id	sid	tid	token	lemma	pos
cana-768	1	1	communications	communication	NOUN
cana-768	1	2	on	on	ADP
cana-768	1	3	applied	apply	VERB
cana-768	1	4	nonlinear	nonlinear	ADJ
cana-768	1	5	analysis	analysis	NOUN
cana-768	1	6	issn	issn	NOUN
cana-768	1	7	:	:	PUNCT
cana-768	1	8	1074	1074	NUM
cana-768	1	9	-	-	PUNCT
cana-768	1	10	133x	133x	NUM
cana-768	1	11	vol	vol	NOUN
cana-768	1	12	31	31	NUM
cana-768	1	13	no	no	NOUN
cana-768	1	14	.	.	PUNCT
cana-768	2	1	3s	3s	NUM
cana-768	2	2	(	(	PUNCT
cana-768	2	3	2024	2024	NUM
cana-768	2	4	)	)	PUNCT
cana-768	2	5	312	312	NUM
cana-768	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	2	7	exponential	exponential	ADJ
cana-768	2	8	b	b	X
cana-768	2	9	-	-	PUNCT
cana-768	2	10	spline	spline	NOUN
cana-768	2	11	method	method	NOUN
cana-768	2	12	for	for	ADP
cana-768	2	13	second	second	ADJ
cana-768	2	14	order	order	NOUN
cana-768	2	15	singularly	singularly	ADV
cana-768	2	16	perturbed	perturb	VERB
cana-768	2	17	boundary	boundary	ADJ
cana-768	2	18	value	value	NOUN
cana-768	2	19	problem	problem	NOUN
cana-768	2	20	with	with	ADP
cana-768	2	21	negative	negative	ADJ
cana-768	2	22	shift	shift	NOUN
cana-768	2	23	1biswajit	1biswajit	NUM
cana-768	2	24	kaushik	kaushik	NOUN
cana-768	2	25	,	,	PUNCT
cana-768	2	26	2myana	2myana	NUM
cana-768	2	27	rajkumar	rajkumar	PROPN
cana-768	2	28	,	,	PUNCT
cana-768	2	29	*	*	PROPN
cana-768	2	30	3diddi	3diddi	NUM
cana-768	2	31	kumara	kumara	NOUN
cana-768	2	32	swamy	swamy	PROPN
cana-768	2	33	1,2,3department	1,2,3department	NUM
cana-768	2	34	of	of	ADP
cana-768	2	35	mathematics	mathematic	NOUN
cana-768	2	36	,	,	PUNCT
cana-768	2	37	indian	indian	PROPN
cana-768	2	38	institute	institute	PROPN
cana-768	2	39	of	of	ADP
cana-768	2	40	information	information	NOUN
cana-768	2	41	technology	technology	NOUN
cana-768	2	42	,	,	PUNCT
cana-768	2	43	sonepat	sonepat	PROPN
cana-768	2	44	,	,	PUNCT
cana-768	2	45	india	india	PROPN
cana-768	2	46	*	*	PUNCT
cana-768	2	47	corresponding	correspond	VERB
cana-768	2	48	author	author	NOUN
cana-768	2	49	:	:	PUNCT
cana-768	2	50	ksdiddi@iiitsonepat.ac.in	ksdiddi@iiitsonepat.ac.in	X
cana-768	2	51	article	article	NOUN
cana-768	2	52	history	history	NOUN
cana-768	2	53	:	:	PUNCT
cana-768	2	54	received	receive	VERB
cana-768	2	55	:	:	PUNCT
cana-768	2	56	12	12	NUM
cana-768	2	57	-	-	PUNCT
cana-768	2	58	04	04	NUM
cana-768	2	59	-	-	PUNCT
cana-768	2	60	2024	2024	NUM
cana-768	2	61	revised	revise	VERB
cana-768	2	62	:	:	PUNCT
cana-768	2	63	26	26	NUM
cana-768	2	64	-	-	SYM
cana-768	2	65	05	05	NUM
cana-768	2	66	-	-	PUNCT
cana-768	2	67	2024	2024	NUM
cana-768	2	68	accepted	accept	VERB
cana-768	2	69	:	:	PUNCT
cana-768	2	70	14	14	NUM
cana-768	2	71	-	-	SYM
cana-768	2	72	06	06	NUM
cana-768	2	73	-	-	PUNCT
cana-768	2	74	2024	2024	NUM
cana-768	2	75	abstract	abstract	NOUN
cana-768	2	76	:	:	PUNCT
cana-768	2	77	in	in	ADP
cana-768	2	78	this	this	DET
cana-768	2	79	paper	paper	NOUN
cana-768	2	80	,	,	PUNCT
cana-768	2	81	we	we	PRON
cana-768	2	82	present	present	VERB
cana-768	2	83	a	a	DET
cana-768	2	84	numerical	numerical	ADJ
cana-768	2	85	scheme	scheme	NOUN
cana-768	2	86	based	base	VERB
cana-768	2	87	on	on	ADP
cana-768	2	88	exponential	exponential	ADJ
cana-768	2	89	b	b	PROPN
cana-768	2	90	-	-	PUNCT
cana-768	2	91	spline	spline	NOUN
cana-768	2	92	method	method	NOUN
cana-768	2	93	for	for	ADP
cana-768	2	94	the	the	DET
cana-768	2	95	solution	solution	NOUN
cana-768	2	96	of	of	ADP
cana-768	2	97	singularly	singularly	ADV
cana-768	2	98	perturbed	perturb	VERB
cana-768	2	99	delay	delay	NOUN
cana-768	2	100	differential	differential	VERB
cana-768	2	101	equation.the	equation.the	DET
cana-768	2	102	equation	equation	NOUN
cana-768	2	103	is	be	AUX
cana-768	2	104	transformed	transform	VERB
cana-768	2	105	to	to	PART
cana-768	2	106	singularly	singularly	ADV
cana-768	2	107	perturbed	perturb	VERB
cana-768	2	108	boundary	boundary	ADJ
cana-768	2	109	value	value	NOUN
cana-768	2	110	problem	problem	NOUN
cana-768	2	111	by	by	ADP
cana-768	2	112	applying	apply	VERB
cana-768	2	113	taylor	taylor	PROPN
cana-768	2	114	's	's	PART
cana-768	2	115	series	series	NOUN
cana-768	2	116	expansion	expansion	NOUN
cana-768	2	117	.	.	PUNCT
cana-768	3	1	a	a	DET
cana-768	3	2	three	three	NUM
cana-768	3	3	term	term	NOUN
cana-768	3	4	recurrence	recurrence	NOUN
cana-768	3	5	relation	relation	NOUN
cana-768	3	6	is	be	AUX
cana-768	3	7	obtained	obtain	VERB
cana-768	3	8	and	and	CCONJ
cana-768	3	9	invariant	invariant	ADJ
cana-768	3	10	embedded	embed	VERB
cana-768	3	11	algorithm	algorithm	NOUN
cana-768	3	12	is	be	AUX
cana-768	3	13	applied	apply	VERB
cana-768	3	14	to	to	PART
cana-768	3	15	get	get	VERB
cana-768	3	16	the	the	DET
cana-768	3	17	approximate	approximate	ADJ
cana-768	3	18	solution	solution	NOUN
cana-768	4	1	.the	.the	PRON
cana-768	4	2	convergence	convergence	NOUN
cana-768	4	3	of	of	ADP
cana-768	4	4	the	the	DET
cana-768	4	5	proposed	propose	VERB
cana-768	4	6	scheme	scheme	NOUN
cana-768	4	7	is	be	AUX
cana-768	4	8	discussed	discuss	VERB
cana-768	4	9	.	.	PUNCT
cana-768	5	1	the	the	DET
cana-768	5	2	efficiency	efficiency	NOUN
cana-768	5	3	of	of	ADP
cana-768	5	4	the	the	DET
cana-768	5	5	scheme	scheme	NOUN
cana-768	5	6	is	be	AUX
cana-768	5	7	illustrated	illustrate	VERB
cana-768	5	8	by	by	ADP
cana-768	5	9	presenting	present	VERB
cana-768	5	10	different	different	ADJ
cana-768	5	11	examples	example	NOUN
cana-768	5	12	.the	.the	PRON
cana-768	5	13	results	result	NOUN
cana-768	5	14	are	be	AUX
cana-768	5	15	compared	compare	VERB
cana-768	5	16	with	with	ADP
cana-768	5	17	available	available	ADJ
cana-768	5	18	literature	literature	NOUN
cana-768	5	19	and	and	CCONJ
cana-768	5	20	comparatively	comparatively	ADV
cana-768	5	21	the	the	DET
cana-768	5	22	method	method	NOUN
cana-768	5	23	yields	yield	VERB
cana-768	5	24	better	well	ADJ
cana-768	5	25	results	result	NOUN
cana-768	5	26	.	.	PUNCT
cana-768	6	1	keywords	keyword	NOUN
cana-768	6	2	:	:	PUNCT
cana-768	6	3	exponential	exponential	ADJ
cana-768	6	4	b	b	X
cana-768	6	5	-	-	PUNCT
cana-768	6	6	spline	spline	ADJ
cana-768	6	7	,	,	PUNCT
cana-768	6	8	negative	negative	ADJ
cana-768	6	9	shift	shift	NOUN
cana-768	6	10	,	,	PUNCT
cana-768	6	11	invariant	invariant	ADJ
cana-768	6	12	embedded	embed	VERB
cana-768	6	13	algorithm	algorithm	NOUN
cana-768	6	14	,	,	PUNCT
cana-768	6	15	tridiagonal	tridiagonal	ADJ
cana-768	6	16	system	system	NOUN
cana-768	6	17	,	,	PUNCT
cana-768	6	18	boundary	boundary	ADJ
cana-768	6	19	layer	layer	NOUN
cana-768	6	20	.	.	PUNCT
cana-768	7	1	1	1	X
cana-768	7	2	.	.	X
cana-768	7	3	introduction	introduction	NOUN
cana-768	7	4	the	the	DET
cana-768	7	5	numerical	numerical	ADJ
cana-768	7	6	treatment	treatment	NOUN
cana-768	7	7	of	of	ADP
cana-768	7	8	a	a	DET
cana-768	7	9	singularly	singularly	ADV
cana-768	7	10	perturbed	perturb	VERB
cana-768	7	11	delay	delay	NOUN
cana-768	7	12	differential	differential	ADJ
cana-768	7	13	equations	equation	NOUN
cana-768	7	14	generated	generate	VERB
cana-768	7	15	lots	lot	NOUN
cana-768	7	16	of	of	ADP
cana-768	7	17	interest	interest	NOUN
cana-768	7	18	in	in	ADP
cana-768	7	19	the	the	DET
cana-768	7	20	recent	recent	ADJ
cana-768	7	21	years	year	NOUN
cana-768	7	22	due	due	ADP
cana-768	7	23	to	to	ADP
cana-768	7	24	applicability	applicability	NOUN
cana-768	7	25	these	these	DET
cana-768	7	26	families	family	NOUN
cana-768	7	27	of	of	ADP
cana-768	7	28	equations	equation	NOUN
cana-768	7	29	in	in	ADP
cana-768	7	30	the	the	DET
cana-768	7	31	process	process	NOUN
cana-768	7	32	of	of	ADP
cana-768	7	33	transforming	transform	VERB
cana-768	7	34	a	a	DET
cana-768	7	35	real	real	ADJ
cana-768	7	36	life	life	NOUN
cana-768	7	37	situation	situation	NOUN
cana-768	7	38	into	into	ADP
cana-768	7	39	a	a	DET
cana-768	7	40	mathematical	mathematical	ADJ
cana-768	7	41	form	form	NOUN
cana-768	7	42	for	for	ADP
cana-768	7	43	numerous	numerous	ADJ
cana-768	7	44	disciplines	discipline	NOUN
cana-768	7	45	of	of	ADP
cana-768	7	46	science	science	NOUN
cana-768	7	47	and	and	CCONJ
cana-768	7	48	technology	technology	NOUN
cana-768	7	49	.	.	PUNCT
cana-768	8	1	an	an	DET
cana-768	8	2	ordinary	ordinary	ADJ
cana-768	8	3	differential	differential	ADJ
cana-768	8	4	equation	equation	NOUN
cana-768	8	5	having	have	VERB
cana-768	8	6	a	a	DET
cana-768	8	7	delay	delay	NOUN
cana-768	8	8	term	term	NOUN
cana-768	8	9	and	and	CCONJ
cana-768	8	10	multiplied	multiply	VERB
cana-768	8	11	the	the	DET
cana-768	8	12	highest	high	ADJ
cana-768	8	13	order	order	NOUN
cana-768	8	14	derivative	derivative	NOUN
cana-768	8	15	by	by	ADP
cana-768	8	16	a	a	DET
cana-768	8	17	small	small	ADJ
cana-768	8	18	positive	positive	ADJ
cana-768	8	19	parameter	parameter	NOUN
cana-768	8	20	,	,	PUNCT
cana-768	8	21	known	know	VERB
cana-768	8	22	as	as	ADP
cana-768	8	23	a	a	DET
cana-768	8	24	singularly	singularly	ADV
cana-768	8	25	perturbed	perturb	VERB
cana-768	8	26	delay	delay	NOUN
cana-768	8	27	differential	differential	ADJ
cana-768	8	28	equation	equation	NOUN
cana-768	8	29	.	.	PUNCT
cana-768	9	1	like	like	INTJ
cana-768	9	2	in	in	ADP
cana-768	9	3	[	[	X
cana-768	9	4	8	8	NUM
cana-768	9	5	]	]	X
cana-768	9	6	lange	lange	NOUN
cana-768	9	7	,	,	PUNCT
cana-768	9	8	c.g	c.g	PROPN
cana-768	9	9	.	.	PROPN
cana-768	9	10	and	and	CCONJ
cana-768	9	11	miura	miura	PROPN
cana-768	9	12	,	,	PUNCT
cana-768	9	13	r.m	r.m	PROPN
cana-768	9	14	.	.	PROPN
cana-768	9	15	had	have	AUX
cana-768	9	16	studied	study	VERB
cana-768	9	17	initial	initial	ADJ
cana-768	9	18	exit	exit	NOUN
cana-768	9	19	time	time	NOUN
cana-768	9	20	problem	problem	NOUN
cana-768	9	21	with	with	ADP
cana-768	9	22	the	the	DET
cana-768	9	23	modelling	modelling	NOUN
cana-768	9	24	of	of	ADP
cana-768	9	25	neuronal	neuronal	ADJ
cana-768	9	26	variability	variability	NOUN
cana-768	9	27	's	's	PART
cana-768	9	28	activation	activation	NOUN
cana-768	9	29	.	.	PUNCT
cana-768	10	1	in	in	ADP
cana-768	10	2	[	[	X
cana-768	10	3	1	1	NUM
cana-768	10	4	]	]	X
cana-768	10	5	derstine	derstine	NOUN
cana-768	10	6	,	,	PUNCT
cana-768	10	7	m.w	m.w	PROPN
cana-768	10	8	studied	study	VERB
cana-768	10	9	problems	problem	NOUN
cana-768	10	10	related	relate	VERB
cana-768	10	11	to	to	ADP
cana-768	10	12	variational	variational	ADJ
cana-768	10	13	and	and	CCONJ
cana-768	10	14	bistable	bistable	ADJ
cana-768	10	15	devices	device	NOUN
cana-768	10	16	problem	problem	NOUN
cana-768	10	17	in	in	ADP
cana-768	10	18	control	control	NOUN
cana-768	10	19	theory	theory	NOUN
cana-768	10	20	.	.	PUNCT
cana-768	11	1	kadalbajoo	kadalbajoo	PROPN
cana-768	11	2	et	et	PROPN
cana-768	11	3	al	al	PROPN
cana-768	11	4	.	.	PUNCT
cana-768	12	1	[	[	X
cana-768	12	2	3	3	NUM
cana-768	12	3	,	,	PUNCT
cana-768	12	4	4	4	NUM
cana-768	12	5	]	]	PUNCT
cana-768	12	6	proposed	propose	VERB
cana-768	12	7	some	some	DET
cana-768	12	8	numerical	numerical	ADJ
cana-768	12	9	approximations	approximation	NOUN
cana-768	12	10	for	for	ADP
cana-768	12	11	a	a	DET
cana-768	12	12	singularly	singularly	ADV
cana-768	12	13	perturbed	perturb	VERB
cana-768	12	14	differential	differential	ADJ
cana-768	12	15	-	-	PUNCT
cana-768	12	16	difference	difference	NOUN
cana-768	12	17	equation	equation	NOUN
cana-768	12	18	containing	contain	VERB
cana-768	12	19	a	a	DET
cana-768	12	20	delay	delay	NOUN
cana-768	12	21	term	term	NOUN
cana-768	12	22	.	.	PUNCT
cana-768	13	1	various	various	ADJ
cana-768	13	2	numerical	numerical	ADJ
cana-768	13	3	approaches	approach	NOUN
cana-768	13	4	were	be	AUX
cana-768	13	5	proposed	propose	VERB
cana-768	13	6	for	for	ADP
cana-768	13	7	differential	differential	ADJ
cana-768	13	8	equations	equation	NOUN
cana-768	13	9	with	with	ADP
cana-768	13	10	negative	negative	ADJ
cana-768	13	11	shifts	shift	NOUN
cana-768	13	12	,	,	PUNCT
cana-768	13	13	mixed	mixed	ADJ
cana-768	13	14	shifts	shift	NOUN
cana-768	13	15	and	and	CCONJ
cana-768	13	16	some	some	DET
cana-768	13	17	schemes	scheme	NOUN
cana-768	13	18	with	with	ADP
cana-768	13	19	fitted	fit	VERB
cana-768	13	20	parameters	parameter	NOUN
cana-768	13	21	by	by	ADP
cana-768	13	22	d.kumara	d.kumara	NOUN
cana-768	13	23	swamy	swamy	PROPN
cana-768	13	24	et	et	PROPN
cana-768	13	25	al	al	PROPN
cana-768	14	1	[	[	X
cana-768	14	2	7,13	7,13	PROPN
cana-768	14	3	,	,	PUNCT
cana-768	14	4	14,15,19].an	14,15,19].an	NUM
cana-768	14	5	integration	integration	NOUN
cana-768	14	6	method	method	NOUN
cana-768	14	7	based	base	VERB
cana-768	14	8	on	on	ADP
cana-768	14	9	numerical	numerical	ADJ
cana-768	14	10	approach	approach	NOUN
cana-768	14	11	was	be	AUX
cana-768	14	12	proposed	propose	VERB
cana-768	14	13	by	by	ADP
cana-768	14	14	y.n	y.n	PROPN
cana-768	14	15	reddy	reddy	PROPN
cana-768	14	16	et	et	PROPN
cana-768	14	17	al.[12	al.[12	PROPN
cana-768	14	18	]	]	PUNCT
cana-768	14	19	for	for	ADP
cana-768	14	20	a	a	DET
cana-768	14	21	singularly	singularly	ADV
cana-768	14	22	perturbed	perturb	VERB
cana-768	14	23	differential	differential	ADJ
cana-768	14	24	equation	equation	NOUN
cana-768	14	25	having	have	VERB
cana-768	14	26	a	a	DET
cana-768	14	27	negative	negative	ADJ
cana-768	14	28	shift	shift	NOUN
cana-768	14	29	.	.	PUNCT
cana-768	15	1	mccartin	mccartin	NOUN
cana-768	15	2	introduced	introduce	VERB
cana-768	15	3	the	the	DET
cana-768	15	4	concept	concept	NOUN
cana-768	15	5	of	of	ADP
cana-768	15	6	exponential	exponential	PROPN
cana-768	15	7	b	b	PROPN
cana-768	15	8	spline[9].he	spline[9].he	PROPN
cana-768	15	9	also	also	ADV
cana-768	15	10	described	describe	VERB
cana-768	15	11	convergent	convergent	NOUN
cana-768	15	12	rates	rate	NOUN
cana-768	15	13	and	and	CCONJ
cana-768	15	14	extremal	extremal	ADJ
cana-768	15	15	features	feature	NOUN
cana-768	15	16	of	of	ADP
cana-768	15	17	the	the	DET
cana-768	15	18	exponential	exponential	ADJ
cana-768	15	19	spline	spline	NOUN
cana-768	15	20	approximation	approximation	NOUN
cana-768	15	21	and	and	CCONJ
cana-768	15	22	also	also	ADV
cana-768	15	23	developed	develop	VERB
cana-768	15	24	cardinal	cardinal	ADJ
cana-768	15	25	bases	basis	NOUN
cana-768	15	26	and	and	CCONJ
cana-768	15	27	b	b	X
cana-768	15	28	-	-	PUNCT
cana-768	15	29	spline	spline	NOUN
cana-768	15	30	bases	basis	NOUN
cana-768	15	31	for	for	ADP
cana-768	15	32	the	the	DET
cana-768	15	33	space	space	NOUN
cana-768	15	34	of	of	ADP
cana-768	15	35	exponential	exponential	ADJ
cana-768	15	36	splines	spline	NOUN
cana-768	15	37	.	.	PUNCT
cana-768	16	1	reza	reza	PROPN
cana-768	16	2	mohammadi[10	mohammadi[10	PROPN
cana-768	16	3	]	]	PUNCT
cana-768	16	4	proposed	propose	VERB
cana-768	16	5	a	a	DET
cana-768	16	6	method	method	NOUN
cana-768	16	7	which	which	PRON
cana-768	16	8	is	be	AUX
cana-768	16	9	based	base	VERB
cana-768	16	10	on	on	ADP
cana-768	16	11	exponential	exponential	ADJ
cana-768	16	12	b	b	NOUN
cana-768	16	13	-	-	NOUN
cana-768	16	14	spline	spline	NOUN
cana-768	16	15	to	to	PART
cana-768	16	16	approximate	approximate	VERB
cana-768	16	17	the	the	DET
cana-768	16	18	soluton	soluton	NOUN
cana-768	16	19	of	of	ADP
cana-768	16	20	partial	partial	ADJ
cana-768	16	21	differential	differential	ADJ
cana-768	16	22	equation	equation	NOUN
cana-768	16	23	of	of	ADP
cana-768	16	24	convectiondiffusion	convectiondiffusion	NOUN
cana-768	16	25	kind	kind	ADV
cana-768	16	26	having	have	VERB
cana-768	16	27	boundary	boundary	ADJ
cana-768	16	28	conditions	condition	NOUN
cana-768	16	29	of	of	ADP
cana-768	16	30	dirichlet	dirichlet	PROPN
cana-768	16	31	’s	’s	PART
cana-768	16	32	type	type	NOUN
cana-768	16	33	.	.	PUNCT
cana-768	17	1	von	von	PROPN
cana-768	17	2	neumann	neumann	PROPN
cana-768	17	3	method	method	PROPN
cana-768	17	4	was	be	AUX
cana-768	17	5	used	use	VERB
cana-768	17	6	to	to	PART
cana-768	17	7	prove	prove	VERB
cana-768	17	8	the	the	DET
cana-768	17	9	stability	stability	NOUN
cana-768	17	10	of	of	ADP
cana-768	17	11	the	the	DET
cana-768	17	12	method	method	NOUN
cana-768	17	13	.	.	PUNCT
cana-768	18	1	a	a	DET
cana-768	18	2	numerical	numerical	ADJ
cana-768	18	3	scheme	scheme	NOUN
cana-768	18	4	for	for	ADP
cana-768	18	5	a	a	DET
cana-768	18	6	family	family	NOUN
cana-768	18	7	of	of	ADP
cana-768	18	8	reaction	reaction	NOUN
cana-768	18	9	-	-	PUNCT
cana-768	18	10	diffusion	diffusion	NOUN
cana-768	18	11	equations	equation	NOUN
cana-768	18	12	was	be	AUX
cana-768	18	13	proposed	propose	VERB
cana-768	18	14	by	by	ADP
cana-768	18	15	a.	a.	PROPN
cana-768	18	16	s.	s.	PROPN
cana-768	18	17	v.	v.	PROPN
cana-768	18	18	ravi	ravi	PROPN
cana-768	18	19	kanth	kanth	PROPN
cana-768	18	20	et	et	PROPN
cana-768	18	21	al.[6	al.[6	PROPN
cana-768	18	22	]	]	PUNCT
cana-768	18	23	based	base	VERB
cana-768	18	24	on	on	ADP
cana-768	18	25	exponential	exponential	ADJ
cana-768	18	26	b	b	NOUN
cana-768	18	27	-	-	NOUN
cana-768	18	28	spline	spline	NOUN
cana-768	18	29	for	for	ADP
cana-768	18	30	space	space	NOUN
cana-768	18	31	derivative	derivative	NOUN
cana-768	18	32	.	.	PUNCT
cana-768	19	1	in	in	ADP
cana-768	19	2	recent	recent	ADJ
cana-768	19	3	years	year	NOUN
cana-768	19	4	,	,	PUNCT
cana-768	19	5	studies	study	NOUN
cana-768	19	6	like	like	ADP
cana-768	19	7	wavelets	wavelet	NOUN
cana-768	19	8	theory	theory	NOUN
cana-768	19	9	,	,	PUNCT
cana-768	19	10	medical	medical	ADJ
cana-768	19	11	imaging	imaging	NOUN
cana-768	19	12	,	,	PUNCT
cana-768	19	13	and	and	CCONJ
cana-768	19	14	image	image	NOUN
cana-768	19	15	processing	processing	NOUN
cana-768	19	16	have	have	AUX
cana-768	19	17	all	all	PRON
cana-768	19	18	greatly	greatly	ADV
cana-768	19	19	benefited	benefit	VERB
cana-768	19	20	from	from	ADP
cana-768	19	21	the	the	DET
cana-768	19	22	application	application	NOUN
cana-768	19	23	of	of	ADP
cana-768	19	24	exponential	exponential	ADJ
cana-768	19	25	splines	spline	NOUN
cana-768	19	26	.	.	PUNCT
cana-768	20	1	sinuk	sinuk	PROPN
cana-768	20	2	kang[5],the	kang[5],the	DET
cana-768	20	3	author	author	NOUN
cana-768	20	4	came	come	VERB
cana-768	20	5	up	up	ADP
cana-768	20	6	with	with	ADP
cana-768	20	7	a	a	DET
cana-768	20	8	communications	communication	NOUN
cana-768	20	9	on	on	ADP
cana-768	20	10	applied	apply	VERB
cana-768	20	11	nonlinear	nonlinear	ADJ
cana-768	20	12	analysis	analysis	NOUN
cana-768	20	13	issn	issn	NOUN
cana-768	20	14	:	:	PUNCT
cana-768	20	15	1074	1074	NUM
cana-768	20	16	-	-	PUNCT
cana-768	20	17	133x	133x	NUM
cana-768	20	18	vol	vol	NOUN
cana-768	20	19	31	31	NUM
cana-768	20	20	no	no	NOUN
cana-768	20	21	.	.	PUNCT
cana-768	21	1	3s	3s	NUM
cana-768	21	2	(	(	PUNCT
cana-768	21	3	2024	2024	NUM
cana-768	21	4	)	)	PUNCT
cana-768	21	5	313	313	NUM
cana-768	21	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	21	7	technique	technique	NOUN
cana-768	21	8	for	for	ADP
cana-768	21	9	the	the	DET
cana-768	21	10	cardinal	cardinal	ADJ
cana-768	21	11	exponential	exponential	ADJ
cana-768	21	12	splines	spline	NOUN
cana-768	21	13	’s	’s	PART
cana-768	21	14	space	space	NOUN
cana-768	21	15	by	by	ADP
cana-768	21	16	using	use	VERB
cana-768	21	17	exponential	exponential	ADJ
cana-768	21	18	b	b	NOUN
cana-768	21	19	-	-	NOUN
cana-768	21	20	spline	spline	NOUN
cana-768	21	21	as	as	ADP
cana-768	21	22	a	a	DET
cana-768	21	23	reisz	reisz	ADJ
cana-768	21	24	basis	basis	NOUN
cana-768	21	25	.	.	PUNCT
cana-768	22	1	w.	w.	PROPN
cana-768	22	2	k.	k.	PROPN
cana-768	22	3	zahra	zahra	PROPN
cana-768	22	4	et	et	PROPN
cana-768	22	5	al	al	PROPN
cana-768	22	6	.	.	PUNCT
cana-768	23	1	[	[	X
cana-768	23	2	18	18	NUM
cana-768	23	3	]	]	PUNCT
cana-768	23	4	developed	develop	VERB
cana-768	23	5	a	a	DET
cana-768	23	6	method	method	NOUN
cana-768	23	7	that	that	PRON
cana-768	23	8	attempted	attempt	VERB
cana-768	23	9	to	to	PART
cana-768	23	10	solve	solve	VERB
cana-768	23	11	a	a	DET
cana-768	23	12	singularly	singularly	ADV
cana-768	23	13	perturbed	perturb	VERB
cana-768	23	14	boundary	boundary	ADJ
cana-768	23	15	value	value	NOUN
cana-768	23	16	problem	problem	NOUN
cana-768	23	17	with	with	ADP
cana-768	23	18	a	a	DET
cana-768	23	19	small	small	ADJ
cana-768	23	20	unknown	unknown	ADJ
cana-768	23	21	perturbation	perturbation	NOUN
cana-768	23	22	parameter	parameter	NOUN
cana-768	23	23	using	use	VERB
cana-768	23	24	exponential	exponential	ADJ
cana-768	23	25	splines	spline	NOUN
cana-768	23	26	and	and	CCONJ
cana-768	23	27	shishkin	shishkin	NOUN
cana-768	23	28	mesh	mesh	NOUN
cana-768	23	29	discretization	discretization	NOUN
cana-768	23	30	.chandra	.chandra	ADP
cana-768	23	31	sekhara	sekhara	PROPN
cana-768	23	32	rao	rao	PROPN
cana-768	23	33	,	,	PUNCT
cana-768	23	34	mukesh	mukesh	PROPN
cana-768	23	35	kumar[11	kumar[11	PROPN
cana-768	23	36	]	]	PUNCT
cana-768	23	37	proposed	propose	VERB
cana-768	23	38	a	a	DET
cana-768	23	39	method	method	NOUN
cana-768	23	40	for	for	SCONJ
cana-768	23	41	a	a	DET
cana-768	23	42	self	self	NOUN
cana-768	23	43	adjoint	adjoint	NOUN
cana-768	23	44	singularly	singularly	ADV
cana-768	23	45	perturbed	perturb	VERB
cana-768	23	46	boundary	boundary	ADJ
cana-768	23	47	value	value	NOUN
cana-768	23	48	problem	problem	NOUN
cana-768	23	49	based	base	VERB
cana-768	23	50	on	on	ADP
cana-768	23	51	the	the	DET
cana-768	23	52	exponential	exponential	ADJ
cana-768	23	53	b	b	PROPN
cana-768	23	54	-	-	PUNCT
cana-768	23	55	spline	spline	NOUN
cana-768	23	56	collocation	collocation	NOUN
cana-768	23	57	approach	approach	NOUN
cana-768	23	58	.	.	PUNCT
cana-768	24	1	we	we	PRON
cana-768	24	2	have	have	AUX
cana-768	24	3	implemented	implement	VERB
cana-768	24	4	exponential	exponential	ADJ
cana-768	24	5	b	b	NOUN
cana-768	24	6	-	-	PUNCT
cana-768	24	7	spline	spline	NOUN
cana-768	24	8	approach	approach	NOUN
cana-768	24	9	to	to	PART
cana-768	24	10	approximate	approximate	VERB
cana-768	24	11	the	the	DET
cana-768	24	12	solution	solution	NOUN
cana-768	24	13	of	of	ADP
cana-768	24	14	a	a	DET
cana-768	24	15	differential	differential	ADJ
cana-768	24	16	equation	equation	NOUN
cana-768	24	17	of	of	ADP
cana-768	24	18	second	second	ADJ
cana-768	24	19	order	order	NOUN
cana-768	24	20	with	with	ADP
cana-768	24	21	negative	negative	ADJ
cana-768	24	22	shift	shift	NOUN
cana-768	24	23	having	have	VERB
cana-768	24	24	a	a	DET
cana-768	24	25	boundary	boundary	NOUN
cana-768	24	26	with	with	ADP
cana-768	24	27	a	a	DET
cana-768	24	28	layer	layer	NOUN
cana-768	24	29	structure	structure	NOUN
cana-768	24	30	.	.	PUNCT
cana-768	25	1	we	we	PRON
cana-768	25	2	have	have	AUX
cana-768	25	3	discussed	discuss	VERB
cana-768	25	4	the	the	DET
cana-768	25	5	problem	problem	NOUN
cana-768	25	6	in	in	ADP
cana-768	25	7	section	section	NOUN
cana-768	25	8	2	2	NUM
cana-768	25	9	of	of	ADP
cana-768	25	10	this	this	DET
cana-768	25	11	paper	paper	NOUN
cana-768	25	12	.	.	PUNCT
cana-768	26	1	the	the	DET
cana-768	26	2	numerical	numerical	ADJ
cana-768	26	3	method	method	NOUN
cana-768	26	4	have	have	AUX
cana-768	26	5	been	be	AUX
cana-768	26	6	developed	develop	VERB
cana-768	26	7	in	in	ADP
cana-768	26	8	section	section	NOUN
cana-768	26	9	3	3	NUM
cana-768	26	10	and	and	CCONJ
cana-768	26	11	the	the	DET
cana-768	26	12	convergence	convergence	NOUN
cana-768	26	13	analysis	analysis	NOUN
cana-768	26	14	was	be	AUX
cana-768	26	15	performed	perform	VERB
cana-768	26	16	in	in	ADP
cana-768	26	17	section	section	NOUN
cana-768	26	18	4	4	NUM
cana-768	26	19	.	.	PUNCT
cana-768	27	1	the	the	DET
cana-768	27	2	effectiveness	effectiveness	NOUN
cana-768	27	3	of	of	ADP
cana-768	27	4	the	the	DET
cana-768	27	5	proposed	propose	VERB
cana-768	27	6	scheme	scheme	NOUN
cana-768	27	7	have	have	AUX
cana-768	27	8	been	be	AUX
cana-768	27	9	covered	cover	VERB
cana-768	27	10	in	in	ADP
cana-768	27	11	section	section	NOUN
cana-768	27	12	5	5	NUM
cana-768	27	13	.	.	NOUN
cana-768	27	14	2	2	NUM
cana-768	27	15	.	.	X
cana-768	27	16	objectives	objective	VERB
cana-768	27	17	the	the	DET
cana-768	27	18	main	main	ADJ
cana-768	27	19	objective	objective	NOUN
cana-768	27	20	of	of	ADP
cana-768	27	21	this	this	DET
cana-768	27	22	paper	paper	NOUN
cana-768	27	23	is	be	AUX
cana-768	27	24	to	to	PART
cana-768	27	25	implement	implement	VERB
cana-768	27	26	exponential	exponential	ADJ
cana-768	27	27	b	b	NOUN
cana-768	27	28	-	-	PUNCT
cana-768	27	29	spline	spline	NOUN
cana-768	27	30	method	method	NOUN
cana-768	27	31	on	on	ADP
cana-768	27	32	a	a	DET
cana-768	27	33	singularly	singularly	ADV
cana-768	27	34	perturbed	perturb	VERB
cana-768	27	35	delay	delay	NOUN
cana-768	27	36	differential	differential	ADJ
cana-768	27	37	equation	equation	NOUN
cana-768	27	38	to	to	PART
cana-768	27	39	approximate	approximate	VERB
cana-768	27	40	its	its	PRON
cana-768	27	41	solution	solution	NOUN
cana-768	27	42	.	.	PUNCT
cana-768	28	1	we	we	PRON
cana-768	28	2	discuss	discuss	VERB
cana-768	28	3	the	the	DET
cana-768	28	4	convergence	convergence	NOUN
cana-768	28	5	analysis	analysis	NOUN
cana-768	28	6	of	of	ADP
cana-768	28	7	the	the	DET
cana-768	28	8	proposed	propose	VERB
cana-768	28	9	method	method	NOUN
cana-768	28	10	.	.	PUNCT
cana-768	29	1	we	we	PRON
cana-768	29	2	consider	consider	VERB
cana-768	29	3	the	the	DET
cana-768	29	4	following	follow	VERB
cana-768	29	5	linear	linear	ADJ
cana-768	29	6	differential	differential	ADJ
cana-768	29	7	equation	equation	NOUN
cana-768	29	8	of	of	ADP
cana-768	29	9	second	second	ADJ
cana-768	29	10	order	order	NOUN
cana-768	29	11	with	with	ADP
cana-768	29	12	negative	negative	ADJ
cana-768	29	13	shift	shift	NOUN
cana-768	29	14	to	to	PART
cana-768	29	15	implement	implement	VERB
cana-768	29	16	the	the	DET
cana-768	29	17	proposed	propose	VERB
cana-768	29	18	method	method	NOUN
cana-768	29	19	,	,	PUNCT
cana-768	29	20	휀𝑢′′(ȶ	휀𝑢′′(ȶ	NOUN
cana-768	29	21	)	)	PUNCT
cana-768	29	22	+	+	CCONJ
cana-768	29	23	𝑚(ȶ)𝑢′(ȶ	𝑚(ȶ)𝑢′(ȶ	PROPN
cana-768	29	24	−	−	ADP
cana-768	29	25	𝛿	𝛿	NOUN
cana-768	29	26	)	)	PUNCT
cana-768	29	27	+	+	NUM
cana-768	29	28	𝑛(ȶ)𝑢(ȶ	𝑛(ȶ)𝑢(ȶ	NOUN
cana-768	29	29	)	)	PUNCT
cana-768	29	30	=	=	SYM
cana-768	29	31	0	0	NUM
cana-768	29	32	,	,	PUNCT
cana-768	29	33	0	0	NUM
cana-768	29	34	≤	≤	NUM
cana-768	30	1	ȶ	ȶ	X
cana-768	30	2	≤	≤	NUM
cana-768	30	3	1	1	NUM
cana-768	30	4	,	,	PUNCT
cana-768	30	5	(	(	PUNCT
cana-768	30	6	2.1	2.1	NUM
cana-768	30	7	)	)	PUNCT
cana-768	30	8	with	with	ADP
cana-768	30	9	imposed	impose	VERB
cana-768	30	10	boundary	boundary	ADJ
cana-768	30	11	conditions	condition	NOUN
cana-768	30	12	,	,	PUNCT
cana-768	30	13	𝓊(ȶ	𝓊(ȶ	NUM
cana-768	30	14	)	)	PUNCT
cana-768	30	15	=	=	SYM
cana-768	30	16	𝜑	𝜑	NOUN
cana-768	30	17	,	,	PUNCT
cana-768	30	18	−𝛿	−𝛿	NOUN
cana-768	30	19	≤	≤	NUM
cana-768	30	20	ȶ	ȶ	X
cana-768	30	21	≤	≤	NUM
cana-768	30	22	0	0	NUM
cana-768	30	23	and	and	CCONJ
cana-768	30	24	𝓊(1	𝓊(1	NOUN
cana-768	30	25	)	)	PUNCT
cana-768	30	26	=	=	SYM
cana-768	30	27	𝜓	𝜓	X
cana-768	30	28	(	(	PUNCT
cana-768	30	29	2.2	2.2	NUM
cana-768	30	30	)	)	PUNCT
cana-768	30	31	where	where	SCONJ
cana-768	30	32	휀	휀	NOUN
cana-768	30	33	and	and	CCONJ
cana-768	30	34	𝛿	𝛿	PROPN
cana-768	30	35	are	be	AUX
cana-768	30	36	perturbation	perturbation	NOUN
cana-768	30	37	parameter	parameter	NOUN
cana-768	30	38	and	and	CCONJ
cana-768	30	39	delay	delay	NOUN
cana-768	30	40	argument	argument	NOUN
cana-768	30	41	respectively	respectively	ADV
cana-768	30	42	such	such	ADJ
cana-768	30	43	that	that	SCONJ
cana-768	30	44	,	,	PUNCT
cana-768	30	45	0	0	PUNCT
cana-768	30	46	<	<	X
cana-768	30	47	휀	휀	X
cana-768	30	48	≪	≪	ADJ
cana-768	30	49	1	1	NUM
cana-768	30	50	,	,	PUNCT
cana-768	30	51	0	0	NUM
cana-768	30	52	<	<	X
cana-768	30	53	𝛿	𝛿	X
cana-768	30	54	<	<	X
cana-768	30	55	1	1	NUM
cana-768	30	56	and	and	CCONJ
cana-768	30	57	𝛿	𝛿	ADJ
cana-768	30	58	=	=	ADJ
cana-768	30	59	𝑜(휀	𝑜(휀	NOUN
cana-768	30	60	)	)	PUNCT
cana-768	30	61	.	.	PUNCT
cana-768	31	1	furthermore	furthermore	ADV
cana-768	31	2	,	,	PUNCT
cana-768	31	3	𝑚(ȶ	𝑚(ȶ	NUM
cana-768	31	4	)	)	PUNCT
cana-768	31	5	and	and	CCONJ
cana-768	31	6	𝑛(ȶ	𝑛(ȶ	VERB
cana-768	31	7	)	)	PUNCT
cana-768	31	8	are	be	AUX
cana-768	31	9	functions	function	NOUN
cana-768	31	10	such	such	ADJ
cana-768	31	11	that	that	SCONJ
cana-768	31	12	they	they	PRON
cana-768	31	13	are	be	AUX
cana-768	31	14	𝑐∞	𝑐∞	PROPN
cana-768	31	15	in	in	ADP
cana-768	31	16	the	the	DET
cana-768	31	17	open	open	ADJ
cana-768	31	18	interval	interval	NOUN
cana-768	31	19	(	(	PUNCT
cana-768	31	20	0,1	0,1	NOUN
cana-768	31	21	)	)	PUNCT
cana-768	31	22	and	and	CCONJ
cana-768	31	23	𝜑	𝜑	NOUN
cana-768	31	24	,	,	PUNCT
cana-768	31	25	𝜓	𝜓	PROPN
cana-768	31	26	are	be	AUX
cana-768	31	27	constants	constant	NOUN
cana-768	31	28	.	.	PUNCT
cana-768	32	1	let	let	VERB
cana-768	32	2	us	we	PRON
cana-768	32	3	assume	assume	VERB
cana-768	32	4	𝑚(ȶ	𝑚(ȶ	NUM
cana-768	32	5	)	)	PUNCT
cana-768	32	6	≥	≥	NOUN
cana-768	32	7	ռ	ռ	X
cana-768	32	8	>	>	X
cana-768	32	9	0	0	PUNCT
cana-768	33	1	throughout	throughout	ADP
cana-768	33	2	the	the	DET
cana-768	33	3	interval	interval	NOUN
cana-768	33	4	[	[	X
cana-768	33	5	0	0	NUM
cana-768	33	6	,	,	PUNCT
cana-768	33	7	1],where	1],where	NUM
cana-768	33	8	,	,	PUNCT
cana-768	33	9	ռ	ռ	PRON
cana-768	33	10	is	be	AUX
cana-768	33	11	a	a	DET
cana-768	33	12	positive	positive	ADJ
cana-768	33	13	constant	constant	ADJ
cana-768	33	14	.the	.the	DET
cana-768	33	15	boundary	boundary	ADJ
cana-768	33	16	layer	layer	NOUN
cana-768	33	17	will	will	AUX
cana-768	33	18	be	be	AUX
cana-768	33	19	in	in	ADP
cana-768	33	20	the	the	DET
cana-768	33	21	neighborhood	neighborhood	NOUN
cana-768	33	22	of	of	ADP
cana-768	33	23	ȶ	ȶ	X
cana-768	34	1	=	=	PUNCT
cana-768	34	2	0.again	0.again	NUM
cana-768	34	3	assuming	assume	VERB
cana-768	34	4	𝑚(ȶ	𝑚(ȶ	NUM
cana-768	34	5	)	)	PUNCT
cana-768	34	6	≤	≤	PUNCT
cana-768	34	7	ռ	ռ	X
cana-768	34	8	<	<	X
cana-768	34	9	0	0	PROPN
cana-768	34	10	throughout	throughout	ADP
cana-768	34	11	the	the	DET
cana-768	34	12	interval	interval	NOUN
cana-768	34	13	[	[	X
cana-768	34	14	0	0	NUM
cana-768	34	15	,	,	PUNCT
cana-768	34	16	1	1	NUM
cana-768	34	17	]	]	PUNCT
cana-768	34	18	,	,	PUNCT
cana-768	34	19	where	where	SCONJ
cana-768	34	20	,	,	PUNCT
cana-768	34	21	ռ	ռ	PROPN
cana-768	34	22	is	be	AUX
cana-768	34	23	a	a	DET
cana-768	34	24	negative	negative	ADJ
cana-768	34	25	constant.the	constant.the	DET
cana-768	34	26	boundary	boundary	ADJ
cana-768	34	27	layer	layer	NOUN
cana-768	34	28	will	will	AUX
cana-768	34	29	be	be	AUX
cana-768	34	30	in	in	ADP
cana-768	34	31	the	the	DET
cana-768	34	32	neighborhood	neighborhood	NOUN
cana-768	34	33	of	of	ADP
cana-768	34	34	ȶ	ȶ	PROPN
cana-768	34	35	=	=	SYM
cana-768	34	36	1	1	X
cana-768	34	37	.	.	X
cana-768	34	38	taylor	taylor	PROPN
cana-768	34	39	's	's	PART
cana-768	34	40	series	series	NOUN
cana-768	34	41	expansion	expansion	NOUN
cana-768	34	42	yields	yield	NOUN
cana-768	34	43	,	,	PUNCT
cana-768	34	44	𝓊′(ȶ	𝓊′(ȶ	PROPN
cana-768	35	1	−	−	NUM
cana-768	35	2	𝛿	𝛿	ADJ
cana-768	35	3	)	)	PUNCT
cana-768	35	4	≈	≈	PROPN
cana-768	35	5	𝓊′(ȶ	𝓊′(ȶ	PROPN
cana-768	35	6	)	)	PUNCT
cana-768	35	7	−	−	PROPN
cana-768	35	8	𝛿𝓊′′(ȶ	𝛿𝓊′′(ȶ	NOUN
cana-768	35	9	)	)	PUNCT
cana-768	35	10	(	(	PUNCT
cana-768	35	11	2.3	2.3	NUM
cana-768	35	12	)	)	PUNCT
cana-768	35	13	using	use	VERB
cana-768	35	14	equation	equation	NOUN
cana-768	35	15	(	(	PUNCT
cana-768	35	16	2.3	2.3	NUM
cana-768	35	17	)	)	PUNCT
cana-768	35	18	in	in	ADP
cana-768	35	19	equation	equation	NOUN
cana-768	35	20	(	(	PUNCT
cana-768	35	21	2.1	2.1	NUM
cana-768	35	22	)	)	PUNCT
cana-768	35	23	,	,	PUNCT
cana-768	35	24	−휀𝓊′′(ȶ	−휀𝓊′′(ȶ	NOUN
cana-768	35	25	)	)	PUNCT
cana-768	35	26	+	+	PUNCT
cana-768	35	27	⨍(ȶ)𝓊′(ȶ	⨍(ȶ)𝓊′(ȶ	ADJ
cana-768	35	28	)	)	PUNCT
cana-768	35	29	+	+	NOUN
cana-768	35	30	𝑔(ȶ)𝓊(ȶ	𝑔(ȶ)𝓊(ȶ	X
cana-768	35	31	)	)	PUNCT
cana-768	35	32	=	=	SYM
cana-768	35	33	0	0	NUM
cana-768	35	34	(	(	PUNCT
cana-768	35	35	2.4	2.4	NUM
cana-768	35	36	)	)	PUNCT
cana-768	35	37	where	where	SCONJ
cana-768	35	38	,	,	PUNCT
cana-768	35	39	⨍(ȶ	⨍(ȶ	PROPN
cana-768	35	40	)	)	PUNCT
cana-768	35	41	=	=	SYM
cana-768	35	42	𝑚(ȶ	𝑚(ȶ	NUM
cana-768	35	43	)	)	PUNCT
cana-768	35	44	𝜎𝑚(ȶ)−1	𝜎𝑚(ȶ)−1	NOUN
cana-768	35	45	,	,	PUNCT
cana-768	35	46	𝑔(ȶ	𝑔(ȶ	X
cana-768	35	47	)	)	PUNCT
cana-768	35	48	=	=	PUNCT
cana-768	35	49	𝑛(ȶ	𝑛(ȶ	VERB
cana-768	35	50	)	)	PUNCT
cana-768	35	51	𝜎𝑚(ȶ)−1	𝜎𝑚(ȶ)−1	NOUN
cana-768	35	52	,	,	PUNCT
cana-768	35	53	𝜎	𝜎	PRON
cana-768	35	54	=	=	PUNCT
cana-768	35	55	𝛿	𝛿	ADJ
cana-768	35	56	with	with	ADP
cana-768	35	57	reference	reference	NOUN
cana-768	35	58	to	to	PART
cana-768	35	59	elsgolt	elsgolt	VERB
cana-768	35	60	’s	’s	PART
cana-768	35	61	and	and	CCONJ
cana-768	35	62	norkin	norkin	X
cana-768	35	63	[	[	X
cana-768	35	64	2	2	NUM
cana-768	35	65	]	]	X
cana-768	35	66	equation	equation	NOUN
cana-768	35	67	(	(	PUNCT
cana-768	35	68	2.4	2.4	NUM
cana-768	35	69	)	)	PUNCT
cana-768	35	70	thus	thus	ADV
cana-768	35	71	obtained	obtain	VERB
cana-768	35	72	from	from	ADP
cana-768	35	73	(	(	PUNCT
cana-768	35	74	2.1	2.1	NUM
cana-768	35	75	)	)	PUNCT
cana-768	35	76	is	be	AUX
cana-768	35	77	valid	valid	ADJ
cana-768	35	78	since	since	SCONJ
cana-768	35	79	,	,	PUNCT
cana-768	35	80	0	0	PUNCT
cana-768	35	81	<	<	X
cana-768	35	82	𝛿	𝛿	X
cana-768	35	83	<	<	X
cana-768	35	84	1	1	NUM
cana-768	35	85	communications	communication	NOUN
cana-768	35	86	on	on	ADP
cana-768	35	87	applied	apply	VERB
cana-768	35	88	nonlinear	nonlinear	ADJ
cana-768	35	89	analysis	analysis	NOUN
cana-768	35	90	issn	issn	NOUN
cana-768	35	91	:	:	PUNCT
cana-768	35	92	1074	1074	NUM
cana-768	35	93	-	-	PUNCT
cana-768	35	94	133x	133x	NUM
cana-768	35	95	vol	vol	NOUN
cana-768	35	96	31	31	NUM
cana-768	35	97	no	no	NOUN
cana-768	35	98	.	.	PUNCT
cana-768	36	1	3s	3s	NUM
cana-768	36	2	(	(	PUNCT
cana-768	36	3	2024	2024	NUM
cana-768	36	4	)	)	PUNCT
cana-768	36	5	314	314	NUM
cana-768	36	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	36	7	3	3	X
cana-768	36	8	.	.	PUNCT
cana-768	36	9	methods	method	NOUN
cana-768	36	10	let	let	VERB
cana-768	36	11	us	we	PRON
cana-768	36	12	consider	consider	VERB
cana-768	36	13	the	the	DET
cana-768	36	14	equation	equation	NOUN
cana-768	36	15	(	(	PUNCT
cana-768	36	16	2.4	2.4	NUM
cana-768	36	17	)	)	PUNCT
cana-768	36	18	,	,	PUNCT
cana-768	36	19	𝐿𝓊	𝐿𝓊	PROPN
cana-768	36	20	≡	≡	PROPN
cana-768	36	21	−휀𝓊′′(ȶ	−휀𝓊′′(ȶ	NOUN
cana-768	36	22	)	)	PUNCT
cana-768	36	23	+	+	CCONJ
cana-768	36	24	⨍(ȶ)𝓊′(ȶ	⨍(ȶ)𝓊′(ȶ	ADJ
cana-768	36	25	)	)	PUNCT
cana-768	37	1	+	+	NOUN
cana-768	37	2	𝑔(ȶ)𝓊(ȶ	𝑔(ȶ)𝓊(ȶ	X
cana-768	37	3	)	)	PUNCT
cana-768	37	4	=	=	SYM
cana-768	37	5	0	0	NUM
cana-768	37	6	,	,	PUNCT
cana-768	37	7	ȶ	ȶ	PROPN
cana-768	37	8	∈	∈	PROPN
cana-768	37	9	[	[	X
cana-768	37	10	0,1	0,1	NUM
cana-768	37	11	]	]	PUNCT
cana-768	37	12	(	(	PUNCT
cana-768	37	13	3.1	3.1	NUM
cana-768	37	14	)	)	PUNCT
cana-768	37	15	let	let	VERB
cana-768	37	16	ω	ω	NUM
cana-768	37	17	:	:	PUNCT
cana-768	37	18	0	0	NUM
cana-768	37	19	=	=	SYM
cana-768	37	20	ȶ0	ȶ0	PROPN
cana-768	37	21	<	<	X
cana-768	37	22	ȶ1	ȶ1	PROPN
cana-768	37	23	<	<	X
cana-768	37	24	⋯⋯	⋯⋯	PROPN
cana-768	37	25	<	<	X
cana-768	37	26	ȶռ	ȶռ	NOUN
cana-768	37	27	=	=	SYM
cana-768	37	28	1	1	NUM
cana-768	37	29	be	be	AUX
cana-768	37	30	partition	partition	NOUN
cana-768	37	31	on	on	ADP
cana-768	37	32	[	[	X
cana-768	37	33	0,1	0,1	NUM
cana-768	37	34	]	]	PUNCT
cana-768	37	35	with	with	ADP
cana-768	37	36	uniform	uniform	ADJ
cana-768	37	37	step	step	NOUN
cana-768	37	38	size	size	NOUN
cana-768	37	39	ɦ	ɦ	X
cana-768	37	40	=	=	NOUN
cana-768	37	41	1	1	NUM
cana-768	37	42	ռ	ռ	NOUN
cana-768	37	43	define	define	VERB
cana-768	37	44	the	the	DET
cana-768	37	45	exponential	exponential	ADJ
cana-768	37	46	b	b	NOUN
cana-768	37	47	-	-	PUNCT
cana-768	37	48	spline	spline	NOUN
cana-768	37	49	function	function	NOUN
cana-768	37	50	ᏸ𝒿(ȶ	ᏸ𝒿(ȶ	NOUN
cana-768	37	51	)	)	PUNCT
cana-768	37	52	,	,	PUNCT
cana-768	37	53	defined	define	VERB
cana-768	37	54	as	as	SCONJ
cana-768	37	55	follows	follow	VERB
cana-768	37	56	[	[	X
cana-768	37	57	9]ռ	9]ռ	NUM
cana-768	37	58	ᏸ𝒿(ȶ	ᏸ𝒿(ȶ	NOUN
cana-768	37	59	)	)	PUNCT
cana-768	38	1	=	=	PRON
cana-768	38	2	{	{	PUNCT
cana-768	38	3	ƙ5	ƙ5	PROPN
cana-768	38	4	[	[	X
cana-768	38	5	(	(	PUNCT
cana-768	38	6	ȶ𝒿−2	ȶ𝒿−2	PROPN
cana-768	38	7	−	−	PROPN
cana-768	38	8	ȶ	ȶ	PROPN
cana-768	38	9	)	)	PUNCT
cana-768	38	10	−	−	PROPN
cana-768	38	11	1	1	NUM
cana-768	38	12	ƥ	ƥ	PROPN
cana-768	38	13	sinh{ƥ(ȶ𝒿−2	sinh{ƥ(ȶ𝒿−2	PROPN
cana-768	38	14	−	−	PROPN
cana-768	38	15	ȶ	ȶ	NOUN
cana-768	38	16	)	)	PUNCT
cana-768	38	17	}	}	PUNCT
cana-768	38	18	]	]	PUNCT
cana-768	38	19	,	,	PUNCT
cana-768	38	20	ȶ	ȶ	PROPN
cana-768	38	21	∈	∈	PROPN
cana-768	39	1	[	[	X
cana-768	39	2	ȶ𝒿−2	ȶ𝒿−2	NOUN
cana-768	39	3	,	,	PUNCT
cana-768	39	4	ȶ𝒿−1	ȶ𝒿−1	PROPN
cana-768	39	5	]	]	PUNCT
cana-768	39	6	,	,	PUNCT
cana-768	39	7	ƙ1	ƙ1	VERB
cana-768	39	8	+	+	CCONJ
cana-768	39	9	ƙ2(ȶ𝒿	ƙ2(ȶ𝒿	NUM
cana-768	39	10	−	−	NOUN
cana-768	39	11	ȶ	ȶ	NOUN
cana-768	39	12	)	)	PUNCT
cana-768	40	1	+	+	CCONJ
cana-768	40	2	ƙ3𝑒	ƙ3𝑒	ADP
cana-768	40	3	ƥ(ȶ𝒿−ȶ	ƥ(ȶ𝒿−ȶ	NUM
cana-768	40	4	)	)	PUNCT
cana-768	41	1	+	+	NUM
cana-768	41	2	ƙ4𝑒	ƙ4𝑒	PROPN
cana-768	41	3	−ƥ(ȶ𝒿−ȶ	−ƥ(ȶ𝒿−ȶ	PROPN
cana-768	41	4	)	)	PUNCT
cana-768	41	5	,	,	PUNCT
cana-768	41	6	ȶ	ȶ	PROPN
cana-768	41	7	∈	∈	PROPN
cana-768	42	1	[	[	X
cana-768	42	2	ȶ𝒿−1	ȶ𝒿−1	PROPN
cana-768	42	3	,	,	PUNCT
cana-768	42	4	ȶ𝒿	ȶ𝒿	ADP
cana-768	42	5	]	]	X
cana-768	42	6	ƙ1	ƙ1	NOUN
cana-768	42	7	+	+	CCONJ
cana-768	42	8	ƙ2(ȶ	ƙ2(ȶ	NOUN
cana-768	42	9	−	−	NOUN
cana-768	43	1	ȶ𝒿	ȶ𝒿	NOUN
cana-768	43	2	)	)	PUNCT
cana-768	44	1	+	+	CCONJ
cana-768	44	2	ƙ3𝑒	ƙ3𝑒	PROPN
cana-768	44	3	ƥ(ȶ−ȶ𝒿	ƥ(ȶ−ȶ𝒿	NOUN
cana-768	44	4	)	)	PUNCT
cana-768	44	5	+	+	CCONJ
cana-768	44	6	ƙ4𝑒	ƙ4𝑒	PROPN
cana-768	44	7	−ƥ(ȶ−ȶ𝒿	−ƥ(ȶ−ȶ𝒿	NOUN
cana-768	44	8	)	)	PUNCT
cana-768	44	9	,	,	PUNCT
cana-768	44	10	ȶ	ȶ	PROPN
cana-768	44	11	∈	∈	PROPN
cana-768	45	1	[	[	X
cana-768	45	2	ȶ𝒿	ȶ𝒿	X
cana-768	45	3	,	,	PUNCT
cana-768	45	4	ȶ𝒿+1	ȶ𝒿+1	PROPN
cana-768	45	5	]	]	X
cana-768	45	6	,	,	PUNCT
cana-768	45	7	ƙ5	ƙ5	NOUN
cana-768	46	1	[	[	X
cana-768	46	2	(	(	PUNCT
cana-768	46	3	ȶ	ȶ	X
cana-768	46	4	−	−	PROPN
cana-768	46	5	ȶ𝒿+2	ȶ𝒿+2	NOUN
cana-768	46	6	)	)	PUNCT
cana-768	46	7	−	−	PROPN
cana-768	46	8	1	1	NUM
cana-768	46	9	ƥ	ƥ	DET
cana-768	46	10	sinh{ƥ(ȶ	sinh{ƥ(ȶ	NOUN
cana-768	46	11	−	−	NOUN
cana-768	46	12	ȶ𝒿+2	ȶ𝒿+2	NOUN
cana-768	46	13	)	)	PUNCT
cana-768	46	14	}	}	PUNCT
cana-768	46	15	]	]	PUNCT
cana-768	46	16	,	,	PUNCT
cana-768	46	17	ȶ	ȶ	PROPN
cana-768	46	18	∈	∈	PROPN
cana-768	47	1	[	[	X
cana-768	47	2	ȶ𝒿−2	ȶ𝒿−2	NOUN
cana-768	47	3	,	,	PUNCT
cana-768	47	4	ȶ𝒿−1	ȶ𝒿−1	PROPN
cana-768	47	5	]	]	PUNCT
cana-768	47	6	,	,	PUNCT
cana-768	47	7	0	0	PUNCT
cana-768	48	1	otherwise	otherwise	ADV
cana-768	48	2	where	where	SCONJ
cana-768	48	3	,	,	PUNCT
cana-768	48	4	ƙ1	ƙ1	NOUN
cana-768	48	5	=	=	SYM
cana-768	48	6	ƥɦ𝚌	ƥɦ𝚌	NOUN
cana-768	48	7	ƥɦ𝚌−𝚜	ƥɦ𝚌−𝚜	PROPN
cana-768	48	8	,	,	PUNCT
cana-768	48	9	ƙ2	ƙ2	NOUN
cana-768	48	10	=	=	SYM
cana-768	48	11	ƥ	ƥ	PRON
cana-768	48	12	2	2	NUM
cana-768	48	13	[	[	PUNCT
cana-768	48	14	𝚌(𝚌−1)+𝚜2	𝚌(𝚌−1)+𝚜2	PROPN
cana-768	48	15	(	(	PUNCT
cana-768	48	16	ƥɦ𝚌−𝚜)(1−𝚌	ƥɦ𝚌−𝚜)(1−𝚌	PROPN
cana-768	48	17	)	)	PUNCT
cana-768	48	18	]	]	PUNCT
cana-768	48	19	,	,	PUNCT
cana-768	48	20	ƙ3	ƙ3	NOUN
cana-768	48	21	=	=	NOUN
cana-768	48	22	1	1	NUM
cana-768	48	23	4	4	NUM
cana-768	48	24	[	[	PUNCT
cana-768	48	25	𝑒−ƥɦ(1−𝚌)+𝚜(𝑒−ƥɦ−1	𝑒−ƥɦ(1−𝚌)+𝚜(𝑒−ƥɦ−1	NOUN
cana-768	48	26	)	)	PUNCT
cana-768	48	27	(	(	PUNCT
cana-768	48	28	ƥɦ𝚌−𝚜)(1−𝚌	ƥɦ𝚌−𝚜)(1−𝚌	PROPN
cana-768	48	29	)	)	PUNCT
cana-768	48	30	]	]	PUNCT
cana-768	48	31	,	,	PUNCT
cana-768	48	32	ƙ4	ƙ4	PROPN
cana-768	48	33	=	=	PUNCT
cana-768	48	34	1	1	NUM
cana-768	48	35	4	4	NUM
cana-768	48	36	[	[	PUNCT
cana-768	48	37	𝑒ƥɦ(𝚌−1)+𝚜(𝑒ƥɦ−1	𝑒ƥɦ(𝚌−1)+𝚜(𝑒ƥɦ−1	NOUN
cana-768	48	38	)	)	PUNCT
cana-768	48	39	(	(	PUNCT
cana-768	48	40	ƥɦ𝚌−𝚜)(1−𝚌	ƥɦ𝚌−𝚜)(1−𝚌	PROPN
cana-768	48	41	)	)	PUNCT
cana-768	48	42	]	]	PUNCT
cana-768	48	43	,	,	PUNCT
cana-768	48	44	ƙ5	ƙ5	NOUN
cana-768	48	45	=	=	SYM
cana-768	48	46	ƥ	ƥ	DET
cana-768	48	47	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	48	48	)	)	PUNCT
cana-768	48	49	where	where	SCONJ
cana-768	48	50	𝚜	𝚜	NOUN
cana-768	48	51	=	=	SYM
cana-768	48	52	sinh(ƥɦ	sinh(ƥɦ	NOUN
cana-768	48	53	)	)	PUNCT
cana-768	48	54	,	,	PUNCT
cana-768	48	55	𝚌	𝚌	X
cana-768	48	56	=	=	SYM
cana-768	48	57	cosh(ƥɦ	cosh(ƥɦ	NOUN
cana-768	48	58	)	)	PUNCT
cana-768	48	59	and	and	CCONJ
cana-768	48	60	ƥ	ƥ	PRON
cana-768	48	61	is	be	AUX
cana-768	48	62	a	a	DET
cana-768	48	63	non	non	ADJ
cana-768	48	64	-	-	ADJ
cana-768	48	65	negative	negative	ADJ
cana-768	48	66	parameter	parameter	NOUN
cana-768	48	67	.	.	PUNCT
cana-768	49	1	let	let	AUX
cana-768	49	2	𝒰(ȶ	𝒰(ȶ	NUM
cana-768	49	3	)	)	PUNCT
cana-768	49	4	approximate	approximate	VERB
cana-768	49	5	the	the	DET
cana-768	49	6	exact	exact	ADJ
cana-768	49	7	solution	solution	NOUN
cana-768	49	8	𝓊(ȶ	𝓊(ȶ	NOUN
cana-768	49	9	)	)	PUNCT
cana-768	49	10	of	of	ADP
cana-768	49	11	the	the	DET
cana-768	49	12	equation	equation	NOUN
cana-768	49	13	(	(	PUNCT
cana-768	49	14	3.1),then	3.1),then	ADV
cana-768	49	15	we	we	PRON
cana-768	49	16	have	have	AUX
cana-768	49	17	,	,	PUNCT
cana-768	49	18	𝒰(ȶ	𝒰(ȶ	PRON
cana-768	49	19	)	)	PUNCT
cana-768	49	20	=	=	PUNCT
cana-768	50	1	∑	∑	ADP
cana-768	50	2	ɤ𝒿	ɤ𝒿	X
cana-768	50	3	ռ+1	ռ+1	ADV
cana-768	50	4	𝒿=−1	𝒿=−1	NUM
cana-768	50	5	ᏸ𝒿(ȶ	ᏸ𝒿(ȶ	NOUN
cana-768	50	6	)	)	PUNCT
cana-768	51	1	[	[	X
cana-768	51	2	mac	mac	NOUN
cana-768	51	3	-	-	PUNCT
cana-768	51	4	cartin	cartin	NOUN
cana-768	51	5	1991	1991	NUM
cana-768	51	6	]	]	PUNCT
cana-768	51	7	(	(	PUNCT
cana-768	51	8	3.2	3.2	NUM
cana-768	51	9	)	)	PUNCT
cana-768	51	10	now	now	ADV
cana-768	51	11	by	by	ADP
cana-768	51	12	using	use	VERB
cana-768	51	13	the	the	DET
cana-768	51	14	conditions	condition	NOUN
cana-768	51	15	(	(	PUNCT
cana-768	51	16	3.2	3.2	NUM
cana-768	51	17	)	)	PUNCT
cana-768	51	18	the	the	DET
cana-768	51	19	values	value	NOUN
cana-768	51	20	of	of	ADP
cana-768	51	21	the	the	DET
cana-768	51	22	unknowns	unknown	NOUN
cana-768	51	23	ɤ𝒿	ɤ𝒿	NOUN
cana-768	51	24	can	can	AUX
cana-768	51	25	be	be	AUX
cana-768	51	26	found	find	VERB
cana-768	51	27	.	.	PUNCT
cana-768	52	1	the	the	DET
cana-768	52	2	values	value	NOUN
cana-768	52	3	of	of	ADP
cana-768	52	4	the	the	DET
cana-768	52	5	𝒰(ȶ	𝒰(ȶ	NOUN
cana-768	52	6	)	)	PUNCT
cana-768	52	7	and	and	CCONJ
cana-768	52	8	its	its	PRON
cana-768	52	9	1st	1st	ADJ
cana-768	52	10	order	order	NOUN
cana-768	52	11	and	and	CCONJ
cana-768	52	12	2nd	2nd	ADJ
cana-768	52	13	order	order	NOUN
cana-768	52	14	derivatives	derivative	NOUN
cana-768	52	15	can	can	AUX
cana-768	52	16	be	be	AUX
cana-768	52	17	determined	determine	VERB
cana-768	52	18	at	at	ADP
cana-768	52	19	the	the	DET
cana-768	52	20	mesh	mesh	NOUN
cana-768	52	21	points	point	NOUN
cana-768	52	22	ȶ𝒿	ȶ𝒿	ADV
cana-768	52	23	as	as	SCONJ
cana-768	52	24	follows	follow	VERB
cana-768	52	25	:	:	PUNCT
cana-768	52	26	𝒰(ȶ𝒿	𝒰(ȶ𝒿	NOUN
cana-768	52	27	)	)	PUNCT
cana-768	52	28	=	=	SYM
cana-768	52	29	ɤ𝒿−1ᏸ𝒿−1(ȶ𝒿	ɤ𝒿−1ᏸ𝒿−1(ȶ𝒿	NOUN
cana-768	52	30	)	)	PUNCT
cana-768	53	1	+	+	CCONJ
cana-768	53	2	ɤ𝒿ᏸ𝒿(ȶ𝒿	ɤ𝒿ᏸ𝒿(ȶ𝒿	NOUN
cana-768	53	3	)	)	PUNCT
cana-768	54	1	+	+	NUM
cana-768	54	2	ɤ𝒿+1ᏸ𝒿+1(ȶ𝒿	ɤ𝒿+1ᏸ𝒿+1(ȶ𝒿	NOUN
cana-768	54	3	)	)	PUNCT
cana-768	54	4	𝒰(ȶ𝒿	𝒰(ȶ𝒿	NOUN
cana-768	54	5	)	)	PUNCT
cana-768	54	6	=	=	SYM
cana-768	54	7	𝚜−ƥɦ	𝚜−ƥɦ	NOUN
cana-768	54	8	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	54	9	)	)	PUNCT
cana-768	54	10	ɤ𝒿−1	ɤ𝒿−1	NOUN
cana-768	54	11	+	+	CCONJ
cana-768	54	12	ɤ𝒿	ɤ𝒿	PRON
cana-768	54	13	+	+	CCONJ
cana-768	54	14	𝚜−ƥɦ	𝚜−ƥɦ	PROPN
cana-768	54	15	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	54	16	)	)	PUNCT
cana-768	54	17	ɤ𝒿+1	ɤ𝒿+1	NOUN
cana-768	54	18	(	(	PUNCT
cana-768	54	19	3.3	3.3	NUM
cana-768	54	20	)	)	PUNCT
cana-768	54	21	𝒰′(ȶ𝒿	𝒰′(ȶ𝒿	NOUN
cana-768	54	22	)	)	PUNCT
cana-768	54	23	=	=	SYM
cana-768	54	24	ƥ(1−𝚌	ƥ(1−𝚌	NOUN
cana-768	54	25	)	)	PUNCT
cana-768	54	26	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	54	27	)	)	PUNCT
cana-768	54	28	ɤ𝒿−1	ɤ𝒿−1	NOUN
cana-768	54	29	−	−	PROPN
cana-768	54	30	ƥ(1−𝚌	ƥ(1−𝚌	NOUN
cana-768	54	31	)	)	PUNCT
cana-768	54	32	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	54	33	)	)	PUNCT
cana-768	54	34	ɤ𝒿+1	ɤ𝒿+1	PROPN
cana-768	54	35	(	(	PUNCT
cana-768	54	36	3.4	3.4	NUM
cana-768	54	37	)	)	PUNCT
cana-768	54	38	communications	communication	NOUN
cana-768	54	39	on	on	ADP
cana-768	54	40	applied	apply	VERB
cana-768	54	41	nonlinear	nonlinear	ADJ
cana-768	54	42	analysis	analysis	NOUN
cana-768	54	43	issn	issn	NOUN
cana-768	54	44	:	:	PUNCT
cana-768	54	45	1074	1074	NUM
cana-768	54	46	-	-	PUNCT
cana-768	54	47	133x	133x	NUM
cana-768	54	48	vol	vol	NOUN
cana-768	54	49	31	31	NUM
cana-768	54	50	no	no	NOUN
cana-768	54	51	.	.	PUNCT
cana-768	55	1	3s	3s	NUM
cana-768	55	2	(	(	PUNCT
cana-768	55	3	2024	2024	NUM
cana-768	55	4	)	)	PUNCT
cana-768	55	5	315	315	NUM
cana-768	55	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	55	7	𝒰′′(ȶ𝒿	𝒰′′(ȶ𝒿	NOUN
cana-768	55	8	)	)	PUNCT
cana-768	55	9	=	=	PUNCT
cana-768	55	10	ƥ2	ƥ2	VERB
cana-768	55	11	𝚜	𝚜	ADP
cana-768	55	12	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	55	13	)	)	PUNCT
cana-768	56	1	[	[	X
cana-768	56	2	ɤ𝒿−1	ɤ𝒿−1	NOUN
cana-768	56	3	−	−	PROPN
cana-768	56	4	2ɤ𝒿	2ɤ𝒿	NOUN
cana-768	56	5	+	+	CCONJ
cana-768	56	6	ɤ𝒿+1	ɤ𝒿+1	NOUN
cana-768	56	7	]	]	X
cana-768	56	8	,	,	PUNCT
cana-768	56	9	0	0	NUM
cana-768	56	10	≤	≤	NUM
cana-768	56	11	𝒿	𝒿	X
cana-768	56	12	≤	≤	NUM
cana-768	56	13	ռ	ռ	PROPN
cana-768	56	14	(	(	PUNCT
cana-768	56	15	3.5	3.5	NUM
cana-768	56	16	)	)	PUNCT
cana-768	56	17	now	now	ADV
cana-768	56	18	,	,	PUNCT
cana-768	56	19	the	the	DET
cana-768	56	20	approximation	approximation	NOUN
cana-768	56	21	of	of	ADP
cana-768	56	22	the	the	DET
cana-768	56	23	equation	equation	NOUN
cana-768	56	24	(	(	PUNCT
cana-768	56	25	3.1	3.1	NUM
cana-768	56	26	)	)	PUNCT
cana-768	56	27	at	at	ADP
cana-768	56	28	the	the	DET
cana-768	56	29	mesh	mesh	NOUN
cana-768	56	30	points	point	NOUN
cana-768	56	31	can	can	AUX
cana-768	56	32	be	be	AUX
cana-768	56	33	described	describe	VERB
cana-768	56	34	as	as	ADP
cana-768	56	35	−휀	−휀	NOUN
cana-768	56	36	𝒰′′(ȶ𝒿	𝒰′′(ȶ𝒿	NOUN
cana-768	56	37	)	)	PUNCT
cana-768	57	1	+	+	CCONJ
cana-768	57	2	⨍(ȶ𝒿	⨍(ȶ𝒿	X
cana-768	57	3	)	)	PUNCT
cana-768	57	4	𝒰	𝒰	NOUN
cana-768	57	5	′(ȶ𝒿	′(ȶ𝒿	NOUN
cana-768	57	6	)	)	PUNCT
cana-768	58	1	+	+	SYM
cana-768	58	2	𝑔(ȶ𝒿)𝒰(ȶ𝒿	𝑔(ȶ𝒿)𝒰(ȶ𝒿	NOUN
cana-768	58	3	)	)	PUNCT
cana-768	58	4	=	=	SYM
cana-768	58	5	0	0	NUM
cana-768	58	6	,	,	PUNCT
cana-768	58	7	ȶ𝒿	ȶ𝒿	PRON
cana-768	58	8	∈	∈	PROPN
cana-768	58	9	[	[	X
cana-768	58	10	0,1	0,1	NUM
cana-768	58	11	]	]	X
cana-768	58	12	−휀	−휀	NOUN
cana-768	58	13	𝒰′′(ȶ𝒿	𝒰′′(ȶ𝒿	NOUN
cana-768	58	14	)	)	PUNCT
cana-768	59	1	+	+	CCONJ
cana-768	59	2	⨍𝒿	⨍𝒿	PROPN
cana-768	59	3	𝒰	𝒰	NOUN
cana-768	59	4	′(ȶ𝒿	′(ȶ𝒿	NOUN
cana-768	59	5	)	)	PUNCT
cana-768	60	1	+	+	CCONJ
cana-768	60	2	𝑔𝒿𝒰(ȶ𝒿	𝑔𝒿𝒰(ȶ𝒿	NOUN
cana-768	60	3	)	)	PUNCT
cana-768	60	4	=	=	SYM
cana-768	60	5	0	0	NUM
cana-768	60	6	,	,	PUNCT
cana-768	60	7	where	where	SCONJ
cana-768	60	8	⨍(ȶ𝒿	⨍(ȶ𝒿	X
cana-768	60	9	)	)	PUNCT
cana-768	60	10	=	=	SYM
cana-768	61	1	⨍𝒿	⨍𝒿	PROPN
cana-768	61	2	,	,	PUNCT
cana-768	61	3	𝑔(ȶ𝒿	𝑔(ȶ𝒿	PROPN
cana-768	61	4	)	)	PUNCT
cana-768	61	5	=	=	SYM
cana-768	61	6	𝑔𝒿	𝑔𝒿	PROPN
cana-768	61	7	(	(	PUNCT
cana-768	61	8	3.6	3.6	NUM
cana-768	61	9	)	)	PUNCT
cana-768	61	10	plugging	plug	VERB
cana-768	61	11	(	(	PUNCT
cana-768	61	12	3.3	3.3	NUM
cana-768	61	13	)	)	PUNCT
cana-768	61	14	,	,	PUNCT
cana-768	61	15	(	(	PUNCT
cana-768	61	16	3.4	3.4	NUM
cana-768	61	17	)	)	PUNCT
cana-768	61	18	and	and	CCONJ
cana-768	61	19	(	(	PUNCT
cana-768	61	20	3.5	3.5	NUM
cana-768	61	21	)	)	PUNCT
cana-768	61	22	into	into	ADP
cana-768	61	23	(	(	PUNCT
cana-768	61	24	3.6	3.6	NUM
cana-768	61	25	)	)	PUNCT
cana-768	61	26	we	we	PRON
cana-768	61	27	get	get	VERB
cana-768	61	28	−	−	NOUN
cana-768	62	1	ƥ2	ƥ2	NOUN
cana-768	62	2	𝚜	𝚜	ADP
cana-768	62	3	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	62	4	)	)	PUNCT
cana-768	63	1	[	[	X
cana-768	63	2	ɤ𝒿−1	ɤ𝒿−1	NOUN
cana-768	63	3	−	−	PROPN
cana-768	63	4	2ɤ𝒿	2ɤ𝒿	NOUN
cana-768	63	5	+	+	CCONJ
cana-768	63	6	ɤ𝒿+1	ɤ𝒿+1	X
cana-768	63	7	]	]	X
cana-768	63	8	+	+	CCONJ
cana-768	63	9	⨍𝒿	⨍𝒿	ADJ
cana-768	63	10	[	[	PUNCT
cana-768	63	11	ƥ(1−𝚌	ƥ(1−𝚌	NOUN
cana-768	63	12	)	)	PUNCT
cana-768	63	13	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	63	14	)	)	PUNCT
cana-768	63	15	ɤ𝒿−1	ɤ𝒿−1	NOUN
cana-768	63	16	−	−	PROPN
cana-768	63	17	ƥ(1−𝚌	ƥ(1−𝚌	NOUN
cana-768	63	18	)	)	PUNCT
cana-768	63	19	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	63	20	)	)	PUNCT
cana-768	63	21	ɤ𝒿+1	ɤ𝒿+1	NOUN
cana-768	63	22	]	]	X
cana-768	64	1	+	+	CCONJ
cana-768	64	2	𝑔𝒿	𝑔𝒿	PROPN
cana-768	64	3	[	[	PUNCT
cana-768	64	4	𝚜−ƥɦ	𝚜−ƥɦ	NUM
cana-768	64	5	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	64	6	)	)	PUNCT
cana-768	64	7	ɤ𝒿−1	ɤ𝒿−1	NOUN
cana-768	64	8	+	+	CCONJ
cana-768	64	9	ɤ𝒿	ɤ𝒿	PRON
cana-768	64	10	+	+	CCONJ
cana-768	64	11	𝚜−ƥɦ	𝚜−ƥɦ	PROPN
cana-768	64	12	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	64	13	)	)	PUNCT
cana-768	64	14	ɤ𝒿+1	ɤ𝒿+1	NOUN
cana-768	64	15	]	]	X
cana-768	64	16	=	=	SYM
cana-768	64	17	0	0	NUM
cana-768	64	18	by	by	ADP
cana-768	64	19	performing	perform	VERB
cana-768	64	20	mathematical	mathematical	ADJ
cana-768	64	21	maneuver	maneuver	NOUN
cana-768	64	22	we	we	PRON
cana-768	64	23	obtain	obtain	VERB
cana-768	64	24	a	a	DET
cana-768	64	25	three	three	NUM
cana-768	64	26	term	term	NOUN
cana-768	64	27	recurrence	recurrence	NOUN
cana-768	64	28	relation	relation	NOUN
cana-768	64	29	as	as	SCONJ
cana-768	64	30	follows	follow	VERB
cana-768	64	31	:	:	PUNCT
cana-768	64	32	𝒦𝒿ɤ𝒿−1	𝒦𝒿ɤ𝒿−1	X
cana-768	65	1	+	+	PUNCT
cana-768	65	2	𝔏𝒿ɤ𝒿	𝔏𝒿ɤ𝒿	ADJ
cana-768	65	3	+	+	NOUN
cana-768	65	4	ϻ𝒿ɤ𝒿+1	ϻ𝒿ɤ𝒿+1	ADJ
cana-768	66	1	=	=	PUNCT
cana-768	66	2	𝘙𝒿	𝘙𝒿	X
cana-768	66	3	(	(	PUNCT
cana-768	66	4	3.7	3.7	NUM
cana-768	66	5	)	)	PUNCT
cana-768	66	6	where	where	SCONJ
cana-768	66	7	,	,	PUNCT
cana-768	66	8	𝒦𝒿	𝒦𝒿	PROPN
cana-768	66	9	=	=	PUNCT
cana-768	66	10	−휀ƥ	−휀ƥ	PROPN
cana-768	66	11	2	2	NUM
cana-768	66	12	𝚜	𝚜	ADP
cana-768	66	13	+	+	NOUN
cana-768	66	14	⨍𝒿ƥ(1	⨍𝒿ƥ(1	ADP
cana-768	66	15	−	−	NOUN
cana-768	66	16	𝚌	𝚌	NOUN
cana-768	66	17	)	)	PUNCT
cana-768	66	18	+	+	CCONJ
cana-768	66	19	𝑔𝒿(𝚜	𝑔𝒿(𝚜	ADP
cana-768	66	20	−	−	NOUN
cana-768	66	21	ƥɦ	ƥɦ	NOUN
cana-768	66	22	)	)	PUNCT
cana-768	67	1	𝔏𝒿	𝔏𝒿	PROPN
cana-768	67	2	=	=	PUNCT
cana-768	67	3	2휀ƥ	2휀ƥ	ADJ
cana-768	67	4	2	2	NUM
cana-768	67	5	𝚜	𝚜	ADP
cana-768	67	6	+	+	PROPN
cana-768	67	7	2𝑔𝒿(ƥɦ𝚌	2𝑔𝒿(ƥɦ𝚌	NUM
cana-768	67	8	−	−	NOUN
cana-768	67	9	𝚜	𝚜	NOUN
cana-768	67	10	)	)	PUNCT
cana-768	67	11	ϻ𝒿	ϻ𝒿	NOUN
cana-768	67	12	=	=	PUNCT
cana-768	67	13	−휀ƥ2	−휀ƥ2	VERB
cana-768	67	14	𝚜	𝚜	ADP
cana-768	67	15	−	−	NOUN
cana-768	67	16	⨍𝒿ƥ(1	⨍𝒿ƥ(1	ADP
cana-768	67	17	−	−	NOUN
cana-768	67	18	𝚌	𝚌	NOUN
cana-768	67	19	)	)	PUNCT
cana-768	67	20	+	+	CCONJ
cana-768	67	21	𝑔𝒿(𝚜	𝑔𝒿(𝚜	ADP
cana-768	67	22	−	−	NOUN
cana-768	67	23	ƥɦ	ƥɦ	NOUN
cana-768	67	24	)	)	PUNCT
cana-768	67	25	𝘙𝒿	𝘙𝒿	NOUN
cana-768	67	26	=	=	SYM
cana-768	67	27	0	0	NUM
cana-768	67	28	system	system	NOUN
cana-768	67	29	(	(	PUNCT
cana-768	67	30	3.7	3.7	NUM
cana-768	67	31	)	)	PUNCT
cana-768	67	32	consists	consist	VERB
cana-768	67	33	of	of	ADP
cana-768	67	34	(	(	PUNCT
cana-768	67	35	ռ	ռ	NOUN
cana-768	67	36	+	+	NOUN
cana-768	67	37	1	1	NUM
cana-768	67	38	)	)	PUNCT
cana-768	67	39	equations	equation	NOUN
cana-768	67	40	with	with	ADP
cana-768	67	41	(	(	PUNCT
cana-768	67	42	ռ	ռ	NOUN
cana-768	67	43	+	+	NOUN
cana-768	67	44	3	3	NUM
cana-768	67	45	)	)	PUNCT
cana-768	67	46	unknowns	unknown	NOUN
cana-768	67	47	,	,	PUNCT
cana-768	67	48	say	say	VERB
cana-768	67	49	ɤ−1	ɤ−1	PROPN
cana-768	67	50	,	,	PUNCT
cana-768	67	51	ɤ0	ɤ0	NOUN
cana-768	67	52	,	,	PUNCT
cana-768	67	53	ɤ1	ɤ1	NOUN
cana-768	67	54	…	…	PUNCT
cana-768	67	55	……	……	NOUN
cana-768	67	56	.	.	PUNCT
cana-768	67	57	.	.	PUNCT
cana-768	68	1	ɤռ+1	ɤռ+1	PUNCT
cana-768	68	2	.	.	PUNCT
cana-768	69	1	plugging	plug	VERB
cana-768	69	2	the	the	DET
cana-768	69	3	boundary	boundary	ADJ
cana-768	69	4	conditions	condition	NOUN
cana-768	69	5	(	(	PUNCT
cana-768	69	6	2.2	2.2	NUM
cana-768	69	7	)	)	PUNCT
cana-768	69	8	in	in	ADP
cana-768	69	9	order	order	NOUN
cana-768	69	10	to	to	PART
cana-768	69	11	solve	solve	VERB
cana-768	69	12	the	the	DET
cana-768	69	13	system	system	NOUN
cana-768	69	14	(	(	PUNCT
cana-768	69	15	3.7	3.7	NUM
cana-768	69	16	)	)	PUNCT
cana-768	69	17	,	,	PUNCT
cana-768	69	18	we	we	PRON
cana-768	69	19	get	get	VERB
cana-768	69	20	two	two	NUM
cana-768	69	21	more	more	ADV
cana-768	69	22	additional	additional	ADJ
cana-768	69	23	equations	equation	NOUN
cana-768	69	24	,	,	PUNCT
cana-768	69	25	{	{	PUNCT
cana-768	69	26	ɤ−1	ɤ−1	X
cana-768	69	27	=	=	SYM
cana-768	69	28	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	69	29	)	)	PUNCT
cana-768	69	30	𝚜−ƥɦ	𝚜−ƥɦ	VERB
cana-768	69	31	(	(	PUNCT
cana-768	69	32	𝜑	𝜑	PROPN
cana-768	69	33	−	−	PROPN
cana-768	69	34	ɤ0	ɤ0	PROPN
cana-768	69	35	)	)	PUNCT
cana-768	69	36	−	−	NOUN
cana-768	69	37	ɤ1	ɤ1	NOUN
cana-768	69	38	ɤռ+1	ɤռ+1	PUNCT
cana-768	69	39	=	=	SYM
cana-768	69	40	2(ƥɦ𝚌−𝚜	2(ƥɦ𝚌−𝚜	NUM
cana-768	69	41	)	)	PUNCT
cana-768	69	42	𝚜−ƥɦ	𝚜−ƥɦ	PROPN
cana-768	69	43	(	(	PUNCT
cana-768	69	44	𝜓	𝜓	NOUN
cana-768	69	45	−	−	PROPN
cana-768	69	46	ɤռ	ɤռ	NOUN
cana-768	69	47	)	)	PUNCT
cana-768	70	1	−	−	PROPN
cana-768	71	1	ɤռ−1	ɤռ−1	PROPN
cana-768	71	2	(	(	PUNCT
cana-768	71	3	3.8	3.8	NUM
cana-768	71	4	)	)	PUNCT
cana-768	71	5	now	now	ADV
cana-768	71	6	(	(	PUNCT
cana-768	71	7	3.8	3.8	NUM
cana-768	71	8	)	)	PUNCT
cana-768	71	9	can	can	AUX
cana-768	71	10	be	be	AUX
cana-768	71	11	used	use	VERB
cana-768	71	12	to	to	PART
cana-768	71	13	eliminate	eliminate	VERB
cana-768	71	14	ɤ−1	ɤ−1	PROPN
cana-768	71	15	and	and	CCONJ
cana-768	71	16	ɤռ+1	ɤռ+1	ADV
cana-768	71	17	from	from	ADP
cana-768	71	18	(	(	PUNCT
cana-768	71	19	3.7	3.7	NUM
cana-768	71	20	)	)	PUNCT
cana-768	71	21	which	which	PRON
cana-768	71	22	yields	yield	VERB
cana-768	71	23	a	a	DET
cana-768	71	24	tridiagonal	tridiagonal	ADJ
cana-768	71	25	system	system	NOUN
cana-768	71	26	in	in	ADP
cana-768	71	27	the	the	DET
cana-768	71	28	unknowns	unknown	NOUN
cana-768	71	29	ɤ0	ɤ0	PROPN
cana-768	71	30	,	,	PUNCT
cana-768	71	31	ɤ1	ɤ1	NOUN
cana-768	71	32	…	…	PUNCT
cana-768	71	33	……	……	NOUN
cana-768	71	34	.	.	PUNCT
cana-768	71	35	.	.	PUNCT
cana-768	72	1	ɤռ	ɤռ	ADP
cana-768	72	2	of	of	ADP
cana-768	72	3	the	the	DET
cana-768	72	4	form	form	NOUN
cana-768	72	5	,	,	PUNCT
cana-768	72	6	𝒜ɤ	𝒜ɤ	PROPN
cana-768	72	7	=	=	SYM
cana-768	72	8	𝔇	𝔇	PROPN
cana-768	72	9	(	(	PUNCT
cana-768	72	10	3.9	3.9	NUM
cana-768	72	11	)	)	PUNCT
cana-768	72	12	where	where	SCONJ
cana-768	72	13	,	,	PUNCT
cana-768	72	14	ɤ	ɤ	X
cana-768	72	15	=	=	SYM
cana-768	72	16	(	(	PUNCT
cana-768	72	17	ɤ0	ɤ0	NOUN
cana-768	72	18	,	,	PUNCT
cana-768	72	19	ɤ1	ɤ1	NOUN
cana-768	72	20	…	…	PUNCT
cana-768	72	21	……	……	NOUN
cana-768	72	22	.	.	PUNCT
cana-768	72	23	.	.	PUNCT
cana-768	73	1	ɤռ	ɤռ	NOUN
cana-768	73	2	)	)	PUNCT
cana-768	73	3	′	′	NUM
cana-768	74	1	𝔇	𝔇	NOUN
cana-768	74	2	=	=	SYM
cana-768	74	3	(	(	PUNCT
cana-768	74	4	−2(ƥɦ𝚌	−2(ƥɦ𝚌	PROPN
cana-768	74	5	−	−	PROPN
cana-768	74	6	𝚜)𝒦0𝜑	𝚜)𝒦0𝜑	NOUN
cana-768	74	7	,	,	PUNCT
cana-768	74	8	0,0	0,0	NOUN
cana-768	74	9	,	,	PUNCT
cana-768	74	10	…	…	PUNCT
cana-768	74	11	…	…	SYM
cana-768	74	12	……	……	X
cana-768	74	13	.	.	PUNCT
cana-768	74	14	,	,	PUNCT
cana-768	74	15	−2(ƥɦ𝚌	−2(ƥɦ𝚌	PROPN
cana-768	74	16	−	−	PROPN
cana-768	74	17	𝚜)ϻռ𝜓	𝚜)ϻռ𝜓	NOUN
cana-768	74	18	)	)	PUNCT
cana-768	75	1	′	′	NUM
cana-768	75	2	communications	communication	NOUN
cana-768	75	3	on	on	ADP
cana-768	75	4	applied	apply	VERB
cana-768	75	5	nonlinear	nonlinear	ADJ
cana-768	75	6	analysis	analysis	NOUN
cana-768	75	7	issn	issn	NOUN
cana-768	75	8	:	:	PUNCT
cana-768	75	9	1074	1074	NUM
cana-768	75	10	-	-	PUNCT
cana-768	75	11	133x	133x	NUM
cana-768	75	12	vol	vol	NOUN
cana-768	75	13	31	31	NUM
cana-768	75	14	no	no	NOUN
cana-768	75	15	.	.	PUNCT
cana-768	76	1	3s	3s	NUM
cana-768	76	2	(	(	PUNCT
cana-768	76	3	2024	2024	NUM
cana-768	76	4	)	)	PUNCT
cana-768	76	5	316	316	NUM
cana-768	76	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	76	7	𝒜	𝒜	NOUN
cana-768	76	8	=	=	SYM
cana-768	76	9	(	(	PUNCT
cana-768	76	10	𝔏0(𝚜	𝔏0(𝚜	ADJ
cana-768	76	11	−	−	PROPN
cana-768	76	12	𝓅ɦ	𝓅ɦ	NUM
cana-768	76	13	)	)	PUNCT
cana-768	76	14	−	−	NOUN
cana-768	76	15	2(𝓅ɦ𝚌	2(𝓅ɦ𝚌	NOUN
cana-768	76	16	−	−	ADP
cana-768	77	1	𝚜)𝒦0	𝚜)𝒦0	ADJ
cana-768	77	2	(	(	PUNCT
cana-768	77	3	ϻ0	ϻ0	NOUN
cana-768	77	4	−	−	NOUN
cana-768	77	5	𝒦0)(𝚜	𝒦0)(𝚜	NOUN
cana-768	77	6	−	−	PROPN
cana-768	77	7	𝓅ɦ	𝓅ɦ	NUM
cana-768	77	8	)	)	PUNCT
cana-768	77	9	0	0	NUM
cana-768	77	10	𝒦1	𝒦1	NOUN
cana-768	77	11	𝔏1	𝔏1	PROPN
cana-768	77	12	ϻ1	ϻ1	X
cana-768	77	13	…	…	PUNCT
cana-768	77	14	…	…	PUNCT
cana-768	77	15	…	…	PUNCT
cana-768	77	16	……	……	NOUN
cana-768	77	17	……	……	NOUN
cana-768	77	18	.	.	PUNCT
cana-768	77	19	.	.	PUNCT
cana-768	78	1	…	…	PUNCT
cana-768	78	2	……	……	NOUN
cana-768	78	3	……	……	NOUN
cana-768	78	4	……	……	NOUN
cana-768	78	5	.	.	PUNCT
cana-768	78	6	.	.	PUNCT
cana-768	79	1	…	…	PUNCT
cana-768	79	2	…	…	PUNCT
cana-768	79	3	…	…	PUNCT
cana-768	79	4	……	……	NOUN
cana-768	79	5	……	……	NOUN
cana-768	79	6	.	.	PUNCT
cana-768	79	7	.	.	PUNCT
cana-768	80	1	…	…	PUNCT
cana-768	80	2	…	…	PUNCT
cana-768	80	3	.	.	PUNCT
cana-768	80	4	.	.	PUNCT
cana-768	81	1	…	…	PUNCT
cana-768	81	2	…	…	PUNCT
cana-768	81	3	……	……	X
cana-768	81	4	.	.	PUNCT
cana-768	81	5	.	.	PUNCT
cana-768	82	1	…	…	PUNCT
cana-768	82	2	…	…	PUNCT
cana-768	82	3	…	…	PUNCT
cana-768	82	4	…	…	PUNCT
cana-768	82	5	……	……	NOUN
cana-768	82	6	……	……	NOUN
cana-768	82	7	(	(	PUNCT
cana-768	82	8	𝒦ռ	𝒦ռ	NOUN
cana-768	82	9	−ϻռ)(𝚜	−ϻռ)(𝚜	NOUN
cana-768	82	10	−	−	PROPN
cana-768	82	11	𝓅ɦ	𝓅ɦ	NUM
cana-768	82	12	)	)	PUNCT
cana-768	83	1	𝔏ռ(𝚜	𝔏ռ(𝚜	ADJ
cana-768	83	2	−	−	PROPN
cana-768	83	3	𝓅ɦ	𝓅ɦ	NUM
cana-768	83	4	)	)	PUNCT
cana-768	83	5	−	−	NOUN
cana-768	83	6	2(𝓅ɦ𝚌	2(𝓅ɦ𝚌	NOUN
cana-768	83	7	−	−	PROPN
cana-768	83	8	𝚜)ϻռ	𝚜)ϻռ	PROPN
cana-768	83	9	)	)	PUNCT
cana-768	83	10	the	the	DET
cana-768	83	11	tridiagonal	tridiagonal	ADJ
cana-768	83	12	system	system	NOUN
cana-768	83	13	(	(	PUNCT
cana-768	83	14	3.7	3.7	NUM
cana-768	83	15	)	)	PUNCT
cana-768	83	16	can	can	AUX
cana-768	83	17	be	be	AUX
cana-768	83	18	solved	solve	VERB
cana-768	83	19	using	use	VERB
cana-768	83	20	invariant	invariant	ADJ
cana-768	83	21	embedded	embed	VERB
cana-768	83	22	algorithm	algorithm	NOUN
cana-768	83	23	.	.	PUNCT
cana-768	84	1	4	4	X
cana-768	84	2	.	.	NOUN
cana-768	84	3	results	result	VERB
cana-768	84	4	convergence	convergence	NOUN
cana-768	84	5	analysis	analysis	NOUN
cana-768	84	6	:	:	PUNCT
cana-768	84	7	the	the	DET
cana-768	84	8	followings	following	NOUN
cana-768	84	9	results	result	NOUN
cana-768	84	10	are	be	AUX
cana-768	84	11	required	require	VERB
cana-768	84	12	to	to	PART
cana-768	84	13	discuss	discuss	VERB
cana-768	84	14	the	the	DET
cana-768	84	15	convergent	convergent	NOUN
cana-768	84	16	analysis	analysis	NOUN
cana-768	84	17	of	of	ADP
cana-768	84	18	the	the	DET
cana-768	84	19	proposed	propose	VERB
cana-768	84	20	scheme	scheme	NOUN
cana-768	84	21	,	,	PUNCT
cana-768	84	22	lemma	lemma	PROPN
cana-768	84	23	1	1	NUM
cana-768	84	24	.	.	PUNCT
cana-768	85	1	if	if	SCONJ
cana-768	85	2	{	{	PUNCT
cana-768	85	3	ᏸ−1,ᏸ0	ᏸ−1,ᏸ0	NOUN
cana-768	85	4	,	,	PUNCT
cana-768	85	5	…	…	PUNCT
cana-768	85	6	…	…	PUNCT
cana-768	85	7	……	……	NOUN
cana-768	85	8	……	……	NOUN
cana-768	85	9	.ᏸռ+1	.ᏸռ+1	PRON
cana-768	85	10	}	}	PUNCT
cana-768	85	11	is	be	AUX
cana-768	85	12	exponential	exponential	ADJ
cana-768	85	13	spline	spline	NOUN
cana-768	85	14	basis	basis	NOUN
cana-768	85	15	,	,	PUNCT
cana-768	85	16	then	then	ADV
cana-768	85	17	see.[11	see.[11	ADV
cana-768	85	18	]	]	X
cana-768	85	19	∑	∑	PUNCT
cana-768	85	20	|ᏸ𝒿(ȶ)|	|ᏸ𝒿(ȶ)|	NOUN
cana-768	85	21	≤	≤	NUM
cana-768	86	1	5	5	NUM
cana-768	86	2	2	2	NUM
cana-768	86	3	ռ+1	ռ+1	NUM
cana-768	86	4	𝒿=−1	𝒿=−1	ADJ
cana-768	86	5	,	,	PUNCT
cana-768	86	6	0	0	NUM
cana-768	86	7	≤	≤	NUM
cana-768	86	8	ȶ	ȶ	X
cana-768	86	9	≤	≤	ADV
cana-768	86	10	1	1	NUM
cana-768	86	11	theorem	theorem	NOUN
cana-768	86	12	1	1	NUM
cana-768	86	13	.	.	PUNCT
cana-768	87	1	let	let	VERB
cana-768	87	2	exact	exact	ADJ
cana-768	87	3	solution	solution	NOUN
cana-768	87	4	𝓊(ȶ	𝓊(ȶ	NOUN
cana-768	87	5	)	)	PUNCT
cana-768	87	6	of	of	ADP
cana-768	87	7	the	the	DET
cana-768	87	8	problem	problem	NOUN
cana-768	87	9	(	(	PUNCT
cana-768	87	10	2.1	2.1	NUM
cana-768	87	11	)	)	PUNCT
cana-768	87	12	can	can	AUX
cana-768	87	13	be	be	AUX
cana-768	87	14	interpolated	interpolate	VERB
cana-768	87	15	using	use	VERB
cana-768	87	16	exponential	exponential	ADJ
cana-768	87	17	bspline	bspline	NOUN
cana-768	87	18	to	to	ADP
cana-768	87	19	a	a	DET
cana-768	87	20	unique	unique	ADJ
cana-768	87	21	𝒰(ȶ	𝒰(ȶ	NOUN
cana-768	87	22	)	)	PUNCT
cana-768	87	23	.	.	PUNCT
cana-768	88	1	and	and	CCONJ
cana-768	88	2	if	if	SCONJ
cana-768	88	3	𝓊(ȶ	𝓊(ȶ	NOUN
cana-768	88	4	)	)	PUNCT
cana-768	88	5	∈	∈	PROPN
cana-768	88	6	𝑐4[0	𝑐4[0	NOUN
cana-768	88	7	,	,	PUNCT
cana-768	88	8	ռ	ռ	NOUN
cana-768	88	9	]	]	PUNCT
cana-768	88	10	and	and	CCONJ
cana-768	88	11	⨍	⨍	NOUN
cana-768	88	12	,	,	PUNCT
cana-768	88	13	𝑔	𝑔	PROPN
cana-768	88	14	∈	∈	PROPN
cana-768	88	15	𝑐2[0	𝑐2[0	PROPN
cana-768	88	16	,	,	PUNCT
cana-768	88	17	ռ	ռ	NOUN
cana-768	88	18	]	]	X
cana-768	88	19	,	,	PUNCT
cana-768	88	20	then	then	ADV
cana-768	88	21	∃	∃	PROPN
cana-768	88	22	a	a	DET
cana-768	88	23	constant	constant	ADJ
cana-768	88	24	ϰ𝒿	ϰ𝒿	ADP
cana-768	88	25	,	,	PUNCT
cana-768	88	26	independent	independent	ADJ
cana-768	88	27	of	of	ADP
cana-768	88	28	ɦ	ɦ	PRON
cana-768	88	29	such	such	ADJ
cana-768	88	30	that	that	PRON
cana-768	88	31	see.[11	see.[11	NOUN
cana-768	88	32	]	]	X
cana-768	88	33	‖𝐷𝒿(𝓊(ȶ	‖𝐷𝒿(𝓊(ȶ	PROPN
cana-768	88	34	)	)	PUNCT
cana-768	88	35	−	−	PROPN
cana-768	88	36	𝒰(ȶ))‖∞	𝒰(ȶ))‖∞	NOUN
cana-768	88	37	≤	≤	NOUN
cana-768	88	38	ϰ𝒿ɦ	ϰ𝒿ɦ	NOUN
cana-768	88	39	𝒿−1	𝒿−1	PROPN
cana-768	88	40	,	,	PUNCT
cana-768	88	41	𝒿	𝒿	PROPN
cana-768	88	42	=	=	PUNCT
cana-768	88	43	0,1,2	0,1,2	NUM
cana-768	88	44	…	…	NUM
cana-768	88	45	.	.	PUNCT
cana-768	89	1	theorem	theorem	NOUN
cana-768	89	2	2	2	NUM
cana-768	89	3	.	.	PUNCT
cana-768	90	1	let	let	VERB
cana-768	90	2	exact	exact	ADJ
cana-768	90	3	solution	solution	NOUN
cana-768	90	4	𝓊(ȶ	𝓊(ȶ	NOUN
cana-768	90	5	)	)	PUNCT
cana-768	90	6	of	of	ADP
cana-768	90	7	the	the	DET
cana-768	90	8	problem	problem	NOUN
cana-768	90	9	(	(	PUNCT
cana-768	90	10	3.1	3.1	NUM
cana-768	90	11	)	)	PUNCT
cana-768	90	12	can	can	AUX
cana-768	90	13	be	be	AUX
cana-768	90	14	approximated	approximate	VERB
cana-768	90	15	using	use	VERB
cana-768	90	16	exponential	exponential	ADJ
cana-768	90	17	bspline	bspline	NOUN
cana-768	90	18	by	by	ADP
cana-768	90	19	𝒰(ȶ	𝒰(ȶ	NOUN
cana-768	90	20	)	)	PUNCT
cana-768	90	21	.	.	PUNCT
cana-768	91	1	if	if	SCONJ
cana-768	91	2	𝓊(ȶ	𝓊(ȶ	NUM
cana-768	91	3	)	)	PUNCT
cana-768	91	4	∈	∈	PROPN
cana-768	91	5	𝑐4[0	𝑐4[0	NOUN
cana-768	91	6	,	,	PUNCT
cana-768	91	7	ռ	ռ	NOUN
cana-768	91	8	]	]	PUNCT
cana-768	91	9	and	and	CCONJ
cana-768	91	10	⨍	⨍	NOUN
cana-768	91	11	,	,	PUNCT
cana-768	91	12	𝑔	𝑔	PROPN
cana-768	91	13	∈	∈	PROPN
cana-768	91	14	𝑐2[0	𝑐2[0	PROPN
cana-768	91	15	,	,	PUNCT
cana-768	91	16	ռ	ռ	NOUN
cana-768	91	17	]	]	X
cana-768	91	18	,	,	PUNCT
cana-768	91	19	then	then	ADV
cana-768	91	20	∃	∃	PROPN
cana-768	91	21	a	a	DET
cana-768	91	22	constant	constant	ADJ
cana-768	91	23	ӄ	ӄ	NOUN
cana-768	91	24	,	,	PUNCT
cana-768	91	25	such	such	ADJ
cana-768	91	26	that	that	SCONJ
cana-768	91	27	‖𝓊(ȶ	‖𝓊(ȶ	NOUN
cana-768	91	28	)	)	PUNCT
cana-768	91	29	−	−	NOUN
cana-768	91	30	𝒰(ȶ)‖∞	𝒰(ȶ)‖∞	ADJ
cana-768	91	31	≤	≤	ADJ
cana-768	91	32	ӄɦ2	ӄɦ2	NOUN
cana-768	91	33	,	,	PUNCT
cana-768	91	34	for	for	ADP
cana-768	91	35	sufficiently	sufficiently	ADV
cana-768	91	36	small	small	ADJ
cana-768	91	37	ɦ	ɦ	X
cana-768	91	38	and	and	CCONJ
cana-768	91	39	ӄ	ӄ	NOUN
cana-768	91	40	is	be	AUX
cana-768	91	41	a	a	DET
cana-768	91	42	positive	positive	ADJ
cana-768	91	43	constant	constant	NOUN
cana-768	91	44	.	.	PUNCT
cana-768	92	1	proof	proof	NOUN
cana-768	92	2	.	.	PUNCT
cana-768	93	1	let	let	VERB
cana-768	93	2	us	we	PRON
cana-768	93	3	consider	consider	VERB
cana-768	93	4	the	the	DET
cana-768	93	5	following	follow	VERB
cana-768	93	6	for	for	ADP
cana-768	93	7	the	the	DET
cana-768	93	8	problem	problem	NOUN
cana-768	93	9	(	(	PUNCT
cana-768	93	10	2.1	2.1	NUM
cana-768	93	11	)	)	PUNCT
cana-768	93	12	.	.	PUNCT
cana-768	94	1	𝓊(ȶ	𝓊(ȶ	NOUN
cana-768	94	2	)	)	PUNCT
cana-768	94	3	be	be	VERB
cana-768	94	4	the	the	DET
cana-768	94	5	exact	exact	ADJ
cana-768	94	6	solution,	solution,	PROPN
cana-768	94	7	�	�	PROPN
cana-768	94	8	̃	̃	PROPN
cana-768	94	9	�	�	NOUN
cana-768	94	10	(ȶ	(ȶ	NOUN
cana-768	94	11	)	)	PUNCT
cana-768	94	12	=	=	PUNCT
cana-768	94	13	∑	∑	PUNCT
cana-768	94	14	ɤ̃𝒿	ɤ̃𝒿	PROPN
cana-768	94	15	ռ+1	ռ+1	ADV
cana-768	94	16	𝒿=−1	𝒿=−1	NUM
cana-768	94	17	ᏸ𝒿(ȶ	ᏸ𝒿(ȶ	NOUN
cana-768	94	18	)	)	PUNCT
cana-768	94	19	be	be	AUX
cana-768	94	20	an	an	DET
cana-768	94	21	unique	unique	ADJ
cana-768	94	22	exponential	exponential	ADJ
cana-768	94	23	b	b	NOUN
cana-768	94	24	-	-	PUNCT
cana-768	94	25	spline	spline	NOUN
cana-768	94	26	interpolating	interpolate	VERB
cana-768	94	27	the	the	DET
cana-768	94	28	solution	solution	NOUN
cana-768	94	29	𝓊(ȶ	𝓊(ȶ	NOUN
cana-768	94	30	)	)	PUNCT
cana-768	94	31	and	and	CCONJ
cana-768	95	1	𝒰(ȶ	𝒰(ȶ	NUM
cana-768	95	2	)	)	PUNCT
cana-768	95	3	=	=	PUNCT
cana-768	95	4	∑	∑	ADP
cana-768	95	5	ɤ𝒿	ɤ𝒿	X
cana-768	95	6	ռ+1	ռ+1	ADV
cana-768	95	7	𝒿=−1	𝒿=−1	NUM
cana-768	95	8	ᏸ𝒿(ȶ	ᏸ𝒿(ȶ	NOUN
cana-768	95	9	)	)	PUNCT
cana-768	95	10	be	be	AUX
cana-768	95	11	the	the	DET
cana-768	95	12	approximate	approximate	ADJ
cana-768	95	13	solution	solution	NOUN
cana-768	95	14	of	of	ADP
cana-768	95	15	the	the	DET
cana-768	95	16	equation	equation	NOUN
cana-768	95	17	.	.	PUNCT
cana-768	96	1	now	now	ADV
cana-768	96	2	,	,	PUNCT
cana-768	96	3	from	from	ADP
cana-768	96	4	lemma	lemma	PROPN
cana-768	96	5	1	1	NUM
cana-768	96	6	we	we	PRON
cana-768	96	7	have	have	VERB
cana-768	96	8	∑|ᏸ𝒿(ȶ)|	∑|ᏸ𝒿(ȶ)|	NOUN
cana-768	96	9	≤	≤	ADV
cana-768	97	1	5	5	NUM
cana-768	97	2	2	2	NUM
cana-768	97	3	ռ+1	ռ+1	NUM
cana-768	97	4	𝒿=−1	𝒿=−1	ADJ
cana-768	97	5	,	,	PUNCT
cana-768	97	6	0	0	NUM
cana-768	97	7	≤	≤	NUM
cana-768	97	8	ȶ	ȶ	SYM
cana-768	97	9	≤	≤	ADV
cana-768	97	10	1	1	NUM
cana-768	97	11	again	again	ADV
cana-768	97	12	,	,	PUNCT
cana-768	97	13	using	use	VERB
cana-768	97	14	theorem	theorem	NOUN
cana-768	97	15	1	1	NUM
cana-768	97	16	|𝐿𝓊(ȶ𝒿	|𝐿𝓊(ȶ𝒿	NOUN
cana-768	97	17	)	)	PUNCT
cana-768	97	18	−	−	PROPN
cana-768	97	19	𝐿𝒰(ȶ𝒿)|	𝐿𝒰(ȶ𝒿)|	NOUN
cana-768	97	20	≤	≤	NUM
cana-768	97	21	|−휀(𝓊′′(ȶ𝒿	|−휀(𝓊′′(ȶ𝒿	NOUN
cana-768	97	22	)	)	PUNCT
cana-768	97	23	−	−	NOUN
cana-768	97	24	𝒰(ȶ𝒿	𝒰(ȶ𝒿	NOUN
cana-768	97	25	)	)	PUNCT
cana-768	97	26	)	)	PUNCT
cana-768	98	1	+	+	CCONJ
cana-768	98	2	⨍(ȶ)(𝓊	⨍(ȶ)(𝓊	NOUN
cana-768	98	3	′(ȶ𝒿	′(ȶ𝒿	NOUN
cana-768	98	4	)	)	PUNCT
cana-768	98	5	−	−	PROPN
cana-768	98	6	𝒰(ȶ𝒿	𝒰(ȶ𝒿	NOUN
cana-768	98	7	)	)	PUNCT
cana-768	98	8	)	)	PUNCT
cana-768	99	1	+	+	CCONJ
cana-768	99	2	𝑔(ȶ)(𝓊(ȶ𝒿	𝑔(ȶ)(𝓊(ȶ𝒿	X
cana-768	99	3	)	)	PUNCT
cana-768	99	4	−	−	PROPN
cana-768	100	1	𝒰(ȶ𝒿))|	𝒰(ȶ𝒿))|	NUM
cana-768	100	2	≤	≤	NUM
cana-768	100	3	(	(	PUNCT
cana-768	100	4	휀ϰ2	휀ϰ2	NOUN
cana-768	100	5	+	+	CCONJ
cana-768	100	6	‖⨍‖∞ϰ1ɦ	‖⨍‖∞ϰ1ɦ	PUNCT
cana-768	100	7	+	+	CCONJ
cana-768	100	8	‖𝑔‖∞ϰ0ɦ	‖𝑔‖∞ϰ0ɦ	PROPN
cana-768	100	9	2)ɦ2=	2)ɦ2=	PROPN
cana-768	101	1	ϰɦ2	ϰɦ2	ADP
cana-768	101	2	where	where	SCONJ
cana-768	101	3	,	,	PUNCT
cana-768	101	4	ϰ	ϰ	NOUN
cana-768	101	5	=	=	PUNCT
cana-768	101	6	휀ϰ2	휀ϰ2	NOUN
cana-768	101	7	+	+	CCONJ
cana-768	101	8	‖⨍‖∞ϰ1ɦ	‖⨍‖∞ϰ1ɦ	PUNCT
cana-768	102	1	+	+	CCONJ
cana-768	102	2	‖𝑔‖∞ϰ0ɦ	‖𝑔‖∞ϰ0ɦ	PROPN
cana-768	102	3	2	2	NUM
cana-768	102	4	thus	thus	ADV
cana-768	102	5	we	we	PRON
cana-768	102	6	obtain	obtain	VERB
cana-768	102	7	,	,	PUNCT
cana-768	102	8	|𝐿𝒰(ȶ𝒿	|𝐿𝒰(ȶ𝒿	NOUN
cana-768	102	9	)	)	PUNCT
cana-768	102	10	−	−	PROPN
cana-768	102	11	𝐿	𝐿	PROPN
cana-768	102	12	�	�	PROPN
cana-768	102	13	̃	̃	PROPN
cana-768	102	14	�	�	PROPN
cana-768	102	15	(ȶ𝒿)|	(ȶ𝒿)|	PUNCT
cana-768	102	16	=	=	SYM
cana-768	102	17	|0	|0	NUM
cana-768	102	18	−	−	PROPN
cana-768	102	19	𝐿	𝐿	PROPN
cana-768	102	20	�	�	PROPN
cana-768	102	21	̃	̃	PROPN
cana-768	102	22	�	�	PROPN
cana-768	102	23	(ȶ𝒿)|	(ȶ𝒿)|	SYM
cana-768	102	24	=	=	SYM
cana-768	102	25	|𝐿𝓊(ȶ𝒿	|𝐿𝓊(ȶ𝒿	NOUN
cana-768	102	26	)	)	PUNCT
cana-768	102	27	−	−	PROPN
cana-768	102	28	𝐿	𝐿	PROPN
cana-768	102	29	�	�	PROPN
cana-768	102	30	̃	̃	PROPN
cana-768	102	31	�	�	PROPN
cana-768	102	32	(ȶ𝒿)|	(ȶ𝒿)|	PUNCT
cana-768	102	33	≤	≤	NUM
cana-768	102	34	ϰɦ2	ϰɦ2	PROPN
cana-768	102	35	(	(	PUNCT
cana-768	102	36	4.1	4.1	NUM
cana-768	102	37	)	)	PUNCT
cana-768	102	38	communications	communication	NOUN
cana-768	102	39	on	on	ADP
cana-768	102	40	applied	apply	VERB
cana-768	102	41	nonlinear	nonlinear	ADJ
cana-768	102	42	analysis	analysis	NOUN
cana-768	102	43	issn	issn	NOUN
cana-768	102	44	:	:	PUNCT
cana-768	102	45	1074	1074	NUM
cana-768	102	46	-	-	PUNCT
cana-768	102	47	133x	133x	NUM
cana-768	102	48	vol	vol	NOUN
cana-768	102	49	31	31	NUM
cana-768	102	50	no	no	NOUN
cana-768	102	51	.	.	PUNCT
cana-768	103	1	3s	3s	NUM
cana-768	103	2	(	(	PUNCT
cana-768	103	3	2024	2024	NUM
cana-768	103	4	)	)	PUNCT
cana-768	103	5	317	317	NUM
cana-768	103	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	103	7	as	as	ADP
cana-768	103	8	𝐿𝒰(ȶ𝒿	𝐿𝒰(ȶ𝒿	PROPN
cana-768	103	9	)	)	PUNCT
cana-768	103	10	=	=	SYM
cana-768	103	11	0	0	NUM
cana-768	103	12	,	,	PUNCT
cana-768	103	13	0	0	NUM
cana-768	103	14	≤	≤	NUM
cana-768	103	15	𝒿	𝒿	X
cana-768	103	16	≤	≤	NUM
cana-768	103	17	ռ	ռ	NOUN
cana-768	103	18	with	with	ADP
cana-768	103	19	the	the	DET
cana-768	103	20	boundary	boundary	ADJ
cana-768	103	21	conditions	condition	NOUN
cana-768	103	22	given	give	VERB
cana-768	103	23	in	in	ADP
cana-768	103	24	(	(	PUNCT
cana-768	103	25	2.2	2.2	NUM
cana-768	103	26	)	)	PUNCT
cana-768	103	27	gives	give	VERB
cana-768	103	28	a	a	DET
cana-768	103	29	system	system	NOUN
cana-768	103	30	of	of	ADP
cana-768	103	31	linear	linear	PROPN
cana-768	103	32	equations	equation	NOUN
cana-768	103	33	,	,	PUNCT
cana-768	103	34	𝒜ɤ	𝒜ɤ	AUX
cana-768	103	35	=	=	SYM
cana-768	103	36	𝔇	𝔇	PROPN
cana-768	103	37	now	now	ADV
cana-768	103	38	,	,	PUNCT
cana-768	103	39	suppose	suppose	VERB
cana-768	103	40	𝐿	𝐿	PROPN
cana-768	103	41	�	�	PROPN
cana-768	103	42	̃	̃	PROPN
cana-768	103	43	�	�	PROPN
cana-768	103	44	(ȶ𝒿	(ȶ𝒿	X
cana-768	103	45	)	)	PUNCT
cana-768	103	46	=	=	SYM
cana-768	103	47	ϣ(ȶ𝒿	ϣ(ȶ𝒿	NOUN
cana-768	103	48	)	)	PUNCT
cana-768	103	49	,	,	PUNCT
cana-768	103	50	0	0	NUM
cana-768	103	51	≤	≤	NUM
cana-768	103	52	𝒿	𝒿	X
cana-768	103	53	≤	≤	NUM
cana-768	103	54	ռ	ռ	NOUN
cana-768	103	55	,	,	PUNCT
cana-768	103	56	with	with	ADP
cana-768	103	57	boundary	boundary	ADJ
cana-768	103	58	conditions	condition	NOUN
cana-768	103	59	�	�	PROPN
cana-768	103	60	̃	̃	PROPN
cana-768	103	61	�	�	NOUN
cana-768	103	62	(ȶ0	(ȶ0	X
cana-768	103	63	)	)	PUNCT
cana-768	103	64	=	=	SYM
cana-768	103	65	𝜑	𝜑	PROPN
cana-768	103	66	and	and	CCONJ
cana-768	103	67	�	�	PROPN
cana-768	103	68	̃	̃	PROPN
cana-768	103	69	�	�	PROPN
cana-768	103	70	(ȶռ	(ȶռ	NOUN
cana-768	103	71	)	)	PUNCT
cana-768	103	72	=	=	SYM
cana-768	103	73	𝜓	𝜓	PROPN
cana-768	103	74	leads	lead	VERB
cana-768	103	75	to	to	ADP
cana-768	103	76	a	a	DET
cana-768	103	77	linear	linear	ADJ
cana-768	103	78	system	system	NOUN
cana-768	103	79	𝒜ɤ̅	𝒜ɤ̅	NOUN
cana-768	103	80	=	=	SYM
cana-768	103	81	�	�	PROPN
cana-768	103	82	̅	̅	NOUN
cana-768	103	83	�	�	NUM
cana-768	103	84	where	where	SCONJ
cana-768	103	85	,	,	PUNCT
cana-768	103	86	ɤ̅	ɤ̅	X
cana-768	103	87	=	=	SYM
cana-768	103	88	(	(	PUNCT
cana-768	103	89	ɤ̅0	ɤ̅0	NOUN
cana-768	103	90	,	,	PUNCT
cana-768	103	91	ɤ̅1	ɤ̅1	NOUN
cana-768	103	92	…	…	SYM
cana-768	103	93	……	……	X
cana-768	103	94	.	.	PUNCT
cana-768	103	95	.	.	PUNCT
cana-768	104	1	ɤ̅ռ	ɤ̅ռ	NOUN
cana-768	104	2	)	)	PUNCT
cana-768	104	3	′	′	NUM
cana-768	104	4	�	�	NOUN
cana-768	104	5	̅	̅	NOUN
cana-768	104	6	�	�	NOUN
cana-768	104	7	=	=	SYM
cana-768	104	8	(	(	PUNCT
cana-768	104	9	�	�	NOUN
cana-768	104	10	̅	̅	NOUN
cana-768	104	11	�	�	NOUN
cana-768	104	12	0(𝚜	0(𝚜	NOUN
cana-768	104	13	−	−	PROPN
cana-768	104	14	ƥɦ	ƥɦ	PROPN
cana-768	104	15	)	)	PUNCT
cana-768	104	16	−	−	PROPN
cana-768	105	1	2(ƥɦ𝚌	2(ƥɦ𝚌	NUM
cana-768	105	2	−	−	PROPN
cana-768	105	3	𝚜)𝒦0𝜑	𝚜)𝒦0𝜑	PROPN
cana-768	105	4	,	,	PUNCT
cana-768	105	5	�	�	PROPN
cana-768	105	6	̅	̅	NOUN
cana-768	105	7	�	�	NOUN
cana-768	105	8	1	1	NUM
cana-768	105	9	,	,	PUNCT
cana-768	105	10	�	�	NOUN
cana-768	105	11	̅	̅	NOUN
cana-768	105	12	�	�	NOUN
cana-768	105	13	2	2	NUM
cana-768	105	14	,	,	PUNCT
cana-768	105	15	…	…	PUNCT
cana-768	105	16	…	…	SYM
cana-768	105	17	……	……	X
cana-768	105	18	.	.	PUNCT
cana-768	106	1	,	,	PUNCT
cana-768	106	2	�	�	NOUN
cana-768	106	3	̅	̅	NOUN
cana-768	106	4	�	�	NOUN
cana-768	106	5	ռ(𝚜	ռ(𝚜	NOUN
cana-768	106	6	−	−	NOUN
cana-768	106	7	ƥɦ	ƥɦ	NOUN
cana-768	106	8	)	)	PUNCT
cana-768	106	9	−	−	PROPN
cana-768	106	10	2(ƥɦ𝚌	2(ƥɦ𝚌	NUM
cana-768	106	11	−	−	PROPN
cana-768	106	12	𝚜)ϻռ𝜓	𝚜)ϻռ𝜓	NOUN
cana-768	106	13	)	)	PUNCT
cana-768	107	1	′	′	NUM
cana-768	107	2	where	where	SCONJ
cana-768	107	3	,	,	PUNCT
cana-768	107	4	�	�	PROPN
cana-768	107	5	̅	̅	NOUN
cana-768	107	6	�	�	NOUN
cana-768	107	7	𝒿	𝒿	NOUN
cana-768	107	8	=	=	SYM
cana-768	107	9	2(ƥɦ𝚌	2(ƥɦ𝚌	NUM
cana-768	107	10	−	−	NOUN
cana-768	107	11	𝚜)ϣ(ȶ𝒿	𝚜)ϣ(ȶ𝒿	NUM
cana-768	107	12	)	)	PUNCT
cana-768	107	13	,	,	PUNCT
cana-768	108	1	0	0	NUM
cana-768	108	2	≤	≤	NUM
cana-768	108	3	𝒿	𝒿	X
cana-768	108	4	≤	≤	NUM
cana-768	108	5	ռ	ռ	NOUN
cana-768	108	6	then	then	ADV
cana-768	108	7	it	it	PRON
cana-768	108	8	follows	follow	VERB
cana-768	108	9	𝒜(ɤ	𝒜(ɤ	PUNCT
cana-768	108	10	−	−	PROPN
cana-768	108	11	ɤ̅	ɤ̅	X
cana-768	108	12	)	)	PUNCT
cana-768	108	13	=	=	SYM
cana-768	108	14	(	(	PUNCT
cana-768	109	1	𝔇	𝔇	PROPN
cana-768	109	2	−	−	PROPN
cana-768	109	3	�	�	PROPN
cana-768	109	4	̅	̅	NOUN
cana-768	109	5	�	�	NOUN
cana-768	109	6	)	)	PUNCT
cana-768	109	7	(	(	PUNCT
cana-768	109	8	4.2	4.2	NUM
cana-768	109	9	)	)	PUNCT
cana-768	110	1	where	where	SCONJ
cana-768	110	2	,	,	PUNCT
cana-768	110	3	(	(	PUNCT
cana-768	110	4	ɤ	ɤ	X
cana-768	110	5	−	−	PROPN
cana-768	110	6	ɤ̅	ɤ̅	X
cana-768	110	7	)	)	PUNCT
cana-768	110	8	=	=	PUNCT
cana-768	110	9	[	[	PUNCT
cana-768	110	10	ɤ0	ɤ0	PROPN
cana-768	110	11	−	−	PROPN
cana-768	110	12	ɤ̅0	ɤ̅0	PROPN
cana-768	110	13	,	,	PUNCT
cana-768	110	14	ɤ1	ɤ1	NOUN
cana-768	110	15	−	−	NOUN
cana-768	110	16	ɤ̅1	ɤ̅1	NOUN
cana-768	110	17	,	,	PUNCT
cana-768	110	18	ɤ2	ɤ2	VERB
cana-768	110	19	−	−	NOUN
cana-768	110	20	ɤ̅2	ɤ̅2	NOUN
cana-768	110	21	,	,	PUNCT
cana-768	110	22	…	…	PUNCT
cana-768	110	23	…	…	PUNCT
cana-768	110	24	…	…	PUNCT
cana-768	110	25	…	…	PUNCT
cana-768	110	26	ɤռ	ɤռ	ADP
cana-768	110	27	−	−	PROPN
cana-768	110	28	ɤ̅ռ	ɤ̅ռ	PROPN
cana-768	110	29	]	]	X
cana-768	110	30	′	′	NUM
cana-768	110	31	(	(	PUNCT
cana-768	110	32	𝔇	𝔇	PROPN
cana-768	110	33	−	−	PROPN
cana-768	110	34	�	�	PROPN
cana-768	110	35	̅	̅	NOUN
cana-768	110	36	�	�	NOUN
cana-768	110	37	)	)	PUNCT
cana-768	111	1	=	=	PUNCT
cana-768	112	1	[	[	X
cana-768	112	2	−2(ƥɦ𝚌	−2(ƥɦ𝚌	X
cana-768	112	3	−	−	ADJ
cana-768	112	4	𝚜)(𝚜	𝚜)(𝚜	NOUN
cana-768	112	5	−	−	NOUN
cana-768	112	6	ƥɦ)ϣ(ȶ0),−2(ƥɦ𝚌	ƥɦ)ϣ(ȶ0),−2(ƥɦ𝚌	NOUN
cana-768	112	7	−	−	NOUN
cana-768	112	8	𝚜)ϣ(ȶ1	𝚜)ϣ(ȶ1	NOUN
cana-768	112	9	)	)	PUNCT
cana-768	112	10	,	,	PUNCT
cana-768	112	11	…	…	PUNCT
cana-768	112	12	,	,	PUNCT
cana-768	112	13	−2(ƥɦ𝚌	−2(ƥɦ𝚌	X
cana-768	112	14	−	−	PROPN
cana-768	112	15	𝚜)(𝚜	𝚜)(𝚜	PROPN
cana-768	112	16	−	−	PROPN
cana-768	112	17	ƥɦ)ϣ(ȶռ	ƥɦ)ϣ(ȶռ	NOUN
cana-768	112	18	)	)	PUNCT
cana-768	112	19	]	]	PUNCT
cana-768	113	1	′	′	NUM
cana-768	113	2	using	use	VERB
cana-768	113	3	(	(	PUNCT
cana-768	113	4	4.1	4.1	NUM
cana-768	113	5	)	)	PUNCT
cana-768	113	6	we	we	PRON
cana-768	113	7	have	have	VERB
cana-768	113	8	,	,	PUNCT
cana-768	113	9	‖𝔇	‖𝔇	PROPN
cana-768	113	10	−	−	PROPN
cana-768	113	11	�	�	PROPN
cana-768	113	12	̅	̅	NOUN
cana-768	113	13	�	�	NOUN
cana-768	113	14	‖∞	‖∞	NOUN
cana-768	113	15	=	=	SYM
cana-768	113	16	max	max	PROPN
cana-768	113	17	0≤𝒿≤ռ	0≤𝒿≤ռ	PROPN
cana-768	113	18	|𝔇𝒿	|𝔇𝒿	PROPN
cana-768	113	19	−	−	PROPN
cana-768	113	20	�	�	NOUN
cana-768	113	21	̅	̅	NOUN
cana-768	113	22	�	�	NOUN
cana-768	113	23	𝒿|	𝒿|	NOUN
cana-768	113	24	≤	≤	NUM
cana-768	113	25	ϰɦ2(ƥɦ)3	ϰɦ2(ƥɦ)3	PROPN
cana-768	113	26	(	(	PUNCT
cana-768	113	27	4.3	4.3	NUM
cana-768	113	28	)	)	PUNCT
cana-768	113	29	as	as	ADP
cana-768	113	30	0	0	X
cana-768	113	31	<	<	X
cana-768	113	32	휀	휀	NOUN
cana-768	113	33	≪	≪	ADJ
cana-768	113	34	1	1	NUM
cana-768	113	35	and	and	CCONJ
cana-768	113	36	with	with	ADP
cana-768	113	37	sufficiently	sufficiently	ADV
cana-768	113	38	small	small	ADJ
cana-768	113	39	ɦ	ɦ	X
cana-768	113	40	it	it	PRON
cana-768	113	41	can	can	AUX
cana-768	113	42	be	be	AUX
cana-768	113	43	verified	verify	VERB
cana-768	113	44	that	that	SCONJ
cana-768	113	45	the	the	DET
cana-768	113	46	coefficient	coefficient	NOUN
cana-768	113	47	matrix	matrix	NOUN
cana-768	113	48	𝒜	𝒜	NOUN
cana-768	113	49	is	be	AUX
cana-768	113	50	irreducible	irreducible	ADJ
cana-768	113	51	and	and	CCONJ
cana-768	113	52	monotone	monotone	ADJ
cana-768	114	1	[	[	X
cana-768	114	2	21	21	NUM
cana-768	114	3	,	,	PUNCT
cana-768	114	4	22	22	NUM
cana-768	114	5	]	]	PUNCT
cana-768	114	6	.	.	PUNCT
cana-768	115	1	hence	hence	ADV
cana-768	115	2	,	,	PUNCT
cana-768	115	3	𝒜−1	𝒜−1	ADV
cana-768	115	4	exists	exist	VERB
cana-768	115	5	.	.	PUNCT
cana-768	116	1	therefore	therefore	ADV
cana-768	116	2	,	,	PUNCT
cana-768	116	3	from	from	ADP
cana-768	116	4	(	(	PUNCT
cana-768	116	5	4.2	4.2	NUM
cana-768	116	6	)	)	PUNCT
cana-768	116	7	we	we	PRON
cana-768	116	8	must	must	AUX
cana-768	116	9	have	have	VERB
cana-768	116	10	‖ɤ	‖ɤ	NOUN
cana-768	116	11	−	−	VERB
cana-768	116	12	ɤ̅‖∞	ɤ̅‖∞	PROPN
cana-768	116	13	≤	≤	PROPN
cana-768	116	14	‖𝒜−1‖∞‖𝔇	‖𝒜−1‖∞‖𝔇	PROPN
cana-768	116	15	−	−	PROPN
cana-768	116	16	�	�	NOUN
cana-768	116	17	̅	̅	NOUN
cana-768	116	18	�	�	NOUN
cana-768	116	19	‖∞	‖∞	NOUN
cana-768	116	20	(	(	PUNCT
cana-768	116	21	4.4	4.4	NUM
cana-768	116	22	)	)	PUNCT
cana-768	116	23	let	let	VERB
cana-768	116	24	𝜌𝒿	𝜌𝒿	INTJ
cana-768	116	25	,	,	PUNCT
cana-768	116	26	0	0	NUM
cana-768	116	27	≤	≤	NUM
cana-768	116	28	𝒿	𝒿	X
cana-768	116	29	≤	≤	NUM
cana-768	116	30	ռ	ռ	PRON
cana-768	116	31	be	be	AUX
cana-768	116	32	the	the	DET
cana-768	116	33	row	row	NOUN
cana-768	116	34	sum	sum	NOUN
cana-768	116	35	of	of	ADP
cana-768	116	36	the	the	DET
cana-768	116	37	matrix	matrix	NOUN
cana-768	116	38	𝒜	𝒜	NOUN
cana-768	116	39	such	such	ADJ
cana-768	116	40	that	that	DET
cana-768	116	41	𝜌0	𝜌0	ADJ
cana-768	116	42	=	=	SYM
cana-768	116	43	𝔏0(𝚜	𝔏0(𝚜	ADJ
cana-768	116	44	−	−	PROPN
cana-768	116	45	ƥɦ	ƥɦ	NOUN
cana-768	116	46	)	)	PUNCT
cana-768	116	47	−	−	PROPN
cana-768	116	48	2(ƥɦ𝚌	2(ƥɦ𝚌	NUM
cana-768	116	49	−	−	PUNCT
cana-768	117	1	𝚜)𝒦0	𝚜)𝒦0	ADJ
cana-768	117	2	+	+	CCONJ
cana-768	117	3	(	(	PUNCT
cana-768	117	4	ϻ0	ϻ0	NOUN
cana-768	117	5	−	−	PROPN
cana-768	117	6	𝒦0)(𝚜	𝒦0)(𝚜	NOUN
cana-768	117	7	−	−	PROPN
cana-768	117	8	ƥɦ	ƥɦ	NOUN
cana-768	117	9	)	)	PUNCT
cana-768	117	10	𝜌𝒿	𝜌𝒿	X
cana-768	118	1	=	=	PUNCT
cana-768	118	2	𝒦𝒿	𝒦𝒿	PROPN
cana-768	118	3	+	+	PUNCT
cana-768	119	1	𝔏𝒿	𝔏𝒿	PROPN
cana-768	119	2	+	+	NOUN
cana-768	119	3	ϻ𝒿	ϻ𝒿	NOUN
cana-768	119	4	𝒿	𝒿	NOUN
cana-768	119	5	=	=	SYM
cana-768	119	6	1,2	1,2	NUM
cana-768	119	7	,	,	PUNCT
cana-768	119	8	…	…	PUNCT
cana-768	119	9	…	…	SYM
cana-768	119	10	……	……	X
cana-768	119	11	.	.	PUNCT
cana-768	120	1	,	,	PUNCT
cana-768	120	2	ռ	ռ	DET
cana-768	120	3	−	−	PROPN
cana-768	120	4	1	1	NUM
cana-768	120	5	𝜌ռ	𝜌ռ	NOUN
cana-768	120	6	=	=	PUNCT
cana-768	120	7	(	(	PUNCT
cana-768	120	8	𝒦ռ	𝒦ռ	PROPN
cana-768	120	9	−ϻռ)(𝚜	−ϻռ)(𝚜	NOUN
cana-768	120	10	−	−	PROPN
cana-768	120	11	ƥɦ	ƥɦ	ADJ
cana-768	120	12	)	)	PUNCT
cana-768	120	13	+	+	CCONJ
cana-768	121	1	𝔏ռ(𝚜	𝔏ռ(𝚜	DET
cana-768	121	2	−	−	NUM
cana-768	121	3	ƥɦ	ƥɦ	NOUN
cana-768	121	4	)	)	PUNCT
cana-768	121	5	−	−	PROPN
cana-768	121	6	2(ƥɦ𝚌	2(ƥɦ𝚌	NUM
cana-768	121	7	−	−	PROPN
cana-768	122	1	𝚜)ϻռ	𝚜)ϻռ	PROPN
cana-768	122	2	now	now	ADV
cana-768	122	3	from	from	ADP
cana-768	122	4	theory	theory	NOUN
cana-768	122	5	of	of	ADP
cana-768	122	6	matrices	matrix	NOUN
cana-768	122	7	we	we	PRON
cana-768	122	8	have	have	VERB
cana-768	122	9	,	,	PUNCT
cana-768	122	10	‖𝒜−1‖∞	‖𝒜−1‖∞	PROPN
cana-768	122	11	≤	≤	NOUN
cana-768	122	12	1	1	NUM
cana-768	122	13	𝜌	𝜌	PART
cana-768	122	14	≤	≤	NUM
cana-768	122	15	1	1	NUM
cana-768	122	16	|𝜌|	|𝜌|	PROPN
cana-768	122	17	≤	≤	NOUN
cana-768	122	18	1	1	NUM
cana-768	122	19	(	(	PUNCT
cana-768	122	20	ƥɦ)3	ƥɦ)3	PROPN
cana-768	122	21	(	(	PUNCT
cana-768	122	22	4.5	4.5	NUM
cana-768	122	23	)	)	PUNCT
cana-768	122	24	where	where	SCONJ
cana-768	122	25	,	,	PUNCT
cana-768	122	26	ρ	ρ	NOUN
cana-768	122	27	=	=	NOUN
cana-768	122	28	min{𝜌0	min{𝜌0	NOUN
cana-768	122	29	,	,	PUNCT
cana-768	122	30	𝜌1	𝜌1	PROPN
cana-768	122	31	,	,	PUNCT
cana-768	122	32	𝜌3	𝜌3	PROPN
cana-768	122	33	,	,	PUNCT
cana-768	122	34	…	…	PUNCT
cana-768	122	35	…	…	PUNCT
cana-768	122	36	…	…	PUNCT
cana-768	122	37	𝜌ռ	𝜌ռ	NOUN
cana-768	122	38	}	}	PUNCT
cana-768	122	39	now	now	ADV
cana-768	122	40	,	,	PUNCT
cana-768	122	41	substituting	substitute	VERB
cana-768	122	42	the	the	DET
cana-768	122	43	values	value	NOUN
cana-768	122	44	of	of	ADP
cana-768	122	45	(	(	PUNCT
cana-768	122	46	4.3	4.3	NUM
cana-768	122	47	)	)	PUNCT
cana-768	122	48	and	and	CCONJ
cana-768	122	49	(	(	PUNCT
cana-768	122	50	4.5	4.5	NUM
cana-768	122	51	)	)	PUNCT
cana-768	122	52	in	in	ADP
cana-768	122	53	(	(	PUNCT
cana-768	122	54	4.4	4.4	NUM
cana-768	122	55	)	)	PUNCT
cana-768	122	56	gives	give	VERB
cana-768	122	57	communications	communication	NOUN
cana-768	122	58	on	on	ADP
cana-768	122	59	applied	apply	VERB
cana-768	122	60	nonlinear	nonlinear	ADJ
cana-768	122	61	analysis	analysis	NOUN
cana-768	122	62	issn	issn	NOUN
cana-768	122	63	:	:	PUNCT
cana-768	122	64	1074	1074	NUM
cana-768	122	65	-	-	PUNCT
cana-768	122	66	133x	133x	NUM
cana-768	122	67	vol	vol	NOUN
cana-768	122	68	31	31	NUM
cana-768	122	69	no	no	NOUN
cana-768	122	70	.	.	PUNCT
cana-768	123	1	3s	3s	NUM
cana-768	123	2	(	(	PUNCT
cana-768	123	3	2024	2024	NUM
cana-768	123	4	)	)	PUNCT
cana-768	123	5	318	318	NUM
cana-768	123	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	123	7	‖ɤ	‖ɤ	X
cana-768	123	8	−	−	PROPN
cana-768	124	1	ɤ̅‖∞	ɤ̅‖∞	PROPN
cana-768	124	2	≤	≤	PROPN
cana-768	124	3	ϰɦ2(ƥɦ)3	ϰɦ2(ƥɦ)3	PROPN
cana-768	124	4	1	1	NUM
cana-768	124	5	|𝜌|	|𝜌|	PROPN
cana-768	124	6	≤	≤	PROPN
cana-768	124	7	ϰɦ2(ƥɦ)3	ϰɦ2(ƥɦ)3	PROPN
cana-768	124	8	1	1	NUM
cana-768	124	9	(	(	PUNCT
cana-768	124	10	ƥɦ)3	ƥɦ)3	PROPN
cana-768	124	11	=	=	SYM
cana-768	124	12	ϰɦ2	ϰɦ2	PROPN
cana-768	124	13	(	(	PUNCT
cana-768	124	14	4.6	4.6	NUM
cana-768	124	15	)	)	PUNCT
cana-768	124	16	using	use	VERB
cana-768	124	17	lemma	lemma	PROPN
cana-768	124	18	1	1	NUM
cana-768	124	19	and	and	CCONJ
cana-768	124	20	equation	equation	NOUN
cana-768	124	21	(	(	PUNCT
cana-768	124	22	4.6	4.6	NUM
cana-768	124	23	)	)	PUNCT
cana-768	124	24	,	,	PUNCT
cana-768	124	25	we	we	PRON
cana-768	124	26	obtained	obtain	VERB
cana-768	124	27	‖𝒰(ȶ	‖𝒰(ȶ	NOUN
cana-768	124	28	)	)	PUNCT
cana-768	124	29	−	−	PROPN
cana-768	124	30	�	�	PROPN
cana-768	124	31	̃	̃	PROPN
cana-768	124	32	�	�	PROPN
cana-768	124	33	(ȶ)‖	(ȶ)‖	PROPN
cana-768	124	34	∞	∞	PROPN
cana-768	124	35	≤	≤	NOUN
cana-768	124	36	∑	∑	PUNCT
cana-768	124	37	(	(	PUNCT
cana-768	124	38	ɤ𝒿	ɤ𝒿	PROPN
cana-768	124	39	−	−	PROPN
cana-768	124	40	ɤ̅𝒿)|ᏸ𝒿(ȶ)|	ɤ̅𝒿)|ᏸ𝒿(ȶ)|	PROPN
cana-768	124	41	ռ+1	ռ+1	ADV
cana-768	124	42	𝒿=−1	𝒿=−1	NUM
cana-768	124	43	≤	≤	NUM
cana-768	124	44	∑	∑	PUNCT
cana-768	124	45	|ᏸ𝒿(ȶ)|‖ɤ	|ᏸ𝒿(ȶ)|‖ɤ	PROPN
cana-768	124	46	−	−	ADP
cana-768	124	47	ɤ̅‖∞	ɤ̅‖∞	NOUN
cana-768	124	48	≤	≤	NOUN
cana-768	124	49	ռ+1	ռ+1	ADV
cana-768	124	50	𝒿=−1	𝒿=−1	NUM
cana-768	124	51	5ϰɦ2	5ϰɦ2	NUM
cana-768	124	52	2	2	NUM
cana-768	124	53	(	(	PUNCT
cana-768	124	54	4.7	4.7	NUM
cana-768	124	55	)	)	PUNCT
cana-768	124	56	applying	apply	VERB
cana-768	124	57	the	the	DET
cana-768	124	58	theorem	theorem	NOUN
cana-768	124	59	1	1	NUM
cana-768	124	60	we	we	PRON
cana-768	124	61	have	have	VERB
cana-768	124	62	‖𝓊(ȶ	‖𝓊(ȶ	NOUN
cana-768	124	63	)	)	PUNCT
cana-768	124	64	−	−	PROPN
cana-768	124	65	�	�	PROPN
cana-768	124	66	̃	̃	PROPN
cana-768	124	67	�	�	PROPN
cana-768	124	68	(ȶ)‖	(ȶ)‖	PROPN
cana-768	124	69	∞	∞	PROPN
cana-768	124	70	≤	≤	NOUN
cana-768	124	71	ϰ0ɦ	ϰ0ɦ	NOUN
cana-768	124	72	4	4	NUM
cana-768	124	73	(	(	PUNCT
cana-768	124	74	4.8	4.8	NUM
cana-768	124	75	)	)	PUNCT
cana-768	124	76	now	now	ADV
cana-768	124	77	combining	combine	VERB
cana-768	124	78	the	the	DET
cana-768	124	79	results	result	NOUN
cana-768	124	80	(	(	PUNCT
cana-768	124	81	4.7	4.7	NUM
cana-768	124	82	)	)	PUNCT
cana-768	124	83	and	and	CCONJ
cana-768	124	84	(	(	PUNCT
cana-768	124	85	4.8	4.8	NUM
cana-768	124	86	)	)	PUNCT
cana-768	124	87	,	,	PUNCT
cana-768	124	88	‖𝓊(ȶ	‖𝓊(ȶ	NOUN
cana-768	124	89	)	)	PUNCT
cana-768	124	90	−	−	NOUN
cana-768	124	91	𝒰(ȶ)‖∞	𝒰(ȶ)‖∞	ADJ
cana-768	124	92	≤	≤	PUNCT
cana-768	124	93	ӄɦ2	ӄɦ2	NOUN
cana-768	124	94	where	where	SCONJ
cana-768	124	95	,	,	PUNCT
cana-768	124	96	ӄ	ӄ	X
cana-768	124	97	=	=	NOUN
cana-768	124	98	ϰ0ɦ	ϰ0ɦ	NOUN
cana-768	124	99	2	2	NUM
cana-768	124	100	+	+	NUM
cana-768	124	101	5ϰ	5ϰ	NUM
cana-768	124	102	2	2	NUM
cana-768	124	103	hence	hence	ADV
cana-768	124	104	,	,	PUNCT
cana-768	124	105	the	the	DET
cana-768	124	106	theorem	theorem	NOUN
cana-768	124	107	is	be	AUX
cana-768	124	108	proved	prove	VERB
cana-768	124	109	.	.	PUNCT
cana-768	125	1	numerical	numerical	ADJ
cana-768	125	2	experiments	experiment	NOUN
cana-768	125	3	:	:	PUNCT
cana-768	125	4	the	the	DET
cana-768	125	5	efficiency	efficiency	NOUN
cana-768	125	6	of	of	ADP
cana-768	125	7	the	the	DET
cana-768	125	8	proposed	propose	VERB
cana-768	125	9	method	method	NOUN
cana-768	125	10	is	be	AUX
cana-768	125	11	demonstrated	demonstrate	VERB
cana-768	125	12	by	by	ADP
cana-768	125	13	the	the	DET
cana-768	125	14	four	four	NUM
cana-768	125	15	model	model	NOUN
cana-768	125	16	problems	problem	NOUN
cana-768	125	17	.	.	PUNCT
cana-768	126	1	our	our	PRON
cana-768	126	2	proposed	propose	VERB
cana-768	126	3	solutions	solution	NOUN
cana-768	126	4	are	be	AUX
cana-768	126	5	compared	compare	VERB
cana-768	126	6	with	with	ADP
cana-768	126	7	the	the	DET
cana-768	126	8	exact	exact	ADJ
cana-768	126	9	solution	solution	NOUN
cana-768	126	10	those	those	PRON
cana-768	126	11	are	be	AUX
cana-768	126	12	available	available	ADJ
cana-768	126	13	in	in	ADP
cana-768	126	14	the	the	DET
cana-768	126	15	literature	literature	NOUN
cana-768	126	16	for	for	ADP
cana-768	126	17	various	various	ADJ
cana-768	126	18	values	value	NOUN
cana-768	126	19	of	of	ADP
cana-768	126	20	휀	휀	NOUN
cana-768	126	21	and	and	CCONJ
cana-768	126	22	δ	δ	PROPN
cana-768	126	23	.	.	PUNCT
cana-768	127	1	we	we	PRON
cana-768	127	2	are	be	AUX
cana-768	127	3	using	use	VERB
cana-768	127	4	double	double	ADJ
cana-768	127	5	mesh	mesh	NOUN
cana-768	127	6	principle	principle	NOUN
cana-768	127	7	given	give	VERB
cana-768	127	8	by	by	ADP
cana-768	127	9	𝐸ռ	𝐸ռ	PROPN
cana-768	127	10	=	=	SYM
cana-768	127	11	max	max	PROPN
cana-768	127	12	0≤𝑖≤ռ	0≤𝑖≤ռ	PROPN
cana-768	127	13	|𝓊𝑖	|𝓊𝑖	X
cana-768	127	14	ռ	ռ	PROPN
cana-768	127	15	−𝓊2𝑖	−𝓊2𝑖	X
cana-768	127	16	2ռ|	2ռ|	NUM
cana-768	127	17	to	to	PART
cana-768	127	18	calculate	calculate	VERB
cana-768	127	19	the	the	DET
cana-768	127	20	absolute	absolute	ADJ
cana-768	127	21	error	error	NOUN
cana-768	127	22	wherein	wherein	SCONJ
cana-768	127	23	the	the	DET
cana-768	127	24	exact	exact	ADJ
cana-768	127	25	solutions	solution	NOUN
cana-768	127	26	are	be	AUX
cana-768	127	27	not	not	PART
cana-768	127	28	available	available	ADJ
cana-768	127	29	.	.	PUNCT
cana-768	128	1	example	example	NOUN
cana-768	128	2	5.1	5.1	NUM
cana-768	128	3	:	:	PUNCT
cana-768	128	4	let	let	VERB
cana-768	128	5	us	we	PRON
cana-768	128	6	take	take	VERB
cana-768	128	7	a	a	DET
cana-768	128	8	differential	differential	ADJ
cana-768	128	9	equation	equation	NOUN
cana-768	128	10	containing	contain	VERB
cana-768	128	11	a	a	DET
cana-768	128	12	negative	negative	ADJ
cana-768	128	13	shift	shift	NOUN
cana-768	128	14	with	with	ADP
cana-768	128	15	left	left	ADJ
cana-768	128	16	end	end	NOUN
cana-768	128	17	layer	layer	NOUN
cana-768	128	18	휀𝓊′′(ȶ	휀𝓊′′(ȶ	NOUN
cana-768	128	19	)	)	PUNCT
cana-768	129	1	+	+	PUNCT
cana-768	130	1	𝓊′(ȶ	𝓊′(ȶ	CCONJ
cana-768	131	1	−	−	ADP
cana-768	131	2	𝛿	𝛿	NOUN
cana-768	131	3	)	)	PUNCT
cana-768	131	4	−	−	PRON
cana-768	131	5	𝓊(ȶ	𝓊(ȶ	NOUN
cana-768	131	6	)	)	PUNCT
cana-768	131	7	=	=	SYM
cana-768	131	8	0	0	NUM
cana-768	131	9	,	,	PUNCT
cana-768	131	10	0	0	NUM
cana-768	131	11	≤	≤	NUM
cana-768	131	12	ȶ	ȶ	X
cana-768	131	13	≤	≤	NUM
cana-768	131	14	1	1	NUM
cana-768	131	15	,	,	PUNCT
cana-768	131	16	with	with	ADP
cana-768	131	17	the	the	DET
cana-768	131	18	boundary	boundary	ADJ
cana-768	131	19	conditions	condition	NOUN
cana-768	131	20	𝓊(0	𝓊(0	PROPN
cana-768	131	21	)	)	PUNCT
cana-768	131	22	=	=	SYM
cana-768	131	23	1	1	NUM
cana-768	131	24	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-768	131	25	𝓊(1	𝓊(1	NOUN
cana-768	131	26	)	)	PUNCT
cana-768	131	27	=	=	SYM
cana-768	131	28	1	1	NUM
cana-768	131	29	we	we	PRON
cana-768	131	30	have	have	VERB
cana-768	131	31	the	the	DET
cana-768	131	32	exact	exact	ADJ
cana-768	131	33	solution	solution	NOUN
cana-768	131	34	as	as	ADP
cana-768	131	35	𝓊(ȶ	𝓊(ȶ	NOUN
cana-768	131	36	)	)	PUNCT
cana-768	131	37	=	=	PUNCT
cana-768	131	38	(	(	PUNCT
cana-768	131	39	1−e𝓌2)e𝓌1ȶ+(e𝓌1−1)e𝓌2ȶ	1−e𝓌2)e𝓌1ȶ+(e𝓌1−1)e𝓌2ȶ	NUM
cana-768	131	40	)	)	PUNCT
cana-768	131	41	(	(	PUNCT
cana-768	131	42	e𝓌1−e𝓌2	e𝓌1−e𝓌2	NOUN
cana-768	131	43	)	)	PUNCT
cana-768	132	1	where	where	SCONJ
cana-768	132	2	,	,	PUNCT
cana-768	132	3	𝓌1	𝓌1	PROPN
cana-768	132	4	=	=	SYM
cana-768	132	5	−	−	PROPN
cana-768	132	6	1	1	NUM
cana-768	132	7	−	−	PROPN
cana-768	132	8	√1	√1	PROPN
cana-768	132	9	+	+	CCONJ
cana-768	132	10	4	4	NUM
cana-768	132	11	(	(	PUNCT
cana-768	132	12	ε−δ	ε−δ	PROPN
cana-768	132	13	)	)	PUNCT
cana-768	132	14	2(ε−δ	2(ε−δ	NOUN
cana-768	132	15	)	)	PUNCT
cana-768	132	16	and	and	CCONJ
cana-768	132	17	𝓌1	𝓌1	NOUN
cana-768	132	18	=	=	SYM
cana-768	132	19	−	−	PROPN
cana-768	132	20	1	1	NUM
cana-768	132	21	+	+	CCONJ
cana-768	132	22	√	√	NUM
cana-768	132	23	1	1	NUM
cana-768	132	24	+	+	X
cana-768	132	25	4(ε−δ	4(ε−δ	PROPN
cana-768	132	26	)	)	PUNCT
cana-768	132	27	2(ε−δ	2(ε−δ	NOUN
cana-768	132	28	)	)	PUNCT
cana-768	132	29	the	the	DET
cana-768	132	30	comparisons	comparison	NOUN
cana-768	132	31	of	of	ADP
cana-768	132	32	the	the	DET
cana-768	132	33	absolute	absolute	ADJ
cana-768	132	34	error	error	NOUN
cana-768	132	35	are	be	AUX
cana-768	132	36	presented	present	VERB
cana-768	132	37	in	in	ADP
cana-768	132	38	the	the	DET
cana-768	132	39	table	table	NOUN
cana-768	132	40	1	1	NUM
cana-768	132	41	and	and	CCONJ
cana-768	132	42	table	table	NOUN
cana-768	132	43	2	2	NUM
cana-768	132	44	with	with	ADP
cana-768	132	45	left	left	ADJ
cana-768	132	46	end	end	NOUN
cana-768	132	47	layer	layer	NOUN
cana-768	132	48	for	for	ADP
cana-768	132	49	various	various	ADJ
cana-768	132	50	values	value	NOUN
cana-768	132	51	of	of	ADP
cana-768	132	52	ε	ε	PROPN
cana-768	132	53	and	and	CCONJ
cana-768	132	54	δ	δ	PROPN
cana-768	132	55	.and	.and	PUNCT
cana-768	133	1	the	the	DET
cana-768	133	2	impact	impact	NOUN
cana-768	133	3	of	of	ADP
cana-768	133	4	the	the	DET
cana-768	133	5	parameter	parameter	NOUN
cana-768	133	6	are	be	AUX
cana-768	133	7	shown	show	VERB
cana-768	133	8	in	in	ADP
cana-768	133	9	graph	graph	NOUN
cana-768	133	10	presented	present	VERB
cana-768	133	11	in	in	ADP
cana-768	133	12	the	the	DET
cana-768	133	13	figure	figure	NOUN
cana-768	133	14	1	1	NUM
cana-768	133	15	and	and	CCONJ
cana-768	133	16	figure	figure	VERB
cana-768	133	17	2	2	NUM
cana-768	133	18	.	.	PUNCT
cana-768	133	19	example	example	NOUN
cana-768	133	20	5.2	5.2	NUM
cana-768	133	21	:	:	PUNCT
cana-768	133	22	let	let	VERB
cana-768	133	23	us	we	PRON
cana-768	133	24	take	take	VERB
cana-768	133	25	a	a	DET
cana-768	133	26	variable	variable	ADJ
cana-768	133	27	coefficient	coefficient	NOUN
cana-768	133	28	differential	differential	ADJ
cana-768	133	29	equation	equation	NOUN
cana-768	133	30	with	with	ADP
cana-768	133	31	negative	negative	ADJ
cana-768	133	32	shift	shift	NOUN
cana-768	133	33	휀𝓊′′(ȶ	휀𝓊′′(ȶ	NOUN
cana-768	133	34	)	)	PUNCT
cana-768	134	1	+	+	NUM
cana-768	134	2	𝑒−0.5ȶ𝓊′(ȶ	𝑒−0.5ȶ𝓊′(ȶ	PRON
cana-768	135	1	−	−	ADP
cana-768	135	2	𝛿	𝛿	NOUN
cana-768	135	3	)	)	PUNCT
cana-768	135	4	−	−	PRON
cana-768	135	5	𝓊(ȶ	𝓊(ȶ	NOUN
cana-768	135	6	)	)	PUNCT
cana-768	135	7	=	=	SYM
cana-768	135	8	0	0	NUM
cana-768	135	9	,	,	PUNCT
cana-768	135	10	with	with	ADP
cana-768	135	11	𝓊(0	𝓊(0	NOUN
cana-768	135	12	)	)	PUNCT
cana-768	135	13	=	=	NOUN
cana-768	135	14	1	1	NUM
cana-768	135	15	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-768	135	16	𝓊(1	𝓊(1	NOUN
cana-768	135	17	)	)	PUNCT
cana-768	135	18	=	=	SYM
cana-768	135	19	1	1	NUM
cana-768	135	20	communications	communication	NOUN
cana-768	135	21	on	on	ADP
cana-768	135	22	applied	apply	VERB
cana-768	135	23	nonlinear	nonlinear	ADJ
cana-768	135	24	analysis	analysis	NOUN
cana-768	135	25	issn	issn	NOUN
cana-768	135	26	:	:	PUNCT
cana-768	135	27	1074	1074	NUM
cana-768	135	28	-	-	PUNCT
cana-768	135	29	133x	133x	NUM
cana-768	135	30	vol	vol	NOUN
cana-768	135	31	31	31	NUM
cana-768	135	32	no	no	NOUN
cana-768	135	33	.	.	PUNCT
cana-768	136	1	3s	3s	NUM
cana-768	136	2	(	(	PUNCT
cana-768	136	3	2024	2024	NUM
cana-768	136	4	)	)	PUNCT
cana-768	136	5	319	319	NUM
cana-768	136	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	137	1	we	we	PRON
cana-768	137	2	are	be	AUX
cana-768	137	3	using	use	VERB
cana-768	137	4	double	double	ADJ
cana-768	137	5	mesh	mesh	NOUN
cana-768	137	6	principle	principle	NOUN
cana-768	137	7	to	to	PART
cana-768	137	8	calculate	calculate	VERB
cana-768	137	9	the	the	DET
cana-768	137	10	maximum	maximum	ADJ
cana-768	137	11	absolute	absolute	ADJ
cana-768	137	12	error	error	NOUN
cana-768	137	13	and	and	CCONJ
cana-768	137	14	presented	present	VERB
cana-768	137	15	in	in	ADP
cana-768	137	16	the	the	DET
cana-768	137	17	table	table	NOUN
cana-768	137	18	3	3	NUM
cana-768	137	19	.	.	X
cana-768	138	1	for	for	ADP
cana-768	138	2	various	various	ADJ
cana-768	138	3	values	value	NOUN
cana-768	138	4	of	of	ADP
cana-768	138	5	ε	ε	PROPN
cana-768	138	6	and	and	CCONJ
cana-768	138	7	δ	δ	PROPN
cana-768	138	8	.	.	PUNCT
cana-768	139	1	the	the	DET
cana-768	139	2	graph	graph	NOUN
cana-768	139	3	of	of	ADP
cana-768	139	4	the	the	DET
cana-768	139	5	computed	compute	VERB
cana-768	139	6	solution	solution	NOUN
cana-768	139	7	is	be	AUX
cana-768	139	8	presented	present	VERB
cana-768	139	9	in	in	ADP
cana-768	139	10	the	the	DET
cana-768	139	11	figure	figure	NOUN
cana-768	139	12	3	3	NUM
cana-768	139	13	.	.	PUNCT
cana-768	139	14	example	example	NOUN
cana-768	139	15	5.3	5.3	NUM
cana-768	139	16	:	:	PUNCT
cana-768	139	17	let	let	VERB
cana-768	139	18	us	we	PRON
cana-768	139	19	take	take	VERB
cana-768	139	20	a	a	DET
cana-768	139	21	differential	differential	ADJ
cana-768	139	22	equation	equation	NOUN
cana-768	139	23	containing	contain	VERB
cana-768	139	24	a	a	DET
cana-768	139	25	negative	negative	ADJ
cana-768	139	26	shift	shift	NOUN
cana-768	139	27	with	with	ADP
cana-768	139	28	right	right	ADJ
cana-768	139	29	end	end	NOUN
cana-768	139	30	layer	layer	NOUN
cana-768	139	31	휀𝓊′′(ȶ	휀𝓊′′(ȶ	NOUN
cana-768	139	32	)	)	PUNCT
cana-768	139	33	−	−	PROPN
cana-768	140	1	𝓊′(ȶ	𝓊′(ȶ	CCONJ
cana-768	141	1	−	−	NUM
cana-768	141	2	𝛿	𝛿	NOUN
cana-768	141	3	)	)	PUNCT
cana-768	141	4	−	−	PRON
cana-768	141	5	𝓊(ȶ	𝓊(ȶ	NOUN
cana-768	141	6	)	)	PUNCT
cana-768	141	7	=	=	SYM
cana-768	141	8	0	0	NUM
cana-768	141	9	,	,	PUNCT
cana-768	141	10	with	with	ADP
cana-768	141	11	the	the	DET
cana-768	141	12	boundary	boundary	ADJ
cana-768	141	13	conditions	condition	NOUN
cana-768	141	14	𝓊(0	𝓊(0	PROPN
cana-768	141	15	)	)	PUNCT
cana-768	141	16	=	=	SYM
cana-768	141	17	1	1	NUM
cana-768	141	18	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-768	141	19	𝓊(1	𝓊(1	NOUN
cana-768	141	20	)	)	PUNCT
cana-768	141	21	=	=	SYM
cana-768	141	22	−1	−1	NOUN
cana-768	141	23	we	we	PRON
cana-768	141	24	have	have	VERB
cana-768	141	25	the	the	DET
cana-768	141	26	exact	exact	ADJ
cana-768	141	27	solution	solution	NOUN
cana-768	141	28	as	as	ADP
cana-768	141	29	𝓊(ȶ	𝓊(ȶ	NOUN
cana-768	141	30	)	)	PUNCT
cana-768	141	31	=	=	PUNCT
cana-768	141	32	(	(	PUNCT
cana-768	141	33	(	(	PUNCT
cana-768	141	34	1+e𝓌2)e𝓌1ȶ−(e𝓌1	1+e𝓌2)e𝓌1ȶ−(e𝓌1	NUM
cana-768	141	35	+	+	NOUN
cana-768	141	36	1)e𝓌2ȶ	1)e𝓌2ȶ	NUM
cana-768	141	37	)	)	PUNCT
cana-768	141	38	(	(	PUNCT
cana-768	141	39	e𝓌2−e𝓌1	e𝓌2−e𝓌1	X
cana-768	141	40	)	)	PUNCT
cana-768	141	41	where	where	SCONJ
cana-768	141	42	𝓌1	𝓌1	PROPN
cana-768	141	43	=	=	NOUN
cana-768	142	1	1	1	NUM
cana-768	142	2	−	−	PROPN
cana-768	142	3	√1	√1	PROPN
cana-768	143	1	+	+	CCONJ
cana-768	143	2	4	4	NUM
cana-768	143	3	(	(	PUNCT
cana-768	143	4	ε−δ	ε−δ	PROPN
cana-768	143	5	)	)	PUNCT
cana-768	143	6	2(ε+δ	2(ε+δ	NUM
cana-768	143	7	)	)	PUNCT
cana-768	143	8	and	and	CCONJ
cana-768	143	9	𝓌1	𝓌1	NOUN
cana-768	143	10	=	=	NOUN
cana-768	143	11	1	1	NUM
cana-768	143	12	+	+	CCONJ
cana-768	143	13	√	√	NUM
cana-768	143	14	1	1	NUM
cana-768	143	15	+	+	X
cana-768	143	16	4(ε−δ	4(ε−δ	PROPN
cana-768	143	17	)	)	PUNCT
cana-768	143	18	2(ε+δ	2(ε+δ	NUM
cana-768	143	19	)	)	PUNCT
cana-768	143	20	the	the	DET
cana-768	143	21	comparison	comparison	NOUN
cana-768	143	22	of	of	ADP
cana-768	143	23	the	the	DET
cana-768	143	24	absolute	absolute	ADJ
cana-768	143	25	errors	error	NOUN
cana-768	143	26	are	be	AUX
cana-768	143	27	presented	present	VERB
cana-768	143	28	in	in	ADP
cana-768	143	29	the	the	DET
cana-768	143	30	table	table	NOUN
cana-768	143	31	4	4	NUM
cana-768	143	32	and	and	CCONJ
cana-768	143	33	table	table	NOUN
cana-768	143	34	5	5	NUM
cana-768	143	35	with	with	ADP
cana-768	143	36	left	left	ADJ
cana-768	143	37	end	end	NOUN
cana-768	143	38	layer	layer	NOUN
cana-768	143	39	for	for	ADP
cana-768	143	40	various	various	ADJ
cana-768	143	41	values	value	NOUN
cana-768	143	42	of	of	ADP
cana-768	143	43	ε	ε	PROPN
cana-768	143	44	and	and	CCONJ
cana-768	143	45	δ	δ	PROPN
cana-768	143	46	.and	.and	PUNCT
cana-768	144	1	the	the	DET
cana-768	144	2	impact	impact	NOUN
cana-768	144	3	of	of	ADP
cana-768	144	4	the	the	DET
cana-768	144	5	parameter	parameter	NOUN
cana-768	144	6	are	be	AUX
cana-768	144	7	shown	show	VERB
cana-768	144	8	in	in	ADP
cana-768	144	9	graph	graph	NOUN
cana-768	144	10	presented	present	VERB
cana-768	144	11	in	in	ADP
cana-768	144	12	the	the	DET
cana-768	144	13	figure	figure	NOUN
cana-768	144	14	4	4	NUM
cana-768	144	15	.	.	PUNCT
cana-768	144	16	and	and	CCONJ
cana-768	144	17	figure	figure	VERB
cana-768	144	18	5	5	NUM
cana-768	144	19	.	.	PUNCT
cana-768	144	20	example	example	NOUN
cana-768	144	21	5.4	5.4	NUM
cana-768	144	22	:	:	PUNCT
cana-768	144	23	let	let	VERB
cana-768	144	24	us	we	PRON
cana-768	144	25	take	take	VERB
cana-768	144	26	a	a	DET
cana-768	144	27	variable	variable	ADJ
cana-768	144	28	coefficient	coefficient	NOUN
cana-768	144	29	differential	differential	NOUN
cana-768	144	30	equation	equation	NOUN
cana-768	144	31	with	with	ADP
cana-768	144	32	a	a	DET
cana-768	144	33	delay	delay	NOUN
cana-768	144	34	term	term	NOUN
cana-768	144	35	휀𝓊′′(ȶ	휀𝓊′′(ȶ	NOUN
cana-768	144	36	)	)	PUNCT
cana-768	145	1	−	−	NOUN
cana-768	145	2	𝑒ȶ𝓊′(ȶ	𝑒ȶ𝓊′(ȶ	NOUN
cana-768	145	3	−	−	PROPN
cana-768	145	4	𝛿	𝛿	NOUN
cana-768	145	5	)	)	PUNCT
cana-768	145	6	−	−	NOUN
cana-768	145	7	ȶ𝓊(ȶ	ȶ𝓊(ȶ	NOUN
cana-768	145	8	)	)	PUNCT
cana-768	146	1	=	=	SYM
cana-768	146	2	0	0	NUM
cana-768	146	3	,	,	PUNCT
cana-768	146	4	with	with	ADP
cana-768	146	5	𝓊(0	𝓊(0	NOUN
cana-768	146	6	)	)	PUNCT
cana-768	146	7	=	=	NOUN
cana-768	146	8	1	1	NUM
cana-768	146	9	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-768	146	10	𝓊(1	𝓊(1	NOUN
cana-768	146	11	)	)	PUNCT
cana-768	146	12	=	=	SYM
cana-768	147	1	1	1	NUM
cana-768	147	2	the	the	DET
cana-768	147	3	maximum	maximum	ADJ
cana-768	147	4	absolute	absolute	ADJ
cana-768	147	5	errors	error	NOUN
cana-768	147	6	are	be	AUX
cana-768	147	7	calculated	calculate	VERB
cana-768	147	8	by	by	ADP
cana-768	147	9	double	double	ADJ
cana-768	147	10	mesh	mesh	NOUN
cana-768	147	11	principle	principle	NOUN
cana-768	147	12	is	be	AUX
cana-768	147	13	presented	present	VERB
cana-768	147	14	in	in	ADP
cana-768	147	15	the	the	DET
cana-768	147	16	table	table	NOUN
cana-768	147	17	6	6	NUM
cana-768	147	18	.	.	PUNCT
cana-768	148	1	for	for	ADP
cana-768	148	2	various	various	ADJ
cana-768	148	3	values	value	NOUN
cana-768	148	4	of	of	ADP
cana-768	148	5	ε	ε	PROPN
cana-768	148	6	and	and	CCONJ
cana-768	148	7	δ	δ	PROPN
cana-768	148	8	.	.	PUNCT
cana-768	149	1	the	the	DET
cana-768	149	2	graph	graph	NOUN
cana-768	149	3	of	of	ADP
cana-768	149	4	the	the	DET
cana-768	149	5	computed	compute	VERB
cana-768	149	6	solution	solution	NOUN
cana-768	149	7	is	be	AUX
cana-768	149	8	presented	present	VERB
cana-768	149	9	in	in	ADP
cana-768	149	10	the	the	DET
cana-768	149	11	figure	figure	NOUN
cana-768	149	12	7	7	NUM
cana-768	149	13	.	.	PUNCT
cana-768	149	14	table	table	NOUN
cana-768	149	15	1	1	NUM
cana-768	149	16	:	:	PUNCT
cana-768	149	17	maximum	maximum	ADJ
cana-768	149	18	absolute	absolute	ADJ
cana-768	149	19	error	error	NOUN
cana-768	149	20	with	with	ADP
cana-768	149	21	휀	휀	NOUN
cana-768	149	22	=	=	SYM
cana-768	149	23	0.1	0.1	NUM
cana-768	149	24	for	for	ADP
cana-768	149	25	various	various	ADJ
cana-768	149	26	values	value	NOUN
cana-768	149	27	of	of	ADP
cana-768	149	28	δ	δ	PROPN
cana-768	149	29	and	and	CCONJ
cana-768	149	30	ռ	ռ	PROPN
cana-768	149	31	(	(	PUNCT
cana-768	149	32	example	example	NOUN
cana-768	149	33	5.1	5.1	NUM
cana-768	149	34	)	)	PUNCT
cana-768	149	35	table	table	NOUN
cana-768	149	36	2	2	NUM
cana-768	149	37	:	:	PUNCT
cana-768	149	38	absolute	absolute	ADJ
cana-768	149	39	error	error	NOUN
cana-768	149	40	with	with	ADP
cana-768	149	41	휀	휀	NOUN
cana-768	149	42	=	=	NOUN
cana-768	149	43	0.02	0.02	NUM
cana-768	149	44	,	,	PUNCT
cana-768	149	45	δ	δ	PROPN
cana-768	149	46	=	=	SYM
cana-768	149	47	0.001and	0.001and	NUM
cana-768	149	48	ɦ	ɦ	X
cana-768	149	49	=	=	NOUN
cana-768	149	50	0.01	0.01	NUM
cana-768	149	51	(	(	PUNCT
cana-768	149	52	example	example	NOUN
cana-768	149	53	5.1	5.1	NUM
cana-768	149	54	)	)	PUNCT
cana-768	149	55	ռ	ռ	NOUN
cana-768	149	56	→	→	SYM
cana-768	149	57	102	102	NUM
cana-768	149	58	103	103	NUM
cana-768	149	59	104	104	NUM
cana-768	149	60	δ	δ	PROPN
cana-768	149	61	↓	↓	NOUN
cana-768	149	62	proposed	propose	VERB
cana-768	149	63	method	method	NOUN
cana-768	149	64	previous	previous	ADJ
cana-768	149	65	result[13	result[13	PROPN
cana-768	149	66	]	]	PUNCT
cana-768	149	67	proposed	propose	VERB
cana-768	149	68	method	method	NOUN
cana-768	149	69	previous	previous	ADJ
cana-768	149	70	result[13	result[13	PROPN
cana-768	149	71	]	]	PUNCT
cana-768	149	72	proposed	propose	VERB
cana-768	149	73	method	method	NOUN
cana-768	149	74	previous	previous	ADJ
cana-768	149	75	result[13	result[13	PROPN
cana-768	149	76	]	]	X
cana-768	149	77	0.01	0.01	NUM
cana-768	149	78	2.5733e-05	2.5733e-05	NUM
cana-768	150	1	1.3798e-04	1.3798e-04	NUM
cana-768	150	2	2.5763e-07	2.5763e-07	NUM
cana-768	150	3	1.3907e-05	1.3907e-05	NUM
cana-768	150	4	2.7092e-09	2.7092e-09	NUM
cana-768	150	5	1.3887e-06	1.3887e-06	NUM
cana-768	150	6	0.03	0.03	NUM
cana-768	150	7	2.9690e-05	2.9690e-05	NUM
cana-768	150	8	1.0765e-04	1.0765e-04	NUM
cana-768	150	9	2.9705e-07	2.9705e-07	NUM
cana-768	150	10	1.0849e-05	1.0849e-05	NUM
cana-768	150	11	2.9838e-09	2.9838e-09	NUM
cana-768	150	12	1.0600e-06	1.0600e-06	NUM
cana-768	150	13	0.06	0.06	NUM
cana-768	150	14	6.1468e-05	6.1468e-05	NUM
cana-768	150	15	6.1798e-05	6.1798e-05	NUM
cana-768	150	16	6.2550e-07	6.2550e-07	NUM
cana-768	150	17	6.2273e-06	6.2273e-06	NUM
cana-768	150	18	6.2161e-09	6.2161e-09	NUM
cana-768	150	19	6.3164e-07	6.3164e-07	NUM
cana-768	150	20	0.08	0.08	NUM
cana-768	150	21	1.4035e-05	1.4035e-05	NUM
cana-768	150	22	3.0995e-05	3.0995e-05	NUM
cana-768	150	23	1.4099e-06	1.4099e-06	NUM
cana-768	150	24	3.1233e-06	3.1233e-06	NUM
cana-768	150	25	1.400e-08	1.400e-08	NUM
cana-768	150	26	3.3537e-07	3.3537e-07	NUM
cana-768	150	27	ȶ	ȶ	PRON
cana-768	150	28	solution	solution	NOUN
cana-768	150	29	by	by	ADP
cana-768	150	30	proposed	propose	VERB
cana-768	150	31	method	method	NOUN
cana-768	150	32	exact	exact	ADJ
cana-768	150	33	solution	solution	NOUN
cana-768	150	34	solution	solution	NOUN
cana-768	150	35	by	by	ADP
cana-768	150	36	method	method	NOUN
cana-768	150	37	[	[	X
cana-768	150	38	15	15	NUM
cana-768	150	39	]	]	X
cana-768	150	40	absolute	absolute	ADJ
cana-768	150	41	error	error	NOUN
cana-768	150	42	by	by	ADP
cana-768	150	43	proposed	propose	VERB
cana-768	150	44	method	method	NOUN
cana-768	150	45	absolute	absolute	ADJ
cana-768	150	46	error	error	NOUN
cana-768	150	47	by	by	ADP
cana-768	150	48	method[15	method[15	NOUN
cana-768	150	49	]	]	PUNCT
cana-768	150	50	0.0	0.0	NUM
cana-768	150	51	1.00000000	1.00000000	NUM
cana-768	150	52	1.00000000	1.00000000	NUM
cana-768	150	53	1.00000000	1.00000000	NUM
cana-768	150	54	0.00000000	0.00000000	NUM
cana-768	150	55	0.00000000	0.00000000	NUM
cana-768	150	56	0.02	0.02	NUM
cana-768	150	57	0.59650758	0.59650758	NUM
cana-768	151	1	0.59611217	0.59611217	NUM
cana-768	151	2	0.40030832	0.40030832	NUM
cana-768	151	3	3.95409e-04	3.95409e-04	NUM
cana-768	151	4	1.95804e-01	1.95804e-01	NUM
cana-768	151	5	0.04	0.04	NUM
cana-768	151	6	0.46326487	0.46326487	NUM
cana-768	151	7	0.46292257	0.46292257	NUM
cana-768	151	8	0.38470877	0.38470877	NUM
cana-768	151	9	3.42308e-04	3.42308e-04	NUM
cana-768	151	10	7.82138e-02	7.82138e-02	NUM
cana-768	151	11	0.06	0.06	NUM
cana-768	151	12	0.42273389	0.42273389	NUM
cana-768	151	13	0.42247446	0.42247446	NUM
cana-768	151	14	0.39155769	0.39155769	NUM
cana-768	151	15	2.59429e-04	2.59429e-04	NUM
cana-768	151	16	3.09168e-02	3.09168e-02	NUM
cana-768	152	1	0.08	0.08	NUM
cana-768	152	2	0.41407601	0.41407601	NUM
cana-768	152	3	0.41386729	0.41386729	NUM
cana-768	152	4	0.39941373	0.39941373	NUM
cana-768	152	5	2.08724e-04	2.08724e-04	NUM
cana-768	152	6	1.44536e-02	1.44536e-02	NUM
cana-768	152	7	0.1	0.1	NUM
cana-768	152	8	0.41644444	0.41644444	NUM
cana-768	152	9	0.41626092	0.41626092	NUM
cana-768	152	10	0.40746127	0.40746127	NUM
cana-768	152	11	1.83512e-04	1.83512e-04	NUM
cana-768	152	12	8.79965e-03	8.79965e-03	NUM
cana-768	152	13	0.2	0.2	NUM
cana-768	152	14	0.45613474	0.45613474	NUM
cana-768	152	15	0.45597317	0.45597317	NUM
cana-768	152	16	0.45020470	0.45020470	NUM
cana-768	152	17	1.61571e-04	1.61571e-04	NUM
cana-768	152	18	5.76847e-03	5.76847e-03	NUM
cana-768	152	19	0.3	0.3	NUM
cana-768	152	20	0.50314705	0.50314705	NUM
cana-768	152	21	0.50299127	0.50299127	NUM
cana-768	152	22	0.49743206	0.49743206	NUM
cana-768	152	23	1.55780e-04	1.55780e-04	NUM
cana-768	152	24	5.55921e-03	5.55921e-03	NUM
cana-768	152	25	communications	communication	NOUN
cana-768	152	26	on	on	ADP
cana-768	152	27	applied	apply	VERB
cana-768	152	28	nonlinear	nonlinear	ADJ
cana-768	152	29	analysis	analysis	NOUN
cana-768	152	30	issn	issn	NOUN
cana-768	152	31	:	:	PUNCT
cana-768	152	32	1074	1074	NUM
cana-768	152	33	-	-	PUNCT
cana-768	152	34	133x	133x	NUM
cana-768	152	35	vol	vol	NOUN
cana-768	152	36	31	31	NUM
cana-768	152	37	no	no	NOUN
cana-768	152	38	.	.	PUNCT
cana-768	153	1	3s	3s	NUM
cana-768	153	2	(	(	PUNCT
cana-768	153	3	2024	2024	NUM
cana-768	153	4	)	)	PUNCT
cana-768	153	5	320	320	NUM
cana-768	153	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	153	7	table	table	NOUN
cana-768	153	8	3	3	NUM
cana-768	153	9	:	:	PUNCT
cana-768	153	10	maximum	maximum	ADJ
cana-768	153	11	absolute	absolute	ADJ
cana-768	153	12	error	error	NOUN
cana-768	153	13	with	with	ADP
cana-768	153	14	휀	휀	NOUN
cana-768	153	15	=	=	SYM
cana-768	153	16	0.1	0.1	NUM
cana-768	153	17	for	for	ADP
cana-768	153	18	various	various	ADJ
cana-768	153	19	values	value	NOUN
cana-768	153	20	of	of	ADP
cana-768	153	21	δ	δ	PROPN
cana-768	153	22	and	and	CCONJ
cana-768	153	23	ռ	ռ	NOUN
cana-768	153	24	using	use	VERB
cana-768	153	25	double	double	ADJ
cana-768	153	26	mesh	mesh	NOUN
cana-768	153	27	principle	principle	NOUN
cana-768	153	28	(	(	PUNCT
cana-768	153	29	for	for	ADP
cana-768	153	30	example	example	NOUN
cana-768	153	31	5.2	5.2	NUM
cana-768	153	32	)	)	PUNCT
cana-768	153	33	ռ	ռ	NOUN
cana-768	153	34	→	→	SYM
cana-768	153	35	102	102	NUM
cana-768	153	36	103	103	NUM
cana-768	153	37	104	104	NUM
cana-768	153	38	δ	δ	PROPN
cana-768	153	39	↓	↓	NOUN
cana-768	153	40	proposed	propose	VERB
cana-768	153	41	method	method	NOUN
cana-768	153	42	proposed	propose	VERB
cana-768	153	43	method	method	NOUN
cana-768	153	44	proposed	propose	VERB
cana-768	153	45	method	method	NOUN
cana-768	153	46	0.001	0.001	NUM
cana-768	153	47	0.0265796	0.0265796	NUM
cana-768	153	48	0.0032995	0.0032995	NUM
cana-768	153	49	3.3605207e-04	3.3605207e-04	NUM
cana-768	153	50	0.003	0.003	NUM
cana-768	153	51	0.0271238	0.0271238	NUM
cana-768	153	52	0.0033683	0.0033683	NUM
cana-768	153	53	3.4306667e-04	3.4306667e-04	NUM
cana-768	153	54	0.006	0.006	NUM
cana-768	153	55	0.0279825	0.0279825	NUM
cana-768	153	56	0.0034768	0.0034768	NUM
cana-768	153	57	3.5414669e-04	3.5414669e-04	NUM
cana-768	153	58	0.008	0.008	NUM
cana-768	153	59	0.0285853	0.0285853	NUM
cana-768	153	60	0.0035531	0.0035531	NUM
cana-768	153	61	3.6193372e-04	3.6193372e-04	NUM
cana-768	153	62	table	table	NOUN
cana-768	153	63	4	4	NUM
cana-768	153	64	:	:	PUNCT
cana-768	153	65	maximum	maximum	ADJ
cana-768	153	66	absolute	absolute	ADJ
cana-768	153	67	error	error	NOUN
cana-768	153	68	with	with	ADP
cana-768	153	69	휀	휀	NOUN
cana-768	153	70	=	=	SYM
cana-768	153	71	0.1	0.1	NUM
cana-768	153	72	for	for	ADP
cana-768	153	73	various	various	ADJ
cana-768	153	74	values	value	NOUN
cana-768	153	75	of	of	ADP
cana-768	153	76	δ	δ	PROPN
cana-768	153	77	and	and	CCONJ
cana-768	153	78	ռ(for	ռ(for	ADP
cana-768	153	79	example	example	NOUN
cana-768	153	80	5.3	5.3	NUM
cana-768	153	81	)	)	PUNCT
cana-768	153	82	ռ	ռ	NOUN
cana-768	153	83	→	→	SYM
cana-768	153	84	102	102	NUM
cana-768	153	85	103	103	NUM
cana-768	153	86	104	104	NUM
cana-768	153	87	δ	δ	PROPN
cana-768	153	88	↓	↓	NOUN
cana-768	153	89	proposed	propose	VERB
cana-768	153	90	method	method	PROPN
cana-768	153	91	results[13	results[13	PROPN
cana-768	153	92	]	]	PUNCT
cana-768	153	93	proposed	propose	VERB
cana-768	153	94	method	method	PROPN
cana-768	153	95	results[13	results[13	PROPN
cana-768	153	96	]	]	PUNCT
cana-768	153	97	proposed	propose	VERB
cana-768	153	98	method	method	PROPN
cana-768	153	99	results[13	results[13	NOUN
cana-768	153	100	]	]	X
cana-768	153	101	0.01	0.01	NUM
cana-768	153	102	1.8402e-05	1.8402e-05	NUM
cana-768	153	103	4.9650e-05	4.9650e-05	NUM
cana-768	153	104	1.8410e-07	1.8410e-07	NUM
cana-768	153	105	4.9729e-06	4.9729e-06	NUM
cana-768	153	106	1.6235e-09	1.6235e-09	NUM
cana-768	153	107	4.9586e-07	4.9586e-07	NUM
cana-768	153	108	0.03	0.03	NUM
cana-768	153	109	1.4093e-05	1.4093e-05	NUM
cana-768	153	110	5.8439e-05	5.8439e-05	NUM
cana-768	153	111	1.4097e-07	1.4097e-07	NUM
cana-768	153	112	5.8534e-06	5.8534e-06	NUM
cana-768	153	113	1.1188e-09	1.1188e-09	NUM
cana-768	153	114	5.8693e-07	5.8693e-07	NUM
cana-768	153	115	0.06	0.06	NUM
cana-768	153	116	9.7089e-06	9.7089e-06	NUM
cana-768	153	117	7.1489e-05	7.1489e-05	NUM
cana-768	153	118	9.7114e-08	9.7114e-08	NUM
cana-768	153	119	7.1607e-06	7.1607e-06	NUM
cana-768	153	120	1.0594e-09	1.0594e-09	NUM
cana-768	153	121	7.2219e-07	7.2219e-07	NUM
cana-768	153	122	0.08	0.08	NUM
cana-768	153	123	7.5492e-06	7.5492e-06	NUM
cana-768	153	124	8.0100e-05	8.0100e-05	NUM
cana-768	154	1	7.5512e-08	7.5512e-08	NUM
cana-768	154	2	8.0235e06	8.0235e06	NUM
cana-768	154	3	6.7766e-10	6.7766e-10	NUM
cana-768	154	4	8.0780e-07	8.0780e-07	NUM
cana-768	154	5	table	table	NOUN
cana-768	154	6	5	5	NUM
cana-768	154	7	:	:	PUNCT
cana-768	154	8	absolute	absolute	ADJ
cana-768	154	9	error	error	NOUN
cana-768	154	10	with	with	ADP
cana-768	154	11	휀	휀	NOUN
cana-768	154	12	=	=	NOUN
cana-768	154	13	0.001	0.001	NUM
cana-768	154	14	,	,	PUNCT
cana-768	154	15	δ	δ	X
cana-768	154	16	=	=	PROPN
cana-768	154	17	0.003	0.003	NUM
cana-768	154	18	and	and	CCONJ
cana-768	154	19	ɦ	ɦ	X
cana-768	154	20	=	=	NOUN
cana-768	154	21	0.01	0.01	NUM
cana-768	154	22	(	(	PUNCT
cana-768	154	23	for	for	ADP
cana-768	154	24	example	example	NOUN
cana-768	154	25	5.3	5.3	NUM
cana-768	154	26	)	)	PUNCT
cana-768	154	27	0.4	0.4	NUM
cana-768	154	28	0.55502160	0.55502160	NUM
cana-768	154	29	0.55487431	0.55487431	NUM
cana-768	154	30	0.54961366	0.54961366	NUM
cana-768	154	31	1.47294e-04	1.47294e-04	NUM
cana-768	154	32	5.26065e-03	5.26065e-03	NUM
cana-768	154	33	0.5	0.5	NUM
cana-768	154	34	0.61224452	0.61224452	NUM
cana-768	154	35	0.61210912	0.61210912	NUM
cana-768	154	36	0.60726922	0.60726922	NUM
cana-768	154	37	1.35403e-04	1.35403e-04	SYM
cana-768	154	38	4.83990e-03	4.83990e-03	NUM
cana-768	154	39	0.6	0.6	NUM
cana-768	154	40	0.67536714	0.67536714	NUM
cana-768	154	41	0.67524765	0.67524765	NUM
cana-768	154	42	0.67097295	0.67097295	NUM
cana-768	154	43	1.19493e-04	1.19493e-04	NUM
cana-768	154	44	4.27470e-03	4.27470e-03	NUM
cana-768	154	45	0.7	0.7	NUM
cana-768	154	46	0.74499772	0.74499772	NUM
cana-768	154	47	0.74489886	0.74489886	NUM
cana-768	154	48	0.74135933	0.74135933	NUM
cana-768	154	49	9.88619e-05	9.88619e-05	NUM
cana-768	154	50	3.53953e-03	3.53953e-03	NUM
cana-768	154	51	0.8	0.8	NUM
cana-768	154	52	0.82180724	0.82180724	NUM
cana-768	154	53	0.82173453	0.82173453	NUM
cana-768	154	54	0.81912938	0.81912938	NUM
cana-768	154	55	7.27047e-05	7.27047e-05	NUM
cana-768	154	56	2.60515e-03	2.60515e-03	NUM
cana-768	154	57	0.9	0.9	NUM
cana-768	154	58	0.90653585	0.90653585	NUM
cana-768	154	59	0.90649574	0.90649574	NUM
cana-768	154	60	0.90505767	0.90505767	NUM
cana-768	154	61	4.01012e-05	4.01012e-05	NUM
cana-768	154	62	1.43807e-03	1.43807e-03	NUM
cana-768	154	63	1.0	1.0	NUM
cana-768	154	64	1.00000000	1.00000000	NUM
cana-768	154	65	1.00000000	1.00000000	NUM
cana-768	154	66	1.00000000	1.00000000	NUM
cana-768	154	67	0.00000000	0.00000000	NUM
cana-768	154	68	0.00000000	0.00000000	NUM
cana-768	154	69	ȶ	ȶ	PRON
cana-768	154	70	solution	solution	NOUN
cana-768	154	71	by	by	ADP
cana-768	154	72	proposed	propose	VERB
cana-768	154	73	method	method	NOUN
cana-768	154	74	exact	exact	ADJ
cana-768	154	75	solution	solution	NOUN
cana-768	154	76	solution	solution	NOUN
cana-768	154	77	by	by	ADP
cana-768	154	78	method	method	NOUN
cana-768	154	79	[	[	X
cana-768	154	80	15	15	NUM
cana-768	154	81	]	]	X
cana-768	154	82	absolute	absolute	ADJ
cana-768	154	83	error	error	NOUN
cana-768	154	84	by	by	ADP
cana-768	154	85	proposed	propose	VERB
cana-768	154	86	method	method	NOUN
cana-768	154	87	absolute	absolute	ADJ
cana-768	154	88	error	error	NOUN
cana-768	154	89	by	by	ADP
cana-768	154	90	method[15	method[15	NOUN
cana-768	154	91	]	]	PUNCT
cana-768	154	92	0.0	0.0	NUM
cana-768	154	93	1.00000000	1.00000000	NUM
cana-768	154	94	1.00000000	1.00000000	NUM
cana-768	154	95	1.00000000	1.00000000	NUM
cana-768	154	96	0.00000000	0.00000000	NUM
cana-768	154	97	0.00000000	0.00000000	NUM
cana-768	154	98	0.1	0.1	NUM
cana-768	154	99	0.90536618	0.90536618	NUM
cana-768	154	100	0.90519656	0.90519656	NUM
cana-768	154	101	0.90493550	0.90493550	NUM
cana-768	154	102	1.69625e-04	1.69625e-04	NUM
cana-768	154	103	4.30683e-04	4.30683e-04	NUM
cana-768	154	104	0.2	0.2	NUM
cana-768	154	105	0.81968792	0.81968792	NUM
cana-768	154	106	0.81938081	0.81938081	NUM
cana-768	154	107	0.81890826	0.81890826	NUM
cana-768	154	108	3.07117e-04	3.07117e-04	NUM
cana-768	154	109	7.79665e-04	7.79665e-04	NUM
cana-768	154	110	0.3	0.3	NUM
cana-768	154	111	0.74211773	0.74211773	NUM
cana-768	154	112	0.74170069	0.74170069	NUM
cana-768	154	113	0.74105916	0.74105916	NUM
cana-768	154	114	4.17042e-04	4.17042e-04	NUM
cana-768	154	115	1.05857e-03	1.05857e-03	NUM
cana-768	155	1	0.4	0.4	NUM
cana-768	155	2	0.67188829	0.67188829	NUM
cana-768	155	3	0.67138491	0.67138491	NUM
cana-768	155	4	0.67061074	0.67061074	NUM
cana-768	155	5	5.03387e-04	5.03387e-04	NUM
cana-768	155	6	1.27755e-03	1.27755e-03	NUM
cana-768	155	7	0.5	0.5	NUM
cana-768	155	8	0.60830494	0.60830494	NUM
cana-768	155	9	0.60773531	0.60773531	NUM
cana-768	155	10	0.60685947	0.60685947	NUM
cana-768	155	11	5.69633e-04	5.69633e-04	NUM
cana-768	155	12	1.44547e-03	1.44547e-03	NUM
cana-768	155	13	0.6	0.6	NUM
cana-768	155	14	0.55073872	0.55073872	NUM
cana-768	155	15	0.55011991	0.55011991	NUM
cana-768	155	16	0.54916868	0.54916868	NUM
cana-768	155	17	6.18814e-04	6.18814e-04	NUM
cana-768	155	18	1.57004e-03	1.57004e-03	NUM
cana-768	155	19	0.7	0.7	NUM
cana-768	155	20	0.49862021	0.49862021	NUM
cana-768	155	21	0.49796665	0.49796665	NUM
cana-768	155	22	0.49696223	0.49696223	NUM
cana-768	155	23	6.53568e-04	6.53568e-04	NUM
cana-768	155	24	1.65798e-03	1.65798e-03	NUM
cana-768	155	25	0.8	0.8	NUM
cana-768	155	26	0.45143388	0.45143388	NUM
cana-768	155	27	0.45075769	0.45075769	NUM
cana-768	155	28	0.44971877	0.44971877	NUM
cana-768	155	29	6.76186e-04	6.76186e-04	NUM
cana-768	155	30	1.71511e-03	1.71511e-03	NUM
cana-768	155	31	0.9	0.9	NUM
cana-768	155	32	0.40871297	0.40871297	NUM
cana-768	155	33	0.40802431	0.40802431	NUM
cana-768	155	34	0.40696648	0.40696648	NUM
cana-768	155	35	6.88656e-04	6.88656e-04	NUM
cana-768	155	36	1.74649e-03	1.74649e-03	NUM
cana-768	155	37	0.92	0.92	NUM
cana-768	155	38	0.40066672	0.40066672	NUM
cana-768	155	39	0.39997663	0.39997663	NUM
cana-768	155	40	0.39891664	0.39891664	NUM
cana-768	155	41	6.90087e-04	6.90087e-04	NUM
cana-768	155	42	1.75008e-03	1.75008e-03	NUM
cana-768	155	43	0.94	0.94	NUM
cana-768	155	44	0.39277848	0.39277848	NUM
cana-768	155	45	0.39208729	0.39208729	NUM
cana-768	155	46	0.39102493	0.39102493	NUM
cana-768	155	47	6.91195e-04	6.91195e-04	NUM
cana-768	155	48	1.75355e-03	1.75355e-03	NUM
cana-768	155	49	0.96	0.96	NUM
cana-768	155	50	0.38498654	0.38498654	NUM
cana-768	155	51	0.38429459	0.38429459	NUM
cana-768	155	52	0.38317158	0.38317158	NUM
cana-768	155	53	6.91948e-04	6.91948e-04	NUM
cana-768	155	54	1.81496e-03	1.81496e-03	NUM
cana-768	155	55	0.98	0.98	NUM
cana-768	155	56	0.36841582	0.36841582	NUM
cana-768	155	57	0.36772893	0.36772893	NUM
cana-768	155	58	0.36289935	0.36289935	NUM
cana-768	155	59	6.86889e-04	6.86889e-04	NUM
cana-768	155	60	5.51647e-03	5.51647e-03	NUM
cana-768	155	61	1.0	1.0	NUM
cana-768	155	62	1.00000000	1.00000000	NUM
cana-768	155	63	1.00000000	1.00000000	NUM
cana-768	155	64	1.00000000	1.00000000	NUM
cana-768	155	65	0.00000000	0.00000000	NUM
cana-768	155	66	0.00000000	0.00000000	NUM
cana-768	155	67	communications	communication	NOUN
cana-768	155	68	on	on	ADP
cana-768	155	69	applied	apply	VERB
cana-768	155	70	nonlinear	nonlinear	ADJ
cana-768	155	71	analysis	analysis	NOUN
cana-768	155	72	issn	issn	NOUN
cana-768	155	73	:	:	PUNCT
cana-768	155	74	1074	1074	NUM
cana-768	155	75	-	-	PUNCT
cana-768	155	76	133x	133x	NUM
cana-768	155	77	vol	vol	NOUN
cana-768	155	78	31	31	NUM
cana-768	155	79	no	no	NOUN
cana-768	155	80	.	.	PUNCT
cana-768	156	1	3s	3s	NUM
cana-768	156	2	(	(	PUNCT
cana-768	156	3	2024	2024	NUM
cana-768	156	4	)	)	PUNCT
cana-768	156	5	321	321	NUM
cana-768	156	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	156	7	table	table	NOUN
cana-768	156	8	6	6	NUM
cana-768	156	9	:	:	PUNCT
cana-768	156	10	maximum	maximum	ADJ
cana-768	156	11	absolute	absolute	ADJ
cana-768	156	12	error	error	NOUN
cana-768	156	13	with	with	ADP
cana-768	156	14	휀	휀	NOUN
cana-768	156	15	=	=	SYM
cana-768	156	16	0.1	0.1	NUM
cana-768	156	17	for	for	ADP
cana-768	156	18	various	various	ADJ
cana-768	156	19	values	value	NOUN
cana-768	156	20	of	of	ADP
cana-768	156	21	δ	δ	PROPN
cana-768	156	22	and	and	CCONJ
cana-768	156	23	ռ	ռ	NOUN
cana-768	156	24	using	use	VERB
cana-768	156	25	double	double	ADJ
cana-768	156	26	mesh	mesh	NOUN
cana-768	156	27	principle	principle	NOUN
cana-768	156	28	(	(	PUNCT
cana-768	156	29	example	example	NOUN
cana-768	156	30	5.4	5.4	NUM
cana-768	156	31	)	)	PUNCT
cana-768	156	32	figure	figure	NOUN
cana-768	156	33	1	1	NUM
cana-768	156	34	.	.	PUNCT
cana-768	156	35	graphical	graphical	ADJ
cana-768	156	36	representation	representation	NOUN
cana-768	156	37	with	with	ADP
cana-768	156	38	휀	휀	NOUN
cana-768	156	39	=	=	SYM
cana-768	156	40	0.1	0.1	NUM
cana-768	156	41	for	for	ADP
cana-768	156	42	various	various	ADJ
cana-768	156	43	values	value	NOUN
cana-768	156	44	of	of	ADP
cana-768	156	45	δ	δ	PROPN
cana-768	156	46	(	(	PUNCT
cana-768	156	47	example5.1	example5.1	X
cana-768	156	48	)	)	PUNCT
cana-768	156	49	figure	figure	NOUN
cana-768	156	50	2	2	NUM
cana-768	156	51	.	.	PUNCT
cana-768	156	52	graphical	graphical	ADJ
cana-768	156	53	representation	representation	NOUN
cana-768	156	54	with	with	ADP
cana-768	156	55	휀	휀	NOUN
cana-768	156	56	=	=	NOUN
cana-768	156	57	0.01	0.01	NUM
cana-768	156	58	for	for	ADP
cana-768	156	59	various	various	ADJ
cana-768	156	60	values	value	NOUN
cana-768	156	61	of	of	ADP
cana-768	156	62	δ	δ	PROPN
cana-768	156	63	(	(	PUNCT
cana-768	156	64	example5.1	example5.1	X
cana-768	156	65	)	)	PUNCT
cana-768	156	66	ռ	ռ	NOUN
cana-768	156	67	→	→	SYM
cana-768	156	68	102	102	NUM
cana-768	156	69	103	103	NUM
cana-768	156	70	104	104	NUM
cana-768	156	71	δ	δ	PROPN
cana-768	156	72	↓	↓	NOUN
cana-768	156	73	proposed	propose	VERB
cana-768	156	74	method	method	NOUN
cana-768	156	75	proposed	propose	VERB
cana-768	156	76	method	method	NOUN
cana-768	156	77	proposed	propose	VERB
cana-768	156	78	method	method	NOUN
cana-768	156	79	0.000	0.000	NUM
cana-768	156	80	0.02230547	0.02230547	NUM
cana-768	156	81	0.00305640	0.00305640	NUM
cana-768	156	82	3.11355660e-04	3.11355660e-04	NUM
cana-768	156	83	0.003	0.003	NUM
cana-768	156	84	0.02081696	0.02081696	NUM
cana-768	156	85	0.00282670	0.00282670	NUM
cana-768	156	86	2.87617565e-04	2.87617565e-04	NUM
cana-768	156	87	0.007	0.007	NUM
cana-768	156	88	0.01910969	0.01910969	NUM
cana-768	156	89	0.00256855	0.00256855	NUM
cana-768	156	90	2.61006577e-04	2.61006577e-04	NUM
cana-768	156	91	0.015	0.015	NUM
cana-768	156	92	0.01639981	0.01639981	NUM
cana-768	156	93	0.00217005	0.00217005	NUM
cana-768	156	94	2.20066455e-04	2.20066455e-04	NUM
cana-768	156	95	communications	communication	NOUN
cana-768	156	96	on	on	ADP
cana-768	156	97	applied	apply	VERB
cana-768	156	98	nonlinear	nonlinear	ADJ
cana-768	156	99	analysis	analysis	NOUN
cana-768	156	100	issn	issn	NOUN
cana-768	156	101	:	:	PUNCT
cana-768	156	102	1074	1074	NUM
cana-768	156	103	-	-	PUNCT
cana-768	156	104	133x	133x	NUM
cana-768	156	105	vol	vol	NOUN
cana-768	156	106	31	31	NUM
cana-768	156	107	no	no	NOUN
cana-768	156	108	.	.	PUNCT
cana-768	157	1	3s	3s	NUM
cana-768	157	2	(	(	PUNCT
cana-768	157	3	2024	2024	NUM
cana-768	157	4	)	)	PUNCT
cana-768	157	5	322	322	NUM
cana-768	157	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	157	7	figure	figure	NOUN
cana-768	157	8	3	3	NUM
cana-768	157	9	.	.	PUNCT
cana-768	157	10	graphical	graphical	ADJ
cana-768	157	11	representation	representation	NOUN
cana-768	157	12	with	with	ADP
cana-768	157	13	휀	휀	NOUN
cana-768	157	14	=	=	SYM
cana-768	157	15	0.1	0.1	NUM
cana-768	157	16	for	for	ADP
cana-768	157	17	various	various	ADJ
cana-768	157	18	values	value	NOUN
cana-768	157	19	of	of	ADP
cana-768	157	20	δ	δ	PROPN
cana-768	157	21	(	(	PUNCT
cana-768	157	22	example5.2	example5.2	NOUN
cana-768	157	23	)	)	PUNCT
cana-768	157	24	figure	figure	NOUN
cana-768	157	25	4	4	NUM
cana-768	157	26	.	.	PUNCT
cana-768	157	27	graphical	graphical	ADJ
cana-768	157	28	representation	representation	NOUN
cana-768	157	29	with	with	ADP
cana-768	157	30	휀	휀	NOUN
cana-768	157	31	=	=	NOUN
cana-768	157	32	0.1	0.1	NUM
cana-768	157	33	for	for	ADP
cana-768	157	34	different	different	ADJ
cana-768	157	35	values	value	NOUN
cana-768	157	36	of	of	ADP
cana-768	157	37	δ	δ	PROPN
cana-768	157	38	(	(	PUNCT
cana-768	157	39	example5.3	example5.3	NOUN
cana-768	157	40	)	)	PUNCT
cana-768	157	41	figure	figure	NOUN
cana-768	157	42	5	5	NUM
cana-768	157	43	.	.	PUNCT
cana-768	157	44	graphical	graphical	ADJ
cana-768	157	45	representation	representation	NOUN
cana-768	157	46	with	with	ADP
cana-768	157	47	휀	휀	NOUN
cana-768	157	48	=	=	NOUN
cana-768	157	49	0.01	0.01	NUM
cana-768	157	50	for	for	ADP
cana-768	157	51	various	various	ADJ
cana-768	157	52	values	value	NOUN
cana-768	157	53	of	of	ADP
cana-768	157	54	δ	δ	PROPN
cana-768	157	55	(	(	PUNCT
cana-768	157	56	example5.3	example5.3	PROPN
cana-768	157	57	)	)	PUNCT
cana-768	157	58	communications	communication	NOUN
cana-768	157	59	on	on	ADP
cana-768	157	60	applied	apply	VERB
cana-768	157	61	nonlinear	nonlinear	ADJ
cana-768	157	62	analysis	analysis	NOUN
cana-768	157	63	issn	issn	NOUN
cana-768	157	64	:	:	PUNCT
cana-768	157	65	1074	1074	NUM
cana-768	157	66	-	-	PUNCT
cana-768	157	67	133x	133x	NUM
cana-768	157	68	vol	vol	NOUN
cana-768	157	69	31	31	NUM
cana-768	157	70	no	no	NOUN
cana-768	157	71	.	.	PUNCT
cana-768	158	1	3s	3s	NUM
cana-768	158	2	(	(	PUNCT
cana-768	158	3	2024	2024	NUM
cana-768	158	4	)	)	PUNCT
cana-768	158	5	323	323	NUM
cana-768	158	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	158	7	figure	figure	NOUN
cana-768	158	8	6	6	NUM
cana-768	158	9	.	.	PUNCT
cana-768	158	10	graphical	graphical	ADJ
cana-768	158	11	representation	representation	NOUN
cana-768	158	12	with	with	ADP
cana-768	158	13	휀	휀	NOUN
cana-768	158	14	=	=	SYM
cana-768	158	15	0.1	0.1	NUM
cana-768	158	16	for	for	ADP
cana-768	158	17	various	various	ADJ
cana-768	158	18	values	value	NOUN
cana-768	158	19	of	of	ADP
cana-768	158	20	δ	δ	PROPN
cana-768	158	21	(	(	PUNCT
cana-768	158	22	example5.4	example5.4	PROPN
cana-768	158	23	)	)	PUNCT
cana-768	158	24	5	5	NUM
cana-768	158	25	.	.	PUNCT
cana-768	158	26	discussion	discussion	NOUN
cana-768	158	27	in	in	ADP
cana-768	158	28	an	an	DET
cana-768	158	29	effort	effort	NOUN
cana-768	158	30	to	to	PART
cana-768	158	31	solve	solve	VERB
cana-768	158	32	delay	delay	NOUN
cana-768	158	33	differential	differential	ADJ
cana-768	158	34	equations	equation	NOUN
cana-768	158	35	with	with	ADP
cana-768	158	36	boundary	boundary	ADJ
cana-768	158	37	layers	layer	NOUN
cana-768	158	38	,	,	PUNCT
cana-768	158	39	we	we	PRON
cana-768	158	40	employed	employ	VERB
cana-768	158	41	the	the	DET
cana-768	158	42	exponential	exponential	ADJ
cana-768	158	43	b	b	NOUN
cana-768	158	44	-	-	PUNCT
cana-768	158	45	spline	spline	NOUN
cana-768	158	46	method	method	NOUN
cana-768	158	47	in	in	ADP
cana-768	158	48	this	this	DET
cana-768	158	49	study	study	NOUN
cana-768	158	50	.	.	PUNCT
cana-768	159	1	with	with	ADP
cana-768	159	2	this	this	DET
cana-768	159	3	approach	approach	NOUN
cana-768	159	4	,	,	PUNCT
cana-768	159	5	we	we	PRON
cana-768	159	6	first	first	ADV
cana-768	159	7	applied	apply	VERB
cana-768	159	8	taylor	taylor	PROPN
cana-768	159	9	's	's	PART
cana-768	159	10	series	series	NOUN
cana-768	159	11	to	to	PART
cana-768	159	12	transform	transform	VERB
cana-768	159	13	a	a	DET
cana-768	159	14	second	second	ADJ
cana-768	159	15	order	order	NOUN
cana-768	159	16	singularly	singularly	ADV
cana-768	159	17	perturbed	perturb	VERB
cana-768	159	18	differential	differential	ADJ
cana-768	159	19	equation	equation	NOUN
cana-768	159	20	with	with	ADP
cana-768	159	21	a	a	DET
cana-768	159	22	delay	delay	NOUN
cana-768	159	23	term	term	NOUN
cana-768	159	24	problem	problem	NOUN
cana-768	159	25	into	into	ADP
cana-768	159	26	a	a	DET
cana-768	159	27	neutral	neutral	ADJ
cana-768	159	28	type	type	NOUN
cana-768	159	29	singularly	singularly	ADV
cana-768	159	30	perturbed	perturb	VERB
cana-768	159	31	differential	differential	ADJ
cana-768	159	32	equation	equation	NOUN
cana-768	159	33	.	.	PUNCT
cana-768	160	1	the	the	DET
cana-768	160	2	suggested	suggest	VERB
cana-768	160	3	approach	approach	NOUN
cana-768	160	4	is	be	AUX
cana-768	160	5	applied	apply	VERB
cana-768	160	6	to	to	ADP
cana-768	160	7	four	four	NUM
cana-768	160	8	model	model	NOUN
cana-768	160	9	problems	problem	NOUN
cana-768	160	10	,	,	PUNCT
cana-768	160	11	and	and	CCONJ
cana-768	160	12	the	the	DET
cana-768	160	13	results	result	NOUN
cana-768	160	14	are	be	AUX
cana-768	160	15	contrasted	contrast	VERB
cana-768	160	16	to	to	ADP
cana-768	160	17	the	the	DET
cana-768	160	18	precise	precise	ADJ
cana-768	160	19	solutions	solution	NOUN
cana-768	160	20	that	that	PRON
cana-768	160	21	were	be	AUX
cana-768	160	22	found	find	VERB
cana-768	160	23	.	.	PUNCT
cana-768	161	1	in	in	ADP
cana-768	161	2	cases	case	NOUN
cana-768	161	3	where	where	SCONJ
cana-768	161	4	exact	exact	ADJ
cana-768	161	5	solutions	solution	NOUN
cana-768	161	6	were	be	AUX
cana-768	161	7	not	not	PART
cana-768	161	8	found	find	VERB
cana-768	161	9	,	,	PUNCT
cana-768	161	10	the	the	DET
cana-768	161	11	absolute	absolute	ADJ
cana-768	161	12	error	error	NOUN
cana-768	161	13	was	be	AUX
cana-768	161	14	calculated	calculate	VERB
cana-768	161	15	using	use	VERB
cana-768	161	16	the	the	DET
cana-768	161	17	double	double	ADJ
cana-768	161	18	mesh	mesh	NOUN
cana-768	161	19	concept	concept	NOUN
cana-768	161	20	.	.	PUNCT
cana-768	162	1	we	we	PRON
cana-768	162	2	have	have	AUX
cana-768	162	3	finally	finally	ADV
cana-768	162	4	drawn	draw	VERB
cana-768	162	5	the	the	DET
cana-768	162	6	graphs	graph	NOUN
cana-768	162	7	showing	show	VERB
cana-768	162	8	the	the	DET
cana-768	162	9	answers	answer	NOUN
cana-768	162	10	for	for	ADP
cana-768	162	11	various	various	ADJ
cana-768	162	12	values	value	NOUN
cana-768	162	13	of	of	ADP
cana-768	162	14	휀	휀	NOUN
cana-768	162	15	and	and	CCONJ
cana-768	162	16	δ	δ	PROPN
cana-768	162	17	.	.	PUNCT
cana-768	162	18	refrences	refrence	VERB
cana-768	163	1	[	[	X
cana-768	163	2	1	1	NUM
cana-768	163	3	]	]	X
cana-768	163	4	derstine	derstine	NOUN
cana-768	163	5	,	,	PUNCT
cana-768	163	6	m.	m.	PROPN
cana-768	163	7	w.	w.	PROPN
cana-768	163	8	,	,	PUNCT
cana-768	163	9	gibbs	gibbs	PROPN
cana-768	163	10	,	,	PUNCT
cana-768	163	11	h.	h.	PROPN
cana-768	163	12	m.	m.	PROPN
cana-768	163	13	,	,	PUNCT
cana-768	163	14	hopf	hopf	PROPN
cana-768	163	15	,	,	PUNCT
cana-768	163	16	f.	f.	PROPN
cana-768	163	17	a.	a.	PROPN
cana-768	163	18	,	,	PUNCT
cana-768	163	19	&	&	CCONJ
cana-768	163	20	kaplan	kaplan	PROPN
cana-768	163	21	,	,	PUNCT
cana-768	163	22	d.	d.	PROPN
cana-768	163	23	l.	l.	PROPN
cana-768	163	24	(	(	PUNCT
cana-768	163	25	1982	1982	NUM
cana-768	163	26	)	)	PUNCT
cana-768	163	27	.	.	PUNCT
cana-768	164	1	bifurcation	bifurcation	NOUN
cana-768	164	2	gap	gap	NOUN
cana-768	164	3	in	in	ADP
cana-768	164	4	a	a	DET
cana-768	164	5	hybrid	hybrid	ADJ
cana-768	164	6	optically	optically	ADV
cana-768	164	7	bistable	bistable	ADJ
cana-768	164	8	system	system	NOUN
cana-768	164	9	.	.	PUNCT
cana-768	165	1	physical	physical	ADJ
cana-768	165	2	review	review	PROPN
cana-768	165	3	a	a	PRON
cana-768	165	4	,	,	PUNCT
cana-768	165	5	26	26	NUM
cana-768	165	6	,	,	PUNCT
cana-768	165	7	3720	3720	NUM
cana-768	165	8	.	.	PUNCT
cana-768	166	1	[	[	X
cana-768	166	2	2	2	NUM
cana-768	166	3	]	]	PUNCT
cana-768	166	4	elsgolt	elsgolt	NOUN
cana-768	166	5	’s	’s	PROPN
cana-768	166	6	,	,	PUNCT
cana-768	166	7	l.	l.	PROPN
cana-768	166	8	e.	e.	PROPN
cana-768	166	9	,	,	PUNCT
cana-768	166	10	norkin	norkin	PROPN
cana-768	166	11	,	,	PUNCT
cana-768	166	12	s.	s.	PROPN
cana-768	166	13	b.	b.	PROPN
cana-768	166	14	,	,	PUNCT
cana-768	166	15	&	&	CCONJ
cana-768	166	16	casti	casti	PROPN
cana-768	166	17	,	,	PUNCT
cana-768	166	18	j.	j.	PROPN
cana-768	166	19	l.	l.	PROPN
cana-768	166	20	(	(	PUNCT
cana-768	166	21	1973	1973	NUM
cana-768	166	22	)	)	PUNCT
cana-768	166	23	.	.	PUNCT
cana-768	167	1	introduction	introduction	NOUN
cana-768	167	2	to	to	ADP
cana-768	167	3	the	the	DET
cana-768	167	4	theory	theory	NOUN
cana-768	167	5	and	and	CCONJ
cana-768	167	6	application	application	NOUN
cana-768	167	7	of	of	ADP
cana-768	167	8	differential	differential	ADJ
cana-768	167	9	equations	equation	NOUN
cana-768	167	10	with	with	ADP
cana-768	167	11	deviating	deviate	VERB
cana-768	167	12	arguments	argument	NOUN
cana-768	167	13	.	.	PUNCT
cana-768	168	1	(	(	PUNCT
cana-768	168	2	academic	academic	ADJ
cana-768	168	3	press	press	NOUN
cana-768	168	4	,	,	PUNCT
cana-768	168	5	new	new	ADJ
cana-768	168	6	work	work	NOUN
cana-768	168	7	.	.	PUNCT
cana-768	169	1	[	[	X
cana-768	169	2	3	3	NUM
cana-768	169	3	]	]	X
cana-768	169	4	kadalbajoo	kadalbajoo	ADJ
cana-768	169	5	,	,	PUNCT
cana-768	169	6	m.	m.	NOUN
cana-768	169	7	k.	k.	PROPN
cana-768	169	8	,	,	PUNCT
cana-768	169	9	&	&	CCONJ
cana-768	169	10	sharma	sharma	PROPN
cana-768	169	11	,	,	PUNCT
cana-768	169	12	k.	k.	PROPN
cana-768	169	13	k.	k.	PROPN
cana-768	169	14	(	(	PUNCT
cana-768	169	15	2004	2004	NUM
cana-768	169	16	)	)	PUNCT
cana-768	169	17	.	.	PUNCT
cana-768	170	1	numerical	numerical	ADJ
cana-768	170	2	analysis	analysis	NOUN
cana-768	170	3	of	of	ADP
cana-768	170	4	singularly	singularly	ADV
cana-768	170	5	perturbed	perturb	VERB
cana-768	170	6	delay	delay	NOUN
cana-768	170	7	differential	differential	ADJ
cana-768	170	8	equations	equation	NOUN
cana-768	170	9	with	with	ADP
cana-768	170	10	layer	layer	NOUN
cana-768	170	11	behavior	behavior	NOUN
cana-768	170	12	.	.	PUNCT
cana-768	171	1	applied	apply	VERB
cana-768	171	2	mathematics	mathematic	NOUN
cana-768	171	3	and	and	CCONJ
cana-768	171	4	computation	computation	NOUN
cana-768	171	5	,	,	PUNCT
cana-768	171	6	157	157	NUM
cana-768	171	7	,	,	PUNCT
cana-768	171	8	11–28	11–28	NUM
cana-768	171	9	.	.	PUNCT
cana-768	172	1	[	[	X
cana-768	172	2	4	4	NUM
cana-768	172	3	]	]	X
cana-768	172	4	kadalbajoo	kadalbajoo	ADJ
cana-768	172	5	,	,	PUNCT
cana-768	172	6	m.	m.	NOUN
cana-768	172	7	k.	k.	PROPN
cana-768	172	8	,	,	PUNCT
cana-768	172	9	&	&	CCONJ
cana-768	172	10	sharma	sharma	PROPN
cana-768	172	11	,	,	PUNCT
cana-768	172	12	k.	k.	PROPN
cana-768	172	13	k.	k.	PROPN
cana-768	172	14	(	(	PUNCT
cana-768	172	15	2008	2008	NUM
cana-768	172	16	)	)	PUNCT
cana-768	172	17	.	.	PUNCT
cana-768	173	1	a	a	DET
cana-768	173	2	numerical	numerical	ADJ
cana-768	173	3	method	method	NOUN
cana-768	173	4	based	base	VERB
cana-768	173	5	on	on	ADP
cana-768	173	6	finite	finite	ADJ
cana-768	173	7	difference	difference	NOUN
cana-768	173	8	for	for	ADP
cana-768	173	9	boundary	boundary	ADJ
cana-768	173	10	value	value	NOUN
cana-768	173	11	problems	problem	NOUN
cana-768	173	12	for	for	ADP
cana-768	173	13	singularly	singularly	ADV
cana-768	173	14	perturbed	perturb	VERB
cana-768	173	15	delay	delay	NOUN
cana-768	173	16	differential	differential	ADJ
cana-768	173	17	equations	equation	NOUN
cana-768	173	18	.	.	PUNCT
cana-768	174	1	applied	apply	VERB
cana-768	174	2	mathematics	mathematic	NOUN
cana-768	174	3	and	and	CCONJ
cana-768	174	4	computation	computation	NOUN
cana-768	174	5	,	,	PUNCT
cana-768	174	6	197	197	NUM
cana-768	174	7	,	,	PUNCT
cana-768	174	8	692	692	NUM
cana-768	174	9	–	–	PUNCT
cana-768	174	10	707	707	NUM
cana-768	174	11	.	.	PUNCT
cana-768	175	1	[	[	X
cana-768	175	2	5	5	NUM
cana-768	175	3	]	]	X
cana-768	175	4	kang	kang	PROPN
cana-768	175	5	,	,	PUNCT
cana-768	175	6	s.	s.	PROPN
cana-768	175	7	(	(	PUNCT
cana-768	175	8	2016	2016	NUM
cana-768	175	9	)	)	PUNCT
cana-768	175	10	.	.	PUNCT
cana-768	176	1	on	on	ADP
cana-768	176	2	the	the	DET
cana-768	176	3	implementation	implementation	NOUN
cana-768	176	4	of	of	ADP
cana-768	176	5	exponential	exponential	ADJ
cana-768	176	6	b	b	NOUN
cana-768	176	7	-	-	PUNCT
cana-768	176	8	splines	spline	NOUN
cana-768	176	9	by	by	ADP
cana-768	176	10	poisson	poisson	NOUN
cana-768	176	11	summation	summation	NOUN
cana-768	176	12	formula	formula	NOUN
cana-768	176	13	.	.	PUNCT
cana-768	177	1	journal	journal	NOUN
cana-768	177	2	of	of	ADP
cana-768	177	3	applied	apply	VERB
cana-768	177	4	mathematics	mathematic	NOUN
cana-768	177	5	and	and	CCONJ
cana-768	177	6	physics	physics	NOUN
cana-768	177	7	,	,	PUNCT
cana-768	177	8	4	4	NUM
cana-768	177	9	,	,	PUNCT
cana-768	177	10	637–640	637–640	NUM
cana-768	177	11	.	.	PUNCT
cana-768	178	1	[	[	X
cana-768	178	2	6	6	NUM
cana-768	178	3	]	]	X
cana-768	178	4	kanth	kanth	ADJ
cana-768	178	5	,	,	PUNCT
cana-768	178	6	a.	a.	PROPN
cana-768	178	7	r.	r.	PROPN
cana-768	178	8	,	,	PUNCT
cana-768	178	9	&	&	CCONJ
cana-768	178	10	garg	garg	PROPN
cana-768	178	11	,	,	PUNCT
cana-768	178	12	n.	n.	PROPN
cana-768	178	13	(	(	PUNCT
cana-768	178	14	2020	2020	NUM
cana-768	178	15	)	)	PUNCT
cana-768	178	16	.	.	PUNCT
cana-768	179	1	a	a	DET
cana-768	179	2	numerical	numerical	ADJ
cana-768	179	3	approach	approach	NOUN
cana-768	179	4	for	for	ADP
cana-768	179	5	a	a	DET
cana-768	179	6	class	class	NOUN
cana-768	179	7	of	of	ADP
cana-768	179	8	time	time	NOUN
cana-768	179	9	-	-	PUNCT
cana-768	179	10	fractional	fractional	ADJ
cana-768	179	11	reaction	reaction	NOUN
cana-768	179	12	–	–	PUNCT
cana-768	179	13	diffusion	diffusion	NOUN
cana-768	179	14	equation	equation	NOUN
cana-768	179	15	through	through	ADP
cana-768	179	16	exponential	exponential	ADJ
cana-768	179	17	b	b	PROPN
cana-768	179	18	-	-	PUNCT
cana-768	179	19	spline	spline	NOUN
cana-768	179	20	method	method	NOUN
cana-768	179	21	.	.	PUNCT
cana-768	180	1	computational	computational	ADJ
cana-768	180	2	and	and	CCONJ
cana-768	180	3	applied	applied	ADJ
cana-768	180	4	mathematics	mathematic	NOUN
cana-768	180	5	,	,	PUNCT
cana-768	180	6	39	39	NUM
cana-768	180	7	,	,	PUNCT
cana-768	180	8	1–24	1–24	PROPN
cana-768	180	9	.	.	PUNCT
cana-768	181	1	[	[	X
cana-768	181	2	7	7	NUM
cana-768	181	3	]	]	X
cana-768	181	4	kumara	kumara	PROPN
cana-768	181	5	swamy	swamy	PROPN
cana-768	181	6	,	,	PUNCT
cana-768	181	7	d.	d.	PROPN
cana-768	181	8	,	,	PUNCT
cana-768	181	9	phaneendra	phaneendra	PROPN
cana-768	181	10	,	,	PUNCT
cana-768	181	11	k.	k.	PROPN
cana-768	181	12	,	,	PUNCT
cana-768	181	13	&	&	CCONJ
cana-768	181	14	reddy	reddy	PROPN
cana-768	181	15	,	,	PUNCT
cana-768	181	16	y.	y.	PROPN
cana-768	181	17	n.	n.	PROPN
cana-768	181	18	(	(	PUNCT
cana-768	181	19	2018	2018	NUM
cana-768	181	20	)	)	PUNCT
cana-768	181	21	.	.	PUNCT
cana-768	182	1	accurate	accurate	ADJ
cana-768	182	2	numerical	numerical	ADJ
cana-768	182	3	method	method	NOUN
cana-768	182	4	for	for	ADP
cana-768	182	5	singularly	singularly	ADV
cana-768	182	6	perturbed	perturb	VERB
cana-768	182	7	differential	differential	ADJ
cana-768	182	8	-	-	PUNCT
cana-768	182	9	difference	difference	NOUN
cana-768	182	10	equations	equation	NOUN
cana-768	182	11	with	with	ADP
cana-768	182	12	mixed	mixed	ADJ
cana-768	182	13	shifts	shift	NOUN
cana-768	182	14	.	.	PUNCT
cana-768	183	1	khayyam	khayyam	PROPN
cana-768	183	2	journal	journal	PROPN
cana-768	183	3	of	of	ADP
cana-768	183	4	mathematics	mathematic	NOUN
cana-768	183	5	,	,	PUNCT
cana-768	183	6	4	4	NUM
cana-768	183	7	,	,	PUNCT
cana-768	183	8	110–122	110–122	NUM
cana-768	183	9	.	.	PUNCT
cana-768	184	1	[	[	X
cana-768	184	2	8	8	NUM
cana-768	184	3	]	]	SYM
cana-768	184	4	lange	lange	NOUN
cana-768	184	5	,	,	PUNCT
cana-768	184	6	c.	c.	PROPN
cana-768	184	7	g.	g.	PROPN
cana-768	184	8	,	,	PUNCT
cana-768	184	9	&	&	CCONJ
cana-768	184	10	miura	miura	PROPN
cana-768	184	11	,	,	PUNCT
cana-768	184	12	r.	r.	PROPN
cana-768	184	13	m.	m.	PROPN
cana-768	184	14	(	(	PUNCT
cana-768	184	15	1994	1994	NUM
cana-768	184	16	)	)	PUNCT
cana-768	184	17	.	.	PUNCT
cana-768	185	1	singular	singular	PROPN
cana-768	185	2	perturbation	perturbation	NOUN
cana-768	185	3	analysis	analysis	NOUN
cana-768	185	4	of	of	ADP
cana-768	185	5	boundary	boundary	ADJ
cana-768	185	6	value	value	NOUN
cana-768	185	7	problems	problem	NOUN
cana-768	185	8	for	for	ADP
cana-768	185	9	differentialdifference	differentialdifference	NOUN
cana-768	185	10	equations	equation	NOUN
cana-768	185	11	.	.	PUNCT
cana-768	186	1	v.	v.	ADP
cana-768	186	2	small	small	ADJ
cana-768	186	3	shifts	shift	NOUN
cana-768	186	4	with	with	ADP
cana-768	186	5	layer	layer	NOUN
cana-768	186	6	behavior	behavior	NOUN
cana-768	186	7	.	.	PUNCT
cana-768	187	1	siam	siam	PROPN
cana-768	187	2	journal	journal	PROPN
cana-768	187	3	on	on	ADP
cana-768	187	4	applied	apply	VERB
cana-768	187	5	mathematics	mathematic	NOUN
cana-768	187	6	,	,	PUNCT
cana-768	187	7	54	54	NUM
cana-768	187	8	,	,	PUNCT
cana-768	187	9	249–272	249–272	NUM
cana-768	187	10	.	.	PUNCT
cana-768	188	1	communications	communication	NOUN
cana-768	188	2	on	on	ADP
cana-768	188	3	applied	apply	VERB
cana-768	188	4	nonlinear	nonlinear	ADJ
cana-768	188	5	analysis	analysis	NOUN
cana-768	188	6	issn	issn	NOUN
cana-768	188	7	:	:	PUNCT
cana-768	188	8	1074	1074	NUM
cana-768	188	9	-	-	PUNCT
cana-768	188	10	133x	133x	NUM
cana-768	188	11	vol	vol	NOUN
cana-768	188	12	31	31	NUM
cana-768	188	13	no	no	NOUN
cana-768	188	14	.	.	PUNCT
cana-768	189	1	3s	3s	NUM
cana-768	189	2	(	(	PUNCT
cana-768	189	3	2024	2024	NUM
cana-768	189	4	)	)	PUNCT
cana-768	189	5	324	324	NUM
cana-768	189	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-768	190	1	[	[	X
cana-768	190	2	9	9	NUM
cana-768	190	3	]	]	X
cana-768	190	4	mccartin	mccartin	NOUN
cana-768	190	5	,	,	PUNCT
cana-768	190	6	b.	b.	PROPN
cana-768	190	7	j.	j.	PROPN
cana-768	190	8	(	(	PUNCT
cana-768	190	9	1991	1991	NUM
cana-768	190	10	)	)	PUNCT
cana-768	190	11	.	.	PUNCT
cana-768	191	1	theory	theory	NOUN
cana-768	191	2	of	of	ADP
cana-768	191	3	exponential	exponential	ADJ
cana-768	191	4	splines	spline	NOUN
cana-768	191	5	.	.	PUNCT
cana-768	192	1	journal	journal	NOUN
cana-768	192	2	of	of	ADP
cana-768	192	3	approximation	approximation	NOUN
cana-768	192	4	theory	theory	NOUN
cana-768	192	5	,	,	PUNCT
cana-768	192	6	66	66	NUM
cana-768	192	7	,	,	PUNCT
cana-768	192	8	1–23	1–23	NOUN
cana-768	192	9	.	.	PUNCT
cana-768	193	1	[	[	X
cana-768	193	2	10	10	NUM
cana-768	193	3	]	]	X
cana-768	193	4	mohammadi	mohammadi	NOUN
cana-768	193	5	,	,	PUNCT
cana-768	193	6	r.	r.	PROPN
cana-768	193	7	(	(	PUNCT
cana-768	193	8	2013	2013	NUM
cana-768	193	9	)	)	PUNCT
cana-768	193	10	.	.	PUNCT
cana-768	194	1	exponential	exponential	PROPN
cana-768	194	2	b	b	X
cana-768	194	3	-	-	PUNCT
cana-768	194	4	spline	spline	NOUN
cana-768	194	5	solution	solution	NOUN
cana-768	194	6	of	of	ADP
cana-768	194	7	convection	convection	NOUN
cana-768	194	8	-	-	PUNCT
cana-768	194	9	diffusion	diffusion	NOUN
cana-768	194	10	equations	equation	NOUN
cana-768	194	11	.	.	PUNCT
cana-768	195	1	appl	appl	PROPN
cana-768	195	2	ma	ma	PROPN
cana-768	195	3	.	.	PUNCT
cana-768	196	1	[	[	X
cana-768	196	2	11	11	NUM
cana-768	196	3	]	]	SYM
cana-768	196	4	rao	rao	PROPN
cana-768	196	5	,	,	PUNCT
cana-768	196	6	s.	s.	PROPN
cana-768	196	7	c.	c.	PROPN
cana-768	196	8	,	,	PUNCT
cana-768	196	9	&	&	CCONJ
cana-768	196	10	kumar	kumar	PROPN
cana-768	196	11	,	,	PUNCT
cana-768	196	12	m.	m.	NOUN
cana-768	196	13	(	(	PUNCT
cana-768	196	14	2008	2008	NUM
cana-768	196	15	)	)	PUNCT
cana-768	196	16	.	.	PUNCT
cana-768	197	1	exponential	exponential	PROPN
cana-768	197	2	b	b	X
cana-768	197	3	-	-	PUNCT
cana-768	197	4	spline	spline	NOUN
cana-768	197	5	collocation	collocation	NOUN
cana-768	197	6	method	method	NOUN
cana-768	197	7	for	for	ADP
cana-768	197	8	self	self	NOUN
cana-768	197	9	-	-	PUNCT
cana-768	197	10	adjoint	adjoint	NOUN
cana-768	197	11	singularly	singularly	ADV
cana-768	197	12	perturbed	perturb	VERB
cana-768	197	13	boundary	boundary	ADJ
cana-768	197	14	value	value	NOUN
cana-768	197	15	problems	problem	NOUN
cana-768	197	16	.	.	PUNCT
cana-768	198	1	applied	apply	VERB
cana-768	198	2	numerical	numerical	ADJ
cana-768	198	3	mathematics	mathematic	NOUN
cana-768	198	4	,	,	PUNCT
cana-768	198	5	58	58	NUM
cana-768	198	6	,	,	PUNCT
cana-768	198	7	1572–1581	1572–1581	NUM
cana-768	198	8	.	.	PUNCT
cana-768	199	1	[	[	X
cana-768	199	2	12	12	NUM
cana-768	199	3	]	]	X
cana-768	199	4	reddy	reddy	NOUN
cana-768	199	5	,	,	PUNCT
cana-768	199	6	y.	y.	PROPN
cana-768	199	7	n.	n.	PROPN
cana-768	199	8	,	,	PUNCT
cana-768	199	9	soujanya	soujanya	PROPN
cana-768	199	10	,	,	PUNCT
cana-768	199	11	g.	g.	PROPN
cana-768	199	12	b.	b.	PROPN
cana-768	199	13	,	,	PUNCT
cana-768	199	14	phaneendra	phaneendra	PROPN
cana-768	199	15	,	,	PUNCT
cana-768	199	16	k.	k.	PROPN
cana-768	199	17	,	,	PUNCT
cana-768	199	18	&	&	CCONJ
cana-768	199	19	others	other	NOUN
cana-768	199	20	.	.	PUNCT
cana-768	200	1	(	(	PUNCT
cana-768	200	2	2012	2012	NUM
cana-768	200	3	)	)	PUNCT
cana-768	200	4	.	.	PUNCT
cana-768	201	1	numerical	numerical	ADJ
cana-768	201	2	integration	integration	NOUN
cana-768	201	3	method	method	NOUN
cana-768	201	4	for	for	ADP
cana-768	201	5	singularly	singularly	ADV
cana-768	201	6	perturbed	perturb	VERB
cana-768	201	7	delay	delay	NOUN
cana-768	201	8	differential	differential	ADJ
cana-768	201	9	equations	equation	NOUN
cana-768	201	10	.	.	PUNCT
cana-768	202	1	international	international	ADJ
cana-768	202	2	journal	journal	PROPN
cana-768	202	3	of	of	ADP
cana-768	202	4	applied	apply	VERB
cana-768	202	5	science	science	NOUN
cana-768	202	6	and	and	CCONJ
cana-768	202	7	engineering	engineering	NOUN
cana-768	202	8	,	,	PUNCT
cana-768	202	9	10	10	NUM
cana-768	202	10	,	,	PUNCT
cana-768	202	11	249–261	249–261	NUM
cana-768	202	12	.	.	PUNCT
cana-768	203	1	[	[	X
cana-768	203	2	13	13	NUM
cana-768	203	3	]	]	SYM
cana-768	203	4	swamy	swamy	NOUN
cana-768	203	5	,	,	PUNCT
cana-768	203	6	d.	d.	PROPN
cana-768	203	7	k.	k.	PROPN
cana-768	203	8	,	,	PUNCT
cana-768	203	9	adilaxmi	adilaxmi	PROPN
cana-768	203	10	,	,	PUNCT
cana-768	203	11	m.	m.	NOUN
cana-768	203	12	,	,	PUNCT
cana-768	203	13	&	&	CCONJ
cana-768	203	14	soujanya	soujanya	PROPN
cana-768	203	15	,	,	PUNCT
cana-768	203	16	g.	g.	PROPN
cana-768	203	17	b.	b.	PROPN
cana-768	203	18	(	(	PUNCT
cana-768	203	19	2020	2020	NUM
cana-768	203	20	)	)	PUNCT
cana-768	203	21	.	.	PUNCT
cana-768	204	1	difference	difference	NOUN
cana-768	204	2	scheme	scheme	NOUN
cana-768	204	3	for	for	ADP
cana-768	204	4	the	the	DET
cana-768	204	5	numerical	numerical	ADJ
cana-768	204	6	solution	solution	NOUN
cana-768	204	7	of	of	ADP
cana-768	204	8	delay	delay	NOUN
cana-768	204	9	differential	differential	ADJ
cana-768	204	10	equations	equation	NOUN
cana-768	204	11	with	with	ADP
cana-768	204	12	layer	layer	NOUN
cana-768	204	13	structure	structure	NOUN
cana-768	204	14	.	.	PUNCT
cana-768	205	1	advances	advance	NOUN
cana-768	205	2	in	in	ADP
cana-768	205	3	mathematics	mathematics	NOUN
cana-768	205	4	scientific	scientific	ADJ
cana-768	205	5	journal	journal	NOUN
cana-768	205	6	,	,	PUNCT
cana-768	205	7	9	9	NUM
cana-768	205	8	,	,	PUNCT
cana-768	205	9	3271–3287	3271–3287	NUM
cana-768	205	10	.	.	PUNCT
cana-768	206	1	[	[	X
cana-768	206	2	14	14	NUM
cana-768	206	3	]	]	X
cana-768	206	4	swamy	swamy	PROPN
cana-768	206	5	,	,	PUNCT
cana-768	206	6	d.	d.	PROPN
cana-768	206	7	k.	k.	PROPN
cana-768	206	8	,	,	PUNCT
cana-768	206	9	phaneendra	phaneendra	PROPN
cana-768	206	10	,	,	PUNCT
cana-768	206	11	k.	k.	PROPN
cana-768	206	12	,	,	PUNCT
cana-768	206	13	babu	babu	PROPN
cana-768	206	14	,	,	PUNCT
cana-768	206	15	a.	a.	PROPN
cana-768	206	16	b.	b.	PROPN
cana-768	206	17	,	,	PUNCT
cana-768	206	18	&	&	CCONJ
cana-768	206	19	reddy	reddy	PROPN
cana-768	206	20	,	,	PUNCT
cana-768	206	21	y.	y.	PROPN
cana-768	206	22	n.	n.	PROPN
cana-768	206	23	(	(	PUNCT
cana-768	206	24	2015	2015	NUM
cana-768	206	25	)	)	PUNCT
cana-768	206	26	.	.	PUNCT
cana-768	207	1	computational	computational	ADJ
cana-768	207	2	method	method	NOUN
cana-768	207	3	for	for	ADP
cana-768	207	4	singularly	singularly	ADV
cana-768	207	5	perturbed	perturb	VERB
cana-768	207	6	delay	delay	NOUN
cana-768	207	7	differential	differential	ADJ
cana-768	207	8	equations	equation	NOUN
cana-768	207	9	with	with	ADP
cana-768	207	10	twin	twin	ADJ
cana-768	207	11	layers	layer	NOUN
cana-768	207	12	or	or	CCONJ
cana-768	207	13	oscillatory	oscillatory	ADJ
cana-768	207	14	behaviour	behaviour	NOUN
cana-768	207	15	.	.	PUNCT
cana-768	208	1	ain	ain	PROPN
cana-768	208	2	shams	sham	VERB
cana-768	208	3	engineering	engineering	NOUN
cana-768	208	4	journal	journal	NOUN
cana-768	208	5	,	,	PUNCT
cana-768	208	6	6	6	NUM
cana-768	208	7	,	,	PUNCT
cana-768	208	8	391–398	391–398	NUM
cana-768	208	9	.	.	PUNCT
cana-768	209	1	[	[	X
cana-768	209	2	15	15	NUM
cana-768	209	3	]	]	X
cana-768	209	4	swamy	swamy	NOUN
cana-768	209	5	,	,	PUNCT
cana-768	209	6	d.	d.	PROPN
cana-768	209	7	k.	k.	PROPN
cana-768	209	8	,	,	PUNCT
cana-768	209	9	singh	singh	PROPN
cana-768	209	10	,	,	PUNCT
cana-768	209	11	r.	r.	PROPN
cana-768	209	12	p.	p.	PROPN
cana-768	209	13	,	,	PUNCT
cana-768	209	14	&	&	CCONJ
cana-768	209	15	reddy	reddy	PROPN
cana-768	209	16	,	,	PUNCT
cana-768	209	17	y.	y.	PROPN
cana-768	209	18	n.	n.	PROPN
cana-768	209	19	(	(	PUNCT
cana-768	209	20	2022	2022	NUM
cana-768	209	21	)	)	PUNCT
cana-768	209	22	.	.	PUNCT
cana-768	210	1	numerical	numerical	ADJ
cana-768	210	2	integration	integration	NOUN
cana-768	210	3	method	method	NOUN
cana-768	210	4	for	for	ADP
cana-768	210	5	a	a	DET
cana-768	210	6	class	class	NOUN
cana-768	210	7	of	of	ADP
cana-768	210	8	singularly	singularly	ADV
cana-768	210	9	perturbed	perturb	VERB
cana-768	210	10	differential	differential	ADJ
cana-768	210	11	-	-	PUNCT
cana-768	210	12	difference	difference	NOUN
cana-768	210	13	equations	equation	NOUN
cana-768	210	14	.	.	PUNCT
cana-768	211	1	mathematical	mathematical	ADJ
cana-768	211	2	statistician	statistician	NOUN
cana-768	211	3	and	and	CCONJ
cana-768	211	4	engineering	engineering	NOUN
cana-768	211	5	applications	application	NOUN
cana-768	211	6	,	,	PUNCT
cana-768	211	7	71	71	NUM
cana-768	211	8	,	,	PUNCT
cana-768	211	9	5771	5771	NUM
cana-768	211	10	–	–	PUNCT
cana-768	211	11	5795	5795	NUM
cana-768	211	12	.	.	PUNCT
cana-768	212	1	[	[	X
cana-768	212	2	16	16	NUM
cana-768	212	3	]	]	X
cana-768	212	4	varga	varga	PROPN
cana-768	212	5	,	,	PUNCT
cana-768	212	6	r.	r.	PROPN
cana-768	212	7	s.	s.	PROPN
cana-768	212	8	(	(	PUNCT
cana-768	212	9	1962	1962	NUM
cana-768	212	10	)	)	PUNCT
cana-768	212	11	.	.	PUNCT
cana-768	213	1	iterative	iterative	NOUN
cana-768	213	2	analysis	analysis	NOUN
cana-768	213	3	.	.	PUNCT
cana-768	214	1	new	new	PROPN
cana-768	214	2	jersey	jersey	PROPN
cana-768	214	3	,	,	PUNCT
cana-768	214	4	322	322	NUM
cana-768	214	5	.	.	PUNCT
cana-768	215	1	[	[	X
cana-768	215	2	17	17	NUM
cana-768	215	3	]	]	X
cana-768	215	4	young	young	ADJ
cana-768	215	5	,	,	PUNCT
cana-768	215	6	d.	d.	PROPN
cana-768	215	7	m.	m.	PROPN
cana-768	215	8	(	(	PUNCT
cana-768	215	9	2014	2014	NUM
cana-768	215	10	)	)	PUNCT
cana-768	215	11	.	.	PUNCT
cana-768	216	1	iterative	iterative	NOUN
cana-768	216	2	solution	solution	NOUN
cana-768	216	3	of	of	ADP
cana-768	216	4	large	large	ADJ
cana-768	216	5	linear	linear	NOUN
cana-768	216	6	systems	system	NOUN
cana-768	216	7	.	.	PUNCT
cana-768	217	1	academic	academic	ADJ
cana-768	217	2	press	press	NOUN
cana-768	217	3	,	,	PUNCT
cana-768	217	4	new	new	ADJ
cana-768	217	5	work	work	NOUN
cana-768	217	6	.	.	PUNCT
cana-768	218	1	[	[	X
cana-768	218	2	18	18	NUM
cana-768	218	3	]	]	X
cana-768	218	4	zahra	zahra	PROPN
cana-768	218	5	,	,	PUNCT
cana-768	218	6	w.	w.	PROPN
cana-768	218	7	k.	k.	PROPN
cana-768	218	8	,	,	PUNCT
cana-768	218	9	el	el	PROPN
cana-768	218	10	-	-	PUNCT
cana-768	218	11	beltagy	beltagy	ADJ
cana-768	218	12	,	,	PUNCT
cana-768	218	13	m.	m.	NOUN
cana-768	218	14	a.	a.	PROPN
cana-768	218	15	,	,	PUNCT
cana-768	218	16	el	el	PROPN
cana-768	218	17	mhlawy	mhlawy	PROPN
cana-768	218	18	,	,	PUNCT
cana-768	218	19	a.	a.	NOUN
cana-768	218	20	m.	m.	NOUN
cana-768	218	21	,	,	PUNCT
cana-768	218	22	&	&	CCONJ
cana-768	218	23	elkhadrawy	elkhadrawy	PROPN
cana-768	218	24	,	,	PUNCT
cana-768	218	25	r.	r.	PROPN
cana-768	218	26	r.	r.	PROPN
cana-768	218	27	(	(	PUNCT
cana-768	218	28	2018	2018	NUM
cana-768	218	29	)	)	PUNCT
cana-768	218	30	.	.	PUNCT
cana-768	219	1	exponential	exponential	ADJ
cana-768	219	2	spline	spline	NOUN
cana-768	219	3	solution	solution	NOUN
cana-768	219	4	for	for	ADP
cana-768	219	5	singularly	singularly	ADV
cana-768	219	6	perturbed	perturb	VERB
cana-768	219	7	boundary	boundary	ADJ
cana-768	219	8	value	value	NOUN
cana-768	219	9	problems	problem	NOUN
cana-768	219	10	with	with	ADP
cana-768	219	11	an	an	DET
cana-768	219	12	uncertain	uncertain	ADJ
cana-768	219	13	—	—	PUNCT
cana-768	219	14	but	but	CCONJ
cana-768	219	15	—	—	PUNCT
cana-768	219	16	bounded	bounded	ADJ
cana-768	219	17	parameter	parameter	NOUN
cana-768	219	18	.	.	PUNCT
cana-768	220	1	journal	journal	PROPN
cana-768	220	2	of	of	ADP
cana-768	220	3	applied	apply	VERB
cana-768	220	4	mathematics	mathematic	NOUN
cana-768	220	5	and	and	CCONJ
cana-768	220	6	physics	physics	NOUN
cana-768	220	7	,	,	PUNCT
cana-768	220	8	6	6	NUM
cana-768	220	9	,	,	PUNCT
cana-768	220	10	854–863	854–863	NUM
cana-768	220	11	.	.	PUNCT
cana-768	221	1	[	[	X
cana-768	221	2	19	19	NUM
cana-768	221	3	]	]	X
cana-768	221	4	kumara	kumara	PROPN
cana-768	221	5	swamy	swamy	PROPN
cana-768	221	6	,	,	PUNCT
cana-768	221	7	d.	d.	PROPN
cana-768	221	8	,	,	PUNCT
cana-768	221	9	phaneendra	phaneendra	PROPN
cana-768	221	10	,	,	PUNCT
cana-768	221	11	k	k	PROPN
cana-768	221	12	.	.	PUNCT
cana-768	221	13	,	,	PUNCT
cana-768	221	14	&	&	CCONJ
cana-768	221	15	reddy	reddy	PROPN
cana-768	221	16	,	,	PUNCT
cana-768	221	17	y.	y.	PROPN
cana-768	221	18	n.	n.	PROPN
cana-768	221	19	(	(	PUNCT
cana-768	221	20	2018	2018	NUM
cana-768	221	21	)	)	PUNCT
cana-768	221	22	.	.	PUNCT
cana-768	222	1	accurate	accurate	ADJ
cana-768	222	2	numerical	numerical	ADJ
cana-768	222	3	method	method	NOUN
cana-768	222	4	for	for	ADP
cana-768	222	5	singularly	singularly	ADV
cana-768	222	6	perturbed	perturb	VERB
cana-768	222	7	differential	differential	ADJ
cana-768	222	8	-	-	PUNCT
cana-768	222	9	difference	difference	NOUN
cana-768	222	10	equations	equation	NOUN
cana-768	222	11	with	with	ADP
cana-768	222	12	mixed	mixed	ADJ
cana-768	222	13	shifts	shift	NOUN
cana-768	222	14	.	.	PUNCT
cana-768	223	1	khayyam	khayyam	PROPN
cana-768	223	2	journal	journal	PROPN
cana-768	223	3	of	of	ADP
cana-768	223	4	mathematics	mathematic	NOUN
cana-768	223	5	,	,	PUNCT
cana-768	223	6	4(2	4(2	NUM
cana-768	223	7	)	)	PUNCT
cana-768	223	8	,	,	PUNCT
cana-768	223	9	110	110	NUM
cana-768	223	10	-	-	SYM
cana-768	223	11	122	122	NUM
cana-768	223	12	.	.	PUNCT