id	sid	tid	token	lemma	pos
iajs-2803	1	1	ibn	ibn	PROPN
iajs-2803	1	2	al	al	PROPN
iajs-2803	1	3	-	-	PUNCT
iajs-2803	1	4	haitham	haitham	PROPN
iajs-2803	1	5	jour	jour	X
iajs-2803	1	6	.	.	PROPN
iajs-2803	1	7	for	for	ADP
iajs-2803	1	8	pure	pure	ADJ
iajs-2803	1	9	&	&	CCONJ
iajs-2803	1	10	appl	appl	PROPN
iajs-2803	1	11	.	.	PUNCT
iajs-2803	2	1	sci	sci	PROPN
iajs-2803	2	2	.	.	PROPN
iajs-2803	3	1	53	53	NUM
iajs-2803	3	2	(	(	PUNCT
iajs-2803	3	3	1)2022	1)2022	PROPN
iajs-2803	3	4	92	92	NUM
iajs-2803	3	5	this	this	DET
iajs-2803	3	6	work	work	NOUN
iajs-2803	3	7	is	be	AUX
iajs-2803	3	8	licensed	license	VERB
iajs-2803	3	9	under	under	ADP
iajs-2803	3	10	a	a	DET
iajs-2803	3	11	creative	creative	ADJ
iajs-2803	3	12	commons	common	NOUN
iajs-2803	3	13	attribution	attribution	NOUN
iajs-2803	3	14	4.0	4.0	NUM
iajs-2803	3	15	international	international	ADJ
iajs-2803	3	16	license	license	NOUN
iajs-2803	3	17	.	.	PUNCT
iajs-2803	4	1	the	the	DET
iajs-2803	4	2	implementations	implementation	NOUN
iajs-2803	4	3	special	special	ADJ
iajs-2803	4	4	third	third	ADJ
iajs-2803	4	5	-	-	PUNCT
iajs-2803	4	6	order	order	NOUN
iajs-2803	4	7	ordinary	ordinary	ADJ
iajs-2803	4	8	differential	differential	ADJ
iajs-2803	4	9	equations	equation	NOUN
iajs-2803	4	10	(	(	PUNCT
iajs-2803	4	11	ode	ode	PROPN
iajs-2803	4	12	)	)	PUNCT
iajs-2803	4	13	for	for	ADP
iajs-2803	4	14	5th	5th	ADJ
iajs-2803	4	15	-	-	PUNCT
iajs-2803	4	16	order	order	NOUN
iajs-2803	4	17	3rd	3rd	ADJ
iajs-2803	4	18	-	-	PUNCT
iajs-2803	4	19	stage	stage	NOUN
iajs-2803	4	20	diagonally	diagonally	ADV
iajs-2803	4	21	implicit	implicit	ADJ
iajs-2803	4	22	type	type	NOUN
iajs-2803	4	23	rungekutta	rungekutta	NOUN
iajs-2803	4	24	method	method	NOUN
iajs-2803	4	25	(	(	PUNCT
iajs-2803	4	26	ditrkm	ditrkm	NOUN
iajs-2803	4	27	)	)	PUNCT
iajs-2803	4	28	department	department	NOUN
iajs-2803	4	29	of	of	ADP
iajs-2803	4	30	mathematics	mathematic	NOUN
iajs-2803	4	31	,	,	PUNCT
iajs-2803	4	32	facultyof	facultyof	NOUN
iajs-2803	4	33	computer	computer	NOUN
iajs-2803	4	34	sciences	science	NOUN
iajs-2803	4	35	and	and	CCONJ
iajs-2803	4	36	mathematics	mathematic	NOUN
iajs-2803	4	37	,	,	PUNCT
iajs-2803	4	38	tikrit	tikrit	NOUN
iajs-2803	4	39	university	university	PROPN
iajs-2803	4	40	,	,	PUNCT
iajs-2803	4	41	iraq	iraq	PROPN
iajs-2803	4	42	.	.	PUNCT
iajs-2803	5	1	abstract	abstract	ADJ
iajs-2803	5	2	the	the	DET
iajs-2803	5	3	derivation	derivation	NOUN
iajs-2803	5	4	of	of	ADP
iajs-2803	5	5	5th	5th	ADJ
iajs-2803	5	6	order	order	NOUN
iajs-2803	5	7	diagonal	diagonal	ADJ
iajs-2803	5	8	implicit	implicit	ADJ
iajs-2803	5	9	type	type	NOUN
iajs-2803	5	10	runge	runge	NOUN
iajs-2803	5	11	kutta	kutta	NOUN
iajs-2803	5	12	methods	method	NOUN
iajs-2803	5	13	(	(	PUNCT
iajs-2803	5	14	ditrkm5	ditrkm5	PROPN
iajs-2803	5	15	)	)	PUNCT
iajs-2803	5	16	for	for	ADP
iajs-2803	5	17	solving	solve	VERB
iajs-2803	5	18	3rd	3rd	ADJ
iajs-2803	5	19	special	special	ADJ
iajs-2803	5	20	order	order	NOUN
iajs-2803	5	21	ordinary	ordinary	ADJ
iajs-2803	5	22	differential	differential	ADJ
iajs-2803	5	23	equations	equation	NOUN
iajs-2803	5	24	(	(	PUNCT
iajs-2803	5	25	odes	ode	NOUN
iajs-2803	5	26	)	)	PUNCT
iajs-2803	5	27	is	be	AUX
iajs-2803	5	28	introduced	introduce	VERB
iajs-2803	5	29	in	in	ADP
iajs-2803	5	30	the	the	DET
iajs-2803	5	31	present	present	ADJ
iajs-2803	5	32	study	study	NOUN
iajs-2803	5	33	.	.	PUNCT
iajs-2803	6	1	the	the	DET
iajs-2803	6	2	ditrkm5	ditrkm5	NOUN
iajs-2803	6	3	techniques	technique	NOUN
iajs-2803	6	4	are	be	AUX
iajs-2803	6	5	the	the	DET
iajs-2803	6	6	name	name	NOUN
iajs-2803	6	7	of	of	ADP
iajs-2803	6	8	the	the	DET
iajs-2803	6	9	approach	approach	NOUN
iajs-2803	6	10	.	.	PUNCT
iajs-2803	7	1	this	this	DET
iajs-2803	7	2	approach	approach	NOUN
iajs-2803	7	3	has	have	VERB
iajs-2803	7	4	three	three	NUM
iajs-2803	7	5	equivalent	equivalent	ADJ
iajs-2803	7	6	non	non	ADJ
iajs-2803	7	7	-	-	ADJ
iajs-2803	7	8	zero	zero	ADJ
iajs-2803	7	9	diagonal	diagonal	ADJ
iajs-2803	7	10	elements	element	NOUN
iajs-2803	7	11	.	.	PUNCT
iajs-2803	8	1	to	to	PART
iajs-2803	8	2	investigate	investigate	VERB
iajs-2803	8	3	the	the	DET
iajs-2803	8	4	current	current	ADJ
iajs-2803	8	5	study	study	NOUN
iajs-2803	8	6	,	,	PUNCT
iajs-2803	8	7	a	a	DET
iajs-2803	8	8	variety	variety	NOUN
iajs-2803	8	9	of	of	ADP
iajs-2803	8	10	tests	test	NOUN
iajs-2803	8	11	for	for	ADP
iajs-2803	8	12	five	five	NUM
iajs-2803	8	13	various	various	ADJ
iajs-2803	8	14	initial	initial	ADJ
iajs-2803	8	15	value	value	NOUN
iajs-2803	8	16	problems	problem	NOUN
iajs-2803	8	17	(	(	PUNCT
iajs-2803	8	18	ivps	ivps	PROPN
iajs-2803	8	19	)	)	PUNCT
iajs-2803	8	20	with	with	ADP
iajs-2803	8	21	different	different	ADJ
iajs-2803	8	22	step	step	NOUN
iajs-2803	8	23	sizes	size	NOUN
iajs-2803	8	24	h	h	NOUN
iajs-2803	8	25	were	be	AUX
iajs-2803	8	26	implemented	implement	VERB
iajs-2803	8	27	.	.	PUNCT
iajs-2803	9	1	then	then	ADV
iajs-2803	9	2	,	,	PUNCT
iajs-2803	9	3	a	a	DET
iajs-2803	9	4	comparison	comparison	NOUN
iajs-2803	9	5	was	be	AUX
iajs-2803	9	6	made	make	VERB
iajs-2803	9	7	with	with	ADP
iajs-2803	9	8	the	the	DET
iajs-2803	9	9	methods	method	NOUN
iajs-2803	9	10	indicated	indicate	VERB
iajs-2803	9	11	in	in	ADP
iajs-2803	9	12	the	the	DET
iajs-2803	9	13	other	other	ADJ
iajs-2803	9	14	literature	literature	NOUN
iajs-2803	9	15	of	of	ADP
iajs-2803	9	16	the	the	DET
iajs-2803	9	17	implicit	implicit	ADJ
iajs-2803	9	18	rk	rk	NOUN
iajs-2803	9	19	techniques	technique	NOUN
iajs-2803	9	20	.	.	PUNCT
iajs-2803	10	1	the	the	DET
iajs-2803	10	2	numerical	numerical	ADJ
iajs-2803	10	3	techniques	technique	NOUN
iajs-2803	10	4	are	be	AUX
iajs-2803	10	5	elucidated	elucidate	VERB
iajs-2803	10	6	as	as	ADP
iajs-2803	10	7	the	the	DET
iajs-2803	10	8	qualification	qualification	NOUN
iajs-2803	10	9	regarding	regard	VERB
iajs-2803	10	10	the	the	DET
iajs-2803	10	11	efficiency	efficiency	NOUN
iajs-2803	10	12	and	and	CCONJ
iajs-2803	10	13	number	number	NOUN
iajs-2803	10	14	of	of	ADP
iajs-2803	10	15	function	function	NOUN
iajs-2803	10	16	evaluations	evaluation	NOUN
iajs-2803	10	17	compared	compare	VERB
iajs-2803	10	18	with	with	ADP
iajs-2803	10	19	another	another	DET
iajs-2803	10	20	literature	literature	NOUN
iajs-2803	10	21	of	of	ADP
iajs-2803	10	22	the	the	DET
iajs-2803	10	23	implicit	implicit	ADJ
iajs-2803	10	24	rk	rk	NOUN
iajs-2803	10	25	approaches	approach	VERB
iajs-2803	10	26	from	from	ADP
iajs-2803	10	27	the	the	DET
iajs-2803	10	28	result	result	NOUN
iajs-2803	10	29	of	of	ADP
iajs-2803	10	30	the	the	DET
iajs-2803	10	31	computations	computation	NOUN
iajs-2803	10	32	.	.	PUNCT
iajs-2803	11	1	in	in	ADP
iajs-2803	11	2	addition	addition	NOUN
iajs-2803	11	3	,	,	PUNCT
iajs-2803	11	4	the	the	DET
iajs-2803	11	5	stability	stability	NOUN
iajs-2803	11	6	polynomial	polynomial	NOUN
iajs-2803	11	7	for	for	ADP
iajs-2803	11	8	ditrk	ditrk	NOUN
iajs-2803	11	9	method	method	NOUN
iajs-2803	11	10	is	be	AUX
iajs-2803	11	11	derived	derive	VERB
iajs-2803	11	12	and	and	CCONJ
iajs-2803	11	13	analyzed	analyze	VERB
iajs-2803	11	14	.	.	PUNCT
iajs-2803	12	1	keywords	keyword	NOUN
iajs-2803	12	2	:	:	PUNCT
iajs-2803	12	3	numerical	numerical	ADJ
iajs-2803	12	4	methods	method	NOUN
iajs-2803	12	5	,	,	PUNCT
iajs-2803	12	6	ordinary	ordinary	ADJ
iajs-2803	12	7	differential	differential	ADJ
iajs-2803	12	8	equations	equation	NOUN
iajs-2803	12	9	,	,	PUNCT
iajs-2803	12	10	diagonal	diagonal	ADJ
iajs-2803	12	11	implicit	implicit	ADJ
iajs-2803	12	12	type	type	NOUN
iajs-2803	12	13	runge	runge	NOUN
iajs-2803	12	14	kutta	kutta	NOUN
iajs-2803	12	15	methods	method	NOUN
iajs-2803	12	16	,	,	PUNCT
iajs-2803	12	17	initial	initial	ADJ
iajs-2803	12	18	value	value	NOUN
iajs-2803	12	19	problems	problem	NOUN
iajs-2803	12	20	,	,	PUNCT
iajs-2803	12	21	stability	stability	NOUN
iajs-2803	12	22	polynomial	polynomial	ADJ
iajs-2803	12	23	analysis	analysis	NOUN
iajs-2803	12	24	.	.	PUNCT
iajs-2803	13	1	1	1	X
iajs-2803	13	2	.	.	X
iajs-2803	13	3	introduction	introduction	NOUN
iajs-2803	13	4	third	third	ADJ
iajs-2803	13	5	-	-	PUNCT
iajs-2803	13	6	order	order	NOUN
iajs-2803	13	7	odes	ode	NOUN
iajs-2803	13	8	are	be	AUX
iajs-2803	13	9	used	use	VERB
iajs-2803	13	10	in	in	ADP
iajs-2803	13	11	neural	neural	ADJ
iajs-2803	13	12	network	network	NOUN
iajs-2803	13	13	engineering	engineering	NOUN
iajs-2803	13	14	and	and	CCONJ
iajs-2803	13	15	applied	apply	VERB
iajs-2803	13	16	sciences	science	NOUN
iajs-2803	13	17	,	,	PUNCT
iajs-2803	13	18	the	the	DET
iajs-2803	13	19	dynamics	dynamic	NOUN
iajs-2803	13	20	of	of	ADP
iajs-2803	13	21	fluid	fluid	ADJ
iajs-2803	13	22	flow	flow	NOUN
iajs-2803	13	23	,	,	PUNCT
iajs-2803	13	24	the	the	DET
iajs-2803	13	25	ship	ship	NOUN
iajs-2803	13	26	's	's	PART
iajs-2803	13	27	motion	motion	NOUN
iajs-2803	13	28	,	,	PUNCT
iajs-2803	13	29	and	and	CCONJ
iajs-2803	13	30	electric	electric	ADJ
iajs-2803	13	31	circuits	circuit	NOUN
iajs-2803	13	32	,	,	PUNCT
iajs-2803	13	33	among	among	ADP
iajs-2803	13	34	other	other	ADJ
iajs-2803	13	35	fields	field	NOUN
iajs-2803	13	36	[	[	X
iajs-2803	13	37	1	1	NUM
iajs-2803	13	38	-	-	SYM
iajs-2803	13	39	6	6	NUM
iajs-2803	13	40	]	]	PUNCT
iajs-2803	13	41	.	.	PUNCT
iajs-2803	14	1	consider	consider	VERB
iajs-2803	14	2	the	the	DET
iajs-2803	14	3	numerical	numerical	ADJ
iajs-2803	14	4	method	method	NOUN
iajs-2803	14	5	for	for	ADP
iajs-2803	14	6	solving	solve	VERB
iajs-2803	14	7	the	the	DET
iajs-2803	14	8	special	special	ADJ
iajs-2803	14	9	"	"	PUNCT
iajs-2803	14	10	initial	initial	ADJ
iajs-2803	14	11	value	value	NOUN
iajs-2803	14	12	problems	problem	NOUN
iajs-2803	14	13	"	"	PUNCT
iajs-2803	14	14	(	(	PUNCT
iajs-2803	14	15	ivps	ivps	PROPN
iajs-2803	14	16	)	)	PUNCT
iajs-2803	14	17	for	for	ADP
iajs-2803	14	18	order	order	NOUN
iajs-2803	14	19	three	three	NUM
iajs-2803	14	20	as	as	ADP
iajs-2803	14	21	the	the	DET
iajs-2803	14	22	following	follow	VERB
iajs-2803	14	23	form	form	NOUN
iajs-2803	14	24	𝑦′′′(𝑥	𝑦′′′(𝑥	NUM
iajs-2803	14	25	)	)	PUNCT
iajs-2803	14	26	=	=	SYM
iajs-2803	14	27	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-2803	14	28	,	,	PUNCT
iajs-2803	14	29	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-2803	14	30	)	)	PUNCT
iajs-2803	14	31	)	)	PUNCT
iajs-2803	14	32	(	(	PUNCT
iajs-2803	14	33	2.1	2.1	NUM
iajs-2803	14	34	)	)	PUNCT
iajs-2803	14	35	𝑦(𝑥0	𝑦(𝑥0	NOUN
iajs-2803	14	36	)	)	PUNCT
iajs-2803	14	37	=	=	SYM
iajs-2803	14	38	𝛼	𝛼	X
iajs-2803	14	39	,	,	PUNCT
iajs-2803	14	40	𝑦′(𝑥0	𝑦′(𝑥0	NUM
iajs-2803	14	41	)	)	PUNCT
iajs-2803	14	42	=	=	SYM
iajs-2803	14	43	𝛽	𝛽	PROPN
iajs-2803	14	44	and	and	CCONJ
iajs-2803	14	45	𝑦′′(𝑥0	𝑦′′(𝑥0	PROPN
iajs-2803	14	46	)	)	PUNCT
iajs-2803	14	47	=	=	PUNCT
iajs-2803	14	48	𝛾	𝛾	PART
iajs-2803	14	49	ibn	ibn	PROPN
iajs-2803	14	50	al	al	PROPN
iajs-2803	14	51	haitham	haitham	PROPN
iajs-2803	14	52	journal	journal	PROPN
iajs-2803	14	53	for	for	ADP
iajs-2803	14	54	pure	pure	ADJ
iajs-2803	14	55	and	and	CCONJ
iajs-2803	14	56	applied	apply	VERB
iajs-2803	14	57	science	science	NOUN
iajs-2803	14	58	journal	journal	PROPN
iajs-2803	14	59	homepage	homepage	NOUN
iajs-2803	14	60	:	:	PUNCT
iajs-2803	14	61	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2803	14	62	doi	doi	NOUN
iajs-2803	14	63	:	:	PUNCT
iajs-2803	14	64	10.30526/35.1.2803	10.30526/35.1.2803	NUM
iajs-2803	14	65	article	article	NOUN
iajs-2803	14	66	history	history	NOUN
iajs-2803	14	67	:	:	PUNCT
iajs-2803	14	68	received	receive	VERB
iajs-2803	14	69	29	29	NUM
iajs-2803	14	70	august	august	PROPN
iajs-2803	14	71	,	,	PUNCT
iajs-2803	14	72	2021	2021	NUM
iajs-2803	14	73	,	,	PUNCT
iajs-2803	14	74	accepted	accept	VERB
iajs-2803	14	75	26	26	NUM
iajs-2803	14	76	,	,	PUNCT
iajs-2803	14	77	september	september	PROPN
iajs-2803	14	78	,	,	PUNCT
iajs-2803	14	79	2021	2021	NUM
iajs-2803	14	80	,	,	PUNCT
iajs-2803	14	81	published	publish	VERB
iajs-2803	14	82	in	in	ADP
iajs-2803	14	83	january	january	PROPN
iajs-2803	14	84	2022	2022	NUM
iajs-2803	14	85	.	.	PUNCT
iajs-2803	15	1	firas	firas	PROPN
iajs-2803	15	2	a.	a.	PROPN
iajs-2803	15	3	fawzi	fawzi	PROPN
iajs-2803	16	1	firasadil01@gmail.com	firasadil01@gmail.com	X
iajs-2803	16	2	mustafa	mustafa	PROPN
iajs-2803	16	3	h.	h.	PROPN
iajs-2803	16	4	jumaa	jumaa	PROPN
iajs-2803	16	5	mustafa.hassan551991@gmail.com	mustafa.hassan551991@gmail.com	PROPN
iajs-2803	16	6	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-2803	16	7	mailto:firasadil01@gmail.com	mailto:firasadil01@gmail.com	PROPN
iajs-2803	16	8	mailto:mustafa.hassan551991@gmail.com	mailto:mustafa.hassan551991@gmail.com	PROPN
iajs-2803	16	9	ibn	ibn	PROPN
iajs-2803	16	10	al	al	PROPN
iajs-2803	16	11	-	-	PUNCT
iajs-2803	16	12	haitham	haitham	PROPN
iajs-2803	16	13	jour	jour	X
iajs-2803	16	14	.	.	PROPN
iajs-2803	17	1	for	for	ADP
iajs-2803	17	2	pure	pure	ADJ
iajs-2803	17	3	&	&	CCONJ
iajs-2803	17	4	appl	appl	PROPN
iajs-2803	17	5	.	.	PUNCT
iajs-2803	18	1	sci	sci	PROPN
iajs-2803	18	2	.	.	PROPN
iajs-2803	19	1	53	53	NUM
iajs-2803	19	2	(	(	PUNCT
iajs-2803	19	3	1)2022	1)2022	PROPN
iajs-2803	19	4	93	93	NUM
iajs-2803	19	5	the	the	DET
iajs-2803	19	6	implicit	implicit	ADJ
iajs-2803	19	7	methods	method	NOUN
iajs-2803	19	8	are	be	AUX
iajs-2803	19	9	important	important	ADJ
iajs-2803	19	10	because	because	SCONJ
iajs-2803	19	11	they	they	PRON
iajs-2803	19	12	can	can	AUX
iajs-2803	19	13	reach	reach	VERB
iajs-2803	19	14	high	high	ADJ
iajs-2803	19	15	orders	order	NOUN
iajs-2803	19	16	of	of	ADP
iajs-2803	19	17	accuracy	accuracy	NOUN
iajs-2803	19	18	at	at	ADP
iajs-2803	19	19	the	the	DET
iajs-2803	19	20	equivalent	equivalent	ADJ
iajs-2803	19	21	number	number	NOUN
iajs-2803	19	22	of	of	ADP
iajs-2803	19	23	stages	stage	NOUN
iajs-2803	19	24	,	,	PUNCT
iajs-2803	19	25	which	which	PRON
iajs-2803	19	26	can	can	AUX
iajs-2803	19	27	be	be	AUX
iajs-2803	19	28	represented	represent	VERB
iajs-2803	19	29	as	as	ADP
iajs-2803	19	30	an	an	DET
iajs-2803	19	31	advantage	advantage	NOUN
iajs-2803	19	32	that	that	PRON
iajs-2803	19	33	leads	lead	VERB
iajs-2803	19	34	to	to	ADP
iajs-2803	19	35	the	the	DET
iajs-2803	19	36	more	more	ADV
iajs-2803	19	37	accurate	accurate	ADJ
iajs-2803	19	38	than	than	ADP
iajs-2803	19	39	the	the	DET
iajs-2803	19	40	explicit	explicit	ADJ
iajs-2803	19	41	approaches	approach	NOUN
iajs-2803	19	42	.	.	PUNCT
iajs-2803	20	1	this	this	PRON
iajs-2803	20	2	manufactures	manufacture	VERB
iajs-2803	20	3	it	it	PRON
iajs-2803	20	4	easier	easy	ADJ
iajs-2803	20	5	to	to	PART
iajs-2803	20	6	exist	exist	VERB
iajs-2803	20	7	the	the	DET
iajs-2803	20	8	solution	solution	NOUN
iajs-2803	20	9	to	to	ADP
iajs-2803	20	10	the	the	DET
iajs-2803	20	11	difficulties	difficulty	NOUN
iajs-2803	20	12	of	of	ADP
iajs-2803	20	13	the	the	DET
iajs-2803	20	14	problems	problem	NOUN
iajs-2803	20	15	.	.	PUNCT
iajs-2803	21	1	so	so	ADV
iajs-2803	21	2	,	,	PUNCT
iajs-2803	21	3	the	the	DET
iajs-2803	21	4	implicit	implicit	ADJ
iajs-2803	21	5	rk	rk	NOUN
iajs-2803	21	6	techniques	technique	NOUN
iajs-2803	21	7	play	play	VERB
iajs-2803	21	8	an	an	DET
iajs-2803	21	9	important	important	ADJ
iajs-2803	21	10	role	role	NOUN
iajs-2803	21	11	for	for	ADP
iajs-2803	21	12	denomination	denomination	NOUN
iajs-2803	21	13	the	the	DET
iajs-2803	21	14	physical	physical	ADJ
iajs-2803	21	15	and	and	CCONJ
iajs-2803	21	16	mathematical	mathematical	ADJ
iajs-2803	21	17	problems	problem	NOUN
iajs-2803	21	18	,	,	PUNCT
iajs-2803	21	19	like	like	ADP
iajs-2803	21	20	a	a	DET
iajs-2803	21	21	differential	differential	ADJ
iajs-2803	21	22	algebraic	algebraic	ADJ
iajs-2803	21	23	equation	equation	NOUN
iajs-2803	21	24	.	.	PUNCT
iajs-2803	22	1	in	in	ADP
iajs-2803	22	2	addition	addition	NOUN
iajs-2803	22	3	,	,	PUNCT
iajs-2803	22	4	diagonal	diagonal	ADJ
iajs-2803	22	5	implicit	implicit	ADJ
iajs-2803	22	6	rk	rk	NOUN
iajs-2803	22	7	(	(	PUNCT
iajs-2803	22	8	dirk	dirk	PROPN
iajs-2803	22	9	)	)	PUNCT
iajs-2803	22	10	techniques	technique	NOUN
iajs-2803	22	11	are	be	AUX
iajs-2803	22	12	also	also	ADV
iajs-2803	22	13	pointed	point	VERB
iajs-2803	22	14	to	to	ADP
iajs-2803	22	15	as	as	ADP
iajs-2803	22	16	semi	semi	ADJ
iajs-2803	22	17	-	-	ADJ
iajs-2803	22	18	implicit	implicit	ADJ
iajs-2803	22	19	approaches	approach	NOUN
iajs-2803	22	20	or	or	CCONJ
iajs-2803	22	21	semi	semi	ADV
iajs-2803	22	22	explicit	explicit	ADJ
iajs-2803	22	23	rk	rk	NOUN
iajs-2803	22	24	techniques	technique	NOUN
iajs-2803	22	25	since	since	SCONJ
iajs-2803	22	26	they	they	PRON
iajs-2803	22	27	obtained	obtain	VERB
iajs-2803	22	28	at	at	ADP
iajs-2803	22	29	minimum	minimum	ADJ
iajs-2803	22	30	one	one	NUM
iajs-2803	22	31	value	value	NOUN
iajs-2803	22	32	does	do	AUX
iajs-2803	22	33	not	not	PART
iajs-2803	22	34	zero	zero	VERB
iajs-2803	22	35	for	for	ADP
iajs-2803	22	36	the	the	DET
iajs-2803	22	37	lower	low	ADJ
iajs-2803	22	38	of	of	ADP
iajs-2803	22	39	the	the	DET
iajs-2803	22	40	triangular	triangular	NOUN
iajs-2803	22	41	diagonal	diagonal	ADJ
iajs-2803	22	42	matrices	matrix	NOUN
iajs-2803	22	43	.	.	PUNCT
iajs-2803	23	1	therefore	therefore	ADV
iajs-2803	23	2	,	,	PUNCT
iajs-2803	23	3	to	to	PART
iajs-2803	23	4	solve	solve	VERB
iajs-2803	23	5	eq	eq	ADP
iajs-2803	23	6	.	.	PUNCT
iajs-2803	24	1	(	(	PUNCT
iajs-2803	24	2	2.1	2.1	NUM
iajs-2803	24	3	)	)	PUNCT
iajs-2803	24	4	,	,	PUNCT
iajs-2803	24	5	two	two	NUM
iajs-2803	24	6	general	general	ADJ
iajs-2803	24	7	strategies	strategy	NOUN
iajs-2803	24	8	can	can	AUX
iajs-2803	24	9	be	be	AUX
iajs-2803	24	10	employed	employ	VERB
iajs-2803	24	11	.	.	PUNCT
iajs-2803	25	1	the	the	DET
iajs-2803	25	2	elementary	elementary	ADJ
iajs-2803	25	3	way	way	NOUN
iajs-2803	25	4	is	be	AUX
iajs-2803	25	5	to	to	PART
iajs-2803	25	6	transfer	transfer	VERB
iajs-2803	25	7	the	the	DET
iajs-2803	25	8	eq	eq	NOUN
iajs-2803	25	9	.	.	PUNCT
iajs-2803	26	1	(	(	PUNCT
iajs-2803	26	2	2.1	2.1	NUM
iajs-2803	26	3	)	)	PUNCT
iajs-2803	26	4	into	into	ADP
iajs-2803	26	5	a	a	DET
iajs-2803	26	6	problem	problem	NOUN
iajs-2803	26	7	with	with	ADP
iajs-2803	26	8	first	first	ADJ
iajs-2803	26	9	-	-	PUNCT
iajs-2803	26	10	order	order	NOUN
iajs-2803	26	11	then	then	ADV
iajs-2803	26	12	apply	apply	VERB
iajs-2803	26	13	any	any	DET
iajs-2803	26	14	pattern	pattern	NOUN
iajs-2803	26	15	of	of	ADP
iajs-2803	26	16	the	the	DET
iajs-2803	26	17	rk	rk	NOUN
iajs-2803	26	18	approach	approach	NOUN
iajs-2803	26	19	to	to	ADP
iajs-2803	26	20	it	it	PRON
iajs-2803	26	21	.	.	PUNCT
iajs-2803	27	1	as	as	ADP
iajs-2803	27	2	a	a	DET
iajs-2803	27	3	result	result	NOUN
iajs-2803	27	4	,	,	PUNCT
iajs-2803	27	5	numerous	numerous	ADJ
iajs-2803	27	6	implicit	implicit	ADJ
iajs-2803	27	7	rk	rk	NOUN
iajs-2803	27	8	approaches	approach	NOUN
iajs-2803	27	9	,	,	PUNCT
iajs-2803	27	10	such	such	ADJ
iajs-2803	27	11	as	as	ADP
iajs-2803	27	12	ismail	ismail	PROPN
iajs-2803	27	13	et	et	PROPN
iajs-2803	27	14	al	al	PROPN
iajs-2803	27	15	.	.	PUNCT
iajs-2803	28	1	[	[	X
iajs-2803	28	2	7	7	X
iajs-2803	28	3	]	]	PUNCT
iajs-2803	28	4	and	and	CCONJ
iajs-2803	28	5	others	other	NOUN
iajs-2803	28	6	,	,	PUNCT
iajs-2803	28	7	have	have	AUX
iajs-2803	28	8	been	be	AUX
iajs-2803	28	9	developed	develop	VERB
iajs-2803	28	10	.	.	PUNCT
iajs-2803	29	1	the	the	DET
iajs-2803	29	2	second	second	ADJ
iajs-2803	29	3	option	option	NOUN
iajs-2803	29	4	is	be	AUX
iajs-2803	29	5	to	to	PART
iajs-2803	29	6	use	use	VERB
iajs-2803	29	7	the	the	DET
iajs-2803	29	8	rk	rk	NOUN
iajs-2803	29	9	type	type	NOUN
iajs-2803	29	10	method	method	NOUN
iajs-2803	29	11	to	to	PART
iajs-2803	29	12	directly	directly	ADV
iajs-2803	29	13	solve	solve	VERB
iajs-2803	29	14	eq	eq	NOUN
iajs-2803	29	15	.	.	PUNCT
iajs-2803	30	1	(	(	PUNCT
iajs-2803	30	2	2.1	2.1	NUM
iajs-2803	30	3	)	)	PUNCT
iajs-2803	30	4	.	.	PUNCT
iajs-2803	31	1	for	for	ADP
iajs-2803	31	2	second	second	ADJ
iajs-2803	31	3	-	-	PUNCT
iajs-2803	31	4	order	order	NOUN
iajs-2803	31	5	systems	system	NOUN
iajs-2803	31	6	,	,	PUNCT
iajs-2803	31	7	several	several	ADJ
iajs-2803	31	8	scholars	scholar	NOUN
iajs-2803	31	9	provided	provide	VERB
iajs-2803	31	10	an	an	DET
iajs-2803	31	11	efficient	efficient	ADJ
iajs-2803	31	12	implicit	implicit	ADJ
iajs-2803	31	13	rk	rk	NOUN
iajs-2803	31	14	technique	technique	NOUN
iajs-2803	31	15	(	(	PUNCT
iajs-2803	31	16	see	see	VERB
iajs-2803	31	17	[	[	X
iajs-2803	31	18	8	8	NUM
iajs-2803	31	19	-	-	SYM
iajs-2803	31	20	13	13	NUM
iajs-2803	31	21	]	]	PUNCT
iajs-2803	31	22	)	)	PUNCT
iajs-2803	31	23	.	.	PUNCT
iajs-2803	32	1	ghawadri	ghawadri	PROPN
iajs-2803	32	2	et	et	PROPN
iajs-2803	32	3	al	al	PROPN
iajs-2803	32	4	.	.	PUNCT
iajs-2803	33	1	[	[	X
iajs-2803	33	2	14	14	NUM
iajs-2803	33	3	]	]	PUNCT
iajs-2803	33	4	,	,	PUNCT
iajs-2803	33	5	constructed	construct	VERB
iajs-2803	33	6	a	a	DET
iajs-2803	33	7	solution	solution	NOUN
iajs-2803	33	8	to	to	ADP
iajs-2803	33	9	the	the	DET
iajs-2803	33	10	ill	ill	ADV
iajs-2803	33	11	-	-	PUNCT
iajs-2803	33	12	posed	pose	VERB
iajs-2803	33	13	issue	issue	NOUN
iajs-2803	33	14	for	for	ADP
iajs-2803	33	15	a	a	DET
iajs-2803	33	16	beam	beam	NOUN
iajs-2803	33	17	with	with	ADP
iajs-2803	33	18	an	an	DET
iajs-2803	33	19	elastically	elastically	ADV
iajs-2803	33	20	base	base	NOUN
iajs-2803	33	21	using	use	VERB
iajs-2803	33	22	special	special	ADJ
iajs-2803	33	23	fourth	fourth	ADJ
iajs-2803	33	24	-	-	PUNCT
iajs-2803	33	25	order	order	NOUN
iajs-2803	33	26	odes	ode	NOUN
iajs-2803	33	27	.	.	PUNCT
iajs-2803	34	1	moreover	moreover	ADV
iajs-2803	34	2	,	,	PUNCT
iajs-2803	34	3	[	[	X
iajs-2803	34	4	15	15	NUM
iajs-2803	34	5	-	-	SYM
iajs-2803	34	6	17	17	NUM
iajs-2803	34	7	]	]	PUNCT
iajs-2803	34	8	developed	develop	VERB
iajs-2803	34	9	a	a	DET
iajs-2803	34	10	solution	solution	NOUN
iajs-2803	34	11	of	of	ADP
iajs-2803	34	12	the	the	DET
iajs-2803	34	13	special	special	ADJ
iajs-2803	34	14	3rd	3rd	ADJ
iajs-2803	34	15	order	order	NOUN
iajs-2803	34	16	for	for	ADP
iajs-2803	34	17	the	the	DET
iajs-2803	34	18	odes	ode	NOUN
iajs-2803	34	19	directly	directly	ADV
iajs-2803	34	20	by	by	ADP
iajs-2803	34	21	rk	rk	NOUN
iajs-2803	34	22	technique	technique	NOUN
iajs-2803	34	23	.	.	PUNCT
iajs-2803	35	1	finally	finally	ADV
iajs-2803	35	2	,	,	PUNCT
iajs-2803	35	3	senu	senu	VERB
iajs-2803	35	4	[	[	X
iajs-2803	35	5	18	18	NUM
iajs-2803	35	6	]	]	PUNCT
iajs-2803	35	7	and	and	CCONJ
iajs-2803	35	8	fawzi	fawzi	VERB
iajs-2803	35	9	et	et	PROPN
iajs-2803	35	10	al	al	PROPN
iajs-2803	35	11	.	.	PUNCT
iajs-2803	36	1	[	[	X
iajs-2803	36	2	19	19	NUM
iajs-2803	36	3	]	]	PUNCT
iajs-2803	36	4	constructed	construct	VERB
iajs-2803	36	5	the	the	DET
iajs-2803	36	6	embedded	embed	VERB
iajs-2803	36	7	the	the	DET
iajs-2803	36	8	rk	rk	NOUN
iajs-2803	36	9	technique	technique	NOUN
iajs-2803	36	10	to	to	PART
iajs-2803	36	11	solve	solve	VERB
iajs-2803	36	12	3rd	3rd	ADJ
iajs-2803	36	13	order	order	NOUN
iajs-2803	36	14	for	for	ADP
iajs-2803	36	15	the	the	DET
iajs-2803	36	16	odes	ode	NOUN
iajs-2803	36	17	.	.	PUNCT
iajs-2803	37	1	a	a	DET
iajs-2803	37	2	significant	significant	ADJ
iajs-2803	37	3	objective	objective	NOUN
iajs-2803	37	4	for	for	ADP
iajs-2803	37	5	current	current	ADJ
iajs-2803	37	6	research	research	NOUN
iajs-2803	37	7	is	be	AUX
iajs-2803	37	8	to	to	PART
iajs-2803	37	9	show	show	VERB
iajs-2803	37	10	how	how	SCONJ
iajs-2803	37	11	particular	particular	ADJ
iajs-2803	37	12	third	third	ADJ
iajs-2803	37	13	-	-	PUNCT
iajs-2803	37	14	order	order	NOUN
iajs-2803	37	15	odes	ode	NOUN
iajs-2803	37	16	are	be	AUX
iajs-2803	37	17	solving	solve	VERB
iajs-2803	37	18	via	via	ADP
iajs-2803	37	19	the	the	DET
iajs-2803	37	20	direct	direct	ADJ
iajs-2803	37	21	method	method	NOUN
iajs-2803	37	22	.	.	PUNCT
iajs-2803	38	1	additionally	additionally	ADV
iajs-2803	38	2	,	,	PUNCT
iajs-2803	38	3	while	while	SCONJ
iajs-2803	38	4	solving	solve	VERB
iajs-2803	38	5	eq	eq	ADP
iajs-2803	38	6	.	.	PUNCT
iajs-2803	39	1	(	(	PUNCT
iajs-2803	39	2	2.1	2.1	NUM
iajs-2803	39	3	)	)	PUNCT
iajs-2803	39	4	numerically	numerically	ADV
iajs-2803	39	5	,	,	PUNCT
iajs-2803	39	6	the	the	DET
iajs-2803	39	7	algebraic	algebraic	ADJ
iajs-2803	39	8	order	order	NOUN
iajs-2803	39	9	of	of	ADP
iajs-2803	39	10	the	the	DET
iajs-2803	39	11	technique	technique	NOUN
iajs-2803	39	12	used	use	VERB
iajs-2803	39	13	must	must	AUX
iajs-2803	39	14	be	be	AUX
iajs-2803	39	15	taken	take	VERB
iajs-2803	39	16	into	into	ADP
iajs-2803	39	17	account	account	NOUN
iajs-2803	39	18	,	,	PUNCT
iajs-2803	39	19	as	as	SCONJ
iajs-2803	39	20	this	this	PRON
iajs-2803	39	21	is	be	AUX
iajs-2803	39	22	the	the	DET
iajs-2803	39	23	most	most	ADV
iajs-2803	39	24	important	important	ADJ
iajs-2803	39	25	factor	factor	NOUN
iajs-2803	39	26	in	in	ADP
iajs-2803	39	27	achieving	achieve	VERB
iajs-2803	39	28	high	high	ADJ
iajs-2803	39	29	accuracy	accuracy	NOUN
iajs-2803	39	30	.	.	PUNCT
iajs-2803	40	1	section	section	NOUN
iajs-2803	40	2	2.2	2.2	NUM
iajs-2803	40	3	demonstrates	demonstrate	VERB
iajs-2803	40	4	the	the	DET
iajs-2803	40	5	basic	basic	ADJ
iajs-2803	40	6	idea	idea	NOUN
iajs-2803	40	7	of	of	ADP
iajs-2803	40	8	construction	construction	NOUN
iajs-2803	40	9	and	and	CCONJ
iajs-2803	40	10	derivation	derivation	NOUN
iajs-2803	40	11	of	of	ADP
iajs-2803	40	12	the	the	DET
iajs-2803	40	13	ditrk	ditrk	NOUN
iajs-2803	40	14	system	system	NOUN
iajs-2803	40	15	for	for	ADP
iajs-2803	40	16	addressing	address	VERB
iajs-2803	40	17	initial	initial	ADJ
iajs-2803	40	18	value	value	NOUN
iajs-2803	40	19	problems	problem	NOUN
iajs-2803	40	20	(	(	PUNCT
iajs-2803	40	21	ivps	ivps	PROPN
iajs-2803	40	22	)	)	PUNCT
iajs-2803	40	23	.	.	PUNCT
iajs-2803	41	1	the	the	DET
iajs-2803	41	2	ditrk	ditrk	NOUN
iajs-2803	41	3	technique	technique	NOUN
iajs-2803	41	4	's	's	PART
iajs-2803	41	5	order	order	NOUN
iajs-2803	41	6	criteria	criterion	NOUN
iajs-2803	41	7	are	be	AUX
iajs-2803	41	8	outlined	outline	VERB
iajs-2803	41	9	in	in	ADP
iajs-2803	41	10	section	section	NOUN
iajs-2803	41	11	2.3	2.3	NUM
iajs-2803	41	12	.	.	PUNCT
iajs-2803	42	1	section	section	NOUN
iajs-2803	42	2	2.4	2.4	NUM
iajs-2803	42	3	describes	describe	VERB
iajs-2803	42	4	the	the	DET
iajs-2803	42	5	3rd	3rd	ADJ
iajs-2803	42	6	stage	stage	NOUN
iajs-2803	42	7	5th	5th	ADJ
iajs-2803	42	8	order	order	NOUN
iajs-2803	42	9	(	(	PUNCT
iajs-2803	42	10	ditrkm5	ditrkm5	NOUN
iajs-2803	42	11	)	)	PUNCT
iajs-2803	42	12	methods	method	NOUN
iajs-2803	42	13	.	.	PUNCT
iajs-2803	43	1	in	in	ADP
iajs-2803	43	2	section	section	NOUN
iajs-2803	43	3	2.5	2.5	NUM
iajs-2803	43	4	,	,	PUNCT
iajs-2803	43	5	the	the	DET
iajs-2803	43	6	analyses	analysis	NOUN
iajs-2803	43	7	of	of	ADP
iajs-2803	43	8	the	the	DET
iajs-2803	43	9	stability	stability	NOUN
iajs-2803	43	10	polynomial	polynomial	NOUN
iajs-2803	43	11	for	for	ADP
iajs-2803	43	12	the	the	DET
iajs-2803	43	13	ditrk	ditrk	NOUN
iajs-2803	43	14	method	method	NOUN
iajs-2803	43	15	are	be	AUX
iajs-2803	43	16	presented	present	VERB
iajs-2803	43	17	.	.	PUNCT
iajs-2803	44	1	in	in	ADP
iajs-2803	44	2	section	section	NOUN
iajs-2803	44	3	2.6	2.6	NUM
iajs-2803	44	4	,	,	PUNCT
iajs-2803	44	5	mentions	mention	VERB
iajs-2803	44	6	the	the	DET
iajs-2803	44	7	ditrk	ditrk	NOUN
iajs-2803	44	8	approach	approach	NOUN
iajs-2803	44	9	with	with	ADP
iajs-2803	44	10	five	five	NUM
iajs-2803	44	11	ivps	ivps	NOUN
iajs-2803	44	12	.	.	PUNCT
iajs-2803	45	1	in	in	ADP
iajs-2803	45	2	section	section	NOUN
iajs-2803	45	3	2.7	2.7	NUM
iajs-2803	45	4	,	,	PUNCT
iajs-2803	45	5	the	the	DET
iajs-2803	45	6	validation	validation	NOUN
iajs-2803	45	7	of	of	ADP
iajs-2803	45	8	the	the	DET
iajs-2803	45	9	current	current	ADJ
iajs-2803	45	10	approach	approach	NOUN
iajs-2803	45	11	compared	compare	VERB
iajs-2803	45	12	with	with	ADP
iajs-2803	45	13	those	those	PRON
iajs-2803	45	14	in	in	ADP
iajs-2803	45	15	the	the	DET
iajs-2803	45	16	other	other	ADJ
iajs-2803	45	17	literatures	literature	NOUN
iajs-2803	45	18	of	of	ADP
iajs-2803	45	19	the	the	DET
iajs-2803	45	20	implicit	implicit	ADJ
iajs-2803	45	21	rk	rk	NOUN
iajs-2803	45	22	techniques	technique	NOUN
iajs-2803	45	23	.	.	PUNCT
iajs-2803	46	1	2	2	X
iajs-2803	46	2	.	.	X
iajs-2803	46	3	the	the	DET
iajs-2803	46	4	methodology	methodology	NOUN
iajs-2803	46	5	of	of	ADP
iajs-2803	46	6	ditrk	ditrk	NOUN
iajs-2803	46	7	techniques	technique	NOUN
iajs-2803	46	8	for	for	ADP
iajs-2803	46	9	solving	solve	VERB
iajs-2803	46	10	ivps	ivps	PROPN
iajs-2803	46	11	in	in	ADP
iajs-2803	46	12	eq	eq	PROPN
iajs-2803	46	13	.	.	PUNCT
iajs-2803	47	1	(	(	PUNCT
iajs-2803	47	2	2.1	2.1	NUM
iajs-2803	47	3	)	)	PUNCT
iajs-2803	47	4	,	,	PUNCT
iajs-2803	47	5	the	the	DET
iajs-2803	47	6	prevalent	prevalent	ADJ
iajs-2803	47	7	formula	formula	NOUN
iajs-2803	47	8	of	of	ADP
iajs-2803	47	9	the	the	DET
iajs-2803	47	10	implicit	implicit	ADJ
iajs-2803	47	11	rk	rk	NOUN
iajs-2803	47	12	approach	approach	NOUN
iajs-2803	47	13	for	for	ADP
iajs-2803	47	14	the	the	DET
iajs-2803	47	15	𝑚	𝑚	PROPN
iajs-2803	47	16	stage	stage	NOUN
iajs-2803	47	17	can	can	AUX
iajs-2803	47	18	be	be	AUX
iajs-2803	47	19	expressed	express	VERB
iajs-2803	47	20	as	as	SCONJ
iajs-2803	47	21	follows	follow	VERB
iajs-2803	47	22	:	:	PUNCT
iajs-2803	48	1	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2803	48	2	=	=	SYM
iajs-2803	48	3	𝑦𝑛	𝑦𝑛	NOUN
iajs-2803	48	4	+	+	NOUN
iajs-2803	48	5	ℎ	ℎ	NOUN
iajs-2803	48	6	𝑦𝑛	𝑦𝑛	AUX
iajs-2803	48	7	′	′	NOUN
iajs-2803	49	1	+	+	CCONJ
iajs-2803	49	2	ℎ2	ℎ2	ADJ
iajs-2803	49	3	2	2	NUM
iajs-2803	49	4	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	49	5	′′	′′	PROPN
iajs-2803	49	6	+	+	CCONJ
iajs-2803	49	7	ℎ3	ℎ3	PROPN
iajs-2803	49	8	∑	∑	PUNCT
iajs-2803	49	9	𝑑𝑖	𝑑𝑖	NOUN
iajs-2803	49	10	𝑚	𝑚	PART
iajs-2803	49	11	𝑖=1	𝑖=1	PROPN
iajs-2803	49	12	𝑘𝑖	𝑘𝑖	X
iajs-2803	49	13	(	(	PUNCT
iajs-2803	49	14	2.2	2.2	NUM
iajs-2803	49	15	)	)	PUNCT
iajs-2803	49	16	𝑦𝑛+1	𝑦𝑛+1	NOUN
iajs-2803	49	17	′	′	NOUN
iajs-2803	49	18	=	=	PUNCT
iajs-2803	49	19	𝑦𝑛	𝑦𝑛	AUX
iajs-2803	49	20	′	′	NOUN
iajs-2803	50	1	+	+	CCONJ
iajs-2803	50	2	ℎ	ℎ	NOUN
iajs-2803	50	3	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	50	4	′′	′′	PROPN
iajs-2803	50	5	+	+	CCONJ
iajs-2803	50	6	ℎ2	ℎ2	NOUN
iajs-2803	50	7	∑	∑	PUNCT
iajs-2803	50	8	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	50	9	𝑚	𝑚	PROPN
iajs-2803	50	10	𝑖=1	𝑖=1	PUNCT
iajs-2803	50	11	𝑘𝑖	𝑘𝑖	X
iajs-2803	50	12	(	(	PUNCT
iajs-2803	50	13	2.3	2.3	NUM
iajs-2803	50	14	)	)	PUNCT
iajs-2803	50	15	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2803	50	16	′′	′′	NOUN
iajs-2803	50	17	=	=	PUNCT
iajs-2803	50	18	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	50	19	′′	′′	PROPN
iajs-2803	50	20	+	+	CCONJ
iajs-2803	50	21	ℎ	ℎ	PROPN
iajs-2803	50	22	∑	∑	PROPN
iajs-2803	50	23	𝑔𝑖	𝑔𝑖	VERB
iajs-2803	50	24	𝑚	𝑚	PROPN
iajs-2803	50	25	𝑖=1	𝑖=1	PUNCT
iajs-2803	50	26	𝑘𝑖	𝑘𝑖	X
iajs-2803	50	27	(	(	PUNCT
iajs-2803	50	28	2.4	2.4	NUM
iajs-2803	50	29	)	)	PUNCT
iajs-2803	50	30	and	and	CCONJ
iajs-2803	50	31	𝑘1	𝑘1	PROPN
iajs-2803	50	32	=	=	SYM
iajs-2803	50	33	𝑓(𝑥𝑛	𝑓(𝑥𝑛	PROPN
iajs-2803	50	34	,	,	PUNCT
iajs-2803	50	35	𝑦𝑛	𝑦𝑛	NOUN
iajs-2803	50	36	)	)	PUNCT
iajs-2803	50	37	(	(	PUNCT
iajs-2803	50	38	2.5	2.5	NUM
iajs-2803	50	39	)	)	PUNCT
iajs-2803	51	1	𝑘𝑖	𝑘𝑖	NOUN
iajs-2803	52	1	=	=	PUNCT
iajs-2803	52	2	𝑓(𝑥𝑛	𝑓(𝑥𝑛	PROPN
iajs-2803	52	3	+	+	CCONJ
iajs-2803	52	4	𝑐𝑖ℎ	𝑐𝑖ℎ	ADJ
iajs-2803	52	5	,	,	PUNCT
iajs-2803	52	6	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	52	7	+	+	ADJ
iajs-2803	52	8	ℎ	ℎ	PART
iajs-2803	52	9	𝑐𝑖𝑦𝑛	𝑐𝑖𝑦𝑛	NOUN
iajs-2803	52	10	′	′	NUM
iajs-2803	52	11	+	+	CCONJ
iajs-2803	52	12	ℎ2	ℎ2	ADJ
iajs-2803	52	13	2	2	NUM
iajs-2803	52	14	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	52	15	2	2	NUM
iajs-2803	52	16	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	52	17	′′	′′	PROPN
iajs-2803	52	18	+	+	CCONJ
iajs-2803	52	19	ℎ3	ℎ3	NOUN
iajs-2803	52	20	∑	∑	PUNCT
iajs-2803	52	21	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-2803	52	22	𝑖−1	𝑖−1	PROPN
iajs-2803	52	23	𝑗=1	𝑗=1	PROPN
iajs-2803	52	24	𝑘𝑗	𝑘𝑗	PROPN
iajs-2803	52	25	)	)	PUNCT
iajs-2803	52	26	(	(	PUNCT
iajs-2803	52	27	2.6	2.6	NUM
iajs-2803	52	28	)	)	PUNCT
iajs-2803	52	29	where	where	SCONJ
iajs-2803	52	30	𝑖	𝑖	ADP
iajs-2803	53	1	=	=	SYM
iajs-2803	54	1	2,3	2,3	NUM
iajs-2803	54	2	,	,	PUNCT
iajs-2803	54	3	…	…	PUNCT
iajs-2803	54	4	,	,	PUNCT
iajs-2803	54	5	𝑚	𝑚	X
iajs-2803	54	6	.	.	PUNCT
iajs-2803	55	1	ibn	ibn	PROPN
iajs-2803	55	2	al	al	PROPN
iajs-2803	55	3	-	-	PUNCT
iajs-2803	55	4	haitham	haitham	PROPN
iajs-2803	55	5	jour	jour	X
iajs-2803	55	6	.	.	PROPN
iajs-2803	55	7	for	for	ADP
iajs-2803	55	8	pure	pure	ADJ
iajs-2803	55	9	&	&	CCONJ
iajs-2803	55	10	appl	appl	PROPN
iajs-2803	55	11	.	.	PUNCT
iajs-2803	56	1	sci	sci	PROPN
iajs-2803	56	2	.	.	PROPN
iajs-2803	57	1	53	53	NUM
iajs-2803	57	2	(	(	PUNCT
iajs-2803	57	3	1)2022	1)2022	PROPN
iajs-2803	57	4	94	94	NUM
iajs-2803	57	5	the	the	DET
iajs-2803	57	6	parameters	parameter	NOUN
iajs-2803	57	7	of	of	ADP
iajs-2803	57	8	diagonal	diagonal	ADJ
iajs-2803	57	9	implicit	implicit	ADJ
iajs-2803	57	10	rk	rk	NOUN
iajs-2803	57	11	type	type	NOUN
iajs-2803	57	12	(	(	PUNCT
iajs-2803	57	13	ditrk	ditrk	NOUN
iajs-2803	57	14	)	)	PUNCT
iajs-2803	57	15	methods	method	NOUN
iajs-2803	57	16	are	be	AUX
iajs-2803	57	17	presumed	presume	VERB
iajs-2803	57	18	as	as	ADP
iajs-2803	57	19	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	57	20	,	,	PUNCT
iajs-2803	57	21	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-2803	57	22	,	,	PUNCT
iajs-2803	57	23	𝑑𝑖	𝑑𝑖	PROPN
iajs-2803	57	24	,	,	PUNCT
iajs-2803	57	25	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	57	26	,	,	PUNCT
iajs-2803	57	27	𝑔𝑖	𝑔𝑖	ADP
iajs-2803	57	28	where	where	SCONJ
iajs-2803	57	29	𝑖	𝑖	X
iajs-2803	57	30	,	,	PUNCT
iajs-2803	57	31	𝑗	𝑗	NOUN
iajs-2803	57	32	=	=	SYM
iajs-2803	57	33	1	1	NUM
iajs-2803	57	34	,	,	PUNCT
iajs-2803	57	35	2	2	NUM
iajs-2803	57	36	,	,	PUNCT
iajs-2803	57	37	3	3	NUM
iajs-2803	57	38	…	…	PUNCT
iajs-2803	57	39	,	,	PUNCT
iajs-2803	57	40	𝑠	𝑠	PROPN
iajs-2803	57	41	are	be	AUX
iajs-2803	57	42	real	real	ADJ
iajs-2803	57	43	numbers	number	NOUN
iajs-2803	57	44	and	and	CCONJ
iajs-2803	57	45	𝑚	𝑚	PROPN
iajs-2803	57	46	is	be	AUX
iajs-2803	57	47	referred	refer	VERB
iajs-2803	57	48	to	to	ADP
iajs-2803	57	49	stage	stage	NOUN
iajs-2803	57	50	digit	digit	NOUN
iajs-2803	57	51	for	for	ADP
iajs-2803	57	52	the	the	DET
iajs-2803	57	53	approach	approach	NOUN
iajs-2803	57	54	.	.	PUNCT
iajs-2803	58	1	this	this	DET
iajs-2803	58	2	scheme	scheme	NOUN
iajs-2803	58	3	is	be	AUX
iajs-2803	58	4	known	know	VERB
iajs-2803	58	5	as	as	ADP
iajs-2803	58	6	diagonal	diagonal	ADJ
iajs-2803	58	7	implicit	implicit	ADJ
iajs-2803	58	8	when	when	SCONJ
iajs-2803	58	9	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-2803	58	10	≠	≠	PROPN
iajs-2803	58	11	0	0	NUM
iajs-2803	58	12	for	for	ADP
iajs-2803	58	13	𝑗	𝑗	INTJ
iajs-2803	58	14	>	>	X
iajs-2803	58	15	𝑖.	𝑖.	NOUN
iajs-2803	58	16	the	the	DET
iajs-2803	58	17	last	last	ADJ
iajs-2803	58	18	denomination	denomination	NOUN
iajs-2803	58	19	includes	include	VERB
iajs-2803	58	20	the	the	DET
iajs-2803	58	21	single	single	ADJ
iajs-2803	58	22	ditrk	ditrk	NOUN
iajs-2803	58	23	techniques	technique	NOUN
iajs-2803	58	24	that	that	PRON
iajs-2803	58	25	𝐴	𝐴	PROPN
iajs-2803	58	26	indicate	indicate	VERB
iajs-2803	58	27	that	that	SCONJ
iajs-2803	58	28	the	the	PRON
iajs-2803	58	29	lower	low	ADJ
iajs-2803	58	30	the	the	DET
iajs-2803	58	31	triangular	triangular	ADJ
iajs-2803	58	32	diagonal	diagonal	ADJ
iajs-2803	58	33	matric	matric	NOUN
iajs-2803	58	34	of	of	ADP
iajs-2803	58	35	𝐴	𝐴	PROPN
iajs-2803	58	36	have	have	VERB
iajs-2803	58	37	same	same	ADJ
iajs-2803	58	38	values	value	NOUN
iajs-2803	58	39	with	with	ADP
iajs-2803	58	40	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-2803	58	41	≠	≠	PROPN
iajs-2803	58	42	0	0	NUM
iajs-2803	58	43	where	where	SCONJ
iajs-2803	58	44	𝑖	𝑖	VERB
iajs-2803	58	45	=	=	PUNCT
iajs-2803	59	1	𝑗	𝑗	PROPN
iajs-2803	59	2	at	at	ADP
iajs-2803	59	3	the	the	DET
iajs-2803	59	4	diagonal	diagonal	NOUN
iajs-2803	59	5	.	.	PUNCT
iajs-2803	60	1	the	the	DET
iajs-2803	60	2	ditrk	ditrk	NOUN
iajs-2803	60	3	approach	approach	NOUN
iajs-2803	60	4	proposed	propose	VERB
iajs-2803	60	5	from	from	ADP
iajs-2803	60	6	the	the	DET
iajs-2803	60	7	work	work	NOUN
iajs-2803	60	8	of	of	ADP
iajs-2803	60	9	butcher	butcher	NOUN
iajs-2803	60	10	,	,	PUNCT
iajs-2803	60	11	as	as	SCONJ
iajs-2803	60	12	illustrated	illustrate	VERB
iajs-2803	60	13	in	in	ADP
iajs-2803	60	14	table	table	NOUN
iajs-2803	60	15	2.1	2.1	NUM
iajs-2803	61	1	[	[	SYM
iajs-2803	61	2	20	20	NUM
iajs-2803	61	3	]	]	PUNCT
iajs-2803	61	4	.	.	PUNCT
iajs-2803	62	1	table	table	NOUN
iajs-2803	62	2	2.1	2.1	NUM
iajs-2803	62	3	:	:	PUNCT
iajs-2803	62	4	butcher	butcher	NOUN
iajs-2803	62	5	form	form	NOUN
iajs-2803	62	6	ditrk	ditrk	NOUN
iajs-2803	62	7	method	method	NOUN
iajs-2803	62	8	.	.	PUNCT
iajs-2803	63	1	3	3	X
iajs-2803	63	2	.	.	X
iajs-2803	63	3	order	order	NOUN
iajs-2803	63	4	conditions	condition	NOUN
iajs-2803	63	5	of	of	ADP
iajs-2803	63	6	the	the	DET
iajs-2803	63	7	ditrk	ditrk	NOUN
iajs-2803	63	8	technique	technique	NOUN
iajs-2803	63	9	according	accord	VERB
iajs-2803	63	10	to	to	ADP
iajs-2803	63	11	mechee	mechee	PROPN
iajs-2803	63	12	et	et	PROPN
iajs-2803	63	13	al	al	PROPN
iajs-2803	63	14	.	.	PUNCT
iajs-2803	64	1	[	[	X
iajs-2803	64	2	17	17	NUM
iajs-2803	64	3	]	]	PUNCT
iajs-2803	64	4	,	,	PUNCT
iajs-2803	64	5	the	the	DET
iajs-2803	64	6	orders	order	NOUN
iajs-2803	64	7	of	of	ADP
iajs-2803	64	8	algebraic	algebraic	ADJ
iajs-2803	64	9	criteria	criterion	NOUN
iajs-2803	64	10	for	for	ADP
iajs-2803	64	11	rkd	rkd	NOUN
iajs-2803	64	12	approached	approach	VERB
iajs-2803	64	13	over	over	ADP
iajs-2803	64	14	order	order	NOUN
iajs-2803	64	15	6	6	NUM
iajs-2803	64	16	are	be	AUX
iajs-2803	64	17	as	as	ADV
iajs-2803	64	18	follow	follow	VERB
iajs-2803	64	19	:	:	PUNCT
iajs-2803	64	20	order	order	NOUN
iajs-2803	64	21	conditions	condition	NOUN
iajs-2803	64	22	of	of	ADP
iajs-2803	64	23	𝑦	𝑦	NOUN
iajs-2803	64	24	:	:	PUNCT
iajs-2803	64	25	order	order	NOUN
iajs-2803	64	26	3	3	NUM
iajs-2803	64	27	∑	∑	PART
iajs-2803	64	28	𝑑𝑖	𝑑𝑖	PROPN
iajs-2803	64	29	=	=	NOUN
iajs-2803	64	30	1	1	NUM
iajs-2803	64	31	6	6	NUM
iajs-2803	64	32	(	(	PUNCT
iajs-2803	64	33	2.7	2.7	NUM
iajs-2803	64	34	)	)	PUNCT
iajs-2803	64	35	order	order	NOUN
iajs-2803	64	36	4	4	NUM
iajs-2803	64	37	∑	∑	PUNCT
iajs-2803	64	38	𝑑𝑖	𝑑𝑖	PROPN
iajs-2803	64	39	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	64	40	=	=	NOUN
iajs-2803	64	41	1	1	NUM
iajs-2803	64	42	24	24	NUM
iajs-2803	64	43	(	(	PUNCT
iajs-2803	64	44	2.8	2.8	NUM
iajs-2803	64	45	)	)	PUNCT
iajs-2803	64	46	order	order	NOUN
iajs-2803	64	47	5	5	NUM
iajs-2803	64	48	∑	∑	PUNCT
iajs-2803	64	49	𝑑𝑖	𝑑𝑖	PROPN
iajs-2803	64	50	𝑐𝑖	𝑐𝑖	ADP
iajs-2803	64	51	2	2	NUM
iajs-2803	64	52	=	=	SYM
iajs-2803	64	53	1	1	NUM
iajs-2803	64	54	60	60	NUM
iajs-2803	64	55	(	(	PUNCT
iajs-2803	64	56	2.9	2.9	NUM
iajs-2803	64	57	)	)	PUNCT
iajs-2803	64	58	order	order	NOUN
iajs-2803	64	59	6	6	NUM
iajs-2803	64	60	∑	∑	PUNCT
iajs-2803	64	61	𝑑𝑖	𝑑𝑖	PROPN
iajs-2803	64	62	𝑐𝑖	𝑐𝑖	ADP
iajs-2803	64	63	3	3	NUM
iajs-2803	64	64	=	=	SYM
iajs-2803	64	65	1	1	NUM
iajs-2803	64	66	120	120	NUM
iajs-2803	64	67	and	and	CCONJ
iajs-2803	64	68	∑	∑	ADJ
iajs-2803	64	69	𝑑𝑖	𝑑𝑖	NOUN
iajs-2803	64	70	𝑎𝑖,𝑗	𝑎𝑖,𝑗	NOUN
iajs-2803	64	71	=	=	NOUN
iajs-2803	64	72	1/720	1/720	NUM
iajs-2803	64	73	.	.	PUNCT
iajs-2803	65	1	(	(	PUNCT
iajs-2803	65	2	2.10	2.10	NUM
iajs-2803	65	3	)	)	PUNCT
iajs-2803	65	4	order	order	NOUN
iajs-2803	65	5	conditions	condition	NOUN
iajs-2803	65	6	of	of	ADP
iajs-2803	65	7	𝒚′	𝒚′	NUM
iajs-2803	65	8	:	:	PUNCT
iajs-2803	65	9	order	order	NOUN
iajs-2803	65	10	2	2	NUM
iajs-2803	65	11	∑	∑	NOUN
iajs-2803	65	12	𝑏𝑖	𝑏𝑖	NOUN
iajs-2803	65	13	=	=	SYM
iajs-2803	65	14	1	1	NUM
iajs-2803	65	15	2	2	NUM
iajs-2803	65	16	(	(	PUNCT
iajs-2803	65	17	2.11	2.11	NUM
iajs-2803	65	18	)	)	PUNCT
iajs-2803	65	19	order	order	NOUN
iajs-2803	65	20	3	3	NUM
iajs-2803	65	21	∑	∑	NOUN
iajs-2803	65	22	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	65	23	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	65	24	=	=	NOUN
iajs-2803	65	25	1	1	NUM
iajs-2803	65	26	6	6	NUM
iajs-2803	65	27	(	(	PUNCT
iajs-2803	65	28	2.12	2.12	NUM
iajs-2803	65	29	)	)	PUNCT
iajs-2803	65	30	order	order	NOUN
iajs-2803	65	31	4	4	NUM
iajs-2803	65	32	∑	∑	NOUN
iajs-2803	65	33	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	65	34	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	65	35	2	2	NUM
iajs-2803	65	36	=	=	SYM
iajs-2803	65	37	1	1	NUM
iajs-2803	65	38	12	12	NUM
iajs-2803	65	39	(	(	PUNCT
iajs-2803	65	40	2.13	2.13	NUM
iajs-2803	65	41	)	)	PUNCT
iajs-2803	65	42	order	order	NOUN
iajs-2803	65	43	5	5	NUM
iajs-2803	65	44	∑	∑	NOUN
iajs-2803	65	45	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	65	46	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	65	47	3	3	NUM
iajs-2803	65	48	=	=	SYM
iajs-2803	65	49	1	1	NUM
iajs-2803	65	50	20	20	NUM
iajs-2803	65	51	and	and	CCONJ
iajs-2803	65	52	∑	∑	ADV
iajs-2803	65	53	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	65	54	𝑎𝑖,𝑗	𝑎𝑖,𝑗	NOUN
iajs-2803	65	55	=	=	NOUN
iajs-2803	65	56	1	1	NUM
iajs-2803	65	57	120	120	NUM
iajs-2803	65	58	(	(	PUNCT
iajs-2803	65	59	2.14	2.14	NUM
iajs-2803	65	60	)	)	PUNCT
iajs-2803	65	61	order	order	NOUN
iajs-2803	65	62	6	6	NUM
iajs-2803	65	63	∑	∑	NOUN
iajs-2803	65	64	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	65	65	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	65	66	4	4	NUM
iajs-2803	65	67	=	=	SYM
iajs-2803	65	68	1	1	NUM
iajs-2803	65	69	30	30	NUM
iajs-2803	65	70	,	,	PUNCT
iajs-2803	65	71	∑	∑	ADP
iajs-2803	65	72	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	65	73	𝑎𝑖,𝑗𝑐𝑗	𝑎𝑖,𝑗𝑐𝑗	NOUN
iajs-2803	65	74	=	=	SYM
iajs-2803	65	75	1	1	NUM
iajs-2803	65	76	720	720	NUM
iajs-2803	65	77	and	and	CCONJ
iajs-2803	65	78	∑	∑	ADP
iajs-2803	65	79	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	65	80	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	65	81	𝑎𝑖,𝑗	𝑎𝑖,𝑗	NOUN
iajs-2803	65	82	=	=	NUM
iajs-2803	65	83	1	1	NUM
iajs-2803	65	84	180	180	NUM
iajs-2803	65	85	.	.	PUNCT
iajs-2803	66	1	(	(	PUNCT
iajs-2803	66	2	2.15	2.15	NUM
iajs-2803	66	3	)	)	PUNCT
iajs-2803	66	4	order	order	NOUN
iajs-2803	66	5	conditions	condition	NOUN
iajs-2803	66	6	of	of	ADP
iajs-2803	66	7	𝒚′′	𝒚′′	NOUN
iajs-2803	66	8	:	:	PUNCT
iajs-2803	66	9	order	order	NOUN
iajs-2803	66	10	1	1	NUM
iajs-2803	66	11	∑	∑	NOUN
iajs-2803	66	12	𝑔𝑖	𝑔𝑖	NOUN
iajs-2803	66	13	=	=	SYM
iajs-2803	66	14	1	1	NUM
iajs-2803	66	15	(	(	PUNCT
iajs-2803	66	16	2.16	2.16	NUM
iajs-2803	66	17	)	)	PUNCT
iajs-2803	66	18	ibn	ibn	PROPN
iajs-2803	66	19	al	al	PROPN
iajs-2803	66	20	-	-	PUNCT
iajs-2803	66	21	haitham	haitham	PROPN
iajs-2803	66	22	jour	jour	X
iajs-2803	66	23	.	.	PROPN
iajs-2803	67	1	for	for	ADP
iajs-2803	67	2	pure	pure	ADJ
iajs-2803	67	3	&	&	CCONJ
iajs-2803	67	4	appl	appl	PROPN
iajs-2803	67	5	.	.	PUNCT
iajs-2803	68	1	sci	sci	PROPN
iajs-2803	68	2	.	.	PROPN
iajs-2803	69	1	53	53	NUM
iajs-2803	69	2	(	(	PUNCT
iajs-2803	69	3	1)2022	1)2022	NOUN
iajs-2803	69	4	95	95	NUM
iajs-2803	69	5	order	order	NOUN
iajs-2803	69	6	2	2	NUM
iajs-2803	69	7	∑	∑	PART
iajs-2803	69	8	𝑔𝑖	𝑔𝑖	VERB
iajs-2803	69	9	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	69	10	=	=	NOUN
iajs-2803	69	11	1	1	NUM
iajs-2803	69	12	2	2	NUM
iajs-2803	69	13	(	(	PUNCT
iajs-2803	69	14	2.17	2.17	NUM
iajs-2803	69	15	)	)	PUNCT
iajs-2803	69	16	order	order	NOUN
iajs-2803	69	17	3	3	NUM
iajs-2803	69	18	∑	∑	PART
iajs-2803	69	19	𝑔𝑖	𝑔𝑖	VERB
iajs-2803	69	20	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	69	21	2	2	NUM
iajs-2803	69	22	=	=	SYM
iajs-2803	69	23	1	1	NUM
iajs-2803	69	24	3	3	NUM
iajs-2803	69	25	(	(	PUNCT
iajs-2803	69	26	2.18	2.18	NUM
iajs-2803	69	27	)	)	PUNCT
iajs-2803	69	28	order	order	NOUN
iajs-2803	69	29	4	4	NUM
iajs-2803	69	30	∑	∑	NOUN
iajs-2803	69	31	𝑔𝑖	𝑔𝑖	NOUN
iajs-2803	69	32	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	69	33	3	3	NUM
iajs-2803	69	34	=	=	SYM
iajs-2803	69	35	1	1	NUM
iajs-2803	69	36	4	4	NUM
iajs-2803	69	37	and	and	CCONJ
iajs-2803	69	38	∑	∑	PUNCT
iajs-2803	69	39	𝑔𝑖	𝑔𝑖	NOUN
iajs-2803	69	40	𝑎𝑖,𝑗	𝑎𝑖,𝑗	NOUN
iajs-2803	69	41	=	=	NOUN
iajs-2803	69	42	1	1	NUM
iajs-2803	69	43	24	24	NUM
iajs-2803	69	44	(	(	PUNCT
iajs-2803	69	45	2.19	2.19	NUM
iajs-2803	69	46	)	)	PUNCT
iajs-2803	69	47	order	order	NOUN
iajs-2803	69	48	5	5	NUM
iajs-2803	69	49	∑	∑	PART
iajs-2803	69	50	𝑔𝑖	𝑔𝑖	VERB
iajs-2803	69	51	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	69	52	4	4	NUM
iajs-2803	69	53	=	=	SYM
iajs-2803	69	54	1	1	NUM
iajs-2803	69	55	5	5	NUM
iajs-2803	69	56	,	,	PUNCT
iajs-2803	69	57	∑	∑	ADP
iajs-2803	69	58	𝑔𝑖	𝑔𝑖	NOUN
iajs-2803	69	59	𝑎𝑖,𝑗𝑐𝑗	𝑎𝑖,𝑗𝑐𝑗	NOUN
iajs-2803	69	60	=	=	SYM
iajs-2803	69	61	1	1	NUM
iajs-2803	69	62	120	120	NUM
iajs-2803	69	63	and	and	CCONJ
iajs-2803	69	64	∑	∑	ADP
iajs-2803	69	65	𝑔𝑖	𝑔𝑖	NOUN
iajs-2803	69	66	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	69	67	𝑎𝑖,𝑗	𝑎𝑖,𝑗	NOUN
iajs-2803	69	68	=	=	NOUN
iajs-2803	69	69	1	1	NUM
iajs-2803	69	70	30	30	NUM
iajs-2803	69	71	(	(	PUNCT
iajs-2803	69	72	2.20	2.20	NUM
iajs-2803	69	73	)	)	PUNCT
iajs-2803	69	74	order	order	NOUN
iajs-2803	69	75	6	6	NUM
iajs-2803	69	76	∑	∑	PART
iajs-2803	69	77	𝑔𝑖	𝑔𝑖	PROPN
iajs-2803	69	78	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	69	79	2𝑎𝑖,𝑗	2𝑎𝑖,𝑗	NUM
iajs-2803	69	80	=	=	SYM
iajs-2803	69	81	1	1	NUM
iajs-2803	69	82	36	36	NUM
iajs-2803	69	83	,	,	PUNCT
iajs-2803	69	84	∑	∑	ADP
iajs-2803	69	85	𝑔𝑖	𝑔𝑖	PROPN
iajs-2803	69	86	𝑎𝑖,𝑗	𝑎𝑖,𝑗	X
iajs-2803	69	87	𝑐𝑗	𝑐𝑗	ADP
iajs-2803	69	88	2	2	NUM
iajs-2803	69	89	+	+	CCONJ
iajs-2803	69	90	∑	∑	ADP
iajs-2803	69	91	𝑔𝑖	𝑔𝑖	ADJ
iajs-2803	69	92	𝑐𝑖𝑎𝑖,𝑗𝑐𝑗	𝑐𝑖𝑎𝑖,𝑗𝑐𝑗	NOUN
iajs-2803	69	93	=	=	PUNCT
iajs-2803	69	94	7	7	NUM
iajs-2803	69	95	720	720	NUM
iajs-2803	69	96	,	,	PUNCT
iajs-2803	69	97	∑	∑	ADP
iajs-2803	69	98	𝑔𝑖	𝑔𝑖	VERB
iajs-2803	69	99	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	69	100	5	5	NUM
iajs-2803	69	101	=	=	SYM
iajs-2803	69	102	1	1	NUM
iajs-2803	69	103	6	6	NUM
iajs-2803	69	104	,	,	PUNCT
iajs-2803	69	105	∑	∑	ADP
iajs-2803	69	106	𝑔𝑖	𝑔𝑖	NOUN
iajs-2803	69	107	𝑎𝑖,𝑗	𝑎𝑖,𝑗	NOUN
iajs-2803	69	108	𝑐𝑗	𝑐𝑗	NOUN
iajs-2803	69	109	2	2	NUM
iajs-2803	69	110	=	=	SYM
iajs-2803	69	111	1	1	NUM
iajs-2803	69	112	360	360	NUM
iajs-2803	69	113	,	,	PUNCT
iajs-2803	69	114	∑	∑	ADP
iajs-2803	69	115	𝑔𝑖	𝑔𝑖	NOUN
iajs-2803	69	116	𝑐𝑖𝑎𝑖,𝑗𝑐𝑗	𝑐𝑖𝑎𝑖,𝑗𝑐𝑗	NOUN
iajs-2803	69	117	=	=	PUNCT
iajs-2803	69	118	1	1	NUM
iajs-2803	69	119	144	144	NUM
iajs-2803	69	120	and	and	CCONJ
iajs-2803	69	121	1	1	NUM
iajs-2803	69	122	2	2	NUM
iajs-2803	69	123	∑	∑	NOUN
iajs-2803	69	124	𝑔𝑖	𝑔𝑖	PROPN
iajs-2803	69	125	𝑎𝑖,𝑗	𝑎𝑖,𝑗	PUNCT
iajs-2803	69	126	𝑐𝑗	𝑐𝑗	ADP
iajs-2803	69	127	2	2	NUM
iajs-2803	69	128	+	+	CCONJ
iajs-2803	69	129	∑	∑	ADP
iajs-2803	69	130	𝑔𝑖	𝑔𝑖	ADJ
iajs-2803	69	131	𝑐𝑖𝑎𝑖,𝑗𝑐𝑗	𝑐𝑖𝑎𝑖,𝑗𝑐𝑗	NOUN
iajs-2803	69	132	=	=	PUNCT
iajs-2803	69	133	1	1	NUM
iajs-2803	69	134	120	120	NUM
iajs-2803	69	135	(	(	PUNCT
iajs-2803	69	136	2.21	2.21	NUM
iajs-2803	69	137	)	)	PUNCT
iajs-2803	69	138	4	4	NUM
iajs-2803	69	139	.	.	PUNCT
iajs-2803	70	1	formation	formation	NOUN
iajs-2803	70	2	of	of	ADP
iajs-2803	70	3	the	the	DET
iajs-2803	70	4	3rd	3rd	ADJ
iajs-2803	70	5	stage	stage	NOUN
iajs-2803	70	6	5th	5th	ADJ
iajs-2803	70	7	order	order	NOUN
iajs-2803	70	8	(	(	PUNCT
iajs-2803	70	9	ditrkm5	ditrkm5	NOUN
iajs-2803	70	10	)	)	PUNCT
iajs-2803	70	11	method	method	NOUN
iajs-2803	70	12	we	we	PRON
iajs-2803	70	13	implement	implement	VERB
iajs-2803	70	14	a	a	DET
iajs-2803	70	15	diagonal	diagonal	ADJ
iajs-2803	70	16	implicit	implicit	ADJ
iajs-2803	70	17	type	type	NOUN
iajs-2803	70	18	runge	runge	NOUN
iajs-2803	70	19	–	–	PUNCT
iajs-2803	70	20	kutta	kutta	NOUN
iajs-2803	70	21	approach	approach	NOUN
iajs-2803	70	22	using	use	VERB
iajs-2803	70	23	order	order	NOUN
iajs-2803	70	24	conditions	condition	NOUN
iajs-2803	70	25	derivations	derivation	NOUN
iajs-2803	70	26	as	as	SCONJ
iajs-2803	70	27	demonstrated	demonstrate	VERB
iajs-2803	70	28	in	in	ADP
iajs-2803	70	29	section	section	NOUN
iajs-2803	70	30	2.3	2.3	NUM
iajs-2803	70	31	,	,	PUNCT
iajs-2803	70	32	which	which	PRON
iajs-2803	70	33	is	be	AUX
iajs-2803	70	34	developed	develop	VERB
iajs-2803	70	35	according	accord	VERB
iajs-2803	70	36	to	to	ADP
iajs-2803	70	37	mechee	mechee	NOUN
iajs-2803	70	38	work	work	NOUN
iajs-2803	70	39	[	[	X
iajs-2803	70	40	17	17	NUM
iajs-2803	70	41	]	]	PUNCT
iajs-2803	70	42	.	.	PUNCT
iajs-2803	71	1	for	for	ADP
iajs-2803	71	2	the	the	DET
iajs-2803	71	3	𝑝	𝑝	PROPN
iajs-2803	71	4	order	order	NOUN
iajs-2803	71	5	ditrk	ditrk	NOUN
iajs-2803	71	6	approach	approach	NOUN
iajs-2803	71	7	,	,	PUNCT
iajs-2803	71	8	the	the	DET
iajs-2803	71	9	local	local	ADJ
iajs-2803	71	10	truncation	truncation	NOUN
iajs-2803	71	11	error	error	NOUN
iajs-2803	71	12	is	be	AUX
iajs-2803	71	13	defined	define	VERB
iajs-2803	71	14	as	as	SCONJ
iajs-2803	71	15	follows	follow	VERB
iajs-2803	71	16	:	:	PUNCT
iajs-2803	71	17	for	for	ADP
iajs-2803	71	18	order	order	NOUN
iajs-2803	71	19	five	five	NUM
iajs-2803	71	20	:	:	PUNCT
iajs-2803	71	21	𝐿𝑇𝐸order	𝐿𝑇𝐸ord	ADJ
iajs-2803	71	22	5	5	NUM
iajs-2803	72	1	=	=	SYM
iajs-2803	72	2	[	[	X
iajs-2803	72	3	(	(	PUNCT
iajs-2803	72	4	∑	∑	INTJ
iajs-2803	72	5	𝑑𝑖	𝑑𝑖	PROPN
iajs-2803	72	6	𝑐𝑖	𝑐𝑖	ADP
iajs-2803	72	7	3	3	NUM
iajs-2803	72	8	−	−	PROPN
iajs-2803	72	9	1	1	NUM
iajs-2803	72	10	120	120	NUM
iajs-2803	72	11	)	)	PUNCT
iajs-2803	72	12	2	2	NUM
iajs-2803	72	13	+	+	CCONJ
iajs-2803	72	14	(	(	PUNCT
iajs-2803	72	15	∑	∑	PROPN
iajs-2803	72	16	𝑑𝑖	𝑑𝑖	PROPN
iajs-2803	72	17	𝑎𝑖,𝑗	𝑎𝑖,𝑗	NOUN
iajs-2803	72	18	−	−	PROPN
iajs-2803	72	19	1	1	NUM
iajs-2803	72	20	720	720	NUM
iajs-2803	72	21	)	)	PUNCT
iajs-2803	72	22	2	2	NUM
iajs-2803	73	1	+	+	CCONJ
iajs-2803	73	2	(	(	PUNCT
iajs-2803	73	3	∑	∑	ADP
iajs-2803	73	4	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	73	5	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	73	6	4	4	NUM
iajs-2803	73	7	−	−	NOUN
iajs-2803	73	8	1	1	NUM
iajs-2803	73	9	30	30	NUM
iajs-2803	73	10	)	)	SYM
iajs-2803	73	11	2	2	NUM
iajs-2803	73	12	+	+	CCONJ
iajs-2803	73	13	(	(	PUNCT
iajs-2803	73	14	∑	∑	INTJ
iajs-2803	73	15	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	73	16	𝑎𝑖,𝑗𝑐𝑗	𝑎𝑖,𝑗𝑐𝑗	PROPN
iajs-2803	73	17	−	−	PROPN
iajs-2803	73	18	1	1	NUM
iajs-2803	73	19	720	720	NUM
iajs-2803	73	20	)	)	PUNCT
iajs-2803	73	21	2	2	NUM
iajs-2803	73	22	+	+	CCONJ
iajs-2803	73	23	(	(	PUNCT
iajs-2803	73	24	∑	∑	ADP
iajs-2803	73	25	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	73	26	𝑎𝑖,𝑗𝑐𝑖	𝑎𝑖,𝑗𝑐𝑖	PROPN
iajs-2803	73	27	−	−	NUM
iajs-2803	73	28	1	1	NUM
iajs-2803	73	29	180	180	NUM
iajs-2803	73	30	)	)	SYM
iajs-2803	73	31	2	2	NUM
iajs-2803	73	32	+	+	CCONJ
iajs-2803	73	33	(	(	PUNCT
iajs-2803	73	34	∑	∑	INTJ
iajs-2803	73	35	𝑔𝑖	𝑔𝑖	NOUN
iajs-2803	73	36	𝑎𝑖,𝑗𝑐𝑖	𝑎𝑖,𝑗𝑐𝑖	PROPN
iajs-2803	73	37	2	2	NUM
iajs-2803	73	38	−	−	NOUN
iajs-2803	73	39	1	1	NUM
iajs-2803	73	40	36	36	NUM
iajs-2803	73	41	)	)	PUNCT
iajs-2803	73	42	2	2	NUM
iajs-2803	73	43	+	+	CCONJ
iajs-2803	73	44	(	(	PUNCT
iajs-2803	73	45	∑	∑	INTJ
iajs-2803	73	46	𝑔𝑖	𝑔𝑖	VERB
iajs-2803	73	47	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	74	1	𝑎𝑖,𝑗𝑐𝑗	𝑎𝑖,𝑗𝑐𝑗	NOUN
iajs-2803	74	2	−	−	PROPN
iajs-2803	74	3	1	1	NUM
iajs-2803	74	4	144	144	NUM
iajs-2803	74	5	)	)	SYM
iajs-2803	74	6	2	2	NUM
iajs-2803	75	1	+	+	CCONJ
iajs-2803	75	2	(	(	PUNCT
iajs-2803	75	3	∑	∑	INTJ
iajs-2803	75	4	𝑔𝑖	𝑔𝑖	VERB
iajs-2803	75	5	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	75	6	5	5	NUM
iajs-2803	75	7	−	−	NOUN
iajs-2803	75	8	1	1	NUM
iajs-2803	75	9	6	6	NUM
iajs-2803	75	10	)	)	SYM
iajs-2803	75	11	2	2	NUM
iajs-2803	75	12	+	+	CCONJ
iajs-2803	75	13	(	(	PUNCT
iajs-2803	75	14	∑	∑	INTJ
iajs-2803	75	15	𝑔𝑖	𝑔𝑖	VERB
iajs-2803	75	16	𝑎𝑖,𝑗𝑐𝑗	𝑎𝑖,𝑗𝑐𝑗	NOUN
iajs-2803	75	17	2	2	NUM
iajs-2803	75	18	−	−	NOUN
iajs-2803	75	19	1	1	NUM
iajs-2803	75	20	360	360	NUM
iajs-2803	75	21	)	)	SYM
iajs-2803	75	22	2	2	NUM
iajs-2803	75	23	+	+	CCONJ
iajs-2803	75	24	(	(	PUNCT
iajs-2803	75	25	∑	∑	INTJ
iajs-2803	75	26	𝑔𝑖	𝑔𝑖	VERB
iajs-2803	75	27	𝑎𝑖,𝑗𝑐𝑗	𝑎𝑖,𝑗𝑐𝑗	ADP
iajs-2803	75	28	2	2	NUM
iajs-2803	75	29	+	+	CCONJ
iajs-2803	75	30	∑	∑	ADP
iajs-2803	75	31	𝑔𝑖	𝑔𝑖	VERB
iajs-2803	75	32	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	76	1	𝑎𝑖,𝑗𝑐𝑗	𝑎𝑖,𝑗𝑐𝑗	NOUN
iajs-2803	76	2	−	−	PROPN
iajs-2803	76	3	1	1	NUM
iajs-2803	76	4	720	720	NUM
iajs-2803	76	5	)	)	PUNCT
iajs-2803	76	6	2	2	NUM
iajs-2803	77	1	+	+	CCONJ
iajs-2803	77	2	(	(	PUNCT
iajs-2803	77	3	1	1	NUM
iajs-2803	77	4	2	2	NUM
iajs-2803	77	5	∑	∑	PUNCT
iajs-2803	77	6	𝑔𝑖	𝑔𝑖	NOUN
iajs-2803	77	7	𝑎𝑖,𝑗𝑐𝑗	𝑎𝑖,𝑗𝑐𝑗	ADP
iajs-2803	77	8	2	2	NUM
iajs-2803	77	9	+	+	CCONJ
iajs-2803	77	10	∑	∑	ADP
iajs-2803	77	11	𝑔𝑖	𝑔𝑖	VERB
iajs-2803	77	12	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	78	1	𝑎𝑖,𝑗𝑐𝑗	𝑎𝑖,𝑗𝑐𝑗	NOUN
iajs-2803	78	2	−	−	PROPN
iajs-2803	78	3	1	1	NUM
iajs-2803	78	4	120	120	NUM
iajs-2803	78	5	)	)	PUNCT
iajs-2803	78	6	2	2	NUM
iajs-2803	78	7	]	]	SYM
iajs-2803	78	8	1	1	NUM
iajs-2803	78	9	2	2	NUM
iajs-2803	78	10	(	(	PUNCT
iajs-2803	78	11	2.22	2.22	NUM
iajs-2803	78	12	)	)	PUNCT
iajs-2803	78	13	the	the	DET
iajs-2803	78	14	error	error	NOUN
iajs-2803	78	15	of	of	ADP
iajs-2803	78	16	local	local	ADJ
iajs-2803	78	17	truncation	truncation	NOUN
iajs-2803	78	18	terms	term	NOUN
iajs-2803	78	19	for	for	ADP
iajs-2803	78	20	𝑦	𝑦	NOUN
iajs-2803	78	21	,	,	PUNCT
iajs-2803	78	22	𝑦′and	𝑦′and	PROPN
iajs-2803	78	23	𝑦′′.	𝑦′′.	PROPN
iajs-2803	78	24	the	the	DET
iajs-2803	78	25	fifth	fifth	ADJ
iajs-2803	78	26	-	-	PUNCT
iajs-2803	78	27	order	order	NOUN
iajs-2803	78	28	three	three	NUM
iajs-2803	78	29	-	-	PUNCT
iajs-2803	78	30	stage	stage	NOUN
iajs-2803	78	31	of	of	ADP
iajs-2803	78	32	the	the	DET
iajs-2803	78	33	ditrkm	ditrkm	NOUN
iajs-2803	78	34	method	method	NOUN
iajs-2803	78	35	in	in	ADP
iajs-2803	78	36	the	the	DET
iajs-2803	78	37	present	present	ADJ
iajs-2803	78	38	study	study	NOUN
iajs-2803	78	39	can	can	AUX
iajs-2803	78	40	be	be	AUX
iajs-2803	78	41	computed	compute	VERB
iajs-2803	78	42	by	by	ADP
iajs-2803	78	43	employing	employ	VERB
iajs-2803	78	44	algebraic	algebraic	ADJ
iajs-2803	78	45	order	order	NOUN
iajs-2803	78	46	conditions	condition	NOUN
iajs-2803	78	47	over	over	ADP
iajs-2803	78	48	5	5	NUM
iajs-2803	78	49	.	.	PUNCT
iajs-2803	79	1	the	the	DET
iajs-2803	79	2	system	system	NOUN
iajs-2803	79	3	of	of	ADP
iajs-2803	79	4	the	the	DET
iajs-2803	79	5	result	result	NOUN
iajs-2803	79	6	includes	include	VERB
iajs-2803	79	7	16	16	NUM
iajs-2803	79	8	nonlinear	nonlinear	ADJ
iajs-2803	79	9	equations	equation	NOUN
iajs-2803	79	10	with	with	ADP
iajs-2803	79	11	16	16	NUM
iajs-2803	79	12	unknown	unknown	ADJ
iajs-2803	79	13	variables	variable	NOUN
iajs-2803	79	14	,	,	PUNCT
iajs-2803	79	15	assuming	assume	VERB
iajs-2803	79	16	𝑎1,1	𝑎1,1	PROPN
iajs-2803	79	17	=	=	SYM
iajs-2803	79	18	𝑎2,2	𝑎2,2	PROPN
iajs-2803	79	19	and	and	CCONJ
iajs-2803	79	20	𝑎2,2	𝑎2,2	PROPN
iajs-2803	79	21	=	=	SYM
iajs-2803	79	22	𝑎3,3	𝑎3,3	PROPN
iajs-2803	79	23	(	(	PUNCT
iajs-2803	79	24	2.23	2.23	NUM
iajs-2803	79	25	)	)	PUNCT
iajs-2803	79	26	thus	thus	ADV
iajs-2803	79	27	,	,	PUNCT
iajs-2803	79	28	the	the	DET
iajs-2803	79	29	calculations	calculation	NOUN
iajs-2803	79	30	of	of	ADP
iajs-2803	79	31	the	the	DET
iajs-2803	79	32	system	system	NOUN
iajs-2803	79	33	products	product	VERB
iajs-2803	79	34	the	the	DET
iajs-2803	79	35	set	set	NOUN
iajs-2803	79	36	of	of	ADP
iajs-2803	79	37	solutions	solution	NOUN
iajs-2803	79	38	in	in	ADP
iajs-2803	79	39	terms	term	NOUN
iajs-2803	79	40	of	of	ADP
iajs-2803	79	41	the	the	DET
iajs-2803	79	42	parameters	parameter	NOUN
iajs-2803	79	43	𝑎1,1	𝑎1,1	PROPN
iajs-2803	79	44	,	,	PUNCT
iajs-2803	79	45	𝑎2,2	𝑎2,2	PROPN
iajs-2803	79	46	and	and	CCONJ
iajs-2803	79	47	𝑐1	𝑐1	NOUN
iajs-2803	79	48	as	as	SCONJ
iajs-2803	79	49	follows	follow	VERB
iajs-2803	79	50	:	:	PUNCT
iajs-2803	79	51	𝑎2,1	𝑎2,1	PROPN
iajs-2803	79	52	=	=	SYM
iajs-2803	79	53	0	0	NUM
iajs-2803	79	54	,	,	PUNCT
iajs-2803	79	55	𝑎3,1	𝑎3,1	NOUN
iajs-2803	79	56	=	=	SYM
iajs-2803	79	57	3	3	NUM
iajs-2803	79	58	20	20	NUM
iajs-2803	79	59	−	−	NOUN
iajs-2803	79	60	3	3	NUM
iajs-2803	79	61	10	10	NUM
iajs-2803	79	62	rootof(10z2	rootof(10z2	PROPN
iajs-2803	79	63	−	−	PROPN
iajs-2803	79	64	10z	10z	NOUN
iajs-2803	79	65	+	+	CCONJ
iajs-2803	79	66	1	1	NUM
iajs-2803	79	67	)	)	PUNCT
iajs-2803	79	68	,	,	PUNCT
iajs-2803	79	69	𝑎3,2	𝑎3,2	NOUN
iajs-2803	79	70	=	=	SYM
iajs-2803	79	71	0	0	PROPN
iajs-2803	79	72	,	,	PUNCT
iajs-2803	79	73	𝑎3,3	𝑎3,3	PROPN
iajs-2803	79	74	=	=	NOUN
iajs-2803	79	75	1	1	NUM
iajs-2803	79	76	120	120	NUM
iajs-2803	79	77	rootof(10z2	rootof(10z2	NOUN
iajs-2803	79	78	−	−	PROPN
iajs-2803	79	79	10z	10z	NOUN
iajs-2803	79	80	+	+	CCONJ
iajs-2803	79	81	1	1	NUM
iajs-2803	79	82	)	)	PUNCT
iajs-2803	79	83	,	,	PUNCT
iajs-2803	79	84	𝑏1	𝑏1	NOUN
iajs-2803	79	85	=	=	SYM
iajs-2803	79	86	−5	−5	PROPN
iajs-2803	79	87	18	18	NUM
iajs-2803	79	88	rootof(10z2	rootof(10z2	PROPN
iajs-2803	79	89	−	−	PROPN
iajs-2803	79	90	10z	10z	NOUN
iajs-2803	79	91	+	+	CCONJ
iajs-2803	79	92	1	1	NUM
iajs-2803	79	93	)	)	PUNCT
iajs-2803	79	94	+	+	CCONJ
iajs-2803	79	95	5	5	NUM
iajs-2803	79	96	18	18	NUM
iajs-2803	79	97	,	,	PUNCT
iajs-2803	79	98	𝑏2	𝑏2	NOUN
iajs-2803	79	99	=	=	NOUN
iajs-2803	79	100	2	2	NUM
iajs-2803	79	101	9	9	NUM
iajs-2803	79	102	,	,	PUNCT
iajs-2803	79	103	𝑏3	𝑏3	NOUN
iajs-2803	79	104	=	=	SYM
iajs-2803	79	105	5	5	NUM
iajs-2803	79	106	18	18	NUM
iajs-2803	79	107	rootof(10z2	rootof(10z2	PROPN
iajs-2803	79	108	−	−	PROPN
iajs-2803	79	109	10z	10z	NOUN
iajs-2803	79	110	+	+	CCONJ
iajs-2803	79	111	1	1	NUM
iajs-2803	79	112	)	)	PUNCT
iajs-2803	79	113	,	,	PUNCT
iajs-2803	79	114	𝑐1	𝑐1	NOUN
iajs-2803	79	115	=	=	PUNCT
iajs-2803	79	116	rootof(10z2	rootof(10z2	PROPN
iajs-2803	79	117	−	−	PROPN
iajs-2803	79	118	10z	10z	NOUN
iajs-2803	79	119	+	+	CCONJ
iajs-2803	79	120	1	1	NUM
iajs-2803	79	121	)	)	PUNCT
iajs-2803	79	122	,	,	PUNCT
iajs-2803	79	123	𝑐2	𝑐2	NOUN
iajs-2803	79	124	=	=	SYM
iajs-2803	79	125	1	1	NUM
iajs-2803	79	126	2	2	NUM
iajs-2803	79	127	,	,	PUNCT
iajs-2803	79	128	𝑐3	𝑐3	NOUN
iajs-2803	79	129	=	=	SYM
iajs-2803	79	130	−rootof(10z2	−rootof(10z2	VERB
iajs-2803	79	131	−	−	PROPN
iajs-2803	79	132	10z	10z	NOUN
iajs-2803	79	133	+	+	CCONJ
iajs-2803	79	134	1	1	NUM
iajs-2803	79	135	)	)	PUNCT
iajs-2803	79	136	+	+	NUM
iajs-2803	79	137	1	1	NUM
iajs-2803	79	138	,	,	PUNCT
iajs-2803	79	139	d1	d1	NOUN
iajs-2803	79	140	=	=	SYM
iajs-2803	79	141	1	1	NUM
iajs-2803	79	142	8	8	NUM
iajs-2803	79	143	−	−	NUM
iajs-2803	79	144	5	5	NUM
iajs-2803	79	145	36	36	NUM
iajs-2803	79	146	rootof(10z2	rootof(10z2	PROPN
iajs-2803	79	147	−	−	PROPN
iajs-2803	79	148	10z	10z	NOUN
iajs-2803	79	149	+	+	CCONJ
iajs-2803	79	150	1	1	NUM
iajs-2803	79	151	)	)	PUNCT
iajs-2803	79	152	,	,	PUNCT
iajs-2803	79	153	d2	d2	PROPN
iajs-2803	79	154	=	=	SYM
iajs-2803	79	155	1	1	NUM
iajs-2803	79	156	18	18	NUM
iajs-2803	79	157	,	,	PUNCT
iajs-2803	79	158	d3	d3	PROPN
iajs-2803	79	159	=	=	SYM
iajs-2803	79	160	5	5	NUM
iajs-2803	79	161	36	36	NUM
iajs-2803	79	162	rootof(10z2	rootof(10z2	PROPN
iajs-2803	79	163	−	−	PROPN
iajs-2803	79	164	10z	10z	NOUN
iajs-2803	79	165	+	+	CCONJ
iajs-2803	79	166	1	1	X
iajs-2803	79	167	)	)	PUNCT
iajs-2803	79	168	−	−	PROPN
iajs-2803	79	169	1	1	NUM
iajs-2803	79	170	72	72	NUM
iajs-2803	79	171	,	,	PUNCT
iajs-2803	79	172	𝑔1	𝑔1	PROPN
iajs-2803	79	173	=	=	PROPN
iajs-2803	79	174	5	5	NUM
iajs-2803	79	175	18	18	NUM
iajs-2803	79	176	,	,	PUNCT
iajs-2803	79	177	𝑔2	𝑔2	NOUN
iajs-2803	79	178	=	=	SYM
iajs-2803	79	179	4	4	NUM
iajs-2803	79	180	9	9	NUM
iajs-2803	79	181	,	,	PUNCT
iajs-2803	79	182	𝑔3	𝑔3	VERB
iajs-2803	79	183	=	=	SYM
iajs-2803	79	184	5	5	NUM
iajs-2803	79	185	18	18	NUM
iajs-2803	79	186	(	(	PUNCT
iajs-2803	79	187	2.24	2.24	NUM
iajs-2803	79	188	)	)	PUNCT
iajs-2803	79	189	ibn	ibn	PROPN
iajs-2803	79	190	al	al	PROPN
iajs-2803	79	191	-	-	PUNCT
iajs-2803	79	192	haitham	haitham	PROPN
iajs-2803	79	193	jour	jour	X
iajs-2803	79	194	.	.	PROPN
iajs-2803	79	195	for	for	ADP
iajs-2803	79	196	pure	pure	ADJ
iajs-2803	79	197	&	&	CCONJ
iajs-2803	79	198	appl	appl	PROPN
iajs-2803	79	199	.	.	PUNCT
iajs-2803	80	1	sci	sci	PROPN
iajs-2803	80	2	.	.	PROPN
iajs-2803	81	1	53	53	NUM
iajs-2803	81	2	(	(	PUNCT
iajs-2803	81	3	1)2022	1)2022	PROPN
iajs-2803	81	4	96	96	NUM
iajs-2803	81	5	finally	finally	ADV
iajs-2803	81	6	,	,	PUNCT
iajs-2803	81	7	coefficients	coefficient	NOUN
iajs-2803	81	8	of	of	ADP
iajs-2803	81	9	the	the	DET
iajs-2803	81	10	ditrkm	ditrkm	NOUN
iajs-2803	81	11	method	method	NOUN
iajs-2803	81	12	for	for	ADP
iajs-2803	81	13	5	5	NUM
iajs-2803	81	14	-	-	PUNCT
iajs-2803	81	15	order	order	NOUN
iajs-2803	81	16	3	3	NUM
iajs-2803	81	17	stages	stage	NOUN
iajs-2803	81	18	indicated	indicate	VERB
iajs-2803	81	19	by	by	ADP
iajs-2803	81	20	ditrkm5	ditrkm5	NOUN
iajs-2803	81	21	can	can	AUX
iajs-2803	81	22	be	be	AUX
iajs-2803	81	23	read	read	VERB
iajs-2803	81	24	as	as	SCONJ
iajs-2803	81	25	shown	show	VERB
iajs-2803	81	26	in	in	ADP
iajs-2803	81	27	table	table	NOUN
iajs-2803	81	28	2.2	2.2	NUM
iajs-2803	81	29	.	.	PUNCT
iajs-2803	81	30	table	table	NOUN
iajs-2803	81	31	2.2	2.2	NUM
iajs-2803	81	32	:	:	PUNCT
iajs-2803	81	33	third	third	ADJ
iajs-2803	81	34	-	-	PUNCT
iajs-2803	81	35	stage	stage	NOUN
iajs-2803	81	36	fifth	fifth	ADJ
iajs-2803	81	37	-	-	PUNCT
iajs-2803	81	38	order	order	NOUN
iajs-2803	81	39	ditrk	ditrk	NOUN
iajs-2803	81	40	method	method	NOUN
iajs-2803	81	41	(	(	PUNCT
iajs-2803	81	42	ditrkm5	ditrkm5	PROPN
iajs-2803	81	43	)	)	PUNCT
iajs-2803	81	44	.	.	PUNCT
iajs-2803	82	1	5	5	X
iajs-2803	82	2	.	.	X
iajs-2803	82	3	the	the	DET
iajs-2803	82	4	stability	stability	NOUN
iajs-2803	82	5	polynomial	polynomial	NOUN
iajs-2803	82	6	of	of	ADP
iajs-2803	82	7	ditrk	ditrk	NOUN
iajs-2803	82	8	method	method	NOUN
iajs-2803	82	9	in	in	ADP
iajs-2803	82	10	order	order	NOUN
iajs-2803	82	11	to	to	PART
iajs-2803	82	12	study	study	VERB
iajs-2803	82	13	the	the	DET
iajs-2803	82	14	stability	stability	NOUN
iajs-2803	82	15	polynomial	polynomial	NOUN
iajs-2803	82	16	of	of	ADP
iajs-2803	82	17	the	the	DET
iajs-2803	82	18	ditrk	ditrk	NOUN
iajs-2803	82	19	method	method	NOUN
iajs-2803	82	20	,	,	PUNCT
iajs-2803	82	21	the	the	DET
iajs-2803	82	22	following	follow	VERB
iajs-2803	82	23	equation	equation	NOUN
iajs-2803	82	24	is	be	AUX
iajs-2803	82	25	suggested	suggest	VERB
iajs-2803	82	26	:	:	PUNCT
iajs-2803	82	27	𝑦′′′	𝑦′′′	PROPN
iajs-2803	82	28	=	=	SYM
iajs-2803	82	29	−𝛾3𝑦	−𝛾3𝑦	X
iajs-2803	82	30	(	(	PUNCT
iajs-2803	82	31	2.25	2.25	NUM
iajs-2803	82	32	)	)	PUNCT
iajs-2803	82	33	by	by	ADP
iajs-2803	82	34	substituting	substitute	VERB
iajs-2803	82	35	the	the	DET
iajs-2803	82	36	ditrk	ditrk	NOUN
iajs-2803	82	37	method	method	NOUN
iajs-2803	82	38	from	from	ADP
iajs-2803	82	39	eqs	eqs	PROPN
iajs-2803	82	40	.	.	PUNCT
iajs-2803	83	1	(	(	PUNCT
iajs-2803	83	2	2.2	2.2	NUM
iajs-2803	83	3	)	)	PUNCT
iajs-2803	83	4	(	(	PUNCT
iajs-2803	83	5	2.4	2.4	NUM
iajs-2803	83	6	)	)	PUNCT
iajs-2803	83	7	to	to	PART
iajs-2803	83	8	exam	exam	VERB
iajs-2803	83	9	eq	eq	ADP
iajs-2803	83	10	.	.	PUNCT
iajs-2803	84	1	(	(	PUNCT
iajs-2803	84	2	2.25	2.25	NUM
iajs-2803	84	3	)	)	PUNCT
iajs-2803	84	4	with	with	ADP
iajs-2803	84	5	stage	stage	NOUN
iajs-2803	84	6	𝑚	𝑚	X
iajs-2803	84	7	=	=	SYM
iajs-2803	84	8	3	3	NUM
iajs-2803	84	9	are	be	AUX
iajs-2803	84	10	yield	yield	NOUN
iajs-2803	84	11	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2803	84	12	=	=	SYM
iajs-2803	84	13	𝑦𝑛	𝑦𝑛	NOUN
iajs-2803	84	14	+	+	NOUN
iajs-2803	84	15	ℎ	ℎ	NOUN
iajs-2803	84	16	𝑦𝑛	𝑦𝑛	AUX
iajs-2803	84	17	′	′	NOUN
iajs-2803	84	18	+	+	CCONJ
iajs-2803	84	19	ℎ2	ℎ2	ADJ
iajs-2803	84	20	2	2	NUM
iajs-2803	84	21	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	84	22	′′	′′	PROPN
iajs-2803	84	23	+	+	CCONJ
iajs-2803	84	24	ℎ3	ℎ3	PROPN
iajs-2803	84	25	∑	∑	PUNCT
iajs-2803	84	26	𝑑𝑖	𝑑𝑖	PART
iajs-2803	84	27	3	3	NUM
iajs-2803	84	28	𝑖=2	𝑖=2	ADV
iajs-2803	84	29	𝑘𝑖	𝑘𝑖	X
iajs-2803	84	30	(	(	PUNCT
iajs-2803	84	31	2.26	2.26	NUM
iajs-2803	84	32	)	)	PUNCT
iajs-2803	84	33	𝑦𝑛+1	𝑦𝑛+1	NOUN
iajs-2803	84	34	′	′	NOUN
iajs-2803	84	35	=	=	PUNCT
iajs-2803	84	36	𝑦𝑛	𝑦𝑛	AUX
iajs-2803	84	37	′	′	NOUN
iajs-2803	85	1	+	+	CCONJ
iajs-2803	85	2	ℎ	ℎ	NOUN
iajs-2803	85	3	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	85	4	′′	′′	PROPN
iajs-2803	85	5	+	+	CCONJ
iajs-2803	85	6	ℎ2	ℎ2	NOUN
iajs-2803	85	7	∑	∑	PUNCT
iajs-2803	85	8	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	85	9	3	3	NUM
iajs-2803	85	10	𝑖=2	𝑖=2	PROPN
iajs-2803	85	11	𝑘𝑖	𝑘𝑖	X
iajs-2803	85	12	(	(	PUNCT
iajs-2803	85	13	2.27	2.27	NUM
iajs-2803	85	14	)	)	PUNCT
iajs-2803	85	15	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2803	85	16	′′	′′	NOUN
iajs-2803	85	17	=	=	PUNCT
iajs-2803	85	18	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	85	19	′′	′′	PROPN
iajs-2803	85	20	+	+	CCONJ
iajs-2803	85	21	ℎ	ℎ	PROPN
iajs-2803	85	22	∑	∑	PROPN
iajs-2803	85	23	𝑔𝑖	𝑔𝑖	PROPN
iajs-2803	85	24	3	3	NUM
iajs-2803	85	25	𝑖=2	𝑖=2	ADV
iajs-2803	85	26	𝑘𝑖	𝑘𝑖	X
iajs-2803	85	27	(	(	PUNCT
iajs-2803	85	28	2.28	2.28	NUM
iajs-2803	85	29	)	)	PUNCT
iajs-2803	85	30	and	and	CCONJ
iajs-2803	85	31	𝑘1	𝑘1	NOUN
iajs-2803	85	32	=	=	SYM
iajs-2803	85	33	𝑓(𝑥𝑛	𝑓(𝑥𝑛	PROPN
iajs-2803	85	34	,	,	PUNCT
iajs-2803	85	35	𝑦𝑛	𝑦𝑛	NOUN
iajs-2803	85	36	)	)	PUNCT
iajs-2803	85	37	𝑘𝑖	𝑘𝑖	NOUN
iajs-2803	85	38	=	=	PUNCT
iajs-2803	85	39	𝑓(𝑥𝑛	𝑓(𝑥𝑛	PROPN
iajs-2803	85	40	+	+	CCONJ
iajs-2803	85	41	𝑐𝑖ℎ	𝑐𝑖ℎ	ADJ
iajs-2803	85	42	,	,	PUNCT
iajs-2803	85	43	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	85	44	+	+	ADJ
iajs-2803	85	45	ℎ	ℎ	PART
iajs-2803	85	46	𝑐𝑖𝑦𝑛	𝑐𝑖𝑦𝑛	NOUN
iajs-2803	85	47	′	′	NUM
iajs-2803	86	1	+	+	CCONJ
iajs-2803	86	2	ℎ2	ℎ2	ADJ
iajs-2803	86	3	2	2	NUM
iajs-2803	86	4	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	86	5	2	2	NUM
iajs-2803	86	6	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	86	7	′′	′′	PROPN
iajs-2803	86	8	+	+	CCONJ
iajs-2803	86	9	ℎ3	ℎ3	NOUN
iajs-2803	86	10	∑	∑	PUNCT
iajs-2803	86	11	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-2803	86	12	𝑖−1	𝑖−1	PROPN
iajs-2803	86	13	𝑗=1	𝑗=1	PROPN
iajs-2803	86	14	𝑘𝑗	𝑘𝑗	PROPN
iajs-2803	86	15	)	)	PUNCT
iajs-2803	86	16	(	(	PUNCT
iajs-2803	86	17	2.29	2.29	NUM
iajs-2803	86	18	)	)	PUNCT
iajs-2803	86	19	where	where	SCONJ
iajs-2803	86	20	𝑖	𝑖	ADP
iajs-2803	86	21	=	=	SYM
iajs-2803	86	22	2,3	2,3	NUM
iajs-2803	86	23	,	,	PUNCT
iajs-2803	86	24	…	…	PUNCT
iajs-2803	86	25	,	,	PUNCT
iajs-2803	86	26	𝑚	𝑚	PROPN
iajs-2803	86	27	and	and	CCONJ
iajs-2803	86	28	𝑌𝑖	𝑌𝑖	PROPN
iajs-2803	86	29	=	=	PUNCT
iajs-2803	87	1	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	87	2	+	+	NOUN
iajs-2803	87	3	ℎ	ℎ	PART
iajs-2803	87	4	𝑐𝑖𝑦𝑛	𝑐𝑖𝑦𝑛	NOUN
iajs-2803	87	5	′	′	NUM
iajs-2803	88	1	+	+	CCONJ
iajs-2803	88	2	ℎ2	ℎ2	ADJ
iajs-2803	88	3	2	2	NUM
iajs-2803	88	4	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	88	5	2	2	NUM
iajs-2803	88	6	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	88	7	′′	′′	PROPN
iajs-2803	88	8	+	+	CCONJ
iajs-2803	88	9	ℎ3	ℎ3	NOUN
iajs-2803	88	10	∑	∑	PUNCT
iajs-2803	88	11	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-2803	88	12	𝑖−1	𝑖−1	PROPN
iajs-2803	88	13	𝑗=1	𝑗=1	PROPN
iajs-2803	88	14	(	(	PUNCT
iajs-2803	88	15	−𝛾3𝑌𝑗	−𝛾3𝑌𝑗	NOUN
iajs-2803	88	16	)	)	PUNCT
iajs-2803	88	17	(	(	PUNCT
iajs-2803	88	18	2.30	2.30	NUM
iajs-2803	88	19	)	)	PUNCT
iajs-2803	88	20	where	where	SCONJ
iajs-2803	88	21	𝑌1	𝑌1	NOUN
iajs-2803	88	22	=	=	SYM
iajs-2803	88	23	𝑦𝑛	𝑦𝑛	X
iajs-2803	88	24	(	(	PUNCT
iajs-2803	88	25	2.31	2.31	NUM
iajs-2803	88	26	)	)	PUNCT
iajs-2803	89	1	𝑌𝑖	𝑌𝑖	NOUN
iajs-2803	89	2	=	=	PUNCT
iajs-2803	90	1	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	90	2	+	+	NOUN
iajs-2803	90	3	ℎ	ℎ	PART
iajs-2803	90	4	𝑐𝑖𝑦𝑛	𝑐𝑖𝑦𝑛	NOUN
iajs-2803	90	5	′	′	NUM
iajs-2803	91	1	+	+	CCONJ
iajs-2803	91	2	ℎ2	ℎ2	ADJ
iajs-2803	91	3	2	2	NUM
iajs-2803	91	4	𝑐𝑖	𝑐𝑖	NOUN
iajs-2803	91	5	2	2	NUM
iajs-2803	91	6	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	91	7	′′	′′	PROPN
iajs-2803	91	8	+	+	CCONJ
iajs-2803	91	9	ℎ3	ℎ3	NOUN
iajs-2803	91	10	∑	∑	PUNCT
iajs-2803	91	11	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-2803	91	12	𝑖−1	𝑖−1	PUNCT
iajs-2803	91	13	𝑗=1	𝑗=1	PROPN
iajs-2803	91	14	𝑓(𝑥𝑛	𝑓(𝑥𝑛	PROPN
iajs-2803	91	15	+	+	CCONJ
iajs-2803	91	16	𝑐𝑖ℎ	𝑐𝑖ℎ	ADJ
iajs-2803	91	17	,	,	PUNCT
iajs-2803	91	18	𝑌𝑖	𝑌𝑖	NOUN
iajs-2803	91	19	)	)	PUNCT
iajs-2803	91	20	(	(	PUNCT
iajs-2803	91	21	2.32	2.32	NUM
iajs-2803	91	22	)	)	PUNCT
iajs-2803	91	23	more	more	ADJ
iajs-2803	91	24	simplification	simplification	NOUN
iajs-2803	91	25	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2803	91	26	=	=	SYM
iajs-2803	91	27	𝑦𝑛	𝑦𝑛	NOUN
iajs-2803	91	28	+	+	NOUN
iajs-2803	91	29	ℎ	ℎ	NOUN
iajs-2803	91	30	𝑦𝑛	𝑦𝑛	AUX
iajs-2803	91	31	′	′	NOUN
iajs-2803	92	1	+	+	CCONJ
iajs-2803	92	2	ℎ2	ℎ2	ADJ
iajs-2803	92	3	2	2	NUM
iajs-2803	92	4	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	92	5	′′	′′	PROPN
iajs-2803	92	6	+	+	CCONJ
iajs-2803	92	7	ℎ3	ℎ3	PROPN
iajs-2803	92	8	∑	∑	PUNCT
iajs-2803	92	9	𝑑𝑖	𝑑𝑖	NOUN
iajs-2803	92	10	𝑚	𝑚	PROPN
iajs-2803	92	11	𝑖=2	𝑖=2	PROPN
iajs-2803	92	12	(	(	PUNCT
iajs-2803	92	13	−𝛾3)𝑌𝑗	−𝛾3)𝑌𝑗	PROPN
iajs-2803	92	14	(	(	PUNCT
iajs-2803	92	15	2.33	2.33	NUM
iajs-2803	92	16	)	)	PUNCT
iajs-2803	92	17	𝑦𝑛+1	𝑦𝑛+1	NOUN
iajs-2803	92	18	′	′	NOUN
iajs-2803	93	1	=	=	PUNCT
iajs-2803	93	2	𝑦𝑛	𝑦𝑛	AUX
iajs-2803	93	3	′	′	NOUN
iajs-2803	94	1	+	+	CCONJ
iajs-2803	94	2	ℎ	ℎ	NOUN
iajs-2803	94	3	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	94	4	′′	′′	PROPN
iajs-2803	94	5	+	+	CCONJ
iajs-2803	94	6	ℎ2	ℎ2	NOUN
iajs-2803	94	7	∑	∑	PUNCT
iajs-2803	94	8	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	94	9	𝑚	𝑚	PROPN
iajs-2803	94	10	𝑖=2	𝑖=2	PUNCT
iajs-2803	95	1	(	(	PUNCT
iajs-2803	95	2	−𝛾3)𝑌𝑗	−𝛾3)𝑌𝑗	PROPN
iajs-2803	95	3	(	(	PUNCT
iajs-2803	95	4	2.34	2.34	NUM
iajs-2803	95	5	)	)	PUNCT
iajs-2803	95	6	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2803	95	7	′′	′′	NOUN
iajs-2803	95	8	=	=	PUNCT
iajs-2803	95	9	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	95	10	′′	′′	PROPN
iajs-2803	95	11	+	+	CCONJ
iajs-2803	95	12	ℎ	ℎ	PROPN
iajs-2803	95	13	∑	∑	PROPN
iajs-2803	95	14	𝑔𝑖	𝑔𝑖	PROPN
iajs-2803	95	15	𝑚	𝑚	PROPN
iajs-2803	95	16	𝑖=2	𝑖=2	PROPN
iajs-2803	95	17	(	(	PUNCT
iajs-2803	95	18	−𝛾3)𝑌𝑗	−𝛾3)𝑌𝑗	PROPN
iajs-2803	95	19	(	(	PUNCT
iajs-2803	95	20	2.35	2.35	NUM
iajs-2803	95	21	)	)	PUNCT
iajs-2803	95	22	from	from	ADP
iajs-2803	95	23	eq	eq	ADP
iajs-2803	95	24	.	.	PUNCT
iajs-2803	95	25	(	(	PUNCT
iajs-2803	95	26	2.25	2.25	NUM
iajs-2803	95	27	)	)	PUNCT
iajs-2803	95	28	,	,	PUNCT
iajs-2803	95	29	the	the	DET
iajs-2803	95	30	above	above	ADJ
iajs-2803	95	31	equations	equation	NOUN
iajs-2803	95	32	can	can	AUX
iajs-2803	95	33	be	be	AUX
iajs-2803	95	34	written	write	VERB
iajs-2803	95	35	as	as	ADP
iajs-2803	95	36	follow	follow	VERB
iajs-2803	95	37	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2803	95	38	=	=	SYM
iajs-2803	95	39	𝑦𝑛	𝑦𝑛	NOUN
iajs-2803	95	40	+	+	NOUN
iajs-2803	95	41	ℎ	ℎ	NOUN
iajs-2803	95	42	𝑦𝑛	𝑦𝑛	AUX
iajs-2803	95	43	′	′	NOUN
iajs-2803	95	44	+	+	CCONJ
iajs-2803	95	45	ℎ2	ℎ2	ADJ
iajs-2803	95	46	2	2	NUM
iajs-2803	95	47	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	95	48	′′	′′	PROPN
iajs-2803	95	49	+	+	CCONJ
iajs-2803	95	50	ℎ3	ℎ3	PROPN
iajs-2803	95	51	∑	∑	PUNCT
iajs-2803	95	52	𝑑𝑖	𝑑𝑖	NOUN
iajs-2803	95	53	𝑚	𝑚	PROPN
iajs-2803	95	54	𝑖=2	𝑖=2	PROPN
iajs-2803	95	55	𝑓(𝑥𝑛	𝑓(𝑥𝑛	PROPN
iajs-2803	95	56	+	+	CCONJ
iajs-2803	95	57	𝑐𝑖ℎ	𝑐𝑖ℎ	ADJ
iajs-2803	95	58	,	,	PUNCT
iajs-2803	95	59	𝑌𝑖	𝑌𝑖	NOUN
iajs-2803	95	60	)	)	PUNCT
iajs-2803	95	61	(	(	PUNCT
iajs-2803	95	62	2.36	2.36	NUM
iajs-2803	95	63	)	)	PUNCT
iajs-2803	95	64	ibn	ibn	PROPN
iajs-2803	95	65	al	al	PROPN
iajs-2803	95	66	-	-	PUNCT
iajs-2803	95	67	haitham	haitham	PROPN
iajs-2803	95	68	jour	jour	X
iajs-2803	95	69	.	.	PROPN
iajs-2803	95	70	for	for	ADP
iajs-2803	95	71	pure	pure	ADJ
iajs-2803	95	72	&	&	CCONJ
iajs-2803	95	73	appl	appl	PROPN
iajs-2803	95	74	.	.	PUNCT
iajs-2803	96	1	sci	sci	PROPN
iajs-2803	96	2	.	.	PROPN
iajs-2803	97	1	53	53	NUM
iajs-2803	97	2	(	(	PUNCT
iajs-2803	97	3	1)2022	1)2022	PROPN
iajs-2803	97	4	97	97	NUM
iajs-2803	97	5	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2803	97	6	′	′	NOUN
iajs-2803	97	7	=	=	PUNCT
iajs-2803	97	8	𝑦𝑛	𝑦𝑛	AUX
iajs-2803	97	9	′	′	NOUN
iajs-2803	98	1	+	+	CCONJ
iajs-2803	98	2	ℎ	ℎ	NOUN
iajs-2803	98	3	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	98	4	′′	′′	PROPN
iajs-2803	98	5	+	+	CCONJ
iajs-2803	98	6	ℎ2	ℎ2	NOUN
iajs-2803	98	7	∑	∑	PUNCT
iajs-2803	98	8	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	98	9	𝑚	𝑚	PROPN
iajs-2803	98	10	𝑖=2	𝑖=2	PROPN
iajs-2803	98	11	𝑓(𝑥𝑛	𝑓(𝑥𝑛	PROPN
iajs-2803	98	12	+	+	CCONJ
iajs-2803	98	13	𝑐𝑖ℎ	𝑐𝑖ℎ	ADJ
iajs-2803	98	14	,	,	PUNCT
iajs-2803	98	15	𝑌𝑖	𝑌𝑖	NOUN
iajs-2803	98	16	)	)	PUNCT
iajs-2803	98	17	(	(	PUNCT
iajs-2803	98	18	2.37	2.37	NUM
iajs-2803	98	19	)	)	PUNCT
iajs-2803	98	20	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2803	99	1	′′	′′	NOUN
iajs-2803	99	2	=	=	PUNCT
iajs-2803	99	3	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	99	4	′′	′′	PROPN
iajs-2803	99	5	+	+	CCONJ
iajs-2803	99	6	ℎ	ℎ	PROPN
iajs-2803	99	7	∑	∑	PROPN
iajs-2803	99	8	𝑔𝑖	𝑔𝑖	PROPN
iajs-2803	99	9	𝑚	𝑚	NOUN
iajs-2803	99	10	𝑖=2	𝑖=2	PROPN
iajs-2803	99	11	𝑓(𝑥𝑛	𝑓(𝑥𝑛	PROPN
iajs-2803	99	12	+	+	CCONJ
iajs-2803	99	13	𝑐𝑖ℎ	𝑐𝑖ℎ	ADJ
iajs-2803	99	14	,	,	PUNCT
iajs-2803	99	15	𝑌𝑖	𝑌𝑖	NOUN
iajs-2803	99	16	)	)	PUNCT
iajs-2803	99	17	(	(	PUNCT
iajs-2803	99	18	2.38	2.38	NUM
iajs-2803	99	19	)	)	PUNCT
iajs-2803	99	20	from	from	ADP
iajs-2803	99	21	eq	eq	ADP
iajs-2803	99	22	.	.	PUNCT
iajs-2803	99	23	(	(	PUNCT
iajs-2803	99	24	2.30	2.30	NUM
iajs-2803	99	25	)	)	PUNCT
iajs-2803	99	26	,	,	PUNCT
iajs-2803	99	27	multiply	multiply	ADP
iajs-2803	99	28	eq	eq	ADP
iajs-2803	99	29	.	.	PUNCT
iajs-2803	100	1	(	(	PUNCT
iajs-2803	100	2	2.34	2.34	NUM
iajs-2803	100	3	)	)	PUNCT
iajs-2803	100	4	by	by	ADP
iajs-2803	100	5	ℎ	ℎ	NOUN
iajs-2803	100	6	and	and	CCONJ
iajs-2803	100	7	eq	eq	NOUN
iajs-2803	100	8	.	.	PUNCT
iajs-2803	101	1	(	(	PUNCT
iajs-2803	101	2	2.35	2.35	NUM
iajs-2803	101	3	)	)	PUNCT
iajs-2803	101	4	by	by	ADP
iajs-2803	101	5	ℎ2,yield	ℎ2,yield	ADP
iajs-2803	101	6	ℎ𝑦𝑛+1	ℎ𝑦𝑛+1	NOUN
iajs-2803	101	7	′	′	NOUN
iajs-2803	101	8	=	=	PUNCT
iajs-2803	101	9	ℎ𝑦𝑛	ℎ𝑦𝑛	NOUN
iajs-2803	101	10	′	′	NOUN
iajs-2803	102	1	+	+	CCONJ
iajs-2803	102	2	ℎ2	ℎ2	ADJ
iajs-2803	102	3	𝑦𝑛	𝑦𝑛	ADP
iajs-2803	102	4	′′	′′	PROPN
iajs-2803	102	5	+	+	CCONJ
iajs-2803	102	6	ℎ3	ℎ3	NOUN
iajs-2803	102	7	∑	∑	ADV
iajs-2803	102	8	𝑏𝑖	𝑏𝑖	ADP
iajs-2803	102	9	𝑚	𝑚	PROPN
iajs-2803	102	10	𝑖=2	𝑖=2	PUNCT
iajs-2803	102	11	(	(	PUNCT
iajs-2803	102	12	−𝛾3)𝑌𝑗	−𝛾3)𝑌𝑗	PROPN
iajs-2803	102	13	(	(	PUNCT
iajs-2803	102	14	2.39	2.39	NUM
iajs-2803	102	15	)	)	PUNCT
iajs-2803	102	16	ℎ2𝑦𝑛+1	ℎ2𝑦𝑛+1	NOUN
iajs-2803	102	17	′′	′′	NOUN
iajs-2803	102	18	=	=	SYM
iajs-2803	102	19	ℎ2𝑦𝑛	ℎ2𝑦𝑛	X
iajs-2803	102	20	′′	′′	PROPN
iajs-2803	102	21	+	+	CCONJ
iajs-2803	102	22	ℎ3	ℎ3	PROPN
iajs-2803	102	23	∑	∑	PUNCT
iajs-2803	102	24	𝑔𝑖	𝑔𝑖	NOUN
iajs-2803	102	25	𝑚	𝑚	PROPN
iajs-2803	102	26	𝑖=2	𝑖=2	PROPN
iajs-2803	102	27	(	(	PUNCT
iajs-2803	102	28	−𝛾3)𝑌𝑗	−𝛾3)𝑌𝑗	PROPN
iajs-2803	102	29	(	(	PUNCT
iajs-2803	102	30	2.40	2.40	NUM
iajs-2803	102	31	)	)	PUNCT
iajs-2803	102	32	then	then	ADV
iajs-2803	102	33	[	[	PUNCT
iajs-2803	102	34	𝑦𝑛+1	𝑦𝑛+1	PROPN
iajs-2803	102	35	ℎ𝑦𝑛+1	ℎ𝑦𝑛+1	ADJ
iajs-2803	102	36	′	′	NOUN
iajs-2803	102	37	ℎ2𝑦𝑛+1	ℎ2𝑦𝑛+1	NOUN
iajs-2803	102	38	′′	′′	PROPN
iajs-2803	102	39	]	]	PUNCT
iajs-2803	103	1	=	=	PUNCT
iajs-2803	103	2	[	[	PUNCT
iajs-2803	103	3	1	1	NUM
iajs-2803	103	4	1	1	NUM
iajs-2803	103	5	1	1	NUM
iajs-2803	103	6	2	2	NUM
iajs-2803	103	7	0	0	NUM
iajs-2803	103	8	1	1	NUM
iajs-2803	103	9	1	1	NUM
iajs-2803	103	10	0	0	NUM
iajs-2803	103	11	0	0	NUM
iajs-2803	103	12	1	1	NUM
iajs-2803	103	13	]	]	PUNCT
iajs-2803	103	14	[	[	PUNCT
iajs-2803	103	15	𝑦𝑛	𝑦𝑛	NOUN
iajs-2803	103	16	ℎ𝑦𝑛	ℎ𝑦𝑛	NOUN
iajs-2803	103	17	′	′	X
iajs-2803	103	18	ℎ2𝑦𝑛	ℎ2𝑦𝑛	X
iajs-2803	104	1	′′	′′	PROPN
iajs-2803	104	2	]	]	PUNCT
iajs-2803	105	1	+	+	CCONJ
iajs-2803	105	2	(	(	PUNCT
iajs-2803	105	3	−𝛾3ℎ3	−𝛾3ℎ3	PROPN
iajs-2803	105	4	)	)	PUNCT
iajs-2803	105	5	[	[	PUNCT
iajs-2803	105	6	𝑑1	𝑑1	NOUN
iajs-2803	105	7	𝑑2	𝑑2	NOUN
iajs-2803	105	8	𝑑3	𝑑3	PROPN
iajs-2803	105	9	𝑏1	𝑏1	ADJ
iajs-2803	105	10	𝑏2	𝑏2	PROPN
iajs-2803	105	11	𝑏3	𝑏3	PROPN
iajs-2803	105	12	𝑔1	𝑔1	PROPN
iajs-2803	105	13	𝑔2	𝑔2	VERB
iajs-2803	105	14	𝑔3	𝑔3	ADJ
iajs-2803	105	15	]	]	PUNCT
iajs-2803	105	16	[	[	PUNCT
iajs-2803	105	17	𝑦𝑛	𝑦𝑛	NOUN
iajs-2803	105	18	ℎ𝑦𝑛	ℎ𝑦𝑛	NOUN
iajs-2803	105	19	′	′	X
iajs-2803	105	20	ℎ2𝑦𝑛	ℎ2𝑦𝑛	X
iajs-2803	106	1	′′	′′	PROPN
iajs-2803	106	2	]	]	PUNCT
iajs-2803	106	3	(	(	PUNCT
iajs-2803	106	4	2.41	2.41	NUM
iajs-2803	106	5	)	)	PUNCT
iajs-2803	106	6	also	also	ADV
iajs-2803	106	7	,	,	PUNCT
iajs-2803	106	8	the	the	DET
iajs-2803	106	9	matrix	matrix	NOUN
iajs-2803	106	10	format	format	NOUN
iajs-2803	106	11	of	of	ADP
iajs-2803	106	12	eq	eq	PROPN
iajs-2803	106	13	.	.	PUNCT
iajs-2803	107	1	(	(	PUNCT
iajs-2803	107	2	2.30	2.30	NUM
iajs-2803	107	3	)	)	PUNCT
iajs-2803	107	4	can	can	AUX
iajs-2803	107	5	be	be	AUX
iajs-2803	107	6	defined	define	VERB
iajs-2803	107	7	as	as	ADP
iajs-2803	107	8	[	[	PUNCT
iajs-2803	107	9	𝑌1	𝑌1	NOUN
iajs-2803	107	10	𝑌2	𝑌2	NOUN
iajs-2803	107	11	⋮	⋮	NOUN
iajs-2803	107	12	𝑌𝑚	𝑌𝑚	PROPN
iajs-2803	107	13	]	]	PUNCT
iajs-2803	108	1	=	=	PUNCT
iajs-2803	108	2	[	[	PUNCT
iajs-2803	108	3	1	1	NUM
iajs-2803	108	4	1	1	NUM
iajs-2803	108	5	⋮	⋮	NOUN
iajs-2803	108	6	1	1	NUM
iajs-2803	108	7	0	0	NUM
iajs-2803	108	8	𝑐2	𝑐2	NOUN
iajs-2803	108	9	⋮	⋮	NOUN
iajs-2803	108	10	𝑐𝑚	𝑐𝑚	X
iajs-2803	108	11	0	0	NUM
iajs-2803	108	12	𝑐2	𝑐2	NOUN
iajs-2803	108	13	2	2	NUM
iajs-2803	108	14	⋮	⋮	NOUN
iajs-2803	108	15	𝑐𝑚	𝑐𝑚	NOUN
iajs-2803	108	16	2	2	NUM
iajs-2803	108	17	]	]	PUNCT
iajs-2803	108	18	[	[	PUNCT
iajs-2803	108	19	𝑦𝑛	𝑦𝑛	NOUN
iajs-2803	108	20	ℎ𝑦𝑛	ℎ𝑦𝑛	NOUN
iajs-2803	108	21	′	′	NOUN
iajs-2803	108	22	⋮	⋮	NOUN
iajs-2803	108	23	ℎ2𝑦𝑛	ℎ2𝑦𝑛	X
iajs-2803	109	1	′′	′′	PROPN
iajs-2803	109	2	]	]	PUNCT
iajs-2803	110	1	+	+	CCONJ
iajs-2803	110	2	(	(	PUNCT
iajs-2803	110	3	−𝛾3ℎ3	−𝛾3ℎ3	PROPN
iajs-2803	110	4	)	)	PUNCT
iajs-2803	110	5	[	[	PUNCT
iajs-2803	110	6	0	0	NUM
iajs-2803	110	7	0	0	NUM
iajs-2803	110	8	⋯	⋯	NOUN
iajs-2803	110	9	0	0	NUM
iajs-2803	110	10	𝑎21	𝑎21	PROPN
iajs-2803	110	11	0	0	NUM
iajs-2803	110	12	⋯	⋯	NOUN
iajs-2803	110	13	0	0	NUM
iajs-2803	110	14	⋮	⋮	PROPN
iajs-2803	110	15	𝑎𝑚1	𝑎𝑚1	PROPN
iajs-2803	110	16	⋮	⋮	PROPN
iajs-2803	110	17	𝑎𝑚2	𝑎𝑚2	NOUN
iajs-2803	110	18	⋱	⋱	PUNCT
iajs-2803	110	19	⋮	⋮	NOUN
iajs-2803	110	20	…	…	PUNCT
iajs-2803	110	21	𝑎𝑚−1	𝑎𝑚−1	NOUN
iajs-2803	110	22	]	]	PUNCT
iajs-2803	110	23	[	[	PUNCT
iajs-2803	110	24	𝑌1	𝑌1	NOUN
iajs-2803	110	25	𝑌2	𝑌2	NOUN
iajs-2803	110	26	⋮	⋮	NOUN
iajs-2803	110	27	𝑌𝑚	𝑌𝑚	PROPN
iajs-2803	110	28	]	]	PUNCT
iajs-2803	110	29	(	(	PUNCT
iajs-2803	110	30	2.42	2.42	NUM
iajs-2803	110	31	)	)	PUNCT
iajs-2803	110	32	where	where	SCONJ
iajs-2803	110	33	𝑚	𝑚	NOUN
iajs-2803	110	34	=	=	SYM
iajs-2803	110	35	3	3	X
iajs-2803	110	36	.	.	PUNCT
iajs-2803	111	1	therefore	therefore	ADV
iajs-2803	111	2	,	,	PUNCT
iajs-2803	111	3	[	[	PUNCT
iajs-2803	111	4	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2803	111	5	ℎ𝑦𝑛+1	ℎ𝑦𝑛+1	ADJ
iajs-2803	111	6	′	′	NOUN
iajs-2803	111	7	ℎ2𝑦𝑛+1	ℎ2𝑦𝑛+1	NOUN
iajs-2803	111	8	′′	′′	PROPN
iajs-2803	111	9	]	]	PUNCT
iajs-2803	111	10	=	=	SYM
iajs-2803	111	11	𝑓(𝐻	𝑓(𝐻	NOUN
iajs-2803	111	12	)	)	PUNCT
iajs-2803	111	13	[	[	PUNCT
iajs-2803	111	14	𝑦𝑛	𝑦𝑛	NOUN
iajs-2803	111	15	ℎ𝑦𝑛	ℎ𝑦𝑛	NOUN
iajs-2803	111	16	′	′	X
iajs-2803	111	17	ℎ2𝑦𝑛	ℎ2𝑦𝑛	X
iajs-2803	112	1	′′	′′	PROPN
iajs-2803	112	2	]	]	PUNCT
iajs-2803	112	3	,	,	PUNCT
iajs-2803	112	4	𝐻	𝐻	PROPN
iajs-2803	112	5	=	=	SYM
iajs-2803	112	6	(	(	PUNCT
iajs-2803	112	7	−𝛾3ℎ3	−𝛾3ℎ3	PROPN
iajs-2803	112	8	)	)	PUNCT
iajs-2803	112	9	(	(	PUNCT
iajs-2803	112	10	2.43	2.43	NUM
iajs-2803	112	11	)	)	PUNCT
iajs-2803	112	12	and	and	CCONJ
iajs-2803	112	13	𝑓(𝐻	𝑓(𝐻	NOUN
iajs-2803	112	14	)	)	PUNCT
iajs-2803	113	1	=	=	PUNCT
iajs-2803	113	2	[	[	PUNCT
iajs-2803	113	3	1	1	NUM
iajs-2803	113	4	+	+	NUM
iajs-2803	113	5	𝐻𝑑𝑇𝑃−1𝐸1	𝐻𝑑𝑇𝑃−1𝐸1	NOUN
iajs-2803	113	6	1	1	NUM
iajs-2803	113	7	+	+	CCONJ
iajs-2803	113	8	𝐻𝑑𝑇𝑃−1𝐸2	𝐻𝑑𝑇𝑃−1𝐸2	PROPN
iajs-2803	113	9	1	1	NUM
iajs-2803	113	10	+	+	CCONJ
iajs-2803	113	11	𝐻𝑑𝑇𝑃−1𝐸3	𝐻𝑑𝑇𝑃−1𝐸3	PROPN
iajs-2803	113	12	𝐻𝑏𝑇𝑃−1𝐸1	𝐻𝑏𝑇𝑃−1𝐸1	NOUN
iajs-2803	113	13	1	1	NUM
iajs-2803	113	14	+	+	CCONJ
iajs-2803	113	15	𝐻𝑏𝑇𝑃−1𝐸2	𝐻𝑏𝑇𝑃−1𝐸2	PROPN
iajs-2803	113	16	1	1	NUM
iajs-2803	113	17	+	+	CCONJ
iajs-2803	113	18	𝐻𝑏𝑇𝑃−1𝐸3	𝐻𝑏𝑇𝑃−1𝐸3	PROPN
iajs-2803	113	19	𝐻𝑔𝑇𝑃−1𝐸1	𝐻𝑔𝑇𝑃−1𝐸1	PROPN
iajs-2803	113	20	𝐻𝑔𝑇𝑃−1𝐸2	𝐻𝑔𝑇𝑃−1𝐸2	PROPN
iajs-2803	113	21	1	1	NUM
iajs-2803	113	22	+	+	CCONJ
iajs-2803	113	23	𝐻𝑏𝑇𝑃−1𝐸3	𝐻𝑏𝑇𝑃−1𝐸3	PROPN
iajs-2803	113	24	]	]	PUNCT
iajs-2803	113	25	(	(	PUNCT
iajs-2803	113	26	2.44	2.44	NUM
iajs-2803	113	27	)	)	PUNCT
iajs-2803	113	28	where	where	SCONJ
iajs-2803	113	29	𝐸1	𝐸1	NOUN
iajs-2803	113	30	=	=	PUNCT
iajs-2803	113	31	[	[	PUNCT
iajs-2803	113	32	1	1	NUM
iajs-2803	113	33	1	1	NUM
iajs-2803	113	34	1	1	NUM
iajs-2803	113	35	]	]	PUNCT
iajs-2803	113	36	,	,	PUNCT
iajs-2803	113	37	𝐸2	𝐸2	PROPN
iajs-2803	113	38	=	=	PUNCT
iajs-2803	113	39	[	[	PUNCT
iajs-2803	113	40	0	0	NUM
iajs-2803	113	41	𝑐2	𝑐2	NOUN
iajs-2803	113	42	𝑐3	𝑐3	NOUN
iajs-2803	113	43	]	]	PUNCT
iajs-2803	113	44	,	,	PUNCT
iajs-2803	113	45	𝐸3	𝐸3	NOUN
iajs-2803	113	46	=	=	PUNCT
iajs-2803	113	47	[	[	PUNCT
iajs-2803	113	48	0	0	NUM
iajs-2803	113	49	𝑐2	𝑐2	NOUN
iajs-2803	113	50	2	2	NUM
iajs-2803	113	51	𝑐𝑚	𝑐𝑚	SYM
iajs-2803	113	52	2	2	NUM
iajs-2803	113	53	]	]	PUNCT
iajs-2803	113	54	and	and	CCONJ
iajs-2803	113	55	𝑃−1	𝑃−1	ADJ
iajs-2803	113	56	=	=	X
iajs-2803	113	57	(	(	PUNCT
iajs-2803	113	58	1	1	NUM
iajs-2803	113	59	−	−	PROPN
iajs-2803	113	60	𝐻𝐴)−1	𝐻𝐴)−1	NOUN
iajs-2803	113	61	(	(	PUNCT
iajs-2803	113	62	2.45	2.45	NUM
iajs-2803	113	63	)	)	PUNCT
iajs-2803	113	64	𝐴	𝐴	NOUN
iajs-2803	113	65	=	=	PUNCT
iajs-2803	114	1	[	[	PUNCT
iajs-2803	114	2	0	0	NUM
iajs-2803	114	3	0	0	NUM
iajs-2803	114	4	⋯	⋯	NOUN
iajs-2803	114	5	0	0	NUM
iajs-2803	114	6	𝑎21	𝑎21	PROPN
iajs-2803	114	7	0	0	NUM
iajs-2803	114	8	⋯	⋯	NOUN
iajs-2803	114	9	0	0	NUM
iajs-2803	114	10	⋮	⋮	PROPN
iajs-2803	114	11	𝑎𝑚1	𝑎𝑚1	PROPN
iajs-2803	114	12	⋮	⋮	PROPN
iajs-2803	114	13	𝑎𝑚2	𝑎𝑚2	NOUN
iajs-2803	114	14	⋱	⋱	PUNCT
iajs-2803	114	15	⋮	⋮	NOUN
iajs-2803	114	16	…	…	PUNCT
iajs-2803	114	17	𝑎𝑚−1	𝑎𝑚−1	PROPN
iajs-2803	114	18	]	]	PUNCT
iajs-2803	114	19	,	,	PUNCT
iajs-2803	114	20	𝐵	𝐵	NOUN
iajs-2803	114	21	=	=	SYM
iajs-2803	114	22	[	[	PUNCT
iajs-2803	114	23	𝑑1	𝑑1	NOUN
iajs-2803	114	24	𝑑2	𝑑2	NOUN
iajs-2803	114	25	𝑑3	𝑑3	PROPN
iajs-2803	114	26	𝑏1	𝑏1	ADJ
iajs-2803	114	27	𝑏2	𝑏2	PROPN
iajs-2803	114	28	𝑏3	𝑏3	PROPN
iajs-2803	114	29	𝑔1	𝑔1	PROPN
iajs-2803	114	30	𝑔2	𝑔2	VERB
iajs-2803	114	31	𝑔3	𝑔3	ADJ
iajs-2803	114	32	]	]	PUNCT
iajs-2803	114	33	(	(	PUNCT
iajs-2803	114	34	2.46	2.46	NUM
iajs-2803	114	35	)	)	PUNCT
iajs-2803	114	36	thus	thus	ADV
iajs-2803	114	37	,	,	PUNCT
iajs-2803	114	38	the	the	DET
iajs-2803	114	39	stability	stability	NOUN
iajs-2803	114	40	polynomial	polynomial	NOUN
iajs-2803	114	41	of	of	ADP
iajs-2803	114	42	the	the	DET
iajs-2803	114	43	ditrk	ditrk	NOUN
iajs-2803	114	44	method	method	NOUN
iajs-2803	114	45	can	can	AUX
iajs-2803	114	46	be	be	AUX
iajs-2803	114	47	written	write	VERB
iajs-2803	114	48	as	as	ADP
iajs-2803	114	49	∅(𝜑	∅(𝜑	PROPN
iajs-2803	114	50	,	,	PUNCT
iajs-2803	114	51	𝐻	𝐻	PROPN
iajs-2803	114	52	)	)	PUNCT
iajs-2803	114	53	=	=	NOUN
iajs-2803	114	54	|𝜑𝐼	|𝜑𝐼	VERB
iajs-2803	114	55	−	−	NUM
iajs-2803	114	56	𝑓(𝐻)|	𝑓(𝐻)|	NOUN
iajs-2803	114	57	(	(	PUNCT
iajs-2803	114	58	2.47	2.47	NUM
iajs-2803	114	59	)	)	PUNCT
iajs-2803	114	60	where	where	SCONJ
iajs-2803	114	61	𝑓(𝐻	𝑓(𝐻	NOUN
iajs-2803	114	62	)	)	PUNCT
iajs-2803	114	63	is	be	AUX
iajs-2803	114	64	given	give	VERB
iajs-2803	114	65	value	value	NOUN
iajs-2803	114	66	,	,	PUNCT
iajs-2803	114	67	the	the	DET
iajs-2803	114	68	characteristic	characteristic	ADJ
iajs-2803	114	69	equation	equation	NOUN
iajs-2803	114	70	is	be	AUX
iajs-2803	114	71	defined	define	VERB
iajs-2803	114	72	as	as	ADP
iajs-2803	114	73	follow	follow	NOUN
iajs-2803	114	74	,	,	PUNCT
iajs-2803	114	75	∅(𝜑	∅(𝜑	NOUN
iajs-2803	114	76	,	,	PUNCT
iajs-2803	114	77	𝐻	𝐻	PROPN
iajs-2803	114	78	)	)	PUNCT
iajs-2803	114	79	=	=	PUNCT
iajs-2803	114	80	𝑃0(𝐻)𝜑3	𝑃0(𝐻)𝜑3	NOUN
iajs-2803	115	1	+	+	CCONJ
iajs-2803	115	2	𝑃1(𝐻)𝜑2	𝑃1(𝐻)𝜑2	X
iajs-2803	115	3	+	+	CCONJ
iajs-2803	115	4	𝑃2(𝐻)𝜑	𝑃2(𝐻)𝜑	NUM
iajs-2803	115	5	+	+	SYM
iajs-2803	115	6	𝑃3(𝐻	𝑃3(𝐻	NOUN
iajs-2803	115	7	)	)	PUNCT
iajs-2803	115	8	(	(	PUNCT
iajs-2803	115	9	2.48	2.48	NUM
iajs-2803	115	10	)	)	PUNCT
iajs-2803	115	11	6	6	NUM
iajs-2803	115	12	.	.	PUNCT
iajs-2803	115	13	test	test	NOUN
iajs-2803	115	14	of	of	ADP
iajs-2803	115	15	problems	problem	NOUN
iajs-2803	115	16	the	the	DET
iajs-2803	115	17	approaches	approach	NOUN
iajs-2803	115	18	that	that	PRON
iajs-2803	115	19	demonstrated	demonstrate	VERB
iajs-2803	115	20	in	in	ADP
iajs-2803	115	21	section	section	NOUN
iajs-2803	115	22	2.3	2.3	NUM
iajs-2803	115	23	tested	test	VERB
iajs-2803	115	24	with	with	ADP
iajs-2803	115	25	5	5	NUM
iajs-2803	115	26	various	various	ADJ
iajs-2803	115	27	problems	problem	NOUN
iajs-2803	115	28	in	in	ADP
iajs-2803	115	29	this	this	DET
iajs-2803	115	30	part	part	NOUN
iajs-2803	115	31	.	.	PUNCT
iajs-2803	116	1	the	the	DET
iajs-2803	116	2	numerical	numerical	ADJ
iajs-2803	116	3	results	result	NOUN
iajs-2803	116	4	of	of	ADP
iajs-2803	116	5	the	the	DET
iajs-2803	116	6	suggested	suggest	VERB
iajs-2803	116	7	approaches	approach	NOUN
iajs-2803	116	8	compared	compare	VERB
iajs-2803	116	9	with	with	ADP
iajs-2803	116	10	those	those	PRON
iajs-2803	116	11	of	of	ADP
iajs-2803	116	12	other	other	ADJ
iajs-2803	116	13	rk	rk	NOUN
iajs-2803	116	14	techniques	technique	NOUN
iajs-2803	116	15	at	at	ADP
iajs-2803	116	16	equivalent	equivalent	ADJ
iajs-2803	116	17	order	order	NOUN
iajs-2803	116	18	which	which	PRON
iajs-2803	116	19	are	be	AUX
iajs-2803	116	20	already	already	ADV
iajs-2803	116	21	available	available	ADJ
iajs-2803	116	22	.	.	PUNCT
iajs-2803	117	1	the	the	DET
iajs-2803	117	2	numerical	numerical	ADJ
iajs-2803	117	3	experiments	experiment	NOUN
iajs-2803	117	4	were	be	AUX
iajs-2803	117	5	conducted	conduct	VERB
iajs-2803	117	6	using	use	VERB
iajs-2803	117	7	the	the	DET
iajs-2803	117	8	following	following	ADJ
iajs-2803	117	9	methods	method	NOUN
iajs-2803	117	10	:	:	PUNCT
iajs-2803	117	11	(	(	PUNCT
iajs-2803	117	12	1	1	X
iajs-2803	117	13	)	)	PUNCT
iajs-2803	117	14	ditrkm5	ditrkm5	NOUN
iajs-2803	117	15	:	:	PUNCT
iajs-2803	117	16	3rd	3rd	ADJ
iajs-2803	117	17	stage	stage	NOUN
iajs-2803	117	18	5th	5th	ADJ
iajs-2803	117	19	order	order	NOUN
iajs-2803	117	20	ditrk	ditrk	NOUN
iajs-2803	117	21	approach	approach	NOUN
iajs-2803	117	22	computed	compute	VERB
iajs-2803	117	23	in	in	ADP
iajs-2803	117	24	the	the	DET
iajs-2803	117	25	present	present	ADJ
iajs-2803	117	26	work	work	NOUN
iajs-2803	117	27	.	.	PUNCT
iajs-2803	118	1	(	(	PUNCT
iajs-2803	118	2	2	2	X
iajs-2803	118	3	)	)	PUNCT
iajs-2803	118	4	radau	radau	NOUN
iajs-2803	118	5	i	i	PRON
iajs-2803	118	6	:	:	PUNCT
iajs-2803	118	7	3rd	3rd	ADJ
iajs-2803	118	8	stage	stage	NOUN
iajs-2803	118	9	5th	5th	ADJ
iajs-2803	118	10	order	order	NOUN
iajs-2803	118	11	rk	rk	NOUN
iajs-2803	118	12	technique	technique	NOUN
iajs-2803	118	13	presented	present	VERB
iajs-2803	118	14	in	in	ADP
iajs-2803	118	15	[	[	X
iajs-2803	118	16	20	20	NUM
iajs-2803	118	17	]	]	PUNCT
iajs-2803	118	18	.	.	PUNCT
iajs-2803	119	1	ibn	ibn	PROPN
iajs-2803	119	2	al	al	PROPN
iajs-2803	119	3	-	-	PUNCT
iajs-2803	119	4	haitham	haitham	PROPN
iajs-2803	119	5	jour	jour	X
iajs-2803	119	6	.	.	PROPN
iajs-2803	119	7	for	for	ADP
iajs-2803	119	8	pure	pure	ADJ
iajs-2803	119	9	&	&	CCONJ
iajs-2803	119	10	appl	appl	PROPN
iajs-2803	119	11	.	.	PUNCT
iajs-2803	120	1	sci	sci	PROPN
iajs-2803	120	2	.	.	PROPN
iajs-2803	121	1	53	53	NUM
iajs-2803	121	2	(	(	PUNCT
iajs-2803	121	3	1)2022	1)2022	PROPN
iajs-2803	121	4	98	98	NUM
iajs-2803	121	5	(	(	PUNCT
iajs-2803	121	6	3	3	NUM
iajs-2803	121	7	)	)	PUNCT
iajs-2803	121	8	radau	radau	NOUN
iajs-2803	121	9	ia	ia	PROPN
iajs-2803	121	10	:	:	PUNCT
iajs-2803	121	11	3rd	3rd	ADJ
iajs-2803	121	12	stage	stage	NOUN
iajs-2803	121	13	5th	5th	ADJ
iajs-2803	121	14	order	order	NOUN
iajs-2803	121	15	rk	rk	NOUN
iajs-2803	121	16	method	method	NOUN
iajs-2803	121	17	studied	study	VERB
iajs-2803	121	18	in	in	ADP
iajs-2803	121	19	[	[	X
iajs-2803	121	20	21	21	NUM
iajs-2803	121	21	]	]	PUNCT
iajs-2803	121	22	.	.	PUNCT
iajs-2803	122	1	(	(	PUNCT
iajs-2803	122	2	4	4	X
iajs-2803	122	3	)	)	PUNCT
iajs-2803	122	4	radau	radau	NOUN
iajs-2803	122	5	ii	ii	PROPN
iajs-2803	122	6	:	:	PUNCT
iajs-2803	122	7	3rd	3rd	ADJ
iajs-2803	122	8	stage	stage	NOUN
iajs-2803	122	9	5th	5th	ADJ
iajs-2803	122	10	order	order	NOUN
iajs-2803	122	11	rk	rk	NOUN
iajs-2803	122	12	scheme	scheme	NOUN
iajs-2803	122	13	tested	test	VERB
iajs-2803	122	14	in	in	ADP
iajs-2803	122	15	[	[	X
iajs-2803	122	16	20	20	NUM
iajs-2803	122	17	]	]	PUNCT
iajs-2803	122	18	.	.	PUNCT
iajs-2803	123	1	(	(	PUNCT
iajs-2803	123	2	5	5	X
iajs-2803	123	3	)	)	PUNCT
iajs-2803	123	4	radau	radau	NOUN
iajs-2803	123	5	iia	iia	VERB
iajs-2803	123	6	:	:	PUNCT
iajs-2803	123	7	3rd	3rd	ADJ
iajs-2803	123	8	stage	stage	NOUN
iajs-2803	123	9	5th	5th	ADJ
iajs-2803	123	10	order	order	NOUN
iajs-2803	123	11	rk	rk	NOUN
iajs-2803	123	12	approach	approach	NOUN
iajs-2803	123	13	noted	note	VERB
iajs-2803	123	14	in	in	ADP
iajs-2803	123	15	[	[	X
iajs-2803	123	16	21	21	NUM
iajs-2803	123	17	]	]	PUNCT
iajs-2803	123	18	.	.	PUNCT
iajs-2803	124	1	problem	problem	NOUN
iajs-2803	124	2	(	(	PUNCT
iajs-2803	124	3	1	1	NUM
iajs-2803	124	4	):	):	PUNCT
iajs-2803	124	5	consider	consider	VERB
iajs-2803	124	6	a	a	DET
iajs-2803	124	7	nonhomogeneous	nonhomogeneous	ADJ
iajs-2803	124	8	linear	linear	NOUN
iajs-2803	124	9	ode	ode	NOUN
iajs-2803	124	10	given	give	VERB
iajs-2803	124	11	in	in	ADP
iajs-2803	124	12	[	[	NOUN
iajs-2803	124	13	23	23	NUM
iajs-2803	124	14	]	]	PUNCT
iajs-2803	124	15	𝑦′′′(𝑥	𝑦′′′(𝑥	PROPN
iajs-2803	124	16	)	)	PUNCT
iajs-2803	124	17	=	=	SYM
iajs-2803	124	18	𝑦(𝑥	𝑦(𝑥	PROPN
iajs-2803	124	19	)	)	PUNCT
iajs-2803	124	20	+	+	SYM
iajs-2803	124	21	cos(𝑥	cos(𝑥	NOUN
iajs-2803	124	22	)	)	PUNCT
iajs-2803	124	23	,	,	PUNCT
iajs-2803	124	24	with	with	ADP
iajs-2803	124	25	𝑦(0	𝑦(0	PROPN
iajs-2803	124	26	)	)	PUNCT
iajs-2803	124	27	=	=	SYM
iajs-2803	124	28	0	0	NUM
iajs-2803	124	29	,	,	PUNCT
iajs-2803	124	30	𝑦′(0	𝑦′(0	NOUN
iajs-2803	124	31	)	)	PUNCT
iajs-2803	124	32	=	=	SYM
iajs-2803	124	33	0	0	NUM
iajs-2803	124	34	,	,	PUNCT
iajs-2803	124	35	𝑦′′(0	𝑦′′(0	NOUN
iajs-2803	124	36	)	)	PUNCT
iajs-2803	125	1	=	=	SYM
iajs-2803	125	2	1	1	NUM
iajs-2803	125	3	where	where	SCONJ
iajs-2803	125	4	𝑥	𝑥	PRON
iajs-2803	125	5	∈	∈	NOUN
iajs-2803	126	1	[	[	X
iajs-2803	126	2	0,1	0,1	NUM
iajs-2803	126	3	]	]	PUNCT
iajs-2803	126	4	,	,	PUNCT
iajs-2803	126	5	and	and	CCONJ
iajs-2803	126	6	analytic	analytic	ADJ
iajs-2803	126	7	solution	solution	NOUN
iajs-2803	126	8	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-2803	126	9	)	)	PUNCT
iajs-2803	126	10	=	=	PUNCT
iajs-2803	126	11	(	(	PUNCT
iajs-2803	126	12	e𝑥	e𝑥	NOUN
iajs-2803	126	13	−cos(𝑥)−sin	−cos(𝑥)−sin	X
iajs-2803	126	14	(	(	PUNCT
iajs-2803	126	15	𝑥	𝑥	NOUN
iajs-2803	126	16	)	)	PUNCT
iajs-2803	126	17	)	)	PUNCT
iajs-2803	126	18	2	2	NUM
iajs-2803	126	19	.	.	PUNCT
iajs-2803	127	1	problem	problem	NOUN
iajs-2803	127	2	(	(	PUNCT
iajs-2803	127	3	2	2	NUM
iajs-2803	127	4	):	):	PUNCT
iajs-2803	127	5	consider	consider	VERB
iajs-2803	127	6	the	the	DET
iajs-2803	127	7	nonhomogeneous	nonhomogeneous	ADJ
iajs-2803	127	8	nonlinear	nonlinear	ADJ
iajs-2803	127	9	ode	ode	PROPN
iajs-2803	127	10	𝑦′′′(𝑥	𝑦′′′(𝑥	PROPN
iajs-2803	127	11	)	)	PUNCT
iajs-2803	127	12	=	=	PUNCT
iajs-2803	127	13	(	(	PUNCT
iajs-2803	127	14	𝑦(𝑥))2	𝑦(𝑥))2	PROPN
iajs-2803	127	15	+	+	CCONJ
iajs-2803	127	16	cos2(𝑥	cos2(𝑥	NOUN
iajs-2803	127	17	)	)	PUNCT
iajs-2803	127	18	−	−	PROPN
iajs-2803	127	19	cos(𝑥	cos(𝑥	PROPN
iajs-2803	127	20	)	)	PUNCT
iajs-2803	127	21	−	−	PROPN
iajs-2803	128	1	1	1	NUM
iajs-2803	128	2	,	,	PUNCT
iajs-2803	128	3	with	with	ADP
iajs-2803	128	4	𝑦(0	𝑦(0	PROPN
iajs-2803	128	5	)	)	PUNCT
iajs-2803	128	6	=	=	SYM
iajs-2803	128	7	0	0	NUM
iajs-2803	128	8	,	,	PUNCT
iajs-2803	128	9	𝑦′(0	𝑦′(0	NOUN
iajs-2803	128	10	)	)	PUNCT
iajs-2803	128	11	=	=	SYM
iajs-2803	128	12	1	1	NUM
iajs-2803	128	13	,	,	PUNCT
iajs-2803	128	14	𝑦′′(0	𝑦′′(0	NOUN
iajs-2803	128	15	)	)	PUNCT
iajs-2803	128	16	=	=	SYM
iajs-2803	129	1	1	1	NUM
iajs-2803	129	2	where	where	SCONJ
iajs-2803	129	3	0	0	NUM
iajs-2803	129	4	≤	≤	NUM
iajs-2803	129	5	𝑥	𝑥	DET
iajs-2803	129	6	≤	≤	NUM
iajs-2803	129	7	2	2	NUM
iajs-2803	129	8	,	,	PUNCT
iajs-2803	129	9	the	the	DET
iajs-2803	129	10	exact	exact	ADJ
iajs-2803	129	11	solution	solution	NOUN
iajs-2803	129	12	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-2803	129	13	)	)	PUNCT
iajs-2803	129	14	=	=	SYM
iajs-2803	129	15	sin	sin	NOUN
iajs-2803	129	16	(	(	PUNCT
iajs-2803	129	17	𝑥	𝑥	NOUN
iajs-2803	129	18	)	)	PUNCT
iajs-2803	129	19	.	.	PUNCT
iajs-2803	130	1	problem	problem	NOUN
iajs-2803	130	2	(	(	PUNCT
iajs-2803	130	3	3	3	NUM
iajs-2803	130	4	):	):	PUNCT
iajs-2803	130	5	the	the	DET
iajs-2803	130	6	nonhomogeneous	nonhomogeneous	ADJ
iajs-2803	130	7	nonlinear	nonlinear	ADJ
iajs-2803	130	8	odes	ode	NOUN
iajs-2803	130	9	is	be	AUX
iajs-2803	130	10	considered	consider	VERB
iajs-2803	130	11	as	as	ADP
iajs-2803	130	12	𝑦1	𝑦1	PROPN
iajs-2803	130	13	′′′(𝑥	′′′(𝑥	PROPN
iajs-2803	130	14	)	)	PUNCT
iajs-2803	130	15	=	=	PUNCT
iajs-2803	130	16	𝑦2(𝑥	𝑦2(𝑥	NUM
iajs-2803	130	17	)	)	PUNCT
iajs-2803	130	18	,	,	PUNCT
iajs-2803	130	19	with	with	ADP
iajs-2803	130	20	𝑦1(0	𝑦1(0	PROPN
iajs-2803	130	21	)	)	PUNCT
iajs-2803	130	22	=	=	SYM
iajs-2803	131	1	1	1	NUM
iajs-2803	131	2	,	,	PUNCT
iajs-2803	131	3	𝑦1	𝑦1	NOUN
iajs-2803	131	4	′	′	NUM
iajs-2803	131	5	(	(	PUNCT
iajs-2803	131	6	0	0	NUM
iajs-2803	131	7	)	)	PUNCT
iajs-2803	131	8	=	=	SYM
iajs-2803	131	9	0	0	NUM
iajs-2803	131	10	,	,	PUNCT
iajs-2803	131	11	𝑦1	𝑦1	NOUN
iajs-2803	131	12	′′(0	′′(0	NOUN
iajs-2803	131	13	)	)	PUNCT
iajs-2803	131	14	=	=	SYM
iajs-2803	131	15	1	1	NUM
iajs-2803	131	16	,	,	PUNCT
iajs-2803	131	17	𝑦2	𝑦2	PROPN
iajs-2803	131	18	′′′(𝑥	′′′(𝑥	PROPN
iajs-2803	131	19	)	)	PUNCT
iajs-2803	131	20	=	=	SYM
iajs-2803	131	21	−𝑦1(𝑥	−𝑦1(𝑥	NOUN
iajs-2803	131	22	)	)	PUNCT
iajs-2803	132	1	−	−	PROPN
iajs-2803	132	2	2	2	NUM
iajs-2803	132	3	𝑦2(𝑥	𝑦2(𝑥	NOUN
iajs-2803	132	4	)	)	PUNCT
iajs-2803	133	1	+	+	CCONJ
iajs-2803	133	2	2	2	NUM
iajs-2803	133	3	𝑦3(𝑥	𝑦3(𝑥	NUM
iajs-2803	133	4	)	)	PUNCT
iajs-2803	133	5	with	with	ADP
iajs-2803	133	6	𝑦2(0	𝑦2(0	PROPN
iajs-2803	133	7	)	)	PUNCT
iajs-2803	133	8	=	=	SYM
iajs-2803	134	1	0	0	NUM
iajs-2803	134	2	,	,	PUNCT
iajs-2803	134	3	𝑦2	𝑦2	PROPN
iajs-2803	134	4	′	′	NUM
iajs-2803	134	5	(	(	PUNCT
iajs-2803	134	6	0	0	NUM
iajs-2803	134	7	)	)	PUNCT
iajs-2803	134	8	=	=	SYM
iajs-2803	134	9	1	1	NUM
iajs-2803	134	10	,	,	PUNCT
iajs-2803	134	11	𝑦2	𝑦2	NOUN
iajs-2803	134	12	′′(0	′′(0	NOUN
iajs-2803	134	13	)	)	PUNCT
iajs-2803	134	14	=	=	SYM
iajs-2803	134	15	0	0	NUM
iajs-2803	134	16	,	,	PUNCT
iajs-2803	134	17	𝑦3	𝑦3	PROPN
iajs-2803	134	18	′′′(𝑥	′′′(𝑥	PROPN
iajs-2803	134	19	)	)	PUNCT
iajs-2803	134	20	=	=	SYM
iajs-2803	134	21	𝑦1(𝑥	𝑦1(𝑥	X
iajs-2803	134	22	)	)	PUNCT
iajs-2803	134	23	+	+	NUM
iajs-2803	134	24	𝑦2(𝑥	𝑦2(𝑥	NUM
iajs-2803	134	25	)	)	PUNCT
iajs-2803	134	26	with	with	ADP
iajs-2803	134	27	𝑦3(0	𝑦3(0	PROPN
iajs-2803	134	28	)	)	PUNCT
iajs-2803	134	29	=	=	SYM
iajs-2803	135	1	1	1	NUM
iajs-2803	135	2	,	,	PUNCT
iajs-2803	135	3	𝑦3	𝑦3	PROPN
iajs-2803	135	4	′	′	PROPN
iajs-2803	135	5	(	(	PUNCT
iajs-2803	135	6	0	0	NUM
iajs-2803	135	7	)	)	PUNCT
iajs-2803	135	8	=	=	SYM
iajs-2803	135	9	1	1	NUM
iajs-2803	135	10	,	,	PUNCT
iajs-2803	135	11	𝑦3	𝑦3	PROPN
iajs-2803	135	12	′′(0	′′(0	PRON
iajs-2803	135	13	)	)	PUNCT
iajs-2803	135	14	=	=	PUNCT
iajs-2803	135	15	1,with	1,with	NUM
iajs-2803	135	16	analytic	analytic	ADJ
iajs-2803	135	17	solution	solution	NOUN
iajs-2803	135	18	𝑦1(𝑥	𝑦1(𝑥	NUM
iajs-2803	135	19	)	)	PUNCT
iajs-2803	135	20	=	=	SYM
iajs-2803	135	21	cosh	cosh	NOUN
iajs-2803	135	22	(	(	PUNCT
iajs-2803	135	23	𝑥	𝑥	NOUN
iajs-2803	135	24	)	)	PUNCT
iajs-2803	135	25	,	,	PUNCT
iajs-2803	135	26	𝑦2(𝑥	𝑦2(𝑥	NUM
iajs-2803	135	27	)	)	PUNCT
iajs-2803	135	28	=	=	VERB
iajs-2803	135	29	sinh	sinh	NOUN
iajs-2803	135	30	(	(	PUNCT
iajs-2803	135	31	𝑥	𝑥	NOUN
iajs-2803	135	32	)	)	PUNCT
iajs-2803	135	33	and	and	CCONJ
iajs-2803	135	34	𝑦3(𝑥	𝑦3(𝑥	NUM
iajs-2803	135	35	)	)	PUNCT
iajs-2803	135	36	=	=	SYM
iajs-2803	135	37	e𝑥	e𝑥	NOUN
iajs-2803	135	38	where	where	SCONJ
iajs-2803	135	39	0	0	NUM
iajs-2803	135	40	≤	≤	NUM
iajs-2803	135	41	𝑥	𝑥	PUNCT
iajs-2803	135	42	≤	≤	NUM
iajs-2803	135	43	1	1	NUM
iajs-2803	135	44	.	.	X
iajs-2803	135	45	7	7	NUM
iajs-2803	135	46	.	.	NOUN
iajs-2803	135	47	numerical	numerical	PROPN
iajs-2803	135	48	results	result	NOUN
iajs-2803	135	49	figure	figure	NOUN
iajs-2803	135	50	(	(	PUNCT
iajs-2803	135	51	2.1	2.1	NUM
iajs-2803	135	52	)	)	PUNCT
iajs-2803	135	53	shows	show	VERB
iajs-2803	135	54	the	the	DET
iajs-2803	135	55	efficiency	efficiency	NOUN
iajs-2803	135	56	of	of	ADP
iajs-2803	135	57	the	the	DET
iajs-2803	135	58	ditrkm	ditrkm	NOUN
iajs-2803	135	59	methods	method	NOUN
iajs-2803	135	60	created	create	VERB
iajs-2803	135	61	by	by	ADP
iajs-2803	135	62	charting	chart	VERB
iajs-2803	135	63	of	of	ADP
iajs-2803	135	64	decimal	decimal	ADJ
iajs-2803	135	65	logarithm	logarithm	NOUN
iajs-2803	135	66	for	for	ADP
iajs-2803	135	67	the	the	DET
iajs-2803	135	68	highest	high	ADJ
iajs-2803	135	69	"	"	PUNCT
iajs-2803	135	70	global	global	ADJ
iajs-2803	135	71	error	error	NOUN
iajs-2803	135	72	"	"	PUNCT
iajs-2803	135	73	versus	versus	ADP
iajs-2803	135	74	logarithm	logarithm	NOUN
iajs-2803	135	75	of	of	ADP
iajs-2803	135	76	function	function	NOUN
iajs-2803	135	77	estimate	estimate	NOUN
iajs-2803	135	78	.	.	PUNCT
iajs-2803	136	1	problem	problem	NOUN
iajs-2803	136	2	1	1	NUM
iajs-2803	136	3	problem	problem	NOUN
iajs-2803	136	4	2	2	NUM
iajs-2803	136	5	problem	problem	NOUN
iajs-2803	136	6	3	3	NUM
iajs-2803	136	7	figure	figure	NOUN
iajs-2803	136	8	2.1	2.1	NUM
iajs-2803	136	9	:	:	PUNCT
iajs-2803	136	10	accuracy	accuracy	NOUN
iajs-2803	136	11	curve	curve	NOUN
iajs-2803	136	12	for	for	ADP
iajs-2803	136	13	ditrkm5	ditrkm5	NOUN
iajs-2803	136	14	,	,	PUNCT
iajs-2803	136	15	radau	radau	NOUN
iajs-2803	136	16	i	i	PRON
iajs-2803	136	17	,	,	PUNCT
iajs-2803	136	18	radau	radau	PROPN
iajs-2803	136	19	ia	ia	PROPN
iajs-2803	136	20	,	,	PUNCT
iajs-2803	136	21	radau	radau	PROPN
iajs-2803	136	22	ii	ii	PROPN
iajs-2803	136	23	and	and	CCONJ
iajs-2803	136	24	radau	radau	NOUN
iajs-2803	136	25	iia	iia	VERB
iajs-2803	136	26	with	with	ADP
iajs-2803	136	27	h	h	NOUN
iajs-2803	136	28	=	=	NOUN
iajs-2803	136	29	0.1	0.1	NUM
iajs-2803	136	30	,	,	PUNCT
iajs-2803	136	31	0.05	0.05	NUM
iajs-2803	136	32	0.025	0.025	NUM
iajs-2803	136	33	,	,	PUNCT
iajs-2803	136	34	0.00125	0.00125	NUM
iajs-2803	136	35	,	,	PUNCT
iajs-2803	136	36	0.00625	0.00625	NUM
iajs-2803	136	37	for	for	ADP
iajs-2803	136	38	the	the	DET
iajs-2803	136	39	problem	problem	NOUN
iajs-2803	136	40	1	1	NUM
iajs-2803	136	41	,	,	PUNCT
iajs-2803	136	42	problem	problem	NOUN
iajs-2803	136	43	2	2	NUM
iajs-2803	136	44	and	and	CCONJ
iajs-2803	136	45	problem	problem	NOUN
iajs-2803	136	46	3	3	X
iajs-2803	136	47	.	.	PUNCT
iajs-2803	137	1	when	when	SCONJ
iajs-2803	137	2	compared	compare	VERB
iajs-2803	137	3	the	the	DET
iajs-2803	137	4	current	current	ADJ
iajs-2803	137	5	study	study	NOUN
iajs-2803	137	6	with	with	ADP
iajs-2803	137	7	another	another	DET
iajs-2803	137	8	implicit	implicit	ADJ
iajs-2803	137	9	rk	rk	NOUN
iajs-2803	137	10	approach	approach	NOUN
iajs-2803	137	11	for	for	ADP
iajs-2803	137	12	equivalent	equivalent	ADJ
iajs-2803	137	13	order	order	NOUN
iajs-2803	137	14	,	,	PUNCT
iajs-2803	137	15	the	the	DET
iajs-2803	137	16	ditrkm5	ditrkm5	NOUN
iajs-2803	137	17	method	method	NOUN
iajs-2803	137	18	requires	require	VERB
iajs-2803	137	19	fewer	few	ADJ
iajs-2803	137	20	"	"	PUNCT
iajs-2803	137	21	function	function	NOUN
iajs-2803	137	22	evaluations	evaluation	NOUN
iajs-2803	137	23	"	"	PUNCT
iajs-2803	137	24	.	.	PUNCT
iajs-2803	138	1	the	the	DET
iajs-2803	138	2	digit	digit	NOUN
iajs-2803	138	3	of	of	ADP
iajs-2803	138	4	equations	equation	NOUN
iajs-2803	138	5	increased	increase	VERB
iajs-2803	138	6	three	three	NUM
iajs-2803	138	7	times	time	NOUN
iajs-2803	138	8	with	with	ADP
iajs-2803	138	9	the	the	DET
iajs-2803	138	10	problems	problem	NOUN
iajs-2803	138	11	turned	turn	VERB
iajs-2803	138	12	to	to	ADP
iajs-2803	138	13	a	a	DET
iajs-2803	138	14	system	system	NOUN
iajs-2803	138	15	of	of	ADP
iajs-2803	138	16	1st	1st	ADJ
iajs-2803	138	17	order	order	NOUN
iajs-2803	138	18	odes	ode	VERB
iajs-2803	138	19	.	.	PUNCT
iajs-2803	139	1	in	in	ADP
iajs-2803	139	2	the	the	DET
iajs-2803	139	3	comparison	comparison	NOUN
iajs-2803	139	4	,	,	PUNCT
iajs-2803	139	5	the	the	DET
iajs-2803	139	6	existing	exist	VERB
iajs-2803	139	7	implicit	implicit	NOUN
iajs-2803	139	8	the	the	DET
iajs-2803	139	9	rk	rk	NOUN
iajs-2803	139	10	approach	approach	NOUN
iajs-2803	139	11	with	with	ADP
iajs-2803	139	12	the	the	DET
iajs-2803	139	13	equivalent	equivalent	ADJ
iajs-2803	139	14	order	order	NOUN
iajs-2803	139	15	,	,	PUNCT
iajs-2803	139	16	the	the	DET
iajs-2803	139	17	"	"	PUNCT
iajs-2803	139	18	global	global	ADJ
iajs-2803	139	19	error	error	NOUN
iajs-2803	139	20	"	"	PUNCT
iajs-2803	139	21	and	and	CCONJ
iajs-2803	139	22	digit	digit	NOUN
iajs-2803	139	23	of	of	ADP
iajs-2803	139	24	"	"	PUNCT
iajs-2803	139	25	function	function	NOUN
iajs-2803	139	26	estimate	estimate	NOUN
iajs-2803	139	27	"	"	PUNCT
iajs-2803	139	28	contain	contain	VERB
iajs-2803	139	29	the	the	DET
iajs-2803	139	30	smallest	small	ADJ
iajs-2803	139	31	maximum	maximum	NOUN
iajs-2803	139	32	for	for	ADP
iajs-2803	139	33	the	the	DET
iajs-2803	139	34	ditrkm5	ditrkm5	NOUN
iajs-2803	139	35	method	method	NOUN
iajs-2803	139	36	at	at	ADP
iajs-2803	139	37	each	each	DET
iajs-2803	139	38	iteration	iteration	NOUN
iajs-2803	139	39	,	,	PUNCT
iajs-2803	139	40	as	as	SCONJ
iajs-2803	139	41	shown	show	VERB
iajs-2803	139	42	in	in	ADP
iajs-2803	139	43	figure	figure	NOUN
iajs-2803	139	44	(	(	PUNCT
iajs-2803	139	45	2.1	2.1	NUM
iajs-2803	139	46	)	)	PUNCT
iajs-2803	139	47	that	that	PRON
iajs-2803	139	48	obtained	obtain	VERB
iajs-2803	139	49	from	from	ADP
iajs-2803	139	50	table	table	NOUN
iajs-2803	139	51	(	(	PUNCT
iajs-2803	139	52	2.1	2.1	NUM
iajs-2803	139	53	)	)	PUNCT
iajs-2803	139	54	.	.	PUNCT
iajs-2803	140	1	as	as	SCONJ
iajs-2803	140	2	shown	show	VERB
iajs-2803	140	3	in	in	ADP
iajs-2803	140	4	figure	figure	NOUN
iajs-2803	140	5	(	(	PUNCT
iajs-2803	140	6	2.1	2.1	NUM
iajs-2803	140	7	)	)	PUNCT
iajs-2803	140	8	,	,	PUNCT
iajs-2803	140	9	the	the	DET
iajs-2803	140	10	fifthorder	fifthorder	ADJ
iajs-2803	140	11	three	three	NUM
iajs-2803	140	12	stage	stage	NOUN
iajs-2803	140	13	results	result	NOUN
iajs-2803	140	14	ditrk	ditrk	VERB
iajs-2803	140	15	method	method	NOUN
iajs-2803	140	16	(	(	PUNCT
iajs-2803	140	17	ditrkm5	ditrkm5	NOUN
iajs-2803	140	18	)	)	PUNCT
iajs-2803	140	19	produces	produce	VERB
iajs-2803	140	20	more	more	ADV
iajs-2803	140	21	accurate	accurate	ADJ
iajs-2803	140	22	findings	finding	NOUN
iajs-2803	140	23	than	than	ADP
iajs-2803	140	24	the	the	DET
iajs-2803	140	25	other	other	ADJ
iajs-2803	140	26	results	result	NOUN
iajs-2803	140	27	in	in	ADP
iajs-2803	140	28	the	the	DET
iajs-2803	140	29	literature	literature	NOUN
iajs-2803	140	30	(	(	PUNCT
iajs-2803	140	31	radau	radau	NOUN
iajs-2803	140	32	i	i	PRON
iajs-2803	140	33	,	,	PUNCT
iajs-2803	140	34	radau	radau	PROPN
iajs-2803	140	35	ia	ia	PROPN
iajs-2803	140	36	,	,	PUNCT
iajs-2803	140	37	radau	radau	PROPN
iajs-2803	140	38	ii	ii	PROPN
iajs-2803	140	39	,	,	PUNCT
iajs-2803	140	40	and	and	CCONJ
iajs-2803	140	41	radau	radau	NOUN
iajs-2803	140	42	iia	iia	VERB
iajs-2803	140	43	)	)	PUNCT
iajs-2803	140	44	.	.	PUNCT
iajs-2803	141	1	in	in	ADP
iajs-2803	141	2	this	this	DET
iajs-2803	141	3	work	work	NOUN
iajs-2803	141	4	,	,	PUNCT
iajs-2803	141	5	the	the	DET
iajs-2803	141	6	logarithm	logarithm	NOUN
iajs-2803	141	7	of	of	ADP
iajs-2803	141	8	"	"	PUNCT
iajs-2803	141	9	maximum	maximum	ADJ
iajs-2803	141	10	global	global	ADJ
iajs-2803	141	11	error	error	NOUN
iajs-2803	141	12	"	"	PUNCT
iajs-2803	141	13	is	be	AUX
iajs-2803	141	14	known	know	VERB
iajs-2803	141	15	as	as	ADP
iajs-2803	141	16	a	a	DET
iajs-2803	141	17	logarithm	logarithm	NOUN
iajs-2803	141	18	function	function	NOUN
iajs-2803	141	19	for	for	ADP
iajs-2803	141	20	"	"	PUNCT
iajs-2803	141	21	function	function	VERB
iajs-2803	141	22	1.8	1.8	NUM
iajs-2803	141	23	2	2	NUM
iajs-2803	141	24	2.2	2.2	NUM
iajs-2803	141	25	2.4	2.4	NUM
iajs-2803	141	26	2.6	2.6	NUM
iajs-2803	141	27	2.8	2.8	NUM
iajs-2803	141	28	3	3	NUM
iajs-2803	141	29	3.2	3.2	NUM
iajs-2803	141	30	-7	-7	NOUN
iajs-2803	142	1	-6	-6	INTJ
iajs-2803	142	2	-5	-5	INTJ
iajs-2803	143	1	-4	-4	INTJ
iajs-2803	143	2	-3	-3	INTJ
iajs-2803	143	3	-2	-2	INTJ
iajs-2803	143	4	-1	-1	INTJ
iajs-2803	143	5	log	log	NOUN
iajs-2803	143	6	(	(	PUNCT
iajs-2803	143	7	number	number	NOUN
iajs-2803	143	8	of	of	ADP
iajs-2803	143	9	function	function	NOUN
iajs-2803	143	10	call	call	NOUN
iajs-2803	143	11	)	)	PUNCT
iajs-2803	143	12	l	l	NOUN
iajs-2803	144	1	o	o	X
iajs-2803	144	2	g	g	NOUN
iajs-2803	144	3	(	(	PUNCT
iajs-2803	144	4	m	m	VERB
iajs-2803	144	5	a	a	PRON
iajs-2803	144	6	x	x	SYM
iajs-2803	144	7	g	g	PROPN
iajs-2803	144	8	lo	lo	PROPN
iajs-2803	144	9	b	b	PROPN
iajs-2803	144	10	a	a	DET
iajs-2803	144	11	l	l	NOUN
iajs-2803	144	12	e	e	NOUN
iajs-2803	144	13	rr	rr	NOUN
iajs-2803	144	14	o	o	NOUN
iajs-2803	144	15	rs	rs	NOUN
iajs-2803	144	16	)	)	PUNCT
iajs-2803	144	17	ditrkm5	ditrkm5	NOUN
iajs-2803	144	18	radau	radau	NOUN
iajs-2803	144	19	i	i	PRON
iajs-2803	144	20	radau	radau	VERB
iajs-2803	144	21	ia	ia	PROPN
iajs-2803	144	22	radau	radau	PROPN
iajs-2803	144	23	ii	ii	PROPN
iajs-2803	144	24	radau	radau	NOUN
iajs-2803	144	25	iia	iia	VERB
iajs-2803	144	26	2	2	NUM
iajs-2803	144	27	2.5	2.5	NUM
iajs-2803	144	28	3	3	NUM
iajs-2803	144	29	3.5	3.5	NUM
iajs-2803	144	30	-6	-6	ADP
iajs-2803	144	31	-5.5	-5.5	PUNCT
iajs-2803	144	32	-5	-5	INTJ
iajs-2803	144	33	-4.5	-4.5	INTJ
iajs-2803	144	34	-4	-4	INTJ
iajs-2803	144	35	-3.5	-3.5	INTJ
iajs-2803	144	36	-3	-3	PUNCT
iajs-2803	144	37	-2.5	-2.5	INTJ
iajs-2803	145	1	-2	-2	INTJ
iajs-2803	145	2	-1.5	-1.5	PUNCT
iajs-2803	145	3	-1	-1	INTJ
iajs-2803	146	1	log	log	NOUN
iajs-2803	146	2	(	(	PUNCT
iajs-2803	146	3	number	number	NOUN
iajs-2803	146	4	of	of	ADP
iajs-2803	146	5	function	function	NOUN
iajs-2803	146	6	call	call	NOUN
iajs-2803	146	7	)	)	PUNCT
iajs-2803	147	1	l	l	NOUN
iajs-2803	147	2	o	o	X
iajs-2803	147	3	g	g	NOUN
iajs-2803	147	4	(	(	PUNCT
iajs-2803	147	5	m	m	VERB
iajs-2803	147	6	a	a	PRON
iajs-2803	147	7	x	x	SYM
iajs-2803	147	8	g	g	PROPN
iajs-2803	147	9	lo	lo	PROPN
iajs-2803	147	10	b	b	PROPN
iajs-2803	147	11	a	a	DET
iajs-2803	147	12	l	l	NOUN
iajs-2803	147	13	e	e	NOUN
iajs-2803	147	14	rr	rr	NOUN
iajs-2803	147	15	o	o	NOUN
iajs-2803	147	16	rs	rs	NOUN
iajs-2803	147	17	)	)	PUNCT
iajs-2803	147	18	ditrkm5	ditrkm5	NOUN
iajs-2803	147	19	radau	radau	NOUN
iajs-2803	147	20	i	i	PRON
iajs-2803	147	21	radau	radau	VERB
iajs-2803	147	22	ia	ia	PROPN
iajs-2803	147	23	radau	radau	PROPN
iajs-2803	147	24	ii	ii	PROPN
iajs-2803	147	25	radau	radau	NOUN
iajs-2803	147	26	iia	iia	VERB
iajs-2803	147	27	1.8	1.8	NUM
iajs-2803	147	28	2	2	NUM
iajs-2803	147	29	2.2	2.2	NUM
iajs-2803	147	30	2.4	2.4	NUM
iajs-2803	147	31	2.6	2.6	NUM
iajs-2803	147	32	2.8	2.8	NUM
iajs-2803	147	33	3	3	NUM
iajs-2803	147	34	3.2	3.2	NUM
iajs-2803	147	35	3.4	3.4	NUM
iajs-2803	147	36	3.6	3.6	NUM
iajs-2803	147	37	-7	-7	NOUN
iajs-2803	148	1	-6	-6	INTJ
iajs-2803	148	2	-5	-5	INTJ
iajs-2803	148	3	-4	-4	INTJ
iajs-2803	148	4	-3	-3	INTJ
iajs-2803	148	5	-2	-2	INTJ
iajs-2803	148	6	-1	-1	INTJ
iajs-2803	148	7	0	0	NUM
iajs-2803	148	8	log	log	NOUN
iajs-2803	148	9	(	(	PUNCT
iajs-2803	148	10	number	number	NOUN
iajs-2803	148	11	of	of	ADP
iajs-2803	148	12	function	function	NOUN
iajs-2803	148	13	call	call	NOUN
iajs-2803	148	14	)	)	PUNCT
iajs-2803	149	1	l	l	NOUN
iajs-2803	149	2	o	o	X
iajs-2803	149	3	g	g	NOUN
iajs-2803	149	4	(	(	PUNCT
iajs-2803	149	5	m	m	VERB
iajs-2803	149	6	a	a	PRON
iajs-2803	149	7	x	x	SYM
iajs-2803	149	8	g	g	PROPN
iajs-2803	149	9	lo	lo	PROPN
iajs-2803	149	10	b	b	PROPN
iajs-2803	149	11	a	a	DET
iajs-2803	149	12	l	l	NOUN
iajs-2803	149	13	e	e	NOUN
iajs-2803	149	14	rr	rr	NOUN
iajs-2803	149	15	o	o	NOUN
iajs-2803	149	16	rs	rs	NOUN
iajs-2803	149	17	)	)	PUNCT
iajs-2803	149	18	ditrkm5	ditrkm5	NOUN
iajs-2803	149	19	radau	radau	NOUN
iajs-2803	149	20	i	i	PRON
iajs-2803	149	21	radau	radau	VERB
iajs-2803	149	22	ia	ia	PROPN
iajs-2803	149	23	radau	radau	PROPN
iajs-2803	149	24	ii	ii	PROPN
iajs-2803	149	25	radau	radau	NOUN
iajs-2803	149	26	iia	iia	VERB
iajs-2803	149	27	ibn	ibn	PROPN
iajs-2803	149	28	al	al	PROPN
iajs-2803	149	29	-	-	PUNCT
iajs-2803	149	30	haitham	haitham	PROPN
iajs-2803	149	31	jour	jour	X
iajs-2803	149	32	.	.	PROPN
iajs-2803	150	1	for	for	ADP
iajs-2803	150	2	pure	pure	ADJ
iajs-2803	150	3	&	&	CCONJ
iajs-2803	150	4	appl	appl	PROPN
iajs-2803	150	5	.	.	PUNCT
iajs-2803	151	1	sci	sci	PROPN
iajs-2803	151	2	.	.	PROPN
iajs-2803	152	1	53	53	NUM
iajs-2803	152	2	(	(	PUNCT
iajs-2803	152	3	1)2022	1)2022	NOUN
iajs-2803	152	4	99	99	NUM
iajs-2803	152	5	evaluation	evaluation	NOUN
iajs-2803	152	6	"	"	PUNCT
iajs-2803	152	7	with	with	ADP
iajs-2803	152	8	different	different	ADJ
iajs-2803	152	9	step	step	NOUN
iajs-2803	152	10	size	size	NOUN
iajs-2803	152	11	ℎ	ℎ	PROPN
iajs-2803	152	12	=	=	NOUN
iajs-2803	152	13	0.1	0.1	NUM
iajs-2803	152	14	,	,	PUNCT
iajs-2803	152	15	0.05	0.05	NUM
iajs-2803	152	16	,	,	PUNCT
iajs-2803	152	17	0.025	0.025	NUM
iajs-2803	152	18	,	,	PUNCT
iajs-2803	152	19	0.0125,0.00625	0.0125,0.00625	NUM
iajs-2803	152	20	for	for	ADP
iajs-2803	152	21	five	five	NUM
iajs-2803	152	22	test	test	NOUN
iajs-2803	152	23	problems	problem	NOUN
iajs-2803	152	24	.	.	PUNCT
iajs-2803	153	1	table	table	NOUN
iajs-2803	153	2	2.1	2.1	NUM
iajs-2803	153	3	:	:	PUNCT
iajs-2803	153	4	comparisons	comparison	NOUN
iajs-2803	153	5	of	of	ADP
iajs-2803	153	6	number	number	NOUN
iajs-2803	153	7	of	of	ADP
iajs-2803	153	8	function	function	NOUN
iajs-2803	153	9	call	call	NOUN
iajs-2803	153	10	and	and	CCONJ
iajs-2803	153	11	maximum	maximum	ADJ
iajs-2803	153	12	global	global	ADJ
iajs-2803	153	13	error	error	NOUN
iajs-2803	153	14	for	for	ADP
iajs-2803	153	15	ditrkm5	ditrkm5	NOUN
iajs-2803	153	16	,	,	PUNCT
iajs-2803	153	17	radau	radau	NOUN
iajs-2803	153	18	i	i	PRON
iajs-2803	153	19	,	,	PUNCT
iajs-2803	153	20	radau	radau	PROPN
iajs-2803	153	21	ia	ia	PROPN
iajs-2803	153	22	,	,	PUNCT
iajs-2803	153	23	radau	radau	PROPN
iajs-2803	153	24	ii	ii	PROPN
iajs-2803	153	25	and	and	CCONJ
iajs-2803	153	26	radau	radau	NOUN
iajs-2803	153	27	iia	iia	VERB
iajs-2803	153	28	methods	method	NOUN
iajs-2803	153	29	with	with	ADP
iajs-2803	153	30	ℎ	ℎ	PROPN
iajs-2803	153	31	=	=	SYM
iajs-2803	153	32	0.1	0.1	NUM
iajs-2803	153	33	,	,	PUNCT
iajs-2803	153	34	0.05	0.05	NUM
iajs-2803	153	35	0.025	0.025	NUM
iajs-2803	153	36	,	,	PUNCT
iajs-2803	153	37	0.00125	0.00125	NUM
iajs-2803	153	38	,	,	PUNCT
iajs-2803	153	39	0.00625	0.00625	NUM
iajs-2803	153	40	for	for	ADP
iajs-2803	153	41	the	the	DET
iajs-2803	153	42	problem	problem	NOUN
iajs-2803	153	43	1	1	NUM
iajs-2803	153	44	,	,	PUNCT
iajs-2803	153	45	problem	problem	NOUN
iajs-2803	153	46	2	2	NUM
iajs-2803	153	47	and	and	CCONJ
iajs-2803	153	48	problem	problem	NOUN
iajs-2803	153	49	3	3	X
iajs-2803	153	50	.	.	PUNCT
iajs-2803	153	51	problem	problem	NOUN
iajs-2803	153	52	3	3	NUM
iajs-2803	153	53	problem	problem	NOUN
iajs-2803	153	54	2	2	NUM
iajs-2803	153	55	problem	problem	NOUN
iajs-2803	153	56	1	1	NUM
iajs-2803	153	57	method	method	NOUN
iajs-2803	153	58	step	step	NOUN
iajs-2803	153	59	size	size	NOUN
iajs-2803	153	60	(	(	PUNCT
iajs-2803	153	61	h	h	NOUN
iajs-2803	153	62	)	)	PUNCT
iajs-2803	153	63	maximum	maximum	ADJ
iajs-2803	153	64	global	global	ADJ
iajs-2803	153	65	error	error	NOUN
iajs-2803	153	66	maximum	maximum	NOUN
iajs-2803	153	67	global	global	ADJ
iajs-2803	153	68	error	error	NOUN
iajs-2803	153	69	maximum	maximum	NOUN
iajs-2803	153	70	global	global	ADJ
iajs-2803	153	71	error	error	NOUN
iajs-2803	153	72	no	no	NOUN
iajs-2803	153	73	.	.	PUNCT
iajs-2803	154	1	of	of	ADP
iajs-2803	154	2	function	function	NOUN
iajs-2803	154	3	call	call	VERB
iajs-2803	154	4	maximum	maximum	ADJ
iajs-2803	154	5	global	global	ADJ
iajs-2803	154	6	error	error	NOUN
iajs-2803	154	7	no	no	NOUN
iajs-2803	154	8	.	.	PUNCT
iajs-2803	155	1	of	of	ADP
iajs-2803	155	2	function	function	NOUN
iajs-2803	155	3	call	call	NOUN
iajs-2803	155	4	9.74073e-05	9.74073e-05	NUM
iajs-2803	155	5	88	88	NUM
iajs-2803	155	6	0.000277124	0.000277124	NUM
iajs-2803	155	7	160	160	NUM
iajs-2803	155	8	9.16352e-05	9.16352e-05	NUM
iajs-2803	155	9	88	88	NUM
iajs-2803	155	10	ditrkm5	ditrkm5	NOUN
iajs-2803	155	11	0.1	0.1	NUM
iajs-2803	155	12	0.05488292	0.05488292	NUM
iajs-2803	155	13	99	99	NUM
iajs-2803	155	14	0.02489423	0.02489423	NUM
iajs-2803	155	15	180	180	NUM
iajs-2803	155	16	0.02986368	0.02986368	NUM
iajs-2803	155	17	99	99	NUM
iajs-2803	155	18	radau	radau	NOUN
iajs-2803	156	1	i	i	PRON
iajs-2803	156	2	0.06335586	0.06335586	NUM
iajs-2803	156	3	99	99	NUM
iajs-2803	156	4	0.02867864	0.02867864	NUM
iajs-2803	156	5	180	180	NUM
iajs-2803	156	6	0.03449261	0.03449261	NUM
iajs-2803	156	7	99	99	NUM
iajs-2803	156	8	radau	radau	NOUN
iajs-2803	156	9	ia	ia	VERB
iajs-2803	156	10	0.05488292	0.05488292	NUM
iajs-2803	156	11	99	99	NUM
iajs-2803	156	12	0.02647426	0.02647426	NUM
iajs-2803	156	13	180	180	NUM
iajs-2803	156	14	0.02878467	0.02878467	NUM
iajs-2803	156	15	99	99	NUM
iajs-2803	156	16	radau	radau	NOUN
iajs-2803	156	17	ii	ii	VERB
iajs-2803	156	18	0.06335586	0.06335586	NUM
iajs-2803	156	19	99	99	NUM
iajs-2803	156	20	0.0298746	0.0298746	NUM
iajs-2803	156	21	180	180	NUM
iajs-2803	156	22	0.03336877	0.03336877	NUM
iajs-2803	156	23	99	99	NUM
iajs-2803	156	24	radau	radau	NOUN
iajs-2803	156	25	iia	iia	VERB
iajs-2803	156	26	1.8304e-05	1.8304e-05	NUM
iajs-2803	156	27	160	160	NUM
iajs-2803	156	28	6.8347e-05	6.8347e-05	NUM
iajs-2803	156	29	320	320	NUM
iajs-2803	156	30	1.74282e-05	1.74282e-05	NUM
iajs-2803	156	31	160	160	NUM
iajs-2803	156	32	ditrkm5	ditrkm5	NOUN
iajs-2803	156	33	0.05	0.05	NUM
iajs-2803	157	1	0.02293305	0.02293305	NUM
iajs-2803	157	2	180	180	NUM
iajs-2803	157	3	0.01292113	0.01292113	NUM
iajs-2803	157	4	360	360	NUM
iajs-2803	157	5	0.01273117	0.01273117	NUM
iajs-2803	157	6	180	180	NUM
iajs-2803	157	7	radau	radau	NOUN
iajs-2803	157	8	i	i	PRON
iajs-2803	157	9	0.02656216	0.02656216	NUM
iajs-2803	157	10	180	180	NUM
iajs-2803	157	11	0.01494992	0.01494992	NUM
iajs-2803	157	12	360	360	NUM
iajs-2803	157	13	0.01475188	0.01475188	NUM
iajs-2803	157	14	180	180	NUM
iajs-2803	157	15	radau	radau	NOUN
iajs-2803	157	16	ia	ia	PROPN
iajs-2803	157	17	0.02293305	0.02293305	NUM
iajs-2803	157	18	180	180	NUM
iajs-2803	157	19	0.01360768	0.01360768	NUM
iajs-2803	157	20	360	360	NUM
iajs-2803	157	21	0.01229666	0.01229666	NUM
iajs-2803	157	22	180	180	NUM
iajs-2803	157	23	radau	radau	NOUN
iajs-2803	157	24	ii	ii	VERB
iajs-2803	157	25	0.02656216	0.02656216	NUM
iajs-2803	157	26	180	180	NUM
iajs-2803	157	27	0.015539	0.015539	NUM
iajs-2803	157	28	360	360	NUM
iajs-2803	157	29	0.0143079	0.0143079	NUM
iajs-2803	157	30	180	180	NUM
iajs-2803	157	31	radau	radau	NOUN
iajs-2803	157	32	iia	iia	VERB
iajs-2803	157	33	4.67234e-06	4.67234e-06	NUM
iajs-2803	157	34	320	320	NUM
iajs-2803	157	35	1.79521e-05	1.79521e-05	NUM
iajs-2803	157	36	648	648	NUM
iajs-2803	157	37	4.45635e-06	4.45635e-06	NUM
iajs-2803	157	38	320	320	NUM
iajs-2803	157	39	ditrkm5	ditrkm5	NOUN
iajs-2803	157	40	0.025	0.025	NUM
iajs-2803	157	41	0.0115538	0.0115538	NUM
iajs-2803	157	42	360	360	NUM
iajs-2803	157	43	0.006847777	0.006847777	NUM
iajs-2803	157	44	729	729	NUM
iajs-2803	157	45	0.006421128	0.006421128	NUM
iajs-2803	157	46	360	360	NUM
iajs-2803	157	47	radau	radau	NOUN
iajs-2803	157	48	i	i	PRON
iajs-2803	157	49	0.01340439	0.01340439	NUM
iajs-2803	157	50	360	360	NUM
iajs-2803	157	51	0.007940234	0.007940234	NUM
iajs-2803	157	52	729	729	NUM
iajs-2803	157	53	0.007451075	0.007451075	NUM
iajs-2803	157	54	360	360	NUM
iajs-2803	157	55	radau	radau	NOUN
iajs-2803	157	56	ia	ia	PROPN
iajs-2803	157	57	0.0115538	0.0115538	NUM
iajs-2803	157	58	360	360	NUM
iajs-2803	157	59	0.007152807	0.007152807	NUM
iajs-2803	157	60	729	729	NUM
iajs-2803	157	61	0.006195875	0.006195875	NUM
iajs-2803	157	62	360	360	NUM
iajs-2803	157	63	radau	radau	NOUN
iajs-2803	157	64	ii	ii	NOUN
iajs-2803	157	65	0.01340439	0.01340439	NUM
iajs-2803	157	66	360	360	NUM
iajs-2803	157	67	0.008219884	0.008219884	NUM
iajs-2803	157	68	729	729	NUM
iajs-2803	157	69	0.007223443	0.007223443	NUM
iajs-2803	157	70	360	360	NUM
iajs-2803	157	71	radau	radau	NOUN
iajs-2803	157	72	iia	iia	VERB
iajs-2803	157	73	1.22981e-06	1.22981e-06	NUM
iajs-2803	157	74	648	648	NUM
iajs-2803	157	75	4.35276e-06	4.35276e-06	NUM
iajs-2803	157	76	1288	1288	NUM
iajs-2803	157	77	1.1728e-06	1.1728e-06	NUM
iajs-2803	157	78	648	648	NUM
iajs-2803	157	79	ditrkm5	ditrkm5	NOUN
iajs-2803	157	80	0.0125	0.0125	NUM
iajs-2803	157	81	0.005945227	0.005945227	NUM
iajs-2803	157	82	729	729	NUM
iajs-2803	157	83	0.003387183	0.003387183	NUM
iajs-2803	157	84	1449	1449	NUM
iajs-2803	157	85	0.003298104	0.003298104	NUM
iajs-2803	157	86	729	729	NUM
iajs-2803	157	87	radau	radau	NOUN
iajs-2803	158	1	i	i	PRON
iajs-2803	158	2	0.006903284	0.006903284	NUM
iajs-2803	158	3	729	729	NUM
iajs-2803	158	4	0.003931975	0.003931975	NUM
iajs-2803	158	5	1449	1449	NUM
iajs-2803	158	6	0.003829934	0.003829934	NUM
iajs-2803	158	7	729	729	NUM
iajs-2803	158	8	radau	radau	NOUN
iajs-2803	158	9	ia	ia	PROPN
iajs-2803	158	10	0.005945227	0.005945227	NUM
iajs-2803	158	11	729	729	NUM
iajs-2803	158	12	0.003535766	0.003535766	NUM
iajs-2803	158	13	1449	1449	NUM
iajs-2803	158	14	0.003179202	0.003179202	NUM
iajs-2803	158	15	729	729	NUM
iajs-2803	158	16	radau	radau	NOUN
iajs-2803	158	17	ii	ii	PROPN
iajs-2803	158	18	0.006903284	0.006903284	NUM
iajs-2803	158	19	729	729	NUM
iajs-2803	158	20	0.004074293	0.004074293	NUM
iajs-2803	158	21	1449	1449	NUM
iajs-2803	158	22	0.003710422	0.003710422	NUM
iajs-2803	158	23	729	729	NUM
iajs-2803	158	24	radau	radau	NOUN
iajs-2803	158	25	iia	iia	VERB
iajs-2803	158	26	3.02667e-07	3.02667e-07	NUM
iajs-2803	158	27	1288	1288	NUM
iajs-2803	158	28	2.88938e-06	2.88938e-06	NUM
iajs-2803	158	29	2560	2560	NUM
iajs-2803	158	30	2.88938e-07	2.88938e-07	NUM
iajs-2803	158	31	1288	1288	NUM
iajs-2803	158	32	ditrkm5	ditrkm5	NOUN
iajs-2803	158	33	0.00625	0.00625	NUM
iajs-2803	158	34	0.002941504	0.002941504	NUM
iajs-2803	158	35	1449	1449	NUM
iajs-2803	158	36	0.001667861	0.001667861	NUM
iajs-2803	158	37	2880	2880	NUM
iajs-2803	158	38	0.00163419	0.00163419	NUM
iajs-2803	158	39	1449	1449	NUM
iajs-2803	158	40	radau	radau	NOUN
iajs-2803	158	41	i	i	PRON
iajs-2803	158	42	0.003416977	0.003416977	NUM
iajs-2803	158	43	1449	1449	NUM
iajs-2803	158	44	0.001937206	0.001937206	NUM
iajs-2803	158	45	2880	2880	NUM
iajs-2803	158	46	0.001898433	0.001898433	NUM
iajs-2803	158	47	1449	1449	NUM
iajs-2803	158	48	radau	radau	NOUN
iajs-2803	158	49	ia	ia	VERB
iajs-2803	158	50	0.002941504	0.002941504	NUM
iajs-2803	158	51	1449	1449	NUM
iajs-2803	158	52	0.001741931	0.001741931	NUM
iajs-2803	158	53	2880	2880	NUM
iajs-2803	158	54	0.001575303	0.001575303	NUM
iajs-2803	158	55	1449	1449	NUM
iajs-2803	158	56	radau	radau	NOUN
iajs-2803	158	57	ii	ii	NOUN
iajs-2803	158	58	0.003416977	0.003416977	NUM
iajs-2803	158	59	1449	1449	NUM
iajs-2803	158	60	0.001741931	0.001741931	NUM
iajs-2803	158	61	2880	2880	NUM
iajs-2803	158	62	0.001839395	0.001839395	NUM
iajs-2803	158	63	1449	1449	NUM
iajs-2803	158	64	radau	radau	NOUN
iajs-2803	158	65	iia	iia	VERB
iajs-2803	158	66	8	8	NUM
iajs-2803	158	67	.	.	PUNCT
iajs-2803	159	1	conclusion	conclusion	VERB
iajs-2803	159	2	the	the	DET
iajs-2803	159	3	test	test	NOUN
iajs-2803	159	4	of	of	ADP
iajs-2803	159	5	the	the	DET
iajs-2803	159	6	fifth	fifth	ADJ
iajs-2803	159	7	-	-	PUNCT
iajs-2803	159	8	order	order	NOUN
iajs-2803	159	9	three	three	NUM
iajs-2803	159	10	-	-	PUNCT
iajs-2803	159	11	stage	stage	NOUN
iajs-2803	159	12	ditrkm5	ditrkm5	NOUN
iajs-2803	159	13	methods	method	NOUN
iajs-2803	159	14	for	for	ADP
iajs-2803	159	15	the	the	DET
iajs-2803	159	16	integration	integration	NOUN
iajs-2803	159	17	of	of	ADP
iajs-2803	159	18	odes	ode	NOUN
iajs-2803	159	19	obtained	obtain	VERB
iajs-2803	159	20	by	by	ADP
iajs-2803	159	21	testing	test	VERB
iajs-2803	159	22	the	the	DET
iajs-2803	159	23	minimized	minimized	ADJ
iajs-2803	159	24	error	error	NOUN
iajs-2803	159	25	norm	norm	NOUN
iajs-2803	159	26	and	and	CCONJ
iajs-2803	159	27	studied	study	VERB
iajs-2803	159	28	the	the	DET
iajs-2803	159	29	digit	digit	NOUN
iajs-2803	159	30	of	of	ADP
iajs-2803	159	31	the	the	DET
iajs-2803	159	32	evaluations	evaluation	NOUN
iajs-2803	159	33	of	of	ADP
iajs-2803	159	34	function	function	NOUN
iajs-2803	159	35	that	that	PRON
iajs-2803	159	36	described	describe	VERB
iajs-2803	159	37	in	in	ADP
iajs-2803	159	38	this	this	DET
iajs-2803	159	39	paper	paper	NOUN
iajs-2803	159	40	.	.	PUNCT
iajs-2803	160	1	the	the	DET
iajs-2803	160	2	digit	digit	NOUN
iajs-2803	160	3	of	of	ADP
iajs-2803	160	4	"	"	PUNCT
iajs-2803	160	5	function	function	NOUN
iajs-2803	160	6	evaluations	evaluation	NOUN
iajs-2803	160	7	"	"	PUNCT
iajs-2803	160	8	and	and	CCONJ
iajs-2803	160	9	the	the	DET
iajs-2803	160	10	maximum	maximum	ADJ
iajs-2803	160	11	error	error	NOUN
iajs-2803	160	12	of	of	ADP
iajs-2803	160	13	the	the	DET
iajs-2803	160	14	supposed	suppose	VERB
iajs-2803	160	15	technique	technique	NOUN
iajs-2803	160	16	is	be	AUX
iajs-2803	160	17	lower	low	ADJ
iajs-2803	160	18	than	than	ADP
iajs-2803	160	19	those	those	PRON
iajs-2803	160	20	in	in	ADP
iajs-2803	160	21	implicit	implicit	NOUN
iajs-2803	160	22	of	of	ADP
iajs-2803	160	23	the	the	DET
iajs-2803	160	24	rk	rk	NOUN
iajs-2803	160	25	approaches	approach	NOUN
iajs-2803	160	26	,	,	PUNCT
iajs-2803	160	27	as	as	SCONJ
iajs-2803	160	28	indicated	indicate	VERB
iajs-2803	160	29	by	by	ADP
iajs-2803	160	30	numerical	numerical	ADJ
iajs-2803	160	31	results	result	NOUN
iajs-2803	160	32	in	in	ADP
iajs-2803	160	33	all	all	DET
iajs-2803	160	34	figure	figure	NOUN
iajs-2803	160	35	(	(	PUNCT
iajs-2803	160	36	2.1	2.1	NUM
iajs-2803	160	37	)	)	PUNCT
iajs-2803	160	38	and	and	CCONJ
iajs-2803	160	39	table	table	NOUN
iajs-2803	160	40	(	(	PUNCT
iajs-2803	160	41	2.1	2.1	NUM
iajs-2803	160	42	)	)	PUNCT
iajs-2803	160	43	,	,	PUNCT
iajs-2803	160	44	and	and	CCONJ
iajs-2803	160	45	the	the	DET
iajs-2803	160	46	introduced	introduce	VERB
iajs-2803	160	47	ibn	ibn	PROPN
iajs-2803	160	48	al	al	PROPN
iajs-2803	160	49	-	-	PUNCT
iajs-2803	160	50	haitham	haitham	PROPN
iajs-2803	160	51	jour	jour	X
iajs-2803	160	52	.	.	PROPN
iajs-2803	160	53	for	for	ADP
iajs-2803	160	54	pure	pure	ADJ
iajs-2803	160	55	&	&	CCONJ
iajs-2803	160	56	appl	appl	PROPN
iajs-2803	160	57	.	.	PUNCT
iajs-2803	161	1	sci	sci	PROPN
iajs-2803	161	2	.	.	PROPN
iajs-2803	162	1	53	53	NUM
iajs-2803	162	2	(	(	PUNCT
iajs-2803	162	3	1)2022	1)2022	NOUN
iajs-2803	162	4	100	100	NUM
iajs-2803	162	5	techniques	technique	NOUN
iajs-2803	162	6	are	be	AUX
iajs-2803	162	7	most	most	ADV
iajs-2803	162	8	accurate	accurate	ADJ
iajs-2803	162	9	by	by	ADP
iajs-2803	162	10	solving	solve	VERB
iajs-2803	162	11	the	the	DET
iajs-2803	162	12	directly	directly	ADV
iajs-2803	162	13	specific	specific	ADJ
iajs-2803	162	14	odes	ode	NOUN
iajs-2803	162	15	of	of	ADP
iajs-2803	162	16	the	the	DET
iajs-2803	162	17	order	order	NOUN
iajs-2803	162	18	of	of	ADP
iajs-2803	162	19	three	three	NUM
iajs-2803	162	20	.	.	PUNCT
iajs-2803	163	1	the	the	DET
iajs-2803	163	2	stability	stability	NOUN
iajs-2803	163	3	polynomial	polynomial	NOUN
iajs-2803	163	4	for	for	ADP
iajs-2803	163	5	ditrk	ditrk	NOUN
iajs-2803	163	6	method	method	NOUN
iajs-2803	163	7	is	be	AUX
iajs-2803	163	8	analyzed	analyze	VERB
iajs-2803	163	9	and	and	CCONJ
iajs-2803	163	10	presented	present	VERB
iajs-2803	163	11	.	.	PUNCT
iajs-2803	164	1	references	reference	NOUN
iajs-2803	164	2	1	1	NUM
iajs-2803	164	3	.	.	PUNCT
iajs-2803	164	4	wu	wu	PROPN
iajs-2803	164	5	,	,	PUNCT
iajs-2803	164	6	x.	x.	PROPN
iajs-2803	164	7	;	;	PUNCT
iajs-2803	164	8	wang	wang	PROPN
iajs-2803	164	9	,	,	PUNCT
iajs-2803	164	10	y.	y.	PROPN
iajs-2803	164	11	;	;	PUNCT
iajs-2803	164	12	price	price	NOUN
iajs-2803	164	13	,	,	PUNCT
iajs-2803	164	14	w.	w.	PROPN
iajs-2803	164	15	multiple	multiple	ADJ
iajs-2803	164	16	resonances	resonance	NOUN
iajs-2803	164	17	,	,	PUNCT
iajs-2803	164	18	responses	response	NOUN
iajs-2803	164	19	,	,	PUNCT
iajs-2803	164	20	and	and	CCONJ
iajs-2803	164	21	parametric	parametric	ADJ
iajs-2803	164	22	instabilities	instability	NOUN
iajs-2803	164	23	in	in	ADP
iajs-2803	164	24	offshore	offshore	ADJ
iajs-2803	164	25	structures	structure	NOUN
iajs-2803	164	26	.	.	PUNCT
iajs-2803	165	1	j.	j.	PROPN
iajs-2803	165	2	ship	ship	PROPN
iajs-2803	165	3	res	res	PROPN
iajs-2803	165	4	.	.	PUNCT
iajs-2803	165	5	1988	1988	NUM
iajs-2803	165	6	,	,	PUNCT
iajs-2803	165	7	32	32	NUM
iajs-2803	165	8	,	,	PUNCT
iajs-2803	165	9	285–296	285–296	NUM
iajs-2803	165	10	.	.	NOUN
iajs-2803	165	11	2	2	NUM
iajs-2803	165	12	.	.	X
iajs-2803	165	13	cortell	cortell	PROPN
iajs-2803	165	14	,	,	PUNCT
iajs-2803	165	15	r.	r.	PROPN
iajs-2803	165	16	application	application	NOUN
iajs-2803	165	17	of	of	ADP
iajs-2803	165	18	the	the	DET
iajs-2803	165	19	fourth	fourth	ADJ
iajs-2803	165	20	-	-	PUNCT
iajs-2803	165	21	order	order	NOUN
iajs-2803	165	22	runge	runge	NOUN
iajs-2803	165	23	–	–	PUNCT
iajs-2803	165	24	kutta	kutta	NOUN
iajs-2803	165	25	method	method	NOUN
iajs-2803	165	26	for	for	ADP
iajs-2803	165	27	the	the	DET
iajs-2803	165	28	solution	solution	NOUN
iajs-2803	165	29	of	of	ADP
iajs-2803	165	30	highorder	highorder	PROPN
iajs-2803	165	31	general	general	ADJ
iajs-2803	165	32	initial	initial	ADJ
iajs-2803	165	33	value	value	NOUN
iajs-2803	165	34	problems	problem	NOUN
iajs-2803	165	35	.	.	PUNCT
iajs-2803	166	1	comput	comput	NOUN
iajs-2803	166	2	.	.	PUNCT
iajs-2803	166	3	struct	struct	NOUN
iajs-2803	166	4	.	.	PUNCT
iajs-2803	167	1	1993	1993	NUM
iajs-2803	167	2	,	,	PUNCT
iajs-2803	167	3	49	49	NUM
iajs-2803	167	4	,	,	PUNCT
iajs-2803	167	5	897–900	897–900	NUM
iajs-2803	167	6	.	.	PUNCT
iajs-2803	168	1	3	3	X
iajs-2803	168	2	.	.	X
iajs-2803	168	3	malek	malek	PROPN
iajs-2803	168	4	,	,	PUNCT
iajs-2803	168	5	a.	a.	NOUN
iajs-2803	168	6	;	;	PUNCT
iajs-2803	168	7	beidokhti	beidokhti	NOUN
iajs-2803	168	8	,	,	PUNCT
iajs-2803	168	9	r.	r.	PROPN
iajs-2803	168	10	numerical	numerical	PROPN
iajs-2803	168	11	solution	solution	NOUN
iajs-2803	168	12	for	for	ADP
iajs-2803	168	13	high	high	ADJ
iajs-2803	168	14	order	order	NOUN
iajs-2803	168	15	differential	differential	ADJ
iajs-2803	168	16	equations	equation	NOUN
iajs-2803	168	17	using	use	VERB
iajs-2803	168	18	a	a	DET
iajs-2803	168	19	hybrid	hybrid	ADJ
iajs-2803	168	20	neural	neural	ADJ
iajs-2803	168	21	network	network	NOUN
iajs-2803	168	22	—	—	PUNCT
iajs-2803	168	23	optimization	optimization	NOUN
iajs-2803	168	24	method	method	NOUN
iajs-2803	168	25	.	.	PUNCT
iajs-2803	169	1	appl	appl	PROPN
iajs-2803	169	2	.	.	PROPN
iajs-2803	169	3	math	math	PROPN
iajs-2803	169	4	.	.	PUNCT
iajs-2803	170	1	comput	comput	NOUN
iajs-2803	170	2	.	.	PUNCT
iajs-2803	171	1	2006	2006	NUM
iajs-2803	171	2	,	,	PUNCT
iajs-2803	171	3	183	183	NUM
iajs-2803	171	4	,	,	PUNCT
iajs-2803	171	5	260–271	260–271	NUM
iajs-2803	171	6	.	.	PUNCT
iajs-2803	172	1	4	4	NUM
iajs-2803	172	2	.	.	X
iajs-2803	172	3	boutayeb	boutayeb	ADJ
iajs-2803	172	4	,	,	PUNCT
iajs-2803	172	5	a.	a.	NOUN
iajs-2803	172	6	;	;	PUNCT
iajs-2803	172	7	chetouani	chetouani	NOUN
iajs-2803	172	8	,	,	PUNCT
iajs-2803	172	9	a.	a.	PROPN
iajs-2803	172	10	a	a	DET
iajs-2803	172	11	mini	mini	NOUN
iajs-2803	172	12	-	-	NOUN
iajs-2803	172	13	review	review	NOUN
iajs-2803	172	14	of	of	ADP
iajs-2803	172	15	numerical	numerical	ADJ
iajs-2803	172	16	methods	method	NOUN
iajs-2803	172	17	for	for	ADP
iajs-2803	172	18	high	high	ADJ
iajs-2803	172	19	-	-	PUNCT
iajs-2803	172	20	order	order	NOUN
iajs-2803	172	21	problems	problem	NOUN
iajs-2803	172	22	.	.	PUNCT
iajs-2803	173	1	int	int	NOUN
iajs-2803	173	2	.	.	PUNCT
iajs-2803	174	1	j.	j.	PROPN
iajs-2803	174	2	comput	comput	PROPN
iajs-2803	174	3	.	.	PUNCT
iajs-2803	175	1	math	math	NOUN
iajs-2803	175	2	.	.	PUNCT
iajs-2803	176	1	2007	2007	NUM
iajs-2803	176	2	,	,	PUNCT
iajs-2803	176	3	84	84	NUM
iajs-2803	176	4	,	,	PUNCT
iajs-2803	176	5	563–579	563–579	NUM
iajs-2803	176	6	.	.	NOUN
iajs-2803	177	1	5	5	NUM
iajs-2803	177	2	.	.	X
iajs-2803	177	3	alomari	alomari	PROPN
iajs-2803	177	4	,	,	PUNCT
iajs-2803	177	5	a.	a.	NOUN
iajs-2803	177	6	;	;	PUNCT
iajs-2803	177	7	anakira	anakira	PROPN
iajs-2803	177	8	,	,	PUNCT
iajs-2803	177	9	n.r	n.r	PROPN
iajs-2803	177	10	.	.	PROPN
iajs-2803	177	11	;	;	PUNCT
iajs-2803	177	12	bataineh	bataineh	PROPN
iajs-2803	177	13	,	,	PUNCT
iajs-2803	177	14	a.s	a.s	PROPN
iajs-2803	177	15	.	.	PROPN
iajs-2803	177	16	;	;	PUNCT
iajs-2803	177	17	hashim	hashim	PROPN
iajs-2803	177	18	,	,	PUNCT
iajs-2803	177	19	i.	i.	PROPN
iajs-2803	177	20	approximate	approximate	ADJ
iajs-2803	177	21	solution	solution	NOUN
iajs-2803	177	22	of	of	ADP
iajs-2803	177	23	nonlinear	nonlinear	ADJ
iajs-2803	177	24	system	system	NOUN
iajs-2803	177	25	of	of	ADP
iajs-2803	177	26	bvp	bvp	NOUN
iajs-2803	177	27	arising	arise	VERB
iajs-2803	177	28	in	in	ADP
iajs-2803	177	29	fluid	fluid	ADJ
iajs-2803	177	30	flow	flow	NOUN
iajs-2803	177	31	problem	problem	NOUN
iajs-2803	177	32	.	.	PUNCT
iajs-2803	178	1	math	math	NOUN
iajs-2803	178	2	.	.	PUNCT
iajs-2803	179	1	probl	probl	PROPN
iajs-2803	179	2	.	.	PUNCT
iajs-2803	180	1	eng	eng	PROPN
iajs-2803	180	2	.	.	PROPN
iajs-2803	180	3	2013	2013	NUM
iajs-2803	180	4	,	,	PUNCT
iajs-2803	180	5	136043	136043	NUM
iajs-2803	180	6	.	.	PUNCT
iajs-2803	181	1	6	6	NUM
iajs-2803	181	2	.	.	X
iajs-2803	181	3	twizell	twizell	PROPN
iajs-2803	181	4	,	,	PUNCT
iajs-2803	181	5	e.	e.	PROPN
iajs-2803	181	6	a	a	DET
iajs-2803	181	7	family	family	NOUN
iajs-2803	181	8	of	of	ADP
iajs-2803	181	9	numerical	numerical	ADJ
iajs-2803	181	10	methods	method	NOUN
iajs-2803	181	11	for	for	ADP
iajs-2803	181	12	the	the	DET
iajs-2803	181	13	solution	solution	NOUN
iajs-2803	181	14	of	of	ADP
iajs-2803	181	15	high	high	ADJ
iajs-2803	181	16	-	-	PUNCT
iajs-2803	181	17	order	order	NOUN
iajs-2803	181	18	general	general	ADJ
iajs-2803	181	19	initial	initial	ADJ
iajs-2803	181	20	value	value	NOUN
iajs-2803	181	21	problems	problem	NOUN
iajs-2803	181	22	.	.	PUNCT
iajs-2803	182	1	comput	comput	NOUN
iajs-2803	182	2	.	.	PUNCT
iajs-2803	183	1	methods	method	NOUN
iajs-2803	183	2	appl	appl	PROPN
iajs-2803	183	3	.	.	PROPN
iajs-2803	183	4	mech	mech	PROPN
iajs-2803	183	5	.	.	PUNCT
iajs-2803	184	1	eng	eng	PROPN
iajs-2803	184	2	.	.	PROPN
iajs-2803	184	3	1988	1988	NUM
iajs-2803	184	4	,	,	PUNCT
iajs-2803	184	5	67	67	NUM
iajs-2803	184	6	,	,	PUNCT
iajs-2803	184	7	15–25	15–25	NUM
iajs-2803	184	8	.	.	PUNCT
iajs-2803	184	9	7	7	X
iajs-2803	184	10	.	.	X
iajs-2803	184	11	ismail	ismail	PROPN
iajs-2803	184	12	,	,	PUNCT
iajs-2803	184	13	f.	f.	PROPN
iajs-2803	184	14	;	;	PUNCT
iajs-2803	184	15	jawias	jawia	NOUN
iajs-2803	184	16	,	,	PUNCT
iajs-2803	184	17	n.i.c	n.i.c	NOUN
iajs-2803	184	18	.	.	PUNCT
iajs-2803	184	19	;	;	PUNCT
iajs-2803	184	20	suleiman	suleiman	PROPN
iajs-2803	184	21	,	,	PUNCT
iajs-2803	184	22	m.	m.	NOUN
iajs-2803	184	23	;	;	PUNCT
iajs-2803	184	24	jaafar	jaafar	ADV
iajs-2803	184	25	,	,	PUNCT
iajs-2803	184	26	a.	a.	NOUN
iajs-2803	184	27	solving	solving	NOUN
iajs-2803	184	28	linear	linear	ADJ
iajs-2803	184	29	ordinary	ordinary	ADJ
iajs-2803	184	30	differential	differential	ADJ
iajs-2803	184	31	equations	equation	NOUN
iajs-2803	184	32	using	use	VERB
iajs-2803	184	33	singly	singly	ADV
iajs-2803	184	34	diagonally	diagonally	ADV
iajs-2803	184	35	implicit	implicit	ADJ
iajs-2803	184	36	runge	runge	NOUN
iajs-2803	184	37	–	–	PUNCT
iajs-2803	184	38	kutta	kutta	X
iajs-2803	184	39	fifth	fifth	ADJ
iajs-2803	184	40	order	order	NOUN
iajs-2803	184	41	five	five	NUM
iajs-2803	184	42	-	-	PUNCT
iajs-2803	184	43	stage	stage	NOUN
iajs-2803	184	44	method	method	NOUN
iajs-2803	184	45	.	.	PUNCT
iajs-2803	185	1	wseas	wseas	PROPN
iajs-2803	185	2	trans	trans	PROPN
iajs-2803	185	3	.	.	PROPN
iajs-2803	185	4	math	math	PROPN
iajs-2803	185	5	.	.	PUNCT
iajs-2803	186	1	2009	2009	NUM
iajs-2803	186	2	,	,	PUNCT
iajs-2803	186	3	8	8	NUM
iajs-2803	186	4	,	,	PUNCT
iajs-2803	186	5	393–402	393–402	NUM
iajs-2803	186	6	.	.	NOUN
iajs-2803	186	7	8	8	NUM
iajs-2803	186	8	.	.	X
iajs-2803	187	1	ismail	ismail	PROPN
iajs-2803	187	2	,	,	PUNCT
iajs-2803	187	3	f.	f.	PROPN
iajs-2803	187	4	diagonally	diagonally	ADV
iajs-2803	187	5	implicit	implicit	ADJ
iajs-2803	187	6	runge	runge	NOUN
iajs-2803	187	7	–	–	PUNCT
iajs-2803	187	8	kutta	kutta	PROPN
iajs-2803	187	9	nystrom	nystrom	PROPN
iajs-2803	187	10	general	general	PROPN
iajs-2803	187	11	method	method	PROPN
iajs-2803	187	12	order	order	NOUN
iajs-2803	187	13	five	five	NUM
iajs-2803	187	14	for	for	ADP
iajs-2803	187	15	solving	solve	VERB
iajs-2803	187	16	second	second	ADJ
iajs-2803	187	17	order	order	NOUN
iajs-2803	187	18	ivps	ivps	PROPN
iajs-2803	187	19	.	.	PUNCT
iajs-2803	187	20	wseas	wseas	PROPN
iajs-2803	187	21	trans	trans	PROPN
iajs-2803	187	22	.	.	PROPN
iajs-2803	188	1	math	math	PROPN
iajs-2803	188	2	.	.	PUNCT
iajs-2803	189	1	2010	2010	NUM
iajs-2803	189	2	,	,	PUNCT
iajs-2803	189	3	9	9	NUM
iajs-2803	189	4	,	,	PUNCT
iajs-2803	189	5	550–560	550–560	NUM
iajs-2803	189	6	.	.	NOUN
iajs-2803	190	1	10	10	NUM
iajs-2803	190	2	.	.	X
iajs-2803	190	3	senu	senu	PROPN
iajs-2803	190	4	,	,	PUNCT
iajs-2803	190	5	n.	n.	NOUN
iajs-2803	190	6	;	;	PUNCT
iajs-2803	190	7	suleiman	suleiman	PROPN
iajs-2803	190	8	,	,	PUNCT
iajs-2803	190	9	m.	m.	NOUN
iajs-2803	190	10	;	;	PUNCT
iajs-2803	190	11	ismail	ismail	PROPN
iajs-2803	190	12	,	,	PUNCT
iajs-2803	190	13	f.	f.	PROPN
iajs-2803	190	14	;	;	PUNCT
iajs-2803	190	15	arifin	arifin	PROPN
iajs-2803	190	16	,	,	PUNCT
iajs-2803	190	17	n.m	n.m	PROPN
iajs-2803	190	18	.	.	PROPN
iajs-2803	190	19	new	new	ADJ
iajs-2803	190	20	4	4	NUM
iajs-2803	190	21	(	(	PUNCT
iajs-2803	190	22	3	3	X
iajs-2803	190	23	)	)	PUNCT
iajs-2803	190	24	pairs	pair	NOUN
iajs-2803	190	25	diagonally	diagonally	ADV
iajs-2803	190	26	implicit	implicit	ADJ
iajs-2803	190	27	runge	runge	NOUN
iajs-2803	190	28	–	–	PUNCT
iajs-2803	190	29	kutta	kutta	NOUN
iajs-2803	190	30	-	-	PUNCT
iajs-2803	190	31	nyström	nyström	NOUN
iajs-2803	190	32	method	method	NOUN
iajs-2803	190	33	for	for	ADP
iajs-2803	190	34	periodic	periodic	ADJ
iajs-2803	190	35	ivps	ivps	PROPN
iajs-2803	190	36	.	.	PUNCT
iajs-2803	191	1	discret	discret	PROPN
iajs-2803	191	2	.	.	PUNCT
iajs-2803	192	1	dyn	dyn	PROPN
iajs-2803	192	2	.	.	PUNCT
iajs-2803	193	1	nat	nat	PROPN
iajs-2803	193	2	.	.	PUNCT
iajs-2803	194	1	soc	soc	PROPN
iajs-2803	194	2	.	.	PUNCT
iajs-2803	195	1	2012	2012	NUM
iajs-2803	195	2	,	,	PUNCT
iajs-2803	195	3	324989	324989	NUM
iajs-2803	195	4	.	.	PUNCT
iajs-2803	196	1	11	11	NUM
iajs-2803	196	2	.	.	X
iajs-2803	196	3	senu	senu	PROPN
iajs-2803	196	4	,	,	PUNCT
iajs-2803	196	5	n.	n.	NOUN
iajs-2803	196	6	;	;	PUNCT
iajs-2803	196	7	suleiman	suleiman	PROPN
iajs-2803	196	8	,	,	PUNCT
iajs-2803	196	9	m.	m.	NOUN
iajs-2803	196	10	;	;	PUNCT
iajs-2803	196	11	ismail	ismail	PROPN
iajs-2803	196	12	,	,	PUNCT
iajs-2803	196	13	f.	f.	PROPN
iajs-2803	196	14	;	;	PUNCT
iajs-2803	196	15	othman	othman	PROPN
iajs-2803	196	16	,	,	PUNCT
iajs-2803	196	17	m.	m.	NOUN
iajs-2803	196	18	a	a	DET
iajs-2803	196	19	singly	singly	ADV
iajs-2803	196	20	diagonally	diagonally	ADV
iajs-2803	196	21	implicit	implicit	ADJ
iajs-2803	196	22	runge	runge	NOUN
iajs-2803	196	23	–	–	PUNCT
iajs-2803	196	24	kutta	kutta	NOUN
iajs-2803	196	25	-	-	PUNCT
iajs-2803	196	26	nyström	nyström	NOUN
iajs-2803	196	27	method	method	NOUN
iajs-2803	196	28	for	for	ADP
iajs-2803	196	29	solving	solve	VERB
iajs-2803	196	30	oscillatory	oscillatory	ADJ
iajs-2803	196	31	problems	problem	NOUN
iajs-2803	196	32	.	.	PUNCT
iajs-2803	197	1	iaeng	iaeng	PROPN
iajs-2803	197	2	int	int	PROPN
iajs-2803	197	3	.	.	PUNCT
iajs-2803	198	1	j.	j.	PROPN
iajs-2803	198	2	appl	appl	PROPN
iajs-2803	198	3	.	.	PROPN
iajs-2803	198	4	math	math	PROPN
iajs-2803	198	5	.	.	PUNCT
iajs-2803	199	1	2011	2011	NUM
iajs-2803	199	2	,	,	PUNCT
iajs-2803	199	3	41	41	NUM
iajs-2803	199	4	,	,	PUNCT
iajs-2803	199	5	155–161	155–161	NUM
iajs-2803	199	6	.	.	PUNCT
iajs-2803	200	1	12	12	NUM
iajs-2803	200	2	.	.	X
iajs-2803	200	3	senu	senu	PROPN
iajs-2803	200	4	,	,	PUNCT
iajs-2803	200	5	n.	n.	NOUN
iajs-2803	200	6	;	;	PUNCT
iajs-2803	200	7	suleiman	suleiman	PROPN
iajs-2803	200	8	,	,	PUNCT
iajs-2803	200	9	m.	m.	NOUN
iajs-2803	200	10	;	;	PUNCT
iajs-2803	200	11	ismail	ismail	PROPN
iajs-2803	200	12	,	,	PUNCT
iajs-2803	200	13	f.	f.	PROPN
iajs-2803	200	14	;	;	PUNCT
iajs-2803	200	15	othman	othman	PROPN
iajs-2803	200	16	,	,	PUNCT
iajs-2803	200	17	m.	m.	NOUN
iajs-2803	200	18	a	a	DET
iajs-2803	200	19	fourth	fourth	ADJ
iajs-2803	200	20	-	-	PUNCT
iajs-2803	200	21	order	order	NOUN
iajs-2803	200	22	diagonally	diagonally	ADV
iajs-2803	200	23	implicit	implicit	ADJ
iajs-2803	200	24	runge	runge	NOUN
iajs-2803	200	25	–	–	PUNCT
iajs-2803	200	26	kutta	kutta	NOUN
iajs-2803	200	27	-	-	PUNCT
iajs-2803	200	28	nyström	nyström	NOUN
iajs-2803	200	29	method	method	NOUN
iajs-2803	200	30	with	with	ADP
iajs-2803	200	31	dispersion	dispersion	NOUN
iajs-2803	200	32	of	of	ADP
iajs-2803	200	33	high	high	ADJ
iajs-2803	200	34	order	order	NOUN
iajs-2803	200	35	.	.	PUNCT
iajs-2803	201	1	in	in	ADP
iajs-2803	201	2	proceedings	proceeding	NOUN
iajs-2803	201	3	of	of	ADP
iajs-2803	201	4	the	the	DET
iajs-2803	201	5	4th	4th	ADJ
iajs-2803	201	6	international	international	ADJ
iajs-2803	201	7	conference	conference	NOUN
iajs-2803	201	8	on	on	ADP
iajs-2803	201	9	applied	applied	ADJ
iajs-2803	201	10	mathematics	mathematic	NOUN
iajs-2803	201	11	,	,	PUNCT
iajs-2803	201	12	simulation	simulation	NOUN
iajs-2803	201	13	,	,	PUNCT
iajs-2803	201	14	modelling	modelling	NOUN
iajs-2803	201	15	(	(	PUNCT
iajs-2803	201	16	asm’10	asm’10	NOUN
iajs-2803	201	17	)	)	PUNCT
iajs-2803	201	18	,	,	PUNCT
iajs-2803	201	19	corfu	corfu	PROPN
iajs-2803	201	20	island	island	PROPN
iajs-2803	201	21	,	,	PUNCT
iajs-2803	201	22	greece	greece	PROPN
iajs-2803	201	23	,	,	PUNCT
iajs-2803	201	24	22–25	22–25	NUM
iajs-2803	201	25	july	july	PROPN
iajs-2803	201	26	2010	2010	NUM
iajs-2803	201	27	;	;	PUNCT
iajs-2803	201	28	78–82	78–82	NUM
iajs-2803	201	29	.	.	NOUN
iajs-2803	201	30	13	13	NUM
iajs-2803	201	31	.	.	PUNCT
iajs-2803	201	32	attili	attili	ADJ
iajs-2803	201	33	,	,	PUNCT
iajs-2803	201	34	b.s	b.s	PROPN
iajs-2803	201	35	.	.	PROPN
iajs-2803	201	36	;	;	PUNCT
iajs-2803	201	37	furati	furati	PROPN
iajs-2803	201	38	,	,	PUNCT
iajs-2803	201	39	k.	k.	PROPN
iajs-2803	201	40	;	;	PUNCT
iajs-2803	201	41	syam	syam	PROPN
iajs-2803	201	42	,	,	PUNCT
iajs-2803	201	43	m.i	m.i	PROPN
iajs-2803	201	44	.	.	PROPN
iajs-2803	201	45	an	an	DET
iajs-2803	201	46	efficient	efficient	ADJ
iajs-2803	201	47	implicit	implicit	ADJ
iajs-2803	201	48	runge	runge	NOUN
iajs-2803	201	49	–	–	PUNCT
iajs-2803	201	50	kutta	kutta	NOUN
iajs-2803	201	51	method	method	NOUN
iajs-2803	201	52	for	for	ADP
iajs-2803	201	53	second	second	ADJ
iajs-2803	201	54	order	order	NOUN
iajs-2803	201	55	systems	system	NOUN
iajs-2803	201	56	.	.	PUNCT
iajs-2803	202	1	appl	appl	PROPN
iajs-2803	202	2	.	.	PROPN
iajs-2803	202	3	math	math	PROPN
iajs-2803	202	4	.	.	PUNCT
iajs-2803	203	1	comput	comput	NOUN
iajs-2803	203	2	.	.	PUNCT
iajs-2803	204	1	2006	2006	NUM
iajs-2803	204	2	,	,	PUNCT
iajs-2803	204	3	178	178	NUM
iajs-2803	204	4	,	,	PUNCT
iajs-2803	204	5	229–238	229–238	NUM
iajs-2803	204	6	.	.	PUNCT
iajs-2803	205	1	14	14	NUM
iajs-2803	205	2	.	.	PUNCT
iajs-2803	206	1	wen	wen	PROPN
iajs-2803	206	2	,	,	PUNCT
iajs-2803	206	3	z.	z.	PROPN
iajs-2803	206	4	;	;	PUNCT
iajs-2803	206	5	zhu	zhu	PROPN
iajs-2803	206	6	,	,	PUNCT
iajs-2803	206	7	t.	t.	PROPN
iajs-2803	206	8	;	;	PUNCT
iajs-2803	206	9	xiao	xiao	PROPN
iajs-2803	206	10	,	,	PUNCT
iajs-2803	206	11	a.	a.	NOUN
iajs-2803	206	12	two	two	NUM
iajs-2803	206	13	classes	class	NOUN
iajs-2803	206	14	of	of	ADP
iajs-2803	206	15	three	three	NUM
iajs-2803	206	16	-	-	PUNCT
iajs-2803	206	17	stage	stage	NOUN
iajs-2803	206	18	diagonally	diagonally	ADV
iajs-2803	206	19	-	-	PUNCT
iajs-2803	206	20	implicit	implicit	ADJ
iajs-2803	206	21	runge	runge	NOUN
iajs-2803	206	22	–	–	PUNCT
iajs-2803	206	23	kutta	kutta	NOUN
iajs-2803	206	24	methods	method	NOUN
iajs-2803	206	25	with	with	ADP
iajs-2803	206	26	an	an	DET
iajs-2803	206	27	explicit	explicit	ADJ
iajs-2803	206	28	stage	stage	NOUN
iajs-2803	206	29	for	for	ADP
iajs-2803	206	30	stiff	stiff	ADJ
iajs-2803	206	31	oscillatory	oscillatory	ADJ
iajs-2803	206	32	problems	problem	NOUN
iajs-2803	206	33	.	.	PUNCT
iajs-2803	207	1	math	math	NOUN
iajs-2803	207	2	.	.	PUNCT
iajs-2803	208	1	appl	appl	PROPN
iajs-2803	208	2	.	.	PUNCT
iajs-2803	209	1	2011	2011	NUM
iajs-2803	209	2	,	,	PUNCT
iajs-2803	209	3	1	1	NUM
iajs-2803	209	4	,	,	PUNCT
iajs-2803	209	5	15	15	NUM
iajs-2803	209	6	.	.	NOUN
iajs-2803	209	7	15	15	NUM
iajs-2803	209	8	.	.	PUNCT
iajs-2803	210	1	ghawadri	ghawadri	PROPN
iajs-2803	210	2	,	,	PUNCT
iajs-2803	210	3	n.	n.	NOUN
iajs-2803	210	4	,	,	PUNCT
iajs-2803	210	5	senu	senu	NOUN
iajs-2803	210	6	,	,	PUNCT
iajs-2803	210	7	n.	n.	NOUN
iajs-2803	210	8	,	,	PUNCT
iajs-2803	210	9	adel	adel	PROPN
iajs-2803	210	10	fawzi	fawzi	PROPN
iajs-2803	210	11	,	,	PUNCT
iajs-2803	210	12	f.	f.	PROPN
iajs-2803	210	13	,	,	PUNCT
iajs-2803	210	14	ismail	ismail	PROPN
iajs-2803	210	15	,	,	PUNCT
iajs-2803	210	16	f.	f.	PROPN
iajs-2803	210	17	,	,	PUNCT
iajs-2803	210	18	&	&	CCONJ
iajs-2803	210	19	ibrahim	ibrahim	PROPN
iajs-2803	210	20	,	,	PUNCT
iajs-2803	210	21	z.	z.	PROPN
iajs-2803	210	22	b.	b.	PROPN
iajs-2803	210	23	diagonally	diagonally	ADV
iajs-2803	210	24	implicit	implicit	ADJ
iajs-2803	210	25	runge	runge	NOUN
iajs-2803	210	26	–	–	PUNCT
iajs-2803	210	27	kutta	kutta	NOUN
iajs-2803	210	28	type	type	NOUN
iajs-2803	210	29	method	method	NOUN
iajs-2803	210	30	for	for	ADP
iajs-2803	210	31	directly	directly	ADV
iajs-2803	210	32	solving	solve	VERB
iajs-2803	210	33	special	special	ADJ
iajs-2803	210	34	fourth	fourth	ADJ
iajs-2803	210	35	-	-	PUNCT
iajs-2803	210	36	order	order	NOUN
iajs-2803	210	37	ordinary	ordinary	ADJ
iajs-2803	210	38	differential	differential	ADJ
iajs-2803	210	39	equations	equation	NOUN
iajs-2803	210	40	with	with	ADP
iajs-2803	210	41	ill	ill	ADV
iajs-2803	210	42	-	-	PUNCT
iajs-2803	210	43	posed	pose	VERB
iajs-2803	210	44	problem	problem	NOUN
iajs-2803	210	45	of	of	ADP
iajs-2803	210	46	a	a	DET
iajs-2803	210	47	beam	beam	NOUN
iajs-2803	210	48	on	on	ADP
iajs-2803	210	49	elastic	elastic	ADJ
iajs-2803	210	50	foundation	foundation	NOUN
iajs-2803	210	51	.	.	PUNCT
iajs-2803	211	1	algorithms	algorithm	NOUN
iajs-2803	211	2	,	,	PUNCT
iajs-2803	211	3	2019	2019	NUM
iajs-2803	211	4	12(1	12(1	NUM
iajs-2803	211	5	)	)	PUNCT
iajs-2803	211	6	,	,	PUNCT
iajs-2803	211	7	10	10	NUM
iajs-2803	211	8	.	.	PUNCT
iajs-2803	212	1	ibn	ibn	PROPN
iajs-2803	212	2	al	al	PROPN
iajs-2803	212	3	-	-	PUNCT
iajs-2803	212	4	haitham	haitham	PROPN
iajs-2803	212	5	jour	jour	X
iajs-2803	212	6	.	.	PROPN
iajs-2803	212	7	for	for	ADP
iajs-2803	212	8	pure	pure	ADJ
iajs-2803	212	9	&	&	CCONJ
iajs-2803	212	10	appl	appl	PROPN
iajs-2803	212	11	.	.	PUNCT
iajs-2803	213	1	sci	sci	PROPN
iajs-2803	213	2	.	.	PROPN
iajs-2803	214	1	53	53	NUM
iajs-2803	214	2	(	(	PUNCT
iajs-2803	214	3	1)2022	1)2022	PROPN
iajs-2803	214	4	101	101	NUM
iajs-2803	214	5	16	16	NUM
iajs-2803	214	6	.	.	PUNCT
iajs-2803	215	1	mechee	mechee	NOUN
iajs-2803	215	2	,	,	PUNCT
iajs-2803	215	3	m.	m.	NOUN
iajs-2803	215	4	,	,	PUNCT
iajs-2803	215	5	senu	senu	NOUN
iajs-2803	215	6	,	,	PUNCT
iajs-2803	215	7	n.	n.	NOUN
iajs-2803	215	8	,	,	PUNCT
iajs-2803	215	9	ismail	ismail	PROPN
iajs-2803	215	10	,	,	PUNCT
iajs-2803	215	11	f.	f.	PROPN
iajs-2803	215	12	,	,	PUNCT
iajs-2803	215	13	nikouravan	nikouravan	PROPN
iajs-2803	215	14	,	,	PUNCT
iajs-2803	215	15	b.	b.	PROPN
iajs-2803	215	16	,	,	PUNCT
iajs-2803	215	17	&	&	CCONJ
iajs-2803	215	18	siri	siri	NOUN
iajs-2803	215	19	,	,	PUNCT
iajs-2803	215	20	z.	z.	PROPN
iajs-2803	215	21	(	(	PUNCT
iajs-2803	215	22	2013	2013	NUM
iajs-2803	215	23	)	)	PUNCT
iajs-2803	215	24	.	.	PUNCT
iajs-2803	216	1	a	a	DET
iajs-2803	216	2	three	three	NUM
iajs-2803	216	3	-	-	PUNCT
iajs-2803	216	4	stage	stage	NOUN
iajs-2803	216	5	fifthorder	fifthorder	NOUN
iajs-2803	216	6	runge	runge	NOUN
iajs-2803	216	7	-	-	PUNCT
iajs-2803	216	8	kutta	kutta	NOUN
iajs-2803	216	9	method	method	NOUN
iajs-2803	216	10	for	for	ADP
iajs-2803	216	11	directly	directly	ADV
iajs-2803	216	12	solving	solve	VERB
iajs-2803	216	13	special	special	ADJ
iajs-2803	216	14	third	third	ADJ
iajs-2803	216	15	-	-	PUNCT
iajs-2803	216	16	order	order	NOUN
iajs-2803	216	17	differential	differential	ADJ
iajs-2803	216	18	equation	equation	NOUN
iajs-2803	216	19	with	with	ADP
iajs-2803	216	20	application	application	NOUN
iajs-2803	216	21	to	to	ADP
iajs-2803	216	22	thin	thin	ADJ
iajs-2803	216	23	film	film	NOUN
iajs-2803	216	24	flow	flow	NOUN
iajs-2803	216	25	problem	problem	NOUN
iajs-2803	216	26	.	.	PUNCT
iajs-2803	217	1	mathematical	mathematical	ADJ
iajs-2803	217	2	problems	problem	NOUN
iajs-2803	217	3	in	in	ADP
iajs-2803	217	4	engineering	engineering	NOUN
iajs-2803	217	5	,	,	PUNCT
iajs-2803	217	6	2013	2013	NUM
iajs-2803	217	7	.	.	PUNCT
iajs-2803	218	1	17	17	NUM
iajs-2803	218	2	.	.	PUNCT
iajs-2803	219	1	f	f	PROPN
iajs-2803	219	2	a	a	DET
iajs-2803	219	3	fawzi	fawzi	NOUN
iajs-2803	219	4	,	,	PUNCT
iajs-2803	219	5	n	n	PRON
iajs-2803	219	6	senu	senu	VERB
iajs-2803	219	7	,	,	PUNCT
iajs-2803	219	8	f	f	PROPN
iajs-2803	219	9	ismail	ismail	PROPN
iajs-2803	219	10	and	and	CCONJ
iajs-2803	219	11	z	z	PROPN
iajs-2803	219	12	a	a	DET
iajs-2803	219	13	majid	majid	PROPN
iajs-2803	220	1	a	a	DET
iajs-2803	220	2	new	new	ADJ
iajs-2803	220	3	integrator	integrator	NOUN
iajs-2803	220	4	of	of	ADP
iajs-2803	220	5	runge	runge	NOUN
iajs-2803	220	6	-	-	PUNCT
iajs-2803	220	7	kutta	kutta	NOUN
iajs-2803	220	8	type	type	NOUN
iajs-2803	220	9	for	for	ADP
iajs-2803	220	10	directly	directly	ADV
iajs-2803	220	11	solving	solve	VERB
iajs-2803	220	12	general	general	ADJ
iajs-2803	220	13	third	third	ADJ
iajs-2803	220	14	-	-	PUNCT
iajs-2803	220	15	order	order	NOUN
iajs-2803	220	16	odes	ode	VERB
iajs-2803	220	17	with	with	ADP
iajs-2803	220	18	application	application	NOUN
iajs-2803	220	19	to	to	ADP
iajs-2803	220	20	thin	thin	ADJ
iajs-2803	220	21	film	film	NOUN
iajs-2803	220	22	flow	flow	NOUN
iajs-2803	220	23	problem	problem	NOUN
iajs-2803	220	24	applied	apply	VERB
iajs-2803	220	25	mathematics	mathematics	PROPN
iajs-2803	220	26	&	&	CCONJ
iajs-2803	220	27	information	information	NOUN
iajs-2803	220	28	sciences	sciences	PROPN
iajs-2803	220	29	,	,	PUNCT
iajs-2803	220	30	2018	2018	NUM
iajs-2803	220	31	.	.	PUNCT
iajs-2803	221	1	12	12	NUM
iajs-2803	221	2	(	(	PUNCT
iajs-2803	221	3	4	4	NUM
iajs-2803	221	4	)	)	PUNCT
iajs-2803	221	5	,	,	PUNCT
iajs-2803	221	6	775	775	NUM
iajs-2803	221	7	-	-	SYM
iajs-2803	221	8	784	784	NUM
iajs-2803	221	9	.	.	PUNCT
iajs-2803	222	1	18	18	NUM
iajs-2803	222	2	.	.	PUNCT
iajs-2803	223	1	f	f	PROPN
iajs-2803	224	1	a	a	DET
iajs-2803	224	2	fawzi	fawzi	NOUN
iajs-2803	224	3	and	and	CCONJ
iajs-2803	224	4	n	n	PRON
iajs-2803	224	5	senu	senu	VERB
iajs-2803	224	6	and	and	CCONJ
iajs-2803	224	7	f	f	PROPN
iajs-2803	224	8	ismail	ismail	NOUN
iajs-2803	224	9	an	an	DET
iajs-2803	224	10	efficient	efficient	ADJ
iajs-2803	224	11	of	of	ADP
iajs-2803	224	12	direct	direct	ADJ
iajs-2803	224	13	integrator	integrator	NOUN
iajs-2803	224	14	of	of	ADP
iajs-2803	224	15	runge	runge	NOUN
iajs-2803	224	16	-	-	PUNCT
iajs-2803	224	17	kutta	kutta	NOUN
iajs-2803	224	18	type	type	NOUN
iajs-2803	224	19	method	method	NOUN
iajs-2803	224	20	for	for	ADP
iajs-2803	224	21	solving	solve	VERB
iajs-2803	224	22	y	y	NOUN
iajs-2803	224	23	''	''	PUNCT
iajs-2803	224	24	'	'	PUNCT
iajs-2803	224	25	=	=	SYM
iajs-2803	224	26	f(x	f(x	PROPN
iajs-2803	224	27	,	,	PUNCT
iajs-2803	224	28	y	y	PROPN
iajs-2803	224	29	,	,	PUNCT
iajs-2803	224	30	y	y	PROPN
iajs-2803	224	31	'	'	PUNCT
iajs-2803	224	32	)	)	PUNCT
iajs-2803	224	33	with	with	ADP
iajs-2803	224	34	application	application	NOUN
iajs-2803	224	35	to	to	ADP
iajs-2803	224	36	thin	thin	ADJ
iajs-2803	224	37	film	film	NOUN
iajs-2803	224	38	flow	flow	NOUN
iajs-2803	224	39	problem	problem	NOUN
iajs-2803	224	40	international	international	ADJ
iajs-2803	224	41	journal	journal	NOUN
iajs-2803	224	42	of	of	ADP
iajs-2803	224	43	pure	pure	ADJ
iajs-2803	224	44	and	and	CCONJ
iajs-2803	224	45	applied	applied	ADJ
iajs-2803	224	46	mathematics	mathematic	NOUN
iajs-2803	224	47	,	,	PUNCT
iajs-2803	224	48	2018	2018	NUM
iajs-2803	224	49	,	,	PUNCT
iajs-2803	224	50	120	120	NUM
iajs-2803	224	51	,	,	PUNCT
iajs-2803	224	52	27	27	NUM
iajs-2803	224	53	-	-	SYM
iajs-2803	224	54	50	50	NUM
iajs-2803	224	55	.	.	PUNCT
iajs-2803	224	56	19	19	NUM
iajs-2803	224	57	.	.	X
iajs-2803	225	1	n	n	PRON
iajs-2803	225	2	senu	senu	VERB
iajs-2803	225	3	,	,	PUNCT
iajs-2803	225	4	m	m	VERB
iajs-2803	225	5	suleiman	suleiman	NOUN
iajs-2803	225	6	,	,	PUNCT
iajs-2803	225	7	f	f	PROPN
iajs-2803	225	8	ismail	ismail	PROPN
iajs-2803	225	9	.	.	PUNCT
iajs-2803	226	1	an	an	DET
iajs-2803	226	2	embedded	embed	VERB
iajs-2803	226	3	explicit	explicit	ADJ
iajs-2803	226	4	runge	runge	NOUN
iajs-2803	226	5	-	-	PUNCT
iajs-2803	226	6	kutta	kutta	NOUN
iajs-2803	226	7	-	-	PUNCT
iajs-2803	226	8	nyström	nyström	NOUN
iajs-2803	226	9	method	method	NOUN
iajs-2803	226	10	for	for	ADP
iajs-2803	226	11	solving	solve	VERB
iajs-2803	226	12	oscillatory	oscillatory	ADJ
iajs-2803	226	13	problems	problem	NOUN
iajs-2803	226	14	,	,	PUNCT
iajs-2803	226	15	physica	physica	PROPN
iajs-2803	226	16	scripta	scripta	PROPN
iajs-2803	226	17	,	,	PUNCT
iajs-2803	226	18	2009	2009	NUM
iajs-2803	226	19	,	,	PUNCT
iajs-2803	226	20	80	80	NUM
iajs-2803	226	21	,	,	PUNCT
iajs-2803	226	22	015005	015005	NUM
iajs-2803	226	23	.	.	PUNCT
iajs-2803	227	1	20	20	NUM
iajs-2803	227	2	.	.	PUNCT
iajs-2803	227	3	fawzi	fawzi	PROPN
iajs-2803	227	4	,	,	PUNCT
iajs-2803	227	5	f.	f.	PROPN
iajs-2803	227	6	a.	a.	PROPN
iajs-2803	227	7	,	,	PUNCT
iajs-2803	227	8	abdullah	abdullah	PROPN
iajs-2803	227	9	,	,	PUNCT
iajs-2803	227	10	z.	z.	PROPN
iajs-2803	227	11	m.	m.	PROPN
iajs-2803	227	12	,	,	PUNCT
iajs-2803	227	13	&	&	CCONJ
iajs-2803	227	14	hussein	hussein	PROPN
iajs-2803	227	15	,	,	PUNCT
iajs-2803	227	16	n.	n.	PROPN
iajs-2803	227	17	k.	k.	PROPN
iajs-2803	228	1	two	two	NUM
iajs-2803	228	2	embedded	embed	VERB
iajs-2803	228	3	pairs	pair	NOUN
iajs-2803	228	4	for	for	ADP
iajs-2803	228	5	solve	solve	NOUN
iajs-2803	228	6	directly	directly	ADV
iajs-2803	228	7	third	third	ADJ
iajs-2803	228	8	-	-	PUNCT
iajs-2803	228	9	order	order	NOUN
iajs-2803	228	10	ordinary	ordinary	ADJ
iajs-2803	228	11	differential	differential	ADJ
iajs-2803	228	12	equation	equation	NOUN
iajs-2803	228	13	by	by	ADP
iajs-2803	228	14	using	use	VERB
iajs-2803	228	15	runge	runge	NOUN
iajs-2803	228	16	-	-	PUNCT
iajs-2803	228	17	kutta	kutta	NOUN
iajs-2803	228	18	type	type	NOUN
iajs-2803	228	19	method	method	NOUN
iajs-2803	228	20	(	(	PUNCT
iajs-2803	228	21	rktgd	rktgd	PROPN
iajs-2803	228	22	)	)	PUNCT
iajs-2803	228	23	,	,	PUNCT
iajs-2803	228	24	journal	journal	NOUN
iajs-2803	228	25	of	of	ADP
iajs-2803	228	26	physics	physics	PROPN
iajs-2803	228	27	:	:	PUNCT
iajs-2803	228	28	conference	conference	NOUN
iajs-2803	228	29	series	series	NOUN
iajs-2803	228	30	(	(	PUNCT
iajs-2803	228	31	vol	vol	NOUN
iajs-2803	228	32	.	.	PROPN
iajs-2803	228	33	1879	1879	NUM
iajs-2803	228	34	,	,	PUNCT
iajs-2803	228	35	no	no	INTJ
iajs-2803	228	36	.	.	NOUN
iajs-2803	228	37	2	2	NUM
iajs-2803	228	38	,	,	PUNCT
iajs-2803	228	39	p.	p.	NOUN
iajs-2803	228	40	022123	022123	NUM
iajs-2803	228	41	)	)	PUNCT
iajs-2803	228	42	.	.	PUNCT
iajs-2803	229	1	iop	iop	PROPN
iajs-2803	229	2	publishing	publishing	NOUN
iajs-2803	229	3	,	,	PUNCT
iajs-2803	229	4	2021	2021	NUM
iajs-2803	229	5	.	.	PUNCT
iajs-2803	230	1	21	21	NUM
iajs-2803	230	2	.	.	PUNCT
iajs-2803	230	3	butcher	butcher	NOUN
iajs-2803	230	4	,	,	PUNCT
iajs-2803	230	5	john	john	PROPN
iajs-2803	230	6	charles	charles	PROPN
iajs-2803	230	7	,	,	PUNCT
iajs-2803	230	8	and	and	CCONJ
iajs-2803	230	9	nicolette	nicolette	PROPN
iajs-2803	230	10	goodwin	goodwin	PROPN
iajs-2803	230	11	.	.	PUNCT
iajs-2803	231	1	numerical	numerical	ADJ
iajs-2803	231	2	methods	method	NOUN
iajs-2803	231	3	for	for	ADP
iajs-2803	231	4	ordinary	ordinary	ADJ
iajs-2803	231	5	differential	differential	ADJ
iajs-2803	231	6	equations	equation	NOUN
iajs-2803	231	7	.	.	PUNCT
iajs-2803	232	1	new	new	PROPN
iajs-2803	232	2	york	york	PROPN
iajs-2803	232	3	:	:	PUNCT
iajs-2803	232	4	wiley	wiley	PROPN
iajs-2803	232	5	,	,	PUNCT
iajs-2803	232	6	2008	2008	NUM
iajs-2803	232	7	.	.	PUNCT
iajs-2803	233	1	2	2	NUM
iajs-2803	233	2	.	.	NUM
iajs-2803	233	3	22	22	NUM
iajs-2803	233	4	.	.	PUNCT
iajs-2803	234	1	dormand	dormand	PROPN
iajs-2803	234	2	,	,	PUNCT
iajs-2803	234	3	j.	j.	PROPN
iajs-2803	234	4	r.	r.	PROPN
iajs-2803	234	5	numerical	numerical	PROPN
iajs-2803	234	6	methods	method	NOUN
iajs-2803	234	7	for	for	ADP
iajs-2803	234	8	differential	differential	ADJ
iajs-2803	234	9	equations	equation	NOUN
iajs-2803	234	10	:	:	PUNCT
iajs-2803	234	11	a	a	DET
iajs-2803	234	12	computational	computational	ADJ
iajs-2803	234	13	approach	approach	NOUN
iajs-2803	234	14	crc	crc	PROPN
iajs-2803	234	15	press	press	NOUN
iajs-2803	234	16	,	,	PUNCT
iajs-2803	234	17	1996.3	1996.3	NUM
iajs-2803	234	18	.	.	PUNCT
iajs-2803	235	1	23	23	NUM
iajs-2803	235	2	.	.	PUNCT
iajs-2803	236	1	hussain	hussain	PROPN
iajs-2803	236	2	,	,	PUNCT
iajs-2803	236	3	k.	k.	PROPN
iajs-2803	236	4	a.	a.	PROPN
iajs-2803	236	5	,	,	PUNCT
iajs-2803	236	6	ismail	ismail	PROPN
iajs-2803	236	7	,	,	PUNCT
iajs-2803	236	8	f.	f.	PROPN
iajs-2803	236	9	,	,	PUNCT
iajs-2803	236	10	senu	senu	VERB
iajs-2803	236	11	,	,	PUNCT
iajs-2803	236	12	n.	n.	NOUN
iajs-2803	236	13	,	,	PUNCT
iajs-2803	236	14	rabiei	rabiei	PROPN
iajs-2803	236	15	,	,	PUNCT
iajs-2803	236	16	f.	f.	PROPN
iajs-2803	236	17	,	,	PUNCT
iajs-2803	236	18	&	&	CCONJ
iajs-2803	236	19	ibrahim	ibrahim	PROPN
iajs-2803	236	20	,	,	PUNCT
iajs-2803	236	21	r.	r.	NOUN
iajs-2803	236	22	integration	integration	NOUN
iajs-2803	236	23	for	for	ADP
iajs-2803	236	24	special	special	ADJ
iajs-2803	236	25	thirdorder	thirdorder	NOUN
iajs-2803	236	26	ordinary	ordinary	ADJ
iajs-2803	236	27	differential	differential	ADJ
iajs-2803	236	28	equations	equation	NOUN
iajs-2803	236	29	using	use	VERB
iajs-2803	236	30	improved	improved	ADJ
iajs-2803	236	31	runge	runge	NOUN
iajs-2803	236	32	-	-	PUNCT
iajs-2803	236	33	kutta	kutta	NOUN
iajs-2803	236	34	direct	direct	ADJ
iajs-2803	236	35	method	method	NOUN
iajs-2803	236	36	,	,	PUNCT
iajs-2803	236	37	mjs	mjs	NOUN
iajs-2803	236	38	,	,	PUNCT
iajs-2803	236	39	2015	2015	NUM
iajs-2803	236	40	34(2	34(2	NUM
iajs-2803	236	41	)	)	PUNCT
iajs-2803	236	42	,	,	PUNCT
iajs-2803	236	43	172	172	NUM
iajs-2803	236	44	-	-	SYM
iajs-2803	236	45	179	179	NUM
iajs-2803	236	46	.	.	PUNCT