id	sid	tid	token	lemma	pos
iajs-3477	1	1	409	409	NUM
iajs-3477	1	2	this	this	DET
iajs-3477	1	3	work	work	NOUN
iajs-3477	1	4	is	be	AUX
iajs-3477	1	5	licensed	license	VERB
iajs-3477	1	6	under	under	ADP
iajs-3477	1	7	a	a	DET
iajs-3477	1	8	creative	creative	ADJ
iajs-3477	1	9	commons	common	NOUN
iajs-3477	1	10	attribution	attribution	NOUN
iajs-3477	1	11	4.0	4.0	NUM
iajs-3477	1	12	international	international	ADJ
iajs-3477	1	13	license	license	NOUN
iajs-3477	1	14	ihjpas.37	ihjpas.37	PROPN
iajs-3477	1	15	(	(	PUNCT
iajs-3477	1	16	2	2	NUM
iajs-3477	1	17	)	)	PUNCT
iajs-3477	1	18	2024	2024	NUM
iajs-3477	1	19	ibn	ibn	PROPN
iajs-3477	1	20	al	al	PROPN
iajs-3477	1	21	-	-	PUNCT
iajs-3477	1	22	haitham	haitham	PROPN
iajs-3477	1	23	journal	journal	PROPN
iajs-3477	1	24	for	for	ADP
iajs-3477	1	25	pure	pure	ADJ
iajs-3477	1	26	and	and	CCONJ
iajs-3477	1	27	applied	applied	ADJ
iajs-3477	1	28	sciences	sciences	PROPN
iajs-3477	1	29	journal	journal	PROPN
iajs-3477	1	30	homepage	homepage	NOUN
iajs-3477	1	31	:	:	PUNCT
iajs-3477	1	32	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	NOUN
iajs-3477	1	33	pissn	pissn	ADJ
iajs-3477	1	34	:	:	PUNCT
iajs-3477	1	35	1609	1609	NUM
iajs-3477	1	36	-	-	SYM
iajs-3477	1	37	4042	4042	NUM
iajs-3477	1	38	,	,	PUNCT
iajs-3477	1	39	eissn	eissn	NOUN
iajs-3477	1	40	:	:	PUNCT
iajs-3477	1	41	2521	2521	NUM
iajs-3477	1	42	-	-	SYM
iajs-3477	1	43	3407	3407	NUM
iajs-3477	1	44	jehan	jehan	PROPN
iajs-3477	1	45	a.qahtan1,2	a.qahtan1,2	NOUN
iajs-3477	1	46	,	,	PUNCT
iajs-3477	1	47	m.	m.	PROPN
iajs-3477	1	48	s.	s.	PROPN
iajs-3477	1	49	hussein*2	hussein*2	PROPN
iajs-3477	1	50	and	and	CCONJ
iajs-3477	1	51	taysir	taysir	PROPN
iajs-3477	1	52	e.	e.	PROPN
iajs-3477	1	53	dyhoum3	dyhoum3	PROPN
iajs-3477	2	1	1ministry	1ministry	NUM
iajs-3477	2	2	of	of	ADP
iajs-3477	2	3	education	education	NOUN
iajs-3477	2	4	,	,	PUNCT
iajs-3477	2	5	general	general	ADJ
iajs-3477	2	6	education	education	NOUN
iajs-3477	2	7	in	in	ADP
iajs-3477	2	8	baghdad	baghdad	PROPN
iajs-3477	2	9	-	-	PUNCT
iajs-3477	2	10	rusafa	rusafa	PROPN
iajs-3477	2	11	ii	ii	PROPN
iajs-3477	2	12	,	,	PUNCT
iajs-3477	2	13	baghdad	baghdad	PROPN
iajs-3477	2	14	,	,	PUNCT
iajs-3477	2	15	iraq	iraq	PROPN
iajs-3477	2	16	.	.	PUNCT
iajs-3477	3	1	2department	2department	NUM
iajs-3477	3	2	of	of	ADP
iajs-3477	3	3	mathematics	mathematic	NOUN
iajs-3477	3	4	,	,	PUNCT
iajs-3477	3	5	college	college	NOUN
iajs-3477	3	6	of	of	ADP
iajs-3477	3	7	science	science	NOUN
iajs-3477	3	8	,	,	PUNCT
iajs-3477	3	9	university	university	NOUN
iajs-3477	3	10	of	of	ADP
iajs-3477	3	11	baghdad	baghdad	PROPN
iajs-3477	3	12	,	,	PUNCT
iajs-3477	3	13	baghdad	baghdad	PROPN
iajs-3477	3	14	,	,	PUNCT
iajs-3477	3	15	iraq	iraq	PROPN
iajs-3477	3	16	.	.	PUNCT
iajs-3477	4	1	3the	3the	DET
iajs-3477	4	2	department	department	NOUN
iajs-3477	4	3	of	of	ADP
iajs-3477	4	4	computing	computing	NOUN
iajs-3477	4	5	and	and	CCONJ
iajs-3477	4	6	mathematics	mathematic	NOUN
iajs-3477	4	7	,	,	PUNCT
iajs-3477	4	8	faculty	faculty	NOUN
iajs-3477	4	9	of	of	ADP
iajs-3477	4	10	science	science	NOUN
iajs-3477	4	11	and	and	CCONJ
iajs-3477	4	12	engineering	engineering	NOUN
iajs-3477	4	13	,	,	PUNCT
iajs-3477	4	14	manchester	manchester	PROPN
iajs-3477	4	15	metropolitan	metropolitan	PROPN
iajs-3477	4	16	university	university	PROPN
iajs-3477	4	17	,	,	PUNCT
iajs-3477	4	18	manchester	manchester	PROPN
iajs-3477	4	19	,	,	PUNCT
iajs-3477	4	20	uk	uk	PROPN
iajs-3477	4	21	.	.	PROPN
iajs-3477	4	22	*	*	PUNCT
iajs-3477	4	23	corresponding	correspond	VERB
iajs-3477	4	24	author	author	NOUN
iajs-3477	4	25	.	.	PUNCT
iajs-3477	5	1	abstract	abstract	ADJ
iajs-3477	5	2	this	this	DET
iajs-3477	5	3	article	article	NOUN
iajs-3477	5	4	studies	study	VERB
iajs-3477	5	5	the	the	DET
iajs-3477	5	6	nonlocal	nonlocal	ADJ
iajs-3477	5	7	inverse	inverse	NOUN
iajs-3477	5	8	boundary	boundary	ADJ
iajs-3477	5	9	value	value	NOUN
iajs-3477	5	10	problem	problem	NOUN
iajs-3477	5	11	for	for	ADP
iajs-3477	5	12	a	a	DET
iajs-3477	5	13	rectangular	rectangular	ADJ
iajs-3477	5	14	domain	domain	NOUN
iajs-3477	5	15	,	,	PUNCT
iajs-3477	5	16	a	a	DET
iajs-3477	5	17	secondorder	secondorder	NOUN
iajs-3477	5	18	,	,	PUNCT
iajs-3477	5	19	elliptic	elliptic	ADJ
iajs-3477	5	20	equation	equation	NOUN
iajs-3477	5	21	and	and	CCONJ
iajs-3477	5	22	a	a	DET
iajs-3477	5	23	two	two	NUM
iajs-3477	5	24	-	-	PUNCT
iajs-3477	5	25	dimensional	dimensional	ADJ
iajs-3477	5	26	equation	equation	NOUN
iajs-3477	5	27	.	.	PUNCT
iajs-3477	6	1	the	the	DET
iajs-3477	6	2	main	main	ADJ
iajs-3477	6	3	objective	objective	NOUN
iajs-3477	6	4	of	of	ADP
iajs-3477	6	5	the	the	DET
iajs-3477	6	6	article	article	NOUN
iajs-3477	6	7	is	be	AUX
iajs-3477	6	8	to	to	PART
iajs-3477	6	9	find	find	VERB
iajs-3477	6	10	the	the	DET
iajs-3477	6	11	unidentified	unidentified	ADJ
iajs-3477	6	12	coefficient	coefficient	NOUN
iajs-3477	6	13	and	and	CCONJ
iajs-3477	6	14	provide	provide	VERB
iajs-3477	6	15	a	a	DET
iajs-3477	6	16	solution	solution	NOUN
iajs-3477	6	17	to	to	ADP
iajs-3477	6	18	the	the	DET
iajs-3477	6	19	problem	problem	NOUN
iajs-3477	6	20	.	.	PUNCT
iajs-3477	7	1	the	the	DET
iajs-3477	7	2	two	two	NUM
iajs-3477	7	3	-	-	PUNCT
iajs-3477	7	4	dimensional	dimensional	ADJ
iajs-3477	7	5	second	second	ADJ
iajs-3477	7	6	-	-	PUNCT
iajs-3477	7	7	order	order	NOUN
iajs-3477	7	8	,	,	PUNCT
iajs-3477	7	9	convection	convection	NOUN
iajs-3477	7	10	equation	equation	NOUN
iajs-3477	7	11	is	be	AUX
iajs-3477	7	12	solved	solve	VERB
iajs-3477	7	13	directly	directly	ADV
iajs-3477	7	14	using	use	VERB
iajs-3477	7	15	the	the	DET
iajs-3477	7	16	finite	finite	ADJ
iajs-3477	7	17	difference	difference	NOUN
iajs-3477	7	18	method	method	NOUN
iajs-3477	7	19	(	(	PUNCT
iajs-3477	7	20	fdm	fdm	NOUN
iajs-3477	7	21	)	)	PUNCT
iajs-3477	7	22	.	.	PUNCT
iajs-3477	8	1	however	however	ADV
iajs-3477	8	2	,	,	PUNCT
iajs-3477	8	3	the	the	DET
iajs-3477	8	4	inverse	inverse	NOUN
iajs-3477	8	5	problem	problem	NOUN
iajs-3477	8	6	was	be	AUX
iajs-3477	8	7	successfully	successfully	ADV
iajs-3477	8	8	solved	solve	VERB
iajs-3477	8	9	the	the	DET
iajs-3477	8	10	matlab	matlab	PROPN
iajs-3477	8	11	subroutine	subroutine	NOUN
iajs-3477	8	12	lsqnonlin	lsqnonlin	NOUN
iajs-3477	8	13	from	from	ADP
iajs-3477	8	14	the	the	DET
iajs-3477	8	15	optimization	optimization	NOUN
iajs-3477	8	16	toolbox	toolbox	NOUN
iajs-3477	8	17	after	after	ADP
iajs-3477	8	18	reformulating	reformulate	VERB
iajs-3477	8	19	it	it	PRON
iajs-3477	8	20	as	as	ADP
iajs-3477	8	21	a	a	DET
iajs-3477	8	22	nonlinear	nonlinear	ADJ
iajs-3477	8	23	regularized	regularize	VERB
iajs-3477	8	24	least	least	ADJ
iajs-3477	8	25	-	-	PUNCT
iajs-3477	8	26	square	square	NOUN
iajs-3477	8	27	optimization	optimization	NOUN
iajs-3477	8	28	problem	problem	NOUN
iajs-3477	8	29	with	with	ADP
iajs-3477	8	30	a	a	DET
iajs-3477	8	31	simple	simple	ADJ
iajs-3477	8	32	bound	bind	VERB
iajs-3477	8	33	on	on	ADP
iajs-3477	8	34	the	the	DET
iajs-3477	8	35	unknown	unknown	ADJ
iajs-3477	8	36	quantity	quantity	NOUN
iajs-3477	8	37	.	.	PUNCT
iajs-3477	9	1	considering	consider	VERB
iajs-3477	9	2	that	that	SCONJ
iajs-3477	9	3	the	the	DET
iajs-3477	9	4	problem	problem	NOUN
iajs-3477	9	5	under	under	ADP
iajs-3477	9	6	study	study	NOUN
iajs-3477	9	7	is	be	AUX
iajs-3477	9	8	often	often	ADV
iajs-3477	9	9	ill	ill	ADV
iajs-3477	9	10	-	-	PUNCT
iajs-3477	9	11	posed	pose	VERB
iajs-3477	9	12	and	and	CCONJ
iajs-3477	9	13	that	that	SCONJ
iajs-3477	9	14	even	even	ADV
iajs-3477	9	15	a	a	DET
iajs-3477	9	16	small	small	ADJ
iajs-3477	9	17	error	error	NOUN
iajs-3477	9	18	in	in	ADP
iajs-3477	9	19	the	the	DET
iajs-3477	9	20	input	input	NOUN
iajs-3477	9	21	data	datum	NOUN
iajs-3477	9	22	can	can	AUX
iajs-3477	9	23	have	have	VERB
iajs-3477	9	24	a	a	DET
iajs-3477	9	25	large	large	ADJ
iajs-3477	9	26	impact	impact	NOUN
iajs-3477	9	27	on	on	ADP
iajs-3477	9	28	the	the	DET
iajs-3477	9	29	outcome	outcome	NOUN
iajs-3477	9	30	,	,	PUNCT
iajs-3477	9	31	tikhonov	tikhonov	NOUN
iajs-3477	9	32	's	's	PART
iajs-3477	9	33	regularization	regularization	NOUN
iajs-3477	9	34	technique	technique	NOUN
iajs-3477	9	35	is	be	AUX
iajs-3477	9	36	used	use	VERB
iajs-3477	9	37	to	to	PART
iajs-3477	9	38	obtain	obtain	VERB
iajs-3477	9	39	stable	stable	ADJ
iajs-3477	9	40	and	and	CCONJ
iajs-3477	9	41	regularized	regularize	VERB
iajs-3477	9	42	results	result	NOUN
iajs-3477	9	43	.	.	PUNCT
iajs-3477	10	1	keywords	keyword	NOUN
iajs-3477	10	2	:	:	PUNCT
iajs-3477	10	3	inverse	inverse	ADJ
iajs-3477	10	4	problem	problem	NOUN
iajs-3477	10	5	,	,	PUNCT
iajs-3477	10	6	two	two	NUM
iajs-3477	10	7	-	-	PUNCT
iajs-3477	10	8	dimensional	dimensional	ADJ
iajs-3477	10	9	parabolic	parabolic	ADJ
iajs-3477	10	10	equation	equation	NOUN
iajs-3477	10	11	,	,	PUNCT
iajs-3477	10	12	overdetermination	overdetermination	NOUN
iajs-3477	10	13	condition	condition	NOUN
iajs-3477	10	14	,	,	PUNCT
iajs-3477	10	15	finite	finite	ADJ
iajs-3477	10	16	difference	difference	NOUN
iajs-3477	10	17	schemes	scheme	NOUN
iajs-3477	10	18	,	,	PUNCT
iajs-3477	10	19	tikhonov	tikhonov	NOUN
iajs-3477	10	20	technique	technique	NOUN
iajs-3477	10	21	.	.	PUNCT
iajs-3477	11	1	1	1	X
iajs-3477	11	2	.	.	X
iajs-3477	11	3	introduction	introduction	NOUN
iajs-3477	11	4	partial	partial	ADJ
iajs-3477	11	5	differential	differential	NOUN
iajs-3477	11	6	equations	equation	NOUN
iajs-3477	11	7	play	play	VERB
iajs-3477	11	8	an	an	DET
iajs-3477	11	9	important	important	ADJ
iajs-3477	11	10	role	role	NOUN
iajs-3477	11	11	in	in	ADP
iajs-3477	11	12	many	many	ADJ
iajs-3477	11	13	areas	area	NOUN
iajs-3477	11	14	of	of	ADP
iajs-3477	11	15	everyday	everyday	ADJ
iajs-3477	11	16	life	life	NOUN
iajs-3477	11	17	.	.	PUNCT
iajs-3477	12	1	in	in	ADP
iajs-3477	12	2	the	the	DET
iajs-3477	12	3	fields	field	NOUN
iajs-3477	12	4	of	of	ADP
iajs-3477	12	5	engineering	engineering	NOUN
iajs-3477	12	6	,	,	PUNCT
iajs-3477	12	7	design	design	NOUN
iajs-3477	12	8	,	,	PUNCT
iajs-3477	12	9	construction	construction	NOUN
iajs-3477	12	10	and	and	CCONJ
iajs-3477	12	11	medicine	medicine	NOUN
iajs-3477	12	12	,	,	PUNCT
iajs-3477	12	13	for	for	ADP
iajs-3477	12	14	example	example	NOUN
iajs-3477	12	15	,	,	PUNCT
iajs-3477	12	16	high	high	ADJ
iajs-3477	12	17	-	-	PUNCT
iajs-3477	12	18	speed	speed	NOUN
iajs-3477	12	19	computers	computer	NOUN
iajs-3477	12	20	have	have	AUX
iajs-3477	12	21	greatly	greatly	ADV
iajs-3477	12	22	influenced	influence	VERB
iajs-3477	12	23	the	the	DET
iajs-3477	12	24	development	development	NOUN
iajs-3477	12	25	of	of	ADP
iajs-3477	12	26	numerical	numerical	ADJ
iajs-3477	12	27	methods	method	NOUN
iajs-3477	12	28	for	for	ADP
iajs-3477	12	29	solving	solve	VERB
iajs-3477	12	30	partial	partial	ADJ
iajs-3477	12	31	differential	differential	NOUN
iajs-3477	12	32	equations	equation	NOUN
iajs-3477	12	33	,	,	PUNCT
iajs-3477	12	34	advancing	advance	VERB
iajs-3477	12	35	and	and	CCONJ
iajs-3477	12	36	modernizing	modernize	VERB
iajs-3477	12	37	them	they	PRON
iajs-3477	12	38	compared	compare	VERB
iajs-3477	12	39	to	to	ADP
iajs-3477	12	40	analytical	analytical	ADJ
iajs-3477	12	41	methods	method	NOUN
iajs-3477	12	42	.	.	PUNCT
iajs-3477	13	1	researchers	researcher	NOUN
iajs-3477	13	2	continue	continue	VERB
iajs-3477	13	3	to	to	PART
iajs-3477	13	4	observe	observe	VERB
iajs-3477	13	5	steady	steady	ADJ
iajs-3477	13	6	progress	progress	NOUN
iajs-3477	13	7	in	in	ADP
iajs-3477	13	8	this	this	DET
iajs-3477	13	9	field	field	NOUN
iajs-3477	13	10	.	.	PUNCT
iajs-3477	14	1	according	accord	VERB
iajs-3477	14	2	to	to	ADP
iajs-3477	14	3	mathematicians	mathematician	NOUN
iajs-3477	14	4	,	,	PUNCT
iajs-3477	14	5	it	it	PRON
iajs-3477	14	6	is	be	AUX
iajs-3477	14	7	the	the	DET
iajs-3477	14	8	first	first	ADJ
iajs-3477	14	9	inverse	inverse	NOUN
iajs-3477	14	10	(	(	PUNCT
iajs-3477	14	11	ill	ill	ADV
iajs-3477	14	12	-	-	PUNCT
iajs-3477	14	13	posed	pose	VERB
iajs-3477	14	14	)	)	PUNCT
iajs-3477	14	15	problem	problem	NOUN
iajs-3477	14	16	in	in	ADP
iajs-3477	14	17	mathematics	mathematic	NOUN
iajs-3477	14	18	,	,	PUNCT
iajs-3477	14	19	(	(	PUNCT
iajs-3477	14	20	hadamard	hadamard	ADJ
iajs-3477	14	21	,	,	PUNCT
iajs-3477	14	22	1902	1902	NUM
iajs-3477	14	23	)	)	PUNCT
iajs-3477	14	24	.	.	PUNCT
iajs-3477	15	1	however	however	ADV
iajs-3477	15	2	,	,	PUNCT
iajs-3477	15	3	this	this	DET
iajs-3477	15	4	problem	problem	NOUN
iajs-3477	15	5	has	have	AUX
iajs-3477	15	6	changed	change	VERB
iajs-3477	15	7	.	.	PUNCT
iajs-3477	16	1	in	in	ADP
iajs-3477	16	2	the	the	DET
iajs-3477	16	3	twentieth	twentieth	ADJ
iajs-3477	16	4	century	century	NOUN
iajs-3477	16	5	,	,	PUNCT
iajs-3477	16	6	practical	practical	ADJ
iajs-3477	16	7	applications	application	NOUN
iajs-3477	16	8	are	be	AUX
iajs-3477	16	9	constantly	constantly	ADV
iajs-3477	16	10	being	be	AUX
iajs-3477	16	11	researched	research	VERB
iajs-3477	16	12	,	,	PUNCT
iajs-3477	16	13	which	which	PRON
iajs-3477	16	14	is	be	AUX
iajs-3477	16	15	of	of	ADP
iajs-3477	16	16	great	great	ADJ
iajs-3477	16	17	interest	interest	NOUN
iajs-3477	16	18	for	for	ADP
iajs-3477	16	19	solving	solve	VERB
iajs-3477	16	20	elliptic	elliptic	ADJ
iajs-3477	16	21	problems	problem	NOUN
iajs-3477	16	22	.	.	PUNCT
iajs-3477	17	1	it	it	PRON
iajs-3477	17	2	has	have	AUX
iajs-3477	17	3	been	be	AUX
iajs-3477	17	4	studied	study	VERB
iajs-3477	17	5	by	by	ADP
iajs-3477	17	6	many	many	ADJ
iajs-3477	17	7	researchers	researcher	NOUN
iajs-3477	17	8	.	.	PUNCT
iajs-3477	18	1	in	in	ADP
iajs-3477	18	2	[	[	X
iajs-3477	18	3	1	1	NUM
iajs-3477	18	4	]	]	PUNCT
iajs-3477	18	5	,	,	PUNCT
iajs-3477	18	6	the	the	DET
iajs-3477	18	7	approximate	approximate	ADJ
iajs-3477	18	8	solution	solution	NOUN
iajs-3477	18	9	of	of	ADP
iajs-3477	18	10	the	the	DET
iajs-3477	18	11	inverse	inverse	NOUN
iajs-3477	18	12	elliptic	elliptic	ADJ
iajs-3477	18	13	problem	problem	NOUN
iajs-3477	18	14	with	with	ADP
iajs-3477	18	15	the	the	DET
iajs-3477	18	16	dirichlet	dirichlet	PROPN
iajs-3477	18	17	condition	condition	NOUN
iajs-3477	18	18	was	be	AUX
iajs-3477	18	19	obtained	obtain	VERB
iajs-3477	18	20	using	use	VERB
iajs-3477	18	21	the	the	DET
iajs-3477	18	22	finite	finite	ADJ
iajs-3477	18	23	difference	difference	NOUN
iajs-3477	18	24	method	method	NOUN
iajs-3477	18	25	.	.	PUNCT
iajs-3477	19	1	in	in	ADP
iajs-3477	19	2	[	[	X
iajs-3477	19	3	2	2	NUM
iajs-3477	19	4	]	]	PUNCT
iajs-3477	19	5	,	,	PUNCT
iajs-3477	19	6	we	we	PRON
iajs-3477	19	7	have	have	AUX
iajs-3477	19	8	used	use	VERB
iajs-3477	19	9	the	the	DET
iajs-3477	19	10	schwarz	schwarz	NOUN
iajs-3477	19	11	-	-	PUNCT
iajs-3477	19	12	alternating	alternate	VERB
iajs-3477	19	13	method	method	NOUN
iajs-3477	19	14	.	.	PUNCT
iajs-3477	20	1	the	the	DET
iajs-3477	20	2	numerical	numerical	ADJ
iajs-3477	20	3	solution	solution	NOUN
iajs-3477	20	4	of	of	ADP
iajs-3477	20	5	the	the	DET
iajs-3477	20	6	inverse	inverse	NOUN
iajs-3477	20	7	problem	problem	NOUN
iajs-3477	20	8	for	for	ADP
iajs-3477	20	9	the	the	DET
iajs-3477	20	10	multidimensional	multidimensional	ADJ
iajs-3477	20	11	elliptic	elliptic	ADJ
iajs-3477	20	12	equation	equation	NOUN
iajs-3477	20	13	with	with	ADP
iajs-3477	20	14	overdetermination	overdetermination	NOUN
iajs-3477	20	15	is	be	AUX
iajs-3477	20	16	obtained	obtain	VERB
iajs-3477	20	17	using	use	VERB
iajs-3477	20	18	a	a	DET
iajs-3477	20	19	finite	finite	ADJ
iajs-3477	20	20	difference	difference	NOUN
iajs-3477	20	21	method	method	NOUN
iajs-3477	20	22	in	in	ADP
iajs-3477	20	23	[	[	X
iajs-3477	20	24	3	3	NUM
iajs-3477	20	25	]	]	PUNCT
iajs-3477	20	26	,	,	PUNCT
iajs-3477	20	27	a	a	DET
iajs-3477	20	28	finite	finite	ADJ
iajs-3477	20	29	element	element	NOUN
iajs-3477	20	30	method	method	NOUN
iajs-3477	20	31	in	in	ADP
iajs-3477	20	32	[	[	X
iajs-3477	20	33	4	4	NUM
iajs-3477	20	34	]	]	PUNCT
iajs-3477	20	35	,	,	PUNCT
iajs-3477	20	36	an	an	DET
iajs-3477	20	37	integral	integral	ADJ
iajs-3477	20	38	equation	equation	NOUN
iajs-3477	20	39	method	method	NOUN
iajs-3477	20	40	in	in	ADP
iajs-3477	20	41	space	space	NOUN
iajs-3477	20	42	[	[	X
iajs-3477	20	43	5	5	NUM
iajs-3477	20	44	]	]	PUNCT
iajs-3477	20	45	,	,	PUNCT
iajs-3477	20	46	the	the	DET
iajs-3477	20	47	tikhonov	tikhonov	NOUN
iajs-3477	20	48	regularization	regularization	NOUN
iajs-3477	20	49	method	method	NOUN
iajs-3477	20	50	in	in	ADP
iajs-3477	20	51	[	[	X
iajs-3477	20	52	6–24	6–24	NOUN
iajs-3477	20	53	]	]	PUNCT
iajs-3477	20	54	,	,	PUNCT
iajs-3477	20	55	and	and	CCONJ
iajs-3477	20	56	the	the	DET
iajs-3477	20	57	lavrentiev	lavrentiev	ADJ
iajs-3477	20	58	regularization	regularization	NOUN
iajs-3477	20	59	method	method	NOUN
iajs-3477	20	60	[	[	X
iajs-3477	20	61	25	25	NUM
iajs-3477	20	62	]	]	PUNCT
iajs-3477	20	63	.	.	PUNCT
iajs-3477	21	1	the	the	DET
iajs-3477	21	2	existence	existence	NOUN
iajs-3477	21	3	and	and	CCONJ
iajs-3477	21	4	uniqueness	uniqueness	NOUN
iajs-3477	21	5	of	of	ADP
iajs-3477	21	6	a	a	DET
iajs-3477	21	7	solution	solution	NOUN
iajs-3477	21	8	to	to	ADP
iajs-3477	21	9	this	this	DET
iajs-3477	21	10	problem	problem	NOUN
iajs-3477	21	11	was	be	AUX
iajs-3477	21	12	proved	prove	VERB
iajs-3477	21	13	in	in	ADP
iajs-3477	21	14	[	[	X
iajs-3477	21	15	26	26	NUM
iajs-3477	21	16	]	]	PUNCT
iajs-3477	21	17	,	,	PUNCT
iajs-3477	21	18	and	and	CCONJ
iajs-3477	21	19	this	this	DET
iajs-3477	21	20	paper	paper	NOUN
iajs-3477	21	21	aims	aim	VERB
iajs-3477	21	22	to	to	ADP
iajs-3477	21	23	an	an	DET
iajs-3477	21	24	approximate	approximate	ADJ
iajs-3477	21	25	solution	solution	NOUN
iajs-3477	21	26	for	for	ADP
iajs-3477	21	27	a	a	DET
iajs-3477	21	28	second	second	ADJ
iajs-3477	21	29	order	order	NOUN
iajs-3477	21	30	elliptic	elliptic	ADJ
iajs-3477	21	31	inverse	inverse	NOUN
iajs-3477	21	32	coefficient	coefficient	NOUN
iajs-3477	21	33	problem	problem	NOUN
iajs-3477	21	34	with	with	ADP
iajs-3477	21	35	nonlocal	nonlocal	ADJ
iajs-3477	21	36	integral	integral	ADJ
iajs-3477	21	37	doi.org/10.30526/37.2.3477	doi.org/10.30526/37.2.3477	NOUN
iajs-3477	21	38	received	receive	VERB
iajs-3477	21	39	:	:	PUNCT
iajs-3477	21	40	8	8	NUM
iajs-3477	21	41	may	may	PROPN
iajs-3477	21	42	2023	2023	NUM
iajs-3477	21	43	accepted	accept	VERB
iajs-3477	21	44	:	:	PUNCT
iajs-3477	21	45	11	11	NUM
iajs-3477	21	46	june	june	PROPN
iajs-3477	21	47	2023	2023	NUM
iajs-3477	21	48	published	publish	VERB
iajs-3477	21	49	:	:	PUNCT
iajs-3477	21	50	20	20	NUM
iajs-3477	21	51	april	april	PROPN
iajs-3477	21	52	2024	2024	NUM
iajs-3477	21	53	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3477	21	54	https://jih.uobaghdad.edu.iq/index.php/j/index#1609-4042	https://jih.uobaghdad.edu.iq/index.php/j/index#1609-4042	NOUN
iajs-3477	21	55	https://jih.uobaghdad.edu.iq/index.php/j/index#2521-3407	https://jih.uobaghdad.edu.iq/index.php/j/index#2521-3407	VERB
iajs-3477	21	56	https://orcid.org/0009-0001-2711-9824	https://orcid.org/0009-0001-2711-9824	ADJ
iajs-3477	21	57	mailto:jehan.adnan.8787@gmail.com	mailto:jehan.adnan.8787@gmail.com	X
iajs-3477	21	58	https://orcid.org/0000-0002-9456-4303	https://orcid.org/0000-0002-9456-4303	PROPN
iajs-3477	21	59	mailto:mmmsh@sc.uobaghdad.edu.iq	mailto:mmmsh@sc.uobaghdad.edu.iq	PROPN
iajs-3477	21	60	https://orcid.org/0000-0002-1761-5904	https://orcid.org/0000-0002-1761-5904	PROPN
iajs-3477	21	61	mailto:t.dyhoum@mmu.ac.uk	mailto:t.dyhoum@mmu.ac.uk	PROPN
iajs-3477	21	62	ihjpas	ihjpa	VERB
iajs-3477	21	63	.	.	PUNCT
iajs-3477	22	1	37	37	NUM
iajs-3477	22	2	(	(	PUNCT
iajs-3477	22	3	2	2	NUM
iajs-3477	22	4	)	)	PUNCT
iajs-3477	22	5	2024	2024	NUM
iajs-3477	22	6	410	410	NUM
iajs-3477	22	7	solve	solve	VERB
iajs-3477	22	8	this	this	DET
iajs-3477	22	9	type	type	NOUN
iajs-3477	22	10	of	of	ADP
iajs-3477	22	11	problem	problem	NOUN
iajs-3477	22	12	numerically	numerically	ADV
iajs-3477	22	13	.	.	PUNCT
iajs-3477	23	1	this	this	DET
iajs-3477	23	2	article	article	NOUN
iajs-3477	23	3	describes	describe	VERB
iajs-3477	23	4	a	a	DET
iajs-3477	23	5	way	way	NOUN
iajs-3477	23	6	to	to	PART
iajs-3477	23	7	solve	solve	VERB
iajs-3477	23	8	this	this	DET
iajs-3477	23	9	type	type	NOUN
iajs-3477	23	10	of	of	ADP
iajs-3477	23	11	inverse	inverse	NOUN
iajs-3477	23	12	coefficient	coefficient	NOUN
iajs-3477	23	13	problem	problem	NOUN
iajs-3477	23	14	numerically	numerically	ADV
iajs-3477	23	15	that	that	PRON
iajs-3477	23	16	is	be	AUX
iajs-3477	23	17	stable	stable	ADJ
iajs-3477	23	18	.	.	PUNCT
iajs-3477	24	1	it	it	PRON
iajs-3477	24	2	uses	use	VERB
iajs-3477	24	3	the	the	DET
iajs-3477	24	4	finite	finite	ADJ
iajs-3477	24	5	difference	difference	NOUN
iajs-3477	24	6	method	method	NOUN
iajs-3477	24	7	(	(	PUNCT
iajs-3477	24	8	fdm	fdm	NOUN
iajs-3477	24	9	)	)	PUNCT
iajs-3477	24	10	,	,	PUNCT
iajs-3477	24	11	an	an	DET
iajs-3477	24	12	optimization	optimization	NOUN
iajs-3477	24	13	method	method	NOUN
iajs-3477	24	14	,	,	PUNCT
iajs-3477	24	15	and	and	CCONJ
iajs-3477	24	16	the	the	DET
iajs-3477	24	17	tikhonov	tikhonov	NOUN
iajs-3477	24	18	regularization	regularization	NOUN
iajs-3477	24	19	.	.	PUNCT
iajs-3477	25	1	the	the	DET
iajs-3477	25	2	direct	direct	ADJ
iajs-3477	25	3	numerical	numerical	ADJ
iajs-3477	25	4	solution	solution	NOUN
iajs-3477	25	5	of	of	ADP
iajs-3477	25	6	the	the	DET
iajs-3477	25	7	problem	problem	NOUN
iajs-3477	25	8	was	be	AUX
iajs-3477	25	9	obtained	obtain	VERB
iajs-3477	25	10	using	use	VERB
iajs-3477	25	11	fdm	fdm	NOUN
iajs-3477	25	12	.	.	PUNCT
iajs-3477	26	1	subsequently	subsequently	ADV
iajs-3477	26	2	,	,	PUNCT
iajs-3477	26	3	we	we	PRON
iajs-3477	26	4	used	use	VERB
iajs-3477	26	5	tikhonov	tikhonov	NOUN
iajs-3477	26	6	's	's	PART
iajs-3477	26	7	approach	approach	NOUN
iajs-3477	26	8	to	to	PART
iajs-3477	26	9	stabilize	stabilize	VERB
iajs-3477	26	10	this	this	DET
iajs-3477	26	11	problem	problem	NOUN
iajs-3477	26	12	.	.	PUNCT
iajs-3477	27	1	section	section	NOUN
iajs-3477	27	2	2	2	NUM
iajs-3477	27	3	presents	present	VERB
iajs-3477	27	4	the	the	DET
iajs-3477	27	5	mathematical	mathematical	ADJ
iajs-3477	27	6	formulation	formulation	NOUN
iajs-3477	27	7	of	of	ADP
iajs-3477	27	8	the	the	DET
iajs-3477	27	9	inverse	inverse	NOUN
iajs-3477	27	10	problem	problem	NOUN
iajs-3477	27	11	.	.	PUNCT
iajs-3477	28	1	in	in	ADP
iajs-3477	28	2	section	section	NOUN
iajs-3477	28	3	2	2	NUM
iajs-3477	28	4	,	,	PUNCT
iajs-3477	28	5	we	we	PRON
iajs-3477	28	6	present	present	VERB
iajs-3477	28	7	the	the	DET
iajs-3477	28	8	mathematical	mathematical	ADJ
iajs-3477	28	9	formulation	formulation	NOUN
iajs-3477	28	10	of	of	ADP
iajs-3477	28	11	the	the	DET
iajs-3477	28	12	inverse	inverse	NOUN
iajs-3477	28	13	problem	problem	NOUN
iajs-3477	28	14	.	.	PUNCT
iajs-3477	29	1	section	section	NOUN
iajs-3477	29	2	3	3	NUM
iajs-3477	29	3	describes	describe	VERB
iajs-3477	29	4	the	the	DET
iajs-3477	29	5	direct	direct	ADJ
iajs-3477	29	6	finite	finite	ADJ
iajs-3477	29	7	difference	difference	NOUN
iajs-3477	29	8	scheme	scheme	NOUN
iajs-3477	29	9	to	to	PART
iajs-3477	29	10	obtain	obtain	VERB
iajs-3477	29	11	the	the	DET
iajs-3477	29	12	numerical	numerical	ADJ
iajs-3477	29	13	solution	solution	NOUN
iajs-3477	29	14	of	of	ADP
iajs-3477	29	15	a	a	DET
iajs-3477	29	16	direct	direct	ADJ
iajs-3477	29	17	problem	problem	NOUN
iajs-3477	29	18	,	,	PUNCT
iajs-3477	29	19	along	along	ADP
iajs-3477	29	20	with	with	ADP
iajs-3477	29	21	numerical	numerical	ADJ
iajs-3477	29	22	test	test	NOUN
iajs-3477	29	23	examples	example	NOUN
iajs-3477	29	24	.	.	PUNCT
iajs-3477	30	1	while	while	SCONJ
iajs-3477	30	2	section	section	NOUN
iajs-3477	30	3	4	4	NUM
iajs-3477	30	4	describes	describe	VERB
iajs-3477	30	5	the	the	DET
iajs-3477	30	6	numerical	numerical	ADJ
iajs-3477	30	7	approach	approach	NOUN
iajs-3477	30	8	to	to	PART
iajs-3477	30	9	solve	solve	VERB
iajs-3477	30	10	an	an	DET
iajs-3477	30	11	inverse	inverse	NOUN
iajs-3477	30	12	problem	problem	NOUN
iajs-3477	30	13	using	use	VERB
iajs-3477	30	14	the	the	DET
iajs-3477	30	15	tikhonov	tikhonov	NOUN
iajs-3477	30	16	technique	technique	NOUN
iajs-3477	30	17	,	,	PUNCT
iajs-3477	30	18	section	section	NOUN
iajs-3477	30	19	5	5	NUM
iajs-3477	30	20	provides	provide	VERB
iajs-3477	30	21	a	a	DET
iajs-3477	30	22	regularized	regularize	VERB
iajs-3477	30	23	solution	solution	NOUN
iajs-3477	30	24	.	.	PUNCT
iajs-3477	31	1	section	section	NOUN
iajs-3477	31	2	5	5	NUM
iajs-3477	31	3	presents	present	NOUN
iajs-3477	31	4	and	and	CCONJ
iajs-3477	31	5	discusses	discuss	VERB
iajs-3477	31	6	the	the	DET
iajs-3477	31	7	quantitative	quantitative	ADJ
iajs-3477	31	8	results	result	NOUN
iajs-3477	31	9	.	.	PUNCT
iajs-3477	32	1	the	the	DET
iajs-3477	32	2	conclusion	conclusion	NOUN
iajs-3477	32	3	of	of	ADP
iajs-3477	32	4	the	the	DET
iajs-3477	32	5	paper	paper	NOUN
iajs-3477	32	6	can	can	AUX
iajs-3477	32	7	be	be	AUX
iajs-3477	32	8	found	find	VERB
iajs-3477	32	9	in	in	ADP
iajs-3477	32	10	section	section	NOUN
iajs-3477	32	11	6	6	NUM
iajs-3477	32	12	.	.	NOUN
iajs-3477	33	1	2	2	NUM
iajs-3477	33	2	.	.	NOUN
iajs-3477	33	3	mathematical	mathematical	ADJ
iajs-3477	33	4	formulation	formulation	NOUN
iajs-3477	33	5	consider	consider	VERB
iajs-3477	33	6	the	the	DET
iajs-3477	33	7	following	follow	VERB
iajs-3477	33	8	inverse	inverse	NOUN
iajs-3477	33	9	problem	problem	NOUN
iajs-3477	33	10	of	of	ADP
iajs-3477	33	11	retrieving	retrieve	VERB
iajs-3477	33	12	an	an	DET
iajs-3477	33	13	unknown	unknown	ADJ
iajs-3477	33	14	time	time	NOUN
iajs-3477	33	15	-	-	PUNCT
iajs-3477	33	16	dependent	dependent	ADJ
iajs-3477	33	17	potential	potential	ADJ
iajs-3477	33	18	coefficient	coefficient	NOUN
iajs-3477	33	19	a(y	a(y	PROPN
iajs-3477	33	20	)	)	PUNCT
iajs-3477	33	21	in	in	ADP
iajs-3477	33	22	the	the	DET
iajs-3477	33	23	two	two	NUM
iajs-3477	33	24	-	-	PUNCT
iajs-3477	33	25	dimensional	dimensional	ADJ
iajs-3477	33	26	second	second	ADJ
iajs-3477	33	27	-	-	PUNCT
iajs-3477	33	28	order	order	NOUN
iajs-3477	33	29	elliptic	elliptic	ADJ
iajs-3477	33	30	equation	equation	NOUN
iajs-3477	33	31	:	:	PUNCT
iajs-3477	33	32	uxx(x	uxx(x	PROPN
iajs-3477	33	33	,	,	PUNCT
iajs-3477	33	34	y	y	NOUN
iajs-3477	33	35	)	)	PUNCT
iajs-3477	34	1	+	+	CCONJ
iajs-3477	34	2	uyy(x	uyy(x	PROPN
iajs-3477	34	3	,	,	PUNCT
iajs-3477	34	4	y	y	NOUN
iajs-3477	34	5	)	)	PUNCT
iajs-3477	34	6	=	=	SYM
iajs-3477	34	7	a(y)u(x	a(y)u(x	NOUN
iajs-3477	34	8	,	,	PUNCT
iajs-3477	34	9	y	y	NOUN
iajs-3477	34	10	)	)	PUNCT
iajs-3477	35	1	+	+	CCONJ
iajs-3477	35	2	f(x	f(x	PROPN
iajs-3477	35	3	,	,	PUNCT
iajs-3477	35	4	y	y	PROPN
iajs-3477	35	5	)	)	PUNCT
iajs-3477	35	6	,	,	PUNCT
iajs-3477	35	7	(	(	PUNCT
iajs-3477	35	8	x	x	X
iajs-3477	35	9	,	,	PUNCT
iajs-3477	35	10	y	y	NOUN
iajs-3477	35	11	)	)	PUNCT
iajs-3477	35	12	∈	∈	PROPN
iajs-3477	35	13	q	q	X
iajs-3477	35	14	(	(	PUNCT
iajs-3477	35	15	1	1	NUM
iajs-3477	35	16	)	)	PUNCT
iajs-3477	35	17	under	under	ADP
iajs-3477	35	18	the	the	DET
iajs-3477	35	19	boundary	boundary	ADJ
iajs-3477	35	20	conditions	condition	NOUN
iajs-3477	35	21	u(x	u(x	NOUN
iajs-3477	35	22	,	,	PUNCT
iajs-3477	35	23	0	0	NUM
iajs-3477	35	24	)	)	PUNCT
iajs-3477	35	25	=	=	SYM
iajs-3477	35	26	φ(x	φ(x	NOUN
iajs-3477	35	27	)	)	PUNCT
iajs-3477	35	28	,	,	PUNCT
iajs-3477	35	29	uy(x	uy(x	X
iajs-3477	35	30	,	,	PUNCT
iajs-3477	35	31	y	y	NOUN
iajs-3477	35	32	)	)	PUNCT
iajs-3477	35	33	=	=	SYM
iajs-3477	35	34	ψ(x	ψ(x	NOUN
iajs-3477	35	35	)	)	PUNCT
iajs-3477	35	36	,	,	PUNCT
iajs-3477	36	1	x	x	PUNCT
iajs-3477	36	2	∈	∈	NOUN
iajs-3477	37	1	[	[	X
iajs-3477	37	2	0,1	0,1	NUM
iajs-3477	37	3	]	]	PUNCT
iajs-3477	37	4	,	,	PUNCT
iajs-3477	37	5	(	(	PUNCT
iajs-3477	37	6	2	2	X
iajs-3477	37	7	)	)	PUNCT
iajs-3477	37	8	ux(0	ux(0	PROPN
iajs-3477	37	9	,	,	PUNCT
iajs-3477	37	10	y	y	NOUN
iajs-3477	37	11	)	)	PUNCT
iajs-3477	37	12	=	=	SYM
iajs-3477	38	1	0	0	NUM
iajs-3477	38	2	,	,	PUNCT
iajs-3477	38	3	y	y	PROPN
iajs-3477	38	4	∈	∈	PROPN
iajs-3477	39	1	[	[	X
iajs-3477	39	2	0	0	NUM
iajs-3477	39	3	,	,	PUNCT
iajs-3477	39	4	y	y	PROPN
iajs-3477	39	5	]	]	X
iajs-3477	39	6	,	,	PUNCT
iajs-3477	39	7	(	(	PUNCT
iajs-3477	39	8	3	3	X
iajs-3477	39	9	)	)	PUNCT
iajs-3477	39	10	with	with	ADP
iajs-3477	39	11	the	the	DET
iajs-3477	39	12	nonlocal	nonlocal	ADJ
iajs-3477	39	13	integral	integral	ADJ
iajs-3477	39	14	condition	condition	NOUN
iajs-3477	39	15	∫u(x	∫u(x	NOUN
iajs-3477	39	16	,	,	PUNCT
iajs-3477	39	17	y)dx	y)dx	PROPN
iajs-3477	39	18	1	1	NUM
iajs-3477	39	19	0	0	NUM
iajs-3477	39	20	=	=	SYM
iajs-3477	39	21	0	0	PROPN
iajs-3477	39	22	,	,	PUNCT
iajs-3477	39	23	y	y	PROPN
iajs-3477	39	24	∈	∈	PROPN
iajs-3477	40	1	[	[	X
iajs-3477	40	2	0	0	NUM
iajs-3477	40	3	,	,	PUNCT
iajs-3477	40	4	y	y	PROPN
iajs-3477	40	5	]	]	X
iajs-3477	40	6	,	,	PUNCT
iajs-3477	40	7	(	(	PUNCT
iajs-3477	40	8	4	4	NUM
iajs-3477	40	9	)	)	PUNCT
iajs-3477	40	10	and	and	CCONJ
iajs-3477	40	11	additional	additional	ADJ
iajs-3477	40	12	measurement	measurement	NOUN
iajs-3477	40	13	condition	condition	NOUN
iajs-3477	40	14	u(0	u(0	PROPN
iajs-3477	40	15	,	,	PUNCT
iajs-3477	40	16	y	y	PROPN
iajs-3477	40	17	)	)	PUNCT
iajs-3477	40	18	=	=	SYM
iajs-3477	40	19	h(y	h(y	ADV
iajs-3477	40	20	)	)	PUNCT
iajs-3477	40	21	,	,	PUNCT
iajs-3477	40	22	y	y	PROPN
iajs-3477	40	23	∈	∈	PROPN
iajs-3477	41	1	[	[	X
iajs-3477	41	2	0	0	NUM
iajs-3477	41	3	,	,	PUNCT
iajs-3477	41	4	y	y	PROPN
iajs-3477	41	5	]	]	X
iajs-3477	41	6	,	,	PUNCT
iajs-3477	41	7	(	(	PUNCT
iajs-3477	41	8	5	5	NUM
iajs-3477	41	9	)	)	PUNCT
iajs-3477	41	10	where	where	SCONJ
iajs-3477	41	11	the	the	DET
iajs-3477	41	12	functions	function	NOUN
iajs-3477	41	13	f(x	f(x	PROPN
iajs-3477	41	14	,	,	PUNCT
iajs-3477	41	15	y	y	PROPN
iajs-3477	41	16	)	)	PUNCT
iajs-3477	41	17	,	,	PUNCT
iajs-3477	41	18	φ(x),ψ(x),ω(x	φ(x),ψ(x),ω(x	NOUN
iajs-3477	41	19	)	)	PUNCT
iajs-3477	41	20	and	and	CCONJ
iajs-3477	41	21	h(y	h(y	NOUN
iajs-3477	41	22	)	)	PUNCT
iajs-3477	41	23	are	be	AUX
iajs-3477	41	24	given	give	VERB
iajs-3477	41	25	and	and	CCONJ
iajs-3477	41	26	q	q	NOUN
iajs-3477	41	27	=	=	X
iajs-3477	41	28	{	{	PUNCT
iajs-3477	41	29	(	(	PUNCT
iajs-3477	41	30	x	x	NOUN
iajs-3477	41	31	,	,	PUNCT
iajs-3477	41	32	y	y	PROPN
iajs-3477	41	33	):	):	PUNCT
iajs-3477	41	34	0	0	PUNCT
iajs-3477	41	35	<	<	X
iajs-3477	41	36	x	x	X
iajs-3477	41	37	<	<	X
iajs-3477	41	38	1	1	NUM
iajs-3477	41	39	,	,	PUNCT
iajs-3477	41	40	0	0	PUNCT
iajs-3477	41	41	<	<	X
iajs-3477	41	42	y	y	X
iajs-3477	41	43	<	<	X
iajs-3477	41	44	y	y	X
iajs-3477	41	45	<	<	X
iajs-3477	41	46	∞	∞	PROPN
iajs-3477	41	47	}	}	PUNCT
iajs-3477	41	48	.	.	PUNCT
iajs-3477	42	1	the	the	DET
iajs-3477	42	2	numerical	numerical	ADJ
iajs-3477	42	3	solution	solution	NOUN
iajs-3477	42	4	of	of	ADP
iajs-3477	42	5	the	the	DET
iajs-3477	42	6	inverse	inverse	NOUN
iajs-3477	42	7	problem	problem	NOUN
iajs-3477	42	8	second	second	ADJ
iajs-3477	42	9	-	-	PUNCT
iajs-3477	42	10	order	order	NOUN
iajs-3477	42	11	elliptic	elliptic	ADJ
iajs-3477	42	12	equation	equation	NOUN
iajs-3477	42	13	(	(	PUNCT
iajs-3477	42	14	1	1	NUM
iajs-3477	42	15	)	)	PUNCT
iajs-3477	42	16	–	–	PUNCT
iajs-3477	42	17	(	(	PUNCT
iajs-3477	42	18	5	5	X
iajs-3477	42	19	)	)	PUNCT
iajs-3477	42	20	is	be	AUX
iajs-3477	42	21	written	write	VERB
iajs-3477	42	22	as	as	ADP
iajs-3477	42	23	{	{	PUNCT
iajs-3477	42	24	a(y	a(y	PROPN
iajs-3477	42	25	)	)	PUNCT
iajs-3477	42	26	,	,	PUNCT
iajs-3477	42	27	u(x	u(x	PROPN
iajs-3477	42	28	,	,	PUNCT
iajs-3477	42	29	y	y	NOUN
iajs-3477	42	30	)	)	PUNCT
iajs-3477	42	31	}	}	PUNCT
iajs-3477	42	32	such	such	ADJ
iajs-3477	42	33	that	that	SCONJ
iajs-3477	42	34	a(y	a(y	PROPN
iajs-3477	42	35	)	)	PUNCT
iajs-3477	42	36	∈	∈	PROPN
iajs-3477	42	37	c[0	c[0	PROPN
iajs-3477	42	38	,	,	PUNCT
iajs-3477	42	39	y	y	NOUN
iajs-3477	42	40	]	]	PUNCT
iajs-3477	42	41	and	and	CCONJ
iajs-3477	42	42	u(x	u(x	PROPN
iajs-3477	42	43	,	,	PUNCT
iajs-3477	42	44	y	y	NOUN
iajs-3477	42	45	)	)	PUNCT
iajs-3477	42	46	∈	∈	PROPN
iajs-3477	42	47	c2(q	c2(q	PROPN
iajs-3477	42	48	)	)	PUNCT
iajs-3477	42	49	.	.	PUNCT
iajs-3477	43	1	the	the	DET
iajs-3477	43	2	existence	existence	NOUN
iajs-3477	43	3	and	and	CCONJ
iajs-3477	43	4	uniqueness	uniqueness	NOUN
iajs-3477	43	5	of	of	ADP
iajs-3477	43	6	theorems	theorem	NOUN
iajs-3477	43	7	have	have	AUX
iajs-3477	43	8	been	be	AUX
iajs-3477	43	9	established	establish	VERB
iajs-3477	43	10	by	by	ADP
iajs-3477	43	11	y.	y.	PROPN
iajs-3477	43	12	mehraliyev	mehraliyev	PROPN
iajs-3477	43	13	in	in	ADP
iajs-3477	43	14	[	[	X
iajs-3477	43	15	26	26	NUM
iajs-3477	43	16	]	]	PUNCT
iajs-3477	43	17	and	and	CCONJ
iajs-3477	43	18	stated	state	VERB
iajs-3477	43	19	as	as	SCONJ
iajs-3477	43	20	follows	follow	VERB
iajs-3477	43	21	:	:	PUNCT
iajs-3477	43	22	2.1	2.1	NUM
iajs-3477	43	23	existence	existence	NOUN
iajs-3477	43	24	of	of	ADP
iajs-3477	43	25	the	the	DET
iajs-3477	43	26	inverse	inverse	NOUN
iajs-3477	43	27	problem	problem	NOUN
iajs-3477	43	28	classical	classical	ADJ
iajs-3477	43	29	solution	solution	NOUN
iajs-3477	43	30	.	.	PUNCT
iajs-3477	44	1	assume	assume	VERB
iajs-3477	44	2	the	the	DET
iajs-3477	44	3	following	follow	VERB
iajs-3477	44	4	conditions	condition	NOUN
iajs-3477	44	5	:	:	PUNCT
iajs-3477	44	6	e1	e1	NOUN
iajs-3477	44	7	)	)	PUNCT
iajs-3477	44	8	φ(x	φ(x	NOUN
iajs-3477	44	9	)	)	PUNCT
iajs-3477	44	10	∈	∈	PROPN
iajs-3477	44	11	c2[0,1	c2[0,1	NOUN
iajs-3477	44	12	]	]	X
iajs-3477	44	13	,	,	PUNCT
iajs-3477	44	14	φ′′′(x	φ′′′(x	PROPN
iajs-3477	44	15	)	)	PUNCT
iajs-3477	44	16	∈	∈	PROPN
iajs-3477	44	17	l2(0,1	l2(0,1	NOUN
iajs-3477	44	18	)	)	PUNCT
iajs-3477	44	19	,	,	PUNCT
iajs-3477	44	20	φ′(0	φ′(0	X
iajs-3477	44	21	)	)	PUNCT
iajs-3477	44	22	=	=	SYM
iajs-3477	44	23	φ′(1	φ′(1	PROPN
iajs-3477	44	24	)	)	PUNCT
iajs-3477	44	25	=	=	SYM
iajs-3477	44	26	0	0	NUM
iajs-3477	44	27	;	;	PUNCT
iajs-3477	45	1	e2	e2	PROPN
iajs-3477	45	2	)	)	PUNCT
iajs-3477	45	3	ψ(x	ψ(x	PROPN
iajs-3477	45	4	)	)	PUNCT
iajs-3477	45	5	∈	∈	PROPN
iajs-3477	45	6	c1[0,1	c1[0,1	PROPN
iajs-3477	45	7	]	]	X
iajs-3477	45	8	,	,	PUNCT
iajs-3477	45	9	ψ′′(x	ψ′′(x	NOUN
iajs-3477	45	10	)	)	PUNCT
iajs-3477	45	11	∈	∈	PROPN
iajs-3477	45	12	l2(0,1	l2(0,1	NOUN
iajs-3477	45	13	)	)	PUNCT
iajs-3477	45	14	,	,	PUNCT
iajs-3477	45	15	ψ′(0	ψ′(0	PRON
iajs-3477	45	16	)	)	PUNCT
iajs-3477	45	17	=	=	SYM
iajs-3477	45	18	ψ′(1	ψ′(1	VERB
iajs-3477	45	19	)	)	PUNCT
iajs-3477	45	20	=	=	SYM
iajs-3477	45	21	0	0	NUM
iajs-3477	45	22	;	;	PUNCT
iajs-3477	45	23	e3	e3	NOUN
iajs-3477	45	24	)	)	PUNCT
iajs-3477	45	25	f(x	f(x	PROPN
iajs-3477	45	26	,	,	PUNCT
iajs-3477	45	27	y	y	PROPN
iajs-3477	45	28	)	)	PUNCT
iajs-3477	45	29	,	,	PUNCT
iajs-3477	45	30	fx	fx	PROPN
iajs-3477	45	31	(	(	PUNCT
iajs-3477	45	32	0	0	NUM
iajs-3477	45	33	,	,	PUNCT
iajs-3477	45	34	y	y	NOUN
iajs-3477	45	35	)	)	PUNCT
iajs-3477	45	36	∈	∈	PROPN
iajs-3477	45	37	c(q	c(q	PROPN
iajs-3477	45	38	)	)	PUNCT
iajs-3477	45	39	,	,	PUNCT
iajs-3477	45	40	fxx	fxx	PROPN
iajs-3477	45	41	(	(	PUNCT
iajs-3477	45	42	x	x	NOUN
iajs-3477	45	43	,	,	PUNCT
iajs-3477	45	44	y	y	NOUN
iajs-3477	45	45	)	)	PUNCT
iajs-3477	45	46	∈	∈	PROPN
iajs-3477	45	47	l2(q	l2(q	PROPN
iajs-3477	45	48	)	)	PUNCT
iajs-3477	45	49	and	and	CCONJ
iajs-3477	45	50	fx	fx	PROPN
iajs-3477	45	51	(	(	PUNCT
iajs-3477	45	52	0	0	NUM
iajs-3477	45	53	,	,	PUNCT
iajs-3477	45	54	y	y	NOUN
iajs-3477	45	55	)	)	PUNCT
iajs-3477	45	56	=	=	SYM
iajs-3477	45	57	fx	fx	NOUN
iajs-3477	45	58	(	(	PUNCT
iajs-3477	45	59	1	1	NUM
iajs-3477	45	60	,	,	PUNCT
iajs-3477	45	61	y	y	NOUN
iajs-3477	45	62	)	)	PUNCT
iajs-3477	45	63	=	=	SYM
iajs-3477	46	1	0	0	NUM
iajs-3477	46	2	,	,	PUNCT
iajs-3477	46	3	y	y	PROPN
iajs-3477	46	4	∈	∈	PROPN
iajs-3477	47	1	[	[	X
iajs-3477	47	2	0	0	NUM
iajs-3477	47	3	,	,	PUNCT
iajs-3477	47	4	y	y	NOUN
iajs-3477	47	5	]	]	X
iajs-3477	47	6	;	;	PUNCT
iajs-3477	47	7	e4	e4	PROPN
iajs-3477	47	8	)	)	PUNCT
iajs-3477	47	9	h(y	h(y	ADV
iajs-3477	47	10	)	)	PUNCT
iajs-3477	47	11	∈	∈	PROPN
iajs-3477	47	12	c2[0	c2[0	PROPN
iajs-3477	47	13	,	,	PUNCT
iajs-3477	47	14	y	y	PROPN
iajs-3477	47	15	]	]	X
iajs-3477	47	16	,	,	PUNCT
iajs-3477	47	17	h(y	h(y	ADJ
iajs-3477	47	18	)	)	PUNCT
iajs-3477	47	19	≠	≠	PROPN
iajs-3477	47	20	0	0	NUM
iajs-3477	47	21	,	,	PUNCT
iajs-3477	47	22	y	y	PROPN
iajs-3477	47	23	∈	∈	PROPN
iajs-3477	48	1	[	[	X
iajs-3477	48	2	0	0	NUM
iajs-3477	48	3	,	,	PUNCT
iajs-3477	48	4	y	y	NOUN
iajs-3477	48	5	]	]	X
iajs-3477	48	6	;	;	PUNCT
iajs-3477	48	7	theorem	theorem	VERB
iajs-3477	48	8	1	1	X
iajs-3477	48	9	.	.	PUNCT
iajs-3477	49	1	let	let	VERB
iajs-3477	49	2	the	the	DET
iajs-3477	49	3	assumptions	assumption	NOUN
iajs-3477	49	4	(	(	PUNCT
iajs-3477	49	5	e1)–(e4	e1)–(e4	NOUN
iajs-3477	49	6	)	)	PUNCT
iajs-3477	49	7	and	and	CCONJ
iajs-3477	49	8	the	the	DET
iajs-3477	49	9	condition	condition	NOUN
iajs-3477	49	10	ihjpas	ihjpa	VERB
iajs-3477	49	11	.	.	PUNCT
iajs-3477	50	1	37	37	NUM
iajs-3477	50	2	(	(	PUNCT
iajs-3477	50	3	2	2	NUM
iajs-3477	50	4	)	)	PUNCT
iajs-3477	50	5	2024	2024	NUM
iajs-3477	50	6	411	411	NUM
iajs-3477	50	7	(	(	PUNCT
iajs-3477	50	8	𝒜1(y	𝒜1(y	PROPN
iajs-3477	50	9	)	)	PUNCT
iajs-3477	51	1	+	+	PUNCT
iajs-3477	51	2	𝒜2(y	𝒜2(y	NOUN
iajs-3477	51	3	)	)	PUNCT
iajs-3477	52	1	+	+	CCONJ
iajs-3477	52	2	2)2	2)2	NUM
iajs-3477	52	3	(	(	PUNCT
iajs-3477	52	4	ℬ1(y	ℬ1(y	PROPN
iajs-3477	52	5	)	)	PUNCT
iajs-3477	52	6	+	+	CCONJ
iajs-3477	52	7	ℬ2(y	ℬ2(y	NOUN
iajs-3477	52	8	)	)	PUNCT
iajs-3477	52	9	)	)	PUNCT
iajs-3477	53	1	<	<	X
iajs-3477	53	2	1	1	NUM
iajs-3477	53	3	,	,	PUNCT
iajs-3477	53	4	(	(	PUNCT
iajs-3477	53	5	6	6	NUM
iajs-3477	53	6	)	)	PUNCT
iajs-3477	53	7	where	where	SCONJ
iajs-3477	53	8	𝒜1(y	𝒜1(y	PROPN
iajs-3477	53	9	)	)	PUNCT
iajs-3477	53	10	=	=	SYM
iajs-3477	53	11	‖φ(x)‖l2(0,1	‖φ(x)‖l2(0,1	NOUN
iajs-3477	53	12	)	)	PUNCT
iajs-3477	54	1	+	+	SYM
iajs-3477	54	2	y‖ψ(x)‖l2(0,1	y‖ψ(x)‖l2(0,1	NOUN
iajs-3477	54	3	)	)	PUNCT
iajs-3477	55	1	+	+	CCONJ
iajs-3477	55	2	2y√y	2y√y	NUM
iajs-3477	55	3	‖f	‖f	PUNCT
iajs-3477	55	4	(	(	PUNCT
iajs-3477	55	5	x	x	X
iajs-3477	55	6	,	,	PUNCT
iajs-3477	55	7	y)‖l2(q	y)‖l2(q	NOUN
iajs-3477	55	8	)	)	PUNCT
iajs-3477	55	9	+2‖φ′′′(x)‖l2(0,1	+2‖φ′′′(x)‖l2(0,1	NOUN
iajs-3477	55	10	)	)	PUNCT
iajs-3477	55	11	+	+	NUM
iajs-3477	55	12	2‖ψ′′(x)‖l2(0,1	2‖ψ′′(x)‖l2(0,1	NOUN
iajs-3477	55	13	)	)	PUNCT
iajs-3477	56	1	+	+	CCONJ
iajs-3477	56	2	2√y‖fxx	2√y‖fxx	NUM
iajs-3477	56	3	(	(	PUNCT
iajs-3477	56	4	x	x	NOUN
iajs-3477	56	5	,	,	PUNCT
iajs-3477	56	6	y)‖l2(q	y)‖l2(q	PROPN
iajs-3477	56	7	)	)	PUNCT
iajs-3477	56	8	,	,	PUNCT
iajs-3477	56	9	𝒜2(y	𝒜2(y	PROPN
iajs-3477	56	10	)	)	PUNCT
iajs-3477	56	11	=	=	SYM
iajs-3477	57	1	‖[h	‖[h	X
iajs-3477	57	2	(	(	PUNCT
iajs-3477	57	3	y)]−1‖c[0,y	y)]−1‖c[0,y	PROPN
iajs-3477	57	4	]	]	X
iajs-3477	57	5	{	{	PUNCT
iajs-3477	57	6	1	1	NUM
iajs-3477	57	7	√6	√6	PROPN
iajs-3477	57	8	[	[	X
iajs-3477	57	9	‖φ′′′(x)‖l2(0,1	‖φ′′′(x)‖l2(0,1	NOUN
iajs-3477	57	10	)	)	PUNCT
iajs-3477	57	11	+	+	CCONJ
iajs-3477	57	12	‖ψ′′(x)‖l2(0,1	‖ψ′′(x)‖l2(0,1	NOUN
iajs-3477	57	13	)	)	PUNCT
iajs-3477	57	14	+	+	CCONJ
iajs-3477	57	15	√y	√y	ADP
iajs-3477	57	16	‖fxx	‖fxx	ADV
iajs-3477	57	17	(	(	PUNCT
iajs-3477	57	18	x	x	NOUN
iajs-3477	57	19	,	,	PUNCT
iajs-3477	57	20	y)‖l2(q	y)‖l2(q	PROPN
iajs-3477	57	21	)	)	PUNCT
iajs-3477	57	22	]	]	PUNCT
iajs-3477	58	1	+	+	CCONJ
iajs-3477	58	2	‖h′′	‖h′′	PROPN
iajs-3477	58	3	(	(	PUNCT
iajs-3477	58	4	y	y	NOUN
iajs-3477	58	5	)	)	PUNCT
iajs-3477	58	6	−	−	PROPN
iajs-3477	58	7	f(0	f(0	NOUN
iajs-3477	58	8	,	,	PUNCT
iajs-3477	58	9	y)‖c[0,y	y)‖c[0,y	NOUN
iajs-3477	58	10	]	]	X
iajs-3477	58	11	}	}	PUNCT
iajs-3477	58	12	,	,	PUNCT
iajs-3477	58	13	ℬ1(y	ℬ1(y	PROPN
iajs-3477	58	14	)	)	PUNCT
iajs-3477	58	15	=	=	SYM
iajs-3477	58	16	2y(1	2y(1	NUM
iajs-3477	58	17	+	+	NUM
iajs-3477	58	18	y	y	NOUN
iajs-3477	58	19	)	)	PUNCT
iajs-3477	58	20	,	,	PUNCT
iajs-3477	58	21	ℬ2(y	ℬ2(y	PROPN
iajs-3477	58	22	)	)	PUNCT
iajs-3477	58	23	=	=	SYM
iajs-3477	58	24	‖[h(y)]−1‖c[0,y	‖[h(y)]−1‖c[0,y	PROPN
iajs-3477	58	25	]	]	X
iajs-3477	58	26	1	1	NUM
iajs-3477	58	27	√6	√6	PROPN
iajs-3477	58	28	y	y	X
iajs-3477	58	29	,	,	PUNCT
iajs-3477	58	30	be	be	AUX
iajs-3477	58	31	satisfied	satisfied	ADJ
iajs-3477	58	32	.	.	PUNCT
iajs-3477	59	1	then	then	ADV
iajs-3477	59	2	problem	problem	NOUN
iajs-3477	59	3	(	(	PUNCT
iajs-3477	59	4	1)–(5	1)–(5	NUM
iajs-3477	59	5	)	)	PUNCT
iajs-3477	59	6	has	have	VERB
iajs-3477	59	7	a	a	DET
iajs-3477	59	8	unique	unique	ADJ
iajs-3477	59	9	classical	classical	ADJ
iajs-3477	59	10	solution	solution	NOUN
iajs-3477	59	11	in	in	ADP
iajs-3477	59	12	the	the	DET
iajs-3477	59	13	ball	ball	NOUN
iajs-3477	59	14	k	k	NOUN
iajs-3477	59	15	=	=	PUNCT
iajs-3477	59	16	kr(‖u‖ey	kr(‖u‖ey	PROPN
iajs-3477	59	17	3	3	NUM
iajs-3477	59	18	≤	≤	NOUN
iajs-3477	60	1	r	r	NOUN
iajs-3477	60	2	=	=	SYM
iajs-3477	60	3	(	(	PUNCT
iajs-3477	60	4	𝒜1(y	𝒜1(y	PROPN
iajs-3477	60	5	)	)	PUNCT
iajs-3477	60	6	+	+	PUNCT
iajs-3477	60	7	𝒜2(y	𝒜2(y	NOUN
iajs-3477	60	8	)	)	PUNCT
iajs-3477	60	9	+	+	CCONJ
iajs-3477	60	10	2	2	X
iajs-3477	60	11	)	)	PUNCT
iajs-3477	60	12	of	of	ADP
iajs-3477	60	13	the	the	DET
iajs-3477	60	14	space	space	NOUN
iajs-3477	60	15	ey	ey	PRON
iajs-3477	60	16	3	3	NUM
iajs-3477	60	17	(	(	PUNCT
iajs-3477	60	18	ey	ey	PRON
iajs-3477	60	19	3	3	NUM
iajs-3477	60	20	is	be	AUX
iajs-3477	60	21	banach	banach	NOUN
iajs-3477	60	22	space	space	NOUN
iajs-3477	60	23	)	)	PUNCT
iajs-3477	60	24	.	.	PUNCT
iajs-3477	61	1	3	3	X
iajs-3477	61	2	.	.	X
iajs-3477	61	3	fdm	fdm	NOUN
iajs-3477	61	4	scheme	scheme	NOUN
iajs-3477	61	5	for	for	ADP
iajs-3477	61	6	direct	direct	ADJ
iajs-3477	61	7	(	(	PUNCT
iajs-3477	61	8	forward	forward	ADJ
iajs-3477	61	9	)	)	PUNCT
iajs-3477	61	10	problem	problem	NOUN
iajs-3477	61	11	in	in	ADP
iajs-3477	61	12	the	the	DET
iajs-3477	61	13	following	follow	VERB
iajs-3477	61	14	section	section	NOUN
iajs-3477	61	15	,	,	PUNCT
iajs-3477	61	16	we	we	PRON
iajs-3477	61	17	will	will	AUX
iajs-3477	61	18	solve	solve	VERB
iajs-3477	61	19	the	the	DET
iajs-3477	61	20	direct	direct	ADJ
iajs-3477	61	21	problem	problem	NOUN
iajs-3477	61	22	,	,	PUNCT
iajs-3477	61	23	i.e.	i.e.	X
iajs-3477	61	24	,	,	PUNCT
iajs-3477	61	25	when	when	SCONJ
iajs-3477	61	26	the	the	DET
iajs-3477	61	27	unknown	unknown	ADJ
iajs-3477	61	28	term	term	NOUN
iajs-3477	61	29	a(y	a(y	PROPN
iajs-3477	61	30	)	)	PUNCT
iajs-3477	61	31	is	be	AUX
iajs-3477	61	32	presumed	presume	VERB
iajs-3477	61	33	to	to	PART
iajs-3477	61	34	be	be	AUX
iajs-3477	61	35	given	give	VERB
iajs-3477	61	36	.	.	PUNCT
iajs-3477	62	1	in	in	ADP
iajs-3477	62	2	order	order	NOUN
iajs-3477	62	3	to	to	PART
iajs-3477	62	4	solve	solve	VERB
iajs-3477	62	5	this	this	DET
iajs-3477	62	6	problem	problem	NOUN
iajs-3477	62	7	,	,	PUNCT
iajs-3477	62	8	we	we	PRON
iajs-3477	62	9	used	use	VERB
iajs-3477	62	10	fdm	fdm	NOUN
iajs-3477	62	11	to	to	PART
iajs-3477	62	12	find	find	VERB
iajs-3477	62	13	the	the	DET
iajs-3477	62	14	numerical	numerical	ADJ
iajs-3477	62	15	solution	solution	NOUN
iajs-3477	62	16	of	of	ADP
iajs-3477	62	17	the	the	DET
iajs-3477	62	18	nonlocal	nonlocal	ADJ
iajs-3477	62	19	problem	problem	NOUN
iajs-3477	62	20	given	give	VERB
iajs-3477	62	21	by	by	ADP
iajs-3477	62	22	equations	equation	NOUN
iajs-3477	62	23	(	(	PUNCT
iajs-3477	62	24	1)-(4	1)-(4	NUM
iajs-3477	62	25	)	)	PUNCT
iajs-3477	62	26	.	.	PUNCT
iajs-3477	63	1	we	we	PRON
iajs-3477	63	2	sub	sub	VERB
iajs-3477	63	3	divide	divide	VERB
iajs-3477	63	4	the	the	DET
iajs-3477	63	5	domain	domain	NOUN
iajs-3477	63	6	q	q	PUNCT
iajs-3477	63	7	into	into	ADP
iajs-3477	63	8	m	m	PROPN
iajs-3477	63	9	×	×	NOUN
iajs-3477	63	10	n	n	PRON
iajs-3477	63	11	mesh	mesh	NOUN
iajs-3477	63	12	with	with	ADP
iajs-3477	63	13	spatial	spatial	ADJ
iajs-3477	63	14	step	step	NOUN
iajs-3477	63	15	size	size	NOUN
iajs-3477	63	16	∆x	∆x	PROPN
iajs-3477	63	17	=	=	SYM
iajs-3477	63	18	1	1	NUM
iajs-3477	63	19	m	m	NOUN
iajs-3477	63	20	,	,	PUNCT
iajs-3477	63	21	and	and	CCONJ
iajs-3477	63	22	∆y	∆y	PROPN
iajs-3477	63	23	=	=	SYM
iajs-3477	63	24	y	y	PROPN
iajs-3477	63	25	n	n	NOUN
iajs-3477	63	26	,	,	PUNCT
iajs-3477	63	27	where	where	SCONJ
iajs-3477	63	28	m	m	VERB
iajs-3477	63	29	and	and	CCONJ
iajs-3477	63	30	n	n	PROPN
iajs-3477	63	31	are	be	AUX
iajs-3477	63	32	given	give	VERB
iajs-3477	63	33	positive	positive	ADJ
iajs-3477	63	34	integers	integer	NOUN
iajs-3477	63	35	.	.	PUNCT
iajs-3477	64	1	the	the	DET
iajs-3477	64	2	grid	grid	NOUN
iajs-3477	64	3	points	point	NOUN
iajs-3477	64	4	are	be	AUX
iajs-3477	64	5	given	give	VERB
iajs-3477	64	6	by	by	ADP
iajs-3477	64	7	xi	xi	PROPN
iajs-3477	64	8	=	=	PUNCT
iajs-3477	64	9	i∆x	i∆x	PROPN
iajs-3477	64	10	,	,	PUNCT
iajs-3477	64	11	i	i	NOUN
iajs-3477	64	12	=	=	NOUN
iajs-3477	64	13	0,1	0,1	NUM
iajs-3477	64	14	,	,	PUNCT
iajs-3477	64	15	…	…	PUNCT
iajs-3477	64	16	,	,	PUNCT
iajs-3477	64	17	m	m	PROPN
iajs-3477	64	18	,	,	PUNCT
iajs-3477	64	19	yj	yj	PROPN
iajs-3477	64	20	=	=	PROPN
iajs-3477	64	21	j∆y	j∆y	PROPN
iajs-3477	64	22	,	,	PUNCT
iajs-3477	64	23	j	j	PROPN
iajs-3477	64	24	=	=	SYM
iajs-3477	64	25	0,1	0,1	NUM
iajs-3477	64	26	,	,	PUNCT
iajs-3477	64	27	…	…	PUNCT
iajs-3477	64	28	,	,	PUNCT
iajs-3477	64	29	n	n	CCONJ
iajs-3477	64	30	,	,	PUNCT
iajs-3477	64	31	we	we	PRON
iajs-3477	64	32	denote	denote	VERB
iajs-3477	64	33	the	the	DET
iajs-3477	64	34	discretized	discretized	ADJ
iajs-3477	64	35	from	from	ADP
iajs-3477	64	36	of	of	ADP
iajs-3477	64	37	the	the	DET
iajs-3477	64	38	quantities	quantity	NOUN
iajs-3477	64	39	as	as	SCONJ
iajs-3477	64	40	follows	follow	VERB
iajs-3477	64	41	;	;	PUNCT
iajs-3477	64	42	u(xi	u(xi	PROPN
iajs-3477	64	43	,	,	PUNCT
iajs-3477	64	44	yj	yj	PROPN
iajs-3477	64	45	)	)	PUNCT
iajs-3477	64	46	=	=	SYM
iajs-3477	64	47	ui	ui	PROPN
iajs-3477	64	48	,	,	PUNCT
iajs-3477	64	49	j	j	PROPN
iajs-3477	64	50	,	,	PUNCT
iajs-3477	64	51	a(yj	a(yj	X
iajs-3477	64	52	)	)	PUNCT
iajs-3477	64	53	=	=	SYM
iajs-3477	64	54	aj	aj	PROPN
iajs-3477	64	55	,	,	PUNCT
iajs-3477	64	56	f(xi	f(xi	PROPN
iajs-3477	64	57	,	,	PUNCT
iajs-3477	64	58	yj	yj	PROPN
iajs-3477	64	59	)	)	PUNCT
iajs-3477	64	60	=	=	SYM
iajs-3477	64	61	fi	fi	PROPN
iajs-3477	64	62	,	,	PUNCT
iajs-3477	64	63	j	j	PROPN
iajs-3477	64	64	,	,	PUNCT
iajs-3477	64	65	ψ(xi	ψ(xi	PROPN
iajs-3477	64	66	)	)	PUNCT
iajs-3477	64	67	=	=	SYM
iajs-3477	64	68	ψi	ψi	ADP
iajs-3477	64	69	and	and	CCONJ
iajs-3477	64	70	φ(xi	φ(xi	NUM
iajs-3477	64	71	)	)	PUNCT
iajs-3477	65	1	=	=	PUNCT
iajs-3477	65	2	φi	φi	ADP
iajs-3477	65	3	for	for	ADP
iajs-3477	65	4	i	i	PROPN
iajs-3477	65	5	=	=	NOUN
iajs-3477	65	6	0,1	0,1	NUM
iajs-3477	65	7	,	,	PUNCT
iajs-3477	65	8	…	…	PUNCT
iajs-3477	65	9	,	,	PUNCT
iajs-3477	65	10	m	m	PROPN
iajs-3477	65	11	,	,	PUNCT
iajs-3477	65	12	j	j	PROPN
iajs-3477	65	13	=	=	SYM
iajs-3477	65	14	0,1	0,1	NUM
iajs-3477	65	15	,	,	PUNCT
iajs-3477	65	16	…	…	PUNCT
iajs-3477	65	17	,	,	PUNCT
iajs-3477	65	18	n.	n.	NOUN
iajs-3477	65	19	then	then	ADV
iajs-3477	65	20	the	the	DET
iajs-3477	65	21	fdm	fdm	NOUN
iajs-3477	65	22	scheme	scheme	NOUN
iajs-3477	65	23	combined	combine	VERB
iajs-3477	65	24	with	with	ADP
iajs-3477	65	25	the	the	DET
iajs-3477	65	26	trapezoidal	trapezoidal	ADJ
iajs-3477	65	27	rule	rule	NOUN
iajs-3477	65	28	quadrature	quadrature	NOUN
iajs-3477	65	29	for	for	ADP
iajs-3477	65	30	nonlocal	nonlocal	ADJ
iajs-3477	65	31	integral	integral	ADJ
iajs-3477	65	32	condition	condition	NOUN
iajs-3477	65	33	,	,	PUNCT
iajs-3477	65	34	the	the	DET
iajs-3477	65	35	discrete	discrete	ADJ
iajs-3477	65	36	expression	expression	NOUN
iajs-3477	65	37	for	for	ADP
iajs-3477	65	38	equation	equation	NOUN
iajs-3477	65	39	(	(	PUNCT
iajs-3477	65	40	1	1	NUM
iajs-3477	65	41	)	)	PUNCT
iajs-3477	65	42	,	,	PUNCT
iajs-3477	65	43	which	which	PRON
iajs-3477	65	44	can	can	AUX
iajs-3477	65	45	be	be	AUX
iajs-3477	65	46	approximated	approximate	VERB
iajs-3477	65	47	via	via	ADP
iajs-3477	65	48	central	central	ADJ
iajs-3477	65	49	fdm	fdm	NOUN
iajs-3477	65	50	expressions	expression	NOUN
iajs-3477	65	51	.	.	PUNCT
iajs-3477	66	1	ui	ui	NOUN
iajs-3477	66	2	,	,	PUNCT
iajs-3477	66	3	j+1	j+1	PROPN
iajs-3477	66	4	−	−	PROPN
iajs-3477	66	5	2ui	2ui	NOUN
iajs-3477	66	6	,	,	PUNCT
iajs-3477	66	7	j	j	PROPN
iajs-3477	66	8	+	+	PROPN
iajs-3477	66	9	ui	ui	PROPN
iajs-3477	66	10	,	,	PUNCT
iajs-3477	66	11	j−1	j−1	PROPN
iajs-3477	66	12	(	(	PUNCT
iajs-3477	66	13	∆y)2	∆y)2	NOUN
iajs-3477	66	14	+	+	NUM
iajs-3477	66	15	ui+1,j	ui+1,j	NOUN
iajs-3477	66	16	−	−	PROPN
iajs-3477	66	17	2ui	2ui	NOUN
iajs-3477	66	18	,	,	PUNCT
iajs-3477	66	19	j	j	PROPN
iajs-3477	66	20	+	+	CCONJ
iajs-3477	66	21	ui−1,j	ui−1,j	X
iajs-3477	66	22	(	(	PUNCT
iajs-3477	66	23	∆x)2	∆x)2	NOUN
iajs-3477	66	24	−	−	NOUN
iajs-3477	66	25	ajui	ajui	NOUN
iajs-3477	66	26	,	,	PUNCT
iajs-3477	66	27	j	j	PROPN
iajs-3477	66	28	=	=	SYM
iajs-3477	66	29	fi	fi	PROPN
iajs-3477	66	30	,	,	PUNCT
iajs-3477	66	31	j	j	PROPN
iajs-3477	66	32	,	,	PUNCT
iajs-3477	66	33	i	i	NOUN
iajs-3477	66	34	=	=	NOUN
iajs-3477	66	35	0,1	0,1	NUM
iajs-3477	66	36	,	,	PUNCT
iajs-3477	66	37	…	…	PUNCT
iajs-3477	66	38	,	,	PUNCT
iajs-3477	66	39	m	m	PROPN
iajs-3477	66	40	,	,	PUNCT
iajs-3477	66	41	j	j	PROPN
iajs-3477	66	42	=	=	SYM
iajs-3477	66	43	0,1	0,1	NUM
iajs-3477	66	44	,	,	PUNCT
iajs-3477	66	45	…	…	PUNCT
iajs-3477	66	46	,	,	PUNCT
iajs-3477	66	47	n.	n.	NOUN
iajs-3477	66	48	simplifying	simplify	VERB
iajs-3477	66	49	the	the	DET
iajs-3477	66	50	above	above	ADJ
iajs-3477	66	51	equation	equation	NOUN
iajs-3477	66	52	,	,	PUNCT
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iajs-3477	66	55	1	1	NUM
iajs-3477	66	56	(	(	PUNCT
iajs-3477	66	57	∆y)2	∆y)2	PROPN
iajs-3477	66	58	(	(	PUNCT
iajs-3477	66	59	ui	ui	PROPN
iajs-3477	66	60	,	,	PUNCT
iajs-3477	66	61	j−1	j−1	PROPN
iajs-3477	66	62	+	+	CCONJ
iajs-3477	66	63	ui	ui	PROPN
iajs-3477	66	64	,	,	PUNCT
iajs-3477	66	65	j+1	j+1	NOUN
iajs-3477	66	66	)	)	PUNCT
iajs-3477	66	67	−	−	PROPN
iajs-3477	66	68	2	2	NUM
iajs-3477	66	69	(	(	PUNCT
iajs-3477	66	70	1	1	NUM
iajs-3477	66	71	(	(	PUNCT
iajs-3477	66	72	∆y)2	∆y)2	PROPN
iajs-3477	66	73	+	+	NOUN
iajs-3477	66	74	1	1	NUM
iajs-3477	66	75	(	(	PUNCT
iajs-3477	66	76	∆x)2	∆x)2	PROPN
iajs-3477	66	77	+	+	CCONJ
iajs-3477	66	78	aj	aj	PROPN
iajs-3477	66	79	2	2	NUM
iajs-3477	66	80	)	)	PUNCT
iajs-3477	66	81	ui	ui	PROPN
iajs-3477	66	82	,	,	PUNCT
iajs-3477	66	83	j	j	PROPN
iajs-3477	67	1	+	+	CCONJ
iajs-3477	67	2	1	1	NUM
iajs-3477	67	3	(	(	PUNCT
iajs-3477	67	4	∆x)2	∆x)2	NOUN
iajs-3477	67	5	(	(	PUNCT
iajs-3477	67	6	ui+1,j	ui+1,j	NOUN
iajs-3477	67	7	+	+	CCONJ
iajs-3477	67	8	ui−1,j	ui−1,j	NOUN
iajs-3477	67	9	)	)	PUNCT
iajs-3477	67	10	=	=	SYM
iajs-3477	68	1	fi	fi	PROPN
iajs-3477	68	2	,	,	PUNCT
iajs-3477	68	3	j	j	PROPN
iajs-3477	68	4	,	,	PUNCT
iajs-3477	68	5	i	i	NOUN
iajs-3477	68	6	=	=	NOUN
iajs-3477	68	7	0,1	0,1	NUM
iajs-3477	68	8	,	,	PUNCT
iajs-3477	68	9	…	…	PUNCT
iajs-3477	68	10	,	,	PUNCT
iajs-3477	68	11	m	m	PROPN
iajs-3477	68	12	,	,	PUNCT
iajs-3477	68	13	j	j	PROPN
iajs-3477	68	14	=	=	SYM
iajs-3477	68	15	0,1	0,1	NUM
iajs-3477	68	16	,	,	PUNCT
iajs-3477	68	17	…	…	PUNCT
iajs-3477	68	18	,	,	PUNCT
iajs-3477	68	19	n.	n.	NOUN
iajs-3477	68	20	(	(	PUNCT
iajs-3477	68	21	7	7	NUM
iajs-3477	68	22	)	)	PUNCT
iajs-3477	68	23	the	the	DET
iajs-3477	68	24	fdm	fdm	NOUN
iajs-3477	68	25	discretizes	discretize	VERB
iajs-3477	68	26	equations	equation	NOUN
iajs-3477	68	27	(	(	PUNCT
iajs-3477	68	28	2	2	NUM
iajs-3477	68	29	)	)	PUNCT
iajs-3477	68	30	(	(	PUNCT
iajs-3477	68	31	3	3	X
iajs-3477	68	32	)	)	PUNCT
iajs-3477	68	33	as	as	ADP
iajs-3477	68	34	ui,0	ui,0	PROPN
iajs-3477	68	35	=	=	SYM
iajs-3477	68	36	φi	φi	PROPN
iajs-3477	68	37	,	,	PUNCT
iajs-3477	68	38	i	i	NOUN
iajs-3477	68	39	=	=	NOUN
iajs-3477	68	40	0,1	0,1	NUM
iajs-3477	68	41	,	,	PUNCT
iajs-3477	68	42	…	…	PUNCT
iajs-3477	68	43	,	,	PUNCT
iajs-3477	68	44	m	m	PROPN
iajs-3477	68	45	,	,	PUNCT
iajs-3477	68	46	(	(	PUNCT
iajs-3477	68	47	8)	8)	NUM
iajs-3477	68	48	ui	ui	NOUN
iajs-3477	68	49	,	,	PUNCT
iajs-3477	68	50	n+1	n+1	PROPN
iajs-3477	68	51	−	−	PROPN
iajs-3477	68	52	ui	ui	PROPN
iajs-3477	68	53	,	,	PUNCT
iajs-3477	68	54	n	n	CCONJ
iajs-3477	68	55	∆y	∆y	NOUN
iajs-3477	68	56	=	=	PUNCT
iajs-3477	68	57	ψi	ψi	NOUN
iajs-3477	68	58	,	,	PUNCT
iajs-3477	68	59	i	i	NOUN
iajs-3477	68	60	=	=	NOUN
iajs-3477	68	61	0,1	0,1	NUM
iajs-3477	68	62	,	,	PUNCT
iajs-3477	68	63	…	…	PUNCT
iajs-3477	68	64	,	,	PUNCT
iajs-3477	68	65	m	m	PROPN
iajs-3477	68	66	,	,	PUNCT
iajs-3477	68	67	(	(	PUNCT
iajs-3477	68	68	9	9	X
iajs-3477	68	69	)	)	PUNCT
iajs-3477	68	70	−3u0,j	−3u0,j	NOUN
iajs-3477	69	1	+	+	CCONJ
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iajs-3477	70	23	4	4	NUM
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iajs-3477	70	32	+	+	CCONJ
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iajs-3477	70	34	,	,	PUNCT
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iajs-3477	70	36	+	+	CCONJ
iajs-3477	70	37	2	2	NUM
iajs-3477	70	38	∑	∑	PROPN
iajs-3477	70	39	ui	ui	PROPN
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iajs-3477	70	41	j	j	PROPN
iajs-3477	70	42	m−1	m−1	PROPN
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iajs-3477	71	1	=	=	SYM
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iajs-3477	71	3	,	,	PUNCT
iajs-3477	71	4	j	j	PROPN
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iajs-3477	71	7	,	,	PUNCT
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iajs-3477	71	10	n.	n.	PROPN
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iajs-3477	72	3	2	2	NUM
iajs-3477	72	4	)	)	PUNCT
iajs-3477	72	5	2024	2024	NUM
iajs-3477	72	6	412	412	NUM
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iajs-3477	72	8	u0,j	u0,j	PROPN
iajs-3477	72	9	=	=	SYM
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iajs-3477	72	12	,	,	PUNCT
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iajs-3477	72	17	.	.	PUNCT
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iajs-3477	73	2	3	3	NUM
iajs-3477	73	3	u1,j	u1,j	NOUN
iajs-3477	73	4	+	+	NUM
iajs-3477	73	5	5	5	NUM
iajs-3477	73	6	3	3	NUM
iajs-3477	73	7	u2,j	u2,j	NOUN
iajs-3477	73	8	+	+	CCONJ
iajs-3477	73	9	2	2	NUM
iajs-3477	73	10	∑	∑	PROPN
iajs-3477	73	11	ui	ui	PROPN
iajs-3477	73	12	,	,	PUNCT
iajs-3477	73	13	j	j	PROPN
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iajs-3477	74	1	+	+	ADJ
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iajs-3477	74	3	,	,	PUNCT
iajs-3477	74	4	j	j	PROPN
iajs-3477	74	5	=	=	SYM
iajs-3477	74	6	0	0	PROPN
iajs-3477	74	7	,	,	PUNCT
iajs-3477	74	8	j	j	PROPN
iajs-3477	74	9	=	=	SYM
iajs-3477	74	10	0,1	0,1	NUM
iajs-3477	74	11	,	,	PUNCT
iajs-3477	74	12	…	…	PUNCT
iajs-3477	74	13	,	,	PUNCT
iajs-3477	74	14	n	n	CCONJ
iajs-3477	74	15	,	,	PUNCT
iajs-3477	74	16	(	(	PUNCT
iajs-3477	74	17	11	11	NUM
iajs-3477	74	18	)	)	PUNCT
iajs-3477	74	19	finally	finally	ADV
iajs-3477	74	20	,	,	PUNCT
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iajs-3477	74	22	discrete	discrete	ADJ
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iajs-3477	74	25	(	(	PUNCT
iajs-3477	74	26	5	5	NUM
iajs-3477	74	27	)	)	PUNCT
iajs-3477	74	28	as	as	ADP
iajs-3477	74	29	.	.	PUNCT
iajs-3477	75	1	u0,j	u0,j	PROPN
iajs-3477	75	2	=	=	SYM
iajs-3477	75	3	hj	hj	PROPN
iajs-3477	75	4	,	,	PUNCT
iajs-3477	75	5	j	j	PROPN
iajs-3477	75	6	=	=	SYM
iajs-3477	75	7	0,1	0,1	NUM
iajs-3477	75	8	,	,	PUNCT
iajs-3477	75	9	…	…	PUNCT
iajs-3477	75	10	,	,	PUNCT
iajs-3477	75	11	n.	n.	NOUN
iajs-3477	75	12	(	(	PUNCT
iajs-3477	75	13	12	12	NUM
iajs-3477	75	14	)	)	PUNCT
iajs-3477	75	15	equations	equation	NOUN
iajs-3477	75	16	(	(	PUNCT
iajs-3477	75	17	7)-(11	7)-(11	NOUN
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iajs-3477	75	34	∆y)2	∆y)2	PROPN
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iajs-3477	75	37	b1ui,1	b1ui,1	PROPN
iajs-3477	76	1	+	+	CCONJ
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iajs-3477	76	3	(	(	PUNCT
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iajs-3477	76	5	(	(	PUNCT
iajs-3477	76	6	ui+1,1	ui+1,1	ADP
iajs-3477	76	7	+	+	PUNCT
iajs-3477	76	8	ui−1,1	ui−1,1	ADJ
iajs-3477	76	9	)	)	PUNCT
iajs-3477	76	10	=	=	SYM
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iajs-3477	76	15	∆y)2	∆y)2	NUM
iajs-3477	76	16	φi	φi	ADV
iajs-3477	76	17	,	,	PUNCT
iajs-3477	76	18	i	i	NOUN
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iajs-3477	76	21	,	,	PUNCT
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iajs-3477	76	28	∆y)2	∆y)2	PROPN
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iajs-3477	76	30	ui,3	ui,3	PROPN
iajs-3477	76	31	+	+	CCONJ
iajs-3477	76	32	ui,1	ui,1	PROPN
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iajs-3477	77	1	+	+	CCONJ
iajs-3477	77	2	b2ui,2	b2ui,2	NOUN
iajs-3477	77	3	+	+	CCONJ
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iajs-3477	78	4	i	i	NOUN
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iajs-3477	78	7	,	,	PUNCT
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iajs-3477	78	15	(	(	PUNCT
iajs-3477	78	16	ui,4	ui,4	PROPN
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iajs-3477	79	7	(	(	PUNCT
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iajs-3477	79	22	,	,	PUNCT
iajs-3477	79	23	⋮	⋮	NOUN
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iajs-3477	79	25	(	(	PUNCT
iajs-3477	79	26	∆y)2	∆y)2	PROPN
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iajs-3477	79	28	ui	ui	PROPN
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iajs-3477	79	34	n−2	n−2	PROPN
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iajs-3477	79	36	+	+	CCONJ
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iajs-3477	79	40	+	+	NUM
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iajs-3477	79	43	∆x)2	∆x)2	X
iajs-3477	79	44	(	(	PUNCT
iajs-3477	79	45	ui+1,n−1	ui+1,n−1	NOUN
iajs-3477	79	46	+	+	X
iajs-3477	79	47	ui−1,n−1	ui−1,n−1	ADJ
iajs-3477	79	48	)	)	PUNCT
iajs-3477	79	49	=	=	SYM
iajs-3477	79	50	fi	fi	NOUN
iajs-3477	79	51	,	,	PUNCT
iajs-3477	79	52	n−1	n−1	PROPN
iajs-3477	79	53	,	,	PUNCT
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iajs-3477	79	57	,	,	PUNCT
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iajs-3477	79	59	,	,	PUNCT
iajs-3477	79	60	m	m	PROPN
iajs-3477	79	61	,	,	PUNCT
iajs-3477	79	62	(	(	PUNCT
iajs-3477	79	63	bn	bn	INTJ
iajs-3477	79	64	+	+	SYM
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iajs-3477	79	66	(	(	PUNCT
iajs-3477	79	67	∆y)2	∆y)2	PROPN
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iajs-3477	79	76	(	(	PUNCT
iajs-3477	79	77	ui+1,n	ui+1,n	NOUN
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iajs-3477	79	79	ui−1,n	ui−1,n	NOUN
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iajs-3477	80	1	+	+	CCONJ
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iajs-3477	80	49	(	(	PUNCT
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iajs-3477	80	51	+	+	NOUN
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iajs-3477	80	55	+	+	CCONJ
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iajs-3477	80	59	,	,	PUNCT
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iajs-3477	81	1	[	[	X
iajs-3477	81	2	u1	u1	NOUN
iajs-3477	81	3	,	,	PUNCT
iajs-3477	81	4	u2	u2	NOUN
iajs-3477	81	5	,	,	PUNCT
iajs-3477	81	6	,	,	PUNCT
iajs-3477	81	7	…	…	PUNCT
iajs-3477	81	8	,	,	PUNCT
iajs-3477	81	9	un−1	un−1	PROPN
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iajs-3477	81	11	un]t	un]t	PROPN
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iajs-3477	82	1	[	[	X
iajs-3477	82	2	u1,j	u1,j	PROPN
iajs-3477	82	3	,	,	PUNCT
iajs-3477	82	4	u2,j	u2,j	PROPN
iajs-3477	82	5	,	,	PUNCT
iajs-3477	82	6	,	,	PUNCT
iajs-3477	82	7	…	…	PUNCT
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iajs-3477	82	16	l=	l=	NOUN
iajs-3477	83	1	[	[	PUNCT
iajs-3477	83	2	𝛤1	𝛤1	NOUN
iajs-3477	83	3	𝛬	𝛬	PROPN
iajs-3477	83	4	𝛩	𝛩	PROPN
iajs-3477	83	5	𝛩	𝛩	NOUN
iajs-3477	83	6	…	…	PUNCT
iajs-3477	83	7	𝛩	𝛩	NOUN
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iajs-3477	83	9	𝛤2	𝛤2	VERB
iajs-3477	83	10	𝛬	𝛬	PROPN
iajs-3477	83	11	𝛩	𝛩	NOUN
iajs-3477	83	12	…	…	PUNCT
iajs-3477	83	13	𝛩	𝛩	NOUN
iajs-3477	83	14	⋱	⋱	PUNCT
iajs-3477	83	15	𝛩	𝛩	NOUN
iajs-3477	83	16	𝛩	𝛩	NOUN
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iajs-3477	83	18	𝛩	𝛩	NOUN
iajs-3477	83	19	…	…	PUNCT
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iajs-3477	83	21	𝛤𝑁−1	𝛤𝑁−1	NOUN
iajs-3477	83	22	𝛬	𝛬	NOUN
iajs-3477	83	23	0	0	NUM
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iajs-3477	83	25	𝛩	𝛩	NOUN
iajs-3477	83	26	𝛩	𝛩	NOUN
iajs-3477	83	27	𝛩	𝛩	NOUN
iajs-3477	83	28	…	…	PUNCT
iajs-3477	83	29	0	0	SYM
iajs-3477	84	1	𝛬	𝛬	NOUN
iajs-3477	84	2	𝛤𝑁	𝛤𝑁	NOUN
iajs-3477	84	3	𝛬	𝛬	NOUN
iajs-3477	84	4	]	]	PUNCT
iajs-3477	84	5	,	,	PUNCT
iajs-3477	84	6	𝑃	𝑃	NOUN
iajs-3477	84	7	=	=	SYM
iajs-3477	84	8	[	[	PUNCT
iajs-3477	84	9	𝐹1	𝐹1	NOUN
iajs-3477	84	10	−	−	PROPN
iajs-3477	85	1	𝛬𝜑𝑖	𝛬𝜑𝑖	PROPN
iajs-3477	85	2	𝐹2	𝐹2	NOUN
iajs-3477	85	3	⋮	⋮	PROPN
iajs-3477	85	4	𝐹𝑁−1	𝐹𝑁−1	NOUN
iajs-3477	86	1	𝐹𝑁	𝐹𝑁	PROPN
iajs-3477	86	2	−	−	PROPN
iajs-3477	86	3	𝛬∆𝑦𝜓𝑖	𝛬∆𝑦𝜓𝑖	NOUN
iajs-3477	86	4	]	]	X
iajs-3477	86	5	,	,	PUNCT
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iajs-3477	86	7	,	,	PUNCT
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iajs-3477	86	12	)	)	PUNCT
iajs-3477	86	13	×(nm	×(nm	PROPN
iajs-3477	86	14	)	)	PUNCT
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iajs-3477	86	18	p	p	NOUN
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iajs-3477	86	25	(	(	PUNCT
iajs-3477	86	26	nm)×	nm)×	PROPN
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iajs-3477	86	28	,	,	PUNCT
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iajs-3477	86	31	λ	λ	PROPN
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iajs-3477	86	33	the	the	DET
iajs-3477	86	34	(	(	PUNCT
iajs-3477	86	35	m	m	PROPN
iajs-3477	86	36	×	×	PROPN
iajs-3477	86	37	m	m	NOUN
iajs-3477	86	38	)	)	PUNCT
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iajs-3477	86	40	,	,	PUNCT
iajs-3477	86	41	θ	θ	NOUN
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iajs-3477	86	44	m	m	PROPN
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iajs-3477	86	46	m	m	NOUN
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iajs-3477	86	48	zero	zero	NUM
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iajs-3477	86	51	fj	fj	PROPN
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iajs-3477	86	53	column	column	NOUN
iajs-3477	86	54	with	with	ADP
iajs-3477	86	55	the	the	DET
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iajs-3477	86	57	(	(	PUNCT
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iajs-3477	86	59	)	)	PUNCT
iajs-3477	86	60	,	,	PUNCT
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iajs-3477	86	62	.	.	PUNCT
iajs-3477	87	1	37	37	NUM
iajs-3477	87	2	(	(	PUNCT
iajs-3477	87	3	2	2	NUM
iajs-3477	87	4	)	)	PUNCT
iajs-3477	87	5	2024	2024	NUM
iajs-3477	87	6	413	413	NUM
iajs-3477	87	7	𝛤𝑗	𝛤𝑗	NOUN
iajs-3477	87	8	=	=	SYM
iajs-3477	87	9	[	[	PUNCT
iajs-3477	87	10	4	4	NUM
iajs-3477	87	11	3(∆𝑥)2	3(∆𝑥)2	NUM
iajs-3477	87	12	+	+	SYM
iajs-3477	87	13	𝑏𝑗	𝑏𝑗	PROPN
iajs-3477	87	14	1	1	NUM
iajs-3477	87	15	3(∆𝑦)2	3(∆𝑦)2	NUM
iajs-3477	87	16	0	0	NUM
iajs-3477	87	17	0	0	NUM
iajs-3477	87	18	0	0	NUM
iajs-3477	87	19	0	0	NUM
iajs-3477	88	1	…	…	PUNCT
iajs-3477	89	1	0	0	NUM
iajs-3477	89	2	0	0	NUM
iajs-3477	89	3	0	0	NUM
iajs-3477	89	4	1	1	NUM
iajs-3477	89	5	(	(	PUNCT
iajs-3477	89	6	∆𝑥)2	∆𝑥)2	PROPN
iajs-3477	89	7	𝑏𝑗	𝑏𝑗	PROPN
iajs-3477	89	8	1	1	NUM
iajs-3477	89	9	(	(	PUNCT
iajs-3477	89	10	∆𝑥)2	∆𝑥)2	PROPN
iajs-3477	89	11	0	0	NUM
iajs-3477	89	12	0	0	NUM
iajs-3477	89	13	0	0	NUM
iajs-3477	89	14	…	…	PUNCT
iajs-3477	89	15	0	0	NUM
iajs-3477	89	16	0	0	NUM
iajs-3477	89	17	0	0	NUM
iajs-3477	89	18	0	0	NUM
iajs-3477	89	19	1	1	NUM
iajs-3477	89	20	(	(	PUNCT
iajs-3477	89	21	∆𝑥)2	∆𝑥)2	PROPN
iajs-3477	89	22	𝑏𝑗	𝑏𝑗	PROPN
iajs-3477	89	23	1	1	NUM
iajs-3477	89	24	(	(	PUNCT
iajs-3477	89	25	∆𝑥)2	∆𝑥)2	PROPN
iajs-3477	89	26	0	0	NUM
iajs-3477	89	27	0	0	NUM
iajs-3477	89	28	…	…	PUNCT
iajs-3477	89	29	0	0	NUM
iajs-3477	89	30	0	0	NUM
iajs-3477	89	31	0	0	NUM
iajs-3477	89	32	⋱	⋱	SYM
iajs-3477	89	33	0	0	NUM
iajs-3477	89	34	0	0	NUM
iajs-3477	89	35	0	0	NUM
iajs-3477	89	36	…	…	SYM
iajs-3477	89	37	0	0	NUM
iajs-3477	89	38	1	1	NUM
iajs-3477	89	39	(	(	PUNCT
iajs-3477	89	40	∆𝑥)2	∆𝑥)2	PROPN
iajs-3477	89	41	𝑏𝑗	𝑏𝑗	PROPN
iajs-3477	89	42	1	1	NUM
iajs-3477	89	43	(	(	PUNCT
iajs-3477	89	44	∆𝑥)2	∆𝑥)2	PROPN
iajs-3477	89	45	10	10	NUM
iajs-3477	89	46	3	3	NUM
iajs-3477	89	47	5	5	NUM
iajs-3477	89	48	3	3	NUM
iajs-3477	89	49	2	2	NUM
iajs-3477	89	50	…	…	SYM
iajs-3477	89	51	2	2	NUM
iajs-3477	89	52	2	2	NUM
iajs-3477	89	53	1	1	NUM
iajs-3477	89	54	]	]	PUNCT
iajs-3477	89	55	,	,	PUNCT
iajs-3477	90	1	𝛬	𝛬	NOUN
iajs-3477	90	2	=	=	X
iajs-3477	90	3	[	[	PUNCT
iajs-3477	90	4	1	1	NUM
iajs-3477	90	5	(	(	PUNCT
iajs-3477	90	6	∆𝑦)2	∆𝑦)2	NOUN
iajs-3477	90	7	0	0	NUM
iajs-3477	90	8	0	0	NUM
iajs-3477	90	9	…	…	SYM
iajs-3477	90	10	0	0	NUM
iajs-3477	90	11	0	0	NUM
iajs-3477	90	12	1	1	NUM
iajs-3477	90	13	(	(	PUNCT
iajs-3477	90	14	∆𝑦)2	∆𝑦)2	NOUN
iajs-3477	90	15	0	0	NUM
iajs-3477	90	16	…	…	SYM
iajs-3477	90	17	0	0	NUM
iajs-3477	90	18	⋱	⋱	SYM
iajs-3477	90	19	0	0	NUM
iajs-3477	90	20	0	0	NUM
iajs-3477	90	21	0	0	NUM
iajs-3477	90	22	…	…	SYM
iajs-3477	90	23	0	0	NUM
iajs-3477	90	24	1	1	NUM
iajs-3477	90	25	(	(	PUNCT
iajs-3477	90	26	∆𝑦)2	∆𝑦)2	NOUN
iajs-3477	90	27	0	0	NUM
iajs-3477	90	28	0	0	NUM
iajs-3477	90	29	0	0	NUM
iajs-3477	90	30	0	0	NUM
iajs-3477	90	31	…	…	PUNCT
iajs-3477	90	32	0	0	NUM
iajs-3477	90	33	0	0	NUM
iajs-3477	90	34	0	0	NUM
iajs-3477	90	35	]	]	PUNCT
iajs-3477	90	36	,	,	PUNCT
iajs-3477	91	1	𝐹𝑗	𝐹𝑗	PROPN
iajs-3477	91	2	=	=	PUNCT
iajs-3477	92	1	[	[	PUNCT
iajs-3477	92	2	𝑓1,𝑗	𝑓1,𝑗	PROPN
iajs-3477	92	3	𝑓2,𝑗	𝑓2,𝑗	PROPN
iajs-3477	92	4	⋱	⋱	PUNCT
iajs-3477	92	5	𝑓𝑀−1,𝑗	𝑓𝑀−1,𝑗	NOUN
iajs-3477	92	6	0	0	NUM
iajs-3477	92	7	]	]	PUNCT
iajs-3477	92	8	,	,	PUNCT
iajs-3477	92	9	3.1	3.1	NUM
iajs-3477	92	10	.	.	PUNCT
iajs-3477	92	11	example	example	NOUN
iajs-3477	92	12	for	for	ADP
iajs-3477	92	13	direct	direct	ADJ
iajs-3477	92	14	problem	problem	NOUN
iajs-3477	92	15	we	we	PRON
iajs-3477	92	16	first	first	ADV
iajs-3477	92	17	investigate	investigate	VERB
iajs-3477	92	18	the	the	DET
iajs-3477	92	19	robustness	robustness	NOUN
iajs-3477	92	20	and	and	CCONJ
iajs-3477	92	21	efficiency	efficiency	NOUN
iajs-3477	92	22	of	of	ADP
iajs-3477	92	23	the	the	DET
iajs-3477	92	24	proposed	propose	VERB
iajs-3477	92	25	fdm	fdm	NOUN
iajs-3477	92	26	method	method	NOUN
iajs-3477	92	27	for	for	ADP
iajs-3477	92	28	a	a	DET
iajs-3477	92	29	direct	direct	ADJ
iajs-3477	92	30	problem	problem	NOUN
iajs-3477	92	31	.	.	PUNCT
iajs-3477	93	1	in	in	ADP
iajs-3477	93	2	cases	case	NOUN
iajs-3477	93	3	where	where	SCONJ
iajs-3477	93	4	the	the	DET
iajs-3477	93	5	unknown	unknown	ADJ
iajs-3477	93	6	coefficient	coefficient	NOUN
iajs-3477	93	7	is	be	AUX
iajs-3477	93	8	given	give	VERB
iajs-3477	93	9	,	,	PUNCT
iajs-3477	93	10	where	where	SCONJ
iajs-3477	93	11	the	the	DET
iajs-3477	93	12	exact	exact	ADJ
iajs-3477	93	13	solution	solution	NOUN
iajs-3477	93	14	is	be	AUX
iajs-3477	93	15	u(x	u(x	NOUN
iajs-3477	93	16	,	,	PUNCT
iajs-3477	93	17	y	y	NOUN
iajs-3477	93	18	)	)	PUNCT
iajs-3477	93	19	=	=	PRON
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iajs-3477	93	21	y	y	PROPN
iajs-3477	93	22	2	2	NUM
iajs-3477	93	23	−	−	NUM
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iajs-3477	93	30	(	(	PUNCT
iajs-3477	93	31	x	x	NOUN
iajs-3477	93	32	,	,	PUNCT
iajs-3477	93	33	y	y	NOUN
iajs-3477	93	34	)	)	PUNCT
iajs-3477	93	35	∈	∈	PROPN
iajs-3477	93	36	q	q	NOUN
iajs-3477	93	37	and	and	CCONJ
iajs-3477	93	38	the	the	DET
iajs-3477	93	39	input	input	NOUN
iajs-3477	93	40	data	datum	NOUN
iajs-3477	93	41	are	be	AUX
iajs-3477	93	42	as	as	SCONJ
iajs-3477	93	43	follows	follow	VERB
iajs-3477	93	44	:	:	PUNCT
iajs-3477	93	45	h	h	NUM
iajs-3477	93	46	(	(	PUNCT
iajs-3477	93	47	y	y	NOUN
iajs-3477	93	48	)	)	PUNCT
iajs-3477	94	1	=	=	PUNCT
iajs-3477	94	2	(	(	PUNCT
iajs-3477	94	3	1	1	NUM
iajs-3477	94	4	20	20	NUM
iajs-3477	94	5	)	)	PUNCT
iajs-3477	94	6	(	(	PUNCT
iajs-3477	94	7	y	y	NOUN
iajs-3477	94	8	−	−	PROPN
iajs-3477	94	9	4	4	NUM
iajs-3477	94	10	)	)	PUNCT
iajs-3477	94	11	,	,	PUNCT
iajs-3477	94	12	φ(x	φ(x	NOUN
iajs-3477	94	13	)	)	PUNCT
iajs-3477	94	14	=	=	SYM
iajs-3477	94	15	−	−	NOUN
iajs-3477	94	16	cos(πx	cos(πx	NOUN
iajs-3477	94	17	)	)	PUNCT
iajs-3477	94	18	5	5	NUM
iajs-3477	94	19	,	,	PUNCT
iajs-3477	94	20	ψ(x	ψ(x	NOUN
iajs-3477	94	21	)	)	PUNCT
iajs-3477	94	22	=	=	SYM
iajs-3477	94	23	cos(πx	cos(πx	NOUN
iajs-3477	94	24	)	)	PUNCT
iajs-3477	94	25	20	20	NUM
iajs-3477	94	26	,	,	PUNCT
iajs-3477	94	27	(	(	PUNCT
iajs-3477	94	28	x	x	NOUN
iajs-3477	94	29	,	,	PUNCT
iajs-3477	94	30	y	y	PROPN
iajs-3477	94	31	)	)	PUNCT
iajs-3477	94	32	∈	∈	PROPN
iajs-3477	95	1	q	q	NOUN
iajs-3477	95	2	,	,	PUNCT
iajs-3477	95	3	a(y	a(y	PROPN
iajs-3477	95	4	)	)	PUNCT
iajs-3477	95	5	=	=	SYM
iajs-3477	95	6	−15y	−15y	PROPN
iajs-3477	95	7	,	,	PUNCT
iajs-3477	95	8	f(x	f(x	PROPN
iajs-3477	95	9	,	,	PUNCT
iajs-3477	95	10	y	y	PROPN
iajs-3477	95	11	)	)	PUNCT
iajs-3477	95	12	=	=	PUNCT
iajs-3477	95	13	(	(	PUNCT
iajs-3477	95	14	1	1	NUM
iajs-3477	95	15	20	20	NUM
iajs-3477	95	16	)	)	PUNCT
iajs-3477	95	17	(	(	PUNCT
iajs-3477	95	18	−π2	−π2	NOUN
iajs-3477	95	19	+	+	CCONJ
iajs-3477	95	20	15y)(y	15y)(y	NUM
iajs-3477	95	21	−	−	NOUN
iajs-3477	95	22	4	4	NUM
iajs-3477	95	23	)	)	PUNCT
iajs-3477	95	24	cos(πx	cos(πx	NOUN
iajs-3477	95	25	)	)	PUNCT
iajs-3477	95	26	,	,	PUNCT
iajs-3477	95	27	(	(	PUNCT
iajs-3477	95	28	x	x	X
iajs-3477	95	29	,	,	PUNCT
iajs-3477	95	30	y	y	NOUN
iajs-3477	95	31	)	)	PUNCT
iajs-3477	95	32	∈	∈	PROPN
iajs-3477	95	33	q.	q.	NOUN
iajs-3477	95	34	figure	figure	NOUN
iajs-3477	95	35	1	1	NUM
iajs-3477	95	36	presents	present	VERB
iajs-3477	95	37	the	the	DET
iajs-3477	95	38	absolute	absolute	ADJ
iajs-3477	95	39	error	error	NOUN
iajs-3477	95	40	diagram	diagram	NOUN
iajs-3477	95	41	of	of	ADP
iajs-3477	95	42	interior	interior	ADJ
iajs-3477	95	43	points	point	NOUN
iajs-3477	96	1	when	when	SCONJ
iajs-3477	96	2	sizes	size	NOUN
iajs-3477	96	3	of	of	ADP
iajs-3477	96	4	mesh	mesh	NOUN
iajs-3477	96	5	n	n	NOUN
iajs-3477	96	6	=	=	SYM
iajs-3477	96	7	m	m	NOUN
iajs-3477	96	8	=	=	PUNCT
iajs-3477	96	9	{	{	PUNCT
iajs-3477	96	10	20	20	NUM
iajs-3477	96	11	,	,	PUNCT
iajs-3477	96	12	40	40	NUM
iajs-3477	96	13	,	,	PUNCT
iajs-3477	96	14	80	80	NUM
iajs-3477	96	15	}	}	PUNCT
iajs-3477	97	1	.	.	PUNCT
iajs-3477	98	1	mesh	mesh	NOUN
iajs-3477	98	2	independence	independence	NOUN
iajs-3477	98	3	has	have	AUX
iajs-3477	98	4	been	be	AUX
iajs-3477	98	5	attained	attain	VERB
iajs-3477	98	6	,	,	PUNCT
iajs-3477	98	7	as	as	ADV
iajs-3477	98	8	well	well	ADV
iajs-3477	98	9	as	as	ADP
iajs-3477	98	10	numerical	numerical	ADJ
iajs-3477	98	11	solution	solution	NOUN
iajs-3477	98	12	convergence	convergence	NOUN
iajs-3477	98	13	toward	toward	ADP
iajs-3477	98	14	the	the	DET
iajs-3477	98	15	exact	exact	ADJ
iajs-3477	98	16	solution	solution	NOUN
iajs-3477	98	17	and	and	CCONJ
iajs-3477	98	18	high	high	ADJ
iajs-3477	98	19	agreement	agreement	NOUN
iajs-3477	98	20	.	.	PUNCT
iajs-3477	99	1	figure	figure	NOUN
iajs-3477	99	2	2	2	NUM
iajs-3477	99	3	,	,	PUNCT
iajs-3477	99	4	as	as	SCONJ
iajs-3477	99	5	the	the	DET
iajs-3477	99	6	number	number	NOUN
iajs-3477	99	7	of	of	ADP
iajs-3477	99	8	discretization	discretization	NOUN
iajs-3477	99	9	rises	rise	VERB
iajs-3477	99	10	,	,	PUNCT
iajs-3477	99	11	the	the	DET
iajs-3477	99	12	findings	finding	NOUN
iajs-3477	99	13	for	for	ADP
iajs-3477	99	14	h(y	h(y	NOUN
iajs-3477	99	15	)	)	PUNCT
iajs-3477	99	16	,	,	PUNCT
iajs-3477	99	17	becomes	become	VERB
iajs-3477	99	18	more	more	ADV
iajs-3477	99	19	accurate	accurate	ADJ
iajs-3477	99	20	and	and	CCONJ
iajs-3477	99	21	showing	show	VERB
iajs-3477	99	22	a	a	DET
iajs-3477	99	23	clear	clear	ADJ
iajs-3477	99	24	convergence	convergence	NOUN
iajs-3477	99	25	.	.	PUNCT
iajs-3477	100	1	ihjpas	ihjpas	PROPN
iajs-3477	100	2	.	.	PUNCT
iajs-3477	101	1	37	37	NUM
iajs-3477	101	2	(	(	PUNCT
iajs-3477	101	3	2	2	NUM
iajs-3477	101	4	)	)	PUNCT
iajs-3477	101	5	2024	2024	NUM
iajs-3477	101	6	414	414	NUM
iajs-3477	101	7	figure	figure	NOUN
iajs-3477	101	8	1	1	NUM
iajs-3477	101	9	.	.	PUNCT
iajs-3477	102	1	the	the	DET
iajs-3477	102	2	absolute	absolute	ADJ
iajs-3477	102	3	errors	error	NOUN
iajs-3477	102	4	for	for	ADP
iajs-3477	102	5	the	the	DET
iajs-3477	102	6	direct	direct	ADJ
iajs-3477	102	7	problem	problem	NOUN
iajs-3477	102	8	(	(	PUNCT
iajs-3477	102	9	1)-(4	1)-(4	NUM
iajs-3477	102	10	)	)	PUNCT
iajs-3477	102	11	,	,	PUNCT
iajs-3477	102	12	when	when	SCONJ
iajs-3477	102	13	sizes	size	NOUN
iajs-3477	102	14	of	of	ADP
iajs-3477	102	15	mesh	mesh	NOUN
iajs-3477	102	16	are	be	AUX
iajs-3477	102	17	m	m	VERB
iajs-3477	102	18	=	=	SYM
iajs-3477	102	19	n	n	SYM
iajs-3477	102	20	∈	∈	PROPN
iajs-3477	102	21	{	{	PUNCT
iajs-3477	102	22	20	20	NUM
iajs-3477	102	23	,	,	PUNCT
iajs-3477	102	24	40	40	NUM
iajs-3477	102	25	,	,	PUNCT
iajs-3477	102	26	80	80	NUM
iajs-3477	102	27	}	}	PUNCT
iajs-3477	102	28	.	.	PUNCT
iajs-3477	103	1	figure	figure	NOUN
iajs-3477	103	2	2	2	NUM
iajs-3477	103	3	.	.	PUNCT
iajs-3477	104	1	the	the	DET
iajs-3477	104	2	numerical	numerical	ADJ
iajs-3477	104	3	value	value	NOUN
iajs-3477	104	4	and	and	CCONJ
iajs-3477	104	5	accurate	accurate	ADJ
iajs-3477	104	6	for	for	ADP
iajs-3477	104	7	desired	desire	VERB
iajs-3477	104	8	output	output	NOUN
iajs-3477	104	9	h(y	h(y	ADV
iajs-3477	104	10	)	)	PUNCT
iajs-3477	104	11	with	with	ADP
iajs-3477	104	12	various	various	ADJ
iajs-3477	104	13	mesh	mesh	NOUN
iajs-3477	104	14	sizes	size	NOUN
iajs-3477	104	15	.	.	PUNCT
iajs-3477	105	1	4	4	X
iajs-3477	105	2	.	.	X
iajs-3477	105	3	inverse	inverse	ADJ
iajs-3477	105	4	problem	problem	NOUN
iajs-3477	105	5	for	for	ADP
iajs-3477	105	6	the	the	DET
iajs-3477	105	7	nonlinear	nonlinear	ADJ
iajs-3477	105	8	inverse	inverse	NOUN
iajs-3477	105	9	problem	problem	NOUN
iajs-3477	105	10	(	(	PUNCT
iajs-3477	105	11	1)-(5	1)-(5	NUM
iajs-3477	105	12	)	)	PUNCT
iajs-3477	105	13	,	,	PUNCT
iajs-3477	105	14	we	we	PRON
iajs-3477	105	15	seek	seek	VERB
iajs-3477	105	16	a	a	DET
iajs-3477	105	17	precise	precise	ADJ
iajs-3477	105	18	and	and	CCONJ
iajs-3477	105	19	stable	stable	ADJ
iajs-3477	105	20	identification	identification	NOUN
iajs-3477	105	21	of	of	ADP
iajs-3477	105	22	u(x	u(x	NOUN
iajs-3477	105	23	,	,	PUNCT
iajs-3477	105	24	y	y	NOUN
iajs-3477	105	25	)	)	PUNCT
iajs-3477	105	26	and	and	CCONJ
iajs-3477	105	27	a(y	a(y	PROPN
iajs-3477	105	28	)	)	PUNCT
iajs-3477	105	29	,	,	PUNCT
iajs-3477	105	30	that	that	PRON
iajs-3477	105	31	mean	mean	VERB
iajs-3477	105	32	a(y	a(y	PROPN
iajs-3477	105	33	)	)	PUNCT
iajs-3477	105	34	be	be	AUX
iajs-3477	105	35	unknown	unknown	ADJ
iajs-3477	105	36	.	.	PUNCT
iajs-3477	106	1	the	the	DET
iajs-3477	106	2	one	one	NUM
iajs-3477	106	3	-	-	PUNCT
iajs-3477	106	4	dimensional	dimensional	ADJ
iajs-3477	106	5	second	second	ADJ
iajs-3477	106	6	-	-	PUNCT
iajs-3477	106	7	order	order	NOUN
iajs-3477	106	8	elliptic	elliptic	ADJ
iajs-3477	106	9	equation	equation	NOUN
iajs-3477	106	10	together	together	ADV
iajs-3477	106	11	with	with	ADP
iajs-3477	106	12	u	u	PROPN
iajs-3477	106	13	(	(	PUNCT
iajs-3477	106	14	x	x	PROPN
iajs-3477	106	15	,	,	PUNCT
iajs-3477	106	16	y	y	NOUN
iajs-3477	106	17	)	)	PUNCT
iajs-3477	106	18	satisfies	satisfy	VERB
iajs-3477	106	19	the	the	DET
iajs-3477	106	20	problem	problem	NOUN
iajs-3477	106	21	given	give	VERB
iajs-3477	106	22	by	by	ADP
iajs-3477	106	23	equations	equation	NOUN
iajs-3477	106	24	(	(	PUNCT
iajs-3477	106	25	1)-(5	1)-(5	NUM
iajs-3477	106	26	)	)	PUNCT
iajs-3477	106	27	.	.	PUNCT
iajs-3477	107	1	during	during	ADP
iajs-3477	107	2	the	the	DET
iajs-3477	107	3	iterative	iterative	NOUN
iajs-3477	107	4	process	process	NOUN
iajs-3477	107	5	to	to	PART
iajs-3477	107	6	solve	solve	VERB
iajs-3477	107	7	the	the	DET
iajs-3477	107	8	inverse	inverse	NOUN
iajs-3477	107	9	problem	problem	NOUN
iajs-3477	107	10	,	,	PUNCT
iajs-3477	107	11	we	we	PRON
iajs-3477	107	12	assume	assume	VERB
iajs-3477	107	13	that	that	SCONJ
iajs-3477	107	14	a(0	a(0	PROPN
iajs-3477	107	15	)	)	PUNCT
iajs-3477	107	16	is	be	AUX
iajs-3477	107	17	a	a	DET
iajs-3477	107	18	constant	constant	ADJ
iajs-3477	107	19	starting	starting	NOUN
iajs-3477	107	20	assumption	assumption	NOUN
iajs-3477	107	21	.	.	PUNCT
iajs-3477	108	1	based	base	VERB
iajs-3477	108	2	on	on	ADP
iajs-3477	108	3	the	the	DET
iajs-3477	108	4	given	give	VERB
iajs-3477	108	5	data	datum	NOUN
iajs-3477	108	6	,	,	PUNCT
iajs-3477	108	7	we	we	PRON
iajs-3477	108	8	can	can	AUX
iajs-3477	108	9	calculate	calculate	VERB
iajs-3477	108	10	this	this	PRON
iajs-3477	108	11	,	,	PUNCT
iajs-3477	108	12	we	we	PRON
iajs-3477	108	13	can	can	AUX
iajs-3477	108	14	calculate	calculate	VERB
iajs-3477	108	15	this	this	PRON
iajs-3477	108	16	at	at	ADP
iajs-3477	108	17	y	y	PROPN
iajs-3477	108	18	=	=	PROPN
iajs-3477	108	19	0	0	PROPN
iajs-3477	108	20	.	.	PUNCT
iajs-3477	108	21	to	to	PART
iajs-3477	108	22	solve	solve	VERB
iajs-3477	108	23	this	this	DET
iajs-3477	108	24	problem	problem	NOUN
iajs-3477	108	25	,	,	PUNCT
iajs-3477	108	26	reformulate	reformulate	VERB
iajs-3477	108	27	it	it	PRON
iajs-3477	108	28	as	as	ADP
iajs-3477	108	29	a	a	DET
iajs-3477	108	30	nonlinear	nonlinear	ADJ
iajs-3477	108	31	minimization	minimization	NOUN
iajs-3477	108	32	problem	problem	NOUN
iajs-3477	108	33	.	.	PUNCT
iajs-3477	109	1	in	in	ADP
iajs-3477	109	2	other	other	ADJ
iajs-3477	109	3	words	word	NOUN
iajs-3477	109	4	:	:	PUNCT
iajs-3477	109	5	we	we	PRON
iajs-3477	109	6	try	try	VERB
iajs-3477	109	7	to	to	PART
iajs-3477	109	8	find	find	VERB
iajs-3477	109	9	the	the	DET
iajs-3477	109	10	smallest	small	ADJ
iajs-3477	109	11	possible	possible	ADJ
iajs-3477	109	12	value	value	NOUN
iajs-3477	109	13	for	for	ADP
iajs-3477	109	14	the	the	DET
iajs-3477	109	15	discrepancy	discrepancy	NOUN
iajs-3477	109	16	between	between	ADP
iajs-3477	109	17	the	the	DET
iajs-3477	109	18	numerically	numerically	ADV
iajs-3477	109	19	calculated	calculate	VERB
iajs-3477	109	20	result	result	NOUN
iajs-3477	109	21	and	and	CCONJ
iajs-3477	109	22	the	the	DET
iajs-3477	109	23	measured	measured	ADJ
iajs-3477	109	24	data	datum	NOUN
iajs-3477	109	25	.	.	PUNCT
iajs-3477	110	1	since	since	SCONJ
iajs-3477	110	2	this	this	PRON
iajs-3477	110	3	is	be	AUX
iajs-3477	110	4	an	an	DET
iajs-3477	110	5	ill	ill	ADV
iajs-3477	110	6	-	-	PUNCT
iajs-3477	110	7	posed	pose	VERB
iajs-3477	110	8	problem	problem	NOUN
iajs-3477	110	9	,	,	PUNCT
iajs-3477	110	10	we	we	PRON
iajs-3477	110	11	need	need	VERB
iajs-3477	110	12	to	to	PART
iajs-3477	110	13	apply	apply	VERB
iajs-3477	110	14	tikhonov	tikhonov	NOUN
iajs-3477	110	15	regularization	regularization	NOUN
iajs-3477	110	16	for	for	ADP
iajs-3477	110	17	a	a	DET
iajs-3477	110	18	robust	robust	ADJ
iajs-3477	110	19	numerical	numerical	ADJ
iajs-3477	110	20	solution	solution	NOUN
iajs-3477	110	21	in	in	ADP
iajs-3477	110	22	order	order	NOUN
iajs-3477	110	23	to	to	PART
iajs-3477	110	24	obtain	obtain	VERB
iajs-3477	110	25	stable	stable	ADJ
iajs-3477	110	26	results	result	NOUN
iajs-3477	110	27	.	.	PUNCT
iajs-3477	111	1	the	the	DET
iajs-3477	111	2	tikhonov	tikhonov	NOUN
iajs-3477	111	3	regularization	regularization	NOUN
iajs-3477	111	4	functional	functional	NOUN
iajs-3477	111	5	can	can	AUX
iajs-3477	111	6	be	be	AUX
iajs-3477	111	7	derived	derive	VERB
iajs-3477	111	8	from	from	ADP
iajs-3477	111	9	condition	condition	NOUN
iajs-3477	111	10	(	(	PUNCT
iajs-3477	111	11	5	5	NUM
iajs-3477	111	12	):	):	PUNCT
iajs-3477	111	13	ihjpas	ihjpa	NOUN
iajs-3477	111	14	.	.	PUNCT
iajs-3477	112	1	37	37	NUM
iajs-3477	112	2	(	(	PUNCT
iajs-3477	112	3	2	2	NUM
iajs-3477	112	4	)	)	PUNCT
iajs-3477	112	5	2024	2024	NUM
iajs-3477	112	6	415	415	NUM
iajs-3477	112	7	f(a	f(a	NOUN
iajs-3477	112	8	)	)	PUNCT
iajs-3477	112	9	=	=	PUNCT
iajs-3477	113	1	‖	‖	PROPN
iajs-3477	113	2	u(0	u(0	PROPN
iajs-3477	113	3	,	,	PUNCT
iajs-3477	113	4	y	y	PROPN
iajs-3477	113	5	)	)	PUNCT
iajs-3477	113	6	−	−	PROPN
iajs-3477	114	1	h(y)‖2	h(y)‖2	X
iajs-3477	114	2	l2[0,y	l2[0,y	NOUN
iajs-3477	114	3	]	]	X
iajs-3477	115	1	+	+	CCONJ
iajs-3477	115	2	β‖a(y)‖2	β‖a(y)‖2	ADJ
iajs-3477	115	3	l2[0,y	l2[0,y	ADJ
iajs-3477	115	4	]	]	PUNCT
iajs-3477	115	5	,	,	PUNCT
iajs-3477	115	6	(	(	PUNCT
iajs-3477	115	7	14	14	NUM
iajs-3477	115	8	)	)	PUNCT
iajs-3477	115	9	where	where	SCONJ
iajs-3477	115	10	β	β	X
iajs-3477	115	11	>	>	X
iajs-3477	115	12	0	0	NUM
iajs-3477	115	13	,	,	PUNCT
iajs-3477	115	14	is	be	AUX
iajs-3477	115	15	a	a	DET
iajs-3477	115	16	regularization	regularization	NOUN
iajs-3477	115	17	parameter	parameter	NOUN
iajs-3477	115	18	.	.	PUNCT
iajs-3477	116	1	the	the	DET
iajs-3477	116	2	discretization	discretization	NOUN
iajs-3477	116	3	of	of	ADP
iajs-3477	116	4	(	(	PUNCT
iajs-3477	116	5	14	14	NUM
iajs-3477	116	6	)	)	PUNCT
iajs-3477	116	7	is	be	AUX
iajs-3477	116	8	f	f	X
iajs-3477	116	9	(	(	PUNCT
iajs-3477	116	10	a	a	NOUN
iajs-3477	116	11	)	)	PUNCT
iajs-3477	116	12	=	=	PUNCT
iajs-3477	117	1	∑[u(0	∑[u(0	PROPN
iajs-3477	117	2	,	,	PUNCT
iajs-3477	117	3	yj	yj	PROPN
iajs-3477	117	4	)	)	PUNCT
iajs-3477	117	5	−	−	PROPN
iajs-3477	117	6	h(yj	h(yj	NOUN
iajs-3477	117	7	)	)	PUNCT
iajs-3477	117	8	]	]	PUNCT
iajs-3477	117	9	2	2	NUM
iajs-3477	117	10	n	n	X
iajs-3477	117	11	j=1	j=1	NOUN
iajs-3477	117	12	+	+	CCONJ
iajs-3477	117	13	β∑aj	β∑aj	X
iajs-3477	117	14	2	2	NUM
iajs-3477	117	15	n	n	NOUN
iajs-3477	117	16	j=1	j=1	NOUN
iajs-3477	117	17	.	.	PUNCT
iajs-3477	118	1	(	(	PUNCT
iajs-3477	118	2	15	15	X
iajs-3477	118	3	)	)	PUNCT
iajs-3477	118	4	the	the	DET
iajs-3477	118	5	unregularized	unregularized	ADJ
iajs-3477	118	6	case	case	NOUN
iajs-3477	118	7	,	,	PUNCT
iajs-3477	118	8	i.e.	i.e.	X
iajs-3477	118	9	,	,	PUNCT
iajs-3477	118	10	β	β	X
iajs-3477	118	11	=	=	SYM
iajs-3477	118	12	0	0	NUM
iajs-3477	118	13	,	,	PUNCT
iajs-3477	118	14	produces	produce	VERB
iajs-3477	118	15	the	the	DET
iajs-3477	118	16	regular	regular	ADJ
iajs-3477	118	17	nonlinear	nonlinear	ADJ
iajs-3477	118	18	least	least	ADJ
iajs-3477	118	19	-	-	PUNCT
iajs-3477	118	20	squares	square	NOUN
iajs-3477	118	21	functional	functional	ADJ
iajs-3477	118	22	,	,	PUNCT
iajs-3477	118	23	which	which	PRON
iajs-3477	118	24	is	be	AUX
iajs-3477	118	25	inherently	inherently	ADV
iajs-3477	118	26	unstable	unstable	ADJ
iajs-3477	118	27	when	when	SCONJ
iajs-3477	118	28	dealing	deal	VERB
iajs-3477	118	29	with	with	ADP
iajs-3477	118	30	noisy	noisy	ADJ
iajs-3477	118	31	data	datum	NOUN
iajs-3477	118	32	.	.	PUNCT
iajs-3477	119	1	the	the	DET
iajs-3477	119	2	matlab	matlab	PROPN
iajs-3477	119	3	toolbox	toolbox	NOUN
iajs-3477	119	4	technique	technique	NOUN
iajs-3477	119	5	lsqnonlin	lsqnonlin	PROPN
iajs-3477	119	6	is	be	AUX
iajs-3477	119	7	used	use	VERB
iajs-3477	119	8	to	to	PART
iajs-3477	119	9	minimize	minimize	VERB
iajs-3477	119	10	f	f	PROPN
iajs-3477	119	11	under	under	ADP
iajs-3477	119	12	the	the	DET
iajs-3477	119	13	physical	physical	ADJ
iajs-3477	119	14	constraint	constraint	NOUN
iajs-3477	119	15	a	a	DET
iajs-3477	119	16	>	>	X
iajs-3477	119	17	0	0	PUNCT
iajs-3477	119	18	and	and	CCONJ
iajs-3477	119	19	does	do	AUX
iajs-3477	119	20	not	not	PART
iajs-3477	119	21	need	need	VERB
iajs-3477	119	22	the	the	DET
iajs-3477	119	23	user	user	NOUN
iajs-3477	119	24	to	to	PART
iajs-3477	119	25	provide	provide	VERB
iajs-3477	119	26	the	the	DET
iajs-3477	119	27	gradient	gradient	NOUN
iajs-3477	119	28	of	of	ADP
iajs-3477	119	29	the	the	DET
iajs-3477	119	30	objective	objective	ADJ
iajs-3477	119	31	functional	functional	ADJ
iajs-3477	119	32	(	(	PUNCT
iajs-3477	119	33	15	15	NUM
iajs-3477	119	34	)	)	PUNCT
iajs-3477	120	1	[	[	X
iajs-3477	120	2	27	27	NUM
iajs-3477	120	3	]	]	PUNCT
iajs-3477	120	4	.	.	PUNCT
iajs-3477	121	1	to	to	PART
iajs-3477	121	2	determine	determine	VERB
iajs-3477	121	3	the	the	DET
iajs-3477	121	4	minimum	minimum	NOUN
iajs-3477	121	5	of	of	ADP
iajs-3477	121	6	a	a	DET
iajs-3477	121	7	scalar	scalar	ADJ
iajs-3477	121	8	function	function	NOUN
iajs-3477	121	9	with	with	ADP
iajs-3477	121	10	several	several	ADJ
iajs-3477	121	11	variables	variable	NOUN
iajs-3477	121	12	,	,	PUNCT
iajs-3477	121	13	the	the	DET
iajs-3477	121	14	lsqnonlin	lsqnonlin	PROPN
iajs-3477	121	15	subroutine	subroutine	NOUN
iajs-3477	121	16	conducts	conduct	VERB
iajs-3477	121	17	a	a	DET
iajs-3477	121	18	constrained	constrained	ADJ
iajs-3477	121	19	nonlinear	nonlinear	ADJ
iajs-3477	121	20	optimization	optimization	NOUN
iajs-3477	121	21	.	.	PUNCT
iajs-3477	122	1	the	the	DET
iajs-3477	122	2	subroutine	subroutine	NOUN
iajs-3477	122	3	is	be	AUX
iajs-3477	122	4	configured	configure	VERB
iajs-3477	122	5	using	use	VERB
iajs-3477	122	6	the	the	DET
iajs-3477	122	7	following	follow	VERB
iajs-3477	122	8	parameters	parameter	NOUN
iajs-3477	122	9	:	:	PUNCT
iajs-3477	122	10	•	•	DET
iajs-3477	122	11	(	(	PUNCT
iajs-3477	122	12	maxlter	maxlter	NOUN
iajs-3477	122	13	)	)	PUNCT
iajs-3477	122	14	maximum	maximum	ADJ
iajs-3477	122	15	number	number	NOUN
iajs-3477	122	16	of	of	ADP
iajs-3477	122	17	iterations	iteration	NOUN
iajs-3477	122	18	=	=	SYM
iajs-3477	122	19	400	400	NUM
iajs-3477	122	20	or	or	CCONJ
iajs-3477	122	21	102	102	NUM
iajs-3477	122	22	×	×	NOUN
iajs-3477	122	23	(	(	PUNCT
iajs-3477	122	24	number	number	NOUN
iajs-3477	122	25	of	of	ADP
iajs-3477	122	26	variables	variable	NOUN
iajs-3477	122	27	)	)	PUNCT
iajs-3477	122	28	•	•	NUM
iajs-3477	122	29	solution	solution	NOUN
iajs-3477	122	30	tolerance	tolerance	NOUN
iajs-3477	122	31	(	(	PUNCT
iajs-3477	122	32	soltol	soltol	NOUN
iajs-3477	122	33	)	)	PUNCT
iajs-3477	122	34	=	=	SYM
iajs-3477	122	35	10−15	10−15	NUM
iajs-3477	122	36	and	and	CCONJ
iajs-3477	122	37	objective	objective	ADJ
iajs-3477	122	38	function	function	NOUN
iajs-3477	122	39	tolerance	tolerance	NOUN
iajs-3477	122	40	(	(	PUNCT
iajs-3477	122	41	funtol	funtol	ADJ
iajs-3477	122	42	)	)	PUNCT
iajs-3477	122	43	=	=	SYM
iajs-3477	122	44	10−15	10−15	NUM
iajs-3477	122	45	.	.	PUNCT
iajs-3477	123	1	the	the	DET
iajs-3477	123	2	solution	solution	NOUN
iajs-3477	123	3	of	of	ADP
iajs-3477	123	4	the	the	DET
iajs-3477	123	5	inverse	inverse	NOUN
iajs-3477	123	6	problem	problem	NOUN
iajs-3477	123	7	(	(	PUNCT
iajs-3477	123	8	1)–(5	1)–(5	NUM
iajs-3477	123	9	)	)	PUNCT
iajs-3477	123	10	is	be	AUX
iajs-3477	123	11	subjected	subject	VERB
iajs-3477	123	12	to	to	ADP
iajs-3477	123	13	both	both	CCONJ
iajs-3477	123	14	accurate	accurate	ADJ
iajs-3477	123	15	and	and	CCONJ
iajs-3477	123	16	noisy	noisy	ADJ
iajs-3477	123	17	measurement	measurement	NOUN
iajs-3477	123	18	data	datum	NOUN
iajs-3477	123	19	(	(	PUNCT
iajs-3477	123	20	5	5	NUM
iajs-3477	123	21	)	)	PUNCT
iajs-3477	123	22	.	.	PUNCT
iajs-3477	124	1	by	by	ADP
iajs-3477	124	2	including	include	VERB
iajs-3477	124	3	a	a	DET
iajs-3477	124	4	random	random	ADJ
iajs-3477	124	5	error	error	NOUN
iajs-3477	124	6	,	,	PUNCT
iajs-3477	124	7	the	the	DET
iajs-3477	124	8	noisy	noisy	ADJ
iajs-3477	124	9	data	datum	NOUN
iajs-3477	124	10	is	be	AUX
iajs-3477	124	11	numerically	numerically	ADV
iajs-3477	124	12	simulated	simulate	VERB
iajs-3477	124	13	as	as	SCONJ
iajs-3477	124	14	follows	follow	VERB
iajs-3477	124	15	:	:	PUNCT
iajs-3477	124	16	hϵ(yj	hϵ(yj	X
iajs-3477	124	17	)	)	PUNCT
iajs-3477	124	18	=	=	PUNCT
iajs-3477	125	1	h(yj	h(yj	NOUN
iajs-3477	125	2	)	)	PUNCT
iajs-3477	126	1	+	+	CCONJ
iajs-3477	126	2	ϵj	ϵj	X
iajs-3477	126	3	,	,	PUNCT
iajs-3477	126	4	j	j	PROPN
iajs-3477	126	5	=	=	SYM
iajs-3477	126	6	0,1	0,1	NUM
iajs-3477	126	7	,	,	PUNCT
iajs-3477	126	8	…	…	PUNCT
iajs-3477	126	9	,	,	PUNCT
iajs-3477	126	10	n	n	CCONJ
iajs-3477	126	11	,	,	PUNCT
iajs-3477	126	12	(	(	PUNCT
iajs-3477	126	13	16	16	NUM
iajs-3477	126	14	)	)	PUNCT
iajs-3477	126	15	where	where	SCONJ
iajs-3477	126	16	ϵ	ϵ	X
iajs-3477	126	17	,	,	PUNCT
iajs-3477	126	18	is	be	AUX
iajs-3477	126	19	random	random	ADJ
iajs-3477	126	20	gaussian	gaussian	ADJ
iajs-3477	126	21	normal	normal	ADJ
iajs-3477	126	22	distribution	distribution	NOUN
iajs-3477	126	23	vectors	vector	NOUN
iajs-3477	126	24	with	with	ADP
iajs-3477	126	25	mean	mean	NOUN
iajs-3477	126	26	zero	zero	NUM
iajs-3477	126	27	and	and	CCONJ
iajs-3477	126	28	standard	standard	ADJ
iajs-3477	126	29	deviations	deviation	NOUN
iajs-3477	126	30	σ	σ	PROPN
iajs-3477	126	31	,	,	PUNCT
iajs-3477	126	32	given	give	VERB
iajs-3477	126	33	by	by	ADP
iajs-3477	126	34	σ	σ	NOUN
iajs-3477	126	35	=	=	SYM
iajs-3477	126	36	p	p	X
iajs-3477	126	37	×	×	PROPN
iajs-3477	126	38	max	max	PROPN
iajs-3477	126	39	y∈[0,y	y∈[0,y	PROPN
iajs-3477	126	40	]	]	X
iajs-3477	126	41	|h(y)|	|h(y)|	PROPN
iajs-3477	126	42	;	;	PUNCT
iajs-3477	126	43	(	(	PUNCT
iajs-3477	126	44	17	17	NUM
iajs-3477	126	45	)	)	PUNCT
iajs-3477	126	46	where	where	SCONJ
iajs-3477	126	47	p	p	NOUN
iajs-3477	126	48	is	be	AUX
iajs-3477	126	49	the	the	DET
iajs-3477	126	50	percentage	percentage	NOUN
iajs-3477	126	51	of	of	ADP
iajs-3477	126	52	noise	noise	NOUN
iajs-3477	126	53	.	.	PUNCT
iajs-3477	127	1	we	we	PRON
iajs-3477	127	2	use	use	VERB
iajs-3477	127	3	the	the	DET
iajs-3477	127	4	matlab	matlab	PROPN
iajs-3477	127	5	bulletin	bulletin	NOUN
iajs-3477	127	6	function	function	NOUN
iajs-3477	127	7	normrnd	normrnd	NOUN
iajs-3477	127	8	to	to	PART
iajs-3477	127	9	generate	generate	VERB
iajs-3477	127	10	the	the	DET
iajs-3477	127	11	random	random	ADJ
iajs-3477	127	12	variables	variable	NOUN
iajs-3477	127	13	ϵ	ϵ	X
iajs-3477	127	14	=	=	SYM
iajs-3477	127	15	(	(	PUNCT
iajs-3477	127	16	ϵj	ϵj	NOUN
iajs-3477	127	17	)	)	PUNCT
iajs-3477	127	18	and	and	CCONJ
iajs-3477	127	19	j	j	PROPN
iajs-3477	127	20	=	=	SYM
iajs-3477	127	21	0,1	0,1	NUM
iajs-3477	127	22	,	,	PUNCT
iajs-3477	127	23	…	…	PUNCT
iajs-3477	127	24	,	,	PUNCT
iajs-3477	127	25	n.	n.	NOUN
iajs-3477	127	26	as	as	SCONJ
iajs-3477	127	27	follows	follow	VERB
iajs-3477	127	28	:	:	PUNCT
iajs-3477	127	29	ϵ	ϵ	X
iajs-3477	127	30	=	=	PUNCT
iajs-3477	127	31	normrnd(0	normrnd(0	PROPN
iajs-3477	127	32	,	,	PUNCT
iajs-3477	127	33	σ	σ	PROPN
iajs-3477	127	34	,	,	PUNCT
iajs-3477	127	35	n	n	CCONJ
iajs-3477	127	36	)	)	PUNCT
iajs-3477	127	37	,	,	PUNCT
iajs-3477	127	38	(	(	PUNCT
iajs-3477	127	39	18	18	NUM
iajs-3477	127	40	)	)	PUNCT
iajs-3477	127	41	4.1	4.1	NUM
iajs-3477	127	42	initial	initial	ADJ
iajs-3477	127	43	guess	guess	NOUN
iajs-3477	127	44	as	as	SCONJ
iajs-3477	127	45	stated	state	VERB
iajs-3477	127	46	previously	previously	ADV
iajs-3477	127	47	,	,	PUNCT
iajs-3477	127	48	to	to	PART
iajs-3477	127	49	begin	begin	VERB
iajs-3477	127	50	the	the	DET
iajs-3477	127	51	iterative	iterative	ADJ
iajs-3477	127	52	process	process	NOUN
iajs-3477	127	53	of	of	ADP
iajs-3477	127	54	solving	solve	VERB
iajs-3477	127	55	the	the	DET
iajs-3477	127	56	inverse	inverse	NOUN
iajs-3477	127	57	problem	problem	NOUN
iajs-3477	127	58	,	,	PUNCT
iajs-3477	127	59	an	an	DET
iajs-3477	127	60	initial	initial	ADJ
iajs-3477	127	61	estimate	estimate	NOUN
iajs-3477	127	62	is	be	AUX
iajs-3477	127	63	required	require	VERB
iajs-3477	127	64	.	.	PUNCT
iajs-3477	128	1	the	the	DET
iajs-3477	128	2	following	follow	VERB
iajs-3477	128	3	values	value	NOUN
iajs-3477	128	4	for	for	ADP
iajs-3477	128	5	a(0	a(0	PROPN
iajs-3477	128	6	)	)	PUNCT
iajs-3477	128	7	can	can	AUX
iajs-3477	128	8	be	be	AUX
iajs-3477	128	9	derived	derive	VERB
iajs-3477	128	10	from	from	ADP
iajs-3477	128	11	input	input	NOUN
iajs-3477	128	12	data	datum	NOUN
iajs-3477	128	13	.	.	PUNCT
iajs-3477	129	1	consider	consider	VERB
iajs-3477	129	2	the	the	DET
iajs-3477	129	3	nonlinear	nonlinear	ADJ
iajs-3477	129	4	inverse	inverse	NOUN
iajs-3477	129	5	problem	problem	NOUN
iajs-3477	129	6	(	(	PUNCT
iajs-3477	129	7	1)-(5	1)-(5	NUM
iajs-3477	129	8	)	)	PUNCT
iajs-3477	129	9	with	with	ADP
iajs-3477	129	10	unknown	unknown	ADJ
iajs-3477	129	11	coefficient	coefficient	NOUN
iajs-3477	129	12	a(y	a(y	PROPN
iajs-3477	129	13	)	)	PUNCT
iajs-3477	129	14	and	and	CCONJ
iajs-3477	129	15	from	from	ADP
iajs-3477	129	16	the	the	DET
iajs-3477	129	17	equation	equation	NOUN
iajs-3477	129	18	(	(	PUNCT
iajs-3477	129	19	28	28	NUM
iajs-3477	129	20	)	)	PUNCT
iajs-3477	129	21	in	in	ADP
iajs-3477	129	22	[	[	X
iajs-3477	129	23	26	26	NUM
iajs-3477	129	24	]	]	PUNCT
iajs-3477	129	25	,	,	PUNCT
iajs-3477	129	26	we	we	PRON
iajs-3477	129	27	have	have	VERB
iajs-3477	129	28	:	:	PUNCT
iajs-3477	129	29	a(y	a(y	PROPN
iajs-3477	129	30	)	)	PUNCT
iajs-3477	130	1	=	=	SYM
iajs-3477	130	2	h−1(y	h−1(y	PROPN
iajs-3477	130	3	)	)	PUNCT
iajs-3477	130	4	{	{	PUNCT
iajs-3477	130	5	h′′(y	h′′(y	NOUN
iajs-3477	130	6	)	)	PUNCT
iajs-3477	130	7	−	−	PROPN
iajs-3477	130	8	f(0	f(0	NOUN
iajs-3477	130	9	,	,	PUNCT
iajs-3477	130	10	y	y	PROPN
iajs-3477	130	11	)	)	PUNCT
iajs-3477	130	12	−	−	PROPN
iajs-3477	130	13	∑λk	∑λk	PROPN
iajs-3477	130	14	2uk(y	2uk(y	NUM
iajs-3477	130	15	)	)	PUNCT
iajs-3477	131	1	∞	∞	NUM
iajs-3477	131	2	k=1	k=1	PROPN
iajs-3477	131	3	}	}	PUNCT
iajs-3477	131	4	,	,	PUNCT
iajs-3477	131	5	y	y	PROPN
iajs-3477	131	6	∈	∈	PROPN
iajs-3477	132	1	[	[	X
iajs-3477	132	2	0	0	NUM
iajs-3477	132	3	,	,	PUNCT
iajs-3477	132	4	y	y	NOUN
iajs-3477	132	5	]	]	PUNCT
iajs-3477	132	6	.	.	PUNCT
iajs-3477	133	1	from	from	ADP
iajs-3477	133	2	equation	equation	NOUN
iajs-3477	133	3	(	(	PUNCT
iajs-3477	133	4	5	5	NUM
iajs-3477	133	5	)	)	PUNCT
iajs-3477	133	6	,	,	PUNCT
iajs-3477	133	7	since	since	SCONJ
iajs-3477	133	8	uk(y	uk(y	NOUN
iajs-3477	133	9	)	)	PUNCT
iajs-3477	133	10	=	=	SYM
iajs-3477	133	11	u(0	u(0	PROPN
iajs-3477	133	12	,	,	PUNCT
iajs-3477	133	13	yk	yk	PROPN
iajs-3477	133	14	)	)	PUNCT
iajs-3477	133	15	=	=	SYM
iajs-3477	133	16	h(yk	h(yk	PROPN
iajs-3477	133	17	)	)	PUNCT
iajs-3477	133	18	and	and	CCONJ
iajs-3477	133	19	λk	λk	ADP
iajs-3477	133	20	2	2	NUM
iajs-3477	133	21	=	=	SYM
iajs-3477	133	22	π2	π2	NOUN
iajs-3477	133	23	,	,	PUNCT
iajs-3477	133	24	therefore	therefore	ADV
iajs-3477	133	25	the	the	DET
iajs-3477	133	26	above	above	ADJ
iajs-3477	133	27	equation	equation	NOUN
iajs-3477	133	28	becomes	become	VERB
iajs-3477	133	29	:	:	PUNCT
iajs-3477	133	30	𝑎(𝑦	𝑎(𝑦	NUM
iajs-3477	133	31	)	)	PUNCT
iajs-3477	133	32	=	=	SYM
iajs-3477	133	33	𝐻−1(𝑦	𝐻−1(𝑦	PROPN
iajs-3477	133	34	)	)	PUNCT
iajs-3477	133	35	{	{	PUNCT
iajs-3477	133	36	𝐻′′(𝑦	𝐻′′(𝑦	PROPN
iajs-3477	133	37	)	)	PUNCT
iajs-3477	133	38	−	−	PROPN
iajs-3477	134	1	𝑓(0	𝑓(0	PROPN
iajs-3477	134	2	,	,	PUNCT
iajs-3477	134	3	𝑦	𝑦	NOUN
iajs-3477	134	4	)	)	PUNCT
iajs-3477	134	5	−	−	PROPN
iajs-3477	134	6	∑	∑	PUNCT
iajs-3477	134	7	𝜋2𝐻(𝑦𝑘	𝜋2𝐻(𝑦𝑘	NOUN
iajs-3477	134	8	)	)	PUNCT
iajs-3477	134	9	∞	∞	PROPN
iajs-3477	134	10	𝑘=1	𝑘=1	PROPN
iajs-3477	134	11	}	}	PUNCT
iajs-3477	134	12	,	,	PUNCT
iajs-3477	134	13	𝑦	𝑦	NOUN
iajs-3477	134	14	∈	∈	NOUN
iajs-3477	135	1	[	[	X
iajs-3477	135	2	0	0	NUM
iajs-3477	135	3	,	,	PUNCT
iajs-3477	135	4	𝑌	𝑌	PROPN
iajs-3477	135	5	]	]	PUNCT
iajs-3477	135	6	.	.	PUNCT
iajs-3477	136	1	the	the	DET
iajs-3477	136	2	above	above	ADJ
iajs-3477	136	3	equations	equation	NOUN
iajs-3477	136	4	at	at	ADP
iajs-3477	136	5	y	y	PROPN
iajs-3477	136	6	=	=	PROPN
iajs-3477	136	7	0	0	NUM
iajs-3477	136	8	,	,	PUNCT
iajs-3477	136	9	we	we	PRON
iajs-3477	136	10	get	get	VERB
iajs-3477	136	11	the	the	DET
iajs-3477	136	12	first	first	ADJ
iajs-3477	136	13	guess	guess	NOUN
iajs-3477	136	14	:	:	PUNCT
iajs-3477	136	15	𝑎0	𝑎0	PROPN
iajs-3477	136	16	=	=	SYM
iajs-3477	136	17	𝐻−1(0	𝐻−1(0	X
iajs-3477	136	18	)	)	PUNCT
iajs-3477	136	19	{	{	PUNCT
iajs-3477	136	20	𝐻′′(0	𝐻′′(0	NUM
iajs-3477	136	21	)	)	PUNCT
iajs-3477	136	22	−	−	ADP
iajs-3477	136	23	𝑓(0,0	𝑓(0,0	NOUN
iajs-3477	136	24	)	)	PUNCT
iajs-3477	136	25	−	−	NOUN
iajs-3477	136	26	∑	∑	PUNCT
iajs-3477	136	27	𝜋2𝐻(0	𝜋2𝐻(0	NUM
iajs-3477	136	28	)	)	PUNCT
iajs-3477	136	29	∞	∞	NUM
iajs-3477	136	30	𝑘=1	𝑘=1	PROPN
iajs-3477	136	31	}	}	PUNCT
iajs-3477	136	32	,	,	PUNCT
iajs-3477	136	33	𝑦	𝑦	NOUN
iajs-3477	136	34	∈	∈	NOUN
iajs-3477	137	1	[	[	X
iajs-3477	137	2	0	0	NUM
iajs-3477	137	3	,	,	PUNCT
iajs-3477	137	4	𝑌	𝑌	PROPN
iajs-3477	137	5	]	]	PUNCT
iajs-3477	137	6	,	,	PUNCT
iajs-3477	137	7	(	(	PUNCT
iajs-3477	137	8	19	19	NUM
iajs-3477	137	9	)	)	PUNCT
iajs-3477	137	10	provided	provide	VERB
iajs-3477	137	11	that	that	SCONJ
iajs-3477	137	12	h(0	h(0	PROPN
iajs-3477	137	13	)	)	PUNCT
iajs-3477	137	14	did	do	AUX
iajs-3477	137	15	not	not	PART
iajs-3477	137	16	vanish	vanish	VERB
iajs-3477	137	17	.	.	PUNCT
iajs-3477	138	1	ihjpas	ihjpas	PROPN
iajs-3477	138	2	.	.	PUNCT
iajs-3477	139	1	37	37	NUM
iajs-3477	139	2	(	(	PUNCT
iajs-3477	139	3	2	2	NUM
iajs-3477	139	4	)	)	PUNCT
iajs-3477	139	5	2024	2024	NUM
iajs-3477	139	6	416	416	NUM
iajs-3477	139	7	5	5	NUM
iajs-3477	139	8	.	.	PUNCT
iajs-3477	139	9	results	result	NOUN
iajs-3477	139	10	and	and	CCONJ
iajs-3477	139	11	discussion	discussion	NOUN
iajs-3477	139	12	we	we	PRON
iajs-3477	139	13	examine	examine	VERB
iajs-3477	139	14	and	and	CCONJ
iajs-3477	139	15	evaluate	evaluate	VERB
iajs-3477	139	16	the	the	DET
iajs-3477	139	17	numerically	numerically	ADV
iajs-3477	139	18	computed	compute	VERB
iajs-3477	139	19	results	result	NOUN
iajs-3477	139	20	using	use	VERB
iajs-3477	139	21	the	the	DET
iajs-3477	139	22	fdm	fdm	NOUN
iajs-3477	139	23	in	in	ADP
iajs-3477	139	24	connection	connection	NOUN
iajs-3477	139	25	with	with	ADP
iajs-3477	139	26	the	the	DET
iajs-3477	139	27	tikhonov	tikhonov	NOUN
iajs-3477	139	28	regularization	regularization	NOUN
iajs-3477	139	29	approach	approach	NOUN
iajs-3477	139	30	,	,	PUNCT
iajs-3477	139	31	as	as	SCONJ
iajs-3477	139	32	described	describe	VERB
iajs-3477	139	33	in	in	ADP
iajs-3477	139	34	the	the	DET
iajs-3477	139	35	previous	previous	ADJ
iajs-3477	139	36	section	section	NOUN
iajs-3477	139	37	.	.	PUNCT
iajs-3477	140	1	the	the	DET
iajs-3477	140	2	root	root	NOUN
iajs-3477	140	3	mean	mean	VERB
iajs-3477	140	4	squares	square	NOUN
iajs-3477	140	5	errors	error	NOUN
iajs-3477	140	6	(	(	PUNCT
iajs-3477	140	7	rmse	rmse	NOUN
iajs-3477	140	8	)	)	PUNCT
iajs-3477	140	9	utilized	utilize	VERB
iajs-3477	140	10	via	via	ADP
iajs-3477	140	11	the	the	DET
iajs-3477	140	12	following	follow	VERB
iajs-3477	140	13	expression	expression	NOUN
iajs-3477	140	14	.	.	PUNCT
iajs-3477	141	1	rmse(𝑎	rmse(𝑎	VERB
iajs-3477	141	2	)	)	PUNCT
iajs-3477	141	3	=	=	PUNCT
iajs-3477	141	4	√	√	ADP
iajs-3477	141	5	1	1	NUM
iajs-3477	141	6	𝑁	𝑁	PROPN
iajs-3477	141	7	∑(𝑎𝑖	∑(𝑎𝑖	ADJ
iajs-3477	141	8	𝑒𝑥𝑎𝑐𝑡	𝑒𝑥𝑎𝑐𝑡	NOUN
iajs-3477	141	9	−	−	PROPN
iajs-3477	141	10	𝑎𝑖	𝑎𝑖	ADP
iajs-3477	141	11	𝑛𝑢𝑚𝑒𝑟𝑖𝑐𝑎𝑙	𝑛𝑢𝑚𝑒𝑟𝑖𝑐𝑎𝑙	NOUN
iajs-3477	141	12	)	)	PUNCT
iajs-3477	141	13	2	2	NUM
iajs-3477	142	1	𝑁	𝑁	PROPN
iajs-3477	142	2	𝑖=1	𝑖=1	PROPN
iajs-3477	142	3	.	.	PUNCT
iajs-3477	143	1	(	(	PUNCT
iajs-3477	143	2	20	20	NUM
iajs-3477	143	3	)	)	PUNCT
iajs-3477	143	4	calculated	calculate	VERB
iajs-3477	143	5	to	to	PART
iajs-3477	143	6	determine	determine	VERB
iajs-3477	143	7	the	the	DET
iajs-3477	143	8	accuracy	accuracy	NOUN
iajs-3477	143	9	of	of	ADP
iajs-3477	143	10	the	the	DET
iajs-3477	143	11	specified	specified	ADJ
iajs-3477	143	12	coefficient	coefficient	NOUN
iajs-3477	143	13	.	.	PUNCT
iajs-3477	144	1	for	for	ADP
iajs-3477	144	2	simplicity	simplicity	NOUN
iajs-3477	144	3	,	,	PUNCT
iajs-3477	144	4	we	we	PRON
iajs-3477	144	5	take	take	VERB
iajs-3477	144	6	y	y	NOUN
iajs-3477	144	7	=	=	NOUN
iajs-3477	144	8	1	1	NUM
iajs-3477	144	9	in	in	ADP
iajs-3477	144	10	all	all	DET
iajs-3477	144	11	examples	example	NOUN
iajs-3477	144	12	.	.	PUNCT
iajs-3477	145	1	first	first	ADV
iajs-3477	145	2	,	,	PUNCT
iajs-3477	145	3	we	we	PRON
iajs-3477	145	4	consider	consider	VERB
iajs-3477	145	5	the	the	DET
iajs-3477	145	6	case	case	NOUN
iajs-3477	145	7	where	where	SCONJ
iajs-3477	145	8	the	the	DET
iajs-3477	145	9	unknown	unknown	ADJ
iajs-3477	145	10	coefficients	coefficient	NOUN
iajs-3477	145	11	are	be	AUX
iajs-3477	145	12	given	give	VERB
iajs-3477	145	13	to	to	PART
iajs-3477	145	14	test	test	VERB
iajs-3477	145	15	the	the	DET
iajs-3477	145	16	stability	stability	NOUN
iajs-3477	145	17	and	and	CCONJ
iajs-3477	145	18	effectiveness	effectiveness	NOUN
iajs-3477	145	19	of	of	ADP
iajs-3477	145	20	the	the	DET
iajs-3477	145	21	proposed	propose	VERB
iajs-3477	145	22	fdm	fdm	NOUN
iajs-3477	145	23	scheme	scheme	NOUN
iajs-3477	145	24	for	for	ADP
iajs-3477	145	25	a	a	DET
iajs-3477	145	26	direct	direct	ADJ
iajs-3477	145	27	problem	problem	NOUN
iajs-3477	145	28	,	,	PUNCT
iajs-3477	145	29	we	we	PRON
iajs-3477	145	30	have	have	VERB
iajs-3477	145	31	a	a	DET
iajs-3477	145	32	direct	direct	ADJ
iajs-3477	145	33	problem	problem	NOUN
iajs-3477	145	34	,	,	PUNCT
iajs-3477	145	35	and	and	CCONJ
iajs-3477	145	36	the	the	DET
iajs-3477	145	37	exact	exact	ADJ
iajs-3477	145	38	solution	solution	NOUN
iajs-3477	145	39	is	be	AUX
iajs-3477	145	40	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3477	145	41	,	,	PUNCT
iajs-3477	145	42	𝑦	𝑦	NOUN
iajs-3477	145	43	)	)	PUNCT
iajs-3477	145	44	=	=	SYM
iajs-3477	145	45	−𝑒	−𝑒	NOUN
iajs-3477	145	46	−7−𝑦	−7−𝑦	NOUN
iajs-3477	145	47	100	100	NUM
iajs-3477	145	48	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3477	145	49	(	(	PUNCT
iajs-3477	145	50	𝑥𝜋	𝑥𝜋	NOUN
iajs-3477	145	51	)	)	PUNCT
iajs-3477	145	52	9	9	NUM
iajs-3477	145	53	,	,	PUNCT
iajs-3477	145	54	and	and	CCONJ
iajs-3477	145	55	the	the	DET
iajs-3477	145	56	input	input	NOUN
iajs-3477	145	57	data	datum	NOUN
iajs-3477	145	58	are	be	AUX
iajs-3477	145	59	as	as	SCONJ
iajs-3477	145	60	follows	follow	VERB
iajs-3477	145	61	:	:	PUNCT
iajs-3477	145	62	𝑎(𝑦	𝑎(𝑦	NUM
iajs-3477	145	63	)	)	PUNCT
iajs-3477	145	64	=	=	SYM
iajs-3477	146	1	−10	−10	X
iajs-3477	146	2	𝑒−	𝑒−	VERB
iajs-3477	146	3	5𝑦	5𝑦	NOUN
iajs-3477	146	4	100	100	NUM
iajs-3477	146	5	,	,	PUNCT
iajs-3477	146	6	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3477	146	7	,	,	PUNCT
iajs-3477	146	8	𝜏	𝜏	NOUN
iajs-3477	146	9	)	)	PUNCT
iajs-3477	146	10	=	=	PUNCT
iajs-3477	146	11	𝑒	𝑒	PROPN
iajs-3477	146	12	1	1	NUM
iajs-3477	146	13	100	100	NUM
iajs-3477	146	14	(	(	PUNCT
iajs-3477	146	15	−7−6𝑦	−7−6𝑦	NUM
iajs-3477	146	16	)	)	PUNCT
iajs-3477	146	17	(	(	PUNCT
iajs-3477	146	18	−100000	−100000	NOUN
iajs-3477	146	19	+	+	CCONJ
iajs-3477	146	20	𝑒𝑦	𝑒𝑦	NOUN
iajs-3477	146	21	20⁄	20⁄	PROPN
iajs-3477	146	22	(	(	PUNCT
iajs-3477	146	23	−1	−1	NOUN
iajs-3477	146	24	+	+	CCONJ
iajs-3477	146	25	10000𝜋2))𝐶𝑜𝑠(𝜋𝑥	10000𝜋2))𝐶𝑜𝑠(𝜋𝑥	NUM
iajs-3477	146	26	)	)	PUNCT
iajs-3477	146	27	90000	90000	NUM
iajs-3477	146	28	𝜑(𝑥	𝜑(𝑥	NOUN
iajs-3477	146	29	)	)	PUNCT
iajs-3477	146	30	=	=	SYM
iajs-3477	146	31	−𝑒	−𝑒	NOUN
iajs-3477	146	32	−7	−7	NOUN
iajs-3477	146	33	100𝑐𝑜𝑠	100𝑐𝑜𝑠	NUM
iajs-3477	146	34	(	(	PUNCT
iajs-3477	146	35	𝑥𝜋	𝑥𝜋	PROPN
iajs-3477	146	36	)	)	PUNCT
iajs-3477	146	37	9	9	NUM
iajs-3477	146	38	,	,	PUNCT
iajs-3477	146	39	𝜓(𝑥	𝜓(𝑥	PROPN
iajs-3477	146	40	)	)	PUNCT
iajs-3477	146	41	=	=	PUNCT
iajs-3477	146	42	𝑒	𝑒	VERB
iajs-3477	146	43	−7	−7	ADP
iajs-3477	146	44	100𝑐𝑜𝑠	100𝑐𝑜𝑠	NUM
iajs-3477	146	45	(	(	PUNCT
iajs-3477	146	46	𝑥𝜋	𝑥𝜋	PROPN
iajs-3477	146	47	)	)	PUNCT
iajs-3477	146	48	900	900	NUM
iajs-3477	146	49	,	,	PUNCT
iajs-3477	146	50	𝐻(𝑦	𝐻(𝑦	NOUN
iajs-3477	146	51	)	)	PUNCT
iajs-3477	147	1	=	=	SYM
iajs-3477	147	2	−𝑒	−𝑒	NOUN
iajs-3477	147	3	−7−𝑦	−7−𝑦	NOUN
iajs-3477	147	4	100	100	NUM
iajs-3477	147	5	9	9	NUM
iajs-3477	147	6	.	.	PUNCT
iajs-3477	148	1	next	next	ADV
iajs-3477	148	2	,	,	PUNCT
iajs-3477	148	3	we	we	PRON
iajs-3477	148	4	consider	consider	VERB
iajs-3477	148	5	the	the	DET
iajs-3477	148	6	inverse	inverse	ADJ
iajs-3477	148	7	elliptic	elliptic	ADJ
iajs-3477	148	8	problem	problem	NOUN
iajs-3477	148	9	(	(	PUNCT
iajs-3477	148	10	1)-(5	1)-(5	NUM
iajs-3477	148	11	)	)	PUNCT
iajs-3477	148	12	with	with	ADP
iajs-3477	148	13	the	the	DET
iajs-3477	148	14	coefficient	coefficient	NOUN
iajs-3477	148	15	a(y	a(y	PROPN
iajs-3477	148	16	)	)	PUNCT
iajs-3477	148	17	is	be	AUX
iajs-3477	148	18	unknown	unknown	ADJ
iajs-3477	148	19	.	.	PUNCT
iajs-3477	149	1	the	the	DET
iajs-3477	149	2	initial	initial	ADJ
iajs-3477	149	3	guess	guess	NOUN
iajs-3477	149	4	was	be	AUX
iajs-3477	149	5	a0	a0	NOUN
iajs-3477	149	6	=	=	PUNCT
iajs-3477	149	7	−10	−10	PRON
iajs-3477	149	8	can	can	AUX
iajs-3477	149	9	be	be	AUX
iajs-3477	149	10	found	find	VERB
iajs-3477	149	11	in	in	ADP
iajs-3477	149	12	the	the	DET
iajs-3477	149	13	equation	equation	NOUN
iajs-3477	149	14	(	(	PUNCT
iajs-3477	149	15	19	19	NUM
iajs-3477	149	16	)	)	PUNCT
iajs-3477	149	17	.	.	PUNCT
iajs-3477	150	1	it	it	PRON
iajs-3477	150	2	is	be	AUX
iajs-3477	150	3	easy	easy	ADJ
iajs-3477	150	4	to	to	PART
iajs-3477	150	5	verify	verify	VERB
iajs-3477	150	6	the	the	DET
iajs-3477	150	7	input	input	NOUN
iajs-3477	150	8	data	datum	NOUN
iajs-3477	150	9	for	for	ADP
iajs-3477	150	10	the	the	DET
iajs-3477	150	11	conditions	condition	NOUN
iajs-3477	150	12	of	of	ADP
iajs-3477	150	13	the	the	DET
iajs-3477	150	14	theorem	theorem	NOUN
iajs-3477	150	15	1	1	NUM
iajs-3477	150	16	.	.	PUNCT
iajs-3477	151	1	hence	hence	ADV
iajs-3477	151	2	,	,	PUNCT
iajs-3477	151	3	the	the	DET
iajs-3477	151	4	inverse	inverse	ADJ
iajs-3477	151	5	elliptic	elliptic	ADJ
iajs-3477	151	6	problem	problem	NOUN
iajs-3477	151	7	(	(	PUNCT
iajs-3477	151	8	1)-(5	1)-(5	NUM
iajs-3477	151	9	)	)	PUNCT
iajs-3477	151	10	with	with	ADP
iajs-3477	151	11	input	input	NOUN
iajs-3477	151	12	data	datum	NOUN
iajs-3477	151	13	above	above	ADV
iajs-3477	151	14	has	have	VERB
iajs-3477	151	15	a	a	DET
iajs-3477	151	16	unique	unique	ADJ
iajs-3477	151	17	solution	solution	NOUN
iajs-3477	151	18	.	.	PUNCT
iajs-3477	152	1	we	we	PRON
iajs-3477	152	2	fix	fix	VERB
iajs-3477	152	3	m=	m=	NOUN
iajs-3477	152	4	n	n	NOUN
iajs-3477	152	5	=	=	NUM
iajs-3477	152	6	40	40	NUM
iajs-3477	152	7	for	for	SCONJ
iajs-3477	152	8	the	the	DET
iajs-3477	152	9	numerical	numerical	ADJ
iajs-3477	152	10	investigation	investigation	NOUN
iajs-3477	152	11	started	start	VERB
iajs-3477	152	12	with	with	ADP
iajs-3477	152	13	the	the	DET
iajs-3477	152	14	situation	situation	NOUN
iajs-3477	152	15	of	of	ADP
iajs-3477	152	16	no	no	DET
iajs-3477	152	17	noise	noise	NOUN
iajs-3477	152	18	included	include	VERB
iajs-3477	152	19	,	,	PUNCT
iajs-3477	152	20	i.e.	i.e.	X
iajs-3477	152	21	,	,	PUNCT
iajs-3477	152	22	p	p	X
iajs-3477	152	23	=	=	NOUN
iajs-3477	152	24	0	0	NUM
iajs-3477	152	25	in	in	ADP
iajs-3477	152	26	(	(	PUNCT
iajs-3477	152	27	17	17	NUM
iajs-3477	152	28	)	)	PUNCT
iajs-3477	152	29	.	.	PUNCT
iajs-3477	153	1	the	the	DET
iajs-3477	153	2	objective	objective	ADJ
iajs-3477	153	3	function	function	NOUN
iajs-3477	153	4	(	(	PUNCT
iajs-3477	153	5	15	15	NUM
iajs-3477	153	6	)	)	PUNCT
iajs-3477	153	7	represented	represent	VERB
iajs-3477	153	8	in	in	ADP
iajs-3477	153	9	figure	figure	NOUN
iajs-3477	153	10	3(a	3(a	NUM
iajs-3477	153	11	)	)	PUNCT
iajs-3477	153	12	,	,	PUNCT
iajs-3477	153	13	and	and	CCONJ
iajs-3477	153	14	a	a	DET
iajs-3477	153	15	speed	speed	NOUN
iajs-3477	153	16	declining	decline	VERB
iajs-3477	153	17	convergence	convergence	NOUN
iajs-3477	153	18	is	be	AUX
iajs-3477	153	19	seen	see	VERB
iajs-3477	153	20	for	for	ADP
iajs-3477	153	21	achieving	achieve	VERB
iajs-3477	153	22	a	a	DET
iajs-3477	153	23	shorter	short	ADJ
iajs-3477	153	24	order	order	NOUN
iajs-3477	153	25	tolerance	tolerance	NOUN
iajs-3477	153	26	o(10−15	o(10−15	PROPN
iajs-3477	153	27	)	)	PUNCT
iajs-3477	153	28	in	in	ADP
iajs-3477	153	29	just	just	ADV
iajs-3477	153	30	9	9	NUM
iajs-3477	153	31	iterations	iteration	NOUN
iajs-3477	153	32	.	.	PUNCT
iajs-3477	154	1	figure	figure	NOUN
iajs-3477	154	2	3(b	3(b	NUM
iajs-3477	154	3	)	)	PUNCT
iajs-3477	154	4	shows	show	VERB
iajs-3477	154	5	numerical	numerical	ADJ
iajs-3477	154	6	results	result	NOUN
iajs-3477	154	7	for	for	ADP
iajs-3477	154	8	the	the	DET
iajs-3477	154	9	coefficient	coefficient	NOUN
iajs-3477	154	10	a(y	a(y	PROPN
iajs-3477	154	11	)	)	PUNCT
iajs-3477	154	12	with	with	ADP
iajs-3477	154	13	rmse(a	rmse(a	NOUN
iajs-3477	154	14	)	)	PUNCT
iajs-3477	154	15	=	=	SYM
iajs-3477	154	16	0.0034	0.0034	NUM
iajs-3477	154	17	.	.	PUNCT
iajs-3477	154	18	ihjpas	ihjpas	PROPN
iajs-3477	154	19	.	.	PUNCT
iajs-3477	155	1	37	37	NUM
iajs-3477	155	2	(	(	PUNCT
iajs-3477	155	3	2	2	NUM
iajs-3477	155	4	)	)	PUNCT
iajs-3477	155	5	2024	2024	NUM
iajs-3477	155	6	417	417	NUM
iajs-3477	155	7	(	(	PUNCT
iajs-3477	155	8	a	a	NOUN
iajs-3477	155	9	)	)	PUNCT
iajs-3477	155	10	(	(	PUNCT
iajs-3477	155	11	b	b	X
iajs-3477	155	12	)	)	PUNCT
iajs-3477	155	13	figure	figure	NOUN
iajs-3477	155	14	3	3	NUM
iajs-3477	155	15	.	.	PUNCT
iajs-3477	156	1	(	(	PUNCT
iajs-3477	156	2	a	a	X
iajs-3477	156	3	)	)	PUNCT
iajs-3477	156	4	objective	objective	ADJ
iajs-3477	156	5	function	function	NOUN
iajs-3477	156	6	(	(	PUNCT
iajs-3477	156	7	15	15	NUM
iajs-3477	156	8	)	)	PUNCT
iajs-3477	156	9	and	and	CCONJ
iajs-3477	156	10	(	(	PUNCT
iajs-3477	156	11	b	b	X
iajs-3477	156	12	)	)	PUNCT
iajs-3477	156	13	a(y	a(y	PROPN
iajs-3477	156	14	)	)	PUNCT
iajs-3477	156	15	with	with	ADP
iajs-3477	156	16	noise	noise	NOUN
iajs-3477	156	17	-	-	PUNCT
iajs-3477	156	18	free	free	ADJ
iajs-3477	156	19	and	and	CCONJ
iajs-3477	156	20	without	without	ADP
iajs-3477	156	21	regularization	regularization	NOUN
iajs-3477	156	22	.	.	PUNCT
iajs-3477	157	1	next	next	ADV
iajs-3477	157	2	,	,	PUNCT
iajs-3477	157	3	we	we	PRON
iajs-3477	157	4	add	add	VERB
iajs-3477	157	5	p	p	X
iajs-3477	157	6	∈	∈	PROPN
iajs-3477	157	7	{	{	PUNCT
iajs-3477	157	8	0.05	0.05	NUM
iajs-3477	157	9	,	,	PUNCT
iajs-3477	157	10	0.5}%	0.5}%	PROPN
iajs-3477	157	11	noise	noise	NOUN
iajs-3477	157	12	as	as	ADP
iajs-3477	157	13	in	in	ADP
iajs-3477	157	14	equation	equation	NOUN
iajs-3477	157	15	(	(	PUNCT
iajs-3477	157	16	17	17	NUM
iajs-3477	157	17	)	)	PUNCT
iajs-3477	157	18	.	.	PUNCT
iajs-3477	158	1	the	the	DET
iajs-3477	158	2	case	case	NOUN
iajs-3477	158	3	of	of	ADP
iajs-3477	158	4	noisy	noisy	ADJ
iajs-3477	158	5	data	datum	NOUN
iajs-3477	158	6	and	and	CCONJ
iajs-3477	158	7	no	no	DET
iajs-3477	158	8	regularization	regularization	NOUN
iajs-3477	158	9	is	be	AUX
iajs-3477	158	10	presented	present	VERB
iajs-3477	158	11	in	in	ADP
iajs-3477	158	12	figures	figure	NOUN
iajs-3477	158	13	4(a)-4(b	4(a)-4(b	NUM
iajs-3477	158	14	)	)	PUNCT
iajs-3477	158	15	.	.	PUNCT
iajs-3477	159	1	figure	figure	NOUN
iajs-3477	159	2	4(a	4(a	NUM
iajs-3477	159	3	)	)	PUNCT
iajs-3477	159	4	,	,	PUNCT
iajs-3477	159	5	from	from	ADP
iajs-3477	159	6	this	this	DET
iajs-3477	159	7	figure	figure	NOUN
iajs-3477	159	8	the	the	DET
iajs-3477	159	9	monotonic	monotonic	ADJ
iajs-3477	159	10	decreasing	decreasing	NOUN
iajs-3477	159	11	achieved	achieve	VERB
iajs-3477	159	12	in	in	ADP
iajs-3477	159	13	about	about	ADV
iajs-3477	159	14	16	16	NUM
iajs-3477	159	15	iterations	iteration	NOUN
iajs-3477	159	16	and	and	CCONJ
iajs-3477	159	17	40	40	NUM
iajs-3477	159	18	iterations	iteration	NOUN
iajs-3477	159	19	respectively	respectively	ADV
iajs-3477	159	20	,	,	PUNCT
iajs-3477	159	21	and	and	CCONJ
iajs-3477	159	22	the	the	DET
iajs-3477	159	23	steady	steady	ADJ
iajs-3477	159	24	convergence	convergence	NOUN
iajs-3477	159	25	for	for	ADP
iajs-3477	159	26	the	the	DET
iajs-3477	159	27	rest	rest	NOUN
iajs-3477	159	28	of	of	ADP
iajs-3477	159	29	iterations	iteration	NOUN
iajs-3477	159	30	to	to	ADP
iajs-3477	159	31	o(10−15	o(10−15	PROPN
iajs-3477	159	32	)	)	PUNCT
iajs-3477	159	33	in	in	ADP
iajs-3477	159	34	40	40	NUM
iajs-3477	159	35	iterations	iteration	NOUN
iajs-3477	159	36	reaching	reach	VERB
iajs-3477	159	37	a	a	DET
iajs-3477	159	38	very	very	ADV
iajs-3477	159	39	low	low	ADJ
iajs-3477	159	40	stationary	stationary	ADJ
iajs-3477	159	41	value	value	NOUN
iajs-3477	159	42	of	of	ADP
iajs-3477	159	43	order	order	NOUN
iajs-3477	159	44	the	the	DET
iajs-3477	159	45	associated	associated	PROPN
iajs-3477	159	46	numerical	numerical	ADJ
iajs-3477	159	47	result	result	NOUN
iajs-3477	159	48	was	be	AUX
iajs-3477	159	49	found	find	VERB
iajs-3477	159	50	stable	stable	ADJ
iajs-3477	159	51	and	and	CCONJ
iajs-3477	159	52	accurate	accurate	ADJ
iajs-3477	159	53	(	(	PUNCT
iajs-3477	159	54	with	with	ADP
iajs-3477	159	55	p	p	NOUN
iajs-3477	159	56	=	=	NOUN
iajs-3477	159	57	0.05	0.05	NUM
iajs-3477	159	58	,	,	PUNCT
iajs-3477	159	59	rmse(a	rmse(a	NOUN
iajs-3477	159	60	)	)	PUNCT
iajs-3477	159	61	=	=	SYM
iajs-3477	159	62	0.2750	0.2750	NUM
iajs-3477	159	63	)	)	PUNCT
iajs-3477	159	64	,	,	PUNCT
iajs-3477	159	65	but	but	CCONJ
iajs-3477	159	66	unstable	unstable	ADJ
iajs-3477	159	67	and	and	CCONJ
iajs-3477	159	68	inaccurate	inaccurate	ADJ
iajs-3477	159	69	(	(	PUNCT
iajs-3477	159	70	with	with	ADP
iajs-3477	159	71	p	p	NOUN
iajs-3477	159	72	=	=	SYM
iajs-3477	159	73	0.5	0.5	NUM
iajs-3477	159	74	,	,	PUNCT
iajs-3477	159	75	rmse(a	rmse(a	NOUN
iajs-3477	159	76	)	)	PUNCT
iajs-3477	159	77	=	=	NOUN
iajs-3477	159	78	27.5397	27.5397	NUM
iajs-3477	159	79	)	)	PUNCT
iajs-3477	159	80	.	.	PUNCT
iajs-3477	160	1	this	this	PRON
iajs-3477	160	2	is	be	AUX
iajs-3477	160	3	expected	expect	VERB
iajs-3477	160	4	since	since	SCONJ
iajs-3477	160	5	the	the	DET
iajs-3477	160	6	problem	problem	NOUN
iajs-3477	160	7	under	under	ADP
iajs-3477	160	8	investigation	investigation	NOUN
iajs-3477	160	9	is	be	AUX
iajs-3477	160	10	ill	ill	ADV
iajs-3477	160	11	-	-	PUNCT
iajs-3477	160	12	posed	pose	VERB
iajs-3477	160	13	problem	problem	NOUN
iajs-3477	160	14	and	and	CCONJ
iajs-3477	160	15	small	small	ADJ
iajs-3477	160	16	errors	error	NOUN
iajs-3477	160	17	(	(	PUNCT
iajs-3477	160	18	noise	noise	NOUN
iajs-3477	160	19	)	)	PUNCT
iajs-3477	160	20	in	in	ADP
iajs-3477	160	21	input	input	NOUN
iajs-3477	160	22	data	datum	NOUN
iajs-3477	160	23	lead	lead	VERB
iajs-3477	160	24	to	to	ADP
iajs-3477	160	25	drastic	drastic	ADJ
iajs-3477	160	26	errors	error	NOUN
iajs-3477	160	27	in	in	ADP
iajs-3477	160	28	outputs	output	NOUN
iajs-3477	160	29	.	.	PUNCT
iajs-3477	161	1	as	as	SCONJ
iajs-3477	161	2	seen	see	VERB
iajs-3477	161	3	in	in	ADP
iajs-3477	161	4	figure	figure	NOUN
iajs-3477	161	5	4(b	4(b	NUM
iajs-3477	161	6	)	)	PUNCT
iajs-3477	161	7	,	,	PUNCT
iajs-3477	161	8	the	the	DET
iajs-3477	161	9	numerical	numerical	ADJ
iajs-3477	161	10	solution	solution	NOUN
iajs-3477	161	11	of	of	ADP
iajs-3477	161	12	the	the	DET
iajs-3477	161	13	a(y	a(y	PROPN
iajs-3477	161	14	)	)	PUNCT
iajs-3477	161	15	stable	stable	ADJ
iajs-3477	161	16	and	and	CCONJ
iajs-3477	161	17	accurate	accurate	ADJ
iajs-3477	161	18	at	at	ADP
iajs-3477	161	19	p	p	NOUN
iajs-3477	161	20	=	=	NOUN
iajs-3477	161	21	0.05	0.05	NUM
iajs-3477	161	22	,	,	PUNCT
iajs-3477	161	23	and	and	CCONJ
iajs-3477	161	24	with	with	ADP
iajs-3477	161	25	p	p	NOUN
iajs-3477	161	26	=	=	SYM
iajs-3477	161	27	0.5	0.5	NUM
iajs-3477	161	28	,	,	PUNCT
iajs-3477	161	29	unstable	unstable	ADJ
iajs-3477	161	30	and	and	CCONJ
iajs-3477	161	31	diverges	diverge	VERB
iajs-3477	161	32	from	from	ADP
iajs-3477	161	33	the	the	DET
iajs-3477	161	34	exact	exact	ADJ
iajs-3477	161	35	solution	solution	NOUN
iajs-3477	161	36	but	but	CCONJ
iajs-3477	161	37	remains	remain	VERB
iajs-3477	161	38	on	on	ADP
iajs-3477	161	39	the	the	DET
iajs-3477	161	40	same	same	ADJ
iajs-3477	161	41	path	path	NOUN
iajs-3477	161	42	when	when	SCONJ
iajs-3477	161	43	the	the	DET
iajs-3477	161	44	value	value	NOUN
iajs-3477	161	45	of	of	ADP
iajs-3477	161	46	additive	additive	ADJ
iajs-3477	161	47	noise	noise	NOUN
iajs-3477	161	48	increases	increase	NOUN
iajs-3477	161	49	in	in	ADP
iajs-3477	161	50	equation	equation	NOUN
iajs-3477	161	51	(	(	PUNCT
iajs-3477	161	52	17	17	NUM
iajs-3477	161	53	)	)	PUNCT
iajs-3477	161	54	.	.	PUNCT
iajs-3477	162	1	in	in	ADP
iajs-3477	162	2	order	order	NOUN
iajs-3477	162	3	to	to	PART
iajs-3477	162	4	restore	restore	VERB
iajs-3477	162	5	the	the	DET
iajs-3477	162	6	deteriorate	deteriorate	ADJ
iajs-3477	162	7	stability	stability	NOUN
iajs-3477	162	8	of	of	ADP
iajs-3477	162	9	the	the	DET
iajs-3477	162	10	coefficient	coefficient	NOUN
iajs-3477	162	11	a(y	a(y	PROPN
iajs-3477	162	12	)	)	PUNCT
iajs-3477	162	13	a	a	DET
iajs-3477	162	14	sort	sort	NOUN
iajs-3477	162	15	of	of	ADP
iajs-3477	162	16	regularization	regularization	NOUN
iajs-3477	162	17	should	should	AUX
iajs-3477	162	18	be	be	AUX
iajs-3477	162	19	applied	apply	VERB
iajs-3477	162	20	.	.	PUNCT
iajs-3477	163	1	the	the	DET
iajs-3477	163	2	l	l	NOUN
iajs-3477	163	3	-	-	ADJ
iajs-3477	163	4	curve	curve	NOUN
iajs-3477	163	5	approach	approach	NOUN
iajs-3477	163	6	developed	develop	VERB
iajs-3477	163	7	by	by	ADP
iajs-3477	163	8	p.	p.	PROPN
iajs-3477	163	9	hansen	hansen	PUNCT
iajs-3477	164	1	[	[	X
iajs-3477	164	2	28	28	NUM
iajs-3477	164	3	]	]	PUNCT
iajs-3477	164	4	,	,	PUNCT
iajs-3477	164	5	morozov	morozov	PROPN
iajs-3477	164	6	's	's	PART
iajs-3477	164	7	discrepancy	discrepancy	NOUN
iajs-3477	164	8	principle	principle	NOUN
iajs-3477	164	9	[	[	X
iajs-3477	164	10	29	29	NUM
iajs-3477	164	11	]	]	PUNCT
iajs-3477	164	12	,	,	PUNCT
iajs-3477	164	13	and	and	CCONJ
iajs-3477	164	14	even	even	ADV
iajs-3477	164	15	just	just	ADV
iajs-3477	164	16	plain	plain	ADJ
iajs-3477	164	17	old	old	ADJ
iajs-3477	164	18	trial	trial	NOUN
iajs-3477	164	19	and	and	CCONJ
iajs-3477	164	20	error	error	NOUN
iajs-3477	164	21	,	,	PUNCT
iajs-3477	164	22	as	as	SCONJ
iajs-3477	164	23	advocated	advocate	VERB
iajs-3477	164	24	for	for	ADP
iajs-3477	164	25	in	in	ADP
iajs-3477	164	26	[	[	X
iajs-3477	164	27	30	30	NUM
iajs-3477	164	28	]	]	PUNCT
iajs-3477	164	29	,	,	PUNCT
iajs-3477	164	30	are	be	AUX
iajs-3477	164	31	just	just	ADV
iajs-3477	164	32	a	a	DET
iajs-3477	164	33	few	few	ADJ
iajs-3477	164	34	of	of	ADP
iajs-3477	164	35	the	the	DET
iajs-3477	164	36	available	available	ADJ
iajs-3477	164	37	options	option	NOUN
iajs-3477	164	38	.	.	PUNCT
iajs-3477	165	1	by	by	ADP
iajs-3477	165	2	incorporating	incorporate	VERB
iajs-3477	165	3	the	the	DET
iajs-3477	165	4	penalty	penalty	NOUN
iajs-3477	165	5	terms	term	NOUN
iajs-3477	165	6	into	into	ADP
iajs-3477	165	7	equation	equation	NOUN
iajs-3477	165	8	(	(	PUNCT
iajs-3477	165	9	15	15	NUM
iajs-3477	165	10	)	)	PUNCT
iajs-3477	165	11	,	,	PUNCT
iajs-3477	165	12	we	we	PRON
iajs-3477	165	13	employ	employ	VERB
iajs-3477	165	14	the	the	DET
iajs-3477	165	15	tikhonov	tikhonov	NOUN
iajs-3477	165	16	regularization	regularization	NOUN
iajs-3477	165	17	technique	technique	NOUN
iajs-3477	165	18	.	.	PUNCT
iajs-3477	166	1	we	we	PRON
iajs-3477	166	2	try	try	VERB
iajs-3477	166	3	out	out	ADP
iajs-3477	166	4	different	different	ADJ
iajs-3477	166	5	values	value	NOUN
iajs-3477	166	6	for	for	ADP
iajs-3477	166	7	the	the	DET
iajs-3477	166	8	regularization	regularization	NOUN
iajs-3477	166	9	parameter	parameter	NOUN
iajs-3477	166	10	β	β	X
iajs-3477	166	11	∈	∈	PROPN
iajs-3477	166	12	{	{	PUNCT
iajs-3477	166	13	10−10	10−10	NUM
iajs-3477	166	14	,	,	PUNCT
iajs-3477	166	15	…	…	PUNCT
iajs-3477	166	16	,	,	PUNCT
iajs-3477	166	17	10−6	10−6	NUM
iajs-3477	166	18	}	}	PUNCT
iajs-3477	166	19	,	,	PUNCT
iajs-3477	166	20	noise	noise	NOUN
iajs-3477	166	21	of	of	ADP
iajs-3477	166	22	p	p	NOUN
iajs-3477	166	23	=	=	NOUN
iajs-3477	166	24	0.05	0.05	NUM
iajs-3477	166	25	%	%	NOUN
iajs-3477	166	26	is	be	AUX
iajs-3477	166	27	added	add	VERB
iajs-3477	166	28	to	to	PART
iajs-3477	166	29	replicate	replicate	VERB
iajs-3477	166	30	real	real	ADJ
iajs-3477	166	31	input	input	NOUN
iajs-3477	166	32	data	datum	NOUN
iajs-3477	166	33	.	.	PUNCT
iajs-3477	167	1	in	in	ADP
iajs-3477	167	2	figures	figure	NOUN
iajs-3477	167	3	5(a	5(a	NUM
iajs-3477	167	4	)	)	PUNCT
iajs-3477	167	5	,	,	PUNCT
iajs-3477	167	6	the	the	DET
iajs-3477	167	7	monotonic	monotonic	ADJ
iajs-3477	167	8	decreasing	decreasing	NOUN
iajs-3477	167	9	achieved	achieve	VERB
iajs-3477	167	10	in	in	ADP
iajs-3477	167	11	about	about	ADV
iajs-3477	167	12	11	11	NUM
iajs-3477	167	13	iterations	iteration	NOUN
iajs-3477	167	14	and	and	CCONJ
iajs-3477	167	15	noise	noise	NOUN
iajs-3477	167	16	of	of	ADP
iajs-3477	167	17	p	p	NOUN
iajs-3477	167	18	=	=	NOUN
iajs-3477	167	19	0.05	0.05	NUM
iajs-3477	167	20	%	%	NOUN
iajs-3477	167	21	.	.	PUNCT
iajs-3477	168	1	in	in	ADP
iajs-3477	168	2	figures	figure	NOUN
iajs-3477	168	3	6(a	6(a	NUM
iajs-3477	168	4	)	)	PUNCT
iajs-3477	168	5	,	,	PUNCT
iajs-3477	168	6	the	the	DET
iajs-3477	168	7	monotonic	monotonic	ADJ
iajs-3477	168	8	decreasing	decreasing	NOUN
iajs-3477	168	9	achieved	achieve	VERB
iajs-3477	168	10	in	in	ADP
iajs-3477	168	11	about	about	ADV
iajs-3477	168	12	28	28	NUM
iajs-3477	168	13	iterations	iteration	NOUN
iajs-3477	168	14	,	,	PUNCT
iajs-3477	168	15	indicating	indicate	VERB
iajs-3477	168	16	that	that	SCONJ
iajs-3477	168	17	the	the	DET
iajs-3477	168	18	objective	objective	ADJ
iajs-3477	168	19	function	function	NOUN
iajs-3477	168	20	minimization	minimization	NOUN
iajs-3477	168	21	(	(	PUNCT
iajs-3477	168	22	15	15	NUM
iajs-3477	168	23	)	)	PUNCT
iajs-3477	168	24	is	be	AUX
iajs-3477	168	25	satisfied	satisfied	ADJ
iajs-3477	168	26	.	.	PUNCT
iajs-3477	169	1	figures	figure	NOUN
iajs-3477	169	2	5(b	5(b	NUM
iajs-3477	169	3	)	)	PUNCT
iajs-3477	169	4	and	and	CCONJ
iajs-3477	169	5	6(b	6(b	NUM
iajs-3477	169	6	)	)	PUNCT
iajs-3477	169	7	depict	depict	VERB
iajs-3477	169	8	the	the	DET
iajs-3477	169	9	unknown	unknown	ADJ
iajs-3477	169	10	potential	potential	ADJ
iajs-3477	169	11	coefficient	coefficient	NOUN
iajs-3477	169	12	a(y	a(y	PROPN
iajs-3477	169	13	)	)	PUNCT
iajs-3477	169	14	.	.	PUNCT
iajs-3477	170	1	these	these	DET
iajs-3477	170	2	figures	figure	NOUN
iajs-3477	170	3	demonstrate	demonstrate	VERB
iajs-3477	170	4	that	that	SCONJ
iajs-3477	170	5	results	result	NOUN
iajs-3477	170	6	are	be	AUX
iajs-3477	170	7	nearly	nearly	ADV
iajs-3477	170	8	perfectly	perfectly	ADV
iajs-3477	170	9	smooth	smooth	ADJ
iajs-3477	170	10	,	,	PUNCT
iajs-3477	170	11	particularly	particularly	ADV
iajs-3477	170	12	in	in	ADP
iajs-3477	170	13	the	the	DET
iajs-3477	170	14	range	range	NOUN
iajs-3477	171	1	[	[	X
iajs-3477	171	2	0.3,1	0.3,1	NOUN
iajs-3477	171	3	]	]	X
iajs-3477	171	4	,	,	PUNCT
iajs-3477	171	5	until	until	SCONJ
iajs-3477	171	6	noise	noise	NOUN
iajs-3477	171	7	levels	level	NOUN
iajs-3477	171	8	increase	increase	VERB
iajs-3477	171	9	from	from	ADP
iajs-3477	171	10	0.05	0.05	NUM
iajs-3477	171	11	%	%	NOUN
iajs-3477	171	12	to	to	PART
iajs-3477	171	13	0.5	0.5	NUM
iajs-3477	171	14	%	%	NOUN
iajs-3477	171	15	and	and	CCONJ
iajs-3477	171	16	instabilities	instability	NOUN
iajs-3477	171	17	appear	appear	VERB
iajs-3477	171	18	.	.	PUNCT
iajs-3477	172	1	in	in	ADP
iajs-3477	172	2	addition	addition	NOUN
iajs-3477	172	3	,	,	PUNCT
iajs-3477	172	4	in	in	ADP
iajs-3477	172	5	table	table	NOUN
iajs-3477	172	6	1	1	NUM
iajs-3477	172	7	rmse(a	rmse(a	NOUN
iajs-3477	172	8	)	)	PUNCT
iajs-3477	172	9	values	value	NOUN
iajs-3477	172	10	reveal	reveal	VERB
iajs-3477	172	11	a	a	DET
iajs-3477	172	12	reasonable	reasonable	ADJ
iajs-3477	172	13	range	range	NOUN
iajs-3477	172	14	of	of	ADP
iajs-3477	172	15	values	value	NOUN
iajs-3477	172	16	,	,	PUNCT
iajs-3477	172	17	with	with	ADP
iajs-3477	172	18	the	the	DET
iajs-3477	172	19	best	good	ADJ
iajs-3477	172	20	retrieval	retrieval	NOUN
iajs-3477	172	21	occurring	occur	VERB
iajs-3477	172	22	at	at	ADP
iajs-3477	172	23	the	the	DET
iajs-3477	172	24	lowest	low	ADJ
iajs-3477	172	25	rmse(a	rmse(a	NOUN
iajs-3477	172	26	)	)	PUNCT
iajs-3477	172	27	.	.	PUNCT
iajs-3477	173	1	for	for	ADP
iajs-3477	173	2	additional	additional	ADJ
iajs-3477	173	3	information	information	NOUN
iajs-3477	173	4	,	,	PUNCT
iajs-3477	173	5	see	see	VERB
iajs-3477	173	6	table	table	NOUN
iajs-3477	173	7	1	1	NUM
iajs-3477	173	8	and	and	CCONJ
iajs-3477	173	9	figure	figure	VERB
iajs-3477	173	10	5	5	NUM
iajs-3477	173	11	-	-	SYM
iajs-3477	173	12	6	6	NUM
iajs-3477	173	13	for	for	ADP
iajs-3477	173	14	numerical	numerical	ADJ
iajs-3477	173	15	results	result	NOUN
iajs-3477	173	16	.	.	PUNCT
iajs-3477	174	1	ihjpas	ihjpas	PROPN
iajs-3477	174	2	.	.	PUNCT
iajs-3477	175	1	37	37	NUM
iajs-3477	175	2	(	(	PUNCT
iajs-3477	175	3	2	2	NUM
iajs-3477	175	4	)	)	PUNCT
iajs-3477	175	5	2024	2024	NUM
iajs-3477	176	1	418	418	NUM
iajs-3477	176	2	table	table	NOUN
iajs-3477	176	3	1	1	NUM
iajs-3477	176	4	.	.	PUNCT
iajs-3477	177	1	the	the	DET
iajs-3477	177	2	rmse(a	rmse(a	NOUN
iajs-3477	177	3	)	)	PUNCT
iajs-3477	177	4	(	(	PUNCT
iajs-3477	177	5	20	20	NUM
iajs-3477	177	6	)	)	PUNCT
iajs-3477	177	7	for	for	ADP
iajs-3477	177	8	the	the	DET
iajs-3477	177	9	noise	noise	NOUN
iajs-3477	177	10	p	p	X
iajs-3477	177	11	∈	∈	PROPN
iajs-3477	177	12	{	{	PUNCT
iajs-3477	177	13	0.05	0.05	NUM
iajs-3477	177	14	,	,	PUNCT
iajs-3477	177	15	0.5	0.5	NUM
iajs-3477	177	16	}	}	PUNCT
iajs-3477	177	17	%	%	NOUN
iajs-3477	177	18	,	,	PUNCT
iajs-3477	177	19	and	and	CCONJ
iajs-3477	177	20	regularization	regularization	NOUN
iajs-3477	177	21	𝛽	𝛽	PROPN
iajs-3477	177	22	∈	∈	PROPN
iajs-3477	177	23	{	{	PUNCT
iajs-3477	177	24	10−10	10−10	NUM
iajs-3477	177	25	,	,	PUNCT
iajs-3477	177	26	…	…	PUNCT
iajs-3477	177	27	,	,	PUNCT
iajs-3477	177	28	10−6	10−6	NUM
iajs-3477	177	29	}	}	PUNCT
iajs-3477	177	30	..	..	PUNCT
iajs-3477	178	1	𝐫𝐦𝐬𝐞(𝐚	𝐫𝐦𝐬𝐞(𝐚	X
iajs-3477	178	2	)	)	PUNCT
iajs-3477	178	3	𝛃	𝛃	PROPN
iajs-3477	179	1	=	=	SYM
iajs-3477	179	2	𝟏𝟎−𝟏𝟎	𝟏𝟎−𝟏𝟎	PROPN
iajs-3477	179	3	𝛃	𝛃	PROPN
iajs-3477	179	4	=	=	SYM
iajs-3477	179	5	𝟏𝟎−𝟗	𝟏𝟎−𝟗	PROPN
iajs-3477	179	6	𝛃	𝛃	X
iajs-3477	180	1	=	=	SYM
iajs-3477	180	2	𝟏𝟎−𝟖	𝟏𝟎−𝟖	PROPN
iajs-3477	180	3	𝛃	𝛃	PROPN
iajs-3477	181	1	=	=	SYM
iajs-3477	181	2	𝟏𝟎−𝟕	𝟏𝟎−𝟕	PROPN
iajs-3477	181	3	𝛃	𝛃	X
iajs-3477	181	4	=	=	SYM
iajs-3477	181	5	𝟏𝟎−𝟔	𝟏𝟎−𝟔	PROPN
iajs-3477	181	6	𝐩	𝐩	SYM
iajs-3477	181	7	=	=	PUNCT
iajs-3477	181	8	𝟎.	𝟎.	PUNCT
iajs-3477	181	9	𝟎𝟓%	𝟎𝟓%	PROPN
iajs-3477	181	10	0.2523	0.2523	NUM
iajs-3477	182	1	0.3709	0.3709	NUM
iajs-3477	182	2	0.8006	0.8006	NUM
iajs-3477	182	3	1.3559	1.3559	NUM
iajs-3477	182	4	2.0580	2.0580	NUM
iajs-3477	182	5	𝐩	𝐩	SYM
iajs-3477	182	6	=	=	PUNCT
iajs-3477	182	7	𝟎.	𝟎.	NOUN
iajs-3477	182	8	𝟓%	𝟓%	VERB
iajs-3477	182	9	21.9455	21.9455	NUM
iajs-3477	182	10	8.6963	8.6963	NUM
iajs-3477	182	11	2.1730	2.1730	NUM
iajs-3477	182	12	1.3343	1.3343	NUM
iajs-3477	182	13	2.0448	2.0448	NUM
iajs-3477	182	14	(	(	PUNCT
iajs-3477	182	15	b	b	NOUN
iajs-3477	182	16	)	)	PUNCT
iajs-3477	182	17	figure	figure	NOUN
iajs-3477	182	18	4	4	NUM
iajs-3477	182	19	.	.	PUNCT
iajs-3477	183	1	(	(	PUNCT
iajs-3477	183	2	a	a	X
iajs-3477	183	3	)	)	PUNCT
iajs-3477	183	4	objective	objective	ADJ
iajs-3477	183	5	function	function	NOUN
iajs-3477	183	6	(	(	PUNCT
iajs-3477	183	7	15	15	NUM
iajs-3477	183	8	)	)	PUNCT
iajs-3477	183	9	and	and	CCONJ
iajs-3477	183	10	(	(	PUNCT
iajs-3477	183	11	b	b	X
iajs-3477	183	12	)	)	PUNCT
iajs-3477	183	13	a(y	a(y	PROPN
iajs-3477	183	14	)	)	PUNCT
iajs-3477	183	15	,	,	PUNCT
iajs-3477	183	16	for	for	ADP
iajs-3477	183	17	different	different	ADJ
iajs-3477	183	18	noise	noise	NOUN
iajs-3477	183	19	level	level	NOUN
iajs-3477	183	20	p	p	NOUN
iajs-3477	183	21	∈	∈	PROPN
iajs-3477	183	22	{	{	PUNCT
iajs-3477	183	23	0.05	0.05	NUM
iajs-3477	183	24	,	,	PUNCT
iajs-3477	183	25	0.5	0.5	NUM
iajs-3477	183	26	}	}	PUNCT
iajs-3477	183	27	%	%	NOUN
iajs-3477	183	28	and	and	CCONJ
iajs-3477	183	29	no	no	DET
iajs-3477	183	30	regularization	regularization	NOUN
iajs-3477	183	31	.	.	PUNCT
iajs-3477	184	1	(	(	PUNCT
iajs-3477	184	2	a	a	X
iajs-3477	184	3	)	)	PUNCT
iajs-3477	184	4	ihjpas	ihjpa	NOUN
iajs-3477	184	5	.	.	PUNCT
iajs-3477	185	1	37	37	NUM
iajs-3477	185	2	(	(	PUNCT
iajs-3477	185	3	2	2	NUM
iajs-3477	185	4	)	)	PUNCT
iajs-3477	185	5	2024	2024	NUM
iajs-3477	185	6	419	419	NUM
iajs-3477	185	7	(	(	PUNCT
iajs-3477	185	8	b	b	NOUN
iajs-3477	185	9	)	)	PUNCT
iajs-3477	185	10	figure	figure	NOUN
iajs-3477	185	11	5	5	NUM
iajs-3477	185	12	.	.	PUNCT
iajs-3477	186	1	(	(	PUNCT
iajs-3477	186	2	a	a	X
iajs-3477	186	3	)	)	PUNCT
iajs-3477	186	4	objective	objective	ADJ
iajs-3477	186	5	function	function	NOUN
iajs-3477	186	6	(	(	PUNCT
iajs-3477	186	7	15	15	NUM
iajs-3477	186	8	)	)	PUNCT
iajs-3477	186	9	and	and	CCONJ
iajs-3477	186	10	(	(	PUNCT
iajs-3477	186	11	b	b	X
iajs-3477	186	12	)	)	PUNCT
iajs-3477	186	13	a(y	a(y	PROPN
iajs-3477	186	14	)	)	PUNCT
iajs-3477	186	15	,	,	PUNCT
iajs-3477	186	16	for	for	ADP
iajs-3477	186	17	p	p	NOUN
iajs-3477	186	18	=	=	NOUN
iajs-3477	186	19	0.05	0.05	NUM
iajs-3477	186	20	%	%	NOUN
iajs-3477	186	21	noise	noise	NOUN
iajs-3477	186	22	and	and	CCONJ
iajs-3477	186	23	β	β	X
iajs-3477	186	24	=	=	SYM
iajs-3477	186	25	10−10	10−10	PROPN
iajs-3477	186	26	.	.	PUNCT
iajs-3477	187	1	(	(	PUNCT
iajs-3477	187	2	a	a	X
iajs-3477	187	3	)	)	PUNCT
iajs-3477	187	4	(	(	PUNCT
iajs-3477	187	5	b	b	X
iajs-3477	187	6	)	)	PUNCT
iajs-3477	187	7	figure	figure	NOUN
iajs-3477	187	8	6	6	NUM
iajs-3477	187	9	.	.	PUNCT
iajs-3477	188	1	(	(	PUNCT
iajs-3477	188	2	a	a	X
iajs-3477	188	3	)	)	PUNCT
iajs-3477	188	4	objective	objective	ADJ
iajs-3477	188	5	function	function	NOUN
iajs-3477	188	6	(	(	PUNCT
iajs-3477	188	7	15	15	NUM
iajs-3477	188	8	)	)	PUNCT
iajs-3477	188	9	and	and	CCONJ
iajs-3477	188	10	(	(	PUNCT
iajs-3477	188	11	b	b	X
iajs-3477	188	12	)	)	PUNCT
iajs-3477	188	13	a(y	a(y	PROPN
iajs-3477	188	14	)	)	PUNCT
iajs-3477	188	15	,	,	PUNCT
iajs-3477	188	16	for	for	ADP
iajs-3477	188	17	p	p	NOUN
iajs-3477	188	18	=	=	SYM
iajs-3477	188	19	0.5	0.5	NUM
iajs-3477	188	20	%	%	NOUN
iajs-3477	188	21	noise	noise	NOUN
iajs-3477	188	22	and	and	CCONJ
iajs-3477	188	23	β	β	X
iajs-3477	188	24	=	=	SYM
iajs-3477	188	25	10−7	10−7	NUM
iajs-3477	188	26	.	.	PUNCT
iajs-3477	189	1	the	the	DET
iajs-3477	189	2	numerical	numerical	ADJ
iajs-3477	189	3	and	and	CCONJ
iajs-3477	189	4	exact	exact	ADJ
iajs-3477	189	5	temperatures	temperature	NOUN
iajs-3477	189	6	u(x	u(x	VERB
iajs-3477	189	7	,	,	PUNCT
iajs-3477	189	8	y	y	NOUN
iajs-3477	189	9	)	)	PUNCT
iajs-3477	189	10	,	,	PUNCT
iajs-3477	189	11	with	with	ADP
iajs-3477	189	12	p	p	NOUN
iajs-3477	189	13	=	=	NOUN
iajs-3477	189	14	0.05	0.05	NUM
iajs-3477	189	15	%	%	NOUN
iajs-3477	189	16	noise	noise	NOUN
iajs-3477	189	17	,	,	PUNCT
iajs-3477	189	18	β	β	X
iajs-3477	189	19	=	=	PUNCT
iajs-3477	189	20	{	{	PUNCT
iajs-3477	189	21	10−10	10−10	NUM
iajs-3477	189	22	}	}	PUNCT
iajs-3477	189	23	,	,	PUNCT
iajs-3477	189	24	p	p	NOUN
iajs-3477	189	25	=	=	NOUN
iajs-3477	189	26	0.5	0.5	NUM
iajs-3477	189	27	%	%	NOUN
iajs-3477	189	28	noise	noise	NOUN
iajs-3477	189	29	,	,	PUNCT
iajs-3477	189	30	β	β	X
iajs-3477	189	31	=	=	PUNCT
iajs-3477	189	32	{	{	PUNCT
iajs-3477	189	33	10−10	10−10	NUM
iajs-3477	189	34	}	}	PUNCT
iajs-3477	189	35	,	,	PUNCT
iajs-3477	189	36	as	as	ADV
iajs-3477	189	37	well	well	ADV
iajs-3477	189	38	as	as	ADP
iajs-3477	189	39	the	the	DET
iajs-3477	189	40	absolute	absolute	ADJ
iajs-3477	189	41	error	error	NOUN
iajs-3477	189	42	between	between	ADP
iajs-3477	189	43	them	they	PRON
iajs-3477	189	44	,	,	PUNCT
iajs-3477	189	45	are	be	AUX
iajs-3477	189	46	illustrated	illustrate	VERB
iajs-3477	189	47	in	in	ADP
iajs-3477	189	48	figure	figure	NOUN
iajs-3477	189	49	7	7	NUM
iajs-3477	189	50	and	and	CCONJ
iajs-3477	189	51	execute	execute	VERB
iajs-3477	189	52	arguments	argument	NOUN
iajs-3477	189	53	obtained	obtain	VERB
iajs-3477	189	54	.	.	PUNCT
iajs-3477	190	1	ihjpas	ihjpas	PROPN
iajs-3477	190	2	.	.	PUNCT
iajs-3477	191	1	37	37	NUM
iajs-3477	191	2	(	(	PUNCT
iajs-3477	191	3	2	2	NUM
iajs-3477	191	4	)	)	PUNCT
iajs-3477	191	5	2024	2024	NUM
iajs-3477	191	6	420	420	NUM
iajs-3477	191	7	(	(	PUNCT
iajs-3477	191	8	a	a	NOUN
iajs-3477	191	9	)	)	PUNCT
iajs-3477	191	10	(	(	PUNCT
iajs-3477	191	11	b	b	X
iajs-3477	191	12	)	)	PUNCT
iajs-3477	191	13	figure	figure	NOUN
iajs-3477	191	14	7	7	NUM
iajs-3477	191	15	.	.	PUNCT
iajs-3477	192	1	the	the	DET
iajs-3477	192	2	exact	exact	ADJ
iajs-3477	192	3	and	and	CCONJ
iajs-3477	192	4	numerical	numerical	ADJ
iajs-3477	192	5	u(x	u(x	PROPN
iajs-3477	192	6	,	,	PUNCT
iajs-3477	192	7	y	y	NOUN
iajs-3477	192	8	)	)	PUNCT
iajs-3477	192	9	with	with	ADP
iajs-3477	192	10	(	(	PUNCT
iajs-3477	192	11	a	a	X
iajs-3477	192	12	)	)	PUNCT
iajs-3477	192	13	p	p	NOUN
iajs-3477	192	14	=	=	NOUN
iajs-3477	192	15	0.05	0.05	NUM
iajs-3477	192	16	%	%	NOUN
iajs-3477	192	17	noise	noise	NOUN
iajs-3477	192	18	β	β	NOUN
iajs-3477	192	19	=	=	SYM
iajs-3477	192	20	10−10	10−10	PROPN
iajs-3477	192	21	,	,	PUNCT
iajs-3477	192	22	(	(	PUNCT
iajs-3477	192	23	b	b	X
iajs-3477	192	24	)	)	PUNCT
iajs-3477	192	25	p	p	NOUN
iajs-3477	192	26	=	=	NOUN
iajs-3477	192	27	0.5	0.5	NUM
iajs-3477	192	28	%	%	NOUN
iajs-3477	192	29	noise	noise	NOUN
iajs-3477	192	30	β	β	X
iajs-3477	192	31	=	=	SYM
iajs-3477	192	32	10−7	10−7	NUM
iajs-3477	192	33	,	,	PUNCT
iajs-3477	192	34	as	as	ADV
iajs-3477	192	35	well	well	ADV
iajs-3477	192	36	as	as	ADP
iajs-3477	192	37	the	the	DET
iajs-3477	192	38	absolute	absolute	ADJ
iajs-3477	192	39	error	error	NOUN
iajs-3477	192	40	between	between	ADP
iajs-3477	192	41	them	they	PRON
iajs-3477	192	42	.	.	PUNCT
iajs-3477	193	1	6	6	NUM
iajs-3477	193	2	.	.	PUNCT
iajs-3477	193	3	conclusions	conclusion	NOUN
iajs-3477	193	4	the	the	DET
iajs-3477	193	5	finite	finite	ADJ
iajs-3477	193	6	difference	difference	NOUN
iajs-3477	193	7	schemes	scheme	NOUN
iajs-3477	193	8	were	be	AUX
iajs-3477	193	9	used	use	VERB
iajs-3477	193	10	for	for	ADP
iajs-3477	193	11	direct	direct	ADJ
iajs-3477	193	12	two	two	NUM
iajs-3477	193	13	-	-	PUNCT
iajs-3477	193	14	dimensional	dimensional	ADJ
iajs-3477	193	15	second	second	ADJ
iajs-3477	193	16	order	order	NOUN
iajs-3477	193	17	elliptic	elliptic	ADJ
iajs-3477	193	18	inverse	inverse	NOUN
iajs-3477	193	19	problems	problem	NOUN
iajs-3477	193	20	in	in	ADP
iajs-3477	193	21	conjunction	conjunction	NOUN
iajs-3477	193	22	with	with	ADP
iajs-3477	193	23	quadrature	quadrature	NOUN
iajs-3477	193	24	by	by	ADP
iajs-3477	193	25	the	the	DET
iajs-3477	193	26	trapezoidal	trapezoidal	ADJ
iajs-3477	193	27	rule	rule	NOUN
iajs-3477	193	28	.	.	PUNCT
iajs-3477	194	1	the	the	DET
iajs-3477	194	2	instability	instability	NOUN
iajs-3477	194	3	induced	induce	VERB
iajs-3477	194	4	by	by	ADP
iajs-3477	194	5	the	the	DET
iajs-3477	194	6	illposed	illpose	VERB
iajs-3477	194	7	problem	problem	NOUN
iajs-3477	194	8	was	be	AUX
iajs-3477	194	9	solved	solve	VERB
iajs-3477	194	10	using	use	VERB
iajs-3477	194	11	tikhonov	tikhonov	NOUN
iajs-3477	194	12	regularization	regularization	NOUN
iajs-3477	194	13	.	.	PUNCT
iajs-3477	195	1	the	the	DET
iajs-3477	195	2	rms	rm	NOUN
iajs-3477	195	3	values	value	NOUN
iajs-3477	195	4	for	for	ADP
iajs-3477	195	5	noise	noise	NOUN
iajs-3477	195	6	p	p	NOUN
iajs-3477	195	7	=	=	PROPN
iajs-3477	195	8	0	0	NUM
iajs-3477	195	9	and	and	CCONJ
iajs-3477	195	10	β	β	X
iajs-3477	195	11	=	=	SYM
iajs-3477	195	12	0	0	NUM
iajs-3477	195	13	were	be	AUX
iajs-3477	195	14	contrasted	contrast	VERB
iajs-3477	195	15	for	for	ADP
iajs-3477	195	16	the	the	DET
iajs-3477	195	17	numerical	numerical	ADJ
iajs-3477	195	18	test	test	NOUN
iajs-3477	195	19	problem	problem	NOUN
iajs-3477	195	20	.	.	PUNCT
iajs-3477	196	1	it	it	PRON
iajs-3477	196	2	was	be	AUX
iajs-3477	196	3	found	find	VERB
iajs-3477	196	4	that	that	SCONJ
iajs-3477	196	5	a	a	DET
iajs-3477	196	6	stable	stable	ADJ
iajs-3477	196	7	solution	solution	NOUN
iajs-3477	196	8	with	with	ADP
iajs-3477	196	9	p	p	NOUN
iajs-3477	196	10	=	=	NOUN
iajs-3477	196	11	0.05	0.05	NUM
iajs-3477	196	12	%	%	NOUN
iajs-3477	196	13	noise	noise	NOUN
iajs-3477	196	14	and	and	CCONJ
iajs-3477	196	15	the	the	DET
iajs-3477	196	16	regularization	regularization	NOUN
iajs-3477	196	17	parameter	parameter	NOUN
iajs-3477	196	18	β	β	PROPN
iajs-3477	196	19	=	=	SYM
iajs-3477	196	20	10−10	10−10	NUM
iajs-3477	196	21	ihjpas	ihjpa	NOUN
iajs-3477	196	22	.	.	PUNCT
iajs-3477	197	1	37	37	NUM
iajs-3477	197	2	(	(	PUNCT
iajs-3477	197	3	2	2	NUM
iajs-3477	197	4	)	)	PUNCT
iajs-3477	197	5	2024	2024	NUM
iajs-3477	197	6	421	421	NUM
iajs-3477	197	7	acknowledgment	acknowledgment	NOUN
iajs-3477	197	8	the	the	DET
iajs-3477	197	9	authors	author	NOUN
iajs-3477	197	10	are	be	AUX
iajs-3477	197	11	greatly	greatly	ADV
iajs-3477	197	12	appreciated	appreciate	VERB
iajs-3477	197	13	the	the	DET
iajs-3477	197	14	referees	referee	NOUN
iajs-3477	197	15	for	for	ADP
iajs-3477	197	16	their	their	PRON
iajs-3477	197	17	valuable	valuable	ADJ
iajs-3477	197	18	comments	comment	NOUN
iajs-3477	197	19	and	and	CCONJ
iajs-3477	197	20	suggestions	suggestion	NOUN
iajs-3477	197	21	for	for	ADP
iajs-3477	197	22	improving	improve	VERB
iajs-3477	197	23	the	the	DET
iajs-3477	197	24	paper	paper	NOUN
iajs-3477	197	25	conflict	conflict	NOUN
iajs-3477	197	26	of	of	ADP
iajs-3477	197	27	interest	interest	NOUN
iajs-3477	197	28	the	the	DET
iajs-3477	197	29	authors	author	NOUN
iajs-3477	197	30	declare	declare	VERB
iajs-3477	197	31	that	that	SCONJ
iajs-3477	197	32	they	they	PRON
iajs-3477	197	33	have	have	VERB
iajs-3477	197	34	no	no	DET
iajs-3477	197	35	conflicts	conflict	NOUN
iajs-3477	197	36	of	of	ADP
iajs-3477	197	37	interest	interest	NOUN
iajs-3477	197	38	.	.	PUNCT
iajs-3477	198	1	funding	funding	NOUN
iajs-3477	198	2	there	there	PRON
iajs-3477	198	3	is	be	VERB
iajs-3477	198	4	no	no	DET
iajs-3477	198	5	financial	financial	ADJ
iajs-3477	198	6	support	support	NOUN
iajs-3477	198	7	in	in	ADP
iajs-3477	198	8	preparation	preparation	NOUN
iajs-3477	198	9	for	for	ADP
iajs-3477	198	10	the	the	DET
iajs-3477	198	11	publication	publication	NOUN
iajs-3477	198	12	.	.	PUNCT
iajs-3477	199	1	references	reference	NOUN
iajs-3477	199	2	1	1	NUM
iajs-3477	199	3	.	.	PUNCT
iajs-3477	199	4	ashyralyyev	ashyralyyev	PROPN
iajs-3477	199	5	,	,	PUNCT
iajs-3477	199	6	c.	c.	PROPN
iajs-3477	199	7	;	;	PUNCT
iajs-3477	199	8	dedeturk	dedeturk	NOUN
iajs-3477	199	9	,	,	PUNCT
iajs-3477	199	10	m.	m.	NOUN
iajs-3477	199	11	a	a	DET
iajs-3477	199	12	finite	finite	ADJ
iajs-3477	199	13	difference	difference	NOUN
iajs-3477	199	14	method	method	NOUN
iajs-3477	199	15	for	for	ADP
iajs-3477	199	16	the	the	DET
iajs-3477	199	17	inverse	inverse	NOUN
iajs-3477	199	18	elliptic	elliptic	ADJ
iajs-3477	199	19	problem	problem	NOUN
iajs-3477	199	20	with	with	ADP
iajs-3477	199	21	the	the	DET
iajs-3477	199	22	dirichlet	dirichlet	PROPN
iajs-3477	199	23	condition	condition	NOUN
iajs-3477	199	24	.	.	PUNCT
iajs-3477	200	1	journal	journal	PROPN
iajs-3477	200	2	of	of	ADP
iajs-3477	200	3	mathematical	mathematical	ADJ
iajs-3477	200	4	engineering	engineering	NOUN
iajs-3477	200	5	.	.	PUNCT
iajs-3477	201	1	2013,1(2	2013,1(2	NUM
iajs-3477	201	2	)	)	PUNCT
iajs-3477	201	3	,	,	PUNCT
iajs-3477	201	4	132	132	NUM
iajs-3477	201	5	-	-	SYM
iajs-3477	201	6	155	155	NUM
iajs-3477	201	7	.	.	NOUN
iajs-3477	202	1	2	2	NUM
iajs-3477	202	2	.	.	X
iajs-3477	202	3	gong	gong	PROPN
iajs-3477	202	4	,	,	PUNCT
iajs-3477	202	5	w.	w.	PROPN
iajs-3477	202	6	;	;	PUNCT
iajs-3477	202	7	kwok	kwok	PROPN
iajs-3477	202	8	,	,	PUNCT
iajs-3477	202	9	f.	f.	PROPN
iajs-3477	202	10	;	;	PUNCT
iajs-3477	202	11	tan	tan	PROPN
iajs-3477	202	12	,	,	PUNCT
iajs-3477	203	1	z.	z.	PROPN
iajs-3477	203	2	convergence	convergence	NOUN
iajs-3477	203	3	analysis	analysis	NOUN
iajs-3477	203	4	of	of	ADP
iajs-3477	203	5	the	the	DET
iajs-3477	203	6	schwarz	schwarz	PROPN
iajs-3477	203	7	alternating	alternate	VERB
iajs-3477	203	8	method	method	NOUN
iajs-3477	203	9	for	for	ADP
iajs-3477	203	10	unconstrained	unconstrained	ADJ
iajs-3477	203	11	elliptic	elliptic	ADJ
iajs-3477	203	12	optimal	optimal	ADJ
iajs-3477	203	13	control	control	NOUN
iajs-3477	203	14	problems	problem	NOUN
iajs-3477	203	15	.	.	PUNCT
iajs-3477	204	1	arxiv	arxiv	PROPN
iajs-3477	204	2	preprint	preprint	NOUN
iajs-3477	204	3	arxiv:2201.00974	arxiv:2201.00974	NUM
iajs-3477	204	4	.2022	.2022	NOUN
iajs-3477	204	5	.	.	PUNCT
iajs-3477	205	1	https://doi.org/10.48550/arxiv.2201.00974	https://doi.org/10.48550/arxiv.2201.00974	PROPN
iajs-3477	205	2	3	3	X
iajs-3477	205	3	.	.	PUNCT
iajs-3477	205	4	ashyralyyev	ashyralyyev	PROPN
iajs-3477	205	5	,	,	PUNCT
iajs-3477	205	6	c.	c.	PROPN
iajs-3477	205	7	;	;	PUNCT
iajs-3477	205	8	dedeturk	dedeturk	NOUN
iajs-3477	205	9	,	,	PUNCT
iajs-3477	205	10	m.	m.	NOUN
iajs-3477	205	11	approximate	approximate	ADJ
iajs-3477	205	12	solution	solution	NOUN
iajs-3477	205	13	of	of	ADP
iajs-3477	205	14	inverse	inverse	ADJ
iajs-3477	205	15	problem	problem	NOUN
iajs-3477	205	16	for	for	ADP
iajs-3477	205	17	elliptic	elliptic	ADJ
iajs-3477	205	18	equation	equation	NOUN
iajs-3477	205	19	with	with	ADP
iajs-3477	205	20	overdetermination	overdetermination	NOUN
iajs-3477	205	21	.	.	PUNCT
iajs-3477	206	1	in	in	ADP
iajs-3477	206	2	abstract	abstract	ADJ
iajs-3477	206	3	and	and	CCONJ
iajs-3477	206	4	applied	apply	VERB
iajs-3477	206	5	analysis	analysis	NOUN
iajs-3477	206	6	.	.	PUNCT
iajs-3477	207	1	hindawi	hindawi	ADJ
iajs-3477	207	2	,	,	PUNCT
iajs-3477	207	3	article	article	NOUN
iajs-3477	207	4	i	i	PROPN
iajs-3477	207	5	d	d	PROPN
iajs-3477	207	6	548017	548017	NUM
iajs-3477	207	7	,	,	PUNCT
iajs-3477	207	8	2013,2013	2013,2013	PROPN
iajs-3477	207	9	.	.	PROPN
iajs-3477	207	10	https://doi.org/10.1155/2013/548017	https://doi.org/10.1155/2013/548017	PROPN
iajs-3477	207	11	4	4	NUM
iajs-3477	207	12	.	.	PUNCT
iajs-3477	207	13	slodička	slodička	NOUN
iajs-3477	207	14	,	,	PUNCT
iajs-3477	207	15	m.	m.	NOUN
iajs-3477	207	16	;	;	PUNCT
iajs-3477	207	17	van	van	PROPN
iajs-3477	207	18	keer	keer	PROPN
iajs-3477	207	19	,	,	PUNCT
iajs-3477	207	20	r.	r.	PROPN
iajs-3477	207	21	a	a	DET
iajs-3477	207	22	numerical	numerical	ADJ
iajs-3477	207	23	approach	approach	NOUN
iajs-3477	207	24	for	for	ADP
iajs-3477	207	25	the	the	DET
iajs-3477	207	26	determination	determination	NOUN
iajs-3477	207	27	of	of	ADP
iajs-3477	207	28	a	a	DET
iajs-3477	207	29	missing	missing	ADJ
iajs-3477	207	30	boundary	boundary	ADJ
iajs-3477	207	31	data	datum	NOUN
iajs-3477	207	32	in	in	ADP
iajs-3477	207	33	elliptic	elliptic	ADJ
iajs-3477	207	34	problems	problem	NOUN
iajs-3477	207	35	.	.	PUNCT
iajs-3477	208	1	applied	apply	VERB
iajs-3477	208	2	mathematics	mathematic	NOUN
iajs-3477	208	3	and	and	CCONJ
iajs-3477	208	4	computation	computation	NOUN
iajs-3477	208	5	,	,	PUNCT
iajs-3477	208	6	2004	2004	NUM
iajs-3477	208	7	,	,	PUNCT
iajs-3477	208	8	147(2	147(2	NUM
iajs-3477	208	9	)	)	PUNCT
iajs-3477	208	10	,	,	PUNCT
iajs-3477	208	11	569–580	569–580	NUM
iajs-3477	208	12	.	.	PUNCT
iajs-3477	209	1	https://doi.org/10.1016/s0096-3003(02)00795-6	https://doi.org/10.1016/s0096-3003(02)00795-6	PROPN
iajs-3477	209	2	5	5	NUM
iajs-3477	209	3	.	.	PUNCT
iajs-3477	209	4	beshley	beshley	PROPN
iajs-3477	209	5	,	,	PUNCT
iajs-3477	209	6	a.	a.	NOUN
iajs-3477	209	7	;	;	PUNCT
iajs-3477	209	8	chapko	chapko	PROPN
iajs-3477	209	9	,	,	PUNCT
iajs-3477	209	10	r.	r.	PROPN
iajs-3477	209	11	;	;	PUNCT
iajs-3477	209	12	and	and	CCONJ
iajs-3477	209	13	johansson	johansson	PROPN
iajs-3477	209	14	,	,	PUNCT
iajs-3477	209	15	b.	b.	PROPN
iajs-3477	209	16	t.	t.	PROPN
iajs-3477	210	1	an	an	DET
iajs-3477	210	2	integral	integral	ADJ
iajs-3477	210	3	equation	equation	NOUN
iajs-3477	210	4	method	method	NOUN
iajs-3477	210	5	for	for	ADP
iajs-3477	210	6	the	the	DET
iajs-3477	210	7	numerical	numerical	ADJ
iajs-3477	210	8	solution	solution	NOUN
iajs-3477	210	9	of	of	ADP
iajs-3477	210	10	a	a	DET
iajs-3477	210	11	dirichlet	dirichlet	NOUN
iajs-3477	210	12	problem	problem	NOUN
iajs-3477	210	13	for	for	ADP
iajs-3477	210	14	second	second	ADJ
iajs-3477	210	15	-	-	PUNCT
iajs-3477	210	16	order	order	NOUN
iajs-3477	210	17	elliptic	elliptic	ADJ
iajs-3477	210	18	equations	equation	NOUN
iajs-3477	210	19	with	with	ADP
iajs-3477	210	20	variable	variable	ADJ
iajs-3477	210	21	coefficients	coefficient	NOUN
iajs-3477	210	22	,	,	PUNCT
iajs-3477	210	23	journal	journal	NOUN
iajs-3477	210	24	of	of	ADP
iajs-3477	210	25	engineering	engineering	NOUN
iajs-3477	210	26	mathematics	mathematic	NOUN
iajs-3477	210	27	,	,	PUNCT
iajs-3477	210	28	2018,112	2018,112	NUM
iajs-3477	210	29	,	,	PUNCT
iajs-3477	210	30	63–73	63–73	NUM
iajs-3477	210	31	.	.	PUNCT
iajs-3477	211	1	https://doi.org/10.1007/s10665-018-9965-7	https://doi.org/10.1007/s10665-018-9965-7	NUM
iajs-3477	211	2	6	6	NUM
iajs-3477	211	3	.	.	PUNCT
iajs-3477	212	1	huntul	huntul	PROPN
iajs-3477	212	2	,	,	PUNCT
iajs-3477	212	3	m.	m.	PROPN
iajs-3477	212	4	j.	j.	PROPN
iajs-3477	212	5	;	;	PUNCT
iajs-3477	212	6	lesnic	lesnic	PROPN
iajs-3477	212	7	,	,	PUNCT
iajs-3477	212	8	d.	d.	PROPN
iajs-3477	212	9	determination	determination	NOUN
iajs-3477	212	10	of	of	ADP
iajs-3477	212	11	a	a	DET
iajs-3477	212	12	time	time	NOUN
iajs-3477	212	13	-	-	PUNCT
iajs-3477	212	14	dependent	dependent	ADJ
iajs-3477	212	15	free	free	ADJ
iajs-3477	212	16	boundary	boundary	NOUN
iajs-3477	212	17	in	in	ADP
iajs-3477	212	18	a	a	DET
iajs-3477	212	19	two	two	NUM
iajs-3477	212	20	-	-	PUNCT
iajs-3477	212	21	dimensional	dimensional	ADJ
iajs-3477	212	22	parabolic	parabolic	ADJ
iajs-3477	212	23	problem	problem	NOUN
iajs-3477	212	24	.	.	PUNCT
iajs-3477	213	1	international	international	ADJ
iajs-3477	213	2	journal	journal	PROPN
iajs-3477	213	3	of	of	ADP
iajs-3477	213	4	applied	applied	ADJ
iajs-3477	213	5	and	and	CCONJ
iajs-3477	213	6	computational	computational	ADJ
iajs-3477	213	7	mathematics	mathematic	NOUN
iajs-3477	213	8	,	,	PUNCT
iajs-3477	213	9	2019	2019	NUM
iajs-3477	213	10	,	,	PUNCT
iajs-3477	213	11	5(4	5(4	NUM
iajs-3477	213	12	)	)	PUNCT
iajs-3477	213	13	,	,	PUNCT
iajs-3477	213	14	118	118	NUM
iajs-3477	213	15	.	.	PUNCT
iajs-3477	213	16	https://doi.org/10.1007/s40819-019-0700-5	https://doi.org/10.1007/s40819-019-0700-5	NUM
iajs-3477	213	17	7	7	NUM
iajs-3477	213	18	.	.	PUNCT
iajs-3477	214	1	hussein	hussein	PROPN
iajs-3477	214	2	,	,	PUNCT
iajs-3477	214	3	s.	s.	PROPN
iajs-3477	214	4	o.	o.	PROPN
iajs-3477	214	5	;	;	PUNCT
iajs-3477	214	6	lesnic	lesnic	PROPN
iajs-3477	214	7	,	,	PUNCT
iajs-3477	214	8	d.	d.	PROPN
iajs-3477	214	9	determination	determination	NOUN
iajs-3477	214	10	of	of	ADP
iajs-3477	214	11	forcing	force	VERB
iajs-3477	214	12	functions	function	NOUN
iajs-3477	214	13	in	in	ADP
iajs-3477	214	14	the	the	DET
iajs-3477	214	15	wave	wave	NOUN
iajs-3477	214	16	equation	equation	NOUN
iajs-3477	214	17	.	.	PUNCT
iajs-3477	215	1	part	part	NOUN
iajs-3477	216	1	i	i	PRON
iajs-3477	216	2	:	:	PUNCT
iajs-3477	216	3	the	the	DET
iajs-3477	216	4	spacedependent	spacedependent	NOUN
iajs-3477	216	5	case.journal	case.journal	PROPN
iajs-3477	216	6	of	of	ADP
iajs-3477	216	7	engineering	engineering	NOUN
iajs-3477	216	8	mathematics	mathematic	NOUN
iajs-3477	216	9	,	,	PUNCT
iajs-3477	216	10	2016	2016	NUM
iajs-3477	216	11	,	,	PUNCT
iajs-3477	216	12	96	96	NUM
iajs-3477	216	13	,	,	PUNCT
iajs-3477	216	14	115–133	115–133	NUM
iajs-3477	216	15	.	.	PUNCT
iajs-3477	217	1	https://doi.org/10.1007/s10665015-9785-y	https://doi.org/10.1007/s10665015-9785-y	PRON
iajs-3477	217	2	8	8	X
iajs-3477	217	3	.	.	PUNCT
iajs-3477	218	1	qassim	qassim	NOUN
iajs-3477	218	2	,	,	PUNCT
iajs-3477	218	3	m.	m.	NOUN
iajs-3477	218	4	;	;	PUNCT
iajs-3477	218	5	hussein	hussein	PROPN
iajs-3477	218	6	,	,	PUNCT
iajs-3477	218	7	m.s	m.s	PROPN
iajs-3477	218	8	.	.	PROPN
iajs-3477	218	9	numerical	numerical	PROPN
iajs-3477	218	10	solution	solution	NOUN
iajs-3477	218	11	to	to	PART
iajs-3477	218	12	recover	recover	VERB
iajs-3477	218	13	time	time	NOUN
iajs-3477	218	14	-	-	PUNCT
iajs-3477	218	15	dependent	dependent	ADJ
iajs-3477	218	16	coefficient	coefficient	NOUN
iajs-3477	218	17	and	and	CCONJ
iajs-3477	218	18	free	free	ADJ
iajs-3477	218	19	boundary	boundary	NOUN
iajs-3477	218	20	from	from	ADP
iajs-3477	218	21	nonlocal	nonlocal	ADJ
iajs-3477	218	22	and	and	CCONJ
iajs-3477	218	23	stefan	stefan	PROPN
iajs-3477	218	24	type	type	PROPN
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iajs-3477	218	26	conditions	condition	NOUN
iajs-3477	218	27	in	in	ADP
iajs-3477	218	28	heat	heat	NOUN
iajs-3477	218	29	equation	equation	NOUN
iajs-3477	218	30	.	.	PUNCT
iajs-3477	219	1	iraqi	iraqi	ADJ
iajs-3477	219	2	journal	journal	PROPN
iajs-3477	219	3	of	of	ADP
iajs-3477	219	4	science	science	NOUN
iajs-3477	219	5	,	,	PUNCT
iajs-3477	219	6	2021	2021	NUM
iajs-3477	219	7	,	,	PUNCT
iajs-3477	219	8	950	950	NUM
iajs-3477	219	9	-	-	SYM
iajs-3477	219	10	960	960	NUM
iajs-3477	219	11	.	.	PUNCT
iajs-3477	220	1	https://doi.org/10.24996/ijs.2021.62.3.25	https://doi.org/10.24996/ijs.2021.62.3.25	PROPN
iajs-3477	221	1	9	9	NUM
iajs-3477	221	2	.	.	PUNCT
iajs-3477	221	3	anwer	anwer	NOUN
iajs-3477	221	4	,	,	PUNCT
iajs-3477	221	5	f.	f.	PROPN
iajs-3477	221	6	;	;	PUNCT
iajs-3477	221	7	hussein	hussein	PROPN
iajs-3477	221	8	,	,	PUNCT
iajs-3477	221	9	m.	m.	NOUN
iajs-3477	221	10	s.	s.	PROPN
iajs-3477	221	11	retrieval	retrieval	PROPN
iajs-3477	221	12	of	of	ADP
iajs-3477	221	13	timewise	timewise	ADJ
iajs-3477	221	14	coefficients	coefficient	NOUN
iajs-3477	221	15	in	in	ADP
iajs-3477	221	16	the	the	DET
iajs-3477	221	17	heat	heat	NOUN
iajs-3477	221	18	equation	equation	NOUN
iajs-3477	221	19	from	from	ADP
iajs-3477	221	20	nonlocal	nonlocal	ADJ
iajs-3477	221	21	overdetermination	overdetermination	NOUN
iajs-3477	221	22	conditions	condition	NOUN
iajs-3477	221	23	.	.	PUNCT
iajs-3477	222	1	iraqi	iraqi	ADJ
iajs-3477	222	2	journal	journal	PROPN
iajs-3477	222	3	of	of	ADP
iajs-3477	222	4	science	science	NOUN
iajs-3477	222	5	,	,	PUNCT
iajs-3477	222	6	2022	2022	NUM
iajs-3477	222	7	,	,	PUNCT
iajs-3477	222	8	1184–1199	1184–1199	NUM
iajs-3477	222	9	.	.	PUNCT
iajs-3477	223	1	https://doi.org/10.24996/ijs.2022.63.3.24	https://doi.org/10.24996/ijs.2022.63.3.24	PROPN
iajs-3477	223	2	10	10	NUM
iajs-3477	223	3	.	.	PUNCT
iajs-3477	224	1	huntul	huntul	PROPN
iajs-3477	224	2	,	,	PUNCT
iajs-3477	224	3	m.j	m.j	PROPN
iajs-3477	224	4	.	.	PROPN
iajs-3477	224	5	;	;	PUNCT
iajs-3477	224	6	hussein	hussein	PROPN
iajs-3477	224	7	,	,	PUNCT
iajs-3477	224	8	m.	m.	NOUN
iajs-3477	224	9	s.	s.	PROPN
iajs-3477	224	10	simultaneous	simultaneous	ADJ
iajs-3477	224	11	identification	identification	NOUN
iajs-3477	224	12	of	of	ADP
iajs-3477	224	13	thermal	thermal	ADJ
iajs-3477	224	14	conductivity	conductivity	NOUN
iajs-3477	224	15	and	and	CCONJ
iajs-3477	224	16	heat	heat	NOUN
iajs-3477	224	17	source	source	NOUN
iajs-3477	224	18	in	in	ADP
iajs-3477	224	19	the	the	DET
iajs-3477	224	20	heat	heat	NOUN
iajs-3477	224	21	equation	equation	NOUN
iajs-3477	224	22	.	.	PUNCT
iajs-3477	225	1	iraqi	iraqi	ADJ
iajs-3477	225	2	journal	journal	PROPN
iajs-3477	225	3	of	of	ADP
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iajs-3477	225	5	,	,	PUNCT
iajs-3477	225	6	2021	2021	NUM
iajs-3477	225	7	,	,	PUNCT
iajs-3477	225	8	1968	1968	NUM
iajs-3477	225	9	-	-	SYM
iajs-3477	225	10	1978	1978	NUM
iajs-3477	225	11	.	.	PUNCT
iajs-3477	226	1	https://doi.org/10.24996/ijs.2021.62.6.22	https://doi.org/10.24996/ijs.2021.62.6.22	PRON
iajs-3477	226	2	11	11	NUM
iajs-3477	226	3	.	.	PUNCT
iajs-3477	227	1	hussein	hussein	PROPN
iajs-3477	227	2	,	,	PUNCT
iajs-3477	227	3	s.	s.	PROPN
iajs-3477	227	4	o.	o.	PROPN
iajs-3477	227	5	;	;	PUNCT
iajs-3477	227	6	hussein	hussein	PROPN
iajs-3477	227	7	,	,	PUNCT
iajs-3477	227	8	m.	m.	NOUN
iajs-3477	227	9	s.	s.	PROPN
iajs-3477	227	10	splitting	split	VERB
iajs-3477	227	11	the	the	DET
iajs-3477	227	12	one	one	NUM
iajs-3477	227	13	-	-	PUNCT
iajs-3477	227	14	dimensional	dimensional	ADJ
iajs-3477	227	15	wave	wave	NOUN
iajs-3477	227	16	equation	equation	NOUN
iajs-3477	227	17	,	,	PUNCT
iajs-3477	227	18	part	part	NOUN
iajs-3477	227	19	ii	ii	PROPN
iajs-3477	227	20	:	:	PUNCT
iajs-3477	227	21	additional	additional	ADJ
iajs-3477	227	22	data	datum	NOUN
iajs-3477	227	23	are	be	AUX
iajs-3477	227	24	given	give	VERB
iajs-3477	227	25	by	by	ADP
iajs-3477	227	26	an	an	DET
iajs-3477	227	27	end	end	NOUN
iajs-3477	227	28	displacement	displacement	NOUN
iajs-3477	227	29	measurement	measurement	NOUN
iajs-3477	227	30	,	,	PUNCT
iajs-3477	227	31	iraqi	iraqi	ADJ
iajs-3477	227	32	journal	journal	NOUN
iajs-3477	227	33	of	of	ADP
iajs-3477	227	34	science	science	NOUN
iajs-3477	227	35	,	,	PUNCT
iajs-3477	227	36	2021	2021	NUM
iajs-3477	227	37	,	,	PUNCT
iajs-3477	227	38	62(1	62(1	NOUN
iajs-3477	227	39	)	)	PUNCT
iajs-3477	227	40	,	,	PUNCT
iajs-3477	227	41	233–239	233–239	NUM
iajs-3477	227	42	.	.	PUNCT
iajs-3477	228	1	https://doi.org/10.24996/ijs.2021.62.1.22	https://doi.org/10.24996/ijs.2021.62.1.22	PROPN
iajs-3477	228	2	12	12	NUM
iajs-3477	228	3	.	.	PUNCT
iajs-3477	229	1	adil	adil	PROPN
iajs-3477	229	2	,	,	PUNCT
iajs-3477	229	3	z.	z.	PROPN
iajs-3477	229	4	;	;	PUNCT
iajs-3477	229	5	hussein	hussein	PROPN
iajs-3477	229	6	,	,	PUNCT
iajs-3477	229	7	m.	m.	NOUN
iajs-3477	229	8	s.	s.	PROPN
iajs-3477	229	9	;	;	PUNCT
iajs-3477	229	10	lesnic	lesnic	PROPN
iajs-3477	229	11	,	,	PUNCT
iajs-3477	229	12	d.	d.	PROPN
iajs-3477	229	13	determination	determination	NOUN
iajs-3477	229	14	of	of	ADP
iajs-3477	229	15	time	time	NOUN
iajs-3477	229	16	-	-	PUNCT
iajs-3477	229	17	dependent	dependent	ADJ
iajs-3477	229	18	coefficients	coefficient	NOUN
iajs-3477	229	19	in	in	ADP
iajs-3477	229	20	moving	move	VERB
iajs-3477	229	21	boundary	boundary	ADJ
iajs-3477	229	22	problems	problem	NOUN
iajs-3477	229	23	under	under	ADP
iajs-3477	229	24	nonlocal	nonlocal	ADJ
iajs-3477	229	25	and	and	CCONJ
iajs-3477	229	26	heat	heat	NOUN
iajs-3477	229	27	moment	moment	NOUN
iajs-3477	229	28	observations	observation	NOUN
iajs-3477	229	29	.	.	PUNCT
iajs-3477	230	1	international	international	ADJ
iajs-3477	230	2	journal	journal	NOUN
iajs-3477	230	3	for	for	ADP
iajs-3477	230	4	computational	computational	ADJ
iajs-3477	230	5	methods	method	NOUN
iajs-3477	230	6	in	in	ADP
iajs-3477	230	7	engineering	engineering	NOUN
iajs-3477	230	8	science	science	NOUN
iajs-3477	230	9	and	and	CCONJ
iajs-3477	230	10	mechanics	mechanic	NOUN
iajs-3477	230	11	,	,	PUNCT
iajs-3477	230	12	2021	2021	NUM
iajs-3477	230	13	,	,	PUNCT
iajs-3477	230	14	22(6	22(6	NUM
iajs-3477	230	15	)	)	PUNCT
iajs-3477	230	16	,	,	PUNCT
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iajs-3477	272	25	equation	equation	NOUN
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iajs-3477	274	2	.	.	PUNCT
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iajs-3477	278	6	.	.	PUNCT
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iajs-3477	283	6	.	.	PUNCT
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iajs-3477	287	5	,	,	PUNCT
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iajs-3477	300	5	2024	2024	NUM
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iajs-3477	300	8	.	.	PUNCT
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iajs-3477	301	40	)	)	PUNCT
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iajs-3477	301	43	.	.	PUNCT
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