id	sid	tid	token	lemma	pos
ejpam-1845	1	1	4_erdem.dvi	4_erdem.dvi	NUM
ejpam-1845	1	2	european	european	ADJ
ejpam-1845	1	3	journal	journal	PROPN
ejpam-1845	1	4	of	of	ADP
ejpam-1845	1	5	pure	pure	ADJ
ejpam-1845	1	6	and	and	CCONJ
ejpam-1845	1	7	applied	apply	VERB
ejpam-1845	1	8	mathematics	mathematic	NOUN
ejpam-1845	1	9	vol	vol	NOUN
ejpam-1845	1	10	.	.	PROPN
ejpam-1845	2	1	6	6	NUM
ejpam-1845	2	2	,	,	PUNCT
ejpam-1845	2	3	no	no	INTJ
ejpam-1845	2	4	.	.	NOUN
ejpam-1845	2	5	1	1	NUM
ejpam-1845	2	6	,	,	PUNCT
ejpam-1845	2	7	2013	2013	NUM
ejpam-1845	2	8	,	,	PUNCT
ejpam-1845	2	9	30	30	NUM
ejpam-1845	2	10	-	-	SYM
ejpam-1845	2	11	43	43	NUM
ejpam-1845	2	12	issn	issn	PROPN
ejpam-1845	2	13	1307	1307	NUM
ejpam-1845	2	14	-	-	SYM
ejpam-1845	2	15	5543	5543	NUM
ejpam-1845	2	16	–	–	PUNCT
ejpam-1845	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1845	2	18	comparative	comparative	ADJ
ejpam-1845	2	19	analysis	analysis	NOUN
ejpam-1845	2	20	of	of	ADP
ejpam-1845	2	21	the	the	DET
ejpam-1845	2	22	modified	modify	VERB
ejpam-1845	2	23	sor	sor	NOUN
ejpam-1845	2	24	and	and	CCONJ
ejpam-1845	2	25	bgc	bgc	NOUN
ejpam-1845	2	26	methods	method	NOUN
ejpam-1845	2	27	applied	apply	VERB
ejpam-1845	2	28	to	to	ADP
ejpam-1845	2	29	the	the	DET
ejpam-1845	2	30	poleness	poleness	ADJ
ejpam-1845	2	31	conservative	conservative	ADJ
ejpam-1845	2	32	finite	finite	ADJ
ejpam-1845	2	33	difference	difference	NOUN
ejpam-1845	2	34	scheme	scheme	NOUN
ejpam-1845	2	35	arzu	arzu	NOUN
ejpam-1845	2	36	erdem	erdem	PROPN
ejpam-1845	2	37	department	department	PROPN
ejpam-1845	2	38	of	of	ADP
ejpam-1845	2	39	mathematics	mathematic	NOUN
ejpam-1845	2	40	,	,	PUNCT
ejpam-1845	2	41	kocaeli	kocaeli	PROPN
ejpam-1845	2	42	university	university	PROPN
ejpam-1845	2	43	,	,	PUNCT
ejpam-1845	2	44	umuttepe	umuttepe	NOUN
ejpam-1845	2	45	campus	campus	PROPN
ejpam-1845	2	46	,	,	PUNCT
ejpam-1845	2	47	izmit	izmit	NOUN
ejpam-1845	2	48	-	-	PUNCT
ejpam-1845	2	49	kocaeli	kocaeli	NOUN
ejpam-1845	2	50	,	,	PUNCT
ejpam-1845	2	51	41380	41380	NUM
ejpam-1845	2	52	,	,	PUNCT
ejpam-1845	2	53	turkey	turkey	NOUN
ejpam-1845	2	54	abstract	abstract	NOUN
ejpam-1845	2	55	.	.	PUNCT
ejpam-1845	3	1	the	the	DET
ejpam-1845	3	2	poleness	poleness	ADJ
ejpam-1845	3	3	conservative	conservative	ADJ
ejpam-1845	3	4	finite	finite	ADJ
ejpam-1845	3	5	difference	difference	NOUN
ejpam-1845	3	6	scheme	scheme	NOUN
ejpam-1845	3	7	based	base	VERB
ejpam-1845	3	8	on	on	ADP
ejpam-1845	3	9	the	the	DET
ejpam-1845	3	10	weak	weak	ADJ
ejpam-1845	3	11	solution	solution	NOUN
ejpam-1845	3	12	of	of	ADP
ejpam-1845	3	13	poisson	poisson	NOUN
ejpam-1845	3	14	equation	equation	NOUN
ejpam-1845	3	15	in	in	ADP
ejpam-1845	3	16	polar	polar	ADJ
ejpam-1845	3	17	coordinates	coordinate	NOUN
ejpam-1845	3	18	is	be	AUX
ejpam-1845	3	19	studied	study	VERB
ejpam-1845	3	20	.	.	PUNCT
ejpam-1845	4	1	due	due	ADP
ejpam-1845	4	2	to	to	ADP
ejpam-1845	4	3	the	the	DET
ejpam-1845	4	4	singularity	singularity	NOUN
ejpam-1845	4	5	at	at	ADP
ejpam-1845	4	6	r	r	NOUN
ejpam-1845	4	7	=	=	SYM
ejpam-1845	4	8	0	0	NUM
ejpam-1845	4	9	in	in	ADP
ejpam-1845	4	10	the	the	DET
ejpam-1845	4	11	considered	consider	VERB
ejpam-1845	4	12	polar	polar	ADJ
ejpam-1845	4	13	domain	domain	NOUN
ejpam-1845	4	14	ωrϕ	ωrϕ	NOUN
ejpam-1845	4	15	,	,	PUNCT
ejpam-1845	4	16	a	a	DET
ejpam-1845	4	17	special	special	ADJ
ejpam-1845	4	18	technique	technique	NOUN
ejpam-1845	4	19	of	of	ADP
ejpam-1845	4	20	deriving	derive	VERB
ejpam-1845	4	21	the	the	DET
ejpam-1845	4	22	finite	finite	ADJ
ejpam-1845	4	23	difference	difference	NOUN
ejpam-1845	4	24	scheme	scheme	NOUN
ejpam-1845	4	25	in	in	ADP
ejpam-1845	4	26	the	the	DET
ejpam-1845	4	27	neighbourhood	neighbourhood	NOUN
ejpam-1845	4	28	of	of	ADP
ejpam-1845	4	29	the	the	DET
ejpam-1845	4	30	pole	pole	NOUN
ejpam-1845	4	31	point	point	NOUN
ejpam-1845	4	32	r	r	NOUN
ejpam-1845	4	33	=	=	SYM
ejpam-1845	4	34	0	0	NUM
ejpam-1845	4	35	is	be	AUX
ejpam-1845	4	36	described	describe	VERB
ejpam-1845	4	37	.	.	PUNCT
ejpam-1845	5	1	the	the	DET
ejpam-1845	5	2	constructed	construct	VERB
ejpam-1845	5	3	scheme	scheme	NOUN
ejpam-1845	5	4	has	have	VERB
ejpam-1845	5	5	the	the	DET
ejpam-1845	5	6	order	order	NOUN
ejpam-1845	5	7	of	of	ADP
ejpam-1845	5	8	approximation	approximation	NOUN
ejpam-1845	5	9	o	o	PROPN
ejpam-1845	5	10	�	�	PROPN
ejpam-1845	5	11	(	(	PUNCT
ejpam-1845	5	12	h2	h2	NOUN
ejpam-1845	5	13	r	r	NOUN
ejpam-1845	5	14	+	+	CCONJ
ejpam-1845	5	15	h2	h2	NOUN
ejpam-1845	5	16	ϕ)/r	ϕ)/r	PROPN
ejpam-1845	5	17	�	�	PROPN
ejpam-1845	5	18	.	.	PUNCT
ejpam-1845	6	1	in	in	ADP
ejpam-1845	6	2	the	the	DET
ejpam-1845	6	3	second	second	ADJ
ejpam-1845	6	4	part	part	NOUN
ejpam-1845	6	5	of	of	ADP
ejpam-1845	6	6	the	the	DET
ejpam-1845	6	7	paper	paper	NOUN
ejpam-1845	6	8	the	the	DET
ejpam-1845	6	9	structure	structure	NOUN
ejpam-1845	6	10	of	of	ADP
ejpam-1845	6	11	the	the	DET
ejpam-1845	6	12	corresponding	corresponding	ADJ
ejpam-1845	6	13	non	non	ADJ
ejpam-1845	6	14	-	-	ADJ
ejpam-1845	6	15	symmetric	symmetric	ADJ
ejpam-1845	6	16	sparse	sparse	ADJ
ejpam-1845	6	17	block	block	NOUN
ejpam-1845	6	18	matrix	matrix	NOUN
ejpam-1845	6	19	is	be	AUX
ejpam-1845	6	20	analyzed	analyze	VERB
ejpam-1845	6	21	.	.	PUNCT
ejpam-1845	7	1	a	a	DET
ejpam-1845	7	2	special	special	ADJ
ejpam-1845	7	3	algorithm	algorithm	NOUN
ejpam-1845	7	4	based	base	VERB
ejpam-1845	7	5	on	on	ADP
ejpam-1845	7	6	sor	sor	NOUN
ejpam-1845	7	7	-	-	PUNCT
ejpam-1845	7	8	method	method	NOUN
ejpam-1845	7	9	is	be	AUX
ejpam-1845	7	10	presented	present	VERB
ejpam-1845	7	11	for	for	ADP
ejpam-1845	7	12	the	the	DET
ejpam-1845	7	13	numerical	numerical	ADJ
ejpam-1845	7	14	solution	solution	NOUN
ejpam-1845	7	15	of	of	ADP
ejpam-1845	7	16	the	the	DET
ejpam-1845	7	17	corresponding	corresponding	ADJ
ejpam-1845	7	18	system	system	NOUN
ejpam-1845	7	19	of	of	ADP
ejpam-1845	7	20	linear	linear	PROPN
ejpam-1845	7	21	algebraic	algebraic	ADJ
ejpam-1845	7	22	equations	equation	NOUN
ejpam-1845	7	23	.	.	PUNCT
ejpam-1845	8	1	the	the	DET
ejpam-1845	8	2	theoretical	theoretical	ADJ
ejpam-1845	8	3	result	result	NOUN
ejpam-1845	8	4	are	be	AUX
ejpam-1845	8	5	illustrated	illustrate	VERB
ejpam-1845	8	6	by	by	ADP
ejpam-1845	8	7	numerical	numerical	ADJ
ejpam-1845	8	8	examples	example	NOUN
ejpam-1845	8	9	for	for	ADP
ejpam-1845	8	10	continuous	continuous	ADJ
ejpam-1845	8	11	as	as	ADV
ejpam-1845	8	12	well	well	ADV
ejpam-1845	8	13	as	as	ADP
ejpam-1845	8	14	discontinuous	discontinuous	ADJ
ejpam-1845	8	15	source	source	NOUN
ejpam-1845	8	16	function	function	NOUN
ejpam-1845	8	17	.	.	PUNCT
ejpam-1845	9	1	2010	2010	NUM
ejpam-1845	9	2	mathematics	mathematic	NOUN
ejpam-1845	9	3	subject	subject	NOUN
ejpam-1845	9	4	classifications	classification	NOUN
ejpam-1845	9	5	:	:	PUNCT
ejpam-1845	9	6	65m06	65m06	NUM
ejpam-1845	9	7	,	,	PUNCT
ejpam-1845	9	8	65f50	65f50	NUM
ejpam-1845	9	9	,	,	PUNCT
ejpam-1845	9	10	65f10	65f10	NUM
ejpam-1845	9	11	key	key	ADJ
ejpam-1845	9	12	words	word	NOUN
ejpam-1845	9	13	and	and	CCONJ
ejpam-1845	9	14	phrases	phrase	NOUN
ejpam-1845	9	15	:	:	PUNCT
ejpam-1845	9	16	finite	finite	ADJ
ejpam-1845	9	17	difference	difference	NOUN
ejpam-1845	9	18	method	method	NOUN
ejpam-1845	9	19	,	,	PUNCT
ejpam-1845	9	20	elliptic	elliptic	ADJ
ejpam-1845	9	21	problem	problem	NOUN
ejpam-1845	9	22	,	,	PUNCT
ejpam-1845	9	23	polar	polar	ADJ
ejpam-1845	9	24	coordinates	coordinate	NOUN
ejpam-1845	9	25	,	,	PUNCT
ejpam-1845	9	26	sparse	sparse	ADJ
ejpam-1845	9	27	matrix	matrix	NOUN
ejpam-1845	9	28	1	1	NUM
ejpam-1845	9	29	.	.	PUNCT
ejpam-1845	10	1	introduction	introduction	NOUN
ejpam-1845	10	2	in	in	ADP
ejpam-1845	10	3	this	this	DET
ejpam-1845	10	4	paper	paper	NOUN
ejpam-1845	10	5	we	we	PRON
ejpam-1845	10	6	consider	consider	VERB
ejpam-1845	10	7	the	the	DET
ejpam-1845	10	8	following	follow	VERB
ejpam-1845	10	9	dirichlet	dirichlet	PROPN
ejpam-1845	10	10	problem	problem	NOUN
ejpam-1845	10	11	for	for	ADP
ejpam-1845	10	12	the	the	DET
ejpam-1845	10	13	poisson	poisson	NOUN
ejpam-1845	10	14	equation	equation	NOUN
ejpam-1845	10	15	in	in	ADP
ejpam-1845	10	16	polar	polar	ADJ
ejpam-1845	10	17	coordinates	coordinate	NOUN
ejpam-1845	10	18	(	(	PUNCT
ejpam-1845	10	19	r,ϕ	r,ϕ	NOUN
ejpam-1845	10	20	):	):	PUNCT
ejpam-1845	10	21			PROPN
ejpam-1845	10	22			NOUN
ejpam-1845	10	23			NOUN
ejpam-1845	10	24	au	au	ADV
ejpam-1845	10	25	:	:	PUNCT
ejpam-1845	10	26	=	=	SYM
ejpam-1845	10	27	−1	−1	NOUN
ejpam-1845	10	28	r	r	NOUN
ejpam-1845	10	29	∂	∂	NOUN
ejpam-1845	10	30	∂	∂	NUM
ejpam-1845	10	31	r	r	NOUN
ejpam-1845	10	32	�	�	PROPN
ejpam-1845	10	33	r	r	NOUN
ejpam-1845	10	34	∂	∂	NUM
ejpam-1845	10	35	u	u	NOUN
ejpam-1845	10	36	∂	∂	NOUN
ejpam-1845	10	37	r	r	NOUN
ejpam-1845	10	38	�	�	NOUN
ejpam-1845	10	39	−	−	PROPN
ejpam-1845	10	40	1	1	NUM
ejpam-1845	10	41	r2	r2	PROPN
ejpam-1845	10	42	∂	∂	NOUN
ejpam-1845	10	43	2u	2u	NOUN
ejpam-1845	10	44	∂	∂	NOUN
ejpam-1845	10	45	ϕ2	ϕ2	ADV
ejpam-1845	10	46	=	=	SYM
ejpam-1845	10	47	f(r,ϕ	f(r,ϕ	NUM
ejpam-1845	10	48	)	)	PUNCT
ejpam-1845	10	49	,	,	PUNCT
ejpam-1845	10	50	(	(	PUNCT
ejpam-1845	10	51	r,ϕ	r,ϕ	NOUN
ejpam-1845	10	52	)	)	PUNCT
ejpam-1845	10	53	∈	∈	PROPN
ejpam-1845	10	54	ωr	ωr	NOUN
ejpam-1845	10	55	,	,	PUNCT
ejpam-1845	10	56	u(r,ϕ	u(r,ϕ	X
ejpam-1845	10	57	)	)	PUNCT
ejpam-1845	10	58	=	=	SYM
ejpam-1845	11	1	0	0	NUM
ejpam-1845	11	2	,	,	PUNCT
ejpam-1845	11	3	(	(	PUNCT
ejpam-1845	11	4	r,ϕ	r,ϕ	NOUN
ejpam-1845	11	5	)	)	PUNCT
ejpam-1845	11	6	∈	∈	PROPN
ejpam-1845	11	7	γϕ	γϕ	ADP
ejpam-1845	11	8	,	,	PUNCT
ejpam-1845	11	9	u(r	u(r	NOUN
ejpam-1845	11	10	,	,	PUNCT
ejpam-1845	11	11	0	0	NUM
ejpam-1845	11	12	)	)	PUNCT
ejpam-1845	11	13	=	=	SYM
ejpam-1845	12	1	u(r	u(r	NOUN
ejpam-1845	12	2	,	,	PUNCT
ejpam-1845	12	3	β	β	NOUN
ejpam-1845	12	4	)	)	PUNCT
ejpam-1845	12	5	,	,	PUNCT
ejpam-1845	12	6	r	r	NOUN
ejpam-1845	12	7	∈	∈	PROPN
ejpam-1845	12	8	(	(	PUNCT
ejpam-1845	12	9	0,r	0,r	NUM
ejpam-1845	12	10	)	)	PUNCT
ejpam-1845	12	11	,	,	PUNCT
ejpam-1845	12	12	.	.	PUNCT
ejpam-1845	13	1	(	(	PUNCT
ejpam-1845	13	2	1	1	X
ejpam-1845	13	3	)	)	PUNCT
ejpam-1845	13	4	where	where	SCONJ
ejpam-1845	13	5	ωr	ωr	ADV
ejpam-1845	13	6	:	:	PUNCT
ejpam-1845	13	7	=	=	SYM
ejpam-1845	13	8	{	{	PUNCT
ejpam-1845	13	9	(	(	PUNCT
ejpam-1845	13	10	r,ϕ	r,ϕ	NOUN
ejpam-1845	13	11	)	)	PUNCT
ejpam-1845	13	12	∈	∈	PROPN
ejpam-1845	13	13	r2	r2	NOUN
ejpam-1845	13	14	:	:	PUNCT
ejpam-1845	14	1	r	r	NOUN
ejpam-1845	14	2	∈	∈	PROPN
ejpam-1845	15	1	[	[	X
ejpam-1845	15	2	0,r	0,r	NUM
ejpam-1845	15	3	)	)	PUNCT
ejpam-1845	15	4	,	,	PUNCT
ejpam-1845	15	5	ϕ	ϕ	PROPN
ejpam-1845	15	6	∈	∈	PROPN
ejpam-1845	16	1	[	[	X
ejpam-1845	16	2	0,β	0,β	NUM
ejpam-1845	16	3	)	)	PUNCT
ejpam-1845	16	4	}	}	PUNCT
ejpam-1845	16	5	,	,	PUNCT
ejpam-1845	16	6	γϕ	γϕ	ADP
ejpam-1845	16	7	:	:	PUNCT
ejpam-1845	16	8	=	=	SYM
ejpam-1845	16	9	{	{	PUNCT
ejpam-1845	16	10	(	(	PUNCT
ejpam-1845	16	11	r,ϕ	r,ϕ	NOUN
ejpam-1845	16	12	)	)	PUNCT
ejpam-1845	16	13	:	:	PUNCT
ejpam-1845	16	14	ϕ	ϕ	PROPN
ejpam-1845	16	15	∈	∈	PROPN
ejpam-1845	17	1	[	[	X
ejpam-1845	17	2	0,β	0,β	NUM
ejpam-1845	17	3	)	)	PUNCT
ejpam-1845	17	4	}	}	PUNCT
ejpam-1845	17	5	,	,	PUNCT
ejpam-1845	17	6	and	and	CCONJ
ejpam-1845	17	7	β	β	X
ejpam-1845	17	8	∈	∈	PROPN
ejpam-1845	17	9	(	(	PUNCT
ejpam-1845	17	10	0,2π	0,2π	NOUN
ejpam-1845	17	11	]	]	PUNCT
ejpam-1845	17	12	.	.	PUNCT
ejpam-1845	18	1	this	this	DET
ejpam-1845	18	2	problem	problem	NOUN
ejpam-1845	18	3	is	be	AUX
ejpam-1845	18	4	a	a	DET
ejpam-1845	18	5	mathematical	mathematical	ADJ
ejpam-1845	18	6	model	model	NOUN
ejpam-1845	18	7	of	of	ADP
ejpam-1845	18	8	various	various	ADJ
ejpam-1845	18	9	physical	physical	ADJ
ejpam-1845	18	10	and	and	CCONJ
ejpam-1845	18	11	engineering	engineering	NOUN
ejpam-1845	18	12	problems	problem	NOUN
ejpam-1845	18	13	arising	arise	VERB
ejpam-1845	18	14	in	in	ADP
ejpam-1845	18	15	steady	steady	ADJ
ejpam-1845	18	16	state	state	NOUN
ejpam-1845	18	17	flow	flow	NOUN
ejpam-1845	18	18	of	of	ADP
ejpam-1845	18	19	an	an	DET
ejpam-1845	18	20	incompressible	incompressible	ADJ
ejpam-1845	18	21	viscous	viscous	ADJ
ejpam-1845	18	22	fluid	fluid	NOUN
ejpam-1845	18	23	in	in	ADP
ejpam-1845	18	24	a	a	DET
ejpam-1845	18	25	duct	duct	NOUN
ejpam-1845	18	26	of	of	ADP
ejpam-1845	18	27	circular	circular	ADJ
ejpam-1845	18	28	cross	cross	NOUN
ejpam-1845	18	29	-	-	NOUN
ejpam-1845	18	30	section	section	NOUN
ejpam-1845	18	31	[	[	X
ejpam-1845	18	32	15	15	NUM
ejpam-1845	18	33	,	,	PUNCT
ejpam-1845	18	34	13	13	NUM
ejpam-1845	18	35	]	]	PUNCT
ejpam-1845	18	36	,	,	PUNCT
ejpam-1845	18	37	in	in	ADP
ejpam-1845	18	38	the	the	DET
ejpam-1845	18	39	determination	determination	NOUN
ejpam-1845	18	40	of	of	ADP
ejpam-1845	18	41	a	a	DET
ejpam-1845	18	42	potential	potential	NOUN
ejpam-1845	18	43	in	in	ADP
ejpam-1845	18	44	electrostatics	electrostatic	NOUN
ejpam-1845	18	45	[	[	X
ejpam-1845	18	46	3	3	NUM
ejpam-1845	18	47	]	]	PUNCT
ejpam-1845	18	48	and	and	CCONJ
ejpam-1845	18	49	in	in	ADP
ejpam-1845	18	50	the	the	DET
ejpam-1845	18	51	elasticity	elasticity	NOUN
ejpam-1845	18	52	theory	theory	NOUN
ejpam-1845	18	53	[	[	X
ejpam-1845	18	54	8	8	NUM
ejpam-1845	18	55	]	]	PUNCT
ejpam-1845	18	56	.	.	PUNCT
ejpam-1845	19	1	the	the	DET
ejpam-1845	19	2	two	two	NUM
ejpam-1845	19	3	circumstances	circumstance	NOUN
ejpam-1845	19	4	may	may	AUX
ejpam-1845	19	5	lead	lead	VERB
ejpam-1845	19	6	to	to	ADP
ejpam-1845	19	7	singularities	singularity	NOUN
ejpam-1845	19	8	:	:	PUNCT
ejpam-1845	19	9	the	the	DET
ejpam-1845	19	10	geometrical	geometrical	ADJ
ejpam-1845	19	11	singularity	singularity	NOUN
ejpam-1845	19	12	related	relate	VERB
ejpam-1845	19	13	to	to	ADP
ejpam-1845	19	14	email	email	NOUN
ejpam-1845	19	15	address	address	NOUN
ejpam-1845	19	16	:	:	PUNCT
ejpam-1845	19	17	erdem.arzu	erdem.arzu	NUM
ejpam-1845	19	18	�	�	NOUN
ejpam-1845	19	19	gmail	gmail	NOUN
ejpam-1845	19	20	.	.	PUNCT
ejpam-1845	20	1	om	om	PROPN
ejpam-1845	20	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1845	21	1	30	30	NUM
ejpam-1845	21	2	c	c	X
ejpam-1845	21	3	©	©	PROPN
ejpam-1845	21	4	2013	2013	NUM
ejpam-1845	21	5	ejpam	ejpam	NOUN
ejpam-1845	21	6	all	all	DET
ejpam-1845	21	7	rights	right	NOUN
ejpam-1845	21	8	reserved	reserve	VERB
ejpam-1845	21	9	.	.	PUNCT
ejpam-1845	22	1	a.	a.	NOUN
ejpam-1845	22	2	erdem	erdem	PROPN
ejpam-1845	22	3	/	/	SYM
ejpam-1845	22	4	eur	eur	PROPN
ejpam-1845	22	5	.	.	PUNCT
ejpam-1845	23	1	j.	j.	PROPN
ejpam-1845	23	2	pure	pure	PROPN
ejpam-1845	23	3	appl	appl	PROPN
ejpam-1845	23	4	.	.	PROPN
ejpam-1845	23	5	math	math	PROPN
ejpam-1845	23	6	,	,	PUNCT
ejpam-1845	23	7	6	6	NUM
ejpam-1845	23	8	(	(	PUNCT
ejpam-1845	23	9	2013	2013	NUM
ejpam-1845	23	10	)	)	PUNCT
ejpam-1845	23	11	,	,	PUNCT
ejpam-1845	23	12	30	30	NUM
ejpam-1845	23	13	-	-	SYM
ejpam-1845	23	14	43	43	NUM
ejpam-1845	23	15	31	31	NUM
ejpam-1845	23	16	the	the	DET
ejpam-1845	23	17	corner	corner	NOUN
ejpam-1845	23	18	β	β	X
ejpam-1845	23	19	∈	∈	PROPN
ejpam-1845	23	20	(	(	PUNCT
ejpam-1845	23	21	0,2π	0,2π	NOUN
ejpam-1845	23	22	)	)	PUNCT
ejpam-1845	23	23	of	of	ADP
ejpam-1845	23	24	the	the	DET
ejpam-1845	23	25	polar	polar	ADJ
ejpam-1845	23	26	domain	domain	NOUN
ejpam-1845	23	27	and	and	CCONJ
ejpam-1845	23	28	the	the	DET
ejpam-1845	23	29	pole	pole	NOUN
ejpam-1845	23	30	point	point	NOUN
ejpam-1845	23	31	r	r	NOUN
ejpam-1845	23	32	=	=	SYM
ejpam-1845	23	33	0	0	NUM
ejpam-1845	23	34	.	.	PUNCT
ejpam-1845	24	1	the	the	DET
ejpam-1845	24	2	first	first	ADJ
ejpam-1845	24	3	type	type	NOUN
ejpam-1845	24	4	of	of	ADP
ejpam-1845	24	5	singularity	singularity	NOUN
ejpam-1845	24	6	means	mean	VERB
ejpam-1845	24	7	that	that	SCONJ
ejpam-1845	24	8	for	for	ADP
ejpam-1845	24	9	some	some	DET
ejpam-1845	24	10	values	value	NOUN
ejpam-1845	24	11	of	of	ADP
ejpam-1845	24	12	the	the	DET
ejpam-1845	24	13	parameter	parameter	NOUN
ejpam-1845	24	14	β	β	PROPN
ejpam-1845	24	15	∈	∈	PROPN
ejpam-1845	24	16	(	(	PUNCT
ejpam-1845	24	17	0,π	0,π	PROPN
ejpam-1845	24	18	)	)	PUNCT
ejpam-1845	24	19	the	the	DET
ejpam-1845	24	20	second	second	ADJ
ejpam-1845	24	21	(	(	PUNCT
ejpam-1845	24	22	and	and	CCONJ
ejpam-1845	24	23	higher	high	ADJ
ejpam-1845	24	24	)	)	PUNCT
ejpam-1845	24	25	derivative	derivative	NOUN
ejpam-1845	24	26	of	of	ADP
ejpam-1845	24	27	the	the	DET
ejpam-1845	24	28	solution	solution	NOUN
ejpam-1845	24	29	u(r,ϕ	u(r,ϕ	PROPN
ejpam-1845	24	30	)	)	PUNCT
ejpam-1845	24	31	with	with	ADP
ejpam-1845	24	32	respect	respect	NOUN
ejpam-1845	24	33	to	to	ADP
ejpam-1845	24	34	r	r	NOUN
ejpam-1845	24	35	∈	∈	PROPN
ejpam-1845	25	1	[	[	X
ejpam-1845	25	2	0,r	0,r	NUM
ejpam-1845	25	3	)	)	PUNCT
ejpam-1845	25	4	is	be	AUX
ejpam-1845	25	5	singular	singular	ADJ
ejpam-1845	25	6	at	at	ADP
ejpam-1845	25	7	r	r	NOUN
ejpam-1845	25	8	=	=	SYM
ejpam-1845	25	9	0	0	NUM
ejpam-1845	25	10	.	.	PUNCT
ejpam-1845	26	1	as	as	SCONJ
ejpam-1845	26	2	show	show	VERB
ejpam-1845	26	3	examples	example	NOUN
ejpam-1845	26	4	below	below	ADP
ejpam-1845	26	5	the	the	DET
ejpam-1845	26	6	regularity	regularity	NOUN
ejpam-1845	26	7	of	of	ADP
ejpam-1845	26	8	the	the	DET
ejpam-1845	26	9	weak	weak	ADJ
ejpam-1845	26	10	solution	solution	NOUN
ejpam-1845	26	11	u	u	PROPN
ejpam-1845	26	12	∈	∈	PROPN
ejpam-1845	26	13	h2(ω	h2(ω	NOUN
ejpam-1845	26	14	)	)	PUNCT
ejpam-1845	26	15	∩	∩	NOUN
ejpam-1845	26	16	�	�	PROPN
ejpam-1845	26	17	h1(ω	h1(ω	PROPN
ejpam-1845	26	18	)	)	PUNCT
ejpam-1845	26	19	of	of	ADP
ejpam-1845	26	20	problem	problem	NOUN
ejpam-1845	26	21	(	(	PUNCT
ejpam-1845	26	22	1	1	X
ejpam-1845	26	23	)	)	PUNCT
ejpam-1845	26	24	depends	depend	VERB
ejpam-1845	26	25	on	on	ADP
ejpam-1845	26	26	the	the	DET
ejpam-1845	26	27	value	value	NOUN
ejpam-1845	26	28	of	of	ADP
ejpam-1845	26	29	the	the	DET
ejpam-1845	26	30	angle	angle	NOUN
ejpam-1845	26	31	β	β	X
ejpam-1845	26	32	∈	∈	PROPN
ejpam-1845	26	33	(	(	PUNCT
ejpam-1845	26	34	0,2π	0,2π	NOUN
ejpam-1845	26	35	)	)	PUNCT
ejpam-1845	26	36	.	.	PUNCT
ejpam-1845	27	1	this	this	DET
ejpam-1845	27	2	behaviour	behaviour	NOUN
ejpam-1845	27	3	is	be	AUX
ejpam-1845	27	4	usual	usual	ADJ
ejpam-1845	27	5	for	for	ADP
ejpam-1845	27	6	second	second	ADJ
ejpam-1845	27	7	order	order	NOUN
ejpam-1845	27	8	elliptic	elliptic	ADJ
ejpam-1845	27	9	problems	problem	NOUN
ejpam-1845	27	10	and	and	CCONJ
ejpam-1845	27	11	is	be	AUX
ejpam-1845	27	12	related	relate	VERB
ejpam-1845	27	13	to	to	ADP
ejpam-1845	27	14	the	the	DET
ejpam-1845	27	15	c2	c2	PROPN
ejpam-1845	27	16	-	-	PUNCT
ejpam-1845	27	17	regularity	regularity	NOUN
ejpam-1845	27	18	property	property	NOUN
ejpam-1845	27	19	of	of	ADP
ejpam-1845	27	20	the	the	DET
ejpam-1845	27	21	boundary	boundary	ADJ
ejpam-1845	27	22	∂ωrβ	∂ωrβ	NOUN
ejpam-1845	27	23	of	of	ADP
ejpam-1845	27	24	the	the	DET
ejpam-1845	27	25	considered	consider	VERB
ejpam-1845	27	26	domain	domain	NOUN
ejpam-1845	27	27	[	[	X
ejpam-1845	27	28	1	1	NUM
ejpam-1845	27	29	,	,	PUNCT
ejpam-1845	27	30	11	11	NUM
ejpam-1845	27	31	]	]	PUNCT
ejpam-1845	27	32	.	.	PUNCT
ejpam-1845	28	1	the	the	DET
ejpam-1845	28	2	singularity	singularity	NOUN
ejpam-1845	28	3	at	at	ADP
ejpam-1845	28	4	the	the	DET
ejpam-1845	28	5	re	re	ADJ
ejpam-1845	28	6	-	-	ADJ
ejpam-1845	28	7	entrant	entrant	ADJ
ejpam-1845	28	8	corner	corner	NOUN
ejpam-1845	28	9	makes	make	VERB
ejpam-1845	28	10	the	the	DET
ejpam-1845	28	11	numerical	numerical	ADJ
ejpam-1845	28	12	solution	solution	NOUN
ejpam-1845	28	13	of	of	ADP
ejpam-1845	28	14	these	these	DET
ejpam-1845	28	15	problems	problem	NOUN
ejpam-1845	28	16	challenging	challenge	VERB
ejpam-1845	28	17	.	.	PUNCT
ejpam-1845	29	1	the	the	DET
ejpam-1845	29	2	second	second	ADJ
ejpam-1845	29	3	type	type	NOUN
ejpam-1845	29	4	of	of	ADP
ejpam-1845	29	5	singularity	singularity	NOUN
ejpam-1845	29	6	is	be	AUX
ejpam-1845	29	7	a	a	DET
ejpam-1845	29	8	reason	reason	NOUN
ejpam-1845	29	9	of	of	ADP
ejpam-1845	29	10	many	many	ADJ
ejpam-1845	29	11	difficulties	difficulty	NOUN
ejpam-1845	29	12	in	in	ADP
ejpam-1845	29	13	constructing	construct	VERB
ejpam-1845	29	14	the	the	DET
ejpam-1845	29	15	standard	standard	ADJ
ejpam-1845	29	16	finite	finite	ADJ
ejpam-1845	29	17	difference	difference	NOUN
ejpam-1845	29	18	(	(	PUNCT
ejpam-1845	29	19	fd	fd	NOUN
ejpam-1845	29	20	)	)	PUNCT
ejpam-1845	29	21	schemes	scheme	NOUN
ejpam-1845	29	22	,	,	PUNCT
ejpam-1845	29	23	when	when	SCONJ
ejpam-1845	29	24	the	the	DET
ejpam-1845	29	25	pole	pole	NOUN
ejpam-1845	29	26	r	r	NOUN
ejpam-1845	29	27	=	=	SYM
ejpam-1845	29	28	0	0	NUM
ejpam-1845	29	29	is	be	AUX
ejpam-1845	29	30	treated	treat	VERB
ejpam-1845	29	31	as	as	ADP
ejpam-1845	29	32	a	a	DET
ejpam-1845	29	33	computational	computational	ADJ
ejpam-1845	29	34	boundary	boundary	NOUN
ejpam-1845	29	35	.	.	PUNCT
ejpam-1845	30	1	to	to	PART
ejpam-1845	30	2	avoid	avoid	VERB
ejpam-1845	30	3	these	these	DET
ejpam-1845	30	4	difficulties	difficulty	NOUN
ejpam-1845	30	5	various	various	ADJ
ejpam-1845	30	6	fd	fd	NOUN
ejpam-1845	30	7	and	and	CCONJ
ejpam-1845	30	8	pseudo	pseudo	NOUN
ejpam-1845	30	9	-	-	ADJ
ejpam-1845	30	10	spectral	spectral	ADJ
ejpam-1845	30	11	(	(	PUNCT
ejpam-1845	30	12	ps	ps	NOUN
ejpam-1845	30	13	)	)	PUNCT
ejpam-1845	30	14	methods	method	NOUN
ejpam-1845	30	15	have	have	AUX
ejpam-1845	30	16	been	be	AUX
ejpam-1845	30	17	suggested	suggest	VERB
ejpam-1845	30	18	in	in	ADP
ejpam-1845	30	19	literature	literature	NOUN
ejpam-1845	30	20	[	[	X
ejpam-1845	30	21	see	see	VERB
ejpam-1845	30	22	4	4	NUM
ejpam-1845	30	23	,	,	PUNCT
ejpam-1845	30	24	14	14	NUM
ejpam-1845	30	25	]	]	PUNCT
ejpam-1845	30	26	.	.	PUNCT
ejpam-1845	31	1	these	these	DET
ejpam-1845	31	2	schemes	scheme	NOUN
ejpam-1845	31	3	include	include	VERB
ejpam-1845	31	4	the	the	DET
ejpam-1845	31	5	necessity	necessity	NOUN
ejpam-1845	31	6	of	of	ADP
ejpam-1845	31	7	special	special	ADJ
ejpam-1845	31	8	boundary	boundary	ADJ
ejpam-1845	31	9	closures	closure	NOUN
ejpam-1845	31	10	,	,	PUNCT
ejpam-1845	31	11	which	which	PRON
ejpam-1845	31	12	leads	lead	VERB
ejpam-1845	31	13	to	to	ADP
ejpam-1845	31	14	undesirable	undesirable	ADJ
ejpam-1845	31	15	clustering	clustering	NOUN
ejpam-1845	31	16	of	of	ADP
ejpam-1845	31	17	grid	grid	NOUN
ejpam-1845	31	18	points	point	NOUN
ejpam-1845	31	19	in	in	ADP
ejpam-1845	31	20	ps	ps	NOUN
ejpam-1845	31	21	schemes	scheme	NOUN
ejpam-1845	31	22	[	[	X
ejpam-1845	31	23	see	see	VERB
ejpam-1845	31	24	4	4	NUM
ejpam-1845	31	25	,	,	PUNCT
ejpam-1845	31	26	6	6	NUM
ejpam-1845	31	27	]	]	PUNCT
ejpam-1845	31	28	.	.	PUNCT
ejpam-1845	32	1	the	the	DET
ejpam-1845	32	2	treatment	treatment	NOUN
ejpam-1845	32	3	of	of	ADP
ejpam-1845	32	4	the	the	DET
ejpam-1845	32	5	singularities	singularity	NOUN
ejpam-1845	32	6	related	relate	VERB
ejpam-1845	32	7	to	to	ADP
ejpam-1845	32	8	the	the	DET
ejpam-1845	32	9	situations	situation	NOUN
ejpam-1845	32	10	r	r	NOUN
ejpam-1845	32	11	→	→	SYM
ejpam-1845	32	12	0	0	NUM
ejpam-1845	32	13	and	and	CCONJ
ejpam-1845	32	14	sinϕ	sinϕ	PROPN
ejpam-1845	32	15	→	→	SYM
ejpam-1845	32	16	0	0	NUM
ejpam-1845	32	17	have	have	AUX
ejpam-1845	32	18	been	be	AUX
ejpam-1845	32	19	given	give	VERB
ejpam-1845	32	20	in	in	ADP
ejpam-1845	32	21	[	[	X
ejpam-1845	32	22	9	9	NUM
ejpam-1845	32	23	,	,	PUNCT
ejpam-1845	32	24	10	10	NUM
ejpam-1845	32	25	]	]	PUNCT
ejpam-1845	32	26	.	.	PUNCT
ejpam-1845	33	1	this	this	DET
ejpam-1845	33	2	paper	paper	NOUN
ejpam-1845	33	3	is	be	AUX
ejpam-1845	33	4	devoted	devote	VERB
ejpam-1845	33	5	to	to	PART
ejpam-1845	33	6	fill	fill	VERB
ejpam-1845	33	7	in	in	ADP
ejpam-1845	33	8	the	the	DET
ejpam-1845	33	9	lack	lack	NOUN
ejpam-1845	33	10	of	of	ADP
ejpam-1845	33	11	result	result	NOUN
ejpam-1845	33	12	for	for	ADP
ejpam-1845	33	13	conservative	conservative	ADJ
ejpam-1845	33	14	finite	finite	ADJ
ejpam-1845	33	15	difference	difference	NOUN
ejpam-1845	33	16	scheme	scheme	NOUN
ejpam-1845	33	17	for	for	ADP
ejpam-1845	33	18	problem	problem	NOUN
ejpam-1845	33	19	(	(	PUNCT
ejpam-1845	33	20	1	1	NUM
ejpam-1845	33	21	)	)	PUNCT
ejpam-1845	33	22	and	and	CCONJ
ejpam-1845	33	23	nonsymmetric	nonsymmetric	ADJ
ejpam-1845	33	24	sparse	sparse	ADJ
ejpam-1845	33	25	block	block	NOUN
ejpam-1845	33	26	matrices	matrix	NOUN
ejpam-1845	33	27	related	relate	VERB
ejpam-1845	33	28	to	to	ADP
ejpam-1845	33	29	finite	finite	VERB
ejpam-1845	33	30	difference	difference	NOUN
ejpam-1845	33	31	equations	equation	NOUN
ejpam-1845	33	32	in	in	ADP
ejpam-1845	33	33	polar	polar	ADJ
ejpam-1845	33	34	coordinates	coordinate	NOUN
ejpam-1845	33	35	.	.	PUNCT
ejpam-1845	34	1	we	we	PRON
ejpam-1845	34	2	present	present	VERB
ejpam-1845	34	3	a	a	DET
ejpam-1845	34	4	conservative	conservative	ADJ
ejpam-1845	34	5	finite	finite	ADJ
ejpam-1845	34	6	difference	difference	NOUN
ejpam-1845	34	7	scheme	scheme	NOUN
ejpam-1845	34	8	for	for	ADP
ejpam-1845	34	9	this	this	DET
ejpam-1845	34	10	problem	problem	NOUN
ejpam-1845	34	11	and	and	CCONJ
ejpam-1845	34	12	prove	prove	VERB
ejpam-1845	34	13	its	its	PRON
ejpam-1845	34	14	convergence	convergence	NOUN
ejpam-1845	34	15	.	.	PUNCT
ejpam-1845	35	1	our	our	PRON
ejpam-1845	35	2	approach	approach	NOUN
ejpam-1845	35	3	is	be	AUX
ejpam-1845	35	4	based	base	VERB
ejpam-1845	35	5	on	on	ADP
ejpam-1845	35	6	the	the	DET
ejpam-1845	35	7	lax	lax	NOUN
ejpam-1845	35	8	-	-	PUNCT
ejpam-1845	35	9	wondroff	wondroff	NOUN
ejpam-1845	35	10	theorem	theorem	NOUN
ejpam-1845	35	11	[	[	X
ejpam-1845	35	12	7	7	NUM
ejpam-1845	35	13	]	]	PUNCT
ejpam-1845	35	14	,	,	PUNCT
ejpam-1845	35	15	which	which	PRON
ejpam-1845	35	16	guarantees	guarantee	VERB
ejpam-1845	35	17	convergence	convergence	NOUN
ejpam-1845	35	18	of	of	ADP
ejpam-1845	35	19	a	a	DET
ejpam-1845	35	20	conservative	conservative	ADJ
ejpam-1845	35	21	fd	fd	ADJ
ejpam-1845	35	22	schemes	scheme	NOUN
ejpam-1845	35	23	in	in	ADP
ejpam-1845	35	24	the	the	DET
ejpam-1845	35	25	class	class	NOUN
ejpam-1845	35	26	of	of	ADP
ejpam-1845	35	27	weak	weak	ADJ
ejpam-1845	35	28	solutions	solution	NOUN
ejpam-1845	35	29	,	,	PUNCT
ejpam-1845	35	30	as	as	SCONJ
ejpam-1845	35	31	the	the	DET
ejpam-1845	35	32	polar	polar	ADJ
ejpam-1845	35	33	mesh	mesh	NOUN
ejpam-1845	35	34	is	be	AUX
ejpam-1845	35	35	refined	refine	VERB
ejpam-1845	35	36	.	.	PUNCT
ejpam-1845	36	1	note	note	VERB
ejpam-1845	36	2	that	that	SCONJ
ejpam-1845	36	3	a	a	DET
ejpam-1845	36	4	similar	similar	ADJ
ejpam-1845	36	5	technique	technique	NOUN
ejpam-1845	36	6	was	be	AUX
ejpam-1845	36	7	used	use	VERB
ejpam-1845	36	8	in	in	ADP
ejpam-1845	36	9	[	[	X
ejpam-1845	36	10	12	12	NUM
ejpam-1845	36	11	]	]	PUNCT
ejpam-1845	36	12	for	for	ADP
ejpam-1845	36	13	problem	problem	NOUN
ejpam-1845	36	14	(	(	PUNCT
ejpam-1845	36	15	1	1	NUM
ejpam-1845	36	16	)	)	PUNCT
ejpam-1845	36	17	,	,	PUNCT
ejpam-1845	36	18	where	where	SCONJ
ejpam-1845	36	19	the	the	DET
ejpam-1845	36	20	classical	classical	ADJ
ejpam-1845	36	21	solution	solution	NOUN
ejpam-1845	36	22	of	of	ADP
ejpam-1845	36	23	the	the	DET
ejpam-1845	36	24	boundary	boundary	ADJ
ejpam-1845	36	25	value	value	NOUN
ejpam-1845	36	26	problem	problem	NOUN
ejpam-1845	36	27	(	(	PUNCT
ejpam-1845	36	28	1	1	X
ejpam-1845	36	29	)	)	PUNCT
ejpam-1845	36	30	is	be	AUX
ejpam-1845	36	31	considered	consider	VERB
ejpam-1845	36	32	.	.	PUNCT
ejpam-1845	37	1	since	since	SCONJ
ejpam-1845	37	2	we	we	PRON
ejpam-1845	37	3	are	be	AUX
ejpam-1845	37	4	interested	interested	ADJ
ejpam-1845	37	5	in	in	ADP
ejpam-1845	37	6	bounded	bounded	ADJ
ejpam-1845	37	7	weak	weak	ADJ
ejpam-1845	37	8	solutions	solution	NOUN
ejpam-1845	37	9	u	u	NOUN
ejpam-1845	37	10	∈	∈	PROPN
ejpam-1845	37	11	h1(ωr	h1(ωr	PROPN
ejpam-1845	37	12	)	)	PUNCT
ejpam-1845	37	13	,	,	PUNCT
ejpam-1845	37	14	we	we	PRON
ejpam-1845	37	15	require	require	VERB
ejpam-1845	37	16	that	that	SCONJ
ejpam-1845	37	17	the	the	DET
ejpam-1845	37	18	solution	solution	NOUN
ejpam-1845	37	19	of	of	ADP
ejpam-1845	37	20	problem	problem	NOUN
ejpam-1845	37	21	(	(	PUNCT
ejpam-1845	37	22	1	1	X
ejpam-1845	37	23	)	)	PUNCT
ejpam-1845	37	24	satisfies	satisfy	VERB
ejpam-1845	37	25	the	the	DET
ejpam-1845	37	26	boundedness	boundedness	NOUN
ejpam-1845	37	27	at	at	ADP
ejpam-1845	37	28	r	r	NOUN
ejpam-1845	37	29	=	=	SYM
ejpam-1845	37	30	0	0	NUM
ejpam-1845	37	31	condition	condition	NOUN
ejpam-1845	37	32	lim	lim	PROPN
ejpam-1845	37	33	r→0	r→0	VERB
ejpam-1845	37	34	r	r	NOUN
ejpam-1845	37	35	∂	∂	NUM
ejpam-1845	37	36	u	u	NOUN
ejpam-1845	37	37	∂	∂	NOUN
ejpam-1845	37	38	r	r	NOUN
ejpam-1845	37	39	=	=	SYM
ejpam-1845	37	40	0	0	NUM
ejpam-1845	37	41	.	.	PUNCT
ejpam-1845	38	1	(	(	PUNCT
ejpam-1845	38	2	2	2	X
ejpam-1845	38	3	)	)	PUNCT
ejpam-1845	38	4	hence	hence	ADV
ejpam-1845	38	5	one	one	NUM
ejpam-1845	38	6	needs	need	VERB
ejpam-1845	38	7	to	to	PART
ejpam-1845	38	8	approximate	approximate	VERB
ejpam-1845	38	9	not	not	PART
ejpam-1845	38	10	only	only	ADV
ejpam-1845	38	11	the	the	DET
ejpam-1845	38	12	elliptic	elliptic	ADJ
ejpam-1845	38	13	equation	equation	NOUN
ejpam-1845	38	14	(	(	PUNCT
ejpam-1845	38	15	1	1	NUM
ejpam-1845	38	16	)	)	PUNCT
ejpam-1845	38	17	,	,	PUNCT
ejpam-1845	38	18	but	but	CCONJ
ejpam-1845	38	19	also	also	ADV
ejpam-1845	38	20	condition	condition	NOUN
ejpam-1845	38	21	(	(	PUNCT
ejpam-1845	38	22	2	2	NUM
ejpam-1845	38	23	)	)	PUNCT
ejpam-1845	38	24	.	.	PUNCT
ejpam-1845	39	1	this	this	DET
ejpam-1845	39	2	condition	condition	NOUN
ejpam-1845	39	3	will	will	AUX
ejpam-1845	39	4	be	be	AUX
ejpam-1845	39	5	used	use	VERB
ejpam-1845	39	6	for	for	ADP
ejpam-1845	39	7	obtaining	obtain	VERB
ejpam-1845	39	8	the	the	DET
ejpam-1845	39	9	conservative	conservative	ADJ
ejpam-1845	39	10	finite	finite	ADJ
ejpam-1845	39	11	difference	difference	NOUN
ejpam-1845	39	12	scheme	scheme	NOUN
ejpam-1845	39	13	in	in	ADP
ejpam-1845	39	14	the	the	DET
ejpam-1845	39	15	neighbourhood	neighbourhood	NOUN
ejpam-1845	39	16	of	of	ADP
ejpam-1845	39	17	the	the	DET
ejpam-1845	39	18	pole	pole	NOUN
ejpam-1845	39	19	point	point	NOUN
ejpam-1845	39	20	r	r	NOUN
ejpam-1845	39	21	=	=	SYM
ejpam-1845	39	22	0	0	NUM
ejpam-1845	39	23	.	.	PUNCT
ejpam-1845	40	1	further	far	ADV
ejpam-1845	40	2	,	,	PUNCT
ejpam-1845	40	3	the	the	DET
ejpam-1845	40	4	fd	fd	ADJ
ejpam-1845	40	5	approximations	approximation	NOUN
ejpam-1845	40	6	of	of	ADP
ejpam-1845	40	7	problem	problem	NOUN
ejpam-1845	40	8	(	(	PUNCT
ejpam-1845	40	9	1)-(2	1)-(2	NUM
ejpam-1845	40	10	)	)	PUNCT
ejpam-1845	40	11	lead	lead	NOUN
ejpam-1845	40	12	to	to	ADP
ejpam-1845	40	13	large	large	ADJ
ejpam-1845	40	14	sparse	sparse	ADJ
ejpam-1845	40	15	system	system	NOUN
ejpam-1845	40	16	of	of	ADP
ejpam-1845	40	17	linear	linear	PROPN
ejpam-1845	40	18	equations	equation	NOUN
ejpam-1845	40	19	,	,	PUNCT
ejpam-1845	40	20	with	with	ADP
ejpam-1845	40	21	the	the	DET
ejpam-1845	40	22	special	special	ADJ
ejpam-1845	40	23	nonsymmetric	nonsymmetric	ADJ
ejpam-1845	40	24	matrix	matrix	NOUN
ejpam-1845	40	25	,	,	PUNCT
ejpam-1845	40	26	due	due	ADP
ejpam-1845	40	27	to	to	ADP
ejpam-1845	40	28	the	the	DET
ejpam-1845	40	29	periodicity	periodicity	NOUN
ejpam-1845	40	30	condition	condition	NOUN
ejpam-1845	40	31	u(r	u(r	PROPN
ejpam-1845	40	32	,	,	PUNCT
ejpam-1845	40	33	0	0	NUM
ejpam-1845	40	34	)	)	PUNCT
ejpam-1845	40	35	=	=	SYM
ejpam-1845	41	1	u(r	u(r	NOUN
ejpam-1845	41	2	,	,	PUNCT
ejpam-1845	41	3	β	β	NOUN
ejpam-1845	41	4	)	)	PUNCT
ejpam-1845	41	5	.	.	PUNCT
ejpam-1845	42	1	these	these	DET
ejpam-1845	42	2	type	type	NOUN
ejpam-1845	42	3	of	of	ADP
ejpam-1845	42	4	linear	linear	PROPN
ejpam-1845	42	5	systems	system	NOUN
ejpam-1845	42	6	require	require	VERB
ejpam-1845	42	7	time	time	NOUN
ejpam-1845	42	8	-	-	PUNCT
ejpam-1845	42	9	consuming	consume	VERB
ejpam-1845	42	10	algorithms	algorithm	NOUN
ejpam-1845	42	11	for	for	ADP
ejpam-1845	42	12	their	their	PRON
ejpam-1845	42	13	effective	effective	ADJ
ejpam-1845	42	14	numerical	numerical	ADJ
ejpam-1845	42	15	solution	solution	NOUN
ejpam-1845	42	16	[	[	X
ejpam-1845	42	17	2	2	NUM
ejpam-1845	42	18	,	,	PUNCT
ejpam-1845	42	19	5	5	NUM
ejpam-1845	42	20	]	]	PUNCT
ejpam-1845	42	21	.	.	PUNCT
ejpam-1845	43	1	we	we	PRON
ejpam-1845	43	2	use	use	VERB
ejpam-1845	43	3	the	the	DET
ejpam-1845	43	4	special	special	ADJ
ejpam-1845	43	5	structure	structure	NOUN
ejpam-1845	43	6	of	of	ADP
ejpam-1845	43	7	the	the	DET
ejpam-1845	43	8	obtained	obtain	VERB
ejpam-1845	43	9	matrix	matrix	NOUN
ejpam-1845	43	10	[	[	X
ejpam-1845	43	11	5	5	NUM
ejpam-1845	43	12	]	]	PUNCT
ejpam-1845	43	13	and	and	CCONJ
ejpam-1845	43	14	construct	construct	VERB
ejpam-1845	43	15	a	a	DET
ejpam-1845	43	16	fast	fast	ADJ
ejpam-1845	43	17	iteration	iteration	NOUN
ejpam-1845	43	18	algorithm	algorithm	NOUN
ejpam-1845	43	19	,	,	PUNCT
ejpam-1845	43	20	based	base	VERB
ejpam-1845	43	21	on	on	ADP
ejpam-1845	43	22	sor	sor	NOUN
ejpam-1845	43	23	-	-	PUNCT
ejpam-1845	43	24	method	method	NOUN
ejpam-1845	43	25	.	.	PUNCT
ejpam-1845	44	1	the	the	DET
ejpam-1845	44	2	paper	paper	NOUN
ejpam-1845	44	3	is	be	AUX
ejpam-1845	44	4	organized	organize	VERB
ejpam-1845	44	5	as	as	SCONJ
ejpam-1845	44	6	follows	follow	VERB
ejpam-1845	44	7	.	.	PUNCT
ejpam-1845	45	1	in	in	ADP
ejpam-1845	45	2	section	section	NOUN
ejpam-1845	45	3	2	2	NUM
ejpam-1845	45	4	the	the	DET
ejpam-1845	45	5	weak	weak	ADJ
ejpam-1845	45	6	solution	solution	NOUN
ejpam-1845	45	7	of	of	ADP
ejpam-1845	45	8	problem	problem	NOUN
ejpam-1845	45	9	(	(	PUNCT
ejpam-1845	45	10	1)-(2	1)-(2	NUM
ejpam-1845	45	11	)	)	PUNCT
ejpam-1845	45	12	is	be	AUX
ejpam-1845	45	13	defined	define	VERB
ejpam-1845	45	14	.	.	PUNCT
ejpam-1845	46	1	the	the	DET
ejpam-1845	46	2	piecewise	piecewise	NOUN
ejpam-1845	46	3	uniform	uniform	NOUN
ejpam-1845	46	4	polar	polar	ADJ
ejpam-1845	46	5	mesh	mesh	NOUN
ejpam-1845	46	6	and	and	CCONJ
ejpam-1845	46	7	the	the	DET
ejpam-1845	46	8	conservative	conservative	ADJ
ejpam-1845	46	9	fd	fd	ADJ
ejpam-1845	46	10	scheme	scheme	NOUN
ejpam-1845	46	11	for	for	ADP
ejpam-1845	46	12	the	the	DET
ejpam-1845	46	13	problem	problem	NOUN
ejpam-1845	46	14	is	be	AUX
ejpam-1845	46	15	constructed	construct	VERB
ejpam-1845	46	16	in	in	ADP
ejpam-1845	46	17	section	section	NOUN
ejpam-1845	46	18	3	3	NUM
ejpam-1845	46	19	.	.	PUNCT
ejpam-1845	47	1	in	in	ADP
ejpam-1845	47	2	section	section	NOUN
ejpam-1845	47	3	4	4	NUM
ejpam-1845	47	4	the	the	DET
ejpam-1845	47	5	structure	structure	NOUN
ejpam-1845	47	6	of	of	ADP
ejpam-1845	47	7	the	the	DET
ejpam-1845	47	8	corresponding	corresponding	ADJ
ejpam-1845	47	9	sparse	sparse	ADJ
ejpam-1845	47	10	matrix	matrix	NOUN
ejpam-1845	47	11	and	and	CCONJ
ejpam-1845	47	12	iteration	iteration	NOUN
ejpam-1845	47	13	algorithm	algorithm	NOUN
ejpam-1845	47	14	is	be	AUX
ejpam-1845	47	15	discussed	discuss	VERB
ejpam-1845	47	16	.	.	PUNCT
ejpam-1845	48	1	numerical	numerical	ADJ
ejpam-1845	48	2	solution	solution	NOUN
ejpam-1845	48	3	of	of	ADP
ejpam-1845	48	4	problem	problem	NOUN
ejpam-1845	48	5	(	(	PUNCT
ejpam-1845	48	6	1)-(2	1)-(2	NUM
ejpam-1845	48	7	)	)	PUNCT
ejpam-1845	48	8	for	for	ADP
ejpam-1845	48	9	different	different	ADJ
ejpam-1845	48	10	types	type	NOUN
ejpam-1845	48	11	of	of	ADP
ejpam-1845	48	12	source	source	NOUN
ejpam-1845	48	13	function	function	NOUN
ejpam-1845	48	14	f(r,ϕ	f(r,ϕ	ADV
ejpam-1845	48	15	)	)	PUNCT
ejpam-1845	48	16	and	and	CCONJ
ejpam-1845	48	17	results	result	NOUN
ejpam-1845	48	18	are	be	AUX
ejpam-1845	48	19	presented	present	VERB
ejpam-1845	48	20	in	in	ADP
ejpam-1845	48	21	section	section	NOUN
ejpam-1845	48	22	5	5	NUM
ejpam-1845	48	23	.	.	PUNCT
ejpam-1845	48	24	a.	a.	NOUN
ejpam-1845	48	25	erdem	erdem	PROPN
ejpam-1845	48	26	/	/	SYM
ejpam-1845	48	27	eur	eur	PROPN
ejpam-1845	48	28	.	.	PUNCT
ejpam-1845	49	1	j.	j.	PROPN
ejpam-1845	49	2	pure	pure	PROPN
ejpam-1845	49	3	appl	appl	PROPN
ejpam-1845	49	4	.	.	PROPN
ejpam-1845	49	5	math	math	PROPN
ejpam-1845	49	6	,	,	PUNCT
ejpam-1845	49	7	6	6	NUM
ejpam-1845	49	8	(	(	PUNCT
ejpam-1845	49	9	2013	2013	NUM
ejpam-1845	49	10	)	)	PUNCT
ejpam-1845	49	11	,	,	PUNCT
ejpam-1845	49	12	30	30	NUM
ejpam-1845	49	13	-	-	SYM
ejpam-1845	49	14	43	43	NUM
ejpam-1845	49	15	32	32	NUM
ejpam-1845	49	16	2	2	NUM
ejpam-1845	49	17	.	.	PUNCT
ejpam-1845	50	1	the	the	DET
ejpam-1845	50	2	weak	weak	ADJ
ejpam-1845	50	3	solution	solution	NOUN
ejpam-1845	50	4	and	and	CCONJ
ejpam-1845	50	5	its	its	PRON
ejpam-1845	50	6	regularity	regularity	NOUN
ejpam-1845	50	7	depending	depend	VERB
ejpam-1845	50	8	on	on	ADP
ejpam-1845	50	9	the	the	DET
ejpam-1845	50	10	parameter	parameter	NOUN
ejpam-1845	50	11	β	β	X
ejpam-1845	50	12	∈	∈	PROPN
ejpam-1845	50	13	(	(	PUNCT
ejpam-1845	50	14	0	0	NUM
ejpam-1845	50	15	,	,	PUNCT
ejpam-1845	50	16	2π	2π	NOUN
ejpam-1845	50	17	)	)	PUNCT
ejpam-1845	50	18	let	let	VERB
ejpam-1845	50	19	v	v	ADP
ejpam-1845	50	20	∈	∈	PROPN
ejpam-1845	50	21	�	�	PROPN
ejpam-1845	50	22	h1(ωrβ	h1(ωrβ	NOUN
ejpam-1845	50	23	)	)	PUNCT
ejpam-1845	50	24	be	be	VERB
ejpam-1845	50	25	an	an	DET
ejpam-1845	50	26	arbitrary	arbitrary	ADJ
ejpam-1845	50	27	function	function	NOUN
ejpam-1845	50	28	,	,	PUNCT
ejpam-1845	50	29	where	where	SCONJ
ejpam-1845	50	30	�	�	NOUN
ejpam-1845	50	31	h1(ωrβ	h1(ωrβ	NOUN
ejpam-1845	50	32	)	)	PUNCT
ejpam-1845	50	33	:	:	PUNCT
ejpam-1845	51	1	=	=	SYM
ejpam-1845	51	2	{	{	PUNCT
ejpam-1845	51	3	v	v	NUM
ejpam-1845	51	4	∈	∈	PROPN
ejpam-1845	51	5	h1(ωrβ	h1(ωrβ	NOUN
ejpam-1845	51	6	)	)	PUNCT
ejpam-1845	51	7	:	:	PUNCT
ejpam-1845	51	8	u(r,ϕ	u(r,ϕ	X
ejpam-1845	51	9	)	)	PUNCT
ejpam-1845	51	10	=	=	PUNCT
ejpam-1845	52	1	0,ϕ	0,ϕ	PUNCT
ejpam-1845	52	2	∈	∈	PROPN
ejpam-1845	52	3	(	(	PUNCT
ejpam-1845	52	4	0,β	0,β	NUM
ejpam-1845	52	5	)	)	PUNCT
ejpam-1845	52	6	;	;	PUNCT
ejpam-1845	53	1	u(r	u(r	ADV
ejpam-1845	53	2	,	,	PUNCT
ejpam-1845	53	3	0	0	NUM
ejpam-1845	53	4	)	)	PUNCT
ejpam-1845	53	5	=	=	SYM
ejpam-1845	54	1	u(r	u(r	NOUN
ejpam-1845	54	2	,	,	PUNCT
ejpam-1845	54	3	β	β	NOUN
ejpam-1845	54	4	)	)	PUNCT
ejpam-1845	54	5	,	,	PUNCT
ejpam-1845	54	6	r	r	NOUN
ejpam-1845	54	7	∈	∈	PROPN
ejpam-1845	54	8	(	(	PUNCT
ejpam-1845	54	9	0,r	0,r	NUM
ejpam-1845	54	10	)	)	PUNCT
ejpam-1845	54	11	}	}	PUNCT
ejpam-1845	54	12	and	and	CCONJ
ejpam-1845	54	13	h1(ωrβ	h1(ωrβ	NOUN
ejpam-1845	54	14	)	)	PUNCT
ejpam-1845	54	15	is	be	AUX
ejpam-1845	54	16	the	the	DET
ejpam-1845	54	17	sobolev	sobolev	ADJ
ejpam-1845	54	18	space	space	NOUN
ejpam-1845	54	19	of	of	ADP
ejpam-1845	54	20	functions	function	NOUN
ejpam-1845	54	21	v	v	ADP
ejpam-1845	54	22	=	=	SYM
ejpam-1845	54	23	v(r,ϕ	v(r,ϕ	PROPN
ejpam-1845	54	24	)	)	PUNCT
ejpam-1845	54	25	with	with	SCONJ
ejpam-1845	54	26	the	the	DET
ejpam-1845	54	27	norm	norm	NOUN
ejpam-1845	54	28	‖u‖1	‖u‖1	VERB
ejpam-1845	54	29	:	:	PUNCT
ejpam-1845	54	30	=	=	SYM
ejpam-1845	54	31			NOUN
ejpam-1845	54	32			PRON
ejpam-1845	54	33			ADJ
ejpam-1845	54	34	∫	∫	PROPN
ejpam-1845	54	35	∫	∫	PROPN
ejpam-1845	54	36	ωrβ	ωrβ	PROPN
ejpam-1845	54	37	�	�	PROPN
ejpam-1845	54	38	u2	u2	PROPN
ejpam-1845	54	39	+	+	CCONJ
ejpam-1845	54	40	|∇u|2	|∇u|2	NOUN
ejpam-1845	54	41	�	�	PROPN
ejpam-1845	54	42	rd	rd	PROPN
ejpam-1845	54	43	rdϕ	rdϕ	NOUN
ejpam-1845	54	44			PROPN
ejpam-1845	54	45			PROPN
ejpam-1845	54	46			NOUN
ejpam-1845	54	47	1/2	1/2	NUM
ejpam-1845	54	48	.	.	PUNCT
ejpam-1845	55	1	let	let	VERB
ejpam-1845	55	2	us	we	PRON
ejpam-1845	55	3	multiply	multiply	VERB
ejpam-1845	55	4	the	the	DET
ejpam-1845	55	5	both	both	DET
ejpam-1845	55	6	sides	side	NOUN
ejpam-1845	55	7	of	of	ADP
ejpam-1845	55	8	equation	equation	NOUN
ejpam-1845	55	9	(	(	PUNCT
ejpam-1845	55	10	1	1	NUM
ejpam-1845	55	11	)	)	PUNCT
ejpam-1845	55	12	to	to	ADP
ejpam-1845	55	13	r	r	PROPN
ejpam-1845	55	14	v(r,ϕ	v(r,ϕ	PROPN
ejpam-1845	55	15	)	)	PUNCT
ejpam-1845	55	16	,	,	PUNCT
ejpam-1845	56	1	r	r	NOUN
ejpam-1845	56	2	∈	∈	PROPN
ejpam-1845	56	3	(	(	PUNCT
ejpam-1845	56	4	0,β	0,β	NUM
ejpam-1845	56	5	)	)	PUNCT
ejpam-1845	56	6	and	and	CCONJ
ejpam-1845	56	7	integrate	integrate	VERB
ejpam-1845	56	8	on	on	ADP
ejpam-1845	56	9	ωrβ	ωrβ	PROPN
ejpam-1845	56	10	:	:	PUNCT
ejpam-1845	56	11	−	−	PROPN
ejpam-1845	56	12	∫	∫	PROPN
ejpam-1845	56	13	∫	∫	PROPN
ejpam-1845	56	14	ωrβ	ωrβ	PROPN
ejpam-1845	56	15	�	�	PROPN
ejpam-1845	56	16	∂	∂	PART
ejpam-1845	56	17	∂	∂	NUM
ejpam-1845	56	18	r	r	NOUN
ejpam-1845	56	19	�	�	PROPN
ejpam-1845	56	20	r	r	NOUN
ejpam-1845	56	21	∂	∂	NUM
ejpam-1845	56	22	u	u	NOUN
ejpam-1845	56	23	∂	∂	NOUN
ejpam-1845	56	24	r	r	NOUN
ejpam-1845	56	25	�	�	NOUN
ejpam-1845	56	26	+	+	CCONJ
ejpam-1845	56	27	1	1	NUM
ejpam-1845	56	28	r	r	NOUN
ejpam-1845	56	29	∂	∂	NOUN
ejpam-1845	56	30	2u	2u	NOUN
ejpam-1845	56	31	∂	∂	NOUN
ejpam-1845	56	32	ϕ2	ϕ2	ADP
ejpam-1845	56	33	�	�	PROPN
ejpam-1845	56	34	vdrdϕ	vdrdϕ	NOUN
ejpam-1845	56	35	=	=	SYM
ejpam-1845	56	36	∫	∫	PROPN
ejpam-1845	56	37	∫	∫	PROPN
ejpam-1845	56	38	ωrβ	ωrβ	PROPN
ejpam-1845	56	39	f(r,ϕ)v	f(r,ϕ)v	PROPN
ejpam-1845	56	40	rdrdϕ.	rdrdϕ.	NOUN
ejpam-1845	56	41	applying	apply	VERB
ejpam-1845	56	42	here	here	ADV
ejpam-1845	56	43	by	by	ADP
ejpam-1845	56	44	part	part	NOUN
ejpam-1845	56	45	integration	integration	NOUN
ejpam-1845	56	46	,	,	PUNCT
ejpam-1845	56	47	using	use	VERB
ejpam-1845	56	48	the	the	DET
ejpam-1845	56	49	boundary	boundary	ADJ
ejpam-1845	56	50	and	and	CCONJ
ejpam-1845	56	51	periodicity	periodicity	NOUN
ejpam-1845	56	52	conditions	condition	NOUN
ejpam-1845	56	53	(	(	PUNCT
ejpam-1845	56	54	2	2	X
ejpam-1845	56	55	)	)	PUNCT
ejpam-1845	56	56	we	we	PRON
ejpam-1845	56	57	get	get	VERB
ejpam-1845	56	58	∫	∫	PROPN
ejpam-1845	56	59	∫	∫	PROPN
ejpam-1845	56	60	ωrβ	ωrβ	PROPN
ejpam-1845	56	61	∇u(r,ϕ	∇u(r,ϕ	PROPN
ejpam-1845	56	62	)	)	PUNCT
ejpam-1845	56	63	·	·	PUNCT
ejpam-1845	57	1	∇v(r,ϕ)rd	∇v(r,ϕ)rd	VERB
ejpam-1845	57	2	rdϕ	rdϕ	NOUN
ejpam-1845	57	3	=	=	SYM
ejpam-1845	57	4	∫	∫	PROPN
ejpam-1845	57	5	∫	∫	PROPN
ejpam-1845	57	6	ωrβ	ωrβ	PROPN
ejpam-1845	57	7	f(r,ϕ)v	f(r,ϕ)v	PROPN
ejpam-1845	57	8	rdrdϕ	rdrdϕ	NOUN
ejpam-1845	57	9	,	,	PUNCT
ejpam-1845	57	10	∀v	∀v	PROPN
ejpam-1845	57	11	∈	∈	PROPN
ejpam-1845	57	12	�	�	NOUN
ejpam-1845	57	13	h1(ωrβ	h1(ωrβ	NOUN
ejpam-1845	57	14	)	)	PUNCT
ejpam-1845	57	15	.	.	PUNCT
ejpam-1845	58	1	(	(	PUNCT
ejpam-1845	58	2	3	3	X
ejpam-1845	58	3	)	)	PUNCT
ejpam-1845	58	4	here	here	ADV
ejpam-1845	58	5	∇u	∇u	PROPN
ejpam-1845	58	6	is	be	AUX
ejpam-1845	58	7	the	the	DET
ejpam-1845	58	8	gradient	gradient	ADJ
ejpam-1845	58	9	vector	vector	NOUN
ejpam-1845	58	10	in	in	ADP
ejpam-1845	58	11	polar	polar	ADJ
ejpam-1845	58	12	coordinates	coordinate	NOUN
ejpam-1845	58	13	,	,	PUNCT
ejpam-1845	58	14	∇u=	∇u=	X
ejpam-1845	58	15	∂	∂	NUM
ejpam-1845	58	16	u	u	NOUN
ejpam-1845	58	17	∂	∂	NOUN
ejpam-1845	58	18	r	r	NOUN
ejpam-1845	58	19	e1	e1	NOUN
ejpam-1845	58	20	+	+	CCONJ
ejpam-1845	58	21	1	1	NUM
ejpam-1845	58	22	r	r	NOUN
ejpam-1845	58	23	∂	∂	NUM
ejpam-1845	58	24	u	u	NOUN
ejpam-1845	58	25	∂	∂	PROPN
ejpam-1845	58	26	ϕ	ϕ	PROPN
ejpam-1845	58	27	e2	e2	PROPN
ejpam-1845	58	28	,	,	PUNCT
ejpam-1845	58	29	�	�	PROPN
ejpam-1845	58	30	e1	e1	PROPN
ejpam-1845	58	31	e2	e2	PROPN
ejpam-1845	58	32	�	�	PROPN
ejpam-1845	58	33	=	=	SYM
ejpam-1845	58	34	�	�	PROPN
ejpam-1845	58	35	cosϕ	cosϕ	NOUN
ejpam-1845	58	36	,	,	PUNCT
ejpam-1845	58	37	sinϕ	sinϕ	NOUN
ejpam-1845	58	38	sinϕ	sinϕ	PROPN
ejpam-1845	58	39	,	,	PUNCT
ejpam-1845	58	40	cosϕ	cosϕ	PROPN
ejpam-1845	58	41	�	�	PROPN
ejpam-1845	58	42	�	�	PROPN
ejpam-1845	58	43	i1	i1	PROPN
ejpam-1845	58	44	i2	i2	PROPN
ejpam-1845	58	45	�	�	PROPN
ejpam-1845	58	46	,	,	PUNCT
ejpam-1845	58	47	and	and	CCONJ
ejpam-1845	58	48	i1	i1	PROPN
ejpam-1845	58	49	,	,	PUNCT
ejpam-1845	58	50	i2	i2	PROPN
ejpam-1845	58	51	are	be	AUX
ejpam-1845	58	52	unit	unit	NOUN
ejpam-1845	58	53	coordinate	coordinate	NOUN
ejpam-1845	58	54	vector	vector	NOUN
ejpam-1845	58	55	in	in	ADP
ejpam-1845	58	56	cartesian	cartesian	ADJ
ejpam-1845	58	57	coordinates	coordinate	NOUN
ejpam-1845	58	58	.	.	PUNCT
ejpam-1845	59	1	the	the	DET
ejpam-1845	59	2	solution	solution	NOUN
ejpam-1845	59	3	u	u	PROPN
ejpam-1845	59	4	∈	∈	PROPN
ejpam-1845	59	5	�	�	PROPN
ejpam-1845	59	6	h1(ωrβ	h1(ωrβ	NOUN
ejpam-1845	59	7	)	)	PUNCT
ejpam-1845	59	8	of	of	ADP
ejpam-1845	59	9	the	the	DET
ejpam-1845	59	10	integral	integral	ADJ
ejpam-1845	59	11	identity	identity	NOUN
ejpam-1845	59	12	(	(	PUNCT
ejpam-1845	59	13	3	3	NUM
ejpam-1845	59	14	)	)	PUNCT
ejpam-1845	59	15	is	be	AUX
ejpam-1845	59	16	defined	define	VERB
ejpam-1845	59	17	as	as	ADP
ejpam-1845	59	18	a	a	DET
ejpam-1845	59	19	weak	weak	ADJ
ejpam-1845	59	20	solution	solution	NOUN
ejpam-1845	59	21	of	of	ADP
ejpam-1845	59	22	the	the	DET
ejpam-1845	59	23	boundary	boundary	ADJ
ejpam-1845	59	24	value	value	NOUN
ejpam-1845	59	25	problem	problem	NOUN
ejpam-1845	59	26	(	(	PUNCT
ejpam-1845	59	27	1)-(2	1)-(2	NUM
ejpam-1845	59	28	)	)	PUNCT
ejpam-1845	59	29	.	.	PUNCT
ejpam-1845	60	1	the	the	DET
ejpam-1845	60	2	integral	integral	ADJ
ejpam-1845	60	3	identity	identity	NOUN
ejpam-1845	60	4	(	(	PUNCT
ejpam-1845	60	5	3	3	X
ejpam-1845	60	6	)	)	PUNCT
ejpam-1845	60	7	shows	show	VERB
ejpam-1845	60	8	that	that	SCONJ
ejpam-1845	60	9	if	if	SCONJ
ejpam-1845	60	10	the	the	DET
ejpam-1845	60	11	function	function	NOUN
ejpam-1845	60	12	u	u	PROPN
ejpam-1845	60	13	∈	∈	PROPN
ejpam-1845	60	14	c2(ωrβ)∩	c2(ωrβ)∩	PROPN
ejpam-1845	60	15	c1(ωrβ	c1(ωrβ	NOUN
ejpam-1845	60	16	)	)	PUNCT
ejpam-1845	60	17	is	be	AUX
ejpam-1845	60	18	the	the	DET
ejpam-1845	60	19	solution	solution	NOUN
ejpam-1845	60	20	of	of	ADP
ejpam-1845	60	21	the	the	DET
ejpam-1845	60	22	boundary	boundary	ADJ
ejpam-1845	60	23	value	value	NOUN
ejpam-1845	60	24	problem	problem	NOUN
ejpam-1845	60	25	(	(	PUNCT
ejpam-1845	60	26	1)-(2	1)-(2	NUM
ejpam-1845	60	27	)	)	PUNCT
ejpam-1845	60	28	,	,	PUNCT
ejpam-1845	60	29	then	then	ADV
ejpam-1845	60	30	for	for	ADP
ejpam-1845	60	31	all	all	DET
ejpam-1845	60	32	v	v	ADP
ejpam-1845	60	33	∈	∈	PROPN
ejpam-1845	60	34	�	�	NOUN
ejpam-1845	60	35	h1(ωrβ	h1(ωrβ	PROPN
ejpam-1845	60	36	)	)	PUNCT
ejpam-1845	60	37	this	this	DET
ejpam-1845	60	38	identity	identity	NOUN
ejpam-1845	60	39	holds	hold	VERB
ejpam-1845	60	40	.	.	PUNCT
ejpam-1845	61	1	hence	hence	ADV
ejpam-1845	61	2	the	the	DET
ejpam-1845	61	3	weak	weak	ADJ
ejpam-1845	61	4	solution	solution	NOUN
ejpam-1845	61	5	of	of	ADP
ejpam-1845	61	6	problem	problem	NOUN
ejpam-1845	61	7	(	(	PUNCT
ejpam-1845	61	8	1)-(2	1)-(2	NUM
ejpam-1845	61	9	)	)	PUNCT
ejpam-1845	61	10	can	can	AUX
ejpam-1845	61	11	be	be	AUX
ejpam-1845	61	12	defined	define	VERB
ejpam-1845	61	13	as	as	ADP
ejpam-1845	61	14	function	function	NOUN
ejpam-1845	61	15	u	u	PROPN
ejpam-1845	61	16	∈	∈	PROPN
ejpam-1845	61	17	�	�	PROPN
ejpam-1845	61	18	h1(ωrβ	h1(ωrβ	NOUN
ejpam-1845	61	19	)	)	PUNCT
ejpam-1845	61	20	satisfying	satisfy	VERB
ejpam-1845	61	21	this	this	DET
ejpam-1845	61	22	integral	integral	ADJ
ejpam-1845	61	23	identity	identity	NOUN
ejpam-1845	61	24	for	for	ADP
ejpam-1845	61	25	all	all	DET
ejpam-1845	61	26	v	v	PROPN
ejpam-1845	61	27	∈	∈	PROPN
ejpam-1845	61	28	�	�	NOUN
ejpam-1845	61	29	h1(ωrβ	h1(ωrβ	NOUN
ejpam-1845	61	30	)	)	PUNCT
ejpam-1845	61	31	.	.	PUNCT
ejpam-1845	62	1	according	accord	VERB
ejpam-1845	62	2	to	to	ADP
ejpam-1845	62	3	the	the	DET
ejpam-1845	62	4	general	general	ADJ
ejpam-1845	62	5	theory	theory	NOUN
ejpam-1845	62	6	for	for	ADP
ejpam-1845	62	7	linear	linear	PROPN
ejpam-1845	62	8	elliptic	elliptic	ADJ
ejpam-1845	62	9	boundary	boundary	ADJ
ejpam-1845	62	10	value	value	NOUN
ejpam-1845	62	11	problems	problem	VERB
ejpam-1845	62	12	the	the	DET
ejpam-1845	62	13	regular	regular	ADJ
ejpam-1845	62	14	weak	weak	ADJ
ejpam-1845	62	15	solution	solution	NOUN
ejpam-1845	62	16	of	of	ADP
ejpam-1845	62	17	problem	problem	NOUN
ejpam-1845	62	18	(	(	PUNCT
ejpam-1845	62	19	1)-(2	1)-(2	NUM
ejpam-1845	62	20	)	)	PUNCT
ejpam-1845	62	21	belongs	belong	VERB
ejpam-1845	62	22	to	to	ADP
ejpam-1845	62	23	h2(ωrβ	h2(ωrβ	PROPN
ejpam-1845	62	24	)	)	PUNCT
ejpam-1845	62	25	∩	∩	PROPN
ejpam-1845	62	26	�	�	PROPN
ejpam-1845	62	27	h1(ωrβ	h1(ωrβ	NOUN
ejpam-1845	62	28	)	)	PUNCT
ejpam-1845	62	29	,	,	PUNCT
ejpam-1845	62	30	if	if	SCONJ
ejpam-1845	62	31	the	the	DET
ejpam-1845	62	32	boundary	boundary	ADJ
ejpam-1845	62	33	∂ωrβ	∂ωrβ	PROPN
ejpam-1845	62	34	is	be	AUX
ejpam-1845	62	35	of	of	ADP
ejpam-1845	62	36	class	class	NOUN
ejpam-1845	62	37	c2	c2	PROPN
ejpam-1845	63	1	[	[	X
ejpam-1845	63	2	4	4	NUM
ejpam-1845	63	3	,	,	PUNCT
ejpam-1845	63	4	11	11	NUM
ejpam-1845	63	5	]	]	PUNCT
ejpam-1845	63	6	.	.	PUNCT
ejpam-1845	64	1	the	the	DET
ejpam-1845	64	2	following	follow	VERB
ejpam-1845	64	3	example	example	NOUN
ejpam-1845	64	4	shows	show	VERB
ejpam-1845	64	5	that	that	SCONJ
ejpam-1845	64	6	depending	depend	VERB
ejpam-1845	64	7	on	on	ADP
ejpam-1845	64	8	the	the	DET
ejpam-1845	64	9	values	value	NOUN
ejpam-1845	64	10	β	β	X
ejpam-1845	64	11	∈	∈	PROPN
ejpam-1845	64	12	(	(	PUNCT
ejpam-1845	64	13	π	π	PROPN
ejpam-1845	64	14	,	,	PUNCT
ejpam-1845	64	15	2π	2π	NOUN
ejpam-1845	64	16	)	)	PUNCT
ejpam-1845	64	17	of	of	ADP
ejpam-1845	64	18	the	the	DET
ejpam-1845	64	19	parameter	parameter	NOUN
ejpam-1845	64	20	β	β	X
ejpam-1845	64	21	the	the	DET
ejpam-1845	64	22	weak	weak	ADJ
ejpam-1845	64	23	solution	solution	NOUN
ejpam-1845	64	24	of	of	ADP
ejpam-1845	64	25	the	the	DET
ejpam-1845	64	26	boundary	boundary	ADJ
ejpam-1845	64	27	value	value	NOUN
ejpam-1845	64	28	problem	problem	NOUN
ejpam-1845	64	29	(	(	PUNCT
ejpam-1845	64	30	1)-(2	1)-(2	NUM
ejpam-1845	64	31	)	)	PUNCT
ejpam-1845	64	32	may	may	AUX
ejpam-1845	64	33	not	not	PART
ejpam-1845	64	34	belong	belong	VERB
ejpam-1845	64	35	to	to	ADP
ejpam-1845	64	36	the	the	DET
ejpam-1845	64	37	class	class	NOUN
ejpam-1845	64	38	h2(ωrβ	h2(ωrβ	PROPN
ejpam-1845	64	39	)	)	PUNCT
ejpam-1845	64	40	.	.	PUNCT
ejpam-1845	65	1	example	example	NOUN
ejpam-1845	66	1	1	1	NUM
ejpam-1845	66	2	.	.	PUNCT
ejpam-1845	67	1	the	the	DET
ejpam-1845	67	2	function	function	NOUN
ejpam-1845	67	3	u(r,ϕ	u(r,ϕ	ADV
ejpam-1845	67	4	)	)	PUNCT
ejpam-1845	68	1	=	=	SYM
ejpam-1845	68	2	rπ	rπ	NOUN
ejpam-1845	68	3	/	/	SYM
ejpam-1845	68	4	βsin(πϕ/β	βsin(πϕ/β	NOUN
ejpam-1845	68	5	)	)	PUNCT
ejpam-1845	68	6	,	,	PUNCT
ejpam-1845	68	7	(	(	PUNCT
ejpam-1845	68	8	r,ϕ	r,ϕ	NOUN
ejpam-1845	68	9	)	)	PUNCT
ejpam-1845	68	10	∈	∈	PROPN
ejpam-1845	68	11	ωrβ	ωrβ	NOUN
ejpam-1845	68	12	(	(	PUNCT
ejpam-1845	68	13	4	4	X
ejpam-1845	68	14	)	)	PUNCT
ejpam-1845	68	15	satisfies	satisfy	VERB
ejpam-1845	68	16	the	the	DET
ejpam-1845	68	17	laplace	laplace	NOUN
ejpam-1845	68	18	equation	equation	NOUN
ejpam-1845	68	19	in	in	ADP
ejpam-1845	68	20	polar	polar	ADJ
ejpam-1845	68	21	coordinates	coordinate	NOUN
ejpam-1845	68	22	and	and	CCONJ
ejpam-1845	68	23	the	the	DET
ejpam-1845	68	24	dirichlet	dirichlet	PROPN
ejpam-1845	68	25	condition	condition	NOUN
ejpam-1845	68	26	u(r,ϕ	u(r,ϕ	ADV
ejpam-1845	68	27	)	)	PUNCT
ejpam-1845	69	1	=	=	SYM
ejpam-1845	69	2	rπ	rπ	NOUN
ejpam-1845	69	3	/	/	SYM
ejpam-1845	69	4	βsin(πϕ/β	βsin(πϕ/β	NOUN
ejpam-1845	69	5	)	)	PUNCT
ejpam-1845	69	6	,	,	PUNCT
ejpam-1845	69	7	ϕ	ϕ	PROPN
ejpam-1845	69	8	∈	∈	PROPN
ejpam-1845	69	9	(	(	PUNCT
ejpam-1845	69	10	0,β	0,β	NUM
ejpam-1845	69	11	)	)	PUNCT
ejpam-1845	69	12	.	.	PUNCT
ejpam-1845	70	1	a.	a.	NOUN
ejpam-1845	70	2	erdem	erdem	PROPN
ejpam-1845	70	3	/	/	SYM
ejpam-1845	70	4	eur	eur	PROPN
ejpam-1845	70	5	.	.	PUNCT
ejpam-1845	71	1	j.	j.	PROPN
ejpam-1845	71	2	pure	pure	PROPN
ejpam-1845	71	3	appl	appl	PROPN
ejpam-1845	71	4	.	.	PROPN
ejpam-1845	71	5	math	math	PROPN
ejpam-1845	71	6	,	,	PUNCT
ejpam-1845	71	7	6	6	NUM
ejpam-1845	71	8	(	(	PUNCT
ejpam-1845	71	9	2013	2013	NUM
ejpam-1845	71	10	)	)	PUNCT
ejpam-1845	71	11	,	,	PUNCT
ejpam-1845	71	12	30	30	NUM
ejpam-1845	71	13	-	-	SYM
ejpam-1845	71	14	43	43	NUM
ejpam-1845	71	15	33	33	NUM
ejpam-1845	71	16	this	this	DET
ejpam-1845	71	17	function	function	NOUN
ejpam-1845	71	18	belongs	belong	VERB
ejpam-1845	71	19	to	to	ADP
ejpam-1845	71	20	the	the	DET
ejpam-1845	71	21	sobolev	sobolev	PROPN
ejpam-1845	71	22	space	space	PROPN
ejpam-1845	71	23	h2(ωrβ	h2(ωrβ	PROPN
ejpam-1845	71	24	)	)	PUNCT
ejpam-1845	71	25	∩	∩	PROPN
ejpam-1845	71	26	h1(ωrβ	h1(ωrβ	PROPN
ejpam-1845	71	27	)	)	PUNCT
ejpam-1845	71	28	,	,	PUNCT
ejpam-1845	71	29	for	for	ADP
ejpam-1845	71	30	all	all	DET
ejpam-1845	71	31	β	β	X
ejpam-1845	71	32	∈	∈	PROPN
ejpam-1845	71	33	(	(	PUNCT
ejpam-1845	71	34	0,π	0,π	NOUN
ejpam-1845	71	35	)	)	PUNCT
ejpam-1845	71	36	.	.	PUNCT
ejpam-1845	72	1	however	however	ADV
ejpam-1845	72	2	for	for	ADP
ejpam-1845	72	3	the	the	DET
ejpam-1845	72	4	values	value	NOUN
ejpam-1845	72	5	β	β	X
ejpam-1845	72	6	∈	∈	PROPN
ejpam-1845	72	7	(	(	PUNCT
ejpam-1845	72	8	π	π	PROPN
ejpam-1845	72	9	,	,	PUNCT
ejpam-1845	72	10	2π	2π	NOUN
ejpam-1845	72	11	)	)	PUNCT
ejpam-1845	72	12	this	this	DET
ejpam-1845	72	13	solution	solution	NOUN
ejpam-1845	72	14	does	do	AUX
ejpam-1845	72	15	n’t	not	PART
ejpam-1845	72	16	belong	belong	VERB
ejpam-1845	72	17	to	to	ADP
ejpam-1845	72	18	h2(ωrβ	h2(ωrβ	PROPN
ejpam-1845	72	19	)	)	PUNCT
ejpam-1845	72	20	,	,	PUNCT
ejpam-1845	72	21	since	since	SCONJ
ejpam-1845	72	22	rα	rα	ADV
ejpam-1845	72	23	/∈	/∈	PUNCT
ejpam-1845	72	24	h2(ωrβ	h2(ωrβ	PROPN
ejpam-1845	72	25	)	)	PUNCT
ejpam-1845	72	26	for	for	ADP
ejpam-1845	72	27	α	α	PRON
ejpam-1845	72	28	<	<	X
ejpam-1845	72	29	1	1	NUM
ejpam-1845	72	30	.	.	PUNCT
ejpam-1845	73	1	the	the	DET
ejpam-1845	73	2	reason	reason	NOUN
ejpam-1845	73	3	,	,	PUNCT
ejpam-1845	73	4	as	as	SCONJ
ejpam-1845	73	5	shown	show	VERB
ejpam-1845	73	6	in	in	ADP
ejpam-1845	73	7	[	[	X
ejpam-1845	73	8	11	11	NUM
ejpam-1845	73	9	]	]	PUNCT
ejpam-1845	73	10	,	,	PUNCT
ejpam-1845	73	11	is	be	AUX
ejpam-1845	73	12	that	that	SCONJ
ejpam-1845	73	13	for	for	SCONJ
ejpam-1845	73	14	β	β	X
ejpam-1845	73	15	∈	∈	PROPN
ejpam-1845	73	16	(	(	PUNCT
ejpam-1845	73	17	π	π	PROPN
ejpam-1845	73	18	,	,	PUNCT
ejpam-1845	73	19	2π	2π	NOUN
ejpam-1845	73	20	)	)	PUNCT
ejpam-1845	73	21	the	the	DET
ejpam-1845	73	22	boundary	boundary	ADJ
ejpam-1845	73	23	∂ωrβ	∂ωrβ	PROPN
ejpam-1845	73	24	does	do	AUX
ejpam-1845	73	25	n’t	not	PART
ejpam-1845	73	26	belong	belong	VERB
ejpam-1845	73	27	to	to	ADP
ejpam-1845	73	28	the	the	DET
ejpam-1845	73	29	class	class	NOUN
ejpam-1845	73	30	c2	c2	PROPN
ejpam-1845	73	31	,	,	PUNCT
ejpam-1845	73	32	as	as	SCONJ
ejpam-1845	73	33	requires	require	VERB
ejpam-1845	73	34	the	the	DET
ejpam-1845	73	35	agmon	agmon	PROPN
ejpam-1845	73	36	-	-	PUNCT
ejpam-1845	73	37	nirenberg	nirenberg	PROPN
ejpam-1845	73	38	regularity	regularity	NOUN
ejpam-1845	73	39	theorem	theorem	NOUN
ejpam-1845	73	40	[	[	X
ejpam-1845	73	41	1	1	NUM
ejpam-1845	73	42	]	]	PUNCT
ejpam-1845	73	43	.	.	PUNCT
ejpam-1845	74	1	note	note	VERB
ejpam-1845	74	2	that	that	SCONJ
ejpam-1845	74	3	the	the	DET
ejpam-1845	74	4	above	above	ADJ
ejpam-1845	74	5	loss	loss	NOUN
ejpam-1845	74	6	of	of	ADP
ejpam-1845	74	7	regularity	regularity	NOUN
ejpam-1845	74	8	of	of	ADP
ejpam-1845	74	9	the	the	DET
ejpam-1845	74	10	boundary	boundary	ADJ
ejpam-1845	74	11	∂ωrβ	∂ωrβ	PROPN
ejpam-1845	74	12	is	be	AUX
ejpam-1845	74	13	a	a	DET
ejpam-1845	74	14	result	result	NOUN
ejpam-1845	74	15	of	of	ADP
ejpam-1845	74	16	the	the	DET
ejpam-1845	74	17	introduced	introduce	VERB
ejpam-1845	74	18	angle	angle	NOUN
ejpam-1845	74	19	α	α	PROPN
ejpam-1845	74	20	=	=	SYM
ejpam-1845	74	21	πϕ/β	πϕ/β	PROPN
ejpam-1845	74	22	.	.	PUNCT
ejpam-1845	75	1	when	when	SCONJ
ejpam-1845	75	2	the	the	DET
ejpam-1845	75	3	parameter	parameter	NOUN
ejpam-1845	75	4	β	β	PROPN
ejpam-1845	75	5	changes	change	NOUN
ejpam-1845	75	6	in	in	ADP
ejpam-1845	75	7	(	(	PUNCT
ejpam-1845	75	8	0,2π	0,2π	ADJ
ejpam-1845	75	9	)	)	PUNCT
ejpam-1845	75	10	the	the	DET
ejpam-1845	75	11	angle	angle	NOUN
ejpam-1845	75	12	α	α	PRON
ejpam-1845	75	13	always	always	ADV
ejpam-1845	75	14	remains	remain	VERB
ejpam-1845	75	15	in	in	ADP
ejpam-1845	75	16	(	(	PUNCT
ejpam-1845	75	17	0,π	0,π	NOUN
ejpam-1845	75	18	)	)	PUNCT
ejpam-1845	75	19	.	.	PUNCT
ejpam-1845	76	1	this	this	PRON
ejpam-1845	76	2	also	also	ADV
ejpam-1845	76	3	implies	imply	VERB
ejpam-1845	76	4	that	that	SCONJ
ejpam-1845	76	5	for	for	ADP
ejpam-1845	76	6	the	the	DET
ejpam-1845	76	7	function	function	NOUN
ejpam-1845	76	8	u(r,ϕ	u(r,ϕ	PROPN
ejpam-1845	76	9	)	)	PUNCT
ejpam-1845	76	10	,	,	PUNCT
ejpam-1845	76	11	given	give	VERB
ejpam-1845	76	12	by	by	ADP
ejpam-1845	76	13	(	(	PUNCT
ejpam-1845	76	14	4	4	NUM
ejpam-1845	76	15	)	)	PUNCT
ejpam-1845	76	16	,	,	PUNCT
ejpam-1845	76	17	the	the	DET
ejpam-1845	76	18	periodicity	periodicity	NOUN
ejpam-1845	76	19	condition	condition	NOUN
ejpam-1845	76	20	∂	∂	NOUN
ejpam-1845	76	21	u(r	u(r	NOUN
ejpam-1845	76	22	,	,	PUNCT
ejpam-1845	76	23	0	0	NUM
ejpam-1845	76	24	)	)	PUNCT
ejpam-1845	76	25	∂	∂	NOUN
ejpam-1845	76	26	ϕ	ϕ	NOUN
ejpam-1845	76	27	=	=	SYM
ejpam-1845	76	28	∂	∂	X
ejpam-1845	76	29	u(r	u(r	NOUN
ejpam-1845	76	30	,	,	PUNCT
ejpam-1845	76	31	β	β	NOUN
ejpam-1845	76	32	)	)	PUNCT
ejpam-1845	76	33	∂	∂	NOUN
ejpam-1845	76	34	ϕ	ϕ	NOUN
ejpam-1845	76	35	,	,	PUNCT
ejpam-1845	76	36	r	r	NOUN
ejpam-1845	76	37	∈	∈	PROPN
ejpam-1845	76	38	(	(	PUNCT
ejpam-1845	76	39	0,r	0,r	NUM
ejpam-1845	76	40	)	)	PUNCT
ejpam-1845	76	41	(	(	PUNCT
ejpam-1845	76	42	5	5	X
ejpam-1845	76	43	)	)	PUNCT
ejpam-1845	76	44	does	do	AUX
ejpam-1845	76	45	n’t	not	PART
ejpam-1845	76	46	hold	hold	VERB
ejpam-1845	76	47	.	.	PUNCT
ejpam-1845	77	1	the	the	DET
ejpam-1845	77	2	next	next	ADJ
ejpam-1845	77	3	example	example	NOUN
ejpam-1845	77	4	shows	show	VERB
ejpam-1845	77	5	that	that	SCONJ
ejpam-1845	77	6	by	by	ADP
ejpam-1845	77	7	introducing	introduce	VERB
ejpam-1845	77	8	the	the	DET
ejpam-1845	77	9	parameter	parameter	NOUN
ejpam-1845	77	10	α	α	NOUN
ejpam-1845	78	1	=	=	X
ejpam-1845	78	2	nπϕ/β	nπϕ/β	NOUN
ejpam-1845	78	3	,	,	PUNCT
ejpam-1845	78	4	n	n	NOUN
ejpam-1845	78	5	=	=	SYM
ejpam-1845	78	6	2	2	NUM
ejpam-1845	78	7	,	,	PUNCT
ejpam-1845	78	8	the	the	DET
ejpam-1845	78	9	fulfilment	fulfilment	NOUN
ejpam-1845	78	10	of	of	ADP
ejpam-1845	78	11	this	this	DET
ejpam-1845	78	12	condition	condition	NOUN
ejpam-1845	78	13	can	can	AUX
ejpam-1845	78	14	be	be	AUX
ejpam-1845	78	15	achieved	achieve	VERB
ejpam-1845	78	16	.	.	PUNCT
ejpam-1845	79	1	example	example	NOUN
ejpam-1845	79	2	2	2	NUM
ejpam-1845	79	3	.	.	X
ejpam-1845	79	4	consider	consider	VERB
ejpam-1845	79	5	now	now	ADV
ejpam-1845	79	6	the	the	DET
ejpam-1845	79	7	function	function	NOUN
ejpam-1845	79	8	u(r,ϕ	u(r,ϕ	ADV
ejpam-1845	79	9	)	)	PUNCT
ejpam-1845	80	1	=	=	PUNCT
ejpam-1845	80	2	r2π	r2π	PROPN
ejpam-1845	80	3	/	/	SYM
ejpam-1845	80	4	βsin(2πϕ/β	βsin(2πϕ/β	PROPN
ejpam-1845	80	5	)	)	PUNCT
ejpam-1845	80	6	,	,	PUNCT
ejpam-1845	80	7	(	(	PUNCT
ejpam-1845	80	8	r,ϕ	r,ϕ	NOUN
ejpam-1845	80	9	)	)	PUNCT
ejpam-1845	80	10	∈	∈	PROPN
ejpam-1845	80	11	ωrβ	ωrβ	PROPN
ejpam-1845	80	12	,	,	PUNCT
ejpam-1845	80	13	(	(	PUNCT
ejpam-1845	80	14	6	6	NUM
ejpam-1845	80	15	)	)	PUNCT
ejpam-1845	80	16	which	which	PRON
ejpam-1845	80	17	evidently	evidently	ADV
ejpam-1845	80	18	belongs	belong	VERB
ejpam-1845	80	19	to	to	ADP
ejpam-1845	80	20	h2(ωrβ	h2(ωrβ	PROPN
ejpam-1845	80	21	)	)	PUNCT
ejpam-1845	80	22	,	,	PUNCT
ejpam-1845	80	23	∀β	∀β	PROPN
ejpam-1845	80	24	∈	∈	PROPN
ejpam-1845	80	25	(	(	PUNCT
ejpam-1845	80	26	0,2π	0,2π	NOUN
ejpam-1845	80	27	)	)	PUNCT
ejpam-1845	80	28	.	.	PUNCT
ejpam-1845	81	1	this	this	DET
ejpam-1845	81	2	function	function	NOUN
ejpam-1845	81	3	satisfies	satisfy	VERB
ejpam-1845	81	4	the	the	DET
ejpam-1845	81	5	laplace	laplace	NOUN
ejpam-1845	81	6	equation	equation	NOUN
ejpam-1845	81	7	and	and	CCONJ
ejpam-1845	81	8	the	the	DET
ejpam-1845	81	9	boundary	boundary	ADJ
ejpam-1845	81	10	conditions	condition	NOUN
ejpam-1845	81	11	(	(	PUNCT
ejpam-1845	81	12	1	1	NUM
ejpam-1845	81	13	)	)	PUNCT
ejpam-1845	81	14	.	.	PUNCT
ejpam-1845	82	1	observe	observe	VERB
ejpam-1845	82	2	that	that	SCONJ
ejpam-1845	82	3	the	the	DET
ejpam-1845	82	4	angle	angle	NOUN
ejpam-1845	82	5	α=	α=	PROPN
ejpam-1845	82	6	2πϕ/β	2πϕ/β	NUM
ejpam-1845	82	7	always	always	ADV
ejpam-1845	82	8	remains	remain	VERB
ejpam-1845	82	9	in	in	ADP
ejpam-1845	82	10	(	(	PUNCT
ejpam-1845	82	11	0,2π	0,2π	ADJ
ejpam-1845	82	12	)	)	PUNCT
ejpam-1845	82	13	,	,	PUNCT
ejpam-1845	82	14	when	when	SCONJ
ejpam-1845	82	15	the	the	DET
ejpam-1845	82	16	parameter	parameter	NOUN
ejpam-1845	82	17	β	β	PROPN
ejpam-1845	82	18	changes	change	NOUN
ejpam-1845	82	19	in	in	ADP
ejpam-1845	82	20	(	(	PUNCT
ejpam-1845	82	21	0,2π	0,2π	NOUN
ejpam-1845	82	22	)	)	PUNCT
ejpam-1845	82	23	.	.	PUNCT
ejpam-1845	83	1	this	this	DET
ejpam-1845	83	2	moment	moment	NOUN
ejpam-1845	83	3	removes	remove	VERB
ejpam-1845	83	4	the	the	DET
ejpam-1845	83	5	lack	lack	NOUN
ejpam-1845	83	6	of	of	ADP
ejpam-1845	83	7	smoothness	smoothness	NOUN
ejpam-1845	83	8	of	of	ADP
ejpam-1845	83	9	the	the	DET
ejpam-1845	83	10	boundary	boundary	ADJ
ejpam-1845	83	11	and	and	CCONJ
ejpam-1845	83	12	as	as	ADP
ejpam-1845	83	13	a	a	DET
ejpam-1845	83	14	result	result	NOUN
ejpam-1845	83	15	the	the	DET
ejpam-1845	83	16	solution	solution	NOUN
ejpam-1845	83	17	u(r,ϕ	u(r,ϕ	NOUN
ejpam-1845	83	18	)	)	PUNCT
ejpam-1845	83	19	∈	∈	PROPN
ejpam-1845	83	20	h2(ωrβ	h2(ωrβ	PROPN
ejpam-1845	83	21	)	)	PUNCT
ejpam-1845	83	22	∩	∩	PROPN
ejpam-1845	83	23	h1(ωrβ	h1(ωrβ	NOUN
ejpam-1845	83	24	)	)	PUNCT
ejpam-1845	83	25	,	,	PUNCT
ejpam-1845	83	26	∀β	∀β	PROPN
ejpam-1845	83	27	∈	∈	PROPN
ejpam-1845	83	28	(	(	PUNCT
ejpam-1845	83	29	0,π	0,π	NOUN
ejpam-1845	83	30	)	)	PUNCT
ejpam-1845	83	31	,	,	PUNCT
ejpam-1845	83	32	given	give	VERB
ejpam-1845	83	33	by	by	ADP
ejpam-1845	83	34	(	(	PUNCT
ejpam-1845	83	35	6	6	NUM
ejpam-1845	83	36	)	)	PUNCT
ejpam-1845	83	37	,	,	PUNCT
ejpam-1845	83	38	also	also	ADV
ejpam-1845	83	39	satisfies	satisfy	VERB
ejpam-1845	83	40	the	the	DET
ejpam-1845	83	41	periodicity	periodicity	NOUN
ejpam-1845	83	42	condition	condition	NOUN
ejpam-1845	83	43	(	(	PUNCT
ejpam-1845	83	44	5	5	NUM
ejpam-1845	83	45	)	)	PUNCT
ejpam-1845	83	46	.	.	PUNCT
ejpam-1845	84	1	these	these	DET
ejpam-1845	84	2	two	two	NUM
ejpam-1845	84	3	solutions	solution	NOUN
ejpam-1845	84	4	show	show	VERB
ejpam-1845	84	5	the	the	DET
ejpam-1845	84	6	main	main	ADJ
ejpam-1845	84	7	distinguished	distinguished	ADJ
ejpam-1845	84	8	features	feature	NOUN
ejpam-1845	84	9	of	of	ADP
ejpam-1845	84	10	the	the	DET
ejpam-1845	84	11	boundary	boundary	ADJ
ejpam-1845	84	12	value	value	NOUN
ejpam-1845	84	13	problem	problem	NOUN
ejpam-1845	84	14	(	(	PUNCT
ejpam-1845	84	15	1)-(2	1)-(2	NUM
ejpam-1845	84	16	)	)	PUNCT
ejpam-1845	84	17	,	,	PUNCT
ejpam-1845	84	18	and	and	CCONJ
ejpam-1845	84	19	they	they	PRON
ejpam-1845	84	20	will	will	AUX
ejpam-1845	84	21	be	be	AUX
ejpam-1845	84	22	used	use	VERB
ejpam-1845	84	23	for	for	ADP
ejpam-1845	84	24	testing	testing	NOUN
ejpam-1845	84	25	of	of	ADP
ejpam-1845	84	26	the	the	DET
ejpam-1845	84	27	presented	present	VERB
ejpam-1845	84	28	finite	finite	ADJ
ejpam-1845	84	29	difference	difference	NOUN
ejpam-1845	84	30	scheme	scheme	NOUN
ejpam-1845	84	31	.	.	PUNCT
ejpam-1845	85	1	3	3	X
ejpam-1845	85	2	.	.	X
ejpam-1845	85	3	the	the	DET
ejpam-1845	85	4	conservative	conservative	ADJ
ejpam-1845	85	5	fd	fd	PROPN
ejpam-1845	85	6	scheme	scheme	NOUN
ejpam-1845	85	7	on	on	ADP
ejpam-1845	85	8	a	a	DET
ejpam-1845	85	9	piecewise	piecewise	NOUN
ejpam-1845	85	10	uniform	uniform	NOUN
ejpam-1845	85	11	polar	polar	ADJ
ejpam-1845	85	12	mesh	mesh	NOUN
ejpam-1845	85	13	we	we	PRON
ejpam-1845	85	14	assume	assume	VERB
ejpam-1845	85	15	here	here	ADV
ejpam-1845	85	16	β	β	X
ejpam-1845	85	17	=	=	PUNCT
ejpam-1845	85	18	2π	2π	NOUN
ejpam-1845	85	19	and	and	CCONJ
ejpam-1845	85	20	introduce	introduce	VERB
ejpam-1845	85	21	the	the	DET
ejpam-1845	85	22	following	follow	VERB
ejpam-1845	85	23	uniform	uniform	NOUN
ejpam-1845	85	24	meshes	mesh	VERB
ejpam-1845	85	25	with	with	ADP
ejpam-1845	85	26	respect	respect	NOUN
ejpam-1845	85	27	to	to	ADP
ejpam-1845	85	28	variables	variable	NOUN
ejpam-1845	85	29	r	r	NOUN
ejpam-1845	85	30	and	and	CCONJ
ejpam-1845	85	31	ϕ	ϕ	NOUN
ejpam-1845	85	32	w	w	NOUN
ejpam-1845	85	33	r	r	NOUN
ejpam-1845	85	34	:	:	PUNCT
ejpam-1845	85	35	=	=	SYM
ejpam-1845	85	36	{	{	PUNCT
ejpam-1845	85	37	rn	rn	PROPN
ejpam-1845	85	38	=	=	PUNCT
ejpam-1845	85	39	(	(	PUNCT
ejpam-1845	85	40	n−	n−	NOUN
ejpam-1845	85	41	0.5)hr	0.5)hr	VERB
ejpam-1845	85	42	:	:	PUNCT
ejpam-1845	85	43	n=	n=	ADJ
ejpam-1845	85	44	1,2	1,2	NUM
ejpam-1845	85	45	,	,	PUNCT
ejpam-1845	85	46	.	.	PUNCT
ejpam-1845	85	47	.	.	PUNCT
ejpam-1845	86	1	.	.	PUNCT
ejpam-1845	87	1	,	,	PUNCT
ejpam-1845	87	2	n	n	PROPN
ejpam-1845	87	3	+	+	NOUN
ejpam-1845	87	4	1	1	NUM
ejpam-1845	87	5	,	,	PUNCT
ejpam-1845	87	6	hr	hr	NOUN
ejpam-1845	87	7	=	=	SYM
ejpam-1845	87	8	(	(	PUNCT
ejpam-1845	87	9	2r)/(2n	2r)/(2n	NUM
ejpam-1845	87	10	+	+	NOUN
ejpam-1845	87	11	1	1	NUM
ejpam-1845	87	12	)	)	PUNCT
ejpam-1845	87	13	}	}	PUNCT
ejpam-1845	87	14	,	,	PUNCT
ejpam-1845	87	15	wϕ	wϕ	NOUN
ejpam-1845	87	16	:	:	PUNCT
ejpam-1845	87	17	=	=	PRON
ejpam-1845	87	18	{	{	PUNCT
ejpam-1845	87	19	ϕm	ϕm	NOUN
ejpam-1845	87	20	=	=	SYM
ejpam-1845	87	21	(	(	PUNCT
ejpam-1845	87	22	m−	m−	PROPN
ejpam-1845	87	23	1)hϕ	1)hϕ	NUM
ejpam-1845	87	24	:	:	PUNCT
ejpam-1845	87	25	m=	m=	X
ejpam-1845	87	26	1,2	1,2	NUM
ejpam-1845	87	27	,	,	PUNCT
ejpam-1845	87	28	.	.	PUNCT
ejpam-1845	87	29	.	.	PUNCT
ejpam-1845	87	30	.	.	PUNCT
ejpam-1845	88	1	,	,	PUNCT
ejpam-1845	88	2	m	m	VERB
ejpam-1845	88	3	+	+	ADJ
ejpam-1845	88	4	1	1	NUM
ejpam-1845	88	5	,	,	PUNCT
ejpam-1845	88	6	hϕ	hϕ	X
ejpam-1845	88	7	=	=	PUNCT
ejpam-1845	88	8	2π	2π	NOUN
ejpam-1845	88	9	/	/	SYM
ejpam-1845	88	10	m	m	VERB
ejpam-1845	88	11	}	}	PUNCT
ejpam-1845	88	12	,	,	PUNCT
ejpam-1845	88	13	with	with	ADP
ejpam-1845	88	14	mesh	mesh	NOUN
ejpam-1845	88	15	steps	step	NOUN
ejpam-1845	88	16	hr	hr	NOUN
ejpam-1845	88	17	,	,	PUNCT
ejpam-1845	88	18	hϕ	hϕ	PROPN
ejpam-1845	88	19	>	>	X
ejpam-1845	88	20	0	0	X
ejpam-1845	88	21	.	.	PUNCT
ejpam-1845	89	1	then	then	ADV
ejpam-1845	89	2	we	we	PRON
ejpam-1845	89	3	obtain	obtain	VERB
ejpam-1845	89	4	the	the	DET
ejpam-1845	89	5	piecewise	piecewise	NOUN
ejpam-1845	89	6	uniform	uniform	NOUN
ejpam-1845	89	7	polar	polar	ADJ
ejpam-1845	89	8	mesh	mesh	NOUN
ejpam-1845	89	9	w	w	NOUN
ejpam-1845	89	10	rϕ	rϕ	NOUN
ejpam-1845	89	11	:	:	PUNCT
ejpam-1845	89	12	=	=	SYM
ejpam-1845	89	13	wr×wϕ	wr×wϕ	PROPN
ejpam-1845	89	14	(	(	PUNCT
ejpam-1845	89	15	fig	fig	NOUN
ejpam-1845	89	16	.	.	PUNCT
ejpam-1845	90	1	1	1	NUM
ejpam-1845	90	2	):	):	PUNCT
ejpam-1845	90	3	w	w	NOUN
ejpam-1845	90	4	rϕ	rϕ	NOUN
ejpam-1845	90	5	:	:	PUNCT
ejpam-1845	90	6	=	=	SYM
ejpam-1845	90	7	{	{	PUNCT
ejpam-1845	90	8	(	(	PUNCT
ejpam-1845	90	9	rn,ϕm	rn,ϕm	ADJ
ejpam-1845	90	10	)	)	PUNCT
ejpam-1845	90	11	∈	∈	PROPN
ejpam-1845	90	12	ωrϕ	ωrϕ	NOUN
ejpam-1845	90	13	:	:	PUNCT
ejpam-1845	90	14	rn	rn	PROPN
ejpam-1845	90	15	∈	∈	PROPN
ejpam-1845	90	16	w	w	PROPN
ejpam-1845	90	17	r	r	NOUN
ejpam-1845	90	18	,	,	PUNCT
ejpam-1845	90	19	ϕm	ϕm	INTJ
ejpam-1845	90	20	∈	∈	PROPN
ejpam-1845	90	21	wϕ	wϕ	PROPN
ejpam-1845	90	22	}	}	PUNCT
ejpam-1845	90	23	,	,	PUNCT
ejpam-1845	90	24	dim	dim	ADJ
ejpam-1845	90	25	wrϕ	wrϕ	NOUN
ejpam-1845	90	26	=	=	SYM
ejpam-1845	90	27	(	(	PUNCT
ejpam-1845	90	28	n	n	PROPN
ejpam-1845	90	29	+	+	NUM
ejpam-1845	90	30	1)×	1)×	NUM
ejpam-1845	90	31	(	(	PUNCT
ejpam-1845	90	32	m	m	VERB
ejpam-1845	90	33	+	+	ADJ
ejpam-1845	90	34	1	1	NUM
ejpam-1845	90	35	)	)	PUNCT
ejpam-1845	90	36	,	,	PUNCT
ejpam-1845	90	37	where	where	SCONJ
ejpam-1845	90	38	w	w	NOUN
ejpam-1845	90	39	rϕ	rϕ	NOUN
ejpam-1845	90	40	:	:	PUNCT
ejpam-1845	90	41	=	=	PUNCT
ejpam-1845	90	42	wrϕ	wrϕ	NOUN
ejpam-1845	90	43	∪	∪	ADP
ejpam-1845	90	44	cγϕ	cγϕ	PROPN
ejpam-1845	90	45	∪	∪	PROPN
ejpam-1845	90	46	γ0	γ0	NOUN
ejpam-1845	90	47	,	,	PUNCT
ejpam-1845	90	48	and	and	CCONJ
ejpam-1845	90	49	wrϕ	wrϕ	NOUN
ejpam-1845	90	50	:	:	PUNCT
ejpam-1845	90	51	=	=	SYM
ejpam-1845	90	52	{	{	PUNCT
ejpam-1845	90	53	(	(	PUNCT
ejpam-1845	90	54	rn,ϕm	rn,ϕm	ADJ
ejpam-1845	90	55	)	)	PUNCT
ejpam-1845	90	56	∈	∈	PROPN
ejpam-1845	90	57	ωrϕ	ωrϕ	NOUN
ejpam-1845	90	58	:	:	PUNCT
ejpam-1845	90	59	n	n	NOUN
ejpam-1845	90	60	=	=	SYM
ejpam-1845	90	61	2	2	NUM
ejpam-1845	90	62	,	,	PUNCT
ejpam-1845	90	63	n	n	PRON
ejpam-1845	90	64	,	,	PUNCT
ejpam-1845	90	65	m	m	VERB
ejpam-1845	90	66	=	=	SYM
ejpam-1845	90	67	2	2	NUM
ejpam-1845	90	68	,	,	PUNCT
ejpam-1845	90	69	m	m	VERB
ejpam-1845	90	70	}	}	PUNCT
ejpam-1845	90	71	.	.	PUNCT
ejpam-1845	91	1	the	the	DET
ejpam-1845	91	2	boundary	boundary	ADJ
ejpam-1845	91	3	mesh	mesh	NOUN
ejpam-1845	91	4	points	point	NOUN
ejpam-1845	91	5	are	be	AUX
ejpam-1845	91	6	defined	define	VERB
ejpam-1845	91	7	as	as	SCONJ
ejpam-1845	91	8	follows	follow	VERB
ejpam-1845	91	9	γϕ	γϕ	ADP
ejpam-1845	91	10	:	:	PUNCT
ejpam-1845	91	11	=	=	SYM
ejpam-1845	91	12	{	{	PUNCT
ejpam-1845	91	13	(	(	PUNCT
ejpam-1845	91	14	r,ϕm	r,ϕm	ADJ
ejpam-1845	91	15	)	)	PUNCT
ejpam-1845	91	16	∈	∈	NOUN
ejpam-1845	91	17	γϕ	γϕ	ADP
ejpam-1845	91	18	:	:	PUNCT
ejpam-1845	91	19	m=	m=	X
ejpam-1845	91	20	1	1	NUM
ejpam-1845	91	21	,	,	PUNCT
ejpam-1845	91	22	m	m	VERB
ejpam-1845	91	23	}	}	PUNCT
ejpam-1845	91	24	,	,	PUNCT
ejpam-1845	91	25	γ0	γ0	NOUN
ejpam-1845	91	26	:	:	PUNCT
ejpam-1845	91	27	=	=	SYM
ejpam-1845	91	28	{	{	PUNCT
ejpam-1845	91	29	(	(	PUNCT
ejpam-1845	91	30	rn	rn	PROPN
ejpam-1845	91	31	,	,	PUNCT
ejpam-1845	91	32	0	0	NUM
ejpam-1845	91	33	)	)	PUNCT
ejpam-1845	91	34	∈	∈	PROPN
ejpam-1845	91	35	γ0	γ0	NOUN
ejpam-1845	91	36	:	:	PUNCT
ejpam-1845	91	37	n=	n=	ADJ
ejpam-1845	91	38	1	1	NUM
ejpam-1845	91	39	,	,	PUNCT
ejpam-1845	91	40	n	n	CCONJ
ejpam-1845	91	41	}	}	PUNCT
ejpam-1845	91	42	.	.	PUNCT
ejpam-1845	92	1	a.	a.	NOUN
ejpam-1845	92	2	erdem	erdem	PROPN
ejpam-1845	92	3	/	/	SYM
ejpam-1845	92	4	eur	eur	PROPN
ejpam-1845	92	5	.	.	PUNCT
ejpam-1845	93	1	j.	j.	PROPN
ejpam-1845	93	2	pure	pure	PROPN
ejpam-1845	93	3	appl	appl	PROPN
ejpam-1845	93	4	.	.	PROPN
ejpam-1845	93	5	math	math	PROPN
ejpam-1845	93	6	,	,	PUNCT
ejpam-1845	93	7	6	6	NUM
ejpam-1845	93	8	(	(	PUNCT
ejpam-1845	93	9	2013	2013	NUM
ejpam-1845	93	10	)	)	PUNCT
ejpam-1845	93	11	,	,	PUNCT
ejpam-1845	93	12	30	30	NUM
ejpam-1845	93	13	-	-	SYM
ejpam-1845	93	14	43	43	NUM
ejpam-1845	93	15	34	34	NUM
ejpam-1845	93	16	1	1	NUM
ejpam-1845	93	17	23	23	NUM
ejpam-1845	93	18	4	4	NUM
ejpam-1845	93	19	5	5	NUM
ejpam-1845	93	20	6	6	NUM
ejpam-1845	93	21	7	7	NUM
ejpam-1845	93	22	8	8	NUM
ejpam-1845	93	23	10	10	NUM
ejpam-1845	93	24	11	11	NUM
ejpam-1845	93	25	12	12	NUM
ejpam-1845	93	26	13	13	NUM
ejpam-1845	93	27	14	14	NUM
ejpam-1845	93	28	15	15	NUM
ejpam-1845	93	29	16	16	NUM
ejpam-1845	93	30	9	9	NUM
ejpam-1845	93	31	18	18	NUM
ejpam-1845	93	32	19	19	NUM
ejpam-1845	93	33	20	20	NUM
ejpam-1845	93	34	21	21	NUM
ejpam-1845	93	35	22	22	NUM
ejpam-1845	93	36	23	23	NUM
ejpam-1845	93	37	24	24	NUM
ejpam-1845	93	38	17β	17β	NUM
ejpam-1845	93	39	0	0	NUM
ejpam-1845	94	1	γ	γ	SYM
ejpam-1845	94	2	0	0	NUM
ejpam-1845	94	3	γφ	γφ	NOUN
ejpam-1845	94	4	rotated	rotate	VERB
ejpam-1845	94	5	mesh	mesh	NOUN
ejpam-1845	94	6	figure	figure	NOUN
ejpam-1845	94	7	1	1	NUM
ejpam-1845	94	8	:	:	PUNCT
ejpam-1845	94	9	geometry	geometry	NOUN
ejpam-1845	94	10	of	of	ADP
ejpam-1845	94	11	the	the	DET
ejpam-1845	94	12	poleness	poleness	ADJ
ejpam-1845	94	13	polar	polar	ADJ
ejpam-1845	94	14	mesh	mesh	NOUN
ejpam-1845	94	15	and	and	CCONJ
ejpam-1845	94	16	its	its	PRON
ejpam-1845	94	17	rotated	rotated	ADJ
ejpam-1845	94	18	form	form	NOUN
ejpam-1845	94	19	due	due	ADP
ejpam-1845	94	20	to	to	ADP
ejpam-1845	94	21	the	the	DET
ejpam-1845	94	22	periodicity	periodicity	NOUN
ejpam-1845	94	23	condition	condition	NOUN
ejpam-1845	94	24	u(r	u(r	PROPN
ejpam-1845	94	25	,	,	PUNCT
ejpam-1845	94	26	0	0	NUM
ejpam-1845	94	27	)	)	PUNCT
ejpam-1845	94	28	=	=	SYM
ejpam-1845	95	1	u(r	u(r	NOUN
ejpam-1845	95	2	,	,	PUNCT
ejpam-1845	95	3	2π	2π	NOUN
ejpam-1845	95	4	)	)	PUNCT
ejpam-1845	95	5	we	we	PRON
ejpam-1845	95	6	will	will	AUX
ejpam-1845	95	7	not	not	PART
ejpam-1845	95	8	include	include	VERB
ejpam-1845	95	9	the	the	DET
ejpam-1845	95	10	values	value	NOUN
ejpam-1845	95	11	u(r	u(r	ADV
ejpam-1845	95	12	,	,	PUNCT
ejpam-1845	95	13	0	0	NUM
ejpam-1845	95	14	)	)	PUNCT
ejpam-1845	95	15	,	,	PUNCT
ejpam-1845	95	16	r	r	NOUN
ejpam-1845	95	17	∈	∈	PROPN
ejpam-1845	96	1	[	[	X
ejpam-1845	96	2	0,r	0,r	X
ejpam-1845	96	3	]	]	X
ejpam-1845	96	4	to	to	ADP
ejpam-1845	96	5	the	the	DET
ejpam-1845	96	6	list	list	NOUN
ejpam-1845	96	7	of	of	ADP
ejpam-1845	96	8	unknowns	unknown	NOUN
ejpam-1845	96	9	in	in	ADP
ejpam-1845	96	10	the	the	DET
ejpam-1845	96	11	discrete	discrete	ADJ
ejpam-1845	96	12	problem	problem	NOUN
ejpam-1845	96	13	.	.	PUNCT
ejpam-1845	97	1	the	the	DET
ejpam-1845	97	2	introduced	introduce	VERB
ejpam-1845	97	3	mesh	mesh	NOUN
ejpam-1845	97	4	w	w	NOUN
ejpam-1845	97	5	rϕ	rϕ	NOUN
ejpam-1845	97	6	does	do	AUX
ejpam-1845	97	7	n’t	not	PART
ejpam-1845	97	8	include	include	VERB
ejpam-1845	97	9	the	the	DET
ejpam-1845	97	10	pole	pole	NOUN
ejpam-1845	97	11	point	point	NOUN
ejpam-1845	97	12	r	r	NOUN
ejpam-1845	97	13	=	=	SYM
ejpam-1845	97	14	0	0	NUM
ejpam-1845	97	15	,	,	PUNCT
ejpam-1845	97	16	that	that	PRON
ejpam-1845	97	17	is	be	AUX
ejpam-1845	97	18	in	in	ADP
ejpam-1845	97	19	the	the	DET
ejpam-1845	97	20	presented	present	VERB
ejpam-1845	97	21	discrete	discrete	ADJ
ejpam-1845	97	22	model	model	NOUN
ejpam-1845	97	23	the	the	DET
ejpam-1845	97	24	domain	domain	NOUN
ejpam-1845	97	25	ωrϕ	ωrϕ	NOUN
ejpam-1845	97	26	is	be	AUX
ejpam-1845	97	27	approximated	approximate	VERB
ejpam-1845	97	28	by	by	ADP
ejpam-1845	97	29	the	the	DET
ejpam-1845	97	30	circular	circular	ADJ
ejpam-1845	97	31	disc	disc	NOUN
ejpam-1845	97	32	o	o	NOUN
ejpam-1845	97	33	ωrϕ.	ωrϕ.	NOUN
ejpam-1845	97	34	thus	thus	ADV
ejpam-1845	97	35	our	our	PRON
ejpam-1845	97	36	discrete	discrete	ADJ
ejpam-1845	97	37	model	model	NOUN
ejpam-1845	97	38	does	do	AUX
ejpam-1845	97	39	not	not	PART
ejpam-1845	97	40	deal	deal	VERB
ejpam-1845	97	41	with	with	ADP
ejpam-1845	97	42	the	the	DET
ejpam-1845	97	43	singularity	singularity	NOUN
ejpam-1845	97	44	at	at	ADP
ejpam-1845	97	45	r	r	NOUN
ejpam-1845	97	46	=	=	SYM
ejpam-1845	97	47	0	0	NUM
ejpam-1845	97	48	,	,	PUNCT
ejpam-1845	97	49	that	that	PRON
ejpam-1845	97	50	is	be	AUX
ejpam-1845	97	51	usual	usual	ADJ
ejpam-1845	97	52	for	for	ADP
ejpam-1845	97	53	the	the	DET
ejpam-1845	97	54	differential	differential	ADJ
ejpam-1845	97	55	problem	problem	NOUN
ejpam-1845	97	56	.	.	PUNCT
ejpam-1845	98	1	instead	instead	ADV
ejpam-1845	98	2	we	we	PRON
ejpam-1845	98	3	will	will	AUX
ejpam-1845	98	4	derive	derive	VERB
ejpam-1845	98	5	an	an	DET
ejpam-1845	98	6	approximation	approximation	NOUN
ejpam-1845	98	7	of	of	ADP
ejpam-1845	98	8	the	the	DET
ejpam-1845	98	9	boundedness	boundedness	NOUN
ejpam-1845	98	10	condition	condition	NOUN
ejpam-1845	98	11	(	(	PUNCT
ejpam-1845	98	12	2	2	NUM
ejpam-1845	98	13	)	)	PUNCT
ejpam-1845	98	14	at	at	ADP
ejpam-1845	98	15	the	the	DET
ejpam-1845	98	16	central	central	ADJ
ejpam-1845	98	17	circle	circle	NOUN
ejpam-1845	98	18	with	with	ADP
ejpam-1845	98	19	radius	radius	NOUN
ejpam-1845	98	20	r	r	NOUN
ejpam-1845	98	21	=	=	SYM
ejpam-1845	98	22	r1	r1	PROPN
ejpam-1845	98	23	,	,	PUNCT
ejpam-1845	98	24	r1	r1	PROPN
ejpam-1845	98	25	=	=	PUNCT
ejpam-1845	98	26	0.5hr	0.5hr	PROPN
ejpam-1845	98	27	.	.	PUNCT
ejpam-1845	99	1	denote	denote	VERB
ejpam-1845	99	2	by	by	ADP
ejpam-1845	99	3	enm	enm	PROPN
ejpam-1845	99	4	=	=	SYM
ejpam-1845	99	5	{	{	PUNCT
ejpam-1845	99	6	(	(	PUNCT
ejpam-1845	99	7	r,ϕ	r,ϕ	NOUN
ejpam-1845	99	8	)	)	PUNCT
ejpam-1845	99	9	∈	∈	PROPN
ejpam-1845	99	10	ωrβ	ωrβ	NOUN
ejpam-1845	99	11	:	:	PUNCT
ejpam-1845	99	12	rn	rn	PROPN
ejpam-1845	99	13	≤	≤	NUM
ejpam-1845	99	14	r	r	NOUN
ejpam-1845	99	15	≤	≤	NOUN
ejpam-1845	99	16	rn+1	rn+1	VERB
ejpam-1845	99	17	,	,	PUNCT
ejpam-1845	99	18	ϕm	ϕm	ADP
ejpam-1845	99	19	≤	≤	PROPN
ejpam-1845	99	20	ϕ	ϕ	X
ejpam-1845	99	21	≤	≤	NUM
ejpam-1845	99	22	ϕm+1	ϕm+1	X
ejpam-1845	99	23	}	}	PUNCT
ejpam-1845	99	24	the	the	DET
ejpam-1845	99	25	polar	polar	ADJ
ejpam-1845	99	26	finite	finite	ADJ
ejpam-1845	99	27	element	element	NOUN
ejpam-1845	99	28	with	with	ADP
ejpam-1845	99	29	four	four	NUM
ejpam-1845	99	30	nodes	node	NOUN
ejpam-1845	99	31	.	.	PUNCT
ejpam-1845	100	1	we	we	PRON
ejpam-1845	100	2	derive	derive	VERB
ejpam-1845	100	3	an	an	DET
ejpam-1845	100	4	error	error	NOUN
ejpam-1845	100	5	approximation	approximation	NOUN
ejpam-1845	100	6	for	for	ADP
ejpam-1845	100	7	each	each	DET
ejpam-1845	100	8	element	element	NOUN
ejpam-1845	100	9	.	.	PUNCT
ejpam-1845	101	1	introducing	introduce	VERB
ejpam-1845	101	2	the	the	DET
ejpam-1845	101	3	halfnodes	halfnode	NOUN
ejpam-1845	101	4	r±n	r±n	PROPN
ejpam-1845	101	5	=	=	SYM
ejpam-1845	101	6	rn	rn	PROPN
ejpam-1845	101	7	±	±	PROPN
ejpam-1845	101	8	hr/2	hr/2	PROPN
ejpam-1845	101	9	,	,	PUNCT
ejpam-1845	101	10	ϕ±m	ϕ±m	PROPN
ejpam-1845	102	1	=	=	PUNCT
ejpam-1845	102	2	ϕm	ϕm	ADP
ejpam-1845	102	3	±	±	NUM
ejpam-1845	102	4	hϕ/2	hϕ/2	ADJ
ejpam-1845	102	5	and	and	CCONJ
ejpam-1845	102	6	integrating	integrate	VERB
ejpam-1845	102	7	equation	equation	NOUN
ejpam-1845	102	8	(	(	PUNCT
ejpam-1845	102	9	1	1	NUM
ejpam-1845	102	10	)	)	PUNCT
ejpam-1845	102	11	on	on	ADP
ejpam-1845	102	12	the	the	DET
ejpam-1845	102	13	finite	finite	PROPN
ejpam-1845	102	14	element	element	NOUN
ejpam-1845	102	15	eenm	eenm	ADV
ejpam-1845	102	16	:	:	PUNCT
ejpam-1845	102	17	=	=	SYM
ejpam-1845	103	1	[	[	X
ejpam-1845	103	2	r−n	r−n	PROPN
ejpam-1845	103	3	,	,	PUNCT
ejpam-1845	103	4	r+n	r+n	PROPN
ejpam-1845	103	5	]	]	X
ejpam-1845	103	6	×	×	NOUN
ejpam-1845	103	7	[	[	X
ejpam-1845	103	8	ϕ−m,ϕ+m	ϕ−m,ϕ+m	X
ejpam-1845	103	9	]	]	X
ejpam-1845	103	10	we	we	PRON
ejpam-1845	103	11	obtain	obtain	VERB
ejpam-1845	103	12	the	the	DET
ejpam-1845	103	13	following	follow	VERB
ejpam-1845	103	14	balance	balance	NOUN
ejpam-1845	103	15	equation	equation	NOUN
ejpam-1845	103	16	:	:	PUNCT
ejpam-1845	103	17	∫	∫	PROPN
ejpam-1845	103	18	ϕ+m	ϕ+m	PROPN
ejpam-1845	104	1	ϕ−m	ϕ−m	PROPN
ejpam-1845	104	2	∫	∫	PROPN
ejpam-1845	105	1	r+n	r+n	PROPN
ejpam-1845	105	2	r−n	r−n	PROPN
ejpam-1845	105	3	∂	∂	NOUN
ejpam-1845	105	4	∂	∂	NUM
ejpam-1845	105	5	r	r	NOUN
ejpam-1845	105	6	�	�	PROPN
ejpam-1845	105	7	r	r	NOUN
ejpam-1845	105	8	∂	∂	NUM
ejpam-1845	105	9	u	u	NOUN
ejpam-1845	105	10	∂	∂	NOUN
ejpam-1845	105	11	r	r	NOUN
ejpam-1845	105	12	�	�	PROPN
ejpam-1845	105	13	drdϕ+	drdϕ+	PRON
ejpam-1845	105	14	∫	∫	PROPN
ejpam-1845	105	15	r+n	r+n	PROPN
ejpam-1845	106	1	r−n	r−n	ADJ
ejpam-1845	106	2	∫	∫	PROPN
ejpam-1845	106	3	ϕ+m	ϕ+m	PROPN
ejpam-1845	107	1	ϕ−m	ϕ−m	NOUN
ejpam-1845	107	2	1	1	NUM
ejpam-1845	107	3	r	r	NOUN
ejpam-1845	107	4	∂	∂	NOUN
ejpam-1845	107	5	2u	2u	NOUN
ejpam-1845	107	6	∂	∂	NOUN
ejpam-1845	107	7	ϕ2	ϕ2	ADV
ejpam-1845	107	8	dϕdr	dϕdr	VERB
ejpam-1845	107	9	=	=	SYM
ejpam-1845	107	10	−	−	PROPN
ejpam-1845	107	11	∫	∫	PROPN
ejpam-1845	107	12	r+n	r+n	PROPN
ejpam-1845	107	13	r−n	r−n	ADJ
ejpam-1845	107	14	∫	∫	PROPN
ejpam-1845	107	15	ϕ+m	ϕ+m	PROPN
ejpam-1845	107	16	ϕ−m	ϕ−m	PROPN
ejpam-1845	107	17	rf(r,ϕ)dϕdr	rf(r,ϕ)dϕdr	PROPN
ejpam-1845	107	18	.	.	PROPN
ejpam-1845	108	1	(	(	PUNCT
ejpam-1845	108	2	7	7	X
ejpam-1845	108	3	)	)	PUNCT
ejpam-1845	108	4	let	let	VERB
ejpam-1845	108	5	us	we	PRON
ejpam-1845	108	6	transform	transform	VERB
ejpam-1845	108	7	the	the	DET
ejpam-1845	108	8	first	first	ADJ
ejpam-1845	108	9	left	leave	VERB
ejpam-1845	108	10	integral	integral	ADJ
ejpam-1845	108	11	i	i	NOUN
ejpam-1845	108	12	r	r	NOUN
ejpam-1845	108	13	nm	nm	NOUN
ejpam-1845	108	14	.	.	PUNCT
ejpam-1845	109	1	i	i	PRON
ejpam-1845	109	2	r	r	VERB
ejpam-1845	109	3	nm	nm	ADJ
ejpam-1845	109	4	=	=	PUNCT
ejpam-1845	110	1	∫	∫	PROPN
ejpam-1845	110	2	ϕ+m	ϕ+m	PROPN
ejpam-1845	111	1	ϕ−m	ϕ−m	PROPN
ejpam-1845	111	2	�	�	PROPN
ejpam-1845	111	3	r	r	NOUN
ejpam-1845	111	4	∂	∂	NUM
ejpam-1845	111	5	u	u	NOUN
ejpam-1845	111	6	∂	∂	NOUN
ejpam-1845	111	7	r	r	NOUN
ejpam-1845	111	8	�	�	PROPN
ejpam-1845	111	9	r	r	NOUN
ejpam-1845	111	10	=	=	NOUN
ejpam-1845	111	11	r+n	r+n	ADJ
ejpam-1845	111	12	r	r	NOUN
ejpam-1845	111	13	=	=	NOUN
ejpam-1845	111	14	r−n	r−n	ADJ
ejpam-1845	111	15	dϕ	dϕ	NOUN
ejpam-1845	111	16	∼=	∼=	PROPN
ejpam-1845	111	17	hϕ	hϕ	NOUN
ejpam-1845	111	18	�	�	PROPN
ejpam-1845	111	19	�	�	PROPN
ejpam-1845	111	20	r	r	NOUN
ejpam-1845	111	21	∂	∂	NUM
ejpam-1845	111	22	u	u	NOUN
ejpam-1845	111	23	∂	∂	NOUN
ejpam-1845	111	24	r	r	NOUN
ejpam-1845	111	25	�	�	PROPN
ejpam-1845	111	26	(	(	PUNCT
ejpam-1845	111	27	r+n	r+n	PROPN
ejpam-1845	111	28	,	,	PUNCT
ejpam-1845	111	29	ϕm)−	ϕm)−	PROPN
ejpam-1845	111	30	�	�	PROPN
ejpam-1845	112	1	r	r	NOUN
ejpam-1845	112	2	∂	∂	NUM
ejpam-1845	112	3	u	u	NOUN
ejpam-1845	112	4	∂	∂	NOUN
ejpam-1845	112	5	r	r	NOUN
ejpam-1845	112	6	�	�	PROPN
ejpam-1845	112	7	(	(	PUNCT
ejpam-1845	112	8	r−n	r−n	PROPN
ejpam-1845	112	9	,	,	PUNCT
ejpam-1845	112	10	ϕm	ϕm	NOUN
ejpam-1845	112	11	)	)	PUNCT
ejpam-1845	112	12	�	�	NOUN
ejpam-1845	112	13	we	we	PRON
ejpam-1845	112	14	use	use	VERB
ejpam-1845	112	15	here	here	ADV
ejpam-1845	112	16	the	the	DET
ejpam-1845	112	17	central	central	ADJ
ejpam-1845	112	18	finite	finite	ADJ
ejpam-1845	112	19	difference	difference	NOUN
ejpam-1845	112	20	formula	formula	NOUN
ejpam-1845	112	21	for	for	ADP
ejpam-1845	112	22	approximation	approximation	NOUN
ejpam-1845	112	23	of	of	ADP
ejpam-1845	112	24	derivatives	derivative	NOUN
ejpam-1845	112	25	on	on	ADP
ejpam-1845	112	26	the	the	DET
ejpam-1845	112	27	right	right	ADJ
ejpam-1845	112	28	hand	hand	NOUN
ejpam-1845	112	29	side	side	NOUN
ejpam-1845	112	30	,	,	PUNCT
ejpam-1845	112	31	by	by	ADP
ejpam-1845	112	32	using	use	VERB
ejpam-1845	112	33	the	the	DET
ejpam-1845	112	34	mesh	mesh	NOUN
ejpam-1845	112	35	points	point	NOUN
ejpam-1845	112	36	rn	rn	PROPN
ejpam-1845	112	37	,	,	PUNCT
ejpam-1845	112	38	rn+1/2	rn+1/2	PROPN
ejpam-1845	112	39	,	,	PUNCT
ejpam-1845	112	40	rn+1	rn+1	VERB
ejpam-1845	112	41	,	,	PUNCT
ejpam-1845	112	42	with	with	ADP
ejpam-1845	112	43	mesh	mesh	NOUN
ejpam-1845	112	44	step	step	NOUN
ejpam-1845	112	45	hr/2	hr/2	NOUN
ejpam-1845	112	46	=	=	SYM
ejpam-1845	112	47	hr/2	hr/2	ADJ
ejpam-1845	112	48	:	:	PUNCT
ejpam-1845	112	49	�	�	PROPN
ejpam-1845	112	50	r	r	NOUN
ejpam-1845	112	51	∂	∂	NUM
ejpam-1845	112	52	u	u	NOUN
ejpam-1845	112	53	∂	∂	NOUN
ejpam-1845	112	54	r	r	NOUN
ejpam-1845	112	55	�	�	PROPN
ejpam-1845	112	56	(	(	PUNCT
ejpam-1845	112	57	r+n	r+n	PROPN
ejpam-1845	112	58	,	,	PUNCT
ejpam-1845	112	59	ϕm	ϕm	X
ejpam-1845	112	60	)	)	PUNCT
ejpam-1845	112	61	∼=	∼=	PROPN
ejpam-1845	112	62	r+n	r+n	ADJ
ejpam-1845	112	63	u(rn+1,ϕm)−	u(rn+1,ϕm)−	PROPN
ejpam-1845	112	64	u(rn,ϕm	u(rn,ϕm	PROPN
ejpam-1845	112	65	)	)	PUNCT
ejpam-1845	112	66	hr	hr	NOUN
ejpam-1845	112	67	,	,	PUNCT
ejpam-1845	112	68	�	�	PROPN
ejpam-1845	112	69	r	r	NOUN
ejpam-1845	112	70	∂	∂	NUM
ejpam-1845	112	71	u	u	NOUN
ejpam-1845	112	72	∂	∂	NOUN
ejpam-1845	112	73	r	r	NOUN
ejpam-1845	112	74	�	�	PROPN
ejpam-1845	112	75	(	(	PUNCT
ejpam-1845	112	76	r−n	r−n	PROPN
ejpam-1845	112	77	,	,	PUNCT
ejpam-1845	112	78	ϕm	ϕm	NOUN
ejpam-1845	112	79	)	)	PUNCT
ejpam-1845	112	80	∼=	∼=	PROPN
ejpam-1845	112	81	r−n	r−n	PROPN
ejpam-1845	112	82	u(rn,ϕm)−	u(rn,ϕm)−	PROPN
ejpam-1845	112	83	u(rn−1,ϕm	u(rn−1,ϕm	PROPN
ejpam-1845	112	84	)	)	PUNCT
ejpam-1845	112	85	hr	hr	NOUN
ejpam-1845	112	86	.	.	PUNCT
ejpam-1845	113	1	a.	a.	PROPN
ejpam-1845	113	2	erdem	erdem	PROPN
ejpam-1845	113	3	/	/	SYM
ejpam-1845	113	4	eur	eur	PROPN
ejpam-1845	113	5	.	.	PUNCT
ejpam-1845	114	1	j.	j.	PROPN
ejpam-1845	114	2	pure	pure	PROPN
ejpam-1845	114	3	appl	appl	PROPN
ejpam-1845	114	4	.	.	PROPN
ejpam-1845	114	5	math	math	PROPN
ejpam-1845	114	6	,	,	PUNCT
ejpam-1845	114	7	6	6	NUM
ejpam-1845	114	8	(	(	PUNCT
ejpam-1845	114	9	2013	2013	NUM
ejpam-1845	114	10	)	)	PUNCT
ejpam-1845	114	11	,	,	PUNCT
ejpam-1845	114	12	30	30	NUM
ejpam-1845	114	13	-	-	SYM
ejpam-1845	114	14	43	43	NUM
ejpam-1845	114	15	35	35	NUM
ejpam-1845	114	16	then	then	ADV
ejpam-1845	114	17	we	we	PRON
ejpam-1845	114	18	have	have	VERB
ejpam-1845	114	19	the	the	DET
ejpam-1845	114	20	following	follow	VERB
ejpam-1845	114	21	variational	variational	ADJ
ejpam-1845	114	22	finite	finite	ADJ
ejpam-1845	114	23	difference	difference	NOUN
ejpam-1845	114	24	approximation	approximation	NOUN
ejpam-1845	114	25	of	of	ADP
ejpam-1845	114	26	the	the	DET
ejpam-1845	114	27	integral	integral	ADJ
ejpam-1845	114	28	operator	operator	NOUN
ejpam-1845	114	29	i	i	PRON
ejpam-1845	114	30	r	r	NOUN
ejpam-1845	114	31	nm	nm	NOUN
ejpam-1845	114	32	:	:	PUNCT
ejpam-1845	114	33	i	i	PRON
ejpam-1845	114	34	r	r	VERB
ejpam-1845	114	35	nm	nm	PRON
ejpam-1845	114	36	∼=	∼=	PROPN
ejpam-1845	114	37	hϕ	hϕ	PART
ejpam-1845	114	38	�	�	PROPN
ejpam-1845	114	39	r+n	r+n	PROPN
ejpam-1845	114	40	ur	ur	INTJ
ejpam-1845	114	41	,	,	PUNCT
ejpam-1845	114	42	nm−	nm−	PROPN
ejpam-1845	114	43	r−n	r−n	ADJ
ejpam-1845	114	44	ur	ur	INTJ
ejpam-1845	114	45	,	,	PUNCT
ejpam-1845	114	46	nm	nm	PROPN
ejpam-1845	114	47	�	�	PROPN
ejpam-1845	114	48	.	.	PUNCT
ejpam-1845	115	1	by	by	ADP
ejpam-1845	115	2	the	the	DET
ejpam-1845	115	3	same	same	ADJ
ejpam-1845	115	4	way	way	NOUN
ejpam-1845	115	5	we	we	PRON
ejpam-1845	115	6	can	can	AUX
ejpam-1845	115	7	derive	derive	VERB
ejpam-1845	115	8	an	an	DET
ejpam-1845	115	9	approximation	approximation	NOUN
ejpam-1845	115	10	of	of	ADP
ejpam-1845	115	11	the	the	DET
ejpam-1845	115	12	second	second	ADJ
ejpam-1845	115	13	integral	integral	ADJ
ejpam-1845	115	14	operator	operator	NOUN
ejpam-1845	115	15	i	i	PRON
ejpam-1845	115	16	ϕ	ϕ	VERB
ejpam-1845	115	17	nm	nm	ADV
ejpam-1845	115	18	on	on	ADP
ejpam-1845	115	19	the	the	DET
ejpam-1845	115	20	left	left	ADJ
ejpam-1845	115	21	hand	hand	NOUN
ejpam-1845	115	22	side	side	NOUN
ejpam-1845	115	23	of	of	ADP
ejpam-1845	115	24	(	(	PUNCT
ejpam-1845	115	25	7	7	NUM
ejpam-1845	115	26	):	):	PUNCT
ejpam-1845	115	27	iϕnmu	iϕnmu	ADJ
ejpam-1845	115	28	∼=	∼=	PROPN
ejpam-1845	115	29	hr	hr	PROPN
ejpam-1845	115	30	rn	rn	PROPN
ejpam-1845	115	31	�	�	PROPN
ejpam-1845	115	32	∂	∂	NUM
ejpam-1845	115	33	u	u	PROPN
ejpam-1845	115	34	∂	∂	PROPN
ejpam-1845	115	35	ϕ	ϕ	NOUN
ejpam-1845	115	36	(	(	PUNCT
ejpam-1845	115	37	rn,ϕ+m)−	rn,ϕ+m)−	NOUN
ejpam-1845	115	38	∂	∂	NUM
ejpam-1845	115	39	u	u	NOUN
ejpam-1845	115	40	∂	∂	PROPN
ejpam-1845	115	41	ϕ	ϕ	NOUN
ejpam-1845	115	42	(	(	PUNCT
ejpam-1845	115	43	rn,ϕ−m	rn,ϕ−m	NOUN
ejpam-1845	115	44	)	)	PUNCT
ejpam-1845	115	45	�	�	PROPN
ejpam-1845	115	46	∼=	∼=	PROPN
ejpam-1845	115	47	hr	hr	PROPN
ejpam-1845	115	48	rn	rn	PROPN
ejpam-1845	115	49	�	�	PROPN
ejpam-1845	115	50	uϕ(rn,ϕm)−	uϕ(rn,ϕm)−	SYM
ejpam-1845	115	51	uϕ(rn,ϕm	uϕ(rn,ϕm	PROPN
ejpam-1845	115	52	)	)	PUNCT
ejpam-1845	115	53	�	�	PROPN
ejpam-1845	115	54	.	.	PUNCT
ejpam-1845	116	1	applying	apply	VERB
ejpam-1845	116	2	to	to	ADP
ejpam-1845	116	3	the	the	DET
ejpam-1845	116	4	right	right	ADJ
ejpam-1845	116	5	hand	hand	NOUN
ejpam-1845	116	6	side	side	NOUN
ejpam-1845	116	7	of	of	ADP
ejpam-1845	116	8	(	(	PUNCT
ejpam-1845	116	9	7	7	X
ejpam-1845	116	10	)	)	PUNCT
ejpam-1845	116	11	the	the	DET
ejpam-1845	116	12	numerical	numerical	ADJ
ejpam-1845	116	13	integration	integration	NOUN
ejpam-1845	116	14	(	(	PUNCT
ejpam-1845	116	15	rectangle	rectangle	NOUN
ejpam-1845	116	16	)	)	PUNCT
ejpam-1845	116	17	formula	formula	NOUN
ejpam-1845	116	18	,	,	PUNCT
ejpam-1845	116	19	finally	finally	ADV
ejpam-1845	116	20	we	we	PRON
ejpam-1845	116	21	have	have	VERB
ejpam-1845	116	22	−hϕ[r	−hϕ[r	NUM
ejpam-1845	116	23	+	+	SYM
ejpam-1845	116	24	n	n	NUM
ejpam-1845	116	25	yr	yr	NOUN
ejpam-1845	116	26	,	,	PUNCT
ejpam-1845	116	27	nm−	nm−	PROPN
ejpam-1845	117	1	r−n	r−n	PROPN
ejpam-1845	117	2	yr	yr	NOUN
ejpam-1845	117	3	,	,	PUNCT
ejpam-1845	117	4	nm]−	nm]−	PROPN
ejpam-1845	117	5	hr	hr	PROPN
ejpam-1845	117	6	rn	rn	PROPN
ejpam-1845	118	1	[	[	X
ejpam-1845	118	2	yϕ,nm	yϕ,nm	NOUN
ejpam-1845	119	1	−	−	PROPN
ejpam-1845	119	2	yϕ,nm	yϕ,nm	NOUN
ejpam-1845	119	3	]	]	X
ejpam-1845	120	1	=	=	SYM
ejpam-1845	120	2	hrhϕ	hrhϕ	PROPN
ejpam-1845	120	3	rnf(rnϕm	rnf(rnϕm	NOUN
ejpam-1845	120	4	)	)	PUNCT
ejpam-1845	120	5	dividing	dividing	NOUN
ejpam-1845	120	6	by	by	ADP
ejpam-1845	120	7	hrhϕ	hrhϕ	PROPN
ejpam-1845	120	8	rn	rn	PROPN
ejpam-1845	120	9	>	>	PROPN
ejpam-1845	120	10	0	0	PUNCT
ejpam-1845	121	1	we	we	PRON
ejpam-1845	121	2	obtain	obtain	VERB
ejpam-1845	121	3	the	the	DET
ejpam-1845	121	4	following	following	ADJ
ejpam-1845	121	5	finite	finite	ADJ
ejpam-1845	121	6	difference	difference	NOUN
ejpam-1845	121	7	equation	equation	NOUN
ejpam-1845	121	8	a	a	DET
ejpam-1845	121	9	nmu	nmu	NOUN
ejpam-1845	121	10	:	:	PUNCT
ejpam-1845	121	11	=	=	SYM
ejpam-1845	121	12	−	−	PROPN
ejpam-1845	121	13	�	�	NOUN
ejpam-1845	121	14	1	1	NUM
ejpam-1845	121	15	r	r	NOUN
ejpam-1845	121	16	(	(	PUNCT
ejpam-1845	121	17	r	r	NOUN
ejpam-1845	121	18	yr	yr	NOUN
ejpam-1845	121	19	)	)	PUNCT
ejpam-1845	121	20	�	�	PROPN
ejpam-1845	122	1	r	r	NOUN
ejpam-1845	122	2	,	,	PUNCT
ejpam-1845	122	3	nm	nm	ADJ
ejpam-1845	122	4	−	−	PROPN
ejpam-1845	122	5	�	�	PROPN
ejpam-1845	122	6	1	1	NUM
ejpam-1845	122	7	r2	r2	PROPN
ejpam-1845	122	8	yϕϕ	yϕϕ	PROPN
ejpam-1845	122	9	�	�	PROPN
ejpam-1845	122	10	nm	nm	PROPN
ejpam-1845	122	11	=	=	SYM
ejpam-1845	122	12	f(rn,ϕm	f(rn,ϕm	NOUN
ejpam-1845	122	13	)	)	PUNCT
ejpam-1845	122	14	,	,	PUNCT
ejpam-1845	122	15	(	(	PUNCT
ejpam-1845	122	16	rn,ϕm	rn,ϕm	NOUN
ejpam-1845	122	17	)	)	PUNCT
ejpam-1845	122	18	∈ωrϕ	∈ωrϕ	NOUN
ejpam-1845	122	19	,	,	PUNCT
ejpam-1845	122	20	n	n	CCONJ
ejpam-1845	122	21	6=	6=	NUM
ejpam-1845	122	22	1	1	NUM
ejpam-1845	122	23	.	.	PUNCT
ejpam-1845	123	1	(	(	PUNCT
ejpam-1845	123	2	8)	8)	NUM
ejpam-1845	123	3	the	the	DET
ejpam-1845	123	4	finite	finite	ADJ
ejpam-1845	123	5	dimensional	dimensional	ADJ
ejpam-1845	123	6	operators	operator	NOUN
ejpam-1845	123	7	a	a	DET
ejpam-1845	123	8	r	r	NOUN
ejpam-1845	123	9	nm	nm	ADJ
ejpam-1845	123	10	y	y	NOUN
ejpam-1845	123	11	:	:	PUNCT
ejpam-1845	123	12	=	=	SYM
ejpam-1845	123	13	�	�	PROPN
ejpam-1845	123	14	1	1	NUM
ejpam-1845	123	15	r	r	NOUN
ejpam-1845	123	16	(	(	PUNCT
ejpam-1845	123	17	r	r	NOUN
ejpam-1845	123	18	yr	yr	NOUN
ejpam-1845	123	19	)	)	PUNCT
ejpam-1845	123	20	�	�	PROPN
ejpam-1845	123	21	r	r	PROPN
ejpam-1845	123	22	,	,	PUNCT
ejpam-1845	123	23	nm	nm	INTJ
ejpam-1845	123	24	,	,	PUNCT
ejpam-1845	123	25	a	a	DET
ejpam-1845	123	26	ϕ	ϕ	PROPN
ejpam-1845	123	27	nm	nm	PUNCT
ejpam-1845	123	28	y	y	PROPN
ejpam-1845	123	29	�	�	PROPN
ejpam-1845	123	30	1	1	NUM
ejpam-1845	123	31	r2	r2	PROPN
ejpam-1845	123	32	yϕϕ	yϕϕ	PROPN
ejpam-1845	123	33	�	�	PROPN
ejpam-1845	123	34	nm	nm	PROPN
ejpam-1845	123	35	are	be	AUX
ejpam-1845	123	36	the	the	DET
ejpam-1845	123	37	finite	finite	ADJ
ejpam-1845	123	38	difference	difference	NOUN
ejpam-1845	123	39	approximations	approximation	NOUN
ejpam-1845	123	40	of	of	ADP
ejpam-1845	123	41	the	the	DET
ejpam-1845	123	42	differential	differential	ADJ
ejpam-1845	123	43	operators	operator	NOUN
ejpam-1845	123	44	aru	aru	VERB
ejpam-1845	123	45	:	:	PUNCT
ejpam-1845	123	46	=	=	SYM
ejpam-1845	123	47	1	1	NUM
ejpam-1845	123	48	r	r	NOUN
ejpam-1845	123	49	∂	∂	NOUN
ejpam-1845	123	50	∂	∂	NUM
ejpam-1845	123	51	r	r	NOUN
ejpam-1845	123	52	�	�	PROPN
ejpam-1845	123	53	k(r	k(r	PROPN
ejpam-1845	123	54	)	)	PUNCT
ejpam-1845	123	55	∂	∂	NUM
ejpam-1845	123	56	u	u	NOUN
ejpam-1845	123	57	∂	∂	NOUN
ejpam-1845	123	58	r	r	NOUN
ejpam-1845	123	59	�	�	PROPN
ejpam-1845	123	60	,	,	PUNCT
ejpam-1845	123	61	aϕu	aϕu	PROPN
ejpam-1845	123	62	:	:	PUNCT
ejpam-1845	124	1	=	=	SYM
ejpam-1845	124	2	1	1	NUM
ejpam-1845	124	3	r2	r2	PROPN
ejpam-1845	124	4	∂	∂	NOUN
ejpam-1845	124	5	2u	2u	PROPN
ejpam-1845	124	6	∂	∂	NOUN
ejpam-1845	124	7	ϕ2	ϕ2	ADV
ejpam-1845	124	8	,	,	PUNCT
ejpam-1845	124	9	(	(	PUNCT
ejpam-1845	124	10	r,ϕ	r,ϕ	NOUN
ejpam-1845	124	11	)	)	PUNCT
ejpam-1845	124	12	∈	∈	PROPN
ejpam-1845	124	13	ωrβ	ωrβ	PROPN
ejpam-1845	124	14	,	,	PUNCT
ejpam-1845	124	15	correspondingly	correspondingly	ADV
ejpam-1845	124	16	.	.	PUNCT
ejpam-1845	125	1	note	note	VERB
ejpam-1845	125	2	that	that	SCONJ
ejpam-1845	125	3	the	the	DET
ejpam-1845	125	4	same	same	ADJ
ejpam-1845	125	5	approximations	approximation	NOUN
ejpam-1845	125	6	can	can	AUX
ejpam-1845	125	7	also	also	ADV
ejpam-1845	125	8	be	be	AUX
ejpam-1845	125	9	obtained	obtain	VERB
ejpam-1845	125	10	from	from	ADP
ejpam-1845	125	11	the	the	DET
ejpam-1845	125	12	direct	direct	ADJ
ejpam-1845	125	13	finite	finite	ADJ
ejpam-1845	125	14	difference	difference	NOUN
ejpam-1845	125	15	approximation	approximation	NOUN
ejpam-1845	125	16	of	of	ADP
ejpam-1845	125	17	the	the	DET
ejpam-1845	125	18	poisson	poisson	NOUN
ejpam-1845	125	19	equation	equation	NOUN
ejpam-1845	125	20	(	(	PUNCT
ejpam-1845	125	21	1	1	NUM
ejpam-1845	125	22	)	)	PUNCT
ejpam-1845	125	23	.	.	PUNCT
ejpam-1845	126	1	the	the	DET
ejpam-1845	126	2	finite	finite	ADJ
ejpam-1845	126	3	difference	difference	NOUN
ejpam-1845	126	4	equation	equation	NOUN
ejpam-1845	126	5	corresponding	correspond	VERB
ejpam-1845	126	6	to	to	ADP
ejpam-1845	126	7	the	the	DET
ejpam-1845	126	8	layer	layer	NOUN
ejpam-1845	126	9	r	r	NOUN
ejpam-1845	126	10	=	=	SYM
ejpam-1845	126	11	r1	r1	NOUN
ejpam-1845	126	12	=	=	SYM
ejpam-1845	126	13	hr/2	hr/2	NOUN
ejpam-1845	126	14	can	can	AUX
ejpam-1845	126	15	be	be	AUX
ejpam-1845	126	16	derived	derive	VERB
ejpam-1845	126	17	by	by	ADP
ejpam-1845	126	18	using	use	VERB
ejpam-1845	126	19	the	the	DET
ejpam-1845	126	20	same	same	ADJ
ejpam-1845	126	21	balance	balance	NOUN
ejpam-1845	126	22	equation	equation	NOUN
ejpam-1845	126	23	(	(	PUNCT
ejpam-1845	126	24	7	7	NUM
ejpam-1845	126	25	)	)	PUNCT
ejpam-1845	126	26	,	,	PUNCT
ejpam-1845	126	27	substituting	substitute	VERB
ejpam-1845	126	28	r−n	r−n	PROPN
ejpam-1845	126	29	=	=	SYM
ejpam-1845	126	30	ǫ	ǫ	NOUN
ejpam-1845	126	31	,	,	PUNCT
ejpam-1845	126	32	r+n	r+n	NOUN
ejpam-1845	126	33	=	=	SYM
ejpam-1845	127	1	hr	hr	NOUN
ejpam-1845	127	2	:	:	PUNCT
ejpam-1845	127	3	∫	∫	PROPN
ejpam-1845	127	4	ϕ+m	ϕ+m	PROPN
ejpam-1845	128	1	ϕ−m	ϕ−m	NOUN
ejpam-1845	128	2	∫	∫	PROPN
ejpam-1845	128	3	hr	hr	PROPN
ejpam-1845	128	4	ǫ	ǫ	PROPN
ejpam-1845	128	5	∂	∂	NOUN
ejpam-1845	128	6	∂	∂	NUM
ejpam-1845	128	7	r	r	NOUN
ejpam-1845	128	8	�	�	PROPN
ejpam-1845	128	9	r	r	NOUN
ejpam-1845	128	10	∂	∂	NUM
ejpam-1845	128	11	u	u	NOUN
ejpam-1845	128	12	∂	∂	NOUN
ejpam-1845	128	13	r	r	NOUN
ejpam-1845	128	14	�	�	PROPN
ejpam-1845	128	15	drdϕ+	drdϕ+	PRON
ejpam-1845	128	16	∫	∫	PROPN
ejpam-1845	128	17	ϕ+m	ϕ+m	PROPN
ejpam-1845	129	1	ϕ−m	ϕ−m	NOUN
ejpam-1845	129	2	∫	∫	PROPN
ejpam-1845	129	3	hr	hr	NOUN
ejpam-1845	129	4	ǫ	ǫ	NOUN
ejpam-1845	129	5	1	1	NUM
ejpam-1845	129	6	r	r	NOUN
ejpam-1845	129	7	∂	∂	NOUN
ejpam-1845	129	8	2u	2u	NOUN
ejpam-1845	129	9	∂	∂	NOUN
ejpam-1845	129	10	ϕ2	ϕ2	ADV
ejpam-1845	129	11	drdϕ	drdϕ	ADJ
ejpam-1845	129	12	=	=	PUNCT
ejpam-1845	130	1	−	−	NOUN
ejpam-1845	130	2	∫	∫	NOUN
ejpam-1845	130	3	ϕ+m	ϕ+m	PROPN
ejpam-1845	131	1	ϕ−m	ϕ−m	NOUN
ejpam-1845	131	2	∫	∫	PROPN
ejpam-1845	131	3	hr	hr	PROPN
ejpam-1845	131	4	ǫ	ǫ	PROPN
ejpam-1845	131	5	rf(r,ϕ)drdϕ.	rf(r,ϕ)drdϕ.	ADV
ejpam-1845	131	6	going	go	VERB
ejpam-1845	131	7	to	to	ADP
ejpam-1845	131	8	the	the	DET
ejpam-1845	131	9	limit	limit	NOUN
ejpam-1845	131	10	ǫ→	ǫ→	X
ejpam-1845	131	11	0	0	NUM
ejpam-1845	131	12	here	here	ADV
ejpam-1845	131	13	and	and	CCONJ
ejpam-1845	131	14	using	use	VERB
ejpam-1845	131	15	condition	condition	NOUN
ejpam-1845	131	16	(	(	PUNCT
ejpam-1845	131	17	2	2	X
ejpam-1845	131	18	)	)	PUNCT
ejpam-1845	131	19	we	we	PRON
ejpam-1845	131	20	obtain	obtain	VERB
ejpam-1845	131	21	∫	∫	PROPN
ejpam-1845	131	22	ϕ+m	ϕ+m	PROPN
ejpam-1845	131	23	ϕ−m	ϕ−m	NOUN
ejpam-1845	131	24	∂	∂	NUM
ejpam-1845	131	25	u(hr	u(hr	PROPN
ejpam-1845	131	26	,	,	PUNCT
ejpam-1845	131	27	ϕ	ϕ	NOUN
ejpam-1845	131	28	)	)	PUNCT
ejpam-1845	131	29	∂	∂	NOUN
ejpam-1845	131	30	r	r	NOUN
ejpam-1845	131	31	dϕ+	dϕ+	PROPN
ejpam-1845	131	32	∫	∫	PROPN
ejpam-1845	131	33	hr	hr	NOUN
ejpam-1845	131	34	0	0	NUM
ejpam-1845	131	35	1	1	NUM
ejpam-1845	131	36	r	r	NOUN
ejpam-1845	131	37	�	�	PROPN
ejpam-1845	131	38	∂	∂	NUM
ejpam-1845	131	39	u(r,ϕ+m	u(r,ϕ+m	PROPN
ejpam-1845	131	40	)	)	PUNCT
ejpam-1845	131	41	∂	∂	PUNCT
ejpam-1845	132	1	ϕ	ϕ	NOUN
ejpam-1845	132	2	−	−	PROPN
ejpam-1845	132	3	∂	∂	X
ejpam-1845	132	4	u(r,ϕ−m	u(r,ϕ−m	PROPN
ejpam-1845	132	5	)	)	PUNCT
ejpam-1845	132	6	∂	∂	PUNCT
ejpam-1845	132	7	ϕ	ϕ	PROPN
ejpam-1845	132	8	�	�	PROPN
ejpam-1845	132	9	dr	dr	PROPN
ejpam-1845	132	10	+	+	PROPN
ejpam-1845	132	11	∫	∫	PROPN
ejpam-1845	132	12	hr	hr	NOUN
ejpam-1845	132	13	0	0	NUM
ejpam-1845	132	14	r	r	NOUN
ejpam-1845	132	15	∫	∫	PROPN
ejpam-1845	132	16	ϕ+m	ϕ+m	PROPN
ejpam-1845	133	1	ϕ−m	ϕ−m	NOUN
ejpam-1845	133	2	f(r,ϕ)dϕdr	f(r,ϕ)dϕdr	NOUN
ejpam-1845	133	3	=	=	SYM
ejpam-1845	133	4	0	0	PROPN
ejpam-1845	133	5	.	.	PUNCT
ejpam-1845	133	6	a.	a.	NOUN
ejpam-1845	133	7	erdem	erdem	PROPN
ejpam-1845	133	8	/	/	SYM
ejpam-1845	133	9	eur	eur	PROPN
ejpam-1845	133	10	.	.	PUNCT
ejpam-1845	134	1	j.	j.	PROPN
ejpam-1845	134	2	pure	pure	PROPN
ejpam-1845	134	3	appl	appl	PROPN
ejpam-1845	134	4	.	.	PROPN
ejpam-1845	134	5	math	math	PROPN
ejpam-1845	134	6	,	,	PUNCT
ejpam-1845	134	7	6	6	NUM
ejpam-1845	134	8	(	(	PUNCT
ejpam-1845	134	9	2013	2013	NUM
ejpam-1845	134	10	)	)	PUNCT
ejpam-1845	134	11	,	,	PUNCT
ejpam-1845	134	12	30	30	NUM
ejpam-1845	134	13	-	-	SYM
ejpam-1845	134	14	43	43	NUM
ejpam-1845	134	15	36	36	NUM
ejpam-1845	134	16	again	again	ADV
ejpam-1845	134	17	using	use	VERB
ejpam-1845	134	18	the	the	DET
ejpam-1845	134	19	numerical	numerical	ADJ
ejpam-1845	134	20	integration	integration	NOUN
ejpam-1845	134	21	formula	formula	NOUN
ejpam-1845	134	22	in	in	ADP
ejpam-1845	134	23	the	the	DET
ejpam-1845	134	24	first	first	ADJ
ejpam-1845	134	25	integral	integral	ADJ
ejpam-1845	134	26	we	we	PRON
ejpam-1845	134	27	get	get	VERB
ejpam-1845	134	28	hrhϕ	hrhϕ	NOUN
ejpam-1845	134	29	∂	∂	NUM
ejpam-1845	134	30	u(hr	u(hr	PROPN
ejpam-1845	134	31	,	,	PUNCT
ejpam-1845	134	32	ϕm	ϕm	NOUN
ejpam-1845	134	33	)	)	PUNCT
ejpam-1845	134	34	∂	∂	NOUN
ejpam-1845	134	35	r	r	NOUN
ejpam-1845	134	36	+	+	CCONJ
ejpam-1845	134	37	2	2	NUM
ejpam-1845	134	38	�	�	PROPN
ejpam-1845	134	39	∂	∂	NUM
ejpam-1845	134	40	u	u	PROPN
ejpam-1845	134	41	∂	∂	PROPN
ejpam-1845	134	42	ϕ	ϕ	PROPN
ejpam-1845	134	43	�	�	PROPN
ejpam-1845	134	44	hr	hr	PROPN
ejpam-1845	134	45	2	2	NUM
ejpam-1845	134	46	,	,	PUNCT
ejpam-1845	134	47	ϕm+	ϕm+	VERB
ejpam-1845	134	48	hϕ	hϕ	PROPN
ejpam-1845	134	49	2	2	NUM
ejpam-1845	134	50	�	�	PROPN
ejpam-1845	134	51	−	−	PROPN
ejpam-1845	134	52	∂	∂	NUM
ejpam-1845	134	53	u	u	PROPN
ejpam-1845	134	54	∂	∂	PROPN
ejpam-1845	134	55	ϕ	ϕ	PROPN
ejpam-1845	134	56	�	�	PROPN
ejpam-1845	134	57	hr	hr	PROPN
ejpam-1845	134	58	2	2	NUM
ejpam-1845	134	59	,	,	PUNCT
ejpam-1845	134	60	ϕm	ϕm	INTJ
ejpam-1845	134	61	−	−	PROPN
ejpam-1845	134	62	hϕ	hϕ	PROPN
ejpam-1845	134	63	2	2	NUM
ejpam-1845	134	64	�	�	PROPN
ejpam-1845	134	65	�	�	PROPN
ejpam-1845	134	66	+	+	CCONJ
ejpam-1845	134	67	h2	h2	NOUN
ejpam-1845	134	68	rhϕ	rhϕ	VERB
ejpam-1845	134	69	2	2	NUM
ejpam-1845	134	70	f	f	PROPN
ejpam-1845	134	71	�	�	PROPN
ejpam-1845	134	72	hr	hr	PROPN
ejpam-1845	134	73	2	2	NUM
ejpam-1845	134	74	,	,	PUNCT
ejpam-1845	134	75	ϕm	ϕm	X
ejpam-1845	134	76	�	�	PROPN
ejpam-1845	135	1	≈	≈	PROPN
ejpam-1845	135	2	0	0	NUM
ejpam-1845	135	3	to	to	PART
ejpam-1845	135	4	derive	derive	VERB
ejpam-1845	135	5	this	this	DET
ejpam-1845	135	6	finite	finite	ADJ
ejpam-1845	135	7	difference	difference	NOUN
ejpam-1845	135	8	equation	equation	NOUN
ejpam-1845	135	9	in	in	ADP
ejpam-1845	135	10	canonical	canonical	ADJ
ejpam-1845	135	11	form	form	NOUN
ejpam-1845	135	12	we	we	PRON
ejpam-1845	135	13	use	use	VERB
ejpam-1845	135	14	the	the	DET
ejpam-1845	135	15	standard	standard	ADJ
ejpam-1845	135	16	definitions	definition	NOUN
ejpam-1845	135	17	yr,1	yr,1	PROPN
ejpam-1845	135	18	m	m	VERB
ejpam-1845	135	19	:	:	PUNCT
ejpam-1845	135	20	=	=	SYM
ejpam-1845	135	21	1	1	NUM
ejpam-1845	135	22	hr	hr	NOUN
ejpam-1845	136	1	[	[	X
ejpam-1845	136	2	y(r1	y(r1	X
ejpam-1845	136	3	+	+	CCONJ
ejpam-1845	136	4	hr	hr	PROPN
ejpam-1845	136	5	,	,	PUNCT
ejpam-1845	136	6	ϕm)−	ϕm)−	PROPN
ejpam-1845	136	7	y(r1,ϕm	y(r1,ϕm	PROPN
ejpam-1845	136	8	)	)	PUNCT
ejpam-1845	136	9	]	]	PUNCT
ejpam-1845	136	10	,	,	PUNCT
ejpam-1845	136	11	yϕ,1	yϕ,1	PROPN
ejpam-1845	136	12	m	m	VERB
ejpam-1845	136	13	:	:	PUNCT
ejpam-1845	136	14	=	=	SYM
ejpam-1845	136	15	1	1	NUM
ejpam-1845	136	16	hϕ	hϕ	NOUN
ejpam-1845	137	1	[	[	X
ejpam-1845	137	2	y(r1,ϕm)−	y(r1,ϕm)−	NOUN
ejpam-1845	137	3	y(r1,ϕm−1	y(r1,ϕm−1	PROPN
ejpam-1845	137	4	)	)	PUNCT
ejpam-1845	137	5	]	]	X
ejpam-1845	137	6	,	,	PUNCT
ejpam-1845	137	7	yϕ,1	yϕ,1	PROPN
ejpam-1845	137	8	m	m	VERB
ejpam-1845	137	9	:	:	PUNCT
ejpam-1845	137	10	=	=	SYM
ejpam-1845	137	11	1	1	NUM
ejpam-1845	137	12	hϕ	hϕ	NOUN
ejpam-1845	137	13	[	[	X
ejpam-1845	137	14	y(r1,ϕm+1)−	y(r1,ϕm+1)−	PROPN
ejpam-1845	137	15	y(r1,ϕm	y(r1,ϕm	PROPN
ejpam-1845	137	16	)	)	PUNCT
ejpam-1845	137	17	]	]	PUNCT
ejpam-1845	137	18	.	.	PUNCT
ejpam-1845	138	1	then	then	ADV
ejpam-1845	138	2	we	we	PRON
ejpam-1845	138	3	have	have	VERB
ejpam-1845	138	4	hrhϕ	hrhϕ	NOUN
ejpam-1845	138	5	yr(r1,ϕm	yr(r1,ϕm	NOUN
ejpam-1845	138	6	)	)	PUNCT
ejpam-1845	139	1	+	+	NUM
ejpam-1845	139	2	2hϕ	2hϕ	ADJ
ejpam-1845	139	3	yϕ,ϕ(r1,ϕm	yϕ,ϕ(r1,ϕm	NOUN
ejpam-1845	139	4	)	)	PUNCT
ejpam-1845	140	1	+	+	NUM
ejpam-1845	140	2	h2	h2	NOUN
ejpam-1845	140	3	rhϕ	rhϕ	VERB
ejpam-1845	140	4	2	2	NUM
ejpam-1845	140	5	f(r1,ϕm	f(r1,ϕm	NUM
ejpam-1845	140	6	)	)	PUNCT
ejpam-1845	140	7	=	=	SYM
ejpam-1845	140	8	0	0	NUM
ejpam-1845	140	9	,	,	PUNCT
ejpam-1845	140	10	m	m	VERB
ejpam-1845	140	11	=	=	NOUN
ejpam-1845	140	12	1,2	1,2	NUM
ejpam-1845	140	13	,	,	PUNCT
ejpam-1845	140	14	.	.	PUNCT
ejpam-1845	140	15	.	.	PUNCT
ejpam-1845	140	16	.	.	PUNCT
ejpam-1845	141	1	,	,	PUNCT
ejpam-1845	141	2	m	m	AUX
ejpam-1845	141	3	dividing	divide	VERB
ejpam-1845	141	4	the	the	DET
ejpam-1845	141	5	both	both	DET
ejpam-1845	141	6	sides	side	NOUN
ejpam-1845	141	7	to	to	ADP
ejpam-1845	141	8	h2	h2	VERB
ejpam-1845	141	9	rhϕ/2	rhϕ/2	X
ejpam-1845	141	10	finally	finally	ADV
ejpam-1845	141	11	we	we	PRON
ejpam-1845	141	12	obtain	obtain	VERB
ejpam-1845	141	13	the	the	DET
ejpam-1845	141	14	finite	finite	ADJ
ejpam-1845	141	15	difference	difference	NOUN
ejpam-1845	141	16	equation	equation	NOUN
ejpam-1845	141	17	corresponding	correspond	VERB
ejpam-1845	141	18	to	to	ADP
ejpam-1845	141	19	the	the	DET
ejpam-1845	141	20	layer	layer	NOUN
ejpam-1845	141	21	r1	r1	NOUN
ejpam-1845	141	22	=	=	SYM
ejpam-1845	141	23	hr/2	hr/2	ADJ
ejpam-1845	141	24	:	:	PUNCT
ejpam-1845	141	25	−	−	PROPN
ejpam-1845	141	26	2	2	NUM
ejpam-1845	141	27	hr	hr	NOUN
ejpam-1845	141	28	yr(r1,ϕm)−	yr(r1,ϕm)−	ADJ
ejpam-1845	141	29	4	4	NUM
ejpam-1845	141	30	h2	h2	NOUN
ejpam-1845	141	31	r	r	NOUN
ejpam-1845	141	32	yϕ,ϕ(r1,ϕm	yϕ,ϕ(r1,ϕm	NOUN
ejpam-1845	141	33	)	)	PUNCT
ejpam-1845	141	34	=	=	SYM
ejpam-1845	141	35	f(r1,ϕm	f(r1,ϕm	NOUN
ejpam-1845	141	36	)	)	PUNCT
ejpam-1845	141	37	=	=	SYM
ejpam-1845	141	38	0	0	NUM
ejpam-1845	141	39	,	,	PUNCT
ejpam-1845	141	40	m=	m=	X
ejpam-1845	141	41	1,2	1,2	NUM
ejpam-1845	141	42	,	,	PUNCT
ejpam-1845	141	43	.	.	PUNCT
ejpam-1845	141	44	.	.	PUNCT
ejpam-1845	142	1	.	.	PUNCT
ejpam-1845	143	1	,	,	PUNCT
ejpam-1845	143	2	m	m	VERB
ejpam-1845	143	3	.	.	PUNCT
ejpam-1845	144	1	(	(	PUNCT
ejpam-1845	144	2	9	9	X
ejpam-1845	144	3	)	)	PUNCT
ejpam-1845	144	4	equations	equation	NOUN
ejpam-1845	144	5	(	(	PUNCT
ejpam-1845	144	6	8)-(9	8)-(9	NOUN
ejpam-1845	144	7	)	)	PUNCT
ejpam-1845	144	8	represent	represent	VERB
ejpam-1845	144	9	the	the	DET
ejpam-1845	144	10	finite	finite	ADJ
ejpam-1845	144	11	difference	difference	NOUN
ejpam-1845	144	12	analogue	analogue	NOUN
ejpam-1845	144	13	of	of	ADP
ejpam-1845	144	14	the	the	DET
ejpam-1845	144	15	poisson	poisson	NOUN
ejpam-1845	144	16	equation	equation	NOUN
ejpam-1845	144	17	(	(	PUNCT
ejpam-1845	144	18	1	1	NUM
ejpam-1845	144	19	)	)	PUNCT
ejpam-1845	144	20	in	in	ADP
ejpam-1845	144	21	the	the	DET
ejpam-1845	144	22	constructed	construct	VERB
ejpam-1845	144	23	polar	polar	ADJ
ejpam-1845	144	24	mesh	mesh	NOUN
ejpam-1845	144	25	ωrϕ.	ωrϕ.	NOUN
ejpam-1845	144	26	lemma	lemma	PROPN
ejpam-1845	144	27	1	1	NUM
ejpam-1845	144	28	.	.	PUNCT
ejpam-1845	145	1	if	if	SCONJ
ejpam-1845	145	2	u	u	PROPN
ejpam-1845	145	3	∈	∈	PROPN
ejpam-1845	145	4	c4(ωrβ	c4(ωrβ	PROPN
ejpam-1845	145	5	)	)	PUNCT
ejpam-1845	145	6	then	then	ADV
ejpam-1845	145	7	the	the	DET
ejpam-1845	145	8	order	order	NOUN
ejpam-1845	145	9	of	of	ADP
ejpam-1845	145	10	the	the	DET
ejpam-1845	145	11	approximation	approximation	NOUN
ejpam-1845	145	12	error	error	NOUN
ejpam-1845	145	13	of	of	ADP
ejpam-1845	145	14	the	the	DET
ejpam-1845	145	15	finite	finite	ADJ
ejpam-1845	145	16	difference	difference	NOUN
ejpam-1845	145	17	schemes	scheme	NOUN
ejpam-1845	145	18	(	(	PUNCT
ejpam-1845	145	19	8)-(9	8)-(9	NOUN
ejpam-1845	145	20	)	)	PUNCT
ejpam-1845	145	21	in	in	ADP
ejpam-1845	145	22	c	c	NOUN
ejpam-1845	145	23	-	-	PUNCT
ejpam-1845	145	24	norm	norm	NOUN
ejpam-1845	145	25	is	be	AUX
ejpam-1845	145	26	ψrϕ	ψrϕ	VERB
ejpam-1845	145	27	:	:	PUNCT
ejpam-1845	145	28	ψrϕ	ψrϕ	VERB
ejpam-1845	145	29	=	=	SYM
ejpam-1845	145	30	o	o	X
ejpam-1845	145	31	�	�	PROPN
ejpam-1845	145	32	(	(	PUNCT
ejpam-1845	145	33	h2	h2	NOUN
ejpam-1845	145	34	r	r	NOUN
ejpam-1845	145	35	+	+	CCONJ
ejpam-1845	145	36	h2	h2	PROPN
ejpam-1845	145	37	ϕ)/rn	ϕ)/rn	PROPN
ejpam-1845	145	38	�	�	PROPN
ejpam-1845	145	39	,	,	PUNCT
ejpam-1845	145	40	where	where	SCONJ
ejpam-1845	145	41	ψrϕ	ψrϕ	NOUN
ejpam-1845	145	42	=	=	SYM
ejpam-1845	145	43	h2	h2	NOUN
ejpam-1845	145	44	r	r	NOUN
ejpam-1845	145	45	6rm	6rm	NOUN
ejpam-1845	145	46			NOUN
ejpam-1845	145	47	∂	∂	VERB
ejpam-1845	145	48	3u	3u	PROPN
ejpam-1845	145	49	∂	∂	NUM
ejpam-1845	145	50	r3	r3	PROPN
ejpam-1845	145	51	+	+	CCONJ
ejpam-1845	145	52	rn	rn	PROPN
ejpam-1845	145	53	+	+	PROPN
ejpam-1845	145	54	hr/2	hr/2	ADJ
ejpam-1845	145	55	4	4	NUM
ejpam-1845	145	56	∂	∂	NUM
ejpam-1845	145	57	4u(ern,ϕm	4u(ern,ϕm	NUM
ejpam-1845	145	58	)	)	PUNCT
ejpam-1845	145	59	∂	∂	PUNCT
ejpam-1845	146	1	r4	r4	NOUN
ejpam-1845	146	2	+	+	CCONJ
ejpam-1845	146	3	rn−	rn−	PRON
ejpam-1845	146	4	hr/2	hr/2	ADJ
ejpam-1845	146	5	4	4	NUM
ejpam-1845	146	6	∂	∂	NUM
ejpam-1845	146	7	4u(eern,ϕ	4u(eern,ϕ	NUM
ejpam-1845	146	8	)	)	PUNCT
ejpam-1845	146	9	∂	∂	NOUN
ejpam-1845	146	10	r4	r4	NOUN
ejpam-1845	146	11			PROPN
ejpam-1845	146	12	+	+	NUM
ejpam-1845	146	13	h2	h2	PROPN
ejpam-1845	146	14	ϕ	ϕ	PROPN
ejpam-1845	146	15	12rm	12rm	PROPN
ejpam-1845	146	16	∂	∂	PROPN
ejpam-1845	146	17	4u(rn	4u(rn	NUM
ejpam-1845	146	18	,	,	PUNCT
ejpam-1845	146	19	eϕm	eϕm	PROPN
ejpam-1845	146	20	)	)	PUNCT
ejpam-1845	146	21	∂	∂	NUM
ejpam-1845	146	22	ϕ4	ϕ4	NOUN
ejpam-1845	146	23	.	.	PUNCT
ejpam-1845	147	1	(	(	PUNCT
ejpam-1845	147	2	10	10	NUM
ejpam-1845	147	3	)	)	PUNCT
ejpam-1845	147	4	the	the	DET
ejpam-1845	147	5	explicit	explicit	ADJ
ejpam-1845	147	6	form	form	NOUN
ejpam-1845	147	7	(	(	PUNCT
ejpam-1845	147	8	10	10	NUM
ejpam-1845	147	9	)	)	PUNCT
ejpam-1845	147	10	of	of	ADP
ejpam-1845	147	11	ψ(hr	ψ(hr	NOUN
ejpam-1845	147	12	,	,	PUNCT
ejpam-1845	147	13	ϕm	ϕm	X
ejpam-1845	147	14	)	)	PUNCT
ejpam-1845	147	15	and	and	CCONJ
ejpam-1845	147	16	the	the	DET
ejpam-1845	147	17	proof	proof	NOUN
ejpam-1845	147	18	of	of	ADP
ejpam-1845	147	19	this	this	DET
ejpam-1845	147	20	result	result	NOUN
ejpam-1845	147	21	is	be	AUX
ejpam-1845	147	22	given	give	VERB
ejpam-1845	147	23	in	in	ADP
ejpam-1845	147	24	[	[	PUNCT
ejpam-1845	147	25	11	11	NUM
ejpam-1845	147	26	]	]	PUNCT
ejpam-1845	147	27	.	.	PUNCT
ejpam-1845	148	1	the	the	DET
ejpam-1845	148	2	lemma	lemma	PROPN
ejpam-1845	148	3	shows	show	VERB
ejpam-1845	148	4	that	that	SCONJ
ejpam-1845	148	5	as	as	SCONJ
ejpam-1845	148	6	r	r	PROPN
ejpam-1845	148	7	→	→	SYM
ejpam-1845	148	8	r1	r1	NOUN
ejpam-1845	148	9	the	the	DET
ejpam-1845	148	10	function	function	NOUN
ejpam-1845	148	11	ψrϕ	ψrϕ	NOUN
ejpam-1845	148	12	increases	increase	NOUN
ejpam-1845	148	13	,	,	PUNCT
ejpam-1845	148	14	and	and	CCONJ
ejpam-1845	148	15	at	at	ADP
ejpam-1845	148	16	the	the	DET
ejpam-1845	148	17	first	first	ADJ
ejpam-1845	148	18	layer	layer	NOUN
ejpam-1845	148	19	r	r	NOUN
ejpam-1845	148	20	=	=	SYM
ejpam-1845	148	21	r1	r1	PROPN
ejpam-1845	148	22	(	(	PUNCT
ejpam-1845	148	23	r1	r1	PROPN
ejpam-1845	148	24	=	=	SYM
ejpam-1845	148	25	hr/2	hr/2	ADJ
ejpam-1845	148	26	)	)	PUNCT
ejpam-1845	148	27	becomes	become	VERB
ejpam-1845	148	28	ψrϕ	ψrϕ	NOUN
ejpam-1845	148	29	=	=	SYM
ejpam-1845	148	30	o(hr	o(hr	NUM
ejpam-1845	148	31	+	+	CCONJ
ejpam-1845	148	32	h2	h2	PROPN
ejpam-1845	148	33	ϕ/hr	ϕ/hr	PROPN
ejpam-1845	148	34	)	)	PUNCT
ejpam-1845	148	35	.	.	PUNCT
ejpam-1845	149	1	note	note	VERB
ejpam-1845	149	2	that	that	SCONJ
ejpam-1845	149	3	the	the	DET
ejpam-1845	149	4	boundedness	boundedness	NOUN
ejpam-1845	149	5	condition	condition	NOUN
ejpam-1845	149	6	(	(	PUNCT
ejpam-1845	149	7	2	2	X
ejpam-1845	149	8	)	)	PUNCT
ejpam-1845	149	9	is	be	AUX
ejpam-1845	149	10	necessary	necessary	ADJ
ejpam-1845	149	11	for	for	ADP
ejpam-1845	149	12	the	the	DET
ejpam-1845	149	13	above	above	ADJ
ejpam-1845	149	14	approximation	approximation	NOUN
ejpam-1845	149	15	,	,	PUNCT
ejpam-1845	149	16	and	and	CCONJ
ejpam-1845	149	17	hence	hence	ADV
ejpam-1845	149	18	for	for	ADP
ejpam-1845	149	19	the	the	DET
ejpam-1845	149	20	convergence	convergence	NOUN
ejpam-1845	149	21	of	of	ADP
ejpam-1845	149	22	the	the	DET
ejpam-1845	149	23	finite	finite	ADJ
ejpam-1845	149	24	difference	difference	NOUN
ejpam-1845	149	25	schemes	scheme	NOUN
ejpam-1845	149	26	(	(	PUNCT
ejpam-1845	149	27	8)-(9	8)-(9	NUM
ejpam-1845	149	28	)	)	PUNCT
ejpam-1845	149	29	,	,	PUNCT
ejpam-1845	149	30	although	although	SCONJ
ejpam-1845	149	31	this	this	DET
ejpam-1845	149	32	condition	condition	NOUN
ejpam-1845	149	33	is	be	AUX
ejpam-1845	149	34	not	not	PART
ejpam-1845	149	35	used	use	VERB
ejpam-1845	149	36	explicitly	explicitly	ADV
ejpam-1845	149	37	on	on	ADP
ejpam-1845	149	38	deriving	derive	VERB
ejpam-1845	149	39	the	the	DET
ejpam-1845	149	40	approximation	approximation	NOUN
ejpam-1845	149	41	error	error	NOUN
ejpam-1845	149	42	.	.	PUNCT
ejpam-1845	150	1	to	to	PART
ejpam-1845	150	2	show	show	VERB
ejpam-1845	150	3	this	this	PRON
ejpam-1845	150	4	,	,	PUNCT
ejpam-1845	150	5	consider	consider	VERB
ejpam-1845	150	6	the	the	DET
ejpam-1845	150	7	following	following	NOUN
ejpam-1845	150	8	:	:	PUNCT
ejpam-1845	150	9	example	example	NOUN
ejpam-1845	151	1	3	3	X
ejpam-1845	151	2	.	.	PUNCT
ejpam-1845	152	1	the	the	DET
ejpam-1845	152	2	function	function	NOUN
ejpam-1845	152	3	u(r,ϕ	u(r,ϕ	ADV
ejpam-1845	152	4	)	)	PUNCT
ejpam-1845	153	1	=	=	PUNCT
ejpam-1845	153	2	ln	ln	ADJ
ejpam-1845	153	3	1	1	NUM
ejpam-1845	153	4	r	r	NOUN
ejpam-1845	153	5	sinϕ	sinϕ	NOUN
ejpam-1845	153	6	,	,	PUNCT
ejpam-1845	153	7	(	(	PUNCT
ejpam-1845	153	8	r,ϕ	r,ϕ	NOUN
ejpam-1845	153	9	)	)	PUNCT
ejpam-1845	153	10	∈	∈	PROPN
ejpam-1845	153	11	ωr,ϕ	ωr,ϕ	PUNCT
ejpam-1845	153	12	,	,	PUNCT
ejpam-1845	153	13	a.	a.	NOUN
ejpam-1845	153	14	erdem	erdem	PROPN
ejpam-1845	153	15	/	/	SYM
ejpam-1845	153	16	eur	eur	PROPN
ejpam-1845	153	17	.	.	PUNCT
ejpam-1845	154	1	j.	j.	PROPN
ejpam-1845	154	2	pure	pure	PROPN
ejpam-1845	154	3	appl	appl	PROPN
ejpam-1845	154	4	.	.	PROPN
ejpam-1845	154	5	math	math	PROPN
ejpam-1845	154	6	,	,	PUNCT
ejpam-1845	154	7	6	6	NUM
ejpam-1845	154	8	(	(	PUNCT
ejpam-1845	154	9	2013	2013	NUM
ejpam-1845	154	10	)	)	PUNCT
ejpam-1845	154	11	,	,	PUNCT
ejpam-1845	154	12	30	30	NUM
ejpam-1845	154	13	-	-	SYM
ejpam-1845	154	14	43	43	NUM
ejpam-1845	154	15	37	37	NUM
ejpam-1845	154	16	satisfies	satisfy	VERB
ejpam-1845	154	17	the	the	DET
ejpam-1845	154	18	poisson	poisson	NOUN
ejpam-1845	154	19	equation	equation	NOUN
ejpam-1845	154	20	(	(	PUNCT
ejpam-1845	154	21	1	1	NUM
ejpam-1845	154	22	)	)	PUNCT
ejpam-1845	154	23	in	in	ADP
ejpam-1845	154	24	ωrβ	ωrβ	PROPN
ejpam-1845	154	25	,	,	PUNCT
ejpam-1845	154	26	with	with	ADP
ejpam-1845	154	27	for	for	ADP
ejpam-1845	154	28	r	r	NOUN
ejpam-1845	154	29	=	=	SYM
ejpam-1845	154	30	1	1	NUM
ejpam-1845	154	31	,	,	PUNCT
ejpam-1845	154	32	β	β	X
ejpam-1845	154	33	=	=	PUNCT
ejpam-1845	154	34	2π	2π	NOUN
ejpam-1845	154	35	,	,	PUNCT
ejpam-1845	154	36	and	and	CCONJ
ejpam-1845	154	37	the	the	DET
ejpam-1845	154	38	right	right	ADJ
ejpam-1845	154	39	hand	hand	NOUN
ejpam-1845	154	40	side	side	NOUN
ejpam-1845	154	41	f(r,ϕ	f(r,ϕ	NOUN
ejpam-1845	154	42	)	)	PUNCT
ejpam-1845	154	43	=	=	SYM
ejpam-1845	154	44	1	1	NUM
ejpam-1845	154	45	r2	r2	NOUN
ejpam-1845	154	46	sinϕ.	sinϕ.	VERB
ejpam-1845	154	47	evidently	evidently	ADV
ejpam-1845	154	48	this	this	DET
ejpam-1845	154	49	solution	solution	NOUN
ejpam-1845	154	50	also	also	ADV
ejpam-1845	154	51	satisfies	satisfy	VERB
ejpam-1845	154	52	the	the	DET
ejpam-1845	154	53	boundary	boundary	ADJ
ejpam-1845	154	54	and	and	CCONJ
ejpam-1845	154	55	periodicity	periodicity	NOUN
ejpam-1845	154	56	conditions	condition	NOUN
ejpam-1845	154	57	(	(	PUNCT
ejpam-1845	154	58	1	1	NUM
ejpam-1845	154	59	)	)	PUNCT
ejpam-1845	154	60	,	,	PUNCT
ejpam-1845	154	61	but	but	CCONJ
ejpam-1845	154	62	does	do	AUX
ejpam-1845	154	63	not	not	PART
ejpam-1845	154	64	satisfy	satisfy	VERB
ejpam-1845	154	65	the	the	DET
ejpam-1845	154	66	boundedness	boundedness	NOUN
ejpam-1845	154	67	condition	condition	NOUN
ejpam-1845	154	68	(	(	PUNCT
ejpam-1845	154	69	2	2	NUM
ejpam-1845	154	70	)	)	PUNCT
ejpam-1845	154	71	,	,	PUNCT
ejpam-1845	154	72	since	since	SCONJ
ejpam-1845	154	73	r∂	r∂	PROPN
ejpam-1845	154	74	u/∂	u/∂	PROPN
ejpam-1845	154	75	r	r	NOUN
ejpam-1845	154	76	=	=	PUNCT
ejpam-1845	154	77	sinϕ	sinϕ	NOUN
ejpam-1845	154	78	6→	6→	NUM
ejpam-1845	154	79	0	0	NUM
ejpam-1845	154	80	,	,	PUNCT
ejpam-1845	154	81	as	as	ADP
ejpam-1845	154	82	r	r	NOUN
ejpam-1845	154	83	→	→	SYM
ejpam-1845	154	84	0	0	NUM
ejpam-1845	154	85	.	.	PUNCT
ejpam-1845	154	86	calculating	calculate	VERB
ejpam-1845	154	87	the	the	DET
ejpam-1845	154	88	right	right	ADJ
ejpam-1845	154	89	hand	hand	NOUN
ejpam-1845	154	90	side	side	NOUN
ejpam-1845	154	91	of	of	ADP
ejpam-1845	154	92	(	(	PUNCT
ejpam-1845	154	93	10	10	NUM
ejpam-1845	154	94	)	)	PUNCT
ejpam-1845	154	95	for	for	ADP
ejpam-1845	154	96	n=	n=	ADJ
ejpam-1845	154	97	1	1	NUM
ejpam-1845	154	98	we	we	PRON
ejpam-1845	154	99	obviously	obviously	ADV
ejpam-1845	154	100	observe	observe	VERB
ejpam-1845	154	101	that	that	SCONJ
ejpam-1845	154	102	for	for	ADP
ejpam-1845	154	103	r	r	NOUN
ejpam-1845	154	104	=	=	SYM
ejpam-1845	154	105	r1	r1	PROPN
ejpam-1845	154	106	ψ(r1,ϕm	ψ(r1,ϕm	PUNCT
ejpam-1845	154	107	)	)	PUNCT
ejpam-1845	155	1	=	=	SYM
ejpam-1845	155	2	h2	h2	PROPN
ejpam-1845	155	3	ϕ	ϕ	PROPN
ejpam-1845	155	4	12r3	12r3	NUM
ejpam-1845	155	5	1	1	NUM
ejpam-1845	155	6	sinϕm	sinϕm	NOUN
ejpam-1845	155	7	.	.	PUNCT
ejpam-1845	156	1	this	this	PRON
ejpam-1845	156	2	shows	show	VERB
ejpam-1845	156	3	that	that	SCONJ
ejpam-1845	156	4	ψ(r1,ϕm	ψ(r1,ϕm	PUNCT
ejpam-1845	156	5	)	)	PUNCT
ejpam-1845	156	6	6→	6→	NUM
ejpam-1845	156	7	0	0	NUM
ejpam-1845	156	8	,	,	PUNCT
ejpam-1845	156	9	as	as	ADP
ejpam-1845	156	10	r1→	r1→	NOUN
ejpam-1845	156	11	0	0	NUM
ejpam-1845	156	12	,	,	PUNCT
ejpam-1845	156	13	and	and	CCONJ
ejpam-1845	156	14	there	there	PRON
ejpam-1845	156	15	is	be	VERB
ejpam-1845	156	16	no	no	DET
ejpam-1845	156	17	approximation	approximation	NOUN
ejpam-1845	156	18	in	in	ADP
ejpam-1845	156	19	the	the	DET
ejpam-1845	156	20	neighbourhood	neighbourhood	NOUN
ejpam-1845	156	21	of	of	ADP
ejpam-1845	156	22	the	the	DET
ejpam-1845	156	23	pole	pole	NOUN
ejpam-1845	156	24	point	point	NOUN
ejpam-1845	156	25	r	r	NOUN
ejpam-1845	156	26	=	=	SYM
ejpam-1845	156	27	0	0	NUM
ejpam-1845	156	28	.	.	PUNCT
ejpam-1845	156	29	to	to	PART
ejpam-1845	156	30	formulate	formulate	VERB
ejpam-1845	156	31	the	the	DET
ejpam-1845	156	32	discrete	discrete	ADJ
ejpam-1845	156	33	problem	problem	NOUN
ejpam-1845	156	34	we	we	PRON
ejpam-1845	156	35	need	need	VERB
ejpam-1845	156	36	to	to	PART
ejpam-1845	156	37	add	add	VERB
ejpam-1845	156	38	to	to	ADP
ejpam-1845	156	39	equations	equation	NOUN
ejpam-1845	156	40	(	(	PUNCT
ejpam-1845	156	41	8)-(9	8)-(9	NUM
ejpam-1845	156	42	)	)	PUNCT
ejpam-1845	156	43	,	,	PUNCT
ejpam-1845	156	44	the	the	DET
ejpam-1845	156	45	equations	equation	NOUN
ejpam-1845	156	46	,	,	PUNCT
ejpam-1845	156	47	obtained	obtain	VERB
ejpam-1845	156	48	from	from	ADP
ejpam-1845	156	49	the	the	DET
ejpam-1845	156	50	periodicity	periodicity	NOUN
ejpam-1845	156	51	condition	condition	NOUN
ejpam-1845	156	52	(	(	PUNCT
ejpam-1845	156	53	1	1	NUM
ejpam-1845	156	54	)	)	PUNCT
ejpam-1845	156	55	.	.	PUNCT
ejpam-1845	157	1	4	4	X
ejpam-1845	157	2	.	.	X
ejpam-1845	157	3	the	the	DET
ejpam-1845	157	4	algebraic	algebraic	ADJ
ejpam-1845	157	5	problem	problem	NOUN
ejpam-1845	157	6	with	with	ADP
ejpam-1845	157	7	nonsymmetric	nonsymmetric	ADJ
ejpam-1845	157	8	sparse	sparse	ADJ
ejpam-1845	157	9	matrix	matrix	NOUN
ejpam-1845	157	10	:	:	PUNCT
ejpam-1845	157	11	iteration	iteration	NOUN
ejpam-1845	157	12	algorithm	algorithm	NOUN
ejpam-1845	157	13	the	the	DET
ejpam-1845	157	14	finite	finite	ADJ
ejpam-1845	157	15	difference	difference	NOUN
ejpam-1845	157	16	equations	equation	NOUN
ejpam-1845	157	17	(	(	PUNCT
ejpam-1845	157	18	8)-(9	8)-(9	NOUN
ejpam-1845	157	19	)	)	PUNCT
ejpam-1845	157	20	compose	compose	VERB
ejpam-1845	157	21	k	k	NOUN
ejpam-1845	157	22	:	:	PUNCT
ejpam-1845	157	23	=	=	NOUN
ejpam-1845	157	24	n	n	CCONJ
ejpam-1845	157	25	m	m	VERB
ejpam-1845	157	26	number	number	NOUN
ejpam-1845	157	27	of	of	ADP
ejpam-1845	157	28	algebraic	algebraic	ADJ
ejpam-1845	157	29	equations	equation	NOUN
ejpam-1845	157	30	with	with	ADP
ejpam-1845	157	31	k	k	PROPN
ejpam-1845	157	32	unknowns	unknowns	PROPN
ejpam-1845	157	33	y	y	PROPN
ejpam-1845	157	34	=	=	SYM
ejpam-1845	157	35	(	(	PUNCT
ejpam-1845	157	36	y11	y11	NOUN
ejpam-1845	157	37	,	,	PUNCT
ejpam-1845	157	38	y12	y12	PROPN
ejpam-1845	157	39	,	,	PUNCT
ejpam-1845	157	40	.	.	PUNCT
ejpam-1845	157	41	.	.	PUNCT
ejpam-1845	158	1	.	.	PUNCT
ejpam-1845	159	1	,	,	PUNCT
ejpam-1845	159	2	y1	y1	NOUN
ejpam-1845	159	3	m	m	PROPN
ejpam-1845	159	4	,	,	PUNCT
ejpam-1845	159	5	y21	y21	PROPN
ejpam-1845	159	6	,	,	PUNCT
ejpam-1845	159	7	.	.	PUNCT
ejpam-1845	159	8	.	.	PUNCT
ejpam-1845	160	1	.	.	PUNCT
ejpam-1845	161	1	,	,	PUNCT
ejpam-1845	161	2	yn	yn	PROPN
ejpam-1845	161	3	m	m	PROPN
ejpam-1845	161	4	)	)	PUNCT
ejpam-1845	161	5	t	t	NOUN
ejpam-1845	161	6	,	,	PUNCT
ejpam-1845	161	7	dim	dim	ADJ
ejpam-1845	161	8	y	y	NOUN
ejpam-1845	161	9	=	=	SYM
ejpam-1845	161	10	k	k	PROPN
ejpam-1845	161	11	.	.	PUNCT
ejpam-1845	162	1	we	we	PRON
ejpam-1845	162	2	can	can	AUX
ejpam-1845	162	3	rewrite	rewrite	VERB
ejpam-1845	162	4	these	these	DET
ejpam-1845	162	5	equations	equation	NOUN
ejpam-1845	162	6	in	in	ADP
ejpam-1845	162	7	the	the	DET
ejpam-1845	162	8	form	form	NOUN
ejpam-1845	162	9	of	of	ADP
ejpam-1845	162	10	the	the	DET
ejpam-1845	162	11	system	system	NOUN
ejpam-1845	162	12	of	of	ADP
ejpam-1845	162	13	linear	linear	PROPN
ejpam-1845	162	14	algebraic	algebraic	ADJ
ejpam-1845	162	15	equations	equation	NOUN
ejpam-1845	162	16	a	a	DET
ejpam-1845	162	17	y	y	PROPN
ejpam-1845	162	18	=	=	SYM
ejpam-1845	162	19	f	f	PROPN
ejpam-1845	162	20	with	with	ADP
ejpam-1845	162	21	the	the	DET
ejpam-1845	162	22	following	follow	VERB
ejpam-1845	162	23	positive	positive	ADJ
ejpam-1845	162	24	band	band	NOUN
ejpam-1845	162	25	matrix	matrix	NOUN
ejpam-1845	162	26	a	a	PRON
ejpam-1845	162	27	,	,	PUNCT
ejpam-1845	162	28	dima	dima	PROPN
ejpam-1845	163	1	=	=	SYM
ejpam-1845	163	2	k	k	PROPN
ejpam-1845	163	3	×	×	PROPN
ejpam-1845	163	4	k	k	NOUN
ejpam-1845	163	5	:	:	PUNCT
ejpam-1845	163	6	a	a	PRON
ejpam-1845	163	7	:	:	PUNCT
ejpam-1845	163	8	=	=	NOUN
ejpam-1845	163	9			PROPN
ejpam-1845	163	10			NOUN
ejpam-1845	163	11	a11	a11	PROPN
ejpam-1845	163	12	a12	a12	NOUN
ejpam-1845	163	13	0	0	NUM
ejpam-1845	163	14	0	0	NUM
ejpam-1845	163	15	.	.	PUNCT
ejpam-1845	163	16	.	.	PUNCT
ejpam-1845	164	1	.	.	PUNCT
ejpam-1845	165	1	0	0	NUM
ejpam-1845	165	2	0	0	NUM
ejpam-1845	165	3	0	0	NUM
ejpam-1845	165	4	a21	a21	PROPN
ejpam-1845	165	5	a22	a22	PROPN
ejpam-1845	165	6	a23	a23	PROPN
ejpam-1845	165	7	0	0	PROPN
ejpam-1845	165	8	.	.	PUNCT
ejpam-1845	165	9	.	.	PUNCT
ejpam-1845	165	10	.	.	PUNCT
ejpam-1845	166	1	0	0	NUM
ejpam-1845	166	2	0	0	NUM
ejpam-1845	166	3	0	0	NUM
ejpam-1845	166	4	0	0	NUM
ejpam-1845	166	5	a32	a32	PROPN
ejpam-1845	166	6	a33	a33	PROPN
ejpam-1845	166	7	a34	a34	NOUN
ejpam-1845	166	8	.	.	PUNCT
ejpam-1845	166	9	.	.	PUNCT
ejpam-1845	166	10	.	.	PUNCT
ejpam-1845	167	1	0	0	NUM
ejpam-1845	168	1	0	0	NUM
ejpam-1845	168	2	0	0	NUM
ejpam-1845	168	3	.	.	PUNCT
ejpam-1845	168	4	.	.	PUNCT
ejpam-1845	168	5	.	.	PUNCT
ejpam-1845	168	6	.	.	PUNCT
ejpam-1845	168	7	.	.	PUNCT
ejpam-1845	168	8	.	.	PUNCT
ejpam-1845	168	9	.	.	PUNCT
ejpam-1845	168	10	.	.	PUNCT
ejpam-1845	168	11	.	.	PUNCT
ejpam-1845	168	12	.	.	PUNCT
ejpam-1845	168	13	.	.	PUNCT
ejpam-1845	168	14	.	.	PUNCT
ejpam-1845	168	15	.	.	PUNCT
ejpam-1845	168	16	.	.	PUNCT
ejpam-1845	168	17	.	.	PUNCT
ejpam-1845	168	18	.	.	PUNCT
ejpam-1845	168	19	.	.	PUNCT
ejpam-1845	168	20	.	.	PUNCT
ejpam-1845	168	21	.	.	PUNCT
ejpam-1845	168	22	.	.	PUNCT
ejpam-1845	168	23	.	.	PUNCT
ejpam-1845	168	24	.	.	PUNCT
ejpam-1845	168	25	.	.	PUNCT
ejpam-1845	169	1	.	.	PUNCT
ejpam-1845	170	1	0	0	NUM
ejpam-1845	171	1	0	0	NUM
ejpam-1845	171	2	0	0	NUM
ejpam-1845	171	3	0	0	NUM
ejpam-1845	171	4	.	.	PUNCT
ejpam-1845	171	5	.	.	PUNCT
ejpam-1845	171	6	.	.	PUNCT
ejpam-1845	172	1	an−1,n−2	an−1,n−2	PROPN
ejpam-1845	172	2	an−1,n−1	an−1,n−1	PROPN
ejpam-1845	172	3	an−1,n	an−1,n	PROPN
ejpam-1845	172	4	0	0	PUNCT
ejpam-1845	172	5	0	0	NUM
ejpam-1845	172	6	0	0	NUM
ejpam-1845	172	7	0	0	NUM
ejpam-1845	172	8	.	.	PUNCT
ejpam-1845	172	9	.	.	PUNCT
ejpam-1845	173	1	.	.	PUNCT
ejpam-1845	173	2	0	0	PUNCT
ejpam-1845	174	1	an	an	DET
ejpam-1845	174	2	,	,	PUNCT
ejpam-1845	174	3	n−1	n−1	PROPN
ejpam-1845	174	4	an	an	PRON
ejpam-1845	174	5	,	,	PUNCT
ejpam-1845	174	6	n	n	PROPN
ejpam-1845	174	7			PROPN
ejpam-1845	174	8			NOUN
ejpam-1845	174	9	.	.	PUNCT
ejpam-1845	175	1	here	here	ADV
ejpam-1845	175	2	m	m	VERB
ejpam-1845	175	3	×m	×m	NOUN
ejpam-1845	175	4	-dimensional	-dimensional	ADJ
ejpam-1845	175	5	block	block	NOUN
ejpam-1845	175	6	matrices	matrix	NOUN
ejpam-1845	175	7	ai	ai	VERB
ejpam-1845	175	8	j	j	PROPN
ejpam-1845	175	9	are	be	AUX
ejpam-1845	175	10	of	of	ADP
ejpam-1845	175	11	the	the	DET
ejpam-1845	175	12	following	follow	VERB
ejpam-1845	175	13	structure	structure	NOUN
ejpam-1845	175	14	:	:	PUNCT
ejpam-1845	175	15	aii	aii	PROPN
ejpam-1845	175	16	=	=	PUNCT
ejpam-1845	175	17			PROPN
ejpam-1845	175	18			NOUN
ejpam-1845	175	19	•	•	NOUN
ejpam-1845	175	20	•	•	NOUN
ejpam-1845	175	21	0	0	NUM
ejpam-1845	175	22	0	0	NUM
ejpam-1845	175	23	.	.	PUNCT
ejpam-1845	175	24	.	.	PUNCT
ejpam-1845	176	1	.	.	PUNCT
ejpam-1845	177	1	0	0	NUM
ejpam-1845	177	2	0	0	NUM
ejpam-1845	178	1	•	•	NUM
ejpam-1845	178	2	•	•	NUM
ejpam-1845	178	3	•	•	NOUN
ejpam-1845	178	4	•	•	NOUN
ejpam-1845	178	5	0	0	NUM
ejpam-1845	178	6	.	.	PUNCT
ejpam-1845	178	7	.	.	PUNCT
ejpam-1845	179	1	.	.	PUNCT
ejpam-1845	180	1	0	0	NUM
ejpam-1845	181	1	0	0	NUM
ejpam-1845	181	2	0	0	NUM
ejpam-1845	181	3	0	0	NUM
ejpam-1845	181	4	•	•	NUM
ejpam-1845	181	5	•	•	NOUN
ejpam-1845	181	6	•	•	NOUN
ejpam-1845	181	7	.	.	PUNCT
ejpam-1845	181	8	.	.	PUNCT
ejpam-1845	181	9	.	.	PUNCT
ejpam-1845	182	1	0	0	NUM
ejpam-1845	183	1	0	0	NUM
ejpam-1845	183	2	0	0	NUM
ejpam-1845	183	3	.	.	PUNCT
ejpam-1845	183	4	.	.	PUNCT
ejpam-1845	183	5	.	.	PUNCT
ejpam-1845	183	6	.	.	PUNCT
ejpam-1845	183	7	.	.	PUNCT
ejpam-1845	183	8	.	.	PUNCT
ejpam-1845	183	9	.	.	PUNCT
ejpam-1845	183	10	.	.	PUNCT
ejpam-1845	183	11	.	.	PUNCT
ejpam-1845	183	12	.	.	PUNCT
ejpam-1845	183	13	.	.	PUNCT
ejpam-1845	183	14	.	.	PUNCT
ejpam-1845	183	15	.	.	PUNCT
ejpam-1845	183	16	.	.	PUNCT
ejpam-1845	183	17	.	.	PUNCT
ejpam-1845	183	18	.	.	PUNCT
ejpam-1845	183	19	.	.	PUNCT
ejpam-1845	183	20	.	.	PUNCT
ejpam-1845	183	21	.	.	PUNCT
ejpam-1845	183	22	.	.	PUNCT
ejpam-1845	183	23	.	.	PUNCT
ejpam-1845	183	24	.	.	PUNCT
ejpam-1845	183	25	.	.	PUNCT
ejpam-1845	184	1	.	.	PUNCT
ejpam-1845	185	1	0	0	NUM
ejpam-1845	186	1	0	0	NUM
ejpam-1845	186	2	0	0	NUM
ejpam-1845	186	3	0	0	NUM
ejpam-1845	186	4	.	.	PUNCT
ejpam-1845	186	5	.	.	PUNCT
ejpam-1845	187	1	.	.	PUNCT
ejpam-1845	188	1	•	•	NUM
ejpam-1845	188	2	•	•	NUM
ejpam-1845	188	3	•	•	NUM
ejpam-1845	188	4	•	•	NOUN
ejpam-1845	188	5	0	0	NUM
ejpam-1845	188	6	0	0	NUM
ejpam-1845	188	7	0	0	NUM
ejpam-1845	188	8	.	.	PUNCT
ejpam-1845	188	9	.	.	PUNCT
ejpam-1845	189	1	.	.	PUNCT
ejpam-1845	190	1	0	0	NUM
ejpam-1845	191	1	•	•	NUM
ejpam-1845	191	2	•	•	PRON
ejpam-1845	191	3			PROPN
ejpam-1845	191	4			NOUN
ejpam-1845	191	5	and	and	CCONJ
ejpam-1845	191	6	aii+1	aii+1	NOUN
ejpam-1845	191	7	=	=	SYM
ejpam-1845	191	8	αi	αi	VERB
ejpam-1845	191	9	i	i	PRON
ejpam-1845	191	10	,	,	PUNCT
ejpam-1845	191	11	ai−1i	ai−1i	VERB
ejpam-1845	191	12	=	=	SYM
ejpam-1845	191	13	βi	βi	VERB
ejpam-1845	191	14	i	i	INTJ
ejpam-1845	191	15	.	.	PUNCT
ejpam-1845	192	1	a.	a.	NOUN
ejpam-1845	192	2	erdem	erdem	PROPN
ejpam-1845	192	3	/	/	SYM
ejpam-1845	192	4	eur	eur	PROPN
ejpam-1845	192	5	.	.	PUNCT
ejpam-1845	193	1	j.	j.	PROPN
ejpam-1845	193	2	pure	pure	PROPN
ejpam-1845	193	3	appl	appl	PROPN
ejpam-1845	193	4	.	.	PROPN
ejpam-1845	193	5	math	math	PROPN
ejpam-1845	193	6	,	,	PUNCT
ejpam-1845	193	7	6	6	NUM
ejpam-1845	193	8	(	(	PUNCT
ejpam-1845	193	9	2013	2013	NUM
ejpam-1845	193	10	)	)	PUNCT
ejpam-1845	193	11	,	,	PUNCT
ejpam-1845	193	12	30	30	NUM
ejpam-1845	193	13	-	-	SYM
ejpam-1845	193	14	43	43	NUM
ejpam-1845	193	15	38	38	NUM
ejpam-1845	193	16	the	the	DET
ejpam-1845	193	17	parameters	parameter	NOUN
ejpam-1845	193	18	αi	αi	ADV
ejpam-1845	193	19	and	and	CCONJ
ejpam-1845	193	20	βi	βi	PRON
ejpam-1845	193	21	can	can	AUX
ejpam-1845	193	22	be	be	AUX
ejpam-1845	193	23	defined	define	VERB
ejpam-1845	193	24	from	from	ADP
ejpam-1845	193	25	the	the	DET
ejpam-1845	193	26	finite	finite	ADJ
ejpam-1845	193	27	difference	difference	NOUN
ejpam-1845	193	28	schemes	scheme	NOUN
ejpam-1845	193	29	(	(	PUNCT
ejpam-1845	193	30	8)-(9	8)-(9	NOUN
ejpam-1845	193	31	)	)	PUNCT
ejpam-1845	193	32	as	as	SCONJ
ejpam-1845	193	33	follows	follow	VERB
ejpam-1845	193	34	:	:	PUNCT
ejpam-1845	193	35	α1	α1	PROPN
ejpam-1845	193	36	=	=	SYM
ejpam-1845	193	37	2	2	NUM
ejpam-1845	193	38	h2	h2	NOUN
ejpam-1845	193	39	r	r	NOUN
ejpam-1845	193	40	;	;	PUNCT
ejpam-1845	193	41	αi	αi	NOUN
ejpam-1845	193	42	=	=	SYM
ejpam-1845	193	43	ki	ki	PROPN
ejpam-1845	193	44	rih	rih	VERB
ejpam-1845	193	45	2	2	NUM
ejpam-1845	193	46	r	r	NOUN
ejpam-1845	193	47	,	,	PUNCT
ejpam-1845	193	48	i	i	NOUN
ejpam-1845	193	49	=	=	NOUN
ejpam-1845	193	50	2	2	NUM
ejpam-1845	193	51	,	,	PUNCT
ejpam-1845	193	52	n	n	NOUN
ejpam-1845	193	53	;	;	PUNCT
ejpam-1845	193	54	βi	βi	PROPN
ejpam-1845	193	55	=	=	SYM
ejpam-1845	193	56	ki+1	ki+1	PROPN
ejpam-1845	193	57	rih	rih	VERB
ejpam-1845	193	58	2	2	NUM
ejpam-1845	193	59	r	r	NOUN
ejpam-1845	193	60	,	,	PUNCT
ejpam-1845	193	61	i	i	NOUN
ejpam-1845	193	62	=	=	NOUN
ejpam-1845	193	63	1	1	NUM
ejpam-1845	193	64	,	,	PUNCT
ejpam-1845	193	65	n	n	NOUN
ejpam-1845	193	66	.	.	PUNCT
ejpam-1845	194	1	since	since	SCONJ
ejpam-1845	194	2	αi	αi	PROPN
ejpam-1845	194	3	6=	6=	ADP
ejpam-1845	194	4	βi	βi	PROPN
ejpam-1845	194	5	,	,	PUNCT
ejpam-1845	194	6	the	the	DET
ejpam-1845	194	7	matrix	matrix	NOUN
ejpam-1845	194	8	a	a	PRON
ejpam-1845	194	9	is	be	AUX
ejpam-1845	194	10	not	not	PART
ejpam-1845	194	11	symmetric	symmetric	ADJ
ejpam-1845	194	12	one	one	NUM
ejpam-1845	194	13	.	.	PUNCT
ejpam-1845	195	1	moreover	moreover	ADV
ejpam-1845	195	2	,	,	PUNCT
ejpam-1845	195	3	a	a	PRON
ejpam-1845	195	4	is	be	AUX
ejpam-1845	195	5	a	a	DET
ejpam-1845	195	6	sparse	sparse	ADJ
ejpam-1845	195	7	matrix	matrix	NOUN
ejpam-1845	195	8	of	of	ADP
ejpam-1845	195	9	special	special	ADJ
ejpam-1845	195	10	structure	structure	NOUN
ejpam-1845	195	11	,	,	PUNCT
ejpam-1845	195	12	corresponding	correspond	VERB
ejpam-1845	195	13	to	to	ADP
ejpam-1845	195	14	the	the	DET
ejpam-1845	195	15	polar	polar	ADJ
ejpam-1845	195	16	mesh	mesh	NOUN
ejpam-1845	195	17	and	and	CCONJ
ejpam-1845	195	18	periodicity	periodicity	NOUN
ejpam-1845	195	19	condition	condition	NOUN
ejpam-1845	195	20	.	.	PUNCT
ejpam-1845	196	1	evidently	evidently	ADV
ejpam-1845	196	2	such	such	DET
ejpam-1845	196	3	a	a	DET
ejpam-1845	196	4	system	system	NOUN
ejpam-1845	196	5	of	of	ADP
ejpam-1845	196	6	linear	linear	PROPN
ejpam-1845	196	7	algebraic	algebraic	ADJ
ejpam-1845	196	8	equations	equation	NOUN
ejpam-1845	196	9	with	with	ADP
ejpam-1845	196	10	non	non	ADJ
ejpam-1845	196	11	-	-	ADJ
ejpam-1845	196	12	symmetric	symmetric	ADJ
ejpam-1845	196	13	sparse	sparse	ADJ
ejpam-1845	196	14	matrix	matrix	NOUN
ejpam-1845	196	15	needs	need	VERB
ejpam-1845	196	16	to	to	PART
ejpam-1845	196	17	be	be	AUX
ejpam-1845	196	18	solved	solve	VERB
ejpam-1845	196	19	by	by	ADP
ejpam-1845	196	20	iteration	iteration	NOUN
ejpam-1845	196	21	methods	method	NOUN
ejpam-1845	196	22	[	[	X
ejpam-1845	196	23	12	12	NUM
ejpam-1845	196	24	,	,	PUNCT
ejpam-1845	196	25	13	13	NUM
ejpam-1845	196	26	,	,	PUNCT
ejpam-1845	196	27	14	14	NUM
ejpam-1845	196	28	]	]	PUNCT
ejpam-1845	196	29	.	.	PUNCT
ejpam-1845	197	1	however	however	ADV
ejpam-1845	197	2	,	,	PUNCT
ejpam-1845	197	3	as	as	SCONJ
ejpam-1845	197	4	the	the	DET
ejpam-1845	197	5	computational	computational	ADJ
ejpam-1845	197	6	experiments	experiment	NOUN
ejpam-1845	197	7	below	below	ADP
ejpam-1845	197	8	show	show	NOUN
ejpam-1845	197	9	,	,	PUNCT
ejpam-1845	197	10	use	use	NOUN
ejpam-1845	197	11	of	of	ADP
ejpam-1845	197	12	compact	compact	ADJ
ejpam-1845	197	13	storage	storage	NOUN
ejpam-1845	197	14	for	for	ADP
ejpam-1845	197	15	the	the	DET
ejpam-1845	197	16	band	band	NOUN
ejpam-1845	197	17	matrix	matrix	NOUN
ejpam-1845	197	18	a	a	PRON
ejpam-1845	197	19	and	and	CCONJ
ejpam-1845	197	20	then	then	ADV
ejpam-1845	197	21	an	an	DET
ejpam-1845	197	22	application	application	NOUN
ejpam-1845	197	23	of	of	ADP
ejpam-1845	197	24	any	any	DET
ejpam-1845	197	25	effective	effective	ADJ
ejpam-1845	197	26	iteration	iteration	NOUN
ejpam-1845	197	27	method	method	NOUN
ejpam-1845	197	28	requires	require	VERB
ejpam-1845	197	29	large	large	ADJ
ejpam-1845	197	30	enough	enough	ADJ
ejpam-1845	197	31	time	time	NOUN
ejpam-1845	197	32	for	for	ADP
ejpam-1845	197	33	the	the	DET
ejpam-1845	197	34	solution	solution	NOUN
ejpam-1845	197	35	of	of	ADP
ejpam-1845	197	36	the	the	DET
ejpam-1845	197	37	linear	linear	ADJ
ejpam-1845	197	38	system	system	NOUN
ejpam-1845	197	39	of	of	ADP
ejpam-1845	197	40	algebraic	algebraic	ADJ
ejpam-1845	197	41	equations	equation	NOUN
ejpam-1845	197	42	a	a	DET
ejpam-1845	197	43	y	y	PROPN
ejpam-1845	197	44	=	=	SYM
ejpam-1845	197	45	f	f	PROPN
ejpam-1845	197	46	.	.	PUNCT
ejpam-1845	198	1	the	the	DET
ejpam-1845	198	2	reason	reason	NOUN
ejpam-1845	198	3	is	be	AUX
ejpam-1845	198	4	that	that	SCONJ
ejpam-1845	198	5	the	the	DET
ejpam-1845	198	6	bandwidth	bandwidth	NOUN
ejpam-1845	198	7	of	of	ADP
ejpam-1845	198	8	the	the	DET
ejpam-1845	198	9	non	non	ADJ
ejpam-1845	198	10	-	-	ADJ
ejpam-1845	198	11	symmetric	symmetric	ADJ
ejpam-1845	198	12	matrix	matrix	NOUN
ejpam-1845	198	13	a	a	PRON
ejpam-1845	198	14	is	be	AUX
ejpam-1845	198	15	bw	bw	NOUN
ejpam-1845	198	16	=	=	PUNCT
ejpam-1845	198	17	3	3	NUM
ejpam-1845	198	18	m	m	VERB
ejpam-1845	198	19	and	and	CCONJ
ejpam-1845	198	20	there	there	PRON
ejpam-1845	198	21	are	be	VERB
ejpam-1845	198	22	many	many	ADJ
ejpam-1845	198	23	null	null	ADJ
ejpam-1845	198	24	terms	term	NOUN
ejpam-1845	198	25	in	in	ADP
ejpam-1845	198	26	the	the	DET
ejpam-1845	198	27	band	band	NOUN
ejpam-1845	198	28	.	.	PUNCT
ejpam-1845	199	1	specifically	specifically	ADV
ejpam-1845	199	2	,	,	PUNCT
ejpam-1845	199	3	the	the	DET
ejpam-1845	199	4	above	above	ADJ
ejpam-1845	199	5	block	block	NOUN
ejpam-1845	199	6	matrices	matrix	NOUN
ejpam-1845	199	7	aii	aii	NOUN
ejpam-1845	199	8	,	,	PUNCT
ejpam-1845	199	9	aii+1	aii+1	ADV
ejpam-1845	199	10	,	,	PUNCT
ejpam-1845	199	11	ai−1i	ai−1i	PROPN
ejpam-1845	199	12	contain	contain	VERB
ejpam-1845	199	13	m2	m2	PROPN
ejpam-1845	199	14	−	−	PROPN
ejpam-1845	199	15	3	3	NUM
ejpam-1845	199	16	m	m	NOUN
ejpam-1845	199	17	,	,	PUNCT
ejpam-1845	199	18	m2	m2	PROPN
ejpam-1845	199	19	−m	−m	PROPN
ejpam-1845	199	20	,	,	PUNCT
ejpam-1845	199	21	m2	m2	PROPN
ejpam-1845	199	22	−m	−m	PROPN
ejpam-1845	199	23	zero	zero	NUM
ejpam-1845	199	24	elements	element	NOUN
ejpam-1845	199	25	,	,	PUNCT
ejpam-1845	199	26	correspondingly	correspondingly	ADV
ejpam-1845	199	27	.	.	PUNCT
ejpam-1845	200	1	hence	hence	ADV
ejpam-1845	200	2	for	for	ADP
ejpam-1845	200	3	m	m	NOUN
ejpam-1845	200	4	=	=	SYM
ejpam-1845	200	5	n	n	NUM
ejpam-1845	200	6	the	the	DET
ejpam-1845	200	7	number	number	NOUN
ejpam-1845	200	8	of	of	ADP
ejpam-1845	200	9	zero	zero	NUM
ejpam-1845	200	10	and	and	CCONJ
ejpam-1845	200	11	non	non	ADJ
ejpam-1845	200	12	-	-	ADJ
ejpam-1845	200	13	zero	zero	NUM
ejpam-1845	200	14	elements	element	NOUN
ejpam-1845	200	15	of	of	ADP
ejpam-1845	200	16	the	the	DET
ejpam-1845	200	17	band	band	NOUN
ejpam-1845	200	18	are	be	AUX
ejpam-1845	200	19	3n3	3n3	NUM
ejpam-1845	200	20	−	−	PROPN
ejpam-1845	200	21	4n2	4n2	NUM
ejpam-1845	201	1	−	−	NOUN
ejpam-1845	201	2	4n	4n	NOUN
ejpam-1845	201	3	and	and	CCONJ
ejpam-1845	201	4	5n2	5n2	NUM
ejpam-1845	201	5	+	+	CCONJ
ejpam-1845	201	6	n	n	CCONJ
ejpam-1845	201	7	,	,	PUNCT
ejpam-1845	201	8	respectively	respectively	ADV
ejpam-1845	201	9	.	.	PUNCT
ejpam-1845	202	1	for	for	ADP
ejpam-1845	202	2	the	the	DET
ejpam-1845	202	3	mesh	mesh	NOUN
ejpam-1845	202	4	with	with	ADP
ejpam-1845	202	5	n	n	NOUN
ejpam-1845	202	6	=	=	SYM
ejpam-1845	202	7	30	30	NUM
ejpam-1845	202	8	,	,	PUNCT
ejpam-1845	202	9	this	this	PRON
ejpam-1845	202	10	means	mean	VERB
ejpam-1845	202	11	that	that	SCONJ
ejpam-1845	202	12	the	the	DET
ejpam-1845	202	13	number	number	NOUN
ejpam-1845	202	14	of	of	ADP
ejpam-1845	202	15	non	non	ADJ
ejpam-1845	202	16	-	-	ADJ
ejpam-1845	202	17	zero	zero	NUM
ejpam-1845	202	18	elements	element	NOUN
ejpam-1845	202	19	of	of	ADP
ejpam-1845	202	20	the	the	DET
ejpam-1845	202	21	band	band	NOUN
ejpam-1845	202	22	matrix	matrix	NOUN
ejpam-1845	202	23	a	a	PRON
ejpam-1845	202	24	is	be	AUX
ejpam-1845	202	25	about	about	ADV
ejpam-1845	202	26	4.3	4.3	NUM
ejpam-1845	202	27	%	%	NOUN
ejpam-1845	202	28	of	of	ADP
ejpam-1845	202	29	all	all	DET
ejpam-1845	202	30	band	band	NOUN
ejpam-1845	202	31	elements	element	NOUN
ejpam-1845	202	32	.	.	PUNCT
ejpam-1845	203	1	therefore	therefore	ADV
ejpam-1845	203	2	one	one	NUM
ejpam-1845	203	3	needs	need	VERB
ejpam-1845	203	4	to	to	PART
ejpam-1845	203	5	construct	construct	VERB
ejpam-1845	203	6	a	a	DET
ejpam-1845	203	7	special	special	ADJ
ejpam-1845	203	8	algorithm	algorithm	NOUN
ejpam-1845	203	9	which	which	PRON
ejpam-1845	203	10	can	can	AUX
ejpam-1845	203	11	store	store	VERB
ejpam-1845	203	12	and	and	CCONJ
ejpam-1845	203	13	operate	operate	VERB
ejpam-1845	203	14	with	with	ADP
ejpam-1845	203	15	only	only	ADV
ejpam-1845	203	16	nonzero	nonzero	ADJ
ejpam-1845	203	17	elements	element	NOUN
ejpam-1845	203	18	αi	αi	ADV
ejpam-1845	203	19	and	and	CCONJ
ejpam-1845	203	20	βi	βi	PRON
ejpam-1845	203	21	,	,	PUNCT
ejpam-1845	203	22	realising	realise	VERB
ejpam-1845	203	23	the	the	DET
ejpam-1845	203	24	multiplications	multiplication	NOUN
ejpam-1845	203	25	u	u	X
ejpam-1845	203	26	y	y	PROPN
ejpam-1845	203	27	and	and	CCONJ
ejpam-1845	203	28	ly	ly	VERB
ejpam-1845	203	29	,	,	PUNCT
ejpam-1845	203	30	to	to	PART
ejpam-1845	203	31	minimize	minimize	VERB
ejpam-1845	203	32	the	the	DET
ejpam-1845	203	33	time	time	NOUN
ejpam-1845	203	34	required	require	VERB
ejpam-1845	203	35	for	for	ADP
ejpam-1845	203	36	the	the	DET
ejpam-1845	203	37	solution	solution	NOUN
ejpam-1845	203	38	of	of	ADP
ejpam-1845	203	39	the	the	DET
ejpam-1845	203	40	considered	consider	VERB
ejpam-1845	203	41	problem	problem	NOUN
ejpam-1845	203	42	by	by	ADP
ejpam-1845	203	43	any	any	DET
ejpam-1845	203	44	iteration	iteration	NOUN
ejpam-1845	203	45	method	method	NOUN
ejpam-1845	203	46	.	.	PUNCT
ejpam-1845	204	1	here	here	ADV
ejpam-1845	204	2	the	the	DET
ejpam-1845	204	3	u	u	NOUN
ejpam-1845	204	4	and	and	CCONJ
ejpam-1845	204	5	l	l	NOUN
ejpam-1845	204	6	are	be	AUX
ejpam-1845	204	7	the	the	DET
ejpam-1845	204	8	upper	upper	ADJ
ejpam-1845	204	9	and	and	CCONJ
ejpam-1845	204	10	lower	low	ADJ
ejpam-1845	204	11	triangular	triangular	NOUN
ejpam-1845	204	12	matrices	matrix	NOUN
ejpam-1845	204	13	:	:	PUNCT
ejpam-1845	204	14	a	a	DET
ejpam-1845	204	15	=	=	NOUN
ejpam-1845	204	16	d+u+	d+u+	NOUN
ejpam-1845	204	17	l.	l.	PROPN
ejpam-1845	204	18	note	note	VERB
ejpam-1845	204	19	that	that	SCONJ
ejpam-1845	204	20	for	for	ADP
ejpam-1845	204	21	some	some	DET
ejpam-1845	204	22	class	class	NOUN
ejpam-1845	204	23	of	of	ADP
ejpam-1845	204	24	systems	system	NOUN
ejpam-1845	204	25	,	,	PUNCT
ejpam-1845	204	26	arising	arise	VERB
ejpam-1845	204	27	from	from	ADP
ejpam-1845	204	28	the	the	DET
ejpam-1845	204	29	finite	finite	ADJ
ejpam-1845	204	30	-	-	ADJ
ejpam-1845	204	31	element	element	ADJ
ejpam-1845	204	32	discretization	discretization	NOUN
ejpam-1845	204	33	,	,	PUNCT
ejpam-1845	204	34	similar	similar	ADJ
ejpam-1845	204	35	algorithm	algorithm	NOUN
ejpam-1845	204	36	was	be	AUX
ejpam-1845	204	37	constructed	construct	VERB
ejpam-1845	204	38	in	in	ADP
ejpam-1845	204	39	[	[	X
ejpam-1845	204	40	15	15	NUM
ejpam-1845	204	41	]	]	PUNCT
ejpam-1845	204	42	.	.	PUNCT
ejpam-1845	205	1	table	table	NOUN
ejpam-1845	205	2	1	1	NUM
ejpam-1845	205	3	illustrates	illustrate	VERB
ejpam-1845	205	4	the	the	DET
ejpam-1845	205	5	comparative	comparative	ADJ
ejpam-1845	205	6	analysis	analysis	NOUN
ejpam-1845	205	7	of	of	ADP
ejpam-1845	205	8	the	the	DET
ejpam-1845	205	9	standard	standard	ADJ
ejpam-1845	205	10	sor	sor	NOUN
ejpam-1845	205	11	method	method	NOUN
ejpam-1845	205	12	yk+1	yk+1	NOUN
ejpam-1845	205	13	=	=	SYM
ejpam-1845	205	14	(	(	PUNCT
ejpam-1845	206	1	d+ωl)−1[(1−ω)d−ωu]yk	d+ωl)−1[(1−ω)d−ωu]yk	ADJ
ejpam-1845	206	2	+	+	NOUN
ejpam-1845	206	3	ω(d+ωl)−1f	ω(d+ωl)−1f	NUM
ejpam-1845	206	4	,	,	PUNCT
ejpam-1845	206	5	(	(	PUNCT
ejpam-1845	206	6	11	11	NUM
ejpam-1845	206	7	)	)	PUNCT
ejpam-1845	206	8	by	by	ADP
ejpam-1845	206	9	using	use	VERB
ejpam-1845	206	10	matlab	matlab	PROPN
ejpam-1845	206	11	code	code	NOUN
ejpam-1845	206	12	,	,	PUNCT
ejpam-1845	206	13	and	and	CCONJ
ejpam-1845	206	14	sor	sor	NOUN
ejpam-1845	206	15	method	method	NOUN
ejpam-1845	206	16	with	with	ADP
ejpam-1845	206	17	the	the	DET
ejpam-1845	206	18	constructed	construct	VERB
ejpam-1845	206	19	here	here	ADV
ejpam-1845	206	20	special	special	ADJ
ejpam-1845	206	21	algorithm	algorithm	NOUN
ejpam-1845	206	22	.	.	PUNCT
ejpam-1845	207	1	as	as	ADP
ejpam-1845	207	2	a	a	DET
ejpam-1845	207	3	test	test	NOUN
ejpam-1845	207	4	example	example	NOUN
ejpam-1845	207	5	the	the	DET
ejpam-1845	207	6	analytical	analytical	ADJ
ejpam-1845	207	7	solution	solution	NOUN
ejpam-1845	207	8	given	give	VERB
ejpam-1845	207	9	in	in	ADP
ejpam-1845	207	10	example	example	NOUN
ejpam-1845	207	11	2	2	NUM
ejpam-1845	207	12	,	,	PUNCT
ejpam-1845	207	13	with	with	ADP
ejpam-1845	207	14	β	β	X
ejpam-1845	207	15	=	=	SYM
ejpam-1845	207	16	2π	2π	NOUN
ejpam-1845	207	17	,	,	PUNCT
ejpam-1845	207	18	is	be	AUX
ejpam-1845	207	19	used	use	VERB
ejpam-1845	207	20	.	.	PUNCT
ejpam-1845	208	1	the	the	DET
ejpam-1845	208	2	iteration	iteration	NOUN
ejpam-1845	208	3	parameter	parameter	NOUN
ejpam-1845	208	4	ω	ω	PROPN
ejpam-1845	208	5	∈	∈	PROPN
ejpam-1845	208	6	(	(	PUNCT
ejpam-1845	208	7	0,2	0,2	NUM
ejpam-1845	208	8	)	)	PUNCT
ejpam-1845	208	9	in	in	ADP
ejpam-1845	208	10	(	(	PUNCT
ejpam-1845	208	11	11	11	NUM
ejpam-1845	208	12	)	)	PUNCT
ejpam-1845	208	13	was	be	AUX
ejpam-1845	208	14	defined	define	VERB
ejpam-1845	208	15	by	by	ADP
ejpam-1845	208	16	the	the	DET
ejpam-1845	208	17	formula	formula	NOUN
ejpam-1845	208	18	ω	ω	NOUN
ejpam-1845	208	19	=	=	SYM
ejpam-1845	209	1	2	2	NUM
ejpam-1845	209	2	1	1	NUM
ejpam-1845	209	3	+	+	NUM
ejpam-1845	209	4	p	p	NOUN
ejpam-1845	209	5	λmin(2−λmin	λmin(2−λmin	NOUN
ejpam-1845	209	6	)	)	PUNCT
ejpam-1845	209	7	,	,	PUNCT
ejpam-1845	209	8	where	where	SCONJ
ejpam-1845	209	9	λmin	λmin	NOUN
ejpam-1845	209	10	is	be	AUX
ejpam-1845	209	11	the	the	DET
ejpam-1845	209	12	minimal	minimal	ADJ
ejpam-1845	209	13	eigenvalue	eigenvalue	NOUN
ejpam-1845	209	14	of	of	ADP
ejpam-1845	209	15	the	the	DET
ejpam-1845	209	16	laplace	laplace	NOUN
ejpam-1845	209	17	operator	operator	NOUN
ejpam-1845	209	18	,	,	PUNCT
ejpam-1845	209	19	and	and	CCONJ
ejpam-1845	209	20	λmin	λmin	NOUN
ejpam-1845	209	21	=	=	SYM
ejpam-1845	209	22	2sin2(π/2n	2sin2(π/2n	NUM
ejpam-1845	209	23	)	)	PUNCT
ejpam-1845	209	24	,	,	PUNCT
ejpam-1845	209	25	for	for	ADP
ejpam-1845	209	26	the	the	DET
ejpam-1845	209	27	square	square	ADJ
ejpam-1845	209	28	mesh	mesh	NOUN
ejpam-1845	209	29	m	m	PROPN
ejpam-1845	209	30	=	=	SYM
ejpam-1845	209	31	n	n	X
ejpam-1845	209	32	.	.	PUNCT
ejpam-1845	210	1	table	table	NOUN
ejpam-1845	210	2	1	1	NUM
ejpam-1845	210	3	shows	show	VERB
ejpam-1845	210	4	that	that	SCONJ
ejpam-1845	210	5	direct	direct	ADJ
ejpam-1845	210	6	application	application	NOUN
ejpam-1845	210	7	of	of	ADP
ejpam-1845	210	8	the	the	DET
ejpam-1845	210	9	sor	sor	NOUN
ejpam-1845	210	10	method	method	NOUN
ejpam-1845	210	11	is	be	AUX
ejpam-1845	210	12	expensive	expensive	ADJ
ejpam-1845	210	13	in	in	ADP
ejpam-1845	210	14	the	the	DET
ejpam-1845	210	15	sense	sense	NOUN
ejpam-1845	210	16	of	of	ADP
ejpam-1845	210	17	the	the	DET
ejpam-1845	210	18	required	require	VERB
ejpam-1845	210	19	cpu	cpu	NOUN
ejpam-1845	210	20	time	time	NOUN
ejpam-1845	210	21	.	.	PUNCT
ejpam-1845	211	1	this	this	DET
ejpam-1845	211	2	time	time	NOUN
ejpam-1845	211	3	increases	increase	VERB
ejpam-1845	211	4	as	as	ADP
ejpam-1845	211	5	the	the	DET
ejpam-1845	211	6	number	number	NOUN
ejpam-1845	211	7	k	k	NOUN
ejpam-1845	212	1	=	=	PUNCT
ejpam-1845	212	2	n	n	PROPN
ejpam-1845	212	3	m	m	NOUN
ejpam-1845	212	4	of	of	ADP
ejpam-1845	212	5	mesh	mesh	NOUN
ejpam-1845	212	6	points	point	NOUN
ejpam-1845	212	7	increases	increase	NOUN
ejpam-1845	212	8	.	.	PUNCT
ejpam-1845	213	1	computational	computational	ADJ
ejpam-1845	213	2	results	result	NOUN
ejpam-1845	213	3	show	show	VERB
ejpam-1845	213	4	that	that	SCONJ
ejpam-1845	213	5	this	this	DET
ejpam-1845	213	6	increase	increase	NOUN
ejpam-1845	213	7	has	have	VERB
ejpam-1845	213	8	the	the	DET
ejpam-1845	213	9	character	character	NOUN
ejpam-1845	213	10	2n	2n	NUM
ejpam-1845	213	11	,	,	PUNCT
ejpam-1845	213	12	i.e.	i.e.	X
ejpam-1845	213	13	n	n	CCONJ
ejpam-1845	213	14	-	-	PUNCT
ejpam-1845	213	15	times	time	NOUN
ejpam-1845	213	16	increase	increase	NOUN
ejpam-1845	213	17	of	of	ADP
ejpam-1845	213	18	the	the	DET
ejpam-1845	213	19	number	number	NOUN
ejpam-1845	213	20	of	of	ADP
ejpam-1845	213	21	mesh	mesh	NOUN
ejpam-1845	213	22	points	point	NOUN
ejpam-1845	213	23	leads	lead	VERB
ejpam-1845	213	24	2n	2n	NUM
ejpam-1845	213	25	-	-	PUNCT
ejpam-1845	213	26	times	time	NOUN
ejpam-1845	213	27	increase	increase	NOUN
ejpam-1845	213	28	of	of	ADP
ejpam-1845	213	29	the	the	DET
ejpam-1845	213	30	cpu	cpu	NOUN
ejpam-1845	213	31	time	time	NOUN
ejpam-1845	213	32	.	.	PUNCT
ejpam-1845	214	1	this	this	PRON
ejpam-1845	214	2	is	be	AUX
ejpam-1845	214	3	due	due	ADJ
ejpam-1845	214	4	to	to	ADP
ejpam-1845	214	5	the	the	DET
ejpam-1845	214	6	moderately	moderately	ADV
ejpam-1845	214	7	ill	ill	ADJ
ejpam-1845	214	8	-	-	PUNCT
ejpam-1845	214	9	conditionedness	conditionedness	NOUN
ejpam-1845	214	10	,	,	PUNCT
ejpam-1845	214	11	according	accord	VERB
ejpam-1845	214	12	to	to	ADP
ejpam-1845	214	13	[	[	X
ejpam-1845	214	14	12	12	NUM
ejpam-1845	214	15	]	]	PUNCT
ejpam-1845	214	16	,	,	PUNCT
ejpam-1845	214	17	of	of	ADP
ejpam-1845	214	18	the	the	DET
ejpam-1845	214	19	matrix	matrix	NOUN
ejpam-1845	214	20	a	a	PRON
ejpam-1845	214	21	,	,	PUNCT
ejpam-1845	214	22	as	as	ADP
ejpam-1845	214	23	the	the	DET
ejpam-1845	214	24	fourth	fourth	ADJ
ejpam-1845	214	25	column	column	NOUN
ejpam-1845	214	26	of	of	ADP
ejpam-1845	214	27	the	the	DET
ejpam-1845	214	28	table	table	NOUN
ejpam-1845	214	29	shows	show	NOUN
ejpam-1845	214	30	.	.	PUNCT
ejpam-1845	215	1	at	at	ADP
ejpam-1845	215	2	the	the	DET
ejpam-1845	215	3	same	same	ADJ
ejpam-1845	215	4	time	time	NOUN
ejpam-1845	215	5	,	,	PUNCT
ejpam-1845	215	6	as	as	ADP
ejpam-1845	215	7	the	the	DET
ejpam-1845	215	8	second	second	ADJ
ejpam-1845	215	9	column	column	NOUN
ejpam-1845	215	10	of	of	ADP
ejpam-1845	215	11	table	table	NOUN
ejpam-1845	215	12	1	1	NUM
ejpam-1845	215	13	shows	show	NOUN
ejpam-1845	215	14	,	,	PUNCT
ejpam-1845	215	15	the	the	DET
ejpam-1845	215	16	sor	sor	NOUN
ejpam-1845	215	17	method	method	NOUN
ejpam-1845	215	18	with	with	ADP
ejpam-1845	215	19	the	the	DET
ejpam-1845	215	20	special	special	ADJ
ejpam-1845	215	21	algorithm	algorithm	NOUN
ejpam-1845	215	22	requires	require	VERB
ejpam-1845	215	23	less	less	ADJ
ejpam-1845	215	24	than	than	ADP
ejpam-1845	215	25	1	1	NUM
ejpam-1845	215	26	second	second	ADJ
ejpam-1845	215	27	for	for	ADP
ejpam-1845	215	28	all	all	DET
ejpam-1845	215	29	considered	consider	VERB
ejpam-1845	215	30	meshes	mesh	NOUN
ejpam-1845	215	31	.	.	PUNCT
ejpam-1845	216	1	a.	a.	PROPN
ejpam-1845	216	2	erdem	erdem	PROPN
ejpam-1845	216	3	/	/	SYM
ejpam-1845	216	4	eur	eur	PROPN
ejpam-1845	216	5	.	.	PUNCT
ejpam-1845	217	1	j.	j.	PROPN
ejpam-1845	217	2	pure	pure	PROPN
ejpam-1845	217	3	appl	appl	PROPN
ejpam-1845	217	4	.	.	PROPN
ejpam-1845	217	5	math	math	PROPN
ejpam-1845	217	6	,	,	PUNCT
ejpam-1845	217	7	6	6	NUM
ejpam-1845	217	8	(	(	PUNCT
ejpam-1845	217	9	2013	2013	NUM
ejpam-1845	217	10	)	)	PUNCT
ejpam-1845	217	11	,	,	PUNCT
ejpam-1845	217	12	30	30	NUM
ejpam-1845	217	13	-	-	SYM
ejpam-1845	217	14	43	43	NUM
ejpam-1845	217	15	39	39	NUM
ejpam-1845	217	16	table	table	NOUN
ejpam-1845	217	17	1	1	NUM
ejpam-1845	217	18	:	:	PUNCT
ejpam-1845	217	19	comparison	comparison	NOUN
ejpam-1845	217	20	of	of	ADP
ejpam-1845	217	21	the	the	DET
ejpam-1845	217	22	standard	standard	ADJ
ejpam-1845	217	23	and	and	CCONJ
ejpam-1845	217	24	modified	modify	VERB
ejpam-1845	217	25	sor	sor	NOUN
ejpam-1845	217	26	algorithms	algorithm	NOUN
ejpam-1845	217	27	n	n	PART
ejpam-1845	217	28	×m	×m	NOUN
ejpam-1845	217	29	sor	sor	NOUN
ejpam-1845	217	30	with	with	ADP
ejpam-1845	217	31	special	special	ADJ
ejpam-1845	217	32	algorithm	algorithm	NOUN
ejpam-1845	217	33	standard	standard	NOUN
ejpam-1845	217	34	sor	sor	NOUN
ejpam-1845	217	35	condition	condition	NOUN
ejpam-1845	217	36	number	number	NOUN
ejpam-1845	217	37	cpu	cpu	PROPN
ejpam-1845	217	38	time(sec	time(sec	NOUN
ejpam-1845	217	39	.	.	PUNCT
ejpam-1845	217	40	)	)	PUNCT
ejpam-1845	218	1	cpu	cpu	PROPN
ejpam-1845	218	2	time(sec	time(sec	PROPN
ejpam-1845	218	3	.	.	PUNCT
ejpam-1845	218	4	)	)	PUNCT
ejpam-1845	218	5	of	of	ADP
ejpam-1845	218	6	the	the	DET
ejpam-1845	218	7	matrix	matrix	NOUN
ejpam-1845	218	8	a	a	DET
ejpam-1845	218	9	20×	20×	NUM
ejpam-1845	218	10	20	20	NUM
ejpam-1845	218	11	0	0	NUM
ejpam-1845	218	12	9	9	NUM
ejpam-1845	218	13	1.5×	1.5×	NUM
ejpam-1845	218	14	104	104	NUM
ejpam-1845	218	15	30×	30×	NUM
ejpam-1845	218	16	30	30	NUM
ejpam-1845	218	17	0	0	NUM
ejpam-1845	218	18	48	48	NUM
ejpam-1845	218	19	8.0×	8.0×	NUM
ejpam-1845	218	20	104	104	NUM
ejpam-1845	218	21	40×	40×	NUM
ejpam-1845	218	22	40	40	NUM
ejpam-1845	218	23	0	0	NUM
ejpam-1845	218	24	126	126	NUM
ejpam-1845	218	25	2.5×	2.5×	NUM
ejpam-1845	218	26	105	105	NUM
ejpam-1845	218	27	5	5	NUM
ejpam-1845	218	28	.	.	PUNCT
ejpam-1845	218	29	numerical	numerical	ADJ
ejpam-1845	218	30	solution	solution	NOUN
ejpam-1845	218	31	of	of	ADP
ejpam-1845	218	32	the	the	DET
ejpam-1845	218	33	elliptic	elliptic	ADJ
ejpam-1845	218	34	problem	problem	NOUN
ejpam-1845	218	35	(	(	PUNCT
ejpam-1845	218	36	1)-(2	1)-(2	NUM
ejpam-1845	218	37	)	)	PUNCT
ejpam-1845	218	38	by	by	ADP
ejpam-1845	218	39	the	the	DET
ejpam-1845	218	40	poleness	poleness	ADJ
ejpam-1845	218	41	conservative	conservative	ADJ
ejpam-1845	218	42	schemes	scheme	NOUN
ejpam-1845	218	43	(	(	PUNCT
ejpam-1845	218	44	8)-(9	8)-(9	NOUN
ejpam-1845	218	45	)	)	PUNCT
ejpam-1845	218	46	in	in	ADP
ejpam-1845	218	47	this	this	DET
ejpam-1845	218	48	section	section	NOUN
ejpam-1845	218	49	we	we	PRON
ejpam-1845	218	50	discuss	discuss	VERB
ejpam-1845	218	51	results	result	NOUN
ejpam-1845	218	52	of	of	ADP
ejpam-1845	218	53	computational	computational	ADJ
ejpam-1845	218	54	experiments	experiment	NOUN
ejpam-1845	218	55	related	relate	VERB
ejpam-1845	218	56	to	to	ADP
ejpam-1845	218	57	numerical	numerical	ADJ
ejpam-1845	218	58	solution	solution	NOUN
ejpam-1845	218	59	of	of	ADP
ejpam-1845	218	60	the	the	DET
ejpam-1845	218	61	dirichlet	dirichlet	PROPN
ejpam-1845	218	62	problem	problem	NOUN
ejpam-1845	218	63	(	(	PUNCT
ejpam-1845	218	64	1)-(2	1)-(2	NUM
ejpam-1845	218	65	)	)	PUNCT
ejpam-1845	218	66	by	by	ADP
ejpam-1845	218	67	the	the	DET
ejpam-1845	218	68	poleness	poleness	ADJ
ejpam-1845	218	69	conservative	conservative	ADJ
ejpam-1845	218	70	scheme	scheme	NOUN
ejpam-1845	218	71	(	(	PUNCT
ejpam-1845	218	72	8)-(9	8)-(9	NUM
ejpam-1845	218	73	)	)	PUNCT
ejpam-1845	218	74	.	.	PUNCT
ejpam-1845	219	1	in	in	ADP
ejpam-1845	219	2	the	the	DET
ejpam-1845	219	3	first	first	ADJ
ejpam-1845	219	4	series	series	NOUN
ejpam-1845	219	5	of	of	ADP
ejpam-1845	219	6	the	the	DET
ejpam-1845	219	7	computational	computational	ADJ
ejpam-1845	219	8	experiments	experiment	NOUN
ejpam-1845	219	9	,	,	PUNCT
ejpam-1845	219	10	the	the	DET
ejpam-1845	219	11	convergence	convergence	NOUN
ejpam-1845	219	12	and	and	CCONJ
ejpam-1845	219	13	accuracy	accuracy	NOUN
ejpam-1845	219	14	of	of	ADP
ejpam-1845	219	15	the	the	DET
ejpam-1845	219	16	numerical	numerical	ADJ
ejpam-1845	219	17	solution	solution	NOUN
ejpam-1845	219	18	of	of	ADP
ejpam-1845	219	19	the	the	DET
ejpam-1845	219	20	dirichlet	dirichlet	PROPN
ejpam-1845	219	21	problem	problem	NOUN
ejpam-1845	219	22	(	(	PUNCT
ejpam-1845	219	23	1)-(2	1)-(2	NUM
ejpam-1845	219	24	)	)	PUNCT
ejpam-1845	219	25	,	,	PUNCT
ejpam-1845	219	26	with	with	ADP
ejpam-1845	219	27	the	the	DET
ejpam-1845	219	28	analytical	analytical	ADJ
ejpam-1845	219	29	solution	solution	NOUN
ejpam-1845	219	30	u(r,ϕ	u(r,ϕ	ADV
ejpam-1845	219	31	)	)	PUNCT
ejpam-1845	220	1	=	=	PRON
ejpam-1845	220	2	(	(	PUNCT
ejpam-1845	220	3	r	r	NOUN
ejpam-1845	220	4	−	−	PROPN
ejpam-1845	220	5	1)sinϕ	1)sinϕ	NUM
ejpam-1845	220	6	,	,	PUNCT
ejpam-1845	220	7	(	(	PUNCT
ejpam-1845	220	8	r,ϕ	r,ϕ	NOUN
ejpam-1845	220	9	)	)	PUNCT
ejpam-1845	220	10	∈	∈	PROPN
ejpam-1845	220	11	ωrβ	ωrβ	PROPN
ejpam-1845	220	12	,	,	PUNCT
ejpam-1845	220	13	r=	r=	ADJ
ejpam-1845	220	14	1	1	NUM
ejpam-1845	220	15	,	,	PUNCT
ejpam-1845	220	16	is	be	AUX
ejpam-1845	220	17	studied	study	VERB
ejpam-1845	220	18	.	.	PUNCT
ejpam-1845	221	1	note	note	VERB
ejpam-1845	221	2	that	that	SCONJ
ejpam-1845	221	3	the	the	DET
ejpam-1845	221	4	corresponding	correspond	VERB
ejpam-1845	221	5	source	source	NOUN
ejpam-1845	221	6	function	function	NOUN
ejpam-1845	221	7	f(r,ϕ	f(r,ϕ	PRON
ejpam-1845	221	8	)	)	PUNCT
ejpam-1845	221	9	=	=	SYM
ejpam-1845	221	10	1	1	NUM
ejpam-1845	221	11	r2	r2	PROPN
ejpam-1845	221	12	sinϕ	sinϕ	NOUN
ejpam-1845	221	13	,	,	PUNCT
ejpam-1845	221	14	(	(	PUNCT
ejpam-1845	221	15	r,ϕ	r,ϕ	NOUN
ejpam-1845	221	16	)	)	PUNCT
ejpam-1845	221	17	∈	∈	PROPN
ejpam-1845	221	18	ωrβ	ωrβ	PROPN
ejpam-1845	221	19	,	,	PUNCT
ejpam-1845	221	20	(	(	PUNCT
ejpam-1845	221	21	12	12	NUM
ejpam-1845	221	22	)	)	PUNCT
ejpam-1845	221	23	has	have	VERB
ejpam-1845	221	24	singularity	singularity	NOUN
ejpam-1845	221	25	at	at	ADP
ejpam-1845	221	26	r	r	NOUN
ejpam-1845	221	27	=	=	SYM
ejpam-1845	221	28	0	0	NUM
ejpam-1845	221	29	.	.	PUNCT
ejpam-1845	222	1	the	the	DET
ejpam-1845	222	2	two	two	NUM
ejpam-1845	222	3	appropriate	appropriate	ADJ
ejpam-1845	222	4	iterative	iterative	NOUN
ejpam-1845	222	5	methods	method	NOUN
ejpam-1845	222	6	sor	sor	NOUN
ejpam-1845	222	7	method	method	NOUN
ejpam-1845	222	8	and	and	CCONJ
ejpam-1845	222	9	bicongugate	bicongugate	VERB
ejpam-1845	222	10	gradient	gradient	NOUN
ejpam-1845	222	11	(	(	PUNCT
ejpam-1845	222	12	bcg	bcg	PROPN
ejpam-1845	222	13	)	)	PUNCT
ejpam-1845	222	14	method	method	NOUN
ejpam-1845	222	15	are	be	AUX
ejpam-1845	222	16	applied	apply	VERB
ejpam-1845	222	17	for	for	ADP
ejpam-1845	222	18	the	the	DET
ejpam-1845	222	19	iterative	iterative	NOUN
ejpam-1845	222	20	solution	solution	NOUN
ejpam-1845	222	21	of	of	ADP
ejpam-1845	222	22	the	the	DET
ejpam-1845	222	23	linear	linear	ADJ
ejpam-1845	222	24	system	system	NOUN
ejpam-1845	222	25	of	of	ADP
ejpam-1845	222	26	algebraic	algebraic	ADJ
ejpam-1845	222	27	equations	equation	NOUN
ejpam-1845	222	28	,	,	PUNCT
ejpam-1845	222	29	corresponding	correspond	VERB
ejpam-1845	222	30	to	to	ADP
ejpam-1845	222	31	the	the	DET
ejpam-1845	222	32	finite	finite	ADJ
ejpam-1845	222	33	difference	difference	NOUN
ejpam-1845	222	34	schemes	scheme	NOUN
ejpam-1845	222	35	(	(	PUNCT
ejpam-1845	222	36	8)-(9	8)-(9	NUM
ejpam-1845	222	37	)	)	PUNCT
ejpam-1845	222	38	.	.	PUNCT
ejpam-1845	223	1	in	in	ADP
ejpam-1845	223	2	all	all	DET
ejpam-1845	223	3	cases	case	NOUN
ejpam-1845	223	4	the	the	DET
ejpam-1845	223	5	matlab	matlab	PROPN
ejpam-1845	223	6	codes	code	NOUN
ejpam-1845	223	7	of	of	ADP
ejpam-1845	223	8	this	this	DET
ejpam-1845	223	9	methods	method	NOUN
ejpam-1845	223	10	with	with	ADP
ejpam-1845	223	11	the	the	DET
ejpam-1845	223	12	above	above	ADJ
ejpam-1845	223	13	mentioned	mention	VERB
ejpam-1845	223	14	special	special	ADJ
ejpam-1845	223	15	algorithm	algorithm	NOUN
ejpam-1845	223	16	is	be	AUX
ejpam-1845	223	17	used	use	VERB
ejpam-1845	223	18	.	.	PUNCT
ejpam-1845	224	1	results	result	NOUN
ejpam-1845	224	2	are	be	AUX
ejpam-1845	224	3	presented	present	VERB
ejpam-1845	224	4	in	in	ADP
ejpam-1845	224	5	the	the	DET
ejpam-1845	224	6	table	table	NOUN
ejpam-1845	224	7	2	2	NUM
ejpam-1845	224	8	.	.	X
ejpam-1845	225	1	for	for	ADP
ejpam-1845	225	2	the	the	DET
ejpam-1845	225	3	comparison	comparison	NOUN
ejpam-1845	225	4	,	,	PUNCT
ejpam-1845	225	5	the	the	DET
ejpam-1845	225	6	numerical	numerical	ADJ
ejpam-1845	225	7	results	result	NOUN
ejpam-1845	225	8	obtained	obtain	VERB
ejpam-1845	225	9	by	by	ADP
ejpam-1845	225	10	the	the	DET
ejpam-1845	225	11	gaussseidel	gaussseidel	NOUN
ejpam-1845	225	12	method	method	NOUN
ejpam-1845	225	13	,	,	PUNCT
ejpam-1845	225	14	are	be	AUX
ejpam-1845	225	15	also	also	ADV
ejpam-1845	225	16	presented	present	VERB
ejpam-1845	225	17	.	.	PUNCT
ejpam-1845	226	1	here	here	ADV
ejpam-1845	226	2	and	and	CCONJ
ejpam-1845	226	3	below	below	ADP
ejpam-1845	226	4	the	the	DET
ejpam-1845	226	5	value	value	NOUN
ejpam-1845	226	6	of	of	ADP
ejpam-1845	226	7	the	the	DET
ejpam-1845	226	8	stopping	stopping	NOUN
ejpam-1845	226	9	parameter	parameter	NOUN
ejpam-1845	226	10	δ	δ	PROPN
ejpam-1845	226	11	>	>	X
ejpam-1845	226	12	0	0	PUNCT
ejpam-1845	227	1	in	in	ADP
ejpam-1845	227	2	‖uni−1	‖uni−1	PROPN
ejpam-1845	227	3	−	−	PROPN
ejpam-1845	227	4	uni‖0	uni‖0	ADJ
ejpam-1845	227	5	≤	≤	PROPN
ejpam-1845	227	6	δ	δ	PROPN
ejpam-1845	227	7	,	,	PUNCT
ejpam-1845	227	8	where	where	SCONJ
ejpam-1845	227	9	‖	‖	PROPN
ejpam-1845	227	10	·	·	SYM
ejpam-1845	227	11	‖0	‖0	NUM
ejpam-1845	227	12	is	be	AUX
ejpam-1845	227	13	the	the	DET
ejpam-1845	227	14	l2	l2	NOUN
ejpam-1845	227	15	-	-	PUNCT
ejpam-1845	227	16	norm	norm	NOUN
ejpam-1845	227	17	,	,	PUNCT
ejpam-1845	227	18	is	be	AUX
ejpam-1845	227	19	taken	take	VERB
ejpam-1845	227	20	δ	δ	PROPN
ejpam-1845	227	21	=	=	SYM
ejpam-1845	227	22	10−5	10−5	NUM
ejpam-1845	227	23	.	.	PUNCT
ejpam-1845	227	24	table	table	NOUN
ejpam-1845	227	25	2	2	NUM
ejpam-1845	227	26	shows	show	VERB
ejpam-1845	227	27	numbers	number	NOUN
ejpam-1845	227	28	of	of	ADP
ejpam-1845	227	29	iterations	iteration	NOUN
ejpam-1845	227	30	corresponding	correspond	VERB
ejpam-1845	227	31	to	to	ADP
ejpam-1845	227	32	all	all	DET
ejpam-1845	227	33	three	three	NUM
ejpam-1845	227	34	iteration	iteration	NOUN
ejpam-1845	227	35	methods	method	NOUN
ejpam-1845	227	36	,	,	PUNCT
ejpam-1845	227	37	with	with	ADP
ejpam-1845	227	38	h1	h1	NOUN
ejpam-1845	227	39	-	-	PUNCT
ejpam-1845	227	40	relative	relative	ADJ
ejpam-1845	227	41	and	and	CCONJ
ejpam-1845	227	42	l∞-absolute	l∞-absolute	NOUN
ejpam-1845	227	43	errors	error	NOUN
ejpam-1845	227	44	.	.	PUNCT
ejpam-1845	228	1	results	result	NOUN
ejpam-1845	228	2	given	give	VERB
ejpam-1845	228	3	in	in	ADP
ejpam-1845	228	4	the	the	DET
ejpam-1845	228	5	table	table	NOUN
ejpam-1845	228	6	show	show	VERB
ejpam-1845	228	7	that	that	SCONJ
ejpam-1845	228	8	for	for	ADP
ejpam-1845	228	9	relatively	relatively	ADV
ejpam-1845	228	10	coarse	coarse	ADJ
ejpam-1845	228	11	meshes	mesh	NOUN
ejpam-1845	228	12	bgc	bgc	NOUN
ejpam-1845	228	13	method	method	NOUN
ejpam-1845	228	14	is	be	AUX
ejpam-1845	228	15	more	more	ADV
ejpam-1845	228	16	effective	effective	ADJ
ejpam-1845	228	17	than	than	ADP
ejpam-1845	228	18	the	the	DET
ejpam-1845	228	19	sor	sor	NOUN
ejpam-1845	228	20	method	method	NOUN
ejpam-1845	228	21	.	.	PUNCT
ejpam-1845	229	1	but	but	CCONJ
ejpam-1845	229	2	for	for	ADP
ejpam-1845	229	3	the	the	DET
ejpam-1845	229	4	meshes	mesh	NOUN
ejpam-1845	229	5	45	45	NUM
ejpam-1845	229	6	×	×	NOUN
ejpam-1845	229	7	45	45	NUM
ejpam-1845	229	8	and	and	CCONJ
ejpam-1845	229	9	higher	high	ADJ
ejpam-1845	229	10	,	,	PUNCT
ejpam-1845	229	11	sor	sor	NOUN
ejpam-1845	229	12	method	method	NOUN
ejpam-1845	229	13	is	be	AUX
ejpam-1845	229	14	more	more	ADV
ejpam-1845	229	15	effective	effective	ADJ
ejpam-1845	229	16	in	in	ADP
ejpam-1845	229	17	the	the	DET
ejpam-1845	229	18	sense	sense	NOUN
ejpam-1845	229	19	of	of	ADP
ejpam-1845	229	20	iterations	iteration	NOUN
ejpam-1845	229	21	.	.	PUNCT
ejpam-1845	230	1	moreover	moreover	ADV
ejpam-1845	230	2	,	,	PUNCT
ejpam-1845	230	3	the	the	DET
ejpam-1845	230	4	number	number	NOUN
ejpam-1845	230	5	of	of	ADP
ejpam-1845	230	6	iterations	iteration	NOUN
ejpam-1845	230	7	ni	ni	PROPN
ejpam-1845	230	8	in	in	ADP
ejpam-1845	230	9	sor	sor	NOUN
ejpam-1845	230	10	method	method	NOUN
ejpam-1845	230	11	increases	increase	VERB
ejpam-1845	230	12	slowly	slowly	ADV
ejpam-1845	230	13	,	,	PUNCT
ejpam-1845	230	14	as	as	SCONJ
ejpam-1845	230	15	increases	increase	VERB
ejpam-1845	230	16	the	the	DET
ejpam-1845	230	17	number	number	NOUN
ejpam-1845	230	18	of	of	ADP
ejpam-1845	230	19	mesh	mesh	NOUN
ejpam-1845	230	20	points	point	NOUN
ejpam-1845	230	21	.	.	PUNCT
ejpam-1845	231	1	thus	thus	ADV
ejpam-1845	231	2	ni	ni	PROPN
ejpam-1845	231	3	=	=	PROPN
ejpam-1845	231	4	234	234	NUM
ejpam-1845	231	5	and	and	CCONJ
ejpam-1845	231	6	ni	ni	PROPN
ejpam-1845	231	7	=	=	PROPN
ejpam-1845	231	8	277	277	NUM
ejpam-1845	231	9	,	,	PUNCT
ejpam-1845	231	10	for	for	ADP
ejpam-1845	231	11	the	the	DET
ejpam-1845	231	12	meshes	mesh	NOUN
ejpam-1845	231	13	40×	40×	NUM
ejpam-1845	231	14	40	40	NUM
ejpam-1845	231	15	and	and	CCONJ
ejpam-1845	231	16	50×	50×	NUM
ejpam-1845	231	17	50	50	NUM
ejpam-1845	231	18	,	,	PUNCT
ejpam-1845	231	19	respectively	respectively	ADV
ejpam-1845	231	20	.	.	PUNCT
ejpam-1845	232	1	as	as	SCONJ
ejpam-1845	232	2	show	show	VERB
ejpam-1845	232	3	the	the	DET
ejpam-1845	232	4	last	last	ADJ
ejpam-1845	232	5	three	three	NUM
ejpam-1845	232	6	columns	column	NOUN
ejpam-1845	232	7	of	of	ADP
ejpam-1845	232	8	the	the	DET
ejpam-1845	232	9	table	table	NOUN
ejpam-1845	232	10	,	,	PUNCT
ejpam-1845	232	11	the	the	DET
ejpam-1845	232	12	h1	h1	NOUN
ejpam-1845	232	13	-	-	PUNCT
ejpam-1845	232	14	relative	relative	ADJ
ejpam-1845	232	15	and	and	CCONJ
ejpam-1845	232	16	l∞-absolute	l∞-absolute	NOUN
ejpam-1845	232	17	errors	error	NOUN
ejpam-1845	232	18	are	be	AUX
ejpam-1845	232	19	small	small	ADJ
ejpam-1845	232	20	enough	enough	ADV
ejpam-1845	232	21	,	,	PUNCT
ejpam-1845	232	22	although	although	SCONJ
ejpam-1845	232	23	the	the	DET
ejpam-1845	232	24	source	source	NOUN
ejpam-1845	232	25	function	function	NOUN
ejpam-1845	232	26	(	(	PUNCT
ejpam-1845	232	27	12	12	NUM
ejpam-1845	232	28	)	)	PUNCT
ejpam-1845	232	29	has	have	VERB
ejpam-1845	232	30	singularity	singularity	NOUN
ejpam-1845	232	31	at	at	ADP
ejpam-1845	232	32	the	the	DET
ejpam-1845	232	33	pole	pole	NOUN
ejpam-1845	232	34	point	point	NOUN
ejpam-1845	232	35	r	r	NOUN
ejpam-1845	232	36	=	=	SYM
ejpam-1845	232	37	0	0	NUM
ejpam-1845	232	38	.	.	PUNCT
ejpam-1845	233	1	the	the	DET
ejpam-1845	233	2	next	next	ADJ
ejpam-1845	233	3	series	series	NOUN
ejpam-1845	233	4	of	of	ADP
ejpam-1845	233	5	computational	computational	ADJ
ejpam-1845	233	6	experiments	experiment	NOUN
ejpam-1845	233	7	is	be	AUX
ejpam-1845	233	8	realized	realize	VERB
ejpam-1845	233	9	for	for	ADP
ejpam-1845	233	10	the	the	DET
ejpam-1845	233	11	smooth	smooth	ADJ
ejpam-1845	233	12	continuous	continuous	ADJ
ejpam-1845	233	13	source	source	NOUN
ejpam-1845	233	14	function	function	NOUN
ejpam-1845	233	15	f̃(x	f̃(x	PROPN
ejpam-1845	233	16	,	,	PUNCT
ejpam-1845	233	17	y	y	NOUN
ejpam-1845	233	18	)	)	PUNCT
ejpam-1845	233	19	=	=	SYM
ejpam-1845	234	1	f(r,ϕ	f(r,ϕ	NUM
ejpam-1845	234	2	)	)	PUNCT
ejpam-1845	235	1	=	=	SYM
ejpam-1845	235	2	(	(	PUNCT
ejpam-1845	235	3	50ex	50ex	PROPN
ejpam-1845	235	4	p(−	p(−	ADJ
ejpam-1845	235	5	ǫ2	ǫ2	PROPN
ejpam-1845	235	6	ǫ2−r2	ǫ2−r2	NUM
ejpam-1845	235	7	)	)	PUNCT
ejpam-1845	235	8	,	,	PUNCT
ejpam-1845	235	9	0	0	NUM
ejpam-1845	235	10	<	<	X
ejpam-1845	235	11	r	r	X
ejpam-1845	235	12	<	<	X
ejpam-1845	235	13	ǫ	ǫ	PRON
ejpam-1845	235	14	0	0	NUM
ejpam-1845	235	15	,	,	PUNCT
ejpam-1845	235	16	ǫ	ǫ	PRON
ejpam-1845	235	17	<	<	X
ejpam-1845	235	18	r	r	NOUN
ejpam-1845	235	19	<	<	X
ejpam-1845	235	20	r	r	NOUN
ejpam-1845	235	21	,	,	PUNCT
ejpam-1845	235	22	r=	r=	ADJ
ejpam-1845	235	23	1	1	NUM
ejpam-1845	235	24	,	,	PUNCT
ejpam-1845	235	25	(	(	PUNCT
ejpam-1845	235	26	13	13	NUM
ejpam-1845	235	27	)	)	PUNCT
ejpam-1845	235	28	a.	a.	NOUN
ejpam-1845	235	29	erdem	erdem	PROPN
ejpam-1845	235	30	/	/	SYM
ejpam-1845	235	31	eur	eur	PROPN
ejpam-1845	235	32	.	.	PUNCT
ejpam-1845	236	1	j.	j.	PROPN
ejpam-1845	236	2	pure	pure	PROPN
ejpam-1845	236	3	appl	appl	PROPN
ejpam-1845	236	4	.	.	PROPN
ejpam-1845	236	5	math	math	PROPN
ejpam-1845	236	6	,	,	PUNCT
ejpam-1845	236	7	6	6	NUM
ejpam-1845	236	8	(	(	PUNCT
ejpam-1845	236	9	2013	2013	NUM
ejpam-1845	236	10	)	)	PUNCT
ejpam-1845	236	11	,	,	PUNCT
ejpam-1845	236	12	30	30	NUM
ejpam-1845	236	13	-	-	SYM
ejpam-1845	236	14	43	43	NUM
ejpam-1845	236	15	40	40	NUM
ejpam-1845	236	16	table	table	NOUN
ejpam-1845	236	17	2	2	NUM
ejpam-1845	236	18	:	:	PUNCT
ejpam-1845	236	19	comparative	comparative	ADJ
ejpam-1845	236	20	analysis	analysis	NOUN
ejpam-1845	236	21	of	of	ADP
ejpam-1845	236	22	the	the	DET
ejpam-1845	236	23	modified	modify	VERB
ejpam-1845	236	24	sor	sor	NOUN
ejpam-1845	236	25	and	and	CCONJ
ejpam-1845	236	26	bgc	bgc	NOUN
ejpam-1845	236	27	methods	method	NOUN
ejpam-1845	236	28	applied	apply	VERB
ejpam-1845	236	29	to	to	ADP
ejpam-1845	236	30	the	the	DET
ejpam-1845	236	31	poleness	poleness	ADJ
ejpam-1845	236	32	conservative	conservative	ADJ
ejpam-1845	236	33	finite	finite	ADJ
ejpam-1845	236	34	difference	difference	NOUN
ejpam-1845	236	35	scheme	scheme	NOUN
ejpam-1845	236	36	(	(	PUNCT
ejpam-1845	236	37	8)-(9	8)-(9	NUM
ejpam-1845	236	38	)	)	PUNCT
ejpam-1845	236	39	methods	method	NOUN
ejpam-1845	236	40	n	n	PART
ejpam-1845	236	41	×m	×m	NOUN
ejpam-1845	236	42	time	time	NOUN
ejpam-1845	236	43	number	number	NOUN
ejpam-1845	236	44	of	of	ADP
ejpam-1845	236	45	rel	rel	NOUN
ejpam-1845	236	46	.	.	PUNCT
ejpam-1845	237	1	error	error	NOUN
ejpam-1845	237	2	abs	ab	NOUN
ejpam-1845	237	3	.	.	PUNCT
ejpam-1845	238	1	error	error	NOUN
ejpam-1845	238	2	abs	ab	NOUN
ejpam-1845	238	3	.	.	PUNCT
ejpam-1845	239	1	error	error	NOUN
ejpam-1845	239	2	(	(	PUNCT
ejpam-1845	239	3	sec	sec	PROPN
ejpam-1845	239	4	.	.	PUNCT
ejpam-1845	239	5	)	)	PUNCT
ejpam-1845	240	1	iterations	iteration	VERB
ejpam-1845	240	2	h1	h1	NOUN
ejpam-1845	240	3	-	-	PUNCT
ejpam-1845	240	4	norm	norm	NOUN
ejpam-1845	240	5	l∞-norm	l∞-norm	NOUN
ejpam-1845	240	6	l∞-norm	l∞-norm	VERB
ejpam-1845	240	7	ni	ni	PROPN
ejpam-1845	240	8	r	r	NOUN
ejpam-1845	240	9	=	=	SYM
ejpam-1845	240	10	r1	r1	NOUN
ejpam-1845	240	11	r	r	NOUN
ejpam-1845	240	12	=	=	PUNCT
ejpam-1845	240	13	r/2	r/2	VERB
ejpam-1845	240	14	30×	30×	NUM
ejpam-1845	240	15	30	30	NUM
ejpam-1845	240	16	0	0	NUM
ejpam-1845	240	17	185	185	NUM
ejpam-1845	240	18	8.0×	8.0×	NUM
ejpam-1845	240	19	10−6	10−6	NUM
ejpam-1845	240	20	3.8×	3.8×	NUM
ejpam-1845	240	21	10−3	10−3	NUM
ejpam-1845	240	22	1.3×	1.3×	NUM
ejpam-1845	240	23	10−3	10−3	NUM
ejpam-1845	240	24	sor	sor	NOUN
ejpam-1845	240	25	40×	40×	NUM
ejpam-1845	240	26	40	40	NUM
ejpam-1845	240	27	1	1	NUM
ejpam-1845	240	28	234	234	NUM
ejpam-1845	240	29	2.7×	2.7×	NUM
ejpam-1845	240	30	10−6	10−6	NUM
ejpam-1845	240	31	2.5×	2.5×	NUM
ejpam-1845	240	32	10−3	10−3	NUM
ejpam-1845	240	33	8.1×	8.1×	NUM
ejpam-1845	240	34	10−4	10−4	NUM
ejpam-1845	240	35	50×	50×	NUM
ejpam-1845	240	36	50	50	NUM
ejpam-1845	240	37	2	2	NUM
ejpam-1845	240	38	277	277	NUM
ejpam-1845	240	39	1.4×	1.4×	NUM
ejpam-1845	240	40	10−6	10−6	NUM
ejpam-1845	240	41	1.9×	1.9×	NUM
ejpam-1845	240	42	10−3	10−3	NUM
ejpam-1845	240	43	5.9×	5.9×	NUM
ejpam-1845	240	44	10−4	10−4	NUM
ejpam-1845	240	45	30×	30×	NUM
ejpam-1845	240	46	30	30	NUM
ejpam-1845	240	47	0	0	NUM
ejpam-1845	240	48	110	110	NUM
ejpam-1845	240	49	8.0×	8.0×	NUM
ejpam-1845	240	50	10−6	10−6	NUM
ejpam-1845	240	51	3.4×	3.4×	NUM
ejpam-1845	240	52	10−3	10−3	NUM
ejpam-1845	240	53	1.2×	1.2×	NUM
ejpam-1845	240	54	10−3	10−3	NUM
ejpam-1845	240	55	bcg	bcg	NOUN
ejpam-1845	240	56	40×	40×	NUM
ejpam-1845	240	57	40	40	NUM
ejpam-1845	240	58	2	2	NUM
ejpam-1845	240	59	224	224	NUM
ejpam-1845	240	60	2.5×	2.5×	NUM
ejpam-1845	240	61	10−6	10−6	NUM
ejpam-1845	240	62	2.0×	2.0×	NUM
ejpam-1845	240	63	10−3	10−3	NUM
ejpam-1845	240	64	6.8×	6.8×	NUM
ejpam-1845	240	65	10−4	10−4	NUM
ejpam-1845	241	1	50×	50×	NUM
ejpam-1845	241	2	50	50	NUM
ejpam-1845	241	3	4	4	NUM
ejpam-1845	241	4	385	385	NUM
ejpam-1845	241	5	1.0×	1.0×	NUM
ejpam-1845	241	6	10−6	10−6	NUM
ejpam-1845	241	7	1.3×	1.3×	NUM
ejpam-1845	241	8	10−3	10−3	NUM
ejpam-1845	241	9	4.3×	4.3×	NUM
ejpam-1845	241	10	10−4	10−4	NUM
ejpam-1845	241	11	30×	30×	NUM
ejpam-1845	241	12	30	30	NUM
ejpam-1845	241	13	33	33	NUM
ejpam-1845	241	14	473	473	NUM
ejpam-1845	241	15	8.5×	8.5×	NUM
ejpam-1845	241	16	10−6	10−6	NUM
ejpam-1845	241	17	4.9×	4.9×	NUM
ejpam-1845	241	18	10−3	10−3	NUM
ejpam-1845	241	19	1.2×	1.2×	NUM
ejpam-1845	241	20	10−3	10−3	NUM
ejpam-1845	241	21	gauss40×	gauss40×	VERB
ejpam-1845	241	22	40	40	NUM
ejpam-1845	241	23	95	95	NUM
ejpam-1845	241	24	762	762	NUM
ejpam-1845	241	25	5.0×	5.0×	NUM
ejpam-1845	241	26	10−6	10−6	NUM
ejpam-1845	241	27	3.0×	3.0×	NUM
ejpam-1845	241	28	10−3	10−3	NUM
ejpam-1845	241	29	7.8×	7.8×	NUM
ejpam-1845	241	30	10−4	10−4	NUM
ejpam-1845	241	31	seidel	seidel	NOUN
ejpam-1845	241	32	50×	50×	NUM
ejpam-1845	241	33	50	50	NUM
ejpam-1845	241	34	219	219	NUM
ejpam-1845	241	35	1105	1105	NUM
ejpam-1845	241	36	1.1×	1.1×	NUM
ejpam-1845	241	37	10−5	10−5	NUM
ejpam-1845	241	38	2.0×	2.0×	NUM
ejpam-1845	241	39	10−3	10−3	NUM
ejpam-1845	241	40	1.6×	1.6×	NUM
ejpam-1845	241	41	10−3	10−3	NUM
ejpam-1845	241	42	with	with	ADP
ejpam-1845	241	43	ǫ	ǫ	NOUN
ejpam-1845	241	44	=	=	SYM
ejpam-1845	241	45	1/2	1/2	NUM
ejpam-1845	241	46	,	,	PUNCT
ejpam-1845	241	47	approximating	approximate	VERB
ejpam-1845	241	48	in	in	ADP
ejpam-1845	241	49	weak	weak	ADJ
ejpam-1845	241	50	sense	sense	NOUN
ejpam-1845	241	51	the	the	DET
ejpam-1845	241	52	dirac	dirac	PROPN
ejpam-1845	241	53	δ	δ	PROPN
ejpam-1845	241	54	-	-	PUNCT
ejpam-1845	241	55	function	function	NOUN
ejpam-1845	241	56	(	(	PUNCT
ejpam-1845	241	57	figure	figure	NOUN
ejpam-1845	241	58	2a	2a	NUM
ejpam-1845	241	59	)	)	PUNCT
ejpam-1845	241	60	.	.	PUNCT
ejpam-1845	242	1	this	this	DET
ejpam-1845	242	2	function	function	NOUN
ejpam-1845	242	3	is	be	AUX
ejpam-1845	242	4	taken	take	VERB
ejpam-1845	242	5	as	as	ADP
ejpam-1845	242	6	a	a	DET
ejpam-1845	242	7	given	give	VERB
ejpam-1845	242	8	data	datum	NOUN
ejpam-1845	242	9	for	for	ADP
ejpam-1845	242	10	the	the	DET
ejpam-1845	242	11	dirichlet	dirichlet	PROPN
ejpam-1845	242	12	problem	problem	NOUN
ejpam-1845	242	13	(	(	PUNCT
ejpam-1845	242	14	1)-(2	1)-(2	NUM
ejpam-1845	242	15	)	)	PUNCT
ejpam-1845	242	16	.	.	PUNCT
ejpam-1845	243	1	the	the	DET
ejpam-1845	243	2	right	right	PROPN
ejpam-1845	243	3	pane	pane	NOUN
ejpam-1845	243	4	,	,	PUNCT
ejpam-1845	243	5	figure	figure	NOUN
ejpam-1845	243	6	2b	2b	NOUN
ejpam-1845	243	7	,	,	PUNCT
ejpam-1845	243	8	illustrates	illustrate	VERB
ejpam-1845	243	9	the	the	DET
ejpam-1845	243	10	numerical	numerical	ADJ
ejpam-1845	243	11	solution	solution	NOUN
ejpam-1845	243	12	ũh(x	ũh(x	NOUN
ejpam-1845	243	13	,	,	PUNCT
ejpam-1845	243	14	y	y	PROPN
ejpam-1845	243	15	)	)	PUNCT
ejpam-1845	243	16	=	=	SYM
ejpam-1845	243	17	uh(r,ϕ	uh(r,ϕ	PROPN
ejpam-1845	243	18	)	)	PUNCT
ejpam-1845	243	19	of	of	ADP
ejpam-1845	243	20	problem	problem	NOUN
ejpam-1845	243	21	(	(	PUNCT
ejpam-1845	243	22	1)-(2	1)-(2	NUM
ejpam-1845	243	23	)	)	PUNCT
ejpam-1845	243	24	by	by	ADP
ejpam-1845	243	25	the	the	DET
ejpam-1845	243	26	poleness	poleness	ADJ
ejpam-1845	243	27	conservative	conservative	ADJ
ejpam-1845	243	28	schemes	scheme	NOUN
ejpam-1845	243	29	(	(	PUNCT
ejpam-1845	243	30	8)-(9	8)-(9	NOUN
ejpam-1845	243	31	)	)	PUNCT
ejpam-1845	243	32	,	,	PUNCT
ejpam-1845	243	33	for	for	ADP
ejpam-1845	243	34	the	the	DET
ejpam-1845	243	35	mesh	mesh	NOUN
ejpam-1845	243	36	size	size	NOUN
ejpam-1845	243	37	30×	30×	NUM
ejpam-1845	243	38	30	30	NUM
ejpam-1845	243	39	.	.	PUNCT
ejpam-1845	244	1	finally	finally	ADV
ejpam-1845	244	2	we	we	PRON
ejpam-1845	244	3	consider	consider	VERB
ejpam-1845	244	4	the	the	DET
ejpam-1845	244	5	weak	weak	ADJ
ejpam-1845	244	6	solution	solution	NOUN
ejpam-1845	244	7	of	of	ADP
ejpam-1845	244	8	the	the	DET
ejpam-1845	244	9	dirichlet	dirichlet	PROPN
ejpam-1845	244	10	problem	problem	NOUN
ejpam-1845	244	11	(	(	PUNCT
ejpam-1845	244	12	1)-(2	1)-(2	NUM
ejpam-1845	244	13	)	)	PUNCT
ejpam-1845	244	14	,	,	PUNCT
ejpam-1845	244	15	when	when	SCONJ
ejpam-1845	244	16	the	the	DET
ejpam-1845	244	17	source	source	NOUN
ejpam-1845	244	18	f(r,ϕ	f(r,ϕ	NOUN
ejpam-1845	244	19	)	)	PUNCT
ejpam-1845	244	20	is	be	AUX
ejpam-1845	244	21	a	a	DET
ejpam-1845	244	22	discontinuous	discontinuous	ADJ
ejpam-1845	244	23	at	at	ADP
ejpam-1845	244	24	r	r	NOUN
ejpam-1845	244	25	=	=	SYM
ejpam-1845	244	26	1/2	1/2	NUM
ejpam-1845	244	27	function	function	NOUN
ejpam-1845	244	28	f̃(x	f̃(x	PROPN
ejpam-1845	244	29	,	,	PUNCT
ejpam-1845	244	30	y	y	NOUN
ejpam-1845	244	31	)	)	PUNCT
ejpam-1845	244	32	=	=	SYM
ejpam-1845	245	1	f(r,ϕ	f(r,ϕ	NUM
ejpam-1845	245	2	)	)	PUNCT
ejpam-1845	246	1	=	=	PUNCT
ejpam-1845	246	2			PROPN
ejpam-1845	246	3			ADJ
ejpam-1845	246	4			PROPN
ejpam-1845	246	5	50ǫ	50ǫ	NOUN
ejpam-1845	246	6	exp(−ǫ2/4r)p	exp(−ǫ2/4r)p	X
ejpam-1845	246	7	4πr3	4πr3	NUM
ejpam-1845	246	8	,	,	PUNCT
ejpam-1845	246	9	0	0	PUNCT
ejpam-1845	246	10	<	<	X
ejpam-1845	246	11	r	r	NOUN
ejpam-1845	246	12	<	<	X
ejpam-1845	246	13	ǫ	ǫ	NOUN
ejpam-1845	246	14	50ǫ	50ǫ	NUM
ejpam-1845	246	15	exp(−ǫ2/4)p	exp(−ǫ2/4)p	NOUN
ejpam-1845	246	16	4π	4π	NUM
ejpam-1845	246	17	,	,	PUNCT
ejpam-1845	246	18	ǫ	ǫ	PRON
ejpam-1845	246	19	<	<	X
ejpam-1845	246	20	r	r	NOUN
ejpam-1845	246	21	<	<	X
ejpam-1845	246	22	r	r	NOUN
ejpam-1845	246	23	,	,	PUNCT
ejpam-1845	246	24	r=	r=	ADJ
ejpam-1845	246	25	1	1	NUM
ejpam-1845	246	26	,	,	PUNCT
ejpam-1845	246	27	given	give	VERB
ejpam-1845	246	28	in	in	ADP
ejpam-1845	246	29	the	the	DET
ejpam-1845	246	30	left	left	ADJ
ejpam-1845	246	31	pane	pane	NOUN
ejpam-1845	246	32	of	of	ADP
ejpam-1845	246	33	figure	figure	NOUN
ejpam-1845	246	34	3	3	NUM
ejpam-1845	246	35	.	.	PUNCT
ejpam-1845	247	1	this	this	DET
ejpam-1845	247	2	function	function	NOUN
ejpam-1845	247	3	with	with	ADP
ejpam-1845	247	4	ǫ	ǫ	NOUN
ejpam-1845	247	5	=	=	SYM
ejpam-1845	247	6	1/2	1/2	NUM
ejpam-1845	247	7	is	be	AUX
ejpam-1845	247	8	taken	take	VERB
ejpam-1845	247	9	as	as	ADP
ejpam-1845	247	10	a	a	DET
ejpam-1845	247	11	given	give	VERB
ejpam-1845	247	12	data	datum	NOUN
ejpam-1845	247	13	for	for	ADP
ejpam-1845	247	14	the	the	DET
ejpam-1845	247	15	dirichlet	dirichlet	PROPN
ejpam-1845	247	16	problem	problem	NOUN
ejpam-1845	247	17	(	(	PUNCT
ejpam-1845	247	18	1)-(2	1)-(2	NUM
ejpam-1845	247	19	)	)	PUNCT
ejpam-1845	247	20	.	.	PUNCT
ejpam-1845	248	1	the	the	DET
ejpam-1845	248	2	numerical	numerical	ADJ
ejpam-1845	248	3	solution	solution	NOUN
ejpam-1845	248	4	ũh(x	ũh(x	NOUN
ejpam-1845	248	5	,	,	PUNCT
ejpam-1845	248	6	y	y	PROPN
ejpam-1845	248	7	)	)	PUNCT
ejpam-1845	248	8	=	=	SYM
ejpam-1845	248	9	uh(r,ϕ	uh(r,ϕ	PROPN
ejpam-1845	248	10	)	)	PUNCT
ejpam-1845	248	11	of	of	ADP
ejpam-1845	248	12	problem	problem	NOUN
ejpam-1845	248	13	(	(	PUNCT
ejpam-1845	248	14	1)-(2	1)-(2	NUM
ejpam-1845	248	15	)	)	PUNCT
ejpam-1845	248	16	obtained	obtain	VERB
ejpam-1845	248	17	for	for	ADP
ejpam-1845	248	18	the	the	DET
ejpam-1845	248	19	mesh	mesh	NOUN
ejpam-1845	248	20	30×	30×	NUM
ejpam-1845	248	21	30	30	NUM
ejpam-1845	248	22	is	be	AUX
ejpam-1845	248	23	plotted	plot	VERB
ejpam-1845	248	24	in	in	ADP
ejpam-1845	248	25	the	the	DET
ejpam-1845	248	26	right	right	ADJ
ejpam-1845	248	27	pane	pane	NOUN
ejpam-1845	248	28	,	,	PUNCT
ejpam-1845	248	29	figure	figure	NOUN
ejpam-1845	248	30	3b	3b	NUM
ejpam-1845	248	31	.	.	PUNCT
ejpam-1845	249	1	to	to	PART
ejpam-1845	249	2	estimate	estimate	VERB
ejpam-1845	249	3	an	an	DET
ejpam-1845	249	4	accuracy	accuracy	NOUN
ejpam-1845	249	5	of	of	ADP
ejpam-1845	249	6	the	the	DET
ejpam-1845	249	7	numerical	numerical	ADJ
ejpam-1845	249	8	solution	solution	NOUN
ejpam-1845	249	9	,	,	PUNCT
ejpam-1845	249	10	in	in	ADP
ejpam-1845	249	11	particular	particular	ADJ
ejpam-1845	249	12	at	at	ADP
ejpam-1845	249	13	the	the	DET
ejpam-1845	249	14	discontinuity	discontinuity	NOUN
ejpam-1845	249	15	point	point	NOUN
ejpam-1845	249	16	r	r	NOUN
ejpam-1845	249	17	=	=	SYM
ejpam-1845	249	18	1/2	1/2	NUM
ejpam-1845	249	19	,	,	PUNCT
ejpam-1845	249	20	the	the	DET
ejpam-1845	249	21	numerical	numerical	ADJ
ejpam-1845	249	22	solutions	solution	NOUN
ejpam-1845	249	23	u	u	PROPN
ejpam-1845	249	24	(	(	PUNCT
ejpam-1845	249	25	1	1	NUM
ejpam-1845	249	26	)	)	PUNCT
ejpam-1845	249	27	h	h	NOUN
ejpam-1845	249	28	(	(	PUNCT
ejpam-1845	249	29	r,ϕ	r,ϕ	NOUN
ejpam-1845	249	30	)	)	PUNCT
ejpam-1845	249	31	=	=	SYM
ejpam-1845	249	32	u	u	NOUN
ejpam-1845	249	33	(	(	PUNCT
ejpam-1845	249	34	2	2	NUM
ejpam-1845	249	35	)	)	PUNCT
ejpam-1845	249	36	h	h	NOUN
ejpam-1845	249	37	(	(	PUNCT
ejpam-1845	249	38	r,ϕ	r,ϕ	NOUN
ejpam-1845	249	39	)	)	PUNCT
ejpam-1845	249	40	corresponding	correspond	VERB
ejpam-1845	249	41	to	to	ADP
ejpam-1845	249	42	two	two	NUM
ejpam-1845	249	43	different	different	ADJ
ejpam-1845	249	44	meshes	mesh	NOUN
ejpam-1845	249	45	w(1	w(1	INTJ
ejpam-1845	249	46	)	)	PUNCT
ejpam-1845	249	47	rϕ	rϕ	NOUN
ejpam-1845	249	48	=	=	NOUN
ejpam-1845	249	49	w(2)rϕ	w(2)rϕ	NOUN
ejpam-1845	249	50	is	be	AUX
ejpam-1845	249	51	compared	compare	VERB
ejpam-1845	249	52	.	.	PUNCT
ejpam-1845	250	1	the	the	DET
ejpam-1845	250	2	relative	relative	ADJ
ejpam-1845	250	3	error	error	NOUN
ejpam-1845	250	4	ǫh	ǫh	ADP
ejpam-1845	250	5	=	=	SYM
ejpam-1845	250	6	u	u	NOUN
ejpam-1845	250	7	(	(	PUNCT
ejpam-1845	250	8	1	1	NUM
ejpam-1845	250	9	)	)	PUNCT
ejpam-1845	250	10	h	h	NOUN
ejpam-1845	250	11	(	(	PUNCT
ejpam-1845	250	12	r,ϕ)−	r,ϕ)−	NOUN
ejpam-1845	250	13	u	u	NOUN
ejpam-1845	250	14	(	(	PUNCT
ejpam-1845	250	15	2	2	NUM
ejpam-1845	250	16	)	)	PUNCT
ejpam-1845	250	17	h	h	NOUN
ejpam-1845	250	18	(	(	PUNCT
ejpam-1845	250	19	r,ϕ	r,ϕ	NOUN
ejpam-1845	250	20	)	)	PUNCT
ejpam-1845	250	21	0.5	0.5	NUM
ejpam-1845	250	22	�	�	PROPN
ejpam-1845	250	23	u	u	PROPN
ejpam-1845	250	24	(	(	PUNCT
ejpam-1845	250	25	1	1	NUM
ejpam-1845	250	26	)	)	PUNCT
ejpam-1845	250	27	h	h	NOUN
ejpam-1845	250	28	(	(	PUNCT
ejpam-1845	250	29	r,ϕ	r,ϕ	NOUN
ejpam-1845	250	30	)	)	PUNCT
ejpam-1845	250	31	+	+	NUM
ejpam-1845	250	32	u	u	NOUN
ejpam-1845	250	33	(	(	PUNCT
ejpam-1845	250	34	2	2	NUM
ejpam-1845	250	35	)	)	PUNCT
ejpam-1845	250	36	h	h	NOUN
ejpam-1845	250	37	(	(	PUNCT
ejpam-1845	250	38	r,ϕ	r,ϕ	PROPN
ejpam-1845	250	39	)	)	PUNCT
ejpam-1845	250	40	�	�	PROPN
ejpam-1845	250	41	∞	∞	PROPN
ejpam-1845	250	42	,	,	PUNCT
ejpam-1845	250	43	is	be	AUX
ejpam-1845	250	44	about	about	ADV
ejpam-1845	250	45	ǫh	ǫh	NUM
ejpam-1845	250	46	=	=	SYM
ejpam-1845	250	47	10−3÷	10−3÷	NUM
ejpam-1845	250	48	10−3	10−3	NUM
ejpam-1845	250	49	,	,	PUNCT
ejpam-1845	250	50	including	include	VERB
ejpam-1845	250	51	the	the	DET
ejpam-1845	250	52	discontinuity	discontinuity	NOUN
ejpam-1845	250	53	point	point	NOUN
ejpam-1845	250	54	.	.	PUNCT
ejpam-1845	251	1	this	this	PRON
ejpam-1845	251	2	shows	show	VERB
ejpam-1845	251	3	high	high	ADJ
ejpam-1845	251	4	accuracy	accuracy	NOUN
ejpam-1845	251	5	of	of	ADP
ejpam-1845	251	6	the	the	DET
ejpam-1845	251	7	numerical	numerical	ADJ
ejpam-1845	251	8	method	method	NOUN
ejpam-1845	251	9	in	in	ADP
ejpam-1845	251	10	the	the	DET
ejpam-1845	251	11	case	case	NOUN
ejpam-1845	251	12	of	of	ADP
ejpam-1845	251	13	discontinuous	discontinuous	ADJ
ejpam-1845	251	14	source	source	NOUN
ejpam-1845	251	15	function	function	NOUN
ejpam-1845	251	16	,	,	PUNCT
ejpam-1845	251	17	also	also	ADV
ejpam-1845	251	18	.	.	PUNCT
ejpam-1845	252	1	a.	a.	NOUN
ejpam-1845	252	2	erdem	erdem	PROPN
ejpam-1845	252	3	/	/	SYM
ejpam-1845	252	4	eur	eur	PROPN
ejpam-1845	252	5	.	.	PUNCT
ejpam-1845	253	1	j.	j.	PROPN
ejpam-1845	253	2	pure	pure	PROPN
ejpam-1845	253	3	appl	appl	PROPN
ejpam-1845	253	4	.	.	PROPN
ejpam-1845	253	5	math	math	PROPN
ejpam-1845	253	6	,	,	PUNCT
ejpam-1845	253	7	6	6	NUM
ejpam-1845	253	8	(	(	PUNCT
ejpam-1845	253	9	2013	2013	NUM
ejpam-1845	253	10	)	)	PUNCT
ejpam-1845	253	11	,	,	PUNCT
ejpam-1845	253	12	30	30	NUM
ejpam-1845	253	13	-	-	SYM
ejpam-1845	253	14	43	43	NUM
ejpam-1845	253	15	41	41	NUM
ejpam-1845	253	16	(	(	PUNCT
ejpam-1845	253	17	a	a	NOUN
ejpam-1845	253	18	)	)	PUNCT
ejpam-1845	253	19	continuous	continuous	ADJ
ejpam-1845	253	20	source	source	NOUN
ejpam-1845	253	21	solution	solution	NOUN
ejpam-1845	253	22	(	(	PUNCT
ejpam-1845	253	23	b	b	NOUN
ejpam-1845	253	24	)	)	PUNCT
ejpam-1845	253	25	numerical	numerical	ADJ
ejpam-1845	253	26	solution	solution	NOUN
ejpam-1845	253	27	figure	figure	NOUN
ejpam-1845	253	28	2	2	NUM
ejpam-1845	253	29	:	:	PUNCT
ejpam-1845	253	30	dirichlet	dirichlet	NOUN
ejpam-1845	253	31	problem	problem	NOUN
ejpam-1845	253	32	in	in	ADP
ejpam-1845	253	33	polar	polar	ADJ
ejpam-1845	253	34	coordinates	coordinate	NOUN
ejpam-1845	253	35	(	(	PUNCT
ejpam-1845	253	36	a	a	X
ejpam-1845	253	37	)	)	PUNCT
ejpam-1845	253	38	discontinuous	discontinuous	ADJ
ejpam-1845	253	39	source	source	NOUN
ejpam-1845	253	40	solution	solution	NOUN
ejpam-1845	253	41	(	(	PUNCT
ejpam-1845	253	42	b	b	NOUN
ejpam-1845	253	43	)	)	PUNCT
ejpam-1845	253	44	numerical	numerical	ADJ
ejpam-1845	253	45	solution	solution	NOUN
ejpam-1845	253	46	figure	figure	NOUN
ejpam-1845	253	47	3	3	NUM
ejpam-1845	253	48	:	:	PUNCT
ejpam-1845	253	49	dirichlet	dirichlet	NOUN
ejpam-1845	253	50	problem	problem	NOUN
ejpam-1845	253	51	in	in	ADP
ejpam-1845	253	52	polar	polar	ADJ
ejpam-1845	253	53	coordinates	coordinate	NOUN
ejpam-1845	253	54	references	reference	VERB
ejpam-1845	253	55	42	42	NUM
ejpam-1845	253	56	6	6	NUM
ejpam-1845	253	57	.	.	PUNCT
ejpam-1845	254	1	conclusion	conclusion	NOUN
ejpam-1845	254	2	we	we	PRON
ejpam-1845	254	3	studied	study	VERB
ejpam-1845	254	4	poleness	poleness	ADJ
ejpam-1845	254	5	conservative	conservative	ADJ
ejpam-1845	254	6	finite	finite	ADJ
ejpam-1845	254	7	difference	difference	NOUN
ejpam-1845	254	8	scheme	scheme	NOUN
ejpam-1845	254	9	for	for	ADP
ejpam-1845	254	10	laplace	laplace	NOUN
ejpam-1845	254	11	operator	operator	NOUN
ejpam-1845	254	12	in	in	ADP
ejpam-1845	254	13	polar	polar	ADJ
ejpam-1845	254	14	coordinates	coordinate	NOUN
ejpam-1845	254	15	.	.	PUNCT
ejpam-1845	255	1	the	the	DET
ejpam-1845	255	2	scheme	scheme	NOUN
ejpam-1845	255	3	with	with	ADP
ejpam-1845	255	4	the	the	DET
ejpam-1845	255	5	modification	modification	NOUN
ejpam-1845	255	6	of	of	ADP
ejpam-1845	255	7	the	the	DET
ejpam-1845	255	8	sor	sor	NOUN
ejpam-1845	255	9	method	method	NOUN
ejpam-1845	255	10	allows	allow	VERB
ejpam-1845	255	11	to	to	PART
ejpam-1845	255	12	construct	construct	VERB
ejpam-1845	255	13	an	an	DET
ejpam-1845	255	14	effective	effective	ADJ
ejpam-1845	255	15	numerical	numerical	ADJ
ejpam-1845	255	16	method	method	NOUN
ejpam-1845	255	17	for	for	ADP
ejpam-1845	255	18	solving	solve	VERB
ejpam-1845	255	19	the	the	DET
ejpam-1845	255	20	dirichlet	dirichlet	PROPN
ejpam-1845	255	21	problem	problem	NOUN
ejpam-1845	255	22	in	in	ADP
ejpam-1845	255	23	the	the	DET
ejpam-1845	255	24	polar	polar	ADJ
ejpam-1845	255	25	coordinates	coordinate	NOUN
ejpam-1845	255	26	,	,	PUNCT
ejpam-1845	255	27	based	base	VERB
ejpam-1845	255	28	on	on	ADP
ejpam-1845	255	29	the	the	DET
ejpam-1845	255	30	weak	weak	ADJ
ejpam-1845	255	31	solution	solution	NOUN
ejpam-1845	255	32	approach	approach	NOUN
ejpam-1845	255	33	.	.	PUNCT
ejpam-1845	256	1	numerical	numerical	ADJ
ejpam-1845	256	2	results	result	NOUN
ejpam-1845	256	3	presented	present	VERB
ejpam-1845	256	4	for	for	ADP
ejpam-1845	256	5	discontinuous	discontinuous	ADJ
ejpam-1845	256	6	source	source	NOUN
ejpam-1845	256	7	function	function	NOUN
ejpam-1845	256	8	shows	show	VERB
ejpam-1845	256	9	high	high	ADJ
ejpam-1845	256	10	accuracy	accuracy	NOUN
ejpam-1845	256	11	of	of	ADP
ejpam-1845	256	12	the	the	DET
ejpam-1845	256	13	method	method	NOUN
ejpam-1845	256	14	on	on	ADP
ejpam-1845	256	15	acceptable	acceptable	ADJ
ejpam-1845	256	16	meshes	mesh	NOUN
ejpam-1845	256	17	.	.	PUNCT
ejpam-1845	257	1	extension	extension	NOUN
ejpam-1845	257	2	of	of	ADP
ejpam-1845	257	3	results	result	NOUN
ejpam-1845	257	4	given	give	VERB
ejpam-1845	257	5	here	here	ADV
ejpam-1845	257	6	can	can	AUX
ejpam-1845	257	7	be	be	AUX
ejpam-1845	257	8	made	make	VERB
ejpam-1845	257	9	for	for	ADP
ejpam-1845	257	10	positive	positive	ADJ
ejpam-1845	257	11	elliptic	elliptic	ADJ
ejpam-1845	257	12	operators	operator	NOUN
ejpam-1845	257	13	with	with	ADP
ejpam-1845	257	14	discontinuous	discontinuous	ADJ
ejpam-1845	257	15	coefficients	coefficient	NOUN
ejpam-1845	257	16	,	,	PUNCT
ejpam-1845	257	17	and	and	CCONJ
ejpam-1845	257	18	for	for	ADP
ejpam-1845	257	19	nonlinear	nonlinear	ADJ
ejpam-1845	257	20	monotone	monotone	ADJ
ejpam-1845	257	21	operators	operator	NOUN
ejpam-1845	257	22	of	of	ADP
ejpam-1845	257	23	plateau	plateau	NOUN
ejpam-1845	257	24	type	type	NOUN
ejpam-1845	257	25	,	,	PUNCT
ejpam-1845	257	26	as	as	ADV
ejpam-1845	257	27	well	well	ADV
ejpam-1845	257	28	.	.	PUNCT
ejpam-1845	258	1	this	this	PRON
ejpam-1845	258	2	require	require	VERB
ejpam-1845	258	3	some	some	DET
ejpam-1845	258	4	additional	additional	ADJ
ejpam-1845	258	5	techniques	technique	NOUN
ejpam-1845	258	6	that	that	PRON
ejpam-1845	258	7	will	will	AUX
ejpam-1845	258	8	be	be	AUX
ejpam-1845	258	9	done	do	VERB
ejpam-1845	258	10	in	in	ADP
ejpam-1845	258	11	next	next	ADJ
ejpam-1845	258	12	studies	study	NOUN
ejpam-1845	258	13	.	.	PUNCT
ejpam-1845	259	1	references	reference	NOUN
ejpam-1845	259	2	[	[	X
ejpam-1845	259	3	1	1	X
ejpam-1845	259	4	]	]	PUNCT
ejpam-1845	259	5	s.	s.	PROPN
ejpam-1845	259	6	agmon	agmon	PROPN
ejpam-1845	259	7	,	,	PUNCT
ejpam-1845	259	8	a.	a.	NOUN
ejpam-1845	259	9	douglis	douglis	PROPN
ejpam-1845	259	10	,	,	PUNCT
ejpam-1845	259	11	and	and	CCONJ
ejpam-1845	259	12	l.	l.	PROPN
ejpam-1845	259	13	nirenberg	nirenberg	PROPN
ejpam-1845	259	14	.	.	PUNCT
ejpam-1845	260	1	estimates	estimate	NOUN
ejpam-1845	260	2	near	near	ADP
ejpam-1845	260	3	the	the	DET
ejpam-1845	260	4	boundary	boundary	NOUN
ejpam-1845	260	5	for	for	ADP
ejpam-1845	260	6	solutions	solution	NOUN
ejpam-1845	260	7	of	of	ADP
ejpam-1845	260	8	elliptic	elliptic	ADJ
ejpam-1845	260	9	partial	partial	ADJ
ejpam-1845	260	10	differential	differential	ADJ
ejpam-1845	260	11	equations	equation	NOUN
ejpam-1845	260	12	satisfying	satisfy	VERB
ejpam-1845	260	13	general	general	ADJ
ejpam-1845	260	14	boundary	boundary	ADJ
ejpam-1845	260	15	conditions	condition	NOUN
ejpam-1845	260	16	.	.	PUNCT
ejpam-1845	261	1	communications	communication	NOUN
ejpam-1845	261	2	on	on	ADP
ejpam-1845	261	3	pure	pure	ADJ
ejpam-1845	261	4	and	and	CCONJ
ejpam-1845	261	5	applied	applied	ADJ
ejpam-1845	261	6	mathematics	mathematic	NOUN
ejpam-1845	261	7	.	.	PUNCT
ejpam-1845	262	1	17	17	NUM
ejpam-1845	262	2	,	,	PUNCT
ejpam-1845	262	3	35	35	NUM
ejpam-1845	262	4	-	-	SYM
ejpam-1845	262	5	92	92	NUM
ejpam-1845	262	6	.	.	PUNCT
ejpam-1845	263	1	1964	1964	NUM
ejpam-1845	263	2	.	.	PUNCT
ejpam-1845	264	1	[	[	X
ejpam-1845	264	2	2	2	NUM
ejpam-1845	264	3	]	]	PUNCT
ejpam-1845	264	4	a.m.	a.m.	NOUN
ejpam-1845	264	5	bruaset	bruaset	PROPN
ejpam-1845	264	6	.	.	PUNCT
ejpam-1845	265	1	a	a	DET
ejpam-1845	265	2	survey	survey	NOUN
ejpam-1845	265	3	of	of	ADP
ejpam-1845	265	4	preconditioned	preconditioned	ADJ
ejpam-1845	265	5	iterative	iterative	NOUN
ejpam-1845	265	6	methods	method	NOUN
ejpam-1845	265	7	.	.	PUNCT
ejpam-1845	266	1	addison	addison	PROPN
ejpam-1845	266	2	-	-	PUNCT
ejpam-1845	266	3	wesley	wesley	PROPN
ejpam-1845	266	4	.	.	PUNCT
ejpam-1845	267	1	1995	1995	NUM
ejpam-1845	267	2	.	.	PUNCT
ejpam-1845	268	1	[	[	X
ejpam-1845	268	2	3	3	NUM
ejpam-1845	268	3	]	]	X
ejpam-1845	268	4	j.d	j.d	PROPN
ejpam-1845	268	5	.	.	PROPN
ejpam-1845	268	6	jackson	jackson	PROPN
ejpam-1845	268	7	.	.	PUNCT
ejpam-1845	269	1	classical	classical	ADJ
ejpam-1845	269	2	electrodynamics	electrodynamic	NOUN
ejpam-1845	269	3	.	.	PUNCT
ejpam-1845	270	1	2nd	2nd	ADJ
ejpam-1845	270	2	ed	ed	NOUN
ejpam-1845	270	3	.	.	PROPN
ejpam-1845	270	4	,	,	PUNCT
ejpam-1845	270	5	wiley	wiley	PROPN
ejpam-1845	270	6	,	,	PUNCT
ejpam-1845	270	7	new	new	PROPN
ejpam-1845	270	8	york	york	PROPN
ejpam-1845	270	9	.	.	PUNCT
ejpam-1845	271	1	1975	1975	NUM
ejpam-1845	271	2	.	.	PUNCT
ejpam-1845	272	1	[	[	X
ejpam-1845	272	2	4	4	NUM
ejpam-1845	272	3	]	]	X
ejpam-1845	272	4	m.d	m.d	PROPN
ejpam-1845	272	5	.	.	PROPN
ejpam-1845	272	6	griffin	griffin	PROPN
ejpam-1845	272	7	,	,	PUNCT
ejpam-1845	272	8	e.	e.	PROPN
ejpam-1845	272	9	jones	jones	PROPN
ejpam-1845	272	10	,	,	PUNCT
ejpam-1845	272	11	and	and	CCONJ
ejpam-1845	272	12	j.d	j.d	PROPN
ejpam-1845	272	13	.	.	PROPN
ejpam-1845	272	14	anderson	anderson	PROPN
ejpam-1845	272	15	.	.	PUNCT
ejpam-1845	273	1	a	a	DET
ejpam-1845	273	2	computational	computational	ADJ
ejpam-1845	273	3	fluid	fluid	ADJ
ejpam-1845	273	4	dynamic	dynamic	ADJ
ejpam-1845	273	5	technique	technique	NOUN
ejpam-1845	273	6	valid	valid	NOUN
ejpam-1845	273	7	at	at	ADP
ejpam-1845	273	8	the	the	DET
ejpam-1845	273	9	centerline	centerline	NOUN
ejpam-1845	273	10	for	for	ADP
ejpam-1845	273	11	non	non	ADJ
ejpam-1845	273	12	-	-	ADJ
ejpam-1845	273	13	axisymmetric	axisymmetric	ADJ
ejpam-1845	273	14	problems	problem	NOUN
ejpam-1845	273	15	in	in	ADP
ejpam-1845	273	16	cylindrical	cylindrical	ADJ
ejpam-1845	273	17	coordinates	coordinate	NOUN
ejpam-1845	273	18	.	.	PUNCT
ejpam-1845	274	1	journal	journal	PROPN
ejpam-1845	274	2	of	of	ADP
ejpam-1845	274	3	computational	computational	ADJ
ejpam-1845	274	4	physics	physic	NOUN
ejpam-1845	274	5	.	.	PUNCT
ejpam-1845	275	1	30	30	NUM
ejpam-1845	275	2	,	,	PUNCT
ejpam-1845	275	3	352	352	NUM
ejpam-1845	275	4	-	-	SYM
ejpam-1845	275	5	364	364	NUM
ejpam-1845	275	6	.	.	PUNCT
ejpam-1845	276	1	1979	1979	NUM
ejpam-1845	276	2	.	.	PUNCT
ejpam-1845	277	1	[	[	X
ejpam-1845	277	2	5	5	X
ejpam-1845	277	3	]	]	PUNCT
ejpam-1845	277	4	w.	w.	PROPN
ejpam-1845	277	5	hackbush	hackbush	PROPN
ejpam-1845	277	6	.	.	PROPN
ejpam-1845	277	7	iterative	iterative	NOUN
ejpam-1845	277	8	solution	solution	NOUN
ejpam-1845	277	9	of	of	ADP
ejpam-1845	277	10	large	large	ADJ
ejpam-1845	277	11	sparse	sparse	ADJ
ejpam-1845	277	12	systems	system	NOUN
ejpam-1845	277	13	of	of	ADP
ejpam-1845	277	14	equations	equation	NOUN
ejpam-1845	277	15	.	.	PUNCT
ejpam-1845	278	1	springer	springer	NOUN
ejpam-1845	278	2	-	-	PUNCT
ejpam-1845	278	3	verlag	verlag	PROPN
ejpam-1845	278	4	,	,	PUNCT
ejpam-1845	278	5	berlin	berlin	PROPN
ejpam-1845	278	6	.	.	PUNCT
ejpam-1845	278	7	1994	1994	NUM
ejpam-1845	278	8	.	.	PUNCT
ejpam-1845	279	1	[	[	X
ejpam-1845	279	2	6	6	NUM
ejpam-1845	279	3	]	]	PUNCT
ejpam-1845	279	4	w.	w.	PROPN
ejpam-1845	279	5	huang	huang	PROPN
ejpam-1845	279	6	and	and	CCONJ
ejpam-1845	279	7	d.m	d.m	PROPN
ejpam-1845	279	8	.	.	PROPN
ejpam-1845	279	9	sloan	sloan	PROPN
ejpam-1845	279	10	.	.	PUNCT
ejpam-1845	280	1	pole	pole	NOUN
ejpam-1845	280	2	condition	condition	NOUN
ejpam-1845	280	3	for	for	ADP
ejpam-1845	280	4	singular	singular	ADJ
ejpam-1845	280	5	problems	problem	NOUN
ejpam-1845	280	6	:	:	PUNCT
ejpam-1845	280	7	the	the	DET
ejpam-1845	280	8	pseudo	pseudo	NOUN
ejpam-1845	280	9	-	-	ADJ
ejpam-1845	280	10	spectral	spectral	ADJ
ejpam-1845	280	11	approximation	approximation	NOUN
ejpam-1845	280	12	.	.	PUNCT
ejpam-1845	281	1	journal	journal	NOUN
ejpam-1845	281	2	of	of	ADP
ejpam-1845	281	3	computational	computational	ADJ
ejpam-1845	281	4	physics	physic	NOUN
ejpam-1845	281	5	.	.	PUNCT
ejpam-1845	282	1	107	107	NUM
ejpam-1845	282	2	,	,	PUNCT
ejpam-1845	282	3	254	254	NUM
ejpam-1845	282	4	-	-	SYM
ejpam-1845	282	5	365	365	NUM
ejpam-1845	282	6	.	.	PUNCT
ejpam-1845	282	7	1993	1993	NUM
ejpam-1845	282	8	.	.	PUNCT
ejpam-1845	283	1	[	[	X
ejpam-1845	283	2	7	7	NUM
ejpam-1845	283	3	]	]	X
ejpam-1845	283	4	p.d	p.d	PROPN
ejpam-1845	283	5	.	.	PROPN
ejpam-1845	283	6	lax	lax	PROPN
ejpam-1845	283	7	and	and	CCONJ
ejpam-1845	283	8	b.	b.	PROPN
ejpam-1845	283	9	wendroff	wendroff	PROPN
ejpam-1845	283	10	.	.	PUNCT
ejpam-1845	284	1	systems	system	NOUN
ejpam-1845	284	2	of	of	ADP
ejpam-1845	284	3	conservation	conservation	NOUN
ejpam-1845	284	4	laws	law	NOUN
ejpam-1845	284	5	.	.	PUNCT
ejpam-1845	285	1	communications	communication	NOUN
ejpam-1845	285	2	on	on	ADP
ejpam-1845	285	3	pure	pure	ADJ
ejpam-1845	285	4	and	and	CCONJ
ejpam-1845	285	5	applied	applied	ADJ
ejpam-1845	285	6	mathematics	mathematic	NOUN
ejpam-1845	285	7	.	.	PUNCT
ejpam-1845	286	1	13	13	NUM
ejpam-1845	286	2	,	,	PUNCT
ejpam-1845	286	3	217	217	NUM
ejpam-1845	286	4	-	-	SYM
ejpam-1845	286	5	237	237	NUM
ejpam-1845	286	6	.	.	PUNCT
ejpam-1845	287	1	1960	1960	NUM
ejpam-1845	287	2	.	.	PUNCT
ejpam-1845	288	1	[	[	X
ejpam-1845	288	2	8	8	NUM
ejpam-1845	288	3	]	]	X
ejpam-1845	288	4	a.i	a.i	PROPN
ejpam-1845	288	5	.	.	PROPN
ejpam-1845	288	6	lurie	lurie	PROPN
ejpam-1845	288	7	.	.	PUNCT
ejpam-1845	289	1	three	three	NUM
ejpam-1845	289	2	-	-	PUNCT
ejpam-1845	289	3	dimensional	dimensional	ADJ
ejpam-1845	289	4	problems	problem	NOUN
ejpam-1845	289	5	of	of	ADP
ejpam-1845	289	6	the	the	DET
ejpam-1845	289	7	theory	theory	NOUN
ejpam-1845	289	8	of	of	ADP
ejpam-1845	289	9	elasticity	elasticity	NOUN
ejpam-1845	289	10	.	.	PUNCT
ejpam-1845	290	1	interscience	interscience	NOUN
ejpam-1845	290	2	publishers	publisher	NOUN
ejpam-1845	290	3	,	,	PUNCT
ejpam-1845	290	4	new	new	PROPN
ejpam-1845	290	5	york	york	PROPN
ejpam-1845	290	6	.	.	PUNCT
ejpam-1845	290	7	1964	1964	NUM
ejpam-1845	290	8	.	.	PUNCT
ejpam-1845	291	1	[	[	X
ejpam-1845	291	2	9	9	NUM
ejpam-1845	291	3	]	]	X
ejpam-1845	291	4	p.e	p.e	PROPN
ejpam-1845	291	5	.	.	PROPN
ejpam-1845	291	6	merilees	merilee	NOUN
ejpam-1845	291	7	.	.	PUNCT
ejpam-1845	292	1	the	the	DET
ejpam-1845	292	2	pseudospectral	pseudospectral	ADJ
ejpam-1845	292	3	approximation	approximation	NOUN
ejpam-1845	292	4	applied	apply	VERB
ejpam-1845	292	5	to	to	ADP
ejpam-1845	292	6	the	the	DET
ejpam-1845	292	7	shallow	shallow	ADJ
ejpam-1845	292	8	water	water	NOUN
ejpam-1845	292	9	equations	equation	NOUN
ejpam-1845	292	10	on	on	ADP
ejpam-1845	292	11	a	a	DET
ejpam-1845	292	12	sphere	sphere	NOUN
ejpam-1845	292	13	.	.	PUNCT
ejpam-1845	293	1	atmosphere	atmosphere	NOUN
ejpam-1845	293	2	,	,	PUNCT
ejpam-1845	293	3	13(1	13(1	NUM
ejpam-1845	293	4	)	)	PUNCT
ejpam-1845	293	5	,	,	PUNCT
ejpam-1845	293	6	897	897	NUM
ejpam-1845	293	7	-	-	SYM
ejpam-1845	293	8	910.1973	910.1973	NUM
ejpam-1845	293	9	.	.	PUNCT
ejpam-1845	294	1	[	[	X
ejpam-1845	294	2	10	10	NUM
ejpam-1845	294	3	]	]	PUNCT
ejpam-1845	294	4	k.	k.	PROPN
ejpam-1845	294	5	mohseni	mohseni	PROPN
ejpam-1845	294	6	and	and	CCONJ
ejpam-1845	294	7	t.	t.	PROPN
ejpam-1845	294	8	colonius	colonius	PROPN
ejpam-1845	294	9	.	.	PUNCT
ejpam-1845	295	1	numerical	numerical	ADJ
ejpam-1845	295	2	treatment	treatment	NOUN
ejpam-1845	295	3	of	of	ADP
ejpam-1845	295	4	polar	polar	ADJ
ejpam-1845	295	5	coordinate	coordinate	NOUN
ejpam-1845	295	6	singularities	singularity	NOUN
ejpam-1845	295	7	.	.	PUNCT
ejpam-1845	296	1	journal	journal	NOUN
ejpam-1845	296	2	of	of	ADP
ejpam-1845	296	3	computational	computational	ADJ
ejpam-1845	296	4	physics	physics	NOUN
ejpam-1845	296	5	.	.	PUNCT
ejpam-1845	297	1	157	157	NUM
ejpam-1845	297	2	,	,	PUNCT
ejpam-1845	297	3	787	787	NUM
ejpam-1845	297	4	-	-	SYM
ejpam-1845	297	5	795	795	NUM
ejpam-1845	297	6	.	.	PUNCT
ejpam-1845	298	1	2000	2000	NUM
ejpam-1845	298	2	.	.	PUNCT
ejpam-1845	299	1	[	[	X
ejpam-1845	299	2	11	11	NUM
ejpam-1845	299	3	]	]	PUNCT
ejpam-1845	299	4	m.	m.	NOUN
ejpam-1845	299	5	renardy	renardy	PROPN
ejpam-1845	299	6	and	and	CCONJ
ejpam-1845	299	7	j.	j.	PROPN
ejpam-1845	299	8	rogers	rogers	PROPN
ejpam-1845	299	9	.	.	PUNCT
ejpam-1845	300	1	introduction	introduction	NOUN
ejpam-1845	300	2	to	to	ADP
ejpam-1845	300	3	partial	partial	ADJ
ejpam-1845	300	4	differential	differential	ADJ
ejpam-1845	300	5	equations	equation	NOUN
ejpam-1845	300	6	.	.	PUNCT
ejpam-1845	301	1	springer	springer	NOUN
ejpam-1845	301	2	-	-	PUNCT
ejpam-1845	301	3	verlag	verlag	PROPN
ejpam-1845	301	4	,	,	PUNCT
ejpam-1845	301	5	new	new	PROPN
ejpam-1845	301	6	york	york	PROPN
ejpam-1845	301	7	,	,	PUNCT
ejpam-1845	301	8	1993	1993	NUM
ejpam-1845	301	9	.	.	PUNCT
ejpam-1845	302	1	references	reference	NOUN
ejpam-1845	302	2	43	43	NUM
ejpam-1845	303	1	[	[	X
ejpam-1845	303	2	12	12	NUM
ejpam-1845	303	3	]	]	X
ejpam-1845	303	4	a.a	a.a	PROPN
ejpam-1845	303	5	.	.	PROPN
ejpam-1845	303	6	samarskii	samarskii	PROPN
ejpam-1845	303	7	and	and	CCONJ
ejpam-1845	303	8	v.b	v.b	PROPN
ejpam-1845	303	9	.	.	PROPN
ejpam-1845	303	10	andreev	andreev	PROPN
ejpam-1845	303	11	.	.	PUNCT
ejpam-1845	304	1	difference	difference	NOUN
ejpam-1845	304	2	methods	method	NOUN
ejpam-1845	304	3	for	for	ADP
ejpam-1845	304	4	elliptic	elliptic	ADJ
ejpam-1845	304	5	problems	problem	NOUN
ejpam-1845	304	6	(	(	PUNCT
ejpam-1845	304	7	in	in	ADP
ejpam-1845	304	8	russian	russian	NOUN
ejpam-1845	304	9	)	)	PUNCT
ejpam-1845	304	10	.	.	PUNCT
ejpam-1845	305	1	nauka	nauka	PROPN
ejpam-1845	305	2	,	,	PUNCT
ejpam-1845	305	3	moscow	moscow	PROPN
ejpam-1845	305	4	.	.	PUNCT
ejpam-1845	305	5	1976	1976	NUM
ejpam-1845	305	6	.	.	PUNCT
ejpam-1845	306	1	[	[	X
ejpam-1845	306	2	13	13	NUM
ejpam-1845	306	3	]	]	X
ejpam-1845	306	4	f.s	f.s	PROPN
ejpam-1845	306	5	.	.	PROPN
ejpam-1845	306	6	sharman	sharman	PROPN
ejpam-1845	306	7	.	.	PUNCT
ejpam-1845	307	1	viscous	viscous	ADJ
ejpam-1845	307	2	flow	flow	NOUN
ejpam-1845	307	3	.	.	PUNCT
ejpam-1845	308	1	mcgraw	mcgraw	PROPN
ejpam-1845	308	2	-	-	PUNCT
ejpam-1845	308	3	hill	hill	PROPN
ejpam-1845	308	4	,	,	PUNCT
ejpam-1845	308	5	new	new	PROPN
ejpam-1845	308	6	york	york	PROPN
ejpam-1845	308	7	.	.	PUNCT
ejpam-1845	308	8	1990	1990	NUM
ejpam-1845	308	9	.	.	PUNCT
ejpam-1845	309	1	[	[	X
ejpam-1845	309	2	14	14	NUM
ejpam-1845	309	3	]	]	X
ejpam-1845	309	4	r.	r.	PROPN
ejpam-1845	309	5	verzicco	verzicco	PROPN
ejpam-1845	309	6	and	and	CCONJ
ejpam-1845	309	7	p.	p.	NOUN
ejpam-1845	309	8	orlandi	orlandi	PROPN
ejpam-1845	309	9	.	.	PUNCT
ejpam-1845	310	1	a	a	DET
ejpam-1845	310	2	finite	finite	ADJ
ejpam-1845	310	3	difference	difference	NOUN
ejpam-1845	310	4	scheme	scheme	NOUN
ejpam-1845	310	5	for	for	ADP
ejpam-1845	310	6	three	three	NUM
ejpam-1845	310	7	dimensional	dimensional	ADJ
ejpam-1845	310	8	incompressible	incompressible	ADJ
ejpam-1845	310	9	flows	flow	NOUN
ejpam-1845	310	10	in	in	ADP
ejpam-1845	310	11	cylindrical	cylindrical	ADJ
ejpam-1845	310	12	coordinates	coordinate	NOUN
ejpam-1845	310	13	.	.	PUNCT
ejpam-1845	311	1	journal	journal	PROPN
ejpam-1845	311	2	of	of	ADP
ejpam-1845	311	3	computational	computational	ADJ
ejpam-1845	311	4	physics	physic	NOUN
ejpam-1845	311	5	.	.	PUNCT
ejpam-1845	312	1	123	123	NUM
ejpam-1845	312	2	,	,	PUNCT
ejpam-1845	312	3	402	402	NUM
ejpam-1845	312	4	-	-	SYM
ejpam-1845	312	5	415	415	NUM
ejpam-1845	312	6	.	.	PUNCT
ejpam-1845	313	1	1996	1996	NUM
ejpam-1845	313	2	.	.	PUNCT
ejpam-1845	314	1	[	[	X
ejpam-1845	314	2	15	15	NUM
ejpam-1845	314	3	]	]	X
ejpam-1845	314	4	f.m	f.m	PROPN
ejpam-1845	314	5	.	.	PROPN
ejpam-1845	314	6	white	white	PROPN
ejpam-1845	314	7	.	.	PUNCT
ejpam-1845	314	8	viscous	viscous	ADJ
ejpam-1845	314	9	fluid	fluid	NOUN
ejpam-1845	314	10	flow	flow	NOUN
ejpam-1845	314	11	.	.	PUNCT
ejpam-1845	315	1	mcgraw	mcgraw	PROPN
ejpam-1845	315	2	-	-	PUNCT
ejpam-1845	315	3	hill	hill	PROPN
ejpam-1845	315	4	,	,	PUNCT
ejpam-1845	315	5	new	new	PROPN
ejpam-1845	315	6	york	york	PROPN
ejpam-1845	315	7	.	.	PROPN
ejpam-1845	315	8	1991	1991	NUM
ejpam-1845	315	9	.	.	PUNCT