id	sid	tid	token	lemma	pos
iajs-3033	1	1	ihjpas	ihjpas	PROPN
iajs-3033	1	2	.	.	PUNCT
iajs-3033	2	1	36	36	NUM
iajs-3033	2	2	(	(	PUNCT
iajs-3033	2	3	3	3	NUM
iajs-3033	2	4	)	)	PUNCT
iajs-3033	2	5	2023	2023	NUM
iajs-3033	2	6	416	416	NUM
iajs-3033	2	7	this	this	DET
iajs-3033	2	8	work	work	NOUN
iajs-3033	2	9	is	be	AUX
iajs-3033	2	10	licensed	license	VERB
iajs-3033	2	11	under	under	ADP
iajs-3033	2	12	a	a	DET
iajs-3033	2	13	creative	creative	ADJ
iajs-3033	2	14	commons	common	NOUN
iajs-3033	2	15	attribution	attribution	NOUN
iajs-3033	2	16	4.0	4.0	NUM
iajs-3033	2	17	international	international	ADJ
iajs-3033	2	18	license	license	NOUN
iajs-3033	2	19	*	*	PUNCT
iajs-3033	2	20	corresponding	correspond	VERB
iajs-3033	2	21	author	author	NOUN
iajs-3033	2	22	:	:	PUNCT
iajs-3033	2	23	mohammeds.abed@uokufa.edu.iq	mohammeds.abed@uokufa.edu.iq	ADJ
iajs-3033	2	24	abstract	abstract	ADV
iajs-3033	2	25	this	this	DET
iajs-3033	2	26	paper	paper	NOUN
iajs-3033	2	27	sheds	shed	VERB
iajs-3033	2	28	light	light	NOUN
iajs-3033	2	29	on	on	ADP
iajs-3033	2	30	the	the	DET
iajs-3033	2	31	vital	vital	ADJ
iajs-3033	2	32	role	role	NOUN
iajs-3033	2	33	that	that	PRON
iajs-3033	2	34	fractional	fractional	ADJ
iajs-3033	2	35	ordinary	ordinary	ADJ
iajs-3033	2	36	differential	differential	ADJ
iajs-3033	2	37	equations	equation	NOUN
iajs-3033	2	38	(	(	PUNCT
iajs-3033	2	39	fodes	fode	NOUN
iajs-3033	2	40	)	)	PUNCT
iajs-3033	2	41	play	play	NOUN
iajs-3033	2	42	in	in	ADP
iajs-3033	2	43	mathematical	mathematical	ADJ
iajs-3033	2	44	modeling	modeling	NOUN
iajs-3033	2	45	and	and	CCONJ
iajs-3033	2	46	in	in	ADP
iajs-3033	2	47	real	real	ADJ
iajs-3033	2	48	life	life	NOUN
iajs-3033	2	49	,	,	PUNCT
iajs-3033	2	50	particularly	particularly	ADV
iajs-3033	2	51	in	in	ADP
iajs-3033	2	52	physical	physical	ADJ
iajs-3033	2	53	conditions	condition	NOUN
iajs-3033	2	54	.	.	PUNCT
iajs-3033	3	1	furthermore	furthermore	ADV
iajs-3033	3	2	,	,	PUNCT
iajs-3033	3	3	if	if	SCONJ
iajs-3033	3	4	the	the	DET
iajs-3033	3	5	problem	problem	NOUN
iajs-3033	3	6	is	be	AUX
iajs-3033	3	7	handled	handle	VERB
iajs-3033	3	8	directly	directly	ADV
iajs-3033	3	9	using	use	VERB
iajs-3033	3	10	the	the	DET
iajs-3033	3	11	numerical	numerical	ADJ
iajs-3033	3	12	method	method	NOUN
iajs-3033	3	13	,	,	PUNCT
iajs-3033	3	14	it	it	PRON
iajs-3033	3	15	is	be	AUX
iajs-3033	3	16	a	a	DET
iajs-3033	3	17	far	far	ADV
iajs-3033	3	18	more	more	ADV
iajs-3033	3	19	powerful	powerful	ADJ
iajs-3033	3	20	and	and	CCONJ
iajs-3033	3	21	efficient	efficient	ADJ
iajs-3033	3	22	numerical	numerical	ADJ
iajs-3033	3	23	method	method	NOUN
iajs-3033	3	24	in	in	ADP
iajs-3033	3	25	terms	term	NOUN
iajs-3033	3	26	of	of	ADP
iajs-3033	3	27	computational	computational	ADJ
iajs-3033	3	28	time	time	NOUN
iajs-3033	3	29	,	,	PUNCT
iajs-3033	3	30	number	number	NOUN
iajs-3033	3	31	of	of	ADP
iajs-3033	3	32	function	function	NOUN
iajs-3033	3	33	evaluations	evaluation	NOUN
iajs-3033	3	34	,	,	PUNCT
iajs-3033	3	35	and	and	CCONJ
iajs-3033	3	36	precision	precision	NOUN
iajs-3033	3	37	.	.	PUNCT
iajs-3033	4	1	in	in	ADP
iajs-3033	4	2	this	this	DET
iajs-3033	4	3	paper	paper	NOUN
iajs-3033	4	4	,	,	PUNCT
iajs-3033	4	5	we	we	PRON
iajs-3033	4	6	concentrate	concentrate	VERB
iajs-3033	4	7	on	on	ADP
iajs-3033	4	8	the	the	DET
iajs-3033	4	9	derivation	derivation	NOUN
iajs-3033	4	10	of	of	ADP
iajs-3033	4	11	the	the	DET
iajs-3033	4	12	direct	direct	ADJ
iajs-3033	4	13	numerical	numerical	ADJ
iajs-3033	4	14	methods	method	NOUN
iajs-3033	4	15	for	for	ADP
iajs-3033	4	16	solving	solve	VERB
iajs-3033	4	17	fifthorder	fifthorder	NOUN
iajs-3033	4	18	fodes	fode	NOUN
iajs-3033	4	19	n	n	PRON
iajs-3033	4	20	one	one	NUM
iajs-3033	4	21	,	,	PUNCT
iajs-3033	4	22	two	two	NUM
iajs-3033	4	23	,	,	PUNCT
iajs-3033	4	24	and	and	CCONJ
iajs-3033	4	25	three	three	NUM
iajs-3033	4	26	stages	stage	NOUN
iajs-3033	4	27	.	.	PUNCT
iajs-3033	5	1	additionally	additionally	ADV
iajs-3033	5	2	,	,	PUNCT
iajs-3033	5	3	it	it	PRON
iajs-3033	5	4	is	be	AUX
iajs-3033	5	5	important	important	ADJ
iajs-3033	5	6	to	to	PART
iajs-3033	5	7	note	note	VERB
iajs-3033	5	8	that	that	SCONJ
iajs-3033	5	9	the	the	DET
iajs-3033	5	10	rkmnumerical	rkmnumerical	ADJ
iajs-3033	5	11	methods	method	NOUN
iajs-3033	5	12	with	with	ADP
iajs-3033	5	13	twoand	twoand	NOUN
iajs-3033	5	14	three	three	NUM
iajs-3033	5	15	-	-	PUNCT
iajs-3033	5	16	stages	stage	NOUN
iajs-3033	5	17	for	for	ADP
iajs-3033	5	18	solving	solve	VERB
iajs-3033	5	19	fifth	fifth	ADJ
iajs-3033	5	20	-	-	PUNCT
iajs-3033	5	21	order	order	NOUN
iajs-3033	5	22	odes	ode	NOUN
iajs-3033	5	23	are	be	AUX
iajs-3033	5	24	convenient	convenient	ADJ
iajs-3033	5	25	.	.	PUNCT
iajs-3033	6	1	numerical	numerical	ADJ
iajs-3033	6	2	examples	example	NOUN
iajs-3033	6	3	have	have	AUX
iajs-3033	6	4	been	be	AUX
iajs-3033	6	5	analyzed	analyze	VERB
iajs-3033	6	6	to	to	PART
iajs-3033	6	7	demonstrate	demonstrate	VERB
iajs-3033	6	8	the	the	DET
iajs-3033	6	9	efficacy	efficacy	NOUN
iajs-3033	6	10	of	of	ADP
iajs-3033	6	11	the	the	DET
iajs-3033	6	12	new	new	ADJ
iajs-3033	6	13	methods	method	NOUN
iajs-3033	6	14	in	in	ADP
iajs-3033	6	15	comparison	comparison	NOUN
iajs-3033	6	16	to	to	ADP
iajs-3033	6	17	the	the	DET
iajs-3033	6	18	analytical	analytical	ADJ
iajs-3033	6	19	method	method	NOUN
iajs-3033	6	20	.	.	PUNCT
iajs-3033	7	1	therefore	therefore	ADV
iajs-3033	7	2	,	,	PUNCT
iajs-3033	7	3	the	the	DET
iajs-3033	7	4	numerical	numerical	ADJ
iajs-3033	7	5	compression	compression	NOUN
iajs-3033	7	6	is	be	AUX
iajs-3033	7	7	carried	carry	VERB
iajs-3033	7	8	out	out	ADP
iajs-3033	7	9	to	to	PART
iajs-3033	7	10	confirm	confirm	VERB
iajs-3033	7	11	the	the	DET
iajs-3033	7	12	efficiency	efficiency	NOUN
iajs-3033	7	13	and	and	CCONJ
iajs-3033	7	14	precision	precision	NOUN
iajs-3033	7	15	of	of	ADP
iajs-3033	7	16	the	the	DET
iajs-3033	7	17	modified	modify	VERB
iajs-3033	7	18	numerical	numerical	ADJ
iajs-3033	7	19	methods	method	NOUN
iajs-3033	7	20	.	.	PUNCT
iajs-3033	8	1	significantly	significantly	ADV
iajs-3033	8	2	,	,	PUNCT
iajs-3033	8	3	the	the	DET
iajs-3033	8	4	study	study	NOUN
iajs-3033	8	5	demonstrates	demonstrate	VERB
iajs-3033	8	6	that	that	SCONJ
iajs-3033	8	7	the	the	DET
iajs-3033	8	8	numerical	numerical	ADJ
iajs-3033	8	9	outcomes	outcome	NOUN
iajs-3033	8	10	of	of	ADP
iajs-3033	8	11	the	the	DET
iajs-3033	8	12	proposed	propose	VERB
iajs-3033	8	13	derived	derive	VERB
iajs-3033	8	14	and	and	CCONJ
iajs-3033	8	15	modified	modify	VERB
iajs-3033	8	16	numerically	numerically	ADV
iajs-3033	8	17	applied	apply	VERB
iajs-3033	8	18	methods	method	NOUN
iajs-3033	8	19	proved	prove	VERB
iajs-3033	8	20	to	to	PART
iajs-3033	8	21	be	be	AUX
iajs-3033	8	22	brilliant	brilliant	ADJ
iajs-3033	8	23	.	.	PUNCT
iajs-3033	9	1	finally	finally	ADV
iajs-3033	9	2	,	,	PUNCT
iajs-3033	9	3	based	base	VERB
iajs-3033	9	4	on	on	ADP
iajs-3033	9	5	the	the	DET
iajs-3033	9	6	findings	finding	NOUN
iajs-3033	9	7	of	of	ADP
iajs-3033	9	8	the	the	DET
iajs-3033	9	9	study	study	NOUN
iajs-3033	9	10	,	,	PUNCT
iajs-3033	9	11	it	it	PRON
iajs-3033	9	12	could	could	AUX
iajs-3033	9	13	be	be	AUX
iajs-3033	9	14	said	say	VERB
iajs-3033	9	15	that	that	SCONJ
iajs-3033	9	16	the	the	DET
iajs-3033	9	17	numerical	numerical	ADJ
iajs-3033	9	18	outcomes	outcome	NOUN
iajs-3033	9	19	of	of	ADP
iajs-3033	9	20	the	the	DET
iajs-3033	9	21	test	test	NOUN
iajs-3033	9	22	-	-	PUNCT
iajs-3033	9	23	problems	problem	NOUN
iajs-3033	9	24	using	use	VERB
iajs-3033	9	25	the	the	DET
iajs-3033	9	26	proposed	propose	VERB
iajs-3033	9	27	and	and	CCONJ
iajs-3033	9	28	modified	modified	ADJ
iajs-3033	9	29	methods	method	NOUN
iajs-3033	9	30	agree	agree	VERB
iajs-3033	9	31	well	well	ADV
iajs-3033	9	32	with	with	ADP
iajs-3033	9	33	the	the	DET
iajs-3033	9	34	analytical	analytical	ADJ
iajs-3033	9	35	solutions	solution	NOUN
iajs-3033	9	36	.	.	PUNCT
iajs-3033	10	1	hence	hence	ADV
iajs-3033	10	2	,	,	PUNCT
iajs-3033	10	3	we	we	PRON
iajs-3033	10	4	can	can	AUX
iajs-3033	10	5	conclude	conclude	VERB
iajs-3033	10	6	that	that	SCONJ
iajs-3033	10	7	the	the	DET
iajs-3033	10	8	proposed	propose	VERB
iajs-3033	10	9	numerical	numerical	ADJ
iajs-3033	10	10	methods	method	NOUN
iajs-3033	10	11	that	that	PRON
iajs-3033	10	12	are	be	AUX
iajs-3033	10	13	derived	derive	VERB
iajs-3033	10	14	or	or	CCONJ
iajs-3033	10	15	modified	modify	VERB
iajs-3033	10	16	in	in	ADP
iajs-3033	10	17	the	the	DET
iajs-3033	10	18	analytic	analytic	ADJ
iajs-3033	10	19	study	study	NOUN
iajs-3033	10	20	of	of	ADP
iajs-3033	10	21	this	this	DET
iajs-3033	10	22	paper	paper	NOUN
iajs-3033	10	23	are	be	AUX
iajs-3033	10	24	quite	quite	ADV
iajs-3033	10	25	efficient	efficient	ADJ
iajs-3033	10	26	.	.	PUNCT
iajs-3033	11	1	keywords	keyword	VERB
iajs-3033	11	2	rkm	rkm	NOUN
iajs-3033	11	3	;	;	PUNCT
iajs-3033	11	4	fractional	fractional	ADJ
iajs-3033	11	5	ordinary	ordinary	ADJ
iajs-3033	11	6	differential	differential	ADJ
iajs-3033	11	7	equations	equation	NOUN
iajs-3033	11	8	;	;	PUNCT
iajs-3033	11	9	fifthorder	fifthorder	NOUN
iajs-3033	11	10	;	;	PUNCT
iajs-3033	11	11	des	des	X
iajs-3033	11	12	;	;	PUNCT
iajs-3033	11	13	fdes	fde	NOUN
iajs-3033	11	14	.	.	PUNCT
iajs-3033	12	1	1	1	X
iajs-3033	12	2	.	.	X
iajs-3033	12	3	introduction	introduction	NOUN
iajs-3033	12	4	undoubtedly	undoubtedly	ADV
iajs-3033	12	5	,	,	PUNCT
iajs-3033	12	6	the	the	DET
iajs-3033	12	7	fractional	fractional	ADJ
iajs-3033	12	8	differential	differential	ADJ
iajs-3033	12	9	equation	equation	NOUN
iajs-3033	12	10	(	(	PUNCT
iajs-3033	12	11	fde	fde	NOUN
iajs-3033	12	12	)	)	PUNCT
iajs-3033	12	13	is	be	AUX
iajs-3033	12	14	considered	consider	VERB
iajs-3033	12	15	the	the	DET
iajs-3033	12	16	most	most	ADV
iajs-3033	12	17	essential	essential	ADJ
iajs-3033	12	18	tool	tool	NOUN
iajs-3033	12	19	of	of	ADP
iajs-3033	12	20	mathematics	mathematic	NOUN
iajs-3033	12	21	,	,	PUNCT
iajs-3033	12	22	with	with	ADP
iajs-3033	12	23	applications	application	NOUN
iajs-3033	12	24	in	in	ADP
iajs-3033	12	25	engineering	engineering	NOUN
iajs-3033	12	26	and	and	CCONJ
iajs-3033	12	27	science	science	NOUN
iajs-3033	12	28	.	.	PUNCT
iajs-3033	13	1	in	in	ADP
iajs-3033	13	2	addition	addition	NOUN
iajs-3033	13	3	to	to	ADP
iajs-3033	13	4	the	the	DET
iajs-3033	13	5	significant	significant	ADJ
iajs-3033	13	6	part	part	NOUN
iajs-3033	13	7	the	the	DET
iajs-3033	13	8	fde	fde	PROPN
iajs-3033	13	9	has	have	AUX
iajs-3033	13	10	concerning	concern	VERB
iajs-3033	13	11	the	the	DET
iajs-3033	13	12	various	various	ADJ
iajs-3033	13	13	branches	branch	NOUN
iajs-3033	13	14	of	of	ADP
iajs-3033	13	15	applied	apply	VERB
iajs-3033	13	16	mathematics	mathematic	NOUN
iajs-3033	13	17	,	,	PUNCT
iajs-3033	13	18	including	include	VERB
iajs-3033	13	19	physics	physics	NOUN
iajs-3033	13	20	,	,	PUNCT
iajs-3033	13	21	economics	economic	NOUN
iajs-3033	13	22	,	,	PUNCT
iajs-3033	13	23	chemistry	chemistry	NOUN
iajs-3033	13	24	,	,	PUNCT
iajs-3033	13	25	engineering	engineering	NOUN
iajs-3033	13	26	,	,	PUNCT
iajs-3033	13	27	medicine	medicine	NOUN
iajs-3033	13	28	,	,	PUNCT
iajs-3033	13	29	and	and	CCONJ
iajs-3033	13	30	biology	biology	NOUN
iajs-3033	13	31	,	,	PUNCT
iajs-3033	13	32	it	it	PRON
iajs-3033	13	33	is	be	AUX
iajs-3033	13	34	to	to	PART
iajs-3033	13	35	be	be	AUX
iajs-3033	13	36	noted	note	VERB
iajs-3033	13	37	that	that	SCONJ
iajs-3033	13	38	the	the	DET
iajs-3033	13	39	larger	large	ADJ
iajs-3033	13	40	part	part	NOUN
iajs-3033	13	41	of	of	ADP
iajs-3033	13	42	mathematical	mathematical	ADJ
iajs-3033	13	43	modeling	modeling	NOUN
iajs-3033	13	44	in	in	ADP
iajs-3033	13	45	engineering	engineering	NOUN
iajs-3033	13	46	and	and	CCONJ
iajs-3033	13	47	science	science	NOUN
iajs-3033	13	48	is	be	AUX
iajs-3033	13	49	related	relate	VERB
iajs-3033	13	50	to	to	ADP
iajs-3033	13	51	different	different	ADJ
iajs-3033	13	52	kinds	kind	NOUN
iajs-3033	13	53	of	of	ADP
iajs-3033	13	54	fdes	fde	NOUN
iajs-3033	13	55	.	.	PUNCT
iajs-3033	14	1	moreover	moreover	ADV
iajs-3033	14	2	,	,	PUNCT
iajs-3033	14	3	solving	solve	VERB
iajs-3033	14	4	the	the	DET
iajs-3033	14	5	doi.org/10.30526/36.3.3033	doi.org/10.30526/36.3.3033	ADJ
iajs-3033	14	6	article	article	NOUN
iajs-3033	14	7	history	history	NOUN
iajs-3033	14	8	:	:	PUNCT
iajs-3033	14	9	received	receive	VERB
iajs-3033	14	10	22	22	NUM
iajs-3033	14	11	september	september	PROPN
iajs-3033	14	12	2022	2022	NUM
iajs-3033	14	13	,	,	PUNCT
iajs-3033	14	14	accepted	accept	VERB
iajs-3033	14	15	23	23	NUM
iajs-3033	14	16	october	october	NOUN
iajs-3033	14	17	2022	2022	NUM
iajs-3033	14	18	,	,	PUNCT
iajs-3033	14	19	published	publish	VERB
iajs-3033	14	20	in	in	ADP
iajs-3033	14	21	july	july	PROPN
iajs-3033	14	22	2023	2023	NUM
iajs-3033	14	23	.	.	PUNCT
iajs-3033	15	1	ibn	ibn	PROPN
iajs-3033	15	2	al	al	PROPN
iajs-3033	15	3	-	-	PUNCT
iajs-3033	15	4	haitham	haitham	PROPN
iajs-3033	15	5	journal	journal	PROPN
iajs-3033	15	6	for	for	ADP
iajs-3033	15	7	pure	pure	ADJ
iajs-3033	15	8	and	and	CCONJ
iajs-3033	15	9	applied	applied	ADJ
iajs-3033	15	10	sciences	sciences	PROPN
iajs-3033	15	11	journal	journal	PROPN
iajs-3033	15	12	homepage	homepage	NOUN
iajs-3033	15	13	:	:	PUNCT
iajs-3033	15	14	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	NOUN
iajs-3033	15	15	constructing	construct	VERB
iajs-3033	15	16	rkm	rkm	NOUN
iajs-3033	15	17	-	-	NOUN
iajs-3033	15	18	method	method	NOUN
iajs-3033	15	19	for	for	ADP
iajs-3033	15	20	solving	solve	VERB
iajs-3033	15	21	fractional	fractional	ADJ
iajs-3033	15	22	ordinary	ordinary	ADJ
iajs-3033	15	23	differential	differential	ADJ
iajs-3033	15	24	equations	equation	NOUN
iajs-3033	15	25	of	of	ADP
iajs-3033	15	26	fifth	fifth	ADJ
iajs-3033	15	27	-	-	PUNCT
iajs-3033	15	28	order	order	NOUN
iajs-3033	15	29	with	with	ADP
iajs-3033	15	30	applications	application	NOUN
iajs-3033	15	31	*	*	PUNCT
iajs-3033	15	32	mohammed	mohammed	PROPN
iajs-3033	15	33	s.	s.	PROPN
iajs-3033	15	34	mechee	mechee	PROPN
iajs-3033	15	35	information	information	NOUN
iajs-3033	15	36	technology	technology	NOUN
iajs-3033	15	37	research	research	NOUN
iajs-3033	15	38	and	and	CCONJ
iajs-3033	15	39	development	development	NOUN
iajs-3033	15	40	center	center	NOUN
iajs-3033	15	41	(	(	PUNCT
iajs-3033	15	42	itrdc	itrdc	NOUN
iajs-3033	15	43	)	)	PUNCT
iajs-3033	15	44	,	,	PUNCT
iajs-3033	15	45	uok	uok	NOUN
iajs-3033	15	46	,	,	PUNCT
iajs-3033	15	47	najaf	najaf	PROPN
iajs-3033	15	48	,	,	PUNCT
iajs-3033	15	49	iraq	iraq	PROPN
iajs-3033	15	50	.	.	PUNCT
iajs-3033	16	1	mohammeds.abed@uokufa.edu.iq	mohammeds.abed@uokufa.edu.iq	PROPN
iajs-3033	16	2	sameeah	sameeah	PROPN
iajs-3033	16	3	h.	h.	PROPN
iajs-3033	16	4	aidi	aidi	PROPN
iajs-3033	16	5	department	department	PROPN
iajs-3033	16	6	of	of	ADP
iajs-3033	16	7	mathematics	mathematics	PROPN
iajs-3033	16	8	,	,	PUNCT
iajs-3033	16	9	college	college	NOUN
iajs-3033	16	10	of	of	ADP
iajs-3033	16	11	education	education	NOUN
iajs-3033	16	12	for	for	ADP
iajs-3033	16	13	for	for	ADP
iajs-3033	16	14	pure	pure	ADJ
iajs-3033	16	15	science	science	NOUN
iajs-3033	16	16	,	,	PUNCT
iajs-3033	16	17	ibn	ibn	PROPN
iajs-3033	16	18	al	al	PROPN
iajs-3033	16	19	-	-	PUNCT
iajs-3033	16	20	haytham	haytham	PROPN
iajs-3033	16	21	,	,	PUNCT
iajs-3033	16	22	university	university	NOUN
iajs-3033	16	23	of	of	ADP
iajs-3033	16	24	baghdad	baghdad	PROPN
iajs-3033	16	25	,	,	PUNCT
iajs-3033	16	26	baghdad	baghdad	PROPN
iajs-3033	16	27	,	,	PUNCT
iajs-3033	16	28	iraq	iraq	PROPN
iajs-3033	16	29	.	.	PUNCT
iajs-3033	17	1	sameeahaidi9@gmail.com	sameeahaidi9@gmail.com	X
iajs-3033	17	2	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3033	17	3	mailto:mohammeds.abed@uokufa.edu.iq	mailto:mohammeds.abed@uokufa.edu.iq	PROPN
iajs-3033	17	4	mailto:mohammeds.abed@uokufa.edu.iq	mailto:mohammeds.abed@uokufa.edu.iq	PROPN
iajs-3033	17	5	mailto:mohammeds.abed@uokufa.edu.iq	mailto:mohammeds.abed@uokufa.edu.iq	PROPN
iajs-3033	17	6	http://en.uobaghdad.edu.iq/?page_id=15060	http://en.uobaghdad.edu.iq/?page_id=15060	NOUN
iajs-3033	17	7	http://en.uobaghdad.edu.iq/?page_id=15060	http://en.uobaghdad.edu.iq/?page_id=15060	NOUN
iajs-3033	17	8	mailto:sameeahaidi9@gmail.com	mailto:sameeahaidi9@gmail.com	X
iajs-3033	17	9	mailto:sameeahaidi9@gmail.com	mailto:sameeahaidi9@gmail.com	X
iajs-3033	17	10	ihjpas	ihjpas	PROPN
iajs-3033	17	11	.	.	PUNCT
iajs-3033	18	1	36	36	NUM
iajs-3033	18	2	(	(	PUNCT
iajs-3033	18	3	3	3	NUM
iajs-3033	18	4	)	)	PUNCT
iajs-3033	18	5	2023	2023	NUM
iajs-3033	18	6	417	417	NUM
iajs-3033	18	7	real	real	ADJ
iajs-3033	18	8	problems	problem	NOUN
iajs-3033	18	9	that	that	PRON
iajs-3033	18	10	might	might	AUX
iajs-3033	18	11	occur	occur	VERB
iajs-3033	18	12	in	in	ADP
iajs-3033	18	13	applied	apply	VERB
iajs-3033	18	14	science	science	NOUN
iajs-3033	18	15	and	and	CCONJ
iajs-3033	18	16	engineering	engineering	NOUN
iajs-3033	18	17	is	be	AUX
iajs-3033	18	18	conducted	conduct	VERB
iajs-3033	18	19	by	by	ADP
iajs-3033	18	20	utilizing	utilize	VERB
iajs-3033	18	21	the	the	DET
iajs-3033	18	22	mathematical	mathematical	ADJ
iajs-3033	18	23	methods	method	NOUN
iajs-3033	18	24	and	and	CCONJ
iajs-3033	18	25	tools	tool	NOUN
iajs-3033	18	26	of	of	ADP
iajs-3033	18	27	fdes	fde	NOUN
iajs-3033	18	28	.	.	PUNCT
iajs-3033	19	1	in	in	ADP
iajs-3033	19	2	the	the	DET
iajs-3033	19	3	last	last	ADJ
iajs-3033	19	4	thirty	thirty	NUM
iajs-3033	19	5	years	year	NOUN
iajs-3033	19	6	,	,	PUNCT
iajs-3033	19	7	numerous	numerous	ADJ
iajs-3033	19	8	significant	significant	ADJ
iajs-3033	19	9	studies	study	NOUN
iajs-3033	19	10	in	in	ADP
iajs-3033	19	11	fractional	fractional	ADJ
iajs-3033	19	12	calculus	calculus	NOUN
iajs-3033	19	13	(	(	PUNCT
iajs-3033	19	14	fc	fc	INTJ
iajs-3033	19	15	)	)	PUNCT
iajs-3033	19	16	have	have	AUX
iajs-3033	19	17	been	be	AUX
iajs-3033	19	18	published	publish	VERB
iajs-3033	19	19	in	in	ADP
iajs-3033	19	20	the	the	DET
iajs-3033	19	21	science	science	NOUN
iajs-3033	19	22	and	and	CCONJ
iajs-3033	19	23	engineering	engineering	NOUN
iajs-3033	19	24	literature	literature	NOUN
iajs-3033	19	25	.	.	PUNCT
iajs-3033	20	1	the	the	DET
iajs-3033	20	2	development	development	NOUN
iajs-3033	20	3	of	of	ADP
iajs-3033	20	4	fc	fc	PROPN
iajs-3033	20	5	is	be	AUX
iajs-3033	20	6	detailed	detail	VERB
iajs-3033	20	7	in	in	ADP
iajs-3033	20	8	different	different	ADJ
iajs-3033	20	9	usages	usage	NOUN
iajs-3033	20	10	in	in	ADP
iajs-3033	20	11	fluid	fluid	ADJ
iajs-3033	20	12	mechanics	mechanic	NOUN
iajs-3033	20	13	studies	study	NOUN
iajs-3033	20	14	,	,	PUNCT
iajs-3033	20	15	electrochemistry	electrochemistry	NOUN
iajs-3033	20	16	,	,	PUNCT
iajs-3033	20	17	biological	biological	ADJ
iajs-3033	20	18	models	model	NOUN
iajs-3033	20	19	,	,	PUNCT
iajs-3033	20	20	and	and	CCONJ
iajs-3033	20	21	viscoelastic	viscoelastic	NOUN
iajs-3033	20	22	models	model	NOUN
iajs-3033	20	23	.	.	PUNCT
iajs-3033	21	1	varied	varied	ADJ
iajs-3033	21	2	numerical	numerical	ADJ
iajs-3033	21	3	or	or	CCONJ
iajs-3033	21	4	analytical	analytical	ADJ
iajs-3033	21	5	approaches	approach	NOUN
iajs-3033	21	6	for	for	ADP
iajs-3033	21	7	solving	solve	VERB
iajs-3033	21	8	differential	differential	ADJ
iajs-3033	21	9	equations	equation	NOUN
iajs-3033	21	10	(	(	PUNCT
iajs-3033	21	11	des	des	PROPN
iajs-3033	21	12	)	)	PUNCT
iajs-3033	21	13	,	,	PUNCT
iajs-3033	21	14	either	either	CCONJ
iajs-3033	21	15	classical	classical	ADJ
iajs-3033	21	16	or	or	CCONJ
iajs-3033	21	17	modernistic	modernistic	ADJ
iajs-3033	21	18	,	,	PUNCT
iajs-3033	21	19	have	have	AUX
iajs-3033	21	20	been	be	AUX
iajs-3033	21	21	the	the	DET
iajs-3033	21	22	subject	subject	NOUN
iajs-3033	21	23	of	of	ADP
iajs-3033	21	24	studies	study	NOUN
iajs-3033	21	25	over	over	ADP
iajs-3033	21	26	the	the	DET
iajs-3033	21	27	years	year	NOUN
iajs-3033	21	28	[	[	X
iajs-3033	21	29	3–7	3–7	NOUN
iajs-3033	21	30	]	]	PUNCT
iajs-3033	21	31	.	.	PUNCT
iajs-3033	22	1	however	however	ADV
iajs-3033	22	2	,	,	PUNCT
iajs-3033	22	3	finding	find	VERB
iajs-3033	22	4	analytical	analytical	ADJ
iajs-3033	22	5	or	or	CCONJ
iajs-3033	22	6	numerical	numerical	ADJ
iajs-3033	22	7	solutions	solution	NOUN
iajs-3033	22	8	to	to	ADP
iajs-3033	22	9	many	many	ADJ
iajs-3033	22	10	types	type	NOUN
iajs-3033	22	11	of	of	ADP
iajs-3033	22	12	des	des	PROPN
iajs-3033	22	13	challenged	challenge	VERB
iajs-3033	22	14	the	the	DET
iajs-3033	22	15	ingenuity	ingenuity	NOUN
iajs-3033	22	16	of	of	ADP
iajs-3033	22	17	mathematicians	mathematician	NOUN
iajs-3033	22	18	.	.	PUNCT
iajs-3033	23	1	at	at	ADP
iajs-3033	23	2	present	present	ADJ
iajs-3033	23	3	,	,	PUNCT
iajs-3033	23	4	engineers	engineer	NOUN
iajs-3033	23	5	and	and	CCONJ
iajs-3033	23	6	scientists	scientist	NOUN
iajs-3033	23	7	can	can	AUX
iajs-3033	23	8	now	now	ADV
iajs-3033	23	9	apply	apply	VERB
iajs-3033	23	10	a	a	DET
iajs-3033	23	11	variety	variety	NOUN
iajs-3033	23	12	of	of	ADP
iajs-3033	23	13	powerful	powerful	ADJ
iajs-3033	23	14	classical	classical	NOUN
iajs-3033	23	15	,	,	PUNCT
iajs-3033	23	16	modern	modern	ADJ
iajs-3033	23	17	numerical	numerical	ADJ
iajs-3033	23	18	,	,	PUNCT
iajs-3033	23	19	and	and	CCONJ
iajs-3033	23	20	analytical	analytical	ADJ
iajs-3033	23	21	approaches	approach	NOUN
iajs-3033	23	22	.	.	PUNCT
iajs-3033	24	1	the	the	DET
iajs-3033	24	2	literature	literature	PROPN
iajs-3033	24	3	review	review	NOUN
iajs-3033	24	4	regarding	regard	VERB
iajs-3033	24	5	various	various	ADJ
iajs-3033	24	6	recent	recent	ADJ
iajs-3033	24	7	strategies	strategy	NOUN
iajs-3033	24	8	for	for	ADP
iajs-3033	24	9	solving	solve	VERB
iajs-3033	24	10	mathematical	mathematical	ADJ
iajs-3033	24	11	models	model	NOUN
iajs-3033	24	12	that	that	PRON
iajs-3033	24	13	incorporate	incorporate	VERB
iajs-3033	24	14	des	de	NOUN
iajs-3033	24	15	is	be	AUX
iajs-3033	24	16	listed	list	VERB
iajs-3033	24	17	as	as	SCONJ
iajs-3033	24	18	follows	follow	VERB
iajs-3033	24	19	:	:	PUNCT
iajs-3033	25	1	mechee	mechee	NOUN
iajs-3033	25	2	,	,	PUNCT
iajs-3033	25	3	m.	m.	NOUN
iajs-3033	25	4	s.	s.	PROPN
iajs-3033	25	5	(	(	PUNCT
iajs-3033	25	6	2019	2019	NUM
iajs-3033	25	7	)	)	PUNCT
iajs-3033	25	8	generalized	generalize	VERB
iajs-3033	25	9	rk	rk	NOUN
iajs-3033	25	10	integrators	integrator	NOUN
iajs-3033	25	11	for	for	ADP
iajs-3033	25	12	solving	solve	VERB
iajs-3033	25	13	a	a	DET
iajs-3033	25	14	lass	lass	NOUN
iajs-3033	25	15	of	of	ADP
iajs-3033	25	16	sixth	sixth	ADJ
iajs-3033	25	17	-	-	PUNCT
iajs-3033	25	18	order	order	NOUN
iajs-3033	25	19	odes	ode	VERB
iajs-3033	25	20	[	[	X
iajs-3033	25	21	8	8	NUM
iajs-3033	25	22	]	]	PUNCT
iajs-3033	25	23	while	while	SCONJ
iajs-3033	25	24	mechee	mechee	X
iajs-3033	25	25	,	,	PUNCT
iajs-3033	25	26	m.	m.	NOUN
iajs-3033	25	27	s.	s.	PROPN
iajs-3033	25	28	,	,	PUNCT
iajs-3033	25	29	&	&	CCONJ
iajs-3033	25	30	senu	senu	PROPN
iajs-3033	25	31	,	,	PUNCT
iajs-3033	25	32	n.	n.	NOUN
iajs-3033	25	33	(	(	PUNCT
iajs-3033	25	34	2012	2012	NUM
iajs-3033	25	35	)	)	PUNCT
iajs-3033	25	36	,	,	PUNCT
iajs-3033	25	37	and	and	CCONJ
iajs-3033	25	38	mechee	mechee	X
iajs-3033	25	39	,	,	PUNCT
iajs-3033	25	40	mohammed	mohammed	PROPN
iajs-3033	25	41	s	s	PROPN
iajs-3033	25	42	et	et	PROPN
iajs-3033	25	43	al	al	PROPN
iajs-3033	25	44	.	.	PROPN
iajs-3033	26	1	(	(	PUNCT
iajs-3033	26	2	2019	2019	NUM
iajs-3033	26	3	)	)	PUNCT
iajs-3033	26	4	studied	study	VERB
iajs-3033	26	5	the	the	DET
iajs-3033	26	6	numerical	numerical	ADJ
iajs-3033	26	7	solutions	solution	NOUN
iajs-3033	26	8	of	of	ADP
iajs-3033	26	9	fodes	fode	NOUN
iajs-3033	26	10	[	[	PUNCT
iajs-3033	26	11	9	9	NUM
iajs-3033	26	12	-	-	SYM
iajs-3033	26	13	10	10	NUM
iajs-3033	26	14	]	]	PUNCT
iajs-3033	26	15	.	.	PUNCT
iajs-3033	27	1	the	the	DET
iajs-3033	27	2	analytical	analytical	ADJ
iajs-3033	27	3	methods	method	NOUN
iajs-3033	27	4	for	for	ADP
iajs-3033	27	5	solving	solve	VERB
iajs-3033	27	6	des	de	NOUN
iajs-3033	27	7	are	be	AUX
iajs-3033	27	8	not	not	PART
iajs-3033	27	9	always	always	ADV
iajs-3033	27	10	capable	capable	ADJ
iajs-3033	27	11	of	of	ADP
iajs-3033	27	12	solving	solve	VERB
iajs-3033	27	13	all	all	DET
iajs-3033	27	14	types	type	NOUN
iajs-3033	27	15	of	of	ADP
iajs-3033	27	16	des	des	PROPN
iajs-3033	27	17	,	,	PUNCT
iajs-3033	27	18	directly	directly	ADV
iajs-3033	27	19	or	or	CCONJ
iajs-3033	27	20	indirectly	indirectly	ADV
iajs-3033	27	21	.	.	PUNCT
iajs-3033	28	1	this	this	DET
iajs-3033	28	2	proposition	proposition	NOUN
iajs-3033	28	3	inspires	inspire	VERB
iajs-3033	28	4	us	we	PRON
iajs-3033	28	5	to	to	PART
iajs-3033	28	6	study	study	VERB
iajs-3033	28	7	the	the	DET
iajs-3033	28	8	derivation	derivation	NOUN
iajs-3033	28	9	of	of	ADP
iajs-3033	28	10	direct	direct	ADJ
iajs-3033	28	11	numerical	numerical	ADJ
iajs-3033	28	12	methods	method	NOUN
iajs-3033	28	13	.	.	PUNCT
iajs-3033	29	1	many	many	ADJ
iajs-3033	29	2	researchers	researcher	NOUN
iajs-3033	29	3	have	have	AUX
iajs-3033	29	4	derived	derive	VERB
iajs-3033	29	5	one	one	NUM
iajs-3033	29	6	-	-	PUNCT
iajs-3033	29	7	step	step	NOUN
iajs-3033	29	8	numerical	numerical	ADJ
iajs-3033	29	9	methods	method	NOUN
iajs-3033	29	10	for	for	ADP
iajs-3033	29	11	solving	solve	VERB
iajs-3033	29	12	ivps	ivps	PROPN
iajs-3033	29	13	of	of	ADP
iajs-3033	29	14	odes	ode	NOUN
iajs-3033	29	15	of	of	ADP
iajs-3033	29	16	different	different	ADJ
iajs-3033	29	17	orders	order	NOUN
iajs-3033	29	18	,	,	PUNCT
iajs-3033	29	19	while	while	SCONJ
iajs-3033	29	20	others	other	NOUN
iajs-3033	29	21	have	have	AUX
iajs-3033	29	22	derived	derive	VERB
iajs-3033	29	23	multistep	multistep	ADJ
iajs-3033	29	24	numerical	numerical	ADJ
iajs-3033	29	25	ways	way	NOUN
iajs-3033	29	26	for	for	ADP
iajs-3033	29	27	solving	solve	VERB
iajs-3033	29	28	this	this	DET
iajs-3033	29	29	problem	problem	NOUN
iajs-3033	29	30	.	.	PUNCT
iajs-3033	30	1	the	the	DET
iajs-3033	30	2	fc	fc	PROPN
iajs-3033	30	3	is	be	AUX
iajs-3033	30	4	an	an	DET
iajs-3033	30	5	efficient	efficient	ADJ
iajs-3033	30	6	mathematical	mathematical	ADJ
iajs-3033	30	7	tool	tool	NOUN
iajs-3033	30	8	to	to	PART
iajs-3033	30	9	solve	solve	VERB
iajs-3033	30	10	different	different	ADJ
iajs-3033	30	11	problems	problem	NOUN
iajs-3033	30	12	in	in	ADP
iajs-3033	30	13	engineering	engineering	NOUN
iajs-3033	30	14	,	,	PUNCT
iajs-3033	30	15	sciences	science	NOUN
iajs-3033	30	16	,	,	PUNCT
iajs-3033	30	17	and	and	CCONJ
iajs-3033	30	18	applied	apply	VERB
iajs-3033	30	19	mathematics	mathematic	NOUN
iajs-3033	30	20	,	,	PUNCT
iajs-3033	30	21	and	and	CCONJ
iajs-3033	30	22	it	it	PRON
iajs-3033	30	23	is	be	AUX
iajs-3033	30	24	used	use	VERB
iajs-3033	30	25	to	to	PART
iajs-3033	30	26	examine	examine	VERB
iajs-3033	30	27	the	the	DET
iajs-3033	30	28	problems	problem	NOUN
iajs-3033	30	29	of	of	ADP
iajs-3033	30	30	nonlinear	nonlinear	ADJ
iajs-3033	30	31	dynamics	dynamic	NOUN
iajs-3033	30	32	of	of	ADP
iajs-3033	30	33	different	different	ADJ
iajs-3033	30	34	.	.	PUNCT
iajs-3033	31	1	principally	principally	ADV
iajs-3033	31	2	,	,	PUNCT
iajs-3033	31	3	exact	exact	ADJ
iajs-3033	31	4	solutions	solution	NOUN
iajs-3033	31	5	can	can	AUX
iajs-3033	31	6	not	not	PART
iajs-3033	31	7	be	be	AUX
iajs-3033	31	8	obtained	obtain	VERB
iajs-3033	31	9	for	for	ADP
iajs-3033	31	10	the	the	DET
iajs-3033	31	11	problems	problem	NOUN
iajs-3033	31	12	of	of	ADP
iajs-3033	31	13	fodes	fode	NOUN
iajs-3033	31	14	,	,	PUNCT
iajs-3033	31	15	so	so	SCONJ
iajs-3033	31	16	it	it	PRON
iajs-3033	31	17	needs	need	VERB
iajs-3033	31	18	to	to	PART
iajs-3033	31	19	find	find	VERB
iajs-3033	31	20	more	more	ADJ
iajs-3033	31	21	semi	semi	ADJ
iajs-3033	31	22	-	-	ADJ
iajs-3033	31	23	numerical	numerical	ADJ
iajs-3033	31	24	and	and	CCONJ
iajs-3033	31	25	analytical	analytical	ADJ
iajs-3033	31	26	methods	method	NOUN
iajs-3033	31	27	and	and	CCONJ
iajs-3033	31	28	acknowledge	acknowledge	VERB
iajs-3033	31	29	the	the	DET
iajs-3033	31	30	impacts	impact	NOUN
iajs-3033	31	31	of	of	ADP
iajs-3033	31	32	the	the	DET
iajs-3033	31	33	nonlinear	nonlinear	ADJ
iajs-3033	31	34	problems	problem	NOUN
iajs-3033	31	35	solutions	solution	NOUN
iajs-3033	31	36	.	.	PUNCT
iajs-3033	32	1	recently	recently	ADV
iajs-3033	32	2	,	,	PUNCT
iajs-3033	32	3	different	different	ADJ
iajs-3033	32	4	approximate	approximate	ADJ
iajs-3033	32	5	methods	method	NOUN
iajs-3033	32	6	have	have	AUX
iajs-3033	32	7	been	be	AUX
iajs-3033	32	8	implemented	implement	VERB
iajs-3033	32	9	to	to	PART
iajs-3033	32	10	solve	solve	VERB
iajs-3033	32	11	dynamical	dynamical	ADJ
iajs-3033	32	12	systems	system	NOUN
iajs-3033	32	13	,	,	PUNCT
iajs-3033	32	14	both	both	CCONJ
iajs-3033	32	15	linear	linear	ADJ
iajs-3033	32	16	and	and	CCONJ
iajs-3033	32	17	nonlinear	nonlinear	ADJ
iajs-3033	32	18	.	.	PUNCT
iajs-3033	33	1	such	such	ADJ
iajs-3033	33	2	approximated	approximate	VERB
iajs-3033	33	3	methods	method	NOUN
iajs-3033	33	4	are	be	AUX
iajs-3033	33	5	the	the	DET
iajs-3033	33	6	variational	variational	ADJ
iajs-3033	33	7	iteration	iteration	NOUN
iajs-3033	33	8	method	method	NOUN
iajs-3033	33	9	(	(	PUNCT
iajs-3033	33	10	vim	vim	NOUN
iajs-3033	33	11	)	)	PUNCT
iajs-3033	33	12	,	,	PUNCT
iajs-3033	33	13	the	the	DET
iajs-3033	33	14	adomian	adomian	NOUN
iajs-3033	33	15	decomposition	decomposition	NOUN
iajs-3033	33	16	method	method	NOUN
iajs-3033	33	17	(	(	PUNCT
iajs-3033	33	18	adm	adm	PROPN
iajs-3033	33	19	)	)	PUNCT
iajs-3033	33	20	,	,	PUNCT
iajs-3033	33	21	the	the	DET
iajs-3033	33	22	homotopy	homotopy	NOUN
iajs-3033	33	23	analysis	analysis	NOUN
iajs-3033	33	24	method	method	NOUN
iajs-3033	33	25	(	(	PUNCT
iajs-3033	33	26	ham	ham	PROPN
iajs-3033	33	27	)	)	PUNCT
iajs-3033	33	28	,	,	PUNCT
iajs-3033	33	29	the	the	DET
iajs-3033	33	30	homotopy	homotopy	NOUN
iajs-3033	33	31	perturbation	perturbation	NOUN
iajs-3033	33	32	method	method	NOUN
iajs-3033	33	33	(	(	PUNCT
iajs-3033	33	34	hpm	hpm	NOUN
iajs-3033	33	35	)	)	PUNCT
iajs-3033	33	36	,	,	PUNCT
iajs-3033	33	37	the	the	DET
iajs-3033	33	38	laplace	laplace	NOUN
iajs-3033	33	39	transform	transform	NOUN
iajs-3033	33	40	method	method	NOUN
iajs-3033	33	41	,	,	PUNCT
iajs-3033	33	42	and	and	CCONJ
iajs-3033	33	43	the	the	DET
iajs-3033	33	44	homotopy	homotopy	NOUN
iajs-3033	33	45	analysis	analysis	NOUN
iajs-3033	33	46	transform	transform	NOUN
iajs-3033	33	47	method	method	NOUN
iajs-3033	33	48	(	(	PUNCT
iajs-3033	33	49	hatm	hatm	ADJ
iajs-3033	33	50	)	)	PUNCT
iajs-3033	33	51	.	.	PUNCT
iajs-3033	34	1	in	in	ADP
iajs-3033	34	2	addition	addition	NOUN
iajs-3033	34	3	,	,	PUNCT
iajs-3033	34	4	utilizing	utilize	VERB
iajs-3033	34	5	the	the	DET
iajs-3033	34	6	generalized	generalized	ADJ
iajs-3033	34	7	taylor	taylor	PROPN
iajs-3033	34	8	series	series	PROPN
iajs-3033	34	9	expansion	expansion	NOUN
iajs-3033	34	10	,	,	PUNCT
iajs-3033	34	11	brought	bring	VERB
iajs-3033	34	12	about	about	ADP
iajs-3033	34	13	a	a	DET
iajs-3033	34	14	new	new	ADJ
iajs-3033	34	15	approach	approach	NOUN
iajs-3033	34	16	in	in	ADP
iajs-3033	34	17	relation	relation	NOUN
iajs-3033	34	18	to	to	ADP
iajs-3033	34	19	the	the	DET
iajs-3033	34	20	fractional	fractional	PROPN
iajs-3033	34	21	euler	euler	NOUN
iajs-3033	34	22	method	method	NOUN
iajs-3033	34	23	and	and	CCONJ
iajs-3033	34	24	the	the	DET
iajs-3033	34	25	modified	modify	VERB
iajs-3033	34	26	trapezoidal	trapezoidal	ADJ
iajs-3033	34	27	rule	rule	NOUN
iajs-3033	34	28	.	.	PUNCT
iajs-3033	35	1	lastly	lastly	ADV
iajs-3033	35	2	,	,	PUNCT
iajs-3033	35	3	mechee	mechee	PROPN
iajs-3033	35	4	&	&	CCONJ
iajs-3033	35	5	senu	senu	PROPN
iajs-3033	35	6	(	(	PUNCT
iajs-3033	35	7	2012	2012	NUM
iajs-3033	35	8	)	)	PUNCT
iajs-3033	35	9	solved	solve	VERB
iajs-3033	35	10	the	the	DET
iajs-3033	35	11	fodes	fode	NOUN
iajs-3033	35	12	lane	lane	NOUN
iajs-3033	35	13	-	-	PUNCT
iajs-3033	35	14	emden	emden	NOUN
iajs-3033	35	15	type	type	NOUN
iajs-3033	35	16	by	by	ADP
iajs-3033	35	17	the	the	DET
iajs-3033	35	18	least	least	ADJ
iajs-3033	35	19	square	square	ADJ
iajs-3033	35	20	method	method	NOUN
iajs-3033	35	21	[	[	X
iajs-3033	35	22	10	10	NUM
iajs-3033	35	23	]	]	PUNCT
iajs-3033	35	24	,	,	PUNCT
iajs-3033	35	25	while	while	SCONJ
iajs-3033	35	26	arshad	arshad	PROPN
iajs-3033	35	27	et	et	PROPN
iajs-3033	35	28	al	al	PROPN
iajs-3033	35	29	.	.	PROPN
iajs-3033	36	1	(	(	PUNCT
iajs-3033	36	2	2020	2020	NUM
iajs-3033	36	3	)	)	PUNCT
iajs-3033	36	4	studied	study	VERB
iajs-3033	36	5	the	the	DET
iajs-3033	36	6	numerical	numerical	ADJ
iajs-3033	36	7	solutions	solution	NOUN
iajs-3033	36	8	of	of	ADP
iajs-3033	36	9	first	first	ADJ
iajs-3033	36	10	order	order	NOUN
iajs-3033	36	11	fodes	fode	NOUN
iajs-3033	36	12	using	use	VERB
iajs-3033	36	13	the	the	DET
iajs-3033	36	14	developed	develop	VERB
iajs-3033	36	15	euler	euler	NOUN
iajs-3033	36	16	method	method	NOUN
iajs-3033	36	17	and	and	CCONJ
iajs-3033	36	18	they	they	PRON
iajs-3033	36	19	derived	derive	VERB
iajs-3033	36	20	2	2	NUM
iajs-3033	36	21	-	-	PUNCT
iajs-3033	36	22	stage	stage	NOUN
iajs-3033	36	23	fractional	fractional	ADJ
iajs-3033	36	24	runge	runge	NOUN
iajs-3033	36	25	-	-	PUNCT
iajs-3033	36	26	kutta	kutta	NOUN
iajs-3033	36	27	(	(	PUNCT
iajs-3033	36	28	frk	frk	PROPN
iajs-3033	36	29	)	)	PUNCT
iajs-3033	36	30	method	method	NOUN
iajs-3033	37	1	[	[	X
iajs-3033	37	2	2	2	NUM
iajs-3033	37	3	]	]	PUNCT
iajs-3033	37	4	.	.	PUNCT
iajs-3033	38	1	in	in	ADP
iajs-3033	38	2	this	this	DET
iajs-3033	38	3	study	study	NOUN
iajs-3033	38	4	,	,	PUNCT
iajs-3033	38	5	euler	euler	NOUN
iajs-3033	38	6	and	and	CCONJ
iajs-3033	38	7	rkm	rkm	PROPN
iajs-3033	38	8	numerical	numerical	PROPN
iajs-3033	38	9	methods	method	NOUN
iajs-3033	38	10	have	have	AUX
iajs-3033	38	11	been	be	AUX
iajs-3033	38	12	derived	derive	VERB
iajs-3033	38	13	or	or	CCONJ
iajs-3033	38	14	developed	develop	VERB
iajs-3033	38	15	to	to	PART
iajs-3033	38	16	be	be	AUX
iajs-3033	38	17	consistent	consistent	ADJ
iajs-3033	38	18	with	with	ADP
iajs-3033	38	19	classes	class	NOUN
iajs-3033	38	20	of	of	ADP
iajs-3033	38	21	fifth	fifth	ADJ
iajs-3033	38	22	-	-	PUNCT
iajs-3033	38	23	order	order	NOUN
iajs-3033	38	24	fodes	fode	NOUN
iajs-3033	38	25	.	.	PUNCT
iajs-3033	39	1	firstly	firstly	ADV
iajs-3033	39	2	,	,	PUNCT
iajs-3033	39	3	the	the	DET
iajs-3033	39	4	generalized	generalize	VERB
iajs-3033	39	5	taylor	taylor	PROPN
iajs-3033	39	6	series	series	PROPN
iajs-3033	39	7	expansion	expansion	NOUN
iajs-3033	39	8	was	be	AUX
iajs-3033	39	9	used	use	VERB
iajs-3033	39	10	to	to	PART
iajs-3033	39	11	develop	develop	VERB
iajs-3033	39	12	a	a	DET
iajs-3033	39	13	one	one	NUM
iajs-3033	39	14	-	-	PUNCT
iajs-3033	39	15	stage	stage	NOUN
iajs-3033	39	16	euler	euler	NOUN
iajs-3033	39	17	method	method	NOUN
iajs-3033	39	18	as	as	ADV
iajs-3033	39	19	well	well	ADV
iajs-3033	39	20	as	as	ADP
iajs-3033	39	21	twoand	twoand	ADP
iajs-3033	39	22	three	three	NUM
iajs-3033	39	23	-	-	PUNCT
iajs-3033	39	24	stage	stage	NOUN
iajs-3033	39	25	rkm	rkm	PROPN
iajs-3033	39	26	techniques	technique	NOUN
iajs-3033	39	27	to	to	PART
iajs-3033	39	28	be	be	AUX
iajs-3033	39	29	suited	suit	VERB
iajs-3033	39	30	for	for	ADP
iajs-3033	39	31	solving	solve	VERB
iajs-3033	39	32	fifth	fifth	ADJ
iajs-3033	39	33	-	-	PUNCT
iajs-3033	39	34	order	order	NOUN
iajs-3033	39	35	fodes	fode	NOUN
iajs-3033	39	36	.	.	PUNCT
iajs-3033	40	1	secondly	secondly	ADV
iajs-3033	40	2	,	,	PUNCT
iajs-3033	40	3	the	the	DET
iajs-3033	40	4	two	two	NUM
iajs-3033	40	5	and	and	CCONJ
iajs-3033	40	6	three	three	NUM
iajs-3033	40	7	-	-	PUNCT
iajs-3033	40	8	stage	stage	NOUN
iajs-3033	40	9	rkm	rkm	PROPN
iajs-3033	40	10	methods	method	NOUN
iajs-3033	40	11	are	be	AUX
iajs-3033	40	12	developed	develop	VERB
iajs-3033	40	13	for	for	ADP
iajs-3033	40	14	solving	solve	VERB
iajs-3033	40	15	fifth	fifth	ADJ
iajs-3033	40	16	-	-	PUNCT
iajs-3033	40	17	order	order	NOUN
iajs-3033	40	18	odes	ode	NOUN
iajs-3033	40	19	in	in	ADP
iajs-3033	40	20	harmony	harmony	NOUN
iajs-3033	40	21	with	with	ADP
iajs-3033	40	22	solving	solve	VERB
iajs-3033	40	23	two	two	NUM
iajs-3033	40	24	kinds	kind	NOUN
iajs-3033	40	25	of	of	ADP
iajs-3033	40	26	fodes	fode	NOUN
iajs-3033	40	27	.	.	PUNCT
iajs-3033	41	1	2	2	X
iajs-3033	41	2	.	.	X
iajs-3033	41	3	preliminary	preliminary	ADJ
iajs-3033	41	4	we	we	PRON
iajs-3033	41	5	recall	recall	VERB
iajs-3033	41	6	some	some	DET
iajs-3033	41	7	special	special	ADJ
iajs-3033	41	8	types	type	NOUN
iajs-3033	41	9	of	of	ADP
iajs-3033	41	10	equation	equation	NOUN
iajs-3033	41	11	,	,	PUNCT
iajs-3033	41	12	some	some	PRON
iajs-3033	41	13	of	of	ADP
iajs-3033	41	14	which	which	PRON
iajs-3033	41	15	will	will	AUX
iajs-3033	41	16	study	study	VERB
iajs-3033	41	17	some	some	PRON
iajs-3033	41	18	of	of	ADP
iajs-3033	41	19	them	they	PRON
iajs-3033	41	20	:	:	PUNCT
iajs-3033	41	21	2.1	2.1	NUM
iajs-3033	41	22	kinds	kind	NOUN
iajs-3033	41	23	of	of	ADP
iajs-3033	41	24	quasi	quasi	ADJ
iajs-3033	41	25	-	-	ADJ
iajs-3033	41	26	linear	linear	ADJ
iajs-3033	41	27	frodes	frode	NOUN
iajs-3033	41	28	of	of	ADP
iajs-3033	41	29	fifth	fifth	NOUN
iajs-3033	41	30	-	-	PUNCT
iajs-3033	41	31	order[8	order[8	NUM
iajs-3033	41	32	]	]	PUNCT
iajs-3033	41	33	:	:	PUNCT
iajs-3033	41	34	in	in	ADP
iajs-3033	41	35	this	this	DET
iajs-3033	41	36	subsection	subsection	NOUN
iajs-3033	41	37	,	,	PUNCT
iajs-3033	41	38	some	some	DET
iajs-3033	41	39	kinds	kind	NOUN
iajs-3033	41	40	of	of	ADP
iajs-3033	41	41	quasi	quasi	ADJ
iajs-3033	41	42	-	-	ADJ
iajs-3033	41	43	linear	linear	ADJ
iajs-3033	41	44	fifth	fifth	ADJ
iajs-3033	41	45	-	-	PUNCT
iajs-3033	41	46	order	order	NOUN
iajs-3033	41	47	fodes	fode	NOUN
iajs-3033	41	48	have	have	AUX
iajs-3033	41	49	been	be	AUX
iajs-3033	41	50	introduced	introduce	VERB
iajs-3033	41	51	.	.	PUNCT
iajs-3033	42	1	2.1.1	2.1.1	NUM
iajs-3033	42	2	kind	kind	NOUN
iajs-3033	42	3	of	of	ADP
iajs-3033	42	4	quasi	quasi	ADJ
iajs-3033	42	5	-	-	ADJ
iajs-3033	42	6	linear	linear	ADJ
iajs-3033	42	7	fodes	fode	NOUN
iajs-3033	42	8	of	of	ADP
iajs-3033	42	9	fifth	fifth	ADJ
iajs-3033	42	10	-	-	PUNCT
iajs-3033	42	11	order[8	order[8	NUM
iajs-3033	42	12	]	]	PUNCT
iajs-3033	42	13	:	:	PUNCT
iajs-3033	42	14	the	the	DET
iajs-3033	42	15	general	general	ADJ
iajs-3033	42	16	kinds	kind	NOUN
iajs-3033	42	17	of	of	ADP
iajs-3033	42	18	quasi	quasi	ADJ
iajs-3033	42	19	-	-	ADJ
iajs-3033	42	20	linear	linear	ADJ
iajs-3033	42	21	fodes	fode	NOUN
iajs-3033	42	22	of	of	ADP
iajs-3033	42	23	fifth	fifth	ADJ
iajs-3033	42	24	-	-	PUNCT
iajs-3033	42	25	order	order	NOUN
iajs-3033	42	26	are	be	AUX
iajs-3033	42	27	written	write	VERB
iajs-3033	42	28	as	as	SCONJ
iajs-3033	42	29	follows	follow	VERB
iajs-3033	42	30	ihjpas	ihjpa	NOUN
iajs-3033	42	31	.	.	PUNCT
iajs-3033	43	1	36	36	NUM
iajs-3033	43	2	(	(	PUNCT
iajs-3033	43	3	3	3	NUM
iajs-3033	43	4	)	)	PUNCT
iajs-3033	43	5	2023	2023	NUM
iajs-3033	43	6	418	418	NUM
iajs-3033	43	7	𝐷5𝛼𝑢(𝜏	𝐷5𝛼𝑢(𝜏	PROPN
iajs-3033	43	8	)	)	PUNCT
iajs-3033	43	9	=	=	SYM
iajs-3033	44	1	𝑓	𝑓	PROPN
iajs-3033	44	2	(	(	PUNCT
iajs-3033	44	3	𝜏	𝜏	NOUN
iajs-3033	44	4	,	,	PUNCT
iajs-3033	44	5	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	44	6	)	)	PUNCT
iajs-3033	44	7	,	,	PUNCT
iajs-3033	44	8	𝑢′(𝜏	𝑢′(𝜏	PROPN
iajs-3033	44	9	)	)	PUNCT
iajs-3033	44	10	,	,	PUNCT
iajs-3033	44	11	𝑢′′(𝑡	𝑢′′(𝑡	NOUN
iajs-3033	44	12	)	)	PUNCT
iajs-3033	44	13	,	,	PUNCT
iajs-3033	44	14	𝑢′′′(𝜏	𝑢′′′(𝜏	PROPN
iajs-3033	44	15	)	)	PUNCT
iajs-3033	44	16	,	,	PUNCT
iajs-3033	44	17	𝑢(4)(𝜏	𝑢(4)(𝜏	NUM
iajs-3033	44	18	)	)	PUNCT
iajs-3033	44	19	)	)	PUNCT
iajs-3033	44	20	,	,	PUNCT
iajs-3033	44	21	(	(	PUNCT
iajs-3033	44	22	1	1	X
iajs-3033	44	23	)	)	PUNCT
iajs-3033	44	24	0	0	PUNCT
iajs-3033	45	1	<	<	X
iajs-3033	45	2	𝛼	𝛼	X
iajs-3033	45	3	<	<	X
iajs-3033	45	4	1	1	NUM
iajs-3033	45	5	,	,	PUNCT
iajs-3033	45	6	𝜏	𝜏	PRON
iajs-3033	45	7	≥	≥	NOUN
iajs-3033	45	8	𝜏0	𝜏0	NOUN
iajs-3033	45	9	when	when	SCONJ
iajs-3033	45	10	the	the	DET
iajs-3033	45	11	initial	initial	ADJ
iajs-3033	45	12	conditions	condition	NOUN
iajs-3033	45	13	𝑢(𝑖𝛼)(0	𝑢(𝑖𝛼)(0	ADJ
iajs-3033	45	14	)	)	PUNCT
iajs-3033	45	15	=	=	PUNCT
iajs-3033	46	1	𝛾𝑖	𝛾𝑖	NOUN
iajs-3033	46	2	,	,	PUNCT
iajs-3033	46	3	𝑖	𝑖	NOUN
iajs-3033	46	4	=	=	SYM
iajs-3033	46	5	0,1	0,1	NUM
iajs-3033	46	6	,	,	PUNCT
iajs-3033	46	7	…	…	PUNCT
iajs-3033	46	8	,	,	PUNCT
iajs-3033	46	9	4	4	X
iajs-3033	46	10	.	.	PUNCT
iajs-3033	46	11	(	(	PUNCT
iajs-3033	46	12	2	2	X
iajs-3033	46	13	)	)	PUNCT
iajs-3033	46	14	2.1.2	2.1.2	NUM
iajs-3033	46	15	kind	kind	NOUN
iajs-3033	46	16	-	-	PUNCT
iajs-3033	46	17	one	one	NUM
iajs-3033	46	18	of	of	ADP
iajs-3033	46	19	quasi	quasi	ADJ
iajs-3033	46	20	-	-	ADJ
iajs-3033	46	21	linear	linear	ADJ
iajs-3033	46	22	frodes	frode	NOUN
iajs-3033	46	23	of	of	ADP
iajs-3033	46	24	fifth	fifth	ADJ
iajs-3033	46	25	-	-	PUNCT
iajs-3033	46	26	order	order	NOUN
iajs-3033	47	1	[	[	X
iajs-3033	47	2	9	9	NUM
iajs-3033	47	3	]	]	PUNCT
iajs-3033	47	4	:	:	PUNCT
iajs-3033	47	5	consider	consider	VERB
iajs-3033	47	6	the	the	DET
iajs-3033	47	7	kind	kind	NOUN
iajs-3033	47	8	-	-	PUNCT
iajs-3033	47	9	one	one	NUM
iajs-3033	47	10	of	of	ADP
iajs-3033	47	11	quasi	quasi	ADJ
iajs-3033	47	12	-	-	ADJ
iajs-3033	47	13	linear	linear	ADJ
iajs-3033	47	14	fodes	fode	NOUN
iajs-3033	47	15	fifth	fifth	ADJ
iajs-3033	47	16	-	-	PUNCT
iajs-3033	47	17	order	order	NOUN
iajs-3033	47	18	as	as	SCONJ
iajs-3033	47	19	follows	follow	VERB
iajs-3033	47	20	:	:	PUNCT
iajs-3033	47	21	𝐷5𝛼𝑢(𝜏	𝐷5𝛼𝑢(𝜏	PROPN
iajs-3033	47	22	)	)	PUNCT
iajs-3033	47	23	=	=	SYM
iajs-3033	48	1	𝑓	𝑓	PROPN
iajs-3033	48	2	(	(	PUNCT
iajs-3033	48	3	𝜏	𝜏	NOUN
iajs-3033	48	4	,	,	PUNCT
iajs-3033	48	5	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	48	6	)	)	PUNCT
iajs-3033	48	7	,	,	PUNCT
iajs-3033	48	8	𝑢′(𝜏	𝑢′(𝜏	PROPN
iajs-3033	48	9	)	)	PUNCT
iajs-3033	48	10	,	,	PUNCT
iajs-3033	48	11	𝑢′′(𝜏	𝑢′′(𝜏	PROPN
iajs-3033	48	12	)	)	PUNCT
iajs-3033	48	13	,	,	PUNCT
iajs-3033	48	14	𝑢′′′(𝜏	𝑢′′′(𝜏	PROPN
iajs-3033	48	15	)	)	PUNCT
iajs-3033	48	16	,	,	PUNCT
iajs-3033	48	17	𝑢(4)(𝜏	𝑢(4)(𝜏	NUM
iajs-3033	48	18	)	)	PUNCT
iajs-3033	48	19	)	)	PUNCT
iajs-3033	48	20	,	,	PUNCT
iajs-3033	48	21	(	(	PUNCT
iajs-3033	48	22	3	3	X
iajs-3033	48	23	)	)	PUNCT
iajs-3033	48	24	0	0	PUNCT
iajs-3033	49	1	<	<	X
iajs-3033	49	2	𝛼	𝛼	X
iajs-3033	49	3	<	<	X
iajs-3033	49	4	1	1	NUM
iajs-3033	49	5	,	,	PUNCT
iajs-3033	49	6	𝜏	𝜏	DET
iajs-3033	49	7	≥	≥	NOUN
iajs-3033	49	8	0	0	NUM
iajs-3033	49	9	when	when	SCONJ
iajs-3033	49	10	the	the	DET
iajs-3033	49	11	initial	initial	ADJ
iajs-3033	49	12	conditions	condition	NOUN
iajs-3033	49	13	are	be	AUX
iajs-3033	49	14	in	in	ADP
iajs-3033	49	15	equation	equation	NOUN
iajs-3033	49	16	(	(	PUNCT
iajs-3033	49	17	2	2	NUM
iajs-3033	49	18	)	)	PUNCT
iajs-3033	49	19	.	.	PUNCT
iajs-3033	50	1	2.1.3	2.1.3	NUM
iajs-3033	50	2	kind	kind	NOUN
iajs-3033	50	3	-	-	PUNCT
iajs-3033	50	4	two	two	NUM
iajs-3033	50	5	of	of	ADP
iajs-3033	50	6	quasi	quasi	ADJ
iajs-3033	50	7	-	-	ADJ
iajs-3033	50	8	linear	linear	ADJ
iajs-3033	50	9	fodes	fode	NOUN
iajs-3033	50	10	of	of	ADP
iajs-3033	50	11	fifth	fifth	ADJ
iajs-3033	50	12	-	-	PUNCT
iajs-3033	50	13	order	order	NOUN
iajs-3033	50	14	[	[	X
iajs-3033	50	15	9	9	NUM
iajs-3033	50	16	]	]	PUNCT
iajs-3033	50	17	:	:	PUNCT
iajs-3033	50	18	consider	consider	VERB
iajs-3033	50	19	the	the	DET
iajs-3033	50	20	kind	kind	NOUN
iajs-3033	50	21	-	-	PUNCT
iajs-3033	50	22	two	two	NUM
iajs-3033	50	23	of	of	ADP
iajs-3033	50	24	quasi	quasi	ADJ
iajs-3033	50	25	-	-	ADJ
iajs-3033	50	26	linear	linear	ADJ
iajs-3033	50	27	fodes	fode	NOUN
iajs-3033	50	28	of	of	ADP
iajs-3033	50	29	fifth	fifth	ADJ
iajs-3033	50	30	-	-	PUNCT
iajs-3033	50	31	order	order	NOUN
iajs-3033	50	32	as	as	SCONJ
iajs-3033	50	33	follows	follow	VERB
iajs-3033	50	34	:	:	PUNCT
iajs-3033	50	35	𝐷5𝛼𝑢(𝜏	𝐷5𝛼𝑢(𝜏	PROPN
iajs-3033	50	36	)	)	PUNCT
iajs-3033	50	37	=	=	SYM
iajs-3033	50	38	𝑓(𝜏	𝑓(𝜏	PROPN
iajs-3033	50	39	,	,	PUNCT
iajs-3033	50	40	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	50	41	)	)	PUNCT
iajs-3033	50	42	,	,	PUNCT
iajs-3033	50	43	𝑢′(𝜏	𝑢′(𝜏	PROPN
iajs-3033	50	44	)	)	PUNCT
iajs-3033	50	45	,	,	PUNCT
iajs-3033	50	46	𝑢′′(𝜏	𝑢′′(𝜏	PROPN
iajs-3033	50	47	)	)	PUNCT
iajs-3033	50	48	,	,	PUNCT
iajs-3033	50	49	𝑢′′′(𝜏	𝑢′′′(𝜏	PROPN
iajs-3033	50	50	)	)	PUNCT
iajs-3033	50	51	)	)	PUNCT
iajs-3033	50	52	,	,	PUNCT
iajs-3033	50	53	0	0	PUNCT
iajs-3033	50	54	<	<	X
iajs-3033	50	55	𝛼	𝛼	X
iajs-3033	50	56	<	<	X
iajs-3033	50	57	1	1	NUM
iajs-3033	50	58	,	,	PUNCT
iajs-3033	50	59	𝜏	𝜏	PRON
iajs-3033	50	60	≥	≥	NOUN
iajs-3033	50	61	𝜏0	𝜏0	NOUN
iajs-3033	50	62	(	(	PUNCT
iajs-3033	50	63	4	4	NUM
iajs-3033	50	64	)	)	PUNCT
iajs-3033	50	65	when	when	SCONJ
iajs-3033	50	66	the	the	DET
iajs-3033	50	67	initial	initial	ADJ
iajs-3033	50	68	conditions	condition	NOUN
iajs-3033	50	69	are	be	AUX
iajs-3033	50	70	in	in	ADP
iajs-3033	50	71	equation	equation	NOUN
iajs-3033	50	72	(	(	PUNCT
iajs-3033	50	73	2	2	NUM
iajs-3033	50	74	)	)	PUNCT
iajs-3033	50	75	.	.	PUNCT
iajs-3033	51	1	2.1.4	2.1.4	NUM
iajs-3033	51	2	kind	kind	NOUN
iajs-3033	51	3	-	-	PUNCT
iajs-3033	51	4	three	three	NUM
iajs-3033	51	5	of	of	ADP
iajs-3033	51	6	quasi	quasi	ADJ
iajs-3033	51	7	-	-	ADJ
iajs-3033	51	8	linear	linear	ADJ
iajs-3033	51	9	fodes	fode	NOUN
iajs-3033	51	10	of	of	ADP
iajs-3033	51	11	fifth	fifth	ADJ
iajs-3033	51	12	-	-	PUNCT
iajs-3033	51	13	order	order	NOUN
iajs-3033	51	14	[	[	X
iajs-3033	51	15	9	9	NUM
iajs-3033	51	16	]	]	PUNCT
iajs-3033	51	17	:	:	PUNCT
iajs-3033	51	18	consider	consider	VERB
iajs-3033	51	19	the	the	DET
iajs-3033	51	20	kind	kind	NOUN
iajs-3033	51	21	-	-	PUNCT
iajs-3033	51	22	three	three	NUM
iajs-3033	51	23	of	of	ADP
iajs-3033	51	24	quasi	quasi	ADJ
iajs-3033	51	25	-	-	ADJ
iajs-3033	51	26	linear	linear	ADJ
iajs-3033	51	27	fodes	fode	NOUN
iajs-3033	51	28	of	of	ADP
iajs-3033	51	29	fifth	fifth	ADJ
iajs-3033	51	30	-	-	PUNCT
iajs-3033	51	31	order	order	NOUN
iajs-3033	51	32	as	as	SCONJ
iajs-3033	51	33	follows	follow	VERB
iajs-3033	51	34	:	:	PUNCT
iajs-3033	51	35	𝐷5𝛼𝑢(𝜏	𝐷5𝛼𝑢(𝜏	PROPN
iajs-3033	51	36	)	)	PUNCT
iajs-3033	52	1	=	=	SYM
iajs-3033	52	2	𝑓(𝜏	𝑓(𝜏	PROPN
iajs-3033	52	3	,	,	PUNCT
iajs-3033	52	4	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	52	5	)	)	PUNCT
iajs-3033	52	6	,	,	PUNCT
iajs-3033	52	7	𝑢′(𝜏	𝑢′(𝜏	PROPN
iajs-3033	52	8	)	)	PUNCT
iajs-3033	52	9	,	,	PUNCT
iajs-3033	52	10	𝑢′′(𝜏	𝑢′′(𝜏	PROPN
iajs-3033	52	11	)	)	PUNCT
iajs-3033	52	12	)	)	PUNCT
iajs-3033	52	13	,	,	PUNCT
iajs-3033	52	14	0	0	PUNCT
iajs-3033	52	15	<	<	X
iajs-3033	52	16	𝛼	𝛼	X
iajs-3033	52	17	<	<	X
iajs-3033	52	18	1	1	NUM
iajs-3033	52	19	,	,	PUNCT
iajs-3033	52	20	𝜏	𝜏	PRON
iajs-3033	52	21	≥	≥	NOUN
iajs-3033	52	22	𝜏0	𝜏0	NOUN
iajs-3033	52	23	(	(	PUNCT
iajs-3033	52	24	5	5	NUM
iajs-3033	52	25	)	)	PUNCT
iajs-3033	52	26	with	with	ADP
iajs-3033	52	27	the	the	DET
iajs-3033	52	28	initial	initial	ADJ
iajs-3033	52	29	conditions	condition	NOUN
iajs-3033	52	30	are	be	AUX
iajs-3033	52	31	in	in	ADP
iajs-3033	52	32	equation	equation	NOUN
iajs-3033	52	33	(	(	PUNCT
iajs-3033	52	34	2	2	NUM
iajs-3033	52	35	)	)	PUNCT
iajs-3033	52	36	.	.	PUNCT
iajs-3033	53	1	2.1.5	2.1.5	NUM
iajs-3033	53	2	kind	kind	NOUN
iajs-3033	53	3	-	-	PUNCT
iajs-3033	53	4	four	four	NUM
iajs-3033	53	5	of	of	ADP
iajs-3033	53	6	quasi	quasi	ADJ
iajs-3033	53	7	-	-	ADJ
iajs-3033	53	8	linear	linear	ADJ
iajs-3033	53	9	fodes	fode	NOUN
iajs-3033	53	10	of	of	ADP
iajs-3033	53	11	fifth	fifth	ADJ
iajs-3033	53	12	-	-	PUNCT
iajs-3033	53	13	order[9	order[9	X
iajs-3033	53	14	]	]	PRON
iajs-3033	53	15	:	:	PUNCT
iajs-3033	53	16	consider	consider	VERB
iajs-3033	53	17	the	the	DET
iajs-3033	53	18	class	class	NOUN
iajs-3033	53	19	-	-	PUNCT
iajs-3033	53	20	four	four	NUM
iajs-3033	53	21	of	of	ADP
iajs-3033	53	22	quasi	quasi	ADJ
iajs-3033	53	23	-	-	ADJ
iajs-3033	53	24	linear	linear	ADJ
iajs-3033	53	25	fodes	fode	NOUN
iajs-3033	53	26	of	of	ADP
iajs-3033	53	27	fifth	fifth	ADJ
iajs-3033	53	28	-	-	PUNCT
iajs-3033	53	29	order	order	NOUN
iajs-3033	53	30	as	as	SCONJ
iajs-3033	53	31	follows	follow	VERB
iajs-3033	53	32	:	:	PUNCT
iajs-3033	53	33	𝐷	𝐷	PROPN
iajs-3033	53	34	5𝛼𝑢(𝜏	5𝛼𝑢(𝜏	NUM
iajs-3033	53	35	)	)	PUNCT
iajs-3033	53	36	=	=	SYM
iajs-3033	53	37	𝑓(𝜏	𝑓(𝜏	PROPN
iajs-3033	53	38	,	,	PUNCT
iajs-3033	53	39	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	53	40	)	)	PUNCT
iajs-3033	53	41	,	,	PUNCT
iajs-3033	53	42	𝑢′(𝜏	𝑢′(𝜏	PROPN
iajs-3033	53	43	)	)	PUNCT
iajs-3033	53	44	)	)	PUNCT
iajs-3033	53	45	,	,	PUNCT
iajs-3033	53	46	0	0	PUNCT
iajs-3033	53	47	<	<	X
iajs-3033	53	48	𝛼	𝛼	X
iajs-3033	53	49	<	<	X
iajs-3033	53	50	1	1	NUM
iajs-3033	53	51	,	,	PUNCT
iajs-3033	53	52	𝜏	𝜏	PRON
iajs-3033	53	53	≥	≥	NOUN
iajs-3033	53	54	𝜏0	𝜏0	NOUN
iajs-3033	53	55	(	(	PUNCT
iajs-3033	53	56	6	6	NUM
iajs-3033	53	57	)	)	PUNCT
iajs-3033	53	58	when	when	SCONJ
iajs-3033	53	59	the	the	DET
iajs-3033	53	60	initial	initial	ADJ
iajs-3033	53	61	conditions	condition	NOUN
iajs-3033	53	62	are	be	AUX
iajs-3033	53	63	in	in	ADP
iajs-3033	53	64	equation	equation	NOUN
iajs-3033	53	65	(	(	PUNCT
iajs-3033	53	66	2	2	NUM
iajs-3033	53	67	)	)	PUNCT
iajs-3033	53	68	.	.	PUNCT
iajs-3033	54	1	2.1.6	2.1.6	NUM
iajs-3033	54	2	kind	kind	NOUN
iajs-3033	54	3	-	-	PUNCT
iajs-3033	54	4	five	five	NUM
iajs-3033	54	5	of	of	ADP
iajs-3033	54	6	quasi	quasi	ADJ
iajs-3033	54	7	-	-	ADJ
iajs-3033	54	8	linear	linear	ADJ
iajs-3033	54	9	fodes	fode	NOUN
iajs-3033	54	10	of	of	ADP
iajs-3033	54	11	fifth	fifth	ADJ
iajs-3033	54	12	-	-	PUNCT
iajs-3033	54	13	order	order	NOUN
iajs-3033	54	14	consider	consider	VERB
iajs-3033	54	15	the	the	DET
iajs-3033	54	16	kind	kind	NOUN
iajs-3033	54	17	-	-	PUNCT
iajs-3033	54	18	five	five	NUM
iajs-3033	54	19	of	of	ADP
iajs-3033	54	20	quasi	quasi	ADJ
iajs-3033	54	21	-	-	ADJ
iajs-3033	54	22	linear	linear	ADJ
iajs-3033	54	23	fodes	fode	NOUN
iajs-3033	54	24	of	of	ADP
iajs-3033	54	25	fifth	fifth	ADJ
iajs-3033	54	26	-	-	PUNCT
iajs-3033	54	27	order	order	NOUN
iajs-3033	54	28	as	as	SCONJ
iajs-3033	54	29	follows	follow	VERB
iajs-3033	54	30	:	:	PUNCT
iajs-3033	54	31	𝐷5𝛼𝑢(𝜏	𝐷5𝛼𝑢(𝜏	PROPN
iajs-3033	54	32	)	)	PUNCT
iajs-3033	54	33	=	=	SYM
iajs-3033	54	34	𝑓(𝜏	𝑓(𝜏	PROPN
iajs-3033	54	35	,	,	PUNCT
iajs-3033	54	36	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	54	37	)	)	PUNCT
iajs-3033	54	38	)	)	PUNCT
iajs-3033	54	39	,	,	PUNCT
iajs-3033	54	40	0	0	PUNCT
iajs-3033	54	41	<	<	X
iajs-3033	54	42	𝛼	𝛼	X
iajs-3033	54	43	<	<	X
iajs-3033	54	44	1	1	NUM
iajs-3033	54	45	,	,	PUNCT
iajs-3033	54	46	𝜏	𝜏	PRON
iajs-3033	54	47	≥	≥	NOUN
iajs-3033	54	48	𝜏0	𝜏0	NOUN
iajs-3033	54	49	(	(	PUNCT
iajs-3033	54	50	7	7	NUM
iajs-3033	54	51	)	)	PUNCT
iajs-3033	54	52	ihjpas	ihjpa	NOUN
iajs-3033	54	53	.	.	PUNCT
iajs-3033	55	1	36	36	NUM
iajs-3033	55	2	(	(	PUNCT
iajs-3033	55	3	3	3	NUM
iajs-3033	55	4	)	)	PUNCT
iajs-3033	55	5	2023	2023	NUM
iajs-3033	55	6	419	419	NUM
iajs-3033	55	7	when	when	SCONJ
iajs-3033	55	8	the	the	DET
iajs-3033	55	9	initial	initial	ADJ
iajs-3033	55	10	conditions	condition	NOUN
iajs-3033	55	11	are	be	AUX
iajs-3033	55	12	in	in	ADP
iajs-3033	55	13	equation	equation	NOUN
iajs-3033	55	14	(	(	PUNCT
iajs-3033	55	15	2	2	NUM
iajs-3033	55	16	)	)	PUNCT
iajs-3033	55	17	.	.	PUNCT
iajs-3033	56	1	2.2	2.2	NUM
iajs-3033	56	2	the	the	DET
iajs-3033	56	3	solving	solving	NOUN
iajs-3033	56	4	of	of	ADP
iajs-3033	56	5	class	class	NOUN
iajs-3033	56	6	-	-	PUNCT
iajs-3033	56	7	five	five	NUM
iajs-3033	56	8	,	,	PUNCT
iajs-3033	56	9	fifth	fifth	ADJ
iajs-3033	56	10	-	-	PUNCT
iajs-3033	56	11	order	order	NOUN
iajs-3033	56	12	odes	ode	NOUN
iajs-3033	56	13	by	by	ADP
iajs-3033	56	14	rkm	rkm	PROPN
iajs-3033	56	15	method	method	PROPN
iajs-3033	56	16	odes	ode	VERB
iajs-3033	56	17	commands	command	NOUN
iajs-3033	56	18	of	of	ADP
iajs-3033	56	19	the	the	DET
iajs-3033	56	20	order	order	NOUN
iajs-3033	56	21	more	more	ADJ
iajs-3033	56	22	than	than	ADP
iajs-3033	56	23	two	two	NUM
iajs-3033	56	24	,	,	PUNCT
iajs-3033	56	25	many	many	ADJ
iajs-3033	56	26	researchers	researcher	NOUN
iajs-3033	56	27	used	use	VERB
iajs-3033	56	28	to	to	PART
iajs-3033	56	29	solve	solve	VERB
iajs-3033	56	30	by	by	ADP
iajs-3033	56	31	transmutation	transmutation	NOUN
iajs-3033	56	32	the	the	DET
iajs-3033	56	33	ode	ode	NOUN
iajs-3033	56	34	into	into	ADP
iajs-3033	56	35	a	a	DET
iajs-3033	56	36	system	system	NOUN
iajs-3033	56	37	of	of	ADP
iajs-3033	56	38	first	first	ADJ
iajs-3033	56	39	-	-	PUNCT
iajs-3033	56	40	order	order	NOUN
iajs-3033	56	41	odes	ode	NOUN
iajs-3033	56	42	where	where	SCONJ
iajs-3033	56	43	the	the	DET
iajs-3033	56	44	dimension	dimension	NOUN
iajs-3033	56	45	of	of	ADP
iajs-3033	56	46	the	the	DET
iajs-3033	56	47	system	system	NOUN
iajs-3033	56	48	are	be	AUX
iajs-3033	56	49	the	the	DET
iajs-3033	56	50	same	same	ADJ
iajs-3033	56	51	in	in	ADP
iajs-3033	56	52	that	that	DET
iajs-3033	56	53	order	order	NOUN
iajs-3033	56	54	.	.	PUNCT
iajs-3033	57	1	2.2.1	2.2.1	NUM
iajs-3033	57	2	the	the	DET
iajs-3033	57	3	solving	solving	NOUN
iajs-3033	57	4	of	of	ADP
iajs-3033	57	5	class	class	NOUN
iajs-3033	57	6	-	-	PUNCT
iajs-3033	57	7	five	five	NUM
iajs-3033	57	8	fifth	fifth	ADJ
iajs-3033	57	9	-	-	PUNCT
iajs-3033	57	10	order	order	NOUN
iajs-3033	57	11	odes	ode	NOUN
iajs-3033	57	12	by	by	ADP
iajs-3033	57	13	rkm	rkm	PROPN
iajs-3033	57	14	method	method	NOUN
iajs-3033	57	15	the	the	DET
iajs-3033	57	16	formula	formula	NOUN
iajs-3033	57	17	of	of	ADP
iajs-3033	57	18	s	s	NOUN
iajs-3033	57	19	-	-	PUNCT
iajs-3033	57	20	stage	stage	NOUN
iajs-3033	57	21	rkm	rkm	PROPN
iajs-3033	57	22	method	method	NOUN
iajs-3033	57	23	to	to	PART
iajs-3033	57	24	solve	solve	VERB
iajs-3033	57	25	kind	kind	ADV
iajs-3033	57	26	-	-	PUNCT
iajs-3033	57	27	five	five	NUM
iajs-3033	57	28	of	of	ADP
iajs-3033	57	29	fifth	fifth	ADJ
iajs-3033	57	30	-	-	PUNCT
iajs-3033	57	31	order	order	NOUN
iajs-3033	57	32	odes	ode	NOUN
iajs-3033	57	33	is	be	AUX
iajs-3033	57	34	proposed	propose	VERB
iajs-3033	57	35	as	as	SCONJ
iajs-3033	57	36	follows	follow	VERB
iajs-3033	57	37	table	table	NOUN
iajs-3033	57	38	1	1	NUM
iajs-3033	57	39	the	the	DET
iajs-3033	57	40	butcher	butcher	NOUN
iajs-3033	57	41	tableau	tableau	PROPN
iajs-3033	57	42	rkm	rkm	PROPN
iajs-3033	57	43	method	method	NOUN
iajs-3033	57	44	of	of	ADP
iajs-3033	57	45	fifth	fifth	ADJ
iajs-3033	57	46	-	-	PUNCT
iajs-3033	57	47	order	order	NOUN
iajs-3033	57	48	0	0	NUM
iajs-3033	57	49	1	1	NUM
iajs-3033	57	50	2	2	NUM
iajs-3033	57	51	0	0	NUM
iajs-3033	57	52	1	1	NUM
iajs-3033	57	53	2	2	NUM
iajs-3033	57	54	1	1	NUM
iajs-3033	57	55	2	2	NUM
iajs-3033	57	56	0	0	NUM
iajs-3033	57	57	0	0	NUM
iajs-3033	57	58	3	3	NUM
iajs-3033	57	59	5	5	NUM
iajs-3033	58	1	+	+	CCONJ
iajs-3033	58	2	√6	√6	PROPN
iajs-3033	58	3	10	10	NUM
iajs-3033	58	4	3	3	NUM
iajs-3033	58	5	5	5	NUM
iajs-3033	58	6	−	−	NOUN
iajs-3033	58	7	√6	√6	PROPN
iajs-3033	58	8	10	10	NUM
iajs-3033	58	9	1	1	NUM
iajs-3033	58	10	0	0	NUM
iajs-3033	59	1	−	−	NOUN
iajs-3033	59	2	119	119	NUM
iajs-3033	59	3	120	120	NUM
iajs-3033	59	4	−	−	NUM
iajs-3033	59	5	1	1	NUM
iajs-3033	59	6	40	40	NUM
iajs-3033	59	7	−	−	NOUN
iajs-3033	60	1	√6	√6	PROPN
iajs-3033	60	2	360	360	NUM
iajs-3033	60	3	1	1	NUM
iajs-3033	60	4	60	60	NUM
iajs-3033	60	5	−	−	NOUN
iajs-3033	60	6	√6	√6	PROPN
iajs-3033	60	7	360	360	NUM
iajs-3033	60	8	0	0	NUM
iajs-3033	60	9	1	1	NUM
iajs-3033	60	10	18	18	NUM
iajs-3033	60	11	1	1	NUM
iajs-3033	60	12	8	8	NUM
iajs-3033	60	13	+	+	CCONJ
iajs-3033	60	14	√6	√6	PROPN
iajs-3033	60	15	48	48	NUM
iajs-3033	60	16	1	1	NUM
iajs-3033	60	17	8	8	NUM
iajs-3033	60	18	+	+	CCONJ
iajs-3033	60	19	√6	√6	PROPN
iajs-3033	60	20	48	48	NUM
iajs-3033	60	21	1	1	NUM
iajs-3033	60	22	9	9	NUM
iajs-3033	60	23	7	7	NUM
iajs-3033	60	24	36	36	NUM
iajs-3033	60	25	−	−	NOUN
iajs-3033	60	26	√6	√6	PROPN
iajs-3033	60	27	48	48	NUM
iajs-3033	60	28	7	7	NUM
iajs-3033	60	29	18	18	NUM
iajs-3033	60	30	+	+	CCONJ
iajs-3033	60	31	√6	√6	PROPN
iajs-3033	60	32	18	18	NUM
iajs-3033	60	33	1	1	NUM
iajs-3033	60	34	9	9	NUM
iajs-3033	60	35	7	7	NUM
iajs-3033	60	36	36	36	NUM
iajs-3033	60	37	−	−	NOUN
iajs-3033	60	38	√6	√6	PROPN
iajs-3033	60	39	48	48	NUM
iajs-3033	60	40	7	7	NUM
iajs-3033	60	41	18	18	NUM
iajs-3033	60	42	+	+	CCONJ
iajs-3033	60	43	√6	√6	PROPN
iajs-3033	60	44	48	48	NUM
iajs-3033	60	45	the	the	DET
iajs-3033	60	46	coefficients	coefficient	NOUN
iajs-3033	60	47	of	of	ADP
iajs-3033	60	48	the	the	DET
iajs-3033	60	49	numerical	numerical	PROPN
iajs-3033	60	50	rkm	rkm	PROPN
iajs-3033	60	51	methods	method	NOUN
iajs-3033	60	52	are	be	AUX
iajs-3033	60	53	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-3033	60	54	;	;	PUNCT
iajs-3033	60	55	𝑐𝑖	𝑐𝑖	NOUN
iajs-3033	60	56	;	;	PUNCT
iajs-3033	60	57	𝑏𝑖	𝑏𝑖	ADP
iajs-3033	60	58	;	;	PUNCT
iajs-3033	60	59	𝑏𝑖	𝑏𝑖	ADP
iajs-3033	60	60	՛	՛	NUM
iajs-3033	60	61	;	;	PUNCT
iajs-3033	60	62	𝑏𝑖	𝑏𝑖	ADP
iajs-3033	60	63	՛՛	՛՛	NOUN
iajs-3033	60	64	;	;	PUNCT
iajs-3033	60	65	𝑏𝑖	𝑏𝑖	ADP
iajs-3033	60	66	՛՛՛	՛՛՛	PROPN
iajs-3033	60	67	;	;	PUNCT
iajs-3033	60	68	ihjpas	ihjpas	PROPN
iajs-3033	60	69	.	.	PUNCT
iajs-3033	61	1	36	36	NUM
iajs-3033	61	2	(	(	PUNCT
iajs-3033	61	3	3	3	NUM
iajs-3033	61	4	)	)	PUNCT
iajs-3033	61	5	2023	2023	NUM
iajs-3033	61	6	420	420	NUM
iajs-3033	61	7	and	and	CCONJ
iajs-3033	61	8	𝑏𝑖	𝑏𝑖	ADP
iajs-3033	61	9	(	(	PUNCT
iajs-3033	61	10	4	4	NUM
iajs-3033	61	11	)	)	PUNCT
iajs-3033	61	12	assumed	assume	VERB
iajs-3033	61	13	to	to	PART
iajs-3033	61	14	be	be	AUX
iajs-3033	61	15	real	real	ADJ
iajs-3033	61	16	for	for	ADP
iajs-3033	61	17	𝑖	𝑖	SYM
iajs-3033	61	18	;	;	PUNCT
iajs-3033	61	19	𝑗	𝑗	NOUN
iajs-3033	61	20	=	=	SYM
iajs-3033	61	21	1,2	1,2	NUM
iajs-3033	61	22	,	,	PUNCT
iajs-3033	61	23	…	…	PUNCT
iajs-3033	61	24	,	,	PUNCT
iajs-3033	61	25	𝑠.	𝑠.	PROPN
iajs-3033	61	26	however	however	ADV
iajs-3033	61	27	,	,	PUNCT
iajs-3033	61	28	mechee	mechee	PROPN
iajs-3033	61	29	&	&	CCONJ
iajs-3033	61	30	kadhim	kadhim	PROPN
iajs-3033	61	31	derived	derive	VERB
iajs-3033	61	32	direct	direct	ADJ
iajs-3033	61	33	numerical	numerical	ADJ
iajs-3033	61	34	three	three	NUM
iajs-3033	61	35	-	-	PUNCT
iajs-3033	61	36	stage	stage	NOUN
iajs-3033	61	37	rkm	rkm	PROPN
iajs-3033	61	38	methods	method	NOUN
iajs-3033	61	39	of	of	ADP
iajs-3033	61	40	fifth	fifth	ADJ
iajs-3033	61	41	-	-	PUNCT
iajs-3033	61	42	order	order	NOUN
iajs-3033	61	43	for	for	ADP
iajs-3033	61	44	solving	solve	VERB
iajs-3033	61	45	fifth	fifth	ADJ
iajs-3033	61	46	-	-	PUNCT
iajs-3033	61	47	order	order	NOUN
iajs-3033	61	48	odes	ode	VERB
iajs-3033	61	49	[	[	X
iajs-3033	61	50	10	10	NUM
iajs-3033	61	51	]	]	PUNCT
iajs-3033	61	52	,	,	PUNCT
iajs-3033	61	53	which	which	PRON
iajs-3033	61	54	expressed	express	VERB
iajs-3033	61	55	in	in	ADP
iajs-3033	61	56	the	the	DET
iajs-3033	61	57	following	following	NOUN
iajs-3033	61	58	.	.	PUNCT
iajs-3033	62	1	3	3	X
iajs-3033	62	2	.	.	NUM
iajs-3033	62	3	proposed	propose	VERB
iajs-3033	62	4	numerical	numerical	ADJ
iajs-3033	62	5	methods	method	NOUN
iajs-3033	62	6	for	for	ADP
iajs-3033	62	7	solving	solve	VERB
iajs-3033	62	8	fodes	fode	NOUN
iajs-3033	62	9	of	of	ADP
iajs-3033	62	10	fifth	fifth	ADJ
iajs-3033	62	11	-	-	PUNCT
iajs-3033	62	12	order	order	NOUN
iajs-3033	62	13	in	in	ADP
iajs-3033	62	14	this	this	DET
iajs-3033	62	15	part	part	NOUN
iajs-3033	62	16	,	,	PUNCT
iajs-3033	62	17	we	we	PRON
iajs-3033	62	18	have	have	AUX
iajs-3033	62	19	established	establish	VERB
iajs-3033	62	20	two	two	NUM
iajs-3033	62	21	numerical	numerical	ADJ
iajs-3033	62	22	methods	method	NOUN
iajs-3033	62	23	and	and	CCONJ
iajs-3033	62	24	modified	modify	VERB
iajs-3033	62	25	another	another	DET
iajs-3033	62	26	two	two	NUM
iajs-3033	62	27	numerical	numerical	ADJ
iajs-3033	62	28	methods	method	NOUN
iajs-3033	62	29	for	for	ADP
iajs-3033	62	30	solving	solve	VERB
iajs-3033	62	31	fifth	fifth	ADJ
iajs-3033	62	32	-	-	PUNCT
iajs-3033	62	33	order	order	NOUN
iajs-3033	62	34	fodes	fode	NOUN
iajs-3033	62	35	which	which	PRON
iajs-3033	62	36	belong	belong	VERB
iajs-3033	62	37	to	to	ADP
iajs-3033	62	38	a	a	DET
iajs-3033	62	39	kind	kind	NOUN
iajs-3033	62	40	of	of	ADP
iajs-3033	62	41	quasi	quasi	ADJ
iajs-3033	62	42	linear	linear	PROPN
iajs-3033	62	43	in	in	ADP
iajs-3033	62	44	equation	equation	NOUN
iajs-3033	62	45	(	(	PUNCT
iajs-3033	62	46	7	7	NUM
iajs-3033	62	47	)	)	PUNCT
iajs-3033	62	48	with	with	ADP
iajs-3033	62	49	the	the	DET
iajs-3033	62	50	ics	ics	NOUN
iajs-3033	62	51	in	in	ADP
iajs-3033	62	52	equation	equation	NOUN
iajs-3033	62	53	(	(	PUNCT
iajs-3033	62	54	2	2	NUM
iajs-3033	62	55	)	)	PUNCT
iajs-3033	62	56	.	.	PUNCT
iajs-3033	63	1	also	also	ADV
iajs-3033	63	2	,	,	PUNCT
iajs-3033	63	3	we	we	PRON
iajs-3033	63	4	give	give	VERB
iajs-3033	63	5	derivation	derivation	NOUN
iajs-3033	63	6	of	of	ADP
iajs-3033	63	7	the	the	DET
iajs-3033	63	8	generalized	generalize	VERB
iajs-3033	63	9	euler	euler	NOUN
iajs-3033	63	10	method	method	NOUN
iajs-3033	63	11	as	as	ADP
iajs-3033	63	12	the	the	DET
iajs-3033	63	13	generalized	generalized	ADJ
iajs-3033	63	14	taylor	taylor	PROPN
iajs-3033	63	15	expansion	expansion	NOUN
iajs-3033	63	16	of	of	ADP
iajs-3033	63	17	𝑢(𝑡	𝑢(𝑡	PROPN
iajs-3033	63	18	+	+	CCONJ
iajs-3033	63	19	ℎ	ℎ	NOUN
iajs-3033	63	20	)	)	PUNCT
iajs-3033	63	21	is	be	AUX
iajs-3033	63	22	:	:	PUNCT
iajs-3033	63	23	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	63	24	+	+	NUM
iajs-3033	63	25	ℎ	ℎ	PROPN
iajs-3033	63	26	)	)	PUNCT
iajs-3033	63	27	=	=	SYM
iajs-3033	63	28	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	63	29	)	)	PUNCT
iajs-3033	63	30	+	+	CCONJ
iajs-3033	63	31	ℎ𝛼	ℎ𝛼	PROPN
iajs-3033	63	32	𝛤((𝛼+1	𝛤((𝛼+1	NUM
iajs-3033	63	33	)	)	PUNCT
iajs-3033	63	34	𝐷𝛼𝑢(𝜏	𝐷𝛼𝑢(𝜏	PROPN
iajs-3033	63	35	)	)	PUNCT
iajs-3033	63	36	+	+	NUM
iajs-3033	63	37	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	63	38	𝛤(2𝛼+1	𝛤(2𝛼+1	NOUN
iajs-3033	63	39	)	)	PUNCT
iajs-3033	63	40	𝐷2𝛼𝑢(𝜏	𝐷2𝛼𝑢(𝜏	PROPN
iajs-3033	63	41	)	)	PUNCT
iajs-3033	64	1	+	+	NUM
iajs-3033	64	2	ℎ3𝛼	ℎ3𝛼	PROPN
iajs-3033	64	3	𝛤(3𝛼+1	𝛤(3𝛼+1	NOUN
iajs-3033	64	4	)	)	PUNCT
iajs-3033	64	5	𝐷3𝛼𝑢(𝜏	𝐷3𝛼𝑢(𝜏	PROPN
iajs-3033	64	6	)	)	PUNCT
iajs-3033	64	7	+	+	PUNCT
iajs-3033	64	8	+	+	CCONJ
iajs-3033	64	9	ℎ4𝛼	ℎ4𝛼	ADJ
iajs-3033	64	10	𝛤(4𝛼+1	𝛤(4𝛼+1	ADJ
iajs-3033	64	11	)	)	PUNCT
iajs-3033	64	12	𝐷4𝛼𝑢(𝜏	𝐷4𝛼𝑢(𝜏	PROPN
iajs-3033	64	13	)	)	PUNCT
iajs-3033	64	14	+	+	CCONJ
iajs-3033	64	15	ℎ5𝛼	ℎ5𝛼	NOUN
iajs-3033	64	16	𝛤(5𝛼+1	𝛤(5𝛼+1	NOUN
iajs-3033	64	17	)	)	PUNCT
iajs-3033	64	18	𝐷5𝛼𝑢(𝜏	𝐷5𝛼𝑢(𝜏	PROPN
iajs-3033	64	19	)	)	PUNCT
iajs-3033	64	20	+	+	PUNCT
iajs-3033	64	21	+	+	CCONJ
iajs-3033	64	22	ℎ6𝛼	ℎ6𝛼	PROPN
iajs-3033	64	23	𝛤(6𝛼+1	𝛤(6𝛼+1	NOUN
iajs-3033	64	24	)	)	PUNCT
iajs-3033	64	25	𝐷6𝛼𝑢(𝜏	𝐷6𝛼𝑢(𝜏	PROPN
iajs-3033	64	26	)	)	PUNCT
iajs-3033	65	1	+	+	CCONJ
iajs-3033	65	2	⋯	⋯	PROPN
iajs-3033	65	3	(	(	PUNCT
iajs-3033	65	4	8)	8)	NUM
iajs-3033	65	5	we	we	PRON
iajs-3033	65	6	ignore	ignore	VERB
iajs-3033	65	7	the	the	DET
iajs-3033	65	8	higher	high	ADJ
iajs-3033	65	9	terms	term	NOUN
iajs-3033	65	10	involving	involve	VERB
iajs-3033	65	11	𝐷5𝛼𝑢(𝜏	𝐷5𝛼𝑢(𝜏	PROPN
iajs-3033	65	12	)	)	PUNCT
iajs-3033	65	13	in	in	ADP
iajs-3033	65	14	equation	equation	NOUN
iajs-3033	65	15	(	(	PUNCT
iajs-3033	65	16	8)	8)	NUM
iajs-3033	65	17	for	for	ADP
iajs-3033	65	18	the	the	DET
iajs-3033	65	19	very	very	ADV
iajs-3033	65	20	small	small	ADJ
iajs-3033	65	21	step	step	NOUN
iajs-3033	65	22	size	size	NOUN
iajs-3033	65	23	.	.	PUNCT
iajs-3033	66	1	substitute	substitute	VERB
iajs-3033	66	2	the	the	DET
iajs-3033	66	3	value	value	NOUN
iajs-3033	66	4	of	of	ADP
iajs-3033	66	5	𝐷5𝛼𝑢(𝜏	𝐷5𝛼𝑢(𝜏	PROPN
iajs-3033	66	6	)	)	PUNCT
iajs-3033	66	7	from	from	ADP
iajs-3033	66	8	equation	equation	NOUN
iajs-3033	66	9	(	(	PUNCT
iajs-3033	66	10	8)	8)	NUM
iajs-3033	66	11	to	to	PART
iajs-3033	66	12	obtain	obtain	VERB
iajs-3033	66	13	the	the	DET
iajs-3033	66	14	following	follow	VERB
iajs-3033	66	15	formula	formula	NOUN
iajs-3033	66	16	:	:	PUNCT
iajs-3033	66	17	𝑢𝑛+1(𝜏	𝑢𝑛+1(𝜏	NOUN
iajs-3033	66	18	)	)	PUNCT
iajs-3033	66	19	=	=	SYM
iajs-3033	66	20	𝑢𝑛(𝜏	𝑢𝑛(𝜏	NUM
iajs-3033	66	21	)	)	PUNCT
iajs-3033	67	1	+	+	CCONJ
iajs-3033	67	2	ℎ𝛼	ℎ𝛼	ADP
iajs-3033	67	3	𝛤(𝛼	𝛤(𝛼	PRON
iajs-3033	67	4	+	+	ADJ
iajs-3033	67	5	1	1	X
iajs-3033	67	6	)	)	PUNCT
iajs-3033	67	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	67	8	𝛼(𝜏	𝛼(𝜏	NOUN
iajs-3033	67	9	)	)	PUNCT
iajs-3033	68	1	+	+	NUM
iajs-3033	68	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	68	3	𝛤(2𝛼	𝛤(2𝛼	X
iajs-3033	68	4	+	+	CCONJ
iajs-3033	68	5	1	1	X
iajs-3033	68	6	)	)	PUNCT
iajs-3033	68	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	68	8	2𝛼(𝜏	2𝛼(𝜏	NUM
iajs-3033	68	9	)	)	PUNCT
iajs-3033	69	1	+	+	CCONJ
iajs-3033	69	2	ℎ3𝛼	ℎ3𝛼	NOUN
iajs-3033	69	3	𝛤(3𝛼	𝛤(3𝛼	VERB
iajs-3033	69	4	+	+	NOUN
iajs-3033	69	5	1	1	X
iajs-3033	69	6	)	)	PUNCT
iajs-3033	69	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	69	8	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	69	9	)	)	PUNCT
iajs-3033	70	1	+	+	CCONJ
iajs-3033	70	2	ℎ4𝛼	ℎ4𝛼	SYM
iajs-3033	70	3	𝛤(4𝛼	𝛤(4𝛼	NOUN
iajs-3033	70	4	+	+	CCONJ
iajs-3033	70	5	1	1	X
iajs-3033	70	6	)	)	PUNCT
iajs-3033	70	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	70	8	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	70	9	)	)	PUNCT
iajs-3033	71	1	+	+	NUM
iajs-3033	71	2	ℎ5𝛼	ℎ5𝛼	NOUN
iajs-3033	71	3	𝛤(5𝛼	𝛤(5𝛼	ADJ
iajs-3033	71	4	+	+	CCONJ
iajs-3033	71	5	1	1	X
iajs-3033	71	6	)	)	PUNCT
iajs-3033	71	7	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	71	8	,	,	PUNCT
iajs-3033	71	9	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	71	10	)	)	PUNCT
iajs-3033	71	11	,	,	PUNCT
iajs-3033	71	12	(	(	PUNCT
iajs-3033	71	13	9	9	X
iajs-3033	71	14	)	)	PUNCT
iajs-3033	71	15	by	by	ADP
iajs-3033	71	16	derivation	derivation	NOUN
iajs-3033	71	17	equation	equation	NOUN
iajs-3033	71	18	(	(	PUNCT
iajs-3033	71	19	16	16	NUM
iajs-3033	71	20	)	)	PUNCT
iajs-3033	71	21	once	once	ADV
iajs-3033	71	22	,	,	PUNCT
iajs-3033	71	23	twice	twice	ADV
iajs-3033	71	24	,	,	PUNCT
iajs-3033	71	25	three	three	NUM
iajs-3033	71	26	and	and	CCONJ
iajs-3033	71	27	four	four	NUM
iajs-3033	71	28	,	,	PUNCT
iajs-3033	71	29	we	we	PRON
iajs-3033	71	30	obtain	obtain	VERB
iajs-3033	71	31	the	the	DET
iajs-3033	71	32	following	following	NOUN
iajs-3033	71	33	:	:	PUNCT
iajs-3033	71	34	𝑢𝑛+1	𝑢𝑛+1	NUM
iajs-3033	71	35	𝛼	𝛼	PART
iajs-3033	71	36	(	(	PUNCT
iajs-3033	71	37	𝜏	𝜏	NOUN
iajs-3033	71	38	)	)	PUNCT
iajs-3033	71	39	=	=	PUNCT
iajs-3033	71	40	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	71	41	𝛼(𝜏	𝛼(𝜏	NOUN
iajs-3033	71	42	)	)	PUNCT
iajs-3033	71	43	+	+	CCONJ
iajs-3033	72	1	ℎ𝛼	ℎ𝛼	PROPN
iajs-3033	72	2	𝛤𝛼	𝛤𝛼	PROPN
iajs-3033	72	3	+	+	NOUN
iajs-3033	72	4	1	1	X
iajs-3033	72	5	)	)	PUNCT
iajs-3033	72	6	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	72	7	2𝛼(𝜏	2𝛼(𝜏	NUM
iajs-3033	72	8	)	)	PUNCT
iajs-3033	73	1	+	+	NUM
iajs-3033	73	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	73	3	𝛤(2𝛼	𝛤(2𝛼	X
iajs-3033	73	4	+	+	CCONJ
iajs-3033	73	5	1	1	X
iajs-3033	73	6	)	)	PUNCT
iajs-3033	73	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	73	8	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	73	9	)	)	PUNCT
iajs-3033	74	1	+	+	CCONJ
iajs-3033	74	2	ℎ3𝛼	ℎ3𝛼	NOUN
iajs-3033	74	3	𝛤(3𝛼	𝛤(3𝛼	VERB
iajs-3033	74	4	+	+	NOUN
iajs-3033	74	5	1	1	X
iajs-3033	74	6	)	)	PUNCT
iajs-3033	74	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	74	8	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	74	9	)	)	PUNCT
iajs-3033	75	1	+	+	CCONJ
iajs-3033	75	2	ℎ4𝛼	ℎ4𝛼	SYM
iajs-3033	75	3	𝛤(4𝛼	𝛤(4𝛼	NOUN
iajs-3033	75	4	+	+	CCONJ
iajs-3033	75	5	1	1	X
iajs-3033	75	6	)	)	PUNCT
iajs-3033	75	7	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	75	8	,	,	PUNCT
iajs-3033	75	9	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	75	10	)	)	PUNCT
iajs-3033	75	11	,	,	PUNCT
iajs-3033	75	12	(	(	PUNCT
iajs-3033	75	13	10	10	NUM
iajs-3033	75	14	)	)	PUNCT
iajs-3033	75	15	𝑢	𝑢	PROPN
iajs-3033	75	16	𝑛+1	𝑛+1	PROPN
iajs-3033	75	17	2𝛼	2𝛼	PROPN
iajs-3033	75	18	(	(	PUNCT
iajs-3033	75	19	𝜏	𝜏	NOUN
iajs-3033	75	20	)	)	PUNCT
iajs-3033	75	21	=	=	SYM
iajs-3033	75	22	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	75	23	2𝛼(𝜏	2𝛼(𝜏	NUM
iajs-3033	75	24	)	)	PUNCT
iajs-3033	76	1	+	+	CCONJ
iajs-3033	76	2	ℎ𝛼	ℎ𝛼	PROPN
iajs-3033	76	3	𝛤𝛼	𝛤𝛼	PROPN
iajs-3033	76	4	+	+	NOUN
iajs-3033	76	5	1	1	NUM
iajs-3033	76	6	)	)	PUNCT
iajs-3033	76	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	76	8	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	76	9	)	)	PUNCT
iajs-3033	77	1	+	+	CCONJ
iajs-3033	77	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	77	3	𝛤(2𝛼	𝛤(2𝛼	X
iajs-3033	77	4	+	+	CCONJ
iajs-3033	77	5	1	1	X
iajs-3033	77	6	)	)	PUNCT
iajs-3033	77	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	77	8	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	77	9	)	)	PUNCT
iajs-3033	78	1	+	+	CCONJ
iajs-3033	78	2	ℎ3𝛼	ℎ3𝛼	NOUN
iajs-3033	78	3	𝛤(3𝛼	𝛤(3𝛼	VERB
iajs-3033	78	4	+	+	NOUN
iajs-3033	78	5	1	1	NUM
iajs-3033	78	6	)	)	PUNCT
iajs-3033	79	1	+	+	CCONJ
iajs-3033	79	2	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	79	3	,	,	PUNCT
iajs-3033	79	4	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	79	5	)	)	PUNCT
iajs-3033	79	6	(	(	PUNCT
iajs-3033	79	7	11	11	NUM
iajs-3033	79	8	)	)	PUNCT
iajs-3033	79	9	𝑢𝑛+1	𝑢𝑛+1	NUM
iajs-3033	79	10	3𝛼	3𝛼	NUM
iajs-3033	79	11	(	(	PUNCT
iajs-3033	79	12	𝜏	𝜏	NOUN
iajs-3033	79	13	)	)	PUNCT
iajs-3033	79	14	=	=	SYM
iajs-3033	79	15	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	79	16	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	79	17	)	)	PUNCT
iajs-3033	80	1	+	+	CCONJ
iajs-3033	80	2	ℎ𝛼	ℎ𝛼	PROPN
iajs-3033	80	3	𝛤𝛼	𝛤𝛼	PROPN
iajs-3033	80	4	+	+	NOUN
iajs-3033	80	5	1	1	X
iajs-3033	80	6	)	)	PUNCT
iajs-3033	80	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	80	8	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	80	9	)	)	PUNCT
iajs-3033	81	1	+	+	NUM
iajs-3033	81	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	81	3	𝛤(2𝛼	𝛤(2𝛼	X
iajs-3033	81	4	+	+	CCONJ
iajs-3033	81	5	1	1	X
iajs-3033	81	6	)	)	PUNCT
iajs-3033	81	7	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	81	8	,	,	PUNCT
iajs-3033	81	9	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	81	10	)	)	PUNCT
iajs-3033	81	11	,	,	PUNCT
iajs-3033	81	12	(	(	PUNCT
iajs-3033	81	13	12	12	NUM
iajs-3033	81	14	)	)	PUNCT
iajs-3033	81	15	𝑢𝑛+1	𝑢𝑛+1	PROPN
iajs-3033	81	16	4𝛼	4𝛼	NOUN
iajs-3033	81	17	(	(	PUNCT
iajs-3033	81	18	𝜏	𝜏	NOUN
iajs-3033	81	19	)	)	PUNCT
iajs-3033	81	20	=	=	SYM
iajs-3033	81	21	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	81	22	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	81	23	)	)	PUNCT
iajs-3033	82	1	+	+	CCONJ
iajs-3033	82	2	ℎ𝛼	ℎ𝛼	PROPN
iajs-3033	82	3	𝛤𝛼	𝛤𝛼	PROPN
iajs-3033	82	4	+	+	NOUN
iajs-3033	82	5	1	1	NUM
iajs-3033	82	6	)	)	PUNCT
iajs-3033	82	7	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	82	8	,	,	PUNCT
iajs-3033	82	9	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	82	10	)	)	PUNCT
iajs-3033	82	11	.	.	PUNCT
iajs-3033	83	1	(	(	PUNCT
iajs-3033	83	2	13	13	NUM
iajs-3033	83	3	)	)	PUNCT
iajs-3033	83	4	in	in	ADP
iajs-3033	83	5	addition	addition	NOUN
iajs-3033	83	6	,	,	PUNCT
iajs-3033	83	7	by	by	ADP
iajs-3033	83	8	introducing	introduce	VERB
iajs-3033	83	9	the	the	DET
iajs-3033	83	10	derivation	derivation	NOUN
iajs-3033	83	11	of	of	ADP
iajs-3033	83	12	developed	develop	VERB
iajs-3033	83	13	rkm	rkm	PROPN
iajs-3033	83	14	method	method	NOUN
iajs-3033	83	15	of	of	ADP
iajs-3033	83	16	two	two	NUM
iajs-3033	83	17	-	-	PUNCT
iajs-3033	83	18	stages	stage	NOUN
iajs-3033	83	19	using	use	VERB
iajs-3033	83	20	the	the	DET
iajs-3033	83	21	chain	chain	NOUN
iajs-3033	83	22	rule	rule	NOUN
iajs-3033	83	23	,	,	PUNCT
iajs-3033	83	24	we	we	PRON
iajs-3033	83	25	get	get	VERB
iajs-3033	83	26	the	the	DET
iajs-3033	83	27	following	following	NOUN
iajs-3033	83	28	:	:	PUNCT
iajs-3033	83	29	ihjpas	ihjpas	PROPN
iajs-3033	83	30	.	.	PUNCT
iajs-3033	84	1	36	36	NUM
iajs-3033	84	2	(	(	PUNCT
iajs-3033	84	3	3	3	NUM
iajs-3033	84	4	)	)	PUNCT
iajs-3033	84	5	2023	2023	NUM
iajs-3033	84	6	421	421	NUM
iajs-3033	84	7	𝐷6𝛼𝑢(𝜏	𝐷6𝛼𝑢(𝜏	PROPN
iajs-3033	84	8	)	)	PUNCT
iajs-3033	84	9	=	=	PUNCT
iajs-3033	84	10	𝐷𝛼(𝐷5𝛼𝑢(𝜏	𝐷𝛼(𝐷5𝛼𝑢(𝜏	NOUN
iajs-3033	84	11	)	)	PUNCT
iajs-3033	84	12	)	)	PUNCT
iajs-3033	85	1	=	=	SYM
iajs-3033	85	2	𝐷𝛼	𝐷𝛼	NOUN
iajs-3033	85	3	(	(	PUNCT
iajs-3033	85	4	𝑓(𝜏	𝑓(𝜏	PROPN
iajs-3033	85	5	,	,	PUNCT
iajs-3033	85	6	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	85	7	)	)	PUNCT
iajs-3033	85	8	)	)	PUNCT
iajs-3033	85	9	)	)	PUNCT
iajs-3033	86	1	=	=	X
iajs-3033	86	2	𝐷𝛼	𝐷𝛼	NOUN
iajs-3033	86	3	(	(	PUNCT
iajs-3033	86	4	𝑓(𝜏	𝑓(𝜏	PROPN
iajs-3033	86	5	,	,	PUNCT
iajs-3033	86	6	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	86	7	)	)	PUNCT
iajs-3033	86	8	)	)	PUNCT
iajs-3033	86	9	)	)	PUNCT
iajs-3033	87	1	+	+	CCONJ
iajs-3033	87	2	𝑓(𝜏	𝑓(𝜏	PROPN
iajs-3033	87	3	,	,	PUNCT
iajs-3033	87	4	𝑢(𝜏))𝐷𝑢	𝑢(𝜏))𝐷𝑢	PROPN
iajs-3033	87	5	𝛼𝑓(𝜏	𝛼𝑓(𝜏	NUM
iajs-3033	87	6	,	,	PUNCT
iajs-3033	87	7	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	87	8	)	)	PUNCT
iajs-3033	87	9	)	)	PUNCT
iajs-3033	87	10	,	,	PUNCT
iajs-3033	87	11	(	(	PUNCT
iajs-3033	87	12	14	14	NUM
iajs-3033	87	13	)	)	PUNCT
iajs-3033	87	14	we	we	PRON
iajs-3033	87	15	ignore	ignore	VERB
iajs-3033	87	16	the	the	DET
iajs-3033	87	17	higher	high	ADJ
iajs-3033	87	18	terms	term	NOUN
iajs-3033	87	19	involving	involve	VERB
iajs-3033	87	20	𝐷6𝛼𝑢(𝑡	𝐷6𝛼𝑢(𝑡	PROPN
iajs-3033	87	21	)	)	PUNCT
iajs-3033	87	22	in	in	ADP
iajs-3033	87	23	equation	equation	NOUN
iajs-3033	87	24	(	(	PUNCT
iajs-3033	87	25	8)	8)	NUM
iajs-3033	87	26	for	for	ADP
iajs-3033	87	27	the	the	DET
iajs-3033	87	28	very	very	ADV
iajs-3033	87	29	small	small	ADJ
iajs-3033	87	30	step	step	NOUN
iajs-3033	87	31	size	size	NOUN
iajs-3033	87	32	and	and	CCONJ
iajs-3033	87	33	substitute	substitute	VERB
iajs-3033	87	34	the	the	DET
iajs-3033	87	35	value	value	NOUN
iajs-3033	87	36	of	of	ADP
iajs-3033	87	37	𝐷5𝛼𝑢(𝑡	𝐷5𝛼𝑢(𝑡	PROPN
iajs-3033	87	38	)	)	PUNCT
iajs-3033	87	39	from	from	ADP
iajs-3033	87	40	equation	equation	NOUN
iajs-3033	87	41	(	(	PUNCT
iajs-3033	87	42	7	7	NUM
iajs-3033	87	43	)	)	PUNCT
iajs-3033	87	44	to	to	PART
iajs-3033	87	45	obtain	obtain	VERB
iajs-3033	87	46	the	the	DET
iajs-3033	87	47	following	follow	VERB
iajs-3033	87	48	formula	formula	NOUN
iajs-3033	87	49	:	:	PUNCT
iajs-3033	87	50	𝑢𝑛+1	𝑢𝑛+1	NUM
iajs-3033	87	51	=	=	SYM
iajs-3033	87	52	𝑢𝑛(𝜏	𝑢𝑛(𝜏	NOUN
iajs-3033	87	53	)	)	PUNCT
iajs-3033	88	1	+	+	CCONJ
iajs-3033	89	1	ℎ𝛼	ℎ𝛼	ADP
iajs-3033	89	2	𝛤(𝛼	𝛤(𝛼	PRON
iajs-3033	89	3	+	+	ADJ
iajs-3033	89	4	1	1	X
iajs-3033	89	5	)	)	PUNCT
iajs-3033	89	6	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	89	7	𝛼(𝜏	𝛼(𝜏	NOUN
iajs-3033	89	8	)	)	PUNCT
iajs-3033	90	1	+	+	NUM
iajs-3033	90	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	90	3	𝛤(2𝛼	𝛤(2𝛼	X
iajs-3033	90	4	+	+	CCONJ
iajs-3033	90	5	1	1	X
iajs-3033	90	6	)	)	PUNCT
iajs-3033	90	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	90	8	2𝛼(𝜏	2𝛼(𝜏	NUM
iajs-3033	90	9	)	)	PUNCT
iajs-3033	91	1	+	+	CCONJ
iajs-3033	91	2	ℎ3𝛼	ℎ3𝛼	NOUN
iajs-3033	91	3	𝛤(3𝛼	𝛤(3𝛼	VERB
iajs-3033	91	4	+	+	NOUN
iajs-3033	91	5	1	1	X
iajs-3033	91	6	)	)	PUNCT
iajs-3033	91	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	91	8	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	91	9	)	)	PUNCT
iajs-3033	92	1	+	+	CCONJ
iajs-3033	92	2	ℎ4𝛼	ℎ4𝛼	SYM
iajs-3033	92	3	𝛤(4𝛼	𝛤(4𝛼	NOUN
iajs-3033	92	4	+	+	CCONJ
iajs-3033	92	5	1	1	X
iajs-3033	92	6	)	)	PUNCT
iajs-3033	92	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	92	8	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	92	9	)	)	PUNCT
iajs-3033	93	1	+	+	NUM
iajs-3033	93	2	ℎ5𝛼	ℎ5𝛼	NOUN
iajs-3033	93	3	𝛤(5𝛼	𝛤(5𝛼	ADJ
iajs-3033	93	4	+	+	CCONJ
iajs-3033	93	5	1	1	X
iajs-3033	93	6	)	)	PUNCT
iajs-3033	93	7	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	93	8	,	,	PUNCT
iajs-3033	93	9	𝑢𝑛(𝜏	𝑢𝑛(𝜏	NUM
iajs-3033	93	10	)	)	PUNCT
iajs-3033	93	11	)	)	PUNCT
iajs-3033	94	1	+	+	CCONJ
iajs-3033	94	2	ℎ6𝛼	ℎ6𝛼	PROPN
iajs-3033	94	3	𝛤(6𝛼	𝛤(6𝛼	VERB
iajs-3033	94	4	+	+	X
iajs-3033	94	5	1	1	X
iajs-3033	94	6	)	)	PUNCT
iajs-3033	94	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	94	8	6𝛼(𝜏	6𝛼(𝜏	NUM
iajs-3033	94	9	)	)	PUNCT
iajs-3033	95	1	+	+	CCONJ
iajs-3033	95	2	ℎ6𝛼	ℎ6𝛼	PROPN
iajs-3033	95	3	𝛤(6𝛼	𝛤(6𝛼	VERB
iajs-3033	95	4	+	+	X
iajs-3033	95	5	1	1	X
iajs-3033	95	6	)	)	PUNCT
iajs-3033	95	7	(	(	PUNCT
iajs-3033	95	8	𝐷𝛼	𝐷𝛼	NOUN
iajs-3033	95	9	(	(	PUNCT
iajs-3033	95	10	𝑓(𝜏	𝑓(𝜏	PROPN
iajs-3033	95	11	,	,	PUNCT
iajs-3033	95	12	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	95	13	)	)	PUNCT
iajs-3033	95	14	)	)	PUNCT
iajs-3033	95	15	)	)	PUNCT
iajs-3033	96	1	+	+	CCONJ
iajs-3033	96	2	𝑓(𝜏	𝑓(𝜏	PROPN
iajs-3033	96	3	,	,	PUNCT
iajs-3033	96	4	𝑢(𝜏))𝐷𝑢	𝑢(𝜏))𝐷𝑢	PROPN
iajs-3033	96	5	𝛼𝑓(𝜏	𝛼𝑓(𝜏	NUM
iajs-3033	96	6	,	,	PUNCT
iajs-3033	96	7	𝑢(𝜏	𝑢(𝜏	PROPN
iajs-3033	96	8	)	)	PUNCT
iajs-3033	96	9	)	)	PUNCT
iajs-3033	96	10	)	)	PUNCT
iajs-3033	97	1	=	=	SYM
iajs-3033	97	2	𝑢𝑛(𝜏	𝑢𝑛(𝜏	X
iajs-3033	97	3	)	)	PUNCT
iajs-3033	98	1	+	+	CCONJ
iajs-3033	98	2	ℎ𝛼	ℎ𝛼	ADP
iajs-3033	98	3	𝛤(𝛼	𝛤(𝛼	PRON
iajs-3033	98	4	+	+	ADJ
iajs-3033	98	5	1	1	X
iajs-3033	98	6	)	)	PUNCT
iajs-3033	98	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	98	8	𝛼(𝜏	𝛼(𝜏	NOUN
iajs-3033	98	9	)	)	PUNCT
iajs-3033	99	1	+	+	NUM
iajs-3033	99	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	99	3	𝛤(2𝛼	𝛤(2𝛼	X
iajs-3033	99	4	+	+	CCONJ
iajs-3033	99	5	1	1	X
iajs-3033	99	6	)	)	PUNCT
iajs-3033	99	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	99	8	2𝛼(𝜏	2𝛼(𝜏	NUM
iajs-3033	99	9	)	)	PUNCT
iajs-3033	100	1	+	+	CCONJ
iajs-3033	100	2	ℎ3𝛼	ℎ3𝛼	NOUN
iajs-3033	100	3	𝛤(3𝛼	𝛤(3𝛼	VERB
iajs-3033	100	4	+	+	NOUN
iajs-3033	100	5	1	1	X
iajs-3033	100	6	)	)	PUNCT
iajs-3033	100	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	100	8	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	100	9	)	)	PUNCT
iajs-3033	101	1	+	+	CCONJ
iajs-3033	101	2	ℎ4𝛼	ℎ4𝛼	SYM
iajs-3033	101	3	𝛤(4𝛼	𝛤(4𝛼	NOUN
iajs-3033	101	4	+	+	CCONJ
iajs-3033	101	5	1	1	X
iajs-3033	101	6	)	)	PUNCT
iajs-3033	101	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	101	8	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	101	9	)	)	PUNCT
iajs-3033	102	1	+	+	NUM
iajs-3033	102	2	ℎ5𝛼	ℎ5𝛼	NOUN
iajs-3033	102	3	𝛤(5𝛼	𝛤(5𝛼	ADJ
iajs-3033	102	4	+	+	CCONJ
iajs-3033	102	5	1	1	X
iajs-3033	102	6	)	)	PUNCT
iajs-3033	102	7	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	102	8	,	,	PUNCT
iajs-3033	102	9	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	102	10	)	)	PUNCT
iajs-3033	102	11	+	+	NUM
iajs-3033	102	12	ℎ5𝛼	ℎ5𝛼	NOUN
iajs-3033	102	13	3	3	NUM
iajs-3033	102	14	!	!	NOUN
iajs-3033	102	15	𝛤(5𝛼	𝛤(5𝛼	AUX
iajs-3033	103	1	+	+	CCONJ
iajs-3033	103	2	1	1	X
iajs-3033	103	3	)	)	PUNCT
iajs-3033	103	4	(	(	PUNCT
iajs-3033	103	5	𝑓	𝑓	X
iajs-3033	103	6	(	(	PUNCT
iajs-3033	103	7	𝜏𝑛	𝜏𝑛	ADP
iajs-3033	103	8	+	+	NOUN
iajs-3033	103	9	6ℎ5𝛼𝛤(5𝛼	6ℎ5𝛼𝛤(5𝛼	NUM
iajs-3033	103	10	+	+	NOUN
iajs-3033	103	11	1	1	NUM
iajs-3033	103	12	)	)	PUNCT
iajs-3033	103	13	𝛤(6𝛼	𝛤(6𝛼	VERB
iajs-3033	104	1	+	+	X
iajs-3033	104	2	1	1	X
iajs-3033	104	3	)	)	PUNCT
iajs-3033	104	4	,	,	PUNCT
iajs-3033	104	5	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	104	6	)	)	PUNCT
iajs-3033	104	7	+	+	PUNCT
iajs-3033	105	1	+	+	CCONJ
iajs-3033	105	2	6ℎ5𝛼𝛤(5𝑎	6ℎ5𝛼𝛤(5𝑎	NUM
iajs-3033	105	3	+	+	CCONJ
iajs-3033	105	4	1	1	NUM
iajs-3033	105	5	)	)	PUNCT
iajs-3033	105	6	𝛤(6𝛼	𝛤(6𝛼	VERB
iajs-3033	106	1	+	+	CCONJ
iajs-3033	106	2	1	1	X
iajs-3033	106	3	)	)	PUNCT
iajs-3033	106	4	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	106	5	,	,	PUNCT
iajs-3033	106	6	𝑢𝑛(𝜏𝑛	𝑢𝑛(𝜏𝑛	NOUN
iajs-3033	106	7	)	)	PUNCT
iajs-3033	106	8	)	)	PUNCT
iajs-3033	106	9	)	)	PUNCT
iajs-3033	106	10	,	,	PUNCT
iajs-3033	106	11	(	(	PUNCT
iajs-3033	106	12	15	15	X
iajs-3033	106	13	)	)	PUNCT
iajs-3033	106	14	taking	take	VERB
iajs-3033	106	15	the	the	DET
iajs-3033	106	16	first	first	ADJ
iajs-3033	106	17	and	and	CCONJ
iajs-3033	106	18	second	second	ADJ
iajs-3033	106	19	derivatives	derivative	NOUN
iajs-3033	106	20	of	of	ADP
iajs-3033	106	21	the	the	DET
iajs-3033	106	22	above	above	ADJ
iajs-3033	106	23	equation	equation	NOUN
iajs-3033	106	24	,	,	PUNCT
iajs-3033	106	25	we	we	PRON
iajs-3033	106	26	get	get	VERB
iajs-3033	106	27	:	:	PUNCT
iajs-3033	106	28	𝑢𝑛+1	𝑢𝑛+1	NUM
iajs-3033	106	29	𝛼	𝛼	PART
iajs-3033	106	30	(	(	PUNCT
iajs-3033	106	31	𝜏	𝜏	NOUN
iajs-3033	106	32	)	)	PUNCT
iajs-3033	106	33	=	=	PUNCT
iajs-3033	106	34	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	106	35	𝛼(𝜏	𝛼(𝜏	NOUN
iajs-3033	106	36	)	)	PUNCT
iajs-3033	106	37	+	+	CCONJ
iajs-3033	107	1	ℎ𝛼	ℎ𝛼	PROPN
iajs-3033	107	2	𝛤𝛼	𝛤𝛼	PROPN
iajs-3033	107	3	+	+	NOUN
iajs-3033	107	4	1	1	X
iajs-3033	107	5	)	)	PUNCT
iajs-3033	107	6	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	107	7	2𝛼(𝜏	2𝛼(𝜏	NUM
iajs-3033	107	8	)	)	PUNCT
iajs-3033	108	1	+	+	CCONJ
iajs-3033	108	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	108	3	𝛤(𝛼	𝛤(𝛼	X
iajs-3033	108	4	+	+	NOUN
iajs-3033	108	5	2	2	NUM
iajs-3033	108	6	)	)	PUNCT
iajs-3033	108	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	108	8	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	108	9	)	)	PUNCT
iajs-3033	109	1	+	+	CCONJ
iajs-3033	109	2	ℎ3𝛼	ℎ3𝛼	NOUN
iajs-3033	109	3	𝛤(𝛼	𝛤(𝛼	PRON
iajs-3033	110	1	+	+	NOUN
iajs-3033	110	2	3	3	X
iajs-3033	110	3	)	)	PUNCT
iajs-3033	110	4	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	110	5	4𝛼(𝑡𝜏	4𝛼(𝑡𝜏	NUM
iajs-3033	110	6	)	)	PUNCT
iajs-3033	110	7	+	+	CCONJ
iajs-3033	110	8	ℎ4𝛼	ℎ4𝛼	PUNCT
iajs-3033	110	9	𝛤(𝛼	𝛤(𝛼	X
iajs-3033	110	10	+	+	ADJ
iajs-3033	110	11	4	4	NUM
iajs-3033	110	12	)	)	PUNCT
iajs-3033	110	13	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	110	14	,	,	PUNCT
iajs-3033	110	15	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	110	16	)	)	PUNCT
iajs-3033	110	17	,	,	PUNCT
iajs-3033	110	18	(	(	PUNCT
iajs-3033	110	19	16	16	NUM
iajs-3033	110	20	)	)	PUNCT
iajs-3033	110	21	𝑢𝑛+1	𝑢𝑛+1	PROPN
iajs-3033	110	22	2𝛼	2𝛼	NUM
iajs-3033	110	23	(	(	PUNCT
iajs-3033	110	24	𝜏	𝜏	NOUN
iajs-3033	110	25	)	)	PUNCT
iajs-3033	110	26	=	=	SYM
iajs-3033	110	27	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	110	28	2𝛼(𝜏	2𝛼(𝜏	NUM
iajs-3033	110	29	)	)	PUNCT
iajs-3033	111	1	+	+	CCONJ
iajs-3033	111	2	ℎ𝛼	ℎ𝛼	PROPN
iajs-3033	111	3	𝛤𝛼	𝛤𝛼	PROPN
iajs-3033	111	4	+	+	NOUN
iajs-3033	111	5	1	1	NUM
iajs-3033	111	6	)	)	PUNCT
iajs-3033	111	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	111	8	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	111	9	)	)	PUNCT
iajs-3033	112	1	+	+	CCONJ
iajs-3033	112	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	112	3	𝛤(𝛼	𝛤(𝛼	X
iajs-3033	112	4	+	+	NOUN
iajs-3033	112	5	2	2	X
iajs-3033	112	6	)	)	PUNCT
iajs-3033	112	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	112	8	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	112	9	)	)	PUNCT
iajs-3033	113	1	+	+	CCONJ
iajs-3033	114	1	ℎ3𝛼	ℎ3𝛼	NOUN
iajs-3033	114	2	𝛤(𝛼	𝛤(𝛼	PRON
iajs-3033	115	1	+	+	NOUN
iajs-3033	115	2	3	3	X
iajs-3033	115	3	)	)	PUNCT
iajs-3033	115	4	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	115	5	,	,	PUNCT
iajs-3033	115	6	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	115	7	)	)	PUNCT
iajs-3033	115	8	,	,	PUNCT
iajs-3033	115	9	(	(	PUNCT
iajs-3033	115	10	17	17	NUM
iajs-3033	115	11	)	)	PUNCT
iajs-3033	115	12	𝑢𝑛+1	𝑢𝑛+1	NUM
iajs-3033	115	13	3𝛼	3𝛼	NUM
iajs-3033	115	14	(	(	PUNCT
iajs-3033	115	15	𝜏	𝜏	NOUN
iajs-3033	115	16	)	)	PUNCT
iajs-3033	115	17	=	=	SYM
iajs-3033	115	18	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	115	19	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	115	20	)	)	PUNCT
iajs-3033	116	1	+	+	CCONJ
iajs-3033	116	2	ℎ𝛼	ℎ𝛼	PROPN
iajs-3033	116	3	𝛤𝛼	𝛤𝛼	PROPN
iajs-3033	116	4	+	+	NOUN
iajs-3033	116	5	1	1	X
iajs-3033	116	6	)	)	PUNCT
iajs-3033	116	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	116	8	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	116	9	)	)	PUNCT
iajs-3033	117	1	+	+	CCONJ
iajs-3033	117	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	117	3	𝛤(𝛼	𝛤(𝛼	X
iajs-3033	117	4	+	+	NOUN
iajs-3033	117	5	2	2	NUM
iajs-3033	117	6	)	)	PUNCT
iajs-3033	117	7	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	117	8	,	,	PUNCT
iajs-3033	117	9	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	117	10	)	)	PUNCT
iajs-3033	117	11	,	,	PUNCT
iajs-3033	117	12	(	(	PUNCT
iajs-3033	117	13	18	18	NUM
iajs-3033	117	14	)	)	PUNCT
iajs-3033	117	15	ihjpas	ihjpa	NOUN
iajs-3033	117	16	.	.	PUNCT
iajs-3033	118	1	36	36	NUM
iajs-3033	118	2	(	(	PUNCT
iajs-3033	118	3	3	3	NUM
iajs-3033	118	4	)	)	PUNCT
iajs-3033	118	5	2023	2023	NUM
iajs-3033	118	6	422	422	NUM
iajs-3033	118	7	𝑢𝑛+1	𝑢𝑛+1	NUM
iajs-3033	118	8	4𝛼	4𝛼	NOUN
iajs-3033	118	9	(	(	PUNCT
iajs-3033	118	10	𝜏	𝜏	NOUN
iajs-3033	118	11	)	)	PUNCT
iajs-3033	118	12	=	=	SYM
iajs-3033	118	13	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	118	14	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	118	15	)	)	PUNCT
iajs-3033	119	1	+	+	CCONJ
iajs-3033	119	2	ℎ𝛼	ℎ𝛼	PROPN
iajs-3033	119	3	𝛤𝛼	𝛤𝛼	PROPN
iajs-3033	119	4	+	+	NOUN
iajs-3033	119	5	1	1	NUM
iajs-3033	119	6	)	)	PUNCT
iajs-3033	119	7	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	119	8	,	,	PUNCT
iajs-3033	119	9	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	119	10	)	)	PUNCT
iajs-3033	119	11	.	.	PUNCT
iajs-3033	120	1	(	(	PUNCT
iajs-3033	120	2	19	19	NUM
iajs-3033	120	3	)	)	PUNCT
iajs-3033	120	4	hence	hence	ADV
iajs-3033	120	5	,	,	PUNCT
iajs-3033	120	6	the	the	DET
iajs-3033	120	7	formulas	formula	NOUN
iajs-3033	120	8	in	in	ADP
iajs-3033	120	9	equations	equation	NOUN
iajs-3033	120	10	(	(	PUNCT
iajs-3033	120	11	15	15	NUM
iajs-3033	120	12	)	)	PUNCT
iajs-3033	120	13	−	−	PROPN
iajs-3033	120	14	(	(	PUNCT
iajs-3033	120	15	19	19	NUM
iajs-3033	120	16	)	)	PUNCT
iajs-3033	120	17	are	be	AUX
iajs-3033	120	18	used	use	VERB
iajs-3033	120	19	to	to	PART
iajs-3033	120	20	produce	produce	VERB
iajs-3033	120	21	convergent	convergent	NOUN
iajs-3033	120	22	sequence	sequence	NOUN
iajs-3033	120	23	for	for	ADP
iajs-3033	120	24	solving	solve	VERB
iajs-3033	120	25	equation	equation	NOUN
iajs-3033	120	26	(	(	PUNCT
iajs-3033	120	27	7	7	NUM
iajs-3033	120	28	)	)	PUNCT
iajs-3033	120	29	with	with	ADP
iajs-3033	120	30	the	the	DET
iajs-3033	120	31	ics	ics	NOUN
iajs-3033	120	32	(	(	PUNCT
iajs-3033	120	33	2	2	NUM
iajs-3033	120	34	)	)	PUNCT
iajs-3033	120	35	.	.	PUNCT
iajs-3033	121	1	finally	finally	ADV
iajs-3033	121	2	,	,	PUNCT
iajs-3033	121	3	we	we	PRON
iajs-3033	121	4	develop	develop	VERB
iajs-3033	121	5	the	the	DET
iajs-3033	121	6	rkm	rkm	PROPN
iajs-3033	121	7	method	method	NOUN
iajs-3033	121	8	of	of	ADP
iajs-3033	121	9	s	s	NOUN
iajs-3033	121	10	-	-	NOUN
iajs-3033	121	11	stage	stage	NOUN
iajs-3033	121	12	,	,	PUNCT
iajs-3033	121	13	and	and	CCONJ
iajs-3033	121	14	improve	improve	VERB
iajs-3033	121	15	equations	equation	NOUN
iajs-3033	121	16	(	(	PUNCT
iajs-3033	121	17	9)-(12	9)-(12	NUM
iajs-3033	121	18	)	)	PUNCT
iajs-3033	121	19	for	for	ADP
iajs-3033	121	20	solving	solve	VERB
iajs-3033	121	21	5𝑡ℎ	5𝑡ℎ	ADJ
iajs-3033	121	22	-order	-order	PROPN
iajs-3033	121	23	odes	ode	VERB
iajs-3033	121	24	to	to	PART
iajs-3033	121	25	be	be	AUX
iajs-3033	121	26	convenient	convenient	ADJ
iajs-3033	121	27	for	for	ADP
iajs-3033	121	28	solving	solve	VERB
iajs-3033	121	29	5𝑡ℎ	5𝑡ℎ	ADJ
iajs-3033	121	30	order	order	NOUN
iajs-3033	121	31	fodes	fode	NOUN
iajs-3033	121	32	;	;	PUNCT
iajs-3033	121	33	the	the	DET
iajs-3033	121	34	following	follow	VERB
iajs-3033	121	35	formula	formula	NOUN
iajs-3033	121	36	has	have	AUX
iajs-3033	121	37	been	be	AUX
iajs-3033	121	38	supposed	suppose	VERB
iajs-3033	121	39	for	for	ADP
iajs-3033	121	40	finding	find	VERB
iajs-3033	121	41	the	the	DET
iajs-3033	121	42	numerical	numerical	ADJ
iajs-3033	121	43	:	:	PUNCT
iajs-3033	121	44	𝑢𝑛+1(𝜏	𝑢𝑛+1(𝜏	ADJ
iajs-3033	121	45	)	)	PUNCT
iajs-3033	121	46	=	=	SYM
iajs-3033	121	47	𝑢𝑛(𝜏	𝑢𝑛(𝜏	NUM
iajs-3033	121	48	)	)	PUNCT
iajs-3033	122	1	+	+	CCONJ
iajs-3033	123	1	ℎ𝛼	ℎ𝛼	ADP
iajs-3033	123	2	𝛤(𝛼	𝛤(𝛼	PRON
iajs-3033	123	3	+	+	ADJ
iajs-3033	123	4	1	1	X
iajs-3033	123	5	)	)	PUNCT
iajs-3033	123	6	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	123	7	𝛼(𝜏	𝛼(𝜏	NOUN
iajs-3033	123	8	)	)	PUNCT
iajs-3033	124	1	+	+	NUM
iajs-3033	124	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	124	3	𝛤(2𝛼	𝛤(2𝛼	X
iajs-3033	124	4	+	+	CCONJ
iajs-3033	124	5	1	1	X
iajs-3033	124	6	)	)	PUNCT
iajs-3033	124	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	124	8	2𝛼(𝜏	2𝛼(𝜏	NUM
iajs-3033	124	9	)	)	PUNCT
iajs-3033	125	1	+	+	CCONJ
iajs-3033	125	2	ℎ3𝛼	ℎ3𝛼	NOUN
iajs-3033	125	3	𝛤(3𝛼	𝛤(3𝛼	VERB
iajs-3033	125	4	+	+	NOUN
iajs-3033	125	5	1	1	X
iajs-3033	125	6	)	)	PUNCT
iajs-3033	125	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	125	8	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	125	9	)	)	PUNCT
iajs-3033	126	1	+	+	CCONJ
iajs-3033	126	2	ℎ4𝛼	ℎ4𝛼	SYM
iajs-3033	126	3	𝛤(4𝛼	𝛤(4𝛼	NOUN
iajs-3033	126	4	+	+	CCONJ
iajs-3033	126	5	1	1	X
iajs-3033	126	6	)	)	PUNCT
iajs-3033	126	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	126	8	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	126	9	)	)	PUNCT
iajs-3033	127	1	+	+	CCONJ
iajs-3033	127	2	ℎ5𝛼	ℎ5𝛼	PROPN
iajs-3033	127	3	∑	∑	PUNCT
iajs-3033	127	4	𝑏𝑖𝑘𝑖	𝑏𝑖𝑘𝑖	PROPN
iajs-3033	127	5	𝑠	𝑠	PROPN
iajs-3033	127	6	𝑖=1	𝑖=1	PROPN
iajs-3033	127	7	 	 	SPACE
iajs-3033	127	8	,	,	PUNCT
iajs-3033	127	9	(	(	PUNCT
iajs-3033	127	10	20	20	X
iajs-3033	127	11	)	)	PUNCT
iajs-3033	127	12	taking	take	VERB
iajs-3033	127	13	the	the	DET
iajs-3033	127	14	first	first	ADJ
iajs-3033	127	15	,	,	PUNCT
iajs-3033	127	16	second	second	ADJ
iajs-3033	127	17	,	,	PUNCT
iajs-3033	127	18	third	third	ADJ
iajs-3033	127	19	,	,	PUNCT
iajs-3033	127	20	and	and	CCONJ
iajs-3033	127	21	fourth	fourth	ADJ
iajs-3033	127	22	derivatives	derivative	NOUN
iajs-3033	127	23	of	of	ADP
iajs-3033	127	24	the	the	DET
iajs-3033	127	25	above	above	ADJ
iajs-3033	127	26	equation	equation	NOUN
iajs-3033	127	27	,	,	PUNCT
iajs-3033	127	28	we	we	PRON
iajs-3033	127	29	get	get	VERB
iajs-3033	127	30	:	:	PUNCT
iajs-3033	127	31	𝑢𝑛+1	𝑢𝑛+1	NUM
iajs-3033	127	32	𝛼	𝛼	PART
iajs-3033	127	33	(	(	PUNCT
iajs-3033	127	34	𝜏	𝜏	NOUN
iajs-3033	127	35	)	)	PUNCT
iajs-3033	127	36	=	=	PUNCT
iajs-3033	127	37	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	127	38	𝛼(𝜏	𝛼(𝜏	NOUN
iajs-3033	127	39	)	)	PUNCT
iajs-3033	128	1	+	+	CCONJ
iajs-3033	128	2	ℎ𝛼	ℎ𝛼	PROPN
iajs-3033	128	3	𝛤(𝛼+1	𝛤(𝛼+1	NOUN
iajs-3033	128	4	)	)	PUNCT
iajs-3033	128	5	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	128	6	2𝛼(𝜏	2𝛼(𝜏	NUM
iajs-3033	128	7	)	)	PUNCT
iajs-3033	129	1	+	+	CCONJ
iajs-3033	129	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	129	3	𝛤(2𝛼+1	𝛤(2𝛼+1	NOUN
iajs-3033	129	4	)	)	PUNCT
iajs-3033	129	5	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	129	6	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	129	7	)	)	PUNCT
iajs-3033	130	1	+	+	CCONJ
iajs-3033	130	2	ℎ3𝛼	ℎ3𝛼	NOUN
iajs-3033	130	3	𝛤(3𝛼	𝛤(3𝛼	VERB
iajs-3033	130	4	+	+	NOUN
iajs-3033	130	5	1	1	X
iajs-3033	130	6	)	)	PUNCT
iajs-3033	130	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	130	8	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	130	9	)	)	PUNCT
iajs-3033	131	1	+	+	CCONJ
iajs-3033	131	2	ℎ4𝛼	ℎ4𝛼	SYM
iajs-3033	131	3	∑	∑	ADP
iajs-3033	131	4	𝑏𝑖	𝑏𝑖	ADP
iajs-3033	131	5	՛	՛	NUM
iajs-3033	131	6	𝑘𝑖	𝑘𝑖	PROPN
iajs-3033	131	7	𝑠	𝑠	PROPN
iajs-3033	131	8	𝑖=1	𝑖=1	PROPN
iajs-3033	131	9	  	  	SPACE
iajs-3033	131	10	,	,	PUNCT
iajs-3033	131	11	(	(	PUNCT
iajs-3033	131	12	21	21	NUM
iajs-3033	131	13	)	)	PUNCT
iajs-3033	131	14	𝑢𝑛+1	𝑢𝑛+1	PROPN
iajs-3033	131	15	2𝛼	2𝛼	NUM
iajs-3033	131	16	(	(	PUNCT
iajs-3033	131	17	𝜏	𝜏	NOUN
iajs-3033	131	18	)	)	PUNCT
iajs-3033	131	19	=	=	SYM
iajs-3033	131	20	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	131	21	2𝛼(𝜏	2𝛼(𝜏	NUM
iajs-3033	131	22	)	)	PUNCT
iajs-3033	132	1	+	+	CCONJ
iajs-3033	132	2	ℎ𝛼	ℎ𝛼	PROPN
iajs-3033	132	3	𝛤𝛼	𝛤𝛼	PROPN
iajs-3033	132	4	+	+	NOUN
iajs-3033	132	5	1	1	NUM
iajs-3033	132	6	)	)	PUNCT
iajs-3033	132	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	132	8	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	132	9	)	)	PUNCT
iajs-3033	133	1	+	+	CCONJ
iajs-3033	133	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	133	3	𝛤(2𝛼	𝛤(2𝛼	X
iajs-3033	133	4	+	+	CCONJ
iajs-3033	133	5	1	1	X
iajs-3033	133	6	)	)	PUNCT
iajs-3033	133	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	133	8	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	133	9	)	)	PUNCT
iajs-3033	134	1	+	+	CCONJ
iajs-3033	134	2	ℎ3𝛼	ℎ3𝛼	NOUN
iajs-3033	134	3	𝛤(3𝛼	𝛤(3𝛼	VERB
iajs-3033	134	4	+	+	NOUN
iajs-3033	134	5	1	1	X
iajs-3033	134	6	)	)	PUNCT
iajs-3033	134	7	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	134	8	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	134	9	)	)	PUNCT
iajs-3033	135	1	+	+	CCONJ
iajs-3033	135	2	ℎ3𝛼	ℎ3𝛼	NOUN
iajs-3033	135	3	∑	∑	ADP
iajs-3033	135	4	𝑏𝑖	𝑏𝑖	ADP
iajs-3033	135	5	′′	′′	PROPN
iajs-3033	135	6	 	 	SPACE
iajs-3033	135	7	𝑘𝑖	𝑘𝑖	NOUN
iajs-3033	135	8	𝑠	𝑠	PROPN
iajs-3033	135	9	𝑖=1	𝑖=1	PUNCT
iajs-3033	135	10	 	 	SPACE
iajs-3033	135	11	,	,	PUNCT
iajs-3033	135	12	(	(	PUNCT
iajs-3033	135	13	22	22	NUM
iajs-3033	135	14	)	)	PUNCT
iajs-3033	135	15	𝑢𝑛+1	𝑢𝑛+1	PROPN
iajs-3033	135	16	3𝛼	3𝛼	NUM
iajs-3033	135	17	(	(	PUNCT
iajs-3033	135	18	𝜏	𝜏	NOUN
iajs-3033	135	19	)	)	PUNCT
iajs-3033	135	20	=	=	SYM
iajs-3033	135	21	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	135	22	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	135	23	)	)	PUNCT
iajs-3033	135	24	+	+	CCONJ
iajs-3033	135	25	ℎ𝛼	ℎ𝛼	PROPN
iajs-3033	136	1	𝛤𝛼	𝛤𝛼	PROPN
iajs-3033	136	2	+	+	NOUN
iajs-3033	136	3	1	1	X
iajs-3033	136	4	)	)	PUNCT
iajs-3033	136	5	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	136	6	4𝛼(𝜏	4𝛼(𝜏	NUM
iajs-3033	136	7	)	)	PUNCT
iajs-3033	137	1	+	+	CCONJ
iajs-3033	137	2	ℎ2𝛼	ℎ2𝛼	NOUN
iajs-3033	137	3	∑	∑	ADP
iajs-3033	137	4	𝑏𝑖	𝑏𝑖	ADP
iajs-3033	137	5	′′′𝑘𝑖	′′′𝑘𝑖	PROPN
iajs-3033	137	6	𝑠	𝑠	PROPN
iajs-3033	137	7	𝑖=1	𝑖=1	PROPN
iajs-3033	137	8	,	,	PUNCT
iajs-3033	137	9	(	(	PUNCT
iajs-3033	137	10	23	23	NUM
iajs-3033	137	11	)	)	PUNCT
iajs-3033	137	12	𝑢𝑛+1	𝑢𝑛+1	PROPN
iajs-3033	137	13	4𝛼	4𝛼	NOUN
iajs-3033	137	14	(	(	PUNCT
iajs-3033	137	15	𝜏	𝜏	NOUN
iajs-3033	137	16	)	)	PUNCT
iajs-3033	137	17	=	=	SYM
iajs-3033	137	18	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	137	19	3𝛼(𝜏	3𝛼(𝜏	NUM
iajs-3033	137	20	)	)	PUNCT
iajs-3033	138	1	+	+	CCONJ
iajs-3033	138	2	ℎ𝛼	ℎ𝛼	ADP
iajs-3033	138	3	 	 	SPACE
iajs-3033	138	4	∑	∑	PROPN
iajs-3033	138	5	𝑏𝑖	𝑏𝑖	ADP
iajs-3033	138	6	(	(	PUNCT
iajs-3033	138	7	4	4	X
iajs-3033	138	8	)	)	PUNCT
iajs-3033	138	9	𝑘𝑖𝑧	𝑘𝑖𝑧	INTJ
iajs-3033	138	10	𝑠	𝑠	INTJ
iajs-3033	138	11	𝑖=1	𝑖=1	PUNCT
iajs-3033	138	12	,	,	PUNCT
iajs-3033	138	13	(	(	PUNCT
iajs-3033	138	14	24	24	NUM
iajs-3033	138	15	)	)	PUNCT
iajs-3033	138	16	𝑘1	𝑘1	NOUN
iajs-3033	138	17	=	=	SYM
iajs-3033	138	18	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	138	19	,	,	PUNCT
iajs-3033	138	20	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	138	21	)	)	PUNCT
iajs-3033	138	22	,	,	PUNCT
iajs-3033	138	23	(	(	PUNCT
iajs-3033	138	24	25	25	NUM
iajs-3033	138	25	)	)	PUNCT
iajs-3033	138	26	𝑘2	𝑘2	NOUN
iajs-3033	138	27	=	=	PUNCT
iajs-3033	138	28	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	138	29	+	+	CCONJ
iajs-3033	138	30	ℎ𝑐2	ℎ𝑐2	ADJ
iajs-3033	138	31	,	,	PUNCT
iajs-3033	138	32	𝑢𝑛	𝑢𝑛	NOUN
iajs-3033	138	33	+	+	PROPN
iajs-3033	138	34	ℎ𝑎21𝑘1	ℎ𝑎21𝑘1	PROPN
iajs-3033	138	35	)	)	PUNCT
iajs-3033	138	36	,	,	PUNCT
iajs-3033	138	37	(	(	PUNCT
iajs-3033	138	38	26	26	NUM
iajs-3033	138	39	)	)	PUNCT
iajs-3033	138	40	and	and	CCONJ
iajs-3033	138	41	𝑘3	𝑘3	PROPN
iajs-3033	138	42	=	=	SYM
iajs-3033	138	43	𝑓(𝜏𝑛	𝑓(𝜏𝑛	PROPN
iajs-3033	138	44	+	+	CCONJ
iajs-3033	138	45	ℎ𝑐3	ℎ𝑐3	ADJ
iajs-3033	138	46	,	,	PUNCT
iajs-3033	138	47	𝑢𝑛	𝑢𝑛	PROPN
iajs-3033	138	48	+	+	PROPN
iajs-3033	138	49	ℎ𝑎31𝑘1	ℎ𝑎31𝑘1	PROPN
iajs-3033	138	50	+	+	CCONJ
iajs-3033	138	51	ℎ𝑎32𝑘2	ℎ𝑎32𝑘2	PROPN
iajs-3033	138	52	)	)	PUNCT
iajs-3033	138	53	.	.	PUNCT
iajs-3033	139	1	(	(	PUNCT
iajs-3033	139	2	27	27	NUM
iajs-3033	139	3	)	)	PUNCT
iajs-3033	139	4	ihjpas	ihjpa	NOUN
iajs-3033	139	5	.	.	PUNCT
iajs-3033	140	1	36	36	NUM
iajs-3033	140	2	(	(	PUNCT
iajs-3033	140	3	3	3	NUM
iajs-3033	140	4	)	)	PUNCT
iajs-3033	140	5	2023	2023	NUM
iajs-3033	140	6	423	423	NUM
iajs-3033	140	7	4	4	NUM
iajs-3033	140	8	.	.	PUNCT
iajs-3033	140	9	applications	application	NOUN
iajs-3033	140	10	and	and	CCONJ
iajs-3033	140	11	results	result	NOUN
iajs-3033	140	12	:	:	PUNCT
iajs-3033	140	13	in	in	ADP
iajs-3033	140	14	this	this	DET
iajs-3033	140	15	section	section	NOUN
iajs-3033	140	16	,	,	PUNCT
iajs-3033	140	17	we	we	PRON
iajs-3033	140	18	demonstrate	demonstrate	VERB
iajs-3033	140	19	the	the	DET
iajs-3033	140	20	effectiveness	effectiveness	NOUN
iajs-3033	140	21	of	of	ADP
iajs-3033	140	22	the	the	DET
iajs-3033	140	23	suggested	suggest	VERB
iajs-3033	140	24	method	method	NOUN
iajs-3033	140	25	using	use	VERB
iajs-3033	140	26	various	various	ADJ
iajs-3033	140	27	numerical	numerical	ADJ
iajs-3033	140	28	examples	example	NOUN
iajs-3033	140	29	.	.	PUNCT
iajs-3033	141	1	example	example	NOUN
iajs-3033	141	2	4.1	4.1	NUM
iajs-3033	141	3	let	let	VERB
iajs-3033	141	4	following	follow	VERB
iajs-3033	141	5	linear	linear	PROPN
iajs-3033	141	6	fode	fode	PROPN
iajs-3033	141	7	of	of	ADP
iajs-3033	141	8	fifth	fifth	ADJ
iajs-3033	141	9	-	-	PUNCT
iajs-3033	141	10	order	order	NOUN
iajs-3033	141	11	:	:	PUNCT
iajs-3033	142	1	𝐷𝑥	𝐷𝑥	PROPN
iajs-3033	142	2	5𝛼𝑦(𝜏	5𝛼𝑦(𝜏	NUM
iajs-3033	142	3	)	)	PUNCT
iajs-3033	142	4	=	=	SYM
iajs-3033	142	5	25𝛼𝑦(𝜏	25𝛼𝑦(𝜏	PROPN
iajs-3033	142	6	)	)	PUNCT
iajs-3033	142	7	,	,	PUNCT
iajs-3033	142	8	0	0	NUM
iajs-3033	142	9	<	<	X
iajs-3033	142	10	𝛼	𝛼	X
iajs-3033	142	11	≤	≤	NUM
iajs-3033	142	12	1	1	NUM
iajs-3033	142	13	,	,	PUNCT
iajs-3033	142	14	𝜏	𝜏	X
iajs-3033	142	15	>	>	X
iajs-3033	142	16	0	0	NUM
iajs-3033	142	17	.	.	PUNCT
iajs-3033	143	1	(	(	PUNCT
iajs-3033	143	2	28	28	NUM
iajs-3033	143	3	)	)	PUNCT
iajs-3033	143	4	when	when	SCONJ
iajs-3033	143	5	initial	initial	ADJ
iajs-3033	143	6	conditions	condition	NOUN
iajs-3033	143	7	𝑦(0	𝑦(0	PROPN
iajs-3033	143	8	)	)	PUNCT
iajs-3033	143	9	=	=	SYM
iajs-3033	143	10	1	1	NUM
iajs-3033	143	11	,	,	PUNCT
iajs-3033	143	12	𝐷𝜏	𝐷𝜏	PROPN
iajs-3033	143	13	𝛼𝑦(0	𝛼𝑦(0	PROPN
iajs-3033	143	14	)	)	PUNCT
iajs-3033	143	15	=	=	SYM
iajs-3033	143	16	2𝛼	2𝛼	NUM
iajs-3033	143	17	,	,	PUNCT
iajs-3033	143	18	𝐷𝜏	𝐷𝜏	PROPN
iajs-3033	143	19	2𝛼𝑦(0	2𝛼𝑦(0	PROPN
iajs-3033	143	20	)	)	PUNCT
iajs-3033	143	21	=	=	SYM
iajs-3033	143	22	22𝛼	22𝛼	NOUN
iajs-3033	143	23	,	,	PUNCT
iajs-3033	143	24	𝐷𝜏	𝐷𝜏	PROPN
iajs-3033	143	25	3𝛼𝑦(0	3𝛼𝑦(0	PROPN
iajs-3033	143	26	)	)	PUNCT
iajs-3033	143	27	=	=	NOUN
iajs-3033	143	28	23𝛼	23𝛼	NOUN
iajs-3033	143	29	,	,	PUNCT
iajs-3033	143	30	𝐷𝜏	𝐷𝜏	PROPN
iajs-3033	143	31	4𝛼𝑦(0	4𝛼𝑦(0	PROPN
iajs-3033	143	32	)	)	PUNCT
iajs-3033	144	1	=	=	SYM
iajs-3033	144	2	24𝛼	24𝛼	NOUN
iajs-3033	144	3	,	,	PUNCT
iajs-3033	144	4	the	the	DET
iajs-3033	144	5	exact	exact	ADJ
iajs-3033	144	6	solution	solution	NOUN
iajs-3033	144	7	:	:	PUNCT
iajs-3033	144	8	𝑦(𝜏	𝑦(𝜏	X
iajs-3033	144	9	)	)	PUNCT
iajs-3033	144	10	=	=	PUNCT
iajs-3033	144	11	𝑒2𝜏.	𝑒2𝜏.	PROPN
iajs-3033	144	12	example	example	NOUN
iajs-3033	144	13	4.2	4.2	NUM
iajs-3033	144	14	let	let	VERB
iajs-3033	144	15	following	follow	VERB
iajs-3033	144	16	linear	linear	PROPN
iajs-3033	144	17	fode	fode	PROPN
iajs-3033	144	18	of	of	ADP
iajs-3033	144	19	fifth	fifth	ADJ
iajs-3033	144	20	-	-	PUNCT
iajs-3033	144	21	order	order	NOUN
iajs-3033	144	22	:	:	PUNCT
iajs-3033	144	23	𝐷𝑥	𝐷𝑥	PROPN
iajs-3033	144	24	5𝛼𝑦(𝜏	5𝛼𝑦(𝜏	NUM
iajs-3033	144	25	)	)	PUNCT
iajs-3033	144	26	+	+	NUM
iajs-3033	145	1	2𝑦(𝜏	2𝑦(𝜏	NUM
iajs-3033	145	2	)	)	PUNCT
iajs-3033	146	1	+	+	SYM
iajs-3033	146	2	𝑦′′(𝜏	𝑦′′(𝜏	NOUN
iajs-3033	146	3	)	)	PUNCT
iajs-3033	146	4	=	=	NOUN
iajs-3033	146	5	25𝛼	25𝛼	NOUN
iajs-3033	146	6	𝑠𝑖𝑛	𝑠𝑖𝑛	VERB
iajs-3033	146	7	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
iajs-3033	146	8	(	(	PUNCT
iajs-3033	146	9	2𝜏	2𝜏	NUM
iajs-3033	146	10	+	+	CCONJ
iajs-3033	146	11	5𝜋	5𝜋	NOUN
iajs-3033	146	12	2	2	NUM
iajs-3033	146	13	𝛼	𝛼	NOUN
iajs-3033	146	14	)	)	PUNCT
iajs-3033	146	15	,	,	PUNCT
iajs-3033	146	16	0	0	PUNCT
iajs-3033	146	17	<	<	X
iajs-3033	146	18	𝛼	𝛼	X
iajs-3033	146	19	≤	≤	NUM
iajs-3033	146	20	1	1	NUM
iajs-3033	146	21	,	,	PUNCT
iajs-3033	146	22	𝜏	𝜏	X
iajs-3033	146	23	>	>	X
iajs-3033	146	24	0	0	PUNCT
iajs-3033	146	25	(	(	PUNCT
iajs-3033	146	26	29	29	NUM
iajs-3033	146	27	)	)	PUNCT
iajs-3033	146	28	when	when	SCONJ
iajs-3033	146	29	initial	initial	ADJ
iajs-3033	146	30	conditions	condition	NOUN
iajs-3033	146	31	𝑦(0	𝑦(0	PROPN
iajs-3033	146	32	)	)	PUNCT
iajs-3033	146	33	=	=	SYM
iajs-3033	146	34	0	0	NUM
iajs-3033	146	35	,	,	PUNCT
iajs-3033	146	36	𝐷𝜏	𝐷𝜏	PROPN
iajs-3033	146	37	𝛼𝑦(0	𝛼𝑦(0	PROPN
iajs-3033	146	38	)	)	PUNCT
iajs-3033	146	39	=	=	SYM
iajs-3033	146	40	2𝛼	2𝛼	PROPN
iajs-3033	146	41	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
iajs-3033	146	42	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
iajs-3033	146	43	(	(	PUNCT
iajs-3033	146	44	𝜋	𝜋	NOUN
iajs-3033	146	45	2	2	NUM
iajs-3033	146	46	𝛼	𝛼	NOUN
iajs-3033	146	47	)	)	PUNCT
iajs-3033	146	48	,	,	PUNCT
iajs-3033	146	49	𝐷𝜏	𝐷𝜏	PROPN
iajs-3033	146	50	2𝛼𝑦(0	2𝛼𝑦(0	PROPN
iajs-3033	146	51	)	)	PUNCT
iajs-3033	147	1	=	=	SYM
iajs-3033	147	2	22𝛼𝑠𝑖𝑛	22𝛼𝑠𝑖𝑛	NUM
iajs-3033	147	3	(	(	PUNCT
iajs-3033	147	4	𝛱𝛼	𝛱𝛼	NOUN
iajs-3033	147	5	)	)	PUNCT
iajs-3033	147	6	,	,	PUNCT
iajs-3033	147	7	𝐷𝜏	𝐷𝜏	PROPN
iajs-3033	147	8	3𝛼𝑦(0	3𝛼𝑦(0	PROPN
iajs-3033	147	9	)	)	PUNCT
iajs-3033	147	10	=	=	NOUN
iajs-3033	147	11	23𝛼	23𝛼	NOUN
iajs-3033	147	12	𝑠𝑖𝑛	𝑠𝑖𝑛	VERB
iajs-3033	147	13	𝑠𝑖𝑛	𝑠𝑖𝑛	PROPN
iajs-3033	147	14	(	(	PUNCT
iajs-3033	147	15	3𝜋	3𝜋	NUM
iajs-3033	147	16	2	2	NUM
iajs-3033	147	17	𝛼	𝛼	NOUN
iajs-3033	147	18	)	)	PUNCT
iajs-3033	147	19	,	,	PUNCT
iajs-3033	147	20	𝐷𝜏	𝐷𝜏	PROPN
iajs-3033	147	21	4𝛼𝑦(0	4𝛼𝑦(0	PROPN
iajs-3033	147	22	)	)	PUNCT
iajs-3033	148	1	=	=	PUNCT
iajs-3033	148	2	24𝛼𝑠𝑖𝑛	24𝛼𝑠𝑖𝑛	NUM
iajs-3033	148	3	(	(	PUNCT
iajs-3033	148	4	2𝛱𝛼	2𝛱𝛼	NUM
iajs-3033	148	5	)	)	PUNCT
iajs-3033	148	6	.	.	PUNCT
iajs-3033	149	1	example	example	NOUN
iajs-3033	149	2	4.3	4.3	NUM
iajs-3033	149	3	let	let	VERB
iajs-3033	149	4	following	follow	VERB
iajs-3033	149	5	linear	linear	PROPN
iajs-3033	149	6	fode	fode	PROPN
iajs-3033	149	7	of	of	ADP
iajs-3033	149	8	fifth	fifth	ADJ
iajs-3033	149	9	-	-	PUNCT
iajs-3033	149	10	order	order	NOUN
iajs-3033	149	11	:	:	PUNCT
iajs-3033	149	12	𝐷5𝛼	𝐷5𝛼	PROPN
iajs-3033	149	13	𝑦(𝜏	𝑦(𝜏	PROPN
iajs-3033	149	14	)	)	PUNCT
iajs-3033	150	1	+	+	CCONJ
iajs-3033	150	2	2𝑦	2𝑦	NOUN
iajs-3033	150	3	՛	՛	VERB
iajs-3033	150	4	+	+	CCONJ
iajs-3033	150	5	𝑦	𝑦	X
iajs-3033	150	6	՛՛	՛՛	PROPN
iajs-3033	150	7	+	+	PROPN
iajs-3033	150	8	𝑦(4	𝑦(4	NOUN
iajs-3033	150	9	)	)	PUNCT
iajs-3033	151	1	=	=	NOUN
iajs-3033	151	2	25𝛼	25𝛼	NOUN
iajs-3033	151	3	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	151	4	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	151	5	(	(	PUNCT
iajs-3033	151	6	2𝜏	2𝜏	NUM
iajs-3033	151	7	+	+	CCONJ
iajs-3033	151	8	5𝜋	5𝜋	NOUN
iajs-3033	151	9	2	2	NUM
iajs-3033	151	10	𝛼	𝛼	NOUN
iajs-3033	151	11	)	)	PUNCT
iajs-3033	151	12	+	+	CCONJ
iajs-3033	151	13	16	16	NUM
iajs-3033	151	14	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	151	15	𝑐𝑜𝑠	𝑐𝑜𝑠	PROPN
iajs-3033	151	16	2𝜏	2𝜏	NUM
iajs-3033	151	17	,	,	PUNCT
iajs-3033	151	18	0	0	PUNCT
iajs-3033	151	19	<	<	X
iajs-3033	151	20	𝛼	𝛼	X
iajs-3033	151	21	≤	≤	NUM
iajs-3033	151	22	1	1	NUM
iajs-3033	151	23	,	,	PUNCT
iajs-3033	151	24	𝜏	𝜏	X
iajs-3033	151	25	>	>	X
iajs-3033	151	26	0	0	PUNCT
iajs-3033	151	27	(	(	PUNCT
iajs-3033	151	28	30	30	NUM
iajs-3033	151	29	)	)	PUNCT
iajs-3033	151	30	when	when	SCONJ
iajs-3033	151	31	initial	initial	ADJ
iajs-3033	151	32	conditions	condition	NOUN
iajs-3033	151	33	:	:	PUNCT
iajs-3033	151	34	𝑦(0	𝑦(0	PROPN
iajs-3033	151	35	)	)	PUNCT
iajs-3033	151	36	=	=	SYM
iajs-3033	151	37	1	1	NUM
iajs-3033	151	38	,	,	PUNCT
iajs-3033	151	39	𝐷𝛼	𝐷𝛼	PROPN
iajs-3033	151	40	𝑦(0	𝑦(0	PROPN
iajs-3033	151	41	)	)	PUNCT
iajs-3033	151	42	=	=	SYM
iajs-3033	151	43	2𝛼	2𝛼	NUM
iajs-3033	151	44	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	151	45	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	151	46	(	(	PUNCT
iajs-3033	151	47	𝜋	𝜋	NOUN
iajs-3033	151	48	2	2	NUM
iajs-3033	151	49	𝛼	𝛼	NOUN
iajs-3033	151	50	)	)	PUNCT
iajs-3033	151	51	,	,	PUNCT
iajs-3033	151	52	𝐷2𝛼	𝐷2𝛼	PROPN
iajs-3033	151	53	𝑦(0	𝑦(0	PROPN
iajs-3033	151	54	)	)	PUNCT
iajs-3033	151	55	=	=	SYM
iajs-3033	151	56	22𝛼	22𝛼	NOUN
iajs-3033	151	57	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	151	58	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	151	59	(	(	PUNCT
iajs-3033	151	60	𝜋	𝜋	NOUN
iajs-3033	151	61	𝛼	𝛼	NOUN
iajs-3033	151	62	)	)	PUNCT
iajs-3033	151	63	,	,	PUNCT
iajs-3033	151	64	𝐷3𝛼	𝐷3𝛼	PROPN
iajs-3033	151	65	𝑦(0	𝑦(0	PROPN
iajs-3033	151	66	)	)	PUNCT
iajs-3033	151	67	=	=	SYM
iajs-3033	151	68	23𝛼	23𝛼	NUM
iajs-3033	151	69	𝑐𝑜𝑠	𝑐𝑜𝑠	PROPN
iajs-3033	151	70	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	152	1	(	(	PUNCT
iajs-3033	152	2	3𝜋	3𝜋	NUM
iajs-3033	152	3	2	2	NUM
iajs-3033	152	4	𝛼	𝛼	NOUN
iajs-3033	152	5	)	)	PUNCT
iajs-3033	152	6	,	,	PUNCT
iajs-3033	152	7	𝐷4𝛼	𝐷4𝛼	PROPN
iajs-3033	152	8	𝑦(0	𝑦(0	PROPN
iajs-3033	152	9	)	)	PUNCT
iajs-3033	152	10	=	=	SYM
iajs-3033	152	11	24𝛼	24𝛼	PROPN
iajs-3033	152	12	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	152	13	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	152	14	(	(	PUNCT
iajs-3033	152	15	2𝜋𝛼	2𝜋𝛼	ADJ
iajs-3033	152	16	)	)	PUNCT
iajs-3033	152	17	ihjpas	ihjpas	PROPN
iajs-3033	152	18	.	.	PUNCT
iajs-3033	153	1	36	36	NUM
iajs-3033	153	2	(	(	PUNCT
iajs-3033	153	3	3	3	NUM
iajs-3033	153	4	)	)	PUNCT
iajs-3033	153	5	2023	2023	NUM
iajs-3033	153	6	424	424	NUM
iajs-3033	153	7	example	example	NOUN
iajs-3033	153	8	4.4	4.4	NUM
iajs-3033	153	9	let	let	VERB
iajs-3033	153	10	following	follow	VERB
iajs-3033	153	11	linear	linear	PROPN
iajs-3033	153	12	fode	fode	PROPN
iajs-3033	153	13	of	of	ADP
iajs-3033	153	14	fifth	fifth	ADJ
iajs-3033	153	15	-	-	PUNCT
iajs-3033	153	16	order	order	NOUN
iajs-3033	153	17	:	:	PUNCT
iajs-3033	153	18	𝐷5𝛼	𝐷5𝛼	PROPN
iajs-3033	153	19	𝑦(𝜏	𝑦(𝜏	PROPN
iajs-3033	153	20	)	)	PUNCT
iajs-3033	154	1	+	+	SYM
iajs-3033	154	2	𝑦	𝑦	NOUN
iajs-3033	154	3	՛	՛	ADJ
iajs-3033	154	4	+	+	CCONJ
iajs-3033	154	5	𝑦	𝑦	X
iajs-3033	154	6	՛՛	՛՛	NOUN
iajs-3033	154	7	=	=	SYM
iajs-3033	154	8	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
iajs-3033	154	9	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
iajs-3033	154	10	(	(	PUNCT
iajs-3033	154	11	2𝜏	2𝜏	NUM
iajs-3033	154	12	+	+	CCONJ
iajs-3033	154	13	5𝜋	5𝜋	NOUN
iajs-3033	154	14	2	2	NUM
iajs-3033	154	15	)	)	PUNCT
iajs-3033	155	1	+	+	ADP
iajs-3033	155	2	𝑐𝑜𝑠	𝑐𝑜𝑠	ADJ
iajs-3033	155	3	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	155	4	(	(	PUNCT
iajs-3033	155	5	2𝜏	2𝜏	NUM
iajs-3033	155	6	+	+	CCONJ
iajs-3033	155	7	5𝜋	5𝜋	NOUN
iajs-3033	155	8	2	2	NUM
iajs-3033	155	9	𝛼	𝛼	NOUN
iajs-3033	155	10	)	)	PUNCT
iajs-3033	155	11	−	−	PROPN
iajs-3033	155	12	2	2	NUM
iajs-3033	155	13	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
iajs-3033	155	14	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
iajs-3033	155	15	(	(	PUNCT
iajs-3033	155	16	𝜏	𝜏	NOUN
iajs-3033	155	17	)	)	PUNCT
iajs-3033	155	18	,	,	PUNCT
iajs-3033	155	19	0	0	NUM
iajs-3033	155	20	<	<	X
iajs-3033	155	21	𝛼	𝛼	X
iajs-3033	155	22	≤	≤	NUM
iajs-3033	155	23	1	1	NUM
iajs-3033	155	24	,	,	PUNCT
iajs-3033	155	25	𝜏	𝜏	X
iajs-3033	155	26	>	>	X
iajs-3033	155	27	0	0	PUNCT
iajs-3033	155	28	(	(	PUNCT
iajs-3033	155	29	31	31	NUM
iajs-3033	155	30	)	)	PUNCT
iajs-3033	155	31	when	when	SCONJ
iajs-3033	155	32	initial	initial	ADJ
iajs-3033	155	33	conditions	condition	NOUN
iajs-3033	155	34	:	:	PUNCT
iajs-3033	155	35	𝑦(0	𝑦(0	PROPN
iajs-3033	155	36	)	)	PUNCT
iajs-3033	155	37	=	=	SYM
iajs-3033	155	38	1	1	NUM
iajs-3033	155	39	,	,	PUNCT
iajs-3033	155	40	𝐷𝛼	𝐷𝛼	PROPN
iajs-3033	155	41	𝑦(0	𝑦(0	PROPN
iajs-3033	155	42	)	)	PUNCT
iajs-3033	155	43	=	=	PUNCT
iajs-3033	155	44	𝜋	𝜋	PRON
iajs-3033	155	45	2	2	NUM
iajs-3033	155	46	𝛼	𝛼	NOUN
iajs-3033	155	47	)	)	PUNCT
iajs-3033	155	48	+	+	CCONJ
iajs-3033	155	49	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	155	50	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	155	51	(	(	PUNCT
iajs-3033	155	52	𝜋	𝜋	NOUN
iajs-3033	155	53	2	2	NUM
iajs-3033	155	54	𝛼	𝛼	NOUN
iajs-3033	155	55	)	)	PUNCT
iajs-3033	155	56	,	,	PUNCT
iajs-3033	155	57	𝐷2𝛼	𝐷2𝛼	PROPN
iajs-3033	155	58	𝑦(0	𝑦(0	PROPN
iajs-3033	155	59	)	)	PUNCT
iajs-3033	155	60	=	=	NOUN
iajs-3033	155	61	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
iajs-3033	155	62	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
iajs-3033	155	63	(	(	PUNCT
iajs-3033	155	64	𝜋𝛼	𝜋𝛼	NOUN
iajs-3033	155	65	)	)	PUNCT
iajs-3033	155	66	+	+	NUM
iajs-3033	155	67	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	155	68	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	155	69	(	(	PUNCT
iajs-3033	155	70	𝜋	𝜋	NOUN
iajs-3033	155	71	𝛼	𝛼	NOUN
iajs-3033	155	72	)	)	PUNCT
iajs-3033	155	73	,	,	PUNCT
iajs-3033	155	74	𝐷3𝛼	𝐷3𝛼	PROPN
iajs-3033	155	75	𝑦(0	𝑦(0	PROPN
iajs-3033	155	76	)	)	PUNCT
iajs-3033	155	77	=	=	SYM
iajs-3033	155	78	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
iajs-3033	155	79	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
iajs-3033	155	80	(	(	PUNCT
iajs-3033	155	81	3𝜋	3𝜋	NUM
iajs-3033	155	82	2	2	NUM
iajs-3033	155	83	𝛼	𝛼	NOUN
iajs-3033	155	84	)	)	PUNCT
iajs-3033	155	85	(	(	PUNCT
iajs-3033	155	86	3𝜋	3𝜋	NUM
iajs-3033	155	87	2	2	NUM
iajs-3033	155	88	𝛼	𝛼	NOUN
iajs-3033	155	89	)	)	PUNCT
iajs-3033	155	90	,	,	PUNCT
iajs-3033	155	91	𝐷4𝛼	𝐷4𝛼	PROPN
iajs-3033	155	92	𝑦(0	𝑦(0	PROPN
iajs-3033	155	93	)	)	PUNCT
iajs-3033	155	94	=	=	SYM
iajs-3033	155	95	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
iajs-3033	155	96	(	(	PUNCT
iajs-3033	155	97	2𝜋𝛼	2𝜋𝛼	NOUN
iajs-3033	155	98	)	)	PUNCT
iajs-3033	156	1	+	+	ADP
iajs-3033	156	2	𝑐𝑜𝑠	𝑐𝑜𝑠	ADJ
iajs-3033	156	3	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	156	4	(	(	PUNCT
iajs-3033	156	5	2𝜋𝛼	2𝜋𝛼	ADJ
iajs-3033	156	6	)	)	PUNCT
iajs-3033	156	7	.	.	PUNCT
iajs-3033	157	1	example	example	NOUN
iajs-3033	157	2	4.5	4.5	NUM
iajs-3033	157	3	let	let	VERB
iajs-3033	157	4	following	follow	VERB
iajs-3033	157	5	linear	linear	PROPN
iajs-3033	157	6	fode	fode	PROPN
iajs-3033	157	7	of	of	ADP
iajs-3033	157	8	fifth	fifth	ADJ
iajs-3033	157	9	-	-	PUNCT
iajs-3033	157	10	order	order	NOUN
iajs-3033	157	11	:	:	PUNCT
iajs-3033	157	12	𝐷5𝛼	𝐷5𝛼	PROPN
iajs-3033	157	13	𝑦(𝜏	𝑦(𝜏	PROPN
iajs-3033	157	14	)	)	PUNCT
iajs-3033	158	1	+	+	NUM
iajs-3033	158	2	9𝑦	9𝑦	NUM
iajs-3033	158	3	՛	՛	NUM
iajs-3033	158	4	+	+	CCONJ
iajs-3033	158	5	𝑦	𝑦	X
iajs-3033	158	6	՛՛	՛՛	NOUN
iajs-3033	158	7	=	=	SYM
iajs-3033	158	8	35𝛼	35𝛼	NUM
iajs-3033	158	9	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	158	10	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	158	11	(	(	PUNCT
iajs-3033	158	12	2𝜏	2𝜏	NUM
iajs-3033	158	13	+	+	CCONJ
iajs-3033	158	14	5𝜋	5𝜋	NOUN
iajs-3033	158	15	2	2	NUM
iajs-3033	158	16	𝛼	𝛼	NOUN
iajs-3033	158	17	)	)	PUNCT
iajs-3033	158	18	,	,	PUNCT
iajs-3033	158	19	0	0	PUNCT
iajs-3033	158	20	<	<	X
iajs-3033	158	21	𝛼	𝛼	X
iajs-3033	158	22	≤	≤	NUM
iajs-3033	158	23	1	1	NUM
iajs-3033	158	24	,	,	PUNCT
iajs-3033	158	25	𝜏	𝜏	X
iajs-3033	158	26	>	>	X
iajs-3033	158	27	0	0	PUNCT
iajs-3033	158	28	(	(	PUNCT
iajs-3033	158	29	32	32	NUM
iajs-3033	158	30	)	)	PUNCT
iajs-3033	158	31	when	when	SCONJ
iajs-3033	158	32	initial	initial	ADJ
iajs-3033	158	33	conditions	condition	NOUN
iajs-3033	158	34	𝑦(0	𝑦(0	PROPN
iajs-3033	158	35	)	)	PUNCT
iajs-3033	158	36	=	=	SYM
iajs-3033	158	37	1	1	NUM
iajs-3033	158	38	,	,	PUNCT
iajs-3033	158	39	𝐷𝛼	𝐷𝛼	PROPN
iajs-3033	158	40	𝑦(0	𝑦(0	PROPN
iajs-3033	158	41	)	)	PUNCT
iajs-3033	158	42	=	=	SYM
iajs-3033	159	1	3𝛼	3𝛼	NOUN
iajs-3033	159	2	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	159	3	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	160	1	(	(	PUNCT
iajs-3033	160	2	𝜋	𝜋	NOUN
iajs-3033	160	3	2	2	NUM
iajs-3033	160	4	𝛼	𝛼	NOUN
iajs-3033	160	5	)	)	PUNCT
iajs-3033	160	6	,	,	PUNCT
iajs-3033	160	7	𝐷2𝛼	𝐷2𝛼	PROPN
iajs-3033	160	8	𝑦(0	𝑦(0	PROPN
iajs-3033	160	9	)	)	PUNCT
iajs-3033	160	10	=	=	SYM
iajs-3033	160	11	32𝛼	32𝛼	PROPN
iajs-3033	160	12	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	160	13	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	160	14	(	(	PUNCT
iajs-3033	160	15	𝜋	𝜋	NOUN
iajs-3033	160	16	𝛼	𝛼	NOUN
iajs-3033	160	17	)	)	PUNCT
iajs-3033	160	18	,	,	PUNCT
iajs-3033	160	19	𝐷3𝛼	𝐷3𝛼	PROPN
iajs-3033	160	20	𝑦(0	𝑦(0	PROPN
iajs-3033	160	21	)	)	PUNCT
iajs-3033	160	22	=	=	NOUN
iajs-3033	160	23	33𝛼	33𝛼	NUM
iajs-3033	160	24	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	160	25	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	160	26	(	(	PUNCT
iajs-3033	160	27	3𝜋	3𝜋	NUM
iajs-3033	160	28	2	2	NUM
iajs-3033	160	29	𝛼	𝛼	NOUN
iajs-3033	160	30	)	)	PUNCT
iajs-3033	160	31	,	,	PUNCT
iajs-3033	160	32	𝐷4𝛼	𝐷4𝛼	PROPN
iajs-3033	160	33	𝑦(0	𝑦(0	PROPN
iajs-3033	160	34	)	)	PUNCT
iajs-3033	160	35	=	=	SYM
iajs-3033	160	36	34𝛼	34𝛼	NUM
iajs-3033	160	37	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	160	38	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3033	160	39	(	(	PUNCT
iajs-3033	160	40	2𝜋𝛼	2𝜋𝛼	ADJ
iajs-3033	160	41	)	)	PUNCT
iajs-3033	160	42	.	.	PUNCT
iajs-3033	161	1	example	example	NOUN
iajs-3033	161	2	4.6	4.6	NUM
iajs-3033	161	3	let	let	VERB
iajs-3033	161	4	following	follow	VERB
iajs-3033	161	5	linear	linear	PROPN
iajs-3033	161	6	fode	fode	PROPN
iajs-3033	161	7	of	of	ADP
iajs-3033	161	8	fifth	fifth	ADJ
iajs-3033	161	9	-	-	PUNCT
iajs-3033	161	10	order	order	NOUN
iajs-3033	161	11	:	:	PUNCT
iajs-3033	162	1	𝐷𝑥	𝐷𝑥	PROPN
iajs-3033	162	2	5𝛼𝑦(𝜏	5𝛼𝑦(𝜏	NUM
iajs-3033	162	3	)	)	PUNCT
iajs-3033	163	1	+	+	CCONJ
iajs-3033	163	2	9𝑦(𝜏	9𝑦(𝜏	NUM
iajs-3033	163	3	)	)	PUNCT
iajs-3033	164	1	+	+	NUM
iajs-3033	164	2	𝑦′′(𝜏	𝑦′′(𝜏	NOUN
iajs-3033	164	3	)	)	PUNCT
iajs-3033	164	4	=	=	NOUN
iajs-3033	164	5	35𝛼	35𝛼	X
iajs-3033	164	6	𝜋	𝜋	X
iajs-3033	164	7	2	2	NUM
iajs-3033	164	8	𝛼	𝛼	NOUN
iajs-3033	164	9	)	)	PUNCT
iajs-3033	164	10	,	,	PUNCT
iajs-3033	164	11	0	0	PUNCT
iajs-3033	164	12	<	<	X
iajs-3033	164	13	𝛼	𝛼	X
iajs-3033	164	14	≤	≤	NUM
iajs-3033	164	15	1	1	NUM
iajs-3033	164	16	,	,	PUNCT
iajs-3033	164	17	𝜏	𝜏	X
iajs-3033	164	18	>	>	X
iajs-3033	164	19	0	0	PUNCT
iajs-3033	164	20	(	(	PUNCT
iajs-3033	164	21	33	33	NUM
iajs-3033	164	22	)	)	PUNCT
iajs-3033	164	23	when	when	SCONJ
iajs-3033	164	24	initial	initial	ADJ
iajs-3033	164	25	conditions	condition	NOUN
iajs-3033	164	26	𝑦(0	𝑦(0	PROPN
iajs-3033	164	27	)	)	PUNCT
iajs-3033	164	28	=	=	SYM
iajs-3033	164	29	0	0	NUM
iajs-3033	164	30	,	,	PUNCT
iajs-3033	164	31	𝐷𝜏	𝐷𝜏	PROPN
iajs-3033	164	32	𝛼𝑦(0	𝛼𝑦(0	PROPN
iajs-3033	164	33	)	)	PUNCT
iajs-3033	164	34	=	=	PUNCT
iajs-3033	164	35	𝜋	𝜋	PRON
iajs-3033	164	36	2	2	NUM
iajs-3033	164	37	𝛼	𝛼	NOUN
iajs-3033	164	38	)	)	PUNCT
iajs-3033	164	39	,	,	PUNCT
iajs-3033	164	40	𝐷𝜏	𝐷𝜏	PROPN
iajs-3033	164	41	2𝛼𝑦(0	2𝛼𝑦(0	PROPN
iajs-3033	164	42	)	)	PUNCT
iajs-3033	165	1	=	=	NOUN
iajs-3033	165	2	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
iajs-3033	165	3	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
iajs-3033	165	4	32𝛼(𝛱𝛼	32𝛼(𝛱𝛼	NUM
iajs-3033	165	5	)	)	PUNCT
iajs-3033	165	6	,	,	PUNCT
iajs-3033	165	7	𝐷𝜏	𝐷𝜏	PROPN
iajs-3033	165	8	3𝛼𝑦(0	3𝛼𝑦(0	PROPN
iajs-3033	165	9	)	)	PUNCT
iajs-3033	165	10	=	=	NOUN
iajs-3033	165	11	33𝛼	33𝛼	NOUN
iajs-3033	165	12	3𝜋	3𝜋	NUM
iajs-3033	165	13	2	2	NUM
iajs-3033	165	14	𝛼	𝛼	NOUN
iajs-3033	165	15	)	)	PUNCT
iajs-3033	165	16	,	,	PUNCT
iajs-3033	165	17	𝐷𝜏	𝐷𝜏	PROPN
iajs-3033	165	18	4𝛼𝑦(0	4𝛼𝑦(0	PROPN
iajs-3033	165	19	)	)	PUNCT
iajs-3033	166	1	=	=	PUNCT
iajs-3033	166	2	3𝛼𝑠𝑖𝑛	3𝛼𝑠𝑖𝑛	NUM
iajs-3033	166	3	(	(	PUNCT
iajs-3033	166	4	2𝛱𝛼	2𝛱𝛼	NUM
iajs-3033	166	5	)	)	PUNCT
iajs-3033	166	6	.	.	PUNCT
iajs-3033	167	1	table	table	NOUN
iajs-3033	167	2	1	1	NUM
iajs-3033	167	3	numerical	numerical	ADJ
iajs-3033	167	4	-	-	PUNCT
iajs-3033	167	5	comparisons	comparison	NOUN
iajs-3033	167	6	on	on	ADP
iajs-3033	167	7	the	the	DET
iajs-3033	167	8	approximated	approximate	VERB
iajs-3033	167	9	-	-	PUNCT
iajs-3033	167	10	solutions	solution	NOUN
iajs-3033	167	11	versus	versus	ADP
iajs-3033	167	12	the	the	DET
iajs-3033	167	13	analytical	analytical	ADJ
iajs-3033	167	14	solutions	solution	NOUN
iajs-3033	167	15	for	for	ADP
iajs-3033	167	16	solving	solve	VERB
iajs-3033	167	17	the	the	DET
iajs-3033	167	18	examples	example	NOUN
iajs-3033	167	19	4.1	4.1	NUM
iajs-3033	167	20	and	and	CCONJ
iajs-3033	167	21	4.2	4.2	NUM
iajs-3033	167	22	using	use	VERB
iajs-3033	167	23	(	(	PUNCT
iajs-3033	167	24	1	1	NUM
iajs-3033	167	25	)	)	PUNCT
iajs-3033	167	26	modified	modify	VERB
iajs-3033	167	27	-	-	PUNCT
iajs-3033	167	28	euler	euler	NOUN
iajs-3033	167	29	-	-	PUNCT
iajs-3033	167	30	method	method	NOUN
iajs-3033	167	31	,	,	PUNCT
iajs-3033	167	32	(	(	PUNCT
iajs-3033	167	33	2	2	X
iajs-3033	167	34	)	)	PUNCT
iajs-3033	167	35	proposed	propose	VERB
iajs-3033	167	36	two	two	NUM
iajs-3033	167	37	-	-	PUNCT
iajs-3033	167	38	stage	stage	NOUN
iajs-3033	167	39	rkm	rkm	NOUN
iajs-3033	167	40	-	-	NOUN
iajs-3033	167	41	method	method	NOUN
iajs-3033	167	42	and	and	CCONJ
iajs-3033	167	43	(	(	PUNCT
iajs-3033	167	44	3	3	X
iajs-3033	167	45	)	)	PUNCT
iajs-3033	167	46	modified	modify	VERB
iajs-3033	167	47	three	three	NUM
iajs-3033	167	48	-	-	PUNCT
iajs-3033	167	49	stage	stage	NOUN
iajs-3033	167	50	rkm	rkm	NOUN
iajs-3033	167	51	-	-	NOUN
iajs-3033	167	52	method	method	NOUN
iajs-3033	167	53	for	for	ADP
iajs-3033	167	54	n=100	n=100	PROPN
iajs-3033	167	55	,	,	PUNCT
iajs-3033	167	56	𝛼	𝛼	X
iajs-3033	167	57	=	=	PROPN
iajs-3033	167	58	0.96	0.96	NUM
iajs-3033	167	59	.	.	PUNCT
iajs-3033	168	1	ihjpas	ihjpas	PROPN
iajs-3033	168	2	.	.	PUNCT
iajs-3033	169	1	36	36	NUM
iajs-3033	169	2	(	(	PUNCT
iajs-3033	169	3	3	3	NUM
iajs-3033	169	4	)	)	PUNCT
iajs-3033	169	5	2023	2023	NUM
iajs-3033	169	6	425	425	NUM
iajs-3033	169	7	5	5	NUM
iajs-3033	169	8	.	.	PUNCT
iajs-3033	169	9	conclusion	conclusion	NOUN
iajs-3033	169	10	the	the	DET
iajs-3033	169	11	fundamental	fundamental	ADJ
iajs-3033	169	12	objective	objective	NOUN
iajs-3033	169	13	is	be	AUX
iajs-3033	169	14	to	to	PART
iajs-3033	169	15	construct	construct	VERB
iajs-3033	169	16	the	the	DET
iajs-3033	169	17	numerical	numerical	PROPN
iajs-3033	169	18	method	method	PROPN
iajs-3033	169	19	rkm	rkm	PROPN
iajs-3033	169	20	for	for	ADP
iajs-3033	169	21	solving	solve	VERB
iajs-3033	169	22	a	a	DET
iajs-3033	169	23	kind	kind	NOUN
iajs-3033	169	24	of	of	ADP
iajs-3033	169	25	fifth	fifth	ADJ
iajs-3033	169	26	-	-	PUNCT
iajs-3033	169	27	order	order	NOUN
iajs-3033	169	28	fractional	fractional	ADJ
iajs-3033	169	29	ordinary	ordinary	ADJ
iajs-3033	169	30	differential	differential	ADJ
iajs-3033	169	31	equation	equation	NOUN
iajs-3033	169	32	.	.	PUNCT
iajs-3033	170	1	for	for	ADP
iajs-3033	170	2	this	this	DET
iajs-3033	170	3	purpose	purpose	NOUN
iajs-3033	170	4	,	,	PUNCT
iajs-3033	170	5	we	we	PRON
iajs-3033	170	6	have	have	AUX
iajs-3033	170	7	derived	derive	VERB
iajs-3033	170	8	the	the	DET
iajs-3033	170	9	threestage	threestage	NOUN
iajs-3033	170	10	rkm	rkm	PROPN
iajs-3033	170	11	method	method	NOUN
iajs-3033	170	12	.	.	PUNCT
iajs-3033	171	1	we	we	PRON
iajs-3033	171	2	introduced	introduce	VERB
iajs-3033	171	3	the	the	DET
iajs-3033	171	4	object	object	NOUN
iajs-3033	171	5	of	of	ADP
iajs-3033	171	6	the	the	DET
iajs-3033	171	7	method	method	NOUN
iajs-3033	171	8	by	by	ADP
iajs-3033	171	9	utilizing	utilize	VERB
iajs-3033	171	10	various	various	ADJ
iajs-3033	171	11	examples	example	NOUN
iajs-3033	171	12	of	of	ADP
iajs-3033	171	13	fifthorder	fifthorder	ADJ
iajs-3033	171	14	fodes	fode	NOUN
iajs-3033	171	15	to	to	PART
iajs-3033	171	16	inquire	inquire	VERB
iajs-3033	171	17	about	about	ADP
iajs-3033	171	18	the	the	DET
iajs-3033	171	19	activity	activity	NOUN
iajs-3033	171	20	of	of	ADP
iajs-3033	171	21	the	the	DET
iajs-3033	171	22	new	new	ADJ
iajs-3033	171	23	method	method	NOUN
iajs-3033	171	24	and	and	CCONJ
iajs-3033	171	25	examine	examine	VERB
iajs-3033	171	26	the	the	DET
iajs-3033	171	27	new	new	ADJ
iajs-3033	171	28	method	method	NOUN
iajs-3033	171	29	's	's	PART
iajs-3033	171	30	effectiveness	effectiveness	NOUN
iajs-3033	171	31	.	.	PUNCT
iajs-3033	172	1	the	the	DET
iajs-3033	172	2	comparison	comparison	NOUN
iajs-3033	172	3	of	of	ADP
iajs-3033	172	4	numerical	numerical	ADJ
iajs-3033	172	5	results	result	NOUN
iajs-3033	172	6	with	with	ADP
iajs-3033	172	7	exact	exact	ADJ
iajs-3033	172	8	solutions	solution	NOUN
iajs-3033	172	9	in	in	ADP
iajs-3033	172	10	table	table	NOUN
iajs-3033	172	11	1	1	NUM
iajs-3033	172	12	shows	show	VERB
iajs-3033	172	13	that	that	SCONJ
iajs-3033	172	14	the	the	DET
iajs-3033	172	15	numerical	numerical	ADJ
iajs-3033	172	16	finding	finding	NOUN
iajs-3033	172	17	of	of	ADP
iajs-3033	172	18	example	example	NOUN
iajs-3033	172	19	4.1	4.1	NUM
iajs-3033	172	20	is	be	AUX
iajs-3033	172	21	more	more	ADV
iajs-3033	172	22	efficacious	efficacious	ADJ
iajs-3033	172	23	and	and	CCONJ
iajs-3033	172	24	precise	precise	ADJ
iajs-3033	172	25	than	than	ADP
iajs-3033	172	26	well	well	ADV
iajs-3033	172	27	-	-	PUNCT
iajs-3033	172	28	known	know	VERB
iajs-3033	172	29	present	present	ADJ
iajs-3033	172	30	methods	method	NOUN
iajs-3033	172	31	.	.	PUNCT
iajs-3033	173	1	references	reference	NOUN
iajs-3033	173	2	1	1	NUM
iajs-3033	173	3	.	.	X
iajs-3033	174	1	akram	akram	PROPN
iajs-3033	174	2	,	,	PUNCT
iajs-3033	174	3	g.	g.	PROPN
iajs-3033	174	4	;	;	PUNCT
iajs-3033	174	5	siddiqi	siddiqi	PROPN
iajs-3033	174	6	,	,	PUNCT
iajs-3033	174	7	s.	s.	PROPN
iajs-3033	174	8	s.	s.	PROPN
iajs-3033	174	9	,	,	PUNCT
iajs-3033	174	10	solution	solution	NOUN
iajs-3033	174	11	of	of	ADP
iajs-3033	174	12	sixth	sixth	ADJ
iajs-3033	174	13	order	order	NOUN
iajs-3033	174	14	boundary	boundary	ADJ
iajs-3033	174	15	value	value	NOUN
iajs-3033	174	16	problems	problem	NOUN
iajs-3033	174	17	using	use	VERB
iajs-3033	174	18	non	non	ADJ
iajs-3033	174	19	polynomial	polynomial	ADJ
iajs-3033	174	20	spline	spline	NOUN
iajs-3033	174	21	technique	technique	NOUN
iajs-3033	174	22	,	,	PUNCT
iajs-3033	174	23	applied	apply	VERB
iajs-3033	174	24	mathematics	mathematic	NOUN
iajs-3033	174	25	and	and	CCONJ
iajs-3033	174	26	computation	computation	NOUN
iajs-3033	174	27	,	,	PUNCT
iajs-3033	174	28	2006	2006	NUM
iajs-3033	174	29	,	,	PUNCT
iajs-3033	174	30	181	181	NUM
iajs-3033	174	31	,	,	PUNCT
iajs-3033	174	32	708	708	NUM
iajs-3033	174	33	2	2	NUM
iajs-3033	174	34	.	.	PUNCT
iajs-3033	175	1	arshad	arshad	ADJ
iajs-3033	175	2	,	,	PUNCT
iajs-3033	175	3	m.	m.	NOUN
iajs-3033	175	4	s.	s.	PROPN
iajs-3033	175	5	;	;	PUNCT
iajs-3033	175	6	baleanu	baleanu	PROPN
iajs-3033	175	7	,	,	PUNCT
iajs-3033	175	8	d.	d.	PROPN
iajs-3033	175	9	,	,	PUNCT
iajs-3033	175	10	riaz	riaz	PROPN
iajs-3033	175	11	,	,	PUNCT
iajs-3033	175	12	m.	m.	PROPN
iajs-3033	175	13	b.	b.	PROPN
iajs-3033	175	14	;	;	PUNCT
iajs-3033	175	15	abbas	abbas	PROPN
iajs-3033	175	16	,	,	PUNCT
iajs-3033	175	17	m.	m.	NOUN
iajs-3033	175	18	a	a	DET
iajs-3033	175	19	novel	novel	ADJ
iajs-3033	175	20	2	2	NUM
iajs-3033	175	21	-	-	PUNCT
iajs-3033	175	22	stage	stage	NOUN
iajs-3033	175	23	fractional	fractional	ADJ
iajs-3033	175	24	runge	runge	NOUN
iajs-3033	175	25	-	-	PUNCT
iajs-3033	175	26	kutta	kutta	NOUN
iajs-3033	175	27	method	method	NOUN
iajs-3033	175	28	for	for	ADP
iajs-3033	175	29	a	a	DET
iajs-3033	175	30	time	time	NOUN
iajs-3033	175	31	-	-	PUNCT
iajs-3033	175	32	fractional	fractional	ADJ
iajs-3033	175	33	logistic	logistic	ADJ
iajs-3033	175	34	growth	growth	NOUN
iajs-3033	175	35	model	model	NOUN
iajs-3033	175	36	,	,	PUNCT
iajs-3033	175	37	discrete	discrete	ADJ
iajs-3033	175	38	dynamics	dynamic	NOUN
iajs-3033	175	39	in	in	ADP
iajs-3033	175	40	nature	nature	NOUN
iajs-3033	175	41	and	and	CCONJ
iajs-3033	175	42	society	society	NOUN
iajs-3033	175	43	,	,	PUNCT
iajs-3033	175	44	2020	2020	NUM
iajs-3033	175	45	.	.	PUNCT
iajs-3033	176	1	3	3	X
iajs-3033	176	2	.	.	X
iajs-3033	176	3	atallah	atallah	PROPN
iajs-3033	176	4	,	,	PUNCT
iajs-3033	176	5	s.	s.	PROPN
iajs-3033	176	6	a.	a.	PROPN
iajs-3033	176	7	,	,	PUNCT
iajs-3033	176	8	a	a	DET
iajs-3033	176	9	finite	finite	ADJ
iajs-3033	176	10	element	element	NOUN
iajs-3033	176	11	method	method	NOUN
iajs-3033	176	12	for	for	ADP
iajs-3033	176	13	time	time	NOUN
iajs-3033	176	14	fractional	fractional	ADJ
iajs-3033	176	15	partial	partial	ADJ
iajs-3033	176	16	differential	differential	NOUN
iajs-3033	176	17	equations	equation	NOUN
iajs-3033	176	18	.	.	PUNCT
iajs-3033	177	1	journal	journal	PROPN
iajs-3033	177	2	of	of	ADP
iajs-3033	177	3	university	university	PROPN
iajs-3033	177	4	of	of	ADP
iajs-3033	177	5	chester	chester	PROPN
iajs-3033	177	6	,	,	PUNCT
iajs-3033	177	7	sprenger	sprenger	NOUN
iajs-3033	177	8	open	open	ADJ
iajs-3033	177	9	,	,	PUNCT
iajs-3033	177	10	2011	2011	NUM
iajs-3033	177	11	.	.	PUNCT
iajs-3033	178	1	ihjpas	ihjpas	PROPN
iajs-3033	178	2	.	.	PUNCT
iajs-3033	179	1	36	36	NUM
iajs-3033	179	2	(	(	PUNCT
iajs-3033	179	3	3	3	NUM
iajs-3033	179	4	)	)	PUNCT
iajs-3033	179	5	2023	2023	NUM
iajs-3033	179	6	426	426	NUM
iajs-3033	179	7	4	4	NUM
iajs-3033	179	8	.	.	PUNCT
iajs-3033	179	9	damor	damor	PROPN
iajs-3033	179	10	,	,	PUNCT
iajs-3033	179	11	r.	r.	PROPN
iajs-3033	179	12	;	;	PUNCT
iajs-3033	179	13	shukla	shukla	NOUN
iajs-3033	179	14	,	,	PUNCT
iajs-3033	179	15	a.	a.	NOUN
iajs-3033	179	16	,	,	PUNCT
iajs-3033	179	17	numerical	numerical	ADJ
iajs-3033	179	18	solution	solution	NOUN
iajs-3033	179	19	of	of	ADP
iajs-3033	179	20	fractional	fractional	ADJ
iajs-3033	179	21	diffusion	diffusion	NOUN
iajs-3033	179	22	equation	equation	NOUN
iajs-3033	179	23	model	model	NOUN
iajs-3033	179	24	for	for	ADP
iajs-3033	179	25	freezing	freeze	VERB
iajs-3033	179	26	in	in	ADP
iajs-3033	179	27	finite	finite	ADJ
iajs-3033	179	28	media	medium	NOUN
iajs-3033	179	29	,	,	PUNCT
iajs-3033	179	30	international	international	ADJ
iajs-3033	179	31	journal	journal	NOUN
iajs-3033	179	32	of	of	ADP
iajs-3033	179	33	engineering	engineering	NOUN
iajs-3033	179	34	mathematics	mathematic	NOUN
iajs-3033	179	35	,	,	PUNCT
iajs-3033	179	36	2013	2013	NUM
iajs-3033	179	37	,	,	PUNCT
iajs-3033	179	38	doi:10.1155/2013/785609	doi:10.1155/2013/785609	PROPN
iajs-3033	179	39	5	5	NUM
iajs-3033	179	40	.	.	PUNCT
iajs-3033	180	1	jafari	jafari	PROPN
iajs-3033	180	2	,	,	PUNCT
iajs-3033	180	3	h.	h.	PROPN
iajs-3033	180	4	;	;	PUNCT
iajs-3033	180	5	jassim	jassim	PROPN
iajs-3033	180	6	,	,	PUNCT
iajs-3033	180	7	h.	h.	PROPN
iajs-3033	180	8	k.	k.	PROPN
iajs-3033	180	9	,	,	PUNCT
iajs-3033	180	10	local	local	ADJ
iajs-3033	180	11	fractional	fractional	ADJ
iajs-3033	180	12	laplace	laplace	NOUN
iajs-3033	180	13	variational	variational	ADJ
iajs-3033	180	14	iteration	iteration	NOUN
iajs-3033	180	15	method	method	NOUN
iajs-3033	180	16	for	for	ADP
iajs-3033	180	17	solving	solve	VERB
iajs-3033	180	18	nonlinear	nonlinear	ADJ
iajs-3033	180	19	partial	partial	ADJ
iajs-3033	180	20	differential	differential	NOUN
iajs-3033	180	21	equations	equation	NOUN
iajs-3033	180	22	on	on	ADP
iajs-3033	180	23	cantor	cantor	PROPN
iajs-3033	180	24	sets	set	NOUN
iajs-3033	180	25	within	within	ADP
iajs-3033	180	26	local	local	ADJ
iajs-3033	180	27	fractional	fractional	ADJ
iajs-3033	180	28	operators	operator	NOUN
iajs-3033	180	29	,	,	PUNCT
iajs-3033	180	30	journal	journal	NOUN
iajs-3033	180	31	of	of	ADP
iajs-3033	180	32	zankoy	zankoy	PROPN
iajs-3033	180	33	sulaimani	sulaimani	PROPN
iajs-3033	180	34	-	-	PUNCT
iajs-3033	180	35	part	part	NOUN
iajs-3033	180	36	a	a	PRON
iajs-3033	180	37	,	,	PUNCT
iajs-3033	180	38	2014	2014	NUM
iajs-3033	180	39	,	,	PUNCT
iajs-3033	180	40	16	16	NUM
iajs-3033	180	41	,	,	PUNCT
iajs-3033	180	42	49	49	NUM
iajs-3033	180	43	6	6	NUM
iajs-3033	180	44	.	.	PUNCT
iajs-3033	181	1	vanani	vanani	NOUN
iajs-3033	181	2	,	,	PUNCT
iajs-3033	181	3	s.	s.	PROPN
iajs-3033	181	4	k.	k.	PROPN
iajs-3033	181	5	;	;	PUNCT
iajs-3033	181	6	aminataei	aminataei	PROPN
iajs-3033	181	7	,	,	PUNCT
iajs-3033	181	8	a.	a.	NOUN
iajs-3033	181	9	tau	tau	PROPN
iajs-3033	181	10	approximate	approximate	ADJ
iajs-3033	181	11	solution	solution	NOUN
iajs-3033	181	12	of	of	ADP
iajs-3033	181	13	fractional	fractional	ADJ
iajs-3033	181	14	partial	partial	ADJ
iajs-3033	181	15	differential	differential	NOUN
iajs-3033	181	16	equations	equation	NOUN
iajs-3033	181	17	,	,	PUNCT
iajs-3033	181	18	computers	computer	NOUN
iajs-3033	181	19	&	&	CCONJ
iajs-3033	181	20	mathematics	mathematics	PROPN
iajs-3033	181	21	with	with	ADP
iajs-3033	181	22	applications	application	NOUN
iajs-3033	181	23	,	,	PUNCT
iajs-3033	181	24	2011	2011	NUM
iajs-3033	181	25	,	,	PUNCT
iajs-3033	181	26	62	62	NUM
iajs-3033	181	27	,	,	PUNCT
iajs-3033	181	28	1075	1075	NUM
iajs-3033	181	29	7	7	NUM
iajs-3033	181	30	.	.	PUNCT
iajs-3033	182	1	khan	khan	PROPN
iajs-3033	182	2	,	,	PUNCT
iajs-3033	182	3	a.	a.	PROPN
iajs-3033	182	4	;	;	PUNCT
iajs-3033	182	5	khan	khan	PROPN
iajs-3033	182	6	,	,	PUNCT
iajs-3033	182	7	a.	a.	PROPN
iajs-3033	182	8	;	;	PUNCT
iajs-3033	182	9	khan	khan	PROPN
iajs-3033	182	10	,	,	PUNCT
iajs-3033	182	11	t.	t.	PROPN
iajs-3033	182	12	;	;	PUNCT
iajs-3033	182	13	zaman	zaman	PROPN
iajs-3033	182	14	,	,	PUNCT
iajs-3033	182	15	g.	g.	PROPN
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iajs-3033	182	17	of	of	ADP
iajs-3033	182	18	triple	triple	ADJ
iajs-3033	182	19	laplace	laplace	NOUN
iajs-3033	182	20	transform	transform	NOUN
iajs-3033	182	21	for	for	ADP
iajs-3033	182	22	solving	solve	VERB
iajs-3033	182	23	fractional	fractional	ADJ
iajs-3033	182	24	differential	differential	ADJ
iajs-3033	182	25	equations	equation	NOUN
iajs-3033	182	26	,	,	PUNCT
iajs-3033	182	27	discrete	discrete	ADJ
iajs-3033	182	28	&	&	CCONJ
iajs-3033	182	29	continuous	continuous	ADJ
iajs-3033	182	30	dynamical	dynamical	ADJ
iajs-3033	182	31	systems	system	NOUN
iajs-3033	182	32	-	-	PUNCT
iajs-3033	182	33	s	s	NOUN
iajs-3033	182	34	,	,	PUNCT
iajs-3033	182	35	2019	2019	NUM
iajs-3033	182	36	,	,	PUNCT
iajs-3033	182	37	15	15	NUM
iajs-3033	182	38	8	8	NUM
iajs-3033	182	39	.	.	PUNCT
iajs-3033	183	1	mechee	mechee	PROPN
iajs-3033	183	2	,	,	PUNCT
iajs-3033	183	3	m.	m.	NOUN
iajs-3033	183	4	s.	s.	PROPN
iajs-3033	183	5	,	,	PUNCT
iajs-3033	183	6	generalized	generalize	VERB
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iajs-3033	183	9	for	for	ADP
iajs-3033	183	10	solving	solve	VERB
iajs-3033	183	11	class	class	NOUN
iajs-3033	183	12	of	of	ADP
iajs-3033	183	13	sixth	sixth	ADJ
iajs-3033	183	14	-	-	PUNCT
iajs-3033	183	15	order	order	NOUN
iajs-3033	183	16	ordinary	ordinary	ADJ
iajs-3033	183	17	differential	differential	ADJ
iajs-3033	183	18	equations	equation	NOUN
iajs-3033	183	19	,	,	PUNCT
iajs-3033	183	20	journal	journal	NOUN
iajs-3033	183	21	of	of	ADP
iajs-3033	183	22	interdisciplinary	interdisciplinary	ADJ
iajs-3033	183	23	mathematics	mathematic	NOUN
iajs-3033	183	24	,	,	PUNCT
iajs-3033	183	25	2019	2019	NUM
iajs-3033	183	26	,	,	PUNCT
iajs-3033	183	27	22	22	NUM
iajs-3033	183	28	,	,	PUNCT
iajs-3033	183	29	1457	1457	NUM
iajs-3033	183	30	9	9	NUM
iajs-3033	183	31	.	.	PUNCT
iajs-3033	184	1	mechee	mechee	PROPN
iajs-3033	184	2	,	,	PUNCT
iajs-3033	184	3	mohammed	mohammed	PROPN
iajs-3033	184	4	;	;	PUNCT
iajs-3033	184	5	s	s	X
iajs-3033	184	6	,	,	PUNCT
iajs-3033	184	7	al	al	PROPN
iajs-3033	184	8	-	-	PUNCT
iajs-3033	184	9	shaher	shaher	PROPN
iajs-3033	184	10	;	;	PUNCT
iajs-3033	184	11	oday	oday	PROPN
iajs-3033	184	12	,	,	PUNCT
iajs-3033	184	13	i.	i.	PROPN
iajs-3033	184	14	;	;	PUNCT
iajs-3033	184	15	al	al	PROPN
iajs-3033	184	16	-	-	PUNCT
iajs-3033	184	17	juaifri	juaifri	PROPN
iajs-3033	184	18	,	,	PUNCT
iajs-3033	184	19	ghassan	ghassan	PROPN
iajs-3033	184	20	a.	a.	PROPN
iajs-3033	184	21	,	,	PUNCT
iajs-3033	184	22	haar	haar	PROPN
iajs-3033	184	23	wavelet	wavelet	NOUN
iajs-3033	184	24	technique	technique	NOUN
iajs-3033	184	25	for	for	ADP
iajs-3033	184	26	solving	solve	VERB
iajs-3033	184	27	fractional	fractional	ADJ
iajs-3033	184	28	differential	differential	ADJ
iajs-3033	184	29	equations	equation	NOUN
iajs-3033	184	30	with	with	ADP
iajs-3033	184	31	an	an	DET
iajs-3033	184	32	application	application	NOUN
iajs-3033	184	33	,	,	PUNCT
iajs-3033	184	34	aip	aip	PROPN
iajs-3033	184	35	conference	conference	NOUN
iajs-3033	184	36	proceedings	proceeding	NOUN
iajs-3033	184	37	,	,	PUNCT
iajs-3033	184	38	aip	aip	PROPN
iajs-3033	184	39	publishing	publishing	PROPN
iajs-3033	184	40	llc	llc	PROPN
iajs-3033	184	41	,	,	PUNCT
iajs-3033	184	42	2019	2019	NUM
iajs-3033	184	43	,	,	PUNCT
iajs-3033	184	44	2086	2086	NUM
iajs-3033	184	45	,	,	PUNCT
iajs-3033	184	46	1	1	NUM
iajs-3033	184	47	,	,	PUNCT
iajs-3033	184	48	030025	030025	NUM
iajs-3033	184	49	.	.	PUNCT
iajs-3033	185	1	10	10	NUM
iajs-3033	185	2	.	.	PUNCT
iajs-3033	186	1	mechee	mechee	PROPN
iajs-3033	186	2	,	,	PUNCT
iajs-3033	186	3	m.	m.	NOUN
iajs-3033	186	4	s.	s.	PROPN
iajs-3033	186	5	;	;	PUNCT
iajs-3033	186	6	senu	senu	PROPN
iajs-3033	186	7	,	,	PUNCT
iajs-3033	186	8	n.	n.	PROPN
iajs-3033	186	9	numerical	numerical	PROPN
iajs-3033	186	10	study	study	PROPN
iajs-3033	186	11	of	of	ADP
iajs-3033	186	12	fractional	fractional	ADJ
iajs-3033	186	13	differential	differential	ADJ
iajs-3033	186	14	equations	equation	NOUN
iajs-3033	186	15	of	of	ADP
iajs-3033	186	16	lane	lane	NOUN
iajs-3033	186	17	-	-	PUNCT
iajs-3033	186	18	emden	emden	NOUN
iajs-3033	186	19	type	type	NOUN
iajs-3033	186	20	by	by	ADP
iajs-3033	186	21	the	the	DET
iajs-3033	186	22	least	least	ADJ
iajs-3033	186	23	square	square	ADJ
iajs-3033	186	24	method	method	NOUN
iajs-3033	186	25	,	,	PUNCT
iajs-3033	186	26	international	international	ADJ
iajs-3033	186	27	journal	journal	NOUN
iajs-3033	186	28	of	of	ADP
iajs-3033	186	29	differential	differential	ADJ
iajs-3033	186	30	equations	equation	NOUN
iajs-3033	186	31	and	and	CCONJ
iajs-3033	186	32	applications	application	NOUN
iajs-3033	186	33	,	,	PUNCT
iajs-3033	186	34	2012	2012	NUM
iajs-3033	186	35	,	,	PUNCT
iajs-3033	186	36	11	11	NUM
iajs-3033	186	37	,	,	PUNCT
iajs-3033	186	38	157	157	NUM
iajs-3033	186	39	.	.	PUNCT