id	sid	tid	token	lemma	pos
cana-1304	1	1	communications	communication	NOUN
cana-1304	1	2	on	on	ADP
cana-1304	1	3	applied	apply	VERB
cana-1304	1	4	nonlinear	nonlinear	ADJ
cana-1304	1	5	analysis	analysis	NOUN
cana-1304	1	6	issn	issn	NOUN
cana-1304	1	7	:	:	PUNCT
cana-1304	1	8	1074	1074	NUM
cana-1304	1	9	-	-	PUNCT
cana-1304	1	10	133x	133x	NUM
cana-1304	1	11	vol	vol	NOUN
cana-1304	1	12	31	31	NUM
cana-1304	1	13	no	no	NOUN
cana-1304	1	14	.	.	PUNCT
cana-1304	2	1	7s	7	NOUN
cana-1304	2	2	(	(	PUNCT
cana-1304	2	3	2024	2024	NUM
cana-1304	2	4	)	)	PUNCT
cana-1304	2	5	286	286	NUM
cana-1304	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1304	2	7	efficiency	efficiency	NOUN
cana-1304	2	8	of	of	ADP
cana-1304	2	9	runge	runge	NOUN
cana-1304	2	10	-	-	PUNCT
cana-1304	2	11	kutta	kutta	NOUN
cana-1304	2	12	-	-	PUNCT
cana-1304	2	13	fehlberg	fehlberg	NOUN
cana-1304	2	14	method	method	NOUN
cana-1304	2	15	in	in	ADP
cana-1304	2	16	resolving	resolve	VERB
cana-1304	2	17	uncertainty	uncertainty	NOUN
cana-1304	2	18	:	:	PUNCT
cana-1304	2	19	a	a	DET
cana-1304	2	20	fuzzy	fuzzy	ADJ
cana-1304	2	21	approach	approach	NOUN
cana-1304	2	22	to	to	PART
cana-1304	2	23	delay	delay	VERB
cana-1304	2	24	differential	differential	ADJ
cana-1304	2	25	equations	equation	NOUN
cana-1304	2	26	1,2	1,2	NUM
cana-1304	2	27	ch	ch	NOUN
cana-1304	2	28	.	.	PUNCT
cana-1304	3	1	subba	subba	PROPN
cana-1304	3	2	reddy	reddy	PROPN
cana-1304	3	3	,	,	PUNCT
cana-1304	3	4	3	3	PROPN
cana-1304	3	5	*	*	PUNCT
cana-1304	3	6	t.	t.	PROPN
cana-1304	3	7	l.	l.	PROPN
cana-1304	3	8	yookesh	yookesh	PROPN
cana-1304	3	9	1	1	NUM
cana-1304	3	10	mentor	mentor	NOUN
cana-1304	3	11	in	in	ADP
cana-1304	3	12	mathematics	mathematic	NOUN
cana-1304	3	13	,	,	PUNCT
cana-1304	3	14	rgukt	rgukt	NOUN
cana-1304	3	15	,	,	PUNCT
cana-1304	3	16	nuzvid	nuzvid	NOUN
cana-1304	3	17	.	.	PUNCT
cana-1304	4	1	2	2	NUM
cana-1304	4	2	research	research	NOUN
cana-1304	4	3	scholar	scholar	NOUN
cana-1304	4	4	,	,	PUNCT
cana-1304	4	5	school	school	NOUN
cana-1304	4	6	of	of	ADP
cana-1304	4	7	applied	apply	VERB
cana-1304	4	8	sciencies	sciencie	NOUN
cana-1304	4	9	and	and	CCONJ
cana-1304	4	10	humanities	humanity	NOUN
cana-1304	4	11	,	,	PUNCT
cana-1304	4	12	deparment	deparment	NOUN
cana-1304	4	13	of	of	ADP
cana-1304	4	14	mathematics	mathematics	PROPN
cana-1304	4	15	&	&	CCONJ
cana-1304	4	16	statistics	statistics	PROPN
cana-1304	4	17	vignan	vignan	PROPN
cana-1304	4	18	’s	’s	PART
cana-1304	4	19	foundation	foundation	PROPN
cana-1304	4	20	for	for	ADP
cana-1304	4	21	science	science	NOUN
cana-1304	4	22	,	,	PUNCT
cana-1304	4	23	technology	technology	NOUN
cana-1304	4	24	&	&	CCONJ
cana-1304	4	25	research	research	NOUN
cana-1304	4	26	,	,	PUNCT
cana-1304	4	27	guntur-522	guntur-522	NOUN
cana-1304	4	28	213	213	NUM
cana-1304	4	29	,	,	PUNCT
cana-1304	4	30	india	india	PROPN
cana-1304	4	31	3	3	NUM
cana-1304	4	32	assistant	assistant	NOUN
cana-1304	4	33	professor	professor	NOUN
cana-1304	4	34	,	,	PUNCT
cana-1304	4	35	school	school	NOUN
cana-1304	4	36	of	of	ADP
cana-1304	4	37	applied	apply	VERB
cana-1304	4	38	sciencies	sciencie	NOUN
cana-1304	4	39	and	and	CCONJ
cana-1304	4	40	humanities	humanity	NOUN
cana-1304	4	41	,	,	PUNCT
cana-1304	4	42	deparment	deparment	NOUN
cana-1304	4	43	of	of	ADP
cana-1304	4	44	mathematics	mathematics	PROPN
cana-1304	4	45	&	&	CCONJ
cana-1304	4	46	statistics	statistics	PROPN
cana-1304	4	47	vignan	vignan	PROPN
cana-1304	4	48	’s	’s	PART
cana-1304	4	49	foundation	foundation	PROPN
cana-1304	4	50	for	for	ADP
cana-1304	4	51	science	science	NOUN
cana-1304	4	52	,	,	PUNCT
cana-1304	4	53	technology	technology	NOUN
cana-1304	4	54	&	&	CCONJ
cana-1304	4	55	research	research	NOUN
cana-1304	4	56	,	,	PUNCT
cana-1304	4	57	guntur-522	guntur-522	NOUN
cana-1304	4	58	213	213	NUM
cana-1304	4	59	,	,	PUNCT
cana-1304	4	60	india	india	PROPN
cana-1304	4	61	e.mail:subbareddych@rguktn.ac.in	e.mail:subbareddych@rguktn.ac.in	PROPN
cana-1304	4	62	anddrytl_sh@vignan.ac.in	anddrytl_sh@vignan.ac.in	NOUN
cana-1304	4	63	*	*	PUNCT
cana-1304	4	64	corresponding	correspond	VERB
cana-1304	4	65	author	author	NOUN
cana-1304	4	66	article	article	NOUN
cana-1304	4	67	history	history	NOUN
cana-1304	4	68	:	:	PUNCT
cana-1304	4	69	received	receive	VERB
cana-1304	4	70	:	:	PUNCT
cana-1304	4	71	01	01	NUM
cana-1304	4	72	-	-	PUNCT
cana-1304	4	73	06	06	NUM
cana-1304	4	74	-	-	PUNCT
cana-1304	4	75	2024	2024	NUM
cana-1304	4	76	revised	revise	VERB
cana-1304	4	77	:	:	PUNCT
cana-1304	4	78	03	03	NUM
cana-1304	4	79	-	-	PUNCT
cana-1304	4	80	07	07	NUM
cana-1304	4	81	-	-	PUNCT
cana-1304	4	82	2024	2024	NUM
cana-1304	4	83	accepted	accept	VERB
cana-1304	4	84	:	:	PUNCT
cana-1304	4	85	29	29	NUM
cana-1304	4	86	-	-	SYM
cana-1304	4	87	07	07	NUM
cana-1304	4	88	-	-	PUNCT
cana-1304	4	89	2024	2024	NUM
cana-1304	4	90	abstract	abstract	NOUN
cana-1304	4	91	:	:	PUNCT
cana-1304	4	92	this	this	DET
cana-1304	4	93	research	research	NOUN
cana-1304	4	94	delves	delve	VERB
cana-1304	4	95	into	into	ADP
cana-1304	4	96	the	the	DET
cana-1304	4	97	examination	examination	NOUN
cana-1304	4	98	of	of	ADP
cana-1304	4	99	the	the	DET
cana-1304	4	100	convergence	convergence	NOUN
cana-1304	4	101	behavior	behavior	NOUN
cana-1304	4	102	of	of	ADP
cana-1304	4	103	the	the	DET
cana-1304	4	104	runge	runge	NOUN
cana-1304	4	105	-	-	PUNCT
cana-1304	4	106	kuttafehlberg	kuttafehlberg	PROPN
cana-1304	4	107	method	method	NOUN
cana-1304	4	108	(	(	PUNCT
cana-1304	4	109	rkfm	rkfm	PROPN
cana-1304	4	110	)	)	PUNCT
cana-1304	4	111	when	when	SCONJ
cana-1304	4	112	applied	apply	VERB
cana-1304	4	113	to	to	PART
cana-1304	4	114	address	address	VERB
cana-1304	4	115	the	the	DET
cana-1304	4	116	challenges	challenge	NOUN
cana-1304	4	117	posed	pose	VERB
cana-1304	4	118	by	by	ADP
cana-1304	4	119	delay	delay	NOUN
cana-1304	4	120	differential	differential	ADJ
cana-1304	4	121	equations	equation	NOUN
cana-1304	4	122	(	(	PUNCT
cana-1304	4	123	dde	dde	PROPN
cana-1304	4	124	)	)	PUNCT
cana-1304	4	125	within	within	ADP
cana-1304	4	126	the	the	DET
cana-1304	4	127	framework	framework	NOUN
cana-1304	4	128	of	of	ADP
cana-1304	4	129	fuzzy	fuzzy	ADJ
cana-1304	4	130	concepts	concept	NOUN
cana-1304	4	131	.	.	PUNCT
cana-1304	5	1	the	the	DET
cana-1304	5	2	integration	integration	NOUN
cana-1304	5	3	of	of	ADP
cana-1304	5	4	fuzzy	fuzzy	ADJ
cana-1304	5	5	logic	logic	NOUN
cana-1304	5	6	is	be	AUX
cana-1304	5	7	explored	explore	VERB
cana-1304	5	8	as	as	ADP
cana-1304	5	9	a	a	DET
cana-1304	5	10	strategic	strategic	ADJ
cana-1304	5	11	means	mean	NOUN
cana-1304	5	12	to	to	PART
cana-1304	5	13	grapple	grapple	VERB
cana-1304	5	14	with	with	ADP
cana-1304	5	15	the	the	DET
cana-1304	5	16	inherent	inherent	ADJ
cana-1304	5	17	uncertainty	uncertainty	NOUN
cana-1304	5	18	in	in	ADP
cana-1304	5	19	obtained	obtain	VERB
cana-1304	5	20	results	result	NOUN
cana-1304	5	21	,	,	PUNCT
cana-1304	5	22	acknowledging	acknowledge	VERB
cana-1304	5	23	the	the	DET
cana-1304	5	24	limitations	limitation	NOUN
cana-1304	5	25	of	of	ADP
cana-1304	5	26	conventional	conventional	ADJ
cana-1304	5	27	approaches	approach	NOUN
cana-1304	5	28	in	in	ADP
cana-1304	5	29	dealing	deal	VERB
cana-1304	5	30	with	with	ADP
cana-1304	5	31	nuanced	nuanced	ADJ
cana-1304	5	32	uncertainties	uncertainty	NOUN
cana-1304	5	33	in	in	ADP
cana-1304	5	34	ddes	dde	NOUN
cana-1304	5	35	.	.	PUNCT
cana-1304	6	1	the	the	DET
cana-1304	6	2	core	core	NOUN
cana-1304	6	3	of	of	ADP
cana-1304	6	4	the	the	DET
cana-1304	6	5	study	study	NOUN
cana-1304	6	6	involves	involve	VERB
cana-1304	6	7	a	a	DET
cana-1304	6	8	meticulous	meticulous	ADJ
cana-1304	6	9	analysis	analysis	NOUN
cana-1304	6	10	of	of	ADP
cana-1304	6	11	numerical	numerical	ADJ
cana-1304	6	12	outcomes	outcome	NOUN
cana-1304	6	13	,	,	PUNCT
cana-1304	6	14	with	with	ADP
cana-1304	6	15	a	a	DET
cana-1304	6	16	specific	specific	ADJ
cana-1304	6	17	emphasis	emphasis	NOUN
cana-1304	6	18	on	on	ADP
cana-1304	6	19	evaluating	evaluate	VERB
cana-1304	6	20	the	the	DET
cana-1304	6	21	effectiveness	effectiveness	NOUN
cana-1304	6	22	and	and	CCONJ
cana-1304	6	23	efficiency	efficiency	NOUN
cana-1304	6	24	of	of	ADP
cana-1304	6	25	the	the	DET
cana-1304	6	26	runge	runge	NOUN
cana-1304	6	27	-	-	PUNCT
cana-1304	6	28	kutta	kutta	NOUN
cana-1304	6	29	-	-	PUNCT
cana-1304	6	30	fehlberg	fehlberg	NOUN
cana-1304	6	31	method	method	NOUN
cana-1304	6	32	.	.	PUNCT
cana-1304	7	1	the	the	DET
cana-1304	7	2	assessment	assessment	NOUN
cana-1304	7	3	includes	include	VERB
cana-1304	7	4	a	a	DET
cana-1304	7	5	thorough	thorough	ADJ
cana-1304	7	6	comparison	comparison	NOUN
cana-1304	7	7	of	of	ADP
cana-1304	7	8	results	result	NOUN
cana-1304	7	9	obtained	obtain	VERB
cana-1304	7	10	through	through	ADP
cana-1304	7	11	the	the	DET
cana-1304	7	12	rkfm	rkfm	NOUN
cana-1304	7	13	against	against	ADP
cana-1304	7	14	those	those	PRON
cana-1304	7	15	derived	derive	VERB
cana-1304	7	16	from	from	ADP
cana-1304	7	17	the	the	DET
cana-1304	7	18	rungekutta	rungekutta	ADJ
cana-1304	7	19	4th	4th	ADJ
cana-1304	7	20	-	-	PUNCT
cana-1304	7	21	order	order	NOUN
cana-1304	7	22	method	method	NOUN
cana-1304	7	23	,	,	PUNCT
cana-1304	7	24	as	as	ADV
cana-1304	7	25	well	well	ADV
cana-1304	7	26	as	as	ADP
cana-1304	7	27	benchmarking	benchmarke	VERB
cana-1304	7	28	against	against	ADP
cana-1304	7	29	the	the	DET
cana-1304	7	30	exact	exact	ADJ
cana-1304	7	31	solution	solution	NOUN
cana-1304	7	32	.	.	PUNCT
cana-1304	8	1	the	the	DET
cana-1304	8	2	findings	finding	NOUN
cana-1304	8	3	of	of	ADP
cana-1304	8	4	this	this	DET
cana-1304	8	5	research	research	NOUN
cana-1304	8	6	not	not	PART
cana-1304	8	7	only	only	ADV
cana-1304	8	8	validate	validate	VERB
cana-1304	8	9	the	the	DET
cana-1304	8	10	suitability	suitability	NOUN
cana-1304	8	11	of	of	ADP
cana-1304	8	12	the	the	DET
cana-1304	8	13	rkfm	rkfm	NOUN
cana-1304	8	14	for	for	ADP
cana-1304	8	15	solving	solve	VERB
cana-1304	8	16	delay	delay	NOUN
cana-1304	8	17	differential	differential	ADJ
cana-1304	8	18	equations	equation	NOUN
cana-1304	8	19	but	but	CCONJ
cana-1304	8	20	also	also	ADV
cana-1304	8	21	highlight	highlight	VERB
cana-1304	8	22	its	its	PRON
cana-1304	8	23	comparative	comparative	ADJ
cana-1304	8	24	advantages	advantage	NOUN
cana-1304	8	25	over	over	ADP
cana-1304	8	26	the	the	DET
cana-1304	8	27	traditional	traditional	ADJ
cana-1304	8	28	runge	runge	NOUN
cana-1304	8	29	-	-	PUNCT
cana-1304	8	30	kutta	kutta	NOUN
cana-1304	8	31	4th	4th	ADJ
cana-1304	8	32	-	-	PUNCT
cana-1304	8	33	order	order	NOUN
cana-1304	8	34	method	method	NOUN
cana-1304	8	35	.	.	PUNCT
cana-1304	9	1	the	the	DET
cana-1304	9	2	results	result	NOUN
cana-1304	9	3	contribute	contribute	VERB
cana-1304	9	4	to	to	ADP
cana-1304	9	5	an	an	DET
cana-1304	9	6	enhanced	enhanced	ADJ
cana-1304	9	7	understanding	understanding	NOUN
cana-1304	9	8	of	of	ADP
cana-1304	9	9	the	the	DET
cana-1304	9	10	performance	performance	NOUN
cana-1304	9	11	and	and	CCONJ
cana-1304	9	12	applicability	applicability	NOUN
cana-1304	9	13	of	of	ADP
cana-1304	9	14	the	the	DET
cana-1304	9	15	rkfm	rkfm	NOUN
cana-1304	9	16	in	in	ADP
cana-1304	9	17	the	the	DET
cana-1304	9	18	context	context	NOUN
cana-1304	9	19	of	of	ADP
cana-1304	9	20	fuzzy	fuzzy	ADJ
cana-1304	9	21	ddes	dde	NOUN
cana-1304	9	22	,	,	PUNCT
cana-1304	9	23	thereby	thereby	ADV
cana-1304	9	24	advancing	advance	VERB
cana-1304	9	25	the	the	DET
cana-1304	9	26	landscape	landscape	NOUN
cana-1304	9	27	of	of	ADP
cana-1304	9	28	numerical	numerical	ADJ
cana-1304	9	29	methods	method	NOUN
cana-1304	9	30	for	for	ADP
cana-1304	9	31	addressing	address	VERB
cana-1304	9	32	complex	complex	ADJ
cana-1304	9	33	dynamic	dynamic	ADJ
cana-1304	9	34	systems	system	NOUN
cana-1304	9	35	.	.	PUNCT
cana-1304	10	1	keywords	keyword	NOUN
cana-1304	10	2	:	:	PUNCT
cana-1304	10	3	approximate	approximate	ADJ
cana-1304	10	4	method	method	NOUN
cana-1304	10	5	,	,	PUNCT
cana-1304	10	6	fuzzy	fuzzy	ADJ
cana-1304	10	7	number	number	NOUN
cana-1304	10	8	,	,	PUNCT
cana-1304	10	9	convergence	convergence	NOUN
cana-1304	10	10	1	1	NUM
cana-1304	10	11	.	.	PUNCT
cana-1304	11	1	introduction	introduction	NOUN
cana-1304	11	2	exploring	explore	VERB
cana-1304	11	3	temporal	temporal	ADJ
cana-1304	11	4	dynamics	dynamic	NOUN
cana-1304	11	5	across	across	ADP
cana-1304	11	6	varied	varied	ADJ
cana-1304	11	7	scenarios	scenario	NOUN
cana-1304	11	8	holds	hold	VERB
cana-1304	11	9	a	a	DET
cana-1304	11	10	central	central	ADJ
cana-1304	11	11	position	position	NOUN
cana-1304	11	12	in	in	ADP
cana-1304	11	13	applied	apply	VERB
cana-1304	11	14	design	design	NOUN
cana-1304	11	15	research	research	NOUN
cana-1304	11	16	.	.	PUNCT
cana-1304	12	1	this	this	PRON
cana-1304	12	2	underscores	underscore	VERB
cana-1304	12	3	the	the	DET
cana-1304	12	4	urgent	urgent	ADJ
cana-1304	12	5	need	need	NOUN
cana-1304	12	6	to	to	PART
cana-1304	12	7	enhance	enhance	VERB
cana-1304	12	8	digital	digital	ADJ
cana-1304	12	9	models	model	NOUN
cana-1304	12	10	and	and	CCONJ
cana-1304	12	11	frameworks	framework	NOUN
cana-1304	12	12	capable	capable	ADJ
cana-1304	12	13	of	of	ADP
cana-1304	12	14	adeptly	adeptly	ADV
cana-1304	12	15	managing	manage	VERB
cana-1304	12	16	frequently	frequently	ADV
cana-1304	12	17	encountered	encounter	VERB
cana-1304	12	18	ambiguous	ambiguous	ADJ
cana-1304	12	19	situations	situation	NOUN
cana-1304	12	20	.	.	PUNCT
cana-1304	13	1	the	the	DET
cana-1304	13	2	utilization	utilization	NOUN
cana-1304	13	3	of	of	ADP
cana-1304	13	4	fuzzy	fuzzy	ADJ
cana-1304	13	5	logic	logic	NOUN
cana-1304	13	6	in	in	ADP
cana-1304	13	7	this	this	DET
cana-1304	13	8	context	context	NOUN
cana-1304	13	9	is	be	AUX
cana-1304	13	10	driven	drive	VERB
cana-1304	13	11	by	by	ADP
cana-1304	13	12	the	the	DET
cana-1304	13	13	recognition	recognition	NOUN
cana-1304	13	14	that	that	SCONJ
cana-1304	13	15	traditional	traditional	ADJ
cana-1304	13	16	methodologies	methodology	NOUN
cana-1304	13	17	may	may	AUX
cana-1304	13	18	fall	fall	VERB
cana-1304	13	19	short	short	ADV
cana-1304	13	20	in	in	ADP
cana-1304	13	21	addressing	address	VERB
cana-1304	13	22	the	the	DET
cana-1304	13	23	nuanced	nuanced	ADJ
cana-1304	13	24	uncertainties	uncertainty	NOUN
cana-1304	13	25	that	that	PRON
cana-1304	13	26	often	often	ADV
cana-1304	13	27	characterize	characterize	VERB
cana-1304	13	28	problems	problem	NOUN
cana-1304	13	29	involving	involve	VERB
cana-1304	13	30	delay	delay	NOUN
cana-1304	13	31	differential	differential	ADJ
cana-1304	13	32	equations	equation	NOUN
cana-1304	13	33	.	.	PUNCT
cana-1304	14	1	by	by	ADP
cana-1304	14	2	introducing	introduce	VERB
cana-1304	14	3	fuzzy	fuzzy	ADJ
cana-1304	14	4	logic	logic	NOUN
cana-1304	14	5	into	into	ADP
cana-1304	14	6	our	our	PRON
cana-1304	14	7	analytical	analytical	ADJ
cana-1304	14	8	framework	framework	NOUN
cana-1304	14	9	,	,	PUNCT
cana-1304	14	10	we	we	PRON
cana-1304	14	11	aim	aim	VERB
cana-1304	14	12	to	to	PART
cana-1304	14	13	enhance	enhance	VERB
cana-1304	14	14	the	the	DET
cana-1304	14	15	robustness	robustness	NOUN
cana-1304	14	16	of	of	ADP
cana-1304	14	17	our	our	PRON
cana-1304	14	18	methodology	methodology	NOUN
cana-1304	14	19	and	and	CCONJ
cana-1304	14	20	foster	foster	VERB
cana-1304	14	21	a	a	DET
cana-1304	14	22	more	more	ADV
cana-1304	14	23	comprehensive	comprehensive	ADJ
cana-1304	14	24	understanding	understanding	NOUN
cana-1304	14	25	of	of	ADP
cana-1304	14	26	the	the	DET
cana-1304	14	27	system	system	NOUN
cana-1304	14	28	's	's	PART
cana-1304	14	29	dynamics.the	dynamics.the	DET
cana-1304	14	30	notion	notion	NOUN
cana-1304	14	31	of	of	ADP
cana-1304	14	32	a	a	DET
cana-1304	14	33	fuzzy	fuzzy	ADJ
cana-1304	14	34	derivative	derivative	NOUN
cana-1304	14	35	,	,	PUNCT
cana-1304	14	36	which	which	PRON
cana-1304	14	37	was	be	AUX
cana-1304	14	38	originally	originally	ADV
cana-1304	14	39	introduced	introduce	VERB
cana-1304	14	40	by	by	ADP
cana-1304	14	41	chang	chang	PROPN
cana-1304	14	42	and	and	CCONJ
cana-1304	14	43	zadeh	zadeh	PROPN
cana-1304	15	1	[	[	X
cana-1304	15	2	7	7	NUM
cana-1304	15	3	]	]	PUNCT
cana-1304	15	4	,	,	PUNCT
cana-1304	15	5	underwent	undergo	VERB
cana-1304	15	6	significant	significant	ADJ
cana-1304	15	7	development	development	NOUN
cana-1304	15	8	through	through	ADP
cana-1304	15	9	the	the	DET
cana-1304	15	10	contributions	contribution	NOUN
cana-1304	15	11	of	of	ADP
cana-1304	15	12	dubois	dubois	PROPN
cana-1304	15	13	and	and	CCONJ
cana-1304	15	14	prade	prade	NOUN
cana-1304	15	15	[	[	X
cana-1304	15	16	8	8	NUM
cana-1304	15	17	]	]	PUNCT
cana-1304	15	18	,	,	PUNCT
cana-1304	15	19	particularly	particularly	ADV
cana-1304	15	20	in	in	ADP
cana-1304	15	21	the	the	DET
cana-1304	15	22	context	context	NOUN
cana-1304	15	23	of	of	ADP
cana-1304	15	24	the	the	DET
cana-1304	15	25	augmentation	augmentation	NOUN
cana-1304	15	26	rule	rule	NOUN
cana-1304	15	27	.	.	PUNCT
cana-1304	16	1	kandel	kandel	NOUN
cana-1304	16	2	and	and	CCONJ
cana-1304	16	3	byat	byat	NOUN
cana-1304	17	1	[	[	X
cana-1304	17	2	13	13	NUM
cana-1304	17	3	]	]	PUNCT
cana-1304	17	4	are	be	AUX
cana-1304	17	5	credited	credit	VERB
cana-1304	17	6	with	with	ADP
cana-1304	17	7	coining	coin	VERB
cana-1304	17	8	the	the	DET
cana-1304	17	9	term	term	NOUN
cana-1304	17	10	"	"	PUNCT
cana-1304	17	11	fuzzy	fuzzy	ADJ
cana-1304	17	12	differential	differential	ADJ
cana-1304	17	13	equation	equation	NOUN
cana-1304	17	14	.	.	PUNCT
cana-1304	17	15	"	"	PUNCT
cana-1304	18	1	subsequently	subsequently	ADV
cana-1304	18	2	,	,	PUNCT
cana-1304	18	3	abbasbandi	abbasbandi	ADJ
cana-1304	18	4	and	and	CCONJ
cana-1304	18	5	allahviranloo	allahviranloo	NOUN
cana-1304	18	6	[	[	X
cana-1304	18	7	2	2	NUM
cana-1304	18	8	]	]	PUNCT
cana-1304	18	9	conducted	conduct	VERB
cana-1304	18	10	mathematical	mathematical	ADJ
cana-1304	18	11	computations	computation	NOUN
cana-1304	18	12	to	to	PART
cana-1304	18	13	address	address	VERB
cana-1304	18	14	fuzzy	fuzzy	ADJ
cana-1304	18	15	differential	differential	NOUN
cana-1304	18	16	conditions	condition	NOUN
cana-1304	18	17	communications	communication	NOUN
cana-1304	18	18	on	on	ADP
cana-1304	18	19	applied	apply	VERB
cana-1304	18	20	nonlinear	nonlinear	ADJ
cana-1304	18	21	analysis	analysis	NOUN
cana-1304	18	22	issn	issn	NOUN
cana-1304	18	23	:	:	PUNCT
cana-1304	18	24	1074	1074	NUM
cana-1304	18	25	-	-	PUNCT
cana-1304	18	26	133x	133x	NUM
cana-1304	18	27	vol	vol	NOUN
cana-1304	18	28	31	31	NUM
cana-1304	18	29	no	no	NOUN
cana-1304	18	30	.	.	PUNCT
cana-1304	19	1	7s	7	NOUN
cana-1304	19	2	(	(	PUNCT
cana-1304	19	3	2024	2024	NUM
cana-1304	19	4	)	)	PUNCT
cana-1304	19	5	287	287	NUM
cana-1304	19	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1304	19	7	related	relate	VERB
cana-1304	19	8	to	to	ADP
cana-1304	19	9	the	the	DET
cana-1304	19	10	seikkala	seikkala	ADJ
cana-1304	19	11	derivative	derivative	NOUN
cana-1304	20	1	[	[	X
cana-1304	20	2	19	19	NUM
cana-1304	20	3	]	]	PUNCT
cana-1304	20	4	.	.	PUNCT
cana-1304	21	1	jafari	jafari	PROPN
cana-1304	21	2	et	et	PROPN
cana-1304	21	3	al	al	PROPN
cana-1304	21	4	.	.	PUNCT
cana-1304	22	1	[	[	X
cana-1304	22	2	10	10	NUM
cana-1304	22	3	]	]	PUNCT
cana-1304	22	4	took	take	VERB
cana-1304	22	5	on	on	ADP
cana-1304	22	6	the	the	DET
cana-1304	22	7	challenging	challenging	ADJ
cana-1304	22	8	task	task	NOUN
cana-1304	22	9	of	of	ADP
cana-1304	22	10	satisfying	satisfy	VERB
cana-1304	22	11	the	the	DET
cana-1304	22	12	𝑛th	𝑛th	NOUN
cana-1304	22	13	requirement	requirement	NOUN
cana-1304	22	14	of	of	ADP
cana-1304	22	15	fuzzy	fuzzy	ADJ
cana-1304	22	16	differential	differential	ADJ
cana-1304	22	17	conditions	condition	NOUN
cana-1304	22	18	using	use	VERB
cana-1304	22	19	the	the	DET
cana-1304	22	20	variational	variational	ADJ
cana-1304	22	21	iteration	iteration	NOUN
cana-1304	22	22	method	method	NOUN
cana-1304	22	23	but	but	CCONJ
cana-1304	22	24	faced	face	VERB
cana-1304	22	25	difficulties	difficulty	NOUN
cana-1304	22	26	in	in	ADP
cana-1304	22	27	the	the	DET
cana-1304	22	28	process	process	NOUN
cana-1304	22	29	.	.	PUNCT
cana-1304	23	1	building	build	VERB
cana-1304	23	2	on	on	ADP
cana-1304	23	3	this	this	PRON
cana-1304	23	4	,	,	PUNCT
cana-1304	23	5	allahviranloo	allahviranloo	NOUN
cana-1304	23	6	et	et	NOUN
cana-1304	23	7	al	al	PROPN
cana-1304	23	8	.	.	PUNCT
cana-1304	24	1	[	[	X
cana-1304	24	2	1	1	NUM
cana-1304	24	3	,	,	PUNCT
cana-1304	24	4	3	3	NUM
cana-1304	24	5	]	]	PUNCT
cana-1304	24	6	employed	employ	VERB
cana-1304	24	7	a	a	DET
cana-1304	24	8	correct	correct	ADJ
cana-1304	24	9	indicator	indicator	NOUN
cana-1304	24	10	strategy	strategy	NOUN
cana-1304	24	11	to	to	PART
cana-1304	24	12	navigate	navigate	VERB
cana-1304	24	13	the	the	DET
cana-1304	24	14	mathematical	mathematical	ADJ
cana-1304	24	15	intricacies	intricacy	NOUN
cana-1304	24	16	of	of	ADP
cana-1304	24	17	differential	differential	ADJ
cana-1304	24	18	equations	equation	NOUN
cana-1304	24	19	with	with	ADP
cana-1304	24	20	fuzziness	fuzziness	NOUN
cana-1304	24	21	.	.	PUNCT
cana-1304	25	1	driver	driver	NOUN
cana-1304	26	1	[	[	X
cana-1304	26	2	9	9	NUM
cana-1304	26	3	]	]	PUNCT
cana-1304	26	4	made	make	VERB
cana-1304	26	5	a	a	DET
cana-1304	26	6	substantial	substantial	ADJ
cana-1304	26	7	contribution	contribution	NOUN
cana-1304	26	8	through	through	ADP
cana-1304	26	9	a	a	DET
cana-1304	26	10	comprehensive	comprehensive	ADJ
cana-1304	26	11	book	book	NOUN
cana-1304	26	12	that	that	PRON
cana-1304	26	13	elucidates	elucidate	VERB
cana-1304	26	14	general	general	ADJ
cana-1304	26	15	differential	differential	ADJ
cana-1304	26	16	conditions	condition	NOUN
cana-1304	26	17	and	and	CCONJ
cana-1304	26	18	differential	differential	ADJ
cana-1304	26	19	delay	delay	NOUN
cana-1304	26	20	conditions	condition	NOUN
cana-1304	26	21	.	.	PUNCT
cana-1304	27	1	bellen	bellen	VERB
cana-1304	27	2	et	et	PROPN
cana-1304	27	3	al	al	PROPN
cana-1304	27	4	.	.	PUNCT
cana-1304	28	1	[	[	X
cana-1304	28	2	5	5	NUM
cana-1304	28	3	,	,	PUNCT
cana-1304	28	4	6	6	NUM
cana-1304	28	5	]	]	PUNCT
cana-1304	28	6	provided	provide	VERB
cana-1304	28	7	mathematical	mathematical	ADJ
cana-1304	28	8	solutions	solution	NOUN
cana-1304	28	9	for	for	ADP
cana-1304	28	10	delay	delay	NOUN
cana-1304	28	11	differential	differential	ADJ
cana-1304	28	12	equations	equation	NOUN
cana-1304	28	13	(	(	PUNCT
cana-1304	28	14	dde	dde	PROPN
cana-1304	28	15	)	)	PUNCT
cana-1304	28	16	.	.	PUNCT
cana-1304	29	1	in	in	ADP
cana-1304	29	2	their	their	PRON
cana-1304	29	3	work	work	NOUN
cana-1304	29	4	[	[	X
cana-1304	29	5	14	14	NUM
cana-1304	29	6	]	]	X
cana-1304	29	7	,	,	PUNCT
cana-1304	29	8	khastan	khastan	PROPN
cana-1304	29	9	et	et	PROPN
cana-1304	29	10	al	al	PROPN
cana-1304	29	11	.	.	PROPN
cana-1304	29	12	deliberated	deliberate	VERB
cana-1304	29	13	on	on	ADP
cana-1304	29	14	the	the	DET
cana-1304	29	15	concepts	concept	NOUN
cana-1304	29	16	of	of	ADP
cana-1304	29	17	differential	differential	ADJ
cana-1304	29	18	conditions	condition	NOUN
cana-1304	29	19	for	for	ADP
cana-1304	29	20	fuzzy	fuzzy	ADJ
cana-1304	29	21	changes	change	NOUN
cana-1304	29	22	under	under	ADP
cana-1304	29	23	summed	sum	VERB
cana-1304	29	24	differentiability	differentiability	PROPN
cana-1304	29	25	.	.	PUNCT
cana-1304	29	26	barzinji	barzinji	PROPN
cana-1304	29	27	et	et	PROPN
cana-1304	29	28	al	al	PROPN
cana-1304	29	29	.	.	PUNCT
cana-1304	30	1	[	[	X
cana-1304	30	2	4	4	X
cana-1304	30	3	]	]	PUNCT
cana-1304	30	4	directed	direct	VERB
cana-1304	30	5	their	their	PRON
cana-1304	30	6	focus	focus	NOUN
cana-1304	30	7	toward	toward	ADP
cana-1304	30	8	linear	linear	ADJ
cana-1304	30	9	differential	differential	ADJ
cana-1304	30	10	differential	differential	NOUN
cana-1304	30	11	frameworks	framework	NOUN
cana-1304	30	12	for	for	ADP
cana-1304	30	13	analyzing	analyze	VERB
cana-1304	30	14	the	the	DET
cana-1304	30	15	stability	stability	NOUN
cana-1304	30	16	of	of	ADP
cana-1304	30	17	a	a	DET
cana-1304	30	18	coherent	coherent	ADJ
cana-1304	30	19	state.abbasbandi	state.abbasbandi	NOUN
cana-1304	30	20	and	and	CCONJ
cana-1304	30	21	allahwiranloo	allahwiranloo	NOUN
cana-1304	31	1	[	[	X
cana-1304	31	2	2	2	X
cana-1304	31	3	]	]	PUNCT
cana-1304	31	4	laid	lay	VERB
cana-1304	31	5	the	the	DET
cana-1304	31	6	foundation	foundation	NOUN
cana-1304	31	7	for	for	ADP
cana-1304	31	8	a	a	DET
cana-1304	31	9	numerical	numerical	ADJ
cana-1304	31	10	technique	technique	NOUN
cana-1304	31	11	by	by	ADP
cana-1304	31	12	introducing	introduce	VERB
cana-1304	31	13	the	the	DET
cana-1304	31	14	fourth	fourth	ADJ
cana-1304	31	15	-	-	PUNCT
cana-1304	31	16	order	order	NOUN
cana-1304	31	17	runge	runge	NOUN
cana-1304	31	18	-	-	PUNCT
cana-1304	31	19	kutta	kutta	NOUN
cana-1304	31	20	methodology	methodology	NOUN
cana-1304	31	21	.	.	PUNCT
cana-1304	32	1	their	their	PRON
cana-1304	32	2	initial	initial	ADJ
cana-1304	32	3	work	work	NOUN
cana-1304	32	4	focused	focus	VERB
cana-1304	32	5	on	on	ADP
cana-1304	32	6	refining	refine	VERB
cana-1304	32	7	fuzzy	fuzzy	ADJ
cana-1304	32	8	differential	differential	ADJ
cana-1304	32	9	conditions	condition	NOUN
cana-1304	32	10	.	.	PUNCT
cana-1304	33	1	building	build	VERB
cana-1304	33	2	upon	upon	SCONJ
cana-1304	33	3	this	this	DET
cana-1304	33	4	groundwork	groundwork	NOUN
cana-1304	33	5	,	,	PUNCT
cana-1304	33	6	pederson	pederson	PROPN
cana-1304	33	7	and	and	CCONJ
cana-1304	33	8	sambandham	sambandham	VERB
cana-1304	33	9	[	[	X
cana-1304	33	10	18	18	NUM
cana-1304	33	11	]	]	PUNCT
cana-1304	33	12	delved	delve	VERB
cana-1304	33	13	into	into	ADP
cana-1304	33	14	the	the	DET
cana-1304	33	15	numerical	numerical	ADJ
cana-1304	33	16	treatment	treatment	NOUN
cana-1304	33	17	of	of	ADP
cana-1304	33	18	fuzzy	fuzzy	ADJ
cana-1304	33	19	differential	differential	ADJ
cana-1304	33	20	delay	delay	NOUN
cana-1304	33	21	scenarios	scenario	NOUN
cana-1304	33	22	.	.	PUNCT
cana-1304	34	1	they	they	PRON
cana-1304	34	2	applied	apply	VERB
cana-1304	34	3	the	the	DET
cana-1304	34	4	runge	runge	NOUN
cana-1304	34	5	-	-	PUNCT
cana-1304	34	6	kutta	kutta	NOUN
cana-1304	34	7	method	method	NOUN
cana-1304	34	8	to	to	PART
cana-1304	34	9	handle	handle	VERB
cana-1304	34	10	these	these	DET
cana-1304	34	11	scenarios	scenario	NOUN
cana-1304	34	12	effectively	effectively	ADV
cana-1304	34	13	.	.	PUNCT
cana-1304	35	1	expanding	expand	VERB
cana-1304	35	2	the	the	DET
cana-1304	35	3	scope	scope	NOUN
cana-1304	35	4	,	,	PUNCT
cana-1304	35	5	al	al	PROPN
cana-1304	35	6	-	-	PUNCT
cana-1304	35	7	rawi	rawi	PROPN
cana-1304	35	8	et	et	PROPN
cana-1304	35	9	al	al	PROPN
cana-1304	35	10	.	.	PUNCT
cana-1304	36	1	[	[	X
cana-1304	36	2	21	21	NUM
cana-1304	36	3	]	]	PUNCT
cana-1304	36	4	extended	extend	VERB
cana-1304	36	5	the	the	DET
cana-1304	36	6	approach	approach	NOUN
cana-1304	36	7	to	to	PART
cana-1304	36	8	address	address	VERB
cana-1304	36	9	numerical	numerical	ADJ
cana-1304	36	10	challenges	challenge	NOUN
cana-1304	36	11	posed	pose	VERB
cana-1304	36	12	by	by	ADP
cana-1304	36	13	differential	differential	ADJ
cana-1304	36	14	carry	carry	NOUN
cana-1304	36	15	constraints	constraint	NOUN
cana-1304	36	16	.	.	PUNCT
cana-1304	37	1	in	in	ADP
cana-1304	37	2	their	their	PRON
cana-1304	37	3	study	study	NOUN
cana-1304	37	4	,	,	PUNCT
cana-1304	37	5	they	they	PRON
cana-1304	37	6	employed	employ	VERB
cana-1304	37	7	the	the	DET
cana-1304	37	8	fourth	fourth	ADJ
cana-1304	37	9	-	-	PUNCT
cana-1304	37	10	order	order	NOUN
cana-1304	37	11	runge	runge	NOUN
cana-1304	37	12	-	-	PUNCT
cana-1304	37	13	kutta	kutta	NOUN
cana-1304	37	14	strategy	strategy	NOUN
cana-1304	37	15	to	to	PART
cana-1304	37	16	enhance	enhance	VERB
cana-1304	37	17	the	the	DET
cana-1304	37	18	resolution	resolution	NOUN
cana-1304	37	19	of	of	ADP
cana-1304	37	20	such	such	ADJ
cana-1304	37	21	challenges	challenge	NOUN
cana-1304	37	22	.	.	PUNCT
cana-1304	38	1	in	in	ADP
cana-1304	38	2	parallel	parallel	ADJ
cana-1304	38	3	investigations	investigation	NOUN
cana-1304	38	4	,	,	PUNCT
cana-1304	38	5	k.	k.	PROPN
cana-1304	38	6	kanagarajan	kanagarajan	PROPN
cana-1304	38	7	et	et	PROPN
cana-1304	38	8	al	al	PROPN
cana-1304	38	9	.	.	PUNCT
cana-1304	39	1	[	[	X
cana-1304	39	2	12	12	NUM
cana-1304	39	3	,	,	PUNCT
cana-1304	39	4	11	11	NUM
cana-1304	39	5	]	]	PUNCT
cana-1304	39	6	explored	explore	VERB
cana-1304	39	7	alternative	alternative	ADJ
cana-1304	39	8	methods	method	NOUN
cana-1304	39	9	for	for	ADP
cana-1304	39	10	handling	handle	VERB
cana-1304	39	11	fuzzy	fuzzy	ADJ
cana-1304	39	12	-	-	PUNCT
cana-1304	39	13	delay	delay	NOUN
cana-1304	39	14	differential	differential	ADJ
cana-1304	39	15	equations	equation	NOUN
cana-1304	39	16	.	.	PUNCT
cana-1304	40	1	specifically	specifically	ADV
cana-1304	40	2	,	,	PUNCT
cana-1304	40	3	they	they	PRON
cana-1304	40	4	investigated	investigate	VERB
cana-1304	40	5	the	the	DET
cana-1304	40	6	runge	runge	NOUN
cana-1304	40	7	-	-	PUNCT
cana-1304	40	8	kutta	kutta	PROPN
cana-1304	40	9	-	-	PUNCT
cana-1304	40	10	nystrom	nystrom	PROPN
cana-1304	40	11	and	and	CCONJ
cana-1304	40	12	the	the	DET
cana-1304	40	13	5th	5th	ADJ
cana-1304	40	14	-	-	PUNCT
cana-1304	40	15	rungekutta	rungekutta	ADJ
cana-1304	40	16	strategies	strategy	NOUN
cana-1304	40	17	to	to	PART
cana-1304	40	18	provide	provide	VERB
cana-1304	40	19	comprehensive	comprehensive	ADJ
cana-1304	40	20	insights	insight	NOUN
cana-1304	40	21	into	into	ADP
cana-1304	40	22	effective	effective	ADJ
cana-1304	40	23	solutions	solution	NOUN
cana-1304	40	24	for	for	ADP
cana-1304	40	25	this	this	DET
cana-1304	40	26	class	class	NOUN
cana-1304	40	27	of	of	ADP
cana-1304	40	28	equations	equation	NOUN
cana-1304	40	29	.	.	PUNCT
cana-1304	41	1	further	far	ADV
cana-1304	41	2	diversifying	diversify	VERB
cana-1304	41	3	the	the	DET
cana-1304	41	4	application	application	NOUN
cana-1304	41	5	of	of	ADP
cana-1304	41	6	runge	runge	NOUN
cana-1304	41	7	-	-	PUNCT
cana-1304	41	8	kutta	kutta	NOUN
cana-1304	41	9	techniques	technique	NOUN
cana-1304	41	10	,	,	PUNCT
cana-1304	41	11	v.	v.	ADP
cana-1304	41	12	parimala	parimala	PROPN
cana-1304	41	13	et	et	PROPN
cana-1304	41	14	al	al	PROPN
cana-1304	41	15	.	.	PUNCT
cana-1304	42	1	[	[	X
cana-1304	42	2	17	17	NUM
cana-1304	42	3	]	]	PUNCT
cana-1304	42	4	employed	employ	VERB
cana-1304	42	5	the	the	DET
cana-1304	42	6	2nd	2nd	ADJ
cana-1304	42	7	-	-	PUNCT
cana-1304	42	8	runge	runge	NOUN
cana-1304	42	9	-	-	PUNCT
cana-1304	42	10	kutta	kutta	NOUN
cana-1304	42	11	technique	technique	NOUN
cana-1304	42	12	to	to	PART
cana-1304	42	13	address	address	VERB
cana-1304	42	14	fuzzy	fuzzy	ADJ
cana-1304	42	15	differential	differential	ADJ
cana-1304	42	16	scenarios	scenario	NOUN
cana-1304	42	17	characterized	characterize	VERB
cana-1304	42	18	by	by	ADP
cana-1304	42	19	fuzzy	fuzzy	ADJ
cana-1304	42	20	initial	initial	ADJ
cana-1304	42	21	conditions	condition	NOUN
cana-1304	42	22	.	.	PUNCT
cana-1304	43	1	this	this	DET
cana-1304	43	2	extension	extension	NOUN
cana-1304	43	3	demonstrates	demonstrate	VERB
cana-1304	43	4	the	the	DET
cana-1304	43	5	versatility	versatility	NOUN
cana-1304	43	6	of	of	ADP
cana-1304	43	7	the	the	DET
cana-1304	43	8	runge	runge	NOUN
cana-1304	43	9	-	-	PUNCT
cana-1304	43	10	kutta	kutta	NOUN
cana-1304	43	11	family	family	NOUN
cana-1304	43	12	of	of	ADP
cana-1304	43	13	methods	method	NOUN
cana-1304	43	14	in	in	ADP
cana-1304	43	15	handling	handle	VERB
cana-1304	43	16	various	various	ADJ
cana-1304	43	17	types	type	NOUN
cana-1304	43	18	of	of	ADP
cana-1304	43	19	fuzzy	fuzzy	ADJ
cana-1304	43	20	scenarios	scenario	NOUN
cana-1304	43	21	.	.	PUNCT
cana-1304	44	1	in	in	ADP
cana-1304	44	2	a	a	DET
cana-1304	44	3	unique	unique	ADJ
cana-1304	44	4	approach	approach	NOUN
cana-1304	44	5	,	,	PUNCT
cana-1304	44	6	narayanamoorthy	narayanamoorthy	ADJ
cana-1304	44	7	et	et	PROPN
cana-1304	44	8	al	al	PROPN
cana-1304	44	9	.	.	PUNCT
cana-1304	45	1	[	[	X
cana-1304	45	2	15	15	NUM
cana-1304	45	3	,	,	PUNCT
cana-1304	45	4	16	16	NUM
cana-1304	45	5	]	]	PUNCT
cana-1304	45	6	combined	combined	ADJ
cana-1304	45	7	runge	runge	NOUN
cana-1304	45	8	-	-	PUNCT
cana-1304	45	9	kutta	kutta	NOUN
cana-1304	45	10	's	's	PART
cana-1304	45	11	third	third	ADJ
cana-1304	45	12	technique	technique	NOUN
cana-1304	45	13	with	with	ADP
cana-1304	45	14	the	the	DET
cana-1304	45	15	seikkal	seikkal	ADJ
cana-1304	45	16	derivative	derivative	NOUN
cana-1304	46	1	[	[	X
cana-1304	46	2	19	19	NUM
cana-1304	46	3	]	]	PUNCT
cana-1304	46	4	to	to	PART
cana-1304	46	5	resolve	resolve	VERB
cana-1304	46	6	fuzzy	fuzzy	ADJ
cana-1304	46	7	differential	differential	ADJ
cana-1304	46	8	situations	situation	NOUN
cana-1304	46	9	.	.	PUNCT
cana-1304	47	1	this	this	DET
cana-1304	47	2	combination	combination	NOUN
cana-1304	47	3	of	of	ADP
cana-1304	47	4	methods	method	NOUN
cana-1304	47	5	showcases	showcase	VERB
cana-1304	47	6	the	the	DET
cana-1304	47	7	innovative	innovative	ADJ
cana-1304	47	8	ways	way	NOUN
cana-1304	47	9	researchers	researcher	NOUN
cana-1304	47	10	are	be	AUX
cana-1304	47	11	exploring	explore	VERB
cana-1304	47	12	to	to	PART
cana-1304	47	13	enhance	enhance	VERB
cana-1304	47	14	the	the	DET
cana-1304	47	15	capabilities	capability	NOUN
cana-1304	47	16	of	of	ADP
cana-1304	47	17	existing	exist	VERB
cana-1304	47	18	numerical	numerical	ADJ
cana-1304	47	19	techniques	technique	NOUN
cana-1304	47	20	for	for	ADP
cana-1304	47	21	tackling	tackle	VERB
cana-1304	47	22	complex	complex	ADJ
cana-1304	47	23	fuzzy	fuzzy	ADJ
cana-1304	47	24	scenarios	scenario	NOUN
cana-1304	47	25	.	.	PUNCT
cana-1304	48	1	this	this	DET
cana-1304	48	2	current	current	ADJ
cana-1304	48	3	article	article	NOUN
cana-1304	48	4	serves	serve	VERB
cana-1304	48	5	as	as	ADP
cana-1304	48	6	an	an	DET
cana-1304	48	7	extension	extension	NOUN
cana-1304	48	8	of	of	ADP
cana-1304	48	9	the	the	DET
cana-1304	48	10	work	work	NOUN
cana-1304	48	11	presented	present	VERB
cana-1304	48	12	in	in	ADP
cana-1304	48	13	[	[	X
cana-1304	48	14	16	16	NUM
cana-1304	48	15	]	]	PUNCT
cana-1304	48	16	,	,	PUNCT
cana-1304	48	17	aiming	aim	VERB
cana-1304	48	18	to	to	PART
cana-1304	48	19	further	far	ADV
cana-1304	48	20	explore	explore	VERB
cana-1304	48	21	the	the	DET
cana-1304	48	22	effectiveness	effectiveness	NOUN
cana-1304	48	23	of	of	ADP
cana-1304	48	24	the	the	DET
cana-1304	48	25	time	time	NOUN
cana-1304	48	26	lag	lag	NOUN
cana-1304	48	27	differential	differential	ADJ
cana-1304	48	28	condition	condition	NOUN
cana-1304	48	29	method	method	NOUN
cana-1304	48	30	within	within	ADP
cana-1304	48	31	a	a	DET
cana-1304	48	32	fuzzy	fuzzy	ADJ
cana-1304	48	33	environment	environment	NOUN
cana-1304	48	34	.	.	PUNCT
cana-1304	49	1	the	the	DET
cana-1304	49	2	crux	crux	NOUN
cana-1304	49	3	of	of	ADP
cana-1304	49	4	our	our	PRON
cana-1304	49	5	endeavor	endeavor	NOUN
cana-1304	49	6	lies	lie	VERB
cana-1304	49	7	in	in	ADP
cana-1304	49	8	the	the	DET
cana-1304	49	9	comprehensive	comprehensive	ADJ
cana-1304	49	10	analysis	analysis	NOUN
cana-1304	49	11	of	of	ADP
cana-1304	49	12	numerical	numerical	ADJ
cana-1304	49	13	outcomes	outcome	NOUN
cana-1304	49	14	,	,	PUNCT
cana-1304	49	15	where	where	SCONJ
cana-1304	49	16	we	we	PRON
cana-1304	49	17	meticulously	meticulously	ADV
cana-1304	49	18	evaluate	evaluate	VERB
cana-1304	49	19	the	the	DET
cana-1304	49	20	performance	performance	NOUN
cana-1304	49	21	of	of	ADP
cana-1304	49	22	the	the	DET
cana-1304	49	23	runge	runge	NOUN
cana-1304	49	24	-	-	PUNCT
cana-1304	49	25	kutta	kutta	NOUN
cana-1304	49	26	-	-	PUNCT
cana-1304	49	27	fehlberg	fehlberg	NOUN
cana-1304	49	28	method	method	NOUN
cana-1304	49	29	.	.	PUNCT
cana-1304	50	1	our	our	PRON
cana-1304	50	2	assessment	assessment	NOUN
cana-1304	50	3	involves	involve	VERB
cana-1304	50	4	a	a	DET
cana-1304	50	5	meticulous	meticulous	ADJ
cana-1304	50	6	comparison	comparison	NOUN
cana-1304	50	7	of	of	ADP
cana-1304	50	8	results	result	NOUN
cana-1304	50	9	obtained	obtain	VERB
cana-1304	50	10	using	use	VERB
cana-1304	50	11	the	the	DET
cana-1304	50	12	rkfm	rkfm	NOUN
cana-1304	50	13	against	against	ADP
cana-1304	50	14	those	those	PRON
cana-1304	50	15	derived	derive	VERB
cana-1304	50	16	from	from	ADP
cana-1304	50	17	the	the	DET
cana-1304	50	18	runge	runge	NOUN
cana-1304	50	19	-	-	PUNCT
cana-1304	50	20	kutta	kutta	NOUN
cana-1304	50	21	4th	4th	ADJ
cana-1304	50	22	order	order	NOUN
cana-1304	50	23	method	method	NOUN
cana-1304	50	24	,	,	PUNCT
cana-1304	50	25	as	as	ADV
cana-1304	50	26	well	well	ADV
cana-1304	50	27	as	as	ADP
cana-1304	50	28	a	a	DET
cana-1304	50	29	benchmarking	benchmarking	NOUN
cana-1304	50	30	against	against	ADP
cana-1304	50	31	the	the	DET
cana-1304	50	32	exact	exact	ADJ
cana-1304	50	33	solution	solution	NOUN
cana-1304	50	34	.	.	PUNCT
cana-1304	51	1	through	through	ADP
cana-1304	51	2	this	this	DET
cana-1304	51	3	rigorous	rigorous	ADJ
cana-1304	51	4	comparative	comparative	ADJ
cana-1304	51	5	analysis	analysis	NOUN
cana-1304	51	6	,	,	PUNCT
cana-1304	51	7	we	we	PRON
cana-1304	51	8	aim	aim	VERB
cana-1304	51	9	to	to	PART
cana-1304	51	10	unveil	unveil	VERB
cana-1304	51	11	the	the	DET
cana-1304	51	12	effectiveness	effectiveness	NOUN
cana-1304	51	13	and	and	CCONJ
cana-1304	51	14	efficiency	efficiency	NOUN
cana-1304	51	15	of	of	ADP
cana-1304	51	16	the	the	DET
cana-1304	51	17	runge	runge	NOUN
cana-1304	51	18	-	-	PUNCT
cana-1304	51	19	kuttafehlberg	kuttafehlberg	PROPN
cana-1304	51	20	method	method	NOUN
cana-1304	51	21	specifically	specifically	ADV
cana-1304	51	22	within	within	ADP
cana-1304	51	23	the	the	DET
cana-1304	51	24	context	context	NOUN
cana-1304	51	25	of	of	ADP
cana-1304	51	26	solving	solve	VERB
cana-1304	51	27	delay	delay	NOUN
cana-1304	51	28	differential	differential	ADJ
cana-1304	51	29	equations	equation	NOUN
cana-1304	51	30	.	.	PUNCT
cana-1304	52	1	the	the	DET
cana-1304	52	2	numerical	numerical	ADJ
cana-1304	52	3	results	result	NOUN
cana-1304	52	4	obtained	obtain	VERB
cana-1304	52	5	not	not	PART
cana-1304	52	6	only	only	ADV
cana-1304	52	7	serve	serve	VERB
cana-1304	52	8	to	to	PART
cana-1304	52	9	validate	validate	VERB
cana-1304	52	10	the	the	DET
cana-1304	52	11	suitability	suitability	NOUN
cana-1304	52	12	of	of	ADP
cana-1304	52	13	the	the	DET
cana-1304	52	14	rkfm	rkfm	NOUN
cana-1304	52	15	but	but	CCONJ
cana-1304	52	16	also	also	ADV
cana-1304	52	17	provide	provide	VERB
cana-1304	52	18	insights	insight	NOUN
cana-1304	52	19	into	into	ADP
cana-1304	52	20	its	its	PRON
cana-1304	52	21	comparative	comparative	ADJ
cana-1304	52	22	advantages	advantage	NOUN
cana-1304	52	23	over	over	ADP
cana-1304	52	24	the	the	DET
cana-1304	52	25	traditional	traditional	ADJ
cana-1304	52	26	runge	runge	NOUN
cana-1304	52	27	-	-	PUNCT
cana-1304	52	28	kutta	kutta	NOUN
cana-1304	52	29	4th	4th	ADJ
cana-1304	52	30	-	-	PUNCT
cana-1304	52	31	order	order	NOUN
cana-1304	52	32	method	method	NOUN
cana-1304	52	33	.	.	PUNCT
cana-1304	53	1	the	the	DET
cana-1304	53	2	meticulous	meticulous	ADJ
cana-1304	53	3	examination	examination	NOUN
cana-1304	53	4	of	of	ADP
cana-1304	53	5	these	these	DET
cana-1304	53	6	results	result	NOUN
cana-1304	53	7	contributes	contribute	VERB
cana-1304	53	8	to	to	ADP
cana-1304	53	9	advancing	advance	VERB
cana-1304	53	10	our	our	PRON
cana-1304	53	11	understanding	understanding	NOUN
cana-1304	53	12	of	of	ADP
cana-1304	53	13	the	the	DET
cana-1304	53	14	applicability	applicability	NOUN
cana-1304	53	15	and	and	CCONJ
cana-1304	53	16	performance	performance	NOUN
cana-1304	53	17	of	of	ADP
cana-1304	53	18	the	the	DET
cana-1304	53	19	rkfm	rkfm	NOUN
cana-1304	53	20	in	in	ADP
cana-1304	53	21	the	the	DET
cana-1304	53	22	realm	realm	NOUN
cana-1304	53	23	of	of	ADP
cana-1304	53	24	fuzzy	fuzzy	ADJ
cana-1304	53	25	delay	delay	NOUN
cana-1304	53	26	differential	differential	ADJ
cana-1304	53	27	equations	equation	NOUN
cana-1304	53	28	,	,	PUNCT
cana-1304	53	29	thereby	thereby	ADV
cana-1304	53	30	enriching	enrich	VERB
cana-1304	53	31	the	the	DET
cana-1304	53	32	landscape	landscape	NOUN
cana-1304	53	33	of	of	ADP
cana-1304	53	34	numerical	numerical	ADJ
cana-1304	53	35	methods	method	NOUN
cana-1304	53	36	for	for	ADP
cana-1304	53	37	addressing	address	VERB
cana-1304	53	38	complex	complex	ADJ
cana-1304	53	39	dynamic	dynamic	ADJ
cana-1304	53	40	systems	system	NOUN
cana-1304	53	41	.	.	PUNCT
cana-1304	54	1	communications	communication	NOUN
cana-1304	54	2	on	on	ADP
cana-1304	54	3	applied	apply	VERB
cana-1304	54	4	nonlinear	nonlinear	ADJ
cana-1304	54	5	analysis	analysis	NOUN
cana-1304	54	6	issn	issn	NOUN
cana-1304	54	7	:	:	PUNCT
cana-1304	54	8	1074	1074	NUM
cana-1304	54	9	-	-	PUNCT
cana-1304	54	10	133x	133x	NUM
cana-1304	54	11	vol	vol	NOUN
cana-1304	54	12	31	31	NUM
cana-1304	54	13	no	no	NOUN
cana-1304	54	14	.	.	PUNCT
cana-1304	55	1	7s	7	NOUN
cana-1304	55	2	(	(	PUNCT
cana-1304	55	3	2024	2024	NUM
cana-1304	55	4	)	)	PUNCT
cana-1304	55	5	288	288	NUM
cana-1304	56	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1304	56	2	2	2	NUM
cana-1304	56	3	.	.	PUNCT
cana-1304	56	4	preliminaries	preliminary	NOUN
cana-1304	56	5	definition	definition	NOUN
cana-1304	56	6	1.a	1.a	NUM
cana-1304	56	7	membership	membership	NOUN
cana-1304	56	8	function	function	NOUN
cana-1304	56	9	is	be	AUX
cana-1304	56	10	a	a	DET
cana-1304	56	11	mathematical	mathematical	ADJ
cana-1304	56	12	representation	representation	NOUN
cana-1304	56	13	in	in	ADP
cana-1304	56	14	fuzzy	fuzzy	ADJ
cana-1304	56	15	logic	logic	NOUN
cana-1304	56	16	that	that	PRON
cana-1304	56	17	assigns	assign	VERB
cana-1304	56	18	a	a	DET
cana-1304	56	19	degree	degree	NOUN
cana-1304	56	20	of	of	ADP
cana-1304	56	21	membership	membership	NOUN
cana-1304	56	22	between	between	ADP
cana-1304	56	23	0	0	NUM
cana-1304	56	24	and	and	CCONJ
cana-1304	56	25	1	1	NUM
cana-1304	56	26	to	to	ADP
cana-1304	56	27	elements	element	NOUN
cana-1304	56	28	in	in	ADP
cana-1304	56	29	a	a	DET
cana-1304	56	30	universe	universe	NOUN
cana-1304	56	31	of	of	ADP
cana-1304	56	32	discourse	discourse	NOUN
cana-1304	56	33	,	,	PUNCT
cana-1304	56	34	indicating	indicate	VERB
cana-1304	56	35	the	the	DET
cana-1304	56	36	extent	extent	NOUN
cana-1304	56	37	to	to	PART
cana-1304	56	38	which	which	PRON
cana-1304	56	39	they	they	PRON
cana-1304	56	40	belong	belong	VERB
cana-1304	56	41	to	to	ADP
cana-1304	56	42	a	a	DET
cana-1304	56	43	specific	specific	ADJ
cana-1304	56	44	fuzzy	fuzzy	ADJ
cana-1304	56	45	set	set	NOUN
cana-1304	56	46	.	.	PUNCT
cana-1304	57	1	it	it	PRON
cana-1304	57	2	quantifies	quantify	VERB
cana-1304	57	3	the	the	DET
cana-1304	57	4	degree	degree	NOUN
cana-1304	57	5	of	of	ADP
cana-1304	57	6	truth	truth	NOUN
cana-1304	57	7	or	or	CCONJ
cana-1304	57	8	membership	membership	NOUN
cana-1304	57	9	for	for	ADP
cana-1304	57	10	each	each	DET
cana-1304	57	11	element	element	NOUN
cana-1304	57	12	,	,	PUNCT
cana-1304	57	13	allowing	allow	VERB
cana-1304	57	14	for	for	ADP
cana-1304	57	15	a	a	DET
cana-1304	57	16	nuanced	nuanced	ADJ
cana-1304	57	17	representation	representation	NOUN
cana-1304	57	18	of	of	ADP
cana-1304	57	19	uncertainty	uncertainty	NOUN
cana-1304	57	20	and	and	CCONJ
cana-1304	57	21	imprecision	imprecision	NOUN
cana-1304	57	22	in	in	ADP
cana-1304	57	23	fuzzy	fuzzy	ADJ
cana-1304	57	24	systems.in	systems.in	X
cana-1304	57	25	general	general	NOUN
cana-1304	57	26	,	,	PUNCT
cana-1304	57	27	a	a	DET
cana-1304	57	28	fuzzy	fuzzy	ADJ
cana-1304	57	29	set	set	VERB
cana-1304	57	30			PROPN
cana-1304	57	31	in	in	ADP
cana-1304	57	32	δ	δ	PROPN
cana-1304	57	33	is	be	AUX
cana-1304	57	34	characterized	characterize	VERB
cana-1304	57	35	by	by	ADP
cana-1304	57	36	its	its	PRON
cana-1304	57	37	membership	membership	NOUN
cana-1304	57	38	function	function	NOUN
cana-1304	57	39	a(x	a(x	NOUN
cana-1304	57	40	)	)	PUNCT
cana-1304	57	41	a	a	PRON
cana-1304	57	42	{	{	PUNCT
cana-1304	57	43	(	(	PUNCT
cana-1304	57	44	,	,	PUNCT
cana-1304	57	45	)	)	PUNCT
cana-1304	57	46	|	|	ADV
cana-1304	57	47	}	}	PUNCT
cana-1304	57	48	x	x	PROPN
cana-1304	58	1	x	x	NUM
cana-1304	58	2			PROPN
cana-1304	58	3			NOUN
cana-1304	58	4	.	.	PUNCT
cana-1304	59	1	definition	definition	NOUN
cana-1304	59	2	2.in	2.in	NUM
cana-1304	59	3	fuzzy	fuzzy	ADJ
cana-1304	59	4	set	set	VERB
cana-1304	59	5	theory	theory	NOUN
cana-1304	59	6	,	,	PUNCT
cana-1304	59	7	an	an	DET
cana-1304	59	8	alpha	alpha	NOUN
cana-1304	59	9	-	-	PUNCT
cana-1304	59	10	cut	cut	NOUN
cana-1304	59	11	is	be	AUX
cana-1304	59	12	a	a	DET
cana-1304	59	13	crisp	crisp	ADJ
cana-1304	59	14	set	set	NOUN
cana-1304	59	15	derived	derive	VERB
cana-1304	59	16	from	from	ADP
cana-1304	59	17	a	a	DET
cana-1304	59	18	fuzzy	fuzzy	ADJ
cana-1304	59	19	set	set	VERB
cana-1304	59	20	by	by	ADP
cana-1304	59	21	retaining	retain	VERB
cana-1304	59	22	only	only	ADV
cana-1304	59	23	those	those	DET
cana-1304	59	24	elements	element	NOUN
cana-1304	59	25	whose	whose	DET
cana-1304	59	26	membership	membership	NOUN
cana-1304	59	27	grades	grade	NOUN
cana-1304	59	28	are	be	AUX
cana-1304	59	29	greater	great	ADJ
cana-1304	59	30	than	than	ADP
cana-1304	59	31	or	or	CCONJ
cana-1304	59	32	equal	equal	ADJ
cana-1304	59	33	to	to	ADP
cana-1304	59	34	a	a	DET
cana-1304	59	35	specified	specify	VERB
cana-1304	59	36	threshold	threshold	NOUN
cana-1304	59	37	value	value	NOUN
cana-1304	59	38	,	,	PUNCT
cana-1304	59	39	denoted	denote	VERB
cana-1304	59	40	as	as	ADP
cana-1304	59	41	"	"	PUNCT
cana-1304	59	42	alpha	alpha	NOUN
cana-1304	59	43	.	.	PUNCT
cana-1304	59	44	"	"	PUNCT
cana-1304	60	1	the	the	DET
cana-1304	60	2	fuzzy	fuzzy	ADJ
cana-1304	60	3	alpha	alpha	NOUN
cana-1304	60	4	-	-	PUNCT
cana-1304	60	5	cut	cut	NOUN
cana-1304	60	6	essentially	essentially	ADV
cana-1304	60	7	transforms	transform	VERB
cana-1304	60	8	a	a	DET
cana-1304	60	9	fuzzy	fuzzy	ADJ
cana-1304	60	10	set	set	VERB
cana-1304	60	11	into	into	ADP
cana-1304	60	12	a	a	DET
cana-1304	60	13	conventional	conventional	ADJ
cana-1304	60	14	,	,	PUNCT
cana-1304	60	15	nonfuzzy	nonfuzzy	NOUN
cana-1304	60	16	set	set	VERB
cana-1304	60	17	by	by	ADP
cana-1304	60	18	considering	consider	VERB
cana-1304	60	19	only	only	ADV
cana-1304	60	20	the	the	DET
cana-1304	60	21	elements	element	NOUN
cana-1304	60	22	that	that	PRON
cana-1304	60	23	exhibit	exhibit	VERB
cana-1304	60	24	a	a	DET
cana-1304	60	25	sufficiently	sufficiently	ADV
cana-1304	60	26	high	high	ADJ
cana-1304	60	27	degree	degree	NOUN
cana-1304	60	28	of	of	ADP
cana-1304	60	29	membership	membership	NOUN
cana-1304	60	30	.	.	PUNCT
cana-1304	61	1	definition	definition	NOUN
cana-1304	61	2	3.the	3.the	DET
cana-1304	61	3	membership	membership	NOUN
cana-1304	61	4	function	function	NOUN
cana-1304	61	5	of	of	ADP
cana-1304	61	6	a	a	DET
cana-1304	61	7	triangular	triangular	NOUN
cana-1304	61	8	fuzzy	fuzzy	ADJ
cana-1304	61	9	number	number	NOUN
cana-1304	61	10	is	be	AUX
cana-1304	61	11	typically	typically	ADV
cana-1304	61	12	represented	represent	VERB
cana-1304	61	13	by	by	ADP
cana-1304	61	14	a	a	DET
cana-1304	61	15	triangle	triangle	NOUN
cana-1304	61	16	on	on	ADP
cana-1304	61	17	the	the	DET
cana-1304	61	18	membership	membership	NOUN
cana-1304	61	19	scale	scale	NOUN
cana-1304	61	20	,	,	PUNCT
cana-1304	61	21	reflecting	reflect	VERB
cana-1304	61	22	the	the	DET
cana-1304	61	23	gradual	gradual	ADJ
cana-1304	61	24	decrease	decrease	NOUN
cana-1304	61	25	in	in	ADP
cana-1304	61	26	membership	membership	NOUN
cana-1304	61	27	from	from	ADP
cana-1304	61	28	the	the	DET
cana-1304	61	29	modal	modal	ADJ
cana-1304	61	30	value	value	NOUN
cana-1304	61	31	towards	towards	ADP
cana-1304	61	32	the	the	DET
cana-1304	61	33	bounds	bound	NOUN
cana-1304	61	34	.	.	PUNCT
cana-1304	62	1	this	this	DET
cana-1304	62	2	type	type	NOUN
cana-1304	62	3	of	of	ADP
cana-1304	62	4	fuzzy	fuzzy	ADJ
cana-1304	62	5	number	number	NOUN
cana-1304	62	6	is	be	AUX
cana-1304	62	7	often	often	ADV
cana-1304	62	8	used	use	VERB
cana-1304	62	9	to	to	PART
cana-1304	62	10	model	model	VERB
cana-1304	62	11	uncertainty	uncertainty	NOUN
cana-1304	62	12	or	or	CCONJ
cana-1304	62	13	imprecision	imprecision	NOUN
cana-1304	62	14	in	in	ADP
cana-1304	62	15	situations	situation	NOUN
cana-1304	62	16	where	where	SCONJ
cana-1304	62	17	the	the	DET
cana-1304	62	18	exact	exact	ADJ
cana-1304	62	19	value	value	NOUN
cana-1304	62	20	is	be	AUX
cana-1304	62	21	uncertain	uncertain	ADJ
cana-1304	62	22	but	but	CCONJ
cana-1304	62	23	can	can	AUX
cana-1304	62	24	be	be	AUX
cana-1304	62	25	estimated	estimate	VERB
cana-1304	62	26	to	to	PART
cana-1304	62	27	lie	lie	VERB
cana-1304	62	28	within	within	ADP
cana-1304	62	29	a	a	DET
cana-1304	62	30	specific	specific	ADJ
cana-1304	62	31	range	range	NOUN
cana-1304	62	32	.	.	PUNCT
cana-1304	63	1	mathematically	mathematically	ADV
cana-1304	63	2	,	,	PUNCT
cana-1304	63	3	a	a	DET
cana-1304	63	4	triangular	triangular	NOUN
cana-1304	63	5	fuzzy	fuzzy	ADJ
cana-1304	63	6	number	number	NOUN
cana-1304	63	7	a	a	PRON
cana-1304	63	8	can	can	AUX
cana-1304	63	9	be	be	AUX
cana-1304	63	10	represented	represent	VERB
cana-1304	63	11	as	as	ADP
cana-1304	63	12	:	:	PUNCT
cana-1304	63	13	{	{	PUNCT
cana-1304	63	14	(	(	PUNCT
cana-1304	63	15	(	(	PUNCT
cana-1304	63	16	}	}	PUNCT
cana-1304	63	17	where	where	SCONJ
cana-1304	63	18	(	(	PUNCT
cana-1304	63	19	is	be	AUX
cana-1304	63	20	the	the	DET
cana-1304	63	21	mathematical	mathematical	ADJ
cana-1304	63	22	function	function	NOUN
cana-1304	63	23	of	of	ADP
cana-1304	63	24	the	the	DET
cana-1304	63	25	triangular	triangular	NOUN
cana-1304	63	26	fuzzy	fuzzy	ADJ
cana-1304	63	27	number	number	NOUN
cana-1304	63	28	,	,	PUNCT
cana-1304	63	29	defined	define	VERB
cana-1304	63	30	as	as	ADP
cana-1304	63	31	:	:	PUNCT
cana-1304	63	32	figure	figure	NOUN
cana-1304	63	33	2.1	2.1	NUM
cana-1304	63	34	:	:	PUNCT
cana-1304	63	35	triangular	triangular	NOUN
cana-1304	63	36	fuzzy	fuzzy	ADJ
cana-1304	63	37	number	number	NOUN
cana-1304	63	38	in	in	ADP
cana-1304	63	39	this	this	DET
cana-1304	63	40	representation	representation	NOUN
cana-1304	63	41	,	,	PUNCT
cana-1304	63	42	a	a	DET
cana-1304	63	43	,	,	PUNCT
cana-1304	63	44	b	b	NOUN
cana-1304	63	45	,	,	PUNCT
cana-1304	63	46	and	and	CCONJ
cana-1304	63	47	c	c	PROPN
cana-1304	63	48	are	be	AUX
cana-1304	63	49	the	the	DET
cana-1304	63	50	lower	lower	ADV
cana-1304	63	51	bound	bind	VERB
cana-1304	63	52	,	,	PUNCT
cana-1304	63	53	modal	modal	ADJ
cana-1304	63	54	value	value	NOUN
cana-1304	63	55	,	,	PUNCT
cana-1304	63	56	and	and	CCONJ
cana-1304	63	57	upper	upper	ADJ
cana-1304	63	58	bound	bind	VERB
cana-1304	63	59	,	,	PUNCT
cana-1304	63	60	respectively	respectively	ADV
cana-1304	63	61	.	.	PUNCT
cana-1304	64	1	triangular	triangular	ADJ
cana-1304	64	2	fuzzy	fuzzy	ADJ
cana-1304	64	3	numbers	number	NOUN
cana-1304	64	4	are	be	AUX
cana-1304	64	5	widely	widely	ADV
cana-1304	64	6	used	use	VERB
cana-1304	64	7	in	in	ADP
cana-1304	64	8	fuzzy	fuzzy	ADJ
cana-1304	64	9	logic	logic	NOUN
cana-1304	64	10	,	,	PUNCT
cana-1304	64	11	fuzzy	fuzzy	ADJ
cana-1304	64	12	systems	system	NOUN
cana-1304	64	13	,	,	PUNCT
cana-1304	64	14	and	and	CCONJ
cana-1304	64	15	decision	decision	NOUN
cana-1304	64	16	-	-	PUNCT
cana-1304	64	17	making	making	NOUN
cana-1304	64	18	under	under	ADP
cana-1304	64	19	uncertainty	uncertainty	NOUN
cana-1304	64	20	.	.	PUNCT
cana-1304	65	1	definition	definition	NOUN
cana-1304	65	2	4.for	4.for	NUM
cana-1304	65	3	arbitraryfuzzynumbers	arbitraryfuzzynumber	VERB
cana-1304	65	4			NOUN
cana-1304	65	5			PUNCT
cana-1304	65	6			PROPN
cana-1304	65	7			PROPN
cana-1304	65	8	,	,	PUNCT
cana-1304	65	9	,	,	PUNCT
cana-1304	65	10	,	,	PUNCT
cana-1304	65	11			PROPN
cana-1304	65	12			PROPN
cana-1304	65	13			PROPN
cana-1304	65	14			PROPN
cana-1304	65	15			NOUN
cana-1304	65	16			NUM
cana-1304	65	17	the	the	DET
cana-1304	65	18	quality	quality	NOUN
cana-1304	65	19			NOUN
cana-1304	65	20			PROPN
cana-1304	65	21	,	,	PUNCT
cana-1304	65	22	sup	sup	NOUN
cana-1304	65	23	(	(	PUNCT
cana-1304	65	24	)	)	PUNCT
cana-1304	65	25	(	(	PUNCT
cana-1304	65	26	)	)	PUNCT
cana-1304	65	27	,	,	PUNCT
cana-1304	65	28	sup	sup	NOUN
cana-1304	65	29	(	(	PUNCT
cana-1304	65	30	)	)	PUNCT
cana-1304	65	31	(	(	PUNCT
cana-1304	65	32	)	)	PUNCT
cana-1304	65	33	0	0	NUM
cana-1304	65	34	1	1	NUM
cana-1304	65	35	0	0	NUM
cana-1304	65	36	1	1	NUM
cana-1304	65	37	d	d	NOUN
cana-1304	65	38			NOUN
cana-1304	65	39			PROPN
cana-1304	65	40			PROPN
cana-1304	65	41			PROPN
cana-1304	65	42			X
cana-1304	65	43			NUM
cana-1304	65	44			NUM
cana-1304	65	45			NUM
cana-1304	65	46			NUM
cana-1304	65	47			PROPN
cana-1304	65	48			NUM
cana-1304	65	49			ADP
cana-1304	66	1			ADP
cana-1304	66	2			NUM
cana-1304	66	3			NUM
cana-1304	66	4			PROPN
cana-1304	66	5			PROPN
cana-1304	66	6			SYM
cana-1304	66	7			INTJ
cana-1304	66	8			NUM
cana-1304	66	9			NUM
cana-1304	66	10			NUM
cana-1304	66	11			NOUN
cana-1304	66	12			NOUN
cana-1304	66	13			PROPN
cana-1304	66	14	is	be	AUX
cana-1304	66	15	the	the	DET
cana-1304	66	16	distance	distance	NOUN
cana-1304	66	17	between	between	ADP
cana-1304	66	18	and	and	NOUN
cana-1304	66	19			PROPN
cana-1304	66	20	.	.	PUNCT
cana-1304	67	1	3	3	X
cana-1304	67	2	.	.	X
cana-1304	67	3	examining	examine	VERB
cana-1304	67	4	the	the	DET
cana-1304	67	5	convergence	convergence	NOUN
cana-1304	67	6	behavior	behavior	NOUN
cana-1304	67	7	of	of	ADP
cana-1304	67	8	fuzzy	fuzzy	ADJ
cana-1304	67	9	delay	delay	NOUN
cana-1304	67	10	differential	differential	ADJ
cana-1304	67	11	equations	equation	NOUN
cana-1304	67	12	on	on	ADP
cana-1304	67	13	considering	consider	VERB
cana-1304	67	14	the	the	DET
cana-1304	67	15	first	first	ADJ
cana-1304	67	16	-	-	PUNCT
cana-1304	67	17	order	order	NOUN
cana-1304	67	18	differential	differential	ADJ
cana-1304	67	19	equation	equation	NOUN
cana-1304	67	20	[	[	X
cana-1304	67	21	16	16	NUM
cana-1304	67	22	]	]	X
cana-1304	67	23	,	,	PUNCT
cana-1304	67	24	1	1	NUM
cana-1304	67	25	<	<	X
cana-1304	67	26	<	<	X
cana-1304	67	27	,	,	PUNCT
cana-1304	67	28	(	(	PUNCT
cana-1304	67	29	)	)	PUNCT
cana-1304	67	30	=	=	SYM
cana-1304	68	1	1	1	NUM
cana-1304	68	2	<	<	X
cana-1304	68	3	<	<	X
cana-1304	68	4	,	,	PUNCT
cana-1304	68	5	0	0	NUM
cana-1304	68	6	.	.	PUNCT
cana-1304	69	1	a	a	DET
cana-1304	69	2	x	x	X
cana-1304	69	3	if	if	SCONJ
cana-1304	69	4	a	a	DET
cana-1304	69	5	x	x	SYM
cana-1304	69	6	a	a	DET
cana-1304	69	7	x	x	NOUN
cana-1304	69	8	ax	ax	NOUN
cana-1304	69	9	if	if	SCONJ
cana-1304	69	10	a	a	DET
cana-1304	69	11	x	x	X
cana-1304	69	12	a	a	DET
cana-1304	69	13	otherwise	otherwise	ADV
cana-1304	69	14			NOUN
cana-1304	69	15			X
cana-1304	69	16			NOUN
cana-1304	69	17			PROPN
cana-1304	69	18			PROPN
cana-1304	69	19			PROPN
cana-1304	69	20			PROPN
cana-1304	69	21			PROPN
cana-1304	69	22			NUM
cana-1304	69	23			NUM
cana-1304	69	24			NUM
cana-1304	69	25			NOUN
cana-1304	69	26			NOUN
cana-1304	69	27			VERB
cana-1304	69	28			DET
cana-1304	69	29			NUM
cana-1304	69	30			NUM
cana-1304	69	31			PRON
cana-1304	69	32			PROPN
cana-1304	69	33	communications	communication	NOUN
cana-1304	69	34	on	on	ADP
cana-1304	69	35	applied	apply	VERB
cana-1304	69	36	nonlinear	nonlinear	ADJ
cana-1304	69	37	analysis	analysis	NOUN
cana-1304	69	38	issn	issn	NOUN
cana-1304	69	39	:	:	PUNCT
cana-1304	69	40	1074	1074	NUM
cana-1304	69	41	-	-	PUNCT
cana-1304	69	42	133x	133x	NUM
cana-1304	69	43	vol	vol	NOUN
cana-1304	69	44	31	31	NUM
cana-1304	69	45	no	no	NOUN
cana-1304	69	46	.	.	PUNCT
cana-1304	70	1	7s	7	NOUN
cana-1304	70	2	(	(	PUNCT
cana-1304	70	3	2024	2024	NUM
cana-1304	70	4	)	)	PUNCT
cana-1304	70	5	289	289	NUM
cana-1304	70	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1304	70	7	{	{	PUNCT
cana-1304	70	8	(	(	PUNCT
cana-1304	70	9	(	(	PUNCT
cana-1304	70	10	(	(	PUNCT
cana-1304	70	11	)	)	PUNCT
cana-1304	70	12	(	(	PUNCT
cana-1304	70	13	where	where	SCONJ
cana-1304	70	14	is	be	AUX
cana-1304	70	15	a	a	DET
cana-1304	70	16	crisp	crisp	ADJ
cana-1304	70	17	function	function	NOUN
cana-1304	70	18	of	of	ADP
cana-1304	70	19	(	(	PUNCT
cana-1304	70	20	.	.	PUNCT
cana-1304	71	1	we	we	PRON
cana-1304	71	2	represent	represent	VERB
cana-1304	71	3	the	the	DET
cana-1304	71	4	fuzzy	fuzzy	ADJ
cana-1304	71	5	function	function	NOUN
cana-1304	71	6	as	as	ADP
cana-1304	71	7	[	[	PUNCT
cana-1304	71	8	]	]	X
cana-1304	71	9	.	.	PUNCT
cana-1304	72	1	we	we	PRON
cana-1304	72	2	have	have	VERB
cana-1304	72	3	(	(	PUNCT
cana-1304	72	4	[	[	PUNCT
cana-1304	72	5	(	(	PUNCT
cana-1304	72	6	(	(	PUNCT
cana-1304	72	7	]	]	X
cana-1304	72	8	where	where	SCONJ
cana-1304	72	9	,	,	PUNCT
cana-1304	72	10	(	(	PUNCT
cana-1304	72	11	[	[	PUNCT
cana-1304	72	12	]	]	X
cana-1304	72	13	(	(	PUNCT
cana-1304	72	14	[	[	PUNCT
cana-1304	72	15	]	]	X
cana-1304	72	16	by	by	ADP
cana-1304	72	17	using	use	VERB
cana-1304	72	18	the	the	DET
cana-1304	72	19	extension	extension	NOUN
cana-1304	72	20	principle	principle	NOUN
cana-1304	72	21	[	[	X
cana-1304	72	22	16	16	NUM
cana-1304	72	23	]	]	PUNCT
cana-1304	72	24	,	,	PUNCT
cana-1304	72	25	(	(	PUNCT
cana-1304	72	26	(	(	PUNCT
cana-1304	72	27	)	)	PUNCT
cana-1304	72	28	(	(	PUNCT
cana-1304	72	29	{	{	PUNCT
cana-1304	72	30	(	(	PUNCT
cana-1304	72	31	(	(	PUNCT
cana-1304	72	32	(	(	PUNCT
cana-1304	72	33	}	}	PUNCT
cana-1304	72	34	from	from	ADP
cana-1304	72	35	this	this	PRON
cana-1304	72	36	it	it	PRON
cana-1304	72	37	follows	follow	VERB
cana-1304	72	38	that	that	SCONJ
cana-1304	72	39	(	(	PUNCT
cana-1304	72	40	(	(	PUNCT
cana-1304	72	41	[	[	PUNCT
cana-1304	72	42	(	(	PUNCT
cana-1304	72	43	(	(	PUNCT
cana-1304	72	44	(	(	PUNCT
cana-1304	72	45	(	(	PUNCT
cana-1304	72	46	]	]	X
cana-1304	72	47	where	where	SCONJ
cana-1304	72	48	(	(	PUNCT
cana-1304	72	49	(	(	PUNCT
cana-1304	72	50	𝑛	𝑛	X
cana-1304	72	51	{	{	PUNCT
cana-1304	72	52	(	(	PUNCT
cana-1304	72	53	(	(	PUNCT
cana-1304	72	54	}	}	PUNCT
cana-1304	72	55	(	(	PUNCT
cana-1304	72	56	(	(	PUNCT
cana-1304	72	57	{	{	PUNCT
cana-1304	72	58	(	(	PUNCT
cana-1304	72	59	(	(	PUNCT
cana-1304	72	60	}	}	PUNCT
cana-1304	72	61	(	(	PUNCT
cana-1304	72	62	3.1	3.1	NUM
cana-1304	72	63	)	)	PUNCT
cana-1304	72	64	theorem	theorem	VERB
cana-1304	72	65	3.1	3.1	NUM
cana-1304	72	66	.	.	PUNCT
cana-1304	73	1	let	let	VERB
cana-1304	73	2	|	|	ADV
cana-1304	73	3	(	(	PUNCT
cana-1304	73	4	)	)	PUNCT
cana-1304	73	5	(	(	PUNCT
cana-1304	73	6	|	|	ADV
cana-1304	73	7	(	(	PUNCT
cana-1304	73	8	|	|	ADV
cana-1304	73	9	|	|	ADV
cana-1304	73	10	)	)	PUNCT
cana-1304	73	11	(	(	PUNCT
cana-1304	73	12	represent	represent	VERB
cana-1304	73	13	a	a	DET
cana-1304	73	14	continuous	continuous	ADJ
cana-1304	73	15	function	function	NOUN
cana-1304	73	16	that	that	PRON
cana-1304	73	17	fulfills	fulfill	VERB
cana-1304	73	18	conditions	condition	NOUN
cana-1304	73	19	and	and	CCONJ
cana-1304	73	20	(	(	PUNCT
cana-1304	73	21	.	.	PUNCT
cana-1304	74	1	this	this	PRON
cana-1304	74	2	guarantees	guarantee	VERB
cana-1304	74	3	the	the	DET
cana-1304	74	4	existence	existence	NOUN
cana-1304	74	5	of	of	ADP
cana-1304	74	6	a	a	DET
cana-1304	74	7	unique	unique	ADJ
cana-1304	74	8	solution	solution	NOUN
cana-1304	74	9	to	to	ADP
cana-1304	74	10	the	the	DET
cana-1304	74	11	initial	initial	ADJ
cana-1304	74	12	value	value	NOUN
cana-1304	74	13	problem	problem	NOUN
cana-1304	74	14	on	on	ADP
cana-1304	74	15	the	the	DET
cana-1304	74	16	domain	domain	NOUN
cana-1304	74	17	,	,	PUNCT
cana-1304	74	18	with	with	ADP
cana-1304	74	19	initial	initial	ADJ
cana-1304	74	20	condition	condition	NOUN
cana-1304	74	21	being	be	AUX
cana-1304	74	22	the	the	DET
cana-1304	74	23	sole	sole	ADJ
cana-1304	74	24	solution	solution	NOUN
cana-1304	74	25	to	to	ADP
cana-1304	74	26	the	the	DET
cana-1304	74	27	differential	differential	ADJ
cana-1304	74	28	equation	equation	NOUN
cana-1304	74	29	(	(	PUNCT
cana-1304	74	30	3.1	3.1	NUM
cana-1304	74	31	)	)	PUNCT
cana-1304	74	32	.	.	PUNCT
cana-1304	75	1	lemma	lemma	PROPN
cana-1304	75	2	3.2	3.2	NUM
cana-1304	75	3	.	.	PUNCT
cana-1304	76	1	the	the	DET
cana-1304	76	2	numbers	number	NOUN
cana-1304	76	3	should	should	AUX
cana-1304	76	4	be	be	AUX
cana-1304	76	5	arranged	arrange	VERB
cana-1304	76	6	in	in	ADP
cana-1304	76	7	sequential	sequential	ADJ
cana-1304	76	8	order	order	NOUN
cana-1304	76	9	{	{	PUNCT
cana-1304	76	10	}	}	PUNCT
cana-1304	76	11	satisfy	satisfy	VERB
cana-1304	76	12	for	for	ADP
cana-1304	76	13	some	some	DET
cana-1304	76	14	given	give	VERB
cana-1304	76	15	constants	constant	NOUN
cana-1304	76	16	and	and	CCONJ
cana-1304	76	17	.	.	PUNCT
cana-1304	77	1	then	then	ADV
cana-1304	77	2	.	.	PUNCT
cana-1304	78	1	lemma3.3	lemma3.3	NOUN
cana-1304	78	2	:	:	PUNCT
cana-1304	78	3	the	the	DET
cana-1304	78	4	numbers	number	NOUN
cana-1304	78	5	should	should	AUX
cana-1304	78	6	be	be	AUX
cana-1304	78	7	arranged	arrange	VERB
cana-1304	78	8	in	in	ADP
cana-1304	78	9	the	the	DET
cana-1304	78	10	following	follow	VERB
cana-1304	78	11	manner	manner	NOUN
cana-1304	78	12	{	{	PUNCT
cana-1304	78	13	}	}	PUNCT
cana-1304	78	14	and	and	CCONJ
cana-1304	78	15	{	{	PUNCT
cana-1304	78	16	}	}	PUNCT
cana-1304	78	17	satisfy	satisfy	VERB
cana-1304	78	18	{	{	PUNCT
cana-1304	78	19	}	}	PUNCT
cana-1304	78	20	{	{	PUNCT
cana-1304	78	21	}	}	PUNCT
cana-1304	78	22	for	for	ADP
cana-1304	78	23	some	some	DET
cana-1304	78	24	given	give	VERB
cana-1304	78	25	positive	positive	ADJ
cana-1304	78	26	constants	constant	NOUN
cana-1304	78	27	and	and	CCONJ
cana-1304	78	28	,	,	PUNCT
cana-1304	78	29	then	then	ADV
cana-1304	78	30	where	where	SCONJ
cana-1304	78	31	and	and	CCONJ
cana-1304	78	32	.	.	PUNCT
cana-1304	79	1	4	4	X
cana-1304	79	2	.	.	X
cana-1304	79	3	runge	runge	NOUN
cana-1304	79	4	-	-	PUNCT
cana-1304	79	5	kutta	kutta	NOUN
cana-1304	79	6	-	-	PUNCT
cana-1304	79	7	fehlberg	fehlberg	NOUN
cana-1304	79	8	method	method	NOUN
cana-1304	79	9	in	in	ADP
cana-1304	79	10	this	this	DET
cana-1304	79	11	current	current	ADJ
cana-1304	79	12	discussion	discussion	NOUN
cana-1304	79	13	,	,	PUNCT
cana-1304	79	14	the	the	DET
cana-1304	79	15	approach	approach	NOUN
cana-1304	79	16	proposed	propose	VERB
cana-1304	79	17	for	for	ADP
cana-1304	79	18	addressing	address	VERB
cana-1304	79	19	the	the	DET
cana-1304	79	20	fuzzy	fuzzy	ADJ
cana-1304	79	21	delay	delay	NOUN
cana-1304	79	22	differential	differential	ADJ
cana-1304	79	23	equation	equation	NOUN
cana-1304	79	24	entails	entail	VERB
cana-1304	79	25	integrating	integrate	VERB
cana-1304	79	26	the	the	DET
cana-1304	79	27	runge	runge	NOUN
cana-1304	79	28	-	-	PUNCT
cana-1304	79	29	kutta	kutta	NOUN
cana-1304	79	30	-	-	PUNCT
cana-1304	79	31	fehlberg	fehlberg	NOUN
cana-1304	79	32	method	method	NOUN
cana-1304	79	33	(	(	PUNCT
cana-1304	79	34	rkfm	rkfm	NOUN
cana-1304	79	35	)	)	PUNCT
cana-1304	79	36	within	within	ADP
cana-1304	79	37	a	a	DET
cana-1304	79	38	fuzzy	fuzzy	ADJ
cana-1304	79	39	framework	framework	NOUN
cana-1304	79	40	.	.	PUNCT
cana-1304	80	1	let	let	AUX
cana-1304	80	2	represent	represent	VERB
cana-1304	80	3	the	the	DET
cana-1304	80	4	exact	exact	ADJ
cana-1304	80	5	solution	solution	NOUN
cana-1304	80	6	,	,	PUNCT
cana-1304	80	7	with	with	ADP
cana-1304	80	8	serving	serve	VERB
cana-1304	80	9	as	as	ADP
cana-1304	80	10	an	an	DET
cana-1304	80	11	approximation	approximation	NOUN
cana-1304	80	12	for	for	ADP
cana-1304	80	13	the	the	DET
cana-1304	80	14	ambiguous	ambiguous	ADJ
cana-1304	80	15	initial	initial	ADJ
cana-1304	80	16	value	value	NOUN
cana-1304	80	17	problem	problem	NOUN
cana-1304	80	18	.	.	PUNCT
cana-1304	81	1	the	the	DET
cana-1304	81	2	resulting	result	VERB
cana-1304	81	3	solution	solution	NOUN
cana-1304	81	4	materializes	materialize	VERB
cana-1304	81	5	as	as	ADP
cana-1304	81	6	the	the	DET
cana-1304	81	7	computed	computed	ADJ
cana-1304	81	8	phase	phase	NOUN
cana-1304	81	9	points	point	NOUN
cana-1304	81	10	.	.	PUNCT
cana-1304	82	1	then	then	ADV
cana-1304	82	2	we	we	PRON
cana-1304	82	3	obtain	obtain	VERB
cana-1304	82	4	the	the	PRON
cana-1304	82	5	,	,	PUNCT
cana-1304	82	6	communications	communication	NOUN
cana-1304	82	7	on	on	ADP
cana-1304	82	8	applied	apply	VERB
cana-1304	82	9	nonlinear	nonlinear	ADJ
cana-1304	82	10	analysis	analysis	NOUN
cana-1304	82	11	issn	issn	NOUN
cana-1304	82	12	:	:	PUNCT
cana-1304	82	13	1074	1074	NUM
cana-1304	82	14	-	-	PUNCT
cana-1304	82	15	133x	133x	NUM
cana-1304	82	16	vol	vol	NOUN
cana-1304	82	17	31	31	NUM
cana-1304	82	18	no	no	NOUN
cana-1304	82	19	.	.	PUNCT
cana-1304	83	1	7s	7	NOUN
cana-1304	83	2	(	(	PUNCT
cana-1304	83	3	2024	2024	NUM
cana-1304	83	4	)	)	PUNCT
cana-1304	83	5	290	290	NUM
cana-1304	83	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1304	83	7	(	(	PUNCT
cana-1304	83	8	𝑛	𝑛	PROPN
cana-1304	83	9	(	(	PUNCT
cana-1304	83	10	)	)	PUNCT
cana-1304	83	11	(	(	PUNCT
cana-1304	83	12	(	(	PUNCT
cana-1304	83	13	)	)	PUNCT
cana-1304	83	14	where	where	SCONJ
cana-1304	83	15	(	(	PUNCT
cana-1304	83	16	{	{	PUNCT
cana-1304	83	17	𝑛	𝑛	PROPN
cana-1304	83	18	(	(	PUNCT
cana-1304	83	19	(	(	PUNCT
cana-1304	83	20	)	)	PUNCT
cana-1304	83	21	(	(	PUNCT
cana-1304	83	22	(	(	PUNCT
cana-1304	83	23	}	}	PUNCT
cana-1304	83	24	(	(	PUNCT
cana-1304	83	25	{	{	PUNCT
cana-1304	83	26	𝑛	𝑛	PROPN
cana-1304	83	27	(	(	PUNCT
cana-1304	83	28	(	(	PUNCT
cana-1304	83	29	)	)	PUNCT
cana-1304	83	30	)	)	PUNCT
cana-1304	83	31	(	(	PUNCT
cana-1304	83	32	(	(	PUNCT
cana-1304	83	33	)	)	PUNCT
cana-1304	83	34	)	)	PUNCT
cana-1304	83	35	}	}	PUNCT
cana-1304	83	36	(	(	PUNCT
cana-1304	83	37	{	{	PUNCT
cana-1304	83	38	𝑛	𝑛	PROPN
cana-1304	83	39	(	(	PUNCT
cana-1304	83	40	(	(	PUNCT
cana-1304	83	41	)	)	PUNCT
cana-1304	83	42	)	)	PUNCT
cana-1304	83	43	(	(	PUNCT
cana-1304	83	44	(	(	PUNCT
cana-1304	83	45	)	)	PUNCT
cana-1304	83	46	)	)	PUNCT
cana-1304	83	47	}	}	PUNCT
cana-1304	83	48	(	(	PUNCT
cana-1304	83	49	{	{	PUNCT
cana-1304	83	50	𝑛	𝑛	PROPN
cana-1304	83	51	(	(	PUNCT
cana-1304	83	52	(	(	PUNCT
cana-1304	83	53	)	)	PUNCT
cana-1304	83	54	)	)	PUNCT
cana-1304	83	55	(	(	PUNCT
cana-1304	83	56	(	(	PUNCT
cana-1304	83	57	)	)	PUNCT
cana-1304	83	58	)	)	PUNCT
cana-1304	83	59	}	}	PUNCT
cana-1304	83	60	(	(	PUNCT
cana-1304	83	61	{	{	PUNCT
cana-1304	83	62	𝑛	𝑛	PROPN
cana-1304	83	63	(	(	PUNCT
cana-1304	83	64	(	(	PUNCT
cana-1304	83	65	)	)	PUNCT
cana-1304	83	66	)	)	PUNCT
cana-1304	83	67	(	(	PUNCT
cana-1304	83	68	(	(	PUNCT
cana-1304	83	69	)	)	PUNCT
cana-1304	83	70	)	)	PUNCT
cana-1304	83	71	}	}	PUNCT
cana-1304	83	72	(	(	PUNCT
cana-1304	83	73	{	{	PUNCT
cana-1304	83	74	𝑛	𝑛	PROPN
cana-1304	83	75	(	(	PUNCT
cana-1304	83	76	(	(	PUNCT
cana-1304	83	77	)	)	PUNCT
cana-1304	83	78	)	)	PUNCT
cana-1304	83	79	(	(	PUNCT
cana-1304	83	80	(	(	PUNCT
cana-1304	83	81	)	)	PUNCT
cana-1304	83	82	)	)	PUNCT
cana-1304	83	83	}	}	PUNCT
cana-1304	83	84	the	the	DET
cana-1304	83	85	parameter	parameter	NOUN
cana-1304	83	86	governing	govern	VERB
cana-1304	83	87	observance	observance	NOUN
cana-1304	83	88	is	be	AUX
cana-1304	83	89	held	hold	VERB
cana-1304	83	90	constant	constant	ADJ
cana-1304	83	91	,	,	PUNCT
cana-1304	83	92	following	follow	VERB
cana-1304	83	93	which	which	PRON
cana-1304	83	94	the	the	DET
cana-1304	83	95	precise	precise	ADJ
cana-1304	83	96	and	and	CCONJ
cana-1304	83	97	approximate	approximate	ADJ
cana-1304	83	98	solutions	solution	NOUN
cana-1304	83	99	for	for	ADP
cana-1304	83	100	are	be	AUX
cana-1304	83	101	expressed	express	VERB
cana-1304	83	102	as	as	SCONJ
cana-1304	83	103	follows	follow	VERB
cana-1304	83	104	:	:	PUNCT
cana-1304	83	105	(	(	PUNCT
cana-1304	83	106	(	(	PUNCT
cana-1304	83	107	(	(	PUNCT
cana-1304	83	108	(	(	PUNCT
cana-1304	83	109	(	(	PUNCT
cana-1304	83	110	(	(	PUNCT
cana-1304	83	111	(	(	PUNCT
cana-1304	83	112	4.1	4.1	NUM
cana-1304	83	113	)	)	PUNCT
cana-1304	83	114	in	in	ADP
cana-1304	83	115	light	light	NOUN
cana-1304	83	116	of	of	ADP
cana-1304	83	117	this	this	PRON
cana-1304	83	118	,	,	PUNCT
cana-1304	83	119	we	we	PRON
cana-1304	83	120	observe	observe	VERB
cana-1304	83	121	the	the	DET
cana-1304	83	122	convergence	convergence	NOUN
cana-1304	83	123	(	(	PUNCT
cana-1304	83	124	(	(	PUNCT
cana-1304	83	125	converges	converge	NOUN
cana-1304	83	126	to	to	ADP
cana-1304	83	127	(	(	PUNCT
cana-1304	83	128	(	(	PUNCT
cana-1304	83	129	with	with	ADP
cana-1304	83	130	respect	respect	NOUN
cana-1304	83	131	to	to	ADP
cana-1304	83	132	.	.	PUNCT
cana-1304	84	1	theorem	theorem	VERB
cana-1304	84	2	4.1	4.1	NUM
cana-1304	84	3	.	.	PUNCT
cana-1304	85	1	assuming	assume	VERB
cana-1304	85	2	the	the	DET
cana-1304	85	3	form	form	NOUN
cana-1304	85	4	(	(	PUNCT
cana-1304	85	5	4.1	4.1	NUM
cana-1304	85	6	)	)	PUNCT
cana-1304	85	7	with	with	ADP
cana-1304	85	8	,	,	PUNCT
cana-1304	85	9	then	then	ADV
cana-1304	85	10	*	*	PUNCT
cana-1304	85	11	(	(	PUNCT
cana-1304	85	12	+	+	X
cana-1304	85	13	(	(	PUNCT
cana-1304	85	14	(	(	PUNCT
cana-1304	85	15	(	(	PUNCT
cana-1304	85	16	.	.	X
cana-1304	85	17	5	5	X
cana-1304	85	18	.	.	X
cana-1304	85	19	illustrative	illustrative	ADJ
cana-1304	85	20	example	example	NOUN
cana-1304	85	21	consider	consider	VERB
cana-1304	85	22	the	the	DET
cana-1304	85	23	a	a	DET
cana-1304	85	24	linear	linear	ADJ
cana-1304	85	25	fuzzy	fuzzy	ADJ
cana-1304	85	26	delay	delay	NOUN
cana-1304	85	27	differential	differential	ADJ
cana-1304	85	28	equation	equation	NOUN
cana-1304	85	29	as	as	ADP
cana-1304	85	30	with	with	ADP
cana-1304	85	31	initial	initial	ADJ
cana-1304	85	32	condition	condition	NOUN
cana-1304	85	33	(	(	PUNCT
cana-1304	85	34	(	(	PUNCT
cana-1304	85	35	⁄	⁄	PROPN
cana-1304	85	36	(	(	PUNCT
cana-1304	85	37	)	)	PUNCT
cana-1304	85	38	(	(	PUNCT
cana-1304	85	39	(	(	PUNCT
cana-1304	85	40	5.1	5.1	NUM
cana-1304	85	41	)	)	PUNCT
cana-1304	85	42	communications	communication	NOUN
cana-1304	85	43	on	on	ADP
cana-1304	85	44	applied	apply	VERB
cana-1304	85	45	nonlinear	nonlinear	ADJ
cana-1304	85	46	analysis	analysis	NOUN
cana-1304	85	47	issn	issn	NOUN
cana-1304	85	48	:	:	PUNCT
cana-1304	85	49	1074	1074	NUM
cana-1304	85	50	-	-	PUNCT
cana-1304	85	51	133x	133x	NUM
cana-1304	85	52	vol	vol	NOUN
cana-1304	85	53	31	31	NUM
cana-1304	85	54	no	no	NOUN
cana-1304	85	55	.	.	PUNCT
cana-1304	86	1	7s	7	NOUN
cana-1304	86	2	(	(	PUNCT
cana-1304	86	3	2024	2024	NUM
cana-1304	86	4	)	)	PUNCT
cana-1304	86	5	291	291	NUM
cana-1304	86	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1304	86	7	with	with	ADP
cana-1304	86	8	(	(	PUNCT
cana-1304	86	9	(	(	PUNCT
cana-1304	86	10	.	.	PUNCT
cana-1304	87	1	under	under	ADP
cana-1304	87	2	the	the	DET
cana-1304	87	3	fuzzy	fuzzy	ADJ
cana-1304	87	4	condition	condition	NOUN
cana-1304	87	5	the	the	DET
cana-1304	87	6	exact	exact	ADJ
cana-1304	87	7	solution	solution	NOUN
cana-1304	87	8	of	of	ADP
cana-1304	87	9	(	(	PUNCT
cana-1304	87	10	5.1	5.1	NUM
cana-1304	87	11	)	)	PUNCT
cana-1304	87	12	are	be	AUX
cana-1304	87	13	(	(	PUNCT
cana-1304	87	14	(	(	PUNCT
cana-1304	87	15	(	(	PUNCT
cana-1304	87	16	(	(	PUNCT
cana-1304	87	17	5.2	5.2	NUM
cana-1304	87	18	)	)	PUNCT
cana-1304	87	19	in	in	ADP
cana-1304	87	20	employing	employ	VERB
cana-1304	87	21	the	the	DET
cana-1304	87	22	runge	runge	NOUN
cana-1304	87	23	-	-	PUNCT
cana-1304	87	24	kutta	kutta	NOUN
cana-1304	87	25	fuzzy	fuzzy	ADJ
cana-1304	87	26	method	method	NOUN
cana-1304	87	27	(	(	PUNCT
cana-1304	87	28	rkfm	rkfm	NOUN
cana-1304	87	29	)	)	PUNCT
cana-1304	87	30	to	to	PART
cana-1304	87	31	approximate	approximate	VERB
cana-1304	87	32	the	the	DET
cana-1304	87	33	solution	solution	NOUN
cana-1304	87	34	for	for	ADP
cana-1304	87	35	the	the	DET
cana-1304	87	36	provided	provide	VERB
cana-1304	87	37	equation	equation	NOUN
cana-1304	87	38	(	(	PUNCT
cana-1304	87	39	5.1	5.1	NUM
cana-1304	87	40	)	)	PUNCT
cana-1304	87	41	,	,	PUNCT
cana-1304	87	42	the	the	DET
cana-1304	87	43	resulting	result	VERB
cana-1304	87	44	fuzzified	fuzzified	ADJ
cana-1304	87	45	form	form	NOUN
cana-1304	87	46	,	,	PUNCT
cana-1304	87	47	as	as	ADP
cana-1304	87	48	per	per	ADP
cana-1304	87	49	definition	definition	NOUN
cana-1304	87	50	3	3	NUM
cana-1304	87	51	,	,	PUNCT
cana-1304	87	52	is	be	AUX
cana-1304	87	53	expressed	express	VERB
cana-1304	87	54	as	as	SCONJ
cana-1304	87	55	follows	follow	VERB
cana-1304	87	56	.	.	PUNCT
cana-1304	88	1	(	(	PUNCT
cana-1304	88	2	⁄	⁄	PROPN
cana-1304	88	3	(	(	PUNCT
cana-1304	88	4	)	)	PUNCT
cana-1304	88	5	(	(	PUNCT
cana-1304	88	6	(	(	PUNCT
cana-1304	88	7	⁄	⁄	PROPN
cana-1304	88	8	(	(	PUNCT
cana-1304	88	9	)	)	PUNCT
cana-1304	88	10	(	(	PUNCT
cana-1304	88	11	(	(	PUNCT
cana-1304	88	12	5.3	5.3	NUM
cana-1304	88	13	)	)	PUNCT
cana-1304	88	14	with	with	ADP
cana-1304	88	15	the	the	DET
cana-1304	88	16	initial	initial	ADJ
cana-1304	88	17	condition	condition	NOUN
cana-1304	88	18	(	(	PUNCT
cana-1304	88	19	(	(	PUNCT
cana-1304	88	20	.	.	PUNCT
cana-1304	89	1	the	the	DET
cana-1304	89	2	numerical	numerical	ADJ
cana-1304	89	3	results	result	NOUN
cana-1304	89	4	derived	derive	VERB
cana-1304	89	5	from	from	ADP
cana-1304	89	6	the	the	DET
cana-1304	89	7	approximate	approximate	ADJ
cana-1304	89	8	method	method	NOUN
cana-1304	89	9	are	be	AUX
cana-1304	89	10	presented	present	VERB
cana-1304	89	11	in	in	ADP
cana-1304	89	12	the	the	DET
cana-1304	89	13	table	table	NOUN
cana-1304	89	14	below	below	ADP
cana-1304	89	15	for	for	ADP
cana-1304	89	16	,	,	PUNCT
cana-1304	89	17	table	table	NOUN
cana-1304	89	18	5.1	5.1	NUM
cana-1304	89	19	:	:	PUNCT
cana-1304	89	20	approximate	approximate	ADJ
cana-1304	89	21	values	value	NOUN
cana-1304	89	22	runge	runge	NOUN
cana-1304	89	23	-	-	PUNCT
cana-1304	89	24	kutta	kutta	PROPN
cana-1304	89	25	fehlberg	fehlberg	PROPN
cana-1304	89	26	method	method	NOUN
cana-1304	89	27	runge	runge	NOUN
cana-1304	89	28	-	-	PUNCT
cana-1304	89	29	kutta	kutta	NOUN
cana-1304	89	30	fourth	fourth	ADJ
cana-1304	89	31	order	order	NOUN
cana-1304	89	32	method	method	NOUN
cana-1304	89	33	(	(	PUNCT
cana-1304	89	34	(	(	PUNCT
cana-1304	89	35	(	(	PUNCT
cana-1304	89	36	(	(	PUNCT
cana-1304	89	37	0	0	NUM
cana-1304	89	38	1.71879	1.71879	NUM
cana-1304	89	39	3.71879	3.71879	NUM
cana-1304	89	40	1.71827	1.71827	NUM
cana-1304	89	41	3.71827	3.71827	NUM
cana-1304	89	42	0.2	0.2	NUM
cana-1304	89	43	1.91879	1.91879	NUM
cana-1304	89	44	3.51879	3.51879	NUM
cana-1304	89	45	1.91827	1.91827	NUM
cana-1304	89	46	3.51827	3.51827	NUM
cana-1304	89	47	0.4	0.4	NUM
cana-1304	89	48	2.11879	2.11879	NUM
cana-1304	89	49	3.31879	3.31879	NUM
cana-1304	89	50	2.11827	2.11827	NUM
cana-1304	89	51	3.31827	3.31827	NUM
cana-1304	89	52	0.6	0.6	NUM
cana-1304	89	53	2.31879	2.31879	NUM
cana-1304	89	54	3.11879	3.11879	NUM
cana-1304	89	55	2.31827	2.31827	NUM
cana-1304	89	56	3.11827	3.11827	NUM
cana-1304	89	57	0.8	0.8	NUM
cana-1304	89	58	2.51879	2.51879	NUM
cana-1304	89	59	2.91879	2.91879	NUM
cana-1304	89	60	2.51827	2.51827	NUM
cana-1304	89	61	2.91827	2.91827	NUM
cana-1304	89	62	1	1	NUM
cana-1304	89	63	2.71879	2.71879	NUM
cana-1304	89	64	2.71879	2.71879	NUM
cana-1304	89	65	2.71827	2.71827	NUM
cana-1304	89	66	2.71827	2.71827	NUM
cana-1304	89	67	table	table	NOUN
cana-1304	89	68	5.2	5.2	NUM
cana-1304	89	69	:	:	PUNCT
cana-1304	89	70	error	error	NOUN
cana-1304	89	71	table	table	NOUN
cana-1304	89	72	exact	exact	ADJ
cana-1304	89	73	solution	solution	NOUN
cana-1304	89	74	rkfm	rkfm	NOUN
cana-1304	89	75	rk	rk	PROPN
cana-1304	89	76	4	4	NUM
cana-1304	89	77	th	th	NOUN
cana-1304	89	78	r	r	NOUN
cana-1304	89	79	(	(	PUNCT
cana-1304	89	80	(	(	PUNCT
cana-1304	89	81	(	(	PUNCT
cana-1304	89	82	(	(	PUNCT
cana-1304	89	83	(	(	PUNCT
cana-1304	89	84	(	(	PUNCT
cana-1304	89	85	0	0	NUM
cana-1304	89	86	0	0	NUM
cana-1304	89	87	5.43657	5.43657	NUM
cana-1304	90	1	1.71902	1.71902	NUM
cana-1304	90	2	1.71756	1.71756	NUM
cana-1304	90	3	1.71828	1.71828	NUM
cana-1304	90	4	1.71829	1.71829	NUM
cana-1304	90	5	0.2	0.2	NUM
cana-1304	90	6	0.54366	0.54366	NUM
cana-1304	90	7	4.89291	4.89291	NUM
cana-1304	90	8	1.37536	1.37536	NUM
cana-1304	90	9	1.37390	1.37390	NUM
cana-1304	90	10	1.37463	1.37463	NUM
cana-1304	90	11	1.37463	1.37463	NUM
cana-1304	90	12	0.4	0.4	NUM
cana-1304	90	13	1.087316	1.087316	NUM
cana-1304	90	14	4.34924	4.34924	NUM
cana-1304	90	15	1.03170	1.03170	NUM
cana-1304	90	16	1.03024	1.03024	NUM
cana-1304	90	17	1.03109	1.03109	NUM
cana-1304	90	18	1.03010	1.03010	NUM
cana-1304	90	19	0.6	0.6	NUM
cana-1304	90	20	1.63097	1.63097	NUM
cana-1304	90	21	3.80560	3.80560	NUM
cana-1304	90	22	0.68094	0.68094	NUM
cana-1304	90	23	0.68659	0.68659	NUM
cana-1304	90	24	0.68732	0.68732	NUM
cana-1304	90	25	0.68732	0.68732	NUM
cana-1304	90	26	0.8	0.8	NUM
cana-1304	90	27	2.17467	2.17467	NUM
cana-1304	90	28	3.26194	3.26194	NUM
cana-1304	90	29	0.33729	0.33729	NUM
cana-1304	90	30	0.34293	0.34293	NUM
cana-1304	90	31	0.34366	0.34366	NUM
cana-1304	90	32	0.34366	0.34366	NUM
cana-1304	90	33	1	1	NUM
cana-1304	90	34	2.71829	2.71829	NUM
cana-1304	90	35	2.71829	2.71829	NUM
cana-1304	90	36	0.00072	0.00072	NUM
cana-1304	90	37	0.00072	0.00072	NUM
cana-1304	90	38	0.00095	0.00095	NUM
cana-1304	90	39	0.00095	0.00095	NUM
cana-1304	90	40	the	the	DET
cana-1304	90	41	validity	validity	NOUN
cana-1304	90	42	of	of	ADP
cana-1304	90	43	the	the	DET
cana-1304	90	44	approximate	approximate	ADJ
cana-1304	90	45	values	value	NOUN
cana-1304	90	46	obtained	obtain	VERB
cana-1304	90	47	through	through	ADP
cana-1304	90	48	the	the	DET
cana-1304	90	49	rkfm	rkfm	PROPN
cana-1304	90	50	(	(	PUNCT
cana-1304	90	51	runge	runge	NOUN
cana-1304	90	52	-	-	PUNCT
cana-1304	90	53	kutta	kutta	NOUN
cana-1304	90	54	fehlberg	fehlberg	NOUN
cana-1304	90	55	method	method	NOUN
cana-1304	90	56	)	)	PUNCT
cana-1304	90	57	and	and	CCONJ
cana-1304	90	58	rh-4th	rh-4th	INTJ
cana-1304	90	59	(	(	PUNCT
cana-1304	90	60	runge	runge	NOUN
cana-1304	90	61	-	-	PUNCT
cana-1304	90	62	hutta	hutta	NOUN
cana-1304	90	63	4th	4th	ADJ
cana-1304	90	64	order	order	NOUN
cana-1304	90	65	)	)	PUNCT
cana-1304	90	66	is	be	AUX
cana-1304	90	67	substantiated	substantiate	VERB
cana-1304	90	68	in	in	ADP
cana-1304	90	69	tables	table	NOUN
cana-1304	90	70	5.1	5.1	NUM
cana-1304	90	71	,	,	PUNCT
cana-1304	90	72	wherein	wherein	SCONJ
cana-1304	90	73	these	these	DET
cana-1304	90	74	values	value	NOUN
cana-1304	90	75	are	be	AUX
cana-1304	90	76	contrasted	contrast	VERB
cana-1304	90	77	with	with	ADP
cana-1304	90	78	the	the	DET
cana-1304	90	79	exact	exact	ADJ
cana-1304	90	80	values	value	NOUN
cana-1304	90	81	presented	present	VERB
cana-1304	90	82	in	in	ADP
cana-1304	90	83	table	table	NOUN
cana-1304	90	84	5.2	5.2	NUM
cana-1304	90	85	.	.	PUNCT
cana-1304	91	1	furthermore	furthermore	ADV
cana-1304	91	2	,	,	PUNCT
cana-1304	91	3	a	a	DET
cana-1304	91	4	visual	visual	ADJ
cana-1304	91	5	representation	representation	NOUN
cana-1304	91	6	of	of	ADP
cana-1304	91	7	the	the	DET
cana-1304	91	8	comparisons	comparison	NOUN
cana-1304	91	9	is	be	AUX
cana-1304	91	10	depicted	depict	VERB
cana-1304	91	11	in	in	ADP
cana-1304	91	12	figures	figure	NOUN
cana-1304	91	13	5.1	5.1	NUM
cana-1304	91	14	and	and	CCONJ
cana-1304	91	15	5.2	5.2	NUM
cana-1304	91	16	.	.	PUNCT
cana-1304	92	1	communications	communication	NOUN
cana-1304	92	2	on	on	ADP
cana-1304	92	3	applied	apply	VERB
cana-1304	92	4	nonlinear	nonlinear	ADJ
cana-1304	92	5	analysis	analysis	NOUN
cana-1304	92	6	issn	issn	NOUN
cana-1304	92	7	:	:	PUNCT
cana-1304	92	8	1074	1074	NUM
cana-1304	92	9	-	-	PUNCT
cana-1304	92	10	133x	133x	NUM
cana-1304	92	11	vol	vol	NOUN
cana-1304	92	12	31	31	NUM
cana-1304	92	13	no	no	NOUN
cana-1304	92	14	.	.	PUNCT
cana-1304	93	1	7s	7	NOUN
cana-1304	93	2	(	(	PUNCT
cana-1304	93	3	2024	2024	NUM
cana-1304	93	4	)	)	PUNCT
cana-1304	93	5	292	292	NUM
cana-1304	93	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1304	93	7	figure	figure	NOUN
cana-1304	93	8	5.1	5.1	NUM
cana-1304	93	9	:	:	PUNCT
cana-1304	93	10	comparison	comparison	NOUN
cana-1304	93	11	between	between	ADP
cana-1304	93	12	approximate	approximate	ADJ
cana-1304	93	13	and	and	CCONJ
cana-1304	93	14	exact	exact	ADJ
cana-1304	93	15	solution	solution	NOUN
cana-1304	93	16	figure	figure	NOUN
cana-1304	93	17	5.2	5.2	NUM
cana-1304	93	18	:	:	PUNCT
cana-1304	93	19	comparision	comparision	NOUN
cana-1304	93	20	between	between	ADP
cana-1304	93	21	rkf	rkf	PROPN
cana-1304	93	22	and	and	CCONJ
cana-1304	93	23	rk4th	rk4th	NUM
cana-1304	93	24	order	order	NOUN
cana-1304	93	25	methods	method	NOUN
cana-1304	93	26	6	6	NUM
cana-1304	93	27	.	.	PUNCT
cana-1304	93	28	conclusion	conclusion	NOUN
cana-1304	93	29	in	in	ADP
cana-1304	93	30	this	this	DET
cana-1304	93	31	investigation	investigation	NOUN
cana-1304	93	32	,	,	PUNCT
cana-1304	93	33	we	we	PRON
cana-1304	93	34	scrutinize	scrutinize	VERB
cana-1304	93	35	the	the	DET
cana-1304	93	36	integration	integration	NOUN
cana-1304	93	37	of	of	ADP
cana-1304	93	38	the	the	DET
cana-1304	93	39	proposed	propose	VERB
cana-1304	93	40	runge	runge	NOUN
cana-1304	93	41	-	-	PUNCT
cana-1304	93	42	kutta	kutta	NOUN
cana-1304	93	43	fuzzy	fuzzy	ADJ
cana-1304	93	44	method	method	NOUN
cana-1304	93	45	(	(	PUNCT
cana-1304	93	46	rkfm	rkfm	NOUN
cana-1304	93	47	)	)	PUNCT
cana-1304	93	48	for	for	ADP
cana-1304	93	49	solving	solve	VERB
cana-1304	93	50	fuzzy	fuzzy	ADJ
cana-1304	93	51	delay	delay	NOUN
cana-1304	93	52	difference	difference	NOUN
cana-1304	93	53	equations	equation	NOUN
cana-1304	93	54	.	.	PUNCT
cana-1304	94	1	the	the	DET
cana-1304	94	2	assessment	assessment	NOUN
cana-1304	94	3	involves	involve	VERB
cana-1304	94	4	a	a	DET
cana-1304	94	5	numerical	numerical	ADJ
cana-1304	94	6	example	example	NOUN
cana-1304	94	7	that	that	PRON
cana-1304	94	8	demonstrates	demonstrate	VERB
cana-1304	94	9	the	the	DET
cana-1304	94	10	efficacy	efficacy	NOUN
cana-1304	94	11	of	of	ADP
cana-1304	94	12	the	the	DET
cana-1304	94	13	implemented	implement	VERB
cana-1304	94	14	approximate	approximate	ADJ
cana-1304	94	15	method	method	NOUN
cana-1304	94	16	.	.	PUNCT
cana-1304	95	1	a	a	DET
cana-1304	95	2	comparative	comparative	ADJ
cana-1304	95	3	evaluation	evaluation	NOUN
cana-1304	95	4	is	be	AUX
cana-1304	95	5	conducted	conduct	VERB
cana-1304	95	6	against	against	ADP
cana-1304	95	7	the	the	DET
cana-1304	95	8	exact	exact	ADJ
cana-1304	95	9	runge	runge	NOUN
cana-1304	95	10	-	-	PUNCT
cana-1304	95	11	kutta	kutta	NOUN
cana-1304	95	12	4th	4th	ADJ
cana-1304	95	13	-	-	PUNCT
cana-1304	95	14	order	order	NOUN
cana-1304	95	15	system	system	NOUN
cana-1304	95	16	,	,	PUNCT
cana-1304	95	17	elucidating	elucidate	VERB
cana-1304	95	18	the	the	DET
cana-1304	95	19	accuracy	accuracy	NOUN
cana-1304	95	20	of	of	ADP
cana-1304	95	21	the	the	DET
cana-1304	95	22	proposed	propose	VERB
cana-1304	95	23	rkfm	rkfm	NOUN
cana-1304	95	24	.	.	PUNCT
cana-1304	96	1	this	this	DET
cana-1304	96	2	rigorous	rigorous	ADJ
cana-1304	96	3	analysis	analysis	NOUN
cana-1304	96	4	serves	serve	VERB
cana-1304	96	5	to	to	PART
cana-1304	96	6	validate	validate	VERB
cana-1304	96	7	and	and	CCONJ
cana-1304	96	8	establish	establish	VERB
cana-1304	96	9	the	the	DET
cana-1304	96	10	stability	stability	NOUN
cana-1304	96	11	of	of	ADP
cana-1304	96	12	the	the	DET
cana-1304	96	13	rkfm	rkfm	NOUN
cana-1304	96	14	in	in	ADP
cana-1304	96	15	the	the	DET
cana-1304	96	16	context	context	NOUN
cana-1304	96	17	of	of	ADP
cana-1304	96	18	solving	solve	VERB
cana-1304	96	19	fuzzy	fuzzy	ADJ
cana-1304	96	20	delay	delay	NOUN
cana-1304	96	21	difference	difference	NOUN
cana-1304	96	22	equations	equation	NOUN
cana-1304	96	23	.	.	PUNCT
cana-1304	97	1	references	reference	NOUN
cana-1304	97	2	[	[	X
cana-1304	97	3	1	1	X
cana-1304	97	4	]	]	PUNCT
cana-1304	97	5	t.	t.	NOUN
cana-1304	97	6	allahviranloo	allahviranloo	NOUN
cana-1304	97	7	,	,	PUNCT
cana-1304	97	8	“	"	PUNCT
cana-1304	97	9	numerical	numerical	ADJ
cana-1304	97	10	methods	method	NOUN
cana-1304	97	11	for	for	ADP
cana-1304	97	12	fuzzy	fuzzy	ADJ
cana-1304	97	13	system	system	NOUN
cana-1304	97	14	of	of	ADP
cana-1304	97	15	linear	linear	PROPN
cana-1304	97	16	equation	equation	NOUN
cana-1304	97	17	”	"	PUNCT
cana-1304	97	18	,	,	PUNCT
cana-1304	97	19	applied	apply	VERB
cana-1304	97	20	mathematics	mathematic	NOUN
cana-1304	97	21	and	and	CCONJ
cana-1304	97	22	computation	computation	NOUN
cana-1304	97	23	,	,	PUNCT
cana-1304	97	24	vol	vol	NOUN
cana-1304	97	25	.	.	PROPN
cana-1304	97	26	155	155	NUM
cana-1304	97	27	,	,	PUNCT
cana-1304	97	28	493	493	NUM
cana-1304	97	29	-	-	SYM
cana-1304	97	30	502	502	NUM
cana-1304	97	31	,	,	PUNCT
cana-1304	97	32	2004	2004	NUM
cana-1304	97	33	.	.	PUNCT
cana-1304	98	1	[	[	X
cana-1304	98	2	2	2	X
cana-1304	98	3	]	]	PUNCT
cana-1304	98	4	s.	s.	PROPN
cana-1304	98	5	abbasbandy	abbasbandy	PROPN
cana-1304	98	6	,	,	PUNCT
cana-1304	98	7	t.	t.	NOUN
cana-1304	98	8	allahviranloo	allahviranloo	NOUN
cana-1304	98	9	,	,	PUNCT
cana-1304	98	10	o.	o.	PROPN
cana-1304	98	11	lopez	lopez	PROPN
cana-1304	98	12	-	-	PUNCT
cana-1304	98	13	pouso	pouso	PROPN
cana-1304	98	14	,	,	PUNCT
cana-1304	98	15	j.j	j.j	PROPN
cana-1304	98	16	.	.	PROPN
cana-1304	98	17	nieto	nieto	PROPN
cana-1304	98	18	,	,	PUNCT
cana-1304	98	19	“	"	PUNCT
cana-1304	98	20	numerical	numerical	ADJ
cana-1304	98	21	methods	method	NOUN
cana-1304	98	22	for	for	ADP
cana-1304	98	23	fuzzy	fuzzy	ADJ
cana-1304	98	24	differential	differential	ADJ
cana-1304	98	25	inclusions	inclusion	NOUN
cana-1304	98	26	”	"	PUNCT
cana-1304	98	27	,	,	PUNCT
cana-1304	98	28	journal	journal	NOUN
cana-1304	98	29	of	of	ADP
cana-1304	98	30	computer	computer	NOUN
cana-1304	98	31	and	and	CCONJ
cana-1304	98	32	mathematics	mathematic	NOUN
cana-1304	98	33	with	with	ADP
cana-1304	98	34	applications	application	NOUN
cana-1304	98	35	,	,	PUNCT
cana-1304	98	36	vol	vol	NOUN
cana-1304	98	37	.	.	PROPN
cana-1304	98	38	48	48	NUM
cana-1304	98	39	,	,	PUNCT
cana-1304	98	40	1633–1644	1633–1644	NUM
cana-1304	98	41	,	,	PUNCT
cana-1304	98	42	2004	2004	NUM
cana-1304	98	43	.	.	PUNCT
cana-1304	99	1	[	[	X
cana-1304	99	2	3	3	X
cana-1304	99	3	]	]	X
cana-1304	99	4	t.	t.	NOUN
cana-1304	99	5	allahviranloo	allahviranloo	PROPN
cana-1304	99	6	,	,	PUNCT
cana-1304	99	7	e.	e.	PROPN
cana-1304	99	8	ahmady	ahmady	PROPN
cana-1304	99	9	,	,	PUNCT
cana-1304	99	10	n.	n.	PROPN
cana-1304	99	11	ahmady	ahmady	PROPN
cana-1304	99	12	,	,	PUNCT
cana-1304	99	13	a	a	DET
cana-1304	99	14	method	method	NOUN
cana-1304	99	15	for	for	ADP
cana-1304	99	16	solving	solve	VERB
cana-1304	99	17	nth	nth	NOUN
cana-1304	99	18	order	order	NOUN
cana-1304	99	19	fuzzy	fuzzy	ADJ
cana-1304	99	20	linear	linear	ADJ
cana-1304	99	21	differential	differential	NOUN
cana-1304	99	22	equations	equation	NOUN
cana-1304	99	23	,	,	PUNCT
cana-1304	99	24	international	international	ADJ
cana-1304	99	25	journal	journal	NOUN
cana-1304	99	26	of	of	ADP
cana-1304	99	27	computer	computer	NOUN
cana-1304	99	28	mathematics	mathematic	NOUN
cana-1304	99	29	,	,	PUNCT
cana-1304	99	30	vol	vol	NOUN
cana-1304	99	31	.	.	PROPN
cana-1304	99	32	86	86	NUM
cana-1304	99	33	,	,	PUNCT
cana-1304	99	34	730	730	NUM
cana-1304	99	35	-	-	SYM
cana-1304	99	36	742	742	NUM
cana-1304	99	37	,	,	PUNCT
cana-1304	99	38	2009	2009	NUM
cana-1304	99	39	.	.	PUNCT
cana-1304	100	1	[	[	X
cana-1304	100	2	4	4	X
cana-1304	100	3	]	]	PUNCT
cana-1304	100	4	k.	k.	PROPN
cana-1304	100	5	barzinji	barzinji	PROPN
cana-1304	100	6	,	,	PUNCT
cana-1304	100	7	n.	n.	PROPN
cana-1304	100	8	maan	maan	PROPN
cana-1304	100	9	,	,	PUNCT
cana-1304	100	10	and	and	CCONJ
cana-1304	100	11	n.	n.	PROPN
cana-1304	100	12	aris	aris	PROPN
cana-1304	100	13	,	,	PUNCT
cana-1304	100	14	“	"	PUNCT
cana-1304	100	15	linear	linear	ADJ
cana-1304	100	16	fuzzy	fuzzy	ADJ
cana-1304	100	17	delay	delay	NOUN
cana-1304	100	18	differential	differential	ADJ
cana-1304	100	19	systems	system	NOUN
cana-1304	100	20	:	:	PUNCT
cana-1304	100	21	analysis	analysis	NOUN
cana-1304	100	22	a	a	DET
cana-1304	100	23	stability	stability	NOUN
cana-1304	100	24	of	of	ADP
cana-1304	100	25	steady	steady	ADJ
cana-1304	100	26	state	state	NOUN
cana-1304	100	27	,	,	PUNCT
cana-1304	100	28	”	"	PUNCT
cana-1304	100	29	matematika	matematika	NOUN
cana-1304	100	30	,	,	PUNCT
cana-1304	100	31	vol	vol	NOUN
cana-1304	100	32	.	.	PROPN
cana-1304	100	33	30	30	NUM
cana-1304	100	34	,	,	PUNCT
cana-1304	100	35	1–7	1–7	NUM
cana-1304	100	36	,	,	PUNCT
cana-1304	100	37	2014	2014	NUM
cana-1304	100	38	.	.	PUNCT
cana-1304	101	1	[	[	X
cana-1304	101	2	5	5	X
cana-1304	101	3	]	]	PUNCT
cana-1304	101	4	r.	r.	NOUN
cana-1304	101	5	bellman	bellman	PROPN
cana-1304	101	6	and	and	CCONJ
cana-1304	101	7	k.	k.	PROPN
cana-1304	101	8	l.	l.	PROPN
cana-1304	101	9	cooke	cooke	PROPN
cana-1304	101	10	,	,	PUNCT
cana-1304	101	11	differential	differential	ADJ
cana-1304	101	12	-	-	PUNCT
cana-1304	101	13	difference	difference	NOUN
cana-1304	101	14	equations	equation	NOUN
cana-1304	101	15	,	,	PUNCT
cana-1304	101	16	academic	academic	ADJ
cana-1304	101	17	press	press	NOUN
cana-1304	101	18	,	,	PUNCT
cana-1304	101	19	new	new	PROPN
cana-1304	101	20	york	york	PROPN
cana-1304	101	21	,	,	PUNCT
cana-1304	101	22	ny	ny	PROPN
cana-1304	101	23	,	,	PUNCT
cana-1304	101	24	usa	usa	PROPN
cana-1304	101	25	,	,	PUNCT
cana-1304	101	26	1963	1963	NUM
cana-1304	101	27	.	.	PUNCT
cana-1304	102	1	[	[	X
cana-1304	102	2	6	6	NUM
cana-1304	102	3	]	]	PUNCT
cana-1304	102	4	a.	a.	NOUN
cana-1304	102	5	bellen	bellen	NOUN
cana-1304	102	6	and	and	CCONJ
cana-1304	102	7	m.	m.	NOUN
cana-1304	102	8	zennaro	zennaro	PROPN
cana-1304	102	9	,	,	PUNCT
cana-1304	102	10	numerical	numerical	ADJ
cana-1304	102	11	methods	method	NOUN
cana-1304	102	12	for	for	ADP
cana-1304	102	13	delay	delay	NOUN
cana-1304	102	14	differential	differential	ADJ
cana-1304	102	15	equations	equation	NOUN
cana-1304	102	16	,	,	PUNCT
cana-1304	102	17	clarendon	clarendon	PROPN
cana-1304	102	18	press	press	NOUN
cana-1304	102	19	,	,	PUNCT
cana-1304	102	20	oxford	oxford	PROPN
cana-1304	102	21	,	,	PUNCT
cana-1304	102	22	uk	uk	PROPN
cana-1304	102	23	,	,	PUNCT
cana-1304	102	24	2003	2003	NUM
cana-1304	102	25	.	.	PUNCT
cana-1304	103	1	[	[	X
cana-1304	103	2	7	7	X
cana-1304	103	3	]	]	PUNCT
cana-1304	103	4	s.	s.	PROPN
cana-1304	103	5	l.	l.	PROPN
cana-1304	103	6	chang	chang	PROPN
cana-1304	103	7	and	and	CCONJ
cana-1304	103	8	l.	l.	PROPN
cana-1304	103	9	a.	a.	PROPN
cana-1304	103	10	zadeh	zadeh	PROPN
cana-1304	103	11	,	,	PUNCT
cana-1304	103	12	“	"	PUNCT
cana-1304	103	13	on	on	ADP
cana-1304	103	14	fuzzy	fuzzy	ADJ
cana-1304	103	15	mapping	mapping	NOUN
cana-1304	103	16	and	and	CCONJ
cana-1304	103	17	control	control	NOUN
cana-1304	103	18	”	"	PUNCT
cana-1304	103	19	,	,	PUNCT
cana-1304	103	20	ieee	ieee	NOUN
cana-1304	103	21	transactions	transaction	NOUN
cana-1304	103	22	on	on	ADP
cana-1304	103	23	systems	system	NOUN
cana-1304	103	24	,	,	PUNCT
cana-1304	103	25	man	man	NOUN
cana-1304	103	26	and	and	CCONJ
cana-1304	103	27	cybernetics	cybernetic	NOUN
cana-1304	103	28	,	,	PUNCT
cana-1304	103	29	vol	vol	NOUN
cana-1304	103	30	.	.	PROPN
cana-1304	103	31	2	2	NUM
cana-1304	103	32	,	,	PUNCT
cana-1304	103	33	no	no	INTJ
cana-1304	103	34	.	.	NOUN
cana-1304	103	35	1	1	NUM
cana-1304	103	36	,	,	PUNCT
cana-1304	103	37	pp	pp	ADJ
cana-1304	103	38	.	.	PUNCT
cana-1304	104	1	30–34	30–34	NUM
cana-1304	104	2	,	,	PUNCT
cana-1304	104	3	1972	1972	NUM
cana-1304	104	4	.	.	PUNCT
cana-1304	105	1	[	[	X
cana-1304	105	2	8	8	NUM
cana-1304	105	3	]	]	X
cana-1304	105	4	d.	d.	PROPN
cana-1304	105	5	dubois	dubois	PROPN
cana-1304	105	6	and	and	CCONJ
cana-1304	105	7	h.	h.	PROPN
cana-1304	105	8	prade	prade	PROPN
cana-1304	105	9	,	,	PUNCT
cana-1304	105	10	“	"	PUNCT
cana-1304	105	11	operations	operation	NOUN
cana-1304	105	12	on	on	ADP
cana-1304	105	13	fuzzy	fuzzy	ADJ
cana-1304	105	14	number	number	NOUN
cana-1304	105	15	,	,	PUNCT
cana-1304	105	16	”	"	PUNCT
cana-1304	105	17	international	international	ADJ
cana-1304	105	18	journal	journal	NOUN
cana-1304	105	19	of	of	ADP
cana-1304	105	20	systems	system	NOUN
cana-1304	105	21	science	science	NOUN
cana-1304	105	22	,	,	PUNCT
cana-1304	105	23	vol	vol	NOUN
cana-1304	105	24	.	.	PROPN
cana-1304	105	25	9	9	NUM
cana-1304	105	26	,	,	PUNCT
cana-1304	105	27	no	no	INTJ
cana-1304	105	28	.	.	NOUN
cana-1304	105	29	6	6	NUM
cana-1304	105	30	,	,	PUNCT
cana-1304	105	31	pp	pp	ADJ
cana-1304	105	32	.	.	PUNCT
cana-1304	106	1	613–626	613–626	NUM
cana-1304	106	2	,	,	PUNCT
cana-1304	106	3	1978	1978	NUM
cana-1304	106	4	.	.	PUNCT
cana-1304	107	1	[	[	X
cana-1304	107	2	9	9	NUM
cana-1304	107	3	]	]	X
cana-1304	107	4	r.	r.	PROPN
cana-1304	107	5	d.	d.	PROPN
cana-1304	107	6	driver	driver	PROPN
cana-1304	107	7	,	,	PUNCT
cana-1304	107	8	ordinary	ordinary	ADJ
cana-1304	107	9	and	and	CCONJ
cana-1304	107	10	delay	delay	VERB
cana-1304	107	11	differential	differential	ADJ
cana-1304	107	12	equations	equation	NOUN
cana-1304	107	13	,	,	PUNCT
cana-1304	107	14	springer	springer	NOUN
cana-1304	107	15	,	,	PUNCT
cana-1304	107	16	newyork	newyork	PROPN
cana-1304	107	17	,	,	PUNCT
cana-1304	107	18	ny	ny	PROPN
cana-1304	107	19	,	,	PUNCT
cana-1304	107	20	usa	usa	PROPN
cana-1304	107	21	,	,	PUNCT
cana-1304	107	22	1977	1977	NUM
cana-1304	107	23	.	.	PUNCT
cana-1304	108	1	[	[	X
cana-1304	108	2	10	10	NUM
cana-1304	108	3	]	]	X
cana-1304	108	4	h.	h.	PROPN
cana-1304	108	5	jafari	jafari	PROPN
cana-1304	108	6	,	,	PUNCT
cana-1304	108	7	m.	m.	NOUN
cana-1304	108	8	saeidy	saeidy	NOUN
cana-1304	108	9	,	,	PUNCT
cana-1304	108	10	and	and	CCONJ
cana-1304	108	11	d.	d.	PROPN
cana-1304	108	12	baleanu	baleanu	PROPN
cana-1304	108	13	,	,	PUNCT
cana-1304	108	14	“	"	PUNCT
cana-1304	108	15	the	the	DET
cana-1304	108	16	variational	variational	ADJ
cana-1304	108	17	iteration	iteration	NOUN
cana-1304	108	18	method	method	NOUN
cana-1304	108	19	for	for	ADP
cana-1304	108	20	solving	solve	VERB
cana-1304	108	21	n	n	CCONJ
cana-1304	108	22	-	-	PUNCT
cana-1304	108	23	th	th	VERB
cana-1304	108	24	order	order	NOUN
cana-1304	108	25	fuzzy	fuzzy	ADJ
cana-1304	108	26	differential	differential	NOUN
cana-1304	108	27	equations,”central	equations,”central	PROPN
cana-1304	108	28	european	european	ADJ
cana-1304	108	29	journal	journal	PROPN
cana-1304	108	30	of	of	ADP
cana-1304	108	31	physics	physics	PROPN
cana-1304	108	32	,	,	PUNCT
cana-1304	108	33	vol	vol	NOUN
cana-1304	108	34	.	.	PROPN
cana-1304	108	35	10	10	NUM
cana-1304	108	36	,	,	PUNCT
cana-1304	108	37	no	no	INTJ
cana-1304	108	38	.	.	NOUN
cana-1304	108	39	1	1	NUM
cana-1304	108	40	,	,	PUNCT
cana-1304	108	41	pp	pp	ADJ
cana-1304	108	42	.	.	PUNCT
cana-1304	109	1	76–85	76–85	NUM
cana-1304	109	2	,	,	PUNCT
cana-1304	109	3	2012	2012	NUM
cana-1304	109	4	.	.	PUNCT
cana-1304	110	1	[	[	X
cana-1304	110	2	11	11	NUM
cana-1304	110	3	]	]	PUNCT
cana-1304	110	4	t.	t.	NOUN
cana-1304	110	5	jayakumar	jayakumar	NOUN
cana-1304	110	6	,	,	PUNCT
cana-1304	110	7	d.maheshkumar	d.maheshkumar	PROPN
cana-1304	110	8	and	and	CCONJ
cana-1304	110	9	k.	k.	PROPN
cana-1304	110	10	kanagarajan	kanagarajan	PROPN
cana-1304	110	11	,	,	PUNCT
cana-1304	110	12	numerical	numerical	ADJ
cana-1304	110	13	solution	solution	NOUN
cana-1304	110	14	of	of	ADP
cana-1304	110	15	fuzzy	fuzzy	ADJ
cana-1304	110	16	differential	differential	ADJ
cana-1304	110	17	equations	equation	NOUN
cana-1304	110	18	by	by	ADP
cana-1304	110	19	runge	runge	VERB
cana-1304	110	20	kutta	kutta	NOUN
cana-1304	110	21	method	method	NOUN
cana-1304	110	22	of	of	ADP
cana-1304	110	23	order	order	NOUN
cana-1304	110	24	five	five	NUM
cana-1304	110	25	,	,	PUNCT
cana-1304	110	26	applied	apply	VERB
cana-1304	110	27	mathematical	mathematical	ADJ
cana-1304	110	28	sciences	science	NOUN
cana-1304	110	29	,	,	PUNCT
cana-1304	110	30	vol	vol	NOUN
cana-1304	110	31	.	.	PROPN
cana-1304	111	1	6	6	NUM
cana-1304	111	2	,	,	PUNCT
cana-1304	111	3	no	no	INTJ
cana-1304	111	4	.	.	NOUN
cana-1304	111	5	60	60	NUM
cana-1304	111	6	,	,	PUNCT
cana-1304	111	7	2989	2989	NUM
cana-1304	111	8	-	-	SYM
cana-1304	111	9	3002	3002	NUM
cana-1304	111	10	,	,	PUNCT
cana-1304	111	11	2012	2012	NUM
cana-1304	111	12	.	.	PUNCT
cana-1304	112	1	[	[	X
cana-1304	112	2	12	12	NUM
cana-1304	112	3	]	]	PUNCT
cana-1304	112	4	k.	k.	PROPN
cana-1304	113	1	kanagarajan	kanagarajan	PROPN
cana-1304	113	2	and	and	CCONJ
cana-1304	113	3	m.	m.	PROPN
cana-1304	113	4	sambath	sambath	PROPN
cana-1304	113	5	,	,	PUNCT
cana-1304	113	6	runge	runge	NOUN
cana-1304	113	7	-	-	PUNCT
cana-1304	113	8	kutta	kutta	PROPN
cana-1304	113	9	nystrom	nystrom	PROPN
cana-1304	113	10	method	method	NOUN
cana-1304	113	11	of	of	ADP
cana-1304	113	12	order	order	NOUN
cana-1304	113	13	three	three	NUM
cana-1304	113	14	for	for	ADP
cana-1304	113	15	solving	solve	VERB
cana-1304	113	16	fuzzy	fuzzy	ADJ
cana-1304	113	17	differential	differential	ADJ
cana-1304	113	18	equations	equation	NOUN
cana-1304	113	19	,	,	PUNCT
cana-1304	113	20	computational	computational	ADJ
cana-1304	113	21	methods	method	NOUN
cana-1304	113	22	in	in	ADP
cana-1304	113	23	applied	applied	ADJ
cana-1304	113	24	mathematics	mathematic	NOUN
cana-1304	113	25	,	,	PUNCT
cana-1304	113	26	vol.10	vol.10	NOUN
cana-1304	113	27	,	,	PUNCT
cana-1304	113	28	no.2	no.2	PROPN
cana-1304	113	29	,	,	PUNCT
cana-1304	113	30	195	195	NUM
cana-1304	113	31	-	-	SYM
cana-1304	113	32	203	203	NUM
cana-1304	113	33	,	,	PUNCT
cana-1304	113	34	2010	2010	NUM
cana-1304	113	35	.	.	PUNCT
cana-1304	114	1	[	[	X
cana-1304	114	2	13	13	NUM
cana-1304	114	3	]	]	PUNCT
cana-1304	114	4	a.	a.	NOUN
cana-1304	114	5	kandel	kandel	PROPN
cana-1304	114	6	,	,	PUNCT
cana-1304	114	7	j.	j.	PROPN
cana-1304	114	8	byatt	byatt	PROPN
cana-1304	114	9	,	,	PUNCT
cana-1304	114	10	fuzzy	fuzzy	ADJ
cana-1304	114	11	processes	process	NOUN
cana-1304	114	12	,	,	PUNCT
cana-1304	114	13	fuzzy	fuzzy	ADJ
cana-1304	114	14	sets	set	NOUN
cana-1304	114	15	and	and	CCONJ
cana-1304	114	16	systems	system	NOUN
cana-1304	114	17	,	,	PUNCT
cana-1304	114	18	vol	vol	NOUN
cana-1304	114	19	.	.	PROPN
cana-1304	114	20	4	4	NUM
cana-1304	114	21	,	,	PUNCT
cana-1304	114	22	117–152	117–152	NUM
cana-1304	114	23	,	,	PUNCT
cana-1304	114	24	1980	1980	NUM
cana-1304	114	25	.	.	PUNCT
cana-1304	115	1	communications	communication	NOUN
cana-1304	115	2	on	on	ADP
cana-1304	115	3	applied	apply	VERB
cana-1304	115	4	nonlinear	nonlinear	ADJ
cana-1304	115	5	analysis	analysis	NOUN
cana-1304	115	6	issn	issn	NOUN
cana-1304	115	7	:	:	PUNCT
cana-1304	115	8	1074	1074	NUM
cana-1304	115	9	-	-	PUNCT
cana-1304	115	10	133x	133x	NUM
cana-1304	115	11	vol	vol	NOUN
cana-1304	115	12	31	31	NUM
cana-1304	115	13	no	no	NOUN
cana-1304	115	14	.	.	PUNCT
cana-1304	116	1	7s	7	NOUN
cana-1304	116	2	(	(	PUNCT
cana-1304	116	3	2024	2024	NUM
cana-1304	116	4	)	)	PUNCT
cana-1304	116	5	293	293	NUM
cana-1304	116	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1304	117	1	[	[	X
cana-1304	117	2	14	14	NUM
cana-1304	117	3	]	]	PUNCT
cana-1304	117	4	a.	a.	PROPN
cana-1304	117	5	khastan	khastan	PROPN
cana-1304	117	6	,	,	PUNCT
cana-1304	117	7	j.	j.	PROPN
cana-1304	117	8	j.	j.	PROPN
cana-1304	117	9	nieto	nieto	PROPN
cana-1304	117	10	,	,	PUNCT
cana-1304	117	11	and	and	CCONJ
cana-1304	117	12	r.	r.	PROPN
cana-1304	117	13	rodr´ıguez	rodr´ıguez	PROPN
cana-1304	117	14	-	-	PUNCT
cana-1304	117	15	l´opez	l´opez	NOUN
cana-1304	117	16	,	,	PUNCT
cana-1304	117	17	“	"	PUNCT
cana-1304	117	18	fuzzy	fuzzy	ADJ
cana-1304	117	19	delay	delay	NOUN
cana-1304	117	20	differential	differential	ADJ
cana-1304	117	21	equations	equation	NOUN
cana-1304	117	22	under	under	ADP
cana-1304	117	23	generalized	generalized	ADJ
cana-1304	117	24	differentiability	differentiability	NOUN
cana-1304	117	25	,	,	PUNCT
cana-1304	117	26	”	"	PUNCT
cana-1304	117	27	information	information	NOUN
cana-1304	117	28	sciences	science	NOUN
cana-1304	117	29	,	,	PUNCT
cana-1304	117	30	vol	vol	NOUN
cana-1304	117	31	.	.	PROPN
cana-1304	117	32	275	275	NUM
cana-1304	117	33	,	,	PUNCT
cana-1304	117	34	145–167	145–167	NUM
cana-1304	117	35	,	,	PUNCT
cana-1304	117	36	2014	2014	NUM
cana-1304	117	37	.	.	PUNCT
cana-1304	118	1	[	[	X
cana-1304	118	2	15	15	NUM
cana-1304	118	3	]	]	X
cana-1304	118	4	narayanamoorthy	narayanamoorthy	ADJ
cana-1304	118	5	,	,	PUNCT
cana-1304	118	6	s.	s.	PROPN
cana-1304	118	7	,	,	PUNCT
cana-1304	118	8	and	and	CCONJ
cana-1304	118	9	t.	t.	PROPN
cana-1304	118	10	l.	l.	PROPN
cana-1304	118	11	yookesh	yookesh	PROPN
cana-1304	118	12	.	.	PUNCT
cana-1304	119	1	"	"	PUNCT
cana-1304	119	2	third	third	ADJ
cana-1304	119	3	order	order	NOUN
cana-1304	119	4	runge	runge	NOUN
cana-1304	119	5	-	-	PUNCT
cana-1304	119	6	kutta	kutta	NOUN
cana-1304	119	7	method	method	NOUN
cana-1304	119	8	for	for	ADP
cana-1304	119	9	solving	solve	VERB
cana-1304	119	10	differential	differential	ADJ
cana-1304	119	11	equation	equation	NOUN
cana-1304	119	12	in	in	ADP
cana-1304	119	13	fuzzy	fuzzy	ADJ
cana-1304	119	14	environment	environment	NOUN
cana-1304	119	15	"	"	PUNCT
cana-1304	119	16	international	international	ADJ
cana-1304	119	17	journal	journal	NOUN
cana-1304	119	18	of	of	ADP
cana-1304	119	19	pure	pure	ADJ
cana-1304	119	20	and	and	CCONJ
cana-1304	119	21	applied	applied	ADJ
cana-1304	119	22	mathematics	mathematic	NOUN
cana-1304	119	23	,	,	PUNCT
cana-1304	119	24	vol	vol	NOUN
cana-1304	119	25	.	.	PROPN
cana-1304	119	26	5	5	NUM
cana-1304	119	27	,	,	PUNCT
cana-1304	119	28	795	795	NUM
cana-1304	119	29	-	-	SYM
cana-1304	119	30	802	802	NUM
cana-1304	119	31	,	,	PUNCT
cana-1304	119	32	2015	2015	NUM
cana-1304	119	33	.	.	PUNCT
cana-1304	120	1	[	[	X
cana-1304	120	2	16	16	NUM
cana-1304	120	3	]	]	X
cana-1304	120	4	s.	s.	PROPN
cana-1304	120	5	narayanamoorthy	narayanamoorthy	PROPN
cana-1304	120	6	,	,	PUNCT
cana-1304	120	7	t.	t.	PROPN
cana-1304	120	8	l.	l.	PROPN
cana-1304	120	9	yookesh	yookesh	PROPN
cana-1304	120	10	,	,	PUNCT
cana-1304	120	11	"	"	PUNCT
cana-1304	120	12	approximate	approximate	ADJ
cana-1304	120	13	method	method	NOUN
cana-1304	120	14	for	for	ADP
cana-1304	120	15	solving	solve	VERB
cana-1304	120	16	the	the	DET
cana-1304	120	17	linear	linear	ADJ
cana-1304	120	18	fuzzy	fuzzy	ADJ
cana-1304	120	19	delay	delay	NOUN
cana-1304	120	20	differential	differential	ADJ
cana-1304	120	21	equations	equation	NOUN
cana-1304	120	22	"	"	PUNCT
cana-1304	120	23	,	,	PUNCT
cana-1304	120	24	discrete	discrete	ADJ
cana-1304	120	25	dynamics	dynamic	NOUN
cana-1304	120	26	in	in	ADP
cana-1304	120	27	nature	nature	NOUN
cana-1304	120	28	and	and	CCONJ
cana-1304	120	29	society	society	NOUN
cana-1304	120	30	,	,	PUNCT
cana-1304	120	31	vol	vol	NOUN
cana-1304	120	32	.	.	NOUN
cana-1304	120	33	2015	2015	NUM
cana-1304	120	34	,	,	PUNCT
cana-1304	120	35	9	9	NUM
cana-1304	120	36	pages	page	NOUN
cana-1304	120	37	,	,	PUNCT
cana-1304	120	38	2015	2015	NUM
cana-1304	120	39	.	.	PUNCT
cana-1304	121	1	[	[	X
cana-1304	121	2	17	17	NUM
cana-1304	121	3	]	]	X
cana-1304	121	4	v.	v.	PROPN
cana-1304	121	5	parimala	parimala	PROPN
cana-1304	121	6	,	,	PUNCT
cana-1304	121	7	p.	p.	NOUN
cana-1304	121	8	rajarajeswari	rajarajeswari	PROPN
cana-1304	121	9	,	,	PUNCT
cana-1304	121	10	v.	v.	PROPN
cana-1304	121	11	nirmala	nirmala	PROPN
cana-1304	121	12	,	,	PUNCT
cana-1304	121	13	a	a	DET
cana-1304	121	14	second	second	ADJ
cana-1304	121	15	order	order	NOUN
cana-1304	121	16	runge	runge	VERB
cana-1304	121	17	kutta	kutta	NOUN
cana-1304	121	18	method	method	NOUN
cana-1304	121	19	to	to	PART
cana-1304	121	20	solve	solve	VERB
cana-1304	121	21	fuzzy	fuzzy	ADJ
cana-1304	121	22	differential	differential	ADJ
cana-1304	121	23	equations	equation	NOUN
cana-1304	121	24	with	with	ADP
cana-1304	121	25	fuzzy	fuzzy	ADJ
cana-1304	121	26	initial	initial	ADJ
cana-1304	121	27	condition	condition	NOUN
cana-1304	121	28	international	international	ADJ
cana-1304	121	29	journal	journal	NOUN
cana-1304	121	30	of	of	ADP
cana-1304	121	31	science	science	NOUN
cana-1304	121	32	and	and	CCONJ
cana-1304	121	33	research	research	NOUN
cana-1304	121	34	(	(	PUNCT
cana-1304	121	35	ijsr	ijsr	NOUN
cana-1304	121	36	)	)	PUNCT
cana-1304	121	37	issn	issn	PROPN
cana-1304	121	38	2319	2319	NUM
cana-1304	121	39	-	-	SYM
cana-1304	121	40	7064	7064	NUM
cana-1304	121	41	.	.	PUNCT
cana-1304	122	1	[	[	X
cana-1304	122	2	18	18	NUM
cana-1304	122	3	]	]	X
cana-1304	122	4	s.	s.	PROPN
cana-1304	122	5	pederson	pederson	PROPN
cana-1304	122	6	and	and	CCONJ
cana-1304	122	7	m.	m.	PROPN
cana-1304	122	8	sambandham	sambandham	PROPN
cana-1304	122	9	,	,	PUNCT
cana-1304	122	10	the	the	DET
cana-1304	122	11	runge	runge	NOUN
cana-1304	122	12	-	-	PUNCT
cana-1304	122	13	kutta	kutta	NOUN
cana-1304	122	14	method	method	NOUN
cana-1304	122	15	for	for	ADP
cana-1304	122	16	hybrid	hybrid	ADJ
cana-1304	122	17	fuzzy	fuzzy	ADJ
cana-1304	122	18	differential	differential	NOUN
cana-1304	122	19	equations	equation	NOUN
cana-1304	122	20	,	,	PUNCT
cana-1304	122	21	nonlinear	nonlinear	ADJ
cana-1304	122	22	analysis	analysis	NOUN
cana-1304	122	23	hybrid	hybrid	NOUN
cana-1304	122	24	systems	system	NOUN
cana-1304	122	25	,	,	PUNCT
cana-1304	122	26	vol	vol	NOUN
cana-1304	122	27	.	.	PROPN
cana-1304	122	28	2	2	NUM
cana-1304	122	29	,	,	PUNCT
cana-1304	122	30	626	626	NUM
cana-1304	122	31	-	-	SYM
cana-1304	122	32	634	634	NUM
cana-1304	122	33	,	,	PUNCT
cana-1304	122	34	2008	2008	NUM
cana-1304	122	35	.	.	PUNCT
cana-1304	123	1	[	[	X
cana-1304	123	2	19	19	NUM
cana-1304	123	3	]	]	X
cana-1304	123	4	s.	s.	PROPN
cana-1304	123	5	seikkala	seikkala	PROPN
cana-1304	123	6	,	,	PUNCT
cana-1304	123	7	on	on	ADP
cana-1304	123	8	the	the	DET
cana-1304	123	9	fuzzy	fuzzy	ADJ
cana-1304	123	10	initial	initial	ADJ
cana-1304	123	11	value	value	NOUN
cana-1304	123	12	problem	problem	NOUN
cana-1304	123	13	,	,	PUNCT
cana-1304	123	14	fuzzy	fuzzy	ADJ
cana-1304	123	15	set	set	NOUN
cana-1304	123	16	and	and	CCONJ
cana-1304	123	17	system	system	NOUN
cana-1304	123	18	,	,	PUNCT
cana-1304	123	19	24	24	NUM
cana-1304	123	20	,	,	PUNCT
cana-1304	123	21	319	319	NUM
cana-1304	123	22	-	-	SYM
cana-1304	123	23	330	330	NUM
cana-1304	123	24	,	,	PUNCT
cana-1304	123	25	1987	1987	NUM
cana-1304	123	26	.	.	PUNCT
cana-1304	124	1	[	[	X
cana-1304	124	2	20	20	NUM
cana-1304	124	3	]	]	X
cana-1304	124	4	suha	suha	PROPN
cana-1304	124	5	najeeb	najeeb	PROPN
cana-1304	124	6	al	al	PROPN
cana-1304	124	7	rawi	rawi	PROPN
cana-1304	124	8	,	,	PUNCT
cana-1304	124	9	raghad	raghad	VERB
cana-1304	124	10	kadhim	kadhim	PROPN
cana-1304	124	11	salih	salih	PROPN
cana-1304	124	12	,	,	PUNCT
cana-1304	124	13	amaal	amaal	PROPN
cana-1304	124	14	ali	ali	PROPN
cana-1304	124	15	mohammed	mohammed	PROPN
cana-1304	124	16	,	,	PUNCT
cana-1304	124	17	numerical	numerical	ADJ
cana-1304	124	18	solution	solution	NOUN
cana-1304	124	19	of	of	ADP
cana-1304	124	20	n	n	PRON
cana-1304	124	21	th	th	X
cana-1304	124	22	order	order	NOUN
cana-1304	124	23	linear	linear	PROPN
cana-1304	124	24	delay	delay	NOUN
cana-1304	124	25	differential	differential	NOUN
cana-1304	124	26	equation	equation	NOUN
cana-1304	124	27	using	use	VERB
cana-1304	124	28	runge	runge	NOUN
cana-1304	124	29	-	-	PUNCT
cana-1304	124	30	kutta	kutta	NOUN
cana-1304	124	31	method	method	NOUN
cana-1304	124	32	,	,	PUNCT
cana-1304	124	33	um	um	INTJ
cana-1304	124	34	salama	salama	PROPN
cana-1304	124	35	science	science	PROPN
cana-1304	124	36	journal	journal	PROPN
cana-1304	124	37	,	,	PUNCT
cana-1304	124	38	vol	vol	NOUN
cana-1304	124	39	.	.	PUNCT
cana-1304	124	40	3(1	3(1	NUM
cana-1304	124	41	)	)	PUNCT
cana-1304	124	42	,	,	PUNCT
cana-1304	124	43	140	140	NUM
cana-1304	124	44	-	-	SYM
cana-1304	124	45	146	146	NUM
cana-1304	124	46	,	,	PUNCT
cana-1304	124	47	2006	2006	NUM
cana-1304	124	48	.	.	PUNCT
cana-1304	125	1	[	[	X
cana-1304	125	2	21	21	NUM
cana-1304	125	3	]	]	X
cana-1304	125	4	l.	l.	PROPN
cana-1304	125	5	a.	a.	PROPN
cana-1304	125	6	zadeh	zadeh	PROPN
cana-1304	125	7	,	,	PUNCT
cana-1304	125	8	“	"	PUNCT
cana-1304	125	9	fuzzy	fuzzy	ADJ
cana-1304	125	10	sets	set	NOUN
cana-1304	125	11	,	,	PUNCT
cana-1304	125	12	”	"	PUNCT
cana-1304	125	13	information	information	NOUN
cana-1304	125	14	and	and	CCONJ
cana-1304	125	15	control	control	NOUN
cana-1304	125	16	,	,	PUNCT
cana-1304	125	17	vol	vol	NOUN
cana-1304	125	18	.	.	PROPN
cana-1304	125	19	8	8	NUM
cana-1304	125	20	,	,	PUNCT
cana-1304	125	21	no	no	INTJ
cana-1304	125	22	.	.	NOUN
cana-1304	125	23	3	3	NUM
cana-1304	125	24	,	,	PUNCT
cana-1304	125	25	pp	pp	ADJ
cana-1304	125	26	.	.	PUNCT
cana-1304	126	1	338–353	338–353	NUM
cana-1304	126	2	,	,	PUNCT
cana-1304	126	3	1965	1965	NUM
cana-1304	126	4	.	.	PUNCT