id	sid	tid	token	lemma	pos
ejpam-3893	1	1	european	european	PROPN
ejpam-3893	1	2	journal	journal	PROPN
ejpam-3893	1	3	of	of	ADP
ejpam-3893	1	4	pure	pure	ADJ
ejpam-3893	1	5	and	and	CCONJ
ejpam-3893	1	6	applied	apply	VERB
ejpam-3893	1	7	mathematics	mathematic	NOUN
ejpam-3893	1	8	vol	vol	NOUN
ejpam-3893	1	9	.	.	PUNCT
ejpam-3893	2	1	14	14	NUM
ejpam-3893	2	2	,	,	PUNCT
ejpam-3893	2	3	no	no	INTJ
ejpam-3893	2	4	.	.	NOUN
ejpam-3893	2	5	3	3	NUM
ejpam-3893	2	6	,	,	PUNCT
ejpam-3893	2	7	2021	2021	NUM
ejpam-3893	2	8	,	,	PUNCT
ejpam-3893	2	9	706	706	NUM
ejpam-3893	2	10	-	-	SYM
ejpam-3893	2	11	722	722	NUM
ejpam-3893	2	12	issn	issn	PROPN
ejpam-3893	2	13	1307	1307	NUM
ejpam-3893	2	14	-	-	SYM
ejpam-3893	2	15	5543	5543	NUM
ejpam-3893	2	16	–	–	PUNCT
ejpam-3893	2	17	ejpam.com	ejpam.com	X
ejpam-3893	2	18	published	publish	VERB
ejpam-3893	2	19	by	by	ADP
ejpam-3893	2	20	new	new	PROPN
ejpam-3893	2	21	york	york	PROPN
ejpam-3893	2	22	business	business	PROPN
ejpam-3893	2	23	global	global	PROPN
ejpam-3893	2	24	a	a	DET
ejpam-3893	2	25	finite	finite	ADJ
ejpam-3893	2	26	difference	difference	NOUN
ejpam-3893	2	27	fictitious	fictitious	ADJ
ejpam-3893	2	28	domain	domain	NOUN
ejpam-3893	2	29	wavelet	wavelet	NOUN
ejpam-3893	2	30	method	method	NOUN
ejpam-3893	2	31	for	for	ADP
ejpam-3893	2	32	solving	solve	VERB
ejpam-3893	2	33	dirichlet	dirichlet	PROPN
ejpam-3893	2	34	boundary	boundary	ADJ
ejpam-3893	2	35	value	value	NOUN
ejpam-3893	2	36	problem	problem	NOUN
ejpam-3893	2	37	francis	francis	PROPN
ejpam-3893	2	38	ohene	ohene	PROPN
ejpam-3893	2	39	boateng1,∗	boateng1,∗	PROPN
ejpam-3893	2	40	,	,	PUNCT
ejpam-3893	2	41	joseph	joseph	PROPN
ejpam-3893	2	42	ackora	ackora	PROPN
ejpam-3893	2	43	-	-	PUNCT
ejpam-3893	2	44	prah2	prah2	PROPN
ejpam-3893	2	45	,	,	PUNCT
ejpam-3893	2	46	benedict	benedict	PROPN
ejpam-3893	2	47	barnes2	barnes2	PROPN
ejpam-3893	2	48	,	,	PUNCT
ejpam-3893	2	49	john	john	PROPN
ejpam-3893	2	50	amoah	amoah	PROPN
ejpam-3893	2	51	-	-	PUNCT
ejpam-3893	2	52	mensah3	mensah3	NOUN
ejpam-3893	2	53	1	1	NUM
ejpam-3893	2	54	department	department	NOUN
ejpam-3893	2	55	of	of	ADP
ejpam-3893	2	56	mathematics	mathematics	PROPN
ejpam-3893	2	57	education	education	NOUN
ejpam-3893	2	58	,	,	PUNCT
ejpam-3893	2	59	faculty	faculty	NOUN
ejpam-3893	2	60	of	of	ADP
ejpam-3893	2	61	applied	apply	VERB
ejpam-3893	2	62	sciences	science	NOUN
ejpam-3893	2	63	and	and	CCONJ
ejpam-3893	2	64	mathematics	mathematic	NOUN
ejpam-3893	2	65	education	education	NOUN
ejpam-3893	2	66	,	,	PUNCT
ejpam-3893	2	67	akenten	akenten	PROPN
ejpam-3893	2	68	appiah	appiah	PROPN
ejpam-3893	2	69	-	-	PUNCT
ejpam-3893	2	70	menka	menka	PROPN
ejpam-3893	2	71	university	university	PROPN
ejpam-3893	2	72	of	of	ADP
ejpam-3893	2	73	skills	skill	NOUN
ejpam-3893	2	74	training	training	NOUN
ejpam-3893	2	75	and	and	CCONJ
ejpam-3893	2	76	entrepreneurial	entrepreneurial	ADJ
ejpam-3893	2	77	development	development	NOUN
ejpam-3893	2	78	,	,	PUNCT
ejpam-3893	2	79	kumasi	kumasi	PROPN
ejpam-3893	2	80	,	,	PUNCT
ejpam-3893	2	81	ghana	ghana	PROPN
ejpam-3893	2	82	2	2	NUM
ejpam-3893	2	83	department	department	NOUN
ejpam-3893	2	84	of	of	ADP
ejpam-3893	2	85	mathematics	mathematic	NOUN
ejpam-3893	2	86	,	,	PUNCT
ejpam-3893	2	87	faculty	faculty	NOUN
ejpam-3893	2	88	of	of	ADP
ejpam-3893	2	89	physical	physical	ADJ
ejpam-3893	2	90	and	and	CCONJ
ejpam-3893	2	91	computational	computational	ADJ
ejpam-3893	2	92	sciences	science	NOUN
ejpam-3893	2	93	,	,	PUNCT
ejpam-3893	2	94	kwame	kwame	PROPN
ejpam-3893	2	95	nkrumah	nkrumah	PROPN
ejpam-3893	2	96	university	university	PROPN
ejpam-3893	2	97	of	of	ADP
ejpam-3893	2	98	science	science	NOUN
ejpam-3893	2	99	and	and	CCONJ
ejpam-3893	2	100	technology	technology	NOUN
ejpam-3893	2	101	,	,	PUNCT
ejpam-3893	2	102	kumasi	kumasi	PROPN
ejpam-3893	2	103	,	,	PUNCT
ejpam-3893	2	104	ghana	ghana	PROPN
ejpam-3893	2	105	3	3	NUM
ejpam-3893	2	106	department	department	PROPN
ejpam-3893	2	107	of	of	ADP
ejpam-3893	2	108	computer	computer	NOUN
ejpam-3893	2	109	science	science	NOUN
ejpam-3893	2	110	,	,	PUNCT
ejpam-3893	2	111	faculty	faculty	NOUN
ejpam-3893	2	112	of	of	ADP
ejpam-3893	2	113	physical	physical	ADJ
ejpam-3893	2	114	sciences	science	NOUN
ejpam-3893	2	115	,	,	PUNCT
ejpam-3893	2	116	sunyani	sunyani	PROPN
ejpam-3893	2	117	technical	technical	PROPN
ejpam-3893	2	118	university	university	PROPN
ejpam-3893	2	119	,	,	PUNCT
ejpam-3893	2	120	sunyani	sunyani	PROPN
ejpam-3893	2	121	,	,	PUNCT
ejpam-3893	2	122	ghana	ghana	PROPN
ejpam-3893	2	123	abstract	abstract	NOUN
ejpam-3893	2	124	.	.	PUNCT
ejpam-3893	3	1	in	in	ADP
ejpam-3893	3	2	this	this	DET
ejpam-3893	3	3	paper	paper	NOUN
ejpam-3893	3	4	,	,	PUNCT
ejpam-3893	3	5	we	we	PRON
ejpam-3893	3	6	introduce	introduce	VERB
ejpam-3893	3	7	a	a	DET
ejpam-3893	3	8	finite	finite	ADJ
ejpam-3893	3	9	difference	difference	NOUN
ejpam-3893	3	10	fictitious	fictitious	ADJ
ejpam-3893	3	11	domain	domain	NOUN
ejpam-3893	3	12	wavelet	wavelet	NOUN
ejpam-3893	3	13	method	method	NOUN
ejpam-3893	3	14	(	(	PUNCT
ejpam-3893	3	15	fdfdwm	fdfdwm	NOUN
ejpam-3893	3	16	)	)	PUNCT
ejpam-3893	3	17	for	for	ADP
ejpam-3893	3	18	solving	solve	VERB
ejpam-3893	3	19	two	two	NUM
ejpam-3893	3	20	dimensional	dimensional	ADJ
ejpam-3893	3	21	(	(	PUNCT
ejpam-3893	3	22	2d	2d	NOUN
ejpam-3893	3	23	)	)	PUNCT
ejpam-3893	3	24	linear	linear	PROPN
ejpam-3893	3	25	elliptic	elliptic	ADJ
ejpam-3893	3	26	partial	partial	ADJ
ejpam-3893	3	27	differential	differential	NOUN
ejpam-3893	3	28	equations	equation	NOUN
ejpam-3893	3	29	(	(	PUNCT
ejpam-3893	3	30	pdes	pde	NOUN
ejpam-3893	3	31	)	)	PUNCT
ejpam-3893	3	32	with	with	ADP
ejpam-3893	3	33	dirichlet	dirichlet	PROPN
ejpam-3893	3	34	boundary	boundary	ADJ
ejpam-3893	3	35	conditions	condition	NOUN
ejpam-3893	3	36	on	on	ADP
ejpam-3893	3	37	regular	regular	ADJ
ejpam-3893	3	38	geometric	geometric	ADJ
ejpam-3893	3	39	domain	domain	NOUN
ejpam-3893	3	40	.	.	PUNCT
ejpam-3893	4	1	the	the	DET
ejpam-3893	4	2	method	method	NOUN
ejpam-3893	4	3	reduces	reduce	VERB
ejpam-3893	4	4	the	the	DET
ejpam-3893	4	5	2d	2d	NUM
ejpam-3893	4	6	pde	pde	NOUN
ejpam-3893	4	7	into	into	ADP
ejpam-3893	4	8	a	a	DET
ejpam-3893	4	9	1d	1d	NUM
ejpam-3893	4	10	system	system	NOUN
ejpam-3893	4	11	of	of	ADP
ejpam-3893	4	12	ordinary	ordinary	ADJ
ejpam-3893	4	13	differential	differential	ADJ
ejpam-3893	4	14	equations	equation	NOUN
ejpam-3893	4	15	and	and	CCONJ
ejpam-3893	4	16	applies	apply	VERB
ejpam-3893	4	17	a	a	DET
ejpam-3893	4	18	compactly	compactly	ADV
ejpam-3893	4	19	supported	support	VERB
ejpam-3893	4	20	wavelet	wavelet	NOUN
ejpam-3893	4	21	to	to	PART
ejpam-3893	4	22	approximate	approximate	VERB
ejpam-3893	4	23	the	the	DET
ejpam-3893	4	24	solution	solution	NOUN
ejpam-3893	4	25	.	.	PUNCT
ejpam-3893	5	1	the	the	DET
ejpam-3893	5	2	problem	problem	NOUN
ejpam-3893	5	3	is	be	AUX
ejpam-3893	5	4	embedded	embed	VERB
ejpam-3893	5	5	in	in	ADP
ejpam-3893	5	6	a	a	DET
ejpam-3893	5	7	fictitious	fictitious	ADJ
ejpam-3893	5	8	domain	domain	NOUN
ejpam-3893	5	9	to	to	PART
ejpam-3893	5	10	aid	aid	VERB
ejpam-3893	5	11	the	the	DET
ejpam-3893	5	12	enforcement	enforcement	NOUN
ejpam-3893	5	13	of	of	ADP
ejpam-3893	5	14	the	the	DET
ejpam-3893	5	15	dirichlet	dirichlet	PROPN
ejpam-3893	5	16	boundary	boundary	PROPN
ejpam-3893	5	17	conditions	condition	NOUN
ejpam-3893	5	18	.	.	PUNCT
ejpam-3893	6	1	we	we	PRON
ejpam-3893	6	2	present	present	VERB
ejpam-3893	6	3	numerical	numerical	ADJ
ejpam-3893	6	4	analysis	analysis	NOUN
ejpam-3893	6	5	and	and	CCONJ
ejpam-3893	6	6	show	show	VERB
ejpam-3893	6	7	that	that	SCONJ
ejpam-3893	6	8	our	our	PRON
ejpam-3893	6	9	method	method	NOUN
ejpam-3893	6	10	yields	yield	VERB
ejpam-3893	6	11	better	well	ADJ
ejpam-3893	6	12	approximation	approximation	NOUN
ejpam-3893	6	13	to	to	ADP
ejpam-3893	6	14	the	the	DET
ejpam-3893	6	15	solution	solution	NOUN
ejpam-3893	6	16	of	of	ADP
ejpam-3893	6	17	the	the	DET
ejpam-3893	6	18	dirichlet	dirichlet	PROPN
ejpam-3893	6	19	problem	problem	NOUN
ejpam-3893	6	20	than	than	ADP
ejpam-3893	6	21	traditional	traditional	ADJ
ejpam-3893	6	22	methods	method	NOUN
ejpam-3893	6	23	like	like	ADP
ejpam-3893	6	24	the	the	DET
ejpam-3893	6	25	finite	finite	ADJ
ejpam-3893	6	26	element	element	NOUN
ejpam-3893	6	27	and	and	CCONJ
ejpam-3893	6	28	finite	finite	ADJ
ejpam-3893	6	29	difference	difference	NOUN
ejpam-3893	6	30	methods	method	NOUN
ejpam-3893	6	31	.	.	PUNCT
ejpam-3893	7	1	2020	2020	NUM
ejpam-3893	7	2	mathematics	mathematic	NOUN
ejpam-3893	7	3	subject	subject	NOUN
ejpam-3893	7	4	classifications	classification	NOUN
ejpam-3893	7	5	:	:	PUNCT
ejpam-3893	7	6	65n06	65n06	NUM
ejpam-3893	7	7	,	,	PUNCT
ejpam-3893	7	8	65n30	65n30	NUM
ejpam-3893	7	9	,	,	PUNCT
ejpam-3893	7	10	65n85	65n85	DET
ejpam-3893	7	11	key	key	ADJ
ejpam-3893	7	12	words	word	NOUN
ejpam-3893	7	13	and	and	CCONJ
ejpam-3893	7	14	phrases	phrase	NOUN
ejpam-3893	7	15	:	:	PUNCT
ejpam-3893	7	16	fictitious	fictitious	ADJ
ejpam-3893	7	17	domain	domain	NOUN
ejpam-3893	7	18	,	,	PUNCT
ejpam-3893	7	19	dirichlet	dirichlet	PROPN
ejpam-3893	7	20	problem	problem	NOUN
ejpam-3893	7	21	,	,	PUNCT
ejpam-3893	7	22	wavelet	wavelet	NOUN
ejpam-3893	7	23	,	,	PUNCT
ejpam-3893	7	24	finite	finite	ADJ
ejpam-3893	7	25	difference	difference	NOUN
ejpam-3893	7	26	,	,	PUNCT
ejpam-3893	7	27	finite	finite	PROPN
ejpam-3893	7	28	element	element	NOUN
ejpam-3893	7	29	1	1	NUM
ejpam-3893	7	30	.	.	PUNCT
ejpam-3893	7	31	introduction	introduction	NOUN
ejpam-3893	7	32	the	the	DET
ejpam-3893	7	33	dirichlet	dirichlet	PROPN
ejpam-3893	7	34	problem	problem	NOUN
ejpam-3893	7	35	(	(	PUNCT
ejpam-3893	7	36	dp	dp	NOUN
ejpam-3893	7	37	)	)	PUNCT
ejpam-3893	7	38	for	for	ADP
ejpam-3893	7	39	linear	linear	PROPN
ejpam-3893	7	40	elliptic	elliptic	ADJ
ejpam-3893	7	41	pde	pde	NOUN
ejpam-3893	7	42	in	in	ADP
ejpam-3893	7	43	2d	2d	PROPN
ejpam-3893	7	44	is	be	AUX
ejpam-3893	7	45	found	find	VERB
ejpam-3893	7	46	in	in	ADP
ejpam-3893	7	47	many	many	ADJ
ejpam-3893	7	48	physical	physical	ADJ
ejpam-3893	7	49	problems	problem	NOUN
ejpam-3893	7	50	that	that	PRON
ejpam-3893	7	51	are	be	AUX
ejpam-3893	7	52	governed	govern	VERB
ejpam-3893	7	53	by	by	ADP
ejpam-3893	7	54	partial	partial	ADJ
ejpam-3893	7	55	differential	differential	ADJ
ejpam-3893	7	56	equations	equation	NOUN
ejpam-3893	7	57	.	.	PUNCT
ejpam-3893	8	1	these	these	DET
ejpam-3893	8	2	physical	physical	ADJ
ejpam-3893	8	3	problems	problem	NOUN
ejpam-3893	8	4	include	include	VERB
ejpam-3893	8	5	vibration	vibration	NOUN
ejpam-3893	8	6	of	of	ADP
ejpam-3893	8	7	solids	solid	NOUN
ejpam-3893	8	8	,	,	PUNCT
ejpam-3893	8	9	flow	flow	NOUN
ejpam-3893	8	10	of	of	ADP
ejpam-3893	8	11	fluids	fluid	NOUN
ejpam-3893	8	12	,	,	PUNCT
ejpam-3893	8	13	diffusion	diffusion	NOUN
ejpam-3893	8	14	of	of	ADP
ejpam-3893	8	15	chemicals	chemical	NOUN
ejpam-3893	8	16	,	,	PUNCT
ejpam-3893	8	17	spread	spread	NOUN
ejpam-3893	8	18	of	of	ADP
ejpam-3893	8	19	heat	heat	NOUN
ejpam-3893	8	20	,	,	PUNCT
ejpam-3893	8	21	structure	structure	NOUN
ejpam-3893	8	22	of	of	ADP
ejpam-3893	8	23	molecules	molecule	NOUN
ejpam-3893	8	24	,	,	PUNCT
ejpam-3893	8	25	propagation	propagation	NOUN
ejpam-3893	8	26	of	of	ADP
ejpam-3893	8	27	waves	wave	NOUN
ejpam-3893	8	28	,	,	PUNCT
ejpam-3893	8	29	laser	laser	NOUN
ejpam-3893	8	30	beam	beam	NOUN
ejpam-3893	8	31	models	model	NOUN
ejpam-3893	8	32	,	,	PUNCT
ejpam-3893	8	33	financial	financial	ADJ
ejpam-3893	8	34	models	model	NOUN
ejpam-3893	8	35	,	,	PUNCT
ejpam-3893	8	36	etc	etc	X
ejpam-3893	9	1	[	[	X
ejpam-3893	9	2	14	14	NUM
ejpam-3893	9	3	]	]	PUNCT
ejpam-3893	9	4	.	.	PUNCT
ejpam-3893	10	1	due	due	ADP
ejpam-3893	10	2	to	to	ADP
ejpam-3893	10	3	the	the	DET
ejpam-3893	10	4	significance	significance	NOUN
ejpam-3893	10	5	of	of	ADP
ejpam-3893	10	6	the	the	DET
ejpam-3893	10	7	dp	dp	NOUN
ejpam-3893	10	8	in	in	ADP
ejpam-3893	10	9	the	the	DET
ejpam-3893	10	10	field	field	NOUN
ejpam-3893	10	11	of	of	ADP
ejpam-3893	10	12	engineering	engineering	NOUN
ejpam-3893	10	13	and	and	CCONJ
ejpam-3893	10	14	the	the	DET
ejpam-3893	10	15	sciences	science	NOUN
ejpam-3893	10	16	,	,	PUNCT
ejpam-3893	10	17	researchers	researcher	NOUN
ejpam-3893	10	18	have	have	AUX
ejpam-3893	10	19	done	do	VERB
ejpam-3893	10	20	a	a	DET
ejpam-3893	10	21	lot	lot	NOUN
ejpam-3893	10	22	of	of	ADP
ejpam-3893	10	23	work	work	NOUN
ejpam-3893	10	24	into	into	ADP
ejpam-3893	10	25	improving	improve	VERB
ejpam-3893	10	26	the	the	DET
ejpam-3893	10	27	solution	solution	NOUN
ejpam-3893	10	28	methods	method	NOUN
ejpam-3893	10	29	,	,	PUNCT
ejpam-3893	10	30	both	both	PRON
ejpam-3893	10	31	analytically	analytically	ADV
ejpam-3893	10	32	and	and	CCONJ
ejpam-3893	10	33	numerically	numerically	ADV
ejpam-3893	10	34	∗corresponding	∗corresponde	VERB
ejpam-3893	10	35	author	author	NOUN
ejpam-3893	10	36	.	.	PUNCT
ejpam-3893	11	1	doi	doi	NOUN
ejpam-3893	11	2	:	:	PUNCT
ejpam-3893	11	3	https://doi.org/10.29020/nybg.ejpam.v14i3.3893	https://doi.org/10.29020/nybg.ejpam.v14i3.3893	ADJ
ejpam-3893	11	4	email	email	NOUN
ejpam-3893	11	5	addresses	address	VERB
ejpam-3893	11	6	:	:	PUNCT
ejpam-3893	12	1	fanbotgh@yahoo.com	fanbotgh@yahoo.com	X
ejpam-3893	12	2	,	,	PUNCT
ejpam-3893	12	3	foboateng@uew.edu.gh	foboateng@uew.edu.gh	PROPN
ejpam-3893	12	4	(	(	PUNCT
ejpam-3893	12	5	f.	f.	PROPN
ejpam-3893	12	6	o.	o.	PROPN
ejpam-3893	12	7	boateng	boateng	PROPN
ejpam-3893	12	8	)	)	PUNCT
ejpam-3893	12	9	,	,	PUNCT
ejpam-3893	12	10	jaackora-prah.cos@knust.edu.gh	jaackora-prah.cos@knust.edu.gh	NUM
ejpam-3893	12	11	(	(	PUNCT
ejpam-3893	12	12	j.	j.	PROPN
ejpam-3893	12	13	ackora	ackora	PROPN
ejpam-3893	12	14	-	-	PUNCT
ejpam-3893	12	15	prah	prah	PROPN
ejpam-3893	12	16	)	)	PUNCT
ejpam-3893	12	17	,	,	PUNCT
ejpam-3893	12	18	ewiekwamina@gmail.com	ewiekwamina@gmail.com	X
ejpam-3893	12	19	(	(	PUNCT
ejpam-3893	12	20	b.	b.	PROPN
ejpam-3893	12	21	barnes),amoahmensahjohn@gmail.com	barnes),amoahmensahjohn@gmail.com	X
ejpam-3893	12	22	(	(	PUNCT
ejpam-3893	12	23	j.	j.	PROPN
ejpam-3893	12	24	amoah	amoah	PROPN
ejpam-3893	12	25	-	-	PUNCT
ejpam-3893	12	26	mensah	mensah	PROPN
ejpam-3893	12	27	)	)	PUNCT
ejpam-3893	12	28	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3893	13	1	706	706	NUM
ejpam-3893	14	1	©	©	PROPN
ejpam-3893	14	2	2021	2021	NUM
ejpam-3893	14	3	ejpam	ejpam	VERB
ejpam-3893	14	4	all	all	DET
ejpam-3893	14	5	rights	right	NOUN
ejpam-3893	14	6	reserved	reserve	VERB
ejpam-3893	14	7	.	.	PUNCT
ejpam-3893	15	1	f.	f.	PROPN
ejpam-3893	15	2	o.	o.	PROPN
ejpam-3893	15	3	boateng	boateng	PROPN
ejpam-3893	15	4	et	et	PROPN
ejpam-3893	15	5	al	al	PROPN
ejpam-3893	15	6	.	.	PUNCT
ejpam-3893	15	7	/	/	SYM
ejpam-3893	15	8	eur	eur	PROPN
ejpam-3893	15	9	.	.	PUNCT
ejpam-3893	16	1	j.	j.	PROPN
ejpam-3893	16	2	pure	pure	PROPN
ejpam-3893	16	3	appl	appl	PROPN
ejpam-3893	16	4	.	.	PROPN
ejpam-3893	16	5	math	math	PROPN
ejpam-3893	16	6	,	,	PUNCT
ejpam-3893	16	7	14	14	NUM
ejpam-3893	16	8	(	(	PUNCT
ejpam-3893	16	9	3	3	NUM
ejpam-3893	16	10	)	)	PUNCT
ejpam-3893	16	11	(	(	PUNCT
ejpam-3893	16	12	2021	2021	NUM
ejpam-3893	16	13	)	)	PUNCT
ejpam-3893	16	14	,	,	PUNCT
ejpam-3893	16	15	706	706	NUM
ejpam-3893	16	16	-	-	SYM
ejpam-3893	16	17	722	722	NUM
ejpam-3893	16	18	707	707	NUM
ejpam-3893	16	19	[	[	X
ejpam-3893	16	20	1	1	NUM
ejpam-3893	16	21	,	,	PUNCT
ejpam-3893	16	22	7	7	NUM
ejpam-3893	16	23	,	,	PUNCT
ejpam-3893	16	24	13	13	NUM
ejpam-3893	16	25	]	]	PUNCT
ejpam-3893	16	26	.	.	PUNCT
ejpam-3893	17	1	however	however	ADV
ejpam-3893	17	2	,	,	PUNCT
ejpam-3893	17	3	challenges	challenge	NOUN
ejpam-3893	17	4	including	include	VERB
ejpam-3893	17	5	difficulty	difficulty	NOUN
ejpam-3893	17	6	in	in	ADP
ejpam-3893	17	7	evaluating	evaluate	VERB
ejpam-3893	17	8	integrals	integral	NOUN
ejpam-3893	17	9	analytically	analytically	ADV
ejpam-3893	17	10	,	,	PUNCT
ejpam-3893	17	11	approximation	approximation	NOUN
ejpam-3893	17	12	based	base	VERB
ejpam-3893	17	13	on	on	ADP
ejpam-3893	17	14	truncation	truncation	NOUN
ejpam-3893	17	15	of	of	ADP
ejpam-3893	17	16	infinite	infinite	ADJ
ejpam-3893	17	17	series	series	NOUN
ejpam-3893	17	18	required	require	VERB
ejpam-3893	17	19	,	,	PUNCT
ejpam-3893	17	20	inappropriate	inappropriate	ADJ
ejpam-3893	17	21	solution	solution	NOUN
ejpam-3893	17	22	space	space	NOUN
ejpam-3893	17	23	and	and	CCONJ
ejpam-3893	17	24	many	many	ADJ
ejpam-3893	17	25	more	more	ADJ
ejpam-3893	17	26	,	,	PUNCT
ejpam-3893	17	27	militate	militate	ADJ
ejpam-3893	17	28	against	against	ADP
ejpam-3893	17	29	analytical	analytical	ADJ
ejpam-3893	17	30	approaches	approach	NOUN
ejpam-3893	17	31	.	.	PUNCT
ejpam-3893	18	1	in	in	ADP
ejpam-3893	18	2	particular	particular	ADJ
ejpam-3893	18	3	,	,	PUNCT
ejpam-3893	18	4	dp	dp	NOUN
ejpam-3893	18	5	for	for	ADP
ejpam-3893	18	6	linear	linear	PROPN
ejpam-3893	18	7	elliptic	elliptic	ADJ
ejpam-3893	18	8	pde	pde	NOUN
ejpam-3893	18	9	in	in	ADP
ejpam-3893	18	10	2d	2d	NOUN
ejpam-3893	18	11	,	,	PUNCT
ejpam-3893	18	12	in	in	ADP
ejpam-3893	18	13	functional	functional	ADJ
ejpam-3893	18	14	space	space	NOUN
ejpam-3893	18	15	may	may	AUX
ejpam-3893	18	16	not	not	PART
ejpam-3893	18	17	have	have	VERB
ejpam-3893	18	18	analytic	analytic	ADJ
ejpam-3893	18	19	solution	solution	NOUN
ejpam-3893	18	20	and	and	CCONJ
ejpam-3893	18	21	so	so	ADV
ejpam-3893	18	22	the	the	DET
ejpam-3893	18	23	solution	solution	NOUN
ejpam-3893	18	24	needs	need	VERB
ejpam-3893	18	25	to	to	PART
ejpam-3893	18	26	be	be	AUX
ejpam-3893	18	27	approximated	approximate	VERB
ejpam-3893	18	28	numerically	numerically	ADV
ejpam-3893	18	29	[	[	X
ejpam-3893	18	30	15	15	NUM
ejpam-3893	18	31	]	]	PUNCT
ejpam-3893	18	32	.	.	PUNCT
ejpam-3893	19	1	with	with	ADP
ejpam-3893	19	2	the	the	DET
ejpam-3893	19	3	availability	availability	NOUN
ejpam-3893	19	4	of	of	ADP
ejpam-3893	19	5	powerful	powerful	ADJ
ejpam-3893	19	6	computers	computer	NOUN
ejpam-3893	19	7	,	,	PUNCT
ejpam-3893	19	8	the	the	DET
ejpam-3893	19	9	emphasis	emphasis	NOUN
ejpam-3893	19	10	on	on	ADP
ejpam-3893	19	11	solving	solve	VERB
ejpam-3893	19	12	dirichlet	dirichlet	PROPN
ejpam-3893	19	13	problem	problem	NOUN
ejpam-3893	19	14	in	in	ADP
ejpam-3893	19	15	2d	2d	NUM
ejpam-3893	19	16	is	be	AUX
ejpam-3893	19	17	gradually	gradually	ADV
ejpam-3893	19	18	shifting	shift	VERB
ejpam-3893	19	19	away	away	ADV
ejpam-3893	19	20	from	from	ADP
ejpam-3893	19	21	the	the	DET
ejpam-3893	19	22	analytical	analytical	ADJ
ejpam-3893	19	23	method	method	NOUN
ejpam-3893	19	24	of	of	ADP
ejpam-3893	19	25	solutions	solution	NOUN
ejpam-3893	19	26	towards	towards	ADP
ejpam-3893	19	27	numerical	numerical	ADJ
ejpam-3893	19	28	computations	computation	NOUN
ejpam-3893	19	29	and	and	CCONJ
ejpam-3893	19	30	analysis	analysis	NOUN
ejpam-3893	19	31	[	[	X
ejpam-3893	19	32	14	14	NUM
ejpam-3893	19	33	]	]	SYM
ejpam-3893	19	34	.	.	PUNCT
ejpam-3893	20	1	numerical	numerical	ADJ
ejpam-3893	20	2	methods	method	NOUN
ejpam-3893	20	3	do	do	AUX
ejpam-3893	20	4	not	not	PART
ejpam-3893	20	5	involve	involve	VERB
ejpam-3893	20	6	the	the	DET
ejpam-3893	20	7	search	search	NOUN
ejpam-3893	20	8	for	for	ADP
ejpam-3893	20	9	an	an	DET
ejpam-3893	20	10	explicit	explicit	ADJ
ejpam-3893	20	11	or	or	CCONJ
ejpam-3893	20	12	implicit	implicit	ADJ
ejpam-3893	20	13	function	function	NOUN
ejpam-3893	20	14	that	that	PRON
ejpam-3893	20	15	describes	describe	VERB
ejpam-3893	20	16	the	the	DET
ejpam-3893	20	17	dirichlet	dirichlet	PROPN
ejpam-3893	20	18	problem	problem	NOUN
ejpam-3893	20	19	.	.	PUNCT
ejpam-3893	21	1	they	they	PRON
ejpam-3893	21	2	largely	largely	ADV
ejpam-3893	21	3	utilize	utilize	VERB
ejpam-3893	21	4	discretization	discretization	NOUN
ejpam-3893	21	5	techniques	technique	NOUN
ejpam-3893	21	6	to	to	PART
ejpam-3893	21	7	reduce	reduce	VERB
ejpam-3893	21	8	the	the	DET
ejpam-3893	21	9	continuous	continuous	ADJ
ejpam-3893	21	10	linear	linear	ADJ
ejpam-3893	21	11	elliptic	elliptic	ADJ
ejpam-3893	21	12	pde	pde	NOUN
ejpam-3893	21	13	and	and	CCONJ
ejpam-3893	21	14	dirichlet	dirichlet	PROPN
ejpam-3893	21	15	boundary	boundary	ADJ
ejpam-3893	21	16	conditions	condition	NOUN
ejpam-3893	21	17	to	to	PART
ejpam-3893	21	18	discrete	discrete	VERB
ejpam-3893	21	19	system	system	NOUN
ejpam-3893	21	20	that	that	PRON
ejpam-3893	21	21	are	be	AUX
ejpam-3893	21	22	suitable	suitable	ADJ
ejpam-3893	21	23	for	for	ADP
ejpam-3893	21	24	high	high	ADJ
ejpam-3893	21	25	speed	speed	NOUN
ejpam-3893	21	26	computer	computer	NOUN
ejpam-3893	21	27	solution	solution	NOUN
ejpam-3893	21	28	.	.	PUNCT
ejpam-3893	22	1	these	these	DET
ejpam-3893	22	2	methods	method	NOUN
ejpam-3893	22	3	are	be	AUX
ejpam-3893	22	4	known	know	VERB
ejpam-3893	22	5	to	to	PART
ejpam-3893	22	6	generate	generate	VERB
ejpam-3893	22	7	approximate	approximate	ADJ
ejpam-3893	22	8	solutions	solution	NOUN
ejpam-3893	22	9	.	.	PUNCT
ejpam-3893	23	1	the	the	DET
ejpam-3893	23	2	finite	finite	PROPN
ejpam-3893	23	3	difference	difference	NOUN
ejpam-3893	23	4	method	method	NOUN
ejpam-3893	23	5	(	(	PUNCT
ejpam-3893	23	6	fdm	fdm	NOUN
ejpam-3893	23	7	)	)	PUNCT
ejpam-3893	23	8	and	and	CCONJ
ejpam-3893	23	9	finite	finite	ADJ
ejpam-3893	23	10	element	element	NOUN
ejpam-3893	23	11	method	method	NOUN
ejpam-3893	23	12	(	(	PUNCT
ejpam-3893	23	13	fem	fem	NOUN
ejpam-3893	23	14	)	)	PUNCT
ejpam-3893	23	15	are	be	AUX
ejpam-3893	23	16	some	some	PRON
ejpam-3893	23	17	of	of	ADP
ejpam-3893	23	18	the	the	DET
ejpam-3893	23	19	traditional	traditional	ADJ
ejpam-3893	23	20	methods	method	NOUN
ejpam-3893	23	21	used	use	VERB
ejpam-3893	23	22	to	to	PART
ejpam-3893	23	23	solve	solve	VERB
ejpam-3893	23	24	this	this	DET
ejpam-3893	23	25	problem	problem	NOUN
ejpam-3893	23	26	.	.	PUNCT
ejpam-3893	24	1	numerical	numerical	ADJ
ejpam-3893	24	2	methods	method	NOUN
ejpam-3893	24	3	that	that	PRON
ejpam-3893	24	4	will	will	AUX
ejpam-3893	24	5	produce	produce	VERB
ejpam-3893	24	6	high	high	ADJ
ejpam-3893	24	7	accurate	accurate	ADJ
ejpam-3893	24	8	,	,	PUNCT
ejpam-3893	24	9	fast	fast	ADJ
ejpam-3893	24	10	convergent	convergent	NOUN
ejpam-3893	24	11	and	and	CCONJ
ejpam-3893	24	12	stable	stable	ADJ
ejpam-3893	24	13	solution	solution	NOUN
ejpam-3893	24	14	to	to	ADP
ejpam-3893	24	15	the	the	DET
ejpam-3893	24	16	dirichlet	dirichlet	PROPN
ejpam-3893	24	17	problem	problem	NOUN
ejpam-3893	24	18	in	in	ADP
ejpam-3893	24	19	2d	2d	NUM
ejpam-3893	24	20	than	than	ADP
ejpam-3893	24	21	the	the	DET
ejpam-3893	24	22	traditional	traditional	ADJ
ejpam-3893	24	23	methods	method	NOUN
ejpam-3893	24	24	is	be	AUX
ejpam-3893	24	25	paramount	paramount	ADJ
ejpam-3893	24	26	.	.	PUNCT
ejpam-3893	25	1	besides	besides	SCONJ
ejpam-3893	25	2	,	,	PUNCT
ejpam-3893	25	3	the	the	DET
ejpam-3893	25	4	method	method	NOUN
ejpam-3893	25	5	must	must	AUX
ejpam-3893	25	6	also	also	ADV
ejpam-3893	25	7	reduce	reduce	VERB
ejpam-3893	25	8	the	the	DET
ejpam-3893	25	9	complexity	complexity	NOUN
ejpam-3893	25	10	in	in	ADP
ejpam-3893	25	11	obtaining	obtain	VERB
ejpam-3893	25	12	the	the	DET
ejpam-3893	25	13	solution	solution	NOUN
ejpam-3893	25	14	to	to	ADP
ejpam-3893	25	15	this	this	DET
ejpam-3893	25	16	problem	problem	NOUN
ejpam-3893	25	17	.	.	PUNCT
ejpam-3893	26	1	in	in	ADP
ejpam-3893	26	2	recent	recent	ADJ
ejpam-3893	26	3	times	time	NOUN
ejpam-3893	26	4	,	,	PUNCT
ejpam-3893	26	5	wavelet	wavelet	NOUN
ejpam-3893	26	6	methods	method	NOUN
ejpam-3893	26	7	are	be	AUX
ejpam-3893	26	8	known	know	VERB
ejpam-3893	26	9	to	to	PART
ejpam-3893	26	10	be	be	AUX
ejpam-3893	26	11	effective	effective	ADJ
ejpam-3893	26	12	and	and	CCONJ
ejpam-3893	26	13	efficient	efficient	ADJ
ejpam-3893	26	14	methods	method	NOUN
ejpam-3893	26	15	for	for	ADP
ejpam-3893	26	16	solving	solve	VERB
ejpam-3893	26	17	dirichlet	dirichlet	PROPN
ejpam-3893	26	18	problem	problem	NOUN
ejpam-3893	26	19	for	for	ADP
ejpam-3893	26	20	linear	linear	PROPN
ejpam-3893	26	21	elliptic	elliptic	ADJ
ejpam-3893	26	22	pdes	pde	NOUN
ejpam-3893	26	23	in	in	ADP
ejpam-3893	26	24	2d	2d	NUM
ejpam-3893	26	25	[	[	X
ejpam-3893	26	26	10	10	NUM
ejpam-3893	26	27	,	,	PUNCT
ejpam-3893	26	28	12	12	NUM
ejpam-3893	26	29	]	]	PUNCT
ejpam-3893	26	30	.	.	PUNCT
ejpam-3893	27	1	in	in	ADP
ejpam-3893	27	2	wavelet	wavelet	NOUN
ejpam-3893	27	3	methods	method	NOUN
ejpam-3893	27	4	,	,	PUNCT
ejpam-3893	27	5	we	we	PRON
ejpam-3893	27	6	are	be	AUX
ejpam-3893	27	7	able	able	ADJ
ejpam-3893	27	8	to	to	PART
ejpam-3893	27	9	obtain	obtain	VERB
ejpam-3893	27	10	information	information	NOUN
ejpam-3893	27	11	in	in	ADP
ejpam-3893	27	12	both	both	CCONJ
ejpam-3893	27	13	frequency	frequency	NOUN
ejpam-3893	27	14	and	and	CCONJ
ejpam-3893	27	15	time	time	NOUN
ejpam-3893	27	16	domains	domain	NOUN
ejpam-3893	27	17	,	,	PUNCT
ejpam-3893	27	18	including	include	VERB
ejpam-3893	27	19	boundary	boundary	ADJ
ejpam-3893	27	20	information	information	NOUN
ejpam-3893	27	21	of	of	ADP
ejpam-3893	27	22	the	the	DET
ejpam-3893	27	23	pde	pde	NOUN
ejpam-3893	27	24	equation	equation	NOUN
ejpam-3893	27	25	.	.	PUNCT
ejpam-3893	28	1	undoubtedly	undoubtedly	ADV
ejpam-3893	28	2	,	,	PUNCT
ejpam-3893	28	3	the	the	DET
ejpam-3893	28	4	vanishing	vanish	VERB
ejpam-3893	28	5	moment	moment	NOUN
ejpam-3893	28	6	property	property	NOUN
ejpam-3893	28	7	of	of	ADP
ejpam-3893	28	8	wavelet	wavelet	NOUN
ejpam-3893	28	9	enables	enable	VERB
ejpam-3893	28	10	the	the	DET
ejpam-3893	28	11	wavelet	wavelet	NOUN
ejpam-3893	28	12	series	series	PROPN
ejpam-3893	28	13	solution	solution	NOUN
ejpam-3893	28	14	to	to	PART
ejpam-3893	28	15	converge	converge	VERB
ejpam-3893	28	16	rapidly	rapidly	ADV
ejpam-3893	28	17	to	to	ADP
ejpam-3893	28	18	a	a	DET
ejpam-3893	28	19	point	point	NOUN
ejpam-3893	28	20	in	in	ADP
ejpam-3893	28	21	the	the	DET
ejpam-3893	28	22	domain	domain	NOUN
ejpam-3893	28	23	as	as	ADP
ejpam-3893	28	24	compared	compare	VERB
ejpam-3893	28	25	to	to	ADP
ejpam-3893	28	26	the	the	DET
ejpam-3893	28	27	afore	afore	NOUN
ejpam-3893	28	28	mentioned	mention	VERB
ejpam-3893	28	29	traditional	traditional	ADJ
ejpam-3893	28	30	numerical	numerical	ADJ
ejpam-3893	28	31	methods	method	NOUN
ejpam-3893	28	32	for	for	ADP
ejpam-3893	28	33	solving	solve	VERB
ejpam-3893	28	34	the	the	DET
ejpam-3893	28	35	dirichlet	dirichlet	PROPN
ejpam-3893	28	36	problem	problem	NOUN
ejpam-3893	28	37	for	for	ADP
ejpam-3893	28	38	linear	linear	PROPN
ejpam-3893	28	39	elliptic	elliptic	ADJ
ejpam-3893	28	40	pde	pde	NOUN
ejpam-3893	28	41	in	in	ADP
ejpam-3893	28	42	2d	2d	NOUN
ejpam-3893	28	43	.	.	PUNCT
ejpam-3893	29	1	2	2	X
ejpam-3893	29	2	.	.	X
ejpam-3893	29	3	the	the	DET
ejpam-3893	29	4	fdfdwm	fdfdwm	NOUN
ejpam-3893	29	5	in	in	ADP
ejpam-3893	29	6	this	this	DET
ejpam-3893	29	7	paper	paper	NOUN
ejpam-3893	29	8	,	,	PUNCT
ejpam-3893	29	9	we	we	PRON
ejpam-3893	29	10	introduce	introduce	VERB
ejpam-3893	29	11	the	the	DET
ejpam-3893	29	12	fdfdwm	fdfdwm	NOUN
ejpam-3893	29	13	as	as	ADP
ejpam-3893	29	14	a	a	DET
ejpam-3893	29	15	numerical	numerical	ADJ
ejpam-3893	29	16	approach	approach	NOUN
ejpam-3893	29	17	to	to	ADP
ejpam-3893	29	18	solving	solve	VERB
ejpam-3893	29	19	the	the	DET
ejpam-3893	29	20	dirichlet	dirichlet	PROPN
ejpam-3893	29	21	problem	problem	NOUN
ejpam-3893	29	22	for	for	ADP
ejpam-3893	29	23	linear	linear	PROPN
ejpam-3893	29	24	elliptic	elliptic	ADJ
ejpam-3893	29	25	pde	pde	NOUN
ejpam-3893	29	26	in	in	ADP
ejpam-3893	29	27	2d	2d	NUM
ejpam-3893	29	28	on	on	ADP
ejpam-3893	29	29	a	a	DET
ejpam-3893	29	30	regular	regular	ADJ
ejpam-3893	29	31	geometric	geometric	ADJ
ejpam-3893	29	32	domain	domain	NOUN
ejpam-3893	29	33	.	.	PUNCT
ejpam-3893	30	1	this	this	DET
ejpam-3893	30	2	method	method	NOUN
ejpam-3893	30	3	aims	aim	VERB
ejpam-3893	30	4	at	at	ADP
ejpam-3893	30	5	providing	provide	VERB
ejpam-3893	30	6	approximate	approximate	ADJ
ejpam-3893	30	7	solution	solution	NOUN
ejpam-3893	30	8	to	to	ADP
ejpam-3893	30	9	the	the	DET
ejpam-3893	30	10	dp	dp	NOUN
ejpam-3893	30	11	,	,	PUNCT
ejpam-3893	30	12	that	that	PRON
ejpam-3893	30	13	is	be	AUX
ejpam-3893	30	14	better	well	ADJ
ejpam-3893	30	15	in	in	ADP
ejpam-3893	30	16	terms	term	NOUN
ejpam-3893	30	17	of	of	ADP
ejpam-3893	30	18	accuracy	accuracy	NOUN
ejpam-3893	30	19	and	and	CCONJ
ejpam-3893	30	20	rate	rate	NOUN
ejpam-3893	30	21	of	of	ADP
ejpam-3893	30	22	convergence	convergence	NOUN
ejpam-3893	30	23	than	than	ADP
ejpam-3893	30	24	that	that	PRON
ejpam-3893	30	25	of	of	ADP
ejpam-3893	30	26	the	the	DET
ejpam-3893	30	27	traditional	traditional	ADJ
ejpam-3893	30	28	methods	method	NOUN
ejpam-3893	30	29	mentioned	mention	VERB
ejpam-3893	30	30	.	.	PUNCT
ejpam-3893	31	1	it	it	PRON
ejpam-3893	31	2	employs	employ	VERB
ejpam-3893	31	3	daubechies	daubechie	NOUN
ejpam-3893	31	4	scaling	scale	VERB
ejpam-3893	31	5	functions	function	NOUN
ejpam-3893	31	6	with	with	ADP
ejpam-3893	31	7	a	a	DET
ejpam-3893	31	8	fictitious	fictitious	ADJ
ejpam-3893	31	9	domain	domain	NOUN
ejpam-3893	31	10	approach	approach	NOUN
ejpam-3893	31	11	.	.	PUNCT
ejpam-3893	32	1	daubechies	daubechie	NOUN
ejpam-3893	32	2	wavelet	wavelet	PROPN
ejpam-3893	32	3	function	function	NOUN
ejpam-3893	32	4	of	of	ADP
ejpam-3893	32	5	order	order	NOUN
ejpam-3893	32	6	n	n	PRON
ejpam-3893	32	7	has	have	VERB
ejpam-3893	32	8	the	the	DET
ejpam-3893	32	9	largest	large	ADJ
ejpam-3893	32	10	number	number	NOUN
ejpam-3893	32	11	of	of	ADP
ejpam-3893	32	12	vanishing	vanish	VERB
ejpam-3893	32	13	moments	moment	NOUN
ejpam-3893	32	14	which	which	PRON
ejpam-3893	32	15	are	be	AUX
ejpam-3893	32	16	compactly	compactly	ADV
ejpam-3893	32	17	supported	support	VERB
ejpam-3893	32	18	on	on	ADP
ejpam-3893	32	19	[	[	X
ejpam-3893	32	20	0	0	NUM
ejpam-3893	32	21	,	,	PUNCT
ejpam-3893	32	22	2n	2n	NUM
ejpam-3893	32	23	−	−	ADP
ejpam-3893	32	24	1	1	NUM
ejpam-3893	32	25	]	]	PUNCT
ejpam-3893	32	26	.	.	PUNCT
ejpam-3893	33	1	moreover	moreover	ADV
ejpam-3893	33	2	,	,	PUNCT
ejpam-3893	33	3	the	the	DET
ejpam-3893	33	4	high	high	ADJ
ejpam-3893	33	5	number	number	NOUN
ejpam-3893	33	6	of	of	ADP
ejpam-3893	33	7	vanishing	vanish	VERB
ejpam-3893	33	8	moments	moment	NOUN
ejpam-3893	33	9	lead	lead	VERB
ejpam-3893	33	10	to	to	ADP
ejpam-3893	33	11	high	high	ADJ
ejpam-3893	33	12	compressibility	compressibility	NOUN
ejpam-3893	33	13	of	of	ADP
ejpam-3893	33	14	orthonormal	orthonormal	ADJ
ejpam-3893	33	15	solution	solution	NOUN
ejpam-3893	33	16	in	in	ADP
ejpam-3893	33	17	ω	ω	PROPN
ejpam-3893	33	18	⊂	⊂	PROPN
ejpam-3893	33	19	h.	h.	PROPN
ejpam-3893	34	1	the	the	DET
ejpam-3893	34	2	use	use	NOUN
ejpam-3893	34	3	of	of	ADP
ejpam-3893	34	4	the	the	DET
ejpam-3893	34	5	daubechies	daubechie	NOUN
ejpam-3893	34	6	scaling	scale	VERB
ejpam-3893	34	7	function	function	NOUN
ejpam-3893	34	8	offers	offer	VERB
ejpam-3893	34	9	the	the	DET
ejpam-3893	34	10	fdfdwm	fdfdwm	NOUN
ejpam-3893	34	11	the	the	DET
ejpam-3893	34	12	flexibility	flexibility	NOUN
ejpam-3893	34	13	to	to	PART
ejpam-3893	34	14	obtain	obtain	VERB
ejpam-3893	34	15	a	a	DET
ejpam-3893	34	16	more	more	ADV
ejpam-3893	34	17	accurate	accurate	ADJ
ejpam-3893	34	18	and	and	CCONJ
ejpam-3893	34	19	stable	stable	ADJ
ejpam-3893	34	20	solution	solution	NOUN
ejpam-3893	34	21	to	to	ADP
ejpam-3893	34	22	the	the	DET
ejpam-3893	34	23	problem	problem	NOUN
ejpam-3893	34	24	at	at	ADP
ejpam-3893	34	25	hand	hand	NOUN
ejpam-3893	34	26	in	in	ADP
ejpam-3893	34	27	a	a	DET
ejpam-3893	34	28	functional	functional	ADJ
ejpam-3893	34	29	space	space	NOUN
ejpam-3893	34	30	[	[	X
ejpam-3893	34	31	2	2	NUM
ejpam-3893	34	32	]	]	PUNCT
ejpam-3893	34	33	.	.	PUNCT
ejpam-3893	35	1	the	the	DET
ejpam-3893	35	2	fictitious	fictitious	ADJ
ejpam-3893	35	3	domain	domain	NOUN
ejpam-3893	35	4	approach	approach	NOUN
ejpam-3893	35	5	of	of	ADP
ejpam-3893	35	6	the	the	DET
ejpam-3893	35	7	fdfdwm	fdfdwm	NOUN
ejpam-3893	35	8	also	also	ADV
ejpam-3893	35	9	makes	make	VERB
ejpam-3893	35	10	it	it	PRON
ejpam-3893	35	11	easier	easy	ADJ
ejpam-3893	35	12	to	to	PART
ejpam-3893	35	13	deal	deal	VERB
ejpam-3893	35	14	with	with	ADP
ejpam-3893	35	15	the	the	DET
ejpam-3893	35	16	dirichlet	dirichlet	PROPN
ejpam-3893	35	17	boundary	boundary	PROPN
ejpam-3893	35	18	condition	condition	NOUN
ejpam-3893	35	19	.	.	PUNCT
ejpam-3893	36	1	notably	notably	ADV
ejpam-3893	36	2	,	,	PUNCT
ejpam-3893	36	3	the	the	DET
ejpam-3893	36	4	fdfdwm	fdfdwm	NOUN
ejpam-3893	36	5	reduces	reduce	VERB
ejpam-3893	36	6	the	the	DET
ejpam-3893	36	7	linear	linear	ADJ
ejpam-3893	36	8	elliptic	elliptic	ADJ
ejpam-3893	36	9	pde	pde	NOUN
ejpam-3893	36	10	in	in	ADP
ejpam-3893	36	11	two	two	NUM
ejpam-3893	36	12	dimensional	dimensional	ADJ
ejpam-3893	36	13	coordinates	coordinate	NOUN
ejpam-3893	36	14	into	into	ADP
ejpam-3893	36	15	a	a	DET
ejpam-3893	36	16	system	system	NOUN
ejpam-3893	36	17	of	of	ADP
ejpam-3893	36	18	one	one	NUM
ejpam-3893	36	19	dimensional	dimensional	ADJ
ejpam-3893	36	20	ordinary	ordinary	ADJ
ejpam-3893	36	21	differential	differential	ADJ
ejpam-3893	36	22	equations	equation	NOUN
ejpam-3893	36	23	.	.	PUNCT
ejpam-3893	37	1	this	this	DET
ejpam-3893	37	2	approach	approach	NOUN
ejpam-3893	37	3	reduces	reduce	VERB
ejpam-3893	37	4	considerably	considerably	ADV
ejpam-3893	37	5	the	the	DET
ejpam-3893	37	6	complexities	complexity	NOUN
ejpam-3893	37	7	involved	involve	VERB
ejpam-3893	37	8	in	in	ADP
ejpam-3893	37	9	the	the	DET
ejpam-3893	37	10	solution	solution	NOUN
ejpam-3893	37	11	process	process	NOUN
ejpam-3893	37	12	,	,	PUNCT
ejpam-3893	37	13	hence	hence	ADV
ejpam-3893	37	14	reduces	reduce	VERB
ejpam-3893	37	15	the	the	DET
ejpam-3893	37	16	computational	computational	ADJ
ejpam-3893	37	17	cost	cost	NOUN
ejpam-3893	37	18	.	.	PUNCT
ejpam-3893	38	1	now	now	ADV
ejpam-3893	38	2	,	,	PUNCT
ejpam-3893	38	3	we	we	PRON
ejpam-3893	38	4	give	give	VERB
ejpam-3893	38	5	the	the	DET
ejpam-3893	38	6	outline	outline	NOUN
ejpam-3893	38	7	of	of	ADP
ejpam-3893	38	8	the	the	DET
ejpam-3893	38	9	fdfdwm	fdfdwm	NOUN
ejpam-3893	38	10	for	for	ADP
ejpam-3893	38	11	solving	solve	VERB
ejpam-3893	38	12	the	the	DET
ejpam-3893	38	13	dirichlet	dirichlet	PROPN
ejpam-3893	38	14	problem	problem	NOUN
ejpam-3893	38	15	on	on	ADP
ejpam-3893	38	16	regular	regular	ADJ
ejpam-3893	38	17	domains	domain	NOUN
ejpam-3893	38	18	.	.	PUNCT
ejpam-3893	39	1	we	we	PRON
ejpam-3893	39	2	consider	consider	VERB
ejpam-3893	39	3	the	the	DET
ejpam-3893	39	4	case	case	NOUN
ejpam-3893	39	5	of	of	ADP
ejpam-3893	39	6	a	a	DET
ejpam-3893	39	7	rectangular	rectangular	ADJ
ejpam-3893	39	8	domain	domain	NOUN
ejpam-3893	39	9	.	.	PUNCT
ejpam-3893	40	1	thus	thus	ADV
ejpam-3893	40	2	;	;	PUNCT
ejpam-3893	40	3	•	•	ADP
ejpam-3893	40	4	the	the	DET
ejpam-3893	40	5	dirichlet	dirichlet	PROPN
ejpam-3893	40	6	problem	problem	NOUN
ejpam-3893	40	7	is	be	AUX
ejpam-3893	40	8	defined	define	VERB
ejpam-3893	40	9	on	on	ADP
ejpam-3893	40	10	an	an	DET
ejpam-3893	40	11	open	open	ADJ
ejpam-3893	40	12	domain	domain	NOUN
ejpam-3893	40	13	with	with	ADP
ejpam-3893	40	14	a	a	DET
ejpam-3893	40	15	rectangular	rectangular	ADJ
ejpam-3893	40	16	boundary	boundary	NOUN
ejpam-3893	40	17	.	.	PUNCT
ejpam-3893	41	1	f.	f.	PROPN
ejpam-3893	41	2	o.	o.	PROPN
ejpam-3893	41	3	boateng	boateng	PROPN
ejpam-3893	41	4	et	et	PROPN
ejpam-3893	41	5	al	al	PROPN
ejpam-3893	41	6	.	.	PUNCT
ejpam-3893	41	7	/	/	SYM
ejpam-3893	41	8	eur	eur	PROPN
ejpam-3893	41	9	.	.	PUNCT
ejpam-3893	42	1	j.	j.	PROPN
ejpam-3893	42	2	pure	pure	PROPN
ejpam-3893	42	3	appl	appl	PROPN
ejpam-3893	42	4	.	.	PROPN
ejpam-3893	42	5	math	math	PROPN
ejpam-3893	42	6	,	,	PUNCT
ejpam-3893	42	7	14	14	NUM
ejpam-3893	42	8	(	(	PUNCT
ejpam-3893	42	9	3	3	NUM
ejpam-3893	42	10	)	)	PUNCT
ejpam-3893	42	11	(	(	PUNCT
ejpam-3893	42	12	2021	2021	NUM
ejpam-3893	42	13	)	)	PUNCT
ejpam-3893	42	14	,	,	PUNCT
ejpam-3893	42	15	706	706	NUM
ejpam-3893	42	16	-	-	SYM
ejpam-3893	42	17	722	722	NUM
ejpam-3893	42	18	708	708	NUM
ejpam-3893	42	19	•	•	NOUN
ejpam-3893	42	20	the	the	DET
ejpam-3893	42	21	two	two	NUM
ejpam-3893	42	22	dimensional	dimensional	ADJ
ejpam-3893	42	23	problem	problem	NOUN
ejpam-3893	42	24	is	be	AUX
ejpam-3893	42	25	reduced	reduce	VERB
ejpam-3893	42	26	to	to	ADP
ejpam-3893	42	27	a	a	DET
ejpam-3893	42	28	one	one	NUM
ejpam-3893	42	29	dimensional	dimensional	ADJ
ejpam-3893	42	30	problem	problem	NOUN
ejpam-3893	42	31	by	by	ADP
ejpam-3893	42	32	discretizing	discretize	VERB
ejpam-3893	42	33	along	along	ADP
ejpam-3893	42	34	one	one	NUM
ejpam-3893	42	35	of	of	ADP
ejpam-3893	42	36	the	the	DET
ejpam-3893	42	37	variables	variable	NOUN
ejpam-3893	42	38	(	(	PUNCT
ejpam-3893	42	39	y−coordinate	y−coordinate	X
ejpam-3893	42	40	or	or	CCONJ
ejpam-3893	42	41	x−coordinate	x−coordinate	NUM
ejpam-3893	42	42	)	)	PUNCT
ejpam-3893	42	43	using	use	VERB
ejpam-3893	42	44	difference	difference	NOUN
ejpam-3893	42	45	quotient	quotient	NOUN
ejpam-3893	42	46	and	and	CCONJ
ejpam-3893	42	47	leaving	leave	VERB
ejpam-3893	42	48	the	the	DET
ejpam-3893	42	49	other	other	ADJ
ejpam-3893	42	50	variable	variable	NOUN
ejpam-3893	42	51	undiscretized	undiscretized	ADJ
ejpam-3893	42	52	.	.	PUNCT
ejpam-3893	43	1	•	•	NUM
ejpam-3893	43	2	the	the	DET
ejpam-3893	43	3	original	original	ADJ
ejpam-3893	43	4	domain	domain	NOUN
ejpam-3893	43	5	of	of	ADP
ejpam-3893	43	6	the	the	DET
ejpam-3893	43	7	problem	problem	NOUN
ejpam-3893	43	8	is	be	AUX
ejpam-3893	43	9	embedded	embed	VERB
ejpam-3893	43	10	in	in	ADP
ejpam-3893	43	11	a	a	DET
ejpam-3893	43	12	slightly	slightly	ADV
ejpam-3893	43	13	larger	large	ADJ
ejpam-3893	43	14	but	but	CCONJ
ejpam-3893	43	15	simple	simple	ADJ
ejpam-3893	43	16	domain	domain	NOUN
ejpam-3893	43	17	,	,	PUNCT
ejpam-3893	43	18	in	in	ADP
ejpam-3893	43	19	this	this	DET
ejpam-3893	43	20	case	case	NOUN
ejpam-3893	43	21	a	a	DET
ejpam-3893	43	22	rectangular	rectangular	ADJ
ejpam-3893	43	23	domain	domain	NOUN
ejpam-3893	43	24	.	.	PUNCT
ejpam-3893	44	1	this	this	DET
ejpam-3893	44	2	extended	extended	ADJ
ejpam-3893	44	3	domain	domain	NOUN
ejpam-3893	44	4	is	be	AUX
ejpam-3893	44	5	termed	term	VERB
ejpam-3893	44	6	as	as	ADP
ejpam-3893	44	7	a	a	DET
ejpam-3893	44	8	fictitious	fictitious	ADJ
ejpam-3893	44	9	domain	domain	NOUN
ejpam-3893	44	10	.	.	PUNCT
ejpam-3893	45	1	•	•	NUM
ejpam-3893	45	2	the	the	DET
ejpam-3893	45	3	one	one	NUM
ejpam-3893	45	4	dimensional	dimensional	ADJ
ejpam-3893	45	5	problem	problem	NOUN
ejpam-3893	45	6	is	be	AUX
ejpam-3893	45	7	formulated	formulate	VERB
ejpam-3893	45	8	as	as	ADP
ejpam-3893	45	9	a	a	DET
ejpam-3893	45	10	variational	variational	ADJ
ejpam-3893	45	11	problem	problem	NOUN
ejpam-3893	45	12	in	in	ADP
ejpam-3893	45	13	the	the	DET
ejpam-3893	45	14	fictitious	fictitious	ADJ
ejpam-3893	45	15	domain	domain	NOUN
ejpam-3893	45	16	.	.	PUNCT
ejpam-3893	46	1	•	•	NUM
ejpam-3893	46	2	a	a	DET
ejpam-3893	46	3	compactly	compactly	ADV
ejpam-3893	46	4	supported	support	VERB
ejpam-3893	46	5	wavelet	wavelet	NOUN
ejpam-3893	46	6	,	,	PUNCT
ejpam-3893	46	7	in	in	ADP
ejpam-3893	46	8	this	this	DET
ejpam-3893	46	9	case	case	NOUN
ejpam-3893	46	10	daubechies	daubechie	NOUN
ejpam-3893	46	11	wavelet	wavelet	NOUN
ejpam-3893	46	12	is	be	AUX
ejpam-3893	46	13	used	use	VERB
ejpam-3893	46	14	for	for	ADP
ejpam-3893	46	15	the	the	DET
ejpam-3893	46	16	numerical	numerical	ADJ
ejpam-3893	46	17	approximation	approximation	NOUN
ejpam-3893	46	18	in	in	ADP
ejpam-3893	46	19	the	the	DET
ejpam-3893	46	20	larger	large	ADJ
ejpam-3893	46	21	domain	domain	NOUN
ejpam-3893	46	22	.	.	PUNCT
ejpam-3893	47	1	•	•	NUM
ejpam-3893	47	2	the	the	DET
ejpam-3893	47	3	resultant	resultant	NOUN
ejpam-3893	47	4	linear	linear	ADJ
ejpam-3893	47	5	system	system	NOUN
ejpam-3893	47	6	in	in	ADP
ejpam-3893	47	7	the	the	DET
ejpam-3893	47	8	large	large	ADJ
ejpam-3893	47	9	domain	domain	NOUN
ejpam-3893	47	10	is	be	AUX
ejpam-3893	47	11	then	then	ADV
ejpam-3893	47	12	solved	solve	VERB
ejpam-3893	47	13	.	.	PUNCT
ejpam-3893	48	1	we	we	PRON
ejpam-3893	48	2	consider	consider	VERB
ejpam-3893	48	3	a	a	DET
ejpam-3893	48	4	general	general	ADJ
ejpam-3893	48	5	linear	linear	ADJ
ejpam-3893	48	6	second	second	ADJ
ejpam-3893	48	7	order	order	NOUN
ejpam-3893	48	8	elliptic	elliptic	ADJ
ejpam-3893	48	9	equation	equation	NOUN
ejpam-3893	48	10	of	of	ADP
ejpam-3893	48	11	the	the	DET
ejpam-3893	48	12	form	form	NOUN
ejpam-3893	48	13	−	−	PROPN
ejpam-3893	49	1	n∑	n∑	NOUN
ejpam-3893	50	1	i	i	PROPN
ejpam-3893	50	2	,	,	PUNCT
ejpam-3893	50	3	j=1	j=1	PROPN
ejpam-3893	50	4	∂	∂	NUM
ejpam-3893	50	5	∂xj	∂xj	NOUN
ejpam-3893	50	6	(	(	PUNCT
ejpam-3893	50	7	aij(x	aij(x	PROPN
ejpam-3893	50	8	)	)	PUNCT
ejpam-3893	50	9	∂φ	∂φ	PROPN
ejpam-3893	50	10	∂xi	∂xi	PROPN
ejpam-3893	50	11	)	)	PUNCT
ejpam-3893	51	1	+	+	NUM
ejpam-3893	51	2	n∑	n∑	X
ejpam-3893	51	3	i=1	i=1	PROPN
ejpam-3893	51	4	bi(x	bi(x	PUNCT
ejpam-3893	51	5	)	)	PUNCT
ejpam-3893	52	1	∂φ	∂φ	PROPN
ejpam-3893	52	2	∂xi	∂xi	PROPN
ejpam-3893	52	3	+	+	CCONJ
ejpam-3893	52	4	c(x)φ	c(x)φ	PROPN
ejpam-3893	52	5	=	=	SYM
ejpam-3893	52	6	f(x	f(x	PROPN
ejpam-3893	52	7	)	)	PUNCT
ejpam-3893	52	8	,	,	PUNCT
ejpam-3893	52	9	x	x	PUNCT
ejpam-3893	52	10	∈	∈	PROPN
ejpam-3893	52	11	ω	ω	X
ejpam-3893	52	12	(	(	PUNCT
ejpam-3893	52	13	1	1	NUM
ejpam-3893	52	14	)	)	PUNCT
ejpam-3893	52	15	where	where	SCONJ
ejpam-3893	52	16	the	the	DET
ejpam-3893	52	17	coefficient	coefficient	NOUN
ejpam-3893	52	18	aij	aij	PROPN
ejpam-3893	52	19	,	,	PUNCT
ejpam-3893	52	20	bi	bi	PROPN
ejpam-3893	52	21	,	,	PUNCT
ejpam-3893	52	22	c	c	PROPN
ejpam-3893	52	23	and	and	CCONJ
ejpam-3893	52	24	f	f	PROPN
ejpam-3893	52	25	satisfy	satisfy	VERB
ejpam-3893	52	26	the	the	DET
ejpam-3893	52	27	following	follow	VERB
ejpam-3893	52	28	conditions	condition	NOUN
ejpam-3893	52	29	:	:	PUNCT
ejpam-3893	52	30	aij	aij	PROPN
ejpam-3893	52	31	∈	∈	PROPN
ejpam-3893	52	32	c1(ω̄	c1(ω̄	NUM
ejpam-3893	52	33	)	)	PUNCT
ejpam-3893	52	34	,	,	PUNCT
ejpam-3893	52	35	i	i	PRON
ejpam-3893	52	36	,	,	PUNCT
ejpam-3893	52	37	j	j	PROPN
ejpam-3893	52	38	=	=	SYM
ejpam-3893	52	39	1	1	NUM
ejpam-3893	52	40	,	,	PUNCT
ejpam-3893	52	41	.	.	PUNCT
ejpam-3893	52	42	.	.	PUNCT
ejpam-3893	52	43	.	.	PUNCT
ejpam-3893	53	1	,	,	PUNCT
ejpam-3893	53	2	n	n	CCONJ
ejpam-3893	53	3	;	;	PUNCT
ejpam-3893	53	4	bi	bi	PROPN
ejpam-3893	53	5	∈	∈	PROPN
ejpam-3893	53	6	c(ω̄	c(ω̄	PROPN
ejpam-3893	53	7	)	)	PUNCT
ejpam-3893	53	8	,	,	PUNCT
ejpam-3893	53	9	i	i	NOUN
ejpam-3893	53	10	=	=	NOUN
ejpam-3893	53	11	1	1	NUM
ejpam-3893	53	12	,	,	PUNCT
ejpam-3893	53	13	.	.	PUNCT
ejpam-3893	53	14	.	.	PUNCT
ejpam-3893	54	1	.	.	PUNCT
ejpam-3893	55	1	,	,	PUNCT
ejpam-3893	55	2	n	n	CCONJ
ejpam-3893	55	3	;	;	PUNCT
ejpam-3893	55	4	c	c	PROPN
ejpam-3893	55	5	∈	∈	PROPN
ejpam-3893	55	6	c(ω̄	c(ω̄	PROPN
ejpam-3893	55	7	)	)	PUNCT
ejpam-3893	55	8	,	,	PUNCT
ejpam-3893	55	9	f(x	f(x	PROPN
ejpam-3893	55	10	)	)	PUNCT
ejpam-3893	55	11	∈	∈	PROPN
ejpam-3893	55	12	c(ω̄	c(ω̄	PROPN
ejpam-3893	55	13	)	)	PUNCT
ejpam-3893	55	14	,	,	PUNCT
ejpam-3893	55	15	and	and	CCONJ
ejpam-3893	55	16	n∑	n∑	PROPN
ejpam-3893	55	17	i	i	PROPN
ejpam-3893	56	1	,	,	PUNCT
ejpam-3893	56	2	j=1	j=1	PROPN
ejpam-3893	56	3	aij(x)ηiηj	aij(x)ηiηj	PROPN
ejpam-3893	56	4	≥	≥	X
ejpam-3893	56	5	τ	τ	PROPN
ejpam-3893	56	6	n∑	n∑	PROPN
ejpam-3893	56	7	i=1	i=1	PROPN
ejpam-3893	56	8	η2	η2	PUNCT
ejpam-3893	56	9	i	i	PRON
ejpam-3893	56	10	,	,	PUNCT
ejpam-3893	56	11	∀η	∀η	X
ejpam-3893	56	12	=	=	SYM
ejpam-3893	56	13	(	(	PUNCT
ejpam-3893	56	14	η1	η1	NOUN
ejpam-3893	56	15	,	,	PUNCT
ejpam-3893	56	16	.	.	PUNCT
ejpam-3893	56	17	.	.	PUNCT
ejpam-3893	56	18	.	.	PUNCT
ejpam-3893	57	1	,	,	PUNCT
ejpam-3893	57	2	ηn	ηn	PROPN
ejpam-3893	57	3	)	)	PUNCT
ejpam-3893	57	4	∈	∈	PROPN
ejpam-3893	57	5	rn	rn	PROPN
ejpam-3893	57	6	,	,	PUNCT
ejpam-3893	57	7	x	x	SYM
ejpam-3893	57	8	∈	∈	NOUN
ejpam-3893	57	9	ω̄	ω̄	ADP
ejpam-3893	57	10	;	;	PUNCT
ejpam-3893	57	11	(	(	PUNCT
ejpam-3893	57	12	2	2	X
ejpam-3893	57	13	)	)	PUNCT
ejpam-3893	57	14	with	with	ADP
ejpam-3893	57	15	τ	τ	PROPN
ejpam-3893	57	16	being	be	AUX
ejpam-3893	57	17	a	a	DET
ejpam-3893	57	18	positive	positive	ADJ
ejpam-3893	57	19	constant	constant	ADJ
ejpam-3893	57	20	independent	independent	NOUN
ejpam-3893	57	21	of	of	ADP
ejpam-3893	57	22	x	x	PROPN
ejpam-3893	57	23	and	and	CCONJ
ejpam-3893	57	24	η	η	PROPN
ejpam-3893	57	25	.	.	PROPN
ejpam-3893	57	26	the	the	DET
ejpam-3893	57	27	fourth	fourth	ADJ
ejpam-3893	57	28	condition	condition	NOUN
ejpam-3893	57	29	(	(	PUNCT
ejpam-3893	57	30	2	2	X
ejpam-3893	57	31	)	)	PUNCT
ejpam-3893	57	32	is	be	AUX
ejpam-3893	57	33	referred	refer	VERB
ejpam-3893	57	34	to	to	ADP
ejpam-3893	57	35	as	as	ADP
ejpam-3893	57	36	uniform	uniform	ADJ
ejpam-3893	57	37	ellipticity	ellipticity	NOUN
ejpam-3893	57	38	.	.	PUNCT
ejpam-3893	58	1	in	in	ADP
ejpam-3893	58	2	this	this	DET
ejpam-3893	58	3	paper	paper	NOUN
ejpam-3893	58	4	,	,	PUNCT
ejpam-3893	58	5	we	we	PRON
ejpam-3893	58	6	restrict	restrict	VERB
ejpam-3893	58	7	ourselves	ourselves	PRON
ejpam-3893	58	8	to	to	ADP
ejpam-3893	58	9	the	the	DET
ejpam-3893	58	10	case	case	NOUN
ejpam-3893	58	11	where	where	SCONJ
ejpam-3893	58	12	the	the	DET
ejpam-3893	58	13	coefficient	coefficient	NOUN
ejpam-3893	58	14	aij(x	aij(x	VERB
ejpam-3893	58	15	)	)	PUNCT
ejpam-3893	58	16	in	in	ADP
ejpam-3893	58	17	equation	equation	NOUN
ejpam-3893	58	18	(	(	PUNCT
ejpam-3893	58	19	1	1	X
ejpam-3893	58	20	)	)	PUNCT
ejpam-3893	58	21	reduces	reduce	VERB
ejpam-3893	58	22	to	to	ADP
ejpam-3893	58	23	a	a	DET
ejpam-3893	58	24	scalar	scalar	ADJ
ejpam-3893	58	25	multiple	multiple	NOUN
ejpam-3893	58	26	,	,	PUNCT
ejpam-3893	58	27	ai	ai	NOUN
ejpam-3893	58	28	of	of	ADP
ejpam-3893	58	29	unit	unit	NOUN
ejpam-3893	58	30	matrix	matrix	NOUN
ejpam-3893	58	31	,	,	PUNCT
ejpam-3893	58	32	were	be	AUX
ejpam-3893	58	33	a	a	DET
ejpam-3893	58	34	is	be	AUX
ejpam-3893	58	35	a	a	DET
ejpam-3893	58	36	smooth	smooth	ADJ
ejpam-3893	58	37	function	function	NOUN
ejpam-3893	58	38	.	.	PUNCT
ejpam-3893	59	1	we	we	PRON
ejpam-3893	59	2	consider	consider	VERB
ejpam-3893	59	3	,	,	PUNCT
ejpam-3893	59	4	the	the	DET
ejpam-3893	59	5	dirichlet	dirichlet	PROPN
ejpam-3893	59	6	problem	problem	NOUN
ejpam-3893	59	7	in	in	ADP
ejpam-3893	59	8	a	a	DET
ejpam-3893	59	9	regular	regular	ADJ
ejpam-3893	59	10	(	(	PUNCT
ejpam-3893	59	11	i.e.	i.e.	X
ejpam-3893	59	12	rectangular	rectangular	ADJ
ejpam-3893	59	13	)	)	PUNCT
ejpam-3893	59	14	domain	domain	NOUN
ejpam-3893	59	15	,	,	PUNCT
ejpam-3893	59	16	ω	ω	NOUN
ejpam-3893	59	17	=	=	PUNCT
ejpam-3893	60	1	[	[	X
ejpam-3893	60	2	p	p	X
ejpam-3893	60	3	,	,	PUNCT
ejpam-3893	60	4	q]×	q]×	PROPN
ejpam-3893	60	5	[	[	X
ejpam-3893	60	6	r	r	X
ejpam-3893	60	7	,	,	PUNCT
ejpam-3893	60	8	s	s	PART
ejpam-3893	60	9	]	]	X
ejpam-3893	60	10	∈	∈	PROPN
ejpam-3893	60	11	r2	r2	PROPN
ejpam-3893	60	12	with	with	ADP
ejpam-3893	60	13	boundary	boundary	ADJ
ejpam-3893	60	14	∂ω	∂ω	PROPN
ejpam-3893	60	15	,	,	PUNCT
ejpam-3893	60	16	given	give	VERB
ejpam-3893	60	17	as	as	ADP
ejpam-3893	60	18	{	{	PUNCT
ejpam-3893	60	19	−∇	−∇	NOUN
ejpam-3893	60	20	·	·	PUNCT
ejpam-3893	60	21	(	(	PUNCT
ejpam-3893	60	22	a∇φ	a∇φ	NOUN
ejpam-3893	60	23	)	)	PUNCT
ejpam-3893	60	24	+	+	CCONJ
ejpam-3893	61	1	b∇φ+	b∇φ+	NUM
ejpam-3893	61	2	cφ	cφ	NOUN
ejpam-3893	61	3	=	=	SYM
ejpam-3893	61	4	f	f	PROPN
ejpam-3893	61	5	in	in	ADP
ejpam-3893	61	6	ω	ω	PROPN
ejpam-3893	61	7	φ(x	φ(x	PROPN
ejpam-3893	61	8	,	,	PUNCT
ejpam-3893	61	9	y	y	NOUN
ejpam-3893	61	10	)	)	PUNCT
ejpam-3893	61	11	=	=	SYM
ejpam-3893	61	12	g	g	NOUN
ejpam-3893	61	13	on	on	ADP
ejpam-3893	61	14	∂ω	∂ω	PROPN
ejpam-3893	61	15	(	(	PUNCT
ejpam-3893	61	16	3	3	NUM
ejpam-3893	61	17	)	)	PUNCT
ejpam-3893	61	18	where	where	SCONJ
ejpam-3893	61	19	the	the	DET
ejpam-3893	61	20	coefficients	coefficient	NOUN
ejpam-3893	61	21	a	a	PRON
ejpam-3893	61	22	=	=	SYM
ejpam-3893	61	23	a(x	a(x	PROPN
ejpam-3893	61	24	,	,	PUNCT
ejpam-3893	61	25	y	y	NOUN
ejpam-3893	61	26	)	)	PUNCT
ejpam-3893	61	27	,	,	PUNCT
ejpam-3893	61	28	b	b	X
ejpam-3893	61	29	=	=	PUNCT
ejpam-3893	61	30	b(x	b(x	PROPN
ejpam-3893	61	31	,	,	PUNCT
ejpam-3893	61	32	y	y	NOUN
ejpam-3893	61	33	)	)	PUNCT
ejpam-3893	61	34	and	and	CCONJ
ejpam-3893	61	35	c	c	X
ejpam-3893	61	36	=	=	SYM
ejpam-3893	61	37	(	(	PUNCT
ejpam-3893	61	38	x	x	X
ejpam-3893	61	39	,	,	PUNCT
ejpam-3893	61	40	y	y	NOUN
ejpam-3893	61	41	)	)	PUNCT
ejpam-3893	61	42	are	be	AUX
ejpam-3893	61	43	smooth	smooth	ADJ
ejpam-3893	61	44	in	in	ADP
ejpam-3893	61	45	∂ω̄	∂ω̄	NOUN
ejpam-3893	61	46	which	which	PRON
ejpam-3893	61	47	satisfy	satisfy	VERB
ejpam-3893	61	48	a(x	a(x	NOUN
ejpam-3893	61	49	,	,	PUNCT
ejpam-3893	61	50	y	y	PROPN
ejpam-3893	61	51	)	)	PUNCT
ejpam-3893	61	52	≥	≥	PROPN
ejpam-3893	61	53	a0	a0	PROPN
ejpam-3893	61	54	>	>	X
ejpam-3893	61	55	0	0	PROPN
ejpam-3893	61	56	,	,	PUNCT
ejpam-3893	61	57	c(x	c(x	NOUN
ejpam-3893	61	58	,	,	PUNCT
ejpam-3893	61	59	y)−	y)−	PROPN
ejpam-3893	61	60	1	1	NUM
ejpam-3893	61	61	2	2	NUM
ejpam-3893	61	62	∇	∇	X
ejpam-3893	61	63	·	·	PUNCT
ejpam-3893	61	64	b(x	b(x	NOUN
ejpam-3893	61	65	,	,	PUNCT
ejpam-3893	61	66	y	y	NOUN
ejpam-3893	61	67	)	)	PUNCT
ejpam-3893	61	68	≥	≥	NOUN
ejpam-3893	61	69	0	0	NUM
ejpam-3893	61	70	,	,	PUNCT
ejpam-3893	61	71	for	for	ADP
ejpam-3893	61	72	all	all	DET
ejpam-3893	61	73	x	x	NOUN
ejpam-3893	61	74	,	,	PUNCT
ejpam-3893	61	75	y	y	PROPN
ejpam-3893	61	76	∈	∈	PROPN
ejpam-3893	61	77	ω	ω	PROPN
ejpam-3893	61	78	(	(	PUNCT
ejpam-3893	61	79	4	4	NUM
ejpam-3893	61	80	)	)	PUNCT
ejpam-3893	61	81	f.	f.	NOUN
ejpam-3893	61	82	o.	o.	PROPN
ejpam-3893	61	83	boateng	boateng	PROPN
ejpam-3893	61	84	et	et	PROPN
ejpam-3893	61	85	al	al	PROPN
ejpam-3893	61	86	.	.	PUNCT
ejpam-3893	61	87	/	/	SYM
ejpam-3893	61	88	eur	eur	PROPN
ejpam-3893	61	89	.	.	PUNCT
ejpam-3893	62	1	j.	j.	PROPN
ejpam-3893	62	2	pure	pure	PROPN
ejpam-3893	62	3	appl	appl	PROPN
ejpam-3893	62	4	.	.	PROPN
ejpam-3893	62	5	math	math	PROPN
ejpam-3893	62	6	,	,	PUNCT
ejpam-3893	62	7	14	14	NUM
ejpam-3893	62	8	(	(	PUNCT
ejpam-3893	62	9	3	3	NUM
ejpam-3893	62	10	)	)	PUNCT
ejpam-3893	62	11	(	(	PUNCT
ejpam-3893	62	12	2021	2021	NUM
ejpam-3893	62	13	)	)	PUNCT
ejpam-3893	62	14	,	,	PUNCT
ejpam-3893	62	15	706	706	NUM
ejpam-3893	62	16	-	-	SYM
ejpam-3893	62	17	722	722	NUM
ejpam-3893	62	18	709	709	NUM
ejpam-3893	62	19	and	and	CCONJ
ejpam-3893	62	20	where	where	SCONJ
ejpam-3893	62	21	f	f	PROPN
ejpam-3893	62	22	is	be	AUX
ejpam-3893	62	23	a	a	DET
ejpam-3893	62	24	given	give	VERB
ejpam-3893	62	25	function	function	NOUN
ejpam-3893	62	26	and	and	CCONJ
ejpam-3893	62	27	g	g	NOUN
ejpam-3893	62	28	is	be	AUX
ejpam-3893	62	29	the	the	DET
ejpam-3893	62	30	boundary	boundary	ADJ
ejpam-3893	62	31	data	datum	NOUN
ejpam-3893	62	32	.	.	PUNCT
ejpam-3893	63	1	the	the	DET
ejpam-3893	63	2	first	first	ADJ
ejpam-3893	63	3	stage	stage	NOUN
ejpam-3893	63	4	of	of	ADP
ejpam-3893	63	5	the	the	DET
ejpam-3893	63	6	fdfdwm	fdfdwm	NOUN
ejpam-3893	63	7	is	be	AUX
ejpam-3893	63	8	to	to	PART
ejpam-3893	63	9	reduce	reduce	VERB
ejpam-3893	63	10	the	the	DET
ejpam-3893	63	11	two	two	NUM
ejpam-3893	63	12	dimensional	dimensional	ADJ
ejpam-3893	63	13	dp	dp	NOUN
ejpam-3893	63	14	in	in	ADP
ejpam-3893	63	15	equation	equation	NOUN
ejpam-3893	63	16	(	(	PUNCT
ejpam-3893	63	17	3	3	NUM
ejpam-3893	63	18	)	)	PUNCT
ejpam-3893	63	19	to	to	ADP
ejpam-3893	63	20	a	a	DET
ejpam-3893	63	21	system	system	NOUN
ejpam-3893	63	22	of	of	ADP
ejpam-3893	63	23	ordinary	ordinary	ADJ
ejpam-3893	63	24	differential	differential	ADJ
ejpam-3893	63	25	equations	equation	NOUN
ejpam-3893	63	26	.	.	PUNCT
ejpam-3893	64	1	to	to	PART
ejpam-3893	64	2	achieve	achieve	VERB
ejpam-3893	64	3	this	this	PRON
ejpam-3893	64	4	,	,	PUNCT
ejpam-3893	64	5	equation	equation	NOUN
ejpam-3893	64	6	(	(	PUNCT
ejpam-3893	64	7	3	3	X
ejpam-3893	64	8	)	)	PUNCT
ejpam-3893	64	9	is	be	AUX
ejpam-3893	64	10	discretized	discretize	VERB
ejpam-3893	64	11	along	along	ADP
ejpam-3893	64	12	one	one	NUM
ejpam-3893	64	13	of	of	ADP
ejpam-3893	64	14	the	the	DET
ejpam-3893	64	15	spatial	spatial	ADJ
ejpam-3893	64	16	variables	variable	NOUN
ejpam-3893	64	17	(	(	PUNCT
ejpam-3893	64	18	say	say	VERB
ejpam-3893	64	19	y	y	PROPN
ejpam-3893	64	20	)	)	PUNCT
ejpam-3893	64	21	,	,	PUNCT
ejpam-3893	64	22	with	with	ADP
ejpam-3893	64	23	equally	equally	ADV
ejpam-3893	64	24	spaced	spaced	ADJ
ejpam-3893	64	25	sample	sample	NOUN
ejpam-3893	64	26	,	,	PUNCT
ejpam-3893	64	27	yi	yi	NOUN
ejpam-3893	64	28	=	=	SYM
ejpam-3893	64	29	i∆y	i∆y	ADJ
ejpam-3893	64	30	.	.	PUNCT
ejpam-3893	65	1	thus	thus	ADV
ejpam-3893	65	2	p	p	X
ejpam-3893	65	3	=	=	SYM
ejpam-3893	65	4	y0	y0	PROPN
ejpam-3893	65	5	<	<	X
ejpam-3893	65	6	y1	y1	X
ejpam-3893	65	7	<	<	X
ejpam-3893	65	8	·	·	PUNCT
ejpam-3893	65	9	·	·	PUNCT
ejpam-3893	65	10	·	·	PUNCT
ejpam-3893	65	11	<	<	X
ejpam-3893	65	12	yny	yny	X
ejpam-3893	65	13	=	=	PUNCT
ejpam-3893	65	14	q	q	NOUN
ejpam-3893	65	15	and	and	CCONJ
ejpam-3893	65	16	∆y	∆y	PROPN
ejpam-3893	65	17	=	=	PUNCT
ejpam-3893	65	18	q	q	NOUN
ejpam-3893	65	19	−	−	PROPN
ejpam-3893	65	20	p	p	NOUN
ejpam-3893	65	21	ny	ny	PROPN
ejpam-3893	65	22	=	=	PUNCT
ejpam-3893	65	23	q	q	PROPN
ejpam-3893	66	1	−	−	PROPN
ejpam-3893	66	2	p	p	NOUN
ejpam-3893	66	3	2	2	NUM
ejpam-3893	66	4	m	m	NOUN
ejpam-3893	66	5	where	where	SCONJ
ejpam-3893	66	6	ny	ny	PROPN
ejpam-3893	66	7	=	=	SYM
ejpam-3893	66	8	2	2	NUM
ejpam-3893	66	9	m	m	NOUN
ejpam-3893	66	10	and	and	CCONJ
ejpam-3893	66	11	m	m	PROPN
ejpam-3893	66	12	is	be	AUX
ejpam-3893	66	13	the	the	DET
ejpam-3893	66	14	resolution	resolution	NOUN
ejpam-3893	66	15	.	.	PUNCT
ejpam-3893	67	1	we	we	PRON
ejpam-3893	67	2	use	use	VERB
ejpam-3893	67	3	central	central	ADJ
ejpam-3893	67	4	difference	difference	NOUN
ejpam-3893	67	5	approximation	approximation	NOUN
ejpam-3893	67	6	:	:	PUNCT
ejpam-3893	67	7	d2φ	d2φ	PROPN
ejpam-3893	67	8	dy2	dy2	PROPN
ejpam-3893	68	1	≈	≈	PROPN
ejpam-3893	68	2	φ(x	φ(x	PROPN
ejpam-3893	68	3	,	,	PUNCT
ejpam-3893	68	4	y	y	PROPN
ejpam-3893	68	5	+	+	PROPN
ejpam-3893	68	6	∆y)−	∆y)−	PROPN
ejpam-3893	68	7	2φ(x	2φ(x	NUM
ejpam-3893	68	8	,	,	PUNCT
ejpam-3893	68	9	y	y	NOUN
ejpam-3893	68	10	)	)	PUNCT
ejpam-3893	69	1	+	+	CCONJ
ejpam-3893	69	2	φ(x	φ(x	PROPN
ejpam-3893	69	3	,	,	PUNCT
ejpam-3893	69	4	y	y	PROPN
ejpam-3893	69	5	−∆y	−∆y	NUM
ejpam-3893	69	6	)	)	PUNCT
ejpam-3893	70	1	∆y2	∆y2	PROPN
ejpam-3893	70	2	(	(	PUNCT
ejpam-3893	70	3	5	5	NUM
ejpam-3893	70	4	)	)	PUNCT
ejpam-3893	70	5	and	and	CCONJ
ejpam-3893	70	6	dφ	dφ	ADP
ejpam-3893	70	7	dy	dy	NOUN
ejpam-3893	70	8	≈	≈	PROPN
ejpam-3893	70	9	φ(x	φ(x	PROPN
ejpam-3893	70	10	,	,	PUNCT
ejpam-3893	70	11	y	y	PROPN
ejpam-3893	70	12	+	+	PROPN
ejpam-3893	70	13	∆y)−	∆y)−	PROPN
ejpam-3893	70	14	φ(x	φ(x	PROPN
ejpam-3893	70	15	,	,	PUNCT
ejpam-3893	70	16	y	y	PROPN
ejpam-3893	70	17	−∆y	−∆y	NUM
ejpam-3893	70	18	)	)	PUNCT
ejpam-3893	70	19	2∆y	2∆y	NUM
ejpam-3893	70	20	(	(	PUNCT
ejpam-3893	70	21	6	6	NUM
ejpam-3893	70	22	)	)	PUNCT
ejpam-3893	70	23	with	with	ADP
ejpam-3893	70	24	an	an	DET
ejpam-3893	70	25	error	error	NOUN
ejpam-3893	70	26	term	term	NOUN
ejpam-3893	70	27	o(y2	o(y2	NOUN
ejpam-3893	70	28	)	)	PUNCT
ejpam-3893	70	29	for	for	ADP
ejpam-3893	70	30	each	each	DET
ejpam-3893	70	31	approximation	approximation	NOUN
ejpam-3893	70	32	.	.	PUNCT
ejpam-3893	71	1	substituting	substitute	VERB
ejpam-3893	71	2	equations	equation	NOUN
ejpam-3893	71	3	(	(	PUNCT
ejpam-3893	71	4	5	5	NUM
ejpam-3893	71	5	)	)	PUNCT
ejpam-3893	71	6	and	and	CCONJ
ejpam-3893	71	7	(	(	PUNCT
ejpam-3893	71	8	6	6	NUM
ejpam-3893	71	9	)	)	PUNCT
ejpam-3893	71	10	into	into	ADP
ejpam-3893	71	11	(	(	PUNCT
ejpam-3893	71	12	3	3	NUM
ejpam-3893	71	13	)	)	PUNCT
ejpam-3893	71	14	,	,	PUNCT
ejpam-3893	71	15	we	we	PRON
ejpam-3893	71	16	have	have	AUX
ejpam-3893	71	17	−a	−a	VERB
ejpam-3893	71	18	[	[	PUNCT
ejpam-3893	71	19	d2φ	d2φ	X
ejpam-3893	71	20	dx2	dx2	X
ejpam-3893	71	21	+	+	CCONJ
ejpam-3893	71	22	φi+1(x)−	φi+1(x)−	PROPN
ejpam-3893	71	23	2φi(x	2φi(x	NUM
ejpam-3893	71	24	)	)	PUNCT
ejpam-3893	72	1	+	+	NUM
ejpam-3893	72	2	φi−1(x	φi−1(x	NOUN
ejpam-3893	72	3	)	)	PUNCT
ejpam-3893	72	4	∆y2	∆y2	PROPN
ejpam-3893	72	5	]	]	PUNCT
ejpam-3893	73	1	+	+	CCONJ
ejpam-3893	73	2	b	b	X
ejpam-3893	73	3	[	[	PUNCT
ejpam-3893	73	4	dφ	dφ	ADP
ejpam-3893	73	5	dx	dx	PROPN
ejpam-3893	73	6	+	+	CCONJ
ejpam-3893	73	7	φi+1(x)−	φi+1(x)−	PROPN
ejpam-3893	73	8	φi−1(x	φi−1(x	NOUN
ejpam-3893	73	9	)	)	PUNCT
ejpam-3893	73	10	2∆y	2∆y	NUM
ejpam-3893	73	11	]	]	PUNCT
ejpam-3893	74	1	+	+	CCONJ
ejpam-3893	74	2	cφi(x	cφi(x	ADJ
ejpam-3893	74	3	)	)	PUNCT
ejpam-3893	74	4	=	=	SYM
ejpam-3893	74	5	f(x	f(x	PROPN
ejpam-3893	74	6	,	,	PUNCT
ejpam-3893	74	7	y	y	NOUN
ejpam-3893	74	8	)	)	PUNCT
ejpam-3893	74	9	(	(	PUNCT
ejpam-3893	74	10	7	7	X
ejpam-3893	74	11	)	)	PUNCT
ejpam-3893	74	12	expanding	expand	VERB
ejpam-3893	74	13	and	and	CCONJ
ejpam-3893	74	14	simplifying	simplify	VERB
ejpam-3893	74	15	(	(	PUNCT
ejpam-3893	74	16	7	7	NUM
ejpam-3893	74	17	)	)	PUNCT
ejpam-3893	74	18	,	,	PUNCT
ejpam-3893	74	19	we	we	PRON
ejpam-3893	74	20	obtain	obtain	VERB
ejpam-3893	74	21	−β1	−β1	NOUN
ejpam-3893	74	22	d2φi	d2φi	NOUN
ejpam-3893	74	23	dx2	dx2	PROPN
ejpam-3893	74	24	+	+	CCONJ
ejpam-3893	74	25	β2	β2	PROPN
ejpam-3893	74	26	dφi	dφi	PROPN
ejpam-3893	74	27	dx	dx	PROPN
ejpam-3893	74	28	+	+	CCONJ
ejpam-3893	74	29	β3φ	β3φ	SYM
ejpam-3893	75	1	i+1	i+1	ADP
ejpam-3893	75	2	+	+	NOUN
ejpam-3893	75	3	β4φ	β4φ	X
ejpam-3893	75	4	i	i	PRON
ejpam-3893	75	5	+	+	X
ejpam-3893	75	6	β5φ	β5φ	X
ejpam-3893	75	7	i−1	i−1	PROPN
ejpam-3893	75	8	=	=	PUNCT
ejpam-3893	75	9	β6f	β6f	PUNCT
ejpam-3893	75	10	i	i	X
ejpam-3893	75	11	(	(	PUNCT
ejpam-3893	75	12	8)	8)	NUM
ejpam-3893	75	13	where	where	SCONJ
ejpam-3893	75	14	β1	β1	PROPN
ejpam-3893	75	15	=	=	SYM
ejpam-3893	75	16	a∆y2	a∆y2	PROPN
ejpam-3893	75	17	,	,	PUNCT
ejpam-3893	75	18	β2	β2	NOUN
ejpam-3893	75	19	=	=	SYM
ejpam-3893	75	20	b∆y2	b∆y2	PROPN
ejpam-3893	75	21	,	,	PUNCT
ejpam-3893	75	22	β3	β3	VERB
ejpam-3893	75	23	=	=	SYM
ejpam-3893	75	24	b	b	X
ejpam-3893	75	25	∆y	∆y	NOUN
ejpam-3893	75	26	2	2	NUM
ejpam-3893	75	27	−	−	NOUN
ejpam-3893	75	28	a	a	PRON
ejpam-3893	75	29	,	,	PUNCT
ejpam-3893	75	30	β4	β4	PROPN
ejpam-3893	75	31	=	=	SYM
ejpam-3893	75	32	2a+	2a+	NUM
ejpam-3893	75	33	c∆y2	c∆y2	PROPN
ejpam-3893	75	34	,	,	PUNCT
ejpam-3893	75	35	β5	β5	NOUN
ejpam-3893	75	36	=	=	NOUN
ejpam-3893	75	37	−(a+	−(a+	NUM
ejpam-3893	75	38	b	b	NOUN
ejpam-3893	75	39	∆y	∆y	NOUN
ejpam-3893	75	40	2	2	NUM
ejpam-3893	75	41	)	)	PUNCT
ejpam-3893	75	42	and	and	CCONJ
ejpam-3893	75	43	β6	β6	PROPN
ejpam-3893	75	44	=	=	PUNCT
ejpam-3893	76	1	∆y2	∆y2	PROPN
ejpam-3893	76	2	now	now	ADV
ejpam-3893	76	3	,	,	PUNCT
ejpam-3893	76	4	we	we	PRON
ejpam-3893	76	5	let	let	VERB
ejpam-3893	76	6	φiς(x	φiς(x	PRON
ejpam-3893	76	7	)	)	PUNCT
ejpam-3893	76	8	=	=	PUNCT
ejpam-3893	77	1	β3φ	β3φ	PUNCT
ejpam-3893	78	1	i+1	i+1	NUM
ejpam-3893	78	2	+	+	NOUN
ejpam-3893	78	3	β4φ	β4φ	X
ejpam-3893	78	4	i	i	PRON
ejpam-3893	78	5	+	+	X
ejpam-3893	78	6	β5φ	β5φ	X
ejpam-3893	78	7	i−1	i−1	PROPN
ejpam-3893	78	8	.	.	PUNCT
ejpam-3893	79	1	(	(	PUNCT
ejpam-3893	79	2	9	9	NUM
ejpam-3893	79	3	)	)	PUNCT
ejpam-3893	79	4	then	then	ADV
ejpam-3893	79	5	equation	equation	NOUN
ejpam-3893	79	6	(	(	PUNCT
ejpam-3893	79	7	8)	8)	NUM
ejpam-3893	79	8	is	be	AUX
ejpam-3893	79	9	−β1	−β1	NOUN
ejpam-3893	79	10	d2φi	d2φi	NOUN
ejpam-3893	79	11	dx2	dx2	PROPN
ejpam-3893	79	12	+	+	CCONJ
ejpam-3893	79	13	β2	β2	PROPN
ejpam-3893	79	14	dφi	dφi	PROPN
ejpam-3893	79	15	dx	dx	PROPN
ejpam-3893	79	16	+	+	CCONJ
ejpam-3893	79	17	φiς(x	φiς(x	PROPN
ejpam-3893	79	18	)	)	PUNCT
ejpam-3893	80	1	=	=	SYM
ejpam-3893	80	2	β6f	β6f	PUNCT
ejpam-3893	81	1	i	i	PRON
ejpam-3893	81	2	,	,	PUNCT
ejpam-3893	81	3	(	(	PUNCT
ejpam-3893	81	4	10	10	NUM
ejpam-3893	81	5	)	)	PUNCT
ejpam-3893	81	6	which	which	PRON
ejpam-3893	81	7	is	be	AUX
ejpam-3893	81	8	represented	represent	VERB
ejpam-3893	81	9	in	in	ADP
ejpam-3893	81	10	a	a	DET
ejpam-3893	81	11	vector	vector	NOUN
ejpam-3893	81	12	form	form	NOUN
ejpam-3893	81	13	as	as	ADP
ejpam-3893	81	14	−∇	−∇	NOUN
ejpam-3893	81	15	·	·	PUNCT
ejpam-3893	81	16	(	(	PUNCT
ejpam-3893	81	17	β1∇φi	β1∇φi	NOUN
ejpam-3893	81	18	)	)	PUNCT
ejpam-3893	81	19	+	+	CCONJ
ejpam-3893	81	20	β2∇φi	β2∇φi	NOUN
ejpam-3893	81	21	+	+	CCONJ
ejpam-3893	81	22	φiς	φiς	ADJ
ejpam-3893	81	23	=	=	PUNCT
ejpam-3893	81	24	β6f	β6f	PUNCT
ejpam-3893	81	25	i	i	PRON
ejpam-3893	81	26	for	for	ADP
ejpam-3893	81	27	i	i	PRON
ejpam-3893	81	28	=	=	NOUN
ejpam-3893	81	29	1	1	NUM
ejpam-3893	81	30	,	,	PUNCT
ejpam-3893	81	31	2	2	NUM
ejpam-3893	81	32	,	,	PUNCT
ejpam-3893	81	33	3	3	NUM
ejpam-3893	81	34	,	,	PUNCT
ejpam-3893	81	35	.	.	PUNCT
ejpam-3893	81	36	.	.	PUNCT
ejpam-3893	81	37	.	.	PUNCT
ejpam-3893	81	38	.	.	PUNCT
ejpam-3893	82	1	(	(	PUNCT
ejpam-3893	82	2	11	11	NUM
ejpam-3893	82	3	)	)	PUNCT
ejpam-3893	82	4	equation	equation	NOUN
ejpam-3893	82	5	(	(	PUNCT
ejpam-3893	82	6	11	11	NUM
ejpam-3893	82	7	)	)	PUNCT
ejpam-3893	82	8	is	be	AUX
ejpam-3893	82	9	a	a	DET
ejpam-3893	82	10	one	one	NUM
ejpam-3893	82	11	dimensional	dimensional	ADJ
ejpam-3893	82	12	system	system	NOUN
ejpam-3893	82	13	of	of	ADP
ejpam-3893	82	14	ordinary	ordinary	ADJ
ejpam-3893	82	15	differential	differential	ADJ
ejpam-3893	82	16	equations	equation	NOUN
ejpam-3893	82	17	obtained	obtain	VERB
ejpam-3893	82	18	as	as	ADP
ejpam-3893	82	19	a	a	DET
ejpam-3893	82	20	result	result	NOUN
ejpam-3893	82	21	of	of	ADP
ejpam-3893	82	22	the	the	DET
ejpam-3893	82	23	reduction	reduction	NOUN
ejpam-3893	82	24	of	of	ADP
ejpam-3893	82	25	(	(	PUNCT
ejpam-3893	82	26	1	1	NUM
ejpam-3893	82	27	)	)	PUNCT
ejpam-3893	82	28	.	.	PUNCT
ejpam-3893	83	1	f.	f.	PROPN
ejpam-3893	83	2	o.	o.	PROPN
ejpam-3893	83	3	boateng	boateng	PROPN
ejpam-3893	83	4	et	et	PROPN
ejpam-3893	83	5	al	al	PROPN
ejpam-3893	83	6	.	.	PUNCT
ejpam-3893	83	7	/	/	SYM
ejpam-3893	83	8	eur	eur	PROPN
ejpam-3893	83	9	.	.	PUNCT
ejpam-3893	84	1	j.	j.	PROPN
ejpam-3893	84	2	pure	pure	PROPN
ejpam-3893	84	3	appl	appl	PROPN
ejpam-3893	84	4	.	.	PROPN
ejpam-3893	84	5	math	math	PROPN
ejpam-3893	84	6	,	,	PUNCT
ejpam-3893	84	7	14	14	NUM
ejpam-3893	84	8	(	(	PUNCT
ejpam-3893	84	9	3	3	NUM
ejpam-3893	84	10	)	)	PUNCT
ejpam-3893	84	11	(	(	PUNCT
ejpam-3893	84	12	2021	2021	NUM
ejpam-3893	84	13	)	)	PUNCT
ejpam-3893	84	14	,	,	PUNCT
ejpam-3893	84	15	706	706	NUM
ejpam-3893	84	16	-	-	SYM
ejpam-3893	84	17	722	722	NUM
ejpam-3893	84	18	710	710	NUM
ejpam-3893	84	19	2.1	2.1	NUM
ejpam-3893	84	20	.	.	PUNCT
ejpam-3893	85	1	variational	variational	ADJ
ejpam-3893	85	2	formulation	formulation	NOUN
ejpam-3893	85	3	of	of	ADP
ejpam-3893	85	4	the	the	DET
ejpam-3893	85	5	dp	dp	NOUN
ejpam-3893	85	6	the	the	DET
ejpam-3893	85	7	next	next	ADJ
ejpam-3893	85	8	stage	stage	NOUN
ejpam-3893	85	9	of	of	ADP
ejpam-3893	85	10	the	the	DET
ejpam-3893	85	11	fdfwdm	fdfwdm	NOUN
ejpam-3893	85	12	is	be	AUX
ejpam-3893	85	13	to	to	PART
ejpam-3893	85	14	write	write	VERB
ejpam-3893	85	15	equation	equation	NOUN
ejpam-3893	85	16	(	(	PUNCT
ejpam-3893	85	17	11	11	NUM
ejpam-3893	85	18	)	)	PUNCT
ejpam-3893	85	19	in	in	ADP
ejpam-3893	85	20	a	a	DET
ejpam-3893	85	21	weak	weak	ADJ
ejpam-3893	85	22	form	form	NOUN
ejpam-3893	85	23	and	and	CCONJ
ejpam-3893	85	24	seek	seek	VERB
ejpam-3893	85	25	a	a	DET
ejpam-3893	85	26	solution	solution	NOUN
ejpam-3893	85	27	in	in	ADP
ejpam-3893	85	28	a	a	DET
ejpam-3893	85	29	sobolev	sobolev	NOUN
ejpam-3893	85	30	space	space	NOUN
ejpam-3893	85	31	h1	h1	PROPN
ejpam-3893	85	32	.	.	PUNCT
ejpam-3893	86	1	we	we	PRON
ejpam-3893	86	2	achieve	achieve	VERB
ejpam-3893	86	3	this	this	PRON
ejpam-3893	86	4	by	by	ADP
ejpam-3893	86	5	multiplying	multiply	VERB
ejpam-3893	86	6	(	(	PUNCT
ejpam-3893	86	7	11	11	NUM
ejpam-3893	86	8	)	)	PUNCT
ejpam-3893	86	9	by	by	ADP
ejpam-3893	86	10	a	a	DET
ejpam-3893	86	11	test	test	NOUN
ejpam-3893	86	12	function	function	NOUN
ejpam-3893	86	13	,	,	PUNCT
ejpam-3893	86	14	v	v	NOUN
ejpam-3893	86	15	∈	∈	PROPN
ejpam-3893	86	16	h1	h1	NOUN
ejpam-3893	86	17	0	0	PUNCT
ejpam-3893	86	18	and	and	CCONJ
ejpam-3893	86	19	integrating	integrate	VERB
ejpam-3893	86	20	over	over	ADP
ejpam-3893	86	21	the	the	DET
ejpam-3893	86	22	domain	domain	NOUN
ejpam-3893	86	23	ω	ω	NOUN
ejpam-3893	86	24	,	,	PUNCT
ejpam-3893	86	25	that	that	SCONJ
ejpam-3893	86	26	is∫	is∫	PROPN
ejpam-3893	86	27	ω	ω	PROPN
ejpam-3893	86	28	(	(	PUNCT
ejpam-3893	86	29	−∇	−∇	NOUN
ejpam-3893	86	30	·	·	PUNCT
ejpam-3893	86	31	(	(	PUNCT
ejpam-3893	86	32	β1∇φi	β1∇φi	NOUN
ejpam-3893	86	33	)	)	PUNCT
ejpam-3893	86	34	+	+	CCONJ
ejpam-3893	86	35	β2∇φi	β2∇φi	PROPN
ejpam-3893	86	36	+	+	CCONJ
ejpam-3893	86	37	φiς	φiς	ADJ
ejpam-3893	86	38	)	)	PUNCT
ejpam-3893	86	39	vdx	vdx	PROPN
ejpam-3893	86	40	=	=	SYM
ejpam-3893	86	41	∫	∫	PROPN
ejpam-3893	86	42	ω	ω	PROPN
ejpam-3893	86	43	β6f	β6f	PROPN
ejpam-3893	86	44	iv	iv	NUM
ejpam-3893	86	45	dx	dx	PROPN
ejpam-3893	86	46	(	(	PUNCT
ejpam-3893	86	47	12	12	NUM
ejpam-3893	86	48	)	)	PUNCT
ejpam-3893	86	49	using	use	VERB
ejpam-3893	86	50	the	the	DET
ejpam-3893	86	51	first	first	ADJ
ejpam-3893	86	52	green	green	NOUN
ejpam-3893	86	53	’s	’s	PART
ejpam-3893	86	54	identity	identity	NOUN
ejpam-3893	86	55	and	and	CCONJ
ejpam-3893	86	56	noting	note	VERB
ejpam-3893	86	57	that	that	SCONJ
ejpam-3893	86	58	v	v	NOUN
ejpam-3893	86	59	=	=	SYM
ejpam-3893	86	60	0	0	NUM
ejpam-3893	86	61	on	on	ADP
ejpam-3893	86	62	the	the	DET
ejpam-3893	86	63	∂ω	∂ω	PROPN
ejpam-3893	86	64	,	,	PUNCT
ejpam-3893	86	65	we	we	PRON
ejpam-3893	86	66	arrive	arrive	VERB
ejpam-3893	86	67	at	at	ADP
ejpam-3893	86	68	the	the	DET
ejpam-3893	86	69	following	following	ADJ
ejpam-3893	86	70	weak	weak	ADJ
ejpam-3893	86	71	form	form	NOUN
ejpam-3893	86	72	,	,	PUNCT
ejpam-3893	86	73	{	{	PUNCT
ejpam-3893	86	74	find	find	VERB
ejpam-3893	86	75	φi	φi	ADP
ejpam-3893	86	76	∈	∈	PROPN
ejpam-3893	86	77	h1(ωf	h1(ωf	PROPN
ejpam-3893	86	78	)	)	PUNCT
ejpam-3893	87	1	such	such	ADJ
ejpam-3893	87	2	that∫	that∫	NOUN
ejpam-3893	87	3	ω	ω	PROPN
ejpam-3893	87	4	(	(	PUNCT
ejpam-3893	87	5	β1∇φi∇v	β1∇φi∇v	PROPN
ejpam-3893	87	6	+	+	NOUN
ejpam-3893	87	7	β2∇φiv	β2∇φiv	NUM
ejpam-3893	87	8	+	+	CCONJ
ejpam-3893	87	9	φiσv	φiσv	ADJ
ejpam-3893	87	10	)	)	PUNCT
ejpam-3893	87	11	dx	dx	PROPN
ejpam-3893	88	1	=	=	SYM
ejpam-3893	88	2	∫	∫	PROPN
ejpam-3893	88	3	ω	ω	PROPN
ejpam-3893	88	4	β6f	β6f	PROPN
ejpam-3893	88	5	iv	iv	NUM
ejpam-3893	88	6	dx	dx	PROPN
ejpam-3893	88	7	∀v	∀v	PROPN
ejpam-3893	88	8	∈	∈	PROPN
ejpam-3893	88	9	h1	h1	NOUN
ejpam-3893	88	10	0	0	NUM
ejpam-3893	88	11	.	.	PUNCT
ejpam-3893	89	1	(	(	PUNCT
ejpam-3893	89	2	13	13	NUM
ejpam-3893	89	3	)	)	PUNCT
ejpam-3893	89	4	we	we	PRON
ejpam-3893	89	5	define	define	VERB
ejpam-3893	89	6	α	α	NOUN
ejpam-3893	89	7	:	:	PUNCT
ejpam-3893	89	8	v	v	NUM
ejpam-3893	89	9	×	×	NOUN
ejpam-3893	89	10	v	v	NOUN
ejpam-3893	89	11	→	→	SYM
ejpam-3893	89	12	r	r	NOUN
ejpam-3893	89	13	and	and	CCONJ
ejpam-3893	89	14	a	a	DET
ejpam-3893	89	15	linear	linear	ADJ
ejpam-3893	89	16	functional	functional	ADJ
ejpam-3893	89	17	l	l	NOUN
ejpam-3893	89	18	:	:	PUNCT
ejpam-3893	89	19	v	v	X
ejpam-3893	89	20	→	→	SYM
ejpam-3893	89	21	r	r	NOUN
ejpam-3893	89	22	,	,	PUNCT
ejpam-3893	89	23	where	where	SCONJ
ejpam-3893	89	24	α	α	X
ejpam-3893	89	25	(	(	PUNCT
ejpam-3893	89	26	·	·	PUNCT
ejpam-3893	89	27	,	,	PUNCT
ejpam-3893	89	28	·	·	PUNCT
ejpam-3893	89	29	)	)	PUNCT
ejpam-3893	89	30	over	over	ADP
ejpam-3893	89	31	space	space	NOUN
ejpam-3893	89	32	v	v	NOUN
ejpam-3893	89	33	is	be	AUX
ejpam-3893	89	34	continuous	continuous	ADJ
ejpam-3893	89	35	.	.	PUNCT
ejpam-3893	90	1	then	then	ADV
ejpam-3893	90	2	we	we	PRON
ejpam-3893	90	3	express	express	VERB
ejpam-3893	90	4	equation	equation	NOUN
ejpam-3893	90	5	(	(	PUNCT
ejpam-3893	90	6	13	13	NUM
ejpam-3893	90	7	)	)	PUNCT
ejpam-3893	90	8	in	in	ADP
ejpam-3893	90	9	a	a	DET
ejpam-3893	90	10	bilinear	bilinear	NOUN
ejpam-3893	90	11	form	form	NOUN
ejpam-3893	90	12	as	as	ADP
ejpam-3893	90	13	α(v	α(v	PROPN
ejpam-3893	90	14	,	,	PUNCT
ejpam-3893	90	15	η	η	NOUN
ejpam-3893	90	16	)	)	PUNCT
ejpam-3893	90	17	=	=	SYM
ejpam-3893	91	1	∫	∫	PROPN
ejpam-3893	91	2	ω	ω	PROPN
ejpam-3893	91	3	(	(	PUNCT
ejpam-3893	91	4	β1∇v∇η	β1∇v∇η	PUNCT
ejpam-3893	91	5	+	+	CCONJ
ejpam-3893	91	6	β2∇vη	β2∇vη	NOUN
ejpam-3893	91	7	+	+	CCONJ
ejpam-3893	91	8	vη	vη	X
ejpam-3893	91	9	)	)	PUNCT
ejpam-3893	91	10	dx	dx	PROPN
ejpam-3893	91	11	∀v	∀v	PROPN
ejpam-3893	91	12	,	,	PUNCT
ejpam-3893	91	13	η	η	PROPN
ejpam-3893	91	14	∈	∈	PROPN
ejpam-3893	91	15	v	v	X
ejpam-3893	91	16	(	(	PUNCT
ejpam-3893	91	17	14	14	NUM
ejpam-3893	91	18	)	)	PUNCT
ejpam-3893	91	19	and	and	CCONJ
ejpam-3893	91	20	l(v	l(v	NOUN
ejpam-3893	91	21	)	)	PUNCT
ejpam-3893	91	22	=	=	SYM
ejpam-3893	92	1	β6	β6	PROPN
ejpam-3893	92	2	∫	∫	PROPN
ejpam-3893	92	3	ω	ω	NUM
ejpam-3893	92	4	fvdx	fvdx	NOUN
ejpam-3893	92	5	(	(	PUNCT
ejpam-3893	92	6	15	15	NUM
ejpam-3893	92	7	)	)	PUNCT
ejpam-3893	92	8	we	we	PRON
ejpam-3893	92	9	note	note	VERB
ejpam-3893	92	10	from	from	ADP
ejpam-3893	92	11	(	(	PUNCT
ejpam-3893	92	12	1	1	NUM
ejpam-3893	92	13	)	)	PUNCT
ejpam-3893	92	14	that	that	SCONJ
ejpam-3893	92	15	when	when	SCONJ
ejpam-3893	92	16	b	b	PROPN
ejpam-3893	92	17	=	=	SYM
ejpam-3893	92	18	0	0	PROPN
ejpam-3893	92	19	,	,	PUNCT
ejpam-3893	92	20	the	the	DET
ejpam-3893	92	21	bilinear	bilinear	NOUN
ejpam-3893	92	22	becomes	become	VERB
ejpam-3893	92	23	symmetrical	symmetrical	ADJ
ejpam-3893	92	24	,	,	PUNCT
ejpam-3893	92	25	that	that	PRON
ejpam-3893	92	26	is	be	AUX
ejpam-3893	92	27	α(v	α(v	NOUN
ejpam-3893	92	28	,	,	PUNCT
ejpam-3893	92	29	η	η	NOUN
ejpam-3893	92	30	)	)	PUNCT
ejpam-3893	92	31	=	=	SYM
ejpam-3893	92	32	α(η	α(η	PROPN
ejpam-3893	92	33	,	,	PUNCT
ejpam-3893	92	34	v	v	NOUN
ejpam-3893	92	35	)	)	PUNCT
ejpam-3893	92	36	.	.	PUNCT
ejpam-3893	93	1	2.2	2.2	NUM
ejpam-3893	93	2	.	.	PUNCT
ejpam-3893	93	3	fictitious	fictitious	ADJ
ejpam-3893	93	4	domain	domain	NOUN
ejpam-3893	93	5	formulation	formulation	NOUN
ejpam-3893	93	6	of	of	ADP
ejpam-3893	93	7	the	the	DET
ejpam-3893	93	8	dp	dp	NOUN
ejpam-3893	93	9	the	the	DET
ejpam-3893	93	10	fdfdwm	fdfdwm	NOUN
ejpam-3893	93	11	uses	use	VERB
ejpam-3893	93	12	the	the	DET
ejpam-3893	93	13	fictitious	fictitious	ADJ
ejpam-3893	93	14	domain	domain	NOUN
ejpam-3893	93	15	approach	approach	NOUN
ejpam-3893	93	16	to	to	PART
ejpam-3893	93	17	handle	handle	VERB
ejpam-3893	93	18	the	the	DET
ejpam-3893	93	19	boundary	boundary	ADJ
ejpam-3893	93	20	conditions	condition	NOUN
ejpam-3893	93	21	.	.	PUNCT
ejpam-3893	94	1	the	the	DET
ejpam-3893	94	2	idea	idea	NOUN
ejpam-3893	94	3	behind	behind	ADP
ejpam-3893	94	4	the	the	DET
ejpam-3893	94	5	fictitious	fictitious	ADJ
ejpam-3893	94	6	domain	domain	NOUN
ejpam-3893	94	7	approach	approach	NOUN
ejpam-3893	94	8	is	be	AUX
ejpam-3893	94	9	to	to	PART
ejpam-3893	94	10	embed	embed	VERB
ejpam-3893	94	11	the	the	DET
ejpam-3893	94	12	original	original	ADJ
ejpam-3893	94	13	domain	domain	NOUN
ejpam-3893	94	14	,	,	PUNCT
ejpam-3893	94	15	ω	ω	NUM
ejpam-3893	94	16	of	of	ADP
ejpam-3893	94	17	the	the	DET
ejpam-3893	94	18	dp	dp	NOUN
ejpam-3893	94	19	(	(	PUNCT
ejpam-3893	94	20	1	1	NUM
ejpam-3893	94	21	)	)	PUNCT
ejpam-3893	94	22	in	in	ADP
ejpam-3893	94	23	a	a	DET
ejpam-3893	94	24	slightly	slightly	ADV
ejpam-3893	94	25	larger	large	ADJ
ejpam-3893	94	26	but	but	CCONJ
ejpam-3893	94	27	simple	simple	ADJ
ejpam-3893	94	28	(	(	PUNCT
ejpam-3893	94	29	rectangular	rectangular	ADJ
ejpam-3893	94	30	)	)	PUNCT
ejpam-3893	94	31	domain	domain	NOUN
ejpam-3893	94	32	,	,	PUNCT
ejpam-3893	94	33	ωf	ωf	X
ejpam-3893	94	34	.	.	PUNCT
ejpam-3893	95	1	this	this	PRON
ejpam-3893	95	2	is	be	AUX
ejpam-3893	95	3	done	do	VERB
ejpam-3893	95	4	in	in	ADP
ejpam-3893	95	5	order	order	NOUN
ejpam-3893	95	6	to	to	PART
ejpam-3893	95	7	handle	handle	VERB
ejpam-3893	95	8	the	the	DET
ejpam-3893	95	9	difficulties	difficulty	NOUN
ejpam-3893	95	10	usually	usually	ADV
ejpam-3893	95	11	associated	associate	VERB
ejpam-3893	95	12	with	with	ADP
ejpam-3893	95	13	taking	take	VERB
ejpam-3893	95	14	care	care	NOUN
ejpam-3893	95	15	of	of	ADP
ejpam-3893	95	16	boundary	boundary	ADJ
ejpam-3893	95	17	conditions	condition	NOUN
ejpam-3893	95	18	.	.	PUNCT
ejpam-3893	96	1	now	now	ADV
ejpam-3893	96	2	,	,	PUNCT
ejpam-3893	96	3	we	we	PRON
ejpam-3893	96	4	let	let	VERB
ejpam-3893	96	5	v	v	PART
ejpam-3893	96	6	be	be	AUX
ejpam-3893	96	7	a	a	DET
ejpam-3893	96	8	closed	closed	ADJ
ejpam-3893	96	9	subspace	subspace	NOUN
ejpam-3893	96	10	h1	h1	PROPN
ejpam-3893	96	11	p	p	X
ejpam-3893	96	12	(	(	PUNCT
ejpam-3893	96	13	ωf	ωf	PROPN
ejpam-3893	96	14	)	)	PUNCT
ejpam-3893	96	15	given	give	VERB
ejpam-3893	96	16	as	as	ADP
ejpam-3893	96	17	{	{	PUNCT
ejpam-3893	96	18	v	v	NOUN
ejpam-3893	96	19	:	:	PUNCT
ejpam-3893	96	20	v	v	NOUN
ejpam-3893	96	21	=	=	SYM
ejpam-3893	96	22	ṽ|ω	ṽ|ω	NOUN
ejpam-3893	96	23	,	,	PUNCT
ejpam-3893	96	24	ṽ	ṽ	PROPN
ejpam-3893	96	25	∈	∈	PROPN
ejpam-3893	96	26	v	v	ADP
ejpam-3893	96	27	}	}	PUNCT
ejpam-3893	96	28	=	=	PUNCT
ejpam-3893	96	29	h1	h1	PROPN
ejpam-3893	96	30	p	p	X
ejpam-3893	96	31	(	(	PUNCT
ejpam-3893	96	32	ωf	ωf	PROPN
ejpam-3893	96	33	)	)	PUNCT
ejpam-3893	96	34	the	the	DET
ejpam-3893	96	35	choice	choice	NOUN
ejpam-3893	96	36	for	for	ADP
ejpam-3893	96	37	v	v	NOUN
ejpam-3893	96	38	,	,	PUNCT
ejpam-3893	96	39	considering	consider	VERB
ejpam-3893	96	40	the	the	DET
ejpam-3893	96	41	dirichlet	dirichlet	PROPN
ejpam-3893	96	42	boundary	boundary	ADJ
ejpam-3893	96	43	condition	condition	NOUN
ejpam-3893	96	44	is	be	AUX
ejpam-3893	96	45	h1	h1	PROPN
ejpam-3893	96	46	0	0	NUM
ejpam-3893	96	47	(	(	PUNCT
ejpam-3893	96	48	ω	ω	NOUN
ejpam-3893	96	49	)	)	PUNCT
ejpam-3893	96	50	.	.	PUNCT
ejpam-3893	97	1	we	we	PRON
ejpam-3893	97	2	also	also	ADV
ejpam-3893	97	3	define	define	VERB
ejpam-3893	97	4	vp	vp	PROPN
ejpam-3893	97	5	(	(	PUNCT
ejpam-3893	97	6	ωf	ωf	PROPN
ejpam-3893	97	7	)	)	PUNCT
ejpam-3893	97	8	by	by	ADP
ejpam-3893	97	9	vp	vp	PROPN
ejpam-3893	97	10	(	(	PUNCT
ejpam-3893	97	11	ωf	ωf	PROPN
ejpam-3893	97	12	)	)	PUNCT
ejpam-3893	97	13	=	=	SYM
ejpam-3893	97	14	{	{	PUNCT
ejpam-3893	97	15	v	v	NUM
ejpam-3893	97	16	∈	∈	PROPN
ejpam-3893	97	17	h1	h1	NOUN
ejpam-3893	97	18	0	0	NUM
ejpam-3893	97	19	(	(	PUNCT
ejpam-3893	97	20	ωf	ωf	PROPN
ejpam-3893	97	21	)	)	PUNCT
ejpam-3893	97	22	:	:	PUNCT
ejpam-3893	97	23	v	v	NOUN
ejpam-3893	97	24	on	on	ADP
ejpam-3893	97	25	∂ω	∂ω	PROPN
ejpam-3893	97	26	is	be	AUX
ejpam-3893	97	27	periodic	periodic	ADJ
ejpam-3893	97	28	on	on	ADP
ejpam-3893	97	29	.	.	PUNCT
ejpam-3893	98	1	(	(	PUNCT
ejpam-3893	98	2	16	16	NUM
ejpam-3893	98	3	)	)	PUNCT
ejpam-3893	98	4	given	give	VERB
ejpam-3893	98	5	some	some	DET
ejpam-3893	98	6	s	s	VERB
ejpam-3893	98	7	>	>	X
ejpam-3893	98	8	0	0	PROPN
ejpam-3893	98	9	,	,	PUNCT
ejpam-3893	98	10	suppose	suppose	VERB
ejpam-3893	98	11	that	that	SCONJ
ejpam-3893	98	12	ωf	ωf	ADV
ejpam-3893	98	13	=	=	SYM
ejpam-3893	98	14	(	(	PUNCT
ejpam-3893	98	15	0	0	NUM
ejpam-3893	98	16	,	,	PUNCT
ejpam-3893	98	17	s)2	s)2	NOUN
ejpam-3893	98	18	then	then	ADV
ejpam-3893	98	19	the	the	DET
ejpam-3893	98	20	periodicity	periodicity	NOUN
ejpam-3893	98	21	property	property	NOUN
ejpam-3893	98	22	in	in	ADP
ejpam-3893	98	23	(	(	PUNCT
ejpam-3893	98	24	16	16	NUM
ejpam-3893	98	25	)	)	PUNCT
ejpam-3893	98	26	implies	imply	VERB
ejpam-3893	98	27	that	that	SCONJ
ejpam-3893	98	28	v	v	X
ejpam-3893	98	29	(	(	PUNCT
ejpam-3893	98	30	0	0	NUM
ejpam-3893	98	31	,	,	PUNCT
ejpam-3893	98	32	y	y	NOUN
ejpam-3893	98	33	)	)	PUNCT
ejpam-3893	98	34	=	=	NOUN
ejpam-3893	99	1	v	v	X
ejpam-3893	99	2	(	(	PUNCT
ejpam-3893	99	3	s	s	PROPN
ejpam-3893	99	4	,	,	PUNCT
ejpam-3893	99	5	y	y	NOUN
ejpam-3893	99	6	)	)	PUNCT
ejpam-3893	99	7	and	and	CCONJ
ejpam-3893	99	8	v	v	NOUN
ejpam-3893	99	9	(	(	PUNCT
ejpam-3893	99	10	x	x	NOUN
ejpam-3893	99	11	,	,	PUNCT
ejpam-3893	99	12	0	0	NUM
ejpam-3893	99	13	)	)	PUNCT
ejpam-3893	99	14	=	=	SYM
ejpam-3893	99	15	v	v	X
ejpam-3893	99	16	(	(	PUNCT
ejpam-3893	99	17	x	x	X
ejpam-3893	99	18	,	,	PUNCT
ejpam-3893	99	19	s	s	PART
ejpam-3893	99	20	)	)	PUNCT
ejpam-3893	99	21	.	.	PUNCT
ejpam-3893	100	1	following	follow	VERB
ejpam-3893	100	2	from	from	ADP
ejpam-3893	100	3	equations	equation	NOUN
ejpam-3893	100	4	(	(	PUNCT
ejpam-3893	100	5	14	14	NUM
ejpam-3893	100	6	)	)	PUNCT
ejpam-3893	100	7	and	and	CCONJ
ejpam-3893	100	8	(	(	PUNCT
ejpam-3893	100	9	15	15	NUM
ejpam-3893	100	10	)	)	PUNCT
ejpam-3893	100	11	,	,	PUNCT
ejpam-3893	100	12	the	the	DET
ejpam-3893	100	13	dp	dp	NOUN
ejpam-3893	100	14	(	(	PUNCT
ejpam-3893	100	15	3	3	NUM
ejpam-3893	100	16	)	)	PUNCT
ejpam-3893	100	17	can	can	AUX
ejpam-3893	100	18	be	be	AUX
ejpam-3893	100	19	formulated	formulate	VERB
ejpam-3893	100	20	as	as	ADP
ejpam-3893	100	21	a	a	DET
ejpam-3893	100	22	variational	variational	ADJ
ejpam-3893	100	23	problem	problem	NOUN
ejpam-3893	100	24	.	.	PUNCT
ejpam-3893	101	1	that	that	PRON
ejpam-3893	101	2	is	be	AUX
ejpam-3893	101	3	,	,	PUNCT
ejpam-3893	101	4	{	{	PUNCT
ejpam-3893	101	5	find	find	VERB
ejpam-3893	101	6	φi	φi	ADP
ejpam-3893	101	7	∈	∈	PROPN
ejpam-3893	101	8	h1(ωf	h1(ωf	PROPN
ejpam-3893	101	9	)	)	PUNCT
ejpam-3893	101	10	,	,	PUNCT
ejpam-3893	101	11	∀v	∀v	PROPN
ejpam-3893	101	12	∈	∈	PROPN
ejpam-3893	101	13	h1	h1	NOUN
ejpam-3893	101	14	0	0	PROPN
ejpam-3893	102	1	so	so	SCONJ
ejpam-3893	102	2	that	that	SCONJ
ejpam-3893	102	3	α(φi	α(φi	NOUN
ejpam-3893	102	4	,	,	PUNCT
ejpam-3893	102	5	v	v	NOUN
ejpam-3893	102	6	)	)	PUNCT
ejpam-3893	102	7	=	=	SYM
ejpam-3893	102	8	l(v	l(v	NOUN
ejpam-3893	102	9	)	)	PUNCT
ejpam-3893	102	10	.	.	PUNCT
ejpam-3893	103	1	(	(	PUNCT
ejpam-3893	103	2	17	17	NUM
ejpam-3893	103	3	)	)	PUNCT
ejpam-3893	103	4	f.	f.	PROPN
ejpam-3893	103	5	o.	o.	PROPN
ejpam-3893	103	6	boateng	boateng	PROPN
ejpam-3893	103	7	et	et	PROPN
ejpam-3893	103	8	al	al	PROPN
ejpam-3893	103	9	.	.	PUNCT
ejpam-3893	103	10	/	/	SYM
ejpam-3893	103	11	eur	eur	PROPN
ejpam-3893	103	12	.	.	PUNCT
ejpam-3893	104	1	j.	j.	PROPN
ejpam-3893	104	2	pure	pure	PROPN
ejpam-3893	104	3	appl	appl	PROPN
ejpam-3893	104	4	.	.	PROPN
ejpam-3893	104	5	math	math	PROPN
ejpam-3893	104	6	,	,	PUNCT
ejpam-3893	104	7	14	14	NUM
ejpam-3893	104	8	(	(	PUNCT
ejpam-3893	104	9	3	3	NUM
ejpam-3893	104	10	)	)	PUNCT
ejpam-3893	104	11	(	(	PUNCT
ejpam-3893	104	12	2021	2021	NUM
ejpam-3893	104	13	)	)	PUNCT
ejpam-3893	104	14	,	,	PUNCT
ejpam-3893	104	15	706	706	NUM
ejpam-3893	104	16	-	-	SYM
ejpam-3893	104	17	722	722	NUM
ejpam-3893	104	18	711	711	NUM
ejpam-3893	104	19	2.3	2.3	NUM
ejpam-3893	104	20	.	.	PUNCT
ejpam-3893	105	1	wavelet	wavelet	NOUN
ejpam-3893	105	2	approximation	approximation	NOUN
ejpam-3893	105	3	of	of	ADP
ejpam-3893	105	4	the	the	DET
ejpam-3893	105	5	dp	dp	NOUN
ejpam-3893	105	6	one	one	NUM
ejpam-3893	105	7	cardinal	cardinal	ADJ
ejpam-3893	105	8	aspect	aspect	NOUN
ejpam-3893	105	9	of	of	ADP
ejpam-3893	105	10	the	the	DET
ejpam-3893	105	11	fdfdwm	fdfdwm	NOUN
ejpam-3893	105	12	is	be	AUX
ejpam-3893	105	13	the	the	DET
ejpam-3893	105	14	approximation	approximation	NOUN
ejpam-3893	105	15	of	of	ADP
ejpam-3893	105	16	the	the	DET
ejpam-3893	105	17	dp	dp	NOUN
ejpam-3893	105	18	using	use	VERB
ejpam-3893	105	19	wavelet	wavelet	NOUN
ejpam-3893	105	20	series	series	NOUN
ejpam-3893	105	21	solution	solution	NOUN
ejpam-3893	105	22	.	.	PUNCT
ejpam-3893	106	1	generally	generally	ADV
ejpam-3893	106	2	,	,	PUNCT
ejpam-3893	106	3	wavelet	wavelet	NOUN
ejpam-3893	106	4	approximations	approximation	NOUN
ejpam-3893	106	5	give	give	VERB
ejpam-3893	106	6	a	a	DET
ejpam-3893	106	7	more	more	ADV
ejpam-3893	106	8	stable	stable	ADJ
ejpam-3893	106	9	and	and	CCONJ
ejpam-3893	106	10	accurate	accurate	ADJ
ejpam-3893	106	11	solutions	solution	NOUN
ejpam-3893	106	12	and	and	CCONJ
ejpam-3893	106	13	also	also	ADV
ejpam-3893	106	14	provide	provide	VERB
ejpam-3893	106	15	information	information	NOUN
ejpam-3893	106	16	on	on	ADP
ejpam-3893	106	17	the	the	DET
ejpam-3893	106	18	boundary	boundary	ADJ
ejpam-3893	106	19	data	datum	NOUN
ejpam-3893	106	20	.	.	PUNCT
ejpam-3893	107	1	we	we	PRON
ejpam-3893	107	2	use	use	VERB
ejpam-3893	107	3	the	the	DET
ejpam-3893	107	4	daubechies	daubechie	NOUN
ejpam-3893	107	5	wavelet	wavelet	NOUN
ejpam-3893	107	6	for	for	ADP
ejpam-3893	107	7	approximating	approximate	VERB
ejpam-3893	107	8	the	the	DET
ejpam-3893	107	9	solution	solution	NOUN
ejpam-3893	107	10	of	of	ADP
ejpam-3893	107	11	the	the	DET
ejpam-3893	107	12	dp	dp	NOUN
ejpam-3893	107	13	due	due	ADP
ejpam-3893	107	14	to	to	ADP
ejpam-3893	107	15	the	the	DET
ejpam-3893	107	16	fact	fact	NOUN
ejpam-3893	107	17	that	that	SCONJ
ejpam-3893	107	18	it	it	PRON
ejpam-3893	107	19	has	have	AUX
ejpam-3893	107	20	the	the	DET
ejpam-3893	107	21	highest	high	ADJ
ejpam-3893	107	22	number	number	NOUN
ejpam-3893	107	23	of	of	ADP
ejpam-3893	107	24	vanishing	vanish	VERB
ejpam-3893	107	25	moments	moment	NOUN
ejpam-3893	107	26	among	among	ADP
ejpam-3893	107	27	the	the	DET
ejpam-3893	107	28	compactly	compactly	ADV
ejpam-3893	107	29	supported	support	VERB
ejpam-3893	107	30	wavelets	wavelet	NOUN
ejpam-3893	107	31	[	[	X
ejpam-3893	107	32	4	4	NUM
ejpam-3893	107	33	,	,	PUNCT
ejpam-3893	107	34	5	5	NUM
ejpam-3893	107	35	]	]	PUNCT
ejpam-3893	107	36	.	.	PUNCT
ejpam-3893	108	1	this	this	PRON
ejpam-3893	108	2	makes	make	VERB
ejpam-3893	108	3	the	the	DET
ejpam-3893	108	4	wavelet	wavelet	NOUN
ejpam-3893	108	5	series	series	PROPN
ejpam-3893	108	6	approximation	approximation	NOUN
ejpam-3893	108	7	converges	converge	VERB
ejpam-3893	108	8	rapidly	rapidly	ADV
ejpam-3893	108	9	to	to	ADP
ejpam-3893	108	10	the	the	DET
ejpam-3893	108	11	desired	desire	VERB
ejpam-3893	108	12	solution	solution	NOUN
ejpam-3893	108	13	.	.	PUNCT
ejpam-3893	109	1	we	we	PRON
ejpam-3893	109	2	begin	begin	VERB
ejpam-3893	109	3	formulating	formulate	VERB
ejpam-3893	109	4	the	the	DET
ejpam-3893	109	5	fdfdwm	fdfdwm	NOUN
ejpam-3893	109	6	solution	solution	NOUN
ejpam-3893	109	7	by	by	ADP
ejpam-3893	109	8	letting	let	VERB
ejpam-3893	109	9	,	,	PUNCT
ejpam-3893	109	10	vj	vj	INTJ
ejpam-3893	109	11	be	be	AUX
ejpam-3893	109	12	a	a	DET
ejpam-3893	109	13	finite	finite	ADJ
ejpam-3893	109	14	dimensional	dimensional	ADJ
ejpam-3893	109	15	subspace	subspace	NOUN
ejpam-3893	109	16	of	of	ADP
ejpam-3893	109	17	v	v	NOUN
ejpam-3893	109	18	.	.	PUNCT
ejpam-3893	110	1	the	the	DET
ejpam-3893	110	2	problem	problem	NOUN
ejpam-3893	110	3	now	now	ADV
ejpam-3893	110	4	becomes	become	VERB
ejpam-3893	110	5	;	;	PUNCT
ejpam-3893	110	6	{	{	PUNCT
ejpam-3893	110	7	find	find	VERB
ejpam-3893	110	8	φij	φij	NOUN
ejpam-3893	110	9	in	in	ADP
ejpam-3893	110	10	vj	vj	ADP
ejpam-3893	110	11	such	such	ADJ
ejpam-3893	110	12	that	that	SCONJ
ejpam-3893	110	13	α(φij	α(φij	PROPN
ejpam-3893	110	14	,	,	PUNCT
ejpam-3893	110	15	vj	vj	PROPN
ejpam-3893	110	16	)	)	PUNCT
ejpam-3893	110	17	=	=	SYM
ejpam-3893	111	1	l(vj	l(vj	X
ejpam-3893	111	2	)	)	PUNCT
ejpam-3893	111	3	∀vj	∀vj	NUM
ejpam-3893	111	4	∈	∈	PROPN
ejpam-3893	111	5	vj	vj	X
ejpam-3893	111	6	.	.	PUNCT
ejpam-3893	112	1	(	(	PUNCT
ejpam-3893	112	2	18	18	NUM
ejpam-3893	112	3	)	)	PUNCT
ejpam-3893	112	4	we	we	PRON
ejpam-3893	112	5	express	express	VERB
ejpam-3893	112	6	equation	equation	NOUN
ejpam-3893	112	7	(	(	PUNCT
ejpam-3893	112	8	18	18	NUM
ejpam-3893	112	9	)	)	PUNCT
ejpam-3893	112	10	in	in	ADP
ejpam-3893	112	11	an	an	DET
ejpam-3893	112	12	expanded	expand	VERB
ejpam-3893	112	13	form	form	NOUN
ejpam-3893	112	14	as	as	ADP
ejpam-3893	112	15	β1	β1	PROPN
ejpam-3893	112	16	∫	∫	PROPN
ejpam-3893	112	17	ωf	ωf	PROPN
ejpam-3893	112	18	∇φij∇vjdx+	∇φij∇vjdx+	PROPN
ejpam-3893	112	19	β2	β2	PROPN
ejpam-3893	112	20	∫	∫	PROPN
ejpam-3893	112	21	ωf	ωf	PROPN
ejpam-3893	113	1	∇φijvjdx+	∇φijvjdx+	PROPN
ejpam-3893	113	2	∫	∫	PROPN
ejpam-3893	113	3	ωf	ωf	PRON
ejpam-3893	113	4	φiς	φiς	ADJ
ejpam-3893	113	5	,	,	PUNCT
ejpam-3893	113	6	jvjdx	jvjdx	ADJ
ejpam-3893	113	7	=	=	SYM
ejpam-3893	113	8	β6	β6	PROPN
ejpam-3893	113	9	∫	∫	PROPN
ejpam-3893	113	10	ωf	ωf	PROPN
ejpam-3893	113	11	f	f	PROPN
ejpam-3893	113	12	ivjdx	ivjdx	PROPN
ejpam-3893	113	13	(	(	PUNCT
ejpam-3893	113	14	19	19	NUM
ejpam-3893	113	15	)	)	PUNCT
ejpam-3893	113	16	substituting	substitute	VERB
ejpam-3893	113	17	equation	equation	NOUN
ejpam-3893	113	18	(	(	PUNCT
ejpam-3893	113	19	9	9	NUM
ejpam-3893	113	20	)	)	PUNCT
ejpam-3893	113	21	into	into	ADP
ejpam-3893	113	22	(	(	PUNCT
ejpam-3893	113	23	19	19	NUM
ejpam-3893	113	24	)	)	PUNCT
ejpam-3893	113	25	,	,	PUNCT
ejpam-3893	113	26	we	we	PRON
ejpam-3893	113	27	obtain	obtain	VERB
ejpam-3893	113	28	β1	β1	PROPN
ejpam-3893	113	29	∫	∫	PROPN
ejpam-3893	113	30	ωf	ωf	PROPN
ejpam-3893	113	31	∇φij∇vjdx+β2	∇φij∇vjdx+β2	PROPN
ejpam-3893	113	32	∫	∫	PROPN
ejpam-3893	114	1	ωf	ωf	PROPN
ejpam-3893	115	1	∇φijvjdx+	∇φijvjdx+	PROPN
ejpam-3893	115	2	∫	∫	PROPN
ejpam-3893	115	3	ωf	ωf	INTJ
ejpam-3893	115	4	(	(	PUNCT
ejpam-3893	115	5	β3φ	β3φ	ADP
ejpam-3893	115	6	i+1	i+1	NUM
ejpam-3893	115	7	j	j	NOUN
ejpam-3893	116	1	+	+	CCONJ
ejpam-3893	116	2	β4φ	β4φ	X
ejpam-3893	117	1	i	i	PRON
ejpam-3893	117	2	j	j	NOUN
ejpam-3893	118	1	+	+	CCONJ
ejpam-3893	118	2	β5φ	β5φ	X
ejpam-3893	118	3	i−1	i−1	PROPN
ejpam-3893	118	4	j	j	PROPN
ejpam-3893	118	5	)	)	PUNCT
ejpam-3893	118	6	vjdx	vjdx	NOUN
ejpam-3893	118	7	=	=	SYM
ejpam-3893	118	8	β6	β6	PROPN
ejpam-3893	118	9	∫	∫	PROPN
ejpam-3893	118	10	ωf	ωf	PROPN
ejpam-3893	118	11	f̃	f̃	PROPN
ejpam-3893	118	12	ivjdx	ivjdx	NOUN
ejpam-3893	118	13	(	(	PUNCT
ejpam-3893	118	14	20	20	NUM
ejpam-3893	118	15	)	)	PUNCT
ejpam-3893	118	16	where	where	SCONJ
ejpam-3893	118	17	f̃	f̃	PROPN
ejpam-3893	118	18	i	i	PRON
ejpam-3893	118	19	∈	∈	PROPN
ejpam-3893	118	20	l2	l2	NOUN
ejpam-3893	118	21	is	be	AUX
ejpam-3893	118	22	an	an	DET
ejpam-3893	118	23	extension	extension	NOUN
ejpam-3893	118	24	of	of	ADP
ejpam-3893	118	25	f(x	f(x	PROPN
ejpam-3893	118	26	,	,	PUNCT
ejpam-3893	118	27	yi	yi	NOUN
ejpam-3893	118	28	)	)	PUNCT
ejpam-3893	118	29	in	in	ADP
ejpam-3893	118	30	the	the	DET
ejpam-3893	118	31	fictitious	fictitious	ADJ
ejpam-3893	118	32	domain	domain	NOUN
ejpam-3893	118	33	,	,	PUNCT
ejpam-3893	118	34	ωf	ωf	ADV
ejpam-3893	118	35	.	.	PUNCT
ejpam-3893	119	1	to	to	PART
ejpam-3893	119	2	obtain	obtain	VERB
ejpam-3893	119	3	approximate	approximate	ADJ
ejpam-3893	119	4	solution	solution	NOUN
ejpam-3893	119	5	of	of	ADP
ejpam-3893	119	6	the	the	DET
ejpam-3893	119	7	dp	dp	NOUN
ejpam-3893	119	8	in	in	ADP
ejpam-3893	119	9	equation	equation	NOUN
ejpam-3893	119	10	(	(	PUNCT
ejpam-3893	119	11	18	18	NUM
ejpam-3893	119	12	)	)	PUNCT
ejpam-3893	119	13	,	,	PUNCT
ejpam-3893	119	14	we	we	PRON
ejpam-3893	119	15	employ	employ	VERB
ejpam-3893	119	16	daubechies	daubechie	NOUN
ejpam-3893	119	17	scaling	scale	VERB
ejpam-3893	119	18	function	function	NOUN
ejpam-3893	119	19	.	.	PUNCT
ejpam-3893	120	1	we	we	PRON
ejpam-3893	120	2	seek	seek	VERB
ejpam-3893	120	3	a	a	DET
ejpam-3893	120	4	solution	solution	NOUN
ejpam-3893	120	5	that	that	PRON
ejpam-3893	120	6	is	be	AUX
ejpam-3893	120	7	written	write	VERB
ejpam-3893	120	8	as	as	ADP
ejpam-3893	120	9	a	a	DET
ejpam-3893	120	10	linear	linear	ADJ
ejpam-3893	120	11	combination	combination	NOUN
ejpam-3893	120	12	of	of	ADP
ejpam-3893	120	13	scaling	scale	VERB
ejpam-3893	120	14	function	function	NOUN
ejpam-3893	120	15	and	and	CCONJ
ejpam-3893	120	16	coefficient	coefficient	NOUN
ejpam-3893	120	17	.	.	PUNCT
ejpam-3893	121	1	thus	thus	ADV
ejpam-3893	121	2	,	,	PUNCT
ejpam-3893	121	3	we	we	PRON
ejpam-3893	121	4	define	define	VERB
ejpam-3893	121	5	the	the	DET
ejpam-3893	121	6	fdfdwm	fdfdwm	ADJ
ejpam-3893	121	7	solution	solution	NOUN
ejpam-3893	121	8	for	for	ADP
ejpam-3893	121	9	resolution	resolution	NOUN
ejpam-3893	121	10	m	m	PROPN
ejpam-3893	121	11	with	with	ADP
ejpam-3893	121	12	a	a	DET
ejpam-3893	121	13	scaling	scale	VERB
ejpam-3893	121	14	parameter	parameter	NOUN
ejpam-3893	121	15	k	k	PROPN
ejpam-3893	121	16	at	at	ADP
ejpam-3893	121	17	a	a	DET
ejpam-3893	121	18	fixed	fixed	ADJ
ejpam-3893	121	19	y−coordinate	y−coordinate	PROPN
ejpam-3893	121	20	,	,	PUNCT
ejpam-3893	121	21	yi	yi	PROPN
ejpam-3893	121	22	,	,	PUNCT
ejpam-3893	121	23	as	as	ADP
ejpam-3893	121	24	φw(x	φw(x	NOUN
ejpam-3893	121	25	,	,	PUNCT
ejpam-3893	121	26	yi	yi	PROPN
ejpam-3893	121	27	)	)	PUNCT
ejpam-3893	121	28	=	=	SYM
ejpam-3893	122	1	2	2	NUM
ejpam-3893	122	2	m	m	NOUN
ejpam-3893	122	3	2	2	NUM
ejpam-3893	122	4	∑	∑	PROPN
ejpam-3893	122	5	k	k	PROPN
ejpam-3893	122	6	ξik	ξik	PROPN
ejpam-3893	122	7	,	,	PUNCT
ejpam-3893	122	8	mϕ(2mx−	mϕ(2mx−	PROPN
ejpam-3893	122	9	k	k	PROPN
ejpam-3893	122	10	)	)	PUNCT
ejpam-3893	122	11	(	(	PUNCT
ejpam-3893	122	12	21	21	NUM
ejpam-3893	122	13	)	)	PUNCT
ejpam-3893	122	14	where	where	SCONJ
ejpam-3893	122	15	φw	φw	PROPN
ejpam-3893	122	16	is	be	AUX
ejpam-3893	122	17	the	the	DET
ejpam-3893	122	18	fdfdwm	fdfdwm	ADJ
ejpam-3893	122	19	solution	solution	NOUN
ejpam-3893	122	20	and	and	CCONJ
ejpam-3893	122	21	ξik	ξik	PROPN
ejpam-3893	122	22	,	,	PUNCT
ejpam-3893	122	23	m	m	VERB
ejpam-3893	122	24	are	be	AUX
ejpam-3893	122	25	the	the	DET
ejpam-3893	122	26	scaling	scaling	ADJ
ejpam-3893	122	27	coefficient	coefficient	NOUN
ejpam-3893	122	28	values	value	NOUN
ejpam-3893	122	29	to	to	PART
ejpam-3893	122	30	be	be	AUX
ejpam-3893	122	31	determined	determine	VERB
ejpam-3893	122	32	.	.	PUNCT
ejpam-3893	123	1	now	now	ADV
ejpam-3893	123	2	,	,	PUNCT
ejpam-3893	123	3	we	we	PRON
ejpam-3893	123	4	set	set	VERB
ejpam-3893	123	5	up	up	ADP
ejpam-3893	123	6	a	a	DET
ejpam-3893	123	7	linear	linear	ADJ
ejpam-3893	123	8	system	system	NOUN
ejpam-3893	123	9	for	for	ADP
ejpam-3893	123	10	equation	equation	NOUN
ejpam-3893	123	11	(	(	PUNCT
ejpam-3893	123	12	20	20	NUM
ejpam-3893	123	13	)	)	PUNCT
ejpam-3893	123	14	to	to	PART
ejpam-3893	123	15	solve	solve	VERB
ejpam-3893	123	16	for	for	ADP
ejpam-3893	123	17	ξik	ξik	NOUN
ejpam-3893	123	18	,	,	PUNCT
ejpam-3893	123	19	m.	m.	NOUN
ejpam-3893	123	20	substituting	substitute	VERB
ejpam-3893	123	21	equation	equation	NOUN
ejpam-3893	123	22	(	(	PUNCT
ejpam-3893	123	23	21	21	NUM
ejpam-3893	123	24	)	)	PUNCT
ejpam-3893	123	25	into	into	ADP
ejpam-3893	123	26	(	(	PUNCT
ejpam-3893	123	27	20	20	NUM
ejpam-3893	123	28	)	)	PUNCT
ejpam-3893	123	29	and	and	CCONJ
ejpam-3893	123	30	simpling	simple	VERB
ejpam-3893	123	31	gives	give	NOUN
ejpam-3893	123	32	,	,	PUNCT
ejpam-3893	124	1	2	2	NUM
ejpam-3893	124	2	m	m	NOUN
ejpam-3893	124	3	2	2	NUM
ejpam-3893	124	4	β1	β1	NOUN
ejpam-3893	124	5	∑	∑	PROPN
ejpam-3893	124	6	k	k	PROPN
ejpam-3893	124	7	ξik	ξik	PROPN
ejpam-3893	124	8	,	,	PUNCT
ejpam-3893	124	9	m	m	PROPN
ejpam-3893	124	10	∫	∫	PROPN
ejpam-3893	124	11	ϕ′(2mx−	ϕ′(2mx−	PRON
ejpam-3893	124	12	k)ϕ′(2mx−	k)ϕ′(2mx−	PROPN
ejpam-3893	124	13	j)dx	j)dx	PROPN
ejpam-3893	124	14	+2	+2	PROPN
ejpam-3893	124	15	m	m	VERB
ejpam-3893	124	16	2	2	NUM
ejpam-3893	124	17	β2	β2	VERB
ejpam-3893	124	18	∑	∑	PROPN
ejpam-3893	124	19	k	k	PROPN
ejpam-3893	124	20	ξik	ξik	PROPN
ejpam-3893	124	21	,	,	PUNCT
ejpam-3893	124	22	m	m	PROPN
ejpam-3893	124	23	∫	∫	PROPN
ejpam-3893	124	24	ϕ′(2mx−	ϕ′(2mx−	PROPN
ejpam-3893	124	25	k)ϕ(2mx−	k)ϕ(2mx−	PROPN
ejpam-3893	125	1	j)dx	j)dx	PROPN
ejpam-3893	125	2	+2	+2	ADP
ejpam-3893	125	3	m	m	VERB
ejpam-3893	125	4	2	2	NUM
ejpam-3893	125	5	β3	β3	PROPN
ejpam-3893	125	6	∑	∑	SYM
ejpam-3893	125	7	k	k	PROPN
ejpam-3893	125	8	ξi+1	ξi+1	PROPN
ejpam-3893	125	9	k	k	PROPN
ejpam-3893	125	10	,	,	PUNCT
ejpam-3893	125	11	m	m	PROPN
ejpam-3893	125	12	∫	∫	PROPN
ejpam-3893	125	13	ϕ(2mx−	ϕ(2mx−	PRON
ejpam-3893	125	14	k)ϕ(2mx−	k)ϕ(2mx−	NOUN
ejpam-3893	126	1	j)dx	j)dx	PROPN
ejpam-3893	126	2	f.	f.	PROPN
ejpam-3893	126	3	o.	o.	PROPN
ejpam-3893	126	4	boateng	boateng	PROPN
ejpam-3893	126	5	et	et	PROPN
ejpam-3893	126	6	al	al	PROPN
ejpam-3893	126	7	.	.	PUNCT
ejpam-3893	126	8	/	/	SYM
ejpam-3893	126	9	eur	eur	PROPN
ejpam-3893	126	10	.	.	PUNCT
ejpam-3893	127	1	j.	j.	PROPN
ejpam-3893	127	2	pure	pure	PROPN
ejpam-3893	127	3	appl	appl	PROPN
ejpam-3893	127	4	.	.	PROPN
ejpam-3893	127	5	math	math	PROPN
ejpam-3893	127	6	,	,	PUNCT
ejpam-3893	127	7	14	14	NUM
ejpam-3893	127	8	(	(	PUNCT
ejpam-3893	127	9	3	3	NUM
ejpam-3893	127	10	)	)	PUNCT
ejpam-3893	127	11	(	(	PUNCT
ejpam-3893	127	12	2021	2021	NUM
ejpam-3893	127	13	)	)	PUNCT
ejpam-3893	127	14	,	,	PUNCT
ejpam-3893	127	15	706	706	NUM
ejpam-3893	127	16	-	-	SYM
ejpam-3893	127	17	722	722	NUM
ejpam-3893	127	18	712	712	NUM
ejpam-3893	127	19	+2	+2	NOUN
ejpam-3893	127	20	m	m	VERB
ejpam-3893	127	21	2	2	NUM
ejpam-3893	127	22	β4	β4	PROPN
ejpam-3893	127	23	∑	∑	PUNCT
ejpam-3893	127	24	k	k	PROPN
ejpam-3893	127	25	ξik	ξik	PROPN
ejpam-3893	127	26	,	,	PUNCT
ejpam-3893	127	27	m	m	PROPN
ejpam-3893	127	28	∫	∫	PROPN
ejpam-3893	127	29	ϕ(2mx−	ϕ(2mx−	PRON
ejpam-3893	127	30	k)ϕ(2mx−	k)ϕ(2mx−	NOUN
ejpam-3893	128	1	j)dx	j)dx	PROPN
ejpam-3893	128	2	+2	+2	PROPN
ejpam-3893	128	3	m	m	VERB
ejpam-3893	128	4	2	2	NUM
ejpam-3893	128	5	β5	β5	NOUN
ejpam-3893	128	6	∑	∑	PUNCT
ejpam-3893	128	7	k	k	PROPN
ejpam-3893	128	8	ξi−1	ξi−1	PROPN
ejpam-3893	128	9	k	k	PROPN
ejpam-3893	128	10	,	,	PUNCT
ejpam-3893	128	11	m	m	PROPN
ejpam-3893	128	12	∫	∫	PROPN
ejpam-3893	128	13	ϕ(2mx−	ϕ(2mx−	DET
ejpam-3893	128	14	k)ϕ(2mx−	k)ϕ(2mx−	NOUN
ejpam-3893	129	1	j)dx	j)dx	PROPN
ejpam-3893	129	2	=	=	SYM
ejpam-3893	129	3	2	2	NUM
ejpam-3893	129	4	m	m	NOUN
ejpam-3893	129	5	2	2	NUM
ejpam-3893	129	6	β6f̃	β6f̃	NOUN
ejpam-3893	130	1	i	i	PRON
ejpam-3893	130	2	∫	∫	PROPN
ejpam-3893	131	1	ϕ(2mx−	ϕ(2mx−	PRON
ejpam-3893	131	2	k)ϕ(2mx−	k)ϕ(2mx−	NOUN
ejpam-3893	132	1	j)dx	j)dx	PROPN
ejpam-3893	132	2	(	(	PUNCT
ejpam-3893	132	3	22	22	NUM
ejpam-3893	132	4	)	)	PUNCT
ejpam-3893	132	5	we	we	PRON
ejpam-3893	132	6	set	set	VERB
ejpam-3893	132	7	up	up	ADP
ejpam-3893	132	8	a	a	DET
ejpam-3893	132	9	linear	linear	ADJ
ejpam-3893	132	10	system	system	NOUN
ejpam-3893	132	11	from	from	ADP
ejpam-3893	132	12	equation	equation	NOUN
ejpam-3893	132	13	(	(	PUNCT
ejpam-3893	132	14	22	22	NUM
ejpam-3893	132	15	)	)	PUNCT
ejpam-3893	132	16	by	by	ADP
ejpam-3893	132	17	introducing	introduce	VERB
ejpam-3893	132	18	connection	connection	NOUN
ejpam-3893	132	19	coefficients	coefficient	NOUN
ejpam-3893	132	20	.	.	PUNCT
ejpam-3893	133	1	that	that	PRON
ejpam-3893	133	2	is	be	AUX
ejpam-3893	133	3	,	,	PUNCT
ejpam-3893	133	4	ω2	ω2	ADJ
ejpam-3893	133	5	k−j	k−j	X
ejpam-3893	133	6	=	=	SYM
ejpam-3893	134	1	∫	∫	PROPN
ejpam-3893	134	2	∞	∞	PROPN
ejpam-3893	135	1	−∞	−∞	PROPN
ejpam-3893	135	2	ϕ′(x	ϕ′(x	PROPN
ejpam-3893	135	3	−	−	PROPN
ejpam-3893	135	4	k)ϕ′(x	k)ϕ′(x	NOUN
ejpam-3893	135	5	−	−	PROPN
ejpam-3893	135	6	j)dx	j)dx	PROPN
ejpam-3893	135	7	,	,	PUNCT
ejpam-3893	135	8	for	for	ADP
ejpam-3893	135	9	derivative	derivative	ADJ
ejpam-3893	135	10	d	d	NOUN
ejpam-3893	135	11	=	=	SYM
ejpam-3893	135	12	2	2	NUM
ejpam-3893	135	13	,	,	PUNCT
ejpam-3893	135	14	ωk−j	ωk−j	NOUN
ejpam-3893	135	15	=	=	SYM
ejpam-3893	136	1	∫	∫	PROPN
ejpam-3893	136	2	∞	∞	PROPN
ejpam-3893	137	1	−∞	−∞	PROPN
ejpam-3893	137	2	ϕ′(x	ϕ′(x	PROPN
ejpam-3893	137	3	−	−	PROPN
ejpam-3893	137	4	k)ϕ(x	k)ϕ(x	X
ejpam-3893	138	1	−	−	PUNCT
ejpam-3893	138	2	j)dx	j)dx	PROPN
ejpam-3893	138	3	,	,	PUNCT
ejpam-3893	138	4	for	for	ADP
ejpam-3893	138	5	derivative	derivative	ADJ
ejpam-3893	138	6	d	d	NOUN
ejpam-3893	138	7	=	=	SYM
ejpam-3893	138	8	1	1	NUM
ejpam-3893	138	9	and	and	CCONJ
ejpam-3893	138	10	the	the	DET
ejpam-3893	138	11	kronecker	kronecker	NOUN
ejpam-3893	138	12	-	-	PUNCT
ejpam-3893	138	13	delta	delta	NOUN
ejpam-3893	138	14	function	function	NOUN
ejpam-3893	138	15	,	,	PUNCT
ejpam-3893	138	16	δk	δk	PROPN
ejpam-3893	138	17	,	,	PUNCT
ejpam-3893	138	18	j	j	PROPN
ejpam-3893	138	19	=	=	SYM
ejpam-3893	138	20	∫	∫	PROPN
ejpam-3893	138	21	∞	∞	PROPN
ejpam-3893	139	1	−∞	−∞	ADP
ejpam-3893	139	2	ϕ(x	ϕ(x	PROPN
ejpam-3893	139	3	−	−	PROPN
ejpam-3893	139	4	k)ϕ(x	k)ϕ(x	X
ejpam-3893	140	1	−	−	PROPN
ejpam-3893	141	1	j)dx	j)dx	PROPN
ejpam-3893	141	2	where	where	SCONJ
ejpam-3893	141	3	we	we	PRON
ejpam-3893	141	4	set	set	VERB
ejpam-3893	141	5	x	x	X
ejpam-3893	141	6	=	=	SYM
ejpam-3893	141	7	2mx	2mx	NOUN
ejpam-3893	141	8	we	we	PRON
ejpam-3893	141	9	handle	handle	VERB
ejpam-3893	141	10	the	the	DET
ejpam-3893	141	11	exterior	exterior	ADJ
ejpam-3893	141	12	nodes	node	NOUN
ejpam-3893	141	13	of	of	ADP
ejpam-3893	141	14	ξi+1	ξi+1	NUM
ejpam-3893	141	15	k	k	NOUN
ejpam-3893	141	16	,	,	PUNCT
ejpam-3893	141	17	m	m	VERB
ejpam-3893	141	18	and	and	CCONJ
ejpam-3893	141	19	ξi−1	ξi−1	PROPN
ejpam-3893	141	20	k	k	PROPN
ejpam-3893	141	21	,	,	PUNCT
ejpam-3893	141	22	m	m	VERB
ejpam-3893	141	23	by	by	ADP
ejpam-3893	141	24	applying	apply	VERB
ejpam-3893	141	25	a	a	DET
ejpam-3893	141	26	shift	shift	NOUN
ejpam-3893	141	27	to	to	ADP
ejpam-3893	141	28	the	the	DET
ejpam-3893	141	29	scaling	scaling	NOUN
ejpam-3893	141	30	functions	function	NOUN
ejpam-3893	141	31	in	in	ADP
ejpam-3893	141	32	the	the	DET
ejpam-3893	141	33	following	following	ADJ
ejpam-3893	141	34	manner	manner	NOUN
ejpam-3893	141	35	:	:	PUNCT
ejpam-3893	141	36	ξi+1	ξi+1	ADV
ejpam-3893	141	37	k	k	X
ejpam-3893	141	38	,	,	PUNCT
ejpam-3893	141	39	mϕ(2mx−	mϕ(2mx−	PROPN
ejpam-3893	141	40	k)ϕ(2mx−	k)ϕ(2mx−	PROPN
ejpam-3893	141	41	j	j	PROPN
ejpam-3893	141	42	)	)	PUNCT
ejpam-3893	141	43	=	=	SYM
ejpam-3893	141	44	ξik	ξik	PROPN
ejpam-3893	141	45	,	,	PUNCT
ejpam-3893	141	46	mϕ(2mx−	mϕ(2mx−	PROPN
ejpam-3893	141	47	k	k	PROPN
ejpam-3893	141	48	+	+	PROPN
ejpam-3893	141	49	1)ϕ(2mx−	1)ϕ(2mx−	NUM
ejpam-3893	141	50	j	j	NOUN
ejpam-3893	141	51	)	)	PUNCT
ejpam-3893	141	52	(	(	PUNCT
ejpam-3893	141	53	23	23	NUM
ejpam-3893	141	54	)	)	PUNCT
ejpam-3893	141	55	and	and	CCONJ
ejpam-3893	141	56	ξi−1	ξi−1	PROPN
ejpam-3893	141	57	k	k	PROPN
ejpam-3893	141	58	,	,	PUNCT
ejpam-3893	141	59	mϕ(2mx−	mϕ(2mx−	PROPN
ejpam-3893	141	60	k)ϕ(2mx−	k)ϕ(2mx−	PROPN
ejpam-3893	141	61	j	j	PROPN
ejpam-3893	141	62	)	)	PUNCT
ejpam-3893	141	63	=	=	SYM
ejpam-3893	141	64	ξik	ξik	PROPN
ejpam-3893	141	65	,	,	PUNCT
ejpam-3893	141	66	mϕ(2mx−	mϕ(2mx−	PROPN
ejpam-3893	141	67	k	k	PROPN
ejpam-3893	142	1	−	−	PROPN
ejpam-3893	142	2	1)ϕ(2mx−	1)ϕ(2mx−	NUM
ejpam-3893	142	3	j	j	NOUN
ejpam-3893	142	4	)	)	PUNCT
ejpam-3893	142	5	(	(	PUNCT
ejpam-3893	142	6	24	24	NUM
ejpam-3893	142	7	)	)	PUNCT
ejpam-3893	142	8	substituting	substitute	VERB
ejpam-3893	142	9	equations	equation	NOUN
ejpam-3893	142	10	(	(	PUNCT
ejpam-3893	142	11	23	23	NUM
ejpam-3893	142	12	)	)	PUNCT
ejpam-3893	142	13	and	and	CCONJ
ejpam-3893	142	14	(	(	PUNCT
ejpam-3893	142	15	24	24	NUM
ejpam-3893	142	16	)	)	PUNCT
ejpam-3893	142	17	into	into	ADP
ejpam-3893	142	18	(	(	PUNCT
ejpam-3893	142	19	22	22	NUM
ejpam-3893	142	20	)	)	PUNCT
ejpam-3893	142	21	,	,	PUNCT
ejpam-3893	142	22	we	we	PRON
ejpam-3893	142	23	obtain∑	obtain∑	VERB
ejpam-3893	142	24	k	k	X
ejpam-3893	142	25	[	[	PUNCT
ejpam-3893	142	26	ξik	ξik	PROPN
ejpam-3893	142	27	,	,	PUNCT
ejpam-3893	142	28	mω2	mω2	PRON
ejpam-3893	142	29	k−j	k−j	X
ejpam-3893	143	1	+	+	CCONJ
ejpam-3893	143	2	β2ξ	β2ξ	PROPN
ejpam-3893	143	3	i	i	PRON
ejpam-3893	143	4	k	k	PROPN
ejpam-3893	143	5	,	,	PUNCT
ejpam-3893	143	6	mωk−j	mωk−j	NOUN
ejpam-3893	144	1	+	+	NUM
ejpam-3893	144	2	β3ξ	β3ξ	PUNCT
ejpam-3893	144	3	i	i	PROPN
ejpam-3893	144	4	k	k	PROPN
ejpam-3893	144	5	,	,	PUNCT
ejpam-3893	144	6	mδk+1,j	mδk+1,j	NOUN
ejpam-3893	144	7	+	+	CCONJ
ejpam-3893	144	8	β4ξ	β4ξ	VERB
ejpam-3893	144	9	i	i	PRON
ejpam-3893	144	10	k	k	PROPN
ejpam-3893	144	11	,	,	PUNCT
ejpam-3893	144	12	mδk	mδk	PROPN
ejpam-3893	144	13	,	,	PUNCT
ejpam-3893	144	14	j	j	PROPN
ejpam-3893	145	1	+	+	CCONJ
ejpam-3893	145	2	β5ξ	β5ξ	PUNCT
ejpam-3893	145	3	i	i	PRON
ejpam-3893	145	4	k	k	NOUN
ejpam-3893	145	5	,	,	PUNCT
ejpam-3893	145	6	mδk−1,j	mδk−1,j	NOUN
ejpam-3893	145	7	]	]	X
ejpam-3893	146	1	=	=	PUNCT
ejpam-3893	146	2	β6f̃	β6f̃	PROPN
ejpam-3893	146	3	iδk	iδk	PROPN
ejpam-3893	146	4	,	,	PUNCT
ejpam-3893	146	5	j	j	PROPN
ejpam-3893	146	6	(	(	PUNCT
ejpam-3893	146	7	25	25	NUM
ejpam-3893	146	8	)	)	PUNCT
ejpam-3893	146	9	we	we	PRON
ejpam-3893	146	10	write	write	VERB
ejpam-3893	146	11	equation	equation	NOUN
ejpam-3893	146	12	(	(	PUNCT
ejpam-3893	146	13	25	25	NUM
ejpam-3893	146	14	)	)	PUNCT
ejpam-3893	146	15	as	as	ADP
ejpam-3893	146	16	a	a	DET
ejpam-3893	146	17	linear	linear	ADJ
ejpam-3893	146	18	system	system	NOUN
ejpam-3893	146	19	in	in	ADP
ejpam-3893	146	20	a	a	DET
ejpam-3893	146	21	vector	vector	NOUN
ejpam-3893	146	22	form	form	NOUN
ejpam-3893	146	23	,	,	PUNCT
ejpam-3893	146	24	given	give	VERB
ejpam-3893	146	25	by	by	ADP
ejpam-3893	146	26	a1	a1	PROPN
ejpam-3893	146	27	~ξ	~ξ	PUNCT
ejpam-3893	146	28	+	+	PROPN
ejpam-3893	146	29	a2	a2	PROPN
ejpam-3893	146	30	~ξ	~ξ	PUNCT
ejpam-3893	146	31	+	+	NOUN
ejpam-3893	146	32	a3	a3	NOUN
ejpam-3893	146	33	~ξ	~ξ	PUNCT
ejpam-3893	146	34	+	+	ADJ
ejpam-3893	146	35	a4	a4	NOUN
ejpam-3893	146	36	~ξ	~ξ	PUNCT
ejpam-3893	146	37	+	+	ADV
ejpam-3893	146	38	a5	a5	NOUN
ejpam-3893	146	39	~ξ	~ξ	PUNCT
ejpam-3893	146	40	=	=	SYM
ejpam-3893	146	41	f	f	PROPN
ejpam-3893	146	42	(	(	PUNCT
ejpam-3893	146	43	26	26	NUM
ejpam-3893	146	44	)	)	PUNCT
ejpam-3893	146	45	where	where	SCONJ
ejpam-3893	146	46	a1	a1	NOUN
ejpam-3893	146	47	=	=	SYM
ejpam-3893	146	48	β1	β1	PROPN
ejpam-3893	146	49	∑	∑	PROPN
ejpam-3893	146	50	k	k	PROPN
ejpam-3893	146	51	ω2	ω2	ADJ
ejpam-3893	146	52	k−j	k−j	PROPN
ejpam-3893	146	53	,	,	PUNCT
ejpam-3893	146	54	a2	a2	PROPN
ejpam-3893	146	55	=	=	PUNCT
ejpam-3893	146	56	β2	β2	VERB
ejpam-3893	146	57	∑	∑	PROPN
ejpam-3893	146	58	k	k	PROPN
ejpam-3893	146	59	ωk−j	ωk−j	PROPN
ejpam-3893	146	60	,	,	PUNCT
ejpam-3893	146	61	a3	a3	NOUN
ejpam-3893	146	62	=	=	PRON
ejpam-3893	146	63	β3	β3	VERB
ejpam-3893	146	64	∑	∑	PROPN
ejpam-3893	146	65	k	k	NOUN
ejpam-3893	146	66	δk+1,j	δk+1,j	NOUN
ejpam-3893	146	67	,	,	PUNCT
ejpam-3893	146	68	a4	a4	NOUN
ejpam-3893	146	69	=	=	SYM
ejpam-3893	146	70	β4	β4	PROPN
ejpam-3893	146	71	∑	∑	PUNCT
ejpam-3893	146	72	k	k	PROPN
ejpam-3893	146	73	δk	δk	PROPN
ejpam-3893	146	74	,	,	PUNCT
ejpam-3893	146	75	j	j	PROPN
ejpam-3893	146	76	,	,	PUNCT
ejpam-3893	147	1	a5	a5	PROPN
ejpam-3893	147	2	=	=	SYM
ejpam-3893	147	3	β5	β5	PROPN
ejpam-3893	147	4	∑	∑	PUNCT
ejpam-3893	147	5	k	k	NOUN
ejpam-3893	147	6	δk−1,j	δk−1,j	NOUN
ejpam-3893	147	7	and	and	CCONJ
ejpam-3893	147	8	f	f	NOUN
ejpam-3893	147	9	=	=	PROPN
ejpam-3893	147	10	β6f̃	β6f̃	PROPN
ejpam-3893	147	11	iδk	iδk	PROPN
ejpam-3893	147	12	,	,	PUNCT
ejpam-3893	147	13	j	j	PROPN
ejpam-3893	147	14	the	the	DET
ejpam-3893	147	15	indexes	index	NOUN
ejpam-3893	147	16	k	k	PROPN
ejpam-3893	147	17	and	and	CCONJ
ejpam-3893	147	18	j	j	PROPN
ejpam-3893	147	19	are	be	AUX
ejpam-3893	147	20	delimited	delimit	VERB
ejpam-3893	147	21	to	to	ADP
ejpam-3893	147	22	the	the	DET
ejpam-3893	147	23	whole	whole	ADJ
ejpam-3893	147	24	domain	domain	NOUN
ejpam-3893	147	25	.	.	PUNCT
ejpam-3893	148	1	we	we	PRON
ejpam-3893	148	2	recall	recall	VERB
ejpam-3893	148	3	that	that	SCONJ
ejpam-3893	148	4	,	,	PUNCT
ejpam-3893	148	5	the	the	DET
ejpam-3893	148	6	original	original	ADJ
ejpam-3893	148	7	domain	domain	NOUN
ejpam-3893	148	8	is	be	AUX
ejpam-3893	148	9	discretized	discretize	VERB
ejpam-3893	148	10	with	with	ADP
ejpam-3893	148	11	nx	nx	NOUN
ejpam-3893	148	12	functions	function	NOUN
ejpam-3893	148	13	.	.	PUNCT
ejpam-3893	149	1	the	the	DET
ejpam-3893	149	2	fictitious	fictitious	ADJ
ejpam-3893	149	3	domain	domain	NOUN
ejpam-3893	149	4	approach	approach	NOUN
ejpam-3893	149	5	requires	require	VERB
ejpam-3893	149	6	that	that	SCONJ
ejpam-3893	149	7	f.	f.	PROPN
ejpam-3893	149	8	o.	o.	PROPN
ejpam-3893	149	9	boateng	boateng	PROPN
ejpam-3893	149	10	et	et	PROPN
ejpam-3893	149	11	al	al	PROPN
ejpam-3893	149	12	.	.	PUNCT
ejpam-3893	149	13	/	/	SYM
ejpam-3893	149	14	eur	eur	PROPN
ejpam-3893	149	15	.	.	PUNCT
ejpam-3893	150	1	j.	j.	PROPN
ejpam-3893	150	2	pure	pure	PROPN
ejpam-3893	150	3	appl	appl	PROPN
ejpam-3893	150	4	.	.	PROPN
ejpam-3893	150	5	math	math	PROPN
ejpam-3893	150	6	,	,	PUNCT
ejpam-3893	150	7	14	14	NUM
ejpam-3893	150	8	(	(	PUNCT
ejpam-3893	150	9	3	3	NUM
ejpam-3893	150	10	)	)	PUNCT
ejpam-3893	150	11	(	(	PUNCT
ejpam-3893	150	12	2021	2021	NUM
ejpam-3893	150	13	)	)	PUNCT
ejpam-3893	150	14	,	,	PUNCT
ejpam-3893	150	15	706	706	NUM
ejpam-3893	150	16	-	-	SYM
ejpam-3893	150	17	722	722	NUM
ejpam-3893	150	18	713	713	NUM
ejpam-3893	150	19	n	n	DET
ejpam-3893	150	20	−	−	NOUN
ejpam-3893	150	21	1	1	NUM
ejpam-3893	150	22	scaling	scaling	NOUN
ejpam-3893	150	23	functions	function	NOUN
ejpam-3893	150	24	be	be	AUX
ejpam-3893	150	25	added	add	VERB
ejpam-3893	150	26	to	to	ADP
ejpam-3893	150	27	each	each	DET
ejpam-3893	150	28	end	end	NOUN
ejpam-3893	150	29	of	of	ADP
ejpam-3893	150	30	the	the	DET
ejpam-3893	150	31	domain	domain	NOUN
ejpam-3893	150	32	,	,	PUNCT
ejpam-3893	150	33	then	then	ADV
ejpam-3893	150	34	the	the	DET
ejpam-3893	150	35	new	new	ADJ
ejpam-3893	150	36	domain	domain	NOUN
ejpam-3893	150	37	,	,	PUNCT
ejpam-3893	150	38	spanned	span	VERB
ejpam-3893	150	39	by	by	ADP
ejpam-3893	150	40	the	the	DET
ejpam-3893	150	41	fictitious	fictitious	ADJ
ejpam-3893	150	42	domain	domain	NOUN
ejpam-3893	150	43	will	will	AUX
ejpam-3893	150	44	expand	expand	VERB
ejpam-3893	150	45	from	from	ADP
ejpam-3893	150	46	−(n−1	−(n−1	PROPN
ejpam-3893	150	47	)	)	PUNCT
ejpam-3893	150	48	to	to	PART
ejpam-3893	150	49	nx−1+(n−1	nx−1+(n−1	PROPN
ejpam-3893	150	50	)	)	PUNCT
ejpam-3893	150	51	.	.	PUNCT
ejpam-3893	151	1	this	this	PRON
ejpam-3893	151	2	will	will	AUX
ejpam-3893	151	3	result	result	VERB
ejpam-3893	151	4	in	in	ADP
ejpam-3893	151	5	a	a	DET
ejpam-3893	151	6	linear	linear	ADJ
ejpam-3893	151	7	system	system	NOUN
ejpam-3893	151	8	with	with	ADP
ejpam-3893	151	9	size	size	NOUN
ejpam-3893	151	10	,	,	PUNCT
ejpam-3893	151	11	nx	nx	PROPN
ejpam-3893	151	12	+2(n	+2(n	PROPN
ejpam-3893	151	13	−1	−1	NOUN
ejpam-3893	151	14	)	)	PUNCT
ejpam-3893	151	15	.	.	PUNCT
ejpam-3893	152	1	thus	thus	ADV
ejpam-3893	152	2	,	,	PUNCT
ejpam-3893	152	3	−(n	−(n	NOUN
ejpam-3893	152	4	−1	−1	NOUN
ejpam-3893	152	5	)	)	PUNCT
ejpam-3893	152	6	≤	≤	PUNCT
ejpam-3893	153	1	k	k	X
ejpam-3893	153	2	≤	≤	NUM
ejpam-3893	153	3	nx	nx	INTJ
ejpam-3893	153	4	−	−	PROPN
ejpam-3893	153	5	1+(n	1+(n	NUM
ejpam-3893	153	6	−1	−1	NOUN
ejpam-3893	153	7	)	)	PUNCT
ejpam-3893	153	8	and	and	CCONJ
ejpam-3893	153	9	−(n	−(n	NOUN
ejpam-3893	153	10	−	−	PROPN
ejpam-3893	153	11	1	1	NUM
ejpam-3893	153	12	)	)	PUNCT
ejpam-3893	153	13	≤	≤	NUM
ejpam-3893	153	14	j	j	PROPN
ejpam-3893	153	15	≤	≤	ADV
ejpam-3893	153	16	nx	nx	NOUN
ejpam-3893	153	17	−	−	PROPN
ejpam-3893	153	18	1	1	NUM
ejpam-3893	153	19	+	+	CCONJ
ejpam-3893	153	20	(	(	PUNCT
ejpam-3893	153	21	n	n	CCONJ
ejpam-3893	153	22	−	−	PROPN
ejpam-3893	153	23	1	1	NUM
ejpam-3893	153	24	)	)	PUNCT
ejpam-3893	153	25	,	,	PUNCT
ejpam-3893	153	26	and	and	CCONJ
ejpam-3893	153	27	so	so	ADV
ejpam-3893	153	28	equation	equation	NOUN
ejpam-3893	153	29	(	(	PUNCT
ejpam-3893	153	30	26	26	NUM
ejpam-3893	153	31	)	)	PUNCT
ejpam-3893	153	32	will	will	AUX
ejpam-3893	153	33	be	be	AUX
ejpam-3893	153	34	an	an	DET
ejpam-3893	153	35	(	(	PUNCT
ejpam-3893	153	36	nx	nx	NOUN
ejpam-3893	153	37	+	+	NOUN
ejpam-3893	153	38	2(n	2(n	NUM
ejpam-3893	153	39	−	−	NUM
ejpam-3893	153	40	1))×	1))×	NUM
ejpam-3893	153	41	(	(	PUNCT
ejpam-3893	153	42	nx	nx	PROPN
ejpam-3893	153	43	+	+	CCONJ
ejpam-3893	153	44	2(n	2(n	NUM
ejpam-3893	153	45	−	−	NOUN
ejpam-3893	153	46	1	1	NUM
ejpam-3893	153	47	)	)	PUNCT
ejpam-3893	153	48	)	)	PUNCT
ejpam-3893	153	49	linear	linear	ADJ
ejpam-3893	153	50	system	system	NOUN
ejpam-3893	153	51	.	.	PUNCT
ejpam-3893	154	1	we	we	PRON
ejpam-3893	154	2	use	use	VERB
ejpam-3893	154	3	daubechies	daubechie	NOUN
ejpam-3893	154	4	scaling	scale	VERB
ejpam-3893	154	5	functions	function	NOUN
ejpam-3893	154	6	of	of	ADP
ejpam-3893	154	7	order	order	NOUN
ejpam-3893	154	8	six	six	NUM
ejpam-3893	154	9	(	(	PUNCT
ejpam-3893	154	10	i.e	i.e	PROPN
ejpam-3893	154	11	dn6	dn6	PROPN
ejpam-3893	154	12	)	)	PUNCT
ejpam-3893	154	13	to	to	PART
ejpam-3893	154	14	construct	construct	VERB
ejpam-3893	154	15	matrices	matrix	NOUN
ejpam-3893	154	16	for	for	ADP
ejpam-3893	154	17	the	the	DET
ejpam-3893	154	18	linear	linear	ADJ
ejpam-3893	154	19	system	system	NOUN
ejpam-3893	154	20	.	.	PUNCT
ejpam-3893	155	1	the	the	DET
ejpam-3893	155	2	matrices	matrix	NOUN
ejpam-3893	155	3	a1	a1	NOUN
ejpam-3893	155	4	and	and	CCONJ
ejpam-3893	155	5	a2	a2	PROPN
ejpam-3893	155	6	are	be	AUX
ejpam-3893	155	7	(	(	PUNCT
ejpam-3893	155	8	2n	2n	NUM
ejpam-3893	155	9	−3)-diagonal	−3)-diagonal	NOUN
ejpam-3893	155	10	(	(	PUNCT
ejpam-3893	155	11	nx	nx	PROPN
ejpam-3893	155	12	+2(n	+2(n	INTJ
ejpam-3893	155	13	−1))×	−1))×	PROPN
ejpam-3893	155	14	(	(	PUNCT
ejpam-3893	155	15	nx	nx	X
ejpam-3893	155	16	+	+	CCONJ
ejpam-3893	155	17	2(n	2(n	NUM
ejpam-3893	155	18	−	−	NOUN
ejpam-3893	155	19	1	1	NUM
ejpam-3893	155	20	)	)	PUNCT
ejpam-3893	155	21	)	)	PUNCT
ejpam-3893	155	22	matrices	matrix	NOUN
ejpam-3893	155	23	.	.	PUNCT
ejpam-3893	156	1	we	we	PRON
ejpam-3893	156	2	reserve	reserve	VERB
ejpam-3893	156	3	the	the	DET
ejpam-3893	156	4	first	first	ADJ
ejpam-3893	156	5	and	and	CCONJ
ejpam-3893	156	6	last	last	ADJ
ejpam-3893	156	7	rows	row	NOUN
ejpam-3893	156	8	for	for	ADP
ejpam-3893	156	9	the	the	DET
ejpam-3893	156	10	enforcement	enforcement	NOUN
ejpam-3893	156	11	of	of	ADP
ejpam-3893	156	12	the	the	DET
ejpam-3893	156	13	dirichlet	dirichlet	PROPN
ejpam-3893	156	14	boundary	boundary	PROPN
ejpam-3893	156	15	condition	condition	NOUN
ejpam-3893	156	16	.	.	PUNCT
ejpam-3893	157	1	we	we	PRON
ejpam-3893	157	2	treat	treat	VERB
ejpam-3893	157	3	thoroughly	thoroughly	ADV
ejpam-3893	157	4	the	the	DET
ejpam-3893	157	5	implementation	implementation	NOUN
ejpam-3893	157	6	of	of	ADP
ejpam-3893	157	7	the	the	DET
ejpam-3893	157	8	boundary	boundary	ADJ
ejpam-3893	157	9	conditions	condition	NOUN
ejpam-3893	157	10	in	in	ADP
ejpam-3893	157	11	section	section	NOUN
ejpam-3893	157	12	2.4	2.4	NUM
ejpam-3893	157	13	we	we	PRON
ejpam-3893	157	14	present	present	VERB
ejpam-3893	157	15	matrices	matrix	NOUN
ejpam-3893	157	16	,	,	PUNCT
ejpam-3893	157	17	a1	a1	NOUN
ejpam-3893	157	18	and	and	CCONJ
ejpam-3893	157	19	a2	a2	PROPN
ejpam-3893	157	20	as	as	SCONJ
ejpam-3893	157	21	follows	follow	VERB
ejpam-3893	157	22	:	:	PUNCT
ejpam-3893	157	23	a1	a1	NOUN
ejpam-3893	157	24	=	=	SYM
ejpam-3893	157	25	β1	β1	NOUN
ejpam-3893	157	26			NOUN
ejpam-3893	157	27	0	0	NUM
ejpam-3893	157	28	0	0	NUM
ejpam-3893	157	29	0	0	NUM
ejpam-3893	157	30	0	0	NUM
ejpam-3893	157	31	0	0	NUM
ejpam-3893	157	32	0	0	NUM
ejpam-3893	157	33	0	0	NUM
ejpam-3893	157	34	·	·	PUNCT
ejpam-3893	157	35	·	·	PUNCT
ejpam-3893	157	36	·	·	PUNCT
ejpam-3893	158	1	ω2	ω2	NUM
ejpam-3893	158	2	−1	−1	NOUN
ejpam-3893	158	3	ω2	ω2	PROPN
ejpam-3893	158	4	0	0	NUM
ejpam-3893	159	1	ω2	ω2	ADJ
ejpam-3893	159	2	1	1	NUM
ejpam-3893	159	3	ω2	ω2	NUM
ejpam-3893	159	4	2	2	NUM
ejpam-3893	159	5	ω2	ω2	NOUN
ejpam-3893	159	6	3	3	NUM
ejpam-3893	159	7	ω2	ω2	CCONJ
ejpam-3893	159	8	4	4	NUM
ejpam-3893	159	9	0	0	NUM
ejpam-3893	159	10	·	·	PUNCT
ejpam-3893	159	11	·	·	PUNCT
ejpam-3893	159	12	·	·	PUNCT
ejpam-3893	160	1	ω2	ω2	ADJ
ejpam-3893	160	2	−2	−2	PROPN
ejpam-3893	160	3	ω2	ω2	ADJ
ejpam-3893	160	4	−1	−1	NOUN
ejpam-3893	160	5	ω2	ω2	PROPN
ejpam-3893	160	6	0	0	NUM
ejpam-3893	161	1	ω2	ω2	ADJ
ejpam-3893	161	2	1	1	NUM
ejpam-3893	161	3	ω2	ω2	NUM
ejpam-3893	161	4	2	2	NUM
ejpam-3893	161	5	ω2	ω2	NOUN
ejpam-3893	161	6	3	3	NUM
ejpam-3893	161	7	ω2	ω2	CCONJ
ejpam-3893	161	8	4	4	NUM
ejpam-3893	161	9	0	0	NUM
ejpam-3893	161	10	·	·	PUNCT
ejpam-3893	161	11	·	·	PUNCT
ejpam-3893	161	12	·	·	PUNCT
ejpam-3893	162	1	ω2	ω2	ADV
ejpam-3893	162	2	−3	−3	PROPN
ejpam-3893	162	3	ω2	ω2	ADJ
ejpam-3893	162	4	−2	−2	PROPN
ejpam-3893	162	5	ω2	ω2	ADJ
ejpam-3893	162	6	−1	−1	NOUN
ejpam-3893	162	7	ω2	ω2	PROPN
ejpam-3893	162	8	0	0	NUM
ejpam-3893	162	9	ω2	ω2	ADJ
ejpam-3893	162	10	1	1	NUM
ejpam-3893	162	11	ω2	ω2	NUM
ejpam-3893	162	12	2	2	NUM
ejpam-3893	162	13	ω2	ω2	NOUN
ejpam-3893	162	14	3	3	NUM
ejpam-3893	162	15	ω2	ω2	CCONJ
ejpam-3893	162	16	4	4	NUM
ejpam-3893	162	17	0	0	NUM
ejpam-3893	162	18	·	·	PUNCT
ejpam-3893	162	19	·	·	PUNCT
ejpam-3893	162	20	·	·	PUNCT
ejpam-3893	163	1	ω2	ω2	ADV
ejpam-3893	163	2	−4	−4	PROPN
ejpam-3893	163	3	ω2	ω2	ADJ
ejpam-3893	163	4	−3	−3	PROPN
ejpam-3893	163	5	ω2	ω2	ADJ
ejpam-3893	163	6	−2	−2	PROPN
ejpam-3893	163	7	ω2	ω2	ADJ
ejpam-3893	163	8	−1	−1	NOUN
ejpam-3893	163	9	ω2	ω2	PROPN
ejpam-3893	163	10	0	0	NUM
ejpam-3893	163	11	ω2	ω2	ADJ
ejpam-3893	163	12	1	1	NUM
ejpam-3893	163	13	ω2	ω2	NUM
ejpam-3893	163	14	2	2	NUM
ejpam-3893	163	15	ω2	ω2	NOUN
ejpam-3893	163	16	3	3	NUM
ejpam-3893	163	17	ω2	ω2	CCONJ
ejpam-3893	163	18	4	4	NUM
ejpam-3893	163	19	0	0	NUM
ejpam-3893	163	20	0	0	NUM
ejpam-3893	163	21	ω2	ω2	ADJ
ejpam-3893	163	22	−4	−4	PROPN
ejpam-3893	163	23	ω2	ω2	PROPN
ejpam-3893	163	24	−3	−3	PROPN
ejpam-3893	163	25	ω2	ω2	ADJ
ejpam-3893	163	26	−2	−2	PROPN
ejpam-3893	163	27	ω2	ω2	ADJ
ejpam-3893	163	28	−1	−1	NOUN
ejpam-3893	163	29	ω2	ω2	PROPN
ejpam-3893	163	30	0	0	NUM
ejpam-3893	163	31	ω2	ω2	ADJ
ejpam-3893	163	32	1	1	NUM
ejpam-3893	163	33	ω2	ω2	NUM
ejpam-3893	163	34	2	2	NUM
ejpam-3893	163	35	ω2	ω2	NOUN
ejpam-3893	163	36	3	3	NUM
ejpam-3893	163	37	ω2	ω2	PROPN
ejpam-3893	163	38	4	4	NUM
ejpam-3893	163	39	...	...	PUNCT
ejpam-3893	163	40	...	...	PUNCT
ejpam-3893	163	41	...	...	PUNCT
ejpam-3893	163	42	...	...	PUNCT
ejpam-3893	163	43	...	...	PUNCT
ejpam-3893	163	44	...	...	PUNCT
ejpam-3893	163	45	...	...	PUNCT
ejpam-3893	163	46	...	...	PUNCT
ejpam-3893	163	47	.	.	PUNCT
ejpam-3893	163	48	.	.	PUNCT
ejpam-3893	163	49	.	.	PUNCT
ejpam-3893	164	1			PUNCT
ejpam-3893	164	2	(	(	PUNCT
ejpam-3893	164	3	27	27	NUM
ejpam-3893	164	4	)	)	PUNCT
ejpam-3893	164	5	a2	a2	PROPN
ejpam-3893	164	6	=	=	SYM
ejpam-3893	164	7	β2	β2	NOUN
ejpam-3893	164	8			VERB
ejpam-3893	164	9	0	0	NUM
ejpam-3893	164	10	0	0	NUM
ejpam-3893	164	11	0	0	NUM
ejpam-3893	164	12	0	0	NUM
ejpam-3893	164	13	0	0	NUM
ejpam-3893	164	14	0	0	NUM
ejpam-3893	164	15	0	0	NUM
ejpam-3893	164	16	·	·	PUNCT
ejpam-3893	164	17	·	·	PUNCT
ejpam-3893	164	18	·	·	PUNCT
ejpam-3893	165	1	ω−1	ω−1	NUM
ejpam-3893	165	2	ω0	ω0	PROPN
ejpam-3893	165	3	ω1	ω1	PROPN
ejpam-3893	165	4	ω2	ω2	PROPN
ejpam-3893	165	5	ω3	ω3	PROPN
ejpam-3893	165	6	ω4	ω4	NUM
ejpam-3893	165	7	0	0	NUM
ejpam-3893	165	8	·	·	PUNCT
ejpam-3893	165	9	·	·	PUNCT
ejpam-3893	166	1	·	·	PUNCT
ejpam-3893	166	2	ω−2	ω−2	PROPN
ejpam-3893	166	3	ω−1	ω−1	NOUN
ejpam-3893	166	4	ω0	ω0	PROPN
ejpam-3893	166	5	ω1	ω1	PROPN
ejpam-3893	166	6	ω2	ω2	PROPN
ejpam-3893	166	7	ω3	ω3	PROPN
ejpam-3893	166	8	ω4	ω4	NUM
ejpam-3893	166	9	0	0	NUM
ejpam-3893	166	10	·	·	PUNCT
ejpam-3893	166	11	·	·	PUNCT
ejpam-3893	166	12	·	·	PUNCT
ejpam-3893	167	1	ω−3	ω−3	PUNCT
ejpam-3893	167	2	ω−2	ω−2	PROPN
ejpam-3893	167	3	ω−1	ω−1	PROPN
ejpam-3893	167	4	ω0	ω0	PROPN
ejpam-3893	167	5	ω1	ω1	PROPN
ejpam-3893	167	6	ω2	ω2	PROPN
ejpam-3893	167	7	ω3	ω3	PROPN
ejpam-3893	167	8	ω4	ω4	NUM
ejpam-3893	167	9	0	0	NUM
ejpam-3893	167	10	·	·	PUNCT
ejpam-3893	167	11	·	·	PUNCT
ejpam-3893	167	12	·	·	PUNCT
ejpam-3893	168	1	ω−4	ω−4	NUM
ejpam-3893	168	2	ω−3	ω−3	PUNCT
ejpam-3893	168	3	ω−2	ω−2	PROPN
ejpam-3893	168	4	ω−1	ω−1	PROPN
ejpam-3893	168	5	ω0	ω0	PROPN
ejpam-3893	168	6	ω1	ω1	PROPN
ejpam-3893	168	7	ω2	ω2	PROPN
ejpam-3893	168	8	ω3	ω3	PROPN
ejpam-3893	168	9	ω4	ω4	NOUN
ejpam-3893	168	10	0	0	NUM
ejpam-3893	168	11	0	0	NUM
ejpam-3893	169	1	ω−4	ω−4	NUM
ejpam-3893	169	2	ω−3	ω−3	PROPN
ejpam-3893	169	3	ω−2	ω−2	PROPN
ejpam-3893	169	4	ω−1	ω−1	PROPN
ejpam-3893	169	5	ω0	ω0	PROPN
ejpam-3893	169	6	ω1	ω1	PROPN
ejpam-3893	169	7	ω2	ω2	PROPN
ejpam-3893	169	8	ω3	ω3	PROPN
ejpam-3893	169	9	ω4	ω4	NUM
ejpam-3893	169	10	...	...	PUNCT
ejpam-3893	169	11	...	...	PUNCT
ejpam-3893	169	12	...	...	PUNCT
ejpam-3893	169	13	...	...	PUNCT
ejpam-3893	169	14	...	...	PUNCT
ejpam-3893	169	15	...	...	PUNCT
ejpam-3893	169	16	...	...	PUNCT
ejpam-3893	169	17	...	...	PUNCT
ejpam-3893	169	18	.	.	PUNCT
ejpam-3893	169	19	.	.	PUNCT
ejpam-3893	169	20	.	.	PUNCT
ejpam-3893	170	1			PUNCT
ejpam-3893	170	2	(	(	PUNCT
ejpam-3893	170	3	28	28	NUM
ejpam-3893	170	4	)	)	PUNCT
ejpam-3893	170	5	it	it	PRON
ejpam-3893	170	6	is	be	AUX
ejpam-3893	170	7	important	important	ADJ
ejpam-3893	170	8	to	to	PART
ejpam-3893	170	9	note	note	VERB
ejpam-3893	170	10	that	that	SCONJ
ejpam-3893	170	11	the	the	DET
ejpam-3893	170	12	values	value	NOUN
ejpam-3893	170	13	of	of	ADP
ejpam-3893	170	14	the	the	DET
ejpam-3893	170	15	connection	connection	NOUN
ejpam-3893	170	16	coefficient	coefficient	NOUN
ejpam-3893	170	17	are	be	AUX
ejpam-3893	170	18	precomputed	precompute	VERB
ejpam-3893	170	19	.	.	PUNCT
ejpam-3893	171	1	in	in	ADP
ejpam-3893	171	2	this	this	DET
ejpam-3893	171	3	case	case	NOUN
ejpam-3893	171	4	a	a	DET
ejpam-3893	171	5	parallelization	parallelization	NOUN
ejpam-3893	171	6	may	may	AUX
ejpam-3893	171	7	be	be	AUX
ejpam-3893	171	8	applied	apply	VERB
ejpam-3893	171	9	in	in	ADP
ejpam-3893	171	10	the	the	DET
ejpam-3893	171	11	implementation	implementation	NOUN
ejpam-3893	171	12	.	.	PUNCT
ejpam-3893	172	1	the	the	DET
ejpam-3893	172	2	rest	rest	NOUN
ejpam-3893	172	3	of	of	ADP
ejpam-3893	172	4	the	the	DET
ejpam-3893	172	5	matrices	matrix	NOUN
ejpam-3893	172	6	,	,	PUNCT
ejpam-3893	172	7	a3	a3	NOUN
ejpam-3893	172	8	,	,	PUNCT
ejpam-3893	172	9	a4	a4	NOUN
ejpam-3893	172	10	and	and	CCONJ
ejpam-3893	172	11	a5	a5	PROPN
ejpam-3893	172	12	are	be	AUX
ejpam-3893	172	13	obtained	obtain	VERB
ejpam-3893	172	14	from	from	ADP
ejpam-3893	172	15	the	the	DET
ejpam-3893	172	16	kronecker	kronecker	NOUN
ejpam-3893	172	17	-	-	PUNCT
ejpam-3893	172	18	delta	delta	NOUN
ejpam-3893	172	19	function	function	NOUN
ejpam-3893	172	20	as	as	ADP
ejpam-3893	172	21	super	super	ADJ
ejpam-3893	172	22	-	-	ADJ
ejpam-3893	172	23	diagonal	diagonal	ADJ
ejpam-3893	172	24	,	,	PUNCT
ejpam-3893	172	25	diagonal	diagonal	ADJ
ejpam-3893	172	26	and	and	CCONJ
ejpam-3893	172	27	subdiagonal	subdiagonal	ADJ
ejpam-3893	172	28	matrices	matrix	NOUN
ejpam-3893	172	29	respectively	respectively	ADV
ejpam-3893	172	30	.	.	PUNCT
ejpam-3893	173	1	that	that	PRON
ejpam-3893	173	2	is	be	AUX
ejpam-3893	173	3	,	,	PUNCT
ejpam-3893	173	4	a3	a3	NOUN
ejpam-3893	173	5	=	=	SYM
ejpam-3893	173	6			NOUN
ejpam-3893	173	7	0	0	SYM
ejpam-3893	174	1	β3	β3	ADJ
ejpam-3893	174	2	0	0	NUM
ejpam-3893	174	3	0	0	NUM
ejpam-3893	174	4	0	0	NUM
ejpam-3893	174	5	0	0	NUM
ejpam-3893	174	6	0	0	NUM
ejpam-3893	174	7	0	0	NUM
ejpam-3893	174	8	0	0	NUM
ejpam-3893	174	9	·	·	PUNCT
ejpam-3893	174	10	·	·	PUNCT
ejpam-3893	174	11	·	·	PUNCT
ejpam-3893	174	12	0	0	NUM
ejpam-3893	174	13	0	0	NUM
ejpam-3893	174	14	β3	β3	NOUN
ejpam-3893	174	15	0	0	NUM
ejpam-3893	174	16	0	0	NUM
ejpam-3893	174	17	0	0	NUM
ejpam-3893	174	18	0	0	NUM
ejpam-3893	174	19	0	0	NUM
ejpam-3893	174	20	0	0	NUM
ejpam-3893	174	21	·	·	PUNCT
ejpam-3893	174	22	·	·	PUNCT
ejpam-3893	174	23	·	·	PUNCT
ejpam-3893	174	24	0	0	NUM
ejpam-3893	174	25	0	0	NUM
ejpam-3893	174	26	0	0	NUM
ejpam-3893	175	1	β3	β3	NOUN
ejpam-3893	175	2	0	0	NUM
ejpam-3893	175	3	0	0	NUM
ejpam-3893	175	4	0	0	NUM
ejpam-3893	175	5	0	0	NUM
ejpam-3893	175	6	0	0	NUM
ejpam-3893	175	7	·	·	PUNCT
ejpam-3893	175	8	·	·	PUNCT
ejpam-3893	175	9	·	·	PUNCT
ejpam-3893	175	10	0	0	NUM
ejpam-3893	175	11	0	0	NUM
ejpam-3893	175	12	0	0	NUM
ejpam-3893	175	13	0	0	NUM
ejpam-3893	175	14	β3	β3	NOUN
ejpam-3893	175	15	0	0	NUM
ejpam-3893	175	16	0	0	NUM
ejpam-3893	175	17	0	0	NUM
ejpam-3893	175	18	0	0	NUM
ejpam-3893	175	19	·	·	PUNCT
ejpam-3893	175	20	·	·	PUNCT
ejpam-3893	175	21	·	·	PUNCT
ejpam-3893	175	22	0	0	NUM
ejpam-3893	176	1	0	0	NUM
ejpam-3893	176	2	0	0	NUM
ejpam-3893	176	3	0	0	NUM
ejpam-3893	176	4	0	0	NUM
ejpam-3893	176	5	β3	β3	NOUN
ejpam-3893	176	6	0	0	NUM
ejpam-3893	176	7	0	0	NUM
ejpam-3893	176	8	0	0	NUM
ejpam-3893	176	9	·	·	PUNCT
ejpam-3893	176	10	·	·	PUNCT
ejpam-3893	176	11	·	·	PUNCT
ejpam-3893	176	12	0	0	NUM
ejpam-3893	177	1	0	0	NUM
ejpam-3893	177	2	0	0	NUM
ejpam-3893	177	3	0	0	NUM
ejpam-3893	177	4	0	0	NUM
ejpam-3893	177	5	0	0	NUM
ejpam-3893	177	6	β3	β3	NOUN
ejpam-3893	177	7	0	0	NUM
ejpam-3893	177	8	0	0	NUM
ejpam-3893	177	9	·	·	PUNCT
ejpam-3893	177	10	·	·	PUNCT
ejpam-3893	177	11	·	·	PUNCT
ejpam-3893	177	12	...	...	PUNCT
ejpam-3893	177	13	...	...	PUNCT
ejpam-3893	177	14	...	...	PUNCT
ejpam-3893	177	15	...	...	PUNCT
ejpam-3893	177	16	...	...	PUNCT
ejpam-3893	177	17	...	...	PUNCT
ejpam-3893	177	18	...	...	PUNCT
ejpam-3893	177	19	...	...	PUNCT
ejpam-3893	177	20	...	...	PUNCT
ejpam-3893	177	21	.	.	PUNCT
ejpam-3893	177	22	.	.	PUNCT
ejpam-3893	177	23	.	.	PUNCT
ejpam-3893	178	1			PUNCT
ejpam-3893	178	2	(	(	PUNCT
ejpam-3893	178	3	29	29	NUM
ejpam-3893	178	4	)	)	PUNCT
ejpam-3893	178	5	f.	f.	NOUN
ejpam-3893	178	6	o.	o.	PROPN
ejpam-3893	178	7	boateng	boateng	PROPN
ejpam-3893	178	8	et	et	PROPN
ejpam-3893	178	9	al	al	PROPN
ejpam-3893	178	10	.	.	PUNCT
ejpam-3893	178	11	/	/	SYM
ejpam-3893	178	12	eur	eur	PROPN
ejpam-3893	178	13	.	.	PUNCT
ejpam-3893	179	1	j.	j.	PROPN
ejpam-3893	179	2	pure	pure	PROPN
ejpam-3893	179	3	appl	appl	PROPN
ejpam-3893	179	4	.	.	PROPN
ejpam-3893	179	5	math	math	PROPN
ejpam-3893	179	6	,	,	PUNCT
ejpam-3893	179	7	14	14	NUM
ejpam-3893	179	8	(	(	PUNCT
ejpam-3893	179	9	3	3	NUM
ejpam-3893	179	10	)	)	PUNCT
ejpam-3893	179	11	(	(	PUNCT
ejpam-3893	179	12	2021	2021	NUM
ejpam-3893	179	13	)	)	PUNCT
ejpam-3893	179	14	,	,	PUNCT
ejpam-3893	179	15	706	706	NUM
ejpam-3893	179	16	-	-	SYM
ejpam-3893	179	17	722	722	NUM
ejpam-3893	179	18	714	714	NUM
ejpam-3893	179	19	a4	a4	NOUN
ejpam-3893	179	20	=	=	SYM
ejpam-3893	179	21			NOUN
ejpam-3893	179	22	β4	β4	VERB
ejpam-3893	179	23	0	0	NUM
ejpam-3893	179	24	0	0	NUM
ejpam-3893	179	25	0	0	NUM
ejpam-3893	179	26	0	0	NUM
ejpam-3893	179	27	0	0	NUM
ejpam-3893	179	28	0	0	NUM
ejpam-3893	179	29	0	0	NUM
ejpam-3893	179	30	0	0	NUM
ejpam-3893	179	31	·	·	PUNCT
ejpam-3893	179	32	·	·	PUNCT
ejpam-3893	179	33	·	·	PUNCT
ejpam-3893	179	34	0	0	NUM
ejpam-3893	180	1	β4	β4	PROPN
ejpam-3893	180	2	0	0	NUM
ejpam-3893	180	3	0	0	NUM
ejpam-3893	180	4	0	0	NUM
ejpam-3893	180	5	0	0	NUM
ejpam-3893	180	6	0	0	NUM
ejpam-3893	180	7	0	0	NUM
ejpam-3893	180	8	0	0	NUM
ejpam-3893	180	9	·	·	PUNCT
ejpam-3893	180	10	·	·	PUNCT
ejpam-3893	180	11	·	·	PUNCT
ejpam-3893	180	12	0	0	NUM
ejpam-3893	181	1	0	0	NUM
ejpam-3893	181	2	β4	β4	PROPN
ejpam-3893	181	3	0	0	NUM
ejpam-3893	181	4	0	0	NUM
ejpam-3893	181	5	0	0	NUM
ejpam-3893	181	6	0	0	NUM
ejpam-3893	181	7	0	0	NUM
ejpam-3893	181	8	0	0	NUM
ejpam-3893	181	9	·	·	PUNCT
ejpam-3893	181	10	·	·	PUNCT
ejpam-3893	181	11	·	·	PUNCT
ejpam-3893	181	12	0	0	NUM
ejpam-3893	181	13	0	0	NUM
ejpam-3893	181	14	0	0	NUM
ejpam-3893	182	1	β4	β4	PROPN
ejpam-3893	182	2	0	0	NUM
ejpam-3893	182	3	0	0	NUM
ejpam-3893	182	4	0	0	NUM
ejpam-3893	182	5	0	0	NUM
ejpam-3893	182	6	0	0	NUM
ejpam-3893	182	7	·	·	PUNCT
ejpam-3893	182	8	·	·	PUNCT
ejpam-3893	182	9	·	·	PUNCT
ejpam-3893	182	10	0	0	NUM
ejpam-3893	182	11	0	0	NUM
ejpam-3893	182	12	0	0	NUM
ejpam-3893	182	13	0	0	NUM
ejpam-3893	183	1	β4	β4	PROPN
ejpam-3893	183	2	0	0	NUM
ejpam-3893	183	3	0	0	NUM
ejpam-3893	183	4	0	0	NUM
ejpam-3893	183	5	0	0	NUM
ejpam-3893	183	6	·	·	PUNCT
ejpam-3893	183	7	·	·	PUNCT
ejpam-3893	183	8	·	·	PUNCT
ejpam-3893	183	9	0	0	NUM
ejpam-3893	184	1	0	0	NUM
ejpam-3893	184	2	0	0	NUM
ejpam-3893	184	3	0	0	NUM
ejpam-3893	184	4	0	0	NUM
ejpam-3893	185	1	β4	β4	PROPN
ejpam-3893	185	2	0	0	NUM
ejpam-3893	185	3	0	0	NUM
ejpam-3893	185	4	0	0	NUM
ejpam-3893	185	5	·	·	PUNCT
ejpam-3893	185	6	·	·	PUNCT
ejpam-3893	185	7	·	·	PUNCT
ejpam-3893	185	8	...	...	PUNCT
ejpam-3893	185	9	...	...	PUNCT
ejpam-3893	185	10	...	...	PUNCT
ejpam-3893	185	11	...	...	PUNCT
ejpam-3893	185	12	...	...	PUNCT
ejpam-3893	185	13	...	...	PUNCT
ejpam-3893	185	14	...	...	PUNCT
ejpam-3893	185	15	...	...	PUNCT
ejpam-3893	185	16	...	...	PUNCT
ejpam-3893	185	17	.	.	PUNCT
ejpam-3893	185	18	.	.	PUNCT
ejpam-3893	185	19	.	.	PUNCT
ejpam-3893	186	1			PUNCT
ejpam-3893	186	2	(	(	PUNCT
ejpam-3893	186	3	30	30	NUM
ejpam-3893	186	4	)	)	PUNCT
ejpam-3893	186	5	and	and	CCONJ
ejpam-3893	186	6	a5	a5	NOUN
ejpam-3893	186	7	=	=	PUNCT
ejpam-3893	186	8			NOUN
ejpam-3893	186	9	0	0	NUM
ejpam-3893	186	10	0	0	NUM
ejpam-3893	186	11	0	0	NUM
ejpam-3893	186	12	0	0	NUM
ejpam-3893	186	13	0	0	NUM
ejpam-3893	186	14	0	0	NUM
ejpam-3893	186	15	0	0	NUM
ejpam-3893	186	16	0	0	NUM
ejpam-3893	186	17	0	0	NUM
ejpam-3893	186	18	·	·	PUNCT
ejpam-3893	186	19	·	·	PUNCT
ejpam-3893	186	20	·	·	PUNCT
ejpam-3893	187	1	β5	β5	VERB
ejpam-3893	187	2	0	0	NUM
ejpam-3893	187	3	0	0	NUM
ejpam-3893	187	4	0	0	NUM
ejpam-3893	187	5	0	0	NUM
ejpam-3893	187	6	0	0	NUM
ejpam-3893	187	7	0	0	NUM
ejpam-3893	187	8	0	0	NUM
ejpam-3893	187	9	0	0	NUM
ejpam-3893	187	10	·	·	PUNCT
ejpam-3893	187	11	·	·	PUNCT
ejpam-3893	187	12	·	·	PUNCT
ejpam-3893	187	13	0	0	NUM
ejpam-3893	188	1	β5	β5	NOUN
ejpam-3893	188	2	0	0	NUM
ejpam-3893	188	3	0	0	NUM
ejpam-3893	188	4	0	0	NUM
ejpam-3893	188	5	0	0	NUM
ejpam-3893	188	6	0	0	NUM
ejpam-3893	188	7	0	0	NUM
ejpam-3893	188	8	0	0	NUM
ejpam-3893	188	9	·	·	PUNCT
ejpam-3893	188	10	·	·	PUNCT
ejpam-3893	188	11	·	·	PUNCT
ejpam-3893	188	12	0	0	NUM
ejpam-3893	188	13	0	0	NUM
ejpam-3893	188	14	β5	β5	NOUN
ejpam-3893	188	15	0	0	NUM
ejpam-3893	188	16	0	0	NUM
ejpam-3893	188	17	0	0	NUM
ejpam-3893	188	18	0	0	NUM
ejpam-3893	188	19	0	0	NUM
ejpam-3893	188	20	0	0	NUM
ejpam-3893	188	21	·	·	PUNCT
ejpam-3893	188	22	·	·	PUNCT
ejpam-3893	188	23	·	·	PUNCT
ejpam-3893	188	24	0	0	NUM
ejpam-3893	188	25	0	0	NUM
ejpam-3893	188	26	0	0	NUM
ejpam-3893	188	27	β5	β5	NOUN
ejpam-3893	188	28	0	0	NUM
ejpam-3893	188	29	0	0	NUM
ejpam-3893	188	30	0	0	NUM
ejpam-3893	188	31	0	0	NUM
ejpam-3893	188	32	0	0	NUM
ejpam-3893	188	33	·	·	PUNCT
ejpam-3893	188	34	·	·	PUNCT
ejpam-3893	188	35	·	·	PUNCT
ejpam-3893	188	36	0	0	NUM
ejpam-3893	188	37	0	0	NUM
ejpam-3893	188	38	0	0	NUM
ejpam-3893	188	39	0	0	NUM
ejpam-3893	188	40	β5	β5	NOUN
ejpam-3893	188	41	0	0	NUM
ejpam-3893	188	42	0	0	NUM
ejpam-3893	188	43	0	0	NUM
ejpam-3893	188	44	0	0	NUM
ejpam-3893	188	45	·	·	PUNCT
ejpam-3893	188	46	·	·	PUNCT
ejpam-3893	188	47	·	·	PUNCT
ejpam-3893	188	48	...	...	PUNCT
ejpam-3893	188	49	...	...	PUNCT
ejpam-3893	188	50	...	...	PUNCT
ejpam-3893	188	51	...	...	PUNCT
ejpam-3893	188	52	...	...	PUNCT
ejpam-3893	188	53	...	...	PUNCT
ejpam-3893	188	54	...	...	PUNCT
ejpam-3893	188	55	...	...	PUNCT
ejpam-3893	188	56	...	...	PUNCT
ejpam-3893	188	57	.	.	PUNCT
ejpam-3893	188	58	.	.	PUNCT
ejpam-3893	188	59	.	.	PUNCT
ejpam-3893	189	1			PUNCT
ejpam-3893	189	2	(	(	PUNCT
ejpam-3893	189	3	31	31	NUM
ejpam-3893	189	4	)	)	PUNCT
ejpam-3893	189	5	combining	combine	VERB
ejpam-3893	189	6	equation	equation	NOUN
ejpam-3893	189	7	(	(	PUNCT
ejpam-3893	189	8	27	27	NUM
ejpam-3893	189	9	)	)	PUNCT
ejpam-3893	189	10	,	,	PUNCT
ejpam-3893	189	11	(	(	PUNCT
ejpam-3893	189	12	28	28	NUM
ejpam-3893	189	13	)	)	PUNCT
ejpam-3893	189	14	,	,	PUNCT
ejpam-3893	189	15	(	(	PUNCT
ejpam-3893	189	16	29	29	NUM
ejpam-3893	189	17	)	)	PUNCT
ejpam-3893	189	18	,	,	PUNCT
ejpam-3893	189	19	(	(	PUNCT
ejpam-3893	189	20	30	30	NUM
ejpam-3893	189	21	)	)	PUNCT
ejpam-3893	189	22	,	,	PUNCT
ejpam-3893	189	23	and	and	CCONJ
ejpam-3893	189	24	(	(	PUNCT
ejpam-3893	189	25	31	31	NUM
ejpam-3893	189	26	)	)	PUNCT
ejpam-3893	189	27	,	,	PUNCT
ejpam-3893	189	28	we	we	PRON
ejpam-3893	189	29	obtain	obtain	VERB
ejpam-3893	189	30	a	a	DET
ejpam-3893	189	31	linear	linear	ADJ
ejpam-3893	189	32	system	system	NOUN
ejpam-3893	189	33	a	a	PRON
ejpam-3893	189	34	~	~	SYM
ejpam-3893	189	35	ξ	ξ	X
ejpam-3893	189	36	=	=	SYM
ejpam-3893	189	37	f	f	PROPN
ejpam-3893	189	38	(	(	PUNCT
ejpam-3893	189	39	32	32	NUM
ejpam-3893	189	40	)	)	PUNCT
ejpam-3893	189	41	where	where	SCONJ
ejpam-3893	189	42	a	a	DET
ejpam-3893	189	43	=	=	SYM
ejpam-3893	189	44	∑5	∑5	NOUN
ejpam-3893	189	45	i=1ai	i=1ai	NUM
ejpam-3893	189	46	in	in	ADP
ejpam-3893	189	47	order	order	NOUN
ejpam-3893	189	48	to	to	PART
ejpam-3893	189	49	construct	construct	VERB
ejpam-3893	189	50	the	the	DET
ejpam-3893	189	51	weak	weak	ADJ
ejpam-3893	189	52	formulation	formulation	NOUN
ejpam-3893	189	53	for	for	ADP
ejpam-3893	189	54	the	the	DET
ejpam-3893	189	55	function	function	NOUN
ejpam-3893	189	56	f(x	f(x	PROPN
ejpam-3893	189	57	,	,	PUNCT
ejpam-3893	189	58	yi	yi	NOUN
ejpam-3893	189	59	)	)	PUNCT
ejpam-3893	189	60	on	on	ADP
ejpam-3893	189	61	the	the	DET
ejpam-3893	189	62	right	right	ADJ
ejpam-3893	189	63	hand	hand	NOUN
ejpam-3893	189	64	side	side	NOUN
ejpam-3893	189	65	of	of	ADP
ejpam-3893	189	66	equation	equation	NOUN
ejpam-3893	189	67	(	(	PUNCT
ejpam-3893	189	68	32	32	NUM
ejpam-3893	189	69	)	)	PUNCT
ejpam-3893	189	70	,	,	PUNCT
ejpam-3893	189	71	we	we	PRON
ejpam-3893	189	72	give	give	VERB
ejpam-3893	189	73	the	the	DET
ejpam-3893	189	74	definitions	definition	NOUN
ejpam-3893	189	75	and	and	CCONJ
ejpam-3893	189	76	state	state	VERB
ejpam-3893	189	77	the	the	DET
ejpam-3893	189	78	theorems	theorem	NOUN
ejpam-3893	189	79	relevant	relevant	ADJ
ejpam-3893	189	80	for	for	ADP
ejpam-3893	189	81	the	the	DET
ejpam-3893	189	82	weak	weak	ADJ
ejpam-3893	189	83	formulation	formulation	NOUN
ejpam-3893	189	84	.	.	PUNCT
ejpam-3893	190	1	definition	definition	NOUN
ejpam-3893	190	2	1	1	NUM
ejpam-3893	190	3	.	.	PUNCT
ejpam-3893	191	1	the	the	DET
ejpam-3893	191	2	orthogonal	orthogonal	ADJ
ejpam-3893	191	3	projection	projection	NOUN
ejpam-3893	191	4	of	of	ADP
ejpam-3893	191	5	the	the	DET
ejpam-3893	191	6	function	function	NOUN
ejpam-3893	191	7	f(x	f(x	PROPN
ejpam-3893	191	8	,	,	PUNCT
ejpam-3893	191	9	y	y	NOUN
ejpam-3893	191	10	)	)	PUNCT
ejpam-3893	191	11	at	at	ADP
ejpam-3893	191	12	a	a	DET
ejpam-3893	191	13	fixed	fix	VERB
ejpam-3893	191	14	y−	y−	NOUN
ejpam-3893	191	15	coordinate	coordinate	NOUN
ejpam-3893	191	16	,	,	PUNCT
ejpam-3893	191	17	yi	yi	VERB
ejpam-3893	191	18	onto	onto	ADP
ejpam-3893	191	19	a	a	DET
ejpam-3893	191	20	subspace	subspace	NOUN
ejpam-3893	191	21	vm	vm	PROPN
ejpam-3893	191	22	is	be	AUX
ejpam-3893	191	23	defined	define	VERB
ejpam-3893	191	24	by	by	ADP
ejpam-3893	191	25	pm	pm	PROPN
ejpam-3893	191	26	{	{	PUNCT
ejpam-3893	191	27	f(x	f(x	PROPN
ejpam-3893	191	28	,	,	PUNCT
ejpam-3893	191	29	yi	yi	PROPN
ejpam-3893	191	30	)	)	PUNCT
ejpam-3893	191	31	}	}	PUNCT
ejpam-3893	192	1	=	=	PUNCT
ejpam-3893	192	2	∑	∑	PUNCT
ejpam-3893	192	3	k	k	PROPN
ejpam-3893	192	4	(	(	PUNCT
ejpam-3893	192	5	∫	∫	PROPN
ejpam-3893	192	6	f(x	f(x	PROPN
ejpam-3893	192	7	,	,	PUNCT
ejpam-3893	192	8	yi)ϕm	yi)ϕm	NOUN
ejpam-3893	192	9	,	,	PUNCT
ejpam-3893	192	10	k(x)dx	k(x)dx	NOUN
ejpam-3893	192	11	)	)	PUNCT
ejpam-3893	192	12	ϕm	ϕm	ADP
ejpam-3893	192	13	,	,	PUNCT
ejpam-3893	192	14	k(x	k(x	PROPN
ejpam-3893	192	15	)	)	PUNCT
ejpam-3893	192	16	(	(	PUNCT
ejpam-3893	192	17	33	33	NUM
ejpam-3893	192	18	)	)	PUNCT
ejpam-3893	192	19	definition	definition	NOUN
ejpam-3893	192	20	2	2	NUM
ejpam-3893	192	21	.	.	PUNCT
ejpam-3893	193	1	the	the	DET
ejpam-3893	193	2	function	function	NOUN
ejpam-3893	193	3	f(x	f(x	PROPN
ejpam-3893	193	4	,	,	PUNCT
ejpam-3893	193	5	y	y	NOUN
ejpam-3893	193	6	)	)	PUNCT
ejpam-3893	193	7	sampled	sample	VERB
ejpam-3893	193	8	at	at	ADP
ejpam-3893	193	9	a	a	DET
ejpam-3893	193	10	fixed	fix	VERB
ejpam-3893	193	11	y−	y−	NOUN
ejpam-3893	193	12	coordinate	coordinate	NOUN
ejpam-3893	193	13	,	,	PUNCT
ejpam-3893	193	14	yi	yi	PROPN
ejpam-3893	193	15	is	be	AUX
ejpam-3893	193	16	also	also	ADV
ejpam-3893	193	17	defined	define	VERB
ejpam-3893	193	18	by	by	ADP
ejpam-3893	193	19	sm	sm	PROPN
ejpam-3893	193	20	{	{	PUNCT
ejpam-3893	193	21	f(x	f(x	PROPN
ejpam-3893	193	22	,	,	PUNCT
ejpam-3893	193	23	yi	yi	PROPN
ejpam-3893	193	24	)	)	PUNCT
ejpam-3893	193	25	}	}	PUNCT
ejpam-3893	194	1	=	=	PUNCT
ejpam-3893	194	2	∑	∑	PUNCT
ejpam-3893	194	3	k	k	PROPN
ejpam-3893	194	4	2	2	NUM
ejpam-3893	194	5	−m	−m	NOUN
ejpam-3893	194	6	2	2	NUM
ejpam-3893	194	7	f(k/2m)ϕm	f(k/2m)ϕm	ADJ
ejpam-3893	194	8	,	,	PUNCT
ejpam-3893	194	9	k(x	k(x	PROPN
ejpam-3893	194	10	)	)	PUNCT
ejpam-3893	194	11	(	(	PUNCT
ejpam-3893	194	12	34	34	NUM
ejpam-3893	194	13	)	)	PUNCT
ejpam-3893	194	14	now	now	ADV
ejpam-3893	194	15	,	,	PUNCT
ejpam-3893	194	16	state	state	NOUN
ejpam-3893	194	17	two	two	NUM
ejpam-3893	194	18	theorems	theorem	NOUN
ejpam-3893	194	19	relevant	relevant	ADJ
ejpam-3893	194	20	to	to	ADP
ejpam-3893	194	21	the	the	DET
ejpam-3893	194	22	approximation	approximation	NOUN
ejpam-3893	194	23	of	of	ADP
ejpam-3893	194	24	the	the	DET
ejpam-3893	194	25	function	function	NOUN
ejpam-3893	194	26	on	on	ADP
ejpam-3893	194	27	the	the	DET
ejpam-3893	194	28	right	right	ADJ
ejpam-3893	194	29	hand	hand	NOUN
ejpam-3893	194	30	side	side	NOUN
ejpam-3893	194	31	.	.	PUNCT
ejpam-3893	195	1	theorem	theorem	NOUN
ejpam-3893	195	2	1	1	NUM
ejpam-3893	195	3	.	.	PUNCT
ejpam-3893	196	1	if	if	SCONJ
ejpam-3893	196	2	m1(τ	m1(τ	PROPN
ejpam-3893	196	3	)	)	PUNCT
ejpam-3893	197	1	=	=	SYM
ejpam-3893	197	2	0	0	NUM
ejpam-3893	197	3	for	for	ADP
ejpam-3893	197	4	τ	τ	PROPN
ejpam-3893	197	5	=	=	SYM
ejpam-3893	197	6	0	0	NUM
ejpam-3893	197	7	,	,	PUNCT
ejpam-3893	197	8	1	1	NUM
ejpam-3893	197	9	,	,	PUNCT
ejpam-3893	197	10	.	.	PUNCT
ejpam-3893	197	11	.	.	PUNCT
ejpam-3893	197	12	.	.	PUNCT
ejpam-3893	198	1	,	,	PUNCT
ejpam-3893	198	2	m	m	PROPN
ejpam-3893	198	3	,	,	PUNCT
ejpam-3893	198	4	then	then	ADV
ejpam-3893	198	5	l2	l2	NOUN
ejpam-3893	198	6	error	error	NOUN
ejpam-3893	198	7	is	be	AUX
ejpam-3893	198	8	:	:	PUNCT
ejpam-3893	198	9	ε1	ε1	VERB
ejpam-3893	198	10	=	=	SYM
ejpam-3893	198	11	‖pm	‖pm	NUM
ejpam-3893	198	12	{	{	PUNCT
ejpam-3893	198	13	f(x	f(x	PROPN
ejpam-3893	198	14	,	,	PUNCT
ejpam-3893	198	15	yi	yi	PROPN
ejpam-3893	198	16	)	)	PUNCT
ejpam-3893	198	17	}	}	PUNCT
ejpam-3893	198	18	−	−	PROPN
ejpam-3893	198	19	f(x	f(x	PROPN
ejpam-3893	198	20	,	,	PUNCT
ejpam-3893	198	21	yi)‖2	yi)‖2	NOUN
ejpam-3893	198	22	≤	≤	NOUN
ejpam-3893	198	23	λ12−m(m+1	λ12−m(m+1	PUNCT
ejpam-3893	198	24	)	)	PUNCT
ejpam-3893	198	25	where	where	SCONJ
ejpam-3893	198	26	λ1	λ1	PROPN
ejpam-3893	198	27	is	be	AUX
ejpam-3893	198	28	a	a	DET
ejpam-3893	198	29	constant	constant	ADJ
ejpam-3893	198	30	dependent	dependent	NOUN
ejpam-3893	198	31	on	on	ADP
ejpam-3893	198	32	f(x	f(x	PROPN
ejpam-3893	198	33	,	,	PUNCT
ejpam-3893	198	34	yi	yi	PROPN
ejpam-3893	198	35	)	)	PUNCT
ejpam-3893	198	36	and	and	CCONJ
ejpam-3893	198	37	the	the	DET
ejpam-3893	198	38	scaling	scale	VERB
ejpam-3893	198	39	functions	function	NOUN
ejpam-3893	198	40	but	but	CCONJ
ejpam-3893	198	41	independent	independent	ADJ
ejpam-3893	198	42	of	of	ADP
ejpam-3893	198	43	m	m	PROPN
ejpam-3893	198	44	and	and	CCONJ
ejpam-3893	198	45	m	m	PROPN
ejpam-3893	198	46	.	.	PUNCT
ejpam-3893	199	1	f.	f.	PROPN
ejpam-3893	199	2	o.	o.	PROPN
ejpam-3893	199	3	boateng	boateng	PROPN
ejpam-3893	199	4	et	et	PROPN
ejpam-3893	199	5	al	al	PROPN
ejpam-3893	199	6	.	.	PUNCT
ejpam-3893	199	7	/	/	SYM
ejpam-3893	199	8	eur	eur	PROPN
ejpam-3893	199	9	.	.	PUNCT
ejpam-3893	200	1	j.	j.	PROPN
ejpam-3893	200	2	pure	pure	PROPN
ejpam-3893	200	3	appl	appl	PROPN
ejpam-3893	200	4	.	.	PROPN
ejpam-3893	200	5	math	math	PROPN
ejpam-3893	200	6	,	,	PUNCT
ejpam-3893	200	7	14	14	NUM
ejpam-3893	200	8	(	(	PUNCT
ejpam-3893	200	9	3	3	NUM
ejpam-3893	200	10	)	)	PUNCT
ejpam-3893	200	11	(	(	PUNCT
ejpam-3893	200	12	2021	2021	NUM
ejpam-3893	200	13	)	)	PUNCT
ejpam-3893	200	14	,	,	PUNCT
ejpam-3893	200	15	706	706	NUM
ejpam-3893	200	16	-	-	SYM
ejpam-3893	200	17	722	722	NUM
ejpam-3893	200	18	715	715	NUM
ejpam-3893	200	19	the	the	DET
ejpam-3893	200	20	proofs	proof	NOUN
ejpam-3893	200	21	of	of	ADP
ejpam-3893	200	22	theorems	theorem	NOUN
ejpam-3893	200	23	1	1	NUM
ejpam-3893	200	24	and	and	CCONJ
ejpam-3893	200	25	2	2	NUM
ejpam-3893	200	26	can	can	AUX
ejpam-3893	200	27	be	be	AUX
ejpam-3893	200	28	found	find	VERB
ejpam-3893	200	29	in	in	ADP
ejpam-3893	200	30	[	[	X
ejpam-3893	200	31	3	3	NUM
ejpam-3893	200	32	]	]	PUNCT
ejpam-3893	200	33	.	.	PUNCT
ejpam-3893	201	1	from	from	ADP
ejpam-3893	201	2	theorem	theorem	NOUN
ejpam-3893	201	3	1	1	NUM
ejpam-3893	201	4	,	,	PUNCT
ejpam-3893	201	5	we	we	PRON
ejpam-3893	201	6	observe	observe	VERB
ejpam-3893	201	7	that	that	SCONJ
ejpam-3893	201	8	for	for	ADP
ejpam-3893	201	9	a	a	DET
ejpam-3893	201	10	given	give	VERB
ejpam-3893	201	11	daubechies	daubechie	NOUN
ejpam-3893	201	12	scaling	scale	VERB
ejpam-3893	201	13	function	function	NOUN
ejpam-3893	201	14	,	,	PUNCT
ejpam-3893	201	15	m	m	VERB
ejpam-3893	201	16	+	+	ADJ
ejpam-3893	201	17	1	1	NUM
ejpam-3893	201	18	represents	represent	VERB
ejpam-3893	201	19	the	the	DET
ejpam-3893	201	20	number	number	NOUN
ejpam-3893	201	21	of	of	ADP
ejpam-3893	201	22	vanishing	vanish	VERB
ejpam-3893	201	23	moments	moment	NOUN
ejpam-3893	201	24	(	(	PUNCT
ejpam-3893	201	25	i.e.	i.e.	X
ejpam-3893	201	26	n	n	X
ejpam-3893	201	27	=	=	SYM
ejpam-3893	201	28	m	m	VERB
ejpam-3893	201	29	+	+	ADJ
ejpam-3893	201	30	1	1	NUM
ejpam-3893	201	31	)	)	PUNCT
ejpam-3893	201	32	.	.	PUNCT
ejpam-3893	202	1	following	follow	VERB
ejpam-3893	202	2	from	from	ADP
ejpam-3893	202	3	definition	definition	NOUN
ejpam-3893	202	4	2	2	NUM
ejpam-3893	202	5	,	,	PUNCT
ejpam-3893	202	6	we	we	PRON
ejpam-3893	202	7	obtain	obtain	AUX
ejpam-3893	202	8	theorem	theorem	ADJ
ejpam-3893	202	9	2	2	NUM
ejpam-3893	202	10	.	.	PUNCT
ejpam-3893	202	11	theorem	theorem	NOUN
ejpam-3893	202	12	2	2	NUM
ejpam-3893	202	13	.	.	PUNCT
ejpam-3893	203	1	if	if	SCONJ
ejpam-3893	203	2	m2(τ	m2(τ	X
ejpam-3893	203	3	)	)	PUNCT
ejpam-3893	203	4	=	=	SYM
ejpam-3893	203	5	0	0	NUM
ejpam-3893	204	1	for	for	ADP
ejpam-3893	204	2	τ	τ	PROPN
ejpam-3893	204	3	=	=	SYM
ejpam-3893	204	4	0	0	NUM
ejpam-3893	204	5	,	,	PUNCT
ejpam-3893	204	6	1	1	NUM
ejpam-3893	204	7	,	,	PUNCT
ejpam-3893	204	8	.	.	PUNCT
ejpam-3893	204	9	.	.	PUNCT
ejpam-3893	204	10	.	.	PUNCT
ejpam-3893	205	1	,	,	PUNCT
ejpam-3893	205	2	m	m	PROPN
ejpam-3893	205	3	,	,	PUNCT
ejpam-3893	205	4	then	then	ADV
ejpam-3893	205	5	l2	l2	NOUN
ejpam-3893	205	6	error	error	NOUN
ejpam-3893	205	7	is	be	AUX
ejpam-3893	205	8	:	:	PUNCT
ejpam-3893	205	9	ε2	ε2	ADJ
ejpam-3893	205	10	=	=	PUNCT
ejpam-3893	205	11	‖pm	‖pm	PUNCT
ejpam-3893	205	12	{	{	PUNCT
ejpam-3893	205	13	f(x	f(x	PROPN
ejpam-3893	205	14	,	,	PUNCT
ejpam-3893	205	15	yi	yi	PROPN
ejpam-3893	205	16	)	)	PUNCT
ejpam-3893	205	17	}	}	PUNCT
ejpam-3893	205	18	−	−	PROPN
ejpam-3893	206	1	sm	sm	INTJ
ejpam-3893	206	2	{	{	PUNCT
ejpam-3893	206	3	f(x	f(x	PROPN
ejpam-3893	206	4	,	,	PUNCT
ejpam-3893	206	5	yi	yi	PROPN
ejpam-3893	206	6	)	)	PUNCT
ejpam-3893	206	7	}	}	PUNCT
ejpam-3893	206	8	‖2	‖2	VERB
ejpam-3893	206	9	≤	≤	NUM
ejpam-3893	206	10	λ22−m(m+1	λ22−m(m+1	NUM
ejpam-3893	206	11	)	)	PUNCT
ejpam-3893	206	12	where	where	SCONJ
ejpam-3893	206	13	λ2	λ2	NOUN
ejpam-3893	206	14	is	be	AUX
ejpam-3893	206	15	a	a	DET
ejpam-3893	206	16	constant	constant	ADJ
ejpam-3893	206	17	independent	independent	NOUN
ejpam-3893	206	18	of	of	ADP
ejpam-3893	206	19	m	m	PROPN
ejpam-3893	206	20	and	and	CCONJ
ejpam-3893	206	21	m	m	PROPN
ejpam-3893	206	22	but	but	CCONJ
ejpam-3893	206	23	dependent	dependent	ADJ
ejpam-3893	206	24	on	on	ADP
ejpam-3893	206	25	f(x	f(x	PROPN
ejpam-3893	206	26	,	,	PUNCT
ejpam-3893	206	27	yi	yi	PROPN
ejpam-3893	206	28	)	)	PUNCT
ejpam-3893	206	29	and	and	CCONJ
ejpam-3893	206	30	the	the	DET
ejpam-3893	206	31	wavelet	wavelet	NOUN
ejpam-3893	206	32	system	system	NOUN
ejpam-3893	206	33	.	.	PUNCT
ejpam-3893	207	1	we	we	PRON
ejpam-3893	207	2	note	note	VERB
ejpam-3893	207	3	that	that	SCONJ
ejpam-3893	207	4	the	the	DET
ejpam-3893	207	5	l2	l2	NOUN
ejpam-3893	207	6	errors	error	NOUN
ejpam-3893	207	7	,	,	PUNCT
ejpam-3893	207	8	ε1	ε1	NOUN
ejpam-3893	207	9	and	and	CCONJ
ejpam-3893	207	10	ε2	ε2	ADJ
ejpam-3893	207	11	in	in	ADP
ejpam-3893	207	12	theorems	theorem	NOUN
ejpam-3893	207	13	1	1	NUM
ejpam-3893	207	14	and	and	CCONJ
ejpam-3893	207	15	2	2	NUM
ejpam-3893	207	16	respectively	respectively	ADV
ejpam-3893	207	17	are	be	AUX
ejpam-3893	207	18	both	both	PRON
ejpam-3893	207	19	bounded	bound	VERB
ejpam-3893	207	20	above	above	ADV
ejpam-3893	207	21	by	by	ADP
ejpam-3893	207	22	2−m(m+1	2−m(m+1	NUM
ejpam-3893	207	23	)	)	PUNCT
ejpam-3893	207	24	.	.	PUNCT
ejpam-3893	208	1	this	this	PRON
ejpam-3893	208	2	means	mean	VERB
ejpam-3893	208	3	nodal	nodal	ADJ
ejpam-3893	208	4	values	value	NOUN
ejpam-3893	208	5	of	of	ADP
ejpam-3893	208	6	the	the	DET
ejpam-3893	208	7	original	original	ADJ
ejpam-3893	208	8	function	function	NOUN
ejpam-3893	208	9	at	at	ADP
ejpam-3893	208	10	fixed	fix	VERB
ejpam-3893	208	11	y−	y−	NOUN
ejpam-3893	208	12	coordinate	coordinate	NOUN
ejpam-3893	208	13	,	,	PUNCT
ejpam-3893	208	14	f(x	f(x	PROPN
ejpam-3893	208	15	,	,	PUNCT
ejpam-3893	208	16	yi	yi	PROPN
ejpam-3893	208	17	)	)	PUNCT
ejpam-3893	208	18	can	can	AUX
ejpam-3893	208	19	be	be	AUX
ejpam-3893	208	20	used	use	VERB
ejpam-3893	208	21	rather	rather	ADV
ejpam-3893	208	22	than	than	ADP
ejpam-3893	208	23	the	the	DET
ejpam-3893	208	24	sampling	sample	VERB
ejpam-3893	208	25	values	value	NOUN
ejpam-3893	208	26	from	from	ADP
ejpam-3893	208	27	sm	sm	PROPN
ejpam-3893	208	28	{	{	PUNCT
ejpam-3893	208	29	f(x	f(x	PROPN
ejpam-3893	208	30	,	,	PUNCT
ejpam-3893	208	31	yi	yi	PROPN
ejpam-3893	208	32	)	)	PUNCT
ejpam-3893	208	33	}	}	PUNCT
ejpam-3893	208	34	which	which	PRON
ejpam-3893	208	35	are	be	AUX
ejpam-3893	208	36	yet	yet	ADV
ejpam-3893	208	37	to	to	PART
ejpam-3893	208	38	be	be	AUX
ejpam-3893	208	39	determined	determine	VERB
ejpam-3893	208	40	.	.	PUNCT
ejpam-3893	209	1	therefore	therefore	ADV
ejpam-3893	209	2	the	the	DET
ejpam-3893	209	3	f(x	f(x	PROPN
ejpam-3893	209	4	,	,	PUNCT
ejpam-3893	209	5	yi	yi	NOUN
ejpam-3893	209	6	)	)	PUNCT
ejpam-3893	209	7	nodal	nodal	NOUN
ejpam-3893	209	8	values	value	NOUN
ejpam-3893	209	9	can	can	AUX
ejpam-3893	209	10	be	be	AUX
ejpam-3893	209	11	utilized	utilize	VERB
ejpam-3893	209	12	at	at	ADP
ejpam-3893	209	13	the	the	DET
ejpam-3893	209	14	right	right	ADJ
ejpam-3893	209	15	hand	hand	NOUN
ejpam-3893	209	16	side	side	NOUN
ejpam-3893	209	17	of	of	ADP
ejpam-3893	209	18	equation	equation	NOUN
ejpam-3893	209	19	(	(	PUNCT
ejpam-3893	209	20	32	32	NUM
ejpam-3893	209	21	)	)	PUNCT
ejpam-3893	209	22	.	.	PUNCT
ejpam-3893	210	1	2.4	2.4	NUM
ejpam-3893	210	2	.	.	PUNCT
ejpam-3893	210	3	incorporating	incorporate	VERB
ejpam-3893	210	4	dirichlet	dirichlet	PROPN
ejpam-3893	210	5	boundary	boundary	ADJ
ejpam-3893	210	6	conditions	condition	NOUN
ejpam-3893	210	7	one	one	NUM
ejpam-3893	210	8	of	of	ADP
ejpam-3893	210	9	the	the	DET
ejpam-3893	210	10	main	main	ADJ
ejpam-3893	210	11	challenges	challenge	NOUN
ejpam-3893	210	12	with	with	ADP
ejpam-3893	210	13	wavelet	wavelet	NOUN
ejpam-3893	210	14	galerkin	galerkin	PROPN
ejpam-3893	210	15	is	be	AUX
ejpam-3893	210	16	the	the	DET
ejpam-3893	210	17	treatment	treatment	NOUN
ejpam-3893	210	18	of	of	ADP
ejpam-3893	210	19	boundary	boundary	ADJ
ejpam-3893	210	20	conditions	condition	NOUN
ejpam-3893	210	21	.	.	PUNCT
ejpam-3893	211	1	in	in	ADP
ejpam-3893	211	2	this	this	DET
ejpam-3893	211	3	paper	paper	NOUN
ejpam-3893	211	4	,	,	PUNCT
ejpam-3893	211	5	we	we	PRON
ejpam-3893	211	6	use	use	VERB
ejpam-3893	211	7	the	the	DET
ejpam-3893	211	8	fictitious	fictitious	ADJ
ejpam-3893	211	9	boundary	boundary	ADJ
ejpam-3893	211	10	condition	condition	NOUN
ejpam-3893	211	11	approach	approach	NOUN
ejpam-3893	211	12	to	to	PART
ejpam-3893	211	13	enforce	enforce	VERB
ejpam-3893	211	14	the	the	DET
ejpam-3893	211	15	dirichlet	dirichlet	PROPN
ejpam-3893	211	16	boundary	boundary	ADJ
ejpam-3893	211	17	condition	condition	NOUN
ejpam-3893	211	18	[	[	X
ejpam-3893	211	19	11	11	NUM
ejpam-3893	211	20	]	]	PUNCT
ejpam-3893	211	21	.	.	PUNCT
ejpam-3893	212	1	we	we	PRON
ejpam-3893	212	2	handle	handle	VERB
ejpam-3893	212	3	the	the	DET
ejpam-3893	212	4	left	left	ADJ
ejpam-3893	212	5	boundary	boundary	NOUN
ejpam-3893	212	6	by	by	ADP
ejpam-3893	212	7	replacing	replace	VERB
ejpam-3893	212	8	the	the	DET
ejpam-3893	212	9	first	first	ADJ
ejpam-3893	212	10	equation	equation	NOUN
ejpam-3893	212	11	of	of	ADP
ejpam-3893	212	12	(	(	PUNCT
ejpam-3893	212	13	32	32	NUM
ejpam-3893	212	14	)	)	PUNCT
ejpam-3893	212	15	by	by	ADP
ejpam-3893	212	16	the	the	DET
ejpam-3893	212	17	following	follow	VERB
ejpam-3893	212	18	equation	equation	NOUN
ejpam-3893	212	19	.	.	PUNCT
ejpam-3893	213	1	φ̃(x	φ̃(x	PROPN
ejpam-3893	213	2	,	,	PUNCT
ejpam-3893	213	3	yi	yi	NOUN
ejpam-3893	213	4	)	)	PUNCT
ejpam-3893	213	5	=	=	PUNCT
ejpam-3893	213	6	∑	∑	PUNCT
ejpam-3893	213	7	k	k	PROPN
ejpam-3893	213	8	ξik	ξik	PROPN
ejpam-3893	213	9	,	,	PUNCT
ejpam-3893	213	10	mϕ(−k	mϕ(−k	NOUN
ejpam-3893	213	11	)	)	PUNCT
ejpam-3893	213	12	=	=	SYM
ejpam-3893	213	13	g(yi	g(yi	PROPN
ejpam-3893	213	14	)	)	PUNCT
ejpam-3893	213	15	we	we	PRON
ejpam-3893	213	16	take	take	VERB
ejpam-3893	213	17	inner	inner	ADJ
ejpam-3893	213	18	product	product	NOUN
ejpam-3893	213	19	of	of	ADP
ejpam-3893	213	20	the	the	DET
ejpam-3893	213	21	rhs	rhs	PROPN
ejpam-3893	213	22	with	with	ADP
ejpam-3893	213	23	ϕ(−j	ϕ(−j	NOUN
ejpam-3893	213	24	)	)	PUNCT
ejpam-3893	213	25	to	to	ADP
ejpam-3893	213	26	obtain,∑	obtain,∑	PROPN
ejpam-3893	213	27	k	k	PROPN
ejpam-3893	213	28	ξik	ξik	PROPN
ejpam-3893	213	29	,	,	PUNCT
ejpam-3893	213	30	m	m	VERB
ejpam-3893	213	31	∫	∫	PROPN
ejpam-3893	213	32	∞	∞	PROPN
ejpam-3893	213	33	−∞	−∞	ADP
ejpam-3893	213	34	ϕ(−k)ϕ(−j)dx	ϕ(−k)ϕ(−j)dx	ADJ
ejpam-3893	213	35	=	=	SYM
ejpam-3893	213	36	g(yi	g(yi	PROPN
ejpam-3893	213	37	)	)	PUNCT
ejpam-3893	213	38	this	this	PRON
ejpam-3893	213	39	results	result	VERB
ejpam-3893	213	40	in	in	ADP
ejpam-3893	213	41	a	a	DET
ejpam-3893	213	42	kronecker	kronecker	NOUN
ejpam-3893	213	43	-	-	PUNCT
ejpam-3893	213	44	delta	delta	NOUN
ejpam-3893	213	45	function	function	NOUN
ejpam-3893	213	46	on	on	ADP
ejpam-3893	213	47	the	the	DET
ejpam-3893	213	48	left,∑	left,∑	INTJ
ejpam-3893	213	49	k	k	PROPN
ejpam-3893	213	50	ξik	ξik	PROPN
ejpam-3893	213	51	,	,	PUNCT
ejpam-3893	213	52	mδk	mδk	PROPN
ejpam-3893	213	53	,	,	PUNCT
ejpam-3893	213	54	j	j	PROPN
ejpam-3893	213	55	=	=	SYM
ejpam-3893	213	56	g(yi	g(yi	PROPN
ejpam-3893	213	57	)	)	PUNCT
ejpam-3893	213	58	(	(	PUNCT
ejpam-3893	213	59	35	35	NUM
ejpam-3893	213	60	)	)	PUNCT
ejpam-3893	213	61	evaluating	evaluate	VERB
ejpam-3893	213	62	the	the	DET
ejpam-3893	213	63	dirichlet	dirichlet	PROPN
ejpam-3893	213	64	boundary	boundary	NOUN
ejpam-3893	213	65	expressed	express	VERB
ejpam-3893	213	66	in	in	ADP
ejpam-3893	213	67	equation	equation	NOUN
ejpam-3893	213	68	(	(	PUNCT
ejpam-3893	213	69	35	35	NUM
ejpam-3893	213	70	)	)	PUNCT
ejpam-3893	213	71	,	,	PUNCT
ejpam-3893	213	72	we	we	PRON
ejpam-3893	213	73	obtain	obtain	VERB
ejpam-3893	213	74	an	an	DET
ejpam-3893	213	75	identity	identity	NOUN
ejpam-3893	213	76	whose	whose	DET
ejpam-3893	213	77	nth	nth	NOUN
ejpam-3893	213	78	column	column	NOUN
ejpam-3893	213	79	has	have	VERB
ejpam-3893	213	80	the	the	DET
ejpam-3893	213	81	value	value	NOUN
ejpam-3893	213	82	1	1	NUM
ejpam-3893	213	83	,	,	PUNCT
ejpam-3893	213	84	and	and	CCONJ
ejpam-3893	213	85	g(yi	g(yi	PROPN
ejpam-3893	213	86	)	)	PUNCT
ejpam-3893	213	87	representing	represent	VERB
ejpam-3893	213	88	the	the	DET
ejpam-3893	213	89	first	first	ADJ
ejpam-3893	213	90	element	element	NOUN
ejpam-3893	213	91	of	of	ADP
ejpam-3893	213	92	the	the	DET
ejpam-3893	213	93	right	right	ADJ
ejpam-3893	213	94	hand	hand	NOUN
ejpam-3893	213	95	side	side	NOUN
ejpam-3893	213	96	.	.	PUNCT
ejpam-3893	214	1	in	in	ADP
ejpam-3893	214	2	similar	similar	ADJ
ejpam-3893	214	3	vein	vein	NOUN
ejpam-3893	214	4	the	the	DET
ejpam-3893	214	5	right	right	ADJ
ejpam-3893	214	6	boundary	boundary	NOUN
ejpam-3893	214	7	of	of	ADP
ejpam-3893	214	8	the	the	DET
ejpam-3893	214	9	system	system	NOUN
ejpam-3893	214	10	is	be	AUX
ejpam-3893	214	11	handled	handle	VERB
ejpam-3893	214	12	.	.	PUNCT
ejpam-3893	215	1	3	3	X
ejpam-3893	215	2	.	.	X
ejpam-3893	215	3	numerical	numerical	ADJ
ejpam-3893	215	4	results	result	NOUN
ejpam-3893	215	5	in	in	ADP
ejpam-3893	215	6	this	this	DET
ejpam-3893	215	7	section	section	NOUN
ejpam-3893	215	8	we	we	PRON
ejpam-3893	215	9	present	present	VERB
ejpam-3893	215	10	the	the	DET
ejpam-3893	215	11	results	result	NOUN
ejpam-3893	215	12	obtained	obtain	VERB
ejpam-3893	215	13	from	from	ADP
ejpam-3893	215	14	numerical	numerical	ADJ
ejpam-3893	215	15	experiments	experiment	NOUN
ejpam-3893	215	16	carried	carry	VERB
ejpam-3893	215	17	out	out	ADP
ejpam-3893	215	18	using	use	VERB
ejpam-3893	215	19	the	the	DET
ejpam-3893	215	20	fdfdwm	fdfdwm	NOUN
ejpam-3893	215	21	on	on	ADP
ejpam-3893	215	22	some	some	DET
ejpam-3893	215	23	linear	linear	ADJ
ejpam-3893	215	24	elliptic	elliptic	ADJ
ejpam-3893	215	25	pdes	pde	NOUN
ejpam-3893	215	26	with	with	ADP
ejpam-3893	215	27	dirichlet	dirichlet	PROPN
ejpam-3893	215	28	boundary	boundary	ADJ
ejpam-3893	215	29	conditions	condition	NOUN
ejpam-3893	215	30	.	.	PUNCT
ejpam-3893	216	1	the	the	DET
ejpam-3893	216	2	results	result	NOUN
ejpam-3893	216	3	from	from	ADP
ejpam-3893	216	4	the	the	DET
ejpam-3893	216	5	fdfdwm	fdfdwm	NOUN
ejpam-3893	216	6	are	be	AUX
ejpam-3893	216	7	compared	compare	VERB
ejpam-3893	216	8	with	with	ADP
ejpam-3893	216	9	the	the	DET
ejpam-3893	216	10	results	result	NOUN
ejpam-3893	216	11	from	from	ADP
ejpam-3893	216	12	two	two	NUM
ejpam-3893	216	13	traditional	traditional	ADJ
ejpam-3893	216	14	methods	method	NOUN
ejpam-3893	216	15	;	;	PUNCT
ejpam-3893	216	16	fdm	fdm	NOUN
ejpam-3893	216	17	and	and	CCONJ
ejpam-3893	216	18	fem	fem	NOUN
ejpam-3893	216	19	,	,	PUNCT
ejpam-3893	216	20	to	to	PART
ejpam-3893	216	21	determine	determine	VERB
ejpam-3893	216	22	the	the	DET
ejpam-3893	216	23	level	level	NOUN
ejpam-3893	216	24	of	of	ADP
ejpam-3893	216	25	accuracy	accuracy	NOUN
ejpam-3893	216	26	of	of	ADP
ejpam-3893	216	27	our	our	PRON
ejpam-3893	216	28	method	method	NOUN
ejpam-3893	216	29	.	.	PUNCT
ejpam-3893	217	1	the	the	DET
ejpam-3893	217	2	outcome	outcome	NOUN
ejpam-3893	217	3	of	of	ADP
ejpam-3893	217	4	the	the	DET
ejpam-3893	217	5	experiments	experiment	NOUN
ejpam-3893	217	6	are	be	AUX
ejpam-3893	217	7	presented	present	VERB
ejpam-3893	217	8	in	in	ADP
ejpam-3893	217	9	a	a	DET
ejpam-3893	217	10	form	form	NOUN
ejpam-3893	217	11	of	of	ADP
ejpam-3893	217	12	two	two	NUM
ejpam-3893	217	13	dimensional	dimensional	ADJ
ejpam-3893	217	14	graphs	graph	NOUN
ejpam-3893	217	15	and	and	CCONJ
ejpam-3893	217	16	tables	table	NOUN
ejpam-3893	217	17	.	.	PUNCT
ejpam-3893	218	1	all	all	DET
ejpam-3893	218	2	numerical	numerical	ADJ
ejpam-3893	218	3	experiments	experiment	NOUN
ejpam-3893	218	4	are	be	AUX
ejpam-3893	218	5	performed	perform	VERB
ejpam-3893	218	6	using	use	VERB
ejpam-3893	218	7	matlab	matlab	PROPN
ejpam-3893	218	8	.	.	PUNCT
ejpam-3893	219	1	f.	f.	PROPN
ejpam-3893	219	2	o.	o.	PROPN
ejpam-3893	219	3	boateng	boateng	PROPN
ejpam-3893	219	4	et	et	PROPN
ejpam-3893	219	5	al	al	PROPN
ejpam-3893	219	6	.	.	PUNCT
ejpam-3893	219	7	/	/	SYM
ejpam-3893	219	8	eur	eur	PROPN
ejpam-3893	219	9	.	.	PUNCT
ejpam-3893	220	1	j.	j.	PROPN
ejpam-3893	220	2	pure	pure	PROPN
ejpam-3893	220	3	appl	appl	PROPN
ejpam-3893	220	4	.	.	PROPN
ejpam-3893	220	5	math	math	PROPN
ejpam-3893	220	6	,	,	PUNCT
ejpam-3893	220	7	14	14	NUM
ejpam-3893	220	8	(	(	PUNCT
ejpam-3893	220	9	3	3	NUM
ejpam-3893	220	10	)	)	PUNCT
ejpam-3893	220	11	(	(	PUNCT
ejpam-3893	220	12	2021	2021	NUM
ejpam-3893	220	13	)	)	PUNCT
ejpam-3893	220	14	,	,	PUNCT
ejpam-3893	220	15	706	706	NUM
ejpam-3893	220	16	-	-	SYM
ejpam-3893	220	17	722	722	NUM
ejpam-3893	220	18	716	716	NUM
ejpam-3893	220	19	3.1	3.1	NUM
ejpam-3893	220	20	.	.	PUNCT
ejpam-3893	221	1	the	the	DET
ejpam-3893	221	2	fdfdwm	fdfdwm	NOUN
ejpam-3893	221	3	test	test	NOUN
ejpam-3893	221	4	cases	case	NOUN
ejpam-3893	221	5	now	now	ADV
ejpam-3893	221	6	,	,	PUNCT
ejpam-3893	221	7	we	we	PRON
ejpam-3893	221	8	consider	consider	VERB
ejpam-3893	221	9	numerical	numerical	ADJ
ejpam-3893	221	10	experiments	experiment	NOUN
ejpam-3893	221	11	performed	perform	VERB
ejpam-3893	221	12	using	use	VERB
ejpam-3893	221	13	fdfdwm	fdfdwm	NOUN
ejpam-3893	221	14	approach	approach	NOUN
ejpam-3893	221	15	on	on	ADP
ejpam-3893	221	16	pdes	pde	NOUN
ejpam-3893	221	17	with	with	ADP
ejpam-3893	221	18	dirichlet	dirichlet	PROPN
ejpam-3893	221	19	boundary	boundary	ADJ
ejpam-3893	221	20	conditions	condition	NOUN
ejpam-3893	221	21	on	on	ADP
ejpam-3893	221	22	rectangular	rectangular	ADJ
ejpam-3893	221	23	domains	domain	NOUN
ejpam-3893	221	24	.	.	PUNCT
ejpam-3893	222	1	in	in	ADP
ejpam-3893	222	2	each	each	PRON
ejpam-3893	222	3	of	of	ADP
ejpam-3893	222	4	the	the	DET
ejpam-3893	222	5	two	two	NUM
ejpam-3893	222	6	cases	case	NOUN
ejpam-3893	222	7	presented	present	VERB
ejpam-3893	222	8	here	here	ADV
ejpam-3893	222	9	,	,	PUNCT
ejpam-3893	222	10	the	the	DET
ejpam-3893	222	11	domain	domain	NOUN
ejpam-3893	222	12	of	of	ADP
ejpam-3893	222	13	the	the	DET
ejpam-3893	222	14	boundary	boundary	ADJ
ejpam-3893	222	15	value	value	NOUN
ejpam-3893	222	16	problem	problem	NOUN
ejpam-3893	222	17	is	be	AUX
ejpam-3893	222	18	placed	place	VERB
ejpam-3893	222	19	in	in	ADP
ejpam-3893	222	20	a	a	DET
ejpam-3893	222	21	slightly	slightly	ADV
ejpam-3893	222	22	larger	large	ADJ
ejpam-3893	222	23	rectangular	rectangular	ADJ
ejpam-3893	222	24	domain	domain	NOUN
ejpam-3893	222	25	referred	refer	VERB
ejpam-3893	222	26	to	to	ADP
ejpam-3893	222	27	as	as	ADP
ejpam-3893	222	28	the	the	DET
ejpam-3893	222	29	fictitious	fictitious	ADJ
ejpam-3893	222	30	domain	domain	NOUN
ejpam-3893	222	31	.	.	PUNCT
ejpam-3893	223	1	the	the	DET
ejpam-3893	223	2	daubechies	daubechie	NOUN
ejpam-3893	223	3	scaling	scale	VERB
ejpam-3893	223	4	functions	function	NOUN
ejpam-3893	223	5	of	of	ADP
ejpam-3893	223	6	orders	order	NOUN
ejpam-3893	223	7	d6	d6	NOUN
ejpam-3893	223	8	,	,	PUNCT
ejpam-3893	223	9	d8	d8	PROPN
ejpam-3893	223	10	,	,	PUNCT
ejpam-3893	223	11	d10	d10	PROPN
ejpam-3893	223	12	,	,	PUNCT
ejpam-3893	223	13	d12	d12	PROPN
ejpam-3893	223	14	,	,	PUNCT
ejpam-3893	223	15	d14	d14	NOUN
ejpam-3893	223	16	,	,	PUNCT
ejpam-3893	223	17	d16	d16	NOUN
ejpam-3893	223	18	,	,	PUNCT
ejpam-3893	223	19	d18	d18	NOUN
ejpam-3893	223	20	and	and	CCONJ
ejpam-3893	223	21	d20	d20	VERB
ejpam-3893	223	22	with	with	ADP
ejpam-3893	223	23	varying	vary	VERB
ejpam-3893	223	24	levels	level	NOUN
ejpam-3893	223	25	of	of	ADP
ejpam-3893	223	26	resolution	resolution	NOUN
ejpam-3893	223	27	(	(	PUNCT
ejpam-3893	223	28	i.e.	i.e.	X
ejpam-3893	223	29	m	m	NOUN
ejpam-3893	223	30	=	=	NOUN
ejpam-3893	223	31	0,m	0,m	PUNCT
ejpam-3893	224	1	=	=	SYM
ejpam-3893	224	2	1,m	1,m	NOUN
ejpam-3893	224	3	=	=	SYM
ejpam-3893	224	4	2	2	NUM
ejpam-3893	224	5	and	and	CCONJ
ejpam-3893	224	6	m	m	PROPN
ejpam-3893	224	7	=	=	NOUN
ejpam-3893	225	1	3	3	X
ejpam-3893	225	2	)	)	PUNCT
ejpam-3893	225	3	are	be	AUX
ejpam-3893	225	4	used	use	VERB
ejpam-3893	225	5	and	and	CCONJ
ejpam-3893	225	6	analyzed	analyze	VERB
ejpam-3893	225	7	in	in	ADP
ejpam-3893	225	8	the	the	DET
ejpam-3893	225	9	experiments	experiment	NOUN
ejpam-3893	225	10	.	.	PUNCT
ejpam-3893	226	1	test	test	NOUN
ejpam-3893	226	2	case	case	NOUN
ejpam-3893	226	3	1	1	NUM
ejpam-3893	226	4	a	a	DET
ejpam-3893	226	5	dirichlet	dirichlet	NOUN
ejpam-3893	226	6	problem	problem	NOUN
ejpam-3893	226	7	defined	define	VERB
ejpam-3893	226	8	on	on	ADP
ejpam-3893	226	9	a	a	DET
ejpam-3893	226	10	rectangular	rectangular	ADJ
ejpam-3893	226	11	domain	domain	NOUN
ejpam-3893	226	12	,	,	PUNCT
ejpam-3893	226	13	ω	ω	NOUN
ejpam-3893	227	1	=	=	PUNCT
ejpam-3893	228	1	[	[	X
ejpam-3893	228	2	−5	−5	NOUN
ejpam-3893	228	3	,	,	PUNCT
ejpam-3893	228	4	5]×	5]×	NOUN
ejpam-3893	229	1	[	[	X
ejpam-3893	229	2	−5	−5	ADJ
ejpam-3893	229	3	,	,	PUNCT
ejpam-3893	229	4	5	5	X
ejpam-3893	229	5	]	]	PUNCT
ejpam-3893	229	6	embedded	embed	VERB
ejpam-3893	229	7	in	in	ADP
ejpam-3893	229	8	a	a	DET
ejpam-3893	229	9	fictitious	fictitious	ADJ
ejpam-3893	229	10	domain	domain	NOUN
ejpam-3893	229	11	ωf	ωf	PRON
ejpam-3893	229	12	=	=	SYM
ejpam-3893	230	1	[	[	X
ejpam-3893	230	2	−8	−8	X
ejpam-3893	230	3	,	,	PUNCT
ejpam-3893	230	4	8]×	8]×	PROPN
ejpam-3893	231	1	[	[	X
ejpam-3893	231	2	−8	−8	X
ejpam-3893	231	3	,	,	PUNCT
ejpam-3893	231	4	8	8	NUM
ejpam-3893	231	5	]	]	PUNCT
ejpam-3893	231	6	with	with	ADP
ejpam-3893	231	7	a	a	DET
ejpam-3893	231	8	dirichlet	dirichlet	PROPN
ejpam-3893	231	9	boundary	boundary	ADJ
ejpam-3893	231	10	condition	condition	NOUN
ejpam-3893	231	11	g	g	PROPN
ejpam-3893	231	12	=	=	SYM
ejpam-3893	231	13	sin(x+y	sin(x+y	PROPN
ejpam-3893	231	14	)	)	PUNCT
ejpam-3893	231	15	is	be	AUX
ejpam-3893	231	16	considered	consider	VERB
ejpam-3893	231	17	for	for	ADP
ejpam-3893	231	18	the	the	DET
ejpam-3893	231	19	first	first	ADJ
ejpam-3893	231	20	numerical	numerical	ADJ
ejpam-3893	231	21	test	test	NOUN
ejpam-3893	231	22	.	.	PUNCT
ejpam-3893	232	1	the	the	DET
ejpam-3893	232	2	problem	problem	NOUN
ejpam-3893	232	3	is	be	AUX
ejpam-3893	232	4	given	give	VERB
ejpam-3893	232	5	as	as	ADP
ejpam-3893	232	6	{	{	PUNCT
ejpam-3893	232	7	−∆φ+	−∆φ+	ADJ
ejpam-3893	232	8	φ	φ	NOUN
ejpam-3893	232	9	=	=	SYM
ejpam-3893	232	10	3	3	NUM
ejpam-3893	232	11	sin(x+	sin(x+	PROPN
ejpam-3893	232	12	y	y	NOUN
ejpam-3893	232	13	)	)	PUNCT
ejpam-3893	232	14	in	in	ADP
ejpam-3893	232	15	ω	ω	NUM
ejpam-3893	232	16	φ(x	φ(x	PROPN
ejpam-3893	232	17	,	,	PUNCT
ejpam-3893	232	18	y	y	NOUN
ejpam-3893	232	19	)	)	PUNCT
ejpam-3893	232	20	=	=	SYM
ejpam-3893	232	21	g	g	NOUN
ejpam-3893	232	22	on	on	ADP
ejpam-3893	232	23	∂ω	∂ω	PROPN
ejpam-3893	232	24	(	(	PUNCT
ejpam-3893	232	25	36	36	NUM
ejpam-3893	232	26	)	)	PUNCT
ejpam-3893	232	27	the	the	DET
ejpam-3893	232	28	dirichlet	dirichlet	PROPN
ejpam-3893	232	29	problem	problem	NOUN
ejpam-3893	232	30	(	(	PUNCT
ejpam-3893	232	31	36	36	NUM
ejpam-3893	232	32	)	)	PUNCT
ejpam-3893	232	33	is	be	AUX
ejpam-3893	232	34	first	first	ADV
ejpam-3893	232	35	solved	solve	VERB
ejpam-3893	232	36	using	use	VERB
ejpam-3893	232	37	fdfdwm	fdfdwm	NOUN
ejpam-3893	232	38	with	with	ADP
ejpam-3893	232	39	d6	d6	NOUN
ejpam-3893	232	40	at	at	ADP
ejpam-3893	232	41	varying	vary	VERB
ejpam-3893	232	42	levels	level	NOUN
ejpam-3893	232	43	of	of	ADP
ejpam-3893	232	44	resolution	resolution	NOUN
ejpam-3893	232	45	,	,	PUNCT
ejpam-3893	232	46	starting	start	VERB
ejpam-3893	232	47	from	from	ADP
ejpam-3893	232	48	m	m	PROPN
ejpam-3893	232	49	=	=	NOUN
ejpam-3893	232	50	0	0	NUM
ejpam-3893	232	51	to	to	ADP
ejpam-3893	232	52	m	m	PROPN
ejpam-3893	232	53	=	=	SYM
ejpam-3893	232	54	3	3	NUM
ejpam-3893	232	55	,	,	PUNCT
ejpam-3893	232	56	corresponding	correspond	VERB
ejpam-3893	232	57	to	to	ADP
ejpam-3893	232	58	a	a	DET
ejpam-3893	232	59	basis	basis	NOUN
ejpam-3893	232	60	of	of	ADP
ejpam-3893	232	61	8	8	NUM
ejpam-3893	232	62	,	,	PUNCT
ejpam-3893	232	63	16	16	NUM
ejpam-3893	232	64	,	,	PUNCT
ejpam-3893	232	65	32	32	NUM
ejpam-3893	232	66	and	and	CCONJ
ejpam-3893	232	67	64	64	NUM
ejpam-3893	232	68	translated	translate	VERB
ejpam-3893	232	69	scaling	scaling	NOUN
ejpam-3893	232	70	functions	function	NOUN
ejpam-3893	232	71	with	with	ADP
ejpam-3893	232	72	support	support	NOUN
ejpam-3893	232	73	intersecting	intersect	VERB
ejpam-3893	232	74	with	with	ADP
ejpam-3893	232	75	[	[	X
ejpam-3893	232	76	−5	−5	ADV
ejpam-3893	232	77	,	,	PUNCT
ejpam-3893	232	78	5	5	NUM
ejpam-3893	232	79	]	]	PUNCT
ejpam-3893	232	80	on	on	ADP
ejpam-3893	232	81	both	both	CCONJ
ejpam-3893	232	82	the	the	DET
ejpam-3893	232	83	horizontal	horizontal	ADJ
ejpam-3893	232	84	and	and	CCONJ
ejpam-3893	232	85	vertical	vertical	ADJ
ejpam-3893	232	86	axes	axis	NOUN
ejpam-3893	232	87	.	.	PUNCT
ejpam-3893	233	1	the	the	DET
ejpam-3893	233	2	values	value	NOUN
ejpam-3893	233	3	of	of	ADP
ejpam-3893	233	4	the	the	DET
ejpam-3893	233	5	approximate	approximate	ADJ
ejpam-3893	233	6	solutions	solution	NOUN
ejpam-3893	233	7	are	be	AUX
ejpam-3893	233	8	used	use	VERB
ejpam-3893	233	9	to	to	PART
ejpam-3893	233	10	generate	generate	VERB
ejpam-3893	233	11	two	two	NUM
ejpam-3893	233	12	dimensional	dimensional	ADJ
ejpam-3893	233	13	coordinates	coordinate	NOUN
ejpam-3893	233	14	surface	surface	NOUN
ejpam-3893	233	15	graphs	graph	NOUN
ejpam-3893	233	16	shown	show	VERB
ejpam-3893	233	17	in	in	ADP
ejpam-3893	233	18	figures	figure	NOUN
ejpam-3893	233	19	1	1	NUM
ejpam-3893	233	20	.	.	PUNCT
ejpam-3893	234	1	this	this	PRON
ejpam-3893	234	2	is	be	AUX
ejpam-3893	234	3	first	first	ADJ
ejpam-3893	234	4	to	to	PART
ejpam-3893	234	5	illustrate	illustrate	VERB
ejpam-3893	234	6	the	the	DET
ejpam-3893	234	7	ability	ability	NOUN
ejpam-3893	234	8	of	of	ADP
ejpam-3893	234	9	the	the	DET
ejpam-3893	234	10	fdfdwm	fdfdwm	NOUN
ejpam-3893	234	11	to	to	PART
ejpam-3893	234	12	approximate	approximate	VERB
ejpam-3893	234	13	the	the	DET
ejpam-3893	234	14	solution	solution	NOUN
ejpam-3893	234	15	to	to	ADP
ejpam-3893	234	16	the	the	DET
ejpam-3893	234	17	dirichlet	dirichlet	PROPN
ejpam-3893	234	18	boundary	boundary	PROPN
ejpam-3893	234	19	value	value	NOUN
ejpam-3893	234	20	problem	problem	NOUN
ejpam-3893	234	21	(	(	PUNCT
ejpam-3893	234	22	36	36	NUM
ejpam-3893	234	23	)	)	PUNCT
ejpam-3893	234	24	.	.	PUNCT
ejpam-3893	235	1	we	we	PRON
ejpam-3893	235	2	demonstrate	demonstrate	VERB
ejpam-3893	235	3	further	far	ADV
ejpam-3893	235	4	the	the	DET
ejpam-3893	235	5	level	level	NOUN
ejpam-3893	235	6	of	of	ADP
ejpam-3893	235	7	accuracy	accuracy	NOUN
ejpam-3893	235	8	of	of	ADP
ejpam-3893	235	9	the	the	DET
ejpam-3893	235	10	fdfdwm	fdfdwm	NOUN
ejpam-3893	235	11	by	by	ADP
ejpam-3893	235	12	comparing	compare	VERB
ejpam-3893	235	13	the	the	DET
ejpam-3893	235	14	approximate	approximate	ADJ
ejpam-3893	235	15	solutions	solution	NOUN
ejpam-3893	235	16	of	of	ADP
ejpam-3893	235	17	fdm	fdm	NOUN
ejpam-3893	235	18	,	,	PUNCT
ejpam-3893	235	19	fem	fem	NOUN
ejpam-3893	235	20	and	and	CCONJ
ejpam-3893	235	21	fdfdwm	fdfdwm	VERB
ejpam-3893	235	22	with	with	ADP
ejpam-3893	235	23	the	the	DET
ejpam-3893	235	24	exact	exact	ADJ
ejpam-3893	235	25	solution	solution	NOUN
ejpam-3893	235	26	of	of	ADP
ejpam-3893	235	27	problem	problem	NOUN
ejpam-3893	235	28	(	(	PUNCT
ejpam-3893	235	29	36	36	NUM
ejpam-3893	235	30	)	)	PUNCT
ejpam-3893	235	31	.	.	PUNCT
ejpam-3893	236	1	test	test	NOUN
ejpam-3893	236	2	case	case	NOUN
ejpam-3893	236	3	2	2	NUM
ejpam-3893	236	4	in	in	ADP
ejpam-3893	236	5	the	the	DET
ejpam-3893	236	6	second	second	ADJ
ejpam-3893	236	7	test	test	NOUN
ejpam-3893	236	8	,	,	PUNCT
ejpam-3893	236	9	we	we	PRON
ejpam-3893	236	10	consider	consider	VERB
ejpam-3893	236	11	another	another	DET
ejpam-3893	236	12	dirichlet	dirichlet	NOUN
ejpam-3893	236	13	problem	problem	NOUN
ejpam-3893	236	14	defined	define	VERB
ejpam-3893	236	15	on	on	ADP
ejpam-3893	236	16	a	a	DET
ejpam-3893	236	17	rectangular	rectangular	ADJ
ejpam-3893	236	18	domain	domain	NOUN
ejpam-3893	236	19	,	,	PUNCT
ejpam-3893	236	20	ω	ω	NOUN
ejpam-3893	236	21	=	=	PUNCT
ejpam-3893	237	1	[	[	X
ejpam-3893	237	2	−3	−3	ADJ
ejpam-3893	237	3	,	,	PUNCT
ejpam-3893	237	4	3]×	3]×	NUM
ejpam-3893	238	1	[	[	X
ejpam-3893	238	2	−3	−3	ADJ
ejpam-3893	238	3	,	,	PUNCT
ejpam-3893	238	4	3	3	X
ejpam-3893	238	5	]	]	PUNCT
ejpam-3893	238	6	embedded	embed	VERB
ejpam-3893	238	7	in	in	ADP
ejpam-3893	238	8	a	a	DET
ejpam-3893	238	9	fictitious	fictitious	ADJ
ejpam-3893	238	10	domain	domain	NOUN
ejpam-3893	238	11	ωf	ωf	PRON
ejpam-3893	238	12	=	=	X
ejpam-3893	239	1	[	[	X
ejpam-3893	239	2	−5	−5	NOUN
ejpam-3893	239	3	,	,	PUNCT
ejpam-3893	239	4	5]×	5]×	NOUN
ejpam-3893	240	1	[	[	X
ejpam-3893	240	2	−5	−5	ADJ
ejpam-3893	240	3	,	,	PUNCT
ejpam-3893	240	4	5	5	NUM
ejpam-3893	240	5	]	]	PUNCT
ejpam-3893	240	6	with	with	ADP
ejpam-3893	240	7	a	a	DET
ejpam-3893	240	8	dirichlet	dirichlet	PROPN
ejpam-3893	240	9	boundary	boundary	ADJ
ejpam-3893	240	10	condition	condition	NOUN
ejpam-3893	240	11	g	g	PROPN
ejpam-3893	240	12	=	=	SYM
ejpam-3893	240	13	x2	x2	PROPN
ejpam-3893	241	1	+	+	CCONJ
ejpam-3893	242	1	y2	y2	NOUN
ejpam-3893	242	2	.	.	PUNCT
ejpam-3893	243	1	we	we	PRON
ejpam-3893	243	2	write	write	VERB
ejpam-3893	243	3	the	the	DET
ejpam-3893	243	4	problem	problem	NOUN
ejpam-3893	243	5	as	as	ADP
ejpam-3893	243	6	{	{	PUNCT
ejpam-3893	243	7	−∆φ+	−∆φ+	ADJ
ejpam-3893	243	8	φ	φ	NOUN
ejpam-3893	243	9	=	=	SYM
ejpam-3893	243	10	x2	x2	PROPN
ejpam-3893	244	1	+	+	CCONJ
ejpam-3893	245	1	y2	y2	INTJ
ejpam-3893	245	2	−	−	NOUN
ejpam-3893	245	3	4	4	NUM
ejpam-3893	245	4	in	in	ADP
ejpam-3893	245	5	ω	ω	NUM
ejpam-3893	245	6	φ(x	φ(x	PROPN
ejpam-3893	245	7	,	,	PUNCT
ejpam-3893	245	8	y	y	NOUN
ejpam-3893	245	9	)	)	PUNCT
ejpam-3893	245	10	=	=	SYM
ejpam-3893	246	1	g	g	NOUN
ejpam-3893	246	2	on	on	ADP
ejpam-3893	246	3	∂ω	∂ω	PROPN
ejpam-3893	246	4	(	(	PUNCT
ejpam-3893	246	5	37	37	NUM
ejpam-3893	246	6	)	)	PUNCT
ejpam-3893	246	7	similar	similar	ADJ
ejpam-3893	246	8	procedure	procedure	NOUN
ejpam-3893	246	9	as	as	SCONJ
ejpam-3893	246	10	used	use	VERB
ejpam-3893	246	11	for	for	ADP
ejpam-3893	246	12	equation	equation	NOUN
ejpam-3893	246	13	(	(	PUNCT
ejpam-3893	246	14	36	36	NUM
ejpam-3893	246	15	)	)	PUNCT
ejpam-3893	246	16	is	be	AUX
ejpam-3893	246	17	also	also	ADV
ejpam-3893	246	18	applied	apply	VERB
ejpam-3893	246	19	to	to	ADP
ejpam-3893	246	20	equation	equation	NOUN
ejpam-3893	246	21	(	(	PUNCT
ejpam-3893	246	22	37	37	NUM
ejpam-3893	246	23	)	)	PUNCT
ejpam-3893	246	24	to	to	PART
ejpam-3893	246	25	generate	generate	VERB
ejpam-3893	246	26	two	two	NUM
ejpam-3893	246	27	dimensional	dimensional	ADJ
ejpam-3893	246	28	coordinates	coordinate	NOUN
ejpam-3893	246	29	surface	surface	NOUN
ejpam-3893	246	30	graphs	graph	NOUN
ejpam-3893	246	31	shown	show	VERB
ejpam-3893	246	32	in	in	ADP
ejpam-3893	246	33	figures	figure	NOUN
ejpam-3893	246	34	3	3	NUM
ejpam-3893	246	35	.	.	PUNCT
ejpam-3893	246	36	test	test	NOUN
ejpam-3893	246	37	case	case	NOUN
ejpam-3893	246	38	3	3	NUM
ejpam-3893	246	39	a	a	DET
ejpam-3893	246	40	poisson	poisson	NOUN
ejpam-3893	246	41	equation	equation	NOUN
ejpam-3893	246	42	is	be	AUX
ejpam-3893	246	43	considered	consider	VERB
ejpam-3893	246	44	for	for	ADP
ejpam-3893	246	45	the	the	DET
ejpam-3893	246	46	third	third	ADJ
ejpam-3893	246	47	numerical	numerical	ADJ
ejpam-3893	246	48	test	test	NOUN
ejpam-3893	246	49	.	.	PUNCT
ejpam-3893	247	1	it	it	PRON
ejpam-3893	247	2	is	be	AUX
ejpam-3893	247	3	defined	define	VERB
ejpam-3893	247	4	on	on	ADP
ejpam-3893	247	5	a	a	DET
ejpam-3893	247	6	rectangular	rectangular	ADJ
ejpam-3893	247	7	domain	domain	NOUN
ejpam-3893	247	8	,	,	PUNCT
ejpam-3893	247	9	ω	ω	NOUN
ejpam-3893	247	10	=	=	PUNCT
ejpam-3893	248	1	[	[	X
ejpam-3893	248	2	0	0	NUM
ejpam-3893	248	3	,	,	PUNCT
ejpam-3893	248	4	1	1	NUM
ejpam-3893	248	5	]	]	SYM
ejpam-3893	248	6	×	×	NOUN
ejpam-3893	249	1	[	[	X
ejpam-3893	249	2	0	0	NUM
ejpam-3893	249	3	,	,	PUNCT
ejpam-3893	249	4	1	1	NUM
ejpam-3893	249	5	]	]	PUNCT
ejpam-3893	249	6	embedded	embed	VERB
ejpam-3893	249	7	in	in	ADP
ejpam-3893	249	8	a	a	DET
ejpam-3893	249	9	fictitious	fictitious	ADJ
ejpam-3893	249	10	domain	domain	NOUN
ejpam-3893	249	11	ωf	ωf	ADP
ejpam-3893	250	1	=	=	X
ejpam-3893	251	1	[	[	X
ejpam-3893	251	2	−0.5	−0.5	PROPN
ejpam-3893	251	3	,	,	PUNCT
ejpam-3893	251	4	1.5	1.5	NUM
ejpam-3893	251	5	]	]	SYM
ejpam-3893	251	6	×	×	NOUN
ejpam-3893	252	1	[	[	X
ejpam-3893	252	2	−0.5	−0.5	PROPN
ejpam-3893	252	3	,	,	PUNCT
ejpam-3893	252	4	1.5	1.5	NUM
ejpam-3893	252	5	]	]	PUNCT
ejpam-3893	252	6	with	with	ADP
ejpam-3893	252	7	a	a	DET
ejpam-3893	252	8	dirichlet	dirichlet	PROPN
ejpam-3893	252	9	boundary	boundary	ADJ
ejpam-3893	252	10	condition	condition	NOUN
ejpam-3893	252	11	g	g	PROPN
ejpam-3893	252	12	=	=	PROPN
ejpam-3893	252	13	sinπx+	sinπx+	ADJ
ejpam-3893	252	14	sinπy	sinπy	NOUN
ejpam-3893	252	15	.	.	PUNCT
ejpam-3893	253	1	the	the	DET
ejpam-3893	253	2	problem	problem	NOUN
ejpam-3893	253	3	is	be	AUX
ejpam-3893	253	4	given	give	VERB
ejpam-3893	253	5	as	as	ADP
ejpam-3893	253	6	{	{	PUNCT
ejpam-3893	253	7	−∆φ	−∆φ	NOUN
ejpam-3893	253	8	=	=	SYM
ejpam-3893	253	9	sinπx+	sinπx+	ADJ
ejpam-3893	253	10	sinπy	sinπy	NOUN
ejpam-3893	253	11	in	in	ADP
ejpam-3893	253	12	ω	ω	PROPN
ejpam-3893	253	13	φ(x	φ(x	PROPN
ejpam-3893	253	14	,	,	PUNCT
ejpam-3893	253	15	y	y	NOUN
ejpam-3893	253	16	)	)	PUNCT
ejpam-3893	253	17	=	=	SYM
ejpam-3893	253	18	0	0	NUM
ejpam-3893	254	1	on	on	ADP
ejpam-3893	254	2	∂ω	∂ω	PROPN
ejpam-3893	254	3	(	(	PUNCT
ejpam-3893	254	4	38	38	NUM
ejpam-3893	254	5	)	)	PUNCT
ejpam-3893	254	6	the	the	DET
ejpam-3893	254	7	fdfdwm	fdfdwm	NOUN
ejpam-3893	254	8	is	be	AUX
ejpam-3893	254	9	used	use	VERB
ejpam-3893	254	10	to	to	PART
ejpam-3893	254	11	compute	compute	VERB
ejpam-3893	254	12	the	the	DET
ejpam-3893	254	13	approximate	approximate	ADJ
ejpam-3893	254	14	solution	solution	NOUN
ejpam-3893	254	15	for	for	ADP
ejpam-3893	254	16	problem	problem	NOUN
ejpam-3893	254	17	(	(	PUNCT
ejpam-3893	254	18	38	38	NUM
ejpam-3893	254	19	)	)	PUNCT
ejpam-3893	254	20	in	in	ADP
ejpam-3893	254	21	similar	similar	ADJ
ejpam-3893	254	22	manner	manner	NOUN
ejpam-3893	254	23	,	,	PUNCT
ejpam-3893	254	24	using	use	VERB
ejpam-3893	254	25	wavelet	wavelet	NOUN
ejpam-3893	254	26	order	order	NOUN
ejpam-3893	254	27	d6	d6	NOUN
ejpam-3893	254	28	and	and	CCONJ
ejpam-3893	254	29	resolution	resolution	NOUN
ejpam-3893	254	30	at	at	ADP
ejpam-3893	254	31	levels	level	NOUN
ejpam-3893	254	32	,	,	PUNCT
ejpam-3893	254	33	m	m	VERB
ejpam-3893	254	34	=	=	SYM
ejpam-3893	255	1	1,m	1,m	X
ejpam-3893	255	2	=	=	SYM
ejpam-3893	255	3	2,m	2,m	NOUN
ejpam-3893	255	4	=	=	SYM
ejpam-3893	255	5	3	3	NUM
ejpam-3893	255	6	and	and	CCONJ
ejpam-3893	255	7	f.	f.	PROPN
ejpam-3893	255	8	o.	o.	PROPN
ejpam-3893	255	9	boateng	boateng	PROPN
ejpam-3893	255	10	et	et	PROPN
ejpam-3893	255	11	al	al	PROPN
ejpam-3893	255	12	.	.	PUNCT
ejpam-3893	255	13	/	/	SYM
ejpam-3893	255	14	eur	eur	PROPN
ejpam-3893	255	15	.	.	PUNCT
ejpam-3893	256	1	j.	j.	PROPN
ejpam-3893	256	2	pure	pure	PROPN
ejpam-3893	256	3	appl	appl	PROPN
ejpam-3893	256	4	.	.	PROPN
ejpam-3893	256	5	math	math	PROPN
ejpam-3893	256	6	,	,	PUNCT
ejpam-3893	256	7	14	14	NUM
ejpam-3893	256	8	(	(	PUNCT
ejpam-3893	256	9	3	3	NUM
ejpam-3893	256	10	)	)	PUNCT
ejpam-3893	256	11	(	(	PUNCT
ejpam-3893	256	12	2021	2021	NUM
ejpam-3893	256	13	)	)	PUNCT
ejpam-3893	256	14	,	,	PUNCT
ejpam-3893	256	15	706	706	NUM
ejpam-3893	256	16	-	-	SYM
ejpam-3893	256	17	722	722	NUM
ejpam-3893	256	18	717	717	NUM
ejpam-3893	256	19	m	m	NOUN
ejpam-3893	256	20	=	=	NOUN
ejpam-3893	256	21	4	4	NUM
ejpam-3893	256	22	respectively	respectively	ADV
ejpam-3893	256	23	.	.	PUNCT
ejpam-3893	257	1	the	the	DET
ejpam-3893	257	2	resulting	result	VERB
ejpam-3893	257	3	approximate	approximate	ADJ
ejpam-3893	257	4	solution	solution	NOUN
ejpam-3893	257	5	is	be	AUX
ejpam-3893	257	6	presented	present	VERB
ejpam-3893	257	7	in	in	ADP
ejpam-3893	257	8	two	two	NUM
ejpam-3893	257	9	dimensional	dimensional	ADJ
ejpam-3893	257	10	co	co	NOUN
ejpam-3893	257	11	-	-	ADJ
ejpam-3893	257	12	ordinates	ordinates	ADJ
ejpam-3893	257	13	surface	surface	NOUN
ejpam-3893	257	14	graph	graph	NOUN
ejpam-3893	257	15	shown	show	VERB
ejpam-3893	257	16	in	in	ADP
ejpam-3893	257	17	figure	figure	NOUN
ejpam-3893	257	18	5	5	NUM
ejpam-3893	257	19	.	.	PUNCT
ejpam-3893	258	1	figure	figure	NOUN
ejpam-3893	258	2	1	1	NUM
ejpam-3893	258	3	:	:	PUNCT
ejpam-3893	258	4	the	the	DET
ejpam-3893	258	5	fwdfdm	fwdfdm	ADJ
ejpam-3893	258	6	approximation	approximation	NOUN
ejpam-3893	258	7	on	on	ADP
ejpam-3893	258	8	a	a	DET
ejpam-3893	258	9	rectangular	rectangular	ADJ
ejpam-3893	258	10	domain	domain	NOUN
ejpam-3893	258	11	for	for	ADP
ejpam-3893	258	12	d6	d6	NOUN
ejpam-3893	258	13	and	and	CCONJ
ejpam-3893	258	14	m	m	NOUN
ejpam-3893	258	15	=	=	SYM
ejpam-3893	258	16	0	0	NUM
ejpam-3893	258	17	,	,	PUNCT
ejpam-3893	258	18	1	1	NUM
ejpam-3893	258	19	,	,	PUNCT
ejpam-3893	258	20	2	2	NUM
ejpam-3893	258	21	and	and	CCONJ
ejpam-3893	258	22	3	3	NUM
ejpam-3893	258	23	it	it	PRON
ejpam-3893	258	24	is	be	AUX
ejpam-3893	258	25	evident	evident	ADJ
ejpam-3893	258	26	from	from	ADP
ejpam-3893	258	27	figures	figure	NOUN
ejpam-3893	258	28	1	1	NUM
ejpam-3893	258	29	and	and	CCONJ
ejpam-3893	258	30	3	3	NUM
ejpam-3893	258	31	that	that	PRON
ejpam-3893	258	32	,	,	PUNCT
ejpam-3893	258	33	as	as	ADP
ejpam-3893	258	34	the	the	DET
ejpam-3893	258	35	level	level	NOUN
ejpam-3893	258	36	of	of	ADP
ejpam-3893	258	37	the	the	DET
ejpam-3893	258	38	resolution	resolution	NOUN
ejpam-3893	258	39	increases	increase	VERB
ejpam-3893	258	40	the	the	DET
ejpam-3893	258	41	fdfdwm	fdfdwm	NOUN
ejpam-3893	258	42	solutions	solution	NOUN
ejpam-3893	258	43	appear	appear	VERB
ejpam-3893	258	44	to	to	PART
ejpam-3893	258	45	better	well	ADV
ejpam-3893	258	46	approximate	approximate	VERB
ejpam-3893	258	47	the	the	DET
ejpam-3893	258	48	exact	exact	ADJ
ejpam-3893	258	49	solution	solution	NOUN
ejpam-3893	258	50	in	in	ADP
ejpam-3893	258	51	both	both	DET
ejpam-3893	258	52	test	test	NOUN
ejpam-3893	258	53	cases	case	NOUN
ejpam-3893	258	54	.	.	PUNCT
ejpam-3893	259	1	this	this	PRON
ejpam-3893	259	2	clearly	clearly	ADV
ejpam-3893	259	3	indicates	indicate	VERB
ejpam-3893	259	4	that	that	SCONJ
ejpam-3893	259	5	the	the	DET
ejpam-3893	259	6	fdfdwm	fdfdwm	NOUN
ejpam-3893	259	7	provides	provide	VERB
ejpam-3893	259	8	reasonable	reasonable	ADJ
ejpam-3893	259	9	approximation	approximation	NOUN
ejpam-3893	259	10	to	to	ADP
ejpam-3893	259	11	the	the	DET
ejpam-3893	259	12	pdes	pde	NOUN
ejpam-3893	259	13	under	under	ADP
ejpam-3893	259	14	consideration	consideration	NOUN
ejpam-3893	259	15	.	.	PUNCT
ejpam-3893	260	1	although	although	SCONJ
ejpam-3893	260	2	the	the	DET
ejpam-3893	260	3	results	result	NOUN
ejpam-3893	260	4	from	from	ADP
ejpam-3893	260	5	the	the	DET
ejpam-3893	260	6	fdfdwm	fdfdwm	NOUN
ejpam-3893	260	7	approximations	approximation	NOUN
ejpam-3893	260	8	look	look	VERB
ejpam-3893	260	9	good	good	ADJ
ejpam-3893	260	10	,	,	PUNCT
ejpam-3893	260	11	we	we	PRON
ejpam-3893	260	12	wish	wish	VERB
ejpam-3893	260	13	to	to	PART
ejpam-3893	260	14	know	know	VERB
ejpam-3893	260	15	the	the	DET
ejpam-3893	260	16	level	level	NOUN
ejpam-3893	260	17	of	of	ADP
ejpam-3893	260	18	accuracy	accuracy	NOUN
ejpam-3893	260	19	of	of	ADP
ejpam-3893	260	20	our	our	PRON
ejpam-3893	260	21	method	method	NOUN
ejpam-3893	260	22	in	in	ADP
ejpam-3893	260	23	relation	relation	NOUN
ejpam-3893	260	24	to	to	ADP
ejpam-3893	260	25	traditional	traditional	ADJ
ejpam-3893	260	26	methods	method	NOUN
ejpam-3893	260	27	like	like	ADP
ejpam-3893	260	28	the	the	DET
ejpam-3893	260	29	fdm	fdm	NOUN
ejpam-3893	260	30	and	and	CCONJ
ejpam-3893	260	31	fem	fem	NOUN
ejpam-3893	260	32	.	.	PUNCT
ejpam-3893	261	1	we	we	PRON
ejpam-3893	261	2	ascertain	ascertain	VERB
ejpam-3893	261	3	this	this	DET
ejpam-3893	261	4	fact	fact	NOUN
ejpam-3893	261	5	by	by	ADP
ejpam-3893	261	6	comparing	compare	VERB
ejpam-3893	261	7	the	the	DET
ejpam-3893	261	8	solution	solution	NOUN
ejpam-3893	261	9	of	of	ADP
ejpam-3893	261	10	fdfdwm	fdfdwm	NOUN
ejpam-3893	261	11	,	,	PUNCT
ejpam-3893	261	12	fdm	fdm	NOUN
ejpam-3893	261	13	and	and	CCONJ
ejpam-3893	261	14	fem	fem	NOUN
ejpam-3893	261	15	with	with	ADP
ejpam-3893	261	16	the	the	DET
ejpam-3893	261	17	exact	exact	ADJ
ejpam-3893	261	18	solution	solution	NOUN
ejpam-3893	261	19	.	.	PUNCT
ejpam-3893	262	1	in	in	ADP
ejpam-3893	262	2	order	order	NOUN
ejpam-3893	262	3	to	to	PART
ejpam-3893	262	4	appreciate	appreciate	VERB
ejpam-3893	262	5	the	the	DET
ejpam-3893	262	6	comparison	comparison	NOUN
ejpam-3893	262	7	,	,	PUNCT
ejpam-3893	262	8	a	a	DET
ejpam-3893	262	9	two	two	NUM
ejpam-3893	262	10	dimensional	dimensional	ADJ
ejpam-3893	262	11	line	line	NOUN
ejpam-3893	262	12	graph	graph	NOUN
ejpam-3893	262	13	is	be	AUX
ejpam-3893	262	14	plotted	plot	VERB
ejpam-3893	262	15	at	at	ADP
ejpam-3893	262	16	fixed	fix	VERB
ejpam-3893	262	17	y	y	PROPN
ejpam-3893	262	18	coordinate	coordinate	NOUN
ejpam-3893	262	19	(	(	PUNCT
ejpam-3893	262	20	y	y	NOUN
ejpam-3893	262	21	=	=	NOUN
ejpam-3893	262	22	0	0	NUM
ejpam-3893	262	23	)	)	PUNCT
ejpam-3893	262	24	to	to	PART
ejpam-3893	262	25	provide	provide	VERB
ejpam-3893	262	26	a	a	DET
ejpam-3893	262	27	cross	cross	ADJ
ejpam-3893	262	28	-	-	ADJ
ejpam-3893	262	29	sectional	sectional	ADJ
ejpam-3893	262	30	view	view	NOUN
ejpam-3893	262	31	.	.	PUNCT
ejpam-3893	263	1	the	the	DET
ejpam-3893	263	2	graphs	graph	NOUN
ejpam-3893	263	3	presented	present	VERB
ejpam-3893	263	4	in	in	ADP
ejpam-3893	263	5	figures	figure	NOUN
ejpam-3893	263	6	2	2	NUM
ejpam-3893	263	7	,	,	PUNCT
ejpam-3893	263	8	4	4	NUM
ejpam-3893	263	9	and	and	CCONJ
ejpam-3893	263	10	6	6	NUM
ejpam-3893	263	11	reveal	reveal	VERB
ejpam-3893	263	12	that	that	SCONJ
ejpam-3893	263	13	,	,	PUNCT
ejpam-3893	263	14	the	the	DET
ejpam-3893	263	15	fdfdwm	fdfdwm	NOUN
ejpam-3893	263	16	performs	perform	VERB
ejpam-3893	263	17	better	well	ADV
ejpam-3893	263	18	in	in	ADP
ejpam-3893	263	19	terms	term	NOUN
ejpam-3893	263	20	of	of	ADP
ejpam-3893	263	21	accuracy	accuracy	NOUN
ejpam-3893	263	22	than	than	ADP
ejpam-3893	263	23	the	the	DET
ejpam-3893	263	24	fem	fem	NOUN
ejpam-3893	263	25	followed	follow	VERB
ejpam-3893	263	26	by	by	ADP
ejpam-3893	263	27	the	the	DET
ejpam-3893	263	28	fdm	fdm	NOUN
ejpam-3893	263	29	.	.	PUNCT
ejpam-3893	264	1	observing	observe	VERB
ejpam-3893	264	2	closely	closely	ADV
ejpam-3893	264	3	figures	figure	NOUN
ejpam-3893	264	4	2	2	NUM
ejpam-3893	264	5	,	,	PUNCT
ejpam-3893	264	6	4	4	NUM
ejpam-3893	264	7	and	and	CCONJ
ejpam-3893	264	8	6	6	NUM
ejpam-3893	264	9	,	,	PUNCT
ejpam-3893	264	10	we	we	PRON
ejpam-3893	264	11	realized	realize	VERB
ejpam-3893	264	12	that	that	SCONJ
ejpam-3893	264	13	as	as	ADP
ejpam-3893	264	14	the	the	DET
ejpam-3893	264	15	resolution	resolution	NOUN
ejpam-3893	264	16	,	,	PUNCT
ejpam-3893	264	17	number	number	NOUN
ejpam-3893	264	18	of	of	ADP
ejpam-3893	264	19	basis	basis	NOUN
ejpam-3893	264	20	functions	function	NOUN
ejpam-3893	264	21	or	or	CCONJ
ejpam-3893	264	22	discretization	discretization	NOUN
ejpam-3893	264	23	points	point	NOUN
ejpam-3893	264	24	increases	increase	VERB
ejpam-3893	264	25	the	the	DET
ejpam-3893	264	26	accuracy	accuracy	NOUN
ejpam-3893	264	27	of	of	ADP
ejpam-3893	264	28	all	all	DET
ejpam-3893	264	29	the	the	DET
ejpam-3893	264	30	methods	method	NOUN
ejpam-3893	264	31	improves	improve	VERB
ejpam-3893	264	32	.	.	PUNCT
ejpam-3893	265	1	however	however	ADV
ejpam-3893	265	2	,	,	PUNCT
ejpam-3893	265	3	by	by	ADP
ejpam-3893	265	4	inspecting	inspect	VERB
ejpam-3893	265	5	the	the	DET
ejpam-3893	265	6	graphs	graph	NOUN
ejpam-3893	265	7	at	at	ADP
ejpam-3893	265	8	resolution	resolution	NOUN
ejpam-3893	265	9	m	m	NOUN
ejpam-3893	265	10	=	=	SYM
ejpam-3893	265	11	3	3	NUM
ejpam-3893	265	12	,	,	PUNCT
ejpam-3893	265	13	the	the	DET
ejpam-3893	265	14	fdfdwm	fdfdwm	NOUN
ejpam-3893	265	15	approximation	approximation	NOUN
ejpam-3893	265	16	and	and	CCONJ
ejpam-3893	265	17	the	the	DET
ejpam-3893	265	18	exact	exact	ADJ
ejpam-3893	265	19	solution	solution	NOUN
ejpam-3893	265	20	are	be	AUX
ejpam-3893	265	21	indistinguishable	indistinguishable	ADJ
ejpam-3893	265	22	.	.	PUNCT
ejpam-3893	266	1	this	this	PRON
ejpam-3893	266	2	can	can	AUX
ejpam-3893	266	3	be	be	AUX
ejpam-3893	266	4	attributed	attribute	VERB
ejpam-3893	266	5	to	to	ADP
ejpam-3893	266	6	the	the	DET
ejpam-3893	266	7	use	use	NOUN
ejpam-3893	266	8	of	of	ADP
ejpam-3893	266	9	the	the	DET
ejpam-3893	266	10	daubechies	daubechie	NOUN
ejpam-3893	266	11	scaling	scale	VERB
ejpam-3893	266	12	functions	function	NOUN
ejpam-3893	266	13	which	which	PRON
ejpam-3893	266	14	offer	offer	VERB
ejpam-3893	266	15	more	more	ADV
ejpam-3893	266	16	accurate	accurate	ADJ
ejpam-3893	266	17	and	and	CCONJ
ejpam-3893	266	18	stable	stable	ADJ
ejpam-3893	266	19	approximation	approximation	NOUN
ejpam-3893	266	20	as	as	SCONJ
ejpam-3893	266	21	opposed	oppose	VERB
ejpam-3893	266	22	to	to	ADP
ejpam-3893	266	23	piece	piece	NOUN
ejpam-3893	266	24	basis	basis	NOUN
ejpam-3893	266	25	functions	function	NOUN
ejpam-3893	266	26	or	or	CCONJ
ejpam-3893	266	27	quadrature	quadrature	NOUN
ejpam-3893	266	28	methods	method	NOUN
ejpam-3893	266	29	often	often	ADV
ejpam-3893	266	30	used	use	VERB
ejpam-3893	266	31	for	for	ADP
ejpam-3893	266	32	the	the	DET
ejpam-3893	266	33	fem	fem	NOUN
ejpam-3893	266	34	and	and	CCONJ
ejpam-3893	266	35	the	the	DET
ejpam-3893	266	36	differencing	difference	VERB
ejpam-3893	266	37	operators	operator	NOUN
ejpam-3893	266	38	used	use	VERB
ejpam-3893	266	39	in	in	ADP
ejpam-3893	266	40	the	the	DET
ejpam-3893	266	41	discretization	discretization	NOUN
ejpam-3893	266	42	process	process	NOUN
ejpam-3893	266	43	of	of	ADP
ejpam-3893	266	44	fdm	fdm	NOUN
ejpam-3893	266	45	.	.	PUNCT
ejpam-3893	267	1	the	the	DET
ejpam-3893	267	2	outcome	outcome	NOUN
ejpam-3893	267	3	of	of	ADP
ejpam-3893	267	4	these	these	DET
ejpam-3893	267	5	results	result	NOUN
ejpam-3893	267	6	are	be	AUX
ejpam-3893	267	7	in	in	ADP
ejpam-3893	267	8	consonance	consonance	NOUN
ejpam-3893	267	9	with	with	ADP
ejpam-3893	267	10	the	the	DET
ejpam-3893	267	11	findings	finding	NOUN
ejpam-3893	267	12	of	of	ADP
ejpam-3893	267	13	a	a	DET
ejpam-3893	267	14	number	number	NOUN
ejpam-3893	267	15	of	of	ADP
ejpam-3893	267	16	related	related	ADJ
ejpam-3893	267	17	studies	study	NOUN
ejpam-3893	267	18	including	include	VERB
ejpam-3893	267	19	;	;	PUNCT
ejpam-3893	268	1	[	[	X
ejpam-3893	268	2	6],[8	6],[8	NOUN
ejpam-3893	268	3	]	]	PUNCT
ejpam-3893	268	4	and	and	CCONJ
ejpam-3893	268	5	[	[	X
ejpam-3893	268	6	9	9	NUM
ejpam-3893	268	7	]	]	PUNCT
ejpam-3893	268	8	.	.	PUNCT
ejpam-3893	269	1	f.	f.	PROPN
ejpam-3893	269	2	o.	o.	PROPN
ejpam-3893	269	3	boateng	boateng	PROPN
ejpam-3893	269	4	et	et	PROPN
ejpam-3893	269	5	al	al	PROPN
ejpam-3893	269	6	.	.	PUNCT
ejpam-3893	269	7	/	/	SYM
ejpam-3893	269	8	eur	eur	PROPN
ejpam-3893	269	9	.	.	PUNCT
ejpam-3893	270	1	j.	j.	PROPN
ejpam-3893	270	2	pure	pure	PROPN
ejpam-3893	270	3	appl	appl	PROPN
ejpam-3893	270	4	.	.	PROPN
ejpam-3893	270	5	math	math	PROPN
ejpam-3893	270	6	,	,	PUNCT
ejpam-3893	270	7	14	14	NUM
ejpam-3893	270	8	(	(	PUNCT
ejpam-3893	270	9	3	3	NUM
ejpam-3893	270	10	)	)	PUNCT
ejpam-3893	270	11	(	(	PUNCT
ejpam-3893	270	12	2021	2021	NUM
ejpam-3893	270	13	)	)	PUNCT
ejpam-3893	270	14	,	,	PUNCT
ejpam-3893	270	15	706	706	NUM
ejpam-3893	270	16	-	-	SYM
ejpam-3893	270	17	722	722	NUM
ejpam-3893	270	18	718	718	NUM
ejpam-3893	270	19	figure	figure	NOUN
ejpam-3893	270	20	2	2	NUM
ejpam-3893	270	21	:	:	PUNCT
ejpam-3893	270	22	comparison	comparison	NOUN
ejpam-3893	270	23	of	of	ADP
ejpam-3893	270	24	fwdfdm	fwdfdm	ADJ
ejpam-3893	270	25	,	,	PUNCT
ejpam-3893	270	26	fdm	fdm	NOUN
ejpam-3893	270	27	and	and	CCONJ
ejpam-3893	270	28	fem	fem	NOUN
ejpam-3893	270	29	solutions	solution	NOUN
ejpam-3893	270	30	with	with	ADP
ejpam-3893	270	31	exact	exact	ADJ
ejpam-3893	270	32	solution	solution	NOUN
ejpam-3893	270	33	φ	φ	NOUN
ejpam-3893	270	34	=	=	SYM
ejpam-3893	270	35	sin(x+y	sin(x+y	PROPN
ejpam-3893	270	36	)	)	PUNCT
ejpam-3893	270	37	on	on	ADP
ejpam-3893	270	38	a	a	DET
ejpam-3893	270	39	rectangular	rectangular	ADJ
ejpam-3893	270	40	domain	domain	NOUN
ejpam-3893	270	41	for	for	ADP
ejpam-3893	270	42	d6	d6	NOUN
ejpam-3893	270	43	and	and	CCONJ
ejpam-3893	270	44	m	m	NOUN
ejpam-3893	270	45	=	=	ADJ
ejpam-3893	270	46	1	1	NUM
ejpam-3893	270	47	,	,	PUNCT
ejpam-3893	270	48	2	2	NUM
ejpam-3893	270	49	and	and	CCONJ
ejpam-3893	270	50	3	3	NUM
ejpam-3893	270	51	figure	figure	NOUN
ejpam-3893	270	52	3	3	NUM
ejpam-3893	270	53	:	:	PUNCT
ejpam-3893	270	54	the	the	DET
ejpam-3893	270	55	fwdfdm	fwdfdm	ADJ
ejpam-3893	270	56	approximation	approximation	NOUN
ejpam-3893	270	57	on	on	ADP
ejpam-3893	270	58	a	a	DET
ejpam-3893	270	59	rectangular	rectangular	ADJ
ejpam-3893	270	60	domain	domain	NOUN
ejpam-3893	270	61	for	for	ADP
ejpam-3893	270	62	d6	d6	NOUN
ejpam-3893	270	63	and	and	CCONJ
ejpam-3893	270	64	m	m	NOUN
ejpam-3893	270	65	=	=	SYM
ejpam-3893	270	66	0	0	NUM
ejpam-3893	270	67	,	,	PUNCT
ejpam-3893	270	68	1	1	NUM
ejpam-3893	270	69	,	,	PUNCT
ejpam-3893	270	70	2	2	NUM
ejpam-3893	270	71	and	and	CCONJ
ejpam-3893	270	72	3	3	NUM
ejpam-3893	270	73	3.2	3.2	NUM
ejpam-3893	270	74	.	.	PUNCT
ejpam-3893	271	1	error	error	NOUN
ejpam-3893	271	2	analysis	analysis	NOUN
ejpam-3893	271	3	for	for	ADP
ejpam-3893	271	4	fdfdwm	fdfdwm	NOUN
ejpam-3893	271	5	here	here	ADV
ejpam-3893	271	6	,	,	PUNCT
ejpam-3893	271	7	the	the	DET
ejpam-3893	271	8	relative	relative	ADJ
ejpam-3893	271	9	error	error	NOUN
ejpam-3893	271	10	using	use	VERB
ejpam-3893	271	11	l2	l2	NOUN
ejpam-3893	271	12	vector	vector	NOUN
ejpam-3893	271	13	norm	norm	NOUN
ejpam-3893	271	14	is	be	AUX
ejpam-3893	271	15	computed	compute	VERB
ejpam-3893	271	16	for	for	ADP
ejpam-3893	271	17	each	each	PRON
ejpam-3893	271	18	of	of	ADP
ejpam-3893	271	19	the	the	DET
ejpam-3893	271	20	test	test	NOUN
ejpam-3893	271	21	cases	case	NOUN
ejpam-3893	271	22	with	with	ADP
ejpam-3893	271	23	varying	vary	VERB
ejpam-3893	271	24	resolutions	resolution	NOUN
ejpam-3893	271	25	(	(	PUNCT
ejpam-3893	271	26	i.e	i.e	X
ejpam-3893	271	27	m	m	NOUN
ejpam-3893	271	28	=	=	ADJ
ejpam-3893	271	29	0	0	NUM
ejpam-3893	271	30	,	,	PUNCT
ejpam-3893	271	31	1	1	NUM
ejpam-3893	271	32	,	,	PUNCT
ejpam-3893	271	33	2	2	NUM
ejpam-3893	271	34	,	,	PUNCT
ejpam-3893	271	35	3	3	NUM
ejpam-3893	271	36	,	,	PUNCT
ejpam-3893	271	37	4	4	NUM
ejpam-3893	271	38	,	,	PUNCT
ejpam-3893	271	39	5	5	NUM
ejpam-3893	271	40	,	,	PUNCT
ejpam-3893	271	41	6	6	NUM
ejpam-3893	271	42	,	,	PUNCT
ejpam-3893	271	43	7	7	NUM
ejpam-3893	271	44	)	)	PUNCT
ejpam-3893	271	45	and	and	CCONJ
ejpam-3893	271	46	scaling	scale	VERB
ejpam-3893	271	47	function	function	NOUN
ejpam-3893	271	48	order	order	NOUN
ejpam-3893	271	49	d6	d6	NOUN
ejpam-3893	271	50	.	.	PUNCT
ejpam-3893	272	1	the	the	DET
ejpam-3893	272	2	f.	f.	PROPN
ejpam-3893	272	3	o.	o.	PROPN
ejpam-3893	272	4	boateng	boateng	PROPN
ejpam-3893	272	5	et	et	PROPN
ejpam-3893	272	6	al	al	PROPN
ejpam-3893	272	7	.	.	PUNCT
ejpam-3893	272	8	/	/	SYM
ejpam-3893	272	9	eur	eur	PROPN
ejpam-3893	272	10	.	.	PUNCT
ejpam-3893	273	1	j.	j.	PROPN
ejpam-3893	273	2	pure	pure	PROPN
ejpam-3893	273	3	appl	appl	PROPN
ejpam-3893	273	4	.	.	PROPN
ejpam-3893	273	5	math	math	PROPN
ejpam-3893	273	6	,	,	PUNCT
ejpam-3893	273	7	14	14	NUM
ejpam-3893	273	8	(	(	PUNCT
ejpam-3893	273	9	3	3	NUM
ejpam-3893	273	10	)	)	PUNCT
ejpam-3893	273	11	(	(	PUNCT
ejpam-3893	273	12	2021	2021	NUM
ejpam-3893	273	13	)	)	PUNCT
ejpam-3893	273	14	,	,	PUNCT
ejpam-3893	273	15	706	706	NUM
ejpam-3893	273	16	-	-	SYM
ejpam-3893	273	17	722	722	NUM
ejpam-3893	273	18	719	719	NUM
ejpam-3893	273	19	figure	figure	NOUN
ejpam-3893	273	20	4	4	NUM
ejpam-3893	273	21	:	:	PUNCT
ejpam-3893	273	22	comparison	comparison	NOUN
ejpam-3893	273	23	of	of	ADP
ejpam-3893	273	24	fwdfdm	fwdfdm	ADJ
ejpam-3893	273	25	,	,	PUNCT
ejpam-3893	273	26	fdm	fdm	NOUN
ejpam-3893	273	27	and	and	CCONJ
ejpam-3893	273	28	fem	fem	NOUN
ejpam-3893	273	29	solutions	solution	NOUN
ejpam-3893	273	30	with	with	ADP
ejpam-3893	273	31	exact	exact	ADJ
ejpam-3893	273	32	solution	solution	NOUN
ejpam-3893	273	33	φ	φ	NOUN
ejpam-3893	273	34	=	=	SYM
ejpam-3893	274	1	x2	x2	PROPN
ejpam-3893	275	1	+	+	CCONJ
ejpam-3893	275	2	y2	y2	NOUN
ejpam-3893	275	3	on	on	ADP
ejpam-3893	275	4	a	a	DET
ejpam-3893	275	5	rectangular	rectangular	ADJ
ejpam-3893	275	6	domain	domain	NOUN
ejpam-3893	275	7	for	for	ADP
ejpam-3893	275	8	d6	d6	NOUN
ejpam-3893	275	9	and	and	CCONJ
ejpam-3893	275	10	m	m	NOUN
ejpam-3893	275	11	=	=	SYM
ejpam-3893	275	12	0	0	NUM
ejpam-3893	275	13	,	,	PUNCT
ejpam-3893	275	14	1	1	NUM
ejpam-3893	275	15	,	,	PUNCT
ejpam-3893	275	16	2	2	NUM
ejpam-3893	275	17	and	and	CCONJ
ejpam-3893	275	18	3	3	NUM
ejpam-3893	275	19	figure	figure	NOUN
ejpam-3893	275	20	5	5	NUM
ejpam-3893	275	21	:	:	PUNCT
ejpam-3893	275	22	the	the	DET
ejpam-3893	275	23	fwdfdm	fwdfdm	ADJ
ejpam-3893	275	24	approximation	approximation	NOUN
ejpam-3893	275	25	on	on	ADP
ejpam-3893	275	26	a	a	DET
ejpam-3893	275	27	rectangular	rectangular	ADJ
ejpam-3893	275	28	domain	domain	NOUN
ejpam-3893	275	29	for	for	ADP
ejpam-3893	275	30	d6	d6	NOUN
ejpam-3893	275	31	and	and	CCONJ
ejpam-3893	275	32	m	m	NOUN
ejpam-3893	275	33	=	=	NOUN
ejpam-3893	275	34	1	1	NUM
ejpam-3893	275	35	,	,	PUNCT
ejpam-3893	275	36	2	2	NUM
ejpam-3893	275	37	,	,	PUNCT
ejpam-3893	275	38	3	3	NUM
ejpam-3893	275	39	and	and	CCONJ
ejpam-3893	275	40	4	4	NUM
ejpam-3893	275	41	relative	relative	ADJ
ejpam-3893	275	42	error	error	NOUN
ejpam-3893	275	43	used	use	VERB
ejpam-3893	275	44	is	be	AUX
ejpam-3893	275	45	provided	provide	VERB
ejpam-3893	275	46	as	as	ADP
ejpam-3893	275	47	e	e	X
ejpam-3893	275	48	=	=	PUNCT
ejpam-3893	275	49	‖φ−	‖φ−	PROPN
ejpam-3893	275	50	φ̃‖l2(ω	φ̃‖l2(ω	ADV
ejpam-3893	275	51	)	)	PUNCT
ejpam-3893	275	52	‖φ‖l2(ω	‖φ‖l2(ω	ADV
ejpam-3893	275	53	)	)	PUNCT
ejpam-3893	276	1	f.	f.	PROPN
ejpam-3893	276	2	o.	o.	PROPN
ejpam-3893	276	3	boateng	boateng	PROPN
ejpam-3893	276	4	et	et	PROPN
ejpam-3893	276	5	al	al	PROPN
ejpam-3893	276	6	.	.	PUNCT
ejpam-3893	276	7	/	/	SYM
ejpam-3893	276	8	eur	eur	PROPN
ejpam-3893	276	9	.	.	PUNCT
ejpam-3893	277	1	j.	j.	PROPN
ejpam-3893	277	2	pure	pure	PROPN
ejpam-3893	277	3	appl	appl	PROPN
ejpam-3893	277	4	.	.	PROPN
ejpam-3893	277	5	math	math	PROPN
ejpam-3893	277	6	,	,	PUNCT
ejpam-3893	277	7	14	14	NUM
ejpam-3893	277	8	(	(	PUNCT
ejpam-3893	277	9	3	3	NUM
ejpam-3893	277	10	)	)	PUNCT
ejpam-3893	277	11	(	(	PUNCT
ejpam-3893	277	12	2021	2021	NUM
ejpam-3893	277	13	)	)	PUNCT
ejpam-3893	277	14	,	,	PUNCT
ejpam-3893	277	15	706	706	NUM
ejpam-3893	277	16	-	-	SYM
ejpam-3893	277	17	722	722	NUM
ejpam-3893	277	18	720	720	NUM
ejpam-3893	277	19	figure	figure	NOUN
ejpam-3893	277	20	6	6	NUM
ejpam-3893	277	21	:	:	PUNCT
ejpam-3893	277	22	comparison	comparison	NOUN
ejpam-3893	277	23	of	of	ADP
ejpam-3893	277	24	fwdfdm	fwdfdm	ADJ
ejpam-3893	277	25	,	,	PUNCT
ejpam-3893	277	26	fdm	fdm	NOUN
ejpam-3893	277	27	and	and	CCONJ
ejpam-3893	277	28	fem	fem	NOUN
ejpam-3893	277	29	solutions	solution	NOUN
ejpam-3893	277	30	with	with	ADP
ejpam-3893	277	31	exact	exact	ADJ
ejpam-3893	277	32	solution	solution	NOUN
ejpam-3893	277	33	(	(	PUNCT
ejpam-3893	277	34	sinπx+	sinπx+	SYM
ejpam-3893	277	35	sinπy)/−	sinπy)/−	VERB
ejpam-3893	277	36	2π2	2π2	NUM
ejpam-3893	277	37	on	on	ADP
ejpam-3893	277	38	a	a	DET
ejpam-3893	277	39	rectangular	rectangular	ADJ
ejpam-3893	277	40	domain	domain	NOUN
ejpam-3893	277	41	for	for	ADP
ejpam-3893	277	42	d6	d6	NOUN
ejpam-3893	277	43	and	and	CCONJ
ejpam-3893	277	44	m	m	NOUN
ejpam-3893	277	45	=	=	NOUN
ejpam-3893	277	46	1	1	NUM
ejpam-3893	277	47	,	,	PUNCT
ejpam-3893	277	48	1	1	NUM
ejpam-3893	277	49	,	,	PUNCT
ejpam-3893	277	50	3	3	NUM
ejpam-3893	277	51	and	and	CCONJ
ejpam-3893	277	52	4	4	NUM
ejpam-3893	277	53	figure	figure	NOUN
ejpam-3893	277	54	7	7	NUM
ejpam-3893	277	55	:	:	PUNCT
ejpam-3893	277	56	relative	relative	ADJ
ejpam-3893	277	57	l2	l2	NOUN
ejpam-3893	277	58	error	error	NOUN
ejpam-3893	277	59	for	for	ADP
ejpam-3893	277	60	test	test	NOUN
ejpam-3893	277	61	case	case	NOUN
ejpam-3893	277	62	1	1	NUM
ejpam-3893	277	63	,	,	PUNCT
ejpam-3893	277	64	2	2	NUM
ejpam-3893	277	65	and	and	CCONJ
ejpam-3893	277	66	3	3	NUM
ejpam-3893	277	67	using	use	VERB
ejpam-3893	277	68	d6	d6	NOUN
ejpam-3893	277	69	and	and	CCONJ
ejpam-3893	277	70	varying	vary	VERB
ejpam-3893	277	71	resolutions	resolution	NOUN
ejpam-3893	277	72	,	,	PUNCT
ejpam-3893	277	73	m	m	VERB
ejpam-3893	277	74	=	=	NOUN
ejpam-3893	277	75	0	0	NUM
ejpam-3893	277	76	to	to	ADP
ejpam-3893	277	77	m	m	NOUN
ejpam-3893	277	78	=	=	NOUN
ejpam-3893	277	79	7	7	NUM
ejpam-3893	277	80	it	it	PRON
ejpam-3893	277	81	is	be	AUX
ejpam-3893	277	82	apparent	apparent	ADJ
ejpam-3893	277	83	from	from	ADP
ejpam-3893	277	84	figure	figure	NOUN
ejpam-3893	277	85	7	7	NUM
ejpam-3893	277	86	that	that	SCONJ
ejpam-3893	277	87	,	,	PUNCT
ejpam-3893	277	88	as	as	SCONJ
ejpam-3893	277	89	the	the	DET
ejpam-3893	277	90	resolution	resolution	NOUN
ejpam-3893	277	91	increases	increase	VERB
ejpam-3893	277	92	the	the	DET
ejpam-3893	277	93	error	error	NOUN
ejpam-3893	277	94	decays	decay	VERB
ejpam-3893	277	95	rapidly	rapidly	ADV
ejpam-3893	277	96	,	,	PUNCT
ejpam-3893	277	97	references	reference	NOUN
ejpam-3893	277	98	721	721	NUM
ejpam-3893	277	99	indicating	indicate	VERB
ejpam-3893	277	100	good	good	ADJ
ejpam-3893	277	101	convergence	convergence	NOUN
ejpam-3893	277	102	of	of	ADP
ejpam-3893	277	103	the	the	DET
ejpam-3893	277	104	approximate	approximate	ADJ
ejpam-3893	277	105	solution	solution	NOUN
ejpam-3893	277	106	to	to	ADP
ejpam-3893	277	107	the	the	DET
ejpam-3893	277	108	exact	exact	ADJ
ejpam-3893	277	109	solution	solution	NOUN
ejpam-3893	277	110	.	.	PUNCT
ejpam-3893	278	1	although	although	SCONJ
ejpam-3893	278	2	using	use	VERB
ejpam-3893	278	3	daubechies	daubechie	NOUN
ejpam-3893	278	4	scaling	scale	VERB
ejpam-3893	278	5	functions	function	NOUN
ejpam-3893	278	6	with	with	ADP
ejpam-3893	278	7	genus	genus	ADJ
ejpam-3893	278	8	d6	d6	NOUN
ejpam-3893	278	9	at	at	ADP
ejpam-3893	278	10	varying	vary	VERB
ejpam-3893	278	11	resolutions	resolution	NOUN
ejpam-3893	278	12	appears	appear	VERB
ejpam-3893	278	13	to	to	PART
ejpam-3893	278	14	generate	generate	VERB
ejpam-3893	278	15	reasonable	reasonable	ADJ
ejpam-3893	278	16	approximation	approximation	NOUN
ejpam-3893	278	17	to	to	ADP
ejpam-3893	278	18	the	the	DET
ejpam-3893	278	19	pdes	pde	NOUN
ejpam-3893	278	20	under	under	ADP
ejpam-3893	278	21	consideration	consideration	NOUN
ejpam-3893	278	22	using	use	VERB
ejpam-3893	278	23	the	the	DET
ejpam-3893	278	24	fdfdwm	fdfdwm	NOUN
ejpam-3893	278	25	,	,	PUNCT
ejpam-3893	278	26	it	it	PRON
ejpam-3893	278	27	is	be	AUX
ejpam-3893	278	28	essential	essential	ADJ
ejpam-3893	278	29	to	to	PART
ejpam-3893	278	30	examine	examine	VERB
ejpam-3893	278	31	instances	instance	NOUN
ejpam-3893	278	32	where	where	SCONJ
ejpam-3893	278	33	the	the	DET
ejpam-3893	278	34	genus	genus	NOUN
ejpam-3893	278	35	of	of	ADP
ejpam-3893	278	36	the	the	DET
ejpam-3893	278	37	scaling	scaling	ADJ
ejpam-3893	278	38	functions	function	NOUN
ejpam-3893	278	39	increases	increase	NOUN
ejpam-3893	278	40	.	.	PUNCT
ejpam-3893	279	1	table	table	NOUN
ejpam-3893	279	2	1	1	NUM
ejpam-3893	279	3	:	:	PUNCT
ejpam-3893	279	4	relative	relative	ADJ
ejpam-3893	279	5	l2	l2	NOUN
ejpam-3893	279	6	error	error	NOUN
ejpam-3893	279	7	for	for	ADP
ejpam-3893	279	8	φ	φ	PROPN
ejpam-3893	279	9	=	=	SYM
ejpam-3893	279	10	(	(	PUNCT
ejpam-3893	279	11	sinπx+sinπy)/−2π2	sinπx+sinπy)/−2π2	ADJ
ejpam-3893	279	12	approximation	approximation	NOUN
ejpam-3893	279	13	and	and	CCONJ
ejpam-3893	279	14	condition	condition	NOUN
ejpam-3893	279	15	number	number	NOUN
ejpam-3893	279	16	of	of	ADP
ejpam-3893	279	17	fdfdwm	fdfdwm	NOUN
ejpam-3893	279	18	’s	’s	PART
ejpam-3893	279	19	system	system	NOUN
ejpam-3893	279	20	matrix	matrix	NOUN
ejpam-3893	279	21	m	m	NOUN
ejpam-3893	279	22	=	=	NOUN
ejpam-3893	279	23	1	1	NUM
ejpam-3893	279	24	m	m	NOUN
ejpam-3893	279	25	=	=	SYM
ejpam-3893	279	26	2	2	NUM
ejpam-3893	279	27	dn	dn	NOUN
ejpam-3893	279	28	error	error	NOUN
ejpam-3893	279	29	(	(	PUNCT
ejpam-3893	279	30	l2	l2	NOUN
ejpam-3893	279	31	)	)	PUNCT
ejpam-3893	279	32	cond	cond	NOUN
ejpam-3893	279	33	.	.	PUNCT
ejpam-3893	280	1	num	num	ADJ
ejpam-3893	280	2	error	error	NOUN
ejpam-3893	280	3	(	(	PUNCT
ejpam-3893	280	4	l2	l2	NOUN
ejpam-3893	280	5	)	)	PUNCT
ejpam-3893	280	6	cond	cond	NOUN
ejpam-3893	280	7	.	.	PUNCT
ejpam-3893	281	1	num	num	ADJ
ejpam-3893	281	2	.	.	NOUN
ejpam-3893	281	3	6	6	NUM
ejpam-3893	281	4	1.72273872e-01	1.72273872e-01	NUM
ejpam-3893	281	5	266545.642	266545.642	NUM
ejpam-3893	281	6	8.59266326e-02	8.59266326e-02	NUM
ejpam-3893	281	7	1216547.557	1216547.557	NUM
ejpam-3893	281	8	8	8	NUM
ejpam-3893	281	9	1.34574728e-01	1.34574728e-01	NUM
ejpam-3893	281	10	299652.198	299652.198	NUM
ejpam-3893	281	11	5.82274887e-02	5.82274887e-02	NUM
ejpam-3893	281	12	2549819.826	2549819.826	NUM
ejpam-3893	281	13	10	10	NUM
ejpam-3893	281	14	1.00084497e-01	1.00084497e-01	NUM
ejpam-3893	281	15	313878.814	313878.814	NUM
ejpam-3893	281	16	2.37372575e-02	2.37372575e-02	NUM
ejpam-3893	281	17	4877499.258	4877499.258	NUM
ejpam-3893	281	18	12	12	NUM
ejpam-3893	281	19	9.03869299e-02	9.03869299e-02	NUM
ejpam-3893	281	20	452164.135	452164.135	NUM
ejpam-3893	281	21	1.00522059e-02	1.00522059e-02	NUM
ejpam-3893	281	22	6225570.392	6225570.392	NUM
ejpam-3893	281	23	14	14	NUM
ejpam-3893	281	24	8.17337237e-02	8.17337237e-02	NUM
ejpam-3893	281	25	724845.847	724845.847	NUM
ejpam-3893	281	26	6.08648401e-03	6.08648401e-03	NUM
ejpam-3893	282	1	9913426.592	9913426.592	NUM
ejpam-3893	282	2	16	16	NUM
ejpam-3893	282	3	7.99390005e-02	7.99390005e-02	NUM
ejpam-3893	282	4	1095616.081	1095616.081	NUM
ejpam-3893	282	5	4.19176077e-03	4.19176077e-03	NUM
ejpam-3893	282	6	12874663.138	12874663.138	NUM
ejpam-3893	282	7	18	18	NUM
ejpam-3893	282	8	7.62888260e-02	7.62888260e-02	NUM
ejpam-3893	282	9	1479906.308	1479906.308	NUM
ejpam-3893	282	10	1.24158634e-03	1.24158634e-03	NUM
ejpam-3893	282	11	19988975.378	19988975.378	NUM
ejpam-3893	282	12	20	20	NUM
ejpam-3893	282	13	7.39675096e-02	7.39675096e-02	NUM
ejpam-3893	283	1	2129604.614	2129604.614	NUM
ejpam-3893	283	2	1.02026987e-04	1.02026987e-04	NUM
ejpam-3893	283	3	31017665.097	31017665.097	NUM
ejpam-3893	283	4	in	in	ADP
ejpam-3893	283	5	table	table	NOUN
ejpam-3893	283	6	1	1	NUM
ejpam-3893	283	7	,	,	PUNCT
ejpam-3893	283	8	we	we	PRON
ejpam-3893	283	9	display	display	VERB
ejpam-3893	283	10	the	the	DET
ejpam-3893	283	11	condition	condition	NOUN
ejpam-3893	283	12	number	number	NOUN
ejpam-3893	283	13	of	of	ADP
ejpam-3893	283	14	the	the	DET
ejpam-3893	283	15	coefficient	coefficient	NOUN
ejpam-3893	283	16	matrix	matrix	NOUN
ejpam-3893	283	17	of	of	ADP
ejpam-3893	283	18	fdfdwm	fdfdwm	NOUN
ejpam-3893	283	19	provided	provide	VERB
ejpam-3893	283	20	in	in	ADP
ejpam-3893	283	21	equation	equation	NOUN
ejpam-3893	283	22	(	(	PUNCT
ejpam-3893	283	23	32	32	NUM
ejpam-3893	283	24	)	)	PUNCT
ejpam-3893	283	25	together	together	ADV
ejpam-3893	283	26	with	with	ADP
ejpam-3893	283	27	the	the	DET
ejpam-3893	283	28	relative	relative	ADJ
ejpam-3893	283	29	l2	l2	NOUN
ejpam-3893	283	30	norm	norm	NOUN
ejpam-3893	283	31	error	error	NOUN
ejpam-3893	283	32	at	at	ADP
ejpam-3893	283	33	m	m	NOUN
ejpam-3893	283	34	=	=	SYM
ejpam-3893	283	35	1	1	NUM
ejpam-3893	283	36	and	and	CCONJ
ejpam-3893	283	37	m	m	PROPN
ejpam-3893	283	38	=	=	ADJ
ejpam-3893	283	39	2	2	NUM
ejpam-3893	283	40	,	,	PUNCT
ejpam-3893	283	41	and	and	CCONJ
ejpam-3893	283	42	varying	vary	VERB
ejpam-3893	283	43	scaling	scale	VERB
ejpam-3893	283	44	function	function	NOUN
ejpam-3893	283	45	genus	genus	NOUN
ejpam-3893	283	46	from	from	ADP
ejpam-3893	283	47	d6	d6	NOUN
ejpam-3893	283	48	to	to	PART
ejpam-3893	283	49	d20	d20	VERB
ejpam-3893	283	50	for	for	ADP
ejpam-3893	283	51	test	test	NOUN
ejpam-3893	283	52	case	case	NOUN
ejpam-3893	283	53	1	1	NUM
ejpam-3893	283	54	.	.	PUNCT
ejpam-3893	284	1	the	the	DET
ejpam-3893	284	2	table	table	NOUN
ejpam-3893	284	3	reveals	reveal	VERB
ejpam-3893	284	4	that	that	SCONJ
ejpam-3893	284	5	the	the	DET
ejpam-3893	284	6	approximation	approximation	NOUN
ejpam-3893	284	7	of	of	ADP
ejpam-3893	284	8	the	the	DET
ejpam-3893	284	9	fdfdwm	fdfdwm	NOUN
ejpam-3893	284	10	gets	get	VERB
ejpam-3893	284	11	better	well	ADJ
ejpam-3893	284	12	as	as	SCONJ
ejpam-3893	284	13	the	the	DET
ejpam-3893	284	14	genus	genus	NOUN
ejpam-3893	284	15	of	of	ADP
ejpam-3893	284	16	the	the	DET
ejpam-3893	284	17	scaling	scale	VERB
ejpam-3893	284	18	functions	function	NOUN
ejpam-3893	284	19	increases	increase	NOUN
ejpam-3893	284	20	from	from	ADP
ejpam-3893	284	21	d6	d6	NOUN
ejpam-3893	284	22	to	to	PART
ejpam-3893	284	23	d20	d20	VERB
ejpam-3893	284	24	.	.	PUNCT
ejpam-3893	285	1	however	however	ADV
ejpam-3893	285	2	,	,	PUNCT
ejpam-3893	285	3	we	we	PRON
ejpam-3893	285	4	realized	realize	VERB
ejpam-3893	285	5	that	that	SCONJ
ejpam-3893	285	6	for	for	ADP
ejpam-3893	285	7	d12	d12	NUM
ejpam-3893	285	8	and	and	CCONJ
ejpam-3893	285	9	above	above	ADV
ejpam-3893	285	10	,	,	PUNCT
ejpam-3893	285	11	the	the	DET
ejpam-3893	285	12	effect	effect	NOUN
ejpam-3893	285	13	of	of	ADP
ejpam-3893	285	14	the	the	DET
ejpam-3893	285	15	increment	increment	NOUN
ejpam-3893	285	16	in	in	ADP
ejpam-3893	285	17	the	the	DET
ejpam-3893	285	18	genus	genus	NOUN
ejpam-3893	285	19	on	on	ADP
ejpam-3893	285	20	the	the	DET
ejpam-3893	285	21	accuracy	accuracy	NOUN
ejpam-3893	285	22	of	of	ADP
ejpam-3893	285	23	the	the	DET
ejpam-3893	285	24	approximation	approximation	NOUN
ejpam-3893	285	25	diminishes	diminish	VERB
ejpam-3893	285	26	.	.	PUNCT
ejpam-3893	286	1	we	we	PRON
ejpam-3893	286	2	noticed	notice	VERB
ejpam-3893	286	3	that	that	SCONJ
ejpam-3893	286	4	the	the	DET
ejpam-3893	286	5	condition	condition	NOUN
ejpam-3893	286	6	number	number	NOUN
ejpam-3893	286	7	grows	grow	VERB
ejpam-3893	286	8	as	as	ADP
ejpam-3893	286	9	the	the	DET
ejpam-3893	286	10	resolution	resolution	NOUN
ejpam-3893	286	11	increases	increase	NOUN
ejpam-3893	286	12	and	and	CCONJ
ejpam-3893	286	13	same	same	ADJ
ejpam-3893	286	14	when	when	SCONJ
ejpam-3893	286	15	the	the	DET
ejpam-3893	286	16	genus	genus	NOUN
ejpam-3893	286	17	of	of	ADP
ejpam-3893	286	18	the	the	DET
ejpam-3893	286	19	scaling	scaling	ADJ
ejpam-3893	286	20	function	function	NOUN
ejpam-3893	286	21	increases	increase	NOUN
ejpam-3893	286	22	.	.	PUNCT
ejpam-3893	287	1	observably	observably	ADV
ejpam-3893	287	2	,	,	PUNCT
ejpam-3893	287	3	we	we	PRON
ejpam-3893	287	4	believe	believe	VERB
ejpam-3893	287	5	that	that	SCONJ
ejpam-3893	287	6	the	the	DET
ejpam-3893	287	7	condition	condition	NOUN
ejpam-3893	287	8	number	number	NOUN
ejpam-3893	287	9	is	be	AUX
ejpam-3893	287	10	one	one	NUM
ejpam-3893	287	11	of	of	ADP
ejpam-3893	287	12	the	the	DET
ejpam-3893	287	13	contributing	contribute	VERB
ejpam-3893	287	14	sources	source	NOUN
ejpam-3893	287	15	of	of	ADP
ejpam-3893	287	16	error	error	NOUN
ejpam-3893	287	17	in	in	ADP
ejpam-3893	287	18	the	the	DET
ejpam-3893	287	19	fdfdwm	fdfdwm	NOUN
ejpam-3893	287	20	.	.	PUNCT
ejpam-3893	288	1	4	4	X
ejpam-3893	288	2	.	.	X
ejpam-3893	288	3	conclusion	conclusion	NOUN
ejpam-3893	288	4	we	we	PRON
ejpam-3893	288	5	have	have	AUX
ejpam-3893	288	6	demonstrated	demonstrate	VERB
ejpam-3893	288	7	in	in	ADP
ejpam-3893	288	8	this	this	DET
ejpam-3893	288	9	paper	paper	NOUN
ejpam-3893	288	10	that	that	SCONJ
ejpam-3893	288	11	the	the	DET
ejpam-3893	288	12	fdfdwm	fdfdwm	NOUN
ejpam-3893	288	13	is	be	AUX
ejpam-3893	288	14	comparable	comparable	ADJ
ejpam-3893	288	15	to	to	ADP
ejpam-3893	288	16	the	the	DET
ejpam-3893	288	17	traditional	traditional	ADJ
ejpam-3893	288	18	fem	fem	NOUN
ejpam-3893	288	19	and	and	CCONJ
ejpam-3893	288	20	fdm	fdm	NOUN
ejpam-3893	288	21	approaches	approach	NOUN
ejpam-3893	288	22	,	,	PUNCT
ejpam-3893	288	23	and	and	CCONJ
ejpam-3893	288	24	has	have	VERB
ejpam-3893	288	25	inherently	inherently	ADV
ejpam-3893	288	26	better	well	ADJ
ejpam-3893	288	27	accuracy	accuracy	NOUN
ejpam-3893	288	28	to	to	ADP
ejpam-3893	288	29	the	the	DET
ejpam-3893	288	30	approximation	approximation	NOUN
ejpam-3893	288	31	of	of	ADP
ejpam-3893	288	32	the	the	DET
ejpam-3893	288	33	dirichlet	dirichlet	PROPN
ejpam-3893	288	34	problem	problem	NOUN
ejpam-3893	288	35	for	for	ADP
ejpam-3893	288	36	linear	linear	PROPN
ejpam-3893	288	37	elliptic	elliptic	ADJ
ejpam-3893	288	38	partial	partial	ADJ
ejpam-3893	288	39	differential	differential	NOUN
ejpam-3893	288	40	equation	equation	NOUN
ejpam-3893	288	41	in	in	ADP
ejpam-3893	288	42	two	two	NUM
ejpam-3893	288	43	dimension	dimension	NOUN
ejpam-3893	288	44	.	.	PUNCT
ejpam-3893	289	1	it	it	PRON
ejpam-3893	289	2	is	be	AUX
ejpam-3893	289	3	much	much	ADV
ejpam-3893	289	4	easier	easy	ADJ
ejpam-3893	289	5	increasing	increase	VERB
ejpam-3893	289	6	the	the	DET
ejpam-3893	289	7	daubechies	daubechie	NOUN
ejpam-3893	289	8	scaling	scale	VERB
ejpam-3893	289	9	function	function	NOUN
ejpam-3893	289	10	order	order	NOUN
ejpam-3893	289	11	and	and	CCONJ
ejpam-3893	289	12	resolution	resolution	NOUN
ejpam-3893	289	13	to	to	PART
ejpam-3893	289	14	obtain	obtain	VERB
ejpam-3893	289	15	more	more	ADV
ejpam-3893	289	16	accurate	accurate	ADJ
ejpam-3893	289	17	solutions	solution	NOUN
ejpam-3893	289	18	.	.	PUNCT
ejpam-3893	290	1	also	also	ADV
ejpam-3893	290	2	the	the	DET
ejpam-3893	290	3	reduction	reduction	NOUN
ejpam-3893	290	4	of	of	ADP
ejpam-3893	290	5	the	the	DET
ejpam-3893	290	6	problem	problem	NOUN
ejpam-3893	290	7	from	from	ADP
ejpam-3893	290	8	2d	2d	NUM
ejpam-3893	290	9	to	to	ADP
ejpam-3893	290	10	1d	1d	NUM
ejpam-3893	290	11	minimizes	minimize	VERB
ejpam-3893	290	12	the	the	DET
ejpam-3893	290	13	complexities	complexity	NOUN
ejpam-3893	290	14	associated	associate	VERB
ejpam-3893	290	15	with	with	ADP
ejpam-3893	290	16	solving	solve	VERB
ejpam-3893	290	17	pdes	pde	NOUN
ejpam-3893	290	18	in	in	ADP
ejpam-3893	290	19	higher	high	ADJ
ejpam-3893	290	20	order	order	NOUN
ejpam-3893	290	21	.	.	PUNCT
ejpam-3893	291	1	references	reference	NOUN
ejpam-3893	291	2	[	[	X
ejpam-3893	291	3	1	1	NUM
ejpam-3893	291	4	]	]	X
ejpam-3893	291	5	j	j	PROPN
ejpam-3893	291	6	d	d	PROPN
ejpam-3893	291	7	anderson	anderson	PROPN
ejpam-3893	291	8	.	.	PUNCT
ejpam-3893	292	1	fundamentals	fundamental	NOUN
ejpam-3893	292	2	of	of	ADP
ejpam-3893	292	3	aerodynamics	aerodynamic	NOUN
ejpam-3893	292	4	,	,	PUNCT
ejpam-3893	292	5	4th	4th	ADJ
ejpam-3893	292	6	ed	ed	NOUN
ejpam-3893	292	7	.	.	PUNCT
ejpam-3893	293	1	mcgraw	mcgraw	PROPN
ejpam-3893	293	2	–	–	PUNCT
ejpam-3893	293	3	hill	hill	PROPN
ejpam-3893	293	4	,	,	PUNCT
ejpam-3893	293	5	2007	2007	NUM
ejpam-3893	293	6	.	.	PUNCT
ejpam-3893	294	1	[	[	X
ejpam-3893	294	2	2	2	NUM
ejpam-3893	294	3	]	]	SYM
ejpam-3893	294	4	b	b	X
ejpam-3893	294	5	barnes	barne	NOUN
ejpam-3893	294	6	,	,	PUNCT
ejpam-3893	294	7	e	e	PROPN
ejpam-3893	294	8	osei	osei	PROPN
ejpam-3893	294	9	-	-	PUNCT
ejpam-3893	294	10	frimpong	frimpong	PROPN
ejpam-3893	294	11	,	,	PUNCT
ejpam-3893	294	12	f	f	PROPN
ejpam-3893	294	13	o	o	X
ejpam-3893	294	14	boateng	boateng	PROPN
ejpam-3893	294	15	,	,	PUNCT
ejpam-3893	294	16	and	and	CCONJ
ejpam-3893	294	17	j	j	PROPN
ejpam-3893	294	18	ackora	ackora	PROPN
ejpam-3893	294	19	-	-	PUNCT
ejpam-3893	294	20	prah	prah	PROPN
ejpam-3893	294	21	.	.	PUNCT
ejpam-3893	295	1	a	a	DET
ejpam-3893	295	2	two	two	NUM
ejpam-3893	295	3	-	-	PUNCT
ejpam-3893	295	4	dimensional	dimensional	ADJ
ejpam-3893	295	5	chebyshev	chebyshev	NOUN
ejpam-3893	295	6	wavelet	wavelet	NOUN
ejpam-3893	295	7	method	method	NOUN
ejpam-3893	295	8	for	for	ADP
ejpam-3893	295	9	solving	solve	VERB
ejpam-3893	295	10	partial	partial	ADJ
ejpam-3893	295	11	differential	differential	ADJ
ejpam-3893	295	12	equations	equation	NOUN
ejpam-3893	295	13	.	.	PUNCT
ejpam-3893	296	1	journal	journal	PROPN
ejpam-3893	296	2	of	of	ADP
ejpam-3893	296	3	mathematical	mathematical	ADJ
ejpam-3893	296	4	theory	theory	NOUN
ejpam-3893	296	5	and	and	CCONJ
ejpam-3893	296	6	modeling	modeling	NOUN
ejpam-3893	296	7	,	,	PUNCT
ejpam-3893	296	8	6(8):124–138	6(8):124–138	NOUN
ejpam-3893	296	9	,	,	PUNCT
ejpam-3893	296	10	2016	2016	NUM
ejpam-3893	296	11	.	.	PUNCT
ejpam-3893	297	1	references	reference	NOUN
ejpam-3893	297	2	722	722	NUM
ejpam-3893	297	3	[	[	X
ejpam-3893	297	4	3	3	NUM
ejpam-3893	297	5	]	]	X
ejpam-3893	297	6	c	c	PROPN
ejpam-3893	297	7	s	s	PART
ejpam-3893	297	8	burrus	burrus	NOUN
ejpam-3893	297	9	,	,	PUNCT
ejpam-3893	297	10	r	r	NOUN
ejpam-3893	297	11	a	a	DET
ejpam-3893	297	12	gophinath	gophinath	NOUN
ejpam-3893	297	13	,	,	PUNCT
ejpam-3893	297	14	and	and	CCONJ
ejpam-3893	297	15	h	h	PROPN
ejpam-3893	297	16	guo	guo	PROPN
ejpam-3893	297	17	.	.	PUNCT
ejpam-3893	298	1	wavelets	wavelet	NOUN
ejpam-3893	298	2	and	and	CCONJ
ejpam-3893	298	3	wavelet	wavelet	NOUN
ejpam-3893	298	4	transforms	transform	VERB
ejpam-3893	298	5	.	.	PUNCT
ejpam-3893	299	1	creative	creative	ADJ
ejpam-3893	299	2	commons	common	NOUN
ejpam-3893	299	3	attribution	attribution	NOUN
ejpam-3893	299	4	license	license	NOUN
ejpam-3893	299	5	,	,	PUNCT
ejpam-3893	299	6	openstax	openstax	NOUN
ejpam-3893	299	7	-	-	PUNCT
ejpam-3893	299	8	cnx	cnx	NOUN
ejpam-3893	299	9	,	,	PUNCT
ejpam-3893	299	10	2015	2015	NUM
ejpam-3893	299	11	.	.	PUNCT
ejpam-3893	300	1	[	[	X
ejpam-3893	300	2	4	4	X
ejpam-3893	300	3	]	]	X
ejpam-3893	300	4	i	i	PRON
ejpam-3893	300	5	daubechies	daubechie	NOUN
ejpam-3893	300	6	.	.	PUNCT
ejpam-3893	301	1	ten	ten	NUM
ejpam-3893	301	2	lectures	lecture	NOUN
ejpam-3893	301	3	on	on	ADP
ejpam-3893	301	4	wavelets	wavelet	NOUN
ejpam-3893	301	5	,	,	PUNCT
ejpam-3893	301	6	volume	volume	NOUN
ejpam-3893	301	7	61	61	NUM
ejpam-3893	301	8	.	.	PUNCT
ejpam-3893	302	1	in	in	ADP
ejpam-3893	302	2	nsf	nsf	NOUN
ejpam-3893	302	3	-	-	PUNCT
ejpam-3893	302	4	cbms	cbms	ADJ
ejpam-3893	302	5	regional	regional	ADJ
ejpam-3893	302	6	conference	conference	NOUN
ejpam-3893	302	7	series	series	NOUN
ejpam-3893	302	8	in	in	ADP
ejpam-3893	302	9	applied	applied	ADJ
ejpam-3893	302	10	mathematics	mathematic	NOUN
ejpam-3893	302	11	,	,	PUNCT
ejpam-3893	302	12	philadelphia	philadelphia	PROPN
ejpam-3893	302	13	,	,	PUNCT
ejpam-3893	302	14	1992	1992	NUM
ejpam-3893	302	15	.	.	PUNCT
ejpam-3893	303	1	society	society	NOUN
ejpam-3893	303	2	for	for	ADP
ejpam-3893	303	3	industrial	industrial	ADJ
ejpam-3893	303	4	and	and	CCONJ
ejpam-3893	303	5	applied	applied	ADJ
ejpam-3893	303	6	mathematics	mathematic	NOUN
ejpam-3893	303	7	.	.	PUNCT
ejpam-3893	304	1	[	[	X
ejpam-3893	304	2	5	5	NUM
ejpam-3893	304	3	]	]	SYM
ejpam-3893	304	4	l	l	NOUN
ejpam-3893	304	5	debnath	debnath	NOUN
ejpam-3893	304	6	and	and	CCONJ
ejpam-3893	304	7	f	f	PROPN
ejpam-3893	304	8	a	a	DET
ejpam-3893	304	9	shah	shah	NOUN
ejpam-3893	304	10	.	.	PUNCT
ejpam-3893	305	1	wavelet	wavelet	NOUN
ejpam-3893	305	2	transforms	transform	VERB
ejpam-3893	305	3	and	and	CCONJ
ejpam-3893	305	4	their	their	PRON
ejpam-3893	305	5	application	application	NOUN
ejpam-3893	305	6	.	.	PUNCT
ejpam-3893	306	1	springer	springer	NOUN
ejpam-3893	306	2	science+business	science+business	PROPN
ejpam-3893	306	3	media	medium	NOUN
ejpam-3893	306	4	new	new	PROPN
ejpam-3893	306	5	york	york	PROPN
ejpam-3893	306	6	,	,	PUNCT
ejpam-3893	306	7	2nd	2nd	PROPN
ejpam-3893	306	8	edition	edition	NOUN
ejpam-3893	306	9	,	,	PUNCT
ejpam-3893	306	10	2015	2015	NUM
ejpam-3893	306	11	.	.	PUNCT
ejpam-3893	307	1	[	[	X
ejpam-3893	307	2	6	6	NUM
ejpam-3893	307	3	]	]	X
ejpam-3893	307	4	r	r	NOUN
ejpam-3893	307	5	k	k	PROPN
ejpam-3893	307	6	deka	deka	NOUN
ejpam-3893	307	7	and	and	CCONJ
ejpam-3893	307	8	a	a	DET
ejpam-3893	307	9	h	h	PROPN
ejpam-3893	307	10	choudhury	choudhury	PROPN
ejpam-3893	307	11	.	.	PUNCT
ejpam-3893	308	1	solution	solution	NOUN
ejpam-3893	308	2	of	of	ADP
ejpam-3893	308	3	two	two	NUM
ejpam-3893	308	4	point	point	NOUN
ejpam-3893	308	5	boundary	boundary	ADJ
ejpam-3893	308	6	value	value	NOUN
ejpam-3893	308	7	problems	problem	NOUN
ejpam-3893	308	8	using	use	VERB
ejpam-3893	308	9	wavelet	wavelet	NOUN
ejpam-3893	308	10	integrals	integral	NOUN
ejpam-3893	308	11	.	.	PUNCT
ejpam-3893	309	1	int	int	NOUN
ejpam-3893	309	2	.	.	PUNCT
ejpam-3893	310	1	j.	j.	PROPN
ejpam-3893	310	2	contemp	contemp	PROPN
ejpam-3893	310	3	.	.	PUNCT
ejpam-3893	311	1	math	math	NOUN
ejpam-3893	311	2	.	.	PUNCT
ejpam-3893	312	1	sciences	science	NOUN
ejpam-3893	312	2	,	,	PUNCT
ejpam-3893	312	3	4(15):695–717	4(15):695–717	NUM
ejpam-3893	312	4	,	,	PUNCT
ejpam-3893	312	5	2009	2009	NUM
ejpam-3893	312	6	.	.	PUNCT
ejpam-3893	313	1	[	[	X
ejpam-3893	313	2	7	7	X
ejpam-3893	313	3	]	]	X
ejpam-3893	313	4	m	m	VERB
ejpam-3893	313	5	eckert	eckert	PROPN
ejpam-3893	313	6	.	.	PUNCT
ejpam-3893	314	1	the	the	DET
ejpam-3893	314	2	dawn	dawn	NOUN
ejpam-3893	314	3	of	of	ADP
ejpam-3893	314	4	fluid	fluid	ADJ
ejpam-3893	314	5	dynamics	dynamic	NOUN
ejpam-3893	314	6	:	:	PUNCT
ejpam-3893	314	7	a	a	DET
ejpam-3893	314	8	discipline	discipline	NOUN
ejpam-3893	314	9	between	between	ADP
ejpam-3893	314	10	science	science	NOUN
ejpam-3893	314	11	and	and	CCONJ
ejpam-3893	314	12	technology	technology	NOUN
ejpam-3893	314	13	.	.	PUNCT
ejpam-3893	315	1	wiley	wiley	PROPN
ejpam-3893	315	2	,	,	PUNCT
ejpam-3893	315	3	2006	2006	NUM
ejpam-3893	315	4	.	.	PUNCT
ejpam-3893	316	1	[	[	X
ejpam-3893	316	2	8	8	NUM
ejpam-3893	316	3	]	]	X
ejpam-3893	316	4	r	r	NOUN
ejpam-3893	316	5	glowinski	glowinski	NOUN
ejpam-3893	316	6	,	,	PUNCT
ejpam-3893	316	7	t	t	PROPN
ejpam-3893	316	8	w	w	PROPN
ejpam-3893	316	9	pan	pan	PROPN
ejpam-3893	316	10	,	,	PUNCT
ejpam-3893	316	11	r	r	NOUN
ejpam-3893	316	12	o	o	NOUN
ejpam-3893	316	13	wells	well	NOUN
ejpam-3893	316	14	,	,	PUNCT
ejpam-3893	316	15	and	and	CCONJ
ejpam-3893	317	1	x	x	PART
ejpam-3893	317	2	zhou	zhou	PROPN
ejpam-3893	317	3	.	.	PUNCT
ejpam-3893	317	4	wavelet	wavelet	NOUN
ejpam-3893	317	5	and	and	CCONJ
ejpam-3893	317	6	finite	finite	PROPN
ejpam-3893	317	7	element	element	NOUN
ejpam-3893	317	8	solutions	solution	NOUN
ejpam-3893	317	9	for	for	ADP
ejpam-3893	317	10	the	the	DET
ejpam-3893	317	11	neumann	neumann	PROPN
ejpam-3893	317	12	problem	problem	NOUN
ejpam-3893	317	13	using	use	VERB
ejpam-3893	317	14	fictitious	fictitious	ADJ
ejpam-3893	317	15	domains	domain	NOUN
ejpam-3893	317	16	.	.	PUNCT
ejpam-3893	318	1	journal	journal	NOUN
ejpam-3893	318	2	of	of	ADP
ejpam-3893	318	3	computational	computational	ADJ
ejpam-3893	318	4	physics	physic	NOUN
ejpam-3893	318	5	,	,	PUNCT
ejpam-3893	318	6	(	(	PUNCT
ejpam-3893	318	7	126):40–51	126):40–51	NUM
ejpam-3893	318	8	,	,	PUNCT
ejpam-3893	318	9	1996	1996	NUM
ejpam-3893	318	10	.	.	PUNCT
ejpam-3893	319	1	[	[	X
ejpam-3893	319	2	9	9	NUM
ejpam-3893	319	3	]	]	SYM
ejpam-3893	319	4	r	r	NOUN
ejpam-3893	319	5	o	o	X
ejpam-3893	319	6	wells	wells	PROPN
ejpam-3893	319	7	jr	jr	PROPN
ejpam-3893	319	8	and	and	CCONJ
ejpam-3893	319	9	x	x	PROPN
ejpam-3893	319	10	zhou	zhou	PROPN
ejpam-3893	319	11	.	.	PUNCT
ejpam-3893	320	1	wavelet	wavelet	NOUN
ejpam-3893	320	2	solutions	solution	NOUN
ejpam-3893	320	3	for	for	ADP
ejpam-3893	320	4	the	the	DET
ejpam-3893	320	5	dirichlet	dirichlet	PROPN
ejpam-3893	320	6	problem	problem	NOUN
ejpam-3893	320	7	.	.	PUNCT
ejpam-3893	321	1	numerical	numerical	PROPN
ejpam-3893	321	2	mathematics	mathematics	PROPN
ejpam-3893	321	3	,	,	PUNCT
ejpam-3893	321	4	70:379–396	70:379–396	NUM
ejpam-3893	321	5	,	,	PUNCT
ejpam-3893	321	6	1995	1995	NUM
ejpam-3893	321	7	.	.	PUNCT
ejpam-3893	322	1	[	[	X
ejpam-3893	322	2	10	10	NUM
ejpam-3893	322	3	]	]	X
ejpam-3893	322	4	a	a	DET
ejpam-3893	322	5	katunin	katunin	NOUN
ejpam-3893	322	6	.	.	PUNCT
ejpam-3893	323	1	solution	solution	NOUN
ejpam-3893	323	2	of	of	ADP
ejpam-3893	323	3	plane	plane	NOUN
ejpam-3893	323	4	dirichlet	dirichlet	PROPN
ejpam-3893	323	5	problem	problem	NOUN
ejpam-3893	323	6	using	use	VERB
ejpam-3893	323	7	compactly	compactly	ADV
ejpam-3893	323	8	supported	support	VERB
ejpam-3893	323	9	2d	2d	NUM
ejpam-3893	323	10	wavelet	wavelet	NOUN
ejpam-3893	323	11	scaling	scaling	NOUN
ejpam-3893	323	12	functions	function	NOUN
ejpam-3893	323	13	.	.	PUNCT
ejpam-3893	324	1	scientific	scientific	ADJ
ejpam-3893	324	2	research	research	NOUN
ejpam-3893	324	3	of	of	ADP
ejpam-3893	324	4	the	the	DET
ejpam-3893	324	5	institute	institute	NOUN
ejpam-3893	324	6	of	of	ADP
ejpam-3893	324	7	mathematics	mathematics	PROPN
ejpam-3893	324	8	and	and	CCONJ
ejpam-3893	324	9	computer	computer	NOUN
ejpam-3893	324	10	science	science	NOUN
ejpam-3893	324	11	,	,	PUNCT
ejpam-3893	324	12	1(11):31–40	1(11):31–40	NUM
ejpam-3893	324	13	,	,	PUNCT
ejpam-3893	324	14	2012	2012	NUM
ejpam-3893	324	15	.	.	PUNCT
ejpam-3893	325	1	[	[	X
ejpam-3893	325	2	11	11	NUM
ejpam-3893	325	3	]	]	X
ejpam-3893	325	4	d	d	PROPN
ejpam-3893	325	5	lu	lu	PROPN
ejpam-3893	325	6	,	,	PUNCT
ejpam-3893	325	7	t	t	PROPN
ejpam-3893	325	8	ohyoshi	ohyoshi	PROPN
ejpam-3893	325	9	,	,	PUNCT
ejpam-3893	325	10	and	and	CCONJ
ejpam-3893	325	11	l	l	PROPN
ejpam-3893	325	12	zhu	zhu	PROPN
ejpam-3893	325	13	.	.	PUNCT
ejpam-3893	326	1	treatment	treatment	NOUN
ejpam-3893	326	2	of	of	ADP
ejpam-3893	326	3	boundary	boundary	ADJ
ejpam-3893	326	4	conditions	condition	NOUN
ejpam-3893	326	5	in	in	ADP
ejpam-3893	326	6	the	the	DET
ejpam-3893	326	7	application	application	NOUN
ejpam-3893	326	8	of	of	ADP
ejpam-3893	326	9	wavelet	wavelet	NOUN
ejpam-3893	326	10	-	-	PUNCT
ejpam-3893	326	11	galerkin	galerkin	PROPN
ejpam-3893	326	12	method	method	NOUN
ejpam-3893	326	13	to	to	ADP
ejpam-3893	326	14	an	an	DET
ejpam-3893	326	15	sh	sh	PROPN
ejpam-3893	326	16	wave	wave	NOUN
ejpam-3893	326	17	problem	problem	NOUN
ejpam-3893	326	18	.	.	PUNCT
ejpam-3893	327	1	international	international	ADJ
ejpam-3893	327	2	journal	journal	NOUN
ejpam-3893	327	3	of	of	ADP
ejpam-3893	327	4	the	the	DET
ejpam-3893	327	5	society	society	NOUN
ejpam-3893	327	6	of	of	ADP
ejpam-3893	327	7	materials	material	NOUN
ejpam-3893	327	8	engineering	engineering	NOUN
ejpam-3893	327	9	for	for	ADP
ejpam-3893	327	10	resources	resource	NOUN
ejpam-3893	327	11	,	,	PUNCT
ejpam-3893	327	12	5(1):15–25	5(1):15–25	NUM
ejpam-3893	327	13	,	,	PUNCT
ejpam-3893	327	14	1997	1997	NUM
ejpam-3893	327	15	.	.	PUNCT
ejpam-3893	328	1	[	[	X
ejpam-3893	328	2	12	12	NUM
ejpam-3893	328	3	]	]	SYM
ejpam-3893	328	4	v	v	PROPN
ejpam-3893	328	5	mishra	mishra	PROPN
ejpam-3893	328	6	and	and	CCONJ
ejpam-3893	328	7	sabina	sabina	PROPN
ejpam-3893	328	8	.	.	PUNCT
ejpam-3893	329	1	wavelet	wavelet	NOUN
ejpam-3893	329	2	-	-	PUNCT
ejpam-3893	329	3	galerkin	galerkin	ADJ
ejpam-3893	329	4	finite	finite	ADJ
ejpam-3893	329	5	difference	difference	NOUN
ejpam-3893	329	6	solutions	solution	NOUN
ejpam-3893	329	7	of	of	ADP
ejpam-3893	329	8	odes	ode	NOUN
ejpam-3893	329	9	.	.	PUNCT
ejpam-3893	330	1	amoadvanced	amoadvance	VERB
ejpam-3893	330	2	modeling	modeling	NOUN
ejpam-3893	330	3	and	and	CCONJ
ejpam-3893	330	4	optimization	optimization	NOUN
ejpam-3893	330	5	,	,	PUNCT
ejpam-3893	330	6	13(3):539–549	13(3):539–549	PROPN
ejpam-3893	330	7	,	,	PUNCT
ejpam-3893	330	8	2011	2011	NUM
ejpam-3893	330	9	.	.	PUNCT
ejpam-3893	331	1	[	[	X
ejpam-3893	331	2	13	13	NUM
ejpam-3893	331	3	]	]	X
ejpam-3893	331	4	s	s	VERB
ejpam-3893	331	5	nazarenko	nazarenko	ADJ
ejpam-3893	331	6	.	.	PUNCT
ejpam-3893	332	1	fluid	fluid	ADJ
ejpam-3893	332	2	dynamics	dynamic	NOUN
ejpam-3893	332	3	via	via	ADP
ejpam-3893	332	4	examples	example	NOUN
ejpam-3893	332	5	and	and	CCONJ
ejpam-3893	332	6	solutions	solution	NOUN
ejpam-3893	332	7	.	.	PUNCT
ejpam-3893	333	1	crc	crc	PROPN
ejpam-3893	333	2	press	press	PROPN
ejpam-3893	333	3	(	(	PUNCT
ejpam-3893	333	4	taylor	taylor	PROPN
ejpam-3893	333	5	and	and	CCONJ
ejpam-3893	333	6	francis	francis	PROPN
ejpam-3893	333	7	group	group	PROPN
ejpam-3893	333	8	)	)	PUNCT
ejpam-3893	333	9	,	,	PUNCT
ejpam-3893	333	10	2014	2014	NUM
ejpam-3893	333	11	.	.	PUNCT
ejpam-3893	334	1	[	[	X
ejpam-3893	334	2	14	14	NUM
ejpam-3893	334	3	]	]	X
ejpam-3893	334	4	w	w	ADP
ejpam-3893	334	5	a	a	DET
ejpam-3893	334	6	strauss	strauss	PROPN
ejpam-3893	334	7	.	.	PUNCT
ejpam-3893	335	1	partial	partial	ADJ
ejpam-3893	335	2	differential	differential	ADJ
ejpam-3893	335	3	equations	equation	NOUN
ejpam-3893	335	4	an	an	DET
ejpam-3893	335	5	introduction	introduction	NOUN
ejpam-3893	335	6	.	.	PUNCT
ejpam-3893	336	1	wiley	wiley	PROPN
ejpam-3893	336	2	,	,	PUNCT
ejpam-3893	336	3	new	new	PROPN
ejpam-3893	336	4	jesse	jesse	PROPN
ejpam-3893	336	5	,	,	PUNCT
ejpam-3893	336	6	2008	2008	NUM
ejpam-3893	336	7	.	.	PUNCT
ejpam-3893	337	1	[	[	X
ejpam-3893	337	2	15	15	NUM
ejpam-3893	337	3	]	]	X
ejpam-3893	337	4	e	e	NOUN
ejpam-3893	337	5	süli	süli	NOUN
ejpam-3893	337	6	.	.	PUNCT
ejpam-3893	338	1	finite	finite	PROPN
ejpam-3893	338	2	element	element	NOUN
ejpam-3893	338	3	methods	method	NOUN
ejpam-3893	338	4	for	for	ADP
ejpam-3893	338	5	partial	partial	ADJ
ejpam-3893	338	6	differential	differential	ADJ
ejpam-3893	338	7	equations	equation	NOUN
ejpam-3893	338	8	.	.	PUNCT
ejpam-3893	339	1	lecture	lecture	NOUN
ejpam-3893	339	2	notes	note	NOUN
ejpam-3893	339	3	.	.	PUNCT
ejpam-3893	340	1	lecture	lecture	NOUN
ejpam-3893	340	2	notes	note	NOUN
ejpam-3893	340	3	.	.	PUNCT
ejpam-3893	341	1	mathematical	mathematical	PROPN
ejpam-3893	341	2	institute	institute	PROPN
ejpam-3893	341	3	university	university	PROPN
ejpam-3893	341	4	of	of	ADP
ejpam-3893	341	5	oxford	oxford	PROPN
ejpam-3893	341	6	,	,	PUNCT
ejpam-3893	341	7	2012	2012	NUM
ejpam-3893	341	8	.	.	PUNCT