractional	ADJ
iajs-856	18	47	number	number	NOUN
iajs-856	18	48	.	.	PUNCT
iajs-856	19	1	q	q	PUNCT
iajs-856	19	2	is	be	AUX
iajs-856	19	3	a	a	DET
iajs-856	19	4	knwon	knwon	VERB
iajs-856	19	5	function	function	NOUN
iajs-856	19	6	of	of	ADP
iajs-856	19	7	x	x	PROPN
iajs-856	19	8	,	,	PUNCT
iajs-856	19	9	y	y	PROPN
iajs-856	19	10	and	and	CCONJ
iajs-856	19	11	t.	t.	NOUN
iajs-856	19	12	we	we	PRON
iajs-856	19	13	use	use	VERB
iajs-856	19	14	a	a	DET
iajs-856	19	15	variation	variation	NOUN
iajs-856	19	16	on	on	ADP
iajs-856	19	17	the	the	DET
iajs-856	19	18	classical	classical	ADJ
iajs-856	19	19	explicit	explicit	ADJ
iajs-856	19	20	euler	euler	NOUN
iajs-856	19	21	method	method	NOUN
iajs-856	19	22	.	.	PUNCT
iajs-856	20	1	we	we	PRON
iajs-856	20	2	prove	prove	VERB
iajs-856	20	3	this	this	DET
iajs-856	20	4	method	method	NOUN
iajs-856	20	5	by	by	ADP
iajs-856	20	6	using	use	VERB
iajs-856	20	7	a	a	DET
iajs-856	20	8	novel	novel	NOUN
iajs-856	20	9	shifted	shift	VERB
iajs-856	20	10	version	version	NOUN
iajs-856	20	11	of	of	ADP
iajs-856	20	12	the	the	DET
iajs-856	20	13	usual	usual	ADJ
iajs-856	20	14	grunwaled	grunwale	VERB
iajs-856	20	15	finite	finite	ADJ
iajs-856	20	16	difference	difference	NOUN
iajs-856	20	17	an	an	DET
iajs-856	20	18	approximation	approximation	NOUN
iajs-856	20	19	for	for	ADP
iajs-856	20	20	the	the	DET
iajs-856	20	21	non	non	ADJ
iajs-856	20	22	-	-	ADJ
iajs-856	20	23	local	local	ADJ
iajs-856	20	24	fractional	fractional	ADJ
iajs-856	20	25	derivative	derivative	ADJ
iajs-856	20	26	operator	operator	NOUN
iajs-856	20	27	.	.	PUNCT
iajs-856	21	1	explicit	explicit	ADJ
iajs-856	21	2	finite	finite	ADJ
iajs-856	21	3	difference	difference	NOUN
iajs-856	21	4	approximation	approximation	NOUN
iajs-856	21	5	for	for	ADP
iajs-856	21	6	solving	solve	VERB
iajs-856	21	7	the	the	DET
iajs-856	21	8	two	two	NUM
iajs-856	21	9	-	-	PUNCT
iajs-856	21	10	dimensional	dimensional	ADJ
iajs-856	21	11	fractional	fractional	ADJ
iajs-856	21	12	dispersion	dispersion	NOUN
iajs-856	21	13	equation	equation	NOUN
iajs-856	21	14	in	in	ADP
iajs-856	21	15	this	this	DET
iajs-856	21	16	section	section	NOUN
iajs-856	21	17	,	,	PUNCT
iajs-856	21	18	we	we	PRON
iajs-856	21	19	propose	propose	VERB
iajs-856	21	20	explicit	explicit	ADJ
iajs-856	21	21	finite	finite	ADJ
iajs-856	21	22	difference	difference	NOUN
iajs-856	21	23	approximation	approximation	NOUN
iajs-856	21	24	for	for	ADP
iajs-856	21	25	solving	solve	VERB
iajs-856	21	26	the	the	DET
iajs-856	21	27	initial	initial	ADJ
iajs-856	21	28	and	and	CCONJ
iajs-856	21	29	boundary	boundary	ADJ
iajs-856	21	30	value	value	NOUN
iajs-856	21	31	problem	problem	NOUN
iajs-856	21	32	two	two	NUM
iajs-856	21	33	-	-	PUNCT
iajs-856	21	34	dimensional	dimensional	ADJ
iajs-856	21	35	fractional	fractional	ADJ
iajs-856	21	36	dispersion	dispersion	NOUN
iajs-856	21	37	equation	equation	NOUN
iajs-856	21	38	(	(	PUNCT
iajs-856	21	39	1)-(3	1)-(3	NUM
iajs-856	21	40	)	)	PUNCT
iajs-856	21	41	.	.	PUNCT
iajs-856	22	1	the	the	DET
iajs-856	22	2	finite	finite	ADJ
iajs-856	22	3	difference	difference	NOUN
iajs-856	22	4	method	method	NOUN
iajs-856	22	5	starts	start	VERB
iajs-856	22	6	by	by	ADP
iajs-856	22	7	dividing	divide	VERB
iajs-856	22	8	the	the	DET
iajs-856	22	9	x	x	NOUN
iajs-856	22	10	-	-	NOUN
iajs-856	22	11	interval	interval	NOUN
iajs-856	23	1	[	[	X
iajs-856	23	2	x0	x0	PROPN
iajs-856	23	3	,	,	PUNCT
iajs-856	23	4	xr	xr	X
iajs-856	23	5	]	]	PUNCT
iajs-856	23	6	into	into	ADP
iajs-856	23	7	n	n	ADP
iajs-856	23	8	subintervals	subinterval	NOUN
iajs-856	23	9	to	to	PART
iajs-856	23	10	get	get	VERB
iajs-856	23	11	the	the	DET
iajs-856	23	12	grid	grid	NOUN
iajs-856	23	13	points	point	NOUN
iajs-856	23	14	xi	xi	X
iajs-856	24	1	=	=	PUNCT
iajs-856	24	2	x0	x0	PROPN
iajs-856	24	3	+	+	CCONJ
iajs-856	24	4	ix	ix	NOUN
iajs-856	24	5	,	,	PUNCT
iajs-856	24	6	where	where	SCONJ
iajs-856	24	7			NOUN
iajs-856	24	8			SYM
iajs-856	24	9	nxxx	nxxx	ADJ
iajs-856	24	10	r	r	NOUN
iajs-856	24	11	0	0	NUM
iajs-856	24	12	and	and	CCONJ
iajs-856	24	13	i=0,1,	i=0,1,	NOUN
iajs-856	24	14	…	…	X
iajs-856	24	15	,n	,n	NOUN
iajs-856	24	16	.	.	PUNCT
iajs-856	25	1	also	also	ADV
iajs-856	25	2	we	we	PRON
iajs-856	25	3	divide	divide	VERB
iajs-856	25	4	the	the	DET
iajs-856	25	5	yinterval	yinterval	NOUN
iajs-856	26	1	[	[	X
iajs-856	26	2	y0	y0	NOUN
iajs-856	26	3	,	,	PUNCT
iajs-856	26	4	yr	yr	NOUN
iajs-856	26	5	]	]	X
iajs-856	26	6	into	into	ADP
iajs-856	26	7	m	m	PROPN
iajs-856	26	8	subintervals	subinterval	NOUN
iajs-856	26	9	to	to	PART
iajs-856	26	10	get	get	VERB
iajs-856	26	11	the	the	DET
iajs-856	26	12	grid	grid	NOUN
iajs-856	26	13	points	point	NOUN
iajs-856	26	14	yj	yj	PROPN
iajs-856	26	15	=	=	SYM
iajs-856	26	16	y0	y0	PROPN
iajs-856	26	17	+	+	CCONJ
iajs-856	26	18	jy	jy	PROPN
iajs-856	26	19	,	,	PUNCT
iajs-856	26	20	where	where	SCONJ
iajs-856	26	21			NOUN
iajs-856	26	22			PROPN
iajs-856	26	23	myyy	myyy	NOUN
iajs-856	26	24	r	r	NOUN
iajs-856	26	25	0	0	NUM
iajs-856	26	26	and	and	CCONJ
iajs-856	26	27	j=0,1,	j=0,1,	NOUN
iajs-856	26	28	…	…	NOUN
iajs-856	26	29	,m	,m	PUNCT
iajs-856	26	30	.	.	PUNCT
iajs-856	27	1	also	also	ADV
iajs-856	27	2	,	,	PUNCT
iajs-856	27	3	the	the	DET
iajs-856	27	4	t	t	NOUN
iajs-856	27	5	-	-	PUNCT
iajs-856	27	6	interval	interval	NOUN
iajs-856	27	7	[	[	X
iajs-856	27	8	0,t	0,t	X
iajs-856	27	9	]	]	X
iajs-856	27	10	is	be	AUX
iajs-856	27	11	divided	divide	VERB
iajs-856	27	12	into	into	ADP
iajs-856	27	13	m	m	PROPN
iajs-856	27	14	subintervals	subinterval	NOUN
iajs-856	27	15	to	to	PART
iajs-856	27	16	get	get	VERB
iajs-856	27	17	the	the	DET
iajs-856	27	18	grid	grid	NOUN
iajs-856	27	19	points	point	NOUN
iajs-856	27	20	ts	ts	ADP
iajs-856	27	21	=	=	PUNCT
iajs-856	27	22	st	st	PROPN
iajs-856	27	23	,	,	PUNCT
iajs-856	27	24	s	s	NOUN
iajs-856	27	25	=	=	NOUN
iajs-856	27	26	0	0	NUM
iajs-856	27	27	,	,	PUNCT
iajs-856	27	28	…	…	PUNCT
iajs-856	27	29	,	,	PUNCT
iajs-856	27	30	m	m	PROPN
iajs-856	27	31	,	,	PUNCT
iajs-856	27	32	where	where	SCONJ
iajs-856	27	33	mtt	mtt	NOUN
iajs-856	27	34			NOUN
iajs-856	27	35	.	.	PUNCT
iajs-856	28	1	now	now	ADV
iajs-856	28	2	,	,	PUNCT
iajs-856	28	3	we	we	PRON
iajs-856	28	4	evaluate	evaluate	VERB
iajs-856	28	5	eq.(1	eq.(1	ADJ
iajs-856	28	6	)	)	PUNCT
iajs-856	28	7	at	at	ADP
iajs-856	28	8	(	(	PUNCT
iajs-856	28	9	x	x	PROPN
iajs-856	28	10	i	i	PROPN
iajs-856	28	11	,	,	PUNCT
iajs-856	28	12	y	y	PROPN
iajs-856	28	13	j	j	PROPN
iajs-856	28	14	,	,	PUNCT
iajs-856	28	15	t	t	PROPN
iajs-856	28	16	s	s	PART
iajs-856	28	17	)	)	PUNCT
iajs-856	28	18	and	and	CCONJ
iajs-856	28	19	we	we	PRON
iajs-856	28	20	use	use	VERB
iajs-856	28	21	the	the	DET
iajs-856	28	22	explicit	explicit	ADJ
iajs-856	28	23	finite	finite	ADJ
iajs-856	28	24	difference	difference	NOUN
iajs-856	28	25	approximation	approximation	NOUN
iajs-856	28	26	to	to	PART
iajs-856	28	27	get	get	VERB
iajs-856	28	28	)	)	PUNCT
iajs-856	28	29	,	,	PUNCT
iajs-856	28	30	,	,	PUNCT
iajs-856	28	31	(	(	PUNCT
iajs-856	28	32	)	)	PUNCT
iajs-856	28	33	,	,	PUNCT
iajs-856	28	34	,	,	PUNCT
iajs-856	28	35	(	(	PUNCT
iajs-856	28	36	)	)	PUNCT
iajs-856	28	37	,	,	PUNCT
iajs-856	28	38	(	(	PUNCT
iajs-856	28	39	)	)	PUNCT
iajs-856	28	40	,	,	PUNCT
iajs-856	28	41	,	,	PUNCT
iajs-856	28	42	(	(	PUNCT
iajs-856	28	43	)	)	PUNCT
iajs-856	28	44	,	,	PUNCT
iajs-856	28	45	(	(	PUNCT
iajs-856	28	46	)	)	PUNCT
iajs-856	28	47	,	,	PUNCT
iajs-856	28	48	,	,	PUNCT
iajs-856	28	49	(	(	PUNCT
iajs-856	28	50	)	)	PUNCT
iajs-856	28	51	,	,	PUNCT
iajs-856	28	52	,	,	PUNCT
iajs-856	28	53	(	(	PUNCT
iajs-856	28	54	1	1	NUM
iajs-856	28	55	sji	sji	NOUN
iajs-856	28	56	sji	sji	NOUN
iajs-856	28	57	ji	ji	PROPN
iajs-856	28	58	sji	sji	PROPN
iajs-856	28	59	ji	ji	PROPN
iajs-856	28	60	sjisji	sjisji	PROPN
iajs-856	28	61	tyxq	tyxq	PROPN
iajs-856	28	62	y	y	PROPN
iajs-856	28	63	tyxu	tyxu	PROPN
iajs-856	28	64	yxb	yxb	NOUN
iajs-856	28	65	x	x	PUNCT
iajs-856	28	66	tyxu	tyxu	VERB
iajs-856	28	67	yxa	yxa	PROPN
iajs-856	28	68	t	t	PROPN
iajs-856	28	69	tyxutyxu	tyxutyxu	NOUN
iajs-856	28	70			ADP
iajs-856	28	71			PROPN
iajs-856	28	72			PROPN
iajs-856	28	73			PROPN
iajs-856	28	74			ADJ
iajs-856	28	75			ADJ
iajs-856	28	76			NUM
iajs-856	28	77			ADJ
iajs-856	28	78			PROPN
iajs-856	28	79			PROPN
iajs-856	28	80			PROPN
iajs-856	28	81			NUM
iajs-856	28	82			NUM
iajs-856	28	83	…	…	PUNCT
iajs-856	28	84	..	..	PUNCT
iajs-856	28	85	(	(	PUNCT
iajs-856	28	86	4	4	X
iajs-856	28	87	)	)	PUNCT
iajs-856	28	88	then	then	ADV
iajs-856	28	89	use	use	VERB
iajs-856	28	90	the	the	DET
iajs-856	28	91	shifted	shift	VERB
iajs-856	28	92	grunwald	grunwald	NOUN
iajs-856	28	93	estimate	estimate	NOUN
iajs-856	28	94	to	to	ADP
iajs-856	28	95	the	the	DET
iajs-856	28	96			NOUN
iajs-856	28	97	,	,	PUNCT
iajs-856	28	98	the	the	DET
iajs-856	28	99	fractional	fractional	ADJ
iajs-856	28	100	derivative	derivative	NOUN
iajs-856	28	101	,	,	PUNCT
iajs-856	29	1	[	[	X
iajs-856	29	2	9	9	NUM
iajs-856	29	3	]	]	NUM
iajs-856	29	4	:	:	PUNCT
iajs-856	29	5	)	)	PUNCT
iajs-856	29	6	(	(	PUNCT
iajs-856	29	7	)	)	PUNCT
iajs-856	29	8	,	,	PUNCT
iajs-856	29	9	,	,	PUNCT
iajs-856	29	10	)	)	PUNCT
iajs-856	29	11	1	1	NUM
iajs-856	29	12	(	(	PUNCT
iajs-856	29	13	(	(	PUNCT
iajs-856	29	14	)	)	PUNCT
iajs-856	29	15	(	(	PUNCT
iajs-856	29	16	1	1	NUM
iajs-856	29	17	)	)	PUNCT
iajs-856	29	18	,	,	PUNCT
iajs-856	29	19	,	,	PUNCT
iajs-856	29	20	(	(	PUNCT
iajs-856	29	21	0	0	NUM
iajs-856	29	22	,	,	PUNCT
iajs-856	29	23	xotyxkxug	xotyxkxug	PROPN
iajs-856	29	24	xx	xx	NUM
iajs-856	30	1	tyxu	tyxu	PROPN
iajs-856	30	2	m	m	VERB
iajs-856	30	3	k	k	PROPN
iajs-856	30	4	k	k	PROPN
iajs-856	30	5			PRON
iajs-856	30	6			PUNCT
iajs-856	30	7			NUM
iajs-856	30	8			ADJ
iajs-856	30	9			PROPN
iajs-856	30	10			X
iajs-856	30	11			NUM
iajs-856	30	12			NUM
iajs-856	30	13			NUM
iajs-856	30	14	…	…	PUNCT
iajs-856	30	15	…	…	PUNCT
iajs-856	30	16	…	…	PUNCT
iajs-856	30	17	…	…	PUNCT
iajs-856	30	18	…	…	SYM
iajs-856	30	19	.(5	.(5	NOUN
iajs-856	30	20	)	)	PUNCT
iajs-856	30	21	)	)	PUNCT
iajs-856	30	22	(	(	PUNCT
iajs-856	30	23	)	)	PUNCT
iajs-856	30	24	,	,	PUNCT
iajs-856	30	25	)	)	PUNCT
iajs-856	30	26	1	1	NUM
iajs-856	30	27	(	(	PUNCT
iajs-856	30	28	,	,	PUNCT
iajs-856	30	29	(	(	PUNCT
iajs-856	30	30	)	)	PUNCT
iajs-856	30	31	(	(	PUNCT
iajs-856	30	32	1	1	NUM
iajs-856	30	33	)	)	PUNCT
iajs-856	30	34	,	,	PUNCT
iajs-856	30	35	,	,	PUNCT
iajs-856	30	36	(	(	PUNCT
iajs-856	30	37	0	0	NUM
iajs-856	30	38	,	,	PUNCT
iajs-856	30	39	yotykyxug	yotykyxug	NOUN
iajs-856	31	1	yy	yy	INTJ
iajs-856	31	2	tyxu	tyxu	PROPN
iajs-856	31	3	m	m	VERB
iajs-856	31	4	k	k	PROPN
iajs-856	31	5	k	k	PROPN
iajs-856	31	6			PRON
iajs-856	31	7			PUNCT
iajs-856	31	8			NUM
iajs-856	31	9			ADJ
iajs-856	31	10			PROPN
iajs-856	31	11			X
iajs-856	31	12			NUM
iajs-856	31	13			NOUN
iajs-856	31	14			NOUN
iajs-856	31	15	to	to	PART
iajs-856	31	16	reduce	reduce	VERB
iajs-856	31	17	eq.(4	eq.(4	PRON
iajs-856	31	18	)	)	PUNCT
iajs-856	31	19	as	as	ADP
iajs-856	31	20	in	in	ADP
iajs-856	31	21	the	the	DET
iajs-856	31	22	following	follow	VERB
iajs-856	31	23	form	form	NOUN
iajs-856	31	24	)	)	PUNCT
iajs-856	31	25	,	,	PUNCT
iajs-856	31	26	,	,	PUNCT
iajs-856	31	27	(	(	PUNCT
iajs-856	31	28	1	1	NUM
iajs-856	31	29	)	)	PUNCT
iajs-856	31	30	,	,	PUNCT
iajs-856	31	31	(	(	PUNCT
iajs-856	31	32	1	1	NUM
iajs-856	31	33	)	)	PUNCT
iajs-856	31	34	,	,	PUNCT
iajs-856	31	35	(	(	PUNCT
iajs-856	31	36	1	1	NUM
iajs-856	31	37	0	0	NUM
iajs-856	31	38	1,,,1	1,,,1	NUM
iajs-856	31	39	1	1	NUM
iajs-856	31	40	0	0	NUM
iajs-856	31	41	,	,	PUNCT
iajs-856	31	42	,	,	PUNCT
iajs-856	31	43	1	1	NUM
iajs-856	31	44	,	,	PUNCT
iajs-856	32	1	sji	sji	NOUN
iajs-856	32	2	j	j	PROPN
iajs-856	32	3	k	k	PROPN
iajs-856	32	4	s	s	VERB
iajs-856	32	5	kjikji	kjikji	NOUN
iajs-856	32	6	s	s	X
iajs-856	32	7	jki	jki	NOUN
iajs-856	33	1	i	i	PRON
iajs-856	33	2	k	k	PROPN
iajs-856	34	1	kji	kji	PROPN
iajs-856	34	2	s	s	VERB
iajs-856	34	3	ji	ji	PROPN
iajs-856	34	4	s	s	X
iajs-856	34	5	ji	ji	PROPN
iajs-856	34	6	tyxqug	tyxqug	PROPN
iajs-856	34	7	y	y	PROPN
iajs-856	34	8	yxbug	yxbug	PROPN
iajs-856	34	9	x	x	SYM
iajs-856	34	10	yxa	yxa	PROPN
iajs-856	34	11	t	t	PROPN
iajs-856	34	12	uu	uu	INTJ
iajs-856	34	13			X
iajs-856	34	14			PROPN
iajs-856	34	15			X
iajs-856	34	16			NOUN
iajs-856	34	17			VERB
iajs-856	34	18			PROPN
iajs-856	34	19			X
iajs-856	34	20			X
iajs-856	34	21			PROPN
iajs-856	34	22			X
iajs-856	34	23			NOUN
iajs-856	34	24			VERB
iajs-856	34	25			PROPN
iajs-856	34	26			NOUN
iajs-856	34	27			NUM
iajs-856	34	28			PUNCT
iajs-856	35	1			NOUN
iajs-856	35	2			ADV
iajs-856	35	3			ADJ
iajs-856	35	4			NUM
iajs-856	35	5			ADP
iajs-856	35	6			ADV
iajs-856	35	7			NUM
iajs-856	35	8			PROPN
iajs-856	35	9			PROPN
iajs-856	35	10	s	s	PROPN
iajs-856	35	11	ji	ji	PROPN
iajs-856	35	12	s	s	PROPN
iajs-856	35	13	kji	kji	NOUN
iajs-856	36	1	j	j	PROPN
iajs-856	36	2	k	k	PROPN
iajs-856	36	3	k	k	PROPN
iajs-856	37	1	ji	ji	INTJ
iajs-856	38	1	i	i	PRON
iajs-856	38	2	k	k	PROPN
iajs-856	39	1	s	s	VERB
iajs-856	39	2	jkik	jkik	NOUN
iajs-856	40	1	ji	ji	PROPN
iajs-856	40	2	s	s	PROPN
iajs-856	40	3	ji	ji	PROPN
iajs-856	40	4	s	s	X
iajs-856	40	5	ji	ji	NOUN
iajs-856	40	6	qug	qug	PROPN
iajs-856	40	7	y	y	PROPN
iajs-856	40	8	b	b	PROPN
iajs-856	41	1	ug	ug	ADP
iajs-856	41	2	x	x	PROPN
iajs-856	41	3	a	a	DET
iajs-856	41	4	t	t	NOUN
iajs-856	41	5	uu	uu	INTJ
iajs-856	41	6	,	,	PUNCT
iajs-856	41	7	1	1	NUM
iajs-856	41	8	,	,	PUNCT
iajs-856	41	9	1	1	NUM
iajs-856	41	10	0	0	NUM
iajs-856	41	11	,	,	PUNCT
iajs-856	41	12	,	,	PUNCT
iajs-856	41	13	1	1	NUM
iajs-856	41	14	0	0	NUM
iajs-856	41	15	,	,	PUNCT
iajs-856	41	16	1	1	NUM
iajs-856	41	17	,	,	PUNCT
iajs-856	41	18	,	,	PUNCT
iajs-856	41	19	,	,	PUNCT
iajs-856	41	20	1	1	NUM
iajs-856	41	21	,	,	PUNCT
iajs-856	41	22			ADV
iajs-856	41	23			NOUN
iajs-856	41	24			X
iajs-856	41	25			PUNCT
iajs-856	41	26			NUM
iajs-856	41	27			PUNCT
iajs-856	41	28			PROPN
iajs-856	41	29			PROPN
iajs-856	41	30			PROPN
iajs-856	41	31			PROPN
iajs-856	41	32			PUNCT
iajs-856	41	33			PROPN
iajs-856	41	34			PROPN
iajs-856	41	35			ADV
iajs-856	41	36			PRON
iajs-856	41	37			PROPN
iajs-856	41	38	,	,	PUNCT
iajs-856	41	39	1,	1,	NUM
iajs-856	41	40	...	...	PUNCT
iajs-856	41	41	,1	,1	PUNCT
iajs-856	41	42			PROPN
iajs-856	41	43	ni	ni	PROPN
iajs-856	41	44	,	,	PUNCT
iajs-856	41	45	msmj	msmj	ADJ
iajs-856	41	46	,	,	PUNCT
iajs-856	41	47	...	...	PUNCT
iajs-856	41	48	,	,	PUNCT
iajs-856	41	49	0,1,	0,1,	NOUN
iajs-856	41	50	...	...	PUNCT
iajs-856	41	51	,1	,1	NOUN
iajs-856	41	52			NOUN
iajs-856	41	53	…	…	PUNCT
iajs-856	41	54	…	…	PUNCT
iajs-856	41	55	…	…	SYM
iajs-856	41	56	……	……	NOUN
iajs-856	41	57	.	.	PUNCT
iajs-856	42	1	(	(	PUNCT
iajs-856	42	2	6	6	NUM
iajs-856	42	3	)	)	PUNCT
iajs-856	42	4	where	where	SCONJ
iajs-856	42	5	)	)	PUNCT
iajs-856	42	6	,	,	PUNCT
iajs-856	42	7	,	,	PUNCT
iajs-856	42	8	(	(	PUNCT
iajs-856	42	9	,	,	PUNCT
iajs-856	42	10	sji	sji	PROPN
iajs-856	42	11	s	s	PART
iajs-856	42	12	ji	ji	NOUN
iajs-856	42	13	tyxuu	tyxuu	VERB
iajs-856	42	14			PROPN
iajs-856	42	15	,	,	PUNCT
iajs-856	42	16	)	)	PUNCT
iajs-856	42	17	,	,	PUNCT
iajs-856	42	18	(	(	PUNCT
iajs-856	42	19	,	,	PUNCT
iajs-856	42	20	jiji	jiji	PROPN
iajs-856	42	21	yxaa	yxaa	VERB
iajs-856	42	22			PROPN
iajs-856	42	23	,	,	PUNCT
iajs-856	42	24	)	)	PUNCT
iajs-856	42	25	,	,	PUNCT
iajs-856	42	26	(	(	PUNCT
iajs-856	42	27	,	,	PUNCT
iajs-856	42	28	jiji	jiji	PROPN
iajs-856	42	29	yxbb	yxbb	PROPN
iajs-856	42	30			PROPN
iajs-856	42	31	,	,	PUNCT
iajs-856	42	32	)	)	PUNCT
iajs-856	42	33	,	,	PUNCT
iajs-856	42	34	,	,	PUNCT
iajs-856	42	35	(	(	PUNCT
iajs-856	42	36	,	,	PUNCT
iajs-856	42	37	sji	sji	PROPN
iajs-856	42	38	s	s	PART
iajs-856	42	39	ji	ji	NOUN
iajs-856	42	40	tyxqq	tyxqq	NOUN
iajs-856	42	41			PRON
iajs-856	42	42	,	,	PUNCT
iajs-856	42	43	!	!	PUNCT
iajs-856	42	44	)	)	PUNCT
iajs-856	43	1	1()1	1()1	NUM
iajs-856	43	2	(	(	PUNCT
iajs-856	43	3	)	)	PUNCT
iajs-856	43	4	1	1	NUM
iajs-856	43	5	(	(	PUNCT
iajs-856	43	6	,	,	PUNCT
iajs-856	43	7	k	k	PROPN
iajs-856	44	1	k	k	PROPN
iajs-856	44	2	g	g	PROPN
iajs-856	44	3	k	k	PROPN
iajs-856	44	4	k	k	PROPN
iajs-856	44	5			PROPN
iajs-856	44	6			PROPN
iajs-856	44	7			NUM
iajs-856	44	8			NUM
iajs-856	44	9			NOUN
iajs-856	44	10	,	,	PUNCT
iajs-856	44	11	k=0,1,2	k=0,1,2	PROPN
iajs-856	44	12	,	,	PUNCT
iajs-856	44	13	…	…	PUNCT
iajs-856	44	14	and	and	CCONJ
iajs-856	44	15	!	!	PUNCT
iajs-856	45	1	)	)	PUNCT
iajs-856	45	2	1()1	1()1	NUM
iajs-856	45	3	(	(	PUNCT
iajs-856	45	4	)	)	PUNCT
iajs-856	45	5	1	1	NUM
iajs-856	45	6	(	(	PUNCT
iajs-856	45	7	,	,	PUNCT
iajs-856	45	8	k	k	PROPN
iajs-856	46	1	k	k	PROPN
iajs-856	46	2	g	g	PROPN
iajs-856	46	3	k	k	PROPN
iajs-856	47	1	k	k	PROPN
iajs-856	47	2			PROPN
iajs-856	47	3			ADJ
iajs-856	47	4			NOUN
iajs-856	47	5			PROPN
iajs-856	47	6			NOUN
iajs-856	47	7	,	,	PUNCT
iajs-856	47	8	k=0,1,2	k=0,1,2	PROPN
iajs-856	47	9	,	,	PUNCT
iajs-856	47	10	…	…	PUNCT
iajs-856	47	11	the	the	DET
iajs-856	47	12	resulting	result	VERB
iajs-856	47	13	equation	equation	NOUN
iajs-856	47	14	can	can	AUX
iajs-856	47	15	be	be	AUX
iajs-856	47	16	explicitly	explicitly	ADV
iajs-856	47	17	solved	solve	VERB
iajs-856	47	18	for	for	ADP
iajs-856	47	19	1	1	NUM
iajs-856	47	20	,	,	PUNCT
iajs-856	47	21	s	s	ADJ
iajs-856	47	22	jiu	jiu	NOUN
iajs-856	47	23	to	to	PART
iajs-856	47	24	give	give	VERB
iajs-856	47	25	s	s	PRON
iajs-856	47	26	ji	ji	NOUN
iajs-856	47	27	s	s	PROPN
iajs-856	47	28	ji	ji	PROPN
iajs-856	47	29	s	s	PROPN
iajs-856	47	30	kji	kji	PROPN
iajs-856	47	31	j	j	PROPN
iajs-856	47	32	k	k	X
iajs-856	48	1	kji	kji	INTJ
iajs-856	49	1	i	i	INTJ
iajs-856	49	2	k	k	PROPN
iajs-856	50	1	s	s	VERB
iajs-856	50	2	jkikji	jkikji	PROPN
iajs-856	50	3	s	s	VERB
iajs-856	50	4	ji	ji	PROPN
iajs-856	50	5	utqug	utqug	PROPN
iajs-856	50	6	y	y	PROPN
iajs-856	50	7	t	t	PROPN
iajs-856	50	8	bug	bug	NOUN
iajs-856	50	9	x	x	PUNCT
iajs-856	50	10	t	t	X
iajs-856	50	11	au	au	ADV
iajs-856	50	12	,	,	PUNCT
iajs-856	50	13	,	,	PUNCT
iajs-856	50	14	1	1	NUM
iajs-856	50	15	,	,	PUNCT
iajs-856	50	16	1	1	NUM
iajs-856	50	17	0	0	NUM
iajs-856	50	18	,	,	PUNCT
iajs-856	50	19	,	,	PUNCT
iajs-856	50	20	1	1	NUM
iajs-856	50	21	0	0	NUM
iajs-856	50	22	,	,	PUNCT
iajs-856	50	23	1	1	NUM
iajs-856	50	24	,	,	PUNCT
iajs-856	50	25	,	,	PUNCT
iajs-856	50	26	1	1	NUM
iajs-856	50	27	,	,	PUNCT
iajs-856	50	28			PRON
iajs-856	50	29			NOUN
iajs-856	50	30			NOUN
iajs-856	50	31			PRON
iajs-856	50	32			PUNCT
iajs-856	50	33			X
iajs-856	51	1			PROPN
iajs-856	51	2			PROPN
iajs-856	51	3			VERB
iajs-856	51	4			PROPN
iajs-856	51	5			PUNCT
iajs-856	51	6			PROPN
iajs-856	51	7			PROPN
iajs-856	51	8			ADV
iajs-856	51	9			PRON
iajs-856	51	10			PROPN
iajs-856	51	11	...............	...............	PUNCT
iajs-856	51	12	(	(	PUNCT
iajs-856	51	13	7	7	X
iajs-856	51	14	)	)	PUNCT
iajs-856	51	15	also	also	ADV
iajs-856	51	16	form	form	VERB
iajs-856	51	17	the	the	DET
iajs-856	51	18	initial	initial	ADJ
iajs-856	51	19	condition	condition	NOUN
iajs-856	51	20	and	and	CCONJ
iajs-856	51	21	boundary	boundary	ADJ
iajs-856	51	22	conditions	condition	NOUN
iajs-856	51	23	one	one	PRON
iajs-856	51	24	can	can	AUX
iajs-856	51	25	get	get	VERB
iajs-856	51	26	ibn	ibn	PROPN
iajs-856	51	27	alhaitham	alhaitham	NOUN
iajs-856	51	28	j.	j.	PROPN
iajs-856	52	1	fo	fo	ADP
iajs-856	52	2	r	r	NOUN
iajs-856	52	3	pure	pure	ADJ
iajs-856	52	4	&	&	CCONJ
iajs-856	52	5	appl	appl	PROPN
iajs-856	52	6	.	.	PUNCT
iajs-856	53	1	sc	sc	PROPN
iajs-856	53	2	i.	i.	PROPN
iajs-856	53	3	vo	vo	PROPN
iajs-856	53	4	l.24	l.24	PROPN
iajs-856	53	5	(	(	PUNCT
iajs-856	53	6	1	1	NUM
iajs-856	53	7	)	)	PUNCT
iajs-856	53	8	2011	2011	NUM
iajs-856	53	9	jiji	jiji	PROPN
iajs-856	53	10	fu	fu	PROPN
iajs-856	53	11	,	,	PUNCT
iajs-856	53	12	0	0	NUM
iajs-856	53	13	,	,	PUNCT
iajs-856	53	14			PRON
iajs-856	53	15	,	,	PUNCT
iajs-856	53	16	i=0	i=0	PROPN
iajs-856	53	17	,	,	PUNCT
iajs-856	53	18	…	…	PUNCT
iajs-856	53	19	,	,	PUNCT
iajs-856	53	20	n	n	PRON
iajs-856	53	21	0,0	0,0	NUM
iajs-856	53	22	s	s	PROPN
iajs-856	53	23	ju	ju	PROPN
iajs-856	53	24	,	,	PUNCT
iajs-856	53	25	j=0	j=0	PROPN
iajs-856	53	26	,	,	PUNCT
iajs-856	53	27	…	…	PUNCT
iajs-856	53	28	,	,	PUNCT
iajs-856	53	29	m	m	VERB
iajs-856	53	30	and	and	CCONJ
iajs-856	53	31	s=1,	s=1,	NOUN
iajs-856	53	32	…	…	PROPN
iajs-856	53	33	,m	,m	PUNCT
iajs-856	53	34	00	00	NUM
iajs-856	53	35	,	,	PUNCT
iajs-856	53	36	s	s	ADV
iajs-856	53	37	iu	iu	ADP
iajs-856	53	38	,	,	PUNCT
iajs-856	53	39	i=0	i=0	PROPN
iajs-856	53	40	,	,	PUNCT
iajs-856	53	41	…	…	PUNCT
iajs-856	53	42	,	,	PUNCT
iajs-856	53	43	n	n	NOUN
iajs-856	53	44	and	and	CCONJ
iajs-856	53	45	s=1,	s=1,	NOUN
iajs-856	53	46	…	…	NUM
iajs-856	53	47	,m	,m	PUNCT
iajs-856	53	48	s	s	VERB
iajs-856	53	49	j	j	PROPN
iajs-856	53	50	s	s	X
iajs-856	53	51	jr	jr	PROPN
iajs-856	53	52	gu	gu	NOUN
iajs-856	53	53			PROPN
iajs-856	53	54	,	,	PUNCT
iajs-856	53	55	,	,	PUNCT
iajs-856	53	56	j=0	j=0	PROPN
iajs-856	53	57	,	,	PUNCT
iajs-856	53	58	…	…	PUNCT
iajs-856	53	59	,	,	PUNCT
iajs-856	53	60	m	m	VERB
iajs-856	53	61	and	and	CCONJ
iajs-856	53	62	s=1,	s=1,	NOUN
iajs-856	53	63	…	…	PROPN
iajs-856	53	64	,m	,m	X
iajs-856	53	65	s	s	VERB
iajs-856	53	66	i	i	PROPN
iajs-856	53	67	s	s	PROPN
iajs-856	53	68	ri	ri	PROPN
iajs-856	53	69	ku	ku	PROPN
iajs-856	53	70			PROPN
iajs-856	53	71	,	,	PUNCT
iajs-856	53	72	,	,	PUNCT
iajs-856	53	73	i=0	i=0	PROPN
iajs-856	53	74	,	,	PUNCT
iajs-856	53	75	…	…	PUNCT
iajs-856	53	76	,	,	PUNCT
iajs-856	53	77	n	n	NOUN
iajs-856	53	78	and	and	CCONJ
iajs-856	53	79	s=1,	s=1,	NOUN
iajs-856	53	80	…	…	PROPN
iajs-856	53	81	,m	,m	PUNCT
iajs-856	53	82	where	where	SCONJ
iajs-856	53	83	)	)	PUNCT
iajs-856	53	84	,	,	PUNCT
iajs-856	53	85	,	,	PUNCT
iajs-856	53	86	(	(	PUNCT
iajs-856	53	87	,	,	PUNCT
iajs-856	53	88	sjiji	sjiji	VERB
iajs-856	53	89	tyxff	tyxff	PROPN
iajs-856	53	90			NOUN
iajs-856	53	91	,	,	PUNCT
iajs-856	53	92	)	)	PUNCT
iajs-856	53	93	,	,	PUNCT
iajs-856	53	94	(	(	PUNCT
iajs-856	53	95	sj	sj	INTJ
iajs-856	53	96	s	s	PROPN
iajs-856	53	97	j	j	PROPN
iajs-856	53	98	tygg	tygg	NOUN
iajs-856	53	99			PROPN
iajs-856	53	100	and	and	CCONJ
iajs-856	53	101	)	)	PUNCT
iajs-856	53	102	,	,	PUNCT
iajs-856	53	103	(	(	PUNCT
iajs-856	53	104	si	si	X
iajs-856	53	105	s	s	X
iajs-856	53	106	i	i	PRON
iajs-856	53	107	txk	txk	VERB
iajs-856	53	108			NUM
iajs-856	53	109	stability	stability	NOUN
iajs-856	53	110	analysis	analysis	NOUN
iajs-856	53	111	of	of	ADP
iajs-856	53	112	the	the	DET
iajs-856	53	113	explicit	explicit	ADJ
iajs-856	53	114	finite	finite	ADJ
iajs-856	53	115	difference	difference	NOUN
iajs-856	53	116	approximation	approximation	NOUN
iajs-856	53	117	define	define	VERB
iajs-856	53	118	the	the	DET
iajs-856	53	119	following	follow	VERB
iajs-856	53	120	fractional	fractional	ADJ
iajs-856	53	121	partial	partial	ADJ
iajs-856	53	122	difference	difference	NOUN
iajs-856	53	123	operators	operator	NOUN
iajs-856	53	124	:	:	PUNCT
iajs-856	53	125			X
iajs-856	53	126			PROPN
iajs-856	53	127			PROPN
iajs-856	53	128			PROPN
iajs-856	53	129			PUNCT
iajs-856	53	130			NUM
iajs-856	53	131	1	1	NUM
iajs-856	53	132	0	0	NUM
iajs-856	53	133	,	,	PUNCT
iajs-856	53	134	1	1	NUM
iajs-856	53	135	,	,	PUNCT
iajs-856	53	136	,	,	PUNCT
iajs-856	53	137	,	,	PUNCT
iajs-856	53	138	,	,	PUNCT
iajs-856	53	139	i	i	PRON
iajs-856	53	140	k	k	PROPN
iajs-856	53	141	s	s	PROPN
iajs-856	53	142	jkik	jkik	NOUN
iajs-856	53	143	jis	ji	VERB
iajs-856	53	144	jix	jix	PROPN
iajs-856	53	145	ug	ug	ADP
iajs-856	53	146	x	x	SYM
iajs-856	53	147	a	a	DET
iajs-856	53	148	u	u	X
iajs-856	53	149			X
iajs-856	53	150	and	and	CCONJ
iajs-856	53	151	s	s	VERB
iajs-856	53	152	kji	kji	NOUN
iajs-856	53	153	j	j	PROPN
iajs-856	53	154	k	k	PROPN
iajs-856	53	155	k	k	PROPN
iajs-856	53	156	jis	jis	PROPN
iajs-856	53	157	jiy	jiy	VERB
iajs-856	53	158	ug	ug	ADP
iajs-856	53	159	y	y	PROPN
iajs-856	53	160	b	b	PROPN
iajs-856	53	161	u	u	PROPN
iajs-856	53	162	1	1	NUM
iajs-856	53	163	,	,	PUNCT
iajs-856	53	164	1	1	NUM
iajs-856	53	165	0	0	NUM
iajs-856	53	166	,	,	PUNCT
iajs-856	53	167	,	,	PUNCT
iajs-856	53	168	,	,	PUNCT
iajs-856	53	169	,	,	PUNCT
iajs-856	53	170			PROPN
iajs-856	53	171			ADV
iajs-856	53	172			PRON
iajs-856	53	173			NOUN
iajs-856	53	174			PUNCT
iajs-856	54	1			NUM
iajs-856	54	2			PRON
iajs-856	54	3	which	which	PRON
iajs-856	54	4	is	be	AUX
iajs-856	54	5	an	an	PRON
iajs-856	54	6	)	)	PUNCT
iajs-856	54	7	(	(	PUNCT
iajs-856	54	8	xo	xo	PROPN
iajs-856	54	9			PROPN
iajs-856	54	10	approximation	approximation	NOUN
iajs-856	54	11	to	to	ADP
iajs-856	54	12	the	the	DET
iajs-856	54	13			NUM
iajs-856	54	14	th	th	X
iajs-856	54	15	fractional	fractional	ADJ
iajs-856	54	16	derivative	derivative	NOUN
iajs-856	54	17	and	and	CCONJ
iajs-856	54	18	)	)	PUNCT
iajs-856	54	19	(	(	PUNCT
iajs-856	55	1	yo	yo	INTJ
iajs-856	55	2			NOUN
iajs-856	55	3	approximation	approximation	NOUN
iajs-856	55	4	to	to	ADP
iajs-856	55	5	the	the	VERB
iajs-856	55	6	th	th	PUNCT
iajs-856	55	7	fractional	fractional	ADJ
iajs-856	55	8	derivative	derivative	ADJ
iajs-856	55	9	term	term	NOUN
iajs-856	55	10	.	.	PUNCT
iajs-856	56	1	then	then	ADV
iajs-856	56	2	eq.(7	eq.(7	VERB
iajs-856	56	3	)	)	PUNCT
iajs-856	56	4	may	may	AUX
iajs-856	56	5	be	be	AUX
iajs-856	56	6	written	write	VERB
iajs-856	56	7	in	in	ADP
iajs-856	56	8	the	the	DET
iajs-856	56	9	operator	operator	NOUN
iajs-856	56	10	form	form	NOUN
iajs-856	56	11	s	s	PART
iajs-856	56	12	ji	ji	PROPN
iajs-856	56	13	s	s	PROPN
iajs-856	56	14	jiyx	jiyx	NOUN
iajs-856	56	15	s	s	PART
iajs-856	56	16	ji	ji	PROPN
iajs-856	56	17	tquttu	tquttu	NOUN
iajs-856	56	18	,	,	PUNCT
iajs-856	56	19	,	,	PUNCT
iajs-856	56	20	,	,	PUNCT
iajs-856	56	21	,	,	PUNCT
iajs-856	56	22	1	1	NUM
iajs-856	56	23	,	,	PUNCT
iajs-856	56	24	)	)	PUNCT
iajs-856	56	25	1	1	NUM
iajs-856	56	26	(	(	PUNCT
iajs-856	56	27			NOUN
iajs-856	56	28			NOUN
iajs-856	56	29			X
iajs-856	56	30	................	................	PUNCT
iajs-856	56	31	(	(	PUNCT
iajs-856	56	32	8)	8)	NOUN
iajs-856	56	33	eq.(8	eq.(8	ADJ
iajs-856	56	34	)	)	PUNCT
iajs-856	56	35	may	may	AUX
iajs-856	56	36	be	be	AUX
iajs-856	56	37	written	write	VERB
iajs-856	56	38	in	in	ADP
iajs-856	56	39	form	form	NOUN
iajs-856	56	40	s	s	PART
iajs-856	56	41	ji	ji	PROPN
iajs-856	56	42	s	s	PROPN
iajs-856	56	43	jiyx	jiyx	NOUN
iajs-856	56	44	s	s	PART
iajs-856	56	45	ji	ji	PROPN
iajs-856	56	46	tquttu	tquttu	NOUN
iajs-856	56	47	,	,	PUNCT
iajs-856	56	48	,	,	PUNCT
iajs-856	56	49	,	,	PUNCT
iajs-856	56	50	,	,	PUNCT
iajs-856	56	51	1	1	NUM
iajs-856	56	52	,	,	PUNCT
iajs-856	56	53	)	)	PUNCT
iajs-856	56	54	1)(1	1)(1	NUM
iajs-856	56	55	(	(	PUNCT
iajs-856	56	56			X
iajs-856	56	57			NOUN
iajs-856	56	58			X
iajs-856	56	59	..................	..................	PUNCT
iajs-856	56	60	(	(	PUNCT
iajs-856	56	61	9	9	NUM
iajs-856	56	62	)	)	PUNCT
iajs-856	56	63	where	where	SCONJ
iajs-856	56	64	ts	ts	ADP
iajs-856	56	65	mn	mn	PROPN
iajs-856	56	66	s	s	PROPN
iajs-856	56	67	m	m	PROPN
iajs-856	56	68	s	s	NOUN
iajs-856	56	69	m	m	PROPN
iajs-856	56	70	s	s	NOUN
iajs-856	56	71	n	n	NUM
iajs-856	56	72	sss	sss	PROPN
iajs-856	56	73	n	n	PRON
iajs-856	56	74	sss	sss	VERB
iajs-856	56	75	uuuuuuuuuu	uuuuuuuuuu	NOUN
iajs-856	56	76	]	]	PUNCT
iajs-856	56	77	,	,	PUNCT
iajs-856	56	78	,	,	PUNCT
iajs-856	56	79	,	,	PUNCT
iajs-856	56	80	,	,	PUNCT
iajs-856	56	81	,	,	PUNCT
iajs-856	56	82	,	,	PUNCT
iajs-856	56	83	,	,	PUNCT
iajs-856	56	84	,	,	PUNCT
iajs-856	56	85	,	,	PUNCT
iajs-856	56	86	,	,	PUNCT
iajs-856	56	87	,	,	PUNCT
iajs-856	56	88	,	,	PUNCT
iajs-856	56	89	[	[	PUNCT
iajs-856	56	90	1,11,21,12,12,22,11,11,21,1	1,11,21,12,12,22,11,11,21,1	NUM
iajs-856	56	91			NOUN
iajs-856	56	92			VERB
iajs-856	56	93	to	to	PART
iajs-856	56	94	solve	solve	VERB
iajs-856	56	95	the	the	DET
iajs-856	56	96	problem	problem	NOUN
iajs-856	56	97	for	for	ADP
iajs-856	56	98	each	each	DET
iajs-856	56	99	fixed	fix	VERB
iajs-856	56	100	yj	yj	PROPN
iajs-856	56	101	to	to	PART
iajs-856	56	102	obtain	obtain	VERB
iajs-856	56	103	an	an	DET
iajs-856	56	104	intermediate	intermediate	ADJ
iajs-856	56	105	solution	solution	NOUN
iajs-856	56	106			PROPN
iajs-856	56	107	jiu	jiu	NOUN
iajs-856	56	108	,	,	PUNCT
iajs-856	56	109	from	from	ADP
iajs-856	56	110	1	1	NUM
iajs-856	56	111	,	,	PUNCT
iajs-856	56	112	,	,	PUNCT
iajs-856	56	113	,	,	PUNCT
iajs-856	56	114	,	,	PUNCT
iajs-856	56	115	)	)	PUNCT
iajs-856	56	116	1	1	NUM
iajs-856	56	117	(	(	PUNCT
iajs-856	56	118			ADV
iajs-856	56	119			PROPN
iajs-856	56	120	s	s	VERB
iajs-856	56	121	ji	ji	PROPN
iajs-856	56	122	s	s	PROPN
iajs-856	56	123	jijix	jijix	PROPN
iajs-856	56	124	utqut	utqut	PROPN
iajs-856	56	125			VERB
iajs-856	56	126	......................	......................	PUNCT
iajs-856	56	127	(	(	PUNCT
iajs-856	56	128	10	10	NUM
iajs-856	56	129	)	)	PUNCT
iajs-856	56	130	then	then	ADV
iajs-856	56	131	solve	solve	VERB
iajs-856	56	132	for	for	ADP
iajs-856	56	133	each	each	DET
iajs-856	56	134	fixed	fix	VERB
iajs-856	56	135	xi	xi	ADP
iajs-856	56	136			NOUN
iajs-856	56	137	ji	ji	PROPN
iajs-856	56	138	s	s	PROPN
iajs-856	56	139	jiy	jiy	PROPN
iajs-856	56	140	uut	uut	PROPN
iajs-856	56	141	,	,	PUNCT
iajs-856	56	142	,	,	PUNCT
iajs-856	56	143	,	,	PUNCT
iajs-856	56	144	)	)	PUNCT
iajs-856	56	145	1	1	NUM
iajs-856	56	146	(	(	PUNCT
iajs-856	56	147			ADJ
iajs-856	56	148	.......................	.......................	PUNCT
iajs-856	56	149	(	(	PUNCT
iajs-856	56	150	11	11	NUM
iajs-856	56	151	)	)	PUNCT
iajs-856	56	152	now	now	ADV
iajs-856	56	153	,	,	PUNCT
iajs-856	56	154	we	we	PRON
iajs-856	56	155	must	must	AUX
iajs-856	56	156	prove	prove	VERB
iajs-856	56	157	each	each	DET
iajs-856	56	158	one	one	NUM
iajs-856	56	159	-	-	PUNCT
iajs-856	56	160	dimensional	dimensional	ADJ
iajs-856	56	161	explicit	explicit	ADJ
iajs-856	56	162	system	system	NOUN
iajs-856	56	163	defined	define	VERB
iajs-856	56	164	by	by	ADP
iajs-856	56	165	the	the	DET
iajs-856	56	166	linear	linear	PROPN
iajs-856	56	167	difference	difference	NOUN
iajs-856	56	168	eqs	eqs	X
iajs-856	56	169	.	.	PUNCT
iajs-856	57	1	(	(	PUNCT
iajs-856	57	2	10	10	NUM
iajs-856	57	3	)	)	PUNCT
iajs-856	57	4	and	and	CCONJ
iajs-856	57	5	(	(	PUNCT
iajs-856	57	6	11	11	NUM
iajs-856	57	7	)	)	PUNCT
iajs-856	57	8	is	be	AUX
iajs-856	57	9	conditionally	conditionally	ADV
iajs-856	57	10	stable	stable	ADJ
iajs-856	57	11	for	for	ADP
iajs-856	57	12	all	all	DET
iajs-856	57	13	1	1	NUM
iajs-856	57	14	<	<	X
iajs-856	57	15			ADP
iajs-856	57	16	<	<	X
iajs-856	57	17	2	2	NUM
iajs-856	57	18	,	,	PUNCT
iajs-856	57	19	1	1	NUM
iajs-856	57	20	<	<	NOUN
iajs-856	57	21			NOUN
iajs-856	57	22	<	<	X
iajs-856	57	23	2	2	NUM
iajs-856	57	24	.	.	PUNCT
iajs-856	57	25	theorem	theorem	VERB
iajs-856	57	26	:	:	PUNCT
iajs-856	57	27	the	the	DET
iajs-856	57	28	explicit	explicit	ADJ
iajs-856	57	29	system	system	NOUN
iajs-856	57	30	defined	define	VERB
iajs-856	57	31	by	by	ADP
iajs-856	57	32	the	the	DET
iajs-856	57	33	linear	linear	PROPN
iajs-856	57	34	difference	difference	NOUN
iajs-856	57	35	eqs.(10	eqs.(10	PROPN
iajs-856	57	36	)	)	PUNCT
iajs-856	57	37	and	and	CCONJ
iajs-856	57	38	(	(	PUNCT
iajs-856	57	39	11	11	NUM
iajs-856	57	40	)	)	PUNCT
iajs-856	57	41	with	with	ADP
iajs-856	57	42	1<	1<	PROPN
iajs-856	57	43	<	<	X
iajs-856	57	44	2	2	NUM
iajs-856	57	45	,	,	PUNCT
iajs-856	57	46	1	1	NUM
iajs-856	57	47	<	<	NOUN
iajs-856	57	48			NOUN
iajs-856	57	49	<	<	X
iajs-856	57	50	2	2	NUM
iajs-856	57	51	is	be	AUX
iajs-856	57	52	conditionally	conditionally	ADV
iajs-856	57	53	stable	stable	ADJ
iajs-856	57	54	if	if	SCONJ
iajs-856	57	55	max	max	PROPN
iajs-856	57	56	1	1	NUM
iajs-856	57	57	ax	ax	NOUN
iajs-856	57	58	t	t	X
iajs-856	57	59			PRON
iajs-856	57	60			NOUN
iajs-856	57	61			NOUN
iajs-856	57	62			NOUN
iajs-856	57	63	and	and	CCONJ
iajs-856	57	64	max	max	PROPN
iajs-856	57	65	1	1	NUM
iajs-856	57	66	by	by	ADP
iajs-856	57	67	t	t	NOUN
iajs-856	57	68			ADJ
iajs-856	57	69			NOUN
iajs-856	57	70			PUNCT
iajs-856	57	71			NOUN
iajs-856	58	1	proof	proof	NOUN
iajs-856	58	2	:	:	PUNCT
iajs-856	58	3	at	at	ADP
iajs-856	58	4	each	each	DET
iajs-856	58	5	grid	grid	NOUN
iajs-856	58	6	point	point	NOUN
iajs-856	58	7	yk	yk	PROPN
iajs-856	58	8	,	,	PUNCT
iajs-856	58	9	for	for	ADP
iajs-856	58	10	1,,1	1,,1	NUM
iajs-856	58	11			PROPN
iajs-856	58	12	mk	mk	NOUN
iajs-856	58	13			NUM
iajs-856	58	14	,	,	PUNCT
iajs-856	58	15	the	the	DET
iajs-856	58	16	system	system	NOUN
iajs-856	58	17	of	of	ADP
iajs-856	58	18	equation	equation	NOUN
iajs-856	58	19	defined	define	VERB
iajs-856	58	20	by	by	ADP
iajs-856	58	21	eq.(10	eq.(10	NOUN
iajs-856	58	22	)	)	PUNCT
iajs-856	58	23	can	can	AUX
iajs-856	58	24	be	be	AUX
iajs-856	58	25	written	write	VERB
iajs-856	58	26	in	in	ADP
iajs-856	58	27	the	the	DET
iajs-856	58	28	explicit	explicit	ADJ
iajs-856	58	29	matrix	matrix	NOUN
iajs-856	58	30	form	form	NOUN
iajs-856	58	31	s	s	PART
iajs-856	58	32	kkk	kkk	PROPN
iajs-856	58	33	s	s	PART
iajs-856	58	34	k	k	PROPN
iajs-856	58	35	qtucu	qtucu	PROPN
iajs-856	58	36			PROPN
iajs-856	58	37	1	1	NOUN
iajs-856	58	38	where	where	SCONJ
iajs-856	58	39	ibn	ibn	PROPN
iajs-856	58	40	alhaitham	alhaitham	NOUN
iajs-856	58	41	j.	j.	PROPN
iajs-856	59	1	fo	fo	ADP
iajs-856	59	2	r	r	NOUN
iajs-856	59	3	pure	pure	ADJ
iajs-856	59	4	&	&	CCONJ
iajs-856	59	5	appl	appl	PROPN
iajs-856	59	6	.	.	PUNCT
iajs-856	60	1	sc	sc	PROPN
iajs-856	60	2	i.	i.	PROPN
iajs-856	60	3	vo	vo	PROPN
iajs-856	61	1	l.24	l.24	PROPN
iajs-856	61	2	(	(	PUNCT
iajs-856	61	3	1	1	NUM
iajs-856	61	4	)	)	PUNCT
iajs-856	61	5	2011	2011	NUM
iajs-856	61	6	,	,	PUNCT
iajs-856	61	7	]	]	PUNCT
iajs-856	61	8	,	,	PUNCT
iajs-856	61	9	,	,	PUNCT
iajs-856	61	10	,	,	PUNCT
iajs-856	61	11	[	[	PUNCT
iajs-856	61	12	1	1	NUM
iajs-856	61	13	,	,	PUNCT
iajs-856	61	14	1	1	NUM
iajs-856	61	15	1	1	NUM
iajs-856	61	16	,	,	PUNCT
iajs-856	61	17	2	2	NUM
iajs-856	61	18	1	1	NUM
iajs-856	61	19	,	,	PUNCT
iajs-856	61	20	1	1	NUM
iajs-856	61	21	1	1	NUM
iajs-856	61	22	ts	ts	ADP
iajs-856	61	23	kn	kn	PROPN
iajs-856	61	24	s	s	PROPN
iajs-856	61	25	k	k	PROPN
iajs-856	61	26	s	s	X
iajs-856	61	27	k	k	PROPN
iajs-856	61	28	s	s	PROPN
iajs-856	61	29	k	k	PROPN
iajs-856	61	30	uuuu	uuuu	PROPN
iajs-856	61	31			PROPN
iajs-856	61	32			X
iajs-856	61	33			ADV
iajs-856	61	34			NOUN
iajs-856	62	1			INTJ
iajs-856	62	2	,	,	PUNCT
iajs-856	62	3	]	]	X
iajs-856	62	4	,	,	PUNCT
iajs-856	62	5	,	,	PUNCT
iajs-856	62	6	,	,	PUNCT
iajs-856	62	7	[	[	PUNCT
iajs-856	62	8	,	,	PUNCT
iajs-856	62	9	1,2,1	1,2,1	NUM
iajs-856	62	10	t	t	PROPN
iajs-856	62	11	knkkk	knkkk	PROPN
iajs-856	62	12	uuuu	uuuu	PROPN
iajs-856	62	13			PROPN
iajs-856	62	14			PROPN
iajs-856	62	15			NOUN
iajs-856	62	16			NUM
iajs-856	62	17			NUM
iajs-856	62	18	ts	ts	ADP
iajs-856	62	19	kn	kn	PROPN
iajs-856	62	20	s	s	PROPN
iajs-856	62	21	k	k	PROPN
iajs-856	62	22	s	s	X
iajs-856	62	23	k	k	PROPN
iajs-856	62	24	s	s	X
iajs-856	62	25	k	k	PROPN
iajs-856	62	26	qqqq	qqqq	PROPN
iajs-856	62	27	]	]	PUNCT
iajs-856	62	28	,	,	PUNCT
iajs-856	62	29	,	,	PUNCT
iajs-856	62	30	,	,	PUNCT
iajs-856	62	31	[	[	PUNCT
iajs-856	62	32	,	,	PUNCT
iajs-856	62	33	1,2,1	1,2,1	NUM
iajs-856	62	34			NOUN
iajs-856	62	35			NUM
iajs-856	62	36	kc	kc	PROPN
iajs-856	62	37	is	be	AUX
iajs-856	62	38	the	the	DET
iajs-856	62	39	matrix	matrix	NOUN
iajs-856	62	40	of	of	ADP
iajs-856	62	41	coefficients	coefficient	NOUN
iajs-856	62	42	,	,	PUNCT
iajs-856	62	43	and	and	CCONJ
iajs-856	62	44	is	be	AUX
iajs-856	62	45	the	the	DET
iajs-856	62	46	sum	sum	NOUN
iajs-856	62	47	of	of	ADP
iajs-856	62	48	a	a	DET
iajs-856	62	49	lower	low	ADJ
iajs-856	62	50	triangular	triangular	NOUN
iajs-856	62	51	matrix	matrix	NOUN
iajs-856	62	52	and	and	CCONJ
iajs-856	62	53	a	a	DET
iajs-856	62	54	super	super	ADV
iajs-856	62	55	diagonal	diagonal	ADJ
iajs-856	62	56	matrix	matrix	NOUN
iajs-856	62	57	at	at	ADP
iajs-856	62	58	the	the	DET
iajs-856	62	59	grid	grid	NOUN
iajs-856	62	60	point	point	NOUN
iajs-856	62	61	y	y	PROPN
iajs-856	62	62	k	k	PROPN
iajs-856	62	63	,	,	PUNCT
iajs-856	62	64	where	where	SCONJ
iajs-856	62	65	the	the	DET
iajs-856	62	66	matrix	matrix	NOUN
iajs-856	62	67	entries	entry	NOUN
iajs-856	62	68	along	along	ADP
iajs-856	62	69	the	the	DET
iajs-856	62	70	ith	ith	PROPN
iajs-856	62	71	row	row	NOUN
iajs-856	62	72	are	be	AUX
iajs-856	62	73	defined	define	VERB
iajs-856	62	74	from	from	ADP
iajs-856	62	75	eq.(10	eq.(10	ADJ
iajs-856	62	76	)	)	PUNCT
iajs-856	62	77	.	.	PUNCT
iajs-856	63	1	for	for	ADP
iajs-856	63	2	example	example	NOUN
iajs-856	63	3	,	,	PUNCT
iajs-856	63	4	for	for	ADP
iajs-856	63	5	i	i	PRON
iajs-856	63	6	=	=	SYM
iajs-856	63	7	1	1	NUM
iajs-856	63	8	the	the	DET
iajs-856	63	9	equation	equation	NOUN
iajs-856	63	10	becomes	become	VERB
iajs-856	63	11	s	s	PROPN
iajs-856	63	12	kkkkkkk	kkkkkkk	PROPN
iajs-856	63	13	s	s	PART
iajs-856	63	14	k	k	PROPN
iajs-856	63	15	tqugugugu	tqugugugu	ADJ
iajs-856	63	16	,	,	PUNCT
iajs-856	63	17	1,20,,1,11,,1,02,,1	1,20,,1,11,,1,02,,1	X
iajs-856	63	18	1	1	NUM
iajs-856	63	19	,	,	PUNCT
iajs-856	63	20	1	1	NUM
iajs-856	63	21	)	)	SYM
iajs-856	63	22	1	1	NUM
iajs-856	63	23	(	(	PUNCT
iajs-856	63	24			NOUN
iajs-856	63	25			PROPN
iajs-856	63	26			NUM
iajs-856	63	27			NOUN
iajs-856	63	28	for	for	ADP
iajs-856	63	29	i	i	PRON
iajs-856	63	30	=	=	NOUN
iajs-856	63	31	2	2	NUM
iajs-856	63	32	we	we	PRON
iajs-856	63	33	have	have	VERB
iajs-856	63	34	s	s	VERB
iajs-856	63	35	kkkkkkkkk	kkkkkkkkk	PROPN
iajs-856	63	36	s	s	PROPN
iajs-856	64	1	k	k	PROPN
iajs-856	64	2	tqugugugugu	tqugugugugu	PROPN
iajs-856	64	3	,	,	PUNCT
iajs-856	64	4	2,30,,2,21,,2,12,,2,03,,2	2,30,,2,21,,2,12,,2,03,,2	NUM
iajs-856	64	5	1	1	NUM
iajs-856	64	6	,	,	PUNCT
iajs-856	64	7	2	2	NUM
iajs-856	64	8	)	)	PUNCT
iajs-856	64	9	1	1	NUM
iajs-856	64	10	(	(	PUNCT
iajs-856	64	11			NOUN
iajs-856	64	12			PUNCT
iajs-856	64	13			X
iajs-856	64	14			X
iajs-856	64	15	and	and	CCONJ
iajs-856	64	16	for	for	ADP
iajs-856	64	17	i	i	PRON
iajs-856	64	18	=	=	SYM
iajs-856	64	19	n	n	NUM
iajs-856	64	20	1	1	NUM
iajs-856	64	21	we	we	PRON
iajs-856	64	22	get	get	VERB
iajs-856	64	23			PROPN
iajs-856	64	24			PROPN
iajs-856	64	25			PROPN
iajs-856	64	26			PROPN
iajs-856	64	27			PROPN
iajs-856	64	28			PROPN
iajs-856	64	29			PROPN
iajs-856	64	30			ADV
iajs-856	64	31			PROPN
iajs-856	64	32	knknknknknkn	knknknknknkn	PROPN
iajs-856	64	33	s	s	VERB
iajs-856	64	34	kn	kn	PROPN
iajs-856	64	35	ugugugu	ugugugu	NOUN
iajs-856	64	36	,	,	PUNCT
iajs-856	64	37	11,,1,22,,1,0,,1	11,,1,22,,1,0,,1	NUM
iajs-856	64	38	1	1	NUM
iajs-856	64	39	,	,	PUNCT
iajs-856	64	40	1	1	NUM
iajs-856	64	41	)	)	SYM
iajs-856	64	42	1	1	NUM
iajs-856	64	43	(	(	PUNCT
iajs-856	64	44			NUM
iajs-856	65	1			PRON
iajs-856	65	2			NOUN
iajs-856	65	3	s	s	VERB
iajs-856	65	4	knknkn	knknkn	NOUN
iajs-856	65	5	tqug	tqug	PROPN
iajs-856	65	6	,	,	PUNCT
iajs-856	65	7	1,0,,1	1,0,,1	NUM
iajs-856	65	8			PROPN
iajs-856	65	9			PROPN
iajs-856	65	10			PROPN
iajs-856	65	11			PROPN
iajs-856	65	12	where	where	SCONJ
iajs-856	65	13	the	the	DET
iajs-856	65	14	coefficients	coefficient	NOUN
iajs-856	65	15			NUM
iajs-856	65	16	x	x	SYM
iajs-856	65	17	t	t	NOUN
iajs-856	65	18	a	a	DET
iajs-856	65	19	jiki	jiki	ADJ
iajs-856	65	20			NOUN
iajs-856	65	21			PUNCT
iajs-856	65	22			NUM
iajs-856	65	23	,	,	PUNCT
iajs-856	65	24	,	,	PUNCT
iajs-856	65	25	,	,	PUNCT
iajs-856	65	26	therefore	therefore	ADV
iajs-856	65	27	the	the	DET
iajs-856	65	28	resulting	result	VERB
iajs-856	65	29	matrix	matrix	NOUN
iajs-856	65	30	entries	entry	NOUN
iajs-856	65	31	jic	jic	PROPN
iajs-856	65	32	,	,	PUNCT
iajs-856	65	33	for	for	ADP
iajs-856	65	34	1,,1	1,,1	NUM
iajs-856	65	35			PROPN
iajs-856	65	36	ni	ni	PROPN
iajs-856	65	37			PROPN
iajs-856	65	38	and	and	CCONJ
iajs-856	65	39	1,,1	1,,1	NUM
iajs-856	65	40			PROPN
iajs-856	65	41	nj	nj	PROPN
iajs-856	65	42			NUM
iajs-856	65	43	by	by	ADP
iajs-856	65	44	are	be	AUX
iajs-856	65	45	defined	define	VERB
iajs-856	65	46	by	by	ADP
iajs-856	65	47			NUM
iajs-856	65	48			NUM
iajs-856	65	49			PROPN
iajs-856	65	50			NUM
iajs-856	65	51			NUM
iajs-856	65	52			NUM
iajs-856	65	53			ADP
iajs-856	65	54			PROPN
iajs-856	65	55			PROPN
iajs-856	65	56	1	1	NOUN
iajs-856	65	57	,	,	PUNCT
iajs-856	65	58	,	,	PUNCT
iajs-856	65	59	0	0	NUM
iajs-856	65	60	,	,	PUNCT
iajs-856	65	61	,	,	PUNCT
iajs-856	65	62	2	2	NUM
iajs-856	65	63	,	,	PUNCT
iajs-856	65	64	,	,	PUNCT
iajs-856	65	65	1	1	NUM
iajs-856	65	66	,	,	PUNCT
iajs-856	65	67	,	,	PUNCT
iajs-856	65	68	,	,	PUNCT
iajs-856	65	69	1	1	NUM
iajs-856	65	70	jki	jki	VERB
iajs-856	65	71	ki	ki	PROPN
iajs-856	66	1	ki	ki	PROPN
iajs-856	66	2	ki	ki	PROPN
iajs-856	67	1	ji	ji	PROPN
iajs-856	68	1	g	g	PROPN
iajs-856	68	2	g	g	PROPN
iajs-856	68	3	g	g	PROPN
iajs-856	68	4	g	g	PROPN
iajs-856	68	5	c	c	PROPN
iajs-856	68	6			NUM
iajs-856	68	7			NUM
iajs-856	68	8			NUM
iajs-856	68	9			NUM
iajs-856	68	10			NUM
iajs-856	68	11			NUM
iajs-856	68	12			NUM
iajs-856	68	13			NUM
iajs-856	68	14	for	for	ADP
iajs-856	68	15	for	for	ADP
iajs-856	68	16	for	for	ADP
iajs-856	68	17	for	for	ADP
iajs-856	68	18	1	1	NUM
iajs-856	68	19	1	1	NUM
iajs-856	68	20	1	1	NUM
iajs-856	68	21			NOUN
iajs-856	68	22			ADJ
iajs-856	68	23			NOUN
iajs-856	69	1			PROPN
iajs-856	69	2	ij	ij	INTJ
iajs-856	69	3	ij	ij	INTJ
iajs-856	69	4	ij	ij	INTJ
iajs-856	69	5	ij	ij	INTJ
iajs-856	69	6	according	accord	VERB
iajs-856	69	7	to	to	ADP
iajs-856	69	8	the	the	DET
iajs-856	69	9	greshgorin	greshgorin	NOUN
iajs-856	69	10	theorem	theorem	VERB
iajs-856	69	11	[	[	PUNCT
iajs-856	69	12	9	9	NUM
iajs-856	69	13	]	]	PUNCT
iajs-856	69	14	,	,	PUNCT
iajs-856	69	15	the	the	DET
iajs-856	69	16	eigenvalues	eigenvalue	NOUN
iajs-856	69	17	of	of	ADP
iajs-856	69	18	the	the	DET
iajs-856	69	19	matrix	matrix	NOUN
iajs-856	69	20	c	c	AUX
iajs-856	69	21	lie	lie	VERB
iajs-856	69	22	in	in	ADP
iajs-856	69	23	the	the	DET
iajs-856	69	24	union	union	NOUN
iajs-856	69	25	of	of	ADP
iajs-856	69	26	the	the	DET
iajs-856	69	27	circles	circle	NOUN
iajs-856	69	28	centered	center	VERB
iajs-856	69	29	at	at	ADP
iajs-856	69	30	iic	iic	PROPN
iajs-856	69	31	,	,	PUNCT
iajs-856	69	32	with	with	ADP
iajs-856	69	33	radius	radius	NOUN
iajs-856	69	34			X
iajs-856	69	35			VERB
iajs-856	69	36			NUM
iajs-856	69	37			NOUN
iajs-856	69	38	n	n	PROPN
iajs-856	69	39	il	il	PROPN
iajs-856	69	40	l	l	NOUN
iajs-856	69	41	lii	lii	NOUN
iajs-856	69	42	cr	cr	PROPN
iajs-856	69	43	0	0	NUM
iajs-856	69	44	,	,	PUNCT
iajs-856	69	45	.	.	PUNCT
iajs-856	70	1	here	here	ADV
iajs-856	70	2	we	we	PRON
iajs-856	70	3	have	have	VERB
iajs-856	70	4			NUM
iajs-856	70	5			NUM
iajs-856	70	6	kikiii	kikiii	NOUN
iajs-856	70	7	gc	gc	PROPN
iajs-856	70	8	,	,	PUNCT
iajs-856	70	9	1	1	NUM
iajs-856	70	10	,	,	PUNCT
iajs-856	70	11	,	,	PUNCT
iajs-856	70	12	,	,	PUNCT
iajs-856	70	13	11	11	NUM
iajs-856	70	14			NOUN
iajs-856	70	15	and	and	CCONJ
iajs-856	70	16			X
iajs-856	71	1			X
iajs-856	71	2			PROPN
iajs-856	71	3			PROPN
iajs-856	71	4			PUNCT
iajs-856	71	5			X
iajs-856	72	1			PROPN
iajs-856	72	2			PROPN
iajs-856	72	3			PROPN
iajs-856	72	4	n	n	CCONJ
iajs-856	72	5	il	il	PROPN
iajs-856	72	6	l	l	NOUN
iajs-856	73	1	i	i	PRON
iajs-856	73	2	il	il	PROPN
iajs-856	73	3	l	l	PROPN
iajs-856	73	4	kilikilii	kilikilii	NOUN
iajs-856	73	5	gcr	gcr	PROPN
iajs-856	73	6	0	0	NUM
iajs-856	73	7	1	1	NUM
iajs-856	73	8	0	0	NUM
iajs-856	73	9	,	,	PUNCT
iajs-856	73	10	1	1	NUM
iajs-856	73	11	,	,	PUNCT
iajs-856	73	12	,	,	PUNCT
iajs-856	73	13	,	,	PUNCT
iajs-856	73	14			NUM
iajs-856	73	15			NUM
iajs-856	73	16	and	and	CCONJ
iajs-856	73	17	therefore	therefore	ADV
iajs-856	73	18	1	1	NUM
iajs-856	73	19	,	,	PUNCT
iajs-856	73	20			PROPN
iajs-856	73	21	iii	iii	PROPN
iajs-856	73	22	rc	rc	PROPN
iajs-856	73	23	.	.	PUNCT
iajs-856	74	1	we	we	PRON
iajs-856	74	2	also	also	ADV
iajs-856	74	3	have	have	VERB
iajs-856	74	4			PROPN
iajs-856	74	5	kikikiiii	kikikiiii	PROPN
iajs-856	74	6	rc	rc	PROPN
iajs-856	74	7	,	,	PUNCT
iajs-856	74	8	,	,	PUNCT
iajs-856	74	9	,	,	PUNCT
iajs-856	74	10	,	,	PUNCT
iajs-856	74	11	211	211	NUM
iajs-856	74	12			NOUN
iajs-856	74	13			NOUN
iajs-856	74	14			NOUN
iajs-856	74	15			PROPN
iajs-856	74	16			PROPN
iajs-856	74	17			NOUN
iajs-856	74	18			PUNCT
iajs-856	74	19			PROPN
iajs-856	74	20	x	x	PROPN
iajs-856	74	21	t	t	PROPN
iajs-856	74	22	a	a	DET
iajs-856	74	23	ki,21	ki,21	NOUN
iajs-856	74	24			NUM
iajs-856	74	25			NUM
iajs-856	74	26			NOUN
iajs-856	74	27			VERB
iajs-856	74	28			PROPN
iajs-856	74	29			PROPN
iajs-856	74	30			NOUN
iajs-856	74	31			PUNCT
iajs-856	74	32			NOUN
iajs-856	74	33	x	x	SYM
iajs-856	74	34	t	t	PROPN
iajs-856	74	35	amax21	amax21	NOUN
iajs-856	74	36	therefore	therefore	ADV
iajs-856	74	37	,	,	PUNCT
iajs-856	74	38	for	for	ADP
iajs-856	74	39	the	the	DET
iajs-856	74	40	spectral	spectral	ADJ
iajs-856	74	41	radius	radius	NOUN
iajs-856	74	42	of	of	ADP
iajs-856	74	43	the	the	DET
iajs-856	74	44	matrix	matrix	NOUN
iajs-856	74	45	c	c	VERB
iajs-856	74	46	to	to	PART
iajs-856	74	47	be	be	AUX
iajs-856	74	48	at	at	ADP
iajs-856	74	49	most	most	ADV
iajs-856	74	50	one	one	NUM
iajs-856	74	51	,	,	PUNCT
iajs-856	74	52	it	it	PRON
iajs-856	74	53	suffices	suffice	VERB
iajs-856	74	54	to	to	PART
iajs-856	74	55	have	have	VERB
iajs-856	74	56	121	121	NUM
iajs-856	74	57	max	max	PROPN
iajs-856	74	58			PRON
iajs-856	74	59			PROPN
iajs-856	74	60			PRON
iajs-856	75	1			NOUN
iajs-856	75	2			VERB
iajs-856	75	3			PROPN
iajs-856	75	4			NOUN
iajs-856	75	5			PUNCT
iajs-856	75	6			NOUN
iajs-856	75	7			NUM
iajs-856	75	8	x	x	NOUN
iajs-856	75	9	t	t	PROPN
iajs-856	75	10	a	a	DET
iajs-856	75	11			NOUN
iajs-856	75	12			NOUN
iajs-856	75	13			NOUN
iajs-856	75	14			PROPN
iajs-856	75	15			PROPN
iajs-856	75	16			NOUN
iajs-856	75	17			X
iajs-856	76	1	1max	1max	NUM
iajs-856	76	2	x	x	NOUN
iajs-856	76	3	t	t	PROPN
iajs-856	76	4	a	a	DET
iajs-856	76	5			PROPN
iajs-856	76	6			ADP
iajs-856	76	7			PROPN
iajs-856	76	8			NOUN
iajs-856	76	9			X
iajs-856	77	1	1max	1max	NUM
iajs-856	77	2			NUM
iajs-856	77	3			NUM
iajs-856	77	4	x	x	X
iajs-856	77	5	t	t	PROPN
iajs-856	77	6	a	a	DET
iajs-856	77	7	max	max	PROPN
iajs-856	77	8	1	1	NUM
iajs-856	77	9	ax	ax	NOUN
iajs-856	77	10	t	t	X
iajs-856	77	11			PRON
iajs-856	77	12			NOUN
iajs-856	77	13			NOUN
iajs-856	77	14			NOUN
iajs-856	77	15	same	same	ADJ
iajs-856	77	16	method	method	NOUN
iajs-856	77	17	above	above	ADV
iajs-856	77	18	,	,	PUNCT
iajs-856	77	19	resulting	result	VERB
iajs-856	77	20	the	the	DET
iajs-856	77	21	system	system	NOUN
iajs-856	77	22	of	of	ADP
iajs-856	77	23	equation	equation	NOUN
iajs-856	77	24	defined	define	VERB
iajs-856	77	25	by	by	ADP
iajs-856	77	26	eq.(11	eq.(11	PROPN
iajs-856	77	27	)	)	PUNCT
iajs-856	77	28	is	be	AUX
iajs-856	77	29	then	then	ADV
iajs-856	77	30	defined	define	VERB
iajs-856	77	31	by	by	ADP
iajs-856	77	32	,	,	PUNCT
iajs-856	77	33			PROPN
iajs-856	77	34	k	k	PROPN
iajs-856	77	35	s	s	X
iajs-856	77	36	kk	kk	PROPN
iajs-856	77	37	uus	uus	PROPN
iajs-856	78	1	where	where	SCONJ
iajs-856	78	2	,	,	PUNCT
iajs-856	78	3	]	]	X
iajs-856	78	4	,	,	PUNCT
iajs-856	78	5	,	,	PUNCT
iajs-856	78	6	,	,	PUNCT
iajs-856	78	7	[	[	PUNCT
iajs-856	78	8	1,2,1	1,2,1	NUM
iajs-856	78	9	,	,	PUNCT
iajs-856	78	10	ts	ts	ADP
iajs-856	78	11	mk	mk	PROPN
iajs-856	78	12	s	s	PROPN
iajs-856	78	13	k	k	PROPN
iajs-856	78	14	s	s	X
iajs-856	78	15	k	k	PROPN
iajs-856	78	16	s	s	PROPN
iajs-856	78	17	k	k	PROPN
iajs-856	78	18	uuuu	uuuu	PROPN
iajs-856	78	19			PROPN
iajs-856	78	20			PRON
iajs-856	78	21	,	,	PUNCT
iajs-856	78	22	]	]	X
iajs-856	78	23	,	,	PUNCT
iajs-856	78	24	,	,	PUNCT
iajs-856	78	25	,	,	PUNCT
iajs-856	78	26	[	[	PUNCT
iajs-856	78	27	1,2,1	1,2,1	NUM
iajs-856	78	28	,	,	PUNCT
iajs-856	78	29	t	t	PROPN
iajs-856	78	30	mkkkk	mkkkk	PROPN
iajs-856	78	31	uuuu	uuuu	PROPN
iajs-856	78	32			PROPN
iajs-856	78	33			PROPN
iajs-856	78	34			NOUN
iajs-856	78	35			NUM
iajs-856	78	36			NUM
iajs-856	78	37	ibn	ibn	PROPN
iajs-856	78	38	alhaitham	alhaitham	NOUN
iajs-856	78	39	j.	j.	PROPN
iajs-856	79	1	fo	fo	ADP
iajs-856	79	2	r	r	NOUN
iajs-856	79	3	pure	pure	ADJ
iajs-856	79	4	&	&	CCONJ
iajs-856	79	5	appl	appl	PROPN
iajs-856	79	6	.	.	PUNCT
iajs-856	80	1	sc	sc	PROPN
iajs-856	80	2	i.	i.	PROPN
iajs-856	80	3	vo	vo	PROPN
iajs-856	80	4	l.24	l.24	PROPN
iajs-856	80	5	(	(	PUNCT
iajs-856	80	6	1	1	NUM
iajs-856	80	7	)	)	PUNCT
iajs-856	80	8	2011	2011	NUM
iajs-856	80	9	ks	ks	NOUN
iajs-856	80	10	is	be	AUX
iajs-856	80	11	the	the	DET
iajs-856	80	12	matrix	matrix	NOUN
iajs-856	80	13	of	of	ADP
iajs-856	80	14	coefficients	coefficient	NOUN
iajs-856	80	15	,	,	PUNCT
iajs-856	80	16	and	and	CCONJ
iajs-856	80	17	is	be	AUX
iajs-856	80	18	the	the	DET
iajs-856	80	19	sum	sum	NOUN
iajs-856	80	20	of	of	ADP
iajs-856	80	21	a	a	DET
iajs-856	80	22	lower	low	ADJ
iajs-856	80	23	triangular	triangular	NOUN
iajs-856	80	24	matrix	matrix	NOUN
iajs-856	80	25	and	and	CCONJ
iajs-856	80	26	a	a	DET
iajs-856	80	27	super	super	ADV
iajs-856	80	28	diagonal	diagonal	ADJ
iajs-856	80	29	matrix	matrix	NOUN
iajs-856	80	30	at	at	ADP
iajs-856	80	31	the	the	DET
iajs-856	80	32	grid	grid	NOUN
iajs-856	80	33	point	point	NOUN
iajs-856	80	34	xk	xk	PROPN
iajs-856	80	35	for	for	ADP
iajs-856	80	36	1,,1	1,,1	NUM
iajs-856	80	37			PROPN
iajs-856	80	38	nk	nk	PROPN
iajs-856	80	39			PROPN
iajs-856	80	40	.	.	PUNCT
iajs-856	81	1	therefore	therefore	ADV
iajs-856	81	2	the	the	DET
iajs-856	81	3	resulting	result	VERB
iajs-856	81	4	matrix	matrix	NOUN
iajs-856	81	5	entries	entry	NOUN
iajs-856	81	6	ks	ks	NOUN
iajs-856	81	7	for	for	ADP
iajs-856	81	8	1,,2,1	1,,2,1	PROPN
iajs-856	81	9			PROPN
iajs-856	81	10	mi	mi	PROPN
iajs-856	81	11			PROPN
iajs-856	81	12	and	and	CCONJ
iajs-856	81	13	1,,1	1,,1	NUM
iajs-856	81	14			NOUN
iajs-856	81	15	mj	mj	PROPN
iajs-856	81	16			NUM
iajs-856	81	17	by	by	ADP
iajs-856	81	18	are	be	AUX
iajs-856	81	19	defined	define	VERB
iajs-856	81	20	by	by	ADP
iajs-856	81	21			NUM
iajs-856	81	22			NUM
iajs-856	81	23			PROPN
iajs-856	81	24			NUM
iajs-856	81	25			NUM
iajs-856	81	26			NUM
iajs-856	81	27			ADP
iajs-856	81	28			PROPN
iajs-856	81	29			PROPN
iajs-856	81	30	1	1	NOUN
iajs-856	81	31	,	,	PUNCT
iajs-856	81	32	,	,	PUNCT
iajs-856	81	33	0	0	NUM
iajs-856	81	34	,	,	PUNCT
iajs-856	81	35	,	,	PUNCT
iajs-856	81	36	2	2	NUM
iajs-856	81	37	,	,	PUNCT
iajs-856	81	38	,	,	PUNCT
iajs-856	81	39	1	1	NUM
iajs-856	81	40	,	,	PUNCT
iajs-856	81	41	,	,	PUNCT
iajs-856	81	42	,	,	PUNCT
iajs-856	81	43	1	1	NUM
iajs-856	81	44	jik	jik	PROPN
iajs-856	81	45	ik	ik	PROPN
iajs-856	81	46	ik	ik	PROPN
iajs-856	81	47	ik	ik	PROPN
iajs-856	81	48	ji	ji	PROPN
iajs-856	82	1	g	g	PROPN
iajs-856	82	2	g	g	PROPN
iajs-856	82	3	g	g	PROPN
iajs-856	82	4	g	g	PROPN
iajs-856	82	5	s	s	PROPN
iajs-856	82	6			PROPN
iajs-856	82	7			PROPN
iajs-856	82	8			PROPN
iajs-856	82	9			PROPN
iajs-856	83	1			NOUN
iajs-856	83	2			NOUN
iajs-856	83	3			NOUN
iajs-856	83	4			NOUN
iajs-856	83	5	for	for	ADP
iajs-856	83	6	for	for	ADP
iajs-856	83	7	for	for	ADP
iajs-856	83	8	for	for	ADP
iajs-856	83	9	1	1	NUM
iajs-856	83	10	1	1	NUM
iajs-856	83	11	1	1	NUM
iajs-856	83	12			NOUN
iajs-856	83	13			ADJ
iajs-856	83	14			NOUN
iajs-856	83	15			PROPN
iajs-856	83	16	ij	ij	INTJ
iajs-856	84	1	ij	ij	INTJ
iajs-856	84	2	ij	ij	INTJ
iajs-856	84	3	ij	ij	INTJ
iajs-856	84	4	where	where	SCONJ
iajs-856	84	5	the	the	DET
iajs-856	84	6	coefficients	coefficient	NOUN
iajs-856	84	7			PROPN
iajs-856	84	8			NOUN
iajs-856	84	9	y	y	PROPN
iajs-856	84	10	t	t	PROPN
iajs-856	84	11	b	b	PROPN
iajs-856	84	12	jiki	jiki	PROPN
iajs-856	84	13			PUNCT
iajs-856	84	14			X
iajs-856	85	1			NUM
iajs-856	85	2	,	,	PUNCT
iajs-856	85	3	,	,	PUNCT
iajs-856	85	4	so	so	ADV
iajs-856	85	5	,	,	PUNCT
iajs-856	85	6	and	and	CCONJ
iajs-856	85	7	in	in	ADP
iajs-856	85	8	the	the	DET
iajs-856	85	9	same	same	ADJ
iajs-856	85	10	way	way	NOUN
iajs-856	85	11	,	,	PUNCT
iajs-856	85	12	according	accord	VERB
iajs-856	85	13	to	to	ADP
iajs-856	85	14	the	the	DET
iajs-856	85	15	greshgorin	greshgorin	NOUN
iajs-856	85	16	theorem	theorem	VERB
iajs-856	85	17	[	[	PUNCT
iajs-856	85	18	9	9	NUM
iajs-856	85	19	]	]	PUNCT
iajs-856	85	20	,	,	PUNCT
iajs-856	85	21	to	to	PART
iajs-856	85	22	get	get	VERB
iajs-856	85	23	max	max	PROPN
iajs-856	85	24	1	1	NUM
iajs-856	85	25	by	by	ADP
iajs-856	85	26	t	t	NOUN
iajs-856	85	27			ADJ
iajs-856	85	28			PROPN
iajs-856	85	29			NOUN
iajs-856	85	30			NOUN
iajs-856	85	31	consistency	consistency	NOUN
iajs-856	85	32	and	and	CCONJ
iajs-856	85	33	convergent	convergent	ADJ
iajs-856	85	34	analysis	analysis	NOUN
iajs-856	85	35	of	of	ADP
iajs-856	85	36	the	the	DET
iajs-856	85	37	explicit	explicit	ADJ
iajs-856	85	38	finite	finite	ADJ
iajs-856	85	39	difference	difference	NOUN
iajs-856	85	40	approximation	approximation	NOUN
iajs-856	85	41	we	we	PRON
iajs-856	85	42	note	note	VERB
iajs-856	85	43	that	that	SCONJ
iajs-856	85	44	the	the	DET
iajs-856	85	45	three	three	NUM
iajs-856	85	46	difference	difference	NOUN
iajs-856	85	47	operators	operator	NOUN
iajs-856	85	48	used	use	VERB
iajs-856	85	49	in	in	ADP
iajs-856	85	50	eq.(6	eq.(6	ADJ
iajs-856	85	51	)	)	PUNCT
iajs-856	85	52	each	each	PRON
iajs-856	85	53	have	have	VERB
iajs-856	85	54	a	a	DET
iajs-856	85	55	local	local	ADJ
iajs-856	85	56	truncation	truncation	NOUN
iajs-856	85	57	error	error	NOUN
iajs-856	85	58	with	with	ADP
iajs-856	85	59	)	)	PUNCT
iajs-856	85	60	,	,	PUNCT
iajs-856	85	61	(	(	PUNCT
iajs-856	85	62	to	to	PART
iajs-856	85	63			NOUN
iajs-856	85	64	)	)	PUNCT
iajs-856	85	65	,	,	PUNCT
iajs-856	85	66	(	(	PUNCT
iajs-856	85	67	xo	xo	PROPN
iajs-856	85	68			NOUN
iajs-856	85	69	and	and	CCONJ
iajs-856	85	70	)	)	PUNCT
iajs-856	85	71	(	(	PUNCT
iajs-856	85	72	yo	yo	INTJ
iajs-856	85	73			X
iajs-856	85	74	respectively	respectively	ADV
iajs-856	85	75	.	.	PUNCT
iajs-856	86	1	the	the	PRON
iajs-856	86	2	)	)	PUNCT
iajs-856	86	3	(	(	PUNCT
iajs-856	86	4	to	to	PART
iajs-856	86	5			PART
iajs-856	86	6	,	,	PUNCT
iajs-856	86	7	for	for	ADP
iajs-856	86	8	the	the	DET
iajs-856	86	9	time	time	NOUN
iajs-856	86	10	derivative	derivative	ADJ
iajs-856	86	11	term	term	NOUN
iajs-856	86	12	,	,	PUNCT
iajs-856	86	13	is	be	AUX
iajs-856	86	14	obtained	obtain	VERB
iajs-856	86	15	from	from	ADP
iajs-856	86	16	the	the	DET
iajs-856	86	17	classical	classical	ADJ
iajs-856	86	18	taylor	taylor	PROPN
iajs-856	86	19	's	's	PART
iajs-856	86	20	expansion	expansion	NOUN
iajs-856	86	21	.	.	PUNCT
iajs-856	87	1	the	the	PRON
iajs-856	87	2	)	)	PUNCT
iajs-856	87	3	(	(	PUNCT
iajs-856	87	4	xo	xo	PROPN
iajs-856	87	5			NOUN
iajs-856	87	6	and	and	CCONJ
iajs-856	87	7	)	)	PUNCT
iajs-856	87	8	(	(	PUNCT
iajs-856	87	9	yo	yo	INTJ
iajs-856	87	10			X
iajs-856	87	11	for	for	ADP
iajs-856	87	12	the	the	DET
iajs-856	87	13	local	local	ADJ
iajs-856	87	14	truncation	truncation	NOUN
iajs-856	87	15	error	error	NOUN
iajs-856	87	16	of	of	ADP
iajs-856	87	17	the	the	DET
iajs-856	87	18	fractional	fractional	ADJ
iajs-856	87	19	derivative	derivative	ADJ
iajs-856	87	20	terms	term	NOUN
iajs-856	87	21	was	be	AUX
iajs-856	87	22	proved	prove	VERB
iajs-856	87	23	in	in	ADP
iajs-856	87	24	[	[	X
iajs-856	87	25	10	10	NUM
iajs-856	87	26	]	]	PUNCT
iajs-856	87	27	.	.	PUNCT
iajs-856	88	1	therefore	therefore	ADV
iajs-856	88	2	,	,	PUNCT
iajs-856	88	3	the	the	DET
iajs-856	88	4	explicit	explicit	ADJ
iajs-856	88	5	finite	finite	ADJ
iajs-856	88	6	difference	difference	NOUN
iajs-856	88	7	approximation	approximation	NOUN
iajs-856	88	8	is	be	AUX
iajs-856	88	9	consistency	consistency	NOUN
iajs-856	88	10	.	.	PUNCT
iajs-856	89	1	theorem	theorem	VERB
iajs-856	89	2	above	above	ADV
iajs-856	89	3	shows	show	VERB
iajs-856	89	4	that	that	SCONJ
iajs-856	89	5	s	s	VERB
iajs-856	89	6	jiyx	jiyx	NOUN
iajs-856	89	7	u	u	NOUN
iajs-856	89	8	,	,	PUNCT
iajs-856	89	9	,	,	PUNCT
iajs-856	89	10	,	,	PUNCT
iajs-856	89	11	)	)	PUNCT
iajs-856	89	12	(	(	PUNCT
iajs-856	89	13			NOUN
iajs-856	89	14			ADP
iajs-856	89	15	converges	converge	NOUN
iajs-856	89	16	to	to	ADP
iajs-856	89	17	the	the	DET
iajs-856	89	18	mixed	mixed	ADJ
iajs-856	89	19	fractional	fractional	ADJ
iajs-856	89	20	derivative	derivative	NOUN
iajs-856	89	21	linearly	linearly	ADV
iajs-856	89	22	,	,	PUNCT
iajs-856	89	23	as	as	ADP
iajs-856	89	24	)	)	PUNCT
iajs-856	89	25	(	(	PUNCT
iajs-856	89	26	)	)	PUNCT
iajs-856	89	27	(	(	PUNCT
iajs-856	89	28	yoxo	yoxo	PROPN
iajs-856	89	29			NOUN
iajs-856	89	30	.	.	PUNCT
iajs-856	90	1	therefore	therefore	ADV
iajs-856	90	2	,	,	PUNCT
iajs-856	90	3	the	the	DET
iajs-856	90	4	local	local	ADJ
iajs-856	90	5	truncation	truncation	NOUN
iajs-856	90	6	error	error	NOUN
iajs-856	90	7	of	of	ADP
iajs-856	90	8	the	the	DET
iajs-856	90	9	explicit	explicit	ADJ
iajs-856	90	10	euler	euler	NOUN
iajs-856	90	11	method	method	NOUN
iajs-856	90	12	eq.(8	eq.(8	X
iajs-856	90	13	)	)	PUNCT
iajs-856	90	14	is	be	AUX
iajs-856	90	15	)	)	PUNCT
iajs-856	90	16	(	(	PUNCT
iajs-856	90	17	)	)	PUNCT
iajs-856	90	18	(	(	PUNCT
iajs-856	90	19	)	)	PUNCT
iajs-856	90	20	(	(	PUNCT
iajs-856	90	21	yoxoto	yoxoto	NOUN
iajs-856	90	22			PROPN
iajs-856	90	23	.	.	PUNCT
iajs-856	91	1	this	this	DET
iajs-856	91	2	consistency	consistency	NOUN
iajs-856	91	3	of	of	ADP
iajs-856	91	4	the	the	DET
iajs-856	91	5	explicit	explicit	ADJ
iajs-856	91	6	finite	finite	ADJ
iajs-856	91	7	difference	difference	NOUN
iajs-856	91	8	approximation	approximation	NOUN
iajs-856	91	9	together	together	ADV
iajs-856	91	10	with	with	ADP
iajs-856	91	11	the	the	DET
iajs-856	91	12	above	above	ADJ
iajs-856	91	13	result	result	NOUN
iajs-856	91	14	on	on	ADP
iajs-856	91	15	conditional	conditional	ADJ
iajs-856	91	16	stability	stability	NOUN
iajs-856	91	17	implies	imply	VERB
iajs-856	91	18	that	that	SCONJ
iajs-856	91	19	the	the	DET
iajs-856	91	20	explicit	explicit	ADJ
iajs-856	91	21	finite	finite	ADJ
iajs-856	91	22	difference	difference	NOUN
iajs-856	91	23	approximation	approximation	NOUN
iajs-856	91	24	is	be	AUX
iajs-856	91	25	convergent	convergent	ADJ
iajs-856	91	26	and	and	CCONJ
iajs-856	91	27	this	this	DET
iajs-856	91	28	convergence	convergence	NOUN
iajs-856	91	29	is	be	AUX
iajs-856	91	30	)	)	PUNCT
iajs-856	91	31	(	(	PUNCT
iajs-856	91	32	tyxo	tyxo	PROPN
iajs-856	91	33			PROPN
iajs-856	91	34	.	.	PUNCT
iajs-856	92	1	numerical	numerical	ADJ
iajs-856	92	2	example	example	NOUN
iajs-856	92	3	in	in	ADP
iajs-856	92	4	this	this	DET
iajs-856	92	5	section	section	NOUN
iajs-856	92	6	,	,	PUNCT
iajs-856	92	7	numerical	numerical	ADJ
iajs-856	92	8	example	example	NOUN
iajs-856	92	9	is	be	AUX
iajs-856	92	10	presented	present	VERB
iajs-856	92	11	which	which	PRON
iajs-856	92	12	confirm	confirm	VERB
iajs-856	92	13	our	our	PRON
iajs-856	92	14	theoretical	theoretical	ADJ
iajs-856	92	15	results	result	NOUN
iajs-856	92	16	.	.	PUNCT
iajs-856	93	1	example	example	NOUN
iajs-856	93	2	:	:	PUNCT
iajs-856	93	3	consider	consider	VERB
iajs-856	93	4	the	the	DET
iajs-856	93	5	two	two	NUM
iajs-856	93	6	-	-	PUNCT
iajs-856	93	7	dimensional	dimensional	ADJ
iajs-856	93	8	fractional	fractional	ADJ
iajs-856	93	9	dispersion	dispersion	NOUN
iajs-856	93	10	equation	equation	NOUN
iajs-856	93	11	:	:	PUNCT
iajs-856	93	12	tt	tt	PROPN
iajs-856	93	13	exyeyx	exyeyx	PROPN
iajs-856	93	14	y	y	PROPN
iajs-856	93	15	tyxuy	tyxuy	NOUN
iajs-856	93	16	x	x	X
iajs-856	93	17	tyxu	tyxu	VERB
iajs-856	93	18	x	x	SYM
iajs-856	93	19	t	t	PROPN
iajs-856	93	20	tyxu	tyxu	VERB
iajs-856	93	21	22225.0	22225.0	NUM
iajs-856	93	22	6.1	6.1	NUM
iajs-856	93	23	6.16.1	6.16.1	NUM
iajs-856	93	24	5.1	5.1	NUM
iajs-856	93	25	5.1	5.1	NUM
iajs-856	93	26	)	)	PUNCT
iajs-856	93	27	,	,	PUNCT
iajs-856	93	28	,	,	PUNCT
iajs-856	93	29	(	(	PUNCT
iajs-856	93	30	2	2	NUM
iajs-856	93	31	)	)	PUNCT
iajs-856	93	32	4.1	4.1	NUM
iajs-856	93	33	(	(	PUNCT
iajs-856	93	34	)	)	PUNCT
iajs-856	93	35	,	,	PUNCT
iajs-856	93	36	,	,	PUNCT
iajs-856	93	37	(	(	PUNCT
iajs-856	93	38	)	)	PUNCT
iajs-856	93	39	5.0	5.0	NUM
iajs-856	93	40	(	(	PUNCT
iajs-856	93	41	)	)	PUNCT
iajs-856	93	42	,	,	PUNCT
iajs-856	93	43	,	,	PUNCT
iajs-856	93	44	(	(	PUNCT
iajs-856	93	45			PROPN
iajs-856	93	46			PROPN
iajs-856	93	47			VERB
iajs-856	93	48			ADJ
iajs-856	94	1			PROPN
iajs-856	94	2			PROPN
iajs-856	94	3			PROPN
iajs-856	94	4			ADJ
iajs-856	94	5			ADJ
iajs-856	94	6	subject	subject	NOUN
iajs-856	94	7	to	to	ADP
iajs-856	94	8	the	the	DET
iajs-856	94	9	initial	initial	ADJ
iajs-856	94	10	condition	condition	NOUN
iajs-856	94	11	u	u	NOUN
iajs-856	94	12	(	(	PUNCT
iajs-856	94	13	x	x	X
iajs-856	94	14	,	,	PUNCT
iajs-856	94	15	y,0	y,0	NUM
iajs-856	94	16	)	)	PUNCT
iajs-856	95	1	=	=	SYM
iajs-856	95	2	xy2	xy2	PROPN
iajs-856	95	3	,	,	PUNCT
iajs-856	95	4	0	0	NUM
iajs-856	95	5			PROPN
iajs-856	95	6	x	x	SYM
iajs-856	95	7			PROPN
iajs-856	95	8	0.5	0.5	NUM
iajs-856	95	9	,	,	PUNCT
iajs-856	95	10	0	0	PUNCT
iajs-856	95	11	<	<	X
iajs-856	95	12	y	y	X
iajs-856	95	13	<	<	X
iajs-856	95	14	0.5	0.5	NUM
iajs-856	95	15	and	and	CCONJ
iajs-856	95	16	the	the	DET
iajs-856	95	17	boundary	boundary	ADJ
iajs-856	95	18	conditions	condition	NOUN
iajs-856	95	19	u	u	SYM
iajs-856	95	20	(	(	PUNCT
iajs-856	95	21	0,y	0,y	PROPN
iajs-856	95	22	,	,	PUNCT
iajs-856	95	23	t	t	PROPN
iajs-856	95	24	)	)	PUNCT
iajs-856	95	25	=	=	SYM
iajs-856	95	26	0	0	NUM
iajs-856	95	27	,	,	PUNCT
iajs-856	95	28	0	0	PUNCT
iajs-856	95	29	<	<	X
iajs-856	95	30	y	y	X
iajs-856	95	31	<	<	X
iajs-856	95	32	0.5	0.5	NUM
iajs-856	95	33	,	,	PUNCT
iajs-856	95	34	0	0	NUM
iajs-856	95	35			NOUN
iajs-856	95	36	t	t	NOUN
iajs-856	95	37	0.025	0.025	NUM
iajs-856	95	38	ibn	ibn	PROPN
iajs-856	95	39	alhaitham	alhaitham	NOUN
iajs-856	95	40	j.	j.	PROPN
iajs-856	95	41	for	for	ADP
iajs-856	95	42	pure	pure	ADJ
iajs-856	95	43	&	&	CCONJ
iajs-856	95	44	appl	appl	PROPN
iajs-856	95	45	.	.	PUNCT
iajs-856	96	1	sci	sci	PROPN
iajs-856	96	2	.	.	PROPN
iajs-856	97	1	vo	vo	INTJ
iajs-856	98	1	l.24	l.24	PROPN
iajs-856	98	2	(	(	PUNCT
iajs-856	98	3	1	1	NUM
iajs-856	98	4	)	)	PUNCT
iajs-856	98	5	2011	2011	NUM
iajs-856	98	6	u	u	NOUN
iajs-856	98	7	(	(	PUNCT
iajs-856	98	8	x,0,t	x,0,t	PROPN
iajs-856	98	9	)	)	PUNCT
iajs-856	98	10	=	=	SYM
iajs-856	98	11	0	0	NUM
iajs-856	98	12	,	,	PUNCT
iajs-856	98	13	0	0	PUNCT
iajs-856	98	14	<	<	X
iajs-856	98	15	x	x	X
iajs-856	98	16	<	<	X
iajs-856	98	17	0.5	0.5	NUM
iajs-856	98	18	,	,	PUNCT
iajs-856	98	19	0	0	NUM
iajs-856	98	20			NOUN
iajs-856	98	21	t	t	NOUN
iajs-856	98	22	0.025	0.025	NUM
iajs-856	98	23	u	u	NOUN
iajs-856	98	24	(	(	PUNCT
iajs-856	98	25	,	,	PUNCT
iajs-856	98	26	0.5,y	0.5,y	NUM
iajs-856	98	27	,	,	PUNCT
iajs-856	98	28	t	t	PROPN
iajs-856	98	29	)	)	PUNCT
iajs-856	98	30	=	=	SYM
iajs-856	98	31	0.5	0.5	NUM
iajs-856	98	32	e	e	NOUN
iajs-856	98	33	2	2	NUM
iajs-856	98	34	t	t	NOUN
iajs-856	98	35	,	,	PUNCT
iajs-856	98	36	0	0	PUNCT
iajs-856	98	37	<	<	X
iajs-856	98	38	y	y	X
iajs-856	98	39	<	<	X
iajs-856	98	40	0.5	0.5	NUM
iajs-856	98	41	,	,	PUNCT
iajs-856	98	42	0	0	NUM
iajs-856	98	43			NOUN
iajs-856	98	44	t	t	NOUN
iajs-856	98	45	0.025	0.025	NUM
iajs-856	98	46	u	u	NOUN
iajs-856	98	47	(	(	PUNCT
iajs-856	98	48	x	x	X
iajs-856	98	49	,	,	PUNCT
iajs-856	98	50	,	,	PUNCT
iajs-856	98	51	0.5,t	0.5,t	NUM
iajs-856	98	52	)	)	PUNCT
iajs-856	98	53	=	=	SYM
iajs-856	99	1	0.25e2tx	0.25e2tx	NUM
iajs-856	99	2	,	,	PUNCT
iajs-856	99	3	0	0	PUNCT
iajs-856	99	4	<	<	X
iajs-856	99	5	x	x	X
iajs-856	99	6	<	<	X
iajs-856	99	7	0.5	0.5	NUM
iajs-856	99	8	,	,	PUNCT
iajs-856	99	9	0	0	NUM
iajs-856	99	10			NOUN
iajs-856	99	11	t	t	NOUN
iajs-856	99	12	0.025	0.025	NUM
iajs-856	99	13	this	this	DET
iajs-856	99	14	fractional	fractional	ADJ
iajs-856	99	15	dispersion	dispersion	NOUN
iajs-856	99	16	equation	equation	NOUN
iajs-856	99	17	together	together	ADV
iajs-856	99	18	with	with	ADP
iajs-856	99	19	the	the	DET
iajs-856	99	20	above	above	ADJ
iajs-856	99	21	initial	initial	ADJ
iajs-856	99	22	and	and	CCONJ
iajs-856	99	23	boundary	boundary	ADJ
iajs-856	99	24	condition	condition	NOUN
iajs-856	99	25	is	be	AUX
iajs-856	99	26	constructed	construct	VERB
iajs-856	99	27	such	such	ADJ
iajs-856	99	28	that	that	SCONJ
iajs-856	99	29	the	the	DET
iajs-856	99	30	exact	exact	ADJ
iajs-856	99	31	solution	solution	NOUN
iajs-856	99	32	is	be	AUX
iajs-856	99	33	u(x	u(x	NOUN
iajs-856	99	34	,	,	PUNCT
iajs-856	99	35	y	y	PROPN
iajs-856	99	36	,	,	PUNCT
iajs-856	99	37	t	t	PROPN
iajs-856	99	38	)	)	PUNCT
iajs-856	99	39	=	=	SYM
iajs-856	99	40	e2txy2	e2txy2	PROPN
iajs-856	99	41	.	.	PROPN
iajs-856	99	42	table	table	NOUN
iajs-856	99	43	(	(	PUNCT
iajs-856	99	44	1	1	NUM
iajs-856	99	45	)	)	PUNCT
iajs-856	99	46	and	and	CCONJ
iajs-856	99	47	(	(	PUNCT
iajs-856	99	48	2	2	X
iajs-856	99	49	)	)	PUNCT
iajs-856	99	50	show	show	VERB
iajs-856	99	51	the	the	DET
iajs-856	99	52	numerical	numerical	ADJ
iajs-856	99	53	solution	solution	NOUN
iajs-856	99	54	using	use	VERB
iajs-856	99	55	the	the	DET
iajs-856	99	56	explicit	explicit	ADJ
iajs-856	99	57	finite	finite	ADJ
iajs-856	99	58	difference	difference	NOUN
iajs-856	99	59	approximation	approximation	NOUN
iajs-856	99	60	.	.	PUNCT
iajs-856	100	1	from	from	ADP
iajs-856	100	2	table	table	NOUN
iajs-856	100	3	(	(	PUNCT
iajs-856	100	4	1	1	NUM
iajs-856	100	5	)	)	PUNCT
iajs-856	100	6	and	and	CCONJ
iajs-856	100	7	(	(	PUNCT
iajs-856	100	8	2	2	NUM
iajs-856	100	9	)	)	PUNCT
iajs-856	100	10	,	,	PUNCT
iajs-856	100	11	it	it	PRON
iajs-856	100	12	can	can	AUX
iajs-856	100	13	be	be	AUX
iajs-856	100	14	seen	see	VERB
iajs-856	100	15	that	that	SCONJ
iajs-856	100	16	thereisa	thereisa	VERB
iajs-856	100	17	good	good	ADJ
iajs-856	100	18	agreement	agreement	NOUN
iajs-856	100	19	between	between	ADP
iajs-856	100	20	the	the	DET
iajs-856	100	21	numerical	numerical	ADJ
iajs-856	100	22	solution	solution	NOUN
iajs-856	100	23	and	and	CCONJ
iajs-856	100	24	exact	exact	ADJ
iajs-856	100	25	solution	solution	NOUN
iajs-856	100	26	.	.	PUNCT
iajs-856	101	1	6	6	X
iajs-856	101	2	.	.	X
iajs-856	101	3	conclusions	conclusion	NOUN
iajs-856	101	4	in	in	ADP
iajs-856	101	5	this	this	DET
iajs-856	101	6	paper	paper	NOUN
iajs-856	101	7	,	,	PUNCT
iajs-856	101	8	a	a	DET
iajs-856	101	9	numerical	numerical	ADJ
iajs-856	101	10	method	method	NOUN
iajs-856	101	11	for	for	ADP
iajs-856	101	12	solving	solve	VERB
iajs-856	101	13	the	the	DET
iajs-856	101	14	two	two	NUM
iajs-856	101	15	-	-	PUNCT
iajs-856	101	16	dimensional	dimensional	ADJ
iajs-856	101	17	fractional	fractional	ADJ
iajs-856	101	18	dispersion	dispersion	NOUN
iajs-856	101	19	equation	equation	NOUN
iajs-856	101	20	has	have	AUX
iajs-856	101	21	been	be	AUX
iajs-856	101	22	described	describe	VERB
iajs-856	101	23	and	and	CCONJ
iajs-856	101	24	demonstrated	demonstrate	VERB
iajs-856	101	25	.	.	PUNCT
iajs-856	102	1	the	the	DET
iajs-856	102	2	explicit	explicit	ADJ
iajs-856	102	3	difference	difference	NOUN
iajs-856	102	4	approximation	approximation	NOUN
iajs-856	102	5	is	be	AUX
iajs-856	102	6	proved	prove	VERB
iajs-856	102	7	to	to	PART
iajs-856	102	8	be	be	AUX
iajs-856	102	9	conditionally	conditionally	ADV
iajs-856	102	10	stable	stable	ADJ
iajs-856	102	11	and	and	CCONJ
iajs-856	102	12	converges	converge	NOUN
iajs-856	102	13	.	.	PUNCT
iajs-856	103	1	furthermore	furthermore	ADV
iajs-856	103	2	numerical	numerical	ADJ
iajs-856	103	3	example	example	NOUN
iajs-856	103	4	is	be	AUX
iajs-856	103	5	presented	present	VERB
iajs-856	103	6	to	to	PART
iajs-856	103	7	show	show	VERB
iajs-856	103	8	that	that	DET
iajs-856	103	9	good	good	ADJ
iajs-856	103	10	agreement	agreement	NOUN
iajs-856	103	11	between	between	ADP
iajs-856	103	12	the	the	DET
iajs-856	103	13	numerical	numerical	ADJ
iajs-856	103	14	solution	solution	NOUN
iajs-856	103	15	and	and	CCONJ
iajs-856	103	16	exact	exact	ADJ
iajs-856	103	17	solution	solution	NOUN
iajs-856	103	18	has	have	AUX
iajs-856	103	19	been	be	AUX
iajs-856	103	20	noted	note	VERB
iajs-856	103	21	.	.	PUNCT
iajs-856	104	1	references	reference	NOUN
iajs-856	104	2	1	1	NUM
iajs-856	104	3	.	.	PUNCT
iajs-856	105	1	huang	huang	PROPN
iajs-856	105	2	,	,	PUNCT
iajs-856	105	3	f.	f.	PROPN
iajs-856	105	4	and	and	CCONJ
iajs-856	105	5	liu	liu	PROPN
iajs-856	105	6	,	,	PUNCT
iajs-856	105	7	f.	f.	PROPN
iajs-856	105	8	(	(	PUNCT
iajs-856	105	9	2005	2005	NUM
iajs-856	105	10	)	)	PUNCT
iajs-856	105	11	,	,	PUNCT
iajs-856	105	12	anziam	anziam	PROPN
iajs-856	105	13	journal	journal	PROPN
iajs-856	105	14	,	,	PUNCT
iajs-856	105	15	46	46	NUM
iajs-856	105	16	:	:	SYM
iajs-856	105	17	1	1	NUM
iajs-856	105	18	-	-	SYM
iajs-856	105	19	14	14	NUM
iajs-856	105	20	.	.	PUNCT
iajs-856	106	1	2	2	NUM
iajs-856	106	2	.	.	X
iajs-856	106	3	shen	shen	PROPN
iajs-856	106	4	,	,	PUNCT
iajs-856	106	5	s.	s.	PROPN
iajs-856	106	6	and	and	CCONJ
iajs-856	106	7	lin	lin	PROPN
iajs-856	106	8	,	,	PUNCT
iajs-856	106	9	f.	f.	PROPN
iajs-856	106	10	(	(	PUNCT
iajs-856	106	11	2005),anziam	2005),anziam	NUM
iajs-856	106	12	j.	j.	PROPN
iajs-856	106	13	,	,	PUNCT
iajs-856	106	14	46(e	46(e	PROPN
iajs-856	106	15	):	):	PUNCT
iajs-856	106	16	871	871	NUM
iajs-856	106	17	-	-	SYM
iajs-856	106	18	887	887	NUM
iajs-856	106	19	.	.	PUNCT
iajs-856	107	1	3	3	X
iajs-856	107	2	.	.	X
iajs-856	107	3	meerschaert	meerschaert	PROPN
iajs-856	107	4	,	,	PUNCT
iajs-856	107	5	m.m	m.m	PROPN
iajs-856	107	6	.	.	PROPN
iajs-856	107	7	;	;	PUNCT
iajs-856	107	8	scheffler	scheffler	PROPN
iajs-856	107	9	,	,	PUNCT
iajs-856	107	10	h.p	h.p	PROPN
iajs-856	107	11	.	.	PROPN
iajs-856	107	12	and	and	CCONJ
iajs-856	107	13	tadjeran	tadjeran	NOUN
iajs-856	107	14	,	,	PUNCT
iajs-856	107	15	c.	c.	PROPN
iajs-856	107	16	(	(	PUNCT
iajs-856	107	17	2006	2006	NUM
iajs-856	107	18	)	)	PUNCT
iajs-856	107	19	,	,	PUNCT
iajs-856	107	20	j.	j.	PROPN
iajs-856	107	21	comput	comput	PROPN
iajs-856	107	22	.	.	PUNCT
iajs-856	108	1	phys	phy	NOUN
iajs-856	108	2	.	.	PUNCT
iajs-856	108	3	,	,	PUNCT
iajs-856	108	4	211:249–261	211:249–261	NUM
iajs-856	108	5	.	.	PUNCT
iajs-856	109	1	4	4	NUM
iajs-856	109	2	.	.	X
iajs-856	110	1	metzler	metzler	PROPN
iajs-856	110	2	,	,	PUNCT
iajs-856	110	3	r.	r.	PROPN
iajs-856	110	4	and	and	CCONJ
iajs-856	110	5	klafter	klafter	PROPN
iajs-856	110	6	,	,	PUNCT
iajs-856	110	7	j.	j.	PROPN
iajs-856	110	8	(	(	PUNCT
iajs-856	110	9	2004	2004	NUM
iajs-856	110	10	)	)	PUNCT
iajs-856	110	11	,	,	PUNCT
iajs-856	110	12	j.	j.	PROPN
iajs-856	110	13	physics	physics	PROPN
iajs-856	110	14	,	,	PUNCT
iajs-856	110	15	a	a	DET
iajs-856	110	16	37	37	NUM
iajs-856	110	17	:	:	PUNCT
iajs-856	110	18	r161	r161	PROPN
iajs-856	110	19	-	-	SYM
iajs-856	110	20	r208	r208	PROPN
iajs-856	110	21	.	.	PROPN
iajs-856	111	1	5	5	NUM
iajs-856	111	2	.	.	NUM
iajs-856	111	3	sabatelli	sabatelli	PROPN
iajs-856	111	4	,	,	PUNCT
iajs-856	111	5	l.	l.	PROPN
iajs-856	111	6	;	;	PUNCT
iajs-856	111	7	keating	keating	PROPN
iajs-856	111	8	,	,	PUNCT
iajs-856	111	9	s.	s.	PROPN
iajs-856	111	10	;	;	PUNCT
iajs-856	111	11	dudley	dudley	PROPN
iajs-856	111	12	,	,	PUNCT
iajs-856	111	13	j.	j.	PROPN
iajs-856	111	14	and	and	CCONJ
iajs-856	111	15	richmond	richmond	PROPN
iajs-856	111	16	,	,	PUNCT
iajs-856	111	17	p.	p.	NOUN
iajs-856	111	18	(	(	PUNCT
iajs-856	111	19	2002	2002	NUM
iajs-856	111	20	)	)	PUNCT
iajs-856	111	21	,	,	PUNCT
iajs-856	111	22	eur	eur	PROPN
iajs-856	111	23	.	.	PUNCT
iajs-856	112	1	phys	phy	NOUN
iajs-856	112	2	.	.	PUNCT
iajs-856	113	1	j.	j.	PROPN
iajs-856	113	2	,	,	PUNCT
iajs-856	113	3	b	b	PROPN
iajs-856	113	4	27	27	NUM
iajs-856	113	5	:	:	PUNCT
iajs-856	113	6	273–275	273–275	NUM
iajs-856	113	7	.	.	NOUN
iajs-856	113	8	6	6	NUM
iajs-856	113	9	.	.	X
iajs-856	113	10	scalas	scalas	PROPN
iajs-856	113	11	,	,	PUNCT
iajs-856	113	12	e.	e.	PROPN
iajs-856	113	13	;	;	PUNCT
iajs-856	113	14	gorenflo	gorenflo	PROPN
iajs-856	113	15	,	,	PUNCT
iajs-856	113	16	r.	r.	PROPN
iajs-856	113	17	and	and	CCONJ
iajs-856	113	18	mainardi	mainardi	PROPN
iajs-856	113	19	,	,	PUNCT
iajs-856	113	20	f.	f.	PROPN
iajs-856	113	21	(	(	PUNCT
iajs-856	113	22	2000	2000	NUM
iajs-856	113	23	)	)	PUNCT
iajs-856	113	24	,	,	PUNCT
iajs-856	113	25	phys	phy	NOUN
iajs-856	113	26	.	.	PUNCT
iajs-856	113	27	,	,	PUNCT
iajs-856	113	28	a	a	DET
iajs-856	113	29	284	284	NUM
iajs-856	113	30	:	:	PUNCT
iajs-856	113	31	376–384	376–384	NUM
iajs-856	113	32	.	.	NOUN
iajs-856	113	33	7	7	X
iajs-856	113	34	.	.	X
iajs-856	114	1	benson	benson	PROPN
iajs-856	114	2	,	,	PUNCT
iajs-856	114	3	d.	d.	PROPN
iajs-856	114	4	;	;	PUNCT
iajs-856	114	5	wheatcraft	wheatcraft	NOUN
iajs-856	114	6	,	,	PUNCT
iajs-856	114	7	s.	s.	PROPN
iajs-856	114	8	and	and	CCONJ
iajs-856	114	9	meerschaert	meerschaert	NOUN
iajs-856	114	10	,	,	PUNCT
iajs-856	114	11	m.	m.	NOUN
iajs-856	114	12	(	(	PUNCT
iajs-856	114	13	2000	2000	NUM
iajs-856	114	14	)	)	PUNCT
iajs-856	114	15	,	,	PUNCT
iajs-856	114	16	water	water	NOUN
iajs-856	114	17	resour	resour	NOUN
iajs-856	114	18	.	.	PUNCT
iajs-856	115	1	res	re	NOUN
iajs-856	115	2	.	.	PROPN
iajs-856	115	3	,	,	PUNCT
iajs-856	116	1	36:1403–1412	36:1403–1412	NUM
iajs-856	116	2	.	.	NOUN
iajs-856	116	3	8	8	NUM
iajs-856	116	4	.	.	X
iajs-856	117	1	schumer	schumer	PROPN
iajs-856	117	2	,	,	PUNCT
iajs-856	117	3	r.	r.	PROPN
iajs-856	117	4	;	;	PUNCT
iajs-856	117	5	benson	benson	PROPN
iajs-856	117	6	,	,	PUNCT
iajs-856	117	7	d.a	d.a	PROPN
iajs-856	117	8	.	.	PROPN
iajs-856	117	9	;	;	PUNCT
iajs-856	117	10	meerschaert	meerschaert	PROPN
iajs-856	117	11	,	,	PUNCT
iajs-856	117	12	m.m	m.m	PROPN
iajs-856	117	13	.	.	PROPN
iajs-856	117	14	and	and	CCONJ
iajs-856	117	15	baeumer	baeumer	PROPN
iajs-856	117	16	,	,	PUNCT
iajs-856	117	17	b.	b.	PROPN
iajs-856	117	18	(	(	PUNCT
iajs-856	117	19	2003	2003	NUM
iajs-856	117	20	)	)	PUNCT
iajs-856	117	21	,	,	PUNCT
iajs-856	117	22	water	water	NOUN
iajs-856	117	23	resour	resour	NOUN
iajs-856	117	24	.	.	PUNCT
iajs-856	118	1	res	re	NOUN
iajs-856	118	2	.	.	PROPN
iajs-856	118	3	,	,	PUNCT
iajs-856	118	4	39	39	NUM
iajs-856	118	5	:	:	SYM
iajs-856	118	6	1022–1032	1022–1032	NUM
iajs-856	118	7	.	.	NOUN
iajs-856	119	1	9	9	X
iajs-856	119	2	.	.	X
iajs-856	119	3	isaacson	isaacson	PROPN
iajs-856	119	4	,	,	PUNCT
iajs-856	119	5	e.	e.	PROPN
iajs-856	119	6	and	and	CCONJ
iajs-856	119	7	keller	keller	PROPN
iajs-856	119	8	,	,	PUNCT
iajs-856	119	9	h.b	h.b	PROPN
iajs-856	119	10	.	.	PROPN
iajs-856	119	11	(	(	PUNCT
iajs-856	119	12	1966	1966	NUM
iajs-856	119	13	)	)	PUNCT
iajs-856	119	14	,	,	PUNCT
iajs-856	119	15	wiley	wiley	NOUN
iajs-856	119	16	,	,	PUNCT
iajs-856	119	17	new	new	PROPN
iajs-856	119	18	york	york	PROPN
iajs-856	119	19	.	.	PUNCT
iajs-856	120	1	10.meerschaert	10.meerschaert	NUM
iajs-856	120	2	,	,	PUNCT
iajs-856	120	3	m.m	m.m	PROPN
iajs-856	120	4	.	.	PROPN
iajs-856	120	5	and	and	CCONJ
iajs-856	120	6	tadjeran	tadjeran	NOUN
iajs-856	120	7	,	,	PUNCT
iajs-856	120	8	c.	c.	PROPN
iajs-856	120	9	(	(	PUNCT
iajs-856	120	10	2004	2004	NUM
iajs-856	120	11	)	)	PUNCT
iajs-856	120	12	,	,	PUNCT
iajs-856	120	13	j.	j.	PROPN
iajs-856	120	14	comput	comput	PROPN
iajs-856	120	15	.	.	PUNCT
iajs-856	121	1	appl	appl	PROPN
iajs-856	121	2	.	.	PROPN
iajs-856	121	3	math	math	PROPN
iajs-856	121	4	.	.	PUNCT
iajs-856	121	5	,	,	PUNCT
iajs-856	122	1	172	172	NUM
iajs-856	122	2	:	:	PUNCT
iajs-856	122	3	65–77	65–77	NUM
iajs-856	122	4	.	.	PUNCT
iajs-856	123	1	table	table	NOUN
iajs-856	123	2	(	(	PUNCT
iajs-856	123	3	1	1	X
iajs-856	123	4	)	)	PUNCT
iajs-856	123	5	the	the	DET
iajs-856	123	6	numerical	numerical	ADJ
iajs-856	123	7	solution	solution	NOUN
iajs-856	123	8	of	of	ADP
iajs-856	123	9	example	example	NOUN
iajs-856	123	10	by	by	ADP
iajs-856	123	11	using	use	VERB
iajs-856	123	12	the	the	DET
iajs-856	123	13	explicit	explicit	ADJ
iajs-856	123	14	finite	finite	ADJ
iajs-856	123	15	difference	difference	NOUN
iajs-856	123	16	approximation	approximation	NOUN
iajs-856	123	17	for	for	ADP
iajs-856	123	18	1.0,1.0	1.0,1.0	PROPN
iajs-856	123	19			PROPN
iajs-856	123	20	yx	yx	PROPN
iajs-856	123	21	and	and	CCONJ
iajs-856	123	22	0125.0t	0125.0t	NUM
iajs-856	123	23	numerical	numerical	ADJ
iajs-856	123	24	solution	solution	NOUN
iajs-856	123	25	exact	exact	ADJ
iajs-856	123	26	solution	solution	NOUN
iajs-856	123	27	error	error	NOUN
iajs-856	123	28	9.730e-4	9.730e-4	NOUN
iajs-856	123	29	1.02532	1.02532	NUM
iajs-856	123	30	e	e	NOUN
iajs-856	123	31	-3	-3	PUNCT
iajs-856	124	1	6.72814	6.72814	NUM
iajs-856	124	2	e	e	NOUN
iajs-856	124	3	-2	-2	X
iajs-856	124	4	7.876e-3	7.876e-3	NUM
iajs-856	124	5	8.20252	8.20252	NUM
iajs-856	124	6	e	e	NOUN
iajs-856	124	7	-3	-3	PUNCT
iajs-856	124	8	3.26521	3.26521	NUM
iajs-856	124	9	e	e	NOUN
iajs-856	124	10	-4	-4	PROPN
iajs-856	124	11	0.027	0.027	NUM
iajs-856	124	12	2.76835	2.76835	NUM
iajs-856	124	13	e	e	NOUN
iajs-856	124	14	-2	-2	X
iajs-856	124	15	6.83508	6.83508	NUM
iajs-856	124	16	e	e	NOUN
iajs-856	124	17	-4	-4	NOUN
iajs-856	124	18	0.064	0.064	NUM
iajs-856	124	19	6.56202	6.56202	NUM
iajs-856	124	20	e	e	NOUN
iajs-856	124	21	-2	-2	X
iajs-856	124	22	1.62017	1.62017	NUM
iajs-856	124	23	e	e	NOUN
iajs-856	124	24	-3	-3	PUNCT
iajs-856	124	25	9.795e-4	9.795e-4	NUM
iajs-856	124	26	1.05127	1.05127	NUM
iajs-856	124	27	e	e	NOUN
iajs-856	124	28	-3	-3	PUNCT
iajs-856	124	29	7.17711	7.17711	NUM
iajs-856	124	30	e	e	NOUN
iajs-856	124	31	-5	-5	NOUN
iajs-856	124	32	7.759e-3	7.759e-3	NUM
iajs-856	124	33	8.41017	8.41017	NUM
iajs-856	124	34	e	e	NOUN
iajs-856	124	35	-3	-3	PUNCT
iajs-856	124	36	6.51169	6.51169	NUM
iajs-856	124	37	e	e	NOUN
iajs-856	124	38	-4	-4	PUNCT
iajs-856	124	39	0.027	0.027	NUM
iajs-856	124	40	2.83843	2.83843	NUM
iajs-856	124	41	e	e	NOUN
iajs-856	124	42	-2	-2	NOUN
iajs-856	124	43	1.38432	1.38432	NUM
iajs-856	124	44	e	e	NOUN
iajs-856	124	45	3	3	NUM
iajs-856	124	46	0.036	0.036	NUM
iajs-856	124	47	6.72814	6.72814	NUM
iajs-856	124	48	e	e	NOUN
iajs-856	124	49	-2	-2	NOUN
iajs-856	124	50	3.12814	3.12814	NUM
iajs-856	124	51	e	e	NOUN
iajs-856	124	52	-2	-2	NOUN
iajs-856	124	53	table	table	NOUN
iajs-856	124	54	(	(	PUNCT
iajs-856	124	55	2	2	NUM
iajs-856	124	56	)	)	PUNCT
iajs-856	124	57	the	the	DET
iajs-856	124	58	numerical	numerical	ADJ
iajs-856	124	59	solution	solution	NOUN
iajs-856	124	60	of	of	ADP
iajs-856	124	61	example	example	NOUN
iajs-856	124	62	by	by	ADP
iajs-856	124	63	using	use	VERB
iajs-856	124	64	the	the	DET
iajs-856	124	65	explicit	explicit	ADJ
iajs-856	124	66	finite	finite	ADJ
iajs-856	124	67	difference	difference	NOUN
iajs-856	124	68	approximation	approximation	NOUN
iajs-856	124	69	for	for	ADP
iajs-856	124	70	125.0,125.0	125.0,125.0	PROPN
iajs-856	124	71			PROPN
iajs-856	124	72	yx	yx	PROPN
iajs-856	124	73	and	and	CCONJ
iajs-856	124	74	0125.0t	0125.0t	NUM
iajs-856	124	75	numerical	numerical	ADJ
iajs-856	124	76	solution	solution	NOUN
iajs-856	124	77	exact	exact	ADJ
iajs-856	124	78	solution	solution	NOUN
iajs-856	124	79	error	error	NOUN
iajs-856	124	80	1.908e-3	1.908e-3	NUM
iajs-856	124	81	2.00257	2.00257	NUM
iajs-856	124	82	e	e	NOUN
iajs-856	124	83	-3	-3	PUNCT
iajs-856	124	84	9.45686	9.45686	NUM
iajs-856	124	85	e	e	NOUN
iajs-856	124	86	-5	-5	NOUN
iajs-856	124	87	0.015	0.015	NUM
iajs-856	124	88	1.60205	1.60205	NUM
iajs-856	124	89	e	e	NOUN
iajs-856	124	90	-2	-2	X
iajs-856	124	91	1.02055	1.02055	NUM
iajs-856	124	92	e	e	NOUN
iajs-856	124	93	-3	-3	PUNCT
iajs-856	124	94	0.052	0.052	NUM
iajs-856	124	95	5.40693	5.40693	NUM
iajs-856	124	96	e	e	NOUN
iajs-856	124	97	-2	-2	X
iajs-856	124	98	2.06935	2.06935	NUM
iajs-856	124	99	e	e	X
iajs-856	124	100	-3	-3	PUNCT
iajs-856	124	101	1.929e-3	1.929e-3	NUM
iajs-856	124	102	2.05326	2.05326	NUM
iajs-856	124	103	e	e	NOUN
iajs-856	124	104	-3	-3	PUNCT
iajs-856	124	105	1.24264	1.24264	NUM
iajs-856	124	106	e	e	NOUN
iajs-856	124	107	-4	-4	PROPN
iajs-856	124	108	0.015	0.015	NUM
iajs-856	124	109	1.64261	1.64261	NUM
iajs-856	124	110	e	e	NOUN
iajs-856	124	111	-2	-2	X
iajs-856	124	112	1.42611	1.42611	NUM
iajs-856	124	113	e	e	NOUN
iajs-856	124	114	-3	-3	PUNCT
iajs-856	124	115	0.036	0.036	NUM
iajs-856	124	116	5.54381	5.54381	NUM
iajs-856	124	117	e	e	NOUN
iajs-856	124	118	-2	-2	X
iajs-856	124	119	1.94381	1.94381	NUM
iajs-856	124	120	e	e	NOUN
iajs-856	124	121	-2	-2	NOUN
iajs-856	124	122	2011	2011	NUM
iajs-856	124	123	)	)	PUNCT
iajs-856	124	124	1	1	NUM
iajs-856	124	125	(	(	PUNCT
iajs-856	124	126	24مجلة	24مجلة	NUM
iajs-856	124	127	ابن	ابن	PROPN
iajs-856	124	128	الھیثم	الھیثم	PROPN
iajs-856	124	129	للعلوم	للعلوم	PROPN
iajs-856	124	130	الصرفة	الصرفة	PROPN
iajs-856	124	131	والتطبیقیة	والتطبیقیة	PROPN
iajs-856	124	132	المجلد	المجلد	PROPN
iajs-856	124	133	تتشتال	تتشتال	VERB
iajs-856	124	134	دلةلمعا	دلةلمعا	PROPN
iajs-856	124	135	الفروق	الفروق	PROPN
iajs-856	124	136	المنتهیة	المنتهیة	PROPN
iajs-856	124	137	الصریحةّ	الصریحةّ	PROPN
iajs-856	124	138	تقریب	تقریب	PROPN
iajs-856	124	139	ذات	ذات	NOUN
iajs-856	124	140	البعدین	البعدین	PROPN
iajs-856	124	141	الكسریة	الكسریة	VERB
iajs-856	124	142	ایمان	ایمان	PROPN
iajs-856	124	143	ایشو	ایشو	PROPN
iajs-856	124	144	كولایر	كولایر	PROPN
iajs-856	124	145	جامعة	جامعة	PROPN
iajs-856	124	146	بغداد	بغداد	PROPN
iajs-856	124	147	،	،	PROPN
iajs-856	124	148	ابن	ابن	PROPN
iajs-856	124	149	الهیثم	الهیثم	PROPN
iajs-856	124	150	-كلیة	-كلیة	PROPN
iajs-856	124	151	التربیة	التربیة	NOUN
iajs-856	124	152	،	،	NOUN
iajs-856	124	153	قسم	قسم	PROPN
iajs-856	125	1	الریاضیات	الریاضیات	NOUN
iajs-856	125	2	2010	2010	NUM
iajs-856	125	3	شباط	شباط	ADV
iajs-856	125	4	7استلم	7استلم	NUM
iajs-856	125	5	البحث	البحث	ADV
iajs-856	125	6	في	في	ADP
iajs-856	125	7	2010	2010	NUM
iajs-856	125	8	ایار	ایار	ADJ
iajs-856	125	9	13قبل	13قبل	PROPN
iajs-856	125	10	البحث	البحث	VERB
iajs-856	125	11	في	في	ADP
iajs-856	125	12	الخالصة	الخالصة	PROPN
iajs-856	125	13	وارزمیــة	وارزمیــة	PROPN
iajs-856	125	14	الحـل	الحـل	PROPN
iajs-856	125	15	العــددي	العــددي	PROPN
iajs-856	125	16	وان	وان	PROPN
iajs-856	125	17	خ	خ	NOUN
iajs-856	125	18	.	.	PUNCT
iajs-856	126	1	البعـدین	البعـدین	PROPN
iajs-856	126	2	ذي	ذي	PROPN
iajs-856	126	3	الكســریة	الكســریة	PROPN
iajs-856	126	4	تتشـتال	تتشـتال	PROPN
iajs-856	126	5	ةلمعادلــفـي	ةلمعادلــفـي	PROPN
iajs-856	126	6	هـذا	هـذا	NOUN
iajs-856	126	7	البحــث	البحــث	PROPN
iajs-856	126	8	قـدمنا	قـدمنا	PROPN
iajs-856	126	9	وناقشــنا	وناقشــنا	PROPN
iajs-856	126	10	خوارزمیـة	خوارزمیـة	PROPN
iajs-856	126	11	للحــل	للحــل	VERB
iajs-856	126	12	العـددي	العـددي	PROPN
iajs-856	126	13	شـرطي	شـرطي	PROPN
iajs-856	126	14	،	،	PROPN
iajs-856	126	15	والتقـارب	والتقـارب	PROPN
iajs-856	126	16	للطریقـة	للطریقـة	PROPN
iajs-856	126	17	السـتقرار	السـتقرار	PROPN
iajs-856	126	18	االو	االو	PROPN
iajs-856	126	19	،	،	PROPN
iajs-856	126	20	تسـاق	تسـاق	PROPN
iajs-856	126	21	اال	اال	NOUN
iajs-856	126	22	اكمـا	اكمـا	NOUN
iajs-856	126	23	ناقشـن	ناقشـن	NOUN
iajs-856	126	24	.	.	PUNCT
iajs-856	127	1	الصـریحة	الصـریحة	PROPN
iajs-856	127	2	الفـروق	الفـروق	VERB
iajs-856	127	3	المنتهیـة	المنتهیـة	PRON
iajs-856	127	4	تقریـب	تقریـب	PROPN
iajs-856	127	5	قائمة	قائمة	PROPN
iajs-856	127	6	على	على	PROPN
iajs-856	127	7	اساس	اساس	PROPN
iajs-856	128	1	دلةالتلك	دلةالتلك	PROPN
iajs-856	128	2	المع	المع	PROPN
iajs-856	128	3	.العددیة	.العددیة	PUNCT
iajs-856	128	4	وبینـا	وبینـا	PROPN
iajs-856	128	5	أن	أن	SCONJ
iajs-856	128	6	تقریـب	تقریـب	AUX
iajs-856	128	7	الفـروق	الفـروق	VERB
iajs-856	128	8	المنتهیـة	المنتهیـة	DET
iajs-856	128	9	الصـریحة	الصـریحة	PROPN
iajs-856	128	10	ةحسـب	ةحسـب	PROPN
iajs-856	128	11	مرتبـة	مرتبـة	PROPN
iajs-856	128	12	االشـتقاق	االشـتقاق	PROPN
iajs-856	128	13	الكسـری	الكسـری	PROPN
iajs-856	128	14	التشـتتسلوك	التشـتتسلوك	PROPN
iajs-856	128	15	ظهرلی	ظهرلی	PROPN
iajs-856	128	16	اعددی	اعددی	PROPN
iajs-856	128	17	اخیرا	اخیرا	PROPN
iajs-856	128	18	قدمنا	قدمنا	PROPN
iajs-856	128	19	مثاال	مثاال	PROPN
iajs-856	128	20	.البعدین	.البعدین	PUNCT
iajs-856	128	21	الكسریة	الكسریة	VERB
iajs-856	128	22	ذي	ذي	PROPN
iajs-856	128	23	التشتت	التشتت	PROPN
iajs-856	128	24	هو	هو	PROPN
iajs-856	128	25	طریقة	طریقة	PROPN
iajs-856	128	26	فعالة	فعالة	PROPN
iajs-856	128	27	حسابیا	حسابیا	PROPN
iajs-856	128	28	لمعادلة	لمعادلة	NOUN
iajs-856	128	29	.التقارب	.التقارب	ADP
iajs-856	129	1	االستقرار	االستقرار	PROPN
iajs-856	129	2	،	،	PROPN
iajs-856	129	3	التشتت	التشتت	PROPN
iajs-856	129	4	الكسریةمعادلة	الكسریةمعادلة	PROPN
iajs-856	129	5	،	،	PROPN
iajs-856	129	6	طریقة	طریقة	PROPN
iajs-856	129	7	اوبلر	اوبلر	PROPN
iajs-856	129	8	الصریحة	الصریحة	PROPN
iajs-856	129	9	،	،	PROPN
iajs-856	129	10	مسألة	مسألة	PROPN
iajs-856	129	11	ذي	ذي	PROPN
iajs-856	129	12	بعدین	بعدین	PROPN
iajs-856	129	13	،	،	PROPN
iajs-856	129	14	كسریة	كسریة	PROPN
iajs-856	129	15	مشتقة	مشتقة	PROPN
iajs-856	130	1	-:الكلمات	-:الكلمات	VERB
iajs-856	130	2	المفتاحیة	المفتاحیة	ADJ