id	sid	tid	token	lemma	pos
american_scientific_journal-1936	1	1	140	140	NUM
american_scientific_journal-1936	1	2	american	american	ADJ
american_scientific_journal-1936	1	3	scientific	scientific	ADJ
american_scientific_journal-1936	1	4	research	research	NOUN
american_scientific_journal-1936	1	5	journal	journal	NOUN
american_scientific_journal-1936	1	6	for	for	ADP
american_scientific_journal-1936	1	7	engineering	engineering	NOUN
american_scientific_journal-1936	1	8	,	,	PUNCT
american_scientific_journal-1936	1	9	technology	technology	NOUN
american_scientific_journal-1936	1	10	,	,	PUNCT
american_scientific_journal-1936	1	11	and	and	CCONJ
american_scientific_journal-1936	1	12	sciences	science	NOUN
american_scientific_journal-1936	1	13	(	(	PUNCT
american_scientific_journal-1936	1	14	asrjets	asrjet	NOUN
american_scientific_journal-1936	1	15	)	)	PUNCT
american_scientific_journal-1936	1	16	issn	issn	PROPN
american_scientific_journal-1936	1	17	(	(	PUNCT
american_scientific_journal-1936	1	18	print	print	NOUN
american_scientific_journal-1936	1	19	)	)	PUNCT
american_scientific_journal-1936	1	20	2313	2313	NUM
american_scientific_journal-1936	1	21	-	-	SYM
american_scientific_journal-1936	1	22	4410	4410	NUM
american_scientific_journal-1936	1	23	,	,	PUNCT
american_scientific_journal-1936	1	24	issn	issn	PROPN
american_scientific_journal-1936	1	25	(	(	PUNCT
american_scientific_journal-1936	1	26	online	online	ADJ
american_scientific_journal-1936	1	27	)	)	PUNCT
american_scientific_journal-1936	1	28	2313	2313	NUM
american_scientific_journal-1936	1	29	-	-	SYM
american_scientific_journal-1936	1	30	4402	4402	NUM
american_scientific_journal-1936	1	31	©	©	PROPN
american_scientific_journal-1936	1	32	global	global	ADJ
american_scientific_journal-1936	1	33	society	society	NOUN
american_scientific_journal-1936	1	34	of	of	ADP
american_scientific_journal-1936	1	35	scientific	scientific	ADJ
american_scientific_journal-1936	1	36	research	research	NOUN
american_scientific_journal-1936	1	37	and	and	CCONJ
american_scientific_journal-1936	1	38	researchers	researcher	NOUN
american_scientific_journal-1936	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-1936	1	40	application	application	NOUN
american_scientific_journal-1936	1	41	of	of	ADP
american_scientific_journal-1936	1	42	some	some	DET
american_scientific_journal-1936	1	43	finite	finite	ADJ
american_scientific_journal-1936	1	44	difference	difference	NOUN
american_scientific_journal-1936	1	45	schemes	scheme	NOUN
american_scientific_journal-1936	1	46	for	for	ADP
american_scientific_journal-1936	1	47	solving	solve	VERB
american_scientific_journal-1936	1	48	one	one	NUM
american_scientific_journal-1936	1	49	dimensional	dimensional	ADJ
american_scientific_journal-1936	1	50	diffusion	diffusion	NOUN
american_scientific_journal-1936	1	51	equation	equation	NOUN
american_scientific_journal-1936	1	52	tsegaye	tsegaye	VERB
american_scientific_journal-1936	1	53	simona	simona	PROPN
american_scientific_journal-1936	1	54	,	,	PUNCT
american_scientific_journal-1936	1	55	purnachandra	purnachandra	VERB
american_scientific_journal-1936	1	56	rao	rao	PROPN
american_scientific_journal-1936	1	57	koyab	koyab	PROPN
american_scientific_journal-1936	1	58	*	*	PROPN
american_scientific_journal-1936	1	59	a	a	X
american_scientific_journal-1936	1	60	,	,	PUNCT
american_scientific_journal-1936	1	61	bschool	bschool	NOUN
american_scientific_journal-1936	1	62	of	of	ADP
american_scientific_journal-1936	1	63	mathematical	mathematical	ADJ
american_scientific_journal-1936	1	64	and	and	CCONJ
american_scientific_journal-1936	1	65	statistical	statistical	ADJ
american_scientific_journal-1936	1	66	sciences	science	NOUN
american_scientific_journal-1936	1	67	,	,	PUNCT
american_scientific_journal-1936	1	68	hawassa	hawassa	ADJ
american_scientific_journal-1936	1	69	university	university	NOUN
american_scientific_journal-1936	1	70	,	,	PUNCT
american_scientific_journal-1936	1	71	hawassa	hawassa	PROPN
american_scientific_journal-1936	1	72	,	,	PUNCT
american_scientific_journal-1936	1	73	ethiopia	ethiopia	PROPN
american_scientific_journal-1936	1	74	aemail	aemail	NOUN
american_scientific_journal-1936	1	75	:	:	PUNCT
american_scientific_journal-1936	1	76	tsegaye_simon@yahoo.com	tsegaye_simon@yahoo.com	X
american_scientific_journal-1936	1	77	bemail	bemail	PROPN
american_scientific_journal-1936	1	78	:	:	PUNCT
american_scientific_journal-1936	1	79	drkpraocecc@yahoo.co.in	drkpraocecc@yahoo.co.in	PUNCT
american_scientific_journal-1936	1	80	abstract	abstract	ADJ
american_scientific_journal-1936	1	81	in	in	ADP
american_scientific_journal-1936	1	82	this	this	DET
american_scientific_journal-1936	1	83	paper	paper	NOUN
american_scientific_journal-1936	1	84	the	the	DET
american_scientific_journal-1936	1	85	numerical	numerical	ADJ
american_scientific_journal-1936	1	86	solutions	solution	NOUN
american_scientific_journal-1936	1	87	of	of	ADP
american_scientific_journal-1936	1	88	one	one	NUM
american_scientific_journal-1936	1	89	dimensional	dimensional	ADJ
american_scientific_journal-1936	1	90	diffusion	diffusion	NOUN
american_scientific_journal-1936	1	91	equation	equation	NOUN
american_scientific_journal-1936	1	92	using	use	VERB
american_scientific_journal-1936	1	93	some	some	DET
american_scientific_journal-1936	1	94	finite	finite	ADJ
american_scientific_journal-1936	1	95	difference	difference	NOUN
american_scientific_journal-1936	1	96	methods	method	NOUN
american_scientific_journal-1936	1	97	have	have	AUX
american_scientific_journal-1936	1	98	been	be	AUX
american_scientific_journal-1936	1	99	considered	consider	VERB
american_scientific_journal-1936	1	100	.	.	PUNCT
american_scientific_journal-1936	2	1	for	for	ADP
american_scientific_journal-1936	2	2	that	that	DET
american_scientific_journal-1936	2	3	purpose	purpose	NOUN
american_scientific_journal-1936	2	4	three	three	NUM
american_scientific_journal-1936	2	5	examples	example	NOUN
american_scientific_journal-1936	2	6	of	of	ADP
american_scientific_journal-1936	2	7	the	the	DET
american_scientific_journal-1936	2	8	diffusion	diffusion	NOUN
american_scientific_journal-1936	2	9	equation	equation	NOUN
american_scientific_journal-1936	2	10	together	together	ADV
american_scientific_journal-1936	2	11	with	with	ADP
american_scientific_journal-1936	2	12	different	different	ADJ
american_scientific_journal-1936	2	13	boundary	boundary	ADJ
american_scientific_journal-1936	2	14	conditions	condition	NOUN
american_scientific_journal-1936	2	15	are	be	AUX
american_scientific_journal-1936	2	16	examined	examine	VERB
american_scientific_journal-1936	2	17	.	.	PUNCT
american_scientific_journal-1936	3	1	the	the	DET
american_scientific_journal-1936	3	2	finite	finite	ADJ
american_scientific_journal-1936	3	3	difference	difference	NOUN
american_scientific_journal-1936	3	4	methods	method	NOUN
american_scientific_journal-1936	3	5	applied	apply	VERB
american_scientific_journal-1936	3	6	on	on	ADP
american_scientific_journal-1936	3	7	each	each	DET
american_scientific_journal-1936	3	8	example	example	NOUN
american_scientific_journal-1936	3	9	are	be	AUX
american_scientific_journal-1936	3	10	(	(	PUNCT
american_scientific_journal-1936	3	11	i	i	NOUN
american_scientific_journal-1936	3	12	)	)	PUNCT
american_scientific_journal-1936	3	13	forward	forward	ADV
american_scientific_journal-1936	3	14	time	time	NOUN
american_scientific_journal-1936	3	15	centered	center	VERB
american_scientific_journal-1936	3	16	space	space	NOUN
american_scientific_journal-1936	3	17	(	(	PUNCT
american_scientific_journal-1936	3	18	ii	ii	NOUN
american_scientific_journal-1936	3	19	)	)	PUNCT
american_scientific_journal-1936	3	20	backward	backward	ADJ
american_scientific_journal-1936	3	21	time	time	NOUN
american_scientific_journal-1936	3	22	centered	center	VERB
american_scientific_journal-1936	3	23	space	space	NOUN
american_scientific_journal-1936	3	24	and	and	CCONJ
american_scientific_journal-1936	3	25	(	(	PUNCT
american_scientific_journal-1936	3	26	iii	iii	NOUN
american_scientific_journal-1936	3	27	)	)	PUNCT
american_scientific_journal-1936	3	28	crank	crank	NOUN
american_scientific_journal-1936	3	29	–	–	PUNCT
american_scientific_journal-1936	3	30	nicolson	nicolson	PROPN
american_scientific_journal-1936	3	31	.	.	PUNCT
american_scientific_journal-1936	4	1	in	in	ADP
american_scientific_journal-1936	4	2	each	each	DET
american_scientific_journal-1936	4	3	case	case	NOUN
american_scientific_journal-1936	4	4	,	,	PUNCT
american_scientific_journal-1936	4	5	we	we	PRON
american_scientific_journal-1936	4	6	have	have	AUX
american_scientific_journal-1936	4	7	studied	study	VERB
american_scientific_journal-1936	4	8	stability	stability	NOUN
american_scientific_journal-1936	4	9	of	of	ADP
american_scientific_journal-1936	4	10	finite	finite	ADJ
american_scientific_journal-1936	4	11	difference	difference	NOUN
american_scientific_journal-1936	4	12	method	method	NOUN
american_scientific_journal-1936	4	13	and	and	CCONJ
american_scientific_journal-1936	4	14	also	also	ADV
american_scientific_journal-1936	4	15	obtained	obtain	VERB
american_scientific_journal-1936	4	16	numerical	numerical	ADJ
american_scientific_journal-1936	4	17	result	result	NOUN
american_scientific_journal-1936	4	18	.	.	PUNCT
american_scientific_journal-1936	5	1	the	the	DET
american_scientific_journal-1936	5	2	performance	performance	NOUN
american_scientific_journal-1936	5	3	of	of	ADP
american_scientific_journal-1936	5	4	each	each	DET
american_scientific_journal-1936	5	5	scheme	scheme	NOUN
american_scientific_journal-1936	5	6	is	be	AUX
american_scientific_journal-1936	5	7	evaluated	evaluate	VERB
american_scientific_journal-1936	5	8	in	in	ADP
american_scientific_journal-1936	5	9	accordance	accordance	NOUN
american_scientific_journal-1936	5	10	with	with	ADP
american_scientific_journal-1936	5	11	both	both	CCONJ
american_scientific_journal-1936	5	12	the	the	DET
american_scientific_journal-1936	5	13	accuracy	accuracy	NOUN
american_scientific_journal-1936	5	14	of	of	ADP
american_scientific_journal-1936	5	15	the	the	DET
american_scientific_journal-1936	5	16	solution	solution	NOUN
american_scientific_journal-1936	5	17	and	and	CCONJ
american_scientific_journal-1936	5	18	programming	programming	NOUN
american_scientific_journal-1936	5	19	efforts	effort	NOUN
american_scientific_journal-1936	5	20	.	.	PUNCT
american_scientific_journal-1936	6	1	the	the	DET
american_scientific_journal-1936	6	2	implementation	implementation	NOUN
american_scientific_journal-1936	6	3	and	and	CCONJ
american_scientific_journal-1936	6	4	behavior	behavior	NOUN
american_scientific_journal-1936	6	5	of	of	ADP
american_scientific_journal-1936	6	6	the	the	DET
american_scientific_journal-1936	6	7	schemes	scheme	NOUN
american_scientific_journal-1936	6	8	have	have	AUX
american_scientific_journal-1936	6	9	been	be	AUX
american_scientific_journal-1936	6	10	compared	compare	VERB
american_scientific_journal-1936	6	11	and	and	CCONJ
american_scientific_journal-1936	6	12	the	the	DET
american_scientific_journal-1936	6	13	results	result	NOUN
american_scientific_journal-1936	6	14	are	be	AUX
american_scientific_journal-1936	6	15	illustrated	illustrate	VERB
american_scientific_journal-1936	6	16	pictorially	pictorially	ADV
american_scientific_journal-1936	6	17	.	.	PUNCT
american_scientific_journal-1936	7	1	it	it	PRON
american_scientific_journal-1936	7	2	is	be	AUX
american_scientific_journal-1936	7	3	found	find	VERB
american_scientific_journal-1936	7	4	in	in	ADP
american_scientific_journal-1936	7	5	case	case	NOUN
american_scientific_journal-1936	7	6	of	of	ADP
american_scientific_journal-1936	7	7	the	the	DET
american_scientific_journal-1936	7	8	test	test	NOUN
american_scientific_journal-1936	7	9	examples	example	NOUN
american_scientific_journal-1936	7	10	studied	study	VERB
american_scientific_journal-1936	7	11	here	here	ADV
american_scientific_journal-1936	7	12	that	that	SCONJ
american_scientific_journal-1936	7	13	the	the	DET
american_scientific_journal-1936	7	14	crank	crank	NOUN
american_scientific_journal-1936	7	15	–	–	PUNCT
american_scientific_journal-1936	7	16	nicolson	nicolson	PROPN
american_scientific_journal-1936	7	17	scheme	scheme	NOUN
american_scientific_journal-1936	7	18	gives	give	VERB
american_scientific_journal-1936	7	19	better	well	ADJ
american_scientific_journal-1936	7	20	approximations	approximation	NOUN
american_scientific_journal-1936	7	21	than	than	ADP
american_scientific_journal-1936	7	22	the	the	DET
american_scientific_journal-1936	7	23	two	two	NUM
american_scientific_journal-1936	7	24	other	other	ADJ
american_scientific_journal-1936	7	25	schemes	scheme	NOUN
american_scientific_journal-1936	7	26	.	.	PUNCT
american_scientific_journal-1936	8	1	keywords	keyword	NOUN
american_scientific_journal-1936	8	2	:	:	PUNCT
american_scientific_journal-1936	8	3	crank	crank	NOUN
american_scientific_journal-1936	8	4	–	–	PUNCT
american_scientific_journal-1936	8	5	nicolson	nicolson	PROPN
american_scientific_journal-1936	8	6	;	;	PUNCT
american_scientific_journal-1936	8	7	diffusion	diffusion	NOUN
american_scientific_journal-1936	8	8	equation	equation	NOUN
american_scientific_journal-1936	8	9	;	;	PUNCT
american_scientific_journal-1936	8	10	forward	forward	ADV
american_scientific_journal-1936	8	11	time	time	NOUN
american_scientific_journal-1936	8	12	centered	center	VERB
american_scientific_journal-1936	8	13	space	space	NOUN
american_scientific_journal-1936	8	14	;	;	PUNCT
american_scientific_journal-1936	8	15	backward	backward	ADJ
american_scientific_journal-1936	8	16	time	time	NOUN
american_scientific_journal-1936	8	17	centered	center	VERB
american_scientific_journal-1936	8	18	space	space	NOUN
american_scientific_journal-1936	8	19	;	;	PUNCT
american_scientific_journal-1936	8	20	stability	stability	NOUN
american_scientific_journal-1936	8	21	.	.	PUNCT
american_scientific_journal-1936	9	1	1	1	X
american_scientific_journal-1936	9	2	.	.	X
american_scientific_journal-1936	9	3	introduction	introduction	NOUN
american_scientific_journal-1936	9	4	one	one	NUM
american_scientific_journal-1936	9	5	dimensional	dimensional	ADJ
american_scientific_journal-1936	9	6	diffusion	diffusion	NOUN
american_scientific_journal-1936	9	7	equation	equation	NOUN
american_scientific_journal-1936	9	8	plays	play	VERB
american_scientific_journal-1936	9	9	an	an	DET
american_scientific_journal-1936	9	10	important	important	ADJ
american_scientific_journal-1936	9	11	role	role	NOUN
american_scientific_journal-1936	9	12	in	in	ADP
american_scientific_journal-1936	9	13	modeling	model	VERB
american_scientific_journal-1936	9	14	numerous	numerous	ADJ
american_scientific_journal-1936	9	15	physical	physical	ADJ
american_scientific_journal-1936	9	16	phenomena	phenomenon	NOUN
american_scientific_journal-1936	9	17	.	.	PUNCT
american_scientific_journal-1936	10	1	the	the	DET
american_scientific_journal-1936	10	2	application	application	NOUN
american_scientific_journal-1936	10	3	of	of	ADP
american_scientific_journal-1936	10	4	such	such	ADJ
american_scientific_journal-1936	10	5	diffusion	diffusion	NOUN
american_scientific_journal-1936	10	6	equation	equation	NOUN
american_scientific_journal-1936	10	7	includes	include	VERB
american_scientific_journal-1936	10	8	a	a	DET
american_scientific_journal-1936	10	9	wide	wide	ADJ
american_scientific_journal-1936	10	10	range	range	NOUN
american_scientific_journal-1936	10	11	of	of	ADP
american_scientific_journal-1936	10	12	areas	area	NOUN
american_scientific_journal-1936	10	13	such	such	ADJ
american_scientific_journal-1936	10	14	as	as	ADP
american_scientific_journal-1936	10	15	physical	physical	ADJ
american_scientific_journal-1936	10	16	,	,	PUNCT
american_scientific_journal-1936	10	17	biological	biological	ADJ
american_scientific_journal-1936	10	18	and	and	CCONJ
american_scientific_journal-1936	10	19	financial	financial	ADJ
american_scientific_journal-1936	10	20	sciences	science	NOUN
american_scientific_journal-1936	10	21	.	.	PUNCT
american_scientific_journal-1936	11	1	one	one	NUM
american_scientific_journal-1936	11	2	of	of	ADP
american_scientific_journal-1936	11	3	the	the	DET
american_scientific_journal-1936	11	4	most	most	ADV
american_scientific_journal-1936	11	5	common	common	ADJ
american_scientific_journal-1936	11	6	applications	application	NOUN
american_scientific_journal-1936	11	7	is	be	AUX
american_scientific_journal-1936	11	8	propagation	propagation	NOUN
american_scientific_journal-1936	11	9	of	of	ADP
american_scientific_journal-1936	11	10	heat	heat	NOUN
american_scientific_journal-1936	11	11	in	in	ADP
american_scientific_journal-1936	11	12	the	the	DET
american_scientific_journal-1936	11	13	environment	environment	NOUN
american_scientific_journal-1936	11	14	,	,	PUNCT
american_scientific_journal-1936	11	15	where	where	SCONJ
american_scientific_journal-1936	11	16	𝑢𝑢(𝑥𝑥	𝑢𝑢(𝑥𝑥	NOUN
american_scientific_journal-1936	11	17	,	,	PUNCT
american_scientific_journal-1936	11	18	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	11	19	)	)	PUNCT
american_scientific_journal-1936	11	20	represents	represent	VERB
american_scientific_journal-1936	11	21	the	the	DET
american_scientific_journal-1936	11	22	temperature	temperature	NOUN
american_scientific_journal-1936	11	23	of	of	ADP
american_scientific_journal-1936	11	24	some	some	DET
american_scientific_journal-1936	11	25	substance	substance	NOUN
american_scientific_journal-1936	11	26	at	at	ADP
american_scientific_journal-1936	11	27	point	point	NOUN
american_scientific_journal-1936	11	28	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	11	29	and	and	CCONJ
american_scientific_journal-1936	11	30	time	time	NOUN
american_scientific_journal-1936	11	31	𝑡𝑡.	𝑡𝑡.	X
american_scientific_journal-1936	11	32	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-1936	12	1	*	*	PUNCT
american_scientific_journal-1936	12	2	corresponding	correspond	VERB
american_scientific_journal-1936	12	3	author	author	NOUN
american_scientific_journal-1936	12	4	.	.	PUNCT
american_scientific_journal-1936	13	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-1936	13	2	american	american	PROPN
american_scientific_journal-1936	13	3	scientific	scientific	PROPN
american_scientific_journal-1936	13	4	research	research	NOUN
american_scientific_journal-1936	13	5	journal	journal	NOUN
american_scientific_journal-1936	13	6	for	for	ADP
american_scientific_journal-1936	13	7	engineering	engineering	NOUN
american_scientific_journal-1936	13	8	,	,	PUNCT
american_scientific_journal-1936	13	9	technology	technology	NOUN
american_scientific_journal-1936	13	10	,	,	PUNCT
american_scientific_journal-1936	13	11	and	and	CCONJ
american_scientific_journal-1936	13	12	sciences	science	NOUN
american_scientific_journal-1936	13	13	(	(	PUNCT
american_scientific_journal-1936	13	14	asrjets	asrjet	NOUN
american_scientific_journal-1936	13	15	)	)	PUNCT
american_scientific_journal-1936	13	16	(	(	PUNCT
american_scientific_journal-1936	13	17	2016	2016	NUM
american_scientific_journal-1936	13	18	)	)	PUNCT
american_scientific_journal-1936	13	19	volume	volume	NOUN
american_scientific_journal-1936	13	20	26	26	NUM
american_scientific_journal-1936	13	21	,	,	PUNCT
american_scientific_journal-1936	13	22	no	no	DET
american_scientific_journal-1936	13	23	3	3	NUM
american_scientific_journal-1936	13	24	,	,	PUNCT
american_scientific_journal-1936	13	25	pp	pp	ADV
american_scientific_journal-1936	13	26	140	140	NUM
american_scientific_journal-1936	13	27	-	-	SYM
american_scientific_journal-1936	13	28	154	154	NUM
american_scientific_journal-1936	13	29	141	141	NUM
american_scientific_journal-1936	13	30	the	the	DET
american_scientific_journal-1936	13	31	diffusion	diffusion	NOUN
american_scientific_journal-1936	13	32	or	or	CCONJ
american_scientific_journal-1936	13	33	heat	heat	NOUN
american_scientific_journal-1936	13	34	equation	equation	NOUN
american_scientific_journal-1936	13	35	is	be	AUX
american_scientific_journal-1936	13	36	applied	apply	VERB
american_scientific_journal-1936	13	37	when	when	SCONJ
american_scientific_journal-1936	13	38	attempting	attempt	VERB
american_scientific_journal-1936	13	39	to	to	PART
american_scientific_journal-1936	13	40	describe	describe	VERB
american_scientific_journal-1936	13	41	the	the	DET
american_scientific_journal-1936	13	42	density	density	NOUN
american_scientific_journal-1936	13	43	fluctuations	fluctuation	NOUN
american_scientific_journal-1936	13	44	in	in	ADP
american_scientific_journal-1936	13	45	a	a	DET
american_scientific_journal-1936	13	46	material	material	NOUN
american_scientific_journal-1936	13	47	that	that	PRON
american_scientific_journal-1936	13	48	undergoes	undergo	VERB
american_scientific_journal-1936	13	49	diffusion	diffusion	NOUN
american_scientific_journal-1936	13	50	[	[	X
american_scientific_journal-1936	13	51	8	8	NUM
american_scientific_journal-1936	13	52	]	]	PUNCT
american_scientific_journal-1936	13	53	.	.	PUNCT
american_scientific_journal-1936	14	1	in	in	ADP
american_scientific_journal-1936	14	2	the	the	DET
american_scientific_journal-1936	14	3	diffusion	diffusion	NOUN
american_scientific_journal-1936	14	4	equation	equation	NOUN
american_scientific_journal-1936	14	5	there	there	PRON
american_scientific_journal-1936	14	6	appear	appear	VERB
american_scientific_journal-1936	14	7	derivatives	derivative	NOUN
american_scientific_journal-1936	14	8	with	with	ADP
american_scientific_journal-1936	14	9	respect	respect	NOUN
american_scientific_journal-1936	14	10	to	to	ADP
american_scientific_journal-1936	14	11	time	time	NOUN
american_scientific_journal-1936	14	12	and	and	CCONJ
american_scientific_journal-1936	14	13	space	space	NOUN
american_scientific_journal-1936	14	14	coordinates	coordinate	NOUN
american_scientific_journal-1936	14	15	.	.	PUNCT
american_scientific_journal-1936	15	1	several	several	ADJ
american_scientific_journal-1936	15	2	finite	finite	ADJ
american_scientific_journal-1936	15	3	difference	difference	NOUN
american_scientific_journal-1936	15	4	techniques	technique	NOUN
american_scientific_journal-1936	15	5	have	have	AUX
american_scientific_journal-1936	15	6	been	be	AUX
american_scientific_journal-1936	15	7	employed	employ	VERB
american_scientific_journal-1936	15	8	to	to	PART
american_scientific_journal-1936	15	9	solve	solve	VERB
american_scientific_journal-1936	15	10	these	these	DET
american_scientific_journal-1936	15	11	equations	equation	NOUN
american_scientific_journal-1936	15	12	so	so	SCONJ
american_scientific_journal-1936	15	13	as	as	SCONJ
american_scientific_journal-1936	15	14	to	to	PART
american_scientific_journal-1936	15	15	fit	fit	VERB
american_scientific_journal-1936	15	16	their	their	PRON
american_scientific_journal-1936	15	17	physical	physical	ADJ
american_scientific_journal-1936	15	18	nature	nature	NOUN
american_scientific_journal-1936	16	1	[	[	X
american_scientific_journal-1936	16	2	1	1	NUM
american_scientific_journal-1936	16	3	–	–	SYM
american_scientific_journal-1936	16	4	2	2	NUM
american_scientific_journal-1936	16	5	,	,	PUNCT
american_scientific_journal-1936	16	6	5	5	NUM
american_scientific_journal-1936	16	7	,	,	PUNCT
american_scientific_journal-1936	16	8	7	7	NUM
american_scientific_journal-1936	16	9	,	,	PUNCT
american_scientific_journal-1936	16	10	13	13	NUM
american_scientific_journal-1936	16	11	,	,	PUNCT
american_scientific_journal-1936	16	12	14	14	NUM
american_scientific_journal-1936	16	13	]	]	PUNCT
american_scientific_journal-1936	16	14	.	.	PUNCT
american_scientific_journal-1936	17	1	the	the	DET
american_scientific_journal-1936	17	2	process	process	NOUN
american_scientific_journal-1936	17	3	of	of	ADP
american_scientific_journal-1936	17	4	solving	solving	NOUN
american_scientific_journal-1936	17	5	requires	require	VERB
american_scientific_journal-1936	17	6	specification	specification	NOUN
american_scientific_journal-1936	17	7	of	of	ADP
american_scientific_journal-1936	17	8	a	a	DET
american_scientific_journal-1936	17	9	suitable	suitable	ADJ
american_scientific_journal-1936	17	10	boundary	boundary	ADJ
american_scientific_journal-1936	17	11	conditions	condition	NOUN
american_scientific_journal-1936	17	12	viz	viz	PROPN
american_scientific_journal-1936	17	13	.	.	PROPN
american_scientific_journal-1936	17	14	,	,	PUNCT
american_scientific_journal-1936	17	15	(	(	PUNCT
american_scientific_journal-1936	17	16	i	i	NOUN
american_scientific_journal-1936	17	17	)	)	PUNCT
american_scientific_journal-1936	17	18	dirichlet	dirichlet	PROPN
american_scientific_journal-1936	17	19	(	(	PUNCT
american_scientific_journal-1936	17	20	ii	ii	PROPN
american_scientific_journal-1936	17	21	)	)	PUNCT
american_scientific_journal-1936	17	22	neumann	neumann	PROPN
american_scientific_journal-1936	17	23	or	or	CCONJ
american_scientific_journal-1936	17	24	gradient	gradient	NOUN
american_scientific_journal-1936	17	25	(	(	PUNCT
american_scientific_journal-1936	17	26	iii	iii	NOUN
american_scientific_journal-1936	17	27	)	)	PUNCT
american_scientific_journal-1936	17	28	mixed	mixed	ADJ
american_scientific_journal-1936	17	29	or	or	CCONJ
american_scientific_journal-1936	17	30	robin	robin	PROPN
american_scientific_journal-1936	17	31	(	(	PUNCT
american_scientific_journal-1936	17	32	iv	iv	NOUN
american_scientific_journal-1936	17	33	)	)	PUNCT
american_scientific_journal-1936	17	34	combination	combination	NOUN
american_scientific_journal-1936	17	35	of	of	ADP
american_scientific_journal-1936	17	36	dirichlet	dirichlet	PROPN
american_scientific_journal-1936	17	37	and	and	CCONJ
american_scientific_journal-1936	17	38	neumann	neumann	PROPN
american_scientific_journal-1936	17	39	.	.	PUNCT
american_scientific_journal-1936	18	1	boundary	boundary	ADJ
american_scientific_journal-1936	18	2	conditions	condition	NOUN
american_scientific_journal-1936	18	3	are	be	AUX
american_scientific_journal-1936	18	4	applied	apply	VERB
american_scientific_journal-1936	18	5	on	on	ADP
american_scientific_journal-1936	18	6	the	the	DET
american_scientific_journal-1936	18	7	spatial	spatial	ADJ
american_scientific_journal-1936	18	8	coordinate	coordinate	NOUN
american_scientific_journal-1936	18	9	at	at	ADP
american_scientific_journal-1936	18	10	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	18	11	=	=	SYM
american_scientific_journal-1936	18	12	0	0	NUM
american_scientific_journal-1936	18	13	and	and	CCONJ
american_scientific_journal-1936	18	14	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	18	15	=	=	PUNCT
american_scientific_journal-1936	18	16	𝐿𝐿	𝐿𝐿	PROPN
american_scientific_journal-1936	18	17	and	and	CCONJ
american_scientific_journal-1936	18	18	initial	initial	ADJ
american_scientific_journal-1936	18	19	conditions	condition	NOUN
american_scientific_journal-1936	18	20	are	be	AUX
american_scientific_journal-1936	18	21	applied	apply	VERB
american_scientific_journal-1936	18	22	on	on	ADP
american_scientific_journal-1936	18	23	the	the	DET
american_scientific_journal-1936	18	24	temporal	temporal	ADJ
american_scientific_journal-1936	18	25	coordinate	coordinate	NOUN
american_scientific_journal-1936	18	26	when	when	SCONJ
american_scientific_journal-1936	18	27	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-1936	18	28	=	=	SYM
american_scientific_journal-1936	19	1	0	0	X
american_scientific_journal-1936	19	2	.	.	PUNCT
american_scientific_journal-1936	20	1	in	in	ADP
american_scientific_journal-1936	20	2	the	the	DET
american_scientific_journal-1936	20	3	process	process	NOUN
american_scientific_journal-1936	20	4	of	of	ADP
american_scientific_journal-1936	20	5	finding	find	VERB
american_scientific_journal-1936	20	6	numerical	numerical	ADJ
american_scientific_journal-1936	20	7	solutions	solution	NOUN
american_scientific_journal-1936	20	8	the	the	DET
american_scientific_journal-1936	20	9	continuous	continuous	ADJ
american_scientific_journal-1936	20	10	partial	partial	ADJ
american_scientific_journal-1936	20	11	differential	differential	NOUN
american_scientific_journal-1936	20	12	equations	equation	NOUN
american_scientific_journal-1936	20	13	are	be	AUX
american_scientific_journal-1936	20	14	replaced	replace	VERB
american_scientific_journal-1936	20	15	by	by	ADP
american_scientific_journal-1936	20	16	their	their	PRON
american_scientific_journal-1936	20	17	discrete	discrete	ADJ
american_scientific_journal-1936	20	18	approximations	approximation	NOUN
american_scientific_journal-1936	20	19	.	.	PUNCT
american_scientific_journal-1936	21	1	in	in	ADP
american_scientific_journal-1936	21	2	the	the	DET
american_scientific_journal-1936	21	3	present	present	ADJ
american_scientific_journal-1936	21	4	context	context	NOUN
american_scientific_journal-1936	21	5	the	the	DET
american_scientific_journal-1936	21	6	word	word	NOUN
american_scientific_journal-1936	21	7	discrete	discrete	ADJ
american_scientific_journal-1936	21	8	indicates	indicate	VERB
american_scientific_journal-1936	21	9	that	that	SCONJ
american_scientific_journal-1936	21	10	the	the	DET
american_scientific_journal-1936	21	11	numerical	numerical	ADJ
american_scientific_journal-1936	21	12	solution	solution	NOUN
american_scientific_journal-1936	21	13	is	be	AUX
american_scientific_journal-1936	21	14	known	know	VERB
american_scientific_journal-1936	21	15	only	only	ADV
american_scientific_journal-1936	21	16	at	at	ADP
american_scientific_journal-1936	21	17	a	a	DET
american_scientific_journal-1936	21	18	finite	finite	ADJ
american_scientific_journal-1936	21	19	number	number	NOUN
american_scientific_journal-1936	21	20	of	of	ADP
american_scientific_journal-1936	21	21	points	point	NOUN
american_scientific_journal-1936	21	22	in	in	ADP
american_scientific_journal-1936	21	23	the	the	DET
american_scientific_journal-1936	21	24	physical	physical	ADJ
american_scientific_journal-1936	21	25	domain	domain	NOUN
american_scientific_journal-1936	21	26	.	.	PUNCT
american_scientific_journal-1936	22	1	the	the	DET
american_scientific_journal-1936	22	2	number	number	NOUN
american_scientific_journal-1936	22	3	of	of	ADP
american_scientific_journal-1936	22	4	those	those	DET
american_scientific_journal-1936	22	5	discrete	discrete	ADJ
american_scientific_journal-1936	22	6	points	point	NOUN
american_scientific_journal-1936	22	7	can	can	AUX
american_scientific_journal-1936	22	8	vary	vary	VERB
american_scientific_journal-1936	22	9	and	and	CCONJ
american_scientific_journal-1936	22	10	can	can	AUX
american_scientific_journal-1936	22	11	be	be	AUX
american_scientific_journal-1936	22	12	fixed	fix	VERB
american_scientific_journal-1936	22	13	by	by	ADP
american_scientific_journal-1936	22	14	the	the	DET
american_scientific_journal-1936	22	15	user	user	NOUN
american_scientific_journal-1936	22	16	of	of	ADP
american_scientific_journal-1936	22	17	the	the	DET
american_scientific_journal-1936	22	18	numerical	numerical	ADJ
american_scientific_journal-1936	22	19	method	method	NOUN
american_scientific_journal-1936	22	20	.	.	PUNCT
american_scientific_journal-1936	23	1	however	however	ADV
american_scientific_journal-1936	23	2	,	,	PUNCT
american_scientific_journal-1936	23	3	increment	increment	VERB
american_scientific_journal-1936	23	4	in	in	ADP
american_scientific_journal-1936	23	5	the	the	DET
american_scientific_journal-1936	23	6	number	number	NOUN
american_scientific_journal-1936	23	7	of	of	ADP
american_scientific_journal-1936	23	8	discrete	discrete	ADJ
american_scientific_journal-1936	23	9	points	point	NOUN
american_scientific_journal-1936	23	10	increases	increase	VERB
american_scientific_journal-1936	23	11	not	not	PART
american_scientific_journal-1936	23	12	only	only	ADV
american_scientific_journal-1936	23	13	the	the	DET
american_scientific_journal-1936	23	14	resolution	resolution	NOUN
american_scientific_journal-1936	23	15	but	but	CCONJ
american_scientific_journal-1936	23	16	also	also	ADV
american_scientific_journal-1936	23	17	the	the	DET
american_scientific_journal-1936	23	18	accuracy	accuracy	NOUN
american_scientific_journal-1936	23	19	of	of	ADP
american_scientific_journal-1936	23	20	the	the	DET
american_scientific_journal-1936	23	21	numerical	numerical	ADJ
american_scientific_journal-1936	23	22	solution	solution	NOUN
american_scientific_journal-1936	23	23	.	.	PUNCT
american_scientific_journal-1936	24	1	the	the	DET
american_scientific_journal-1936	24	2	process	process	NOUN
american_scientific_journal-1936	24	3	of	of	ADP
american_scientific_journal-1936	24	4	discretization	discretization	NOUN
american_scientific_journal-1936	24	5	of	of	ADP
american_scientific_journal-1936	24	6	a	a	DET
american_scientific_journal-1936	24	7	diffusion	diffusion	NOUN
american_scientific_journal-1936	24	8	equation	equation	NOUN
american_scientific_journal-1936	24	9	leads	lead	VERB
american_scientific_journal-1936	24	10	to	to	ADP
american_scientific_journal-1936	24	11	a	a	DET
american_scientific_journal-1936	24	12	set	set	NOUN
american_scientific_journal-1936	24	13	of	of	ADP
american_scientific_journal-1936	24	14	algebraic	algebraic	ADJ
american_scientific_journal-1936	24	15	equations	equation	NOUN
american_scientific_journal-1936	24	16	.	.	PUNCT
american_scientific_journal-1936	25	1	these	these	DET
american_scientific_journal-1936	25	2	algebraic	algebraic	ADJ
american_scientific_journal-1936	25	3	equations	equation	NOUN
american_scientific_journal-1936	25	4	are	be	AUX
american_scientific_journal-1936	25	5	evaluated	evaluate	VERB
american_scientific_journal-1936	25	6	so	so	SCONJ
american_scientific_journal-1936	25	7	as	as	SCONJ
american_scientific_journal-1936	25	8	to	to	PART
american_scientific_journal-1936	25	9	obtain	obtain	VERB
american_scientific_journal-1936	25	10	values	value	NOUN
american_scientific_journal-1936	25	11	for	for	ADP
american_scientific_journal-1936	25	12	the	the	DET
american_scientific_journal-1936	25	13	unknown	unknown	ADJ
american_scientific_journal-1936	25	14	quantities	quantity	NOUN
american_scientific_journal-1936	25	15	of	of	ADP
american_scientific_journal-1936	25	16	the	the	DET
american_scientific_journal-1936	25	17	discretization	discretization	NOUN
american_scientific_journal-1936	25	18	.	.	PUNCT
american_scientific_journal-1936	26	1	in	in	ADP
american_scientific_journal-1936	26	2	turn	turn	NOUN
american_scientific_journal-1936	26	3	,	,	PUNCT
american_scientific_journal-1936	26	4	the	the	DET
american_scientific_journal-1936	26	5	values	value	NOUN
american_scientific_journal-1936	26	6	of	of	ADP
american_scientific_journal-1936	26	7	unknowns	unknown	NOUN
american_scientific_journal-1936	26	8	provide	provide	VERB
american_scientific_journal-1936	26	9	an	an	DET
american_scientific_journal-1936	26	10	approximate	approximate	ADJ
american_scientific_journal-1936	26	11	solution	solution	NOUN
american_scientific_journal-1936	26	12	to	to	ADP
american_scientific_journal-1936	26	13	the	the	DET
american_scientific_journal-1936	26	14	original	original	ADJ
american_scientific_journal-1936	26	15	diffusion	diffusion	NOUN
american_scientific_journal-1936	26	16	equation	equation	NOUN
american_scientific_journal-1936	26	17	.	.	PUNCT
american_scientific_journal-1936	27	1	we	we	PRON
american_scientific_journal-1936	27	2	now	now	ADV
american_scientific_journal-1936	27	3	divide	divide	VERB
american_scientific_journal-1936	27	4	the	the	DET
american_scientific_journal-1936	27	5	𝑥𝑥𝑡𝑡	𝑥𝑥𝑡𝑡	NOUN
american_scientific_journal-1936	27	6	domain	domain	NOUN
american_scientific_journal-1936	27	7	into	into	ADP
american_scientific_journal-1936	27	8	a	a	DET
american_scientific_journal-1936	27	9	mesh	mesh	NOUN
american_scientific_journal-1936	27	10	.	.	PUNCT
american_scientific_journal-1936	28	1	the	the	DET
american_scientific_journal-1936	28	2	coordinate	coordinate	NOUN
american_scientific_journal-1936	28	3	axes	axis	NOUN
american_scientific_journal-1936	28	4	are	be	AUX
american_scientific_journal-1936	28	5	divided	divide	VERB
american_scientific_journal-1936	28	6	into	into	ADP
american_scientific_journal-1936	28	7	steps	step	NOUN
american_scientific_journal-1936	28	8	of	of	ADP
american_scientific_journal-1936	28	9	uniform	uniform	ADJ
american_scientific_journal-1936	28	10	lengths	length	NOUN
american_scientific_journal-1936	28	11	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	28	12	and	and	CCONJ
american_scientific_journal-1936	28	13	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	28	14	along	along	ADP
american_scientific_journal-1936	28	15	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	28	16	and	and	CCONJ
american_scientific_journal-1936	28	17	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	28	18	axis	axis	NOUN
american_scientific_journal-1936	28	19	respectively	respectively	ADV
american_scientific_journal-1936	28	20	.	.	PUNCT
american_scientific_journal-1936	29	1	when	when	SCONJ
american_scientific_journal-1936	29	2	horizontal	horizontal	ADJ
american_scientific_journal-1936	29	3	and	and	CCONJ
american_scientific_journal-1936	29	4	vertical	vertical	ADJ
american_scientific_journal-1936	29	5	lines	line	NOUN
american_scientific_journal-1936	29	6	are	be	AUX
american_scientific_journal-1936	29	7	drawn	draw	VERB
american_scientific_journal-1936	29	8	along	along	ADP
american_scientific_journal-1936	29	9	the	the	DET
american_scientific_journal-1936	29	10	step	step	NOUN
american_scientific_journal-1936	29	11	nodes	nod	VERB
american_scientific_journal-1936	29	12	the	the	DET
american_scientific_journal-1936	29	13	resulting	result	VERB
american_scientific_journal-1936	29	14	image	image	NOUN
american_scientific_journal-1936	29	15	would	would	AUX
american_scientific_journal-1936	29	16	resemble	resemble	VERB
american_scientific_journal-1936	29	17	as	as	ADP
american_scientific_journal-1936	29	18	a	a	DET
american_scientific_journal-1936	29	19	net	net	NOUN
american_scientific_journal-1936	29	20	or	or	CCONJ
american_scientific_journal-1936	29	21	mesh	mesh	NOUN
american_scientific_journal-1936	29	22	.	.	PUNCT
american_scientific_journal-1936	30	1	the	the	DET
american_scientific_journal-1936	30	2	two	two	NUM
american_scientific_journal-1936	30	3	key	key	ADJ
american_scientific_journal-1936	30	4	parameters	parameter	NOUN
american_scientific_journal-1936	30	5	of	of	ADP
american_scientific_journal-1936	30	6	the	the	DET
american_scientific_journal-1936	30	7	mesh	mesh	NOUN
american_scientific_journal-1936	30	8	are	be	AUX
american_scientific_journal-1936	30	9	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	30	10	and	and	CCONJ
american_scientific_journal-1936	30	11	∆𝑡𝑡.	∆𝑡𝑡.	PROPN
american_scientific_journal-1936	30	12	the	the	DET
american_scientific_journal-1936	30	13	former	former	ADJ
american_scientific_journal-1936	30	14	denotes	denote	VERB
american_scientific_journal-1936	30	15	the	the	DET
american_scientific_journal-1936	30	16	local	local	ADJ
american_scientific_journal-1936	30	17	distance	distance	NOUN
american_scientific_journal-1936	30	18	between	between	ADP
american_scientific_journal-1936	30	19	adjacent	adjacent	ADJ
american_scientific_journal-1936	30	20	points	point	NOUN
american_scientific_journal-1936	30	21	in	in	ADP
american_scientific_journal-1936	30	22	space	space	NOUN
american_scientific_journal-1936	30	23	while	while	SCONJ
american_scientific_journal-1936	30	24	the	the	DET
american_scientific_journal-1936	30	25	latter	latter	ADJ
american_scientific_journal-1936	30	26	denotes	denote	NOUN
american_scientific_journal-1936	30	27	local	local	ADJ
american_scientific_journal-1936	30	28	distance	distance	NOUN
american_scientific_journal-1936	30	29	between	between	ADP
american_scientific_journal-1936	30	30	adjacent	adjacent	ADJ
american_scientific_journal-1936	30	31	time	time	NOUN
american_scientific_journal-1936	30	32	steps	step	NOUN
american_scientific_journal-1936	30	33	.	.	PUNCT
american_scientific_journal-1936	31	1	the	the	DET
american_scientific_journal-1936	31	2	intersection	intersection	NOUN
american_scientific_journal-1936	31	3	points	point	NOUN
american_scientific_journal-1936	31	4	of	of	ADP
american_scientific_journal-1936	31	5	this	this	DET
american_scientific_journal-1936	31	6	mesh	mesh	NOUN
american_scientific_journal-1936	31	7	are	be	AUX
american_scientific_journal-1936	31	8	called	call	VERB
american_scientific_journal-1936	31	9	nodes	node	NOUN
american_scientific_journal-1936	31	10	.	.	PUNCT
american_scientific_journal-1936	32	1	the	the	DET
american_scientific_journal-1936	32	2	discrete	discrete	ADJ
american_scientific_journal-1936	32	3	solutions	solution	NOUN
american_scientific_journal-1936	32	4	are	be	AUX
american_scientific_journal-1936	32	5	computed	compute	VERB
american_scientific_journal-1936	32	6	at	at	ADP
american_scientific_journal-1936	32	7	the	the	DET
american_scientific_journal-1936	32	8	mesh	mesh	NOUN
american_scientific_journal-1936	32	9	nodes	node	NOUN
american_scientific_journal-1936	32	10	.	.	PUNCT
american_scientific_journal-1936	33	1	the	the	DET
american_scientific_journal-1936	33	2	core	core	ADJ
american_scientific_journal-1936	33	3	idea	idea	NOUN
american_scientific_journal-1936	33	4	of	of	ADP
american_scientific_journal-1936	33	5	the	the	DET
american_scientific_journal-1936	33	6	finite	finite	ADJ
american_scientific_journal-1936	33	7	difference	difference	NOUN
american_scientific_journal-1936	33	8	scheme	scheme	NOUN
american_scientific_journal-1936	33	9	is	be	AUX
american_scientific_journal-1936	33	10	to	to	PART
american_scientific_journal-1936	33	11	replace	replace	VERB
american_scientific_journal-1936	33	12	continuous	continuous	ADJ
american_scientific_journal-1936	33	13	derivatives	derivative	NOUN
american_scientific_journal-1936	33	14	with	with	ADP
american_scientific_journal-1936	33	15	difference	difference	NOUN
american_scientific_journal-1936	33	16	formulae	formulae	NOUN
american_scientific_journal-1936	33	17	.	.	PUNCT
american_scientific_journal-1936	34	1	difference	difference	NOUN
american_scientific_journal-1936	34	2	formulae	formulae	NOUN
american_scientific_journal-1936	34	3	provide	provide	VERB
american_scientific_journal-1936	34	4	discrete	discrete	ADJ
american_scientific_journal-1936	34	5	values	value	NOUN
american_scientific_journal-1936	34	6	of	of	ADP
american_scientific_journal-1936	34	7	the	the	DET
american_scientific_journal-1936	34	8	function	function	NOUN
american_scientific_journal-1936	34	9	at	at	ADP
american_scientific_journal-1936	34	10	nodes	node	NOUN
american_scientific_journal-1936	34	11	of	of	ADP
american_scientific_journal-1936	34	12	the	the	DET
american_scientific_journal-1936	34	13	mesh	mesh	NOUN
american_scientific_journal-1936	34	14	.	.	PUNCT
american_scientific_journal-1936	35	1	a	a	DET
american_scientific_journal-1936	35	2	variety	variety	NOUN
american_scientific_journal-1936	35	3	of	of	ADP
american_scientific_journal-1936	35	4	finite	finite	ADJ
american_scientific_journal-1936	35	5	difference	difference	NOUN
american_scientific_journal-1936	35	6	schemes	scheme	NOUN
american_scientific_journal-1936	35	7	are	be	AUX
american_scientific_journal-1936	35	8	popular	popular	ADJ
american_scientific_journal-1936	35	9	and	and	CCONJ
american_scientific_journal-1936	35	10	widely	widely	ADV
american_scientific_journal-1936	35	11	used	use	VERB
american_scientific_journal-1936	35	12	.	.	PUNCT
american_scientific_journal-1936	36	1	use	use	NOUN
american_scientific_journal-1936	36	2	of	of	ADP
american_scientific_journal-1936	36	3	different	different	ADJ
american_scientific_journal-1936	36	4	combinations	combination	NOUN
american_scientific_journal-1936	36	5	of	of	ADP
american_scientific_journal-1936	36	6	mesh	mesh	NOUN
american_scientific_journal-1936	36	7	points	point	NOUN
american_scientific_journal-1936	36	8	in	in	ADP
american_scientific_journal-1936	36	9	the	the	DET
american_scientific_journal-1936	36	10	difference	difference	NOUN
american_scientific_journal-1936	36	11	formulas	formula	NOUN
american_scientific_journal-1936	36	12	results	result	VERB
american_scientific_journal-1936	36	13	in	in	ADP
american_scientific_journal-1936	36	14	different	different	ADJ
american_scientific_journal-1936	36	15	schemes	scheme	NOUN
american_scientific_journal-1936	36	16	.	.	PUNCT
american_scientific_journal-1936	37	1	in	in	ADP
american_scientific_journal-1936	37	2	the	the	DET
american_scientific_journal-1936	37	3	limit	limit	NOUN
american_scientific_journal-1936	37	4	of	of	ADP
american_scientific_journal-1936	37	5	the	the	DET
american_scientific_journal-1936	37	6	mesh	mesh	NOUN
american_scientific_journal-1936	37	7	step	step	NOUN
american_scientific_journal-1936	37	8	spacing	space	VERB
american_scientific_journal-1936	37	9	tending	tend	VERB
american_scientific_journal-1936	37	10	to	to	ADP
american_scientific_journal-1936	37	11	zero	zero	NUM
american_scientific_journal-1936	37	12	i.e.	i.e.	X
american_scientific_journal-1936	37	13	,	,	PUNCT
american_scientific_journal-1936	37	14	as	as	ADP
american_scientific_journal-1936	37	15	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	37	16	→	→	SYM
american_scientific_journal-1936	37	17	0	0	NUM
american_scientific_journal-1936	37	18	and	and	CCONJ
american_scientific_journal-1936	37	19	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	37	20	→	→	SYM
american_scientific_journal-1936	37	21	0	0	NUM
american_scientific_journal-1936	37	22	,	,	PUNCT
american_scientific_journal-1936	37	23	the	the	DET
american_scientific_journal-1936	37	24	numerical	numerical	ADJ
american_scientific_journal-1936	37	25	solution	solution	NOUN
american_scientific_journal-1936	37	26	obtained	obtain	VERB
american_scientific_journal-1936	37	27	by	by	ADP
american_scientific_journal-1936	37	28	any	any	DET
american_scientific_journal-1936	37	29	useful	useful	ADJ
american_scientific_journal-1936	37	30	scheme	scheme	NOUN
american_scientific_journal-1936	37	31	will	will	AUX
american_scientific_journal-1936	37	32	approach	approach	VERB
american_scientific_journal-1936	37	33	the	the	DET
american_scientific_journal-1936	37	34	true	true	ADJ
american_scientific_journal-1936	37	35	solution	solution	NOUN
american_scientific_journal-1936	37	36	of	of	ADP
american_scientific_journal-1936	37	37	the	the	DET
american_scientific_journal-1936	37	38	differential	differential	ADJ
american_scientific_journal-1936	37	39	equation	equation	NOUN
american_scientific_journal-1936	37	40	.	.	PUNCT
american_scientific_journal-1936	38	1	however	however	ADV
american_scientific_journal-1936	38	2	,	,	PUNCT
american_scientific_journal-1936	38	3	the	the	DET
american_scientific_journal-1936	38	4	rate	rate	NOUN
american_scientific_journal-1936	38	5	at	at	ADP
american_scientific_journal-1936	38	6	which	which	PRON
american_scientific_journal-1936	38	7	the	the	DET
american_scientific_journal-1936	38	8	numerical	numerical	ADJ
american_scientific_journal-1936	38	9	solution	solution	NOUN
american_scientific_journal-1936	38	10	converges	converge	VERB
american_scientific_journal-1936	38	11	to	to	ADP
american_scientific_journal-1936	38	12	the	the	DET
american_scientific_journal-1936	38	13	true	true	ADJ
american_scientific_journal-1936	38	14	solution	solution	NOUN
american_scientific_journal-1936	38	15	varies	vary	VERB
american_scientific_journal-1936	38	16	with	with	ADP
american_scientific_journal-1936	38	17	the	the	DET
american_scientific_journal-1936	38	18	scheme	scheme	NOUN
american_scientific_journal-1936	38	19	.	.	PUNCT
american_scientific_journal-1936	39	1	in	in	ADP
american_scientific_journal-1936	39	2	addition	addition	NOUN
american_scientific_journal-1936	39	3	,	,	PUNCT
american_scientific_journal-1936	39	4	there	there	PRON
american_scientific_journal-1936	39	5	are	be	VERB
american_scientific_journal-1936	39	6	some	some	DET
american_scientific_journal-1936	39	7	practically	practically	ADV
american_scientific_journal-1936	39	8	useful	useful	ADJ
american_scientific_journal-1936	39	9	schemes	scheme	NOUN
american_scientific_journal-1936	39	10	which	which	PRON
american_scientific_journal-1936	39	11	may	may	AUX
american_scientific_journal-1936	39	12	fail	fail	VERB
american_scientific_journal-1936	39	13	to	to	PART
american_scientific_journal-1936	39	14	yield	yield	VERB
american_scientific_journal-1936	39	15	a	a	DET
american_scientific_journal-1936	39	16	solution	solution	NOUN
american_scientific_journal-1936	39	17	for	for	ADP
american_scientific_journal-1936	39	18	bad	bad	ADJ
american_scientific_journal-1936	39	19	combinations	combination	NOUN
american_scientific_journal-1936	39	20	of	of	ADP
american_scientific_journal-1936	39	21	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	39	22	and	and	CCONJ
american_scientific_journal-1936	39	23	∆𝑡𝑡.	∆𝑡𝑡.	PROPN
american_scientific_journal-1936	39	24	hence	hence	ADV
american_scientific_journal-1936	39	25	,	,	PUNCT
american_scientific_journal-1936	39	26	the	the	DET
american_scientific_journal-1936	39	27	selection	selection	NOUN
american_scientific_journal-1936	39	28	of	of	ADP
american_scientific_journal-1936	39	29	combinations	combination	NOUN
american_scientific_journal-1936	39	30	of	of	ADP
american_scientific_journal-1936	39	31	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	39	32	and	and	CCONJ
american_scientific_journal-1936	39	33	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	39	34	plays	play	VERB
american_scientific_journal-1936	39	35	an	an	DET
american_scientific_journal-1936	39	36	important	important	ADJ
american_scientific_journal-1936	39	37	role	role	NOUN
american_scientific_journal-1936	39	38	[	[	X
american_scientific_journal-1936	39	39	3	3	NUM
american_scientific_journal-1936	39	40	]	]	PUNCT
american_scientific_journal-1936	39	41	.	.	PUNCT
american_scientific_journal-1936	40	1	further	far	ADV
american_scientific_journal-1936	40	2	,	,	PUNCT
american_scientific_journal-1936	40	3	considerable	considerable	ADJ
american_scientific_journal-1936	40	4	attention	attention	NOUN
american_scientific_journal-1936	40	5	is	be	AUX
american_scientific_journal-1936	40	6	required	require	VERB
american_scientific_journal-1936	40	7	so	so	SCONJ
american_scientific_journal-1936	40	8	that	that	SCONJ
american_scientific_journal-1936	40	9	the	the	DET
american_scientific_journal-1936	40	10	physical	physical	ADJ
american_scientific_journal-1936	40	11	interpretations	interpretation	NOUN
american_scientific_journal-1936	40	12	of	of	ADP
american_scientific_journal-1936	40	13	solutions	solution	NOUN
american_scientific_journal-1936	40	14	of	of	ADP
american_scientific_journal-1936	40	15	diffusion	diffusion	NOUN
american_scientific_journal-1936	40	16	equation	equation	NOUN
american_scientific_journal-1936	40	17	remain	remain	VERB
american_scientific_journal-1936	40	18	meaningful	meaningful	ADJ
american_scientific_journal-1936	40	19	.	.	PUNCT
american_scientific_journal-1936	41	1	that	that	PRON
american_scientific_journal-1936	41	2	is	is	ADV
american_scientific_journal-1936	41	3	,	,	PUNCT
american_scientific_journal-1936	41	4	we	we	PRON
american_scientific_journal-1936	41	5	have	have	VERB
american_scientific_journal-1936	41	6	to	to	PART
american_scientific_journal-1936	41	7	select	select	VERB
american_scientific_journal-1936	41	8	such	such	DET
american_scientific_journal-1936	41	9	a	a	DET
american_scientific_journal-1936	41	10	combination	combination	NOUN
american_scientific_journal-1936	41	11	of	of	ADP
american_scientific_journal-1936	41	12	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	41	13	and	and	CCONJ
american_scientific_journal-1936	41	14	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	41	15	that	that	PRON
american_scientific_journal-1936	41	16	provides	provide	VERB
american_scientific_journal-1936	41	17	physically	physically	ADV
american_scientific_journal-1936	41	18	meaningful	meaningful	ADJ
american_scientific_journal-1936	41	19	approximate	approximate	ADJ
american_scientific_journal-1936	41	20	solution	solution	NOUN
american_scientific_journal-1936	41	21	for	for	ADP
american_scientific_journal-1936	41	22	the	the	DET
american_scientific_journal-1936	41	23	diffusion	diffusion	NOUN
american_scientific_journal-1936	41	24	equation	equation	NOUN
american_scientific_journal-1936	41	25	.	.	PUNCT
american_scientific_journal-1936	42	1	2	2	X
american_scientific_journal-1936	42	2	.	.	X
american_scientific_journal-1936	42	3	governing	govern	VERB
american_scientific_journal-1936	42	4	equation	equation	NOUN
american_scientific_journal-1936	42	5	and	and	CCONJ
american_scientific_journal-1936	42	6	finite	finite	ADJ
american_scientific_journal-1936	42	7	difference	difference	NOUN
american_scientific_journal-1936	42	8	schemes	scheme	NOUN
american_scientific_journal-1936	42	9	here	here	ADV
american_scientific_journal-1936	42	10	we	we	PRON
american_scientific_journal-1936	42	11	now	now	ADV
american_scientific_journal-1936	42	12	introduce	introduce	VERB
american_scientific_journal-1936	42	13	and	and	CCONJ
american_scientific_journal-1936	42	14	discuss	discuss	VERB
american_scientific_journal-1936	42	15	governing	govern	VERB
american_scientific_journal-1936	42	16	equation	equation	NOUN
american_scientific_journal-1936	42	17	describing	describe	VERB
american_scientific_journal-1936	42	18	one	one	NUM
american_scientific_journal-1936	42	19	dimensional	dimensional	ADJ
american_scientific_journal-1936	42	20	diffusion	diffusion	NOUN
american_scientific_journal-1936	42	21	.	.	PUNCT
american_scientific_journal-1936	43	1	also	also	ADV
american_scientific_journal-1936	43	2	we	we	PRON
american_scientific_journal-1936	43	3	present	present	VERB
american_scientific_journal-1936	43	4	american	american	ADJ
american_scientific_journal-1936	43	5	scientific	scientific	ADJ
american_scientific_journal-1936	43	6	research	research	NOUN
american_scientific_journal-1936	43	7	journal	journal	NOUN
american_scientific_journal-1936	43	8	for	for	ADP
american_scientific_journal-1936	43	9	engineering	engineering	NOUN
american_scientific_journal-1936	43	10	,	,	PUNCT
american_scientific_journal-1936	43	11	technology	technology	NOUN
american_scientific_journal-1936	43	12	,	,	PUNCT
american_scientific_journal-1936	43	13	and	and	CCONJ
american_scientific_journal-1936	43	14	sciences	science	NOUN
american_scientific_journal-1936	43	15	(	(	PUNCT
american_scientific_journal-1936	43	16	asrjets	asrjet	NOUN
american_scientific_journal-1936	43	17	)	)	PUNCT
american_scientific_journal-1936	43	18	(	(	PUNCT
american_scientific_journal-1936	43	19	2016	2016	NUM
american_scientific_journal-1936	43	20	)	)	PUNCT
american_scientific_journal-1936	43	21	volume	volume	NOUN
american_scientific_journal-1936	43	22	26	26	NUM
american_scientific_journal-1936	43	23	,	,	PUNCT
american_scientific_journal-1936	43	24	no	no	DET
american_scientific_journal-1936	43	25	3	3	NUM
american_scientific_journal-1936	43	26	,	,	PUNCT
american_scientific_journal-1936	43	27	pp	pp	ADV
american_scientific_journal-1936	43	28	140	140	NUM
american_scientific_journal-1936	43	29	-	-	SYM
american_scientific_journal-1936	43	30	154	154	NUM
american_scientific_journal-1936	43	31	142	142	NUM
american_scientific_journal-1936	43	32	the	the	DET
american_scientific_journal-1936	43	33	finite	finite	ADJ
american_scientific_journal-1936	43	34	difference	difference	NOUN
american_scientific_journal-1936	43	35	methods	method	NOUN
american_scientific_journal-1936	43	36	viz	viz	PROPN
american_scientific_journal-1936	43	37	.	.	PUNCT
american_scientific_journal-1936	43	38	,	,	PUNCT
american_scientific_journal-1936	43	39	forward	forward	ADV
american_scientific_journal-1936	43	40	time	time	NOUN
american_scientific_journal-1936	43	41	centered	center	VERB
american_scientific_journal-1936	43	42	space	space	NOUN
american_scientific_journal-1936	43	43	or	or	CCONJ
american_scientific_journal-1936	43	44	ftcs	ftcs	NOUN
american_scientific_journal-1936	43	45	,	,	PUNCT
american_scientific_journal-1936	43	46	backward	backward	ADJ
american_scientific_journal-1936	43	47	time	time	NOUN
american_scientific_journal-1936	43	48	centered	center	VERB
american_scientific_journal-1936	43	49	space	space	NOUN
american_scientific_journal-1936	43	50	or	or	CCONJ
american_scientific_journal-1936	43	51	btcs	btcs	NOUN
american_scientific_journal-1936	43	52	and	and	CCONJ
american_scientific_journal-1936	43	53	crank	crank	NOUN
american_scientific_journal-1936	43	54	–	–	PUNCT
american_scientific_journal-1936	43	55	nicolson	nicolson	PROPN
american_scientific_journal-1936	43	56	schemes	scheme	NOUN
american_scientific_journal-1936	43	57	.	.	PUNCT
american_scientific_journal-1936	44	1	2.1	2.1	NUM
american_scientific_journal-1936	44	2	governing	govern	VERB
american_scientific_journal-1936	44	3	equation	equation	NOUN
american_scientific_journal-1936	44	4	the	the	DET
american_scientific_journal-1936	44	5	more	more	ADV
american_scientific_journal-1936	44	6	general	general	ADJ
american_scientific_journal-1936	44	7	diffusion	diffusion	NOUN
american_scientific_journal-1936	44	8	equation	equation	NOUN
american_scientific_journal-1936	44	9	is	be	AUX
american_scientific_journal-1936	44	10	a	a	DET
american_scientific_journal-1936	44	11	partial	partial	ADJ
american_scientific_journal-1936	44	12	differential	differential	NOUN
american_scientific_journal-1936	44	13	equation	equation	NOUN
american_scientific_journal-1936	44	14	and	and	CCONJ
american_scientific_journal-1936	44	15	it	it	PRON
american_scientific_journal-1936	44	16	describes	describe	VERB
american_scientific_journal-1936	44	17	the	the	DET
american_scientific_journal-1936	44	18	density	density	NOUN
american_scientific_journal-1936	44	19	fluctuations	fluctuation	NOUN
american_scientific_journal-1936	44	20	in	in	ADP
american_scientific_journal-1936	44	21	the	the	DET
american_scientific_journal-1936	44	22	material	material	NOUN
american_scientific_journal-1936	44	23	undergoing	undergo	VERB
american_scientific_journal-1936	44	24	diffusion	diffusion	NOUN
american_scientific_journal-1936	44	25	.	.	PUNCT
american_scientific_journal-1936	45	1	the	the	DET
american_scientific_journal-1936	45	2	equation	equation	NOUN
american_scientific_journal-1936	45	3	can	can	AUX
american_scientific_journal-1936	45	4	be	be	AUX
american_scientific_journal-1936	45	5	expressed	express	VERB
american_scientific_journal-1936	45	6	as	as	ADP
american_scientific_journal-1936	45	7	:	:	PUNCT
american_scientific_journal-1936	45	8	𝜕𝜕𝜕𝜕	𝜕𝜕𝜕𝜕	NOUN
american_scientific_journal-1936	45	9	𝜕𝜕𝜕𝜕	𝜕𝜕𝜕𝜕	NOUN
american_scientific_journal-1936	45	10	=	=	SYM
american_scientific_journal-1936	45	11	∇.	∇.	X
american_scientific_journal-1936	45	12	(	(	PUNCT
american_scientific_journal-1936	45	13	𝐷𝐷∇𝑢𝑢	𝐷𝐷∇𝑢𝑢	NOUN
american_scientific_journal-1936	45	14	)	)	PUNCT
american_scientific_journal-1936	45	15	(	(	PUNCT
american_scientific_journal-1936	45	16	1	1	X
american_scientific_journal-1936	45	17	)	)	PUNCT
american_scientific_journal-1936	45	18	here	here	ADV
american_scientific_journal-1936	45	19	in	in	ADP
american_scientific_journal-1936	45	20	(	(	PUNCT
american_scientific_journal-1936	45	21	1	1	NUM
american_scientific_journal-1936	45	22	)	)	PUNCT
american_scientific_journal-1936	45	23	,	,	PUNCT
american_scientific_journal-1936	45	24	𝑢𝑢	𝑢𝑢	PROPN
american_scientific_journal-1936	45	25	≡	≡	PROPN
american_scientific_journal-1936	45	26	𝑢𝑢(𝒙𝒙	𝑢𝑢(𝒙𝒙	PROPN
american_scientific_journal-1936	45	27	,	,	PUNCT
american_scientific_journal-1936	45	28	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	45	29	)	)	PUNCT
american_scientific_journal-1936	45	30	denotes	denote	VERB
american_scientific_journal-1936	45	31	the	the	DET
american_scientific_journal-1936	45	32	density	density	NOUN
american_scientific_journal-1936	45	33	of	of	ADP
american_scientific_journal-1936	45	34	the	the	DET
american_scientific_journal-1936	45	35	diffusing	diffuse	VERB
american_scientific_journal-1936	45	36	material	material	NOUN
american_scientific_journal-1936	45	37	at	at	ADP
american_scientific_journal-1936	45	38	location	location	NOUN
american_scientific_journal-1936	45	39	𝒙𝒙	𝒙𝒙	NOUN
american_scientific_journal-1936	45	40	=	=	PUNCT
american_scientific_journal-1936	45	41	(	(	PUNCT
american_scientific_journal-1936	45	42	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	45	43	,	,	PUNCT
american_scientific_journal-1936	45	44	𝑦𝑦	𝑦𝑦	PROPN
american_scientific_journal-1936	45	45	,	,	PUNCT
american_scientific_journal-1936	45	46	𝑧𝑧	𝑧𝑧	NOUN
american_scientific_journal-1936	45	47	)	)	PUNCT
american_scientific_journal-1936	45	48	and	and	CCONJ
american_scientific_journal-1936	45	49	at	at	ADP
american_scientific_journal-1936	45	50	time	time	NOUN
american_scientific_journal-1936	45	51	𝑡𝑡.	𝑡𝑡.	X
american_scientific_journal-1936	45	52	also	also	ADV
american_scientific_journal-1936	45	53	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	45	54	≡	≡	PROPN
american_scientific_journal-1936	45	55	𝐷𝐷(𝑢𝑢(𝒙𝒙	𝐷𝐷(𝑢𝑢(𝒙𝒙	PROPN
american_scientific_journal-1936	45	56	,	,	PUNCT
american_scientific_journal-1936	45	57	𝑡𝑡	𝑡𝑡	NOUN
american_scientific_journal-1936	45	58	)	)	PUNCT
american_scientific_journal-1936	45	59	,	,	PUNCT
american_scientific_journal-1936	45	60	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	45	61	)	)	PUNCT
american_scientific_journal-1936	45	62	denotes	denote	VERB
american_scientific_journal-1936	45	63	the	the	DET
american_scientific_journal-1936	45	64	collective	collective	ADJ
american_scientific_journal-1936	45	65	diffusion	diffusion	NOUN
american_scientific_journal-1936	45	66	coefficient	coefficient	NOUN
american_scientific_journal-1936	45	67	for	for	ADP
american_scientific_journal-1936	45	68	the	the	DET
american_scientific_journal-1936	45	69	density	density	NOUN
american_scientific_journal-1936	45	70	𝑢𝑢	𝑢𝑢	PROPN
american_scientific_journal-1936	45	71	at	at	ADP
american_scientific_journal-1936	45	72	location	location	NOUN
american_scientific_journal-1936	45	73	𝐱𝐱.	𝐱𝐱.	VERB
american_scientific_journal-1936	45	74	now	now	ADV
american_scientific_journal-1936	45	75	for	for	ADP
american_scientific_journal-1936	45	76	simplicity	simplicity	NOUN
american_scientific_journal-1936	45	77	let	let	VERB
american_scientific_journal-1936	45	78	the	the	DET
american_scientific_journal-1936	45	79	diffusion	diffusion	NOUN
american_scientific_journal-1936	45	80	coefficient	coefficient	NOUN
american_scientific_journal-1936	45	81	be	be	AUX
american_scientific_journal-1936	45	82	independent	independent	ADJ
american_scientific_journal-1936	45	83	of	of	ADP
american_scientific_journal-1936	45	84	both	both	DET
american_scientific_journal-1936	45	85	density	density	NOUN
american_scientific_journal-1936	45	86	and	and	CCONJ
american_scientific_journal-1936	45	87	location	location	NOUN
american_scientific_journal-1936	45	88	i.e.	i.e.	ADV
american_scientific_journal-1936	45	89	,	,	PUNCT
american_scientific_journal-1936	45	90	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	45	91	is	be	AUX
american_scientific_journal-1936	45	92	a	a	DET
american_scientific_journal-1936	45	93	constant	constant	ADJ
american_scientific_journal-1936	45	94	.	.	PUNCT
american_scientific_journal-1936	46	1	thus	thus	ADV
american_scientific_journal-1936	46	2	equation	equation	NOUN
american_scientific_journal-1936	46	3	(	(	PUNCT
american_scientific_journal-1936	46	4	1	1	X
american_scientific_journal-1936	46	5	)	)	PUNCT
american_scientific_journal-1936	46	6	reduces	reduce	VERB
american_scientific_journal-1936	46	7	to	to	ADP
american_scientific_journal-1936	46	8	a	a	DET
american_scientific_journal-1936	46	9	linear	linear	ADJ
american_scientific_journal-1936	46	10	form	form	NOUN
american_scientific_journal-1936	46	11	as	as	ADP
american_scientific_journal-1936	46	12	𝜕𝜕𝜕𝜕	𝜕𝜕𝜕𝜕	NOUN
american_scientific_journal-1936	46	13	𝜕𝜕𝜕𝜕	𝜕𝜕𝜕𝜕	NOUN
american_scientific_journal-1936	46	14	=	=	SYM
american_scientific_journal-1936	46	15	𝐷𝐷∇2𝑢𝑢	𝐷𝐷∇2𝑢𝑢	X
american_scientific_journal-1936	46	16	.	.	PUNCT
american_scientific_journal-1936	47	1	(	(	PUNCT
american_scientific_journal-1936	47	2	2	2	X
american_scientific_journal-1936	47	3	)	)	PUNCT
american_scientific_journal-1936	47	4	equation	equation	NOUN
american_scientific_journal-1936	47	5	(	(	PUNCT
american_scientific_journal-1936	47	6	2	2	X
american_scientific_journal-1936	47	7	)	)	PUNCT
american_scientific_journal-1936	47	8	is	be	AUX
american_scientific_journal-1936	47	9	a	a	DET
american_scientific_journal-1936	47	10	diffusion	diffusion	NOUN
american_scientific_journal-1936	47	11	or	or	CCONJ
american_scientific_journal-1936	47	12	heat	heat	NOUN
american_scientific_journal-1936	47	13	equation	equation	NOUN
american_scientific_journal-1936	47	14	and	and	CCONJ
american_scientific_journal-1936	47	15	describes	describe	VERB
american_scientific_journal-1936	47	16	the	the	DET
american_scientific_journal-1936	47	17	distribution	distribution	NOUN
american_scientific_journal-1936	47	18	of	of	ADP
american_scientific_journal-1936	47	19	material	material	NOUN
american_scientific_journal-1936	47	20	or	or	CCONJ
american_scientific_journal-1936	47	21	heat	heat	NOUN
american_scientific_journal-1936	47	22	in	in	ADP
american_scientific_journal-1936	47	23	a	a	DET
american_scientific_journal-1936	47	24	given	give	VERB
american_scientific_journal-1936	47	25	region	region	NOUN
american_scientific_journal-1936	47	26	over	over	ADP
american_scientific_journal-1936	47	27	time	time	NOUN
american_scientific_journal-1936	47	28	with	with	ADP
american_scientific_journal-1936	47	29	constant	constant	ADJ
american_scientific_journal-1936	47	30	diffusion	diffusion	NOUN
american_scientific_journal-1936	47	31	coefficient	coefficient	NOUN
american_scientific_journal-1936	47	32	.	.	PUNCT
american_scientific_journal-1936	48	1	in	in	ADP
american_scientific_journal-1936	48	2	the	the	DET
american_scientific_journal-1936	48	3	present	present	ADJ
american_scientific_journal-1936	48	4	study	study	NOUN
american_scientific_journal-1936	48	5	we	we	PRON
american_scientific_journal-1936	48	6	further	far	ADV
american_scientific_journal-1936	48	7	simplify	simplify	VERB
american_scientific_journal-1936	48	8	(	(	PUNCT
american_scientific_journal-1936	48	9	2	2	NUM
american_scientific_journal-1936	48	10	)	)	PUNCT
american_scientific_journal-1936	48	11	and	and	CCONJ
american_scientific_journal-1936	48	12	consider	consider	VERB
american_scientific_journal-1936	48	13	one	one	NUM
american_scientific_journal-1936	48	14	–	–	PUNCT
american_scientific_journal-1936	48	15	dimensional	dimensional	ADJ
american_scientific_journal-1936	48	16	diffusion	diffusion	NOUN
american_scientific_journal-1936	48	17	with	with	ADP
american_scientific_journal-1936	48	18	constant	constant	ADJ
american_scientific_journal-1936	48	19	diffusion	diffusion	NOUN
american_scientific_journal-1936	48	20	coefficient	coefficient	NOUN
american_scientific_journal-1936	48	21	𝐷𝐷.	𝐷𝐷.	NUM
american_scientific_journal-1936	48	22	this	this	DET
american_scientific_journal-1936	48	23	consideration	consideration	NOUN
american_scientific_journal-1936	48	24	simplifies	simplifie	NOUN
american_scientific_journal-1936	48	25	(	(	PUNCT
american_scientific_journal-1936	48	26	2	2	NUM
american_scientific_journal-1936	48	27	)	)	PUNCT
american_scientific_journal-1936	48	28	to	to	PART
american_scientific_journal-1936	48	29	give	give	VERB
american_scientific_journal-1936	48	30	𝜕𝜕𝜕𝜕	𝜕𝜕𝜕𝜕	NOUN
american_scientific_journal-1936	48	31	𝜕𝜕𝜕𝜕	𝜕𝜕𝜕𝜕	NOUN
american_scientific_journal-1936	48	32	=	=	SYM
american_scientific_journal-1936	48	33	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	48	34	𝜕𝜕2𝜕𝜕	𝜕𝜕2𝜕𝜕	PROPN
american_scientific_journal-1936	48	35	𝜕𝜕𝑥𝑥2	𝜕𝜕𝑥𝑥2	PUNCT
american_scientific_journal-1936	48	36	(	(	PUNCT
american_scientific_journal-1936	48	37	3	3	X
american_scientific_journal-1936	48	38	)	)	PUNCT
american_scientific_journal-1936	48	39	here	here	ADV
american_scientific_journal-1936	48	40	in	in	ADP
american_scientific_journal-1936	48	41	(	(	PUNCT
american_scientific_journal-1936	48	42	3	3	NUM
american_scientific_journal-1936	48	43	)	)	PUNCT
american_scientific_journal-1936	48	44	,	,	PUNCT
american_scientific_journal-1936	48	45	𝑢𝑢	𝑢𝑢	PROPN
american_scientific_journal-1936	48	46	is	be	AUX
american_scientific_journal-1936	48	47	the	the	DET
american_scientific_journal-1936	48	48	density	density	NOUN
american_scientific_journal-1936	48	49	of	of	ADP
american_scientific_journal-1936	48	50	the	the	DET
american_scientific_journal-1936	48	51	diffusing	diffuse	VERB
american_scientific_journal-1936	48	52	material	material	NOUN
american_scientific_journal-1936	48	53	at	at	ADP
american_scientific_journal-1936	48	54	location	location	NOUN
american_scientific_journal-1936	48	55	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	48	56	and	and	CCONJ
american_scientific_journal-1936	48	57	time	time	NOUN
american_scientific_journal-1936	48	58	𝑡𝑡.	𝑡𝑡.	PRON
american_scientific_journal-1936	48	59	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	48	60	is	be	AUX
american_scientific_journal-1936	48	61	the	the	DET
american_scientific_journal-1936	48	62	diffusivity	diffusivity	NOUN
american_scientific_journal-1936	48	63	coefficient	coefficient	NOUN
american_scientific_journal-1936	48	64	in	in	ADP
american_scientific_journal-1936	48	65	the	the	DET
american_scientific_journal-1936	48	66	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	48	67	–	–	PUNCT
american_scientific_journal-1936	48	68	direction	direction	NOUN
american_scientific_journal-1936	48	69	.	.	PUNCT
american_scientific_journal-1936	49	1	we	we	PRON
american_scientific_journal-1936	49	2	impose	impose	VERB
american_scientific_journal-1936	49	3	appropriate	appropriate	ADJ
american_scientific_journal-1936	49	4	initial	initial	ADJ
american_scientific_journal-1936	49	5	and	and	CCONJ
american_scientific_journal-1936	49	6	boundary	boundary	ADJ
american_scientific_journal-1936	49	7	conditions	condition	NOUN
american_scientific_journal-1936	49	8	on	on	ADP
american_scientific_journal-1936	49	9	(	(	PUNCT
american_scientific_journal-1936	49	10	3	3	X
american_scientific_journal-1936	49	11	)	)	PUNCT
american_scientific_journal-1936	49	12	in	in	ADP
american_scientific_journal-1936	49	13	order	order	NOUN
american_scientific_journal-1936	49	14	to	to	PART
american_scientific_journal-1936	49	15	evaluate	evaluate	VERB
american_scientific_journal-1936	49	16	a	a	DET
american_scientific_journal-1936	49	17	numerical	numerical	ADJ
american_scientific_journal-1936	49	18	or	or	CCONJ
american_scientific_journal-1936	49	19	approximate	approximate	ADJ
american_scientific_journal-1936	49	20	solution	solution	NOUN
american_scientific_journal-1936	49	21	of	of	ADP
american_scientific_journal-1936	49	22	it	it	PRON
american_scientific_journal-1936	49	23	.	.	PUNCT
american_scientific_journal-1936	50	1	several	several	ADJ
american_scientific_journal-1936	50	2	combinations	combination	NOUN
american_scientific_journal-1936	50	3	of	of	ADP
american_scientific_journal-1936	50	4	boundary	boundary	ADJ
american_scientific_journal-1936	50	5	conditions	condition	NOUN
american_scientific_journal-1936	50	6	are	be	AUX
american_scientific_journal-1936	50	7	possible	possible	ADJ
american_scientific_journal-1936	50	8	.	.	PUNCT
american_scientific_journal-1936	51	1	we	we	PRON
american_scientific_journal-1936	51	2	consider	consider	VERB
american_scientific_journal-1936	51	3	three	three	NUM
american_scientific_journal-1936	51	4	distinct	distinct	ADJ
american_scientific_journal-1936	51	5	cases	case	NOUN
american_scientific_journal-1936	51	6	and	and	CCONJ
american_scientific_journal-1936	51	7	apply	apply	VERB
american_scientific_journal-1936	51	8	them	they	PRON
american_scientific_journal-1936	51	9	in	in	ADP
american_scientific_journal-1936	51	10	a	a	DET
american_scientific_journal-1936	51	11	finite	finite	ADJ
american_scientific_journal-1936	51	12	domain	domain	NOUN
american_scientific_journal-1936	51	13	as	as	SCONJ
american_scientific_journal-1936	51	14	follows	follow	VERB
american_scientific_journal-1936	51	15	:	:	PUNCT
american_scientific_journal-1936	51	16	case	case	NOUN
american_scientific_journal-1936	51	17	1	1	NUM
american_scientific_journal-1936	51	18	:	:	PUNCT
american_scientific_journal-1936	51	19	dirichlet	dirichlet	ADJ
american_scientific_journal-1936	51	20	type	type	NOUN
american_scientific_journal-1936	51	21	of	of	ADP
american_scientific_journal-1936	51	22	boundary	boundary	ADJ
american_scientific_journal-1936	51	23	conditions	condition	NOUN
american_scientific_journal-1936	51	24	𝑢𝑢(𝑥𝑥	𝑢𝑢(𝑥𝑥	PROPN
american_scientific_journal-1936	51	25	,	,	PUNCT
american_scientific_journal-1936	51	26	0	0	NUM
american_scientific_journal-1936	51	27	)	)	PUNCT
american_scientific_journal-1936	51	28	=	=	SYM
american_scientific_journal-1936	51	29	𝑓𝑓(𝑥𝑥	𝑓𝑓(𝑥𝑥	PROPN
american_scientific_journal-1936	51	30	)	)	PUNCT
american_scientific_journal-1936	51	31	(	(	PUNCT
american_scientific_journal-1936	51	32	4	4	X
american_scientific_journal-1936	51	33	)	)	PUNCT
american_scientific_journal-1936	51	34	𝑢𝑢(0	𝑢𝑢(0	PROPN
american_scientific_journal-1936	51	35	,	,	PUNCT
american_scientific_journal-1936	51	36	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	51	37	)	)	PUNCT
american_scientific_journal-1936	51	38	=	=	PUNCT
american_scientific_journal-1936	51	39	𝑢𝑢0	𝑢𝑢0	NOUN
american_scientific_journal-1936	51	40	𝑢𝑢(𝐿𝐿	𝑢𝑢(𝐿𝐿	NOUN
american_scientific_journal-1936	51	41	,	,	PUNCT
american_scientific_journal-1936	51	42	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	51	43	)	)	PUNCT
american_scientific_journal-1936	51	44	=	=	SYM
american_scientific_journal-1936	51	45	𝑢𝑢𝐿𝐿	𝑢𝑢𝐿𝐿	NOUN
american_scientific_journal-1936	51	46	case	case	NOUN
american_scientific_journal-1936	51	47	2	2	NUM
american_scientific_journal-1936	51	48	:	:	PUNCT
american_scientific_journal-1936	51	49	neumann	neumann	PROPN
american_scientific_journal-1936	51	50	type	type	NOUN
american_scientific_journal-1936	51	51	of	of	ADP
american_scientific_journal-1936	51	52	boundary	boundary	ADJ
american_scientific_journal-1936	51	53	conditions	condition	NOUN
american_scientific_journal-1936	51	54	𝑢𝑢(𝑥𝑥	𝑢𝑢(𝑥𝑥	PROPN
american_scientific_journal-1936	51	55	,	,	PUNCT
american_scientific_journal-1936	51	56	0	0	NUM
american_scientific_journal-1936	51	57	)	)	PUNCT
american_scientific_journal-1936	51	58	=	=	SYM
american_scientific_journal-1936	51	59	𝑓𝑓(𝑥𝑥	𝑓𝑓(𝑥𝑥	PROPN
american_scientific_journal-1936	51	60	)	)	PUNCT
american_scientific_journal-1936	51	61	(	(	PUNCT
american_scientific_journal-1936	51	62	5	5	X
american_scientific_journal-1936	51	63	)	)	PUNCT
american_scientific_journal-1936	51	64	𝜕𝜕𝜕𝜕	𝜕𝜕𝜕𝜕	NOUN
american_scientific_journal-1936	51	65	𝜕𝜕𝑥𝑥	𝜕𝜕𝑥𝑥	X
american_scientific_journal-1936	51	66	(	(	PUNCT
american_scientific_journal-1936	51	67	0	0	NUM
american_scientific_journal-1936	51	68	,	,	PUNCT
american_scientific_journal-1936	51	69	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	51	70	)	)	PUNCT
american_scientific_journal-1936	51	71	=	=	PUNCT
american_scientific_journal-1936	51	72	𝑢𝑢0	𝑢𝑢0	VERB
american_scientific_journal-1936	51	73	american	american	ADJ
american_scientific_journal-1936	51	74	scientific	scientific	ADJ
american_scientific_journal-1936	51	75	research	research	NOUN
american_scientific_journal-1936	51	76	journal	journal	NOUN
american_scientific_journal-1936	51	77	for	for	ADP
american_scientific_journal-1936	51	78	engineering	engineering	NOUN
american_scientific_journal-1936	51	79	,	,	PUNCT
american_scientific_journal-1936	51	80	technology	technology	NOUN
american_scientific_journal-1936	51	81	,	,	PUNCT
american_scientific_journal-1936	51	82	and	and	CCONJ
american_scientific_journal-1936	51	83	sciences	science	NOUN
american_scientific_journal-1936	51	84	(	(	PUNCT
american_scientific_journal-1936	51	85	asrjets	asrjet	NOUN
american_scientific_journal-1936	51	86	)	)	PUNCT
american_scientific_journal-1936	51	87	(	(	PUNCT
american_scientific_journal-1936	51	88	2016	2016	NUM
american_scientific_journal-1936	51	89	)	)	PUNCT
american_scientific_journal-1936	51	90	volume	volume	NOUN
american_scientific_journal-1936	51	91	26	26	NUM
american_scientific_journal-1936	51	92	,	,	PUNCT
american_scientific_journal-1936	51	93	no	no	DET
american_scientific_journal-1936	51	94	3	3	NUM
american_scientific_journal-1936	51	95	,	,	PUNCT
american_scientific_journal-1936	51	96	pp	pp	ADV
american_scientific_journal-1936	51	97	140	140	NUM
american_scientific_journal-1936	51	98	-	-	SYM
american_scientific_journal-1936	51	99	154	154	NUM
american_scientific_journal-1936	51	100	143	143	NUM
american_scientific_journal-1936	51	101	𝜕𝜕𝜕𝜕	𝜕𝜕𝜕𝜕	NOUN
american_scientific_journal-1936	51	102	𝜕𝜕𝑥𝑥	𝜕𝜕𝑥𝑥	X
american_scientific_journal-1936	51	103	(	(	PUNCT
american_scientific_journal-1936	51	104	𝐿𝐿	𝐿𝐿	PROPN
american_scientific_journal-1936	51	105	,	,	PUNCT
american_scientific_journal-1936	51	106	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	51	107	)	)	PUNCT
american_scientific_journal-1936	51	108	=	=	SYM
american_scientific_journal-1936	51	109	𝑢𝑢𝐿𝐿	𝑢𝑢𝐿𝐿	NOUN
american_scientific_journal-1936	51	110	case	case	NOUN
american_scientific_journal-1936	51	111	3	3	NUM
american_scientific_journal-1936	51	112	:	:	PUNCT
american_scientific_journal-1936	51	113	one	one	NUM
american_scientific_journal-1936	51	114	end	end	NOUN
american_scientific_journal-1936	51	115	neumann	neumann	PROPN
american_scientific_journal-1936	51	116	and	and	CCONJ
american_scientific_journal-1936	51	117	other	other	ADJ
american_scientific_journal-1936	51	118	end	end	NOUN
american_scientific_journal-1936	51	119	dirichlet	dirichlet	PROPN
american_scientific_journal-1936	51	120	type	type	NOUN
american_scientific_journal-1936	51	121	of	of	ADP
american_scientific_journal-1936	51	122	boundary	boundary	ADJ
american_scientific_journal-1936	51	123	conditions	condition	NOUN
american_scientific_journal-1936	51	124	:	:	PUNCT
american_scientific_journal-1936	51	125	𝑢𝑢(𝑥𝑥	𝑢𝑢(𝑥𝑥	NOUN
american_scientific_journal-1936	51	126	,	,	PUNCT
american_scientific_journal-1936	51	127	0	0	NUM
american_scientific_journal-1936	51	128	)	)	PUNCT
american_scientific_journal-1936	51	129	=	=	SYM
american_scientific_journal-1936	51	130	𝑓𝑓(𝑥𝑥	𝑓𝑓(𝑥𝑥	PROPN
american_scientific_journal-1936	51	131	)	)	PUNCT
american_scientific_journal-1936	51	132	(	(	PUNCT
american_scientific_journal-1936	51	133	6	6	NUM
american_scientific_journal-1936	51	134	)	)	PUNCT
american_scientific_journal-1936	51	135	𝜕𝜕𝜕𝜕	𝜕𝜕𝜕𝜕	NOUN
american_scientific_journal-1936	51	136	𝜕𝜕𝑥𝑥	𝜕𝜕𝑥𝑥	X
american_scientific_journal-1936	51	137	(	(	PUNCT
american_scientific_journal-1936	51	138	0	0	NUM
american_scientific_journal-1936	51	139	,	,	PUNCT
american_scientific_journal-1936	51	140	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	51	141	)	)	PUNCT
american_scientific_journal-1936	51	142	=	=	SYM
american_scientific_journal-1936	51	143	0	0	NUM
american_scientific_journal-1936	51	144	𝑢𝑢(𝐿𝐿	𝑢𝑢(𝐿𝐿	NOUN
american_scientific_journal-1936	51	145	,	,	PUNCT
american_scientific_journal-1936	51	146	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	51	147	)	)	PUNCT
american_scientific_journal-1936	51	148	=	=	VERB
american_scientific_journal-1936	52	1	𝑢𝑢𝐿𝐿	𝑢𝑢𝐿𝐿	NOUN
american_scientific_journal-1936	52	2	here	here	ADV
american_scientific_journal-1936	52	3	in	in	ADP
american_scientific_journal-1936	52	4	(	(	PUNCT
american_scientific_journal-1936	52	5	4	4	NUM
american_scientific_journal-1936	52	6	)	)	PUNCT
american_scientific_journal-1936	52	7	to	to	ADP
american_scientific_journal-1936	52	8	(	(	PUNCT
american_scientific_journal-1936	52	9	6	6	NUM
american_scientific_journal-1936	52	10	)	)	PUNCT
american_scientific_journal-1936	52	11	,	,	PUNCT
american_scientific_journal-1936	52	12	the	the	DET
american_scientific_journal-1936	52	13	quantities	quantity	NOUN
american_scientific_journal-1936	52	14	𝑢𝑢0	𝑢𝑢0	NOUN
american_scientific_journal-1936	52	15	and	and	CCONJ
american_scientific_journal-1936	52	16	𝑢𝑢𝐿𝐿	𝑢𝑢𝐿𝐿	ADV
american_scientific_journal-1936	52	17	represent	represent	VERB
american_scientific_journal-1936	52	18	constant	constant	ADJ
american_scientific_journal-1936	52	19	densities	density	NOUN
american_scientific_journal-1936	52	20	of	of	ADP
american_scientific_journal-1936	52	21	the	the	DET
american_scientific_journal-1936	52	22	diffusing	diffuse	VERB
american_scientific_journal-1936	52	23	material	material	NOUN
american_scientific_journal-1936	52	24	respectively	respectively	ADV
american_scientific_journal-1936	52	25	at	at	ADP
american_scientific_journal-1936	52	26	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	52	27	=	=	SYM
american_scientific_journal-1936	52	28	0	0	NUM
american_scientific_journal-1936	52	29	and	and	CCONJ
american_scientific_journal-1936	52	30	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	52	31	=	=	NOUN
american_scientific_journal-1936	52	32	𝐿𝐿.	𝐿𝐿.	X
american_scientific_journal-1936	52	33	the	the	DET
american_scientific_journal-1936	52	34	function	function	NOUN
american_scientific_journal-1936	52	35	𝑓𝑓(𝑥𝑥	𝑓𝑓(𝑥𝑥	PROPN
american_scientific_journal-1936	52	36	)	)	PUNCT
american_scientific_journal-1936	52	37	is	be	AUX
american_scientific_journal-1936	52	38	an	an	DET
american_scientific_journal-1936	52	39	arbitrary	arbitrary	ADJ
american_scientific_journal-1936	52	40	one	one	NUM
american_scientific_journal-1936	52	41	of	of	ADP
american_scientific_journal-1936	52	42	its	its	PRON
american_scientific_journal-1936	52	43	argument	argument	NOUN
american_scientific_journal-1936	52	44	.	.	PUNCT
american_scientific_journal-1936	53	1	2.2	2.2	NUM
american_scientific_journal-1936	53	2	forward	forward	ADJ
american_scientific_journal-1936	53	3	time	time	NOUN
american_scientific_journal-1936	53	4	centered	center	VERB
american_scientific_journal-1936	53	5	space	space	NOUN
american_scientific_journal-1936	53	6	explicit	explicit	ADJ
american_scientific_journal-1936	53	7	scheme	scheme	NOUN
american_scientific_journal-1936	53	8	the	the	DET
american_scientific_journal-1936	53	9	equation	equation	NOUN
american_scientific_journal-1936	53	10	(	(	PUNCT
american_scientific_journal-1936	53	11	3	3	X
american_scientific_journal-1936	53	12	)	)	PUNCT
american_scientific_journal-1936	53	13	does	do	AUX
american_scientific_journal-1936	53	14	not	not	PART
american_scientific_journal-1936	53	15	always	always	ADV
american_scientific_journal-1936	53	16	exhibit	exhibit	VERB
american_scientific_journal-1936	53	17	an	an	DET
american_scientific_journal-1936	53	18	analytical	analytical	ADJ
american_scientific_journal-1936	53	19	solution	solution	NOUN
american_scientific_journal-1936	53	20	and	and	CCONJ
american_scientific_journal-1936	53	21	even	even	ADV
american_scientific_journal-1936	53	22	if	if	SCONJ
american_scientific_journal-1936	53	23	it	it	PRON
american_scientific_journal-1936	53	24	exhibits	exhibit	VERB
american_scientific_journal-1936	53	25	finding	finding	NOUN
american_scientific_journal-1936	53	26	is	be	AUX
american_scientific_journal-1936	53	27	not	not	PART
american_scientific_journal-1936	53	28	easy	easy	ADJ
american_scientific_journal-1936	53	29	.	.	PUNCT
american_scientific_journal-1936	54	1	hence	hence	ADV
american_scientific_journal-1936	54	2	,	,	PUNCT
american_scientific_journal-1936	54	3	finite	finite	ADJ
american_scientific_journal-1936	54	4	difference	difference	NOUN
american_scientific_journal-1936	54	5	schemes	scheme	NOUN
american_scientific_journal-1936	54	6	are	be	AUX
american_scientific_journal-1936	54	7	applied	apply	VERB
american_scientific_journal-1936	54	8	for	for	ADP
american_scientific_journal-1936	54	9	finding	find	VERB
american_scientific_journal-1936	54	10	approximate	approximate	ADJ
american_scientific_journal-1936	54	11	solutions	solution	NOUN
american_scientific_journal-1936	54	12	.	.	PUNCT
american_scientific_journal-1936	55	1	we	we	PRON
american_scientific_journal-1936	55	2	now	now	ADV
american_scientific_journal-1936	55	3	approximate	approximate	ADJ
american_scientific_journal-1936	55	4	equation	equation	NOUN
american_scientific_journal-1936	55	5	(	(	PUNCT
american_scientific_journal-1936	55	6	3	3	NUM
american_scientific_journal-1936	55	7	)	)	PUNCT
american_scientific_journal-1936	55	8	by	by	ADP
american_scientific_journal-1936	55	9	applying	apply	VERB
american_scientific_journal-1936	55	10	forward	forward	ADV
american_scientific_journal-1936	55	11	difference	difference	NOUN
american_scientific_journal-1936	55	12	on	on	ADP
american_scientific_journal-1936	55	13	time	time	NOUN
american_scientific_journal-1936	55	14	derivative	derivative	ADJ
american_scientific_journal-1936	55	15	and	and	CCONJ
american_scientific_journal-1936	55	16	central	central	ADJ
american_scientific_journal-1936	55	17	difference	difference	NOUN
american_scientific_journal-1936	55	18	on	on	ADP
american_scientific_journal-1936	55	19	space	space	NOUN
american_scientific_journal-1936	55	20	derivative	derivative	NOUN
american_scientific_journal-1936	55	21	.	.	PUNCT
american_scientific_journal-1936	56	1	thus	thus	ADV
american_scientific_journal-1936	56	2	equation	equation	NOUN
american_scientific_journal-1936	56	3	(	(	PUNCT
american_scientific_journal-1936	56	4	3	3	X
american_scientific_journal-1936	56	5	)	)	PUNCT
american_scientific_journal-1936	56	6	takes	take	VERB
american_scientific_journal-1936	56	7	the	the	DET
american_scientific_journal-1936	56	8	form	form	NOUN
american_scientific_journal-1936	56	9	as	as	ADP
american_scientific_journal-1936	56	10	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	NOUN
american_scientific_journal-1936	56	11	𝑛𝑛+1−	𝑛𝑛+1−	PROPN
american_scientific_journal-1936	56	12	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	NOUN
american_scientific_journal-1936	56	13	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-1936	56	14	∆𝜕𝜕	∆𝜕𝜕	NOUN
american_scientific_journal-1936	56	15	=	=	PROPN
american_scientific_journal-1936	56	16	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	56	17	�	�	PROPN
american_scientific_journal-1936	56	18	𝜕𝜕𝑖𝑖−1	𝜕𝜕𝑖𝑖−1	PROPN
american_scientific_journal-1936	56	19	𝑛𝑛	𝑛𝑛	ADP
american_scientific_journal-1936	56	20	−2	−2	PROPN
american_scientific_journal-1936	56	21	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	INTJ
american_scientific_journal-1936	56	22	𝑛𝑛+	𝑛𝑛+	ADJ
american_scientific_journal-1936	56	23	𝜕𝜕𝑖𝑖+1	𝜕𝜕𝑖𝑖+1	PUNCT
american_scientific_journal-1936	56	24	𝑛𝑛	𝑛𝑛	ADP
american_scientific_journal-1936	56	25	∆𝑥𝑥2	∆𝑥𝑥2	PROPN
american_scientific_journal-1936	56	26	�	�	PROPN
american_scientific_journal-1936	56	27	+	+	CCONJ
american_scientific_journal-1936	56	28	𝑂𝑂(∆𝑡𝑡	𝑂𝑂(∆𝑡𝑡	NOUN
american_scientific_journal-1936	56	29	)	)	PUNCT
american_scientific_journal-1936	56	30	+	+	PUNCT
american_scientific_journal-1936	56	31	𝑂𝑂(∆𝑥𝑥2	𝑂𝑂(∆𝑥𝑥2	NUM
american_scientific_journal-1936	56	32	)	)	PUNCT
american_scientific_journal-1936	56	33	.	.	PUNCT
american_scientific_journal-1936	57	1	(	(	PUNCT
american_scientific_journal-1936	57	2	7	7	X
american_scientific_journal-1936	57	3	)	)	PUNCT
american_scientific_journal-1936	57	4	the	the	DET
american_scientific_journal-1936	57	5	temporal	temporal	ADJ
american_scientific_journal-1936	57	6	error	error	NOUN
american_scientific_journal-1936	57	7	𝑂𝑂(∆𝑡𝑡	𝑂𝑂(∆𝑡𝑡	NOUN
american_scientific_journal-1936	57	8	)	)	PUNCT
american_scientific_journal-1936	57	9	and	and	CCONJ
american_scientific_journal-1936	57	10	spatial	spatial	ADJ
american_scientific_journal-1936	57	11	error	error	NOUN
american_scientific_journal-1936	57	12	𝑂𝑂(∆𝑥𝑥2	𝑂𝑂(∆𝑥𝑥2	NUM
american_scientific_journal-1936	57	13	)	)	PUNCT
american_scientific_journal-1936	57	14	have	have	VERB
american_scientific_journal-1936	57	15	different	different	ADJ
american_scientific_journal-1936	57	16	orders	order	NOUN
american_scientific_journal-1936	57	17	.	.	PUNCT
american_scientific_journal-1936	58	1	their	their	PRON
american_scientific_journal-1936	58	2	values	value	NOUN
american_scientific_journal-1936	58	3	are	be	AUX
american_scientific_journal-1936	58	4	very	very	ADV
american_scientific_journal-1936	58	5	small	small	ADJ
american_scientific_journal-1936	58	6	and	and	CCONJ
american_scientific_journal-1936	58	7	their	their	PRON
american_scientific_journal-1936	58	8	influence	influence	NOUN
american_scientific_journal-1936	58	9	on	on	ADP
american_scientific_journal-1936	58	10	the	the	DET
american_scientific_journal-1936	58	11	solution	solution	NOUN
american_scientific_journal-1936	58	12	is	be	AUX
american_scientific_journal-1936	58	13	negligible	negligible	ADJ
american_scientific_journal-1936	58	14	.	.	PUNCT
american_scientific_journal-1936	59	1	the	the	DET
american_scientific_journal-1936	59	2	big	big	ADJ
american_scientific_journal-1936	59	3	o	o	PROPN
american_scientific_journal-1936	59	4	notation	notation	NOUN
american_scientific_journal-1936	59	5	expresses	express	VERB
american_scientific_journal-1936	59	6	the	the	DET
american_scientific_journal-1936	59	7	rate	rate	NOUN
american_scientific_journal-1936	59	8	at	at	ADP
american_scientific_journal-1936	59	9	which	which	PRON
american_scientific_journal-1936	59	10	the	the	DET
american_scientific_journal-1936	59	11	truncation	truncation	NOUN
american_scientific_journal-1936	59	12	error	error	NOUN
american_scientific_journal-1936	59	13	goes	go	VERB
american_scientific_journal-1936	59	14	to	to	ADP
american_scientific_journal-1936	59	15	zero	zero	NUM
american_scientific_journal-1936	59	16	.	.	PUNCT
american_scientific_journal-1936	60	1	hence	hence	ADV
american_scientific_journal-1936	60	2	drop	drop	VERB
american_scientific_journal-1936	60	3	the	the	DET
american_scientific_journal-1936	60	4	truncation	truncation	NOUN
american_scientific_journal-1936	60	5	error	error	NOUN
american_scientific_journal-1936	60	6	terms	term	NOUN
american_scientific_journal-1936	60	7	from	from	ADP
american_scientific_journal-1936	60	8	equation	equation	NOUN
american_scientific_journal-1936	60	9	(	(	PUNCT
american_scientific_journal-1936	60	10	7	7	NUM
american_scientific_journal-1936	60	11	)	)	PUNCT
american_scientific_journal-1936	60	12	and	and	CCONJ
american_scientific_journal-1936	60	13	after	after	ADP
american_scientific_journal-1936	60	14	a	a	DET
american_scientific_journal-1936	60	15	rearrangement	rearrangement	NOUN
american_scientific_journal-1936	60	16	it	it	PRON
american_scientific_journal-1936	60	17	leads	lead	VERB
american_scientific_journal-1936	60	18	to	to	ADP
american_scientific_journal-1936	60	19	𝑢𝑢𝑖𝑖𝑛𝑛+1	𝑢𝑢𝑖𝑖𝑛𝑛+1	PROPN
american_scientific_journal-1936	60	20	=	=	SYM
american_scientific_journal-1936	60	21	𝑟𝑟𝑢𝑢𝑖𝑖−1𝑛𝑛	𝑟𝑟𝑢𝑢𝑖𝑖−1𝑛𝑛	PROPN
american_scientific_journal-1936	60	22	+	+	CCONJ
american_scientific_journal-1936	60	23	(	(	PUNCT
american_scientific_journal-1936	60	24	1	1	NUM
american_scientific_journal-1936	60	25	−	−	NUM
american_scientific_journal-1936	60	26	2𝑟𝑟)𝑢𝑢𝑖𝑖𝑛𝑛	2𝑟𝑟)𝑢𝑢𝑖𝑖𝑛𝑛	NUM
american_scientific_journal-1936	60	27	+	+	CCONJ
american_scientific_journal-1936	60	28	𝑟𝑟𝑢𝑢𝑖𝑖+1𝑛𝑛	𝑟𝑟𝑢𝑢𝑖𝑖+1𝑛𝑛	PROPN
american_scientific_journal-1936	60	29	(	(	PUNCT
american_scientific_journal-1936	60	30	8)	8)	NUM
american_scientific_journal-1936	60	31	in	in	ADP
american_scientific_journal-1936	60	32	(	(	PUNCT
american_scientific_journal-1936	60	33	8)	8)	NUM
american_scientific_journal-1936	60	34	,	,	PUNCT
american_scientific_journal-1936	60	35	we	we	PRON
american_scientific_journal-1936	60	36	have	have	AUX
american_scientific_journal-1936	60	37	used	use	VERB
american_scientific_journal-1936	60	38	the	the	DET
american_scientific_journal-1936	60	39	notation	notation	NOUN
american_scientific_journal-1936	60	40	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1936	60	41	=	=	SYM
american_scientific_journal-1936	60	42	𝐷𝐷(∆𝑡𝑡	𝐷𝐷(∆𝑡𝑡	PROPN
american_scientific_journal-1936	60	43	∆𝑥𝑥2⁄	∆𝑥𝑥2⁄	NOUN
american_scientific_journal-1936	60	44	)	)	PUNCT
american_scientific_journal-1936	60	45	.	.	PUNCT
american_scientific_journal-1936	61	1	furthermore	furthermore	ADV
american_scientific_journal-1936	61	2	,	,	PUNCT
american_scientific_journal-1936	61	3	equation	equation	NOUN
american_scientific_journal-1936	61	4	(	(	PUNCT
american_scientific_journal-1936	61	5	8)	8)	NUM
american_scientific_journal-1936	61	6	can	can	AUX
american_scientific_journal-1936	61	7	be	be	AUX
american_scientific_journal-1936	61	8	expressed	express	VERB
american_scientific_journal-1936	61	9	in	in	ADP
american_scientific_journal-1936	61	10	terms	term	NOUN
american_scientific_journal-1936	61	11	of	of	ADP
american_scientific_journal-1936	61	12	matrix	matrix	NOUN
american_scientific_journal-1936	61	13	multiplication	multiplication	NOUN
american_scientific_journal-1936	61	14	as	as	ADP
american_scientific_journal-1936	61	15	𝑢𝑢𝑛𝑛+1	𝑢𝑢𝑛𝑛+1	NOUN
american_scientific_journal-1936	61	16	=	=	PUNCT
american_scientific_journal-1936	61	17	(	(	PUNCT
american_scientific_journal-1936	61	18	𝐼𝐼	𝐼𝐼	PROPN
american_scientific_journal-1936	61	19	+	+	CCONJ
american_scientific_journal-1936	61	20	𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟	NUM
american_scientific_journal-1936	61	21	)	)	PUNCT
american_scientific_journal-1936	61	22	𝑢𝑢𝑛𝑛	𝑢𝑢𝑛𝑛	NOUN
american_scientific_journal-1936	61	23	(	(	PUNCT
american_scientific_journal-1936	61	24	9	9	NUM
american_scientific_journal-1936	61	25	)	)	PUNCT
american_scientific_journal-1936	61	26	in	in	ADP
american_scientific_journal-1936	61	27	(	(	PUNCT
american_scientific_journal-1936	61	28	9	9	NUM
american_scientific_journal-1936	61	29	)	)	PUNCT
american_scientific_journal-1936	61	30	,	,	PUNCT
american_scientific_journal-1936	61	31	we	we	PRON
american_scientific_journal-1936	61	32	have	have	AUX
american_scientific_journal-1936	61	33	used	use	VERB
american_scientific_journal-1936	61	34	the	the	DET
american_scientific_journal-1936	61	35	following	follow	VERB
american_scientific_journal-1936	61	36	matrix	matrix	NOUN
american_scientific_journal-1936	61	37	notations	notation	NOUN
american_scientific_journal-1936	61	38	𝑢𝑢𝑛𝑛+1	𝑢𝑢𝑛𝑛+1	NOUN
american_scientific_journal-1936	61	39	=	=	PUNCT
american_scientific_journal-1936	62	1	[	[	X
american_scientific_journal-1936	62	2	𝑢𝑢1𝑛𝑛+1	𝑢𝑢1𝑛𝑛+1	NOUN
american_scientific_journal-1936	62	3	,	,	PUNCT
american_scientific_journal-1936	62	4	𝑢𝑢2𝑛𝑛+1	𝑢𝑢2𝑛𝑛+1	PROPN
american_scientific_journal-1936	62	5	,	,	PUNCT
american_scientific_journal-1936	62	6	.	.	PUNCT
american_scientific_journal-1936	62	7	.	.	PUNCT
american_scientific_journal-1936	63	1	.	.	PUNCT
american_scientific_journal-1936	64	1	,	,	PUNCT
american_scientific_journal-1936	64	2	𝑢𝑢𝑁𝑁−1𝑛𝑛+1	𝑢𝑢𝑁𝑁−1𝑛𝑛+1	PROPN
american_scientific_journal-1936	64	3	]	]	SYM
american_scientific_journal-1936	64	4	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-1936	64	5	𝑢𝑢𝑛𝑛	𝑢𝑢𝑛𝑛	NOUN
american_scientific_journal-1936	64	6	=	=	PUNCT
american_scientific_journal-1936	65	1	[	[	X
american_scientific_journal-1936	65	2	𝑢𝑢1𝑛𝑛	𝑢𝑢1𝑛𝑛	NOUN
american_scientific_journal-1936	65	3	+	+	X
american_scientific_journal-1936	65	4	𝑟𝑟𝑢𝑢0𝑛𝑛	𝑟𝑟𝑢𝑢0𝑛𝑛	PROPN
american_scientific_journal-1936	65	5	,	,	PUNCT
american_scientific_journal-1936	65	6	𝑢𝑢2𝑛𝑛	𝑢𝑢2𝑛𝑛	PROPN
american_scientific_journal-1936	65	7	,	,	PUNCT
american_scientific_journal-1936	65	8	.	.	PUNCT
american_scientific_journal-1936	65	9	.	.	PUNCT
american_scientific_journal-1936	66	1	.	.	PUNCT
american_scientific_journal-1936	66	2	,	,	PUNCT
american_scientific_journal-1936	66	3	𝑢𝑢𝑁𝑁−1𝑛𝑛	𝑢𝑢𝑁𝑁−1𝑛𝑛	VERB
american_scientific_journal-1936	66	4	+	+	CCONJ
american_scientific_journal-1936	66	5	𝑢𝑢𝑁𝑁𝑛𝑛	𝑢𝑢𝑁𝑁𝑛𝑛	X
american_scientific_journal-1936	66	6	]	]	X
american_scientific_journal-1936	66	7	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-1936	66	8	𝐼𝐼	𝐼𝐼	PROPN
american_scientific_journal-1936	66	9	=	=	SYM
american_scientific_journal-1936	66	10	�	�	PROPN
american_scientific_journal-1936	67	1	1	1	NUM
american_scientific_journal-1936	67	2	0	0	NUM
american_scientific_journal-1936	67	3	0	0	NUM
american_scientific_journal-1936	67	4	.	.	PUNCT
american_scientific_journal-1936	67	5	.	.	PUNCT
american_scientific_journal-1936	67	6	.	.	PUNCT
american_scientific_journal-1936	68	1	0	0	NUM
american_scientific_journal-1936	69	1	0	0	NUM
american_scientific_journal-1936	69	2	1	1	NUM
american_scientific_journal-1936	69	3	0	0	NUM
american_scientific_journal-1936	69	4	.	.	PUNCT
american_scientific_journal-1936	69	5	.	.	PUNCT
american_scientific_journal-1936	69	6	.	.	PUNCT
american_scientific_journal-1936	70	1	0	0	PUNCT
american_scientific_journal-1936	70	2	.	.	PUNCT
american_scientific_journal-1936	70	3	.	.	PUNCT
american_scientific_journal-1936	70	4	.	.	PUNCT
american_scientific_journal-1936	70	5	.	.	PUNCT
american_scientific_journal-1936	70	6	.	.	PUNCT
american_scientific_journal-1936	70	7	.	.	PUNCT
american_scientific_journal-1936	71	1	.	.	PUNCT
american_scientific_journal-1936	72	1	0	0	NUM
american_scientific_journal-1936	73	1	0	0	NUM
american_scientific_journal-1936	73	2	0	0	NUM
american_scientific_journal-1936	73	3	.	.	PUNCT
american_scientific_journal-1936	73	4	.	.	PUNCT
american_scientific_journal-1936	73	5	.	.	PUNCT
american_scientific_journal-1936	74	1	1	1	NUM
american_scientific_journal-1936	74	2	�	�	PROPN
american_scientific_journal-1936	74	3	american	american	ADJ
american_scientific_journal-1936	74	4	scientific	scientific	ADJ
american_scientific_journal-1936	74	5	research	research	NOUN
american_scientific_journal-1936	74	6	journal	journal	NOUN
american_scientific_journal-1936	74	7	for	for	ADP
american_scientific_journal-1936	74	8	engineering	engineering	NOUN
american_scientific_journal-1936	74	9	,	,	PUNCT
american_scientific_journal-1936	74	10	technology	technology	NOUN
american_scientific_journal-1936	74	11	,	,	PUNCT
american_scientific_journal-1936	74	12	and	and	CCONJ
american_scientific_journal-1936	74	13	sciences	science	NOUN
american_scientific_journal-1936	74	14	(	(	PUNCT
american_scientific_journal-1936	74	15	asrjets	asrjet	NOUN
american_scientific_journal-1936	74	16	)	)	PUNCT
american_scientific_journal-1936	74	17	(	(	PUNCT
american_scientific_journal-1936	74	18	2016	2016	NUM
american_scientific_journal-1936	74	19	)	)	PUNCT
american_scientific_journal-1936	74	20	volume	volume	NOUN
american_scientific_journal-1936	74	21	26	26	NUM
american_scientific_journal-1936	74	22	,	,	PUNCT
american_scientific_journal-1936	74	23	no	no	DET
american_scientific_journal-1936	74	24	3	3	NUM
american_scientific_journal-1936	74	25	,	,	PUNCT
american_scientific_journal-1936	74	26	pp	pp	ADV
american_scientific_journal-1936	74	27	140	140	NUM
american_scientific_journal-1936	74	28	-	-	SYM
american_scientific_journal-1936	74	29	154	154	NUM
american_scientific_journal-1936	74	30	144	144	NUM
american_scientific_journal-1936	74	31	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1936	74	32	=	=	SYM
american_scientific_journal-1936	75	1	⎣	⎣	ADJ
american_scientific_journal-1936	75	2	⎢	⎢	NOUN
american_scientific_journal-1936	75	3	⎢	⎢	NOUN
american_scientific_journal-1936	75	4	⎢	⎢	NOUN
american_scientific_journal-1936	75	5	⎡	⎡	NOUN
american_scientific_journal-1936	75	6	−2	−2	NOUN
american_scientific_journal-1936	75	7	1	1	NUM
american_scientific_journal-1936	75	8	0	0	NUM
american_scientific_journal-1936	75	9	.	.	PUNCT
american_scientific_journal-1936	75	10	.	.	PUNCT
american_scientific_journal-1936	75	11	.	.	PUNCT
american_scientific_journal-1936	76	1	0	0	NUM
american_scientific_journal-1936	77	1	0	0	NUM
american_scientific_journal-1936	77	2	0	0	NUM
american_scientific_journal-1936	77	3	1	1	NUM
american_scientific_journal-1936	77	4	−	−	NUM
american_scientific_journal-1936	77	5	2	2	NUM
american_scientific_journal-1936	77	6	1	1	NUM
american_scientific_journal-1936	77	7	.	.	PUNCT
american_scientific_journal-1936	77	8	.	.	PUNCT
american_scientific_journal-1936	77	9	.	.	PUNCT
american_scientific_journal-1936	78	1	0	0	NUM
american_scientific_journal-1936	79	1	0	0	NUM
american_scientific_journal-1936	79	2	0	0	NUM
american_scientific_journal-1936	79	3	.	.	PUNCT
american_scientific_journal-1936	79	4	.	.	PUNCT
american_scientific_journal-1936	79	5	.	.	PUNCT
american_scientific_journal-1936	79	6	.	.	PUNCT
american_scientific_journal-1936	79	7	.	.	PUNCT
american_scientific_journal-1936	79	8	.	.	PUNCT
american_scientific_journal-1936	79	9	.	.	PUNCT
american_scientific_journal-1936	79	10	.	.	PUNCT
american_scientific_journal-1936	79	11	.	.	PUNCT
american_scientific_journal-1936	80	1	0	0	NUM
american_scientific_journal-1936	81	1	0	0	NUM
american_scientific_journal-1936	81	2	0	0	NUM
american_scientific_journal-1936	81	3	.	.	PUNCT
american_scientific_journal-1936	81	4	.	.	PUNCT
american_scientific_journal-1936	82	1	.	.	PUNCT
american_scientific_journal-1936	83	1	1	1	NUM
american_scientific_journal-1936	83	2	−	−	NUM
american_scientific_journal-1936	83	3	2	2	NUM
american_scientific_journal-1936	83	4	1	1	NUM
american_scientific_journal-1936	83	5	0	0	NUM
american_scientific_journal-1936	83	6	0	0	NUM
american_scientific_journal-1936	83	7	0	0	NUM
american_scientific_journal-1936	83	8	.	.	PUNCT
american_scientific_journal-1936	83	9	.	.	PUNCT
american_scientific_journal-1936	83	10	.	.	PUNCT
american_scientific_journal-1936	84	1	0	0	NUM
american_scientific_journal-1936	85	1	1	1	NUM
american_scientific_journal-1936	85	2	−	−	PROPN
american_scientific_journal-1936	86	1	2⎦	2⎦	PROPN
american_scientific_journal-1936	86	2	⎥	⎥	PROPN
american_scientific_journal-1936	86	3	⎥	⎥	PROPN
american_scientific_journal-1936	86	4	⎥	⎥	PROPN
american_scientific_journal-1936	86	5	⎤	⎤	PROPN
american_scientific_journal-1936	86	6	.	.	PUNCT
american_scientific_journal-1936	87	1	(	(	PUNCT
american_scientific_journal-1936	87	2	10	10	NUM
american_scientific_journal-1936	87	3	)	)	PUNCT
american_scientific_journal-1936	87	4	in	in	ADP
american_scientific_journal-1936	87	5	(	(	PUNCT
american_scientific_journal-1936	87	6	9	9	NUM
american_scientific_journal-1936	87	7	)	)	PUNCT
american_scientific_journal-1936	87	8	,	,	PUNCT
american_scientific_journal-1936	87	9	both	both	CCONJ
american_scientific_journal-1936	87	10	𝑢𝑢𝑛𝑛	𝑢𝑢𝑛𝑛	NOUN
american_scientific_journal-1936	87	11	and	and	CCONJ
american_scientific_journal-1936	87	12	𝑢𝑢𝑛𝑛+1	𝑢𝑢𝑛𝑛+1	NOUN
american_scientific_journal-1936	87	13	are	be	AUX
american_scientific_journal-1936	87	14	column	column	NOUN
american_scientific_journal-1936	87	15	vectors	vector	NOUN
american_scientific_journal-1936	87	16	of	of	ADP
american_scientific_journal-1936	87	17	dimension	dimension	NOUN
american_scientific_journal-1936	87	18	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-1936	87	19	−	−	PROPN
american_scientific_journal-1936	87	20	1	1	NUM
american_scientific_journal-1936	87	21	.	.	PUNCT
american_scientific_journal-1936	88	1	the	the	DET
american_scientific_journal-1936	88	2	superscript	superscript	ADJ
american_scientific_journal-1936	88	3	𝑇𝑇	𝑇𝑇	PROPN
american_scientific_journal-1936	88	4	denotes	denote	NOUN
american_scientific_journal-1936	88	5	transpose	transpose	ADV
american_scientific_journal-1936	88	6	of	of	ADP
american_scientific_journal-1936	88	7	the	the	DET
american_scientific_journal-1936	88	8	matrix	matrix	NOUN
american_scientific_journal-1936	88	9	.	.	PUNCT
american_scientific_journal-1936	89	1	the	the	DET
american_scientific_journal-1936	89	2	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-1936	89	3	−	−	NOUN
american_scientific_journal-1936	89	4	1	1	NUM
american_scientific_journal-1936	89	5	dimensional	dimensional	ADJ
american_scientific_journal-1936	89	6	square	square	ADJ
american_scientific_journal-1936	89	7	matrices	matrix	NOUN
american_scientific_journal-1936	89	8	𝐼𝐼	𝐼𝐼	PROPN
american_scientific_journal-1936	89	9	and	and	CCONJ
american_scientific_journal-1936	89	10	𝑟𝑟	𝑟𝑟	ADV
american_scientific_journal-1936	89	11	respectively	respectively	ADV
american_scientific_journal-1936	89	12	denote	denote	VERB
american_scientific_journal-1936	89	13	an	an	DET
american_scientific_journal-1936	89	14	identity	identity	NOUN
american_scientific_journal-1936	89	15	and	and	CCONJ
american_scientific_journal-1936	89	16	a	a	DET
american_scientific_journal-1936	89	17	tridiagonal	tridiagonal	ADJ
american_scientific_journal-1936	89	18	matrices	matrix	NOUN
american_scientific_journal-1936	89	19	.	.	PUNCT
american_scientific_journal-1936	90	1	to	to	PART
american_scientific_journal-1936	90	2	find	find	VERB
american_scientific_journal-1936	90	3	the	the	DET
american_scientific_journal-1936	90	4	stability	stability	NOUN
american_scientific_journal-1936	90	5	condition	condition	NOUN
american_scientific_journal-1936	90	6	of	of	ADP
american_scientific_journal-1936	90	7	equation	equation	NOUN
american_scientific_journal-1936	90	8	(	(	PUNCT
american_scientific_journal-1936	90	9	8)	8)	NUM
american_scientific_journal-1936	90	10	,	,	PUNCT
american_scientific_journal-1936	90	11	we	we	PRON
american_scientific_journal-1936	90	12	substitute	substitute	VERB
american_scientific_journal-1936	90	13	a	a	DET
american_scientific_journal-1936	90	14	trial	trial	NOUN
american_scientific_journal-1936	90	15	solution	solution	NOUN
american_scientific_journal-1936	90	16	or	or	CCONJ
american_scientific_journal-1936	90	17	a	a	DET
american_scientific_journal-1936	90	18	fourier	fourier	NOUN
american_scientific_journal-1936	90	19	mode	mode	NOUN
american_scientific_journal-1936	90	20	𝑢𝑢𝑖𝑖𝑛𝑛	𝑢𝑢𝑖𝑖𝑛𝑛	NOUN
american_scientific_journal-1936	90	21	=	=	SYM
american_scientific_journal-1936	90	22	𝜆𝜆𝑛𝑛𝑒𝑒[𝑛𝑛𝑖𝑖𝑛𝑛	𝜆𝜆𝑛𝑛𝑒𝑒[𝑛𝑛𝑖𝑖𝑛𝑛	PUNCT
american_scientific_journal-1936	90	23	𝑝𝑝⁄	𝑝𝑝⁄	X
american_scientific_journal-1936	90	24	]	]	PUNCT
american_scientific_journal-1936	90	25	(	(	PUNCT
american_scientific_journal-1936	90	26	11	11	NUM
american_scientific_journal-1936	90	27	)	)	PUNCT
american_scientific_journal-1936	90	28	to	to	PART
american_scientific_journal-1936	90	29	get	get	VERB
american_scientific_journal-1936	90	30	𝜆𝜆	𝜆𝜆	NOUN
american_scientific_journal-1936	90	31	=	=	SYM
american_scientific_journal-1936	90	32	𝑟𝑟	𝑟𝑟	PROPN
american_scientific_journal-1936	90	33	�	�	PROPN
american_scientific_journal-1936	90	34	𝑒𝑒𝑛𝑛𝑛𝑛	𝑒𝑒𝑛𝑛𝑛𝑛	PROPN
american_scientific_journal-1936	90	35	𝑝𝑝⁄	𝑝𝑝⁄	PROPN
american_scientific_journal-1936	90	36	+	+	CCONJ
american_scientific_journal-1936	90	37	𝑒𝑒	𝑒𝑒	PROPN
american_scientific_journal-1936	90	38	−𝑛𝑛𝑛𝑛	−𝑛𝑛𝑛𝑛	PROPN
american_scientific_journal-1936	90	39	𝑝𝑝⁄	𝑝𝑝⁄	PROPN
american_scientific_journal-1936	90	40	�	�	PROPN
american_scientific_journal-1936	91	1	+	+	CCONJ
american_scientific_journal-1936	91	2	1	1	NUM
american_scientific_journal-1936	91	3	−	−	NOUN
american_scientific_journal-1936	91	4	2𝑟𝑟	2𝑟𝑟	NOUN
american_scientific_journal-1936	91	5	=	=	SYM
american_scientific_journal-1936	92	1	1	1	NUM
american_scientific_journal-1936	92	2	−	−	PROPN
american_scientific_journal-1936	92	3	2𝑟𝑟[1	2𝑟𝑟[1	NUM
american_scientific_journal-1936	92	4	−	−	PROPN
american_scientific_journal-1936	92	5	cos	cos	PROPN
american_scientific_journal-1936	92	6	(	(	PUNCT
american_scientific_journal-1936	92	7	𝜋𝜋	𝜋𝜋	X
american_scientific_journal-1936	92	8	𝑝𝑝⁄	𝑝𝑝⁄	X
american_scientific_journal-1936	92	9	)	)	PUNCT
american_scientific_journal-1936	92	10	]	]	PUNCT
american_scientific_journal-1936	92	11	here	here	ADV
american_scientific_journal-1936	92	12	𝑝𝑝	𝑝𝑝	PROPN
american_scientific_journal-1936	92	13	is	be	AUX
american_scientific_journal-1936	92	14	any	any	DET
american_scientific_journal-1936	92	15	non	non	ADJ
american_scientific_journal-1936	92	16	-	-	ADJ
american_scientific_journal-1936	92	17	zero	zero	NUM
american_scientific_journal-1936	92	18	integer	integer	NOUN
american_scientific_journal-1936	92	19	.	.	PUNCT
american_scientific_journal-1936	93	1	since	since	SCONJ
american_scientific_journal-1936	93	2	we	we	PRON
american_scientific_journal-1936	93	3	must	must	AUX
american_scientific_journal-1936	93	4	have	have	VERB
american_scientific_journal-1936	93	5	|𝜆𝜆|	|𝜆𝜆|	PROPN
american_scientific_journal-1936	93	6	≤	≤	NUM
american_scientific_journal-1936	93	7	1	1	NUM
american_scientific_journal-1936	93	8	for	for	ADP
american_scientific_journal-1936	93	9	non	non	X
american_scientific_journal-1936	93	10	–	–	PUNCT
american_scientific_journal-1936	93	11	divergence	divergence	NOUN
american_scientific_journal-1936	93	12	,	,	PUNCT
american_scientific_journal-1936	93	13	the	the	DET
american_scientific_journal-1936	93	14	stability	stability	NOUN
american_scientific_journal-1936	93	15	condition	condition	NOUN
american_scientific_journal-1936	93	16	turns	turn	VERB
american_scientific_journal-1936	93	17	out	out	ADP
american_scientific_journal-1936	93	18	to	to	PART
american_scientific_journal-1936	93	19	be	be	AUX
american_scientific_journal-1936	93	20	𝑟𝑟	𝑟𝑟	X
american_scientific_journal-1936	93	21	=	=	PUNCT
american_scientific_journal-1936	94	1	[	[	X
american_scientific_journal-1936	94	2	𝐷𝐷∆𝑡𝑡	𝐷𝐷∆𝑡𝑡	X
american_scientific_journal-1936	94	3	∆𝑥𝑥2⁄	∆𝑥𝑥2⁄	NOUN
american_scientific_journal-1936	94	4	]	]	PUNCT
american_scientific_journal-1936	94	5	≤	≤	NUM
american_scientific_journal-1936	94	6	1	1	NUM
american_scientific_journal-1936	94	7	2⁄	2⁄	NUM
american_scientific_journal-1936	94	8	.	.	PUNCT
american_scientific_journal-1936	95	1	that	that	ADV
american_scientific_journal-1936	95	2	is	is	ADV
american_scientific_journal-1936	95	3	,	,	PUNCT
american_scientific_journal-1936	95	4	the	the	DET
american_scientific_journal-1936	95	5	equation	equation	NOUN
american_scientific_journal-1936	95	6	(	(	PUNCT
american_scientific_journal-1936	95	7	8)	8)	NUM
american_scientific_journal-1936	95	8	is	be	AUX
american_scientific_journal-1936	95	9	stable	stable	ADJ
american_scientific_journal-1936	95	10	as	as	ADV
american_scientific_journal-1936	95	11	long	long	ADV
american_scientific_journal-1936	95	12	as	as	SCONJ
american_scientific_journal-1936	95	13	the	the	DET
american_scientific_journal-1936	95	14	spatial	spatial	ADJ
american_scientific_journal-1936	95	15	interval	interval	NOUN
american_scientific_journal-1936	95	16	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	95	17	satisfies	satisfy	VERB
american_scientific_journal-1936	95	18	the	the	DET
american_scientific_journal-1936	95	19	condition	condition	NOUN
american_scientific_journal-1936	95	20	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	95	21	≤	≤	NUM
american_scientific_journal-1936	95	22	√2𝐷𝐷	√2𝐷𝐷	NOUN
american_scientific_journal-1936	95	23	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	95	24	for	for	ADP
american_scientific_journal-1936	95	25	any	any	DET
american_scientific_journal-1936	95	26	given	give	VERB
american_scientific_journal-1936	95	27	time	time	NOUN
american_scientific_journal-1936	95	28	interval	interval	NOUN
american_scientific_journal-1936	95	29	∆𝑡𝑡.	∆𝑡𝑡.	PROPN
american_scientific_journal-1936	95	30	otherwise	otherwise	ADV
american_scientific_journal-1936	95	31	(	(	PUNCT
american_scientific_journal-1936	95	32	8)	8)	NOUN
american_scientific_journal-1936	95	33	will	will	AUX
american_scientific_journal-1936	95	34	not	not	PART
american_scientific_journal-1936	95	35	be	be	AUX
american_scientific_journal-1936	95	36	stable	stable	ADJ
american_scientific_journal-1936	95	37	[	[	X
american_scientific_journal-1936	95	38	13	13	NUM
american_scientific_journal-1936	95	39	]	]	PUNCT
american_scientific_journal-1936	95	40	.	.	PUNCT
american_scientific_journal-1936	96	1	further	far	ADV
american_scientific_journal-1936	96	2	,	,	PUNCT
american_scientific_journal-1936	96	3	the	the	DET
american_scientific_journal-1936	96	4	truncation	truncation	NOUN
american_scientific_journal-1936	96	5	error	error	NOUN
american_scientific_journal-1936	96	6	𝑇𝑇𝑖𝑖,𝑛𝑛	𝑇𝑇𝑖𝑖,𝑛𝑛	VERB
american_scientific_journal-1936	96	7	for	for	ADP
american_scientific_journal-1936	96	8	the	the	DET
american_scientific_journal-1936	96	9	equation	equation	NOUN
american_scientific_journal-1936	96	10	(	(	PUNCT
american_scientific_journal-1936	96	11	8)	8)	NUM
american_scientific_journal-1936	96	12	can	can	AUX
american_scientific_journal-1936	96	13	be	be	AUX
american_scientific_journal-1936	96	14	derived	derive	VERB
american_scientific_journal-1936	96	15	and	and	CCONJ
american_scientific_journal-1936	96	16	expressed	express	VERB
american_scientific_journal-1936	96	17	as	as	ADP
american_scientific_journal-1936	96	18	[	[	X
american_scientific_journal-1936	96	19	14	14	NUM
american_scientific_journal-1936	96	20	]	]	X
american_scientific_journal-1936	96	21	𝑇𝑇𝑖𝑖,𝑛𝑛	𝑇𝑇𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	96	22	=	=	SYM
american_scientific_journal-1936	96	23	�	�	PROPN
american_scientific_journal-1936	96	24	𝜕𝜕𝑢𝑢	𝜕𝜕𝑢𝑢	NOUN
american_scientific_journal-1936	96	25	𝜕𝜕𝑡𝑡	𝜕𝜕𝑡𝑡	PROPN
american_scientific_journal-1936	97	1	−	−	PROPN
american_scientific_journal-1936	97	2	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	97	3	𝜕𝜕2𝑢𝑢	𝜕𝜕2𝑢𝑢	PROPN
american_scientific_journal-1936	97	4	𝜕𝜕𝑥𝑥2	𝜕𝜕𝑥𝑥2	ADP
american_scientific_journal-1936	97	5	�	�	PROPN
american_scientific_journal-1936	97	6	𝑖𝑖,𝑛𝑛	𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	98	1	+	+	CCONJ
american_scientific_journal-1936	98	2	1	1	NUM
american_scientific_journal-1936	98	3	2	2	NUM
american_scientific_journal-1936	98	4	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	98	5	�	�	PROPN
american_scientific_journal-1936	98	6	𝜕𝜕2𝑢𝑢	𝜕𝜕2𝑢𝑢	PROPN
american_scientific_journal-1936	98	7	𝜕𝜕𝑡𝑡2	𝜕𝜕𝑡𝑡2	PRON
american_scientific_journal-1936	98	8	�	�	PROPN
american_scientific_journal-1936	98	9	𝑖𝑖,𝑛𝑛	𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	99	1	+	+	CCONJ
american_scientific_journal-1936	99	2	1	1	NUM
american_scientific_journal-1936	99	3	12	12	NUM
american_scientific_journal-1936	99	4	(	(	PUNCT
american_scientific_journal-1936	99	5	∆𝑥𝑥)2	∆𝑥𝑥)2	PUNCT
american_scientific_journal-1936	99	6	�	�	PROPN
american_scientific_journal-1936	99	7	𝜕𝜕4𝑢𝑢	𝜕𝜕4𝑢𝑢	PROPN
american_scientific_journal-1936	99	8	𝜕𝜕𝑥𝑥4	𝜕𝜕𝑥𝑥4	PROPN
american_scientific_journal-1936	99	9	�	�	PROPN
american_scientific_journal-1936	99	10	𝑖𝑖,𝑛𝑛	𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	99	11	+	+	X
american_scientific_journal-1936	99	12	𝑂𝑂((∆𝑡𝑡)2	𝑂𝑂((∆𝑡𝑡)2	PROPN
american_scientific_journal-1936	99	13	)	)	PUNCT
american_scientific_journal-1936	100	1	+	+	NUM
american_scientific_journal-1936	100	2	𝑂𝑂((∆𝑥𝑥)4	𝑂𝑂((∆𝑥𝑥)4	NOUN
american_scientific_journal-1936	100	3	)	)	PUNCT
american_scientific_journal-1936	100	4	.	.	PUNCT
american_scientific_journal-1936	101	1	it	it	PRON
american_scientific_journal-1936	101	2	can	can	AUX
american_scientific_journal-1936	101	3	be	be	AUX
american_scientific_journal-1936	101	4	observed	observe	VERB
american_scientific_journal-1936	101	5	that	that	SCONJ
american_scientific_journal-1936	101	6	the	the	DET
american_scientific_journal-1936	101	7	truncation	truncation	NOUN
american_scientific_journal-1936	101	8	error	error	NOUN
american_scientific_journal-1936	101	9	𝑇𝑇𝑖𝑖,𝑛𝑛	𝑇𝑇𝑖𝑖,𝑛𝑛	NOUN
american_scientific_journal-1936	101	10	goes	go	VERB
american_scientific_journal-1936	101	11	to	to	ADP
american_scientific_journal-1936	101	12	zero	zero	NUM
american_scientific_journal-1936	101	13	as	as	SCONJ
american_scientific_journal-1936	101	14	both	both	CCONJ
american_scientific_journal-1936	101	15	temporal	temporal	ADJ
american_scientific_journal-1936	101	16	and	and	CCONJ
american_scientific_journal-1936	101	17	spatial	spatial	ADJ
american_scientific_journal-1936	101	18	intervals	interval	NOUN
american_scientific_journal-1936	101	19	go	go	VERB
american_scientific_journal-1936	101	20	to	to	ADP
american_scientific_journal-1936	101	21	zero	zero	NUM
american_scientific_journal-1936	101	22	.	.	PUNCT
american_scientific_journal-1936	102	1	that	that	PRON
american_scientific_journal-1936	102	2	is	be	AUX
american_scientific_journal-1936	102	3	𝑇𝑇𝑖𝑖,𝑛𝑛	𝑇𝑇𝑖𝑖,𝑛𝑛	X
american_scientific_journal-1936	102	4	→	→	SYM
american_scientific_journal-1936	102	5	0	0	NUM
american_scientific_journal-1936	102	6	as	as	ADP
american_scientific_journal-1936	102	7	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	102	8	→	→	SYM
american_scientific_journal-1936	102	9	0	0	NUM
american_scientific_journal-1936	102	10	and	and	CCONJ
american_scientific_journal-1936	102	11	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	102	12	→	→	SYM
american_scientific_journal-1936	102	13	0	0	X
american_scientific_journal-1936	102	14	.	.	PUNCT
american_scientific_journal-1936	103	1	it	it	PRON
american_scientific_journal-1936	103	2	shows	show	VERB
american_scientific_journal-1936	103	3	that	that	SCONJ
american_scientific_journal-1936	103	4	the	the	DET
american_scientific_journal-1936	103	5	ftcs	ftcs	NOUN
american_scientific_journal-1936	103	6	scheme	scheme	NOUN
american_scientific_journal-1936	103	7	is	be	AUX
american_scientific_journal-1936	103	8	consistent	consistent	ADJ
american_scientific_journal-1936	103	9	with	with	ADP
american_scientific_journal-1936	103	10	partial	partial	ADJ
american_scientific_journal-1936	103	11	differential	differential	NOUN
american_scientific_journal-1936	103	12	equation	equation	NOUN
american_scientific_journal-1936	103	13	(	(	PUNCT
american_scientific_journal-1936	103	14	3	3	NUM
american_scientific_journal-1936	103	15	)	)	PUNCT
american_scientific_journal-1936	103	16	.	.	PUNCT
american_scientific_journal-1936	104	1	2.3	2.3	NUM
american_scientific_journal-1936	104	2	backward	backward	ADJ
american_scientific_journal-1936	104	3	time	time	NOUN
american_scientific_journal-1936	104	4	centered	center	VERB
american_scientific_journal-1936	104	5	space	space	NOUN
american_scientific_journal-1936	104	6	implicit	implicit	ADJ
american_scientific_journal-1936	104	7	scheme	scheme	NOUN
american_scientific_journal-1936	104	8	to	to	PART
american_scientific_journal-1936	104	9	discretize	discretize	VERB
american_scientific_journal-1936	104	10	equation	equation	NOUN
american_scientific_journal-1936	104	11	(	(	PUNCT
american_scientific_journal-1936	104	12	3	3	NUM
american_scientific_journal-1936	104	13	)	)	PUNCT
american_scientific_journal-1936	104	14	,	,	PUNCT
american_scientific_journal-1936	104	15	we	we	PRON
american_scientific_journal-1936	104	16	substitute	substitute	VERB
american_scientific_journal-1936	104	17	the	the	DET
american_scientific_journal-1936	104	18	backward	backward	ADJ
american_scientific_journal-1936	104	19	difference	difference	NOUN
american_scientific_journal-1936	104	20	approximation	approximation	NOUN
american_scientific_journal-1936	104	21	for	for	ADP
american_scientific_journal-1936	104	22	the	the	DET
american_scientific_journal-1936	104	23	first	first	ADJ
american_scientific_journal-1936	104	24	partial	partial	ADJ
american_scientific_journal-1936	104	25	derivative	derivative	ADJ
american_scientific_journal-1936	104	26	and	and	CCONJ
american_scientific_journal-1936	104	27	central	central	ADJ
american_scientific_journal-1936	104	28	difference	difference	NOUN
american_scientific_journal-1936	104	29	approximation	approximation	NOUN
american_scientific_journal-1936	104	30	for	for	ADP
american_scientific_journal-1936	104	31	the	the	DET
american_scientific_journal-1936	104	32	second	second	ADJ
american_scientific_journal-1936	104	33	partial	partial	ADJ
american_scientific_journal-1936	104	34	derivative	derivative	NOUN
american_scientific_journal-1936	104	35	,	,	PUNCT
american_scientific_journal-1936	104	36	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	PRON
american_scientific_journal-1936	104	37	𝑛𝑛−	𝑛𝑛−	NUM
american_scientific_journal-1936	104	38	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	ADV
american_scientific_journal-1936	104	39	𝑛𝑛−1	𝑛𝑛−1	PROPN
american_scientific_journal-1936	104	40	∆𝜕𝜕	∆𝜕𝜕	NOUN
american_scientific_journal-1936	104	41	=	=	PROPN
american_scientific_journal-1936	104	42	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	104	43	�	�	PROPN
american_scientific_journal-1936	104	44	𝜕𝜕𝑖𝑖−1	𝜕𝜕𝑖𝑖−1	PROPN
american_scientific_journal-1936	104	45	𝑛𝑛	𝑛𝑛	ADP
american_scientific_journal-1936	104	46	−2	−2	PROPN
american_scientific_journal-1936	104	47	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	INTJ
american_scientific_journal-1936	104	48	𝑛𝑛+	𝑛𝑛+	ADJ
american_scientific_journal-1936	104	49	𝜕𝜕𝑖𝑖+1	𝜕𝜕𝑖𝑖+1	PUNCT
american_scientific_journal-1936	104	50	𝑛𝑛	𝑛𝑛	ADP
american_scientific_journal-1936	104	51	∆𝑥𝑥2	∆𝑥𝑥2	PROPN
american_scientific_journal-1936	104	52	�	�	PROPN
american_scientific_journal-1936	104	53	+	+	CCONJ
american_scientific_journal-1936	104	54	𝑂𝑂(∆𝑡𝑡	𝑂𝑂(∆𝑡𝑡	NOUN
american_scientific_journal-1936	104	55	)	)	PUNCT
american_scientific_journal-1936	104	56	+	+	PUNCT
american_scientific_journal-1936	104	57	𝑂𝑂(∆𝑥𝑥2	𝑂𝑂(∆𝑥𝑥2	NUM
american_scientific_journal-1936	104	58	)	)	PUNCT
american_scientific_journal-1936	104	59	(	(	PUNCT
american_scientific_journal-1936	104	60	12	12	NUM
american_scientific_journal-1936	104	61	)	)	PUNCT
american_scientific_journal-1936	104	62	to	to	PART
american_scientific_journal-1936	104	63	present	present	VERB
american_scientific_journal-1936	104	64	the	the	DET
american_scientific_journal-1936	104	65	system	system	NOUN
american_scientific_journal-1936	104	66	of	of	ADP
american_scientific_journal-1936	104	67	equations	equation	NOUN
american_scientific_journal-1936	104	68	in	in	ADP
american_scientific_journal-1936	104	69	a	a	DET
american_scientific_journal-1936	104	70	simple	simple	ADJ
american_scientific_journal-1936	104	71	manner	manner	NOUN
american_scientific_journal-1936	104	72	let	let	VERB
american_scientific_journal-1936	104	73	us	we	PRON
american_scientific_journal-1936	104	74	drop	drop	VERB
american_scientific_journal-1936	104	75	the	the	DET
american_scientific_journal-1936	104	76	truncation	truncation	NOUN
american_scientific_journal-1936	104	77	error	error	NOUN
american_scientific_journal-1936	104	78	terms	term	NOUN
american_scientific_journal-1936	104	79	from	from	ADP
american_scientific_journal-1936	104	80	(	(	PUNCT
american_scientific_journal-1936	104	81	12	12	NUM
american_scientific_journal-1936	104	82	)	)	PUNCT
american_scientific_journal-1936	104	83	and	and	CCONJ
american_scientific_journal-1936	104	84	rearrange	rearrange	VERB
american_scientific_journal-1936	104	85	the	the	DET
american_scientific_journal-1936	104	86	resulting	result	VERB
american_scientific_journal-1936	104	87	equation	equation	NOUN
american_scientific_journal-1936	104	88	to	to	PART
american_scientific_journal-1936	104	89	get	get	VERB
american_scientific_journal-1936	104	90	𝑢𝑢𝑖𝑖𝑛𝑛−1	𝑢𝑢𝑖𝑖𝑛𝑛−1	PROPN
american_scientific_journal-1936	104	91	=	=	SYM
american_scientific_journal-1936	104	92	−	−	PROPN
american_scientific_journal-1936	104	93	𝑟𝑟𝑢𝑢𝑖𝑖−1𝑛𝑛	𝑟𝑟𝑢𝑢𝑖𝑖−1𝑛𝑛	NOUN
american_scientific_journal-1936	104	94	+	+	CCONJ
american_scientific_journal-1936	104	95	(	(	PUNCT
american_scientific_journal-1936	104	96	1	1	NUM
american_scientific_journal-1936	104	97	+	+	CCONJ
american_scientific_journal-1936	104	98	2𝑟𝑟	2𝑟𝑟	ADJ
american_scientific_journal-1936	104	99	)	)	PUNCT
american_scientific_journal-1936	104	100	𝑢𝑢𝑖𝑖𝑛𝑛	𝑢𝑢𝑖𝑖𝑛𝑛	NOUN
american_scientific_journal-1936	104	101	−	−	PROPN
american_scientific_journal-1936	104	102	𝑟𝑟𝑢𝑢𝑖𝑖+1𝑛𝑛	𝑟𝑟𝑢𝑢𝑖𝑖+1𝑛𝑛	PROPN
american_scientific_journal-1936	104	103	(	(	PUNCT
american_scientific_journal-1936	104	104	13	13	NUM
american_scientific_journal-1936	104	105	)	)	PUNCT
american_scientific_journal-1936	104	106	american	american	ADJ
american_scientific_journal-1936	104	107	scientific	scientific	ADJ
american_scientific_journal-1936	104	108	research	research	NOUN
american_scientific_journal-1936	104	109	journal	journal	NOUN
american_scientific_journal-1936	104	110	for	for	ADP
american_scientific_journal-1936	104	111	engineering	engineering	NOUN
american_scientific_journal-1936	104	112	,	,	PUNCT
american_scientific_journal-1936	104	113	technology	technology	NOUN
american_scientific_journal-1936	104	114	,	,	PUNCT
american_scientific_journal-1936	104	115	and	and	CCONJ
american_scientific_journal-1936	104	116	sciences	science	NOUN
american_scientific_journal-1936	104	117	(	(	PUNCT
american_scientific_journal-1936	104	118	asrjets	asrjet	NOUN
american_scientific_journal-1936	104	119	)	)	PUNCT
american_scientific_journal-1936	104	120	(	(	PUNCT
american_scientific_journal-1936	104	121	2016	2016	NUM
american_scientific_journal-1936	104	122	)	)	PUNCT
american_scientific_journal-1936	104	123	volume	volume	NOUN
american_scientific_journal-1936	104	124	26	26	NUM
american_scientific_journal-1936	104	125	,	,	PUNCT
american_scientific_journal-1936	104	126	no	no	DET
american_scientific_journal-1936	104	127	3	3	NUM
american_scientific_journal-1936	104	128	,	,	PUNCT
american_scientific_journal-1936	104	129	pp	pp	ADV
american_scientific_journal-1936	104	130	140	140	NUM
american_scientific_journal-1936	104	131	-	-	SYM
american_scientific_journal-1936	104	132	154	154	NUM
american_scientific_journal-1936	104	133	145	145	NUM
american_scientific_journal-1936	104	134	here	here	ADV
american_scientific_journal-1936	104	135	in	in	ADP
american_scientific_journal-1936	104	136	(	(	PUNCT
american_scientific_journal-1936	104	137	12	12	NUM
american_scientific_journal-1936	104	138	)	)	PUNCT
american_scientific_journal-1936	104	139	and	and	CCONJ
american_scientific_journal-1936	104	140	(	(	PUNCT
american_scientific_journal-1936	104	141	13	13	NUM
american_scientific_journal-1936	104	142	)	)	PUNCT
american_scientific_journal-1936	104	143	,	,	PUNCT
american_scientific_journal-1936	104	144	we	we	PRON
american_scientific_journal-1936	104	145	denote	denote	VERB
american_scientific_journal-1936	104	146	𝑖𝑖	𝑖𝑖	ADP
american_scientific_journal-1936	104	147	is	be	AUX
american_scientific_journal-1936	104	148	an	an	DET
american_scientific_journal-1936	104	149	index	index	NOUN
american_scientific_journal-1936	104	150	number	number	NOUN
american_scientific_journal-1936	104	151	taking	take	VERB
american_scientific_journal-1936	104	152	the	the	DET
american_scientific_journal-1936	104	153	values	value	NOUN
american_scientific_journal-1936	104	154	𝑖𝑖	𝑖𝑖	X
american_scientific_journal-1936	105	1	=	=	SYM
american_scientific_journal-1936	105	2	1	1	NUM
american_scientific_journal-1936	105	3	,	,	PUNCT
american_scientific_journal-1936	105	4	2	2	NUM
american_scientific_journal-1936	105	5	,	,	PUNCT
american_scientific_journal-1936	105	6	3	3	NUM
american_scientific_journal-1936	105	7	,	,	PUNCT
american_scientific_journal-1936	105	8	.	.	PUNCT
american_scientific_journal-1936	105	9	.	.	PUNCT
american_scientific_journal-1936	106	1	.	.	PUNCT
american_scientific_journal-1936	107	1	,	,	PUNCT
american_scientific_journal-1936	107	2	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-1936	107	3	−	−	PROPN
american_scientific_journal-1936	108	1	1	1	NUM
american_scientific_journal-1936	108	2	.	.	PUNCT
american_scientific_journal-1936	109	1	if	if	SCONJ
american_scientific_journal-1936	109	2	the	the	DET
american_scientific_journal-1936	109	3	dirichlet	dirichlet	PROPN
american_scientific_journal-1936	109	4	type	type	NOUN
american_scientific_journal-1936	109	5	of	of	ADP
american_scientific_journal-1936	109	6	boundary	boundary	ADJ
american_scientific_journal-1936	109	7	condition	condition	NOUN
american_scientific_journal-1936	109	8	are	be	AUX
american_scientific_journal-1936	109	9	given	give	VERB
american_scientific_journal-1936	109	10	i.e.	i.e.	ADV
american_scientific_journal-1936	109	11	,	,	PUNCT
american_scientific_journal-1936	109	12	values	value	NOUN
american_scientific_journal-1936	109	13	of	of	ADP
american_scientific_journal-1936	109	14	the	the	DET
american_scientific_journal-1936	109	15	end	end	NOUN
american_scientific_journal-1936	109	16	points	point	NOUN
american_scientific_journal-1936	109	17	𝑢𝑢0	𝑢𝑢0	NOUN
american_scientific_journal-1936	109	18	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-1936	109	19	and	and	CCONJ
american_scientific_journal-1936	109	20	𝑢𝑢𝑁𝑁	𝑢𝑢𝑁𝑁	PRON
american_scientific_journal-1936	109	21	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-1936	109	22	are	be	AUX
american_scientific_journal-1936	109	23	given	give	VERB
american_scientific_journal-1936	109	24	,	,	PUNCT
american_scientific_journal-1936	109	25	then	then	ADV
american_scientific_journal-1936	109	26	(	(	PUNCT
american_scientific_journal-1936	109	27	13	13	NUM
american_scientific_journal-1936	109	28	)	)	PUNCT
american_scientific_journal-1936	109	29	can	can	AUX
american_scientific_journal-1936	109	30	be	be	AUX
american_scientific_journal-1936	109	31	reduced	reduce	VERB
american_scientific_journal-1936	109	32	into	into	ADP
american_scientific_journal-1936	109	33	a	a	DET
american_scientific_journal-1936	109	34	compact	compact	ADJ
american_scientific_journal-1936	109	35	form	form	NOUN
american_scientific_journal-1936	109	36	as	as	ADP
american_scientific_journal-1936	109	37	𝑢𝑢𝑛𝑛−1	𝑢𝑢𝑛𝑛−1	NOUN
american_scientific_journal-1936	109	38	=	=	PUNCT
american_scientific_journal-1936	109	39	(	(	PUNCT
american_scientific_journal-1936	109	40	𝐼𝐼	𝐼𝐼	PROPN
american_scientific_journal-1936	109	41	−	−	PROPN
american_scientific_journal-1936	109	42	𝑟𝑟𝑟𝑟)𝑢𝑢𝑛𝑛	𝑟𝑟𝑟𝑟)𝑢𝑢𝑛𝑛	PROPN
american_scientific_journal-1936	109	43	,	,	PUNCT
american_scientific_journal-1936	109	44	(	(	PUNCT
american_scientific_journal-1936	109	45	14	14	NUM
american_scientific_journal-1936	109	46	)	)	PUNCT
american_scientific_journal-1936	109	47	here	here	ADV
american_scientific_journal-1936	109	48	in	in	ADP
american_scientific_journal-1936	109	49	(	(	PUNCT
american_scientific_journal-1936	109	50	14	14	NUM
american_scientific_journal-1936	109	51	)	)	PUNCT
american_scientific_journal-1936	109	52	,	,	PUNCT
american_scientific_journal-1936	109	53	both	both	DET
american_scientific_journal-1936	109	54	𝑢𝑢𝑛𝑛−1	𝑢𝑢𝑛𝑛−1	NOUN
american_scientific_journal-1936	109	55	and	and	CCONJ
american_scientific_journal-1936	109	56	𝑢𝑢𝑛𝑛	𝑢𝑢𝑛𝑛	NOUN
american_scientific_journal-1936	109	57	represent	represent	VERB
american_scientific_journal-1936	109	58	(	(	PUNCT
american_scientific_journal-1936	109	59	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-1936	109	60	−	−	PROPN
american_scientific_journal-1936	109	61	1	1	NUM
american_scientific_journal-1936	109	62	)	)	PUNCT
american_scientific_journal-1936	109	63	dimensional	dimensional	ADJ
american_scientific_journal-1936	109	64	column	column	NOUN
american_scientific_journal-1936	109	65	vectors	vector	NOUN
american_scientific_journal-1936	109	66	.	.	PUNCT
american_scientific_journal-1936	110	1	that	that	PRON
american_scientific_journal-1936	110	2	is	be	AUX
american_scientific_journal-1936	110	3	,	,	PUNCT
american_scientific_journal-1936	110	4	𝑢𝑢𝑛𝑛−1	𝑢𝑢𝑛𝑛−1	PROPN
american_scientific_journal-1936	110	5	=	=	SYM
american_scientific_journal-1936	110	6	[	[	X
american_scientific_journal-1936	110	7	𝑢𝑢1𝑛𝑛−1	𝑢𝑢1𝑛𝑛−1	PROPN
american_scientific_journal-1936	110	8	,	,	PUNCT
american_scientific_journal-1936	110	9	𝑢𝑢2𝑛𝑛−1	𝑢𝑢2𝑛𝑛−1	PROPN
american_scientific_journal-1936	110	10	,	,	PUNCT
american_scientific_journal-1936	110	11	.	.	PUNCT
american_scientific_journal-1936	110	12	.	.	PUNCT
american_scientific_journal-1936	110	13	.	.	PUNCT
american_scientific_journal-1936	111	1	,	,	PUNCT
american_scientific_journal-1936	111	2	𝑢𝑢𝑁𝑁−1𝑛𝑛−1]𝑇𝑇	𝑢𝑢𝑁𝑁−1𝑛𝑛−1]𝑇𝑇	ADV
american_scientific_journal-1936	111	3	and	and	CCONJ
american_scientific_journal-1936	111	4	𝑢𝑢𝑛𝑛	𝑢𝑢𝑛𝑛	NOUN
american_scientific_journal-1936	111	5	=	=	SYM
american_scientific_journal-1936	111	6	[	[	X
american_scientific_journal-1936	111	7	(	(	PUNCT
american_scientific_journal-1936	111	8	𝑢𝑢1𝑛𝑛	𝑢𝑢1𝑛𝑛	NOUN
american_scientific_journal-1936	111	9	−	−	PROPN
american_scientific_journal-1936	111	10	𝑟𝑟𝑢𝑢0𝑛𝑛	𝑟𝑟𝑢𝑢0𝑛𝑛	PROPN
american_scientific_journal-1936	111	11	)	)	PUNCT
american_scientific_journal-1936	111	12	,	,	PUNCT
american_scientific_journal-1936	111	13	𝑢𝑢2𝑛𝑛	𝑢𝑢2𝑛𝑛	PROPN
american_scientific_journal-1936	111	14	,	,	PUNCT
american_scientific_journal-1936	111	15	.	.	PUNCT
american_scientific_journal-1936	111	16	.	.	PUNCT
american_scientific_journal-1936	112	1	.	.	PUNCT
american_scientific_journal-1936	113	1	,	,	PUNCT
american_scientific_journal-1936	113	2	𝑢𝑢𝑁𝑁−2𝑛𝑛	𝑢𝑢𝑁𝑁−2𝑛𝑛	PROPN
american_scientific_journal-1936	113	3	,	,	PUNCT
american_scientific_journal-1936	113	4	(	(	PUNCT
american_scientific_journal-1936	113	5	𝑢𝑢𝑁𝑁−1𝑛𝑛	𝑢𝑢𝑁𝑁−1𝑛𝑛	VERB
american_scientific_journal-1936	113	6	−	−	NOUN
american_scientific_journal-1936	114	1	𝑢𝑢𝑁𝑁𝑛𝑛)]𝑇𝑇	𝑢𝑢𝑁𝑁𝑛𝑛)]𝑇𝑇	ADV
american_scientific_journal-1936	114	2	now	now	ADV
american_scientific_journal-1936	114	3	up	up	ADP
american_scientific_journal-1936	114	4	on	on	ADP
american_scientific_journal-1936	114	5	substitution	substitution	NOUN
american_scientific_journal-1936	114	6	of	of	ADP
american_scientific_journal-1936	114	7	the	the	DET
american_scientific_journal-1936	114	8	fourier	fourier	ADJ
american_scientific_journal-1936	114	9	mode	mode	NOUN
american_scientific_journal-1936	114	10	(	(	PUNCT
american_scientific_journal-1936	114	11	11	11	NUM
american_scientific_journal-1936	114	12	)	)	PUNCT
american_scientific_journal-1936	114	13	in	in	ADP
american_scientific_journal-1936	114	14	(	(	PUNCT
american_scientific_journal-1936	114	15	13	13	NUM
american_scientific_journal-1936	114	16	)	)	PUNCT
american_scientific_journal-1936	114	17	yields	yield	VERB
american_scientific_journal-1936	114	18	1	1	NUM
american_scientific_journal-1936	114	19	𝜆𝜆⁄	𝜆𝜆⁄	NOUN
american_scientific_journal-1936	114	20	=	=	SYM
american_scientific_journal-1936	114	21	−𝑟𝑟𝑒𝑒−(𝑛𝑛𝑛𝑛	−𝑟𝑟𝑒𝑒−(𝑛𝑛𝑛𝑛	PROPN
american_scientific_journal-1936	114	22	𝑝𝑝⁄	𝑝𝑝⁄	X
american_scientific_journal-1936	114	23	)	)	PUNCT
american_scientific_journal-1936	115	1	+	+	CCONJ
american_scientific_journal-1936	115	2	(	(	PUNCT
american_scientific_journal-1936	115	3	1	1	NUM
american_scientific_journal-1936	115	4	+	+	NUM
american_scientific_journal-1936	115	5	2𝑟𝑟	2𝑟𝑟	ADJ
american_scientific_journal-1936	115	6	)	)	PUNCT
american_scientific_journal-1936	115	7	–	–	PUNCT
american_scientific_journal-1936	115	8	𝑟𝑟𝑒𝑒(𝑛𝑛𝑛𝑛	𝑟𝑟𝑒𝑒(𝑛𝑛𝑛𝑛	X
american_scientific_journal-1936	115	9	𝑝𝑝⁄	𝑝𝑝⁄	NOUN
american_scientific_journal-1936	115	10	)	)	PUNCT
american_scientific_journal-1936	115	11	or	or	CCONJ
american_scientific_journal-1936	115	12	equivalently	equivalently	ADV
american_scientific_journal-1936	115	13	𝜆𝜆	𝜆𝜆	VERB
american_scientific_journal-1936	115	14	=	=	SYM
american_scientific_journal-1936	115	15	{	{	PUNCT
american_scientific_journal-1936	115	16	1	1	NUM
american_scientific_journal-1936	115	17	+	+	SYM
american_scientific_journal-1936	115	18	2𝑟𝑟[1	2𝑟𝑟[1	NUM
american_scientific_journal-1936	115	19	−	−	NOUN
american_scientific_journal-1936	115	20	cos	cos	PROPN
american_scientific_journal-1936	115	21	(	(	PUNCT
american_scientific_journal-1936	115	22	𝜋𝜋	𝜋𝜋	X
american_scientific_journal-1936	115	23	𝑝𝑝⁄	𝑝𝑝⁄	X
american_scientific_journal-1936	115	24	)	)	PUNCT
american_scientific_journal-1936	115	25	]	]	PUNCT
american_scientific_journal-1936	115	26	}	}	PUNCT
american_scientific_journal-1936	115	27	−1	−1	NOUN
american_scientific_journal-1936	115	28	and	and	CCONJ
american_scientific_journal-1936	115	29	thus	thus	ADV
american_scientific_journal-1936	115	30	|𝜆𝜆|	|𝜆𝜆|	PROPN
american_scientific_journal-1936	115	31	≤	≤	NUM
american_scientific_journal-1936	115	32	1	1	NUM
american_scientific_journal-1936	115	33	.	.	PUNCT
american_scientific_journal-1936	116	1	this	this	PRON
american_scientific_journal-1936	116	2	indicates	indicate	VERB
american_scientific_journal-1936	116	3	that	that	SCONJ
american_scientific_journal-1936	116	4	the	the	DET
american_scientific_journal-1936	116	5	btcs	btcs	NOUN
american_scientific_journal-1936	116	6	scheme	scheme	NOUN
american_scientific_journal-1936	116	7	is	be	AUX
american_scientific_journal-1936	116	8	unconditionally	unconditionally	ADV
american_scientific_journal-1936	116	9	stable	stable	ADJ
american_scientific_journal-1936	116	10	.	.	PUNCT
american_scientific_journal-1936	117	1	further	far	ADV
american_scientific_journal-1936	117	2	,	,	PUNCT
american_scientific_journal-1936	117	3	the	the	DET
american_scientific_journal-1936	117	4	advantage	advantage	NOUN
american_scientific_journal-1936	117	5	of	of	ADP
american_scientific_journal-1936	117	6	this	this	DET
american_scientific_journal-1936	117	7	scheme	scheme	NOUN
american_scientific_journal-1936	117	8	is	be	AUX
american_scientific_journal-1936	117	9	it	it	PRON
american_scientific_journal-1936	117	10	removes	remove	VERB
american_scientific_journal-1936	117	11	the	the	DET
american_scientific_journal-1936	117	12	stability	stability	NOUN
american_scientific_journal-1936	117	13	limitation	limitation	NOUN
american_scientific_journal-1936	117	14	associated	associate	VERB
american_scientific_journal-1936	117	15	with	with	ADP
american_scientific_journal-1936	117	16	the	the	DET
american_scientific_journal-1936	117	17	diffusion	diffusion	NOUN
american_scientific_journal-1936	117	18	operator	operator	NOUN
american_scientific_journal-1936	117	19	.	.	PUNCT
american_scientific_journal-1936	118	1	the	the	DET
american_scientific_journal-1936	118	2	disadvantage	disadvantage	NOUN
american_scientific_journal-1936	118	3	is	be	AUX
american_scientific_journal-1936	118	4	that	that	SCONJ
american_scientific_journal-1936	118	5	the	the	DET
american_scientific_journal-1936	118	6	problem	problem	NOUN
american_scientific_journal-1936	118	7	becomes	become	VERB
american_scientific_journal-1936	118	8	more	more	ADV
american_scientific_journal-1936	118	9	expensive	expensive	ADJ
american_scientific_journal-1936	118	10	to	to	PART
american_scientific_journal-1936	118	11	solve	solve	VERB
american_scientific_journal-1936	118	12	numerically	numerically	ADV
american_scientific_journal-1936	118	13	[	[	X
american_scientific_journal-1936	118	14	3	3	NUM
american_scientific_journal-1936	118	15	]	]	PUNCT
american_scientific_journal-1936	118	16	.	.	PUNCT
american_scientific_journal-1936	119	1	the	the	DET
american_scientific_journal-1936	119	2	truncation	truncation	NOUN
american_scientific_journal-1936	119	3	error	error	NOUN
american_scientific_journal-1936	119	4	𝑇𝑇𝑖𝑖,𝑛𝑛	𝑇𝑇𝑖𝑖,𝑛𝑛	VERB
american_scientific_journal-1936	119	5	for	for	ADP
american_scientific_journal-1936	119	6	the	the	DET
american_scientific_journal-1936	119	7	btcs	btcs	NOUN
american_scientific_journal-1936	119	8	solution	solution	NOUN
american_scientific_journal-1936	119	9	of	of	ADP
american_scientific_journal-1936	119	10	the	the	DET
american_scientific_journal-1936	119	11	diffusion	diffusion	NOUN
american_scientific_journal-1936	119	12	equation	equation	NOUN
american_scientific_journal-1936	119	13	is	be	AUX
american_scientific_journal-1936	119	14	[	[	X
american_scientific_journal-1936	119	15	14	14	NUM
american_scientific_journal-1936	119	16	]	]	X
american_scientific_journal-1936	120	1	𝑇𝑇𝑖𝑖,𝑛𝑛	𝑇𝑇𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	120	2	=	=	SYM
american_scientific_journal-1936	120	3	�	�	PROPN
american_scientific_journal-1936	120	4	𝜕𝜕𝑢𝑢	𝜕𝜕𝑢𝑢	NOUN
american_scientific_journal-1936	120	5	𝜕𝜕𝑡𝑡	𝜕𝜕𝑡𝑡	PROPN
american_scientific_journal-1936	121	1	−	−	PROPN
american_scientific_journal-1936	121	2	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	121	3	𝜕𝜕2𝑢𝑢	𝜕𝜕2𝑢𝑢	PROPN
american_scientific_journal-1936	121	4	𝜕𝜕𝑥𝑥2	𝜕𝜕𝑥𝑥2	ADP
american_scientific_journal-1936	121	5	�	�	PROPN
american_scientific_journal-1936	121	6	𝑖𝑖,𝑛𝑛	𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	122	1	+	+	CCONJ
american_scientific_journal-1936	122	2	1	1	NUM
american_scientific_journal-1936	122	3	2	2	NUM
american_scientific_journal-1936	122	4	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	122	5	�	�	PROPN
american_scientific_journal-1936	122	6	𝜕𝜕2𝑢𝑢	𝜕𝜕2𝑢𝑢	PROPN
american_scientific_journal-1936	122	7	𝜕𝜕𝑡𝑡2	𝜕𝜕𝑡𝑡2	PROPN
american_scientific_journal-1936	122	8	�	�	PROPN
american_scientific_journal-1936	122	9	𝑖𝑖,𝑛𝑛	𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	123	1	−	−	PROPN
american_scientific_journal-1936	123	2	1	1	NUM
american_scientific_journal-1936	123	3	12	12	NUM
american_scientific_journal-1936	123	4	(	(	PUNCT
american_scientific_journal-1936	123	5	∆𝑥𝑥)2	∆𝑥𝑥)2	PUNCT
american_scientific_journal-1936	123	6	�	�	PROPN
american_scientific_journal-1936	123	7	𝜕𝜕4𝑢𝑢	𝜕𝜕4𝑢𝑢	PROPN
american_scientific_journal-1936	123	8	𝜕𝜕𝑥𝑥4	𝜕𝜕𝑥𝑥4	PROPN
american_scientific_journal-1936	123	9	�	�	PROPN
american_scientific_journal-1936	123	10	𝑖𝑖,𝑛𝑛	𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	123	11	+	+	X
american_scientific_journal-1936	123	12	𝑂𝑂((∆𝑡𝑡)2	𝑂𝑂((∆𝑡𝑡)2	PROPN
american_scientific_journal-1936	123	13	)	)	PUNCT
american_scientific_journal-1936	124	1	+	+	NUM
american_scientific_journal-1936	124	2	𝑂𝑂((∆𝑥𝑥)4	𝑂𝑂((∆𝑥𝑥)4	NOUN
american_scientific_journal-1936	124	3	)	)	PUNCT
american_scientific_journal-1936	124	4	.	.	PUNCT
american_scientific_journal-1936	125	1	it	it	PRON
american_scientific_journal-1936	125	2	can	can	AUX
american_scientific_journal-1936	125	3	be	be	AUX
american_scientific_journal-1936	125	4	observed	observe	VERB
american_scientific_journal-1936	125	5	that	that	SCONJ
american_scientific_journal-1936	125	6	the	the	DET
american_scientific_journal-1936	125	7	truncation	truncation	NOUN
american_scientific_journal-1936	125	8	error	error	NOUN
american_scientific_journal-1936	125	9	𝑇𝑇𝑖𝑖,𝑛𝑛	𝑇𝑇𝑖𝑖,𝑛𝑛	NOUN
american_scientific_journal-1936	125	10	goes	go	VERB
american_scientific_journal-1936	125	11	to	to	ADP
american_scientific_journal-1936	125	12	zero	zero	NUM
american_scientific_journal-1936	125	13	as	as	SCONJ
american_scientific_journal-1936	125	14	both	both	CCONJ
american_scientific_journal-1936	125	15	temporal	temporal	ADJ
american_scientific_journal-1936	125	16	and	and	CCONJ
american_scientific_journal-1936	125	17	spatial	spatial	ADJ
american_scientific_journal-1936	125	18	intervals	interval	NOUN
american_scientific_journal-1936	125	19	go	go	VERB
american_scientific_journal-1936	125	20	to	to	ADP
american_scientific_journal-1936	125	21	zero	zero	NUM
american_scientific_journal-1936	125	22	.	.	PUNCT
american_scientific_journal-1936	126	1	that	that	PRON
american_scientific_journal-1936	126	2	is	be	AUX
american_scientific_journal-1936	126	3	𝑇𝑇𝑖𝑖,𝑛𝑛	𝑇𝑇𝑖𝑖,𝑛𝑛	X
american_scientific_journal-1936	126	4	→	→	SYM
american_scientific_journal-1936	126	5	0	0	NUM
american_scientific_journal-1936	126	6	as	as	ADP
american_scientific_journal-1936	126	7	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	126	8	→	→	SYM
american_scientific_journal-1936	126	9	0	0	NUM
american_scientific_journal-1936	126	10	and	and	CCONJ
american_scientific_journal-1936	126	11	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	126	12	→	→	SYM
american_scientific_journal-1936	126	13	0	0	X
american_scientific_journal-1936	126	14	.	.	PUNCT
american_scientific_journal-1936	127	1	it	it	PRON
american_scientific_journal-1936	127	2	shows	show	VERB
american_scientific_journal-1936	127	3	that	that	SCONJ
american_scientific_journal-1936	127	4	the	the	DET
american_scientific_journal-1936	127	5	btcs	btcs	NOUN
american_scientific_journal-1936	127	6	scheme	scheme	NOUN
american_scientific_journal-1936	127	7	is	be	AUX
american_scientific_journal-1936	127	8	consistent	consistent	ADJ
american_scientific_journal-1936	127	9	with	with	ADP
american_scientific_journal-1936	127	10	partial	partial	ADJ
american_scientific_journal-1936	127	11	differential	differential	NOUN
american_scientific_journal-1936	127	12	equation	equation	NOUN
american_scientific_journal-1936	127	13	(	(	PUNCT
american_scientific_journal-1936	127	14	3	3	NUM
american_scientific_journal-1936	127	15	)	)	PUNCT
american_scientific_journal-1936	127	16	.	.	PUNCT
american_scientific_journal-1936	128	1	2.4	2.4	NUM
american_scientific_journal-1936	128	2	crank	crank	NOUN
american_scientific_journal-1936	128	3	–	–	PUNCT
american_scientific_journal-1936	128	4	nicolson	nicolson	PROPN
american_scientific_journal-1936	128	5	scheme	scheme	NOUN
american_scientific_journal-1936	128	6	as	as	SCONJ
american_scientific_journal-1936	128	7	we	we	PRON
american_scientific_journal-1936	128	8	have	have	AUX
american_scientific_journal-1936	128	9	already	already	ADV
american_scientific_journal-1936	128	10	seen	see	VERB
american_scientific_journal-1936	128	11	both	both	CCONJ
american_scientific_journal-1936	128	12	the	the	DET
american_scientific_journal-1936	128	13	ftcs	ftcs	NOUN
american_scientific_journal-1936	128	14	and	and	CCONJ
american_scientific_journal-1936	128	15	btcs	btcs	NOUN
american_scientific_journal-1936	128	16	schemes	scheme	NOUN
american_scientific_journal-1936	128	17	have	have	VERB
american_scientific_journal-1936	128	18	temporal	temporal	ADJ
american_scientific_journal-1936	128	19	truncation	truncation	NOUN
american_scientific_journal-1936	128	20	errors	error	NOUN
american_scientific_journal-1936	128	21	of	of	ADP
american_scientific_journal-1936	128	22	order	order	NOUN
american_scientific_journal-1936	128	23	𝑂𝑂(∆𝑡𝑡	𝑂𝑂(∆𝑡𝑡	NOUN
american_scientific_journal-1936	128	24	)	)	PUNCT
american_scientific_journal-1936	128	25	.	.	PUNCT
american_scientific_journal-1936	129	1	however	however	ADV
american_scientific_journal-1936	129	2	,	,	PUNCT
american_scientific_journal-1936	129	3	the	the	DET
american_scientific_journal-1936	129	4	crank	crank	NOUN
american_scientific_journal-1936	129	5	–	–	PUNCT
american_scientific_journal-1936	129	6	nicolson	nicolson	PROPN
american_scientific_journal-1936	129	7	scheme	scheme	NOUN
american_scientific_journal-1936	129	8	has	have	VERB
american_scientific_journal-1936	129	9	the	the	DET
american_scientific_journal-1936	129	10	error	error	NOUN
american_scientific_journal-1936	129	11	of	of	ADP
american_scientific_journal-1936	129	12	order	order	NOUN
american_scientific_journal-1936	129	13	𝑂𝑂(∆𝑡𝑡2	𝑂𝑂(∆𝑡𝑡2	NOUN
american_scientific_journal-1936	129	14	)	)	PUNCT
american_scientific_journal-1936	129	15	.	.	PUNCT
american_scientific_journal-1936	130	1	also	also	ADV
american_scientific_journal-1936	130	2	the	the	DET
american_scientific_journal-1936	130	3	crank	crank	NOUN
american_scientific_journal-1936	130	4	–	–	PUNCT
american_scientific_journal-1936	130	5	nicolson	nicolson	PROPN
american_scientific_journal-1936	130	6	scheme	scheme	NOUN
american_scientific_journal-1936	130	7	is	be	AUX
american_scientific_journal-1936	130	8	not	not	PART
american_scientific_journal-1936	130	9	significantly	significantly	ADV
american_scientific_journal-1936	130	10	more	more	ADV
american_scientific_journal-1936	130	11	difficult	difficult	ADJ
american_scientific_journal-1936	130	12	to	to	PART
american_scientific_journal-1936	130	13	implement	implement	VERB
american_scientific_journal-1936	130	14	than	than	ADP
american_scientific_journal-1936	130	15	the	the	DET
american_scientific_journal-1936	130	16	btcs	btcs	NOUN
american_scientific_journal-1936	130	17	schemes	scheme	NOUN
american_scientific_journal-1936	130	18	.	.	PUNCT
american_scientific_journal-1936	131	1	further	far	ADV
american_scientific_journal-1936	131	2	,	,	PUNCT
american_scientific_journal-1936	131	3	the	the	DET
american_scientific_journal-1936	131	4	crank	crank	NOUN
american_scientific_journal-1936	131	5	–	–	PUNCT
american_scientific_journal-1936	131	6	nicolson	nicolson	PROPN
american_scientific_journal-1936	131	7	scheme	scheme	NOUN
american_scientific_journal-1936	131	8	has	have	VERB
american_scientific_journal-1936	131	9	significant	significant	ADJ
american_scientific_journal-1936	131	10	advantages	advantage	NOUN
american_scientific_journal-1936	131	11	whenever	whenever	SCONJ
american_scientific_journal-1936	131	12	the	the	DET
american_scientific_journal-1936	131	13	time	time	NOUN
american_scientific_journal-1936	131	14	–	–	PUNCT
american_scientific_journal-1936	131	15	accurate	accurate	ADJ
american_scientific_journal-1936	131	16	solutions	solution	NOUN
american_scientific_journal-1936	131	17	play	play	VERB
american_scientific_journal-1936	131	18	an	an	DET
american_scientific_journal-1936	131	19	important	important	ADJ
american_scientific_journal-1936	131	20	role	role	NOUN
american_scientific_journal-1936	131	21	.	.	PUNCT
american_scientific_journal-1936	132	1	the	the	DET
american_scientific_journal-1936	132	2	crank	crank	NOUN
american_scientific_journal-1936	132	3	–	–	PUNCT
american_scientific_journal-1936	132	4	nicolson	nicolson	PROPN
american_scientific_journal-1936	132	5	scheme	scheme	NOUN
american_scientific_journal-1936	132	6	,	,	PUNCT
american_scientific_journal-1936	132	7	like	like	ADP
american_scientific_journal-1936	132	8	btcs	btcs	NOUN
american_scientific_journal-1936	132	9	,	,	PUNCT
american_scientific_journal-1936	132	10	is	be	AUX
american_scientific_journal-1936	132	11	also	also	ADV
american_scientific_journal-1936	132	12	implicit	implicit	ADJ
american_scientific_journal-1936	132	13	and	and	CCONJ
american_scientific_journal-1936	132	14	unconditionally	unconditionally	ADV
american_scientific_journal-1936	132	15	stable	stable	ADJ
american_scientific_journal-1936	132	16	.	.	PUNCT
american_scientific_journal-1936	133	1	the	the	DET
american_scientific_journal-1936	133	2	crank	crank	NOUN
american_scientific_journal-1936	133	3	–	–	PUNCT
american_scientific_journal-1936	133	4	nicolson	nicolson	PROPN
american_scientific_journal-1936	133	5	scheme	scheme	NOUN
american_scientific_journal-1936	133	6	approximates	approximate	VERB
american_scientific_journal-1936	133	7	equation	equation	NOUN
american_scientific_journal-1936	133	8	(	(	PUNCT
american_scientific_journal-1936	133	9	3	3	X
american_scientific_journal-1936	133	10	)	)	PUNCT
american_scientific_journal-1936	133	11	using	use	VERB
american_scientific_journal-1936	133	12	central	central	ADJ
american_scientific_journal-1936	133	13	differences	difference	NOUN
american_scientific_journal-1936	133	14	of	of	ADP
american_scientific_journal-1936	133	15	time	time	NOUN
american_scientific_journal-1936	133	16	intervals	interval	NOUN
american_scientific_journal-1936	133	17	.	.	PUNCT
american_scientific_journal-1936	134	1	the	the	DET
american_scientific_journal-1936	134	2	spatial	spatial	ADJ
american_scientific_journal-1936	134	3	derivatives	derivative	NOUN
american_scientific_journal-1936	134	4	are	be	AUX
american_scientific_journal-1936	134	5	estimated	estimate	VERB
american_scientific_journal-1936	134	6	by	by	ADP
american_scientific_journal-1936	134	7	the	the	DET
american_scientific_journal-1936	134	8	average	average	NOUN
american_scientific_journal-1936	134	9	of	of	ADP
american_scientific_journal-1936	134	10	their	their	PRON
american_scientific_journal-1936	134	11	values	value	NOUN
american_scientific_journal-1936	134	12	at	at	ADP
american_scientific_journal-1936	134	13	time	time	NOUN
american_scientific_journal-1936	134	14	steps	step	NOUN
american_scientific_journal-1936	134	15	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-1936	134	16	and	and	CCONJ
american_scientific_journal-1936	134	17	𝑛𝑛	𝑛𝑛	VERB
american_scientific_journal-1936	134	18	+	+	CCONJ
american_scientific_journal-1936	134	19	1	1	NUM
american_scientific_journal-1936	134	20	as	as	ADP
american_scientific_journal-1936	134	21	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	NOUN
american_scientific_journal-1936	134	22	𝑛𝑛+1−	𝑛𝑛+1−	PROPN
american_scientific_journal-1936	134	23	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	NOUN
american_scientific_journal-1936	134	24	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-1936	134	25	∆𝜕𝜕	∆𝜕𝜕	NOUN
american_scientific_journal-1936	134	26	=	=	SYM
american_scientific_journal-1936	134	27	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	134	28	2	2	NUM
american_scientific_journal-1936	134	29	�	�	PROPN
american_scientific_journal-1936	134	30	𝜕𝜕𝑖𝑖+1	𝜕𝜕𝑖𝑖+1	NUM
american_scientific_journal-1936	134	31	𝑛𝑛+1−2𝜕𝜕𝑖𝑖	𝑛𝑛+1−2𝜕𝜕𝑖𝑖	PROPN
american_scientific_journal-1936	134	32	𝑛𝑛+1	𝑛𝑛+1	ADP
american_scientific_journal-1936	134	33	+	+	PROPN
american_scientific_journal-1936	134	34	𝜕𝜕𝑖𝑖−1	𝜕𝜕𝑖𝑖−1	PRON
american_scientific_journal-1936	134	35	𝑛𝑛+1	𝑛𝑛+1	X
american_scientific_journal-1936	134	36	(	(	PUNCT
american_scientific_journal-1936	134	37	∆𝑥𝑥)2	∆𝑥𝑥)2	PROPN
american_scientific_journal-1936	134	38	+	+	NUM
american_scientific_journal-1936	134	39	𝜕𝜕𝑖𝑖+1	𝜕𝜕𝑖𝑖+1	NUM
american_scientific_journal-1936	134	40	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-1936	134	41	−2𝜕𝜕𝑖𝑖	−2𝜕𝜕𝑖𝑖	ADP
american_scientific_journal-1936	134	42	𝑛𝑛+	𝑛𝑛+	NOUN
american_scientific_journal-1936	134	43	𝜕𝜕𝑖𝑖−1	𝜕𝜕𝑖𝑖−1	DET
american_scientific_journal-1936	134	44	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-1936	134	45	(	(	PUNCT
american_scientific_journal-1936	134	46	∆𝑥𝑥)2	∆𝑥𝑥)2	PUNCT
american_scientific_journal-1936	134	47	�	�	PROPN
american_scientific_journal-1936	134	48	+	+	CCONJ
american_scientific_journal-1936	134	49	𝑂𝑂((∆𝑡𝑡)2	𝑂𝑂((∆𝑡𝑡)2	PROPN
american_scientific_journal-1936	134	50	)	)	PUNCT
american_scientific_journal-1936	135	1	+	+	CCONJ
american_scientific_journal-1936	135	2	𝑂𝑂((∆𝑥𝑥)2	𝑂𝑂((∆𝑥𝑥)2	X
american_scientific_journal-1936	135	3	)	)	PUNCT
american_scientific_journal-1936	135	4	(	(	PUNCT
american_scientific_journal-1936	135	5	15	15	NUM
american_scientific_journal-1936	135	6	)	)	PUNCT
american_scientific_journal-1936	135	7	the	the	DET
american_scientific_journal-1936	135	8	crank	crank	NOUN
american_scientific_journal-1936	135	9	–	–	PUNCT
american_scientific_journal-1936	135	10	nicolson	nicolson	PROPN
american_scientific_journal-1936	135	11	scheme	scheme	NOUN
american_scientific_journal-1936	135	12	has	have	VERB
american_scientific_journal-1936	135	13	a	a	DET
american_scientific_journal-1936	135	14	truncation	truncation	NOUN
american_scientific_journal-1936	135	15	error	error	NOUN
american_scientific_journal-1936	135	16	of	of	ADP
american_scientific_journal-1936	135	17	temporal	temporal	ADJ
american_scientific_journal-1936	135	18	order	order	NOUN
american_scientific_journal-1936	135	19	𝑂𝑂(∆𝑡𝑡2	𝑂𝑂(∆𝑡𝑡2	PUNCT
american_scientific_journal-1936	135	20	)	)	PUNCT
american_scientific_journal-1936	135	21	and	and	CCONJ
american_scientific_journal-1936	135	22	spatial	spatial	ADJ
american_scientific_journal-1936	135	23	order	order	NOUN
american_scientific_journal-1936	135	24	𝑂𝑂(∆𝑥𝑥2	𝑂𝑂(∆𝑥𝑥2	NOUN
american_scientific_journal-1936	135	25	)	)	PUNCT
american_scientific_journal-1936	135	26	.	.	PUNCT
american_scientific_journal-1936	136	1	drop	drop	VERB
american_scientific_journal-1936	136	2	the	the	DET
american_scientific_journal-1936	136	3	truncation	truncation	NOUN
american_scientific_journal-1936	136	4	error	error	NOUN
american_scientific_journal-1936	136	5	terms	term	NOUN
american_scientific_journal-1936	136	6	from	from	ADP
american_scientific_journal-1936	136	7	(	(	PUNCT
american_scientific_journal-1936	136	8	15	15	NUM
american_scientific_journal-1936	136	9	)	)	PUNCT
american_scientific_journal-1936	136	10	and	and	CCONJ
american_scientific_journal-1936	136	11	rearranging	rearrange	VERB
american_scientific_journal-1936	136	12	the	the	DET
american_scientific_journal-1936	136	13	terms	term	NOUN
american_scientific_journal-1936	136	14	so	so	SCONJ
american_scientific_journal-1936	136	15	that	that	SCONJ
american_scientific_journal-1936	136	16	values	value	NOUN
american_scientific_journal-1936	136	17	of	of	ADP
american_scientific_journal-1936	136	18	𝑢𝑢	𝑢𝑢	PRON
american_scientific_journal-1936	136	19	at	at	ADP
american_scientific_journal-1936	136	20	time	time	NOUN
american_scientific_journal-1936	136	21	𝑛𝑛	𝑛𝑛	PRON
american_scientific_journal-1936	136	22	are	be	AUX
american_scientific_journal-1936	136	23	on	on	ADP
american_scientific_journal-1936	136	24	the	the	DET
american_scientific_journal-1936	136	25	left	left	NOUN
american_scientific_journal-1936	136	26	and	and	CCONJ
american_scientific_journal-1936	136	27	values	value	NOUN
american_scientific_journal-1936	136	28	of	of	ADP
american_scientific_journal-1936	136	29	𝑢𝑢	𝑢𝑢	PRON
american_scientific_journal-1936	136	30	at	at	ADP
american_scientific_journal-1936	136	31	time	time	NOUN
american_scientific_journal-1936	136	32	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-1936	136	33	+	+	CCONJ
american_scientific_journal-1936	136	34	1	1	NUM
american_scientific_journal-1936	136	35	are	be	AUX
american_scientific_journal-1936	136	36	on	on	ADP
american_scientific_journal-1936	136	37	the	the	DET
american_scientific_journal-1936	136	38	right	right	NOUN
american_scientific_journal-1936	136	39	gives	give	VERB
american_scientific_journal-1936	136	40	american	american	ADJ
american_scientific_journal-1936	136	41	scientific	scientific	ADJ
american_scientific_journal-1936	136	42	research	research	NOUN
american_scientific_journal-1936	136	43	journal	journal	NOUN
american_scientific_journal-1936	136	44	for	for	ADP
american_scientific_journal-1936	136	45	engineering	engineering	NOUN
american_scientific_journal-1936	136	46	,	,	PUNCT
american_scientific_journal-1936	136	47	technology	technology	NOUN
american_scientific_journal-1936	136	48	,	,	PUNCT
american_scientific_journal-1936	136	49	and	and	CCONJ
american_scientific_journal-1936	136	50	sciences	science	NOUN
american_scientific_journal-1936	136	51	(	(	PUNCT
american_scientific_journal-1936	136	52	asrjets	asrjet	NOUN
american_scientific_journal-1936	136	53	)	)	PUNCT
american_scientific_journal-1936	136	54	(	(	PUNCT
american_scientific_journal-1936	136	55	2016	2016	NUM
american_scientific_journal-1936	136	56	)	)	PUNCT
american_scientific_journal-1936	136	57	volume	volume	NOUN
american_scientific_journal-1936	136	58	26	26	NUM
american_scientific_journal-1936	136	59	,	,	PUNCT
american_scientific_journal-1936	136	60	no	no	DET
american_scientific_journal-1936	136	61	3	3	NUM
american_scientific_journal-1936	136	62	,	,	PUNCT
american_scientific_journal-1936	136	63	pp	pp	ADV
american_scientific_journal-1936	136	64	140	140	NUM
american_scientific_journal-1936	136	65	-	-	SYM
american_scientific_journal-1936	136	66	154	154	NUM
american_scientific_journal-1936	136	67	146	146	NUM
american_scientific_journal-1936	136	68	𝑟𝑟𝑢𝑢𝑖𝑖−1𝑛𝑛	𝑟𝑟𝑢𝑢𝑖𝑖−1𝑛𝑛	NOUN
american_scientific_journal-1936	137	1	+	+	CCONJ
american_scientific_journal-1936	137	2	(	(	PUNCT
american_scientific_journal-1936	137	3	2	2	NUM
american_scientific_journal-1936	137	4	−	−	NUM
american_scientific_journal-1936	137	5	2𝑟𝑟)𝑢𝑢𝑖𝑖𝑛𝑛	2𝑟𝑟)𝑢𝑢𝑖𝑖𝑛𝑛	NUM
american_scientific_journal-1936	137	6	+	+	CCONJ
american_scientific_journal-1936	137	7	𝑟𝑟𝑢𝑢𝑖𝑖+1𝑛𝑛	𝑟𝑟𝑢𝑢𝑖𝑖+1𝑛𝑛	NOUN
american_scientific_journal-1936	137	8	=	=	SYM
american_scientific_journal-1936	137	9	−𝑟𝑟𝑢𝑢𝑖𝑖−1𝑛𝑛+1	−𝑟𝑟𝑢𝑢𝑖𝑖−1𝑛𝑛+1	PROPN
american_scientific_journal-1936	137	10	+	+	CCONJ
american_scientific_journal-1936	137	11	(	(	PUNCT
american_scientific_journal-1936	137	12	2	2	NUM
american_scientific_journal-1936	137	13	+	+	NUM
american_scientific_journal-1936	137	14	2𝑟𝑟)𝑢𝑢𝑖𝑖𝑛𝑛+1	2𝑟𝑟)𝑢𝑢𝑖𝑖𝑛𝑛+1	NUM
american_scientific_journal-1936	137	15	−	−	NOUN
american_scientific_journal-1936	137	16	𝑟𝑟𝑢𝑢𝑖𝑖+1𝑛𝑛+1	𝑟𝑟𝑢𝑢𝑖𝑖+1𝑛𝑛+1	NOUN
american_scientific_journal-1936	137	17	(	(	PUNCT
american_scientific_journal-1936	137	18	16	16	NUM
american_scientific_journal-1936	137	19	)	)	PUNCT
american_scientific_journal-1936	137	20	the	the	DET
american_scientific_journal-1936	137	21	left	left	ADJ
american_scientific_journal-1936	137	22	hand	hand	NOUN
american_scientific_journal-1936	137	23	side	side	NOUN
american_scientific_journal-1936	137	24	of	of	ADP
american_scientific_journal-1936	137	25	(	(	PUNCT
american_scientific_journal-1936	137	26	16	16	NUM
american_scientific_journal-1936	137	27	)	)	PUNCT
american_scientific_journal-1936	137	28	contains	contain	VERB
american_scientific_journal-1936	137	29	three	three	NUM
american_scientific_journal-1936	137	30	known	know	VERB
american_scientific_journal-1936	137	31	values	value	NOUN
american_scientific_journal-1936	137	32	and	and	CCONJ
american_scientific_journal-1936	137	33	the	the	DET
american_scientific_journal-1936	137	34	right	right	ADJ
american_scientific_journal-1936	137	35	hand	hand	NOUN
american_scientific_journal-1936	137	36	contains	contain	VERB
american_scientific_journal-1936	137	37	three	three	NUM
american_scientific_journal-1936	137	38	unknowns	unknown	NOUN
american_scientific_journal-1936	137	39	.	.	PUNCT
american_scientific_journal-1936	138	1	this	this	DET
american_scientific_journal-1936	138	2	scheme	scheme	NOUN
american_scientific_journal-1936	138	3	generates	generate	VERB
american_scientific_journal-1936	138	4	a	a	DET
american_scientific_journal-1936	138	5	set	set	NOUN
american_scientific_journal-1936	138	6	of	of	ADP
american_scientific_journal-1936	138	7	(	(	PUNCT
american_scientific_journal-1936	138	8	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-1936	138	9	−	−	PROPN
american_scientific_journal-1936	138	10	1	1	NUM
american_scientific_journal-1936	138	11	)	)	PUNCT
american_scientific_journal-1936	138	12	linear	linear	ADJ
american_scientific_journal-1936	138	13	equation	equation	NOUN
american_scientific_journal-1936	138	14	and	and	CCONJ
american_scientific_journal-1936	138	15	those	those	PRON
american_scientific_journal-1936	138	16	have	have	VERB
american_scientific_journal-1936	138	17	to	to	PART
american_scientific_journal-1936	138	18	be	be	AUX
american_scientific_journal-1936	138	19	solved	solve	VERB
american_scientific_journal-1936	138	20	at	at	ADP
american_scientific_journal-1936	138	21	each	each	DET
american_scientific_journal-1936	138	22	time	time	NOUN
american_scientific_journal-1936	138	23	level	level	NOUN
american_scientific_journal-1936	138	24	.	.	PUNCT
american_scientific_journal-1936	139	1	applying	apply	VERB
american_scientific_journal-1936	139	2	(	(	PUNCT
american_scientific_journal-1936	139	3	16	16	NUM
american_scientific_journal-1936	139	4	)	)	PUNCT
american_scientific_journal-1936	139	5	for	for	ADP
american_scientific_journal-1936	139	6	all	all	DET
american_scientific_journal-1936	139	7	the	the	DET
american_scientific_journal-1936	139	8	internal	internal	ADJ
american_scientific_journal-1936	139	9	mesh	mesh	NOUN
american_scientific_journal-1936	139	10	points	point	NOUN
american_scientific_journal-1936	139	11	at	at	ADP
american_scientific_journal-1936	139	12	𝑖𝑖	𝑖𝑖	NOUN
american_scientific_journal-1936	139	13	=	=	NOUN
american_scientific_journal-1936	139	14	1,2,3	1,2,3	NUM
american_scientific_journal-1936	139	15	,	,	PUNCT
american_scientific_journal-1936	139	16	.	.	PUNCT
american_scientific_journal-1936	139	17	.	.	PUNCT
american_scientific_journal-1936	139	18	.	.	PUNCT
american_scientific_journal-1936	140	1	,	,	PUNCT
american_scientific_journal-1936	140	2	𝑁𝑁	𝑁𝑁	PROPN
american_scientific_journal-1936	140	3	−	−	PROPN
american_scientific_journal-1936	140	4	1	1	NUM
american_scientific_journal-1936	140	5	and	and	CCONJ
american_scientific_journal-1936	140	6	using	use	VERB
american_scientific_journal-1936	140	7	the	the	DET
american_scientific_journal-1936	140	8	boundary	boundary	ADJ
american_scientific_journal-1936	140	9	conditions	condition	NOUN
american_scientific_journal-1936	140	10	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	140	11	=	=	SYM
american_scientific_journal-1936	140	12	0	0	NUM
american_scientific_journal-1936	140	13	and	and	CCONJ
american_scientific_journal-1936	140	14	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	140	15	=	=	PUNCT
american_scientific_journal-1936	140	16	𝐿𝐿	𝐿𝐿	PROPN
american_scientific_journal-1936	140	17	we	we	PRON
american_scientific_journal-1936	140	18	obtain	obtain	VERB
american_scientific_journal-1936	140	19	a	a	DET
american_scientific_journal-1936	140	20	tridiagonal	tridiagonal	ADJ
american_scientific_journal-1936	140	21	set	set	NOUN
american_scientific_journal-1936	140	22	of	of	ADP
american_scientific_journal-1936	140	23	linear	linear	PROPN
american_scientific_journal-1936	140	24	algebraic	algebraic	ADJ
american_scientific_journal-1936	140	25	equations	equation	NOUN
american_scientific_journal-1936	140	26	.	.	PUNCT
american_scientific_journal-1936	141	1	these	these	DET
american_scientific_journal-1936	141	2	equations	equation	NOUN
american_scientific_journal-1936	141	3	have	have	VERB
american_scientific_journal-1936	141	4	to	to	PART
american_scientific_journal-1936	141	5	be	be	AUX
american_scientific_journal-1936	141	6	solved	solve	VERB
american_scientific_journal-1936	141	7	at	at	ADP
american_scientific_journal-1936	141	8	each	each	DET
american_scientific_journal-1936	141	9	time	time	NOUN
american_scientific_journal-1936	141	10	level	level	NOUN
american_scientific_journal-1936	141	11	.	.	PUNCT
american_scientific_journal-1936	142	1	the	the	DET
american_scientific_journal-1936	142	2	compact	compact	ADJ
american_scientific_journal-1936	142	3	form	form	NOUN
american_scientific_journal-1936	142	4	of	of	ADP
american_scientific_journal-1936	142	5	such	such	ADJ
american_scientific_journal-1936	142	6	tridiagonal	tridiagonal	ADJ
american_scientific_journal-1936	142	7	set	set	NOUN
american_scientific_journal-1936	142	8	of	of	ADP
american_scientific_journal-1936	142	9	linear	linear	PROPN
american_scientific_journal-1936	142	10	algebraic	algebraic	ADJ
american_scientific_journal-1936	142	11	equations	equation	NOUN
american_scientific_journal-1936	142	12	can	can	AUX
american_scientific_journal-1936	142	13	be	be	AUX
american_scientific_journal-1936	142	14	written	write	VERB
american_scientific_journal-1936	142	15	as	as	ADP
american_scientific_journal-1936	142	16	𝑢𝑢𝑛𝑛+1	𝑢𝑢𝑛𝑛+1	NOUN
american_scientific_journal-1936	142	17	=	=	PUNCT
american_scientific_journal-1936	142	18	(	(	PUNCT
american_scientific_journal-1936	142	19	2𝐼𝐼	2𝐼𝐼	NUM
american_scientific_journal-1936	142	20	−	−	NOUN
american_scientific_journal-1936	142	21	𝑟𝑟𝑟𝑟)−1(2𝐼𝐼	𝑟𝑟𝑟𝑟)−1(2𝐼𝐼	NOUN
american_scientific_journal-1936	142	22	+	+	CCONJ
american_scientific_journal-1936	142	23	𝑟𝑟𝑟𝑟)𝑢𝑢𝑛𝑛	𝑟𝑟𝑟𝑟)𝑢𝑢𝑛𝑛	PROPN
american_scientific_journal-1936	142	24	(	(	PUNCT
american_scientific_journal-1936	142	25	17	17	NUM
american_scientific_journal-1936	142	26	)	)	PUNCT
american_scientific_journal-1936	142	27	the	the	DET
american_scientific_journal-1936	142	28	system	system	NOUN
american_scientific_journal-1936	142	29	of	of	ADP
american_scientific_journal-1936	142	30	equations	equation	NOUN
american_scientific_journal-1936	142	31	(	(	PUNCT
american_scientific_journal-1936	142	32	17	17	NUM
american_scientific_journal-1936	142	33	)	)	PUNCT
american_scientific_journal-1936	142	34	can	can	AUX
american_scientific_journal-1936	142	35	be	be	AUX
american_scientific_journal-1936	142	36	solved	solve	VERB
american_scientific_journal-1936	142	37	very	very	ADV
american_scientific_journal-1936	142	38	efficiently	efficiently	ADV
american_scientific_journal-1936	142	39	.	.	PUNCT
american_scientific_journal-1936	143	1	also	also	ADV
american_scientific_journal-1936	143	2	its	its	PRON
american_scientific_journal-1936	143	3	unconditional	unconditional	ADJ
american_scientific_journal-1936	143	4	stability	stability	NOUN
american_scientific_journal-1936	143	5	can	can	AUX
american_scientific_journal-1936	143	6	be	be	AUX
american_scientific_journal-1936	143	7	shown	show	VERB
american_scientific_journal-1936	143	8	by	by	ADP
american_scientific_journal-1936	143	9	substituting	substitute	VERB
american_scientific_journal-1936	143	10	(	(	PUNCT
american_scientific_journal-1936	143	11	11	11	NUM
american_scientific_journal-1936	143	12	)	)	PUNCT
american_scientific_journal-1936	143	13	into	into	ADP
american_scientific_journal-1936	143	14	(	(	PUNCT
american_scientific_journal-1936	143	15	16	16	NUM
american_scientific_journal-1936	143	16	)	)	PUNCT
american_scientific_journal-1936	143	17	.	.	PUNCT
american_scientific_journal-1936	144	1	thus	thus	ADV
american_scientific_journal-1936	144	2	,	,	PUNCT
american_scientific_journal-1936	144	3	2𝜆𝜆	2𝜆𝜆	ADJ
american_scientific_journal-1936	144	4	�	�	NOUN
american_scientific_journal-1936	144	5	1	1	NUM
american_scientific_journal-1936	144	6	+	+	CCONJ
american_scientific_journal-1936	144	7	𝑟𝑟	𝑟𝑟	NUM
american_scientific_journal-1936	144	8	�	�	NOUN
american_scientific_journal-1936	144	9	1	1	NUM
american_scientific_journal-1936	144	10	−	−	PROPN
american_scientific_journal-1936	144	11	cos	cos	PROPN
american_scientific_journal-1936	144	12	�	�	PROPN
american_scientific_journal-1936	144	13	𝑛𝑛	𝑛𝑛	PROPN
american_scientific_journal-1936	144	14	𝑝𝑝	𝑝𝑝	PROPN
american_scientific_journal-1936	144	15	�	�	PROPN
american_scientific_journal-1936	144	16	�	�	PROPN
american_scientific_journal-1936	144	17	�	�	PROPN
american_scientific_journal-1936	144	18	=	=	SYM
american_scientific_journal-1936	144	19	2	2	NUM
american_scientific_journal-1936	144	20	�	�	PROPN
american_scientific_journal-1936	144	21	1	1	NUM
american_scientific_journal-1936	144	22	−	−	PROPN
american_scientific_journal-1936	144	23	𝑟𝑟	𝑟𝑟	NUM
american_scientific_journal-1936	144	24	�	�	PROPN
american_scientific_journal-1936	144	25	1	1	NUM
american_scientific_journal-1936	144	26	−	−	PROPN
american_scientific_journal-1936	144	27	cos	cos	PROPN
american_scientific_journal-1936	144	28	�	�	PROPN
american_scientific_journal-1936	144	29	𝑛𝑛	𝑛𝑛	PROPN
american_scientific_journal-1936	144	30	𝑝𝑝	𝑝𝑝	PROPN
american_scientific_journal-1936	144	31	�	�	PROPN
american_scientific_journal-1936	144	32	�	�	PROPN
american_scientific_journal-1936	144	33	�	�	PROPN
american_scientific_journal-1936	144	34	,	,	PUNCT
american_scientific_journal-1936	144	35	𝜆𝜆	𝜆𝜆	NOUN
american_scientific_journal-1936	144	36	=	=	SYM
american_scientific_journal-1936	145	1	1	1	NUM
american_scientific_journal-1936	145	2	−	−	NOUN
american_scientific_journal-1936	145	3	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1936	145	4	�	�	PROPN
american_scientific_journal-1936	145	5	1	1	NUM
american_scientific_journal-1936	145	6	−	−	PROPN
american_scientific_journal-1936	145	7	cos	cos	PROPN
american_scientific_journal-1936	145	8	�	�	PROPN
american_scientific_journal-1936	145	9	𝜋𝜋𝑝𝑝	𝜋𝜋𝑝𝑝	PROPN
american_scientific_journal-1936	145	10	�	�	PROPN
american_scientific_journal-1936	145	11	�	�	PROPN
american_scientific_journal-1936	145	12	1	1	NUM
american_scientific_journal-1936	145	13	+	+	CCONJ
american_scientific_journal-1936	145	14	𝑟𝑟	𝑟𝑟	PROPN
american_scientific_journal-1936	145	15	�	�	PROPN
american_scientific_journal-1936	145	16	1	1	NUM
american_scientific_journal-1936	145	17	−cos	−co	NOUN
american_scientific_journal-1936	145	18	�	�	PROPN
american_scientific_journal-1936	145	19	𝜋𝜋𝑝𝑝	𝜋𝜋𝑝𝑝	PROPN
american_scientific_journal-1936	145	20	�	�	PROPN
american_scientific_journal-1936	145	21	�	�	PROPN
american_scientific_journal-1936	145	22	|𝜆𝜆|	|𝜆𝜆|	PROPN
american_scientific_journal-1936	145	23	≤	≤	NOUN
american_scientific_journal-1936	145	24	1	1	NUM
american_scientific_journal-1936	145	25	the	the	DET
american_scientific_journal-1936	145	26	truncation	truncation	NOUN
american_scientific_journal-1936	145	27	error	error	NOUN
american_scientific_journal-1936	145	28	𝑇𝑇𝑖𝑖,𝑛𝑛	𝑇𝑇𝑖𝑖,𝑛𝑛	VERB
american_scientific_journal-1936	145	29	for	for	ADP
american_scientific_journal-1936	145	30	the	the	DET
american_scientific_journal-1936	145	31	crank	crank	NOUN
american_scientific_journal-1936	145	32	–	–	PUNCT
american_scientific_journal-1936	145	33	nicolson	nicolson	PROPN
american_scientific_journal-1936	145	34	solution	solution	NOUN
american_scientific_journal-1936	145	35	of	of	ADP
american_scientific_journal-1936	145	36	the	the	DET
american_scientific_journal-1936	145	37	diffusion	diffusion	NOUN
american_scientific_journal-1936	145	38	equation	equation	NOUN
american_scientific_journal-1936	145	39	is	be	AUX
american_scientific_journal-1936	145	40	[	[	X
american_scientific_journal-1936	145	41	14	14	NUM
american_scientific_journal-1936	145	42	]	]	X
american_scientific_journal-1936	146	1	𝑇𝑇𝑖𝑖,𝑛𝑛	𝑇𝑇𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	146	2	=	=	SYM
american_scientific_journal-1936	146	3	�	�	PROPN
american_scientific_journal-1936	146	4	𝜕𝜕𝑢𝑢	𝜕𝜕𝑢𝑢	NOUN
american_scientific_journal-1936	146	5	𝜕𝜕𝑡𝑡	𝜕𝜕𝑡𝑡	PROPN
american_scientific_journal-1936	147	1	−	−	PROPN
american_scientific_journal-1936	147	2	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	147	3	𝜕𝜕2𝑢𝑢	𝜕𝜕2𝑢𝑢	PROPN
american_scientific_journal-1936	147	4	𝜕𝜕𝑥𝑥2	𝜕𝜕𝑥𝑥2	ADP
american_scientific_journal-1936	147	5	�	�	PROPN
american_scientific_journal-1936	147	6	𝑖𝑖,𝑛𝑛	𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	147	7	+	+	CCONJ
american_scientific_journal-1936	147	8	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	147	9	2	2	NUM
american_scientific_journal-1936	147	10	𝜕𝜕	𝜕𝜕	X
american_scientific_journal-1936	147	11	𝜕𝜕𝑡𝑡	𝜕𝜕𝑡𝑡	NUM
american_scientific_journal-1936	147	12	�	�	PROPN
american_scientific_journal-1936	147	13	𝜕𝜕𝑢𝑢	𝜕𝜕𝑢𝑢	NOUN
american_scientific_journal-1936	147	14	𝜕𝜕𝑡𝑡	𝜕𝜕𝑡𝑡	PROPN
american_scientific_journal-1936	148	1	−	−	PROPN
american_scientific_journal-1936	148	2	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	148	3	𝜕𝜕2𝑢𝑢	𝜕𝜕2𝑢𝑢	PROPN
american_scientific_journal-1936	148	4	𝜕𝜕𝑥𝑥2	𝜕𝜕𝑥𝑥2	ADP
american_scientific_journal-1936	148	5	�	�	PROPN
american_scientific_journal-1936	148	6	𝑖𝑖,𝑛𝑛	𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	148	7	+	+	CCONJ
american_scientific_journal-1936	148	8	(	(	PUNCT
american_scientific_journal-1936	148	9	∆𝑡𝑡)2	∆𝑡𝑡)2	PROPN
american_scientific_journal-1936	148	10	6	6	NUM
american_scientific_journal-1936	148	11	�	�	PROPN
american_scientific_journal-1936	148	12	𝜕𝜕3𝑢𝑢	𝜕𝜕3𝑢𝑢	NOUN
american_scientific_journal-1936	148	13	𝜕𝜕𝑡𝑡3	𝜕𝜕𝑡𝑡3	VERB
american_scientific_journal-1936	148	14	�	�	PROPN
american_scientific_journal-1936	148	15	𝑖𝑖,𝑛𝑛	𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	149	1	−	−	PROPN
american_scientific_journal-1936	149	2	1	1	NUM
american_scientific_journal-1936	149	3	12	12	NUM
american_scientific_journal-1936	149	4	(	(	PUNCT
american_scientific_journal-1936	149	5	∆𝑥𝑥)2	∆𝑥𝑥)2	PUNCT
american_scientific_journal-1936	149	6	�	�	PROPN
american_scientific_journal-1936	149	7	𝜕𝜕4𝑢𝑢	𝜕𝜕4𝑢𝑢	PROPN
american_scientific_journal-1936	149	8	𝜕𝜕𝑥𝑥4	𝜕𝜕𝑥𝑥4	PROPN
american_scientific_journal-1936	149	9	�	�	PROPN
american_scientific_journal-1936	149	10	𝑖𝑖,𝑛𝑛	𝑖𝑖,𝑛𝑛	PROPN
american_scientific_journal-1936	149	11	+	+	X
american_scientific_journal-1936	149	12	𝑂𝑂((∆𝑡𝑡)3	𝑂𝑂((∆𝑡𝑡)3	ADJ
american_scientific_journal-1936	149	13	)	)	PUNCT
american_scientific_journal-1936	150	1	+	+	NUM
american_scientific_journal-1936	150	2	𝑂𝑂((∆𝑥𝑥)3	𝑂𝑂((∆𝑥𝑥)3	NOUN
american_scientific_journal-1936	150	3	)	)	PUNCT
american_scientific_journal-1936	150	4	.	.	PUNCT
american_scientific_journal-1936	151	1	it	it	PRON
american_scientific_journal-1936	151	2	can	can	AUX
american_scientific_journal-1936	151	3	be	be	AUX
american_scientific_journal-1936	151	4	observed	observe	VERB
american_scientific_journal-1936	151	5	that	that	SCONJ
american_scientific_journal-1936	151	6	the	the	DET
american_scientific_journal-1936	151	7	truncation	truncation	NOUN
american_scientific_journal-1936	151	8	error	error	NOUN
american_scientific_journal-1936	151	9	𝑇𝑇𝑖𝑖,𝑛𝑛	𝑇𝑇𝑖𝑖,𝑛𝑛	NOUN
american_scientific_journal-1936	151	10	goes	go	VERB
american_scientific_journal-1936	151	11	to	to	ADP
american_scientific_journal-1936	151	12	zero	zero	NUM
american_scientific_journal-1936	151	13	as	as	SCONJ
american_scientific_journal-1936	151	14	both	both	CCONJ
american_scientific_journal-1936	151	15	temporal	temporal	ADJ
american_scientific_journal-1936	151	16	and	and	CCONJ
american_scientific_journal-1936	151	17	spatial	spatial	ADJ
american_scientific_journal-1936	151	18	intervals	interval	NOUN
american_scientific_journal-1936	151	19	go	go	VERB
american_scientific_journal-1936	151	20	to	to	ADP
american_scientific_journal-1936	151	21	zero	zero	NUM
american_scientific_journal-1936	151	22	.	.	PUNCT
american_scientific_journal-1936	152	1	that	that	PRON
american_scientific_journal-1936	152	2	is	be	AUX
american_scientific_journal-1936	152	3	𝑇𝑇𝑖𝑖,𝑛𝑛	𝑇𝑇𝑖𝑖,𝑛𝑛	X
american_scientific_journal-1936	152	4	→	→	SYM
american_scientific_journal-1936	152	5	0	0	NUM
american_scientific_journal-1936	152	6	as	as	ADP
american_scientific_journal-1936	152	7	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	152	8	→	→	SYM
american_scientific_journal-1936	152	9	0	0	NUM
american_scientific_journal-1936	152	10	and	and	CCONJ
american_scientific_journal-1936	152	11	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	152	12	→	→	SYM
american_scientific_journal-1936	152	13	0	0	X
american_scientific_journal-1936	152	14	.	.	PUNCT
american_scientific_journal-1936	153	1	it	it	PRON
american_scientific_journal-1936	153	2	shows	show	VERB
american_scientific_journal-1936	153	3	that	that	SCONJ
american_scientific_journal-1936	153	4	the	the	DET
american_scientific_journal-1936	153	5	crank	crank	NOUN
american_scientific_journal-1936	153	6	–	–	PUNCT
american_scientific_journal-1936	153	7	nicolson	nicolson	PROPN
american_scientific_journal-1936	153	8	scheme	scheme	NOUN
american_scientific_journal-1936	153	9	is	be	AUX
american_scientific_journal-1936	153	10	consistent	consistent	ADJ
american_scientific_journal-1936	153	11	with	with	ADP
american_scientific_journal-1936	153	12	partial	partial	ADJ
american_scientific_journal-1936	153	13	differential	differential	NOUN
american_scientific_journal-1936	153	14	equation	equation	NOUN
american_scientific_journal-1936	153	15	(	(	PUNCT
american_scientific_journal-1936	153	16	3	3	NUM
american_scientific_journal-1936	153	17	)	)	PUNCT
american_scientific_journal-1936	153	18	.	.	PUNCT
american_scientific_journal-1936	154	1	3	3	X
american_scientific_journal-1936	154	2	.	.	X
american_scientific_journal-1936	154	3	numerical	numerical	ADJ
american_scientific_journal-1936	154	4	results	result	NOUN
american_scientific_journal-1936	154	5	consider	consider	VERB
american_scientific_journal-1936	154	6	the	the	DET
american_scientific_journal-1936	154	7	special	special	ADJ
american_scientific_journal-1936	154	8	case	case	NOUN
american_scientific_journal-1936	154	9	of	of	ADP
american_scientific_journal-1936	154	10	the	the	DET
american_scientific_journal-1936	154	11	diffusion	diffusion	NOUN
american_scientific_journal-1936	154	12	equation	equation	NOUN
american_scientific_journal-1936	154	13	(	(	PUNCT
american_scientific_journal-1936	154	14	3	3	NUM
american_scientific_journal-1936	154	15	)	)	PUNCT
american_scientific_journal-1936	154	16	with	with	ADP
american_scientific_journal-1936	154	17	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	154	18	=	=	NOUN
american_scientific_journal-1936	154	19	1	1	NUM
american_scientific_journal-1936	154	20	to	to	PART
american_scientific_journal-1936	154	21	obtain	obtain	VERB
american_scientific_journal-1936	154	22	𝜕𝜕𝑢𝑢	𝜕𝜕𝑢𝑢	PUNCT
american_scientific_journal-1936	154	23	𝜕𝜕𝑡𝑡⁄	𝜕𝜕𝑡𝑡⁄	PROPN
american_scientific_journal-1936	154	24	=	=	PUNCT
american_scientific_journal-1936	154	25	𝜕𝜕2𝑢𝑢	𝜕𝜕2𝑢𝑢	NOUN
american_scientific_journal-1936	154	26	𝜕𝜕𝑥𝑥2⁄	𝜕𝜕𝑥𝑥2⁄	PROPN
american_scientific_journal-1936	154	27	(	(	PUNCT
american_scientific_journal-1936	154	28	18	18	NUM
american_scientific_journal-1936	154	29	)	)	PUNCT
american_scientific_journal-1936	154	30	the	the	DET
american_scientific_journal-1936	154	31	numerical	numerical	ADJ
american_scientific_journal-1936	154	32	solutions	solution	NOUN
american_scientific_journal-1936	154	33	of	of	ADP
american_scientific_journal-1936	154	34	(	(	PUNCT
american_scientific_journal-1936	154	35	18	18	NUM
american_scientific_journal-1936	154	36	)	)	PUNCT
american_scientific_journal-1936	154	37	together	together	ADV
american_scientific_journal-1936	154	38	with	with	ADP
american_scientific_journal-1936	154	39	appropriate	appropriate	ADJ
american_scientific_journal-1936	154	40	initial	initial	ADJ
american_scientific_journal-1936	154	41	and	and	CCONJ
american_scientific_journal-1936	154	42	boundary	boundary	ADJ
american_scientific_journal-1936	154	43	conditions	condition	NOUN
american_scientific_journal-1936	154	44	are	be	AUX
american_scientific_journal-1936	154	45	drawn	draw	VERB
american_scientific_journal-1936	154	46	using	use	VERB
american_scientific_journal-1936	154	47	finite	finite	ADJ
american_scientific_journal-1936	154	48	difference	difference	NOUN
american_scientific_journal-1936	154	49	schemes	scheme	NOUN
american_scientific_journal-1936	154	50	(	(	PUNCT
american_scientific_journal-1936	154	51	i	i	NOUN
american_scientific_journal-1936	154	52	)	)	PUNCT
american_scientific_journal-1936	154	53	ftcs	ftcs	NOUN
american_scientific_journal-1936	154	54	(	(	PUNCT
american_scientific_journal-1936	154	55	ii	ii	NOUN
american_scientific_journal-1936	154	56	)	)	PUNCT
american_scientific_journal-1936	154	57	btcs	btcs	NOUN
american_scientific_journal-1936	154	58	and	and	CCONJ
american_scientific_journal-1936	154	59	(	(	PUNCT
american_scientific_journal-1936	154	60	iii	iii	NOUN
american_scientific_journal-1936	154	61	)	)	PUNCT
american_scientific_journal-1936	154	62	crank	crank	NOUN
american_scientific_journal-1936	154	63	–	–	PUNCT
american_scientific_journal-1936	154	64	nicolson	nicolson	PROPN
american_scientific_journal-1936	154	65	.	.	PUNCT
american_scientific_journal-1936	155	1	the	the	DET
american_scientific_journal-1936	155	2	details	detail	NOUN
american_scientific_journal-1936	155	3	are	be	AUX
american_scientific_journal-1936	155	4	given	give	VERB
american_scientific_journal-1936	155	5	in	in	ADP
american_scientific_journal-1936	155	6	what	what	PRON
american_scientific_journal-1936	155	7	follows	follow	VERB
american_scientific_journal-1936	155	8	from	from	ADP
american_scientific_journal-1936	155	9	sections	section	NOUN
american_scientific_journal-1936	155	10	3.1	3.1	NUM
american_scientific_journal-1936	155	11	to	to	ADP
american_scientific_journal-1936	155	12	3.3	3.3	NUM
american_scientific_journal-1936	155	13	.	.	PUNCT
american_scientific_journal-1936	156	1	in	in	ADP
american_scientific_journal-1936	156	2	our	our	PRON
american_scientific_journal-1936	156	3	computations	computation	NOUN
american_scientific_journal-1936	156	4	0.1	0.1	NUM
american_scientific_journal-1936	156	5	and	and	CCONJ
american_scientific_journal-1936	156	6	0.125	0.125	NUM
american_scientific_journal-1936	156	7	are	be	AUX
american_scientific_journal-1936	156	8	assigned	assign	VERB
american_scientific_journal-1936	156	9	to	to	ADP
american_scientific_journal-1936	156	10	the	the	DET
american_scientific_journal-1936	156	11	spatial	spatial	ADJ
american_scientific_journal-1936	156	12	interval	interval	NOUN
american_scientific_journal-1936	156	13	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	156	14	and	and	CCONJ
american_scientific_journal-1936	156	15	the	the	DET
american_scientific_journal-1936	156	16	values	value	NOUN
american_scientific_journal-1936	156	17	0.4	0.4	NUM
american_scientific_journal-1936	156	18	and	and	CCONJ
american_scientific_journal-1936	156	19	0.625	0.625	NUM
american_scientific_journal-1936	156	20	for	for	ADP
american_scientific_journal-1936	156	21	parameter	parameter	NOUN
american_scientific_journal-1936	156	22	𝑟𝑟	𝑟𝑟	PROPN
american_scientific_journal-1936	156	23	are	be	AUX
american_scientific_journal-1936	156	24	used	use	VERB
american_scientific_journal-1936	156	25	.	.	PUNCT
american_scientific_journal-1936	157	1	american	american	ADJ
american_scientific_journal-1936	157	2	scientific	scientific	ADJ
american_scientific_journal-1936	157	3	research	research	PROPN
american_scientific_journal-1936	157	4	journal	journal	NOUN
american_scientific_journal-1936	157	5	for	for	ADP
american_scientific_journal-1936	157	6	engineering	engineering	NOUN
american_scientific_journal-1936	157	7	,	,	PUNCT
american_scientific_journal-1936	157	8	technology	technology	NOUN
american_scientific_journal-1936	157	9	,	,	PUNCT
american_scientific_journal-1936	157	10	and	and	CCONJ
american_scientific_journal-1936	157	11	sciences	science	NOUN
american_scientific_journal-1936	157	12	(	(	PUNCT
american_scientific_journal-1936	157	13	asrjets	asrjet	NOUN
american_scientific_journal-1936	157	14	)	)	PUNCT
american_scientific_journal-1936	157	15	(	(	PUNCT
american_scientific_journal-1936	157	16	2016	2016	NUM
american_scientific_journal-1936	157	17	)	)	PUNCT
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american_scientific_journal-1936	157	19	26	26	NUM
american_scientific_journal-1936	157	20	,	,	PUNCT
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american_scientific_journal-1936	157	22	3	3	NUM
american_scientific_journal-1936	157	23	,	,	PUNCT
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american_scientific_journal-1936	157	27	154	154	NUM
american_scientific_journal-1936	157	28	147	147	NUM
american_scientific_journal-1936	157	29	3.1	3.1	NUM
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american_scientific_journal-1936	157	33	this	this	DET
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american_scientific_journal-1936	157	35	,	,	PUNCT
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american_scientific_journal-1936	157	37	(	(	PUNCT
american_scientific_journal-1936	157	38	18	18	NUM
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american_scientific_journal-1936	157	45	and	and	CCONJ
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american_scientific_journal-1936	157	48	𝑢𝑢(𝑥𝑥	𝑢𝑢(𝑥𝑥	PROPN
american_scientific_journal-1936	157	49	,	,	PUNCT
american_scientific_journal-1936	157	50	0	0	NUM
american_scientific_journal-1936	157	51	)	)	PUNCT
american_scientific_journal-1936	157	52	=	=	SYM
american_scientific_journal-1936	158	1	sin(𝜋𝜋𝑥𝑥	sin(𝜋𝜋𝑥𝑥	X
american_scientific_journal-1936	158	2	)	)	PUNCT
american_scientific_journal-1936	158	3	,	,	PUNCT
american_scientific_journal-1936	159	1	0	0	NUM
american_scientific_journal-1936	159	2	<	<	X
american_scientific_journal-1936	159	3	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	159	4	<	<	X
american_scientific_journal-1936	159	5	1	1	NUM
american_scientific_journal-1936	159	6	,	,	PUNCT
american_scientific_journal-1936	159	7	(	(	PUNCT
american_scientific_journal-1936	159	8	19	19	NUM
american_scientific_journal-1936	159	9	)	)	PUNCT
american_scientific_journal-1936	159	10	𝑢𝑢(0	𝑢𝑢(0	PROPN
american_scientific_journal-1936	159	11	,	,	PUNCT
american_scientific_journal-1936	159	12	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	159	13	)	)	PUNCT
american_scientific_journal-1936	159	14	=	=	SYM
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american_scientific_journal-1936	159	16	,	,	PUNCT
american_scientific_journal-1936	159	17	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	159	18	)	)	PUNCT
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american_scientific_journal-1936	159	20	0	0	NUM
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american_scientific_journal-1936	160	2	20	20	NUM
american_scientific_journal-1936	160	3	)	)	PUNCT
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american_scientific_journal-1936	160	5	the	the	DET
american_scientific_journal-1936	160	6	analytical	analytical	ADJ
american_scientific_journal-1936	160	7	solution	solution	NOUN
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american_scientific_journal-1936	160	9	(	(	PUNCT
american_scientific_journal-1936	160	10	18	18	NUM
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american_scientific_journal-1936	160	13	the	the	DET
american_scientific_journal-1936	160	14	initial	initial	ADJ
american_scientific_journal-1936	160	15	boundary	boundary	ADJ
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american_scientific_journal-1936	160	17	problem	problem	NOUN
american_scientific_journal-1936	160	18	(	(	PUNCT
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american_scientific_journal-1936	160	26	be	be	AUX
american_scientific_journal-1936	160	27	easily	easily	ADV
american_scientific_journal-1936	160	28	found	find	VERB
american_scientific_journal-1936	160	29	using	use	VERB
american_scientific_journal-1936	160	30	the	the	DET
american_scientific_journal-1936	160	31	method	method	NOUN
american_scientific_journal-1936	160	32	of	of	ADP
american_scientific_journal-1936	160	33	separation	separation	NOUN
american_scientific_journal-1936	160	34	of	of	ADP
american_scientific_journal-1936	160	35	variables	variable	NOUN
american_scientific_journal-1936	160	36	as	as	ADP
american_scientific_journal-1936	160	37	𝑢𝑢(𝑥𝑥	𝑢𝑢(𝑥𝑥	PROPN
american_scientific_journal-1936	160	38	,	,	PUNCT
american_scientific_journal-1936	160	39	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	160	40	)	)	PUNCT
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american_scientific_journal-1936	160	42	𝑒𝑒−𝑛𝑛2𝜕𝜕	𝑒𝑒−𝑛𝑛2𝜕𝜕	PROPN
american_scientific_journal-1936	160	43	sin(𝜋𝜋𝑥𝑥	sin(𝜋𝜋𝑥𝑥	NOUN
american_scientific_journal-1936	160	44	)	)	PUNCT
american_scientific_journal-1936	160	45	.	.	PUNCT
american_scientific_journal-1936	161	1	(	(	PUNCT
american_scientific_journal-1936	161	2	21	21	NUM
american_scientific_journal-1936	161	3	)	)	PUNCT
american_scientific_journal-1936	161	4	the	the	DET
american_scientific_journal-1936	161	5	numerical	numerical	ADJ
american_scientific_journal-1936	161	6	solutions	solution	NOUN
american_scientific_journal-1936	161	7	and	and	CCONJ
american_scientific_journal-1936	161	8	errors	error	NOUN
american_scientific_journal-1936	161	9	of	of	ADP
american_scientific_journal-1936	161	10	(	(	PUNCT
american_scientific_journal-1936	161	11	18	18	NUM
american_scientific_journal-1936	161	12	)	)	PUNCT
american_scientific_journal-1936	161	13	together	together	ADV
american_scientific_journal-1936	161	14	with	with	ADP
american_scientific_journal-1936	161	15	(	(	PUNCT
american_scientific_journal-1936	161	16	19	19	NUM
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american_scientific_journal-1936	161	18	and	and	CCONJ
american_scientific_journal-1936	161	19	(	(	PUNCT
american_scientific_journal-1936	161	20	20	20	NUM
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american_scientific_journal-1936	161	24	in	in	ADP
american_scientific_journal-1936	161	25	the	the	DET
american_scientific_journal-1936	161	26	following	follow	VERB
american_scientific_journal-1936	161	27	plots	plot	NOUN
american_scientific_journal-1936	161	28	.	.	PUNCT
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american_scientific_journal-1936	162	2	1	1	NUM
american_scientific_journal-1936	162	3	:	:	PUNCT
american_scientific_journal-1936	162	4	numerical	numerical	ADJ
american_scientific_journal-1936	162	5	solutions	solution	NOUN
american_scientific_journal-1936	162	6	and	and	CCONJ
american_scientific_journal-1936	162	7	errors	error	NOUN
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american_scientific_journal-1936	162	9	(	(	PUNCT
american_scientific_journal-1936	162	10	18	18	NUM
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american_scientific_journal-1936	162	22	using	use	VERB
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american_scientific_journal-1936	162	25	different	different	ADJ
american_scientific_journal-1936	162	26	schemes	scheme	NOUN
american_scientific_journal-1936	162	27	when	when	SCONJ
american_scientific_journal-1936	162	28	𝑟𝑟	𝑟𝑟	ADV
american_scientific_journal-1936	162	29	=	=	SYM
american_scientific_journal-1936	162	30	0.4	0.4	NUM
american_scientific_journal-1936	162	31	and	and	CCONJ
american_scientific_journal-1936	162	32	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	162	33	=	=	SYM
american_scientific_journal-1936	162	34	0.125	0.125	NUM
american_scientific_journal-1936	162	35	.	.	NOUN
american_scientific_journal-1936	162	36	0	0	NUM
american_scientific_journal-1936	162	37	0.2	0.2	NUM
american_scientific_journal-1936	162	38	0.4	0.4	NUM
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american_scientific_journal-1936	162	51	)	)	PUNCT
american_scientific_journal-1936	162	52	btcs	btcs	NOUN
american_scientific_journal-1936	162	53	scheme	scheme	NOUN
american_scientific_journal-1936	162	54	t	t	PROPN
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american_scientific_journal-1936	162	57	0.2	0.2	NUM
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american_scientific_journal-1936	164	28	0.6	0.6	NUM
american_scientific_journal-1936	164	29	0.8	0.8	NUM
american_scientific_journal-1936	164	30	1	1	NUM
american_scientific_journal-1936	164	31	0	0	NUM
american_scientific_journal-1936	164	32	0.5	0.5	NUM
american_scientific_journal-1936	164	33	1	1	NUM
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american_scientific_journal-1936	164	36	5	5	NUM
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american_scientific_journal-1936	164	42	f	f	X
american_scientific_journal-1936	164	43	)	)	PUNCT
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american_scientific_journal-1936	164	46	crank	crank	NOUN
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american_scientific_journal-1936	164	50	t	t	PROPN
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american_scientific_journal-1936	164	52	rr	rr	NOUN
american_scientific_journal-1936	164	53	o	o	NOUN
american_scientific_journal-1936	164	54	r	r	NOUN
american_scientific_journal-1936	164	55	0	0	NUM
american_scientific_journal-1936	164	56	0.2	0.2	NUM
american_scientific_journal-1936	164	57	0.4	0.4	NUM
american_scientific_journal-1936	164	58	0.6	0.6	NUM
american_scientific_journal-1936	164	59	0.8	0.8	NUM
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american_scientific_journal-1936	164	70	)	)	PUNCT
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american_scientific_journal-1936	164	78	0.6	0.6	NUM
american_scientific_journal-1936	164	79	0.8	0.8	NUM
american_scientific_journal-1936	164	80	1	1	NUM
american_scientific_journal-1936	164	81	0	0	NUM
american_scientific_journal-1936	164	82	0.5	0.5	NUM
american_scientific_journal-1936	164	83	1	1	NUM
american_scientific_journal-1936	164	84	0	0	NUM
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american_scientific_journal-1936	164	90	)	)	PUNCT
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american_scientific_journal-1936	164	105	engineering	engineering	NOUN
american_scientific_journal-1936	164	106	,	,	PUNCT
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american_scientific_journal-1936	164	108	,	,	PUNCT
american_scientific_journal-1936	164	109	and	and	CCONJ
american_scientific_journal-1936	164	110	sciences	science	NOUN
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american_scientific_journal-1936	164	115	2016	2016	NUM
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american_scientific_journal-1936	164	118	26	26	NUM
american_scientific_journal-1936	164	119	,	,	PUNCT
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american_scientific_journal-1936	164	121	3	3	NUM
american_scientific_journal-1936	164	122	,	,	PUNCT
american_scientific_journal-1936	164	123	pp	pp	ADV
american_scientific_journal-1936	164	124	140	140	NUM
american_scientific_journal-1936	164	125	-	-	SYM
american_scientific_journal-1936	164	126	154	154	NUM
american_scientific_journal-1936	164	127	148	148	NUM
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american_scientific_journal-1936	164	129	2	2	NUM
american_scientific_journal-1936	164	130	:	:	PUNCT
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american_scientific_journal-1936	164	132	solutions	solution	NOUN
american_scientific_journal-1936	164	133	and	and	CCONJ
american_scientific_journal-1936	164	134	errors	error	NOUN
american_scientific_journal-1936	164	135	of	of	ADP
american_scientific_journal-1936	164	136	(	(	PUNCT
american_scientific_journal-1936	164	137	18	18	NUM
american_scientific_journal-1936	164	138	)	)	PUNCT
american_scientific_journal-1936	164	139	together	together	ADV
american_scientific_journal-1936	164	140	with	with	ADP
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american_scientific_journal-1936	164	142	19	19	NUM
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american_scientific_journal-1936	164	145	(	(	PUNCT
american_scientific_journal-1936	164	146	20	20	NUM
american_scientific_journal-1936	164	147	)	)	PUNCT
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american_scientific_journal-1936	164	154	when	when	SCONJ
american_scientific_journal-1936	164	155	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1936	164	156	=	=	SYM
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american_scientific_journal-1936	164	158	and	and	CCONJ
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american_scientific_journal-1936	164	160	=	=	SYM
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american_scientific_journal-1936	164	165	2	2	NUM
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american_scientific_journal-1936	164	167	this	this	DET
american_scientific_journal-1936	164	168	problem	problem	NOUN
american_scientific_journal-1936	164	169	,	,	PUNCT
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american_scientific_journal-1936	164	171	(	(	PUNCT
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american_scientific_journal-1936	165	2	)	)	PUNCT
american_scientific_journal-1936	165	3	,	,	PUNCT
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american_scientific_journal-1936	165	6	𝑥𝑥	𝑥𝑥	ADP
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american_scientific_journal-1936	165	15	(	(	PUNCT
american_scientific_journal-1936	165	16	0	0	NUM
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american_scientific_journal-1936	165	27	)	)	PUNCT
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american_scientific_journal-1936	165	29	0	0	NUM
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american_scientific_journal-1936	165	31	0	0	NUM
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american_scientific_journal-1936	165	33	𝑡𝑡	𝑡𝑡	ADJ
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american_scientific_journal-1936	166	12	1	1	NUM
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american_scientific_journal-1936	166	15	1	1	NUM
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american_scientific_journal-1936	166	30	0	0	NUM
american_scientific_journal-1936	166	31	0.5	0.5	NUM
american_scientific_journal-1936	166	32	1	1	NUM
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american_scientific_journal-1936	166	34	0	0	NUM
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american_scientific_journal-1936	167	1	o	o	NOUN
american_scientific_journal-1936	167	2	r	r	NOUN
american_scientific_journal-1936	167	3	0	0	NUM
american_scientific_journal-1936	167	4	0.2	0.2	NUM
american_scientific_journal-1936	167	5	0.4	0.4	NUM
american_scientific_journal-1936	167	6	0.6	0.6	NUM
american_scientific_journal-1936	167	7	0.8	0.8	NUM
american_scientific_journal-1936	167	8	1	1	NUM
american_scientific_journal-1936	167	9	0	0	NUM
american_scientific_journal-1936	167	10	0.5	0.5	NUM
american_scientific_journal-1936	167	11	1	1	NUM
american_scientific_journal-1936	167	12	0	0	NUM
american_scientific_journal-1936	167	13	0.5	0.5	NUM
american_scientific_journal-1936	167	14	1	1	NUM
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american_scientific_journal-1936	167	18	)	)	PUNCT
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american_scientific_journal-1936	167	20	-	-	PUNCT
american_scientific_journal-1936	167	21	nicholson	nicholson	PROPN
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american_scientific_journal-1936	167	23	t	t	PROPN
american_scientific_journal-1936	167	24	u	u	PROPN
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american_scientific_journal-1936	167	26	0.2	0.2	NUM
american_scientific_journal-1936	167	27	0.4	0.4	NUM
american_scientific_journal-1936	167	28	0.6	0.6	NUM
american_scientific_journal-1936	167	29	0.8	0.8	NUM
american_scientific_journal-1936	167	30	1	1	NUM
american_scientific_journal-1936	167	31	0	0	NUM
american_scientific_journal-1936	167	32	0.5	0.5	NUM
american_scientific_journal-1936	167	33	1	1	NUM
american_scientific_journal-1936	167	34	-5	-5	NOUN
american_scientific_journal-1936	167	35	0	0	NUM
american_scientific_journal-1936	167	36	5	5	NUM
american_scientific_journal-1936	167	37	x	x	SYM
american_scientific_journal-1936	167	38	10	10	NUM
american_scientific_journal-1936	167	39	-3	-3	INTJ
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american_scientific_journal-1936	167	42	f	f	X
american_scientific_journal-1936	167	43	)	)	PUNCT
american_scientific_journal-1936	167	44	error	error	NOUN
american_scientific_journal-1936	167	45	of	of	ADP
american_scientific_journal-1936	167	46	crank	crank	NOUN
american_scientific_journal-1936	167	47	-	-	PUNCT
american_scientific_journal-1936	167	48	nicolson	nicolson	PROPN
american_scientific_journal-1936	167	49	scheme	scheme	PROPN
american_scientific_journal-1936	167	50	t	t	PROPN
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american_scientific_journal-1936	167	52	rr	rr	NOUN
american_scientific_journal-1936	167	53	o	o	NOUN
american_scientific_journal-1936	167	54	r	r	NOUN
american_scientific_journal-1936	167	55	0	0	NUM
american_scientific_journal-1936	167	56	0.2	0.2	NUM
american_scientific_journal-1936	167	57	0.4	0.4	NUM
american_scientific_journal-1936	167	58	0.6	0.6	NUM
american_scientific_journal-1936	167	59	0.8	0.8	NUM
american_scientific_journal-1936	167	60	1	1	NUM
american_scientific_journal-1936	167	61	0	0	NUM
american_scientific_journal-1936	167	62	0.5	0.5	NUM
american_scientific_journal-1936	167	63	1	1	NUM
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american_scientific_journal-1936	167	65	0	0	NUM
american_scientific_journal-1936	167	66	5	5	NUM
american_scientific_journal-1936	167	67	x	x	SYM
american_scientific_journal-1936	167	68	10	10	NUM
american_scientific_journal-1936	167	69	8	8	NUM
american_scientific_journal-1936	167	70	x	x	SYM
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american_scientific_journal-1936	167	72	a	a	PRON
american_scientific_journal-1936	167	73	)	)	PUNCT
american_scientific_journal-1936	167	74	ftcs	ftcs	NOUN
american_scientific_journal-1936	167	75	scheme	scheme	NOUN
american_scientific_journal-1936	167	76	t	t	PROPN
american_scientific_journal-1936	167	77	u	u	NOUN
american_scientific_journal-1936	167	78	0	0	NUM
american_scientific_journal-1936	167	79	0.2	0.2	NUM
american_scientific_journal-1936	167	80	0.4	0.4	NUM
american_scientific_journal-1936	167	81	0.6	0.6	NUM
american_scientific_journal-1936	167	82	0.8	0.8	NUM
american_scientific_journal-1936	167	83	1	1	NUM
american_scientific_journal-1936	167	84	0	0	NUM
american_scientific_journal-1936	167	85	0.5	0.5	NUM
american_scientific_journal-1936	167	86	1	1	NUM
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american_scientific_journal-1936	167	88	0	0	NUM
american_scientific_journal-1936	167	89	5	5	NUM
american_scientific_journal-1936	167	90	x	x	SYM
american_scientific_journal-1936	167	91	10	10	NUM
american_scientific_journal-1936	167	92	8	8	NUM
american_scientific_journal-1936	167	93	x	x	SYM
american_scientific_journal-1936	167	94	(	(	PUNCT
american_scientific_journal-1936	167	95	b	b	NOUN
american_scientific_journal-1936	167	96	)	)	PUNCT
american_scientific_journal-1936	167	97	error	error	NOUN
american_scientific_journal-1936	167	98	of	of	ADP
american_scientific_journal-1936	167	99	ftcs	ftcs	NOUN
american_scientific_journal-1936	167	100	scheme	scheme	NOUN
american_scientific_journal-1936	167	101	t	t	PROPN
american_scientific_journal-1936	167	102	e	e	NOUN
american_scientific_journal-1936	167	103	rr	rr	NOUN
american_scientific_journal-1936	167	104	o	o	NOUN
american_scientific_journal-1936	167	105	r	r	NOUN
american_scientific_journal-1936	167	106	american	american	PROPN
american_scientific_journal-1936	167	107	scientific	scientific	ADJ
american_scientific_journal-1936	167	108	research	research	NOUN
american_scientific_journal-1936	167	109	journal	journal	NOUN
american_scientific_journal-1936	167	110	for	for	ADP
american_scientific_journal-1936	167	111	engineering	engineering	NOUN
american_scientific_journal-1936	167	112	,	,	PUNCT
american_scientific_journal-1936	167	113	technology	technology	NOUN
american_scientific_journal-1936	167	114	,	,	PUNCT
american_scientific_journal-1936	167	115	and	and	CCONJ
american_scientific_journal-1936	167	116	sciences	science	NOUN
american_scientific_journal-1936	167	117	(	(	PUNCT
american_scientific_journal-1936	167	118	asrjets	asrjet	NOUN
american_scientific_journal-1936	167	119	)	)	PUNCT
american_scientific_journal-1936	167	120	(	(	PUNCT
american_scientific_journal-1936	167	121	2016	2016	NUM
american_scientific_journal-1936	167	122	)	)	PUNCT
american_scientific_journal-1936	167	123	volume	volume	NOUN
american_scientific_journal-1936	167	124	26	26	NUM
american_scientific_journal-1936	167	125	,	,	PUNCT
american_scientific_journal-1936	167	126	no	no	DET
american_scientific_journal-1936	167	127	3	3	NUM
american_scientific_journal-1936	167	128	,	,	PUNCT
american_scientific_journal-1936	167	129	pp	pp	ADV
american_scientific_journal-1936	167	130	140	140	NUM
american_scientific_journal-1936	167	131	-	-	SYM
american_scientific_journal-1936	167	132	154	154	NUM
american_scientific_journal-1936	167	133	149	149	NUM
american_scientific_journal-1936	167	134	however	however	ADV
american_scientific_journal-1936	167	135	,	,	PUNCT
american_scientific_journal-1936	167	136	the	the	DET
american_scientific_journal-1936	167	137	analytical	analytical	ADJ
american_scientific_journal-1936	167	138	solution	solution	NOUN
american_scientific_journal-1936	167	139	of	of	ADP
american_scientific_journal-1936	167	140	(	(	PUNCT
american_scientific_journal-1936	167	141	18	18	NUM
american_scientific_journal-1936	167	142	)	)	PUNCT
american_scientific_journal-1936	167	143	with	with	ADP
american_scientific_journal-1936	167	144	the	the	DET
american_scientific_journal-1936	167	145	initial	initial	ADJ
american_scientific_journal-1936	167	146	boundary	boundary	ADJ
american_scientific_journal-1936	167	147	value	value	NOUN
american_scientific_journal-1936	167	148	problem	problem	NOUN
american_scientific_journal-1936	167	149	(	(	PUNCT
american_scientific_journal-1936	167	150	22	22	NUM
american_scientific_journal-1936	167	151	)	)	PUNCT
american_scientific_journal-1936	167	152	and	and	CCONJ
american_scientific_journal-1936	167	153	(	(	PUNCT
american_scientific_journal-1936	167	154	23	23	NUM
american_scientific_journal-1936	167	155	)	)	PUNCT
american_scientific_journal-1936	167	156	can	can	AUX
american_scientific_journal-1936	167	157	be	be	AUX
american_scientific_journal-1936	167	158	easily	easily	ADV
american_scientific_journal-1936	167	159	found	find	VERB
american_scientific_journal-1936	167	160	using	use	VERB
american_scientific_journal-1936	167	161	the	the	DET
american_scientific_journal-1936	167	162	method	method	NOUN
american_scientific_journal-1936	167	163	of	of	ADP
american_scientific_journal-1936	167	164	separation	separation	NOUN
american_scientific_journal-1936	167	165	of	of	ADP
american_scientific_journal-1936	167	166	variables	variable	NOUN
american_scientific_journal-1936	167	167	as	as	ADP
american_scientific_journal-1936	167	168	𝑢𝑢(𝑥𝑥	𝑢𝑢(𝑥𝑥	PROPN
american_scientific_journal-1936	167	169	,	,	PUNCT
american_scientific_journal-1936	167	170	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	167	171	)	)	PUNCT
american_scientific_journal-1936	167	172	=	=	SYM
american_scientific_journal-1936	167	173	𝑒𝑒−𝑛𝑛2𝜕𝜕	𝑒𝑒−𝑛𝑛2𝜕𝜕	PROPN
american_scientific_journal-1936	167	174	cos(𝜋𝜋𝑥𝑥	cos(𝜋𝜋𝑥𝑥	ADJ
american_scientific_journal-1936	167	175	)	)	PUNCT
american_scientific_journal-1936	167	176	.	.	PUNCT
american_scientific_journal-1936	168	1	(	(	PUNCT
american_scientific_journal-1936	168	2	24	24	NUM
american_scientific_journal-1936	168	3	)	)	PUNCT
american_scientific_journal-1936	168	4	the	the	DET
american_scientific_journal-1936	168	5	numerical	numerical	ADJ
american_scientific_journal-1936	168	6	solutions	solution	NOUN
american_scientific_journal-1936	168	7	and	and	CCONJ
american_scientific_journal-1936	168	8	errors	error	NOUN
american_scientific_journal-1936	168	9	of	of	ADP
american_scientific_journal-1936	168	10	(	(	PUNCT
american_scientific_journal-1936	168	11	18	18	NUM
american_scientific_journal-1936	168	12	)	)	PUNCT
american_scientific_journal-1936	168	13	together	together	ADV
american_scientific_journal-1936	168	14	with	with	ADP
american_scientific_journal-1936	168	15	(	(	PUNCT
american_scientific_journal-1936	168	16	22	22	NUM
american_scientific_journal-1936	168	17	)	)	PUNCT
american_scientific_journal-1936	168	18	and	and	CCONJ
american_scientific_journal-1936	168	19	(	(	PUNCT
american_scientific_journal-1936	168	20	23	23	NUM
american_scientific_journal-1936	168	21	)	)	PUNCT
american_scientific_journal-1936	168	22	are	be	AUX
american_scientific_journal-1936	168	23	illustrated	illustrate	VERB
american_scientific_journal-1936	168	24	in	in	ADP
american_scientific_journal-1936	168	25	the	the	DET
american_scientific_journal-1936	168	26	following	follow	VERB
american_scientific_journal-1936	168	27	plots	plot	NOUN
american_scientific_journal-1936	168	28	:	:	PUNCT
american_scientific_journal-1936	168	29	figure	figure	VERB
american_scientific_journal-1936	168	30	3	3	NUM
american_scientific_journal-1936	168	31	:	:	PUNCT
american_scientific_journal-1936	168	32	numerical	numerical	ADJ
american_scientific_journal-1936	168	33	solutions	solution	NOUN
american_scientific_journal-1936	168	34	and	and	CCONJ
american_scientific_journal-1936	168	35	errors	error	NOUN
american_scientific_journal-1936	168	36	of	of	ADP
american_scientific_journal-1936	168	37	(	(	PUNCT
american_scientific_journal-1936	168	38	18	18	NUM
american_scientific_journal-1936	168	39	)	)	PUNCT
american_scientific_journal-1936	168	40	together	together	ADV
american_scientific_journal-1936	168	41	with	with	ADP
american_scientific_journal-1936	168	42	(	(	PUNCT
american_scientific_journal-1936	168	43	22	22	NUM
american_scientific_journal-1936	168	44	)	)	PUNCT
american_scientific_journal-1936	168	45	and	and	CCONJ
american_scientific_journal-1936	168	46	(	(	PUNCT
american_scientific_journal-1936	168	47	23	23	NUM
american_scientific_journal-1936	168	48	)	)	PUNCT
american_scientific_journal-1936	168	49	obtained	obtain	VERB
american_scientific_journal-1936	168	50	using	use	VERB
american_scientific_journal-1936	168	51	the	the	DET
american_scientific_journal-1936	168	52	three	three	NUM
american_scientific_journal-1936	168	53	different	different	ADJ
american_scientific_journal-1936	168	54	schemes	scheme	NOUN
american_scientific_journal-1936	168	55	when	when	SCONJ
american_scientific_journal-1936	168	56	𝑟𝑟	𝑟𝑟	ADV
american_scientific_journal-1936	168	57	=	=	SYM
american_scientific_journal-1936	168	58	0.4	0.4	NUM
american_scientific_journal-1936	168	59	and	and	CCONJ
american_scientific_journal-1936	168	60	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	168	61	=	=	SYM
american_scientific_journal-1936	168	62	0.125	0.125	NUM
american_scientific_journal-1936	168	63	.	.	NOUN
american_scientific_journal-1936	168	64	0	0	NUM
american_scientific_journal-1936	169	1	0.2	0.2	NUM
american_scientific_journal-1936	169	2	0.4	0.4	NUM
american_scientific_journal-1936	169	3	0.6	0.6	NUM
american_scientific_journal-1936	169	4	0.8	0.8	NUM
american_scientific_journal-1936	169	5	1	1	NUM
american_scientific_journal-1936	169	6	0	0	NUM
american_scientific_journal-1936	169	7	0.5	0.5	NUM
american_scientific_journal-1936	169	8	1	1	NUM
american_scientific_journal-1936	169	9	-1	-1	SYM
american_scientific_journal-1936	169	10	0	0	NUM
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american_scientific_journal-1936	169	15	)	)	PUNCT
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american_scientific_journal-1936	169	17	scheme	scheme	NOUN
american_scientific_journal-1936	169	18	t	t	PROPN
american_scientific_journal-1936	169	19	u	u	NOUN
american_scientific_journal-1936	169	20	0	0	NUM
american_scientific_journal-1936	169	21	0.2	0.2	NUM
american_scientific_journal-1936	169	22	0.4	0.4	NUM
american_scientific_journal-1936	169	23	0.6	0.6	NUM
american_scientific_journal-1936	169	24	0.8	0.8	NUM
american_scientific_journal-1936	169	25	1	1	NUM
american_scientific_journal-1936	169	26	0	0	NUM
american_scientific_journal-1936	169	27	0.5	0.5	NUM
american_scientific_journal-1936	169	28	1	1	NUM
american_scientific_journal-1936	169	29	-1	-1	SYM
american_scientific_journal-1936	169	30	0	0	NUM
american_scientific_journal-1936	169	31	1	1	NUM
american_scientific_journal-1936	169	32	x	x	SYM
american_scientific_journal-1936	169	33	(	(	PUNCT
american_scientific_journal-1936	169	34	b	b	NOUN
american_scientific_journal-1936	169	35	)	)	PUNCT
american_scientific_journal-1936	169	36	error	error	NOUN
american_scientific_journal-1936	169	37	of	of	ADP
american_scientific_journal-1936	169	38	ftcs	ftcs	NOUN
american_scientific_journal-1936	169	39	scheme	scheme	NOUN
american_scientific_journal-1936	170	1	t	t	NOUN
american_scientific_journal-1936	170	2	e	e	NOUN
american_scientific_journal-1936	170	3	r	r	NOUN
american_scientific_journal-1936	170	4	r	r	NOUN
american_scientific_journal-1936	170	5	o	o	NOUN
american_scientific_journal-1936	170	6	r	r	NOUN
american_scientific_journal-1936	170	7	0	0	NUM
american_scientific_journal-1936	170	8	0.2	0.2	NUM
american_scientific_journal-1936	170	9	0.4	0.4	NUM
american_scientific_journal-1936	170	10	0.6	0.6	NUM
american_scientific_journal-1936	170	11	0.8	0.8	NUM
american_scientific_journal-1936	170	12	1	1	NUM
american_scientific_journal-1936	170	13	0	0	NUM
american_scientific_journal-1936	170	14	0.5	0.5	NUM
american_scientific_journal-1936	170	15	1	1	NUM
american_scientific_journal-1936	170	16	-1	-1	SYM
american_scientific_journal-1936	170	17	0	0	NUM
american_scientific_journal-1936	170	18	1	1	NUM
american_scientific_journal-1936	170	19	x	x	SYM
american_scientific_journal-1936	170	20	(	(	PUNCT
american_scientific_journal-1936	170	21	c	c	NOUN
american_scientific_journal-1936	170	22	)	)	PUNCT
american_scientific_journal-1936	170	23	btcs	btcs	NOUN
american_scientific_journal-1936	170	24	scheme	scheme	NOUN
american_scientific_journal-1936	170	25	t	t	PROPN
american_scientific_journal-1936	170	26	u	u	NOUN
american_scientific_journal-1936	170	27	0	0	NUM
american_scientific_journal-1936	170	28	0.2	0.2	NUM
american_scientific_journal-1936	170	29	0.4	0.4	NUM
american_scientific_journal-1936	170	30	0.6	0.6	NUM
american_scientific_journal-1936	170	31	0.8	0.8	NUM
american_scientific_journal-1936	170	32	1	1	NUM
american_scientific_journal-1936	170	33	0	0	NUM
american_scientific_journal-1936	170	34	0.5	0.5	NUM
american_scientific_journal-1936	170	35	1	1	NUM
american_scientific_journal-1936	170	36	-1	-1	SYM
american_scientific_journal-1936	170	37	-0.5	-0.5	X
american_scientific_journal-1936	170	38	0	0	PUNCT
american_scientific_journal-1936	170	39	x	x	SYM
american_scientific_journal-1936	170	40	(	(	PUNCT
american_scientific_journal-1936	170	41	d	d	NOUN
american_scientific_journal-1936	170	42	)	)	PUNCT
american_scientific_journal-1936	170	43	error	error	NOUN
american_scientific_journal-1936	170	44	of	of	ADP
american_scientific_journal-1936	170	45	btcs	btcs	NOUN
american_scientific_journal-1936	170	46	scheme	scheme	NOUN
american_scientific_journal-1936	170	47	t	t	NOUN
american_scientific_journal-1936	170	48	e	e	NOUN
american_scientific_journal-1936	171	1	r	r	NOUN
american_scientific_journal-1936	171	2	r	r	NOUN
american_scientific_journal-1936	171	3	o	o	NOUN
american_scientific_journal-1936	171	4	r	r	NOUN
american_scientific_journal-1936	171	5	0	0	NUM
american_scientific_journal-1936	171	6	0.2	0.2	NUM
american_scientific_journal-1936	171	7	0.4	0.4	NUM
american_scientific_journal-1936	171	8	0.6	0.6	NUM
american_scientific_journal-1936	171	9	0.8	0.8	NUM
american_scientific_journal-1936	171	10	1	1	NUM
american_scientific_journal-1936	171	11	0	0	NUM
american_scientific_journal-1936	171	12	0.5	0.5	NUM
american_scientific_journal-1936	171	13	1	1	NUM
american_scientific_journal-1936	171	14	-1	-1	SYM
american_scientific_journal-1936	171	15	0	0	NUM
american_scientific_journal-1936	171	16	1	1	NUM
american_scientific_journal-1936	171	17	x	x	SYM
american_scientific_journal-1936	171	18	(	(	PUNCT
american_scientific_journal-1936	171	19	e	e	NOUN
american_scientific_journal-1936	171	20	)	)	PUNCT
american_scientific_journal-1936	171	21	crank	crank	NOUN
american_scientific_journal-1936	171	22	-	-	PUNCT
american_scientific_journal-1936	171	23	nicolson	nicolson	PROPN
american_scientific_journal-1936	171	24	scheme	scheme	PROPN
american_scientific_journal-1936	171	25	t	t	PROPN
american_scientific_journal-1936	171	26	u	u	NOUN
american_scientific_journal-1936	171	27	0	0	NUM
american_scientific_journal-1936	171	28	0.2	0.2	NUM
american_scientific_journal-1936	171	29	0.4	0.4	NUM
american_scientific_journal-1936	171	30	0.6	0.6	NUM
american_scientific_journal-1936	171	31	0.8	0.8	NUM
american_scientific_journal-1936	171	32	1	1	NUM
american_scientific_journal-1936	171	33	0	0	NUM
american_scientific_journal-1936	171	34	0.5	0.5	NUM
american_scientific_journal-1936	171	35	1	1	NUM
american_scientific_journal-1936	171	36	-1	-1	SYM
american_scientific_journal-1936	171	37	-0.5	-0.5	X
american_scientific_journal-1936	171	38	0	0	PUNCT
american_scientific_journal-1936	171	39	x	x	SYM
american_scientific_journal-1936	171	40	(	(	PUNCT
american_scientific_journal-1936	171	41	f	f	X
american_scientific_journal-1936	171	42	)	)	PUNCT
american_scientific_journal-1936	171	43	error	error	NOUN
american_scientific_journal-1936	171	44	of	of	ADP
american_scientific_journal-1936	171	45	crank	crank	NOUN
american_scientific_journal-1936	171	46	-	-	PUNCT
american_scientific_journal-1936	171	47	nicolson	nicolson	PROPN
american_scientific_journal-1936	171	48	scheme	scheme	PROPN
american_scientific_journal-1936	171	49	t	t	PROPN
american_scientific_journal-1936	171	50	e	e	NOUN
american_scientific_journal-1936	171	51	r	r	NOUN
american_scientific_journal-1936	171	52	r	r	NOUN
american_scientific_journal-1936	171	53	o	o	NOUN
american_scientific_journal-1936	171	54	r	r	NOUN
american_scientific_journal-1936	171	55	american	american	ADJ
american_scientific_journal-1936	171	56	scientific	scientific	ADJ
american_scientific_journal-1936	171	57	research	research	NOUN
american_scientific_journal-1936	171	58	journal	journal	NOUN
american_scientific_journal-1936	171	59	for	for	ADP
american_scientific_journal-1936	171	60	engineering	engineering	NOUN
american_scientific_journal-1936	171	61	,	,	PUNCT
american_scientific_journal-1936	171	62	technology	technology	NOUN
american_scientific_journal-1936	171	63	,	,	PUNCT
american_scientific_journal-1936	171	64	and	and	CCONJ
american_scientific_journal-1936	171	65	sciences	science	NOUN
american_scientific_journal-1936	171	66	(	(	PUNCT
american_scientific_journal-1936	171	67	asrjets	asrjet	NOUN
american_scientific_journal-1936	171	68	)	)	PUNCT
american_scientific_journal-1936	171	69	(	(	PUNCT
american_scientific_journal-1936	171	70	2016	2016	NUM
american_scientific_journal-1936	171	71	)	)	PUNCT
american_scientific_journal-1936	171	72	volume	volume	NOUN
american_scientific_journal-1936	171	73	26	26	NUM
american_scientific_journal-1936	171	74	,	,	PUNCT
american_scientific_journal-1936	171	75	no	no	DET
american_scientific_journal-1936	171	76	3	3	NUM
american_scientific_journal-1936	171	77	,	,	PUNCT
american_scientific_journal-1936	171	78	pp	pp	ADV
american_scientific_journal-1936	171	79	140	140	NUM
american_scientific_journal-1936	171	80	-	-	SYM
american_scientific_journal-1936	171	81	154	154	NUM
american_scientific_journal-1936	171	82	150	150	NUM
american_scientific_journal-1936	171	83	figure	figure	NOUN
american_scientific_journal-1936	171	84	4	4	NUM
american_scientific_journal-1936	171	85	:	:	PUNCT
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american_scientific_journal-1936	171	89	errors	error	NOUN
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american_scientific_journal-1936	171	92	18	18	NUM
american_scientific_journal-1936	171	93	)	)	PUNCT
american_scientific_journal-1936	171	94	together	together	ADV
american_scientific_journal-1936	171	95	with	with	ADP
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american_scientific_journal-1936	171	97	22	22	NUM
american_scientific_journal-1936	171	98	)	)	PUNCT
american_scientific_journal-1936	171	99	and	and	CCONJ
american_scientific_journal-1936	171	100	(	(	PUNCT
american_scientific_journal-1936	171	101	23	23	NUM
american_scientific_journal-1936	171	102	)	)	PUNCT
american_scientific_journal-1936	171	103	obtained	obtain	VERB
american_scientific_journal-1936	171	104	using	use	VERB
american_scientific_journal-1936	171	105	the	the	DET
american_scientific_journal-1936	171	106	three	three	NUM
american_scientific_journal-1936	171	107	different	different	ADJ
american_scientific_journal-1936	171	108	schemes	scheme	NOUN
american_scientific_journal-1936	171	109	when	when	SCONJ
american_scientific_journal-1936	171	110	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1936	171	111	=	=	SYM
american_scientific_journal-1936	171	112	0.625	0.625	NUM
american_scientific_journal-1936	171	113	and	and	CCONJ
american_scientific_journal-1936	171	114	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	171	115	=	=	SYM
american_scientific_journal-1936	171	116	0.1	0.1	NUM
american_scientific_journal-1936	171	117	.	.	X
american_scientific_journal-1936	171	118	3.3	3.3	NUM
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american_scientific_journal-1936	171	120	3	3	NUM
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american_scientific_journal-1936	171	122	this	this	DET
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american_scientific_journal-1936	171	124	,	,	PUNCT
american_scientific_journal-1936	171	125	consider	consider	VERB
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american_scientific_journal-1936	171	127	18	18	NUM
american_scientific_journal-1936	171	128	)	)	PUNCT
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american_scientific_journal-1936	171	130	with	with	ADP
american_scientific_journal-1936	171	131	the	the	DET
american_scientific_journal-1936	171	132	following	following	ADJ
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american_scientific_journal-1936	171	135	boundary	boundary	ADJ
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american_scientific_journal-1936	171	137	𝑢𝑢(𝑥𝑥	𝑢𝑢(𝑥𝑥	PROPN
american_scientific_journal-1936	171	138	,	,	PUNCT
american_scientific_journal-1936	171	139	0	0	NUM
american_scientific_journal-1936	171	140	)	)	PUNCT
american_scientific_journal-1936	171	141	=	=	SYM
american_scientific_journal-1936	171	142	cos(𝑥𝑥	cos(𝑥𝑥	NUM
american_scientific_journal-1936	171	143	)	)	PUNCT
american_scientific_journal-1936	171	144	,	,	PUNCT
american_scientific_journal-1936	171	145	0	0	PUNCT
american_scientific_journal-1936	171	146	<	<	X
american_scientific_journal-1936	171	147	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-1936	171	148	<	<	X
american_scientific_journal-1936	171	149	1	1	NUM
american_scientific_journal-1936	171	150	(	(	PUNCT
american_scientific_journal-1936	171	151	25	25	NUM
american_scientific_journal-1936	171	152	)	)	PUNCT
american_scientific_journal-1936	171	153	𝜕𝜕𝜕𝜕	𝜕𝜕𝜕𝜕	NOUN
american_scientific_journal-1936	171	154	𝜕𝜕𝑥𝑥	𝜕𝜕𝑥𝑥	X
american_scientific_journal-1936	171	155	(	(	PUNCT
american_scientific_journal-1936	171	156	0	0	NUM
american_scientific_journal-1936	171	157	,	,	PUNCT
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american_scientific_journal-1936	171	159	)	)	PUNCT
american_scientific_journal-1936	171	160	=	=	SYM
american_scientific_journal-1936	171	161	𝑢𝑢	𝑢𝑢	PROPN
american_scientific_journal-1936	171	162	�	�	PROPN
american_scientific_journal-1936	171	163	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-1936	171	164	2	2	NUM
american_scientific_journal-1936	171	165	,	,	PUNCT
american_scientific_journal-1936	171	166	𝑡𝑡	𝑡𝑡	NOUN
american_scientific_journal-1936	171	167	�	�	X
american_scientific_journal-1936	171	168	=	=	SYM
american_scientific_journal-1936	171	169	0	0	NUM
american_scientific_journal-1936	171	170	,	,	PUNCT
american_scientific_journal-1936	171	171	𝑡𝑡	𝑡𝑡	ADJ
american_scientific_journal-1936	171	172	≥	≥	NOUN
american_scientific_journal-1936	171	173	0	0	NUM
american_scientific_journal-1936	171	174	.	.	PUNCT
american_scientific_journal-1936	172	1	(	(	PUNCT
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american_scientific_journal-1936	172	3	)	)	PUNCT
american_scientific_journal-1936	172	4	however	however	ADV
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american_scientific_journal-1936	172	6	analytical	analytical	ADJ
american_scientific_journal-1936	172	7	solution	solution	NOUN
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american_scientific_journal-1936	172	19	25	25	NUM
american_scientific_journal-1936	172	20	)	)	PUNCT
american_scientific_journal-1936	172	21	and	and	CCONJ
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american_scientific_journal-1936	172	26	be	be	AUX
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american_scientific_journal-1936	172	28	0	0	NUM
american_scientific_journal-1936	172	29	0.2	0.2	NUM
american_scientific_journal-1936	172	30	0.4	0.4	NUM
american_scientific_journal-1936	172	31	0.6	0.6	NUM
american_scientific_journal-1936	172	32	0.8	0.8	NUM
american_scientific_journal-1936	172	33	1	1	NUM
american_scientific_journal-1936	172	34	0	0	NUM
american_scientific_journal-1936	172	35	0.5	0.5	NUM
american_scientific_journal-1936	172	36	1	1	NUM
american_scientific_journal-1936	172	37	-5	-5	NOUN
american_scientific_journal-1936	172	38	0	0	NUM
american_scientific_journal-1936	172	39	5	5	NUM
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american_scientific_journal-1936	172	41	10	10	NUM
american_scientific_journal-1936	172	42	25	25	NUM
american_scientific_journal-1936	172	43	x	x	SYM
american_scientific_journal-1936	172	44	(	(	PUNCT
american_scientific_journal-1936	172	45	a	a	PRON
american_scientific_journal-1936	172	46	)	)	PUNCT
american_scientific_journal-1936	172	47	ftcs	ftcs	NOUN
american_scientific_journal-1936	172	48	scheme	scheme	NOUN
american_scientific_journal-1936	172	49	t	t	PROPN
american_scientific_journal-1936	172	50	u	u	NOUN
american_scientific_journal-1936	172	51	0	0	NUM
american_scientific_journal-1936	172	52	0.2	0.2	NUM
american_scientific_journal-1936	172	53	0.4	0.4	NUM
american_scientific_journal-1936	172	54	0.6	0.6	NUM
american_scientific_journal-1936	172	55	0.8	0.8	NUM
american_scientific_journal-1936	172	56	1	1	NUM
american_scientific_journal-1936	172	57	0	0	NUM
american_scientific_journal-1936	172	58	0.5	0.5	NUM
american_scientific_journal-1936	172	59	1	1	NUM
american_scientific_journal-1936	172	60	-5	-5	NOUN
american_scientific_journal-1936	172	61	0	0	NUM
american_scientific_journal-1936	172	62	5	5	NUM
american_scientific_journal-1936	172	63	x	x	SYM
american_scientific_journal-1936	172	64	10	10	NUM
american_scientific_journal-1936	172	65	25	25	NUM
american_scientific_journal-1936	172	66	x	x	SYM
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american_scientific_journal-1936	173	1	t	t	PROPN
american_scientific_journal-1936	173	2	e	e	NOUN
american_scientific_journal-1936	173	3	rr	rr	NOUN
american_scientific_journal-1936	173	4	o	o	NOUN
american_scientific_journal-1936	173	5	r	r	NOUN
american_scientific_journal-1936	173	6	0	0	NUM
american_scientific_journal-1936	173	7	0.2	0.2	NUM
american_scientific_journal-1936	173	8	0.4	0.4	NUM
american_scientific_journal-1936	173	9	0.6	0.6	NUM
american_scientific_journal-1936	173	10	0.8	0.8	NUM
american_scientific_journal-1936	173	11	1	1	NUM
american_scientific_journal-1936	173	12	0	0	NUM
american_scientific_journal-1936	173	13	0.5	0.5	NUM
american_scientific_journal-1936	173	14	1	1	NUM
american_scientific_journal-1936	173	15	-1	-1	SYM
american_scientific_journal-1936	173	16	0	0	NUM
american_scientific_journal-1936	173	17	1	1	NUM
american_scientific_journal-1936	173	18	x	x	SYM
american_scientific_journal-1936	173	19	(	(	PUNCT
american_scientific_journal-1936	173	20	c	c	NOUN
american_scientific_journal-1936	173	21	)	)	PUNCT
american_scientific_journal-1936	173	22	btcs	btcs	NOUN
american_scientific_journal-1936	173	23	scheme	scheme	NOUN
american_scientific_journal-1936	173	24	t	t	PROPN
american_scientific_journal-1936	173	25	u	u	NOUN
american_scientific_journal-1936	173	26	0	0	NUM
american_scientific_journal-1936	173	27	0.2	0.2	NUM
american_scientific_journal-1936	173	28	0.4	0.4	NUM
american_scientific_journal-1936	173	29	0.6	0.6	NUM
american_scientific_journal-1936	173	30	0.8	0.8	NUM
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american_scientific_journal-1936	173	140	)	)	PUNCT
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american_scientific_journal-1936	176	192	(	(	PUNCT
american_scientific_journal-1936	176	193	25	25	NUM
american_scientific_journal-1936	176	194	)	)	PUNCT
american_scientific_journal-1936	176	195	and	and	CCONJ
american_scientific_journal-1936	176	196	(	(	PUNCT
american_scientific_journal-1936	176	197	26	26	NUM
american_scientific_journal-1936	176	198	)	)	PUNCT
american_scientific_journal-1936	176	199	obtained	obtain	VERB
american_scientific_journal-1936	176	200	using	use	VERB
american_scientific_journal-1936	176	201	the	the	DET
american_scientific_journal-1936	176	202	three	three	NUM
american_scientific_journal-1936	176	203	different	different	ADJ
american_scientific_journal-1936	176	204	schemes	scheme	NOUN
american_scientific_journal-1936	176	205	when	when	SCONJ
american_scientific_journal-1936	176	206	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1936	176	207	=	=	SYM
american_scientific_journal-1936	176	208	0.625	0.625	NUM
american_scientific_journal-1936	176	209	and	and	CCONJ
american_scientific_journal-1936	176	210	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	176	211	=	=	SYM
american_scientific_journal-1936	176	212	0.1	0.1	NUM
american_scientific_journal-1936	176	213	performance	performance	NOUN
american_scientific_journal-1936	176	214	of	of	ADP
american_scientific_journal-1936	176	215	the	the	DET
american_scientific_journal-1936	176	216	three	three	NUM
american_scientific_journal-1936	176	217	finite	finite	ADJ
american_scientific_journal-1936	176	218	difference	difference	NOUN
american_scientific_journal-1936	176	219	schemes	scheme	NOUN
american_scientific_journal-1936	176	220	can	can	AUX
american_scientific_journal-1936	176	221	be	be	AUX
american_scientific_journal-1936	176	222	evaluated	evaluate	VERB
american_scientific_journal-1936	176	223	up	up	ADP
american_scientific_journal-1936	176	224	on	on	ADP
american_scientific_journal-1936	176	225	comparing	compare	VERB
american_scientific_journal-1936	176	226	some	some	DET
american_scientific_journal-1936	176	227	factors	factor	NOUN
american_scientific_journal-1936	176	228	viz	viz	VERB
american_scientific_journal-1936	176	229	.	.	PUNCT
american_scientific_journal-1936	177	1	(	(	PUNCT
american_scientific_journal-1936	177	2	i	i	NOUN
american_scientific_journal-1936	177	3	)	)	PUNCT
american_scientific_journal-1936	177	4	stability	stability	NOUN
american_scientific_journal-1936	177	5	of	of	ADP
american_scientific_journal-1936	177	6	numerical	numerical	ADJ
american_scientific_journal-1936	177	7	schemes	scheme	NOUN
american_scientific_journal-1936	177	8	and	and	CCONJ
american_scientific_journal-1936	177	9	(	(	PUNCT
american_scientific_journal-1936	177	10	ii	ii	NOUN
american_scientific_journal-1936	177	11	)	)	PUNCT
american_scientific_journal-1936	177	12	error	error	NOUN
american_scientific_journal-1936	177	13	.	.	PUNCT
american_scientific_journal-1936	178	1	stability	stability	NOUN
american_scientific_journal-1936	178	2	criteria	criterion	NOUN
american_scientific_journal-1936	178	3	and	and	CCONJ
american_scientific_journal-1936	178	4	numerical	numerical	ADJ
american_scientific_journal-1936	178	5	solutions	solution	NOUN
american_scientific_journal-1936	178	6	show	show	VERB
american_scientific_journal-1936	178	7	that	that	SCONJ
american_scientific_journal-1936	178	8	the	the	DET
american_scientific_journal-1936	178	9	three	three	NUM
american_scientific_journal-1936	178	10	schemes	scheme	NOUN
american_scientific_journal-1936	178	11	work	work	VERB
american_scientific_journal-1936	178	12	well	well	ADV
american_scientific_journal-1936	178	13	and	and	CCONJ
american_scientific_journal-1936	178	14	each	each	PRON
american_scientific_journal-1936	178	15	produces	produce	VERB
american_scientific_journal-1936	178	16	reasonable	reasonable	ADJ
american_scientific_journal-1936	178	17	results	result	NOUN
american_scientific_journal-1936	178	18	in	in	ADP
american_scientific_journal-1936	178	19	case	case	NOUN
american_scientific_journal-1936	178	20	of	of	ADP
american_scientific_journal-1936	178	21	all	all	DET
american_scientific_journal-1936	178	22	test	test	NOUN
american_scientific_journal-1936	178	23	examples	example	NOUN
american_scientific_journal-1936	178	24	.	.	PUNCT
american_scientific_journal-1936	179	1	the	the	DET
american_scientific_journal-1936	179	2	numerical	numerical	ADJ
american_scientific_journal-1936	179	3	results	result	NOUN
american_scientific_journal-1936	179	4	are	be	AUX
american_scientific_journal-1936	179	5	obtained	obtain	VERB
american_scientific_journal-1936	179	6	using	use	VERB
american_scientific_journal-1936	179	7	matlab	matlab	PROPN
american_scientific_journal-1936	179	8	programming	programming	NOUN
american_scientific_journal-1936	179	9	and	and	CCONJ
american_scientific_journal-1936	179	10	the	the	DET
american_scientific_journal-1936	179	11	outcomes	outcome	NOUN
american_scientific_journal-1936	179	12	are	be	AUX
american_scientific_journal-1936	179	13	illustrated	illustrate	VERB
american_scientific_journal-1936	179	14	in	in	ADP
american_scientific_journal-1936	179	15	figures	figure	NOUN
american_scientific_journal-1936	179	16	1	1	NUM
american_scientific_journal-1936	179	17	–	–	SYM
american_scientific_journal-1936	179	18	6	6	NUM
american_scientific_journal-1936	179	19	.	.	PUNCT
american_scientific_journal-1936	180	1	the	the	DET
american_scientific_journal-1936	180	2	selection	selection	NOUN
american_scientific_journal-1936	180	3	of	of	ADP
american_scientific_journal-1936	180	4	spatial	spatial	ADJ
american_scientific_journal-1936	180	5	interval	interval	NOUN
american_scientific_journal-1936	180	6	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	180	7	=	=	SYM
american_scientific_journal-1936	180	8	0.125	0.125	NUM
american_scientific_journal-1936	180	9	and	and	CCONJ
american_scientific_journal-1936	180	10	the	the	DET
american_scientific_journal-1936	180	11	time	time	NOUN
american_scientific_journal-1936	180	12	step	step	NOUN
american_scientific_journal-1936	180	13	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	180	14	=	=	SYM
american_scientific_journal-1936	180	15	0.00625	0.00625	NUM
american_scientific_journal-1936	180	16	,	,	PUNCT
american_scientific_journal-1936	180	17	leads	lead	VERB
american_scientific_journal-1936	180	18	to	to	ADP
american_scientific_journal-1936	180	19	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1936	180	20	=	=	SYM
american_scientific_journal-1936	180	21	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	181	1	[	[	X
american_scientific_journal-1936	181	2	∆𝑡𝑡	∆𝑡𝑡	X
american_scientific_journal-1936	181	3	(	(	PUNCT
american_scientific_journal-1936	181	4	∆𝑥𝑥)2⁄	∆𝑥𝑥)2⁄	NOUN
american_scientific_journal-1936	181	5	]	]	X
american_scientific_journal-1936	181	6	=	=	PUNCT
american_scientific_journal-1936	181	7	0.4	0.4	NUM
american_scientific_journal-1936	181	8	<	<	X
american_scientific_journal-1936	181	9	1	1	NUM
american_scientific_journal-1936	181	10	2⁄	2⁄	NUM
american_scientific_journal-1936	181	11	.	.	PUNCT
american_scientific_journal-1936	182	1	the	the	DET
american_scientific_journal-1936	182	2	stability	stability	NOUN
american_scientific_journal-1936	182	3	analysis	analysis	NOUN
american_scientific_journal-1936	182	4	ftcs	ftcs	NOUN
american_scientific_journal-1936	182	5	scheme	scheme	NOUN
american_scientific_journal-1936	182	6	guarantees	guarantee	VERB
american_scientific_journal-1936	182	7	that	that	SCONJ
american_scientific_journal-1936	182	8	if	if	SCONJ
american_scientific_journal-1936	182	9	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1936	182	10	≤	≤	ADV
american_scientific_journal-1936	182	11	1	1	NUM
american_scientific_journal-1936	182	12	2⁄	2⁄	NUM
american_scientific_journal-1936	182	13	then	then	ADV
american_scientific_journal-1936	182	14	the	the	DET
american_scientific_journal-1936	182	15	condition	condition	NOUN
american_scientific_journal-1936	182	16	is	be	AUX
american_scientific_journal-1936	182	17	stable	stable	ADJ
american_scientific_journal-1936	182	18	.	.	PUNCT
american_scientific_journal-1936	183	1	this	this	DET
american_scientific_journal-1936	183	2	stability	stability	NOUN
american_scientific_journal-1936	183	3	criterion	criterion	NOUN
american_scientific_journal-1936	183	4	is	be	AUX
american_scientific_journal-1936	183	5	well	well	ADV
american_scientific_journal-1936	183	6	supported	support	VERB
american_scientific_journal-1936	183	7	by	by	ADP
american_scientific_journal-1936	183	8	the	the	DET
american_scientific_journal-1936	183	9	solutions	solution	NOUN
american_scientific_journal-1936	183	10	provided	provide	VERB
american_scientific_journal-1936	183	11	by	by	ADP
american_scientific_journal-1936	183	12	all	all	DET
american_scientific_journal-1936	183	13	the	the	DET
american_scientific_journal-1936	183	14	three	three	NUM
american_scientific_journal-1936	183	15	schemes	scheme	NOUN
american_scientific_journal-1936	183	16	in	in	ADP
american_scientific_journal-1936	183	17	case	case	NOUN
american_scientific_journal-1936	183	18	of	of	ADP
american_scientific_journal-1936	183	19	all	all	DET
american_scientific_journal-1936	183	20	problems	problem	NOUN
american_scientific_journal-1936	183	21	.	.	PUNCT
american_scientific_journal-1936	184	1	the	the	DET
american_scientific_journal-1936	184	2	same	same	ADJ
american_scientific_journal-1936	184	3	fact	fact	NOUN
american_scientific_journal-1936	184	4	has	have	AUX
american_scientific_journal-1936	184	5	observed	observe	VERB
american_scientific_journal-1936	184	6	in	in	ADP
american_scientific_journal-1936	184	7	figures	figure	NOUN
american_scientific_journal-1936	184	8	1	1	NUM
american_scientific_journal-1936	184	9	,	,	PUNCT
american_scientific_journal-1936	184	10	3	3	NUM
american_scientific_journal-1936	184	11	and	and	CCONJ
american_scientific_journal-1936	184	12	5	5	NUM
american_scientific_journal-1936	184	13	.	.	PUNCT
american_scientific_journal-1936	185	1	but	but	CCONJ
american_scientific_journal-1936	185	2	if	if	SCONJ
american_scientific_journal-1936	185	3	we	we	PRON
american_scientific_journal-1936	185	4	decrease	decrease	VERB
american_scientific_journal-1936	185	5	the	the	DET
american_scientific_journal-1936	185	6	spatial	spatial	ADJ
american_scientific_journal-1936	185	7	interval	interval	NOUN
american_scientific_journal-1936	185	8	to	to	ADP
american_scientific_journal-1936	185	9	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	186	1	=	=	SYM
american_scientific_journal-1936	186	2	0.1	0.1	NUM
american_scientific_journal-1936	186	3	for	for	ADP
american_scientific_journal-1936	186	4	better	well	ADJ
american_scientific_journal-1936	186	5	resolution	resolution	NOUN
american_scientific_journal-1936	186	6	and	and	CCONJ
american_scientific_journal-1936	186	7	considering	consider	VERB
american_scientific_journal-1936	186	8	the	the	DET
american_scientific_journal-1936	186	9	same	same	ADJ
american_scientific_journal-1936	186	10	time	time	NOUN
american_scientific_journal-1936	186	11	step	step	NOUN
american_scientific_journal-1936	186	12	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	187	1	=	=	SYM
american_scientific_journal-1936	187	2	0.00625	0.00625	NUM
american_scientific_journal-1936	187	3	,	,	PUNCT
american_scientific_journal-1936	187	4	leads	lead	VERB
american_scientific_journal-1936	187	5	to	to	ADP
american_scientific_journal-1936	187	6	𝑟𝑟	𝑟𝑟	NOUN
american_scientific_journal-1936	187	7	=	=	SYM
american_scientific_journal-1936	187	8	𝐷𝐷	𝐷𝐷	PROPN
american_scientific_journal-1936	188	1	[	[	X
american_scientific_journal-1936	188	2	∆𝑡𝑡	∆𝑡𝑡	X
american_scientific_journal-1936	188	3	(	(	PUNCT
american_scientific_journal-1936	188	4	∆𝑥𝑥)2⁄	∆𝑥𝑥)2⁄	NOUN
american_scientific_journal-1936	188	5	]	]	X
american_scientific_journal-1936	188	6	=	=	PUNCT
american_scientific_journal-1936	188	7	0.625	0.625	NUM
american_scientific_journal-1936	188	8	>	>	SYM
american_scientific_journal-1936	188	9	1	1	NUM
american_scientific_journal-1936	188	10	2⁄	2⁄	NUM
american_scientific_journal-1936	188	11	.	.	PUNCT
american_scientific_journal-1936	189	1	the	the	DET
american_scientific_journal-1936	189	2	stability	stability	NOUN
american_scientific_journal-1936	189	3	analysis	analysis	NOUN
american_scientific_journal-1936	189	4	of	of	ADP
american_scientific_journal-1936	189	5	ftcs	ftcs	NOUN
american_scientific_journal-1936	189	6	scheme	scheme	NOUN
american_scientific_journal-1936	189	7	0	0	NUM
american_scientific_journal-1936	189	8	0.2	0.2	NUM
american_scientific_journal-1936	189	9	0.4	0.4	NUM
american_scientific_journal-1936	189	10	0.6	0.6	NUM
american_scientific_journal-1936	189	11	0.8	0.8	NUM
american_scientific_journal-1936	189	12	1	1	NUM
american_scientific_journal-1936	189	13	0	0	NUM
american_scientific_journal-1936	189	14	0.51	0.51	NUM
american_scientific_journal-1936	189	15	1.52	1.52	NUM
american_scientific_journal-1936	189	16	0	0	NUM
american_scientific_journal-1936	189	17	0.5	0.5	NUM
american_scientific_journal-1936	189	18	1	1	NUM
american_scientific_journal-1936	189	19	x	x	SYM
american_scientific_journal-1936	189	20	(	(	PUNCT
american_scientific_journal-1936	189	21	a	a	PRON
american_scientific_journal-1936	189	22	)	)	PUNCT
american_scientific_journal-1936	189	23	ftcs	ftcs	NOUN
american_scientific_journal-1936	189	24	scheme	scheme	NOUN
american_scientific_journal-1936	189	25	t	t	PROPN
american_scientific_journal-1936	189	26	u	u	NOUN
american_scientific_journal-1936	189	27	0	0	NUM
american_scientific_journal-1936	189	28	0.2	0.2	NUM
american_scientific_journal-1936	189	29	0.4	0.4	NUM
american_scientific_journal-1936	189	30	0.6	0.6	NUM
american_scientific_journal-1936	189	31	0.8	0.8	NUM
american_scientific_journal-1936	189	32	1	1	NUM
american_scientific_journal-1936	189	33	0	0	NUM
american_scientific_journal-1936	189	34	0.51	0.51	NUM
american_scientific_journal-1936	189	35	1.52	1.52	NUM
american_scientific_journal-1936	189	36	0	0	NUM
american_scientific_journal-1936	189	37	2	2	NUM
american_scientific_journal-1936	189	38	4	4	NUM
american_scientific_journal-1936	189	39	x	x	SYM
american_scientific_journal-1936	189	40	10	10	NUM
american_scientific_journal-1936	189	41	-4	-4	NOUN
american_scientific_journal-1936	189	42	x	x	SYM
american_scientific_journal-1936	189	43	(	(	PUNCT
american_scientific_journal-1936	189	44	b	b	NOUN
american_scientific_journal-1936	189	45	)	)	PUNCT
american_scientific_journal-1936	189	46	error	error	NOUN
american_scientific_journal-1936	189	47	of	of	ADP
american_scientific_journal-1936	189	48	ftcs	ftcs	NOUN
american_scientific_journal-1936	189	49	scheme	scheme	NOUN
american_scientific_journal-1936	189	50	t	t	PROPN
american_scientific_journal-1936	189	51	e	e	NOUN
american_scientific_journal-1936	189	52	rr	rr	NOUN
american_scientific_journal-1936	190	1	o	o	NOUN
american_scientific_journal-1936	190	2	r	r	NOUN
american_scientific_journal-1936	190	3	0	0	NUM
american_scientific_journal-1936	190	4	0.2	0.2	NUM
american_scientific_journal-1936	190	5	0.4	0.4	NUM
american_scientific_journal-1936	190	6	0.6	0.6	NUM
american_scientific_journal-1936	190	7	0.8	0.8	NUM
american_scientific_journal-1936	190	8	1	1	NUM
american_scientific_journal-1936	190	9	0	0	NUM
american_scientific_journal-1936	190	10	0.51	0.51	NUM
american_scientific_journal-1936	190	11	1.52	1.52	NUM
american_scientific_journal-1936	190	12	0	0	NUM
american_scientific_journal-1936	190	13	0.5	0.5	NUM
american_scientific_journal-1936	190	14	1	1	NUM
american_scientific_journal-1936	190	15	x	x	SYM
american_scientific_journal-1936	190	16	(	(	PUNCT
american_scientific_journal-1936	190	17	c	c	NOUN
american_scientific_journal-1936	190	18	)	)	PUNCT
american_scientific_journal-1936	190	19	btcs	btcs	NOUN
american_scientific_journal-1936	190	20	scheme	scheme	NOUN
american_scientific_journal-1936	190	21	t	t	PROPN
american_scientific_journal-1936	190	22	u	u	NOUN
american_scientific_journal-1936	190	23	0	0	NUM
american_scientific_journal-1936	190	24	0.2	0.2	NUM
american_scientific_journal-1936	190	25	0.4	0.4	NUM
american_scientific_journal-1936	190	26	0.6	0.6	NUM
american_scientific_journal-1936	190	27	0.8	0.8	NUM
american_scientific_journal-1936	190	28	1	1	NUM
american_scientific_journal-1936	190	29	0	0	NUM
american_scientific_journal-1936	190	30	0.51	0.51	NUM
american_scientific_journal-1936	190	31	1.52	1.52	NUM
american_scientific_journal-1936	190	32	-2	-2	NOUN
american_scientific_journal-1936	190	33	0	0	NUM
american_scientific_journal-1936	190	34	2	2	NUM
american_scientific_journal-1936	190	35	x	x	SYM
american_scientific_journal-1936	190	36	10	10	NUM
american_scientific_journal-1936	190	37	-3	-3	INTJ
american_scientific_journal-1936	190	38	x	x	X
american_scientific_journal-1936	190	39	(	(	PUNCT
american_scientific_journal-1936	190	40	d	d	NOUN
american_scientific_journal-1936	190	41	)	)	PUNCT
american_scientific_journal-1936	190	42	error	error	NOUN
american_scientific_journal-1936	190	43	of	of	ADP
american_scientific_journal-1936	190	44	btcs	btcs	NOUN
american_scientific_journal-1936	190	45	scheme	scheme	NOUN
american_scientific_journal-1936	190	46	t	t	PROPN
american_scientific_journal-1936	190	47	e	e	NOUN
american_scientific_journal-1936	190	48	rr	rr	NOUN
american_scientific_journal-1936	190	49	o	o	NOUN
american_scientific_journal-1936	190	50	r	r	NOUN
american_scientific_journal-1936	190	51	0	0	NUM
american_scientific_journal-1936	190	52	0.2	0.2	NUM
american_scientific_journal-1936	190	53	0.4	0.4	NUM
american_scientific_journal-1936	190	54	0.6	0.6	NUM
american_scientific_journal-1936	190	55	0.8	0.8	NUM
american_scientific_journal-1936	190	56	1	1	NUM
american_scientific_journal-1936	190	57	0	0	NUM
american_scientific_journal-1936	190	58	0.51	0.51	NUM
american_scientific_journal-1936	190	59	1.52	1.52	NUM
american_scientific_journal-1936	190	60	0	0	NUM
american_scientific_journal-1936	190	61	0.5	0.5	NUM
american_scientific_journal-1936	190	62	1	1	NUM
american_scientific_journal-1936	190	63	x	x	SYM
american_scientific_journal-1936	190	64	(	(	PUNCT
american_scientific_journal-1936	190	65	e	e	NOUN
american_scientific_journal-1936	190	66	)	)	PUNCT
american_scientific_journal-1936	190	67	crank	crank	NOUN
american_scientific_journal-1936	190	68	-	-	PUNCT
american_scientific_journal-1936	190	69	nicolson	nicolson	PROPN
american_scientific_journal-1936	190	70	scheme	scheme	PROPN
american_scientific_journal-1936	190	71	t	t	PROPN
american_scientific_journal-1936	190	72	u	u	NOUN
american_scientific_journal-1936	190	73	0	0	NUM
american_scientific_journal-1936	190	74	0.2	0.2	NUM
american_scientific_journal-1936	190	75	0.4	0.4	NUM
american_scientific_journal-1936	190	76	0.6	0.6	NUM
american_scientific_journal-1936	190	77	0.8	0.8	NUM
american_scientific_journal-1936	190	78	1	1	NUM
american_scientific_journal-1936	190	79	0	0	NUM
american_scientific_journal-1936	190	80	0.51	0.51	NUM
american_scientific_journal-1936	190	81	1.52	1.52	NUM
american_scientific_journal-1936	190	82	-1	-1	SYM
american_scientific_journal-1936	190	83	0	0	NUM
american_scientific_journal-1936	190	84	1	1	NUM
american_scientific_journal-1936	190	85	x	x	SYM
american_scientific_journal-1936	190	86	10	10	NUM
american_scientific_journal-1936	190	87	-3	-3	INTJ
american_scientific_journal-1936	190	88	x	x	X
american_scientific_journal-1936	190	89	(	(	PUNCT
american_scientific_journal-1936	190	90	f	f	X
american_scientific_journal-1936	190	91	)	)	PUNCT
american_scientific_journal-1936	190	92	error	error	NOUN
american_scientific_journal-1936	190	93	of	of	ADP
american_scientific_journal-1936	190	94	crank	crank	NOUN
american_scientific_journal-1936	190	95	-	-	PUNCT
american_scientific_journal-1936	190	96	nicolson	nicolson	PROPN
american_scientific_journal-1936	190	97	scheme	scheme	PROPN
american_scientific_journal-1936	190	98	t	t	PROPN
american_scientific_journal-1936	190	99	e	e	NOUN
american_scientific_journal-1936	190	100	rr	rr	NOUN
american_scientific_journal-1936	190	101	o	o	NOUN
american_scientific_journal-1936	190	102	r	r	NOUN
american_scientific_journal-1936	190	103	american	american	PROPN
american_scientific_journal-1936	190	104	scientific	scientific	ADJ
american_scientific_journal-1936	190	105	research	research	NOUN
american_scientific_journal-1936	190	106	journal	journal	NOUN
american_scientific_journal-1936	190	107	for	for	ADP
american_scientific_journal-1936	190	108	engineering	engineering	NOUN
american_scientific_journal-1936	190	109	,	,	PUNCT
american_scientific_journal-1936	190	110	technology	technology	NOUN
american_scientific_journal-1936	190	111	,	,	PUNCT
american_scientific_journal-1936	190	112	and	and	CCONJ
american_scientific_journal-1936	190	113	sciences	science	NOUN
american_scientific_journal-1936	190	114	(	(	PUNCT
american_scientific_journal-1936	190	115	asrjets	asrjet	NOUN
american_scientific_journal-1936	190	116	)	)	PUNCT
american_scientific_journal-1936	190	117	(	(	PUNCT
american_scientific_journal-1936	190	118	2016	2016	NUM
american_scientific_journal-1936	190	119	)	)	PUNCT
american_scientific_journal-1936	190	120	volume	volume	NOUN
american_scientific_journal-1936	190	121	26	26	NUM
american_scientific_journal-1936	190	122	,	,	PUNCT
american_scientific_journal-1936	190	123	no	no	DET
american_scientific_journal-1936	190	124	3	3	NUM
american_scientific_journal-1936	190	125	,	,	PUNCT
american_scientific_journal-1936	190	126	pp	pp	ADV
american_scientific_journal-1936	190	127	140	140	NUM
american_scientific_journal-1936	190	128	-	-	SYM
american_scientific_journal-1936	190	129	154	154	NUM
american_scientific_journal-1936	190	130	153	153	NUM
american_scientific_journal-1936	190	131	predicts	predict	NOUN
american_scientific_journal-1936	190	132	that	that	SCONJ
american_scientific_journal-1936	190	133	if	if	SCONJ
american_scientific_journal-1936	190	134	𝑟𝑟	𝑟𝑟	ADV
american_scientific_journal-1936	190	135	>	>	X
american_scientific_journal-1936	190	136	1	1	NUM
american_scientific_journal-1936	190	137	2⁄	2⁄	NUM
american_scientific_journal-1936	190	138	then	then	ADV
american_scientific_journal-1936	190	139	the	the	DET
american_scientific_journal-1936	190	140	condition	condition	NOUN
american_scientific_journal-1936	190	141	is	be	AUX
american_scientific_journal-1936	190	142	unstable	unstable	ADJ
american_scientific_journal-1936	190	143	.	.	PUNCT
american_scientific_journal-1936	191	1	hence	hence	ADV
american_scientific_journal-1936	191	2	,	,	PUNCT
american_scientific_journal-1936	191	3	the	the	DET
american_scientific_journal-1936	191	4	ftcs	ftcs	NOUN
american_scientific_journal-1936	191	5	scheme	scheme	NOUN
american_scientific_journal-1936	191	6	provides	provide	VERB
american_scientific_journal-1936	191	7	unstable	unstable	ADJ
american_scientific_journal-1936	191	8	solution	solution	NOUN
american_scientific_journal-1936	191	9	and	and	CCONJ
american_scientific_journal-1936	191	10	as	as	ADP
american_scientific_journal-1936	191	11	a	a	DET
american_scientific_journal-1936	191	12	result	result	NOUN
american_scientific_journal-1936	191	13	the	the	DET
american_scientific_journal-1936	191	14	error	error	NOUN
american_scientific_journal-1936	191	15	blows	blow	VERB
american_scientific_journal-1936	191	16	up	up	ADP
american_scientific_journal-1936	191	17	as	as	SCONJ
american_scientific_journal-1936	191	18	shown	show	VERB
american_scientific_journal-1936	191	19	in	in	ADP
american_scientific_journal-1936	191	20	figures	figure	NOUN
american_scientific_journal-1936	191	21	2a	2a	NUM
american_scientific_journal-1936	191	22	–	–	PUNCT
american_scientific_journal-1936	191	23	2b	2b	NUM
american_scientific_journal-1936	191	24	and	and	CCONJ
american_scientific_journal-1936	191	25	4a	4a	NUM
american_scientific_journal-1936	191	26	–	–	PUNCT
american_scientific_journal-1936	191	27	4b	4b	PROPN
american_scientific_journal-1936	191	28	.	.	PUNCT
american_scientific_journal-1936	192	1	however	however	ADV
american_scientific_journal-1936	192	2	,	,	PUNCT
american_scientific_journal-1936	192	3	the	the	DET
american_scientific_journal-1936	192	4	btcs	btcs	NOUN
american_scientific_journal-1936	192	5	and	and	CCONJ
american_scientific_journal-1936	192	6	crank	crank	NOUN
american_scientific_journal-1936	192	7	–	–	PUNCT
american_scientific_journal-1936	192	8	nicolson	nicolson	PROPN
american_scientific_journal-1936	192	9	schemes	scheme	NOUN
american_scientific_journal-1936	192	10	work	work	VERB
american_scientific_journal-1936	192	11	quite	quite	ADV
american_scientific_journal-1936	192	12	well	well	ADV
american_scientific_journal-1936	192	13	and	and	CCONJ
american_scientific_journal-1936	192	14	provide	provide	VERB
american_scientific_journal-1936	192	15	stable	stable	ADJ
american_scientific_journal-1936	192	16	solutions	solution	NOUN
american_scientific_journal-1936	192	17	as	as	SCONJ
american_scientific_journal-1936	192	18	shown	show	VERB
american_scientific_journal-1936	192	19	in	in	ADP
american_scientific_journal-1936	192	20	figures	figure	NOUN
american_scientific_journal-1936	192	21	2c	2c	NUM
american_scientific_journal-1936	192	22	–	–	PUNCT
american_scientific_journal-1936	192	23	2f	2f	NUM
american_scientific_journal-1936	192	24	and	and	CCONJ
american_scientific_journal-1936	192	25	4c	4c	NOUN
american_scientific_journal-1936	192	26	–	–	PUNCT
american_scientific_journal-1936	192	27	4f	4f	NUM
american_scientific_journal-1936	192	28	.	.	PUNCT
american_scientific_journal-1936	193	1	with	with	ADP
american_scientific_journal-1936	193	2	the	the	DET
american_scientific_journal-1936	193	3	same	same	ADJ
american_scientific_journal-1936	193	4	spatial	spatial	ADJ
american_scientific_journal-1936	193	5	interval	interval	NOUN
american_scientific_journal-1936	193	6	∆𝑥𝑥	∆𝑥𝑥	NOUN
american_scientific_journal-1936	193	7	=	=	SYM
american_scientific_journal-1936	193	8	0.1	0.1	NUM
american_scientific_journal-1936	193	9	and	and	CCONJ
american_scientific_journal-1936	193	10	time	time	NOUN
american_scientific_journal-1936	193	11	step	step	NOUN
american_scientific_journal-1936	193	12	∆𝑡𝑡	∆𝑡𝑡	PROPN
american_scientific_journal-1936	194	1	=	=	SYM
american_scientific_journal-1936	195	1	0.00625	0.00625	NUM
american_scientific_journal-1936	195	2	,	,	PUNCT
american_scientific_journal-1936	195	3	all	all	DET
american_scientific_journal-1936	195	4	the	the	DET
american_scientific_journal-1936	195	5	three	three	NUM
american_scientific_journal-1936	195	6	schemes	scheme	NOUN
american_scientific_journal-1936	195	7	including	include	VERB
american_scientific_journal-1936	195	8	ftcs	ftcs	NOUN
american_scientific_journal-1936	195	9	produce	produce	VERB
american_scientific_journal-1936	195	10	stable	stable	ADJ
american_scientific_journal-1936	195	11	solutions	solution	NOUN
american_scientific_journal-1936	195	12	.	.	PUNCT
american_scientific_journal-1936	196	1	despite	despite	SCONJ
american_scientific_journal-1936	196	2	of	of	ADP
american_scientific_journal-1936	196	3	the	the	DET
american_scientific_journal-1936	196	4	fact	fact	NOUN
american_scientific_journal-1936	196	5	that	that	SCONJ
american_scientific_journal-1936	196	6	𝑟𝑟	𝑟𝑟	AUX
american_scientific_journal-1936	196	7	=	=	SYM
american_scientific_journal-1936	196	8	0.625	0.625	NUM
american_scientific_journal-1936	196	9	does	do	AUX
american_scientific_journal-1936	196	10	n’t	not	PART
american_scientific_journal-1936	196	11	strictly	strictly	ADV
american_scientific_journal-1936	196	12	satisfy	satisfy	VERB
american_scientific_journal-1936	196	13	the	the	DET
american_scientific_journal-1936	196	14	stability	stability	NOUN
american_scientific_journal-1936	196	15	condition	condition	NOUN
american_scientific_journal-1936	196	16	𝑟𝑟	𝑟𝑟	ADP
american_scientific_journal-1936	196	17	≤	≤	NUM
american_scientific_journal-1936	196	18	1	1	NUM
american_scientific_journal-1936	196	19	2⁄	2⁄	NUM
american_scientific_journal-1936	196	20	as	as	SCONJ
american_scientific_journal-1936	196	21	shown	show	VERB
american_scientific_journal-1936	196	22	in	in	ADP
american_scientific_journal-1936	196	23	figures	figure	NOUN
american_scientific_journal-1936	196	24	6a	6a	NOUN
american_scientific_journal-1936	196	25	–	–	PUNCT
american_scientific_journal-1936	196	26	6f	6f	NUM
american_scientific_journal-1936	196	27	.	.	PUNCT
american_scientific_journal-1936	197	1	this	this	PRON
american_scientific_journal-1936	197	2	implies	imply	VERB
american_scientific_journal-1936	197	3	that	that	SCONJ
american_scientific_journal-1936	197	4	the	the	DET
american_scientific_journal-1936	197	5	stability	stability	NOUN
american_scientific_journal-1936	197	6	of	of	ADP
american_scientific_journal-1936	197	7	the	the	DET
american_scientific_journal-1936	197	8	ftcs	ftcs	NOUN
american_scientific_journal-1936	197	9	scheme	scheme	NOUN
american_scientific_journal-1936	197	10	is	be	AUX
american_scientific_journal-1936	197	11	not	not	PART
american_scientific_journal-1936	197	12	a	a	DET
american_scientific_journal-1936	197	13	necessary	necessary	ADJ
american_scientific_journal-1936	197	14	condition	condition	NOUN
american_scientific_journal-1936	197	15	,	,	PUNCT
american_scientific_journal-1936	197	16	but	but	CCONJ
american_scientific_journal-1936	197	17	only	only	ADV
american_scientific_journal-1936	197	18	sufficient	sufficient	ADJ
american_scientific_journal-1936	197	19	one	one	NUM
american_scientific_journal-1936	197	20	.	.	PUNCT
american_scientific_journal-1936	198	1	besides	besides	SCONJ
american_scientific_journal-1936	198	2	,	,	PUNCT
american_scientific_journal-1936	198	3	if	if	SCONJ
american_scientific_journal-1936	198	4	it	it	PRON
american_scientific_journal-1936	198	5	converges	converge	VERB
american_scientific_journal-1936	198	6	then	then	ADV
american_scientific_journal-1936	198	7	the	the	DET
american_scientific_journal-1936	198	8	accuracy	accuracy	NOUN
american_scientific_journal-1936	198	9	of	of	ADP
american_scientific_journal-1936	198	10	ftcs	ftcs	NOUN
american_scientific_journal-1936	198	11	may	may	AUX
american_scientific_journal-1936	198	12	be	be	AUX
american_scientific_journal-1936	198	13	better	well	ADJ
american_scientific_journal-1936	198	14	than	than	ADP
american_scientific_journal-1936	198	15	that	that	PRON
american_scientific_journal-1936	198	16	of	of	ADP
american_scientific_journal-1936	198	17	btcs	btcs	NOUN
american_scientific_journal-1936	198	18	scheme	scheme	NOUN
american_scientific_journal-1936	198	19	,	,	PUNCT
american_scientific_journal-1936	198	20	but	but	CCONJ
american_scientific_journal-1936	198	21	generally	generally	ADV
american_scientific_journal-1936	198	22	not	not	PART
american_scientific_journal-1936	198	23	better	well	ADJ
american_scientific_journal-1936	198	24	than	than	ADP
american_scientific_journal-1936	198	25	that	that	PRON
american_scientific_journal-1936	198	26	of	of	ADP
american_scientific_journal-1936	198	27	the	the	DET
american_scientific_journal-1936	198	28	crank	crank	NOUN
american_scientific_journal-1936	198	29	–	–	PUNCT
american_scientific_journal-1936	198	30	nicolson	nicolson	PROPN
american_scientific_journal-1936	198	31	scheme	scheme	NOUN
american_scientific_journal-1936	198	32	.	.	PUNCT
american_scientific_journal-1936	199	1	the	the	DET
american_scientific_journal-1936	199	2	observations	observation	NOUN
american_scientific_journal-1936	199	3	regarding	regard	VERB
american_scientific_journal-1936	199	4	stability	stability	NOUN
american_scientific_journal-1936	199	5	of	of	ADP
american_scientific_journal-1936	199	6	the	the	DET
american_scientific_journal-1936	199	7	solutions	solution	NOUN
american_scientific_journal-1936	199	8	made	make	VERB
american_scientific_journal-1936	199	9	from	from	ADP
american_scientific_journal-1936	199	10	the	the	DET
american_scientific_journal-1936	199	11	figures	figure	NOUN
american_scientific_journal-1936	199	12	are	be	AUX
american_scientific_journal-1936	199	13	summarized	summarize	VERB
american_scientific_journal-1936	199	14	in	in	ADP
american_scientific_journal-1936	199	15	a	a	DET
american_scientific_journal-1936	199	16	tabular	tabular	NOUN
american_scientific_journal-1936	199	17	form	form	NOUN
american_scientific_journal-1936	199	18	as	as	ADP
american_scientific_journal-1936	199	19	below	below	ADV
american_scientific_journal-1936	199	20	:	:	PUNCT
american_scientific_journal-1936	199	21	table	table	NOUN
american_scientific_journal-1936	199	22	1	1	NUM
american_scientific_journal-1936	199	23	:	:	PUNCT
american_scientific_journal-1936	199	24	stability	stability	NOUN
american_scientific_journal-1936	199	25	of	of	ADP
american_scientific_journal-1936	199	26	the	the	DET
american_scientific_journal-1936	199	27	solutions	solution	NOUN
american_scientific_journal-1936	199	28	of	of	ADP
american_scientific_journal-1936	199	29	one	one	NUM
american_scientific_journal-1936	199	30	dimensional	dimensional	ADJ
american_scientific_journal-1936	199	31	diffusion	diffusion	NOUN
american_scientific_journal-1936	199	32	equation	equation	NOUN
american_scientific_journal-1936	199	33	problems	problem	NOUN
american_scientific_journal-1936	199	34	finite	finite	VERB
american_scientific_journal-1936	199	35	difference	difference	NOUN
american_scientific_journal-1936	199	36	schemes	scheme	NOUN
american_scientific_journal-1936	199	37	stability	stability	NOUN
american_scientific_journal-1936	199	38	condition	condition	NOUN
american_scientific_journal-1936	199	39	for	for	ADP
american_scientific_journal-1936	199	40	𝒓𝒓	𝒓𝒓	PROPN
american_scientific_journal-1936	199	41	≤	≤	NOUN
american_scientific_journal-1936	199	42	𝟎𝟎.𝟓𝟓	𝟎𝟎.𝟓𝟓	NUM
american_scientific_journal-1936	199	43	stability	stability	NOUN
american_scientific_journal-1936	199	44	condition	condition	NOUN
american_scientific_journal-1936	199	45	for	for	ADP
american_scientific_journal-1936	199	46	𝒓𝒓	𝒓𝒓	PROPN
american_scientific_journal-1936	199	47	>	>	SYM
american_scientific_journal-1936	199	48	0.5	0.5	NUM
american_scientific_journal-1936	199	49	problem	problem	NOUN
american_scientific_journal-1936	199	50	1	1	NUM
american_scientific_journal-1936	199	51	ftcs	ftcs	NOUN
american_scientific_journal-1936	199	52	stable	stable	ADJ
american_scientific_journal-1936	199	53	(	(	PUNCT
american_scientific_journal-1936	199	54	fig	fig	NOUN
american_scientific_journal-1936	199	55	.	.	PUNCT
american_scientific_journal-1936	200	1	1a	1a	X
american_scientific_journal-1936	200	2	)	)	PUNCT
american_scientific_journal-1936	200	3	unstable	unstable	ADJ
american_scientific_journal-1936	200	4	(	(	PUNCT
american_scientific_journal-1936	200	5	fig	fig	NOUN
american_scientific_journal-1936	200	6	.	.	PUNCT
american_scientific_journal-1936	201	1	2a	2a	NUM
american_scientific_journal-1936	201	2	)	)	PUNCT
american_scientific_journal-1936	201	3	btcs	btcs	NOUN
american_scientific_journal-1936	201	4	stable	stable	ADJ
american_scientific_journal-1936	201	5	(	(	PUNCT
american_scientific_journal-1936	201	6	fig	fig	NOUN
american_scientific_journal-1936	201	7	.	.	PUNCT
american_scientific_journal-1936	202	1	1c	1c	NOUN
american_scientific_journal-1936	202	2	)	)	PUNCT
american_scientific_journal-1936	202	3	stable	stable	ADJ
american_scientific_journal-1936	202	4	(	(	PUNCT
american_scientific_journal-1936	202	5	fig	fig	NOUN
american_scientific_journal-1936	202	6	.	.	PUNCT
american_scientific_journal-1936	203	1	2c	2c	NUM
american_scientific_journal-1936	203	2	)	)	PUNCT
american_scientific_journal-1936	204	1	cn	cn	PROPN
american_scientific_journal-1936	204	2	stable	stable	ADJ
american_scientific_journal-1936	204	3	(	(	PUNCT
american_scientific_journal-1936	204	4	fig	fig	NOUN
american_scientific_journal-1936	204	5	.	.	PUNCT
american_scientific_journal-1936	205	1	1e	1e	NUM
american_scientific_journal-1936	205	2	)	)	PUNCT
american_scientific_journal-1936	205	3	stable	stable	ADJ
american_scientific_journal-1936	205	4	(	(	PUNCT
american_scientific_journal-1936	205	5	fig	fig	NOUN
american_scientific_journal-1936	205	6	.	.	PUNCT
american_scientific_journal-1936	206	1	2e	2e	NUM
american_scientific_journal-1936	206	2	)	)	PUNCT
american_scientific_journal-1936	206	3	problem	problem	NOUN
american_scientific_journal-1936	206	4	2	2	NUM
american_scientific_journal-1936	206	5	ftcs	ftcs	NOUN
american_scientific_journal-1936	206	6	stable	stable	ADJ
american_scientific_journal-1936	206	7	(	(	PUNCT
american_scientific_journal-1936	206	8	fig	fig	NOUN
american_scientific_journal-1936	206	9	.	.	PUNCT
american_scientific_journal-1936	207	1	3a	3a	NUM
american_scientific_journal-1936	207	2	)	)	PUNCT
american_scientific_journal-1936	207	3	unstable	unstable	ADJ
american_scientific_journal-1936	207	4	(	(	PUNCT
american_scientific_journal-1936	207	5	fig	fig	NOUN
american_scientific_journal-1936	207	6	.	.	PUNCT
american_scientific_journal-1936	208	1	4a	4a	NUM
american_scientific_journal-1936	208	2	)	)	PUNCT
american_scientific_journal-1936	208	3	btcs	btcs	NOUN
american_scientific_journal-1936	208	4	stable	stable	ADJ
american_scientific_journal-1936	208	5	(	(	PUNCT
american_scientific_journal-1936	208	6	fig	fig	NOUN
american_scientific_journal-1936	208	7	.	.	PUNCT
american_scientific_journal-1936	209	1	3c	3c	NUM
american_scientific_journal-1936	209	2	)	)	PUNCT
american_scientific_journal-1936	209	3	stable	stable	ADJ
american_scientific_journal-1936	209	4	(	(	PUNCT
american_scientific_journal-1936	209	5	fig	fig	NOUN
american_scientific_journal-1936	209	6	.	.	PUNCT
american_scientific_journal-1936	210	1	4c	4c	NOUN
american_scientific_journal-1936	210	2	)	)	PUNCT
american_scientific_journal-1936	211	1	cn	cn	PROPN
american_scientific_journal-1936	211	2	stable	stable	ADJ
american_scientific_journal-1936	211	3	(	(	PUNCT
american_scientific_journal-1936	211	4	fig	fig	NOUN
american_scientific_journal-1936	211	5	.	.	PUNCT
american_scientific_journal-1936	212	1	3e	3e	X
american_scientific_journal-1936	212	2	)	)	PUNCT
american_scientific_journal-1936	212	3	stable	stable	ADJ
american_scientific_journal-1936	212	4	(	(	PUNCT
american_scientific_journal-1936	212	5	fig	fig	NOUN
american_scientific_journal-1936	212	6	.	.	PUNCT
american_scientific_journal-1936	213	1	4e	4e	NOUN
american_scientific_journal-1936	213	2	)	)	PUNCT
american_scientific_journal-1936	213	3	problem	problem	NOUN
american_scientific_journal-1936	213	4	3	3	NUM
american_scientific_journal-1936	213	5	ftcs	ftcs	NOUN
american_scientific_journal-1936	213	6	stable	stable	ADJ
american_scientific_journal-1936	213	7	(	(	PUNCT
american_scientific_journal-1936	213	8	fig	fig	NOUN
american_scientific_journal-1936	213	9	.	.	PUNCT
american_scientific_journal-1936	214	1	5a	5a	NUM
american_scientific_journal-1936	214	2	)	)	PUNCT
american_scientific_journal-1936	214	3	stable	stable	ADJ
american_scientific_journal-1936	214	4	(	(	PUNCT
american_scientific_journal-1936	214	5	fig	fig	NOUN
american_scientific_journal-1936	214	6	.	.	PUNCT
american_scientific_journal-1936	215	1	6a	6a	NOUN
american_scientific_journal-1936	215	2	)	)	PUNCT
american_scientific_journal-1936	215	3	btcs	btcs	NOUN
american_scientific_journal-1936	215	4	stable	stable	ADJ
american_scientific_journal-1936	215	5	(	(	PUNCT
american_scientific_journal-1936	215	6	fig	fig	NOUN
american_scientific_journal-1936	215	7	.	.	PUNCT
american_scientific_journal-1936	216	1	5c	5c	NUM
american_scientific_journal-1936	216	2	)	)	PUNCT
american_scientific_journal-1936	216	3	stable	stable	ADJ
american_scientific_journal-1936	216	4	(	(	PUNCT
american_scientific_journal-1936	216	5	fig	fig	NOUN
american_scientific_journal-1936	216	6	.	.	PUNCT
american_scientific_journal-1936	217	1	6c	6c	NOUN
american_scientific_journal-1936	217	2	)	)	PUNCT
american_scientific_journal-1936	218	1	cn	cn	PROPN
american_scientific_journal-1936	218	2	stable	stable	ADJ
american_scientific_journal-1936	218	3	(	(	PUNCT
american_scientific_journal-1936	218	4	fig	fig	NOUN
american_scientific_journal-1936	218	5	.	.	PUNCT
american_scientific_journal-1936	219	1	5e	5e	NOUN
american_scientific_journal-1936	219	2	)	)	PUNCT
american_scientific_journal-1936	219	3	stable	stable	ADJ
american_scientific_journal-1936	219	4	(	(	PUNCT
american_scientific_journal-1936	219	5	fig	fig	NOUN
american_scientific_journal-1936	219	6	.	.	PUNCT
american_scientific_journal-1936	220	1	6e	6e	NOUN
american_scientific_journal-1936	220	2	)	)	PUNCT
american_scientific_journal-1936	220	3	4	4	NUM
american_scientific_journal-1936	220	4	.	.	PUNCT
american_scientific_journal-1936	221	1	conclusions	conclusion	NOUN
american_scientific_journal-1936	221	2	in	in	ADP
american_scientific_journal-1936	221	3	this	this	DET
american_scientific_journal-1936	221	4	study	study	NOUN
american_scientific_journal-1936	221	5	,	,	PUNCT
american_scientific_journal-1936	221	6	we	we	PRON
american_scientific_journal-1936	221	7	have	have	AUX
american_scientific_journal-1936	221	8	discussed	discuss	VERB
american_scientific_journal-1936	221	9	application	application	NOUN
american_scientific_journal-1936	221	10	of	of	ADP
american_scientific_journal-1936	221	11	numerical	numerical	ADJ
american_scientific_journal-1936	221	12	schemes	scheme	NOUN
american_scientific_journal-1936	221	13	on	on	ADP
american_scientific_journal-1936	221	14	one	one	NUM
american_scientific_journal-1936	221	15	dimensional	dimensional	ADJ
american_scientific_journal-1936	221	16	diffusion	diffusion	NOUN
american_scientific_journal-1936	221	17	equation	equation	NOUN
american_scientific_journal-1936	221	18	.	.	PUNCT
american_scientific_journal-1936	222	1	it	it	PRON
american_scientific_journal-1936	222	2	is	be	AUX
american_scientific_journal-1936	222	3	observed	observe	VERB
american_scientific_journal-1936	222	4	from	from	ADP
american_scientific_journal-1936	222	5	numerical	numerical	ADJ
american_scientific_journal-1936	222	6	computation	computation	NOUN
american_scientific_journal-1936	222	7	that	that	SCONJ
american_scientific_journal-1936	222	8	all	all	DET
american_scientific_journal-1936	222	9	the	the	DET
american_scientific_journal-1936	222	10	three	three	NUM
american_scientific_journal-1936	222	11	schemes	scheme	NOUN
american_scientific_journal-1936	222	12	worked	work	VERB
american_scientific_journal-1936	222	13	well	well	ADV
american_scientific_journal-1936	222	14	according	accord	VERB
american_scientific_journal-1936	222	15	to	to	ADP
american_scientific_journal-1936	222	16	the	the	DET
american_scientific_journal-1936	222	17	stability	stability	NOUN
american_scientific_journal-1936	222	18	criteria	criterion	NOUN
american_scientific_journal-1936	222	19	and	and	CCONJ
american_scientific_journal-1936	222	20	each	each	DET
american_scientific_journal-1936	222	21	scheme	scheme	NOUN
american_scientific_journal-1936	222	22	produced	produce	VERB
american_scientific_journal-1936	222	23	reasonable	reasonable	ADJ
american_scientific_journal-1936	222	24	approximation	approximation	NOUN
american_scientific_journal-1936	222	25	for	for	ADP
american_scientific_journal-1936	222	26	the	the	DET
american_scientific_journal-1936	222	27	density	density	NOUN
american_scientific_journal-1936	222	28	variable	variable	PROPN
american_scientific_journal-1936	222	29	𝑢𝑢(𝑥𝑥	𝑢𝑢(𝑥𝑥	PROPN
american_scientific_journal-1936	222	30	,	,	PUNCT
american_scientific_journal-1936	222	31	𝑡𝑡	𝑡𝑡	NOUN
american_scientific_journal-1936	222	32	)	)	PUNCT
american_scientific_journal-1936	222	33	.	.	PUNCT
american_scientific_journal-1936	223	1	the	the	DET
american_scientific_journal-1936	223	2	three	three	NUM
american_scientific_journal-1936	223	3	schemes	scheme	NOUN
american_scientific_journal-1936	223	4	are	be	AUX
american_scientific_journal-1936	223	5	compared	compare	VERB
american_scientific_journal-1936	223	6	based	base	VERB
american_scientific_journal-1936	223	7	on	on	ADP
american_scientific_journal-1936	223	8	the	the	DET
american_scientific_journal-1936	223	9	results	result	NOUN
american_scientific_journal-1936	223	10	of	of	ADP
american_scientific_journal-1936	223	11	the	the	DET
american_scientific_journal-1936	223	12	three	three	NUM
american_scientific_journal-1936	223	13	test	test	NOUN
american_scientific_journal-1936	223	14	problems	problem	NOUN
american_scientific_journal-1936	223	15	.	.	PUNCT
american_scientific_journal-1936	224	1	the	the	DET
american_scientific_journal-1936	224	2	comparison	comparison	NOUN
american_scientific_journal-1936	224	3	indicates	indicate	VERB
american_scientific_journal-1936	224	4	that	that	SCONJ
american_scientific_journal-1936	224	5	the	the	DET
american_scientific_journal-1936	224	6	approximate	approximate	ADJ
american_scientific_journal-1936	224	7	solution	solution	NOUN
american_scientific_journal-1936	224	8	provided	provide	VERB
american_scientific_journal-1936	224	9	by	by	ADP
american_scientific_journal-1936	224	10	crank	crank	NOUN
american_scientific_journal-1936	224	11	–	–	PUNCT
american_scientific_journal-1936	224	12	nicolson	nicolson	PROPN
american_scientific_journal-1936	224	13	scheme	scheme	NOUN
american_scientific_journal-1936	224	14	is	be	AUX
american_scientific_journal-1936	224	15	better	well	ADJ
american_scientific_journal-1936	224	16	than	than	ADP
american_scientific_journal-1936	224	17	the	the	DET
american_scientific_journal-1936	224	18	other	other	ADJ
american_scientific_journal-1936	224	19	two	two	NUM
american_scientific_journal-1936	224	20	schemes	scheme	NOUN
american_scientific_journal-1936	224	21	.	.	PUNCT
american_scientific_journal-1936	225	1	hence	hence	ADV
american_scientific_journal-1936	225	2	,	,	PUNCT
american_scientific_journal-1936	225	3	crank	crank	NOUN
american_scientific_journal-1936	225	4	–	–	PUNCT
american_scientific_journal-1936	225	5	nicolson	nicolson	PROPN
american_scientific_journal-1936	225	6	scheme	scheme	NOUN
american_scientific_journal-1936	225	7	is	be	AUX
american_scientific_journal-1936	225	8	recommended	recommend	VERB
american_scientific_journal-1936	225	9	for	for	ADP
american_scientific_journal-1936	225	10	solving	solve	VERB
american_scientific_journal-1936	225	11	one	one	NUM
american_scientific_journal-1936	225	12	–	–	PUNCT
american_scientific_journal-1936	225	13	dimensional	dimensional	ADJ
american_scientific_journal-1936	225	14	equation	equation	NOUN
american_scientific_journal-1936	225	15	for	for	ADP
american_scientific_journal-1936	225	16	a	a	DET
american_scientific_journal-1936	225	17	better	well	ADJ
american_scientific_journal-1936	225	18	approximation	approximation	NOUN
american_scientific_journal-1936	225	19	.	.	PUNCT
american_scientific_journal-1936	226	1	references	reference	NOUN
american_scientific_journal-1936	226	2	[	[	X
american_scientific_journal-1936	226	3	1	1	NUM
american_scientific_journal-1936	226	4	]	]	PUNCT
american_scientific_journal-1936	226	5	bergara	bergara	ADJ
american_scientific_journal-1936	226	6	a.	a.	NOUN
american_scientific_journal-1936	226	7	finite	finite	PROPN
american_scientific_journal-1936	226	8	–	–	PUNCT
american_scientific_journal-1936	226	9	difference	difference	NOUN
american_scientific_journal-1936	226	10	numerical	numerical	ADJ
american_scientific_journal-1936	226	11	methods	method	NOUN
american_scientific_journal-1936	226	12	of	of	ADP
american_scientific_journal-1936	226	13	partial	partial	ADJ
american_scientific_journal-1936	226	14	differential	differential	ADJ
american_scientific_journal-1936	226	15	equation	equation	NOUN
american_scientific_journal-1936	226	16	in	in	ADP
american_scientific_journal-1936	226	17	finance	finance	NOUN
american_scientific_journal-1936	226	18	with	with	ADP
american_scientific_journal-1936	226	19	american	american	ADJ
american_scientific_journal-1936	226	20	scientific	scientific	ADJ
american_scientific_journal-1936	226	21	research	research	NOUN
american_scientific_journal-1936	226	22	journal	journal	NOUN
american_scientific_journal-1936	226	23	for	for	ADP
american_scientific_journal-1936	226	24	engineering	engineering	NOUN
american_scientific_journal-1936	226	25	,	,	PUNCT
american_scientific_journal-1936	226	26	technology	technology	NOUN
american_scientific_journal-1936	226	27	,	,	PUNCT
american_scientific_journal-1936	226	28	and	and	CCONJ
american_scientific_journal-1936	226	29	sciences	science	NOUN
american_scientific_journal-1936	226	30	(	(	PUNCT
american_scientific_journal-1936	226	31	asrjets	asrjet	NOUN
american_scientific_journal-1936	226	32	)	)	PUNCT
american_scientific_journal-1936	226	33	(	(	PUNCT
american_scientific_journal-1936	226	34	2016	2016	NUM
american_scientific_journal-1936	226	35	)	)	PUNCT
american_scientific_journal-1936	226	36	volume	volume	NOUN
american_scientific_journal-1936	226	37	26	26	NUM
american_scientific_journal-1936	226	38	,	,	PUNCT
american_scientific_journal-1936	226	39	no	no	DET
american_scientific_journal-1936	226	40	3	3	NUM
american_scientific_journal-1936	226	41	,	,	PUNCT
american_scientific_journal-1936	226	42	pp	pp	ADV
american_scientific_journal-1936	226	43	140	140	NUM
american_scientific_journal-1936	226	44	-	-	SYM
american_scientific_journal-1936	226	45	154	154	NUM
american_scientific_journal-1936	226	46	154	154	NUM
american_scientific_journal-1936	226	47	matlab	matlab	NOUN
american_scientific_journal-1936	226	48	,	,	PUNCT
american_scientific_journal-1936	226	49	epv	epv	PROPN
american_scientific_journal-1936	226	50	/	/	SYM
american_scientific_journal-1936	226	51	ehu	ehu	PROPN
american_scientific_journal-1936	226	52	,	,	PUNCT
american_scientific_journal-1936	226	53	http://www.ehu.es/aitor	http://www.ehu.es/aitor	NOUN
american_scientific_journal-1936	227	1	[	[	X
american_scientific_journal-1936	227	2	2	2	NUM
american_scientific_journal-1936	227	3	]	]	PUNCT
american_scientific_journal-1936	227	4	evans	evans	PROPN
american_scientific_journal-1936	227	5	g.	g.	PROPN
american_scientific_journal-1936	227	6	,	,	PUNCT
american_scientific_journal-1936	227	7	blackdge	blackdge	PROPN
american_scientific_journal-1936	227	8	j.	j.	PROPN
american_scientific_journal-1936	227	9	and	and	CCONJ
american_scientific_journal-1936	227	10	yardley	yardley	PROPN
american_scientific_journal-1936	227	11	p.	p.	PROPN
american_scientific_journal-1936	227	12	(	(	PUNCT
american_scientific_journal-1936	227	13	2000	2000	NUM
american_scientific_journal-1936	227	14	)	)	PUNCT
american_scientific_journal-1936	227	15	.	.	PUNCT
american_scientific_journal-1936	228	1	numerical	numerical	ADJ
american_scientific_journal-1936	228	2	methods	method	NOUN
american_scientific_journal-1936	228	3	for	for	ADP
american_scientific_journal-1936	228	4	partial	partial	ADJ
american_scientific_journal-1936	228	5	differential	differential	NOUN
american_scientific_journal-1936	228	6	equations	equation	NOUN
american_scientific_journal-1936	228	7	,	,	PUNCT
american_scientific_journal-1936	228	8	springer	springer	NOUN
american_scientific_journal-1936	228	9	–	–	PUNCT
american_scientific_journal-1936	228	10	verlag	verlag	PROPN
american_scientific_journal-1936	228	11	,	,	PUNCT
american_scientific_journal-1936	228	12	berlin	berlin	PROPN
american_scientific_journal-1936	228	13	,	,	PUNCT
american_scientific_journal-1936	228	14	heidelberg	heidelberg	PROPN
american_scientific_journal-1936	228	15	,	,	PUNCT
american_scientific_journal-1936	228	16	new	new	PROPN
american_scientific_journal-1936	228	17	york	york	PROPN
american_scientific_journal-1936	228	18	.	.	PUNCT
american_scientific_journal-1936	229	1	isbn	isbn	PROPN
american_scientific_journal-1936	229	2	3	3	NUM
american_scientific_journal-1936	229	3	-	-	SYM
american_scientific_journal-1936	229	4	540	540	NUM
american_scientific_journal-1936	229	5	-	-	PUNCT
american_scientific_journal-1936	229	6	76125	76125	NUM
american_scientific_journal-1936	229	7	-	-	PUNCT
american_scientific_journal-1936	229	8	x.	x.	NOUN
american_scientific_journal-1936	230	1	[	[	X
american_scientific_journal-1936	230	2	3	3	X
american_scientific_journal-1936	230	3	]	]	X
american_scientific_journal-1936	230	4	gerald	gerald	PROPN
american_scientific_journal-1936	230	5	w.	w.	PROPN
american_scientific_journal-1936	230	6	(	(	PUNCT
american_scientific_journal-1936	230	7	2011	2011	NUM
american_scientific_journal-1936	230	8	)	)	PUNCT
american_scientific_journal-1936	230	9	.	.	PUNCT
american_scientific_journal-1936	231	1	finite	finite	ADJ
american_scientific_journal-1936	231	2	–	–	PUNCT
american_scientific_journal-1936	231	3	difference	difference	NOUN
american_scientific_journal-1936	231	4	approximations	approximation	NOUN
american_scientific_journal-1936	231	5	to	to	ADP
american_scientific_journal-1936	231	6	the	the	DET
american_scientific_journal-1936	231	7	heat	heat	NOUN
american_scientific_journal-1936	231	8	equation	equation	NOUN
american_scientific_journal-1936	231	9	,	,	PUNCT
american_scientific_journal-1936	231	10	portland	portland	PROPN
american_scientific_journal-1936	231	11	state	state	PROPN
american_scientific_journal-1936	231	12	university	university	PROPN
american_scientific_journal-1936	231	13	,	,	PUNCT
american_scientific_journal-1936	231	14	portland	portland	PROPN
american_scientific_journal-1936	231	15	,	,	PUNCT
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american_scientific_journal-1936	231	17	.	.	PUNCT
american_scientific_journal-1936	232	1	[	[	X
american_scientific_journal-1936	232	2	4	4	X
american_scientific_journal-1936	232	3	]	]	PUNCT
american_scientific_journal-1936	232	4	h.	h.	PROPN
american_scientific_journal-1936	232	5	saberi	saberi	PROPN
american_scientific_journal-1936	232	6	najafi	najafi	PROPN
american_scientific_journal-1936	232	7	(	(	PUNCT
american_scientific_journal-1936	232	8	2008	2008	NUM
american_scientific_journal-1936	232	9	)	)	PUNCT
american_scientific_journal-1936	232	10	.	.	PUNCT
american_scientific_journal-1936	233	1	solving	solve	VERB
american_scientific_journal-1936	233	2	one	one	NUM
american_scientific_journal-1936	233	3	–	–	PUNCT
american_scientific_journal-1936	233	4	dimensional	dimensional	ADJ
american_scientific_journal-1936	233	5	advection	advection	NOUN
american_scientific_journal-1936	233	6	–	–	PUNCT
american_scientific_journal-1936	233	7	dispersion	dispersion	NOUN
american_scientific_journal-1936	233	8	with	with	ADP
american_scientific_journal-1936	233	9	reaction	reaction	NOUN
american_scientific_journal-1936	233	10	using	use	VERB
american_scientific_journal-1936	233	11	some	some	DET
american_scientific_journal-1936	233	12	finite	finite	ADJ
american_scientific_journal-1936	233	13	–	–	PUNCT
american_scientific_journal-1936	233	14	difference	difference	NOUN
american_scientific_journal-1936	233	15	methods	method	NOUN
american_scientific_journal-1936	233	16	,	,	PUNCT
american_scientific_journal-1936	233	17	applied	apply	VERB
american_scientific_journal-1936	233	18	mathematical	mathematical	ADJ
american_scientific_journal-1936	233	19	sciences	science	NOUN
american_scientific_journal-1936	233	20	,	,	PUNCT
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american_scientific_journal-1936	233	22	.	.	PROPN
american_scientific_journal-1936	234	1	2	2	NUM
american_scientific_journal-1936	234	2	,	,	PUNCT
american_scientific_journal-1936	234	3	pp	pp	ADJ
american_scientific_journal-1936	234	4	.	.	PUNCT
american_scientific_journal-1936	235	1	2611	2611	NUM
american_scientific_journal-1936	235	2	–	–	PUNCT
american_scientific_journal-1936	235	3	18	18	NUM
american_scientific_journal-1936	235	4	.	.	PUNCT
american_scientific_journal-1936	236	1	[	[	X
american_scientific_journal-1936	236	2	5	5	NUM
american_scientific_journal-1936	236	3	]	]	X
american_scientific_journal-1936	236	4	karantonis	karantonis	X
american_scientific_journal-1936	236	5	a.	a.	NOUN
american_scientific_journal-1936	236	6	(	(	PUNCT
american_scientific_journal-1936	236	7	2001	2001	NUM
american_scientific_journal-1936	236	8	)	)	PUNCT
american_scientific_journal-1936	236	9	.	.	PUNCT
american_scientific_journal-1936	237	1	numerical	numerical	ADJ
american_scientific_journal-1936	237	2	solution	solution	NOUN
american_scientific_journal-1936	237	3	of	of	ADP
american_scientific_journal-1936	237	4	reaction	reaction	NOUN
american_scientific_journal-1936	237	5	–	–	PUNCT
american_scientific_journal-1936	237	6	diffusion	diffusion	NOUN
american_scientific_journal-1936	237	7	equations	equation	NOUN
american_scientific_journal-1936	237	8	by	by	ADP
american_scientific_journal-1936	237	9	the	the	DET
american_scientific_journal-1936	237	10	finite	finite	ADJ
american_scientific_journal-1936	237	11	difference	difference	NOUN
american_scientific_journal-1936	237	12	method	method	NOUN
american_scientific_journal-1936	237	13	.	.	PUNCT
american_scientific_journal-1936	238	1	[	[	X
american_scientific_journal-1936	238	2	6	6	NUM
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american_scientific_journal-1936	238	4	kværnø	kværnø	PROPN
american_scientific_journal-1936	238	5	a.	a.	PROPN
american_scientific_journal-1936	238	6	(	(	PUNCT
american_scientific_journal-1936	238	7	2009	2009	NUM
american_scientific_journal-1936	238	8	)	)	PUNCT
american_scientific_journal-1936	238	9	.	.	PUNCT
american_scientific_journal-1936	239	1	numerical	numerical	PROPN
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american_scientific_journal-1936	239	3	,	,	PUNCT
american_scientific_journal-1936	239	4	lecture	lecture	NOUN
american_scientific_journal-1936	239	5	notes	note	NOUN
american_scientific_journal-1936	239	6	,	,	PUNCT
american_scientific_journal-1936	239	7	ntnu	ntnu	INTJ
american_scientific_journal-1936	239	8	,	,	PUNCT
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american_scientific_journal-1936	239	10	of	of	ADP
american_scientific_journal-1936	239	11	oslo	oslo	PROPN
american_scientific_journal-1936	239	12	.	.	PUNCT
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american_scientific_journal-1936	240	6	(	(	PUNCT
american_scientific_journal-1936	240	7	2011	2011	NUM
american_scientific_journal-1936	240	8	)	)	PUNCT
american_scientific_journal-1936	240	9	.	.	PUNCT
american_scientific_journal-1936	241	1	numerical	numerical	ADJ
american_scientific_journal-1936	241	2	solution	solution	NOUN
american_scientific_journal-1936	241	3	of	of	ADP
american_scientific_journal-1936	241	4	partial	partial	ADJ
american_scientific_journal-1936	241	5	differential	differential	ADJ
american_scientific_journal-1936	241	6	equations	equation	NOUN
american_scientific_journal-1936	241	7	with	with	ADP
american_scientific_journal-1936	241	8	finite	finite	ADJ
american_scientific_journal-1936	241	9	difference	difference	NOUN
american_scientific_journal-1936	241	10	methods	method	NOUN
american_scientific_journal-1936	241	11	,	,	PUNCT
american_scientific_journal-1936	241	12	lecture	lecture	NOUN
american_scientific_journal-1936	241	13	notes	note	NOUN
american_scientific_journal-1936	241	14	,	,	PUNCT
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american_scientific_journal-1936	241	18	of	of	ADP
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american_scientific_journal-1936	241	20	.	.	PUNCT
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american_scientific_journal-1936	242	5	h.	h.	PROPN
american_scientific_journal-1936	242	6	p.	p.	PROPN
american_scientific_journal-1936	242	7	(	(	PUNCT
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american_scientific_journal-1936	242	10	.	.	PUNCT
american_scientific_journal-1936	243	1	finite	finite	ADJ
american_scientific_journal-1936	243	2	difference	difference	NOUN
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american_scientific_journal-1936	243	4	for	for	ADP
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american_scientific_journal-1936	243	6	processes	process	NOUN
american_scientific_journal-1936	243	7	,	,	PUNCT
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american_scientific_journal-1936	243	9	of	of	ADP
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american_scientific_journal-1936	244	7	and	and	CCONJ
american_scientific_journal-1936	244	8	ataie	ataie	PROPN
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american_scientific_journal-1936	244	11	2009	2009	NUM
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american_scientific_journal-1936	244	13	.	.	PUNCT
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american_scientific_journal-1936	245	2	of	of	ADP
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american_scientific_journal-1936	245	5	schemes	scheme	NOUN
american_scientific_journal-1936	245	6	for	for	ADP
american_scientific_journal-1936	245	7	water	water	NOUN
american_scientific_journal-1936	245	8	flow	flow	NOUN
american_scientific_journal-1936	245	9	in	in	ADP
american_scientific_journal-1936	245	10	unsaturated	unsaturated	ADJ
american_scientific_journal-1936	245	11	soils	soil	NOUN
american_scientific_journal-1936	245	12	,	,	PUNCT
american_scientific_journal-1936	245	13	international	international	ADJ
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american_scientific_journal-1936	245	15	of	of	ADP
american_scientific_journal-1936	245	16	aerospace	aerospace	NOUN
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american_scientific_journal-1936	245	20	,	,	PUNCT
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american_scientific_journal-1936	245	25	,	,	PUNCT
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american_scientific_journal-1936	245	27	–	–	PUNCT
american_scientific_journal-1936	245	28	5	5	NUM
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american_scientific_journal-1936	246	2	10	10	NUM
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american_scientific_journal-1936	246	7	,	,	PUNCT
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american_scientific_journal-1936	247	2	–	–	PUNCT
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american_scientific_journal-1936	248	8	–	–	PUNCT
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american_scientific_journal-1936	248	12	,	,	PUNCT
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american_scientific_journal-1936	248	23	,	,	PUNCT
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american_scientific_journal-1936	248	27	,	,	PUNCT
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american_scientific_journal-1936	248	30	1	1	NUM
american_scientific_journal-1936	248	31	–	–	PUNCT
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american_scientific_journal-1936	249	5	m.	m.	NOUN
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american_scientific_journal-1936	249	12	.	.	PUNCT
american_scientific_journal-1936	250	1	a	a	DET
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american_scientific_journal-1936	253	2	,	,	PUNCT
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american_scientific_journal-1936	255	5	–	–	PUNCT
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american_scientific_journal-1936	259	9	-	-	PUNCT
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american_scientific_journal-1936	259	11	-	-	PUNCT
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american_scientific_journal-1936	259	13	-	-	SYM
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american_scientific_journal-1936	259	15	(	(	PUNCT
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