id	sid	tid	token	lemma	pos
ma-64	1	1	2022	2022	NUM
ma-64	1	2	ada	ada	PROPN
ma-64	1	3	academica	academica	PROPN
ma-64	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-64	1	5	.	.	PUNCT
ma-64	2	1	j.	j.	PROPN
ma-64	2	2	math	math	PROPN
ma-64	2	3	.	.	PUNCT
ma-64	3	1	anal	anal	ADJ
ma-64	3	2	.	.	PUNCT
ma-64	3	3	2	2	NUM
ma-64	3	4	(	(	PUNCT
ma-64	3	5	2022	2022	NUM
ma-64	3	6	)	)	PUNCT
ma-64	3	7	9doi	9doi	NOUN
ma-64	3	8	:	:	PUNCT
ma-64	3	9	10.28924	10.28924	NUM
ma-64	3	10	/	/	SYM
ma-64	3	11	ada	ada	PROPN
ma-64	3	12	/	/	SYM
ma-64	3	13	ma.2.9	ma.2.9	PROPN
ma-64	3	14	efficient	efficient	ADJ
ma-64	3	15	numerical	numerical	ADJ
ma-64	3	16	schemes	scheme	NOUN
ma-64	3	17	for	for	ADP
ma-64	3	18	computations	computation	NOUN
ma-64	3	19	of	of	ADP
ma-64	3	20	european	european	ADJ
ma-64	3	21	options	option	NOUN
ma-64	3	22	with	with	ADP
ma-64	3	23	transaction	transaction	NOUN
ma-64	3	24	costs	cost	VERB
ma-64	4	1	md	md	PROPN
ma-64	4	2	.	.	PROPN
ma-64	4	3	shorif	shorif	PROPN
ma-64	4	4	hossan1	hossan1	PROPN
ma-64	4	5	,	,	PUNCT
ma-64	4	6	md	md	PROPN
ma-64	4	7	.	.	PROPN
ma-64	4	8	shafiqul	shafiqul	PROPN
ma-64	4	9	islam1	islam1	PROPN
ma-64	4	10	,	,	PUNCT
ma-64	4	11	md	md	PROPN
ma-64	4	12	.	.	PROPN
ma-64	4	13	kamrujjaman2,∗	kamrujjaman2,∗	PROPN
ma-64	4	14	1department	1department	NUM
ma-64	4	15	of	of	ADP
ma-64	4	16	applied	apply	VERB
ma-64	4	17	mathematics	mathematic	NOUN
ma-64	4	18	,	,	PUNCT
ma-64	4	19	university	university	NOUN
ma-64	4	20	of	of	ADP
ma-64	4	21	dhaka	dhaka	PROPN
ma-64	4	22	,	,	PUNCT
ma-64	4	23	dhaka	dhaka	PROPN
ma-64	4	24	,	,	PUNCT
ma-64	4	25	bangladesh	bangladesh	NOUN
ma-64	4	26	shorif@du.ac.bd	shorif@du.ac.bd	ADJ
ma-64	4	27	,	,	PUNCT
ma-64	4	28	mdshafiqul@du.ac.bd	mdshafiqul@du.ac.bd	VERB
ma-64	4	29	2department	2department	NUM
ma-64	4	30	of	of	ADP
ma-64	4	31	mathematics	mathematic	NOUN
ma-64	4	32	,	,	PUNCT
ma-64	4	33	university	university	NOUN
ma-64	4	34	of	of	ADP
ma-64	4	35	dhaka	dhaka	PROPN
ma-64	4	36	,	,	PUNCT
ma-64	4	37	dhaka	dhaka	PROPN
ma-64	4	38	,	,	PUNCT
ma-64	4	39	bangladesh	bangladesh	PROPN
ma-64	4	40	kamrujjaman@du.ac.bd	kamrujjaman@du.ac.bd	VERB
ma-64	4	41	∗correspondence	∗correspondence	NOUN
ma-64	4	42	:	:	PUNCT
ma-64	4	43	kamrujjaman@du.ac.bd	kamrujjaman@du.ac.bd	VERB
ma-64	4	44	abstract	abstract	NOUN
ma-64	4	45	.	.	PUNCT
ma-64	5	1	this	this	DET
ma-64	5	2	paper	paper	NOUN
ma-64	5	3	aims	aim	VERB
ma-64	5	4	to	to	PART
ma-64	5	5	find	find	VERB
ma-64	5	6	numerical	numerical	ADJ
ma-64	5	7	solutions	solution	NOUN
ma-64	5	8	of	of	ADP
ma-64	5	9	the	the	DET
ma-64	5	10	non	non	ADJ
ma-64	5	11	-	-	ADJ
ma-64	5	12	linear	linear	ADJ
ma-64	5	13	black	black	ADJ
ma-64	5	14	-	-	PUNCT
ma-64	5	15	scholes	schole	NOUN
ma-64	5	16	partial	partial	ADJ
ma-64	5	17	dif	dif	X
ma-64	5	18	-	-	ADJ
ma-64	5	19	ferential	ferential	ADJ
ma-64	5	20	equation	equation	NOUN
ma-64	5	21	(	(	PUNCT
ma-64	5	22	pde	pde	NOUN
ma-64	5	23	)	)	PUNCT
ma-64	5	24	,	,	PUNCT
ma-64	5	25	which	which	PRON
ma-64	5	26	often	often	ADV
ma-64	5	27	appears	appear	VERB
ma-64	5	28	in	in	ADP
ma-64	5	29	financial	financial	ADJ
ma-64	5	30	markets	market	NOUN
ma-64	5	31	,	,	PUNCT
ma-64	5	32	for	for	ADP
ma-64	5	33	european	european	ADJ
ma-64	5	34	option	option	NOUN
ma-64	5	35	pricing	pricing	NOUN
ma-64	5	36	inthe	inthe	DET
ma-64	5	37	appearance	appearance	NOUN
ma-64	5	38	of	of	ADP
ma-64	5	39	the	the	DET
ma-64	5	40	transaction	transaction	NOUN
ma-64	5	41	costs	cost	NOUN
ma-64	5	42	.	.	PUNCT
ma-64	6	1	here	here	ADV
ma-64	6	2	we	we	PRON
ma-64	6	3	exploit	exploit	VERB
ma-64	6	4	the	the	DET
ma-64	6	5	transformations	transformation	NOUN
ma-64	6	6	for	for	ADP
ma-64	6	7	the	the	DET
ma-64	6	8	computationalpurpose	computationalpurpose	NOUN
ma-64	6	9	of	of	ADP
ma-64	6	10	a	a	DET
ma-64	6	11	non	non	ADJ
ma-64	6	12	-	-	ADJ
ma-64	6	13	linear	linear	ADJ
ma-64	6	14	black	black	ADJ
ma-64	6	15	-	-	PUNCT
ma-64	6	16	scholes	schole	NOUN
ma-64	6	17	pde	pde	NOUN
ma-64	6	18	to	to	PART
ma-64	6	19	modify	modify	VERB
ma-64	6	20	as	as	ADP
ma-64	6	21	a	a	DET
ma-64	6	22	non	non	ADJ
ma-64	6	23	-	-	ADJ
ma-64	6	24	linear	linear	ADJ
ma-64	6	25	parabolic	parabolic	ADJ
ma-64	6	26	type	type	NOUN
ma-64	6	27	pde	pde	NOUN
ma-64	6	28	with	with	ADP
ma-64	6	29	reli	reli	NOUN
ma-64	6	30	-	-	PUNCT
ma-64	6	31	able	able	ADJ
ma-64	6	32	initial	initial	ADJ
ma-64	6	33	and	and	CCONJ
ma-64	6	34	boundary	boundary	ADJ
ma-64	6	35	conditions	condition	NOUN
ma-64	6	36	for	for	ADP
ma-64	6	37	call	call	NOUN
ma-64	6	38	and	and	CCONJ
ma-64	6	39	put	put	ADJ
ma-64	6	40	options	option	NOUN
ma-64	6	41	.	.	PUNCT
ma-64	7	1	several	several	ADJ
ma-64	7	2	schemes	scheme	NOUN
ma-64	7	3	are	be	AUX
ma-64	7	4	derived	derive	VERB
ma-64	7	5	rigorouslyusing	rigorouslyuse	VERB
ma-64	7	6	the	the	DET
ma-64	7	7	finite	finite	ADJ
ma-64	7	8	volume	volume	NOUN
ma-64	7	9	method	method	NOUN
ma-64	7	10	(	(	PUNCT
ma-64	7	11	fvm	fvm	ADV
ma-64	7	12	)	)	PUNCT
ma-64	7	13	and	and	CCONJ
ma-64	7	14	finite	finite	ADJ
ma-64	7	15	difference	difference	NOUN
ma-64	7	16	method	method	NOUN
ma-64	7	17	(	(	PUNCT
ma-64	7	18	fdm	fdm	NOUN
ma-64	7	19	)	)	PUNCT
ma-64	7	20	,	,	PUNCT
ma-64	7	21	which	which	PRON
ma-64	7	22	is	be	AUX
ma-64	7	23	the	the	DET
ma-64	7	24	novelty	novelty	NOUN
ma-64	7	25	of	of	ADP
ma-64	7	26	thispaper	thispaper	NOUN
ma-64	7	27	.	.	PUNCT
ma-64	8	1	stability	stability	NOUN
ma-64	8	2	and	and	CCONJ
ma-64	8	3	consistency	consistency	NOUN
ma-64	8	4	analysis	analysis	NOUN
ma-64	8	5	assure	assure	VERB
ma-64	8	6	the	the	DET
ma-64	8	7	convergence	convergence	NOUN
ma-64	8	8	of	of	ADP
ma-64	8	9	these	these	DET
ma-64	8	10	schemes	scheme	NOUN
ma-64	8	11	.	.	PUNCT
ma-64	9	1	we	we	PRON
ma-64	9	2	apply	apply	VERB
ma-64	9	3	theseschemes	thesescheme	NOUN
ma-64	9	4	to	to	ADP
ma-64	9	5	various	various	ADJ
ma-64	9	6	volatility	volatility	NOUN
ma-64	9	7	models	model	NOUN
ma-64	9	8	,	,	PUNCT
ma-64	9	9	such	such	ADJ
ma-64	9	10	as	as	ADP
ma-64	9	11	the	the	DET
ma-64	9	12	leland	leland	PROPN
ma-64	9	13	,	,	PUNCT
ma-64	9	14	boyle	boyle	PROPN
ma-64	9	15	and	and	CCONJ
ma-64	9	16	vorst	vorst	PROPN
ma-64	9	17	,	,	PUNCT
ma-64	9	18	barles	barle	NOUN
ma-64	9	19	and	and	CCONJ
ma-64	9	20	soner	soner	NOUN
ma-64	9	21	,	,	PUNCT
ma-64	9	22	andrisk	andrisk	NOUN
ma-64	9	23	-	-	PUNCT
ma-64	9	24	adjusted	adjust	VERB
ma-64	9	25	pricing	pricing	NOUN
ma-64	9	26	methodology	methodology	NOUN
ma-64	9	27	(	(	PUNCT
ma-64	9	28	rapm	rapm	NOUN
ma-64	9	29	)	)	PUNCT
ma-64	9	30	.	.	PUNCT
ma-64	10	1	all	all	DET
ma-64	10	2	the	the	DET
ma-64	10	3	schemes	scheme	NOUN
ma-64	10	4	are	be	AUX
ma-64	10	5	tested	test	VERB
ma-64	10	6	numerically	numerically	ADV
ma-64	10	7	.	.	PUNCT
ma-64	11	1	the	the	DET
ma-64	11	2	convergenceof	convergenceof	NOUN
ma-64	11	3	the	the	DET
ma-64	11	4	obtained	obtain	VERB
ma-64	11	5	results	result	NOUN
ma-64	11	6	is	be	AUX
ma-64	11	7	observed	observe	VERB
ma-64	11	8	,	,	PUNCT
ma-64	11	9	and	and	CCONJ
ma-64	11	10	we	we	PRON
ma-64	11	11	find	find	VERB
ma-64	11	12	that	that	SCONJ
ma-64	11	13	they	they	PRON
ma-64	11	14	are	be	AUX
ma-64	11	15	also	also	ADV
ma-64	11	16	reliable	reliable	ADJ
ma-64	11	17	.	.	PUNCT
ma-64	12	1	finally	finally	ADV
ma-64	12	2	,	,	PUNCT
ma-64	12	3	we	we	PRON
ma-64	12	4	display	display	VERB
ma-64	12	5	allthe	allthe	DET
ma-64	12	6	approximate	approximate	ADJ
ma-64	12	7	results	result	NOUN
ma-64	12	8	together	together	ADV
ma-64	12	9	with	with	ADP
ma-64	12	10	the	the	DET
ma-64	12	11	exact	exact	ADJ
ma-64	12	12	values	value	NOUN
ma-64	12	13	through	through	ADP
ma-64	12	14	graphical	graphical	ADJ
ma-64	12	15	and	and	CCONJ
ma-64	12	16	tabular	tabular	ADJ
ma-64	12	17	representations	representation	NOUN
ma-64	12	18	.	.	PUNCT
ma-64	13	1	1	1	X
ma-64	13	2	.	.	X
ma-64	13	3	introduction	introduction	NOUN
ma-64	13	4	understanding	understanding	NOUN
ma-64	13	5	and	and	CCONJ
ma-64	13	6	accurately	accurately	ADV
ma-64	13	7	evaluating	evaluate	VERB
ma-64	13	8	transaction	transaction	NOUN
ma-64	13	9	costs	cost	NOUN
ma-64	13	10	in	in	ADP
ma-64	13	11	a	a	DET
ma-64	13	12	financial	financial	ADJ
ma-64	13	13	market	market	NOUN
ma-64	13	14	is	be	AUX
ma-64	13	15	vital	vital	ADJ
ma-64	13	16	forsecurity	forsecurity	NOUN
ma-64	13	17	trading	trading	NOUN
ma-64	13	18	,	,	PUNCT
ma-64	13	19	asset	asset	NOUN
ma-64	13	20	pricing	pricing	NOUN
ma-64	13	21	,	,	PUNCT
ma-64	13	22	stock	stock	NOUN
ma-64	13	23	market	market	NOUN
ma-64	13	24	regulation	regulation	NOUN
ma-64	13	25	,	,	PUNCT
ma-64	13	26	and	and	CCONJ
ma-64	13	27	many	many	ADJ
ma-64	13	28	other	other	ADJ
ma-64	13	29	issues	issue	NOUN
ma-64	13	30	.	.	PUNCT
ma-64	14	1	during	during	ADP
ma-64	14	2	the	the	DET
ma-64	14	3	last	last	ADJ
ma-64	14	4	fewdecades	fewdecade	NOUN
ma-64	14	5	,	,	PUNCT
ma-64	14	6	pricing	pricing	NOUN
ma-64	14	7	options	option	NOUN
ma-64	14	8	more	more	ADV
ma-64	14	9	accurately	accurately	ADV
ma-64	14	10	after	after	ADP
ma-64	14	11	including	include	VERB
ma-64	14	12	realistic	realistic	ADJ
ma-64	14	13	assumptions	assumption	NOUN
ma-64	14	14	-	-	PUNCT
ma-64	14	15	such	such	ADJ
ma-64	14	16	as	as	ADP
ma-64	14	17	transactioncost	transactioncost	NOUN
ma-64	14	18	,	,	PUNCT
ma-64	14	19	getting	get	VERB
ma-64	14	20	more	more	ADJ
ma-64	14	21	importance	importance	NOUN
ma-64	14	22	from	from	ADP
ma-64	14	23	both	both	CCONJ
ma-64	14	24	the	the	DET
ma-64	14	25	traders	trader	NOUN
ma-64	14	26	and	and	CCONJ
ma-64	14	27	the	the	DET
ma-64	14	28	investors.the	investors.the	DET
ma-64	14	29	literature	literature	NOUN
ma-64	14	30	’s	’s	PART
ma-64	15	1	[	[	X
ma-64	15	2	1–6	1–6	NUM
ma-64	15	3	]	]	X
ma-64	15	4	,	,	PUNCT
ma-64	15	5	contains	contain	VERB
ma-64	15	6	descriptive	descriptive	ADJ
ma-64	15	7	discussions	discussion	NOUN
ma-64	15	8	of	of	ADP
ma-64	15	9	options	option	NOUN
ma-64	15	10	.	.	PUNCT
ma-64	16	1	fischer	fischer	PROPN
ma-64	16	2	black	black	PROPN
ma-64	16	3	and	and	CCONJ
ma-64	16	4	myronscholes	myronschole	NOUN
ma-64	16	5	[	[	X
ma-64	16	6	7	7	NUM
ma-64	16	7	]	]	PUNCT
ma-64	16	8	worked	work	VERB
ma-64	16	9	jointly	jointly	ADV
ma-64	16	10	,	,	PUNCT
ma-64	16	11	and	and	CCONJ
ma-64	16	12	first	first	ADV
ma-64	16	13	disclosed	disclose	VERB
ma-64	16	14	the	the	DET
ma-64	16	15	concept	concept	NOUN
ma-64	16	16	of	of	ADP
ma-64	16	17	the	the	DET
ma-64	16	18	black	black	ADJ
ma-64	16	19	-	-	PUNCT
ma-64	16	20	scholes	schole	NOUN
ma-64	16	21	model	model	NOUN
ma-64	16	22	for	for	ADP
ma-64	16	23	options	option	NOUN
ma-64	16	24	pricing	pricing	NOUN
ma-64	16	25	and	and	CCONJ
ma-64	16	26	corporate	corporate	ADJ
ma-64	16	27	liabilities	liability	NOUN
ma-64	16	28	,	,	PUNCT
ma-64	16	29	and	and	CCONJ
ma-64	16	30	was	be	AUX
ma-64	16	31	published	publish	VERB
ma-64	16	32	in	in	ADP
ma-64	16	33	1973	1973	NUM
ma-64	16	34	,	,	PUNCT
ma-64	16	35	while	while	SCONJ
ma-64	16	36	robert	robert	PROPN
ma-64	16	37	merton	merton	PROPN
ma-64	16	38	[	[	X
ma-64	16	39	8	8	NUM
ma-64	16	40	]	]	X
ma-64	16	41	advanced	advanced	ADJ
ma-64	16	42	thismodel	thismodel	NOUN
ma-64	16	43	in	in	ADP
ma-64	16	44	the	the	DET
ma-64	16	45	article	article	NOUN
ma-64	16	46	"	"	PUNCT
ma-64	16	47	theory	theory	NOUN
ma-64	16	48	of	of	ADP
ma-64	16	49	rational	rational	ADJ
ma-64	16	50	option	option	NOUN
ma-64	16	51	pricing	pricing	NOUN
ma-64	16	52	"	"	PUNCT
ma-64	16	53	in	in	ADP
ma-64	16	54	the	the	DET
ma-64	16	55	same	same	ADJ
ma-64	16	56	year	year	NOUN
ma-64	16	57	.	.	PUNCT
ma-64	17	1	their	their	PRON
ma-64	17	2	derived	derived	ADJ
ma-64	17	3	equation	equation	NOUN
ma-64	17	4	isbased	isbase	VERB
ma-64	17	5	on	on	ADP
ma-64	17	6	the	the	DET
ma-64	17	7	assumption	assumption	NOUN
ma-64	17	8	that	that	SCONJ
ma-64	17	9	there	there	PRON
ma-64	17	10	are	be	VERB
ma-64	17	11	no	no	DET
ma-64	17	12	fees	fee	NOUN
ma-64	17	13	for	for	ADP
ma-64	17	14	buying	buy	VERB
ma-64	17	15	and	and	CCONJ
ma-64	17	16	selling	sell	VERB
ma-64	17	17	options	option	NOUN
ma-64	17	18	and	and	CCONJ
ma-64	17	19	stocks	stock	NOUN
ma-64	17	20	,	,	PUNCT
ma-64	17	21	as	as	SCONJ
ma-64	17	22	wellas	wella	NOUN
ma-64	17	23	no	no	DET
ma-64	17	24	trade	trade	NOUN
ma-64	17	25	barriers	barrier	NOUN
ma-64	17	26	(	(	PUNCT
ma-64	17	27	i.e.	i.e.	X
ma-64	17	28	,	,	PUNCT
ma-64	17	29	no	no	DET
ma-64	17	30	commissions	commission	NOUN
ma-64	17	31	and	and	CCONJ
ma-64	17	32	transaction	transaction	NOUN
ma-64	17	33	costs	cost	NOUN
ma-64	17	34	)	)	PUNCT
ma-64	17	35	.	.	PUNCT
ma-64	18	1	in	in	ADP
ma-64	18	2	other	other	ADJ
ma-64	18	3	words	word	NOUN
ma-64	18	4	,	,	PUNCT
ma-64	18	5	this	this	DET
ma-64	18	6	model	model	NOUN
ma-64	18	7	makes	make	VERB
ma-64	18	8	received	receive	VERB
ma-64	18	9	:	:	PUNCT
ma-64	18	10	20	20	NUM
ma-64	18	11	dec	dec	PROPN
ma-64	18	12	2021	2021	NUM
ma-64	18	13	.	.	PUNCT
ma-64	19	1	key	key	ADJ
ma-64	19	2	words	word	NOUN
ma-64	19	3	and	and	CCONJ
ma-64	19	4	phrases	phrase	NOUN
ma-64	19	5	.	.	PUNCT
ma-64	20	1	nonlinear	nonlinear	ADJ
ma-64	20	2	black	black	ADJ
ma-64	20	3	-	-	PUNCT
ma-64	20	4	scholes	schole	NOUN
ma-64	20	5	pde	pde	NOUN
ma-64	20	6	;	;	PUNCT
ma-64	20	7	option	option	NOUN
ma-64	20	8	pricing	pricing	NOUN
ma-64	20	9	;	;	PUNCT
ma-64	20	10	volatility	volatility	NOUN
ma-64	20	11	model	model	NOUN
ma-64	20	12	;	;	PUNCT
ma-64	20	13	finite	finite	PROPN
ma-64	20	14	volume	volume	NOUN
ma-64	20	15	method	method	NOUN
ma-64	20	16	;	;	PUNCT
ma-64	20	17	finitedifference	finitedifference	NOUN
ma-64	20	18	method	method	NOUN
ma-64	20	19	.	.	PUNCT
ma-64	21	1	1	1	NUM
ma-64	21	2	https://adac.ee	https://adac.ee	PROPN
ma-64	21	3	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	21	4	https://orcid.org/0000-0003-4115-9002	https://orcid.org/0000-0003-4115-9002	NOUN
ma-64	21	5	https://orcid.org/0000-0001-7121-3386	https://orcid.org/0000-0001-7121-3386	VERB
ma-64	21	6	https://orcid.org/0000-0002-4892-745x	https://orcid.org/0000-0002-4892-745x	ADJ
ma-64	21	7	eur	eur	NOUN
ma-64	21	8	.	.	PUNCT
ma-64	22	1	j.	j.	PROPN
ma-64	22	2	math	math	PROPN
ma-64	22	3	.	.	PUNCT
ma-64	23	1	anal	anal	PROPN
ma-64	23	2	.	.	PUNCT
ma-64	24	1	10.28924	10.28924	NUM
ma-64	24	2	/	/	SYM
ma-64	24	3	ada	ada	PROPN
ma-64	24	4	/	/	SYM
ma-64	24	5	ma.2.9	ma.2.9	PROPN
ma-64	24	6	2a	2a	NUM
ma-64	24	7	friction	friction	NOUN
ma-64	24	8	-	-	PUNCT
ma-64	24	9	less	less	ADJ
ma-64	24	10	assumption	assumption	NOUN
ma-64	24	11	(	(	PUNCT
ma-64	24	12	which	which	PRON
ma-64	24	13	is	be	AUX
ma-64	24	14	indispensable	indispensable	ADJ
ma-64	24	15	,	,	PUNCT
ma-64	24	16	as	as	ADP
ma-64	24	17	actual	actual	ADJ
ma-64	24	18	costs	cost	NOUN
ma-64	24	19	correlated	correlate	VERB
ma-64	24	20	with	with	ADP
ma-64	24	21	practical	practical	ADJ
ma-64	24	22	marketapplications	marketapplication	NOUN
ma-64	24	23	)	)	PUNCT
ma-64	24	24	to	to	PART
ma-64	24	25	implement	implement	VERB
ma-64	24	26	a	a	DET
ma-64	24	27	hedging	hedging	NOUN
ma-64	24	28	plan	plan	NOUN
ma-64	24	29	for	for	ADP
ma-64	24	30	any	any	DET
ma-64	24	31	contingent	contingent	ADJ
ma-64	24	32	claim	claim	NOUN
ma-64	24	33	of	of	ADP
ma-64	24	34	the	the	DET
ma-64	24	35	european	european	ADJ
ma-64	24	36	type.various	type.various	ADJ
ma-64	24	37	studies	study	NOUN
ma-64	24	38	have	have	AUX
ma-64	24	39	been	be	AUX
ma-64	24	40	conducted	conduct	VERB
ma-64	24	41	about	about	ADP
ma-64	24	42	the	the	DET
ma-64	24	43	linear	linear	ADJ
ma-64	24	44	black	black	ADJ
ma-64	24	45	-	-	PUNCT
ma-64	24	46	scholes	schole	NOUN
ma-64	24	47	model	model	NOUN
ma-64	24	48	[	[	X
ma-64	24	49	9–15	9–15	X
ma-64	24	50	]	]	PUNCT
ma-64	24	51	though	though	SCONJ
ma-64	24	52	itadopts	itadopt	NOUN
ma-64	24	53	the	the	DET
ma-64	24	54	unrealistic	unrealistic	ADJ
ma-64	24	55	assumption	assumption	NOUN
ma-64	24	56	of	of	ADP
ma-64	24	57	no	no	DET
ma-64	24	58	transaction	transaction	NOUN
ma-64	24	59	costs	cost	NOUN
ma-64	24	60	.	.	PUNCT
ma-64	25	1	several	several	ADJ
ma-64	25	2	studies	study	NOUN
ma-64	25	3	have	have	AUX
ma-64	25	4	been	be	AUX
ma-64	25	5	attempted	attempt	VERB
ma-64	25	6	toevaluate	toevaluate	VERB
ma-64	25	7	the	the	DET
ma-64	25	8	price	price	NOUN
ma-64	25	9	of	of	ADP
ma-64	25	10	european	european	ADJ
ma-64	25	11	options	option	NOUN
ma-64	26	1	[	[	X
ma-64	26	2	16–23	16–23	NUM
ma-64	26	3	]	]	X
ma-64	26	4	,	,	PUNCT
ma-64	26	5	american	american	ADJ
ma-64	26	6	options	option	NOUN
ma-64	26	7	[	[	X
ma-64	26	8	24–28	24–28	NUM
ma-64	26	9	]	]	PUNCT
ma-64	26	10	,	,	PUNCT
ma-64	26	11	asian	asian	ADJ
ma-64	26	12	options	option	NOUN
ma-64	26	13	[	[	X
ma-64	26	14	29	29	NUM
ma-64	26	15	,	,	PUNCT
ma-64	26	16	30],and	30],and	NUM
ma-64	26	17	barrier	barrier	NOUN
ma-64	26	18	options	option	NOUN
ma-64	26	19	[	[	X
ma-64	26	20	31	31	NUM
ma-64	26	21	]	]	PUNCT
ma-64	26	22	in	in	ADP
ma-64	26	23	a	a	DET
ma-64	26	24	completely	completely	ADV
ma-64	26	25	friction	friction	NOUN
ma-64	26	26	-	-	PUNCT
ma-64	26	27	less	less	ADJ
ma-64	26	28	market	market	NOUN
ma-64	26	29	.	.	PUNCT
ma-64	27	1	recently	recently	ADV
ma-64	27	2	,	,	PUNCT
ma-64	27	3	the	the	DET
ma-64	27	4	fractional	fractional	ADJ
ma-64	27	5	black	black	ADJ
ma-64	27	6	-	-	PUNCT
ma-64	27	7	scholesmodel	scholesmodel	NOUN
ma-64	27	8	[	[	X
ma-64	27	9	32–34	32–34	NUM
ma-64	27	10	]	]	PUNCT
ma-64	27	11	received	receive	VERB
ma-64	27	12	some	some	PRON
ma-64	27	13	attention.contrastingly	attention.contrastingly	ADV
ma-64	27	14	,	,	PUNCT
ma-64	27	15	the	the	DET
ma-64	27	16	non	non	ADJ
ma-64	27	17	-	-	ADJ
ma-64	27	18	linear	linear	ADJ
ma-64	27	19	black	black	ADJ
ma-64	27	20	-	-	PUNCT
ma-64	27	21	scholes	schole	NOUN
ma-64	27	22	pde	pde	NOUN
ma-64	27	23	,	,	PUNCT
ma-64	27	24	where	where	SCONJ
ma-64	27	25	the	the	DET
ma-64	27	26	non	non	ADJ
ma-64	27	27	-	-	ADJ
ma-64	27	28	linear	linear	ADJ
ma-64	27	29	term	term	NOUN
ma-64	27	30	denotes	denote	VERB
ma-64	27	31	the	the	DET
ma-64	27	32	pres	pre	NOUN
ma-64	27	33	-	-	NOUN
ma-64	27	34	ence	ence	NOUN
ma-64	27	35	of	of	ADP
ma-64	27	36	transaction	transaction	NOUN
ma-64	27	37	costs	cost	NOUN
ma-64	27	38	,	,	PUNCT
ma-64	27	39	is	be	AUX
ma-64	27	40	of	of	ADP
ma-64	27	41	great	great	ADJ
ma-64	27	42	importance	importance	NOUN
ma-64	27	43	to	to	ADP
ma-64	27	44	our	our	PRON
ma-64	27	45	contemporary	contemporary	ADJ
ma-64	27	46	world	world	NOUN
ma-64	27	47	over	over	ADP
ma-64	27	48	some	some	DET
ma-64	27	49	time	time	NOUN
ma-64	27	50	both	both	DET
ma-64	27	51	interms	interm	NOUN
ma-64	27	52	of	of	ADP
ma-64	27	53	approach	approach	NOUN
ma-64	27	54	and	and	CCONJ
ma-64	27	55	applicability	applicability	NOUN
ma-64	27	56	.	.	PUNCT
ma-64	28	1	several	several	ADJ
ma-64	28	2	models	model	NOUN
ma-64	28	3	[	[	X
ma-64	28	4	35	35	NUM
ma-64	28	5	]	]	PUNCT
ma-64	28	6	consider	consider	VERB
ma-64	28	7	transaction	transaction	NOUN
ma-64	28	8	costs	cost	NOUN
ma-64	28	9	:	:	PUNCT
ma-64	28	10	leland	leland	PROPN
ma-64	28	11	model	model	NOUN
ma-64	28	12	,	,	PUNCT
ma-64	28	13	paras	paras	X
ma-64	28	14	,	,	PUNCT
ma-64	28	15	and	and	CCONJ
ma-64	28	16	avellaneda	avellaneda	PROPN
ma-64	28	17	model	model	PROPN
ma-64	28	18	,	,	PUNCT
ma-64	28	19	boyle	boyle	PROPN
ma-64	28	20	and	and	CCONJ
ma-64	28	21	vorst	vorst	PROPN
ma-64	28	22	model	model	PROPN
ma-64	28	23	,	,	PUNCT
ma-64	28	24	hodges	hodge	NOUN
ma-64	28	25	and	and	CCONJ
ma-64	28	26	neuberger	neuberger	PROPN
ma-64	28	27	model	model	PROPN
ma-64	28	28	,	,	PUNCT
ma-64	28	29	barles	barles	PROPN
ma-64	28	30	andsoner	andsoner	PROPN
ma-64	28	31	model	model	PROPN
ma-64	28	32	,	,	PUNCT
ma-64	28	33	and	and	CCONJ
ma-64	28	34	rapm	rapm	NOUN
ma-64	28	35	(	(	PUNCT
ma-64	28	36	risk	risk	NOUN
ma-64	28	37	-	-	PUNCT
ma-64	28	38	adjusted	adjust	VERB
ma-64	28	39	pricing	pricing	NOUN
ma-64	28	40	methodology	methodology	NOUN
ma-64	28	41	)	)	PUNCT
ma-64	28	42	model	model	NOUN
ma-64	28	43	.	.	PUNCT
ma-64	29	1	if	if	SCONJ
ma-64	29	2	the	the	DET
ma-64	29	3	transaction	transaction	NOUN
ma-64	29	4	cost	cost	VERB
ma-64	29	5	pa	pa	PROPN
ma-64	29	6	-	-	NOUN
ma-64	29	7	rameters	rameter	NOUN
ma-64	29	8	are	be	AUX
ma-64	29	9	equal	equal	ADJ
ma-64	29	10	to	to	ADP
ma-64	29	11	zero	zero	NUM
ma-64	29	12	,	,	PUNCT
ma-64	29	13	all	all	PRON
ma-64	29	14	of	of	ADP
ma-64	29	15	these	these	DET
ma-64	29	16	non	non	ADJ
ma-64	29	17	-	-	ADJ
ma-64	29	18	linear	linear	ADJ
ma-64	29	19	transaction	transaction	NOUN
ma-64	29	20	cost	cost	NOUN
ma-64	29	21	models	model	NOUN
ma-64	29	22	are	be	AUX
ma-64	29	23	unvarying	unvarye	VERB
ma-64	29	24	with	with	ADP
ma-64	29	25	thelinear	thelinear	NOUN
ma-64	29	26	model.soner	model.soner	PROPN
ma-64	29	27	et	et	PROPN
ma-64	29	28	al	al	PROPN
ma-64	29	29	.	.	PUNCT
ma-64	30	1	[	[	X
ma-64	30	2	36	36	NUM
ma-64	30	3	]	]	PUNCT
ma-64	30	4	showed	show	VERB
ma-64	30	5	that	that	SCONJ
ma-64	30	6	there	there	PRON
ma-64	30	7	is	be	VERB
ma-64	30	8	no	no	DET
ma-64	30	9	nontrivial	nontrivial	ADJ
ma-64	30	10	hedging	hedge	VERB
ma-64	30	11	portfolio	portfolio	NOUN
ma-64	30	12	for	for	ADP
ma-64	30	13	option	option	NOUN
ma-64	30	14	pricing	pricing	NOUN
ma-64	30	15	withtransaction	withtransaction	NOUN
ma-64	30	16	costs	cost	NOUN
ma-64	30	17	.	.	PUNCT
ma-64	31	1	they	they	PRON
ma-64	31	2	also	also	ADV
ma-64	31	3	suggested	suggest	VERB
ma-64	31	4	that	that	SCONJ
ma-64	31	5	the	the	DET
ma-64	31	6	best	good	ADJ
ma-64	31	7	hedging	hedging	NOUN
ma-64	31	8	strategy	strategy	NOUN
ma-64	31	9	is	be	AUX
ma-64	31	10	buying	buy	VERB
ma-64	31	11	an	an	DET
ma-64	31	12	asset	asset	NOUN
ma-64	31	13	andtaking	andtake	VERB
ma-64	31	14	on	on	ADP
ma-64	31	15	it	it	PRON
ma-64	31	16	for	for	ADP
ma-64	31	17	a	a	DET
ma-64	31	18	certain	certain	ADJ
ma-64	31	19	period	period	NOUN
ma-64	31	20	as	as	ADP
ma-64	31	21	a	a	DET
ma-64	31	22	call	call	NOUN
ma-64	31	23	or	or	CCONJ
ma-64	31	24	put	put	NOUN
ma-64	31	25	option	option	NOUN
ma-64	31	26	.	.	PUNCT
ma-64	32	1	leland	leland	PROPN
ma-64	33	1	[	[	X
ma-64	33	2	37	37	NUM
ma-64	33	3	]	]	PUNCT
ma-64	33	4	inaugurates	inaugurate	VERB
ma-64	33	5	the	the	DET
ma-64	33	6	idea	idea	NOUN
ma-64	33	7	of	of	ADP
ma-64	33	8	usingtransaction	usingtransaction	NOUN
ma-64	33	9	costs	cost	NOUN
ma-64	33	10	at	at	ADP
ma-64	33	11	discrete	discrete	ADJ
ma-64	33	12	times	time	NOUN
ma-64	33	13	.	.	PUNCT
ma-64	34	1	he	he	PRON
ma-64	34	2	also	also	ADV
ma-64	34	3	indicated	indicate	VERB
ma-64	34	4	that	that	SCONJ
ma-64	34	5	the	the	DET
ma-64	34	6	hedging	hedging	NOUN
ma-64	34	7	error	error	NOUN
ma-64	34	8	could	could	AUX
ma-64	34	9	be	be	AUX
ma-64	34	10	minimized	minimize	VERB
ma-64	34	11	ifthe	ifthe	NOUN
ma-64	34	12	length	length	NOUN
ma-64	34	13	of	of	ADP
ma-64	34	14	re	re	VERB
ma-64	34	15	-	-	ADJ
ma-64	34	16	balancing	balancing	ADJ
ma-64	34	17	frequency	frequency	NOUN
ma-64	34	18	approaches	approach	NOUN
ma-64	34	19	zero	zero	NUM
ma-64	34	20	.	.	PUNCT
ma-64	35	1	later	later	ADV
ma-64	35	2	,	,	PUNCT
ma-64	35	3	boyle	boyle	NOUN
ma-64	35	4	and	and	CCONJ
ma-64	35	5	vorst	vorst	PROPN
ma-64	36	1	[	[	X
ma-64	36	2	38	38	NUM
ma-64	36	3	]	]	PUNCT
ma-64	36	4	demonstrated	demonstrate	VERB
ma-64	36	5	fur	fur	NOUN
ma-64	36	6	-	-	PUNCT
ma-64	36	7	ther	ther	ADJ
ma-64	36	8	in	in	ADP
ma-64	36	9	a	a	DET
ma-64	36	10	discrete	discrete	ADJ
ma-64	36	11	-	-	PUNCT
ma-64	36	12	time	time	NOUN
ma-64	36	13	framework	framework	NOUN
ma-64	36	14	with	with	ADP
ma-64	36	15	a	a	DET
ma-64	36	16	binomial	binomial	ADJ
ma-64	36	17	tree	tree	NOUN
ma-64	36	18	model	model	NOUN
ma-64	36	19	for	for	ADP
ma-64	36	20	the	the	DET
ma-64	36	21	option	option	NOUN
ma-64	36	22	prices	price	NOUN
ma-64	36	23	with	with	ADP
ma-64	36	24	proportionaltransaction	proportionaltransaction	NOUN
ma-64	36	25	costs	cost	NOUN
ma-64	36	26	,	,	PUNCT
ma-64	36	27	and	and	CCONJ
ma-64	36	28	it	it	PRON
ma-64	36	29	is	be	AUX
ma-64	36	30	pretty	pretty	ADV
ma-64	36	31	accurate	accurate	ADJ
ma-64	36	32	for	for	ADP
ma-64	36	33	possible	possible	ADJ
ma-64	36	34	parameter	parameter	NOUN
ma-64	36	35	values	value	NOUN
ma-64	36	36	.	.	PUNCT
ma-64	37	1	besides	besides	SCONJ
ma-64	37	2	,	,	PUNCT
ma-64	37	3	dewynne	dewynne	NOUN
ma-64	37	4	etal	etal	NOUN
ma-64	37	5	.	.	PUNCT
ma-64	38	1	[	[	X
ma-64	38	2	39	39	NUM
ma-64	38	3	]	]	PUNCT
ma-64	38	4	considered	consider	VERB
ma-64	38	5	path	path	NOUN
ma-64	38	6	-	-	PUNCT
ma-64	38	7	dependent	dependent	ADJ
ma-64	38	8	and	and	CCONJ
ma-64	38	9	exotic	exotic	ADJ
ma-64	38	10	options	option	NOUN
ma-64	38	11	with	with	ADP
ma-64	38	12	transaction	transaction	NOUN
ma-64	38	13	costs	cost	NOUN
ma-64	38	14	.	.	PUNCT
ma-64	39	1	recently	recently	ADV
ma-64	39	2	,	,	PUNCT
ma-64	39	3	asymptoticanalysis	asymptoticanalysis	NOUN
ma-64	39	4	[	[	X
ma-64	39	5	40	40	NUM
ma-64	39	6	]	]	PUNCT
ma-64	39	7	and	and	CCONJ
ma-64	39	8	markov	markov	NOUN
ma-64	39	9	chain	chain	NOUN
ma-64	39	10	approximation	approximation	NOUN
ma-64	40	1	[	[	X
ma-64	40	2	41	41	NUM
ma-64	40	3	]	]	PUNCT
ma-64	40	4	were	be	AUX
ma-64	40	5	also	also	ADV
ma-64	40	6	studied	study	VERB
ma-64	40	7	for	for	ADP
ma-64	40	8	pricing	price	VERB
ma-64	40	9	european	european	ADJ
ma-64	40	10	optionswith	optionswith	ADP
ma-64	40	11	transaction	transaction	NOUN
ma-64	40	12	costs	cost	NOUN
ma-64	40	13	in	in	ADP
ma-64	40	14	some	some	DET
ma-64	40	15	previous	previous	ADJ
ma-64	40	16	literature.on	literature.on	NOUN
ma-64	40	17	the	the	DET
ma-64	40	18	other	other	ADJ
ma-64	40	19	hand	hand	NOUN
ma-64	40	20	,	,	PUNCT
ma-64	40	21	few	few	ADJ
ma-64	40	22	researchers	researcher	NOUN
ma-64	40	23	[	[	X
ma-64	40	24	42–46	42–46	NUM
ma-64	40	25	,	,	PUNCT
ma-64	40	26	49–51	49–51	NUM
ma-64	40	27	]	]	PUNCT
ma-64	40	28	paid	pay	VERB
ma-64	40	29	their	their	PRON
ma-64	40	30	attention	attention	NOUN
ma-64	40	31	to	to	PART
ma-64	40	32	solve	solve	VERB
ma-64	40	33	the	the	DET
ma-64	40	34	non	non	ADJ
ma-64	40	35	-	-	ADJ
ma-64	40	36	linearblack	linearblack	ADJ
ma-64	40	37	-	-	PUNCT
ma-64	40	38	scholes	schole	NOUN
ma-64	40	39	equation	equation	NOUN
ma-64	40	40	numerically	numerically	ADV
ma-64	40	41	.	.	PUNCT
ma-64	41	1	for	for	ADP
ma-64	41	2	example	example	NOUN
ma-64	41	3	,	,	PUNCT
ma-64	41	4	the	the	DET
ma-64	41	5	exponential	exponential	ADJ
ma-64	41	6	time	time	NOUN
ma-64	41	7	differencing	differencing	NOUN
ma-64	41	8	(	(	PUNCT
ma-64	41	9	etd	etd	NOUN
ma-64	41	10	)	)	PUNCT
ma-64	41	11	method[44	method[44	PROPN
ma-64	41	12	]	]	PUNCT
ma-64	41	13	was	be	AUX
ma-64	41	14	applied	apply	VERB
ma-64	41	15	to	to	PART
ma-64	41	16	solve	solve	VERB
ma-64	41	17	the	the	DET
ma-64	41	18	non	non	ADJ
ma-64	41	19	-	-	ADJ
ma-64	41	20	linear	linear	ADJ
ma-64	41	21	black	black	ADJ
ma-64	41	22	–	–	PUNCT
ma-64	41	23	scholes	schole	NOUN
ma-64	41	24	model	model	NOUN
ma-64	41	25	for	for	ADP
ma-64	41	26	pricing	price	VERB
ma-64	41	27	american	american	ADJ
ma-64	41	28	options	option	NOUN
ma-64	41	29	with	with	ADP
ma-64	41	30	ahighly	ahighly	ADV
ma-64	41	31	stable	stable	ADJ
ma-64	41	32	and	and	CCONJ
ma-64	41	33	efficient	efficient	ADJ
ma-64	41	34	transaction	transaction	NOUN
ma-64	41	35	cost	cost	NOUN
ma-64	41	36	.	.	PUNCT
ma-64	42	1	lesmana	lesmana	PROPN
ma-64	42	2	and	and	CCONJ
ma-64	42	3	wang	wang	PROPN
ma-64	43	1	[	[	X
ma-64	43	2	45	45	NUM
ma-64	43	3	]	]	PUNCT
ma-64	43	4	developed	develop	VERB
ma-64	43	5	the	the	DET
ma-64	43	6	numerical	numerical	ADJ
ma-64	43	7	methodbased	methodbase	VERB
ma-64	43	8	on	on	ADP
ma-64	43	9	an	an	DET
ma-64	43	10	upwind	upwind	ADJ
ma-64	43	11	finite	finite	ADJ
ma-64	43	12	difference	difference	NOUN
ma-64	43	13	scheme	scheme	NOUN
ma-64	43	14	for	for	ADP
ma-64	43	15	a	a	DET
ma-64	43	16	non	non	ADJ
ma-64	43	17	-	-	ADJ
ma-64	43	18	linear	linear	ADJ
ma-64	43	19	parabolic	parabolic	ADJ
ma-64	43	20	pde	pde	NOUN
ma-64	43	21	,	,	PUNCT
ma-64	43	22	and	and	CCONJ
ma-64	43	23	they	they	PRON
ma-64	43	24	attemptedto	attemptedto	VERB
ma-64	43	25	pricing	price	VERB
ma-64	43	26	european	european	ADJ
ma-64	43	27	options	option	NOUN
ma-64	43	28	under	under	ADP
ma-64	43	29	transaction	transaction	NOUN
ma-64	43	30	costs	cost	NOUN
ma-64	43	31	.	.	PUNCT
ma-64	44	1	ankudinova	ankudinova	PROPN
ma-64	44	2	and	and	CCONJ
ma-64	44	3	ehrhardt	ehrhardt	ADJ
ma-64	45	1	[	[	X
ma-64	45	2	46	46	NUM
ma-64	45	3	]	]	PUNCT
ma-64	45	4	focused	focus	VERB
ma-64	45	5	on	on	ADP
ma-64	45	6	thenon	thenon	ADJ
ma-64	45	7	-	-	ADJ
ma-64	45	8	linear	linear	ADJ
ma-64	45	9	black	black	ADJ
ma-64	45	10	-	-	PUNCT
ma-64	45	11	scholes	schole	NOUN
ma-64	45	12	equation	equation	NOUN
ma-64	45	13	for	for	ADP
ma-64	45	14	european	european	ADJ
ma-64	45	15	call	call	NOUN
ma-64	45	16	options	option	NOUN
ma-64	45	17	using	use	VERB
ma-64	45	18	several	several	ADJ
ma-64	45	19	transaction	transaction	NOUN
ma-64	45	20	cost	cost	NOUN
ma-64	45	21	modelsas	modelsa	NOUN
ma-64	45	22	well	well	ADV
ma-64	45	23	as	as	ADP
ma-64	45	24	crank	crank	NOUN
ma-64	45	25	–	–	PUNCT
ma-64	45	26	nicolson	nicolson	PROPN
ma-64	45	27	and	and	CCONJ
ma-64	45	28	rigal	rigal	ADJ
ma-64	45	29	compact	compact	ADJ
ma-64	45	30	schemes	scheme	NOUN
ma-64	45	31	.	.	PUNCT
ma-64	46	1	r.	r.	PROPN
ma-64	46	2	l.	l.	PROPN
ma-64	46	3	valkov	valkov	PROPN
ma-64	47	1	[	[	X
ma-64	47	2	47	47	NUM
ma-64	47	3	]	]	PUNCT
ma-64	47	4	has	have	AUX
ma-64	47	5	solved	solve	VERB
ma-64	47	6	the	the	DET
ma-64	47	7	non	non	ADJ
ma-64	47	8	-	-	ADJ
ma-64	47	9	linearblack	linearblack	ADJ
ma-64	47	10	–	–	PUNCT
ma-64	47	11	scholes	schole	NOUN
ma-64	47	12	-	-	PUNCT
ma-64	47	13	bellman	bellman	NOUN
ma-64	47	14	model	model	NOUN
ma-64	47	15	numerically	numerically	ADV
ma-64	47	16	as	as	ADV
ma-64	47	17	well	well	ADV
ma-64	47	18	as	as	ADP
ma-64	47	19	discuss	discuss	VERB
ma-64	47	20	the	the	DET
ma-64	47	21	monotonicity	monotonicity	NOUN
ma-64	47	22	and	and	CCONJ
ma-64	47	23	consistency	consistency	NOUN
ma-64	47	24	ofhis	ofhis	NOUN
ma-64	47	25	suggested	suggest	VERB
ma-64	47	26	scheme	scheme	NOUN
ma-64	47	27	in	in	ADP
ma-64	47	28	considerable	considerable	ADJ
ma-64	47	29	detail	detail	NOUN
ma-64	47	30	.	.	PUNCT
ma-64	48	1	a	a	DET
ma-64	48	2	monotone	monotone	ADJ
ma-64	48	3	finite	finite	NOUN
ma-64	48	4	volume	volume	NOUN
ma-64	48	5	spatial	spatial	ADJ
ma-64	48	6	discretization	discretization	NOUN
ma-64	48	7	and	and	CCONJ
ma-64	48	8	asecond	asecond	NOUN
ma-64	48	9	-	-	PUNCT
ma-64	48	10	order	order	NOUN
ma-64	48	11	predictor	predictor	NOUN
ma-64	48	12	-	-	PUNCT
ma-64	48	13	corrector	corrector	NOUN
ma-64	48	14	scheme	scheme	NOUN
ma-64	48	15	in	in	ADP
ma-64	48	16	time	time	NOUN
ma-64	48	17	are	be	AUX
ma-64	48	18	considered	consider	VERB
ma-64	48	19	by	by	ADP
ma-64	48	20	radoslas	radoslas	ADJ
ma-64	48	21	valkov	valkov	NOUN
ma-64	49	1	[	[	X
ma-64	49	2	48	48	NUM
ma-64	49	3	]	]	PUNCT
ma-64	49	4	to	to	ADP
ma-64	49	5	handlethe	handlethe	PRON
ma-64	49	6	black	black	ADJ
ma-64	49	7	–	–	PUNCT
ma-64	49	8	scholes	schole	NOUN
ma-64	49	9	equation	equation	NOUN
ma-64	49	10	with	with	ADP
ma-64	49	11	uncertain	uncertain	ADJ
ma-64	49	12	volatility	volatility	NOUN
ma-64	49	13	and	and	CCONJ
ma-64	49	14	dividend	dividend	NOUN
ma-64	49	15	.	.	PUNCT
ma-64	50	1	the	the	DET
ma-64	50	2	applicability	applicability	NOUN
ma-64	50	3	of	of	ADP
ma-64	50	4	implicit	implicit	ADJ
ma-64	50	5	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	50	6	eur	eur	NOUN
ma-64	50	7	.	.	PUNCT
ma-64	51	1	j.	j.	PROPN
ma-64	51	2	math	math	PROPN
ma-64	51	3	.	.	PUNCT
ma-64	52	1	anal	anal	PROPN
ma-64	52	2	.	.	PUNCT
ma-64	53	1	10.28924	10.28924	NUM
ma-64	53	2	/	/	SYM
ma-64	53	3	ada	ada	PROPN
ma-64	53	4	/	/	SYM
ma-64	53	5	ma.2.9	ma.2.9	PROPN
ma-64	53	6	3numerical	3numerical	NUM
ma-64	53	7	schemes	scheme	NOUN
ma-64	53	8	for	for	ADP
ma-64	53	9	the	the	DET
ma-64	53	10	valuation	valuation	NOUN
ma-64	53	11	of	of	ADP
ma-64	53	12	contingent	contingent	ADJ
ma-64	53	13	claims	claim	NOUN
ma-64	53	14	in	in	ADP
ma-64	53	15	non	non	ADJ
ma-64	53	16	-	-	ADJ
ma-64	53	17	linear	linear	ADJ
ma-64	53	18	black	black	ADJ
ma-64	53	19	–	–	PUNCT
ma-64	53	20	scholes	schole	NOUN
ma-64	53	21	models	model	NOUN
ma-64	53	22	hasbeen	hasbeen	ADJ
ma-64	53	23	discussed	discuss	VERB
ma-64	53	24	by	by	ADP
ma-64	53	25	pascal	pascal	ADJ
ma-64	53	26	heider	heider	NOUN
ma-64	53	27	[	[	X
ma-64	53	28	49	49	NUM
ma-64	53	29	]	]	PUNCT
ma-64	53	30	.	.	PUNCT
ma-64	54	1	he	he	PRON
ma-64	54	2	also	also	ADV
ma-64	54	3	studied	study	VERB
ma-64	54	4	the	the	DET
ma-64	54	5	practical	practical	ADJ
ma-64	54	6	implications	implication	NOUN
ma-64	54	7	of	of	ADP
ma-64	54	8	the	the	DET
ma-64	54	9	derivedstability	derivedstability	NOUN
ma-64	54	10	criteria	criterion	NOUN
ma-64	54	11	on	on	ADP
ma-64	54	12	relevant	relevant	ADJ
ma-64	54	13	numerical	numerical	ADJ
ma-64	54	14	examples	example	NOUN
ma-64	54	15	.	.	PUNCT
ma-64	55	1	he	he	PRON
ma-64	55	2	claimed	claim	VERB
ma-64	55	3	that	that	SCONJ
ma-64	55	4	if	if	SCONJ
ma-64	55	5	certain	certain	ADJ
ma-64	55	6	stability	stability	NOUN
ma-64	55	7	requirementsare	requirementsare	VERB
ma-64	55	8	satisfied	satisfied	ADJ
ma-64	55	9	,	,	PUNCT
ma-64	55	10	it	it	PRON
ma-64	55	11	is	be	AUX
ma-64	55	12	possible	possible	ADJ
ma-64	55	13	to	to	PART
ma-64	55	14	construct	construct	VERB
ma-64	55	15	convergent	convergent	ADJ
ma-64	55	16	implicit	implicit	ADJ
ma-64	55	17	algorithms	algorithm	NOUN
ma-64	55	18	for	for	ADP
ma-64	55	19	non	non	ADJ
ma-64	55	20	-	-	ADJ
ma-64	55	21	linear	linear	ADJ
ma-64	55	22	black	black	ADJ
ma-64	55	23	–	–	PUNCT
ma-64	55	24	scholesequations	scholesequation	NOUN
ma-64	55	25	.	.	PUNCT
ma-64	56	1	ekaterina	ekaterina	PROPN
ma-64	56	2	dremkova	dremkova	VERB
ma-64	56	3	and	and	CCONJ
ma-64	56	4	matthias	matthias	PROPN
ma-64	56	5	ehrhardt	ehrhardt	NOUN
ma-64	57	1	[	[	X
ma-64	57	2	50	50	NUM
ma-64	57	3	]	]	PUNCT
ma-64	57	4	have	have	AUX
ma-64	57	5	solved	solve	VERB
ma-64	57	6	non	non	ADJ
ma-64	57	7	-	-	ADJ
ma-64	57	8	linear	linear	ADJ
ma-64	57	9	black	black	ADJ
ma-64	57	10	–	–	PUNCT
ma-64	57	11	scholesequations	scholesequation	NOUN
ma-64	57	12	for	for	ADP
ma-64	57	13	american	american	ADJ
ma-64	57	14	options	option	NOUN
ma-64	57	15	with	with	ADP
ma-64	57	16	a	a	DET
ma-64	57	17	non	non	ADJ
ma-64	57	18	-	-	ADJ
ma-64	57	19	linear	linear	ADJ
ma-64	57	20	volatility	volatility	NOUN
ma-64	57	21	function	function	NOUN
ma-64	57	22	using	use	VERB
ma-64	57	23	various	various	ADJ
ma-64	57	24	compact	compact	ADJ
ma-64	57	25	finitedifference	finitedifference	NOUN
ma-64	57	26	techniques	technique	NOUN
ma-64	57	27	to	to	PART
ma-64	57	28	improve	improve	VERB
ma-64	57	29	the	the	DET
ma-64	57	30	order	order	NOUN
ma-64	57	31	of	of	ADP
ma-64	57	32	the	the	DET
ma-64	57	33	accuracy	accuracy	NOUN
ma-64	57	34	.	.	PUNCT
ma-64	58	1	the	the	DET
ma-64	58	2	existence	existence	NOUN
ma-64	58	3	and	and	CCONJ
ma-64	58	4	uniqueness	uniqueness	ADJ
ma-64	58	5	ofsolutions	ofsolution	NOUN
ma-64	58	6	to	to	ADP
ma-64	58	7	the	the	DET
ma-64	58	8	well	well	ADV
ma-64	58	9	-	-	PUNCT
ma-64	58	10	known	know	VERB
ma-64	58	11	non	non	ADJ
ma-64	58	12	-	-	ADJ
ma-64	58	13	linear	linear	ADJ
ma-64	58	14	black	black	ADJ
ma-64	58	15	-	-	PUNCT
ma-64	58	16	scholes	schole	NOUN
ma-64	58	17	equation	equation	NOUN
ma-64	58	18	have	have	AUX
ma-64	58	19	been	be	AUX
ma-64	58	20	demonstrated	demonstrate	VERB
ma-64	58	21	by	by	ADP
ma-64	58	22	naoyukiishimura	naoyukiishimura	NOUN
ma-64	58	23	[	[	X
ma-64	58	24	51	51	NUM
ma-64	58	25	]	]	PUNCT
ma-64	58	26	for	for	ADP
ma-64	58	27	both	both	PRON
ma-64	58	28	in	in	ADP
ma-64	58	29	the	the	DET
ma-64	58	30	classical	classical	ADJ
ma-64	58	31	and	and	CCONJ
ma-64	58	32	weak	weak	ADJ
ma-64	58	33	senses.however	senses.however	ADV
ma-64	58	34	,	,	PUNCT
ma-64	58	35	in	in	ADP
ma-64	58	36	this	this	DET
ma-64	58	37	paper	paper	NOUN
ma-64	58	38	,	,	PUNCT
ma-64	58	39	we	we	PRON
ma-64	58	40	work	work	VERB
ma-64	58	41	on	on	ADP
ma-64	58	42	approximating	approximate	VERB
ma-64	58	43	non	non	ADJ
ma-64	58	44	-	-	ADJ
ma-64	58	45	linear	linear	ADJ
ma-64	58	46	black	black	ADJ
ma-64	58	47	-	-	PUNCT
ma-64	58	48	scholes	schole	NOUN
ma-64	58	49	pde	pde	NOUN
ma-64	58	50	for	for	ADP
ma-64	58	51	valuingeuropean	valuingeuropean	ADJ
ma-64	58	52	options	option	NOUN
ma-64	58	53	when	when	SCONJ
ma-64	58	54	there	there	PRON
ma-64	58	55	are	be	VERB
ma-64	58	56	transaction	transaction	NOUN
ma-64	58	57	costs	cost	NOUN
ma-64	58	58	.	.	PUNCT
ma-64	59	1	for	for	ADP
ma-64	59	2	this	this	PRON
ma-64	59	3	,	,	PUNCT
ma-64	59	4	we	we	PRON
ma-64	59	5	organize	organize	VERB
ma-64	59	6	the	the	DET
ma-64	59	7	present	present	ADJ
ma-64	59	8	research	research	NOUN
ma-64	59	9	workas	workas	PROPN
ma-64	59	10	follows	follow	VERB
ma-64	59	11	:	:	PUNCT
ma-64	59	12	we	we	PRON
ma-64	59	13	modify	modify	VERB
ma-64	59	14	the	the	DET
ma-64	59	15	original	original	ADJ
ma-64	59	16	model	model	NOUN
ma-64	59	17	into	into	ADP
ma-64	59	18	parabolic	parabolic	ADJ
ma-64	59	19	type	type	NOUN
ma-64	59	20	pde	pde	NOUN
ma-64	59	21	exploiting	exploit	VERB
ma-64	59	22	the	the	DET
ma-64	59	23	transformations	transformation	NOUN
ma-64	59	24	[	[	X
ma-64	59	25	46]which	46]which	NUM
ma-64	59	26	are	be	AUX
ma-64	59	27	written	write	VERB
ma-64	59	28	in	in	ADP
ma-64	59	29	section	section	NOUN
ma-64	59	30	2	2	NUM
ma-64	59	31	.	.	PUNCT
ma-64	60	1	a	a	DET
ma-64	60	2	brief	brief	ADJ
ma-64	60	3	description	description	NOUN
ma-64	60	4	of	of	ADP
ma-64	60	5	different	different	ADJ
ma-64	60	6	volatility	volatility	NOUN
ma-64	60	7	models	model	NOUN
ma-64	60	8	is	be	AUX
ma-64	60	9	given	give	VERB
ma-64	60	10	in	in	ADP
ma-64	60	11	section3	section3	ADV
ma-64	60	12	subsequently	subsequently	ADV
ma-64	60	13	.	.	PUNCT
ma-64	61	1	section	section	NOUN
ma-64	61	2	4	4	NUM
ma-64	61	3	is	be	AUX
ma-64	61	4	devoted	devote	VERB
ma-64	61	5	to	to	PART
ma-64	61	6	discretize	discretize	VERB
ma-64	61	7	the	the	DET
ma-64	61	8	transformed	transform	VERB
ma-64	61	9	parabolic	parabolic	ADJ
ma-64	61	10	type	type	NOUN
ma-64	61	11	equation	equation	NOUN
ma-64	61	12	byusing	byuse	VERB
ma-64	61	13	some	some	DET
ma-64	61	14	numerical	numerical	ADJ
ma-64	61	15	schemes	scheme	NOUN
ma-64	61	16	.	.	PUNCT
ma-64	62	1	stability	stability	NOUN
ma-64	62	2	and	and	CCONJ
ma-64	62	3	consistency	consistency	NOUN
ma-64	62	4	analysis	analysis	NOUN
ma-64	62	5	are	be	AUX
ma-64	62	6	included	include	VERB
ma-64	62	7	in	in	ADP
ma-64	62	8	sections	section	NOUN
ma-64	62	9	5	5	NUM
ma-64	62	10	and6	and6	PROPN
ma-64	62	11	,	,	PUNCT
ma-64	62	12	respectively	respectively	ADV
ma-64	62	13	.	.	PUNCT
ma-64	63	1	in	in	ADP
ma-64	63	2	section	section	NOUN
ma-64	63	3	7	7	NUM
ma-64	63	4	,	,	PUNCT
ma-64	63	5	numerical	numerical	ADJ
ma-64	63	6	examples	example	NOUN
ma-64	63	7	are	be	AUX
ma-64	63	8	given	give	VERB
ma-64	63	9	to	to	PART
ma-64	63	10	show	show	VERB
ma-64	63	11	the	the	DET
ma-64	63	12	efficacy	efficacy	NOUN
ma-64	63	13	of	of	ADP
ma-64	63	14	the	the	DET
ma-64	63	15	proposedschemes	proposedscheme	NOUN
ma-64	63	16	.	.	PUNCT
ma-64	64	1	subsequently	subsequently	ADV
ma-64	64	2	,	,	PUNCT
ma-64	64	3	a	a	DET
ma-64	64	4	general	general	ADJ
ma-64	64	5	conclusion	conclusion	NOUN
ma-64	64	6	is	be	AUX
ma-64	64	7	drawn	draw	VERB
ma-64	64	8	in	in	ADP
ma-64	64	9	section	section	NOUN
ma-64	64	10	8	8	NUM
ma-64	64	11	.	.	PUNCT
ma-64	65	1	finally	finally	ADV
ma-64	65	2	,	,	PUNCT
ma-64	65	3	all	all	DET
ma-64	65	4	relevant	relevant	ADJ
ma-64	65	5	referencesare	referencesare	NOUN
ma-64	65	6	included	include	VERB
ma-64	65	7	.	.	PUNCT
ma-64	66	1	2	2	X
ma-64	66	2	.	.	X
ma-64	66	3	the	the	DET
ma-64	66	4	model	model	NOUN
ma-64	66	5	equation	equation	NOUN
ma-64	66	6	this	this	DET
ma-64	66	7	section	section	NOUN
ma-64	66	8	considers	consider	VERB
ma-64	66	9	a	a	DET
ma-64	66	10	non	non	ADJ
ma-64	66	11	-	-	ADJ
ma-64	66	12	linear	linear	ADJ
ma-64	66	13	black	black	ADJ
ma-64	66	14	-	-	PUNCT
ma-64	66	15	scholes	schole	NOUN
ma-64	66	16	pde	pde	NOUN
ma-64	66	17	and	and	CCONJ
ma-64	66	18	modifies	modify	VERB
ma-64	66	19	it	it	PRON
ma-64	66	20	to	to	ADP
ma-64	66	21	a	a	DET
ma-64	66	22	non	non	ADJ
ma-64	66	23	-	-	ADJ
ma-64	66	24	linear	linear	ADJ
ma-64	66	25	parabolictype	parabolictype	NOUN
ma-64	66	26	equation	equation	NOUN
ma-64	66	27	with	with	ADP
ma-64	66	28	appropriate	appropriate	ADJ
ma-64	66	29	and	and	CCONJ
ma-64	66	30	available	available	ADJ
ma-64	66	31	transformations	transformation	NOUN
ma-64	66	32	,	,	PUNCT
ma-64	66	33	which	which	PRON
ma-64	66	34	would	would	AUX
ma-64	66	35	be	be	AUX
ma-64	66	36	easy	easy	ADJ
ma-64	66	37	to	to	PART
ma-64	66	38	computenumerically	computenumerically	ADV
ma-64	66	39	.	.	PUNCT
ma-64	67	1	let	let	VERB
ma-64	67	2	us	we	PRON
ma-64	67	3	consider	consider	VERB
ma-64	67	4	the	the	DET
ma-64	67	5	non	non	ADJ
ma-64	67	6	-	-	ADJ
ma-64	67	7	linear	linear	ADJ
ma-64	67	8	black	black	ADJ
ma-64	67	9	-	-	PUNCT
ma-64	67	10	scholes	schole	NOUN
ma-64	67	11	pde	pde	NOUN
ma-64	68	1	[	[	X
ma-64	68	2	46	46	NUM
ma-64	68	3	]	]	X
ma-64	68	4	,	,	PUNCT
ma-64	68	5	∂f	∂f	PROPN
ma-64	68	6	∂t	∂t	PROPN
ma-64	69	1	+	+	NUM
ma-64	69	2	rs	rs	ADJ
ma-64	69	3	∂f	∂f	PROPN
ma-64	69	4	∂s	∂s	PROPN
ma-64	69	5	+	+	CCONJ
ma-64	69	6	1	1	NUM
ma-64	69	7	2	2	NUM
ma-64	69	8	σ̃2s2	σ̃2s2	PROPN
ma-64	69	9	∂	∂	NUM
ma-64	69	10	2f	2f	NUM
ma-64	69	11	∂s2	∂s2	NOUN
ma-64	69	12	−	−	PROPN
ma-64	69	13	rf	rf	NOUN
ma-64	69	14	=	=	NOUN
ma-64	69	15	0	0	NUM
ma-64	69	16	,	,	PUNCT
ma-64	69	17	0	0	PUNCT
ma-64	69	18	<	<	X
ma-64	69	19	s	s	X
ma-64	69	20	<	<	X
ma-64	69	21	∞	∞	PROPN
ma-64	69	22	,	,	PUNCT
ma-64	69	23	t	t	PROPN
ma-64	69	24	∈	∈	PROPN
ma-64	69	25	(	(	PUNCT
ma-64	69	26	0	0	NUM
ma-64	69	27	,	,	PUNCT
ma-64	69	28	t	t	NOUN
ma-64	69	29	)	)	PUNCT
ma-64	69	30	(	(	PUNCT
ma-64	69	31	1	1	X
ma-64	69	32	)	)	PUNCT
ma-64	69	33	subject	subject	NOUN
ma-64	69	34	to	to	ADP
ma-64	69	35	the	the	DET
ma-64	69	36	terminal	terminal	ADJ
ma-64	69	37	and	and	CCONJ
ma-64	69	38	boundary	boundary	ADJ
ma-64	69	39	conditions	condition	NOUN
ma-64	69	40	for	for	ADP
ma-64	69	41	european	european	ADJ
ma-64	69	42	call	call	NOUN
ma-64	69	43	and	and	CCONJ
ma-64	69	44	put	put	VERB
ma-64	69	45	options	option	NOUN
ma-64	69	46	:	:	PUNCT
ma-64	69	47	f	f	PROPN
ma-64	69	48	(	(	PUNCT
ma-64	69	49	s	s	PROPN
ma-64	69	50	,	,	PUNCT
ma-64	69	51	t	t	NOUN
ma-64	69	52	)	)	PUNCT
ma-64	70	1	=	=	SYM
ma-64	71	1	max(s	max(s	PROPN
ma-64	71	2	−	−	NUM
ma-64	71	3	k	k	NOUN
ma-64	71	4	,	,	PUNCT
ma-64	71	5	0	0	NUM
ma-64	71	6	)	)	PUNCT
ma-64	71	7	,	,	PUNCT
ma-64	71	8	f	f	PROPN
ma-64	71	9	(	(	PUNCT
ma-64	71	10	s	s	PROPN
ma-64	71	11	,	,	PUNCT
ma-64	71	12	t	t	PROPN
ma-64	71	13	)	)	PUNCT
ma-64	71	14	=	=	SYM
ma-64	72	1	0	0	PUNCT
ma-64	72	2	when	when	SCONJ
ma-64	72	3	s	s	VERB
ma-64	72	4	=	=	SYM
ma-64	72	5	0	0	PROPN
ma-64	72	6	,	,	PUNCT
ma-64	72	7	f	f	X
ma-64	72	8	(	(	PUNCT
ma-64	72	9	s	s	PROPN
ma-64	72	10	,	,	PUNCT
ma-64	72	11	t	t	PROPN
ma-64	72	12	)	)	PUNCT
ma-64	72	13	=	=	SYM
ma-64	72	14	s	s	PART
ma-64	72	15	−	−	NOUN
ma-64	72	16	ke−r(t−t	ke−r(t−t	PROPN
ma-64	72	17	)	)	PUNCT
ma-64	72	18	,	,	PUNCT
ma-64	72	19	when	when	SCONJ
ma-64	72	20	s	s	X
ma-64	72	21	→	→	SYM
ma-64	72	22	∞and	∞and	ADJ
ma-64	72	23	f	f	X
ma-64	72	24	(	(	PUNCT
ma-64	72	25	s	s	PROPN
ma-64	72	26	,	,	PUNCT
ma-64	72	27	t	t	NOUN
ma-64	72	28	)	)	PUNCT
ma-64	73	1	=	=	PUNCT
ma-64	73	2	max(k	max(k	NOUN
ma-64	73	3	−	−	NOUN
ma-64	73	4	s	s	PROPN
ma-64	73	5	,	,	PUNCT
ma-64	73	6	0	0	NUM
ma-64	73	7	)	)	PUNCT
ma-64	73	8	,	,	PUNCT
ma-64	73	9	f	f	PROPN
ma-64	73	10	(	(	PUNCT
ma-64	73	11	s	s	PROPN
ma-64	73	12	,	,	PUNCT
ma-64	73	13	t	t	PROPN
ma-64	73	14	)	)	PUNCT
ma-64	73	15	=	=	SYM
ma-64	73	16	ke−r(t−t	ke−r(t−t	PROPN
ma-64	73	17	)	)	PUNCT
ma-64	73	18	,	,	PUNCT
ma-64	73	19	when	when	SCONJ
ma-64	73	20	s	s	VERB
ma-64	73	21	=	=	SYM
ma-64	73	22	0	0	PROPN
ma-64	73	23	,	,	PUNCT
ma-64	73	24	f	f	X
ma-64	73	25	(	(	PUNCT
ma-64	73	26	s	s	PROPN
ma-64	73	27	,	,	PUNCT
ma-64	73	28	t	t	PROPN
ma-64	73	29	)	)	PUNCT
ma-64	73	30	=	=	SYM
ma-64	74	1	0	0	NUM
ma-64	74	2	,	,	PUNCT
ma-64	74	3	when	when	SCONJ
ma-64	74	4	s	s	X
ma-64	74	5	→	→	SYM
ma-64	74	6	∞respectively	∞respectively	ADV
ma-64	74	7	.	.	PUNCT
ma-64	75	1	throughout	throughout	ADP
ma-64	75	2	this	this	DET
ma-64	75	3	paper	paper	NOUN
ma-64	75	4	,	,	PUNCT
ma-64	75	5	we	we	PRON
ma-64	75	6	use	use	VERB
ma-64	75	7	the	the	DET
ma-64	75	8	notations	notation	NOUN
ma-64	75	9	:	:	PUNCT
ma-64	76	1	f	f	PROPN
ma-64	76	2	=	=	SYM
ma-64	76	3	f	f	PROPN
ma-64	76	4	(	(	PUNCT
ma-64	76	5	s	s	PROPN
ma-64	76	6	,	,	PUNCT
ma-64	76	7	t	t	PROPN
ma-64	76	8	)	)	PUNCT
ma-64	76	9	=	=	NOUN
ma-64	77	1	the	the	DET
ma-64	77	2	option	option	NOUN
ma-64	77	3	price	price	NOUN
ma-64	77	4	,	,	PUNCT
ma-64	77	5	s	s	NOUN
ma-64	77	6	=	=	NOUN
ma-64	77	7	stock	stock	NOUN
ma-64	77	8	price	price	NOUN
ma-64	77	9	,	,	PUNCT
ma-64	77	10	k	k	NOUN
ma-64	77	11	=	=	PUNCT
ma-64	77	12	strike	strike	NOUN
ma-64	77	13	price	price	NOUN
ma-64	77	14	,	,	PUNCT
ma-64	77	15	t	t	NOUN
ma-64	77	16	=	=	SYM
ma-64	77	17	maturity	maturity	NOUN
ma-64	77	18	time	time	NOUN
ma-64	77	19	,	,	PUNCT
ma-64	77	20	r	r	NOUN
ma-64	77	21	=	=	SYM
ma-64	77	22	interest	interest	NOUN
ma-64	77	23	rate	rate	NOUN
ma-64	77	24	,	,	PUNCT
ma-64	77	25	t	t	NOUN
ma-64	77	26	=	=	PUNCT
ma-64	77	27	time	time	NOUN
ma-64	77	28	in	in	ADP
ma-64	77	29	years	year	NOUN
ma-64	77	30	,	,	PUNCT
ma-64	77	31	and	and	CCONJ
ma-64	78	1	σ̃	σ̃	PROPN
ma-64	78	2	=	=	SYM
ma-64	78	3	σ̃	σ̃	PROPN
ma-64	78	4	(	(	PUNCT
ma-64	78	5	t	t	PROPN
ma-64	78	6	,	,	PUNCT
ma-64	78	7	s	s	PROPN
ma-64	78	8	,	,	PUNCT
ma-64	78	9	∂f∂s	∂f∂s	VERB
ma-64	78	10	,	,	PUNCT
ma-64	78	11	∂2f	∂2f	VERB
ma-64	78	12	∂s2	∂s2	NOUN
ma-64	78	13	)	)	PUNCT
ma-64	78	14	depends	depend	VERB
ma-64	78	15	on	on	ADP
ma-64	78	16	the	the	DET
ma-64	78	17	volatility	volatility	NOUN
ma-64	78	18	model	model	NOUN
ma-64	78	19	.	.	PUNCT
ma-64	79	1	now	now	ADV
ma-64	79	2	consider	consider	VERB
ma-64	79	3	the	the	DET
ma-64	79	4	transformations	transformation	NOUN
ma-64	79	5	[	[	X
ma-64	79	6	46	46	NUM
ma-64	79	7	]	]	PUNCT
ma-64	79	8	as	as	SCONJ
ma-64	79	9	given	give	VERB
ma-64	79	10	below	below	ADV
ma-64	79	11	,	,	PUNCT
ma-64	79	12	y	y	PROPN
ma-64	79	13	=	=	PUNCT
ma-64	79	14	ln	ln	PROPN
ma-64	79	15	(	(	PUNCT
ma-64	79	16	k−1s	k−1s	NOUN
ma-64	79	17	)	)	PUNCT
ma-64	79	18	,	,	PUNCT
ma-64	80	1	τ	τ	PROPN
ma-64	80	2	=	=	SYM
ma-64	80	3	1	1	NUM
ma-64	80	4	2	2	NUM
ma-64	80	5	σ2(t	σ2(t	NOUN
ma-64	80	6	−	−	PROPN
ma-64	80	7	t	t	PROPN
ma-64	80	8	)	)	PUNCT
ma-64	80	9	and	and	CCONJ
ma-64	80	10	u(y	u(y	PROPN
ma-64	80	11	,	,	PUNCT
ma-64	80	12	t	t	PROPN
ma-64	80	13	)	)	PUNCT
ma-64	80	14	=	=	VERB
ma-64	81	1	k−1e−yf	k−1e−yf	VERB
ma-64	81	2	(	(	PUNCT
ma-64	81	3	s	s	PROPN
ma-64	81	4	,	,	PUNCT
ma-64	81	5	t	t	PROPN
ma-64	81	6	)	)	PUNCT
ma-64	81	7	and	and	CCONJ
ma-64	81	8	substituting	substitute	VERB
ma-64	81	9	these	these	PRON
ma-64	81	10	into	into	ADP
ma-64	81	11	equation	equation	NOUN
ma-64	81	12	(	(	PUNCT
ma-64	81	13	1	1	NUM
ma-64	81	14	)	)	PUNCT
ma-64	81	15	to	to	PART
ma-64	81	16	obtain	obtain	VERB
ma-64	81	17	the	the	DET
ma-64	81	18	following	follow	VERB
ma-64	81	19	non	non	ADJ
ma-64	81	20	-	-	ADJ
ma-64	81	21	linear	linear	ADJ
ma-64	81	22	parabolic	parabolic	ADJ
ma-64	81	23	pde	pde	NOUN
ma-64	81	24	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	81	25	eur	eur	PROPN
ma-64	81	26	.	.	PUNCT
ma-64	82	1	j.	j.	PROPN
ma-64	82	2	math	math	PROPN
ma-64	82	3	.	.	PUNCT
ma-64	83	1	anal	anal	PROPN
ma-64	83	2	.	.	PUNCT
ma-64	84	1	10.28924	10.28924	NUM
ma-64	84	2	/	/	SYM
ma-64	84	3	ada	ada	PROPN
ma-64	84	4	/	/	SYM
ma-64	84	5	ma.2.9	ma.2.9	PROPN
ma-64	84	6	4	4	NUM
ma-64	84	7	∂u	∂u	NOUN
ma-64	84	8	∂τ	∂τ	PROPN
ma-64	84	9	=	=	SYM
ma-64	84	10	2r	2r	NUM
ma-64	84	11	σ2	σ2	PROPN
ma-64	84	12	∂u	∂u	PROPN
ma-64	84	13	∂y	∂y	PRON
ma-64	85	1	+	+	CCONJ
ma-64	85	2	(	(	PUNCT
ma-64	85	3	σ̃	σ̃	PROPN
ma-64	85	4	σ	σ	PROPN
ma-64	85	5	)	)	PUNCT
ma-64	85	6	2(∂2u	2(∂2u	NUM
ma-64	85	7	∂y2	∂y2	ADJ
ma-64	85	8	+	+	CCONJ
ma-64	85	9	∂u	∂u	PROPN
ma-64	85	10	∂y	∂y	PROPN
ma-64	85	11	)	)	PUNCT
ma-64	86	1	,	,	PUNCT
ma-64	86	2	ymin	ymin	VERB
ma-64	86	3	<	<	X
ma-64	86	4	y	y	X
ma-64	86	5	<	<	X
ma-64	86	6	ymax	ymax	PROPN
ma-64	86	7	,	,	PUNCT
ma-64	86	8	τ	τ	PROPN
ma-64	86	9	∈	∈	PROPN
ma-64	86	10	(	(	PUNCT
ma-64	86	11	0	0	NUM
ma-64	86	12	,	,	PUNCT
ma-64	86	13	σ2	σ2	NOUN
ma-64	86	14	2	2	NUM
ma-64	86	15	t	t	NOUN
ma-64	86	16	)	)	PUNCT
ma-64	86	17	(	(	PUNCT
ma-64	86	18	2	2	X
ma-64	86	19	)	)	PUNCT
ma-64	86	20	with	with	ADP
ma-64	86	21	the	the	DET
ma-64	86	22	modified	modify	VERB
ma-64	86	23	initial	initial	ADJ
ma-64	86	24	and	and	CCONJ
ma-64	86	25	boundary	boundary	ADJ
ma-64	86	26	conditions	condition	NOUN
ma-64	86	27	for	for	ADP
ma-64	86	28	european	european	ADJ
ma-64	86	29	call	call	NOUN
ma-64	86	30	and	and	CCONJ
ma-64	86	31	put	put	VERB
ma-64	86	32	options	option	NOUN
ma-64	86	33	:	:	PUNCT
ma-64	86	34	u(y	u(y	NOUN
ma-64	86	35	,	,	PUNCT
ma-64	86	36	0	0	NUM
ma-64	86	37	)	)	PUNCT
ma-64	87	1	=	=	SYM
ma-64	87	2	max	max	PROPN
ma-64	87	3	(	(	PUNCT
ma-64	87	4	1−	1−	NUM
ma-64	87	5	e−y	e−y	PROPN
ma-64	87	6	,	,	PUNCT
ma-64	87	7	0	0	NUM
ma-64	87	8	)	)	PUNCT
ma-64	87	9	as	as	ADP
ma-64	87	10	y	y	PROPN
ma-64	87	11	∈	∈	PROPN
ma-64	87	12	(	(	PUNCT
ma-64	87	13	−∞,∞	−∞,∞	NOUN
ma-64	87	14	)	)	PUNCT
ma-64	87	15	,	,	PUNCT
ma-64	87	16	u(y	u(y	PROPN
ma-64	87	17	,	,	PUNCT
ma-64	87	18	τ	τ	PROPN
ma-64	87	19	)	)	PUNCT
ma-64	87	20	=	=	SYM
ma-64	87	21	0	0	PUNCT
ma-64	88	1	as	as	ADP
ma-64	88	2	y	y	PROPN
ma-64	88	3	→	→	SYM
ma-64	88	4	−∞	−∞	PROPN
ma-64	88	5	,	,	PUNCT
ma-64	88	6	u(y	u(y	PROPN
ma-64	88	7	,	,	PUNCT
ma-64	88	8	τ	τ	PROPN
ma-64	88	9	)	)	PUNCT
ma-64	88	10	=	=	SYM
ma-64	88	11	1−	1−	NUM
ma-64	88	12	e−(y+2rτ	e−(y+2rτ	NOUN
ma-64	88	13	/	/	SYM
ma-64	88	14	σ2)as	σ2)as	PROPN
ma-64	88	15	y	y	PROPN
ma-64	88	16	→∞	→∞	PROPN
ma-64	88	17	,	,	PUNCT
ma-64	88	18	and	and	CCONJ
ma-64	88	19	u(y	u(y	PROPN
ma-64	88	20	,	,	PUNCT
ma-64	88	21	0	0	NUM
ma-64	88	22	)	)	PUNCT
ma-64	88	23	=	=	SYM
ma-64	88	24	max	max	PROPN
ma-64	88	25	(	(	PUNCT
ma-64	88	26	e−y	e−y	PROPN
ma-64	88	27	−	−	PROPN
ma-64	88	28	1	1	NUM
ma-64	88	29	,	,	PUNCT
ma-64	88	30	0	0	NUM
ma-64	88	31	)	)	PUNCT
ma-64	88	32	as	as	ADP
ma-64	88	33	y	y	PROPN
ma-64	88	34	∈	∈	PROPN
ma-64	88	35	(	(	PUNCT
ma-64	88	36	−∞,∞	−∞,∞	NOUN
ma-64	88	37	)	)	PUNCT
ma-64	88	38	,	,	PUNCT
ma-64	88	39	u(y	u(y	PROPN
ma-64	88	40	,	,	PUNCT
ma-64	88	41	τ	τ	PROPN
ma-64	88	42	)	)	PUNCT
ma-64	88	43	=	=	PUNCT
ma-64	88	44	e−(y+2rτ	e−(y+2rτ	PUNCT
ma-64	88	45	/	/	SYM
ma-64	88	46	σ2	σ2	NOUN
ma-64	88	47	)	)	PUNCT
ma-64	88	48	as	as	ADP
ma-64	88	49	y	y	PROPN
ma-64	88	50	→	→	SYM
ma-64	88	51	−∞	−∞	PROPN
ma-64	88	52	,	,	PUNCT
ma-64	88	53	u(y	u(y	PROPN
ma-64	88	54	,	,	PUNCT
ma-64	88	55	τ	τ	PROPN
ma-64	88	56	)	)	PUNCT
ma-64	88	57	=	=	SYM
ma-64	88	58	0	0	PUNCT
ma-64	88	59	as	as	ADP
ma-64	88	60	y	y	PROPN
ma-64	88	61	→∞	→∞	PROPN
ma-64	88	62	,	,	PUNCT
ma-64	88	63	respectively	respectively	ADV
ma-64	88	64	.	.	PUNCT
ma-64	89	1	3	3	X
ma-64	89	2	.	.	X
ma-64	89	3	volatility	volatility	NOUN
ma-64	89	4	models	model	NOUN
ma-64	89	5	this	this	DET
ma-64	89	6	section	section	NOUN
ma-64	89	7	concerns	concern	VERB
ma-64	89	8	four	four	NUM
ma-64	89	9	stochastic	stochastic	ADJ
ma-64	89	10	volatility	volatility	NOUN
ma-64	89	11	models	model	NOUN
ma-64	89	12	to	to	PART
ma-64	89	13	discretize	discretize	VERB
ma-64	89	14	the	the	DET
ma-64	89	15	non	non	ADJ
ma-64	89	16	-	-	ADJ
ma-64	89	17	linear	linear	ADJ
ma-64	89	18	black	black	NOUN
ma-64	89	19	-	-	PUNCT
ma-64	89	20	scholespde	scholespde	NOUN
ma-64	89	21	,	,	PUNCT
ma-64	89	22	whose	whose	DET
ma-64	89	23	solution	solution	NOUN
ma-64	89	24	provides	provide	VERB
ma-64	89	25	the	the	DET
ma-64	89	26	option	option	NOUN
ma-64	89	27	price	price	NOUN
ma-64	89	28	for	for	ADP
ma-64	89	29	transaction	transaction	NOUN
ma-64	89	30	fees	fee	NOUN
ma-64	89	31	.	.	PUNCT
ma-64	90	1	we	we	PRON
ma-64	90	2	give	give	VERB
ma-64	90	3	a	a	DET
ma-64	90	4	short	short	ADJ
ma-64	90	5	description	description	NOUN
ma-64	90	6	,	,	PUNCT
ma-64	90	7	but	but	CCONJ
ma-64	90	8	details	detail	NOUN
ma-64	90	9	are	be	AUX
ma-64	90	10	available	available	ADJ
ma-64	90	11	in	in	ADP
ma-64	90	12	some	some	DET
ma-64	90	13	previous	previous	ADJ
ma-64	90	14	literature	literature	NOUN
ma-64	90	15	[	[	X
ma-64	90	16	46	46	NUM
ma-64	90	17	]	]	PUNCT
ma-64	90	18	.	.	PUNCT
ma-64	91	1	leland	leland	PROPN
ma-64	91	2	volatility	volatility	PROPN
ma-64	91	3	model	model	NOUN
ma-64	91	4	(	(	PUNCT
ma-64	91	5	lvm	lvm	NOUN
ma-64	91	6	)	)	PUNCT
ma-64	91	7	.	.	PUNCT
ma-64	92	1	leland	leland	PROPN
ma-64	93	1	[	[	X
ma-64	93	2	37	37	NUM
ma-64	93	3	]	]	PUNCT
ma-64	93	4	developed	develop	VERB
ma-64	93	5	a	a	DET
ma-64	93	6	technique	technique	NOUN
ma-64	93	7	for	for	ADP
ma-64	93	8	replicating	replicate	VERB
ma-64	93	9	options	option	NOUN
ma-64	93	10	in	in	ADP
ma-64	93	11	thepresence	thepresence	NOUN
ma-64	93	12	of	of	ADP
ma-64	93	13	transactions	transaction	NOUN
ma-64	93	14	costs	cost	NOUN
ma-64	93	15	for	for	ADP
ma-64	93	16	a	a	DET
ma-64	93	17	small	small	ADJ
ma-64	93	18	time	time	NOUN
ma-64	93	19	interval	interval	NOUN
ma-64	93	20	.	.	PUNCT
ma-64	94	1	he	he	PRON
ma-64	94	2	proposed	propose	VERB
ma-64	94	3	that	that	SCONJ
ma-64	94	4	the	the	DET
ma-64	94	5	option	option	NOUN
ma-64	94	6	price	price	NOUN
ma-64	94	7	isthe	isthe	ADJ
ma-64	94	8	solution	solution	NOUN
ma-64	94	9	of	of	ADP
ma-64	94	10	the	the	DET
ma-64	94	11	non	non	ADJ
ma-64	94	12	-	-	ADJ
ma-64	94	13	linear	linear	ADJ
ma-64	94	14	black	black	ADJ
ma-64	94	15	-	-	PUNCT
ma-64	94	16	scholes	schole	NOUN
ma-64	94	17	equation	equation	NOUN
ma-64	94	18	(	(	PUNCT
ma-64	94	19	1	1	NUM
ma-64	94	20	)	)	PUNCT
ma-64	94	21	but	but	CCONJ
ma-64	94	22	with	with	ADP
ma-64	94	23	the	the	DET
ma-64	94	24	adjusted	adjusted	ADJ
ma-64	94	25	volatility	volatility	NOUN
ma-64	94	26	[	[	X
ma-64	94	27	46	46	NUM
ma-64	94	28	]	]	X
ma-64	94	29	asfollows	asfollow	VERB
ma-64	94	30	:	:	PUNCT
ma-64	94	31	σ̃	σ̃	PROPN
ma-64	94	32	=	=	PUNCT
ma-64	94	33	σ	σ	NOUN
ma-64	94	34	√	√	NOUN
ma-64	94	35	1	1	NUM
ma-64	94	36	+	+	CCONJ
ma-64	94	37	√	√	NUM
ma-64	94	38	2	2	NUM
ma-64	94	39	π	π	PROPN
ma-64	94	40	µ	µ	X
ma-64	94	41	σ	σ	NOUN
ma-64	94	42	√	√	CCONJ
ma-64	94	43	∆t	∆t	PROPN
ma-64	94	44	sign	sign	NOUN
ma-64	94	45	(	(	PUNCT
ma-64	94	46	fss	fss	NOUN
ma-64	94	47	)	)	PUNCT
ma-64	94	48	(	(	PUNCT
ma-64	94	49	3	3	X
ma-64	94	50	)	)	PUNCT
ma-64	94	51	where	where	SCONJ
ma-64	94	52	,	,	PUNCT
ma-64	94	53	σ	σ	PROPN
ma-64	94	54	is	be	AUX
ma-64	94	55	the	the	DET
ma-64	94	56	original	original	ADJ
ma-64	94	57	volatility	volatility	NOUN
ma-64	94	58	,	,	PUNCT
ma-64	94	59	µ	µ	X
ma-64	94	60	is	be	AUX
ma-64	94	61	the	the	DET
ma-64	94	62	round	round	ADJ
ma-64	94	63	-	-	PUNCT
ma-64	94	64	trip	trip	NOUN
ma-64	94	65	transaction	transaction	NOUN
ma-64	94	66	cost	cost	NOUN
ma-64	94	67	per	per	ADP
ma-64	94	68	unit	unit	NOUN
ma-64	94	69	dollar	dollar	NOUN
ma-64	94	70	of	of	ADP
ma-64	94	71	the	the	DET
ma-64	94	72	trans	trans	NOUN
ma-64	94	73	-	-	NOUN
ma-64	94	74	action	action	NOUN
ma-64	94	75	,	,	PUNCT
ma-64	94	76	and	and	CCONJ
ma-64	94	77	∆t	∆t	PROPN
ma-64	94	78	is	be	AUX
ma-64	94	79	the	the	DET
ma-64	94	80	transaction	transaction	NOUN
ma-64	94	81	frequency	frequency	NOUN
ma-64	94	82	.	.	PUNCT
ma-64	95	1	in	in	ADP
ma-64	95	2	this	this	DET
ma-64	95	3	formula	formula	NOUN
ma-64	95	4	,	,	PUNCT
ma-64	95	5	both	both	PRON
ma-64	95	6	µ	µ	NOUN
ma-64	95	7	and	and	CCONJ
ma-64	95	8	∆t	∆t	PROPN
ma-64	95	9	are	be	AUX
ma-64	95	10	assumed	assume	VERB
ma-64	95	11	to	to	PART
ma-64	95	12	be	be	AUX
ma-64	95	13	smallwhile	smallwhile	NOUN
ma-64	95	14	keeping	keep	VERB
ma-64	95	15	the	the	DET
ma-64	95	16	ratio	ratio	NOUN
ma-64	95	17	µ√	µ√	NOUN
ma-64	95	18	∆t	∆t	PROPN
ma-64	95	19	of	of	ADP
ma-64	95	20	order	order	NOUN
ma-64	95	21	one	one	NUM
ma-64	95	22	.	.	PUNCT
ma-64	96	1	boyle	boyle	PROPN
ma-64	96	2	and	and	CCONJ
ma-64	96	3	vorst	vorst	PROPN
ma-64	96	4	volatility	volatility	NOUN
ma-64	96	5	model	model	NOUN
ma-64	96	6	(	(	PUNCT
ma-64	96	7	bvvm	bvvm	NOUN
ma-64	96	8	)	)	PUNCT
ma-64	96	9	.	.	PUNCT
ma-64	97	1	boyle	boyle	PROPN
ma-64	97	2	and	and	CCONJ
ma-64	97	3	vorst	vorst	PROPN
ma-64	98	1	[	[	X
ma-64	98	2	38	38	NUM
ma-64	98	3	]	]	PUNCT
ma-64	98	4	derived	derive	VERB
ma-64	98	5	a	a	DET
ma-64	98	6	method	method	NOUN
ma-64	98	7	for	for	ADP
ma-64	98	8	calculatingoption	calculatingoption	NOUN
ma-64	98	9	prices	price	NOUN
ma-64	98	10	in	in	ADP
ma-64	98	11	a	a	DET
ma-64	98	12	discrete	discrete	ADJ
ma-64	98	13	-	-	PUNCT
ma-64	98	14	time	time	NOUN
ma-64	98	15	where	where	SCONJ
ma-64	98	16	option	option	NOUN
ma-64	98	17	price	price	NOUN
ma-64	98	18	meets	meet	VERB
ma-64	98	19	to	to	ADP
ma-64	98	20	black	black	ADJ
ma-64	98	21	-	-	PUNCT
ma-64	98	22	scholes	schole	NOUN
ma-64	98	23	price	price	NOUN
ma-64	98	24	with	with	ADP
ma-64	98	25	the	the	DET
ma-64	98	26	modifiedvolatility	modifiedvolatility	NOUN
ma-64	98	27	[	[	X
ma-64	98	28	46	46	NUM
ma-64	98	29	]	]	PUNCT
ma-64	98	30	given	give	VERB
ma-64	98	31	by	by	ADP
ma-64	98	32	σ̃	σ̃	PROPN
ma-64	98	33	=	=	SYM
ma-64	98	34	σ	σ	NOUN
ma-64	98	35	√	√	ADV
ma-64	98	36	1	1	NUM
ma-64	98	37	+	+	SYM
ma-64	98	38	µ	µ	PROPN
ma-64	98	39	σ	σ	PRON
ma-64	98	40	√	√	CCONJ
ma-64	98	41	∆t	∆t	PROPN
ma-64	98	42	sign	sign	NOUN
ma-64	98	43	(	(	PUNCT
ma-64	98	44	fss	fss	NOUN
ma-64	98	45	)	)	PUNCT
ma-64	98	46	(	(	PUNCT
ma-64	98	47	4	4	X
ma-64	98	48	)	)	PUNCT
ma-64	98	49	where	where	SCONJ
ma-64	98	50	,	,	PUNCT
ma-64	98	51	σ	σ	PROPN
ma-64	98	52	,	,	PUNCT
ma-64	98	53	µ	µ	NOUN
ma-64	98	54	,	,	PUNCT
ma-64	98	55	and	and	CCONJ
ma-64	98	56	∆t	∆t	PROPN
ma-64	98	57	represents	represent	VERB
ma-64	98	58	the	the	DET
ma-64	98	59	same	same	ADJ
ma-64	98	60	meaning	meaning	NOUN
ma-64	98	61	as	as	ADP
ma-64	98	62	leland	leland	PROPN
ma-64	98	63	.	.	PUNCT
ma-64	99	1	barles	barle	NOUN
ma-64	99	2	and	and	CCONJ
ma-64	99	3	soner	soner	NOUN
ma-64	99	4	volatility	volatility	NOUN
ma-64	99	5	model	model	NOUN
ma-64	99	6	(	(	PUNCT
ma-64	99	7	bsvm	bsvm	PROPN
ma-64	99	8	)	)	PUNCT
ma-64	99	9	.	.	PUNCT
ma-64	100	1	barles	barle	NOUN
ma-64	100	2	and	and	CCONJ
ma-64	100	3	soner	soner	NOUN
ma-64	100	4	[	[	X
ma-64	100	5	43	43	NUM
ma-64	100	6	]	]	PUNCT
ma-64	100	7	evolved	evolve	VERB
ma-64	100	8	a	a	DET
ma-64	100	9	model	model	NOUN
ma-64	100	10	using	use	VERB
ma-64	100	11	theutility	theutility	NOUN
ma-64	100	12	function	function	NOUN
ma-64	100	13	approach	approach	NOUN
ma-64	100	14	of	of	ADP
ma-64	100	15	hodges	hodge	NOUN
ma-64	100	16	and	and	CCONJ
ma-64	100	17	neuberger	neuberger	NOUN
ma-64	101	1	[	[	X
ma-64	101	2	52	52	NUM
ma-64	101	3	]	]	PUNCT
ma-64	101	4	along	along	ADP
ma-64	101	5	with	with	ADP
ma-64	101	6	asymptotic	asymptotic	ADJ
ma-64	101	7	analysis	analysis	NOUN
ma-64	101	8	of	of	ADP
ma-64	101	9	partialdifferential	partialdifferential	ADJ
ma-64	101	10	equations	equation	NOUN
ma-64	101	11	.	.	PUNCT
ma-64	102	1	for	for	ADP
ma-64	102	2	this	this	DET
ma-64	102	3	case	case	NOUN
ma-64	102	4	,	,	PUNCT
ma-64	102	5	the	the	DET
ma-64	102	6	formula	formula	NOUN
ma-64	102	7	for	for	ADP
ma-64	102	8	the	the	DET
ma-64	102	9	modified	modify	VERB
ma-64	102	10	volatility	volatility	NOUN
ma-64	102	11	[	[	X
ma-64	102	12	46	46	NUM
ma-64	102	13	]	]	PUNCT
ma-64	102	14	is	be	AUX
ma-64	102	15	given	give	VERB
ma-64	102	16	by	by	ADP
ma-64	102	17	σ̃	σ̃	PROPN
ma-64	102	18	=	=	SYM
ma-64	102	19	σ	σ	NOUN
ma-64	102	20	√	√	NOUN
ma-64	102	21	1	1	NUM
ma-64	102	22	+	+	CCONJ
ma-64	102	23	er(t−t)a2s2fss	er(t−t)a2s2fss	ADV
ma-64	102	24	(	(	PUNCT
ma-64	102	25	5	5	NUM
ma-64	102	26	)	)	PUNCT
ma-64	102	27	where	where	SCONJ
ma-64	102	28	,	,	PUNCT
ma-64	102	29	µ	µ	X
ma-64	102	30	=	=	SYM
ma-64	102	31	a	a	DET
ma-64	102	32	√	√	NUM
ma-64	102	33	∈	∈	NOUN
ma-64	102	34	is	be	AUX
ma-64	102	35	the	the	DET
ma-64	102	36	round	round	ADJ
ma-64	102	37	-	-	PUNCT
ma-64	102	38	trip	trip	NOUN
ma-64	102	39	transaction	transaction	NOUN
ma-64	102	40	cost	cost	NOUN
ma-64	102	41	per	per	ADP
ma-64	102	42	unit	unit	NOUN
ma-64	102	43	dollar	dollar	NOUN
ma-64	102	44	of	of	ADP
ma-64	102	45	the	the	DET
ma-64	102	46	transaction	transaction	NOUN
ma-64	102	47	for	for	ADP
ma-64	102	48	someconstant	someconstant	NOUN
ma-64	102	49	a	a	DET
ma-64	102	50	>	>	X
ma-64	102	51	0	0	NUM
ma-64	102	52	and	and	CCONJ
ma-64	102	53	∈→	∈→	NOUN
ma-64	102	54	0	0	NUM
ma-64	102	55	.	.	PUNCT
ma-64	103	1	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	103	2	eur	eur	PROPN
ma-64	103	3	.	.	PUNCT
ma-64	104	1	j.	j.	PROPN
ma-64	104	2	math	math	PROPN
ma-64	104	3	.	.	PUNCT
ma-64	105	1	anal	anal	PROPN
ma-64	105	2	.	.	PUNCT
ma-64	106	1	10.28924	10.28924	NUM
ma-64	106	2	/	/	SYM
ma-64	106	3	ada	ada	PROPN
ma-64	106	4	/	/	SYM
ma-64	106	5	ma.2.9	ma.2.9	PROPN
ma-64	106	6	5	5	NUM
ma-64	106	7	rapm	rapm	ADJ
ma-64	106	8	volatility	volatility	NOUN
ma-64	106	9	model	model	NOUN
ma-64	106	10	(	(	PUNCT
ma-64	106	11	rapmvm	rapmvm	PROPN
ma-64	106	12	)	)	PUNCT
ma-64	106	13	.	.	PUNCT
ma-64	107	1	kratka	kratka	PROPN
ma-64	108	1	[	[	X
ma-64	108	2	53	53	NUM
ma-64	108	3	]	]	PUNCT
ma-64	108	4	took	take	VERB
ma-64	108	5	the	the	DET
ma-64	108	6	first	first	ADJ
ma-64	108	7	step	step	NOUN
ma-64	108	8	for	for	ADP
ma-64	108	9	this	this	DET
ma-64	108	10	model	model	NOUN
ma-64	108	11	and	and	CCONJ
ma-64	108	12	laterimproved	laterimprove	VERB
ma-64	108	13	by	by	ADP
ma-64	108	14	jandačka	jandačka	NOUN
ma-64	108	15	and	and	CCONJ
ma-64	108	16	ševčovič	ševčovič	PROPN
ma-64	108	17	[	[	X
ma-64	108	18	54	54	NUM
ma-64	108	19	]	]	PUNCT
ma-64	108	20	.	.	PUNCT
ma-64	109	1	here	here	ADV
ma-64	109	2	the	the	DET
ma-64	109	3	modified	modified	ADJ
ma-64	109	4	volatility	volatility	NOUN
ma-64	109	5	is	be	AUX
ma-64	109	6	of	of	ADP
ma-64	109	7	the	the	DET
ma-64	109	8	form	form	NOUN
ma-64	109	9	[	[	X
ma-64	109	10	46	46	NUM
ma-64	109	11	]	]	X
ma-64	110	1	σ̃	σ̃	PROPN
ma-64	110	2	=	=	PUNCT
ma-64	110	3	σ	σ	NOUN
ma-64	110	4	√	√	NOUN
ma-64	110	5	1	1	NUM
ma-64	111	1	+	+	NUM
ma-64	111	2	3×	3×	NUM
ma-64	111	3	3	3	NUM
ma-64	111	4	√	√	PROPN
ma-64	111	5	c2	c2	PROPN
ma-64	111	6	m	m	PROPN
ma-64	111	7	2π	2π	PROPN
ma-64	111	8	sfss	sfss	NOUN
ma-64	111	9	(	(	PUNCT
ma-64	111	10	6	6	NUM
ma-64	111	11	)	)	PUNCT
ma-64	111	12	where	where	SCONJ
ma-64	111	13	,	,	PUNCT
ma-64	111	14	m	m	VERB
ma-64	111	15	≥	≥	NOUN
ma-64	111	16	0	0	NUM
ma-64	111	17	is	be	AUX
ma-64	111	18	the	the	DET
ma-64	111	19	transaction	transaction	NOUN
ma-64	111	20	cost	cost	NOUN
ma-64	111	21	measure	measure	NOUN
ma-64	111	22	and	and	CCONJ
ma-64	111	23	c	c	X
ma-64	111	24	≥	≥	X
ma-64	111	25	0	0	NUM
ma-64	111	26	is	be	AUX
ma-64	111	27	the	the	DET
ma-64	111	28	risk	risk	NOUN
ma-64	111	29	premium	premium	NOUN
ma-64	111	30	measure	measure	NOUN
ma-64	111	31	.	.	PUNCT
ma-64	112	1	4	4	X
ma-64	112	2	.	.	X
ma-64	112	3	derivations	derivation	NOUN
ma-64	112	4	of	of	ADP
ma-64	112	5	computational	computational	ADJ
ma-64	112	6	schemes	scheme	NOUN
ma-64	112	7	in	in	ADP
ma-64	112	8	this	this	DET
ma-64	112	9	section	section	NOUN
ma-64	112	10	,	,	PUNCT
ma-64	112	11	we	we	PRON
ma-64	112	12	derive	derive	VERB
ma-64	112	13	five	five	NUM
ma-64	112	14	computational	computational	ADJ
ma-64	112	15	schemes	scheme	NOUN
ma-64	112	16	,	,	PUNCT
ma-64	112	17	in	in	ADP
ma-64	112	18	detail	detail	NOUN
ma-64	112	19	,	,	PUNCT
ma-64	112	20	for	for	ADP
ma-64	112	21	equation	equation	NOUN
ma-64	112	22	(	(	PUNCT
ma-64	112	23	2	2	X
ma-64	112	24	)	)	PUNCT
ma-64	112	25	using	use	VERB
ma-64	112	26	twowell	twowell	NOUN
ma-64	112	27	-	-	PUNCT
ma-64	112	28	known	know	VERB
ma-64	112	29	numerical	numerical	ADJ
ma-64	112	30	methods	method	NOUN
ma-64	112	31	.	.	PUNCT
ma-64	113	1	4.1	4.1	NUM
ma-64	113	2	.	.	PUNCT
ma-64	113	3	dufort	dufort	NOUN
ma-64	113	4	-	-	PUNCT
ma-64	113	5	frankel	frankel	NOUN
ma-64	113	6	finite	finite	ADJ
ma-64	113	7	difference	difference	NOUN
ma-64	113	8	scheme	scheme	NOUN
ma-64	113	9	.	.	PUNCT
ma-64	114	1	the	the	DET
ma-64	114	2	dufort	dufort	NOUN
ma-64	114	3	-	-	PUNCT
ma-64	114	4	frankel	frankel	NOUN
ma-64	114	5	fd	fd	PROPN
ma-64	114	6	scheme	scheme	NOUN
ma-64	114	7	[	[	X
ma-64	114	8	55	55	NUM
ma-64	114	9	]	]	PUNCT
ma-64	114	10	can	can	AUX
ma-64	114	11	be	be	AUX
ma-64	114	12	appliedto	appliedto	ADJ
ma-64	114	13	solve	solve	VERB
ma-64	114	14	various	various	ADJ
ma-64	114	15	kinds	kind	NOUN
ma-64	114	16	of	of	ADP
ma-64	114	17	problems	problem	NOUN
ma-64	114	18	which	which	PRON
ma-64	114	19	occur	occur	VERB
ma-64	114	20	in	in	ADP
ma-64	114	21	finance	finance	NOUN
ma-64	114	22	.	.	PUNCT
ma-64	115	1	this	this	DET
ma-64	115	2	scheme	scheme	NOUN
ma-64	115	3	is	be	AUX
ma-64	115	4	a	a	DET
ma-64	115	5	multi	multi	ADJ
ma-64	115	6	-	-	ADJ
ma-64	115	7	step	step	ADJ
ma-64	115	8	method	method	NOUN
ma-64	115	9	,	,	PUNCT
ma-64	115	10	andrequires	andrequire	VERB
ma-64	115	11	another	another	DET
ma-64	115	12	scheme	scheme	NOUN
ma-64	115	13	for	for	ADP
ma-64	115	14	simulating	simulate	VERB
ma-64	115	15	the	the	DET
ma-64	115	16	first	first	ADJ
ma-64	115	17	temporal	temporal	ADJ
ma-64	115	18	vector	vector	NOUN
ma-64	115	19	.	.	PUNCT
ma-64	116	1	in	in	ADP
ma-64	116	2	this	this	DET
ma-64	116	3	formulation	formulation	NOUN
ma-64	116	4	∂u	∂u	PROPN
ma-64	116	5	∂τ	∂τ	PROPN
ma-64	116	6	,	,	PUNCT
ma-64	116	7	∂u	∂u	PROPN
ma-64	116	8	∂y	∂y	PROPN
ma-64	116	9	,	,	PUNCT
ma-64	116	10	and	and	CCONJ
ma-64	116	11	∂2u	∂2u	PROPN
ma-64	116	12	∂y2are	∂y2are	PROPN
ma-64	116	13	discretized	discretize	VERB
ma-64	116	14	by	by	ADP
ma-64	116	15	central	central	ADJ
ma-64	116	16	difference	difference	NOUN
ma-64	116	17	and	and	CCONJ
ma-64	116	18	uji	uji	NOUN
ma-64	116	19	is	be	AUX
ma-64	116	20	replaced	replace	VERB
ma-64	116	21	by	by	ADP
ma-64	116	22	(	(	PUNCT
ma-64	116	23	uj+1	uj+1	NOUN
ma-64	117	1	i	i	PRON
ma-64	118	1	+	+	CCONJ
ma-64	119	1	uj−1	uj−1	PROPN
ma-64	119	2	i	i	PROPN
ma-64	119	3	)	)	PUNCT
ma-64	119	4	/2	/2	PUNCT
ma-64	119	5	.	.	PUNCT
ma-64	120	1	thus	thus	ADV
ma-64	120	2	,	,	PUNCT
ma-64	120	3	discretizingequation	discretizingequation	NOUN
ma-64	120	4	(	(	PUNCT
ma-64	120	5	2	2	NUM
ma-64	120	6	)	)	PUNCT
ma-64	120	7	by	by	ADP
ma-64	120	8	dufort	dufort	NOUN
ma-64	120	9	-	-	PUNCT
ma-64	120	10	frankel	frankel	NOUN
ma-64	120	11	fdm	fdm	NOUN
ma-64	120	12	,	,	PUNCT
ma-64	120	13	we	we	PRON
ma-64	120	14	obtain	obtain	VERB
ma-64	120	15	1	1	NUM
ma-64	120	16	2∆τ	2∆τ	NUM
ma-64	120	17	(	(	PUNCT
ma-64	120	18	uj+1	uj+1	NUM
ma-64	121	1	i	i	PRON
ma-64	121	2	−	−	VERB
ma-64	121	3	uj−1	uj−1	INTJ
ma-64	122	1	i	i	PRON
ma-64	122	2	)	)	PUNCT
ma-64	123	1	=	=	PUNCT
ma-64	123	2	(	(	PUNCT
ma-64	123	3	σ̃	σ̃	PROPN
ma-64	123	4	σ	σ	PROPN
ma-64	123	5	)	)	PUNCT
ma-64	123	6	2	2	NUM
ma-64	123	7	[	[	PUNCT
ma-64	123	8	1	1	NUM
ma-64	123	9	(	(	PUNCT
ma-64	123	10	∆y)2	∆y)2	PROPN
ma-64	123	11	(	(	PUNCT
ma-64	123	12	uji−1	uji−1	PROPN
ma-64	123	13	−	−	PROPN
ma-64	123	14	(	(	PUNCT
ma-64	123	15	uj+1	uj+1	X
ma-64	124	1	i	i	PRON
ma-64	124	2	+	+	CCONJ
ma-64	124	3	uj−1	uj−1	PROPN
ma-64	124	4	i	i	NOUN
ma-64	124	5	)	)	PUNCT
ma-64	125	1	+	+	CCONJ
ma-64	125	2	uji+1	uji+1	X
ma-64	125	3	)	)	PUNCT
ma-64	125	4	]	]	PUNCT
ma-64	126	1	+	+	CCONJ
ma-64	126	2	(	(	PUNCT
ma-64	126	3	σ̃	σ̃	PROPN
ma-64	126	4	σ	σ	PROPN
ma-64	126	5	)	)	PUNCT
ma-64	126	6	2	2	NUM
ma-64	126	7	[	[	PUNCT
ma-64	126	8	1	1	NUM
ma-64	126	9	2∆y	2∆y	NUM
ma-64	126	10	(	(	PUNCT
ma-64	126	11	uji+1	uji+1	ADP
ma-64	126	12	−	−	NOUN
ma-64	126	13	u	u	NOUN
ma-64	126	14	j	j	PROPN
ma-64	126	15	i−1	i−1	PROPN
ma-64	126	16	)	)	PUNCT
ma-64	126	17	]	]	PUNCT
ma-64	127	1	+	+	CCONJ
ma-64	127	2	r	r	NOUN
ma-64	127	3	σ2∆y	σ2∆y	NOUN
ma-64	127	4	(	(	PUNCT
ma-64	127	5	uji+1	uji+1	ADP
ma-64	127	6	−	−	PROPN
ma-64	127	7	u	u	NOUN
ma-64	127	8	j	j	PROPN
ma-64	127	9	i−1	i−1	PROPN
ma-64	127	10	)	)	PUNCT
ma-64	127	11	or	or	CCONJ
ma-64	127	12	,	,	PUNCT
ma-64	127	13	equivalently	equivalently	ADV
ma-64	127	14	uj+1	uj+1	X
ma-64	127	15	i	i	NOUN
ma-64	127	16	=	=	AUX
ma-64	127	17	uj−1	uj−1	INTJ
ma-64	127	18	i	i	PRON
ma-64	127	19	+	+	NOUN
ma-64	127	20	2r(∆τ)(∆y	2r(∆τ)(∆y	X
ma-64	127	21	)	)	PUNCT
ma-64	127	22	σ2	σ2	NOUN
ma-64	127	23	(	(	PUNCT
ma-64	127	24	uji+1	uji+1	ADP
ma-64	127	25	−	−	PROPN
ma-64	127	26	u	u	NOUN
ma-64	127	27	j	j	PROPN
ma-64	127	28	i−1	i−1	PROPN
ma-64	127	29	)	)	PUNCT
ma-64	128	1	+	+	CCONJ
ma-64	128	2	∆τ	∆τ	NOUN
ma-64	128	3	∆y	∆y	NOUN
ma-64	128	4	(	(	PUNCT
ma-64	128	5	σ̃	σ̃	PROPN
ma-64	128	6	σ	σ	PROPN
ma-64	128	7	)	)	PUNCT
ma-64	128	8	2	2	NUM
ma-64	128	9	(	(	PUNCT
ma-64	128	10	uji+1	uji+1	ADP
ma-64	128	11	−	−	PROPN
ma-64	128	12	u	u	NOUN
ma-64	128	13	j	j	PROPN
ma-64	128	14	i−1	i−1	PROPN
ma-64	128	15	)	)	PUNCT
ma-64	129	1	+	+	PUNCT
ma-64	130	1	2(∆τ	2(∆τ	X
ma-64	130	2	)	)	PUNCT
ma-64	130	3	(	(	PUNCT
ma-64	130	4	∆y)2	∆y)2	PROPN
ma-64	130	5	(	(	PUNCT
ma-64	130	6	σ̃	σ̃	PROPN
ma-64	130	7	σ	σ	PROPN
ma-64	130	8	)	)	PUNCT
ma-64	130	9	2	2	NUM
ma-64	130	10	(	(	PUNCT
ma-64	130	11	uji−1	uji−1	PROPN
ma-64	130	12	−	−	PROPN
ma-64	130	13	u	u	NOUN
ma-64	130	14	j+1	j+1	PROPN
ma-64	131	1	i	i	PRON
ma-64	131	2	−	−	VERB
ma-64	132	1	uj−1	uj−1	INTJ
ma-64	132	2	i	i	PRON
ma-64	132	3	+	+	X
ma-64	132	4	uji+1	uji+1	X
ma-64	132	5	)	)	PUNCT
ma-64	132	6	which	which	PRON
ma-64	132	7	can	can	AUX
ma-64	132	8	be	be	AUX
ma-64	132	9	written	write	VERB
ma-64	132	10	as	as	ADP
ma-64	132	11	uj+1	uj+1	NUM
ma-64	132	12	i	i	NOUN
ma-64	132	13	=	=	PUNCT
ma-64	133	1	aiu	aiu	PROPN
ma-64	133	2	j	j	PROPN
ma-64	134	1	i−1	i−1	PROPN
ma-64	134	2	+	+	PROPN
ma-64	134	3	biu	biu	PROPN
ma-64	134	4	j	j	PROPN
ma-64	134	5	i+1	i+1	PRON
ma-64	134	6	+	+	CCONJ
ma-64	134	7	ciu	ciu	ADJ
ma-64	134	8	j−1	j−1	PROPN
ma-64	134	9	i	i	PRON
ma-64	134	10	;	;	PUNCT
ma-64	134	11	i	i	PROPN
ma-64	134	12	=	=	NOUN
ma-64	134	13	0	0	NUM
ma-64	134	14	,	,	PUNCT
ma-64	134	15	1	1	NUM
ma-64	134	16	,	,	PUNCT
ma-64	134	17	2	2	NUM
ma-64	134	18	,	,	PUNCT
ma-64	134	19	.	.	PUNCT
ma-64	134	20	.	.	PUNCT
ma-64	134	21	.	.	PUNCT
ma-64	135	1	,	,	PUNCT
ma-64	136	1	n	n	CCONJ
ma-64	136	2	−	−	PROPN
ma-64	136	3	1	1	NUM
ma-64	136	4	;	;	PUNCT
ma-64	136	5	j	j	PROPN
ma-64	136	6	=	=	SYM
ma-64	136	7	0	0	NUM
ma-64	136	8	,	,	PUNCT
ma-64	136	9	1	1	NUM
ma-64	136	10	,	,	PUNCT
ma-64	136	11	2	2	NUM
ma-64	136	12	,	,	PUNCT
ma-64	136	13	.	.	PUNCT
ma-64	136	14	.	.	PUNCT
ma-64	136	15	.	.	PUNCT
ma-64	137	1	,	,	PUNCT
ma-64	137	2	m	m	VERB
ma-64	137	3	−	−	NOUN
ma-64	137	4	1	1	NUM
ma-64	137	5	(	(	PUNCT
ma-64	137	6	7	7	NUM
ma-64	137	7	)	)	PUNCT
ma-64	137	8	where	where	SCONJ
ma-64	137	9	ai	ai	VERB
ma-64	137	10	=	=	X
ma-64	137	11	[	[	PUNCT
ma-64	137	12	(	(	PUNCT
ma-64	137	13	∆y)2	∆y)2	PROPN
ma-64	137	14	+	+	NOUN
ma-64	137	15	2(∆τ	2(∆τ	NUM
ma-64	137	16	)	)	PUNCT
ma-64	137	17	(	(	PUNCT
ma-64	137	18	σ̃	σ̃	PROPN
ma-64	137	19	σ	σ	PROPN
ma-64	137	20	)	)	PUNCT
ma-64	137	21	2	2	NUM
ma-64	137	22	]	]	SYM
ma-64	137	23	−1	−1	NOUN
ma-64	137	24	×	×	NOUN
ma-64	137	25	[	[	PUNCT
ma-64	137	26	(	(	PUNCT
ma-64	137	27	∆τ	∆τ	PROPN
ma-64	137	28	)	)	PUNCT
ma-64	137	29	(	(	PUNCT
ma-64	137	30	σ̃	σ̃	PROPN
ma-64	137	31	σ	σ	PROPN
ma-64	137	32	)	)	PUNCT
ma-64	137	33	2	2	NUM
ma-64	137	34	(	(	PUNCT
ma-64	137	35	2−	2−	NUM
ma-64	137	36	∆y)−	∆y)−	PRON
ma-64	137	37	(	(	PUNCT
ma-64	137	38	∆y)(∆τ	∆y)(∆τ	NOUN
ma-64	137	39	)	)	PUNCT
ma-64	137	40	2r	2r	NUM
ma-64	137	41	σ2	σ2	PROPN
ma-64	137	42	]	]	PUNCT
ma-64	137	43	,	,	PUNCT
ma-64	137	44	bi	bi	NOUN
ma-64	137	45	=	=	PUNCT
ma-64	137	46	[	[	PUNCT
ma-64	137	47	(	(	PUNCT
ma-64	137	48	∆y)2	∆y)2	PROPN
ma-64	137	49	+	+	NOUN
ma-64	137	50	2(∆τ	2(∆τ	NUM
ma-64	137	51	)	)	PUNCT
ma-64	137	52	(	(	PUNCT
ma-64	137	53	σ̃	σ̃	PROPN
ma-64	137	54	σ	σ	PROPN
ma-64	137	55	)	)	PUNCT
ma-64	137	56	2	2	NUM
ma-64	137	57	]	]	SYM
ma-64	137	58	−1	−1	NOUN
ma-64	137	59	×	×	NOUN
ma-64	137	60	[	[	PUNCT
ma-64	137	61	(	(	PUNCT
ma-64	137	62	∆τ	∆τ	PROPN
ma-64	137	63	)	)	PUNCT
ma-64	137	64	(	(	PUNCT
ma-64	137	65	σ̃	σ̃	PROPN
ma-64	137	66	σ	σ	PROPN
ma-64	137	67	)	)	PUNCT
ma-64	137	68	2	2	NUM
ma-64	137	69	(	(	PUNCT
ma-64	137	70	2	2	NUM
ma-64	137	71	+	+	SYM
ma-64	137	72	∆y	∆y	NOUN
ma-64	137	73	)	)	PUNCT
ma-64	138	1	+	+	CCONJ
ma-64	138	2	(	(	PUNCT
ma-64	138	3	∆y)(∆τ	∆y)(∆τ	NOUN
ma-64	138	4	)	)	PUNCT
ma-64	138	5	2r	2r	NUM
ma-64	138	6	σ2	σ2	PROPN
ma-64	138	7	]	]	PUNCT
ma-64	138	8	,	,	PUNCT
ma-64	138	9	and	and	CCONJ
ma-64	138	10	ci	ci	NOUN
ma-64	138	11	=	=	PUNCT
ma-64	139	1	[	[	PUNCT
ma-64	139	2	(	(	PUNCT
ma-64	139	3	∆y)2	∆y)2	PROPN
ma-64	139	4	+	+	NOUN
ma-64	139	5	2(∆τ	2(∆τ	NUM
ma-64	139	6	)	)	PUNCT
ma-64	139	7	(	(	PUNCT
ma-64	139	8	σ̃	σ̃	PROPN
ma-64	139	9	σ	σ	PROPN
ma-64	139	10	)	)	PUNCT
ma-64	139	11	2	2	NUM
ma-64	139	12	]	]	SYM
ma-64	139	13	−1	−1	NOUN
ma-64	139	14	×	×	NOUN
ma-64	139	15	[	[	PUNCT
ma-64	139	16	(	(	PUNCT
ma-64	139	17	∆y)2	∆y)2	ADP
ma-64	139	18	−	−	PROPN
ma-64	139	19	2(∆τ	2(∆τ	NUM
ma-64	139	20	)	)	PUNCT
ma-64	139	21	(	(	PUNCT
ma-64	139	22	σ̃	σ̃	PROPN
ma-64	139	23	σ	σ	PROPN
ma-64	139	24	)	)	PUNCT
ma-64	139	25	2	2	NUM
ma-64	139	26	]	]	PUNCT
ma-64	139	27	which	which	PRON
ma-64	139	28	is	be	AUX
ma-64	139	29	our	our	PRON
ma-64	139	30	proposed	propose	VERB
ma-64	139	31	dufort	dufort	NOUN
ma-64	139	32	-	-	PUNCT
ma-64	139	33	frankel	frankel	NOUN
ma-64	139	34	finite	finite	ADJ
ma-64	139	35	difference	difference	NOUN
ma-64	139	36	scheme	scheme	NOUN
ma-64	139	37	(	(	PUNCT
ma-64	139	38	dffds	dffds	PROPN
ma-64	139	39	)	)	PUNCT
ma-64	139	40	.	.	PUNCT
ma-64	140	1	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	140	2	eur	eur	PROPN
ma-64	140	3	.	.	PUNCT
ma-64	141	1	j.	j.	PROPN
ma-64	141	2	math	math	PROPN
ma-64	141	3	.	.	PUNCT
ma-64	142	1	anal	anal	PROPN
ma-64	142	2	.	.	PUNCT
ma-64	143	1	10.28924	10.28924	NUM
ma-64	143	2	/	/	SYM
ma-64	143	3	ada	ada	PROPN
ma-64	143	4	/	/	SYM
ma-64	143	5	ma.2.9	ma.2.9	PROPN
ma-64	143	6	64.2	64.2	NUM
ma-64	143	7	.	.	PUNCT
ma-64	144	1	laasonen	laasonen	PROPN
ma-64	144	2	finite	finite	PROPN
ma-64	144	3	difference	difference	NOUN
ma-64	144	4	scheme	scheme	NOUN
ma-64	144	5	.	.	PUNCT
ma-64	145	1	the	the	DET
ma-64	145	2	laasonen	laasonen	PROPN
ma-64	145	3	finite	finite	PROPN
ma-64	145	4	difference	difference	NOUN
ma-64	145	5	scheme	scheme	NOUN
ma-64	145	6	[	[	X
ma-64	145	7	55	55	NUM
ma-64	145	8	]	]	PUNCT
ma-64	145	9	can	can	AUX
ma-64	145	10	be	be	AUX
ma-64	145	11	ap	ap	VERB
ma-64	145	12	-	-	PUNCT
ma-64	145	13	plied	plied	ADJ
ma-64	145	14	to	to	PART
ma-64	145	15	solve	solve	VERB
ma-64	145	16	linear	linear	ADJ
ma-64	145	17	and	and	CCONJ
ma-64	145	18	non	non	ADJ
ma-64	145	19	-	-	ADJ
ma-64	145	20	linear	linear	ADJ
ma-64	145	21	partial	partial	ADJ
ma-64	145	22	differential	differential	NOUN
ma-64	145	23	equations	equation	NOUN
ma-64	145	24	.	.	PUNCT
ma-64	146	1	this	this	DET
ma-64	146	2	method	method	ADJ
ma-64	146	3	metamorphosedpartial	metamorphosedpartial	ADJ
ma-64	146	4	differential	differential	NOUN
ma-64	146	5	equations	equation	NOUN
ma-64	146	6	into	into	ADP
ma-64	146	7	a	a	DET
ma-64	146	8	system	system	NOUN
ma-64	146	9	of	of	ADP
ma-64	146	10	linear	linear	ADJ
ma-64	146	11	algebraic	algebraic	ADJ
ma-64	146	12	equations	equation	NOUN
ma-64	146	13	.	.	PUNCT
ma-64	147	1	in	in	ADP
ma-64	147	2	this	this	DET
ma-64	147	3	formulation	formulation	NOUN
ma-64	147	4	∂u	∂u	PROPN
ma-64	147	5	∂τis	∂τis	NUM
ma-64	147	6	approximated	approximate	VERB
ma-64	147	7	by	by	ADP
ma-64	147	8	a	a	DET
ma-64	147	9	central	central	ADJ
ma-64	147	10	differencing	differencing	NOUN
ma-64	147	11	at	at	ADP
ma-64	147	12	a	a	DET
ma-64	147	13	step	step	NOUN
ma-64	147	14	∆τ	∆τ	NOUN
ma-64	147	15	2	2	NUM
ma-64	147	16	,	,	PUNCT
ma-64	147	17	and	and	CCONJ
ma-64	147	18	∂u	∂u	PROPN
ma-64	147	19	∂y	∂y	PROPN
ma-64	147	20	,	,	PUNCT
ma-64	147	21	∂2u	∂2u	PROPN
ma-64	147	22	∂y2	∂y2	ADJ
ma-64	147	23	are	be	AUX
ma-64	147	24	approximated	approximate	VERB
ma-64	147	25	by	by	ADP
ma-64	147	26	centraldifferences	centraldifference	NOUN
ma-64	147	27	at	at	ADP
ma-64	147	28	time	time	NOUN
ma-64	147	29	levels	level	NOUN
ma-64	147	30	j	j	PROPN
ma-64	147	31	+	+	CCONJ
ma-64	147	32	1	1	X
ma-64	147	33	.	.	PUNCT
ma-64	147	34	now	now	ADV
ma-64	147	35	the	the	DET
ma-64	147	36	discretized	discretized	ADJ
ma-64	147	37	form	form	NOUN
ma-64	147	38	of	of	ADP
ma-64	147	39	equation	equation	NOUN
ma-64	147	40	(	(	PUNCT
ma-64	147	41	2	2	X
ma-64	147	42	)	)	PUNCT
ma-64	147	43	is	be	AUX
ma-64	147	44	as	as	SCONJ
ma-64	147	45	follows	follow	VERB
ma-64	147	46	1	1	NUM
ma-64	147	47	∆τ	∆τ	NOUN
ma-64	147	48	(	(	PUNCT
ma-64	147	49	uj+1	uj+1	NOUN
ma-64	147	50	i	i	PRON
ma-64	147	51	−	−	PROPN
ma-64	147	52	uji	uji	PROPN
ma-64	147	53	)	)	PUNCT
ma-64	147	54	=	=	PUNCT
ma-64	148	1	1	1	NUM
ma-64	148	2	2(∆y)2	2(∆y)2	NUM
ma-64	148	3	(	(	PUNCT
ma-64	148	4	σ̃	σ̃	PROPN
ma-64	148	5	σ	σ	PROPN
ma-64	148	6	)	)	PUNCT
ma-64	148	7	2	2	NUM
ma-64	148	8	[	[	PUNCT
ma-64	148	9	2	2	NUM
ma-64	148	10	(	(	PUNCT
ma-64	148	11	uj+1	uj+1	NOUN
ma-64	148	12	i−1	i−1	PROPN
ma-64	148	13	−	−	PROPN
ma-64	149	1	2uj+1	2uj+1	NUM
ma-64	149	2	i	i	PRON
ma-64	149	3	+	+	PUNCT
ma-64	149	4	uj+1	uj+1	NUM
ma-64	149	5	i+1	i+1	NOUN
ma-64	149	6	)	)	PUNCT
ma-64	150	1	+	+	CCONJ
ma-64	150	2	∆y	∆y	PROPN
ma-64	150	3	(	(	PUNCT
ma-64	150	4	uj+1	uj+1	NUM
ma-64	150	5	i+1	i+1	ADV
ma-64	150	6	−	−	PROPN
ma-64	150	7	u	u	NOUN
ma-64	150	8	j+1	j+1	PROPN
ma-64	150	9	i−1	i−1	PROPN
ma-64	150	10	)	)	PUNCT
ma-64	150	11	]	]	PUNCT
ma-64	151	1	+	+	CCONJ
ma-64	151	2	r	r	NOUN
ma-64	151	3	σ2∆y	σ2∆y	NOUN
ma-64	151	4	(	(	PUNCT
ma-64	151	5	uj+1	uj+1	NUM
ma-64	151	6	i+1	i+1	SYM
ma-64	151	7	−	−	PROPN
ma-64	151	8	u	u	NOUN
ma-64	151	9	j+1	j+1	PROPN
ma-64	151	10	i−1	i−1	PROPN
ma-64	151	11	)	)	PUNCT
ma-64	151	12	after	after	ADP
ma-64	151	13	simplification	simplification	NOUN
ma-64	151	14	,	,	PUNCT
ma-64	151	15	we	we	PRON
ma-64	151	16	get	get	VERB
ma-64	151	17	[	[	PUNCT
ma-64	151	18	r∆τ	r∆τ	VERB
ma-64	151	19	∆yσ2	∆yσ2	NOUN
ma-64	151	20	+	+	CCONJ
ma-64	151	21	∆τ	∆τ	PROPN
ma-64	151	22	2(∆y)2	2(∆y)2	PROPN
ma-64	151	23	(	(	PUNCT
ma-64	151	24	σ̃	σ̃	PROPN
ma-64	151	25	σ	σ	PROPN
ma-64	151	26	)	)	PUNCT
ma-64	151	27	2	2	NUM
ma-64	151	28	(	(	PUNCT
ma-64	151	29	∆y	∆y	NOUN
ma-64	151	30	−	−	PROPN
ma-64	151	31	2	2	NUM
ma-64	151	32	)	)	PUNCT
ma-64	151	33	]	]	PUNCT
ma-64	152	1	uj+1	uj+1	X
ma-64	152	2	i−1	i−1	PROPN
ma-64	152	3	+	+	CCONJ
ma-64	152	4	[	[	PUNCT
ma-64	152	5	1	1	NUM
ma-64	152	6	+	+	NUM
ma-64	152	7	2∆τ	2∆τ	NUM
ma-64	152	8	(	(	PUNCT
ma-64	152	9	∆y)2	∆y)2	PROPN
ma-64	152	10	(	(	PUNCT
ma-64	152	11	σ̃	σ̃	PROPN
ma-64	152	12	σ	σ	PROPN
ma-64	152	13	)	)	PUNCT
ma-64	152	14	2	2	NUM
ma-64	152	15	]	]	PUNCT
ma-64	152	16	uj+1	uj+1	NUM
ma-64	153	1	i	i	PRON
ma-64	153	2	−	−	PROPN
ma-64	153	3	[	[	PUNCT
ma-64	153	4	r∆τ	r∆τ	VERB
ma-64	153	5	∆yσ2	∆yσ2	NOUN
ma-64	153	6	+	+	CCONJ
ma-64	153	7	∆τ	∆τ	PROPN
ma-64	153	8	2(∆y)2	2(∆y)2	PROPN
ma-64	153	9	(	(	PUNCT
ma-64	153	10	σ̃	σ̃	PROPN
ma-64	153	11	σ	σ	PROPN
ma-64	153	12	)	)	PUNCT
ma-64	153	13	2	2	NUM
ma-64	153	14	(	(	PUNCT
ma-64	153	15	∆y	∆y	NOUN
ma-64	153	16	+	+	NOUN
ma-64	153	17	2	2	NUM
ma-64	153	18	)	)	PUNCT
ma-64	153	19	]	]	PUNCT
ma-64	154	1	uj+1	uj+1	PRON
ma-64	154	2	i+1	i+1	NOUN
ma-64	154	3	=	=	SYM
ma-64	154	4	uji	uji	PROPN
ma-64	154	5	the	the	DET
ma-64	154	6	above	above	ADJ
ma-64	154	7	equation	equation	NOUN
ma-64	154	8	reduces	reduce	VERB
ma-64	154	9	to	to	PART
ma-64	154	10	diu	diu	VERB
ma-64	154	11	j+1	j+1	PROPN
ma-64	154	12	i−1	i−1	PROPN
ma-64	154	13	+	+	CCONJ
ma-64	154	14	(	(	PUNCT
ma-64	154	15	1	1	NUM
ma-64	154	16	+	+	NUM
ma-64	154	17	ei	ei	NOUN
ma-64	154	18	)	)	PUNCT
ma-64	154	19	u	u	NOUN
ma-64	154	20	j+1	j+1	PROPN
ma-64	154	21	i	i	PROPN
ma-64	154	22	+	+	NUM
ma-64	154	23	fiu	fiu	PROPN
ma-64	155	1	j+1	j+1	PROPN
ma-64	155	2	i+1	i+1	NUM
ma-64	155	3	=	=	SYM
ma-64	155	4	uji	uji	PROPN
ma-64	155	5	;	;	PUNCT
ma-64	155	6	i	i	PROPN
ma-64	155	7	=	=	NOUN
ma-64	155	8	0	0	NUM
ma-64	155	9	,	,	PUNCT
ma-64	155	10	1	1	NUM
ma-64	155	11	,	,	PUNCT
ma-64	155	12	2	2	NUM
ma-64	155	13	,	,	PUNCT
ma-64	155	14	.	.	PUNCT
ma-64	155	15	.	.	PUNCT
ma-64	155	16	.	.	PUNCT
ma-64	156	1	,	,	PUNCT
ma-64	157	1	n	n	CCONJ
ma-64	157	2	−	−	PROPN
ma-64	157	3	1	1	NUM
ma-64	157	4	;	;	PUNCT
ma-64	157	5	j	j	PROPN
ma-64	157	6	=	=	SYM
ma-64	157	7	0	0	NUM
ma-64	157	8	,	,	PUNCT
ma-64	157	9	1	1	NUM
ma-64	157	10	,	,	PUNCT
ma-64	157	11	2	2	NUM
ma-64	157	12	,	,	PUNCT
ma-64	157	13	.	.	PUNCT
ma-64	157	14	.	.	PUNCT
ma-64	157	15	.	.	PUNCT
ma-64	158	1	,	,	PUNCT
ma-64	158	2	m	m	AUX
ma-64	158	3	−	−	NOUN
ma-64	158	4	1	1	NUM
ma-64	158	5	(	(	PUNCT
ma-64	158	6	8)	8)	NUM
ma-64	158	7	where	where	SCONJ
ma-64	158	8	di	di	X
ma-64	158	9	=	=	NOUN
ma-64	158	10	r∆τ	r∆τ	VERB
ma-64	158	11	∆yσ2	∆yσ2	NOUN
ma-64	158	12	+	+	CCONJ
ma-64	158	13	∆τ	∆τ	PROPN
ma-64	158	14	2(∆y)2	2(∆y)2	PROPN
ma-64	158	15	(	(	PUNCT
ma-64	158	16	σ̃	σ̃	PROPN
ma-64	158	17	σ	σ	PROPN
ma-64	158	18	)	)	PUNCT
ma-64	158	19	2	2	NUM
ma-64	158	20	(	(	PUNCT
ma-64	158	21	∆y	∆y	NOUN
ma-64	158	22	−	−	PROPN
ma-64	158	23	2	2	NUM
ma-64	158	24	)	)	PUNCT
ma-64	158	25	,	,	PUNCT
ma-64	158	26	ei	ei	NOUN
ma-64	158	27	=	=	SYM
ma-64	158	28	2∆τ	2∆τ	NUM
ma-64	158	29	(	(	PUNCT
ma-64	158	30	∆y)2	∆y)2	PROPN
ma-64	158	31	(	(	PUNCT
ma-64	158	32	σ̃	σ̃	PROPN
ma-64	158	33	σ	σ	PROPN
ma-64	158	34	)	)	PUNCT
ma-64	158	35	2	2	NUM
ma-64	158	36	and	and	CCONJ
ma-64	158	37	fi	fi	NOUN
ma-64	158	38	=	=	NOUN
ma-64	158	39	−	−	NOUN
ma-64	158	40	r∆τ	r∆τ	VERB
ma-64	158	41	∆yσ2	∆yσ2	NOUN
ma-64	158	42	−	−	PROPN
ma-64	158	43	∆τ	∆τ	PROPN
ma-64	158	44	2(∆y)2	2(∆y)2	PROPN
ma-64	158	45	(	(	PUNCT
ma-64	158	46	σ̃	σ̃	PROPN
ma-64	158	47	σ	σ	PROPN
ma-64	158	48	)	)	PUNCT
ma-64	158	49	2	2	NUM
ma-64	158	50	(	(	PUNCT
ma-64	158	51	∆y	∆y	NOUN
ma-64	158	52	+	+	CCONJ
ma-64	158	53	2	2	NUM
ma-64	158	54	)	)	PUNCT
ma-64	158	55	4.3	4.3	NUM
ma-64	158	56	.	.	PUNCT
ma-64	159	1	finite	finite	PROPN
ma-64	159	2	volume	volume	NOUN
ma-64	159	3	schemes	scheme	NOUN
ma-64	159	4	.	.	PUNCT
ma-64	160	1	the	the	DET
ma-64	160	2	finite	finite	PROPN
ma-64	160	3	volume	volume	NOUN
ma-64	160	4	scheme	scheme	NOUN
ma-64	160	5	is	be	AUX
ma-64	160	6	a	a	DET
ma-64	160	7	scheme	scheme	NOUN
ma-64	160	8	of	of	ADP
ma-64	160	9	solving	solve	VERB
ma-64	160	10	different	different	ADJ
ma-64	160	11	kinds	kind	NOUN
ma-64	160	12	oftime	oftime	ADV
ma-64	160	13	-	-	PUNCT
ma-64	160	14	dependent	dependent	ADJ
ma-64	160	15	or	or	CCONJ
ma-64	160	16	independent	independent	ADJ
ma-64	160	17	partial	partial	ADJ
ma-64	160	18	differential	differential	NOUN
ma-64	160	19	equations	equation	NOUN
ma-64	160	20	in	in	ADP
ma-64	160	21	algebraic	algebraic	ADJ
ma-64	160	22	equations	equation	NOUN
ma-64	160	23	.	.	PUNCT
ma-64	161	1	in	in	ADP
ma-64	161	2	this	this	DET
ma-64	161	3	scheme	scheme	NOUN
ma-64	161	4	,	,	PUNCT
ma-64	161	5	we	we	PRON
ma-64	161	6	divide	divide	VERB
ma-64	161	7	the	the	DET
ma-64	161	8	physical	physical	ADJ
ma-64	161	9	space	space	NOUN
ma-64	161	10	into	into	ADP
ma-64	161	11	a	a	DET
ma-64	161	12	finite	finite	ADJ
ma-64	161	13	number	number	NOUN
ma-64	161	14	of	of	ADP
ma-64	161	15	control	control	NOUN
ma-64	161	16	volumes	volume	NOUN
ma-64	161	17	.	.	PUNCT
ma-64	162	1	in	in	ADP
ma-64	162	2	this	this	DET
ma-64	162	3	section	section	NOUN
ma-64	162	4	,	,	PUNCT
ma-64	162	5	we	we	PRON
ma-64	162	6	describeit	describeit	VERB
ma-64	162	7	in	in	ADP
ma-64	162	8	a	a	DET
ma-64	162	9	few	few	ADJ
ma-64	162	10	lines	line	NOUN
ma-64	162	11	,	,	PUNCT
ma-64	162	12	but	but	CCONJ
ma-64	162	13	details	detail	NOUN
ma-64	162	14	are	be	AUX
ma-64	162	15	available	available	ADJ
ma-64	162	16	in	in	ADP
ma-64	162	17	the	the	DET
ma-64	162	18	previous	previous	ADJ
ma-64	162	19	study	study	NOUN
ma-64	162	20	[	[	X
ma-64	162	21	56	56	NUM
ma-64	162	22	]	]	PUNCT
ma-64	162	23	conducted	conduct	VERB
ma-64	162	24	by	by	ADP
ma-64	162	25	malalasekera	malalasekera	NOUN
ma-64	162	26	etal	etal	NOUN
ma-64	162	27	.	.	PUNCT
ma-64	163	1	applying	apply	VERB
ma-64	163	2	the	the	DET
ma-64	163	3	finite	finite	ADJ
ma-64	163	4	volume	volume	NOUN
ma-64	163	5	integration	integration	NOUN
ma-64	163	6	in	in	ADP
ma-64	163	7	equation	equation	NOUN
ma-64	163	8	(	(	PUNCT
ma-64	163	9	2	2	NUM
ma-64	163	10	)	)	PUNCT
ma-64	163	11	over	over	ADP
ma-64	163	12	a	a	DET
ma-64	163	13	control	control	NOUN
ma-64	163	14	volume	volume	NOUN
ma-64	163	15	(	(	PUNCT
ma-64	163	16	cv	cv	PROPN
ma-64	163	17	)	)	PUNCT
ma-64	163	18	with	with	ADP
ma-64	163	19	a	a	DET
ma-64	163	20	finite	finite	ADJ
ma-64	163	21	timestep	timestep	NOUN
ma-64	163	22	∆τ	∆τ	NOUN
ma-64	163	23	,	,	PUNCT
ma-64	163	24	we	we	PRON
ma-64	163	25	obtain	obtain	VERB
ma-64	163	26	∫	∫	PROPN
ma-64	163	27	τ+∆τ	τ+∆τ	PROPN
ma-64	163	28	τ	τ	PROPN
ma-64	163	29	∫	∫	PROPN
ma-64	163	30	cv	cv	PROPN
ma-64	163	31	∂u	∂u	PROPN
ma-64	163	32	∂τ	∂τ	PROPN
ma-64	163	33	dv	dv	PROPN
ma-64	163	34	dτ	dτ	PROPN
ma-64	164	1	=	=	SYM
ma-64	165	1	(	(	PUNCT
ma-64	165	2	2r	2r	NUM
ma-64	165	3	σ2	σ2	PROPN
ma-64	165	4	+	+	CCONJ
ma-64	165	5	(	(	PUNCT
ma-64	165	6	σ̃	σ̃	PROPN
ma-64	165	7	σ	σ	PROPN
ma-64	165	8	)	)	PUNCT
ma-64	165	9	2	2	NUM
ma-64	165	10	)	)	PUNCT
ma-64	165	11	∫	∫	PROPN
ma-64	166	1	τ+∆τ	τ+∆τ	PROPN
ma-64	166	2	τ	τ	PROPN
ma-64	166	3	∫	∫	PROPN
ma-64	166	4	cv	cv	PROPN
ma-64	166	5	∂u	∂u	PROPN
ma-64	166	6	∂y	∂y	PROPN
ma-64	166	7	dv	dv	PROPN
ma-64	166	8	dτ	dτ	PROPN
ma-64	167	1	+	+	CCONJ
ma-64	167	2	(	(	PUNCT
ma-64	167	3	σ̃	σ̃	PROPN
ma-64	167	4	σ	σ	PROPN
ma-64	167	5	)	)	PUNCT
ma-64	167	6	2	2	NUM
ma-64	167	7	∫	∫	NOUN
ma-64	168	1	τ+∆τ	τ+∆τ	PROPN
ma-64	168	2	τ	τ	PROPN
ma-64	168	3	∫	∫	PROPN
ma-64	168	4	cv	cv	PROPN
ma-64	168	5	∂2u	∂2u	PROPN
ma-64	168	6	∂y2	∂y2	PROPN
ma-64	168	7	dv	dv	PROPN
ma-64	168	8	dτ	dτ	PROPN
ma-64	168	9	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	168	10	eur	eur	PROPN
ma-64	168	11	.	.	PUNCT
ma-64	169	1	j.	j.	PROPN
ma-64	169	2	math	math	PROPN
ma-64	169	3	.	.	PUNCT
ma-64	170	1	anal	anal	PROPN
ma-64	170	2	.	.	PUNCT
ma-64	171	1	10.28924	10.28924	NUM
ma-64	171	2	/	/	SYM
ma-64	171	3	ada	ada	PROPN
ma-64	171	4	/	/	SYM
ma-64	171	5	ma.2.9	ma.2.9	PROPN
ma-64	171	6	7after	7after	NUM
ma-64	171	7	rearranging	rearrange	VERB
ma-64	171	8	,	,	PUNCT
ma-64	171	9	we	we	PRON
ma-64	171	10	get∫	get∫	VERB
ma-64	171	11	cv	cv	PROPN
ma-64	172	1	[	[	X
ma-64	172	2	∫	∫	X
ma-64	172	3	τ+∆τ	τ+∆τ	X
ma-64	172	4	τ	τ	PROPN
ma-64	172	5	∂u	∂u	PROPN
ma-64	172	6	∂τ	∂τ	PROPN
ma-64	172	7	dτ	dτ	NOUN
ma-64	172	8	]	]	PUNCT
ma-64	172	9	dv	dv	PROPN
ma-64	172	10	=	=	PUNCT
ma-64	172	11	(	(	PUNCT
ma-64	172	12	2r	2r	NUM
ma-64	172	13	σ2	σ2	PROPN
ma-64	172	14	+	+	CCONJ
ma-64	172	15	(	(	PUNCT
ma-64	172	16	σ̃	σ̃	PROPN
ma-64	172	17	σ	σ	PROPN
ma-64	172	18	)	)	PUNCT
ma-64	172	19	2	2	NUM
ma-64	172	20	)	)	PUNCT
ma-64	172	21	∫	∫	PROPN
ma-64	173	1	τ+∆τ	τ+∆τ	PROPN
ma-64	173	2	τ	τ	PROPN
ma-64	174	1	[	[	X
ma-64	174	2	∫	∫	PROPN
ma-64	174	3	cv	cv	PROPN
ma-64	174	4	∂u	∂u	PROPN
ma-64	174	5	∂y	∂y	PROPN
ma-64	175	1	dv	dv	PROPN
ma-64	175	2	]	]	X
ma-64	175	3	dτ	dτ	PROPN
ma-64	175	4	+	+	CCONJ
ma-64	175	5	(	(	PUNCT
ma-64	175	6	σ̃	σ̃	PROPN
ma-64	175	7	σ	σ	PROPN
ma-64	175	8	)	)	PUNCT
ma-64	175	9	2	2	NUM
ma-64	175	10	∫	∫	NOUN
ma-64	175	11	τ+∆	τ+∆	PUNCT
ma-64	175	12	τ	τ	PROPN
ma-64	176	1	[	[	X
ma-64	176	2	∫	∫	PROPN
ma-64	176	3	cv	cv	PROPN
ma-64	176	4	∂2u	∂2u	PROPN
ma-64	176	5	∂y2	∂y2	PROPN
ma-64	176	6	dv	dv	PROPN
ma-64	176	7	]	]	X
ma-64	176	8	dτ	dτ	X
ma-64	176	9	applying	apply	VERB
ma-64	176	10	gauss	gauss	NOUN
ma-64	176	11	’s	’s	PART
ma-64	176	12	divergence	divergence	NOUN
ma-64	176	13	theorem	theorem	PROPN
ma-64	176	14	,	,	PUNCT
ma-64	176	15	the	the	DET
ma-64	176	16	above	above	ADJ
ma-64	176	17	equation	equation	NOUN
ma-64	176	18	leads	lead	VERB
ma-64	176	19	(	(	PUNCT
ma-64	176	20	up	up	ADP
ma-64	176	21	−	−	PROPN
ma-64	176	22	u0	u0	ADJ
ma-64	176	23	p	p	NOUN
ma-64	176	24	)	)	PUNCT
ma-64	176	25	∆v	∆v	PROPN
ma-64	176	26	=	=	SYM
ma-64	176	27	1	1	NUM
ma-64	176	28	2	2	NUM
ma-64	176	29	(	(	PUNCT
ma-64	176	30	2r	2r	NUM
ma-64	176	31	σ2	σ2	PROPN
ma-64	176	32	+	+	CCONJ
ma-64	176	33	(	(	PUNCT
ma-64	176	34	σ̃	σ̃	PROPN
ma-64	176	35	σ	σ	PROPN
ma-64	176	36	)	)	PUNCT
ma-64	176	37	2	2	NUM
ma-64	176	38	)	)	PUNCT
ma-64	176	39	a	a	DET
ma-64	176	40	∫	∫	PROPN
ma-64	176	41	τ+∆τ	τ+∆τ	PROPN
ma-64	176	42	τ	τ	PROPN
ma-64	176	43	(	(	PUNCT
ma-64	176	44	ue	ue	INTJ
ma-64	176	45	−	−	PROPN
ma-64	176	46	uw	uw	PROPN
ma-64	176	47	)	)	PUNCT
ma-64	176	48	dτ	dτ	PROPN
ma-64	176	49	+	+	CCONJ
ma-64	176	50	(	(	PUNCT
ma-64	176	51	σ̃	σ̃	PROPN
ma-64	176	52	σ	σ	PROPN
ma-64	176	53	)	)	PUNCT
ma-64	176	54	2	2	NUM
ma-64	176	55	∫	∫	NOUN
ma-64	176	56	τ+∆τ	τ+∆τ	PROPN
ma-64	176	57	τ	τ	X
ma-64	177	1	[	[	X
ma-64	177	2	(	(	PUNCT
ma-64	177	3	a	a	DET
ma-64	177	4	ue	ue	ADJ
ma-64	177	5	−	−	NOUN
ma-64	177	6	up	up	ADP
ma-64	177	7	δype	δype	NOUN
ma-64	177	8	)	)	PUNCT
ma-64	177	9	−	−	PROPN
ma-64	178	1	[	[	X
ma-64	178	2	(	(	PUNCT
ma-64	178	3	a	a	DET
ma-64	178	4	up	up	ADJ
ma-64	178	5	−	−	PROPN
ma-64	178	6	uw	uw	PROPN
ma-64	178	7	δywp	δywp	NOUN
ma-64	178	8	)	)	PUNCT
ma-64	178	9	]	]	X
ma-64	178	10	]	]	X
ma-64	178	11	dτ	dτ	INTJ
ma-64	178	12	(	(	PUNCT
ma-64	178	13	9	9	NUM
ma-64	178	14	)	)	PUNCT
ma-64	178	15	for	for	ADP
ma-64	178	16	0	0	NUM
ma-64	178	17	≤	≤	NUM
ma-64	178	18	θ	θ	PROPN
ma-64	178	19	≤	≤	NUM
ma-64	178	20	1	1	NUM
ma-64	178	21	,	,	PUNCT
ma-64	178	22	we	we	PRON
ma-64	178	23	assume	assume	VERB
ma-64	178	24	∫	∫	PROPN
ma-64	178	25	τ+∆τ	τ+∆τ	PROPN
ma-64	178	26	τ	τ	PROPN
ma-64	178	27	up	up	ADV
ma-64	178	28	dτ	dτ	NOUN
ma-64	178	29	=	=	SYM
ma-64	178	30	[	[	PUNCT
ma-64	178	31	θup	θup	NOUN
ma-64	178	32	+	+	CCONJ
ma-64	178	33	(	(	PUNCT
ma-64	178	34	1−	1−	NUM
ma-64	178	35	θ)u0	θ)u0	NOUN
ma-64	178	36	p	p	X
ma-64	178	37	]	]	X
ma-64	178	38	∆τ	∆τ	PROPN
ma-64	178	39	(	(	PUNCT
ma-64	178	40	10	10	NUM
ma-64	178	41	)	)	PUNCT
ma-64	178	42	applying	apply	VERB
ma-64	178	43	equation	equation	NOUN
ma-64	178	44	(	(	PUNCT
ma-64	178	45	10	10	NUM
ma-64	178	46	)	)	PUNCT
ma-64	178	47	into	into	ADP
ma-64	178	48	equation	equation	NOUN
ma-64	178	49	(	(	PUNCT
ma-64	178	50	9	9	NUM
ma-64	178	51	)	)	PUNCT
ma-64	178	52	and	and	CCONJ
ma-64	178	53	dividing	divide	VERB
ma-64	178	54	by	by	ADP
ma-64	178	55	we	we	PRON
ma-64	178	56	get	get	VERB
ma-64	178	57	(	(	PUNCT
ma-64	178	58	up	up	ADP
ma-64	178	59	−	−	PROPN
ma-64	178	60	u0	u0	ADJ
ma-64	178	61	p	p	NOUN
ma-64	178	62	)	)	PUNCT
ma-64	178	63	∆y	∆y	PROPN
ma-64	178	64	∆τ	∆τ	NOUN
ma-64	178	65	=	=	SYM
ma-64	178	66	1	1	NUM
ma-64	178	67	2	2	NUM
ma-64	178	68	(	(	PUNCT
ma-64	178	69	2r	2r	NUM
ma-64	178	70	σ2	σ2	PROPN
ma-64	178	71	+	+	CCONJ
ma-64	178	72	(	(	PUNCT
ma-64	178	73	σ̃	σ̃	PROPN
ma-64	178	74	σ	σ	PROPN
ma-64	178	75	)	)	PUNCT
ma-64	178	76	2	2	NUM
ma-64	178	77	)	)	PUNCT
ma-64	178	78	[	[	PUNCT
ma-64	178	79	θ	θ	PROPN
ma-64	178	80	(	(	PUNCT
ma-64	178	81	ue	ue	INTJ
ma-64	178	82	−	−	PROPN
ma-64	178	83	uw	uw	PROPN
ma-64	178	84	)	)	PUNCT
ma-64	179	1	+	+	CCONJ
ma-64	179	2	(	(	PUNCT
ma-64	179	3	1−	1−	NUM
ma-64	179	4	θ	θ	NOUN
ma-64	179	5	)	)	PUNCT
ma-64	179	6	(	(	PUNCT
ma-64	179	7	u0	u0	PROPN
ma-64	179	8	e	e	PROPN
ma-64	179	9	−	−	NOUN
ma-64	179	10	u0	u0	ADJ
ma-64	179	11	w	w	PROPN
ma-64	179	12	)	)	PUNCT
ma-64	179	13	]	]	PUNCT
ma-64	180	1	+	+	CCONJ
ma-64	180	2	(	(	PUNCT
ma-64	180	3	σ̃	σ̃	PROPN
ma-64	180	4	σ	σ	PROPN
ma-64	180	5	)	)	PUNCT
ma-64	180	6	2	2	NUM
ma-64	180	7	θ	θ	NOUN
ma-64	180	8	(	(	PUNCT
ma-64	180	9	ue	ue	INTJ
ma-64	180	10	−	−	PROPN
ma-64	180	11	up	up	ADJ
ma-64	180	12	δype	δype	NOUN
ma-64	180	13	−	−	PROPN
ma-64	180	14	up	up	ADP
ma-64	180	15	−	−	PROPN
ma-64	180	16	uw	uw	PROPN
ma-64	180	17	δywp	δywp	NOUN
ma-64	180	18	)	)	PUNCT
ma-64	181	1	+	+	CCONJ
ma-64	181	2	(	(	PUNCT
ma-64	181	3	σ̃	σ̃	PROPN
ma-64	181	4	σ	σ	PROPN
ma-64	181	5	)	)	PUNCT
ma-64	181	6	2	2	NUM
ma-64	181	7	(	(	PUNCT
ma-64	181	8	1−	1−	NUM
ma-64	181	9	θ	θ	NOUN
ma-64	181	10	)	)	PUNCT
ma-64	181	11	(	(	PUNCT
ma-64	181	12	u0	u0	PROPN
ma-64	181	13	e	e	PROPN
ma-64	181	14	−	−	PROPN
ma-64	181	15	u0	u0	ADJ
ma-64	181	16	p	p	NOUN
ma-64	181	17	δype	δype	NOUN
ma-64	181	18	−	−	NOUN
ma-64	181	19	u0	u0	ADJ
ma-64	181	20	p	p	NOUN
ma-64	181	21	−	−	PROPN
ma-64	181	22	u0	u0	ADJ
ma-64	181	23	w	w	PROPN
ma-64	181	24	δywp	δywp	PROPN
ma-64	181	25	)	)	PUNCT
ma-64	181	26	(	(	PUNCT
ma-64	181	27	11	11	NUM
ma-64	181	28	)	)	PUNCT
ma-64	181	29	for	for	ADP
ma-64	181	30	convenience	convenience	NOUN
ma-64	181	31	,	,	PUNCT
ma-64	181	32	we	we	PRON
ma-64	181	33	put	put	VERB
ma-64	181	34	δywp	δywp	NOUN
ma-64	181	35	=	=	NOUN
ma-64	181	36	δype	δype	NOUN
ma-64	181	37	=	=	SYM
ma-64	181	38	∆y	∆y	PROPN
ma-64	181	39	on	on	ADP
ma-64	181	40	the	the	DET
ma-64	181	41	following	follow	VERB
ma-64	181	42	three	three	NUM
ma-64	181	43	schemes	scheme	NOUN
ma-64	181	44	.	.	PUNCT
ma-64	182	1	explicit	explicit	ADJ
ma-64	182	2	scheme	scheme	NOUN
ma-64	182	3	.	.	PUNCT
ma-64	182	4	substitution	substitution	NOUN
ma-64	182	5	of	of	ADP
ma-64	182	6	θ	θ	PROPN
ma-64	182	7	=	=	SYM
ma-64	182	8	0	0	PUNCT
ma-64	182	9	into	into	ADP
ma-64	182	10	equation	equation	NOUN
ma-64	182	11	(	(	PUNCT
ma-64	182	12	11	11	NUM
ma-64	182	13	)	)	PUNCT
ma-64	182	14	gives	give	VERB
ma-64	182	15	the	the	DET
ma-64	182	16	following	follow	VERB
ma-64	182	17	explicit	explicit	ADJ
ma-64	182	18	discretizedequation	discretizedequation	NOUN
ma-64	182	19	,	,	PUNCT
ma-64	182	20	(	(	PUNCT
ma-64	182	21	up	up	ADP
ma-64	182	22	−	−	PROPN
ma-64	182	23	u0	u0	ADJ
ma-64	182	24	p	p	NOUN
ma-64	182	25	)	)	PUNCT
ma-64	182	26	∆y	∆y	PROPN
ma-64	182	27	∆τ	∆τ	NOUN
ma-64	182	28	=	=	SYM
ma-64	182	29	1	1	NUM
ma-64	182	30	2	2	NUM
ma-64	182	31	(	(	PUNCT
ma-64	182	32	2r	2r	NUM
ma-64	182	33	σ2	σ2	PROPN
ma-64	182	34	+	+	CCONJ
ma-64	182	35	(	(	PUNCT
ma-64	182	36	σ̃	σ̃	PROPN
ma-64	182	37	σ	σ	PROPN
ma-64	182	38	)	)	PUNCT
ma-64	182	39	2	2	NUM
ma-64	182	40	)	)	PUNCT
ma-64	182	41	(	(	PUNCT
ma-64	182	42	u0	u0	PROPN
ma-64	182	43	e	e	PROPN
ma-64	182	44	−	−	PROPN
ma-64	182	45	u0	u0	ADJ
ma-64	182	46	w	w	PROPN
ma-64	182	47	)	)	PUNCT
ma-64	183	1	+	+	CCONJ
ma-64	183	2	1	1	NUM
ma-64	183	3	∆y	∆y	NOUN
ma-64	183	4	(	(	PUNCT
ma-64	183	5	σ̃	σ̃	PROPN
ma-64	183	6	σ	σ	PROPN
ma-64	183	7	)	)	PUNCT
ma-64	183	8	2	2	NUM
ma-64	183	9	(	(	PUNCT
ma-64	183	10	u0	u0	NOUN
ma-64	183	11	e	e	NOUN
ma-64	183	12	−	−	PROPN
ma-64	183	13	2u0	2u0	NUM
ma-64	183	14	p	p	NOUN
ma-64	183	15	+	+	CCONJ
ma-64	183	16	u0	u0	ADJ
ma-64	183	17	w	w	PROPN
ma-64	183	18	)	)	PUNCT
ma-64	183	19	this	this	DET
ma-64	183	20	equation	equation	NOUN
ma-64	183	21	may	may	AUX
ma-64	183	22	be	be	AUX
ma-64	183	23	re	re	NOUN
ma-64	183	24	-	-	NOUN
ma-64	183	25	writtens	written	NOUN
ma-64	183	26	as	as	ADP
ma-64	183	27	up	up	ADV
ma-64	183	28	=	=	NOUN
ma-64	183	29	αiu	αiu	NOUN
ma-64	183	30	0	0	NUM
ma-64	184	1	w	w	NOUN
ma-64	184	2	+	+	CCONJ
ma-64	184	3	(	(	PUNCT
ma-64	184	4	1	1	NUM
ma-64	184	5	+	+	NUM
ma-64	184	6	βi	βi	NOUN
ma-64	184	7	)	)	PUNCT
ma-64	184	8	u	u	NOUN
ma-64	184	9	0	0	NUM
ma-64	185	1	p	p	NOUN
ma-64	185	2	+	+	CCONJ
ma-64	185	3	γiu	γiu	NOUN
ma-64	185	4	0	0	NUM
ma-64	185	5	e	e	X
ma-64	185	6	(	(	PUNCT
ma-64	185	7	12	12	NUM
ma-64	185	8	)	)	PUNCT
ma-64	185	9	where	where	SCONJ
ma-64	185	10	αi	αi	ADV
ma-64	185	11	=	=	SYM
ma-64	185	12	∆τ	∆τ	PROPN
ma-64	185	13	(	(	PUNCT
ma-64	185	14	∆y)2	∆y)2	PROPN
ma-64	185	15	(	(	PUNCT
ma-64	185	16	σ̃	σ̃	PROPN
ma-64	185	17	σ	σ	PROPN
ma-64	185	18	)	)	PUNCT
ma-64	185	19	2	2	NUM
ma-64	185	20	−	−	NOUN
ma-64	185	21	∆τ	∆τ	PROPN
ma-64	185	22	2∆y	2∆y	NUM
ma-64	185	23	(	(	PUNCT
ma-64	185	24	2r	2r	NUM
ma-64	185	25	σ2	σ2	PROPN
ma-64	185	26	+	+	CCONJ
ma-64	185	27	(	(	PUNCT
ma-64	185	28	σ̃	σ̃	PROPN
ma-64	185	29	σ	σ	PROPN
ma-64	185	30	)	)	PUNCT
ma-64	185	31	2	2	NUM
ma-64	185	32	)	)	PUNCT
ma-64	185	33	,	,	PUNCT
ma-64	186	1	βi	βi	PROPN
ma-64	186	2	=	=	SYM
ma-64	186	3	−	−	PROPN
ma-64	186	4	2∆τ	2∆τ	NUM
ma-64	186	5	(	(	PUNCT
ma-64	186	6	∆y)2	∆y)2	PROPN
ma-64	186	7	(	(	PUNCT
ma-64	186	8	σ̃	σ̃	PROPN
ma-64	186	9	σ	σ	PROPN
ma-64	186	10	)	)	PUNCT
ma-64	186	11	2	2	NUM
ma-64	186	12	and	and	CCONJ
ma-64	186	13	γi	γi	NOUN
ma-64	186	14	=	=	SYM
ma-64	186	15	∆τ	∆τ	PROPN
ma-64	186	16	(	(	PUNCT
ma-64	186	17	∆y)2	∆y)2	PROPN
ma-64	186	18	(	(	PUNCT
ma-64	186	19	σ̃	σ̃	PROPN
ma-64	186	20	σ	σ	PROPN
ma-64	186	21	)	)	PUNCT
ma-64	186	22	2	2	PROPN
ma-64	186	23	+	+	CCONJ
ma-64	186	24	∆τ	∆τ	PROPN
ma-64	186	25	2∆y	2∆y	NUM
ma-64	186	26	(	(	PUNCT
ma-64	186	27	2r	2r	NUM
ma-64	186	28	σ2	σ2	PROPN
ma-64	186	29	+	+	CCONJ
ma-64	186	30	(	(	PUNCT
ma-64	186	31	σ̃	σ̃	PROPN
ma-64	186	32	σ	σ	PROPN
ma-64	186	33	)	)	PUNCT
ma-64	186	34	2	2	NUM
ma-64	186	35	)	)	PUNCT
ma-64	186	36	which	which	PRON
ma-64	186	37	is	be	AUX
ma-64	186	38	the	the	DET
ma-64	186	39	desired	desire	VERB
ma-64	186	40	finite	finite	ADJ
ma-64	186	41	volume	volume	NOUN
ma-64	186	42	explicit	explicit	ADJ
ma-64	186	43	scheme	scheme	NOUN
ma-64	186	44	(	(	PUNCT
ma-64	186	45	fves	fve	NOUN
ma-64	186	46	)	)	PUNCT
ma-64	186	47	.	.	PUNCT
ma-64	187	1	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	187	2	eur	eur	PROPN
ma-64	187	3	.	.	PUNCT
ma-64	188	1	j.	j.	PROPN
ma-64	188	2	math	math	PROPN
ma-64	188	3	.	.	PUNCT
ma-64	189	1	anal	anal	PROPN
ma-64	189	2	.	.	PUNCT
ma-64	190	1	10.28924	10.28924	NUM
ma-64	190	2	/	/	SYM
ma-64	190	3	ada	ada	PROPN
ma-64	190	4	/	/	SYM
ma-64	190	5	ma.2.9	ma.2.9	PROPN
ma-64	190	6	8	8	NUM
ma-64	190	7	crank	crank	NOUN
ma-64	190	8	-	-	PUNCT
ma-64	190	9	nicolson	nicolson	PROPN
ma-64	190	10	scheme	scheme	NOUN
ma-64	190	11	.	.	PUNCT
ma-64	191	1	putting	put	VERB
ma-64	191	2	θ	θ	NOUN
ma-64	191	3	=	=	SYM
ma-64	191	4	1	1	NUM
ma-64	191	5	2	2	NUM
ma-64	191	6	into	into	ADP
ma-64	191	7	equation	equation	NOUN
ma-64	191	8	(	(	PUNCT
ma-64	191	9	11	11	NUM
ma-64	191	10	)	)	PUNCT
ma-64	191	11	,	,	PUNCT
ma-64	191	12	we	we	PRON
ma-64	191	13	get	get	VERB
ma-64	191	14	the	the	DET
ma-64	191	15	following	follow	VERB
ma-64	191	16	crank	crank	NOUN
ma-64	191	17	-	-	PUNCT
ma-64	191	18	nicolsondiscretized	nicolsondiscretize	VERB
ma-64	191	19	equation	equation	NOUN
ma-64	191	20	,	,	PUNCT
ma-64	191	21	(	(	PUNCT
ma-64	191	22	up	up	ADP
ma-64	191	23	−	−	PROPN
ma-64	191	24	u0	u0	ADJ
ma-64	191	25	p	p	NOUN
ma-64	191	26	)	)	PUNCT
ma-64	191	27	∆y	∆y	PROPN
ma-64	191	28	∆τ	∆τ	NOUN
ma-64	191	29	=	=	SYM
ma-64	191	30	1	1	NUM
ma-64	191	31	4	4	NUM
ma-64	191	32	(	(	PUNCT
ma-64	191	33	2r	2r	NUM
ma-64	191	34	σ2	σ2	PROPN
ma-64	191	35	+	+	CCONJ
ma-64	191	36	(	(	PUNCT
ma-64	191	37	σ̃	σ̃	PROPN
ma-64	191	38	σ	σ	PROPN
ma-64	191	39	)	)	PUNCT
ma-64	191	40	2	2	NUM
ma-64	191	41	)	)	PUNCT
ma-64	191	42	(	(	PUNCT
ma-64	191	43	ue	ue	INTJ
ma-64	191	44	−	−	PROPN
ma-64	191	45	uw	uw	PROPN
ma-64	192	1	+	+	NUM
ma-64	192	2	u0	u0	PROPN
ma-64	192	3	e	e	PROPN
ma-64	192	4	−	−	NOUN
ma-64	192	5	u0	u0	ADJ
ma-64	192	6	w	w	PROPN
ma-64	192	7	)	)	PUNCT
ma-64	193	1	+	+	CCONJ
ma-64	193	2	1	1	NUM
ma-64	193	3	2∆y	2∆y	NUM
ma-64	193	4	(	(	PUNCT
ma-64	193	5	σ̃	σ̃	PROPN
ma-64	193	6	σ	σ	PROPN
ma-64	193	7	)	)	PUNCT
ma-64	193	8	2	2	NUM
ma-64	193	9	(	(	PUNCT
ma-64	193	10	ue	ue	INTJ
ma-64	193	11	−	−	NOUN
ma-64	193	12	2up	2up	PROPN
ma-64	194	1	+	+	CCONJ
ma-64	194	2	uw	uw	PROPN
ma-64	194	3	+	+	NUM
ma-64	194	4	u0	u0	PROPN
ma-64	194	5	e	e	NOUN
ma-64	194	6	−	−	PROPN
ma-64	194	7	2u0	2u0	NUM
ma-64	195	1	p	p	NOUN
ma-64	195	2	+	+	NUM
ma-64	195	3	u0	u0	PROPN
ma-64	195	4	w	w	PROPN
ma-64	195	5	)	)	PUNCT
ma-64	195	6	after	after	ADP
ma-64	195	7	simplification	simplification	NOUN
ma-64	195	8	,	,	PUNCT
ma-64	195	9	we	we	PRON
ma-64	195	10	get	get	VERB
ma-64	195	11	the	the	DET
ma-64	195	12	following	follow	VERB
ma-64	195	13	equation	equation	NOUN
ma-64	195	14	λiuw	λiuw	NOUN
ma-64	195	15	+	+	CCONJ
ma-64	195	16	(	(	PUNCT
ma-64	195	17	1	1	NUM
ma-64	195	18	+	+	NUM
ma-64	195	19	ξi	ξi	NOUN
ma-64	195	20	)	)	PUNCT
ma-64	195	21	up	up	ADP
ma-64	196	1	+	+	CCONJ
ma-64	196	2	ηiue	ηiue	NOUN
ma-64	196	3	=	=	PUNCT
ma-64	196	4	−λiu0	−λiu0	NUM
ma-64	196	5	π	π	X
ma-64	196	6	+	+	CCONJ
ma-64	196	7	(	(	PUNCT
ma-64	196	8	1−	1−	NUM
ma-64	196	9	ξi	ξi	NOUN
ma-64	196	10	)	)	PUNCT
ma-64	196	11	u0	u0	NOUN
ma-64	196	12	p	p	NOUN
ma-64	196	13	−	−	PROPN
ma-64	196	14	ηiu0	ηiu0	NOUN
ma-64	196	15	e	e	X
ma-64	196	16	(	(	PUNCT
ma-64	196	17	13	13	NUM
ma-64	196	18	)	)	PUNCT
ma-64	196	19	where	where	SCONJ
ma-64	196	20	λi	λi	ADP
ma-64	196	21	=	=	SYM
ma-64	196	22	∆τ	∆τ	PROPN
ma-64	196	23	4∆y	4∆y	NUM
ma-64	196	24	(	(	PUNCT
ma-64	196	25	2r	2r	NUM
ma-64	196	26	σ2	σ2	PROPN
ma-64	196	27	+	+	CCONJ
ma-64	196	28	(	(	PUNCT
ma-64	196	29	σ̃	σ̃	PROPN
ma-64	196	30	σ	σ	PROPN
ma-64	196	31	)	)	PUNCT
ma-64	196	32	2	2	NUM
ma-64	196	33	)	)	PUNCT
ma-64	196	34	−	−	PROPN
ma-64	196	35	∆τ	∆τ	PROPN
ma-64	196	36	2(∆y)2	2(∆y)2	PROPN
ma-64	196	37	(	(	PUNCT
ma-64	196	38	σ̃	σ̃	PROPN
ma-64	196	39	σ	σ	PROPN
ma-64	196	40	)	)	PUNCT
ma-64	196	41	2	2	NUM
ma-64	196	42	,	,	PUNCT
ma-64	196	43	ξi	ξi	NOUN
ma-64	196	44	=	=	SYM
ma-64	196	45	∆τ	∆τ	PROPN
ma-64	196	46	(	(	PUNCT
ma-64	196	47	∆y)2	∆y)2	PROPN
ma-64	196	48	(	(	PUNCT
ma-64	196	49	σ̃	σ̃	PROPN
ma-64	196	50	σ	σ	PROPN
ma-64	196	51	)	)	PUNCT
ma-64	196	52	2	2	NUM
ma-64	196	53	and	and	CCONJ
ma-64	196	54	ηi	ηi	NOUN
ma-64	196	55	=	=	SYM
ma-64	196	56	−	−	PROPN
ma-64	196	57	[	[	PUNCT
ma-64	196	58	∆τ	∆τ	PROPN
ma-64	196	59	4∆y	4∆y	NUM
ma-64	196	60	(	(	PUNCT
ma-64	196	61	2r	2r	NUM
ma-64	196	62	σ2	σ2	PROPN
ma-64	196	63	+	+	CCONJ
ma-64	196	64	(	(	PUNCT
ma-64	196	65	σ̃	σ̃	PROPN
ma-64	196	66	σ	σ	PROPN
ma-64	196	67	)	)	PUNCT
ma-64	196	68	2	2	NUM
ma-64	196	69	)	)	PUNCT
ma-64	197	1	+	+	CCONJ
ma-64	197	2	∆τ	∆τ	PROPN
ma-64	197	3	2(∆y)2	2(∆y)2	PROPN
ma-64	197	4	(	(	PUNCT
ma-64	197	5	σ̃	σ̃	PROPN
ma-64	197	6	σ	σ	PROPN
ma-64	197	7	)	)	PUNCT
ma-64	197	8	2	2	NUM
ma-64	197	9	]	]	PUNCT
ma-64	197	10	which	which	PRON
ma-64	197	11	is	be	AUX
ma-64	197	12	the	the	DET
ma-64	197	13	proposed	propose	VERB
ma-64	197	14	finite	finite	PROPN
ma-64	197	15	volume	volume	PROPN
ma-64	197	16	crank	crank	PROPN
ma-64	197	17	-	-	PUNCT
ma-64	197	18	nicolson	nicolson	PROPN
ma-64	197	19	scheme	scheme	PROPN
ma-64	197	20	(	(	PUNCT
ma-64	197	21	fvcns	fvcns	PROPN
ma-64	197	22	)	)	PUNCT
ma-64	197	23	.	.	PUNCT
ma-64	198	1	fully	fully	ADV
ma-64	198	2	implicit	implicit	ADJ
ma-64	198	3	scheme	scheme	NOUN
ma-64	198	4	.	.	PUNCT
ma-64	198	5	substitution	substitution	NOUN
ma-64	198	6	of	of	ADP
ma-64	198	7	θ	θ	PROPN
ma-64	198	8	=	=	SYM
ma-64	198	9	1	1	NUM
ma-64	198	10	into	into	ADP
ma-64	198	11	equation	equation	NOUN
ma-64	198	12	(	(	PUNCT
ma-64	198	13	11	11	NUM
ma-64	198	14	)	)	PUNCT
ma-64	198	15	leads	lead	VERB
ma-64	198	16	to	to	ADP
ma-64	198	17	the	the	DET
ma-64	198	18	following	follow	VERB
ma-64	198	19	form	form	NOUN
ma-64	198	20	:(	:(	PUNCT
ma-64	198	21	up	up	ADP
ma-64	198	22	−	−	PROPN
ma-64	198	23	u0	u0	ADJ
ma-64	198	24	p	p	NOUN
ma-64	198	25	)	)	PUNCT
ma-64	198	26	∆y	∆y	PROPN
ma-64	198	27	∆τ	∆τ	NOUN
ma-64	198	28	=	=	SYM
ma-64	198	29	1	1	NUM
ma-64	198	30	2	2	NUM
ma-64	198	31	(	(	PUNCT
ma-64	198	32	2r	2r	NUM
ma-64	198	33	σ2	σ2	PROPN
ma-64	198	34	+	+	CCONJ
ma-64	198	35	(	(	PUNCT
ma-64	198	36	σ̃	σ̃	PROPN
ma-64	198	37	σ	σ	PROPN
ma-64	198	38	)	)	PUNCT
ma-64	198	39	2	2	NUM
ma-64	198	40	)	)	PUNCT
ma-64	198	41	(	(	PUNCT
ma-64	198	42	ue	ue	INTJ
ma-64	198	43	−	−	PROPN
ma-64	198	44	uw	uw	PROPN
ma-64	198	45	)	)	PUNCT
ma-64	199	1	+	+	CCONJ
ma-64	199	2	1	1	NUM
ma-64	199	3	∆y	∆y	NOUN
ma-64	199	4	(	(	PUNCT
ma-64	199	5	σ̃	σ̃	PROPN
ma-64	199	6	σ	σ	PROPN
ma-64	199	7	)	)	PUNCT
ma-64	199	8	2	2	NUM
ma-64	199	9	(	(	PUNCT
ma-64	199	10	ue	ue	INTJ
ma-64	199	11	−	−	NOUN
ma-64	199	12	2up	2up	PROPN
ma-64	200	1	+	+	CCONJ
ma-64	200	2	uw	uw	PROPN
ma-64	200	3	)	)	PUNCT
ma-64	200	4	and	and	CCONJ
ma-64	200	5	the	the	DET
ma-64	200	6	reduced	reduce	VERB
ma-64	200	7	formula	formula	NOUN
ma-64	200	8	is	be	AUX
ma-64	200	9	then	then	ADV
ma-64	200	10	qiuw	qiuw	NOUN
ma-64	200	11	+	+	CCONJ
ma-64	200	12	(	(	PUNCT
ma-64	200	13	1	1	NUM
ma-64	200	14	+	+	NUM
ma-64	200	15	ri	ri	NOUN
ma-64	200	16	)	)	PUNCT
ma-64	200	17	up	up	ADP
ma-64	201	1	+	+	CCONJ
ma-64	201	2	siue	siue	NOUN
ma-64	201	3	=	=	PUNCT
ma-64	201	4	u0	u0	PROPN
ma-64	201	5	p	p	X
ma-64	201	6	(	(	PUNCT
ma-64	201	7	14	14	NUM
ma-64	201	8	)	)	PUNCT
ma-64	201	9	where	where	SCONJ
ma-64	201	10	qi	qi	NOUN
ma-64	201	11	=	=	SYM
ma-64	201	12	∆τ	∆τ	PROPN
ma-64	201	13	2∆y	2∆y	NUM
ma-64	201	14	(	(	PUNCT
ma-64	201	15	2r	2r	NUM
ma-64	201	16	σ2	σ2	PROPN
ma-64	201	17	+	+	CCONJ
ma-64	201	18	(	(	PUNCT
ma-64	201	19	σ̃	σ̃	PROPN
ma-64	201	20	σ	σ	PROPN
ma-64	201	21	)	)	PUNCT
ma-64	201	22	2	2	NUM
ma-64	201	23	)	)	PUNCT
ma-64	201	24	−	−	PROPN
ma-64	202	1	∆τ	∆τ	PROPN
ma-64	202	2	(	(	PUNCT
ma-64	202	3	∆y)2	∆y)2	PROPN
ma-64	202	4	(	(	PUNCT
ma-64	202	5	σ̃	σ̃	PROPN
ma-64	202	6	σ	σ	PROPN
ma-64	202	7	)	)	PUNCT
ma-64	202	8	2	2	NUM
ma-64	202	9	,	,	PUNCT
ma-64	202	10	ri	ri	NOUN
ma-64	202	11	=	=	SYM
ma-64	202	12	2∆τ	2∆τ	NUM
ma-64	202	13	(	(	PUNCT
ma-64	202	14	∆y)2	∆y)2	PROPN
ma-64	202	15	(	(	PUNCT
ma-64	202	16	σ̃	σ̃	PROPN
ma-64	202	17	σ	σ	PROPN
ma-64	202	18	)	)	PUNCT
ma-64	202	19	2	2	NUM
ma-64	202	20	and	and	CCONJ
ma-64	202	21	si	si	NOUN
ma-64	202	22	=	=	SYM
ma-64	202	23	−	−	PROPN
ma-64	202	24	∆τ	∆τ	PROPN
ma-64	202	25	2∆y	2∆y	NUM
ma-64	202	26	(	(	PUNCT
ma-64	202	27	2r	2r	NUM
ma-64	202	28	σ2	σ2	PROPN
ma-64	202	29	+	+	CCONJ
ma-64	202	30	(	(	PUNCT
ma-64	202	31	σ̃	σ̃	PROPN
ma-64	202	32	σ	σ	PROPN
ma-64	202	33	)	)	PUNCT
ma-64	202	34	2	2	NUM
ma-64	202	35	)	)	PUNCT
ma-64	202	36	−	−	PROPN
ma-64	203	1	∆τ	∆τ	PROPN
ma-64	203	2	(	(	PUNCT
ma-64	203	3	∆y)2	∆y)2	PROPN
ma-64	203	4	(	(	PUNCT
ma-64	203	5	σ̃	σ̃	PROPN
ma-64	203	6	σ	σ	PROPN
ma-64	203	7	)	)	PUNCT
ma-64	203	8	2	2	NUM
ma-64	203	9	which	which	PRON
ma-64	203	10	is	be	AUX
ma-64	203	11	our	our	PRON
ma-64	203	12	proposed	propose	VERB
ma-64	203	13	finite	finite	NOUN
ma-64	203	14	volume	volume	NOUN
ma-64	203	15	fully	fully	ADV
ma-64	203	16	implicit	implicit	ADJ
ma-64	203	17	scheme	scheme	NOUN
ma-64	203	18	(	(	PUNCT
ma-64	203	19	fvfis	fvfis	PROPN
ma-64	203	20	)	)	PUNCT
ma-64	203	21	.	.	PUNCT
ma-64	204	1	5	5	X
ma-64	204	2	.	.	X
ma-64	204	3	stability	stability	NOUN
ma-64	204	4	of	of	ADP
ma-64	204	5	the	the	DET
ma-64	204	6	numerical	numerical	ADJ
ma-64	204	7	schemes	scheme	NOUN
ma-64	204	8	to	to	PART
ma-64	204	9	test	test	VERB
ma-64	204	10	the	the	DET
ma-64	204	11	stability	stability	NOUN
ma-64	204	12	of	of	ADP
ma-64	204	13	the	the	DET
ma-64	204	14	derived	derive	VERB
ma-64	204	15	schemes	scheme	NOUN
ma-64	204	16	in	in	ADP
ma-64	204	17	section	section	NOUN
ma-64	204	18	4	4	NUM
ma-64	204	19	,	,	PUNCT
ma-64	204	20	with	with	ADP
ma-64	204	21	the	the	DET
ma-64	204	22	help	help	NOUN
ma-64	204	23	of	of	ADP
ma-64	204	24	the	the	DET
ma-64	204	25	von	von	PROPN
ma-64	204	26	-	-	PUNCT
ma-64	204	27	neumannstability	neumannstability	NOUN
ma-64	204	28	method	method	NOUN
ma-64	204	29	[	[	X
ma-64	204	30	55	55	NUM
ma-64	204	31	]	]	PUNCT
ma-64	204	32	,	,	PUNCT
ma-64	204	33	let	let	VERB
ma-64	204	34	us	we	PRON
ma-64	204	35	consider	consider	VERB
ma-64	204	36	a	a	DET
ma-64	204	37	fourier	fouri	ADJ
ma-64	204	38	component	component	NOUN
ma-64	204	39	for	for	ADP
ma-64	204	40	uji	uji	PROPN
ma-64	204	41	and	and	CCONJ
ma-64	204	42	u0	u0	PROPN
ma-64	204	43	p	p	PROPN
ma-64	204	44	as	as	ADP
ma-64	204	45	uji	uji	PROPN
ma-64	204	46	=	=	SYM
ma-64	204	47	u	u	NOUN
ma-64	204	48	jeiθi	jeiθi	NOUN
ma-64	204	49	and	and	CCONJ
ma-64	204	50	u0	u0	ADJ
ma-64	204	51	p	p	NOUN
ma-64	204	52	=	=	PUNCT
ma-64	204	53	u	u	NOUN
ma-64	204	54	jeiθi	jeiθi	NOUN
ma-64	204	55	(	(	PUNCT
ma-64	204	56	15	15	NUM
ma-64	204	57	)	)	PUNCT
ma-64	204	58	where	where	SCONJ
ma-64	204	59	i	i	PRON
ma-64	204	60	=	=	VERB
ma-64	204	61	√	√	NUM
ma-64	204	62	−1	−1	NOUN
ma-64	204	63	,	,	PUNCT
ma-64	204	64	i.e.	i.e.	X
ma-64	204	65	,	,	PUNCT
ma-64	204	66	imaginary	imaginary	ADJ
ma-64	204	67	unit	unit	NOUN
ma-64	204	68	,	,	PUNCT
ma-64	204	69	u	u	PROPN
ma-64	204	70	j	j	PROPN
ma-64	204	71	is	be	AUX
ma-64	204	72	the	the	DET
ma-64	204	73	amplitude	amplitude	NOUN
ma-64	204	74	at	at	ADP
ma-64	204	75	a	a	DET
ma-64	204	76	time	time	NOUN
ma-64	204	77	level	level	NOUN
ma-64	204	78	j	j	PROPN
ma-64	204	79	,	,	PUNCT
ma-64	204	80	θ(=	θ(=	PROPN
ma-64	204	81	r∆y	r∆y	NOUN
ma-64	204	82	)	)	PUNCT
ma-64	204	83	is	be	AUX
ma-64	204	84	the	the	DET
ma-64	204	85	phaseangle	phaseangle	NOUN
ma-64	204	86	,	,	PUNCT
ma-64	204	87	r	r	NOUN
ma-64	204	88	is	be	AUX
ma-64	204	89	the	the	DET
ma-64	204	90	wave	wave	NOUN
ma-64	204	91	number	number	NOUN
ma-64	204	92	in	in	ADP
ma-64	204	93	the	the	DET
ma-64	204	94	x	x	NOUN
ma-64	204	95	-	-	NOUN
ma-64	204	96	direction	direction	NOUN
ma-64	204	97	,	,	PUNCT
ma-64	204	98	and	and	CCONJ
ma-64	204	99	i	i	PRON
ma-64	204	100	represents	represent	VERB
ma-64	204	101	the	the	DET
ma-64	204	102	index	index	NOUN
ma-64	204	103	of	of	ADP
ma-64	204	104	the	the	DET
ma-64	204	105	node	node	NOUN
ma-64	204	106	.	.	PUNCT
ma-64	205	1	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	205	2	eur	eur	PROPN
ma-64	205	3	.	.	PUNCT
ma-64	206	1	j.	j.	PROPN
ma-64	206	2	math	math	PROPN
ma-64	206	3	.	.	PUNCT
ma-64	207	1	anal	anal	PROPN
ma-64	207	2	.	.	PUNCT
ma-64	208	1	10.28924	10.28924	NUM
ma-64	208	2	/	/	SYM
ma-64	208	3	ada	ada	PROPN
ma-64	208	4	/	/	SYM
ma-64	208	5	ma.2.9	ma.2.9	PROPN
ma-64	209	1	9similarly	9similarly	ADV
ma-64	209	2	,	,	PUNCT
ma-64	209	3	uj∓1	uj∓1	ADV
ma-64	209	4	i±1	i±1	X
ma-64	209	5	=	=	SYM
ma-64	209	6	u	u	PROPN
ma-64	209	7	j∓1eiθ(i±1	j∓1eiθ(i±1	NOUN
ma-64	209	8	)	)	PUNCT
ma-64	209	9	u0	u0	PROPN
ma-64	209	10	w	w	PROPN
ma-64	209	11	=	=	SYM
ma-64	209	12	u	u	PROPN
ma-64	209	13	jeiθ(i−1	jeiθ(i−1	PROPN
ma-64	209	14	)	)	PUNCT
ma-64	209	15	u0	u0	PROPN
ma-64	209	16	e	e	NOUN
ma-64	209	17	=	=	SYM
ma-64	209	18	u	u	X
ma-64	209	19	jeiθ(i+1	jeiθ(i+1	NOUN
ma-64	209	20	)	)	PUNCT
ma-64	209	21	up	up	ADP
ma-64	209	22	=	=	SYM
ma-64	209	23	u	u	NOUN
ma-64	209	24	j+1eiθi	j+1eiθi	VERB
ma-64	209	25	uw	uw	PROPN
ma-64	209	26	=	=	PROPN
ma-64	209	27	u	u	PROPN
ma-64	209	28	j+1eiθ(i−1	j+1eiθ(i−1	PROPN
ma-64	209	29	)	)	PUNCT
ma-64	209	30	ue	ue	PROPN
ma-64	210	1	=	=	PUNCT
ma-64	210	2	u	u	PROPN
ma-64	210	3	j+1eiθ(i+1	j+1eiθ(i+1	PROPN
ma-64	210	4	)	)	PUNCT
ma-64	210	5	(	(	PUNCT
ma-64	210	6	16	16	NUM
ma-64	210	7	)	)	PUNCT
ma-64	210	8	for	for	ADP
ma-64	210	9	convenience	convenience	NOUN
ma-64	210	10	,	,	PUNCT
ma-64	210	11	let	let	VERB
ma-64	210	12	us	we	PRON
ma-64	210	13	suppose	suppose	VERB
ma-64	210	14	that	that	SCONJ
ma-64	210	15	g	g	PROPN
ma-64	210	16	=	=	SYM
ma-64	210	17	u	u	PROPN
ma-64	210	18	j+1	j+1	PROPN
ma-64	210	19	u	u	PROPN
ma-64	210	20	j	j	PROPN
ma-64	210	21	.	.	PUNCT
ma-64	211	1	thus	thus	ADV
ma-64	211	2	,	,	PUNCT
ma-64	211	3	the	the	DET
ma-64	211	4	stability	stability	NOUN
ma-64	211	5	requirement	requirement	NOUN
ma-64	211	6	is	be	AUX
ma-64	211	7	|g|2	|g|2	PROPN
ma-64	211	8	≤	≤	NOUN
ma-64	211	9	1.applying	1.applying	NUM
ma-64	211	10	equation	equation	NOUN
ma-64	211	11	(	(	PUNCT
ma-64	211	12	15	15	NUM
ma-64	211	13	)	)	PUNCT
ma-64	211	14	and	and	CCONJ
ma-64	211	15	equation	equation	NOUN
ma-64	211	16	(	(	PUNCT
ma-64	211	17	16	16	NUM
ma-64	211	18	)	)	PUNCT
ma-64	211	19	into	into	ADP
ma-64	211	20	equation	equation	NOUN
ma-64	211	21	(	(	PUNCT
ma-64	211	22	7	7	NUM
ma-64	211	23	)	)	PUNCT
ma-64	211	24	,	,	PUNCT
ma-64	211	25	and	and	CCONJ
ma-64	211	26	dividing	divide	VERB
ma-64	211	27	by	by	ADP
ma-64	211	28	eiθi	eiθi	NOUN
ma-64	211	29	,	,	PUNCT
ma-64	211	30	we	we	PRON
ma-64	211	31	get	get	VERB
ma-64	211	32	|g|2	|g|2	PROPN
ma-64	211	33	=	=	SYM
ma-64	211	34	1	1	NUM
ma-64	211	35	4	4	NUM
ma-64	211	36	{4∆τ	{4∆τ	X
ma-64	211	37	(	(	PUNCT
ma-64	211	38	σ̃	σ̃	PROPN
ma-64	211	39	σ	σ	PROPN
ma-64	211	40	)	)	PUNCT
ma-64	211	41	2	2	PROPN
ma-64	211	42	cos	cos	PROPN
ma-64	211	43	θ	θ	PROPN
ma-64	211	44	±	±	NUM
ma-64	211	45	√	√	PROPN
ma-64	211	46	a	a	DET
ma-64	211	47	}	}	PUNCT
ma-64	211	48	2	2	NUM
ma-64	211	49	+	+	NUM
ma-64	211	50	4(∆τ)2(∆y)2	4(∆τ)2(∆y)2	NUM
ma-64	211	51	(	(	PUNCT
ma-64	211	52	2r	2r	NUM
ma-64	211	53	σ2	σ2	PROPN
ma-64	211	54	+	+	CCONJ
ma-64	211	55	(	(	PUNCT
ma-64	211	56	σ̃	σ̃	PROPN
ma-64	211	57	σ	σ	PROPN
ma-64	211	58	)	)	PUNCT
ma-64	211	59	2	2	NUM
ma-64	211	60	)	)	SYM
ma-64	211	61	2	2	NUM
ma-64	211	62	(	(	PUNCT
ma-64	211	63	1−	1−	NUM
ma-64	211	64	cos2	cos2	PROPN
ma-64	211	65	θ	θ	PROPN
ma-64	211	66	)	)	PUNCT
ma-64	211	67			NOUN
ma-64	211	68	×	×	NOUN
ma-64	211	69	(	(	PUNCT
ma-64	211	70	(	(	PUNCT
ma-64	211	71	∆y)2	∆y)2	PROPN
ma-64	211	72	+	+	ADJ
ma-64	211	73	2∆τ	2∆τ	NUM
ma-64	211	74	(	(	PUNCT
ma-64	211	75	σ̃	σ̃	PROPN
ma-64	211	76	σ	σ	PROPN
ma-64	211	77	)	)	PUNCT
ma-64	211	78	2	2	NUM
ma-64	211	79	)	)	PUNCT
ma-64	211	80	−2	−2	NOUN
ma-64	211	81	(	(	PUNCT
ma-64	211	82	17	17	NUM
ma-64	211	83	)	)	PUNCT
ma-64	211	84	where	where	SCONJ
ma-64	211	85	a	a	DET
ma-64	211	86	=	=	NOUN
ma-64	211	87	16(∆τ)2	16(∆τ)2	NOUN
ma-64	211	88	(	(	PUNCT
ma-64	211	89	σ̃	σ̃	PROPN
ma-64	211	90	σ	σ	PROPN
ma-64	211	91	)	)	PUNCT
ma-64	211	92	4	4	NUM
ma-64	211	93	cos2	cos2	NOUN
ma-64	211	94	θ	θ	PROPN
ma-64	211	95	−	−	PROPN
ma-64	211	96	4(∆τ)2(∆y)2	4(∆τ)2(∆y)2	PROPN
ma-64	212	1	(	(	PUNCT
ma-64	212	2	2r	2r	NUM
ma-64	212	3	σ2	σ2	PROPN
ma-64	212	4	+	+	CCONJ
ma-64	212	5	(	(	PUNCT
ma-64	212	6	σ̃	σ̃	PROPN
ma-64	212	7	σ	σ	PROPN
ma-64	212	8	)	)	PUNCT
ma-64	212	9	2	2	NUM
ma-64	212	10	)	)	SYM
ma-64	212	11	2	2	NUM
ma-64	212	12	(	(	PUNCT
ma-64	212	13	1−	1−	NUM
ma-64	212	14	cos2	cos2	PROPN
ma-64	212	15	θ	θ	PROPN
ma-64	212	16	)	)	PUNCT
ma-64	213	1	+	+	CCONJ
ma-64	214	1	4(∆y)4	4(∆y)4	NUM
ma-64	214	2	−	−	NOUN
ma-64	214	3	16(∆τ)2	16(∆τ)2	NUM
ma-64	214	4	(	(	PUNCT
ma-64	214	5	σ̃	σ̃	PROPN
ma-64	214	6	σ	σ	PROPN
ma-64	214	7	)	)	PUNCT
ma-64	214	8	4	4	NUM
ma-64	214	9	+	+	CCONJ
ma-64	214	10	i16(∆τ)2(∆y	i16(∆τ)2(∆y	NOUN
ma-64	214	11	)	)	PUNCT
ma-64	214	12	(	(	PUNCT
ma-64	214	13	σ̃	σ̃	PROPN
ma-64	214	14	σ	σ	PROPN
ma-64	214	15	)	)	PUNCT
ma-64	214	16	2	2	NUM
ma-64	214	17	(	(	PUNCT
ma-64	214	18	2r	2r	NUM
ma-64	214	19	σ2	σ2	PROPN
ma-64	214	20	+	+	CCONJ
ma-64	214	21	(	(	PUNCT
ma-64	214	22	σ̃	σ̃	PROPN
ma-64	214	23	σ	σ	PROPN
ma-64	214	24	)	)	PUNCT
ma-64	214	25	2	2	NUM
ma-64	214	26	)	)	PUNCT
ma-64	214	27	cos	cos	ADP
ma-64	214	28	θ	θ	PROPN
ma-64	214	29	√	√	ADP
ma-64	214	30	1−	1−	NUM
ma-64	214	31	cos2	cos2	PROPN
ma-64	214	32	θ	θ	PROPN
ma-64	214	33	for	for	ADP
ma-64	214	34	extremum	extremum	ADJ
ma-64	214	35	value	value	NOUN
ma-64	214	36	of	of	ADP
ma-64	214	37	|g|2	|g|2	PROPN
ma-64	214	38	,	,	PUNCT
ma-64	214	39	solving	solve	VERB
ma-64	214	40	d	d	PROPN
ma-64	214	41	|g|2	|g|2	PROPN
ma-64	214	42	d(cos	d(cos	PROPN
ma-64	214	43	θ	θ	PROPN
ma-64	214	44	)	)	PUNCT
ma-64	214	45	=	=	SYM
ma-64	214	46	0	0	NUM
ma-64	214	47	for	for	ADP
ma-64	214	48	cos	cos	PROPN
ma-64	214	49	θ	θ	PROPN
ma-64	214	50	,	,	PUNCT
ma-64	214	51	and	and	CCONJ
ma-64	214	52	substituting	substitute	VERB
ma-64	214	53	it	it	PRON
ma-64	214	54	into	into	ADP
ma-64	214	55	d2|g|2	d2|g|2	PROPN
ma-64	214	56	d(cos	d(cos	PROPN
ma-64	214	57	θ)2	θ)2	NOUN
ma-64	214	58	<	<	X
ma-64	214	59	0	0	NUM
ma-64	214	60	.	.	X
ma-64	215	1	thenfrom	thenfrom	ADP
ma-64	215	2	equation	equation	NOUN
ma-64	215	3	(	(	PUNCT
ma-64	215	4	17	17	NUM
ma-64	215	5	)	)	PUNCT
ma-64	215	6	,	,	PUNCT
ma-64	215	7	we	we	PRON
ma-64	215	8	can	can	AUX
ma-64	215	9	not	not	PART
ma-64	215	10	confirm	confirm	VERB
ma-64	215	11	that	that	SCONJ
ma-64	215	12	the	the	DET
ma-64	215	13	maximum	maximum	ADJ
ma-64	215	14	value	value	NOUN
ma-64	215	15	of	of	ADP
ma-64	215	16	|g|2	|g|2	PROPN
ma-64	215	17	would	would	AUX
ma-64	215	18	occur	occur	VERB
ma-64	215	19	.	.	PUNCT
ma-64	216	1	however	however	ADV
ma-64	216	2	,	,	PUNCT
ma-64	216	3	theextreme	theextreme	PROPN
ma-64	216	4	values	value	NOUN
ma-64	216	5	of	of	ADP
ma-64	216	6	cos	cos	ADP
ma-64	216	7	θ	θ	PROPN
ma-64	216	8	must	must	AUX
ma-64	216	9	yet	yet	ADV
ma-64	216	10	be	be	AUX
ma-64	216	11	investigated	investigate	VERB
ma-64	216	12	.	.	PUNCT
ma-64	217	1	for	for	ADP
ma-64	217	2	cos	cos	PROPN
ma-64	217	3	θ	θ	PROPN
ma-64	217	4	=	=	SYM
ma-64	217	5	1	1	NUM
ma-64	217	6	,	,	PUNCT
ma-64	217	7	equation	equation	NOUN
ma-64	217	8	(	(	PUNCT
ma-64	217	9	17	17	NUM
ma-64	217	10	)	)	PUNCT
ma-64	217	11	gives	give	VERB
ma-64	217	12	|g|2	|g|2	PROPN
ma-64	217	13	=	=	SYM
ma-64	217	14	1	1	NUM
ma-64	217	15	,	,	PUNCT
ma-64	217	16	andthe	andthe	ADJ
ma-64	217	17	stability	stability	NOUN
ma-64	217	18	requirement	requirement	NOUN
ma-64	217	19	is	be	AUX
ma-64	217	20	satisfied	satisfied	ADJ
ma-64	217	21	.	.	PUNCT
ma-64	218	1	for	for	ADP
ma-64	218	2	cos	cos	PROPN
ma-64	218	3	θ	θ	PROPN
ma-64	218	4	=	=	SYM
ma-64	218	5	−1	−1	NOUN
ma-64	218	6	,	,	PUNCT
ma-64	218	7	equation	equation	NOUN
ma-64	218	8	(	(	PUNCT
ma-64	218	9	17	17	NUM
ma-64	218	10	)	)	PUNCT
ma-64	218	11	also	also	ADV
ma-64	218	12	yields	yield	VERB
ma-64	218	13	|g|2	|g|2	PROPN
ma-64	218	14	=	=	SYM
ma-64	218	15	1	1	NUM
ma-64	218	16	and	and	CCONJ
ma-64	218	17	,	,	PUNCT
ma-64	218	18	andthe	andthe	ADJ
ma-64	218	19	stability	stability	NOUN
ma-64	218	20	requirement	requirement	NOUN
ma-64	218	21	is	be	AUX
ma-64	218	22	satisfied	satisfied	ADJ
ma-64	218	23	.	.	PUNCT
ma-64	219	1	thus	thus	ADV
ma-64	219	2	,	,	PUNCT
ma-64	219	3	the	the	DET
ma-64	219	4	dffds	dffds	NOUN
ma-64	219	5	proposed	propose	VERB
ma-64	219	6	in	in	ADP
ma-64	219	7	equation	equation	NOUN
ma-64	219	8	(	(	PUNCT
ma-64	219	9	7	7	X
ma-64	219	10	)	)	PUNCT
ma-64	219	11	is	be	AUX
ma-64	219	12	unconditionallystable	unconditionallystable	ADJ
ma-64	219	13	.	.	PUNCT
ma-64	220	1	similarly	similarly	ADV
ma-64	220	2	,	,	PUNCT
ma-64	220	3	we	we	PRON
ma-64	220	4	can	can	AUX
ma-64	220	5	show	show	VERB
ma-64	220	6	that	that	SCONJ
ma-64	220	7	lfds	lfds	PROPN
ma-64	220	8	and	and	CCONJ
ma-64	220	9	fvfis	fvfis	PROPN
ma-64	220	10	wrote	write	VERB
ma-64	220	11	in	in	ADP
ma-64	220	12	equation	equation	NOUN
ma-64	220	13	(	(	PUNCT
ma-64	220	14	8)	8)	NUM
ma-64	220	15	and	and	CCONJ
ma-64	220	16	equation	equation	NOUN
ma-64	220	17	(	(	PUNCT
ma-64	220	18	14	14	NUM
ma-64	220	19	)	)	PUNCT
ma-64	220	20	,	,	PUNCT
ma-64	220	21	respectively	respectively	ADV
ma-64	220	22	,	,	PUNCT
ma-64	220	23	both	both	PRON
ma-64	220	24	are	be	AUX
ma-64	220	25	unconditionally	unconditionally	ADV
ma-64	220	26	stable	stable	ADJ
ma-64	220	27	.	.	PUNCT
ma-64	221	1	again	again	ADV
ma-64	221	2	,	,	PUNCT
ma-64	221	3	applying	apply	VERB
ma-64	221	4	equation	equation	NOUN
ma-64	221	5	(	(	PUNCT
ma-64	221	6	15	15	NUM
ma-64	221	7	)	)	PUNCT
ma-64	221	8	and	and	CCONJ
ma-64	221	9	equation	equation	NOUN
ma-64	221	10	(	(	PUNCT
ma-64	221	11	16	16	NUM
ma-64	221	12	)	)	PUNCT
ma-64	221	13	into	into	ADP
ma-64	221	14	equation	equation	NOUN
ma-64	221	15	(	(	PUNCT
ma-64	221	16	12	12	NUM
ma-64	221	17	)	)	PUNCT
ma-64	221	18	and	and	CCONJ
ma-64	221	19	dividing	divide	VERB
ma-64	221	20	by	by	ADP
ma-64	221	21	eiθi	eiθi	NOUN
ma-64	221	22	,	,	PUNCT
ma-64	221	23	we	we	PRON
ma-64	221	24	get	get	VERB
ma-64	221	25	g	g	NOUN
ma-64	221	26	=	=	NOUN
ma-64	221	27	1	1	NUM
ma-64	221	28	+	+	NUM
ma-64	221	29	2∆τ	2∆τ	NUM
ma-64	221	30	(	(	PUNCT
ma-64	221	31	∆y)2	∆y)2	PROPN
ma-64	221	32	(	(	PUNCT
ma-64	221	33	σ̃	σ̃	PROPN
ma-64	221	34	σ	σ	PROPN
ma-64	221	35	)	)	PUNCT
ma-64	221	36	2	2	NUM
ma-64	221	37	(	(	PUNCT
ma-64	221	38	cos	cos	X
ma-64	221	39	θ	θ	PROPN
ma-64	221	40	−	−	PROPN
ma-64	221	41	1	1	NUM
ma-64	221	42	)	)	PUNCT
ma-64	222	1	+	+	CCONJ
ma-64	222	2	i	i	PRON
ma-64	222	3	∆τ	∆τ	NOUN
ma-64	222	4	∆y	∆y	PROPN
ma-64	222	5	(	(	PUNCT
ma-64	222	6	2r	2r	NUM
ma-64	222	7	σ2	σ2	PROPN
ma-64	222	8	+	+	CCONJ
ma-64	222	9	(	(	PUNCT
ma-64	222	10	σ̃	σ̃	PROPN
ma-64	222	11	σ	σ	PROPN
ma-64	222	12	)	)	PUNCT
ma-64	222	13	2	2	NUM
ma-64	222	14	)	)	PUNCT
ma-64	222	15	sin	sin	NOUN
ma-64	222	16	θ	θ	PROPN
ma-64	222	17	then	then	ADV
ma-64	222	18	we	we	PRON
ma-64	222	19	may	may	AUX
ma-64	222	20	obtain	obtain	VERB
ma-64	222	21	easily	easily	ADV
ma-64	222	22	,	,	PUNCT
ma-64	222	23	|g|2	|g|2	PROPN
ma-64	222	24	=	=	PUNCT
ma-64	222	25	{	{	PUNCT
ma-64	222	26	1	1	NUM
ma-64	222	27	+	+	NUM
ma-64	222	28	2∆τ	2∆τ	NUM
ma-64	222	29	(	(	PUNCT
ma-64	222	30	∆y)2	∆y)2	PROPN
ma-64	222	31	(	(	PUNCT
ma-64	222	32	σ̃	σ̃	PROPN
ma-64	222	33	σ	σ	PROPN
ma-64	222	34	)	)	PUNCT
ma-64	222	35	2	2	NUM
ma-64	222	36	(	(	PUNCT
ma-64	222	37	cos	cos	X
ma-64	222	38	θ	θ	PROPN
ma-64	222	39	−	−	PROPN
ma-64	222	40	1	1	NUM
ma-64	222	41	)	)	PUNCT
ma-64	222	42	}	}	PUNCT
ma-64	222	43	2	2	NUM
ma-64	222	44	+	+	CCONJ
ma-64	222	45	(	(	PUNCT
ma-64	222	46	∆τ	∆τ	PROPN
ma-64	222	47	∆y	∆y	PROPN
ma-64	222	48	)	)	PUNCT
ma-64	222	49	2	2	NUM
ma-64	222	50	(	(	PUNCT
ma-64	222	51	2r	2r	NUM
ma-64	222	52	σ2	σ2	PROPN
ma-64	222	53	+	+	CCONJ
ma-64	222	54	(	(	PUNCT
ma-64	222	55	σ̃	σ̃	PROPN
ma-64	222	56	σ	σ	PROPN
ma-64	222	57	)	)	PUNCT
ma-64	222	58	2	2	NUM
ma-64	222	59	)	)	SYM
ma-64	222	60	2	2	NUM
ma-64	222	61	(	(	PUNCT
ma-64	222	62	1−	1−	NUM
ma-64	222	63	cos2	cos2	PROPN
ma-64	222	64	θ	θ	PROPN
ma-64	222	65	)	)	PUNCT
ma-64	222	66	(	(	PUNCT
ma-64	222	67	18	18	NUM
ma-64	222	68	)	)	PUNCT
ma-64	222	69	for	for	ADP
ma-64	222	70	extremum	extremum	ADJ
ma-64	222	71	value	value	NOUN
ma-64	222	72	of	of	ADP
ma-64	222	73	|g|2	|g|2	PROPN
ma-64	222	74	such	such	ADJ
ma-64	222	75	that	that	SCONJ
ma-64	222	76	d	d	PROPN
ma-64	222	77	|g|2	|g|2	PROPN
ma-64	222	78	d(cos	d(cos	PROPN
ma-64	222	79	θ	θ	PROPN
ma-64	222	80	)	)	PUNCT
ma-64	222	81	=	=	SYM
ma-64	222	82	0	0	NUM
ma-64	222	83	,	,	PUNCT
ma-64	222	84	we	we	PRON
ma-64	222	85	can	can	AUX
ma-64	222	86	find	find	VERB
ma-64	222	87	cos	cos	ADP
ma-64	222	88	θ	θ	PROPN
ma-64	222	89	=	=	SYM
ma-64	222	90	1	1	NUM
ma-64	222	91	∆τ	∆τ	PROPN
ma-64	222	92	×	×	NOUN
ma-64	222	93	[	[	PUNCT
ma-64	222	94	2	2	NUM
ma-64	222	95	(	(	PUNCT
ma-64	222	96	σ̃	σ̃	PROPN
ma-64	222	97	σ	σ	PROPN
ma-64	222	98	)	)	PUNCT
ma-64	222	99	2	2	NUM
ma-64	222	100	−	−	PROPN
ma-64	222	101	4	4	NUM
ma-64	222	102	∆τ	∆τ	NOUN
ma-64	222	103	(	(	PUNCT
ma-64	222	104	∆y)2	∆y)2	PROPN
ma-64	222	105	(	(	PUNCT
ma-64	222	106	σ̃	σ̃	PROPN
ma-64	222	107	σ	σ	PROPN
ma-64	222	108	)	)	PUNCT
ma-64	222	109	4	4	NUM
ma-64	222	110	]	]	SYM
ma-64	222	111	×	×	NOUN
ma-64	222	112	(2r	(2r	NOUN
ma-64	222	113	σ2	σ2	PROPN
ma-64	222	114	+	+	CCONJ
ma-64	222	115	(	(	PUNCT
ma-64	222	116	σ̃	σ̃	PROPN
ma-64	222	117	σ	σ	PROPN
ma-64	222	118	)	)	PUNCT
ma-64	222	119	2	2	NUM
ma-64	222	120	)	)	SYM
ma-64	222	121	2	2	NUM
ma-64	222	122	−	−	PROPN
ma-64	222	123	4	4	NUM
ma-64	222	124	∆τ	∆τ	NOUN
ma-64	222	125	(	(	PUNCT
ma-64	222	126	∆y)2	∆y)2	PROPN
ma-64	222	127	(	(	PUNCT
ma-64	222	128	σ̃	σ̃	PROPN
ma-64	222	129	σ	σ	PROPN
ma-64	222	130	)	)	PUNCT
ma-64	222	131	4	4	NUM
ma-64	222	132	−1	−1	NOUN
ma-64	222	133	(	(	PUNCT
ma-64	222	134	19	19	NUM
ma-64	222	135	)	)	PUNCT
ma-64	222	136	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	222	137	eur	eur	PROPN
ma-64	222	138	.	.	PUNCT
ma-64	223	1	j.	j.	PROPN
ma-64	223	2	math	math	PROPN
ma-64	223	3	.	.	PUNCT
ma-64	224	1	anal	anal	PROPN
ma-64	224	2	.	.	PUNCT
ma-64	225	1	10.28924	10.28924	NUM
ma-64	225	2	/	/	SYM
ma-64	225	3	ada	ada	PROPN
ma-64	225	4	/	/	SYM
ma-64	225	5	ma.2.9	ma.2.9	PROPN
ma-64	225	6	10	10	NUM
ma-64	225	7	considering	consider	VERB
ma-64	225	8	d2|g|2	d2|g|2	PROPN
ma-64	225	9	d(cos	d(cos	PROPN
ma-64	225	10	θ)2	θ)2	NOUN
ma-64	225	11	<	<	X
ma-64	225	12	0	0	PROPN
ma-64	225	13	,	,	PUNCT
ma-64	225	14	and	and	CCONJ
ma-64	225	15	substituting	substitute	VERB
ma-64	225	16	the	the	DET
ma-64	225	17	value	value	NOUN
ma-64	225	18	of	of	ADP
ma-64	225	19	cos	cos	PROPN
ma-64	225	20	θ	θ	PROPN
ma-64	225	21	from	from	ADP
ma-64	225	22	equation	equation	NOUN
ma-64	225	23	(	(	PUNCT
ma-64	225	24	19	19	NUM
ma-64	225	25	)	)	PUNCT
ma-64	225	26	into	into	ADP
ma-64	225	27	equation	equation	NOUN
ma-64	225	28	(	(	PUNCT
ma-64	225	29	18),which	18),which	NUM
ma-64	225	30	does	do	AUX
ma-64	225	31	not	not	PART
ma-64	225	32	provide	provide	VERB
ma-64	225	33	us	we	PRON
ma-64	225	34	the	the	DET
ma-64	225	35	maximum	maximum	ADJ
ma-64	225	36	value	value	NOUN
ma-64	225	37	of	of	ADP
ma-64	225	38	|g|2	|g|2	PROPN
ma-64	225	39	.	.	PUNCT
ma-64	226	1	but	but	CCONJ
ma-64	226	2	,	,	PUNCT
ma-64	226	3	the	the	DET
ma-64	226	4	extreme	extreme	ADJ
ma-64	226	5	values	value	NOUN
ma-64	226	6	of	of	ADP
ma-64	226	7	cos	cos	ADP
ma-64	226	8	θ	θ	PROPN
ma-64	226	9	must	must	AUX
ma-64	226	10	beinvestigated	beinvestigate	VERB
ma-64	226	11	.	.	PUNCT
ma-64	227	1	for	for	ADP
ma-64	227	2	cos	cos	PROPN
ma-64	227	3	θ	θ	PROPN
ma-64	227	4	=	=	SYM
ma-64	227	5	1	1	NUM
ma-64	227	6	,	,	PUNCT
ma-64	227	7	equation	equation	NOUN
ma-64	227	8	(	(	PUNCT
ma-64	227	9	18	18	NUM
ma-64	227	10	)	)	PUNCT
ma-64	227	11	gives	give	VERB
ma-64	227	12	|g|2	|g|2	PROPN
ma-64	227	13	=	=	SYM
ma-64	227	14	1	1	NUM
ma-64	227	15	,	,	PUNCT
ma-64	227	16	and	and	CCONJ
ma-64	227	17	the	the	DET
ma-64	227	18	stability	stability	NOUN
ma-64	227	19	requirement	requirement	NOUN
ma-64	227	20	is	be	AUX
ma-64	227	21	satisfied.for	satisfied.for	X
ma-64	228	1	cos	cos	PROPN
ma-64	228	2	θ	θ	PROPN
ma-64	228	3	=	=	SYM
ma-64	228	4	−1	−1	NOUN
ma-64	228	5	,	,	PUNCT
ma-64	228	6	equation	equation	NOUN
ma-64	228	7	(	(	PUNCT
ma-64	228	8	18	18	NUM
ma-64	228	9	)	)	PUNCT
ma-64	228	10	yields	yield	VERB
ma-64	228	11	|g|2	|g|2	PROPN
ma-64	229	1	=	=	PUNCT
ma-64	230	1	{	{	PUNCT
ma-64	231	1	1−	1−	NUM
ma-64	231	2	4∆τ	4∆τ	NUM
ma-64	231	3	(	(	PUNCT
ma-64	231	4	∆y)2	∆y)2	PROPN
ma-64	231	5	(	(	PUNCT
ma-64	231	6	σ̃	σ̃	PROPN
ma-64	231	7	σ	σ	PROPN
ma-64	231	8	)	)	PUNCT
ma-64	231	9	2	2	NUM
ma-64	231	10	}	}	SYM
ma-64	231	11	2	2	NUM
ma-64	231	12	and	and	CCONJ
ma-64	231	13	,	,	PUNCT
ma-64	231	14	imposing	impose	VERB
ma-64	231	15	the	the	DET
ma-64	231	16	requirement	requirement	NOUN
ma-64	231	17	of	of	ADP
ma-64	231	18	|g|2	|g|2	PROPN
ma-64	231	19	≤	≤	PROPN
ma-64	231	20	1	1	NUM
ma-64	231	21	,	,	PUNCT
ma-64	231	22	yields	yield	NOUN
ma-64	231	23	,	,	PUNCT
ma-64	231	24	fves	fve	NOUN
ma-64	231	25	in	in	ADP
ma-64	231	26	equation	equation	NOUN
ma-64	231	27	(	(	PUNCT
ma-64	231	28	12	12	NUM
ma-64	231	29	)	)	PUNCT
ma-64	231	30	is	be	AUX
ma-64	231	31	conditionally	conditionally	ADV
ma-64	231	32	stable	stable	ADJ
ma-64	231	33	and	and	CCONJ
ma-64	231	34	the	the	DET
ma-64	231	35	condition	condition	NOUN
ma-64	231	36	is	be	AUX
ma-64	231	37	(	(	PUNCT
ma-64	231	38	σ̃	σ̃	PROPN
ma-64	231	39	σ	σ	PROPN
ma-64	231	40	)	)	PUNCT
ma-64	231	41	2	2	NUM
ma-64	231	42	≤	≤	NOUN
ma-64	231	43	(	(	PUNCT
ma-64	231	44	∆y)2	∆y)2	NUM
ma-64	231	45	2∆τ	2∆τ	NUM
ma-64	231	46	(	(	PUNCT
ma-64	231	47	20	20	NUM
ma-64	231	48	)	)	PUNCT
ma-64	231	49	similarly	similarly	ADV
ma-64	231	50	,	,	PUNCT
ma-64	231	51	we	we	PRON
ma-64	231	52	can	can	AUX
ma-64	231	53	state	state	VERB
ma-64	231	54	that	that	DET
ma-64	231	55	fvcns	fvcns	PROPN
ma-64	231	56	,	,	PUNCT
ma-64	231	57	equation	equation	NOUN
ma-64	231	58	(	(	PUNCT
ma-64	231	59	13	13	NUM
ma-64	231	60	)	)	PUNCT
ma-64	231	61	is	be	AUX
ma-64	231	62	also	also	ADV
ma-64	231	63	conditionally	conditionally	ADV
ma-64	231	64	stable	stable	ADJ
ma-64	231	65	and	and	CCONJ
ma-64	231	66	the	the	DET
ma-64	231	67	conditionis	conditionis	NOUN
ma-64	231	68	(	(	PUNCT
ma-64	231	69	σ̃	σ̃	PROPN
ma-64	231	70	σ	σ	PROPN
ma-64	231	71	)	)	PUNCT
ma-64	231	72	2	2	NUM
ma-64	231	73	≤	≤	NOUN
ma-64	231	74	(	(	PUNCT
ma-64	231	75	∆y)2	∆y)2	PROPN
ma-64	231	76	∆τ	∆τ	PROPN
ma-64	231	77	(	(	PUNCT
ma-64	231	78	21	21	NUM
ma-64	231	79	)	)	PUNCT
ma-64	231	80	6	6	NUM
ma-64	231	81	.	.	PUNCT
ma-64	232	1	consistency	consistency	NOUN
ma-64	232	2	of	of	ADP
ma-64	232	3	the	the	DET
ma-64	232	4	numerical	numerical	ADJ
ma-64	232	5	schemes	scheme	NOUN
ma-64	232	6	for	for	ADP
ma-64	232	7	consistency	consistency	NOUN
ma-64	232	8	,	,	PUNCT
ma-64	232	9	the	the	DET
ma-64	232	10	finite	finite	ADJ
ma-64	232	11	difference	difference	NOUN
ma-64	232	12	equation	equation	NOUN
ma-64	232	13	(	(	PUNCT
ma-64	232	14	fde	fde	NOUN
ma-64	232	15	)	)	PUNCT
ma-64	232	16	approximation	approximation	NOUN
ma-64	232	17	of	of	ADP
ma-64	232	18	a	a	DET
ma-64	232	19	pde	pde	NOUN
ma-64	232	20	must	must	AUX
ma-64	232	21	reduce	reduce	VERB
ma-64	232	22	tothe	tothe	ADJ
ma-64	232	23	original	original	ADJ
ma-64	232	24	pde	pde	NOUN
ma-64	232	25	as	as	SCONJ
ma-64	232	26	the	the	DET
ma-64	232	27	step	step	NOUN
ma-64	232	28	sizes	size	NOUN
ma-64	232	29	approach	approach	VERB
ma-64	232	30	zero	zero	NUM
ma-64	232	31	[	[	X
ma-64	232	32	55	55	NUM
ma-64	232	33	]	]	PUNCT
ma-64	232	34	.	.	PUNCT
ma-64	233	1	now	now	ADV
ma-64	233	2	expanding	expand	VERB
ma-64	233	3	each	each	DET
ma-64	233	4	u(y	u(y	PROPN
ma-64	233	5	,	,	PUNCT
ma-64	233	6	τ	τ	PROPN
ma-64	233	7	)	)	PUNCT
ma-64	233	8	in	in	ADP
ma-64	233	9	a	a	DET
ma-64	233	10	taylor	taylor	PROPN
ma-64	233	11	series	series	NOUN
ma-64	233	12	expansion	expansion	NOUN
ma-64	233	13	about	about	ADP
ma-64	233	14	uji	uji	PROPN
ma-64	233	15	,	,	PUNCT
ma-64	233	16	we	we	PRON
ma-64	233	17	get	get	VERB
ma-64	233	18	uj+1	uj+1	NUM
ma-64	233	19	i	i	NOUN
ma-64	233	20	=	=	PUNCT
ma-64	233	21	uji	uji	PROPN
ma-64	234	1	+	+	CCONJ
ma-64	234	2	∆τ	∆τ	PROPN
ma-64	234	3	∂u	∂u	PROPN
ma-64	234	4	∂τ	∂τ	PROPN
ma-64	234	5	+	+	CCONJ
ma-64	234	6	(	(	PUNCT
ma-64	234	7	∆τ)2	∆τ)2	NOUN
ma-64	234	8	2	2	NUM
ma-64	234	9	!	!	PUNCT
ma-64	234	10	∂2u	∂2u	PROPN
ma-64	234	11	∂τ2	∂τ2	PROPN
ma-64	235	1	+	+	CCONJ
ma-64	235	2	(	(	PUNCT
ma-64	235	3	∆τ)3	∆τ)3	ADJ
ma-64	235	4	3	3	NUM
ma-64	235	5	!	!	NOUN
ma-64	235	6	∂3u	∂3u	ADJ
ma-64	235	7	∂τ3	∂τ3	NOUN
ma-64	235	8	+	+	PROPN
ma-64	235	9	o(∆τ)4	o(∆τ)4	NOUN
ma-64	235	10	(	(	PUNCT
ma-64	235	11	22	22	NUM
ma-64	235	12	)	)	PUNCT
ma-64	235	13	uj+1	uj+1	NOUN
ma-64	235	14	i+1	i+1	NOUN
ma-64	235	15	=	=	ADJ
ma-64	235	16	uji	uji	ADJ
ma-64	235	17	+	+	CCONJ
ma-64	235	18	∆τ	∆τ	PROPN
ma-64	235	19	∂u	∂u	PROPN
ma-64	235	20	∂τ	∂τ	PROPN
ma-64	235	21	+	+	NUM
ma-64	235	22	∆y	∆y	PROPN
ma-64	235	23	∂u	∂u	PROPN
ma-64	235	24	∂y	∂y	NOUN
ma-64	236	1	+	+	CCONJ
ma-64	236	2	1	1	NUM
ma-64	236	3	2	2	NUM
ma-64	236	4	!	!	PUNCT
ma-64	236	5	(	(	PUNCT
ma-64	236	6	∆τ	∆τ	PROPN
ma-64	236	7	∂	∂	NOUN
ma-64	236	8	∂τ	∂τ	NOUN
ma-64	236	9	+	+	CCONJ
ma-64	236	10	∆y	∆y	PROPN
ma-64	236	11	∂	∂	NOUN
ma-64	236	12	∂y	∂y	NOUN
ma-64	236	13	)	)	PUNCT
ma-64	236	14	2	2	NUM
ma-64	236	15	u	u	NOUN
ma-64	236	16	+	+	NOUN
ma-64	236	17	1	1	NUM
ma-64	236	18	3	3	NUM
ma-64	236	19	!	!	PUNCT
ma-64	237	1	(	(	PUNCT
ma-64	237	2	∆τ	∆τ	PROPN
ma-64	237	3	∂	∂	NOUN
ma-64	237	4	∂τ	∂τ	NOUN
ma-64	237	5	+	+	CCONJ
ma-64	237	6	∆y	∆y	PROPN
ma-64	237	7	∂	∂	X
ma-64	237	8	∂y	∂y	NOUN
ma-64	237	9	)	)	PUNCT
ma-64	237	10	3	3	NUM
ma-64	237	11	u	u	NOUN
ma-64	237	12	+	+	NOUN
ma-64	237	13	o	o	X
ma-64	237	14	[	[	PUNCT
ma-64	237	15	(	(	PUNCT
ma-64	237	16	∆τ)4	∆τ)4	X
ma-64	237	17	,	,	PUNCT
ma-64	237	18	(	(	PUNCT
ma-64	237	19	∆y)4	∆y)4	X
ma-64	237	20	]	]	PUNCT
ma-64	237	21	(	(	PUNCT
ma-64	237	22	23	23	NUM
ma-64	237	23	)	)	PUNCT
ma-64	237	24	uj+1	uj+1	NOUN
ma-64	237	25	i−1	i−1	PROPN
ma-64	237	26	=	=	PRON
ma-64	237	27	uji	uji	PROPN
ma-64	237	28	+	+	CCONJ
ma-64	237	29	∆τ	∆τ	PROPN
ma-64	237	30	∂u	∂u	PROPN
ma-64	237	31	∂τ	∂τ	PROPN
ma-64	237	32	−	−	PROPN
ma-64	237	33	∆y	∆y	PROPN
ma-64	237	34	∂u	∂u	PROPN
ma-64	237	35	∂y	∂y	PRON
ma-64	238	1	+	+	CCONJ
ma-64	238	2	1	1	NUM
ma-64	238	3	2	2	NUM
ma-64	238	4	!	!	PUNCT
ma-64	238	5	(	(	PUNCT
ma-64	238	6	∆τ	∆τ	PROPN
ma-64	238	7	∂	∂	NUM
ma-64	238	8	∂τ	∂τ	PROPN
ma-64	238	9	−∆y	−∆y	NOUN
ma-64	238	10	∂	∂	X
ma-64	238	11	∂y	∂y	X
ma-64	238	12	)	)	PUNCT
ma-64	238	13	2	2	NUM
ma-64	238	14	u	u	NOUN
ma-64	238	15	+	+	NOUN
ma-64	238	16	1	1	NUM
ma-64	238	17	3	3	NUM
ma-64	238	18	!	!	PUNCT
ma-64	239	1	(	(	PUNCT
ma-64	239	2	∆τ	∆τ	PROPN
ma-64	239	3	∂	∂	NOUN
ma-64	239	4	∂τ	∂τ	PROPN
ma-64	239	5	−	−	NOUN
ma-64	239	6	∆y	∆y	PROPN
ma-64	239	7	∂	∂	X
ma-64	239	8	∂y	∂y	NOUN
ma-64	239	9	)	)	PUNCT
ma-64	239	10	3	3	NUM
ma-64	239	11	u	u	NOUN
ma-64	239	12	+	+	NOUN
ma-64	239	13	o	o	X
ma-64	239	14	[	[	PUNCT
ma-64	239	15	(	(	PUNCT
ma-64	239	16	∆τ)4	∆τ)4	X
ma-64	239	17	,	,	PUNCT
ma-64	239	18	(	(	PUNCT
ma-64	239	19	∆y)4	∆y)4	X
ma-64	239	20	]	]	PUNCT
ma-64	239	21	(	(	PUNCT
ma-64	239	22	24	24	NUM
ma-64	239	23	)	)	PUNCT
ma-64	239	24	applying	apply	VERB
ma-64	239	25	equations	equation	NOUN
ma-64	239	26	(	(	PUNCT
ma-64	239	27	22	22	NUM
ma-64	239	28	)	)	PUNCT
ma-64	239	29	,	,	PUNCT
ma-64	239	30	(	(	PUNCT
ma-64	239	31	23	23	NUM
ma-64	239	32	)	)	PUNCT
ma-64	239	33	,	,	PUNCT
ma-64	239	34	and	and	CCONJ
ma-64	239	35	(	(	PUNCT
ma-64	239	36	24	24	NUM
ma-64	239	37	)	)	PUNCT
ma-64	239	38	into	into	ADP
ma-64	239	39	equation	equation	NOUN
ma-64	239	40	(	(	PUNCT
ma-64	239	41	8)	8)	NUM
ma-64	239	42	yields	yield	NOUN
ma-64	239	43	(	(	PUNCT
ma-64	239	44	di	di	NOUN
ma-64	239	45	+	+	NOUN
ma-64	239	46	ei	ei	NOUN
ma-64	239	47	+	+	NUM
ma-64	239	48	fi	fi	NOUN
ma-64	239	49	)	)	PUNCT
ma-64	239	50	u	u	NOUN
ma-64	239	51	j	j	PROPN
ma-64	240	1	i	i	PRON
ma-64	240	2	+	+	CCONJ
ma-64	240	3	(	(	PUNCT
ma-64	240	4	1	1	NUM
ma-64	240	5	+	+	CCONJ
ma-64	240	6	di	di	X
ma-64	240	7	+	+	NOUN
ma-64	240	8	ei	ei	NOUN
ma-64	240	9	+	+	CCONJ
ma-64	240	10	fi	fi	NOUN
ma-64	240	11	)	)	PUNCT
ma-64	240	12	∆τ	∆τ	PROPN
ma-64	240	13	∂u	∂u	PROPN
ma-64	240	14	∂τ	∂τ	PROPN
ma-64	240	15	+	+	CCONJ
ma-64	240	16	(	(	PUNCT
ma-64	240	17	1	1	NUM
ma-64	240	18	+	+	CCONJ
ma-64	240	19	di	di	X
ma-64	240	20	+	+	NOUN
ma-64	240	21	ei	ei	NOUN
ma-64	240	22	+	+	NUM
ma-64	240	23	fi	fi	NOUN
ma-64	240	24	)	)	PUNCT
ma-64	240	25	(	(	PUNCT
ma-64	240	26	∆τ)2	∆τ)2	SYM
ma-64	240	27	2	2	NUM
ma-64	240	28	∂2u	∂2u	X
ma-64	240	29	∂τ2	∂τ2	PROPN
ma-64	240	30	+	+	CCONJ
ma-64	240	31	(	(	PUNCT
ma-64	240	32	−di	−di	NOUN
ma-64	240	33	+	+	CCONJ
ma-64	240	34	fi	fi	NOUN
ma-64	240	35	)	)	PUNCT
ma-64	240	36	∆y	∆y	PROPN
ma-64	240	37	∂u	∂u	PROPN
ma-64	240	38	∂y	∂y	PRON
ma-64	241	1	+	+	CCONJ
ma-64	241	2	(	(	PUNCT
ma-64	241	3	−di	−di	NOUN
ma-64	241	4	+	+	CCONJ
ma-64	241	5	fi	fi	NOUN
ma-64	241	6	)	)	PUNCT
ma-64	241	7	∆τ∆y	∆τ∆y	PROPN
ma-64	241	8	∂2u	∂2u	PROPN
ma-64	241	9	∂τ∂y	∂τ∂y	PROPN
ma-64	241	10	+	+	CCONJ
ma-64	241	11	(	(	PUNCT
ma-64	241	12	di	di	NOUN
ma-64	241	13	+	+	NOUN
ma-64	241	14	fi	fi	NOUN
ma-64	241	15	)	)	PUNCT
ma-64	241	16	(	(	PUNCT
ma-64	241	17	∆y)2	∆y)2	PROPN
ma-64	241	18	2	2	NUM
ma-64	241	19	∂2u	∂2u	NOUN
ma-64	241	20	∂y2	∂y2	ADV
ma-64	242	1	+	+	PROPN
ma-64	242	2	o	o	X
ma-64	242	3	[	[	PUNCT
ma-64	242	4	(	(	PUNCT
ma-64	242	5	∆τ)3	∆τ)3	ADJ
ma-64	242	6	,	,	PUNCT
ma-64	242	7	(	(	PUNCT
ma-64	242	8	∆y)3	∆y)3	X
ma-64	242	9	]	]	PUNCT
ma-64	242	10	=	=	SYM
ma-64	242	11	0from	0from	NUM
ma-64	243	1	which	which	PRON
ma-64	243	2	we	we	PRON
ma-64	243	3	get	get	VERB
ma-64	243	4	∂u	∂u	PROPN
ma-64	243	5	∂τ	∂τ	PROPN
ma-64	243	6	+	+	CCONJ
ma-64	243	7	∆τ	∆τ	PROPN
ma-64	243	8	2	2	NUM
ma-64	243	9	∂2u	∂2u	NOUN
ma-64	243	10	∂τ2	∂τ2	PROPN
ma-64	244	1	−	−	PROPN
ma-64	245	1	(	(	PUNCT
ma-64	245	2	2r	2r	NUM
ma-64	245	3	σ2	σ2	PROPN
ma-64	245	4	+	+	CCONJ
ma-64	245	5	(	(	PUNCT
ma-64	245	6	σ̃	σ̃	PROPN
ma-64	245	7	σ	σ	PROPN
ma-64	245	8	)	)	PUNCT
ma-64	245	9	2	2	NUM
ma-64	245	10	)	)	PUNCT
ma-64	245	11	∂u	∂u	PROPN
ma-64	245	12	∂y	∂y	SYM
ma-64	245	13	−	−	NOUN
ma-64	245	14	∆τ	∆τ	PROPN
ma-64	245	15	(	(	PUNCT
ma-64	245	16	2r	2r	NUM
ma-64	245	17	σ2	σ2	PROPN
ma-64	245	18	+	+	CCONJ
ma-64	245	19	(	(	PUNCT
ma-64	245	20	σ̃	σ̃	PROPN
ma-64	245	21	σ	σ	PROPN
ma-64	245	22	)	)	PUNCT
ma-64	245	23	2	2	NUM
ma-64	245	24	)	)	PUNCT
ma-64	245	25	∂2u	∂2u	PROPN
ma-64	245	26	∂y∂τ	∂y∂τ	PRON
ma-64	245	27	−	−	PROPN
ma-64	246	1	(	(	PUNCT
ma-64	246	2	σ̃	σ̃	PROPN
ma-64	246	3	σ	σ	PROPN
ma-64	246	4	)	)	PUNCT
ma-64	246	5	2	2	NUM
ma-64	246	6	∂2u	∂2u	NOUN
ma-64	246	7	∂y2	∂y2	ADV
ma-64	247	1	+	+	PROPN
ma-64	247	2	o	o	X
ma-64	247	3	[	[	PUNCT
ma-64	247	4	(	(	PUNCT
ma-64	247	5	∆τ)2	∆τ)2	NOUN
ma-64	247	6	,	,	PUNCT
ma-64	247	7	(	(	PUNCT
ma-64	247	8	∆y)2	∆y)2	PART
ma-64	247	9	]	]	PUNCT
ma-64	247	10	=	=	SYM
ma-64	247	11	0	0	NUM
ma-64	247	12	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	247	13	eur	eur	PROPN
ma-64	247	14	.	.	PUNCT
ma-64	248	1	j.	j.	PROPN
ma-64	248	2	math	math	PROPN
ma-64	248	3	.	.	PUNCT
ma-64	249	1	anal	anal	PROPN
ma-64	249	2	.	.	PUNCT
ma-64	250	1	10.28924	10.28924	NUM
ma-64	250	2	/	/	SYM
ma-64	250	3	ada	ada	PROPN
ma-64	250	4	/	/	SYM
ma-64	250	5	ma.2.9	ma.2.9	PROPN
ma-64	250	6	11it	11it	NOUN
ma-64	250	7	is	be	AUX
ma-64	250	8	obvious	obvious	ADJ
ma-64	250	9	that	that	SCONJ
ma-64	250	10	if	if	SCONJ
ma-64	250	11	∆τ,∆y	∆τ,∆y	PROPN
ma-64	250	12	→	→	SYM
ma-64	250	13	0	0	NUM
ma-64	250	14	,	,	PUNCT
ma-64	250	15	then	then	ADV
ma-64	250	16	the	the	DET
ma-64	250	17	original	original	ADJ
ma-64	250	18	pde	pde	NOUN
ma-64	250	19	(	(	PUNCT
ma-64	250	20	2	2	NUM
ma-64	250	21	)	)	PUNCT
ma-64	250	22	is	be	AUX
ma-64	250	23	recovered	recover	VERB
ma-64	250	24	.	.	PUNCT
ma-64	251	1	therefore	therefore	ADV
ma-64	251	2	,	,	PUNCT
ma-64	251	3	the	the	DET
ma-64	251	4	laasonenfinite	laasonenfinite	ADJ
ma-64	251	5	difference	difference	NOUN
ma-64	251	6	scheme	scheme	NOUN
ma-64	251	7	,	,	PUNCT
ma-64	251	8	equation	equation	NOUN
ma-64	251	9	(	(	PUNCT
ma-64	251	10	8)	8)	NUM
ma-64	251	11	,	,	PUNCT
ma-64	251	12	is	be	AUX
ma-64	251	13	consistent	consistent	ADJ
ma-64	251	14	.	.	PUNCT
ma-64	252	1	now	now	ADV
ma-64	252	2	according	accord	VERB
ma-64	252	3	to	to	ADP
ma-64	252	4	lax	lax	PROPN
ma-64	252	5	’s	’s	PART
ma-64	252	6	equivalence	equivalence	NOUN
ma-64	252	7	theorem,[55	theorem,[55	VERB
ma-64	252	8	]	]	PUNCT
ma-64	252	9	,	,	PUNCT
ma-64	252	10	lfds	lfds	PROPN
ma-64	252	11	is	be	AUX
ma-64	252	12	convergent	convergent	ADJ
ma-64	252	13	for	for	ADP
ma-64	252	14	all	all	DET
ma-64	252	15	values	value	NOUN
ma-64	252	16	of	of	ADP
ma-64	252	17	the	the	DET
ma-64	252	18	parameters	parameter	NOUN
ma-64	252	19	.	.	PUNCT
ma-64	253	1	similar	similar	ADJ
ma-64	253	2	arguments	argument	NOUN
ma-64	253	3	hold	hold	VERB
ma-64	253	4	for	for	ADP
ma-64	253	5	dffds	dffds	NOUN
ma-64	253	6	andfvfis	andfvfis	PROPN
ma-64	253	7	.	.	PUNCT
ma-64	254	1	on	on	ADP
ma-64	254	2	the	the	DET
ma-64	254	3	other	other	ADJ
ma-64	254	4	hand	hand	NOUN
ma-64	254	5	,	,	PUNCT
ma-64	254	6	fves	fve	NOUN
ma-64	254	7	and	and	CCONJ
ma-64	254	8	fvcns	fvcns	PROPN
ma-64	254	9	are	be	AUX
ma-64	254	10	also	also	ADV
ma-64	254	11	convergent	convergent	ADJ
ma-64	254	12	if	if	SCONJ
ma-64	254	13	the	the	DET
ma-64	254	14	conditions	condition	NOUN
ma-64	254	15	(	(	PUNCT
ma-64	254	16	20	20	NUM
ma-64	254	17	)	)	PUNCT
ma-64	254	18	and	and	CCONJ
ma-64	254	19	(	(	PUNCT
ma-64	254	20	21)respectively	21)respectively	ADV
ma-64	254	21	,	,	PUNCT
ma-64	254	22	are	be	AUX
ma-64	254	23	satisfied	satisfied	ADJ
ma-64	254	24	.	.	PUNCT
ma-64	255	1	table	table	NOUN
ma-64	255	2	1	1	NUM
ma-64	255	3	.	.	PUNCT
ma-64	256	1	call	call	NOUN
ma-64	256	2	option	option	NOUN
ma-64	256	3	prices	price	NOUN
ma-64	256	4	using	use	VERB
ma-64	256	5	the	the	DET
ma-64	256	6	leland	leland	PROPN
ma-64	256	7	volatility	volatility	NOUN
ma-64	256	8	model	model	NOUN
ma-64	256	9	.	.	PUNCT
ma-64	257	1	s0	s0	PROPN
ma-64	257	2	exact	exact	ADJ
ma-64	257	3	finite	finite	ADJ
ma-64	257	4	difference	difference	NOUN
ma-64	257	5	schemes	scheme	NOUN
ma-64	257	6	finite	finite	VERB
ma-64	257	7	volume	volume	NOUN
ma-64	257	8	schemes(linear	schemes(linear	PROPN
ma-64	257	9	)	)	PUNCT
ma-64	257	10	dffds	dffds	NOUN
ma-64	257	11	lfds	lfds	PROPN
ma-64	257	12	fves	fve	NOUN
ma-64	257	13	fvfis	fvfi	VERB
ma-64	257	14	fvcns37.00	fvcns37.00	VERB
ma-64	257	15	0.00001	0.00001	NUM
ma-64	257	16	0.04734	0.04734	NUM
ma-64	257	17	0.04893	0.04893	NUM
ma-64	257	18	0.00000	0.00000	NUM
ma-64	257	19	0.00054	0.00054	NUM
ma-64	257	20	0.0005047.00	0.0005047.00	NOUN
ma-64	257	21	0.00182	0.00182	NUM
ma-64	257	22	0.30914	0.30914	NUM
ma-64	257	23	0.31368	0.31368	NUM
ma-64	258	1	0.00006	0.00006	NUM
ma-64	258	2	0.01340	0.01340	NUM
ma-64	258	3	0.0129757.00	0.0129757.00	NUM
ma-64	258	4	0.05078	0.05078	NUM
ma-64	258	5	1.09349	1.09349	NUM
ma-64	258	6	1.09949	1.09949	NUM
ma-64	258	7	0.00036	0.00036	NUM
ma-64	258	8	0.10771	0.10771	NUM
ma-64	258	9	0.1058867.00	0.1058867.00	NUM
ma-64	258	10	0.45226	0.45226	NUM
ma-64	258	11	2.93576	2.93576	NUM
ma-64	258	12	2.94472	2.94472	NUM
ma-64	258	13	0.00335	0.00335	NUM
ma-64	258	14	0.65191	0.65191	NUM
ma-64	258	15	0.6479577.00	0.6479577.00	NUM
ma-64	258	16	1.97686	1.97686	NUM
ma-64	258	17	6.06630	6.06630	NUM
ma-64	258	18	6.07104	6.07104	NUM
ma-64	258	19	0.01709	0.01709	NUM
ma-64	258	20	2.26632	2.26632	NUM
ma-64	258	21	2.2623087.00	2.2623087.00	NUM
ma-64	258	22	5.46222	5.46222	NUM
ma-64	258	23	10.56460	10.56460	NUM
ma-64	258	24	10.56947	10.56947	NUM
ma-64	258	25	1.25649	1.25649	NUM
ma-64	258	26	5.63768	5.63768	NUM
ma-64	258	27	5.6368897.00	5.6368897.00	NUM
ma-64	258	28	11.17037	11.17037	NUM
ma-64	258	29	16.34912	16.34912	NUM
ma-64	258	30	16.34757	16.34757	NUM
ma-64	258	31	6.49278	6.49278	NUM
ma-64	258	32	11.07370	11.07370	NUM
ma-64	258	33	11.07714107.00	11.07714107.00	NUM
ma-64	258	34	18.71972	18.71972	NUM
ma-64	258	35	23.33442	23.33442	NUM
ma-64	258	36	23.33541	23.33541	NUM
ma-64	258	37	16.15278	16.15278	NUM
ma-64	258	38	18.66210	18.66210	NUM
ma-64	258	39	18.66616117.00	18.66616117.00	NUM
ma-64	258	40	27.48006	27.48006	NUM
ma-64	258	41	31.19401	31.19401	NUM
ma-64	258	42	31.19406	31.19406	NUM
ma-64	258	43	26.33380	26.33380	NUM
ma-64	258	44	27.42028	27.42028	NUM
ma-64	258	45	27.42359127.00	27.42359127.00	NUM
ma-64	258	46	36.91158	36.91158	NUM
ma-64	258	47	39.65579	39.65579	NUM
ma-64	258	48	39.65486	39.65486	NUM
ma-64	258	49	36.72393	36.72393	NUM
ma-64	258	50	36.83405	36.83405	NUM
ma-64	258	51	36.83640137.00	36.83640137.00	NUM
ma-64	258	52	46.67034	46.67034	NUM
ma-64	258	53	48.63231	48.63231	NUM
ma-64	258	54	48.63285	48.63285	NUM
ma-64	258	55	46.68664	46.68664	NUM
ma-64	258	56	46.59745	46.59745	NUM
ma-64	258	57	46.59938147.00	46.59938147.00	NUM
ma-64	258	58	56.57397	56.57397	NUM
ma-64	258	59	57.89847	57.89847	NUM
ma-64	258	60	57.89955	57.89955	NUM
ma-64	258	61	56.61703	56.61703	NUM
ma-64	258	62	56.45705	56.45705	NUM
ma-64	258	63	56.45879157.00	56.45879157.00	NUM
ma-64	258	64	66.53723	66.53723	NUM
ma-64	258	65	67.45340	67.45340	NUM
ma-64	258	66	67.45432	67.45432	NUM
ma-64	258	67	66.59903	66.59903	NUM
ma-64	258	68	66.46595	66.46595	NUM
ma-64	258	69	66.46767167.00	66.46767167.00	NUM
ma-64	258	70	76.52370	76.52370	NUM
ma-64	258	71	77.08904	77.08904	NUM
ma-64	258	72	77.08984	77.08984	NUM
ma-64	258	73	76.50332	76.50332	NUM
ma-64	258	74	76.39766	76.39766	NUM
ma-64	258	75	76.39940177.00	76.39940177.00	NUM
ma-64	258	76	86.51886	86.51886	NUM
ma-64	258	77	86.88858	86.88858	NUM
ma-64	258	78	86.88931	86.88931	NUM
ma-64	258	79	86.48557	86.48557	NUM
ma-64	258	80	86.40846	86.40846	NUM
ma-64	258	81	86.41023187.00	86.41023187.00	NUM
ma-64	258	82	96.51716	96.51716	NUM
ma-64	258	83	96.75424	96.75424	NUM
ma-64	258	84	96.75478	96.75478	NUM
ma-64	258	85	96.48843	96.48843	NUM
ma-64	258	86	96.43330	96.43330	NUM
ma-64	258	87	96.43508197.00	96.43508197.00	NUM
ma-64	258	88	106.51657	106.51657	NUM
ma-64	258	89	106.59706	106.59706	NUM
ma-64	258	90	106.59728	106.59728	NUM
ma-64	258	91	106.40288	106.40288	NUM
ma-64	258	92	106.36023	106.36023	NUM
ma-64	258	93	106.36202207.00	106.36202207.00	NUM
ma-64	258	94	116.51636	116.51636	NUM
ma-64	258	95	116.67091	116.67091	NUM
ma-64	258	96	116.67078	116.67078	NUM
ma-64	258	97	116.55261	116.55261	NUM
ma-64	258	98	116.52319	116.52319	NUM
ma-64	258	99	116.52499217.00	116.52499217.00	NUM
ma-64	258	100	126.51629	126.51629	NUM
ma-64	258	101	126.48888	126.48888	NUM
ma-64	258	102	126.48906	126.48906	NUM
ma-64	258	103	126.39973	126.39973	NUM
ma-64	258	104	126.37558	126.37558	NUM
ma-64	258	105	126.37738227.00	126.37738227.00	NUM
ma-64	258	106	136.51627	136.51627	NUM
ma-64	258	107	136.46008	136.46008	NUM
ma-64	258	108	136.46065	136.46065	NUM
ma-64	258	109	136.39791	136.39791	NUM
ma-64	258	110	136.37870	136.37870	NUM
ma-64	258	111	136.38049237.00	136.38049237.00	NUM
ma-64	258	112	146.51626	146.51626	NUM
ma-64	258	113	146.57401	146.57401	NUM
ma-64	258	114	146.57489	146.57489	NUM
ma-64	258	115	146.53847	146.53847	NUM
ma-64	258	116	146.52419	146.52419	NUM
ma-64	258	117	146.52597247.00	146.52597247.00	NUM
ma-64	258	118	156.51626	156.51626	NUM
ma-64	258	119	156.41475	156.41475	NUM
ma-64	258	120	156.41484	156.41484	NUM
ma-64	258	121	156.38607	156.38607	NUM
ma-64	258	122	156.37369	156.37369	NUM
ma-64	258	123	156.37545257.00	156.37545257.00	NUM
ma-64	258	124	166.51626	166.51626	NUM
ma-64	258	125	166.40053	166.40053	NUM
ma-64	258	126	166.39979	166.39979	NUM
ma-64	258	127	166.37904	166.37904	NUM
ma-64	258	128	166.36868	166.36868	NUM
ma-64	258	129	166.37039267.00	166.37039267.00	NUM
ma-64	258	130	176.51626	176.51626	NUM
ma-64	258	131	176.52571	176.52571	NUM
ma-64	258	132	176.52411	176.52411	NUM
ma-64	258	133	176.51173	176.51173	NUM
ma-64	258	134	176.50347	176.50347	NUM
ma-64	258	135	176.50515	176.50515	NUM
ma-64	258	136	7	7	NUM
ma-64	258	137	.	.	NOUN
ma-64	258	138	results	result	NOUN
ma-64	258	139	and	and	CCONJ
ma-64	258	140	discussions	discussion	NOUN
ma-64	258	141	in	in	ADP
ma-64	258	142	this	this	DET
ma-64	258	143	section	section	NOUN
ma-64	258	144	,	,	PUNCT
ma-64	258	145	we	we	PRON
ma-64	258	146	choose	choose	VERB
ma-64	258	147	the	the	DET
ma-64	258	148	same	same	ADJ
ma-64	258	149	parameters	parameter	NOUN
ma-64	258	150	:	:	PUNCT
ma-64	258	151	r	r	NOUN
ma-64	258	152	=	=	SYM
ma-64	258	153	0.1	0.1	NUM
ma-64	258	154	,	,	PUNCT
ma-64	258	155	σ	σ	NOUN
ma-64	258	156	=	=	NUM
ma-64	258	157	0.2	0.2	NUM
ma-64	258	158	,	,	PUNCT
ma-64	258	159	k	k	PROPN
ma-64	258	160	=	=	SYM
ma-64	258	161	100	100	NUM
ma-64	258	162	,	,	PUNCT
ma-64	258	163	t	t	NOUN
ma-64	258	164	=	=	SYM
ma-64	258	165	1	1	NUM
ma-64	258	166	,	,	PUNCT
ma-64	258	167	µ	µ	X
ma-64	258	168	=	=	SYM
ma-64	258	169	0.05	0.05	NUM
ma-64	258	170	,	,	PUNCT
ma-64	258	171	∆t	∆t	PROPN
ma-64	258	172	=	=	SYM
ma-64	258	173	0.01	0.01	NUM
ma-64	258	174	,	,	PUNCT
ma-64	258	175	a	a	DET
ma-64	258	176	=	=	NOUN
ma-64	258	177	0.02	0.02	NUM
ma-64	258	178	,	,	PUNCT
ma-64	258	179	m	m	VERB
ma-64	258	180	=	=	NOUN
ma-64	258	181	0.01	0.01	NUM
ma-64	258	182	,	,	PUNCT
ma-64	258	183	and	and	CCONJ
ma-64	258	184	c	c	NOUN
ma-64	258	185	=	=	SYM
ma-64	258	186	30	30	NUM
ma-64	258	187	,	,	PUNCT
ma-64	258	188	as	as	SCONJ
ma-64	258	189	illustrated	illustrate	VERB
ma-64	258	190	in	in	ADP
ma-64	258	191	the	the	DET
ma-64	258	192	literature	literature	NOUN
ma-64	258	193	[	[	X
ma-64	258	194	46	46	NUM
ma-64	258	195	]	]	PUNCT
ma-64	258	196	.	.	PUNCT
ma-64	259	1	then	then	ADV
ma-64	259	2	wecalculate	wecalculate	VERB
ma-64	259	3	the	the	DET
ma-64	259	4	call	call	NOUN
ma-64	259	5	option	option	NOUN
ma-64	259	6	values	value	NOUN
ma-64	259	7	using	use	VERB
ma-64	259	8	the	the	DET
ma-64	259	9	proposed	propose	VERB
ma-64	259	10	schemes	scheme	NOUN
ma-64	259	11	,	,	PUNCT
ma-64	259	12	described	describe	VERB
ma-64	259	13	in	in	ADP
ma-64	259	14	previous	previous	ADJ
ma-64	259	15	section	section	NOUN
ma-64	259	16	4	4	NUM
ma-64	259	17	,	,	PUNCT
ma-64	259	18	fordifferent	fordifferent	ADJ
ma-64	259	19	volatility	volatility	NOUN
ma-64	259	20	models	model	NOUN
ma-64	259	21	.	.	PUNCT
ma-64	260	1	we	we	PRON
ma-64	260	2	compare	compare	VERB
ma-64	260	3	the	the	DET
ma-64	260	4	approximate	approximate	ADJ
ma-64	260	5	results	result	NOUN
ma-64	260	6	with	with	ADP
ma-64	260	7	the	the	DET
ma-64	260	8	exact	exact	ADJ
ma-64	260	9	value	value	NOUN
ma-64	260	10	of	of	ADP
ma-64	260	11	the	the	DET
ma-64	260	12	linearblack	linearblack	NOUN
ma-64	260	13	-	-	PUNCT
ma-64	260	14	scholes	schole	NOUN
ma-64	260	15	model	model	NOUN
ma-64	260	16	and	and	CCONJ
ma-64	260	17	among	among	ADP
ma-64	260	18	themselves	themselves	PRON
ma-64	260	19	also	also	ADV
ma-64	260	20	.	.	PUNCT
ma-64	261	1	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	261	2	eur	eur	PROPN
ma-64	261	3	.	.	PUNCT
ma-64	262	1	j.	j.	PROPN
ma-64	262	2	math	math	PROPN
ma-64	262	3	.	.	PUNCT
ma-64	263	1	anal	anal	PROPN
ma-64	263	2	.	.	PUNCT
ma-64	264	1	10.28924	10.28924	NUM
ma-64	264	2	/	/	SYM
ma-64	264	3	ada	ada	PROPN
ma-64	264	4	/	/	SYM
ma-64	264	5	ma.2.9	ma.2.9	PROPN
ma-64	264	6	12	12	NUM
ma-64	264	7	figure	figure	NOUN
ma-64	264	8	1	1	NUM
ma-64	264	9	.	.	NUM
ma-64	264	10	approximate	approximate	ADJ
ma-64	264	11	results	result	NOUN
ma-64	264	12	of	of	ADP
ma-64	264	13	equation	equation	NOUN
ma-64	264	14	(	(	PUNCT
ma-64	264	15	1	1	NUM
ma-64	264	16	)	)	PUNCT
ma-64	264	17	by	by	ADP
ma-64	264	18	using	use	VERB
ma-64	264	19	(	(	PUNCT
ma-64	264	20	a	a	PRON
ma-64	264	21	)	)	PUNCT
ma-64	264	22	boyle	boyle	NOUN
ma-64	264	23	and	and	CCONJ
ma-64	264	24	vorst	vorst	PROPN
ma-64	264	25	volatilitymodel	volatilitymodel	PROPN
ma-64	264	26	,	,	PUNCT
ma-64	264	27	and	and	CCONJ
ma-64	264	28	(	(	PUNCT
ma-64	264	29	b	b	NOUN
ma-64	264	30	)	)	PUNCT
ma-64	264	31	barles	barle	NOUN
ma-64	264	32	and	and	CCONJ
ma-64	264	33	soner	soner	NOUN
ma-64	264	34	volatility	volatility	NOUN
ma-64	264	35	model	model	NOUN
ma-64	264	36	.	.	PUNCT
ma-64	265	1	from	from	ADP
ma-64	265	2	table	table	NOUN
ma-64	265	3	1	1	NUM
ma-64	265	4	and	and	CCONJ
ma-64	265	5	figure	figure	VERB
ma-64	265	6	8.7	8.7	NUM
ma-64	265	7	(	(	PUNCT
ma-64	265	8	see	see	VERB
ma-64	265	9	appendix	appendix	NOUN
ma-64	265	10	)	)	PUNCT
ma-64	265	11	,	,	PUNCT
ma-64	265	12	we	we	PRON
ma-64	265	13	observe	observe	VERB
ma-64	265	14	that	that	SCONJ
ma-64	265	15	fully	fully	ADV
ma-64	265	16	implicit	implicit	ADJ
ma-64	265	17	fvs	fvs	ADJ
ma-64	265	18	and	and	CCONJ
ma-64	265	19	crank	crank	NOUN
ma-64	265	20	-	-	PUNCT
ma-64	265	21	nicolson	nicolson	PROPN
ma-64	265	22	fvs	fvs	NOUN
ma-64	265	23	provide	provide	VERB
ma-64	265	24	comparatively	comparatively	ADV
ma-64	265	25	better	well	ADJ
ma-64	265	26	results	result	NOUN
ma-64	265	27	than	than	ADP
ma-64	265	28	the	the	DET
ma-64	265	29	other	other	ADJ
ma-64	265	30	methods	method	NOUN
ma-64	265	31	.	.	PUNCT
ma-64	266	1	note	note	VERB
ma-64	266	2	that	that	SCONJ
ma-64	266	3	all	all	PRON
ma-64	266	4	of	of	ADP
ma-64	266	5	themethods	themethod	NOUN
ma-64	266	6	provide	provide	VERB
ma-64	266	7	poor	poor	ADJ
ma-64	266	8	results	result	NOUN
ma-64	266	9	when	when	SCONJ
ma-64	266	10	the	the	DET
ma-64	266	11	initial	initial	ADJ
ma-64	266	12	stock	stock	NOUN
ma-64	266	13	price	price	NOUN
ma-64	266	14	is	be	AUX
ma-64	266	15	less	less	ADJ
ma-64	266	16	than	than	ADP
ma-64	266	17	the	the	DET
ma-64	266	18	strike	strike	NOUN
ma-64	266	19	price	price	NOUN
ma-64	266	20	(	(	PUNCT
ma-64	266	21	here	here	ADV
ma-64	266	22	strikeprice	strikeprice	NOUN
ma-64	266	23	,	,	PUNCT
ma-64	266	24	in	in	ADP
ma-64	266	25	comparison	comparison	NOUN
ma-64	266	26	with	with	ADP
ma-64	266	27	the	the	DET
ma-64	266	28	exact	exact	ADJ
ma-64	266	29	value	value	NOUN
ma-64	266	30	of	of	ADP
ma-64	266	31	the	the	DET
ma-64	266	32	linear	linear	ADJ
ma-64	266	33	black	black	NOUN
ma-64	266	34	-	-	PUNCT
ma-64	266	35	scholes	schole	NOUN
ma-64	266	36	model.from	model.from	PRON
ma-64	266	37	table	table	NOUN
ma-64	266	38	8.3	8.3	NUM
ma-64	266	39	in	in	ADP
ma-64	266	40	appendix	appendix	NOUN
ma-64	266	41	8	8	NUM
ma-64	266	42	and	and	CCONJ
ma-64	266	43	figure	figure	VERB
ma-64	266	44	1	1	NUM
ma-64	266	45	(	(	PUNCT
ma-64	266	46	a	a	X
ma-64	266	47	)	)	PUNCT
ma-64	266	48	,	,	PUNCT
ma-64	266	49	we	we	PRON
ma-64	266	50	can	can	AUX
ma-64	266	51	make	make	VERB
ma-64	266	52	similar	similar	ADJ
ma-64	266	53	comments	comment	NOUN
ma-64	266	54	,	,	PUNCT
ma-64	266	55	but	but	CCONJ
ma-64	266	56	here	here	ADV
ma-64	266	57	thefves	thefve	NOUN
ma-64	266	58	gives	give	VERB
ma-64	266	59	a	a	DET
ma-64	266	60	very	very	ADV
ma-64	266	61	poor	poor	ADJ
ma-64	266	62	approximation	approximation	NOUN
ma-64	266	63	than	than	ADP
ma-64	266	64	the	the	DET
ma-64	266	65	other	other	ADJ
ma-64	266	66	methods	method	NOUN
ma-64	266	67	when	when	SCONJ
ma-64	266	68	the	the	DET
ma-64	266	69	initial	initial	ADJ
ma-64	266	70	stock	stock	NOUN
ma-64	266	71	price	price	NOUN
ma-64	266	72	is	be	AUX
ma-64	266	73	lessthan	lessthan	NOUN
ma-64	266	74	the	the	DET
ma-64	266	75	strike	strike	NOUN
ma-64	266	76	price	price	NOUN
ma-64	266	77	(	(	PUNCT
ma-64	266	78	k	k	NOUN
ma-64	266	79	=	=	NOUN
ma-64	266	80	100	100	NUM
ma-64	266	81	)	)	PUNCT
ma-64	266	82	.	.	PUNCT
ma-64	267	1	table	table	NOUN
ma-64	267	2	8.4	8.4	NUM
ma-64	267	3	in	in	ADP
ma-64	267	4	appendix	appendix	NOUN
ma-64	267	5	8	8	NUM
ma-64	267	6	and	and	CCONJ
ma-64	267	7	figure	figure	VERB
ma-64	267	8	1(b	1(b	NUM
ma-64	267	9	)	)	PUNCT
ma-64	267	10	show	show	VERB
ma-64	267	11	that	that	SCONJ
ma-64	267	12	all	all	PRON
ma-64	267	13	of	of	ADP
ma-64	267	14	themethods	themethod	NOUN
ma-64	267	15	provide	provide	VERB
ma-64	267	16	a	a	DET
ma-64	267	17	closer	close	ADJ
ma-64	267	18	approximation	approximation	NOUN
ma-64	267	19	to	to	ADP
ma-64	267	20	the	the	DET
ma-64	267	21	exact	exact	ADJ
ma-64	267	22	value	value	NOUN
ma-64	267	23	of	of	ADP
ma-64	267	24	the	the	DET
ma-64	267	25	linear	linear	ADJ
ma-64	267	26	black	black	ADJ
ma-64	267	27	-	-	PUNCT
ma-64	267	28	scholes	schole	NOUN
ma-64	267	29	model	model	NOUN
ma-64	267	30	forall	forall	NOUN
ma-64	267	31	of	of	ADP
ma-64	267	32	the	the	DET
ma-64	267	33	initial	initial	ADJ
ma-64	267	34	stock	stock	NOUN
ma-64	267	35	price	price	NOUN
ma-64	267	36	,	,	PUNCT
ma-64	267	37	whether	whether	SCONJ
ma-64	267	38	it	it	PRON
ma-64	267	39	is	be	AUX
ma-64	267	40	greater	great	ADJ
ma-64	267	41	than	than	ADP
ma-64	267	42	the	the	DET
ma-64	267	43	strike	strike	NOUN
ma-64	267	44	price	price	NOUN
ma-64	267	45	,	,	PUNCT
ma-64	267	46	k	k	PROPN
ma-64	267	47	=	=	SYM
ma-64	267	48	100	100	NUM
ma-64	267	49	.	.	PUNCT
ma-64	267	50	table	table	NOUN
ma-64	267	51	2	2	NUM
ma-64	267	52	.	.	PUNCT
ma-64	267	53	call	call	NOUN
ma-64	267	54	option	option	NOUN
ma-64	267	55	prices	price	NOUN
ma-64	267	56	using	use	VERB
ma-64	267	57	rapm	rapm	ADJ
ma-64	267	58	volatility	volatility	NOUN
ma-64	267	59	model	model	NOUN
ma-64	267	60	.	.	PUNCT
ma-64	268	1	s0	s0	PROPN
ma-64	268	2	exact	exact	ADJ
ma-64	268	3	finite	finite	ADJ
ma-64	268	4	difference	difference	NOUN
ma-64	268	5	schemes	scheme	NOUN
ma-64	268	6	finite	finite	VERB
ma-64	268	7	volume	volume	NOUN
ma-64	268	8	schemes(linear	schemes(linear	PROPN
ma-64	268	9	)	)	PUNCT
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ma-64	271	1	j.	j.	PROPN
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ma-64	273	13	corresponding	correspond	VERB
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ma-64	273	16	in	in	ADP
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ma-64	273	18	8	8	NUM
ma-64	273	19	,	,	PUNCT
ma-64	273	20	we	we	PRON
ma-64	273	21	may	may	AUX
ma-64	273	22	observe	observe	VERB
ma-64	273	23	thatfor	thatfor	ADP
ma-64	273	24	the	the	DET
ma-64	273	25	rapm	rapm	ADJ
ma-64	273	26	volatility	volatility	NOUN
ma-64	273	27	model	model	NOUN
ma-64	273	28	,	,	PUNCT
ma-64	273	29	the	the	DET
ma-64	273	30	fvcns	fvcns	NOUN
ma-64	273	31	and	and	CCONJ
ma-64	273	32	fvfis	fvfi	VERB
ma-64	273	33	give	give	VERB
ma-64	273	34	better	well	ADJ
ma-64	273	35	approximation	approximation	NOUN
ma-64	273	36	than	than	ADP
ma-64	273	37	the	the	DET
ma-64	273	38	othernumerical	othernumerical	ADJ
ma-64	273	39	schemes	scheme	NOUN
ma-64	273	40	when	when	SCONJ
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ma-64	273	42	initial	initial	ADJ
ma-64	273	43	stock	stock	NOUN
ma-64	273	44	price	price	NOUN
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ma-64	273	46	closer	close	ADJ
ma-64	273	47	to	to	ADP
ma-64	273	48	and/or	and/or	CCONJ
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ma-64	273	50	than	than	ADP
ma-64	273	51	the	the	DET
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ma-64	273	53	price.on	price.on	PROPN
ma-64	273	54	the	the	DET
ma-64	273	55	other	other	ADJ
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ma-64	273	65	,	,	PUNCT
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ma-64	273	69	that	that	SCONJ
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ma-64	273	75	results	result	NOUN
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ma-64	273	77	the	the	DET
ma-64	273	78	other	other	ADJ
ma-64	273	79	schemes	scheme	NOUN
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ma-64	273	81	all	all	PRON
ma-64	273	82	of	of	ADP
ma-64	273	83	the	the	DET
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ma-64	273	85	models	model	NOUN
ma-64	273	86	.	.	PUNCT
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ma-64	274	3	,	,	PUNCT
ma-64	274	4	6	6	NUM
ma-64	274	5	depict	depict	VERB
ma-64	274	6	the	the	DET
ma-64	274	7	optionprices	optionprice	NOUN
ma-64	274	8	at	at	ADP
ma-64	274	9	various	various	ADJ
ma-64	274	10	time	time	NOUN
ma-64	274	11	periods	period	NOUN
ma-64	274	12	(	(	PUNCT
ma-64	274	13	from	from	ADP
ma-64	274	14	initial	initial	ADJ
ma-64	274	15	time	time	NOUN
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ma-64	274	18	0	0	NUM
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ma-64	274	21	time	time	NOUN
ma-64	274	22	,	,	PUNCT
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ma-64	274	25	t	t	PROPN
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ma-64	275	5	solution	solution	NOUN
ma-64	275	6	surface	surface	NOUN
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ma-64	275	8	option	option	NOUN
ma-64	275	9	price	price	NOUN
ma-64	275	10	by	by	ADP
ma-64	275	11	using	use	VERB
ma-64	275	12	barles	barle	NOUN
ma-64	275	13	and	and	CCONJ
ma-64	275	14	sonervolatility	sonervolatility	NOUN
ma-64	275	15	model	model	NOUN
ma-64	275	16	and	and	CCONJ
ma-64	275	17	rapm	rapm	ADJ
ma-64	275	18	volatility	volatility	NOUN
ma-64	275	19	model	model	NOUN
ma-64	275	20	are	be	AUX
ma-64	275	21	presented	present	VERB
ma-64	275	22	in	in	ADP
ma-64	275	23	appendix	appendix	NOUN
ma-64	275	24	8	8	NUM
ma-64	275	25	,	,	PUNCT
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ma-64	275	27	figures	figure	NOUN
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ma-64	275	29	.	.	PUNCT
ma-64	275	30	figure	figure	NOUN
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ma-64	275	34	results	result	NOUN
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ma-64	275	37	(	(	PUNCT
ma-64	275	38	1	1	X
ma-64	275	39	)	)	PUNCT
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ma-64	275	41	(	(	PUNCT
ma-64	275	42	a	a	DET
ma-64	275	43	)	)	PUNCT
ma-64	275	44	dufort	dufort	NOUN
ma-64	275	45	-	-	PUNCT
ma-64	275	46	frankel	frankel	NOUN
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ma-64	275	48	dif	dif	X
ma-64	275	49	-	-	PUNCT
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ma-64	275	51	scheme	scheme	NOUN
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ma-64	275	53	and	and	CCONJ
ma-64	275	54	(	(	PUNCT
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ma-64	275	56	)	)	PUNCT
ma-64	275	57	laasonen	laasonen	PROPN
ma-64	275	58	finite	finite	PROPN
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ma-64	275	60	scheme	scheme	NOUN
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ma-64	276	1	figure	figure	NOUN
ma-64	276	2	3	3	NUM
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ma-64	276	5	results	result	NOUN
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ma-64	276	8	(	(	PUNCT
ma-64	276	9	1	1	X
ma-64	276	10	)	)	PUNCT
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ma-64	276	12	(	(	PUNCT
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ma-64	276	14	)	)	PUNCT
ma-64	276	15	finite	finite	PROPN
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ma-64	277	1	figure	figure	NOUN
ma-64	277	2	4	4	NUM
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ma-64	281	25	(	(	PUNCT
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ma-64	281	30	)	)	PUNCT
ma-64	281	31	lvm	lvm	NOUN
ma-64	281	32	(	(	PUNCT
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ma-64	281	35	(	(	PUNCT
ma-64	281	36	e	e	NOUN
ma-64	281	37	)	)	PUNCT
ma-64	281	38	lvm	lvm	NOUN
ma-64	281	39	(	(	PUNCT
ma-64	281	40	fvfis	fvfis	ADJ
ma-64	281	41	)	)	PUNCT
ma-64	281	42	figure	figure	NOUN
ma-64	281	43	5	5	NUM
ma-64	281	44	.	.	PUNCT
ma-64	281	45	solution	solution	NOUN
ma-64	281	46	surface	surface	NOUN
ma-64	281	47	for	for	ADP
ma-64	281	48	option	option	NOUN
ma-64	281	49	price	price	NOUN
ma-64	281	50	by	by	ADP
ma-64	281	51	using	use	VERB
ma-64	281	52	leland	leland	PROPN
ma-64	281	53	volatility	volatility	NOUN
ma-64	281	54	model	model	NOUN
ma-64	281	55	.	.	PUNCT
ma-64	282	1	(	(	PUNCT
ma-64	282	2	a	a	X
ma-64	282	3	)	)	PUNCT
ma-64	282	4	bvvm	bvvm	NOUN
ma-64	282	5	(	(	PUNCT
ma-64	282	6	dffds	dffds	PROPN
ma-64	282	7	)	)	PUNCT
ma-64	282	8	(	(	PUNCT
ma-64	282	9	b	b	X
ma-64	282	10	)	)	PUNCT
ma-64	282	11	bvvm	bvvm	NOUN
ma-64	282	12	(	(	PUNCT
ma-64	282	13	lds	lds	PROPN
ma-64	282	14	)	)	PUNCT
ma-64	282	15	(	(	PUNCT
ma-64	282	16	c	c	X
ma-64	282	17	)	)	PUNCT
ma-64	282	18	bvvm	bvvm	NOUN
ma-64	282	19	(	(	PUNCT
ma-64	282	20	fves	fve	NOUN
ma-64	282	21	)	)	PUNCT
ma-64	282	22	(	(	PUNCT
ma-64	282	23	d	d	X
ma-64	282	24	)	)	PUNCT
ma-64	282	25	bvvm	bvvm	NOUN
ma-64	282	26	(	(	PUNCT
ma-64	282	27	fvcns	fvcns	PROPN
ma-64	282	28	)	)	PUNCT
ma-64	282	29	(	(	PUNCT
ma-64	282	30	e	e	NOUN
ma-64	282	31	)	)	PUNCT
ma-64	282	32	bvvm	bvvm	NOUN
ma-64	282	33	(	(	PUNCT
ma-64	282	34	fvfis	fvfis	PROPN
ma-64	282	35	)	)	PUNCT
ma-64	282	36	figure	figure	NOUN
ma-64	282	37	6	6	NUM
ma-64	282	38	.	.	PUNCT
ma-64	282	39	solution	solution	NOUN
ma-64	282	40	surface	surface	NOUN
ma-64	282	41	for	for	ADP
ma-64	282	42	option	option	NOUN
ma-64	282	43	price	price	NOUN
ma-64	282	44	by	by	ADP
ma-64	282	45	using	use	VERB
ma-64	282	46	boyle	boyle	PROPN
ma-64	282	47	and	and	CCONJ
ma-64	282	48	vorst	vorst	PROPN
ma-64	282	49	volatilitymodel	volatilitymodel	PROPN
ma-64	282	50	.	.	PROPN
ma-64	283	1	8	8	NUM
ma-64	283	2	.	.	X
ma-64	283	3	conclusion	conclusion	NOUN
ma-64	283	4	in	in	ADP
ma-64	283	5	this	this	DET
ma-64	283	6	research	research	NOUN
ma-64	283	7	work	work	NOUN
ma-64	283	8	,	,	PUNCT
ma-64	283	9	we	we	PRON
ma-64	283	10	have	have	AUX
ma-64	283	11	derived	derive	VERB
ma-64	283	12	some	some	DET
ma-64	283	13	numerical	numerical	ADJ
ma-64	283	14	schemes	scheme	NOUN
ma-64	283	15	using	use	VERB
ma-64	283	16	the	the	DET
ma-64	283	17	fvm	fvm	ADJ
ma-64	283	18	and	and	CCONJ
ma-64	283	19	fdm	fdm	NOUN
ma-64	283	20	tosolve	tosolve	VERB
ma-64	283	21	the	the	DET
ma-64	283	22	non	non	ADJ
ma-64	283	23	-	-	ADJ
ma-64	283	24	linear	linear	ADJ
ma-64	283	25	black	black	ADJ
ma-64	283	26	-	-	PUNCT
ma-64	283	27	scholes	schole	NOUN
ma-64	283	28	pde	pde	NOUN
ma-64	283	29	for	for	ADP
ma-64	283	30	european	european	ADJ
ma-64	283	31	option	option	NOUN
ma-64	283	32	pricing	pricing	NOUN
ma-64	283	33	with	with	ADP
ma-64	283	34	the	the	DET
ma-64	283	35	transaction	transaction	NOUN
ma-64	283	36	costs	cost	NOUN
ma-64	283	37	byexploiting	byexploite	VERB
ma-64	283	38	the	the	DET
ma-64	283	39	transformations	transformation	NOUN
ma-64	283	40	available	available	ADJ
ma-64	283	41	in	in	ADP
ma-64	283	42	the	the	DET
ma-64	283	43	existing	exist	VERB
ma-64	283	44	literature	literature	NOUN
ma-64	283	45	[	[	X
ma-64	283	46	46	46	NUM
ma-64	283	47	]	]	PUNCT
ma-64	283	48	.	.	PUNCT
ma-64	284	1	thus	thus	ADV
ma-64	284	2	we	we	PRON
ma-64	284	3	have	have	AUX
ma-64	284	4	modified	modify	VERB
ma-64	284	5	themodel	themodel	NOUN
ma-64	284	6	equation	equation	NOUN
ma-64	284	7	accordingly	accordingly	ADV
ma-64	284	8	to	to	ADP
ma-64	284	9	a	a	DET
ma-64	284	10	non	non	ADJ
ma-64	284	11	-	-	ADJ
ma-64	284	12	linear	linear	ADJ
ma-64	284	13	parabolic	parabolic	ADJ
ma-64	284	14	pde	pde	NOUN
ma-64	284	15	.	.	PUNCT
ma-64	285	1	for	for	ADP
ma-64	285	2	the	the	DET
ma-64	285	3	convergence	convergence	NOUN
ma-64	285	4	of	of	ADP
ma-64	285	5	these	these	DET
ma-64	285	6	schemes	scheme	NOUN
ma-64	285	7	,	,	PUNCT
ma-64	285	8	stability	stability	NOUN
ma-64	285	9	and	and	CCONJ
ma-64	285	10	consistency	consistency	NOUN
ma-64	285	11	have	have	AUX
ma-64	285	12	been	be	AUX
ma-64	285	13	shown	show	VERB
ma-64	285	14	rigorously	rigorously	ADV
ma-64	285	15	.	.	PUNCT
ma-64	286	1	then	then	ADV
ma-64	286	2	these	these	DET
ma-64	286	3	schemes	scheme	NOUN
ma-64	286	4	have	have	AUX
ma-64	286	5	been	be	AUX
ma-64	286	6	applied	apply	VERB
ma-64	286	7	tovarious	tovarious	ADJ
ma-64	286	8	volatility	volatility	NOUN
ma-64	286	9	models	model	NOUN
ma-64	286	10	.	.	PUNCT
ma-64	287	1	according	accord	VERB
ma-64	287	2	to	to	ADP
ma-64	287	3	the	the	DET
ma-64	287	4	visible	visible	ADJ
ma-64	287	5	results	result	NOUN
ma-64	287	6	,	,	PUNCT
ma-64	287	7	as	as	SCONJ
ma-64	287	8	presented	present	VERB
ma-64	287	9	in	in	ADP
ma-64	287	10	the	the	DET
ma-64	287	11	earlier	early	ADJ
ma-64	287	12	sections	section	NOUN
ma-64	287	13	,	,	PUNCT
ma-64	287	14	it	it	PRON
ma-64	287	15	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	287	16	eur	eur	PROPN
ma-64	287	17	.	.	PUNCT
ma-64	288	1	j.	j.	PROPN
ma-64	288	2	math	math	PROPN
ma-64	288	3	.	.	PUNCT
ma-64	289	1	anal	anal	PROPN
ma-64	289	2	.	.	PUNCT
ma-64	290	1	10.28924	10.28924	NUM
ma-64	290	2	/	/	SYM
ma-64	290	3	ada	ada	PROPN
ma-64	290	4	/	/	SYM
ma-64	290	5	ma.2.9	ma.2.9	PROPN
ma-64	290	6	15is	15is	PROPN
ma-64	290	7	noted	note	VERB
ma-64	290	8	that	that	SCONJ
ma-64	290	9	all	all	PRON
ma-64	290	10	of	of	ADP
ma-64	290	11	the	the	DET
ma-64	290	12	proposed	propose	VERB
ma-64	290	13	schemes	scheme	NOUN
ma-64	290	14	provide	provide	VERB
ma-64	290	15	the	the	DET
ma-64	290	16	best	good	ADJ
ma-64	290	17	approximation	approximation	NOUN
ma-64	290	18	to	to	ADP
ma-64	290	19	the	the	DET
ma-64	290	20	exact	exact	ADJ
ma-64	290	21	value	value	NOUN
ma-64	290	22	of	of	ADP
ma-64	290	23	thelinear	thelinear	ADJ
ma-64	290	24	black	black	ADJ
ma-64	290	25	-	-	PUNCT
ma-64	290	26	scholes	schole	NOUN
ma-64	290	27	model	model	NOUN
ma-64	290	28	for	for	ADP
ma-64	290	29	all	all	DET
ma-64	290	30	initial	initial	ADJ
ma-64	290	31	stock	stock	NOUN
ma-64	290	32	prices	price	NOUN
ma-64	290	33	,	,	PUNCT
ma-64	290	34	regardless	regardless	ADV
ma-64	290	35	of	of	ADP
ma-64	290	36	whether	whether	SCONJ
ma-64	290	37	they	they	PRON
ma-64	290	38	are	be	AUX
ma-64	290	39	closer	close	ADJ
ma-64	290	40	to	to	PART
ma-64	290	41	orgreater	orgreater	VERB
ma-64	290	42	than	than	ADP
ma-64	290	43	the	the	DET
ma-64	290	44	strike	strike	NOUN
ma-64	290	45	price	price	NOUN
ma-64	290	46	;	;	PUNCT
ma-64	290	47	particularly	particularly	ADV
ma-64	290	48	in	in	ADP
ma-64	290	49	the	the	DET
ma-64	290	50	case	case	NOUN
ma-64	290	51	of	of	ADP
ma-64	290	52	barles	barle	NOUN
ma-64	290	53	and	and	CCONJ
ma-64	290	54	soner	soner	NOUN
ma-64	290	55	volatility	volatility	NOUN
ma-64	290	56	model	model	NOUN
ma-64	290	57	.	.	PUNCT
ma-64	291	1	wemay	wemay	ADJ
ma-64	291	2	claim	claim	VERB
ma-64	291	3	that	that	SCONJ
ma-64	291	4	the	the	DET
ma-64	291	5	fvfis	fvfis	NOUN
ma-64	291	6	and	and	CCONJ
ma-64	291	7	fvcns	fvcns	PROPN
ma-64	291	8	approximate	approximate	NOUN
ma-64	291	9	better	well	ADV
ma-64	291	10	than	than	ADP
ma-64	291	11	the	the	DET
ma-64	291	12	other	other	ADJ
ma-64	291	13	methods	method	NOUN
ma-64	291	14	for	for	ADP
ma-64	291	15	all	all	DET
ma-64	291	16	four	four	NUM
ma-64	291	17	-	-	PUNCT
ma-64	291	18	volatility	volatility	NOUN
ma-64	291	19	models	model	NOUN
ma-64	291	20	.	.	PUNCT
ma-64	292	1	thus	thus	ADV
ma-64	292	2	,	,	PUNCT
ma-64	292	3	it	it	PRON
ma-64	292	4	is	be	AUX
ma-64	292	5	observed	observe	VERB
ma-64	292	6	that	that	SCONJ
ma-64	292	7	the	the	DET
ma-64	292	8	fvfis	fvfis	NOUN
ma-64	292	9	and	and	CCONJ
ma-64	292	10	fvcns	fvcns	PROPN
ma-64	292	11	are	be	AUX
ma-64	292	12	very	very	ADV
ma-64	292	13	effective	effective	ADJ
ma-64	292	14	and	and	CCONJ
ma-64	292	15	proficientin	proficientin	ADJ
ma-64	292	16	locating	locate	VERB
ma-64	292	17	approximate	approximate	ADJ
ma-64	292	18	solutions	solution	NOUN
ma-64	292	19	to	to	ADP
ma-64	292	20	non	non	ADJ
ma-64	292	21	-	-	ADJ
ma-64	292	22	linear	linear	ADJ
ma-64	292	23	black	black	ADJ
ma-64	292	24	-	-	PUNCT
ma-64	292	25	scholes	schole	NOUN
ma-64	292	26	models	model	NOUN
ma-64	292	27	.	.	PUNCT
ma-64	293	1	notice	notice	VERB
ma-64	293	2	that	that	SCONJ
ma-64	293	3	the	the	DET
ma-64	293	4	limitationof	limitationof	NOUN
ma-64	293	5	these	these	DET
ma-64	293	6	schemes	scheme	NOUN
ma-64	293	7	is	be	AUX
ma-64	293	8	that	that	SCONJ
ma-64	293	9	they	they	PRON
ma-64	293	10	may	may	AUX
ma-64	293	11	offer	offer	VERB
ma-64	293	12	poor	poor	ADJ
ma-64	293	13	results	result	NOUN
ma-64	293	14	sometimes	sometimes	ADV
ma-64	293	15	when	when	SCONJ
ma-64	293	16	the	the	DET
ma-64	293	17	initial	initial	ADJ
ma-64	293	18	stock	stock	NOUN
ma-64	293	19	price	price	NOUN
ma-64	293	20	is	be	AUX
ma-64	293	21	lessthan	lessthan	NOUN
ma-64	293	22	the	the	DET
ma-64	293	23	strike	strike	NOUN
ma-64	293	24	price	price	NOUN
ma-64	293	25	compared	compare	VERB
ma-64	293	26	to	to	ADP
ma-64	293	27	the	the	DET
ma-64	293	28	exact	exact	ADJ
ma-64	293	29	value	value	NOUN
ma-64	293	30	of	of	ADP
ma-64	293	31	the	the	DET
ma-64	293	32	linear	linear	ADJ
ma-64	293	33	black	black	ADJ
ma-64	293	34	-	-	PUNCT
ma-64	293	35	scholes	schole	NOUN
ma-64	293	36	model	model	NOUN
ma-64	293	37	.	.	PUNCT
ma-64	294	1	finally	finally	ADV
ma-64	294	2	,	,	PUNCT
ma-64	294	3	wemay	wemay	AUX
ma-64	294	4	conclude	conclude	VERB
ma-64	294	5	that	that	SCONJ
ma-64	294	6	the	the	DET
ma-64	294	7	proposed	propose	VERB
ma-64	294	8	schemes	scheme	NOUN
ma-64	294	9	may	may	AUX
ma-64	294	10	be	be	AUX
ma-64	294	11	applied	apply	VERB
ma-64	294	12	to	to	ADP
ma-64	294	13	other	other	ADJ
ma-64	294	14	non	non	ADJ
ma-64	294	15	-	-	ADJ
ma-64	294	16	linear	linear	ADJ
ma-64	294	17	partial	partial	ADJ
ma-64	294	18	differentialequations	differentialequation	NOUN
ma-64	294	19	to	to	PART
ma-64	294	20	compute	compute	VERB
ma-64	294	21	the	the	DET
ma-64	294	22	numerical	numerical	ADJ
ma-64	294	23	solutions	solution	NOUN
ma-64	294	24	with	with	ADP
ma-64	294	25	the	the	DET
ma-64	294	26	desired	desire	VERB
ma-64	294	27	accuracy	accuracy	NOUN
ma-64	294	28	.	.	PUNCT
ma-64	295	1	conflicts	conflict	NOUN
ma-64	295	2	of	of	ADP
ma-64	295	3	interest	interest	NOUN
ma-64	295	4	.	.	PUNCT
ma-64	296	1	the	the	DET
ma-64	296	2	authors	author	NOUN
ma-64	296	3	declare	declare	VERB
ma-64	296	4	no	no	DET
ma-64	296	5	competing	compete	VERB
ma-64	296	6	interests	interest	NOUN
ma-64	296	7	exist	exist	VERB
ma-64	296	8	.	.	PUNCT
ma-64	297	1	funding	funding	NOUN
ma-64	297	2	statement	statement	NOUN
ma-64	297	3	.	.	PUNCT
ma-64	298	1	this	this	DET
ma-64	298	2	research	research	NOUN
ma-64	298	3	received	receive	VERB
ma-64	298	4	no	no	DET
ma-64	298	5	external	external	ADJ
ma-64	298	6	funding	funding	NOUN
ma-64	298	7	.	.	PUNCT
ma-64	299	1	references	reference	NOUN
ma-64	299	2	[	[	X
ma-64	299	3	1	1	X
ma-64	299	4	]	]	PUNCT
ma-64	299	5	j.	j.	PROPN
ma-64	299	6	c.	c.	PROPN
ma-64	299	7	hull	hull	PROPN
ma-64	299	8	,	,	PUNCT
ma-64	299	9	options	option	NOUN
ma-64	299	10	,	,	PUNCT
ma-64	299	11	futures	future	NOUN
ma-64	299	12	,	,	PUNCT
ma-64	299	13	and	and	CCONJ
ma-64	299	14	other	other	ADJ
ma-64	299	15	derivatives	derivative	NOUN
ma-64	299	16	,	,	PUNCT
ma-64	299	17	8th	8th	ADJ
ma-64	299	18	ed	ed	NOUN
ma-64	299	19	.	.	PROPN
ma-64	299	20	,	,	PUNCT
ma-64	299	21	pearson	pearson	PROPN
ma-64	299	22	prentice	prentice	PROPN
ma-64	299	23	hall	hall	PROPN
ma-64	299	24	,	,	PUNCT
ma-64	299	25	new	new	PROPN
ma-64	299	26	jersey	jersey	PROPN
ma-64	299	27	,	,	PUNCT
ma-64	299	28	usa	usa	PROPN
ma-64	299	29	,	,	PUNCT
ma-64	299	30	2009.[2	2009.[2	NUM
ma-64	299	31	]	]	X
ma-64	299	32	n.	n.	NOUN
ma-64	299	33	privault	privault	NOUN
ma-64	299	34	,	,	PUNCT
ma-64	299	35	stochastic	stochastic	NOUN
ma-64	299	36	&	&	CCONJ
ma-64	299	37	finance	finance	VERB
ma-64	299	38	an	an	DET
ma-64	299	39	introduction	introduction	NOUN
ma-64	299	40	with	with	ADP
ma-64	299	41	market	market	NOUN
ma-64	299	42	examples	example	NOUN
ma-64	299	43	,	,	PUNCT
ma-64	300	1	1st	1st	ADJ
ma-64	300	2	ed	ed	NOUN
ma-64	300	3	.	.	PROPN
ma-64	300	4	,	,	PUNCT
ma-64	300	5	crc	crc	NOUN
ma-64	300	6	press	press	NOUN
ma-64	300	7	,	,	PUNCT
ma-64	300	8	2013.[3	2013.[3	NUM
ma-64	300	9	]	]	X
ma-64	300	10	j.	j.	PROPN
ma-64	300	11	monique	monique	PROPN
ma-64	300	12	,	,	PUNCT
ma-64	300	13	y.	y.	PROPN
ma-64	300	14	marc	marc	PROPN
ma-64	300	15	,	,	PUNCT
ma-64	300	16	c.	c.	PROPN
ma-64	300	17	march	march	PROPN
ma-64	300	18	,	,	PUNCT
ma-64	300	19	mathematical	mathematical	ADJ
ma-64	300	20	methods	method	NOUN
ma-64	300	21	for	for	ADP
ma-64	300	22	financial	financial	ADJ
ma-64	300	23	markets	market	NOUN
ma-64	300	24	,	,	PUNCT
ma-64	300	25	springer	springer	NOUN
ma-64	300	26	science	science	PROPN
ma-64	300	27	&	&	CCONJ
ma-64	300	28	business	business	PROPN
ma-64	300	29	media,2009.[4	media,2009.[4	PROPN
ma-64	300	30	]	]	PUNCT
ma-64	300	31	j.	j.	PROPN
ma-64	300	32	r.	r.	PROPN
ma-64	300	33	buchanan	buchanan	PROPN
ma-64	300	34	,	,	PUNCT
ma-64	300	35	an	an	DET
ma-64	300	36	undergraduate	undergraduate	ADJ
ma-64	300	37	introduction	introduction	NOUN
ma-64	300	38	to	to	ADP
ma-64	300	39	financial	financial	ADJ
ma-64	300	40	mathematics	mathematic	NOUN
ma-64	300	41	,	,	PUNCT
ma-64	300	42	3rd	3rd	ADJ
ma-64	300	43	ed	ed	NOUN
ma-64	300	44	.	.	PROPN
ma-64	300	45	,	,	PUNCT
ma-64	300	46	world	world	NOUN
ma-64	300	47	scientific	scientific	ADJ
ma-64	300	48	publishing	publishing	NOUN
ma-64	300	49	com	com	NOUN
ma-64	300	50	-	-	PUNCT
ma-64	300	51	pany	pany	NOUN
ma-64	300	52	,	,	PUNCT
ma-64	300	53	2012.[5	2012.[5	NUM
ma-64	300	54	]	]	PUNCT
ma-64	300	55	a.	a.	NOUN
ma-64	300	56	yves	yve	NOUN
ma-64	300	57	,	,	PUNCT
ma-64	300	58	p.	p.	NOUN
ma-64	300	59	olivier	olivier	NOUN
ma-64	300	60	,	,	PUNCT
ma-64	300	61	computational	computational	ADJ
ma-64	300	62	methods	method	NOUN
ma-64	300	63	for	for	ADP
ma-64	300	64	option	option	NOUN
ma-64	300	65	pricing	pricing	NOUN
ma-64	300	66	,	,	PUNCT
ma-64	300	67	society	society	NOUN
ma-64	300	68	for	for	ADP
ma-64	300	69	industrial	industrial	ADJ
ma-64	300	70	and	and	CCONJ
ma-64	300	71	applied	applied	ADJ
ma-64	300	72	mathematics	mathematic	NOUN
ma-64	300	73	,	,	PUNCT
ma-64	300	74	2005.[6	2005.[6	NUM
ma-64	300	75	]	]	X
ma-64	300	76	j.	j.	PROPN
ma-64	300	77	guyon	guyon	PROPN
ma-64	300	78	,	,	PUNCT
ma-64	300	79	p.	p.	PROPN
ma-64	300	80	henry	henry	PROPN
ma-64	300	81	-	-	PUNCT
ma-64	300	82	labordere	labordere	PROPN
ma-64	300	83	,	,	PUNCT
ma-64	300	84	nonlinear	nonlinear	ADJ
ma-64	300	85	option	option	NOUN
ma-64	300	86	pricing	pricing	NOUN
ma-64	300	87	,	,	PUNCT
ma-64	300	88	crc	crc	NOUN
ma-64	300	89	press	press	NOUN
ma-64	300	90	,	,	PUNCT
ma-64	300	91	2014.[7	2014.[7	NUM
ma-64	300	92	]	]	X
ma-64	300	93	f.	f.	PROPN
ma-64	300	94	black	black	PROPN
ma-64	300	95	,	,	PUNCT
ma-64	300	96	m.	m.	NOUN
ma-64	300	97	scholes	schole	NOUN
ma-64	300	98	,	,	PUNCT
ma-64	300	99	the	the	DET
ma-64	300	100	pricing	pricing	NOUN
ma-64	300	101	of	of	ADP
ma-64	300	102	options	option	NOUN
ma-64	300	103	and	and	CCONJ
ma-64	300	104	corporate	corporate	ADJ
ma-64	300	105	liabilities	liability	NOUN
ma-64	300	106	,	,	PUNCT
ma-64	300	107	j.	j.	PROPN
ma-64	300	108	polit	polit	PROPN
ma-64	300	109	.	.	PROPN
ma-64	300	110	econ	econ	PROPN
ma-64	300	111	.	.	PUNCT
ma-64	301	1	81	81	NUM
ma-64	301	2	(	(	PUNCT
ma-64	301	3	1973	1973	NUM
ma-64	301	4	)	)	PUNCT
ma-64	302	1	637–654	637–654	NUM
ma-64	302	2	.	.	PUNCT
ma-64	302	3	https	https	NOUN
ma-64	302	4	:	:	PUNCT
ma-64	302	5	//www.jstor.org	//www.jstor.org	PUNCT
ma-64	302	6	/	/	SYM
ma-64	302	7	stable/1831029.[8	stable/1831029.[8	PROPN
ma-64	302	8	]	]	PUNCT
ma-64	302	9	r.	r.	PROPN
ma-64	302	10	c.	c.	PROPN
ma-64	302	11	merton	merton	PROPN
ma-64	302	12	,	,	PUNCT
ma-64	302	13	theory	theory	NOUN
ma-64	302	14	of	of	ADP
ma-64	302	15	rational	rational	ADJ
ma-64	302	16	option	option	NOUN
ma-64	302	17	pricing	pricing	NOUN
ma-64	302	18	,	,	PUNCT
ma-64	302	19	bell	bell	PROPN
ma-64	302	20	j.	j.	PROPN
ma-64	302	21	econ	econ	PROPN
ma-64	302	22	.	.	PUNCT
ma-64	303	1	manag	manag	PROPN
ma-64	303	2	.	.	PUNCT
ma-64	304	1	sci	sci	PROPN
ma-64	304	2	.	.	PROPN
ma-64	304	3	4	4	NUM
ma-64	304	4	(	(	PUNCT
ma-64	304	5	1973	1973	NUM
ma-64	304	6	)	)	PUNCT
ma-64	305	1	141–183	141–183	NUM
ma-64	305	2	.	.	PUNCT
ma-64	305	3	https://doi.org/	https://doi.org/	PROPN
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ma-64	305	5	]	]	X
ma-64	305	6	m.	m.	NOUN
ma-64	305	7	m.	m.	PROPN
ma-64	305	8	chawla	chawla	PROPN
ma-64	305	9	,	,	PUNCT
ma-64	305	10	m.	m.	PROPN
ma-64	305	11	a.	a.	PROPN
ma-64	305	12	al	al	PROPN
ma-64	305	13	-	-	PUNCT
ma-64	305	14	zanaidi	zanaidi	PROPN
ma-64	305	15	,	,	PUNCT
ma-64	305	16	d.	d.	PROPN
ma-64	305	17	j.	j.	PROPN
ma-64	305	18	evans	evans	PROPN
ma-64	305	19	,	,	PUNCT
ma-64	305	20	generalized	generalized	ADJ
ma-64	305	21	trapezoidal	trapezoidal	ADJ
ma-64	305	22	formulas	formula	NOUN
ma-64	305	23	for	for	ADP
ma-64	305	24	the	the	DET
ma-64	305	25	black	black	ADJ
ma-64	305	26	-	-	PUNCT
ma-64	305	27	scholes	schole	NOUN
ma-64	305	28	equation	equation	NOUN
ma-64	305	29	ofoption	ofoption	NOUN
ma-64	305	30	pricing	pricing	NOUN
ma-64	305	31	,	,	PUNCT
ma-64	305	32	int	int	NOUN
ma-64	305	33	.	.	PUNCT
ma-64	306	1	j.	j.	PROPN
ma-64	306	2	comput	comput	PROPN
ma-64	306	3	.	.	PUNCT
ma-64	307	1	math	math	NOUN
ma-64	307	2	.	.	PUNCT
ma-64	308	1	80	80	NUM
ma-64	308	2	(	(	PUNCT
ma-64	308	3	2003	2003	NUM
ma-64	308	4	)	)	PUNCT
ma-64	308	5	1521–1526	1521–1526	NUM
ma-64	308	6	.	.	PUNCT
ma-64	309	1	https://doi.org/10.1080/00207160310001603299.[10	https://doi.org/10.1080/00207160310001603299.[10	NOUN
ma-64	309	2	]	]	PUNCT
ma-64	309	3	a.	a.	PROPN
ma-64	309	4	s.	s.	PROPN
ma-64	309	5	shinde	shinde	PROPN
ma-64	309	6	,	,	PUNCT
ma-64	309	7	k.	k.	PROPN
ma-64	309	8	c.	c.	PROPN
ma-64	309	9	takale	takale	PROPN
ma-64	309	10	,	,	PUNCT
ma-64	309	11	study	study	NOUN
ma-64	309	12	of	of	ADP
ma-64	309	13	black	black	ADJ
ma-64	309	14	-	-	PUNCT
ma-64	309	15	scholes	schole	NOUN
ma-64	309	16	model	model	NOUN
ma-64	309	17	and	and	CCONJ
ma-64	309	18	its	its	PRON
ma-64	309	19	applications	application	NOUN
ma-64	309	20	,	,	PUNCT
ma-64	309	21	procedia	procedia	PROPN
ma-64	309	22	eng	eng	PROPN
ma-64	309	23	.	.	PROPN
ma-64	310	1	38	38	NUM
ma-64	310	2	(	(	PUNCT
ma-64	310	3	2012	2012	NUM
ma-64	310	4	)	)	PUNCT
ma-64	311	1	270–279	270–279	NUM
ma-64	311	2	.	.	PUNCT
ma-64	312	1	http://dx.doi.org/10.1016/j.proeng.2012.06.035.[11	http://dx.doi.org/10.1016/j.proeng.2012.06.035.[11	PROPN
ma-64	312	2	]	]	X
ma-64	312	3	l.	l.	PROPN
ma-64	312	4	jódar	jódar	PROPN
ma-64	312	5	,	,	PUNCT
ma-64	312	6	p.	p.	PROPN
ma-64	312	7	sevilla	sevilla	PROPN
ma-64	312	8	-	-	PUNCT
ma-64	312	9	peris	peris	PROPN
ma-64	312	10	,	,	PUNCT
ma-64	312	11	j.	j.	PROPN
ma-64	312	12	c.	c.	PROPN
ma-64	312	13	cortés	cortés	PROPN
ma-64	312	14	,	,	PUNCT
ma-64	312	15	r.	r.	PROPN
ma-64	312	16	saha	saha	PROPN
ma-64	312	17	,	,	PUNCT
ma-64	312	18	a	a	DET
ma-64	312	19	new	new	ADJ
ma-64	312	20	direct	direct	ADJ
ma-64	312	21	method	method	NOUN
ma-64	312	22	for	for	ADP
ma-64	312	23	solving	solve	VERB
ma-64	312	24	the	the	DET
ma-64	312	25	black	black	ADJ
ma-64	312	26	-	-	PUNCT
ma-64	312	27	scholes	schole	NOUN
ma-64	312	28	equation	equation	NOUN
ma-64	312	29	,	,	PUNCT
ma-64	312	30	appl.math	appl.math	PROPN
ma-64	312	31	.	.	PUNCT
ma-64	312	32	lett	lett	PROPN
ma-64	312	33	.	.	PROPN
ma-64	313	1	18	18	NUM
ma-64	313	2	(	(	PUNCT
ma-64	313	3	2005	2005	NUM
ma-64	313	4	)	)	PUNCT
ma-64	313	5	29–32	29–32	NUM
ma-64	313	6	.	.	PUNCT
ma-64	314	1	http://dx.doi.org/10.1016/j.aml.2002.12.016.[12	http://dx.doi.org/10.1016/j.aml.2002.12.016.[12	PROPN
ma-64	314	2	]	]	PUNCT
ma-64	314	3	k.	k.	PROPN
ma-64	314	4	s.	s.	PROPN
ma-64	314	5	patel	patel	PROPN
ma-64	314	6	,	,	PUNCT
ma-64	314	7	m.	m.	PROPN
ma-64	314	8	mehra	mehra	PROPN
ma-64	314	9	,	,	PUNCT
ma-64	314	10	high	high	ADJ
ma-64	314	11	-	-	PUNCT
ma-64	314	12	order	order	NOUN
ma-64	314	13	compact	compact	ADJ
ma-64	314	14	finite	finite	ADJ
ma-64	314	15	difference	difference	NOUN
ma-64	314	16	method	method	NOUN
ma-64	314	17	for	for	ADP
ma-64	314	18	black	black	ADJ
ma-64	314	19	-	-	PUNCT
ma-64	314	20	scholes	schole	NOUN
ma-64	314	21	pde	pde	NOUN
ma-64	314	22	,	,	PUNCT
ma-64	314	23	springer	springer	NOUN
ma-64	314	24	proc	proc	NOUN
ma-64	314	25	.	.	PUNCT
ma-64	315	1	math.stat	math.stat	PROPN
ma-64	315	2	.	.	PROPN
ma-64	316	1	143	143	NUM
ma-64	316	2	(	(	PUNCT
ma-64	316	3	2015	2015	NUM
ma-64	316	4	)	)	PUNCT
ma-64	317	1	393–403	393–403	NUM
ma-64	317	2	.	.	PUNCT
ma-64	318	1	10.1007/978	10.1007/978	NUM
ma-64	318	2	-	-	PUNCT
ma-64	318	3	81	81	NUM
ma-64	318	4	-	-	PUNCT
ma-64	318	5	322	322	NUM
ma-64	318	6	-	-	PUNCT
ma-64	318	7	2485	2485	NUM
ma-64	318	8	-	-	PUNCT
ma-64	318	9	3_32.[13	3_32.[13	NUM
ma-64	318	10	]	]	PUNCT
ma-64	318	11	p.	p.	NOUN
ma-64	318	12	roul	roul	PROPN
ma-64	318	13	,	,	PUNCT
ma-64	318	14	v.	v.	ADP
ma-64	318	15	m.	m.	PROPN
ma-64	318	16	k.	k.	PROPN
ma-64	318	17	prasad	prasad	PROPN
ma-64	318	18	goura	goura	PROPN
ma-64	318	19	,	,	PUNCT
ma-64	318	20	a	a	DET
ma-64	318	21	sixth	sixth	ADJ
ma-64	318	22	order	order	NOUN
ma-64	318	23	numerical	numerical	ADJ
ma-64	318	24	method	method	NOUN
ma-64	318	25	and	and	CCONJ
ma-64	318	26	its	its	PRON
ma-64	318	27	convergence	convergence	NOUN
ma-64	318	28	for	for	ADP
ma-64	318	29	generalized	generalized	ADJ
ma-64	318	30	black	black	ADJ
ma-64	318	31	–	–	PUNCT
ma-64	318	32	scholespde	scholespde	NOUN
ma-64	318	33	,	,	PUNCT
ma-64	318	34	j.	j.	PROPN
ma-64	318	35	comput	comput	PROPN
ma-64	318	36	.	.	PUNCT
ma-64	319	1	appl	appl	PROPN
ma-64	319	2	.	.	PROPN
ma-64	319	3	math	math	NOUN
ma-64	319	4	.	.	PUNCT
ma-64	320	1	377	377	NUM
ma-64	320	2	(	(	PUNCT
ma-64	320	3	2020	2020	NUM
ma-64	320	4	)	)	PUNCT
ma-64	320	5	112881	112881	NUM
ma-64	320	6	.	.	PUNCT
ma-64	321	1	https://doi.org/10.1016/j.cam.2020.112881.[14	https://doi.org/10.1016/j.cam.2020.112881.[14	PROPN
ma-64	321	2	]	]	PUNCT
ma-64	321	3	m.	m.	NOUN
ma-64	321	4	brenner	brenner	PROPN
ma-64	321	5	,	,	PUNCT
ma-64	321	6	m.	m.	NOUN
ma-64	321	7	g.	g.	PROPN
ma-64	321	8	subrahmanyam	subrahmanyam	PROPN
ma-64	321	9	,	,	PUNCT
ma-64	321	10	a	a	DET
ma-64	321	11	simple	simple	ADJ
ma-64	321	12	approach	approach	NOUN
ma-64	321	13	to	to	ADP
ma-64	321	14	option	option	NOUN
ma-64	321	15	valuation	valuation	NOUN
ma-64	321	16	and	and	CCONJ
ma-64	321	17	hedging	hedging	NOUN
ma-64	321	18	in	in	ADP
ma-64	321	19	the	the	DET
ma-64	321	20	black	black	ADJ
ma-64	321	21	-	-	PUNCT
ma-64	321	22	scholes	schole	NOUN
ma-64	321	23	model	model	NOUN
ma-64	321	24	,	,	PUNCT
ma-64	321	25	financ	financ	PROPN
ma-64	321	26	.	.	PUNCT
ma-64	322	1	anal	anal	PROPN
ma-64	322	2	.	.	PUNCT
ma-64	323	1	j.	j.	PROPN
ma-64	323	2	50	50	NUM
ma-64	323	3	(	(	PUNCT
ma-64	323	4	1994	1994	NUM
ma-64	323	5	)	)	PUNCT
ma-64	323	6	25–28	25–28	NUM
ma-64	323	7	.	.	PUNCT
ma-64	323	8	https://www.jstor.org/stable/4479727.[15	https://www.jstor.org/stable/4479727.[15	PROPN
ma-64	323	9	]	]	PUNCT
ma-64	324	1	j.	j.	PROPN
ma-64	324	2	d.	d.	PROPN
ma-64	324	3	macbeth	macbeth	PROPN
ma-64	324	4	,	,	PUNCT
ma-64	324	5	l.	l.	PROPN
ma-64	324	6	j.	j.	PROPN
ma-64	324	7	merville	merville	PROPN
ma-64	324	8	,	,	PUNCT
ma-64	324	9	an	an	DET
ma-64	324	10	empirical	empirical	ADJ
ma-64	324	11	examination	examination	NOUN
ma-64	324	12	of	of	ADP
ma-64	324	13	the	the	DET
ma-64	324	14	black	black	ADJ
ma-64	324	15	-	-	PUNCT
ma-64	324	16	scholes	schole	NOUN
ma-64	324	17	call	call	NOUN
ma-64	324	18	option	option	NOUN
ma-64	324	19	pricing	pricing	NOUN
ma-64	324	20	model	model	NOUN
ma-64	324	21	,	,	PUNCT
ma-64	324	22	j.	j.	PROPN
ma-64	324	23	finance,34	finance,34	PROPN
ma-64	324	24	(	(	PUNCT
ma-64	324	25	1979	1979	NUM
ma-64	324	26	)	)	PUNCT
ma-64	324	27	1173–1186	1173–1186	NUM
ma-64	324	28	.	.	PUNCT
ma-64	325	1	https://doi.org/10.2307/2327242	https://doi.org/10.2307/2327242	PROPN
ma-64	325	2	.	.	PUNCT
ma-64	326	1	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	326	2	https://www.jstor.org/stable/1831029	https://www.jstor.org/stable/1831029	NOUN
ma-64	326	3	https://www.jstor.org/stable/1831029	https://www.jstor.org/stable/1831029	NOUN
ma-64	326	4	https://doi.org/10.2307/3003143	https://doi.org/10.2307/3003143	NOUN
ma-64	326	5	https://doi.org/10.2307/3003143	https://doi.org/10.2307/3003143	NOUN
ma-64	326	6	https://doi.org/10.1080/00207160310001603299	https://doi.org/10.1080/00207160310001603299	NOUN
ma-64	326	7	http://dx.doi.org/10.1016/j.proeng.2012.06.035	http://dx.doi.org/10.1016/j.proeng.2012.06.035	PROPN
ma-64	326	8	http://dx.doi.org/10.1016/j.aml.2002.12.016	http://dx.doi.org/10.1016/j.aml.2002.12.016	PROPN
ma-64	327	1	10.1007/978	10.1007/978	NUM
ma-64	327	2	-	-	PUNCT
ma-64	327	3	81	81	NUM
ma-64	327	4	-	-	PUNCT
ma-64	327	5	322	322	NUM
ma-64	327	6	-	-	PUNCT
ma-64	327	7	2485	2485	NUM
ma-64	327	8	-	-	SYM
ma-64	327	9	3_32	3_32	NUM
ma-64	327	10	https://doi.org/10.1016/j.cam.2020.112881	https://doi.org/10.1016/j.cam.2020.112881	PROPN
ma-64	327	11	https://www.jstor.org/stable/4479727	https://www.jstor.org/stable/4479727	PROPN
ma-64	327	12	https://doi.org/10.2307/2327242	https://doi.org/10.2307/2327242	NUM
ma-64	327	13	eur	eur	PROPN
ma-64	327	14	.	.	PUNCT
ma-64	328	1	j.	j.	PROPN
ma-64	328	2	math	math	PROPN
ma-64	328	3	.	.	PUNCT
ma-64	329	1	anal	anal	PROPN
ma-64	329	2	.	.	PUNCT
ma-64	330	1	10.28924	10.28924	NUM
ma-64	330	2	/	/	SYM
ma-64	330	3	ada	ada	PROPN
ma-64	330	4	/	/	SYM
ma-64	330	5	ma.2.9	ma.2.9	PROPN
ma-64	330	6	16	16	NUM
ma-64	331	1	[	[	X
ma-64	331	2	16	16	NUM
ma-64	331	3	]	]	PUNCT
ma-64	331	4	j.	j.	PROPN
ma-64	331	5	hok	hok	PROPN
ma-64	331	6	,	,	PUNCT
ma-64	331	7	t.	t.	PROPN
ma-64	331	8	l.	l.	PROPN
ma-64	331	9	r.	r.	PROPN
ma-64	331	10	chan	chan	PROPN
ma-64	331	11	,	,	PUNCT
ma-64	331	12	option	option	NOUN
ma-64	331	13	pricing	pricing	NOUN
ma-64	331	14	with	with	ADP
ma-64	331	15	legendre	legendre	PROPN
ma-64	331	16	polynomials	polynomials	PROPN
ma-64	331	17	,	,	PUNCT
ma-64	331	18	j.	j.	PROPN
ma-64	331	19	comput	comput	PROPN
ma-64	331	20	.	.	PUNCT
ma-64	332	1	appl	appl	PROPN
ma-64	332	2	.	.	PROPN
ma-64	332	3	math	math	PROPN
ma-64	332	4	.	.	PUNCT
ma-64	333	1	322	322	NUM
ma-64	333	2	(	(	PUNCT
ma-64	333	3	2017	2017	NUM
ma-64	333	4	)	)	PUNCT
ma-64	333	5	25–45	25–45	NUM
ma-64	333	6	.	.	PUNCT
ma-64	334	1	http	http	PROPN
ma-64	334	2	:	:	PUNCT
ma-64	334	3	//dx.doi.org/10.1016	//dx.doi.org/10.1016	X
ma-64	334	4	/	/	SYM
ma-64	334	5	j.cam.2017.03.027.[17	j.cam.2017.03.027.[17	NUM
ma-64	334	6	]	]	PUNCT
ma-64	334	7	m.	m.	NOUN
ma-64	334	8	s.	s.	PROPN
ma-64	334	9	hossan	hossan	PROPN
ma-64	334	10	,	,	PUNCT
ma-64	334	11	a.	a.	PROPN
ma-64	334	12	b.	b.	PROPN
ma-64	334	13	m.	m.	PROPN
ma-64	334	14	hossain	hossain	PROPN
ma-64	334	15	,	,	PUNCT
ma-64	334	16	m.	m.	PROPN
ma-64	334	17	s.	s.	PROPN
ma-64	334	18	islam	islam	PROPN
ma-64	334	19	,	,	PUNCT
ma-64	334	20	numerical	numerical	ADJ
ma-64	334	21	solutions	solution	NOUN
ma-64	334	22	of	of	ADP
ma-64	334	23	black	black	ADJ
ma-64	334	24	-	-	PUNCT
ma-64	334	25	scholes	schole	NOUN
ma-64	334	26	model	model	NOUN
ma-64	334	27	by	by	ADP
ma-64	334	28	du	du	PROPN
ma-64	334	29	fort	fort	PROPN
ma-64	334	30	-	-	PUNCT
ma-64	334	31	frankel	frankel	PROPN
ma-64	334	32	fdmand	fdmand	NOUN
ma-64	334	33	galerkin	galerkin	PROPN
ma-64	334	34	wrm	wrm	PROPN
ma-64	334	35	,	,	PUNCT
ma-64	334	36	int	int	PROPN
ma-64	334	37	.	.	PUNCT
ma-64	335	1	j.	j.	PROPN
ma-64	335	2	math	math	PROPN
ma-64	335	3	.	.	PUNCT
ma-64	336	1	res	re	NOUN
ma-64	336	2	.	.	PROPN
ma-64	337	1	9	9	NUM
ma-64	337	2	(	(	PUNCT
ma-64	337	3	2020	2020	NUM
ma-64	337	4	)	)	PUNCT
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ma-64	337	6	.	.	PUNCT
ma-64	338	1	https://doi.org/10.18488/journal.24.2020.91.1.10.[18	https://doi.org/10.18488/journal.24.2020.91.1.10.[18	X
ma-64	338	2	]	]	X
ma-64	338	3	s.	s.	PROPN
ma-64	338	4	alrabeei	alrabeei	PROPN
ma-64	338	5	,	,	PUNCT
ma-64	338	6	m.	m.	PROPN
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ma-64	338	8	,	,	PUNCT
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ma-64	338	10	european	european	ADJ
ma-64	338	11	options	option	NOUN
ma-64	338	12	under	under	ADP
ma-64	338	13	jump	jump	NOUN
ma-64	338	14	diffusion	diffusion	NOUN
ma-64	338	15	models	model	NOUN
ma-64	338	16	with	with	ADP
ma-64	338	17	fast	fast	ADJ
ma-64	338	18	l	l	ADJ
ma-64	338	19	-	-	ADJ
ma-64	338	20	stable	stable	ADJ
ma-64	338	21	pade	pade	NOUN
ma-64	338	22	scheme	scheme	NOUN
ma-64	338	23	,	,	PUNCT
ma-64	338	24	int.j	int.j	PROPN
ma-64	338	25	.	.	PROPN
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ma-64	338	27	.	.	PUNCT
ma-64	339	1	comput	comput	NOUN
ma-64	339	2	.	.	PUNCT
ma-64	340	1	sci	sci	PROPN
ma-64	340	2	.	.	PROPN
ma-64	341	1	14	14	NUM
ma-64	341	2	(	(	PUNCT
ma-64	341	3	2020	2020	NUM
ma-64	341	4	)	)	PUNCT
ma-64	341	5	111	111	NUM
ma-64	341	6	-	-	SYM
ma-64	341	7	115.[19	115.[19	NUM
ma-64	341	8	]	]	PUNCT
ma-64	341	9	p.	p.	NOUN
ma-64	341	10	p.	p.	PROPN
ma-64	341	11	boyle	boyle	PROPN
ma-64	341	12	,	,	PUNCT
ma-64	341	13	options	option	NOUN
ma-64	341	14	:	:	PUNCT
ma-64	341	15	a	a	DET
ma-64	341	16	monte	monte	PROPN
ma-64	341	17	carlo	carlo	PROPN
ma-64	341	18	approach	approach	NOUN
ma-64	341	19	,	,	PUNCT
ma-64	341	20	j.	j.	PROPN
ma-64	341	21	financ	financ	PROPN
ma-64	341	22	.	.	PUNCT
ma-64	341	23	econ	econ	PROPN
ma-64	341	24	.	.	PUNCT
ma-64	342	1	4	4	NUM
ma-64	342	2	(	(	PUNCT
ma-64	342	3	1977	1977	NUM
ma-64	342	4	)	)	PUNCT
ma-64	342	5	323–338	323–338	NUM
ma-64	342	6	.	.	PUNCT
ma-64	343	1	https://doi.org/10.1016/	https://doi.org/10.1016/	PROPN
ma-64	343	2	0304	0304	NUM
ma-64	343	3	-	-	PUNCT
ma-64	343	4	405x(77)90005	405x(77)90005	NUM
ma-64	343	5	-	-	PUNCT
ma-64	343	6	8.[20	8.[20	NUM
ma-64	343	7	]	]	PUNCT
ma-64	343	8	p.	p.	PROPN
ma-64	343	9	carr	carr	PROPN
ma-64	343	10	,	,	PUNCT
ma-64	343	11	d.	d.	PROPN
ma-64	343	12	madan	madan	PROPN
ma-64	343	13	,	,	PUNCT
ma-64	343	14	option	option	NOUN
ma-64	343	15	valuation	valuation	NOUN
ma-64	343	16	using	use	VERB
ma-64	343	17	the	the	DET
ma-64	343	18	fast	fast	ADJ
ma-64	343	19	fourier	fourier	NOUN
ma-64	343	20	transform	transform	NOUN
ma-64	343	21	,	,	PUNCT
ma-64	343	22	j.	j.	PROPN
ma-64	343	23	comput	comput	PROPN
ma-64	343	24	.	.	PUNCT
ma-64	344	1	financ	financ	PROPN
ma-64	344	2	.	.	PUNCT
ma-64	345	1	2	2	NUM
ma-64	345	2	(	(	PUNCT
ma-64	345	3	1999	1999	NUM
ma-64	345	4	)	)	PUNCT
ma-64	346	1	61–73	61–73	NUM
ma-64	346	2	.	.	PUNCT
ma-64	347	1	https	https	NOUN
ma-64	347	2	:	:	PUNCT
ma-64	347	3	//doi.org/10.21314	//doi.org/10.21314	NOUN
ma-64	347	4	/	/	SYM
ma-64	347	5	jcf.1999.043.[21	jcf.1999.043.[21	NOUN
ma-64	347	6	]	]	PUNCT
ma-64	347	7	p.	p.	PROPN
ma-64	347	8	roul	roul	PROPN
ma-64	347	9	,	,	PUNCT
ma-64	347	10	v.	v.	ADP
ma-64	347	11	m.	m.	PROPN
ma-64	347	12	k.	k.	PROPN
ma-64	347	13	prasad	prasad	PROPN
ma-64	347	14	goura	goura	PROPN
ma-64	347	15	,	,	PUNCT
ma-64	347	16	a	a	DET
ma-64	347	17	new	new	ADJ
ma-64	347	18	higher	high	ADJ
ma-64	347	19	order	order	NOUN
ma-64	347	20	compact	compact	ADJ
ma-64	347	21	finite	finite	ADJ
ma-64	347	22	difference	difference	NOUN
ma-64	347	23	method	method	NOUN
ma-64	347	24	for	for	ADP
ma-64	347	25	generalised	generalised	ADJ
ma-64	347	26	black	black	ADJ
ma-64	347	27	–	–	PUNCT
ma-64	347	28	scholespartial	scholespartial	ADJ
ma-64	347	29	differential	differential	NOUN
ma-64	347	30	equation	equation	NOUN
ma-64	347	31	:	:	PUNCT
ma-64	347	32	european	european	ADJ
ma-64	347	33	call	call	NOUN
ma-64	347	34	option	option	NOUN
ma-64	347	35	,	,	PUNCT
ma-64	347	36	j.	j.	PROPN
ma-64	347	37	comput	comput	PROPN
ma-64	347	38	.	.	PUNCT
ma-64	348	1	appl	appl	PROPN
ma-64	348	2	.	.	PROPN
ma-64	348	3	math	math	NOUN
ma-64	348	4	.	.	PUNCT
ma-64	349	1	363	363	NUM
ma-64	349	2	(	(	PUNCT
ma-64	349	3	2020	2020	NUM
ma-64	349	4	)	)	PUNCT
ma-64	350	1	464–484	464–484	NUM
ma-64	350	2	.	.	PUNCT
ma-64	350	3	https://doi.org/	https://doi.org/	VERB
ma-64	350	4	10.1016	10.1016	NUM
ma-64	350	5	/	/	SYM
ma-64	350	6	j.cam.2019.06.015.[22	j.cam.2019.06.015.[22	NOUN
ma-64	350	7	]	]	PUNCT
ma-64	351	1	s.	s.	PROPN
ma-64	351	2	wang	wang	PROPN
ma-64	351	3	,	,	PUNCT
ma-64	351	4	a	a	DET
ma-64	351	5	novel	novel	NOUN
ma-64	351	6	fitted	fit	VERB
ma-64	351	7	finite	finite	NOUN
ma-64	351	8	volume	volume	NOUN
ma-64	351	9	method	method	NOUN
ma-64	351	10	for	for	ADP
ma-64	351	11	the	the	DET
ma-64	351	12	black	black	ADJ
ma-64	351	13	-	-	PUNCT
ma-64	351	14	scholes	schole	NOUN
ma-64	351	15	equation	equation	NOUN
ma-64	351	16	governing	govern	VERB
ma-64	351	17	option	option	NOUN
ma-64	351	18	pricing	pricing	NOUN
ma-64	351	19	,	,	PUNCT
ma-64	351	20	i	i	PRON
ma-64	351	21	m	m	VERB
ma-64	351	22	a	a	PROPN
ma-64	351	23	j.	j.	PROPN
ma-64	351	24	numer.anal	numer.anal	PROPN
ma-64	351	25	.	.	PROPN
ma-64	351	26	24	24	NUM
ma-64	351	27	(	(	PUNCT
ma-64	351	28	2004	2004	NUM
ma-64	351	29	)	)	PUNCT
ma-64	351	30	699–720	699–720	NUM
ma-64	351	31	.	.	PUNCT
ma-64	352	1	https://doi.org/10.1093/imanum/24.4.699.[23	https://doi.org/10.1093/imanum/24.4.699.[23	PROPN
ma-64	352	2	]	]	X
ma-64	352	3	f.	f.	PROPN
ma-64	352	4	soleymani	soleymani	PROPN
ma-64	352	5	,	,	PUNCT
ma-64	352	6	a.	a.	NOUN
ma-64	352	7	akgül	akgül	NOUN
ma-64	352	8	,	,	PUNCT
ma-64	352	9	european	european	ADJ
ma-64	352	10	option	option	NOUN
ma-64	352	11	valuation	valuation	NOUN
ma-64	352	12	under	under	ADP
ma-64	352	13	the	the	DET
ma-64	352	14	bates	bate	NOUN
ma-64	352	15	pide	pide	PROPN
ma-64	352	16	in	in	ADP
ma-64	352	17	finance	finance	NOUN
ma-64	352	18	:	:	PUNCT
ma-64	352	19	a	a	DET
ma-64	352	20	numerical	numerical	ADJ
ma-64	352	21	implementation	implementation	NOUN
ma-64	352	22	ofthe	ofthe	PRON
ma-64	352	23	gaussian	gaussian	ADJ
ma-64	352	24	scheme	scheme	NOUN
ma-64	352	25	,	,	PUNCT
ma-64	352	26	discrete	discrete	ADJ
ma-64	352	27	cont	cont	NOUN
ma-64	352	28	.	.	PUNCT
ma-64	353	1	dyn	dyn	PROPN
ma-64	353	2	-	-	PUNCT
ma-64	353	3	s.	s.	PROPN
ma-64	353	4	13	13	NUM
ma-64	353	5	(	(	PUNCT
ma-64	353	6	2020	2020	NUM
ma-64	353	7	)	)	PUNCT
ma-64	353	8	889–909	889–909	NUM
ma-64	353	9	.	.	PUNCT
ma-64	354	1	http://dx.doi.org/10.3934/dcdss.2020052.[24	http://dx.doi.org/10.3934/dcdss.2020052.[24	PROPN
ma-64	354	2	]	]	PUNCT
ma-64	354	3	y.	y.	PROPN
ma-64	354	4	fadaei	fadaei	PROPN
ma-64	354	5	,	,	PUNCT
ma-64	354	6	z.	z.	PROPN
ma-64	354	7	a.	a.	PROPN
ma-64	354	8	khan	khan	PROPN
ma-64	354	9	,	,	PUNCT
ma-64	354	10	a.	a.	NOUN
ma-64	354	11	akgül	akgül	NOUN
ma-64	354	12	,	,	PUNCT
ma-64	354	13	a	a	DET
ma-64	354	14	greedy	greedy	ADJ
ma-64	354	15	algorithm	algorithm	NOUN
ma-64	354	16	for	for	ADP
ma-64	354	17	partition	partition	NOUN
ma-64	354	18	of	of	ADP
ma-64	354	19	unity	unity	NOUN
ma-64	354	20	collocation	collocation	NOUN
ma-64	354	21	method	method	NOUN
ma-64	354	22	in	in	ADP
ma-64	354	23	pricing	pricing	NOUN
ma-64	354	24	americanoptions	americanoption	NOUN
ma-64	354	25	.	.	PUNCT
ma-64	355	1	math	math	NOUN
ma-64	355	2	.	.	PUNCT
ma-64	356	1	methods	method	NOUN
ma-64	356	2	appl	appl	PROPN
ma-64	356	3	.	.	PUNCT
ma-64	357	1	sci	sci	PROPN
ma-64	357	2	.	.	PROPN
ma-64	358	1	42	42	NUM
ma-64	358	2	(	(	PUNCT
ma-64	358	3	2019	2019	NUM
ma-64	358	4	)	)	PUNCT
ma-64	358	5	5595–5606	5595–5606	NUM
ma-64	358	6	.	.	PUNCT
ma-64	359	1	https://doi.org/10.1002/mma.5757.[25	https://doi.org/10.1002/mma.5757.[25	X
ma-64	359	2	]	]	X
ma-64	359	3	a.	a.	PROPN
ma-64	359	4	q.	q.	PROPN
ma-64	359	5	m.	m.	PROPN
ma-64	359	6	khaliq	khaliq	PROPN
ma-64	359	7	,	,	PUNCT
ma-64	359	8	b.	b.	PROPN
ma-64	359	9	kleefeld	kleefeld	PROPN
ma-64	359	10	,	,	PUNCT
ma-64	359	11	r.	r.	PROPN
ma-64	359	12	h.	h.	PROPN
ma-64	359	13	liu	liu	PROPN
ma-64	359	14	,	,	PUNCT
ma-64	359	15	solving	solve	VERB
ma-64	359	16	complex	complex	ADJ
ma-64	359	17	pde	pde	NOUN
ma-64	359	18	systems	system	NOUN
ma-64	359	19	for	for	ADP
ma-64	359	20	pricing	price	VERB
ma-64	359	21	american	american	ADJ
ma-64	359	22	options	option	NOUN
ma-64	359	23	with	with	ADP
ma-64	359	24	regime	regime	NOUN
ma-64	359	25	-	-	PUNCT
ma-64	359	26	switching	switching	NOUN
ma-64	359	27	by	by	ADP
ma-64	359	28	efficient	efficient	ADJ
ma-64	359	29	exponential	exponential	ADJ
ma-64	359	30	time	time	NOUN
ma-64	359	31	differencing	difference	VERB
ma-64	359	32	schemes	scheme	NOUN
ma-64	359	33	,	,	PUNCT
ma-64	359	34	numer	numer	NOUN
ma-64	359	35	.	.	PUNCT
ma-64	360	1	methods	method	NOUN
ma-64	360	2	partial	partial	ADJ
ma-64	360	3	differ	differ	VERB
ma-64	360	4	.	.	PUNCT
ma-64	361	1	equ	equ	PROPN
ma-64	361	2	.	.	PROPN
ma-64	361	3	29	29	NUM
ma-64	361	4	(	(	PUNCT
ma-64	361	5	2013	2013	NUM
ma-64	361	6	)	)	PUNCT
ma-64	361	7	320	320	NUM
ma-64	361	8	-	-	SYM
ma-64	361	9	336	336	NUM
ma-64	361	10	.	.	PUNCT
ma-64	362	1	https://doi.org/10.1002/num.21714.[26	https://doi.org/10.1002/num.21714.[26	ADJ
ma-64	362	2	]	]	PUNCT
ma-64	362	3	a.	a.	PROPN
ma-64	362	4	q.	q.	PROPN
ma-64	362	5	khaliq	khaliq	PROPN
ma-64	362	6	,	,	PUNCT
ma-64	363	1	r.	r.	PROPN
ma-64	363	2	h.	h.	PROPN
ma-64	363	3	liu	liu	PROPN
ma-64	363	4	,	,	PUNCT
ma-64	363	5	new	new	PROPN
ma-64	363	6	numerical	numerical	ADJ
ma-64	363	7	scheme	scheme	NOUN
ma-64	363	8	for	for	ADP
ma-64	363	9	pricing	price	VERB
ma-64	363	10	american	american	ADJ
ma-64	363	11	option	option	NOUN
ma-64	363	12	with	with	ADP
ma-64	363	13	regime	regime	NOUN
ma-64	363	14	-	-	PUNCT
ma-64	363	15	switching	switching	NOUN
ma-64	363	16	,	,	PUNCT
ma-64	363	17	int	int	NOUN
ma-64	363	18	.	.	PUNCT
ma-64	364	1	j.	j.	PROPN
ma-64	364	2	theor.appl	theor.appl	PROPN
ma-64	364	3	.	.	PROPN
ma-64	364	4	finance	finance	NOUN
ma-64	364	5	.	.	PUNCT
ma-64	365	1	12	12	NUM
ma-64	365	2	(	(	PUNCT
ma-64	365	3	2009	2009	NUM
ma-64	365	4	)	)	PUNCT
ma-64	365	5	319	319	NUM
ma-64	365	6	-	-	SYM
ma-64	365	7	340	340	NUM
ma-64	365	8	.	.	PUNCT
ma-64	366	1	https://doi.org/10.1142/s0219024909005245.[27	https://doi.org/10.1142/s0219024909005245.[27	X
ma-64	366	2	]	]	PUNCT
ma-64	366	3	m.	m.	PROPN
ma-64	366	4	yousuf	yousuf	PROPN
ma-64	366	5	,	,	PUNCT
ma-64	366	6	high	high	ADJ
ma-64	366	7	-	-	PUNCT
ma-64	366	8	order	order	NOUN
ma-64	366	9	time	time	NOUN
ma-64	366	10	-	-	PUNCT
ma-64	366	11	stepping	step	VERB
ma-64	366	12	scheme	scheme	NOUN
ma-64	366	13	for	for	ADP
ma-64	366	14	pricing	price	VERB
ma-64	366	15	american	american	ADJ
ma-64	366	16	option	option	NOUN
ma-64	366	17	under	under	ADP
ma-64	366	18	bates	bates	PROPN
ma-64	366	19	model	model	PROPN
ma-64	366	20	,	,	PUNCT
ma-64	366	21	int	int	PROPN
ma-64	366	22	.	.	PUNCT
ma-64	367	1	j.	j.	PROPN
ma-64	367	2	comput	comput	PROPN
ma-64	367	3	.	.	PUNCT
ma-64	368	1	math.96	math.96	PROPN
ma-64	368	2	(	(	PUNCT
ma-64	368	3	2019	2019	NUM
ma-64	368	4	)	)	PUNCT
ma-64	368	5	18	18	NUM
ma-64	368	6	-	-	SYM
ma-64	368	7	32	32	NUM
ma-64	368	8	.	.	PUNCT
ma-64	369	1	https://doi.org/10.1080/00207160.2017.1420785.[28	https://doi.org/10.1080/00207160.2017.1420785.[28	X
ma-64	369	2	]	]	PUNCT
ma-64	369	3	m.	m.	PROPN
ma-64	369	4	yousuf	yousuf	PROPN
ma-64	369	5	,	,	PUNCT
ma-64	369	6	a.	a.	PROPN
ma-64	369	7	q.	q.	PROPN
ma-64	369	8	m.	m.	PROPN
ma-64	369	9	khaliq	khaliq	PROPN
ma-64	369	10	,	,	PUNCT
ma-64	370	1	r.	r.	PROPN
ma-64	370	2	h.	h.	PROPN
ma-64	370	3	liu	liu	PROPN
ma-64	370	4	,	,	PUNCT
ma-64	370	5	pricing	price	VERB
ma-64	370	6	american	american	ADJ
ma-64	370	7	options	option	NOUN
ma-64	370	8	under	under	ADP
ma-64	370	9	multi	multi	ADJ
ma-64	370	10	-	-	ADJ
ma-64	370	11	state	state	ADJ
ma-64	370	12	regime	regime	NOUN
ma-64	370	13	switching	switch	VERB
ma-64	370	14	with	with	ADP
ma-64	370	15	an	an	DET
ma-64	370	16	efficient	efficient	ADJ
ma-64	370	17	l	l	ADJ
ma-64	370	18	-	-	ADJ
ma-64	370	19	stable	stable	ADJ
ma-64	370	20	method	method	NOUN
ma-64	370	21	,	,	PUNCT
ma-64	370	22	int	int	NOUN
ma-64	370	23	.	.	PUNCT
ma-64	371	1	j.	j.	PROPN
ma-64	371	2	comput	comput	PROPN
ma-64	371	3	.	.	PUNCT
ma-64	372	1	math	math	NOUN
ma-64	372	2	.	.	PUNCT
ma-64	373	1	92	92	NUM
ma-64	373	2	(	(	PUNCT
ma-64	373	3	2015	2015	NUM
ma-64	373	4	)	)	PUNCT
ma-64	373	5	2530	2530	NUM
ma-64	373	6	-	-	SYM
ma-64	373	7	2550	2550	NUM
ma-64	373	8	.	.	PUNCT
ma-64	374	1	https://doi.org/10.1080/00207160.2015.1071799.[29	https://doi.org/10.1080/00207160.2015.1071799.[29	PROPN
ma-64	374	2	]	]	X
ma-64	374	3	p.	p.	PROPN
ma-64	374	4	roul	roul	PROPN
ma-64	374	5	,	,	PUNCT
ma-64	374	6	a	a	DET
ma-64	374	7	fourth	fourth	ADJ
ma-64	374	8	order	order	NOUN
ma-64	374	9	numerical	numerical	ADJ
ma-64	374	10	method	method	NOUN
ma-64	374	11	based	base	VERB
ma-64	374	12	on	on	ADP
ma-64	374	13	b	b	X
ma-64	374	14	-	-	PUNCT
ma-64	374	15	spline	spline	NOUN
ma-64	374	16	functions	function	NOUN
ma-64	374	17	for	for	ADP
ma-64	374	18	pricing	price	VERB
ma-64	374	19	asian	asian	ADJ
ma-64	374	20	options	option	NOUN
ma-64	374	21	,	,	PUNCT
ma-64	374	22	comput	comput	NOUN
ma-64	374	23	.	.	PUNCT
ma-64	375	1	math	math	NOUN
ma-64	375	2	.	.	PUNCT
ma-64	376	1	withappl	withappl	PROPN
ma-64	376	2	.	.	PUNCT
ma-64	377	1	80	80	NUM
ma-64	377	2	(	(	PUNCT
ma-64	377	3	2020	2020	NUM
ma-64	377	4	)	)	PUNCT
ma-64	378	1	504–521	504–521	NUM
ma-64	378	2	.	.	PUNCT
ma-64	379	1	https://doi.org/10.1016/j.camwa.2020.04.001.[30	https://doi.org/10.1016/j.camwa.2020.04.001.[30	NOUN
ma-64	379	2	]	]	PUNCT
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ma-64	379	19	asian	asian	ADJ
ma-64	379	20	option	option	NOUN
ma-64	379	21	with	with	ADP
ma-64	379	22	moving	move	VERB
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ma-64	379	24	,	,	PUNCT
ma-64	379	25	differ	differ	VERB
ma-64	379	26	.	.	PUNCT
ma-64	380	1	equations	equations	PROPN
ma-64	380	2	dyn	dyn	PROPN
ma-64	380	3	.	.	PUNCT
ma-64	381	1	syst	syst	PROPN
ma-64	381	2	.	.	PUNCT
ma-64	382	1	27	27	NUM
ma-64	382	2	(	(	PUNCT
ma-64	382	3	2019	2019	NUM
ma-64	382	4	)	)	PUNCT
ma-64	382	5	39–56	39–56	NUM
ma-64	382	6	.	.	PUNCT
ma-64	383	1	https://doi.org/10.1007/s12591-017-0372-8.[31	https://doi.org/10.1007/s12591-017-0372-8.[31	X
ma-64	383	2	]	]	X
ma-64	383	3	b.	b.	PROPN
ma-64	383	4	a.	a.	PROPN
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ma-64	383	6	,	,	PUNCT
ma-64	383	7	a.	a.	PROPN
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ma-64	383	9	m.	m.	PROPN
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ma-64	383	11	,	,	PUNCT
ma-64	383	12	m.	m.	PROPN
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ma-64	383	14	,	,	PUNCT
ma-64	383	15	j.	j.	PROPN
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ma-64	383	20	r.	r.	PROPN
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ma-64	383	22	,	,	PUNCT
ma-64	383	23	on	on	ADP
ma-64	383	24	smoothing	smoothing	NOUN
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ma-64	383	26	the	the	DET
ma-64	383	27	crank	crank	NOUN
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ma-64	383	29	nicolson	nicolson	PROPN
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ma-64	383	32	-	-	PUNCT
ma-64	383	33	order	order	NOUN
ma-64	383	34	schemes	scheme	NOUN
ma-64	383	35	for	for	ADP
ma-64	383	36	pricing	pricing	NOUN
ma-64	383	37	barrier	barrier	NOUN
ma-64	383	38	options	option	NOUN
ma-64	383	39	,	,	PUNCT
ma-64	383	40	j.	j.	PROPN
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ma-64	383	42	.	.	PUNCT
ma-64	384	1	appl	appl	PROPN
ma-64	384	2	.	.	PROPN
ma-64	384	3	math	math	NOUN
ma-64	384	4	.	.	PUNCT
ma-64	385	1	204	204	NUM
ma-64	385	2	(	(	PUNCT
ma-64	385	3	2007	2007	NUM
ma-64	385	4	)	)	PUNCT
ma-64	385	5	144	144	NUM
ma-64	385	6	-	-	SYM
ma-64	385	7	158	158	NUM
ma-64	385	8	.	.	PUNCT
ma-64	386	1	https://doi	https://doi	X
ma-64	386	2	.	.	PUNCT
ma-64	387	1	org/10.1016	org/10.1016	PROPN
ma-64	387	2	/	/	SYM
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ma-64	387	4	]	]	PUNCT
ma-64	387	5	m.	m.	NOUN
ma-64	387	6	h.	h.	PROPN
ma-64	387	7	akrami	akrami	PROPN
ma-64	387	8	,	,	PUNCT
ma-64	387	9	g.	g.	PROPN
ma-64	387	10	h.	h.	PROPN
ma-64	387	11	erjaee	erjaee	PROPN
ma-64	387	12	,	,	PUNCT
ma-64	387	13	numerical	numerical	ADJ
ma-64	387	14	solutions	solution	NOUN
ma-64	387	15	for	for	ADP
ma-64	387	16	fractional	fractional	ADJ
ma-64	387	17	black	black	ADJ
ma-64	387	18	-	-	PUNCT
ma-64	387	19	scholes	schole	NOUN
ma-64	387	20	option	option	NOUN
ma-64	387	21	pricing	pricing	NOUN
ma-64	387	22	equation	equation	NOUN
ma-64	387	23	,	,	PUNCT
ma-64	387	24	glob	glob	NOUN
ma-64	387	25	.	.	PUNCT
ma-64	387	26	anal.discret	anal.discret	PROPN
ma-64	387	27	.	.	PROPN
ma-64	387	28	math	math	NOUN
ma-64	387	29	.	.	PUNCT
ma-64	388	1	1	1	NUM
ma-64	388	2	(	(	PUNCT
ma-64	388	3	2016	2016	NUM
ma-64	388	4	)	)	PUNCT
ma-64	388	5	9–14	9–14	NOUN
ma-64	388	6	.	.	PUNCT
ma-64	389	1	https://doi.org/10.1016/j.camwa.2016.02.007.[33	https://doi.org/10.1016/j.camwa.2016.02.007.[33	PROPN
ma-64	389	2	]	]	PUNCT
ma-64	389	3	s.	s.	PROPN
ma-64	389	4	kumar	kumar	PROPN
ma-64	389	5	,	,	PUNCT
ma-64	389	6	a.	a.	PROPN
ma-64	389	7	yildirim	yildirim	PROPN
ma-64	389	8	,	,	PUNCT
ma-64	389	9	y.	y.	PROPN
ma-64	389	10	khan	khan	PROPN
ma-64	389	11	,	,	PUNCT
ma-64	389	12	h.	h.	PROPN
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ma-64	389	14	,	,	PUNCT
ma-64	389	15	k.	k.	PROPN
ma-64	389	16	sayevand	sayevand	PROPN
ma-64	389	17	,	,	PUNCT
ma-64	389	18	l.	l.	PROPN
ma-64	389	19	wei	wei	PROPN
ma-64	389	20	,	,	PUNCT
ma-64	389	21	analytical	analytical	ADJ
ma-64	389	22	solution	solution	NOUN
ma-64	389	23	of	of	ADP
ma-64	389	24	fractional	fractional	ADJ
ma-64	389	25	black	black	ADJ
ma-64	389	26	-	-	PUNCT
ma-64	389	27	scholeseuropean	scholeseuropean	ADJ
ma-64	389	28	option	option	NOUN
ma-64	389	29	pricing	pricing	NOUN
ma-64	389	30	equation	equation	NOUN
ma-64	389	31	by	by	ADP
ma-64	389	32	using	use	VERB
ma-64	389	33	laplace	laplace	NOUN
ma-64	389	34	transform	transform	NOUN
ma-64	389	35	,	,	PUNCT
ma-64	389	36	j.	j.	PROPN
ma-64	389	37	fract	fract	PROPN
ma-64	389	38	.	.	PUNCT
ma-64	390	1	calc	calc	PROPN
ma-64	390	2	.	.	PUNCT
ma-64	391	1	appl	appl	PROPN
ma-64	391	2	.	.	PROPN
ma-64	392	1	2	2	NUM
ma-64	392	2	(	(	PUNCT
ma-64	392	3	2012	2012	NUM
ma-64	392	4	)	)	PUNCT
ma-64	392	5	1–9.[34	1–9.[34	NUM
ma-64	392	6	]	]	PUNCT
ma-64	392	7	m.	m.	NOUN
ma-64	392	8	h.	h.	PROPN
ma-64	392	9	akrami	akrami	PROPN
ma-64	392	10	,	,	PUNCT
ma-64	392	11	g.	g.	PROPN
ma-64	392	12	h.	h.	PROPN
ma-64	392	13	erjaee	erjaee	PROPN
ma-64	392	14	,	,	PUNCT
ma-64	392	15	examples	example	NOUN
ma-64	392	16	of	of	ADP
ma-64	392	17	analytical	analytical	ADJ
ma-64	392	18	solutions	solution	NOUN
ma-64	392	19	by	by	ADP
ma-64	392	20	means	mean	NOUN
ma-64	392	21	of	of	ADP
ma-64	392	22	mittag	mittag	ADJ
ma-64	392	23	-	-	PUNCT
ma-64	392	24	leffler	leffler	NOUN
ma-64	392	25	function	function	NOUN
ma-64	392	26	of	of	ADP
ma-64	392	27	fractionalblack	fractionalblack	NOUN
ma-64	392	28	-	-	PUNCT
ma-64	392	29	scholes	schole	NOUN
ma-64	392	30	option	option	NOUN
ma-64	392	31	pricing	pricing	NOUN
ma-64	392	32	equation	equation	NOUN
ma-64	392	33	,	,	PUNCT
ma-64	392	34	fract	fract	PROPN
ma-64	392	35	.	.	PUNCT
ma-64	393	1	calc	calc	PROPN
ma-64	393	2	.	.	PUNCT
ma-64	394	1	appl	appl	PROPN
ma-64	394	2	.	.	PUNCT
ma-64	395	1	anal	anal	PROPN
ma-64	395	2	.	.	PUNCT
ma-64	396	1	18	18	NUM
ma-64	396	2	(	(	PUNCT
ma-64	396	3	2015	2015	NUM
ma-64	396	4	)	)	PUNCT
ma-64	396	5	38–47	38–47	NUM
ma-64	396	6	.	.	PUNCT
ma-64	397	1	https://doi.org/10.1515/	https://doi.org/10.1515/	PROPN
ma-64	397	2	fca-2015	fca-2015	NOUN
ma-64	397	3	-	-	PUNCT
ma-64	397	4	0004.[35	0004.[35	PROPN
ma-64	397	5	]	]	PUNCT
ma-64	397	6	p.	p.	NOUN
ma-64	397	7	ehrhardt	ehrhardt	PROPN
ma-64	397	8	,	,	PUNCT
ma-64	397	9	a.	a.	NOUN
ma-64	397	10	unterreiter	unterreiter	NOUN
ma-64	397	11	,	,	PUNCT
ma-64	397	12	the	the	DET
ma-64	397	13	numerical	numerical	ADJ
ma-64	397	14	solution	solution	NOUN
ma-64	397	15	of	of	ADP
ma-64	397	16	nonlinear	nonlinear	ADJ
ma-64	397	17	black	black	ADJ
ma-64	397	18	–	–	PUNCT
ma-64	397	19	scholes	schole	NOUN
ma-64	397	20	equations	equation	NOUN
ma-64	397	21	,	,	PUNCT
ma-64	397	22	technische	technische	PROPN
ma-64	397	23	universitatberlin	universitatberlin	PROPN
ma-64	397	24	,	,	PUNCT
ma-64	397	25	28	28	NUM
ma-64	397	26	(	(	PUNCT
ma-64	397	27	2008	2008	NUM
ma-64	397	28	)	)	PUNCT
ma-64	397	29	.	.	PUNCT
ma-64	398	1	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	398	2	http://dx.doi.org/10.1016/j.cam.2017.03.027	http://dx.doi.org/10.1016/j.cam.2017.03.027	PROPN
ma-64	398	3	http://dx.doi.org/10.1016/j.cam.2017.03.027	http://dx.doi.org/10.1016/j.cam.2017.03.027	PROPN
ma-64	398	4	https://doi.org/10.18488/journal.24.2020.91.1.10	https://doi.org/10.18488/journal.24.2020.91.1.10	NOUN
ma-64	398	5	https://doi.org/10.1016/0304-405x(77)90005-8	https://doi.org/10.1016/0304-405x(77)90005-8	PROPN
ma-64	398	6	https://doi.org/10.1016/0304-405x(77)90005-8	https://doi.org/10.1016/0304-405x(77)90005-8	PROPN
ma-64	398	7	https://doi.org/10.21314/jcf.1999.043	https://doi.org/10.21314/jcf.1999.043	PROPN
ma-64	398	8	https://doi.org/10.21314/jcf.1999.043	https://doi.org/10.21314/jcf.1999.043	PROPN
ma-64	398	9	https://doi.org/10.1016/j.cam.2019.06.015	https://doi.org/10.1016/j.cam.2019.06.015	PROPN
ma-64	398	10	https://doi.org/10.1016/j.cam.2019.06.015	https://doi.org/10.1016/j.cam.2019.06.015	PROPN
ma-64	398	11	https://doi.org/10.1093/imanum/24.4.699	https://doi.org/10.1093/imanum/24.4.699	PROPN
ma-64	398	12	http://dx.doi.org/10.3934/dcdss.2020052	http://dx.doi.org/10.3934/dcdss.2020052	PRON
ma-64	398	13	https://doi.org/10.1002/mma.5757	https://doi.org/10.1002/mma.5757	PROPN
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ma-64	398	16	https://doi.org/10.1080/00207160.2017.1420785	https://doi.org/10.1080/00207160.2017.1420785	PUNCT
ma-64	399	1	https://doi.org/10.1080/00207160.2015.1071799	https://doi.org/10.1080/00207160.2015.1071799	PROPN
ma-64	400	1	https://doi.org/10.1016/j.camwa.2020.04.001	https://doi.org/10.1016/j.camwa.2020.04.001	NOUN
ma-64	400	2	https://doi.org/10.1007/s12591-017-0372-8	https://doi.org/10.1007/s12591-017-0372-8	NUM
ma-64	400	3	https://doi.org/10.1016/j.cam.2006.04.034	https://doi.org/10.1016/j.cam.2006.04.034	NOUN
ma-64	400	4	https://doi.org/10.1016/j.cam.2006.04.034	https://doi.org/10.1016/j.cam.2006.04.034	NOUN
ma-64	400	5	https://doi.org/10.1016/j.camwa.2016.02.007	https://doi.org/10.1016/j.camwa.2016.02.007	VERB
ma-64	400	6	https://doi.org/10.1515/fca-2015-0004	https://doi.org/10.1515/fca-2015-0004	VERB
ma-64	400	7	https://doi.org/10.1515/fca-2015-0004	https://doi.org/10.1515/fca-2015-0004	VERB
ma-64	400	8	eur	eur	PROPN
ma-64	400	9	.	.	PUNCT
ma-64	401	1	j.	j.	PROPN
ma-64	401	2	math	math	PROPN
ma-64	401	3	.	.	PUNCT
ma-64	402	1	anal	anal	PROPN
ma-64	402	2	.	.	PUNCT
ma-64	403	1	10.28924	10.28924	NUM
ma-64	403	2	/	/	SYM
ma-64	403	3	ada	ada	PROPN
ma-64	403	4	/	/	SYM
ma-64	403	5	ma.2.9	ma.2.9	PROPN
ma-64	403	6	17	17	NUM
ma-64	404	1	[	[	SYM
ma-64	404	2	36	36	NUM
ma-64	404	3	]	]	X
ma-64	404	4	h.	h.	PROPN
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ma-64	404	6	,	,	PUNCT
ma-64	404	7	s.	s.	PROPN
ma-64	404	8	shreve	shreve	PROPN
ma-64	404	9	,	,	PUNCT
ma-64	404	10	j.	j.	PROPN
ma-64	404	11	cvitanic	cvitanic	PROPN
ma-64	404	12	,	,	PUNCT
ma-64	404	13	there	there	PRON
ma-64	404	14	is	be	VERB
ma-64	404	15	no	no	DET
ma-64	404	16	nontrivial	nontrivial	ADJ
ma-64	404	17	hedging	hedge	VERB
ma-64	404	18	portfolio	portfolio	NOUN
ma-64	404	19	for	for	ADP
ma-64	404	20	option	option	NOUN
ma-64	404	21	pricing	pricing	NOUN
ma-64	404	22	with	with	ADP
ma-64	404	23	transaction	transaction	NOUN
ma-64	404	24	costs	cost	NOUN
ma-64	404	25	,	,	PUNCT
ma-64	404	26	ann	ann	PROPN
ma-64	404	27	.	.	PROPN
ma-64	404	28	appl	appl	PROPN
ma-64	404	29	.	.	PUNCT
ma-64	405	1	probab	probab	PROPN
ma-64	405	2	.	.	PUNCT
ma-64	406	1	5	5	NUM
ma-64	406	2	(	(	PUNCT
ma-64	406	3	1995	1995	NUM
ma-64	406	4	)	)	PUNCT
ma-64	406	5	5327–355	5327–355	NOUN
ma-64	406	6	.	.	PUNCT
ma-64	406	7	https://www.jstor.org/stable/2245301.[37	https://www.jstor.org/stable/2245301.[37	PROPN
ma-64	406	8	]	]	PUNCT
ma-64	407	1	h.	h.	PROPN
ma-64	407	2	e.	e.	PROPN
ma-64	407	3	leland	leland	PROPN
ma-64	407	4	,	,	PUNCT
ma-64	407	5	option	option	NOUN
ma-64	407	6	pricing	pricing	NOUN
ma-64	407	7	and	and	CCONJ
ma-64	407	8	replication	replication	NOUN
ma-64	407	9	with	with	ADP
ma-64	407	10	transactions	transaction	NOUN
ma-64	407	11	costs	cost	NOUN
ma-64	407	12	,	,	PUNCT
ma-64	407	13	j.	j.	PROPN
ma-64	407	14	finance	finance	PROPN
ma-64	407	15	.	.	PUNCT
ma-64	408	1	40	40	NUM
ma-64	408	2	(	(	PUNCT
ma-64	408	3	1985	1985	NUM
ma-64	408	4	)	)	PUNCT
ma-64	408	5	1283–1301	1283–1301	NUM
ma-64	408	6	.	.	PUNCT
ma-64	408	7	https	https	NOUN
ma-64	408	8	:	:	PUNCT
ma-64	409	1	//doi.org/10.1111	//doi.org/10.1111	PROPN
ma-64	409	2	/	/	SYM
ma-64	409	3	j.1540	j.1540	PROPN
ma-64	409	4	-	-	PUNCT
ma-64	409	5	6261.1985.tb02383.x.[38	6261.1985.tb02383.x.[38	NOUN
ma-64	409	6	]	]	PUNCT
ma-64	409	7	p.	p.	NOUN
ma-64	409	8	p.	p.	PROPN
ma-64	409	9	boyle	boyle	PROPN
ma-64	409	10	,	,	PUNCT
ma-64	409	11	t.	t.	PROPN
ma-64	409	12	vorst	vorst	PROPN
ma-64	409	13	,	,	PUNCT
ma-64	409	14	option	option	NOUN
ma-64	409	15	replication	replication	NOUN
ma-64	409	16	in	in	ADP
ma-64	409	17	discrete	discrete	ADJ
ma-64	409	18	time	time	NOUN
ma-64	409	19	with	with	ADP
ma-64	409	20	transaction	transaction	NOUN
ma-64	409	21	costs	cost	NOUN
ma-64	409	22	,	,	PUNCT
ma-64	409	23	j.	j.	PROPN
ma-64	409	24	finance	finance	PROPN
ma-64	409	25	.	.	PUNCT
ma-64	410	1	47	47	NUM
ma-64	410	2	(	(	PUNCT
ma-64	410	3	1992	1992	NUM
ma-64	410	4	)	)	PUNCT
ma-64	410	5	271–293	271–293	NUM
ma-64	410	6	.	.	PUNCT
ma-64	411	1	https://doi.org/10.1111/j.1540-6261.1992.tb03986.x.[39	https://doi.org/10.1111/j.1540-6261.1992.tb03986.x.[39	PROPN
ma-64	411	2	]	]	X
ma-64	411	3	j.	j.	PROPN
ma-64	411	4	dewynne	dewynne	PROPN
ma-64	411	5	,	,	PUNCT
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ma-64	411	7	whalley	whalley	PROPN
ma-64	411	8	,	,	PUNCT
ma-64	411	9	p.	p.	PROPN
ma-64	411	10	wilmott	wilmott	PROPN
ma-64	411	11	,	,	PUNCT
ma-64	411	12	path	path	NOUN
ma-64	411	13	-	-	PUNCT
ma-64	411	14	dependent	dependent	ADJ
ma-64	411	15	options	option	NOUN
ma-64	411	16	and	and	CCONJ
ma-64	411	17	transaction	transaction	NOUN
ma-64	411	18	costs	cost	NOUN
ma-64	411	19	,	,	PUNCT
ma-64	411	20	phil	phil	PROPN
ma-64	411	21	.	.	PUNCT
ma-64	412	1	trans	trans	PROPN
ma-64	412	2	.	.	PUNCT
ma-64	412	3	r.	r.	PROPN
ma-64	412	4	soc	soc	PROPN
ma-64	412	5	.	.	PUNCT
ma-64	413	1	lond	lond	PROPN
ma-64	413	2	.	.	PUNCT
ma-64	414	1	a.347	a.347	PROPN
ma-64	414	2	(	(	PUNCT
ma-64	414	3	1994	1994	NUM
ma-64	414	4	)	)	PUNCT
ma-64	415	1	517–529	517–529	NUM
ma-64	415	2	.	.	PUNCT
ma-64	415	3	https://www.jstor.org/stable/54362.[40	https://www.jstor.org/stable/54362.[40	PROPN
ma-64	415	4	]	]	X
ma-64	415	5	a.	a.	PROPN
ma-64	415	6	e.	e.	PROPN
ma-64	415	7	whalley	whalley	PROPN
ma-64	415	8	,	,	PUNCT
ma-64	415	9	p.	p.	PROPN
ma-64	415	10	wilmott	wilmott	PROPN
ma-64	415	11	,	,	PUNCT
ma-64	415	12	an	an	DET
ma-64	415	13	asymptotic	asymptotic	ADJ
ma-64	415	14	analysis	analysis	NOUN
ma-64	415	15	of	of	ADP
ma-64	415	16	an	an	DET
ma-64	415	17	optimal	optimal	ADJ
ma-64	415	18	hedging	hedging	NOUN
ma-64	415	19	model	model	NOUN
ma-64	415	20	for	for	ADP
ma-64	415	21	option	option	NOUN
ma-64	415	22	pricing	pricing	NOUN
ma-64	415	23	with	with	ADP
ma-64	415	24	transactioncosts	transactioncost	NOUN
ma-64	415	25	,	,	PUNCT
ma-64	415	26	math	math	NOUN
ma-64	415	27	.	.	PUNCT
ma-64	416	1	financ	financ	PROPN
ma-64	416	2	.	.	PUNCT
ma-64	417	1	7	7	NUM
ma-64	417	2	(	(	PUNCT
ma-64	417	3	1997	1997	NUM
ma-64	417	4	)	)	PUNCT
ma-64	418	1	307–324	307–324	NUM
ma-64	418	2	.	.	PUNCT
ma-64	419	1	https://doi.org/10.1111/1467-9965.00034.[41	https://doi.org/10.1111/1467-9965.00034.[41	PROPN
ma-64	419	2	]	]	X
ma-64	419	3	m.	m.	NOUN
ma-64	419	4	monoyios	monoyio	NOUN
ma-64	419	5	,	,	PUNCT
ma-64	419	6	option	option	NOUN
ma-64	419	7	pricing	pricing	NOUN
ma-64	419	8	with	with	ADP
ma-64	419	9	transaction	transaction	NOUN
ma-64	419	10	costs	cost	NOUN
ma-64	419	11	using	use	VERB
ma-64	419	12	a	a	DET
ma-64	419	13	markov	markov	NOUN
ma-64	419	14	chain	chain	NOUN
ma-64	419	15	approximation	approximation	NOUN
ma-64	419	16	,	,	PUNCT
ma-64	419	17	j.	j.	PROPN
ma-64	419	18	econ	econ	PROPN
ma-64	419	19	.	.	PUNCT
ma-64	420	1	dyn	dyn	PROPN
ma-64	420	2	.	.	PUNCT
ma-64	421	1	control	control	PROPN
ma-64	421	2	.	.	PUNCT
ma-64	422	1	28(2004	28(2004	NUM
ma-64	422	2	)	)	PUNCT
ma-64	423	1	889–913	889–913	NUM
ma-64	423	2	.	.	PUNCT
ma-64	424	1	https://doi.org/10.1016/s0165-1889(03)00059-9.[42	https://doi.org/10.1016/s0165-1889(03)00059-9.[42	PROPN
ma-64	424	2	]	]	PUNCT
ma-64	424	3	r.	r.	PROPN
ma-64	424	4	company	company	PROPN
ma-64	424	5	,	,	PUNCT
ma-64	424	6	e.	e.	PROPN
ma-64	424	7	navarro	navarro	PROPN
ma-64	424	8	,	,	PUNCT
ma-64	424	9	j.	j.	PROPN
ma-64	424	10	ramón	ramón	PROPN
ma-64	424	11	pintos	pintos	PROPN
ma-64	424	12	,	,	PUNCT
ma-64	424	13	e.	e.	PROPN
ma-64	424	14	ponsoda	ponsoda	PROPN
ma-64	424	15	,	,	PUNCT
ma-64	424	16	numerical	numerical	ADJ
ma-64	424	17	solution	solution	NOUN
ma-64	424	18	of	of	ADP
ma-64	424	19	linear	linear	PROPN
ma-64	424	20	and	and	CCONJ
ma-64	424	21	nonlinear	nonlinear	ADJ
ma-64	424	22	black	black	ADJ
ma-64	424	23	-	-	PUNCT
ma-64	424	24	scholesoption	scholesoption	NOUN
ma-64	424	25	pricing	pricing	NOUN
ma-64	424	26	equations	equation	NOUN
ma-64	424	27	,	,	PUNCT
ma-64	424	28	comput	comput	NOUN
ma-64	424	29	.	.	PUNCT
ma-64	425	1	math	math	NOUN
ma-64	425	2	.	.	PUNCT
ma-64	426	1	with	with	ADP
ma-64	426	2	appl	appl	PROPN
ma-64	426	3	.	.	PUNCT
ma-64	427	1	56	56	NUM
ma-64	427	2	(	(	PUNCT
ma-64	427	3	2008	2008	NUM
ma-64	427	4	)	)	PUNCT
ma-64	428	1	813–821	813–821	NUM
ma-64	428	2	.	.	PUNCT
ma-64	429	1	https://doi.org/10.1016/j.camwa	https://doi.org/10.1016/j.camwa	PROPN
ma-64	429	2	.	.	PUNCT
ma-64	430	1	2008.02.010.[43	2008.02.010.[43	PROPN
ma-64	430	2	]	]	X
ma-64	430	3	g.	g.	PROPN
ma-64	430	4	barles	barle	NOUN
ma-64	430	5	,	,	PUNCT
ma-64	430	6	h.	h.	PROPN
ma-64	430	7	m.	m.	PROPN
ma-64	430	8	soner	soner	NOUN
ma-64	430	9	,	,	PUNCT
ma-64	430	10	option	option	NOUN
ma-64	430	11	pricing	pricing	NOUN
ma-64	430	12	with	with	ADP
ma-64	430	13	transaction	transaction	NOUN
ma-64	430	14	costs	cost	NOUN
ma-64	430	15	and	and	CCONJ
ma-64	430	16	a	a	DET
ma-64	430	17	nonlinear	nonlinear	ADJ
ma-64	430	18	black	black	ADJ
ma-64	430	19	-	-	PUNCT
ma-64	430	20	scholes	schole	NOUN
ma-64	430	21	equation	equation	NOUN
ma-64	430	22	,	,	PUNCT
ma-64	430	23	financ.stochastic	financ.stochastic	PROPN
ma-64	430	24	.	.	NOUN
ma-64	430	25	2	2	NUM
ma-64	430	26	(	(	PUNCT
ma-64	430	27	1998	1998	NUM
ma-64	430	28	)	)	PUNCT
ma-64	430	29	369–397	369–397	NUM
ma-64	430	30	.	.	PUNCT
ma-64	431	1	https://doi.org/10.1007/s007800050046.[44	https://doi.org/10.1007/s007800050046.[44	PROPN
ma-64	431	2	]	]	PUNCT
ma-64	431	3	m.	m.	PROPN
ma-64	431	4	yousuf	yousuf	PROPN
ma-64	431	5	,	,	PUNCT
ma-64	431	6	a.	a.	PROPN
ma-64	431	7	q.	q.	PROPN
ma-64	431	8	m.	m.	PROPN
ma-64	431	9	khaliq	khaliq	PROPN
ma-64	431	10	,	,	PUNCT
ma-64	431	11	b.	b.	PROPN
ma-64	431	12	kleefeld	kleefeld	PROPN
ma-64	431	13	,	,	PUNCT
ma-64	431	14	the	the	DET
ma-64	431	15	numerical	numerical	ADJ
ma-64	431	16	approximation	approximation	NOUN
ma-64	431	17	of	of	ADP
ma-64	431	18	nonlinear	nonlinear	ADJ
ma-64	431	19	black	black	ADJ
ma-64	431	20	-	-	PUNCT
ma-64	431	21	scholes	schole	NOUN
ma-64	431	22	model	model	NOUN
ma-64	431	23	for	for	ADP
ma-64	431	24	exoticpath	exoticpath	NOUN
ma-64	431	25	-	-	PUNCT
ma-64	431	26	dependent	dependent	ADJ
ma-64	431	27	american	american	ADJ
ma-64	431	28	options	option	NOUN
ma-64	431	29	with	with	ADP
ma-64	431	30	transaction	transaction	NOUN
ma-64	431	31	cost	cost	NOUN
ma-64	431	32	,	,	PUNCT
ma-64	431	33	int	int	NOUN
ma-64	431	34	.	.	PUNCT
ma-64	432	1	j.	j.	PROPN
ma-64	432	2	comput	comput	PROPN
ma-64	432	3	.	.	PUNCT
ma-64	433	1	math	math	NOUN
ma-64	433	2	.	.	PUNCT
ma-64	434	1	89	89	NUM
ma-64	434	2	(	(	PUNCT
ma-64	434	3	2012	2012	NUM
ma-64	434	4	)	)	PUNCT
ma-64	434	5	1239–1254	1239–1254	NUM
ma-64	434	6	.	.	PUNCT
ma-64	435	1	https://doi	https://doi	PROPN
ma-64	435	2	.	.	PUNCT
ma-64	435	3	org/10.1080/00207160.2012.688115.[45	org/10.1080/00207160.2012.688115.[45	PROPN
ma-64	435	4	]	]	PUNCT
ma-64	435	5	d.	d.	PROPN
ma-64	435	6	c.	c.	PROPN
ma-64	435	7	lesmana	lesmana	PROPN
ma-64	435	8	,	,	PUNCT
ma-64	435	9	s.	s.	PROPN
ma-64	435	10	wang	wang	PROPN
ma-64	435	11	,	,	PUNCT
ma-64	435	12	an	an	DET
ma-64	435	13	upwind	upwind	ADJ
ma-64	435	14	finite	finite	ADJ
ma-64	435	15	difference	difference	NOUN
ma-64	435	16	method	method	NOUN
ma-64	435	17	for	for	ADP
ma-64	435	18	a	a	DET
ma-64	435	19	nonlinear	nonlinear	ADJ
ma-64	435	20	black	black	ADJ
ma-64	435	21	-	-	PUNCT
ma-64	435	22	scholes	schole	NOUN
ma-64	435	23	equation	equation	NOUN
ma-64	435	24	governingeuropean	governingeuropean	NOUN
ma-64	435	25	option	option	NOUN
ma-64	435	26	valuation	valuation	NOUN
ma-64	435	27	under	under	ADP
ma-64	435	28	transaction	transaction	NOUN
ma-64	435	29	costs	cost	NOUN
ma-64	435	30	,	,	PUNCT
ma-64	435	31	appl	appl	PROPN
ma-64	435	32	.	.	PROPN
ma-64	435	33	math	math	NOUN
ma-64	435	34	.	.	PUNCT
ma-64	436	1	comput	comput	NOUN
ma-64	436	2	.	.	PUNCT
ma-64	437	1	219	219	NUM
ma-64	437	2	(	(	PUNCT
ma-64	437	3	2013	2013	NUM
ma-64	437	4	)	)	PUNCT
ma-64	437	5	8811–8828	8811–8828	NOUN
ma-64	437	6	.	.	PUNCT
ma-64	438	1	https://doi	https://doi	X
ma-64	438	2	.	.	PUNCT
ma-64	439	1	org/10.1016	org/10.1016	PROPN
ma-64	439	2	/	/	SYM
ma-64	439	3	j.amc.2012.12.077.[46	j.amc.2012.12.077.[46	PROPN
ma-64	439	4	]	]	PUNCT
ma-64	439	5	j.	j.	PROPN
ma-64	439	6	ankudinova	ankudinova	PROPN
ma-64	439	7	,	,	PUNCT
ma-64	439	8	m.	m.	NOUN
ma-64	439	9	ehrhardt	ehrhardt	PROPN
ma-64	439	10	,	,	PUNCT
ma-64	439	11	on	on	ADP
ma-64	439	12	the	the	DET
ma-64	439	13	numerical	numerical	ADJ
ma-64	439	14	solution	solution	NOUN
ma-64	439	15	of	of	ADP
ma-64	439	16	nonlinear	nonlinear	ADJ
ma-64	439	17	black	black	ADJ
ma-64	439	18	-	-	PUNCT
ma-64	439	19	scholes	schole	NOUN
ma-64	439	20	equations	equation	NOUN
ma-64	439	21	,	,	PUNCT
ma-64	439	22	comput	comput	NOUN
ma-64	439	23	.	.	PUNCT
ma-64	440	1	math	math	NOUN
ma-64	440	2	.	.	PUNCT
ma-64	441	1	withappl	withappl	NOUN
ma-64	441	2	.	.	PUNCT
ma-64	442	1	56	56	NUM
ma-64	442	2	(	(	PUNCT
ma-64	442	3	2008	2008	NUM
ma-64	442	4	)	)	PUNCT
ma-64	443	1	799–812	799–812	NUM
ma-64	443	2	.	.	PUNCT
ma-64	444	1	https://doi.org/10.1016/j.camwa.2008.02.005.[47	https://doi.org/10.1016/j.camwa.2008.02.005.[47	X
ma-64	444	2	]	]	X
ma-64	444	3	r.	r.	PROPN
ma-64	444	4	l.	l.	PROPN
ma-64	444	5	valkov	valkov	PROPN
ma-64	444	6	,	,	PUNCT
ma-64	444	7	fitted	fit	VERB
ma-64	444	8	strong	strong	ADJ
ma-64	444	9	stability	stability	NOUN
ma-64	444	10	-	-	PUNCT
ma-64	444	11	preserving	preserve	VERB
ma-64	444	12	schemes	scheme	NOUN
ma-64	444	13	for	for	ADP
ma-64	444	14	the	the	DET
ma-64	444	15	black	black	ADJ
ma-64	444	16	-	-	PUNCT
ma-64	444	17	scholes	schole	NOUN
ma-64	444	18	barenblatt	barenblatt	PROPN
ma-64	444	19	equation	equation	NOUN
ma-64	444	20	,	,	PUNCT
ma-64	444	21	int	int	NOUN
ma-64	444	22	.	.	PUNCT
ma-64	445	1	j.	j.	PROPN
ma-64	445	2	comput.math	comput.math	PROPN
ma-64	445	3	.	.	PUNCT
ma-64	446	1	92	92	NUM
ma-64	446	2	(	(	PUNCT
ma-64	446	3	2015	2015	NUM
ma-64	446	4	)	)	PUNCT
ma-64	446	5	2475–2497	2475–2497	NUM
ma-64	446	6	.	.	PUNCT
ma-64	447	1	https://doi.org/10.1080/00207160.2015.1069818.[48	https://doi.org/10.1080/00207160.2015.1069818.[48	PROPN
ma-64	447	2	]	]	X
ma-64	447	3	r.	r.	PROPN
ma-64	447	4	valkov	valkov	PROPN
ma-64	447	5	,	,	PUNCT
ma-64	447	6	predictor	predictor	NOUN
ma-64	447	7	-	-	PUNCT
ma-64	447	8	corrector	corrector	NOUN
ma-64	447	9	balance	balance	NOUN
ma-64	447	10	method	method	NOUN
ma-64	447	11	for	for	ADP
ma-64	447	12	the	the	DET
ma-64	447	13	worst	bad	ADJ
ma-64	447	14	-	-	PUNCT
ma-64	447	15	case	case	NOUN
ma-64	447	16	1d	1d	NUM
ma-64	447	17	option	option	NOUN
ma-64	447	18	pricing	pricing	NOUN
ma-64	447	19	,	,	PUNCT
ma-64	447	20	comput	comput	NOUN
ma-64	447	21	.	.	PUNCT
ma-64	448	1	methods	method	NOUN
ma-64	448	2	appl	appl	PROPN
ma-64	448	3	.	.	PUNCT
ma-64	449	1	math.16	math.16	PROPN
ma-64	449	2	(	(	PUNCT
ma-64	449	3	2016	2016	NUM
ma-64	449	4	)	)	PUNCT
ma-64	449	5	175–186	175–186	NUM
ma-64	449	6	.	.	PUNCT
ma-64	450	1	https://doi.org/10.1515/cmam-2015-0029.[49	https://doi.org/10.1515/cmam-2015-0029.[49	PROPN
ma-64	450	2	]	]	X
ma-64	450	3	p.	p.	NOUN
ma-64	450	4	heider	heider	NOUN
ma-64	450	5	,	,	PUNCT
ma-64	450	6	numerical	numerical	ADJ
ma-64	450	7	methods	method	NOUN
ma-64	450	8	for	for	ADP
ma-64	450	9	non	non	ADJ
ma-64	450	10	-	-	ADJ
ma-64	450	11	linear	linear	ADJ
ma-64	450	12	black	black	ADJ
ma-64	450	13	–	–	PUNCT
ma-64	450	14	scholes	schole	NOUN
ma-64	450	15	equations	equation	NOUN
ma-64	450	16	,	,	PUNCT
ma-64	450	17	appl	appl	PROPN
ma-64	450	18	.	.	PROPN
ma-64	450	19	math	math	PROPN
ma-64	450	20	.	.	PUNCT
ma-64	451	1	finance	finance	NOUN
ma-64	451	2	.	.	PUNCT
ma-64	452	1	17	17	NUM
ma-64	452	2	(	(	PUNCT
ma-64	452	3	2010	2010	NUM
ma-64	452	4	)	)	PUNCT
ma-64	452	5	59	59	NUM
ma-64	452	6	-	-	SYM
ma-64	452	7	81	81	NUM
ma-64	452	8	.	.	PUNCT
ma-64	453	1	https://doi.org/10.1080/13504860903075670.[50	https://doi.org/10.1080/13504860903075670.[50	PROPN
ma-64	453	2	]	]	PUNCT
ma-64	453	3	e.	e.	PROPN
ma-64	453	4	dremkova	dremkova	PROPN
ma-64	453	5	,	,	PUNCT
ma-64	453	6	m.	m.	NOUN
ma-64	453	7	ehrhardt	ehrhardt	PROPN
ma-64	453	8	,	,	PUNCT
ma-64	453	9	a	a	DET
ma-64	453	10	high	high	ADJ
ma-64	453	11	-	-	PUNCT
ma-64	453	12	order	order	NOUN
ma-64	453	13	compact	compact	ADJ
ma-64	453	14	method	method	NOUN
ma-64	453	15	for	for	ADP
ma-64	453	16	nonlinear	nonlinear	ADJ
ma-64	453	17	black	black	ADJ
ma-64	453	18	–	–	PUNCT
ma-64	453	19	scholes	schole	NOUN
ma-64	453	20	option	option	NOUN
ma-64	453	21	pricing	pricing	NOUN
ma-64	453	22	equationsof	equationsof	VERB
ma-64	453	23	american	american	ADJ
ma-64	453	24	options	option	NOUN
ma-64	453	25	,	,	PUNCT
ma-64	453	26	int	int	NOUN
ma-64	453	27	.	.	PUNCT
ma-64	454	1	j.	j.	PROPN
ma-64	454	2	comput	comput	PROPN
ma-64	454	3	.	.	PUNCT
ma-64	455	1	math	math	NOUN
ma-64	455	2	.	.	PUNCT
ma-64	456	1	88	88	NUM
ma-64	456	2	(	(	PUNCT
ma-64	456	3	2011	2011	NUM
ma-64	456	4	)	)	PUNCT
ma-64	456	5	2782	2782	NUM
ma-64	456	6	-	-	SYM
ma-64	456	7	2797	2797	NUM
ma-64	456	8	.	.	PUNCT
ma-64	457	1	https://doi.org/10.1080/00207160.2011	https://doi.org/10.1080/00207160.2011	X
ma-64	457	2	.	.	PUNCT
ma-64	458	1	558574.[51	558574.[51	NUM
ma-64	458	2	]	]	X
ma-64	458	3	n.	n.	NOUN
ma-64	458	4	ishimura	ishimura	PROPN
ma-64	458	5	,	,	PUNCT
ma-64	458	6	remarks	remark	NOUN
ma-64	458	7	on	on	ADP
ma-64	458	8	the	the	DET
ma-64	458	9	nonlinear	nonlinear	ADJ
ma-64	458	10	black	black	ADJ
ma-64	458	11	-	-	PUNCT
ma-64	458	12	scholes	schole	NOUN
ma-64	458	13	equations	equation	NOUN
ma-64	458	14	with	with	ADP
ma-64	458	15	the	the	DET
ma-64	458	16	effect	effect	NOUN
ma-64	458	17	of	of	ADP
ma-64	458	18	transaction	transaction	NOUN
ma-64	458	19	costs	cost	NOUN
ma-64	458	20	,	,	PUNCT
ma-64	458	21	asia	asia	PROPN
ma-64	458	22	-	-	PUNCT
ma-64	458	23	pac	pac	PROPN
ma-64	458	24	.	.	PROPN
ma-64	458	25	fin.mark	fin.mark	PROPN
ma-64	458	26	.	.	PUNCT
ma-64	459	1	17	17	NUM
ma-64	459	2	(	(	PUNCT
ma-64	459	3	2010	2010	NUM
ma-64	459	4	)	)	PUNCT
ma-64	459	5	241	241	NUM
ma-64	459	6	-	-	SYM
ma-64	459	7	259	259	NUM
ma-64	459	8	.	.	PUNCT
ma-64	460	1	https://doi.org/10.1007/s10690-010-9115-3.[52	https://doi.org/10.1007/s10690-010-9115-3.[52	NOUN
ma-64	460	2	]	]	PUNCT
ma-64	460	3	s.	s.	PROPN
ma-64	460	4	d.	d.	PROPN
ma-64	460	5	hodges	hodges	PROPN
ma-64	460	6	,	,	PUNCT
ma-64	460	7	a.	a.	NOUN
ma-64	460	8	neuberger	neuberger	NOUN
ma-64	460	9	,	,	PUNCT
ma-64	460	10	optimal	optimal	ADJ
ma-64	460	11	replication	replication	NOUN
ma-64	460	12	of	of	ADP
ma-64	460	13	contingent	contingent	ADJ
ma-64	460	14	claims	claim	NOUN
ma-64	460	15	under	under	ADP
ma-64	460	16	transactions	transaction	NOUN
ma-64	460	17	costs	cost	NOUN
ma-64	460	18	,	,	PUNCT
ma-64	460	19	rev	rev	PROPN
ma-64	460	20	.	.	PROPN
ma-64	460	21	futures	futures	PROPN
ma-64	460	22	mark.8	mark.8	PROPN
ma-64	460	23	(	(	PUNCT
ma-64	460	24	1989	1989	NUM
ma-64	460	25	)	)	PUNCT
ma-64	460	26	222–239.[53	222–239.[53	NOUN
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ma-64	460	28	m.	m.	NOUN
ma-64	460	29	kratka	kratka	PROPN
ma-64	460	30	,	,	PUNCT
ma-64	460	31	no	no	DET
ma-64	460	32	mystery	mystery	NOUN
ma-64	460	33	behind	behind	ADP
ma-64	460	34	the	the	DET
ma-64	460	35	smile	smile	NOUN
ma-64	460	36	.	.	PUNCT
ma-64	461	1	risk	risk	NOUN
ma-64	461	2	-	-	PUNCT
ma-64	461	3	london	london	NOUN
ma-64	461	4	-	-	PUNCT
ma-64	461	5	risk	risk	NOUN
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ma-64	461	7	limited	limit	VERB
ma-64	461	8	,	,	PUNCT
ma-64	461	9	11	11	NUM
ma-64	461	10	(	(	PUNCT
ma-64	461	11	1998	1998	NUM
ma-64	461	12	)	)	PUNCT
ma-64	461	13	67	67	NUM
ma-64	461	14	-	-	SYM
ma-64	461	15	71.[54	71.[54	PROPN
ma-64	461	16	]	]	X
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ma-64	461	19	,	,	PUNCT
ma-64	461	20	d.	d.	PROPN
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ma-64	461	22	,	,	PUNCT
ma-64	461	23	on	on	ADP
ma-64	461	24	the	the	DET
ma-64	461	25	risk	risk	NOUN
ma-64	461	26	-	-	PUNCT
ma-64	461	27	adjusted	adjust	VERB
ma-64	461	28	pricing	pricing	NOUN
ma-64	461	29	-	-	PUNCT
ma-64	461	30	methodology	methodology	NOUN
ma-64	461	31	-	-	PUNCT
ma-64	461	32	based	base	VERB
ma-64	461	33	valuation	valuation	NOUN
ma-64	461	34	of	of	ADP
ma-64	461	35	vanilla	vanilla	NOUN
ma-64	461	36	options	option	NOUN
ma-64	461	37	and	and	CCONJ
ma-64	461	38	expla	expla	NOUN
ma-64	461	39	-	-	PUNCT
ma-64	461	40	nation	nation	NOUN
ma-64	461	41	of	of	ADP
ma-64	461	42	the	the	DET
ma-64	461	43	volatility	volatility	NOUN
ma-64	461	44	smile	smile	NOUN
ma-64	461	45	,	,	PUNCT
ma-64	461	46	j.	j.	PROPN
ma-64	461	47	appl	appl	PROPN
ma-64	461	48	.	.	PROPN
ma-64	461	49	math	math	PROPN
ma-64	461	50	.	.	PUNCT
ma-64	462	1	2005	2005	NUM
ma-64	463	1	235–258	235–258	NUM
ma-64	463	2	.	.	PUNCT
ma-64	464	1	https://doi.org/10.1155/jam.2005.235.[55	https://doi.org/10.1155/jam.2005.235.[55	NOUN
ma-64	464	2	]	]	X
ma-64	464	3	k.	k.	PROPN
ma-64	464	4	a.	a.	PROPN
ma-64	464	5	hoffmann	hoffmann	PROPN
ma-64	464	6	,	,	PUNCT
ma-64	464	7	s.	s.	PROPN
ma-64	464	8	t.	t.	PROPN
ma-64	464	9	chiang	chiang	PROPN
ma-64	464	10	,	,	PUNCT
ma-64	464	11	computational	computational	ADJ
ma-64	464	12	fluid	fluid	ADJ
ma-64	464	13	dynamics	dynamic	NOUN
ma-64	464	14	volume	volume	NOUN
ma-64	464	15	i	i	PRON
ma-64	464	16	,	,	PUNCT
ma-64	464	17	engineering	engineer	VERB
ma-64	464	18	education	education	NOUN
ma-64	464	19	system	system	NOUN
ma-64	464	20	,	,	PUNCT
ma-64	464	21	2000.[56	2000.[56	NUM
ma-64	464	22	]	]	PUNCT
ma-64	464	23	w.	w.	PROPN
ma-64	464	24	malalasekera	malalasekera	PROPN
ma-64	464	25	,	,	PUNCT
ma-64	464	26	h.	h.	PROPN
ma-64	464	27	k.	k.	PROPN
ma-64	464	28	versteeg	versteeg	PROPN
ma-64	464	29	,	,	PUNCT
ma-64	464	30	an	an	DET
ma-64	464	31	introduction	introduction	NOUN
ma-64	464	32	to	to	ADP
ma-64	464	33	computational	computational	ADJ
ma-64	464	34	fluid	fluid	ADJ
ma-64	464	35	dynamics	dynamic	NOUN
ma-64	464	36	:	:	PUNCT
ma-64	464	37	the	the	DET
ma-64	464	38	finite	finite	PROPN
ma-64	464	39	volume	volume	NOUN
ma-64	464	40	method	method	NOUN
ma-64	464	41	,	,	PUNCT
ma-64	464	42	pearsoneducation	pearsoneducation	NOUN
ma-64	464	43	,	,	PUNCT
ma-64	464	44	2007	2007	NUM
ma-64	464	45	.	.	PUNCT
ma-64	465	1	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	465	2	https://www.jstor.org/stable/2245301	https://www.jstor.org/stable/2245301	NOUN
ma-64	466	1	https://doi.org/10.1111/j.1540-6261.1985.tb02383.x	https://doi.org/10.1111/j.1540-6261.1985.tb02383.x	PROPN
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ma-64	466	4	https://www.jstor.org/stable/54362	https://www.jstor.org/stable/54362	PROPN
ma-64	466	5	https://doi.org/10.1111/1467-9965.00034	https://doi.org/10.1111/1467-9965.00034	PROPN
ma-64	466	6	https://doi.org/10.1016/s0165-1889(03)00059-9	https://doi.org/10.1016/s0165-1889(03)00059-9	PROPN
ma-64	466	7	https://doi.org/10.1016/j.camwa.2008.02.010	https://doi.org/10.1016/j.camwa.2008.02.010	PROPN
ma-64	466	8	https://doi.org/10.1016/j.camwa.2008.02.010	https://doi.org/10.1016/j.camwa.2008.02.010	VERB
ma-64	466	9	https://doi.org/10.1007/s007800050046	https://doi.org/10.1007/s007800050046	NUM
ma-64	466	10	https://doi.org/10.1080/00207160.2012.688115	https://doi.org/10.1080/00207160.2012.688115	PROPN
ma-64	466	11	https://doi.org/10.1080/00207160.2012.688115	https://doi.org/10.1080/00207160.2012.688115	PROPN
ma-64	467	1	https://doi.org/10.1016/j.amc.2012.12.077	https://doi.org/10.1016/j.amc.2012.12.077	PROPN
ma-64	467	2	https://doi.org/10.1016/j.amc.2012.12.077	https://doi.org/10.1016/j.amc.2012.12.077	PROPN
ma-64	467	3	https://doi.org/10.1016/j.camwa.2008.02.005	https://doi.org/10.1016/j.camwa.2008.02.005	PROPN
ma-64	467	4	https://doi.org/10.1080/00207160.2015.1069818	https://doi.org/10.1080/00207160.2015.1069818	PROPN
ma-64	468	1	https://doi.org/10.1515/cmam-2015-0029	https://doi.org/10.1515/cmam-2015-0029	PROPN
ma-64	468	2	https://doi.org/10.1080/13504860903075670	https://doi.org/10.1080/13504860903075670	ADP
ma-64	468	3	https://doi.org/10.1080/00207160.2011.558574	https://doi.org/10.1080/00207160.2011.558574	PROPN
ma-64	468	4	https://doi.org/10.1080/00207160.2011.558574	https://doi.org/10.1080/00207160.2011.558574	PROPN
ma-64	468	5	https://doi.org/10.1007/s10690-010-9115-3	https://doi.org/10.1007/s10690-010-9115-3	NUM
ma-64	468	6	https://doi.org/10.1155/jam.2005.235	https://doi.org/10.1155/jam.2005.235	PROPN
ma-64	468	7	eur	eur	PROPN
ma-64	468	8	.	.	PUNCT
ma-64	469	1	j.	j.	PROPN
ma-64	469	2	math	math	PROPN
ma-64	469	3	.	.	PUNCT
ma-64	470	1	anal	anal	PROPN
ma-64	470	2	.	.	PUNCT
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ma-64	471	8	section	section	NOUN
ma-64	471	9	contains	contain	VERB
ma-64	471	10	the	the	DET
ma-64	471	11	supporting	support	VERB
ma-64	471	12	figures	figure	NOUN
ma-64	471	13	and	and	CCONJ
ma-64	471	14	tables	table	NOUN
ma-64	471	15	to	to	PART
ma-64	471	16	observe	observe	VERB
ma-64	471	17	the	the	DET
ma-64	471	18	accuracy	accuracy	NOUN
ma-64	471	19	of	of	ADP
ma-64	471	20	the	the	DET
ma-64	471	21	solutionmethodologies	solutionmethodologie	NOUN
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ma-64	472	1	figure	figure	VERB
ma-64	472	2	8.7	8.7	NUM
ma-64	472	3	.	.	PUNCT
ma-64	472	4	approximate	approximate	ADJ
ma-64	472	5	results	result	NOUN
ma-64	472	6	of	of	ADP
ma-64	472	7	equation	equation	NOUN
ma-64	472	8	(	(	PUNCT
ma-64	472	9	1	1	NUM
ma-64	472	10	)	)	PUNCT
ma-64	472	11	by	by	ADP
ma-64	472	12	using	use	VERB
ma-64	472	13	leland	leland	PROPN
ma-64	472	14	volatility	volatility	NOUN
ma-64	472	15	model	model	PROPN
ma-64	472	16	.	.	PUNCT
ma-64	473	1	figure	figure	VERB
ma-64	473	2	8.8	8.8	NUM
ma-64	473	3	.	.	PUNCT
ma-64	474	1	approximate	approximate	ADJ
ma-64	474	2	results	result	NOUN
ma-64	474	3	of	of	ADP
ma-64	474	4	equation	equation	NOUN
ma-64	474	5	(	(	PUNCT
ma-64	474	6	1	1	NUM
ma-64	474	7	)	)	PUNCT
ma-64	474	8	by	by	ADP
ma-64	474	9	using	use	VERB
ma-64	474	10	rapm	rapm	ADJ
ma-64	474	11	volatility	volatility	NOUN
ma-64	474	12	model	model	NOUN
ma-64	474	13	.	.	PUNCT
ma-64	475	1	https://doi.org/10.28924/ada/ma.2.9	https://doi.org/10.28924/ada/ma.2.9	PROPN
ma-64	475	2	eur	eur	PROPN
ma-64	475	3	.	.	PUNCT
ma-64	476	1	j.	j.	PROPN
ma-64	476	2	math	math	PROPN
ma-64	476	3	.	.	PUNCT
ma-64	477	1	anal	anal	PROPN
ma-64	477	2	.	.	PUNCT
ma-64	478	1	10.28924	10.28924	NUM
ma-64	478	2	/	/	SYM
ma-64	478	3	ada	ada	PROPN
ma-64	478	4	/	/	SYM
ma-64	478	5	ma.2.9	ma.2.9	PROPN
ma-64	478	6	19	19	NUM
ma-64	478	7	table	table	NOUN
ma-64	478	8	8.3	8.3	NUM
ma-64	478	9	.	.	PUNCT
ma-64	479	1	call	call	NOUN
ma-64	479	2	option	option	NOUN
ma-64	479	3	prices	price	NOUN
ma-64	479	4	using	use	VERB
ma-64	479	5	boyle	boyle	PROPN
ma-64	479	6	and	and	CCONJ
ma-64	479	7	vorst	vorst	PROPN
ma-64	479	8	volatility	volatility	NOUN
ma-64	479	9	model	model	NOUN
ma-64	479	10	.	.	PUNCT
ma-64	480	1	s0	s0	PROPN
ma-64	480	2	exact	exact	ADJ
ma-64	480	3	finite	finite	ADJ
ma-64	480	4	difference	difference	NOUN
ma-64	480	5	schemes	scheme	NOUN
ma-64	480	6	finite	finite	VERB
ma-64	480	7	volume	volume	NOUN
ma-64	480	8	schemes(linear	schemes(linear	PROPN
ma-64	480	9	)	)	PUNCT
ma-64	480	10	dffds	dffds	NOUN
ma-64	480	11	lfds	lfds	PROPN
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ma-64	480	13	fvfis	fvfi	VERB
ma-64	480	14	fvcns37.00	fvcns37.00	VERB
ma-64	480	15	0.00001	0.00001	NUM
ma-64	480	16	0.08130	0.08130	NUM
ma-64	480	17	0.08362	0.08362	NUM
ma-64	480	18	0.00000	0.00000	NUM
ma-64	481	1	0.00054	0.00054	NUM
ma-64	481	2	0.0005047.00	0.0005047.00	NOUN
ma-64	482	1	0.00182	0.00182	NUM
ma-64	482	2	0.44919	0.44919	NUM
ma-64	482	3	0.45475	0.45475	NUM
ma-64	482	4	0.00016	0.00016	NUM
ma-64	482	5	0.01340	0.01340	NUM
ma-64	482	6	0.0129757.00	0.0129757.00	NUM
ma-64	482	7	0.05078	0.05078	NUM
ma-64	482	8	1.43187	1.43187	NUM
ma-64	482	9	1.43827	1.43827	NUM
ma-64	482	10	0.00137	0.00137	NUM
ma-64	482	11	0.10771	0.10771	NUM
ma-64	482	12	0.1058867.00	0.1058867.00	NUM
ma-64	482	13	0.45226	0.45226	NUM
ma-64	482	14	3.52436	3.52436	NUM
ma-64	482	15	3.53389	3.53389	NUM
ma-64	482	16	0.00181	0.00181	NUM
ma-64	482	17	0.65191	0.65191	NUM
ma-64	482	18	0.6479577.00	0.6479577.00	NUM
ma-64	482	19	1.97686	1.97686	NUM
ma-64	482	20	6.88032	6.88032	NUM
ma-64	482	21	6.88512	6.88512	NUM
ma-64	482	22	-0.01095	-0.01095	NOUN
ma-64	483	1	2.26632	2.26632	NUM
ma-64	483	2	2.2623087.00	2.2623087.00	NUM
ma-64	483	3	5.46222	5.46222	NUM
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ma-64	483	5	11.53065	11.53065	NUM
ma-64	483	6	-0.03314	-0.03314	NOUN
ma-64	483	7	5.63768	5.63768	NUM
ma-64	483	8	5.6368897.00	5.6368897.00	NUM
ma-64	483	9	11.17037	11.17037	NUM
ma-64	483	10	17.36380	17.36380	NUM
ma-64	483	11	17.36252	17.36252	NUM
ma-64	483	12	1.18226	1.18226	NUM
ma-64	483	13	11.07370	11.07370	NUM
ma-64	483	14	11.07714107.00	11.07714107.00	NUM
ma-64	483	15	18.71972	18.71972	NUM
ma-64	483	16	24.30605	24.30605	NUM
ma-64	483	17	24.30805	24.30805	NUM
ma-64	483	18	14.49730	14.49730	NUM
ma-64	483	19	18.66210	18.66210	NUM
ma-64	483	20	18.66616117.00	18.66616117.00	NUM
ma-64	483	21	27.48006	27.48006	NUM
ma-64	483	22	32.07120	32.07120	NUM
ma-64	483	23	32.07189	32.07189	NUM
ma-64	483	24	26.66264	26.66264	NUM
ma-64	483	25	27.42028	27.42028	NUM
ma-64	483	26	27.42359127.00	27.42359127.00	NUM
ma-64	483	27	36.91158	36.91158	NUM
ma-64	483	28	40.41514	40.41514	NUM
ma-64	483	29	40.41449	40.41449	NUM
ma-64	483	30	37.98090	37.98090	NUM
ma-64	483	31	36.83405	36.83405	NUM
ma-64	483	32	36.83640137.00	36.83640137.00	NUM
ma-64	483	33	46.67034	46.67034	NUM
ma-64	483	34	49.26375	49.26375	NUM
ma-64	483	35	49.26507	49.26507	NUM
ma-64	483	36	47.25031	47.25031	NUM
ma-64	483	37	46.59745	46.59745	NUM
ma-64	483	38	46.59938147.00	46.59938147.00	NUM
ma-64	483	39	56.57397	56.57397	NUM
ma-64	483	40	58.41457	58.41457	NUM
ma-64	483	41	58.41649	58.41649	NUM
ma-64	483	42	56.80881	56.80881	NUM
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ma-64	483	50	66.46767167.00	66.46767167.00	NUM
ma-64	483	51	76.52370	76.52370	NUM
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ma-64	483	56	76.39940177.00	76.39940177.00	NUM
ma-64	483	57	86.51886	86.51886	NUM
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ma-64	483	61	86.40846	86.40846	NUM
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ma-64	483	63	96.51716	96.51716	NUM
ma-64	483	64	96.94695	96.94695	NUM
ma-64	483	65	96.94884	96.94884	NUM
ma-64	483	66	96.47214	96.47214	NUM
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ma-64	483	84	126.39087	126.39087	NUM
ma-64	483	85	126.37558	126.37558	NUM
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ma-64	483	89	136.53250	136.53250	NUM
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ma-64	483	93	146.51626	146.51626	NUM
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ma-64	483	97	146.52418	146.52418	NUM
ma-64	483	98	146.52596247.00	146.52596247.00	NUM
ma-64	483	99	156.51626	156.51626	NUM
ma-64	483	100	156.45839	156.45839	NUM
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ma-64	496	14	(	(	PUNCT
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ma-64	496	22	(	(	PUNCT
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ma-64	498	5	.	.	PUNCT
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ma-64	499	7	.	.	PUNCT
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ma-64	500	11	8	8	NUM
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ma-64	501	1	conclusion	conclusion	NOUN
ma-64	501	2	conflicts	conflict	NOUN
ma-64	501	3	of	of	ADP
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