id	sid	tid	token	lemma	pos
ap-6304	1	1	acta	acta	PROPN
ap-6304	1	2	polytechnica	polytechnica	PROPN
ap-6304	1	3	https://doi.org/10.14311/ap.2021.61.0049	https://doi.org/10.14311/ap.2021.61.0049	PROPN
ap-6304	1	4	acta	acta	PROPN
ap-6304	1	5	polytechnica	polytechnica	PROPN
ap-6304	1	6	61(si):49–58	61(si):49–58	NUM
ap-6304	1	7	,	,	PUNCT
ap-6304	1	8	2021	2021	NUM
ap-6304	1	9	©	©	ADP
ap-6304	1	10	2021	2021	NUM
ap-6304	1	11	the	the	DET
ap-6304	1	12	author(s	author(s	NOUN
ap-6304	1	13	)	)	PUNCT
ap-6304	1	14	.	.	PUNCT
ap-6304	2	1	licensed	license	VERB
ap-6304	2	2	under	under	ADP
ap-6304	2	3	a	a	DET
ap-6304	2	4	cc	cc	NOUN
ap-6304	2	5	-	-	PUNCT
ap-6304	2	6	by	by	ADP
ap-6304	2	7	4.0	4.0	NUM
ap-6304	2	8	licence	licence	NOUN
ap-6304	2	9	published	publish	VERB
ap-6304	2	10	by	by	ADP
ap-6304	2	11	the	the	DET
ap-6304	2	12	czech	czech	PROPN
ap-6304	2	13	technical	technical	PROPN
ap-6304	2	14	university	university	PROPN
ap-6304	2	15	in	in	ADP
ap-6304	2	16	prague	prague	PROPN
ap-6304	2	17	modified	modify	VERB
ap-6304	2	18	equation	equation	NOUN
ap-6304	2	19	for	for	ADP
ap-6304	2	20	a	a	DET
ap-6304	2	21	class	class	NOUN
ap-6304	2	22	of	of	ADP
ap-6304	2	23	explicit	explicit	ADJ
ap-6304	2	24	and	and	CCONJ
ap-6304	2	25	implicit	implicit	ADJ
ap-6304	2	26	schemes	scheme	NOUN
ap-6304	2	27	solving	solve	VERB
ap-6304	2	28	one	one	NUM
ap-6304	2	29	-	-	PUNCT
ap-6304	2	30	dimensional	dimensional	ADJ
ap-6304	2	31	advection	advection	NOUN
ap-6304	2	32	problem	problem	NOUN
ap-6304	2	33	tomáš	tomáš	ADP
ap-6304	2	34	bodnára	bodnára	PROPN
ap-6304	2	35	,	,	PUNCT
ap-6304	2	36	b,∗	b,∗	NOUN
ap-6304	2	37	,	,	PUNCT
ap-6304	2	38	philippe	philippe	PROPN
ap-6304	2	39	frauniéc	frauniéc	NOUN
ap-6304	2	40	,	,	PUNCT
ap-6304	2	41	karel	karel	PROPN
ap-6304	2	42	kozela	kozela	VERB
ap-6304	2	43	a	a	DET
ap-6304	2	44	czech	czech	PROPN
ap-6304	2	45	technical	technical	PROPN
ap-6304	2	46	university	university	PROPN
ap-6304	2	47	in	in	ADP
ap-6304	2	48	prague	prague	PROPN
ap-6304	2	49	,	,	PUNCT
ap-6304	2	50	faculty	faculty	NOUN
ap-6304	2	51	of	of	ADP
ap-6304	2	52	mechanical	mechanical	ADJ
ap-6304	2	53	engineering	engineering	NOUN
ap-6304	2	54	,	,	PUNCT
ap-6304	2	55	karlovo	karlovo	PROPN
ap-6304	2	56	náměstí	náměstí	NOUN
ap-6304	2	57	13	13	NUM
ap-6304	2	58	,	,	PUNCT
ap-6304	2	59	121	121	NUM
ap-6304	2	60	35	35	NUM
ap-6304	2	61	prague	prague	NOUN
ap-6304	2	62	,	,	PUNCT
ap-6304	2	63	czech	czech	PROPN
ap-6304	2	64	republic	republic	PROPN
ap-6304	2	65	b	b	PROPN
ap-6304	2	66	czech	czech	PROPN
ap-6304	2	67	academy	academy	PROPN
ap-6304	2	68	of	of	ADP
ap-6304	2	69	sciences	sciences	PROPN
ap-6304	2	70	,	,	PUNCT
ap-6304	2	71	institute	institute	NOUN
ap-6304	2	72	of	of	ADP
ap-6304	2	73	mathematics	mathematics	PROPN
ap-6304	2	74	,	,	PUNCT
ap-6304	2	75	žitná	žitná	NOUN
ap-6304	2	76	25	25	NUM
ap-6304	2	77	,	,	PUNCT
ap-6304	2	78	115	115	NUM
ap-6304	2	79	67	67	NUM
ap-6304	2	80	prague	prague	NOUN
ap-6304	2	81	,	,	PUNCT
ap-6304	2	82	czech	czech	PROPN
ap-6304	2	83	republic	republic	NOUN
ap-6304	2	84	c	c	PROPN
ap-6304	2	85	université	université	PROPN
ap-6304	2	86	de	de	PROPN
ap-6304	2	87	toulon	toulon	PROPN
ap-6304	2	88	,	,	PUNCT
ap-6304	2	89	mediterranean	mediterranean	PROPN
ap-6304	2	90	institute	institute	PROPN
ap-6304	2	91	of	of	ADP
ap-6304	2	92	oceanography	oceanography	PROPN
ap-6304	2	93	mio	mio	PROPN
ap-6304	2	94	,	,	PUNCT
ap-6304	2	95	bp	bp	PROPN
ap-6304	2	96	20132	20132	NUM
ap-6304	2	97	f-83957	f-83957	PROPN
ap-6304	2	98	la	la	PROPN
ap-6304	2	99	garde	garde	PROPN
ap-6304	2	100	cedex	cedex	PROPN
ap-6304	2	101	,	,	PUNCT
ap-6304	2	102	france	france	PROPN
ap-6304	2	103	∗	∗	NOUN
ap-6304	2	104	corresponding	correspond	VERB
ap-6304	2	105	author	author	NOUN
ap-6304	2	106	:	:	PUNCT
ap-6304	2	107	tomas.bodnar@fs.cvut.cz	tomas.bodnar@fs.cvut.cz	NOUN
ap-6304	2	108	abstract	abstract	NOUN
ap-6304	2	109	.	.	PUNCT
ap-6304	3	1	this	this	DET
ap-6304	3	2	paper	paper	NOUN
ap-6304	3	3	presents	present	VERB
ap-6304	3	4	the	the	DET
ap-6304	3	5	general	general	ADJ
ap-6304	3	6	modified	modify	VERB
ap-6304	3	7	equation	equation	NOUN
ap-6304	3	8	for	for	ADP
ap-6304	3	9	a	a	DET
ap-6304	3	10	family	family	NOUN
ap-6304	3	11	of	of	ADP
ap-6304	3	12	finite	finite	ADJ
ap-6304	3	13	-	-	PUNCT
ap-6304	3	14	difference	difference	NOUN
ap-6304	3	15	schemes	scheme	NOUN
ap-6304	3	16	solving	solve	VERB
ap-6304	3	17	one	one	NUM
ap-6304	3	18	-	-	PUNCT
ap-6304	3	19	dimensional	dimensional	ADJ
ap-6304	3	20	advection	advection	NOUN
ap-6304	3	21	equation	equation	NOUN
ap-6304	3	22	.	.	PUNCT
ap-6304	4	1	the	the	DET
ap-6304	4	2	whole	whole	ADJ
ap-6304	4	3	family	family	NOUN
ap-6304	4	4	of	of	ADP
ap-6304	4	5	explicit	explicit	ADJ
ap-6304	4	6	and	and	CCONJ
ap-6304	4	7	implicit	implicit	ADJ
ap-6304	4	8	schemes	scheme	NOUN
ap-6304	4	9	working	work	VERB
ap-6304	4	10	at	at	ADP
ap-6304	4	11	two	two	NUM
ap-6304	4	12	time	time	NOUN
ap-6304	4	13	-	-	PUNCT
ap-6304	4	14	levels	level	NOUN
ap-6304	4	15	and	and	CCONJ
ap-6304	4	16	having	have	VERB
ap-6304	4	17	three	three	NUM
ap-6304	4	18	point	point	NOUN
ap-6304	4	19	spatial	spatial	ADJ
ap-6304	4	20	support	support	NOUN
ap-6304	4	21	is	be	AUX
ap-6304	4	22	considered	consider	VERB
ap-6304	4	23	.	.	PUNCT
ap-6304	5	1	some	some	PRON
ap-6304	5	2	of	of	ADP
ap-6304	5	3	the	the	DET
ap-6304	5	4	classical	classical	ADJ
ap-6304	5	5	schemes	scheme	NOUN
ap-6304	5	6	(	(	PUNCT
ap-6304	5	7	upwind	upwind	NOUN
ap-6304	5	8	,	,	PUNCT
ap-6304	5	9	lax	lax	NOUN
ap-6304	5	10	-	-	PUNCT
ap-6304	5	11	friedrichs	friedrich	NOUN
ap-6304	5	12	,	,	PUNCT
ap-6304	5	13	lax	lax	NOUN
ap-6304	5	14	-	-	PUNCT
ap-6304	5	15	wendroff	wendroff	NOUN
ap-6304	5	16	)	)	PUNCT
ap-6304	5	17	are	be	AUX
ap-6304	5	18	discussed	discuss	VERB
ap-6304	5	19	as	as	ADP
ap-6304	5	20	examples	example	NOUN
ap-6304	5	21	,	,	PUNCT
ap-6304	5	22	showing	show	VERB
ap-6304	5	23	the	the	DET
ap-6304	5	24	possible	possible	ADJ
ap-6304	5	25	implications	implication	NOUN
ap-6304	5	26	arising	arise	VERB
ap-6304	5	27	from	from	ADP
ap-6304	5	28	the	the	DET
ap-6304	5	29	modified	modify	VERB
ap-6304	5	30	equation	equation	NOUN
ap-6304	5	31	to	to	ADP
ap-6304	5	32	the	the	DET
ap-6304	5	33	properties	property	NOUN
ap-6304	5	34	of	of	ADP
ap-6304	5	35	the	the	DET
ap-6304	5	36	considered	consider	VERB
ap-6304	5	37	numerical	numerical	ADJ
ap-6304	5	38	methods	method	NOUN
ap-6304	5	39	.	.	PUNCT
ap-6304	6	1	keywords	keyword	NOUN
ap-6304	6	2	:	:	PUNCT
ap-6304	6	3	modified	modify	VERB
ap-6304	6	4	equation	equation	NOUN
ap-6304	6	5	,	,	PUNCT
ap-6304	6	6	finite	finite	ADJ
ap-6304	6	7	difference	difference	NOUN
ap-6304	6	8	,	,	PUNCT
ap-6304	6	9	advection	advection	NOUN
ap-6304	6	10	equation	equation	NOUN
ap-6304	6	11	.	.	PUNCT
ap-6304	7	1	1	1	X
ap-6304	7	2	.	.	X
ap-6304	7	3	introduction	introduction	NOUN
ap-6304	7	4	numerical	numerical	ADJ
ap-6304	7	5	solution	solution	NOUN
ap-6304	7	6	of	of	ADP
ap-6304	7	7	differential	differential	ADJ
ap-6304	7	8	equations	equation	NOUN
ap-6304	7	9	became	become	VERB
ap-6304	7	10	a	a	DET
ap-6304	7	11	standard	standard	ADJ
ap-6304	7	12	tool	tool	NOUN
ap-6304	7	13	in	in	ADP
ap-6304	7	14	many	many	ADJ
ap-6304	7	15	disciplines	discipline	NOUN
ap-6304	7	16	of	of	ADP
ap-6304	7	17	theoretical	theoretical	ADJ
ap-6304	7	18	science	science	NOUN
ap-6304	7	19	as	as	ADV
ap-6304	7	20	well	well	ADV
ap-6304	7	21	as	as	ADP
ap-6304	7	22	in	in	ADP
ap-6304	7	23	applied	applied	ADJ
ap-6304	7	24	sciences	science	NOUN
ap-6304	7	25	and	and	CCONJ
ap-6304	7	26	engineering	engineering	NOUN
ap-6304	7	27	.	.	PUNCT
ap-6304	8	1	numerical	numerical	ADJ
ap-6304	8	2	and	and	CCONJ
ap-6304	8	3	computational	computational	ADJ
ap-6304	8	4	methods	method	NOUN
ap-6304	8	5	brought	bring	VERB
ap-6304	8	6	the	the	DET
ap-6304	8	7	possibility	possibility	NOUN
ap-6304	8	8	to	to	PART
ap-6304	8	9	solve	solve	VERB
ap-6304	8	10	non	non	ADJ
ap-6304	8	11	-	-	ADJ
ap-6304	8	12	trivial	trivial	ADJ
ap-6304	8	13	problems	problem	NOUN
ap-6304	8	14	described	describe	VERB
ap-6304	8	15	by	by	ADP
ap-6304	8	16	ordinary	ordinary	ADJ
ap-6304	8	17	and	and	CCONJ
ap-6304	8	18	partial	partial	ADJ
ap-6304	8	19	differential	differential	ADJ
ap-6304	8	20	equations	equation	NOUN
ap-6304	8	21	for	for	ADP
ap-6304	8	22	which	which	PRON
ap-6304	8	23	it	it	PRON
ap-6304	8	24	was	be	AUX
ap-6304	8	25	impossible	impossible	ADJ
ap-6304	8	26	to	to	PART
ap-6304	8	27	obtain	obtain	VERB
ap-6304	8	28	an	an	DET
ap-6304	8	29	analytical	analytical	ADJ
ap-6304	8	30	solution	solution	NOUN
ap-6304	8	31	by	by	ADP
ap-6304	8	32	standard	standard	ADJ
ap-6304	8	33	mathematical	mathematical	ADJ
ap-6304	8	34	methods	method	NOUN
ap-6304	8	35	.	.	PUNCT
ap-6304	9	1	a	a	DET
ap-6304	9	2	wide	wide	ADJ
ap-6304	9	3	range	range	NOUN
ap-6304	9	4	of	of	ADP
ap-6304	9	5	numerical	numerical	ADJ
ap-6304	9	6	methods	method	NOUN
ap-6304	9	7	was	be	AUX
ap-6304	9	8	developed	develop	VERB
ap-6304	9	9	during	during	ADP
ap-6304	9	10	the	the	DET
ap-6304	9	11	years	year	NOUN
ap-6304	9	12	for	for	ADP
ap-6304	9	13	specific	specific	ADJ
ap-6304	9	14	problems	problem	NOUN
ap-6304	9	15	.	.	PUNCT
ap-6304	10	1	typically	typically	ADV
ap-6304	10	2	the	the	DET
ap-6304	10	3	physical	physical	ADJ
ap-6304	10	4	problem	problem	NOUN
ap-6304	10	5	is	be	AUX
ap-6304	10	6	first	first	ADV
ap-6304	10	7	described	describe	VERB
ap-6304	10	8	mathematically	mathematically	ADV
ap-6304	10	9	,	,	PUNCT
ap-6304	10	10	so	so	CCONJ
ap-6304	10	11	the	the	DET
ap-6304	10	12	mathematical	mathematical	ADJ
ap-6304	10	13	model	model	NOUN
ap-6304	10	14	is	be	AUX
ap-6304	10	15	created	create	VERB
ap-6304	10	16	.	.	PUNCT
ap-6304	11	1	then	then	ADV
ap-6304	11	2	this	this	DET
ap-6304	11	3	mathematical	mathematical	ADJ
ap-6304	11	4	model	model	NOUN
ap-6304	11	5	is	be	AUX
ap-6304	11	6	solved	solve	VERB
ap-6304	11	7	numerically	numerically	ADV
ap-6304	11	8	.	.	PUNCT
ap-6304	12	1	the	the	DET
ap-6304	12	2	obtained	obtain	VERB
ap-6304	12	3	numerical	numerical	ADJ
ap-6304	12	4	solution	solution	NOUN
ap-6304	12	5	is	be	AUX
ap-6304	12	6	an	an	DET
ap-6304	12	7	approximation	approximation	NOUN
ap-6304	12	8	to	to	ADP
ap-6304	12	9	the	the	DET
ap-6304	12	10	solution	solution	NOUN
ap-6304	12	11	of	of	ADP
ap-6304	12	12	the	the	DET
ap-6304	12	13	mathematical	mathematical	ADJ
ap-6304	12	14	model	model	NOUN
ap-6304	12	15	,	,	PUNCT
ap-6304	12	16	which	which	PRON
ap-6304	12	17	itself	itself	PRON
ap-6304	12	18	is	be	AUX
ap-6304	12	19	just	just	ADV
ap-6304	12	20	an	an	DET
ap-6304	12	21	approximation	approximation	NOUN
ap-6304	12	22	of	of	ADP
ap-6304	12	23	the	the	DET
ap-6304	12	24	physical	physical	ADJ
ap-6304	12	25	problem	problem	NOUN
ap-6304	12	26	.	.	PUNCT
ap-6304	13	1	we	we	PRON
ap-6304	13	2	keep	keep	VERB
ap-6304	13	3	aside	aside	ADV
ap-6304	13	4	the	the	DET
ap-6304	13	5	error	error	NOUN
ap-6304	13	6	introduced	introduce	VERB
ap-6304	13	7	by	by	ADP
ap-6304	13	8	the	the	DET
ap-6304	13	9	inaccuracies	inaccuracy	NOUN
ap-6304	13	10	and	and	CCONJ
ap-6304	13	11	approximations	approximation	NOUN
ap-6304	13	12	made	make	VERB
ap-6304	13	13	when	when	SCONJ
ap-6304	13	14	developing	develop	VERB
ap-6304	13	15	the	the	DET
ap-6304	13	16	mathematical	mathematical	ADJ
ap-6304	13	17	model	model	NOUN
ap-6304	13	18	from	from	ADP
ap-6304	13	19	the	the	DET
ap-6304	13	20	physical	physical	ADJ
ap-6304	13	21	problem	problem	NOUN
ap-6304	13	22	.	.	PUNCT
ap-6304	14	1	here	here	ADV
ap-6304	14	2	the	the	DET
ap-6304	14	3	focus	focus	NOUN
ap-6304	14	4	is	be	AUX
ap-6304	14	5	on	on	ADP
ap-6304	14	6	the	the	DET
ap-6304	14	7	difference	difference	NOUN
ap-6304	14	8	between	between	ADP
ap-6304	14	9	the	the	DET
ap-6304	14	10	discrete	discrete	ADJ
ap-6304	14	11	numerical	numerical	ADJ
ap-6304	14	12	solution	solution	NOUN
ap-6304	14	13	of	of	ADP
ap-6304	14	14	the	the	DET
ap-6304	14	15	mathematical	mathematical	ADJ
ap-6304	14	16	model	model	NOUN
ap-6304	14	17	and	and	CCONJ
ap-6304	14	18	its	its	PRON
ap-6304	14	19	exact	exact	ADJ
ap-6304	14	20	(	(	PUNCT
ap-6304	14	21	analytical	analytical	ADJ
ap-6304	14	22	)	)	PUNCT
ap-6304	14	23	solution	solution	NOUN
ap-6304	14	24	.	.	PUNCT
ap-6304	15	1	the	the	DET
ap-6304	15	2	numerical	numerical	ADJ
ap-6304	15	3	solution	solution	NOUN
ap-6304	15	4	strongly	strongly	ADV
ap-6304	15	5	depends	depend	VERB
ap-6304	15	6	on	on	ADP
ap-6304	15	7	the	the	DET
ap-6304	15	8	method	method	NOUN
ap-6304	15	9	used	use	VERB
ap-6304	15	10	to	to	PART
ap-6304	15	11	obtain	obtain	VERB
ap-6304	15	12	it	it	PRON
ap-6304	15	13	.	.	PUNCT
ap-6304	16	1	so	so	ADV
ap-6304	16	2	the	the	DET
ap-6304	16	3	properties	property	NOUN
ap-6304	16	4	and	and	CCONJ
ap-6304	16	5	quality	quality	NOUN
ap-6304	16	6	of	of	ADP
ap-6304	16	7	the	the	DET
ap-6304	16	8	numerical	numerical	ADJ
ap-6304	16	9	solution	solution	NOUN
ap-6304	16	10	may	may	AUX
ap-6304	16	11	differ	differ	VERB
ap-6304	16	12	from	from	ADP
ap-6304	16	13	the	the	DET
ap-6304	16	14	solution	solution	NOUN
ap-6304	16	15	of	of	ADP
ap-6304	16	16	the	the	DET
ap-6304	16	17	original	original	ADJ
ap-6304	16	18	mathematical	mathematical	ADJ
ap-6304	16	19	model	model	NOUN
ap-6304	16	20	.	.	PUNCT
ap-6304	17	1	the	the	DET
ap-6304	17	2	aim	aim	NOUN
ap-6304	17	3	of	of	ADP
ap-6304	17	4	this	this	DET
ap-6304	17	5	paper	paper	NOUN
ap-6304	17	6	is	be	AUX
ap-6304	17	7	to	to	PART
ap-6304	17	8	show	show	VERB
ap-6304	17	9	that	that	SCONJ
ap-6304	17	10	the	the	DET
ap-6304	17	11	numerical	numerical	ADJ
ap-6304	17	12	solution	solution	NOUN
ap-6304	17	13	of	of	ADP
ap-6304	17	14	certain	certain	ADJ
ap-6304	17	15	problems	problem	NOUN
ap-6304	17	16	(	(	PUNCT
ap-6304	17	17	equations	equation	NOUN
ap-6304	17	18	)	)	PUNCT
ap-6304	17	19	is	be	AUX
ap-6304	17	20	much	much	ADV
ap-6304	17	21	closer	close	ADJ
ap-6304	17	22	to	to	ADP
ap-6304	17	23	the	the	DET
ap-6304	17	24	solution	solution	NOUN
ap-6304	17	25	of	of	ADP
ap-6304	17	26	some	some	DET
ap-6304	17	27	modified	modify	VERB
ap-6304	17	28	equation	equation	NOUN
ap-6304	17	29	,	,	PUNCT
ap-6304	17	30	rather	rather	ADV
ap-6304	17	31	than	than	ADP
ap-6304	17	32	to	to	ADP
ap-6304	17	33	the	the	DET
ap-6304	17	34	solution	solution	NOUN
ap-6304	17	35	of	of	ADP
ap-6304	17	36	the	the	DET
ap-6304	17	37	original	original	ADJ
ap-6304	17	38	problem	problem	NOUN
ap-6304	17	39	.	.	PUNCT
ap-6304	18	1	many	many	ADJ
ap-6304	18	2	important	important	ADJ
ap-6304	18	3	properties	property	NOUN
ap-6304	18	4	of	of	ADP
ap-6304	18	5	the	the	DET
ap-6304	18	6	numerical	numerical	ADJ
ap-6304	18	7	solution	solution	NOUN
ap-6304	18	8	can	can	AUX
ap-6304	18	9	than	than	ADP
ap-6304	18	10	be	be	AUX
ap-6304	18	11	easily	easily	ADV
ap-6304	18	12	seen	see	VERB
ap-6304	18	13	(	(	PUNCT
ap-6304	18	14	and	and	CCONJ
ap-6304	18	15	a	a	X
ap-6304	18	16	-	-	PUNCT
ap-6304	18	17	priori	priori	NOUN
ap-6304	18	18	expected	expect	VERB
ap-6304	18	19	)	)	PUNCT
ap-6304	18	20	from	from	ADP
ap-6304	18	21	the	the	DET
ap-6304	18	22	behavior	behavior	NOUN
ap-6304	18	23	of	of	ADP
ap-6304	18	24	the	the	DET
ap-6304	18	25	known	know	VERB
ap-6304	18	26	solution	solution	NOUN
ap-6304	18	27	of	of	ADP
ap-6304	18	28	the	the	DET
ap-6304	18	29	modified	modify	VERB
ap-6304	18	30	problem	problem	NOUN
ap-6304	18	31	.	.	PUNCT
ap-6304	19	1	this	this	DET
ap-6304	19	2	rather	rather	ADV
ap-6304	19	3	general	general	ADJ
ap-6304	19	4	principle	principle	NOUN
ap-6304	19	5	will	will	AUX
ap-6304	19	6	be	be	AUX
ap-6304	19	7	demonstrated	demonstrate	VERB
ap-6304	19	8	on	on	ADP
ap-6304	19	9	a	a	DET
ap-6304	19	10	finite	finite	ADJ
ap-6304	19	11	-	-	PUNCT
ap-6304	19	12	difference	difference	NOUN
ap-6304	19	13	approximation	approximation	NOUN
ap-6304	19	14	of	of	ADP
ap-6304	19	15	the	the	DET
ap-6304	19	16	solution	solution	NOUN
ap-6304	19	17	of	of	ADP
ap-6304	19	18	one	one	NUM
ap-6304	19	19	-	-	PUNCT
ap-6304	19	20	dimensional	dimensional	ADJ
ap-6304	19	21	advection	advection	NOUN
ap-6304	19	22	equation	equation	NOUN
ap-6304	19	23	.	.	PUNCT
ap-6304	20	1	the	the	DET
ap-6304	20	2	structure	structure	NOUN
ap-6304	20	3	of	of	ADP
ap-6304	20	4	the	the	DET
ap-6304	20	5	paper	paper	NOUN
ap-6304	20	6	is	be	AUX
ap-6304	20	7	as	as	SCONJ
ap-6304	20	8	follows	follow	VERB
ap-6304	20	9	.	.	PUNCT
ap-6304	21	1	first	first	ADV
ap-6304	21	2	the	the	DET
ap-6304	21	3	advection	advection	NOUN
ap-6304	21	4	,	,	PUNCT
ap-6304	21	5	diffusion	diffusion	NOUN
ap-6304	21	6	and	and	CCONJ
ap-6304	21	7	dispersion	dispersion	NOUN
ap-6304	21	8	equations	equation	NOUN
ap-6304	21	9	are	be	AUX
ap-6304	21	10	introduced	introduce	VERB
ap-6304	21	11	and	and	CCONJ
ap-6304	21	12	discussed	discuss	VERB
ap-6304	21	13	.	.	PUNCT
ap-6304	22	1	then	then	ADV
ap-6304	22	2	several	several	ADJ
ap-6304	22	3	explicit	explicit	ADJ
ap-6304	22	4	schemes	scheme	NOUN
ap-6304	22	5	for	for	ADP
ap-6304	22	6	advection	advection	NOUN
ap-6304	22	7	equation	equation	NOUN
ap-6304	22	8	are	be	AUX
ap-6304	22	9	presented	present	VERB
ap-6304	22	10	and	and	CCONJ
ap-6304	22	11	analyzed	analyze	VERB
ap-6304	22	12	at	at	ADP
ap-6304	22	13	the	the	DET
ap-6304	22	14	discrete	discrete	ADJ
ap-6304	22	15	level	level	NOUN
ap-6304	22	16	.	.	PUNCT
ap-6304	23	1	modified	modify	VERB
ap-6304	23	2	equation	equation	NOUN
ap-6304	23	3	is	be	AUX
ap-6304	23	4	first	first	ADV
ap-6304	23	5	derived	derive	VERB
ap-6304	23	6	for	for	ADP
ap-6304	23	7	upwind	upwind	NOUN
ap-6304	23	8	scheme	scheme	NOUN
ap-6304	23	9	and	and	CCONJ
ap-6304	23	10	then	then	ADV
ap-6304	23	11	extended	extend	VERB
ap-6304	23	12	for	for	ADP
ap-6304	23	13	a	a	DET
ap-6304	23	14	general	general	ADJ
ap-6304	23	15	class	class	NOUN
ap-6304	23	16	of	of	ADP
ap-6304	23	17	explicit	explicit	ADJ
ap-6304	23	18	and	and	CCONJ
ap-6304	23	19	implicit	implicit	ADJ
ap-6304	23	20	schemes	scheme	NOUN
ap-6304	23	21	.	.	PUNCT
ap-6304	24	1	finally	finally	ADV
ap-6304	24	2	the	the	DET
ap-6304	24	3	modified	modify	VERB
ap-6304	24	4	equations	equation	NOUN
ap-6304	24	5	are	be	AUX
ap-6304	24	6	discussed	discuss	VERB
ap-6304	24	7	from	from	ADP
ap-6304	24	8	the	the	DET
ap-6304	24	9	point	point	NOUN
ap-6304	24	10	of	of	ADP
ap-6304	24	11	view	view	NOUN
ap-6304	24	12	of	of	ADP
ap-6304	24	13	numerical	numerical	ADJ
ap-6304	24	14	diffusion	diffusion	NOUN
ap-6304	24	15	and	and	CCONJ
ap-6304	24	16	dispersion	dispersion	NOUN
ap-6304	24	17	.	.	PUNCT
ap-6304	25	1	2	2	X
ap-6304	25	2	.	.	X
ap-6304	25	3	model	model	NOUN
ap-6304	25	4	problems	problem	NOUN
ap-6304	25	5	in	in	ADP
ap-6304	25	6	order	order	NOUN
ap-6304	25	7	to	to	PART
ap-6304	25	8	be	be	AUX
ap-6304	25	9	able	able	ADJ
ap-6304	25	10	to	to	PART
ap-6304	25	11	explain	explain	VERB
ap-6304	25	12	the	the	DET
ap-6304	25	13	properties	property	NOUN
ap-6304	25	14	of	of	ADP
ap-6304	25	15	modified	modify	VERB
ap-6304	25	16	equations	equation	NOUN
ap-6304	25	17	and	and	CCONJ
ap-6304	25	18	the	the	DET
ap-6304	25	19	underlying	underlying	ADJ
ap-6304	25	20	numerical	numerical	ADJ
ap-6304	25	21	schemes	scheme	NOUN
ap-6304	25	22	three	three	NUM
ap-6304	25	23	model	model	NOUN
ap-6304	25	24	problems	problem	NOUN
ap-6304	25	25	are	be	AUX
ap-6304	25	26	introduced	introduce	VERB
ap-6304	25	27	.	.	PUNCT
ap-6304	26	1	they	they	PRON
ap-6304	26	2	describe	describe	VERB
ap-6304	26	3	the	the	DET
ap-6304	26	4	physical	physical	ADJ
ap-6304	26	5	phenomena	phenomenon	NOUN
ap-6304	26	6	of	of	ADP
ap-6304	26	7	advection	advection	NOUN
ap-6304	26	8	,	,	PUNCT
ap-6304	26	9	diffusion	diffusion	NOUN
ap-6304	26	10	and	and	CCONJ
ap-6304	26	11	dispersion	dispersion	NOUN
ap-6304	26	12	.	.	PUNCT
ap-6304	27	1	all	all	DET
ap-6304	27	2	these	these	DET
ap-6304	27	3	problems	problem	NOUN
ap-6304	27	4	can	can	AUX
ap-6304	27	5	be	be	AUX
ap-6304	27	6	mathematically	mathematically	ADV
ap-6304	27	7	formulated	formulate	VERB
ap-6304	27	8	using	use	VERB
ap-6304	27	9	a	a	DET
ap-6304	27	10	linear	linear	ADJ
ap-6304	27	11	evolutionary	evolutionary	ADJ
ap-6304	27	12	partial	partial	ADJ
ap-6304	27	13	differential	differential	NOUN
ap-6304	27	14	equation	equation	NOUN
ap-6304	27	15	.	.	PUNCT
ap-6304	28	1	in	in	ADP
ap-6304	28	2	all	all	DET
ap-6304	28	3	cases	case	NOUN
ap-6304	28	4	the	the	DET
ap-6304	28	5	unknown	unknown	ADJ
ap-6304	28	6	function	function	NOUN
ap-6304	28	7	u(x	u(x	NOUN
ap-6304	28	8	,	,	PUNCT
ap-6304	28	9	t	t	PROPN
ap-6304	28	10	)	)	PUNCT
ap-6304	28	11	is	be	AUX
ap-6304	28	12	the	the	DET
ap-6304	28	13	sought	seek	VERB
ap-6304	28	14	subject	subject	NOUN
ap-6304	28	15	to	to	ADP
ap-6304	28	16	the	the	DET
ap-6304	28	17	initial	initial	ADJ
ap-6304	28	18	data	datum	NOUN
ap-6304	28	19	u(x	u(x	NOUN
ap-6304	28	20	,	,	PUNCT
ap-6304	28	21	t	t	NOUN
ap-6304	28	22	=	=	SYM
ap-6304	28	23	0	0	NUM
ap-6304	28	24	)	)	PUNCT
ap-6304	28	25	=	=	SYM
ap-6304	28	26	η(x	η(x	NOUN
ap-6304	28	27	)	)	PUNCT
ap-6304	28	28	.	.	PUNCT
ap-6304	29	1	for	for	ADP
ap-6304	29	2	a	a	DET
ap-6304	29	3	sketch	sketch	NOUN
ap-6304	29	4	of	of	ADP
ap-6304	29	5	an	an	DET
ap-6304	29	6	example	example	NOUN
ap-6304	29	7	of	of	ADP
ap-6304	29	8	initial	initial	ADJ
ap-6304	29	9	data	datum	NOUN
ap-6304	29	10	see	see	VERB
ap-6304	29	11	fig	fig	NOUN
ap-6304	29	12	.	.	PUNCT
ap-6304	30	1	1	1	X
ap-6304	30	2	.	.	X
ap-6304	30	3	the	the	DET
ap-6304	30	4	initial	initial	ADJ
ap-6304	30	5	value	value	NOUN
ap-6304	30	6	problem	problem	NOUN
ap-6304	30	7	can	can	AUX
ap-6304	30	8	be	be	AUX
ap-6304	30	9	thus	thus	ADV
ap-6304	30	10	solved	solve	VERB
ap-6304	30	11	analytically	analytically	ADV
ap-6304	30	12	using	use	VERB
ap-6304	30	13	the	the	DET
ap-6304	30	14	fourier	fourier	NOUN
ap-6304	30	15	transform	transform	NOUN
ap-6304	30	16	method	method	NOUN
ap-6304	30	17	.	.	PUNCT
ap-6304	31	1	the	the	DET
ap-6304	31	2	fourier	fourier	NOUN
ap-6304	31	3	transform	transform	NOUN
ap-6304	31	4	(	(	PUNCT
ap-6304	31	5	in	in	ADP
ap-6304	31	6	space	space	NOUN
ap-6304	31	7	)	)	PUNCT
ap-6304	31	8	needed	need	VERB
ap-6304	31	9	to	to	PART
ap-6304	31	10	obtain	obtain	VERB
ap-6304	31	11	the	the	DET
ap-6304	31	12	analytical	analytical	ADJ
ap-6304	31	13	solutions	solution	NOUN
ap-6304	31	14	is	be	AUX
ap-6304	31	15	defined	define	VERB
ap-6304	31	16	by	by	ADP
ap-6304	31	17	:	:	PUNCT
ap-6304	31	18	û(ξ	û(ξ	ADJ
ap-6304	31	19	,	,	PUNCT
ap-6304	31	20	t	t	PROPN
ap-6304	31	21	)	)	PUNCT
ap-6304	31	22	=	=	SYM
ap-6304	32	1	1√	1√	NUM
ap-6304	32	2	2π	2π	NUM
ap-6304	32	3	∫	∫	PROPN
ap-6304	33	1	+	+	NUM
ap-6304	33	2	∞	∞	PROPN
ap-6304	33	3	−∞	−∞	ADP
ap-6304	33	4	u(x	u(x	NOUN
ap-6304	33	5	,	,	PUNCT
ap-6304	33	6	t)e−iξxdx	t)e−iξxdx	PROPN
ap-6304	33	7	,	,	PUNCT
ap-6304	33	8	while	while	SCONJ
ap-6304	33	9	the	the	DET
ap-6304	33	10	inverse	inverse	NOUN
ap-6304	33	11	is	be	AUX
ap-6304	33	12	u(x	u(x	NOUN
ap-6304	33	13	,	,	PUNCT
ap-6304	33	14	t	t	NOUN
ap-6304	33	15	)	)	PUNCT
ap-6304	33	16	=	=	SYM
ap-6304	34	1	1√	1√	NUM
ap-6304	34	2	2π	2π	NUM
ap-6304	34	3	∫	∫	PROPN
ap-6304	35	1	+	+	NUM
ap-6304	35	2	∞	∞	PROPN
ap-6304	35	3	−∞	−∞	ADP
ap-6304	35	4	û(ξ	û(ξ	ADJ
ap-6304	35	5	,	,	PUNCT
ap-6304	35	6	t)eiξxdξ	t)eiξxdξ	PROPN
ap-6304	35	7	.	.	PUNCT
ap-6304	36	1	49	49	NUM
ap-6304	36	2	https://doi.org/10.14311/ap.2021.61.0049	https://doi.org/10.14311/ap.2021.61.0049	NOUN
ap-6304	36	3	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-6304	36	4	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-6304	36	5	t.	t.	NOUN
ap-6304	36	6	bodnár	bodnár	PROPN
ap-6304	36	7	,	,	PUNCT
ap-6304	36	8	ph	ph	PROPN
ap-6304	36	9	.	.	PROPN
ap-6304	36	10	fraunié	fraunié	PROPN
ap-6304	36	11	,	,	PUNCT
ap-6304	36	12	k.	k.	PROPN
ap-6304	36	13	kozel	kozel	PROPN
ap-6304	37	1	acta	acta	PROPN
ap-6304	37	2	polytechnica	polytechnica	PROPN
ap-6304	37	3	u	u	PROPN
ap-6304	37	4	x	x	PROPN
ap-6304	37	5	u(x	u(x	PROPN
ap-6304	37	6	,	,	PUNCT
ap-6304	37	7	t	t	NOUN
ap-6304	37	8	)	)	PUNCT
ap-6304	37	9	=	=	SYM
ap-6304	38	1	(	(	PUNCT
ap-6304	38	2	x)η0	x)η0	PROPN
ap-6304	38	3	figure	figure	NOUN
ap-6304	38	4	1	1	NUM
ap-6304	38	5	.	.	PUNCT
ap-6304	38	6	initial	initial	ADJ
ap-6304	38	7	condition	condition	NOUN
ap-6304	38	8	.	.	PUNCT
ap-6304	39	1	using	use	VERB
ap-6304	39	2	this	this	DET
ap-6304	39	3	transformation	transformation	NOUN
ap-6304	39	4	,	,	PUNCT
ap-6304	39	5	the	the	DET
ap-6304	39	6	analytical	analytical	ADJ
ap-6304	39	7	solutions	solution	NOUN
ap-6304	39	8	of	of	ADP
ap-6304	39	9	model	model	NOUN
ap-6304	39	10	linear	linear	PROPN
ap-6304	39	11	problems	problem	NOUN
ap-6304	39	12	(	(	PUNCT
ap-6304	39	13	discussed	discuss	VERB
ap-6304	39	14	further	far	ADV
ap-6304	39	15	)	)	PUNCT
ap-6304	39	16	can	can	AUX
ap-6304	39	17	be	be	AUX
ap-6304	39	18	derived	derive	VERB
ap-6304	39	19	.	.	PUNCT
ap-6304	40	1	the	the	DET
ap-6304	40	2	details	detail	NOUN
ap-6304	40	3	can	can	AUX
ap-6304	40	4	be	be	AUX
ap-6304	40	5	found	find	VERB
ap-6304	40	6	for	for	ADP
ap-6304	40	7	example	example	NOUN
ap-6304	40	8	in	in	ADP
ap-6304	40	9	the	the	DET
ap-6304	40	10	appendix	appendix	NOUN
ap-6304	40	11	of	of	ADP
ap-6304	40	12	the	the	DET
ap-6304	40	13	book	book	NOUN
ap-6304	40	14	[	[	X
ap-6304	40	15	1	1	NUM
ap-6304	40	16	]	]	PUNCT
ap-6304	40	17	.	.	PUNCT
ap-6304	41	1	2.1	2.1	NUM
ap-6304	41	2	.	.	PUNCT
ap-6304	41	3	advection	advection	NOUN
ap-6304	41	4	equation	equation	NOUN
ap-6304	41	5	the	the	DET
ap-6304	41	6	advection	advection	NOUN
ap-6304	41	7	problem	problem	NOUN
ap-6304	41	8	can	can	AUX
ap-6304	41	9	be	be	AUX
ap-6304	41	10	described	describe	VERB
ap-6304	41	11	by	by	ADP
ap-6304	41	12	a	a	DET
ap-6304	41	13	first	first	ADJ
ap-6304	41	14	order	order	NOUN
ap-6304	41	15	pde	pde	NOUN
ap-6304	41	16	of	of	ADP
ap-6304	41	17	the	the	DET
ap-6304	41	18	form	form	NOUN
ap-6304	41	19	:	:	PUNCT
ap-6304	41	20	ut	ut	PROPN
ap-6304	42	1	+	+	CCONJ
ap-6304	42	2	aux	aux	X
ap-6304	42	3	=	=	NOUN
ap-6304	42	4	0	0	NUM
ap-6304	42	5	in	in	ADP
ap-6304	42	6	this	this	DET
ap-6304	42	7	paper	paper	NOUN
ap-6304	42	8	we	we	PRON
ap-6304	42	9	consider	consider	VERB
ap-6304	42	10	the	the	DET
ap-6304	42	11	advection	advection	NOUN
ap-6304	42	12	velocity	velocity	NOUN
ap-6304	42	13	a	a	DET
ap-6304	42	14	>	>	X
ap-6304	42	15	0	0	NUM
ap-6304	42	16	,	,	PUNCT
ap-6304	42	17	but	but	CCONJ
ap-6304	42	18	for	for	ADP
ap-6304	42	19	a	a	DET
ap-6304	42	20	≤	≤	NUM
ap-6304	42	21	0	0	NUM
ap-6304	43	1	the	the	DET
ap-6304	43	2	solution	solution	NOUN
ap-6304	43	3	can	can	AUX
ap-6304	43	4	be	be	AUX
ap-6304	43	5	obtained	obtain	VERB
ap-6304	43	6	as	as	ADV
ap-6304	43	7	well	well	ADV
ap-6304	43	8	.	.	PUNCT
ap-6304	44	1	this	this	DET
ap-6304	44	2	advection	advection	NOUN
ap-6304	44	3	equation	equation	NOUN
ap-6304	44	4	is	be	AUX
ap-6304	44	5	supplemented	supplement	VERB
ap-6304	44	6	by	by	ADP
ap-6304	44	7	the	the	DET
ap-6304	44	8	initial	initial	ADJ
ap-6304	44	9	data	datum	NOUN
ap-6304	44	10	u(x	u(x	NOUN
ap-6304	44	11	,	,	PUNCT
ap-6304	44	12	t	t	NOUN
ap-6304	44	13	=	=	SYM
ap-6304	44	14	0	0	NUM
ap-6304	44	15	)	)	PUNCT
ap-6304	44	16	=	=	SYM
ap-6304	44	17	η(x	η(x	X
ap-6304	44	18	)	)	PUNCT
ap-6304	44	19	.	.	PUNCT
ap-6304	45	1	applying	apply	VERB
ap-6304	45	2	the	the	DET
ap-6304	45	3	fourier	fourier	NOUN
ap-6304	45	4	transform	transform	NOUN
ap-6304	45	5	we	we	PRON
ap-6304	45	6	can	can	AUX
ap-6304	45	7	get	get	VERB
ap-6304	45	8	the	the	DET
ap-6304	45	9	expression	expression	NOUN
ap-6304	45	10	for	for	ADP
ap-6304	45	11	the	the	DET
ap-6304	45	12	fourier	fourier	ADJ
ap-6304	45	13	image	image	NOUN
ap-6304	45	14	of	of	ADP
ap-6304	45	15	the	the	DET
ap-6304	45	16	solution	solution	NOUN
ap-6304	45	17	û(ξ	û(ξ	PROPN
ap-6304	45	18	,	,	PUNCT
ap-6304	45	19	t	t	PROPN
ap-6304	45	20	)	)	PUNCT
ap-6304	45	21	=	=	SYM
ap-6304	45	22	e−iξatη̂(ξ	e−iξatη̂(ξ	NOUN
ap-6304	45	23	)	)	PUNCT
ap-6304	45	24	.	.	PUNCT
ap-6304	46	1	using	use	VERB
ap-6304	46	2	the	the	DET
ap-6304	46	3	inverse	inverse	NOUN
ap-6304	46	4	transform	transform	NOUN
ap-6304	46	5	,	,	PUNCT
ap-6304	46	6	the	the	DET
ap-6304	46	7	solution	solution	NOUN
ap-6304	46	8	can	can	AUX
ap-6304	46	9	be	be	AUX
ap-6304	46	10	written	write	VERB
ap-6304	46	11	in	in	ADP
ap-6304	46	12	the	the	DET
ap-6304	46	13	form	form	NOUN
ap-6304	46	14	u(x	u(x	NOUN
ap-6304	46	15	,	,	PUNCT
ap-6304	46	16	t	t	NOUN
ap-6304	46	17	)	)	PUNCT
ap-6304	46	18	=	=	SYM
ap-6304	47	1	1√	1√	NUM
ap-6304	47	2	2π	2π	NUM
ap-6304	47	3	∫	∫	PROPN
ap-6304	48	1	+	+	NUM
ap-6304	48	2	∞	∞	PROPN
ap-6304	48	3	−∞	−∞	ADP
ap-6304	48	4	e−iξatη̂(ξ)eiξxdξ	e−iξatη̂(ξ)eiξxdξ	NOUN
ap-6304	48	5	and	and	CCONJ
ap-6304	48	6	finally	finally	ADV
ap-6304	48	7	u(x	u(x	NOUN
ap-6304	48	8	,	,	PUNCT
ap-6304	48	9	t	t	NOUN
ap-6304	48	10	)	)	PUNCT
ap-6304	48	11	=	=	SYM
ap-6304	49	1	1√	1√	NUM
ap-6304	49	2	2π	2π	NUM
ap-6304	49	3	∫	∫	PROPN
ap-6304	50	1	+	+	NUM
ap-6304	50	2	∞	∞	PROPN
ap-6304	50	3	−∞	−∞	X
ap-6304	50	4	η̂(ξ)eiξ(x−at)dξ	η̂(ξ)eiξ(x−at)dξ	NOUN
ap-6304	50	5	it	it	PRON
ap-6304	50	6	’s	’	VERB
ap-6304	50	7	not	not	PART
ap-6304	50	8	difficult	difficult	ADJ
ap-6304	50	9	to	to	PART
ap-6304	50	10	see	see	VERB
ap-6304	50	11	that	that	SCONJ
ap-6304	50	12	the	the	DET
ap-6304	50	13	solution	solution	NOUN
ap-6304	50	14	corresponds	correspond	VERB
ap-6304	50	15	in	in	ADP
ap-6304	50	16	fact	fact	NOUN
ap-6304	50	17	to	to	ADP
ap-6304	50	18	the	the	DET
ap-6304	50	19	initial	initial	ADJ
ap-6304	50	20	data	datum	NOUN
ap-6304	50	21	η(x	η(x	NOUN
ap-6304	50	22	)	)	PUNCT
ap-6304	50	23	shifted	shift	VERB
ap-6304	50	24	along	along	ADP
ap-6304	50	25	the	the	DET
ap-6304	50	26	x	x	NOUN
ap-6304	50	27	-	-	NOUN
ap-6304	50	28	axis	axis	NOUN
ap-6304	50	29	at	at	ADP
ap-6304	50	30	velocity	velocity	NOUN
ap-6304	50	31	a	a	DET
ap-6304	50	32	,	,	PUNCT
ap-6304	50	33	i.e.	i.e.	X
ap-6304	50	34	u(x	u(x	PROPN
ap-6304	50	35	,	,	PUNCT
ap-6304	50	36	t	t	PROPN
ap-6304	50	37	)	)	PUNCT
ap-6304	51	1	=	=	PUNCT
ap-6304	51	2	η(x−	η(x−	NOUN
ap-6304	51	3	at	at	ADP
ap-6304	51	4	)	)	PUNCT
ap-6304	51	5	.	.	PUNCT
ap-6304	52	1	an	an	DET
ap-6304	52	2	illustration	illustration	NOUN
ap-6304	52	3	of	of	ADP
ap-6304	52	4	such	such	DET
ap-6304	52	5	a	a	DET
ap-6304	52	6	situation	situation	NOUN
ap-6304	52	7	can	can	AUX
ap-6304	52	8	be	be	AUX
ap-6304	52	9	seen	see	VERB
ap-6304	52	10	in	in	ADP
ap-6304	52	11	fig	fig	NOUN
ap-6304	52	12	.	.	PUNCT
ap-6304	53	1	2	2	NUM
ap-6304	53	2	.	.	X
ap-6304	53	3	when	when	SCONJ
ap-6304	53	4	the	the	DET
ap-6304	53	5	advection	advection	NOUN
ap-6304	53	6	equation	equation	NOUN
ap-6304	53	7	is	be	AUX
ap-6304	53	8	solved	solve	VERB
ap-6304	53	9	numerically	numerically	ADV
ap-6304	53	10	the	the	DET
ap-6304	53	11	discrete	discrete	ADJ
ap-6304	53	12	solution	solution	NOUN
ap-6304	53	13	differs	differ	VERB
ap-6304	53	14	from	from	ADP
ap-6304	53	15	the	the	DET
ap-6304	53	16	exact	exact	ADJ
ap-6304	53	17	one	one	NOUN
ap-6304	53	18	,	,	PUNCT
ap-6304	53	19	depending	depend	VERB
ap-6304	53	20	on	on	ADP
ap-6304	53	21	the	the	DET
ap-6304	53	22	numerical	numerical	ADJ
ap-6304	53	23	method	method	NOUN
ap-6304	53	24	used	use	VERB
ap-6304	53	25	.	.	PUNCT
ap-6304	54	1	the	the	DET
ap-6304	54	2	numerical	numerical	ADJ
ap-6304	54	3	solution	solution	NOUN
ap-6304	54	4	often	often	ADV
ap-6304	54	5	exhibits	exhibit	VERB
ap-6304	54	6	some	some	DET
ap-6304	54	7	non	non	ADJ
ap-6304	54	8	-	-	ADJ
ap-6304	54	9	physical	physical	ADJ
ap-6304	54	10	oscillations	oscillation	NOUN
ap-6304	54	11	(	(	PUNCT
ap-6304	54	12	due	due	ADP
ap-6304	54	13	to	to	ADP
ap-6304	54	14	dispersion	dispersion	NOUN
ap-6304	54	15	)	)	PUNCT
ap-6304	54	16	or	or	CCONJ
ap-6304	54	17	smeared	smear	VERB
ap-6304	54	18	solution	solution	NOUN
ap-6304	54	19	gradients	gradient	NOUN
ap-6304	54	20	(	(	PUNCT
ap-6304	54	21	due	due	ADP
ap-6304	54	22	to	to	ADP
ap-6304	54	23	diffusion	diffusion	NOUN
ap-6304	54	24	)	)	PUNCT
ap-6304	54	25	.	.	PUNCT
ap-6304	55	1	this	this	PRON
ap-6304	55	2	is	be	AUX
ap-6304	55	3	why	why	SCONJ
ap-6304	55	4	the	the	DET
ap-6304	55	5	diffusion	diffusion	NOUN
ap-6304	55	6	and	and	CCONJ
ap-6304	55	7	dispersion	dispersion	NOUN
ap-6304	55	8	equations	equation	NOUN
ap-6304	55	9	are	be	AUX
ap-6304	55	10	briefly	briefly	ADV
ap-6304	55	11	presented	present	VERB
ap-6304	55	12	hereafter	hereafter	ADV
ap-6304	55	13	.	.	PUNCT
ap-6304	56	1	0t	0t	X
ap-6304	57	1	=	=	SYM
ap-6304	57	2	t	t	PROPN
ap-6304	57	3	+2	+2	PROPN
ap-6304	58	1	tδt	tδt	PROPN
ap-6304	58	2	=	=	PROPN
ap-6304	58	3	t	t	PROPN
ap-6304	58	4	+	+	X
ap-6304	58	5	t0	t0	PROPN
ap-6304	58	6	δt	δt	NOUN
ap-6304	58	7	=	=	SYM
ap-6304	58	8	t0	t0	NUM
ap-6304	58	9	u	u	NOUN
ap-6304	58	10	x	x	X
ap-6304	58	11	a	a	DET
ap-6304	58	12	figure	figure	NOUN
ap-6304	58	13	2	2	NUM
ap-6304	58	14	.	.	PUNCT
ap-6304	58	15	advection	advection	NOUN
ap-6304	58	16	equation	equation	NOUN
ap-6304	58	17	solution	solution	NOUN
ap-6304	58	18	evolution	evolution	NOUN
ap-6304	58	19	.	.	PUNCT
ap-6304	59	1	0t	0t	X
ap-6304	60	1	=	=	SYM
ap-6304	60	2	t	t	X
ap-6304	60	3	δ0t	δ0t	PROPN
ap-6304	60	4	=	=	PROPN
ap-6304	60	5	t	t	PROPN
ap-6304	60	6	+2	+2	PROPN
ap-6304	60	7	t	t	PROPN
ap-6304	60	8	t	t	PROPN
ap-6304	60	9	=	=	PROPN
ap-6304	60	10	t	t	PROPN
ap-6304	60	11	+	+	NUM
ap-6304	60	12	t0	t0	PRON
ap-6304	60	13	δu	δu	ADP
ap-6304	60	14	x	x	NOUN
ap-6304	60	15	figure	figure	NOUN
ap-6304	60	16	3	3	NUM
ap-6304	60	17	.	.	PUNCT
ap-6304	60	18	diffusion	diffusion	NOUN
ap-6304	60	19	equation	equation	NOUN
ap-6304	60	20	solution	solution	NOUN
ap-6304	60	21	evolution	evolution	NOUN
ap-6304	60	22	.	.	PUNCT
ap-6304	61	1	2.2	2.2	NUM
ap-6304	61	2	.	.	PUNCT
ap-6304	61	3	diffusion	diffusion	NOUN
ap-6304	61	4	equation	equation	NOUN
ap-6304	61	5	the	the	DET
ap-6304	61	6	diffusion	diffusion	NOUN
ap-6304	61	7	equation	equation	NOUN
ap-6304	61	8	contains	contain	VERB
ap-6304	61	9	second	second	ADJ
ap-6304	61	10	spatial	spatial	ADJ
ap-6304	61	11	derivative	derivative	NOUN
ap-6304	61	12	,	,	PUNCT
ap-6304	61	13	multiplied	multiply	VERB
ap-6304	61	14	by	by	ADP
ap-6304	61	15	a	a	DET
ap-6304	61	16	diffusion	diffusion	NOUN
ap-6304	61	17	coefficient	coefficient	PROPN
ap-6304	61	18	b.	b.	PROPN
ap-6304	61	19	ut	ut	PROPN
ap-6304	62	1	+	+	PROPN
ap-6304	62	2	buxx	buxx	PROPN
ap-6304	62	3	=	=	SYM
ap-6304	62	4	0	0	PUNCT
ap-6304	62	5	also	also	ADV
ap-6304	62	6	this	this	DET
ap-6304	62	7	linear	linear	ADJ
ap-6304	62	8	pde	pde	NOUN
ap-6304	62	9	can	can	AUX
ap-6304	62	10	easily	easily	ADV
ap-6304	62	11	be	be	AUX
ap-6304	62	12	solved	solve	VERB
ap-6304	62	13	analytically	analytically	ADV
ap-6304	62	14	using	use	VERB
ap-6304	62	15	the	the	DET
ap-6304	62	16	fourier	fourier	NOUN
ap-6304	62	17	transform	transform	NOUN
ap-6304	62	18	to	to	PART
ap-6304	62	19	obtain	obtain	VERB
ap-6304	62	20	û(ξ	û(ξ	ADP
ap-6304	62	21	,	,	PUNCT
ap-6304	62	22	t	t	PROPN
ap-6304	62	23	)	)	PUNCT
ap-6304	62	24	=	=	SYM
ap-6304	62	25	e−i2ξ2btη̂(ξ	e−i2ξ2btη̂(ξ	PROPN
ap-6304	62	26	)	)	PUNCT
ap-6304	62	27	and	and	CCONJ
ap-6304	62	28	after	after	SCONJ
ap-6304	62	29	the	the	DET
ap-6304	62	30	inverse	inverse	NOUN
ap-6304	62	31	transform	transform	VERB
ap-6304	62	32	the	the	DET
ap-6304	62	33	solution	solution	NOUN
ap-6304	62	34	u(x	u(x	NOUN
ap-6304	62	35	,	,	PUNCT
ap-6304	62	36	t	t	NOUN
ap-6304	62	37	)	)	PUNCT
ap-6304	62	38	=	=	SYM
ap-6304	63	1	1√	1√	NUM
ap-6304	63	2	2π	2π	NUM
ap-6304	63	3	∫	∫	PROPN
ap-6304	64	1	+	+	X
ap-6304	64	2	∞	∞	PROPN
ap-6304	64	3	−∞	−∞	ADP
ap-6304	64	4	eξ	eξ	PROPN
ap-6304	64	5	2btη̂(ξ)eiξxdξ	2btη̂(ξ)eiξxdξ	NUM
ap-6304	64	6	.	.	PUNCT
ap-6304	65	1	a	a	DET
ap-6304	65	2	straightforward	straightforward	ADJ
ap-6304	65	3	comparison	comparison	NOUN
ap-6304	65	4	with	with	ADP
ap-6304	65	5	the	the	DET
ap-6304	65	6	solution	solution	NOUN
ap-6304	65	7	of	of	ADP
ap-6304	65	8	the	the	DET
ap-6304	65	9	advection	advection	NOUN
ap-6304	65	10	equation	equation	NOUN
ap-6304	65	11	reveals	reveal	VERB
ap-6304	65	12	that	that	SCONJ
ap-6304	65	13	now	now	ADV
ap-6304	65	14	the	the	DET
ap-6304	65	15	individual	individual	ADJ
ap-6304	65	16	fourier	fourier	NOUN
ap-6304	65	17	modes	mode	NOUN
ap-6304	65	18	found	find	VERB
ap-6304	65	19	in	in	ADP
ap-6304	65	20	the	the	DET
ap-6304	65	21	initial	initial	ADJ
ap-6304	65	22	data	datum	NOUN
ap-6304	65	23	η(x	η(x	NOUN
ap-6304	65	24	)	)	PUNCT
ap-6304	65	25	do	do	AUX
ap-6304	65	26	not	not	PART
ap-6304	65	27	change	change	VERB
ap-6304	65	28	their	their	PRON
ap-6304	65	29	position	position	NOUN
ap-6304	65	30	.	.	PUNCT
ap-6304	66	1	they	they	PRON
ap-6304	66	2	only	only	ADV
ap-6304	66	3	change	change	VERB
ap-6304	66	4	their	their	PRON
ap-6304	66	5	amplitude	amplitude	NOUN
ap-6304	66	6	by	by	ADP
ap-6304	66	7	the	the	DET
ap-6304	66	8	factor	factor	NOUN
ap-6304	66	9	eξ2bt	eξ2bt	PROPN
ap-6304	66	10	,	,	PUNCT
ap-6304	66	11	which	which	PRON
ap-6304	66	12	means	mean	VERB
ap-6304	66	13	the	the	DET
ap-6304	66	14	exponential	exponential	ADJ
ap-6304	66	15	decay	decay	NOUN
ap-6304	66	16	for	for	ADP
ap-6304	66	17	b	b	NOUN
ap-6304	66	18	<	<	X
ap-6304	66	19	0	0	NUM
ap-6304	66	20	and	and	CCONJ
ap-6304	66	21	growth	growth	NOUN
ap-6304	66	22	for	for	ADP
ap-6304	66	23	b	b	PROPN
ap-6304	66	24	>	>	X
ap-6304	66	25	0	0	PROPN
ap-6304	66	26	.	.	PUNCT
ap-6304	67	1	this	this	PRON
ap-6304	67	2	is	be	AUX
ap-6304	67	3	why	why	SCONJ
ap-6304	67	4	only	only	ADV
ap-6304	67	5	the	the	DET
ap-6304	67	6	decaying	decay	VERB
ap-6304	67	7	case	case	NOUN
ap-6304	67	8	with	with	ADP
ap-6304	67	9	b	b	PROPN
ap-6304	67	10	<	<	X
ap-6304	67	11	0	0	X
ap-6304	67	12	is	be	AUX
ap-6304	67	13	usually	usually	ADV
ap-6304	67	14	physically	physically	ADV
ap-6304	67	15	acceptable	acceptable	ADJ
ap-6304	67	16	leading	lead	VERB
ap-6304	67	17	to	to	ADP
ap-6304	67	18	an	an	DET
ap-6304	67	19	asymptotically	asymptotically	ADV
ap-6304	67	20	stable	stable	ADJ
ap-6304	67	21	evolution	evolution	NOUN
ap-6304	67	22	in	in	ADP
ap-6304	67	23	time	time	NOUN
ap-6304	67	24	.	.	PUNCT
ap-6304	68	1	it	it	PRON
ap-6304	68	2	should	should	AUX
ap-6304	68	3	also	also	ADV
ap-6304	68	4	be	be	AUX
ap-6304	68	5	noted	note	VERB
ap-6304	68	6	that	that	SCONJ
ap-6304	68	7	the	the	DET
ap-6304	68	8	decay	decay	NOUN
ap-6304	68	9	depends	depend	VERB
ap-6304	68	10	on	on	ADP
ap-6304	68	11	the	the	DET
ap-6304	68	12	square	square	NOUN
ap-6304	68	13	of	of	ADP
ap-6304	68	14	wave	wave	NOUN
ap-6304	68	15	number	number	NOUN
ap-6304	68	16	ξ	ξ	PROPN
ap-6304	68	17	and	and	CCONJ
ap-6304	68	18	thus	thus	ADV
ap-6304	68	19	the	the	DET
ap-6304	68	20	rapidly	rapidly	ADV
ap-6304	68	21	oscillating	oscillate	VERB
ap-6304	68	22	modes	mode	NOUN
ap-6304	68	23	decay	decay	VERB
ap-6304	68	24	much	much	ADV
ap-6304	68	25	faster	fast	ADV
ap-6304	68	26	.	.	PUNCT
ap-6304	69	1	an	an	DET
ap-6304	69	2	illustration	illustration	NOUN
ap-6304	69	3	of	of	ADP
ap-6304	69	4	the	the	DET
ap-6304	69	5	diffusion	diffusion	NOUN
ap-6304	69	6	process	process	NOUN
ap-6304	69	7	and	and	CCONJ
ap-6304	69	8	diffusion	diffusion	NOUN
ap-6304	69	9	equation	equation	NOUN
ap-6304	69	10	solution	solution	NOUN
ap-6304	69	11	is	be	AUX
ap-6304	69	12	shown	show	VERB
ap-6304	69	13	in	in	ADP
ap-6304	69	14	fig	fig	NOUN
ap-6304	69	15	.	.	PUNCT
ap-6304	70	1	3	3	NUM
ap-6304	70	2	.	.	X
ap-6304	70	3	2.3	2.3	NUM
ap-6304	70	4	.	.	PUNCT
ap-6304	71	1	dispersion	dispersion	NOUN
ap-6304	71	2	equation	equation	NOUN
ap-6304	71	3	the	the	DET
ap-6304	71	4	linear	linear	ADJ
ap-6304	71	5	dispersion	dispersion	NOUN
ap-6304	71	6	equation	equation	NOUN
ap-6304	71	7	can	can	AUX
ap-6304	71	8	be	be	AUX
ap-6304	71	9	written	write	VERB
ap-6304	71	10	as	as	ADP
ap-6304	71	11	ut	ut	PROPN
ap-6304	71	12	+	+	CCONJ
ap-6304	71	13	cuxxx	cuxxx	X
ap-6304	71	14	=	=	SYM
ap-6304	71	15	0	0	NUM
ap-6304	71	16	where	where	SCONJ
ap-6304	71	17	c	c	PROPN
ap-6304	71	18	is	be	AUX
ap-6304	71	19	the	the	DET
ap-6304	71	20	dispersion	dispersion	NOUN
ap-6304	71	21	coefficient	coefficient	NOUN
ap-6304	71	22	.	.	PUNCT
ap-6304	72	1	the	the	DET
ap-6304	72	2	fourier	fourier	ADJ
ap-6304	72	3	image	image	NOUN
ap-6304	72	4	of	of	ADP
ap-6304	72	5	the	the	DET
ap-6304	72	6	solution	solution	NOUN
ap-6304	72	7	is	be	AUX
ap-6304	72	8	û(ξ	û(ξ	ADJ
ap-6304	72	9	,	,	PUNCT
ap-6304	72	10	t	t	PROPN
ap-6304	72	11	)	)	PUNCT
ap-6304	72	12	=	=	SYM
ap-6304	72	13	e−i3ξ3ctη̂(ξ	e−i3ξ3ctη̂(ξ	X
ap-6304	72	14	)	)	PUNCT
ap-6304	72	15	50	50	NUM
ap-6304	72	16	vol	vol	NOUN
ap-6304	72	17	.	.	PUNCT
ap-6304	73	1	61	61	NUM
ap-6304	73	2	special	special	ADJ
ap-6304	73	3	issue/2021	issue/2021	NOUN
ap-6304	73	4	modified	modify	VERB
ap-6304	73	5	equation	equation	NOUN
ap-6304	73	6	for	for	ADP
ap-6304	73	7	explicit	explicit	ADJ
ap-6304	73	8	and	and	CCONJ
ap-6304	73	9	implicit	implicit	ADJ
ap-6304	73	10	schemes	scheme	NOUN
ap-6304	73	11	from	from	ADP
ap-6304	73	12	which	which	PRON
ap-6304	73	13	follows	follow	VERB
ap-6304	73	14	the	the	DET
ap-6304	73	15	solution	solution	NOUN
ap-6304	73	16	u(x	u(x	NOUN
ap-6304	73	17	,	,	PUNCT
ap-6304	73	18	t	t	NOUN
ap-6304	73	19	)	)	PUNCT
ap-6304	73	20	=	=	SYM
ap-6304	74	1	1√	1√	NUM
ap-6304	74	2	2π	2π	NUM
ap-6304	74	3	∫	∫	PROPN
ap-6304	75	1	+	+	X
ap-6304	75	2	∞	∞	PROPN
ap-6304	75	3	−∞	−∞	ADP
ap-6304	75	4	eiξ3ctη̂(ξ)eiξxdξ	eiξ3ctη̂(ξ)eiξxdξ	NOUN
ap-6304	75	5	that	that	PRON
ap-6304	75	6	can	can	AUX
ap-6304	75	7	be	be	AUX
ap-6304	75	8	rearranged	rearrange	VERB
ap-6304	75	9	to	to	ADP
ap-6304	75	10	u(x	u(x	PROPN
ap-6304	75	11	,	,	PUNCT
ap-6304	75	12	t	t	PROPN
ap-6304	75	13	)	)	PUNCT
ap-6304	75	14	=	=	SYM
ap-6304	76	1	1√	1√	NUM
ap-6304	76	2	2π	2π	NUM
ap-6304	76	3	∫	∫	PROPN
ap-6304	77	1	+	+	NUM
ap-6304	77	2	∞	∞	PROPN
ap-6304	77	3	−∞	−∞	ADP
ap-6304	77	4	η̂(ξ)eiξ(x+c	η̂(ξ)eiξ(x+c	NOUN
ap-6304	77	5	ξ2t)dξ	ξ2t)dξ	NOUN
ap-6304	77	6	this	this	DET
ap-6304	77	7	form	form	NOUN
ap-6304	77	8	is	be	AUX
ap-6304	77	9	very	very	ADV
ap-6304	77	10	similar	similar	ADJ
ap-6304	77	11	to	to	ADP
ap-6304	77	12	the	the	DET
ap-6304	77	13	solution	solution	NOUN
ap-6304	77	14	of	of	ADP
ap-6304	77	15	the	the	DET
ap-6304	77	16	advection	advection	NOUN
ap-6304	77	17	equation	equation	NOUN
ap-6304	77	18	u(x	u(x	NOUN
ap-6304	77	19	,	,	PUNCT
ap-6304	77	20	t	t	PROPN
ap-6304	77	21	)	)	PUNCT
ap-6304	78	1	=	=	SYM
ap-6304	79	1	1√	1√	NUM
ap-6304	79	2	2π	2π	NUM
ap-6304	79	3	∫	∫	PROPN
ap-6304	80	1	+	+	NUM
ap-6304	80	2	∞	∞	PROPN
ap-6304	80	3	−∞	−∞	X
ap-6304	80	4	η̂(ξ)eiξ(x−at)dξ	η̂(ξ)eiξ(x−at)dξ	NOUN
ap-6304	80	5	.	.	PUNCT
ap-6304	81	1	comparing	compare	VERB
ap-6304	81	2	the	the	DET
ap-6304	81	3	corresponding	corresponding	ADJ
ap-6304	81	4	expressions	expression	NOUN
ap-6304	81	5	in	in	ADP
ap-6304	81	6	the	the	DET
ap-6304	81	7	exponential	exponential	NOUN
ap-6304	81	8	,	,	PUNCT
ap-6304	81	9	it	it	PRON
ap-6304	81	10	can	can	AUX
ap-6304	81	11	be	be	AUX
ap-6304	81	12	seen	see	VERB
ap-6304	81	13	that	that	SCONJ
ap-6304	81	14	during	during	ADP
ap-6304	81	15	the	the	DET
ap-6304	81	16	dispersive	dispersive	ADJ
ap-6304	81	17	evolution	evolution	NOUN
ap-6304	81	18	the	the	DET
ap-6304	81	19	fourier	fourier	NOUN
ap-6304	81	20	modes	mode	NOUN
ap-6304	81	21	are	be	AUX
ap-6304	81	22	also	also	ADV
ap-6304	81	23	shifted	shift	VERB
ap-6304	81	24	along	along	ADP
ap-6304	81	25	the	the	DET
ap-6304	81	26	x	x	NOUN
ap-6304	81	27	-	-	NOUN
ap-6304	81	28	axis	axis	ADJ
ap-6304	81	29	,	,	PUNCT
ap-6304	81	30	but	but	CCONJ
ap-6304	81	31	each	each	DET
ap-6304	81	32	mode	mode	NOUN
ap-6304	81	33	is	be	AUX
ap-6304	81	34	shifted	shift	VERB
ap-6304	81	35	at	at	ADP
ap-6304	81	36	a	a	DET
ap-6304	81	37	different	different	ADJ
ap-6304	81	38	velocity	velocity	NOUN
ap-6304	81	39	depending	depend	VERB
ap-6304	81	40	on	on	ADP
ap-6304	81	41	the	the	DET
ap-6304	81	42	wave	wave	NOUN
ap-6304	81	43	number	number	NOUN
ap-6304	81	44	as	as	ADP
ap-6304	81	45	−c	−c	NOUN
ap-6304	81	46	ξ2	ξ2	NOUN
ap-6304	81	47	.	.	PUNCT
ap-6304	82	1	the	the	DET
ap-6304	82	2	minus	minus	PROPN
ap-6304	82	3	sign	sign	NOUN
ap-6304	82	4	indicates	indicate	VERB
ap-6304	82	5	that	that	SCONJ
ap-6304	82	6	for	for	ADP
ap-6304	82	7	c	c	PROPN
ap-6304	82	8	>	>	X
ap-6304	82	9	0	0	NUM
ap-6304	82	10	the	the	DET
ap-6304	82	11	modes	mode	NOUN
ap-6304	82	12	propagate	propagate	VERB
ap-6304	82	13	against	against	ADP
ap-6304	82	14	the	the	DET
ap-6304	82	15	sense	sense	NOUN
ap-6304	82	16	of	of	ADP
ap-6304	82	17	the	the	DET
ap-6304	82	18	x	x	NOUN
ap-6304	82	19	-	-	NOUN
ap-6304	82	20	axis	axis	ADJ
ap-6304	82	21	.	.	PUNCT
ap-6304	83	1	in	in	ADP
ap-6304	83	2	general	general	ADJ
ap-6304	83	3	it	it	PRON
ap-6304	83	4	means	mean	VERB
ap-6304	83	5	that	that	SCONJ
ap-6304	83	6	the	the	DET
ap-6304	83	7	initial	initial	ADJ
ap-6304	83	8	data	datum	NOUN
ap-6304	83	9	are	be	AUX
ap-6304	83	10	decomposed	decompose	VERB
ap-6304	83	11	into	into	ADP
ap-6304	83	12	individual	individual	ADJ
ap-6304	83	13	modes	mode	NOUN
ap-6304	83	14	and	and	CCONJ
ap-6304	83	15	each	each	PRON
ap-6304	83	16	of	of	ADP
ap-6304	83	17	them	they	PRON
ap-6304	83	18	propagates	propagate	VERB
ap-6304	83	19	at	at	ADP
ap-6304	83	20	a	a	DET
ap-6304	83	21	different	different	ADJ
ap-6304	83	22	speed	speed	NOUN
ap-6304	83	23	,	,	PUNCT
ap-6304	83	24	proportional	proportional	ADJ
ap-6304	83	25	to	to	ADP
ap-6304	83	26	ξ2	ξ2	VERB
ap-6304	83	27	.	.	PUNCT
ap-6304	84	1	2.4	2.4	NUM
ap-6304	84	2	.	.	PUNCT
ap-6304	84	3	advection	advection	NOUN
ap-6304	84	4	-	-	PUNCT
ap-6304	84	5	diffusion	diffusion	NOUN
ap-6304	84	6	-	-	PUNCT
ap-6304	84	7	dispersion	dispersion	NOUN
ap-6304	84	8	equation	equation	NOUN
ap-6304	84	9	the	the	DET
ap-6304	84	10	above	above	ADV
ap-6304	84	11	described	describe	VERB
ap-6304	84	12	model	model	NOUN
ap-6304	84	13	problems	problem	NOUN
ap-6304	84	14	involving	involve	VERB
ap-6304	84	15	the	the	DET
ap-6304	84	16	advection	advection	NOUN
ap-6304	84	17	,	,	PUNCT
ap-6304	84	18	diffusion	diffusion	NOUN
ap-6304	84	19	and	and	CCONJ
ap-6304	84	20	dispersion	dispersion	NOUN
ap-6304	84	21	can	can	AUX
ap-6304	84	22	be	be	AUX
ap-6304	84	23	combined	combine	VERB
ap-6304	84	24	into	into	ADP
ap-6304	84	25	advection	advection	NOUN
ap-6304	84	26	-	-	PUNCT
ap-6304	84	27	diffusion	diffusion	NOUN
ap-6304	84	28	or	or	CCONJ
ap-6304	84	29	advection	advection	NOUN
ap-6304	84	30	-	-	PUNCT
ap-6304	84	31	dispersion	dispersion	NOUN
ap-6304	84	32	equations	equation	NOUN
ap-6304	84	33	.	.	PUNCT
ap-6304	85	1	the	the	DET
ap-6304	85	2	solutions	solution	NOUN
ap-6304	85	3	of	of	ADP
ap-6304	85	4	these	these	DET
ap-6304	85	5	combined	combine	VERB
ap-6304	85	6	equations	equation	NOUN
ap-6304	85	7	can	can	AUX
ap-6304	85	8	also	also	ADV
ap-6304	85	9	be	be	AUX
ap-6304	85	10	derived	derive	VERB
ap-6304	85	11	analytically	analytically	ADV
ap-6304	85	12	.	.	PUNCT
ap-6304	86	1	they	they	PRON
ap-6304	86	2	will	will	AUX
ap-6304	86	3	share	share	VERB
ap-6304	86	4	the	the	DET
ap-6304	86	5	properties	property	NOUN
ap-6304	86	6	and	and	CCONJ
ap-6304	86	7	behavior	behavior	NOUN
ap-6304	86	8	of	of	ADP
ap-6304	86	9	both	both	CCONJ
ap-6304	86	10	original	original	ADJ
ap-6304	86	11	equations	equation	NOUN
ap-6304	86	12	solutions	solution	NOUN
ap-6304	86	13	.	.	PUNCT
ap-6304	87	1	these	these	DET
ap-6304	87	2	combinations	combination	NOUN
ap-6304	87	3	will	will	AUX
ap-6304	87	4	be	be	AUX
ap-6304	87	5	important	important	ADJ
ap-6304	87	6	later	later	ADV
ap-6304	87	7	in	in	ADP
ap-6304	87	8	this	this	DET
ap-6304	87	9	paper	paper	NOUN
ap-6304	87	10	while	while	SCONJ
ap-6304	87	11	discussing	discuss	VERB
ap-6304	87	12	the	the	DET
ap-6304	87	13	properties	property	NOUN
ap-6304	87	14	of	of	ADP
ap-6304	87	15	the	the	DET
ap-6304	87	16	modified	modify	VERB
ap-6304	87	17	equations	equation	NOUN
ap-6304	87	18	,	,	PUNCT
ap-6304	87	19	where	where	SCONJ
ap-6304	87	20	often	often	ADV
ap-6304	87	21	the	the	DET
ap-6304	87	22	diffusive	diffusive	ADJ
ap-6304	87	23	and	and	CCONJ
ap-6304	87	24	dispersive	dispersive	ADJ
ap-6304	87	25	term	term	NOUN
ap-6304	87	26	appear	appear	VERB
ap-6304	87	27	due	due	ADJ
ap-6304	87	28	to	to	ADP
ap-6304	87	29	the	the	DET
ap-6304	87	30	discretization	discretization	NOUN
ap-6304	87	31	of	of	ADP
ap-6304	87	32	advection	advection	NOUN
ap-6304	87	33	equation	equation	NOUN
ap-6304	87	34	.	.	PUNCT
ap-6304	88	1	see	see	VERB
ap-6304	88	2	the	the	DET
ap-6304	88	3	discussions	discussion	NOUN
ap-6304	88	4	in	in	ADP
ap-6304	88	5	the	the	DET
ap-6304	88	6	sections	section	NOUN
ap-6304	88	7	4.1–5	4.1–5	ADJ
ap-6304	88	8	.	.	PUNCT
ap-6304	89	1	3	3	X
ap-6304	89	2	.	.	X
ap-6304	89	3	discrete	discrete	VERB
ap-6304	89	4	analysis	analysis	NOUN
ap-6304	89	5	the	the	DET
ap-6304	89	6	problem	problem	NOUN
ap-6304	89	7	of	of	ADP
ap-6304	89	8	numerical	numerical	ADJ
ap-6304	89	9	solution	solution	NOUN
ap-6304	89	10	of	of	ADP
ap-6304	89	11	advection	advection	NOUN
ap-6304	89	12	equation	equation	NOUN
ap-6304	89	13	is	be	AUX
ap-6304	89	14	one	one	NUM
ap-6304	89	15	of	of	ADP
ap-6304	89	16	the	the	DET
ap-6304	89	17	classical	classical	ADJ
ap-6304	89	18	topics	topic	NOUN
ap-6304	89	19	in	in	ADP
ap-6304	89	20	numerical	numerical	ADJ
ap-6304	89	21	mathematics	mathematic	NOUN
ap-6304	89	22	.	.	PUNCT
ap-6304	90	1	there	there	PRON
ap-6304	90	2	exists	exist	VERB
ap-6304	90	3	a	a	DET
ap-6304	90	4	wide	wide	ADJ
ap-6304	90	5	range	range	NOUN
ap-6304	90	6	of	of	ADP
ap-6304	90	7	numerical	numerical	ADJ
ap-6304	90	8	schemes	scheme	NOUN
ap-6304	90	9	to	to	PART
ap-6304	90	10	discretize	discretize	VERB
ap-6304	90	11	this	this	DET
ap-6304	90	12	problem	problem	NOUN
ap-6304	90	13	.	.	PUNCT
ap-6304	91	1	here	here	ADV
ap-6304	91	2	we	we	PRON
ap-6304	91	3	only	only	ADV
ap-6304	91	4	show	show	VERB
ap-6304	91	5	a	a	DET
ap-6304	91	6	few	few	ADJ
ap-6304	91	7	classical	classical	ADJ
ap-6304	91	8	methods	method	NOUN
ap-6304	91	9	as	as	ADP
ap-6304	91	10	an	an	DET
ap-6304	91	11	illustration	illustration	NOUN
ap-6304	91	12	.	.	PUNCT
ap-6304	92	1	further	far	ADV
ap-6304	92	2	we	we	PRON
ap-6304	92	3	will	will	AUX
ap-6304	92	4	consider	consider	VERB
ap-6304	92	5	advection	advection	NOUN
ap-6304	92	6	in	in	ADP
ap-6304	92	7	one	one	NUM
ap-6304	92	8	spatial	spatial	ADJ
ap-6304	92	9	dimension	dimension	NOUN
ap-6304	92	10	ut	ut	PROPN
ap-6304	93	1	+	+	CCONJ
ap-6304	93	2	aux	aux	X
ap-6304	93	3	=	=	NOUN
ap-6304	93	4	0	0	PROPN
ap-6304	93	5	a	a	DET
ap-6304	93	6	>	>	X
ap-6304	93	7	0	0	NUM
ap-6304	93	8	,	,	PUNCT
ap-6304	93	9	where	where	SCONJ
ap-6304	93	10	u(x	u(x	NOUN
ap-6304	93	11	,	,	PUNCT
ap-6304	93	12	t	t	PROPN
ap-6304	93	13	)	)	PUNCT
ap-6304	93	14	is	be	AUX
ap-6304	93	15	the	the	DET
ap-6304	93	16	sought	seek	VERB
ap-6304	93	17	solution	solution	NOUN
ap-6304	93	18	and	and	CCONJ
ap-6304	93	19	uni	uni	PROPN
ap-6304	94	1	≈	≈	PROPN
ap-6304	94	2	u(xi	u(xi	PROPN
ap-6304	94	3	,	,	PUNCT
ap-6304	94	4	tn	tn	NOUN
ap-6304	94	5	)	)	PUNCT
ap-6304	94	6	is	be	AUX
ap-6304	94	7	its	its	PRON
ap-6304	94	8	discrete	discrete	ADJ
ap-6304	94	9	numerical	numerical	ADJ
ap-6304	94	10	approximation	approximation	NOUN
ap-6304	94	11	at	at	ADP
ap-6304	94	12	point	point	NOUN
ap-6304	94	13	xi	xi	INTJ
ap-6304	94	14	=	=	PUNCT
ap-6304	94	15	i∆x	i∆x	VERB
ap-6304	94	16	and	and	CCONJ
ap-6304	94	17	time	time	NOUN
ap-6304	94	18	instant	instant	PROPN
ap-6304	94	19	tn	tn	PROPN
ap-6304	94	20	=	=	SYM
ap-6304	94	21	n∆t	n∆t	PROPN
ap-6304	94	22	,	,	PUNCT
ap-6304	94	23	i	i	PRON
ap-6304	94	24	,	,	PUNCT
ap-6304	94	25	n	n	PRON
ap-6304	94	26	being	be	AUX
ap-6304	94	27	integer	integer	NOUN
ap-6304	94	28	indices	index	NOUN
ap-6304	94	29	in	in	ADP
ap-6304	94	30	spatial	spatial	ADJ
ap-6304	94	31	and	and	CCONJ
ap-6304	94	32	temporal	temporal	ADJ
ap-6304	94	33	coordinates	coordinate	NOUN
ap-6304	94	34	respectively	respectively	ADV
ap-6304	94	35	.	.	PUNCT
ap-6304	95	1	the	the	DET
ap-6304	95	2	numerical	numerical	ADJ
ap-6304	95	3	approximation	approximation	NOUN
ap-6304	95	4	of	of	ADP
ap-6304	95	5	the	the	DET
ap-6304	95	6	solution	solution	NOUN
ap-6304	95	7	can	can	AUX
ap-6304	95	8	be	be	AUX
ap-6304	95	9	constructed	construct	VERB
ap-6304	95	10	e.g.	e.g.	ADV
ap-6304	95	11	using	use	VERB
ap-6304	95	12	the	the	DET
ap-6304	95	13	finite	finite	ADJ
ap-6304	95	14	-	-	PUNCT
ap-6304	95	15	difference	difference	ADJ
ap-6304	95	16	discretization	discretization	NOUN
ap-6304	95	17	,	,	PUNCT
ap-6304	95	18	replacing	replace	VERB
ap-6304	95	19	the	the	DET
ap-6304	95	20	derivatives	derivative	NOUN
ap-6304	95	21	in	in	ADP
ap-6304	95	22	the	the	DET
ap-6304	95	23	original	original	ADJ
ap-6304	95	24	equation	equation	NOUN
ap-6304	95	25	by	by	ADP
ap-6304	95	26	the	the	DET
ap-6304	95	27	corresponding	corresponding	ADJ
ap-6304	95	28	divided	divide	VERB
ap-6304	95	29	differences	difference	NOUN
ap-6304	95	30	formulas	formula	NOUN
ap-6304	95	31	developed	develop	VERB
ap-6304	95	32	from	from	ADP
ap-6304	95	33	the	the	DET
ap-6304	95	34	taylor	taylor	PROPN
ap-6304	95	35	expansions	expansion	NOUN
ap-6304	95	36	.	.	PUNCT
ap-6304	96	1	the	the	DET
ap-6304	96	2	x	x	SYM
ap-6304	96	3	t	t	NOUN
ap-6304	96	4	i−1	i−1	PROPN
ap-6304	96	5	i+1i	i+1i	PROPN
ap-6304	96	6	n+1	n+1	PROPN
ap-6304	96	7	n	n	PRON
ap-6304	96	8	figure	figure	VERB
ap-6304	96	9	4	4	NUM
ap-6304	96	10	.	.	PUNCT
ap-6304	96	11	initial	initial	ADJ
ap-6304	96	12	condition	condition	NOUN
ap-6304	96	13	.	.	PUNCT
ap-6304	97	1	final	final	ADJ
ap-6304	97	2	formulas	formula	NOUN
ap-6304	97	3	for	for	ADP
ap-6304	97	4	few	few	ADJ
ap-6304	97	5	classical	classical	ADJ
ap-6304	97	6	schemes	scheme	NOUN
ap-6304	97	7	are	be	AUX
ap-6304	97	8	shown	show	VERB
ap-6304	97	9	in	in	ADP
ap-6304	97	10	the	the	DET
ap-6304	97	11	table	table	NOUN
ap-6304	97	12	1	1	NUM
ap-6304	97	13	.	.	PUNCT
ap-6304	98	1	some	some	DET
ap-6304	98	2	details	detail	NOUN
ap-6304	98	3	concerning	concern	VERB
ap-6304	98	4	the	the	DET
ap-6304	98	5	process	process	NOUN
ap-6304	98	6	of	of	ADP
ap-6304	98	7	derivation	derivation	NOUN
ap-6304	98	8	of	of	ADP
ap-6304	98	9	some	some	PRON
ap-6304	98	10	of	of	ADP
ap-6304	98	11	these	these	DET
ap-6304	98	12	schemes	scheme	NOUN
ap-6304	98	13	will	will	AUX
ap-6304	98	14	be	be	AUX
ap-6304	98	15	shown	show	VERB
ap-6304	98	16	in	in	ADP
ap-6304	98	17	the	the	DET
ap-6304	98	18	following	follow	VERB
ap-6304	98	19	sections	section	NOUN
ap-6304	98	20	.	.	PUNCT
ap-6304	99	1	more	more	ADJ
ap-6304	99	2	details	detail	NOUN
ap-6304	99	3	can	can	AUX
ap-6304	99	4	be	be	AUX
ap-6304	99	5	found	find	VERB
ap-6304	99	6	e.g.	e.g.	ADV
ap-6304	99	7	in	in	ADP
ap-6304	99	8	the	the	DET
ap-6304	99	9	classical	classical	ADJ
ap-6304	99	10	textbooks	textbook	NOUN
ap-6304	99	11	[	[	X
ap-6304	99	12	2	2	NUM
ap-6304	99	13	]	]	PUNCT
ap-6304	99	14	,	,	PUNCT
ap-6304	99	15	[	[	X
ap-6304	99	16	3	3	NUM
ap-6304	99	17	]	]	PUNCT
ap-6304	99	18	or	or	CCONJ
ap-6304	99	19	[	[	X
ap-6304	99	20	4	4	NUM
ap-6304	99	21	]	]	PUNCT
ap-6304	99	22	.	.	PUNCT
ap-6304	100	1	3.1	3.1	NUM
ap-6304	100	2	.	.	PUNCT
ap-6304	100	3	up	up	ADP
ap-6304	100	4	-	-	PUNCT
ap-6304	100	5	wind	wind	NOUN
ap-6304	100	6	&	&	CCONJ
ap-6304	100	7	down	down	ADP
ap-6304	100	8	-	-	PUNCT
ap-6304	100	9	wind	wind	NOUN
ap-6304	100	10	decomposition	decomposition	NOUN
ap-6304	100	11	a	a	DET
ap-6304	100	12	family	family	NOUN
ap-6304	100	13	of	of	ADP
ap-6304	100	14	simple	simple	ADJ
ap-6304	100	15	explicit	explicit	ADJ
ap-6304	100	16	schemes	scheme	NOUN
ap-6304	100	17	working	work	VERB
ap-6304	100	18	on	on	ADP
ap-6304	100	19	a	a	DET
ap-6304	100	20	three	three	NUM
ap-6304	100	21	-	-	PUNCT
ap-6304	100	22	point	point	NOUN
ap-6304	100	23	spatial	spatial	ADJ
ap-6304	100	24	stencil	stencil	NOUN
ap-6304	100	25	and	and	CCONJ
ap-6304	100	26	two	two	NUM
ap-6304	100	27	time	time	NOUN
ap-6304	100	28	levels	level	NOUN
ap-6304	100	29	(	(	PUNCT
ap-6304	100	30	see	see	VERB
ap-6304	100	31	fig	fig	NOUN
ap-6304	100	32	.	.	PUNCT
ap-6304	101	1	4	4	X
ap-6304	101	2	)	)	PUNCT
ap-6304	101	3	can	can	AUX
ap-6304	101	4	be	be	AUX
ap-6304	101	5	derived	derive	VERB
ap-6304	101	6	using	use	VERB
ap-6304	101	7	forward	forward	ADV
ap-6304	101	8	and	and	CCONJ
ap-6304	101	9	backward	backward	ADJ
ap-6304	101	10	difference	difference	NOUN
ap-6304	101	11	approximations	approximation	NOUN
ap-6304	101	12	of	of	ADP
ap-6304	101	13	the	the	DET
ap-6304	101	14	spatial	spatial	ADJ
ap-6304	101	15	derivative	derivative	NOUN
ap-6304	101	16	.	.	PUNCT
ap-6304	102	1	when	when	SCONJ
ap-6304	102	2	a	a	DET
ap-6304	102	3	general	general	ADJ
ap-6304	102	4	(	(	PUNCT
ap-6304	102	5	convex	convex	NOUN
ap-6304	102	6	)	)	PUNCT
ap-6304	102	7	combination	combination	NOUN
ap-6304	102	8	of	of	ADP
ap-6304	102	9	forward	forward	ADJ
ap-6304	102	10	and	and	CCONJ
ap-6304	102	11	backward	backward	ADJ
ap-6304	102	12	differences	difference	NOUN
ap-6304	102	13	is	be	AUX
ap-6304	102	14	used	use	VERB
ap-6304	102	15	,	,	PUNCT
ap-6304	102	16	with	with	ADP
ap-6304	102	17	weighting	weight	VERB
ap-6304	102	18	factor	factor	NOUN
ap-6304	102	19	α	α	NOUN
ap-6304	102	20	,	,	PUNCT
ap-6304	102	21	the	the	DET
ap-6304	102	22	explicit	explicit	ADJ
ap-6304	102	23	finite	finite	ADJ
ap-6304	102	24	difference	difference	NOUN
ap-6304	102	25	approximation	approximation	NOUN
ap-6304	102	26	will	will	AUX
ap-6304	102	27	take	take	VERB
ap-6304	102	28	the	the	DET
ap-6304	102	29	form	form	NOUN
ap-6304	102	30	un+1	un+1	NOUN
ap-6304	103	1	i	i	PRON
ap-6304	103	2	−	−	VERB
ap-6304	103	3	uni	uni	PROPN
ap-6304	103	4	∆t	∆t	PROPN
ap-6304	104	1	+	+	CCONJ
ap-6304	104	2	a	a	DET
ap-6304	104	3	[	[	PUNCT
ap-6304	104	4	α	α	X
ap-6304	104	5	(	(	PUNCT
ap-6304	104	6	uni+1	uni+1	NOUN
ap-6304	104	7	−	−	PROPN
ap-6304	104	8	uni	uni	PROPN
ap-6304	104	9	∆x	∆x	PROPN
ap-6304	104	10	)	)	PUNCT
ap-6304	105	1	+	+	CCONJ
ap-6304	106	1	+	+	ADJ
ap-6304	106	2	(	(	PUNCT
ap-6304	106	3	1−	1−	NUM
ap-6304	106	4	α	α	NOUN
ap-6304	106	5	)	)	PUNCT
ap-6304	106	6	(	(	PUNCT
ap-6304	106	7	uni	uni	INTJ
ap-6304	106	8	−	−	PROPN
ap-6304	106	9	uni−1	uni−1	PROPN
ap-6304	106	10	∆x	∆x	PROPN
ap-6304	106	11	)	)	PUNCT
ap-6304	106	12	]	]	PUNCT
ap-6304	107	1	=	=	PUNCT
ap-6304	107	2	0	0	PUNCT
ap-6304	107	3	this	this	DET
ap-6304	107	4	family	family	NOUN
ap-6304	107	5	of	of	ADP
ap-6304	107	6	schemes	scheme	NOUN
ap-6304	107	7	can	can	AUX
ap-6304	107	8	be	be	AUX
ap-6304	107	9	formally	formally	ADV
ap-6304	107	10	written	write	VERB
ap-6304	107	11	using	use	VERB
ap-6304	107	12	the	the	DET
ap-6304	107	13	forward	forward	ADJ
ap-6304	107	14	(	(	PUNCT
ap-6304	107	15	down	down	ADJ
ap-6304	107	16	-	-	PUNCT
ap-6304	107	17	wind	wind	NOUN
ap-6304	107	18	)	)	PUNCT
ap-6304	107	19	difference	difference	NOUN
ap-6304	107	20	{	{	PUNCT
ap-6304	107	21	d	d	NOUN
ap-6304	107	22	}	}	PUNCT
ap-6304	107	23	and	and	CCONJ
ap-6304	107	24	backward	backward	ADJ
ap-6304	107	25	(	(	PUNCT
ap-6304	107	26	up	up	ADP
ap-6304	107	27	-	-	PUNCT
ap-6304	107	28	wind	wind	NOUN
ap-6304	107	29	)	)	PUNCT
ap-6304	107	30	difference	difference	NOUN
ap-6304	107	31	{	{	PUNCT
ap-6304	107	32	u	u	NOUN
ap-6304	107	33	}	}	PUNCT
ap-6304	107	34	as	as	ADP
ap-6304	107	35	un+1	un+1	PROPN
ap-6304	108	1	i	i	PRON
ap-6304	108	2	−	−	VERB
ap-6304	108	3	uni	uni	PROPN
ap-6304	108	4	∆t	∆t	PROPN
ap-6304	109	1	+	+	CCONJ
ap-6304	109	2	a	a	DET
ap-6304	109	3	[	[	PUNCT
ap-6304	109	4	α{d}+	α{d}+	PROPN
ap-6304	109	5	(	(	PUNCT
ap-6304	109	6	1−	1−	NUM
ap-6304	109	7	α){u	α){u	NUM
ap-6304	109	8	}	}	PUNCT
ap-6304	109	9	]	]	PUNCT
ap-6304	109	10	=	=	PUNCT
ap-6304	109	11	0	0	X
ap-6304	109	12	.	.	PUNCT
ap-6304	110	1	it	it	PRON
ap-6304	110	2	’s	’	VERB
ap-6304	110	3	evident	evident	ADJ
ap-6304	110	4	,	,	PUNCT
ap-6304	110	5	that	that	SCONJ
ap-6304	110	6	the	the	DET
ap-6304	110	7	classical	classical	ADJ
ap-6304	110	8	upwind	upwind	NOUN
ap-6304	110	9	and	and	CCONJ
ap-6304	110	10	downwind	downwind	ADJ
ap-6304	110	11	schemes	scheme	NOUN
ap-6304	110	12	can	can	AUX
ap-6304	110	13	be	be	AUX
ap-6304	110	14	recovered	recover	VERB
ap-6304	110	15	for	for	ADP
ap-6304	110	16	special	special	ADJ
ap-6304	110	17	choices	choice	NOUN
ap-6304	110	18	of	of	ADP
ap-6304	110	19	α	α	NOUN
ap-6304	110	20	=	=	SYM
ap-6304	110	21	0	0	PROPN
ap-6304	110	22	and	and	CCONJ
ap-6304	110	23	α	α	NOUN
ap-6304	110	24	=	=	NOUN
ap-6304	110	25	1	1	NUM
ap-6304	110	26	respectively	respectively	ADV
ap-6304	110	27	.	.	PUNCT
ap-6304	111	1	the	the	DET
ap-6304	111	2	simple	simple	ADJ
ap-6304	111	3	central	central	ADJ
ap-6304	111	4	scheme	scheme	NOUN
ap-6304	111	5	can	can	AUX
ap-6304	111	6	be	be	AUX
ap-6304	111	7	obtained	obtain	VERB
ap-6304	111	8	for	for	ADP
ap-6304	111	9	a	a	DET
ap-6304	111	10	symmetric	symmetric	ADJ
ap-6304	111	11	choice	choice	NOUN
ap-6304	111	12	represented	represent	VERB
ap-6304	111	13	by	by	ADP
ap-6304	111	14	α	α	PROPN
ap-6304	111	15	=	=	SYM
ap-6304	111	16	1/2	1/2	NUM
ap-6304	111	17	.	.	PUNCT
ap-6304	112	1	a	a	DET
ap-6304	112	2	little	little	ADJ
ap-6304	112	3	bit	bit	NOUN
ap-6304	112	4	less	less	ADV
ap-6304	112	5	apparent	apparent	ADJ
ap-6304	112	6	,	,	PUNCT
ap-6304	112	7	but	but	CCONJ
ap-6304	112	8	still	still	ADV
ap-6304	112	9	easy	easy	ADJ
ap-6304	112	10	to	to	PART
ap-6304	112	11	verify	verify	VERB
ap-6304	113	1	is	be	AUX
ap-6304	113	2	the	the	DET
ap-6304	113	3	representation	representation	NOUN
ap-6304	113	4	of	of	ADP
ap-6304	113	5	lax	lax	NOUN
ap-6304	113	6	-	-	PUNCT
ap-6304	113	7	friedrichs	friedrich	NOUN
ap-6304	113	8	and	and	CCONJ
ap-6304	113	9	lax	lax	ADJ
ap-6304	113	10	-	-	PUNCT
ap-6304	113	11	wendroff	wendroff	NOUN
ap-6304	113	12	schemes	scheme	NOUN
ap-6304	113	13	,	,	PUNCT
ap-6304	113	14	that	that	PRON
ap-6304	113	15	also	also	ADV
ap-6304	113	16	belong	belong	VERB
ap-6304	113	17	to	to	ADP
ap-6304	113	18	this	this	DET
ap-6304	113	19	family	family	NOUN
ap-6304	113	20	.	.	PUNCT
ap-6304	114	1	values	value	NOUN
ap-6304	114	2	of	of	ADP
ap-6304	114	3	the	the	DET
ap-6304	114	4	upwind	upwind	NOUN
ap-6304	114	5	/	/	SYM
ap-6304	114	6	downwind	downwind	NOUN
ap-6304	114	7	blending	blend	VERB
ap-6304	114	8	coefficient	coefficient	NOUN
ap-6304	114	9	α	α	PROPN
ap-6304	114	10	for	for	ADP
ap-6304	114	11	all	all	DET
ap-6304	114	12	these	these	DET
ap-6304	114	13	schemes	scheme	NOUN
ap-6304	114	14	are	be	AUX
ap-6304	114	15	summarized	summarize	VERB
ap-6304	114	16	in	in	ADP
ap-6304	114	17	the	the	DET
ap-6304	114	18	tab	tab	NOUN
ap-6304	114	19	.	.	PUNCT
ap-6304	115	1	2	2	NUM
ap-6304	115	2	.	.	NOUN
ap-6304	115	3	3.2	3.2	NUM
ap-6304	115	4	.	.	PUNCT
ap-6304	116	1	central	central	ADJ
ap-6304	116	2	&	&	CCONJ
ap-6304	116	3	upwind	upwind	NOUN
ap-6304	116	4	decomposition	decomposition	NOUN
ap-6304	116	5	in	in	ADP
ap-6304	116	6	the	the	DET
ap-6304	116	7	same	same	ADJ
ap-6304	116	8	way	way	NOUN
ap-6304	116	9	as	as	SCONJ
ap-6304	116	10	every	every	DET
ap-6304	116	11	explicit	explicit	ADJ
ap-6304	116	12	scheme	scheme	NOUN
ap-6304	116	13	with	with	ADP
ap-6304	116	14	a	a	DET
ap-6304	116	15	threepoint	threepoint	NOUN
ap-6304	116	16	stencil	stencil	NOUN
ap-6304	116	17	can	can	AUX
ap-6304	116	18	be	be	AUX
ap-6304	116	19	written	write	VERB
ap-6304	116	20	in	in	ADP
ap-6304	116	21	the	the	DET
ap-6304	116	22	form	form	NOUN
ap-6304	116	23	of	of	ADP
ap-6304	116	24	convex	convex	ADJ
ap-6304	116	25	combination	combination	NOUN
ap-6304	116	26	of	of	ADP
ap-6304	116	27	forward	forward	ADJ
ap-6304	116	28	and	and	CCONJ
ap-6304	116	29	backward	backward	ADJ
ap-6304	116	30	differences	difference	NOUN
ap-6304	116	31	,	,	PUNCT
ap-6304	116	32	it	it	PRON
ap-6304	116	33	can	can	AUX
ap-6304	116	34	also	also	ADV
ap-6304	116	35	be	be	AUX
ap-6304	116	36	formally	formally	ADV
ap-6304	116	37	rewritten	rewrite	VERB
ap-6304	116	38	as	as	ADP
ap-6304	116	39	a	a	DET
ap-6304	116	40	weighted	weighted	ADJ
ap-6304	116	41	sum	sum	NOUN
ap-6304	116	42	of	of	ADP
ap-6304	116	43	central	central	ADJ
ap-6304	116	44	and	and	CCONJ
ap-6304	116	45	upwind	upwind	ADJ
ap-6304	116	46	difference	difference	NOUN
ap-6304	116	47	approximations	approximation	NOUN
ap-6304	116	48	.	.	PUNCT
ap-6304	117	1	the	the	DET
ap-6304	117	2	central	central	ADJ
ap-6304	117	3	approximation	approximation	NOUN
ap-6304	117	4	{	{	PUNCT
ap-6304	117	5	c	c	NOUN
ap-6304	117	6	}	}	PUNCT
ap-6304	117	7	can	can	AUX
ap-6304	117	8	simply	simply	ADV
ap-6304	117	9	be	be	AUX
ap-6304	117	10	expressed	express	VERB
ap-6304	117	11	as	as	ADP
ap-6304	117	12	an	an	DET
ap-6304	117	13	average	average	NOUN
ap-6304	117	14	of	of	ADP
ap-6304	117	15	upwind	upwind	NOUN
ap-6304	117	16	and	and	CCONJ
ap-6304	117	17	downwind	downwind	NOUN
ap-6304	117	18	(	(	PUNCT
ap-6304	117	19	backward	backward	ADJ
ap-6304	117	20	and	and	CCONJ
ap-6304	117	21	forward	forward	ADJ
ap-6304	117	22	)	)	PUNCT
ap-6304	117	23	differences	difference	NOUN
ap-6304	117	24	as	as	ADP
ap-6304	117	25	{	{	PUNCT
ap-6304	117	26	c	c	NOUN
ap-6304	117	27	}	}	PUNCT
ap-6304	117	28	=	=	SYM
ap-6304	117	29	{	{	PUNCT
ap-6304	117	30	d}+	d}+	X
ap-6304	117	31	{	{	PUNCT
ap-6304	117	32	u	u	NOUN
ap-6304	117	33	}	}	PUNCT
ap-6304	117	34	2	2	NUM
ap-6304	117	35	=	=	NOUN
ap-6304	117	36	⇒	⇒	NOUN
ap-6304	117	37	{	{	PUNCT
ap-6304	117	38	d	d	NOUN
ap-6304	117	39	}	}	PUNCT
ap-6304	117	40	=	=	SYM
ap-6304	117	41	2{c	2{c	NUM
ap-6304	117	42	}	}	PUNCT
ap-6304	117	43	−	−	PROPN
ap-6304	117	44	{	{	PUNCT
ap-6304	117	45	u	u	NOUN
ap-6304	117	46	}	}	PUNCT
ap-6304	117	47	.	.	PUNCT
ap-6304	118	1	51	51	NUM
ap-6304	118	2	t.	t.	NOUN
ap-6304	118	3	bodnár	bodnár	NOUN
ap-6304	118	4	,	,	PUNCT
ap-6304	118	5	ph	ph	PROPN
ap-6304	118	6	.	.	PROPN
ap-6304	118	7	fraunié	fraunié	PROPN
ap-6304	118	8	,	,	PUNCT
ap-6304	118	9	k.	k.	PROPN
ap-6304	118	10	kozel	kozel	PROPN
ap-6304	118	11	acta	acta	PROPN
ap-6304	118	12	polytechnica	polytechnica	PROPN
ap-6304	118	13	scheme	scheme	NOUN
ap-6304	118	14	formula	formula	NOUN
ap-6304	118	15	up	up	ADP
ap-6304	118	16	-	-	PUNCT
ap-6304	118	17	wind	wind	NOUN
ap-6304	118	18	[	[	X
ap-6304	118	19	u	u	X
ap-6304	118	20	]	]	X
ap-6304	118	21	un+1	un+1	NOUN
ap-6304	119	1	i	i	NOUN
ap-6304	119	2	=	=	PUNCT
ap-6304	119	3	uni	uni	PROPN
ap-6304	119	4	−	−	PROPN
ap-6304	119	5	a∆t	a∆t	VERB
ap-6304	119	6	∆x	∆x	PROPN
ap-6304	119	7	(	(	PUNCT
ap-6304	119	8	uni	uni	PROPN
ap-6304	119	9	−	−	PROPN
ap-6304	119	10	uni−1	uni−1	PROPN
ap-6304	119	11	)	)	PUNCT
ap-6304	119	12	down	down	ADP
ap-6304	119	13	-	-	PUNCT
ap-6304	119	14	wind	wind	NOUN
ap-6304	119	15	[	[	X
ap-6304	119	16	d	d	X
ap-6304	119	17	]	]	X
ap-6304	119	18	un+1	un+1	NOUN
ap-6304	120	1	i	i	NOUN
ap-6304	120	2	=	=	PUNCT
ap-6304	120	3	uni	uni	PROPN
ap-6304	120	4	−	−	PROPN
ap-6304	120	5	a∆t	a∆t	VERB
ap-6304	120	6	∆x	∆x	PROPN
ap-6304	120	7	(	(	PUNCT
ap-6304	120	8	uni+1	uni+1	NOUN
ap-6304	120	9	−	−	X
ap-6304	120	10	uni	uni	ADJ
ap-6304	120	11	)	)	PUNCT
ap-6304	120	12	central	central	ADJ
ap-6304	121	1	[	[	X
ap-6304	121	2	c	c	X
ap-6304	121	3	]	]	X
ap-6304	121	4	un+1	un+1	NOUN
ap-6304	122	1	i	i	NOUN
ap-6304	122	2	=	=	PUNCT
ap-6304	122	3	uni	uni	PROPN
ap-6304	122	4	−	−	NOUN
ap-6304	122	5	a∆t	a∆t	VERB
ap-6304	122	6	2∆x	2∆x	NUM
ap-6304	122	7	(	(	PUNCT
ap-6304	122	8	uni+1	uni+1	NOUN
ap-6304	122	9	−	−	PROPN
ap-6304	122	10	uni−1	uni−1	PROPN
ap-6304	122	11	)	)	PUNCT
ap-6304	122	12	lax	lax	NOUN
ap-6304	122	13	-	-	PUNCT
ap-6304	122	14	friedrichs	friedrich	NOUN
ap-6304	123	1	[	[	X
ap-6304	123	2	lf	lf	X
ap-6304	123	3	]	]	X
ap-6304	123	4	un+1	un+1	NOUN
ap-6304	124	1	i	i	NOUN
ap-6304	124	2	=	=	NOUN
ap-6304	124	3	1	1	NUM
ap-6304	124	4	2	2	NUM
ap-6304	124	5	(	(	PUNCT
ap-6304	124	6	uni+1	uni+1	NOUN
ap-6304	124	7	+	+	CCONJ
ap-6304	124	8	uni−1)−	uni−1)−	ADJ
ap-6304	124	9	a∆t	a∆t	NOUN
ap-6304	124	10	2∆x	2∆x	NUM
ap-6304	124	11	(	(	PUNCT
ap-6304	124	12	uni+1	uni+1	NOUN
ap-6304	124	13	−	−	PROPN
ap-6304	124	14	uni−1	uni−1	PROPN
ap-6304	124	15	)	)	PUNCT
ap-6304	124	16	lax	lax	NOUN
ap-6304	124	17	-	-	PUNCT
ap-6304	124	18	wendroff	wendroff	NOUN
ap-6304	124	19	[	[	X
ap-6304	124	20	lw	lw	X
ap-6304	124	21	]	]	X
ap-6304	124	22	un+1	un+1	NOUN
ap-6304	125	1	i	i	PRON
ap-6304	125	2	=	=	PUNCT
ap-6304	125	3	uni	uni	PROPN
ap-6304	125	4	−	−	NOUN
ap-6304	125	5	a∆t	a∆t	VERB
ap-6304	125	6	2∆x	2∆x	NUM
ap-6304	125	7	(	(	PUNCT
ap-6304	125	8	uni+1	uni+1	NOUN
ap-6304	125	9	−	−	PROPN
ap-6304	125	10	uni−1	uni−1	PROPN
ap-6304	125	11	)	)	PUNCT
ap-6304	126	1	+	+	CCONJ
ap-6304	126	2	a2∆t2	a2∆t2	ADJ
ap-6304	126	3	2∆x2	2∆x2	NUM
ap-6304	126	4	(	(	PUNCT
ap-6304	126	5	uni+1	uni+1	NOUN
ap-6304	126	6	−	−	PROPN
ap-6304	126	7	2uni	2uni	NUM
ap-6304	126	8	+	+	CCONJ
ap-6304	126	9	uni−1	uni−1	PROPN
ap-6304	126	10	)	)	PUNCT
ap-6304	126	11	table	table	NOUN
ap-6304	126	12	1	1	NUM
ap-6304	126	13	.	.	PUNCT
ap-6304	127	1	examples	example	NOUN
ap-6304	127	2	of	of	ADP
ap-6304	127	3	some	some	DET
ap-6304	127	4	simple	simple	ADJ
ap-6304	127	5	classical	classical	ADJ
ap-6304	127	6	discretizations	discretization	NOUN
ap-6304	127	7	for	for	ADP
ap-6304	127	8	advection	advection	NOUN
ap-6304	127	9	equation	equation	NOUN
ap-6304	127	10	.	.	PUNCT
ap-6304	128	1	scheme	scheme	NOUN
ap-6304	128	2	coefficient	coefficient	NOUN
ap-6304	128	3	α	α	X
ap-6304	129	1	[	[	X
ap-6304	129	2	u	u	X
ap-6304	129	3	]	]	X
ap-6304	129	4	0	0	PUNCT
ap-6304	130	1	[	[	X
ap-6304	130	2	d	d	X
ap-6304	130	3	]	]	X
ap-6304	130	4	1	1	NUM
ap-6304	131	1	[	[	X
ap-6304	131	2	c	c	X
ap-6304	131	3	]	]	X
ap-6304	131	4	1	1	NUM
ap-6304	131	5	2	2	NUM
ap-6304	131	6	[	[	X
ap-6304	131	7	lf	lf	X
ap-6304	131	8	]	]	SYM
ap-6304	131	9	1	1	NUM
ap-6304	131	10	2	2	NUM
ap-6304	131	11	−	−	PROPN
ap-6304	131	12	∆x	∆x	PROPN
ap-6304	131	13	2a∆t	2a∆t	NUM
ap-6304	132	1	[	[	X
ap-6304	132	2	lw	lw	X
ap-6304	132	3	]	]	X
ap-6304	132	4	1	1	NUM
ap-6304	132	5	2	2	NUM
ap-6304	132	6	−	−	NOUN
ap-6304	132	7	a∆t	a∆t	VERB
ap-6304	132	8	2∆x	2∆x	NUM
ap-6304	132	9	table	table	NOUN
ap-6304	132	10	2	2	NUM
ap-6304	132	11	.	.	PUNCT
ap-6304	133	1	coefficient	coefficient	NOUN
ap-6304	133	2	of	of	ADP
ap-6304	133	3	up	up	ADP
ap-6304	133	4	-	-	PUNCT
ap-6304	133	5	wind	wind	NOUN
ap-6304	133	6	/	/	SYM
ap-6304	133	7	down	down	ADP
ap-6304	133	8	-	-	PUNCT
ap-6304	133	9	wind	wind	NOUN
ap-6304	133	10	decomposition	decomposition	NOUN
ap-6304	133	11	of	of	ADP
ap-6304	133	12	classical	classical	ADJ
ap-6304	133	13	schemes	scheme	NOUN
ap-6304	133	14	.	.	PUNCT
ap-6304	134	1	the	the	DET
ap-6304	134	2	family	family	NOUN
ap-6304	134	3	of	of	ADP
ap-6304	134	4	explicit	explicit	ADJ
ap-6304	134	5	schemes	scheme	NOUN
ap-6304	134	6	can	can	AUX
ap-6304	134	7	thus	thus	ADV
ap-6304	134	8	be	be	AUX
ap-6304	134	9	rewritten	rewrite	VERB
ap-6304	134	10	using	use	VERB
ap-6304	134	11	the	the	DET
ap-6304	134	12	central	central	ADJ
ap-6304	134	13	difference	difference	NOUN
ap-6304	134	14	approximation	approximation	NOUN
ap-6304	134	15	{	{	PUNCT
ap-6304	134	16	c	c	NOUN
ap-6304	134	17	}	}	PUNCT
ap-6304	134	18	and	and	CCONJ
ap-6304	134	19	additional	additional	ADJ
ap-6304	134	20	upwinding	upwinding	NOUN
ap-6304	134	21	{	{	PUNCT
ap-6304	134	22	u	u	NOUN
ap-6304	134	23	}	}	PUNCT
ap-6304	134	24	,	,	PUNCT
ap-6304	134	25	where	where	SCONJ
ap-6304	134	26	the	the	DET
ap-6304	134	27	blending	blend	VERB
ap-6304	134	28	parameter	parameter	NOUN
ap-6304	134	29	now	now	ADV
ap-6304	134	30	has	have	VERB
ap-6304	134	31	the	the	DET
ap-6304	134	32	value	value	NOUN
ap-6304	134	33	2α	2α	NOUN
ap-6304	134	34	.	.	PUNCT
ap-6304	135	1	un+1	un+1	NOUN
ap-6304	136	1	i	i	PRON
ap-6304	136	2	−	−	VERB
ap-6304	136	3	uni	uni	PROPN
ap-6304	136	4	∆t	∆t	PROPN
ap-6304	137	1	+	+	CCONJ
ap-6304	137	2	a	a	DET
ap-6304	137	3	[	[	X
ap-6304	137	4	2α{c}+	2α{c}+	NUM
ap-6304	137	5	(	(	PUNCT
ap-6304	137	6	1−	1−	NUM
ap-6304	137	7	2α){u	2α){u	NUM
ap-6304	137	8	}	}	PUNCT
ap-6304	137	9	]	]	PUNCT
ap-6304	137	10	=	=	PUNCT
ap-6304	137	11	0	0	NUM
ap-6304	137	12	3.3	3.3	NUM
ap-6304	137	13	.	.	PUNCT
ap-6304	138	1	central	central	ADJ
ap-6304	138	2	&	&	CCONJ
ap-6304	138	3	viscous	viscous	ADJ
ap-6304	138	4	decomposition	decomposition	NOUN
ap-6304	138	5	by	by	ADP
ap-6304	138	6	taking	take	VERB
ap-6304	138	7	a	a	DET
ap-6304	138	8	divided	divide	VERB
ap-6304	138	9	difference	difference	NOUN
ap-6304	138	10	of	of	ADP
ap-6304	138	11	forward	forward	ADJ
ap-6304	138	12	and	and	CCONJ
ap-6304	138	13	backward	backward	ADJ
ap-6304	138	14	differences	difference	NOUN
ap-6304	138	15	(	(	PUNCT
ap-6304	138	16	approximations	approximation	NOUN
ap-6304	138	17	of	of	ADP
ap-6304	138	18	ux	ux	PROPN
ap-6304	138	19	)	)	PUNCT
ap-6304	138	20	,	,	PUNCT
ap-6304	138	21	the	the	DET
ap-6304	138	22	central	central	ADJ
ap-6304	138	23	approximation	approximation	NOUN
ap-6304	138	24	of	of	ADP
ap-6304	138	25	the	the	DET
ap-6304	138	26	second	second	ADJ
ap-6304	138	27	derivative	derivative	ADJ
ap-6304	138	28	uxx	uxx	NOUN
ap-6304	138	29	can	can	AUX
ap-6304	138	30	be	be	AUX
ap-6304	138	31	constructed	construct	VERB
ap-6304	138	32	.	.	PUNCT
ap-6304	139	1	this	this	PRON
ap-6304	139	2	is	be	AUX
ap-6304	139	3	often	often	ADV
ap-6304	139	4	used	use	VERB
ap-6304	139	5	in	in	ADP
ap-6304	139	6	approximation	approximation	NOUN
ap-6304	139	7	of	of	ADP
ap-6304	139	8	diffusive	diffusive	ADJ
ap-6304	139	9	(	(	PUNCT
ap-6304	139	10	or	or	CCONJ
ap-6304	139	11	viscous	viscous	ADJ
ap-6304	139	12	terms	term	NOUN
ap-6304	139	13	)	)	PUNCT
ap-6304	139	14	containing	contain	VERB
ap-6304	139	15	second	second	ADJ
ap-6304	139	16	derivatives	derivative	NOUN
ap-6304	139	17	.	.	PUNCT
ap-6304	140	1	this	this	DET
ap-6304	140	2	viscous	viscous	ADJ
ap-6304	140	3	-	-	PUNCT
ap-6304	140	4	like	like	ADJ
ap-6304	140	5	term	term	NOUN
ap-6304	140	6	{	{	PUNCT
ap-6304	140	7	v	v	NOUN
ap-6304	140	8	}	}	PUNCT
ap-6304	140	9	can	can	AUX
ap-6304	140	10	be	be	AUX
ap-6304	140	11	formally	formally	ADV
ap-6304	140	12	written	write	VERB
ap-6304	140	13	as	as	ADP
ap-6304	140	14	{	{	PUNCT
ap-6304	140	15	v	v	NOUN
ap-6304	140	16	}	}	PUNCT
ap-6304	140	17	=	=	PUNCT
ap-6304	140	18	{	{	PUNCT
ap-6304	140	19	d	d	NOUN
ap-6304	140	20	}	}	PUNCT
ap-6304	140	21	−	−	PROPN
ap-6304	140	22	{	{	PUNCT
ap-6304	140	23	u}∆x	u}∆x	X
ap-6304	141	1	=	=	AUX
ap-6304	141	2	⇒	⇒	NOUN
ap-6304	141	3	{	{	PUNCT
ap-6304	141	4	u	u	NOUN
ap-6304	141	5	}	}	PUNCT
ap-6304	141	6	=	=	SYM
ap-6304	141	7	{	{	PUNCT
ap-6304	141	8	c	c	NOUN
ap-6304	141	9	}	}	PUNCT
ap-6304	141	10	−	−	PROPN
ap-6304	141	11	∆x	∆x	PROPN
ap-6304	141	12	2	2	NUM
ap-6304	141	13	{	{	PUNCT
ap-6304	141	14	v	v	NOUN
ap-6304	141	15	}	}	PUNCT
ap-6304	141	16	.	.	PUNCT
ap-6304	142	1	using	use	VERB
ap-6304	142	2	this	this	DET
ap-6304	142	3	definition	definition	NOUN
ap-6304	142	4	of	of	ADP
ap-6304	142	5	{	{	PUNCT
ap-6304	142	6	v	v	NOUN
ap-6304	142	7	}	}	PUNCT
ap-6304	142	8	,	,	PUNCT
ap-6304	142	9	the	the	DET
ap-6304	142	10	whole	whole	ADJ
ap-6304	142	11	family	family	NOUN
ap-6304	142	12	of	of	ADP
ap-6304	142	13	schemes	scheme	NOUN
ap-6304	142	14	can	can	AUX
ap-6304	142	15	be	be	AUX
ap-6304	142	16	written	write	VERB
ap-6304	142	17	as	as	ADP
ap-6304	142	18	a	a	DET
ap-6304	142	19	combination	combination	NOUN
ap-6304	142	20	of	of	ADP
ap-6304	142	21	the	the	DET
ap-6304	142	22	central	central	ADJ
ap-6304	142	23	approximation	approximation	NOUN
ap-6304	142	24	part	part	NOUN
ap-6304	142	25	and	and	CCONJ
ap-6304	142	26	a	a	DET
ap-6304	142	27	viscous	viscous	ADJ
ap-6304	142	28	(	(	PUNCT
ap-6304	142	29	diffusive	diffusive	ADJ
ap-6304	142	30	)	)	PUNCT
ap-6304	142	31	part	part	NOUN
ap-6304	142	32	.	.	PUNCT
ap-6304	143	1	un+1	un+1	ADV
ap-6304	144	1	i	i	PRON
ap-6304	144	2	−	−	VERB
ap-6304	144	3	uni	uni	PROPN
ap-6304	144	4	∆t	∆t	PROPN
ap-6304	145	1	+	+	CCONJ
ap-6304	145	2	a	a	DET
ap-6304	145	3	[	[	PUNCT
ap-6304	145	4	{	{	PUNCT
ap-6304	145	5	c	c	NOUN
ap-6304	145	6	}	}	PUNCT
ap-6304	145	7	−	−	PROPN
ap-6304	145	8	(	(	PUNCT
ap-6304	145	9	1−	1−	NUM
ap-6304	145	10	2α)a∆x	2α)a∆x	NUM
ap-6304	145	11	2	2	NUM
ap-6304	145	12	{	{	PUNCT
ap-6304	145	13	v	v	NOUN
ap-6304	145	14	}	}	PUNCT
ap-6304	145	15	]	]	PUNCT
ap-6304	145	16	=	=	SYM
ap-6304	145	17	0	0	NUM
ap-6304	145	18	3.3.1	3.3.1	NUM
ap-6304	145	19	.	.	PUNCT
ap-6304	145	20	numerical	numerical	ADJ
ap-6304	145	21	viscosity	viscosity	NOUN
ap-6304	145	22	by	by	ADP
ap-6304	145	23	a	a	DET
ap-6304	145	24	simple	simple	ADJ
ap-6304	145	25	rearrangement	rearrangement	NOUN
ap-6304	145	26	of	of	ADP
ap-6304	145	27	this	this	DET
ap-6304	145	28	formula	formula	NOUN
ap-6304	145	29	,	,	PUNCT
ap-6304	145	30	it	it	PRON
ap-6304	145	31	’s	’	VERB
ap-6304	145	32	easy	easy	ADJ
ap-6304	145	33	to	to	PART
ap-6304	145	34	see	see	VERB
ap-6304	145	35	that	that	SCONJ
ap-6304	145	36	all	all	DET
ap-6304	145	37	the	the	DET
ap-6304	145	38	schemes	scheme	NOUN
ap-6304	145	39	from	from	ADP
ap-6304	145	40	the	the	DET
ap-6304	145	41	considered	consider	VERB
ap-6304	145	42	explicit	explicit	ADJ
ap-6304	145	43	family	family	NOUN
ap-6304	145	44	can	can	AUX
ap-6304	145	45	be	be	AUX
ap-6304	145	46	written	write	VERB
ap-6304	145	47	in	in	ADP
ap-6304	145	48	the	the	DET
ap-6304	145	49	form	form	NOUN
ap-6304	145	50	,	,	PUNCT
ap-6304	145	51	where	where	SCONJ
ap-6304	145	52	only	only	ADV
ap-6304	145	53	the	the	DET
ap-6304	145	54	central	central	ADJ
ap-6304	145	55	approximation	approximation	NOUN
ap-6304	145	56	of	of	ADP
ap-6304	145	57	the	the	DET
ap-6304	145	58	first	first	ADJ
ap-6304	145	59	derivative	derivative	NOUN
ap-6304	145	60	is	be	AUX
ap-6304	145	61	kept	keep	VERB
ap-6304	145	62	on	on	ADP
ap-6304	145	63	left	left	ADJ
ap-6304	145	64	,	,	PUNCT
ap-6304	145	65	while	while	SCONJ
ap-6304	145	66	the	the	DET
ap-6304	145	67	remaining	remain	VERB
ap-6304	145	68	viscous	viscous	ADJ
ap-6304	145	69	-	-	PUNCT
ap-6304	145	70	like	like	ADJ
ap-6304	145	71	part	part	NOUN
ap-6304	145	72	is	be	AUX
ap-6304	145	73	moved	move	VERB
ap-6304	145	74	to	to	ADP
ap-6304	145	75	the	the	DET
ap-6304	145	76	right	right	ADJ
ap-6304	145	77	-	-	PUNCT
ap-6304	145	78	hand	hand	NOUN
ap-6304	145	79	side	side	NOUN
ap-6304	145	80	un+1	un+1	ADV
ap-6304	146	1	i	i	PRON
ap-6304	146	2	−	−	VERB
ap-6304	146	3	uni	uni	PROPN
ap-6304	146	4	∆t	∆t	PROPN
ap-6304	147	1	+	+	CCONJ
ap-6304	148	1	a{c	a{c	NOUN
ap-6304	148	2	}	}	PUNCT
ap-6304	148	3	=	=	PUNCT
ap-6304	148	4	(	(	PUNCT
ap-6304	148	5	1−	1−	NUM
ap-6304	148	6	2α)a∆x	2α)a∆x	NUM
ap-6304	148	7	2	2	NUM
ap-6304	148	8	{	{	PUNCT
ap-6304	148	9	v	v	NOUN
ap-6304	148	10	}	}	PUNCT
ap-6304	148	11	,	,	PUNCT
ap-6304	148	12	scheme	scheme	NOUN
ap-6304	148	13	coefficient	coefficient	NOUN
ap-6304	148	14	α	α	PROPN
ap-6304	148	15	ε	ε	PROPN
ap-6304	148	16	µ	µ	X
ap-6304	148	17	[	[	X
ap-6304	148	18	u	u	X
ap-6304	148	19	]	]	X
ap-6304	148	20	0	0	NUM
ap-6304	148	21	1	1	NUM
ap-6304	148	22	a∆x	a∆x	ADP
ap-6304	148	23	2	2	NUM
ap-6304	148	24	[	[	X
ap-6304	148	25	d	d	X
ap-6304	148	26	]	]	X
ap-6304	148	27	1	1	NUM
ap-6304	148	28	−1	−1	NOUN
ap-6304	148	29	−a∆x	−a∆x	PROPN
ap-6304	148	30	2	2	NUM
ap-6304	149	1	[	[	X
ap-6304	149	2	c	c	X
ap-6304	149	3	]	]	X
ap-6304	149	4	1	1	NUM
ap-6304	149	5	2	2	NUM
ap-6304	149	6	0	0	NUM
ap-6304	149	7	0	0	NUM
ap-6304	150	1	[	[	X
ap-6304	150	2	lf	lf	X
ap-6304	150	3	]	]	SYM
ap-6304	150	4	1	1	NUM
ap-6304	150	5	2	2	NUM
ap-6304	150	6	−	−	PROPN
ap-6304	150	7	∆x	∆x	PROPN
ap-6304	150	8	2a∆t	2a∆t	NUM
ap-6304	150	9	1	1	NUM
ap-6304	150	10	γ	γ	X
ap-6304	150	11	∆x2	∆x2	PRON
ap-6304	150	12	2∆t	2∆t	NUM
ap-6304	150	13	[	[	X
ap-6304	150	14	lw	lw	X
ap-6304	150	15	]	]	X
ap-6304	150	16	1	1	NUM
ap-6304	150	17	2	2	NUM
ap-6304	150	18	−	−	NOUN
ap-6304	150	19	a∆t	a∆t	ADJ
ap-6304	150	20	2∆x	2∆x	NUM
ap-6304	150	21	γ	γ	NOUN
ap-6304	150	22	a2∆t	a2∆t	NOUN
ap-6304	150	23	2	2	NUM
ap-6304	150	24	table	table	NOUN
ap-6304	150	25	3	3	NUM
ap-6304	150	26	.	.	PUNCT
ap-6304	150	27	numerical	numerical	ADJ
ap-6304	150	28	viscosity	viscosity	NOUN
ap-6304	150	29	coefficients	coefficient	VERB
ap-6304	150	30	for	for	ADP
ap-6304	150	31	some	some	DET
ap-6304	150	32	classical	classical	ADJ
ap-6304	150	33	schemes	scheme	NOUN
ap-6304	150	34	.	.	PUNCT
ap-6304	151	1	or	or	CCONJ
ap-6304	151	2	shortly	shortly	ADV
ap-6304	151	3	un+1	un+1	ADV
ap-6304	152	1	i	i	PRON
ap-6304	152	2	−	−	VERB
ap-6304	152	3	uni	uni	PROPN
ap-6304	152	4	∆t	∆t	PROPN
ap-6304	153	1	+	+	CCONJ
ap-6304	154	1	a{c	a{c	NOUN
ap-6304	154	2	}	}	PUNCT
ap-6304	154	3	=	=	SYM
ap-6304	154	4	µ{v	µ{v	PROPN
ap-6304	154	5	}	}	PUNCT
ap-6304	154	6	.	.	PUNCT
ap-6304	155	1	it	it	PRON
ap-6304	155	2	’s	’	VERB
ap-6304	155	3	not	not	PART
ap-6304	155	4	difficult	difficult	ADJ
ap-6304	155	5	to	to	PART
ap-6304	155	6	see	see	VERB
ap-6304	155	7	that	that	SCONJ
ap-6304	155	8	this	this	DET
ap-6304	155	9	discrete	discrete	ADJ
ap-6304	155	10	equation	equation	NOUN
ap-6304	155	11	corresponds	correspond	VERB
ap-6304	155	12	to	to	ADP
ap-6304	155	13	a	a	DET
ap-6304	155	14	finite	finite	ADJ
ap-6304	155	15	-	-	PUNCT
ap-6304	155	16	difference	difference	NOUN
ap-6304	155	17	approximation	approximation	NOUN
ap-6304	155	18	of	of	ADP
ap-6304	155	19	the	the	DET
ap-6304	155	20	advection	advection	NOUN
ap-6304	155	21	-	-	PUNCT
ap-6304	155	22	diffusion	diffusion	NOUN
ap-6304	155	23	equation	equation	NOUN
ap-6304	155	24	rather	rather	ADV
ap-6304	155	25	than	than	ADP
ap-6304	155	26	just	just	ADV
ap-6304	155	27	to	to	ADP
ap-6304	155	28	the	the	DET
ap-6304	155	29	original	original	ADJ
ap-6304	155	30	advection	advection	NOUN
ap-6304	155	31	equation	equation	NOUN
ap-6304	155	32	.	.	PUNCT
ap-6304	156	1	ut	ut	PROPN
ap-6304	157	1	+	+	CCONJ
ap-6304	157	2	aux	aux	X
ap-6304	157	3	=	=	SYM
ap-6304	157	4	0	0	PUNCT
ap-6304	157	5	−→	−→	NOUN
ap-6304	157	6	ut	ut	PROPN
ap-6304	157	7	+	+	CCONJ
ap-6304	157	8	aux	aux	X
ap-6304	157	9	=	=	NOUN
ap-6304	157	10	µuxx	µuxx	PROPN
ap-6304	157	11	the	the	DET
ap-6304	157	12	extra	extra	ADJ
ap-6304	157	13	term	term	NOUN
ap-6304	157	14	on	on	ADP
ap-6304	157	15	the	the	DET
ap-6304	157	16	right	right	ADJ
ap-6304	157	17	hand	hand	NOUN
ap-6304	157	18	side	side	NOUN
ap-6304	157	19	corresponds	correspond	VERB
ap-6304	157	20	to	to	ADP
ap-6304	157	21	the	the	DET
ap-6304	157	22	numerical	numerical	ADJ
ap-6304	157	23	diffusion	diffusion	NOUN
ap-6304	157	24	(	(	PUNCT
ap-6304	157	25	viscosity	viscosity	NOUN
ap-6304	157	26	)	)	PUNCT
ap-6304	157	27	,	,	PUNCT
ap-6304	157	28	where	where	SCONJ
ap-6304	157	29	the	the	DET
ap-6304	157	30	coefficient	coefficient	NOUN
ap-6304	157	31	µ	µ	NOUN
ap-6304	157	32	depends	depend	VERB
ap-6304	157	33	on	on	ADP
ap-6304	157	34	the	the	DET
ap-6304	157	35	method	method	NOUN
ap-6304	157	36	being	be	AUX
ap-6304	157	37	used	use	VERB
ap-6304	157	38	.	.	PUNCT
ap-6304	158	1	µ	µ	X
ap-6304	158	2	=	=	SYM
ap-6304	158	3	(	(	PUNCT
ap-6304	158	4	1−	1−	NUM
ap-6304	158	5	2α)︸	2α)︸	NUM
ap-6304	158	6	︷︷	︷︷	PROPN
ap-6304	158	7	︸	︸	X
ap-6304	158	8	ε	ε	PROPN
ap-6304	158	9	a∆x	a∆x	VERB
ap-6304	158	10	2	2	NUM
ap-6304	158	11	values	value	NOUN
ap-6304	158	12	of	of	ADP
ap-6304	158	13	this	this	DET
ap-6304	158	14	numerical	numerical	ADJ
ap-6304	158	15	viscosity	viscosity	NOUN
ap-6304	158	16	coefficient	coefficient	NOUN
ap-6304	158	17	for	for	ADP
ap-6304	158	18	few	few	ADJ
ap-6304	158	19	classical	classical	ADJ
ap-6304	158	20	explicit	explicit	ADJ
ap-6304	158	21	methods	method	NOUN
ap-6304	158	22	are	be	AUX
ap-6304	158	23	listed	list	VERB
ap-6304	158	24	in	in	ADP
ap-6304	158	25	the	the	DET
ap-6304	158	26	table	table	NOUN
ap-6304	159	1	3	3	X
ap-6304	159	2	.	.	PUNCT
ap-6304	160	1	in	in	ADP
ap-6304	160	2	this	this	DET
ap-6304	160	3	context	context	NOUN
ap-6304	160	4	,	,	PUNCT
ap-6304	160	5	each	each	DET
ap-6304	160	6	scheme	scheme	NOUN
ap-6304	160	7	within	within	ADP
ap-6304	160	8	this	this	DET
ap-6304	160	9	explicit	explicit	ADJ
ap-6304	160	10	family	family	NOUN
ap-6304	160	11	can	can	AUX
ap-6304	160	12	be	be	AUX
ap-6304	160	13	considered	consider	VERB
ap-6304	160	14	as	as	ADP
ap-6304	160	15	a	a	DET
ap-6304	160	16	simple	simple	ADJ
ap-6304	160	17	central	central	ADJ
ap-6304	160	18	scheme	scheme	NOUN
ap-6304	160	19	with	with	ADP
ap-6304	160	20	different	different	ADJ
ap-6304	160	21	amounts	amount	NOUN
ap-6304	160	22	of	of	ADP
ap-6304	160	23	added	add	VERB
ap-6304	160	24	numerical	numerical	ADJ
ap-6304	160	25	viscosity	viscosity	NOUN
ap-6304	160	26	(	(	PUNCT
ap-6304	160	27	or	or	CCONJ
ap-6304	160	28	upwinding	upwinde	VERB
ap-6304	160	29	,	,	PUNCT
ap-6304	160	30	alternatively	alternatively	ADV
ap-6304	160	31	)	)	PUNCT
ap-6304	160	32	.	.	PUNCT
ap-6304	161	1	when	when	SCONJ
ap-6304	161	2	taking	take	VERB
ap-6304	161	3	into	into	ADP
ap-6304	161	4	account	account	NOUN
ap-6304	161	5	the	the	DET
ap-6304	161	6	definition	definition	NOUN
ap-6304	161	7	of	of	ADP
ap-6304	161	8	the	the	DET
ap-6304	161	9	non	non	ADJ
ap-6304	161	10	-	-	ADJ
ap-6304	161	11	dimensional	dimensional	ADJ
ap-6304	161	12	courant	courant	ADJ
ap-6304	161	13	-	-	PUNCT
ap-6304	161	14	friedrichslewy	friedrichslewy	ADJ
ap-6304	161	15	parameter	parameter	NOUN
ap-6304	161	16	γ	γ	X
ap-6304	161	17	=	=	PROPN
ap-6304	161	18	a∆t	a∆t	PROPN
ap-6304	161	19	∆x	∆x	PROPN
ap-6304	161	20	,	,	PUNCT
ap-6304	161	21	which	which	PRON
ap-6304	161	22	is	be	AUX
ap-6304	161	23	positive	positive	ADJ
ap-6304	161	24	(	(	PUNCT
ap-6304	161	25	and	and	CCONJ
ap-6304	161	26	bounded	bound	VERB
ap-6304	161	27	by	by	ADP
ap-6304	161	28	stability	stability	NOUN
ap-6304	161	29	conditions	condition	NOUN
ap-6304	161	30	)	)	PUNCT
ap-6304	161	31	,	,	PUNCT
ap-6304	161	32	the	the	DET
ap-6304	161	33	non	non	ADJ
ap-6304	161	34	-	-	ADJ
ap-6304	161	35	dimensional	dimensional	ADJ
ap-6304	161	36	viscosity	viscosity	NOUN
ap-6304	161	37	coefficient	coefficient	NOUN
ap-6304	161	38	ε	ε	PROPN
ap-6304	161	39	can	can	AUX
ap-6304	161	40	be	be	AUX
ap-6304	161	41	defined	define	VERB
ap-6304	161	42	.	.	PUNCT
ap-6304	162	1	the	the	DET
ap-6304	162	2	value	value	NOUN
ap-6304	162	3	of	of	ADP
ap-6304	162	4	the	the	DET
ap-6304	162	5	numerical	numerical	ADJ
ap-6304	162	6	viscosity	viscosity	NOUN
ap-6304	162	7	coefficient	coefficient	NOUN
ap-6304	162	8	determines	determine	VERB
ap-6304	162	9	the	the	DET
ap-6304	162	10	essential	essential	ADJ
ap-6304	162	11	behavior	behavior	NOUN
ap-6304	162	12	and	and	CCONJ
ap-6304	162	13	properties	property	NOUN
ap-6304	162	14	of	of	ADP
ap-6304	162	15	the	the	DET
ap-6304	162	16	specific	specific	ADJ
ap-6304	162	17	numerical	numerical	ADJ
ap-6304	162	18	method	method	NOUN
ap-6304	162	19	.	.	PUNCT
ap-6304	163	1	just	just	ADV
ap-6304	163	2	by	by	ADP
ap-6304	163	3	changing	change	VERB
ap-6304	163	4	the	the	DET
ap-6304	163	5	parameter	parameter	NOUN
ap-6304	163	6	µ	µ	NOUN
ap-6304	163	7	,	,	PUNCT
ap-6304	163	8	the	the	DET
ap-6304	163	9	schemes	scheme	NOUN
ap-6304	163	10	can	can	AUX
ap-6304	163	11	become	become	VERB
ap-6304	163	12	more	more	ADV
ap-6304	163	13	diffusive	diffusive	ADJ
ap-6304	163	14	or	or	CCONJ
ap-6304	163	15	dispersive	dispersive	ADJ
ap-6304	163	16	,	,	PUNCT
ap-6304	163	17	stable	stable	ADJ
ap-6304	163	18	or	or	CCONJ
ap-6304	163	19	unstable	unstable	ADJ
ap-6304	163	20	and	and	CCONJ
ap-6304	163	21	also	also	ADV
ap-6304	163	22	their	their	PRON
ap-6304	163	23	order	order	NOUN
ap-6304	163	24	of	of	ADP
ap-6304	163	25	accuracy	accuracy	NOUN
ap-6304	163	26	will	will	AUX
ap-6304	163	27	change	change	VERB
ap-6304	163	28	.	.	PUNCT
ap-6304	164	1	these	these	DET
ap-6304	164	2	properties	property	NOUN
ap-6304	164	3	for	for	ADP
ap-6304	164	4	some	some	DET
ap-6304	164	5	schemes	scheme	NOUN
ap-6304	164	6	are	be	AUX
ap-6304	164	7	summarized	summarize	VERB
ap-6304	164	8	in	in	ADP
ap-6304	164	9	the	the	DET
ap-6304	164	10	table	table	NOUN
ap-6304	164	11	4	4	NUM
ap-6304	164	12	.	.	NOUN
ap-6304	164	13	52	52	NUM
ap-6304	164	14	vol	vol	NOUN
ap-6304	164	15	.	.	PUNCT
ap-6304	165	1	61	61	NUM
ap-6304	165	2	special	special	ADJ
ap-6304	165	3	issue/2021	issue/2021	NOUN
ap-6304	165	4	modified	modify	VERB
ap-6304	165	5	equation	equation	NOUN
ap-6304	165	6	for	for	ADP
ap-6304	165	7	explicit	explicit	ADJ
ap-6304	165	8	and	and	CCONJ
ap-6304	165	9	implicit	implicit	ADJ
ap-6304	165	10	schemes	scheme	NOUN
ap-6304	165	11	scheme	scheme	NOUN
ap-6304	165	12	ε	ε	PROPN
ap-6304	165	13	µ	µ	PRON
ap-6304	165	14	accuracy	accuracy	NOUN
ap-6304	165	15	stability	stability	NOUN
ap-6304	165	16	behavior	behavior	NOUN
ap-6304	165	17	[	[	X
ap-6304	165	18	d	d	X
ap-6304	165	19	]	]	X
ap-6304	165	20	−1	−1	NOUN
ap-6304	165	21	−a∆x	−a∆x	PROPN
ap-6304	165	22	2	2	NUM
ap-6304	165	23	<	<	X
ap-6304	165	24	0	0	NUM
ap-6304	165	25	(	(	PUNCT
ap-6304	165	26	∆t)1/(∆x)1	∆t)1/(∆x)1	X
ap-6304	165	27	unstable	unstable	ADJ
ap-6304	165	28	dispersive	dispersive	NOUN
ap-6304	166	1	[	[	X
ap-6304	166	2	c	c	X
ap-6304	166	3	]	]	X
ap-6304	166	4	0	0	NUM
ap-6304	166	5	0	0	NUM
ap-6304	166	6	(	(	PUNCT
ap-6304	166	7	∆t)1/(∆x)2	∆t)1/(∆x)2	VERB
ap-6304	166	8	unstable	unstable	ADJ
ap-6304	166	9	dispersive	dispersive	NOUN
ap-6304	166	10	[	[	X
ap-6304	166	11	lw	lw	X
ap-6304	166	12	]	]	X
ap-6304	166	13	γ	γ	X
ap-6304	166	14	<	<	X
ap-6304	166	15	1	1	NUM
ap-6304	166	16	a2∆t	a2∆t	NOUN
ap-6304	166	17	2	2	NUM
ap-6304	166	18	(	(	PUNCT
ap-6304	166	19	∆t)2/(∆x)2	∆t)2/(∆x)2	NOUN
ap-6304	166	20	stable	stable	ADJ
ap-6304	166	21	dispersive	dispersive	ADJ
ap-6304	166	22	[	[	X
ap-6304	166	23	u	u	X
ap-6304	166	24	]	]	X
ap-6304	166	25	1	1	NUM
ap-6304	166	26	a∆x	a∆x	X
ap-6304	166	27	2	2	NUM
ap-6304	166	28	(	(	PUNCT
ap-6304	166	29	∆t)1/(∆x)1	∆t)1/(∆x)1	X
ap-6304	166	30	stable	stable	ADJ
ap-6304	166	31	diffusive	diffusive	NOUN
ap-6304	167	1	[	[	X
ap-6304	167	2	lf	lf	X
ap-6304	167	3	]	]	X
ap-6304	167	4	1	1	NUM
ap-6304	167	5	γ	γ	X
ap-6304	167	6	>	>	X
ap-6304	167	7	1	1	NUM
ap-6304	167	8	∆x2	∆x2	NOUN
ap-6304	167	9	2∆t	2∆t	NUM
ap-6304	167	10	(	(	PUNCT
ap-6304	167	11	∆t)1/(∆x)1	∆t)1/(∆x)1	X
ap-6304	167	12	stable	stable	ADJ
ap-6304	167	13	diffusive	diffusive	ADJ
ap-6304	167	14	table	table	NOUN
ap-6304	167	15	4	4	NUM
ap-6304	167	16	.	.	PUNCT
ap-6304	167	17	properties	property	NOUN
ap-6304	167	18	and	and	CCONJ
ap-6304	167	19	behavior	behavior	NOUN
ap-6304	167	20	of	of	ADP
ap-6304	167	21	selected	select	VERB
ap-6304	167	22	explicit	explicit	ADJ
ap-6304	167	23	numerical	numerical	ADJ
ap-6304	167	24	schemes	scheme	NOUN
ap-6304	167	25	.	.	PUNCT
ap-6304	168	1	the	the	DET
ap-6304	168	2	schemes	scheme	NOUN
ap-6304	168	3	in	in	ADP
ap-6304	168	4	the	the	DET
ap-6304	168	5	table	table	NOUN
ap-6304	168	6	4	4	NUM
ap-6304	168	7	are	be	AUX
ap-6304	168	8	sorted	sort	VERB
ap-6304	168	9	from	from	ADP
ap-6304	168	10	top	top	NOUN
ap-6304	168	11	to	to	ADP
ap-6304	168	12	bottom	bottom	NOUN
ap-6304	168	13	according	accord	VERB
ap-6304	168	14	to	to	ADP
ap-6304	168	15	increasing	increase	VERB
ap-6304	168	16	numerical	numerical	ADJ
ap-6304	168	17	viscosity	viscosity	NOUN
ap-6304	168	18	.	.	PUNCT
ap-6304	169	1	it	it	PRON
ap-6304	169	2	can	can	AUX
ap-6304	169	3	be	be	AUX
ap-6304	169	4	seen	see	VERB
ap-6304	169	5	(	(	PUNCT
ap-6304	169	6	as	as	SCONJ
ap-6304	169	7	expected	expect	VERB
ap-6304	169	8	)	)	PUNCT
ap-6304	169	9	that	that	SCONJ
ap-6304	169	10	when	when	SCONJ
ap-6304	169	11	the	the	DET
ap-6304	169	12	numerical	numerical	ADJ
ap-6304	169	13	viscosity	viscosity	NOUN
ap-6304	169	14	coefficient	coefficient	NOUN
ap-6304	169	15	is	be	AUX
ap-6304	169	16	negative	negative	ADJ
ap-6304	169	17	,	,	PUNCT
ap-6304	169	18	the	the	DET
ap-6304	169	19	scheme	scheme	NOUN
ap-6304	169	20	is	be	AUX
ap-6304	169	21	unstable	unstable	ADJ
ap-6304	169	22	.	.	PUNCT
ap-6304	170	1	by	by	ADP
ap-6304	170	2	increasing	increase	VERB
ap-6304	170	3	its	its	PRON
ap-6304	170	4	value	value	NOUN
ap-6304	170	5	,	,	PUNCT
ap-6304	170	6	the	the	DET
ap-6304	170	7	scheme	scheme	NOUN
ap-6304	170	8	becomes	become	VERB
ap-6304	170	9	stable	stable	ADJ
ap-6304	170	10	and	and	CCONJ
ap-6304	170	11	also	also	ADV
ap-6304	170	12	can	can	AUX
ap-6304	170	13	improve	improve	VERB
ap-6304	170	14	its	its	PRON
ap-6304	170	15	accuracy	accuracy	NOUN
ap-6304	170	16	.	.	PUNCT
ap-6304	171	1	however	however	ADV
ap-6304	171	2	by	by	ADP
ap-6304	171	3	further	further	ADJ
ap-6304	171	4	increase	increase	NOUN
ap-6304	171	5	of	of	ADP
ap-6304	171	6	the	the	DET
ap-6304	171	7	numerical	numerical	ADJ
ap-6304	171	8	viscosity	viscosity	NOUN
ap-6304	171	9	,	,	PUNCT
ap-6304	171	10	the	the	DET
ap-6304	171	11	behavior	behavior	NOUN
ap-6304	171	12	of	of	ADP
ap-6304	171	13	the	the	DET
ap-6304	171	14	method	method	NOUN
ap-6304	171	15	becomes	become	VERB
ap-6304	171	16	more	more	ADV
ap-6304	171	17	diffusive	diffusive	ADJ
ap-6304	171	18	and	and	CCONJ
ap-6304	171	19	the	the	DET
ap-6304	171	20	formal	formal	ADJ
ap-6304	171	21	order	order	NOUN
ap-6304	171	22	of	of	ADP
ap-6304	171	23	accuracy	accuracy	NOUN
ap-6304	171	24	drops	drop	VERB
ap-6304	171	25	down	down	ADP
ap-6304	171	26	again	again	ADV
ap-6304	171	27	.	.	PUNCT
ap-6304	172	1	in	in	ADP
ap-6304	172	2	summary	summary	NOUN
ap-6304	172	3	,	,	PUNCT
ap-6304	172	4	the	the	DET
ap-6304	172	5	identification	identification	NOUN
ap-6304	172	6	of	of	ADP
ap-6304	172	7	the	the	DET
ap-6304	172	8	amount	amount	NOUN
ap-6304	172	9	of	of	ADP
ap-6304	172	10	numerical	numerical	ADJ
ap-6304	172	11	viscosity	viscosity	NOUN
ap-6304	172	12	embedded	embed	VERB
ap-6304	172	13	in	in	ADP
ap-6304	172	14	a	a	DET
ap-6304	172	15	numerical	numerical	ADJ
ap-6304	172	16	scheme	scheme	NOUN
ap-6304	172	17	is	be	AUX
ap-6304	172	18	the	the	DET
ap-6304	172	19	key	key	ADJ
ap-6304	172	20	point	point	NOUN
ap-6304	172	21	in	in	ADP
ap-6304	172	22	understanding	understand	VERB
ap-6304	172	23	its	its	PRON
ap-6304	172	24	behavior	behavior	NOUN
ap-6304	172	25	.	.	PUNCT
ap-6304	173	1	here	here	ADV
ap-6304	173	2	it	it	PRON
ap-6304	173	3	was	be	AUX
ap-6304	173	4	done	do	VERB
ap-6304	173	5	at	at	ADP
ap-6304	173	6	the	the	DET
ap-6304	173	7	discrete	discrete	ADJ
ap-6304	173	8	level	level	NOUN
ap-6304	173	9	,	,	PUNCT
ap-6304	173	10	by	by	ADP
ap-6304	173	11	identifying	identify	VERB
ap-6304	173	12	the	the	DET
ap-6304	173	13	discrete	discrete	ADJ
ap-6304	173	14	diffusive	diffusive	ADJ
ap-6304	173	15	term	term	NOUN
ap-6304	173	16	in	in	ADP
ap-6304	173	17	the	the	DET
ap-6304	173	18	scheme	scheme	NOUN
ap-6304	173	19	.	.	PUNCT
ap-6304	174	1	similarly	similarly	ADV
ap-6304	174	2	even	even	ADV
ap-6304	174	3	more	more	ADV
ap-6304	174	4	detailed	detailed	ADJ
ap-6304	174	5	analysis	analysis	NOUN
ap-6304	174	6	can	can	AUX
ap-6304	174	7	be	be	AUX
ap-6304	174	8	performed	perform	VERB
ap-6304	174	9	at	at	ADP
ap-6304	174	10	the	the	DET
ap-6304	174	11	continuous	continuous	ADJ
ap-6304	174	12	level	level	NOUN
ap-6304	174	13	,	,	PUNCT
ap-6304	174	14	leading	lead	VERB
ap-6304	174	15	to	to	ADP
ap-6304	174	16	so	so	ADV
ap-6304	174	17	called	call	VERB
ap-6304	174	18	modified	modified	ADJ
ap-6304	174	19	equation	equation	NOUN
ap-6304	174	20	.	.	PUNCT
ap-6304	175	1	4	4	X
ap-6304	175	2	.	.	NUM
ap-6304	175	3	modified	modify	VERB
ap-6304	175	4	equation	equation	NOUN
ap-6304	175	5	the	the	DET
ap-6304	175	6	modified	modify	VERB
ap-6304	175	7	equation	equation	NOUN
ap-6304	175	8	approach	approach	NOUN
ap-6304	175	9	is	be	AUX
ap-6304	175	10	well	well	ADV
ap-6304	175	11	known	know	VERB
ap-6304	175	12	,	,	PUNCT
ap-6304	175	13	often	often	ADV
ap-6304	175	14	used	use	VERB
ap-6304	175	15	to	to	PART
ap-6304	175	16	assess	assess	VERB
ap-6304	175	17	the	the	DET
ap-6304	175	18	order	order	NOUN
ap-6304	175	19	of	of	ADP
ap-6304	175	20	accuracy	accuracy	NOUN
ap-6304	175	21	for	for	ADP
ap-6304	175	22	finite	finite	ADJ
ap-6304	175	23	-	-	PUNCT
ap-6304	175	24	difference	difference	NOUN
ap-6304	175	25	schemes	scheme	NOUN
ap-6304	175	26	.	.	PUNCT
ap-6304	176	1	when	when	SCONJ
ap-6304	176	2	doing	do	VERB
ap-6304	176	3	the	the	DET
ap-6304	176	4	taylor	taylor	PROPN
ap-6304	176	5	expansions	expansion	NOUN
ap-6304	176	6	to	to	PART
ap-6304	176	7	develop	develop	VERB
ap-6304	176	8	the	the	DET
ap-6304	176	9	finite	finite	ADJ
ap-6304	176	10	-	-	PUNCT
ap-6304	176	11	difference	difference	NOUN
ap-6304	176	12	approximations	approximation	NOUN
ap-6304	176	13	,	,	PUNCT
ap-6304	176	14	it	it	PRON
ap-6304	176	15	is	be	AUX
ap-6304	176	16	possible	possible	ADJ
ap-6304	176	17	to	to	PART
ap-6304	176	18	go	go	VERB
ap-6304	176	19	beyond	beyond	ADP
ap-6304	176	20	just	just	ADV
ap-6304	176	21	finding	find	VERB
ap-6304	176	22	the	the	DET
ap-6304	176	23	order	order	NOUN
ap-6304	176	24	of	of	ADP
ap-6304	176	25	the	the	DET
ap-6304	176	26	leading	lead	VERB
ap-6304	176	27	term	term	NOUN
ap-6304	176	28	in	in	ADP
ap-6304	176	29	the	the	DET
ap-6304	176	30	truncated	truncated	ADJ
ap-6304	176	31	taylor	taylor	PROPN
ap-6304	176	32	series	series	PROPN
ap-6304	176	33	.	.	PUNCT
ap-6304	177	1	it	it	PRON
ap-6304	177	2	’s	’	VERB
ap-6304	177	3	possible	possible	ADJ
ap-6304	177	4	to	to	PART
ap-6304	177	5	find	find	VERB
ap-6304	177	6	analytically	analytically	ADV
ap-6304	177	7	the	the	DET
ap-6304	177	8	form	form	NOUN
ap-6304	177	9	of	of	ADP
ap-6304	177	10	the	the	DET
ap-6304	177	11	leading	lead	VERB
ap-6304	177	12	term	term	NOUN
ap-6304	177	13	,	,	PUNCT
ap-6304	177	14	add	add	VERB
ap-6304	177	15	it	it	PRON
ap-6304	177	16	to	to	PART
ap-6304	177	17	(	(	PUNCT
ap-6304	177	18	keep	keep	VERB
ap-6304	177	19	it	it	PRON
ap-6304	177	20	in	in	ADP
ap-6304	177	21	)	)	PUNCT
ap-6304	177	22	the	the	DET
ap-6304	177	23	original	original	ADJ
ap-6304	177	24	equation	equation	NOUN
ap-6304	177	25	and	and	CCONJ
ap-6304	177	26	study	study	VERB
ap-6304	177	27	the	the	DET
ap-6304	177	28	behavior	behavior	NOUN
ap-6304	177	29	of	of	ADP
ap-6304	177	30	the	the	DET
ap-6304	177	31	modified	modify	VERB
ap-6304	177	32	equation	equation	NOUN
ap-6304	177	33	that	that	PRON
ap-6304	177	34	includes	include	VERB
ap-6304	177	35	this	this	DET
ap-6304	177	36	extra	extra	ADJ
ap-6304	177	37	term	term	NOUN
ap-6304	177	38	introduced	introduce	VERB
ap-6304	177	39	by	by	ADP
ap-6304	177	40	the	the	DET
ap-6304	177	41	discretization	discretization	NOUN
ap-6304	177	42	of	of	ADP
ap-6304	177	43	the	the	DET
ap-6304	177	44	problem	problem	NOUN
ap-6304	177	45	.	.	PUNCT
ap-6304	178	1	the	the	DET
ap-6304	178	2	properties	property	NOUN
ap-6304	178	3	of	of	ADP
ap-6304	178	4	the	the	DET
ap-6304	178	5	modified	modify	VERB
ap-6304	178	6	problem	problem	NOUN
ap-6304	178	7	solution	solution	NOUN
ap-6304	178	8	will	will	AUX
ap-6304	178	9	be	be	AUX
ap-6304	178	10	close	close	ADJ
ap-6304	178	11	to	to	ADP
ap-6304	178	12	the	the	DET
ap-6304	178	13	properties	property	NOUN
ap-6304	178	14	of	of	ADP
ap-6304	178	15	the	the	DET
ap-6304	178	16	numerical	numerical	ADJ
ap-6304	178	17	solution	solution	NOUN
ap-6304	178	18	of	of	ADP
ap-6304	178	19	the	the	DET
ap-6304	178	20	original	original	ADJ
ap-6304	178	21	problem	problem	NOUN
ap-6304	178	22	.	.	PUNCT
ap-6304	179	1	4.1	4.1	NUM
ap-6304	179	2	.	.	PUNCT
ap-6304	179	3	modified	modify	VERB
ap-6304	179	4	equation	equation	NOUN
ap-6304	179	5	for	for	ADP
ap-6304	179	6	upwind	upwind	NOUN
ap-6304	179	7	scheme	scheme	NOUN
ap-6304	179	8	when	when	SCONJ
ap-6304	179	9	solving	solve	VERB
ap-6304	179	10	the	the	DET
ap-6304	179	11	the	the	DET
ap-6304	179	12	advection	advection	NOUN
ap-6304	179	13	equation	equation	NOUN
ap-6304	179	14	ut	ut	PROPN
ap-6304	180	1	+	+	CCONJ
ap-6304	180	2	aux	aux	X
ap-6304	180	3	=	=	NOUN
ap-6304	180	4	0	0	PROPN
ap-6304	180	5	a	a	DET
ap-6304	180	6	>	>	X
ap-6304	180	7	0	0	PUNCT
ap-6304	181	1	the	the	DET
ap-6304	181	2	up	up	ADJ
ap-6304	181	3	-	-	PUNCT
ap-6304	181	4	wind	wind	NOUN
ap-6304	181	5	scheme	scheme	NOUN
ap-6304	181	6	can	can	AUX
ap-6304	181	7	be	be	AUX
ap-6304	181	8	written	write	VERB
ap-6304	181	9	as	as	ADP
ap-6304	181	10	un+1	un+1	NOUN
ap-6304	181	11	i	i	PRON
ap-6304	181	12	−	−	X
ap-6304	181	13	uni	uni	PROPN
ap-6304	181	14	∆t	∆t	PROPN
ap-6304	182	1	+	+	CCONJ
ap-6304	182	2	a	a	DET
ap-6304	182	3	[	[	PUNCT
ap-6304	182	4	uni	uni	NOUN
ap-6304	182	5	−	−	PROPN
ap-6304	182	6	uni−1	uni−1	PROPN
ap-6304	182	7	∆x	∆x	PROPN
ap-6304	182	8	]	]	PUNCT
ap-6304	182	9	=	=	PUNCT
ap-6304	182	10	0	0	NUM
ap-6304	182	11	,	,	PUNCT
ap-6304	182	12	using	use	VERB
ap-6304	182	13	the	the	DET
ap-6304	182	14	explicit	explicit	ADJ
ap-6304	182	15	euler	euler	NOUN
ap-6304	182	16	discretization	discretization	NOUN
ap-6304	182	17	in	in	ADP
ap-6304	182	18	time	time	NOUN
ap-6304	182	19	and	and	CCONJ
ap-6304	182	20	backward	backward	ADJ
ap-6304	182	21	difference	difference	NOUN
ap-6304	182	22	in	in	ADP
ap-6304	182	23	space	space	NOUN
ap-6304	182	24	(	(	PUNCT
ap-6304	182	25	i.e.	i.e.	X
ap-6304	182	26	upwind	upwind	NOUN
ap-6304	182	27	when	when	SCONJ
ap-6304	182	28	the	the	DET
ap-6304	182	29	advection	advection	NOUN
ap-6304	182	30	velocity	velocity	NOUN
ap-6304	182	31	a	a	PRON
ap-6304	182	32	>	>	X
ap-6304	182	33	0	0	NUM
ap-6304	182	34	)	)	PUNCT
ap-6304	182	35	.	.	PUNCT
ap-6304	183	1	considering	consider	VERB
ap-6304	183	2	a	a	DET
ap-6304	183	3	sufficiently	sufficiently	ADV
ap-6304	183	4	smooth	smooth	ADJ
ap-6304	183	5	interpolant	interpolant	NOUN
ap-6304	183	6	u(xi	u(xi	PROPN
ap-6304	183	7	,	,	PUNCT
ap-6304	183	8	tn	tn	PROPN
ap-6304	183	9	)	)	PUNCT
ap-6304	183	10	=	=	SYM
ap-6304	183	11	uni	uni	INTJ
ap-6304	183	12	,	,	PUNCT
ap-6304	183	13	the	the	DET
ap-6304	183	14	taylor	taylor	PROPN
ap-6304	183	15	expansions	expansion	NOUN
ap-6304	183	16	can	can	AUX
ap-6304	183	17	be	be	AUX
ap-6304	183	18	used	use	VERB
ap-6304	183	19	to	to	PART
ap-6304	183	20	derive	derive	VERB
ap-6304	183	21	the	the	DET
ap-6304	183	22	corresponding	correspond	VERB
ap-6304	183	23	approximation	approximation	NOUN
ap-6304	183	24	formulas	formula	NOUN
ap-6304	183	25	.	.	PUNCT
ap-6304	184	1	u(xi	u(xi	PROPN
ap-6304	184	2	,	,	PUNCT
ap-6304	184	3	tn+1)−u(xi	tn+1)−u(xi	PROPN
ap-6304	184	4	,	,	PUNCT
ap-6304	184	5	tn	tn	PROPN
ap-6304	184	6	)	)	PUNCT
ap-6304	184	7	∆t	∆t	PROPN
ap-6304	185	1	+	+	NOUN
ap-6304	185	2	a	a	DET
ap-6304	185	3	[	[	PUNCT
ap-6304	185	4	u(xi	u(xi	PROPN
ap-6304	185	5	,	,	PUNCT
ap-6304	185	6	tn)−u(xi−1	tn)−u(xi−1	PROPN
ap-6304	185	7	,	,	PUNCT
ap-6304	185	8	tn	tn	PROPN
ap-6304	185	9	)	)	PUNCT
ap-6304	185	10	∆x	∆x	PROPN
ap-6304	185	11	]	]	PUNCT
ap-6304	186	1	=	=	X
ap-6304	186	2	0	0	X
ap-6304	186	3	the	the	DET
ap-6304	186	4	terms	term	NOUN
ap-6304	186	5	u(xi	u(xi	PROPN
ap-6304	186	6	,	,	PUNCT
ap-6304	186	7	tn+1	tn+1	NOUN
ap-6304	186	8	)	)	PUNCT
ap-6304	186	9	and	and	CCONJ
ap-6304	186	10	u(xi	u(xi	PROPN
ap-6304	186	11	,	,	PUNCT
ap-6304	186	12	tn+1	tn+1	NOUN
ap-6304	186	13	)	)	PUNCT
ap-6304	186	14	appearing	appear	VERB
ap-6304	186	15	in	in	ADP
ap-6304	186	16	this	this	DET
ap-6304	186	17	formula	formula	NOUN
ap-6304	186	18	are	be	AUX
ap-6304	186	19	then	then	ADV
ap-6304	186	20	obtained	obtain	VERB
ap-6304	186	21	from	from	ADP
ap-6304	186	22	(	(	PUNCT
ap-6304	186	23	truncated	truncated	ADJ
ap-6304	186	24	)	)	PUNCT
ap-6304	186	25	the	the	DET
ap-6304	186	26	taylor	taylor	PROPN
ap-6304	186	27	series	series	PROPN
ap-6304	186	28	u(xi	u(xi	PROPN
ap-6304	186	29	,	,	PUNCT
ap-6304	186	30	tn+1	tn+1	NOUN
ap-6304	186	31	)	)	PUNCT
ap-6304	186	32	=	=	SYM
ap-6304	187	1	u(xi	u(xi	X
ap-6304	187	2	,	,	PUNCT
ap-6304	187	3	tn	tn	NOUN
ap-6304	187	4	)	)	PUNCT
ap-6304	188	1	+	+	X
ap-6304	188	2	∆tut(xi	∆tut(xi	ADJ
ap-6304	188	3	,	,	PUNCT
ap-6304	188	4	tn)+	tn)+	NOUN
ap-6304	188	5	+	+	CCONJ
ap-6304	188	6	∆t2	∆t2	PROPN
ap-6304	188	7	2	2	NUM
ap-6304	188	8	utt(xi	utt(xi	NOUN
ap-6304	188	9	,	,	PUNCT
ap-6304	188	10	tn	tn	PROPN
ap-6304	188	11	)	)	PUNCT
ap-6304	189	1	+	+	ADJ
ap-6304	189	2	∆t3	∆t3	X
ap-6304	189	3	6	6	NUM
ap-6304	189	4	uttt(xi	uttt(xi	PROPN
ap-6304	189	5	,	,	PUNCT
ap-6304	189	6	tn	tn	PROPN
ap-6304	189	7	)	)	PUNCT
ap-6304	189	8	+	+	NOUN
ap-6304	189	9	o(∆t4	o(∆t4	NOUN
ap-6304	189	10	)	)	PUNCT
ap-6304	189	11	u(xi−1	u(xi−1	PROPN
ap-6304	189	12	,	,	PUNCT
ap-6304	189	13	tn	tn	PROPN
ap-6304	189	14	)	)	PUNCT
ap-6304	189	15	=	=	SYM
ap-6304	190	1	u(xi	u(xi	X
ap-6304	190	2	,	,	PUNCT
ap-6304	190	3	tn)−∆xux(xi	tn)−∆xux(xi	PROPN
ap-6304	190	4	,	,	PUNCT
ap-6304	190	5	tn)+	tn)+	NOUN
ap-6304	190	6	+	+	CCONJ
ap-6304	190	7	∆x2	∆x2	NOUN
ap-6304	190	8	2	2	NUM
ap-6304	190	9	uxx(xi	uxx(xi	NOUN
ap-6304	190	10	,	,	PUNCT
ap-6304	190	11	tn)−	tn)−	X
ap-6304	190	12	∆x3	∆x3	X
ap-6304	190	13	6	6	NUM
ap-6304	190	14	uxxx(xi	uxxx(xi	PROPN
ap-6304	190	15	,	,	PUNCT
ap-6304	190	16	tn	tn	PROPN
ap-6304	190	17	)	)	PUNCT
ap-6304	190	18	+	+	NOUN
ap-6304	190	19	o(∆x4	o(∆x4	NUM
ap-6304	190	20	)	)	PUNCT
ap-6304	190	21	.	.	PUNCT
ap-6304	191	1	using	use	VERB
ap-6304	191	2	these	these	DET
ap-6304	191	3	values	value	NOUN
ap-6304	191	4	,	,	PUNCT
ap-6304	191	5	the	the	DET
ap-6304	191	6	corresponding	corresponding	ADJ
ap-6304	191	7	difference	difference	NOUN
ap-6304	191	8	approximations	approximation	NOUN
ap-6304	191	9	can	can	AUX
ap-6304	191	10	be	be	AUX
ap-6304	191	11	obtained	obtain	VERB
ap-6304	191	12	for	for	ADP
ap-6304	191	13	temporal	temporal	ADJ
ap-6304	191	14	and	and	CCONJ
ap-6304	191	15	spatial	spatial	ADJ
ap-6304	191	16	derivatives	derivative	NOUN
ap-6304	191	17	.	.	PUNCT
ap-6304	192	1	u(xi	u(xi	NOUN
ap-6304	192	2	,	,	PUNCT
ap-6304	192	3	tn+1)−	tn+1)−	PROPN
ap-6304	192	4	u(xi	u(xi	PROPN
ap-6304	192	5	,	,	PUNCT
ap-6304	192	6	tn	tn	NOUN
ap-6304	192	7	)	)	PUNCT
ap-6304	192	8	∆t	∆t	PROPN
ap-6304	192	9	=	=	SYM
ap-6304	192	10	ut(xi	ut(xi	PROPN
ap-6304	192	11	,	,	PUNCT
ap-6304	192	12	tn)+	tn)+	NOUN
ap-6304	192	13	+	+	CCONJ
ap-6304	192	14	∆t	∆t	PROPN
ap-6304	192	15	2	2	NUM
ap-6304	192	16	utt(xi	utt(xi	NOUN
ap-6304	192	17	,	,	PUNCT
ap-6304	192	18	tn	tn	PROPN
ap-6304	192	19	)	)	PUNCT
ap-6304	192	20	+	+	CCONJ
ap-6304	192	21	∆t2	∆t2	VERB
ap-6304	192	22	6	6	NUM
ap-6304	192	23	uttt(xi	uttt(xi	ADJ
ap-6304	192	24	,	,	PUNCT
ap-6304	192	25	tn	tn	PROPN
ap-6304	192	26	)	)	PUNCT
ap-6304	193	1	+	+	NOUN
ap-6304	193	2	o(∆t3	o(∆t3	NOUN
ap-6304	193	3	)	)	PUNCT
ap-6304	193	4	u(xi	u(xi	NOUN
ap-6304	193	5	,	,	PUNCT
ap-6304	193	6	tn)−	tn)−	NOUN
ap-6304	193	7	u(xi−1	u(xi−1	PROPN
ap-6304	193	8	,	,	PUNCT
ap-6304	193	9	tn	tn	PROPN
ap-6304	193	10	)	)	PUNCT
ap-6304	193	11	∆x	∆x	PROPN
ap-6304	193	12	=	=	SYM
ap-6304	193	13	ux(xi	ux(xi	PROPN
ap-6304	193	14	,	,	PUNCT
ap-6304	193	15	tn)−	tn)−	PUNCT
ap-6304	193	16	−	−	PROPN
ap-6304	193	17	∆x	∆x	PROPN
ap-6304	193	18	2	2	NUM
ap-6304	193	19	uxx(xi	uxx(xi	NOUN
ap-6304	193	20	,	,	PUNCT
ap-6304	193	21	tn	tn	PROPN
ap-6304	193	22	)	)	PUNCT
ap-6304	193	23	+	+	CCONJ
ap-6304	193	24	∆x2	∆x2	PRON
ap-6304	193	25	6	6	NUM
ap-6304	193	26	uxxx(xi	uxxx(xi	NOUN
ap-6304	193	27	,	,	PUNCT
ap-6304	193	28	tn	tn	PROPN
ap-6304	193	29	)	)	PUNCT
ap-6304	193	30	+	+	NOUN
ap-6304	193	31	o(∆x3	o(∆x3	NUM
ap-6304	193	32	)	)	PUNCT
ap-6304	193	33	when	when	SCONJ
ap-6304	193	34	these	these	DET
ap-6304	193	35	difference	difference	NOUN
ap-6304	193	36	approximations	approximation	NOUN
ap-6304	193	37	are	be	AUX
ap-6304	193	38	put	put	VERB
ap-6304	193	39	together	together	ADV
ap-6304	193	40	as	as	ADP
ap-6304	193	41	in	in	ADP
ap-6304	193	42	the	the	DET
ap-6304	193	43	numerical	numerical	ADJ
ap-6304	193	44	scheme	scheme	NOUN
ap-6304	193	45	,	,	PUNCT
ap-6304	193	46	the	the	DET
ap-6304	193	47	original	original	ADJ
ap-6304	193	48	advection	advection	NOUN
ap-6304	193	49	equation	equation	NOUN
ap-6304	193	50	appears	appear	VERB
ap-6304	193	51	on	on	ADP
ap-6304	193	52	the	the	DET
ap-6304	193	53	right	right	ADJ
ap-6304	193	54	hand	hand	NOUN
ap-6304	193	55	side	side	NOUN
ap-6304	193	56	,	,	PUNCT
ap-6304	193	57	together	together	ADV
ap-6304	193	58	with	with	ADP
ap-6304	193	59	some	some	DET
ap-6304	193	60	extra	extra	ADJ
ap-6304	193	61	terms	term	NOUN
ap-6304	193	62	,	,	PUNCT
ap-6304	193	63	representing	represent	VERB
ap-6304	193	64	the	the	DET
ap-6304	193	65	leading	lead	VERB
ap-6304	193	66	order	order	NOUN
ap-6304	193	67	terms	term	NOUN
ap-6304	193	68	in	in	ADP
ap-6304	193	69	the	the	DET
ap-6304	193	70	remainder	remainder	NOUN
ap-6304	193	71	of	of	ADP
ap-6304	193	72	the	the	DET
ap-6304	193	73	truncated	truncated	ADJ
ap-6304	193	74	taylor	taylor	PROPN
ap-6304	193	75	series	series	PROPN
ap-6304	193	76	.	.	PUNCT
ap-6304	194	1	u(xi	u(xi	PROPN
ap-6304	194	2	,	,	PUNCT
ap-6304	194	3	tn+1)−u(xi	tn+1)−u(xi	PROPN
ap-6304	194	4	,	,	PUNCT
ap-6304	194	5	tn	tn	PROPN
ap-6304	194	6	)	)	PUNCT
ap-6304	194	7	∆t	∆t	PROPN
ap-6304	195	1	+	+	NOUN
ap-6304	195	2	a	a	DET
ap-6304	195	3	[	[	PUNCT
ap-6304	195	4	u(xi	u(xi	PROPN
ap-6304	195	5	,	,	PUNCT
ap-6304	195	6	tn)−u(xi−1	tn)−u(xi−1	PROPN
ap-6304	195	7	,	,	PUNCT
ap-6304	195	8	tn	tn	PROPN
ap-6304	195	9	)	)	PUNCT
ap-6304	195	10	∆x	∆x	PROPN
ap-6304	195	11	]	]	PUNCT
ap-6304	196	1	=	=	PUNCT
ap-6304	196	2	=	=	SYM
ap-6304	196	3	ut(xi	ut(xi	PROPN
ap-6304	196	4	,	,	PUNCT
ap-6304	196	5	tn	tn	PROPN
ap-6304	196	6	)	)	PUNCT
ap-6304	196	7	+	+	CCONJ
ap-6304	196	8	aux(xi	aux(xi	ADJ
ap-6304	196	9	,	,	PUNCT
ap-6304	196	10	tn	tn	NOUN
ap-6304	196	11	)	)	PUNCT
ap-6304	196	12	+	+	CCONJ
ap-6304	196	13	.	.	PUNCT
ap-6304	196	14	.	.	PUNCT
ap-6304	196	15	.	.	PUNCT
ap-6304	196	16	.	.	PUNCT
ap-6304	196	17	.	.	PUNCT
ap-6304	196	18	.	.	PUNCT
ap-6304	196	19	.	.	PUNCT
ap-6304	196	20	.	.	PUNCT
ap-6304	196	21	.	.	PUNCT
ap-6304	197	1	=	=	PUNCT
ap-6304	197	2	0	0	NUM
ap-6304	198	1	it	it	PRON
ap-6304	198	2	means	mean	VERB
ap-6304	198	3	that	that	SCONJ
ap-6304	198	4	although	although	SCONJ
ap-6304	198	5	the	the	DET
ap-6304	198	6	difference	difference	NOUN
ap-6304	198	7	scheme	scheme	NOUN
ap-6304	198	8	approximates	approximate	VERB
ap-6304	198	9	the	the	DET
ap-6304	198	10	advection	advection	NOUN
ap-6304	198	11	equation	equation	NOUN
ap-6304	198	12	,	,	PUNCT
ap-6304	198	13	some	some	DET
ap-6304	198	14	extra	extra	ADJ
ap-6304	198	15	(	(	PUNCT
ap-6304	198	16	higher	high	ADJ
ap-6304	198	17	order	order	NOUN
ap-6304	198	18	)	)	PUNCT
ap-6304	198	19	terms	term	NOUN
ap-6304	198	20	appear	appear	VERB
ap-6304	198	21	on	on	ADP
ap-6304	198	22	the	the	DET
ap-6304	198	23	right	right	ADJ
ap-6304	198	24	hand	hand	NOUN
ap-6304	198	25	side	side	NOUN
ap-6304	198	26	due	due	ADP
ap-6304	198	27	to	to	ADP
ap-6304	198	28	discretization	discretization	NOUN
ap-6304	198	29	.	.	PUNCT
ap-6304	199	1	ut(xi	ut(xi	PROPN
ap-6304	199	2	,	,	PUNCT
ap-6304	199	3	tn	tn	PROPN
ap-6304	199	4	)	)	PUNCT
ap-6304	200	1	+	+	CCONJ
ap-6304	200	2	aux(xi	aux(xi	ADJ
ap-6304	200	3	,	,	PUNCT
ap-6304	200	4	tn	tn	NOUN
ap-6304	200	5	)	)	PUNCT
ap-6304	200	6	=	=	SYM
ap-6304	200	7	−	−	ADP
ap-6304	200	8	∆t	∆t	PROPN
ap-6304	200	9	2	2	NUM
ap-6304	200	10	utt(xi	utt(xi	NOUN
ap-6304	200	11	,	,	PUNCT
ap-6304	200	12	tn)−	tn)−	NOUN
ap-6304	200	13	∆t2	∆t2	VERB
ap-6304	200	14	6	6	NUM
ap-6304	200	15	uttt(xi	uttt(xi	ADJ
ap-6304	200	16	,	,	PUNCT
ap-6304	200	17	tn	tn	PROPN
ap-6304	200	18	)	)	PUNCT
ap-6304	200	19	+	+	VERB
ap-6304	200	20	o(∆t3)+	o(∆t3)+	NOUN
ap-6304	200	21	+	+	CCONJ
ap-6304	200	22	a∆x	a∆x	X
ap-6304	200	23	2	2	NUM
ap-6304	200	24	uxx(xi	uxx(xi	NOUN
ap-6304	200	25	,	,	PUNCT
ap-6304	200	26	tn)−	tn)−	PUNCT
ap-6304	200	27	a∆x2	a∆x2	ADP
ap-6304	200	28	6	6	NUM
ap-6304	200	29	uxxx(xi	uxxx(xi	NOUN
ap-6304	200	30	,	,	PUNCT
ap-6304	200	31	tn	tn	PROPN
ap-6304	200	32	)	)	PUNCT
ap-6304	201	1	+	+	NOUN
ap-6304	201	2	o(∆x3	o(∆x3	NUM
ap-6304	201	3	)	)	PUNCT
ap-6304	201	4	53	53	NUM
ap-6304	201	5	t.	t.	NOUN
ap-6304	201	6	bodnár	bodnár	NOUN
ap-6304	201	7	,	,	PUNCT
ap-6304	201	8	ph	ph	PROPN
ap-6304	201	9	.	.	PROPN
ap-6304	201	10	fraunié	fraunié	PROPN
ap-6304	201	11	,	,	PUNCT
ap-6304	201	12	k.	k.	PROPN
ap-6304	201	13	kozel	kozel	PROPN
ap-6304	201	14	acta	acta	PROPN
ap-6304	201	15	polytechnica	polytechnica	PROPN
ap-6304	201	16	partial	partial	ADJ
ap-6304	201	17	derivatives	derivative	NOUN
ap-6304	201	18	with	with	ADP
ap-6304	201	19	respect	respect	NOUN
ap-6304	201	20	to	to	ADP
ap-6304	201	21	time	time	NOUN
ap-6304	201	22	and	and	CCONJ
ap-6304	201	23	also	also	ADV
ap-6304	201	24	space	space	NOUN
ap-6304	201	25	,	,	PUNCT
ap-6304	201	26	both	both	PRON
ap-6304	201	27	appear	appear	VERB
ap-6304	201	28	on	on	ADP
ap-6304	201	29	the	the	DET
ap-6304	201	30	right	right	ADJ
ap-6304	201	31	hand	hand	NOUN
ap-6304	201	32	side	side	NOUN
ap-6304	201	33	.	.	PUNCT
ap-6304	202	1	the	the	DET
ap-6304	202	2	derivatives	derivative	NOUN
ap-6304	202	3	with	with	ADP
ap-6304	202	4	respect	respect	NOUN
ap-6304	202	5	to	to	ADP
ap-6304	202	6	time	time	NOUN
ap-6304	202	7	can	can	AUX
ap-6304	202	8	be	be	AUX
ap-6304	202	9	converted	convert	VERB
ap-6304	202	10	to	to	ADP
ap-6304	202	11	spatial	spatial	ADJ
ap-6304	202	12	derivatives	derivative	NOUN
ap-6304	202	13	using	use	VERB
ap-6304	202	14	the	the	DET
ap-6304	202	15	original	original	ADJ
ap-6304	202	16	advection	advection	NOUN
ap-6304	202	17	equation	equation	NOUN
ap-6304	202	18	(	(	PUNCT
ap-6304	202	19	or	or	CCONJ
ap-6304	202	20	corresponding	correspond	VERB
ap-6304	202	21	scheme	scheme	PROPN
ap-6304	202	22	taylor	taylor	PROPN
ap-6304	202	23	’s	’s	PART
ap-6304	202	24	expansions	expansion	NOUN
ap-6304	202	25	):	):	PUNCT
ap-6304	202	26	ut	ut	PROPN
ap-6304	203	1	+	+	CCONJ
ap-6304	203	2	aux	aux	X
ap-6304	203	3	=	=	SYM
ap-6304	203	4	0	0	PUNCT
ap-6304	203	5	=	=	NOUN
ap-6304	203	6	⇒	⇒	NOUN
ap-6304	203	7	∂	∂	X
ap-6304	203	8	·	·	PUNCT
ap-6304	203	9	∂t	∂t	PROPN
ap-6304	203	10	=	=	SYM
ap-6304	203	11	−a∂	−a∂	PROPN
ap-6304	203	12	·	·	PUNCT
ap-6304	203	13	∂x	∂x	PROPN
ap-6304	203	14	utt	utt	ADJ
ap-6304	203	15	=	=	SYM
ap-6304	203	16	a2uxx	a2uxx	PROPN
ap-6304	203	17	&	&	CCONJ
ap-6304	203	18	uttt	uttt	NOUN
ap-6304	203	19	=	=	SYM
ap-6304	203	20	−a3uxxx	−a3uxxx	NOUN
ap-6304	203	21	this	this	PRON
ap-6304	203	22	leads	lead	VERB
ap-6304	203	23	to	to	ADP
ap-6304	203	24	ut(xi	ut(xi	PROPN
ap-6304	203	25	,	,	PUNCT
ap-6304	203	26	tn	tn	PROPN
ap-6304	203	27	)	)	PUNCT
ap-6304	204	1	+	+	CCONJ
ap-6304	204	2	aux(xi	aux(xi	ADJ
ap-6304	204	3	,	,	PUNCT
ap-6304	204	4	tn	tn	NOUN
ap-6304	204	5	)	)	PUNCT
ap-6304	204	6	=	=	SYM
ap-6304	205	1	−	−	NOUN
ap-6304	205	2	a2∆t	a2∆t	NOUN
ap-6304	205	3	2	2	NUM
ap-6304	205	4	uxx(xi	uxx(xi	NOUN
ap-6304	205	5	,	,	PUNCT
ap-6304	205	6	tn	tn	PROPN
ap-6304	205	7	)	)	PUNCT
ap-6304	206	1	+	+	CCONJ
ap-6304	206	2	a3∆t2	a3∆t2	ADV
ap-6304	206	3	6	6	NUM
ap-6304	206	4	uxxx(xi	uxxx(xi	NOUN
ap-6304	206	5	,	,	PUNCT
ap-6304	206	6	tn	tn	PROPN
ap-6304	206	7	)	)	PUNCT
ap-6304	207	1	+	+	VERB
ap-6304	207	2	o(∆t3)+	o(∆t3)+	NOUN
ap-6304	207	3	+	+	CCONJ
ap-6304	207	4	a∆x	a∆x	X
ap-6304	207	5	2	2	NUM
ap-6304	207	6	uxx(xi	uxx(xi	NOUN
ap-6304	207	7	,	,	PUNCT
ap-6304	207	8	tn)−	tn)−	PUNCT
ap-6304	207	9	a∆x2	a∆x2	ADP
ap-6304	207	10	6	6	NUM
ap-6304	207	11	uxxx(xi	uxxx(xi	NOUN
ap-6304	207	12	,	,	PUNCT
ap-6304	207	13	tn	tn	PROPN
ap-6304	207	14	)	)	PUNCT
ap-6304	207	15	+	+	NOUN
ap-6304	207	16	o(∆x3	o(∆x3	NUM
ap-6304	207	17	)	)	PUNCT
ap-6304	207	18	.	.	PUNCT
ap-6304	208	1	when	when	SCONJ
ap-6304	208	2	only	only	ADV
ap-6304	208	3	the	the	DET
ap-6304	208	4	leading	lead	VERB
ap-6304	208	5	order	order	NOUN
ap-6304	208	6	term	term	NOUN
ap-6304	208	7	is	be	AUX
ap-6304	208	8	kept	keep	VERB
ap-6304	208	9	,	,	PUNCT
ap-6304	208	10	the	the	DET
ap-6304	208	11	modified	modify	VERB
ap-6304	208	12	equation	equation	NOUN
ap-6304	208	13	takes	take	VERB
ap-6304	208	14	the	the	DET
ap-6304	208	15	form	form	NOUN
ap-6304	208	16	:	:	PUNCT
ap-6304	208	17	ut(xi	ut(xi	PROPN
ap-6304	208	18	,	,	PUNCT
ap-6304	208	19	tn	tn	PROPN
ap-6304	208	20	)	)	PUNCT
ap-6304	209	1	+	+	CCONJ
ap-6304	209	2	aux(xi	aux(xi	ADJ
ap-6304	209	3	,	,	PUNCT
ap-6304	209	4	tn	tn	NOUN
ap-6304	209	5	)	)	PUNCT
ap-6304	209	6	=	=	PUNCT
ap-6304	210	1	=	=	PUNCT
ap-6304	210	2	(	(	PUNCT
ap-6304	210	3	a∆x	a∆x	ADP
ap-6304	210	4	2	2	NUM
ap-6304	210	5	−	−	NOUN
ap-6304	210	6	a2∆t	a2∆t	NOUN
ap-6304	210	7	2	2	NUM
ap-6304	210	8	)	)	PUNCT
ap-6304	210	9	uxx(xi	uxx(xi	NOUN
ap-6304	210	10	,	,	PUNCT
ap-6304	210	11	tn	tn	PROPN
ap-6304	210	12	)	)	PUNCT
ap-6304	211	1	+	+	NOUN
ap-6304	211	2	o(∆t2	o(∆t2	ADJ
ap-6304	211	3	;	;	PUNCT
ap-6304	211	4	∆x2	∆x2	NOUN
ap-6304	211	5	)	)	PUNCT
ap-6304	211	6	.	.	PUNCT
ap-6304	212	1	in	in	ADP
ap-6304	212	2	the	the	DET
ap-6304	212	3	approximate	approximate	ADJ
ap-6304	212	4	version	version	NOUN
ap-6304	212	5	,	,	PUNCT
ap-6304	212	6	the	the	DET
ap-6304	212	7	extra	extra	ADJ
ap-6304	212	8	term	term	NOUN
ap-6304	212	9	containing	contain	VERB
ap-6304	212	10	second	second	ADJ
ap-6304	212	11	(	(	PUNCT
ap-6304	212	12	spatial	spatial	ADJ
ap-6304	212	13	)	)	PUNCT
ap-6304	212	14	derivative	derivative	ADJ
ap-6304	212	15	uxx	uxx	NOUN
ap-6304	212	16	appears	appear	VERB
ap-6304	212	17	on	on	ADP
ap-6304	212	18	the	the	DET
ap-6304	212	19	right	right	ADJ
ap-6304	212	20	hand	hand	NOUN
ap-6304	212	21	side	side	NOUN
ap-6304	212	22	.	.	PUNCT
ap-6304	213	1	ut(xi	ut(xi	PROPN
ap-6304	213	2	,	,	PUNCT
ap-6304	213	3	tn	tn	PROPN
ap-6304	213	4	)	)	PUNCT
ap-6304	214	1	+	+	CCONJ
ap-6304	214	2	aux(xi	aux(xi	ADJ
ap-6304	214	3	,	,	PUNCT
ap-6304	214	4	tn	tn	PROPN
ap-6304	214	5	)	)	PUNCT
ap-6304	214	6	.=	.=	PROPN
ap-6304	214	7	a∆x	a∆x	PROPN
ap-6304	214	8	2	2	NUM
ap-6304	214	9	(	(	PUNCT
ap-6304	214	10	1−	1−	NUM
ap-6304	214	11	γ)uxx(xi	γ)uxx(xi	PROPN
ap-6304	214	12	,	,	PUNCT
ap-6304	214	13	tn	tn	PROPN
ap-6304	214	14	)	)	PUNCT
ap-6304	214	15	it	it	PRON
ap-6304	214	16	means	mean	VERB
ap-6304	214	17	that	that	SCONJ
ap-6304	214	18	while	while	SCONJ
ap-6304	214	19	solving	solve	VERB
ap-6304	214	20	the	the	DET
ap-6304	214	21	advection	advection	NOUN
ap-6304	214	22	equation	equation	NOUN
ap-6304	214	23	by	by	ADP
ap-6304	214	24	the	the	DET
ap-6304	214	25	up	up	ADJ
ap-6304	214	26	-	-	PUNCT
ap-6304	214	27	wind	wind	NOUN
ap-6304	214	28	scheme	scheme	NOUN
ap-6304	214	29	,	,	PUNCT
ap-6304	214	30	we	we	PRON
ap-6304	214	31	obtain	obtain	VERB
ap-6304	214	32	rather	rather	ADV
ap-6304	214	33	the	the	DET
ap-6304	214	34	solution	solution	NOUN
ap-6304	214	35	of	of	ADP
ap-6304	214	36	the	the	DET
ap-6304	214	37	advection	advection	NOUN
ap-6304	214	38	-	-	PUNCT
ap-6304	214	39	diffusion	diffusion	NOUN
ap-6304	214	40	equation	equation	NOUN
ap-6304	214	41	with	with	ADP
ap-6304	214	42	the	the	DET
ap-6304	214	43	diffusion	diffusion	NOUN
ap-6304	214	44	coefficient	coefficient	NOUN
ap-6304	214	45	corresponding	correspond	VERB
ap-6304	214	46	to	to	ADP
ap-6304	214	47	the	the	DET
ap-6304	214	48	numerical	numerical	ADJ
ap-6304	214	49	viscosity	viscosity	PROPN
ap-6304	215	1	µ	µ	X
ap-6304	215	2	ut	ut	PROPN
ap-6304	215	3	+	+	CCONJ
ap-6304	215	4	aux	aux	X
ap-6304	215	5	=	=	SYM
ap-6304	215	6	0	0	PUNCT
ap-6304	215	7	−→	−→	NOUN
ap-6304	215	8	ut	ut	PROPN
ap-6304	215	9	+	+	CCONJ
ap-6304	215	10	aux	aux	PROPN
ap-6304	215	11	=	=	PUNCT
ap-6304	215	12	a∆x	a∆x	X
ap-6304	215	13	2	2	NUM
ap-6304	215	14	(	(	PUNCT
ap-6304	215	15	1−	1−	NUM
ap-6304	215	16	γ)︸	γ)︸	PROPN
ap-6304	215	17	︷︷	︷︷	PROPN
ap-6304	215	18	︸	︸	ADP
ap-6304	215	19	µ	µ	X
ap-6304	215	20	uxx	uxx	NOUN
ap-6304	215	21	in	in	ADP
ap-6304	215	22	more	more	ADJ
ap-6304	215	23	detail	detail	NOUN
ap-6304	215	24	,	,	PUNCT
ap-6304	215	25	instead	instead	ADV
ap-6304	215	26	of	of	ADP
ap-6304	215	27	the	the	DET
ap-6304	215	28	first	first	ADJ
ap-6304	215	29	order	order	NOUN
ap-6304	215	30	approximation	approximation	NOUN
ap-6304	215	31	of	of	ADP
ap-6304	215	32	the	the	DET
ap-6304	215	33	advection	advection	NOUN
ap-6304	215	34	equation	equation	NOUN
ap-6304	215	35	we	we	PRON
ap-6304	215	36	have	have	AUX
ap-6304	215	37	obtained	obtain	VERB
ap-6304	215	38	a	a	DET
ap-6304	215	39	second	second	ADJ
ap-6304	215	40	order	order	NOUN
ap-6304	215	41	approximation	approximation	NOUN
ap-6304	215	42	of	of	ADP
ap-6304	215	43	the	the	DET
ap-6304	215	44	advection	advection	NOUN
ap-6304	215	45	-	-	PUNCT
ap-6304	215	46	diffusion	diffusion	NOUN
ap-6304	215	47	equation	equation	NOUN
ap-6304	215	48	.	.	PUNCT
ap-6304	216	1	1st	1st	ADJ
ap-6304	216	2	order	order	NOUN
ap-6304	216	3	approximation	approximation	NOUN
ap-6304	216	4	of	of	ADP
ap-6304	216	5	original	original	ADJ
ap-6304	216	6	equation	equation	NOUN
ap-6304	216	7	ut	ut	PROPN
ap-6304	217	1	+	+	CCONJ
ap-6304	217	2	aux	aux	X
ap-6304	217	3	=	=	X
ap-6304	217	4	0	0	PUNCT
ap-6304	218	1	+	+	NUM
ap-6304	218	2	o(∆t	o(∆t	NOUN
ap-6304	218	3	;	;	PUNCT
ap-6304	218	4	∆x	∆x	NUM
ap-6304	218	5	)	)	PUNCT
ap-6304	218	6	2nd	2nd	ADJ
ap-6304	218	7	order	order	NOUN
ap-6304	218	8	approximation	approximation	NOUN
ap-6304	218	9	of	of	ADP
ap-6304	218	10	modified	modify	VERB
ap-6304	218	11	equation	equation	NOUN
ap-6304	218	12	ut	ut	PROPN
ap-6304	218	13	+	+	CCONJ
ap-6304	218	14	aux	aux	PROPN
ap-6304	218	15	=	=	PUNCT
ap-6304	218	16	a∆x	a∆x	X
ap-6304	218	17	2	2	NUM
ap-6304	218	18	(	(	PUNCT
ap-6304	218	19	1−	1−	NUM
ap-6304	218	20	γ)uxx	γ)uxx	PROPN
ap-6304	218	21	+	+	PROPN
ap-6304	218	22	o(∆t2	o(∆t2	ADJ
ap-6304	218	23	;	;	PUNCT
ap-6304	218	24	∆x2	∆x2	NOUN
ap-6304	218	25	)	)	PUNCT
ap-6304	218	26	so	so	SCONJ
ap-6304	218	27	the	the	DET
ap-6304	218	28	numerical	numerical	ADJ
ap-6304	218	29	solution	solution	NOUN
ap-6304	218	30	of	of	ADP
ap-6304	218	31	the	the	DET
ap-6304	218	32	original	original	ADJ
ap-6304	218	33	(	(	PUNCT
ap-6304	218	34	advection	advection	NOUN
ap-6304	218	35	)	)	PUNCT
ap-6304	218	36	problem	problem	NOUN
ap-6304	218	37	is	be	AUX
ap-6304	218	38	in	in	ADP
ap-6304	218	39	fact	fact	NOUN
ap-6304	218	40	much	much	ADV
ap-6304	218	41	closer	close	ADJ
ap-6304	218	42	to	to	ADP
ap-6304	218	43	the	the	DET
ap-6304	218	44	solution	solution	NOUN
ap-6304	218	45	of	of	ADP
ap-6304	218	46	the	the	DET
ap-6304	218	47	modified	modify	VERB
ap-6304	218	48	(	(	PUNCT
ap-6304	218	49	advection	advection	NOUN
ap-6304	218	50	-	-	PUNCT
ap-6304	218	51	diffusion	diffusion	NOUN
ap-6304	218	52	)	)	PUNCT
ap-6304	218	53	problem	problem	NOUN
ap-6304	218	54	,	,	PUNCT
ap-6304	218	55	with	with	ADP
ap-6304	218	56	all	all	DET
ap-6304	218	57	the	the	DET
ap-6304	218	58	consequences	consequence	NOUN
ap-6304	218	59	it	it	PRON
ap-6304	218	60	may	may	AUX
ap-6304	218	61	have	have	VERB
ap-6304	218	62	on	on	ADP
ap-6304	218	63	the	the	DET
ap-6304	218	64	solution	solution	NOUN
ap-6304	218	65	behavior	behavior	NOUN
ap-6304	218	66	.	.	PUNCT
ap-6304	219	1	from	from	ADP
ap-6304	219	2	the	the	DET
ap-6304	219	3	form	form	NOUN
ap-6304	219	4	of	of	ADP
ap-6304	219	5	the	the	DET
ap-6304	219	6	modified	modify	VERB
ap-6304	219	7	equation	equation	NOUN
ap-6304	219	8	we	we	PRON
ap-6304	219	9	can	can	AUX
ap-6304	219	10	see	see	VERB
ap-6304	219	11	the	the	DET
ap-6304	219	12	order	order	NOUN
ap-6304	219	13	of	of	ADP
ap-6304	219	14	accuracy	accuracy	NOUN
ap-6304	219	15	of	of	ADP
ap-6304	219	16	the	the	DET
ap-6304	219	17	approximation	approximation	NOUN
ap-6304	219	18	of	of	ADP
ap-6304	219	19	the	the	DET
ap-6304	219	20	original	original	ADJ
ap-6304	219	21	problem	problem	NOUN
ap-6304	219	22	,	,	PUNCT
ap-6304	219	23	the	the	DET
ap-6304	219	24	diffusive	diffusive	ADJ
ap-6304	219	25	(	(	PUNCT
ap-6304	219	26	or	or	CCONJ
ap-6304	219	27	possibly	possibly	ADV
ap-6304	219	28	dispersive	dispersive	VERB
ap-6304	219	29	)	)	PUNCT
ap-6304	219	30	x	x	SYM
ap-6304	220	1	t	t	NOUN
ap-6304	220	2	i−1	i−1	PROPN
ap-6304	220	3	i+1i	i+1i	PROPN
ap-6304	220	4	n+1	n+1	PROPN
ap-6304	220	5	n	n	NUM
ap-6304	220	6	α4	α4	VERB
ap-6304	220	7	α	α	NOUN
ap-6304	220	8	α	α	NOUN
ap-6304	220	9	α1	α1	PROPN
ap-6304	220	10	3	3	NUM
ap-6304	220	11	2	2	NUM
ap-6304	220	12	figure	figure	NOUN
ap-6304	220	13	5	5	NUM
ap-6304	220	14	.	.	PUNCT
ap-6304	220	15	computational	computational	ADJ
ap-6304	220	16	stencil	stencil	PROPN
ap-6304	220	17	for	for	ADP
ap-6304	220	18	general	general	ADJ
ap-6304	220	19	implicit	implicit	ADJ
ap-6304	220	20	and	and	CCONJ
ap-6304	220	21	explicit	explicit	ADJ
ap-6304	220	22	schemes	scheme	NOUN
ap-6304	220	23	.	.	PUNCT
ap-6304	221	1	character	character	NOUN
ap-6304	221	2	of	of	ADP
ap-6304	221	3	the	the	DET
ap-6304	221	4	modified	modify	VERB
ap-6304	221	5	equation	equation	NOUN
ap-6304	221	6	,	,	PUNCT
ap-6304	221	7	representing	represent	VERB
ap-6304	221	8	the	the	DET
ap-6304	221	9	behavior	behavior	NOUN
ap-6304	221	10	of	of	ADP
ap-6304	221	11	the	the	DET
ap-6304	221	12	numerical	numerical	ADJ
ap-6304	221	13	solution	solution	NOUN
ap-6304	221	14	.	.	PUNCT
ap-6304	222	1	it	it	PRON
ap-6304	222	2	’s	’	VERB
ap-6304	222	3	also	also	ADV
ap-6304	222	4	possible	possible	ADJ
ap-6304	222	5	to	to	PART
ap-6304	222	6	see	see	VERB
ap-6304	222	7	e.g.	e.g.	ADV
ap-6304	222	8	how	how	SCONJ
ap-6304	222	9	the	the	DET
ap-6304	222	10	numerical	numerical	ADJ
ap-6304	222	11	viscosity	viscosity	NOUN
ap-6304	222	12	coefficient	coefficient	VERB
ap-6304	222	13	µ	µ	DET
ap-6304	222	14	scales	scale	NOUN
ap-6304	222	15	with	with	ADP
ap-6304	222	16	time	time	NOUN
ap-6304	222	17	-	-	PUNCT
ap-6304	222	18	step	step	NOUN
ap-6304	222	19	∆t	∆t	PROPN
ap-6304	222	20	and	and	CCONJ
ap-6304	222	21	spatial	spatial	ADJ
ap-6304	222	22	step	step	NOUN
ap-6304	222	23	∆x	∆x	PROPN
ap-6304	222	24	.	.	PUNCT
ap-6304	223	1	from	from	ADP
ap-6304	223	2	the	the	DET
ap-6304	223	3	requirement	requirement	NOUN
ap-6304	223	4	of	of	ADP
ap-6304	223	5	positivity	positivity	NOUN
ap-6304	223	6	of	of	ADP
ap-6304	223	7	the	the	DET
ap-6304	223	8	diffusion	diffusion	NOUN
ap-6304	223	9	coefficient	coefficient	NOUN
ap-6304	223	10	µ	µ	X
ap-6304	223	11	>	>	SYM
ap-6304	223	12	0	0	PUNCT
ap-6304	224	1	it	it	PRON
ap-6304	224	2	’s	’	VERB
ap-6304	224	3	possible	possible	ADJ
ap-6304	224	4	to	to	PART
ap-6304	224	5	estimate	estimate	VERB
ap-6304	224	6	the	the	DET
ap-6304	224	7	stability	stability	NOUN
ap-6304	224	8	of	of	ADP
ap-6304	224	9	the	the	DET
ap-6304	224	10	underlying	underlying	ADJ
ap-6304	224	11	numerical	numerical	ADJ
ap-6304	224	12	scheme	scheme	NOUN
ap-6304	224	13	,	,	PUNCT
ap-6304	224	14	i.e.	i.e.	X
ap-6304	224	15	the	the	DET
ap-6304	224	16	limitations	limitation	NOUN
ap-6304	224	17	for	for	ADP
ap-6304	224	18	the	the	DET
ap-6304	224	19	cfl	cfl	NOUN
ap-6304	224	20	parameter	parameter	PROPN
ap-6304	224	21	γ	γ	PROPN
ap-6304	224	22	(	(	PUNCT
ap-6304	224	23	evidently	evidently	ADV
ap-6304	224	24	γ	γ	X
ap-6304	224	25	<	<	X
ap-6304	224	26	1	1	NUM
ap-6304	224	27	is	be	AUX
ap-6304	224	28	required	require	VERB
ap-6304	224	29	for	for	ADP
ap-6304	224	30	the	the	DET
ap-6304	224	31	up	up	ADJ
ap-6304	224	32	-	-	PUNCT
ap-6304	224	33	wind	wind	NOUN
ap-6304	224	34	scheme	scheme	NOUN
ap-6304	224	35	)	)	PUNCT
ap-6304	224	36	.	.	PUNCT
ap-6304	225	1	4.2	4.2	NUM
ap-6304	225	2	.	.	PUNCT
ap-6304	225	3	general	general	ADJ
ap-6304	225	4	modified	modify	VERB
ap-6304	225	5	equation	equation	NOUN
ap-6304	225	6	the	the	DET
ap-6304	225	7	procedure	procedure	NOUN
ap-6304	225	8	of	of	ADP
ap-6304	225	9	deriving	derive	VERB
ap-6304	225	10	the	the	DET
ap-6304	225	11	modified	modify	VERB
ap-6304	225	12	equation	equation	NOUN
ap-6304	225	13	can	can	AUX
ap-6304	225	14	be	be	AUX
ap-6304	225	15	applied	apply	VERB
ap-6304	225	16	to	to	ADP
ap-6304	225	17	all	all	DET
ap-6304	225	18	explicit	explicit	ADJ
ap-6304	225	19	schemes	scheme	NOUN
ap-6304	225	20	discussed	discuss	VERB
ap-6304	225	21	so	so	ADV
ap-6304	225	22	far	far	ADV
ap-6304	225	23	.	.	PUNCT
ap-6304	226	1	in	in	ADP
ap-6304	226	2	fact	fact	NOUN
ap-6304	226	3	it	it	PRON
ap-6304	226	4	can	can	AUX
ap-6304	226	5	be	be	AUX
ap-6304	226	6	applied	apply	VERB
ap-6304	226	7	to	to	ADP
ap-6304	226	8	a	a	DET
ap-6304	226	9	much	much	ADV
ap-6304	226	10	larger	large	ADJ
ap-6304	226	11	family	family	NOUN
ap-6304	226	12	including	include	VERB
ap-6304	226	13	also	also	ADV
ap-6304	226	14	implicit	implicit	ADJ
ap-6304	226	15	schemes	scheme	NOUN
ap-6304	226	16	.	.	PUNCT
ap-6304	227	1	further	far	ADV
ap-6304	227	2	we	we	PRON
ap-6304	227	3	will	will	AUX
ap-6304	227	4	work	work	VERB
ap-6304	227	5	with	with	ADP
ap-6304	227	6	a	a	DET
ap-6304	227	7	family	family	NOUN
ap-6304	227	8	of	of	ADP
ap-6304	227	9	explicit	explicit	ADJ
ap-6304	227	10	and	and	CCONJ
ap-6304	227	11	implicit	implicit	ADJ
ap-6304	227	12	schemes	scheme	NOUN
ap-6304	227	13	,	,	PUNCT
ap-6304	227	14	where	where	SCONJ
ap-6304	227	15	the	the	DET
ap-6304	227	16	approximation	approximation	NOUN
ap-6304	227	17	of	of	ADP
ap-6304	227	18	the	the	DET
ap-6304	227	19	spatial	spatial	ADJ
ap-6304	227	20	derivative	derivative	NOUN
ap-6304	227	21	is	be	AUX
ap-6304	227	22	obtained	obtain	VERB
ap-6304	227	23	as	as	ADP
ap-6304	227	24	a	a	DET
ap-6304	227	25	linear	linear	ADJ
ap-6304	227	26	combination	combination	NOUN
ap-6304	227	27	of	of	ADP
ap-6304	227	28	the	the	DET
ap-6304	227	29	forward	forward	ADJ
ap-6304	227	30	and	and	CCONJ
ap-6304	227	31	backward	backward	ADJ
ap-6304	227	32	differences	difference	NOUN
ap-6304	227	33	at	at	ADP
ap-6304	227	34	time	time	NOUN
ap-6304	227	35	levels	level	NOUN
ap-6304	227	36	n	n	CCONJ
ap-6304	227	37	and	and	CCONJ
ap-6304	227	38	n	n	PROPN
ap-6304	227	39	+	+	NOUN
ap-6304	228	1	1	1	X
ap-6304	228	2	.	.	PUNCT
ap-6304	228	3	the	the	DET
ap-6304	228	4	whole	whole	ADJ
ap-6304	228	5	family	family	NOUN
ap-6304	228	6	of	of	ADP
ap-6304	228	7	such	such	ADJ
ap-6304	228	8	schemes	scheme	NOUN
ap-6304	228	9	can	can	AUX
ap-6304	228	10	be	be	AUX
ap-6304	228	11	written	write	VERB
ap-6304	228	12	in	in	ADP
ap-6304	228	13	the	the	DET
ap-6304	228	14	form	form	NOUN
ap-6304	228	15	:	:	PUNCT
ap-6304	228	16	un+1	un+1	NOUN
ap-6304	229	1	i	i	PRON
ap-6304	229	2	−	−	VERB
ap-6304	229	3	uni	uni	PROPN
ap-6304	229	4	∆t	∆t	PROPN
ap-6304	229	5	+	+	PROPN
ap-6304	230	1	+	+	CCONJ
ap-6304	230	2	a	a	DET
ap-6304	230	3	[	[	PUNCT
ap-6304	230	4	α1	α1	PROPN
ap-6304	230	5	(	(	PUNCT
ap-6304	230	6	uni+1	uni+1	NOUN
ap-6304	230	7	−	−	PROPN
ap-6304	230	8	uni	uni	PROPN
ap-6304	230	9	∆x	∆x	PROPN
ap-6304	230	10	)	)	PUNCT
ap-6304	231	1	+	+	CCONJ
ap-6304	231	2	α2	α2	ADJ
ap-6304	231	3	(	(	PUNCT
ap-6304	231	4	uni	uni	INTJ
ap-6304	231	5	−	−	PROPN
ap-6304	231	6	uni−1	uni−1	PROPN
ap-6304	231	7	∆x	∆x	PROPN
ap-6304	231	8	)	)	PUNCT
ap-6304	231	9	]	]	PUNCT
ap-6304	232	1	+	+	CCONJ
ap-6304	232	2	+	+	PUNCT
ap-6304	232	3	a	a	DET
ap-6304	232	4	[	[	PUNCT
ap-6304	232	5	α3	α3	NOUN
ap-6304	232	6	(	(	PUNCT
ap-6304	232	7	un+1	un+1	PROPN
ap-6304	232	8	i+1	i+1	NUM
ap-6304	232	9	−	−	PROPN
ap-6304	232	10	u	u	NOUN
ap-6304	232	11	n+1	n+1	PROPN
ap-6304	232	12	i	i	PRON
ap-6304	232	13	∆x	∆x	PROPN
ap-6304	232	14	)	)	PUNCT
ap-6304	233	1	+	+	NOUN
ap-6304	233	2	α4	α4	NOUN
ap-6304	233	3	(	(	PUNCT
ap-6304	233	4	un+1	un+1	NOUN
ap-6304	233	5	i	i	PRON
ap-6304	233	6	−	−	PROPN
ap-6304	233	7	un+1	un+1	ADV
ap-6304	233	8	i−1	i−1	PROPN
ap-6304	233	9	∆x	∆x	PROPN
ap-6304	233	10	)	)	PUNCT
ap-6304	233	11	]	]	PUNCT
ap-6304	234	1	=	=	PUNCT
ap-6304	234	2	0	0	NUM
ap-6304	234	3	.	.	PUNCT
ap-6304	235	1	the	the	DET
ap-6304	235	2	computational	computational	ADJ
ap-6304	235	3	stencil	stencil	NOUN
ap-6304	235	4	for	for	ADP
ap-6304	235	5	such	such	ADJ
ap-6304	235	6	family	family	NOUN
ap-6304	235	7	of	of	ADP
ap-6304	235	8	schemes	scheme	NOUN
ap-6304	235	9	is	be	AUX
ap-6304	235	10	shown	show	VERB
ap-6304	235	11	in	in	ADP
ap-6304	235	12	the	the	DET
ap-6304	235	13	fig	fig	NOUN
ap-6304	235	14	.	.	PUNCT
ap-6304	236	1	5	5	NUM
ap-6304	236	2	,	,	PUNCT
ap-6304	236	3	introducing	introduce	VERB
ap-6304	236	4	also	also	ADV
ap-6304	236	5	the	the	DET
ap-6304	236	6	weights	weight	NOUN
ap-6304	236	7	α1	α1	PROPN
ap-6304	236	8	–	–	PUNCT
ap-6304	236	9	α4	α4	NOUN
ap-6304	236	10	used	use	VERB
ap-6304	236	11	for	for	ADP
ap-6304	236	12	blending	blend	VERB
ap-6304	236	13	the	the	DET
ap-6304	236	14	individual	individual	ADJ
ap-6304	236	15	differences	difference	NOUN
ap-6304	236	16	in	in	ADP
ap-6304	236	17	the	the	DET
ap-6304	236	18	linear	linear	ADJ
ap-6304	236	19	combination	combination	NOUN
ap-6304	236	20	.	.	PUNCT
ap-6304	237	1	due	due	ADP
ap-6304	237	2	to	to	PART
ap-6304	237	3	consistency	consistency	VERB
ap-6304	237	4	the	the	DET
ap-6304	237	5	condition	condition	NOUN
ap-6304	237	6	α1	α1	PROPN
ap-6304	237	7	+	+	CCONJ
ap-6304	237	8	α2	α2	ADJ
ap-6304	237	9	+	+	CCONJ
ap-6304	237	10	α3	α3	ADJ
ap-6304	237	11	+	+	CCONJ
ap-6304	237	12	α4	α4	NOUN
ap-6304	237	13	=	=	SYM
ap-6304	237	14	1	1	NUM
ap-6304	237	15	should	should	AUX
ap-6304	237	16	be	be	AUX
ap-6304	237	17	verified	verify	VERB
ap-6304	237	18	,	,	PUNCT
ap-6304	237	19	moreover	moreover	ADV
ap-6304	237	20	obviously	obviously	ADV
ap-6304	237	21	|α3|+	|α3|+	CCONJ
ap-6304	237	22	|α4|	|α4|	NOUN
ap-6304	237	23	=	=	SYM
ap-6304	237	24	0	0	NUM
ap-6304	237	25	for	for	ADP
ap-6304	237	26	explicit	explicit	ADJ
ap-6304	237	27	schemes	scheme	NOUN
ap-6304	237	28	,	,	PUNCT
ap-6304	237	29	while	while	SCONJ
ap-6304	237	30	the	the	DET
ap-6304	237	31	opposite	opposite	ADJ
ap-6304	237	32	|α3|+	|α3|+	ADJ
ap-6304	237	33	|α4|	|α4|	NOUN
ap-6304	237	34	6=	6=	PRON
ap-6304	237	35	0	0	NUM
ap-6304	237	36	characterizes	characterize	VERB
ap-6304	237	37	the	the	DET
ap-6304	237	38	implicit	implicit	ADJ
ap-6304	237	39	schemes	scheme	NOUN
ap-6304	237	40	.	.	PUNCT
ap-6304	238	1	for	for	ADP
ap-6304	238	2	simplicity	simplicity	NOUN
ap-6304	238	3	,	,	PUNCT
ap-6304	238	4	the	the	DET
ap-6304	238	5	coefficients	coefficient	NOUN
ap-6304	238	6	of	of	ADP
ap-6304	238	7	the	the	DET
ap-6304	238	8	explicit	explicit	ADJ
ap-6304	238	9	part	part	NOUN
ap-6304	238	10	are	be	AUX
ap-6304	238	11	marked	mark	VERB
ap-6304	238	12	in	in	ADP
ap-6304	238	13	blue	blue	ADJ
ap-6304	238	14	,	,	PUNCT
ap-6304	238	15	while	while	SCONJ
ap-6304	238	16	the	the	DET
ap-6304	238	17	implicit	implicit	ADJ
ap-6304	238	18	part	part	NOUN
ap-6304	238	19	is	be	AUX
ap-6304	238	20	green	green	ADJ
ap-6304	238	21	.	.	PUNCT
ap-6304	239	1	the	the	DET
ap-6304	239	2	coefficients	coefficient	NOUN
ap-6304	239	3	α1	α1	PROPN
ap-6304	239	4	–	–	PUNCT
ap-6304	239	5	α4	α4	NOUN
ap-6304	239	6	for	for	ADP
ap-6304	239	7	some	some	DET
ap-6304	239	8	examples	example	NOUN
ap-6304	239	9	of	of	ADP
ap-6304	239	10	classical	classical	ADJ
ap-6304	239	11	explicit	explicit	ADJ
ap-6304	239	12	and	and	CCONJ
ap-6304	239	13	implicit	implicit	ADJ
ap-6304	239	14	schemes	scheme	NOUN
ap-6304	239	15	are	be	AUX
ap-6304	239	16	shown	show	VERB
ap-6304	239	17	in	in	ADP
ap-6304	239	18	the	the	DET
ap-6304	239	19	tab	tab	NOUN
ap-6304	239	20	.	.	PUNCT
ap-6304	240	1	5	5	NUM
ap-6304	240	2	.	.	X
ap-6304	240	3	the	the	DET
ap-6304	240	4	last	last	ADJ
ap-6304	240	5	two	two	NUM
ap-6304	240	6	rows	row	NOUN
ap-6304	240	7	in	in	ADP
ap-6304	240	8	the	the	DET
ap-6304	240	9	table	table	NOUN
ap-6304	240	10	correspond	correspond	VERB
ap-6304	240	11	to	to	ADP
ap-6304	240	12	the	the	DET
ap-6304	240	13	wendroff	wendroff	PROPN
ap-6304	240	14	scheme	scheme	NOUN
ap-6304	240	15	denoted	denote	VERB
ap-6304	240	16	by	by	ADP
ap-6304	240	17	[	[	X
ap-6304	240	18	w	w	X
ap-6304	240	19	]	]	PUNCT
ap-6304	240	20	and	and	CCONJ
ap-6304	240	21	cranknicolson	cranknicolson	NOUN
ap-6304	240	22	scheme	scheme	NOUN
ap-6304	240	23	denoted	denote	VERB
ap-6304	240	24	by	by	ADP
ap-6304	240	25	[	[	X
ap-6304	240	26	cn	cn	X
ap-6304	240	27	]	]	X
ap-6304	240	28	.	.	PUNCT
ap-6304	241	1	these	these	DET
ap-6304	241	2	two	two	NUM
ap-6304	241	3	schemes	scheme	NOUN
ap-6304	241	4	are	be	AUX
ap-6304	241	5	examples	example	NOUN
ap-6304	241	6	of	of	ADP
ap-6304	241	7	implicit	implicit	ADJ
ap-6304	241	8	schemes	scheme	NOUN
ap-6304	241	9	,	,	PUNCT
ap-6304	241	10	using	use	VERB
ap-6304	241	11	the	the	DET
ap-6304	241	12	difference	difference	NOUN
ap-6304	241	13	approximations	approximation	NOUN
ap-6304	241	14	at	at	ADP
ap-6304	241	15	both	both	DET
ap-6304	241	16	time	time	NOUN
ap-6304	241	17	levels	level	NOUN
ap-6304	241	18	n	n	PRON
ap-6304	241	19	and	and	CCONJ
ap-6304	241	20	n+	n+	NUM
ap-6304	241	21	1	1	X
ap-6304	241	22	.	.	X
ap-6304	241	23	for	for	ADP
ap-6304	241	24	54	54	NUM
ap-6304	241	25	vol	vol	NOUN
ap-6304	241	26	.	.	PUNCT
ap-6304	242	1	61	61	NUM
ap-6304	242	2	special	special	ADJ
ap-6304	242	3	issue/2021	issue/2021	NOUN
ap-6304	242	4	modified	modify	VERB
ap-6304	242	5	equation	equation	NOUN
ap-6304	242	6	for	for	ADP
ap-6304	242	7	explicit	explicit	ADJ
ap-6304	242	8	and	and	CCONJ
ap-6304	242	9	implicit	implicit	ADJ
ap-6304	242	10	schemes	scheme	NOUN
ap-6304	242	11	scheme	scheme	NOUN
ap-6304	242	12	α1	α1	PROPN
ap-6304	242	13	α2	α2	ADJ
ap-6304	242	14	α3	α3	PROPN
ap-6304	242	15	α4	α4	NOUN
ap-6304	242	16	[	[	X
ap-6304	242	17	u	u	X
ap-6304	242	18	]	]	X
ap-6304	242	19	0	0	NUM
ap-6304	242	20	1	1	NUM
ap-6304	242	21	0	0	NUM
ap-6304	242	22	0	0	NUM
ap-6304	243	1	[	[	X
ap-6304	243	2	d	d	X
ap-6304	243	3	]	]	X
ap-6304	243	4	1	1	NUM
ap-6304	243	5	0	0	NUM
ap-6304	243	6	0	0	NUM
ap-6304	243	7	0	0	NUM
ap-6304	244	1	[	[	X
ap-6304	244	2	c	c	X
ap-6304	244	3	]	]	X
ap-6304	244	4	1	1	NUM
ap-6304	244	5	2	2	NUM
ap-6304	244	6	1	1	NUM
ap-6304	244	7	2	2	NUM
ap-6304	244	8	0	0	NUM
ap-6304	244	9	0	0	NUM
ap-6304	245	1	[	[	X
ap-6304	245	2	lf	lf	X
ap-6304	245	3	]	]	SYM
ap-6304	245	4	1	1	NUM
ap-6304	245	5	2	2	NUM
ap-6304	245	6	−	−	PROPN
ap-6304	245	7	∆x	∆x	PROPN
ap-6304	245	8	2a∆t	2a∆t	NUM
ap-6304	245	9	1	1	NUM
ap-6304	245	10	2	2	NUM
ap-6304	245	11	+	+	CCONJ
ap-6304	245	12	∆x	∆x	PROPN
ap-6304	245	13	2a∆t	2a∆t	NUM
ap-6304	245	14	0	0	NUM
ap-6304	245	15	0	0	NUM
ap-6304	246	1	[	[	X
ap-6304	246	2	lw	lw	X
ap-6304	246	3	]	]	X
ap-6304	246	4	1	1	NUM
ap-6304	246	5	2	2	NUM
ap-6304	246	6	−	−	NOUN
ap-6304	246	7	a∆t	a∆t	VERB
ap-6304	246	8	2∆x	2∆x	NUM
ap-6304	246	9	1	1	NUM
ap-6304	246	10	2	2	NUM
ap-6304	246	11	+	+	CCONJ
ap-6304	246	12	a∆t	a∆t	VERB
ap-6304	246	13	2∆x	2∆x	NUM
ap-6304	246	14	0	0	NUM
ap-6304	246	15	0	0	PUNCT
ap-6304	247	1	[	[	X
ap-6304	247	2	w	w	X
ap-6304	247	3	]	]	SYM
ap-6304	247	4	1	1	NUM
ap-6304	247	5	2	2	NUM
ap-6304	247	6	0	0	NUM
ap-6304	247	7	0	0	NUM
ap-6304	247	8	1	1	NUM
ap-6304	247	9	2	2	NUM
ap-6304	247	10	[	[	X
ap-6304	247	11	cn	cn	X
ap-6304	247	12	]	]	X
ap-6304	247	13	1	1	NUM
ap-6304	247	14	4	4	NUM
ap-6304	247	15	1	1	NUM
ap-6304	247	16	4	4	NUM
ap-6304	247	17	1	1	NUM
ap-6304	247	18	4	4	NUM
ap-6304	247	19	1	1	NUM
ap-6304	247	20	4	4	NUM
ap-6304	247	21	table	table	NOUN
ap-6304	247	22	5	5	NUM
ap-6304	247	23	.	.	PUNCT
ap-6304	247	24	coefficients	coefficient	NOUN
ap-6304	247	25	of	of	ADP
ap-6304	247	26	some	some	DET
ap-6304	247	27	explicit	explicit	ADJ
ap-6304	247	28	and	and	CCONJ
ap-6304	247	29	implicit	implicit	ADJ
ap-6304	247	30	schemes	scheme	NOUN
ap-6304	247	31	with	with	ADP
ap-6304	247	32	three	three	NUM
ap-6304	247	33	-	-	PUNCT
ap-6304	247	34	point	point	NOUN
ap-6304	247	35	stencil	stencil	PROPN
ap-6304	247	36	.	.	PUNCT
ap-6304	248	1	scheme	scheme	NOUN
ap-6304	248	2	modified	modify	VERB
ap-6304	248	3	equation	equation	NOUN
ap-6304	248	4	[	[	X
ap-6304	248	5	u	u	X
ap-6304	248	6	]	]	X
ap-6304	248	7	ut	ut	PROPN
ap-6304	249	1	+	+	CCONJ
ap-6304	249	2	aux	aux	PROPN
ap-6304	249	3	=	=	PUNCT
ap-6304	249	4	(	(	PUNCT
ap-6304	249	5	1−	1−	NUM
ap-6304	249	6	γ)a∆x	γ)a∆x	NUM
ap-6304	249	7	2	2	NUM
ap-6304	249	8	uxx	uxx	X
ap-6304	250	1	[	[	X
ap-6304	250	2	d	d	X
ap-6304	250	3	]	]	X
ap-6304	250	4	ut	ut	PROPN
ap-6304	250	5	+	+	CCONJ
ap-6304	250	6	aux	aux	X
ap-6304	250	7	=	=	PUNCT
ap-6304	251	1	−(1	−(1	PROPN
ap-6304	251	2	+	+	NUM
ap-6304	251	3	γ)a∆x	γ)a∆x	NUM
ap-6304	251	4	2	2	NUM
ap-6304	251	5	uxx	uxx	X
ap-6304	252	1	[	[	X
ap-6304	252	2	c	c	X
ap-6304	252	3	]	]	X
ap-6304	252	4	ut	ut	PROPN
ap-6304	252	5	+	+	CCONJ
ap-6304	252	6	aux	aux	PROPN
ap-6304	252	7	=	=	PUNCT
ap-6304	252	8	−γ	−γ	NOUN
ap-6304	252	9	a∆x	a∆x	PROPN
ap-6304	252	10	2	2	NUM
ap-6304	252	11	uxx	uxx	X
ap-6304	253	1	[	[	X
ap-6304	253	2	lf	lf	X
ap-6304	253	3	]	]	X
ap-6304	253	4	ut	ut	PROPN
ap-6304	254	1	+	+	CCONJ
ap-6304	254	2	aux	aux	PROPN
ap-6304	254	3	=	=	PUNCT
ap-6304	254	4	(	(	PUNCT
ap-6304	254	5	1	1	NUM
ap-6304	254	6	γ	γ	NOUN
ap-6304	254	7	−	−	NOUN
ap-6304	254	8	γ)a∆x	γ)a∆x	NUM
ap-6304	254	9	2	2	NUM
ap-6304	254	10	uxx	uxx	X
ap-6304	254	11	[	[	X
ap-6304	254	12	lw	lw	X
ap-6304	254	13	]	]	X
ap-6304	254	14	ut	ut	PROPN
ap-6304	255	1	+	+	CCONJ
ap-6304	255	2	aux	aux	PROPN
ap-6304	255	3	=	=	PUNCT
ap-6304	255	4	−(1−	−(1−	NOUN
ap-6304	255	5	γ2)a∆x2	γ2)a∆x2	PROPN
ap-6304	255	6	6	6	NUM
ap-6304	255	7	uxxx	uxxx	NOUN
ap-6304	256	1	[	[	X
ap-6304	256	2	w	w	X
ap-6304	256	3	]	]	X
ap-6304	256	4	ut	ut	PROPN
ap-6304	256	5	+	+	CCONJ
ap-6304	256	6	aux	aux	X
ap-6304	256	7	=	=	PUNCT
ap-6304	256	8	−(2	−(2	PROPN
ap-6304	256	9	+	+	NUM
ap-6304	256	10	3γ	3γ	NUM
ap-6304	256	11	+	+	CCONJ
ap-6304	256	12	γ2)a∆x2	γ2)a∆x2	SYM
ap-6304	256	13	12	12	NUM
ap-6304	256	14	uxxx	uxxx	PROPN
ap-6304	256	15	[	[	X
ap-6304	256	16	cn	cn	X
ap-6304	256	17	]	]	X
ap-6304	256	18	ut	ut	PROPN
ap-6304	256	19	+	+	CCONJ
ap-6304	256	20	aux	aux	X
ap-6304	256	21	=	=	PUNCT
ap-6304	256	22	−(2	−(2	PROPN
ap-6304	256	23	+	+	CCONJ
ap-6304	256	24	γ2)a∆x2	γ2)a∆x2	SYM
ap-6304	256	25	12	12	NUM
ap-6304	256	26	uxxx	uxxx	ADJ
ap-6304	256	27	table	table	NOUN
ap-6304	256	28	6	6	NUM
ap-6304	256	29	.	.	PUNCT
ap-6304	256	30	modified	modify	VERB
ap-6304	256	31	equations	equation	NOUN
ap-6304	256	32	for	for	ADP
ap-6304	256	33	some	some	DET
ap-6304	256	34	explicit	explicit	ADJ
ap-6304	256	35	and	and	CCONJ
ap-6304	256	36	implicit	implicit	ADJ
ap-6304	256	37	schemes	scheme	NOUN
ap-6304	256	38	.	.	PUNCT
ap-6304	257	1	each	each	PRON
ap-6304	257	2	of	of	ADP
ap-6304	257	3	these	these	DET
ap-6304	257	4	schemes	scheme	NOUN
ap-6304	257	5	it	it	PRON
ap-6304	257	6	’s	’	VERB
ap-6304	257	7	possible	possible	ADJ
ap-6304	257	8	to	to	PART
ap-6304	257	9	derive	derive	VERB
ap-6304	257	10	the	the	DET
ap-6304	257	11	modified	modify	VERB
ap-6304	257	12	equation	equation	NOUN
ap-6304	257	13	similarly	similarly	ADV
ap-6304	257	14	as	as	ADP
ap-6304	257	15	in	in	ADP
ap-6304	257	16	the	the	DET
ap-6304	257	17	case	case	NOUN
ap-6304	257	18	of	of	ADP
ap-6304	257	19	the	the	DET
ap-6304	257	20	up	up	ADJ
ap-6304	257	21	-	-	PUNCT
ap-6304	257	22	wind	wind	NOUN
ap-6304	257	23	scheme	scheme	NOUN
ap-6304	257	24	.	.	PUNCT
ap-6304	258	1	these	these	DET
ap-6304	258	2	modified	modify	VERB
ap-6304	258	3	equations	equation	NOUN
ap-6304	258	4	are	be	AUX
ap-6304	258	5	listed	list	VERB
ap-6304	258	6	in	in	ADP
ap-6304	258	7	the	the	DET
ap-6304	258	8	tab	tab	NOUN
ap-6304	258	9	.	.	PUNCT
ap-6304	259	1	6	6	NUM
ap-6304	259	2	using	use	VERB
ap-6304	259	3	the	the	DET
ap-6304	259	4	same	same	ADJ
ap-6304	259	5	procedure	procedure	NOUN
ap-6304	259	6	a	a	DET
ap-6304	259	7	general	general	ADJ
ap-6304	259	8	modified	modify	VERB
ap-6304	259	9	equation	equation	NOUN
ap-6304	259	10	(	(	PUNCT
ap-6304	259	11	with	with	ADP
ap-6304	259	12	up	up	ADP
ap-6304	259	13	to	to	ADP
ap-6304	259	14	3rd	3rd	ADJ
ap-6304	259	15	order	order	NOUN
ap-6304	259	16	terms	term	NOUN
ap-6304	259	17	)	)	PUNCT
ap-6304	259	18	for	for	SCONJ
ap-6304	259	19	the	the	DET
ap-6304	259	20	whole	whole	ADJ
ap-6304	259	21	family	family	NOUN
ap-6304	259	22	of	of	ADP
ap-6304	259	23	considered	consider	VERB
ap-6304	259	24	schemes	scheme	NOUN
ap-6304	259	25	can	can	AUX
ap-6304	259	26	be	be	AUX
ap-6304	259	27	obtained	obtain	VERB
ap-6304	259	28	in	in	ADP
ap-6304	259	29	the	the	DET
ap-6304	259	30	form	form	NOUN
ap-6304	259	31	:	:	PUNCT
ap-6304	259	32	ut	ut	PROPN
ap-6304	259	33	+	+	CCONJ
ap-6304	259	34	aux	aux	X
ap-6304	259	35	=	=	PUNCT
ap-6304	259	36	ε2uxx	ε2uxx	X
ap-6304	260	1	+	+	NUM
ap-6304	260	2	ε3uxxx	ε3uxxx	NOUN
ap-6304	260	3	.	.	PUNCT
ap-6304	261	1	this	this	PRON
ap-6304	261	2	is	be	AUX
ap-6304	261	3	formally	formally	ADV
ap-6304	261	4	an	an	DET
ap-6304	261	5	advection	advection	NOUN
ap-6304	261	6	-	-	PUNCT
ap-6304	261	7	diffusion	diffusion	NOUN
ap-6304	261	8	-	-	PUNCT
ap-6304	261	9	dispersion	dispersion	NOUN
ap-6304	261	10	equation	equation	NOUN
ap-6304	261	11	with	with	ADP
ap-6304	261	12	the	the	DET
ap-6304	261	13	numerical	numerical	PROPN
ap-6304	261	14	diffusion	diffusion	PROPN
ap-6304	261	15	coefficient	coefficient	NOUN
ap-6304	261	16	ε2	ε2	NOUN
ap-6304	261	17	and	and	CCONJ
ap-6304	261	18	dispersion	dispersion	NOUN
ap-6304	261	19	coefficient	coefficient	NOUN
ap-6304	261	20	ε3	ε3	PROPN
ap-6304	261	21	.	.	PUNCT
ap-6304	262	1	these	these	DET
ap-6304	262	2	coefficients	coefficient	NOUN
ap-6304	262	3	can	can	AUX
ap-6304	262	4	be	be	AUX
ap-6304	262	5	derived	derive	VERB
ap-6304	262	6	analytically	analytically	ADV
ap-6304	262	7	to	to	ADP
ap-6304	262	8	the	the	DET
ap-6304	262	9	form	form	NOUN
ap-6304	262	10	of	of	ADP
ap-6304	262	11	functions	function	NOUN
ap-6304	262	12	depending	depend	VERB
ap-6304	262	13	on	on	ADP
ap-6304	262	14	the	the	DET
ap-6304	262	15	blending	blend	VERB
ap-6304	262	16	weights	weight	NOUN
ap-6304	262	17	α1	α1	PROPN
ap-6304	262	18	–	–	PUNCT
ap-6304	262	19	α4	α4	NOUN
ap-6304	262	20	.	.	PUNCT
ap-6304	263	1	ε2	ε2	PROPN
ap-6304	263	2	=	=	SYM
ap-6304	263	3	−a∆x	−a∆x	PROPN
ap-6304	263	4	2	2	NUM
ap-6304	263	5	{	{	PUNCT
ap-6304	263	6	(	(	PUNCT
ap-6304	263	7	α1	α1	PROPN
ap-6304	263	8	−	−	PROPN
ap-6304	263	9	α2	α2	PROPN
ap-6304	263	10	)	)	PUNCT
ap-6304	264	1	+	+	CCONJ
ap-6304	264	2	(	(	PUNCT
ap-6304	264	3	α3	α3	PROPN
ap-6304	264	4	−	−	PROPN
ap-6304	264	5	α4)+	α4)+	NOUN
ap-6304	264	6	+	+	CCONJ
ap-6304	264	7	γ	γ	X
ap-6304	264	8	[	[	PUNCT
ap-6304	264	9	(	(	PUNCT
ap-6304	264	10	α1	α1	PROPN
ap-6304	264	11	+	+	CCONJ
ap-6304	264	12	α2)2	α2)2	NUM
ap-6304	264	13	−	−	PROPN
ap-6304	264	14	(	(	PUNCT
ap-6304	264	15	α3	α3	NOUN
ap-6304	264	16	+	+	CCONJ
ap-6304	264	17	α4)2	α4)2	PROPN
ap-6304	264	18	]	]	X
ap-6304	264	19	}	}	PUNCT
ap-6304	264	20	ε3	ε3	PROPN
ap-6304	264	21	=	=	SYM
ap-6304	264	22	−a∆x2	−a∆x2	PROPN
ap-6304	264	23	6	6	NUM
ap-6304	264	24	{	{	SYM
ap-6304	264	25	1	1	NUM
ap-6304	264	26	+	+	NUM
ap-6304	264	27	3γ	3γ	NUM
ap-6304	264	28	[	[	PUNCT
ap-6304	264	29	(	(	PUNCT
ap-6304	264	30	α2	α2	ADJ
ap-6304	264	31	1	1	NUM
ap-6304	264	32	−	−	NOUN
ap-6304	264	33	α2	α2	PROPN
ap-6304	264	34	2)−	2)−	PROPN
ap-6304	264	35	(	(	PUNCT
ap-6304	264	36	α2	α2	NOUN
ap-6304	264	37	3	3	NUM
ap-6304	264	38	−	−	ADV
ap-6304	264	39	α2	α2	ADJ
ap-6304	264	40	4	4	NUM
ap-6304	264	41	)	)	PUNCT
ap-6304	264	42	]	]	PUNCT
ap-6304	265	1	+	+	PUNCT
ap-6304	266	1	+	+	NUM
ap-6304	266	2	2γ2	2γ2	NUM
ap-6304	266	3	[	[	X
ap-6304	266	4	(	(	PUNCT
ap-6304	266	5	α1	α1	PROPN
ap-6304	266	6	+	+	CCONJ
ap-6304	266	7	α2)3	α2)3	PUNCT
ap-6304	266	8	+	+	CCONJ
ap-6304	266	9	(	(	PUNCT
ap-6304	266	10	α3	α3	PROPN
ap-6304	266	11	+	+	NOUN
ap-6304	266	12	α4)3	α4)3	NUM
ap-6304	266	13	]	]	X
ap-6304	266	14	}	}	PUNCT
ap-6304	266	15	5	5	NUM
ap-6304	266	16	.	.	PUNCT
ap-6304	266	17	numerical	numerical	ADJ
ap-6304	266	18	diffusion	diffusion	NOUN
ap-6304	266	19	and	and	CCONJ
ap-6304	266	20	dispersion	dispersion	NOUN
ap-6304	266	21	the	the	DET
ap-6304	266	22	general	general	ADJ
ap-6304	266	23	modified	modify	VERB
ap-6304	266	24	equation	equation	NOUN
ap-6304	266	25	for	for	ADP
ap-6304	266	26	the	the	DET
ap-6304	266	27	whole	whole	ADJ
ap-6304	266	28	explicit	explicit	ADJ
ap-6304	266	29	/	/	SYM
ap-6304	266	30	implicit	implicit	ADJ
ap-6304	266	31	family	family	NOUN
ap-6304	266	32	of	of	ADP
ap-6304	266	33	schemes	scheme	NOUN
ap-6304	266	34	can	can	AUX
ap-6304	266	35	be	be	AUX
ap-6304	266	36	rewritten	rewrite	VERB
ap-6304	266	37	in	in	ADP
ap-6304	266	38	0	0	NUM
ap-6304	266	39	0.5	0.5	NUM
ap-6304	266	40	1	1	NUM
ap-6304	266	41	1.5	1.5	NUM
ap-6304	266	42	2	2	NUM
ap-6304	266	43	0.8	0.8	NUM
ap-6304	266	44	1	1	NUM
ap-6304	266	45	1.2	1.2	NUM
ap-6304	266	46	1.4	1.4	NUM
ap-6304	266	47	1.6	1.6	NUM
ap-6304	266	48	1.8	1.8	NUM
ap-6304	266	49	2	2	NUM
ap-6304	266	50	2.2	2.2	NUM
ap-6304	266	51	x−coordinate	x−coordinate	NOUN
ap-6304	266	52	u	u	PROPN
ap-6304	266	53	ut	ut	PROPN
ap-6304	266	54	+	+	PROPN
ap-6304	266	55	aux	aux	X
ap-6304	266	56	=	=	PUNCT
ap-6304	266	57	(	(	PUNCT
ap-6304	266	58	1−	1−	NUM
ap-6304	266	59	γ)a∆x	γ)a∆x	NUM
ap-6304	266	60	2	2	NUM
ap-6304	266	61	uxx	uxx	NOUN
ap-6304	266	62	figure	figure	NOUN
ap-6304	266	63	6	6	NUM
ap-6304	266	64	.	.	PUNCT
ap-6304	266	65	up	up	ADP
ap-6304	266	66	-	-	PUNCT
ap-6304	266	67	wind	wind	NOUN
ap-6304	266	68	[	[	X
ap-6304	266	69	u	u	X
ap-6304	266	70	]	]	X
ap-6304	266	71	scheme	scheme	NOUN
ap-6304	266	72	solution	solution	NOUN
ap-6304	266	73	and	and	CCONJ
ap-6304	266	74	modified	modify	VERB
ap-6304	266	75	equation	equation	NOUN
ap-6304	266	76	.	.	PUNCT
ap-6304	267	1	the	the	DET
ap-6304	267	2	form	form	NOUN
ap-6304	267	3	ut	ut	PROPN
ap-6304	267	4	+	+	CCONJ
ap-6304	267	5	aux	aux	X
ap-6304	267	6	=	=	PUNCT
ap-6304	267	7	ε2uxx	ε2uxx	X
ap-6304	267	8	+	+	NUM
ap-6304	267	9	ε3uxxx	ε3uxxx	NOUN
ap-6304	267	10	=	=	SYM
ap-6304	267	11	=	=	SYM
ap-6304	267	12	ε̃2	ε̃2	PROPN
ap-6304	267	13	a∆x	a∆x	PROPN
ap-6304	267	14	2	2	NUM
ap-6304	267	15	uxx	uxx	NOUN
ap-6304	267	16	+	+	X
ap-6304	267	17	ε̃3	ε̃3	PROPN
ap-6304	267	18	a∆x2	a∆x2	ADP
ap-6304	267	19	6	6	NUM
ap-6304	267	20	uxxx	uxxx	NOUN
ap-6304	267	21	where	where	SCONJ
ap-6304	267	22	the	the	DET
ap-6304	267	23	non	non	ADJ
ap-6304	267	24	-	-	ADJ
ap-6304	267	25	dimensional	dimensional	ADJ
ap-6304	267	26	coefficients	coefficient	NOUN
ap-6304	267	27	ε̃2	ε̃2	PROPN
ap-6304	267	28	and	and	CCONJ
ap-6304	267	29	ε̃3	ε̃3	PROPN
ap-6304	267	30	are	be	AUX
ap-6304	267	31	functions	function	NOUN
ap-6304	267	32	of	of	ADP
ap-6304	267	33	the	the	DET
ap-6304	267	34	cfl	cfl	NOUN
ap-6304	267	35	parameter	parameter	PROPN
ap-6304	267	36	γ	γ	PROPN
ap-6304	267	37	.	.	PUNCT
ap-6304	268	1	this	this	DET
ap-6304	268	2	dependence	dependence	NOUN
ap-6304	268	3	of	of	ADP
ap-6304	268	4	numerical	numerical	ADJ
ap-6304	268	5	diffusion	diffusion	NOUN
ap-6304	268	6	and	and	CCONJ
ap-6304	268	7	dispersion	dispersion	NOUN
ap-6304	268	8	coefficients	coefficient	NOUN
ap-6304	268	9	is	be	AUX
ap-6304	268	10	obvious	obvious	ADJ
ap-6304	268	11	from	from	ADP
ap-6304	268	12	the	the	DET
ap-6304	268	13	tab	tab	NOUN
ap-6304	268	14	.	.	PUNCT
ap-6304	269	1	7	7	X
ap-6304	269	2	.	.	X
ap-6304	269	3	as	as	SCONJ
ap-6304	269	4	already	already	ADV
ap-6304	269	5	noted	note	VERB
ap-6304	269	6	in	in	ADP
ap-6304	269	7	the	the	DET
ap-6304	269	8	case	case	NOUN
ap-6304	269	9	of	of	ADP
ap-6304	269	10	the	the	DET
ap-6304	269	11	discrete	discrete	ADJ
ap-6304	269	12	analysis	analysis	NOUN
ap-6304	269	13	of	of	ADP
ap-6304	269	14	classical	classical	ADJ
ap-6304	269	15	schemes	scheme	NOUN
ap-6304	269	16	(	(	PUNCT
ap-6304	269	17	end	end	NOUN
ap-6304	269	18	of	of	ADP
ap-6304	269	19	section	section	NOUN
ap-6304	269	20	3	3	NUM
ap-6304	269	21	)	)	PUNCT
ap-6304	269	22	,	,	PUNCT
ap-6304	269	23	the	the	DET
ap-6304	269	24	amount	amount	NOUN
ap-6304	269	25	of	of	ADP
ap-6304	269	26	added	add	VERB
ap-6304	269	27	numerical	numerical	ADJ
ap-6304	269	28	viscosity	viscosity	NOUN
ap-6304	269	29	(	(	PUNCT
ap-6304	269	30	diffusion	diffusion	NOUN
ap-6304	269	31	)	)	PUNCT
ap-6304	269	32	is	be	AUX
ap-6304	269	33	responsible	responsible	ADJ
ap-6304	269	34	for	for	ADP
ap-6304	269	35	the	the	DET
ap-6304	269	36	essential	essential	ADJ
ap-6304	269	37	properties	property	NOUN
ap-6304	269	38	and	and	CCONJ
ap-6304	269	39	behavior	behavior	NOUN
ap-6304	269	40	of	of	ADP
ap-6304	269	41	each	each	DET
ap-6304	269	42	scheme	scheme	NOUN
ap-6304	269	43	.	.	PUNCT
ap-6304	270	1	5.1	5.1	NUM
ap-6304	270	2	.	.	PUNCT
ap-6304	271	1	diffusive	diffusive	ADJ
ap-6304	271	2	schemes	scheme	NOUN
ap-6304	271	3	the	the	DET
ap-6304	271	4	schemes	scheme	NOUN
ap-6304	271	5	,	,	PUNCT
ap-6304	271	6	for	for	ADP
ap-6304	271	7	which	which	PRON
ap-6304	271	8	the	the	DET
ap-6304	271	9	leading	lead	VERB
ap-6304	271	10	order	order	NOUN
ap-6304	271	11	term	term	NOUN
ap-6304	271	12	on	on	ADP
ap-6304	271	13	the	the	DET
ap-6304	271	14	right	right	ADJ
ap-6304	271	15	-	-	PUNCT
ap-6304	271	16	hand	hand	NOUN
ap-6304	271	17	side	side	NOUN
ap-6304	271	18	of	of	ADP
ap-6304	271	19	the	the	DET
ap-6304	271	20	modified	modify	VERB
ap-6304	271	21	equation	equation	NOUN
ap-6304	271	22	is	be	AUX
ap-6304	271	23	the	the	DET
ap-6304	271	24	diffusive	diffusive	ADJ
ap-6304	271	25	term	term	NOUN
ap-6304	271	26	ε̃2	ε̃2	PROPN
ap-6304	271	27	a∆x	a∆x	ADP
ap-6304	271	28	2	2	NUM
ap-6304	271	29	uxx	uxx	NOUN
ap-6304	271	30	are	be	AUX
ap-6304	271	31	of	of	ADP
ap-6304	271	32	the	the	DET
ap-6304	271	33	first	first	ADJ
ap-6304	271	34	order	order	NOUN
ap-6304	271	35	of	of	ADP
ap-6304	271	36	accuracy	accuracy	NOUN
ap-6304	271	37	.	.	PUNCT
ap-6304	272	1	if	if	SCONJ
ap-6304	272	2	the	the	DET
ap-6304	272	3	sign	sign	NOUN
ap-6304	272	4	of	of	ADP
ap-6304	272	5	the	the	DET
ap-6304	272	6	numerical	numerical	ADJ
ap-6304	272	7	viscosity	viscosity	NOUN
ap-6304	272	8	coefficient	coefficient	NOUN
ap-6304	272	9	ε̃2	ε̃2	PROPN
ap-6304	272	10	is	be	AUX
ap-6304	272	11	positive	positive	ADJ
ap-6304	272	12	,	,	PUNCT
ap-6304	272	13	the	the	DET
ap-6304	272	14	scheme	scheme	NOUN
ap-6304	272	15	is	be	AUX
ap-6304	272	16	stable	stable	ADJ
ap-6304	272	17	and	and	CCONJ
ap-6304	272	18	it	it	PRON
ap-6304	272	19	’s	’	VERB
ap-6304	272	20	behavior	behavior	NOUN
ap-6304	272	21	is	be	AUX
ap-6304	272	22	diffusive	diffusive	ADJ
ap-6304	272	23	.	.	PUNCT
ap-6304	273	1	the	the	DET
ap-6304	273	2	negative	negative	ADJ
ap-6304	273	3	sign	sign	NOUN
ap-6304	273	4	of	of	ADP
ap-6304	273	5	ε̃2	ε̃2	PROPN
ap-6304	273	6	indicates	indicate	VERB
ap-6304	273	7	that	that	SCONJ
ap-6304	273	8	the	the	DET
ap-6304	273	9	scheme	scheme	NOUN
ap-6304	273	10	is	be	AUX
ap-6304	273	11	unstable	unstable	ADJ
ap-6304	273	12	.	.	PUNCT
ap-6304	274	1	the	the	DET
ap-6304	274	2	typical	typical	ADJ
ap-6304	274	3	behavior	behavior	NOUN
ap-6304	274	4	of	of	ADP
ap-6304	274	5	first	first	ADJ
ap-6304	274	6	order	order	NOUN
ap-6304	274	7	schemes	scheme	NOUN
ap-6304	274	8	is	be	AUX
ap-6304	274	9	shown	show	VERB
ap-6304	274	10	in	in	ADP
ap-6304	274	11	the	the	DET
ap-6304	274	12	fig	fig	NOUN
ap-6304	274	13	.	.	PUNCT
ap-6304	275	1	6	6	NUM
ap-6304	275	2	for	for	ADP
ap-6304	275	3	up	up	NOUN
ap-6304	275	4	-	-	PUNCT
ap-6304	275	5	wind	wind	NOUN
ap-6304	275	6	and	and	CCONJ
ap-6304	275	7	in	in	ADP
ap-6304	275	8	fig	fig	NOUN
ap-6304	275	9	.	.	PUNCT
ap-6304	276	1	7	7	NUM
ap-6304	276	2	for	for	ADP
ap-6304	276	3	laxfriedrichs	laxfriedrichs	ADJ
ap-6304	276	4	scheme	scheme	NOUN
ap-6304	276	5	.	.	PUNCT
ap-6304	277	1	the	the	DET
ap-6304	277	2	same	same	ADJ
ap-6304	277	3	initial	initial	ADJ
ap-6304	277	4	value	value	NOUN
ap-6304	277	5	problem	problem	NOUN
ap-6304	277	6	is	be	AUX
ap-6304	277	7	solved	solve	VERB
ap-6304	277	8	for	for	ADP
ap-6304	277	9	piece	piece	NOUN
ap-6304	277	10	-	-	PUNCT
ap-6304	277	11	wise	wise	ADJ
ap-6304	277	12	constant	constant	ADJ
ap-6304	277	13	initial	initial	ADJ
ap-6304	277	14	data	datum	NOUN
ap-6304	277	15	.	.	PUNCT
ap-6304	278	1	the	the	DET
ap-6304	278	2	analytical	analytical	ADJ
ap-6304	278	3	solution	solution	NOUN
ap-6304	278	4	corresponds	correspond	VERB
ap-6304	278	5	to	to	ADP
ap-6304	278	6	the	the	DET
ap-6304	278	7	"	"	PUNCT
ap-6304	278	8	shifted	shift	VERB
ap-6304	278	9	"	"	PUNCT
ap-6304	278	10	original	original	ADJ
ap-6304	278	11	data	datum	NOUN
ap-6304	278	12	.	.	PUNCT
ap-6304	279	1	the	the	DET
ap-6304	279	2	discrete	discrete	ADJ
ap-6304	279	3	numerical	numerical	ADJ
ap-6304	279	4	solution	solution	NOUN
ap-6304	279	5	obtained	obtain	VERB
ap-6304	279	6	using	use	VERB
ap-6304	279	7	each	each	DET
ap-6304	279	8	scheme	scheme	NOUN
ap-6304	279	9	is	be	AUX
ap-6304	279	10	marked	mark	VERB
ap-6304	279	11	by	by	ADP
ap-6304	279	12	circles	circle	NOUN
ap-6304	279	13	in	in	ADP
ap-6304	279	14	the	the	DET
ap-6304	279	15	corresponding	corresponding	ADJ
ap-6304	279	16	plots	plot	NOUN
ap-6304	279	17	.	.	PUNCT
ap-6304	280	1	while	while	SCONJ
ap-6304	280	2	the	the	DET
ap-6304	280	3	sign	sign	NOUN
ap-6304	280	4	of	of	ADP
ap-6304	280	5	ε̃2	ε̃2	PROPN
ap-6304	280	6	determines	determine	VERB
ap-6304	280	7	the	the	DET
ap-6304	280	8	stability	stability	NOUN
ap-6304	280	9	of	of	ADP
ap-6304	280	10	the	the	DET
ap-6304	280	11	numerical	numerical	ADJ
ap-6304	280	12	method	method	NOUN
ap-6304	280	13	,	,	PUNCT
ap-6304	280	14	the	the	DET
ap-6304	280	15	size	size	NOUN
ap-6304	280	16	of	of	ADP
ap-6304	280	17	ε̃2	ε̃2	PROPN
ap-6304	280	18	is	be	AUX
ap-6304	280	19	responsible	responsible	ADJ
ap-6304	280	20	for	for	ADP
ap-6304	280	21	the	the	DET
ap-6304	280	22	amount	amount	NOUN
ap-6304	280	23	of	of	ADP
ap-6304	280	24	added	add	VERB
ap-6304	280	25	numerical	numerical	ADJ
ap-6304	280	26	diffusion	diffusion	NOUN
ap-6304	280	27	.	.	PUNCT
ap-6304	281	1	the	the	PRON
ap-6304	281	2	higher	high	ADJ
ap-6304	281	3	the	the	DET
ap-6304	281	4	coefficient	coefficient	NOUN
ap-6304	281	5	,	,	PUNCT
ap-6304	281	6	the	the	DET
ap-6304	281	7	more	more	ADV
ap-6304	281	8	diffused	diffused	ADJ
ap-6304	281	9	(	(	PUNCT
ap-6304	281	10	smeared	smeared	NOUN
ap-6304	281	11	)	)	PUNCT
ap-6304	281	12	the	the	DET
ap-6304	281	13	solution	solution	NOUN
ap-6304	281	14	will	will	AUX
ap-6304	281	15	be	be	AUX
ap-6304	281	16	.	.	PUNCT
ap-6304	282	1	by	by	ADP
ap-6304	282	2	comparing	compare	VERB
ap-6304	282	3	the	the	DET
ap-6304	282	4	lax	lax	NOUN
ap-6304	282	5	-	-	PUNCT
ap-6304	282	6	friedrichs	friedrich	NOUN
ap-6304	282	7	and	and	CCONJ
ap-6304	282	8	the	the	DET
ap-6304	282	9	upwind	upwind	NOUN
ap-6304	282	10	schemes	scheme	NOUN
ap-6304	282	11	modified	modify	VERB
ap-6304	282	12	equations	equation	NOUN
ap-6304	282	13	it	it	PRON
ap-6304	282	14	is	be	AUX
ap-6304	282	15	clear	clear	ADJ
ap-6304	282	16	that	that	SCONJ
ap-6304	282	17	for	for	ADP
ap-6304	282	18	given	give	VERB
ap-6304	282	19	cfl	cfl	NOUN
ap-6304	282	20	parameter	parameter	NOUN
ap-6304	282	21	γ	γ	PROPN
ap-6304	282	22	the	the	DET
ap-6304	282	23	numerical	numerical	ADJ
ap-6304	282	24	viscosity	viscosity	NOUN
ap-6304	282	25	coefficient	coefficient	NOUN
ap-6304	282	26	ε̃2	ε̃2	X
ap-6304	282	27	=	=	SYM
ap-6304	282	28	(	(	PUNCT
ap-6304	282	29	1	1	NUM
ap-6304	282	30	γ	γ	NOUN
ap-6304	282	31	−	−	PROPN
ap-6304	282	32	γ	γ	NOUN
ap-6304	282	33	)	)	PUNCT
ap-6304	282	34	of	of	ADP
ap-6304	282	35	the	the	DET
ap-6304	282	36	[	[	X
ap-6304	282	37	lf	lf	NOUN
ap-6304	282	38	]	]	X
ap-6304	282	39	scheme	scheme	NOUN
ap-6304	282	40	is	be	AUX
ap-6304	282	41	always	always	ADV
ap-6304	282	42	greater	great	ADJ
ap-6304	282	43	than	than	ADP
ap-6304	282	44	the	the	DET
ap-6304	282	45	ε̃2	ε̃2	PROPN
ap-6304	282	46	=	=	SYM
ap-6304	282	47	(	(	PUNCT
ap-6304	282	48	1−γ	1−γ	NUM
ap-6304	282	49	)	)	PUNCT
ap-6304	282	50	of	of	ADP
ap-6304	282	51	the	the	DET
ap-6304	282	52	[	[	X
ap-6304	282	53	u	u	X
ap-6304	282	54	]	]	X
ap-6304	282	55	scheme	scheme	NOUN
ap-6304	282	56	.	.	PUNCT
ap-6304	283	1	so	so	ADV
ap-6304	283	2	the	the	DET
ap-6304	283	3	lax	lax	NOUN
ap-6304	283	4	-	-	PUNCT
ap-6304	283	5	friedrichs	friedrich	NOUN
ap-6304	283	6	will	will	AUX
ap-6304	283	7	be	be	AUX
ap-6304	283	8	more	more	ADV
ap-6304	283	9	diffusive	diffusive	ADJ
ap-6304	283	10	than	than	ADP
ap-6304	283	11	the	the	DET
ap-6304	283	12	up	up	ADJ
ap-6304	283	13	-	-	PUNCT
ap-6304	283	14	wind	wind	NOUN
ap-6304	283	15	scheme	scheme	NOUN
ap-6304	283	16	.	.	PUNCT
ap-6304	284	1	this	this	PRON
ap-6304	284	2	is	be	AUX
ap-6304	284	3	also	also	ADV
ap-6304	284	4	well	well	ADV
ap-6304	284	5	visible	visible	ADJ
ap-6304	284	6	in	in	ADP
ap-6304	284	7	the	the	DET
ap-6304	284	8	corresponding	corresponding	ADJ
ap-6304	284	9	numerical	numerical	ADJ
ap-6304	284	10	solutions	solution	NOUN
ap-6304	284	11	in	in	ADP
ap-6304	284	12	the	the	DET
ap-6304	284	13	figs	fig	NOUN
ap-6304	284	14	.	.	PUNCT
ap-6304	285	1	6	6	NUM
ap-6304	285	2	and	and	CCONJ
ap-6304	285	3	7	7	NUM
ap-6304	285	4	.	.	X
ap-6304	285	5	55	55	NUM
ap-6304	285	6	t.	t.	NOUN
ap-6304	285	7	bodnár	bodnár	NOUN
ap-6304	285	8	,	,	PUNCT
ap-6304	285	9	ph	ph	PROPN
ap-6304	285	10	.	.	PROPN
ap-6304	285	11	fraunié	fraunié	PROPN
ap-6304	285	12	,	,	PUNCT
ap-6304	285	13	k.	k.	PROPN
ap-6304	285	14	kozel	kozel	PROPN
ap-6304	285	15	acta	acta	PROPN
ap-6304	285	16	polytechnica	polytechnica	PROPN
ap-6304	285	17	scheme	scheme	PROPN
ap-6304	285	18	ε̃2	ε̃2	PROPN
ap-6304	285	19	ε̃3	ε̃3	PROPN
ap-6304	285	20	behavior	behavior	NOUN
ap-6304	286	1	[	[	X
ap-6304	286	2	u	u	X
ap-6304	286	3	]	]	X
ap-6304	286	4	1−	1−	NUM
ap-6304	286	5	γ	γ	X
ap-6304	286	6	·	·	PUNCT
ap-6304	286	7	·	·	PUNCT
ap-6304	286	8	·	·	PUNCT
ap-6304	286	9	ε2	ε2	ADV
ap-6304	286	10	>	>	X
ap-6304	286	11	0	0	PUNCT
ap-6304	286	12	diffusive	diffusive	ADJ
ap-6304	287	1	[	[	X
ap-6304	287	2	d	d	X
ap-6304	287	3	]	]	X
ap-6304	287	4	−(1	−(1	NOUN
ap-6304	287	5	+	+	CCONJ
ap-6304	287	6	γ	γ	X
ap-6304	287	7	)	)	PUNCT
ap-6304	287	8	·	·	PUNCT
ap-6304	287	9	·	·	PUNCT
ap-6304	287	10	·	·	PUNCT
ap-6304	288	1	ε2	ε2	ADV
ap-6304	288	2	<	<	X
ap-6304	288	3	0	0	PUNCT
ap-6304	288	4	unstable	unstable	ADJ
ap-6304	288	5	[	[	X
ap-6304	288	6	c	c	X
ap-6304	288	7	]	]	X
ap-6304	288	8	−γ	−γ	NOUN
ap-6304	288	9	·	·	PUNCT
ap-6304	288	10	·	·	PUNCT
ap-6304	288	11	·	·	PUNCT
ap-6304	289	1	ε2	ε2	ADV
ap-6304	289	2	<	<	X
ap-6304	289	3	0	0	PUNCT
ap-6304	290	1	unstable	unstable	ADJ
ap-6304	290	2	[	[	X
ap-6304	290	3	lf	lf	X
ap-6304	290	4	]	]	X
ap-6304	290	5	1	1	NUM
ap-6304	290	6	γ	γ	NOUN
ap-6304	290	7	−	−	PROPN
ap-6304	290	8	γ	γ	X
ap-6304	290	9	·	·	PUNCT
ap-6304	290	10	·	·	PUNCT
ap-6304	290	11	·	·	PUNCT
ap-6304	291	1	ε2	ε2	ADV
ap-6304	291	2	>	>	X
ap-6304	291	3	0	0	PUNCT
ap-6304	291	4	diffusive	diffusive	ADJ
ap-6304	291	5	[	[	X
ap-6304	291	6	lw	lw	X
ap-6304	291	7	]	]	PUNCT
ap-6304	291	8	0	0	PUNCT
ap-6304	291	9	−(1−	−(1−	ADP
ap-6304	291	10	γ2	γ2	ADJ
ap-6304	291	11	)	)	PUNCT
ap-6304	291	12	ε3	ε3	PROPN
ap-6304	291	13	6=	6=	ADP
ap-6304	291	14	0	0	NUM
ap-6304	291	15	dispersive	dispersive	ADJ
ap-6304	292	1	[	[	X
ap-6304	292	2	w	w	X
ap-6304	292	3	]	]	X
ap-6304	292	4	0	0	NUM
ap-6304	293	1	−	−	NOUN
ap-6304	293	2	1	1	NUM
ap-6304	293	3	2	2	NUM
ap-6304	293	4	(	(	PUNCT
ap-6304	293	5	2	2	NUM
ap-6304	293	6	+	+	NUM
ap-6304	293	7	3γ	3γ	NUM
ap-6304	293	8	+	+	CCONJ
ap-6304	293	9	γ2	γ2	ADJ
ap-6304	293	10	)	)	PUNCT
ap-6304	293	11	ε3	ε3	PROPN
ap-6304	293	12	6=	6=	ADP
ap-6304	293	13	0	0	NUM
ap-6304	293	14	dispersive	dispersive	NOUN
ap-6304	294	1	[	[	X
ap-6304	294	2	cn	cn	X
ap-6304	294	3	]	]	X
ap-6304	294	4	0	0	NUM
ap-6304	294	5	−	−	NOUN
ap-6304	294	6	1	1	NUM
ap-6304	294	7	2	2	NUM
ap-6304	294	8	(	(	PUNCT
ap-6304	294	9	2	2	NUM
ap-6304	294	10	+	+	CCONJ
ap-6304	294	11	γ2	γ2	ADJ
ap-6304	294	12	)	)	PUNCT
ap-6304	294	13	ε3	ε3	PROPN
ap-6304	294	14	6=	6=	NUM
ap-6304	294	15	0	0	NUM
ap-6304	294	16	dispersive	dispersive	ADJ
ap-6304	294	17	table	table	NOUN
ap-6304	294	18	7	7	NUM
ap-6304	294	19	.	.	PUNCT
ap-6304	294	20	coefficients	coefficient	NOUN
ap-6304	294	21	of	of	ADP
ap-6304	294	22	numerical	numerical	ADJ
ap-6304	294	23	diffusion	diffusion	NOUN
ap-6304	294	24	and	and	CCONJ
ap-6304	294	25	dispersion	dispersion	NOUN
ap-6304	294	26	for	for	ADP
ap-6304	294	27	selected	select	VERB
ap-6304	294	28	schemes	scheme	NOUN
ap-6304	294	29	.	.	PUNCT
ap-6304	295	1	0	0	NUM
ap-6304	295	2	0.5	0.5	NUM
ap-6304	295	3	1	1	NUM
ap-6304	295	4	1.5	1.5	NUM
ap-6304	295	5	2	2	NUM
ap-6304	295	6	0.8	0.8	NUM
ap-6304	295	7	1	1	NUM
ap-6304	295	8	1.2	1.2	NUM
ap-6304	295	9	1.4	1.4	NUM
ap-6304	295	10	1.6	1.6	NUM
ap-6304	295	11	1.8	1.8	NUM
ap-6304	295	12	2	2	NUM
ap-6304	295	13	2.2	2.2	NUM
ap-6304	295	14	x−coordinate	x−coordinate	NOUN
ap-6304	295	15	u	u	PROPN
ap-6304	295	16	ut	ut	PROPN
ap-6304	295	17	+	+	PROPN
ap-6304	295	18	aux	aux	X
ap-6304	295	19	=	=	PUNCT
ap-6304	295	20	(	(	PUNCT
ap-6304	295	21	1	1	NUM
ap-6304	295	22	γ	γ	NOUN
ap-6304	295	23	−	−	PROPN
ap-6304	295	24	γ	γ	NOUN
ap-6304	295	25	)	)	PUNCT
ap-6304	295	26	a∆x	a∆x	PROPN
ap-6304	295	27	2	2	NUM
ap-6304	295	28	uxx	uxx	NOUN
ap-6304	295	29	figure	figure	NOUN
ap-6304	295	30	7	7	NUM
ap-6304	295	31	.	.	PUNCT
ap-6304	295	32	lax	lax	NOUN
ap-6304	295	33	-	-	PUNCT
ap-6304	295	34	friedrichs	friedrich	NOUN
ap-6304	295	35	[	[	X
ap-6304	295	36	lf	lf	X
ap-6304	295	37	]	]	PUNCT
ap-6304	295	38	scheme	scheme	NOUN
ap-6304	295	39	solution	solution	NOUN
ap-6304	295	40	and	and	CCONJ
ap-6304	295	41	modified	modify	VERB
ap-6304	295	42	equation	equation	NOUN
ap-6304	295	43	.	.	PUNCT
ap-6304	296	1	5.2	5.2	NUM
ap-6304	296	2	.	.	PUNCT
ap-6304	297	1	dispersive	dispersive	ADJ
ap-6304	297	2	schemes	scheme	NOUN
ap-6304	297	3	for	for	ADP
ap-6304	297	4	some	some	DET
ap-6304	297	5	schemes	scheme	NOUN
ap-6304	297	6	the	the	DET
ap-6304	297	7	first	first	ADJ
ap-6304	297	8	-	-	PUNCT
ap-6304	297	9	order	order	NOUN
ap-6304	297	10	diffusive	diffusive	ADJ
ap-6304	297	11	term	term	NOUN
ap-6304	297	12	vanishes	vanish	VERB
ap-6304	297	13	and	and	CCONJ
ap-6304	297	14	the	the	DET
ap-6304	297	15	dominant	dominant	ADJ
ap-6304	297	16	role	role	NOUN
ap-6304	297	17	in	in	ADP
ap-6304	297	18	the	the	DET
ap-6304	297	19	modified	modify	VERB
ap-6304	297	20	equation	equation	NOUN
ap-6304	297	21	is	be	AUX
ap-6304	297	22	played	play	VERB
ap-6304	297	23	by	by	ADP
ap-6304	297	24	the	the	DET
ap-6304	297	25	dispersive	dispersive	ADJ
ap-6304	297	26	term	term	NOUN
ap-6304	297	27	ε̃3	ε̃3	PROPN
ap-6304	297	28	a∆x2	a∆x2	CCONJ
ap-6304	297	29	6	6	NUM
ap-6304	297	30	uxxx	uxxx	NOUN
ap-6304	297	31	.	.	PUNCT
ap-6304	298	1	due	due	ADP
ap-6304	298	2	to	to	ADP
ap-6304	298	3	this	this	PRON
ap-6304	298	4	,	,	PUNCT
ap-6304	298	5	such	such	ADJ
ap-6304	298	6	schemes	scheme	NOUN
ap-6304	298	7	are	be	AUX
ap-6304	298	8	of	of	ADP
ap-6304	298	9	a	a	DET
ap-6304	298	10	second	second	ADJ
ap-6304	298	11	order	order	NOUN
ap-6304	298	12	and	and	CCONJ
ap-6304	298	13	their	their	PRON
ap-6304	298	14	behavior	behavior	NOUN
ap-6304	298	15	is	be	AUX
ap-6304	298	16	dispersive	dispersive	ADJ
ap-6304	298	17	.	.	PUNCT
ap-6304	299	1	the	the	DET
ap-6304	299	2	numerical	numerical	ADJ
ap-6304	299	3	solution	solution	NOUN
ap-6304	299	4	behaves	behave	VERB
ap-6304	299	5	much	much	ADV
ap-6304	299	6	more	more	ADJ
ap-6304	299	7	like	like	ADP
ap-6304	299	8	the	the	DET
ap-6304	299	9	solution	solution	NOUN
ap-6304	299	10	of	of	ADP
ap-6304	299	11	the	the	DET
ap-6304	299	12	advectiondispersion	advectiondispersion	NOUN
ap-6304	299	13	equation	equation	NOUN
ap-6304	299	14	.	.	PUNCT
ap-6304	300	1	it	it	PRON
ap-6304	300	2	means	mean	VERB
ap-6304	300	3	that	that	SCONJ
ap-6304	300	4	the	the	DET
ap-6304	300	5	advected	advected	ADJ
ap-6304	300	6	initial	initial	ADJ
ap-6304	300	7	data	datum	NOUN
ap-6304	300	8	are	be	AUX
ap-6304	300	9	decomposed	decompose	VERB
ap-6304	300	10	into	into	ADP
ap-6304	300	11	individual	individual	ADJ
ap-6304	300	12	fourier	fourier	NOUN
ap-6304	300	13	modes	mode	NOUN
ap-6304	300	14	and	and	CCONJ
ap-6304	300	15	each	each	PRON
ap-6304	300	16	of	of	ADP
ap-6304	300	17	them	they	PRON
ap-6304	300	18	propagates	propagate	VERB
ap-6304	300	19	at	at	ADP
ap-6304	300	20	a	a	DET
ap-6304	300	21	different	different	ADJ
ap-6304	300	22	velocity	velocity	NOUN
ap-6304	300	23	,	,	PUNCT
ap-6304	300	24	depending	depend	VERB
ap-6304	300	25	on	on	ADP
ap-6304	300	26	the	the	DET
ap-6304	300	27	corresponding	corresponding	ADJ
ap-6304	300	28	wave	wave	NOUN
ap-6304	300	29	-	-	PUNCT
ap-6304	300	30	number	number	NOUN
ap-6304	300	31	.	.	PUNCT
ap-6304	301	1	this	this	DET
ap-6304	301	2	kind	kind	NOUN
ap-6304	301	3	of	of	ADP
ap-6304	301	4	behavior	behavior	NOUN
ap-6304	301	5	can	can	AUX
ap-6304	301	6	be	be	AUX
ap-6304	301	7	observed	observe	VERB
ap-6304	301	8	for	for	ADP
ap-6304	301	9	lax	lax	NOUN
ap-6304	301	10	-	-	PUNCT
ap-6304	301	11	wendroff	wendroff	NOUN
ap-6304	301	12	and	and	CCONJ
ap-6304	301	13	wendroff	wendroff	VERB
ap-6304	301	14	schemes	scheme	NOUN
ap-6304	301	15	in	in	ADP
ap-6304	301	16	the	the	DET
ap-6304	301	17	fig	fig	NOUN
ap-6304	301	18	.	.	PUNCT
ap-6304	302	1	8	8	NUM
ap-6304	302	2	and	and	CCONJ
ap-6304	302	3	9	9	NUM
ap-6304	302	4	respectively	respectively	ADV
ap-6304	302	5	.	.	PUNCT
ap-6304	303	1	again	again	ADV
ap-6304	303	2	,	,	PUNCT
ap-6304	303	3	for	for	ADP
ap-6304	303	4	a	a	DET
ap-6304	303	5	given	give	VERB
ap-6304	303	6	cfl	cfl	NOUN
ap-6304	303	7	parameter	parameter	NOUN
ap-6304	303	8	γ	γ	PROPN
ap-6304	303	9	the	the	DET
ap-6304	303	10	numerical	numerical	ADJ
ap-6304	303	11	dispersion	dispersion	NOUN
ap-6304	303	12	coefficient	coefficient	NOUN
ap-6304	303	13	ε̃3	ε̃3	PROPN
ap-6304	303	14	=	=	PUNCT
ap-6304	303	15	−(1−	−(1−	ADP
ap-6304	303	16	γ2	γ2	NOUN
ap-6304	303	17	)	)	PUNCT
ap-6304	303	18	of	of	ADP
ap-6304	303	19	the	the	DET
ap-6304	303	20	[	[	X
ap-6304	303	21	lw	lw	X
ap-6304	303	22	]	]	X
ap-6304	303	23	scheme	scheme	NOUN
ap-6304	303	24	is	be	AUX
ap-6304	303	25	smaller	small	ADJ
ap-6304	303	26	(	(	PUNCT
ap-6304	303	27	in	in	ADP
ap-6304	303	28	the	the	DET
ap-6304	303	29	absolute	absolute	ADJ
ap-6304	303	30	value	value	NOUN
ap-6304	303	31	)	)	PUNCT
ap-6304	303	32	than	than	ADP
ap-6304	303	33	the	the	DET
ap-6304	303	34	coefficient	coefficient	NOUN
ap-6304	303	35	ε̃3	ε̃3	PROPN
ap-6304	303	36	=	=	SYM
ap-6304	303	37	−(2	−(2	PROPN
ap-6304	303	38	+	+	ADJ
ap-6304	303	39	3γ+γ2)/2	3γ+γ2)/2	NUM
ap-6304	303	40	for	for	ADP
ap-6304	303	41	the	the	DET
ap-6304	303	42	[	[	X
ap-6304	303	43	w	w	NOUN
ap-6304	303	44	]	]	X
ap-6304	303	45	scheme	scheme	NOUN
ap-6304	303	46	.	.	PUNCT
ap-6304	304	1	this	this	PRON
ap-6304	304	2	results	result	VERB
ap-6304	304	3	in	in	ADP
ap-6304	304	4	a	a	DET
ap-6304	304	5	less	less	ADV
ap-6304	304	6	dispersive	dispersive	ADJ
ap-6304	304	7	(	(	PUNCT
ap-6304	304	8	less	less	ADJ
ap-6304	304	9	oscillatory	oscillatory	ADJ
ap-6304	304	10	)	)	PUNCT
ap-6304	304	11	solution	solution	NOUN
ap-6304	304	12	obtained	obtain	VERB
ap-6304	304	13	using	use	VERB
ap-6304	304	14	the	the	DET
ap-6304	304	15	lax	lax	ADJ
ap-6304	304	16	-	-	PUNCT
ap-6304	304	17	wendroff	wendroff	NOUN
ap-6304	304	18	scheme	scheme	NOUN
ap-6304	304	19	.	.	PUNCT
ap-6304	305	1	6	6	NUM
ap-6304	305	2	.	.	NUM
ap-6304	305	3	limitations	limitation	NOUN
ap-6304	305	4	and	and	CCONJ
ap-6304	305	5	extensions	extension	NOUN
ap-6304	305	6	in	in	ADP
ap-6304	305	7	this	this	DET
ap-6304	305	8	paper	paper	NOUN
ap-6304	305	9	the	the	DET
ap-6304	305	10	presentation	presentation	NOUN
ap-6304	305	11	was	be	AUX
ap-6304	305	12	limited	limit	VERB
ap-6304	305	13	to	to	ADP
ap-6304	305	14	the	the	DET
ap-6304	305	15	finite	finite	ADJ
ap-6304	305	16	-	-	PUNCT
ap-6304	305	17	difference	difference	NOUN
ap-6304	305	18	approximation	approximation	NOUN
ap-6304	305	19	of	of	ADP
ap-6304	305	20	linear	linear	ADJ
ap-6304	305	21	advection	advection	NOUN
ap-6304	305	22	,	,	PUNCT
ap-6304	305	23	using	use	VERB
ap-6304	305	24	schemes	scheme	NOUN
ap-6304	305	25	with	with	ADP
ap-6304	305	26	three	three	NUM
ap-6304	305	27	-	-	PUNCT
ap-6304	305	28	point	point	NOUN
ap-6304	305	29	stencil	stencil	NOUN
ap-6304	305	30	operating	operate	VERB
ap-6304	305	31	at	at	ADP
ap-6304	305	32	two	two	NUM
ap-6304	305	33	time	time	NOUN
ap-6304	305	34	levels	level	NOUN
ap-6304	305	35	.	.	PUNCT
ap-6304	306	1	most	most	ADJ
ap-6304	306	2	of	of	ADP
ap-6304	306	3	these	these	DET
ap-6304	306	4	limiting	limit	VERB
ap-6304	306	5	assumptions	assumption	NOUN
ap-6304	306	6	can	can	AUX
ap-6304	306	7	be	be	AUX
ap-6304	306	8	removed	remove	VERB
ap-6304	306	9	or	or	CCONJ
ap-6304	306	10	relaxed	relaxed	ADJ
ap-6304	306	11	.	.	PUNCT
ap-6304	307	1	larger	large	ADJ
ap-6304	307	2	stencil	stencil	PROPN
ap-6304	307	3	and	and	CCONJ
ap-6304	307	4	more	more	ADJ
ap-6304	307	5	time	time	NOUN
ap-6304	307	6	levels	level	NOUN
ap-6304	307	7	can	can	AUX
ap-6304	307	8	be	be	AUX
ap-6304	307	9	used	use	VERB
ap-6304	307	10	to	to	PART
ap-6304	307	11	construct	construct	VERB
ap-6304	307	12	the	the	DET
ap-6304	307	13	scheme	scheme	NOUN
ap-6304	307	14	,	,	PUNCT
ap-6304	307	15	it	it	PRON
ap-6304	307	16	will	will	AUX
ap-6304	307	17	only	only	ADV
ap-6304	307	18	make	make	VERB
ap-6304	307	19	the	the	DET
ap-6304	307	20	analysis	analysis	NOUN
ap-6304	307	21	of	of	ADP
ap-6304	307	22	the	the	DET
ap-6304	307	23	scheme	scheme	NOUN
ap-6304	307	24	and	and	CCONJ
ap-6304	307	25	its	its	PRON
ap-6304	307	26	modified	modified	ADJ
ap-6304	307	27	0	0	NUM
ap-6304	307	28	0.5	0.5	NUM
ap-6304	307	29	1	1	NUM
ap-6304	307	30	1.5	1.5	NUM
ap-6304	307	31	2	2	NUM
ap-6304	307	32	0.8	0.8	NUM
ap-6304	307	33	1	1	NUM
ap-6304	307	34	1.2	1.2	NUM
ap-6304	307	35	1.4	1.4	NUM
ap-6304	307	36	1.6	1.6	NUM
ap-6304	307	37	1.8	1.8	NUM
ap-6304	307	38	2	2	NUM
ap-6304	307	39	2.2	2.2	NUM
ap-6304	307	40	x−coordinate	x−coordinate	NOUN
ap-6304	307	41	u	u	PROPN
ap-6304	307	42	ut	ut	PROPN
ap-6304	307	43	+	+	CCONJ
ap-6304	307	44	aux	aux	X
ap-6304	307	45	=	=	PUNCT
ap-6304	307	46	−(1−	−(1−	NOUN
ap-6304	307	47	γ2)a∆x2	γ2)a∆x2	PROPN
ap-6304	307	48	6	6	NUM
ap-6304	307	49	uxxx	uxxx	ADJ
ap-6304	307	50	figure	figure	NOUN
ap-6304	307	51	8	8	NUM
ap-6304	307	52	.	.	PUNCT
ap-6304	308	1	lax	lax	NOUN
ap-6304	308	2	-	-	PUNCT
ap-6304	308	3	wendroff	wendroff	NOUN
ap-6304	308	4	[	[	X
ap-6304	308	5	lw	lw	X
ap-6304	308	6	]	]	PUNCT
ap-6304	308	7	scheme	scheme	NOUN
ap-6304	308	8	solution	solution	NOUN
ap-6304	308	9	and	and	CCONJ
ap-6304	308	10	modified	modify	VERB
ap-6304	308	11	equation	equation	NOUN
ap-6304	308	12	.	.	PUNCT
ap-6304	309	1	0	0	NUM
ap-6304	309	2	0.5	0.5	NUM
ap-6304	309	3	1	1	NUM
ap-6304	309	4	1.5	1.5	NUM
ap-6304	309	5	2	2	NUM
ap-6304	309	6	0.8	0.8	NUM
ap-6304	309	7	1	1	NUM
ap-6304	309	8	1.2	1.2	NUM
ap-6304	309	9	1.4	1.4	NUM
ap-6304	309	10	1.6	1.6	NUM
ap-6304	309	11	1.8	1.8	NUM
ap-6304	309	12	2	2	NUM
ap-6304	309	13	2.2	2.2	NUM
ap-6304	309	14	x−coordinate	x−coordinate	NOUN
ap-6304	309	15	u	u	PROPN
ap-6304	309	16	ut	ut	PROPN
ap-6304	309	17	+	+	CCONJ
ap-6304	309	18	aux	aux	X
ap-6304	309	19	=	=	PUNCT
ap-6304	309	20	−(2	−(2	PROPN
ap-6304	309	21	+	+	NUM
ap-6304	309	22	3γ	3γ	NUM
ap-6304	309	23	+	+	CCONJ
ap-6304	309	24	γ2)a∆x2	γ2)a∆x2	SYM
ap-6304	309	25	12	12	NUM
ap-6304	309	26	uxxx	uxxx	ADJ
ap-6304	309	27	figure	figure	NOUN
ap-6304	309	28	9	9	NUM
ap-6304	309	29	.	.	PUNCT
ap-6304	310	1	wendroff	wendroff	PROPN
ap-6304	311	1	[	[	X
ap-6304	311	2	w	w	X
ap-6304	311	3	]	]	X
ap-6304	311	4	scheme	scheme	NOUN
ap-6304	311	5	solution	solution	NOUN
ap-6304	311	6	and	and	CCONJ
ap-6304	311	7	modified	modify	VERB
ap-6304	311	8	equation	equation	NOUN
ap-6304	311	9	.	.	PUNCT
ap-6304	312	1	equation	equation	NOUN
ap-6304	312	2	derivation	derivation	NOUN
ap-6304	312	3	more	more	ADV
ap-6304	312	4	difficult	difficult	ADJ
ap-6304	312	5	(	(	PUNCT
ap-6304	312	6	time	time	NOUN
ap-6304	312	7	consuming	consume	VERB
ap-6304	312	8	)	)	PUNCT
ap-6304	312	9	,	,	PUNCT
ap-6304	312	10	however	however	ADV
ap-6304	312	11	it	it	PRON
ap-6304	312	12	can	can	AUX
ap-6304	312	13	easily	easily	ADV
ap-6304	312	14	be	be	AUX
ap-6304	312	15	done	do	VERB
ap-6304	312	16	.	.	PUNCT
ap-6304	313	1	the	the	DET
ap-6304	313	2	only	only	ADJ
ap-6304	313	3	important	important	ADJ
ap-6304	313	4	limitation	limitation	NOUN
ap-6304	313	5	is	be	AUX
ap-6304	313	6	that	that	SCONJ
ap-6304	313	7	the	the	DET
ap-6304	313	8	schemes	scheme	NOUN
ap-6304	313	9	should	should	AUX
ap-6304	313	10	be	be	AUX
ap-6304	313	11	linear	linear	ADJ
ap-6304	313	12	in	in	ADP
ap-6304	313	13	the	the	DET
ap-6304	313	14	sense	sense	NOUN
ap-6304	313	15	that	that	SCONJ
ap-6304	313	16	their	their	PRON
ap-6304	313	17	coefficients	coefficient	NOUN
ap-6304	313	18	ca	can	AUX
ap-6304	313	19	n’t	not	PART
ap-6304	313	20	depend	depend	VERB
ap-6304	313	21	on	on	ADP
ap-6304	313	22	the	the	DET
ap-6304	313	23	solution	solution	NOUN
ap-6304	313	24	.	.	PUNCT
ap-6304	314	1	the	the	DET
ap-6304	314	2	non	non	ADJ
ap-6304	314	3	-	-	ADJ
ap-6304	314	4	linear	linear	ADJ
ap-6304	314	5	schemes	scheme	NOUN
ap-6304	314	6	case	case	NOUN
ap-6304	314	7	will	will	AUX
ap-6304	314	8	be	be	AUX
ap-6304	314	9	significantly	significantly	ADV
ap-6304	314	10	more	more	ADV
ap-6304	314	11	complicated	complicated	ADJ
ap-6304	314	12	,	,	PUNCT
ap-6304	314	13	although	although	SCONJ
ap-6304	314	14	some	some	DET
ap-6304	314	15	kind	kind	NOUN
ap-6304	314	16	of	of	ADP
ap-6304	314	17	local	local	ADJ
ap-6304	314	18	linearization	linearization	NOUN
ap-6304	314	19	(	(	PUNCT
ap-6304	314	20	frozen	frozen	ADJ
ap-6304	314	21	coefficients	coefficient	NOUN
ap-6304	314	22	)	)	PUNCT
ap-6304	314	23	would	would	AUX
ap-6304	314	24	probably	probably	ADV
ap-6304	314	25	give	give	VERB
ap-6304	314	26	at	at	ADP
ap-6304	314	27	least	least	ADJ
ap-6304	314	28	some	some	PRON
ap-6304	314	29	basic	basic	ADJ
ap-6304	314	30	information	information	NOUN
ap-6304	314	31	.	.	PUNCT
ap-6304	315	1	multidimensional	multidimensional	ADJ
ap-6304	315	2	schemes	scheme	NOUN
ap-6304	315	3	can	can	AUX
ap-6304	315	4	be	be	AUX
ap-6304	315	5	analyzed	analyze	VERB
ap-6304	315	6	in	in	ADP
ap-6304	315	7	a	a	DET
ap-6304	315	8	very	very	ADV
ap-6304	315	9	similar	similar	ADJ
ap-6304	315	10	way	way	NOUN
ap-6304	315	11	,	,	PUNCT
ap-6304	315	12	at	at	ADP
ap-6304	315	13	least	least	ADJ
ap-6304	315	14	on	on	ADP
ap-6304	315	15	regular	regular	ADJ
ap-6304	315	16	,	,	PUNCT
ap-6304	315	17	non	non	ADJ
ap-6304	315	18	-	-	ADJ
ap-6304	315	19	distorted	distorted	ADJ
ap-6304	315	20	grids	grid	NOUN
ap-6304	315	21	.	.	PUNCT
ap-6304	316	1	for	for	ADP
ap-6304	316	2	finite	finite	ADJ
ap-6304	316	3	-	-	PUNCT
ap-6304	316	4	volume	volume	NOUN
ap-6304	316	5	schemes	scheme	NOUN
ap-6304	316	6	such	such	ADJ
ap-6304	316	7	analysis	analysis	NOUN
ap-6304	316	8	can	can	AUX
ap-6304	316	9	be	be	AUX
ap-6304	316	10	performed	perform	VERB
ap-6304	316	11	on	on	ADP
ap-6304	316	12	arbitrary	arbitrary	ADJ
ap-6304	316	13	grids	grid	NOUN
ap-6304	316	14	,	,	PUNCT
ap-6304	316	15	based	base	VERB
ap-6304	316	16	on	on	ADP
ap-6304	316	17	the	the	DET
ap-6304	316	18	expression	expression	NOUN
ap-6304	316	19	and	and	CCONJ
ap-6304	316	20	splitting	splitting	NOUN
ap-6304	316	21	of	of	ADP
ap-6304	316	22	the	the	DET
ap-6304	316	23	numerical	numerical	ADJ
ap-6304	316	24	flux	flux	PROPN
ap-6304	316	25	as	as	ADP
ap-6304	316	26	a	a	DET
ap-6304	316	27	sum	sum	NOUN
ap-6304	316	28	of	of	ADP
ap-6304	316	29	the	the	DET
ap-6304	316	30	simple	simple	ADJ
ap-6304	316	31	56	56	NUM
ap-6304	316	32	vol	vol	NOUN
ap-6304	316	33	.	.	PUNCT
ap-6304	317	1	61	61	NUM
ap-6304	317	2	special	special	ADJ
ap-6304	317	3	issue/2021	issue/2021	NOUN
ap-6304	317	4	modified	modify	VERB
ap-6304	317	5	equation	equation	NOUN
ap-6304	317	6	for	for	ADP
ap-6304	317	7	explicit	explicit	ADJ
ap-6304	317	8	and	and	CCONJ
ap-6304	317	9	implicit	implicit	ADJ
ap-6304	317	10	schemes	scheme	NOUN
ap-6304	317	11	average	average	ADJ
ap-6304	317	12	central	central	ADJ
ap-6304	317	13	flux	flux	NOUN
ap-6304	317	14	and	and	CCONJ
ap-6304	317	15	a	a	DET
ap-6304	317	16	dissipative	dissipative	ADJ
ap-6304	317	17	stabilizing	stabilizing	NOUN
ap-6304	317	18	part	part	NOUN
ap-6304	317	19	[	[	X
ap-6304	317	20	5	5	NUM
ap-6304	317	21	,	,	PUNCT
ap-6304	317	22	6	6	NUM
ap-6304	317	23	]	]	PUNCT
ap-6304	317	24	.	.	PUNCT
ap-6304	318	1	based	base	VERB
ap-6304	318	2	on	on	ADP
ap-6304	318	3	the	the	DET
ap-6304	318	4	extra	extra	ADJ
ap-6304	318	5	dissipation	dissipation	NOUN
ap-6304	318	6	,	,	PUNCT
ap-6304	318	7	the	the	DET
ap-6304	318	8	properties	property	NOUN
ap-6304	318	9	of	of	ADP
ap-6304	318	10	the	the	DET
ap-6304	318	11	scheme	scheme	NOUN
ap-6304	318	12	can	can	AUX
ap-6304	318	13	be	be	AUX
ap-6304	318	14	shown	show	VERB
ap-6304	318	15	.	.	PUNCT
ap-6304	319	1	7	7	X
ap-6304	319	2	.	.	X
ap-6304	319	3	remark	remark	NOUN
ap-6304	319	4	on	on	ADP
ap-6304	319	5	applications	application	NOUN
ap-6304	319	6	based	base	VERB
ap-6304	319	7	on	on	ADP
ap-6304	319	8	a	a	DET
ap-6304	319	9	detailed	detailed	ADJ
ap-6304	319	10	knowledge	knowledge	NOUN
ap-6304	319	11	of	of	ADP
ap-6304	319	12	the	the	DET
ap-6304	319	13	diffusive	diffusive	ADJ
ap-6304	319	14	/	/	SYM
ap-6304	319	15	dispersive	dispersive	ADJ
ap-6304	319	16	behavior	behavior	NOUN
ap-6304	319	17	of	of	ADP
ap-6304	319	18	numerical	numerical	ADJ
ap-6304	319	19	schemes	scheme	NOUN
ap-6304	319	20	,	,	PUNCT
ap-6304	319	21	suitable	suitable	ADJ
ap-6304	319	22	strategy	strategy	NOUN
ap-6304	319	23	can	can	AUX
ap-6304	319	24	be	be	AUX
ap-6304	319	25	chosen	choose	VERB
ap-6304	319	26	to	to	PART
ap-6304	319	27	improve	improve	VERB
ap-6304	319	28	their	their	PRON
ap-6304	319	29	properties	property	NOUN
ap-6304	319	30	,	,	PUNCT
ap-6304	319	31	namely	namely	ADV
ap-6304	319	32	the	the	DET
ap-6304	319	33	stability	stability	NOUN
ap-6304	319	34	and	and	CCONJ
ap-6304	319	35	resolution	resolution	NOUN
ap-6304	319	36	.	.	PUNCT
ap-6304	320	1	the	the	DET
ap-6304	320	2	classical	classical	ADJ
ap-6304	320	3	way	way	NOUN
ap-6304	320	4	is	be	AUX
ap-6304	320	5	to	to	PART
ap-6304	320	6	modify	modify	VERB
ap-6304	320	7	the	the	DET
ap-6304	320	8	embedded	embed	VERB
ap-6304	320	9	numerical	numerical	ADJ
ap-6304	320	10	viscosity	viscosity	NOUN
ap-6304	320	11	of	of	ADP
ap-6304	320	12	the	the	DET
ap-6304	320	13	scheme	scheme	NOUN
ap-6304	320	14	.	.	PUNCT
ap-6304	321	1	it	it	PRON
ap-6304	321	2	can	can	AUX
ap-6304	321	3	be	be	AUX
ap-6304	321	4	done	do	VERB
ap-6304	321	5	for	for	ADP
ap-6304	321	6	example	example	NOUN
ap-6304	321	7	by	by	ADP
ap-6304	321	8	the	the	DET
ap-6304	321	9	following	follow	VERB
ap-6304	321	10	approaches	approach	NOUN
ap-6304	321	11	:	:	PUNCT
ap-6304	321	12	(	(	PUNCT
ap-6304	321	13	1	1	X
ap-6304	321	14	.	.	PUNCT
ap-6304	321	15	)	)	PUNCT
ap-6304	321	16	modify	modify	VERB
ap-6304	321	17	the	the	DET
ap-6304	321	18	coefficients	coefficient	NOUN
ap-6304	321	19	–	–	PUNCT
ap-6304	321	20	as	as	SCONJ
ap-6304	321	21	it	it	PRON
ap-6304	321	22	was	be	AUX
ap-6304	321	23	shown	show	VERB
ap-6304	321	24	in	in	ADP
ap-6304	321	25	section	section	NOUN
ap-6304	321	26	3	3	NUM
ap-6304	321	27	,	,	PUNCT
ap-6304	321	28	each	each	DET
ap-6304	321	29	scheme	scheme	NOUN
ap-6304	321	30	can	can	AUX
ap-6304	321	31	be	be	AUX
ap-6304	321	32	written	write	VERB
ap-6304	321	33	as	as	ADP
ap-6304	321	34	a	a	DET
ap-6304	321	35	sum	sum	NOUN
ap-6304	321	36	of	of	ADP
ap-6304	321	37	the	the	DET
ap-6304	321	38	central	central	ADJ
ap-6304	321	39	(	(	PUNCT
ap-6304	321	40	non	non	ADJ
ap-6304	321	41	-	-	ADJ
ap-6304	321	42	diffusive	diffusive	ADJ
ap-6304	321	43	)	)	PUNCT
ap-6304	321	44	part	part	NOUN
ap-6304	321	45	and	and	CCONJ
ap-6304	321	46	additional	additional	ADJ
ap-6304	321	47	internal	internal	ADJ
ap-6304	321	48	dissipative	dissipative	ADJ
ap-6304	321	49	part	part	NOUN
ap-6304	321	50	(	(	PUNCT
ap-6304	321	51	or	or	CCONJ
ap-6304	321	52	sum	sum	NOUN
ap-6304	321	53	of	of	ADP
ap-6304	321	54	down	down	NOUN
ap-6304	321	55	-	-	PUNCT
ap-6304	321	56	wind	wind	NOUN
ap-6304	321	57	and	and	CCONJ
ap-6304	321	58	up	up	ADJ
ap-6304	321	59	-	-	PUNCT
ap-6304	321	60	wind	wind	NOUN
ap-6304	321	61	parts	part	NOUN
ap-6304	321	62	alternatively	alternatively	ADV
ap-6304	321	63	)	)	PUNCT
ap-6304	321	64	.	.	PUNCT
ap-6304	322	1	the	the	DET
ap-6304	322	2	coefficient	coefficient	NOUN
ap-6304	322	3	of	of	ADP
ap-6304	322	4	internal	internal	ADJ
ap-6304	322	5	numerical	numerical	ADJ
ap-6304	322	6	viscosity	viscosity	NOUN
ap-6304	322	7	embedded	embed	VERB
ap-6304	322	8	in	in	ADP
ap-6304	322	9	the	the	DET
ap-6304	322	10	scheme	scheme	NOUN
ap-6304	322	11	can	can	AUX
ap-6304	322	12	be	be	AUX
ap-6304	322	13	modified	modify	VERB
ap-6304	322	14	and	and	CCONJ
ap-6304	322	15	adjusted	adjust	VERB
ap-6304	322	16	by	by	ADP
ap-6304	322	17	varying	vary	VERB
ap-6304	322	18	e.g.	e.g.	ADV
ap-6304	322	19	the	the	DET
ap-6304	322	20	blending	blend	VERB
ap-6304	322	21	parameter	parameter	NOUN
ap-6304	322	22	α	α	PROPN
ap-6304	322	23	and	and	CCONJ
ap-6304	322	24	balancing	balance	VERB
ap-6304	322	25	the	the	DET
ap-6304	322	26	amount	amount	NOUN
ap-6304	322	27	of	of	ADP
ap-6304	322	28	forward	forward	ADJ
ap-6304	322	29	and	and	CCONJ
ap-6304	322	30	backward	backward	ADJ
ap-6304	322	31	differences	difference	NOUN
ap-6304	322	32	in	in	ADP
ap-6304	322	33	the	the	DET
ap-6304	322	34	approximation	approximation	NOUN
ap-6304	322	35	.	.	PUNCT
ap-6304	323	1	for	for	ADP
ap-6304	323	2	modified	modify	VERB
ap-6304	323	3	lax	lax	ADJ
ap-6304	323	4	-	-	PUNCT
ap-6304	323	5	friedrichs	friedrichs	NOUN
ap-6304	323	6	scheme	scheme	NOUN
ap-6304	323	7	with	with	ADP
ap-6304	323	8	reduced	reduce	VERB
ap-6304	323	9	numerical	numerical	ADJ
ap-6304	323	10	viscosity	viscosity	NOUN
ap-6304	323	11	see	see	VERB
ap-6304	323	12	e.g.	e.g.	ADV
ap-6304	323	13	[	[	X
ap-6304	323	14	7	7	NUM
ap-6304	323	15	]	]	PUNCT
ap-6304	323	16	.	.	PUNCT
ap-6304	324	1	(	(	PUNCT
ap-6304	324	2	2	2	NUM
ap-6304	324	3	.	.	PUNCT
ap-6304	324	4	)	)	PUNCT
ap-6304	324	5	build	build	VERB
ap-6304	324	6	a	a	DET
ap-6304	324	7	composite	composite	ADJ
ap-6304	324	8	scheme	scheme	NOUN
ap-6304	324	9	–	–	PUNCT
ap-6304	324	10	two	two	NUM
ap-6304	324	11	schemes	scheme	NOUN
ap-6304	324	12	are	be	AUX
ap-6304	324	13	used	use	VERB
ap-6304	324	14	,	,	PUNCT
ap-6304	324	15	one	one	NUM
ap-6304	324	16	with	with	ADP
ap-6304	324	17	higher	high	ADJ
ap-6304	324	18	accuracy	accuracy	NOUN
ap-6304	324	19	(	(	PUNCT
ap-6304	324	20	typically	typically	ADV
ap-6304	324	21	dispersive	dispersive	VERB
ap-6304	324	22	)	)	PUNCT
ap-6304	324	23	and	and	CCONJ
ap-6304	324	24	one	one	NUM
ap-6304	324	25	with	with	ADP
ap-6304	324	26	lower	low	ADJ
ap-6304	324	27	accuracy	accuracy	NOUN
ap-6304	324	28	(	(	PUNCT
ap-6304	324	29	typically	typically	ADV
ap-6304	324	30	diffusive	diffusive	ADJ
ap-6304	324	31	)	)	PUNCT
ap-6304	324	32	.	.	PUNCT
ap-6304	325	1	during	during	ADP
ap-6304	325	2	the	the	DET
ap-6304	325	3	time	time	NOUN
ap-6304	325	4	-	-	PUNCT
ap-6304	325	5	stepping	step	VERB
ap-6304	325	6	process	process	NOUN
ap-6304	325	7	,	,	PUNCT
ap-6304	325	8	several	several	ADJ
ap-6304	325	9	steps	step	NOUN
ap-6304	325	10	are	be	AUX
ap-6304	325	11	performed	perform	VERB
ap-6304	325	12	using	use	VERB
ap-6304	325	13	the	the	DET
ap-6304	325	14	higher	high	ADJ
ap-6304	325	15	order	order	NOUN
ap-6304	325	16	(	(	PUNCT
ap-6304	325	17	but	but	CCONJ
ap-6304	325	18	usually	usually	ADV
ap-6304	325	19	oscillatory	oscillatory	ADJ
ap-6304	325	20	)	)	PUNCT
ap-6304	325	21	scheme	scheme	NOUN
ap-6304	325	22	,	,	PUNCT
ap-6304	325	23	followed	follow	VERB
ap-6304	325	24	by	by	ADP
ap-6304	325	25	a	a	DET
ap-6304	325	26	"	"	PUNCT
ap-6304	325	27	smoothing	smoothing	NOUN
ap-6304	325	28	"	"	PUNCT
ap-6304	325	29	step	step	NOUN
ap-6304	325	30	performed	perform	VERB
ap-6304	325	31	using	use	VERB
ap-6304	325	32	a	a	DET
ap-6304	325	33	lower	low	ADJ
ap-6304	325	34	order	order	NOUN
ap-6304	325	35	diffusive	diffusive	ADJ
ap-6304	325	36	scheme	scheme	NOUN
ap-6304	325	37	.	.	PUNCT
ap-6304	326	1	the	the	DET
ap-6304	326	2	ratio	ratio	NOUN
ap-6304	326	3	of	of	ADP
ap-6304	326	4	high	high	ADJ
ap-6304	326	5	/	/	SYM
ap-6304	326	6	low	low	ADJ
ap-6304	326	7	order	order	NOUN
ap-6304	326	8	steps	step	NOUN
ap-6304	326	9	can	can	AUX
ap-6304	326	10	be	be	AUX
ap-6304	326	11	tuned	tune	VERB
ap-6304	326	12	to	to	PART
ap-6304	326	13	optimize	optimize	VERB
ap-6304	326	14	the	the	DET
ap-6304	326	15	performance	performance	NOUN
ap-6304	326	16	of	of	ADP
ap-6304	326	17	the	the	DET
ap-6304	326	18	combined	combine	VERB
ap-6304	326	19	composite	composite	ADJ
ap-6304	326	20	method	method	NOUN
ap-6304	326	21	.	.	PUNCT
ap-6304	327	1	an	an	DET
ap-6304	327	2	example	example	NOUN
ap-6304	327	3	of	of	ADP
ap-6304	327	4	this	this	DET
ap-6304	327	5	technique	technique	NOUN
ap-6304	327	6	using	use	VERB
ap-6304	327	7	a	a	DET
ap-6304	327	8	combination	combination	NOUN
ap-6304	327	9	of	of	ADP
ap-6304	327	10	lax	lax	NOUN
ap-6304	327	11	-	-	PUNCT
ap-6304	327	12	wendroff	wendroff	NOUN
ap-6304	327	13	and	and	CCONJ
ap-6304	327	14	lax	lax	ADJ
ap-6304	327	15	-	-	PUNCT
ap-6304	327	16	friedrichs	friedrich	NOUN
ap-6304	327	17	scheme	scheme	NOUN
ap-6304	327	18	can	can	AUX
ap-6304	327	19	be	be	AUX
ap-6304	327	20	found	find	VERB
ap-6304	327	21	in	in	ADP
ap-6304	327	22	[	[	X
ap-6304	327	23	8	8	NUM
ap-6304	327	24	]	]	PUNCT
ap-6304	327	25	.	.	PUNCT
ap-6304	328	1	(	(	PUNCT
ap-6304	328	2	3	3	NUM
ap-6304	328	3	.	.	PUNCT
ap-6304	328	4	)	)	PUNCT
ap-6304	328	5	use	use	VERB
ap-6304	328	6	artificial	artificial	ADJ
ap-6304	328	7	viscosity	viscosity	NOUN
ap-6304	328	8	–	–	PUNCT
ap-6304	328	9	the	the	DET
ap-6304	328	10	splitting	splitting	NOUN
ap-6304	328	11	of	of	ADP
ap-6304	328	12	numerical	numerical	ADJ
ap-6304	328	13	methods	method	NOUN
ap-6304	328	14	into	into	ADP
ap-6304	328	15	the	the	DET
ap-6304	328	16	central	central	ADJ
ap-6304	328	17	and	and	CCONJ
ap-6304	328	18	viscous	viscous	ADJ
ap-6304	328	19	(	(	PUNCT
ap-6304	328	20	diffusive	diffusive	ADJ
ap-6304	328	21	)	)	PUNCT
ap-6304	328	22	part	part	NOUN
ap-6304	328	23	offers	offer	VERB
ap-6304	328	24	the	the	DET
ap-6304	328	25	possibility	possibility	NOUN
ap-6304	328	26	to	to	PART
ap-6304	328	27	use	use	VERB
ap-6304	328	28	always	always	ADV
ap-6304	328	29	the	the	DET
ap-6304	328	30	(	(	PUNCT
ap-6304	328	31	accurate	accurate	ADJ
ap-6304	328	32	but	but	CCONJ
ap-6304	328	33	unstable	unstable	ADJ
ap-6304	328	34	)	)	PUNCT
ap-6304	328	35	central	central	ADJ
ap-6304	328	36	scheme	scheme	NOUN
ap-6304	328	37	,	,	PUNCT
ap-6304	328	38	followed	follow	VERB
ap-6304	328	39	by	by	ADP
ap-6304	328	40	a	a	DET
ap-6304	328	41	separate	separate	ADJ
ap-6304	328	42	stabilizing	stabilizing	NOUN
ap-6304	328	43	step	step	NOUN
ap-6304	328	44	applying	apply	VERB
ap-6304	328	45	an	an	DET
ap-6304	328	46	artificial	artificial	ADJ
ap-6304	328	47	viscosity	viscosity	NOUN
ap-6304	328	48	term	term	NOUN
ap-6304	328	49	.	.	PUNCT
ap-6304	329	1	in	in	ADP
ap-6304	329	2	this	this	DET
ap-6304	329	3	way	way	NOUN
ap-6304	329	4	,	,	PUNCT
ap-6304	329	5	the	the	DET
ap-6304	329	6	numerical	numerical	ADJ
ap-6304	329	7	viscosity	viscosity	NOUN
ap-6304	329	8	is	be	AUX
ap-6304	329	9	separated	separate	VERB
ap-6304	329	10	and	and	CCONJ
ap-6304	329	11	no	no	ADV
ap-6304	329	12	longer	long	ADV
ap-6304	329	13	relies	rely	VERB
ap-6304	329	14	on	on	ADP
ap-6304	329	15	the	the	DET
ap-6304	329	16	form	form	NOUN
ap-6304	329	17	embedded	embed	VERB
ap-6304	329	18	(	(	PUNCT
ap-6304	329	19	hidden	hide	VERB
ap-6304	329	20	)	)	PUNCT
ap-6304	329	21	in	in	ADP
ap-6304	329	22	the	the	DET
ap-6304	329	23	numerical	numerical	ADJ
ap-6304	329	24	discretization	discretization	NOUN
ap-6304	329	25	.	.	PUNCT
ap-6304	330	1	the	the	DET
ap-6304	330	2	separate	separate	ADJ
ap-6304	330	3	,	,	PUNCT
ap-6304	330	4	stand	stand	VERB
ap-6304	330	5	alone	alone	ADV
ap-6304	330	6	,	,	PUNCT
ap-6304	330	7	numerical	numerical	ADJ
ap-6304	330	8	viscosity	viscosity	NOUN
ap-6304	330	9	can	can	AUX
ap-6304	330	10	be	be	AUX
ap-6304	330	11	designed	design	VERB
ap-6304	330	12	and	and	CCONJ
ap-6304	330	13	tuned	tune	VERB
ap-6304	330	14	for	for	ADP
ap-6304	330	15	the	the	DET
ap-6304	330	16	specific	specific	ADJ
ap-6304	330	17	problem	problem	NOUN
ap-6304	330	18	and	and	CCONJ
ap-6304	330	19	best	good	ADJ
ap-6304	330	20	performance	performance	NOUN
ap-6304	330	21	.	.	PUNCT
ap-6304	331	1	typically	typically	ADV
ap-6304	331	2	the	the	DET
ap-6304	331	3	second	second	ADJ
ap-6304	331	4	and	and	CCONJ
ap-6304	331	5	fourth	fourth	ADJ
ap-6304	331	6	order	order	NOUN
ap-6304	331	7	damping	damp	VERB
ap-6304	331	8	terms	term	NOUN
ap-6304	331	9	were	be	AUX
ap-6304	331	10	used	use	VERB
ap-6304	331	11	proportional	proportional	ADJ
ap-6304	331	12	to	to	ADP
ap-6304	331	13	second	second	ADJ
ap-6304	331	14	and	and	CCONJ
ap-6304	331	15	fourth	fourth	ADJ
ap-6304	331	16	order	order	NOUN
ap-6304	331	17	derivatives	derivative	NOUN
ap-6304	331	18	ε2uxx	ε2uxx	NUM
ap-6304	331	19	and	and	CCONJ
ap-6304	331	20	ε4uxxxx	ε4uxxxx	NOUN
ap-6304	331	21	.	.	PUNCT
ap-6304	332	1	more	more	ADV
ap-6304	332	2	efficient	efficient	ADJ
ap-6304	332	3	non	non	ADJ
ap-6304	332	4	-	-	ADJ
ap-6304	332	5	linear	linear	ADJ
ap-6304	332	6	numerical	numerical	ADJ
ap-6304	332	7	viscosities	viscosity	NOUN
ap-6304	332	8	can	can	AUX
ap-6304	332	9	be	be	AUX
ap-6304	332	10	constructed	construct	VERB
ap-6304	332	11	easily	easily	ADV
ap-6304	332	12	by	by	ADP
ap-6304	332	13	considering	consider	VERB
ap-6304	332	14	variable	variable	ADJ
ap-6304	332	15	,	,	PUNCT
ap-6304	332	16	solution	solution	NOUN
ap-6304	332	17	dependent	dependent	ADJ
ap-6304	332	18	,	,	PUNCT
ap-6304	332	19	numerical	numerical	ADJ
ap-6304	332	20	viscosity	viscosity	NOUN
ap-6304	332	21	coefficients	coefficient	VERB
ap-6304	332	22	ε2(u	ε2(u	PROPN
ap-6304	332	23	)	)	PUNCT
ap-6304	332	24	,	,	PUNCT
ap-6304	332	25	ε4(u	ε4(u	PROPN
ap-6304	332	26	)	)	PUNCT
ap-6304	332	27	.	.	PUNCT
ap-6304	333	1	when	when	SCONJ
ap-6304	333	2	these	these	DET
ap-6304	333	3	coefficients	coefficient	NOUN
ap-6304	333	4	are	be	AUX
ap-6304	333	5	kept	keep	VERB
ap-6304	333	6	small	small	ADJ
ap-6304	333	7	on	on	ADP
ap-6304	333	8	the	the	DET
ap-6304	333	9	smooth	smooth	ADJ
ap-6304	333	10	solution	solution	NOUN
ap-6304	333	11	and	and	CCONJ
ap-6304	333	12	only	only	ADV
ap-6304	333	13	locally	locally	ADV
ap-6304	333	14	increased	increase	VERB
ap-6304	333	15	where	where	SCONJ
ap-6304	333	16	the	the	DET
ap-6304	333	17	solution	solution	NOUN
ap-6304	333	18	has	have	VERB
ap-6304	333	19	high	high	ADJ
ap-6304	333	20	gradients	gradient	NOUN
ap-6304	333	21	or	or	CCONJ
ap-6304	333	22	is	be	AUX
ap-6304	333	23	oscillatory	oscillatory	ADJ
ap-6304	333	24	,	,	PUNCT
ap-6304	333	25	a	a	DET
ap-6304	333	26	good	good	ADJ
ap-6304	333	27	resolution	resolution	NOUN
ap-6304	333	28	properties	property	NOUN
ap-6304	333	29	can	can	AUX
ap-6304	333	30	be	be	AUX
ap-6304	333	31	preserved	preserve	VERB
ap-6304	333	32	while	while	SCONJ
ap-6304	333	33	the	the	DET
ap-6304	333	34	stability	stability	NOUN
ap-6304	333	35	and	and	CCONJ
ap-6304	333	36	robustness	robustness	NOUN
ap-6304	333	37	of	of	ADP
ap-6304	333	38	the	the	DET
ap-6304	333	39	method	method	NOUN
ap-6304	333	40	is	be	AUX
ap-6304	333	41	improved	improve	VERB
ap-6304	333	42	.	.	PUNCT
ap-6304	334	1	see	see	VERB
ap-6304	334	2	e.g.	e.g.	ADV
ap-6304	334	3	[	[	X
ap-6304	334	4	9	9	NUM
ap-6304	334	5	]	]	PUNCT
ap-6304	334	6	for	for	ADP
ap-6304	334	7	artificial	artificial	ADJ
ap-6304	334	8	viscosity	viscosity	NOUN
ap-6304	334	9	example	example	NOUN
ap-6304	334	10	and	and	CCONJ
ap-6304	334	11	application	application	NOUN
ap-6304	334	12	or	or	CCONJ
ap-6304	334	13	[	[	X
ap-6304	334	14	10	10	NUM
ap-6304	334	15	]	]	PUNCT
ap-6304	334	16	or	or	CCONJ
ap-6304	334	17	alternative	alternative	ADJ
ap-6304	334	18	filtering	filter	VERB
ap-6304	334	19	techniques	technique	NOUN
ap-6304	334	20	.	.	PUNCT
ap-6304	335	1	8	8	X
ap-6304	335	2	.	.	PUNCT
ap-6304	335	3	conclusions	conclusion	NOUN
ap-6304	335	4	and	and	CCONJ
ap-6304	335	5	remarks	remark	VERB
ap-6304	335	6	the	the	DET
ap-6304	335	7	discrete	discrete	ADJ
ap-6304	335	8	analysis	analysis	NOUN
ap-6304	335	9	based	base	VERB
ap-6304	335	10	on	on	ADP
ap-6304	335	11	a	a	DET
ap-6304	335	12	decomposition	decomposition	NOUN
ap-6304	335	13	of	of	ADP
ap-6304	335	14	the	the	DET
ap-6304	335	15	scheme	scheme	NOUN
ap-6304	335	16	into	into	ADP
ap-6304	335	17	a	a	DET
ap-6304	335	18	central	central	ADJ
ap-6304	335	19	and	and	CCONJ
ap-6304	335	20	diffusive	diffusive	ADJ
ap-6304	335	21	(	(	PUNCT
ap-6304	335	22	or	or	CCONJ
ap-6304	335	23	upwind	upwind	NOUN
ap-6304	335	24	)	)	PUNCT
ap-6304	335	25	part	part	NOUN
ap-6304	335	26	was	be	AUX
ap-6304	335	27	shown	show	VERB
ap-6304	335	28	for	for	ADP
ap-6304	335	29	a	a	DET
ap-6304	335	30	family	family	NOUN
ap-6304	335	31	of	of	ADP
ap-6304	335	32	explicit	explicit	ADJ
ap-6304	335	33	schemes	scheme	NOUN
ap-6304	335	34	.	.	PUNCT
ap-6304	336	1	a	a	DET
ap-6304	336	2	general	general	ADJ
ap-6304	336	3	modified	modify	VERB
ap-6304	336	4	equation	equation	NOUN
ap-6304	336	5	was	be	AUX
ap-6304	336	6	developed	develop	VERB
ap-6304	336	7	for	for	ADP
ap-6304	336	8	a	a	DET
ap-6304	336	9	large	large	ADJ
ap-6304	336	10	family	family	NOUN
ap-6304	336	11	of	of	ADP
ap-6304	336	12	explicit	explicit	ADJ
ap-6304	336	13	and	and	CCONJ
ap-6304	336	14	implicit	implicit	ADJ
ap-6304	336	15	schemes	scheme	NOUN
ap-6304	336	16	.	.	PUNCT
ap-6304	337	1	this	this	PRON
ap-6304	337	2	led	lead	VERB
ap-6304	337	3	to	to	ADP
ap-6304	337	4	a	a	DET
ap-6304	337	5	discussion	discussion	NOUN
ap-6304	337	6	concerning	concern	VERB
ap-6304	337	7	the	the	DET
ap-6304	337	8	diffusive	diffusive	ADJ
ap-6304	337	9	and	and	CCONJ
ap-6304	337	10	dispersive	dispersive	ADJ
ap-6304	337	11	properties	property	NOUN
ap-6304	337	12	of	of	ADP
ap-6304	337	13	numerical	numerical	ADJ
ap-6304	337	14	schemes	scheme	NOUN
ap-6304	337	15	.	.	PUNCT
ap-6304	338	1	most	most	ADJ
ap-6304	338	2	of	of	ADP
ap-6304	338	3	the	the	DET
ap-6304	338	4	partial	partial	ADJ
ap-6304	338	5	conclusions	conclusion	NOUN
ap-6304	338	6	were	be	AUX
ap-6304	338	7	already	already	ADV
ap-6304	338	8	formulated	formulate	VERB
ap-6304	338	9	in	in	ADP
ap-6304	338	10	the	the	DET
ap-6304	338	11	above	above	ADJ
ap-6304	338	12	sections	section	NOUN
ap-6304	338	13	.	.	PUNCT
ap-6304	339	1	let	let	VERB
ap-6304	339	2	’s	’s	PRON
ap-6304	339	3	just	just	ADV
ap-6304	339	4	point	point	VERB
ap-6304	339	5	out	out	ADP
ap-6304	339	6	again	again	ADV
ap-6304	339	7	some	some	DET
ap-6304	339	8	key	key	ADJ
ap-6304	339	9	points	point	NOUN
ap-6304	339	10	.	.	PUNCT
ap-6304	340	1	the	the	DET
ap-6304	340	2	numerical	numerical	ADJ
ap-6304	340	3	solution	solution	NOUN
ap-6304	340	4	of	of	ADP
ap-6304	340	5	the	the	DET
ap-6304	340	6	advection	advection	NOUN
ap-6304	340	7	equation	equation	NOUN
ap-6304	340	8	is	be	AUX
ap-6304	340	9	“	"	PUNCT
ap-6304	340	10	much	much	ADV
ap-6304	340	11	closer	close	ADJ
ap-6304	340	12	”	"	PUNCT
ap-6304	340	13	to	to	ADP
ap-6304	340	14	the	the	DET
ap-6304	340	15	solution	solution	NOUN
ap-6304	340	16	of	of	ADP
ap-6304	340	17	advection	advection	NOUN
ap-6304	340	18	-	-	PUNCT
ap-6304	340	19	diffusion	diffusion	NOUN
ap-6304	340	20	or	or	CCONJ
ap-6304	340	21	advection	advection	NOUN
ap-6304	340	22	-	-	PUNCT
ap-6304	340	23	dispersion	dispersion	NOUN
ap-6304	340	24	equation	equation	NOUN
ap-6304	340	25	,	,	PUNCT
ap-6304	340	26	depending	depend	VERB
ap-6304	340	27	which	which	PRON
ap-6304	340	28	is	be	AUX
ap-6304	340	29	the	the	DET
ap-6304	340	30	leading	lead	VERB
ap-6304	340	31	order	order	NOUN
ap-6304	340	32	term	term	NOUN
ap-6304	340	33	in	in	ADP
ap-6304	340	34	the	the	DET
ap-6304	340	35	discretization	discretization	NOUN
ap-6304	340	36	error	error	NOUN
ap-6304	340	37	.	.	PUNCT
ap-6304	341	1	the	the	DET
ap-6304	341	2	behavior	behavior	NOUN
ap-6304	341	3	and	and	CCONJ
ap-6304	341	4	quality	quality	NOUN
ap-6304	341	5	of	of	ADP
ap-6304	341	6	the	the	DET
ap-6304	341	7	numerical	numerical	ADJ
ap-6304	341	8	solution	solution	NOUN
ap-6304	341	9	heavily	heavily	ADV
ap-6304	341	10	depends	depend	VERB
ap-6304	341	11	on	on	ADP
ap-6304	341	12	the	the	DET
ap-6304	341	13	coefficients	coefficient	NOUN
ap-6304	341	14	of	of	ADP
ap-6304	341	15	the	the	DET
ap-6304	341	16	modified	modify	VERB
ap-6304	341	17	equation	equation	NOUN
ap-6304	341	18	.	.	PUNCT
ap-6304	342	1	their	their	PRON
ap-6304	342	2	knowledge	knowledge	NOUN
ap-6304	342	3	can	can	AUX
ap-6304	342	4	help	help	VERB
ap-6304	342	5	to	to	PART
ap-6304	342	6	assess	assess	VERB
ap-6304	342	7	a	a	DET
ap-6304	342	8	-	-	PUNCT
ap-6304	342	9	priori	priori	VERB
ap-6304	342	10	the	the	DET
ap-6304	342	11	behavior	behavior	NOUN
ap-6304	342	12	of	of	ADP
ap-6304	342	13	a	a	DET
ap-6304	342	14	numerical	numerical	ADJ
ap-6304	342	15	method	method	NOUN
ap-6304	342	16	.	.	PUNCT
ap-6304	343	1	the	the	DET
ap-6304	343	2	detailed	detailed	ADJ
ap-6304	343	3	knowledge	knowledge	NOUN
ap-6304	343	4	of	of	ADP
ap-6304	343	5	the	the	DET
ap-6304	343	6	structure	structure	NOUN
ap-6304	343	7	of	of	ADP
ap-6304	343	8	the	the	DET
ap-6304	343	9	leading	lead	VERB
ap-6304	343	10	order	order	NOUN
ap-6304	343	11	terms	term	NOUN
ap-6304	343	12	on	on	ADP
ap-6304	343	13	the	the	DET
ap-6304	343	14	right	right	ADJ
ap-6304	343	15	-	-	PUNCT
ap-6304	343	16	hand	hand	NOUN
ap-6304	343	17	side	side	NOUN
ap-6304	343	18	of	of	ADP
ap-6304	343	19	the	the	DET
ap-6304	343	20	modified	modify	VERB
ap-6304	343	21	equation	equation	NOUN
ap-6304	343	22	can	can	AUX
ap-6304	343	23	be	be	AUX
ap-6304	343	24	used	use	VERB
ap-6304	343	25	to	to	PART
ap-6304	343	26	construct	construct	VERB
ap-6304	343	27	the	the	DET
ap-6304	343	28	“	"	PUNCT
ap-6304	343	29	high(er	high(er	ADJ
ap-6304	343	30	)	)	PUNCT
ap-6304	343	31	resolution	resolution	NOUN
ap-6304	343	32	”	"	PUNCT
ap-6304	343	33	numerical	numerical	ADJ
ap-6304	343	34	methods	method	NOUN
ap-6304	343	35	.	.	PUNCT
ap-6304	344	1	acknowledgements	acknowledgement	NOUN
ap-6304	344	2	t.	t.	PROPN
ap-6304	344	3	bodnár	bodnár	PROPN
ap-6304	344	4	is	be	AUX
ap-6304	344	5	greatful	greatful	ADJ
ap-6304	344	6	for	for	ADP
ap-6304	344	7	the	the	DET
ap-6304	344	8	support	support	NOUN
ap-6304	344	9	provided	provide	VERB
ap-6304	344	10	by	by	ADP
ap-6304	344	11	the	the	DET
ap-6304	344	12	european	european	PROPN
ap-6304	344	13	regional	regional	PROPN
ap-6304	344	14	development	development	PROPN
ap-6304	344	15	fund	fund	NOUN
ap-6304	344	16	-	-	PUNCT
ap-6304	344	17	project	project	NOUN
ap-6304	344	18	“	"	PUNCT
ap-6304	344	19	center	center	NOUN
ap-6304	344	20	for	for	ADP
ap-6304	344	21	advanced	advanced	ADJ
ap-6304	344	22	applied	apply	VERB
ap-6304	344	23	science	science	NOUN
ap-6304	344	24	”	"	PUNCT
ap-6304	344	25	no.cz.02.1.01/0.0/0.0/16	no.cz.02.1.01/0.0/0.0/16	NOUN
ap-6304	344	26	019/0000778	019/0000778	NUM
ap-6304	344	27	and	and	CCONJ
ap-6304	344	28	partly	partly	ADV
ap-6304	344	29	by	by	ADP
ap-6304	344	30	the	the	DET
ap-6304	344	31	czech	czech	PROPN
ap-6304	344	32	science	science	NOUN
ap-6304	344	33	foundation	foundation	NOUN
ap-6304	344	34	under	under	ADP
ap-6304	344	35	the	the	DET
ap-6304	344	36	grant	grant	NOUN
ap-6304	344	37	no	no	NOUN
ap-6304	344	38	.	.	PUNCT
ap-6304	345	1	p201	p201	NUM
ap-6304	345	2	-	-	SYM
ap-6304	345	3	19	19	NUM
ap-6304	345	4	-	-	PUNCT
ap-6304	345	5	04243s	04243s	NUM
ap-6304	345	6	.	.	PUNCT
ap-6304	346	1	references	reference	NOUN
ap-6304	346	2	[	[	X
ap-6304	346	3	1	1	NUM
ap-6304	346	4	]	]	PUNCT
ap-6304	346	5	r.	r.	PROPN
ap-6304	346	6	j.	j.	PROPN
ap-6304	346	7	leveque	leveque	PROPN
ap-6304	346	8	.	.	PUNCT
ap-6304	347	1	finite	finite	ADJ
ap-6304	347	2	difference	difference	NOUN
ap-6304	347	3	methods	method	NOUN
ap-6304	347	4	for	for	ADP
ap-6304	347	5	ordinary	ordinary	ADJ
ap-6304	347	6	and	and	CCONJ
ap-6304	347	7	partial	partial	ADJ
ap-6304	347	8	differential	differential	ADJ
ap-6304	347	9	equations	equation	NOUN
ap-6304	347	10	:	:	PUNCT
ap-6304	347	11	steady	steady	ADJ
ap-6304	347	12	-	-	PUNCT
ap-6304	347	13	state	state	NOUN
ap-6304	347	14	and	and	CCONJ
ap-6304	347	15	time	time	NOUN
ap-6304	347	16	-	-	PUNCT
ap-6304	347	17	dependent	dependent	ADJ
ap-6304	347	18	problems	problem	NOUN
ap-6304	347	19	.	.	PUNCT
ap-6304	348	1	siam	siam	PROPN
ap-6304	348	2	,	,	PUNCT
ap-6304	348	3	2007	2007	NUM
ap-6304	348	4	.	.	PUNCT
ap-6304	349	1	[	[	X
ap-6304	349	2	2	2	X
ap-6304	349	3	]	]	PUNCT
ap-6304	349	4	c.	c.	PROPN
ap-6304	349	5	hirsch	hirsch	PROPN
ap-6304	349	6	.	.	PUNCT
ap-6304	350	1	numerical	numerical	PROPN
ap-6304	350	2	computation	computation	NOUN
ap-6304	350	3	of	of	ADP
ap-6304	350	4	internal	internal	ADJ
ap-6304	350	5	and	and	CCONJ
ap-6304	350	6	external	external	ADJ
ap-6304	350	7	flows	flow	NOUN
ap-6304	350	8	,	,	PUNCT
ap-6304	350	9	vol	vol	NOUN
ap-6304	350	10	.	.	PUNCT
ap-6304	350	11	1,2	1,2	NUM
ap-6304	350	12	.	.	PUNCT
ap-6304	351	1	john	john	PROPN
ap-6304	351	2	willey	willey	PROPN
ap-6304	351	3	&	&	CCONJ
ap-6304	351	4	sons	son	NOUN
ap-6304	351	5	,	,	PUNCT
ap-6304	351	6	1988	1988	NUM
ap-6304	351	7	.	.	PUNCT
ap-6304	352	1	[	[	X
ap-6304	352	2	3	3	X
ap-6304	352	3	]	]	X
ap-6304	352	4	j.	j.	PROPN
ap-6304	352	5	d.	d.	PROPN
ap-6304	352	6	anderson	anderson	PROPN
ap-6304	352	7	.	.	PUNCT
ap-6304	353	1	computational	computational	ADJ
ap-6304	353	2	techniques	technique	NOUN
ap-6304	353	3	for	for	ADP
ap-6304	353	4	fluid	fluid	ADJ
ap-6304	353	5	dynamics	dynamic	NOUN
ap-6304	353	6	,	,	PUNCT
ap-6304	353	7	vol	vol	NOUN
ap-6304	353	8	.	.	PROPN
ap-6304	353	9	1	1	NUM
ap-6304	353	10	-	-	SYM
ap-6304	353	11	2	2	NUM
ap-6304	353	12	of	of	ADP
ap-6304	353	13	springer	springer	NOUN
ap-6304	353	14	series	series	NOUN
ap-6304	353	15	in	in	ADP
ap-6304	353	16	computational	computational	ADJ
ap-6304	353	17	physics	physic	NOUN
ap-6304	353	18	.	.	PUNCT
ap-6304	354	1	springer	springer	NOUN
ap-6304	354	2	-	-	PUNCT
ap-6304	354	3	verlag	verlag	PROPN
ap-6304	354	4	berlin	berlin	PROPN
ap-6304	354	5	heidelberg	heidelberg	PROPN
ap-6304	354	6	,	,	PUNCT
ap-6304	354	7	2nd	2nd	ADJ
ap-6304	354	8	edn	edn	PROPN
ap-6304	354	9	.	.	PUNCT
ap-6304	354	10	,	,	PUNCT
ap-6304	354	11	1991	1991	NUM
ap-6304	354	12	.	.	PUNCT
ap-6304	355	1	[	[	X
ap-6304	355	2	4	4	X
ap-6304	355	3	]	]	PUNCT
ap-6304	355	4	c.	c.	PROPN
ap-6304	355	5	a.	a.	PROPN
ap-6304	355	6	j.	j.	PROPN
ap-6304	355	7	fletcher	fletcher	PROPN
ap-6304	355	8	.	.	PUNCT
ap-6304	356	1	computational	computational	ADJ
ap-6304	356	2	fluid	fluid	ADJ
ap-6304	356	3	dynamics	dynamic	NOUN
ap-6304	356	4	the	the	DET
ap-6304	356	5	basics	basic	NOUN
ap-6304	356	6	with	with	ADP
ap-6304	356	7	applications	application	NOUN
ap-6304	356	8	.	.	PUNCT
ap-6304	357	1	mcgraw	mcgraw	PROPN
ap-6304	357	2	-	-	PUNCT
ap-6304	357	3	hill	hill	PROPN
ap-6304	357	4	,	,	PUNCT
ap-6304	357	5	1995	1995	NUM
ap-6304	357	6	.	.	PUNCT
ap-6304	358	1	[	[	X
ap-6304	358	2	5	5	NUM
ap-6304	358	3	]	]	PUNCT
ap-6304	358	4	r.	r.	PROPN
ap-6304	358	5	j.	j.	PROPN
ap-6304	358	6	leveque	leveque	PROPN
ap-6304	358	7	.	.	PUNCT
ap-6304	359	1	numerical	numerical	ADJ
ap-6304	359	2	methods	method	NOUN
ap-6304	359	3	for	for	ADP
ap-6304	359	4	conservation	conservation	NOUN
ap-6304	359	5	laws	law	NOUN
ap-6304	359	6	.	.	PUNCT
ap-6304	360	1	lectures	lecture	NOUN
ap-6304	360	2	in	in	ADP
ap-6304	360	3	mathematics	mathematic	NOUN
ap-6304	360	4	.	.	PUNCT
ap-6304	361	1	birkhäuser	birkhäuser	PROPN
ap-6304	361	2	verlag	verlag	PROPN
ap-6304	361	3	,	,	PUNCT
ap-6304	361	4	1990	1990	NUM
ap-6304	361	5	.	.	PUNCT
ap-6304	362	1	[	[	X
ap-6304	362	2	6	6	NUM
ap-6304	362	3	]	]	PUNCT
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ap-6304	362	5	j.	j.	PROPN
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ap-6304	363	2	volume	volume	NOUN
ap-6304	363	3	methods	method	NOUN
ap-6304	363	4	for	for	ADP
ap-6304	363	5	hyperbolic	hyperbolic	ADJ
ap-6304	363	6	problems	problem	NOUN
ap-6304	363	7	.	.	PUNCT
ap-6304	364	1	cambridge	cambridge	NOUN
ap-6304	364	2	texts	text	NOUN
ap-6304	364	3	in	in	ADP
ap-6304	364	4	applied	applied	ADJ
ap-6304	364	5	mathematics	mathematic	NOUN
ap-6304	364	6	.	.	PUNCT
ap-6304	365	1	cambridge	cambridge	PROPN
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ap-6304	365	4	,	,	PUNCT
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ap-6304	365	6	.	.	PUNCT
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ap-6304	366	2	7	7	X
ap-6304	366	3	]	]	X
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ap-6304	366	5	dvořák	dvořák	PROPN
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ap-6304	366	7	k.	k.	PROPN
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ap-6304	366	9	.	.	PUNCT
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ap-6304	367	2	modeling	modeling	NOUN
ap-6304	367	3	in	in	ADP
ap-6304	367	4	aerodynamics	aerodynamic	NOUN
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ap-6304	367	6	in	in	ADP
ap-6304	367	7	czech	czech	PROPN
ap-6304	367	8	)	)	PUNCT
ap-6304	367	9	.	.	PUNCT
ap-6304	368	1	vydavatelství	vydavatelství	PROPN
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ap-6304	368	3	,	,	PUNCT
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ap-6304	368	5	.	.	PUNCT
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ap-6304	369	9	.	.	PUNCT
ap-6304	370	1	composite	composite	ADJ
ap-6304	370	2	schemes	scheme	NOUN
ap-6304	370	3	for	for	ADP
ap-6304	370	4	conservation	conservation	NOUN
ap-6304	370	5	laws	law	NOUN
ap-6304	370	6	.	.	PUNCT
ap-6304	371	1	siam	siam	PROPN
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ap-6304	371	3	on	on	ADP
ap-6304	371	4	numerical	numerical	ADJ
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ap-6304	371	6	35(6):2250–2271	35(6):2250–2271	NUM
ap-6304	371	7	,	,	PUNCT
ap-6304	371	8	1998	1998	NUM
ap-6304	371	9	.	.	PUNCT
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ap-6304	373	6	,	,	PUNCT
ap-6304	373	7	l.	l.	PROPN
ap-6304	373	8	beneš	beneš	PROPN
ap-6304	373	9	,	,	PUNCT
ap-6304	373	10	k.	k.	PROPN
ap-6304	373	11	kozel	kozel	PROPN
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ap-6304	373	13	numerical	numerical	PROPN
ap-6304	373	14	simulation	simulation	PROPN
ap-6304	373	15	of	of	ADP
ap-6304	373	16	flow	flow	NOUN
ap-6304	373	17	over	over	ADP
ap-6304	373	18	barriers	barrier	NOUN
ap-6304	373	19	in	in	ADP
ap-6304	373	20	complex	complex	ADJ
ap-6304	373	21	terrain	terrain	NOUN
ap-6304	373	22	.	.	PUNCT
ap-6304	374	1	il	il	PROPN
ap-6304	374	2	nuovo	nuovo	PROPN
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ap-6304	374	8	.	.	PUNCT
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ap-6304	375	3	ncc	ncc	NOUN
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ap-6304	375	5	i2008	i2008	PROPN
ap-6304	375	6	-	-	PUNCT
ap-6304	375	7	10323	10323	NUM
ap-6304	375	8	-	-	PUNCT
ap-6304	375	9	4	4	NUM
ap-6304	375	10	.	.	NOUN
ap-6304	375	11	57	57	NUM
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ap-6304	375	14	t.	t.	PROPN
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ap-6304	375	21	k.	k.	PROPN
ap-6304	375	22	kozel	kozel	PROPN
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ap-6304	376	3	]	]	PUNCT
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ap-6304	376	6	,	,	PUNCT
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ap-6304	376	8	bodnár	bodnár	PROPN
ap-6304	376	9	.	.	PUNCT
ap-6304	377	1	on	on	ADP
ap-6304	377	2	the	the	DET
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ap-6304	377	4	of	of	ADP
ap-6304	377	5	spurious	spurious	ADJ
ap-6304	377	6	oscillations	oscillation	NOUN
ap-6304	377	7	in	in	ADP
ap-6304	377	8	the	the	DET
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ap-6304	377	10	simulations	simulation	NOUN
ap-6304	377	11	of	of	ADP
ap-6304	377	12	convection	convection	NOUN
ap-6304	377	13	dominated	dominate	VERB
ap-6304	377	14	problems	problem	NOUN
ap-6304	377	15	.	.	PUNCT
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ap-6304	378	2	journal	journal	PROPN
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ap-6304	378	4	mathematics	mathematics	PROPN
ap-6304	378	5	47:851–864	47:851–864	PROPN
ap-6304	378	6	,	,	PUNCT
ap-6304	378	7	2019	2019	NUM
ap-6304	378	8	.	.	PUNCT
ap-6304	379	1	doi:10.1007	doi:10.1007	VERB
ap-6304	379	2	/	/	SYM
ap-6304	379	3	s10013	s10013	VERB
ap-6304	379	4	-	-	PUNCT
ap-6304	379	5	019	019	NUM
ap-6304	379	6	-	-	PUNCT
ap-6304	379	7	00369	00369	NUM
ap-6304	379	8	-	-	PUNCT
ap-6304	379	9	z.	z.	PROPN
ap-6304	379	10	58	58	NUM
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ap-6304	379	12	acta	acta	PROPN
ap-6304	379	13	polytechnica	polytechnica	PROPN
ap-6304	379	14	61(si):49–58	61(si):49–58	NUM
ap-6304	379	15	,	,	PUNCT
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ap-6304	379	17	1	1	NUM
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ap-6304	379	19	2	2	NUM
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ap-6304	379	30	equation	equation	NOUN
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ap-6304	379	33	-	-	PUNCT
ap-6304	379	34	diffusion	diffusion	NOUN
ap-6304	379	35	-	-	PUNCT
ap-6304	379	36	dispersion	dispersion	NOUN
ap-6304	379	37	equation	equation	NOUN
ap-6304	379	38	3	3	NUM
ap-6304	379	39	discrete	discrete	ADJ
ap-6304	379	40	analysis	analysis	NOUN
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ap-6304	379	42	up	up	ADP
ap-6304	379	43	-	-	PUNCT
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ap-6304	379	45	&	&	CCONJ
ap-6304	379	46	down	down	ADP
ap-6304	379	47	-	-	PUNCT
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ap-6304	379	49	decomposition	decomposition	NOUN
ap-6304	379	50	3.2	3.2	NUM
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ap-6304	379	52	&	&	CCONJ
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ap-6304	379	54	decomposition	decomposition	NOUN
ap-6304	379	55	3.3	3.3	NUM
ap-6304	379	56	central	central	ADJ
ap-6304	379	57	&	&	CCONJ
ap-6304	379	58	viscous	viscous	ADJ
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ap-6304	379	60	3.3.1	3.3.1	NUM
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ap-6304	379	62	viscosity	viscosity	NOUN
ap-6304	379	63	4	4	NUM
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ap-6304	379	74	modified	modify	VERB
ap-6304	379	75	equation	equation	NOUN
ap-6304	379	76	5	5	NUM
ap-6304	379	77	numerical	numerical	ADJ
ap-6304	379	78	diffusion	diffusion	NOUN
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ap-6304	379	80	dispersion	dispersion	NOUN
ap-6304	379	81	5.1	5.1	NUM
ap-6304	379	82	diffusive	diffusive	ADJ
ap-6304	379	83	schemes	scheme	NOUN
ap-6304	379	84	5.2	5.2	NUM
ap-6304	379	85	dispersive	dispersive	ADJ
ap-6304	379	86	schemes	scheme	NOUN
ap-6304	379	87	6	6	NUM
ap-6304	379	88	limitations	limitation	NOUN
ap-6304	379	89	and	and	CCONJ
ap-6304	379	90	extensions	extension	NOUN
ap-6304	379	91	7	7	NUM
ap-6304	379	92	remark	remark	NOUN
ap-6304	379	93	on	on	ADP
ap-6304	379	94	applications	application	NOUN
ap-6304	379	95	8	8	NUM
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ap-6304	379	97	and	and	CCONJ
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ap-6304	379	99	acknowledgements	acknowledgement	NOUN
ap-6304	379	100	references	reference	NOUN