id	sid	tid	token	lemma	pos
american_scientific_journal-2216	1	1	261	261	NUM
american_scientific_journal-2216	1	2	american	american	ADJ
american_scientific_journal-2216	1	3	scientific	scientific	ADJ
american_scientific_journal-2216	1	4	research	research	NOUN
american_scientific_journal-2216	1	5	journal	journal	NOUN
american_scientific_journal-2216	1	6	for	for	ADP
american_scientific_journal-2216	1	7	engineering	engineering	NOUN
american_scientific_journal-2216	1	8	,	,	PUNCT
american_scientific_journal-2216	1	9	technology	technology	NOUN
american_scientific_journal-2216	1	10	,	,	PUNCT
american_scientific_journal-2216	1	11	and	and	CCONJ
american_scientific_journal-2216	1	12	sciences	science	NOUN
american_scientific_journal-2216	1	13	(	(	PUNCT
american_scientific_journal-2216	1	14	asrjets	asrjet	NOUN
american_scientific_journal-2216	1	15	)	)	PUNCT
american_scientific_journal-2216	1	16	issn	issn	PROPN
american_scientific_journal-2216	1	17	(	(	PUNCT
american_scientific_journal-2216	1	18	print	print	NOUN
american_scientific_journal-2216	1	19	)	)	PUNCT
american_scientific_journal-2216	1	20	2313	2313	NUM
american_scientific_journal-2216	1	21	-	-	SYM
american_scientific_journal-2216	1	22	4410	4410	NUM
american_scientific_journal-2216	1	23	,	,	PUNCT
american_scientific_journal-2216	1	24	issn	issn	PROPN
american_scientific_journal-2216	1	25	(	(	PUNCT
american_scientific_journal-2216	1	26	online	online	ADJ
american_scientific_journal-2216	1	27	)	)	PUNCT
american_scientific_journal-2216	1	28	2313	2313	NUM
american_scientific_journal-2216	1	29	-	-	SYM
american_scientific_journal-2216	1	30	4402	4402	NUM
american_scientific_journal-2216	1	31	©	©	PROPN
american_scientific_journal-2216	1	32	global	global	ADJ
american_scientific_journal-2216	1	33	society	society	NOUN
american_scientific_journal-2216	1	34	of	of	ADP
american_scientific_journal-2216	1	35	scientific	scientific	ADJ
american_scientific_journal-2216	1	36	research	research	NOUN
american_scientific_journal-2216	1	37	and	and	CCONJ
american_scientific_journal-2216	1	38	researchers	researcher	NOUN
american_scientific_journal-2216	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PRON
american_scientific_journal-2216	1	40	improved	improve	VERB
american_scientific_journal-2216	1	41	rotated	rotate	VERB
american_scientific_journal-2216	1	42	finite	finite	ADJ
american_scientific_journal-2216	1	43	difference	difference	NOUN
american_scientific_journal-2216	1	44	method	method	NOUN
american_scientific_journal-2216	1	45	for	for	ADP
american_scientific_journal-2216	1	46	solving	solve	VERB
american_scientific_journal-2216	1	47	fractional	fractional	ADJ
american_scientific_journal-2216	1	48	elliptic	elliptic	ADJ
american_scientific_journal-2216	1	49	partial	partial	ADJ
american_scientific_journal-2216	1	50	differential	differential	ADJ
american_scientific_journal-2216	1	51	equations	equation	NOUN
american_scientific_journal-2216	1	52	abdulkafi	abdulkafi	PROPN
american_scientific_journal-2216	1	53	mohammed	mohammed	PROPN
american_scientific_journal-2216	1	54	saeed	saeed	PROPN
american_scientific_journal-2216	1	55	*	*	PROPN
american_scientific_journal-2216	1	56	department	department	PROPN
american_scientific_journal-2216	1	57	of	of	ADP
american_scientific_journal-2216	1	58	mathematics	mathematics	PROPN
american_scientific_journal-2216	1	59	,	,	PUNCT
american_scientific_journal-2216	1	60	college	college	NOUN
american_scientific_journal-2216	1	61	of	of	ADP
american_scientific_journal-2216	1	62	science	science	NOUN
american_scientific_journal-2216	1	63	,	,	PUNCT
american_scientific_journal-2216	1	64	qassim	qassim	PROPN
american_scientific_journal-2216	1	65	university	university	PROPN
american_scientific_journal-2216	1	66	,	,	PUNCT
american_scientific_journal-2216	1	67	saudi	saudi	PROPN
american_scientific_journal-2216	1	68	arabia	arabia	PROPN
american_scientific_journal-2216	1	69	email	email	NOUN
american_scientific_journal-2216	1	70	:	:	PUNCT
american_scientific_journal-2216	1	71	abdulkafi.ahmed@qu.edu.sa	abdulkafi.ahmed@qu.edu.sa	PROPN
american_scientific_journal-2216	1	72	,	,	PUNCT
american_scientific_journal-2216	1	73	email	email	NOUN
american_scientific_journal-2216	1	74	:	:	PUNCT
american_scientific_journal-2216	1	75	abdelkafe@yahoo.com	abdelkafe@yahoo.com	X
american_scientific_journal-2216	2	1	abstract	abstract	ADJ
american_scientific_journal-2216	2	2	real	real	ADJ
american_scientific_journal-2216	2	3	life	life	NOUN
american_scientific_journal-2216	2	4	problems	problem	NOUN
american_scientific_journal-2216	2	5	with	with	ADP
american_scientific_journal-2216	2	6	fractional	fractional	ADJ
american_scientific_journal-2216	2	7	partial	partial	ADJ
american_scientific_journal-2216	2	8	differential	differential	NOUN
american_scientific_journal-2216	2	9	equations	equation	NOUN
american_scientific_journal-2216	2	10	(	(	PUNCT
american_scientific_journal-2216	2	11	fpde	fpde	NOUN
american_scientific_journal-2216	2	12	's	's	PART
american_scientific_journal-2216	2	13	)	)	PUNCT
american_scientific_journal-2216	2	14	are	be	AUX
american_scientific_journal-2216	2	15	of	of	ADP
american_scientific_journal-2216	2	16	great	great	ADJ
american_scientific_journal-2216	2	17	importance	importance	NOUN
american_scientific_journal-2216	2	18	,	,	PUNCT
american_scientific_journal-2216	2	19	since	since	SCONJ
american_scientific_journal-2216	2	20	fractional	fractional	ADJ
american_scientific_journal-2216	2	21	differential	differential	ADJ
american_scientific_journal-2216	2	22	equations	equation	NOUN
american_scientific_journal-2216	2	23	accumulate	accumulate	VERB
american_scientific_journal-2216	2	24	the	the	DET
american_scientific_journal-2216	2	25	whole	whole	ADJ
american_scientific_journal-2216	2	26	information	information	NOUN
american_scientific_journal-2216	2	27	of	of	ADP
american_scientific_journal-2216	2	28	the	the	DET
american_scientific_journal-2216	2	29	function	function	NOUN
american_scientific_journal-2216	2	30	in	in	ADP
american_scientific_journal-2216	2	31	a	a	DET
american_scientific_journal-2216	2	32	weighted	weight	VERB
american_scientific_journal-2216	2	33	form	form	NOUN
american_scientific_journal-2216	2	34	.	.	PUNCT
american_scientific_journal-2216	3	1	this	this	PRON
american_scientific_journal-2216	3	2	has	have	VERB
american_scientific_journal-2216	3	3	many	many	ADJ
american_scientific_journal-2216	3	4	applications	application	NOUN
american_scientific_journal-2216	3	5	in	in	ADP
american_scientific_journal-2216	3	6	physics	physics	NOUN
american_scientific_journal-2216	3	7	,	,	PUNCT
american_scientific_journal-2216	3	8	chemistry	chemistry	NOUN
american_scientific_journal-2216	3	9	,	,	PUNCT
american_scientific_journal-2216	3	10	engineering	engineering	NOUN
american_scientific_journal-2216	3	11	,	,	PUNCT
american_scientific_journal-2216	3	12	etc	etc	X
american_scientific_journal-2216	3	13	.	.	X
american_scientific_journal-2216	3	14	for	for	ADP
american_scientific_journal-2216	3	15	that	that	DET
american_scientific_journal-2216	3	16	reason	reason	NOUN
american_scientific_journal-2216	3	17	,	,	PUNCT
american_scientific_journal-2216	3	18	we	we	PRON
american_scientific_journal-2216	3	19	need	need	VERB
american_scientific_journal-2216	3	20	a	a	DET
american_scientific_journal-2216	3	21	method	method	NOUN
american_scientific_journal-2216	3	22	for	for	ADP
american_scientific_journal-2216	3	23	solving	solve	VERB
american_scientific_journal-2216	3	24	such	such	ADJ
american_scientific_journal-2216	3	25	equations	equation	NOUN
american_scientific_journal-2216	3	26	,	,	PUNCT
american_scientific_journal-2216	3	27	effectively	effectively	ADV
american_scientific_journal-2216	3	28	,	,	PUNCT
american_scientific_journal-2216	3	29	easy	easy	ADJ
american_scientific_journal-2216	3	30	use	use	NOUN
american_scientific_journal-2216	3	31	and	and	CCONJ
american_scientific_journal-2216	3	32	applied	apply	VERB
american_scientific_journal-2216	3	33	for	for	ADP
american_scientific_journal-2216	3	34	different	different	ADJ
american_scientific_journal-2216	3	35	problems	problem	NOUN
american_scientific_journal-2216	3	36	.	.	PUNCT
american_scientific_journal-2216	4	1	the	the	DET
american_scientific_journal-2216	4	2	objective	objective	NOUN
american_scientific_journal-2216	4	3	of	of	ADP
american_scientific_journal-2216	4	4	this	this	DET
american_scientific_journal-2216	4	5	paper	paper	NOUN
american_scientific_journal-2216	4	6	is	be	AUX
american_scientific_journal-2216	4	7	to	to	PART
american_scientific_journal-2216	4	8	solve	solve	VERB
american_scientific_journal-2216	4	9	fractional	fractional	ADJ
american_scientific_journal-2216	4	10	elliptic	elliptic	ADJ
american_scientific_journal-2216	4	11	partial	partial	ADJ
american_scientific_journal-2216	4	12	differential	differential	NOUN
american_scientific_journal-2216	4	13	equations	equation	NOUN
american_scientific_journal-2216	4	14	,	,	PUNCT
american_scientific_journal-2216	4	15	by	by	ADP
american_scientific_journal-2216	4	16	using	use	VERB
american_scientific_journal-2216	4	17	new	new	ADJ
american_scientific_journal-2216	4	18	accelerated	accelerate	VERB
american_scientific_journal-2216	4	19	version	version	NOUN
american_scientific_journal-2216	4	20	of	of	ADP
american_scientific_journal-2216	4	21	rotated	rotate	VERB
american_scientific_journal-2216	4	22	five	five	NUM
american_scientific_journal-2216	4	23	point	point	NOUN
american_scientific_journal-2216	4	24	’s	’s	PART
american_scientific_journal-2216	4	25	approximation	approximation	NOUN
american_scientific_journal-2216	4	26	method	method	NOUN
american_scientific_journal-2216	4	27	.	.	PUNCT
american_scientific_journal-2216	5	1	experiment	experiment	NOUN
american_scientific_journal-2216	5	2	results	result	NOUN
american_scientific_journal-2216	5	3	of	of	ADP
american_scientific_journal-2216	5	4	the	the	DET
american_scientific_journal-2216	5	5	test	test	NOUN
american_scientific_journal-2216	5	6	problem	problem	NOUN
american_scientific_journal-2216	5	7	are	be	AUX
american_scientific_journal-2216	5	8	given	give	VERB
american_scientific_journal-2216	5	9	in	in	ADP
american_scientific_journal-2216	5	10	order	order	NOUN
american_scientific_journal-2216	5	11	to	to	PART
american_scientific_journal-2216	5	12	confirm	confirm	VERB
american_scientific_journal-2216	5	13	the	the	DET
american_scientific_journal-2216	5	14	superiority	superiority	NOUN
american_scientific_journal-2216	5	15	of	of	ADP
american_scientific_journal-2216	5	16	our	our	PRON
american_scientific_journal-2216	5	17	proposed	propose	VERB
american_scientific_journal-2216	5	18	method	method	NOUN
american_scientific_journal-2216	5	19	.	.	PUNCT
american_scientific_journal-2216	6	1	keywords	keyword	NOUN
american_scientific_journal-2216	6	2	:	:	PUNCT
american_scientific_journal-2216	6	3	rotated	rotate	VERB
american_scientific_journal-2216	6	4	finite	finite	ADJ
american_scientific_journal-2216	6	5	difference	difference	NOUN
american_scientific_journal-2216	6	6	approximation	approximation	NOUN
american_scientific_journal-2216	6	7	method	method	NOUN
american_scientific_journal-2216	6	8	;	;	PUNCT
american_scientific_journal-2216	6	9	fractional	fractional	ADJ
american_scientific_journal-2216	6	10	elliptic	elliptic	ADJ
american_scientific_journal-2216	6	11	partial	partial	ADJ
american_scientific_journal-2216	6	12	differential	differential	NOUN
american_scientific_journal-2216	6	13	equations	equation	NOUN
american_scientific_journal-2216	6	14	.	.	PUNCT
american_scientific_journal-2216	7	1	1	1	X
american_scientific_journal-2216	7	2	.	.	X
american_scientific_journal-2216	7	3	introduction	introduction	NOUN
american_scientific_journal-2216	7	4	fast	fast	ADJ
american_scientific_journal-2216	7	5	computational	computational	ADJ
american_scientific_journal-2216	7	6	methods	method	NOUN
american_scientific_journal-2216	7	7	for	for	ADP
american_scientific_journal-2216	7	8	solving	solve	VERB
american_scientific_journal-2216	7	9	partial	partial	ADJ
american_scientific_journal-2216	7	10	differential	differential	ADJ
american_scientific_journal-2216	7	11	equations	equation	NOUN
american_scientific_journal-2216	7	12	using	use	VERB
american_scientific_journal-2216	7	13	finite	finite	ADJ
american_scientific_journal-2216	7	14	difference	difference	NOUN
american_scientific_journal-2216	7	15	schemes	scheme	NOUN
american_scientific_journal-2216	7	16	derived	derive	VERB
american_scientific_journal-2216	7	17	from	from	ADP
american_scientific_journal-2216	7	18	skewed	skewed	ADJ
american_scientific_journal-2216	7	19	(	(	PUNCT
american_scientific_journal-2216	7	20	rotated	rotate	VERB
american_scientific_journal-2216	7	21	)	)	PUNCT
american_scientific_journal-2216	7	22	difference	difference	NOUN
american_scientific_journal-2216	7	23	operators	operator	NOUN
american_scientific_journal-2216	7	24	have	have	AUX
american_scientific_journal-2216	7	25	been	be	AUX
american_scientific_journal-2216	7	26	extensively	extensively	ADV
american_scientific_journal-2216	7	27	investigated	investigate	VERB
american_scientific_journal-2216	7	28	over	over	ADP
american_scientific_journal-2216	7	29	the	the	DET
american_scientific_journal-2216	7	30	years	year	NOUN
american_scientific_journal-2216	7	31	.	.	PUNCT
american_scientific_journal-2216	8	1	these	these	DET
american_scientific_journal-2216	8	2	iterative	iterative	ADJ
american_scientific_journal-2216	8	3	methods	method	NOUN
american_scientific_journal-2216	8	4	based	base	VERB
american_scientific_journal-2216	8	5	on	on	ADP
american_scientific_journal-2216	8	6	the	the	DET
american_scientific_journal-2216	8	7	rotated	rotate	VERB
american_scientific_journal-2216	8	8	finite	finite	ADJ
american_scientific_journal-2216	8	9	difference	difference	NOUN
american_scientific_journal-2216	8	10	approximations	approximation	NOUN
american_scientific_journal-2216	8	11	have	have	AUX
american_scientific_journal-2216	8	12	been	be	AUX
american_scientific_journal-2216	8	13	shown	show	VERB
american_scientific_journal-2216	8	14	to	to	PART
american_scientific_journal-2216	8	15	be	be	AUX
american_scientific_journal-2216	8	16	much	much	ADV
american_scientific_journal-2216	8	17	faster	fast	ADJ
american_scientific_journal-2216	8	18	than	than	ADP
american_scientific_journal-2216	8	19	the	the	DET
american_scientific_journal-2216	8	20	methods	method	NOUN
american_scientific_journal-2216	8	21	based	base	VERB
american_scientific_journal-2216	8	22	on	on	ADP
american_scientific_journal-2216	8	23	the	the	DET
american_scientific_journal-2216	8	24	standard	standard	ADJ
american_scientific_journal-2216	8	25	five	five	NUM
american_scientific_journal-2216	8	26	-	-	PUNCT
american_scientific_journal-2216	8	27	point	point	NOUN
american_scientific_journal-2216	8	28	formula	formula	NOUN
american_scientific_journal-2216	8	29	in	in	ADP
american_scientific_journal-2216	8	30	solving	solve	VERB
american_scientific_journal-2216	8	31	the	the	DET
american_scientific_journal-2216	8	32	partial	partial	ADJ
american_scientific_journal-2216	8	33	differential	differential	NOUN
american_scientific_journal-2216	8	34	equations	equation	NOUN
american_scientific_journal-2216	8	35	which	which	PRON
american_scientific_journal-2216	8	36	is	be	AUX
american_scientific_journal-2216	8	37	due	due	ADJ
american_scientific_journal-2216	8	38	to	to	ADP
american_scientific_journal-2216	8	39	the	the	DET
american_scientific_journal-2216	8	40	formers	former	NOUN
american_scientific_journal-2216	8	41	’	’	PART
american_scientific_journal-2216	8	42	overall	overall	ADV
american_scientific_journal-2216	8	43	lower	low	ADJ
american_scientific_journal-2216	8	44	computational	computational	ADJ
american_scientific_journal-2216	8	45	complexities	complexity	NOUN
american_scientific_journal-2216	8	46	(	(	PUNCT
american_scientific_journal-2216	8	47	[	[	X
american_scientific_journal-2216	8	48	1,2,3,4,5	1,2,3,4,5	NUM
american_scientific_journal-2216	8	49	]	]	NUM
american_scientific_journal-2216	8	50	)	)	PUNCT
american_scientific_journal-2216	8	51	.	.	PUNCT
american_scientific_journal-2216	9	1	fractional	fractional	ADJ
american_scientific_journal-2216	9	2	partial	partial	ADJ
american_scientific_journal-2216	9	3	differential	differential	NOUN
american_scientific_journal-2216	9	4	equations	equation	NOUN
american_scientific_journal-2216	9	5	(	(	PUNCT
american_scientific_journal-2216	9	6	fpde	fpde	NOUN
american_scientific_journal-2216	9	7	's	's	PART
american_scientific_journal-2216	9	8	)	)	PUNCT
american_scientific_journal-2216	9	9	can	can	AUX
american_scientific_journal-2216	9	10	be	be	AUX
american_scientific_journal-2216	9	11	seen	see	VERB
american_scientific_journal-2216	9	12	as	as	ADP
american_scientific_journal-2216	9	13	a	a	DET
american_scientific_journal-2216	9	14	generalization	generalization	NOUN
american_scientific_journal-2216	9	15	of	of	ADP
american_scientific_journal-2216	9	16	the	the	DET
american_scientific_journal-2216	9	17	classical	classical	ADJ
american_scientific_journal-2216	9	18	partial	partial	ADJ
american_scientific_journal-2216	9	19	differential	differential	NOUN
american_scientific_journal-2216	9	20	equations	equation	NOUN
american_scientific_journal-2216	9	21	(	(	PUNCT
american_scientific_journal-2216	9	22	pde	pde	NOUN
american_scientific_journal-2216	9	23	's	's	PART
american_scientific_journal-2216	9	24	)	)	PUNCT
american_scientific_journal-2216	9	25	in	in	ADP
american_scientific_journal-2216	9	26	the	the	DET
american_scientific_journal-2216	9	27	sense	sense	NOUN
american_scientific_journal-2216	9	28	that	that	SCONJ
american_scientific_journal-2216	9	29	it	it	PRON
american_scientific_journal-2216	9	30	takes	take	VERB
american_scientific_journal-2216	9	31	into	into	ADP
american_scientific_journal-2216	9	32	account	account	NOUN
american_scientific_journal-2216	9	33	the	the	DET
american_scientific_journal-2216	9	34	memory	memory	NOUN
american_scientific_journal-2216	9	35	and	and	CCONJ
american_scientific_journal-2216	9	36	hereditary	hereditary	ADJ
american_scientific_journal-2216	9	37	properties	property	NOUN
american_scientific_journal-2216	9	38	of	of	ADP
american_scientific_journal-2216	9	39	the	the	DET
american_scientific_journal-2216	9	40	physical	physical	ADJ
american_scientific_journal-2216	9	41	phenomena	phenomenon	NOUN
american_scientific_journal-2216	9	42	(	(	PUNCT
american_scientific_journal-2216	9	43	[	[	X
american_scientific_journal-2216	9	44	6,7	6,7	NUM
american_scientific_journal-2216	9	45	]	]	PUNCT
american_scientific_journal-2216	9	46	)	)	PUNCT
american_scientific_journal-2216	9	47	.	.	PUNCT
american_scientific_journal-2216	10	1	as	as	SCONJ
american_scientific_journal-2216	10	2	it	it	PRON
american_scientific_journal-2216	10	3	was	be	AUX
american_scientific_journal-2216	10	4	in	in	ADP
american_scientific_journal-2216	10	5	the	the	DET
american_scientific_journal-2216	10	6	classical	classical	ADJ
american_scientific_journal-2216	10	7	pde	pde	NOUN
american_scientific_journal-2216	10	8	's	's	PART
american_scientific_journal-2216	10	9	there	there	PRON
american_scientific_journal-2216	10	10	is	be	VERB
american_scientific_journal-2216	10	11	no	no	DET
american_scientific_journal-2216	10	12	general	general	ADJ
american_scientific_journal-2216	10	13	method	method	NOUN
american_scientific_journal-2216	10	14	that	that	PRON
american_scientific_journal-2216	10	15	can	can	AUX
american_scientific_journal-2216	10	16	be	be	AUX
american_scientific_journal-2216	10	17	used	use	VERB
american_scientific_journal-2216	10	18	in	in	ADP
american_scientific_journal-2216	10	19	solving	solve	VERB
american_scientific_journal-2216	10	20	fpde	fpde	NOUN
american_scientific_journal-2216	10	21	's	's	PART
american_scientific_journal-2216	10	22	.	.	PUNCT
american_scientific_journal-2216	11	1	numerical	numerical	ADJ
american_scientific_journal-2216	11	2	solution	solution	NOUN
american_scientific_journal-2216	11	3	of	of	ADP
american_scientific_journal-2216	11	4	fpde	fpde	NOUN
american_scientific_journal-2216	11	5	's	's	PART
american_scientific_journal-2216	11	6	has	have	AUX
american_scientific_journal-2216	11	7	received	receive	VERB
american_scientific_journal-2216	11	8	great	great	ADJ
american_scientific_journal-2216	11	9	progress	progress	NOUN
american_scientific_journal-2216	11	10	in	in	ADP
american_scientific_journal-2216	11	11	the	the	DET
american_scientific_journal-2216	11	12	recent	recent	ADJ
american_scientific_journal-2216	11	13	years	year	NOUN
american_scientific_journal-2216	11	14	(	(	PUNCT
american_scientific_journal-2216	11	15	[	[	X
american_scientific_journal-2216	11	16	8,9	8,9	NUM
american_scientific_journal-2216	11	17	]	]	PUNCT
american_scientific_journal-2216	11	18	)	)	PUNCT
american_scientific_journal-2216	11	19	.	.	PUNCT
american_scientific_journal-2216	12	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-2216	13	1	*	*	PUNCT
american_scientific_journal-2216	13	2	corresponding	correspond	VERB
american_scientific_journal-2216	13	3	author	author	NOUN
american_scientific_journal-2216	13	4	.	.	PUNCT
american_scientific_journal-2216	14	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-2216	14	2	american	american	PROPN
american_scientific_journal-2216	14	3	scientific	scientific	PROPN
american_scientific_journal-2216	14	4	research	research	NOUN
american_scientific_journal-2216	14	5	journal	journal	NOUN
american_scientific_journal-2216	14	6	for	for	ADP
american_scientific_journal-2216	14	7	engineering	engineering	NOUN
american_scientific_journal-2216	14	8	,	,	PUNCT
american_scientific_journal-2216	14	9	technology	technology	NOUN
american_scientific_journal-2216	14	10	,	,	PUNCT
american_scientific_journal-2216	14	11	and	and	CCONJ
american_scientific_journal-2216	14	12	sciences	science	NOUN
american_scientific_journal-2216	14	13	(	(	PUNCT
american_scientific_journal-2216	14	14	asrjets	asrjet	NOUN
american_scientific_journal-2216	14	15	)	)	PUNCT
american_scientific_journal-2216	14	16	(	(	PUNCT
american_scientific_journal-2216	14	17	2016	2016	NUM
american_scientific_journal-2216	14	18	)	)	PUNCT
american_scientific_journal-2216	14	19	volume	volume	NOUN
american_scientific_journal-2216	14	20	26	26	NUM
american_scientific_journal-2216	14	21	,	,	PUNCT
american_scientific_journal-2216	14	22	no	no	DET
american_scientific_journal-2216	14	23	1	1	NUM
american_scientific_journal-2216	14	24	,	,	PUNCT
american_scientific_journal-2216	14	25	pp	pp	ADV
american_scientific_journal-2216	14	26	261	261	NUM
american_scientific_journal-2216	14	27	-	-	SYM
american_scientific_journal-2216	14	28	270	270	NUM
american_scientific_journal-2216	14	29	262	262	NUM
american_scientific_journal-2216	14	30	the	the	DET
american_scientific_journal-2216	14	31	time	time	NOUN
american_scientific_journal-2216	14	32	and	and	CCONJ
american_scientific_journal-2216	14	33	space	space	NOUN
american_scientific_journal-2216	14	34	-	-	PUNCT
american_scientific_journal-2216	14	35	fractional	fractional	ADJ
american_scientific_journal-2216	14	36	partial	partial	ADJ
american_scientific_journal-2216	14	37	differential	differential	NOUN
american_scientific_journal-2216	14	38	equation	equation	NOUN
american_scientific_journal-2216	14	39	describe	describe	VERB
american_scientific_journal-2216	14	40	transport	transport	NOUN
american_scientific_journal-2216	14	41	dynamics	dynamic	NOUN
american_scientific_journal-2216	14	42	in	in	ADP
american_scientific_journal-2216	14	43	complex	complex	ADJ
american_scientific_journal-2216	14	44	systems	system	NOUN
american_scientific_journal-2216	14	45	governed	govern	VERB
american_scientific_journal-2216	14	46	by	by	ADP
american_scientific_journal-2216	14	47	anomalous	anomalous	ADJ
american_scientific_journal-2216	14	48	dispersion	dispersion	NOUN
american_scientific_journal-2216	14	49	and	and	CCONJ
american_scientific_journal-2216	14	50	non	non	ADJ
american_scientific_journal-2216	14	51	-	-	ADJ
american_scientific_journal-2216	14	52	exponential	exponential	ADJ
american_scientific_journal-2216	14	53	relaxation	relaxation	NOUN
american_scientific_journal-2216	14	54	[	[	X
american_scientific_journal-2216	14	55	10	10	NUM
american_scientific_journal-2216	14	56	]	]	PUNCT
american_scientific_journal-2216	14	57	.	.	PUNCT
american_scientific_journal-2216	15	1	because	because	SCONJ
american_scientific_journal-2216	15	2	of	of	ADP
american_scientific_journal-2216	15	3	complexity	complexity	NOUN
american_scientific_journal-2216	15	4	in	in	ADP
american_scientific_journal-2216	15	5	the	the	DET
american_scientific_journal-2216	15	6	theoretic	theoretic	ADJ
american_scientific_journal-2216	15	7	analysis	analysis	NOUN
american_scientific_journal-2216	15	8	of	of	ADP
american_scientific_journal-2216	15	9	numerical	numerical	ADJ
american_scientific_journal-2216	15	10	approximation	approximation	NOUN
american_scientific_journal-2216	15	11	of	of	ADP
american_scientific_journal-2216	15	12	fractional	fractional	ADJ
american_scientific_journal-2216	15	13	systems	system	NOUN
american_scientific_journal-2216	15	14	,	,	PUNCT
american_scientific_journal-2216	15	15	the	the	DET
american_scientific_journal-2216	15	16	common	common	ADJ
american_scientific_journal-2216	15	17	approach	approach	NOUN
american_scientific_journal-2216	15	18	is	be	AUX
american_scientific_journal-2216	15	19	to	to	PART
american_scientific_journal-2216	15	20	apply	apply	VERB
american_scientific_journal-2216	15	21	the	the	DET
american_scientific_journal-2216	15	22	finite	finite	ADJ
american_scientific_journal-2216	15	23	difference	difference	NOUN
american_scientific_journal-2216	15	24	method	method	NOUN
american_scientific_journal-2216	15	25	to	to	PART
american_scientific_journal-2216	15	26	discretize	discretize	VERB
american_scientific_journal-2216	15	27	fractional	fractional	ADJ
american_scientific_journal-2216	15	28	derivative	derivative	ADJ
american_scientific_journal-2216	15	29	operators	operator	NOUN
american_scientific_journal-2216	15	30	,	,	PUNCT
american_scientific_journal-2216	15	31	and	and	CCONJ
american_scientific_journal-2216	15	32	then	then	ADV
american_scientific_journal-2216	15	33	obtain	obtain	VERB
american_scientific_journal-2216	15	34	the	the	DET
american_scientific_journal-2216	15	35	numerical	numerical	ADJ
american_scientific_journal-2216	15	36	solutions	solution	NOUN
american_scientific_journal-2216	15	37	of	of	ADP
american_scientific_journal-2216	15	38	the	the	DET
american_scientific_journal-2216	15	39	fractional	fractional	ADJ
american_scientific_journal-2216	15	40	partial	partial	ADJ
american_scientific_journal-2216	15	41	differential	differential	NOUN
american_scientific_journal-2216	15	42	equations	equation	NOUN
american_scientific_journal-2216	15	43	.	.	PUNCT
american_scientific_journal-2216	16	1	furthermore	furthermore	ADV
american_scientific_journal-2216	16	2	,	,	PUNCT
american_scientific_journal-2216	16	3	goloviznin	goloviznin	NOUN
american_scientific_journal-2216	16	4	and	and	CCONJ
american_scientific_journal-2216	16	5	his	his	PRON
american_scientific_journal-2216	16	6	colleagues	colleague	NOUN
american_scientific_journal-2216	17	1	[	[	X
american_scientific_journal-2216	17	2	11	11	NUM
american_scientific_journal-2216	17	3	]	]	PUNCT
american_scientific_journal-2216	17	4	developed	develop	VERB
american_scientific_journal-2216	17	5	a	a	DET
american_scientific_journal-2216	17	6	numerical	numerical	ADJ
american_scientific_journal-2216	17	7	method	method	NOUN
american_scientific_journal-2216	17	8	for	for	ADP
american_scientific_journal-2216	17	9	solving	solve	VERB
american_scientific_journal-2216	17	10	some	some	DET
american_scientific_journal-2216	17	11	1	1	NUM
american_scientific_journal-2216	17	12	-	-	PUNCT
american_scientific_journal-2216	17	13	d	d	NOUN
american_scientific_journal-2216	17	14	equations	equation	NOUN
american_scientific_journal-2216	17	15	with	with	ADP
american_scientific_journal-2216	17	16	fractional	fractional	ADJ
american_scientific_journal-2216	17	17	derivatives	derivative	NOUN
american_scientific_journal-2216	17	18	.	.	PUNCT
american_scientific_journal-2216	18	1	the	the	DET
american_scientific_journal-2216	18	2	paper	paper	NOUN
american_scientific_journal-2216	18	3	is	be	AUX
american_scientific_journal-2216	18	4	organized	organize	VERB
american_scientific_journal-2216	18	5	in	in	ADP
american_scientific_journal-2216	18	6	five	five	NUM
american_scientific_journal-2216	18	7	sections	section	NOUN
american_scientific_journal-2216	18	8	:	:	PUNCT
american_scientific_journal-2216	18	9	section	section	NOUN
american_scientific_journal-2216	18	10	2	2	NUM
american_scientific_journal-2216	18	11	describes	describe	VERB
american_scientific_journal-2216	18	12	the	the	DET
american_scientific_journal-2216	18	13	formulation	formulation	NOUN
american_scientific_journal-2216	18	14	of	of	ADP
american_scientific_journal-2216	18	15	the	the	DET
american_scientific_journal-2216	18	16	rotated	rotate	VERB
american_scientific_journal-2216	18	17	point	point	NOUN
american_scientific_journal-2216	18	18	iterative	iterative	NOUN
american_scientific_journal-2216	18	19	method	method	NOUN
american_scientific_journal-2216	18	20	for	for	ADP
american_scientific_journal-2216	18	21	solving	solve	VERB
american_scientific_journal-2216	18	22	the	the	DET
american_scientific_journal-2216	18	23	fractional	fractional	ADJ
american_scientific_journal-2216	18	24	poisson	poisson	NOUN
american_scientific_journal-2216	18	25	’s	’s	PART
american_scientific_journal-2216	18	26	equation	equation	NOUN
american_scientific_journal-2216	18	27	.	.	PUNCT
american_scientific_journal-2216	19	1	in	in	ADP
american_scientific_journal-2216	19	2	section	section	NOUN
american_scientific_journal-2216	19	3	3	3	NUM
american_scientific_journal-2216	19	4	,	,	PUNCT
american_scientific_journal-2216	19	5	the	the	DET
american_scientific_journal-2216	19	6	proposed	propose	VERB
american_scientific_journal-2216	19	7	accelerated	accelerate	VERB
american_scientific_journal-2216	19	8	version	version	NOUN
american_scientific_journal-2216	19	9	of	of	ADP
american_scientific_journal-2216	19	10	rotated	rotate	VERB
american_scientific_journal-2216	19	11	five	five	NUM
american_scientific_journal-2216	19	12	point	point	NOUN
american_scientific_journal-2216	19	13	’s	’s	PART
american_scientific_journal-2216	19	14	approximation	approximation	NOUN
american_scientific_journal-2216	19	15	method	method	NOUN
american_scientific_journal-2216	19	16	will	will	AUX
american_scientific_journal-2216	19	17	be	be	AUX
american_scientific_journal-2216	19	18	given	give	VERB
american_scientific_journal-2216	19	19	.	.	PUNCT
american_scientific_journal-2216	20	1	in	in	ADP
american_scientific_journal-2216	20	2	section	section	NOUN
american_scientific_journal-2216	20	3	4	4	NUM
american_scientific_journal-2216	20	4	,	,	PUNCT
american_scientific_journal-2216	20	5	the	the	DET
american_scientific_journal-2216	20	6	numerical	numerical	ADJ
american_scientific_journal-2216	20	7	results	result	NOUN
american_scientific_journal-2216	20	8	are	be	AUX
american_scientific_journal-2216	20	9	presented	present	VERB
american_scientific_journal-2216	20	10	in	in	ADP
american_scientific_journal-2216	20	11	order	order	NOUN
american_scientific_journal-2216	20	12	to	to	PART
american_scientific_journal-2216	20	13	show	show	VERB
american_scientific_journal-2216	20	14	the	the	DET
american_scientific_journal-2216	20	15	efficiency	efficiency	NOUN
american_scientific_journal-2216	20	16	of	of	ADP
american_scientific_journal-2216	20	17	the	the	DET
american_scientific_journal-2216	20	18	new	new	ADJ
american_scientific_journal-2216	20	19	proposed	propose	VERB
american_scientific_journal-2216	20	20	method	method	NOUN
american_scientific_journal-2216	20	21	.	.	PUNCT
american_scientific_journal-2216	21	1	finally	finally	ADV
american_scientific_journal-2216	21	2	,	,	PUNCT
american_scientific_journal-2216	21	3	the	the	DET
american_scientific_journal-2216	21	4	conclusion	conclusion	NOUN
american_scientific_journal-2216	21	5	is	be	AUX
american_scientific_journal-2216	21	6	given	give	VERB
american_scientific_journal-2216	21	7	in	in	ADP
american_scientific_journal-2216	21	8	section	section	NOUN
american_scientific_journal-2216	21	9	5	5	NUM
american_scientific_journal-2216	21	10	.	.	NOUN
american_scientific_journal-2216	21	11	2	2	NUM
american_scientific_journal-2216	21	12	.	.	X
american_scientific_journal-2216	21	13	formulation	formulation	NOUN
american_scientific_journal-2216	21	14	of	of	ADP
american_scientific_journal-2216	21	15	the	the	DET
american_scientific_journal-2216	21	16	rotated	rotate	VERB
american_scientific_journal-2216	21	17	point	point	NOUN
american_scientific_journal-2216	21	18	iterative	iterative	NOUN
american_scientific_journal-2216	21	19	method	method	NOUN
american_scientific_journal-2216	21	20	for	for	ADP
american_scientific_journal-2216	21	21	solving	solve	VERB
american_scientific_journal-2216	21	22	the	the	DET
american_scientific_journal-2216	21	23	fractional	fractional	ADJ
american_scientific_journal-2216	21	24	poisson	poisson	NOUN
american_scientific_journal-2216	21	25	’s	’s	PART
american_scientific_journal-2216	21	26	equation	equation	NOUN
american_scientific_journal-2216	21	27	consider	consider	VERB
american_scientific_journal-2216	21	28	the	the	DET
american_scientific_journal-2216	21	29	poisson	poisson	NOUN
american_scientific_journal-2216	21	30	’s	’s	PART
american_scientific_journal-2216	21	31	equation	equation	NOUN
american_scientific_journal-2216	21	32	in	in	ADP
american_scientific_journal-2216	21	33	the	the	DET
american_scientific_journal-2216	21	34	form	form	NOUN
american_scientific_journal-2216	21	35	:	:	PUNCT
american_scientific_journal-2216	21	36	(	(	PUNCT
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american_scientific_journal-2216	21	38	(	(	PUNCT
american_scientific_journal-2216	21	39	,	,	PUNCT
american_scientific_journal-2216	21	40	)	)	PUNCT
american_scientific_journal-2216	21	41	(	(	PUNCT
american_scientific_journal-2216	21	42	,	,	PUNCT
american_scientific_journal-2216	21	43	)	)	PUNCT
american_scientific_journal-2216	21	44	,	,	PUNCT
american_scientific_journal-2216	22	1	α	α	PROPN
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american_scientific_journal-2216	22	3	α	α	NOUN
american_scientific_journal-2216	22	4	α	α	PROPN
american_scientific_journal-2216	22	5	∂	∂	NOUN
american_scientific_journal-2216	22	6	∂	∂	NUM
american_scientific_journal-2216	22	7	−	−	PROPN
american_scientific_journal-2216	22	8	+	+	CCONJ
american_scientific_journal-2216	22	9	=	=	SYM
american_scientific_journal-2216	22	10	∂	∂	NUM
american_scientific_journal-2216	22	11	∂	∂	NUM
american_scientific_journal-2216	22	12	u	u	NOUN
american_scientific_journal-2216	22	13	x	x	PROPN
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american_scientific_journal-2216	22	16	x	x	X
american_scientific_journal-2216	22	17	y	y	NOUN
american_scientific_journal-2216	22	18	x	x	SYM
american_scientific_journal-2216	22	19	y	y	PROPN
american_scientific_journal-2216	22	20	(	(	PUNCT
american_scientific_journal-2216	22	21	,	,	PUNCT
american_scientific_journal-2216	22	22	)	)	PUNCT
american_scientific_journal-2216	22	23	∈x	∈x	VERB
american_scientific_journal-2216	22	24	y	y	PROPN
american_scientific_journal-2216	22	25	d	d	X
american_scientific_journal-2216	22	26	(	(	PUNCT
american_scientific_journal-2216	22	27	2.1	2.1	NUM
american_scientific_journal-2216	22	28	)	)	PUNCT
american_scientific_journal-2216	23	1	where	where	SCONJ
american_scientific_journal-2216	23	2	:	:	PUNCT
american_scientific_journal-2216	23	3	{	{	PUNCT
american_scientific_journal-2216	23	4	(	(	PUNCT
american_scientific_journal-2216	23	5	,	,	PUNCT
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american_scientific_journal-2216	23	7	:	:	PUNCT
american_scientific_journal-2216	23	8	(	(	PUNCT
american_scientific_journal-2216	23	9	,	,	PUNCT
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american_scientific_journal-2216	24	1	[	[	X
american_scientific_journal-2216	24	2	0	0	NUM
american_scientific_journal-2216	24	3	,	,	PUNCT
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american_scientific_journal-2216	25	1	[	[	X
american_scientific_journal-2216	25	2	0	0	NUM
american_scientific_journal-2216	25	3	,	,	PUNCT
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american_scientific_journal-2216	25	6	=	=	SYM
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american_scientific_journal-2216	25	9	x	x	PUNCT
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american_scientific_journal-2216	25	12	y	y	PROPN
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american_scientific_journal-2216	26	5	-	-	PUNCT
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american_scientific_journal-2216	26	10	0	0	NUM
american_scientific_journal-2216	26	11	,	,	PUNCT
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american_scientific_journal-2216	26	15	0	0	NUM
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american_scientific_journal-2216	26	20	0,u	0,u	VERB
american_scientific_journal-2216	27	1	y	y	PROPN
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american_scientific_journal-2216	27	4	u	u	NOUN
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american_scientific_journal-2216	27	6	y=	y=	NUM
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american_scientific_journal-2216	28	1	=	=	PUNCT
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american_scientific_journal-2216	28	3	(	(	PUNCT
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american_scientific_journal-2216	29	2	8	8	NUM
american_scientific_journal-2216	29	3	]	]	PUNCT
american_scientific_journal-2216	29	4	considered	consider	VERB
american_scientific_journal-2216	29	5	the	the	DET
american_scientific_journal-2216	29	6	fractional	fractional	ADJ
american_scientific_journal-2216	29	7	poisson	poisson	NOUN
american_scientific_journal-2216	29	8	’s	’s	PART
american_scientific_journal-2216	29	9	equation	equation	NOUN
american_scientific_journal-2216	29	10	in	in	ADP
american_scientific_journal-2216	29	11	the	the	DET
american_scientific_journal-2216	29	12	form	form	NOUN
american_scientific_journal-2216	29	13	:	:	PUNCT
american_scientific_journal-2216	29	14	(	(	PUNCT
american_scientific_journal-2216	29	15	)	)	PUNCT
american_scientific_journal-2216	29	16	(	(	PUNCT
american_scientific_journal-2216	29	17	,	,	PUNCT
american_scientific_journal-2216	29	18	)	)	PUNCT
american_scientific_journal-2216	29	19	(	(	PUNCT
american_scientific_journal-2216	29	20	,	,	PUNCT
american_scientific_journal-2216	29	21	)	)	PUNCT
american_scientific_journal-2216	29	22	u	u	NOUN
american_scientific_journal-2216	29	23	x	x	X
american_scientific_journal-2216	29	24	y	y	NOUN
american_scientific_journal-2216	29	25	f	f	PROPN
american_scientific_journal-2216	29	26	x	x	X
american_scientific_journal-2216	29	27	y	y	NOUN
american_scientific_journal-2216	29	28	x	x	PUNCT
american_scientific_journal-2216	29	29	y	y	NOUN
american_scientific_journal-2216	29	30	α	α	NOUN
american_scientific_journal-2216	29	31	α	α	NOUN
american_scientific_journal-2216	29	32	α	α	NOUN
american_scientific_journal-2216	29	33	α	α	PROPN
american_scientific_journal-2216	29	34	∂	∂	NOUN
american_scientific_journal-2216	29	35	∂	∂	NUM
american_scientific_journal-2216	29	36	−	−	PROPN
american_scientific_journal-2216	30	1	+	+	CCONJ
american_scientific_journal-2216	30	2	=	=	SYM
american_scientific_journal-2216	30	3	∂	∂	NUM
american_scientific_journal-2216	30	4	∂	∂	NOUN
american_scientific_journal-2216	30	5	,	,	PUNCT
american_scientific_journal-2216	30	6	where	where	SCONJ
american_scientific_journal-2216	30	7	1	1	NUM
american_scientific_journal-2216	30	8	2,α≤	2,α≤	NUM
american_scientific_journal-2216	30	9	≤	≤	NOUN
american_scientific_journal-2216	30	10	(	(	PUNCT
american_scientific_journal-2216	30	11	2.2	2.2	NUM
american_scientific_journal-2216	30	12	)	)	PUNCT
american_scientific_journal-2216	30	13	subject	subject	NOUN
american_scientific_journal-2216	30	14	to	to	ADP
american_scientific_journal-2216	30	15	the	the	DET
american_scientific_journal-2216	30	16	same	same	ADJ
american_scientific_journal-2216	30	17	dirichlet	dirichlet	ADJ
american_scientific_journal-2216	30	18	-	-	PUNCT
american_scientific_journal-2216	30	19	boundary	boundary	ADJ
american_scientific_journal-2216	30	20	conditions	condition	NOUN
american_scientific_journal-2216	30	21	of	of	ADP
american_scientific_journal-2216	30	22	equation	equation	NOUN
american_scientific_journal-2216	30	23	(	(	PUNCT
american_scientific_journal-2216	30	24	2.1	2.1	NUM
american_scientific_journal-2216	30	25	)	)	PUNCT
american_scientific_journal-2216	30	26	.	.	PUNCT
american_scientific_journal-2216	31	1	now	now	ADV
american_scientific_journal-2216	31	2	,	,	PUNCT
american_scientific_journal-2216	31	3	we	we	PRON
american_scientific_journal-2216	31	4	consider	consider	VERB
american_scientific_journal-2216	31	5	the	the	DET
american_scientific_journal-2216	31	6	corresponding	corresponding	ADJ
american_scientific_journal-2216	31	7	fractional	fractional	ADJ
american_scientific_journal-2216	31	8	order	order	NOUN
american_scientific_journal-2216	31	9	elliptic	elliptic	ADJ
american_scientific_journal-2216	31	10	by	by	ADP
american_scientific_journal-2216	31	11	the	the	DET
american_scientific_journal-2216	31	12	form	form	NOUN
american_scientific_journal-2216	31	13	:	:	PUNCT
american_scientific_journal-2216	31	14	(	(	PUNCT
american_scientific_journal-2216	31	15	)	)	PUNCT
american_scientific_journal-2216	31	16	(	(	PUNCT
american_scientific_journal-2216	31	17	,	,	PUNCT
american_scientific_journal-2216	31	18	)	)	PUNCT
american_scientific_journal-2216	31	19	(	(	PUNCT
american_scientific_journal-2216	31	20	,	,	PUNCT
american_scientific_journal-2216	31	21	)	)	PUNCT
american_scientific_journal-2216	31	22	∂	∂	NUM
american_scientific_journal-2216	31	23	∂	∂	NUM
american_scientific_journal-2216	31	24	−	−	PROPN
american_scientific_journal-2216	32	1	+	+	CCONJ
american_scientific_journal-2216	32	2	=	=	SYM
american_scientific_journal-2216	32	3	∂	∂	NUM
american_scientific_journal-2216	32	4	∂	∂	NUM
american_scientific_journal-2216	32	5	u	u	NOUN
american_scientific_journal-2216	32	6	x	x	PROPN
american_scientific_journal-2216	32	7	y	y	NOUN
american_scientific_journal-2216	32	8	f	f	PROPN
american_scientific_journal-2216	32	9	x	x	X
american_scientific_journal-2216	32	10	y	y	NOUN
american_scientific_journal-2216	32	11	x	x	X
american_scientific_journal-2216	32	12	y	y	NOUN
american_scientific_journal-2216	32	13	α	α	X
american_scientific_journal-2216	32	14	β	β	X
american_scientific_journal-2216	32	15	α	α	X
american_scientific_journal-2216	32	16	β	β	X
american_scientific_journal-2216	32	17	,	,	PUNCT
american_scientific_journal-2216	32	18	where	where	SCONJ
american_scientific_journal-2216	32	19	(	(	PUNCT
american_scientific_journal-2216	32	20	1	1	NUM
american_scientific_journal-2216	32	21	,	,	PUNCT
american_scientific_journal-2216	32	22	2)α	2)α	NUM
american_scientific_journal-2216	32	23	β≤	β≤	PROPN
american_scientific_journal-2216	32	24	≤	≤	NOUN
american_scientific_journal-2216	32	25	(	(	PUNCT
american_scientific_journal-2216	32	26	2.3	2.3	NUM
american_scientific_journal-2216	32	27	)	)	PUNCT
american_scientific_journal-2216	32	28	it	it	PRON
american_scientific_journal-2216	32	29	can	can	AUX
american_scientific_journal-2216	32	30	be	be	AUX
american_scientific_journal-2216	32	31	seen	see	VERB
american_scientific_journal-2216	32	32	that	that	SCONJ
american_scientific_journal-2216	32	33	equation	equation	NOUN
american_scientific_journal-2216	32	34	(	(	PUNCT
american_scientific_journal-2216	32	35	2.3	2.3	NUM
american_scientific_journal-2216	32	36	)	)	PUNCT
american_scientific_journal-2216	32	37	is	be	AUX
american_scientific_journal-2216	32	38	a	a	DET
american_scientific_journal-2216	32	39	generalization	generalization	NOUN
american_scientific_journal-2216	32	40	to	to	ADP
american_scientific_journal-2216	32	41	equations	equation	NOUN
american_scientific_journal-2216	32	42	(	(	PUNCT
american_scientific_journal-2216	32	43	2.1	2.1	NUM
american_scientific_journal-2216	32	44	)	)	PUNCT
american_scientific_journal-2216	32	45	and	and	CCONJ
american_scientific_journal-2216	32	46	(	(	PUNCT
american_scientific_journal-2216	32	47	2.2	2.2	NUM
american_scientific_journal-2216	32	48	)	)	PUNCT
american_scientific_journal-2216	32	49	.	.	PUNCT
american_scientific_journal-2216	33	1	the	the	DET
american_scientific_journal-2216	33	2	simplest	simple	ADJ
american_scientific_journal-2216	33	3	standard	standard	ADJ
american_scientific_journal-2216	33	4	five	five	NUM
american_scientific_journal-2216	33	5	-	-	PUNCT
american_scientific_journal-2216	33	6	point	point	NOUN
american_scientific_journal-2216	33	7	finite	finite	ADJ
american_scientific_journal-2216	33	8	difference	difference	NOUN
american_scientific_journal-2216	33	9	approximation	approximation	NOUN
american_scientific_journal-2216	33	10	of	of	ADP
american_scientific_journal-2216	33	11	the	the	DET
american_scientific_journal-2216	33	12	laplacian	laplacian	NOUN
american_scientific_journal-2216	33	13	is	be	AUX
american_scientific_journal-2216	33	14	american	american	ADJ
american_scientific_journal-2216	33	15	scientific	scientific	ADJ
american_scientific_journal-2216	33	16	research	research	NOUN
american_scientific_journal-2216	33	17	journal	journal	NOUN
american_scientific_journal-2216	33	18	for	for	ADP
american_scientific_journal-2216	33	19	engineering	engineering	NOUN
american_scientific_journal-2216	33	20	,	,	PUNCT
american_scientific_journal-2216	33	21	technology	technology	NOUN
american_scientific_journal-2216	33	22	,	,	PUNCT
american_scientific_journal-2216	33	23	and	and	CCONJ
american_scientific_journal-2216	33	24	sciences	science	NOUN
american_scientific_journal-2216	33	25	(	(	PUNCT
american_scientific_journal-2216	33	26	asrjets	asrjet	NOUN
american_scientific_journal-2216	33	27	)	)	PUNCT
american_scientific_journal-2216	33	28	(	(	PUNCT
american_scientific_journal-2216	33	29	2016	2016	NUM
american_scientific_journal-2216	33	30	)	)	PUNCT
american_scientific_journal-2216	33	31	volume	volume	NOUN
american_scientific_journal-2216	33	32	26	26	NUM
american_scientific_journal-2216	33	33	,	,	PUNCT
american_scientific_journal-2216	33	34	no	no	DET
american_scientific_journal-2216	33	35	1	1	NUM
american_scientific_journal-2216	33	36	,	,	PUNCT
american_scientific_journal-2216	33	37	pp	pp	ADV
american_scientific_journal-2216	33	38	261	261	NUM
american_scientific_journal-2216	33	39	-	-	SYM
american_scientific_journal-2216	33	40	270	270	NUM
american_scientific_journal-2216	33	41	263	263	NUM
american_scientific_journal-2216	33	42	ij	ij	NOUN
american_scientific_journal-2216	33	43	jiijjijiijji	jiijjijiijji	NOUN
american_scientific_journal-2216	34	1	fho	fho	VERB
american_scientific_journal-2216	34	2	y	y	PROPN
american_scientific_journal-2216	34	3	u	u	NOUN
american_scientific_journal-2216	34	4	x	x	PROPN
american_scientific_journal-2216	34	5	uh	uh	INTJ
american_scientific_journal-2216	34	6	h	h	NOUN
american_scientific_journal-2216	34	7	uuu	uuu	PROPN
american_scientific_journal-2216	34	8	h	h	PROPN
american_scientific_journal-2216	34	9	uuu	uuu	PROPN
american_scientific_journal-2216	35	1	=	=	X
american_scientific_journal-2216	35	2	−	−	PROPN
american_scientific_journal-2216	35	3			PUNCT
american_scientific_journal-2216	36	1			PROPN
american_scientific_journal-2216	37	1			INTJ
american_scientific_journal-2216	37	2			NOUN
american_scientific_journal-2216	37	3			VERB
american_scientific_journal-2216	37	4	∂	∂	NUM
american_scientific_journal-2216	37	5	∂	∂	NUM
american_scientific_journal-2216	37	6	+	+	NUM
american_scientific_journal-2216	37	7	∂	∂	NUM
american_scientific_journal-2216	37	8	∂	∂	NOUN
american_scientific_journal-2216	37	9	−	−	NOUN
american_scientific_journal-2216	38	1	+	+	NOUN
american_scientific_journal-2216	38	2	−	−	NOUN
american_scientific_journal-2216	38	3	+	+	X
american_scientific_journal-2216	39	1	+	+	ADJ
american_scientific_journal-2216	39	2	−	−	PROPN
american_scientific_journal-2216	39	3	−+−+	−+−+	NOUN
american_scientific_journal-2216	39	4	)	)	PUNCT
american_scientific_journal-2216	39	5	(	(	PUNCT
american_scientific_journal-2216	39	6	12	12	NUM
american_scientific_journal-2216	39	7	122	122	NUM
american_scientific_journal-2216	39	8	4	4	NUM
american_scientific_journal-2216	39	9	4	4	NUM
american_scientific_journal-2216	39	10	4	4	NUM
american_scientific_journal-2216	39	11	4	4	NUM
american_scientific_journal-2216	39	12	4	4	NUM
american_scientific_journal-2216	39	13	2	2	NUM
american_scientific_journal-2216	39	14	2	2	NUM
american_scientific_journal-2216	39	15	1,1	1,1	NUM
american_scientific_journal-2216	39	16	,	,	PUNCT
american_scientific_journal-2216	39	17	2	2	NUM
american_scientific_journal-2216	39	18	,	,	PUNCT
american_scientific_journal-2216	39	19	1,1	1,1	NUM
american_scientific_journal-2216	39	20	(	(	PUNCT
american_scientific_journal-2216	39	21	2.4	2.4	NUM
american_scientific_journal-2216	39	22	)	)	PUNCT
american_scientific_journal-2216	39	23	here	here	ADV
american_scientific_journal-2216	39	24	,	,	PUNCT
american_scientific_journal-2216	39	25	)	)	PUNCT
american_scientific_journal-2216	39	26	,	,	PUNCT
american_scientific_journal-2216	39	27	(	(	PUNCT
american_scientific_journal-2216	39	28	jiij	jiij	PROPN
american_scientific_journal-2216	39	29	yxuu	yxuu	PROPN
american_scientific_journal-2216	39	30	=	=	PUNCT
american_scientific_journal-2216	39	31	.	.	PUNCT
american_scientific_journal-2216	40	1	another	another	DET
american_scientific_journal-2216	40	2	approximation	approximation	NOUN
american_scientific_journal-2216	40	3	to	to	ADP
american_scientific_journal-2216	40	4	equation	equation	NOUN
american_scientific_journal-2216	40	5	(	(	PUNCT
american_scientific_journal-2216	40	6	2.1	2.1	NUM
american_scientific_journal-2216	40	7	)	)	PUNCT
american_scientific_journal-2216	40	8	can	can	AUX
american_scientific_journal-2216	40	9	be	be	AUX
american_scientific_journal-2216	40	10	derived	derive	VERB
american_scientific_journal-2216	40	11	from	from	ADP
american_scientific_journal-2216	40	12	the	the	DET
american_scientific_journal-2216	40	13	rotated	rotated	ADJ
american_scientific_journal-2216	40	14	five	five	NUM
american_scientific_journal-2216	40	15	-	-	PUNCT
american_scientific_journal-2216	40	16	point	point	NOUN
american_scientific_journal-2216	40	17	finite	finite	ADJ
american_scientific_journal-2216	40	18	difference	difference	NOUN
american_scientific_journal-2216	40	19	approximation	approximation	NOUN
american_scientific_journal-2216	40	20	to	to	PART
american_scientific_journal-2216	40	21	give	give	VERB
american_scientific_journal-2216	40	22	[	[	PUNCT
american_scientific_journal-2216	40	23	1	1	NUM
american_scientific_journal-2216	40	24	]	]	SYM
american_scientific_journal-2216	40	25	1	1	NUM
american_scientific_journal-2216	40	26	,	,	PUNCT
american_scientific_journal-2216	40	27	1	1	NUM
american_scientific_journal-2216	40	28	1	1	NUM
american_scientific_journal-2216	40	29	,	,	PUNCT
american_scientific_journal-2216	40	30	1	1	NUM
american_scientific_journal-2216	40	31	1	1	NUM
american_scientific_journal-2216	40	32	,	,	PUNCT
american_scientific_journal-2216	40	33	1	1	NUM
american_scientific_journal-2216	40	34	1	1	NUM
american_scientific_journal-2216	40	35	,	,	PUNCT
american_scientific_journal-2216	40	36	1	1	NUM
american_scientific_journal-2216	40	37	2	2	NUM
american_scientific_journal-2216	40	38	4	4	NUM
american_scientific_journal-2216	40	39	4	4	NUM
american_scientific_journal-2216	40	40	4	4	NUM
american_scientific_journal-2216	40	41	2	2	NUM
american_scientific_journal-2216	40	42	4	4	NUM
american_scientific_journal-2216	40	43	2	2	NUM
american_scientific_journal-2216	40	44	2	2	NUM
american_scientific_journal-2216	40	45	4	4	NUM
american_scientific_journal-2216	40	46	4	4	NUM
american_scientific_journal-2216	40	47	4	4	NUM
american_scientific_journal-2216	40	48	2	2	NUM
american_scientific_journal-2216	40	49	1	1	NUM
american_scientific_journal-2216	40	50	1	1	NUM
american_scientific_journal-2216	40	51	(	(	PUNCT
american_scientific_journal-2216	40	52	)	)	PUNCT
american_scientific_journal-2216	40	53	.	.	PUNCT
american_scientific_journal-2216	41	1	2	2	NUM
american_scientific_journal-2216	41	2	12	12	NUM
american_scientific_journal-2216	42	1	i	i	PRON
american_scientific_journal-2216	42	2	j	j	PROPN
american_scientific_journal-2216	43	1	i	i	PRON
american_scientific_journal-2216	43	2	j	j	VERB
american_scientific_journal-2216	44	1	i	i	PRON
american_scientific_journal-2216	44	2	j	j	VERB
american_scientific_journal-2216	45	1	i	i	PRON
american_scientific_journal-2216	45	2	j	j	PROPN
american_scientific_journal-2216	46	1	ij	ij	INTJ
american_scientific_journal-2216	46	2	ij	ij	INTJ
american_scientific_journal-2216	46	3	u	u	NOUN
american_scientific_journal-2216	46	4	u	u	X
american_scientific_journal-2216	46	5	u	u	X
american_scientific_journal-2216	46	6	u	u	NOUN
american_scientific_journal-2216	46	7	u	u	NOUN
american_scientific_journal-2216	46	8	h	h	NOUN
american_scientific_journal-2216	46	9	u	u	NOUN
american_scientific_journal-2216	46	10	u	u	NOUN
american_scientific_journal-2216	46	11	uh	uh	INTJ
american_scientific_journal-2216	46	12	o	o	NOUN
american_scientific_journal-2216	47	1	h	h	NOUN
american_scientific_journal-2216	48	1	f	f	NOUN
american_scientific_journal-2216	48	2	x	x	X
american_scientific_journal-2216	48	3	y	y	NOUN
american_scientific_journal-2216	48	4	x	x	PUNCT
american_scientific_journal-2216	48	5	y	y	PROPN
american_scientific_journal-2216	48	6	+	+	PUNCT
american_scientific_journal-2216	49	1	+	+	CCONJ
american_scientific_journal-2216	49	2	−	−	ADP
american_scientific_journal-2216	49	3	−	−	PROPN
american_scientific_journal-2216	50	1	+	+	CCONJ
american_scientific_journal-2216	50	2	−	−	PROPN
american_scientific_journal-2216	50	3	−	−	PROPN
american_scientific_journal-2216	51	1	+	+	NOUN
american_scientific_journal-2216	51	2	+	+	PROPN
american_scientific_journal-2216	51	3	+	+	ADJ
american_scientific_journal-2216	51	4	+	+	CCONJ
american_scientific_journal-2216	51	5	−	−	NOUN
american_scientific_journal-2216	51	6			VERB
american_scientific_journal-2216	51	7			PROPN
american_scientific_journal-2216	51	8	∂	∂	PROPN
american_scientific_journal-2216	51	9	∂	∂	NOUN
american_scientific_journal-2216	51	10	∂	∂	NOUN
american_scientific_journal-2216	51	11	−	−	PROPN
american_scientific_journal-2216	52	1	+	+	CCONJ
american_scientific_journal-2216	52	2	+	+	NUM
american_scientific_journal-2216	52	3	−	−	NOUN
american_scientific_journal-2216	52	4	=	=	SYM
american_scientific_journal-2216	52	5			NOUN
american_scientific_journal-2216	52	6			ADJ
american_scientific_journal-2216	52	7			NOUN
american_scientific_journal-2216	52	8	∂	∂	NUM
american_scientific_journal-2216	52	9	∂	∂	NUM
american_scientific_journal-2216	52	10	∂	∂	NUM
american_scientific_journal-2216	52	11	∂	∂	NOUN
american_scientific_journal-2216	52	12			NOUN
american_scientific_journal-2216	52	13			NOUN
american_scientific_journal-2216	52	14			PROPN
american_scientific_journal-2216	52	15	(	(	PUNCT
american_scientific_journal-2216	52	16	2.5	2.5	NUM
american_scientific_journal-2216	52	17	)	)	PUNCT
american_scientific_journal-2216	52	18	in	in	ADP
american_scientific_journal-2216	52	19	order	order	NOUN
american_scientific_journal-2216	52	20	to	to	PART
american_scientific_journal-2216	52	21	obtain	obtain	VERB
american_scientific_journal-2216	52	22	the	the	DET
american_scientific_journal-2216	52	23	finite	finite	ADJ
american_scientific_journal-2216	52	24	difference	difference	NOUN
american_scientific_journal-2216	52	25	approximation	approximation	NOUN
american_scientific_journal-2216	52	26	of	of	ADP
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american_scientific_journal-2216	53	1	≈	≈	PROPN
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american_scientific_journal-2216	57	4	u	u	X
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american_scientific_journal-2216	57	7	u	u	X
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american_scientific_journal-2216	57	20	)	)	PUNCT
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american_scientific_journal-2216	57	25	αα	αα	ADP
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american_scientific_journal-2216	57	27	+	+	PUNCT
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american_scientific_journal-2216	62	7	u	u	X
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american_scientific_journal-2216	62	45	1	1	NUM
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american_scientific_journal-2216	62	54	,	,	PUNCT
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american_scientific_journal-2216	63	7	αα	αα	ADP
american_scientific_journal-2216	63	8	+	+	PUNCT
american_scientific_journal-2216	64	1	−	−	X
american_scientific_journal-2216	64	2	+	+	NUM
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american_scientific_journal-2216	65	1	≈	≈	PROPN
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american_scientific_journal-2216	72	2	u	u	X
american_scientific_journal-2216	72	3	d	d	X
american_scientific_journal-2216	72	4	u	u	X
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american_scientific_journal-2216	72	16	,	,	PUNCT
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american_scientific_journal-2216	72	36	+	+	PUNCT
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american_scientific_journal-2216	72	40	+	+	SYM
american_scientific_journal-2216	73	1	≈	≈	PROPN
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american_scientific_journal-2216	79	16	-	-	PUNCT
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american_scientific_journal-2216	88	2	j	j	PROPN
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american_scientific_journal-2216	89	2	u	u	X
american_scientific_journal-2216	89	3	u	u	X
american_scientific_journal-2216	89	4	u	u	X
american_scientific_journal-2216	89	5	u	u	NOUN
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american_scientific_journal-2216	89	11	αα	αα	PROPN
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american_scientific_journal-2216	89	14	can	can	AUX
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american_scientific_journal-2216	89	21	american	american	PROPN
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american_scientific_journal-2216	89	40	,	,	PUNCT
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american_scientific_journal-2216	89	42	1	1	NUM
american_scientific_journal-2216	89	43	,	,	PUNCT
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american_scientific_journal-2216	90	2	+	+	CCONJ
american_scientific_journal-2216	90	3	−−	−−	NOUN
american_scientific_journal-2216	90	4	−	−	NOUN
american_scientific_journal-2216	90	5	−	−	NOUN
american_scientific_journal-2216	90	6	−	−	PROPN
american_scientific_journal-2216	91	1	=	=	SYM
american_scientific_journal-2216	91	2	−ij	−ij	NOUN
american_scientific_journal-2216	92	1	i	i	PRON
american_scientific_journal-2216	92	2	j	j	PROPN
american_scientific_journal-2216	93	1	i	i	PRON
american_scientific_journal-2216	93	2	j	j	VERB
american_scientific_journal-2216	94	1	i	i	PRON
american_scientific_journal-2216	94	2	j	j	VERB
american_scientific_journal-2216	95	1	i	i	PRON
american_scientific_journal-2216	95	2	j	j	VERB
american_scientific_journal-2216	96	1	iju	iju	NUM
american_scientific_journal-2216	96	2	u	u	NOUN
american_scientific_journal-2216	96	3	u	u	NOUN
american_scientific_journal-2216	96	4	u	u	NOUN
american_scientific_journal-2216	96	5	u	u	NOUN
american_scientific_journal-2216	96	6	h	h	NOUN
american_scientific_journal-2216	96	7	f	f	PROPN
american_scientific_journal-2216	96	8	(	(	PUNCT
american_scientific_journal-2216	96	9	2.8	2.8	NUM
american_scientific_journal-2216	96	10	)	)	PUNCT
american_scientific_journal-2216	96	11	by	by	ADP
american_scientific_journal-2216	96	12	the	the	DET
american_scientific_journal-2216	96	13	same	same	ADJ
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american_scientific_journal-2216	96	15	,	,	PUNCT
american_scientific_journal-2216	96	16	the	the	DET
american_scientific_journal-2216	96	17	rotated	rotate	VERB
american_scientific_journal-2216	96	18	five	five	NUM
american_scientific_journal-2216	96	19	-	-	PUNCT
american_scientific_journal-2216	96	20	point	point	NOUN
american_scientific_journal-2216	96	21	finite	finite	ADJ
american_scientific_journal-2216	96	22	difference	difference	NOUN
american_scientific_journal-2216	96	23	approximation	approximation	NOUN
american_scientific_journal-2216	96	24	can	can	AUX
american_scientific_journal-2216	96	25	be	be	AUX
american_scientific_journal-2216	96	26	written	write	VERB
american_scientific_journal-2216	96	27	as	as	ADP
american_scientific_journal-2216	96	28	:	:	PUNCT
american_scientific_journal-2216	96	29	1	1	NUM
american_scientific_journal-2216	96	30	,	,	PUNCT
american_scientific_journal-2216	96	31	1	1	NUM
american_scientific_journal-2216	96	32	1	1	NUM
american_scientific_journal-2216	96	33	,	,	PUNCT
american_scientific_journal-2216	96	34	1	1	NUM
american_scientific_journal-2216	96	35	1	1	NUM
american_scientific_journal-2216	96	36	,	,	PUNCT
american_scientific_journal-2216	96	37	1	1	NUM
american_scientific_journal-2216	96	38	1	1	NUM
american_scientific_journal-2216	96	39	,	,	PUNCT
american_scientific_journal-2216	96	40	14	14	NUM
american_scientific_journal-2216	96	41	(	(	PUNCT
american_scientific_journal-2216	96	42	3	3	X
american_scientific_journal-2216	96	43	)	)	PUNCT
american_scientific_journal-2216	96	44	αα+	αα+	NOUN
american_scientific_journal-2216	97	1	+	+	CCONJ
american_scientific_journal-2216	98	1	−	−	ADP
american_scientific_journal-2216	98	2	−	−	NOUN
american_scientific_journal-2216	98	3	−	−	PROPN
american_scientific_journal-2216	99	1	+	+	CCONJ
american_scientific_journal-2216	99	2	+	+	CCONJ
american_scientific_journal-2216	99	3	−−	−−	NOUN
american_scientific_journal-2216	99	4	−	−	NOUN
american_scientific_journal-2216	99	5	−	−	NOUN
american_scientific_journal-2216	99	6	−	−	PROPN
american_scientific_journal-2216	99	7	=	=	SYM
american_scientific_journal-2216	99	8	−ij	−ij	NOUN
american_scientific_journal-2216	100	1	i	i	PRON
american_scientific_journal-2216	100	2	j	j	PROPN
american_scientific_journal-2216	101	1	i	i	PRON
american_scientific_journal-2216	101	2	j	j	VERB
american_scientific_journal-2216	102	1	i	i	PRON
american_scientific_journal-2216	102	2	j	j	VERB
american_scientific_journal-2216	103	1	i	i	PRON
american_scientific_journal-2216	103	2	j	j	VERB
american_scientific_journal-2216	104	1	iju	iju	NUM
american_scientific_journal-2216	104	2	u	u	NOUN
american_scientific_journal-2216	104	3	u	u	NOUN
american_scientific_journal-2216	104	4	u	u	NOUN
american_scientific_journal-2216	104	5	u	u	NOUN
american_scientific_journal-2216	104	6	h	h	NOUN
american_scientific_journal-2216	104	7	f	f	PROPN
american_scientific_journal-2216	104	8	(	(	PUNCT
american_scientific_journal-2216	104	9	2.9	2.9	NUM
american_scientific_journal-2216	104	10	)	)	PUNCT
american_scientific_journal-2216	104	11	there	there	PRON
american_scientific_journal-2216	104	12	are	be	VERB
american_scientific_journal-2216	104	13	two	two	NUM
american_scientific_journal-2216	104	14	ways	way	NOUN
american_scientific_journal-2216	104	15	to	to	ADP
american_scientific_journal-2216	104	16	approximating	approximate	VERB
american_scientific_journal-2216	104	17	equation	equation	NOUN
american_scientific_journal-2216	104	18	(	(	PUNCT
american_scientific_journal-2216	104	19	2.3	2.3	NUM
american_scientific_journal-2216	104	20	)	)	PUNCT
american_scientific_journal-2216	104	21	,	,	PUNCT
american_scientific_journal-2216	104	22	the	the	DET
american_scientific_journal-2216	104	23	first	first	ADJ
american_scientific_journal-2216	104	24	one	one	NUM
american_scientific_journal-2216	104	25	by	by	ADP
american_scientific_journal-2216	104	26	using	use	VERB
american_scientific_journal-2216	104	27	caputo	caputo	PROPN
american_scientific_journal-2216	104	28	’s	’s	PART
american_scientific_journal-2216	104	29	formula	formula	NOUN
american_scientific_journal-2216	104	30	which	which	PRON
american_scientific_journal-2216	104	31	is	be	AUX
american_scientific_journal-2216	104	32	replaced	replace	VERB
american_scientific_journal-2216	104	33	by	by	ADP
american_scientific_journal-2216	104	34	a	a	DET
american_scientific_journal-2216	104	35	finite	finite	ADJ
american_scientific_journal-2216	104	36	sum	sum	NOUN
american_scientific_journal-2216	104	37	of	of	ADP
american_scientific_journal-2216	104	38	integrals	integral	NOUN
american_scientific_journal-2216	104	39	at	at	ADP
american_scientific_journal-2216	104	40	the	the	DET
american_scientific_journal-2216	104	41	discretization	discretization	NOUN
american_scientific_journal-2216	104	42	points	point	NOUN
american_scientific_journal-2216	104	43	,	,	PUNCT
american_scientific_journal-2216	104	44	and	and	CCONJ
american_scientific_journal-2216	104	45	approximate	approximate	VERB
american_scientific_journal-2216	104	46	the	the	DET
american_scientific_journal-2216	104	47	second	second	ADJ
american_scientific_journal-2216	104	48	order	order	NOUN
american_scientific_journal-2216	104	49	derivative	derivative	NOUN
american_scientific_journal-2216	104	50	by	by	ADP
american_scientific_journal-2216	104	51	using	use	VERB
american_scientific_journal-2216	104	52	the	the	DET
american_scientific_journal-2216	104	53	standard	standard	ADJ
american_scientific_journal-2216	104	54	five	five	NUM
american_scientific_journal-2216	104	55	-	-	PUNCT
american_scientific_journal-2216	104	56	point	point	NOUN
american_scientific_journal-2216	104	57	finite	finite	ADJ
american_scientific_journal-2216	104	58	difference	difference	NOUN
american_scientific_journal-2216	104	59	formula	formula	NOUN
american_scientific_journal-2216	104	60	(	(	PUNCT
american_scientific_journal-2216	104	61	2.8	2.8	NUM
american_scientific_journal-2216	104	62	)	)	PUNCT
american_scientific_journal-2216	104	63	or	or	CCONJ
american_scientific_journal-2216	104	64	rotated	rotate	VERB
american_scientific_journal-2216	104	65	five	five	NUM
american_scientific_journal-2216	104	66	-	-	PUNCT
american_scientific_journal-2216	104	67	point	point	NOUN
american_scientific_journal-2216	104	68	finite	finite	ADJ
american_scientific_journal-2216	104	69	difference	difference	NOUN
american_scientific_journal-2216	104	70	formula	formula	NOUN
american_scientific_journal-2216	104	71	(	(	PUNCT
american_scientific_journal-2216	104	72	2.9	2.9	NUM
american_scientific_journal-2216	104	73	)	)	PUNCT
american_scientific_journal-2216	104	74	.	.	PUNCT
american_scientific_journal-2216	105	1	if	if	SCONJ
american_scientific_journal-2216	105	2	the	the	DET
american_scientific_journal-2216	105	3	standard	standard	ADJ
american_scientific_journal-2216	105	4	five	five	NUM
american_scientific_journal-2216	105	5	-	-	PUNCT
american_scientific_journal-2216	105	6	point	point	NOUN
american_scientific_journal-2216	105	7	finite	finite	ADJ
american_scientific_journal-2216	105	8	difference	difference	NOUN
american_scientific_journal-2216	105	9	is	be	AUX
american_scientific_journal-2216	105	10	used	use	VERB
american_scientific_journal-2216	105	11	,	,	PUNCT
american_scientific_journal-2216	105	12	then	then	ADV
american_scientific_journal-2216	105	13	the	the	DET
american_scientific_journal-2216	105	14	finite	finite	ADJ
american_scientific_journal-2216	105	15	difference	difference	NOUN
american_scientific_journal-2216	105	16	formula	formula	NOUN
american_scientific_journal-2216	105	17	of	of	ADP
american_scientific_journal-2216	105	18	caputo	caputo	PROPN
american_scientific_journal-2216	105	19	’s	’s	PART
american_scientific_journal-2216	105	20	fractional	fractional	ADJ
american_scientific_journal-2216	105	21	derivative	derivative	NOUN
american_scientific_journal-2216	105	22	will	will	AUX
american_scientific_journal-2216	105	23	take	take	VERB
american_scientific_journal-2216	105	24	the	the	DET
american_scientific_journal-2216	105	25	form	form	NOUN
american_scientific_journal-2216	105	26	:	:	PUNCT
american_scientific_journal-2216	105	27	1	1	NUM
american_scientific_journal-2216	105	28	1	1	NUM
american_scientific_journal-2216	105	29	2	2	NUM
american_scientific_journal-2216	105	30	2	2	NUM
american_scientific_journal-2216	105	31	1	1	NUM
american_scientific_journal-2216	105	32	0	0	NUM
american_scientific_journal-2216	105	33	2	2	NUM
american_scientific_journal-2216	105	34	0	0	NUM
american_scientific_journal-2216	105	35	1	1	NUM
american_scientific_journal-2216	105	36	(	(	PUNCT
american_scientific_journal-2216	105	37	,	,	PUNCT
american_scientific_journal-2216	105	38	)	)	PUNCT
american_scientific_journal-2216	105	39	(	(	PUNCT
american_scientific_journal-2216	105	40	,	,	PUNCT
american_scientific_journal-2216	105	41	)	)	PUNCT
american_scientific_journal-2216	105	42	(	(	PUNCT
american_scientific_journal-2216	105	43	)	)	PUNCT
american_scientific_journal-2216	105	44	(	(	PUNCT
american_scientific_journal-2216	105	45	2	2	NUM
american_scientific_journal-2216	105	46	)	)	PUNCT
american_scientific_journal-2216	106	1	+	+	CCONJ
american_scientific_journal-2216	106	2	−	−	ADP
american_scientific_journal-2216	106	3	−	−	NOUN
american_scientific_journal-2216	107	1	−	−	PROPN
american_scientific_journal-2216	107	2	=	=	SYM
american_scientific_journal-2216	107	3	∂	∂	NUM
american_scientific_journal-2216	107	4	≅	≅	NUM
american_scientific_journal-2216	107	5	−	−	PROPN
american_scientific_journal-2216	107	6	γ	γ	PROPN
american_scientific_journal-2216	107	7	−	−	PROPN
american_scientific_journal-2216	107	8	∂∑∫	∂∑∫	NOUN
american_scientific_journal-2216	108	1	k	k	PROPN
american_scientific_journal-2216	108	2	k	k	PROPN
american_scientific_journal-2216	109	1	i	i	PRON
american_scientific_journal-2216	109	2	xc	xc	X
american_scientific_journal-2216	110	1	x	x	PUNCT
american_scientific_journal-2216	110	2	x	x	PUNCT
american_scientific_journal-2216	110	3	k	k	X
american_scientific_journal-2216	110	4	u	u	NOUN
american_scientific_journal-2216	110	5	s	s	NOUN
american_scientific_journal-2216	110	6	yd	yd	NOUN
american_scientific_journal-2216	110	7	u	u	NOUN
american_scientific_journal-2216	110	8	x	x	PROPN
american_scientific_journal-2216	110	9	y	y	NOUN
american_scientific_journal-2216	110	10	x	x	SYM
american_scientific_journal-2216	110	11	s	s	PRON
american_scientific_journal-2216	110	12	ds	ds	X
american_scientific_journal-2216	110	13	s	s	NOUN
american_scientific_journal-2216	110	14	α	α	NOUN
american_scientific_journal-2216	110	15	α	α	NOUN
american_scientific_journal-2216	110	16	α	α	NOUN
american_scientific_journal-2216	110	17	1	1	NUM
american_scientific_journal-2216	110	18	0	0	NUM
american_scientific_journal-2216	110	19	,	,	PUNCT
american_scientific_journal-2216	110	20	1	1	NUM
american_scientific_journal-2216	110	21	,	,	PUNCT
american_scientific_journal-2216	110	22	,	,	PUNCT
american_scientific_journal-2216	110	23	1	1	NUM
american_scientific_journal-2216	110	24	,	,	PUNCT
american_scientific_journal-2216	110	25	0	0	NUM
american_scientific_journal-2216	110	26	1	1	NUM
american_scientific_journal-2216	110	27	(	(	PUNCT
american_scientific_journal-2216	110	28	2	2	NUM
american_scientific_journal-2216	110	29	)	)	PUNCT
american_scientific_journal-2216	110	30	(	(	PUNCT
american_scientific_journal-2216	110	31	3	3	X
american_scientific_journal-2216	110	32	)	)	PUNCT
american_scientific_journal-2216	110	33	−	−	NOUN
american_scientific_journal-2216	111	1	−	−	PROPN
american_scientific_journal-2216	112	1	+	+	CCONJ
american_scientific_journal-2216	112	2	−	−	PROPN
american_scientific_journal-2216	112	3	−	−	NOUN
american_scientific_journal-2216	113	1	−	−	PROPN
american_scientific_journal-2216	113	2	=	=	SYM
american_scientific_journal-2216	113	3	≅	≅	PROPN
american_scientific_journal-2216	113	4	−	−	PROPN
american_scientific_journal-2216	114	1	+	+	CCONJ
american_scientific_journal-2216	114	2	γ	γ	X
american_scientific_journal-2216	114	3	−	−	PROPN
american_scientific_journal-2216	114	4	∑	∑	PROPN
american_scientific_journal-2216	114	5	i	i	PRON
american_scientific_journal-2216	114	6	c	c	NOUN
american_scientific_journal-2216	114	7	x	x	VERB
american_scientific_journal-2216	115	1	i	i	PRON
american_scientific_journal-2216	115	2	j	j	PROPN
american_scientific_journal-2216	116	1	k	k	INTJ
american_scientific_journal-2216	117	1	i	i	PRON
american_scientific_journal-2216	117	2	k	k	PROPN
american_scientific_journal-2216	118	1	j	j	PROPN
american_scientific_journal-2216	119	1	i	i	PRON
american_scientific_journal-2216	119	2	k	k	PROPN
american_scientific_journal-2216	120	1	j	j	PROPN
american_scientific_journal-2216	121	1	i	i	PRON
american_scientific_journal-2216	121	2	k	k	PROPN
american_scientific_journal-2216	122	1	j	j	PROPN
american_scientific_journal-2216	123	1	k	k	PROPN
american_scientific_journal-2216	123	2	d	d	PUNCT
american_scientific_journal-2216	123	3	u	u	PROPN
american_scientific_journal-2216	123	4	b	b	PROPN
american_scientific_journal-2216	123	5	u	u	X
american_scientific_journal-2216	123	6	u	u	NOUN
american_scientific_journal-2216	123	7	u	u	NOUN
american_scientific_journal-2216	123	8	h	h	NOUN
american_scientific_journal-2216	123	9	α	α	NOUN
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american_scientific_journal-2216	123	13	(	(	PUNCT
american_scientific_journal-2216	123	14	2.10	2.10	NUM
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american_scientific_journal-2216	123	16	where	where	SCONJ
american_scientific_journal-2216	123	17	2	2	NUM
american_scientific_journal-2216	123	18	2	2	NUM
american_scientific_journal-2216	123	19	[	[	X
american_scientific_journal-2216	123	20	(	(	PUNCT
american_scientific_journal-2216	123	21	1	1	NUM
american_scientific_journal-2216	123	22	)	)	PUNCT
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american_scientific_journal-2216	123	24	−	−	PROPN
american_scientific_journal-2216	124	1	−=	−=	NOUN
american_scientific_journal-2216	124	2	+	+	CCONJ
american_scientific_journal-2216	124	3	−kb	−kb	PROPN
american_scientific_journal-2216	125	1	k	k	NOUN
american_scientific_journal-2216	125	2	kα	kα	PROPN
american_scientific_journal-2216	125	3	α	α	PROPN
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american_scientific_journal-2216	125	5	,	,	PUNCT
american_scientific_journal-2216	125	6	let	let	VERB
american_scientific_journal-2216	125	7	*	*	PUNCT
american_scientific_journal-2216	125	8	(	(	PUNCT
american_scientific_journal-2216	125	9	3	3	NUM
american_scientific_journal-2216	125	10	)	)	PUNCT
american_scientific_journal-2216	125	11	−	−	NOUN
american_scientific_journal-2216	126	1	=	=	PUNCT
american_scientific_journal-2216	126	2	γ	γ	X
american_scientific_journal-2216	126	3	−	−	PROPN
american_scientific_journal-2216	126	4	s	s	NOUN
american_scientific_journal-2216	126	5	s	s	X
american_scientific_journal-2216	126	6	bb	bb	NOUN
american_scientific_journal-2216	126	7	h	h	NOUN
american_scientific_journal-2216	126	8	β	β	X
american_scientific_journal-2216	126	9	β	β	X
american_scientific_journal-2216	126	10	β	β	X
american_scientific_journal-2216	126	11	,	,	PUNCT
american_scientific_journal-2216	126	12	(	(	PUNCT
american_scientific_journal-2216	126	13	3	3	X
american_scientific_journal-2216	126	14	)	)	PUNCT
american_scientific_journal-2216	126	15	−	−	NOUN
american_scientific_journal-2216	127	1	=	=	PUNCT
american_scientific_journal-2216	127	2	γ	γ	X
american_scientific_journal-2216	127	3	−	−	PROPN
american_scientific_journal-2216	128	1	k	k	NOUN
american_scientific_journal-2216	129	1	k	k	PROPN
american_scientific_journal-2216	130	1	bb	bb	INTJ
american_scientific_journal-2216	131	1	h	h	NOUN
american_scientific_journal-2216	132	1	α	α	NOUN
american_scientific_journal-2216	132	2	α	α	NOUN
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american_scientific_journal-2216	132	5	,	,	PUNCT
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american_scientific_journal-2216	132	7	finite	finite	ADJ
american_scientific_journal-2216	132	8	difference	difference	NOUN
american_scientific_journal-2216	132	9	scheme	scheme	NOUN
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american_scientific_journal-2216	132	11	equation	equation	NOUN
american_scientific_journal-2216	132	12	(	(	PUNCT
american_scientific_journal-2216	132	13	2.3	2.3	NUM
american_scientific_journal-2216	132	14	)	)	PUNCT
american_scientific_journal-2216	132	15	will	will	AUX
american_scientific_journal-2216	132	16	be	be	AUX
american_scientific_journal-2216	132	17	given	give	VERB
american_scientific_journal-2216	132	18	in	in	ADP
american_scientific_journal-2216	132	19	the	the	DET
american_scientific_journal-2216	132	20	form	form	NOUN
american_scientific_journal-2216	132	21	:	:	PUNCT
american_scientific_journal-2216	132	22	11	11	NUM
american_scientific_journal-2216	132	23	*	*	SYM
american_scientific_journal-2216	132	24	1	1	NUM
american_scientific_journal-2216	132	25	,	,	PUNCT
american_scientific_journal-2216	132	26	,	,	PUNCT
american_scientific_journal-2216	132	27	1	1	NUM
american_scientific_journal-2216	132	28	,	,	PUNCT
american_scientific_journal-2216	132	29	,	,	PUNCT
american_scientific_journal-2216	132	30	1	1	NUM
american_scientific_journal-2216	132	31	,	,	PUNCT
american_scientific_journal-2216	132	32	,	,	PUNCT
american_scientific_journal-2216	132	33	1	1	NUM
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american_scientific_journal-2216	171	3	∑	∑	PROPN
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american_scientific_journal-2216	178	9	-	-	PUNCT
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american_scientific_journal-2216	178	28	:	:	PUNCT
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american_scientific_journal-2216	179	2	+	+	NUM
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american_scientific_journal-2216	182	2	∑	∑	PUNCT
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american_scientific_journal-2216	204	27	represented	represent	VERB
american_scientific_journal-2216	204	28	as	as	ADP
american_scientific_journal-2216	204	29	in	in	ADP
american_scientific_journal-2216	204	30	figure	figure	NOUN
american_scientific_journal-2216	204	31	1	1	NUM
american_scientific_journal-2216	204	32	whereas	whereas	SCONJ
american_scientific_journal-2216	204	33	the	the	DET
american_scientific_journal-2216	204	34	computational	computational	ADJ
american_scientific_journal-2216	204	35	molecule	molecule	NOUN
american_scientific_journal-2216	204	36	of	of	ADP
american_scientific_journal-2216	204	37	standard	standard	ADJ
american_scientific_journal-2216	204	38	finite	finite	ADJ
american_scientific_journal-2216	204	39	difference	difference	NOUN
american_scientific_journal-2216	204	40	approximation	approximation	NOUN
american_scientific_journal-2216	204	41	for	for	ADP
american_scientific_journal-2216	204	42	fpde	fpde	NOUN
american_scientific_journal-2216	204	43	's	's	PART
american_scientific_journal-2216	204	44	can	can	AUX
american_scientific_journal-2216	204	45	be	be	AUX
american_scientific_journal-2216	204	46	represented	represent	VERB
american_scientific_journal-2216	204	47	as	as	ADP
american_scientific_journal-2216	204	48	in	in	ADP
american_scientific_journal-2216	204	49	figure	figure	NOUN
american_scientific_journal-2216	204	50	2	2	NUM
american_scientific_journal-2216	204	51	.	.	PUNCT
american_scientific_journal-2216	204	52	american	american	PROPN
american_scientific_journal-2216	204	53	scientific	scientific	ADJ
american_scientific_journal-2216	204	54	research	research	PROPN
american_scientific_journal-2216	204	55	journal	journal	NOUN
american_scientific_journal-2216	204	56	for	for	ADP
american_scientific_journal-2216	204	57	engineering	engineering	NOUN
american_scientific_journal-2216	204	58	,	,	PUNCT
american_scientific_journal-2216	204	59	technology	technology	NOUN
american_scientific_journal-2216	204	60	,	,	PUNCT
american_scientific_journal-2216	204	61	and	and	CCONJ
american_scientific_journal-2216	204	62	sciences	science	NOUN
american_scientific_journal-2216	204	63	(	(	PUNCT
american_scientific_journal-2216	204	64	asrjets	asrjet	NOUN
american_scientific_journal-2216	204	65	)	)	PUNCT
american_scientific_journal-2216	204	66	(	(	PUNCT
american_scientific_journal-2216	204	67	2016	2016	NUM
american_scientific_journal-2216	204	68	)	)	PUNCT
american_scientific_journal-2216	204	69	volume	volume	NOUN
american_scientific_journal-2216	204	70	26	26	NUM
american_scientific_journal-2216	204	71	,	,	PUNCT
american_scientific_journal-2216	204	72	no	no	DET
american_scientific_journal-2216	204	73	1	1	NUM
american_scientific_journal-2216	204	74	,	,	PUNCT
american_scientific_journal-2216	204	75	pp	pp	ADV
american_scientific_journal-2216	204	76	261	261	NUM
american_scientific_journal-2216	204	77	-	-	SYM
american_scientific_journal-2216	204	78	270	270	NUM
american_scientific_journal-2216	204	79	266	266	NUM
american_scientific_journal-2216	204	80	figure	figure	NOUN
american_scientific_journal-2216	204	81	1	1	NUM
american_scientific_journal-2216	204	82	:	:	PUNCT
american_scientific_journal-2216	204	83	computational	computational	ADJ
american_scientific_journal-2216	204	84	molecule	molecule	NOUN
american_scientific_journal-2216	204	85	of	of	ADP
american_scientific_journal-2216	204	86	eq	eq	PROPN
american_scientific_journal-2216	204	87	.	.	PUNCT
american_scientific_journal-2216	205	1	(	(	PUNCT
american_scientific_journal-2216	205	2	2.4	2.4	NUM
american_scientific_journal-2216	205	3	)	)	PUNCT
american_scientific_journal-2216	205	4	figure	figure	NOUN
american_scientific_journal-2216	205	5	2	2	NUM
american_scientific_journal-2216	205	6	:	:	PUNCT
american_scientific_journal-2216	205	7	computational	computational	ADJ
american_scientific_journal-2216	205	8	molecule	molecule	NOUN
american_scientific_journal-2216	205	9	of	of	ADP
american_scientific_journal-2216	205	10	eq	eq	PROPN
american_scientific_journal-2216	205	11	.	.	PUNCT
american_scientific_journal-2216	206	1	(	(	PUNCT
american_scientific_journal-2216	206	2	2.8	2.8	NUM
american_scientific_journal-2216	206	3	)	)	PUNCT
american_scientific_journal-2216	206	4	also	also	ADV
american_scientific_journal-2216	206	5	,	,	PUNCT
american_scientific_journal-2216	206	6	we	we	PRON
american_scientific_journal-2216	206	7	can	can	AUX
american_scientific_journal-2216	206	8	observe	observe	VERB
american_scientific_journal-2216	206	9	that	that	SCONJ
american_scientific_journal-2216	206	10	for	for	ADP
american_scientific_journal-2216	206	11	the	the	DET
american_scientific_journal-2216	206	12	rotated	rotate	VERB
american_scientific_journal-2216	206	13	five	five	NUM
american_scientific_journal-2216	206	14	-	-	PUNCT
american_scientific_journal-2216	206	15	point	point	NOUN
american_scientific_journal-2216	206	16	finite	finite	ADJ
american_scientific_journal-2216	206	17	difference	difference	NOUN
american_scientific_journal-2216	206	18	approximation	approximation	NOUN
american_scientific_journal-2216	206	19	the	the	DET
american_scientific_journal-2216	206	20	following	follow	VERB
american_scientific_journal-2216	206	21	transformations	transformation	NOUN
american_scientific_journal-2216	206	22	take	take	VERB
american_scientific_journal-2216	206	23	place	place	NOUN
american_scientific_journal-2216	206	24	1	1	NUM
american_scientific_journal-2216	206	25	1	1	NUM
american_scientific_journal-2216	206	26	1i	1i	NOUN
american_scientific_journal-2216	206	27	,	,	PUNCT
american_scientific_journal-2216	206	28	j	j	PROPN
american_scientific_journal-2216	206	29	i	i	PRON
american_scientific_journal-2216	206	30	,	,	PUNCT
american_scientific_journal-2216	206	31	j±	j±	PROPN
american_scientific_journal-2216	206	32	→	→	SYM
american_scientific_journal-2216	206	33	±	±	NUM
american_scientific_journal-2216	206	34	±	±	NUM
american_scientific_journal-2216	206	35	1	1	NUM
american_scientific_journal-2216	206	36	1	1	NUM
american_scientific_journal-2216	206	37	1i	1i	NOUN
american_scientific_journal-2216	206	38	,	,	PUNCT
american_scientific_journal-2216	206	39	j	j	PROPN
american_scientific_journal-2216	207	1	i	i	PRON
american_scientific_journal-2216	207	2	,	,	PUNCT
american_scientific_journal-2216	207	3	j±	j±	PROPN
american_scientific_journal-2216	207	4	→	→	SYM
american_scientific_journal-2216	207	5	±	±	NOUN
american_scientific_journal-2216	207	6			NOUN
american_scientific_journal-2216	207	7	2h	2h	NUM
american_scientific_journal-2216	207	8	h.→	h.→	PUNCT
american_scientific_journal-2216	208	1	therefore	therefore	ADV
american_scientific_journal-2216	208	2	,	,	PUNCT
american_scientific_journal-2216	208	3	the	the	DET
american_scientific_journal-2216	208	4	computational	computational	ADJ
american_scientific_journal-2216	208	5	molecule	molecule	NOUN
american_scientific_journal-2216	208	6	of	of	ADP
american_scientific_journal-2216	208	7	the	the	DET
american_scientific_journal-2216	208	8	rotated	rotated	ADJ
american_scientific_journal-2216	208	9	five	five	NUM
american_scientific_journal-2216	208	10	-	-	PUNCT
american_scientific_journal-2216	208	11	point	point	NOUN
american_scientific_journal-2216	208	12	finite	finite	ADJ
american_scientific_journal-2216	208	13	difference	difference	NOUN
american_scientific_journal-2216	208	14	approximation	approximation	NOUN
american_scientific_journal-2216	208	15	for	for	ADP
american_scientific_journal-2216	208	16	pde	pde	NOUN
american_scientific_journal-2216	208	17	and	and	CCONJ
american_scientific_journal-2216	208	18	fpde	fpde	NOUN
american_scientific_journal-2216	208	19	can	can	AUX
american_scientific_journal-2216	208	20	be	be	AUX
american_scientific_journal-2216	208	21	shown	show	VERB
american_scientific_journal-2216	208	22	in	in	ADP
american_scientific_journal-2216	208	23	figure	figure	NOUN
american_scientific_journal-2216	208	24	3	3	NUM
american_scientific_journal-2216	208	25	and	and	CCONJ
american_scientific_journal-2216	208	26	figure	figure	VERB
american_scientific_journal-2216	208	27	4	4	NUM
american_scientific_journal-2216	208	28	respectively	respectively	ADV
american_scientific_journal-2216	208	29	.	.	PUNCT
american_scientific_journal-2216	209	1	figure	figure	VERB
american_scientific_journal-2216	209	2	3	3	NUM
american_scientific_journal-2216	209	3	:	:	PUNCT
american_scientific_journal-2216	209	4	computational	computational	ADJ
american_scientific_journal-2216	209	5	molecule	molecule	NOUN
american_scientific_journal-2216	209	6	of	of	ADP
american_scientific_journal-2216	209	7	eq	eq	PROPN
american_scientific_journal-2216	209	8	.	.	PUNCT
american_scientific_journal-2216	210	1	(	(	PUNCT
american_scientific_journal-2216	210	2	2.5	2.5	NUM
american_scientific_journal-2216	210	3	)	)	PUNCT
american_scientific_journal-2216	210	4	figure	figure	NOUN
american_scientific_journal-2216	210	5	4	4	NUM
american_scientific_journal-2216	210	6	:	:	PUNCT
american_scientific_journal-2216	210	7	computational	computational	ADJ
american_scientific_journal-2216	210	8	molecule	molecule	NOUN
american_scientific_journal-2216	210	9	of	of	ADP
american_scientific_journal-2216	210	10	eq	eq	PROPN
american_scientific_journal-2216	210	11	.	.	PUNCT
american_scientific_journal-2216	211	1	(	(	PUNCT
american_scientific_journal-2216	211	2	2.9	2.9	NUM
american_scientific_journal-2216	211	3	)	)	PUNCT
american_scientific_journal-2216	211	4	it	it	PRON
american_scientific_journal-2216	211	5	is	be	AUX
american_scientific_journal-2216	211	6	clear	clear	ADJ
american_scientific_journal-2216	211	7	that	that	SCONJ
american_scientific_journal-2216	211	8	the	the	DET
american_scientific_journal-2216	211	9	coefficients	coefficient	NOUN
american_scientific_journal-2216	211	10	matrix	matrix	NOUN
american_scientific_journal-2216	211	11	for	for	ADP
american_scientific_journal-2216	211	12	the	the	DET
american_scientific_journal-2216	211	13	fractional	fractional	ADJ
american_scientific_journal-2216	211	14	order	order	NOUN
american_scientific_journal-2216	211	15	case	case	NOUN
american_scientific_journal-2216	211	16	0f	0f	NOUN
american_scientific_journal-2216	211	17	equations	equation	NOUN
american_scientific_journal-2216	211	18	(	(	PUNCT
american_scientific_journal-2216	211	19	2.8	2.8	NUM
american_scientific_journal-2216	211	20	)	)	PUNCT
american_scientific_journal-2216	211	21	and	and	CCONJ
american_scientific_journal-2216	211	22	(	(	PUNCT
american_scientific_journal-2216	211	23	2.9	2.9	NUM
american_scientific_journal-2216	211	24	)	)	PUNCT
american_scientific_journal-2216	211	25	have	have	VERB
american_scientific_journal-2216	211	26	the	the	DET
american_scientific_journal-2216	211	27	same	same	ADJ
american_scientific_journal-2216	211	28	structure	structure	NOUN
american_scientific_journal-2216	211	29	as	as	ADP
american_scientific_journal-2216	211	30	in	in	ADP
american_scientific_journal-2216	211	31	equations	equation	NOUN
american_scientific_journal-2216	211	32	(	(	PUNCT
american_scientific_journal-2216	211	33	2.4	2.4	NUM
american_scientific_journal-2216	211	34	)	)	PUNCT
american_scientific_journal-2216	211	35	and	and	CCONJ
american_scientific_journal-2216	211	36	(	(	PUNCT
american_scientific_journal-2216	211	37	2.5	2.5	NUM
american_scientific_journal-2216	211	38	)	)	PUNCT
american_scientific_journal-2216	211	39	except	except	SCONJ
american_scientific_journal-2216	211	40	the	the	DET
american_scientific_journal-2216	211	41	free	free	ADJ
american_scientific_journal-2216	211	42	column	column	NOUN
american_scientific_journal-2216	211	43	f	f	PROPN
american_scientific_journal-2216	211	44	in	in	ADP
american_scientific_journal-2216	211	45	the	the	DET
american_scientific_journal-2216	211	46	right	right	ADJ
american_scientific_journal-2216	211	47	side	side	NOUN
american_scientific_journal-2216	211	48	of	of	ADP
american_scientific_journal-2216	211	49	system	system	NOUN
american_scientific_journal-2216	211	50	(	(	PUNCT
american_scientific_journal-2216	211	51	3.1	3.1	NUM
american_scientific_journal-2216	211	52	)	)	PUNCT
american_scientific_journal-2216	211	53	.	.	PUNCT
american_scientific_journal-2216	212	1	theoretically	theoretically	ADV
american_scientific_journal-2216	212	2	,	,	PUNCT
american_scientific_journal-2216	212	3	it	it	PRON
american_scientific_journal-2216	212	4	can	can	AUX
american_scientific_journal-2216	212	5	be	be	AUX
american_scientific_journal-2216	212	6	seen	see	VERB
american_scientific_journal-2216	212	7	that	that	SCONJ
american_scientific_journal-2216	212	8	the	the	DET
american_scientific_journal-2216	212	9	coefficients	coefficient	NOUN
american_scientific_journal-2216	212	10	matrices	matrix	NOUN
american_scientific_journal-2216	212	11	resulting	result	VERB
american_scientific_journal-2216	212	12	from	from	ADP
american_scientific_journal-2216	212	13	systems	system	NOUN
american_scientific_journal-2216	212	14	(	(	PUNCT
american_scientific_journal-2216	212	15	2.4	2.4	NUM
american_scientific_journal-2216	212	16	)	)	PUNCT
american_scientific_journal-2216	212	17	and	and	CCONJ
american_scientific_journal-2216	212	18	(	(	PUNCT
american_scientific_journal-2216	212	19	2.5	2.5	NUM
american_scientific_journal-2216	212	20	)	)	PUNCT
american_scientific_journal-2216	212	21	are	be	AUX
american_scientific_journal-2216	212	22	nonsingulars	nonsingular	NOUN
american_scientific_journal-2216	212	23	,	,	PUNCT
american_scientific_journal-2216	212	24	so	so	SCONJ
american_scientific_journal-2216	212	25	the	the	DET
american_scientific_journal-2216	212	26	system	system	NOUN
american_scientific_journal-2216	212	27	(	(	PUNCT
american_scientific_journal-2216	212	28	3.1	3.1	NUM
american_scientific_journal-2216	212	29	)	)	PUNCT
american_scientific_journal-2216	212	30	has	have	VERB
american_scientific_journal-2216	212	31	unique	unique	ADJ
american_scientific_journal-2216	212	32	solution	solution	NOUN
american_scientific_journal-2216	212	33	(	(	PUNCT
american_scientific_journal-2216	212	34	[	[	X
american_scientific_journal-2216	212	35	5	5	NUM
american_scientific_journal-2216	212	36	]	]	PUNCT
american_scientific_journal-2216	212	37	)	)	PUNCT
american_scientific_journal-2216	212	38	.	.	PUNCT
american_scientific_journal-2216	213	1	in	in	ADP
american_scientific_journal-2216	213	2	addition	addition	NOUN
american_scientific_journal-2216	213	3	to	to	ADP
american_scientific_journal-2216	213	4	that	that	SCONJ
american_scientific_journal-2216	213	5	the	the	DET
american_scientific_journal-2216	213	6	coefficients	coefficient	NOUN
american_scientific_journal-2216	213	7	matrix	matrix	VERB
american_scientific_journal-2216	213	8	a	a	PRON
american_scientific_journal-2216	213	9	is	be	AUX
american_scientific_journal-2216	213	10	strictly	strictly	ADV
american_scientific_journal-2216	213	11	diagonal	diagonal	ADJ
american_scientific_journal-2216	213	12	dominant	dominant	NOUN
american_scientific_journal-2216	213	13	,	,	PUNCT
american_scientific_journal-2216	213	14	then	then	ADV
american_scientific_journal-2216	213	15	a	a	PRON
american_scientific_journal-2216	213	16	is	be	AUX
american_scientific_journal-2216	213	17	non	non	ADJ
american_scientific_journal-2216	213	18	-	-	ADJ
american_scientific_journal-2216	213	19	singular	singular	ADJ
american_scientific_journal-2216	213	20	and	and	CCONJ
american_scientific_journal-2216	213	21	systems	system	NOUN
american_scientific_journal-2216	213	22	(	(	PUNCT
american_scientific_journal-2216	213	23	2.8	2.8	NUM
american_scientific_journal-2216	213	24	)	)	PUNCT
american_scientific_journal-2216	213	25	and	and	CCONJ
american_scientific_journal-2216	213	26	(	(	PUNCT
american_scientific_journal-2216	213	27	2.9	2.9	NUM
american_scientific_journal-2216	213	28	)	)	PUNCT
american_scientific_journal-2216	213	29	have	have	VERB
american_scientific_journal-2216	213	30	a	a	DET
american_scientific_journal-2216	213	31	unique	unique	ADJ
american_scientific_journal-2216	213	32	solution	solution	NOUN
american_scientific_journal-2216	213	33	for	for	ADP
american_scientific_journal-2216	213	34	(	(	PUNCT
american_scientific_journal-2216	213	35	1	1	NUM
american_scientific_journal-2216	213	36	<	<	X
american_scientific_journal-2216	213	37	α	α	NOUN
american_scientific_journal-2216	213	38	,	,	PUNCT
american_scientific_journal-2216	213	39	β	β	X
american_scientific_journal-2216	213	40	<	<	X
american_scientific_journal-2216	213	41	2	2	NUM
american_scientific_journal-2216	213	42	)	)	PUNCT
american_scientific_journal-2216	213	43	.	.	PUNCT
american_scientific_journal-2216	214	1	since	since	SCONJ
american_scientific_journal-2216	214	2	it	it	PRON
american_scientific_journal-2216	214	3	is	be	AUX
american_scientific_journal-2216	214	4	well	well	ADV
american_scientific_journal-2216	214	5	known	know	VERB
american_scientific_journal-2216	214	6	that	that	SCONJ
american_scientific_journal-2216	214	7	preconditioners	preconditioner	NOUN
american_scientific_journal-2216	214	8	play	play	VERB
american_scientific_journal-2216	214	9	a	a	DET
american_scientific_journal-2216	214	10	vital	vital	ADJ
american_scientific_journal-2216	214	11	role	role	NOUN
american_scientific_journal-2216	214	12	in	in	ADP
american_scientific_journal-2216	214	13	accelerating	accelerate	VERB
american_scientific_journal-2216	214	14	the	the	DET
american_scientific_journal-2216	214	15	convergence	convergence	NOUN
american_scientific_journal-2216	214	16	rates	rate	NOUN
american_scientific_journal-2216	214	17	of	of	ADP
american_scientific_journal-2216	214	18	iterative	iterative	ADJ
american_scientific_journal-2216	214	19	methods	method	NOUN
american_scientific_journal-2216	214	20	,	,	PUNCT
american_scientific_journal-2216	214	21	several	several	ADJ
american_scientific_journal-2216	214	22	preconditioned	preconditioned	ADJ
american_scientific_journal-2216	214	23	strategies	strategy	NOUN
american_scientific_journal-2216	214	24	have	have	AUX
american_scientific_journal-2216	214	25	been	be	AUX
american_scientific_journal-2216	214	26	used	use	VERB
american_scientific_journal-2216	214	27	for	for	ADP
american_scientific_journal-2216	214	28	improving	improve	VERB
american_scientific_journal-2216	214	29	the	the	DET
american_scientific_journal-2216	214	30	convergence	convergence	NOUN
american_scientific_journal-2216	214	31	rate	rate	NOUN
american_scientific_journal-2216	214	32	of	of	ADP
american_scientific_journal-2216	214	33	the	the	DET
american_scientific_journal-2216	214	34	iterative	iterative	NOUN
american_scientific_journal-2216	214	35	methods	method	NOUN
american_scientific_journal-2216	214	36	derived	derive	VERB
american_scientific_journal-2216	214	37	from	from	ADP
american_scientific_journal-2216	214	38	the	the	DET
american_scientific_journal-2216	214	39	standard	standard	NOUN
american_scientific_journal-2216	214	40	and	and	CCONJ
american_scientific_journal-2216	214	41	skewed	skewed	ADJ
american_scientific_journal-2216	214	42	(	(	PUNCT
american_scientific_journal-2216	214	43	rotated	rotated	ADJ
american_scientific_journal-2216	214	44	)	)	PUNCT
american_scientific_journal-2216	214	45	finite	finite	ADJ
american_scientific_journal-2216	214	46	difference	difference	NOUN
american_scientific_journal-2216	214	47	operators	operator	NOUN
american_scientific_journal-2216	214	48	(	(	PUNCT
american_scientific_journal-2216	214	49	[	[	X
american_scientific_journal-2216	214	50	4	4	NUM
american_scientific_journal-2216	214	51	]	]	PUNCT
american_scientific_journal-2216	214	52	,	,	PUNCT
american_scientific_journal-2216	214	53	[	[	X
american_scientific_journal-2216	214	54	5	5	NUM
american_scientific_journal-2216	214	55	]	]	NUM
american_scientific_journal-2216	214	56	)	)	PUNCT
american_scientific_journal-2216	214	57	.	.	PUNCT
american_scientific_journal-2216	215	1	a	a	DET
american_scientific_journal-2216	215	2	well	well	ADV
american_scientific_journal-2216	215	3	-	-	PUNCT
american_scientific_journal-2216	215	4	designed	design	VERB
american_scientific_journal-2216	215	5	i+1,j	i+1,j	NOUN
american_scientific_journal-2216	215	6	i-1,j	i-1,j	NOUN
american_scientific_journal-2216	216	1	i	i	PRON
american_scientific_journal-2216	216	2	,	,	PUNCT
american_scientific_journal-2216	216	3	j-1	j-1	ADV
american_scientific_journal-2216	216	4	i	i	PRON
american_scientific_journal-2216	216	5	,	,	PUNCT
american_scientific_journal-2216	216	6	j	j	PROPN
american_scientific_journal-2216	216	7	i	i	PROPN
american_scientific_journal-2216	216	8	,	,	PUNCT
american_scientific_journal-2216	216	9	j+1	j+1	PROPN
american_scientific_journal-2216	216	10	i+1,j	i+1,j	NOUN
american_scientific_journal-2216	216	11	0,j	0,j	NOUN
american_scientific_journal-2216	216	12	i,0	i,0	X
american_scientific_journal-2216	217	1	i	i	PRON
american_scientific_journal-2216	217	2	,	,	PUNCT
american_scientific_journal-2216	217	3	j	j	PROPN
american_scientific_journal-2216	217	4	i	i	PROPN
american_scientific_journal-2216	217	5	,	,	PUNCT
american_scientific_journal-2216	217	6	j+1	j+1	ADJ
american_scientific_journal-2216	217	7	i+1,j+1	i+1,j+1	NOUN
american_scientific_journal-2216	217	8	i-1,j-1	i-1,j-1	NOUN
american_scientific_journal-2216	217	9	i+1,j-1	i+1,j-1	ADV
american_scientific_journal-2216	217	10	i	i	PRON
american_scientific_journal-2216	217	11	,	,	PUNCT
american_scientific_journal-2216	217	12	j	j	PROPN
american_scientific_journal-2216	217	13	i-1	i-1	NUM
american_scientific_journal-2216	217	14	,	,	PUNCT
american_scientific_journal-2216	217	15	j+1	j+1	PROPN
american_scientific_journal-2216	217	16	i+1,j+1	i+1,j+1	NOUN
american_scientific_journal-2216	218	1	i-1,0	i-1,0	NOUN
american_scientific_journal-2216	218	2	i+1,j-1	i+1,j-1	ADV
american_scientific_journal-2216	218	3	i	i	PRON
american_scientific_journal-2216	218	4	,	,	PUNCT
american_scientific_journal-2216	218	5	j	j	PROPN
american_scientific_journal-2216	218	6	0	0	NUM
american_scientific_journal-2216	218	7	,	,	PUNCT
american_scientific_journal-2216	218	8	j+1	j+1	ADJ
american_scientific_journal-2216	218	9	american	american	ADJ
american_scientific_journal-2216	218	10	scientific	scientific	ADJ
american_scientific_journal-2216	218	11	research	research	NOUN
american_scientific_journal-2216	218	12	journal	journal	NOUN
american_scientific_journal-2216	218	13	for	for	ADP
american_scientific_journal-2216	218	14	engineering	engineering	NOUN
american_scientific_journal-2216	218	15	,	,	PUNCT
american_scientific_journal-2216	218	16	technology	technology	NOUN
american_scientific_journal-2216	218	17	,	,	PUNCT
american_scientific_journal-2216	218	18	and	and	CCONJ
american_scientific_journal-2216	218	19	sciences	science	NOUN
american_scientific_journal-2216	218	20	(	(	PUNCT
american_scientific_journal-2216	218	21	asrjets	asrjet	NOUN
american_scientific_journal-2216	218	22	)	)	PUNCT
american_scientific_journal-2216	218	23	(	(	PUNCT
american_scientific_journal-2216	218	24	2016	2016	NUM
american_scientific_journal-2216	218	25	)	)	PUNCT
american_scientific_journal-2216	218	26	volume	volume	NOUN
american_scientific_journal-2216	218	27	26	26	NUM
american_scientific_journal-2216	218	28	,	,	PUNCT
american_scientific_journal-2216	218	29	no	no	DET
american_scientific_journal-2216	218	30	1	1	NUM
american_scientific_journal-2216	218	31	,	,	PUNCT
american_scientific_journal-2216	218	32	pp	pp	ADV
american_scientific_journal-2216	218	33	261	261	NUM
american_scientific_journal-2216	218	34	-	-	SYM
american_scientific_journal-2216	218	35	270	270	NUM
american_scientific_journal-2216	218	36	267	267	NUM
american_scientific_journal-2216	218	37	preconditioning	preconditioning	NOUN
american_scientific_journal-2216	218	38	of	of	ADP
american_scientific_journal-2216	218	39	the	the	DET
american_scientific_journal-2216	218	40	pde	pde	NOUN
american_scientific_journal-2216	218	41	and	and	CCONJ
american_scientific_journal-2216	218	42	fpde	fpde	NOUN
american_scientific_journal-2216	218	43	problems	problem	NOUN
american_scientific_journal-2216	218	44	reduces	reduce	VERB
american_scientific_journal-2216	218	45	the	the	DET
american_scientific_journal-2216	218	46	number	number	NOUN
american_scientific_journal-2216	218	47	of	of	ADP
american_scientific_journal-2216	218	48	iterations	iteration	NOUN
american_scientific_journal-2216	218	49	to	to	PART
american_scientific_journal-2216	218	50	reach	reach	VERB
american_scientific_journal-2216	218	51	convergence	convergence	NOUN
american_scientific_journal-2216	218	52	.	.	PUNCT
american_scientific_journal-2216	219	1	dramatic	dramatic	ADJ
american_scientific_journal-2216	219	2	improvements	improvement	NOUN
american_scientific_journal-2216	219	3	are	be	AUX
american_scientific_journal-2216	219	4	possible	possible	ADJ
american_scientific_journal-2216	219	5	,	,	PUNCT
american_scientific_journal-2216	219	6	but	but	CCONJ
american_scientific_journal-2216	219	7	the	the	DET
american_scientific_journal-2216	219	8	difficulty	difficulty	NOUN
american_scientific_journal-2216	219	9	is	be	AUX
american_scientific_journal-2216	219	10	to	to	PART
american_scientific_journal-2216	219	11	construct	construct	VERB
american_scientific_journal-2216	219	12	the	the	DET
american_scientific_journal-2216	219	13	suitable	suitable	ADJ
american_scientific_journal-2216	219	14	preconditioner	preconditioner	NOUN
american_scientific_journal-2216	219	15	.	.	PUNCT
american_scientific_journal-2216	220	1	in	in	ADP
american_scientific_journal-2216	220	2	general	general	ADJ
american_scientific_journal-2216	220	3	,	,	PUNCT
american_scientific_journal-2216	220	4	a	a	DET
american_scientific_journal-2216	220	5	good	good	ADJ
american_scientific_journal-2216	220	6	preconditioner	preconditioner	NOUN
american_scientific_journal-2216	220	7	should	should	AUX
american_scientific_journal-2216	220	8	satisfy	satisfy	VERB
american_scientific_journal-2216	220	9	the	the	DET
american_scientific_journal-2216	220	10	following	follow	VERB
american_scientific_journal-2216	220	11	prosperities	prosperity	NOUN
american_scientific_journal-2216	220	12	:	:	PUNCT
american_scientific_journal-2216	220	13	the	the	DET
american_scientific_journal-2216	220	14	first	first	ADJ
american_scientific_journal-2216	220	15	one	one	NUM
american_scientific_journal-2216	220	16	is	be	AUX
american_scientific_journal-2216	220	17	that	that	SCONJ
american_scientific_journal-2216	220	18	,	,	PUNCT
american_scientific_journal-2216	220	19	the	the	DET
american_scientific_journal-2216	220	20	preconditioned	preconditioned	ADJ
american_scientific_journal-2216	220	21	system	system	NOUN
american_scientific_journal-2216	220	22	should	should	AUX
american_scientific_journal-2216	220	23	be	be	AUX
american_scientific_journal-2216	220	24	easy	easy	ADJ
american_scientific_journal-2216	220	25	to	to	PART
american_scientific_journal-2216	220	26	solve	solve	VERB
american_scientific_journal-2216	220	27	and	and	CCONJ
american_scientific_journal-2216	220	28	the	the	DET
american_scientific_journal-2216	220	29	second	second	ADJ
american_scientific_journal-2216	220	30	one	one	NOUN
american_scientific_journal-2216	220	31	is	be	AUX
american_scientific_journal-2216	220	32	that	that	SCONJ
american_scientific_journal-2216	220	33	the	the	DET
american_scientific_journal-2216	220	34	preconditioner	preconditioner	NOUN
american_scientific_journal-2216	220	35	should	should	AUX
american_scientific_journal-2216	220	36	be	be	AUX
american_scientific_journal-2216	220	37	cheap	cheap	ADJ
american_scientific_journal-2216	220	38	to	to	PART
american_scientific_journal-2216	220	39	construct	construct	VERB
american_scientific_journal-2216	220	40	and	and	CCONJ
american_scientific_journal-2216	220	41	apply	apply	VERB
american_scientific_journal-2216	220	42	.	.	PUNCT
american_scientific_journal-2216	221	1	usually	usually	ADV
american_scientific_journal-2216	221	2	the	the	DET
american_scientific_journal-2216	221	3	system	system	NOUN
american_scientific_journal-2216	221	4	(	(	PUNCT
american_scientific_journal-2216	221	5	3.1	3.1	NUM
american_scientific_journal-2216	221	6	)	)	PUNCT
american_scientific_journal-2216	221	7	is	be	AUX
american_scientific_journal-2216	221	8	large	large	ADJ
american_scientific_journal-2216	221	9	and	and	CCONJ
american_scientific_journal-2216	221	10	the	the	DET
american_scientific_journal-2216	221	11	matrix	matrix	NOUN
american_scientific_journal-2216	221	12	a	a	PRON
american_scientific_journal-2216	221	13	is	be	AUX
american_scientific_journal-2216	221	14	sparse	sparse	ADJ
american_scientific_journal-2216	221	15	.	.	PUNCT
american_scientific_journal-2216	222	1	furthermore	furthermore	ADV
american_scientific_journal-2216	222	2	,	,	PUNCT
american_scientific_journal-2216	222	3	matrix	matrix	VERB
american_scientific_journal-2216	222	4	a	a	PRON
american_scientific_journal-2216	222	5	can	can	AUX
american_scientific_journal-2216	222	6	be	be	AUX
american_scientific_journal-2216	222	7	write	write	ADJ
american_scientific_journal-2216	222	8	as	as	ADP
american_scientific_journal-2216	222	9	a	a	DET
american_scientific_journal-2216	222	10	d	d	NOUN
american_scientific_journal-2216	222	11	l	l	NOUN
american_scientific_journal-2216	222	12	u=	u=	NOUN
american_scientific_journal-2216	222	13	−	−	PROPN
american_scientific_journal-2216	222	14	−	−	PROPN
american_scientific_journal-2216	222	15	(	(	PUNCT
american_scientific_journal-2216	222	16	3.2	3.2	NUM
american_scientific_journal-2216	222	17	)	)	PUNCT
american_scientific_journal-2216	222	18	where	where	SCONJ
american_scientific_journal-2216	222	19	d	d	NOUN
american_scientific_journal-2216	222	20	is	be	AUX
american_scientific_journal-2216	222	21	diagonal	diagonal	ADJ
american_scientific_journal-2216	222	22	matrix	matrix	NOUN
american_scientific_journal-2216	222	23	a	a	PRON
american_scientific_journal-2216	222	24	,	,	PUNCT
american_scientific_journal-2216	222	25	l−	l−	NOUN
american_scientific_journal-2216	222	26	is	be	AUX
american_scientific_journal-2216	222	27	strictly	strictly	ADV
american_scientific_journal-2216	222	28	lower	low	ADJ
american_scientific_journal-2216	222	29	triangular	triangular	NOUN
american_scientific_journal-2216	222	30	parts	part	NOUN
american_scientific_journal-2216	222	31	of	of	ADP
american_scientific_journal-2216	222	32	a	a	PRON
american_scientific_journal-2216	222	33	and	and	CCONJ
american_scientific_journal-2216	222	34	u−	u−	PROPN
american_scientific_journal-2216	222	35	is	be	AUX
american_scientific_journal-2216	222	36	strictly	strictly	ADV
american_scientific_journal-2216	222	37	upper	upper	ADJ
american_scientific_journal-2216	222	38	triangular	triangular	NOUN
american_scientific_journal-2216	222	39	parts	part	NOUN
american_scientific_journal-2216	222	40	of	of	ADP
american_scientific_journal-2216	222	41	a.	a.	NOUN
american_scientific_journal-2216	222	42	a	a	DET
american_scientific_journal-2216	222	43	preconditioner	preconditioner	NOUN
american_scientific_journal-2216	222	44	(	(	PUNCT
american_scientific_journal-2216	222	45	)	)	PUNCT
american_scientific_journal-2216	223	1	+	+	ADV
american_scientific_journal-2216	223	2	i	i	PRON
american_scientific_journal-2216	223	3	ml	ml	VERB
american_scientific_journal-2216	223	4	where	where	SCONJ
american_scientific_journal-2216	223	5	0	0	NUM
american_scientific_journal-2216	223	6	2≤	2≤	NUM
american_scientific_journal-2216	223	7	<	<	X
american_scientific_journal-2216	223	8	m	m	PROPN
american_scientific_journal-2216	223	9	is	be	AUX
american_scientific_journal-2216	223	10	used	use	VERB
american_scientific_journal-2216	223	11	to	to	PART
american_scientific_journal-2216	223	12	modify	modify	VERB
american_scientific_journal-2216	223	13	the	the	DET
american_scientific_journal-2216	223	14	original	original	ADJ
american_scientific_journal-2216	223	15	system	system	NOUN
american_scientific_journal-2216	223	16	(	(	PUNCT
american_scientific_journal-2216	223	17	3.1	3.1	NUM
american_scientific_journal-2216	223	18	)	)	PUNCT
american_scientific_journal-2216	223	19	to	to	ADP
american_scientific_journal-2216	223	20	the	the	DET
american_scientific_journal-2216	223	21	following	follow	VERB
american_scientific_journal-2216	223	22	system	system	NOUN
american_scientific_journal-2216	223	23	:	:	PUNCT
american_scientific_journal-2216	223	24	(	(	PUNCT
american_scientific_journal-2216	223	25	)	)	PUNCT
american_scientific_journal-2216	223	26	(	(	PUNCT
american_scientific_journal-2216	223	27	)	)	PUNCT
american_scientific_journal-2216	224	1	+	+	X
american_scientific_journal-2216	224	2	=	=	PUNCT
american_scientific_journal-2216	225	1	+	+	NOUN
american_scientific_journal-2216	225	2	i	i	PRON
american_scientific_journal-2216	225	3	ml	ml	X
american_scientific_journal-2216	225	4	au	au	VERB
american_scientific_journal-2216	226	1	i	i	PRON
american_scientific_journal-2216	226	2	ml	ml	PROPN
american_scientific_journal-2216	226	3	f	f	PROPN
american_scientific_journal-2216	226	4	(	(	PUNCT
american_scientific_journal-2216	226	5	3.3	3.3	NUM
american_scientific_journal-2216	226	6	)	)	PUNCT
american_scientific_journal-2216	226	7	a	a	DET
american_scientific_journal-2216	226	8	preconditioner	preconditioner	NOUN
american_scientific_journal-2216	226	9	(	(	PUNCT
american_scientific_journal-2216	226	10	)	)	PUNCT
american_scientific_journal-2216	226	11	=	=	PUNCT
american_scientific_journal-2216	227	1	+	+	ADP
american_scientific_journal-2216	227	2	p	p	X
american_scientific_journal-2216	227	3	i	i	PRON
american_scientific_journal-2216	227	4	ml	ml	INTJ
american_scientific_journal-2216	227	5	is	be	AUX
american_scientific_journal-2216	227	6	a	a	DET
american_scientific_journal-2216	227	7	matrix	matrix	NOUN
american_scientific_journal-2216	227	8	that	that	PRON
american_scientific_journal-2216	227	9	transforms	transform	VERB
american_scientific_journal-2216	227	10	the	the	DET
american_scientific_journal-2216	227	11	original	original	ADJ
american_scientific_journal-2216	227	12	system	system	NOUN
american_scientific_journal-2216	227	13	(	(	PUNCT
american_scientific_journal-2216	227	14	3.1	3.1	NUM
american_scientific_journal-2216	227	15	)	)	PUNCT
american_scientific_journal-2216	227	16	into	into	ADP
american_scientific_journal-2216	227	17	new	new	ADJ
american_scientific_journal-2216	227	18	system	system	NOUN
american_scientific_journal-2216	227	19	(	(	PUNCT
american_scientific_journal-2216	227	20	3.3	3.3	NUM
american_scientific_journal-2216	227	21	)	)	PUNCT
american_scientific_journal-2216	227	22	that	that	PRON
american_scientific_journal-2216	227	23	is	be	AUX
american_scientific_journal-2216	227	24	equivalent	equivalent	ADJ
american_scientific_journal-2216	227	25	in	in	ADP
american_scientific_journal-2216	227	26	the	the	DET
american_scientific_journal-2216	227	27	sense	sense	NOUN
american_scientific_journal-2216	227	28	that	that	SCONJ
american_scientific_journal-2216	227	29	it	it	PRON
american_scientific_journal-2216	227	30	has	have	AUX
american_scientific_journal-2216	227	31	the	the	DET
american_scientific_journal-2216	227	32	same	same	ADJ
american_scientific_journal-2216	227	33	solution	solution	NOUN
american_scientific_journal-2216	227	34	,	,	PUNCT
american_scientific_journal-2216	227	35	but	but	CCONJ
american_scientific_journal-2216	227	36	that	that	PRON
american_scientific_journal-2216	227	37	has	have	VERB
american_scientific_journal-2216	227	38	more	more	ADV
american_scientific_journal-2216	227	39	favourable	favourable	ADJ
american_scientific_journal-2216	227	40	spectral	spectral	ADJ
american_scientific_journal-2216	227	41	properties	property	NOUN
american_scientific_journal-2216	227	42	.	.	PUNCT
american_scientific_journal-2216	228	1	4	4	X
american_scientific_journal-2216	228	2	.	.	X
american_scientific_journal-2216	228	3	numerical	numerical	ADJ
american_scientific_journal-2216	228	4	results	result	NOUN
american_scientific_journal-2216	228	5	and	and	CCONJ
american_scientific_journal-2216	228	6	discussion	discussion	NOUN
american_scientific_journal-2216	228	7	in	in	ADP
american_scientific_journal-2216	228	8	the	the	DET
american_scientific_journal-2216	228	9	first	first	ADJ
american_scientific_journal-2216	228	10	part	part	NOUN
american_scientific_journal-2216	228	11	of	of	ADP
american_scientific_journal-2216	228	12	this	this	DET
american_scientific_journal-2216	228	13	section	section	NOUN
american_scientific_journal-2216	228	14	,	,	PUNCT
american_scientific_journal-2216	228	15	we	we	PRON
american_scientific_journal-2216	228	16	have	have	AUX
american_scientific_journal-2216	228	17	compared	compare	VERB
american_scientific_journal-2216	228	18	between	between	ADP
american_scientific_journal-2216	228	19	the	the	DET
american_scientific_journal-2216	228	20	spectral	spectral	ADJ
american_scientific_journal-2216	228	21	radiuses	radius	NOUN
american_scientific_journal-2216	228	22	of	of	ADP
american_scientific_journal-2216	228	23	the	the	DET
american_scientific_journal-2216	228	24	iteration	iteration	NOUN
american_scientific_journal-2216	228	25	matrix	matrix	NOUN
american_scientific_journal-2216	228	26	corresponding	correspond	VERB
american_scientific_journal-2216	228	27	to	to	ADP
american_scientific_journal-2216	228	28	the	the	DET
american_scientific_journal-2216	228	29	resulting	result	VERB
american_scientific_journal-2216	228	30	system	system	NOUN
american_scientific_journal-2216	228	31	of	of	ADP
american_scientific_journal-2216	228	32	rotated	rotate	VERB
american_scientific_journal-2216	228	33	five	five	NUM
american_scientific_journal-2216	228	34	-	-	PUNCT
american_scientific_journal-2216	228	35	point	point	NOUN
american_scientific_journal-2216	228	36	finite	finite	ADJ
american_scientific_journal-2216	228	37	difference	difference	NOUN
american_scientific_journal-2216	228	38	(	(	PUNCT
american_scientific_journal-2216	228	39	original	original	ADJ
american_scientific_journal-2216	228	40	system	system	NOUN
american_scientific_journal-2216	228	41	)	)	PUNCT
american_scientific_journal-2216	228	42	and	and	CCONJ
american_scientific_journal-2216	228	43	the	the	DET
american_scientific_journal-2216	228	44	preconditioned	preconditioned	ADJ
american_scientific_journal-2216	228	45	system	system	NOUN
american_scientific_journal-2216	228	46	for	for	ADP
american_scientific_journal-2216	228	47	different	different	ADJ
american_scientific_journal-2216	228	48	values	value	NOUN
american_scientific_journal-2216	228	49	of	of	ADP
american_scientific_journal-2216	228	50	,	,	PUNCT
american_scientific_journal-2216	228	51	α	α	PROPN
american_scientific_journal-2216	228	52	β	β	NOUN
american_scientific_journal-2216	228	53	such	such	ADJ
american_scientific_journal-2216	228	54	that	that	SCONJ
american_scientific_journal-2216	228	55	(	(	PUNCT
american_scientific_journal-2216	228	56	1	1	NUM
american_scientific_journal-2216	228	57	,	,	PUNCT
american_scientific_journal-2216	228	58	2)α	2)α	NUM
american_scientific_journal-2216	228	59	β≤	β≤	PROPN
american_scientific_journal-2216	228	60	≤	≤	NUM
american_scientific_journal-2216	228	61	.	.	PUNCT
american_scientific_journal-2216	229	1	table	table	NOUN
american_scientific_journal-2216	229	2	1	1	NUM
american_scientific_journal-2216	229	3	shows	show	VERB
american_scientific_journal-2216	229	4	the	the	DET
american_scientific_journal-2216	229	5	comparison	comparison	NOUN
american_scientific_journal-2216	229	6	of	of	ADP
american_scientific_journal-2216	229	7	the	the	DET
american_scientific_journal-2216	229	8	spectral	spectral	ADJ
american_scientific_journal-2216	229	9	radius	radius	NOUN
american_scientific_journal-2216	229	10	between	between	ADP
american_scientific_journal-2216	229	11	the	the	DET
american_scientific_journal-2216	229	12	original	original	ADJ
american_scientific_journal-2216	229	13	and	and	CCONJ
american_scientific_journal-2216	229	14	the	the	DET
american_scientific_journal-2216	229	15	preconditioned	preconditioned	ADJ
american_scientific_journal-2216	229	16	systems	system	NOUN
american_scientific_journal-2216	229	17	.	.	PUNCT
american_scientific_journal-2216	230	1	clearly	clearly	ADV
american_scientific_journal-2216	230	2	it	it	PRON
american_scientific_journal-2216	230	3	can	can	AUX
american_scientific_journal-2216	230	4	be	be	AUX
american_scientific_journal-2216	230	5	seen	see	VERB
american_scientific_journal-2216	230	6	that	that	SCONJ
american_scientific_journal-2216	230	7	the	the	DET
american_scientific_journal-2216	230	8	spectral	spectral	ADJ
american_scientific_journal-2216	230	9	radius	radius	NOUN
american_scientific_journal-2216	230	10	of	of	ADP
american_scientific_journal-2216	230	11	the	the	DET
american_scientific_journal-2216	230	12	preconditioned	preconditioned	ADJ
american_scientific_journal-2216	230	13	system	system	NOUN
american_scientific_journal-2216	230	14	is	be	AUX
american_scientific_journal-2216	230	15	smaller	small	ADJ
american_scientific_journal-2216	230	16	compared	compare	VERB
american_scientific_journal-2216	230	17	to	to	ADP
american_scientific_journal-2216	230	18	the	the	DET
american_scientific_journal-2216	230	19	original	original	ADJ
american_scientific_journal-2216	230	20	system	system	NOUN
american_scientific_journal-2216	230	21	,	,	PUNCT
american_scientific_journal-2216	230	22	thus	thus	ADV
american_scientific_journal-2216	230	23	justifying	justify	VERB
american_scientific_journal-2216	230	24	the	the	DET
american_scientific_journal-2216	230	25	superiority	superiority	NOUN
american_scientific_journal-2216	230	26	of	of	ADP
american_scientific_journal-2216	230	27	the	the	DET
american_scientific_journal-2216	230	28	preconditioned	preconditioned	ADJ
american_scientific_journal-2216	230	29	system	system	NOUN
american_scientific_journal-2216	230	30	against	against	ADP
american_scientific_journal-2216	230	31	the	the	DET
american_scientific_journal-2216	230	32	original	original	ADJ
american_scientific_journal-2216	230	33	system	system	NOUN
american_scientific_journal-2216	230	34	which	which	PRON
american_scientific_journal-2216	230	35	is	be	AUX
american_scientific_journal-2216	230	36	quite	quite	ADV
american_scientific_journal-2216	230	37	agreeing	agree	VERB
american_scientific_journal-2216	230	38	with	with	ADP
american_scientific_journal-2216	230	39	the	the	DET
american_scientific_journal-2216	230	40	results	result	NOUN
american_scientific_journal-2216	230	41	obtained	obtain	VERB
american_scientific_journal-2216	230	42	in	in	ADP
american_scientific_journal-2216	230	43	the	the	DET
american_scientific_journal-2216	230	44	previous	previous	ADJ
american_scientific_journal-2216	230	45	work	work	NOUN
american_scientific_journal-2216	230	46	(	(	PUNCT
american_scientific_journal-2216	230	47	[	[	X
american_scientific_journal-2216	230	48	3,4,8	3,4,8	NOUN
american_scientific_journal-2216	230	49	]	]	PUNCT
american_scientific_journal-2216	230	50	)	)	PUNCT
american_scientific_journal-2216	230	51	.	.	PUNCT
american_scientific_journal-2216	231	1	table	table	NOUN
american_scientific_journal-2216	231	2	1	1	NUM
american_scientific_journal-2216	231	3	:	:	PUNCT
american_scientific_journal-2216	231	4	comparison	comparison	NOUN
american_scientific_journal-2216	231	5	of	of	ADP
american_scientific_journal-2216	231	6	the	the	DET
american_scientific_journal-2216	231	7	spectral	spectral	ADJ
american_scientific_journal-2216	231	8	radiuses	radius	NOUN
american_scientific_journal-2216	231	9	of	of	ADP
american_scientific_journal-2216	231	10	the	the	DET
american_scientific_journal-2216	231	11	iteration	iteration	NOUN
american_scientific_journal-2216	231	12	matrix	matrix	NOUN
american_scientific_journal-2216	231	13	corresponding	correspond	VERB
american_scientific_journal-2216	231	14	to	to	ADP
american_scientific_journal-2216	231	15	the	the	DET
american_scientific_journal-2216	231	16	original	original	ADJ
american_scientific_journal-2216	231	17	and	and	CCONJ
american_scientific_journal-2216	231	18	the	the	DET
american_scientific_journal-2216	231	19	preconditioned	preconditioned	ADJ
american_scientific_journal-2216	231	20	systems	system	NOUN
american_scientific_journal-2216	231	21	n	n	PRON
american_scientific_journal-2216	231	22	order	order	VERB
american_scientific_journal-2216	231	23	original	original	ADJ
american_scientific_journal-2216	231	24	system	system	NOUN
american_scientific_journal-2216	231	25	preconditioned	precondition	VERB
american_scientific_journal-2216	231	26	system	system	NOUN
american_scientific_journal-2216	231	27	α	α	X
american_scientific_journal-2216	231	28	β	β	X
american_scientific_journal-2216	231	29	(	(	PUNCT
american_scientific_journal-2216	231	30	)	)	PUNCT
american_scientific_journal-2216	231	31	aρ	aρ	INTJ
american_scientific_journal-2216	231	32	(	(	PUNCT
american_scientific_journal-2216	231	33	)	)	PUNCT
american_scientific_journal-2216	231	34	paρ	paρ	VERB
american_scientific_journal-2216	231	35	42	42	NUM
american_scientific_journal-2216	231	36	1.2	1.2	NUM
american_scientific_journal-2216	231	37	1.4	1.4	NUM
american_scientific_journal-2216	231	38	0.053	0.053	NUM
american_scientific_journal-2216	231	39	0.041	0.041	NUM
american_scientific_journal-2216	231	40	74	74	NUM
american_scientific_journal-2216	231	41	1.4	1.4	NUM
american_scientific_journal-2216	231	42	1.4	1.4	NUM
american_scientific_journal-2216	231	43	0.091	0.091	NUM
american_scientific_journal-2216	231	44	0.083	0.083	NUM
american_scientific_journal-2216	231	45	114	114	NUM
american_scientific_journal-2216	231	46	1.6	1.6	NUM
american_scientific_journal-2216	231	47	1.4	1.4	NUM
american_scientific_journal-2216	231	48	0.141	0.141	NUM
american_scientific_journal-2216	231	49	0.112	0.112	NUM
american_scientific_journal-2216	231	50	186	186	NUM
american_scientific_journal-2216	231	51	1.8	1.8	NUM
american_scientific_journal-2216	231	52	1.4	1.4	NUM
american_scientific_journal-2216	231	53	0.184	0.184	NUM
american_scientific_journal-2216	231	54	0.171	0.171	NUM
american_scientific_journal-2216	231	55	american	american	ADJ
american_scientific_journal-2216	231	56	scientific	scientific	ADJ
american_scientific_journal-2216	231	57	research	research	NOUN
american_scientific_journal-2216	231	58	journal	journal	NOUN
american_scientific_journal-2216	231	59	for	for	ADP
american_scientific_journal-2216	231	60	engineering	engineering	NOUN
american_scientific_journal-2216	231	61	,	,	PUNCT
american_scientific_journal-2216	231	62	technology	technology	NOUN
american_scientific_journal-2216	231	63	,	,	PUNCT
american_scientific_journal-2216	231	64	and	and	CCONJ
american_scientific_journal-2216	231	65	sciences	science	NOUN
american_scientific_journal-2216	231	66	(	(	PUNCT
american_scientific_journal-2216	231	67	asrjets	asrjet	NOUN
american_scientific_journal-2216	231	68	)	)	PUNCT
american_scientific_journal-2216	231	69	(	(	PUNCT
american_scientific_journal-2216	231	70	2016	2016	NUM
american_scientific_journal-2216	231	71	)	)	PUNCT
american_scientific_journal-2216	231	72	volume	volume	NOUN
american_scientific_journal-2216	231	73	26	26	NUM
american_scientific_journal-2216	231	74	,	,	PUNCT
american_scientific_journal-2216	231	75	no	no	DET
american_scientific_journal-2216	231	76	1	1	NUM
american_scientific_journal-2216	231	77	,	,	PUNCT
american_scientific_journal-2216	231	78	pp	pp	ADV
american_scientific_journal-2216	231	79	261	261	NUM
american_scientific_journal-2216	231	80	-	-	SYM
american_scientific_journal-2216	231	81	270	270	NUM
american_scientific_journal-2216	231	82	268	268	NUM
american_scientific_journal-2216	231	83	the	the	DET
american_scientific_journal-2216	231	84	second	second	ADJ
american_scientific_journal-2216	231	85	part	part	NOUN
american_scientific_journal-2216	231	86	of	of	ADP
american_scientific_journal-2216	231	87	this	this	DET
american_scientific_journal-2216	231	88	section	section	NOUN
american_scientific_journal-2216	231	89	has	have	AUX
american_scientific_journal-2216	231	90	discussed	discuss	VERB
american_scientific_journal-2216	231	91	the	the	DET
american_scientific_journal-2216	231	92	numerical	numerical	ADJ
american_scientific_journal-2216	231	93	solution	solution	NOUN
american_scientific_journal-2216	231	94	of	of	ADP
american_scientific_journal-2216	231	95	the	the	DET
american_scientific_journal-2216	231	96	following	follow	VERB
american_scientific_journal-2216	231	97	modal	modal	ADJ
american_scientific_journal-2216	231	98	problem	problem	NOUN
american_scientific_journal-2216	231	99	using	use	VERB
american_scientific_journal-2216	231	100	the	the	DET
american_scientific_journal-2216	231	101	proposed	propose	VERB
american_scientific_journal-2216	231	102	iterative	iterative	NOUN
american_scientific_journal-2216	231	103	method	method	NOUN
american_scientific_journal-2216	231	104	:	:	PUNCT
american_scientific_journal-2216	231	105	2	2	NUM
american_scientific_journal-2216	231	106	2	2	NUM
american_scientific_journal-2216	231	107	(	(	PUNCT
american_scientific_journal-2216	231	108	,	,	PUNCT
american_scientific_journal-2216	231	109	)	)	PUNCT
american_scientific_journal-2216	231	110	(	(	PUNCT
american_scientific_journal-2216	231	111	,	,	PUNCT
american_scientific_journal-2216	231	112	)	)	PUNCT
american_scientific_journal-2216	231	113	10[4	10[4	NUM
american_scientific_journal-2216	231	114	(	(	PUNCT
american_scientific_journal-2216	231	115	2	2	NUM
american_scientific_journal-2216	231	116	)	)	PUNCT
american_scientific_journal-2216	231	117	]	]	PUNCT
american_scientific_journal-2216	232	1	sin+	sin+	PROPN
american_scientific_journal-2216	233	1	+	+	PROPN
american_scientific_journal-2216	233	2	+	+	PROPN
american_scientific_journal-2216	233	3	=	=	SYM
american_scientific_journal-2216	233	4	−	−	PROPN
american_scientific_journal-2216	233	5	+	+	NUM
american_scientific_journal-2216	233	6	−c	−c	NOUN
american_scientific_journal-2216	233	7	c	c	NOUN
american_scientific_journal-2216	233	8	x	x	PUNCT
american_scientific_journal-2216	233	9	y	y	PROPN
american_scientific_journal-2216	233	10	d	d	PUNCT
american_scientific_journal-2216	233	11	u	u	NOUN
american_scientific_journal-2216	233	12	x	x	PROPN
american_scientific_journal-2216	233	13	y	y	NOUN
american_scientific_journal-2216	233	14	d	d	PROPN
american_scientific_journal-2216	233	15	u	u	NOUN
american_scientific_journal-2216	233	16	x	x	PROPN
american_scientific_journal-2216	233	17	y	y	NOUN
american_scientific_journal-2216	233	18	x	x	PUNCT
american_scientific_journal-2216	233	19	x	x	X
american_scientific_journal-2216	233	20	yβ	yβ	NOUN
american_scientific_journal-2216	233	21	β	β	PROPN
american_scientific_journal-2216	233	22	π	π	PROPN
american_scientific_journal-2216	233	23	π	π	X
american_scientific_journal-2216	233	24	defined	define	VERB
american_scientific_journal-2216	233	25	in	in	ADP
american_scientific_journal-2216	233	26	{	{	PUNCT
american_scientific_journal-2216	233	27	0	0	NUM
american_scientific_journal-2216	233	28	0.5	0.5	NUM
american_scientific_journal-2216	233	29	,	,	PUNCT
american_scientific_journal-2216	233	30	0	0	NUM
american_scientific_journal-2216	233	31	1}=	1}=	NUM
american_scientific_journal-2216	233	32	<	<	X
american_scientific_journal-2216	233	33	<	<	X
american_scientific_journal-2216	233	34	<	<	X
american_scientific_journal-2216	233	35	<	<	X
american_scientific_journal-2216	233	36	d	d	X
american_scientific_journal-2216	233	37	x	x	SYM
american_scientific_journal-2216	233	38	y	y	NOUN
american_scientific_journal-2216	233	39	with	with	ADP
american_scientific_journal-2216	233	40	the	the	DET
american_scientific_journal-2216	233	41	boundary	boundary	ADJ
american_scientific_journal-2216	233	42	condition	condition	NOUN
american_scientific_journal-2216	233	43	0γ	0γ	NOUN
american_scientific_journal-2216	234	1	=	=	PUNCT
american_scientific_journal-2216	234	2	u	u	NOUN
american_scientific_journal-2216	234	3	such	such	ADJ
american_scientific_journal-2216	234	4	that	that	SCONJ
american_scientific_journal-2216	234	5	:	:	PUNCT
american_scientific_journal-2216	234	6	γ	γ	X
american_scientific_journal-2216	234	7	is	be	AUX
american_scientific_journal-2216	234	8	the	the	DET
american_scientific_journal-2216	234	9	boundary	boundary	NOUN
american_scientific_journal-2216	234	10	of	of	ADP
american_scientific_journal-2216	234	11	the	the	DET
american_scientific_journal-2216	234	12	area	area	NOUN
american_scientific_journal-2216	234	13	d	d	NOUN
american_scientific_journal-2216	234	14	,	,	PUNCT
american_scientific_journal-2216	234	15	and	and	CCONJ
american_scientific_journal-2216	234	16	the	the	DET
american_scientific_journal-2216	234	17	fractional	fractional	ADJ
american_scientific_journal-2216	234	18	order	order	NOUN
american_scientific_journal-2216	234	19	is	be	AUX
american_scientific_journal-2216	234	20	1	1	NUM
american_scientific_journal-2216	234	21	2	2	NUM
american_scientific_journal-2216	234	22	.	.	PUNCT
american_scientific_journal-2216	235	1	<	<	X
american_scientific_journal-2216	235	2	≤β	≤β	PROPN
american_scientific_journal-2216	235	3	table	table	NOUN
american_scientific_journal-2216	235	4	2	2	NUM
american_scientific_journal-2216	235	5	:	:	PUNCT
american_scientific_journal-2216	235	6	solution	solution	NOUN
american_scientific_journal-2216	235	7	of	of	ADP
american_scientific_journal-2216	235	8	the	the	DET
american_scientific_journal-2216	235	9	modal	modal	ADJ
american_scientific_journal-2216	235	10	problem	problem	NOUN
american_scientific_journal-2216	235	11	for	for	ADP
american_scientific_journal-2216	235	12	1.5	1.5	NUM
american_scientific_journal-2216	235	13	=	=	NOUN
american_scientific_journal-2216	235	14	β	β	NOUN
american_scientific_journal-2216	235	15	by	by	ADP
american_scientific_journal-2216	235	16	the	the	DET
american_scientific_journal-2216	235	17	original	original	ADJ
american_scientific_journal-2216	235	18	and	and	CCONJ
american_scientific_journal-2216	235	19	the	the	DET
american_scientific_journal-2216	235	20	preconditioned	preconditioned	ADJ
american_scientific_journal-2216	235	21	systems	system	NOUN
american_scientific_journal-2216	235	22	numerical	numerical	PROPN
american_scientific_journal-2216	235	23	data	datum	NOUN
american_scientific_journal-2216	235	24	of	of	ADP
american_scientific_journal-2216	235	25	the	the	DET
american_scientific_journal-2216	235	26	original	original	ADJ
american_scientific_journal-2216	235	27	and	and	CCONJ
american_scientific_journal-2216	235	28	the	the	DET
american_scientific_journal-2216	235	29	preconditioned	preconditioned	ADJ
american_scientific_journal-2216	235	30	systems	system	NOUN
american_scientific_journal-2216	235	31	are	be	AUX
american_scientific_journal-2216	235	32	summarized	summarize	VERB
american_scientific_journal-2216	235	33	in	in	ADP
american_scientific_journal-2216	235	34	tables	table	NOUN
american_scientific_journal-2216	235	35	(	(	PUNCT
american_scientific_journal-2216	235	36	2	2	NUM
american_scientific_journal-2216	235	37	-	-	SYM
american_scientific_journal-2216	235	38	3	3	NUM
american_scientific_journal-2216	235	39	)	)	PUNCT
american_scientific_journal-2216	235	40	for	for	ADP
american_scientific_journal-2216	235	41	two	two	NUM
american_scientific_journal-2216	235	42	fractional	fractional	ADJ
american_scientific_journal-2216	235	43	orders	order	NOUN
american_scientific_journal-2216	235	44	for	for	ADP
american_scientific_journal-2216	235	45	1.5	1.5	NUM
american_scientific_journal-2216	235	46	=	=	NOUN
american_scientific_journal-2216	235	47	β	β	NOUN
american_scientific_journal-2216	235	48	and	and	CCONJ
american_scientific_journal-2216	235	49	2	2	NUM
american_scientific_journal-2216	235	50	.=β	.=β	PUNCT
american_scientific_journal-2216	235	51	it	it	PRON
american_scientific_journal-2216	235	52	can	can	AUX
american_scientific_journal-2216	235	53	be	be	AUX
american_scientific_journal-2216	235	54	observed	observe	VERB
american_scientific_journal-2216	235	55	that	that	SCONJ
american_scientific_journal-2216	235	56	in	in	ADP
american_scientific_journal-2216	235	57	all	all	DET
american_scientific_journal-2216	235	58	cases	case	NOUN
american_scientific_journal-2216	235	59	illustrated	illustrate	VERB
american_scientific_journal-2216	235	60	the	the	DET
american_scientific_journal-2216	235	61	increase	increase	NOUN
american_scientific_journal-2216	235	62	in	in	ADP
american_scientific_journal-2216	235	63	the	the	DET
american_scientific_journal-2216	235	64	fractional	fractional	ADJ
american_scientific_journal-2216	235	65	order	order	NOUN
american_scientific_journal-2216	235	66	2	2	NUM
american_scientific_journal-2216	235	67	=	=	NOUN
american_scientific_journal-2216	235	68	β	β	NOUN
american_scientific_journal-2216	235	69	reduces	reduce	VERB
american_scientific_journal-2216	235	70	the	the	DET
american_scientific_journal-2216	235	71	magnitudes	magnitude	NOUN
american_scientific_journal-2216	235	72	of	of	ADP
american_scientific_journal-2216	235	73	the	the	DET
american_scientific_journal-2216	235	74	peaks	peak	NOUN
american_scientific_journal-2216	235	75	.	.	PUNCT
american_scientific_journal-2216	236	1	throughout	throughout	ADP
american_scientific_journal-2216	236	2	the	the	DET
american_scientific_journal-2216	236	3	two	two	NUM
american_scientific_journal-2216	236	4	sections	section	NOUN
american_scientific_journal-2216	236	5	of	of	ADP
american_scientific_journal-2216	236	6	our	our	PRON
american_scientific_journal-2216	236	7	experiments	experiment	NOUN
american_scientific_journal-2216	236	8	,	,	PUNCT
american_scientific_journal-2216	236	9	the	the	DET
american_scientific_journal-2216	236	10	results	result	NOUN
american_scientific_journal-2216	236	11	reveal	reveal	VERB
american_scientific_journal-2216	236	12	that	that	SCONJ
american_scientific_journal-2216	236	13	the	the	DET
american_scientific_journal-2216	236	14	proposed	propose	VERB
american_scientific_journal-2216	236	15	preconditioned	precondition	VERB
american_scientific_journal-2216	236	16	is	be	AUX
american_scientific_journal-2216	236	17	superior	superior	ADJ
american_scientific_journal-2216	236	18	to	to	ADP
american_scientific_journal-2216	236	19	the	the	DET
american_scientific_journal-2216	236	20	original	original	ADJ
american_scientific_journal-2216	236	21	system	system	NOUN
american_scientific_journal-2216	236	22	in	in	ADP
american_scientific_journal-2216	236	23	solving	solve	VERB
american_scientific_journal-2216	236	24	fractional	fractional	ADJ
american_scientific_journal-2216	236	25	elliptic	elliptic	ADJ
american_scientific_journal-2216	236	26	partial	partial	ADJ
american_scientific_journal-2216	236	27	differential	differential	NOUN
american_scientific_journal-2216	236	28	equations	equation	NOUN
american_scientific_journal-2216	236	29	.	.	PUNCT
american_scientific_journal-2216	237	1	original	original	ADJ
american_scientific_journal-2216	237	2	system	system	NOUN
american_scientific_journal-2216	237	3	preconditioned	precondition	VERB
american_scientific_journal-2216	237	4	system	system	NOUN
american_scientific_journal-2216	237	5	0	0	NUM
american_scientific_journal-2216	237	6	0.1	0.1	NUM
american_scientific_journal-2216	237	7	0.2	0.2	NUM
american_scientific_journal-2216	237	8	0.3	0.3	NUM
american_scientific_journal-2216	237	9	0.4	0.4	NUM
american_scientific_journal-2216	237	10	0.5	0.5	NUM
american_scientific_journal-2216	237	11	0	0	NUM
american_scientific_journal-2216	237	12	0.1	0.1	NUM
american_scientific_journal-2216	237	13	0.2	0.2	NUM
american_scientific_journal-2216	237	14	0.3	0.3	NUM
american_scientific_journal-2216	237	15	0.4	0.4	NUM
american_scientific_journal-2216	237	16	0.5	0.5	NUM
american_scientific_journal-2216	237	17	0	0	NUM
american_scientific_journal-2216	237	18	0	0	NUM
american_scientific_journal-2216	237	19	0	0	NUM
american_scientific_journal-2216	237	20	0	0	NUM
american_scientific_journal-2216	237	21	0	0	NUM
american_scientific_journal-2216	237	22	0	0	NUM
american_scientific_journal-2216	237	23	0	0	NUM
american_scientific_journal-2216	237	24	0	0	NUM
american_scientific_journal-2216	237	25	0	0	NUM
american_scientific_journal-2216	237	26	0	0	NUM
american_scientific_journal-2216	237	27	0	0	NUM
american_scientific_journal-2216	237	28	0	0	NUM
american_scientific_journal-2216	237	29	0	0	NUM
american_scientific_journal-2216	237	30	0.1	0.1	NUM
american_scientific_journal-2216	237	31	0	0	NUM
american_scientific_journal-2216	237	32	1.846	1.846	NUM
american_scientific_journal-2216	237	33	2.831	2.831	NUM
american_scientific_journal-2216	237	34	3.046	3.046	NUM
american_scientific_journal-2216	237	35	1.984	1.984	NUM
american_scientific_journal-2216	237	36	0	0	NUM
american_scientific_journal-2216	237	37	0	0	NUM
american_scientific_journal-2216	237	38	1.561	1.561	NUM
american_scientific_journal-2216	237	39	2.503	2.503	NUM
american_scientific_journal-2216	237	40	2.883	2.883	NUM
american_scientific_journal-2216	237	41	1.552	1.552	NUM
american_scientific_journal-2216	237	42	0	0	NUM
american_scientific_journal-2216	237	43	0.2	0.2	NUM
american_scientific_journal-2216	237	44	0	0	NUM
american_scientific_journal-2216	237	45	2.692	2.692	NUM
american_scientific_journal-2216	237	46	5.411	5.411	NUM
american_scientific_journal-2216	237	47	5.662	5.662	NUM
american_scientific_journal-2216	237	48	3.784	3.784	NUM
american_scientific_journal-2216	237	49	0	0	NUM
american_scientific_journal-2216	237	50	0	0	NUM
american_scientific_journal-2216	237	51	2.341	2.341	NUM
american_scientific_journal-2216	237	52	4.854	4.854	NUM
american_scientific_journal-2216	237	53	5.404	5.404	NUM
american_scientific_journal-2216	237	54	3.334	3.334	NUM
american_scientific_journal-2216	237	55	0	0	NUM
american_scientific_journal-2216	237	56	0.3	0.3	NUM
american_scientific_journal-2216	237	57	0	0	NUM
american_scientific_journal-2216	237	58	3.147	3.147	NUM
american_scientific_journal-2216	237	59	7.604	7.604	NUM
american_scientific_journal-2216	237	60	7.934	7.934	NUM
american_scientific_journal-2216	237	61	4.527	4.527	NUM
american_scientific_journal-2216	237	62	0	0	NUM
american_scientific_journal-2216	237	63	0	0	NUM
american_scientific_journal-2216	237	64	2.733	2.733	NUM
american_scientific_journal-2216	237	65	6.931	6.931	NUM
american_scientific_journal-2216	237	66	7.663	7.663	NUM
american_scientific_journal-2216	237	67	4.416	4.416	NUM
american_scientific_journal-2216	237	68	0	0	NUM
american_scientific_journal-2216	237	69	0.4	0.4	NUM
american_scientific_journal-2216	237	70	0	0	NUM
american_scientific_journal-2216	237	71	4.533	4.533	NUM
american_scientific_journal-2216	237	72	7.599	7.599	NUM
american_scientific_journal-2216	237	73	7.962	7.962	NUM
american_scientific_journal-2216	237	74	5.681	5.681	NUM
american_scientific_journal-2216	237	75	0	0	NUM
american_scientific_journal-2216	237	76	0	0	NUM
american_scientific_journal-2216	237	77	3.883	3.883	NUM
american_scientific_journal-2216	237	78	7.201	7.201	NUM
american_scientific_journal-2216	237	79	7.533	7.533	NUM
american_scientific_journal-2216	237	80	5.334	5.334	NUM
american_scientific_journal-2216	237	81	0	0	NUM
american_scientific_journal-2216	237	82	0.5	0.5	NUM
american_scientific_journal-2216	237	83	0	0	NUM
american_scientific_journal-2216	237	84	5.703	5.703	NUM
american_scientific_journal-2216	237	85	8.104	8.104	NUM
american_scientific_journal-2216	237	86	8.544	8.544	NUM
american_scientific_journal-2216	237	87	6.571	6.571	NUM
american_scientific_journal-2216	237	88	0	0	NUM
american_scientific_journal-2216	237	89	0	0	NUM
american_scientific_journal-2216	237	90	4.914	4.914	NUM
american_scientific_journal-2216	237	91	7.995	7.995	NUM
american_scientific_journal-2216	237	92	8.212	8.212	NUM
american_scientific_journal-2216	237	93	6.204	6.204	NUM
american_scientific_journal-2216	237	94	0	0	NUM
american_scientific_journal-2216	237	95	0.6	0.6	NUM
american_scientific_journal-2216	237	96	0	0	NUM
american_scientific_journal-2216	237	97	6.342	6.342	NUM
american_scientific_journal-2216	237	98	8.212	8.212	NUM
american_scientific_journal-2216	237	99	8.704	8.704	NUM
american_scientific_journal-2216	237	100	7.364	7.364	NUM
american_scientific_journal-2216	237	101	0	0	NUM
american_scientific_journal-2216	237	102	0	0	NUM
american_scientific_journal-2216	237	103	5.683	5.683	NUM
american_scientific_journal-2216	237	104	8.113	8.113	NUM
american_scientific_journal-2216	237	105	8.673	8.673	NUM
american_scientific_journal-2216	237	106	6.677	6.677	NUM
american_scientific_journal-2216	237	107	0	0	NUM
american_scientific_journal-2216	237	108	0.7	0.7	NUM
american_scientific_journal-2216	237	109	0	0	NUM
american_scientific_journal-2216	237	110	5.425	5.425	NUM
american_scientific_journal-2216	237	111	6.425	6.425	NUM
american_scientific_journal-2216	237	112	6.225	6.225	NUM
american_scientific_journal-2216	237	113	6.225	6.225	NUM
american_scientific_journal-2216	237	114	0	0	NUM
american_scientific_journal-2216	237	115	0	0	NUM
american_scientific_journal-2216	237	116	4.842	4.842	NUM
american_scientific_journal-2216	237	117	5.524	5.524	NUM
american_scientific_journal-2216	237	118	5.791	5.791	NUM
american_scientific_journal-2216	237	119	5.875	5.875	NUM
american_scientific_journal-2216	237	120	0	0	NUM
american_scientific_journal-2216	237	121	0.8	0.8	NUM
american_scientific_journal-2216	237	122	0	0	NUM
american_scientific_journal-2216	237	123	3.843	3.843	NUM
american_scientific_journal-2216	237	124	4.511	4.511	NUM
american_scientific_journal-2216	237	125	4.341	4.341	NUM
american_scientific_journal-2216	237	126	4.542	4.542	NUM
american_scientific_journal-2216	237	127	0	0	NUM
american_scientific_journal-2216	237	128	0	0	NUM
american_scientific_journal-2216	237	129	2.661	2.661	NUM
american_scientific_journal-2216	237	130	3.641	3.641	NUM
american_scientific_journal-2216	237	131	3.973	3.973	NUM
american_scientific_journal-2216	237	132	4.341	4.341	NUM
american_scientific_journal-2216	237	133	0	0	NUM
american_scientific_journal-2216	237	134	0.9	0.9	NUM
american_scientific_journal-2216	237	135	0	0	NUM
american_scientific_journal-2216	237	136	1.846	1.846	NUM
american_scientific_journal-2216	237	137	2.831	2.831	NUM
american_scientific_journal-2216	237	138	3.046	3.046	NUM
american_scientific_journal-2216	237	139	1.984	1.984	NUM
american_scientific_journal-2216	237	140	0	0	NUM
american_scientific_journal-2216	237	141	0	0	NUM
american_scientific_journal-2216	237	142	1.543	1.543	NUM
american_scientific_journal-2216	237	143	2.492	2.492	NUM
american_scientific_journal-2216	237	144	2.785	2.785	NUM
american_scientific_journal-2216	237	145	1.473	1.473	NUM
american_scientific_journal-2216	237	146	0	0	NUM
american_scientific_journal-2216	237	147	1	1	NUM
american_scientific_journal-2216	237	148	0	0	NUM
american_scientific_journal-2216	237	149	0	0	NUM
american_scientific_journal-2216	237	150	0	0	NUM
american_scientific_journal-2216	237	151	0	0	NUM
american_scientific_journal-2216	237	152	0	0	NUM
american_scientific_journal-2216	237	153	0	0	NUM
american_scientific_journal-2216	237	154	0	0	NUM
american_scientific_journal-2216	237	155	0	0	NUM
american_scientific_journal-2216	237	156	0	0	NUM
american_scientific_journal-2216	237	157	0	0	NUM
american_scientific_journal-2216	237	158	0	0	NUM
american_scientific_journal-2216	237	159	0	0	NUM
american_scientific_journal-2216	238	1	x	x	SYM
american_scientific_journal-2216	238	2	y	y	PROPN
american_scientific_journal-2216	238	3	american	american	PROPN
american_scientific_journal-2216	238	4	scientific	scientific	PROPN
american_scientific_journal-2216	238	5	research	research	PROPN
american_scientific_journal-2216	238	6	journal	journal	NOUN
american_scientific_journal-2216	238	7	for	for	ADP
american_scientific_journal-2216	238	8	engineering	engineering	NOUN
american_scientific_journal-2216	238	9	,	,	PUNCT
american_scientific_journal-2216	238	10	technology	technology	NOUN
american_scientific_journal-2216	238	11	,	,	PUNCT
american_scientific_journal-2216	238	12	and	and	CCONJ
american_scientific_journal-2216	238	13	sciences	science	NOUN
american_scientific_journal-2216	238	14	(	(	PUNCT
american_scientific_journal-2216	238	15	asrjets	asrjet	NOUN
american_scientific_journal-2216	238	16	)	)	PUNCT
american_scientific_journal-2216	238	17	(	(	PUNCT
american_scientific_journal-2216	238	18	2016	2016	NUM
american_scientific_journal-2216	238	19	)	)	PUNCT
american_scientific_journal-2216	238	20	volume	volume	NOUN
american_scientific_journal-2216	238	21	26	26	NUM
american_scientific_journal-2216	238	22	,	,	PUNCT
american_scientific_journal-2216	238	23	no	no	DET
american_scientific_journal-2216	238	24	1	1	NUM
american_scientific_journal-2216	238	25	,	,	PUNCT
american_scientific_journal-2216	238	26	pp	pp	ADV
american_scientific_journal-2216	238	27	261	261	NUM
american_scientific_journal-2216	238	28	-	-	SYM
american_scientific_journal-2216	238	29	270	270	NUM
american_scientific_journal-2216	238	30	269	269	NUM
american_scientific_journal-2216	238	31	table	table	NOUN
american_scientific_journal-2216	238	32	(	(	PUNCT
american_scientific_journal-2216	238	33	3	3	NUM
american_scientific_journal-2216	238	34	):	):	PUNCT
american_scientific_journal-2216	238	35	solution	solution	NOUN
american_scientific_journal-2216	238	36	of	of	ADP
american_scientific_journal-2216	238	37	the	the	DET
american_scientific_journal-2216	238	38	modal	modal	ADJ
american_scientific_journal-2216	238	39	problem	problem	NOUN
american_scientific_journal-2216	238	40	for	for	ADP
american_scientific_journal-2216	238	41	2	2	NUM
american_scientific_journal-2216	238	42	=	=	NOUN
american_scientific_journal-2216	238	43	β	β	NOUN
american_scientific_journal-2216	238	44	by	by	ADP
american_scientific_journal-2216	238	45	the	the	DET
american_scientific_journal-2216	238	46	original	original	ADJ
american_scientific_journal-2216	238	47	and	and	CCONJ
american_scientific_journal-2216	238	48	the	the	DET
american_scientific_journal-2216	238	49	preconditioned	preconditioned	ADJ
american_scientific_journal-2216	238	50	systems	system	NOUN
american_scientific_journal-2216	238	51	5	5	NUM
american_scientific_journal-2216	238	52	.	.	PUNCT
american_scientific_journal-2216	238	53	conclusion	conclusion	NOUN
american_scientific_journal-2216	238	54	and	and	CCONJ
american_scientific_journal-2216	238	55	future	future	ADJ
american_scientific_journal-2216	238	56	works	work	NOUN
american_scientific_journal-2216	238	57	in	in	ADP
american_scientific_journal-2216	238	58	this	this	DET
american_scientific_journal-2216	238	59	paper	paper	NOUN
american_scientific_journal-2216	238	60	,	,	PUNCT
american_scientific_journal-2216	238	61	we	we	PRON
american_scientific_journal-2216	238	62	have	have	AUX
american_scientific_journal-2216	238	63	formulated	formulate	VERB
american_scientific_journal-2216	238	64	new	new	ADJ
american_scientific_journal-2216	238	65	preconditioned	preconditioned	ADJ
american_scientific_journal-2216	238	66	iterative	iterative	NOUN
american_scientific_journal-2216	238	67	method	method	NOUN
american_scientific_journal-2216	238	68	based	base	VERB
american_scientific_journal-2216	238	69	on	on	ADP
american_scientific_journal-2216	238	70	rotated	rotate	VERB
american_scientific_journal-2216	238	71	finite	finite	ADJ
american_scientific_journal-2216	238	72	difference	difference	NOUN
american_scientific_journal-2216	238	73	method	method	NOUN
american_scientific_journal-2216	238	74	for	for	ADP
american_scientific_journal-2216	238	75	solving	solve	VERB
american_scientific_journal-2216	238	76	fractional	fractional	ADJ
american_scientific_journal-2216	238	77	elliptic	elliptic	ADJ
american_scientific_journal-2216	238	78	partial	partial	ADJ
american_scientific_journal-2216	238	79	differential	differential	NOUN
american_scientific_journal-2216	238	80	equations	equation	NOUN
american_scientific_journal-2216	238	81	.	.	PUNCT
american_scientific_journal-2216	239	1	from	from	ADP
american_scientific_journal-2216	239	2	observation	observation	NOUN
american_scientific_journal-2216	239	3	of	of	ADP
american_scientific_journal-2216	239	4	all	all	DET
american_scientific_journal-2216	239	5	experimental	experimental	ADJ
american_scientific_journal-2216	239	6	results	result	NOUN
american_scientific_journal-2216	239	7	,	,	PUNCT
american_scientific_journal-2216	239	8	it	it	PRON
american_scientific_journal-2216	239	9	can	can	AUX
american_scientific_journal-2216	239	10	be	be	AUX
american_scientific_journal-2216	239	11	concluded	conclude	VERB
american_scientific_journal-2216	239	12	that	that	SCONJ
american_scientific_journal-2216	239	13	the	the	DET
american_scientific_journal-2216	239	14	proposed	propose	VERB
american_scientific_journal-2216	239	15	scheme	scheme	NOUN
american_scientific_journal-2216	239	16	may	may	AUX
american_scientific_journal-2216	239	17	be	be	AUX
american_scientific_journal-2216	239	18	a	a	DET
american_scientific_journal-2216	239	19	good	good	ADJ
american_scientific_journal-2216	239	20	alternative	alternative	NOUN
american_scientific_journal-2216	239	21	to	to	PART
american_scientific_journal-2216	239	22	solve	solve	VERB
american_scientific_journal-2216	239	23	fractional	fractional	ADJ
american_scientific_journal-2216	239	24	elliptic	elliptic	ADJ
american_scientific_journal-2216	239	25	partial	partial	ADJ
american_scientific_journal-2216	239	26	differential	differential	NOUN
american_scientific_journal-2216	239	27	equation	equation	NOUN
american_scientific_journal-2216	239	28	and	and	CCONJ
american_scientific_journal-2216	239	29	many	many	ADJ
american_scientific_journal-2216	239	30	other	other	ADJ
american_scientific_journal-2216	239	31	numerical	numerical	ADJ
american_scientific_journal-2216	239	32	problems	problem	NOUN
american_scientific_journal-2216	239	33	.	.	PUNCT
american_scientific_journal-2216	240	1	the	the	DET
american_scientific_journal-2216	240	2	idea	idea	NOUN
american_scientific_journal-2216	240	3	of	of	ADP
american_scientific_journal-2216	240	4	this	this	DET
american_scientific_journal-2216	240	5	proposed	propose	VERB
american_scientific_journal-2216	240	6	method	method	NOUN
american_scientific_journal-2216	240	7	can	can	AUX
american_scientific_journal-2216	240	8	be	be	AUX
american_scientific_journal-2216	240	9	extended	extend	VERB
american_scientific_journal-2216	240	10	to	to	ADP
american_scientific_journal-2216	240	11	group	group	NOUN
american_scientific_journal-2216	240	12	iterative	iterative	NOUN
american_scientific_journal-2216	240	13	solver	solver	NOUN
american_scientific_journal-2216	240	14	which	which	PRON
american_scientific_journal-2216	240	15	will	will	AUX
american_scientific_journal-2216	240	16	be	be	AUX
american_scientific_journal-2216	240	17	reported	report	VERB
american_scientific_journal-2216	240	18	separately	separately	ADV
american_scientific_journal-2216	240	19	in	in	ADP
american_scientific_journal-2216	240	20	the	the	DET
american_scientific_journal-2216	240	21	future	future	NOUN
american_scientific_journal-2216	240	22	.	.	PUNCT
american_scientific_journal-2216	241	1	acknowledgements	acknowledgement	NOUN
american_scientific_journal-2216	241	2	financial	financial	ADJ
american_scientific_journal-2216	241	3	support	support	NOUN
american_scientific_journal-2216	241	4	provided	provide	VERB
american_scientific_journal-2216	241	5	by	by	ADP
american_scientific_journal-2216	241	6	qassim	qassim	PROPN
american_scientific_journal-2216	241	7	university	university	PROPN
american_scientific_journal-2216	241	8	for	for	ADP
american_scientific_journal-2216	241	9	the	the	DET
american_scientific_journal-2216	241	10	completion	completion	NOUN
american_scientific_journal-2216	241	11	of	of	ADP
american_scientific_journal-2216	241	12	this	this	DET
american_scientific_journal-2216	241	13	research	research	NOUN
american_scientific_journal-2216	241	14	is	be	AUX
american_scientific_journal-2216	241	15	gratefully	gratefully	ADV
american_scientific_journal-2216	241	16	acknowledged	acknowledge	VERB
american_scientific_journal-2216	241	17	.	.	PUNCT
american_scientific_journal-2216	242	1	references	reference	NOUN
american_scientific_journal-2216	242	2	[	[	X
american_scientific_journal-2216	242	3	1	1	NUM
american_scientific_journal-2216	242	4	]	]	PUNCT
american_scientific_journal-2216	242	5	a.	a.	PROPN
american_scientific_journal-2216	242	6	r.	r.	PROPN
american_scientific_journal-2216	242	7	abdullah	abdullah	PROPN
american_scientific_journal-2216	242	8	,	,	PUNCT
american_scientific_journal-2216	242	9	“	"	PUNCT
american_scientific_journal-2216	242	10	the	the	DET
american_scientific_journal-2216	242	11	four	four	NUM
american_scientific_journal-2216	242	12	point	point	NOUN
american_scientific_journal-2216	242	13	explicit	explicit	ADJ
american_scientific_journal-2216	242	14	decoupled	decouple	VERB
american_scientific_journal-2216	242	15	group	group	NOUN
american_scientific_journal-2216	242	16	(	(	PUNCT
american_scientific_journal-2216	242	17	edg	edg	PROPN
american_scientific_journal-2216	242	18	)	)	PUNCT
american_scientific_journal-2216	242	19	method	method	NOUN
american_scientific_journal-2216	242	20	:	:	PUNCT
american_scientific_journal-2216	242	21	a	a	DET
american_scientific_journal-2216	242	22	fast	fast	ADJ
american_scientific_journal-2216	242	23	poisson	poisson	NOUN
american_scientific_journal-2216	242	24	solver	solver	X
american_scientific_journal-2216	242	25	”	"	PUNCT
american_scientific_journal-2216	242	26	international	international	ADJ
american_scientific_journal-2216	242	27	journal	journal	NOUN
american_scientific_journal-2216	242	28	of	of	ADP
american_scientific_journal-2216	242	29	comp	comp	PROPN
american_scientific_journal-2216	242	30	.	.	PUNCT
american_scientific_journal-2216	243	1	math	math	NOUN
american_scientific_journal-2216	243	2	.	.	PUNCT
american_scientific_journal-2216	244	1	vol	vol	NOUN
american_scientific_journal-2216	244	2	.	.	PROPN
american_scientific_journal-2216	245	1	38	38	NUM
american_scientific_journal-2216	245	2	,	,	PUNCT
american_scientific_journal-2216	245	3	pp	pp	ADJ
american_scientific_journal-2216	245	4	.	.	PUNCT
american_scientific_journal-2216	246	1	61	61	NUM
american_scientific_journal-2216	246	2	-	-	SYM
american_scientific_journal-2216	246	3	70	70	NUM
american_scientific_journal-2216	246	4	,	,	PUNCT
american_scientific_journal-2216	246	5	1991	1991	NUM
american_scientific_journal-2216	246	6	.	.	PUNCT
american_scientific_journal-2216	247	1	[	[	X
american_scientific_journal-2216	247	2	2	2	NUM
american_scientific_journal-2216	247	3	]	]	PUNCT
american_scientific_journal-2216	247	4	a.	a.	NOUN
american_scientific_journal-2216	247	5	gunawardena	gunawardena	PROPN
american_scientific_journal-2216	247	6	,	,	PUNCT
american_scientific_journal-2216	247	7	s.	s.	PROPN
american_scientific_journal-2216	247	8	jain	jain	PROPN
american_scientific_journal-2216	247	9	,	,	PUNCT
american_scientific_journal-2216	247	10	l.	l.	PROPN
american_scientific_journal-2216	247	11	snyder	snyder	PROPN
american_scientific_journal-2216	247	12	,	,	PUNCT
american_scientific_journal-2216	247	13	”	"	PUNCT
american_scientific_journal-2216	247	14	modified	modify	VERB
american_scientific_journal-2216	247	15	iterative	iterative	NOUN
american_scientific_journal-2216	247	16	methods	method	NOUN
american_scientific_journal-2216	247	17	for	for	ADP
american_scientific_journal-2216	247	18	consistent	consistent	ADJ
american_scientific_journal-2216	247	19	linear	linear	PROPN
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american_scientific_journal-2216	247	22	.	.	PUNCT
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american_scientific_journal-2216	249	5	,	,	PUNCT
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american_scientific_journal-2216	251	9	,	,	PUNCT
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american_scientific_journal-2216	251	11	,	,	PUNCT
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american_scientific_journal-2216	251	13	sciences	science	NOUN
american_scientific_journal-2216	251	14	(	(	PUNCT
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american_scientific_journal-2216	251	17	(	(	PUNCT
american_scientific_journal-2216	251	18	2016	2016	NUM
american_scientific_journal-2216	251	19	)	)	PUNCT
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american_scientific_journal-2216	251	21	26	26	NUM
american_scientific_journal-2216	251	22	,	,	PUNCT
american_scientific_journal-2216	251	23	no	no	DET
american_scientific_journal-2216	251	24	1	1	NUM
american_scientific_journal-2216	251	25	,	,	PUNCT
american_scientific_journal-2216	251	26	pp	pp	ADV
american_scientific_journal-2216	251	27	261	261	NUM
american_scientific_journal-2216	251	28	-	-	SYM
american_scientific_journal-2216	251	29	270	270	NUM
american_scientific_journal-2216	251	30	270	270	NUM
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american_scientific_journal-2216	253	1	,	,	PUNCT
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american_scientific_journal-2216	256	5	-	-	SYM
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american_scientific_journal-2216	259	2	-	-	SYM
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american_scientific_journal-2216	262	5	i.	i.	PROPN
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american_scientific_journal-2216	262	7	,	,	PUNCT
american_scientific_journal-2216	262	8	o.	o.	PROPN
american_scientific_journal-2216	262	9	p.	p.	PROPN
american_scientific_journal-2216	262	10	agrawal	agrawal	PROPN
american_scientific_journal-2216	262	11	,	,	PUNCT
american_scientific_journal-2216	262	12	“	"	PUNCT
american_scientific_journal-2216	262	13	riesz	riesz	VERB
american_scientific_journal-2216	262	14	fractional	fractional	ADJ
american_scientific_journal-2216	262	15	derivatives	derivative	NOUN
american_scientific_journal-2216	262	16	and	and	CCONJ
american_scientific_journal-2216	262	17	dimensional	dimensional	ADJ
american_scientific_journal-2216	262	18	space	space	NOUN
american_scientific_journal-2216	262	19	”	"	PUNCT
american_scientific_journal-2216	262	20	,	,	PUNCT
american_scientific_journal-2216	262	21	int	int	PROPN
american_scientific_journal-2216	262	22	j	j	PROPN
american_scientific_journal-2216	262	23	theor	theor	PROPN
american_scientific_journal-2216	262	24	phys	phys	PROPN
american_scientific_journal-2216	262	25	,	,	PUNCT
american_scientific_journal-2216	262	26	vol	vol	NOUN
american_scientific_journal-2216	262	27	.	.	PUNCT
american_scientific_journal-2216	263	1	49(2	49(2	NUM
american_scientific_journal-2216	263	2	)	)	PUNCT
american_scientific_journal-2216	263	3	,	,	PUNCT
american_scientific_journal-2216	264	1	pp	pp	PROPN
american_scientific_journal-2216	264	2	.	.	PUNCT
american_scientific_journal-2216	265	1	270	270	NUM
american_scientific_journal-2216	265	2	-	-	SYM
american_scientific_journal-2216	265	3	275	275	NUM
american_scientific_journal-2216	265	4	,	,	PUNCT
american_scientific_journal-2216	265	5	2010	2010	NUM
american_scientific_journal-2216	265	6	.	.	PUNCT
american_scientific_journal-2216	266	1	[	[	X
american_scientific_journal-2216	266	2	7	7	X
american_scientific_journal-2216	266	3	]	]	X
american_scientific_journal-2216	266	4	j.	j.	PROPN
american_scientific_journal-2216	266	5	hristov	hristov	PROPN
american_scientific_journal-2216	266	6	,	,	PUNCT
american_scientific_journal-2216	266	7	“	"	PUNCT
american_scientific_journal-2216	266	8	approximate	approximate	ADJ
american_scientific_journal-2216	266	9	solutions	solution	NOUN
american_scientific_journal-2216	266	10	to	to	ADP
american_scientific_journal-2216	266	11	fractional	fractional	ADJ
american_scientific_journal-2216	266	12	subdiffusion	subdiffusion	NOUN
american_scientific_journal-2216	266	13	equations	equation	NOUN
american_scientific_journal-2216	266	14	”	"	PUNCT
american_scientific_journal-2216	266	15	,	,	PUNCT
american_scientific_journal-2216	266	16	european	european	PROPN
american_scientific_journal-2216	266	17	physical	physical	PROPN
american_scientific_journal-2216	266	18	journal	journal	PROPN
american_scientific_journal-2216	266	19	,	,	PUNCT
american_scientific_journal-2216	266	20	vol	vol	NOUN
american_scientific_journal-2216	266	21	.	.	PUNCT
american_scientific_journal-2216	266	22	193(1	193(1	NUM
american_scientific_journal-2216	266	23	)	)	PUNCT
american_scientific_journal-2216	266	24	pp	pp	ADP
american_scientific_journal-2216	266	25	.	.	PUNCT
american_scientific_journal-2216	267	1	229	229	NUM
american_scientific_journal-2216	267	2	-	-	SYM
american_scientific_journal-2216	267	3	243	243	NUM
american_scientific_journal-2216	267	4	,	,	PUNCT
american_scientific_journal-2216	267	5	2011	2011	NUM
american_scientific_journal-2216	267	6	.	.	PUNCT
american_scientific_journal-2216	268	1	[	[	X
american_scientific_journal-2216	268	2	8	8	X
american_scientific_journal-2216	268	3	]	]	X
american_scientific_journal-2216	268	4	v.	v.	PROPN
american_scientific_journal-2216	268	5	d.	d.	PROPN
american_scientific_journal-2216	268	6	beibalaev	beibalaev	PROPN
american_scientific_journal-2216	268	7	,	,	PUNCT
american_scientific_journal-2216	268	8	p.	p.	PROPN
american_scientific_journal-2216	268	9	ruslan	ruslan	PROPN
american_scientific_journal-2216	268	10	,	,	PUNCT
american_scientific_journal-2216	268	11	meilanov	meilanov	NOUN
american_scientific_journal-2216	268	12	,	,	PUNCT
american_scientific_journal-2216	268	13	“	"	PUNCT
american_scientific_journal-2216	268	14	the	the	DET
american_scientific_journal-2216	268	15	dirihlet	dirihlet	PROPN
american_scientific_journal-2216	268	16	problem	problem	NOUN
american_scientific_journal-2216	268	17	for	for	ADP
american_scientific_journal-2216	268	18	the	the	DET
american_scientific_journal-2216	268	19	fractional	fractional	ADJ
american_scientific_journal-2216	268	20	poisson	poisson	NOUN
american_scientific_journal-2216	268	21	’s	’s	PART
american_scientific_journal-2216	268	22	equation	equation	NOUN
american_scientific_journal-2216	268	23	with	with	ADP
american_scientific_journal-2216	268	24	caputo	caputo	PROPN
american_scientific_journal-2216	268	25	derivatives	derivative	NOUN
american_scientific_journal-2216	268	26	:	:	PUNCT
american_scientific_journal-2216	268	27	afinite	afinite	NOUN
american_scientific_journal-2216	268	28	difference	difference	NOUN
american_scientific_journal-2216	268	29	approximation	approximation	NOUN
american_scientific_journal-2216	268	30	and	and	CCONJ
american_scientific_journal-2216	268	31	a	a	DET
american_scientific_journal-2216	268	32	numerical	numerical	ADJ
american_scientific_journal-2216	268	33	solution	solution	NOUN
american_scientific_journal-2216	268	34	”	"	PUNCT
american_scientific_journal-2216	268	35	,	,	PUNCT
american_scientific_journal-2216	268	36	thermal	thermal	ADJ
american_scientific_journal-2216	268	37	science	science	NOUN
american_scientific_journal-2216	268	38	,	,	PUNCT
american_scientific_journal-2216	268	39	vol	vol	NOUN
american_scientific_journal-2216	268	40	.	.	PROPN
american_scientific_journal-2216	268	41	16(2	16(2	NUM
american_scientific_journal-2216	268	42	)	)	PUNCT
american_scientific_journal-2216	268	43	,	,	PUNCT
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american_scientific_journal-2216	268	45	-	-	PUNCT
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american_scientific_journal-2216	268	47	,	,	PUNCT
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american_scientific_journal-2216	268	49	.	.	PUNCT
american_scientific_journal-2216	269	1	[	[	X
american_scientific_journal-2216	269	2	9	9	NUM
american_scientific_journal-2216	269	3	]	]	PUNCT
american_scientific_journal-2216	269	4	z.	z.	PROPN
american_scientific_journal-2216	269	5	b.	b.	PROPN
american_scientific_journal-2216	269	6	li	li	PROPN
american_scientific_journal-2216	269	7	,	,	PUNCT
american_scientific_journal-2216	269	8	j.	j.	PROPN
american_scientific_journal-2216	269	9	h.	h.	PROPN
american_scientific_journal-2216	269	10	he	he	PRON
american_scientific_journal-2216	269	11	,	,	PUNCT
american_scientific_journal-2216	269	12	“	"	PUNCT
american_scientific_journal-2216	269	13	fractional	fractional	ADJ
american_scientific_journal-2216	269	14	complex	complex	ADJ
american_scientific_journal-2216	269	15	transform	transform	NOUN
american_scientific_journal-2216	269	16	for	for	ADP
american_scientific_journal-2216	269	17	fractional	fractional	ADJ
american_scientific_journal-2216	269	18	differential	differential	ADJ
american_scientific_journal-2216	269	19	equations	equation	NOUN
american_scientific_journal-2216	269	20	”	"	PUNCT
american_scientific_journal-2216	269	21	,	,	PUNCT
american_scientific_journal-2216	269	22	mathematical	mathematical	ADJ
american_scientific_journal-2216	269	23	and	and	CCONJ
american_scientific_journal-2216	269	24	computational	computational	ADJ
american_scientific_journal-2216	269	25	applications	application	NOUN
american_scientific_journal-2216	269	26	,	,	PUNCT
american_scientific_journal-2216	269	27	vol	vol	NOUN
american_scientific_journal-2216	269	28	.	.	PUNCT
american_scientific_journal-2216	269	29	15(5	15(5	NUM
american_scientific_journal-2216	269	30	)	)	PUNCT
american_scientific_journal-2216	269	31	,	,	PUNCT
american_scientific_journal-2216	269	32	pp	pp	ADP
american_scientific_journal-2216	269	33	.	.	PUNCT
american_scientific_journal-2216	270	1	970	970	NUM
american_scientific_journal-2216	270	2	-	-	SYM
american_scientific_journal-2216	270	3	973	973	NUM
american_scientific_journal-2216	270	4	,	,	PUNCT
american_scientific_journal-2216	270	5	2010	2010	NUM
american_scientific_journal-2216	270	6	.	.	PUNCT
american_scientific_journal-2216	271	1	[	[	X
american_scientific_journal-2216	271	2	10	10	NUM
american_scientific_journal-2216	271	3	]	]	X
american_scientific_journal-2216	271	4	r.	r.	PROPN
american_scientific_journal-2216	271	5	metzler	metzler	PROPN
american_scientific_journal-2216	271	6	,	,	PUNCT
american_scientific_journal-2216	271	7	j.	j.	PROPN
american_scientific_journal-2216	271	8	klafter	klafter	PROPN
american_scientific_journal-2216	271	9	,	,	PUNCT
american_scientific_journal-2216	271	10	“	"	PUNCT
american_scientific_journal-2216	271	11	the	the	DET
american_scientific_journal-2216	271	12	random	random	ADJ
american_scientific_journal-2216	271	13	walk	walk	NOUN
american_scientific_journal-2216	271	14	’s	’s	PART
american_scientific_journal-2216	271	15	guide	guide	NOUN
american_scientific_journal-2216	271	16	to	to	ADP
american_scientific_journal-2216	271	17	anomalous	anomalous	ADJ
american_scientific_journal-2216	271	18	diffusion	diffusion	NOUN
american_scientific_journal-2216	271	19	:	:	PUNCT
american_scientific_journal-2216	271	20	a	a	DET
american_scientific_journal-2216	271	21	fractional	fractional	ADJ
american_scientific_journal-2216	271	22	dynamics	dynamic	NOUN
american_scientific_journal-2216	271	23	approach	approach	NOUN
american_scientific_journal-2216	271	24	”	"	PUNCT
american_scientific_journal-2216	271	25	.	.	PUNCT
american_scientific_journal-2216	272	1	phys	phy	NOUN
american_scientific_journal-2216	272	2	.	.	PUNCT
american_scientific_journal-2216	273	1	rep	rep	PROPN
american_scientific_journal-2216	273	2	.	.	PROPN
american_scientific_journal-2216	273	3	,	,	PUNCT
american_scientific_journal-2216	273	4	vol.339(1	vol.339(1	PROPN
american_scientific_journal-2216	273	5	)	)	PUNCT
american_scientific_journal-2216	273	6	,	,	PUNCT
american_scientific_journal-2216	273	7	pp.1	pp.1	PROPN
american_scientific_journal-2216	273	8	-	-	PUNCT
american_scientific_journal-2216	273	9	77	77	NUM
american_scientific_journal-2216	273	10	,	,	PUNCT
american_scientific_journal-2216	273	11	2000	2000	NUM
american_scientific_journal-2216	273	12	.	.	PUNCT
american_scientific_journal-2216	274	1	[	[	X
american_scientific_journal-2216	274	2	11	11	NUM
american_scientific_journal-2216	274	3	]	]	PUNCT
american_scientific_journal-2216	274	4	v.	v.	ADP
american_scientific_journal-2216	274	5	m.	m.	PROPN
american_scientific_journal-2216	274	6	goloviznin	goloviznin	PROPN
american_scientific_journal-2216	274	7	,	,	PUNCT
american_scientific_journal-2216	274	8	i.	i.	PROPN
american_scientific_journal-2216	274	9	a.	a.	PROPN
american_scientific_journal-2216	274	10	korotkin	korotkin	PROPN
american_scientific_journal-2216	274	11	,	,	PUNCT
american_scientific_journal-2216	274	12	“	"	PUNCT
american_scientific_journal-2216	274	13	methods	method	NOUN
american_scientific_journal-2216	274	14	of	of	ADP
american_scientific_journal-2216	274	15	the	the	DET
american_scientific_journal-2216	274	16	numerical	numerical	ADJ
american_scientific_journal-2216	274	17	solutions	solution	NOUN
american_scientific_journal-2216	274	18	some	some	DET
american_scientific_journal-2216	274	19	one	one	NUM
american_scientific_journal-2216	274	20	-	-	PUNCT
american_scientific_journal-2216	274	21	dimensional	dimensional	ADJ
american_scientific_journal-2216	274	22	equations	equation	NOUN
american_scientific_journal-2216	274	23	with	with	ADP
american_scientific_journal-2216	274	24	fractional	fractional	ADJ
american_scientific_journal-2216	274	25	derivatives	derivative	NOUN
american_scientific_journal-2216	274	26	”	"	PUNCT
american_scientific_journal-2216	274	27	,	,	PUNCT
american_scientific_journal-2216	274	28	differential	differential	ADJ
american_scientific_journal-2216	274	29	equations	equation	NOUN
american_scientific_journal-2216	274	30	,	,	PUNCT
american_scientific_journal-2216	274	31	vol.42(7	vol.42(7	NOUN
american_scientific_journal-2216	274	32	)	)	PUNCT
american_scientific_journal-2216	274	33	,	,	PUNCT
american_scientific_journal-2216	274	34	pp	pp	PROPN
american_scientific_journal-2216	274	35	.	.	PUNCT
american_scientific_journal-2216	275	1	21	21	NUM
american_scientific_journal-2216	275	2	-	-	SYM
american_scientific_journal-2216	275	3	130	130	NUM
american_scientific_journal-2216	275	4	,	,	PUNCT
american_scientific_journal-2216	275	5	2006	2006	NUM
american_scientific_journal-2216	275	6	.	.	PUNCT
american_scientific_journal-2216	276	1	[	[	X
american_scientific_journal-2216	276	2	12	12	NUM
american_scientific_journal-2216	276	3	]	]	PUNCT
american_scientific_journal-2216	276	4	k.	k.	PROPN
american_scientific_journal-2216	276	5	b.	b.	PROPN
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american_scientific_journal-2216	276	7	,	,	PUNCT
american_scientific_journal-2216	276	8	j.	j.	PROPN
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american_scientific_journal-2216	276	10	,	,	PUNCT
american_scientific_journal-2216	276	11	the	the	DET
american_scientific_journal-2216	276	12	fractional	fractional	ADJ
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american_scientific_journal-2216	276	14	,	,	PUNCT
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american_scientific_journal-2216	276	17	,	,	PUNCT
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american_scientific_journal-2216	276	20	,	,	PUNCT
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american_scientific_journal-2216	276	22	,	,	PUNCT
american_scientific_journal-2216	276	23	1974	1974	NUM
american_scientific_journal-2216	276	24	.	.	PUNCT