id	sid	tid	token	lemma	pos
iajs-3409	1	1	388	388	NUM
iajs-3409	1	2	this	this	DET
iajs-3409	1	3	work	work	NOUN
iajs-3409	1	4	is	be	AUX
iajs-3409	1	5	licensed	license	VERB
iajs-3409	1	6	under	under	ADP
iajs-3409	1	7	a	a	DET
iajs-3409	1	8	creative	creative	ADJ
iajs-3409	1	9	commons	common	NOUN
iajs-3409	1	10	attribution	attribution	NOUN
iajs-3409	1	11	4.0	4.0	NUM
iajs-3409	1	12	international	international	ADJ
iajs-3409	1	13	license	license	NOUN
iajs-3409	1	14	ihjpas	ihjpa	NOUN
iajs-3409	1	15	.	.	PUNCT
iajs-3409	2	1	37	37	NUM
iajs-3409	2	2	(	(	PUNCT
iajs-3409	2	3	2	2	NUM
iajs-3409	2	4	)	)	PUNCT
iajs-3409	2	5	2024	2024	NUM
iajs-3409	2	6	ibn	ibn	PROPN
iajs-3409	2	7	al	al	PROPN
iajs-3409	2	8	-	-	PUNCT
iajs-3409	2	9	haitham	haitham	PROPN
iajs-3409	2	10	journal	journal	PROPN
iajs-3409	2	11	for	for	ADP
iajs-3409	2	12	pure	pure	ADJ
iajs-3409	2	13	and	and	CCONJ
iajs-3409	2	14	applied	applied	ADJ
iajs-3409	2	15	sciences	sciences	PROPN
iajs-3409	2	16	journal	journal	PROPN
iajs-3409	2	17	homepage	homepage	NOUN
iajs-3409	2	18	:	:	PUNCT
iajs-3409	2	19	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	NOUN
iajs-3409	2	20	pissn	pissn	ADJ
iajs-3409	2	21	:	:	PUNCT
iajs-3409	2	22	1609	1609	NUM
iajs-3409	2	23	-	-	SYM
iajs-3409	2	24	4042	4042	NUM
iajs-3409	2	25	,	,	PUNCT
iajs-3409	2	26	eissn	eissn	NOUN
iajs-3409	2	27	:	:	PUNCT
iajs-3409	2	28	2521	2521	NUM
iajs-3409	2	29	-	-	SYM
iajs-3409	2	30	3407	3407	NUM
iajs-3409	2	31	firas	firas	PROPN
iajs-3409	2	32	a.	a.	PROPN
iajs-3409	2	33	fawzi*1	fawzi*1	PROPN
iajs-3409	2	34	,	,	PUNCT
iajs-3409	2	35	hadeer	hadeer	NOUN
iajs-3409	2	36	m.	m.	NOUN
iajs-3409	2	37	globe2	globe2	PROPN
iajs-3409	2	38	and	and	CCONJ
iajs-3409	2	39	nizam	nizam	PROPN
iajs-3409	2	40	g.	g.	PROPN
iajs-3409	2	41	ghawadri	ghawadri	PROPN
iajs-3409	2	42	3	3	NUM
iajs-3409	2	43	1,2	1,2	NUM
iajs-3409	2	44	department	department	NOUN
iajs-3409	2	45	of	of	ADP
iajs-3409	2	46	mathematics	mathematic	NOUN
iajs-3409	2	47	,	,	PUNCT
iajs-3409	2	48	faculty	faculty	NOUN
iajs-3409	2	49	of	of	ADP
iajs-3409	2	50	computer	computer	NOUN
iajs-3409	2	51	science	science	NOUN
iajs-3409	2	52	and	and	CCONJ
iajs-3409	2	53	mathematics	mathematic	NOUN
iajs-3409	2	54	,	,	PUNCT
iajs-3409	2	55	tikrit	tikrit	NOUN
iajs-3409	2	56	university	university	NOUN
iajs-3409	2	57	,	,	PUNCT
iajs-3409	2	58	salah	salah	PROPN
iajs-3409	2	59	al	al	PROPN
iajs-3409	2	60	-	-	PUNCT
iajs-3409	2	61	din	din	PROPN
iajs-3409	2	62	,	,	PUNCT
iajs-3409	2	63	iraq	iraq	PROPN
iajs-3409	2	64	.	.	PUNCT
iajs-3409	3	1	3	3	NUM
iajs-3409	3	2	doctor	doctor	NOUN
iajs-3409	3	3	of	of	ADP
iajs-3409	3	4	mathematics	mathematic	NOUN
iajs-3409	3	5	,	,	PUNCT
iajs-3409	3	6	ministry	ministry	PROPN
iajs-3409	3	7	of	of	ADP
iajs-3409	3	8	education	education	PROPN
iajs-3409	3	9	,	,	PUNCT
iajs-3409	3	10	jenin	jenin	PROPN
iajs-3409	3	11	,	,	PUNCT
iajs-3409	3	12	palestine	palestine	PROPN
iajs-3409	3	13	.	.	PUNCT
iajs-3409	4	1	*	*	PUNCT
iajs-3409	4	2	corresponding	correspond	VERB
iajs-3409	4	3	author	author	NOUN
iajs-3409	4	4	.	.	PUNCT
iajs-3409	5	1	abstract	abstract	ADJ
iajs-3409	5	2	this	this	DET
iajs-3409	5	3	paper	paper	NOUN
iajs-3409	5	4	presents	present	VERB
iajs-3409	5	5	two	two	NUM
iajs-3409	5	6	important	important	ADJ
iajs-3409	5	7	contributions	contribution	NOUN
iajs-3409	5	8	to	to	ADP
iajs-3409	5	9	the	the	DET
iajs-3409	5	10	field	field	NOUN
iajs-3409	5	11	of	of	ADP
iajs-3409	5	12	numerical	numerical	ADJ
iajs-3409	5	13	analysis	analysis	NOUN
iajs-3409	5	14	for	for	ADP
iajs-3409	5	15	third	third	ADJ
iajs-3409	5	16	-	-	PUNCT
iajs-3409	5	17	order	order	NOUN
iajs-3409	5	18	ordinary	ordinary	ADJ
iajs-3409	5	19	differential	differential	ADJ
iajs-3409	5	20	equations	equation	NOUN
iajs-3409	5	21	(	(	PUNCT
iajs-3409	5	22	odes	ode	NOUN
iajs-3409	5	23	)	)	PUNCT
iajs-3409	5	24	.	.	PUNCT
iajs-3409	6	1	first	first	ADV
iajs-3409	6	2	,	,	PUNCT
iajs-3409	6	3	a	a	DET
iajs-3409	6	4	new	new	ADJ
iajs-3409	6	5	class	class	NOUN
iajs-3409	6	6	of	of	ADP
iajs-3409	6	7	direct	direct	ADJ
iajs-3409	6	8	implicit	implicit	ADJ
iajs-3409	6	9	runge	runge	NOUN
iajs-3409	6	10	-	-	PUNCT
iajs-3409	6	11	kutta	kutta	NOUN
iajs-3409	6	12	(	(	PUNCT
iajs-3409	6	13	rk	rk	NOUN
iajs-3409	6	14	)	)	PUNCT
iajs-3409	6	15	processes	process	NOUN
iajs-3409	6	16	,	,	PUNCT
iajs-3409	6	17	called	call	VERB
iajs-3409	6	18	rktdio	rktdio	NOUN
iajs-3409	6	19	,	,	PUNCT
iajs-3409	6	20	is	be	AUX
iajs-3409	6	21	introduced	introduce	VERB
iajs-3409	6	22	as	as	ADP
iajs-3409	6	23	solutions	solution	NOUN
iajs-3409	6	24	to	to	ADP
iajs-3409	6	25	third	third	ADJ
iajs-3409	6	26	-	-	PUNCT
iajs-3409	6	27	order	order	NOUN
iajs-3409	6	28	odes	ode	NOUN
iajs-3409	6	29	.	.	PUNCT
iajs-3409	7	1	secondly	secondly	ADV
iajs-3409	7	2	,	,	PUNCT
iajs-3409	7	3	it	it	PRON
iajs-3409	7	4	develops	develop	VERB
iajs-3409	7	5	the	the	DET
iajs-3409	7	6	erktdio	erktdio	NOUN
iajs-3409	7	7	method	method	NOUN
iajs-3409	7	8	,	,	PUNCT
iajs-3409	7	9	which	which	PRON
iajs-3409	7	10	is	be	AUX
iajs-3409	7	11	an	an	DET
iajs-3409	7	12	embedded	embed	VERB
iajs-3409	7	13	pairwise	pairwise	NOUN
iajs-3409	7	14	diagonal	diagonal	ADJ
iajs-3409	7	15	implicit	implicit	ADJ
iajs-3409	7	16	rk	rk	NOUN
iajs-3409	7	17	method	method	NOUN
iajs-3409	7	18	.	.	PUNCT
iajs-3409	8	1	the	the	DET
iajs-3409	8	2	study	study	NOUN
iajs-3409	8	3	begins	begin	VERB
iajs-3409	8	4	by	by	ADP
iajs-3409	8	5	introducing	introduce	VERB
iajs-3409	8	6	the	the	DET
iajs-3409	8	7	theory	theory	NOUN
iajs-3409	8	8	of	of	ADP
iajs-3409	8	9	relevant	relevant	ADJ
iajs-3409	8	10	-	-	PUNCT
iajs-3409	8	11	colored	colored	ADJ
iajs-3409	8	12	trees	tree	NOUN
iajs-3409	8	13	and	and	CCONJ
iajs-3409	8	14	b	b	NOUN
iajs-3409	8	15	-	-	PUNCT
iajs-3409	8	16	series	series	NOUN
iajs-3409	8	17	as	as	ADP
iajs-3409	8	18	fundamental	fundamental	ADJ
iajs-3409	8	19	concepts	concept	NOUN
iajs-3409	8	20	.	.	PUNCT
iajs-3409	9	1	by	by	ADP
iajs-3409	9	2	utilizing	utilize	VERB
iajs-3409	9	3	the	the	DET
iajs-3409	9	4	order	order	NOUN
iajs-3409	9	5	constraints	constraint	NOUN
iajs-3409	9	6	,	,	PUNCT
iajs-3409	9	7	two	two	NUM
iajs-3409	9	8	rktdio	rktdio	NOUN
iajs-3409	9	9	methods	method	NOUN
iajs-3409	9	10	are	be	AUX
iajs-3409	9	11	derived	derive	VERB
iajs-3409	9	12	:	:	PUNCT
iajs-3409	9	13	a	a	DET
iajs-3409	9	14	fifth	fifth	ADJ
iajs-3409	9	15	-	-	PUNCT
iajs-3409	9	16	order	order	NOUN
iajs-3409	9	17	method	method	NOUN
iajs-3409	9	18	with	with	ADP
iajs-3409	9	19	three	three	NUM
iajs-3409	9	20	stages	stage	NOUN
iajs-3409	9	21	and	and	CCONJ
iajs-3409	9	22	a	a	DET
iajs-3409	9	23	sixth	sixth	ADJ
iajs-3409	9	24	-	-	PUNCT
iajs-3409	9	25	order	order	NOUN
iajs-3409	9	26	method	method	NOUN
iajs-3409	9	27	with	with	ADP
iajs-3409	9	28	four	four	NUM
iajs-3409	9	29	stages	stage	NOUN
iajs-3409	9	30	.	.	PUNCT
iajs-3409	10	1	in	in	ADP
iajs-3409	10	2	addition	addition	NOUN
iajs-3409	10	3	,	,	PUNCT
iajs-3409	10	4	an	an	DET
iajs-3409	10	5	embedded	embed	VERB
iajs-3409	10	6	method	method	NOUN
iajs-3409	10	7	called	call	VERB
iajs-3409	10	8	erktdio6(5	erktdio6(5	PROPN
iajs-3409	10	9	)	)	PUNCT
iajs-3409	10	10	is	be	AUX
iajs-3409	10	11	derived	derive	VERB
iajs-3409	10	12	,	,	PUNCT
iajs-3409	10	13	which	which	PRON
iajs-3409	10	14	has	have	VERB
iajs-3409	10	15	orders	order	NOUN
iajs-3409	10	16	six	six	NUM
iajs-3409	10	17	and	and	CCONJ
iajs-3409	10	18	five	five	NUM
iajs-3409	10	19	.	.	PUNCT
iajs-3409	11	1	the	the	DET
iajs-3409	11	2	derivation	derivation	NOUN
iajs-3409	11	3	of	of	ADP
iajs-3409	11	4	the	the	DET
iajs-3409	11	5	embedded	embed	VERB
iajs-3409	11	6	method	method	NOUN
iajs-3409	11	7	includes	include	VERB
iajs-3409	11	8	strategies	strategy	NOUN
iajs-3409	11	9	to	to	PART
iajs-3409	11	10	ensure	ensure	VERB
iajs-3409	11	11	that	that	SCONJ
iajs-3409	11	12	the	the	DET
iajs-3409	11	13	higher	high	ADJ
iajs-3409	11	14	-	-	PUNCT
iajs-3409	11	15	order	order	NOUN
iajs-3409	11	16	method	method	NOUN
iajs-3409	11	17	achieves	achieve	VERB
iajs-3409	11	18	high	high	ADJ
iajs-3409	11	19	accuracy	accuracy	NOUN
iajs-3409	11	20	while	while	SCONJ
iajs-3409	11	21	the	the	DET
iajs-3409	11	22	lowerorder	lowerorder	NOUN
iajs-3409	11	23	method	method	NOUN
iajs-3409	11	24	provides	provide	VERB
iajs-3409	11	25	optimal	optimal	ADJ
iajs-3409	11	26	error	error	NOUN
iajs-3409	11	27	estimates	estimate	NOUN
iajs-3409	11	28	.	.	PUNCT
iajs-3409	12	1	to	to	PART
iajs-3409	12	2	evaluate	evaluate	VERB
iajs-3409	12	3	the	the	DET
iajs-3409	12	4	effectiveness	effectiveness	NOUN
iajs-3409	12	5	of	of	ADP
iajs-3409	12	6	the	the	DET
iajs-3409	12	7	proposed	propose	VERB
iajs-3409	12	8	methods	method	NOUN
iajs-3409	12	9	,	,	PUNCT
iajs-3409	12	10	variable	variable	ADJ
iajs-3409	12	11	step	step	NOUN
iajs-3409	12	12	-	-	PUNCT
iajs-3409	12	13	size	size	NOUN
iajs-3409	12	14	codes	code	NOUN
iajs-3409	12	15	are	be	AUX
iajs-3409	12	16	developed	develop	VERB
iajs-3409	12	17	and	and	CCONJ
iajs-3409	12	18	applied	apply	VERB
iajs-3409	12	19	to	to	ADP
iajs-3409	12	20	a	a	DET
iajs-3409	12	21	set	set	NOUN
iajs-3409	12	22	of	of	ADP
iajs-3409	12	23	specific	specific	ADJ
iajs-3409	12	24	third	third	ADJ
iajs-3409	12	25	-	-	PUNCT
iajs-3409	12	26	order	order	NOUN
iajs-3409	12	27	problems	problem	NOUN
iajs-3409	12	28	.	.	PUNCT
iajs-3409	13	1	the	the	DET
iajs-3409	13	2	numerical	numerical	ADJ
iajs-3409	13	3	evaluation	evaluation	NOUN
iajs-3409	13	4	involves	involve	VERB
iajs-3409	13	5	converting	convert	VERB
iajs-3409	13	6	the	the	DET
iajs-3409	13	7	problems	problem	NOUN
iajs-3409	13	8	into	into	ADP
iajs-3409	13	9	a	a	DET
iajs-3409	13	10	system	system	NOUN
iajs-3409	13	11	of	of	ADP
iajs-3409	13	12	first	first	ADJ
iajs-3409	13	13	-	-	PUNCT
iajs-3409	13	14	order	order	NOUN
iajs-3409	13	15	odes	ode	NOUN
iajs-3409	13	16	and	and	CCONJ
iajs-3409	13	17	comparing	compare	VERB
iajs-3409	13	18	the	the	DET
iajs-3409	13	19	results	result	NOUN
iajs-3409	13	20	with	with	ADP
iajs-3409	13	21	existing	exist	VERB
iajs-3409	13	22	methods	method	NOUN
iajs-3409	13	23	in	in	ADP
iajs-3409	13	24	terms	term	NOUN
iajs-3409	13	25	of	of	ADP
iajs-3409	13	26	accuracy	accuracy	NOUN
iajs-3409	13	27	and	and	CCONJ
iajs-3409	13	28	function	function	NOUN
iajs-3409	13	29	evaluations	evaluation	NOUN
iajs-3409	13	30	.	.	PUNCT
iajs-3409	14	1	the	the	DET
iajs-3409	14	2	numerical	numerical	ADJ
iajs-3409	14	3	demonstrations	demonstration	NOUN
iajs-3409	14	4	emphasise	emphasise	VERB
iajs-3409	14	5	the	the	DET
iajs-3409	14	6	superior	superior	ADJ
iajs-3409	14	7	performance	performance	NOUN
iajs-3409	14	8	and	and	CCONJ
iajs-3409	14	9	efficiency	efficiency	NOUN
iajs-3409	14	10	of	of	ADP
iajs-3409	14	11	the	the	DET
iajs-3409	14	12	new	new	ADJ
iajs-3409	14	13	methods	method	NOUN
iajs-3409	14	14	in	in	ADP
iajs-3409	14	15	solving	solve	VERB
iajs-3409	14	16	third	third	ADJ
iajs-3409	14	17	-	-	PUNCT
iajs-3409	14	18	order	order	NOUN
iajs-3409	14	19	odes	ode	NOUN
iajs-3409	14	20	.	.	PUNCT
iajs-3409	15	1	the	the	DET
iajs-3409	15	2	comparative	comparative	ADJ
iajs-3409	15	3	analysis	analysis	NOUN
iajs-3409	15	4	shows	show	VERB
iajs-3409	15	5	the	the	DET
iajs-3409	15	6	accuracy	accuracy	NOUN
iajs-3409	15	7	achieved	achieve	VERB
iajs-3409	15	8	by	by	ADP
iajs-3409	15	9	the	the	DET
iajs-3409	15	10	higher	high	ADJ
iajs-3409	15	11	-	-	PUNCT
iajs-3409	15	12	order	order	NOUN
iajs-3409	15	13	method	method	NOUN
iajs-3409	15	14	and	and	CCONJ
iajs-3409	15	15	the	the	DET
iajs-3409	15	16	improved	improve	VERB
iajs-3409	15	17	error	error	NOUN
iajs-3409	15	18	estimation	estimation	NOUN
iajs-3409	15	19	of	of	ADP
iajs-3409	15	20	the	the	DET
iajs-3409	15	21	lower	low	ADJ
iajs-3409	15	22	-	-	PUNCT
iajs-3409	15	23	order	order	NOUN
iajs-3409	15	24	method	method	NOUN
iajs-3409	15	25	.	.	PUNCT
iajs-3409	16	1	the	the	DET
iajs-3409	16	2	results	result	NOUN
iajs-3409	16	3	validate	validate	VERB
iajs-3409	16	4	the	the	DET
iajs-3409	16	5	efficacy	efficacy	NOUN
iajs-3409	16	6	of	of	ADP
iajs-3409	16	7	the	the	DET
iajs-3409	16	8	proposed	propose	VERB
iajs-3409	16	9	approaches	approach	NOUN
iajs-3409	16	10	and	and	CCONJ
iajs-3409	16	11	their	their	PRON
iajs-3409	16	12	potential	potential	NOUN
iajs-3409	16	13	for	for	ADP
iajs-3409	16	14	practical	practical	ADJ
iajs-3409	16	15	applications	application	NOUN
iajs-3409	16	16	in	in	ADP
iajs-3409	16	17	various	various	ADJ
iajs-3409	16	18	domains	domain	NOUN
iajs-3409	16	19	.	.	PUNCT
iajs-3409	17	1	keywords	keyword	NOUN
iajs-3409	17	2	:	:	PUNCT
iajs-3409	17	3	third	third	ADJ
iajs-3409	17	4	-	-	PUNCT
iajs-3409	17	5	order	order	NOUN
iajs-3409	17	6	odes	ode	NOUN
iajs-3409	17	7	,	,	PUNCT
iajs-3409	17	8	order	order	NOUN
iajs-3409	17	9	conditions	condition	NOUN
iajs-3409	17	10	,	,	PUNCT
iajs-3409	17	11	b	b	X
iajs-3409	17	12	-	-	PUNCT
iajs-3409	17	13	series	series	NOUN
iajs-3409	17	14	,	,	PUNCT
iajs-3409	17	15	relevant	relevant	ADJ
iajs-3409	17	16	-	-	PUNCT
iajs-3409	17	17	colored	colored	ADJ
iajs-3409	17	18	trees	tree	NOUN
iajs-3409	17	19	.	.	PUNCT
iajs-3409	18	1	1	1	X
iajs-3409	18	2	.	.	X
iajs-3409	18	3	introduction	introduction	NOUN
iajs-3409	18	4	third	third	ADJ
iajs-3409	18	5	-	-	PUNCT
iajs-3409	18	6	order	order	NOUN
iajs-3409	18	7	differential	differential	ADJ
iajs-3409	18	8	equations	equation	NOUN
iajs-3409	18	9	can	can	AUX
iajs-3409	18	10	be	be	AUX
iajs-3409	18	11	found	find	VERB
iajs-3409	18	12	in	in	ADP
iajs-3409	18	13	various	various	ADJ
iajs-3409	18	14	fields	field	NOUN
iajs-3409	18	15	,	,	PUNCT
iajs-3409	18	16	such	such	ADJ
iajs-3409	18	17	as	as	ADP
iajs-3409	18	18	applied	applied	ADJ
iajs-3409	18	19	sciences	science	NOUN
iajs-3409	18	20	,	,	PUNCT
iajs-3409	18	21	neural	neural	ADJ
iajs-3409	18	22	network	network	NOUN
iajs-3409	18	23	engineering	engineering	NOUN
iajs-3409	18	24	[	[	X
iajs-3409	18	25	1,2	1,2	NUM
iajs-3409	18	26	]	]	PUNCT
iajs-3409	18	27	,	,	PUNCT
iajs-3409	18	28	fluid	fluid	ADJ
iajs-3409	18	29	dynamics	dynamic	NOUN
iajs-3409	18	30	[	[	X
iajs-3409	18	31	3	3	NUM
iajs-3409	18	32	]	]	PUNCT
iajs-3409	18	33	and	and	CCONJ
iajs-3409	18	34	thin	thin	ADJ
iajs-3409	18	35	film	film	NOUN
iajs-3409	18	36	flow	flow	NOUN
iajs-3409	18	37	[	[	X
iajs-3409	18	38	4	4	NUM
iajs-3409	18	39	]	]	PUNCT
iajs-3409	18	40	.	.	PUNCT
iajs-3409	19	1	the	the	DET
iajs-3409	19	2	aim	aim	NOUN
iajs-3409	19	3	of	of	ADP
iajs-3409	19	4	this	this	DET
iajs-3409	19	5	paper	paper	NOUN
iajs-3409	19	6	is	be	AUX
iajs-3409	19	7	to	to	PART
iajs-3409	19	8	develop	develop	VERB
iajs-3409	19	9	and	and	CCONJ
iajs-3409	19	10	explain	explain	VERB
iajs-3409	19	11	a	a	DET
iajs-3409	19	12	computational	computational	ADJ
iajs-3409	19	13	method	method	NOUN
iajs-3409	19	14	for	for	ADP
iajs-3409	19	15	solving	solve	VERB
iajs-3409	19	16	initial	initial	ADJ
iajs-3409	19	17	value	value	NOUN
iajs-3409	19	18	problems	problem	NOUN
iajs-3409	19	19	of	of	ADP
iajs-3409	19	20	third	third	ADJ
iajs-3409	19	21	-	-	PUNCT
iajs-3409	19	22	order	order	NOUN
iajs-3409	19	23	differential	differential	ADJ
iajs-3409	19	24	equations	equation	NOUN
iajs-3409	19	25	.	.	PUNCT
iajs-3409	20	1	𝛼′′′(𝑥	𝛼′′′(𝑥	NUM
iajs-3409	20	2	)	)	PUNCT
iajs-3409	20	3	=	=	SYM
iajs-3409	20	4	𝜇	𝜇	X
iajs-3409	20	5	(	(	PUNCT
iajs-3409	20	6	𝑥	𝑥	PROPN
iajs-3409	20	7	,	,	PUNCT
iajs-3409	20	8	𝛼(𝑥	𝛼(𝑥	PROPN
iajs-3409	20	9	)	)	PUNCT
iajs-3409	20	10	)	)	PUNCT
iajs-3409	20	11	,	,	PUNCT
iajs-3409	21	1	𝑥	𝑥	PRON
iajs-3409	21	2	≥	≥	NOUN
iajs-3409	21	3	𝑥0	𝑥0	NOUN
iajs-3409	21	4	,	,	PUNCT
iajs-3409	21	5	(	(	PUNCT
iajs-3409	21	6	1	1	X
iajs-3409	21	7	)	)	PUNCT
iajs-3409	21	8	with	with	ADP
iajs-3409	21	9	initial	initial	ADJ
iajs-3409	21	10	conditions	condition	NOUN
iajs-3409	21	11	α(xn	α(xn	NOUN
iajs-3409	21	12	)	)	PUNCT
iajs-3409	21	13	=	=	SYM
iajs-3409	21	14	αn	αn	NOUN
iajs-3409	21	15	,	,	PUNCT
iajs-3409	21	16	β(xn	β(xn	NUM
iajs-3409	21	17	)	)	PUNCT
iajs-3409	21	18	=	=	SYM
iajs-3409	21	19	𝛼𝑛	𝛼𝑛	ADP
iajs-3409	21	20	′	′	NUM
iajs-3409	21	21	,	,	PUNCT
iajs-3409	21	22	γ(xn	γ(xn	NUM
iajs-3409	21	23	)	)	PUNCT
iajs-3409	21	24	=	=	SYM
iajs-3409	21	25	α𝑛	α𝑛	NUM
iajs-3409	21	26	′′	′′	PROPN
iajs-3409	21	27	.	.	PUNCT
iajs-3409	22	1	received	receive	VERB
iajs-3409	22	2	:	:	PUNCT
iajs-3409	22	3	13	13	NUM
iajs-3409	22	4	april	april	PROPN
iajs-3409	22	5	2023	2023	NUM
iajs-3409	22	6	accepted	accept	VERB
iajs-3409	22	7	:	:	PUNCT
iajs-3409	22	8	12	12	NUM
iajs-3409	22	9	june	june	PROPN
iajs-3409	22	10	2023	2023	NUM
iajs-3409	22	11	published	publish	VERB
iajs-3409	22	12	:	:	PUNCT
iajs-3409	22	13	20	20	NUM
iajs-3409	22	14	april	april	PROPN
iajs-3409	22	15	2024	2024	NUM
iajs-3409	22	16	efficient	efficient	ADJ
iajs-3409	22	17	embedded	embed	VERB
iajs-3409	22	18	diagonal	diagonal	ADJ
iajs-3409	22	19	implicit	implicit	ADJ
iajs-3409	22	20	runge	runge	NOUN
iajs-3409	22	21	-	-	PUNCT
iajs-3409	22	22	kutta	kutta	NOUN
iajs-3409	22	23	method	method	NOUN
iajs-3409	22	24	for	for	ADP
iajs-3409	22	25	directly	directly	ADV
iajs-3409	22	26	solving	solve	VERB
iajs-3409	22	27	third	third	ADJ
iajs-3409	22	28	order	order	NOUN
iajs-3409	22	29	odes	ode	NOUN
iajs-3409	22	30	doi.org/10.30526/37.2.3409	doi.org/10.30526/37.2.3409	AUX
iajs-3409	22	31	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3409	22	32	https://jih.uobaghdad.edu.iq/index.php/j/index#1609-4042	https://jih.uobaghdad.edu.iq/index.php/j/index#1609-4042	NOUN
iajs-3409	22	33	https://jih.uobaghdad.edu.iq/index.php/j/index#2521-3407	https://jih.uobaghdad.edu.iq/index.php/j/index#2521-3407	VERB
iajs-3409	23	1	https://orcid.org/my-orcid?orcid=0000-0003-0939-7940	https://orcid.org/my-orcid?orcid=0000-0003-0939-7940	ADV
iajs-3409	23	2	mailto:firasadil01@tu.edu.iq	mailto:firasadil01@tu.edu.iq	ADJ
iajs-3409	23	3	https://orcid.org/0009-0008-2163-2484	https://orcid.org/0009-0008-2163-2484	NOUN
iajs-3409	23	4	mailto:hadeermohamadjalob@gmail.com	mailto:hadeermohamadjalob@gmail.com	X
iajs-3409	23	5	https://orcid.org/0000-0002-4335-1789	https://orcid.org/0000-0002-4335-1789	ADJ
iajs-3409	23	6	mailto:nizamghawadri@gmail.com	mailto:nizamghawadri@gmail.com	PROPN
iajs-3409	23	7	ihjpas	ihjpa	VERB
iajs-3409	23	8	.	.	PUNCT
iajs-3409	24	1	37	37	NUM
iajs-3409	24	2	(	(	PUNCT
iajs-3409	24	3	2	2	NUM
iajs-3409	24	4	)	)	PUNCT
iajs-3409	24	5	2024	2024	NUM
iajs-3409	24	6	389	389	NUM
iajs-3409	24	7	where	where	SCONJ
iajs-3409	24	8	(	(	PUNCT
iajs-3409	24	9	𝑥)∈	𝑥)∈	PROPN
iajs-3409	24	10	𝑅𝑑	𝑅𝑑	PROPN
iajs-3409	24	11	,	,	PUNCT
iajs-3409	24	12	𝑓	𝑓	X
iajs-3409	24	13	:	:	PUNCT
iajs-3409	24	14	𝑅𝑑×	𝑅𝑑×	X
iajs-3409	24	15	𝑅𝑑	𝑅𝑑	PROPN
iajs-3409	24	16	→	→	SYM
iajs-3409	24	17	𝑅𝑑	𝑅𝑑	PROPN
iajs-3409	24	18	has	have	VERB
iajs-3409	24	19	a	a	DET
iajs-3409	24	20	continuous	continuous	ADJ
iajs-3409	24	21	value	value	NOUN
iajs-3409	24	22	but	but	CCONJ
iajs-3409	24	23	lacks	lack	VERB
iajs-3409	24	24	the	the	DET
iajs-3409	24	25	first	first	ADJ
iajs-3409	24	26	and	and	CCONJ
iajs-3409	24	27	second	second	ADJ
iajs-3409	24	28	derivatives	derivative	NOUN
iajs-3409	24	29	.	.	PUNCT
iajs-3409	25	1	numerical	numerical	ADJ
iajs-3409	25	2	solutions	solution	NOUN
iajs-3409	25	3	are	be	AUX
iajs-3409	25	4	often	often	ADV
iajs-3409	25	5	necessary	necessary	ADJ
iajs-3409	25	6	for	for	ADP
iajs-3409	25	7	third	third	ADJ
iajs-3409	25	8	-	-	PUNCT
iajs-3409	25	9	order	order	NOUN
iajs-3409	25	10	differential	differential	ADJ
iajs-3409	25	11	equations	equation	NOUN
iajs-3409	25	12	since	since	SCONJ
iajs-3409	25	13	analytical	analytical	ADJ
iajs-3409	25	14	solutions	solution	NOUN
iajs-3409	25	15	are	be	AUX
iajs-3409	25	16	often	often	ADV
iajs-3409	25	17	not	not	PART
iajs-3409	25	18	available	available	ADJ
iajs-3409	25	19	.	.	PUNCT
iajs-3409	26	1	some	some	DET
iajs-3409	26	2	researchers	researcher	NOUN
iajs-3409	26	3	have	have	AUX
iajs-3409	26	4	used	use	VERB
iajs-3409	26	5	classical	classical	ADJ
iajs-3409	26	6	methods	method	NOUN
iajs-3409	26	7	to	to	PART
iajs-3409	26	8	solve	solve	VERB
iajs-3409	26	9	higherorder	higherorder	NOUN
iajs-3409	26	10	differential	differential	ADJ
iajs-3409	26	11	equations	equation	NOUN
iajs-3409	26	12	by	by	ADP
iajs-3409	26	13	converting	convert	VERB
iajs-3409	26	14	them	they	PRON
iajs-3409	26	15	into	into	ADP
iajs-3409	26	16	a	a	DET
iajs-3409	26	17	system	system	NOUN
iajs-3409	26	18	of	of	ADP
iajs-3409	26	19	first	first	ADJ
iajs-3409	26	20	-	-	PUNCT
iajs-3409	26	21	order	order	NOUN
iajs-3409	26	22	differential	differential	ADJ
iajs-3409	26	23	equations	equation	NOUN
iajs-3409	27	1	[	[	X
iajs-3409	27	2	5	5	NUM
iajs-3409	27	3	-	-	SYM
iajs-3409	27	4	16,27	16,27	NUM
iajs-3409	27	5	]	]	PUNCT
iajs-3409	27	6	.	.	PUNCT
iajs-3409	28	1	however	however	ADV
iajs-3409	28	2	,	,	PUNCT
iajs-3409	28	3	this	this	DET
iajs-3409	28	4	method	method	NOUN
iajs-3409	28	5	can	can	AUX
iajs-3409	28	6	be	be	AUX
iajs-3409	28	7	computationally	computationally	ADV
iajs-3409	28	8	intensive	intensive	ADJ
iajs-3409	28	9	and	and	CCONJ
iajs-3409	28	10	time	time	NOUN
iajs-3409	28	11	consuming	consume	VERB
iajs-3409	28	12	.	.	PUNCT
iajs-3409	29	1	direct	direct	ADJ
iajs-3409	29	2	numerical	numerical	ADJ
iajs-3409	29	3	approaches	approach	NOUN
iajs-3409	29	4	have	have	AUX
iajs-3409	29	5	been	be	AUX
iajs-3409	29	6	proposed	propose	VERB
iajs-3409	29	7	to	to	PART
iajs-3409	29	8	reduce	reduce	VERB
iajs-3409	29	9	the	the	DET
iajs-3409	29	10	computation	computation	NOUN
iajs-3409	29	11	time	time	NOUN
iajs-3409	29	12	,	,	PUNCT
iajs-3409	29	13	but	but	CCONJ
iajs-3409	29	14	they	they	PRON
iajs-3409	29	15	require	require	VERB
iajs-3409	29	16	a	a	DET
iajs-3409	29	17	second	second	ADJ
iajs-3409	29	18	method	method	NOUN
iajs-3409	29	19	to	to	PART
iajs-3409	29	20	obtain	obtain	VERB
iajs-3409	29	21	initial	initial	ADJ
iajs-3409	29	22	values	value	NOUN
iajs-3409	29	23	for	for	ADP
iajs-3409	29	24	the	the	DET
iajs-3409	29	25	numerical	numerical	ADJ
iajs-3409	29	26	solutions	solution	NOUN
iajs-3409	29	27	.	.	PUNCT
iajs-3409	30	1	implicit	implicit	ADJ
iajs-3409	30	2	methods	method	NOUN
iajs-3409	30	3	are	be	AUX
iajs-3409	30	4	useful	useful	ADJ
iajs-3409	30	5	because	because	SCONJ
iajs-3409	30	6	they	they	PRON
iajs-3409	30	7	can	can	AUX
iajs-3409	30	8	achieve	achieve	VERB
iajs-3409	30	9	high	high	ADJ
iajs-3409	30	10	accuracy	accuracy	NOUN
iajs-3409	30	11	with	with	ADP
iajs-3409	30	12	fewer	few	ADJ
iajs-3409	30	13	steps	step	NOUN
iajs-3409	30	14	,	,	PUNCT
iajs-3409	30	15	making	make	VERB
iajs-3409	30	16	it	it	PRON
iajs-3409	30	17	easier	easy	ADJ
iajs-3409	30	18	to	to	PART
iajs-3409	30	19	find	find	VERB
iajs-3409	30	20	solutions	solution	NOUN
iajs-3409	30	21	to	to	ADP
iajs-3409	30	22	complex	complex	ADJ
iajs-3409	30	23	problems	problem	NOUN
iajs-3409	30	24	.	.	PUNCT
iajs-3409	31	1	several	several	ADJ
iajs-3409	31	2	researchers	researcher	NOUN
iajs-3409	31	3	have	have	AUX
iajs-3409	31	4	developed	develop	VERB
iajs-3409	31	5	embedded	embed	VERB
iajs-3409	31	6	runge	runge	NOUN
iajs-3409	31	7	-	-	PUNCT
iajs-3409	31	8	kutta	kutta	NOUN
iajs-3409	31	9	methods	method	NOUN
iajs-3409	31	10	with	with	ADP
iajs-3409	31	11	high	high	ADJ
iajs-3409	31	12	algebraic	algebraic	ADJ
iajs-3409	31	13	orders	order	NOUN
iajs-3409	31	14	for	for	ADP
iajs-3409	31	15	solving	solve	VERB
iajs-3409	31	16	third	third	ADJ
iajs-3409	31	17	-	-	PUNCT
iajs-3409	31	18	order	order	NOUN
iajs-3409	31	19	differential	differential	ADJ
iajs-3409	31	20	equations	equation	NOUN
iajs-3409	32	1	[	[	X
iajs-3409	32	2	17	17	NUM
iajs-3409	32	3	-	-	SYM
iajs-3409	32	4	18	18	NUM
iajs-3409	32	5	]	]	PUNCT
iajs-3409	32	6	.	.	PUNCT
iajs-3409	33	1	ismail	ismail	PROPN
iajs-3409	33	2	et	et	PROPN
iajs-3409	33	3	.	.	PUNCT
iajs-3409	34	1	al	al	PROPN
iajs-3409	35	1	[	[	X
iajs-3409	35	2	19	19	NUM
iajs-3409	35	3	]	]	PUNCT
iajs-3409	35	4	proposed	propose	VERB
iajs-3409	35	5	the	the	DET
iajs-3409	35	6	singly	singly	ADV
iajs-3409	35	7	embedded	embed	VERB
iajs-3409	35	8	diagonally	diagonally	ADV
iajs-3409	35	9	implicit	implicit	ADJ
iajs-3409	35	10	runge	runge	NOUN
iajs-3409	35	11	-	-	PUNCT
iajs-3409	35	12	kutta	kutta	NOUN
iajs-3409	35	13	(	(	PUNCT
iajs-3409	35	14	sdirk	sdirk	ADJ
iajs-3409	35	15	)	)	PUNCT
iajs-3409	35	16	method	method	NOUN
iajs-3409	35	17	to	to	PART
iajs-3409	35	18	combine	combine	VERB
iajs-3409	35	19	delay	delay	VERB
iajs-3409	35	20	differential	differential	ADJ
iajs-3409	35	21	equations	equation	NOUN
iajs-3409	35	22	(	(	PUNCT
iajs-3409	35	23	ddes	ddes	PROPN
iajs-3409	35	24	)	)	PUNCT
iajs-3409	35	25	and	and	CCONJ
iajs-3409	35	26	compared	compare	VERB
iajs-3409	35	27	the	the	DET
iajs-3409	35	28	computational	computational	ADJ
iajs-3409	35	29	results	result	NOUN
iajs-3409	35	30	.	.	PUNCT
iajs-3409	36	1	the	the	DET
iajs-3409	36	2	researchers	researcher	NOUN
iajs-3409	36	3	in	in	ADP
iajs-3409	36	4	[	[	X
iajs-3409	36	5	20,21,26	20,21,26	NUM
iajs-3409	36	6	]	]	PUNCT
iajs-3409	36	7	developed	develop	VERB
iajs-3409	36	8	a	a	DET
iajs-3409	36	9	novel	novel	NOUN
iajs-3409	36	10	embedded	embed	VERB
iajs-3409	36	11	explicit	explicit	ADJ
iajs-3409	36	12	and	and	CCONJ
iajs-3409	36	13	implicit	implicit	ADJ
iajs-3409	36	14	runge	runge	NOUN
iajs-3409	36	15	-	-	PUNCT
iajs-3409	36	16	kutta	kutta	NOUN
iajs-3409	36	17	method	method	NOUN
iajs-3409	36	18	for	for	ADP
iajs-3409	36	19	solving	solve	VERB
iajs-3409	36	20	special	special	ADJ
iajs-3409	36	21	third	third	ADJ
iajs-3409	36	22	and	and	CCONJ
iajs-3409	36	23	fourth	fourth	ADJ
iajs-3409	36	24	-	-	PUNCT
iajs-3409	36	25	order	order	NOUN
iajs-3409	36	26	problems	problem	NOUN
iajs-3409	36	27	.	.	PUNCT
iajs-3409	37	1	the	the	DET
iajs-3409	37	2	main	main	ADJ
iajs-3409	37	3	objective	objective	NOUN
iajs-3409	37	4	of	of	ADP
iajs-3409	37	5	this	this	DET
iajs-3409	37	6	work	work	NOUN
iajs-3409	37	7	is	be	AUX
iajs-3409	37	8	to	to	PART
iajs-3409	37	9	develop	develop	VERB
iajs-3409	37	10	a	a	DET
iajs-3409	37	11	new	new	ADJ
iajs-3409	37	12	method	method	NOUN
iajs-3409	37	13	called	call	VERB
iajs-3409	37	14	rktdio	rktdio	NOUN
iajs-3409	37	15	,	,	PUNCT
iajs-3409	37	16	an	an	DET
iajs-3409	37	17	implicit	implicit	ADJ
iajs-3409	37	18	one	one	NUM
iajs-3409	37	19	-	-	PUNCT
iajs-3409	37	20	step	step	NOUN
iajs-3409	37	21	runge	runge	NOUN
iajs-3409	37	22	-	-	PUNCT
iajs-3409	37	23	kutta	kutta	NOUN
iajs-3409	37	24	method	method	NOUN
iajs-3409	37	25	designed	design	VERB
iajs-3409	37	26	for	for	ADP
iajs-3409	37	27	directly	directly	ADV
iajs-3409	37	28	solving	solve	VERB
iajs-3409	37	29	specific	specific	ADJ
iajs-3409	37	30	third	third	ADJ
iajs-3409	37	31	-	-	PUNCT
iajs-3409	37	32	order	order	NOUN
iajs-3409	37	33	differential	differential	ADJ
iajs-3409	37	34	equations	equation	NOUN
iajs-3409	37	35	.	.	PUNCT
iajs-3409	38	1	this	this	DET
iajs-3409	38	2	method	method	NOUN
iajs-3409	38	3	is	be	AUX
iajs-3409	38	4	developed	develop	VERB
iajs-3409	38	5	using	use	VERB
iajs-3409	38	6	the	the	DET
iajs-3409	38	7	theory	theory	NOUN
iajs-3409	38	8	of	of	ADP
iajs-3409	38	9	relevant	relevant	ADJ
iajs-3409	38	10	-	-	PUNCT
iajs-3409	38	11	colored	colored	ADJ
iajs-3409	38	12	trees	tree	NOUN
iajs-3409	38	13	theory	theory	NOUN
iajs-3409	38	14	and	and	CCONJ
iajs-3409	38	15	also	also	ADV
iajs-3409	38	16	involves	involve	VERB
iajs-3409	38	17	the	the	DET
iajs-3409	38	18	derivation	derivation	NOUN
iajs-3409	38	19	of	of	ADP
iajs-3409	38	20	embedded	embed	VERB
iajs-3409	38	21	diagonally	diagonally	ADV
iajs-3409	38	22	implicit	implicit	ADJ
iajs-3409	38	23	runge	runge	NOUN
iajs-3409	38	24	-	-	PUNCT
iajs-3409	38	25	kutta	kutta	NOUN
iajs-3409	38	26	methods	method	NOUN
iajs-3409	38	27	for	for	ADP
iajs-3409	38	28	the	the	DET
iajs-3409	38	29	direct	direct	ADJ
iajs-3409	38	30	integration	integration	NOUN
iajs-3409	38	31	of	of	ADP
iajs-3409	38	32	certain	certain	ADJ
iajs-3409	38	33	third	third	ADJ
iajs-3409	38	34	-	-	PUNCT
iajs-3409	38	35	order	order	NOUN
iajs-3409	38	36	differential	differential	ADJ
iajs-3409	38	37	equations	equation	NOUN
iajs-3409	38	38	.	.	PUNCT
iajs-3409	39	1	the	the	DET
iajs-3409	39	2	structure	structure	NOUN
iajs-3409	39	3	of	of	ADP
iajs-3409	39	4	this	this	DET
iajs-3409	39	5	paper	paper	NOUN
iajs-3409	39	6	is	be	AUX
iajs-3409	39	7	as	as	SCONJ
iajs-3409	39	8	follows	follow	VERB
iajs-3409	39	9	:	:	PUNCT
iajs-3409	39	10	section	section	NOUN
iajs-3409	39	11	2	2	NUM
iajs-3409	39	12	provides	provide	VERB
iajs-3409	39	13	the	the	DET
iajs-3409	39	14	formulation	formulation	NOUN
iajs-3409	39	15	concept	concept	NOUN
iajs-3409	39	16	for	for	ADP
iajs-3409	39	17	the	the	DET
iajs-3409	39	18	rktdio	rktdio	NOUN
iajs-3409	39	19	approach	approach	NOUN
iajs-3409	39	20	for	for	ADP
iajs-3409	39	21	the	the	DET
iajs-3409	39	22	direct	direct	ADJ
iajs-3409	39	23	integration	integration	NOUN
iajs-3409	39	24	of	of	ADP
iajs-3409	39	25	certain	certain	ADJ
iajs-3409	39	26	third	third	ADJ
iajs-3409	39	27	-	-	PUNCT
iajs-3409	39	28	order	order	NOUN
iajs-3409	39	29	odes	ode	NOUN
iajs-3409	39	30	.	.	PUNCT
iajs-3409	40	1	in	in	ADP
iajs-3409	40	2	section	section	NOUN
iajs-3409	40	3	3	3	NUM
iajs-3409	40	4	,	,	PUNCT
iajs-3409	40	5	we	we	PRON
iajs-3409	40	6	develop	develop	VERB
iajs-3409	40	7	the	the	DET
iajs-3409	40	8	novel	novel	ADJ
iajs-3409	40	9	theory	theory	NOUN
iajs-3409	40	10	of	of	ADP
iajs-3409	40	11	relevant	relevant	ADJ
iajs-3409	40	12	-	-	PUNCT
iajs-3409	40	13	colored	colored	ADJ
iajs-3409	40	14	trees	tree	NOUN
iajs-3409	40	15	theory	theory	NOUN
iajs-3409	40	16	and	and	CCONJ
iajs-3409	40	17	the	the	DET
iajs-3409	40	18	corresponding	corresponding	ADJ
iajs-3409	40	19	b	b	X
iajs-3409	40	20	-	-	PUNCT
iajs-3409	40	21	series	series	NOUN
iajs-3409	40	22	theory	theory	NOUN
iajs-3409	40	23	.	.	PUNCT
iajs-3409	41	1	section	section	NOUN
iajs-3409	41	2	4	4	NUM
iajs-3409	41	3	contains	contain	VERB
iajs-3409	41	4	the	the	DET
iajs-3409	41	5	derivation	derivation	NOUN
iajs-3409	41	6	of	of	ADP
iajs-3409	41	7	the	the	DET
iajs-3409	41	8	ordering	ordering	NOUN
iajs-3409	41	9	criteria	criterion	NOUN
iajs-3409	41	10	of	of	ADP
iajs-3409	41	11	the	the	DET
iajs-3409	41	12	rktdio	rktdio	NOUN
iajs-3409	41	13	method	method	NOUN
iajs-3409	41	14	.	.	PUNCT
iajs-3409	42	1	section	section	NOUN
iajs-3409	42	2	5	5	NUM
iajs-3409	42	3	presents	present	VERB
iajs-3409	42	4	the	the	DET
iajs-3409	42	5	construction	construction	NOUN
iajs-3409	42	6	of	of	ADP
iajs-3409	42	7	a	a	DET
iajs-3409	42	8	three	three	NUM
iajs-3409	42	9	-	-	PUNCT
iajs-3409	42	10	stage	stage	NOUN
iajs-3409	42	11	rktdio	rktdio	NOUN
iajs-3409	42	12	approach	approach	NOUN
iajs-3409	42	13	for	for	ADP
iajs-3409	42	14	order	order	NOUN
iajs-3409	42	15	five	five	NUM
iajs-3409	42	16	and	and	CCONJ
iajs-3409	42	17	a	a	DET
iajs-3409	42	18	four	four	NUM
iajs-3409	42	19	-	-	PUNCT
iajs-3409	42	20	stage	stage	NOUN
iajs-3409	42	21	method	method	NOUN
iajs-3409	42	22	for	for	ADP
iajs-3409	42	23	order	order	NOUN
iajs-3409	42	24	six	six	NUM
iajs-3409	42	25	.	.	PUNCT
iajs-3409	42	26	section	section	NOUN
iajs-3409	42	27	6	6	NUM
iajs-3409	42	28	describes	describe	VERB
iajs-3409	42	29	the	the	DET
iajs-3409	42	30	derivation	derivation	NOUN
iajs-3409	42	31	of	of	ADP
iajs-3409	42	32	the	the	DET
iajs-3409	42	33	embedded	embed	VERB
iajs-3409	42	34	erktdio6(5	erktdio6(5	PROPN
iajs-3409	42	35	)	)	PUNCT
iajs-3409	42	36	method	method	NOUN
iajs-3409	42	37	.	.	PUNCT
iajs-3409	43	1	to	to	PART
iajs-3409	43	2	demonstrate	demonstrate	VERB
iajs-3409	43	3	the	the	DET
iajs-3409	43	4	efficiency	efficiency	NOUN
iajs-3409	43	5	and	and	CCONJ
iajs-3409	43	6	effectiveness	effectiveness	NOUN
iajs-3409	43	7	of	of	ADP
iajs-3409	43	8	the	the	DET
iajs-3409	43	9	rktdio	rktdio	NOUN
iajs-3409	43	10	and	and	CCONJ
iajs-3409	43	11	erktdio6(5	erktdio6(5	PROPN
iajs-3409	43	12	)	)	PUNCT
iajs-3409	43	13	methods	method	NOUN
iajs-3409	43	14	compared	compare	VERB
iajs-3409	43	15	to	to	ADP
iajs-3409	43	16	the	the	DET
iajs-3409	43	17	methods	method	NOUN
iajs-3409	43	18	currently	currently	ADV
iajs-3409	43	19	used	use	VERB
iajs-3409	43	20	in	in	ADP
iajs-3409	43	21	the	the	DET
iajs-3409	43	22	scientific	scientific	ADJ
iajs-3409	43	23	literature	literature	NOUN
iajs-3409	43	24	,	,	PUNCT
iajs-3409	43	25	we	we	PRON
iajs-3409	43	26	give	give	VERB
iajs-3409	43	27	numerical	numerical	ADJ
iajs-3409	43	28	findings	finding	NOUN
iajs-3409	43	29	in	in	ADP
iajs-3409	43	30	section	section	NOUN
iajs-3409	43	31	7	7	NUM
iajs-3409	43	32	.	.	PUNCT
iajs-3409	43	33	section	section	NOUN
iajs-3409	43	34	8	8	NUM
iajs-3409	43	35	provides	provide	VERB
iajs-3409	43	36	conclusions	conclusion	NOUN
iajs-3409	43	37	.	.	PUNCT
iajs-3409	44	1	2	2	X
iajs-3409	44	2	.	.	X
iajs-3409	44	3	the	the	DET
iajs-3409	44	4	formulation	formulation	NOUN
iajs-3409	44	5	of	of	ADP
iajs-3409	44	6	rktdio	rktdio	NOUN
iajs-3409	44	7	method	method	NOUN
iajs-3409	44	8	by	by	ADP
iajs-3409	44	9	turning	turn	VERB
iajs-3409	44	10	it	it	PRON
iajs-3409	44	11	into	into	ADP
iajs-3409	44	12	a	a	DET
iajs-3409	44	13	system	system	NOUN
iajs-3409	44	14	of	of	ADP
iajs-3409	44	15	first	first	ADJ
iajs-3409	44	16	-	-	PUNCT
iajs-3409	44	17	order	order	NOUN
iajs-3409	44	18	odes	ode	NOUN
iajs-3409	44	19	,	,	PUNCT
iajs-3409	44	20	the	the	DET
iajs-3409	44	21	special	special	ADJ
iajs-3409	44	22	third	third	ADJ
iajs-3409	44	23	-	-	PUNCT
iajs-3409	44	24	order	order	NOUN
iajs-3409	44	25	ivp	ivp	X
iajs-3409	44	26	(	(	PUNCT
iajs-3409	44	27	1	1	X
iajs-3409	44	28	)	)	PUNCT
iajs-3409	44	29	can	can	AUX
iajs-3409	44	30	be	be	AUX
iajs-3409	44	31	solved	solve	VERB
iajs-3409	44	32	as	as	SCONJ
iajs-3409	44	33	follows	follow	VERB
iajs-3409	44	34	:	:	PUNCT
iajs-3409	44	35	(	(	PUNCT
iajs-3409	44	36	α(x	α(x	NOUN
iajs-3409	44	37	)	)	PUNCT
iajs-3409	44	38	β(x	β(x	NOUN
iajs-3409	44	39	)	)	PUNCT
iajs-3409	44	40	γ(x	γ(x	NOUN
iajs-3409	44	41	)	)	PUNCT
iajs-3409	44	42	)	)	PUNCT
iajs-3409	45	1	′	′	NUM
iajs-3409	46	1	=	=	PUNCT
iajs-3409	46	2	(	(	PUNCT
iajs-3409	46	3	β(x	β(x	NOUN
iajs-3409	46	4	)	)	PUNCT
iajs-3409	46	5	γ(x	γ(x	NOUN
iajs-3409	46	6	)	)	PUNCT
iajs-3409	46	7	μ(x	μ(x	PROPN
iajs-3409	46	8	,	,	PUNCT
iajs-3409	46	9	α(x	α(x	NOUN
iajs-3409	46	10	)	)	PUNCT
iajs-3409	46	11	)	)	PUNCT
iajs-3409	46	12	)	)	PUNCT
iajs-3409	47	1	(	(	PUNCT
iajs-3409	47	2	2	2	X
iajs-3409	47	3	)	)	PUNCT
iajs-3409	47	4	with	with	ADP
iajs-3409	47	5	initial	initial	ADJ
iajs-3409	47	6	conditions	condition	NOUN
iajs-3409	47	7	α(xn	α(xn	NOUN
iajs-3409	47	8	)	)	PUNCT
iajs-3409	47	9	=	=	SYM
iajs-3409	47	10	αn	αn	NOUN
iajs-3409	47	11	,	,	PUNCT
iajs-3409	47	12	β(xn	β(xn	NUM
iajs-3409	47	13	)	)	PUNCT
iajs-3409	47	14	=	=	SYM
iajs-3409	48	1	𝛼𝑛	𝛼𝑛	ADP
iajs-3409	48	2	′	′	NUM
iajs-3409	48	3	,	,	PUNCT
iajs-3409	48	4	γ(xn	γ(xn	NUM
iajs-3409	48	5	)	)	PUNCT
iajs-3409	48	6	=	=	SYM
iajs-3409	48	7	α𝑛	α𝑛	NOUN
iajs-3409	48	8	′′.	′′.	VERB
iajs-3409	48	9	the	the	DET
iajs-3409	48	10	runge	runge	NOUN
iajs-3409	48	11	-	-	PUNCT
iajs-3409	48	12	kutta	kutta	NOUN
iajs-3409	48	13	method	method	NOUN
iajs-3409	48	14	first	first	ADJ
iajs-3409	48	15	-	-	PUNCT
iajs-3409	48	16	order	order	NOUN
iajs-3409	48	17	is	be	AUX
iajs-3409	48	18	used	use	VERB
iajs-3409	48	19	to	to	PART
iajs-3409	48	20	obtain	obtain	VERB
iajs-3409	48	21	the	the	DET
iajs-3409	48	22	following	follow	VERB
iajs-3409	48	23	system	system	NOUN
iajs-3409	48	24	of	of	ADP
iajs-3409	48	25	equations	equation	NOUN
iajs-3409	48	26	αi=	αi=	PROPN
iajs-3409	48	27	αn	αn	NOUN
iajs-3409	49	1	+	+	CCONJ
iajs-3409	49	2	h	h	NOUN
iajs-3409	49	3	∑	∑	PROPN
iajs-3409	49	4	aijα′j	aijα′j	PROPN
iajs-3409	49	5	s	s	PART
iajs-3409	49	6	j=1	j=1	NOUN
iajs-3409	49	7	,	,	PUNCT
iajs-3409	49	8	(	(	PUNCT
iajs-3409	49	9	3	3	X
iajs-3409	49	10	)	)	PUNCT
iajs-3409	49	11	α′i	α′i	PROPN
iajs-3409	49	12	=	=	SYM
iajs-3409	49	13	𝛼𝑛	𝛼𝑛	NOUN
iajs-3409	49	14	′	′	NOUN
iajs-3409	50	1	+	+	CCONJ
iajs-3409	50	2	h	h	NOUN
iajs-3409	50	3	∑	∑	NOUN
iajs-3409	50	4	aijα′′j	aijα′′j	NOUN
iajs-3409	50	5	,	,	PUNCT
iajs-3409	50	6	s	s	PART
iajs-3409	50	7	j=1	j=1	NOUN
iajs-3409	50	8	(	(	PUNCT
iajs-3409	50	9	4	4	NUM
iajs-3409	50	10	)	)	PUNCT
iajs-3409	50	11	α𝑖	α𝑖	ADP
iajs-3409	51	1	′′	′′	NOUN
iajs-3409	51	2	=	=	SYM
iajs-3409	51	3	α𝑛	α𝑛	NUM
iajs-3409	51	4	′′	′′	PROPN
iajs-3409	51	5	+	+	CCONJ
iajs-3409	51	6	h	h	PROPN
iajs-3409	51	7	∑	∑	PUNCT
iajs-3409	51	8	aij	aij	PROPN
iajs-3409	51	9	μ(xn	μ(xn	PROPN
iajs-3409	51	10	+	+	CCONJ
iajs-3409	51	11	cjh	cjh	PROPN
iajs-3409	51	12	,	,	PUNCT
iajs-3409	51	13	αj	αj	NOUN
iajs-3409	51	14	)	)	PUNCT
iajs-3409	51	15	,	,	PUNCT
iajs-3409	51	16	s	s	PART
iajs-3409	51	17	j=1	j=1	NOUN
iajs-3409	51	18	(	(	PUNCT
iajs-3409	51	19	5	5	NUM
iajs-3409	51	20	)	)	PUNCT
iajs-3409	51	21	αn+1	αn+1	NUM
iajs-3409	52	1	=	=	SYM
iajs-3409	52	2	αn	αn	NOUN
iajs-3409	53	1	+	+	NUM
iajs-3409	53	2	h	h	NOUN
iajs-3409	53	3	∑	∑	PUNCT
iajs-3409	53	4	biα𝑖	biα𝑖	NOUN
iajs-3409	53	5	′	′	NUM
iajs-3409	53	6	,	,	PUNCT
iajs-3409	53	7	(	(	PUNCT
iajs-3409	53	8	6)s	6)s	NOUN
iajs-3409	53	9	i=1	i=1	PROPN
iajs-3409	53	10	ihjpas	ihjpas	PROPN
iajs-3409	53	11	.	.	PUNCT
iajs-3409	54	1	37	37	NUM
iajs-3409	54	2	(	(	PUNCT
iajs-3409	54	3	2	2	NUM
iajs-3409	54	4	)	)	PUNCT
iajs-3409	54	5	2024	2024	NUM
iajs-3409	54	6	390	390	NUM
iajs-3409	54	7	α𝑛+1	α𝑛+1	NUM
iajs-3409	54	8	′	′	NUM
iajs-3409	54	9	=	=	PUNCT
iajs-3409	54	10	α𝑛	α𝑛	NOUN
iajs-3409	54	11	′	′	NUM
iajs-3409	55	1	+	+	CCONJ
iajs-3409	55	2	h	h	NOUN
iajs-3409	55	3	∑	∑	PUNCT
iajs-3409	55	4	biα𝑖	biα𝑖	NOUN
iajs-3409	55	5	′′s	′′s	NOUN
iajs-3409	55	6	i=1	i=1	PRON
iajs-3409	55	7	,	,	PUNCT
iajs-3409	55	8	(	(	PUNCT
iajs-3409	55	9	7	7	NUM
iajs-3409	55	10	)	)	PUNCT
iajs-3409	55	11	α𝑛+1	α𝑛+1	NUM
iajs-3409	56	1	′′	′′	NOUN
iajs-3409	56	2	=	=	SYM
iajs-3409	56	3	α𝑛	α𝑛	NUM
iajs-3409	56	4	′′	′′	PROPN
iajs-3409	56	5	+	+	CCONJ
iajs-3409	56	6	h	h	PROPN
iajs-3409	56	7	∑	∑	VERB
iajs-3409	56	8	biμ	biμ	PROPN
iajs-3409	56	9	s	s	X
iajs-3409	56	10	i=1	i=1	PROPN
iajs-3409	56	11	(	(	PUNCT
iajs-3409	56	12	xn	xn	PROPN
iajs-3409	56	13	+	+	PROPN
iajs-3409	56	14	cih	cih	PROPN
iajs-3409	56	15	,	,	PUNCT
iajs-3409	56	16	αi	αi	NOUN
iajs-3409	56	17	)	)	PUNCT
iajs-3409	56	18	.	.	PUNCT
iajs-3409	57	1	(	(	PUNCT
iajs-3409	57	2	8)	8)	NUM
iajs-3409	57	3	when	when	SCONJ
iajs-3409	57	4	we	we	PRON
iajs-3409	57	5	ignore	ignore	VERB
iajs-3409	57	6	𝛼𝑖	𝛼𝑖	ADP
iajs-3409	57	7	′	′	NOUN
iajs-3409	57	8	,	,	PUNCT
iajs-3409	57	9	𝛼𝑖	𝛼𝑖	ADP
iajs-3409	57	10	′′	′′	PROPN
iajs-3409	57	11	and	and	CCONJ
iajs-3409	57	12	α𝑖	α𝑖	AUX
iajs-3409	57	13	′′′	′′′	ADV
iajs-3409	57	14	,	,	PUNCT
iajs-3409	57	15	from	from	ADP
iajs-3409	57	16	(	(	PUNCT
iajs-3409	57	17	3	3	NUM
iajs-3409	57	18	)	)	PUNCT
iajs-3409	57	19	–	–	PUNCT
iajs-3409	57	20	(	(	PUNCT
iajs-3409	57	21	8)	8)	NUM
iajs-3409	57	22	we	we	PRON
iajs-3409	57	23	conclude	conclude	VERB
iajs-3409	57	24	αi	αi	VERB
iajs-3409	57	25	=	=	PUNCT
iajs-3409	57	26	αn	αn	NOUN
iajs-3409	58	1	+	+	NUM
iajs-3409	58	2	h	h	NOUN
iajs-3409	58	3	∑	∑	PUNCT
iajs-3409	58	4	aij	aij	PROPN
iajs-3409	58	5	s	s	PROPN
iajs-3409	58	6	j=1	j=1	NOUN
iajs-3409	58	7	α𝑛	α𝑛	NOUN
iajs-3409	58	8	′	′	NUM
iajs-3409	58	9	+	+	CCONJ
iajs-3409	58	10	h2	h2	PROPN
iajs-3409	58	11	∑	∑	PUNCT
iajs-3409	58	12	aij	aij	PROPN
iajs-3409	58	13	s	s	PROPN
iajs-3409	58	14	j	j	PROPN
iajs-3409	58	15	,	,	PUNCT
iajs-3409	58	16	k=1	k=1	PROPN
iajs-3409	58	17	αjkα𝑛	αjkα𝑛	VERB
iajs-3409	58	18	′′	′′	PROPN
iajs-3409	58	19	+	+	CCONJ
iajs-3409	58	20	h3	h3	NOUN
iajs-3409	58	21	∑	∑	PROPN
iajs-3409	58	22	aijajkakl	aijajkakl	PROPN
iajs-3409	58	23	μ(xn	μ(xn	PROPN
iajs-3409	58	24	+	+	CCONJ
iajs-3409	58	25	cih	cih	PROPN
iajs-3409	58	26	,	,	PUNCT
iajs-3409	58	27	αl	αl	ADP
iajs-3409	58	28	)	)	PUNCT
iajs-3409	58	29	,	,	PUNCT
iajs-3409	58	30	i	i	PRON
iajs-3409	58	31	=	=	NOUN
iajs-3409	58	32	1	1	NUM
iajs-3409	58	33	,	,	PUNCT
iajs-3409	58	34	…	…	PUNCT
iajs-3409	58	35	,	,	PUNCT
iajs-3409	58	36	s.	s.	PROPN
iajs-3409	58	37	(	(	PUNCT
iajs-3409	58	38	9	9	NUM
iajs-3409	58	39	)	)	PUNCT
iajs-3409	58	40	s	s	PART
iajs-3409	58	41	j	j	PROPN
iajs-3409	58	42	,	,	PUNCT
iajs-3409	58	43	k	k	PROPN
iajs-3409	58	44	,	,	PUNCT
iajs-3409	58	45	l	l	NOUN
iajs-3409	58	46	𝛼𝑛+1	𝛼𝑛+1	NUM
iajs-3409	58	47	=	=	SYM
iajs-3409	58	48	𝛼𝑛	𝛼𝑛	NOUN
iajs-3409	59	1	+	+	NUM
iajs-3409	59	2	ℎ	ℎ	PROPN
iajs-3409	59	3	∑	∑	ADV
iajs-3409	59	4	𝑏𝑖𝛼𝑛	𝑏𝑖𝛼𝑛	NOUN
iajs-3409	59	5	′	′	NOUN
iajs-3409	59	6	+	+	CCONJ
iajs-3409	59	7	ℎ2	ℎ2	NOUN
iajs-3409	59	8	∑	∑	PUNCT
iajs-3409	59	9	𝑏𝑖	𝑏𝑖	ADP
iajs-3409	59	10	𝑠	𝑠	PROPN
iajs-3409	59	11	𝑖,𝑗=1	𝑖,𝑗=1	NOUN
iajs-3409	59	12	𝑎𝑖𝑗𝛼𝑛	𝑎𝑖𝑗𝛼𝑛	VERB
iajs-3409	59	13	′′	′′	PROPN
iajs-3409	59	14	𝑠	𝑠	NUM
iajs-3409	59	15	𝑖=1	𝑖=1	PROPN
iajs-3409	59	16	+	+	CCONJ
iajs-3409	59	17	ℎ3	ℎ3	PROPN
iajs-3409	59	18	∑	∑	PUNCT
iajs-3409	59	19	𝑏𝑖𝑎𝑖𝑗𝑎𝑗𝑘	𝑏𝑖𝑎𝑖𝑗𝑎𝑗𝑘	NOUN
iajs-3409	59	20	𝜇(𝑥𝑛	𝜇(𝑥𝑛	PROPN
iajs-3409	59	21	+	+	CCONJ
iajs-3409	59	22	𝑐𝑘ℎ	𝑐𝑘ℎ	NUM
iajs-3409	59	23	,	,	PUNCT
iajs-3409	59	24	𝑠	𝑠	PROPN
iajs-3409	59	25	𝑖,𝑗,𝑘=1	𝑖,𝑗,𝑘=1	ADV
iajs-3409	59	26	𝛼𝑘	𝛼𝑘	NOUN
iajs-3409	59	27	)	)	PUNCT
iajs-3409	59	28	,	,	PUNCT
iajs-3409	59	29	(	(	PUNCT
iajs-3409	59	30	10	10	NUM
iajs-3409	59	31	)	)	PUNCT
iajs-3409	59	32	𝛼′𝑛+1	𝛼′𝑛+1	NOUN
iajs-3409	59	33	=	=	SYM
iajs-3409	59	34	𝛼𝑛	𝛼𝑛	NOUN
iajs-3409	60	1	′	′	NOUN
iajs-3409	61	1	+	+	CCONJ
iajs-3409	61	2	ℎ	ℎ	PROPN
iajs-3409	61	3	∑	∑	ADV
iajs-3409	61	4	𝑏𝑖𝛼𝑛	𝑏𝑖𝛼𝑛	NOUN
iajs-3409	61	5	′′	′′	PROPN
iajs-3409	61	6	+	+	CCONJ
iajs-3409	61	7	ℎ2	ℎ2	ADJ
iajs-3409	61	8	∑	∑	PUNCT
iajs-3409	61	9	𝑏𝑖𝑎𝑖𝑗	𝑏𝑖𝑎𝑖𝑗	NOUN
iajs-3409	61	10	𝜇𝑠	𝜇𝑠	ADP
iajs-3409	61	11	𝑖.𝑗=1	𝑖.𝑗=1	PROPN
iajs-3409	61	12	(	(	PUNCT
iajs-3409	61	13	𝑥𝑛	𝑥𝑛	PROPN
iajs-3409	61	14	+	+	CCONJ
iajs-3409	61	15	𝑐𝑗ℎ𝑠	𝑐𝑗ℎ𝑠	NOUN
iajs-3409	61	16	𝑖=1	𝑖=1	PROPN
iajs-3409	61	17	,	,	PUNCT
iajs-3409	61	18	𝛼𝑗	𝛼𝑗	PROPN
iajs-3409	61	19	)	)	PUNCT
iajs-3409	61	20	,	,	PUNCT
iajs-3409	61	21	(	(	PUNCT
iajs-3409	61	22	11	11	NUM
iajs-3409	61	23	)	)	PUNCT
iajs-3409	61	24	𝛼𝑛+1	𝛼𝑛+1	NUM
iajs-3409	62	1	′′	′′	PROPN
iajs-3409	62	2	=	=	SYM
iajs-3409	62	3	𝛼𝑛	𝛼𝑛	PROPN
iajs-3409	62	4	′′	′′	PROPN
iajs-3409	62	5	+	+	CCONJ
iajs-3409	62	6	h	h	PROPN
iajs-3409	62	7	∑	∑	PROPN
iajs-3409	62	8	bi	bi	PROPN
iajs-3409	62	9	μ(xn	μ(xn	PROPN
iajs-3409	62	10	+	+	CCONJ
iajs-3409	62	11	cih	cih	PROPN
iajs-3409	62	12	,	,	PUNCT
iajs-3409	62	13	s	s	PART
iajs-3409	62	14	i=1	i=1	PROPN
iajs-3409	62	15	αi	αi	PROPN
iajs-3409	62	16	)	)	PUNCT
iajs-3409	62	17	.	.	PUNCT
iajs-3409	63	1	(	(	PUNCT
iajs-3409	63	2	12	12	NUM
iajs-3409	63	3	)	)	PUNCT
iajs-3409	63	4	we	we	PRON
iajs-3409	63	5	assume	assume	VERB
iajs-3409	63	6	that	that	SCONJ
iajs-3409	63	7	∑	∑	PUNCT
iajs-3409	63	8	aij	aij	PROPN
iajs-3409	63	9	=	=	SYM
iajs-3409	63	10	ci	ci	PROPN
iajs-3409	63	11	,	,	PUNCT
iajs-3409	63	12	s	s	PART
iajs-3409	63	13	j=1	j=1	NOUN
iajs-3409	63	14	∑	∑	PUNCT
iajs-3409	63	15	aijajk	aijajk	NOUN
iajs-3409	63	16	=	=	SYM
iajs-3409	63	17	1	1	NUM
iajs-3409	63	18	2	2	NUM
iajs-3409	63	19	s	s	NOUN
iajs-3409	63	20	j	j	PROPN
iajs-3409	63	21	,	,	PUNCT
iajs-3409	63	22	k=1	k=1	PROPN
iajs-3409	63	23	ci	ci	PROPN
iajs-3409	63	24	2	2	NUM
iajs-3409	63	25	,	,	PUNCT
iajs-3409	63	26	∑	∑	PUNCT
iajs-3409	63	27	bi	bi	NOUN
iajs-3409	63	28	=	=	NOUN
iajs-3409	63	29	1	1	NUM
iajs-3409	63	30	s	s	NOUN
iajs-3409	63	31	i=1	i=1	PROPN
iajs-3409	63	32	,	,	PUNCT
iajs-3409	63	33	∑	∑	PUNCT
iajs-3409	63	34	biaij	biaij	NOUN
iajs-3409	63	35	=	=	SYM
iajs-3409	63	36	1	1	NUM
iajs-3409	63	37	2	2	NUM
iajs-3409	63	38	s	s	VERB
iajs-3409	63	39	i	i	PRON
iajs-3409	63	40	,	,	PUNCT
iajs-3409	63	41	j=1	j=1	PROPN
iajs-3409	63	42	,	,	PUNCT
iajs-3409	63	43	∑	∑	PUNCT
iajs-3409	63	44	biaij	biaij	NOUN
iajs-3409	63	45	=	=	PUNCT
iajs-3409	63	46	b𝑖	b𝑖	PROPN
iajs-3409	63	47	′′	′′	PROPN
iajs-3409	63	48	,	,	PUNCT
iajs-3409	63	49	∑	∑	ADV
iajs-3409	64	1	bjajkakl	bjajkakl	ADJ
iajs-3409	64	2	=	=	SYM
iajs-3409	64	3	b𝑖	b𝑖	PROPN
iajs-3409	64	4	′′	′′	PROPN
iajs-3409	64	5	s	s	PROPN
iajs-3409	64	6	j	j	PROPN
iajs-3409	64	7	,	,	PUNCT
iajs-3409	64	8	k=1	k=1	PROPN
iajs-3409	64	9	s	s	AUX
iajs-3409	64	10	j=1	j=1	NOUN
iajs-3409	64	11	,	,	PUNCT
iajs-3409	64	12	∑	∑	PUNCT
iajs-3409	64	13	aik	aik	PROPN
iajs-3409	64	14	s	s	PART
iajs-3409	64	15	k	k	PROPN
iajs-3409	64	16	,	,	PUNCT
iajs-3409	64	17	l	l	NOUN
iajs-3409	64	18	,	,	PUNCT
iajs-3409	64	19	r=1	r=1	NOUN
iajs-3409	64	20	aklalr	aklalr	NOUN
iajs-3409	64	21	=	=	SYM
iajs-3409	64	22	�	�	PROPN
iajs-3409	64	23	̂	̂	NOUN
iajs-3409	64	24	�	�	NOUN
iajs-3409	64	25	𝑖𝑗	𝑖𝑗	NOUN
iajs-3409	64	26	,	,	PUNCT
iajs-3409	64	27	𝑖	𝑖	NOUN
iajs-3409	64	28	=	=	NOUN
iajs-3409	64	29	1	1	NUM
iajs-3409	64	30	,	,	PUNCT
iajs-3409	64	31	…	…	PUNCT
iajs-3409	64	32	,	,	PUNCT
iajs-3409	64	33	𝑠.	𝑠.	NOUN
iajs-3409	64	34	as	as	ADP
iajs-3409	64	35	a	a	DET
iajs-3409	64	36	result	result	NOUN
iajs-3409	64	37	,	,	PUNCT
iajs-3409	64	38	we	we	PRON
iajs-3409	64	39	are	be	AUX
iajs-3409	64	40	able	able	ADJ
iajs-3409	64	41	to	to	PART
iajs-3409	64	42	solve	solve	VERB
iajs-3409	64	43	the	the	DET
iajs-3409	64	44	specific	specific	ADJ
iajs-3409	64	45	third	third	ADJ
iajs-3409	64	46	-	-	PUNCT
iajs-3409	64	47	order	order	NOUN
iajs-3409	64	48	ivp	ivp	X
iajs-3409	64	49	(	(	PUNCT
iajs-3409	64	50	1	1	NUM
iajs-3409	64	51	)	)	PUNCT
iajs-3409	64	52	,	,	PUNCT
iajs-3409	64	53	indicated	indicate	VERB
iajs-3409	64	54	by	by	ADP
iajs-3409	64	55	the	the	DET
iajs-3409	64	56	rktdio	rktdio	NOUN
iajs-3409	64	57	approach	approach	NOUN
iajs-3409	64	58	,	,	PUNCT
iajs-3409	64	59	using	use	VERB
iajs-3409	64	60	the	the	DET
iajs-3409	64	61	following	follow	VERB
iajs-3409	64	62	direct	direct	ADJ
iajs-3409	64	63	integration	integration	NOUN
iajs-3409	64	64	method	method	NOUN
iajs-3409	64	65	.	.	PUNCT
iajs-3409	65	1	thus	thus	ADV
iajs-3409	65	2	,	,	PUNCT
iajs-3409	65	3	the	the	DET
iajs-3409	65	4	following	follow	VERB
iajs-3409	65	5	formula	formula	NOUN
iajs-3409	65	6	is	be	AUX
iajs-3409	65	7	used	use	VERB
iajs-3409	65	8	to	to	PART
iajs-3409	65	9	represent	represent	VERB
iajs-3409	65	10	the	the	DET
iajs-3409	65	11	s	s	NOUN
iajs-3409	65	12	-	-	PUNCT
iajs-3409	65	13	stage	stage	NOUN
iajs-3409	65	14	rktdio	rktdio	NOUN
iajs-3409	65	15	approach	approach	NOUN
iajs-3409	65	16	for	for	ADP
iajs-3409	65	17	the	the	DET
iajs-3409	65	18	numerical	numerical	ADJ
iajs-3409	65	19	solution	solution	NOUN
iajs-3409	65	20	of	of	ADP
iajs-3409	65	21	the	the	DET
iajs-3409	65	22	ivp	ivp	NOUN
iajs-3409	65	23	(	(	PUNCT
iajs-3409	65	24	1	1	NUM
iajs-3409	65	25	):	):	SYM
iajs-3409	65	26	αn+1	αn+1	NUM
iajs-3409	65	27	=	=	SYM
iajs-3409	65	28	αn	αn	NOUN
iajs-3409	66	1	+	+	CCONJ
iajs-3409	66	2	h𝛼𝑛	h𝛼𝑛	NOUN
iajs-3409	66	3	′	′	NOUN
iajs-3409	67	1	+	+	CCONJ
iajs-3409	67	2	1	1	NUM
iajs-3409	67	3	2	2	NUM
iajs-3409	67	4	h2𝛼𝑛	h2𝛼𝑛	X
iajs-3409	67	5	′′	′′	PROPN
iajs-3409	67	6	+	+	CCONJ
iajs-3409	67	7	h3	h3	NOUN
iajs-3409	67	8	∑	∑	PUNCT
iajs-3409	67	9	bi	bi	PROPN
iajs-3409	67	10	s	s	PROPN
iajs-3409	67	11	i=1	i=1	PROPN
iajs-3409	67	12	μ(xn	μ(xn	PROPN
iajs-3409	67	13	+	+	CCONJ
iajs-3409	67	14	cih	cih	PROPN
iajs-3409	67	15	,	,	PUNCT
iajs-3409	67	16	αi	αi	NOUN
iajs-3409	67	17	)	)	PUNCT
iajs-3409	67	18	,	,	PUNCT
iajs-3409	67	19	(	(	PUNCT
iajs-3409	67	20	13	13	NUM
iajs-3409	67	21	)	)	PUNCT
iajs-3409	67	22	𝛼′𝑛+1	𝛼′𝑛+1	NOUN
iajs-3409	67	23	=	=	SYM
iajs-3409	67	24	𝛼𝑛	𝛼𝑛	NOUN
iajs-3409	67	25	′	′	NOUN
iajs-3409	68	1	+	+	CCONJ
iajs-3409	68	2	h𝛼𝑛	h𝛼𝑛	VERB
iajs-3409	68	3	′′	′′	PROPN
iajs-3409	68	4	+	+	CCONJ
iajs-3409	68	5	h2	h2	PROPN
iajs-3409	68	6	∑	∑	PROPN
iajs-3409	68	7	b𝑖	b𝑖	PROPN
iajs-3409	68	8	′	′	NUM
iajs-3409	68	9	μ(xn	μ(xn	PROPN
iajs-3409	68	10	+	+	CCONJ
iajs-3409	68	11	cih	cih	PROPN
iajs-3409	68	12	,	,	PUNCT
iajs-3409	68	13	s	s	VERB
iajs-3409	68	14	i=1	i=1	PROPN
iajs-3409	68	15	α𝑖	α𝑖	PROPN
iajs-3409	68	16	′	′	NUM
iajs-3409	68	17	)	)	PUNCT
iajs-3409	68	18	,	,	PUNCT
iajs-3409	68	19	(	(	PUNCT
iajs-3409	68	20	14	14	NUM
iajs-3409	68	21	)	)	PUNCT
iajs-3409	68	22	𝛼𝑛+1	𝛼𝑛+1	NUM
iajs-3409	68	23	′′	′′	PROPN
iajs-3409	68	24	=	=	SYM
iajs-3409	68	25	𝛼𝑛	𝛼𝑛	PROPN
iajs-3409	68	26	′′	′′	PROPN
iajs-3409	68	27	+	+	CCONJ
iajs-3409	68	28	h	h	PROPN
iajs-3409	68	29	∑	∑	PROPN
iajs-3409	68	30	b𝑖	b𝑖	PROPN
iajs-3409	68	31	′′	′′	PROPN
iajs-3409	68	32	s	s	PART
iajs-3409	68	33	i=1	i=1	PROPN
iajs-3409	68	34	μ	μ	PROPN
iajs-3409	68	35	(	(	PUNCT
iajs-3409	68	36	xn	xn	PROPN
iajs-3409	68	37	+	+	X
iajs-3409	68	38	cih	cih	PROPN
iajs-3409	68	39	,	,	PUNCT
iajs-3409	68	40	α𝑖	α𝑖	NOUN
iajs-3409	68	41	′	′	NUM
iajs-3409	68	42	)	)	PUNCT
iajs-3409	68	43	,	,	PUNCT
iajs-3409	68	44	(	(	PUNCT
iajs-3409	68	45	15	15	X
iajs-3409	68	46	)	)	PUNCT
iajs-3409	68	47	αi	αi	VERB
iajs-3409	68	48	=	=	PUNCT
iajs-3409	68	49	αn	αn	NOUN
iajs-3409	69	1	+	+	NUM
iajs-3409	69	2	cih𝛼𝑛	cih𝛼𝑛	NOUN
iajs-3409	69	3	′	′	NUM
iajs-3409	70	1	+	+	CCONJ
iajs-3409	70	2	1	1	NUM
iajs-3409	70	3	2	2	NUM
iajs-3409	70	4	ci	ci	NOUN
iajs-3409	70	5	2h2𝛼𝑛	2h2𝛼𝑛	NUM
iajs-3409	70	6	′′	′′	NOUN
iajs-3409	70	7	+	+	CCONJ
iajs-3409	70	8	h3	h3	NOUN
iajs-3409	70	9	+	+	CCONJ
iajs-3409	70	10	∑	∑	PROPN
iajs-3409	70	11	�	�	PROPN
iajs-3409	70	12	̂	̂	NOUN
iajs-3409	70	13	�	�	PROPN
iajs-3409	70	14	ij	ij	NOUN
iajs-3409	70	15	μ(xn	μ(xn	PROPN
iajs-3409	70	16	+	+	CCONJ
iajs-3409	70	17	cih	cih	PROPN
iajs-3409	70	18	,	,	PUNCT
iajs-3409	70	19	s	s	PART
iajs-3409	70	20	i	i	PROPN
iajs-3409	70	21	,	,	PUNCT
iajs-3409	70	22	j=1	j=1	PROPN
iajs-3409	70	23	α𝑗	α𝑗	PROPN
iajs-3409	70	24	′	′	NOUN
iajs-3409	70	25	)	)	PUNCT
iajs-3409	70	26	.	.	PUNCT
iajs-3409	71	1	(	(	PUNCT
iajs-3409	71	2	16	16	NUM
iajs-3409	71	3	)	)	PUNCT
iajs-3409	71	4	all	all	DET
iajs-3409	71	5	rktdio	rktdio	NOUN
iajs-3409	71	6	parameters	parameter	NOUN
iajs-3409	71	7	aij	aij	PROPN
iajs-3409	71	8	,	,	PUNCT
iajs-3409	71	9	bi	bi	NOUN
iajs-3409	71	10	,	,	PUNCT
iajs-3409	71	11	b𝑖	b𝑖	PROPN
iajs-3409	71	12	′	′	PROPN
iajs-3409	71	13	,	,	PUNCT
iajs-3409	71	14	b𝑖	b𝑖	PROPN
iajs-3409	71	15	′′	′′	PROPN
iajs-3409	71	16	,	,	PUNCT
iajs-3409	71	17	and	and	CCONJ
iajs-3409	71	18	ci	ci	PROPN
iajs-3409	71	19	are	be	AUX
iajs-3409	71	20	real	real	ADJ
iajs-3409	71	21	numbers	number	NOUN
iajs-3409	71	22	and	and	CCONJ
iajs-3409	71	23	i	i	PRON
iajs-3409	71	24	,	,	PUNCT
iajs-3409	71	25	j	j	PROPN
iajs-3409	71	26	=	=	SYM
iajs-3409	71	27	1	1	NUM
iajs-3409	71	28	,	,	PUNCT
iajs-3409	71	29	2	2	NUM
iajs-3409	71	30	,	,	PUNCT
iajs-3409	71	31	.	.	PUNCT
iajs-3409	71	32	.	.	PUNCT
iajs-3409	72	1	.	.	PUNCT
iajs-3409	73	1	,	,	PUNCT
iajs-3409	73	2	s.	s.	PROPN
iajs-3409	73	3	the	the	DET
iajs-3409	73	4	rktdio	rktdio	NOUN
iajs-3409	73	5	method	method	NOUN
iajs-3409	73	6	(	(	PUNCT
iajs-3409	73	7	13)–(16	13)–(16	NUM
iajs-3409	73	8	)	)	PUNCT
iajs-3409	73	9	can	can	AUX
iajs-3409	73	10	be	be	AUX
iajs-3409	73	11	expressed	express	VERB
iajs-3409	73	12	in	in	ADP
iajs-3409	73	13	butcher	butcher	PROPN
iajs-3409	73	14	tableau	tableau	PROPN
iajs-3409	73	15	as	as	SCONJ
iajs-3409	73	16	follows	follow	VERB
iajs-3409	73	17	ihjpas	ihjpa	NOUN
iajs-3409	73	18	.	.	PUNCT
iajs-3409	74	1	37	37	NUM
iajs-3409	74	2	(	(	PUNCT
iajs-3409	74	3	2	2	NUM
iajs-3409	74	4	)	)	PUNCT
iajs-3409	74	5	2024	2024	NUM
iajs-3409	74	6	391	391	NUM
iajs-3409	74	7	:	:	PUNCT
iajs-3409	74	8	3	3	NUM
iajs-3409	74	9	.	.	X
iajs-3409	74	10	b	b	X
iajs-3409	74	11	-	-	PUNCT
iajs-3409	74	12	series	series	NOUN
iajs-3409	74	13	and	and	CCONJ
iajs-3409	74	14	associated	associate	VERB
iajs-3409	74	15	relevant	relevant	ADJ
iajs-3409	74	16	-	-	PUNCT
iajs-3409	74	17	colored	colored	ADJ
iajs-3409	74	18	trees	tree	NOUN
iajs-3409	74	19	the	the	DET
iajs-3409	74	20	essential	essential	ADJ
iajs-3409	74	21	definitions	definition	NOUN
iajs-3409	74	22	of	of	ADP
iajs-3409	74	23	lemmas	lemmas	PROPN
iajs-3409	74	24	and	and	CCONJ
iajs-3409	74	25	associated	associated	ADJ
iajs-3409	74	26	theorems	theorem	NOUN
iajs-3409	74	27	that	that	PRON
iajs-3409	74	28	are	be	AUX
iajs-3409	74	29	utilized	utilize	VERB
iajs-3409	74	30	throughout	throughout	ADP
iajs-3409	74	31	this	this	DET
iajs-3409	74	32	article	article	NOUN
iajs-3409	74	33	will	will	AUX
iajs-3409	74	34	be	be	AUX
iajs-3409	74	35	covered	cover	VERB
iajs-3409	74	36	in	in	ADP
iajs-3409	74	37	this	this	DET
iajs-3409	74	38	part	part	NOUN
iajs-3409	74	39	.	.	PUNCT
iajs-3409	75	1	definition	definition	NOUN
iajs-3409	75	2	3.1	3.1	NUM
iajs-3409	76	1	[	[	X
iajs-3409	76	2	22,23	22,23	NOUN
iajs-3409	76	3	]	]	PUNCT
iajs-3409	76	4	:	:	PUNCT
iajs-3409	76	5	order	order	NOUN
iajs-3409	76	6	of	of	ADP
iajs-3409	76	7	the	the	DET
iajs-3409	76	8	rktdio	rktdio	NOUN
iajs-3409	76	9	method	method	NOUN
iajs-3409	76	10	for	for	ADP
iajs-3409	76	11	third	third	ADJ
iajs-3409	76	12	-	-	PUNCT
iajs-3409	76	13	order	order	NOUN
iajs-3409	76	14	odes	ode	VERB
iajs-3409	76	15	the	the	DET
iajs-3409	76	16	rktdio	rktdio	NOUN
iajs-3409	76	17	method	method	NOUN
iajs-3409	76	18	(	(	PUNCT
iajs-3409	76	19	13)-(16	13)-(16	NOUN
iajs-3409	76	20	)	)	PUNCT
iajs-3409	76	21	has	have	VERB
iajs-3409	76	22	order	order	NOUN
iajs-3409	76	23	𝑝	𝑝	NOUN
iajs-3409	76	24	when	when	SCONJ
iajs-3409	76	25	the	the	DET
iajs-3409	76	26	third	third	ADJ
iajs-3409	76	27	-	-	PUNCT
iajs-3409	76	28	order	order	NOUN
iajs-3409	76	29	ode	ode	NOUN
iajs-3409	76	30	(	(	PUNCT
iajs-3409	76	31	1	1	NUM
iajs-3409	76	32	)	)	PUNCT
iajs-3409	76	33	with	with	ADP
iajs-3409	76	34	the	the	DET
iajs-3409	76	35	assumption	assumption	NOUN
iajs-3409	76	36	α(xn	α(xn	NUM
iajs-3409	76	37	)	)	PUNCT
iajs-3409	76	38	=	=	SYM
iajs-3409	76	39	αn	αn	NUM
iajs-3409	76	40	,	,	PUNCT
iajs-3409	76	41	α′(xn	α′(xn	NOUN
iajs-3409	76	42	)	)	PUNCT
iajs-3409	76	43	=	=	PUNCT
iajs-3409	76	44	α′	α′	NUM
iajs-3409	76	45	n	n	CCONJ
iajs-3409	76	46	,	,	PUNCT
iajs-3409	76	47	α′′(xn	α′′(xn	NOUN
iajs-3409	76	48	)	)	PUNCT
iajs-3409	77	1	=	=	SYM
iajs-3409	77	2	α′′	α′′	NOUN
iajs-3409	77	3	n	n	PRON
iajs-3409	77	4	hence	hence	ADV
iajs-3409	77	5	the	the	DET
iajs-3409	77	6	local	local	ADJ
iajs-3409	77	7	truncation	truncation	NOUN
iajs-3409	77	8	error	error	NOUN
iajs-3409	77	9	norms	norm	NOUN
iajs-3409	77	10	of	of	ADP
iajs-3409	77	11	the	the	DET
iajs-3409	77	12	exact	exact	ADJ
iajs-3409	77	13	solution	solution	NOUN
iajs-3409	77	14	and	and	CCONJ
iajs-3409	77	15	the	the	DET
iajs-3409	77	16	first	first	ADJ
iajs-3409	77	17	,	,	PUNCT
iajs-3409	77	18	and	and	CCONJ
iajs-3409	77	19	second	second	ADJ
iajs-3409	77	20	derivatives	derivative	NOUN
iajs-3409	77	21	of	of	ADP
iajs-3409	77	22	the	the	DET
iajs-3409	77	23	solution	solution	NOUN
iajs-3409	77	24	must	must	AUX
iajs-3409	77	25	satisfied	satisfied	ADJ
iajs-3409	77	26	.	.	PUNCT
iajs-3409	78	1	α(xn	α(xn	NOUN
iajs-3409	78	2	+	+	NUM
iajs-3409	78	3	h	h	X
iajs-3409	78	4	)	)	PUNCT
iajs-3409	78	5	−	−	NOUN
iajs-3409	78	6	αn+1	αn+1	NUM
iajs-3409	78	7	=	=	SYM
iajs-3409	78	8	o(hp+1	o(hp+1	NOUN
iajs-3409	78	9	)	)	PUNCT
iajs-3409	78	10	,	,	PUNCT
iajs-3409	78	11	α′(xn	α′(xn	PROPN
iajs-3409	78	12	+	+	CCONJ
iajs-3409	78	13	h	h	NOUN
iajs-3409	78	14	)	)	PUNCT
iajs-3409	78	15	−	−	PROPN
iajs-3409	78	16	α′n+1	α′n+1	NOUN
iajs-3409	78	17	=	=	SYM
iajs-3409	78	18	o(hp+1	o(hp+1	NOUN
iajs-3409	78	19	)	)	PUNCT
iajs-3409	78	20	,	,	PUNCT
iajs-3409	78	21	α′′(xn	α′′(xn	NOUN
iajs-3409	79	1	+	+	CCONJ
iajs-3409	79	2	h	h	NOUN
iajs-3409	79	3	)	)	PUNCT
iajs-3409	79	4	−	−	PROPN
iajs-3409	79	5	α′′	α′′	NOUN
iajs-3409	79	6	n+1	n+1	PUNCT
iajs-3409	79	7	=	=	SYM
iajs-3409	79	8	o(hp+1	o(hp+1	NOUN
iajs-3409	79	9	)	)	PUNCT
iajs-3409	79	10	,	,	PUNCT
iajs-3409	79	11	(	(	PUNCT
iajs-3409	79	12	17	17	NUM
iajs-3409	79	13	)	)	PUNCT
iajs-3409	79	14	the	the	DET
iajs-3409	79	15	following	follow	VERB
iajs-3409	79	16	autonomous	autonomous	ADJ
iajs-3409	79	17	form	form	NOUN
iajs-3409	79	18	of	of	ADP
iajs-3409	79	19	third	third	ADJ
iajs-3409	79	20	-	-	PUNCT
iajs-3409	79	21	order	order	NOUN
iajs-3409	79	22	ivp	ivp	NOUN
iajs-3409	79	23	must	must	AUX
iajs-3409	79	24	be	be	AUX
iajs-3409	79	25	used	use	VERB
iajs-3409	79	26	in	in	ADP
iajs-3409	79	27	order	order	NOUN
iajs-3409	79	28	to	to	PART
iajs-3409	79	29	derive	derive	VERB
iajs-3409	79	30	the	the	DET
iajs-3409	79	31	algebraic	algebraic	ADJ
iajs-3409	79	32	order	order	NOUN
iajs-3409	79	33	conditions	condition	NOUN
iajs-3409	79	34	for	for	ADP
iajs-3409	79	35	the	the	DET
iajs-3409	79	36	rktdio	rktdio	NOUN
iajs-3409	79	37	technique	technique	NOUN
iajs-3409	79	38	(	(	PUNCT
iajs-3409	79	39	13)–(16	13)–(16	NUM
iajs-3409	79	40	)	)	PUNCT
iajs-3409	79	41	.	.	PUNCT
iajs-3409	80	1	α(3)(x	α(3)(x	NOUN
iajs-3409	80	2	)	)	PUNCT
iajs-3409	80	3	=	=	SYM
iajs-3409	80	4	ρ(α(x	ρ(α(x	PROPN
iajs-3409	80	5	)	)	PUNCT
iajs-3409	80	6	)	)	PUNCT
iajs-3409	80	7	,	,	PUNCT
iajs-3409	80	8	(	(	PUNCT
iajs-3409	80	9	18	18	NUM
iajs-3409	80	10	)	)	PUNCT
iajs-3409	80	11	with	with	ADP
iajs-3409	80	12	initial	initial	ADJ
iajs-3409	80	13	conditions	condition	NOUN
iajs-3409	80	14	α(xn	α(xn	NOUN
iajs-3409	80	15	)	)	PUNCT
iajs-3409	80	16	=	=	SYM
iajs-3409	81	1	αn	αn	NUM
iajs-3409	81	2	,	,	PUNCT
iajs-3409	81	3	α′(xn	α′(xn	NOUN
iajs-3409	81	4	)	)	PUNCT
iajs-3409	81	5	=	=	PUNCT
iajs-3409	82	1	α′	α′	NUM
iajs-3409	82	2	n	n	CCONJ
iajs-3409	82	3	,	,	PUNCT
iajs-3409	82	4	α′′(xn	α′′(xn	NOUN
iajs-3409	82	5	)	)	PUNCT
iajs-3409	82	6	=	=	SYM
iajs-3409	83	1	α𝑛	α𝑛	NOUN
iajs-3409	83	2	′′.	′′.	NOUN
iajs-3409	83	3	by	by	ADP
iajs-3409	83	4	extending	extend	VERB
iajs-3409	83	5	ivp	ivp	NOUN
iajs-3409	83	6	(	(	PUNCT
iajs-3409	83	7	1	1	NUM
iajs-3409	83	8	)	)	PUNCT
iajs-3409	83	9	with	with	ADP
iajs-3409	83	10	a	a	DET
iajs-3409	83	11	one	one	NUM
iajs-3409	83	12	-	-	PUNCT
iajs-3409	83	13	dimensional	dimensional	ADJ
iajs-3409	83	14	vector	vector	NOUN
iajs-3409	83	15	𝑤	𝑤	ADP
iajs-3409	83	16	=	=	SYM
iajs-3409	83	17	𝑥	𝑥	PROPN
iajs-3409	83	18	,	,	PUNCT
iajs-3409	83	19	the	the	DET
iajs-3409	83	20	autonomous	autonomous	ADJ
iajs-3409	83	21	problem	problem	NOUN
iajs-3409	83	22	can	can	AUX
iajs-3409	83	23	be	be	AUX
iajs-3409	83	24	expressed	express	VERB
iajs-3409	83	25	equivalently	equivalently	ADV
iajs-3409	83	26	to	to	ADP
iajs-3409	83	27	the	the	DET
iajs-3409	83	28	third	third	ADJ
iajs-3409	83	29	-	-	PUNCT
iajs-3409	83	30	order	order	NOUN
iajs-3409	83	31	initial	initial	ADJ
iajs-3409	83	32	value	value	NOUN
iajs-3409	83	33	problem	problem	NOUN
iajs-3409	83	34	(	(	PUNCT
iajs-3409	83	35	1	1	X
iajs-3409	83	36	)	)	PUNCT
iajs-3409	83	37	as	as	SCONJ
iajs-3409	83	38	follows	follow	VERB
iajs-3409	83	39	:	:	PUNCT
iajs-3409	83	40	w3	w3	PROPN
iajs-3409	83	41	=	=	PUNCT
iajs-3409	83	42	0	0	PROPN
iajs-3409	83	43	,	,	PUNCT
iajs-3409	83	44	(	(	PUNCT
iajs-3409	83	45	19	19	NUM
iajs-3409	83	46	)	)	PUNCT
iajs-3409	83	47	α(3	α(3	NOUN
iajs-3409	83	48	)	)	PUNCT
iajs-3409	83	49	=	=	SYM
iajs-3409	84	1	ρ(w	ρ(w	NOUN
iajs-3409	84	2	,	,	PUNCT
iajs-3409	84	3	α	α	NOUN
iajs-3409	84	4	)	)	PUNCT
iajs-3409	84	5	,	,	PUNCT
iajs-3409	84	6	(	(	PUNCT
iajs-3409	84	7	20	20	NUM
iajs-3409	84	8	)	)	PUNCT
iajs-3409	84	9	w(xn	w(xn	NOUN
iajs-3409	84	10	)	)	PUNCT
iajs-3409	84	11	=	=	SYM
iajs-3409	84	12	wn	wn	PROPN
iajs-3409	84	13	w′(xn	w′(xn	PROPN
iajs-3409	84	14	)	)	PUNCT
iajs-3409	85	1	=	=	SYM
iajs-3409	85	2	w′	w′	PROPN
iajs-3409	85	3	n	n	X
iajs-3409	85	4	=	=	SYM
iajs-3409	85	5	1	1	NUM
iajs-3409	85	6	,	,	PUNCT
iajs-3409	85	7	w′′(xn	w′′(xn	NOUN
iajs-3409	85	8	)	)	PUNCT
iajs-3409	85	9	=	=	PUNCT
iajs-3409	86	1	w′′	w′′	NOUN
iajs-3409	86	2	n	n	NOUN
iajs-3409	86	3	=	=	SYM
iajs-3409	86	4	0	0	NUM
iajs-3409	86	5	,	,	PUNCT
iajs-3409	86	6	(	(	PUNCT
iajs-3409	86	7	21	21	NUM
iajs-3409	86	8	)	)	PUNCT
iajs-3409	86	9	α(xn	α(xn	NUM
iajs-3409	86	10	)	)	PUNCT
iajs-3409	86	11	=	=	SYM
iajs-3409	86	12	αn	αn	NUM
iajs-3409	86	13	,	,	PUNCT
iajs-3409	86	14	α′(xn	α′(xn	NOUN
iajs-3409	86	15	)	)	PUNCT
iajs-3409	86	16	=	=	PUNCT
iajs-3409	86	17	α′	α′	NUM
iajs-3409	86	18	n	n	CCONJ
iajs-3409	86	19	,	,	PUNCT
iajs-3409	86	20	α′′(xn	α′′(xn	NOUN
iajs-3409	86	21	)	)	PUNCT
iajs-3409	86	22	=	=	SYM
iajs-3409	86	23	α′′n	α′′n	NOUN
iajs-3409	86	24	.	.	PUNCT
iajs-3409	87	1	(	(	PUNCT
iajs-3409	87	2	22	22	NUM
iajs-3409	87	3	)	)	PUNCT
iajs-3409	87	4	applying	apply	VERB
iajs-3409	87	5	rktdio	rktdio	NOUN
iajs-3409	87	6	method	method	NOUN
iajs-3409	87	7	(	(	PUNCT
iajs-3409	87	8	13)–(16	13)–(16	NUM
iajs-3409	87	9	)	)	PUNCT
iajs-3409	87	10	to	to	ADP
iajs-3409	87	11	the	the	DET
iajs-3409	87	12	scheme	scheme	NOUN
iajs-3409	87	13	(	(	PUNCT
iajs-3409	87	14	19)–(22	19)–(22	NUM
iajs-3409	87	15	)	)	PUNCT
iajs-3409	87	16	,	,	PUNCT
iajs-3409	87	17	we	we	PRON
iajs-3409	87	18	obtain	obtain	VERB
iajs-3409	87	19	wi	wi	PROPN
iajs-3409	87	20	=	=	SYM
iajs-3409	87	21	wn	wn	PROPN
iajs-3409	87	22	+	+	CCONJ
iajs-3409	87	23	cih	cih	X
iajs-3409	87	24	w′	w′	PROPN
iajs-3409	87	25	n	n	PROPN
iajs-3409	87	26	+	+	CCONJ
iajs-3409	87	27	1	1	NUM
iajs-3409	87	28	2	2	NUM
iajs-3409	87	29	ci	ci	NOUN
iajs-3409	87	30	2h2	2h2	NUM
iajs-3409	87	31	w′′	w′′	NOUN
iajs-3409	87	32	n	n	PRON
iajs-3409	87	33	,	,	PUNCT
iajs-3409	87	34	(	(	PUNCT
iajs-3409	87	35	23	23	NUM
iajs-3409	87	36	)	)	PUNCT
iajs-3409	87	37	αi	αi	VERB
iajs-3409	88	1	=	=	PUNCT
iajs-3409	88	2	αn	αn	NOUN
iajs-3409	89	1	+	+	CCONJ
iajs-3409	89	2	cihα′	cihα′	NOUN
iajs-3409	89	3	n	n	X
iajs-3409	89	4	+	+	CCONJ
iajs-3409	89	5	1	1	NUM
iajs-3409	89	6	2	2	NUM
iajs-3409	89	7	ci	ci	NOUN
iajs-3409	89	8	2h2	2h2	NUM
iajs-3409	89	9	α′′	α′′	NOUN
iajs-3409	89	10	n	n	CCONJ
iajs-3409	89	11	+	+	NUM
iajs-3409	89	12	h3	h3	NOUN
iajs-3409	89	13	∑	∑	PUNCT
iajs-3409	89	14	aij	aij	PROPN
iajs-3409	89	15	μ(wj	μ(wj	NUM
iajs-3409	89	16	,	,	PUNCT
iajs-3409	89	17	αj	αj	NOUN
iajs-3409	89	18	)	)	PUNCT
iajs-3409	89	19	,	,	PUNCT
iajs-3409	89	20	s	s	VERB
iajs-3409	89	21	i	i	PROPN
iajs-3409	89	22	,	,	PUNCT
iajs-3409	89	23	j=1	j=1	PROPN
iajs-3409	89	24	(	(	PUNCT
iajs-3409	89	25	24	24	NUM
iajs-3409	89	26	)	)	PUNCT
iajs-3409	89	27	wn+1	wn+1	PROPN
iajs-3409	89	28	=	=	SYM
iajs-3409	89	29	wn	wn	PROPN
iajs-3409	89	30	+	+	CCONJ
iajs-3409	89	31	h	h	PROPN
iajs-3409	89	32	w′	w′	PROPN
iajs-3409	89	33	n	n	PROPN
iajs-3409	89	34	+	+	CCONJ
iajs-3409	89	35	1	1	NUM
iajs-3409	89	36	2	2	NUM
iajs-3409	89	37	h2w′′	h2w′′	NOUN
iajs-3409	89	38	n	n	NOUN
iajs-3409	89	39	,	,	PUNCT
iajs-3409	89	40	(	(	PUNCT
iajs-3409	89	41	25	25	NUM
iajs-3409	89	42	)	)	PUNCT
iajs-3409	89	43	w′	w′	NOUN
iajs-3409	89	44	n+1	n+1	PART
iajs-3409	90	1	=	=	PUNCT
iajs-3409	90	2	w′	w′	PROPN
iajs-3409	90	3	n	n	NOUN
iajs-3409	90	4	+	+	NUM
iajs-3409	90	5	h	h	NOUN
iajs-3409	90	6	w′′	w′′	PROPN
iajs-3409	90	7	n	n	PROPN
iajs-3409	90	8	,	,	PUNCT
iajs-3409	90	9	(	(	PUNCT
iajs-3409	90	10	26	26	NUM
iajs-3409	90	11	)	)	PUNCT
iajs-3409	90	12	w′′	w′′	NOUN
iajs-3409	90	13	n+1	n+1	PUNCT
iajs-3409	90	14	=	=	PUNCT
iajs-3409	90	15	w′′	w′′	PROPN
iajs-3409	90	16	n	n	PRON
iajs-3409	90	17	,	,	PUNCT
iajs-3409	90	18	(	(	PUNCT
iajs-3409	90	19	27	27	NUM
iajs-3409	90	20	)	)	PUNCT
iajs-3409	90	21	αn+1	αn+1	NUM
iajs-3409	90	22	=	=	SYM
iajs-3409	90	23	αn	αn	NOUN
iajs-3409	91	1	+	+	NUM
iajs-3409	91	2	h	h	PROPN
iajs-3409	91	3	α′	α′	NUM
iajs-3409	91	4	n	n	NOUN
iajs-3409	91	5	+	+	CCONJ
iajs-3409	91	6	1	1	NUM
iajs-3409	91	7	2	2	NUM
iajs-3409	91	8	h2α′′	h2α′′	NOUN
iajs-3409	91	9	n	n	PRON
iajs-3409	91	10	+	+	NUM
iajs-3409	91	11	h3	h3	NOUN
iajs-3409	91	12	∑	∑	PUNCT
iajs-3409	91	13	bi	bi	PROPN
iajs-3409	91	14	μ(wi	μ(wi	PROPN
iajs-3409	91	15	s	s	PROPN
iajs-3409	91	16	i=1	i=1	PROPN
iajs-3409	91	17	,	,	PUNCT
iajs-3409	91	18	αi	αi	PROPN
iajs-3409	91	19	)	)	PUNCT
iajs-3409	91	20	,	,	PUNCT
iajs-3409	91	21	(	(	PUNCT
iajs-3409	91	22	28	28	NUM
iajs-3409	91	23	)	)	PUNCT
iajs-3409	91	24	α′n+1	α′n+1	NOUN
iajs-3409	91	25	=	=	SYM
iajs-3409	91	26	α′	α′	NUM
iajs-3409	91	27	n	n	NOUN
iajs-3409	91	28	+	+	NUM
iajs-3409	91	29	h	h	NOUN
iajs-3409	91	30	α′′	α′′	NOUN
iajs-3409	91	31	n	n	PROPN
iajs-3409	91	32	+	+	CCONJ
iajs-3409	91	33	h2	h2	NOUN
iajs-3409	91	34	∑	∑	PUNCT
iajs-3409	91	35	b′	b′	NOUN
iajs-3409	91	36	i	i	PRON
iajs-3409	91	37	μ(wi	μ(wi	PROPN
iajs-3409	91	38	,	,	PUNCT
iajs-3409	91	39	s	s	VERB
iajs-3409	91	40	i=1	i=1	PROPN
iajs-3409	91	41	αi	αi	PROPN
iajs-3409	91	42	)	)	PUNCT
iajs-3409	91	43	,	,	PUNCT
iajs-3409	91	44	(	(	PUNCT
iajs-3409	91	45	29	29	X
iajs-3409	91	46	)	)	PUNCT
iajs-3409	91	47	𝑐1	𝑐1	NOUN
iajs-3409	91	48	⋮	⋮	NOUN
iajs-3409	91	49	𝑐𝑠	𝑐𝑠	PRON
iajs-3409	91	50	�	�	PROPN
iajs-3409	91	51	̂	̂	NOUN
iajs-3409	91	52	�	�	NOUN
iajs-3409	91	53	11	11	NUM
iajs-3409	91	54	…	…	PUNCT
iajs-3409	91	55	�	�	NOUN
iajs-3409	91	56	̂	̂	SYM
iajs-3409	91	57	�	�	NOUN
iajs-3409	91	58	1𝑠	1𝑠	ADJ
iajs-3409	91	59	⋮	⋮	NOUN
iajs-3409	91	60	⋱	⋱	PUNCT
iajs-3409	91	61	⋮	⋮	NOUN
iajs-3409	91	62	�	�	PROPN
iajs-3409	91	63	̂	̂	PROPN
iajs-3409	91	64	�	�	NOUN
iajs-3409	91	65	𝑠1	𝑠1	PROPN
iajs-3409	91	66	…	…	PUNCT
iajs-3409	91	67	�	�	PROPN
iajs-3409	91	68	̂	̂	NUM
iajs-3409	91	69	�	�	NOUN
iajs-3409	91	70	𝑠𝑠	𝑠𝑠	ADV
iajs-3409	91	71	𝑏1	𝑏1	ADJ
iajs-3409	91	72	…	…	PUNCT
iajs-3409	91	73	𝑏𝑠	𝑏𝑠	NOUN
iajs-3409	91	74	𝑏1	𝑏1	NOUN
iajs-3409	91	75	′	′	NUM
iajs-3409	92	1	…	…	PUNCT
iajs-3409	92	2	𝑏𝑠	𝑏𝑠	NOUN
iajs-3409	92	3	′	′	NOUN
iajs-3409	92	4	𝑏1	𝑏1	NOUN
iajs-3409	92	5	′′	′′	PROPN
iajs-3409	92	6	…	…	PUNCT
iajs-3409	92	7	𝑏𝑠	𝑏𝑠	NOUN
iajs-3409	92	8	′′	′′	PROPN
iajs-3409	92	9	ihjpas	ihjpa	VERB
iajs-3409	92	10	.	.	PUNCT
iajs-3409	93	1	37	37	NUM
iajs-3409	93	2	(	(	PUNCT
iajs-3409	93	3	2	2	NUM
iajs-3409	93	4	)	)	PUNCT
iajs-3409	93	5	2024	2024	NUM
iajs-3409	93	6	392	392	NUM
iajs-3409	93	7	α′′	α′′	NOUN
iajs-3409	93	8	n+1	n+1	PUNCT
iajs-3409	93	9	=	=	SYM
iajs-3409	93	10	α′′	α′′	NOUN
iajs-3409	93	11	n	n	NOUN
iajs-3409	93	12	+	+	NUM
iajs-3409	93	13	h	h	NOUN
iajs-3409	93	14	∑	∑	PUNCT
iajs-3409	93	15	b′′	b′′	VERB
iajs-3409	93	16	i	i	PRON
iajs-3409	93	17	s	s	VERB
iajs-3409	93	18	i=1	i=1	PROPN
iajs-3409	93	19	μ(wi	μ(wi	PROPN
iajs-3409	93	20	,	,	PUNCT
iajs-3409	93	21	αi	αi	NOUN
iajs-3409	93	22	)	)	PUNCT
iajs-3409	93	23	.	.	PUNCT
iajs-3409	94	1	(	(	PUNCT
iajs-3409	94	2	30	30	X
iajs-3409	94	3	)	)	PUNCT
iajs-3409	94	4	substituting	substitute	VERB
iajs-3409	94	5	eq	eq	PROPN
iajs-3409	94	6	.	.	PUNCT
iajs-3409	95	1	(	(	PUNCT
iajs-3409	95	2	21	21	NUM
iajs-3409	95	3	)	)	PUNCT
iajs-3409	95	4	into	into	ADP
iajs-3409	95	5	system	system	NOUN
iajs-3409	95	6	of	of	ADP
iajs-3409	95	7	eqs	eqs	PROPN
iajs-3409	95	8	.	.	PUNCT
iajs-3409	96	1	(	(	PUNCT
iajs-3409	96	2	23)–(30	23)–(30	NUM
iajs-3409	96	3	)	)	PUNCT
iajs-3409	96	4	,	,	PUNCT
iajs-3409	96	5	we	we	PRON
iajs-3409	96	6	get	get	VERB
iajs-3409	96	7	wi	wi	PROPN
iajs-3409	96	8	=	=	PUNCT
iajs-3409	96	9	xn	xn	PROPN
iajs-3409	97	1	+	+	CCONJ
iajs-3409	97	2	cih	cih	PROPN
iajs-3409	97	3	,	,	PUNCT
iajs-3409	97	4	(	(	PUNCT
iajs-3409	97	5	31	31	NUM
iajs-3409	97	6	)	)	PUNCT
iajs-3409	97	7	wn+1	wn+1	NOUN
iajs-3409	97	8	=	=	SYM
iajs-3409	97	9	xn	xn	PROPN
iajs-3409	98	1	+	+	NUM
iajs-3409	98	2	h	h	NOUN
iajs-3409	98	3	,	,	PUNCT
iajs-3409	98	4	(	(	PUNCT
iajs-3409	98	5	32	32	NUM
iajs-3409	98	6	)	)	PUNCT
iajs-3409	98	7	w′	w′	VERB
iajs-3409	98	8	n+1	n+1	X
iajs-3409	98	9	=	=	SYM
iajs-3409	98	10	1	1	NUM
iajs-3409	98	11	,	,	PUNCT
iajs-3409	98	12	(	(	PUNCT
iajs-3409	98	13	33	33	NUM
iajs-3409	98	14	)	)	PUNCT
iajs-3409	98	15	w′′	w′′	NOUN
iajs-3409	98	16	n+1	n+1	PROPN
iajs-3409	98	17	=	=	SYM
iajs-3409	98	18	0	0	NUM
iajs-3409	98	19	,	,	PUNCT
iajs-3409	98	20	(	(	PUNCT
iajs-3409	98	21	34	34	NUM
iajs-3409	98	22	)	)	PUNCT
iajs-3409	98	23	αn+1	αn+1	NUM
iajs-3409	99	1	=	=	SYM
iajs-3409	99	2	αn	αn	NOUN
iajs-3409	100	1	+	+	NUM
iajs-3409	100	2	hα′	hα′	NOUN
iajs-3409	100	3	n	n	CCONJ
iajs-3409	100	4	+	+	CCONJ
iajs-3409	100	5	1	1	NUM
iajs-3409	100	6	2	2	NUM
iajs-3409	100	7	h2α′′	h2α′′	NOUN
iajs-3409	100	8	n	n	PRON
iajs-3409	100	9	+	+	NUM
iajs-3409	100	10	h3	h3	NOUN
iajs-3409	100	11	∑	∑	PUNCT
iajs-3409	100	12	bi	bi	PROPN
iajs-3409	100	13	s	s	PROPN
iajs-3409	100	14	i=1	i=1	PROPN
iajs-3409	100	15	μ(xn	μ(xn	PROPN
iajs-3409	100	16	+	+	CCONJ
iajs-3409	100	17	cih	cih	PROPN
iajs-3409	100	18	,	,	PUNCT
iajs-3409	100	19	αi	αi	NOUN
iajs-3409	100	20	)	)	PUNCT
iajs-3409	100	21	,	,	PUNCT
iajs-3409	100	22	(	(	PUNCT
iajs-3409	100	23	35	35	NUM
iajs-3409	100	24	)	)	PUNCT
iajs-3409	100	25	α′	α′	NUM
iajs-3409	100	26	n+1	n+1	PUNCT
iajs-3409	100	27	=	=	PUNCT
iajs-3409	100	28	α′	α′	NUM
iajs-3409	100	29	n	n	NOUN
iajs-3409	100	30	+	+	NUM
iajs-3409	100	31	hα′′	hα′′	NOUN
iajs-3409	100	32	n	n	CCONJ
iajs-3409	100	33	+	+	CCONJ
iajs-3409	100	34	h2	h2	NOUN
iajs-3409	100	35	∑	∑	PUNCT
iajs-3409	100	36	b′	b′	PROPN
iajs-3409	101	1	i	i	PRON
iajs-3409	101	2	s	s	VERB
iajs-3409	101	3	i=1	i=1	PROPN
iajs-3409	101	4	μ(xn	μ(xn	PROPN
iajs-3409	101	5	+	+	CCONJ
iajs-3409	101	6	cih	cih	PROPN
iajs-3409	101	7	,	,	PUNCT
iajs-3409	101	8	αi	αi	NOUN
iajs-3409	101	9	)	)	PUNCT
iajs-3409	101	10	,	,	PUNCT
iajs-3409	101	11	(	(	PUNCT
iajs-3409	101	12	36	36	NUM
iajs-3409	101	13	)	)	PUNCT
iajs-3409	101	14	α′′	α′′	NOUN
iajs-3409	101	15	n+1	n+1	PART
iajs-3409	101	16	=	=	SYM
iajs-3409	101	17	α′′	α′′	NOUN
iajs-3409	101	18	n	n	NOUN
iajs-3409	101	19	+	+	NUM
iajs-3409	101	20	h	h	NOUN
iajs-3409	101	21	∑	∑	PUNCT
iajs-3409	101	22	b′′	b′′	VERB
iajs-3409	102	1	i	i	PRON
iajs-3409	102	2	s	s	VERB
iajs-3409	102	3	i=1	i=1	PROPN
iajs-3409	102	4	μ(xn	μ(xn	PROPN
iajs-3409	102	5	+	+	CCONJ
iajs-3409	102	6	cih	cih	PROPN
iajs-3409	102	7	,	,	PUNCT
iajs-3409	102	8	αi	αi	NOUN
iajs-3409	102	9	)	)	PUNCT
iajs-3409	102	10	,	,	PUNCT
iajs-3409	102	11	(	(	PUNCT
iajs-3409	102	12	37	37	NUM
iajs-3409	102	13	)	)	PUNCT
iajs-3409	102	14	αi	αi	VERB
iajs-3409	102	15	=	=	PUNCT
iajs-3409	103	1	αn	αn	NOUN
iajs-3409	104	1	+	+	CCONJ
iajs-3409	104	2	cihα′	cihα′	NOUN
iajs-3409	104	3	n	n	X
iajs-3409	104	4	+	+	CCONJ
iajs-3409	104	5	1	1	NUM
iajs-3409	104	6	2	2	NUM
iajs-3409	104	7	ci	ci	NOUN
iajs-3409	104	8	2h2α′′	2h2α′′	NUM
iajs-3409	104	9	n	n	ADP
iajs-3409	104	10	+	+	NUM
iajs-3409	104	11	h3	h3	NOUN
iajs-3409	104	12	∑	∑	PUNCT
iajs-3409	104	13	�	�	PROPN
iajs-3409	104	14	̂	̂	NOUN
iajs-3409	104	15	�	�	PROPN
iajs-3409	104	16	𝑖𝑗	𝑖𝑗	ADP
iajs-3409	104	17	μ(xn	μ(xn	PROPN
iajs-3409	104	18	+	+	CCONJ
iajs-3409	104	19	cih	cih	PROPN
iajs-3409	104	20	s	s	X
iajs-3409	104	21	i	i	PROPN
iajs-3409	104	22	,	,	PUNCT
iajs-3409	104	23	j=1	j=1	PROPN
iajs-3409	104	24	,	,	PUNCT
iajs-3409	104	25	αj	αj	NOUN
iajs-3409	104	26	)	)	PUNCT
iajs-3409	104	27	.	.	PUNCT
iajs-3409	105	1	(	(	PUNCT
iajs-3409	105	2	38	38	NUM
iajs-3409	105	3	)	)	PUNCT
iajs-3409	105	4	we	we	PRON
iajs-3409	105	5	find	find	VERB
iajs-3409	105	6	that	that	SCONJ
iajs-3409	105	7	the	the	DET
iajs-3409	105	8	system	system	NOUN
iajs-3409	105	9	of	of	ADP
iajs-3409	105	10	equations	equation	NOUN
iajs-3409	105	11	(	(	PUNCT
iajs-3409	105	12	13)–(16	13)–(16	NUM
iajs-3409	105	13	)	)	PUNCT
iajs-3409	105	14	,	,	PUNCT
iajs-3409	105	15	which	which	PRON
iajs-3409	105	16	is	be	AUX
iajs-3409	105	17	generated	generate	VERB
iajs-3409	105	18	by	by	ADP
iajs-3409	105	19	using	use	VERB
iajs-3409	105	20	the	the	DET
iajs-3409	105	21	rktdio	rktdio	NOUN
iajs-3409	105	22	approach	approach	NOUN
iajs-3409	105	23	on	on	ADP
iajs-3409	105	24	the	the	DET
iajs-3409	105	25	non	non	ADJ
iajs-3409	105	26	-	-	ADJ
iajs-3409	105	27	autonomous	autonomous	ADJ
iajs-3409	105	28	problem	problem	NOUN
iajs-3409	105	29	(	(	PUNCT
iajs-3409	105	30	1	1	NUM
iajs-3409	105	31	)	)	PUNCT
iajs-3409	105	32	,	,	PUNCT
iajs-3409	105	33	is	be	AUX
iajs-3409	105	34	totally	totally	ADV
iajs-3409	105	35	similar	similar	ADJ
iajs-3409	105	36	to	to	ADP
iajs-3409	105	37	eqs	eqs	PROPN
iajs-3409	105	38	.	.	PUNCT
iajs-3409	106	1	(	(	PUNCT
iajs-3409	106	2	35	35	NUM
iajs-3409	106	3	)	)	PUNCT
iajs-3409	106	4	–	–	PUNCT
iajs-3409	106	5	(	(	PUNCT
iajs-3409	106	6	38	38	NUM
iajs-3409	106	7	)	)	PUNCT
iajs-3409	106	8	.	.	PUNCT
iajs-3409	107	1	hence	hence	ADV
iajs-3409	107	2	,	,	PUNCT
iajs-3409	107	3	discussing	discuss	VERB
iajs-3409	107	4	the	the	DET
iajs-3409	107	5	numerical	numerical	ADJ
iajs-3409	107	6	solutions	solution	NOUN
iajs-3409	107	7	of	of	ADP
iajs-3409	107	8	autonomous	autonomous	ADJ
iajs-3409	107	9	form	form	NOUN
iajs-3409	107	10	is	be	AUX
iajs-3409	107	11	sufficient	sufficient	ADJ
iajs-3409	107	12	(	(	PUNCT
iajs-3409	107	13	18	18	NUM
iajs-3409	107	14	)	)	PUNCT
iajs-3409	107	15	.	.	PUNCT
iajs-3409	108	1	hence	hence	ADV
iajs-3409	108	2	,	,	PUNCT
iajs-3409	108	3	the	the	DET
iajs-3409	108	4	rktdio	rktdio	NOUN
iajs-3409	108	5	method	method	NOUN
iajs-3409	108	6	(	(	PUNCT
iajs-3409	108	7	13)–(16	13)–(16	NUM
iajs-3409	108	8	)	)	PUNCT
iajs-3409	108	9	can	can	AUX
iajs-3409	108	10	be	be	AUX
iajs-3409	108	11	implemented	implement	VERB
iajs-3409	108	12	as	as	SCONJ
iajs-3409	108	13	follows	follow	VERB
iajs-3409	108	14	.	.	PUNCT
iajs-3409	108	15	αn+1	αn+1	NUM
iajs-3409	109	1	=	=	NUM
iajs-3409	109	2	αn	αn	NOUN
iajs-3409	110	1	+	+	NUM
iajs-3409	110	2	h	h	PROPN
iajs-3409	110	3	α′	α′	NUM
iajs-3409	110	4	n	n	NOUN
iajs-3409	110	5	+	+	CCONJ
iajs-3409	110	6	1	1	NUM
iajs-3409	110	7	2	2	NUM
iajs-3409	110	8	h2α′′	h2α′′	NOUN
iajs-3409	110	9	n	n	PRON
iajs-3409	110	10	+	+	NUM
iajs-3409	110	11	h3	h3	NOUN
iajs-3409	110	12	∑	∑	PUNCT
iajs-3409	110	13	bi	bi	PROPN
iajs-3409	110	14	s	s	PROPN
iajs-3409	110	15	i=1	i=1	PROPN
iajs-3409	110	16	μ(αi	μ(αi	NUM
iajs-3409	110	17	)	)	PUNCT
iajs-3409	110	18	,	,	PUNCT
iajs-3409	110	19	α′	α′	SYM
iajs-3409	110	20	n+1	n+1	PUNCT
iajs-3409	110	21	=	=	PUNCT
iajs-3409	110	22	α′	α′	NUM
iajs-3409	110	23	n	n	NOUN
iajs-3409	110	24	+	+	NUM
iajs-3409	110	25	hα′′	hα′′	NOUN
iajs-3409	110	26	n	n	CCONJ
iajs-3409	110	27	+	+	CCONJ
iajs-3409	110	28	h2	h2	NOUN
iajs-3409	110	29	∑	∑	PUNCT
iajs-3409	110	30	b′	b′	NOUN
iajs-3409	111	1	i	i	PRON
iajs-3409	111	2	s	s	VERB
iajs-3409	111	3	i=1	i=1	PROPN
iajs-3409	111	4	μ(αi	μ(αi	NOUN
iajs-3409	111	5	)	)	PUNCT
iajs-3409	111	6	,	,	PUNCT
iajs-3409	111	7	α′′	α′′	NOUN
iajs-3409	111	8	n+1	n+1	PUNCT
iajs-3409	111	9	=	=	SYM
iajs-3409	111	10	α′′	α′′	NOUN
iajs-3409	111	11	n	n	NOUN
iajs-3409	111	12	+	+	NUM
iajs-3409	111	13	h	h	NOUN
iajs-3409	111	14	∑	∑	PUNCT
iajs-3409	111	15	b′′	b′′	VERB
iajs-3409	112	1	i	i	PRON
iajs-3409	112	2	s	s	VERB
iajs-3409	112	3	i=1	i=1	PROPN
iajs-3409	112	4	μ(αi	μ(αi	NUM
iajs-3409	112	5	)	)	PUNCT
iajs-3409	112	6	,	,	PUNCT
iajs-3409	112	7	αi	αi	VERB
iajs-3409	112	8	=	=	PUNCT
iajs-3409	112	9	αn	αn	NOUN
iajs-3409	113	1	+	+	CCONJ
iajs-3409	113	2	cihα′	cihα′	NOUN
iajs-3409	113	3	n	n	X
iajs-3409	114	1	+	+	CCONJ
iajs-3409	114	2	1	1	NUM
iajs-3409	114	3	2	2	NUM
iajs-3409	114	4	ci	ci	NOUN
iajs-3409	114	5	2h2α′′	2h2α′′	NUM
iajs-3409	114	6	n	n	ADP
iajs-3409	114	7	+	+	NUM
iajs-3409	114	8	h3	h3	NOUN
iajs-3409	114	9	∑	∑	PUNCT
iajs-3409	114	10	�	�	PROPN
iajs-3409	114	11	̂	̂	NOUN
iajs-3409	114	12	�	�	NOUN
iajs-3409	114	13	𝑖𝑗	𝑖𝑗	NOUN
iajs-3409	114	14	s	s	VERB
iajs-3409	114	15	i	i	PROPN
iajs-3409	114	16	,	,	PUNCT
iajs-3409	114	17	j=1	j=1	ADJ
iajs-3409	114	18	μ(αj	μ(αj	PROPN
iajs-3409	114	19	)	)	PUNCT
iajs-3409	114	20	.	.	PUNCT
iajs-3409	115	1	(	(	PUNCT
iajs-3409	115	2	39	39	NUM
iajs-3409	115	3	)	)	PUNCT
iajs-3409	115	4	the	the	DET
iajs-3409	115	5	following	follow	VERB
iajs-3409	115	6	elementary	elementary	ADJ
iajs-3409	115	7	differentials	differential	NOUN
iajs-3409	115	8	are	be	AUX
iajs-3409	115	9	obtained	obtain	VERB
iajs-3409	115	10	by	by	ADP
iajs-3409	115	11	using	use	VERB
iajs-3409	115	12	the	the	DET
iajs-3409	115	13	elementary	elementary	ADJ
iajs-3409	115	14	differential	differential	ADJ
iajs-3409	115	15	notation	notation	NOUN
iajs-3409	115	16	on	on	ADP
iajs-3409	115	17	the	the	DET
iajs-3409	115	18	analytical	analytical	ADJ
iajs-3409	115	19	solution	solution	NOUN
iajs-3409	115	20	𝛼(𝑥	𝛼(𝑥	PROPN
iajs-3409	115	21	)	)	PUNCT
iajs-3409	115	22	.	.	PUNCT
iajs-3409	116	1	[	[	X
iajs-3409	116	2	15	15	NUM
iajs-3409	116	3	]	]	X
iajs-3409	116	4	α(1	α(1	PROPN
iajs-3409	116	5	)	)	PUNCT
iajs-3409	116	6	=	=	SYM
iajs-3409	116	7	α′	α′	NUM
iajs-3409	116	8	,	,	PUNCT
iajs-3409	116	9	α(2	α(2	PROPN
iajs-3409	116	10	)	)	PUNCT
iajs-3409	116	11	=	=	SYM
iajs-3409	116	12	α′′	α′′	NOUN
iajs-3409	116	13	,	,	PUNCT
iajs-3409	116	14	α(3	α(3	PROPN
iajs-3409	116	15	)	)	PUNCT
iajs-3409	116	16	=	=	SYM
iajs-3409	116	17	μ	μ	PROPN
iajs-3409	116	18	,	,	PUNCT
iajs-3409	116	19	α(4	α(4	PROPN
iajs-3409	116	20	)	)	PUNCT
iajs-3409	116	21	=	=	PUNCT
iajs-3409	116	22	μ′α′	μ′α′	NOUN
iajs-3409	116	23	,	,	PUNCT
iajs-3409	116	24	α(5	α(5	NOUN
iajs-3409	116	25	)	)	PUNCT
iajs-3409	116	26	=	=	SYM
iajs-3409	116	27	μ′′(α′	μ′′(α′	PROPN
iajs-3409	116	28	,	,	PUNCT
iajs-3409	116	29	α′	α′	NUM
iajs-3409	116	30	)	)	PUNCT
iajs-3409	117	1	+	+	CCONJ
iajs-3409	117	2	μ′α′′(𝛼′	μ′α′′(𝛼′	PROPN
iajs-3409	117	3	,	,	PUNCT
iajs-3409	117	4	𝛼′	𝛼′	NUM
iajs-3409	117	5	)	)	PUNCT
iajs-3409	117	6	,	,	PUNCT
iajs-3409	117	7	α(6	α(6	PROPN
iajs-3409	117	8	)	)	PUNCT
iajs-3409	117	9	=	=	SYM
iajs-3409	117	10	3𝛼′′(𝛼′	3𝛼′′(𝛼′	NUM
iajs-3409	117	11	,	,	PUNCT
iajs-3409	117	12	𝛼′′	𝛼′′	NOUN
iajs-3409	117	13	)	)	PUNCT
iajs-3409	117	14	+	+	SYM
iajs-3409	117	15	μ′′′(𝛼′	μ′′′(𝛼′	NOUN
iajs-3409	117	16	,	,	PUNCT
iajs-3409	117	17	𝛼′	𝛼′	NUM
iajs-3409	117	18	,	,	PUNCT
iajs-3409	117	19	𝛼′	𝛼′	NUM
iajs-3409	117	20	)	)	PUNCT
iajs-3409	118	1	+	+	CCONJ
iajs-3409	118	2	μ′α′′.	μ′α′′.	NOUN
iajs-3409	118	3	(	(	PUNCT
iajs-3409	118	4	40	40	NUM
iajs-3409	118	5	)	)	PUNCT
iajs-3409	118	6	these	these	DET
iajs-3409	118	7	processes	process	NOUN
iajs-3409	118	8	very	very	ADV
iajs-3409	118	9	quickly	quickly	ADV
iajs-3409	118	10	get	get	VERB
iajs-3409	118	11	more	more	ADV
iajs-3409	118	12	difficult	difficult	ADJ
iajs-3409	118	13	as	as	SCONJ
iajs-3409	118	14	the	the	DET
iajs-3409	118	15	order	order	NOUN
iajs-3409	118	16	increases	increase	VERB
iajs-3409	118	17	.	.	PUNCT
iajs-3409	119	1	the	the	DET
iajs-3409	119	2	optimum	optimum	ADJ
iajs-3409	119	3	method	method	NOUN
iajs-3409	119	4	for	for	ADP
iajs-3409	119	5	overcoming	overcome	VERB
iajs-3409	119	6	this	this	DET
iajs-3409	119	7	challenge	challenge	NOUN
iajs-3409	119	8	,	,	PUNCT
iajs-3409	119	9	according	accord	VERB
iajs-3409	119	10	to	to	ADP
iajs-3409	119	11	[	[	X
iajs-3409	119	12	25	25	NUM
iajs-3409	119	13	]	]	PUNCT
iajs-3409	119	14	,	,	PUNCT
iajs-3409	119	15	will	will	AUX
iajs-3409	119	16	be	be	AUX
iajs-3409	119	17	to	to	PART
iajs-3409	119	18	use	use	VERB
iajs-3409	119	19	a	a	DET
iajs-3409	119	20	graphical	graphical	ADJ
iajs-3409	119	21	representation	representation	NOUN
iajs-3409	119	22	with	with	ADP
iajs-3409	119	23	a	a	DET
iajs-3409	119	24	few	few	ADJ
iajs-3409	119	25	modifications	modification	NOUN
iajs-3409	119	26	for	for	ADP
iajs-3409	119	27	third	third	ADJ
iajs-3409	119	28	-	-	PUNCT
iajs-3409	119	29	order	order	NOUN
iajs-3409	119	30	odes	ode	NOUN
iajs-3409	119	31	,	,	PUNCT
iajs-3409	119	32	denoted	denote	VERB
iajs-3409	119	33	by	by	ADP
iajs-3409	119	34	relevant	relevant	ADJ
iajs-3409	119	35	-	-	PUNCT
iajs-3409	119	36	colored	colored	ADJ
iajs-3409	119	37	trees	tree	NOUN
iajs-3409	119	38	.	.	PUNCT
iajs-3409	120	1	the	the	DET
iajs-3409	120	2	three	three	NUM
iajs-3409	120	3	sorts	sort	NOUN
iajs-3409	120	4	of	of	ADP
iajs-3409	120	5	nodes	node	NOUN
iajs-3409	120	6	in	in	ADP
iajs-3409	120	7	the	the	DET
iajs-3409	120	8	relevant	relevant	ADJ
iajs-3409	120	9	-	-	PUNCT
iajs-3409	120	10	colored	colored	ADJ
iajs-3409	120	11	trees	tree	NOUN
iajs-3409	120	12	are	be	AUX
iajs-3409	120	13	"	"	PUNCT
iajs-3409	120	14	meager	meager	ADJ
iajs-3409	120	15	,	,	PUNCT
iajs-3409	120	16	"	"	PUNCT
iajs-3409	120	17	"	"	PUNCT
iajs-3409	120	18	black	black	ADJ
iajs-3409	120	19	ball	ball	NOUN
iajs-3409	120	20	"	"	PUNCT
iajs-3409	120	21	,	,	PUNCT
iajs-3409	120	22	and	and	CCONJ
iajs-3409	120	23	"	"	PUNCT
iajs-3409	120	24	white	white	ADJ
iajs-3409	120	25	ball	ball	NOUN
iajs-3409	120	26	"	"	PUNCT
iajs-3409	120	27	,	,	PUNCT
iajs-3409	120	28	and	and	CCONJ
iajs-3409	120	29	they	they	PRON
iajs-3409	120	30	are	be	AUX
iajs-3409	120	31	connected	connect	VERB
iajs-3409	120	32	by	by	ADP
iajs-3409	120	33	arcs	arc	NOUN
iajs-3409	120	34	.	.	PUNCT
iajs-3409	121	1	in	in	ADP
iajs-3409	121	2	these	these	DET
iajs-3409	121	3	trees	tree	NOUN
iajs-3409	121	4	,	,	PUNCT
iajs-3409	121	5	we	we	PRON
iajs-3409	121	6	specifically	specifically	ADV
iajs-3409	121	7	use	use	VERB
iajs-3409	121	8	the	the	DET
iajs-3409	121	9	end	end	NOUN
iajs-3409	121	10	meager	meager	ADJ
iajs-3409	121	11	node	node	NOUN
iajs-3409	121	12	to	to	PART
iajs-3409	121	13	denote	denote	VERB
iajs-3409	121	14	each	each	DET
iajs-3409	121	15	𝛼′	𝛼′	NUM
iajs-3409	121	16	,	,	PUNCT
iajs-3409	121	17	the	the	DET
iajs-3409	121	18	end	end	NOUN
iajs-3409	121	19	black	black	ADJ
iajs-3409	121	20	ball	ball	NOUN
iajs-3409	121	21	node	node	VERB
iajs-3409	121	22	to	to	PART
iajs-3409	121	23	denote	denote	VERB
iajs-3409	121	24	each	each	DET
iajs-3409	121	25	𝛼′′	𝛼′′	NOUN
iajs-3409	121	26	,	,	PUNCT
iajs-3409	121	27	the	the	DET
iajs-3409	121	28	end	end	NOUN
iajs-3409	121	29	white	white	PROPN
iajs-3409	121	30	ball	ball	PROPN
iajs-3409	121	31	to	to	PART
iajs-3409	121	32	denote	denote	VERB
iajs-3409	121	33	each	each	PRON
iajs-3409	121	34	𝜇	𝜇	ADP
iajs-3409	121	35	,	,	PUNCT
iajs-3409	121	36	and	and	CCONJ
iajs-3409	121	37	each	each	DET
iajs-3409	121	38	arc	arc	NOUN
iajs-3409	121	39	to	to	PART
iajs-3409	121	40	denote	denote	VERB
iajs-3409	121	41	each	each	DET
iajs-3409	121	42	arc	arc	NOUN
iajs-3409	121	43	,	,	PUNCT
iajs-3409	121	44	leaving	leave	VERB
iajs-3409	121	45	this	this	DET
iajs-3409	121	46	node	node	NOUN
iajs-3409	121	47	to	to	PART
iajs-3409	121	48	represent	represent	VERB
iajs-3409	121	49	the	the	DET
iajs-3409	121	50	𝑚	𝑚	PROPN
iajs-3409	121	51	−	−	PROPN
iajs-3409	121	52	𝑡ℎ	𝑡ℎ	NOUN
iajs-3409	121	53	derivative	derivative	NOUN
iajs-3409	121	54	of	of	ADP
iajs-3409	121	55	𝜇	𝜇	ADP
iajs-3409	121	56	with	with	ADP
iajs-3409	121	57	respect	respect	NOUN
iajs-3409	121	58	to	to	ADP
iajs-3409	121	59	𝛼.	𝛼.	NOUN
iajs-3409	121	60	in	in	ADP
iajs-3409	121	61	addition	addition	NOUN
iajs-3409	121	62	,	,	PUNCT
iajs-3409	121	63	the	the	DET
iajs-3409	121	64	symbols	symbol	NOUN
iajs-3409	121	65	𝑡1	𝑡1	VERB
iajs-3409	121	66	and	and	CCONJ
iajs-3409	121	67	𝑡2	𝑡2	PROPN
iajs-3409	121	68	denote	denote	VERB
iajs-3409	121	69	the	the	DET
iajs-3409	121	70	first	first	ADJ
iajs-3409	121	71	-	-	PUNCT
iajs-3409	121	72	order	order	NOUN
iajs-3409	121	73	and	and	CCONJ
iajs-3409	121	74	the	the	DET
iajs-3409	121	75	second	second	ADJ
iajs-3409	121	76	-	-	PUNCT
iajs-3409	121	77	order	order	NOUN
iajs-3409	121	78	tree	tree	NOUN
iajs-3409	121	79	and	and	CCONJ
iajs-3409	121	80	𝑡3	𝑡3	VERB
iajs-3409	121	81	the	the	DET
iajs-3409	121	82	third	third	ADJ
iajs-3409	121	83	-	-	PUNCT
iajs-3409	121	84	order	order	NOUN
iajs-3409	121	85	tree	tree	NOUN
iajs-3409	121	86	,	,	PUNCT
iajs-3409	121	87	respectively	respectively	ADV
iajs-3409	121	88	(	(	PUNCT
iajs-3409	121	89	see	see	VERB
iajs-3409	121	90	figure	figure	NOUN
iajs-3409	121	91	1	1	NUM
iajs-3409	121	92	)	)	PUNCT
iajs-3409	121	93	ihjpas	ihjpa	NOUN
iajs-3409	121	94	.	.	PUNCT
iajs-3409	122	1	37	37	NUM
iajs-3409	122	2	(	(	PUNCT
iajs-3409	122	3	2	2	NUM
iajs-3409	122	4	)	)	PUNCT
iajs-3409	122	5	2024	2024	NUM
iajs-3409	122	6	393	393	NUM
iajs-3409	122	7	𝜏1	𝜏1	NOUN
iajs-3409	122	8	=	=	SYM
iajs-3409	122	9	𝜏2	𝜏2	NOUN
iajs-3409	122	10	=	=	SYM
iajs-3409	122	11	𝜏3	𝜏3	NOUN
iajs-3409	122	12	=	=	NOUN
iajs-3409	122	13	figure	figure	NOUN
iajs-3409	122	14	1	1	NUM
iajs-3409	122	15	.	.	PUNCT
iajs-3409	123	1	the	the	DET
iajs-3409	123	2	relevant	relevant	ADJ
iajs-3409	123	3	-	-	PUNCT
iajs-3409	123	4	colored	colored	ADJ
iajs-3409	123	5	trees	tree	NOUN
iajs-3409	123	6	here	here	ADV
iajs-3409	123	7	,	,	PUNCT
iajs-3409	123	8	we	we	PRON
iajs-3409	123	9	'll	will	AUX
iajs-3409	123	10	go	go	VERB
iajs-3409	123	11	through	through	ADP
iajs-3409	123	12	some	some	DET
iajs-3409	123	13	essential	essential	ADJ
iajs-3409	123	14	definitions	definition	NOUN
iajs-3409	123	15	for	for	ADP
iajs-3409	123	16	the	the	DET
iajs-3409	123	17	relevant	relevant	ADJ
iajs-3409	123	18	-	-	PUNCT
iajs-3409	123	19	colored	colored	ADJ
iajs-3409	123	20	trees	tree	NOUN
iajs-3409	123	21	and	and	CCONJ
iajs-3409	123	22	related	relate	VERB
iajs-3409	123	23	b	b	NOUN
iajs-3409	123	24	-	-	PUNCT
iajs-3409	123	25	series	series	NOUN
iajs-3409	123	26	that	that	PRON
iajs-3409	123	27	are	be	AUX
iajs-3409	123	28	necessary	necessary	ADJ
iajs-3409	123	29	for	for	ADP
iajs-3409	123	30	this	this	DET
iajs-3409	123	31	work	work	NOUN
iajs-3409	123	32	.	.	PUNCT
iajs-3409	124	1	definition	definition	NOUN
iajs-3409	124	2	3.2	3.2	NUM
iajs-3409	125	1	[	[	X
iajs-3409	125	2	22,23	22,23	NOUN
iajs-3409	125	3	]	]	X
iajs-3409	125	4	:	:	PUNCT
iajs-3409	125	5	relevant	relevant	ADJ
iajs-3409	125	6	-	-	PUNCT
iajs-3409	125	7	colored	colored	ADJ
iajs-3409	125	8	trees	tree	NOUN
iajs-3409	125	9	(	(	PUNCT
iajs-3409	125	10	rt	rt	NOUN
iajs-3409	125	11	)	)	PUNCT
iajs-3409	125	12	and	and	CCONJ
iajs-3409	125	13	meager	meager	ADJ
iajs-3409	125	14	node	node	VERB
iajs-3409	125	15	the	the	DET
iajs-3409	125	16	following	follow	VERB
iajs-3409	125	17	definitions	definition	NOUN
iajs-3409	125	18	are	be	AUX
iajs-3409	125	19	repeated	repeat	VERB
iajs-3409	125	20	for	for	ADP
iajs-3409	125	21	the	the	DET
iajs-3409	125	22	set	set	NOUN
iajs-3409	125	23	of	of	ADP
iajs-3409	125	24	relevant	relevant	ADJ
iajs-3409	125	25	-	-	PUNCT
iajs-3409	125	26	colored	colored	ADJ
iajs-3409	125	27	trees	tree	NOUN
iajs-3409	125	28	(	(	PUNCT
iajs-3409	125	29	rt	rt	NOUN
iajs-3409	125	30	):	):	PUNCT
iajs-3409	125	31	1the	1the	PROPN
iajs-3409	125	32	trees	tree	NOUN
iajs-3409	125	33	𝑡1	𝑡1	VERB
iajs-3409	125	34	,	,	PUNCT
iajs-3409	125	35	𝑡2	𝑡2	NOUN
iajs-3409	125	36	and	and	CCONJ
iajs-3409	125	37	𝑡3	𝑡3	PROPN
iajs-3409	125	38	above	above	ADV
iajs-3409	125	39	are	be	AUX
iajs-3409	125	40	all	all	ADV
iajs-3409	125	41	in	in	ADP
iajs-3409	125	42	rt	rt	PROPN
iajs-3409	125	43	,	,	PUNCT
iajs-3409	125	44	and	and	CCONJ
iajs-3409	125	45	the	the	DET
iajs-3409	125	46	tree	tree	NOUN
iajs-3409	125	47	𝑡1	𝑡1	NOUN
iajs-3409	125	48	includes	include	VERB
iajs-3409	125	49	only	only	ADV
iajs-3409	125	50	one	one	NUM
iajs-3409	125	51	meager	meager	ADJ
iajs-3409	125	52	node	node	NOUN
iajs-3409	125	53	(	(	PUNCT
iajs-3409	125	54	known	know	VERB
iajs-3409	125	55	as	as	ADP
iajs-3409	125	56	the	the	DET
iajs-3409	125	57	root	root	NOUN
iajs-3409	125	58	)	)	PUNCT
iajs-3409	125	59	.	.	PUNCT
iajs-3409	126	1	2if	2if	PROPN
iajs-3409	126	2	𝜏1	𝜏1	NOUN
iajs-3409	126	3	,	,	PUNCT
iajs-3409	126	4	𝜏2	𝜏2	PROPN
iajs-3409	126	5	,	,	PUNCT
iajs-3409	126	6	.	.	PUNCT
iajs-3409	126	7	.	.	PUNCT
iajs-3409	126	8	.	.	PUNCT
iajs-3409	127	1	,	,	PUNCT
iajs-3409	127	2	𝜏𝑚	𝜏𝑚	PROPN
iajs-3409	127	3	∈	∈	PROPN
iajs-3409	127	4	𝑅𝑇	𝑅𝑇	PROPN
iajs-3409	127	5	,	,	PUNCT
iajs-3409	127	6	then	then	ADV
iajs-3409	127	7	𝜏	𝜏	X
iajs-3409	127	8	=	=	PUNCT
iajs-3409	128	1	[	[	X
iajs-3409	128	2	𝜏1	𝜏1	NOUN
iajs-3409	128	3	,	,	PUNCT
iajs-3409	128	4	𝜏2	𝜏2	PROPN
iajs-3409	128	5	,	,	PUNCT
iajs-3409	128	6	…	…	PUNCT
iajs-3409	128	7	,	,	PUNCT
iajs-3409	128	8	𝜏𝑚]3	𝜏𝑚]3	PROPN
iajs-3409	128	9	is	be	AUX
iajs-3409	128	10	the	the	DET
iajs-3409	128	11	tree	tree	NOUN
iajs-3409	128	12	obtained	obtain	VERB
iajs-3409	128	13	by	by	ADP
iajs-3409	128	14	linking	link	VERB
iajs-3409	128	15	the	the	DET
iajs-3409	128	16	roots	root	NOUN
iajs-3409	128	17	𝜏1	𝜏1	NOUN
iajs-3409	128	18	,	,	PUNCT
iajs-3409	128	19	𝜏2	𝜏2	PROPN
iajs-3409	128	20	,	,	PUNCT
iajs-3409	128	21	.	.	PUNCT
iajs-3409	128	22	.	.	PUNCT
iajs-3409	128	23	.	.	PUNCT
iajs-3409	129	1	,	,	PUNCT
iajs-3409	129	2	𝜏𝑚	𝜏𝑚	PROPN
iajs-3409	129	3	and	and	CCONJ
iajs-3409	129	4	the	the	DET
iajs-3409	129	5	root	root	NOUN
iajs-3409	129	6	is	be	AUX
iajs-3409	129	7	the	the	DET
iajs-3409	129	8	‘	'	PUNCT
iajs-3409	129	9	‘	'	PUNCT
iajs-3409	129	10	meager	meager	ADJ
iajs-3409	129	11	node	node	NOUN
iajs-3409	129	12	’’	’'	PUNCT
iajs-3409	129	13	𝑡1	𝑡1	NOUN
iajs-3409	129	14	is	be	AUX
iajs-3409	129	15	at	at	ADP
iajs-3409	129	16	the	the	DET
iajs-3409	129	17	bottom	bottom	NOUN
iajs-3409	129	18	.	.	PUNCT
iajs-3409	130	1	the	the	DET
iajs-3409	130	2	subscript	subscript	NOUN
iajs-3409	130	3	3	3	NUM
iajs-3409	130	4	is	be	AUX
iajs-3409	130	5	to	to	PART
iajs-3409	130	6	mention	mention	VERB
iajs-3409	130	7	that	that	SCONJ
iajs-3409	130	8	the	the	DET
iajs-3409	130	9	trees	tree	NOUN
iajs-3409	130	10	of	of	ADP
iajs-3409	130	11	the	the	DET
iajs-3409	130	12	roots	root	NOUN
iajs-3409	130	13	of	of	ADP
iajs-3409	130	14	𝜏1	𝜏1	NOUN
iajs-3409	130	15	,	,	PUNCT
iajs-3409	130	16	𝜏2	𝜏2	PROPN
iajs-3409	130	17	,	,	PUNCT
iajs-3409	130	18	.	.	PUNCT
iajs-3409	130	19	.	.	PUNCT
iajs-3409	131	1	.	.	PUNCT
iajs-3409	132	1	,	,	PUNCT
iajs-3409	132	2	𝜏𝑚	𝜏𝑚	INTJ
iajs-3409	132	3	onto	onto	ADP
iajs-3409	132	4	the	the	DET
iajs-3409	132	5	tree	tree	NOUN
iajs-3409	132	6	𝑡3	𝑡3	PROPN
iajs-3409	132	7	contain	contain	VERB
iajs-3409	132	8	a	a	DET
iajs-3409	132	9	chain	chain	NOUN
iajs-3409	132	10	of	of	ADP
iajs-3409	132	11	three	three	NUM
iajs-3409	132	12	nodes	node	NOUN
iajs-3409	132	13	.	.	PUNCT
iajs-3409	133	1	we	we	PRON
iajs-3409	133	2	will	will	AUX
iajs-3409	133	3	employ	employ	VERB
iajs-3409	133	4	the	the	DET
iajs-3409	133	5	following	follow	VERB
iajs-3409	133	6	principles	principle	NOUN
iajs-3409	133	7	to	to	PART
iajs-3409	133	8	create	create	VERB
iajs-3409	133	9	the	the	DET
iajs-3409	133	10	appropriate	appropriate	ADJ
iajs-3409	133	11	colored	colored	ADJ
iajs-3409	133	12	trees	tree	NOUN
iajs-3409	133	13	:	:	PUNCT
iajs-3409	133	14	1the	1the	DET
iajs-3409	133	15	‘	'	PUNCT
iajs-3409	133	16	‘	'	PUNCT
iajs-3409	133	17	meager	meager	ADJ
iajs-3409	133	18	’’	’'	PUNCT
iajs-3409	133	19	node	node	NOUN
iajs-3409	133	20	is	be	AUX
iajs-3409	133	21	always	always	ADV
iajs-3409	133	22	the	the	DET
iajs-3409	133	23	root	root	NOUN
iajs-3409	133	24	.	.	PUNCT
iajs-3409	134	1	2a	2a	NUM
iajs-3409	134	2	‘	'	PUNCT
iajs-3409	134	3	‘	'	PUNCT
iajs-3409	134	4	meager	meager	ADJ
iajs-3409	134	5	’’	’'	PUNCT
iajs-3409	134	6	node	node	NOUN
iajs-3409	134	7	has	have	VERB
iajs-3409	134	8	only	only	ADV
iajs-3409	134	9	single	single	ADJ
iajs-3409	134	10	child	child	NOUN
iajs-3409	134	11	and	and	CCONJ
iajs-3409	134	12	that	that	DET
iajs-3409	134	13	child	child	NOUN
iajs-3409	134	14	should	should	AUX
iajs-3409	134	15	be	be	AUX
iajs-3409	134	16	‘	'	PUNCT
iajs-3409	134	17	‘	'	PUNCT
iajs-3409	134	18	black	black	ADJ
iajs-3409	134	19	ball	ball	NOUN
iajs-3409	134	20	’’	’'	PUNCT
iajs-3409	134	21	.	.	PUNCT
iajs-3409	135	1	3a	3a	PROPN
iajs-3409	135	2	‘	'	PUNCT
iajs-3409	135	3	‘	'	PUNCT
iajs-3409	135	4	black	black	ADJ
iajs-3409	135	5	ball	ball	NOUN
iajs-3409	135	6	’’	’'	PUNCT
iajs-3409	135	7	node	node	NOUN
iajs-3409	135	8	has	have	VERB
iajs-3409	135	9	only	only	ADV
iajs-3409	135	10	single	single	ADJ
iajs-3409	135	11	child	child	NOUN
iajs-3409	135	12	and	and	CCONJ
iajs-3409	135	13	that	that	DET
iajs-3409	135	14	child	child	NOUN
iajs-3409	135	15	should	should	AUX
iajs-3409	135	16	be	be	AUX
iajs-3409	135	17	‘	'	PUNCT
iajs-3409	135	18	‘	'	PUNCT
iajs-3409	135	19	white	white	ADJ
iajs-3409	135	20	ball	ball	NOUN
iajs-3409	135	21	’’	’'	PUNCT
iajs-3409	135	22	.	.	PUNCT
iajs-3409	136	1	definition	definition	NOUN
iajs-3409	136	2	3.3	3.3	NUM
iajs-3409	137	1	[	[	X
iajs-3409	137	2	13,14	13,14	NUM
iajs-3409	137	3	]	]	PUNCT
iajs-3409	137	4	:	:	PUNCT
iajs-3409	137	5	order	order	NOUN
iajs-3409	137	6	function	function	VERB
iajs-3409	137	7	𝝆(𝝉	𝝆(𝝉	PROPN
iajs-3409	137	8	)	)	PUNCT
iajs-3409	137	9	for	for	ADP
iajs-3409	137	10	relevant	relevant	ADJ
iajs-3409	137	11	-	-	PUNCT
iajs-3409	137	12	colored	colored	ADJ
iajs-3409	137	13	trees	tree	NOUN
iajs-3409	137	14	(	(	PUNCT
iajs-3409	137	15	rt	rt	PROPN
iajs-3409	137	16	)	)	PUNCT
iajs-3409	137	17	the	the	DET
iajs-3409	137	18	order	order	NOUN
iajs-3409	137	19	𝜌(𝜏	𝜌(𝜏	X
iajs-3409	137	20	)	)	PUNCT
iajs-3409	137	21	and	and	CCONJ
iajs-3409	137	22	symmetry	symmetry	NOUN
iajs-3409	137	23	𝜎(𝜏	𝜎(𝜏	PROPN
iajs-3409	137	24	)	)	PUNCT
iajs-3409	137	25	functions	function	NOUN
iajs-3409	137	26	are	be	AUX
iajs-3409	137	27	defined	define	VERB
iajs-3409	137	28	recursively	recursively	ADV
iajs-3409	137	29	as	as	SCONJ
iajs-3409	137	30	follows	follow	VERB
iajs-3409	137	31	:	:	PUNCT
iajs-3409	137	32	1	1	NUM
iajs-3409	137	33	𝜌(𝑡1	𝜌(𝑡1	ADV
iajs-3409	137	34	)	)	PUNCT
iajs-3409	138	1	=	=	SYM
iajs-3409	138	2	1	1	NUM
iajs-3409	138	3	,	,	PUNCT
iajs-3409	138	4	𝜌(𝑡2	𝜌(𝑡2	X
iajs-3409	138	5	)	)	PUNCT
iajs-3409	138	6	=	=	SYM
iajs-3409	138	7	2	2	NUM
iajs-3409	138	8	,	,	PUNCT
iajs-3409	138	9	𝜌(𝑡3	𝜌(𝑡3	NOUN
iajs-3409	138	10	)	)	PUNCT
iajs-3409	138	11	=	=	SYM
iajs-3409	139	1	3	3	NUM
iajs-3409	139	2	,	,	PUNCT
iajs-3409	139	3	2𝜎(𝑡1	2𝜎(𝑡1	NUM
iajs-3409	139	4	)	)	PUNCT
iajs-3409	139	5	=	=	SYM
iajs-3409	139	6	1	1	NUM
iajs-3409	139	7	,	,	PUNCT
iajs-3409	139	8	𝜎(𝑡2	𝜎(𝑡2	NUM
iajs-3409	139	9	)	)	PUNCT
iajs-3409	139	10	=	=	SYM
iajs-3409	140	1	1	1	NUM
iajs-3409	140	2	,	,	PUNCT
iajs-3409	140	3	𝜎(𝑡3	𝜎(𝑡3	NOUN
iajs-3409	140	4	)	)	PUNCT
iajs-3409	140	5	=	=	SYM
iajs-3409	141	1	1	1	NUM
iajs-3409	141	2	,	,	PUNCT
iajs-3409	141	3	3if	3if	ADJ
iajs-3409	141	4	𝜏	𝜏	X
iajs-3409	141	5	=	=	PUNCT
iajs-3409	142	1	[	[	X
iajs-3409	142	2	𝜏1	𝜏1	NOUN
iajs-3409	142	3	,	,	PUNCT
iajs-3409	142	4	𝜏2	𝜏2	PROPN
iajs-3409	142	5	,	,	PUNCT
iajs-3409	142	6	…	…	PUNCT
iajs-3409	142	7	,	,	PUNCT
iajs-3409	142	8	𝜏𝑚]3	𝜏𝑚]3	VERB
iajs-3409	142	9	for	for	ADP
iajs-3409	142	10	each	each	DET
iajs-3409	142	11	𝜏	𝜏	PROPN
iajs-3409	142	12	∈	∈	PRON
iajs-3409	142	13	𝑅𝑇	𝑅𝑇	PROPN
iajs-3409	142	14	,	,	PUNCT
iajs-3409	142	15	then	then	ADV
iajs-3409	142	16	ρ(τ	ρ(τ	VERB
iajs-3409	142	17	)	)	PUNCT
iajs-3409	142	18	=	=	SYM
iajs-3409	142	19	3	3	NUM
iajs-3409	142	20	+	+	CCONJ
iajs-3409	142	21	∑	∑	ADP
iajs-3409	142	22	ρ(τi	ρ(τi	ADJ
iajs-3409	142	23	)	)	PUNCT
iajs-3409	142	24	m	m	VERB
iajs-3409	142	25	i=1	i=1	PROPN
iajs-3409	142	26	and	and	CCONJ
iajs-3409	142	27	𝜎(𝜏	𝜎(𝜏	PROPN
iajs-3409	142	28	)	)	PUNCT
iajs-3409	143	1	=	=	SYM
iajs-3409	143	2	∏	∏	NUM
iajs-3409	143	3	𝜎(𝜏𝑖)(𝑣1	𝜎(𝜏𝑖)(𝑣1	PROPN
iajs-3409	143	4	!	!	PUNCT
iajs-3409	144	1	𝑣2!𝑚	𝑣2!𝑚	PROPN
iajs-3409	144	2	𝑖=1	𝑖=1	PROPN
iajs-3409	144	3	…	…	PUNCT
iajs-3409	144	4	)	)	PUNCT
iajs-3409	145	1	where	where	SCONJ
iajs-3409	145	2	𝜌(𝜏	𝜌(𝜏	NOUN
iajs-3409	145	3	)	)	PUNCT
iajs-3409	145	4	is	be	AUX
iajs-3409	145	5	the	the	DET
iajs-3409	145	6	number	number	NOUN
iajs-3409	145	7	of	of	ADP
iajs-3409	145	8	nodes	node	NOUN
iajs-3409	145	9	of	of	ADP
iajs-3409	145	10	𝜏	𝜏	NOUN
iajs-3409	145	11	,	,	PUNCT
iajs-3409	145	12	∀τ	∀τ	SYM
iajs-3409	145	13	∈	∈	PROPN
iajs-3409	145	14	rt	rt	PROPN
iajs-3409	145	15	and	and	CCONJ
iajs-3409	145	16	ν1	ν1	NOUN
iajs-3409	145	17	!	!	PUNCT
iajs-3409	146	1	ν2	ν2	PROPN
iajs-3409	146	2	!	!	PUNCT
iajs-3409	147	1	…	…	PUNCT
iajs-3409	147	2	count	count	VERB
iajs-3409	147	3	equal	equal	ADJ
iajs-3409	147	4	trees	tree	NOUN
iajs-3409	147	5	among	among	ADP
iajs-3409	147	6	𝜏1	𝜏1	NOUN
iajs-3409	147	7	,	,	PUNCT
iajs-3409	147	8	𝜏2	𝜏2	PROPN
iajs-3409	147	9	,	,	PUNCT
iajs-3409	147	10	.	.	PUNCT
iajs-3409	147	11	.	.	PUNCT
iajs-3409	148	1	.	.	PUNCT
iajs-3409	149	1	,	,	PUNCT
iajs-3409	149	2	𝜏𝑚.	𝜏𝑚.	NOUN
iajs-3409	149	3	then	then	ADV
iajs-3409	149	4	we	we	PRON
iajs-3409	149	5	can	can	AUX
iajs-3409	149	6	define	define	VERB
iajs-3409	149	7	the	the	DET
iajs-3409	149	8	set	set	NOUN
iajs-3409	149	9	𝑆𝑟	𝑆𝑟	PROPN
iajs-3409	149	10	which	which	PRON
iajs-3409	149	11	consist	consist	NOUN
iajs-3409	149	12	of	of	ADP
iajs-3409	149	13	every	every	DET
iajs-3409	149	14	trees	tree	NOUN
iajs-3409	149	15	𝑅𝑇	𝑅𝑇	PROPN
iajs-3409	149	16	of	of	ADP
iajs-3409	149	17	order	order	NOUN
iajs-3409	149	18	𝑟.	𝑟.	NOUN
iajs-3409	149	19	definition	definition	NOUN
iajs-3409	149	20	3.4	3.4	NUM
iajs-3409	149	21	[	[	X
iajs-3409	149	22	22,23	22,23	NOUN
iajs-3409	149	23	]	]	X
iajs-3409	149	24	:	:	PUNCT
iajs-3409	149	25	elementary	elementary	ADJ
iajs-3409	149	26	differential	differential	PROPN
iajs-3409	149	27	and	and	CCONJ
iajs-3409	149	28	b	b	NOUN
iajs-3409	149	29	-	-	PUNCT
iajs-3409	149	30	series	series	NOUN
iajs-3409	149	31	on	on	ADP
iajs-3409	149	32	relevant	relevant	ADJ
iajs-3409	149	33	-	-	PUNCT
iajs-3409	149	34	colored	colored	ADJ
iajs-3409	149	35	trees	tree	NOUN
iajs-3409	149	36	(	(	PUNCT
iajs-3409	149	37	rt	rt	PROPN
iajs-3409	149	38	)	)	PUNCT
iajs-3409	149	39	for	for	ADP
iajs-3409	149	40	the	the	DET
iajs-3409	149	41	rktdio	rktdio	NOUN
iajs-3409	149	42	approach	approach	VERB
iajs-3409	149	43	the	the	DET
iajs-3409	149	44	elementary	elementary	ADJ
iajs-3409	149	45	differential	differential	NOUN
iajs-3409	149	46	for	for	ADP
iajs-3409	149	47	every	every	DET
iajs-3409	149	48	tree	tree	NOUN
iajs-3409	149	49	𝜏	𝜏	NOUN
iajs-3409	149	50	∈	∈	PRON
iajs-3409	149	51	𝑅𝑇	𝑅𝑇	PROPN
iajs-3409	149	52	is	be	AUX
iajs-3409	149	53	a	a	DET
iajs-3409	149	54	function	function	NOUN
iajs-3409	149	55	f(τ	f(τ	PROPN
iajs-3409	149	56	):	):	PUNCT
iajs-3409	149	57	rd	rd	PROPN
iajs-3409	149	58	×	×	PROPN
iajs-3409	149	59	rd	rd	PROPN
iajs-3409	149	60	×	×	PROPN
iajs-3409	149	61	rd	rd	PROPN
iajs-3409	149	62	→	→	SYM
iajs-3409	149	63	rd	rd	PROPN
iajs-3409	149	64	,	,	PUNCT
iajs-3409	149	65	recursively	recursively	ADV
iajs-3409	149	66	defined	define	VERB
iajs-3409	149	67	on	on	ADP
iajs-3409	149	68	rt	rt	PROPN
iajs-3409	149	69	as	as	SCONJ
iajs-3409	149	70	follows	follow	VERB
iajs-3409	149	71	1𝕌(𝑡1)(𝛼	1𝕌(𝑡1)(𝛼	NUM
iajs-3409	149	72	,	,	PUNCT
iajs-3409	149	73	𝛼′	𝛼′	PROPN
iajs-3409	149	74	,	,	PUNCT
iajs-3409	149	75	𝛼′′	𝛼′′	NOUN
iajs-3409	149	76	)	)	PUNCT
iajs-3409	149	77	=	=	SYM
iajs-3409	149	78	𝛼′	𝛼′	PROPN
iajs-3409	149	79	,	,	PUNCT
iajs-3409	149	80	𝕌(𝑡2)(𝛼	𝕌(𝑡2)(𝛼	PROPN
iajs-3409	149	81	,	,	PUNCT
iajs-3409	149	82	𝛼′	𝛼′	PROPN
iajs-3409	149	83	,	,	PUNCT
iajs-3409	149	84	𝛼′′	𝛼′′	NOUN
iajs-3409	149	85	)	)	PUNCT
iajs-3409	149	86	=	=	SYM
iajs-3409	149	87	𝛼′′	𝛼′′	NOUN
iajs-3409	149	88	,	,	PUNCT
iajs-3409	149	89	𝕌(𝑡3	𝕌(𝑡3	NOUN
iajs-3409	149	90	)	)	PUNCT
iajs-3409	149	91	(	(	PUNCT
iajs-3409	149	92	𝛼	𝛼	PROPN
iajs-3409	149	93	,	,	PUNCT
iajs-3409	149	94	𝛼′	𝛼′	NUM
iajs-3409	149	95	,	,	PUNCT
iajs-3409	149	96	𝛼′′	𝛼′′	NOUN
iajs-3409	149	97	)	)	PUNCT
iajs-3409	149	98	=	=	SYM
iajs-3409	149	99	𝜇(𝛼	𝜇(𝛼	PROPN
iajs-3409	149	100	)	)	PUNCT
iajs-3409	149	101	,	,	PUNCT
iajs-3409	149	102	2𝕌	2𝕌	NOUN
iajs-3409	149	103	(	(	PUNCT
iajs-3409	149	104	𝜏	𝜏	NOUN
iajs-3409	149	105	)	)	PUNCT
iajs-3409	149	106	=	=	SYM
iajs-3409	149	107	𝜇(𝑚)(𝛼	𝜇(𝑚)(𝛼	NOUN
iajs-3409	149	108	)	)	PUNCT
iajs-3409	149	109	(	(	PUNCT
iajs-3409	149	110	𝕌	𝕌	PROPN
iajs-3409	149	111	(	(	PUNCT
iajs-3409	149	112	𝜏1)(𝛼	𝜏1)(𝛼	PROPN
iajs-3409	149	113	,	,	PUNCT
iajs-3409	149	114	𝛼′	𝛼′	PROPN
iajs-3409	149	115	,	,	PUNCT
iajs-3409	149	116	𝛼′′	𝛼′′	NOUN
iajs-3409	149	117	)	)	PUNCT
iajs-3409	149	118	,	,	PUNCT
iajs-3409	149	119	.	.	PUNCT
iajs-3409	149	120	.	.	PUNCT
iajs-3409	150	1	.	.	PUNCT
iajs-3409	151	1	,	,	PUNCT
iajs-3409	151	2	𝕌	𝕌	PROPN
iajs-3409	151	3	(	(	PUNCT
iajs-3409	151	4	𝜏𝑚)(𝛼	𝜏𝑚)(𝛼	PROPN
iajs-3409	151	5	,	,	PUNCT
iajs-3409	151	6	𝛼′	𝛼′	PROPN
iajs-3409	151	7	,	,	PUNCT
iajs-3409	151	8	𝛼′′	𝛼′′	NOUN
iajs-3409	151	9	)	)	PUNCT
iajs-3409	151	10	)	)	PUNCT
iajs-3409	151	11	for	for	ADP
iajs-3409	151	12	𝜏	𝜏	NOUN
iajs-3409	151	13	=	=	PUNCT
iajs-3409	151	14	[	[	X
iajs-3409	151	15	𝜏1	𝜏1	NOUN
iajs-3409	151	16	,	,	PUNCT
iajs-3409	151	17	𝜏2	𝜏2	PROPN
iajs-3409	151	18	,	,	PUNCT
iajs-3409	151	19	…	…	PUNCT
iajs-3409	151	20	,	,	PUNCT
iajs-3409	151	21	𝜏𝑚]3	𝜏𝑚]3	X
iajs-3409	151	22	.	.	X
iajs-3409	152	1	we	we	PRON
iajs-3409	152	2	expanded	expand	VERB
iajs-3409	152	3	these	these	DET
iajs-3409	152	4	definitions	definition	NOUN
iajs-3409	152	5	to	to	PART
iajs-3409	152	6	provide	provide	VERB
iajs-3409	152	7	the	the	DET
iajs-3409	152	8	definition	definition	NOUN
iajs-3409	152	9	of	of	ADP
iajs-3409	152	10	b	b	NOUN
iajs-3409	152	11	-	-	PUNCT
iajs-3409	152	12	series	series	NOUN
iajs-3409	152	13	on	on	ADP
iajs-3409	152	14	the	the	DET
iajs-3409	152	15	set	set	NOUN
iajs-3409	152	16	rt	rt	PROPN
iajs-3409	152	17	of	of	ADP
iajs-3409	152	18	the	the	DET
iajs-3409	152	19	relevantcolored	relevantcolore	VERB
iajs-3409	152	20	trees	tree	NOUN
iajs-3409	152	21	for	for	ADP
iajs-3409	152	22	the	the	DET
iajs-3409	152	23	rktdio	rktdio	NOUN
iajs-3409	152	24	approach	approach	NOUN
iajs-3409	152	25	,	,	PUNCT
iajs-3409	152	26	which	which	PRON
iajs-3409	152	27	was	be	AUX
iajs-3409	152	28	motivated	motivate	VERB
iajs-3409	152	29	by	by	ADP
iajs-3409	152	30	the	the	DET
iajs-3409	152	31	definitions	definition	NOUN
iajs-3409	152	32	of	of	ADP
iajs-3409	152	33	b	b	NOUN
iajs-3409	152	34	-	-	PUNCT
iajs-3409	152	35	series	series	NOUN
iajs-3409	152	36	on	on	ADP
iajs-3409	152	37	the	the	DET
iajs-3409	152	38	root	root	NOUN
iajs-3409	152	39	trees	tree	NOUN
iajs-3409	152	40	in	in	ADP
iajs-3409	152	41	[	[	X
iajs-3409	152	42	23	23	NUM
iajs-3409	152	43	]	]	PUNCT
iajs-3409	152	44	and	and	CCONJ
iajs-3409	152	45	the	the	DET
iajs-3409	152	46	tri	tri	ADJ
iajs-3409	152	47	-	-	ADJ
iajs-3409	152	48	colored	colored	ADJ
iajs-3409	152	49	trees	tree	NOUN
iajs-3409	152	50	in	in	ADP
iajs-3409	152	51	[	[	X
iajs-3409	152	52	24	24	NUM
iajs-3409	152	53	]	]	PUNCT
iajs-3409	152	54	.	.	PUNCT
iajs-3409	153	1	definition	definition	NOUN
iajs-3409	153	2	3.5	3.5	NUM
iajs-3409	153	3	[	[	X
iajs-3409	153	4	22,23	22,23	NOUN
iajs-3409	153	5	]	]	X
iajs-3409	153	6	:	:	PUNCT
iajs-3409	153	7	b	b	X
iajs-3409	153	8	-	-	PUNCT
iajs-3409	153	9	series	series	NOUN
iajs-3409	153	10	representation	representation	NOUN
iajs-3409	153	11	let	let	VERB
iajs-3409	153	12	δ	δ	PRON
iajs-3409	153	13	:	:	PUNCT
iajs-3409	153	14	rt	rt	NOUN
iajs-3409	153	15	∪	∪	ADP
iajs-3409	153	16	{	{	PUNCT
iajs-3409	153	17	∅	∅	NOUN
iajs-3409	153	18	}	}	PUNCT
iajs-3409	153	19	→	→	SYM
iajs-3409	153	20	rd	rd	NOUN
iajs-3409	153	21	be	be	AUX
iajs-3409	153	22	a	a	DET
iajs-3409	153	23	mapping	mapping	NOUN
iajs-3409	153	24	,	,	PUNCT
iajs-3409	153	25	then	then	ADV
iajs-3409	153	26	we	we	PRON
iajs-3409	153	27	can	can	AUX
iajs-3409	153	28	give	give	VERB
iajs-3409	153	29	the	the	DET
iajs-3409	153	30	form	form	NOUN
iajs-3409	153	31	of	of	ADP
iajs-3409	153	32	a	a	DET
iajs-3409	153	33	formal	formal	ADJ
iajs-3409	153	34	series	series	NOUN
iajs-3409	153	35	as	as	SCONJ
iajs-3409	153	36	follows	follow	VERB
iajs-3409	153	37	:	:	PUNCT
iajs-3409	153	38	b(δ	b(δ	PROPN
iajs-3409	153	39	,	,	PUNCT
iajs-3409	153	40	y	y	NOUN
iajs-3409	153	41	)	)	PUNCT
iajs-3409	153	42	=	=	SYM
iajs-3409	153	43	δ(∅	δ(∅	NOUN
iajs-3409	153	44	)	)	PUNCT
iajs-3409	154	1	+	+	CCONJ
iajs-3409	154	2	∑	∑	PUNCT
iajs-3409	154	3	hρ(τ	hρ(τ	NOUN
iajs-3409	154	4	)	)	PUNCT
iajs-3409	154	5	σ(τ	σ(τ	PROPN
iajs-3409	154	6	)	)	PUNCT
iajs-3409	154	7	δ(τ)τ∈rt	δ(τ)τ∈rt	PROPN
iajs-3409	154	8	𝕌(τ)(α	𝕌(τ)(α	NOUN
iajs-3409	154	9	,	,	PUNCT
iajs-3409	154	10	α′α′′	α′α′′	NUM
iajs-3409	154	11	)	)	PUNCT
iajs-3409	154	12	,	,	PUNCT
iajs-3409	154	13	(	(	PUNCT
iajs-3409	154	14	41	41	NUM
iajs-3409	154	15	)	)	PUNCT
iajs-3409	154	16	which	which	PRON
iajs-3409	154	17	is	be	AUX
iajs-3409	154	18	called	call	VERB
iajs-3409	154	19	the	the	DET
iajs-3409	154	20	b	b	NOUN
iajs-3409	154	21	-	-	PUNCT
iajs-3409	154	22	series	series	NOUN
iajs-3409	154	23	.	.	PUNCT
iajs-3409	155	1	ihjpas	ihjpas	PROPN
iajs-3409	155	2	.	.	PUNCT
iajs-3409	156	1	37	37	NUM
iajs-3409	156	2	(	(	PUNCT
iajs-3409	156	3	2	2	NUM
iajs-3409	156	4	)	)	PUNCT
iajs-3409	156	5	2024	2024	NUM
iajs-3409	156	6	394	394	NUM
iajs-3409	156	7	we	we	PRON
iajs-3409	156	8	present	present	VERB
iajs-3409	156	9	the	the	DET
iajs-3409	156	10	following	follow	VERB
iajs-3409	156	11	crucial	crucial	ADJ
iajs-3409	156	12	lemma	lemma	PROPN
iajs-3409	156	13	that	that	PRON
iajs-3409	156	14	is	be	AUX
iajs-3409	156	15	important	important	ADJ
iajs-3409	156	16	to	to	ADP
iajs-3409	156	17	this	this	DET
iajs-3409	156	18	derivation	derivation	NOUN
iajs-3409	156	19	in	in	ADP
iajs-3409	156	20	order	order	NOUN
iajs-3409	156	21	to	to	PART
iajs-3409	156	22	accomplish	accomplish	VERB
iajs-3409	156	23	the	the	DET
iajs-3409	156	24	main	main	ADJ
iajs-3409	156	25	goal	goal	NOUN
iajs-3409	156	26	of	of	ADP
iajs-3409	156	27	this	this	DET
iajs-3409	156	28	research	research	NOUN
iajs-3409	156	29	,	,	PUNCT
iajs-3409	156	30	which	which	PRON
iajs-3409	156	31	is	be	AUX
iajs-3409	156	32	the	the	DET
iajs-3409	156	33	derivation	derivation	NOUN
iajs-3409	156	34	of	of	ADP
iajs-3409	156	35	the	the	DET
iajs-3409	156	36	order	order	NOUN
iajs-3409	156	37	conditions	condition	NOUN
iajs-3409	156	38	of	of	ADP
iajs-3409	156	39	the	the	DET
iajs-3409	156	40	rktdio	rktdio	NOUN
iajs-3409	156	41	technique	technique	NOUN
iajs-3409	156	42	.	.	PUNCT
iajs-3409	157	1	lemma	lemma	PROPN
iajs-3409	157	2	3.1	3.1	NUM
iajs-3409	158	1	[	[	X
iajs-3409	158	2	22,23	22,23	NOUN
iajs-3409	158	3	]	]	X
iajs-3409	158	4	:	:	PUNCT
iajs-3409	158	5	let	let	VERB
iajs-3409	158	6	𝛿	𝛿	PRON
iajs-3409	158	7	be	be	AUX
iajs-3409	158	8	a	a	DET
iajs-3409	158	9	function	function	NOUN
iajs-3409	158	10	𝛿	𝛿	DET
iajs-3409	158	11	∶	∶	NOUN
iajs-3409	158	12	𝑅𝑇	𝑅𝑇	PROPN
iajs-3409	158	13	∪	∪	VERB
iajs-3409	158	14	{	{	PUNCT
iajs-3409	158	15	∅	∅	NOUN
iajs-3409	158	16	}	}	PUNCT
iajs-3409	158	17	→	→	SYM
iajs-3409	158	18	𝑅𝑑	𝑅𝑑	NOUN
iajs-3409	158	19	with	with	ADP
iajs-3409	158	20	𝛿(∅	𝛿(∅	NOUN
iajs-3409	158	21	)	)	PUNCT
iajs-3409	158	22	=	=	SYM
iajs-3409	159	1	1	1	X
iajs-3409	159	2	.	.	PUNCT
iajs-3409	159	3	thus	thus	ADV
iajs-3409	159	4	ℎ3𝜇(𝐵(𝛿	ℎ3𝜇(𝐵(𝛿	VERB
iajs-3409	159	5	,	,	PUNCT
iajs-3409	159	6	𝛼	𝛼	NOUN
iajs-3409	159	7	)	)	PUNCT
iajs-3409	159	8	)	)	PUNCT
iajs-3409	159	9	is	be	AUX
iajs-3409	159	10	also	also	ADV
iajs-3409	159	11	a	a	DET
iajs-3409	159	12	b	b	NUM
iajs-3409	159	13	-	-	PUNCT
iajs-3409	159	14	series	series	NOUN
iajs-3409	159	15	ℎ3𝜇(𝐵(𝛿	ℎ3𝜇(𝐵(𝛿	PROPN
iajs-3409	159	16	,	,	PUNCT
iajs-3409	159	17	𝛼	𝛼	NOUN
iajs-3409	159	18	)	)	PUNCT
iajs-3409	159	19	)	)	PUNCT
iajs-3409	160	1	=	=	PUNCT
iajs-3409	160	2	𝐵(𝛿′	𝐵(𝛿′	VERB
iajs-3409	160	3	,	,	PUNCT
iajs-3409	160	4	𝛼	𝛼	NOUN
iajs-3409	160	5	)	)	PUNCT
iajs-3409	160	6	where	where	SCONJ
iajs-3409	160	7	𝛿′(∅	𝛿′(∅	ADJ
iajs-3409	160	8	)	)	PUNCT
iajs-3409	160	9	=	=	SYM
iajs-3409	160	10	0	0	NUM
iajs-3409	160	11	,	,	PUNCT
iajs-3409	160	12	𝛿′(𝑡1	𝛿′(𝑡1	VERB
iajs-3409	160	13	)	)	PUNCT
iajs-3409	160	14	=	=	SYM
iajs-3409	160	15	0	0	NUM
iajs-3409	160	16	,	,	PUNCT
iajs-3409	160	17	𝛿′(𝑡2	𝛿′(𝑡2	ADJ
iajs-3409	160	18	)	)	PUNCT
iajs-3409	160	19	=	=	SYM
iajs-3409	160	20	0	0	NUM
iajs-3409	160	21	,	,	PUNCT
iajs-3409	160	22	𝛿′(𝑡3	𝛿′(𝑡3	NOUN
iajs-3409	160	23	)	)	PUNCT
iajs-3409	160	24	=	=	PUNCT
iajs-3409	160	25	1	1	NUM
iajs-3409	160	26	,	,	PUNCT
iajs-3409	160	27	and	and	CCONJ
iajs-3409	160	28	for	for	ADP
iajs-3409	160	29	𝜏	𝜏	NOUN
iajs-3409	160	30	=	=	PUNCT
iajs-3409	161	1	[	[	X
iajs-3409	161	2	𝜏1	𝜏1	NOUN
iajs-3409	161	3	,	,	PUNCT
iajs-3409	161	4	𝜏2	𝜏2	PROPN
iajs-3409	161	5	,	,	PUNCT
iajs-3409	161	6	…	…	PUNCT
iajs-3409	161	7	,	,	PUNCT
iajs-3409	161	8	𝜏𝑚]3	𝜏𝑚]3	PROPN
iajs-3409	161	9	∈	∈	PROPN
iajs-3409	161	10	𝑅𝑇	𝑅𝑇	PROPN
iajs-3409	161	11	,	,	PUNCT
iajs-3409	161	12	𝛿′(𝜏	𝛿′(𝜏	PROPN
iajs-3409	161	13	)	)	PUNCT
iajs-3409	161	14	=	=	NOUN
iajs-3409	161	15	𝛿(𝜏1	𝛿(𝜏1	ADJ
iajs-3409	161	16	)	)	PUNCT
iajs-3409	161	17	,	,	PUNCT
iajs-3409	161	18	.	.	PUNCT
iajs-3409	161	19	.	.	PUNCT
iajs-3409	161	20	.	.	PUNCT
iajs-3409	162	1	𝛿(𝜏𝑚	𝛿(𝜏𝑚	ADJ
iajs-3409	162	2	)	)	PUNCT
iajs-3409	162	3	.	.	PUNCT
iajs-3409	163	1	lemma	lemma	PROPN
iajs-3409	163	2	3.2	3.2	NUM
iajs-3409	164	1	[	[	X
iajs-3409	164	2	22,23	22,23	NOUN
iajs-3409	164	3	]	]	X
iajs-3409	164	4	:	:	PUNCT
iajs-3409	164	5	if	if	SCONJ
iajs-3409	164	6	we	we	PRON
iajs-3409	164	7	suppose	suppose	VERB
iajs-3409	164	8	that	that	SCONJ
iajs-3409	164	9	the	the	DET
iajs-3409	164	10	analytic	analytic	ADJ
iajs-3409	164	11	solution	solution	NOUN
iajs-3409	164	12	of	of	ADP
iajs-3409	164	13	(	(	PUNCT
iajs-3409	164	14	18	18	NUM
iajs-3409	164	15	)	)	PUNCT
iajs-3409	164	16	is	be	AUX
iajs-3409	164	17	a	a	DET
iajs-3409	164	18	b	b	NOUN
iajs-3409	164	19	-	-	PUNCT
iajs-3409	164	20	series	series	NOUN
iajs-3409	164	21	𝐵(𝜗	𝐵(𝜗	NOUN
iajs-3409	164	22	,	,	PUNCT
iajs-3409	164	23	𝛼0	𝛼0	PROPN
iajs-3409	164	24	)	)	PUNCT
iajs-3409	164	25	with	with	ADP
iajs-3409	164	26	a	a	DET
iajs-3409	164	27	real	real	ADJ
iajs-3409	164	28	function	function	NOUN
iajs-3409	164	29	𝜗	𝜗	NOUN
iajs-3409	164	30	which	which	PRON
iajs-3409	164	31	is	be	AUX
iajs-3409	164	32	defined	define	VERB
iajs-3409	164	33	on	on	ADP
iajs-3409	164	34	𝑅𝑇	𝑅𝑇	PROPN
iajs-3409	164	35	∪	∪	ADJ
iajs-3409	164	36	{	{	PUNCT
iajs-3409	164	37	∅	∅	NOUN
iajs-3409	164	38	}	}	PUNCT
iajs-3409	164	39	,	,	PUNCT
iajs-3409	164	40	then	then	ADV
iajs-3409	164	41	𝜗(∅	𝜗(∅	NUM
iajs-3409	164	42	)	)	PUNCT
iajs-3409	165	1	=	=	SYM
iajs-3409	165	2	1	1	NUM
iajs-3409	165	3	,	,	PUNCT
iajs-3409	165	4	𝜗(𝑡1	𝜗(𝑡1	NOUN
iajs-3409	165	5	)	)	PUNCT
iajs-3409	165	6	=	=	SYM
iajs-3409	165	7	1	1	NUM
iajs-3409	165	8	,	,	PUNCT
iajs-3409	165	9	𝜗(𝑡2	𝜗(𝑡2	ADJ
iajs-3409	165	10	)	)	PUNCT
iajs-3409	165	11	=	=	SYM
iajs-3409	165	12	1	1	NUM
iajs-3409	165	13	,	,	PUNCT
iajs-3409	165	14	𝜗(𝑡3	𝜗(𝑡3	NOUN
iajs-3409	165	15	)	)	PUNCT
iajs-3409	165	16	=	=	SYM
iajs-3409	165	17	1	1	NUM
iajs-3409	165	18	,	,	PUNCT
iajs-3409	165	19	and	and	CCONJ
iajs-3409	165	20	𝜏	𝜏	X
iajs-3409	165	21	=	=	PUNCT
iajs-3409	166	1	[	[	X
iajs-3409	166	2	𝜏1	𝜏1	NOUN
iajs-3409	166	3	,	,	PUNCT
iajs-3409	166	4	𝜏2	𝜏2	PROPN
iajs-3409	166	5	,	,	PUNCT
iajs-3409	166	6	…	…	PUNCT
iajs-3409	166	7	,	,	PUNCT
iajs-3409	166	8	𝜏𝑚]3	𝜏𝑚]3	PROPN
iajs-3409	166	9	∈	∈	PROPN
iajs-3409	166	10	𝑅𝑇	𝑅𝑇	PROPN
iajs-3409	166	11	,	,	PUNCT
iajs-3409	166	12	we	we	PRON
iajs-3409	166	13	have	have	VERB
iajs-3409	166	14	𝜗(𝜏	𝜗(𝜏	NOUN
iajs-3409	166	15	)	)	PUNCT
iajs-3409	166	16	=	=	SYM
iajs-3409	166	17	1	1	NUM
iajs-3409	166	18	𝜌(𝜏)(𝜌(𝜏	𝜌(𝜏)(𝜌(𝜏	NUM
iajs-3409	166	19	)	)	PUNCT
iajs-3409	167	1	−	−	ADP
iajs-3409	167	2	1)(𝜌(𝜏	1)(𝜌(𝜏	NUM
iajs-3409	167	3	)	)	PUNCT
iajs-3409	167	4	−	−	PROPN
iajs-3409	168	1	2	2	NUM
iajs-3409	168	2	)	)	PUNCT
iajs-3409	168	3	(	(	PUNCT
iajs-3409	168	4	𝜗(𝜏1	𝜗(𝜏1	NOUN
iajs-3409	168	5	)	)	PUNCT
iajs-3409	168	6	,	,	PUNCT
iajs-3409	168	7	.	.	PUNCT
iajs-3409	168	8	.	.	PUNCT
iajs-3409	168	9	.	.	PUNCT
iajs-3409	169	1	𝜗(𝜏𝑚	𝜗(𝜏𝑚	X
iajs-3409	169	2	)	)	PUNCT
iajs-3409	169	3	)	)	PUNCT
iajs-3409	169	4	.	.	PUNCT
iajs-3409	170	1	proposition	proposition	NOUN
iajs-3409	170	2	3.2.1	3.2.1	NUM
iajs-3409	171	1	[	[	X
iajs-3409	171	2	22,23	22,23	NOUN
iajs-3409	171	3	]	]	X
iajs-3409	171	4	:	:	PUNCT
iajs-3409	171	5	the	the	DET
iajs-3409	171	6	density	density	NOUN
iajs-3409	171	7	𝜎(𝜏	𝜎(𝜏	PROPN
iajs-3409	171	8	)	)	PUNCT
iajs-3409	171	9	is	be	AUX
iajs-3409	171	10	the	the	DET
iajs-3409	171	11	non	non	ADJ
iajs-3409	171	12	negative	negative	ADJ
iajs-3409	171	13	integer	integer	NOUN
iajs-3409	171	14	factors	factor	NOUN
iajs-3409	171	15	defined	define	VERB
iajs-3409	171	16	on	on	ADP
iajs-3409	171	17	trees	tree	NOUN
iajs-3409	171	18	𝑅𝑇	𝑅𝑇	PROPN
iajs-3409	171	19	,	,	PUNCT
iajs-3409	171	20	∀𝜏	∀𝜏	PROPN
iajs-3409	171	21	∈	∈	NOUN
iajs-3409	171	22	𝑅𝑇	𝑅𝑇	NOUN
iajs-3409	171	23	satisfy	satisfy	VERB
iajs-3409	171	24	1𝜎(𝑡1	1𝜎(𝑡1	NUM
iajs-3409	171	25	)	)	PUNCT
iajs-3409	172	1	=	=	SYM
iajs-3409	172	2	1	1	NUM
iajs-3409	172	3	,	,	PUNCT
iajs-3409	172	4	𝜎(𝑡2	𝜎(𝑡2	NUM
iajs-3409	172	5	)	)	PUNCT
iajs-3409	172	6	=	=	SYM
iajs-3409	172	7	2	2	NUM
iajs-3409	172	8	,	,	PUNCT
iajs-3409	172	9	𝜎(𝑡3	𝜎(𝑡3	NOUN
iajs-3409	172	10	)	)	PUNCT
iajs-3409	172	11	=	=	SYM
iajs-3409	173	1	6	6	NUM
iajs-3409	173	2	,	,	PUNCT
iajs-3409	173	3	2with	2with	PROPN
iajs-3409	173	4	𝜏	𝜏	NOUN
iajs-3409	173	5	=	=	PUNCT
iajs-3409	173	6	[	[	X
iajs-3409	173	7	𝜏1	𝜏1	NOUN
iajs-3409	173	8	,	,	PUNCT
iajs-3409	173	9	𝜏2	𝜏2	PROPN
iajs-3409	173	10	,	,	PUNCT
iajs-3409	173	11	…	…	PUNCT
iajs-3409	173	12	,	,	PUNCT
iajs-3409	173	13	𝜏𝑚]3	𝜏𝑚]3	PROPN
iajs-3409	173	14	,	,	PUNCT
iajs-3409	173	15	we	we	PRON
iajs-3409	173	16	have	have	VERB
iajs-3409	173	17	𝜎(𝜏	𝜎(𝜏	NUM
iajs-3409	173	18	)	)	PUNCT
iajs-3409	173	19	=	=	SYM
iajs-3409	173	20	𝜌(𝜏)(𝜌(𝜏	𝜌(𝜏)(𝜌(𝜏	PROPN
iajs-3409	173	21	)	)	PUNCT
iajs-3409	174	1	−	−	ADP
iajs-3409	174	2	1)(𝜌(𝜏	1)(𝜌(𝜏	NUM
iajs-3409	174	3	)	)	PUNCT
iajs-3409	174	4	−	−	PROPN
iajs-3409	175	1	2)(𝜎(𝜏1	2)(𝜎(𝜏1	NUM
iajs-3409	175	2	)	)	PUNCT
iajs-3409	175	3	,	,	PUNCT
iajs-3409	175	4	…	…	PUNCT
iajs-3409	175	5	,	,	PUNCT
iajs-3409	175	6	𝜎(𝜏𝑚	𝜎(𝜏𝑚	ADJ
iajs-3409	175	7	)	)	PUNCT
iajs-3409	175	8	)	)	PUNCT
iajs-3409	175	9	.	.	PUNCT
iajs-3409	176	1	proposition	proposition	NOUN
iajs-3409	176	2	3.2.2	3.2.2	NUM
iajs-3409	177	1	[	[	X
iajs-3409	177	2	22,23	22,23	NOUN
iajs-3409	177	3	]	]	X
iajs-3409	177	4	:	:	PUNCT
iajs-3409	177	5	the	the	DET
iajs-3409	177	6	non	non	ADJ
iajs-3409	177	7	-	-	ADJ
iajs-3409	177	8	negative	negative	ADJ
iajs-3409	177	9	integer	integer	NOUN
iajs-3409	177	10	휀(𝜏	휀(𝜏	NOUN
iajs-3409	177	11	)	)	PUNCT
iajs-3409	177	12	,	,	PUNCT
iajs-3409	177	13	∀𝜏	∀𝜏	PROPN
iajs-3409	177	14	∈	∈	NOUN
iajs-3409	177	15	𝑅𝑇	𝑅𝑇	NOUN
iajs-3409	177	16	satisfy	satisfy	VERB
iajs-3409	177	17	1𝜖(𝑡1	1𝜖(𝑡1	NUM
iajs-3409	177	18	)	)	PUNCT
iajs-3409	178	1	=	=	SYM
iajs-3409	178	2	1	1	NUM
iajs-3409	178	3	,	,	PUNCT
iajs-3409	178	4	휀(𝑡2	휀(𝑡2	VERB
iajs-3409	178	5	)	)	PUNCT
iajs-3409	178	6	=	=	SYM
iajs-3409	178	7	1	1	NUM
iajs-3409	178	8	,	,	PUNCT
iajs-3409	178	9	𝜖(𝑡3	𝜖(𝑡3	NOUN
iajs-3409	178	10	)	)	PUNCT
iajs-3409	178	11	=	=	SYM
iajs-3409	179	1	1	1	NUM
iajs-3409	179	2	,	,	PUNCT
iajs-3409	179	3	2for	2for	ADP
iajs-3409	179	4	the	the	DET
iajs-3409	179	5	tree	tree	NOUN
iajs-3409	179	6	𝜏	𝜏	NOUN
iajs-3409	179	7	=	=	PUNCT
iajs-3409	180	1	[	[	X
iajs-3409	180	2	𝜏1	𝜏1	NOUN
iajs-3409	180	3	𝑣1	𝑣1	NOUN
iajs-3409	180	4	,	,	PUNCT
iajs-3409	180	5	…	…	PUNCT
iajs-3409	180	6	,	,	PUNCT
iajs-3409	180	7	𝜏𝑚	𝜏𝑚	PROPN
iajs-3409	180	8	𝑣𝑚	𝑣𝑚	VERB
iajs-3409	180	9	]	]	X
iajs-3409	180	10	3	3	NUM
iajs-3409	180	11	∈	∈	PROPN
iajs-3409	180	12	𝑅𝑇	𝑅𝑇	PROPN
iajs-3409	180	13	,	,	PUNCT
iajs-3409	180	14	with	with	ADP
iajs-3409	180	15	distinct	distinct	ADJ
iajs-3409	180	16	𝜏𝑖	𝜏𝑖	NOUN
iajs-3409	180	17	we	we	PRON
iajs-3409	180	18	have	have	VERB
iajs-3409	180	19	휀(𝜏	휀(𝜏	NOUN
iajs-3409	180	20	)	)	PUNCT
iajs-3409	180	21	=	=	SYM
iajs-3409	180	22	(	(	PUNCT
iajs-3409	180	23	𝜌(𝜏	𝜌(𝜏	NOUN
iajs-3409	180	24	)	)	PUNCT
iajs-3409	180	25	−	−	PROPN
iajs-3409	180	26	3	3	NUM
iajs-3409	180	27	)	)	PUNCT
iajs-3409	180	28	!	!	PUNCT
iajs-3409	181	1	∏	∏	PROPN
iajs-3409	181	2	1	1	NUM
iajs-3409	181	3	𝑣𝑖	𝑣𝑖	ADP
iajs-3409	181	4	(	(	PUNCT
iajs-3409	181	5	𝜀(𝜏𝑖	𝜀(𝜏𝑖	PROPN
iajs-3409	181	6	)	)	PUNCT
iajs-3409	181	7	𝜌(𝜏𝑖	𝜌(𝜏𝑖	PROPN
iajs-3409	181	8	)	)	PUNCT
iajs-3409	181	9	!	!	PUNCT
iajs-3409	181	10	)	)	PUNCT
iajs-3409	182	1	𝑣𝑖	𝑣𝑖	ADV
iajs-3409	182	2	,	,	PUNCT
iajs-3409	182	3	𝑚	𝑚	X
iajs-3409	182	4	𝑖=1	𝑖=1	VERB
iajs-3409	182	5	where	where	SCONJ
iajs-3409	182	6	𝑣𝑖	𝑣𝑖	ADP
iajs-3409	182	7	count	count	VERB
iajs-3409	182	8	similar	similar	ADJ
iajs-3409	182	9	tree	tree	NOUN
iajs-3409	182	10	of	of	ADP
iajs-3409	182	11	𝜏𝑖	𝜏𝑖	NOUN
iajs-3409	182	12	,	,	PUNCT
iajs-3409	182	13	𝑖	𝑖	NOUN
iajs-3409	182	14	=	=	NOUN
iajs-3409	182	15	1	1	NUM
iajs-3409	182	16	,	,	PUNCT
iajs-3409	182	17	.	.	PUNCT
iajs-3409	182	18	.	.	PUNCT
iajs-3409	182	19	.	.	PUNCT
iajs-3409	183	1	,	,	PUNCT
iajs-3409	183	2	𝑚.	𝑚.	ADV
iajs-3409	183	3	therefore	therefore	ADV
iajs-3409	183	4	we	we	PRON
iajs-3409	183	5	can	can	AUX
iajs-3409	183	6	represent	represent	VERB
iajs-3409	183	7	b	b	NUM
iajs-3409	183	8	-	-	PUNCT
iajs-3409	183	9	series	series	NOUN
iajs-3409	183	10	(	(	PUNCT
iajs-3409	183	11	41	41	NUM
iajs-3409	183	12	)	)	PUNCT
iajs-3409	183	13	as	as	SCONJ
iajs-3409	183	14	follows	follow	VERB
iajs-3409	183	15	:	:	PUNCT
iajs-3409	183	16	𝐵(𝛿	𝐵(𝛿	NOUN
iajs-3409	183	17	,	,	PUNCT
iajs-3409	183	18	𝛼	𝛼	NOUN
iajs-3409	183	19	)	)	PUNCT
iajs-3409	183	20	=	=	SYM
iajs-3409	183	21	𝛿(∅	𝛿(∅	PROPN
iajs-3409	183	22	)	)	PUNCT
iajs-3409	184	1	+	+	CCONJ
iajs-3409	184	2	∑	∑	X
iajs-3409	184	3	ℎ𝜌(𝜏	ℎ𝜌(𝜏	NUM
iajs-3409	184	4	)	)	PUNCT
iajs-3409	184	5	𝜌(𝜏	𝜌(𝜏	NOUN
iajs-3409	184	6	)	)	PUNCT
iajs-3409	184	7	!	!	PUNCT
iajs-3409	185	1	𝛿(𝜏	𝛿(𝜏	NOUN
iajs-3409	185	2	)	)	PUNCT
iajs-3409	185	3	휀(𝜏	휀(𝜏	NOUN
iajs-3409	185	4	)	)	PUNCT
iajs-3409	185	5	𝜎(𝜏	𝜎(𝜏	NOUN
iajs-3409	185	6	)	)	PUNCT
iajs-3409	185	7	𝜇(𝜏)(𝛼	𝜇(𝜏)(𝛼	NUM
iajs-3409	185	8	,	,	PUNCT
iajs-3409	185	9	𝛼′	𝛼′	NUM
iajs-3409	185	10	,	,	PUNCT
iajs-3409	185	11	𝛼′′).𝜏∈𝑅𝑇	𝛼′′).𝜏∈𝑅𝑇	NUM
iajs-3409	185	12	(	(	PUNCT
iajs-3409	185	13	42	42	NUM
iajs-3409	185	14	)	)	PUNCT
iajs-3409	185	15	the	the	DET
iajs-3409	185	16	previous	previous	ADJ
iajs-3409	185	17	analysis	analysis	NOUN
iajs-3409	185	18	results	result	NOUN
iajs-3409	185	19	in	in	ADP
iajs-3409	185	20	the	the	DET
iajs-3409	185	21	following	follow	VERB
iajs-3409	185	22	theorem	theorem	PROPN
iajs-3409	185	23	.	.	PUNCT
iajs-3409	185	24	theorem	theorem	VERB
iajs-3409	185	25	3.1	3.1	NUM
iajs-3409	186	1	[	[	X
iajs-3409	186	2	22,23	22,23	NOUN
iajs-3409	186	3	]	]	X
iajs-3409	186	4	:	:	PUNCT
iajs-3409	186	5	the	the	DET
iajs-3409	186	6	exact	exact	ADJ
iajs-3409	186	7	solution	solution	NOUN
iajs-3409	186	8	of	of	ADP
iajs-3409	186	9	(	(	PUNCT
iajs-3409	186	10	18	18	NUM
iajs-3409	186	11	)	)	PUNCT
iajs-3409	186	12	is	be	AUX
iajs-3409	186	13	a	a	DET
iajs-3409	186	14	b	b	NOUN
iajs-3409	186	15	-	-	PUNCT
iajs-3409	186	16	series	series	NOUN
iajs-3409	186	17	𝛼(𝑥0	𝛼(𝑥0	VERB
iajs-3409	186	18	+	+	CCONJ
iajs-3409	186	19	ℎ	ℎ	X
iajs-3409	186	20	)	)	PUNCT
iajs-3409	186	21	=	=	SYM
iajs-3409	186	22	∑	∑	PUNCT
iajs-3409	186	23	ℎ𝜌(𝜏	ℎ𝜌(𝜏	NOUN
iajs-3409	186	24	)	)	PUNCT
iajs-3409	187	1	𝜌(𝜏)!𝜏∈𝑅𝑇	𝜌(𝜏)!𝜏∈𝑅𝑇	PROPN
iajs-3409	187	2	휀(𝜏)𝕌(𝜏)(𝛼0	휀(𝜏)𝕌(𝜏)(𝛼0	NOUN
iajs-3409	187	3	,	,	PUNCT
iajs-3409	187	4	𝛼0	𝛼0	PROPN
iajs-3409	187	5	′	′	NUM
iajs-3409	187	6	,	,	PUNCT
iajs-3409	187	7	𝛼0	𝛼0	PROPN
iajs-3409	187	8	′′	′′	PROPN
iajs-3409	187	9	)	)	PUNCT
iajs-3409	187	10	,	,	PUNCT
iajs-3409	187	11	(	(	PUNCT
iajs-3409	187	12	43	43	NUM
iajs-3409	187	13	)	)	PUNCT
iajs-3409	187	14	and	and	CCONJ
iajs-3409	187	15	the	the	DET
iajs-3409	187	16	first	first	ADJ
iajs-3409	187	17	and	and	CCONJ
iajs-3409	187	18	second	second	ADJ
iajs-3409	187	19	derivatives	derivative	NOUN
iajs-3409	187	20	have	have	VERB
iajs-3409	187	21	the	the	DET
iajs-3409	187	22	following	follow	VERB
iajs-3409	187	23	b	b	NOUN
iajs-3409	187	24	-	-	PUNCT
iajs-3409	187	25	series	series	NOUN
iajs-3409	187	26	respectively	respectively	ADV
iajs-3409	187	27	,	,	PUNCT
iajs-3409	187	28	𝛼′(𝑥0	𝛼′(𝑥0	NOUN
iajs-3409	187	29	+	+	CCONJ
iajs-3409	187	30	ℎ	ℎ	NOUN
iajs-3409	187	31	)	)	PUNCT
iajs-3409	187	32	=	=	SYM
iajs-3409	187	33	∑	∑	PUNCT
iajs-3409	187	34	ℎ𝜌(𝜏)−1	ℎ𝜌(𝜏)−1	PUNCT
iajs-3409	187	35	(	(	PUNCT
iajs-3409	187	36	𝜌(𝜏)−1)!𝜏∈𝑅𝑇	𝜌(𝜏)−1)!𝜏∈𝑅𝑇	PROPN
iajs-3409	187	37	휀(𝜏)𝕌(𝜏)(𝛼0	휀(𝜏)𝕌(𝜏)(𝛼0	PROPN
iajs-3409	187	38	,	,	PUNCT
iajs-3409	187	39	𝛼0	𝛼0	PROPN
iajs-3409	187	40	′	′	NUM
iajs-3409	187	41	,	,	PUNCT
iajs-3409	187	42	𝛼0	𝛼0	PROPN
iajs-3409	187	43	′′	′′	PROPN
iajs-3409	187	44	)	)	PUNCT
iajs-3409	187	45	,	,	PUNCT
iajs-3409	187	46	(	(	PUNCT
iajs-3409	187	47	44	44	X
iajs-3409	187	48	)	)	PUNCT
iajs-3409	187	49	𝛼′′(𝑥0	𝛼′′(𝑥0	PROPN
iajs-3409	187	50	+	+	NUM
iajs-3409	187	51	ℎ	ℎ	NOUN
iajs-3409	187	52	)	)	PUNCT
iajs-3409	187	53	=	=	SYM
iajs-3409	187	54	∑	∑	PUNCT
iajs-3409	187	55	ℎ𝜌(𝜏)−2	ℎ𝜌(𝜏)−2	NOUN
iajs-3409	187	56	(	(	PUNCT
iajs-3409	187	57	𝜌(𝜏)−2)!𝜏∈𝑅𝑇/[𝑡1	𝜌(𝜏)−2)!𝜏∈𝑅𝑇/[𝑡1	NUM
iajs-3409	187	58	]	]	SYM
iajs-3409	187	59	휀(𝜏)𝕌(𝜏)(𝛼0	휀(𝜏)𝕌(𝜏)(𝛼0	PROPN
iajs-3409	187	60	,	,	PUNCT
iajs-3409	187	61	𝛼0	𝛼0	PROPN
iajs-3409	187	62	′	′	NUM
iajs-3409	187	63	,	,	PUNCT
iajs-3409	187	64	𝛼0	𝛼0	PROPN
iajs-3409	187	65	′′	′′	PROPN
iajs-3409	187	66	)	)	PUNCT
iajs-3409	187	67	.	.	PUNCT
iajs-3409	188	1	(	(	PUNCT
iajs-3409	188	2	45	45	NUM
iajs-3409	188	3	)	)	PUNCT
iajs-3409	188	4	lemma	lemma	PROPN
iajs-3409	188	5	3.3	3.3	NUM
iajs-3409	189	1	[	[	X
iajs-3409	189	2	22,23	22,23	NOUN
iajs-3409	189	3	]	]	X
iajs-3409	189	4	:	:	PUNCT
iajs-3409	189	5	we	we	PRON
iajs-3409	189	6	can	can	AUX
iajs-3409	189	7	calculate	calculate	VERB
iajs-3409	189	8	the	the	DET
iajs-3409	189	9	function	function	NOUN
iajs-3409	189	10	𝜂𝑖(𝜏	𝜂𝑖(𝜏	PUNCT
iajs-3409	189	11	)	)	PUNCT
iajs-3409	189	12	on	on	ADP
iajs-3409	189	13	∈	∈	PROPN
iajs-3409	189	14	𝑅𝑇/[𝑡1	𝑅𝑇/[𝑡1	NOUN
iajs-3409	189	15	,	,	PUNCT
iajs-3409	189	16	𝑡2	𝑡2	NOUN
iajs-3409	189	17	]	]	PUNCT
iajs-3409	189	18	recursively	recursively	ADV
iajs-3409	189	19	as	as	ADP
iajs-3409	189	20	1𝜂𝑖(𝑡3	1𝜂𝑖(𝑡3	NUM
iajs-3409	189	21	)	)	PUNCT
iajs-3409	190	1	=	=	SYM
iajs-3409	190	2	1	1	NUM
iajs-3409	190	3	,	,	PUNCT
iajs-3409	190	4	2for	2for	ADP
iajs-3409	190	5	the	the	DET
iajs-3409	190	6	tree	tree	NOUN
iajs-3409	190	7	𝜏	𝜏	NOUN
iajs-3409	191	1	=	=	PUNCT
iajs-3409	192	1	[	[	X
iajs-3409	192	2	𝜏1	𝜏1	NOUN
iajs-3409	192	3	𝑣1	𝑣1	NOUN
iajs-3409	192	4	,	,	PUNCT
iajs-3409	192	5	𝑡2	𝑡2	PROPN
iajs-3409	192	6	𝑣2	𝑣2	NUM
iajs-3409	192	7	,	,	PUNCT
iajs-3409	192	8	𝑡3	𝑡3	PROPN
iajs-3409	192	9	𝑣3	𝑣3	PROPN
iajs-3409	192	10	,	,	PUNCT
iajs-3409	192	11	.	.	PUNCT
iajs-3409	192	12	.	.	PUNCT
iajs-3409	192	13	.	.	PUNCT
iajs-3409	193	1	,	,	PUNCT
iajs-3409	193	2	𝜏𝑚	𝜏𝑚	PROPN
iajs-3409	193	3	𝑣𝑚]3	𝑣𝑚]3	PROPN
iajs-3409	193	4	∈	∈	PROPN
iajs-3409	193	5	𝑅𝑇	𝑅𝑇	PROPN
iajs-3409	193	6	,	,	PUNCT
iajs-3409	193	7	with	with	ADP
iajs-3409	193	8	distinct	distinct	ADJ
iajs-3409	193	9	𝜏𝑖	𝜏𝑖	NOUN
iajs-3409	193	10	,	,	PUNCT
iajs-3409	193	11	𝑖	𝑖	NOUN
iajs-3409	193	12	=	=	NOUN
iajs-3409	193	13	1	1	NUM
iajs-3409	193	14	,	,	PUNCT
iajs-3409	193	15	.	.	PUNCT
iajs-3409	193	16	.	.	PUNCT
iajs-3409	193	17	.	.	PUNCT
iajs-3409	194	1	,	,	PUNCT
iajs-3409	194	2	𝑚	𝑚	PROPN
iajs-3409	194	3	and	and	CCONJ
iajs-3409	194	4	different	different	ADJ
iajs-3409	194	5	𝑡1	𝑡1	NOUN
iajs-3409	194	6	,	,	PUNCT
iajs-3409	194	7	and	and	CCONJ
iajs-3409	194	8	𝑡2	𝑡2	PROPN
iajs-3409	194	9	,	,	PUNCT
iajs-3409	194	10	𝜂𝑗	𝜂𝑗	NOUN
iajs-3409	194	11	=	=	NOUN
iajs-3409	194	12	1	1	NUM
iajs-3409	194	13	2𝑣2	2𝑣2	NUM
iajs-3409	194	14	𝑐𝑗	𝑐𝑗	ADP
iajs-3409	194	15	𝑣1	𝑣1	NOUN
iajs-3409	194	16	+	+	PROPN
iajs-3409	194	17	2𝑣2	2𝑣2	PROPN
iajs-3409	194	18	∏	∏	PROPN
iajs-3409	194	19	(	(	PUNCT
iajs-3409	194	20	∑	∑	X
iajs-3409	194	21	�	�	PROPN
iajs-3409	194	22	̂	̂	NOUN
iajs-3409	194	23	�	�	NOUN
iajs-3409	194	24	𝑗𝑘𝜂𝑘(𝜏𝑖))𝑣𝑖𝑠	𝑗𝑘𝜂𝑘(𝜏𝑖))𝑣𝑖𝑠	NOUN
iajs-3409	194	25	𝑘=1	𝑘=1	NOUN
iajs-3409	194	26	𝑚	𝑚	X
iajs-3409	194	27	𝑖=3	𝑖=3	PROPN
iajs-3409	194	28	.	.	PUNCT
iajs-3409	195	1	now	now	ADV
iajs-3409	195	2	,	,	PUNCT
iajs-3409	195	3	we	we	PRON
iajs-3409	195	4	denote	denote	VERB
iajs-3409	195	5	the	the	DET
iajs-3409	195	6	vector	vector	NOUN
iajs-3409	195	7	𝜂(𝜏	𝜂(𝜏	NOUN
iajs-3409	195	8	)	)	PUNCT
iajs-3409	195	9	=	=	SYM
iajs-3409	195	10	(	(	PUNCT
iajs-3409	195	11	𝜂1(𝜏)(𝜏	𝜂1(𝜏)(𝜏	NOUN
iajs-3409	195	12	)	)	PUNCT
iajs-3409	195	13	,	,	PUNCT
iajs-3409	195	14	.	.	PUNCT
iajs-3409	195	15	.	.	PUNCT
iajs-3409	196	1	.	.	PUNCT
iajs-3409	197	1	,	,	PUNCT
iajs-3409	197	2	𝜂𝑠(𝜏)(𝜏))𝑇	𝜂𝑠(𝜏)(𝜏))𝑇	PROPN
iajs-3409	197	3	,	,	PUNCT
iajs-3409	197	4	∀𝛼	∀𝛼	PROPN
iajs-3409	197	5	∈	∈	PROPN
iajs-3409	197	6	𝑅𝑇\	𝑅𝑇\	X
iajs-3409	197	7	{	{	PUNCT
iajs-3409	197	8	𝑡1	𝑡1	PROPN
iajs-3409	197	9	,	,	PUNCT
iajs-3409	197	10	𝑡2	𝑡2	PROPN
iajs-3409	197	11	}	}	PUNCT
iajs-3409	197	12	.	.	PUNCT
iajs-3409	198	1	the	the	DET
iajs-3409	198	2	initial	initial	ADJ
iajs-3409	198	3	weight	weight	NOUN
iajs-3409	198	4	associated	associate	VERB
iajs-3409	198	5	to	to	ADP
iajs-3409	198	6	𝛼𝑛+1	𝛼𝑛+1	PROPN
iajs-3409	198	7	is	be	AUX
iajs-3409	198	8	indicated	indicate	VERB
iajs-3409	198	9	by	by	ADP
iajs-3409	198	10	𝜕(𝜏	𝜕(𝜏	NOUN
iajs-3409	198	11	)	)	PUNCT
iajs-3409	198	12	and	and	CCONJ
iajs-3409	198	13	is	be	AUX
iajs-3409	198	14	defined	define	VERB
iajs-3409	198	15	as	as	SCONJ
iajs-3409	198	16	follows	follow	VERB
iajs-3409	198	17	:	:	PUNCT
iajs-3409	198	18	𝜕(𝜏	𝜕(𝜏	NUM
iajs-3409	198	19	)	)	PUNCT
iajs-3409	198	20	=	=	PUNCT
iajs-3409	198	21	∑	∑	PUNCT
iajs-3409	198	22	𝑠𝑖	𝑠𝑖	VERB
iajs-3409	198	23	𝜂𝑖(𝜏)𝑠	𝜂𝑖(𝜏)𝑠	X
iajs-3409	198	24	𝑖=1	𝑖=1	PUNCT
iajs-3409	198	25	=	=	PUNCT
iajs-3409	198	26	𝑠𝑇	𝑠𝑇	PROPN
iajs-3409	198	27	𝜂(𝜏	𝜂(𝜏	NOUN
iajs-3409	198	28	)	)	PUNCT
iajs-3409	198	29	,	,	PUNCT
iajs-3409	198	30	𝜕′(𝜏	𝜕′(𝜏	NUM
iajs-3409	198	31	)	)	PUNCT
iajs-3409	198	32	is	be	AUX
iajs-3409	198	33	indicated	indicate	VERB
iajs-3409	198	34	to	to	ADP
iajs-3409	198	35	the	the	DET
iajs-3409	198	36	initial	initial	ADJ
iajs-3409	198	37	weight	weight	NOUN
iajs-3409	198	38	associated	associate	VERB
iajs-3409	198	39	with	with	ADP
iajs-3409	198	40	𝛼′	𝛼′	PROPN
iajs-3409	198	41	𝑛+1	𝑛+1	PROPN
iajs-3409	198	42	and	and	CCONJ
iajs-3409	198	43	is	be	AUX
iajs-3409	198	44	defined	define	VERB
iajs-3409	198	45	as	as	ADP
iajs-3409	198	46	follows	follow	VERB
iajs-3409	198	47	:	:	PUNCT
iajs-3409	198	48	𝜕′(𝜏	𝜕′(𝜏	NUM
iajs-3409	198	49	)	)	PUNCT
iajs-3409	198	50	=	=	PUNCT
iajs-3409	199	1	∑	∑	PUNCT
iajs-3409	199	2	𝑠𝑖′	𝑠𝑖′	PROPN
iajs-3409	200	1	𝜂𝑖(𝜏)𝑠	𝜂𝑖(𝜏)𝑠	X
iajs-3409	200	2	𝑖=1	𝑖=1	PUNCT
iajs-3409	200	3	=	=	SYM
iajs-3409	200	4	𝑠′𝑇	𝑠′𝑇	NOUN
iajs-3409	200	5	𝜂(𝜏	𝜂(𝜏	NOUN
iajs-3409	200	6	)	)	PUNCT
iajs-3409	200	7	,	,	PUNCT
iajs-3409	200	8	and	and	CCONJ
iajs-3409	200	9	the	the	DET
iajs-3409	200	10	initial	initial	ADJ
iajs-3409	200	11	weight	weight	NOUN
iajs-3409	200	12	associated	associate	VERB
iajs-3409	200	13	with	with	ADP
iajs-3409	200	14	𝛼′′	𝛼′′	NOUN
iajs-3409	200	15	𝑛+1	𝑛+1	AUX
iajs-3409	200	16	indicated	indicate	VERB
iajs-3409	200	17	by	by	ADP
iajs-3409	200	18	𝜕′′(𝜏	𝜕′′(𝜏	PROPN
iajs-3409	200	19	)	)	PUNCT
iajs-3409	200	20	and	and	CCONJ
iajs-3409	200	21	is	be	AUX
iajs-3409	200	22	defined	define	VERB
iajs-3409	200	23	as	as	ADP
iajs-3409	200	24	follows	follow	VERB
iajs-3409	200	25	:	:	PUNCT
iajs-3409	200	26	ihjpas	ihjpas	PROPN
iajs-3409	200	27	.	.	PUNCT
iajs-3409	201	1	37	37	NUM
iajs-3409	201	2	(	(	PUNCT
iajs-3409	201	3	2	2	NUM
iajs-3409	201	4	)	)	PUNCT
iajs-3409	201	5	2024	2024	NUM
iajs-3409	201	6	395	395	NUM
iajs-3409	201	7	𝜕′′(𝜏	𝜕′′(𝜏	PROPN
iajs-3409	201	8	)	)	PUNCT
iajs-3409	201	9	=	=	PUNCT
iajs-3409	201	10	∑	∑	PUNCT
iajs-3409	201	11	𝑠𝑖′′	𝑠𝑖′′	PROPN
iajs-3409	201	12	𝜂𝑖(𝜏)𝑠	𝜂𝑖(𝜏)𝑠	NUM
iajs-3409	201	13	𝑖=1	𝑖=1	PUNCT
iajs-3409	201	14	=	=	SYM
iajs-3409	201	15	𝑠′′𝑇	𝑠′′𝑇	NOUN
iajs-3409	201	16	𝜂(𝜏	𝜂(𝜏	NOUN
iajs-3409	201	17	)	)	PUNCT
iajs-3409	201	18	.	.	PUNCT
iajs-3409	202	1	as	as	ADP
iajs-3409	202	2	a	a	DET
iajs-3409	202	3	result	result	NOUN
iajs-3409	202	4	,	,	PUNCT
iajs-3409	202	5	we	we	PRON
iajs-3409	202	6	obtain	obtain	VERB
iajs-3409	202	7	the	the	DET
iajs-3409	202	8	following	follow	VERB
iajs-3409	202	9	fundamental	fundamental	ADJ
iajs-3409	202	10	theorem	theorem	NOUN
iajs-3409	202	11	for	for	ADP
iajs-3409	202	12	the	the	DET
iajs-3409	202	13	numerical	numerical	ADJ
iajs-3409	202	14	solution	solution	NOUN
iajs-3409	202	15	and	and	CCONJ
iajs-3409	202	16	rktdio	rktdio	NOUN
iajs-3409	202	17	technique	technique	NOUN
iajs-3409	202	18	numerical	numerical	ADJ
iajs-3409	202	19	derivatives	derivative	NOUN
iajs-3409	202	20	.	.	PUNCT
iajs-3409	203	1	theorem	theorem	VERB
iajs-3409	203	2	3.2	3.2	NUM
iajs-3409	204	1	[	[	X
iajs-3409	204	2	22,23	22,23	NOUN
iajs-3409	204	3	]	]	X
iajs-3409	204	4	:	:	PUNCT
iajs-3409	204	5	when	when	SCONJ
iajs-3409	204	6	we	we	PRON
iajs-3409	204	7	apply	apply	VERB
iajs-3409	204	8	the	the	DET
iajs-3409	204	9	rktdio	rktdio	NOUN
iajs-3409	204	10	method	method	NOUN
iajs-3409	204	11	(	(	PUNCT
iajs-3409	204	12	39	39	NUM
iajs-3409	204	13	)	)	PUNCT
iajs-3409	204	14	on	on	ADP
iajs-3409	204	15	the	the	DET
iajs-3409	204	16	autonomous	autonomous	ADJ
iajs-3409	204	17	problem	problem	NOUN
iajs-3409	204	18	(	(	PUNCT
iajs-3409	204	19	18	18	NUM
iajs-3409	204	20	)	)	PUNCT
iajs-3409	204	21	yields	yield	VERB
iajs-3409	204	22	the	the	DET
iajs-3409	204	23	numerical	numerical	ADJ
iajs-3409	204	24	solution	solution	NOUN
iajs-3409	204	25	𝛼𝑛+1	𝛼𝑛+1	NUM
iajs-3409	204	26	and	and	CCONJ
iajs-3409	204	27	numerical	numerical	ADJ
iajs-3409	204	28	derivatives	derivative	NOUN
iajs-3409	204	29	𝛼′𝑛+1	𝛼′𝑛+1	PROPN
iajs-3409	204	30	,	,	PUNCT
iajs-3409	204	31	𝛼′′𝑛+1	𝛼′′𝑛+1	PROPN
iajs-3409	204	32	which	which	PRON
iajs-3409	204	33	have	have	VERB
iajs-3409	204	34	the	the	DET
iajs-3409	204	35	bseries	bserie	NOUN
iajs-3409	204	36	as	as	SCONJ
iajs-3409	204	37	follows	follow	VERB
iajs-3409	204	38	:	:	PUNCT
iajs-3409	204	39	𝛼𝑛+1	𝛼𝑛+1	NUM
iajs-3409	204	40	=	=	SYM
iajs-3409	204	41	𝛼𝑛	𝛼𝑛	PROPN
iajs-3409	204	42	+	+	NUM
iajs-3409	204	43	ℎ𝛼𝑛	ℎ𝛼𝑛	NOUN
iajs-3409	204	44	′	′	NOUN
iajs-3409	205	1	+	+	CCONJ
iajs-3409	205	2	1	1	NUM
iajs-3409	205	3	2	2	NUM
iajs-3409	205	4	ℎ2𝛼𝑛	ℎ2𝛼𝑛	NUM
iajs-3409	205	5	′′	′′	PROPN
iajs-3409	205	6	+	+	CCONJ
iajs-3409	205	7	∑	∑	PUNCT
iajs-3409	205	8	ℎ𝜌(𝜏	ℎ𝜌(𝜏	NOUN
iajs-3409	205	9	)	)	PUNCT
iajs-3409	205	10	𝜌(𝜏)!𝜏∈	𝜌(𝜏)!𝜏∈	VERB
iajs-3409	205	11	𝑅𝑇	𝑅𝑇	PROPN
iajs-3409	205	12	{	{	PUNCT
iajs-3409	205	13	𝑡1,𝑡2	𝑡1,𝑡2	PROPN
iajs-3409	205	14	}	}	PUNCT
iajs-3409	205	15	휀(𝜏)𝜎(𝜏)𝜃(𝜏	휀(𝜏)𝜎(𝜏)𝜃(𝜏	NOUN
iajs-3409	205	16	)	)	PUNCT
iajs-3409	205	17	.	.	PUNCT
iajs-3409	206	1	𝕌(𝜏)(𝛼0	𝕌(𝜏)(𝛼0	PROPN
iajs-3409	206	2	,	,	PUNCT
iajs-3409	206	3	𝛼0	𝛼0	PROPN
iajs-3409	206	4	′	′	NUM
iajs-3409	206	5	,	,	PUNCT
iajs-3409	206	6	𝛼0	𝛼0	PROPN
iajs-3409	206	7	′′	′′	PROPN
iajs-3409	206	8	)	)	PUNCT
iajs-3409	206	9	,	,	PUNCT
iajs-3409	206	10	(	(	PUNCT
iajs-3409	206	11	45	45	NUM
iajs-3409	206	12	)	)	PUNCT
iajs-3409	206	13	𝛼𝑛+1	𝛼𝑛+1	NOUN
iajs-3409	206	14	′	′	NOUN
iajs-3409	206	15	=	=	SYM
iajs-3409	206	16	𝛼𝑛	𝛼𝑛	NOUN
iajs-3409	206	17	′	′	NOUN
iajs-3409	206	18	+	+	CCONJ
iajs-3409	206	19	ℎ𝛼𝑛	ℎ𝛼𝑛	NOUN
iajs-3409	206	20	′′	′′	PROPN
iajs-3409	206	21	+	+	CCONJ
iajs-3409	206	22	∑	∑	PUNCT
iajs-3409	206	23	ℎ𝜌(𝜏)−1	ℎ𝜌(𝜏)−1	ADJ
iajs-3409	206	24	)	)	PUNCT
iajs-3409	206	25	𝜌(𝜏)!𝜏∈𝑅𝑇/{𝑡1,𝑡2	𝜌(𝜏)!𝜏∈𝑅𝑇/{𝑡1,𝑡2	NUM
iajs-3409	206	26	}	}	PUNCT
iajs-3409	206	27	휀(𝜏)𝜎(𝜏)𝜃′(𝜏	휀(𝜏)𝜎(𝜏)𝜃′(𝜏	PROPN
iajs-3409	206	28	)	)	PUNCT
iajs-3409	206	29	.	.	PUNCT
iajs-3409	207	1	𝕌(𝜏)(𝛼0	𝕌(𝜏)(𝛼0	PROPN
iajs-3409	207	2	,	,	PUNCT
iajs-3409	207	3	𝛼0	𝛼0	PROPN
iajs-3409	207	4	′	′	NUM
iajs-3409	207	5	,	,	PUNCT
iajs-3409	207	6	𝛼0	𝛼0	PROPN
iajs-3409	207	7	′′	′′	PROPN
iajs-3409	207	8	)	)	PUNCT
iajs-3409	207	9	,	,	PUNCT
iajs-3409	207	10	(	(	PUNCT
iajs-3409	207	11	46	46	NUM
iajs-3409	207	12	)	)	PUNCT
iajs-3409	207	13	𝛼𝑛+1	𝛼𝑛+1	NUM
iajs-3409	207	14	′′	′′	PROPN
iajs-3409	207	15	=	=	SYM
iajs-3409	207	16	𝛼𝑛	𝛼𝑛	PROPN
iajs-3409	208	1	′′	′′	PROPN
iajs-3409	208	2	+	+	CCONJ
iajs-3409	208	3	∑	∑	NOUN
iajs-3409	208	4	ℎ𝜌(𝜏)−2	ℎ𝜌(𝜏)−2	NOUN
iajs-3409	208	5	)	)	PUNCT
iajs-3409	208	6	𝜌(𝜏)!𝜏∈𝑅𝑇/{𝑡1,𝑡2	𝜌(𝜏)!𝜏∈𝑅𝑇/{𝑡1,𝑡2	NUM
iajs-3409	208	7	}	}	PUNCT
iajs-3409	208	8	휀(𝜏)𝜎(𝜏)𝜃′′(𝜏	휀(𝜏)𝜎(𝜏)𝜃′′(𝜏	PROPN
iajs-3409	208	9	)	)	PUNCT
iajs-3409	208	10	.	.	PUNCT
iajs-3409	209	1	𝕌(𝜏)(𝛼0	𝕌(𝜏)(𝛼0	PROPN
iajs-3409	209	2	,	,	PUNCT
iajs-3409	209	3	𝛼0	𝛼0	PROPN
iajs-3409	209	4	′	′	NUM
iajs-3409	209	5	,	,	PUNCT
iajs-3409	209	6	𝛼0	𝛼0	PROPN
iajs-3409	209	7	′′	′′	PROPN
iajs-3409	209	8	)	)	PUNCT
iajs-3409	209	9	.	.	PUNCT
iajs-3409	210	1	(	(	PUNCT
iajs-3409	210	2	47	47	NUM
iajs-3409	210	3	)	)	PUNCT
iajs-3409	210	4	4	4	NUM
iajs-3409	210	5	.	.	PUNCT
iajs-3409	211	1	algebraic	algebraic	ADJ
iajs-3409	211	2	order	order	NOUN
iajs-3409	211	3	conditions	condition	NOUN
iajs-3409	211	4	we	we	PRON
iajs-3409	211	5	arrive	arrive	VERB
iajs-3409	211	6	at	at	ADP
iajs-3409	211	7	this	this	DET
iajs-3409	211	8	paper	paper	NOUN
iajs-3409	211	9	's	's	PART
iajs-3409	211	10	main	main	ADJ
iajs-3409	211	11	contribution	contribution	NOUN
iajs-3409	211	12	—	—	PUNCT
iajs-3409	211	13	the	the	DET
iajs-3409	211	14	order	order	NOUN
iajs-3409	211	15	conditions	condition	NOUN
iajs-3409	211	16	of	of	ADP
iajs-3409	211	17	the	the	DET
iajs-3409	211	18	rktdio	rktdio	NOUN
iajs-3409	211	19	method	method	NOUN
iajs-3409	211	20	-	-	PUNCT
iajs-3409	211	21	through	through	ADP
iajs-3409	211	22	theorems	theorem	NOUN
iajs-3409	211	23	3.1	3.1	NUM
iajs-3409	211	24	and	and	CCONJ
iajs-3409	211	25	3.2	3.2	NUM
iajs-3409	211	26	.	.	PUNCT
iajs-3409	212	1	in	in	ADP
iajs-3409	212	2	table	table	NOUN
iajs-3409	212	3	1	1	NUM
iajs-3409	212	4	,	,	PUNCT
iajs-3409	212	5	the	the	DET
iajs-3409	212	6	relevant	relevant	ADJ
iajs-3409	212	7	-	-	PUNCT
iajs-3409	212	8	colored	colored	ADJ
iajs-3409	212	9	trees	tree	NOUN
iajs-3409	212	10	of	of	ADP
iajs-3409	212	11	orders	order	NOUN
iajs-3409	212	12	up	up	ADP
iajs-3409	212	13	to	to	PART
iajs-3409	212	14	six	six	NUM
iajs-3409	212	15	are	be	AUX
iajs-3409	212	16	listed	list	VERB
iajs-3409	212	17	together	together	ADV
iajs-3409	212	18	with	with	ADP
iajs-3409	212	19	the	the	DET
iajs-3409	212	20	accompanying	accompanying	ADJ
iajs-3409	212	21	function	function	NOUN
iajs-3409	212	22	values	value	NOUN
iajs-3409	212	23	.	.	PUNCT
iajs-3409	213	1	theorem	theorem	VERB
iajs-3409	213	2	4.1	4.1	NUM
iajs-3409	213	3	:	:	PUNCT
iajs-3409	213	4	the	the	DET
iajs-3409	213	5	rktdio	rktdio	NOUN
iajs-3409	213	6	method	method	NOUN
iajs-3409	213	7	has	have	VERB
iajs-3409	213	8	order	order	NOUN
iajs-3409	213	9	𝑝	𝑝	NOUN
iajs-3409	213	10	(	(	PUNCT
iajs-3409	213	11	𝑝	𝑝	PROPN
iajs-3409	213	12	≥	≥	NOUN
iajs-3409	213	13	3	3	NUM
iajs-3409	213	14	)	)	PUNCT
iajs-3409	214	1	if	if	SCONJ
iajs-3409	214	2	and	and	CCONJ
iajs-3409	214	3	only	only	ADV
iajs-3409	214	4	if	if	SCONJ
iajs-3409	214	5	it	it	PRON
iajs-3409	214	6	satisfies	satisfy	VERB
iajs-3409	214	7	the	the	DET
iajs-3409	214	8	following	follow	VERB
iajs-3409	214	9	conditions	condition	NOUN
iajs-3409	214	10	.	.	PUNCT
iajs-3409	215	1	1𝜃(𝜏	1𝜃(𝜏	NUM
iajs-3409	215	2	)	)	PUNCT
iajs-3409	216	1	=	=	SYM
iajs-3409	216	2	1	1	NUM
iajs-3409	216	3	𝜎(𝜏	𝜎(𝜏	NOUN
iajs-3409	216	4	)	)	PUNCT
iajs-3409	216	5	,	,	PUNCT
iajs-3409	216	6	𝜏	𝜏	NOUN
iajs-3409	216	7	∈	∈	NOUN
iajs-3409	216	8	⋃	⋃	PROPN
iajs-3409	216	9	𝑠𝑟	𝑠𝑟	NOUN
iajs-3409	216	10	𝑝	𝑝	PROPN
iajs-3409	216	11	𝑟=4	𝑟=4	PROPN
iajs-3409	216	12	,	,	PUNCT
iajs-3409	216	13	(	(	PUNCT
iajs-3409	216	14	48	48	NUM
iajs-3409	216	15	)	)	PUNCT
iajs-3409	216	16	2𝜃′(𝜏	2𝜃′(𝜏	NUM
iajs-3409	216	17	)	)	PUNCT
iajs-3409	216	18	=	=	SYM
iajs-3409	216	19	𝜌(𝜏	𝜌(𝜏	X
iajs-3409	216	20	)	)	PUNCT
iajs-3409	216	21	𝜎(𝜏	𝜎(𝜏	PROPN
iajs-3409	216	22	)	)	PUNCT
iajs-3409	216	23	,	,	PUNCT
iajs-3409	216	24	𝜏	𝜏	NOUN
iajs-3409	216	25	∈	∈	NOUN
iajs-3409	216	26	⋃	⋃	PUNCT
iajs-3409	216	27	𝑠𝑟	𝑠𝑟	NOUN
iajs-3409	216	28	𝑝+1	𝑝+1	NOUN
iajs-3409	216	29	𝑟=4	𝑟=4	NUM
iajs-3409	216	30	,	,	PUNCT
iajs-3409	216	31	(	(	PUNCT
iajs-3409	216	32	49	49	NUM
iajs-3409	216	33	)	)	PUNCT
iajs-3409	216	34	3𝜃′′(𝜏	3𝜃′′(𝜏	NUM
iajs-3409	216	35	)	)	PUNCT
iajs-3409	216	36	=	=	SYM
iajs-3409	216	37	𝜌(𝜏)(𝜌(𝜏)−1	𝜌(𝜏)(𝜌(𝜏)−1	X
iajs-3409	216	38	)	)	PUNCT
iajs-3409	216	39	𝜎(𝜏	𝜎(𝜏	PROPN
iajs-3409	216	40	)	)	PUNCT
iajs-3409	216	41	,	,	PUNCT
iajs-3409	216	42	𝜏	𝜏	NOUN
iajs-3409	216	43	∈	∈	NOUN
iajs-3409	216	44	⋃	⋃	NOUN
iajs-3409	216	45	𝑠𝑟	𝑠𝑟	NOUN
iajs-3409	216	46	𝑝+2	𝑝+2	PROPN
iajs-3409	216	47	𝑟=4	𝑟=4	PROPN
iajs-3409	216	48	.	.	PUNCT
iajs-3409	217	1	(	(	PUNCT
iajs-3409	217	2	50	50	NUM
iajs-3409	217	3	)	)	PUNCT
iajs-3409	217	4	even	even	ADV
iajs-3409	217	5	though	though	SCONJ
iajs-3409	217	6	some	some	PRON
iajs-3409	217	7	of	of	ADP
iajs-3409	217	8	the	the	DET
iajs-3409	217	9	trees	tree	NOUN
iajs-3409	217	10	in	in	ADP
iajs-3409	217	11	the	the	DET
iajs-3409	217	12	set	set	NOUN
iajs-3409	217	13	rt	rt	PROPN
iajs-3409	217	14	provide	provide	VERB
iajs-3409	217	15	the	the	DET
iajs-3409	217	16	same	same	ADJ
iajs-3409	217	17	order	order	NOUN
iajs-3409	217	18	criteria	criterion	NOUN
iajs-3409	217	19	and	and	CCONJ
iajs-3409	217	20	pertain	pertain	VERB
iajs-3409	217	21	to	to	ADP
iajs-3409	217	22	various	various	ADJ
iajs-3409	217	23	elementary	elementary	ADJ
iajs-3409	217	24	differentials	differential	NOUN
iajs-3409	217	25	,	,	PUNCT
iajs-3409	217	26	it	it	PRON
iajs-3409	217	27	is	be	AUX
iajs-3409	217	28	still	still	ADV
iajs-3409	217	29	unnecessary	unnecessary	ADJ
iajs-3409	217	30	.	.	PUNCT
iajs-3409	218	1	in	in	ADP
iajs-3409	218	2	general	general	ADJ
iajs-3409	218	3	,	,	PUNCT
iajs-3409	218	4	the	the	DET
iajs-3409	218	5	following	follow	VERB
iajs-3409	218	6	corollary	corollary	NOUN
iajs-3409	218	7	,	,	PUNCT
iajs-3409	218	8	which	which	PRON
iajs-3409	218	9	may	may	AUX
iajs-3409	218	10	be	be	AUX
iajs-3409	218	11	derived	derive	VERB
iajs-3409	218	12	from	from	ADP
iajs-3409	218	13	the	the	DET
iajs-3409	218	14	definition	definition	NOUN
iajs-3409	218	15	of	of	ADP
iajs-3409	218	16	density	density	NOUN
iajs-3409	218	17	and	and	CCONJ
iajs-3409	218	18	order	order	NOUN
iajs-3409	218	19	,	,	PUNCT
iajs-3409	218	20	and	and	CCONJ
iajs-3409	218	21	from	from	ADP
iajs-3409	218	22	lemma	lemma	PROPN
iajs-3409	218	23	3.3	3.3	NUM
iajs-3409	218	24	,	,	PUNCT
iajs-3409	218	25	can	can	AUX
iajs-3409	218	26	be	be	AUX
iajs-3409	218	27	used	use	VERB
iajs-3409	218	28	to	to	PART
iajs-3409	218	29	overcome	overcome	VERB
iajs-3409	218	30	the	the	DET
iajs-3409	218	31	similarity	similarity	NOUN
iajs-3409	218	32	between	between	ADP
iajs-3409	218	33	the	the	DET
iajs-3409	218	34	order	order	NOUN
iajs-3409	218	35	criteria	criterion	NOUN
iajs-3409	218	36	.	.	PUNCT
iajs-3409	219	1	table	table	NOUN
iajs-3409	219	2	1	1	NUM
iajs-3409	219	3	.	.	NUM
iajs-3409	219	4	lists	list	VERB
iajs-3409	219	5	elementary	elementary	ADJ
iajs-3409	219	6	differentials	differential	NOUN
iajs-3409	219	7	,	,	PUNCT
iajs-3409	219	8	relevant	relevant	ADJ
iajs-3409	219	9	-	-	PUNCT
iajs-3409	219	10	colored	colored	ADJ
iajs-3409	219	11	trees	tree	NOUN
iajs-3409	219	12	of	of	ADP
iajs-3409	219	13	up	up	ADP
iajs-3409	219	14	to	to	PART
iajs-3409	219	15	six	six	NUM
iajs-3409	219	16	orders	order	NOUN
iajs-3409	219	17	,	,	PUNCT
iajs-3409	219	18	and	and	CCONJ
iajs-3409	219	19	related	related	ADJ
iajs-3409	219	20	functions	function	NOUN
iajs-3409	219	21	.	.	PUNCT
iajs-3409	220	1	order	order	NOUN
iajs-3409	220	2	𝝉	𝝉	DET
iajs-3409	220	3	tree	tree	NOUN
iajs-3409	220	4	𝜶(𝝉	𝜶(𝝉	NOUN
iajs-3409	220	5	)	)	PUNCT
iajs-3409	220	6	density	density	NOUN
iajs-3409	220	7	𝒏(𝝉	𝒏(𝝉	PROPN
iajs-3409	220	8	)	)	PUNCT
iajs-3409	220	9	elementary	elementary	NOUN
iajs-3409	220	10	0	0	NUM
iajs-3409	220	11	∅	∅	NOUN
iajs-3409	220	12	∅	∅	NOUN
iajs-3409	220	13	1	1	NUM
iajs-3409	220	14	1	1	NUM
iajs-3409	220	15	𝛼	𝛼	SYM
iajs-3409	220	16	1	1	NUM
iajs-3409	220	17	𝑡1	𝑡1	NOUN
iajs-3409	220	18	1	1	NUM
iajs-3409	220	19	1	1	NUM
iajs-3409	220	20	𝛼′	𝛼′	NUM
iajs-3409	220	21	2	2	NUM
iajs-3409	220	22	𝑡2	𝑡2	NOUN
iajs-3409	220	23	1	1	NUM
iajs-3409	220	24	2	2	NUM
iajs-3409	220	25	𝛼′′	𝛼′′	NOUN
iajs-3409	220	26	3	3	NUM
iajs-3409	220	27	𝑡3	𝑡3	PROPN
iajs-3409	220	28	1	1	NUM
iajs-3409	220	29	6	6	NUM
iajs-3409	220	30	𝜇	𝜇	ADP
iajs-3409	220	31	4	4	NUM
iajs-3409	220	32	𝜏41	𝜏41	NOUN
iajs-3409	220	33	1	1	NUM
iajs-3409	220	34	24	24	NUM
iajs-3409	220	35	𝑐	𝑐	PROPN
iajs-3409	220	36	𝜇′𝛼′	𝜇′𝛼′	PROPN
iajs-3409	220	37	ihjpas	ihjpa	NOUN
iajs-3409	220	38	.	.	PUNCT
iajs-3409	221	1	37	37	NUM
iajs-3409	221	2	(	(	PUNCT
iajs-3409	221	3	2	2	NUM
iajs-3409	221	4	)	)	PUNCT
iajs-3409	221	5	2024	2024	NUM
iajs-3409	221	6	396	396	NUM
iajs-3409	221	7	5	5	NUM
iajs-3409	221	8	𝜏51	𝜏51	NOUN
iajs-3409	221	9	1	1	NUM
iajs-3409	221	10	60	60	NUM
iajs-3409	221	11	𝑐2	𝑐2	NOUN
iajs-3409	221	12	𝜇′𝛼′′	𝜇′𝛼′′	ADP
iajs-3409	221	13	5	5	NUM
iajs-3409	221	14	𝜏52	𝜏52	NOUN
iajs-3409	221	15	1	1	NUM
iajs-3409	221	16	120	120	NUM
iajs-3409	221	17	1	1	NUM
iajs-3409	221	18	2	2	NUM
iajs-3409	221	19	𝑐2	𝑐2	NOUN
iajs-3409	221	20	𝜇′′(𝛼′	𝜇′′(𝛼′	NOUN
iajs-3409	221	21	,	,	PUNCT
iajs-3409	221	22	𝛼′	𝛼′	NUM
iajs-3409	221	23	)	)	PUNCT
iajs-3409	221	24	6	6	NUM
iajs-3409	221	25	𝜏61	𝜏61	NOUN
iajs-3409	221	26	3	3	NUM
iajs-3409	221	27	120	120	NUM
iajs-3409	221	28	𝑐3	𝑐3	NOUN
iajs-3409	221	29	𝜇′′(𝛼′	𝜇′′(𝛼′	VERB
iajs-3409	221	30	,	,	PUNCT
iajs-3409	221	31	𝛼′′	𝛼′′	NOUN
iajs-3409	221	32	)	)	PUNCT
iajs-3409	221	33	6	6	NUM
iajs-3409	221	34	𝜏62	𝜏62	NOUN
iajs-3409	221	35	1	1	NUM
iajs-3409	221	36	240	240	NUM
iajs-3409	221	37	1	1	NUM
iajs-3409	221	38	2	2	NUM
iajs-3409	221	39	𝑐3	𝑐3	NOUN
iajs-3409	221	40	𝜇′′′(𝛼′	𝜇′′′(𝛼′	PROPN
iajs-3409	221	41	,	,	PUNCT
iajs-3409	221	42	𝛼′	𝛼′	PROPN
iajs-3409	221	43	,	,	PUNCT
iajs-3409	221	44	𝛼′	𝛼′	NUM
iajs-3409	221	45	)	)	PUNCT
iajs-3409	221	46	6	6	NUM
iajs-3409	221	47	𝜏63	𝜏63	NUM
iajs-3409	221	48	1	1	NUM
iajs-3409	221	49	720	720	NUM
iajs-3409	221	50	1	1	NUM
iajs-3409	221	51	6	6	NUM
iajs-3409	221	52	𝑐3	𝑐3	NOUN
iajs-3409	221	53	𝜇′𝛼′′	𝜇′𝛼′′	ADP
iajs-3409	221	54	the	the	DET
iajs-3409	221	55	order	order	NOUN
iajs-3409	221	56	criteria	criterion	NOUN
iajs-3409	221	57	for	for	ADP
iajs-3409	221	58	the	the	DET
iajs-3409	221	59	rktdio	rktdio	NOUN
iajs-3409	221	60	technique	technique	NOUN
iajs-3409	221	61	up	up	ADP
iajs-3409	221	62	to	to	ADP
iajs-3409	221	63	the	the	DET
iajs-3409	221	64	sixth	sixth	ADJ
iajs-3409	221	65	order	order	NOUN
iajs-3409	221	66	can	can	AUX
iajs-3409	221	67	be	be	AUX
iajs-3409	221	68	expressed	express	VERB
iajs-3409	221	69	as	as	SCONJ
iajs-3409	221	70	follows	follow	VERB
iajs-3409	221	71	using	use	VERB
iajs-3409	221	72	theorem	theorem	NOUN
iajs-3409	221	73	4.1	4.1	NUM
iajs-3409	221	74	as	as	ADP
iajs-3409	221	75	a	a	DET
iajs-3409	221	76	foundation	foundation	NOUN
iajs-3409	221	77	:	:	PUNCT
iajs-3409	221	78	order	order	NOUN
iajs-3409	221	79	condition	condition	NOUN
iajs-3409	221	80	for	for	ADP
iajs-3409	221	81	𝜶	𝜶	PRON
iajs-3409	221	82	order	order	NOUN
iajs-3409	221	83	3	3	NUM
iajs-3409	221	84	∑	∑	PUNCT
iajs-3409	221	85	𝑘𝑖	𝑘𝑖	NOUN
iajs-3409	221	86	=	=	SYM
iajs-3409	221	87	1	1	NUM
iajs-3409	221	88	6	6	NUM
iajs-3409	221	89	(	(	PUNCT
iajs-3409	221	90	51	51	NUM
iajs-3409	221	91	)	)	PUNCT
iajs-3409	221	92	order	order	NOUN
iajs-3409	221	93	4	4	NUM
iajs-3409	221	94	∑	∑	PART
iajs-3409	221	95	𝑘𝑖	𝑘𝑖	VERB
iajs-3409	221	96	𝑠𝑖	𝑠𝑖	NOUN
iajs-3409	221	97	=	=	SYM
iajs-3409	221	98	1	1	NUM
iajs-3409	221	99	24	24	NUM
iajs-3409	221	100	(	(	PUNCT
iajs-3409	221	101	52	52	NUM
iajs-3409	221	102	)	)	PUNCT
iajs-3409	221	103	order	order	NOUN
iajs-3409	221	104	5	5	NUM
iajs-3409	221	105	∑	∑	PUNCT
iajs-3409	221	106	𝑘𝑖𝑠𝑖	𝑘𝑖𝑠𝑖	ADJ
iajs-3409	221	107	2	2	NUM
iajs-3409	221	108	=	=	SYM
iajs-3409	221	109	1	1	NUM
iajs-3409	221	110	60	60	NUM
iajs-3409	221	111	(	(	PUNCT
iajs-3409	221	112	53	53	NUM
iajs-3409	221	113	)	)	PUNCT
iajs-3409	221	114	order	order	NOUN
iajs-3409	221	115	6	6	NUM
iajs-3409	221	116	∑	∑	PUNCT
iajs-3409	221	117	𝑘𝑖𝑠𝑖	𝑘𝑖𝑠𝑖	ADV
iajs-3409	221	118	3	3	NUM
iajs-3409	221	119	=	=	SYM
iajs-3409	221	120	1	1	NUM
iajs-3409	221	121	120	120	NUM
iajs-3409	221	122	,	,	PUNCT
iajs-3409	221	123	∑	∑	NUM
iajs-3409	221	124	𝑘𝑖𝑎𝑖𝑗	𝑘𝑖𝑎𝑖𝑗	NOUN
iajs-3409	221	125	=	=	SYM
iajs-3409	221	126	1	1	NUM
iajs-3409	221	127	720	720	NUM
iajs-3409	221	128	(	(	PUNCT
iajs-3409	221	129	54	54	NUM
iajs-3409	221	130	)	)	PUNCT
iajs-3409	221	131	order	order	NOUN
iajs-3409	221	132	condition	condition	NOUN
iajs-3409	221	133	for	for	ADP
iajs-3409	221	134	𝜶′	𝜶′	ADJ
iajs-3409	221	135	order	order	NOUN
iajs-3409	221	136	2	2	NUM
iajs-3409	221	137	∑	∑	PUNCT
iajs-3409	221	138	𝑘′𝑖	𝑘′𝑖	VERB
iajs-3409	221	139	=	=	SYM
iajs-3409	221	140	1	1	NUM
iajs-3409	221	141	2	2	NUM
iajs-3409	221	142	(	(	PUNCT
iajs-3409	221	143	55	55	NUM
iajs-3409	221	144	)	)	PUNCT
iajs-3409	221	145	order	order	NOUN
iajs-3409	221	146	3	3	NUM
iajs-3409	221	147	∑	∑	PUNCT
iajs-3409	221	148	𝑘𝑖′	𝑘𝑖′	PROPN
iajs-3409	221	149	𝑠𝑖	𝑠𝑖	NOUN
iajs-3409	221	150	=	=	NOUN
iajs-3409	222	1	1	1	NUM
iajs-3409	222	2	6	6	NUM
iajs-3409	222	3	(	(	PUNCT
iajs-3409	222	4	56	56	NUM
iajs-3409	222	5	)	)	PUNCT
iajs-3409	222	6	order	order	NOUN
iajs-3409	222	7	4	4	NUM
iajs-3409	222	8	ihjpas	ihjpa	NOUN
iajs-3409	222	9	.	.	PUNCT
iajs-3409	223	1	37	37	NUM
iajs-3409	223	2	(	(	PUNCT
iajs-3409	223	3	2	2	NUM
iajs-3409	223	4	)	)	PUNCT
iajs-3409	223	5	2024	2024	NUM
iajs-3409	223	6	397	397	NUM
iajs-3409	223	7	∑	∑	SYM
iajs-3409	223	8	𝑘𝑖′𝑠𝑖	𝑘𝑖′𝑠𝑖	X
iajs-3409	223	9	2	2	NUM
iajs-3409	223	10	=	=	SYM
iajs-3409	223	11	1	1	NUM
iajs-3409	223	12	12	12	NUM
iajs-3409	223	13	(	(	PUNCT
iajs-3409	223	14	57	57	NUM
iajs-3409	223	15	)	)	PUNCT
iajs-3409	223	16	order	order	NOUN
iajs-3409	223	17	5	5	NUM
iajs-3409	223	18	∑	∑	PUNCT
iajs-3409	223	19	𝑘𝑖′𝑠𝑖	𝑘𝑖′𝑠𝑖	NOUN
iajs-3409	223	20	3	3	NUM
iajs-3409	223	21	=	=	SYM
iajs-3409	223	22	1	1	NUM
iajs-3409	223	23	20	20	NUM
iajs-3409	223	24	,	,	PUNCT
iajs-3409	223	25	∑	∑	SYM
iajs-3409	223	26	𝑘𝑖′𝑎𝑖𝑗	𝑘𝑖′𝑎𝑖𝑗	X
iajs-3409	223	27	=	=	SYM
iajs-3409	223	28	1	1	NUM
iajs-3409	223	29	120	120	NUM
iajs-3409	223	30	(	(	PUNCT
iajs-3409	223	31	58	58	NUM
iajs-3409	223	32	)	)	PUNCT
iajs-3409	223	33	order	order	NOUN
iajs-3409	223	34	6	6	NUM
iajs-3409	223	35	∑	∑	PUNCT
iajs-3409	223	36	𝑘𝑖′𝑠𝑖	𝑘𝑖′𝑠𝑖	X
iajs-3409	223	37	4	4	NUM
iajs-3409	223	38	=	=	SYM
iajs-3409	223	39	1	1	NUM
iajs-3409	223	40	30	30	NUM
iajs-3409	223	41	,	,	PUNCT
iajs-3409	223	42	∑	∑	PUNCT
iajs-3409	223	43	𝑘𝑖′𝑎𝑖𝑗𝑠𝑗	𝑘𝑖′𝑎𝑖𝑗𝑠𝑗	NOUN
iajs-3409	223	44	=	=	SYM
iajs-3409	223	45	1	1	NUM
iajs-3409	223	46	720	720	NUM
iajs-3409	223	47	,	,	PUNCT
iajs-3409	223	48	∑	∑	PUNCT
iajs-3409	223	49	𝑘𝑖′𝑠𝑗𝑎𝑖𝑗	𝑘𝑖′𝑠𝑗𝑎𝑖𝑗	NOUN
iajs-3409	223	50	=	=	SYM
iajs-3409	223	51	1	1	NUM
iajs-3409	223	52	180	180	NUM
iajs-3409	223	53	(	(	PUNCT
iajs-3409	223	54	59	59	NUM
iajs-3409	223	55	)	)	PUNCT
iajs-3409	223	56	order	order	NOUN
iajs-3409	223	57	condition	condition	NOUN
iajs-3409	223	58	for	for	ADP
iajs-3409	223	59	𝜶′′	𝜶′′	ADJ
iajs-3409	223	60	order	order	NOUN
iajs-3409	223	61	1	1	NUM
iajs-3409	223	62	∑	∑	PUNCT
iajs-3409	223	63	𝑘𝑖	𝑘𝑖	ADP
iajs-3409	223	64	′′	′′	NOUN
iajs-3409	223	65	=	=	PUNCT
iajs-3409	223	66	1	1	NUM
iajs-3409	223	67	(	(	PUNCT
iajs-3409	223	68	60	60	NUM
iajs-3409	223	69	)	)	PUNCT
iajs-3409	223	70	order	order	NOUN
iajs-3409	223	71	2	2	NUM
iajs-3409	223	72	∑	∑	PUNCT
iajs-3409	223	73	𝑘𝑖′′	𝑘𝑖′′	ADV
iajs-3409	223	74	𝑠𝑖	𝑠𝑖	VERB
iajs-3409	223	75	=	=	NOUN
iajs-3409	223	76	1	1	NUM
iajs-3409	223	77	2	2	NUM
iajs-3409	223	78	(	(	PUNCT
iajs-3409	223	79	61	61	NUM
iajs-3409	223	80	)	)	PUNCT
iajs-3409	223	81	order	order	NOUN
iajs-3409	223	82	3	3	NUM
iajs-3409	223	83	∑	∑	NOUN
iajs-3409	223	84	𝑘𝑖′′𝑠𝑖	𝑘𝑖′′𝑠𝑖	ADP
iajs-3409	223	85	2	2	NUM
iajs-3409	223	86	=	=	SYM
iajs-3409	223	87	1	1	NUM
iajs-3409	223	88	3	3	NUM
iajs-3409	223	89	(	(	PUNCT
iajs-3409	223	90	62	62	NUM
iajs-3409	223	91	)	)	PUNCT
iajs-3409	223	92	order	order	NOUN
iajs-3409	223	93	4	4	NUM
iajs-3409	223	94	∑	∑	NOUN
iajs-3409	223	95	𝑘𝑖′′𝑠𝑖	𝑘𝑖′′𝑠𝑖	ADP
iajs-3409	223	96	3	3	NUM
iajs-3409	223	97	=	=	SYM
iajs-3409	223	98	1	1	NUM
iajs-3409	223	99	4	4	NUM
iajs-3409	223	100	,	,	PUNCT
iajs-3409	223	101	∑	∑	PUNCT
iajs-3409	223	102	𝑘𝑖′′𝑎𝑖𝑗	𝑘𝑖′′𝑎𝑖𝑗	X
iajs-3409	223	103	=	=	SYM
iajs-3409	223	104	1	1	NUM
iajs-3409	223	105	24	24	NUM
iajs-3409	223	106	(	(	PUNCT
iajs-3409	223	107	63	63	NUM
iajs-3409	223	108	)	)	PUNCT
iajs-3409	223	109	order	order	NOUN
iajs-3409	223	110	5	5	NUM
iajs-3409	223	111	∑	∑	PUNCT
iajs-3409	223	112	𝑘𝑖′′𝑠𝑖	𝑘𝑖′′𝑠𝑖	ADP
iajs-3409	223	113	4	4	NUM
iajs-3409	223	114	=	=	SYM
iajs-3409	223	115	1	1	NUM
iajs-3409	223	116	5	5	NUM
iajs-3409	223	117	,	,	PUNCT
iajs-3409	223	118	∑	∑	ADV
iajs-3409	223	119	𝑘𝑖′′𝑎𝑖𝑗𝑠𝑗	𝑘𝑖′′𝑎𝑖𝑗𝑠𝑗	X
iajs-3409	223	120	=	=	SYM
iajs-3409	223	121	1	1	NUM
iajs-3409	223	122	120	120	NUM
iajs-3409	223	123	,	,	PUNCT
iajs-3409	223	124	∑	∑	PUNCT
iajs-3409	223	125	𝑘𝑖′′𝑠𝑗𝑎𝑖𝑗	𝑘𝑖′′𝑠𝑗𝑎𝑖𝑗	NOUN
iajs-3409	223	126	=	=	SYM
iajs-3409	223	127	1	1	NUM
iajs-3409	223	128	30	30	NUM
iajs-3409	223	129	(	(	PUNCT
iajs-3409	223	130	64	64	NUM
iajs-3409	223	131	)	)	PUNCT
iajs-3409	223	132	order	order	NOUN
iajs-3409	223	133	6	6	NUM
iajs-3409	223	134	∑	∑	PUNCT
iajs-3409	223	135	𝑘𝑖	𝑘𝑖	ADP
iajs-3409	223	136	′′𝑠𝑖	′′𝑠𝑖	PRON
iajs-3409	223	137	2𝑎𝑖𝑗	2𝑎𝑖𝑗	NOUN
iajs-3409	223	138	=	=	SYM
iajs-3409	223	139	1	1	NUM
iajs-3409	223	140	36	36	NUM
iajs-3409	223	141	,	,	PUNCT
iajs-3409	223	142	∑	∑	PROPN
iajs-3409	223	143	𝑘𝑖′′𝑠𝑖	𝑘𝑖′′𝑠𝑖	ADP
iajs-3409	223	144	5	5	NUM
iajs-3409	223	145	=	=	SYM
iajs-3409	223	146	1	1	NUM
iajs-3409	223	147	6	6	NUM
iajs-3409	223	148	,	,	PUNCT
iajs-3409	223	149	∑	∑	PROPN
iajs-3409	223	150	𝑘𝑖′′𝑎𝑖𝑗𝑠𝑗	𝑘𝑖′′𝑎𝑖𝑗𝑠𝑗	ADP
iajs-3409	223	151	2	2	NUM
iajs-3409	223	152	=	=	SYM
iajs-3409	223	153	1	1	NUM
iajs-3409	223	154	360	360	NUM
iajs-3409	223	155	,	,	PUNCT
iajs-3409	223	156	∑	∑	PUNCT
iajs-3409	223	157	𝑘𝑖′′𝑠𝑖𝑎𝑖𝑗𝑠𝑗	𝑘𝑖′′𝑠𝑖𝑎𝑖𝑗𝑠𝑗	NOUN
iajs-3409	223	158	=	=	PUNCT
iajs-3409	223	159	1	1	NUM
iajs-3409	223	160	144	144	NUM
iajs-3409	223	161	(	(	PUNCT
iajs-3409	223	162	65	65	NUM
iajs-3409	223	163	)	)	PUNCT
iajs-3409	223	164	5	5	NUM
iajs-3409	223	165	.	.	PUNCT
iajs-3409	224	1	the	the	DET
iajs-3409	224	2	construction	construction	NOUN
iajs-3409	224	3	of	of	ADP
iajs-3409	224	4	rktdio	rktdio	NOUN
iajs-3409	224	5	method	method	NOUN
iajs-3409	224	6	when	when	SCONJ
iajs-3409	224	7	creating	create	VERB
iajs-3409	224	8	implicit	implicit	ADJ
iajs-3409	224	9	rktdio	rktdio	ADJ
iajs-3409	224	10	methods	method	NOUN
iajs-3409	224	11	,	,	PUNCT
iajs-3409	224	12	the	the	DET
iajs-3409	224	13	order	order	NOUN
iajs-3409	224	14	conditions	condition	NOUN
iajs-3409	224	15	listed	list	VERB
iajs-3409	224	16	in	in	ADP
iajs-3409	224	17	section	section	NOUN
iajs-3409	224	18	3.2	3.2	NUM
iajs-3409	224	19	must	must	AUX
iajs-3409	224	20	be	be	AUX
iajs-3409	224	21	met	meet	VERB
iajs-3409	224	22	.	.	PUNCT
iajs-3409	225	1	for	for	ADP
iajs-3409	225	2	the	the	DET
iajs-3409	225	3	𝑞-order	𝑞-order	NOUN
iajs-3409	225	4	rktdio	rktdio	NOUN
iajs-3409	225	5	method	method	NOUN
iajs-3409	225	6	,	,	PUNCT
iajs-3409	225	7	the	the	DET
iajs-3409	225	8	local	local	ADJ
iajs-3409	225	9	truncated	truncated	ADJ
iajs-3409	225	10	error	error	NOUN
iajs-3409	225	11	is	be	AUX
iajs-3409	225	12	defined	define	VERB
iajs-3409	225	13	as	as	SCONJ
iajs-3409	225	14	follows	follow	VERB
iajs-3409	225	15	:	:	PUNCT
iajs-3409	225	16	‖𝐿𝑔	‖𝐿𝑔	NOUN
iajs-3409	225	17	(	(	PUNCT
iajs-3409	225	18	𝑞+1)‖2	𝑞+1)‖2	ADJ
iajs-3409	225	19	=	=	SYM
iajs-3409	225	20	(	(	PUNCT
iajs-3409	225	21	∑	∑	PUNCT
iajs-3409	225	22	(	(	PUNCT
iajs-3409	225	23	𝐿𝑖	𝐿𝑖	PROPN
iajs-3409	225	24	(	(	PUNCT
iajs-3409	225	25	𝑞+1	𝑞+1	NUM
iajs-3409	225	26	)	)	PUNCT
iajs-3409	225	27	)	)	PUNCT
iajs-3409	225	28	2	2	NUM
iajs-3409	226	1	+	+	CCONJ
iajs-3409	226	2	(	(	PUNCT
iajs-3409	226	3	∑	∑	PROPN
iajs-3409	226	4	(	(	PUNCT
iajs-3409	226	5	𝐿𝑖′	𝐿𝑖′	PROPN
iajs-3409	226	6	(	(	PUNCT
iajs-3409	226	7	𝑞+1	𝑞+1	NUM
iajs-3409	226	8	)	)	PUNCT
iajs-3409	226	9	)	)	PUNCT
iajs-3409	226	10	2	2	NUM
iajs-3409	226	11	+	+	CCONJ
iajs-3409	226	12	(	(	PUNCT
iajs-3409	226	13	∑	∑	INTJ
iajs-3409	226	14	(	(	PUNCT
iajs-3409	226	15	𝐿𝑖′′	𝐿𝑖′′	ADV
iajs-3409	226	16	(	(	PUNCT
iajs-3409	226	17	𝑞+1	𝑞+1	NUM
iajs-3409	226	18	)	)	PUNCT
iajs-3409	226	19	)	)	PUNCT
iajs-3409	226	20	2𝑛′′	2𝑛′′	NUM
iajs-3409	226	21	𝑞+1	𝑞+1	NUM
iajs-3409	226	22	𝑖=1	𝑖=1	PROPN
iajs-3409	226	23	𝑛′	𝑛′	ADP
iajs-3409	226	24	𝑞+1	𝑞+1	SYM
iajs-3409	226	25	𝑖=1	𝑖=1	PROPN
iajs-3409	226	26	𝑛𝑞+1	𝑛𝑞+1	X
iajs-3409	226	27	𝑖=1	𝑖=1	PUNCT
iajs-3409	226	28	(	(	PUNCT
iajs-3409	226	29	66	66	NUM
iajs-3409	226	30	)	)	PUNCT
iajs-3409	226	31	where	where	SCONJ
iajs-3409	226	32	𝐿(𝑞+1	𝐿(𝑞+1	NOUN
iajs-3409	226	33	)	)	PUNCT
iajs-3409	226	34	,	,	PUNCT
iajs-3409	226	35	𝐿′(𝑞+1	𝐿′(𝑞+1	PROPN
iajs-3409	226	36	)	)	PUNCT
iajs-3409	226	37	,	,	PUNCT
iajs-3409	226	38	𝐿′′(𝑞+1	𝐿′′(𝑞+1	NOUN
iajs-3409	226	39	)	)	PUNCT
iajs-3409	226	40	the	the	DET
iajs-3409	226	41	local	local	ADJ
iajs-3409	226	42	truncation	truncation	NOUN
iajs-3409	226	43	error	error	NOUN
iajs-3409	226	44	are	be	AUX
iajs-3409	226	45	terms	term	NOUN
iajs-3409	226	46	respectively	respectively	ADV
iajs-3409	226	47	,	,	PUNCT
iajs-3409	226	48	𝐿𝑔	𝐿𝑔	PROPN
iajs-3409	226	49	(	(	PUNCT
iajs-3409	226	50	𝑞+1	𝑞+1	NUM
iajs-3409	226	51	)	)	PUNCT
iajs-3409	226	52	is	be	AUX
iajs-3409	226	53	the	the	DET
iajs-3409	226	54	global	global	ADJ
iajs-3409	226	55	local	local	ADJ
iajs-3409	226	56	truncation	truncation	NOUN
iajs-3409	226	57	error	error	NOUN
iajs-3409	226	58	.	.	PUNCT
iajs-3409	227	1	5.1	5.1	NUM
iajs-3409	227	2	a	a	DET
iajs-3409	227	3	three	three	NUM
iajs-3409	227	4	-	-	PUNCT
iajs-3409	227	5	stage	stage	NOUN
iajs-3409	227	6	fifth	fifth	ADJ
iajs-3409	227	7	-	-	PUNCT
iajs-3409	227	8	order	order	NOUN
iajs-3409	227	9	rktdio	rktdio	NOUN
iajs-3409	227	10	method	method	NOUN
iajs-3409	227	11	in	in	ADP
iajs-3409	227	12	this	this	DET
iajs-3409	227	13	subsection	subsection	NOUN
iajs-3409	227	14	,	,	PUNCT
iajs-3409	227	15	the	the	DET
iajs-3409	227	16	derivation	derivation	NOUN
iajs-3409	227	17	of	of	ADP
iajs-3409	227	18	the	the	DET
iajs-3409	227	19	three	three	NUM
iajs-3409	227	20	-	-	PUNCT
iajs-3409	227	21	stage	stage	NOUN
iajs-3409	227	22	rktdio	rktdio	NOUN
iajs-3409	227	23	technique	technique	NOUN
iajs-3409	227	24	of	of	ADP
iajs-3409	227	25	order	order	NOUN
iajs-3409	227	26	five	five	NUM
iajs-3409	227	27	by	by	ADP
iajs-3409	227	28	using	use	VERB
iajs-3409	227	29	the	the	DET
iajs-3409	227	30	algebraic	algebraic	ADJ
iajs-3409	227	31	order	order	NOUN
iajs-3409	227	32	conditions	condition	NOUN
iajs-3409	227	33	up	up	ADP
iajs-3409	227	34	to	to	PART
iajs-3409	227	35	order	order	VERB
iajs-3409	227	36	five	five	NUM
iajs-3409	227	37	will	will	AUX
iajs-3409	227	38	be	be	AUX
iajs-3409	227	39	considered	consider	VERB
iajs-3409	227	40	.	.	PUNCT
iajs-3409	228	1	the	the	DET
iajs-3409	228	2	resulting	result	VERB
iajs-3409	228	3	system	system	NOUN
iajs-3409	228	4	consists	consist	VERB
iajs-3409	228	5	of	of	ADP
iajs-3409	228	6	16	16	NUM
iajs-3409	228	7	nonlinear	nonlinear	ADJ
iajs-3409	228	8	equations	equation	NOUN
iajs-3409	228	9	with	with	ADP
iajs-3409	228	10	16	16	NUM
iajs-3409	228	11	unknown	unknown	ADJ
iajs-3409	228	12	variables	variable	NOUN
iajs-3409	228	13	,	,	PUNCT
iajs-3409	228	14	solving	solve	VERB
iajs-3409	228	15	the	the	DET
iajs-3409	228	16	system	system	NOUN
iajs-3409	228	17	simultaneously	simultaneously	ADV
iajs-3409	228	18	,	,	PUNCT
iajs-3409	228	19	and	and	CCONJ
iajs-3409	228	20	assuming	assume	VERB
iajs-3409	228	21	𝑎11	𝑎11	ADJ
iajs-3409	228	22	=	=	SYM
iajs-3409	228	23	𝑎22	𝑎22	NOUN
iajs-3409	228	24	and	and	CCONJ
iajs-3409	228	25	𝑎22	𝑎22	NOUN
iajs-3409	228	26	=	=	PUNCT
iajs-3409	228	27	𝑎33	𝑎33	NOUN
iajs-3409	228	28	𝑎21	𝑎21	NOUN
iajs-3409	228	29	=	=	SYM
iajs-3409	228	30	𝑎21	𝑎21	PROPN
iajs-3409	228	31	,	,	PUNCT
iajs-3409	228	32	𝑎31	𝑎31	NOUN
iajs-3409	228	33	=	=	SYM
iajs-3409	228	34	𝑎21	𝑎21	PROPN
iajs-3409	228	35	,	,	PUNCT
iajs-3409	228	36	𝑎32	𝑎32	NOUN
iajs-3409	228	37	=	=	SYM
iajs-3409	228	38	3	3	NUM
iajs-3409	228	39	20	20	NUM
iajs-3409	229	1	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	229	2	𝑂𝑓	𝑂𝑓	PROPN
iajs-3409	229	3	(	(	PUNCT
iajs-3409	229	4	5	5	NUM
iajs-3409	229	5	−	−	PROPN
iajs-3409	229	6	𝑧2	𝑧2	NOUN
iajs-3409	229	7	−	−	PROPN
iajs-3409	229	8	3	3	NUM
iajs-3409	229	9	)	)	PUNCT
iajs-3409	229	10	,	,	PUNCT
iajs-3409	229	11	𝑎33	𝑎33	VERB
iajs-3409	229	12	=	=	SYM
iajs-3409	229	13	−	−	PROPN
iajs-3409	229	14	5	5	NUM
iajs-3409	229	15	9	9	NUM
iajs-3409	229	16	𝑎21	𝑎21	NOUN
iajs-3409	229	17	−	−	PROPN
iajs-3409	229	18	1	1	NUM
iajs-3409	229	19	24	24	NUM
iajs-3409	229	20	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	229	21	𝑂𝑓(5	𝑂𝑓(5	NOUN
iajs-3409	229	22	−	−	PROPN
iajs-3409	229	23	𝑧2	𝑧2	NOUN
iajs-3409	229	24	−	−	PROPN
iajs-3409	229	25	3	3	NUM
iajs-3409	229	26	)	)	PUNCT
iajs-3409	229	27	+	+	CCONJ
iajs-3409	229	28	1	1	NUM
iajs-3409	229	29	24	24	NUM
iajs-3409	229	30	,	,	PUNCT
iajs-3409	229	31	𝑏1	𝑏1	NOUN
iajs-3409	229	32	=	=	SYM
iajs-3409	229	33	2	2	NUM
iajs-3409	229	34	9	9	NUM
iajs-3409	229	35	,	,	PUNCT
iajs-3409	229	36	𝑏2	𝑏2	NOUN
iajs-3409	229	37	=	=	NOUN
iajs-3409	229	38	1	1	NUM
iajs-3409	229	39	36	36	NUM
iajs-3409	229	40	200	200	NUM
iajs-3409	229	41	𝑎21𝑅𝑜𝑜𝑡	𝑎21𝑅𝑜𝑜𝑡	NOUN
iajs-3409	229	42	𝑂𝑓(5−𝑧2−3)+15𝑅𝑜𝑜𝑡	𝑂𝑓(5−𝑧2−3)+15𝑅𝑜𝑜𝑡	PROPN
iajs-3409	230	1	𝑂𝑓(5−𝑧2−3)+200	𝑂𝑓(5−𝑧2−3)+200	PROPN
iajs-3409	230	2	𝑎21	𝑎21	PROPN
iajs-3409	230	3	+	+	PROPN
iajs-3409	230	4	9	9	NUM
iajs-3409	230	5	40	40	NUM
iajs-3409	230	6	𝑎21	𝑎21	NOUN
iajs-3409	230	7	+	+	PROPN
iajs-3409	230	8	3	3	NUM
iajs-3409	230	9	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	230	10	𝑂𝑓	𝑂𝑓	PROPN
iajs-3409	230	11	(	(	PUNCT
iajs-3409	230	12	5−𝑧2−3	5−𝑧2−3	NUM
iajs-3409	230	13	)	)	PUNCT
iajs-3409	230	14	,	,	PUNCT
iajs-3409	230	15	𝑏3	𝑏3	NOUN
iajs-3409	230	16	=	=	SYM
iajs-3409	230	17	−	−	PROPN
iajs-3409	230	18	1	1	NUM
iajs-3409	230	19	36	36	NUM
iajs-3409	230	20	200	200	NUM
iajs-3409	230	21	𝑎21𝑅𝑜𝑜𝑡	𝑎21𝑅𝑜𝑜𝑡	NOUN
iajs-3409	230	22	𝑂𝑓(5−𝑧2−3)−15𝑅𝑜𝑜𝑡	𝑂𝑓(5−𝑧2−3)−15𝑅𝑜𝑜𝑡	NOUN
iajs-3409	231	1	𝑂𝑓(5−𝑧2−3)+200	𝑂𝑓(5−𝑧2−3)+200	PROPN
iajs-3409	231	2	𝑎21	𝑎21	PROPN
iajs-3409	231	3	+	+	PROPN
iajs-3409	231	4	9	9	NUM
iajs-3409	231	5	40	40	NUM
iajs-3409	231	6	𝑎21	𝑎21	NOUN
iajs-3409	231	7	+	+	PROPN
iajs-3409	231	8	3	3	NUM
iajs-3409	231	9	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	231	10	𝑂𝑓	𝑂𝑓	PROPN
iajs-3409	231	11	(	(	PUNCT
iajs-3409	231	12	5−𝑧2−3	5−𝑧2−3	NUM
iajs-3409	231	13	)	)	PUNCT
iajs-3409	231	14	,	,	PUNCT
iajs-3409	231	15	𝑐1	𝑐1	NOUN
iajs-3409	231	16	=	=	NOUN
iajs-3409	231	17	1	1	NUM
iajs-3409	231	18	2	2	NUM
iajs-3409	231	19	,	,	PUNCT
iajs-3409	231	20	𝑐2	𝑐2	NOUN
iajs-3409	231	21	=	=	SYM
iajs-3409	231	22	1	1	NUM
iajs-3409	231	23	2	2	NUM
iajs-3409	231	24	−	−	NOUN
iajs-3409	231	25	1	1	NUM
iajs-3409	231	26	2	2	NUM
iajs-3409	231	27	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	231	28	𝑂𝑓	𝑂𝑓	PROPN
iajs-3409	231	29	(	(	PUNCT
iajs-3409	231	30	5	5	NUM
iajs-3409	231	31	−	−	NOUN
iajs-3409	231	32	𝑧2	𝑧2	NOUN
iajs-3409	231	33	−	−	PROPN
iajs-3409	231	34	3	3	NUM
iajs-3409	231	35	)	)	PUNCT
iajs-3409	231	36	,	,	PUNCT
iajs-3409	231	37	𝑐3	𝑐3	NOUN
iajs-3409	231	38	=	=	SYM
iajs-3409	231	39	1	1	NUM
iajs-3409	231	40	2	2	NUM
iajs-3409	231	41	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	231	42	𝑂𝑓	𝑂𝑓	PROPN
iajs-3409	231	43	(	(	PUNCT
iajs-3409	231	44	5	5	NUM
iajs-3409	231	45	−	−	NOUN
iajs-3409	231	46	𝑧2	𝑧2	NOUN
iajs-3409	231	47	−	−	NOUN
iajs-3409	231	48	3	3	NUM
iajs-3409	231	49	)	)	PUNCT
iajs-3409	231	50	+	+	CCONJ
iajs-3409	231	51	1	1	NUM
iajs-3409	231	52	2	2	NUM
iajs-3409	231	53	,	,	PUNCT
iajs-3409	231	54	𝑑1	𝑑1	NOUN
iajs-3409	231	55	=	=	SYM
iajs-3409	231	56	1	1	NUM
iajs-3409	231	57	18	18	NUM
iajs-3409	231	58	,	,	PUNCT
iajs-3409	231	59	𝑑2	𝑑2	NOUN
iajs-3409	231	60	=	=	SYM
iajs-3409	231	61	5	5	NUM
iajs-3409	231	62	72	72	NUM
iajs-3409	231	63	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	231	64	𝑂𝑓	𝑂𝑓	PROPN
iajs-3409	231	65	(	(	PUNCT
iajs-3409	231	66	5	5	NUM
iajs-3409	231	67	−	−	NOUN
iajs-3409	231	68	𝑧2	𝑧2	NOUN
iajs-3409	231	69	−	−	NOUN
iajs-3409	231	70	3	3	NUM
iajs-3409	231	71	)	)	PUNCT
iajs-3409	231	72	+	+	CCONJ
iajs-3409	231	73	1	1	NUM
iajs-3409	231	74	18	18	NUM
iajs-3409	231	75	,	,	PUNCT
iajs-3409	231	76	𝑑3	𝑑3	NOUN
iajs-3409	231	77	=	=	SYM
iajs-3409	231	78	−	−	PROPN
iajs-3409	231	79	5	5	NUM
iajs-3409	231	80	72	72	NUM
iajs-3409	231	81	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	231	82	𝑂𝑓	𝑂𝑓	PROPN
iajs-3409	231	83	(	(	PUNCT
iajs-3409	231	84	5	5	NUM
iajs-3409	231	85	−	−	NOUN
iajs-3409	231	86	𝑧2	𝑧2	NOUN
iajs-3409	231	87	−	−	NOUN
iajs-3409	231	88	3	3	NUM
iajs-3409	231	89	)	)	PUNCT
iajs-3409	231	90	+	+	CCONJ
iajs-3409	231	91	1	1	NUM
iajs-3409	231	92	18	18	NUM
iajs-3409	231	93	,	,	PUNCT
iajs-3409	231	94	𝑔1	𝑔1	PROPN
iajs-3409	231	95	=	=	PUNCT
iajs-3409	231	96	4	4	NUM
iajs-3409	231	97	9	9	NUM
iajs-3409	231	98	,	,	PUNCT
iajs-3409	231	99	𝑔2	𝑔2	NOUN
iajs-3409	231	100	=	=	SYM
iajs-3409	231	101	5	5	NUM
iajs-3409	231	102	18	18	NUM
iajs-3409	231	103	,	,	PUNCT
iajs-3409	231	104	𝑔3	𝑔3	VERB
iajs-3409	231	105	=	=	SYM
iajs-3409	231	106	5	5	NUM
iajs-3409	231	107	18	18	NUM
iajs-3409	231	108	.	.	PUNCT
iajs-3409	232	1	next	next	ADV
iajs-3409	232	2	,	,	PUNCT
iajs-3409	232	3	we	we	PRON
iajs-3409	232	4	minimize	minimize	VERB
iajs-3409	232	5	the	the	DET
iajs-3409	232	6	truncation	truncation	NOUN
iajs-3409	232	7	error	error	NOUN
iajs-3409	232	8	term	term	NOUN
iajs-3409	232	9	by	by	ADP
iajs-3409	232	10	using	use	VERB
iajs-3409	232	11	minimize	minimize	VERB
iajs-3409	232	12	command	command	NOUN
iajs-3409	232	13	in	in	ADP
iajs-3409	232	14	maple	maple	NOUN
iajs-3409	232	15	.	.	PUNCT
iajs-3409	233	1	thus	thus	ADV
iajs-3409	233	2	,	,	PUNCT
iajs-3409	233	3	for	for	ADP
iajs-3409	233	4	the	the	DET
iajs-3409	233	5	optimized	optimize	VERB
iajs-3409	233	6	value	value	NOUN
iajs-3409	233	7	of	of	ADP
iajs-3409	233	8	coefficients	coefficient	NOUN
iajs-3409	233	9	in	in	ADP
iajs-3409	233	10	fractional	fractional	ADJ
iajs-3409	233	11	we	we	PRON
iajs-3409	233	12	chose	choose	VERB
iajs-3409	233	13	𝑎21	𝑎21	NOUN
iajs-3409	233	14	=	=	SYM
iajs-3409	233	15	−	−	PROPN
iajs-3409	233	16	1	1	NUM
iajs-3409	233	17	125	125	NUM
iajs-3409	233	18	with	with	ADP
iajs-3409	233	19	this	this	DET
iajs-3409	233	20	value	value	NOUN
iajs-3409	233	21	‖𝜋𝑔	‖𝜋𝑔	NUM
iajs-3409	233	22	(	(	PUNCT
iajs-3409	233	23	5)‖	5)‖	NUM
iajs-3409	233	24	2	2	NUM
iajs-3409	233	25	=	=	NOUN
iajs-3409	233	26	ihjpas	ihjpa	NOUN
iajs-3409	233	27	.	.	PUNCT
iajs-3409	234	1	37	37	NUM
iajs-3409	234	2	(	(	PUNCT
iajs-3409	234	3	2	2	NUM
iajs-3409	234	4	)	)	PUNCT
iajs-3409	234	5	2024	2024	NUM
iajs-3409	234	6	398	398	NUM
iajs-3409	234	7	0.001366343866	0.001366343866	NUM
iajs-3409	234	8	.	.	PUNCT
iajs-3409	235	1	finally	finally	ADV
iajs-3409	235	2	,	,	PUNCT
iajs-3409	235	3	all	all	DET
iajs-3409	235	4	the	the	DET
iajs-3409	235	5	parameters	parameter	NOUN
iajs-3409	235	6	of	of	ADP
iajs-3409	235	7	three	three	NUM
iajs-3409	235	8	-	-	PUNCT
iajs-3409	235	9	stage	stage	NOUN
iajs-3409	235	10	fifth	fifth	ADJ
iajs-3409	235	11	-	-	PUNCT
iajs-3409	235	12	order	order	NOUN
iajs-3409	235	13	rktdio	rktdio	NOUN
iajs-3409	235	14	approach	approach	NOUN
iajs-3409	235	15	that	that	PRON
iajs-3409	235	16	will	will	AUX
iajs-3409	235	17	be	be	AUX
iajs-3409	235	18	denoted	denote	VERB
iajs-3409	235	19	as	as	ADP
iajs-3409	235	20	rktdio5	rktdio5	NOUN
iajs-3409	235	21	can	can	AUX
iajs-3409	235	22	be	be	AUX
iajs-3409	235	23	written	write	VERB
iajs-3409	235	24	as	as	SCONJ
iajs-3409	235	25	follows	follow	VERB
iajs-3409	235	26	(	(	PUNCT
iajs-3409	235	27	see	see	VERB
iajs-3409	235	28	table	table	NOUN
iajs-3409	235	29	2	2	NUM
iajs-3409	235	30	):	):	PUNCT
iajs-3409	235	31	table	table	NOUN
iajs-3409	235	32	2	2	NUM
iajs-3409	235	33	.	.	PUNCT
iajs-3409	236	1	the	the	DET
iajs-3409	236	2	rktdio5	rktdio5	PROPN
iajs-3409	236	3	method	method	NOUN
iajs-3409	236	4	1	1	NUM
iajs-3409	236	5	2	2	NUM
iajs-3409	236	6	83	83	NUM
iajs-3409	236	7	1800	1800	NUM
iajs-3409	236	8	−	−	NOUN
iajs-3409	237	1	√15	√15	PROPN
iajs-3409	237	2	120	120	NUM
iajs-3409	237	3	1	1	NUM
iajs-3409	237	4	2	2	NUM
iajs-3409	237	5	−	−	NOUN
iajs-3409	237	6	√15	√15	PROPN
iajs-3409	237	7	10	10	NUM
iajs-3409	238	1	−	−	NOUN
iajs-3409	238	2	1	1	NUM
iajs-3409	238	3	125	125	NUM
iajs-3409	238	4	83	83	NUM
iajs-3409	238	5	1800	1800	NUM
iajs-3409	238	6	−	−	NOUN
iajs-3409	238	7	√15	√15	PROPN
iajs-3409	238	8	120	120	NUM
iajs-3409	238	9	1	1	NUM
iajs-3409	238	10	2	2	NUM
iajs-3409	238	11	+	+	CCONJ
iajs-3409	238	12	√15	√15	PROPN
iajs-3409	239	1	10	10	NUM
iajs-3409	239	2	−	−	NOUN
iajs-3409	239	3	1	1	NUM
iajs-3409	239	4	125	125	NUM
iajs-3409	239	5	3√15	3√15	NUM
iajs-3409	239	6	100	100	NUM
iajs-3409	239	7	83	83	NUM
iajs-3409	239	8	1800	1800	NUM
iajs-3409	239	9	−	−	NOUN
iajs-3409	239	10	√15	√15	PROPN
iajs-3409	239	11	120	120	NUM
iajs-3409	239	12	1	1	NUM
iajs-3409	239	13	18	18	NUM
iajs-3409	239	14	1	1	NUM
iajs-3409	239	15	18	18	NUM
iajs-3409	239	16	+	+	CCONJ
iajs-3409	239	17	√15	√15	PROPN
iajs-3409	239	18	72	72	NUM
iajs-3409	239	19	1	1	NUM
iajs-3409	239	20	18	18	NUM
iajs-3409	239	21	−	−	NOUN
iajs-3409	239	22	√15	√15	PROPN
iajs-3409	239	23	72	72	NUM
iajs-3409	239	24	2	2	NUM
iajs-3409	239	25	9	9	NUM
iajs-3409	239	26	5	5	NUM
iajs-3409	239	27	36	36	NUM
iajs-3409	239	28	+	+	CCONJ
iajs-3409	239	29	√15	√15	PROPN
iajs-3409	239	30	36	36	NUM
iajs-3409	239	31	5	5	NUM
iajs-3409	239	32	36	36	NUM
iajs-3409	239	33	−	−	NOUN
iajs-3409	239	34	√15	√15	PROPN
iajs-3409	239	35	36	36	NUM
iajs-3409	239	36	4	4	NUM
iajs-3409	239	37	9	9	NUM
iajs-3409	239	38	5	5	NUM
iajs-3409	239	39	18	18	NUM
iajs-3409	239	40	5	5	NUM
iajs-3409	239	41	18	18	NUM
iajs-3409	239	42	5.2	5.2	NUM
iajs-3409	239	43	a	a	DET
iajs-3409	239	44	four	four	NUM
iajs-3409	239	45	-	-	PUNCT
iajs-3409	239	46	stage	stage	NOUN
iajs-3409	239	47	rdtdio	rdtdio	NOUN
iajs-3409	239	48	method	method	NOUN
iajs-3409	239	49	of	of	ADP
iajs-3409	239	50	order	order	NOUN
iajs-3409	239	51	six	six	NUM
iajs-3409	239	52	for	for	ADP
iajs-3409	239	53	the	the	DET
iajs-3409	239	54	four	four	NUM
iajs-3409	239	55	-	-	PUNCT
iajs-3409	239	56	stage	stage	NOUN
iajs-3409	239	57	rktdio	rktdio	NOUN
iajs-3409	239	58	technique	technique	NOUN
iajs-3409	239	59	of	of	ADP
iajs-3409	239	60	order	order	NOUN
iajs-3409	239	61	six	six	NUM
iajs-3409	239	62	,	,	PUNCT
iajs-3409	239	63	the	the	DET
iajs-3409	239	64	algebraic	algebraic	ADJ
iajs-3409	239	65	conditions	condition	NOUN
iajs-3409	239	66	up	up	ADP
iajs-3409	239	67	to	to	PART
iajs-3409	239	68	order	order	VERB
iajs-3409	239	69	six	six	NUM
iajs-3409	239	70	will	will	AUX
iajs-3409	239	71	be	be	AUX
iajs-3409	239	72	solved	solve	VERB
iajs-3409	239	73	.	.	PUNCT
iajs-3409	240	1	the	the	DET
iajs-3409	240	2	resulting	result	VERB
iajs-3409	240	3	system	system	NOUN
iajs-3409	240	4	consists	consist	VERB
iajs-3409	240	5	of	of	ADP
iajs-3409	240	6	25	25	NUM
iajs-3409	240	7	nonlinear	nonlinear	ADJ
iajs-3409	240	8	equations	equation	NOUN
iajs-3409	240	9	with	with	ADP
iajs-3409	240	10	23	23	NUM
iajs-3409	240	11	unknown	unknown	ADJ
iajs-3409	240	12	variables	variable	NOUN
iajs-3409	240	13	,	,	PUNCT
iajs-3409	240	14	and	and	CCONJ
iajs-3409	240	15	using	use	VERB
iajs-3409	240	16	simplifying	simplify	VERB
iajs-3409	240	17	assumption	assumption	NOUN
iajs-3409	240	18	𝑏𝑖	𝑏𝑖	ADP
iajs-3409	240	19	′	′	NOUN
iajs-3409	240	20	=	=	PUNCT
iajs-3409	241	1	𝑏𝑖	𝑏𝑖	ADP
iajs-3409	241	2	′′(1	′′(1	PRON
iajs-3409	241	3	−	−	PROPN
iajs-3409	241	4	𝑐𝑖	𝑐𝑖	NOUN
iajs-3409	241	5	)	)	PUNCT
iajs-3409	241	6	,	,	PUNCT
iajs-3409	241	7	𝑖	𝑖	NOUN
iajs-3409	241	8	=	=	SYM
iajs-3409	241	9	1	1	NUM
iajs-3409	241	10	,	,	PUNCT
iajs-3409	241	11	…	…	PUNCT
iajs-3409	241	12	,	,	PUNCT
iajs-3409	241	13	𝑠	𝑠	INTJ
iajs-3409	241	14	,	,	PUNCT
iajs-3409	241	15	and	and	CCONJ
iajs-3409	241	16	supposing	suppose	VERB
iajs-3409	241	17	𝑏2	𝑏2	PROPN
iajs-3409	241	18	′′	′′	PROPN
iajs-3409	241	19	=	=	SYM
iajs-3409	241	20	0	0	NUM
iajs-3409	241	21	,	,	PUNCT
iajs-3409	241	22	and	and	CCONJ
iajs-3409	241	23	𝑏2	𝑏2	PROPN
iajs-3409	241	24	′′′	′′′	PROPN
iajs-3409	242	1	=	=	SYM
iajs-3409	242	2	0	0	NUM
iajs-3409	242	3	𝑎21	𝑎21	NOUN
iajs-3409	242	4	=	=	SYM
iajs-3409	242	5	3	3	NUM
iajs-3409	242	6	20	20	NUM
iajs-3409	242	7	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	242	8	𝑂𝑓	𝑂𝑓	PROPN
iajs-3409	242	9	(	(	PUNCT
iajs-3409	242	10	10	10	NUM
iajs-3409	242	11	−	−	PROPN
iajs-3409	242	12	𝑧2	𝑧2	NOUN
iajs-3409	242	13	−	−	PROPN
iajs-3409	242	14	10	10	NUM
iajs-3409	242	15	−	−	NOUN
iajs-3409	242	16	𝑧	𝑧	PROPN
iajs-3409	242	17	+	+	ADJ
iajs-3409	242	18	1	1	NUM
iajs-3409	242	19	)	)	PUNCT
iajs-3409	242	20	−	−	PROPN
iajs-3409	242	21	3	3	NUM
iajs-3409	242	22	80	80	NUM
iajs-3409	242	23	,	,	PUNCT
iajs-3409	242	24	𝑎31	𝑎31	NOUN
iajs-3409	242	25	=	=	SYM
iajs-3409	242	26	−	−	PROPN
iajs-3409	242	27	1	1	NUM
iajs-3409	242	28	40	40	NUM
iajs-3409	242	29	,	,	PUNCT
iajs-3409	242	30	𝑎32	𝑎32	NOUN
iajs-3409	242	31	=	=	SYM
iajs-3409	242	32	11	11	NUM
iajs-3409	242	33	80	80	NUM
iajs-3409	242	34	−	−	NOUN
iajs-3409	242	35	3	3	NUM
iajs-3409	242	36	20	20	NUM
iajs-3409	242	37	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	242	38	𝑂𝑓(10	𝑂𝑓(10	NUM
iajs-3409	243	1	−	−	PROPN
iajs-3409	244	1	𝑧2	𝑧2	NOUN
iajs-3409	244	2	−	−	PROPN
iajs-3409	244	3	10	10	NUM
iajs-3409	244	4	−	−	NOUN
iajs-3409	244	5	𝑧	𝑧	PROPN
iajs-3409	244	6	+	+	ADJ
iajs-3409	244	7	1	1	NUM
iajs-3409	244	8	)	)	PUNCT
iajs-3409	244	9	,	,	PUNCT
iajs-3409	244	10	𝑎41	𝑎41	NOUN
iajs-3409	244	11	=	=	SYM
iajs-3409	244	12	1	1	NUM
iajs-3409	244	13	40	40	NUM
iajs-3409	244	14	,	,	PUNCT
iajs-3409	244	15	𝑎42	𝑎42	NOUN
iajs-3409	244	16	=	=	SYM
iajs-3409	244	17	−	−	PROPN
iajs-3409	244	18	1	1	NUM
iajs-3409	244	19	40	40	NUM
iajs-3409	244	20	,	,	PUNCT
iajs-3409	244	21	𝑎43	𝑎43	ADJ
iajs-3409	244	22	=	=	SYM
iajs-3409	244	23	3	3	NUM
iajs-3409	244	24	20	20	NUM
iajs-3409	244	25	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	244	26	𝑂𝑓(10	𝑂𝑓(10	NUM
iajs-3409	245	1	−	−	PROPN
iajs-3409	246	1	𝑧2	𝑧2	NOUN
iajs-3409	246	2	−	−	PROPN
iajs-3409	246	3	10	10	NUM
iajs-3409	246	4	−	−	NOUN
iajs-3409	246	5	𝑧	𝑧	PROPN
iajs-3409	246	6	+	+	ADJ
iajs-3409	246	7	1	1	NUM
iajs-3409	246	8	)	)	PUNCT
iajs-3409	246	9	−	−	PROPN
iajs-3409	246	10	3	3	NUM
iajs-3409	246	11	80	80	NUM
iajs-3409	246	12	,	,	PUNCT
iajs-3409	246	13	𝑎44	𝑎44	NOUN
iajs-3409	246	14	=	=	SYM
iajs-3409	246	15	1	1	NUM
iajs-3409	246	16	48	48	NUM
iajs-3409	246	17	,	,	PUNCT
iajs-3409	246	18	𝑏1	𝑏1	NOUN
iajs-3409	246	19	=	=	SYM
iajs-3409	246	20	2	2	NUM
iajs-3409	246	21	9	9	NUM
iajs-3409	246	22	,	,	PUNCT
iajs-3409	246	23	𝑏2	𝑏2	NOUN
iajs-3409	246	24	=	=	SYM
iajs-3409	246	25	0	0	NUM
iajs-3409	246	26	,	,	PUNCT
iajs-3409	246	27	𝑏3	𝑏3	NOUN
iajs-3409	246	28	=	=	SYM
iajs-3409	246	29	5	5	NUM
iajs-3409	246	30	18	18	NUM
iajs-3409	246	31	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	246	32	𝑂𝑓(10	𝑂𝑓(10	PUNCT
iajs-3409	247	1	−	−	PROPN
iajs-3409	248	1	𝑧2	𝑧2	NOUN
iajs-3409	248	2	−	−	PROPN
iajs-3409	248	3	10	10	NUM
iajs-3409	248	4	−	−	NOUN
iajs-3409	248	5	𝑧	𝑧	PROPN
iajs-3409	248	6	+	+	ADJ
iajs-3409	248	7	1	1	NUM
iajs-3409	248	8	)	)	PUNCT
iajs-3409	249	1	,	,	PUNCT
iajs-3409	249	2	𝑏4	𝑏4	PROPN
iajs-3409	249	3	=	=	PUNCT
iajs-3409	249	4	−	−	PROPN
iajs-3409	249	5	5	5	NUM
iajs-3409	249	6	18	18	NUM
iajs-3409	249	7	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	249	8	𝑂𝑓(10	𝑂𝑓(10	PUNCT
iajs-3409	250	1	−	−	PROPN
iajs-3409	251	1	𝑧2	𝑧2	NOUN
iajs-3409	251	2	−	−	PROPN
iajs-3409	251	3	10	10	NUM
iajs-3409	251	4	−	−	NOUN
iajs-3409	251	5	𝑧	𝑧	PROPN
iajs-3409	251	6	+	+	NOUN
iajs-3409	251	7	1	1	NUM
iajs-3409	251	8	)	)	PUNCT
iajs-3409	251	9	+	+	CCONJ
iajs-3409	251	10	5	5	NUM
iajs-3409	251	11	36	36	NUM
iajs-3409	251	12	,	,	PUNCT
iajs-3409	251	13	𝑐1	𝑐1	NOUN
iajs-3409	251	14	=	=	NOUN
iajs-3409	251	15	1	1	NUM
iajs-3409	251	16	2	2	NUM
iajs-3409	251	17	,	,	PUNCT
iajs-3409	251	18	𝑐2	𝑐2	NOUN
iajs-3409	251	19	=	=	SYM
iajs-3409	251	20	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	251	21	𝑂𝑓(10	𝑂𝑓(10	PUNCT
iajs-3409	252	1	−	−	PRON
iajs-3409	252	2	𝑧2	𝑧2	NOUN
iajs-3409	252	3	−	−	PROPN
iajs-3409	252	4	10	10	NUM
iajs-3409	252	5	−	−	NOUN
iajs-3409	252	6	𝑧	𝑧	PROPN
iajs-3409	252	7	+	+	ADJ
iajs-3409	252	8	1	1	NUM
iajs-3409	252	9	)	)	PUNCT
iajs-3409	252	10	,	,	PUNCT
iajs-3409	252	11	𝑐3	𝑐3	NOUN
iajs-3409	252	12	=	=	SYM
iajs-3409	252	13	1	1	NUM
iajs-3409	252	14	−	−	PROPN
iajs-3409	252	15	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	252	16	𝑂𝑓(10	𝑂𝑓(10	PUNCT
iajs-3409	253	1	−	−	PROPN
iajs-3409	253	2	𝑧2	𝑧2	NOUN
iajs-3409	253	3	−	−	PROPN
iajs-3409	253	4	10	10	NUM
iajs-3409	253	5	−	−	NOUN
iajs-3409	253	6	𝑧	𝑧	PROPN
iajs-3409	253	7	+	+	ADJ
iajs-3409	253	8	1	1	NUM
iajs-3409	253	9	)	)	PUNCT
iajs-3409	253	10	,	,	PUNCT
iajs-3409	254	1	𝑐4	𝑐4	NOUN
iajs-3409	254	2	=	=	SYM
iajs-3409	254	3	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	254	4	𝑂𝑓(10	𝑂𝑓(10	PUNCT
iajs-3409	255	1	−	−	PRON
iajs-3409	255	2	𝑧2	𝑧2	NOUN
iajs-3409	255	3	−	−	PROPN
iajs-3409	255	4	10	10	NUM
iajs-3409	255	5	−	−	NOUN
iajs-3409	255	6	𝑧	𝑧	PROPN
iajs-3409	255	7	+	+	ADJ
iajs-3409	255	8	1	1	NUM
iajs-3409	255	9	)	)	PUNCT
iajs-3409	255	10	,	,	PUNCT
iajs-3409	255	11	𝑑1	𝑑1	NOUN
iajs-3409	255	12	=	=	SYM
iajs-3409	255	13	1	1	NUM
iajs-3409	255	14	18	18	NUM
iajs-3409	255	15	,	,	PUNCT
iajs-3409	255	16	𝑑2	𝑑2	NOUN
iajs-3409	255	17	=	=	PUNCT
iajs-3409	255	18	𝑑2	𝑑2	NOUN
iajs-3409	255	19	,	,	PUNCT
iajs-3409	255	20	𝑑3	𝑑3	NOUN
iajs-3409	255	21	=	=	SYM
iajs-3409	255	22	5	5	NUM
iajs-3409	255	23	36	36	NUM
iajs-3409	255	24	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	255	25	𝑂𝑓(10	𝑂𝑓(10	PUNCT
iajs-3409	256	1	−	−	PROPN
iajs-3409	257	1	𝑧2	𝑧2	NOUN
iajs-3409	257	2	−	−	PROPN
iajs-3409	257	3	10	10	NUM
iajs-3409	257	4	−	−	NOUN
iajs-3409	257	5	𝑧	𝑧	PROPN
iajs-3409	257	6	+	+	ADJ
iajs-3409	257	7	1	1	NUM
iajs-3409	257	8	)	)	PUNCT
iajs-3409	257	9	−	−	PROPN
iajs-3409	257	10	1	1	NUM
iajs-3409	257	11	72	72	NUM
iajs-3409	257	12	,	,	PUNCT
iajs-3409	257	13	𝑑4	𝑑4	ADV
iajs-3409	257	14	=	=	PUNCT
iajs-3409	257	15	−𝑑2	−𝑑2	NOUN
iajs-3409	257	16	−	−	NOUN
iajs-3409	257	17	5	5	NUM
iajs-3409	257	18	36	36	NUM
iajs-3409	257	19	𝑅𝑜𝑜𝑡	𝑅𝑜𝑜𝑡	PROPN
iajs-3409	257	20	𝑂𝑓(10	𝑂𝑓(10	PUNCT
iajs-3409	258	1	−	−	PROPN
iajs-3409	259	1	𝑧2	𝑧2	NOUN
iajs-3409	259	2	−	−	PROPN
iajs-3409	259	3	10	10	NUM
iajs-3409	259	4	−	−	NOUN
iajs-3409	259	5	𝑧	𝑧	PROPN
iajs-3409	259	6	+	+	ADJ
iajs-3409	259	7	1	1	NUM
iajs-3409	259	8	)	)	PUNCT
iajs-3409	259	9	−	−	PROPN
iajs-3409	259	10	1	1	NUM
iajs-3409	259	11	8	8	NUM
iajs-3409	259	12	,	,	PUNCT
iajs-3409	259	13	𝑔1	𝑔1	PROPN
iajs-3409	259	14	=	=	PUNCT
iajs-3409	259	15	4	4	NUM
iajs-3409	259	16	9	9	NUM
iajs-3409	259	17	,	,	PUNCT
iajs-3409	259	18	𝑔2	𝑔2	NOUN
iajs-3409	259	19	=	=	SYM
iajs-3409	259	20	0	0	NUM
iajs-3409	259	21	,	,	PUNCT
iajs-3409	259	22	𝑔3	𝑔3	VERB
iajs-3409	259	23	=	=	SYM
iajs-3409	259	24	5	5	NUM
iajs-3409	259	25	18	18	NUM
iajs-3409	259	26	,	,	PUNCT
iajs-3409	259	27	𝑔4	𝑔4	NOUN
iajs-3409	259	28	=	=	NOUN
iajs-3409	259	29	5	5	NUM
iajs-3409	259	30	18	18	NUM
iajs-3409	259	31	lastly	lastly	ADV
iajs-3409	259	32	,	,	PUNCT
iajs-3409	259	33	all	all	DET
iajs-3409	259	34	the	the	DET
iajs-3409	259	35	parameters	parameter	NOUN
iajs-3409	259	36	of	of	ADP
iajs-3409	259	37	four	four	NUM
iajs-3409	259	38	-	-	PUNCT
iajs-3409	259	39	stage	stage	NOUN
iajs-3409	259	40	sixth	sixth	ADJ
iajs-3409	259	41	-	-	PUNCT
iajs-3409	259	42	order	order	NOUN
iajs-3409	259	43	rktdio	rktdio	NOUN
iajs-3409	259	44	method	method	NOUN
iajs-3409	259	45	indicated	indicate	VERB
iajs-3409	259	46	by	by	ADP
iajs-3409	259	47	rktdio6	rktdio6	NOUN
iajs-3409	259	48	can	can	AUX
iajs-3409	259	49	be	be	AUX
iajs-3409	259	50	written	write	VERB
iajs-3409	259	51	as	as	SCONJ
iajs-3409	259	52	follows	follow	VERB
iajs-3409	259	53	:	:	PUNCT
iajs-3409	259	54	table	table	NOUN
iajs-3409	259	55	3	3	NUM
iajs-3409	259	56	.	.	PUNCT
iajs-3409	260	1	the	the	DET
iajs-3409	260	2	rktdio6	rktdio6	NOUN
iajs-3409	260	3	method	method	NOUN
iajs-3409	260	4	.	.	PUNCT
iajs-3409	261	1	1	1	NUM
iajs-3409	261	2	2	2	NUM
iajs-3409	261	3	1	1	NUM
iajs-3409	261	4	48	48	NUM
iajs-3409	261	5	1	1	NUM
iajs-3409	261	6	2	2	NUM
iajs-3409	261	7	−	−	NOUN
iajs-3409	261	8	√15	√15	PROPN
iajs-3409	261	9	10	10	NUM
iajs-3409	261	10	3	3	NUM
iajs-3409	261	11	80	80	NUM
iajs-3409	261	12	−	−	NUM
iajs-3409	261	13	3√15	3√15	NUM
iajs-3409	261	14	200	200	NUM
iajs-3409	261	15	1	1	NUM
iajs-3409	261	16	48	48	NUM
iajs-3409	261	17	1	1	NUM
iajs-3409	261	18	2	2	NUM
iajs-3409	261	19	+	+	CCONJ
iajs-3409	261	20	√15	√15	PROPN
iajs-3409	262	1	10	10	NUM
iajs-3409	262	2	−	−	NOUN
iajs-3409	262	3	1	1	NUM
iajs-3409	262	4	40	40	NUM
iajs-3409	262	5	1	1	NUM
iajs-3409	262	6	16	16	NUM
iajs-3409	262	7	+	+	CCONJ
iajs-3409	262	8	3√15	3√15	NUM
iajs-3409	262	9	200	200	NUM
iajs-3409	262	10	1	1	NUM
iajs-3409	262	11	48	48	NUM
iajs-3409	262	12	1	1	NUM
iajs-3409	262	13	2	2	NUM
iajs-3409	262	14	−	−	NOUN
iajs-3409	262	15	√15	√15	PROPN
iajs-3409	262	16	10	10	NUM
iajs-3409	262	17	1	1	NUM
iajs-3409	262	18	40	40	NUM
iajs-3409	262	19	−	−	NOUN
iajs-3409	262	20	1	1	NUM
iajs-3409	262	21	40	40	NUM
iajs-3409	262	22	3	3	NUM
iajs-3409	262	23	80	80	NUM
iajs-3409	262	24	−	−	NUM
iajs-3409	263	1	3√15	3√15	NUM
iajs-3409	263	2	200	200	NUM
iajs-3409	263	3	1	1	NUM
iajs-3409	263	4	18	18	NUM
iajs-3409	263	5	+	+	CCONJ
iajs-3409	263	6	√15	√15	PROPN
iajs-3409	263	7	72	72	NUM
iajs-3409	263	8	ihjpas	ihjpa	NOUN
iajs-3409	263	9	.	.	PUNCT
iajs-3409	264	1	37	37	NUM
iajs-3409	264	2	(	(	PUNCT
iajs-3409	264	3	2	2	NUM
iajs-3409	264	4	)	)	PUNCT
iajs-3409	264	5	2024	2024	NUM
iajs-3409	264	6	399	399	NUM
iajs-3409	264	7	1	1	NUM
iajs-3409	264	8	18	18	NUM
iajs-3409	264	9	0	0	NUM
iajs-3409	264	10	1	1	NUM
iajs-3409	264	11	18	18	NUM
iajs-3409	264	12	−	−	NOUN
iajs-3409	264	13	√15	√15	PROPN
iajs-3409	264	14	72	72	NUM
iajs-3409	264	15	1	1	NUM
iajs-3409	264	16	18	18	NUM
iajs-3409	264	17	−	−	NOUN
iajs-3409	264	18	√15	√15	PROPN
iajs-3409	264	19	72	72	NUM
iajs-3409	264	20	2	2	NUM
iajs-3409	264	21	9	9	NUM
iajs-3409	264	22	0	0	NUM
iajs-3409	264	23	5	5	NUM
iajs-3409	264	24	36	36	NUM
iajs-3409	264	25	−	−	NOUN
iajs-3409	264	26	√15	√15	PROPN
iajs-3409	264	27	36	36	NUM
iajs-3409	264	28	5	5	NUM
iajs-3409	264	29	36	36	NUM
iajs-3409	264	30	+	+	CCONJ
iajs-3409	264	31	√15	√15	PROPN
iajs-3409	264	32	36	36	NUM
iajs-3409	264	33	4	4	NUM
iajs-3409	264	34	9	9	NUM
iajs-3409	264	35	0	0	NUM
iajs-3409	264	36	5	5	NUM
iajs-3409	264	37	18	18	NUM
iajs-3409	264	38	5	5	NUM
iajs-3409	264	39	18	18	NUM
iajs-3409	264	40	6	6	NUM
iajs-3409	264	41	.	.	PUNCT
iajs-3409	265	1	derivation	derivation	NOUN
iajs-3409	265	2	embedded	embed	VERB
iajs-3409	265	3	erktdio6(5	erktdio6(5	PROPN
iajs-3409	265	4	)	)	PUNCT
iajs-3409	265	5	method	method	NOUN
iajs-3409	265	6	the	the	DET
iajs-3409	265	7	rktdio	rktdio	NOUN
iajs-3409	265	8	method	method	NOUN
iajs-3409	265	9	with	with	ADP
iajs-3409	265	10	𝔰-stages	𝔰-stage	NOUN
iajs-3409	265	11	for	for	ADP
iajs-3409	265	12	solving	solve	VERB
iajs-3409	265	13	equation	equation	NOUN
iajs-3409	265	14	(	(	PUNCT
iajs-3409	265	15	1	1	X
iajs-3409	265	16	)	)	PUNCT
iajs-3409	265	17	is	be	AUX
iajs-3409	265	18	presented	present	VERB
iajs-3409	265	19	in	in	ADP
iajs-3409	265	20	its	its	PRON
iajs-3409	265	21	general	general	ADJ
iajs-3409	265	22	form	form	NOUN
iajs-3409	265	23	.	.	PUNCT
iajs-3409	266	1	subsequently	subsequently	ADV
iajs-3409	266	2	,	,	PUNCT
iajs-3409	266	3	the	the	DET
iajs-3409	266	4	development	development	NOUN
iajs-3409	266	5	of	of	ADP
iajs-3409	266	6	the	the	DET
iajs-3409	266	7	embedded	embed	VERB
iajs-3409	266	8	pair	pair	NOUN
iajs-3409	266	9	rk	rk	NOUN
iajs-3409	266	10	approach	approach	NOUN
iajs-3409	266	11	is	be	AUX
iajs-3409	266	12	discussed	discuss	VERB
iajs-3409	266	13	,	,	PUNCT
iajs-3409	266	14	which	which	PRON
iajs-3409	266	15	is	be	AUX
iajs-3409	266	16	an	an	DET
iajs-3409	266	17	area	area	NOUN
iajs-3409	266	18	of	of	ADP
iajs-3409	266	19	active	active	ADJ
iajs-3409	266	20	research	research	NOUN
iajs-3409	266	21	aimed	aim	VERB
iajs-3409	266	22	at	at	ADP
iajs-3409	266	23	improving	improve	VERB
iajs-3409	266	24	existing	exist	VERB
iajs-3409	266	25	codes	code	NOUN
iajs-3409	266	26	.	.	PUNCT
iajs-3409	267	1	to	to	PART
iajs-3409	267	2	estimate	estimate	VERB
iajs-3409	267	3	the	the	DET
iajs-3409	267	4	minimum	minimum	NOUN
iajs-3409	267	5	error	error	NOUN
iajs-3409	267	6	,	,	PUNCT
iajs-3409	267	7	implicit	implicit	ADJ
iajs-3409	267	8	rktdio	rktdio	NOUN
iajs-3409	267	9	techniques	technique	NOUN
iajs-3409	267	10	are	be	AUX
iajs-3409	267	11	used	use	VERB
iajs-3409	267	12	,	,	PUNCT
iajs-3409	267	13	employing	employ	VERB
iajs-3409	267	14	pairs	pair	NOUN
iajs-3409	267	15	of	of	ADP
iajs-3409	267	16	𝒫(𝒬	𝒫(𝒬	NOUN
iajs-3409	267	17	)	)	PUNCT
iajs-3409	267	18	orders	order	NOUN
iajs-3409	267	19	in	in	ADP
iajs-3409	267	20	the	the	DET
iajs-3409	267	21	values	value	NOUN
iajs-3409	267	22	of	of	ADP
iajs-3409	267	23	step	step	NOUN
iajs-3409	267	24	size	size	NOUN
iajs-3409	267	25	codes	code	NOUN
iajs-3409	267	26	.	.	PUNCT
iajs-3409	268	1	these	these	DET
iajs-3409	268	2	methods	method	NOUN
iajs-3409	268	3	are	be	AUX
iajs-3409	268	4	based	base	VERB
iajs-3409	268	5	on	on	ADP
iajs-3409	268	6	the	the	DET
iajs-3409	268	7	𝒫-order	𝒫-order	PROPN
iajs-3409	268	8	method	method	NOUN
iajs-3409	268	9	(	(	PUNCT
iajs-3409	268	10	𝐶	𝐶	PROPN
iajs-3409	268	11	,	,	PUNCT
iajs-3409	268	12	𝐴	𝐴	PROPN
iajs-3409	268	13	,	,	PUNCT
iajs-3409	268	14	𝑏	𝑏	PROPN
iajs-3409	268	15	,	,	PUNCT
iajs-3409	268	16	𝑏′	𝑏′	PROPN
iajs-3409	268	17	,	,	PUNCT
iajs-3409	268	18	𝑏′′	𝑏′′	NOUN
iajs-3409	268	19	)	)	PUNCT
iajs-3409	268	20	and	and	CCONJ
iajs-3409	268	21	the	the	DET
iajs-3409	268	22	𝒬-order	𝒬-order	PROPN
iajs-3409	268	23	method	method	NOUN
iajs-3409	268	24	(	(	PUNCT
iajs-3409	268	25	𝐶	𝐶	PROPN
iajs-3409	268	26	,	,	PUNCT
iajs-3409	268	27	𝐴	𝐴	PROPN
iajs-3409	268	28	,	,	PUNCT
iajs-3409	268	29	�	�	PROPN
iajs-3409	268	30	̈	̈	X
iajs-3409	268	31	�	�	PROPN
iajs-3409	268	32	,	,	PUNCT
iajs-3409	268	33	�	�	PROPN
iajs-3409	268	34	̈	̈	X
iajs-3409	268	35	�	�	NOUN
iajs-3409	268	36	′	′	NUM
iajs-3409	268	37	,	,	PUNCT
iajs-3409	268	38	�	�	PROPN
iajs-3409	268	39	̈	̈	X
iajs-3409	268	40	�	�	PROPN
iajs-3409	268	41	′′	′′	PROPN
iajs-3409	268	42	)	)	PUNCT
iajs-3409	268	43	,	,	PUNCT
iajs-3409	268	44	and	and	CCONJ
iajs-3409	268	45	can	can	AUX
iajs-3409	268	46	be	be	AUX
iajs-3409	268	47	represented	represent	VERB
iajs-3409	268	48	using	use	VERB
iajs-3409	268	49	the	the	DET
iajs-3409	268	50	butcher	butcher	NOUN
iajs-3409	268	51	tabular	tabular	PROPN
iajs-3409	268	52	notation	notation	NOUN
iajs-3409	268	53	.	.	PUNCT
iajs-3409	269	1	the	the	DET
iajs-3409	269	2	embedded	embed	VERB
iajs-3409	269	3	pair	pair	NOUN
iajs-3409	269	4	can	can	AUX
iajs-3409	269	5	be	be	AUX
iajs-3409	269	6	initialized	initialize	VERB
iajs-3409	269	7	in	in	ADP
iajs-3409	269	8	the	the	DET
iajs-3409	269	9	following	follow	VERB
iajs-3409	269	10	manner	manner	NOUN
iajs-3409	269	11	:	:	PUNCT
iajs-3409	269	12	c	c	PROPN
iajs-3409	269	13	a	a	DET
iajs-3409	269	14	𝑏	𝑏	PROPN
iajs-3409	269	15	𝑇	𝑇	PROPN
iajs-3409	269	16	𝑏′	𝑏′	PUNCT
iajs-3409	269	17	𝑇	𝑇	PROPN
iajs-3409	269	18	𝑏′′	𝑏′′	PROPN
iajs-3409	269	19	𝑇	𝑇	PROPN
iajs-3409	269	20	�	�	PROPN
iajs-3409	269	21	̈	̈	SYM
iajs-3409	269	22	�	�	PROPN
iajs-3409	269	23	𝑇	𝑇	PROPN
iajs-3409	269	24	�	�	PROPN
iajs-3409	269	25	̈	̈	SYM
iajs-3409	269	26	�	�	PROPN
iajs-3409	269	27	′	′	NOUN
iajs-3409	269	28	𝑇	𝑇	PROPN
iajs-3409	269	29	�	�	PROPN
iajs-3409	269	30	̈	̈	X
iajs-3409	269	31	�	�	NOUN
iajs-3409	269	32	′′	′′	NOUN
iajs-3409	269	33	𝑇	𝑇	VERB
iajs-3409	269	34	the	the	DET
iajs-3409	269	35	main	main	ADJ
iajs-3409	269	36	objective	objective	NOUN
iajs-3409	269	37	of	of	ADP
iajs-3409	269	38	constructing	construct	VERB
iajs-3409	269	39	the	the	DET
iajs-3409	269	40	embedded	embed	VERB
iajs-3409	269	41	pair	pair	NOUN
iajs-3409	269	42	of	of	ADP
iajs-3409	269	43	implicit	implicit	ADJ
iajs-3409	269	44	rktdio	rktdio	NOUN
iajs-3409	269	45	techniques	technique	NOUN
iajs-3409	269	46	is	be	AUX
iajs-3409	269	47	to	to	PART
iajs-3409	269	48	obtain	obtain	VERB
iajs-3409	269	49	a	a	DET
iajs-3409	269	50	single	single	ADJ
iajs-3409	269	51	error	error	NOUN
iajs-3409	269	52	estimate	estimate	NOUN
iajs-3409	269	53	that	that	PRON
iajs-3409	269	54	can	can	AUX
iajs-3409	269	55	be	be	AUX
iajs-3409	269	56	used	use	VERB
iajs-3409	269	57	in	in	ADP
iajs-3409	269	58	step	step	NOUN
iajs-3409	269	59	-	-	PUNCT
iajs-3409	269	60	size	size	NOUN
iajs-3409	269	61	approaches	approach	NOUN
iajs-3409	269	62	.	.	PUNCT
iajs-3409	270	1	this	this	PRON
iajs-3409	270	2	is	be	AUX
iajs-3409	270	3	achieved	achieve	VERB
iajs-3409	270	4	by	by	ADP
iajs-3409	270	5	improving	improve	VERB
iajs-3409	270	6	the	the	DET
iajs-3409	270	7	existing	exist	VERB
iajs-3409	270	8	pairs	pair	NOUN
iajs-3409	270	9	and	and	CCONJ
iajs-3409	270	10	local	local	ADJ
iajs-3409	270	11	error	error	NOUN
iajs-3409	270	12	estimates	estimate	NOUN
iajs-3409	270	13	and	and	CCONJ
iajs-3409	270	14	then	then	ADV
iajs-3409	270	15	restricting	restrict	VERB
iajs-3409	270	16	the	the	DET
iajs-3409	270	17	step	step	NOUN
iajs-3409	270	18	size	size	NOUN
iajs-3409	271	1	𝓀.	𝓀.	NOUN
iajs-3409	271	2	𝒽𝑛+1	𝒽𝑛+1	NUM
iajs-3409	271	3	=	=	SYM
iajs-3409	271	4	0.9𝓀𝑛	0.9𝓀𝑛	PROPN
iajs-3409	271	5	(	(	PUNCT
iajs-3409	271	6	𝑇𝑜𝑙	𝑇𝑜𝑙	PROPN
iajs-3409	271	7	𝐿𝑇𝐸	𝐿𝑇𝐸	PROPN
iajs-3409	271	8	)	)	PUNCT
iajs-3409	271	9	1	1	NUM
iajs-3409	271	10	𝒬+1	𝒬+1	NUM
iajs-3409	271	11	(	(	PUNCT
iajs-3409	271	12	67	67	NUM
iajs-3409	271	13	)	)	PUNCT
iajs-3409	271	14	a	a	DET
iajs-3409	271	15	safety	safety	NOUN
iajs-3409	271	16	factor	factor	NOUN
iajs-3409	271	17	of	of	ADP
iajs-3409	271	18	0.9	0.9	NUM
iajs-3409	271	19	is	be	AUX
iajs-3409	271	20	used	use	VERB
iajs-3409	271	21	to	to	PART
iajs-3409	271	22	determine	determine	VERB
iajs-3409	271	23	the	the	DET
iajs-3409	271	24	local	local	ADJ
iajs-3409	271	25	error	error	NOUN
iajs-3409	271	26	estimate	estimate	NOUN
iajs-3409	271	27	at	at	ADP
iajs-3409	271	28	each	each	DET
iajs-3409	271	29	step	step	NOUN
iajs-3409	271	30	,	,	PUNCT
iajs-3409	271	31	and	and	CCONJ
iajs-3409	271	32	𝑇𝑜𝑙	𝑇𝑜𝑙	PROPN
iajs-3409	271	33	represents	represent	VERB
iajs-3409	271	34	the	the	DET
iajs-3409	271	35	maximum	maximum	ADJ
iajs-3409	271	36	allowable	allowable	ADJ
iajs-3409	271	37	local	local	ADJ
iajs-3409	271	38	error	error	NOUN
iajs-3409	271	39	that	that	PRON
iajs-3409	271	40	ensures	ensure	VERB
iajs-3409	271	41	the	the	DET
iajs-3409	271	42	necessary	necessary	ADJ
iajs-3409	271	43	accuracy	accuracy	NOUN
iajs-3409	271	44	.	.	PUNCT
iajs-3409	272	1	if	if	SCONJ
iajs-3409	272	2	the	the	DET
iajs-3409	272	3	local	local	ADJ
iajs-3409	272	4	truncation	truncation	NOUN
iajs-3409	272	5	error	error	NOUN
iajs-3409	272	6	(	(	PUNCT
iajs-3409	272	7	lte	lte	PROPN
iajs-3409	272	8	)	)	PUNCT
iajs-3409	272	9	is	be	AUX
iajs-3409	272	10	less	less	ADJ
iajs-3409	272	11	than	than	ADP
iajs-3409	272	12	or	or	CCONJ
iajs-3409	272	13	equal	equal	ADJ
iajs-3409	272	14	to	to	ADP
iajs-3409	272	15	𝑇𝑜𝑙	𝑇𝑜𝑙	PROPN
iajs-3409	272	16	,	,	PUNCT
iajs-3409	272	17	the	the	DET
iajs-3409	272	18	step	step	NOUN
iajs-3409	272	19	is	be	AUX
iajs-3409	272	20	accepted	accept	VERB
iajs-3409	272	21	and	and	CCONJ
iajs-3409	272	22	the	the	DET
iajs-3409	272	23	higher	high	ADJ
iajs-3409	272	24	order	order	NOUN
iajs-3409	272	25	method	method	NOUN
iajs-3409	272	26	(	(	PUNCT
iajs-3409	272	27	or	or	CCONJ
iajs-3409	272	28	local	local	ADJ
iajs-3409	272	29	extrapolation	extrapolation	NOUN
iajs-3409	272	30	)	)	PUNCT
iajs-3409	272	31	is	be	AUX
iajs-3409	272	32	used	use	VERB
iajs-3409	272	33	,	,	PUNCT
iajs-3409	272	34	where	where	SCONJ
iajs-3409	272	35	a	a	DET
iajs-3409	272	36	more	more	ADV
iajs-3409	272	37	accurate	accurate	ADJ
iajs-3409	272	38	approximation	approximation	NOUN
iajs-3409	272	39	is	be	AUX
iajs-3409	272	40	applied	apply	VERB
iajs-3409	272	41	to	to	PART
iajs-3409	272	42	drive	drive	VERB
iajs-3409	272	43	the	the	DET
iajs-3409	272	44	integration	integration	NOUN
iajs-3409	272	45	and	and	CCONJ
iajs-3409	272	46	update	update	VERB
iajs-3409	272	47	𝓀	𝓀	PRON
iajs-3409	272	48	using	use	VERB
iajs-3409	272	49	equation	equation	NOUN
iajs-3409	272	50	(	(	PUNCT
iajs-3409	272	51	67	67	NUM
iajs-3409	272	52	)	)	PUNCT
iajs-3409	272	53	.	.	PUNCT
iajs-3409	273	1	on	on	ADP
iajs-3409	273	2	the	the	DET
iajs-3409	273	3	other	other	ADJ
iajs-3409	273	4	hand	hand	NOUN
iajs-3409	273	5	,	,	PUNCT
iajs-3409	273	6	if	if	SCONJ
iajs-3409	273	7	lte	lte	PROPN
iajs-3409	273	8	is	be	AUX
iajs-3409	273	9	greater	great	ADJ
iajs-3409	273	10	than	than	ADP
iajs-3409	273	11	𝑇𝑜𝑙	𝑇𝑜𝑙	PROPN
iajs-3409	273	12	,	,	PUNCT
iajs-3409	273	13	the	the	DET
iajs-3409	273	14	step	step	NOUN
iajs-3409	273	15	is	be	AUX
iajs-3409	273	16	rejected	reject	VERB
iajs-3409	273	17	and	and	CCONJ
iajs-3409	273	18	the	the	DET
iajs-3409	273	19	step	step	NOUN
iajs-3409	273	20	size	size	NOUN
iajs-3409	273	21	𝓀	𝓀	PRON
iajs-3409	273	22	is	be	AUX
iajs-3409	273	23	reduced	reduce	VERB
iajs-3409	273	24	by	by	ADP
iajs-3409	273	25	half	half	NOUN
iajs-3409	273	26	.	.	PUNCT
iajs-3409	274	1	the	the	DET
iajs-3409	274	2	rktdio	rktdio	NOUN
iajs-3409	274	3	method	method	NOUN
iajs-3409	274	4	is	be	AUX
iajs-3409	274	5	an	an	DET
iajs-3409	274	6	embedded	embed	VERB
iajs-3409	274	7	rungekutta	rungekutta	NOUN
iajs-3409	274	8	method	method	NOUN
iajs-3409	274	9	developed	develop	VERB
iajs-3409	274	10	for	for	ADP
iajs-3409	274	11	solving	solve	VERB
iajs-3409	274	12	third	third	ADJ
iajs-3409	274	13	-	-	PUNCT
iajs-3409	274	14	order	order	NOUN
iajs-3409	274	15	odes	ode	NOUN
iajs-3409	274	16	.	.	PUNCT
iajs-3409	275	1	to	to	PART
iajs-3409	275	2	ensure	ensure	VERB
iajs-3409	275	3	high	high	ADJ
iajs-3409	275	4	accuracy	accuracy	NOUN
iajs-3409	275	5	for	for	ADP
iajs-3409	275	6	the	the	DET
iajs-3409	275	7	higherorder	higherorder	NOUN
iajs-3409	275	8	method	method	NOUN
iajs-3409	275	9	and	and	CCONJ
iajs-3409	275	10	the	the	DET
iajs-3409	275	11	most	most	ADV
iajs-3409	275	12	accurate	accurate	ADJ
iajs-3409	275	13	error	error	NOUN
iajs-3409	275	14	estimates	estimate	NOUN
iajs-3409	275	15	for	for	ADP
iajs-3409	275	16	the	the	DET
iajs-3409	275	17	lower	low	ADJ
iajs-3409	275	18	-	-	PUNCT
iajs-3409	275	19	order	order	NOUN
iajs-3409	275	20	methods	method	NOUN
iajs-3409	275	21	,	,	PUNCT
iajs-3409	275	22	fractions	fraction	NOUN
iajs-3409	275	23	were	be	AUX
iajs-3409	275	24	used	use	VERB
iajs-3409	275	25	to	to	PART
iajs-3409	275	26	develop	develop	VERB
iajs-3409	275	27	orders	order	NOUN
iajs-3409	275	28	6	6	NUM
iajs-3409	275	29	and	and	CCONJ
iajs-3409	275	30	5	5	NUM
iajs-3409	275	31	,	,	PUNCT
iajs-3409	275	32	respectively	respectively	ADV
iajs-3409	275	33	.	.	PUNCT
iajs-3409	276	1	the	the	DET
iajs-3409	276	2	step	step	NOUN
iajs-3409	276	3	size	size	NOUN
iajs-3409	276	4	𝓀	𝓀	PRON
iajs-3409	276	5	plays	play	VERB
iajs-3409	276	6	a	a	DET
iajs-3409	276	7	crucial	crucial	ADJ
iajs-3409	276	8	role	role	NOUN
iajs-3409	276	9	in	in	ADP
iajs-3409	276	10	obtaining	obtain	VERB
iajs-3409	276	11	accurate	accurate	ADJ
iajs-3409	276	12	results	result	NOUN
iajs-3409	276	13	and	and	CCONJ
iajs-3409	276	14	can	can	AUX
iajs-3409	276	15	be	be	AUX
iajs-3409	276	16	doubled	double	VERB
iajs-3409	276	17	to	to	PART
iajs-3409	276	18	achieve	achieve	VERB
iajs-3409	276	19	this	this	DET
iajs-3409	276	20	goal	goal	NOUN
iajs-3409	276	21	.	.	PUNCT
iajs-3409	277	1	the	the	DET
iajs-3409	277	2	embedded	embed	VERB
iajs-3409	277	3	rktdio6(5	rktdio6(5	NOUN
iajs-3409	277	4	)	)	PUNCT
iajs-3409	277	5	method	method	NOUN
iajs-3409	277	6	is	be	AUX
iajs-3409	277	7	derived	derive	VERB
iajs-3409	277	8	in	in	ADP
iajs-3409	277	9	table	table	NOUN
iajs-3409	277	10	4	4	NUM
iajs-3409	277	11	for	for	ADP
iajs-3409	277	12	this	this	DET
iajs-3409	277	13	study	study	NOUN
iajs-3409	277	14	.	.	PUNCT
iajs-3409	278	1	in	in	ADP
iajs-3409	278	2	rktdio6(5	rktdio6(5	PROPN
iajs-3409	278	3	)	)	PUNCT
iajs-3409	278	4	,	,	PUNCT
iajs-3409	278	5	the	the	DET
iajs-3409	278	6	𝐴	𝐴	PROPN
iajs-3409	278	7	and	and	CCONJ
iajs-3409	278	8	𝐶	𝐶	PROPN
iajs-3409	278	9	values	value	NOUN
iajs-3409	278	10	is	be	AUX
iajs-3409	278	11	computed	compute	VERB
iajs-3409	278	12	from	from	ADP
iajs-3409	278	13	the	the	DET
iajs-3409	278	14	6th	6th	ADJ
iajs-3409	278	15	-	-	PUNCT
iajs-3409	278	16	order	order	NOUN
iajs-3409	278	17	solution	solution	NOUN
iajs-3409	278	18	then	then	ADV
iajs-3409	278	19	derived	derive	VERB
iajs-3409	278	20	the	the	DET
iajs-3409	278	21	four	four	NUM
iajs-3409	278	22	-	-	PUNCT
iajs-3409	278	23	stage	stage	NOUN
iajs-3409	278	24	5rd	5rd	NOUN
iajs-3409	278	25	-	-	PUNCT
iajs-3409	278	26	order	order	NOUN
iajs-3409	278	27	embedded	embed	VERB
iajs-3409	278	28	equation	equation	NOUN
iajs-3409	278	29	.	.	PUNCT
iajs-3409	279	1	solving	solve	VERB
iajs-3409	279	2	of	of	ADP
iajs-3409	279	3	the	the	DET
iajs-3409	279	4	eqs	eqs	PROPN
iajs-3409	279	5	.	.	PUNCT
iajs-3409	280	1	(	(	PUNCT
iajs-3409	280	2	51	51	NUM
iajs-3409	280	3	-	-	SYM
iajs-3409	280	4	53	53	NUM
iajs-3409	280	5	)	)	PUNCT
iajs-3409	280	6	,	,	PUNCT
iajs-3409	280	7	(	(	PUNCT
iajs-3409	280	8	55	55	NUM
iajs-3409	280	9	-	-	SYM
iajs-3409	280	10	58	58	NUM
iajs-3409	280	11	)	)	PUNCT
iajs-3409	280	12	,	,	PUNCT
iajs-3409	280	13	and	and	CCONJ
iajs-3409	280	14	(	(	PUNCT
iajs-3409	280	15	60	60	NUM
iajs-3409	280	16	-	-	SYM
iajs-3409	280	17	64	64	NUM
iajs-3409	280	18	)	)	PUNCT
iajs-3409	280	19	ihjpas	ihjpa	NOUN
iajs-3409	280	20	.	.	PUNCT
iajs-3409	281	1	37	37	NUM
iajs-3409	281	2	(	(	PUNCT
iajs-3409	281	3	2	2	NUM
iajs-3409	281	4	)	)	PUNCT
iajs-3409	281	5	2024	2024	NUM
iajs-3409	281	6	400	400	NUM
iajs-3409	281	7	simultaneously	simultaneously	ADV
iajs-3409	281	8	then	then	ADV
iajs-3409	281	9	the	the	DET
iajs-3409	281	10	solution	solution	NOUN
iajs-3409	281	11	for	for	ADP
iajs-3409	281	12	�	�	PROPN
iajs-3409	281	13	̈	̈	SYM
iajs-3409	281	14	�	�	PROPN
iajs-3409	281	15	and	and	CCONJ
iajs-3409	281	16	�	�	PROPN
iajs-3409	281	17	̈	̈	X
iajs-3409	281	18	�	�	NOUN
iajs-3409	281	19	′	′	NUM
iajs-3409	281	20	while	while	SCONJ
iajs-3409	281	21	�	�	PROPN
iajs-3409	281	22	̈	̈	X
iajs-3409	281	23	�	�	NOUN
iajs-3409	281	24	′′	′′	PROPN
iajs-3409	281	25	have	have	VERB
iajs-3409	281	26	the	the	DET
iajs-3409	281	27	same	same	ADJ
iajs-3409	281	28	values	value	NOUN
iajs-3409	281	29	as	as	ADP
iajs-3409	281	30	the	the	DET
iajs-3409	281	31	6th	6th	ADJ
iajs-3409	281	32	-order	-order	NOUN
iajs-3409	281	33	.	.	PUNCT
iajs-3409	282	1	the	the	DET
iajs-3409	282	2	solutions	solution	NOUN
iajs-3409	282	3	are	be	AUX
iajs-3409	282	4	obtained	obtain	VERB
iajs-3409	282	5	as	as	ADP
iajs-3409	282	6	�	�	PROPN
iajs-3409	282	7	̈	̈	X
iajs-3409	282	8	�	�	NOUN
iajs-3409	282	9	1	1	NUM
iajs-3409	282	10	′	′	NOUN
iajs-3409	282	11	=	=	SYM
iajs-3409	282	12	2	2	NUM
iajs-3409	282	13	9	9	NUM
iajs-3409	282	14	,	,	PUNCT
iajs-3409	282	15	�	�	PROPN
iajs-3409	282	16	̈	̈	X
iajs-3409	282	17	�	�	NOUN
iajs-3409	282	18	2	2	NUM
iajs-3409	282	19	′	′	NOUN
iajs-3409	282	20	=	=	SYM
iajs-3409	282	21	0	0	NUM
iajs-3409	282	22	,	,	PUNCT
iajs-3409	282	23	�	�	NOUN
iajs-3409	282	24	̈	̈	X
iajs-3409	282	25	�	�	NOUN
iajs-3409	282	26	3	3	NUM
iajs-3409	283	1	′	′	NOUN
iajs-3409	283	2	=	=	SYM
iajs-3409	283	3	5	5	NUM
iajs-3409	283	4	36	36	NUM
iajs-3409	283	5	−	−	NOUN
iajs-3409	283	6	√15	√15	PROPN
iajs-3409	283	7	36	36	NUM
iajs-3409	283	8	,	,	PUNCT
iajs-3409	283	9	�	�	PROPN
iajs-3409	283	10	̈	̈	X
iajs-3409	283	11	�	�	NOUN
iajs-3409	283	12	4	4	NUM
iajs-3409	283	13	′	′	NOUN
iajs-3409	283	14	=	=	SYM
iajs-3409	283	15	5	5	NUM
iajs-3409	283	16	36	36	NUM
iajs-3409	284	1	+	+	CCONJ
iajs-3409	284	2	√15	√15	PROPN
iajs-3409	284	3	36	36	NUM
iajs-3409	284	4	,	,	PUNCT
iajs-3409	284	5	�	�	PROPN
iajs-3409	284	6	̈	̈	X
iajs-3409	284	7	�	�	NOUN
iajs-3409	284	8	1	1	NUM
iajs-3409	284	9	=	=	SYM
iajs-3409	284	10	1	1	NUM
iajs-3409	284	11	18	18	NUM
iajs-3409	284	12	,	,	PUNCT
iajs-3409	284	13	�	�	PROPN
iajs-3409	284	14	̈	̈	X
iajs-3409	284	15	�	�	NOUN
iajs-3409	284	16	2	2	NUM
iajs-3409	284	17	=	=	SYM
iajs-3409	284	18	1	1	NUM
iajs-3409	284	19	18	18	NUM
iajs-3409	284	20	+	+	CCONJ
iajs-3409	284	21	√15	√15	PROPN
iajs-3409	284	22	72	72	NUM
iajs-3409	284	23	,	,	PUNCT
iajs-3409	284	24	�	�	PROPN
iajs-3409	284	25	̈	̈	X
iajs-3409	284	26	�	�	NOUN
iajs-3409	284	27	3	3	NUM
iajs-3409	284	28	=	=	SYM
iajs-3409	284	29	1	1	NUM
iajs-3409	284	30	18	18	NUM
iajs-3409	284	31	−	−	NOUN
iajs-3409	284	32	√15	√15	PROPN
iajs-3409	284	33	72	72	NUM
iajs-3409	284	34	,	,	PUNCT
iajs-3409	284	35	�	�	PROPN
iajs-3409	284	36	̈	̈	X
iajs-3409	284	37	�	�	NOUN
iajs-3409	284	38	4	4	NUM
iajs-3409	284	39	=	=	SYM
iajs-3409	284	40	�	�	PROPN
iajs-3409	284	41	̈	̈	X
iajs-3409	284	42	�	�	NOUN
iajs-3409	284	43	4	4	NUM
iajs-3409	284	44	,	,	PUNCT
iajs-3409	284	45	�	�	NOUN
iajs-3409	284	46	̈	̈	X
iajs-3409	284	47	�	�	NOUN
iajs-3409	284	48	1	1	NUM
iajs-3409	284	49	′′	′′	NOUN
iajs-3409	284	50	=	=	NOUN
iajs-3409	284	51	4	4	NUM
iajs-3409	284	52	9	9	NUM
iajs-3409	284	53	,	,	PUNCT
iajs-3409	284	54	�	�	PROPN
iajs-3409	284	55	̈	̈	NOUN
iajs-3409	284	56	�	�	NOUN
iajs-3409	284	57	2	2	NUM
iajs-3409	284	58	′′	′′	PROPN
iajs-3409	284	59	=	=	SYM
iajs-3409	284	60	0	0	NUM
iajs-3409	284	61	,	,	PUNCT
iajs-3409	284	62	�	�	PROPN
iajs-3409	284	63	̈	̈	X
iajs-3409	284	64	�	�	NOUN
iajs-3409	284	65	3	3	NUM
iajs-3409	284	66	′′	′′	PROPN
iajs-3409	284	67	=	=	PUNCT
iajs-3409	284	68	5	5	NUM
iajs-3409	284	69	18	18	NUM
iajs-3409	284	70	,	,	PUNCT
iajs-3409	284	71	�	�	PROPN
iajs-3409	284	72	̈	̈	X
iajs-3409	284	73	�	�	NOUN
iajs-3409	284	74	4	4	NUM
iajs-3409	284	75	′′	′′	NOUN
iajs-3409	284	76	=	=	NOUN
iajs-3409	284	77	5	5	NUM
iajs-3409	284	78	18	18	NUM
iajs-3409	284	79	.	.	PUNCT
iajs-3409	285	1	the	the	DET
iajs-3409	285	2	following	follow	VERB
iajs-3409	285	3	simplifying	simplify	VERB
iajs-3409	285	4	assumption	assumption	NOUN
iajs-3409	285	5	is	be	AUX
iajs-3409	285	6	used	use	VERB
iajs-3409	285	7	in	in	ADP
iajs-3409	285	8	order	order	NOUN
iajs-3409	285	9	to	to	PART
iajs-3409	285	10	reduce	reduce	VERB
iajs-3409	285	11	the	the	DET
iajs-3409	285	12	number	number	NOUN
iajs-3409	285	13	of	of	ADP
iajs-3409	285	14	equations	equation	NOUN
iajs-3409	285	15	to	to	PART
iajs-3409	285	16	be	be	AUX
iajs-3409	285	17	solved	solve	VERB
iajs-3409	285	18	:	:	PUNCT
iajs-3409	285	19	𝑏𝑖	𝑏𝑖	ADP
iajs-3409	285	20	′	′	NOUN
iajs-3409	285	21	=	=	PUNCT
iajs-3409	286	1	𝑏𝑖	𝑏𝑖	ADP
iajs-3409	286	2	′′(1	′′(1	PRON
iajs-3409	286	3	−	−	PROPN
iajs-3409	286	4	𝑐𝑖	𝑐𝑖	NOUN
iajs-3409	286	5	)	)	PUNCT
iajs-3409	286	6	,	,	PUNCT
iajs-3409	286	7	𝑖	𝑖	NOUN
iajs-3409	286	8	=	=	SYM
iajs-3409	286	9	1	1	NUM
iajs-3409	286	10	,	,	PUNCT
iajs-3409	286	11	…	…	PUNCT
iajs-3409	286	12	,	,	PUNCT
iajs-3409	286	13	𝔰.	𝔰.	NOUN
iajs-3409	286	14	(	(	PUNCT
iajs-3409	286	15	68	68	NUM
iajs-3409	286	16	)	)	PUNCT
iajs-3409	286	17	initially	initially	ADV
iajs-3409	286	18	,	,	PUNCT
iajs-3409	286	19	we	we	PRON
iajs-3409	286	20	have	have	VERB
iajs-3409	286	21	16	16	NUM
iajs-3409	286	22	nonlinear	nonlinear	ADJ
iajs-3409	286	23	equations	equation	NOUN
iajs-3409	286	24	with	with	ADP
iajs-3409	286	25	12	12	NUM
iajs-3409	286	26	unknown	unknown	ADJ
iajs-3409	286	27	variables	variable	NOUN
iajs-3409	286	28	that	that	PRON
iajs-3409	286	29	we	we	PRON
iajs-3409	286	30	need	need	VERB
iajs-3409	286	31	to	to	PART
iajs-3409	286	32	find	find	VERB
iajs-3409	286	33	a	a	DET
iajs-3409	286	34	solution	solution	NOUN
iajs-3409	286	35	for	for	ADP
iajs-3409	286	36	.	.	PUNCT
iajs-3409	287	1	however	however	ADV
iajs-3409	287	2	,	,	PUNCT
iajs-3409	287	3	as	as	SCONJ
iajs-3409	287	4	the	the	DET
iajs-3409	287	5	number	number	NOUN
iajs-3409	287	6	of	of	ADP
iajs-3409	287	7	equations	equation	NOUN
iajs-3409	287	8	is	be	AUX
iajs-3409	287	9	greater	great	ADJ
iajs-3409	287	10	than	than	ADP
iajs-3409	287	11	the	the	DET
iajs-3409	287	12	number	number	NOUN
iajs-3409	287	13	of	of	ADP
iajs-3409	287	14	unknowns	unknown	NOUN
iajs-3409	287	15	,	,	PUNCT
iajs-3409	287	16	there	there	PRON
iajs-3409	287	17	is	be	VERB
iajs-3409	287	18	no	no	DET
iajs-3409	287	19	solution	solution	NOUN
iajs-3409	287	20	.	.	PUNCT
iajs-3409	288	1	to	to	PART
iajs-3409	288	2	tackle	tackle	VERB
iajs-3409	288	3	this	this	DET
iajs-3409	288	4	issue	issue	NOUN
iajs-3409	288	5	,	,	PUNCT
iajs-3409	288	6	we	we	PRON
iajs-3409	288	7	make	make	VERB
iajs-3409	288	8	the	the	DET
iajs-3409	288	9	simplifying	simplifying	NOUN
iajs-3409	288	10	assumption	assumption	NOUN
iajs-3409	288	11	(	(	PUNCT
iajs-3409	288	12	68	68	NUM
iajs-3409	288	13	)	)	PUNCT
iajs-3409	288	14	which	which	PRON
iajs-3409	288	15	reduces	reduce	VERB
iajs-3409	288	16	the	the	DET
iajs-3409	288	17	number	number	NOUN
iajs-3409	288	18	of	of	ADP
iajs-3409	288	19	equations	equation	NOUN
iajs-3409	288	20	to	to	ADP
iajs-3409	288	21	12	12	NUM
iajs-3409	288	22	with	with	ADP
iajs-3409	288	23	11	11	NUM
iajs-3409	288	24	unknowns	unknown	NOUN
iajs-3409	288	25	,	,	PUNCT
iajs-3409	288	26	enabling	enable	VERB
iajs-3409	288	27	us	we	PRON
iajs-3409	288	28	to	to	PART
iajs-3409	288	29	solve	solve	VERB
iajs-3409	288	30	the	the	DET
iajs-3409	288	31	system	system	NOUN
iajs-3409	288	32	.	.	PUNCT
iajs-3409	289	1	we	we	PRON
iajs-3409	289	2	choose	choose	VERB
iajs-3409	289	3	�	�	PROPN
iajs-3409	289	4	̈	̈	X
iajs-3409	289	5	�	�	NOUN
iajs-3409	289	6	=	=	SYM
iajs-3409	289	7	1	1	NUM
iajs-3409	289	8	10	10	NUM
iajs-3409	289	9	as	as	ADP
iajs-3409	289	10	the	the	DET
iajs-3409	289	11	free	free	ADJ
iajs-3409	289	12	parameter	parameter	NOUN
iajs-3409	289	13	,	,	PUNCT
iajs-3409	289	14	and	and	CCONJ
iajs-3409	289	15	as	as	ADP
iajs-3409	289	16	a	a	DET
iajs-3409	289	17	result	result	NOUN
iajs-3409	289	18	,	,	PUNCT
iajs-3409	289	19	we	we	PRON
iajs-3409	289	20	can	can	AUX
iajs-3409	289	21	express	express	VERB
iajs-3409	289	22	the	the	DET
iajs-3409	289	23	coefficients	coefficient	NOUN
iajs-3409	289	24	of	of	ADP
iajs-3409	289	25	the	the	DET
iajs-3409	289	26	4	4	NUM
iajs-3409	289	27	-	-	PUNCT
iajs-3409	289	28	stage	stage	NOUN
iajs-3409	289	29	embedded	embed	VERB
iajs-3409	289	30	erktdio6(5	erktdio6(5	PROPN
iajs-3409	289	31	)	)	PUNCT
iajs-3409	289	32	technique	technique	NOUN
iajs-3409	289	33	.	.	PUNCT
iajs-3409	290	1	table	table	NOUN
iajs-3409	290	2	4	4	NUM
iajs-3409	290	3	:	:	PUNCT
iajs-3409	290	4	table	table	NOUN
iajs-3409	290	5	of	of	ADP
iajs-3409	290	6	erktdio6(5	erktdio6(5	PROPN
iajs-3409	290	7	)	)	PUNCT
iajs-3409	290	8	method	method	NOUN
iajs-3409	290	9	.	.	PUNCT
iajs-3409	291	1	7	7	X
iajs-3409	291	2	.	.	NOUN
iajs-3409	291	3	numerical	numerical	ADJ
iajs-3409	291	4	experiments	experiment	NOUN
iajs-3409	291	5	7.1	7.1	NUM
iajs-3409	291	6	constant	constant	ADJ
iajs-3409	291	7	methods	method	NOUN
iajs-3409	291	8	in	in	ADP
iajs-3409	291	9	order	order	NOUN
iajs-3409	291	10	to	to	PART
iajs-3409	291	11	evaluate	evaluate	VERB
iajs-3409	291	12	the	the	DET
iajs-3409	291	13	performance	performance	NOUN
iajs-3409	291	14	of	of	ADP
iajs-3409	291	15	the	the	DET
iajs-3409	291	16	new	new	ADJ
iajs-3409	291	17	rktdio	rktdio	NOUN
iajs-3409	291	18	methods	method	NOUN
iajs-3409	291	19	to	to	ADP
iajs-3409	291	20	the	the	DET
iajs-3409	291	21	established	establish	VERB
iajs-3409	291	22	rk	rk	NOUN
iajs-3409	291	23	methods	method	NOUN
iajs-3409	291	24	in	in	ADP
iajs-3409	291	25	the	the	DET
iajs-3409	291	26	scientific	scientific	ADJ
iajs-3409	291	27	literature	literature	NOUN
iajs-3409	291	28	,	,	PUNCT
iajs-3409	291	29	a	a	DET
iajs-3409	291	30	series	series	NOUN
iajs-3409	291	31	of	of	ADP
iajs-3409	291	32	test	test	NOUN
iajs-3409	291	33	problems	problem	NOUN
iajs-3409	291	34	are	be	AUX
iajs-3409	291	35	addressed	address	VERB
iajs-3409	291	36	in	in	ADP
iajs-3409	291	37	this	this	DET
iajs-3409	291	38	part	part	NOUN
iajs-3409	291	39	.	.	PUNCT
iajs-3409	292	1	the	the	DET
iajs-3409	292	2	following	follow	VERB
iajs-3409	292	3	methods	method	NOUN
iajs-3409	292	4	have	have	AUX
iajs-3409	292	5	been	be	AUX
iajs-3409	292	6	selected	select	VERB
iajs-3409	292	7	for	for	ADP
iajs-3409	292	8	comparison	comparison	NOUN
iajs-3409	292	9	:	:	PUNCT
iajs-3409	292	10			X
iajs-3409	293	1	rktdio5	rktdio5	PROPN
iajs-3409	293	2	:	:	PUNCT
iajs-3409	293	3	the	the	DET
iajs-3409	293	4	implicit	implicit	ADJ
iajs-3409	293	5	rktdio	rktdio	NOUN
iajs-3409	293	6	method	method	NOUN
iajs-3409	293	7	of	of	ADP
iajs-3409	293	8	order	order	NOUN
iajs-3409	293	9	five	five	NUM
iajs-3409	293	10	with	with	ADP
iajs-3409	293	11	three	three	NUM
iajs-3409	293	12	-	-	PUNCT
iajs-3409	293	13	stage	stage	NOUN
iajs-3409	293	14	derived	derive	VERB
iajs-3409	293	15	in	in	ADP
iajs-3409	293	16	this	this	DET
iajs-3409	293	17	paper	paper	NOUN
iajs-3409	293	18	.	.	PUNCT
iajs-3409	294	1			PRON
iajs-3409	294	2	rktdio6	rktdio6	NOUN
iajs-3409	294	3	:	:	PUNCT
iajs-3409	294	4	the	the	DET
iajs-3409	294	5	implicit	implicit	ADJ
iajs-3409	294	6	rktdio	rktdio	NOUN
iajs-3409	294	7	method	method	NOUN
iajs-3409	294	8	of	of	ADP
iajs-3409	294	9	order	order	NOUN
iajs-3409	294	10	six	six	NUM
iajs-3409	294	11	with	with	ADP
iajs-3409	294	12	four	four	NUM
iajs-3409	294	13	-	-	PUNCT
iajs-3409	294	14	stage	stage	NOUN
iajs-3409	294	15	derived	derive	VERB
iajs-3409	294	16	in	in	ADP
iajs-3409	294	17	this	this	DET
iajs-3409	294	18	paper	paper	NOUN
iajs-3409	294	19	.	.	PUNCT
iajs-3409	295	1	ihjpas	ihjpas	PROPN
iajs-3409	295	2	.	.	PUNCT
iajs-3409	296	1	37	37	NUM
iajs-3409	296	2	(	(	PUNCT
iajs-3409	296	3	2	2	NUM
iajs-3409	296	4	)	)	PUNCT
iajs-3409	296	5	2024	2024	NUM
iajs-3409	296	6	401	401	NUM
iajs-3409	296	7			NOUN
iajs-3409	296	8	ditrkm5	ditrkm5	NOUN
iajs-3409	296	9	:	:	PUNCT
iajs-3409	296	10	three	three	NUM
iajs-3409	296	11	-	-	PUNCT
iajs-3409	296	12	stage	stage	NOUN
iajs-3409	296	13	fifth	fifth	ADJ
iajs-3409	296	14	-	-	PUNCT
iajs-3409	296	15	order	order	NOUN
iajs-3409	296	16	implicit	implicit	ADJ
iajs-3409	296	17	rk	rk	NOUN
iajs-3409	296	18	derived	derive	VERB
iajs-3409	296	19	by	by	ADP
iajs-3409	296	20	[	[	X
iajs-3409	296	21	25	25	NUM
iajs-3409	296	22	]	]	PUNCT
iajs-3409	296	23	.	.	PUNCT
iajs-3409	297	1			NOUN
iajs-3409	297	2	radau	radau	VERB
iajs-3409	298	1	i	i	PRON
iajs-3409	298	2	:	:	PUNCT
iajs-3409	298	3	three	three	NUM
iajs-3409	298	4	-	-	PUNCT
iajs-3409	298	5	stage	stage	NOUN
iajs-3409	298	6	fifth	fifth	ADJ
iajs-3409	298	7	-	-	PUNCT
iajs-3409	298	8	order	order	NOUN
iajs-3409	298	9	implicit	implicit	ADJ
iajs-3409	298	10	rk	rk	NOUN
iajs-3409	298	11	method	method	NOUN
iajs-3409	298	12	presented	present	VERB
iajs-3409	298	13	in	in	ADP
iajs-3409	298	14	[	[	X
iajs-3409	298	15	28	28	NUM
iajs-3409	298	16	]	]	PUNCT
iajs-3409	298	17	.	.	PUNCT
iajs-3409	299	1			PROPN
iajs-3409	299	2	radau	radau	PROPN
iajs-3409	299	3	ia	ia	PROPN
iajs-3409	299	4	:	:	PUNCT
iajs-3409	299	5	three	three	NUM
iajs-3409	299	6	-	-	PUNCT
iajs-3409	299	7	stage	stage	NOUN
iajs-3409	299	8	fifth	fifth	ADJ
iajs-3409	299	9	-	-	PUNCT
iajs-3409	299	10	order	order	NOUN
iajs-3409	299	11	implicit	implicit	ADJ
iajs-3409	299	12	rk	rk	NOUN
iajs-3409	299	13	method	method	NOUN
iajs-3409	299	14	presented	present	VERB
iajs-3409	299	15	in	in	ADP
iajs-3409	299	16	[	[	X
iajs-3409	299	17	24	24	NUM
iajs-3409	299	18	]	]	PUNCT
iajs-3409	299	19	.	.	PUNCT
iajs-3409	300	1			PROPN
iajs-3409	300	2	lobatto	lobatto	PROPN
iajs-3409	300	3	iii	iii	PROPN
iajs-3409	300	4	:	:	PUNCT
iajs-3409	300	5	the	the	DET
iajs-3409	300	6	sixth	sixth	ADJ
iajs-3409	300	7	-	-	PUNCT
iajs-3409	300	8	order	order	NOUN
iajs-3409	300	9	four	four	NUM
iajs-3409	300	10	-	-	PUNCT
iajs-3409	300	11	stage	stage	NOUN
iajs-3409	300	12	implicit	implicit	ADJ
iajs-3409	300	13	runge	runge	NOUN
iajs-3409	300	14	–	–	PUNCT
iajs-3409	300	15	kutta	kutta	NOUN
iajs-3409	300	16	method	method	NOUN
iajs-3409	300	17	as	as	SCONJ
iajs-3409	300	18	given	give	VERB
iajs-3409	300	19	by	by	ADP
iajs-3409	300	20	[	[	X
iajs-3409	300	21	30	30	NUM
iajs-3409	300	22	]	]	PUNCT
iajs-3409	300	23	.	.	PUNCT
iajs-3409	301	1			PROPN
iajs-3409	301	2	lobatto	lobatto	PROPN
iajs-3409	301	3	iiib	iiib	NOUN
iajs-3409	301	4	:	:	PUNCT
iajs-3409	301	5	the	the	DET
iajs-3409	301	6	sixth	sixth	ADJ
iajs-3409	301	7	-	-	PUNCT
iajs-3409	301	8	order	order	NOUN
iajs-3409	301	9	four	four	NUM
iajs-3409	301	10	-	-	PUNCT
iajs-3409	301	11	stage	stage	NOUN
iajs-3409	301	12	implicit	implicit	ADJ
iajs-3409	301	13	runge	runge	NOUN
iajs-3409	301	14	–	–	PUNCT
iajs-3409	301	15	kutta	kutta	NOUN
iajs-3409	301	16	method	method	NOUN
iajs-3409	301	17	as	as	SCONJ
iajs-3409	301	18	given	give	VERB
iajs-3409	301	19	by	by	ADP
iajs-3409	301	20	[	[	X
iajs-3409	301	21	29	29	NUM
iajs-3409	301	22	]	]	PUNCT
iajs-3409	301	23	.	.	PUNCT
iajs-3409	302	1	problem	problem	NOUN
iajs-3409	302	2	(	(	PUNCT
iajs-3409	302	3	1	1	NUM
iajs-3409	302	4	):	):	PUNCT
iajs-3409	302	5	consider	consider	VERB
iajs-3409	302	6	a	a	DET
iajs-3409	302	7	nonhomogeneous	nonhomogeneous	ADJ
iajs-3409	302	8	linear	linear	NOUN
iajs-3409	302	9	ode	ode	NOUN
iajs-3409	302	10	given	give	VERB
iajs-3409	302	11	in	in	ADP
iajs-3409	302	12	[	[	X
iajs-3409	302	13	22	22	NUM
iajs-3409	302	14	]	]	SYM
iajs-3409	302	15	α′′′(x	α′′′(x	NUM
iajs-3409	302	16	)	)	PUNCT
iajs-3409	302	17	=	=	SYM
iajs-3409	302	18	α(x	α(x	NOUN
iajs-3409	302	19	)	)	PUNCT
iajs-3409	302	20	+	+	SYM
iajs-3409	302	21	cos(x	cos(x	PROPN
iajs-3409	302	22	)	)	PUNCT
iajs-3409	302	23	,	,	PUNCT
iajs-3409	302	24	with	with	ADP
iajs-3409	302	25	𝛼(0	𝛼(0	PROPN
iajs-3409	302	26	)	)	PUNCT
iajs-3409	302	27	=	=	SYM
iajs-3409	302	28	0	0	NUM
iajs-3409	302	29	,	,	PUNCT
iajs-3409	302	30	𝛼′(0	𝛼′(0	NOUN
iajs-3409	302	31	)	)	PUNCT
iajs-3409	302	32	=	=	SYM
iajs-3409	302	33	0	0	NUM
iajs-3409	302	34	,	,	PUNCT
iajs-3409	302	35	𝛼′′(0	𝛼′′(0	X
iajs-3409	302	36	)	)	PUNCT
iajs-3409	303	1	=	=	SYM
iajs-3409	303	2	1	1	NUM
iajs-3409	303	3	where	where	SCONJ
iajs-3409	303	4	x	x	X
iajs-3409	303	5	∈	∈	PROPN
iajs-3409	304	1	[	[	X
iajs-3409	304	2	0,1	0,1	NUM
iajs-3409	304	3	]	]	PUNCT
iajs-3409	304	4	,	,	PUNCT
iajs-3409	304	5	and	and	CCONJ
iajs-3409	304	6	analytic	analytic	ADJ
iajs-3409	304	7	solution	solution	NOUN
iajs-3409	304	8	𝛼(𝑥	𝛼(𝑥	PROPN
iajs-3409	304	9	)	)	PUNCT
iajs-3409	304	10	=	=	PUNCT
iajs-3409	304	11	(	(	PUNCT
iajs-3409	304	12	𝑒𝑥−cos(𝑥)−sin(𝑥	𝑒𝑥−cos(𝑥)−sin(𝑥	NOUN
iajs-3409	304	13	)	)	PUNCT
iajs-3409	304	14	)	)	PUNCT
iajs-3409	305	1	2	2	NUM
iajs-3409	305	2	.	.	PUNCT
iajs-3409	305	3	problem	problem	NOUN
iajs-3409	305	4	(	(	PUNCT
iajs-3409	305	5	2	2	NUM
iajs-3409	305	6	):	):	PUNCT
iajs-3409	305	7	consider	consider	VERB
iajs-3409	305	8	the	the	DET
iajs-3409	305	9	nonhomogeneous	nonhomogeneous	ADJ
iajs-3409	305	10	nonlinear	nonlinear	ADJ
iajs-3409	305	11	ode	ode	PROPN
iajs-3409	305	12	α′′′(x	α′′′(x	NUM
iajs-3409	305	13	)	)	PUNCT
iajs-3409	305	14	=	=	PUNCT
iajs-3409	306	1	(	(	PUNCT
iajs-3409	306	2	α(x))2	α(x))2	X
iajs-3409	306	3	+	+	CCONJ
iajs-3409	306	4	cos2(x	cos2(x	NOUN
iajs-3409	306	5	)	)	PUNCT
iajs-3409	306	6	−	−	PROPN
iajs-3409	307	1	cos(x	cos(x	PROPN
iajs-3409	307	2	)	)	PUNCT
iajs-3409	308	1	−	−	NOUN
iajs-3409	308	2	1	1	NUM
iajs-3409	308	3	,	,	PUNCT
iajs-3409	308	4	with	with	ADP
iajs-3409	308	5	𝛼(0	𝛼(0	PROPN
iajs-3409	308	6	)	)	PUNCT
iajs-3409	308	7	=	=	SYM
iajs-3409	309	1	0	0	NUM
iajs-3409	309	2	,	,	PUNCT
iajs-3409	309	3	𝛼′(0	𝛼′(0	NOUN
iajs-3409	309	4	)	)	PUNCT
iajs-3409	309	5	=	=	SYM
iajs-3409	309	6	1	1	NUM
iajs-3409	309	7	,	,	PUNCT
iajs-3409	309	8	𝛼′′(0	𝛼′′(0	NOUN
iajs-3409	309	9	)	)	PUNCT
iajs-3409	309	10	=	=	SYM
iajs-3409	309	11	1	1	NUM
iajs-3409	309	12	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	NOUN
iajs-3409	309	13	0	0	NUM
iajs-3409	309	14	≤	≤	NUM
iajs-3409	309	15	𝑥	𝑥	DET
iajs-3409	309	16	≤	≤	NUM
iajs-3409	309	17	2	2	NUM
iajs-3409	309	18	,	,	PUNCT
iajs-3409	309	19	and	and	CCONJ
iajs-3409	309	20	analytic	analytic	ADJ
iajs-3409	309	21	solution	solution	NOUN
iajs-3409	309	22	𝛼(𝑥	𝛼(𝑥	PROPN
iajs-3409	309	23	)	)	PUNCT
iajs-3409	309	24	=	=	PUNCT
iajs-3409	309	25	sin	sin	NOUN
iajs-3409	309	26	(	(	PUNCT
iajs-3409	309	27	𝑥	𝑥	NOUN
iajs-3409	309	28	)	)	PUNCT
iajs-3409	309	29	.	.	PUNCT
iajs-3409	310	1	problem	problem	NOUN
iajs-3409	310	2	(	(	PUNCT
iajs-3409	310	3	3	3	NUM
iajs-3409	310	4	):	):	PUNCT
iajs-3409	310	5	the	the	DET
iajs-3409	310	6	nonhomogeneous	nonhomogeneous	ADJ
iajs-3409	310	7	nonlinear	nonlinear	ADJ
iajs-3409	310	8	odes	ode	NOUN
iajs-3409	310	9	is	be	AUX
iajs-3409	310	10	considered	consider	VERB
iajs-3409	310	11	as	as	ADP
iajs-3409	310	12	α′′′(x	α′′′(x	NUM
iajs-3409	310	13	)	)	PUNCT
iajs-3409	310	14	=	=	SYM
iajs-3409	310	15	8	8	NUM
iajs-3409	310	16	(	(	PUNCT
iajs-3409	310	17	𝛼2(𝑥	𝛼2(𝑥	NOUN
iajs-3409	310	18	)	)	PUNCT
iajs-3409	310	19	𝑒2𝑥	𝑒2𝑥	NOUN
iajs-3409	310	20	)	)	PUNCT
iajs-3409	310	21	with	with	ADP
iajs-3409	310	22	𝛼(0	𝛼(0	PROPN
iajs-3409	310	23	)	)	PUNCT
iajs-3409	310	24	=	=	NOUN
iajs-3409	310	25	1	1	NUM
iajs-3409	310	26	,	,	PUNCT
iajs-3409	310	27	𝛼′(0	𝛼′(0	NOUN
iajs-3409	310	28	)	)	PUNCT
iajs-3409	310	29	=	=	SYM
iajs-3409	310	30	2	2	NUM
iajs-3409	310	31	,	,	PUNCT
iajs-3409	310	32	𝛼′′(0	𝛼′′(0	NOUN
iajs-3409	310	33	)	)	PUNCT
iajs-3409	310	34	=	=	SYM
iajs-3409	310	35	4	4	NUM
iajs-3409	310	36	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	NOUN
iajs-3409	310	37	0	0	NUM
iajs-3409	310	38	≤	≤	NUM
iajs-3409	310	39	𝑥	𝑥	DET
iajs-3409	310	40	≤	≤	NUM
iajs-3409	310	41	1	1	NUM
iajs-3409	310	42	,	,	PUNCT
iajs-3409	310	43	and	and	CCONJ
iajs-3409	310	44	analytic	analytic	ADJ
iajs-3409	310	45	solution	solution	NOUN
iajs-3409	310	46	𝛼(𝑥	𝛼(𝑥	PROPN
iajs-3409	310	47	)	)	PUNCT
iajs-3409	311	1	=	=	NOUN
iajs-3409	311	2	𝑒2𝑥	𝑒2𝑥	NOUN
iajs-3409	311	3	.	.	PUNCT
iajs-3409	312	1	figure	figure	VERB
iajs-3409	312	2	2	2	NUM
iajs-3409	312	3	.	.	PUNCT
iajs-3409	312	4	accuracy	accuracy	NOUN
iajs-3409	312	5	curve	curve	NOUN
iajs-3409	312	6	for	for	ADP
iajs-3409	312	7	rktdio5	rktdio5	PROPN
iajs-3409	312	8	,	,	PUNCT
iajs-3409	312	9	ditrkm5	ditrkm5	PROPN
iajs-3409	312	10	,	,	PUNCT
iajs-3409	312	11	radau	radau	NOUN
iajs-3409	312	12	i	i	PRON
iajs-3409	312	13	,	,	PUNCT
iajs-3409	312	14	radau	radau	PROPN
iajs-3409	312	15	ia	ia	VERB
iajs-3409	312	16	with	with	ADP
iajs-3409	312	17	ℎ	ℎ	X
iajs-3409	312	18	=	=	SYM
iajs-3409	312	19	0.1	0.1	NUM
iajs-3409	312	20	,	,	PUNCT
iajs-3409	312	21	0.05	0.05	NUM
iajs-3409	312	22	,	,	PUNCT
iajs-3409	312	23	0.025	0.025	NUM
iajs-3409	312	24	,	,	PUNCT
iajs-3409	312	25	0.00125	0.00125	NUM
iajs-3409	312	26	,	,	PUNCT
iajs-3409	312	27	0.00625	0.00625	NUM
iajs-3409	312	28	for	for	ADP
iajs-3409	312	29	problem1	problem1	NOUN
iajs-3409	312	30	.	.	PUNCT
iajs-3409	313	1	ihjpas	ihjpas	PROPN
iajs-3409	313	2	.	.	PUNCT
iajs-3409	314	1	37	37	NUM
iajs-3409	314	2	(	(	PUNCT
iajs-3409	314	3	2	2	NUM
iajs-3409	314	4	)	)	PUNCT
iajs-3409	314	5	2024	2024	NUM
iajs-3409	314	6	402	402	NUM
iajs-3409	314	7	figure3	figure3	NOUN
iajs-3409	314	8	.	.	PUNCT
iajs-3409	315	1	accuracy	accuracy	NOUN
iajs-3409	315	2	curve	curve	NOUN
iajs-3409	315	3	for	for	ADP
iajs-3409	315	4	rktdio5	rktdio5	PROPN
iajs-3409	315	5	,	,	PUNCT
iajs-3409	315	6	ditrkm5	ditrkm5	PROPN
iajs-3409	315	7	,	,	PUNCT
iajs-3409	315	8	radau	radau	NOUN
iajs-3409	315	9	i	i	PRON
iajs-3409	315	10	,	,	PUNCT
iajs-3409	315	11	radau	radau	PROPN
iajs-3409	315	12	ia	ia	VERB
iajs-3409	315	13	with	with	ADP
iajs-3409	315	14	ℎ	ℎ	X
iajs-3409	315	15	=	=	SYM
iajs-3409	315	16	0.1	0.1	NUM
iajs-3409	315	17	,	,	PUNCT
iajs-3409	315	18	0.05	0.05	NUM
iajs-3409	315	19	,	,	PUNCT
iajs-3409	315	20	0.025	0.025	NUM
iajs-3409	315	21	,	,	PUNCT
iajs-3409	315	22	0.00125	0.00125	NUM
iajs-3409	315	23	,	,	PUNCT
iajs-3409	315	24	0.00625	0.00625	NUM
iajs-3409	315	25	for	for	ADP
iajs-3409	315	26	problem2	problem2	NOUN
iajs-3409	315	27	.	.	PUNCT
iajs-3409	316	1	figure4	figure4	ADJ
iajs-3409	316	2	.	.	PUNCT
iajs-3409	316	3	accuracy	accuracy	NOUN
iajs-3409	316	4	curve	curve	NOUN
iajs-3409	316	5	for	for	ADP
iajs-3409	316	6	rktdio5	rktdio5	PROPN
iajs-3409	316	7	,	,	PUNCT
iajs-3409	316	8	ditrkm5	ditrkm5	PROPN
iajs-3409	316	9	,	,	PUNCT
iajs-3409	316	10	radau	radau	NOUN
iajs-3409	316	11	i	i	PRON
iajs-3409	316	12	,	,	PUNCT
iajs-3409	316	13	radau	radau	PROPN
iajs-3409	316	14	ia	ia	VERB
iajs-3409	316	15	with	with	ADP
iajs-3409	316	16	ℎ	ℎ	X
iajs-3409	316	17	=	=	SYM
iajs-3409	316	18	0.1	0.1	NUM
iajs-3409	316	19	,	,	PUNCT
iajs-3409	316	20	0.05	0.05	NUM
iajs-3409	316	21	,	,	PUNCT
iajs-3409	316	22	0.025	0.025	NUM
iajs-3409	316	23	,	,	PUNCT
iajs-3409	316	24	0.00125	0.00125	NUM
iajs-3409	316	25	,	,	PUNCT
iajs-3409	316	26	0.00625	0.00625	NUM
iajs-3409	316	27	for	for	ADP
iajs-3409	316	28	problem3	problem3	PROPN
iajs-3409	316	29	.	.	PUNCT
iajs-3409	317	1	figure	figure	NOUN
iajs-3409	317	2	5	5	NUM
iajs-3409	317	3	.	.	PUNCT
iajs-3409	317	4	accuracy	accuracy	NOUN
iajs-3409	317	5	curve	curve	NOUN
iajs-3409	317	6	for	for	ADP
iajs-3409	317	7	rktdio6	rktdio6	NOUN
iajs-3409	317	8	,	,	PUNCT
iajs-3409	317	9	lobattoo	lobattoo	PROPN
iajs-3409	317	10	iii	iii	NOUN
iajs-3409	317	11	,	,	PUNCT
iajs-3409	317	12	lobattoo	lobattoo	ADJ
iajs-3409	317	13	iiib	iiib	NOUN
iajs-3409	317	14	with	with	ADP
iajs-3409	317	15	ℎ	ℎ	PROPN
iajs-3409	317	16	=	=	SYM
iajs-3409	317	17	0.1	0.1	NUM
iajs-3409	317	18	,	,	PUNCT
iajs-3409	317	19	0.05	0.05	NUM
iajs-3409	317	20	,	,	PUNCT
iajs-3409	317	21	0.025	0.025	NUM
iajs-3409	317	22	,	,	PUNCT
iajs-3409	317	23	0.00125	0.00125	NUM
iajs-3409	317	24	,	,	PUNCT
iajs-3409	317	25	0.00625	0.00625	NUM
iajs-3409	317	26	for	for	ADP
iajs-3409	317	27	problem1	problem1	NOUN
iajs-3409	317	28	.	.	PUNCT
iajs-3409	318	1	ihjpas	ihjpas	PROPN
iajs-3409	318	2	.	.	PUNCT
iajs-3409	319	1	37	37	NUM
iajs-3409	319	2	(	(	PUNCT
iajs-3409	319	3	2	2	NUM
iajs-3409	319	4	)	)	PUNCT
iajs-3409	319	5	2024	2024	NUM
iajs-3409	320	1	403	403	NUM
iajs-3409	320	2	figure	figure	NOUN
iajs-3409	320	3	6	6	NUM
iajs-3409	320	4	.	.	PUNCT
iajs-3409	320	5	accuracy	accuracy	NOUN
iajs-3409	320	6	curve	curve	NOUN
iajs-3409	320	7	for	for	ADP
iajs-3409	320	8	rktdio6	rktdio6	NOUN
iajs-3409	320	9	,	,	PUNCT
iajs-3409	320	10	lobattoo	lobattoo	PROPN
iajs-3409	320	11	iii	iii	NOUN
iajs-3409	320	12	,	,	PUNCT
iajs-3409	320	13	lobattoo	lobattoo	ADJ
iajs-3409	320	14	iiib	iiib	NOUN
iajs-3409	320	15	with	with	ADP
iajs-3409	320	16	ℎ	ℎ	PROPN
iajs-3409	320	17	=	=	SYM
iajs-3409	320	18	0.1	0.1	NUM
iajs-3409	320	19	,	,	PUNCT
iajs-3409	320	20	0.05	0.05	NUM
iajs-3409	320	21	,	,	PUNCT
iajs-3409	320	22	0.025	0.025	NUM
iajs-3409	320	23	,	,	PUNCT
iajs-3409	320	24	0.00125	0.00125	NUM
iajs-3409	320	25	,	,	PUNCT
iajs-3409	320	26	0.00625	0.00625	NUM
iajs-3409	320	27	for	for	ADP
iajs-3409	320	28	problem2	problem2	NOUN
iajs-3409	320	29	.	.	PUNCT
iajs-3409	321	1	figure	figure	NOUN
iajs-3409	321	2	7	7	NUM
iajs-3409	321	3	.	.	PUNCT
iajs-3409	321	4	accuracy	accuracy	NOUN
iajs-3409	321	5	curve	curve	NOUN
iajs-3409	321	6	for	for	ADP
iajs-3409	321	7	rktdio6	rktdio6	NOUN
iajs-3409	321	8	,	,	PUNCT
iajs-3409	321	9	lobattoo	lobattoo	PROPN
iajs-3409	321	10	iii	iii	NOUN
iajs-3409	321	11	,	,	PUNCT
iajs-3409	321	12	lobattoo	lobattoo	ADJ
iajs-3409	321	13	iiib	iiib	NOUN
iajs-3409	321	14	with	with	ADP
iajs-3409	321	15	ℎ	ℎ	PROPN
iajs-3409	321	16	=	=	SYM
iajs-3409	321	17	0.1	0.1	NUM
iajs-3409	321	18	,	,	PUNCT
iajs-3409	321	19	0.05	0.05	NUM
iajs-3409	321	20	,	,	PUNCT
iajs-3409	321	21	0.025	0.025	NUM
iajs-3409	321	22	,	,	PUNCT
iajs-3409	321	23	0.00125	0.00125	NUM
iajs-3409	321	24	,	,	PUNCT
iajs-3409	321	25	0.00625	0.00625	NUM
iajs-3409	321	26	for	for	ADP
iajs-3409	321	27	problem3	problem3	PROPN
iajs-3409	321	28	.	.	PUNCT
iajs-3409	322	1	7.2	7.2	NUM
iajs-3409	322	2	variable	variable	ADJ
iajs-3409	322	3	method	method	NOUN
iajs-3409	322	4	this	this	DET
iajs-3409	322	5	subsection	subsection	NOUN
iajs-3409	322	6	will	will	AUX
iajs-3409	322	7	apply	apply	VERB
iajs-3409	322	8	the	the	DET
iajs-3409	322	9	new	new	ADJ
iajs-3409	322	10	embedded	embed	VERB
iajs-3409	322	11	method	method	NOUN
iajs-3409	322	12	to	to	ADP
iajs-3409	322	13	the	the	DET
iajs-3409	322	14	same	same	ADJ
iajs-3409	322	15	third	third	ADJ
iajs-3409	322	16	-	-	PUNCT
iajs-3409	322	17	order	order	NOUN
iajs-3409	322	18	differential	differential	ADJ
iajs-3409	322	19	equation	equation	NOUN
iajs-3409	322	20	problems	problem	NOUN
iajs-3409	322	21	in	in	ADP
iajs-3409	322	22	the	the	DET
iajs-3409	322	23	previous	previous	ADJ
iajs-3409	322	24	subsection	subsection	NOUN
iajs-3409	322	25	.	.	PUNCT
iajs-3409	323	1	the	the	DET
iajs-3409	323	2	following	follow	VERB
iajs-3409	323	3	implicit	implicit	ADJ
iajs-3409	323	4	diagonally	diagonally	ADJ
iajs-3409	323	5	rk	rk	NOUN
iajs-3409	323	6	method	method	NOUN
iajs-3409	323	7	is	be	AUX
iajs-3409	323	8	selected	select	VERB
iajs-3409	323	9	for	for	ADP
iajs-3409	323	10	the	the	DET
iajs-3409	323	11	numerical	numerical	ADJ
iajs-3409	323	12	comparisons	comparison	NOUN
iajs-3409	323	13	.	.	PUNCT
iajs-3409	324	1	the	the	DET
iajs-3409	324	2	approximation	approximation	NOUN
iajs-3409	324	3	results	result	NOUN
iajs-3409	324	4	are	be	AUX
iajs-3409	324	5	illustrated	illustrate	VERB
iajs-3409	324	6	in	in	ADP
iajs-3409	324	7	the	the	DET
iajs-3409	324	8	tables	table	NOUN
iajs-3409	324	9	below	below	ADV
iajs-3409	324	10	for	for	ADP
iajs-3409	324	11	solving	solve	VERB
iajs-3409	324	12	problems	problem	NOUN
iajs-3409	324	13	.	.	PUNCT
iajs-3409	325	1	the	the	DET
iajs-3409	325	2	following	follow	VERB
iajs-3409	325	3	abbreviations	abbreviation	NOUN
iajs-3409	325	4	will	will	AUX
iajs-3409	325	5	be	be	AUX
iajs-3409	325	6	used	use	VERB
iajs-3409	325	7	in	in	ADP
iajs-3409	325	8	the	the	DET
iajs-3409	325	9	tables	table	NOUN
iajs-3409	325	10	:	:	PUNCT
iajs-3409	325	11			X
iajs-3409	326	1	𝑻𝒐𝒍	𝑻𝒐𝒍	NOUN
iajs-3409	326	2	:	:	PUNCT
iajs-3409	326	3	tolerance	tolerance	NOUN
iajs-3409	326	4	.	.	PUNCT
iajs-3409	327	1			PROPN
iajs-3409	327	2	method	method	PROPN
iajs-3409	327	3	:	:	PUNCT
iajs-3409	327	4	method	method	NOUN
iajs-3409	327	5	employed	employ	VERB
iajs-3409	327	6	step	step	NOUN
iajs-3409	327	7	sizes	size	NOUN
iajs-3409	327	8	between	between	ADP
iajs-3409	327	9	two	two	NUM
iajs-3409	327	10	points	point	NOUN
iajs-3409	327	11	or	or	CCONJ
iajs-3409	327	12	positions	position	NOUN
iajs-3409	327	13	.	.	PUNCT
iajs-3409	328	1			PROPN
iajs-3409	328	2	f.	f.	PROPN
iajs-3409	328	3	n	n	CCONJ
iajs-3409	328	4	:	:	PUNCT
iajs-3409	328	5	number	number	NOUN
iajs-3409	328	6	of	of	ADP
iajs-3409	328	7	the	the	DET
iajs-3409	328	8	function	function	NOUN
iajs-3409	328	9	call	call	NOUN
iajs-3409	328	10	.	.	PUNCT
iajs-3409	329	1			PRON
iajs-3409	329	2	step	step	NOUN
iajs-3409	329	3	:	:	PUNCT
iajs-3409	329	4	the	the	DET
iajs-3409	329	5	number	number	NOUN
iajs-3409	329	6	of	of	ADP
iajs-3409	329	7	successful	successful	ADJ
iajs-3409	329	8	steps	step	NOUN
iajs-3409	329	9	.	.	PUNCT
iajs-3409	330	1			PRON
iajs-3409	330	2	fstep	fstep	NOUN
iajs-3409	330	3	:	:	PUNCT
iajs-3409	330	4	the	the	DET
iajs-3409	330	5	number	number	NOUN
iajs-3409	330	6	of	of	ADP
iajs-3409	330	7	failed	fail	VERB
iajs-3409	330	8	steps	step	NOUN
iajs-3409	330	9	.	.	PUNCT
iajs-3409	331	1			PRON
iajs-3409	331	2	time	time	NOUN
iajs-3409	331	3	:	:	PUNCT
iajs-3409	331	4	execution	execution	NOUN
iajs-3409	331	5	time	time	NOUN
iajs-3409	331	6	.	.	PUNCT
iajs-3409	332	1			PUNCT
iajs-3409	333	1	erktdio6(5	erktdio6(5	PROPN
iajs-3409	333	2	):	):	PUNCT
iajs-3409	333	3	the	the	DET
iajs-3409	333	4	novel	novel	NOUN
iajs-3409	333	5	embedded	embed	VERB
iajs-3409	333	6	6(5	6(5	NUM
iajs-3409	333	7	)	)	PUNCT
iajs-3409	333	8	derived	derive	VERB
iajs-3409	333	9	in	in	ADP
iajs-3409	333	10	this	this	DET
iajs-3409	333	11	study	study	NOUN
iajs-3409	333	12	.	.	PUNCT
iajs-3409	334	1			X
iajs-3409	335	1	editrk5(4	editrk5(4	NOUN
iajs-3409	335	2	):	):	PUNCT
iajs-3409	335	3	the	the	DET
iajs-3409	335	4	embedded	embed	VERB
iajs-3409	335	5	diagonally	diagonally	ADV
iajs-3409	335	6	implicit	implicit	ADJ
iajs-3409	335	7	5(4	5(4	NOUN
iajs-3409	335	8	)	)	PUNCT
iajs-3409	335	9	rk	rk	NOUN
iajs-3409	335	10	derived	derive	VERB
iajs-3409	335	11	in	in	ADP
iajs-3409	335	12	[	[	X
iajs-3409	335	13	7	7	NUM
iajs-3409	335	14	]	]	PUNCT
iajs-3409	335	15	.	.	PUNCT
iajs-3409	336	1	ihjpas	ihjpas	PROPN
iajs-3409	336	2	.	.	PUNCT
iajs-3409	337	1	37	37	NUM
iajs-3409	337	2	(	(	PUNCT
iajs-3409	337	3	2	2	NUM
iajs-3409	337	4	)	)	PUNCT
iajs-3409	337	5	2024	2024	NUM
iajs-3409	337	6	404	404	NUM
iajs-3409	337	7	table	table	NOUN
iajs-3409	337	8	4	4	NUM
iajs-3409	337	9	.	.	PUNCT
iajs-3409	337	10	comparisons	comparison	NOUN
iajs-3409	337	11	of	of	ADP
iajs-3409	337	12	number	number	NOUN
iajs-3409	337	13	of	of	ADP
iajs-3409	337	14	function	function	NOUN
iajs-3409	337	15	call	call	NOUN
iajs-3409	337	16	and	and	CCONJ
iajs-3409	337	17	time	time	NOUN
iajs-3409	337	18	of	of	ADP
iajs-3409	337	19	erktdio6(5	erktdio6(5	PROPN
iajs-3409	337	20	)	)	PUNCT
iajs-3409	337	21	and	and	CCONJ
iajs-3409	337	22	editrk	editrk	NOUN
iajs-3409	337	23	5(4	5(4	NUM
iajs-3409	337	24	)	)	PUNCT
iajs-3409	337	25	with	with	ADP
iajs-3409	337	26	h	h	NOUN
iajs-3409	337	27	=	=	SYM
iajs-3409	337	28	10−6	10−6	NUM
iajs-3409	337	29	,	,	PUNCT
iajs-3409	337	30	10−8	10−8	NUM
iajs-3409	337	31	,	,	PUNCT
iajs-3409	337	32	10−10	10−10	NUM
iajs-3409	337	33	for	for	ADP
iajs-3409	337	34	the	the	DET
iajs-3409	337	35	problem	problem	NOUN
iajs-3409	337	36	1	1	NUM
iajs-3409	337	37	.	.	X
iajs-3409	337	38	fstep	fstep	NOUN
iajs-3409	337	39	step	step	NOUN
iajs-3409	337	40	time	time	NOUN
iajs-3409	337	41	no	no	INTJ
iajs-3409	337	42	.	.	PUNCT
iajs-3409	338	1	of	of	ADP
iajs-3409	338	2	function	function	NOUN
iajs-3409	338	3	call	call	NOUN
iajs-3409	338	4	method	method	NOUN
iajs-3409	338	5	𝑻𝑶𝑳(𝓴	𝑻𝑶𝑳(𝓴	PROPN
iajs-3409	338	6	)	)	PUNCT
iajs-3409	338	7	2	2	NUM
iajs-3409	338	8	5	5	NUM
iajs-3409	338	9	0.025	0.025	NUM
iajs-3409	338	10	270	270	NUM
iajs-3409	338	11	erktdio6(5	erktdio6(5	PROPN
iajs-3409	338	12	)	)	PUNCT
iajs-3409	338	13	10−6	10−6	NUM
iajs-3409	338	14	0	0	NUM
iajs-3409	338	15	13	13	NUM
iajs-3409	338	16	0.033	0.033	NUM
iajs-3409	338	17	421	421	NUM
iajs-3409	338	18	editrk	editrk	NOUN
iajs-3409	338	19	5(4	5(4	NUM
iajs-3409	338	20	)	)	PUNCT
iajs-3409	338	21	2	2	NUM
iajs-3409	338	22	16	16	NUM
iajs-3409	338	23	0.038	0.038	NUM
iajs-3409	338	24	1210	1210	NUM
iajs-3409	338	25	erktdio6(5	erktdio6(5	SYM
iajs-3409	338	26	)	)	PUNCT
iajs-3409	338	27	10−8	10−8	NUM
iajs-3409	338	28	0	0	NUM
iajs-3409	338	29	40	40	NUM
iajs-3409	338	30	0.047	0.047	NUM
iajs-3409	338	31	1962	1962	NUM
iajs-3409	338	32	editrk	editrk	NOUN
iajs-3409	338	33	5(4	5(4	NUM
iajs-3409	338	34	)	)	PUNCT
iajs-3409	338	35	2	2	NUM
iajs-3409	338	36	72	72	NUM
iajs-3409	338	37	0.060	0.060	NUM
iajs-3409	338	38	6353	6353	NUM
iajs-3409	338	39	erktdio6(5	erktdio6(5	SYM
iajs-3409	338	40	)	)	PUNCT
iajs-3409	338	41	10−10	10−10	NUM
iajs-3409	338	42	1	1	NUM
iajs-3409	338	43	128	128	NUM
iajs-3409	338	44	0.074	0.074	NUM
iajs-3409	338	45	9105	9105	NUM
iajs-3409	338	46	editrk	editrk	NOUN
iajs-3409	338	47	5(4	5(4	NUM
iajs-3409	338	48	)	)	PUNCT
iajs-3409	338	49	table	table	NOUN
iajs-3409	338	50	5	5	NUM
iajs-3409	338	51	.	.	PUNCT
iajs-3409	338	52	comparisons	comparison	NOUN
iajs-3409	338	53	of	of	ADP
iajs-3409	338	54	number	number	NOUN
iajs-3409	338	55	of	of	ADP
iajs-3409	338	56	function	function	NOUN
iajs-3409	338	57	call	call	NOUN
iajs-3409	338	58	and	and	CCONJ
iajs-3409	338	59	time	time	NOUN
iajs-3409	338	60	of	of	ADP
iajs-3409	338	61	editrkm	editrkm	NOUN
iajs-3409	338	62	4(3	4(3	NUM
iajs-3409	338	63	)	)	PUNCT
iajs-3409	338	64	and	and	CCONJ
iajs-3409	338	65	editrkm	editrkm	PROPN
iajs-3409	338	66	5(4	5(4	PROPN
iajs-3409	338	67	)	)	PUNCT
iajs-3409	338	68	with	with	ADP
iajs-3409	338	69	h	h	NOUN
iajs-3409	338	70	=	=	SYM
iajs-3409	338	71	10−2	10−2	NUM
iajs-3409	338	72	,	,	PUNCT
iajs-3409	338	73	10−4	10−4	NUM
iajs-3409	338	74	,	,	PUNCT
iajs-3409	338	75	10−6	10−6	NUM
iajs-3409	338	76	for	for	ADP
iajs-3409	338	77	the	the	DET
iajs-3409	338	78	problem	problem	NOUN
iajs-3409	338	79	2	2	NUM
iajs-3409	338	80	.	.	NOUN
iajs-3409	338	81	fstep	fstep	NOUN
iajs-3409	338	82	step	step	NOUN
iajs-3409	338	83	time	time	NOUN
iajs-3409	338	84	no	no	INTJ
iajs-3409	338	85	.	.	PUNCT
iajs-3409	338	86	of	of	ADP
iajs-3409	338	87	function	function	NOUN
iajs-3409	338	88	call	call	NOUN
iajs-3409	338	89	method	method	NOUN
iajs-3409	338	90	𝑻𝑶𝑳(𝓴	𝑻𝑶𝑳(𝓴	PROPN
iajs-3409	338	91	)	)	PUNCT
iajs-3409	338	92	0	0	NUM
iajs-3409	338	93	3	3	NUM
iajs-3409	338	94	0.032	0.032	NUM
iajs-3409	338	95	183	183	NUM
iajs-3409	338	96	erktdio6(5	erktdio6(5	PROPN
iajs-3409	338	97	)	)	PUNCT
iajs-3409	338	98	10−6	10−6	NUM
iajs-3409	338	99	0	0	NUM
iajs-3409	338	100	7	7	NUM
iajs-3409	338	101	0.062	0.062	NUM
iajs-3409	338	102	166	166	NUM
iajs-3409	338	103	editrk	editrk	NOUN
iajs-3409	338	104	5(4	5(4	NUM
iajs-3409	338	105	)	)	PUNCT
iajs-3409	338	106	0	0	NUM
iajs-3409	338	107	8	8	NUM
iajs-3409	338	108	0.045	0.045	NUM
iajs-3409	338	109	662	662	NUM
iajs-3409	338	110	erktdio6(5	erktdio6(5	SYM
iajs-3409	338	111	)	)	PUNCT
iajs-3409	338	112	10−8	10−8	NUM
iajs-3409	338	113	0	0	NUM
iajs-3409	338	114	22	22	NUM
iajs-3409	338	115	0.083	0.083	NUM
iajs-3409	338	116	759	759	NUM
iajs-3409	338	117	editrk	editrk	NOUN
iajs-3409	338	118	5(4	5(4	NUM
iajs-3409	338	119	)	)	PUNCT
iajs-3409	338	120	0	0	NUM
iajs-3409	338	121	29	29	NUM
iajs-3409	338	122	0.080	0.080	NUM
iajs-3409	338	123	2533	2533	NUM
iajs-3409	338	124	erktdio6(5	erktdio6(5	PROPN
iajs-3409	338	125	)	)	PUNCT
iajs-3409	338	126	10−10	10−10	NUM
iajs-3409	338	127	1	1	NUM
iajs-3409	338	128	69	69	NUM
iajs-3409	338	129	0.119	0.119	NUM
iajs-3409	338	130	3495	3495	NUM
iajs-3409	338	131	editrk	editrk	NOUN
iajs-3409	338	132	5(4	5(4	NOUN
iajs-3409	338	133	)	)	PUNCT
iajs-3409	338	134	table	table	NOUN
iajs-3409	338	135	6	6	NUM
iajs-3409	338	136	.	.	PUNCT
iajs-3409	338	137	comparisons	comparison	NOUN
iajs-3409	338	138	of	of	ADP
iajs-3409	338	139	number	number	NOUN
iajs-3409	338	140	of	of	ADP
iajs-3409	338	141	function	function	NOUN
iajs-3409	338	142	call	call	NOUN
iajs-3409	338	143	and	and	CCONJ
iajs-3409	338	144	time	time	NOUN
iajs-3409	338	145	of	of	ADP
iajs-3409	338	146	editrkm	editrkm	NOUN
iajs-3409	338	147	4(3	4(3	NUM
iajs-3409	338	148	)	)	PUNCT
iajs-3409	338	149	and	and	CCONJ
iajs-3409	338	150	editrkm	editrkm	PROPN
iajs-3409	338	151	5(4	5(4	PROPN
iajs-3409	338	152	)	)	PUNCT
iajs-3409	338	153	with	with	ADP
iajs-3409	338	154	h	h	NOUN
iajs-3409	338	155	=	=	SYM
iajs-3409	338	156	10−2	10−2	NUM
iajs-3409	338	157	,	,	PUNCT
iajs-3409	338	158	10−4	10−4	NUM
iajs-3409	338	159	,	,	PUNCT
iajs-3409	338	160	10−6	10−6	NUM
iajs-3409	338	161	for	for	ADP
iajs-3409	338	162	the	the	DET
iajs-3409	338	163	problem	problem	NOUN
iajs-3409	338	164	3	3	X
iajs-3409	338	165	.	.	NOUN
iajs-3409	338	166	fstep	fstep	NOUN
iajs-3409	338	167	step	step	NOUN
iajs-3409	338	168	time	time	NOUN
iajs-3409	338	169	no	no	INTJ
iajs-3409	338	170	.	.	PUNCT
iajs-3409	338	171	of	of	ADP
iajs-3409	338	172	function	function	NOUN
iajs-3409	338	173	call	call	NOUN
iajs-3409	338	174	method	method	NOUN
iajs-3409	338	175	𝑻𝑶𝑳(𝓴	𝑻𝑶𝑳(𝓴	PROPN
iajs-3409	338	176	)	)	PUNCT
iajs-3409	338	177	1	1	NUM
iajs-3409	338	178	97	97	NUM
iajs-3409	338	179	0.012	0.012	NUM
iajs-3409	338	180	466	466	NUM
iajs-3409	338	181	erktdio6(5	erktdio6(5	PROPN
iajs-3409	338	182	)	)	PUNCT
iajs-3409	338	183	10−6	10−6	NUM
iajs-3409	338	184	0	0	NUM
iajs-3409	338	185	29	29	NUM
iajs-3409	338	186	0.035	0.035	NUM
iajs-3409	338	187	882	882	NUM
iajs-3409	338	188	editrk	editrk	NOUN
iajs-3409	338	189	5(4	5(4	NUM
iajs-3409	338	190	)	)	PUNCT
iajs-3409	338	191	1	1	NUM
iajs-3409	338	192	315	315	NUM
iajs-3409	338	193	0.031	0.031	NUM
iajs-3409	338	194	2511	2511	NUM
iajs-3409	338	195	erktdio6(5	erktdio6(5	SYM
iajs-3409	338	196	)	)	PUNCT
iajs-3409	338	197	10−8	10−8	NUM
iajs-3409	338	198	1	1	NUM
iajs-3409	338	199	152	152	NUM
iajs-3409	338	200	0.059	0.059	NUM
iajs-3409	338	201	4101	4101	NUM
iajs-3409	338	202	editrk	editrk	NOUN
iajs-3409	338	203	5(4	5(4	NOUN
iajs-3409	338	204	)	)	PUNCT
iajs-3409	338	205	1	1	NUM
iajs-3409	338	206	1260	1260	NUM
iajs-3409	338	207	0.075	0.075	NUM
iajs-3409	338	208	13325	13325	NUM
iajs-3409	338	209	erktdio6(5	erktdio6(5	PROPN
iajs-3409	338	210	)	)	PUNCT
iajs-3409	338	211	10−10	10−10	NUM
iajs-3409	338	212	2	2	NUM
iajs-3409	338	213	725	725	NUM
iajs-3409	338	214	0.095	0.095	NUM
iajs-3409	338	215	19044	19044	NUM
iajs-3409	338	216	editrk	editrk	NOUN
iajs-3409	338	217	5(4	5(4	NOUN
iajs-3409	338	218	)	)	PUNCT
iajs-3409	338	219	ihjpas	ihjpa	NOUN
iajs-3409	338	220	.	.	PUNCT
iajs-3409	339	1	37	37	NUM
iajs-3409	339	2	(	(	PUNCT
iajs-3409	339	3	2	2	NUM
iajs-3409	339	4	)	)	PUNCT
iajs-3409	339	5	2024	2024	NUM
iajs-3409	339	6	405	405	NUM
iajs-3409	339	7	problem	problem	NOUN
iajs-3409	339	8	1	1	NUM
iajs-3409	339	9	problem	problem	NOUN
iajs-3409	339	10	2	2	NUM
iajs-3409	339	11	problem	problem	NOUN
iajs-3409	339	12	3	3	NUM
iajs-3409	339	13	figure	figure	NOUN
iajs-3409	339	14	8	8	NUM
iajs-3409	339	15	:	:	PUNCT
iajs-3409	339	16	accuracy	accuracy	NOUN
iajs-3409	339	17	curve	curve	NOUN
iajs-3409	339	18	for	for	ADP
iajs-3409	339	19	erktdio6(5	erktdio6(5	PROPN
iajs-3409	339	20	)	)	PUNCT
iajs-3409	339	21	and	and	CCONJ
iajs-3409	339	22	editrk5(4	editrk5(4	PROPN
iajs-3409	339	23	)	)	PUNCT
iajs-3409	339	24	with	with	ADP
iajs-3409	339	25	ℎ	ℎ	PROPN
iajs-3409	339	26	=	=	SYM
iajs-3409	339	27	10−6	10−6	NUM
iajs-3409	339	28	,	,	PUNCT
iajs-3409	339	29	10−8	10−8	NUM
iajs-3409	339	30	,	,	PUNCT
iajs-3409	339	31	10−10	10−10	NUM
iajs-3409	339	32	.	.	PUNCT
iajs-3409	340	1	ihjpas	ihjpas	PROPN
iajs-3409	340	2	.	.	PUNCT
iajs-3409	341	1	37	37	NUM
iajs-3409	341	2	(	(	PUNCT
iajs-3409	341	3	2	2	NUM
iajs-3409	341	4	)	)	PUNCT
iajs-3409	341	5	2024	2024	NUM
iajs-3409	341	6	406	406	NUM
iajs-3409	341	7	8	8	NUM
iajs-3409	341	8	.	.	PUNCT
iajs-3409	342	1	discussions	discussion	NOUN
iajs-3409	342	2	the	the	DET
iajs-3409	342	3	objective	objective	NOUN
iajs-3409	342	4	of	of	ADP
iajs-3409	342	5	our	our	PRON
iajs-3409	342	6	research	research	NOUN
iajs-3409	342	7	was	be	AUX
iajs-3409	342	8	to	to	PART
iajs-3409	342	9	directly	directly	ADV
iajs-3409	342	10	solve	solve	VERB
iajs-3409	342	11	third	third	ADJ
iajs-3409	342	12	-	-	PUNCT
iajs-3409	342	13	order	order	NOUN
iajs-3409	342	14	ordinary	ordinary	ADJ
iajs-3409	342	15	differential	differential	ADJ
iajs-3409	342	16	equations	equation	NOUN
iajs-3409	342	17	(	(	PUNCT
iajs-3409	342	18	odes	ode	NOUN
iajs-3409	342	19	)	)	PUNCT
iajs-3409	342	20	using	use	VERB
iajs-3409	342	21	the	the	DET
iajs-3409	342	22	rktdio	rktdio	NOUN
iajs-3409	342	23	approach	approach	NOUN
iajs-3409	342	24	,	,	PUNCT
iajs-3409	342	25	which	which	PRON
iajs-3409	342	26	is	be	AUX
iajs-3409	342	27	based	base	VERB
iajs-3409	342	28	on	on	ADP
iajs-3409	342	29	the	the	DET
iajs-3409	342	30	algebraic	algebraic	ADJ
iajs-3409	342	31	theory	theory	NOUN
iajs-3409	342	32	of	of	ADP
iajs-3409	342	33	order	order	NOUN
iajs-3409	342	34	conditions	condition	NOUN
iajs-3409	342	35	.	.	PUNCT
iajs-3409	343	1	previous	previous	ADJ
iajs-3409	343	2	research	research	NOUN
iajs-3409	343	3	has	have	AUX
iajs-3409	343	4	primarily	primarily	ADV
iajs-3409	343	5	concentrated	concentrate	VERB
iajs-3409	343	6	on	on	ADP
iajs-3409	343	7	defining	define	VERB
iajs-3409	343	8	algebraic	algebraic	ADJ
iajs-3409	343	9	order	order	NOUN
iajs-3409	343	10	conditions	condition	NOUN
iajs-3409	343	11	and	and	CCONJ
iajs-3409	343	12	b	b	X
iajs-3409	343	13	-	-	PUNCT
iajs-3409	343	14	series	series	NOUN
iajs-3409	343	15	theory	theory	NOUN
iajs-3409	343	16	to	to	PART
iajs-3409	343	17	solve	solve	VERB
iajs-3409	343	18	firstand	firstand	NOUN
iajs-3409	343	19	second	second	ADJ
iajs-3409	343	20	-	-	PUNCT
iajs-3409	343	21	order	order	NOUN
iajs-3409	343	22	ordinary	ordinary	ADJ
iajs-3409	343	23	differential	differential	ADJ
iajs-3409	343	24	equations	equation	NOUN
iajs-3409	343	25	(	(	PUNCT
iajs-3409	343	26	odes	ode	NOUN
iajs-3409	343	27	)	)	PUNCT
iajs-3409	343	28	.	.	PUNCT
iajs-3409	344	1	however	however	ADV
iajs-3409	344	2	,	,	PUNCT
iajs-3409	344	3	we	we	PRON
iajs-3409	344	4	were	be	AUX
iajs-3409	344	5	inspired	inspire	VERB
iajs-3409	344	6	to	to	PART
iajs-3409	344	7	expand	expand	VERB
iajs-3409	344	8	upon	upon	SCONJ
iajs-3409	344	9	these	these	DET
iajs-3409	344	10	ideas	idea	NOUN
iajs-3409	344	11	and	and	CCONJ
iajs-3409	344	12	create	create	VERB
iajs-3409	344	13	the	the	DET
iajs-3409	344	14	rktdio	rktdio	NOUN
iajs-3409	344	15	formula	formula	NOUN
iajs-3409	344	16	specifically	specifically	ADV
iajs-3409	344	17	designed	design	VERB
iajs-3409	344	18	for	for	ADP
iajs-3409	344	19	third	third	ADJ
iajs-3409	344	20	-	-	PUNCT
iajs-3409	344	21	order	order	NOUN
iajs-3409	344	22	odes	ode	NOUN
iajs-3409	344	23	.	.	PUNCT
iajs-3409	345	1	as	as	ADP
iajs-3409	345	2	a	a	DET
iajs-3409	345	3	result	result	NOUN
iajs-3409	345	4	,	,	PUNCT
iajs-3409	345	5	the	the	DET
iajs-3409	345	6	rktdio5	rktdio5	NOUN
iajs-3409	345	7	and	and	CCONJ
iajs-3409	345	8	rktdio6	rktdio6	NOUN
iajs-3409	345	9	methods	method	NOUN
iajs-3409	345	10	were	be	AUX
iajs-3409	345	11	developed	develop	VERB
iajs-3409	345	12	,	,	PUNCT
iajs-3409	345	13	offering	offer	VERB
iajs-3409	345	14	improved	improved	ADJ
iajs-3409	345	15	computing	computing	NOUN
iajs-3409	345	16	efficiency	efficiency	NOUN
iajs-3409	345	17	and	and	CCONJ
iajs-3409	345	18	accuracy	accuracy	NOUN
iajs-3409	345	19	for	for	ADP
iajs-3409	345	20	solving	solve	VERB
iajs-3409	345	21	certain	certain	ADJ
iajs-3409	345	22	third	third	ADJ
iajs-3409	345	23	-	-	PUNCT
iajs-3409	345	24	order	order	NOUN
iajs-3409	345	25	odes	ode	NOUN
iajs-3409	345	26	as	as	ADP
iajs-3409	345	27	compared	compare	VERB
iajs-3409	345	28	to	to	ADP
iajs-3409	345	29	other	other	ADJ
iajs-3409	345	30	current	current	ADJ
iajs-3409	345	31	approaches	approach	NOUN
iajs-3409	345	32	.	.	PUNCT
iajs-3409	346	1	in	in	ADP
iajs-3409	346	2	addition	addition	NOUN
iajs-3409	346	3	,	,	PUNCT
iajs-3409	346	4	we	we	PRON
iajs-3409	346	5	shared	share	VERB
iajs-3409	346	6	the	the	DET
iajs-3409	346	7	results	result	NOUN
iajs-3409	346	8	of	of	ADP
iajs-3409	346	9	our	our	PRON
iajs-3409	346	10	study	study	NOUN
iajs-3409	346	11	on	on	ADP
iajs-3409	346	12	the	the	DET
iajs-3409	346	13	embedded	embed	VERB
iajs-3409	346	14	diagonal	diagonal	ADJ
iajs-3409	346	15	implicit	implicit	ADJ
iajs-3409	346	16	type	type	NOUN
iajs-3409	346	17	rungekutta	rungekutta	NOUN
iajs-3409	346	18	technique	technique	NOUN
iajs-3409	346	19	(	(	PUNCT
iajs-3409	346	20	erktdio	erktdio	NOUN
iajs-3409	346	21	)	)	PUNCT
iajs-3409	346	22	.	.	PUNCT
iajs-3409	347	1	we	we	PRON
iajs-3409	347	2	assessed	assess	VERB
iajs-3409	347	3	the	the	DET
iajs-3409	347	4	performance	performance	NOUN
iajs-3409	347	5	of	of	ADP
iajs-3409	347	6	our	our	PRON
iajs-3409	347	7	method	method	NOUN
iajs-3409	347	8	(	(	PUNCT
iajs-3409	347	9	erktdio6(5	erktdio6(5	PROPN
iajs-3409	347	10	)	)	PUNCT
iajs-3409	347	11	)	)	PUNCT
iajs-3409	347	12	in	in	ADP
iajs-3409	347	13	comparison	comparison	NOUN
iajs-3409	347	14	to	to	ADP
iajs-3409	347	15	other	other	ADJ
iajs-3409	347	16	approaches	approach	NOUN
iajs-3409	347	17	by	by	ADP
iajs-3409	347	18	examining	examine	VERB
iajs-3409	347	19	the	the	DET
iajs-3409	347	20	decimal	decimal	ADJ
iajs-3409	347	21	logarithm	logarithm	NOUN
iajs-3409	347	22	of	of	ADP
iajs-3409	347	23	the	the	DET
iajs-3409	347	24	highest	high	ADJ
iajs-3409	347	25	time	time	NOUN
iajs-3409	347	26	curve	curve	NOUN
iajs-3409	347	27	and	and	CCONJ
iajs-3409	347	28	the	the	DET
iajs-3409	347	29	logarithm	logarithm	NOUN
iajs-3409	347	30	of	of	ADP
iajs-3409	347	31	the	the	DET
iajs-3409	347	32	function	function	NOUN
iajs-3409	347	33	call	call	NOUN
iajs-3409	347	34	estimates	estimate	NOUN
iajs-3409	347	35	obtained	obtain	VERB
iajs-3409	347	36	from	from	ADP
iajs-3409	347	37	tables	table	NOUN
iajs-3409	347	38	4	4	NUM
iajs-3409	347	39	-	-	SYM
iajs-3409	347	40	6	6	NUM
iajs-3409	347	41	.	.	PUNCT
iajs-3409	348	1	we	we	PRON
iajs-3409	348	2	utilised	utilise	VERB
iajs-3409	348	3	three	three	NUM
iajs-3409	348	4	separate	separate	ADJ
iajs-3409	348	5	test	test	NOUN
iajs-3409	348	6	problems	problem	NOUN
iajs-3409	348	7	and	and	CCONJ
iajs-3409	348	8	calculated	calculate	VERB
iajs-3409	348	9	the	the	DET
iajs-3409	348	10	logarithm	logarithm	NOUN
iajs-3409	348	11	of	of	ADP
iajs-3409	348	12	the	the	DET
iajs-3409	348	13	time	time	NOUN
iajs-3409	348	14	curve	curve	NOUN
iajs-3409	348	15	utilising	utilise	VERB
iajs-3409	348	16	various	various	ADJ
iajs-3409	348	17	tolerance	tolerance	NOUN
iajs-3409	348	18	values	value	NOUN
iajs-3409	348	19	.	.	PUNCT
iajs-3409	349	1	figure	figure	NOUN
iajs-3409	349	2	10	10	NUM
iajs-3409	349	3	was	be	AUX
iajs-3409	349	4	generated	generate	VERB
iajs-3409	349	5	using	use	VERB
iajs-3409	349	6	the	the	DET
iajs-3409	349	7	numerical	numerical	ADJ
iajs-3409	349	8	data	data	PROPN
iajs-3409	349	9	obtained	obtain	VERB
iajs-3409	349	10	from	from	ADP
iajs-3409	349	11	tables	table	NOUN
iajs-3409	349	12	4	4	NUM
iajs-3409	349	13	-	-	SYM
iajs-3409	349	14	6	6	NUM
iajs-3409	349	15	.	.	PUNCT
iajs-3409	350	1	it	it	PRON
iajs-3409	350	2	presents	present	VERB
iajs-3409	350	3	the	the	DET
iajs-3409	350	4	number	number	NOUN
iajs-3409	350	5	of	of	ADP
iajs-3409	350	6	successful	successful	ADJ
iajs-3409	350	7	and	and	CCONJ
iajs-3409	350	8	failed	fail	VERB
iajs-3409	350	9	steps	step	NOUN
iajs-3409	350	10	that	that	PRON
iajs-3409	350	11	occurred	occur	VERB
iajs-3409	350	12	during	during	ADP
iajs-3409	350	13	the	the	DET
iajs-3409	350	14	calculations	calculation	NOUN
iajs-3409	350	15	.	.	PUNCT
iajs-3409	351	1	our	our	PRON
iajs-3409	351	2	work	work	NOUN
iajs-3409	351	3	has	have	AUX
iajs-3409	351	4	enhanced	enhance	VERB
iajs-3409	351	5	and	and	CCONJ
iajs-3409	351	6	refined	refine	VERB
iajs-3409	351	7	the	the	DET
iajs-3409	351	8	method	method	NOUN
iajs-3409	351	9	by	by	ADP
iajs-3409	351	10	transitioning	transition	VERB
iajs-3409	351	11	from	from	ADP
iajs-3409	351	12	an	an	DET
iajs-3409	351	13	explicit	explicit	ADJ
iajs-3409	351	14	to	to	ADP
iajs-3409	351	15	an	an	DET
iajs-3409	351	16	implicit	implicit	ADJ
iajs-3409	351	17	approach	approach	NOUN
iajs-3409	351	18	and	and	CCONJ
iajs-3409	351	19	from	from	ADP
iajs-3409	351	20	a	a	DET
iajs-3409	351	21	direct	direct	ADJ
iajs-3409	351	22	to	to	ADP
iajs-3409	351	23	a	a	DET
iajs-3409	351	24	diagonal	diagonal	ADJ
iajs-3409	351	25	scheme	scheme	NOUN
iajs-3409	351	26	.	.	PUNCT
iajs-3409	352	1	9	9	X
iajs-3409	352	2	.	.	X
iajs-3409	352	3	conclusions	conclusion	NOUN
iajs-3409	352	4	ultimately	ultimately	ADV
iajs-3409	352	5	,	,	PUNCT
iajs-3409	352	6	our	our	PRON
iajs-3409	352	7	research	research	NOUN
iajs-3409	352	8	has	have	AUX
iajs-3409	352	9	made	make	VERB
iajs-3409	352	10	a	a	DET
iajs-3409	352	11	significant	significant	ADJ
iajs-3409	352	12	contribution	contribution	NOUN
iajs-3409	352	13	to	to	ADP
iajs-3409	352	14	the	the	DET
iajs-3409	352	15	progress	progress	NOUN
iajs-3409	352	16	of	of	ADP
iajs-3409	352	17	numerical	numerical	ADJ
iajs-3409	352	18	methods	method	NOUN
iajs-3409	352	19	for	for	ADP
iajs-3409	352	20	solving	solve	VERB
iajs-3409	352	21	third	third	ADJ
iajs-3409	352	22	-	-	PUNCT
iajs-3409	352	23	order	order	NOUN
iajs-3409	352	24	ordinary	ordinary	ADJ
iajs-3409	352	25	differential	differential	ADJ
iajs-3409	352	26	equations	equation	NOUN
iajs-3409	352	27	.	.	PUNCT
iajs-3409	353	1	the	the	DET
iajs-3409	353	2	introduction	introduction	NOUN
iajs-3409	353	3	of	of	ADP
iajs-3409	353	4	the	the	DET
iajs-3409	353	5	rktdio5	rktdio5	NOUN
iajs-3409	353	6	and	and	CCONJ
iajs-3409	353	7	rktdio6	rktdio6	NOUN
iajs-3409	353	8	techniques	technique	NOUN
iajs-3409	353	9	provides	provide	VERB
iajs-3409	353	10	improved	improved	ADJ
iajs-3409	353	11	computational	computational	ADJ
iajs-3409	353	12	efficiency	efficiency	NOUN
iajs-3409	353	13	and	and	CCONJ
iajs-3409	353	14	precision	precision	NOUN
iajs-3409	353	15	for	for	ADP
iajs-3409	353	16	particular	particular	ADJ
iajs-3409	353	17	third	third	ADJ
iajs-3409	353	18	-	-	PUNCT
iajs-3409	353	19	order	order	NOUN
iajs-3409	353	20	ordinary	ordinary	ADJ
iajs-3409	353	21	differential	differential	ADJ
iajs-3409	353	22	equations	equation	NOUN
iajs-3409	353	23	(	(	PUNCT
iajs-3409	353	24	odes	ode	NOUN
iajs-3409	353	25	)	)	PUNCT
iajs-3409	353	26	.	.	PUNCT
iajs-3409	354	1	furthermore	furthermore	ADV
iajs-3409	354	2	,	,	PUNCT
iajs-3409	354	3	our	our	PRON
iajs-3409	354	4	examination	examination	NOUN
iajs-3409	354	5	of	of	ADP
iajs-3409	354	6	the	the	DET
iajs-3409	354	7	erktdio	erktdio	NOUN
iajs-3409	354	8	technique	technique	NOUN
iajs-3409	354	9	showcases	showcase	VERB
iajs-3409	354	10	its	its	PRON
iajs-3409	354	11	efficacy	efficacy	NOUN
iajs-3409	354	12	in	in	ADP
iajs-3409	354	13	comparison	comparison	NOUN
iajs-3409	354	14	to	to	ADP
iajs-3409	354	15	alternative	alternative	ADJ
iajs-3409	354	16	methods	method	NOUN
iajs-3409	354	17	,	,	PUNCT
iajs-3409	354	18	especially	especially	ADV
iajs-3409	354	19	in	in	ADP
iajs-3409	354	20	terms	term	NOUN
iajs-3409	354	21	of	of	ADP
iajs-3409	354	22	the	the	DET
iajs-3409	354	23	number	number	NOUN
iajs-3409	354	24	of	of	ADP
iajs-3409	354	25	successful	successful	ADJ
iajs-3409	354	26	steps	step	NOUN
iajs-3409	354	27	in	in	ADP
iajs-3409	354	28	computations	computation	NOUN
iajs-3409	354	29	.	.	PUNCT
iajs-3409	355	1	our	our	PRON
iajs-3409	355	2	methods	method	NOUN
iajs-3409	355	3	provide	provide	VERB
iajs-3409	355	4	the	the	DET
iajs-3409	355	5	potential	potential	NOUN
iajs-3409	355	6	for	for	ADP
iajs-3409	355	7	enhanced	enhanced	ADJ
iajs-3409	355	8	solutions	solution	NOUN
iajs-3409	355	9	of	of	ADP
iajs-3409	355	10	third	third	ADJ
iajs-3409	355	11	-	-	PUNCT
iajs-3409	355	12	order	order	NOUN
iajs-3409	355	13	odes	ode	NOUN
iajs-3409	355	14	by	by	ADP
iajs-3409	355	15	adopting	adopt	VERB
iajs-3409	355	16	implicit	implicit	ADJ
iajs-3409	355	17	and	and	CCONJ
iajs-3409	355	18	diagonal	diagonal	ADJ
iajs-3409	355	19	schemes	scheme	NOUN
iajs-3409	355	20	.	.	PUNCT
iajs-3409	356	1	in	in	ADP
iajs-3409	356	2	summary	summary	NOUN
iajs-3409	356	3	,	,	PUNCT
iajs-3409	356	4	these	these	DET
iajs-3409	356	5	discoveries	discovery	NOUN
iajs-3409	356	6	expand	expand	VERB
iajs-3409	356	7	the	the	DET
iajs-3409	356	8	current	current	ADJ
iajs-3409	356	9	understanding	understanding	NOUN
iajs-3409	356	10	of	of	ADP
iajs-3409	356	11	numerical	numerical	ADJ
iajs-3409	356	12	analysis	analysis	NOUN
iajs-3409	356	13	and	and	CCONJ
iajs-3409	356	14	computational	computational	ADJ
iajs-3409	356	15	mathematics	mathematic	NOUN
iajs-3409	356	16	,	,	PUNCT
iajs-3409	356	17	offering	offer	VERB
iajs-3409	356	18	useful	useful	ADJ
iajs-3409	356	19	insights	insight	NOUN
iajs-3409	356	20	for	for	ADP
iajs-3409	356	21	future	future	ADJ
iajs-3409	356	22	investigations	investigation	NOUN
iajs-3409	356	23	in	in	ADP
iajs-3409	356	24	this	this	DET
iajs-3409	356	25	field	field	NOUN
iajs-3409	356	26	.	.	PUNCT
iajs-3409	357	1	acknowledgment	acknowledgment	NOUN
iajs-3409	357	2	the	the	DET
iajs-3409	357	3	authors	author	NOUN
iajs-3409	357	4	have	have	AUX
iajs-3409	357	5	greatly	greatly	ADV
iajs-3409	357	6	appreciated	appreciate	VERB
iajs-3409	357	7	the	the	DET
iajs-3409	357	8	referees	referee	NOUN
iajs-3409	357	9	for	for	ADP
iajs-3409	357	10	their	their	PRON
iajs-3409	357	11	valuable	valuable	ADJ
iajs-3409	357	12	comments	comment	NOUN
iajs-3409	357	13	and	and	CCONJ
iajs-3409	357	14	suggestions	suggestion	NOUN
iajs-3409	357	15	for	for	ADP
iajs-3409	357	16	improving	improve	VERB
iajs-3409	357	17	the	the	DET
iajs-3409	357	18	paper	paper	NOUN
iajs-3409	357	19	.	.	PUNCT
iajs-3409	358	1	conflict	conflict	NOUN
iajs-3409	358	2	of	of	ADP
iajs-3409	358	3	interest	interest	NOUN
iajs-3409	358	4	the	the	DET
iajs-3409	358	5	authors	author	NOUN
iajs-3409	358	6	declare	declare	VERB
iajs-3409	358	7	that	that	SCONJ
iajs-3409	358	8	they	they	PRON
iajs-3409	358	9	have	have	VERB
iajs-3409	358	10	no	no	DET
iajs-3409	358	11	conflicts	conflict	NOUN
iajs-3409	358	12	of	of	ADP
iajs-3409	358	13	interest	interest	NOUN
iajs-3409	358	14	.	.	PUNCT
iajs-3409	359	1	funding	funding	NOUN
iajs-3409	359	2	there	there	PRON
iajs-3409	359	3	is	be	VERB
iajs-3409	359	4	no	no	DET
iajs-3409	359	5	financial	financial	ADJ
iajs-3409	359	6	support	support	NOUN
iajs-3409	359	7	in	in	ADP
iajs-3409	359	8	preparation	preparation	NOUN
iajs-3409	359	9	for	for	ADP
iajs-3409	359	10	the	the	DET
iajs-3409	359	11	publication	publication	NOUN
iajs-3409	359	12	.	.	PUNCT
iajs-3409	360	1	references	reference	NOUN
iajs-3409	360	2	1	1	NUM
iajs-3409	360	3	.	.	PUNCT
iajs-3409	361	1	boutayeb	boutayeb	ADJ
iajs-3409	361	2	,	,	PUNCT
iajs-3409	361	3	a.	a.	NOUN
iajs-3409	361	4	;	;	PUNCT
iajs-3409	361	5	chetouani	chetouani	PROPN
iajs-3409	361	6	a.	a.	PROPN
iajs-3409	361	7	a	a	DET
iajs-3409	361	8	mini	mini	NOUN
iajs-3409	361	9	-	-	NOUN
iajs-3409	361	10	review	review	NOUN
iajs-3409	361	11	of	of	ADP
iajs-3409	361	12	numerical	numerical	ADJ
iajs-3409	361	13	methods	method	NOUN
iajs-3409	361	14	for	for	ADP
iajs-3409	361	15	high	high	ADJ
iajs-3409	361	16	-	-	PUNCT
iajs-3409	361	17	order	order	NOUN
iajs-3409	361	18	problems	problem	NOUN
iajs-3409	361	19	.	.	PUNCT
iajs-3409	362	1	international	international	ADJ
iajs-3409	362	2	journal	journal	PROPN
iajs-3409	362	3	of	of	ADP
iajs-3409	362	4	computer	computer	NOUN
iajs-3409	362	5	mathematics	mathematic	NOUN
iajs-3409	362	6	.	.	PUNCT
iajs-3409	363	1	2007	2007	NUM
iajs-3409	363	2	,	,	PUNCT
iajs-3409	363	3	84(4	84(4	NUM
iajs-3409	363	4	)	)	PUNCT
iajs-3409	363	5	,	,	PUNCT
iajs-3409	363	6	563	563	NUM
iajs-3409	363	7	-	-	SYM
iajs-3409	363	8	579	579	NUM
iajs-3409	363	9	,	,	PUNCT
iajs-3409	363	10	https://doi.org/10.1080/00207160701242250	https://doi.org/10.1080/00207160701242250	NUM
iajs-3409	363	11	.	.	PUNCT
iajs-3409	364	1	https://doi.org/10.1080/00207160701242250	https://doi.org/10.1080/00207160701242250	PROPN
iajs-3409	364	2	ihjpas	ihjpas	PROPN
iajs-3409	364	3	.	.	PUNCT
iajs-3409	365	1	37	37	NUM
iajs-3409	365	2	(	(	PUNCT
iajs-3409	365	3	2	2	NUM
iajs-3409	365	4	)	)	PUNCT
iajs-3409	365	5	2024	2024	NUM
iajs-3409	365	6	407	407	NUM
iajs-3409	365	7	2	2	NUM
iajs-3409	365	8	.	.	PUNCT
iajs-3409	365	9	wu	wu	PROPN
iajs-3409	365	10	,	,	PUNCT
iajs-3409	365	11	xiong	xiong	PROPN
iajs-3409	365	12	-	-	PUNCT
iajs-3409	365	13	jian	jian	PROPN
iajs-3409	365	14	;	;	PUNCT
iajs-3409	365	15	yigong	yigong	PROPN
iajs-3409	365	16	wang	wang	PROPN
iajs-3409	365	17	;	;	PUNCT
iajs-3409	365	18	w.	w.	PROPN
iajs-3409	365	19	g.	g.	PROPN
iajs-3409	365	20	price	price	PROPN
iajs-3409	365	21	.	.	PUNCT
iajs-3409	366	1	multiple	multiple	ADJ
iajs-3409	366	2	resonances	resonance	NOUN
iajs-3409	366	3	,	,	PUNCT
iajs-3409	366	4	responses	response	NOUN
iajs-3409	366	5	,	,	PUNCT
iajs-3409	366	6	and	and	CCONJ
iajs-3409	366	7	parametric	parametric	ADJ
iajs-3409	366	8	instabilities	instability	NOUN
iajs-3409	366	9	in	in	ADP
iajs-3409	366	10	offshore	offshore	ADJ
iajs-3409	366	11	structures	structure	NOUN
iajs-3409	366	12	.	.	PUNCT
iajs-3409	367	1	journal	journal	NOUN
iajs-3409	367	2	of	of	ADP
iajs-3409	367	3	ship	ship	NOUN
iajs-3409	367	4	research	research	NOUN
iajs-3409	367	5	.	.	PUNCT
iajs-3409	368	1	1988	1988	NUM
iajs-3409	368	2	,	,	PUNCT
iajs-3409	368	3	32(04	32(04	NUM
iajs-3409	368	4	)	)	PUNCT
iajs-3409	368	5	,	,	PUNCT
iajs-3409	368	6	285	285	NUM
iajs-3409	368	7	-	-	SYM
iajs-3409	368	8	296	296	NUM
iajs-3409	368	9	,	,	PUNCT
iajs-3409	368	10	https://doi.org/10.5957/jsr.1988.32.4.285	https://doi.org/10.5957/jsr.1988.32.4.285	PROPN
iajs-3409	368	11	3	3	X
iajs-3409	368	12	.	.	PUNCT
iajs-3409	368	13	cortell	cortell	PROPN
iajs-3409	368	14	,	,	PUNCT
iajs-3409	368	15	r.	r.	PROPN
iajs-3409	368	16	application	application	NOUN
iajs-3409	368	17	of	of	ADP
iajs-3409	368	18	the	the	DET
iajs-3409	368	19	fourth	fourth	ADJ
iajs-3409	368	20	-	-	PUNCT
iajs-3409	368	21	order	order	NOUN
iajs-3409	368	22	runge	runge	NOUN
iajs-3409	368	23	-	-	PUNCT
iajs-3409	368	24	kutta	kutta	NOUN
iajs-3409	368	25	method	method	NOUN
iajs-3409	368	26	for	for	ADP
iajs-3409	368	27	the	the	DET
iajs-3409	368	28	solution	solution	NOUN
iajs-3409	368	29	of	of	ADP
iajs-3409	368	30	high	high	ADJ
iajs-3409	368	31	-	-	PUNCT
iajs-3409	368	32	order	order	NOUN
iajs-3409	368	33	general	general	ADJ
iajs-3409	368	34	initial	initial	ADJ
iajs-3409	368	35	value	value	NOUN
iajs-3409	368	36	problems	problem	NOUN
iajs-3409	368	37	.	.	PUNCT
iajs-3409	369	1	computers	computer	NOUN
iajs-3409	369	2	&	&	CCONJ
iajs-3409	369	3	structures	structure	NOUN
iajs-3409	369	4	.	.	PUNCT
iajs-3409	370	1	1993	1993	NUM
iajs-3409	370	2	,	,	PUNCT
iajs-3409	370	3	49(5	49(5	NUM
iajs-3409	370	4	)	)	PUNCT
iajs-3409	370	5	,	,	PUNCT
iajs-3409	370	6	897	897	NUM
iajs-3409	370	7	-	-	SYM
iajs-3409	370	8	900	900	NUM
iajs-3409	370	9	,	,	PUNCT
iajs-3409	370	10	https://doi.org/10.1016/00457949(93)90036-d	https://doi.org/10.1016/00457949(93)90036-d	NOUN
iajs-3409	370	11	4	4	NUM
iajs-3409	370	12	.	.	PUNCT
iajs-3409	371	1	malek	malek	PROPN
iajs-3409	371	2	,	,	PUNCT
iajs-3409	371	3	a.	a.	PROPN
iajs-3409	371	4	;	;	PUNCT
iajs-3409	371	5	r.	r.	PROPN
iajs-3409	371	6	shekari	shekari	PROPN
iajs-3409	371	7	beidokhti	beidokhti	PROPN
iajs-3409	371	8	.	.	PUNCT
iajs-3409	372	1	numerical	numerical	ADJ
iajs-3409	372	2	solution	solution	NOUN
iajs-3409	372	3	for	for	ADP
iajs-3409	372	4	high	high	ADJ
iajs-3409	372	5	order	order	NOUN
iajs-3409	372	6	differential	differential	ADJ
iajs-3409	372	7	equations	equation	NOUN
iajs-3409	372	8	using	use	VERB
iajs-3409	372	9	a	a	DET
iajs-3409	372	10	hybrid	hybrid	ADJ
iajs-3409	372	11	neural	neural	ADJ
iajs-3409	372	12	network	network	NOUN
iajs-3409	372	13	-	-	PUNCT
iajs-3409	372	14	optimization	optimization	NOUN
iajs-3409	372	15	method	method	NOUN
iajs-3409	372	16	.	.	PUNCT
iajs-3409	373	1	applied	apply	VERB
iajs-3409	373	2	mathematics	mathematic	NOUN
iajs-3409	373	3	and	and	CCONJ
iajs-3409	373	4	computation	computation	NOUN
iajs-3409	373	5	.	.	PUNCT
iajs-3409	374	1	2006	2006	NUM
iajs-3409	374	2	,	,	PUNCT
iajs-3409	374	3	183(1	183(1	NUM
iajs-3409	374	4	)	)	PUNCT
iajs-3409	374	5	,	,	PUNCT
iajs-3409	374	6	260	260	NUM
iajs-3409	374	7	-	-	SYM
iajs-3409	374	8	271	271	NUM
iajs-3409	374	9	,	,	PUNCT
iajs-3409	374	10	https://doi.org/10.1016/j.amc.2006.05.068	https://doi.org/10.1016/j.amc.2006.05.068	PROPN
iajs-3409	374	11	.	.	PUNCT
iajs-3409	375	1	5	5	NUM
iajs-3409	375	2	.	.	X
iajs-3409	375	3	awoyemi	awoyemi	PROPN
iajs-3409	375	4	,	,	PUNCT
iajs-3409	375	5	d.	d.	PROPN
iajs-3409	375	6	o.	o.	PROPN
iajs-3409	375	7	algorithmic	algorithmic	ADJ
iajs-3409	375	8	collocation	collocation	NOUN
iajs-3409	375	9	approach	approach	NOUN
iajs-3409	375	10	for	for	ADP
iajs-3409	375	11	direct	direct	ADJ
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iajs-3409	375	13	of	of	ADP
iajs-3409	375	14	fourth	fourth	ADJ
iajs-3409	375	15	-	-	PUNCT
iajs-3409	375	16	order	order	NOUN
iajs-3409	375	17	initial	initial	ADJ
iajs-3409	375	18	-	-	PUNCT
iajs-3409	375	19	value	value	NOUN
iajs-3409	375	20	problems	problem	NOUN
iajs-3409	375	21	of	of	ADP
iajs-3409	375	22	ordinary	ordinary	ADJ
iajs-3409	375	23	differential	differential	ADJ
iajs-3409	375	24	equations	equation	NOUN
iajs-3409	375	25	.	.	PUNCT
iajs-3409	376	1	international	international	ADJ
iajs-3409	376	2	journal	journal	PROPN
iajs-3409	376	3	of	of	ADP
iajs-3409	376	4	computer	computer	NOUN
iajs-3409	376	5	mathematics	mathematic	NOUN
iajs-3409	376	6	.	.	PUNCT
iajs-3409	377	1	2005	2005	NUM
iajs-3409	377	2	,	,	PUNCT
iajs-3409	377	3	82(3	82(3	NUM
iajs-3409	377	4	)	)	PUNCT
iajs-3409	377	5	,	,	PUNCT
iajs-3409	377	6	321	321	NUM
iajs-3409	377	7	-	-	SYM
iajs-3409	377	8	329	329	NUM
iajs-3409	377	9	,	,	PUNCT
iajs-3409	377	10	https://doi.org/10.1080/00207160412331296634	https://doi.org/10.1080/00207160412331296634	NOUN
iajs-3409	377	11	.	.	PUNCT
iajs-3409	378	1	6	6	NUM
iajs-3409	378	2	.	.	X
iajs-3409	378	3	adel	adel	PROPN
iajs-3409	378	4	,	,	PUNCT
iajs-3409	378	5	f.	f.	PROPN
iajs-3409	378	6	;	;	PUNCT
iajs-3409	378	7	senu	senu	X
iajs-3409	378	8	,	,	PUNCT
iajs-3409	378	9	n.	n.	NOUN
iajs-3409	378	10	;	;	PUNCT
iajs-3409	378	11	ismail	ismail	PROPN
iajs-3409	378	12	,	,	PUNCT
iajs-3409	378	13	f.	f.	PROPN
iajs-3409	378	14	;	;	PUNCT
iajs-3409	378	15	majid	majid	PROPN
iajs-3409	378	16	,	,	PUNCT
iajs-3409	378	17	z.	z.	PROPN
iajs-3409	378	18	a.	a.	PROPN
iajs-3409	378	19	new	new	ADJ
iajs-3409	378	20	efficient	efficient	ADJ
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iajs-3409	378	22	-	-	PUNCT
iajs-3409	378	23	fitted	fit	VERB
iajs-3409	378	24	and	and	CCONJ
iajs-3409	378	25	amplification	amplification	NOUN
iajs-3409	378	26	-	-	PUNCT
iajs-3409	378	27	fitted	fit	VERB
iajs-3409	378	28	rungekutta	rungekutta	NOUN
iajs-3409	378	29	method	method	NOUN
iajs-3409	378	30	for	for	ADP
iajs-3409	378	31	oscillatory	oscillatory	ADJ
iajs-3409	378	32	problems	problem	NOUN
iajs-3409	378	33	.	.	PUNCT
iajs-3409	379	1	international	international	ADJ
iajs-3409	379	2	j	j	PROPN
iajs-3409	379	3	pure	pure	ADJ
iajs-3409	379	4	appl	appl	PROPN
iajs-3409	379	5	math	math	NOUN
iajs-3409	379	6	,	,	PUNCT
iajs-3409	379	7	2016	2016	NUM
iajs-3409	379	8	,	,	PUNCT
iajs-3409	379	9	107(1	107(1	NUM
iajs-3409	379	10	)	)	PUNCT
iajs-3409	379	11	,	,	PUNCT
iajs-3409	379	12	69	69	NUM
iajs-3409	379	13	-	-	SYM
iajs-3409	379	14	86	86	NUM
iajs-3409	379	15	,	,	PUNCT
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iajs-3409	379	17	7	7	NUM
iajs-3409	379	18	.	.	X
iajs-3409	379	19	hussain	hussain	PROPN
iajs-3409	379	20	,	,	PUNCT
iajs-3409	379	21	k.	k.	PROPN
iajs-3409	379	22	;	;	PUNCT
iajs-3409	379	23	ismail	ismail	PROPN
iajs-3409	379	24	,	,	PUNCT
iajs-3409	379	25	f.	f.	PROPN
iajs-3409	379	26	,	,	PUNCT
iajs-3409	379	27	;	;	PUNCT
iajs-3409	379	28	senu	senu	NOUN
iajs-3409	379	29	,	,	PUNCT
iajs-3409	379	30	n.	n.	NOUN
iajs-3409	379	31	a	a	DET
iajs-3409	379	32	new	new	ADJ
iajs-3409	379	33	optimized	optimize	VERB
iajs-3409	379	34	runge	runge	NOUN
iajs-3409	379	35	-	-	PUNCT
iajs-3409	379	36	kutta	kutta	NOUN
iajs-3409	379	37	-	-	PUNCT
iajs-3409	379	38	nyström	nyström	NOUN
iajs-3409	379	39	method	method	NOUN
iajs-3409	379	40	to	to	PART
iajs-3409	379	41	solve	solve	VERB
iajs-3409	379	42	oscillation	oscillation	NOUN
iajs-3409	379	43	problems	problem	NOUN
iajs-3409	379	44	.	.	PUNCT
iajs-3409	380	1	world	world	NOUN
iajs-3409	380	2	applied	apply	VERB
iajs-3409	380	3	sciences	science	NOUN
iajs-3409	380	4	journal	journal	NOUN
iajs-3409	380	5	,	,	PUNCT
iajs-3409	380	6	2015	2015	NUM
iajs-3409	380	7	,	,	PUNCT
iajs-3409	380	8	33(10	33(10	NUM
iajs-3409	380	9	)	)	PUNCT
iajs-3409	380	10	,	,	PUNCT
iajs-3409	380	11	1614	1614	NUM
iajs-3409	380	12	-	-	SYM
iajs-3409	380	13	1622	1622	NUM
iajs-3409	380	14	,	,	PUNCT
iajs-3409	380	15	https://doi.org/10.5829/idosi.wasj.2015.33.10.300	https://doi.org/10.5829/idosi.wasj.2015.33.10.300	PROPN
iajs-3409	380	16	.	.	PUNCT
iajs-3409	381	1	8	8	NUM
iajs-3409	381	2	.	.	X
iajs-3409	381	3	hussain	hussain	PROPN
iajs-3409	381	4	,	,	PUNCT
iajs-3409	381	5	k.	k.	PROPN
iajs-3409	381	6	a.	a.	PROPN
iajs-3409	381	7	;	;	PUNCT
iajs-3409	381	8	abdulnaby	abdulnaby	PROPN
iajs-3409	381	9	,	,	PUNCT
iajs-3409	381	10	z.	z.	PROPN
iajs-3409	382	1	e	e	X
iajs-3409	382	2	..	..	PUNCT
iajs-3409	382	3	a	a	DET
iajs-3409	382	4	new	new	ADJ
iajs-3409	382	5	two	two	NUM
iajs-3409	382	6	derivative	derivative	ADJ
iajs-3409	382	7	fsal	fsal	NOUN
iajs-3409	382	8	runge	runge	NOUN
iajs-3409	382	9	-	-	PUNCT
iajs-3409	382	10	kutta	kutta	NOUN
iajs-3409	382	11	method	method	NOUN
iajs-3409	382	12	of	of	ADP
iajs-3409	382	13	order	order	NOUN
iajs-3409	382	14	five	five	NUM
iajs-3409	382	15	in	in	ADP
iajs-3409	382	16	four	four	NUM
iajs-3409	382	17	stages	stage	NOUN
iajs-3409	382	18	.	.	PUNCT
iajs-3409	383	1	order	order	NOUN
iajs-3409	383	2	,	,	PUNCT
iajs-3409	383	3	2020	2020	NUM
iajs-3409	383	4	,	,	PUNCT
iajs-3409	383	5	17(1	17(1	NUM
iajs-3409	383	6	)	)	PUNCT
iajs-3409	383	7	.	.	PUNCT
iajs-3409	384	1	https://doi.org/10.21123/bsj.2020.17.1.0166	https://doi.org/10.21123/bsj.2020.17.1.0166	NOUN
iajs-3409	384	2	9	9	NUM
iajs-3409	384	3	.	.	PUNCT
iajs-3409	384	4	lee	lee	PROPN
iajs-3409	384	5	,	,	PUNCT
iajs-3409	384	6	k.	k.	PROPN
iajs-3409	384	7	c.	c.	PROPN
iajs-3409	384	8	;	;	PUNCT
iajs-3409	384	9	senu	senu	NOUN
iajs-3409	384	10	,	,	PUNCT
iajs-3409	384	11	n.	n.	NOUN
iajs-3409	384	12	,	,	PUNCT
iajs-3409	384	13	ahmadian	ahmadian	ADJ
iajs-3409	384	14	,	,	PUNCT
iajs-3409	384	15	a.	a.	PROPN
iajs-3409	384	16	,	,	PUNCT
iajs-3409	384	17	ibrahim	ibrahim	PROPN
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iajs-3409	384	19	s.	s.	PROPN
iajs-3409	384	20	n.	n.	PROPN
iajs-3409	384	21	i.	i.	PROPN
iajs-3409	384	22	,	,	PUNCT
iajs-3409	384	23	&	&	CCONJ
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iajs-3409	384	25	,	,	PUNCT
iajs-3409	384	26	d.	d.	PROPN
iajs-3409	384	27	numerical	numerical	PROPN
iajs-3409	384	28	study	study	PROPN
iajs-3409	384	29	of	of	ADP
iajs-3409	384	30	third	third	ADJ
iajs-3409	384	31	-	-	PUNCT
iajs-3409	384	32	order	order	NOUN
iajs-3409	384	33	ordinary	ordinary	ADJ
iajs-3409	384	34	differential	differential	ADJ
iajs-3409	384	35	equations	equation	NOUN
iajs-3409	384	36	using	use	VERB
iajs-3409	384	37	a	a	DET
iajs-3409	384	38	new	new	ADJ
iajs-3409	384	39	class	class	NOUN
iajs-3409	384	40	of	of	ADP
iajs-3409	384	41	two	two	NUM
iajs-3409	384	42	derivative	derivative	ADJ
iajs-3409	384	43	runge	runge	NOUN
iajs-3409	384	44	-	-	PUNCT
iajs-3409	384	45	kutta	kutta	NOUN
iajs-3409	384	46	type	type	NOUN
iajs-3409	384	47	methods	method	NOUN
iajs-3409	384	48	.	.	PUNCT
iajs-3409	385	1	alexandria	alexandria	PROPN
iajs-3409	385	2	engineering	engineering	PROPN
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iajs-3409	385	4	,	,	PUNCT
iajs-3409	385	5	2020	2020	NUM
iajs-3409	385	6	,	,	PUNCT
iajs-3409	385	7	59(4	59(4	NUM
iajs-3409	385	8	)	)	PUNCT
iajs-3409	385	9	,	,	PUNCT
iajs-3409	385	10	2449	2449	NUM
iajs-3409	385	11	-	-	SYM
iajs-3409	385	12	2467	2467	NUM
iajs-3409	385	13	,	,	PUNCT
iajs-3409	385	14	https://doi.org/10.1016/j.aej.2020.03.008	https://doi.org/10.1016/j.aej.2020.03.008	NOUN
iajs-3409	385	15	.	.	PUNCT
iajs-3409	386	1	10	10	NUM
iajs-3409	386	2	.	.	X
iajs-3409	387	1	ahmad	ahmad	PROPN
iajs-3409	387	2	,	,	PUNCT
iajs-3409	387	3	n.	n.	PROPN
iajs-3409	387	4	a.	a.	PROPN
iajs-3409	387	5	;	;	PUNCT
iajs-3409	387	6	senu	senu	NOUN
iajs-3409	387	7	,	,	PUNCT
iajs-3409	387	8	n.	n.	NOUN
iajs-3409	387	9	;	;	PUNCT
iajs-3409	387	10	ismail	ismail	PROPN
iajs-3409	387	11	,	,	PUNCT
iajs-3409	387	12	f.	f.	PROPN
iajs-3409	387	13	phase	phase	PROPN
iajs-3409	387	14	-	-	PUNCT
iajs-3409	387	15	fitted	fit	VERB
iajs-3409	387	16	and	and	CCONJ
iajs-3409	387	17	amplification	amplification	NOUN
iajs-3409	387	18	-	-	PUNCT
iajs-3409	387	19	fitted	fit	VERB
iajs-3409	387	20	higher	high	ADJ
iajs-3409	387	21	order	order	NOUN
iajs-3409	387	22	two	two	NUM
iajs-3409	387	23	-	-	PUNCT
iajs-3409	387	24	derivative	derivative	NOUN
iajs-3409	387	25	runge	runge	NOUN
iajs-3409	387	26	-	-	PUNCT
iajs-3409	387	27	kutta	kutta	NOUN
iajs-3409	387	28	method	method	NOUN
iajs-3409	387	29	for	for	ADP
iajs-3409	387	30	the	the	DET
iajs-3409	387	31	numerical	numerical	ADJ
iajs-3409	387	32	solution	solution	NOUN
iajs-3409	387	33	of	of	ADP
iajs-3409	387	34	orbital	orbital	ADJ
iajs-3409	387	35	and	and	CCONJ
iajs-3409	387	36	related	relate	VERB
iajs-3409	387	37	periodical	periodical	ADJ
iajs-3409	387	38	ivps	ivps	PROPN
iajs-3409	387	39	.	.	PUNCT
iajs-3409	388	1	mathematical	mathematical	ADJ
iajs-3409	388	2	problems	problem	NOUN
iajs-3409	388	3	in	in	ADP
iajs-3409	388	4	engineering	engineering	NOUN
iajs-3409	388	5	,	,	PUNCT
iajs-3409	388	6	2017	2017	NUM
iajs-3409	388	7	.	.	PUNCT
iajs-3409	389	1	10.1109	10.1109	NUM
iajs-3409	389	2	/	/	SYM
iajs-3409	389	3	icrem.2015.7357020	icrem.2015.7357020	NOUN
iajs-3409	389	4	.	.	PUNCT
iajs-3409	390	1	11	11	NUM
iajs-3409	390	2	.	.	X
iajs-3409	391	1	senu	senu	PROPN
iajs-3409	391	2	,	,	PUNCT
iajs-3409	391	3	n.	n.	NOUN
iajs-3409	391	4	;	;	PUNCT
iajs-3409	391	5	ahmad	ahmad	PROPN
iajs-3409	391	6	,	,	PUNCT
iajs-3409	391	7	n.	n.	PROPN
iajs-3409	391	8	a.	a.	PROPN
iajs-3409	391	9	,	,	PUNCT
iajs-3409	391	10	;	;	PUNCT
iajs-3409	391	11	zarina	zarina	PROPN
iajs-3409	391	12	,	,	PUNCT
iajs-3409	391	13	b.	b.	PROPN
iajs-3409	391	14	i.	i.	PROPN
iajs-3409	391	15	b.	b.	PROPN
iajs-3409	391	16	i.	i.	PROPN
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iajs-3409	391	20	phase	phase	NOUN
iajs-3409	391	21	-	-	PUNCT
iajs-3409	391	22	fitted	fit	VERB
iajs-3409	391	23	and	and	CCONJ
iajs-3409	391	24	amplification	amplification	NOUN
iajs-3409	391	25	-	-	PUNCT
iajs-3409	391	26	fitted	fit	VERB
iajs-3409	391	27	diagonally	diagonally	ADV
iajs-3409	391	28	implicit	implicit	ADJ
iajs-3409	391	29	two	two	NUM
iajs-3409	391	30	derivative	derivative	ADJ
iajs-3409	391	31	runge	runge	NOUN
iajs-3409	391	32	-	-	PUNCT
iajs-3409	391	33	kutta	kutta	NOUN
iajs-3409	391	34	method	method	NOUN
iajs-3409	391	35	for	for	ADP
iajs-3409	391	36	periodic	periodic	ADJ
iajs-3409	391	37	ivps	ivps	PROPN
iajs-3409	391	38	.	.	PUNCT
iajs-3409	392	1	sains	sain	NOUN
iajs-3409	392	2	malaysiana	malaysiana	PROPN
iajs-3409	392	3	,	,	PUNCT
iajs-3409	392	4	2021	2021	NUM
iajs-3409	392	5	,	,	PUNCT
iajs-3409	392	6	50(6	50(6	NUM
iajs-3409	392	7	)	)	PUNCT
iajs-3409	392	8	,	,	PUNCT
iajs-3409	392	9	1799	1799	NUM
iajs-3409	392	10	-	-	SYM
iajs-3409	392	11	1814	1814	NUM
iajs-3409	392	12	,	,	PUNCT
iajs-3409	392	13	10.17576	10.17576	NUM
iajs-3409	392	14	/	/	SYM
iajs-3409	392	15	jsm-2021	jsm-2021	NOUN
iajs-3409	392	16	-	-	PUNCT
iajs-3409	392	17	5006	5006	NUM
iajs-3409	392	18	-	-	SYM
iajs-3409	392	19	25	25	NUM
iajs-3409	392	20	.	.	NOUN
iajs-3409	392	21	12	12	NUM
iajs-3409	392	22	.	.	PUNCT
iajs-3409	393	1	fawzi	fawzi	PROPN
iajs-3409	393	2	,	,	PUNCT
iajs-3409	393	3	f.	f.	PROPN
iajs-3409	393	4	a.	a.	PROPN
iajs-3409	394	1	an	an	DET
iajs-3409	394	2	embedded	embed	VERB
iajs-3409	394	3	5	5	NUM
iajs-3409	394	4	(	(	PUNCT
iajs-3409	394	5	4	4	NUM
iajs-3409	394	6	)	)	PUNCT
iajs-3409	394	7	pair	pair	NOUN
iajs-3409	394	8	of	of	ADP
iajs-3409	394	9	optimized	optimize	VERB
iajs-3409	394	10	runge	runge	NOUN
iajs-3409	394	11	-	-	PUNCT
iajs-3409	394	12	kutta	kutta	NOUN
iajs-3409	394	13	method	method	NOUN
iajs-3409	394	14	for	for	ADP
iajs-3409	394	15	the	the	DET
iajs-3409	394	16	numerical	numerical	ADJ
iajs-3409	394	17	solution	solution	NOUN
iajs-3409	394	18	of	of	ADP
iajs-3409	394	19	periodic	periodic	ADJ
iajs-3409	394	20	initial	initial	ADJ
iajs-3409	394	21	value	value	NOUN
iajs-3409	394	22	problems	problem	NOUN
iajs-3409	394	23	.	.	PUNCT
iajs-3409	395	1	iraqi	iraqi	ADJ
iajs-3409	395	2	journal	journal	PROPN
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iajs-3409	395	4	science	science	NOUN
iajs-3409	395	5	,	,	PUNCT
iajs-3409	395	6	2022	2022	NUM
iajs-3409	395	7	,	,	PUNCT
iajs-3409	395	8	3889	3889	NUM
iajs-3409	395	9	-	-	SYM
iajs-3409	395	10	3901	3901	NUM
iajs-3409	395	11	,	,	PUNCT
iajs-3409	395	12	https://doi.org/10.24996/ijs.2022.63.9.21	https://doi.org/10.24996/ijs.2022.63.9.21	PROPN
iajs-3409	395	13	.	.	PROPN
iajs-3409	395	14	13	13	NUM
iajs-3409	395	15	.	.	X
iajs-3409	395	16	senu	senu	PROPN
iajs-3409	395	17	,	,	PUNCT
iajs-3409	395	18	n.	n.	NOUN
iajs-3409	395	19	;	;	PUNCT
iajs-3409	395	20	ahmad	ahmad	PROPN
iajs-3409	395	21	,	,	PUNCT
iajs-3409	395	22	n.	n.	PROPN
iajs-3409	395	23	;	;	PUNCT
iajs-3409	395	24	ismail	ismail	PROPN
iajs-3409	395	25	,	,	PUNCT
iajs-3409	395	26	f.	f.	PROPN
iajs-3409	395	27	embedded	embed	VERB
iajs-3409	395	28	5	5	NUM
iajs-3409	395	29	(	(	PUNCT
iajs-3409	395	30	4	4	NUM
iajs-3409	395	31	)	)	PUNCT
iajs-3409	395	32	pair	pair	NOUN
iajs-3409	395	33	trigonometrically	trigonometrically	ADV
iajs-3409	395	34	-	-	PUNCT
iajs-3409	395	35	fitted	fit	VERB
iajs-3409	395	36	two	two	NUM
iajs-3409	395	37	derivative	derivative	ADJ
iajs-3409	395	38	runge	runge	NOUN
iajs-3409	395	39	-	-	PUNCT
iajs-3409	395	40	kutta	kutta	NOUN
iajs-3409	395	41	method	method	NOUN
iajs-3409	395	42	with	with	ADP
iajs-3409	395	43	fsal	fsal	ADJ
iajs-3409	395	44	property	property	NOUN
iajs-3409	395	45	for	for	ADP
iajs-3409	395	46	numerical	numerical	ADJ
iajs-3409	395	47	solution	solution	NOUN
iajs-3409	395	48	of	of	ADP
iajs-3409	395	49	oscillatory	oscillatory	ADJ
iajs-3409	395	50	problems	problem	NOUN
iajs-3409	395	51	,	,	PUNCT
iajs-3409	395	52	wseas	wseas	VERB
iajs-3409	395	53	transactions	transaction	NOUN
iajs-3409	395	54	on	on	ADP
iajs-3409	395	55	computers	computer	NOUN
iajs-3409	395	56	,	,	PUNCT
iajs-3409	395	57	2017,16	2017,16	NUM
iajs-3409	395	58	,	,	PUNCT
iajs-3409	395	59	155	155	NUM
iajs-3409	395	60	-	-	SYM
iajs-3409	395	61	162	162	NUM
iajs-3409	395	62	.	.	PUNCT
iajs-3409	396	1	14	14	NUM
iajs-3409	396	2	.	.	PUNCT
iajs-3409	396	3	jikantoro	jikantoro	PROPN
iajs-3409	396	4	,	,	PUNCT
iajs-3409	396	5	y.	y.	PROPN
iajs-3409	396	6	d.	d.	PROPN
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iajs-3409	396	8	ismail	ismail	PROPN
iajs-3409	396	9	,	,	PUNCT
iajs-3409	396	10	f.	f.	PROPN
iajs-3409	396	11	,	,	PUNCT
iajs-3409	396	12	senu	senu	VERB
iajs-3409	396	13	,	,	PUNCT
iajs-3409	396	14	n.	n.	NOUN
iajs-3409	396	15	,	,	PUNCT
iajs-3409	396	16	;	;	PUNCT
iajs-3409	396	17	ibrahim	ibrahim	PROPN
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iajs-3409	396	19	z.	z.	PROPN
iajs-3409	396	20	b.	b.	PROPN
iajs-3409	396	21	,	,	PUNCT
iajs-3409	396	22	hybrid	hybrid	ADJ
iajs-3409	396	23	methods	method	NOUN
iajs-3409	396	24	for	for	ADP
iajs-3409	396	25	direct	direct	ADJ
iajs-3409	396	26	integration	integration	NOUN
iajs-3409	396	27	of	of	ADP
iajs-3409	396	28	special	special	ADJ
iajs-3409	396	29	third	third	ADJ
iajs-3409	396	30	order	order	NOUN
iajs-3409	396	31	ordinary	ordinary	ADJ
iajs-3409	396	32	differential	differential	ADJ
iajs-3409	396	33	equations	equation	NOUN
iajs-3409	396	34	.	.	PUNCT
iajs-3409	397	1	applied	apply	VERB
iajs-3409	397	2	mathematics	mathematic	NOUN
iajs-3409	397	3	and	and	CCONJ
iajs-3409	397	4	computation	computation	NOUN
iajs-3409	397	5	,	,	PUNCT
iajs-3409	397	6	2018	2018	NUM
iajs-3409	397	7	,	,	PUNCT
iajs-3409	397	8	320	320	NUM
iajs-3409	397	9	,	,	PUNCT
iajs-3409	397	10	452	452	NUM
iajs-3409	397	11	-	-	SYM
iajs-3409	397	12	463	463	NUM
iajs-3409	397	13	,	,	PUNCT
iajs-3409	397	14	https://doi.org/10.1016/j.amc.2017.10.003	https://doi.org/10.1016/j.amc.2017.10.003	PROPN
iajs-3409	397	15	.	.	NOUN
iajs-3409	397	16	15	15	NUM
iajs-3409	397	17	.	.	X
iajs-3409	397	18	shokri	shokri	PROPN
iajs-3409	397	19	,	,	PUNCT
iajs-3409	397	20	a.	a.	NOUN
iajs-3409	397	21	;	;	PUNCT
iajs-3409	397	22	mehdizadeh	mehdizadeh	PROPN
iajs-3409	397	23	khalsaraei	khalsaraei	PROPN
iajs-3409	397	24	,	,	PUNCT
iajs-3409	397	25	m.	m.	NOUN
iajs-3409	397	26	a	a	DET
iajs-3409	397	27	new	new	ADJ
iajs-3409	397	28	efficient	efficient	ADJ
iajs-3409	397	29	high	high	ADJ
iajs-3409	397	30	order	order	NOUN
iajs-3409	397	31	four	four	NUM
iajs-3409	397	32	-	-	PUNCT
iajs-3409	397	33	step	step	NOUN
iajs-3409	397	34	multiderivative	multiderivative	ADJ
iajs-3409	397	35	method	method	NOUN
iajs-3409	397	36	for	for	ADP
iajs-3409	397	37	the	the	DET
iajs-3409	397	38	numerical	numerical	ADJ
iajs-3409	397	39	solution	solution	NOUN
iajs-3409	397	40	of	of	ADP
iajs-3409	397	41	second	second	ADJ
iajs-3409	397	42	-	-	PUNCT
iajs-3409	397	43	order	order	NOUN
iajs-3409	397	44	ivps	ivps	PROPN
iajs-3409	397	45	with	with	ADP
iajs-3409	397	46	oscillating	oscillate	VERB
iajs-3409	397	47	solutions	solution	NOUN
iajs-3409	397	48	.	.	PUNCT
iajs-3409	398	1	mathematics	mathematic	NOUN
iajs-3409	398	2	interdisciplinary	interdisciplinary	ADJ
iajs-3409	398	3	research	research	NOUN
iajs-3409	398	4	,	,	PUNCT
iajs-3409	398	5	2020	2020	NUM
iajs-3409	398	6	,	,	PUNCT
iajs-3409	398	7	5(2	5(2	NUM
iajs-3409	398	8	)	)	PUNCT
iajs-3409	398	9	,	,	PUNCT
iajs-3409	398	10	157	157	NUM
iajs-3409	398	11	-	-	SYM
iajs-3409	398	12	172	172	NUM
iajs-3409	398	13	,	,	PUNCT
iajs-3409	398	14	10.22052	10.22052	NUM
iajs-3409	398	15	/	/	SYM
iajs-3409	398	16	mir.2020.211603.1185	mir.2020.211603.1185	PROPN
iajs-3409	398	17	.	.	PROPN
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iajs-3409	398	19	.	.	PUNCT
iajs-3409	399	1	mechee	mechee	NOUN
iajs-3409	399	2	,	,	PUNCT
iajs-3409	399	3	m.	m.	NOUN
iajs-3409	399	4	;	;	PUNCT
iajs-3409	399	5	senu	senu	NOUN
iajs-3409	399	6	,	,	PUNCT
iajs-3409	399	7	n.	n.	NOUN
iajs-3409	399	8	;	;	PUNCT
iajs-3409	399	9	ismail	ismail	PROPN
iajs-3409	399	10	,	,	PUNCT
iajs-3409	399	11	f.	f.	PROPN
iajs-3409	399	12	;	;	PUNCT
iajs-3409	399	13	nikouravan	nikouravan	PROPN
iajs-3409	399	14	,	,	PUNCT
iajs-3409	399	15	b.	b.	PROPN
iajs-3409	399	16	;	;	PUNCT
iajs-3409	399	17	siri	siri	NOUN
iajs-3409	399	18	,	,	PUNCT
iajs-3409	399	19	z.	z.	PROPN
iajs-3409	399	20	a	a	DET
iajs-3409	399	21	three	three	NUM
iajs-3409	399	22	-	-	PUNCT
iajs-3409	399	23	stage	stage	NOUN
iajs-3409	399	24	fifth	fifth	ADJ
iajs-3409	399	25	-	-	PUNCT
iajs-3409	399	26	order	order	NOUN
iajs-3409	399	27	runge	runge	NOUN
iajs-3409	399	28	-	-	PUNCT
iajs-3409	399	29	kutta	kutta	NOUN
iajs-3409	399	30	method	method	NOUN
iajs-3409	399	31	for	for	ADP
iajs-3409	399	32	directly	directly	ADV
iajs-3409	399	33	solving	solve	VERB
iajs-3409	399	34	special	special	ADJ
iajs-3409	399	35	third	third	ADJ
iajs-3409	399	36	-	-	PUNCT
iajs-3409	399	37	order	order	NOUN
iajs-3409	399	38	differential	differential	ADJ
iajs-3409	399	39	equation	equation	NOUN
iajs-3409	399	40	with	with	ADP
iajs-3409	399	41	application	application	NOUN
iajs-3409	399	42	to	to	ADP
iajs-3409	399	43	thin	thin	ADJ
iajs-3409	399	44	film	film	NOUN
iajs-3409	399	45	flow	flow	NOUN
iajs-3409	399	46	problem	problem	NOUN
iajs-3409	399	47	.	.	PUNCT
iajs-3409	400	1	mathematical	mathematical	ADJ
iajs-3409	400	2	problems	problem	NOUN
iajs-3409	400	3	in	in	ADP
iajs-3409	400	4	engineering	engineering	NOUN
iajs-3409	400	5	.	.	PUNCT
iajs-3409	401	1	2013	2013	NUM
iajs-3409	401	2	,	,	PUNCT
iajs-3409	401	3	2013	2013	NUM
iajs-3409	401	4	,	,	PUNCT
iajs-3409	401	5	https://doi.org/10.1155/2013/795397	https://doi.org/10.1155/2013/795397	NOUN
iajs-3409	401	6	.	.	PUNCT
iajs-3409	402	1	17	17	NUM
iajs-3409	402	2	.	.	PUNCT
iajs-3409	402	3	fawzi	fawzi	PROPN
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iajs-3409	402	5	f.	f.	PROPN
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iajs-3409	402	11	h.	h.	PROPN
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iajs-3409	403	4	third	third	ADJ
iajs-3409	403	5	-	-	PUNCT
iajs-3409	403	6	order	order	NOUN
iajs-3409	403	7	ordinary	ordinary	ADJ
iajs-3409	403	8	differential	differential	ADJ
iajs-3409	403	9	equations	equation	NOUN
iajs-3409	403	10	(	(	PUNCT
iajs-3409	403	11	ode	ode	PROPN
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iajs-3409	403	13	for	for	ADP
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iajs-3409	403	15	-	-	PUNCT
iajs-3409	403	16	order	order	NOUN
iajs-3409	403	17	3rd	3rd	ADJ
iajs-3409	403	18	-	-	PUNCT
iajs-3409	403	19	stage	stage	NOUN
iajs-3409	403	20	diagonally	diagonally	ADV
iajs-3409	403	21	implicit	implicit	ADJ
iajs-3409	403	22	type	type	NOUN
iajs-3409	403	23	runge	runge	NOUN
iajs-3409	403	24	-	-	PUNCT
iajs-3409	403	25	kutta	kutta	NOUN
iajs-3409	403	26	method	method	NOUN
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iajs-3409	403	28	ditrkm	ditrkm	NOUN
iajs-3409	403	29	)	)	PUNCT
iajs-3409	403	30	.	.	PUNCT
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iajs-3409	405	3	https://doi.org/10.1016/j.amc.2006.05.068	https://doi.org/10.1016/j.amc.2006.05.068	VERB
iajs-3409	405	4	https://doi.org/10.1080/00207160412331296634	https://doi.org/10.1080/00207160412331296634	NOUN
iajs-3409	405	5	http://dx.doi.org/10.12732/ijpam.v107i1.7	http://dx.doi.org/10.12732/ijpam.v107i1.7	ADJ
iajs-3409	405	6	https://doi.org/10.21123/bsj.2020.17.1.0166	https://doi.org/10.21123/bsj.2020.17.1.0166	NOUN
iajs-3409	405	7	https://doi.org/10.1016/j.aej.2020.03.008	https://doi.org/10.1016/j.aej.2020.03.008	NOUN
iajs-3409	405	8	http://dx.doi.org/10.1109/icrem.2015.7357020	http://dx.doi.org/10.1109/icrem.2015.7357020	NOUN
iajs-3409	405	9	http://dx.doi.org/10.17576/jsm-2021-5006-25	http://dx.doi.org/10.17576/jsm-2021-5006-25	VERB
iajs-3409	405	10	https://doi.org/10.24996/ijs.2022.63.9.21	https://doi.org/10.24996/ijs.2022.63.9.21	PROPN
iajs-3409	405	11	https://doi.org/10.1016/j.amc.2017.10.003	https://doi.org/10.1016/j.amc.2017.10.003	PROPN
iajs-3409	405	12	http://dx.doi.org/10.22052/mir.2020.211603.1185	http://dx.doi.org/10.22052/mir.2020.211603.1185	PUNCT
iajs-3409	405	13	https://doi.org/10.1155/2013/795397	https://doi.org/10.1155/2013/795397	NOUN
iajs-3409	405	14	ihjpas	ihjpa	NOUN
iajs-3409	405	15	.	.	PUNCT
iajs-3409	406	1	37	37	NUM
iajs-3409	406	2	(	(	PUNCT
iajs-3409	406	3	2	2	NUM
iajs-3409	406	4	)	)	PUNCT
iajs-3409	406	5	2024	2024	NUM
iajs-3409	406	6	408	408	NUM
iajs-3409	406	7	haitham	haitham	PROPN
iajs-3409	406	8	journal	journal	PROPN
iajs-3409	406	9	for	for	ADP
iajs-3409	406	10	pure	pure	ADJ
iajs-3409	406	11	and	and	CCONJ
iajs-3409	406	12	applied	applied	ADJ
iajs-3409	406	13	sciences	science	NOUN
iajs-3409	406	14	.	.	PUNCT
iajs-3409	406	15	2022	2022	NUM
iajs-3409	406	16	,	,	PUNCT
iajs-3409	406	17	35(1	35(1	NUM
iajs-3409	406	18	)	)	PUNCT
iajs-3409	406	19	,	,	PUNCT
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iajs-3409	406	21	-	-	SYM
iajs-3409	406	22	101	101	NUM
iajs-3409	406	23	,	,	PUNCT
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iajs-3409	406	27	.	.	PUNCT
iajs-3409	407	1	ismail	ismail	PROPN
iajs-3409	407	2	f.	f.	PROPN
iajs-3409	407	3	;	;	PUNCT
iajs-3409	407	4	al	al	PROPN
iajs-3409	407	5	-	-	PUNCT
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iajs-3409	407	8	r.	r.	PROPN
iajs-3409	407	9	a.	a.	NOUN
iajs-3409	407	10	solving	solving	NOUN
iajs-3409	407	11	delay	delay	NOUN
iajs-3409	407	12	differential	differential	ADJ
iajs-3409	407	13	equations	equation	NOUN
iajs-3409	407	14	using	use	VERB
iajs-3409	407	15	embedded	embed	VERB
iajs-3409	407	16	singly	singly	ADV
iajs-3409	407	17	diagonally	diagonally	ADV
iajs-3409	407	18	implicit	implicit	ADJ
iajs-3409	407	19	runge	runge	NOUN
iajs-3409	407	20	-	-	PUNCT
iajs-3409	407	21	kutta	kutta	NOUN
iajs-3409	407	22	methods	method	NOUN
iajs-3409	407	23	.	.	PUNCT
iajs-3409	408	1	acta	acta	PROPN
iajs-3409	408	2	mathematica	mathematica	PROPN
iajs-3409	408	3	vietnamica	vietnamica	PROPN
iajs-3409	408	4	.	.	PUNCT
iajs-3409	409	1	2008	2008	NUM
iajs-3409	409	2	,	,	PUNCT
iajs-3409	409	3	33(2	33(2	NUM
iajs-3409	409	4	)	)	PUNCT
iajs-3409	409	5	,	,	PUNCT
iajs-3409	409	6	95	95	NUM
iajs-3409	409	7	-	-	SYM
iajs-3409	409	8	105	105	NUM
iajs-3409	409	9	.	.	PUNCT
iajs-3409	410	1	19	19	NUM
iajs-3409	410	2	.	.	PUNCT
iajs-3409	410	3	jikantoro	jikantoro	PROPN
iajs-3409	410	4	,	,	PUNCT
iajs-3409	410	5	y.	y.	PROPN
iajs-3409	410	6	d.	d.	PROPN
iajs-3409	410	7	,	,	PUNCT
iajs-3409	410	8	ismail	ismail	PROPN
iajs-3409	410	9	,	,	PUNCT
iajs-3409	410	10	f.	f.	PROPN
iajs-3409	410	11	,	,	PUNCT
iajs-3409	410	12	senu	senu	VERB
iajs-3409	410	13	,	,	PUNCT
iajs-3409	410	14	n.	n.	NOUN
iajs-3409	410	15	,	,	PUNCT
iajs-3409	410	16	&	&	CCONJ
iajs-3409	410	17	ibrahim	ibrahim	PROPN
iajs-3409	410	18	,	,	PUNCT
iajs-3409	410	19	z.	z.	PROPN
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iajs-3409	410	21	,	,	PUNCT
iajs-3409	410	22	.	.	PUNCT
iajs-3409	411	1	a	a	DET
iajs-3409	411	2	new	new	ADJ
iajs-3409	411	3	integrator	integrator	NOUN
iajs-3409	411	4	for	for	ADP
iajs-3409	411	5	special	special	ADJ
iajs-3409	411	6	third	third	ADJ
iajs-3409	411	7	order	order	NOUN
iajs-3409	411	8	differential	differential	ADJ
iajs-3409	411	9	equations	equation	NOUN
iajs-3409	411	10	with	with	ADP
iajs-3409	411	11	application	application	NOUN
iajs-3409	411	12	to	to	ADP
iajs-3409	411	13	thin	thin	ADJ
iajs-3409	411	14	film	film	NOUN
iajs-3409	411	15	flow	flow	NOUN
iajs-3409	411	16	problem	problem	NOUN
iajs-3409	411	17	.	.	PUNCT
iajs-3409	412	1	indian	indian	ADJ
iajs-3409	412	2	journal	journal	PROPN
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iajs-3409	412	4	pure	pure	ADJ
iajs-3409	412	5	and	and	CCONJ
iajs-3409	412	6	applied	applied	ADJ
iajs-3409	412	7	mathematics	mathematic	NOUN
iajs-3409	412	8	,	,	PUNCT
iajs-3409	412	9	2018	2018	NUM
iajs-3409	412	10	,	,	PUNCT
iajs-3409	412	11	49	49	NUM
iajs-3409	412	12	,	,	PUNCT
iajs-3409	412	13	151	151	NUM
iajs-3409	412	14	-	-	SYM
iajs-3409	412	15	167	167	NUM
iajs-3409	412	16	,	,	PUNCT
iajs-3409	412	17	10.1007	10.1007	NUM
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iajs-3409	412	19	s13226	s13226	NUM
iajs-3409	412	20	-	-	PUNCT
iajs-3409	412	21	018	018	NUM
iajs-3409	412	22	-	-	PUNCT
iajs-3409	412	23	0259	0259	NUM
iajs-3409	412	24	-	-	PUNCT
iajs-3409	412	25	6	6	NUM
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iajs-3409	412	27	20	20	NUM
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iajs-3409	413	1	lee	lee	PROPN
iajs-3409	413	2	,	,	PUNCT
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iajs-3409	413	4	c.	c.	PROPN
iajs-3409	413	5	;	;	PUNCT
iajs-3409	413	6	senu	senu	PROPN
iajs-3409	413	7	,	,	PUNCT
iajs-3409	413	8	;	;	PUNCT
iajs-3409	413	9	ahmadian	ahmadian	ADJ
iajs-3409	413	10	,	,	PUNCT
iajs-3409	413	11	a.	a.	NOUN
iajs-3409	413	12	;	;	PUNCT
iajs-3409	413	13	ibrahim	ibrahim	PROPN
iajs-3409	413	14	,	,	PUNCT
iajs-3409	413	15	s.	s.	PROPN
iajs-3409	413	16	n.	n.	PROPN
iajs-3409	413	17	i.	i.	PROPN
iajs-3409	413	18	,	,	PUNCT
iajs-3409	413	19	on	on	ADP
iajs-3409	413	20	two	two	NUM
iajs-3409	413	21	-	-	PUNCT
iajs-3409	413	22	derivative	derivative	NOUN
iajs-3409	413	23	runge	runge	NOUN
iajs-3409	413	24	–	–	PUNCT
iajs-3409	413	25	kutta	kutta	NOUN
iajs-3409	413	26	type	type	NOUN
iajs-3409	413	27	methods	method	NOUN
iajs-3409	413	28	for	for	ADP
iajs-3409	413	29	solving	solve	VERB
iajs-3409	413	30	u‴=	u‴=	PROPN
iajs-3409	413	31	f	f	PROPN
iajs-3409	413	32	(	(	PUNCT
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iajs-3409	413	34	,	,	PUNCT
iajs-3409	413	35	u	u	NOUN
iajs-3409	413	36	(	(	PUNCT
iajs-3409	413	37	x	x	NOUN
iajs-3409	413	38	)	)	PUNCT
iajs-3409	413	39	)	)	PUNCT
iajs-3409	413	40	with	with	ADP
iajs-3409	413	41	application	application	NOUN
iajs-3409	413	42	to	to	ADP
iajs-3409	413	43	thin	thin	ADJ
iajs-3409	413	44	film	film	NOUN
iajs-3409	413	45	flow	flow	NOUN
iajs-3409	413	46	problem	problem	NOUN
iajs-3409	413	47	.	.	PUNCT
iajs-3409	414	1	symmetry	symmetry	NOUN
iajs-3409	414	2	,	,	PUNCT
iajs-3409	414	3	2020	2020	NUM
iajs-3409	414	4	,	,	PUNCT
iajs-3409	414	5	12(6	12(6	NUM
iajs-3409	414	6	)	)	PUNCT
iajs-3409	414	7	,	,	PUNCT
iajs-3409	414	8	924	924	NUM
iajs-3409	414	9	,	,	PUNCT
iajs-3409	414	10	https://doi.org/10.3390/sym12060924	https://doi.org/10.3390/sym12060924	NOUN
iajs-3409	414	11	.	.	PROPN
iajs-3409	415	1	21	21	NUM
iajs-3409	415	2	.	.	PUNCT
iajs-3409	415	3	hussain	hussain	PROPN
iajs-3409	415	4	,	,	PUNCT
iajs-3409	415	5	k.	k.	PROPN
iajs-3409	415	6	;	;	PUNCT
iajs-3409	415	7	ismail	ismail	PROPN
iajs-3409	415	8	,	,	PUNCT
iajs-3409	415	9	f.	f.	PROPN
iajs-3409	415	10	;	;	PUNCT
iajs-3409	415	11	senu	senu	X
iajs-3409	415	12	,	,	PUNCT
iajs-3409	415	13	n.	n.	NOUN
iajs-3409	415	14	solving	solve	VERB
iajs-3409	415	15	directly	directly	ADV
iajs-3409	415	16	special	special	ADJ
iajs-3409	415	17	fourth	fourth	ADJ
iajs-3409	415	18	-	-	PUNCT
iajs-3409	415	19	order	order	NOUN
iajs-3409	415	20	ordinary	ordinary	ADJ
iajs-3409	415	21	differential	differential	ADJ
iajs-3409	415	22	equations	equation	NOUN
iajs-3409	415	23	using	use	VERB
iajs-3409	415	24	runge	runge	NOUN
iajs-3409	415	25	–	–	PUNCT
iajs-3409	415	26	kutta	kutta	NOUN
iajs-3409	415	27	type	type	NOUN
iajs-3409	415	28	method	method	NOUN
iajs-3409	415	29	.	.	PUNCT
iajs-3409	416	1	journal	journal	NOUN
iajs-3409	416	2	of	of	ADP
iajs-3409	416	3	computational	computational	ADJ
iajs-3409	416	4	and	and	CCONJ
iajs-3409	416	5	applied	applied	ADJ
iajs-3409	416	6	mathematics	mathematic	NOUN
iajs-3409	416	7	.	.	PUNCT
iajs-3409	417	1	2016	2016	NUM
iajs-3409	417	2	,	,	PUNCT
iajs-3409	417	3	306	306	NUM
iajs-3409	417	4	,	,	PUNCT
iajs-3409	417	5	179199	179199	NUM
iajs-3409	417	6	,	,	PUNCT
iajs-3409	417	7	https://doi.org/10.1016/j.cam.2016.04.002	https://doi.org/10.1016/j.cam.2016.04.002	NOUN
iajs-3409	417	8	.	.	PROPN
iajs-3409	418	1	22	22	NUM
iajs-3409	418	2	.	.	PUNCT
iajs-3409	419	1	ghawadri	ghawadri	PROPN
iajs-3409	419	2	,	,	PUNCT
iajs-3409	419	3	n.	n.	NOUN
iajs-3409	419	4	;	;	PUNCT
iajs-3409	419	5	senu	senu	NOUN
iajs-3409	419	6	,	,	PUNCT
iajs-3409	419	7	n.	n.	NOUN
iajs-3409	419	8	;	;	PUNCT
iajs-3409	419	9	adel	adel	PROPN
iajs-3409	419	10	fawzi	fawzi	PROPN
iajs-3409	419	11	,	,	PUNCT
iajs-3409	419	12	f.	f.	PROPN
iajs-3409	419	13	;	;	PUNCT
iajs-3409	419	14	ismail	ismail	PROPN
iajs-3409	419	15	,	,	PUNCT
iajs-3409	419	16	f.	f.	PROPN
iajs-3409	419	17	;	;	PUNCT
iajs-3409	419	18	ibrahim	ibrahim	PROPN
iajs-3409	419	19	,	,	PUNCT
iajs-3409	420	1	z.	z.	PROPN
iajs-3409	420	2	b.	b.	PROPN
iajs-3409	420	3	explicit	explicit	ADJ
iajs-3409	420	4	integrator	integrator	NOUN
iajs-3409	420	5	of	of	ADP
iajs-3409	420	6	runge	runge	NOUN
iajs-3409	420	7	-	-	PUNCT
iajs-3409	420	8	kutta	kutta	NOUN
iajs-3409	420	9	type	type	NOUN
iajs-3409	420	10	for	for	ADP
iajs-3409	420	11	direct	direct	ADJ
iajs-3409	420	12	solution	solution	NOUN
iajs-3409	420	13	of	of	ADP
iajs-3409	420	14	𝑢(4	𝑢(4	PROPN
iajs-3409	420	15	)	)	PUNCT
iajs-3409	421	1	=	=	SYM
iajs-3409	421	2	𝑓	𝑓	PROPN
iajs-3409	421	3	(	(	PUNCT
iajs-3409	421	4	𝑥	𝑥	NOUN
iajs-3409	421	5	,	,	PUNCT
iajs-3409	421	6	𝑢	𝑢	PROPN
iajs-3409	421	7	,	,	PUNCT
iajs-3409	421	8	𝑢′	𝑢′	NUM
iajs-3409	421	9	,	,	PUNCT
iajs-3409	421	10	𝑢′′	𝑢′′	PROPN
iajs-3409	421	11	)	)	PUNCT
iajs-3409	421	12	.	.	PUNCT
iajs-3409	421	13	symmetry	symmetry	PROPN
iajs-3409	421	14	.	.	PUNCT
iajs-3409	422	1	2019	2019	NUM
iajs-3409	422	2	,	,	PUNCT
iajs-3409	422	3	11(2	11(2	NUM
iajs-3409	422	4	)	)	PUNCT
iajs-3409	422	5	,	,	PUNCT
iajs-3409	422	6	246	246	NUM
iajs-3409	422	7	,	,	PUNCT
iajs-3409	422	8	https://doi.org/10.3390/sym11020246	https://doi.org/10.3390/sym11020246	PROPN
iajs-3409	422	9	.	.	PUNCT
iajs-3409	423	1	23	23	NUM
iajs-3409	423	2	.	.	PUNCT
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iajs-3409	424	2	,	,	PUNCT
iajs-3409	424	3	j.	j.	PROPN
iajs-3409	424	4	r.	r.	PROPN
iajs-3409	424	5	numerical	numerical	PROPN
iajs-3409	424	6	methods	method	NOUN
iajs-3409	424	7	for	for	ADP
iajs-3409	424	8	differential	differential	ADJ
iajs-3409	424	9	equations	equation	NOUN
iajs-3409	424	10	:	:	PUNCT
iajs-3409	424	11	a	a	DET
iajs-3409	424	12	computational	computational	ADJ
iajs-3409	424	13	approach	approach	NOUN
iajs-3409	424	14	.	.	PUNCT
iajs-3409	425	1	crc	crc	PROPN
iajs-3409	425	2	press	press	PROPN
iajs-3409	425	3	,	,	PUNCT
iajs-3409	425	4	1996	1996	NUM
iajs-3409	425	5	,	,	PUNCT
iajs-3409	425	6	https://doi.org/10.1201/9781351075107	https://doi.org/10.1201/9781351075107	PROPN
iajs-3409	425	7	.	.	PUNCT
iajs-3409	426	1	24	24	NUM
iajs-3409	426	2	.	.	PUNCT
iajs-3409	426	3	fawzi	fawzi	PROPN
iajs-3409	426	4	,	,	PUNCT
iajs-3409	426	5	f.	f.	PROPN
iajs-3409	426	6	a.	a.	PROPN
iajs-3409	426	7	;	;	PUNCT
iajs-3409	426	8	jaleel	jaleel	PROPN
iajs-3409	426	9	,	,	PUNCT
iajs-3409	426	10	n.	n.	PROPN
iajs-3409	426	11	w.	w.	PROPN
iajs-3409	426	12	exponentially	exponentially	ADV
iajs-3409	426	13	fitted	fit	VERB
iajs-3409	426	14	diagonally	diagonally	ADV
iajs-3409	426	15	implicit	implicit	ADJ
iajs-3409	426	16	editrk	editrk	NOUN
iajs-3409	426	17	method	method	NOUN
iajs-3409	426	18	for	for	ADP
iajs-3409	426	19	solving	solve	VERB
iajs-3409	426	20	odes	ode	NOUN
iajs-3409	426	21	.	.	PUNCT
iajs-3409	427	1	ibn	ibn	PROPN
iajs-3409	427	2	al	al	PROPN
iajs-3409	427	3	-	-	PUNCT
iajs-3409	427	4	haitham	haitham	PROPN
iajs-3409	427	5	journal	journal	PROPN
iajs-3409	427	6	for	for	ADP
iajs-3409	427	7	pure	pure	ADJ
iajs-3409	427	8	and	and	CCONJ
iajs-3409	427	9	applied	applied	ADJ
iajs-3409	427	10	sciences	science	NOUN
iajs-3409	427	11	.	.	PUNCT
iajs-3409	428	1	2023	2023	NUM
iajs-3409	428	2	,	,	PUNCT
iajs-3409	428	3	36(1	36(1	NUM
iajs-3409	428	4	)	)	PUNCT
iajs-3409	428	5	,	,	PUNCT
iajs-3409	428	6	389	389	NUM
iajs-3409	428	7	-	-	SYM
iajs-3409	428	8	399	399	NUM
iajs-3409	428	9	,	,	PUNCT
iajs-3409	428	10	https://doi.org/10.30526/36.1.2883	https://doi.org/10.30526/36.1.2883	PROPN
iajs-3409	428	11	.	.	PUNCT
iajs-3409	429	1	25	25	NUM
iajs-3409	429	2	.	.	X
iajs-3409	429	3	saleh	saleh	NOUN
iajs-3409	429	4	,	,	PUNCT
iajs-3409	429	5	o.	o.	PROPN
iajs-3409	429	6	m.	m.	NOUN
iajs-3409	429	7	;	;	PUNCT
iajs-3409	429	8	fawzi	fawzi	PROPN
iajs-3409	429	9	,	,	PUNCT
iajs-3409	429	10	f.	f.	PROPN
iajs-3409	429	11	a.	a.	PROPN
iajs-3409	429	12	;	;	PUNCT
iajs-3409	429	13	hussain	hussain	PROPN
iajs-3409	429	14	,	,	PUNCT
iajs-3409	429	15	k.	k.	PROPN
iajs-3409	429	16	a.	a.	PROPN
iajs-3409	429	17	;	;	PUNCT
iajs-3409	429	18	ghawadri	ghawadri	PROPN
iajs-3409	429	19	,	,	PUNCT
iajs-3409	429	20	n.	n.	NOUN
iajs-3409	429	21	g.	g.	PROPN
iajs-3409	429	22	derivation	derivation	NOUN
iajs-3409	429	23	of	of	ADP
iajs-3409	429	24	embedded	embed	VERB
iajs-3409	429	25	diagonally	diagonally	ADV
iajs-3409	429	26	implicit	implicit	ADJ
iajs-3409	429	27	methods	method	NOUN
iajs-3409	429	28	for	for	ADP
iajs-3409	429	29	directly	directly	ADV
iajs-3409	429	30	solving	solve	VERB
iajs-3409	429	31	fourth	fourth	ADJ
iajs-3409	429	32	-	-	PUNCT
iajs-3409	429	33	order	order	NOUN
iajs-3409	429	34	odes	ode	NOUN
iajs-3409	429	35	.	.	PUNCT
iajs-3409	430	1	ibn	ibn	PROPN
iajs-3409	430	2	al	al	PROPN
iajs-3409	430	3	-	-	PUNCT
iajs-3409	430	4	haitham	haitham	PROPN
iajs-3409	430	5	journal	journal	PROPN
iajs-3409	430	6	for	for	ADP
iajs-3409	430	7	pure	pure	ADJ
iajs-3409	430	8	and	and	CCONJ
iajs-3409	430	9	applied	applied	ADJ
iajs-3409	430	10	sciences	science	NOUN
iajs-3409	430	11	,	,	PUNCT
iajs-3409	430	12	2024	2024	NUM
iajs-3409	430	13	,	,	PUNCT
iajs-3409	430	14	37(1	37(1	NUM
iajs-3409	430	15	)	)	PUNCT
iajs-3409	430	16	,	,	PUNCT
iajs-3409	430	17	375	375	NUM
iajs-3409	430	18	-	-	SYM
iajs-3409	430	19	385	385	NUM
iajs-3409	430	20	,	,	PUNCT
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iajs-3409	430	22	.	.	PROPN
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iajs-3409	430	24	.	.	X
iajs-3409	430	25	senu	senu	PROPN
iajs-3409	430	26	,	,	PUNCT
iajs-3409	430	27	n.	n.	NOUN
iajs-3409	430	28	;	;	PUNCT
iajs-3409	430	29	suleiman	suleiman	PROPN
iajs-3409	430	30	,	,	PUNCT
iajs-3409	430	31	m.	m.	NOUN
iajs-3409	430	32	;	;	PUNCT
iajs-3409	430	33	ismail	ismail	PROPN
iajs-3409	430	34	,	,	PUNCT
iajs-3409	430	35	f.	f.	PROPN
iajs-3409	430	36	an	an	DET
iajs-3409	430	37	embedded	embed	VERB
iajs-3409	430	38	explicit	explicit	ADJ
iajs-3409	430	39	runge	runge	NOUN
iajs-3409	430	40	–	–	PUNCT
iajs-3409	430	41	kutta	kutta	NOUN
iajs-3409	430	42	–	–	PUNCT
iajs-3409	430	43	nyström	nyström	NOUN
iajs-3409	430	44	method	method	NOUN
iajs-3409	430	45	for	for	ADP
iajs-3409	430	46	solving	solve	VERB
iajs-3409	430	47	oscillatory	oscillatory	ADJ
iajs-3409	430	48	problems	problem	NOUN
iajs-3409	430	49	.	.	PUNCT
iajs-3409	431	1	physica	physica	PROPN
iajs-3409	431	2	scripta	scripta	PROPN
iajs-3409	431	3	.	.	PROPN
iajs-3409	431	4	2009	2009	NUM
iajs-3409	431	5	,	,	PUNCT
iajs-3409	431	6	80(1	80(1	NUM
iajs-3409	431	7	)	)	PUNCT
iajs-3409	431	8	,	,	PUNCT
iajs-3409	431	9	015005	015005	NUM
iajs-3409	431	10	.	.	PUNCT
iajs-3409	432	1	https://doi.org/10.1088/00318949/80/01/015005	https://doi.org/10.1088/00318949/80/01/015005	NUM
iajs-3409	432	2	27	27	NUM
iajs-3409	432	3	.	.	PUNCT
iajs-3409	433	1	hairer	hairer	PROPN
iajs-3409	433	2	e.	e.	PROPN
iajs-3409	433	3	;	;	PUNCT
iajs-3409	433	4	hochbruck	hochbruck	NOUN
iajs-3409	433	5	,	,	PUNCT
iajs-3409	433	6	m.	m.	NOUN
iajs-3409	433	7	;	;	PUNCT
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iajs-3409	433	9	,	,	PUNCT
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iajs-3409	433	18	;	;	PUNCT
iajs-3409	433	19	oberwolfach	oberwolfach	NOUN
iajs-3409	433	20	reports	report	VERB
iajs-3409	433	21	.	.	PUNCT
iajs-3409	434	1	2006	2006	NUM
iajs-3409	434	2	,	,	PUNCT
iajs-3409	434	3	3(1	3(1	NUM
iajs-3409	434	4	)	)	PUNCT
iajs-3409	434	5	,	,	PUNCT
iajs-3409	434	6	805	805	NUM
iajs-3409	434	7	-	-	SYM
iajs-3409	434	8	882	882	NUM
iajs-3409	434	9	.	.	PUNCT
iajs-3409	435	1	https://doi.org/10.1017/s0962492902000144	https://doi.org/10.1017/s0962492902000144	NUM
iajs-3409	435	2	.	.	NOUN
iajs-3409	436	1	28	28	NUM
iajs-3409	436	2	.	.	PUNCT
iajs-3409	437	1	hairer	hairer	PROPN
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iajs-3409	437	3	,	,	PUNCT
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iajs-3409	437	12	equations	equation	NOUN
iajs-3409	437	13	i	i	PRON
iajs-3409	437	14	:	:	PUNCT
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iajs-3409	437	17	,	,	PUNCT
iajs-3409	437	18	ii	ii	PROPN
iajs-3409	437	19	:	:	PUNCT
iajs-3409	437	20	stiff	stiff	ADJ
iajs-3409	437	21	problems	problem	NOUN
iajs-3409	437	22	.	.	PUNCT
iajs-3409	438	1	springer	springer	NOUN
iajs-3409	438	2	,	,	PUNCT
iajs-3409	438	3	1987	1987	NUM
iajs-3409	438	4	.	.	PUNCT
iajs-3409	439	1	https://doi.org/10.1007/978-3-540-78862-1	https://doi.org/10.1007/978-3-540-78862-1	PROPN
iajs-3409	439	2	.	.	PROPN
iajs-3409	439	3	29	29	NUM
iajs-3409	439	4	.	.	PUNCT
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iajs-3409	440	9	differential	differential	ADJ
iajs-3409	440	10	systems	system	NOUN
iajs-3409	440	11	.	.	PUNCT
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iajs-3409	441	3	:	:	PUNCT
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iajs-3409	441	5	,	,	PUNCT
iajs-3409	441	6	1991	1991	NUM
iajs-3409	441	7	.	.	PUNCT
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iajs-3409	443	4	https://doi.org/10.1016/j.cam.2016.04.002	https://doi.org/10.1016/j.cam.2016.04.002	NOUN
iajs-3409	443	5	https://doi.org/10.3390/sym11020246	https://doi.org/10.3390/sym11020246	PROPN
iajs-3409	443	6	https://doi.org/10.1201/9781351075107	https://doi.org/10.1201/9781351075107	PROPN
iajs-3409	443	7	https://doi.org/10.30526/36.1.2883	https://doi.org/10.30526/36.1.2883	PROPN
iajs-3409	443	8	https://doi.org/10.30526/37.1.3288	https://doi.org/10.30526/37.1.3288	NUM
iajs-3409	443	9	http://dx.doi.org/10.1088/0031-8949/80/01/015005	http://dx.doi.org/10.1088/0031-8949/80/01/015005	NOUN
iajs-3409	443	10	http://dx.doi.org/10.1088/0031-8949/80/01/015005	http://dx.doi.org/10.1088/0031-8949/80/01/015005	X
iajs-3409	443	11	http://dx.doi.org/10.1017/s0962492902000144	http://dx.doi.org/10.1017/s0962492902000144	X
iajs-3409	443	12	http://dx.doi.org/10.1007/978-3-540-78862-1	http://dx.doi.org/10.1007/978-3-540-78862-1	X