id	sid	tid	token	lemma	pos
iajs-2883	1	1	ihjpas	ihjpas	PROPN
iajs-2883	1	2	.	.	PUNCT
iajs-2883	2	1	36(1)2023	36(1)2023	NUM
iajs-2883	2	2	389	389	NUM
iajs-2883	2	3	this	this	DET
iajs-2883	2	4	work	work	NOUN
iajs-2883	2	5	is	be	AUX
iajs-2883	2	6	licensed	license	VERB
iajs-2883	2	7	under	under	ADP
iajs-2883	2	8	a	a	DET
iajs-2883	2	9	creative	creative	ADJ
iajs-2883	2	10	commons	common	NOUN
iajs-2883	2	11	attribution	attribution	NOUN
iajs-2883	2	12	4.0	4.0	NUM
iajs-2883	2	13	international	international	ADJ
iajs-2883	2	14	license	license	NOUN
iajs-2883	2	15	exponentially	exponentially	ADV
iajs-2883	2	16	fitted	fit	VERB
iajs-2883	2	17	diagonally	diagonally	ADV
iajs-2883	2	18	implicit	implicit	ADJ
iajs-2883	2	19	editrk	editrk	NOUN
iajs-2883	2	20	method	method	NOUN
iajs-2883	2	21	for	for	ADP
iajs-2883	2	22	solving	solve	VERB
iajs-2883	2	23	odes	ode	NOUN
iajs-2883	2	24	abstract	abstract	ADV
iajs-2883	2	25	this	this	DET
iajs-2883	2	26	paper	paper	NOUN
iajs-2883	2	27	derives	derive	VERB
iajs-2883	2	28	the	the	DET
iajs-2883	2	29	editrk4	editrk4	PROPN
iajs-2883	2	30	technique	technique	NOUN
iajs-2883	2	31	,	,	PUNCT
iajs-2883	2	32	which	which	PRON
iajs-2883	2	33	is	be	AUX
iajs-2883	2	34	an	an	DET
iajs-2883	2	35	exponentially	exponentially	ADV
iajs-2883	2	36	fitted	fit	VERB
iajs-2883	2	37	diagonally	diagonally	ADV
iajs-2883	2	38	implicit	implicit	ADJ
iajs-2883	2	39	rk	rk	NOUN
iajs-2883	2	40	method	method	NOUN
iajs-2883	2	41	for	for	ADP
iajs-2883	2	42	solving	solve	VERB
iajs-2883	2	43	odes	ode	NOUN
iajs-2883	2	44	𝑦′′′(𝑥	𝑦′′′(𝑥	NUM
iajs-2883	2	45	)	)	PUNCT
iajs-2883	2	46	=	=	SYM
iajs-2883	3	1	𝑓	𝑓	PROPN
iajs-2883	3	2	(	(	PUNCT
iajs-2883	3	3	𝑥	𝑥	PROPN
iajs-2883	3	4	,	,	PUNCT
iajs-2883	3	5	𝑦	𝑦	NOUN
iajs-2883	3	6	)	)	PUNCT
iajs-2883	3	7	.	.	PUNCT
iajs-2883	4	1	this	this	DET
iajs-2883	4	2	approach	approach	NOUN
iajs-2883	4	3	is	be	AUX
iajs-2883	4	4	intended	intend	VERB
iajs-2883	4	5	to	to	PART
iajs-2883	4	6	integrate	integrate	VERB
iajs-2883	4	7	exactly	exactly	ADV
iajs-2883	4	8	initial	initial	ADJ
iajs-2883	4	9	value	value	NOUN
iajs-2883	4	10	problems	problem	NOUN
iajs-2883	4	11	(	(	PUNCT
iajs-2883	4	12	ivps	ivps	PROPN
iajs-2883	4	13	)	)	PUNCT
iajs-2883	4	14	,	,	PUNCT
iajs-2883	4	15	their	their	PRON
iajs-2883	4	16	solutions	solution	NOUN
iajs-2883	4	17	consist	consist	VERB
iajs-2883	4	18	of	of	ADP
iajs-2883	4	19	linear	linear	ADJ
iajs-2883	4	20	combinations	combination	NOUN
iajs-2883	4	21	of	of	ADP
iajs-2883	4	22	the	the	DET
iajs-2883	4	23	group	group	NOUN
iajs-2883	4	24	functions	function	NOUN
iajs-2883	4	25	𝑒𝑤𝑥	𝑒𝑤𝑥	NOUN
iajs-2883	4	26	and	and	CCONJ
iajs-2883	4	27	𝑒−𝑤𝑥	𝑒−𝑤𝑥	NOUN
iajs-2883	4	28	for	for	ADP
iajs-2883	4	29	exponentially	exponentially	ADV
iajs-2883	4	30	fitting	fitting	ADJ
iajs-2883	4	31	problems	problem	NOUN
iajs-2883	4	32	,	,	PUNCT
iajs-2883	4	33	with	with	ADP
iajs-2883	4	34	𝑤	𝑤	ADP
iajs-2883	4	35	∈	∈	PROPN
iajs-2883	4	36	𝑅	𝑅	PROPN
iajs-2883	4	37	being	be	AUX
iajs-2883	4	38	the	the	DET
iajs-2883	4	39	problem	problem	NOUN
iajs-2883	4	40	’s	’s	PART
iajs-2883	4	41	major	major	ADJ
iajs-2883	4	42	frequency	frequency	NOUN
iajs-2883	4	43	utilized	utilize	VERB
iajs-2883	4	44	to	to	PART
iajs-2883	4	45	improve	improve	VERB
iajs-2883	4	46	the	the	DET
iajs-2883	4	47	precision	precision	NOUN
iajs-2883	4	48	of	of	ADP
iajs-2883	4	49	the	the	DET
iajs-2883	4	50	method	method	NOUN
iajs-2883	4	51	.	.	PUNCT
iajs-2883	5	1	the	the	DET
iajs-2883	5	2	modified	modify	VERB
iajs-2883	5	3	method	method	NOUN
iajs-2883	5	4	editrk4	editrk4	PROPN
iajs-2883	5	5	is	be	AUX
iajs-2883	5	6	a	a	DET
iajs-2883	5	7	new	new	ADJ
iajs-2883	5	8	threestage	threestage	NOUN
iajs-2883	5	9	fourth	fourth	ADJ
iajs-2883	5	10	-	-	PUNCT
iajs-2883	5	11	order	order	NOUN
iajs-2883	5	12	exponentially	exponentially	ADV
iajs-2883	5	13	-	-	PUNCT
iajs-2883	5	14	fitted	fit	VERB
iajs-2883	5	15	diagonally	diagonally	ADV
iajs-2883	5	16	implicit	implicit	ADJ
iajs-2883	5	17	approach	approach	NOUN
iajs-2883	5	18	for	for	ADP
iajs-2883	5	19	solving	solve	VERB
iajs-2883	5	20	ivps	ivps	PROPN
iajs-2883	5	21	with	with	ADP
iajs-2883	5	22	functions	function	NOUN
iajs-2883	5	23	that	that	PRON
iajs-2883	5	24	are	be	AUX
iajs-2883	5	25	exponential	exponential	ADJ
iajs-2883	5	26	as	as	ADP
iajs-2883	5	27	solutions	solution	NOUN
iajs-2883	5	28	.	.	PUNCT
iajs-2883	6	1	different	different	ADJ
iajs-2883	6	2	forms	form	NOUN
iajs-2883	6	3	of	of	ADP
iajs-2883	6	4	3𝑟𝑑-order	3𝑟𝑑-order	NUM
iajs-2883	6	5	odes	ode	NOUN
iajs-2883	6	6	must	must	AUX
iajs-2883	6	7	be	be	AUX
iajs-2883	6	8	derived	derive	VERB
iajs-2883	6	9	using	use	VERB
iajs-2883	6	10	the	the	DET
iajs-2883	6	11	modified	modify	VERB
iajs-2883	6	12	system	system	NOUN
iajs-2883	6	13	,	,	PUNCT
iajs-2883	6	14	and	and	CCONJ
iajs-2883	6	15	when	when	SCONJ
iajs-2883	6	16	the	the	DET
iajs-2883	6	17	same	same	ADJ
iajs-2883	6	18	issue	issue	NOUN
iajs-2883	6	19	is	be	AUX
iajs-2883	6	20	reduced	reduce	VERB
iajs-2883	6	21	to	to	ADP
iajs-2883	6	22	a	a	DET
iajs-2883	6	23	1𝑠𝑡	1𝑠𝑡	ADJ
iajs-2883	6	24	framework	framework	NOUN
iajs-2883	6	25	of	of	ADP
iajs-2883	6	26	equations	equation	NOUN
iajs-2883	6	27	that	that	PRON
iajs-2883	6	28	can	can	AUX
iajs-2883	6	29	be	be	AUX
iajs-2883	6	30	solved	solve	VERB
iajs-2883	6	31	using	use	VERB
iajs-2883	6	32	conventional	conventional	ADJ
iajs-2883	6	33	rk	rk	NOUN
iajs-2883	6	34	approaches	approach	NOUN
iajs-2883	6	35	,	,	PUNCT
iajs-2883	6	36	numerical	numerical	ADJ
iajs-2883	6	37	comparisons	comparison	NOUN
iajs-2883	6	38	must	must	AUX
iajs-2883	6	39	be	be	AUX
iajs-2883	6	40	done	do	VERB
iajs-2883	6	41	.	.	PUNCT
iajs-2883	7	1	the	the	DET
iajs-2883	7	2	findings	finding	NOUN
iajs-2883	7	3	show	show	VERB
iajs-2883	7	4	that	that	SCONJ
iajs-2883	7	5	the	the	DET
iajs-2883	7	6	novel	novel	ADJ
iajs-2883	7	7	approach	approach	NOUN
iajs-2883	7	8	is	be	AUX
iajs-2883	7	9	more	more	ADV
iajs-2883	7	10	efficacious	efficacious	ADJ
iajs-2883	7	11	than	than	ADP
iajs-2883	7	12	previously	previously	ADV
iajs-2883	7	13	published	publish	VERB
iajs-2883	7	14	methods	method	NOUN
iajs-2883	7	15	.	.	PUNCT
iajs-2883	8	1	keyword	keyword	NOUN
iajs-2883	8	2	:	:	PUNCT
iajs-2883	8	3	numerical	numerical	ADJ
iajs-2883	8	4	methods	method	NOUN
iajs-2883	8	5	,	,	PUNCT
iajs-2883	8	6	exponentially	exponentially	ADV
iajs-2883	8	7	fitted	fit	VERB
iajs-2883	8	8	,	,	PUNCT
iajs-2883	8	9	ordinary	ordinary	ADJ
iajs-2883	8	10	differential	differential	ADJ
iajs-2883	8	11	equations	equation	NOUN
iajs-2883	8	12	,	,	PUNCT
iajs-2883	8	13	diagonal	diagonal	ADJ
iajs-2883	8	14	implicit	implicit	ADJ
iajs-2883	8	15	type	type	NOUN
iajs-2883	8	16	runge	runge	NOUN
iajs-2883	8	17	kutta	kutta	NOUN
iajs-2883	8	18	methods	method	NOUN
iajs-2883	8	19	,	,	PUNCT
iajs-2883	8	20	initial	initial	ADJ
iajs-2883	8	21	value	value	NOUN
iajs-2883	8	22	problems	problem	NOUN
iajs-2883	8	23	.	.	PUNCT
iajs-2883	9	1	1.introduction	1.introduction	NUM
iajs-2883	9	2	this	this	DET
iajs-2883	9	3	paper	paper	NOUN
iajs-2883	9	4	is	be	AUX
iajs-2883	9	5	about	about	ADP
iajs-2883	9	6	rk	rk	NOUN
iajs-2883	9	7	type	type	NOUN
iajs-2883	9	8	methods	method	NOUN
iajs-2883	9	9	directly	directly	ADV
iajs-2883	9	10	for	for	ADP
iajs-2883	9	11	solving	solve	VERB
iajs-2883	9	12	3𝑟𝑑-order	3𝑟𝑑-order	NUM
iajs-2883	9	13	odes	ode	NOUN
iajs-2883	9	14	that	that	PRON
iajs-2883	9	15	are	be	AUX
iajs-2883	9	16	exponentially	exponentially	ADV
iajs-2883	9	17	-	-	PUNCT
iajs-2883	9	18	fitted	fit	VERB
iajs-2883	9	19	diagonally	diagonally	ADV
iajs-2883	9	20	implicit	implicit	ADJ
iajs-2883	9	21	in	in	ADP
iajs-2883	9	22	the	the	DET
iajs-2883	9	23	form	form	NOUN
iajs-2883	9	24	:	:	PUNCT
iajs-2883	9	25	𝑣′′′(𝑡	𝑣′′′(𝑡	NUM
iajs-2883	9	26	)	)	PUNCT
iajs-2883	9	27	=	=	SYM
iajs-2883	9	28	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-2883	9	29	,	,	PUNCT
iajs-2883	9	30	𝑣(𝑡	𝑣(𝑡	NOUN
iajs-2883	9	31	)	)	PUNCT
iajs-2883	9	32	)	)	PUNCT
iajs-2883	9	33	,	,	PUNCT
iajs-2883	9	34	𝑣(𝑡0	𝑣(𝑡0	NOUN
iajs-2883	9	35	)	)	PUNCT
iajs-2883	10	1	=	=	SYM
iajs-2883	10	2	𝑣0	𝑣0	PROPN
iajs-2883	10	3	,	,	PUNCT
iajs-2883	10	4	𝑣′(𝑡0	𝑣′(𝑡0	NOUN
iajs-2883	10	5	)	)	PUNCT
iajs-2883	11	1	=	=	PUNCT
iajs-2883	11	2	𝑣0	𝑣0	PROPN
iajs-2883	11	3	′	′	NOUN
iajs-2883	11	4	,	,	PUNCT
iajs-2883	11	5	𝑣′′(𝑡0	𝑣′′(𝑡0	PROPN
iajs-2883	11	6	)	)	PUNCT
iajs-2883	11	7	=	=	PUNCT
iajs-2883	11	8	𝑣0	𝑣0	PROPN
iajs-2883	11	9	′′	′′	PROPN
iajs-2883	11	10	,	,	PUNCT
iajs-2883	11	11	𝑡	𝑡	PROPN
iajs-2883	11	12	≥	≥	PROPN
iajs-2883	11	13	𝑡0	𝑡0	NOUN
iajs-2883	11	14	(	(	PUNCT
iajs-2883	11	15	1	1	NUM
iajs-2883	11	16	)	)	PUNCT
iajs-2883	12	1	where	where	SCONJ
iajs-2883	12	2	𝑣	𝑣	PRON
iajs-2883	12	3	∈	∈	PROPN
iajs-2883	12	4	𝑅𝑑	𝑅𝑑	PROPN
iajs-2883	12	5	,	,	PUNCT
iajs-2883	12	6	𝑓	𝑓	DET
iajs-2883	12	7	∶	∶	NOUN
iajs-2883	12	8	𝑅	𝑅	PROPN
iajs-2883	12	9	×	×	NOUN
iajs-2883	12	10	𝑅𝑑	𝑅𝑑	PROPN
iajs-2883	12	11	→	→	SYM
iajs-2883	12	12	𝑅𝑑	𝑅𝑑	PROPN
iajs-2883	12	13	is	be	AUX
iajs-2883	12	14	a	a	DET
iajs-2883	12	15	continuous	continuous	ADJ
iajs-2883	12	16	vector	vector	NOUN
iajs-2883	12	17	-	-	PUNCT
iajs-2883	12	18	valued	value	VERB
iajs-2883	12	19	operation	operation	NOUN
iajs-2883	12	20	that	that	PRON
iajs-2883	12	21	does	do	AUX
iajs-2883	12	22	not	not	PART
iajs-2883	12	23	rely	rely	VERB
iajs-2883	12	24	on	on	ADP
iajs-2883	12	25	the	the	DET
iajs-2883	12	26	second	second	ADJ
iajs-2883	12	27	derivatives	derivative	NOUN
iajs-2883	12	28	directly	directly	ADV
iajs-2883	12	29	.	.	PUNCT
iajs-2883	13	1	numerous	numerous	ADJ
iajs-2883	13	2	physical	physical	ADJ
iajs-2883	13	3	issues	issue	NOUN
iajs-2883	13	4	,	,	PUNCT
iajs-2883	13	5	such	such	ADJ
iajs-2883	13	6	as	as	ADP
iajs-2883	13	7	thin	thin	ADJ
iajs-2883	13	8	-	-	PUNCT
iajs-2883	13	9	film	film	NOUN
iajs-2883	13	10	flow	flow	NOUN
iajs-2883	13	11	and	and	CCONJ
iajs-2883	13	12	gravitydriven	gravitydriven	ADJ
iajs-2883	13	13	fluxes	flux	NOUN
iajs-2883	13	14	,	,	PUNCT
iajs-2883	13	15	need	need	VERB
iajs-2883	13	16	to	to	PART
iajs-2883	13	17	be	be	AUX
iajs-2883	13	18	addressed	address	VERB
iajs-2883	13	19	,	,	PUNCT
iajs-2883	13	20	and	and	CCONJ
iajs-2883	13	21	so	so	ADV
iajs-2883	13	22	on	on	ADV
iajs-2883	13	23	,	,	PUNCT
iajs-2883	13	24	have	have	VERB
iajs-2883	13	25	this	this	DET
iajs-2883	13	26	type	type	NOUN
iajs-2883	13	27	of	of	ADP
iajs-2883	13	28	problem	problem	NOUN
iajs-2883	13	29	[	[	X
iajs-2883	13	30	1	1	NUM
iajs-2883	13	31	-	-	SYM
iajs-2883	13	32	3	3	NUM
iajs-2883	13	33	]	]	PUNCT
iajs-2883	13	34	.	.	PUNCT
iajs-2883	14	1	then	then	ADV
iajs-2883	14	2	,	,	PUNCT
iajs-2883	14	3	some	some	DET
iajs-2883	14	4	researchers	researcher	NOUN
iajs-2883	14	5	have	have	AUX
iajs-2883	14	6	constructed	construct	VERB
iajs-2883	14	7	explicit	explicit	ADJ
iajs-2883	14	8	rk	rk	NOUN
iajs-2883	14	9	methods	method	NOUN
iajs-2883	14	10	for	for	ADP
iajs-2883	14	11	solving	solve	VERB
iajs-2883	14	12	1𝑠𝑡-order	1𝑠𝑡-order	NUM
iajs-2883	14	13	and	and	CCONJ
iajs-2883	14	14	2𝑛𝑑-order	2𝑛𝑑-order	NUM
iajs-2883	14	15	odes	ode	VERB
iajs-2883	14	16	that	that	DET
iajs-2883	14	17	doi.org/10.30526/36.1.2883	doi.org/10.30526/36.1.2883	NOUN
iajs-2883	14	18	article	article	NOUN
iajs-2883	14	19	history	history	NOUN
iajs-2883	14	20	:	:	PUNCT
iajs-2883	14	21	received	receive	VERB
iajs-2883	14	22	21	21	NUM
iajs-2883	14	23	june	june	PROPN
iajs-2883	14	24	2022	2022	NUM
iajs-2883	14	25	,	,	PUNCT
iajs-2883	14	26	accepted	accept	VERB
iajs-2883	14	27	21	21	NUM
iajs-2883	14	28	augest	augest	NOUN
iajs-2883	14	29	2022	2022	NUM
iajs-2883	14	30	,	,	PUNCT
iajs-2883	14	31	published	publish	VERB
iajs-2883	14	32	in	in	ADP
iajs-2883	14	33	january	january	PROPN
iajs-2883	14	34	2023	2023	NUM
iajs-2883	14	35	.	.	PUNCT
iajs-2883	15	1	ibn	ibn	PROPN
iajs-2883	15	2	al	al	PROPN
iajs-2883	15	3	-	-	PUNCT
iajs-2883	15	4	haitham	haitham	PROPN
iajs-2883	15	5	journal	journal	PROPN
iajs-2883	15	6	for	for	ADP
iajs-2883	15	7	pure	pure	ADJ
iajs-2883	15	8	and	and	CCONJ
iajs-2883	15	9	applied	applied	ADJ
iajs-2883	15	10	sciences	sciences	PROPN
iajs-2883	15	11	journal	journal	PROPN
iajs-2883	15	12	homepage	homepage	NOUN
iajs-2883	15	13	:	:	PUNCT
iajs-2883	15	14	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	NOUN
iajs-2883	15	15	firas	firas	PROPN
iajs-2883	15	16	adel	adel	PROPN
iajs-2883	15	17	fawzi	fawzi	PROPN
iajs-2883	15	18	department	department	PROPN
iajs-2883	15	19	of	of	ADP
iajs-2883	15	20	mathematics	mathematic	NOUN
iajs-2883	15	21	,	,	PUNCT
iajs-2883	15	22	faculty	faculty	NOUN
iajs-2883	15	23	of	of	ADP
iajs-2883	15	24	computer	computer	NOUN
iajs-2883	15	25	science	science	NOUN
iajs-2883	15	26	and	and	CCONJ
iajs-2883	15	27	mathematics	mathematic	NOUN
iajs-2883	15	28	,	,	PUNCT
iajs-2883	15	29	university	university	NOUN
iajs-2883	15	30	of	of	ADP
iajs-2883	15	31	tikrit	tikrit	NOUN
iajs-2883	15	32	,	,	PUNCT
iajs-2883	15	33	iraq	iraq	PROPN
iajs-2883	15	34	.	.	PUNCT
iajs-2883	16	1	firasadil01@tu.edu.iq	firasadil01@tu.edu.iq	PROPN
iajs-2883	16	2	nour	nour	PROPN
iajs-2883	16	3	w.	w.	PROPN
iajs-2883	16	4	jaleel	jaleel	PROPN
iajs-2883	16	5	department	department	PROPN
iajs-2883	16	6	of	of	ADP
iajs-2883	16	7	mathematics	mathematic	NOUN
iajs-2883	16	8	,	,	PUNCT
iajs-2883	16	9	faculty	faculty	NOUN
iajs-2883	16	10	of	of	ADP
iajs-2883	16	11	computer	computer	NOUN
iajs-2883	16	12	science	science	NOUN
iajs-2883	16	13	and	and	CCONJ
iajs-2883	16	14	mathematics	mathematic	NOUN
iajs-2883	16	15	,	,	PUNCT
iajs-2883	16	16	university	university	NOUN
iajs-2883	16	17	of	of	ADP
iajs-2883	16	18	tikrit	tikrit	NOUN
iajs-2883	16	19	,	,	PUNCT
iajs-2883	16	20	iraq	iraq	PROPN
iajs-2883	16	21	.	.	PUNCT
iajs-2883	17	1	ur.w.jaleel35433@st.tu.edu.iq	ur.w.jaleel35433@st.tu.edu.iq	PROPN
iajs-2883	18	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-2883	18	2	mailto:firasadil01@tu.edu.iq	mailto:firasadil01@tu.edu.iq	PROPN
iajs-2883	18	3	ihjpas	ihjpas	PROPN
iajs-2883	18	4	.	.	PUNCT
iajs-2883	19	1	36(1)2023	36(1)2023	NUM
iajs-2883	19	2	390	390	NUM
iajs-2883	19	3	are	be	AUX
iajs-2883	19	4	exponentially	exponentially	ADV
iajs-2883	19	5	and	and	CCONJ
iajs-2883	19	6	trigonometrically	trigonometrically	ADV
iajs-2883	19	7	fitted	fit	VERB
iajs-2883	19	8	in	in	ADP
iajs-2883	19	9	recent	recent	ADJ
iajs-2883	19	10	years	year	NOUN
iajs-2883	19	11	.	.	PUNCT
iajs-2883	20	1	because	because	SCONJ
iajs-2883	20	2	implicit	implicit	ADJ
iajs-2883	20	3	techniques	technique	NOUN
iajs-2883	20	4	can	can	AUX
iajs-2883	20	5	attain	attain	VERB
iajs-2883	20	6	higher	high	ADJ
iajs-2883	20	7	levels	level	NOUN
iajs-2883	20	8	of	of	ADP
iajs-2883	20	9	accuracy	accuracy	NOUN
iajs-2883	20	10	for	for	ADP
iajs-2883	20	11	the	the	DET
iajs-2883	20	12	same	same	ADJ
iajs-2883	20	13	stage	stage	NOUN
iajs-2883	20	14	number	number	NOUN
iajs-2883	20	15	as	as	ADP
iajs-2883	20	16	explicit	explicit	ADJ
iajs-2883	20	17	methods	method	NOUN
iajs-2883	20	18	,	,	PUNCT
iajs-2883	20	19	they	they	PRON
iajs-2883	20	20	are	be	AUX
iajs-2883	20	21	essential	essential	ADJ
iajs-2883	20	22	.	.	PUNCT
iajs-2883	21	1	it	it	PRON
iajs-2883	21	2	becomes	become	VERB
iajs-2883	21	3	easier	easy	ADJ
iajs-2883	21	4	to	to	PART
iajs-2883	21	5	resolve	resolve	VERB
iajs-2883	21	6	challenging	challenging	ADJ
iajs-2883	21	7	problems	problem	NOUN
iajs-2883	21	8	as	as	ADP
iajs-2883	21	9	a	a	DET
iajs-2883	21	10	result	result	NOUN
iajs-2883	21	11	of	of	ADP
iajs-2883	21	12	this	this	PRON
iajs-2883	21	13	.	.	PUNCT
iajs-2883	22	1	implicit	implicit	ADJ
iajs-2883	22	2	(	(	PUNCT
iajs-2883	22	3	rk	rk	NOUN
iajs-2883	22	4	)	)	PUNCT
iajs-2883	22	5	approaches	approach	NOUN
iajs-2883	22	6	,	,	PUNCT
iajs-2883	22	7	on	on	ADP
iajs-2883	22	8	the	the	DET
iajs-2883	22	9	other	other	ADJ
iajs-2883	22	10	hand	hand	NOUN
iajs-2883	22	11	,	,	PUNCT
iajs-2883	22	12	play	play	VERB
iajs-2883	22	13	a	a	DET
iajs-2883	22	14	crucial	crucial	ADJ
iajs-2883	22	15	role	role	NOUN
iajs-2883	22	16	in	in	ADP
iajs-2883	22	17	other	other	ADJ
iajs-2883	22	18	types	type	NOUN
iajs-2883	22	19	of	of	ADP
iajs-2883	22	20	problems	problem	NOUN
iajs-2883	22	21	,	,	PUNCT
iajs-2883	22	22	such	such	ADJ
iajs-2883	22	23	as	as	ADP
iajs-2883	22	24	differential	differential	ADJ
iajs-2883	22	25	-	-	PUNCT
iajs-2883	22	26	algebraic	algebraic	ADJ
iajs-2883	22	27	neutralization	neutralization	NOUN
iajs-2883	22	28	.	.	PUNCT
iajs-2883	23	1	furthermore	furthermore	ADV
iajs-2883	23	2	,	,	PUNCT
iajs-2883	23	3	because	because	SCONJ
iajs-2883	23	4	they	they	PRON
iajs-2883	23	5	have	have	VERB
iajs-2883	23	6	a	a	DET
iajs-2883	23	7	lower	low	ADJ
iajs-2883	23	8	triangular	triangular	NOUN
iajs-2883	23	9	a	a	DET
iajs-2883	23	10	-	-	PUNCT
iajs-2883	23	11	matrix	matrix	NOUN
iajs-2883	23	12	with	with	ADP
iajs-2883	23	13	at	at	ADV
iajs-2883	23	14	least	least	ADV
iajs-2883	23	15	one	one	NUM
iajs-2883	23	16	nonzero	nonzero	NOUN
iajs-2883	23	17	diagonal	diagonal	ADJ
iajs-2883	23	18	element	element	NOUN
iajs-2883	23	19	,	,	PUNCT
iajs-2883	23	20	diagonally	diagonally	ADV
iajs-2883	23	21	implicit	implicit	ADJ
iajs-2883	23	22	rk	rk	NOUN
iajs-2883	23	23	methods	method	NOUN
iajs-2883	23	24	are	be	AUX
iajs-2883	23	25	sometimes	sometimes	ADV
iajs-2883	23	26	known	know	VERB
iajs-2883	23	27	as	as	ADP
iajs-2883	23	28	semi-(implicit	semi-(implicit	ADJ
iajs-2883	23	29	or	or	CCONJ
iajs-2883	23	30	explicit	explicit	ADJ
iajs-2883	23	31	)	)	PUNCT
iajs-2883	23	32	rk	rk	NOUN
iajs-2883	23	33	approaches	approach	NOUN
iajs-2883	23	34	.	.	PUNCT
iajs-2883	24	1	for	for	SCONJ
iajs-2883	24	2	trigonometric	trigonometric	ADJ
iajs-2883	24	3	polynomial	polynomial	ADJ
iajs-2883	24	4	periodic	periodic	ADJ
iajs-2883	24	5	solutions	solution	NOUN
iajs-2883	24	6	to	to	PART
iajs-2883	24	7	odes	ode	NOUN
iajs-2883	24	8	,	,	PUNCT
iajs-2883	24	9	[	[	X
iajs-2883	24	10	4	4	NUM
iajs-2883	24	11	]	]	PUNCT
iajs-2883	24	12	developed	develop	VERB
iajs-2883	24	13	runge	runge	NOUN
iajs-2883	24	14	-	-	PUNCT
iajs-2883	24	15	kutta	kutta	NOUN
iajs-2883	24	16	-	-	PUNCT
iajs-2883	24	17	nyström	nyström	NOUN
iajs-2883	24	18	techniques	technique	NOUN
iajs-2883	24	19	.	.	PUNCT
iajs-2883	25	1	exponentially	exponentially	ADV
iajs-2883	25	2	adapted	adapt	VERB
iajs-2883	25	3	rk	rk	NOUN
iajs-2883	25	4	algorithms	algorithm	NOUN
iajs-2883	25	5	were	be	AUX
iajs-2883	25	6	developed	develop	VERB
iajs-2883	25	7	by	by	ADP
iajs-2883	25	8	[	[	X
iajs-2883	25	9	5	5	NUM
iajs-2883	25	10	]	]	PUNCT
iajs-2883	25	11	.	.	PUNCT
iajs-2883	26	1	while	while	SCONJ
iajs-2883	26	2	[	[	X
iajs-2883	26	3	6	6	NUM
iajs-2883	26	4	]	]	PUNCT
iajs-2883	26	5	presents	present	VERB
iajs-2883	26	6	an	an	DET
iajs-2883	26	7	extended	extended	ADJ
iajs-2883	26	8	version	version	NOUN
iajs-2883	26	9	of	of	ADP
iajs-2883	26	10	the	the	DET
iajs-2883	26	11	rk	rk	NOUN
iajs-2883	26	12	method	method	NOUN
iajs-2883	26	13	that	that	PRON
iajs-2883	26	14	tackles	tackle	VERB
iajs-2883	26	15	the	the	DET
iajs-2883	26	16	problems	problem	NOUN
iajs-2883	26	17	of	of	ADP
iajs-2883	26	18	the	the	DET
iajs-2883	26	19	schrödinger	schrödinger	ADJ
iajs-2883	26	20	equation	equation	NOUN
iajs-2883	26	21	.	.	PUNCT
iajs-2883	27	1	the	the	DET
iajs-2883	27	2	majority	majority	NOUN
iajs-2883	27	3	of	of	ADP
iajs-2883	27	4	scientists	scientist	NOUN
iajs-2883	27	5	,	,	PUNCT
iajs-2883	27	6	engineers	engineer	NOUN
iajs-2883	27	7	,	,	PUNCT
iajs-2883	27	8	and	and	CCONJ
iajs-2883	27	9	researchers	researcher	NOUN
iajs-2883	27	10	utilized	utilize	VERB
iajs-2883	27	11	to	to	PART
iajs-2883	27	12	resolve	resolve	VERB
iajs-2883	27	13	(	(	PUNCT
iajs-2883	27	14	1	1	NUM
iajs-2883	27	15	)	)	PUNCT
iajs-2883	27	16	by	by	ADP
iajs-2883	27	17	reducing	reduce	VERB
iajs-2883	27	18	third	third	ADJ
iajs-2883	27	19	-	-	PUNCT
iajs-2883	27	20	order	order	NOUN
iajs-2883	27	21	differential	differential	ADJ
iajs-2883	27	22	equations	equation	NOUN
iajs-2883	27	23	to	to	ADP
iajs-2883	27	24	a	a	DET
iajs-2883	27	25	three	three	NUM
iajs-2883	27	26	-	-	PUNCT
iajs-2883	27	27	dimensional	dimensional	ADJ
iajs-2883	27	28	system	system	NOUN
iajs-2883	27	29	of	of	ADP
iajs-2883	27	30	1𝑠𝑡-order	1𝑠𝑡-order	NUM
iajs-2883	27	31	equations	equation	NOUN
iajs-2883	27	32	.	.	PUNCT
iajs-2883	28	1	however	however	ADV
iajs-2883	28	2	,	,	PUNCT
iajs-2883	28	3	if	if	SCONJ
iajs-2883	28	4	the	the	DET
iajs-2883	28	5	problem	problem	NOUN
iajs-2883	28	6	can	can	AUX
iajs-2883	28	7	be	be	AUX
iajs-2883	28	8	solved	solve	VERB
iajs-2883	28	9	directly	directly	ADV
iajs-2883	28	10	using	use	VERB
iajs-2883	28	11	numerical	numerical	ADJ
iajs-2883	28	12	methods	method	NOUN
iajs-2883	28	13	,	,	PUNCT
iajs-2883	28	14	it	it	PRON
iajs-2883	28	15	is	be	AUX
iajs-2883	28	16	more	more	ADV
iajs-2883	28	17	efficient	efficient	ADJ
iajs-2883	28	18	.	.	PUNCT
iajs-2883	29	1	in	in	ADP
iajs-2883	29	2	[	[	PUNCT
iajs-2883	29	3	7	7	NUM
iajs-2883	29	4	-	-	SYM
iajs-2883	29	5	9	9	NUM
iajs-2883	29	6	]	]	PUNCT
iajs-2883	29	7	are	be	AUX
iajs-2883	29	8	examples	example	NOUN
iajs-2883	29	9	of	of	ADP
iajs-2883	29	10	this	this	DET
iajs-2883	29	11	type	type	NOUN
iajs-2883	29	12	of	of	ADP
iajs-2883	29	13	work	work	NOUN
iajs-2883	29	14	.	.	PUNCT
iajs-2883	30	1	two	two	NUM
iajs-2883	30	2	explicit	explicit	ADJ
iajs-2883	30	3	two	two	NUM
iajs-2883	30	4	-	-	PUNCT
iajs-2883	30	5	derivative	derivative	ADJ
iajs-2883	30	6	rkn	rkn	NOUN
iajs-2883	30	7	techniques	technique	NOUN
iajs-2883	30	8	,	,	PUNCT
iajs-2883	30	9	one	one	NUM
iajs-2883	30	10	exponentially	exponentially	ADV
iajs-2883	30	11	fitted	fit	VERB
iajs-2883	30	12	and	and	CCONJ
iajs-2883	30	13	the	the	DET
iajs-2883	30	14	other	other	ADJ
iajs-2883	30	15	trigonometrically	trigonometrically	ADV
iajs-2883	30	16	fitted	fit	VERB
iajs-2883	30	17	,	,	PUNCT
iajs-2883	30	18	are	be	AUX
iajs-2883	30	19	constructed	construct	VERB
iajs-2883	30	20	in	in	ADP
iajs-2883	30	21	[	[	X
iajs-2883	30	22	10	10	NUM
iajs-2883	30	23	]	]	PUNCT
iajs-2883	30	24	.	.	PUNCT
iajs-2883	31	1	then	then	ADV
iajs-2883	31	2	,	,	PUNCT
iajs-2883	31	3	using	use	VERB
iajs-2883	31	4	the	the	DET
iajs-2883	31	5	simos	simos	ADJ
iajs-2883	31	6	technique	technique	NOUN
iajs-2883	31	7	,	,	PUNCT
iajs-2883	31	8	demba	demba	PROPN
iajs-2883	31	9	et	et	PROPN
iajs-2883	31	10	al	al	PROPN
iajs-2883	31	11	.	.	PUNCT
iajs-2883	32	1	[	[	X
iajs-2883	32	2	11	11	NUM
iajs-2883	32	3	]	]	PUNCT
iajs-2883	32	4	implemented	implement	VERB
iajs-2883	32	5	an	an	DET
iajs-2883	32	6	explicit	explicit	ADJ
iajs-2883	32	7	trigonometrically	trigonometrically	ADV
iajs-2883	32	8	fitted	fit	VERB
iajs-2883	32	9	rkn	rkn	NOUN
iajs-2883	32	10	method	method	NOUN
iajs-2883	32	11	.	.	PUNCT
iajs-2883	33	1	furthermore	furthermore	ADV
iajs-2883	33	2	,	,	PUNCT
iajs-2883	33	3	[	[	X
iajs-2883	33	4	12	12	NUM
iajs-2883	33	5	]	]	PUNCT
iajs-2883	33	6	and	and	CCONJ
iajs-2883	33	7	[	[	X
iajs-2883	33	8	13	13	NUM
iajs-2883	33	9	]	]	PUNCT
iajs-2883	33	10	are	be	AUX
iajs-2883	33	11	to	to	PART
iajs-2883	33	12	demonstrate	demonstrate	VERB
iajs-2883	33	13	how	how	SCONJ
iajs-2883	33	14	the	the	DET
iajs-2883	33	15	direct	direct	ADJ
iajs-2883	33	16	method	method	NOUN
iajs-2883	33	17	is	be	AUX
iajs-2883	33	18	used	use	VERB
iajs-2883	33	19	to	to	PART
iajs-2883	33	20	solve	solve	VERB
iajs-2883	33	21	specific	specific	ADJ
iajs-2883	33	22	third	third	ADJ
iajs-2883	33	23	and	and	CCONJ
iajs-2883	33	24	fourth	fourth	ADJ
iajs-2883	33	25	-	-	PUNCT
iajs-2883	33	26	order	order	NOUN
iajs-2883	33	27	odes	ode	NOUN
iajs-2883	33	28	.	.	PUNCT
iajs-2883	34	1	the	the	DET
iajs-2883	34	2	major	major	ADJ
iajs-2883	34	3	purpose	purpose	NOUN
iajs-2883	34	4	of	of	ADP
iajs-2883	34	5	this	this	DET
iajs-2883	34	6	research	research	NOUN
iajs-2883	34	7	is	be	AUX
iajs-2883	34	8	to	to	PART
iajs-2883	34	9	show	show	VERB
iajs-2883	34	10	how	how	SCONJ
iajs-2883	34	11	to	to	PART
iajs-2883	34	12	solve	solve	VERB
iajs-2883	34	13	special	special	ADJ
iajs-2883	34	14	3𝑟𝑑-order	3𝑟𝑑-order	NUM
iajs-2883	34	15	odes	ode	NOUN
iajs-2883	34	16	using	use	VERB
iajs-2883	34	17	an	an	DET
iajs-2883	34	18	exponentially	exponentially	ADV
iajs-2883	34	19	-	-	PUNCT
iajs-2883	34	20	fitted	fit	VERB
iajs-2883	34	21	diagonally	diagonally	ADV
iajs-2883	34	22	implicit	implicit	ADJ
iajs-2883	34	23	rk	rk	NOUN
iajs-2883	34	24	method	method	NOUN
iajs-2883	34	25	.	.	PUNCT
iajs-2883	35	1	in	in	ADP
iajs-2883	35	2	addition	addition	NOUN
iajs-2883	35	3	,	,	PUNCT
iajs-2883	35	4	(	(	PUNCT
iajs-2883	35	5	1	1	X
iajs-2883	35	6	)	)	PUNCT
iajs-2883	35	7	is	be	AUX
iajs-2883	35	8	solved	solve	VERB
iajs-2883	35	9	numerically	numerically	ADV
iajs-2883	35	10	using	use	VERB
iajs-2883	35	11	the	the	DET
iajs-2883	35	12	approach	approach	NOUN
iajs-2883	35	13	's	's	PART
iajs-2883	35	14	algebraic	algebraic	ADJ
iajs-2883	35	15	order	order	NOUN
iajs-2883	35	16	must	must	AUX
iajs-2883	35	17	be	be	AUX
iajs-2883	35	18	considered	consider	VERB
iajs-2883	35	19	,	,	PUNCT
iajs-2883	35	20	as	as	SCONJ
iajs-2883	35	21	it	it	PRON
iajs-2883	35	22	is	be	AUX
iajs-2883	35	23	the	the	DET
iajs-2883	35	24	most	most	ADV
iajs-2883	35	25	essential	essential	ADJ
iajs-2883	35	26	aspect	aspect	NOUN
iajs-2883	35	27	in	in	ADP
iajs-2883	35	28	achieving	achieve	VERB
iajs-2883	35	29	high	high	ADJ
iajs-2883	35	30	accuracy	accuracy	NOUN
iajs-2883	35	31	.	.	PUNCT
iajs-2883	36	1	the	the	DET
iajs-2883	36	2	required	require	VERB
iajs-2883	36	3	criteria	criterion	NOUN
iajs-2883	36	4	and	and	CCONJ
iajs-2883	36	5	derivation	derivation	NOUN
iajs-2883	36	6	for	for	ADP
iajs-2883	36	7	exponentially	exponentially	ADV
iajs-2883	36	8	fitted	fit	VERB
iajs-2883	36	9	3𝑟𝑑-order	3𝑟𝑑-order	NUM
iajs-2883	36	10	odes	ode	NOUN
iajs-2883	36	11	are	be	AUX
iajs-2883	36	12	solved	solve	VERB
iajs-2883	36	13	using	use	VERB
iajs-2883	36	14	rk	rk	NOUN
iajs-2883	36	15	techniques	technique	NOUN
iajs-2883	36	16	and	and	CCONJ
iajs-2883	36	17	presented	present	VERB
iajs-2883	36	18	in	in	ADP
iajs-2883	36	19	part	part	NOUN
iajs-2883	36	20	3	3	NUM
iajs-2883	36	21	.	.	PUNCT
iajs-2883	36	22	section	section	NOUN
iajs-2883	36	23	4	4	NUM
iajs-2883	36	24	compares	compare	VERB
iajs-2883	36	25	the	the	DET
iajs-2883	36	26	effectiveness	effectiveness	NOUN
iajs-2883	36	27	of	of	ADP
iajs-2883	36	28	the	the	DET
iajs-2883	36	29	new	new	ADJ
iajs-2883	36	30	method	method	NOUN
iajs-2883	36	31	to	to	ADP
iajs-2883	36	32	that	that	PRON
iajs-2883	36	33	of	of	ADP
iajs-2883	36	34	previous	previous	ADJ
iajs-2883	36	35	methods	method	NOUN
iajs-2883	36	36	.	.	PUNCT
iajs-2883	37	1	for	for	ADP
iajs-2883	37	2	addressing	address	VERB
iajs-2883	37	3	the	the	DET
iajs-2883	37	4	ivps	ivps	PROPN
iajs-2883	37	5	problem	problem	NOUN
iajs-2883	37	6	(	(	PUNCT
iajs-2883	37	7	1	1	NUM
iajs-2883	37	8	)	)	PUNCT
iajs-2883	37	9	,	,	PUNCT
iajs-2883	37	10	the	the	DET
iajs-2883	37	11	general	general	ADJ
iajs-2883	37	12	structure	structure	NOUN
iajs-2883	37	13	of	of	ADP
iajs-2883	37	14	the	the	DET
iajs-2883	37	15	editrk4	editrk4	PROPN
iajs-2883	37	16	approach	approach	NOUN
iajs-2883	37	17	with	with	ADP
iajs-2883	37	18	an	an	DET
iajs-2883	37	19	m	m	NOUN
iajs-2883	37	20	-	-	NOUN
iajs-2883	37	21	stage	stage	NOUN
iajs-2883	37	22	:	:	PUNCT
iajs-2883	37	23	𝑣𝑛+1	𝑣𝑛+1	NUM
iajs-2883	37	24	=	=	SYM
iajs-2883	37	25	𝑣𝑛	𝑣𝑛	PROPN
iajs-2883	37	26	+	+	CCONJ
iajs-2883	37	27	ℎ𝑣𝑛	ℎ𝑣𝑛	PROPN
iajs-2883	37	28	′	′	NOUN
iajs-2883	38	1	+	+	CCONJ
iajs-2883	38	2	ℎ2	ℎ2	ADJ
iajs-2883	38	3	2	2	NUM
iajs-2883	38	4	𝑣𝑛	𝑣𝑛	ADP
iajs-2883	38	5	′′	′′	PROPN
iajs-2883	38	6	+	+	CCONJ
iajs-2883	38	7	ℎ3	ℎ3	NOUN
iajs-2883	38	8	∑	∑	ADV
iajs-2883	38	9	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	38	10	𝑚	𝑚	PROPN
iajs-2883	38	11	𝑖=1	𝑖=1	PROPN
iajs-2883	38	12	𝑘𝑖	𝑘𝑖	ADP
iajs-2883	38	13	,	,	PUNCT
iajs-2883	38	14	(	(	PUNCT
iajs-2883	38	15	2	2	X
iajs-2883	38	16	)	)	PUNCT
iajs-2883	38	17	𝑣𝑛+1	𝑣𝑛+1	NOUN
iajs-2883	38	18	′	′	NOUN
iajs-2883	38	19	=	=	SYM
iajs-2883	38	20	𝑣𝑛	𝑣𝑛	NOUN
iajs-2883	38	21	′	′	NOUN
iajs-2883	38	22	+	+	CCONJ
iajs-2883	38	23	ℎ𝑣𝑛	ℎ𝑣𝑛	PROPN
iajs-2883	38	24	′′	′′	PROPN
iajs-2883	38	25	+	+	CCONJ
iajs-2883	38	26	ℎ2	ℎ2	NOUN
iajs-2883	38	27	∑	∑	PUNCT
iajs-2883	38	28	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	38	29	′𝑚	′𝑚	NOUN
iajs-2883	38	30	𝑖=1	𝑖=1	PROPN
iajs-2883	38	31	𝑘𝑖	𝑘𝑖	VERB
iajs-2883	38	32	,	,	PUNCT
iajs-2883	38	33	(	(	PUNCT
iajs-2883	38	34	3	3	X
iajs-2883	38	35	)	)	PUNCT
iajs-2883	38	36	𝑣𝑛+1	𝑣𝑛+1	NUM
iajs-2883	39	1	′′	′′	NOUN
iajs-2883	39	2	=	=	SYM
iajs-2883	39	3	𝑣𝑛	𝑣𝑛	PROPN
iajs-2883	39	4	′′	′′	PROPN
iajs-2883	39	5	+	+	CCONJ
iajs-2883	39	6	ℎ	ℎ	PROPN
iajs-2883	39	7	∑	∑	PUNCT
iajs-2883	39	8	𝑏𝑖	𝑏𝑖	PROPN
iajs-2883	39	9	′′𝑚	′′𝑚	NOUN
iajs-2883	39	10	𝑖=1	𝑖=1	PROPN
iajs-2883	39	11	𝑘𝑖	𝑘𝑖	X
iajs-2883	39	12	.	.	PUNCT
iajs-2883	40	1	(	(	PUNCT
iajs-2883	40	2	4	4	X
iajs-2883	40	3	)	)	PUNCT
iajs-2883	40	4	where	where	SCONJ
iajs-2883	40	5	𝑘𝑖	𝑘𝑖	NOUN
iajs-2883	40	6	=	=	SYM
iajs-2883	40	7	𝑓	𝑓	PROPN
iajs-2883	40	8	(	(	PUNCT
iajs-2883	40	9	𝑥𝑛	𝑥𝑛	PROPN
iajs-2883	40	10	+	+	CCONJ
iajs-2883	40	11	𝑐𝑖ℎ	𝑐𝑖ℎ	ADJ
iajs-2883	40	12	,	,	PUNCT
iajs-2883	40	13	𝑣𝑛	𝑣𝑛	ADP
iajs-2883	40	14	+	+	CCONJ
iajs-2883	40	15	𝑐𝑖ℎ𝑣𝑛	𝑐𝑖ℎ𝑣𝑛	NOUN
iajs-2883	40	16	′	′	NOUN
iajs-2883	41	1	+	+	CCONJ
iajs-2883	41	2	ℎ2	ℎ2	ADJ
iajs-2883	41	3	2	2	NUM
iajs-2883	41	4	𝑐𝑖	𝑐𝑖	NOUN
iajs-2883	41	5	2	2	NUM
iajs-2883	41	6	𝑣𝑛	𝑣𝑛	ADP
iajs-2883	41	7	′′	′′	PROPN
iajs-2883	41	8	+	+	CCONJ
iajs-2883	41	9	ℎ3	ℎ3	PROPN
iajs-2883	41	10	∑	∑	PUNCT
iajs-2883	41	11	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-2883	41	12	𝑖−1	𝑖−1	PROPN
iajs-2883	41	13	𝑗=1	𝑗=1	PROPN
iajs-2883	41	14	𝑘𝑗	𝑘𝑗	PROPN
iajs-2883	41	15	)	)	PUNCT
iajs-2883	41	16	,	,	PUNCT
iajs-2883	41	17	(	(	PUNCT
iajs-2883	41	18	5	5	X
iajs-2883	41	19	)	)	PUNCT
iajs-2883	41	20	for	for	ADP
iajs-2883	41	21	𝑖	𝑖	NOUN
iajs-2883	41	22	=	=	SYM
iajs-2883	41	23	2,3	2,3	NUM
iajs-2883	41	24	,	,	PUNCT
iajs-2883	41	25	…	…	PUNCT
iajs-2883	41	26	,	,	PUNCT
iajs-2883	41	27	𝑚.	𝑚.	VERB
iajs-2883	41	28	the	the	DET
iajs-2883	41	29	diagonal	diagonal	ADJ
iajs-2883	41	30	implicit	implicit	ADJ
iajs-2883	41	31	rk	rk	NOUN
iajs-2883	41	32	type	type	NOUN
iajs-2883	41	33	parameters	parameter	NOUN
iajs-2883	41	34	(	(	PUNCT
iajs-2883	41	35	editrk4	editrk4	PROPN
iajs-2883	41	36	)	)	PUNCT
iajs-2883	41	37	techniques	technique	NOUN
iajs-2883	41	38	are	be	AUX
iajs-2883	41	39	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	41	40	,	,	PUNCT
iajs-2883	41	41	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	41	42	′	′	NUM
iajs-2883	41	43	,	,	PUNCT
iajs-2883	41	44	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	41	45	′′	′′	PROPN
iajs-2883	41	46	,	,	PUNCT
iajs-2883	41	47	𝑎𝑖,𝑗	𝑎𝑖,𝑗	PUNCT
iajs-2883	41	48	and	and	CCONJ
iajs-2883	41	49	𝑐𝑖	𝑐𝑖	NOUN
iajs-2883	41	50	of	of	ADP
iajs-2883	41	51	where	where	SCONJ
iajs-2883	41	52	𝑖	𝑖	NOUN
iajs-2883	41	53	=	=	SYM
iajs-2883	41	54	2	2	NUM
iajs-2883	41	55	,	,	PUNCT
iajs-2883	41	56	3	3	NUM
iajs-2883	41	57	,	,	PUNCT
iajs-2883	41	58	.	.	PUNCT
iajs-2883	41	59	.	.	PUNCT
iajs-2883	42	1	.	.	PUNCT
iajs-2883	43	1	,	,	PUNCT
iajs-2883	43	2	𝑚	𝑚	X
iajs-2883	43	3	,	,	PUNCT
iajs-2883	43	4	are	be	AUX
iajs-2883	43	5	genuine	genuine	ADJ
iajs-2883	43	6	integers	integer	NOUN
iajs-2883	43	7	as	as	ADV
iajs-2883	43	8	well	well	ADV
iajs-2883	43	9	as	as	ADP
iajs-2883	43	10	𝑚	𝑚	PROPN
iajs-2883	43	11	is	be	AUX
iajs-2883	43	12	the	the	DET
iajs-2883	43	13	approach	approach	NOUN
iajs-2883	43	14	's	's	PART
iajs-2883	43	15	digit	digit	NOUN
iajs-2883	43	16	of	of	ADP
iajs-2883	43	17	the	the	DET
iajs-2883	43	18	stage	stage	NOUN
iajs-2883	43	19	.	.	PUNCT
iajs-2883	44	1	when	when	SCONJ
iajs-2883	44	2	𝑎𝑖,𝑗	𝑎𝑖,𝑗	X
iajs-2883	44	3	≠	≠	PROPN
iajs-2883	44	4	0	0	NUM
iajs-2883	44	5	for	for	ADP
iajs-2883	44	6	𝑖	𝑖	SYM
iajs-2883	44	7	≤	≤	NUM
iajs-2883	44	8	𝑗	𝑗	ADP
iajs-2883	44	9	,	,	PUNCT
iajs-2883	44	10	this	this	DET
iajs-2883	44	11	method	method	NOUN
iajs-2883	44	12	is	be	AUX
iajs-2883	44	13	known	know	VERB
iajs-2883	44	14	as	as	ADP
iajs-2883	44	15	diagonal	diagonal	ADJ
iajs-2883	44	16	implicit	implicit	NOUN
iajs-2883	44	17	.	.	PUNCT
iajs-2883	45	1	the	the	DET
iajs-2883	45	2	final	final	ADJ
iajs-2883	45	3	designation	designation	NOUN
iajs-2883	45	4	comprises	comprise	VERB
iajs-2883	45	5	the	the	DET
iajs-2883	45	6	single	single	ADJ
iajs-2883	45	7	editrk4	editrk4	PROPN
iajs-2883	45	8	techniques	technique	NOUN
iajs-2883	45	9	,	,	PUNCT
iajs-2883	45	10	it	it	PRON
iajs-2883	45	11	means	mean	VERB
iajs-2883	45	12	that	that	SCONJ
iajs-2883	45	13	the	the	DET
iajs-2883	45	14	values	value	NOUN
iajs-2883	45	15	of	of	ADP
iajs-2883	45	16	𝐴	𝐴	PROPN
iajs-2883	45	17	in	in	ADP
iajs-2883	45	18	lower	low	ADJ
iajs-2883	45	19	triangle	triangle	NOUN
iajs-2883	45	20	diagonal	diagonal	ADJ
iajs-2883	45	21	matrices	matrix	NOUN
iajs-2883	45	22	are	be	AUX
iajs-2883	45	23	the	the	DET
iajs-2883	45	24	same	same	ADJ
iajs-2883	45	25	as	as	ADP
iajs-2883	45	26	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-2883	45	27	≠	≠	PROPN
iajs-2883	45	28	0	0	NUM
iajs-2883	45	29	where	where	SCONJ
iajs-2883	45	30	𝑖	𝑖	VERB
iajs-2883	45	31	=	=	PUNCT
iajs-2883	45	32	𝑗	𝑗	PROPN
iajs-2883	45	33	in	in	ADP
iajs-2883	45	34	the	the	DET
iajs-2883	45	35	diagonal	diagonal	NOUN
iajs-2883	45	36	.	.	PUNCT
iajs-2883	46	1	file:///c:/users	file:///c:/user	NOUN
iajs-2883	46	2	/	/	SYM
iajs-2883	46	3	newfuture	newfuture	NOUN
iajs-2883	46	4	/	/	SYM
iajs-2883	46	5	onedrive	onedrive	ADJ
iajs-2883	46	6	/	/	SYM
iajs-2883	46	7	desktop	desktop	NOUN
iajs-2883	46	8	/	/	SYM
iajs-2883	46	9	نور%20جليل%20القصاب	نور%20جليل%20القصاب	NOUN
iajs-2883	46	10	/	/	SYM
iajs-2883	46	11	النسخة%20بالتفاصيل.docx%23_bookmark15	النسخة%20بالتفاصيل.docx%23_bookmark15	NOUN
iajs-2883	46	12	file:///c:/users	file:///c:/users	PROPN
iajs-2883	46	13	/	/	SYM
iajs-2883	46	14	newfuture	newfuture	NOUN
iajs-2883	46	15	/	/	SYM
iajs-2883	46	16	onedrive	onedrive	ADJ
iajs-2883	46	17	/	/	SYM
iajs-2883	46	18	desktop	desktop	NOUN
iajs-2883	46	19	/	/	SYM
iajs-2883	46	20	نور%20جليل%20القصاب	نور%20جليل%20القصاب	NOUN
iajs-2883	46	21	/	/	SYM
iajs-2883	46	22	النسخة%20بالتفاصيل.docx%23_bookmark15	النسخة%20بالتفاصيل.docx%23_bookmark15	NOUN
iajs-2883	46	23	file:///c:/users	file:///c:/users	PROPN
iajs-2883	46	24	/	/	SYM
iajs-2883	46	25	newfuture	newfuture	NOUN
iajs-2883	46	26	/	/	SYM
iajs-2883	46	27	onedrive	onedrive	ADJ
iajs-2883	46	28	/	/	SYM
iajs-2883	46	29	desktop	desktop	NOUN
iajs-2883	46	30	/	/	SYM
iajs-2883	46	31	نور%20جليل%20القصاب	نور%20جليل%20القصاب	NOUN
iajs-2883	46	32	/	/	SYM
iajs-2883	46	33	النسخة%20بالتفاصيل.docx%23_bookmark16	النسخة%20بالتفاصيل.docx%23_bookmark16	NOUN
iajs-2883	46	34	file:///c:/users	file:///c:/user	NOUN
iajs-2883	46	35	/	/	SYM
iajs-2883	46	36	newfuture	newfuture	NOUN
iajs-2883	46	37	/	/	SYM
iajs-2883	46	38	onedrive	onedrive	ADJ
iajs-2883	46	39	/	/	SYM
iajs-2883	46	40	desktop	desktop	NOUN
iajs-2883	46	41	/	/	SYM
iajs-2883	46	42	نور%20جليل%20القصاب	نور%20جليل%20القصاب	NOUN
iajs-2883	46	43	/	/	SYM
iajs-2883	46	44	النسخة%20بالتفاصيل.docx%23_bookmark17	النسخة%20بالتفاصيل.docx%23_bookmark17	VERB
iajs-2883	46	45	file:///c:/users	file:///c:/user	NOUN
iajs-2883	46	46	/	/	SYM
iajs-2883	46	47	newfuture	newfuture	NOUN
iajs-2883	46	48	/	/	SYM
iajs-2883	46	49	onedrive	onedrive	ADJ
iajs-2883	46	50	/	/	SYM
iajs-2883	46	51	desktop	desktop	NOUN
iajs-2883	46	52	/	/	SYM
iajs-2883	46	53	نور%20جليل%20القصاب	نور%20جليل%20القصاب	NOUN
iajs-2883	46	54	/	/	SYM
iajs-2883	46	55	النسخة%20بالتفاصيل.docx%23_bookmark22	النسخة%20بالتفاصيل.docx%23_bookmark22	NOUN
iajs-2883	46	56	file:///c:/users	file:///c:/users	PROPN
iajs-2883	46	57	/	/	SYM
iajs-2883	46	58	newfuture	newfuture	NOUN
iajs-2883	46	59	/	/	SYM
iajs-2883	46	60	onedrive	onedrive	ADJ
iajs-2883	46	61	/	/	SYM
iajs-2883	46	62	desktop	desktop	NOUN
iajs-2883	46	63	/	/	SYM
iajs-2883	46	64	نور%20جليل%20القصاب	نور%20جليل%20القصاب	NOUN
iajs-2883	46	65	/	/	SYM
iajs-2883	46	66	النسخة%20بالتفاصيل.docx%23_bookmark24	النسخة%20بالتفاصيل.docx%23_bookmark24	ADJ
iajs-2883	46	67	ihjpas	ihjpa	NOUN
iajs-2883	46	68	.	.	PUNCT
iajs-2883	47	1	36(1)2023	36(1)2023	NUM
iajs-2883	47	2	391	391	NUM
iajs-2883	47	3	table	table	NOUN
iajs-2883	47	4	1	1	NUM
iajs-2883	47	5	.	.	PUNCT
iajs-2883	47	6	butcher	butcher	NOUN
iajs-2883	47	7	form	form	VERB
iajs-2883	47	8	editrk4	editrk4	PROPN
iajs-2883	47	9	method	method	NOUN
iajs-2883	47	10	.	.	PUNCT
iajs-2883	48	1	𝑐1	𝑐1	NOUN
iajs-2883	48	2	𝑎11	𝑎11	VERB
iajs-2883	48	3	𝑐2	𝑐2	NOUN
iajs-2883	48	4	𝑎21	𝑎21	PROPN
iajs-2883	48	5	𝑎22	𝑎22	NOUN
iajs-2883	48	6	𝑐3	𝑐3	VERB
iajs-2883	48	7	𝑎31	𝑎31	ADJ
iajs-2883	48	8	𝑎32	𝑎32	NOUN
iajs-2883	48	9	𝑎33	𝑎33	NOUN
iajs-2883	48	10	𝑏1	𝑏1	ADJ
iajs-2883	48	11	𝑏2	𝑏2	NOUN
iajs-2883	48	12	𝑏3	𝑏3	NOUN
iajs-2883	48	13	𝑏1	𝑏1	VERB
iajs-2883	48	14	′	′	NOUN
iajs-2883	48	15	𝑏1	𝑏1	NOUN
iajs-2883	48	16	′′	′′	PROPN
iajs-2883	48	17	𝑏2	𝑏2	PROPN
iajs-2883	48	18	′	′	PROPN
iajs-2883	48	19	𝑏2	𝑏2	PROPN
iajs-2883	48	20	′′	′′	PROPN
iajs-2883	48	21	𝑏3	𝑏3	VERB
iajs-2883	48	22	′	′	ADJ
iajs-2883	48	23	𝑏3	𝑏3	NOUN
iajs-2883	48	24	′′	′′	PROPN
iajs-2883	48	25	the	the	DET
iajs-2883	48	26	parameters	parameter	NOUN
iajs-2883	48	27	of	of	ADP
iajs-2883	48	28	the	the	DET
iajs-2883	48	29	new	new	ADJ
iajs-2883	48	30	method	method	NOUN
iajs-2883	48	31	supplied	supply	VERB
iajs-2883	48	32	by	by	ADP
iajs-2883	48	33	(	(	PUNCT
iajs-2883	48	34	2)-(5	2)-(5	NUM
iajs-2883	48	35	)	)	PUNCT
iajs-2883	48	36	are	be	AUX
iajs-2883	48	37	obtained	obtain	VERB
iajs-2883	48	38	by	by	ADP
iajs-2883	48	39	expanding	expand	VERB
iajs-2883	48	40	the	the	DET
iajs-2883	48	41	editrk4	editrk4	PROPN
iajs-2883	48	42	method	method	NOUN
iajs-2883	48	43	statement	statement	NOUN
iajs-2883	48	44	using	use	VERB
iajs-2883	48	45	taylor	taylor	PROPN
iajs-2883	48	46	's	's	PART
iajs-2883	48	47	series	series	NOUN
iajs-2883	48	48	enlargement	enlargement	NOUN
iajs-2883	48	49	.	.	PUNCT
iajs-2883	49	1	in	in	ADP
iajs-2883	49	2	accordance	accordance	NOUN
iajs-2883	49	3	with	with	ADP
iajs-2883	49	4	a	a	DET
iajs-2883	49	5	few	few	ADJ
iajs-2883	49	6	algebraic	algebraic	ADJ
iajs-2883	49	7	adjustments	adjustment	NOUN
iajs-2883	49	8	,	,	PUNCT
iajs-2883	49	9	this	this	DET
iajs-2883	49	10	enlargement	enlargement	NOUN
iajs-2883	49	11	equals	equal	VERB
iajs-2883	49	12	the	the	DET
iajs-2883	49	13	correct	correct	ADJ
iajs-2883	49	14	solution	solution	NOUN
iajs-2883	49	15	found	find	VERB
iajs-2883	49	16	through	through	ADP
iajs-2883	49	17	taylor	taylor	PROPN
iajs-2883	49	18	's	's	PART
iajs-2883	49	19	series	series	NOUN
iajs-2883	49	20	expansion	expansion	NOUN
iajs-2883	49	21	.	.	PUNCT
iajs-2883	50	1	the	the	DET
iajs-2883	50	2	general	general	ADJ
iajs-2883	50	3	order	order	NOUN
iajs-2883	50	4	criteria	criterion	NOUN
iajs-2883	50	5	for	for	ADP
iajs-2883	50	6	the	the	DET
iajs-2883	50	7	new	new	ADJ
iajs-2883	50	8	technique	technique	NOUN
iajs-2883	50	9	were	be	AUX
iajs-2883	50	10	derived	derive	VERB
iajs-2883	50	11	using	use	VERB
iajs-2883	50	12	the	the	DET
iajs-2883	50	13	direct	direct	ADJ
iajs-2883	50	14	truncation	truncation	NOUN
iajs-2883	50	15	error	error	NOUN
iajs-2883	50	16	on	on	ADP
iajs-2883	50	17	the	the	DET
iajs-2883	50	18	local	local	ADJ
iajs-2883	50	19	level	level	NOUN
iajs-2883	50	20	.	.	PUNCT
iajs-2883	51	1	this	this	DET
iajs-2883	51	2	idea	idea	NOUN
iajs-2883	51	3	is	be	AUX
iajs-2883	51	4	founded	found	VERB
iajs-2883	51	5	on	on	ADP
iajs-2883	51	6	the	the	DET
iajs-2883	51	7	derivation	derivation	NOUN
iajs-2883	51	8	of	of	ADP
iajs-2883	51	9	order	order	NOUN
iajs-2883	51	10	criteria	criterion	NOUN
iajs-2883	51	11	to	to	ADP
iajs-2883	51	12	the	the	DET
iajs-2883	51	13	rk	rk	NOUN
iajs-2883	51	14	technique	technique	NOUN
iajs-2883	51	15	see	see	VERB
iajs-2883	51	16	[	[	X
iajs-2883	51	17	14	14	NUM
iajs-2883	51	18	]	]	PUNCT
iajs-2883	51	19	and	and	CCONJ
iajs-2883	51	20	[	[	X
iajs-2883	51	21	15	15	NUM
iajs-2883	51	22	]	]	PUNCT
iajs-2883	51	23	.	.	PUNCT
iajs-2883	52	1	the	the	DET
iajs-2883	52	2	new	new	ADJ
iajs-2883	52	3	editrk4	editrk4	PROPN
iajs-2883	52	4	technique	technique	NOUN
iajs-2883	52	5	is	be	AUX
iajs-2883	52	6	formed	form	VERB
iajs-2883	52	7	as	as	SCONJ
iajs-2883	52	8	follows	follow	VERB
iajs-2883	52	9	:	:	PUNCT
iajs-2883	52	10	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2883	52	11	=	=	SYM
iajs-2883	52	12	𝑦𝑛	𝑦𝑛	PROPN
iajs-2883	52	13	+	+	CCONJ
iajs-2883	52	14	ℎ𝛷(𝑥𝑛	ℎ𝛷(𝑥𝑛	ADV
iajs-2883	52	15	,	,	PUNCT
iajs-2883	52	16	𝑦𝑛	𝑦𝑛	NOUN
iajs-2883	52	17	)	)	PUNCT
iajs-2883	52	18	,	,	PUNCT
iajs-2883	52	19	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2883	52	20	′	′	NUM
iajs-2883	52	21	=	=	PUNCT
iajs-2883	52	22	𝑦𝑛	𝑦𝑛	AUX
iajs-2883	52	23	′	′	NOUN
iajs-2883	52	24	+	+	CCONJ
iajs-2883	52	25	ℎ𝛷′(𝑥𝑛	ℎ𝛷′(𝑥𝑛	NOUN
iajs-2883	52	26	,	,	PUNCT
iajs-2883	52	27	𝑦𝑛	𝑦𝑛	NOUN
iajs-2883	52	28	)	)	PUNCT
iajs-2883	52	29	,	,	PUNCT
iajs-2883	52	30	𝑦𝑛+1	𝑦𝑛+1	NUM
iajs-2883	52	31	′′	′′	PROPN
iajs-2883	52	32	=	=	PUNCT
iajs-2883	52	33	𝑦𝑛	𝑦𝑛	ADP
iajs-2883	52	34	′′	′′	PROPN
iajs-2883	52	35	+	+	CCONJ
iajs-2883	52	36	ℎ𝛷′′(𝑥𝑛	ℎ𝛷′′(𝑥𝑛	PROPN
iajs-2883	52	37	,	,	PUNCT
iajs-2883	52	38	𝑦𝑛	𝑦𝑛	NOUN
iajs-2883	52	39	)	)	PUNCT
iajs-2883	52	40	,	,	PUNCT
iajs-2883	52	41	(	(	PUNCT
iajs-2883	52	42	6	6	NUM
iajs-2883	52	43	)	)	PUNCT
iajs-2883	52	44	where	where	SCONJ
iajs-2883	52	45	the	the	DET
iajs-2883	52	46	increment	increment	NOUN
iajs-2883	52	47	functions	function	NOUN
iajs-2883	52	48	are	be	AUX
iajs-2883	52	49	:	:	PUNCT
iajs-2883	52	50	𝛷(𝑥𝑛	𝛷(𝑥𝑛	ADV
iajs-2883	52	51	,	,	PUNCT
iajs-2883	52	52	𝑦𝑛	𝑦𝑛	NOUN
iajs-2883	52	53	)	)	PUNCT
iajs-2883	52	54	=	=	VERB
iajs-2883	52	55	𝑦𝑛	𝑦𝑛	AUX
iajs-2883	52	56	′	′	NOUN
iajs-2883	53	1	+	+	CCONJ
iajs-2883	53	2	ℎ	ℎ	NOUN
iajs-2883	53	3	2	2	NUM
iajs-2883	53	4	𝑦𝑛	𝑦𝑛	ADP
iajs-2883	53	5	′′	′′	NOUN
iajs-2883	53	6	+	+	CCONJ
iajs-2883	53	7	ℎ2	ℎ2	NOUN
iajs-2883	53	8	∑	∑	PUNCT
iajs-2883	53	9	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	53	10	𝑚	𝑚	PROPN
iajs-2883	53	11	𝑖=1	𝑖=1	PUNCT
iajs-2883	53	12	𝑘𝑖	𝑘𝑖	ADP
iajs-2883	53	13	,	,	PUNCT
iajs-2883	53	14	𝛷′(𝑥𝑛	𝛷′(𝑥𝑛	NUM
iajs-2883	53	15	,	,	PUNCT
iajs-2883	53	16	𝑦𝑛	𝑦𝑛	NOUN
iajs-2883	53	17	)	)	PUNCT
iajs-2883	53	18	=	=	SYM
iajs-2883	53	19	𝑦𝑛	𝑦𝑛	ADP
iajs-2883	53	20	′′	′′	PROPN
iajs-2883	53	21	+	+	CCONJ
iajs-2883	53	22	ℎ	ℎ	PROPN
iajs-2883	53	23	∑	∑	NOUN
iajs-2883	53	24	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	53	25	′	′	NUM
iajs-2883	53	26	𝑚	𝑚	PROPN
iajs-2883	53	27	𝑖=1	𝑖=1	PUNCT
iajs-2883	54	1	𝑘𝑖	𝑘𝑖	NOUN
iajs-2883	54	2	,	,	PUNCT
iajs-2883	54	3	𝛷′′(𝑥𝑛	𝛷′′(𝑥𝑛	NOUN
iajs-2883	54	4	,	,	PUNCT
iajs-2883	54	5	𝑦𝑛	𝑦𝑛	NOUN
iajs-2883	54	6	)	)	PUNCT
iajs-2883	54	7	=	=	SYM
iajs-2883	55	1	∑	∑	PROPN
iajs-2883	55	2	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	55	3	′′	′′	PROPN
iajs-2883	55	4	𝑚	𝑚	X
iajs-2883	55	5	𝑖=1	𝑖=1	PROPN
iajs-2883	55	6	𝑘𝑖	𝑘𝑖	NOUN
iajs-2883	55	7	.	.	PUNCT
iajs-2883	56	1	(	(	PUNCT
iajs-2883	56	2	7	7	X
iajs-2883	56	3	)	)	PUNCT
iajs-2883	56	4	in	in	ADP
iajs-2883	56	5	which	which	PRON
iajs-2883	56	6	𝑘𝑖	𝑘𝑖	PART
iajs-2883	56	7	is	be	AUX
iajs-2883	56	8	shown	show	VERB
iajs-2883	56	9	in	in	ADP
iajs-2883	56	10	(	(	PUNCT
iajs-2883	56	11	5	5	NUM
iajs-2883	56	12	)	)	PUNCT
iajs-2883	56	13	.	.	PUNCT
iajs-2883	57	1	if	if	SCONJ
iajs-2883	57	2	we	we	PRON
iajs-2883	57	3	suppose	suppose	VERB
iajs-2883	57	4	the	the	DET
iajs-2883	57	5	taylor	taylor	PROPN
iajs-2883	57	6	increment	increment	NOUN
iajs-2883	57	7	function	function	NOUN
iajs-2883	57	8	is	be	AUX
iajs-2883	57	9	∆	∆	PROPN
iajs-2883	57	10	,	,	PUNCT
iajs-2883	57	11	∆′and	∆′and	PROPN
iajs-2883	57	12	∆′′	∆′′	PROPN
iajs-2883	57	13	.	.	PUNCT
iajs-2883	58	1	thus	thus	ADV
iajs-2883	58	2	,	,	PUNCT
iajs-2883	58	3	by	by	ADP
iajs-2883	58	4	inserting	insert	VERB
iajs-2883	58	5	the	the	DET
iajs-2883	58	6	exact	exact	ADJ
iajs-2883	58	7	solution	solution	NOUN
iajs-2883	58	8	of	of	ADP
iajs-2883	58	9	(	(	PUNCT
iajs-2883	58	10	1	1	NUM
iajs-2883	58	11	)	)	PUNCT
iajs-2883	58	12	into	into	ADP
iajs-2883	58	13	(	(	PUNCT
iajs-2883	58	14	7	7	NUM
iajs-2883	58	15	)	)	PUNCT
iajs-2883	58	16	,	,	PUNCT
iajs-2883	58	17	the	the	DET
iajs-2883	58	18	local	local	ADJ
iajs-2883	58	19	truncation	truncation	NOUN
iajs-2883	58	20	error	error	NOUN
iajs-2883	58	21	(	(	PUNCT
iajs-2883	58	22	lte	lte	PROPN
iajs-2883	58	23	)	)	PUNCT
iajs-2883	58	24	of	of	ADP
iajs-2883	58	25	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-2883	58	26	)	)	PUNCT
iajs-2883	58	27	,	,	PUNCT
iajs-2883	58	28	𝑦′(𝑥	𝑦′(𝑥	PROPN
iajs-2883	58	29	)	)	PUNCT
iajs-2883	58	30	and	and	CCONJ
iajs-2883	58	31	𝑦′′(𝑥	𝑦′′(𝑥	NOUN
iajs-2883	58	32	)	)	PUNCT
iajs-2883	58	33	can	can	AUX
iajs-2883	58	34	be	be	AUX
iajs-2883	58	35	obtained	obtain	VERB
iajs-2883	58	36	:	:	PUNCT
iajs-2883	58	37	𝜏𝑛+1	𝜏𝑛+1	NUM
iajs-2883	58	38	=	=	SYM
iajs-2883	59	1	ℎ[𝛷	ℎ[𝛷	NOUN
iajs-2883	59	2	−	−	NOUN
iajs-2883	59	3	∆	∆	PROPN
iajs-2883	59	4	]	]	PUNCT
iajs-2883	59	5	,	,	PUNCT
iajs-2883	59	6	𝜏𝑛+1	𝜏𝑛+1	NOUN
iajs-2883	59	7	′	′	NOUN
iajs-2883	59	8	=	=	PUNCT
iajs-2883	59	9	ℎ[𝛷′	ℎ[𝛷′	PROPN
iajs-2883	59	10	−	−	PROPN
iajs-2883	59	11	∆′	∆′	PROPN
iajs-2883	59	12	]	]	PUNCT
iajs-2883	59	13	,	,	PUNCT
iajs-2883	59	14	𝜏𝑛+1	𝜏𝑛+1	X
iajs-2883	59	15	′′	′′	PROPN
iajs-2883	59	16	=	=	PUNCT
iajs-2883	59	17	ℎ[𝛷′′	ℎ[𝛷′′	PROPN
iajs-2883	59	18	−	−	NOUN
iajs-2883	59	19	∆′′	∆′′	ADP
iajs-2883	59	20	]	]	PUNCT
iajs-2883	59	21	.	.	PUNCT
iajs-2883	60	1	(	(	PUNCT
iajs-2883	60	2	8)	8)	NUM
iajs-2883	60	3	in	in	ADP
iajs-2883	60	4	the	the	DET
iajs-2883	60	5	terms	term	NOUN
iajs-2883	60	6	of	of	ADP
iajs-2883	60	7	elementary	elementary	ADJ
iajs-2883	60	8	differentials	differential	NOUN
iajs-2883	60	9	,	,	PUNCT
iajs-2883	60	10	these	these	DET
iajs-2883	60	11	expressions	expression	NOUN
iajs-2883	60	12	are	be	AUX
iajs-2883	60	13	best	well	ADV
iajs-2883	60	14	given	give	VERB
iajs-2883	60	15	and	and	CCONJ
iajs-2883	60	16	the	the	DET
iajs-2883	60	17	taylor	taylor	PROPN
iajs-2883	60	18	series	series	NOUN
iajs-2883	60	19	can	can	AUX
iajs-2883	60	20	be	be	AUX
iajs-2883	60	21	expressed	express	VERB
iajs-2883	60	22	as	as	SCONJ
iajs-2883	60	23	follows	follow	VERB
iajs-2883	60	24	:	:	PUNCT
iajs-2883	60	25	∆=	∆=	VERB
iajs-2883	60	26	𝑦′	𝑦′	X
iajs-2883	60	27	+	+	SYM
iajs-2883	60	28	1	1	NUM
iajs-2883	60	29	2	2	NUM
iajs-2883	60	30	ℎ𝑦′′	ℎ𝑦′′	NOUN
iajs-2883	60	31	+	+	CCONJ
iajs-2883	60	32	1	1	NUM
iajs-2883	60	33	6	6	NUM
iajs-2883	60	34	ℎ2𝐹1	ℎ2𝐹1	X
iajs-2883	60	35	(	(	PUNCT
iajs-2883	60	36	3	3	NUM
iajs-2883	60	37	)	)	PUNCT
iajs-2883	60	38	+	+	CCONJ
iajs-2883	60	39	1	1	NUM
iajs-2883	60	40	24	24	NUM
iajs-2883	60	41	ℎ3𝐹1	ℎ3𝐹1	PUNCT
iajs-2883	60	42	(	(	PUNCT
iajs-2883	60	43	4	4	NUM
iajs-2883	60	44	)	)	PUNCT
iajs-2883	60	45	+	+	CCONJ
iajs-2883	60	46	𝑂(ℎ4	𝑂(ℎ4	NOUN
iajs-2883	60	47	)	)	PUNCT
iajs-2883	60	48	,	,	PUNCT
iajs-2883	60	49	ihjpas	ihjpa	VERB
iajs-2883	60	50	.	.	PUNCT
iajs-2883	61	1	36(1)2023	36(1)2023	NUM
iajs-2883	61	2	392	392	NUM
iajs-2883	61	3	∆′=	∆′=	NOUN
iajs-2883	61	4	𝑦′′	𝑦′′	NOUN
iajs-2883	62	1	+	+	CCONJ
iajs-2883	62	2	1	1	NUM
iajs-2883	62	3	2	2	NUM
iajs-2883	62	4	ℎ𝐹1	ℎ𝐹1	PROPN
iajs-2883	62	5	(	(	PUNCT
iajs-2883	62	6	3	3	NUM
iajs-2883	62	7	)	)	PUNCT
iajs-2883	62	8	+	+	CCONJ
iajs-2883	62	9	1	1	NUM
iajs-2883	62	10	6	6	NUM
iajs-2883	62	11	ℎ2𝐹1	ℎ2𝐹1	X
iajs-2883	62	12	(	(	PUNCT
iajs-2883	62	13	4	4	NUM
iajs-2883	62	14	)	)	PUNCT
iajs-2883	62	15	+	+	CCONJ
iajs-2883	62	16	1	1	NUM
iajs-2883	62	17	24	24	NUM
iajs-2883	62	18	ℎ3𝐹1	ℎ3𝐹1	PUNCT
iajs-2883	62	19	(	(	PUNCT
iajs-2883	62	20	5	5	NUM
iajs-2883	62	21	)	)	PUNCT
iajs-2883	62	22	+	+	CCONJ
iajs-2883	62	23	𝑂(ℎ4	𝑂(ℎ4	NOUN
iajs-2883	62	24	)	)	PUNCT
iajs-2883	62	25	,	,	PUNCT
iajs-2883	62	26	∆′′=	∆′′=	PROPN
iajs-2883	62	27	𝐹1	𝐹1	PROPN
iajs-2883	62	28	(	(	PUNCT
iajs-2883	62	29	3	3	NUM
iajs-2883	62	30	)	)	PUNCT
iajs-2883	62	31	+	+	CCONJ
iajs-2883	62	32	1	1	NUM
iajs-2883	62	33	2	2	NUM
iajs-2883	62	34	ℎ𝐹1	ℎ𝐹1	PROPN
iajs-2883	62	35	(	(	PUNCT
iajs-2883	62	36	4	4	NUM
iajs-2883	62	37	)	)	PUNCT
iajs-2883	62	38	+	+	CCONJ
iajs-2883	62	39	1	1	NUM
iajs-2883	62	40	6	6	NUM
iajs-2883	62	41	ℎ2𝐹1	ℎ2𝐹1	X
iajs-2883	62	42	(	(	PUNCT
iajs-2883	62	43	5	5	NUM
iajs-2883	62	44	)	)	PUNCT
iajs-2883	62	45	+	+	CCONJ
iajs-2883	62	46	𝑂(ℎ3	𝑂(ℎ3	NOUN
iajs-2883	62	47	)	)	PUNCT
iajs-2883	62	48	.	.	PUNCT
iajs-2883	63	1	(	(	PUNCT
iajs-2883	63	2	9	9	X
iajs-2883	63	3	)	)	PUNCT
iajs-2883	63	4	the	the	DET
iajs-2883	63	5	first	first	ADJ
iajs-2883	63	6	few	few	ADJ
iajs-2883	63	7	basic	basic	ADJ
iajs-2883	63	8	differentials	differential	NOUN
iajs-2883	63	9	in	in	ADP
iajs-2883	63	10	the	the	DET
iajs-2883	63	11	scalar	scalar	ADJ
iajs-2883	63	12	case	case	NOUN
iajs-2883	63	13	are	be	AUX
iajs-2883	63	14	as	as	SCONJ
iajs-2883	63	15	follows	follow	VERB
iajs-2883	63	16	:	:	PUNCT
iajs-2883	63	17	𝐹1	𝐹1	PROPN
iajs-2883	63	18	(	(	PUNCT
iajs-2883	63	19	3	3	NUM
iajs-2883	63	20	)	)	PUNCT
iajs-2883	63	21	=	=	SYM
iajs-2883	64	1	𝑓	𝑓	PROPN
iajs-2883	64	2	,	,	PUNCT
iajs-2883	64	3	𝐹1	𝐹1	X
iajs-2883	64	4	(	(	PUNCT
iajs-2883	64	5	4	4	NUM
iajs-2883	64	6	)	)	PUNCT
iajs-2883	64	7	=	=	SYM
iajs-2883	64	8	𝑓𝑥	𝑓𝑥	PROPN
iajs-2883	64	9	+	+	NUM
iajs-2883	64	10	𝑓𝑦𝑦′	𝑓𝑦𝑦′	NOUN
iajs-2883	64	11	,	,	PUNCT
iajs-2883	64	12	𝐹1	𝐹1	X
iajs-2883	64	13	(	(	PUNCT
iajs-2883	64	14	5	5	NUM
iajs-2883	64	15	)	)	PUNCT
iajs-2883	64	16	=	=	VERB
iajs-2883	64	17	𝑓𝑥𝑥	𝑓𝑥𝑥	NOUN
iajs-2883	64	18	+	+	CCONJ
iajs-2883	64	19	2𝑓𝑥𝑦𝑦′	2𝑓𝑥𝑦𝑦′	NUM
iajs-2883	64	20	+	+	CCONJ
iajs-2883	64	21	𝑓𝑥𝑦′𝑦𝑥𝑥	𝑓𝑥𝑦′𝑦𝑥𝑥	PROPN
iajs-2883	64	22	+	+	CCONJ
iajs-2883	64	23	𝑓𝑦𝑦′′	𝑓𝑦𝑦′′	NOUN
iajs-2883	64	24	+	+	CCONJ
iajs-2883	64	25	𝑓𝑦𝑦(𝑦′)2	𝑓𝑦𝑦(𝑦′)2	NUM
iajs-2883	64	26	.	.	PUNCT
iajs-2883	65	1	(	(	PUNCT
iajs-2883	65	2	10	10	NUM
iajs-2883	65	3	)	)	PUNCT
iajs-2883	65	4	substituting	substituting	NOUN
iajs-2883	65	5	(	(	PUNCT
iajs-2883	65	6	10	10	NUM
iajs-2883	65	7	)	)	PUNCT
iajs-2883	65	8	into	into	ADP
iajs-2883	65	9	(	(	PUNCT
iajs-2883	65	10	7	7	NUM
iajs-2883	65	11	)	)	PUNCT
iajs-2883	65	12	,	,	PUNCT
iajs-2883	65	13	for	for	ADP
iajs-2883	65	14	new	new	ADJ
iajs-2883	65	15	method	method	NOUN
iajs-2883	65	16	,	,	PUNCT
iajs-2883	65	17	the	the	DET
iajs-2883	65	18	increment	increment	NOUN
iajs-2883	65	19	functions	function	NOUN
iajs-2883	65	20	φ	φ	PROPN
iajs-2883	65	21	,	,	PUNCT
iajs-2883	65	22	φ	φ	PROPN
iajs-2883	65	23	'	'	PUNCT
iajs-2883	65	24	and	and	CCONJ
iajs-2883	65	25	φ	φ	NUM
iajs-2883	65	26	''	''	PUNCT
iajs-2883	65	27	will	will	AUX
iajs-2883	65	28	become	become	VERB
iajs-2883	65	29	∑	∑	PUNCT
iajs-2883	65	30	𝑏𝑖𝑘𝑖	𝑏𝑖𝑘𝑖	VERB
iajs-2883	65	31	𝑚	𝑚	NOUN
iajs-2883	65	32	𝑖=1	𝑖=1	PUNCT
iajs-2883	65	33	=	=	PUNCT
iajs-2883	66	1	∑	∑	PROPN
iajs-2883	66	2	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	66	3	𝑚	𝑚	PROPN
iajs-2883	66	4	𝑖=1	𝑖=1	PUNCT
iajs-2883	67	1	𝑓	𝑓	PROPN
iajs-2883	67	2	+	+	NUM
iajs-2883	67	3	∑	∑	AUX
iajs-2883	67	4	𝑏𝑖𝑐𝑖	𝑏𝑖𝑐𝑖	VERB
iajs-2883	67	5	𝑚	𝑚	PROPN
iajs-2883	67	6	𝑖=1	𝑖=1	PROPN
iajs-2883	67	7	(	(	PUNCT
iajs-2883	67	8	𝑓𝑥	𝑓𝑥	PROPN
iajs-2883	67	9	+	+	NUM
iajs-2883	67	10	𝑓𝑦𝑦′)ℎ	𝑓𝑦𝑦′)ℎ	NOUN
iajs-2883	68	1	+	+	CCONJ
iajs-2883	68	2	1	1	NUM
iajs-2883	68	3	2	2	NUM
iajs-2883	68	4	∑	∑	NOUN
iajs-2883	68	5	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	68	6	𝑚	𝑚	X
iajs-2883	68	7	𝑖=1	𝑖=1	PROPN
iajs-2883	68	8	𝑐𝑖	𝑐𝑖	NOUN
iajs-2883	68	9	2(𝑓𝑥𝑥	2(𝑓𝑥𝑥	NOUN
iajs-2883	69	1	+	+	CCONJ
iajs-2883	69	2	2𝑓𝑥𝑦𝑦′	2𝑓𝑥𝑦𝑦′	NUM
iajs-2883	69	3	+	+	CCONJ
iajs-2883	69	4	𝑓𝑥𝑦′𝑦𝑥𝑥	𝑓𝑥𝑦′𝑦𝑥𝑥	PROPN
iajs-2883	69	5	+	+	CCONJ
iajs-2883	69	6	𝑓𝑦𝑦′′	𝑓𝑦𝑦′′	NOUN
iajs-2883	69	7	+	+	CCONJ
iajs-2883	70	1	𝑓𝑦𝑦(𝑦′)2)ℎ2	𝑓𝑦𝑦(𝑦′)2)ℎ2	X
iajs-2883	70	2	+	+	X
iajs-2883	70	3	𝑂(ℎ3	𝑂(ℎ3	NUM
iajs-2883	70	4	)	)	PUNCT
iajs-2883	70	5	,	,	PUNCT
iajs-2883	70	6	∑	∑	ADP
iajs-2883	70	7	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	70	8	′𝑘𝑖	′𝑘𝑖	NOUN
iajs-2883	70	9	𝑚	𝑚	X
iajs-2883	70	10	𝑖=1	𝑖=1	PUNCT
iajs-2883	70	11	=	=	PUNCT
iajs-2883	71	1	∑	∑	PROPN
iajs-2883	71	2	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	71	3	′	′	NUM
iajs-2883	71	4	𝑚	𝑚	PROPN
iajs-2883	71	5	𝑖=1	𝑖=1	PUNCT
iajs-2883	72	1	𝑓	𝑓	PROPN
iajs-2883	72	2	+	+	NOUN
iajs-2883	72	3	∑	∑	PROPN
iajs-2883	72	4	𝑏𝑖	𝑏𝑖	INTJ
iajs-2883	72	5	′𝑐𝑖	′𝑐𝑖	NOUN
iajs-2883	72	6	𝑚	𝑚	X
iajs-2883	72	7	𝑖=1	𝑖=1	PROPN
iajs-2883	72	8	(	(	PUNCT
iajs-2883	72	9	𝑓𝑥	𝑓𝑥	PROPN
iajs-2883	72	10	+	+	NUM
iajs-2883	72	11	𝑓𝑦𝑦′)ℎ	𝑓𝑦𝑦′)ℎ	NOUN
iajs-2883	72	12	+	+	CCONJ
iajs-2883	72	13	1	1	NUM
iajs-2883	72	14	2	2	NUM
iajs-2883	72	15	∑	∑	NOUN
iajs-2883	72	16	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	72	17	′	′	NUM
iajs-2883	72	18	𝑚	𝑚	PROPN
iajs-2883	72	19	𝑖=1	𝑖=1	PUNCT
iajs-2883	72	20	𝑐𝑖	𝑐𝑖	NOUN
iajs-2883	72	21	2(𝑓𝑥𝑥	2(𝑓𝑥𝑥	NOUN
iajs-2883	72	22	+	+	CCONJ
iajs-2883	72	23	2𝑓𝑥𝑦𝑦′	2𝑓𝑥𝑦𝑦′	NUM
iajs-2883	72	24	+	+	CCONJ
iajs-2883	72	25	𝑓𝑥𝑦′𝑦𝑥𝑥	𝑓𝑥𝑦′𝑦𝑥𝑥	PROPN
iajs-2883	72	26	+	+	CCONJ
iajs-2883	72	27	𝑓𝑦𝑦′′	𝑓𝑦𝑦′′	NOUN
iajs-2883	72	28	+	+	CCONJ
iajs-2883	73	1	𝑓𝑦𝑦(𝑦′)2)ℎ2	𝑓𝑦𝑦(𝑦′)2)ℎ2	X
iajs-2883	73	2	+	+	X
iajs-2883	73	3	𝑂(ℎ3	𝑂(ℎ3	NUM
iajs-2883	73	4	)	)	PUNCT
iajs-2883	73	5	,	,	PUNCT
iajs-2883	73	6	∑	∑	ADP
iajs-2883	73	7	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	73	8	′′𝑘𝑖	′′𝑘𝑖	NOUN
iajs-2883	73	9	𝑚	𝑚	X
iajs-2883	73	10	𝑖=1	𝑖=1	PUNCT
iajs-2883	73	11	=	=	PUNCT
iajs-2883	73	12	∑	∑	ADP
iajs-2883	74	1	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	74	2	′′𝑚	′′𝑚	NOUN
iajs-2883	74	3	𝑖=1	𝑖=1	PROPN
iajs-2883	75	1	𝑓	𝑓	PRON
iajs-2883	76	1	+	+	CCONJ
iajs-2883	76	2	∑	∑	PROPN
iajs-2883	76	3	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	76	4	′′𝑐𝑖	′′𝑐𝑖	NOUN
iajs-2883	76	5	𝑚	𝑚	X
iajs-2883	76	6	𝑖=1	𝑖=1	PROPN
iajs-2883	76	7	(	(	PUNCT
iajs-2883	76	8	𝑓𝑥	𝑓𝑥	PROPN
iajs-2883	76	9	+	+	NUM
iajs-2883	76	10	𝑓𝑦𝑦′)ℎ	𝑓𝑦𝑦′)ℎ	NOUN
iajs-2883	76	11	+	+	CCONJ
iajs-2883	76	12	1	1	NUM
iajs-2883	76	13	2	2	NUM
iajs-2883	76	14	∑	∑	ADV
iajs-2883	76	15	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	76	16	′′𝑚	′′𝑚	NOUN
iajs-2883	76	17	𝑖=1	𝑖=1	PROPN
iajs-2883	76	18	𝑐𝑖	𝑐𝑖	NOUN
iajs-2883	76	19	2(𝑓𝑥𝑥	2(𝑓𝑥𝑥	NOUN
iajs-2883	76	20	+	+	CCONJ
iajs-2883	76	21	2𝑓𝑥𝑦𝑦′	2𝑓𝑥𝑦𝑦′	NUM
iajs-2883	76	22	+	+	CCONJ
iajs-2883	76	23	𝑓𝑥𝑦′𝑦𝑥𝑥	𝑓𝑥𝑦′𝑦𝑥𝑥	PROPN
iajs-2883	76	24	+	+	CCONJ
iajs-2883	76	25	𝑓𝑦𝑦′′	𝑓𝑦𝑦′′	NOUN
iajs-2883	76	26	+	+	CCONJ
iajs-2883	77	1	𝑓𝑦𝑦(𝑦′)2)ℎ2	𝑓𝑦𝑦(𝑦′)2)ℎ2	X
iajs-2883	77	2	+	+	X
iajs-2883	77	3	𝑂(ℎ3	𝑂(ℎ3	NUM
iajs-2883	77	4	)	)	PUNCT
iajs-2883	77	5	,	,	PUNCT
iajs-2883	77	6	from	from	ADP
iajs-2883	77	7	(	(	PUNCT
iajs-2883	77	8	9	9	NUM
iajs-2883	77	9	)	)	PUNCT
iajs-2883	77	10	and	and	CCONJ
iajs-2883	77	11	(	(	PUNCT
iajs-2883	77	12	11	11	NUM
iajs-2883	77	13	)	)	PUNCT
iajs-2883	77	14	,	,	PUNCT
iajs-2883	77	15	the	the	DET
iajs-2883	77	16	following	follow	VERB
iajs-2883	77	17	is	be	AUX
iajs-2883	77	18	how	how	SCONJ
iajs-2883	77	19	lte	lte	PROPN
iajs-2883	77	20	in	in	ADP
iajs-2883	77	21	(	(	PUNCT
iajs-2883	77	22	8)	8)	NUM
iajs-2883	77	23	is	be	AUX
iajs-2883	77	24	expressed	express	VERB
iajs-2883	77	25	:	:	PUNCT
iajs-2883	77	26	𝜏𝑛+1	𝜏𝑛+1	NUM
iajs-2883	77	27	=	=	SYM
iajs-2883	77	28	ℎ3	ℎ3	NOUN
iajs-2883	77	29	[	[	X
iajs-2883	77	30	∑	∑	X
iajs-2883	77	31	𝑏𝑖𝑘𝑖	𝑏𝑖𝑘𝑖	NOUN
iajs-2883	77	32	𝑚	𝑚	PART
iajs-2883	77	33	𝑖=1	𝑖=1	PROPN
iajs-2883	78	1	−	−	PROPN
iajs-2883	79	1	(	(	PUNCT
iajs-2883	79	2	1	1	NUM
iajs-2883	79	3	6	6	NUM
iajs-2883	79	4	𝐹1	𝐹1	NOUN
iajs-2883	79	5	(	(	PUNCT
iajs-2883	79	6	3	3	NUM
iajs-2883	79	7	)	)	PUNCT
iajs-2883	79	8	+	+	CCONJ
iajs-2883	79	9	1	1	NUM
iajs-2883	79	10	24	24	NUM
iajs-2883	79	11	ℎ𝐹1	ℎ𝐹1	PROPN
iajs-2883	79	12	(	(	PUNCT
iajs-2883	79	13	4	4	NUM
iajs-2883	79	14	)	)	PUNCT
iajs-2883	79	15	+	+	CCONJ
iajs-2883	79	16	⋯	⋯	NOUN
iajs-2883	79	17	)	)	PUNCT
iajs-2883	79	18	]	]	PUNCT
iajs-2883	79	19	,	,	PUNCT
iajs-2883	79	20	𝜏𝑛+1	𝜏𝑛+1	NUM
iajs-2883	79	21	′	′	NOUN
iajs-2883	79	22	=	=	NOUN
iajs-2883	79	23	ℎ2	ℎ2	NOUN
iajs-2883	80	1	[	[	X
iajs-2883	80	2	∑	∑	ADP
iajs-2883	80	3	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	80	4	′𝑘𝑖	′𝑘𝑖	NOUN
iajs-2883	80	5	𝑚	𝑚	PROPN
iajs-2883	80	6	𝑖=1	𝑖=1	PUNCT
iajs-2883	80	7	−	−	PROPN
iajs-2883	80	8	(	(	PUNCT
iajs-2883	80	9	1	1	NUM
iajs-2883	80	10	2	2	NUM
iajs-2883	80	11	𝐹1	𝐹1	NOUN
iajs-2883	80	12	(	(	PUNCT
iajs-2883	80	13	3	3	NUM
iajs-2883	80	14	)	)	PUNCT
iajs-2883	80	15	+	+	CCONJ
iajs-2883	80	16	1	1	NUM
iajs-2883	80	17	6	6	NUM
iajs-2883	80	18	ℎ𝐹1	ℎ𝐹1	PROPN
iajs-2883	80	19	(	(	PUNCT
iajs-2883	80	20	4	4	NUM
iajs-2883	80	21	)	)	PUNCT
iajs-2883	81	1	+	+	CCONJ
iajs-2883	81	2	⋯	⋯	NOUN
iajs-2883	81	3	)	)	PUNCT
iajs-2883	81	4	]	]	PUNCT
iajs-2883	81	5	,	,	PUNCT
iajs-2883	81	6	𝜏𝑛+1	𝜏𝑛+1	X
iajs-2883	81	7	′′	′′	PROPN
iajs-2883	81	8	=	=	SYM
iajs-2883	81	9	ℎ	ℎ	PROPN
iajs-2883	82	1	[	[	X
iajs-2883	82	2	∑	∑	ADP
iajs-2883	82	3	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	82	4	′′𝑘𝑖	′′𝑘𝑖	NOUN
iajs-2883	82	5	𝑚	𝑚	PROPN
iajs-2883	82	6	𝑖=1	𝑖=1	PUNCT
iajs-2883	82	7	−	−	PROPN
iajs-2883	82	8	(	(	PUNCT
iajs-2883	82	9	𝐹1	𝐹1	PROPN
iajs-2883	82	10	(	(	PUNCT
iajs-2883	82	11	3	3	NUM
iajs-2883	82	12	)	)	PUNCT
iajs-2883	82	13	+	+	CCONJ
iajs-2883	82	14	1	1	NUM
iajs-2883	82	15	2	2	NUM
iajs-2883	82	16	ℎ𝐹1	ℎ𝐹1	PROPN
iajs-2883	82	17	(	(	PUNCT
iajs-2883	82	18	4	4	NUM
iajs-2883	82	19	)	)	PUNCT
iajs-2883	82	20	+	+	CCONJ
iajs-2883	82	21	1	1	NUM
iajs-2883	82	22	6	6	NUM
iajs-2883	82	23	ℎ2𝐹1	ℎ2𝐹1	X
iajs-2883	82	24	(	(	PUNCT
iajs-2883	82	25	5	5	NUM
iajs-2883	82	26	)	)	PUNCT
iajs-2883	82	27	…	…	PUNCT
iajs-2883	82	28	)	)	PUNCT
iajs-2883	82	29	]	]	PUNCT
iajs-2883	82	30	.	.	PUNCT
iajs-2883	82	31	(	(	PUNCT
iajs-2883	82	32	12	12	NUM
iajs-2883	82	33	)	)	PUNCT
iajs-2883	82	34	the	the	DET
iajs-2883	82	35	lte	lte	PROPN
iajs-2883	82	36	or	or	CCONJ
iajs-2883	82	37	the	the	DET
iajs-2883	82	38	order	order	NOUN
iajs-2883	82	39	conditions	condition	NOUN
iajs-2883	82	40	up	up	ADP
iajs-2883	82	41	to	to	PART
iajs-2883	82	42	order	order	VERB
iajs-2883	82	43	six	six	NUM
iajs-2883	82	44	for	for	ADP
iajs-2883	82	45	m	m	NOUN
iajs-2883	82	46	-	-	NOUN
iajs-2883	82	47	stage	stage	NOUN
iajs-2883	82	48	for	for	ADP
iajs-2883	82	49	the	the	DET
iajs-2883	82	50	new	new	ADJ
iajs-2883	82	51	technique	technique	NOUN
iajs-2883	82	52	can	can	AUX
iajs-2883	82	53	be	be	AUX
iajs-2883	82	54	solved	solve	VERB
iajs-2883	82	55	by	by	ADP
iajs-2883	82	56	substituting	substitute	VERB
iajs-2883	82	57	(	(	PUNCT
iajs-2883	82	58	11	11	NUM
iajs-2883	82	59	)	)	PUNCT
iajs-2883	82	60	into	into	ADP
iajs-2883	82	61	(	(	PUNCT
iajs-2883	82	62	12	12	NUM
iajs-2883	82	63	)	)	PUNCT
iajs-2883	82	64	and	and	CCONJ
iajs-2883	82	65	expanding	expand	VERB
iajs-2883	82	66	as	as	ADP
iajs-2883	82	67	a	a	DET
iajs-2883	82	68	taylor	taylor	NOUN
iajs-2883	82	69	expansion	expansion	NOUN
iajs-2883	82	70	using	use	VERB
iajs-2883	82	71	the	the	DET
iajs-2883	82	72	maple	maple	NOUN
iajs-2883	82	73	package	package	NOUN
iajs-2883	82	74	see	see	VERB
iajs-2883	82	75	[	[	X
iajs-2883	82	76	14	14	NUM
iajs-2883	82	77	]	]	PUNCT
iajs-2883	82	78	and	and	CCONJ
iajs-2883	82	79	[	[	X
iajs-2883	82	80	12	12	NUM
iajs-2883	82	81	]	]	PUNCT
iajs-2883	82	82	.	.	PUNCT
iajs-2883	83	1	file:///c:/users	file:///c:/user	NOUN
iajs-2883	83	2	/	/	SYM
iajs-2883	83	3	newfuture	newfuture	NOUN
iajs-2883	83	4	/	/	SYM
iajs-2883	83	5	onedrive	onedrive	ADJ
iajs-2883	83	6	/	/	SYM
iajs-2883	83	7	desktop	desktop	NOUN
iajs-2883	83	8	/	/	SYM
iajs-2883	83	9	نور%20جليل%20القصاب	نور%20جليل%20القصاب	NOUN
iajs-2883	83	10	/	/	SYM
iajs-2883	83	11	النسخة%20بالتفاصيل.docx%23_bookmark7	النسخة%20بالتفاصيل.docx%23_bookmark7	NOUN
iajs-2883	83	12	file:///c:/users	file:///c:/users	PROPN
iajs-2883	83	13	/	/	SYM
iajs-2883	83	14	newfuture	newfuture	NOUN
iajs-2883	83	15	/	/	SYM
iajs-2883	83	16	onedrive	onedrive	ADJ
iajs-2883	83	17	/	/	SYM
iajs-2883	83	18	desktop	desktop	NOUN
iajs-2883	83	19	/	/	SYM
iajs-2883	83	20	نور%20جليل%20القصاب	نور%20جليل%20القصاب	NOUN
iajs-2883	83	21	/	/	SYM
iajs-2883	83	22	النسخة%20بالتفاصيل.docx%23_bookmark4	النسخة%20بالتفاصيل.docx%23_bookmark4	PROPN
iajs-2883	83	23	ihjpas	ihjpa	NOUN
iajs-2883	83	24	.	.	PUNCT
iajs-2883	84	1	36(1)2023	36(1)2023	NUM
iajs-2883	84	2	393	393	NUM
iajs-2883	84	3	2.exponentially	2.exponentially	NUM
iajs-2883	84	4	fitted	fit	VERB
iajs-2883	84	5	editrk4	editrk4	PROPN
iajs-2883	84	6	method	method	NOUN
iajs-2883	84	7	definition	definition	NOUN
iajs-2883	84	8	1	1	NUM
iajs-2883	84	9	:	:	PUNCT
iajs-2883	84	10	to	to	PART
iajs-2883	84	11	create	create	VERB
iajs-2883	84	12	the	the	DET
iajs-2883	84	13	exponentially	exponentially	ADV
iajs-2883	84	14	fitted	fit	VERB
iajs-2883	84	15	rk	rk	NOUN
iajs-2883	84	16	kind	kind	ADJ
iajs-2883	84	17	3	3	NUM
iajs-2883	84	18	-	-	PUNCT
iajs-2883	84	19	stage	stage	NOUN
iajs-2883	84	20	4𝑡ℎ-order	4𝑡ℎ-order	NUM
iajs-2883	84	21	technique	technique	NOUN
iajs-2883	84	22	,	,	PUNCT
iajs-2883	84	23	the	the	DET
iajs-2883	84	24	functions	function	NOUN
iajs-2883	84	25	𝑒𝑤	𝑒𝑤	X
iajs-2883	84	26	and	and	CCONJ
iajs-2883	84	27	𝑒−𝑤	𝑒−𝑤	PROPN
iajs-2883	84	28	must	must	AUX
iajs-2883	84	29	integrate	integrate	VERB
iajs-2883	84	30	perfectly	perfectly	ADV
iajs-2883	84	31	at	at	ADP
iajs-2883	84	32	each	each	DET
iajs-2883	84	33	stage	stage	NOUN
iajs-2883	84	34	;	;	PUNCT
iajs-2883	84	35	consequently	consequently	ADV
iajs-2883	84	36	,	,	PUNCT
iajs-2883	84	37	the	the	DET
iajs-2883	84	38	following	follow	VERB
iajs-2883	84	39	equations	equation	NOUN
iajs-2883	84	40	are	be	AUX
iajs-2883	84	41	derived	derive	VERB
iajs-2883	84	42	for	for	ADP
iajs-2883	84	43	𝑦	𝑦	NOUN
iajs-2883	84	44	,	,	PUNCT
iajs-2883	84	45	𝑦′	𝑦′	X
iajs-2883	84	46	and	and	CCONJ
iajs-2883	84	47	𝑦′′	𝑦′′	PROPN
iajs-2883	84	48	𝑒±𝑣	𝑒±𝑣	PUNCT
iajs-2883	85	1	=	=	SYM
iajs-2883	85	2	1	1	NUM
iajs-2883	85	3	±	±	NUM
iajs-2883	85	4	𝑣	𝑣	DET
iajs-2883	85	5	+	+	NOUN
iajs-2883	85	6	1	1	NUM
iajs-2883	85	7	2	2	NUM
iajs-2883	85	8	𝑣2	𝑣2	NUM
iajs-2883	85	9	±	±	NUM
iajs-2883	85	10	𝑣3	𝑣3	PROPN
iajs-2883	85	11	∑	∑	PUNCT
iajs-2883	85	12	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	85	13	𝑚	𝑚	X
iajs-2883	85	14	𝑖=1	𝑖=1	PROPN
iajs-2883	85	15	𝑒±𝑐𝑖𝑣	𝑒±𝑐𝑖𝑣	X
iajs-2883	85	16	,	,	PUNCT
iajs-2883	85	17	(	(	PUNCT
iajs-2883	85	18	13	13	NUM
iajs-2883	85	19	)	)	PUNCT
iajs-2883	85	20	e±v	e±v	PROPN
iajs-2883	85	21	=	=	SYM
iajs-2883	85	22	1	1	NUM
iajs-2883	85	23	±	±	NUM
iajs-2883	85	24	v	v	NOUN
iajs-2883	85	25	+	+	CCONJ
iajs-2883	85	26	v2	v2	PROPN
iajs-2883	85	27	∑	∑	NOUN
iajs-2883	85	28	bi	bi	NOUN
iajs-2883	85	29	′	′	NUM
iajs-2883	85	30	m	m	VERB
iajs-2883	85	31	i=1	i=1	PROPN
iajs-2883	85	32	e±civ	e±civ	PROPN
iajs-2883	85	33	,	,	PUNCT
iajs-2883	85	34	(	(	PUNCT
iajs-2883	85	35	14	14	NUM
iajs-2883	85	36	)	)	PUNCT
iajs-2883	85	37	𝑒±𝑣	𝑒±𝑣	PUNCT
iajs-2883	86	1	=	=	SYM
iajs-2883	86	2	1	1	NUM
iajs-2883	86	3	±	±	NUM
iajs-2883	86	4	𝑣	𝑣	PRON
iajs-2883	86	5	∑	∑	PROPN
iajs-2883	86	6	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	86	7	′′𝑚	′′𝑚	NOUN
iajs-2883	86	8	𝑖=1	𝑖=1	PROPN
iajs-2883	86	9	𝑒±𝑐𝑖𝑣.	𝑒±𝑐𝑖𝑣.	PROPN
iajs-2883	86	10	(	(	PUNCT
iajs-2883	86	11	15	15	NUM
iajs-2883	86	12	)	)	PUNCT
iajs-2883	86	13	where	where	SCONJ
iajs-2883	86	14	𝑣	𝑣	ADP
iajs-2883	86	15	=	=	SYM
iajs-2883	86	16	𝑤ℎ	𝑤ℎ	NOUN
iajs-2883	86	17	,	,	PUNCT
iajs-2883	86	18	𝑤	𝑤	ADP
iajs-2883	86	19	∈	∈	NOUN
iajs-2883	86	20	𝑅.	𝑅.	NOUN
iajs-2883	86	21	the	the	DET
iajs-2883	86	22	relations	relation	NOUN
iajs-2883	86	23	cosh(𝑣	cosh(𝑣	VERB
iajs-2883	86	24	)	)	PUNCT
iajs-2883	86	25	=	=	SYM
iajs-2883	87	1	𝑒𝑣+𝑒−𝑣	𝑒𝑣+𝑒−𝑣	NOUN
iajs-2883	87	2	2	2	NUM
iajs-2883	87	3	and	and	CCONJ
iajs-2883	87	4	sinh(𝑣	sinh(𝑣	NOUN
iajs-2883	87	5	)	)	PUNCT
iajs-2883	87	6	=	=	SYM
iajs-2883	88	1	𝑒𝑣−𝑒−𝑣	𝑒𝑣−𝑒−𝑣	ADJ
iajs-2883	88	2	2	2	NUM
iajs-2883	88	3	will	will	AUX
iajs-2883	88	4	be	be	AUX
iajs-2883	88	5	used	use	VERB
iajs-2883	88	6	in	in	ADP
iajs-2883	88	7	the	the	DET
iajs-2883	88	8	derivation	derivation	NOUN
iajs-2883	88	9	process	process	NOUN
iajs-2883	88	10	.	.	PUNCT
iajs-2883	89	1	the	the	DET
iajs-2883	89	2	following	follow	VERB
iajs-2883	89	3	equations	equation	NOUN
iajs-2883	89	4	corresponding	correspond	VERB
iajs-2883	89	5	𝑦	𝑦	NOUN
iajs-2883	89	6	,	,	PUNCT
iajs-2883	89	7	𝑦′	𝑦′	X
iajs-2883	89	8	and	and	CCONJ
iajs-2883	89	9	𝑦′′	𝑦′′	ADV
iajs-2883	89	10	are	be	AUX
iajs-2883	89	11	:	:	PUNCT
iajs-2883	89	12	cos(𝑣	cos(𝑣	X
iajs-2883	89	13	)	)	PUNCT
iajs-2883	89	14	=	=	SYM
iajs-2883	90	1	1	1	NUM
iajs-2883	90	2	+	+	CCONJ
iajs-2883	90	3	1	1	NUM
iajs-2883	90	4	2	2	NUM
iajs-2883	90	5	𝑣2	𝑣2	NOUN
iajs-2883	90	6	+	+	CCONJ
iajs-2883	90	7	𝑣3	𝑣3	ADV
iajs-2883	90	8	∑	∑	ADP
iajs-2883	90	9	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	90	10	𝑚	𝑚	PROPN
iajs-2883	90	11	𝑖=1	𝑖=1	PROPN
iajs-2883	90	12	sin	sin	PROPN
iajs-2883	90	13	ℎ(𝑣𝑐𝑖	ℎ(𝑣𝑐𝑖	PROPN
iajs-2883	90	14	)	)	PUNCT
iajs-2883	90	15	,	,	PUNCT
iajs-2883	90	16	(	(	PUNCT
iajs-2883	90	17	16	16	X
iajs-2883	90	18	)	)	PUNCT
iajs-2883	90	19	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
iajs-2883	90	20	ℎ(𝑣	ℎ(𝑣	NOUN
iajs-2883	90	21	)	)	PUNCT
iajs-2883	90	22	=	=	SYM
iajs-2883	91	1	𝑣	𝑣	ADP
iajs-2883	91	2	+	+	CCONJ
iajs-2883	91	3	𝑣3	𝑣3	ADV
iajs-2883	91	4	∑	∑	ADP
iajs-2883	91	5	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	91	6	𝑚	𝑚	X
iajs-2883	91	7	𝑖=1	𝑖=1	PROPN
iajs-2883	91	8	𝑐𝑜𝑠ℎ(𝑣𝑐𝑖	𝑐𝑜𝑠ℎ(𝑣𝑐𝑖	PROPN
iajs-2883	91	9	)	)	PUNCT
iajs-2883	91	10	,	,	PUNCT
iajs-2883	91	11	(	(	PUNCT
iajs-2883	91	12	17	17	NUM
iajs-2883	91	13	)	)	PUNCT
iajs-2883	91	14	𝑐𝑜𝑠ℎ(𝑣	𝑐𝑜𝑠ℎ(𝑣	ADP
iajs-2883	91	15	)	)	PUNCT
iajs-2883	91	16	=	=	SYM
iajs-2883	92	1	1	1	NUM
iajs-2883	93	1	+	+	CCONJ
iajs-2883	93	2	𝑣2	𝑣2	X
iajs-2883	93	3	∑	∑	PUNCT
iajs-2883	93	4	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	93	5	′	′	NUM
iajs-2883	93	6	𝑚	𝑚	VERB
iajs-2883	93	7	𝑖=1	𝑖=1	PROPN
iajs-2883	93	8	𝑐𝑜𝑠ℎ(𝑣𝑐𝑖	𝑐𝑜𝑠ℎ(𝑣𝑐𝑖	PROPN
iajs-2883	93	9	)	)	PUNCT
iajs-2883	93	10	,	,	PUNCT
iajs-2883	93	11	(	(	PUNCT
iajs-2883	93	12	18	18	NUM
iajs-2883	93	13	)	)	PUNCT
iajs-2883	93	14	sinh(𝑣	sinh(𝑣	NOUN
iajs-2883	93	15	)	)	PUNCT
iajs-2883	93	16	=	=	SYM
iajs-2883	94	1	𝑣	𝑣	ADP
iajs-2883	94	2	+	+	CCONJ
iajs-2883	94	3	𝑣2	𝑣2	X
iajs-2883	94	4	∑	∑	PUNCT
iajs-2883	94	5	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	94	6	′	′	NUM
iajs-2883	94	7	𝑚	𝑚	VERB
iajs-2883	94	8	𝑖=1	𝑖=1	PROPN
iajs-2883	94	9	sinh(𝑣𝑐𝑖	sinh(𝑣𝑐𝑖	NOUN
iajs-2883	94	10	)	)	PUNCT
iajs-2883	94	11	,	,	PUNCT
iajs-2883	94	12	(	(	PUNCT
iajs-2883	94	13	19	19	NUM
iajs-2883	94	14	)	)	PUNCT
iajs-2883	94	15	cosh(𝑣	cosh(𝑣	NOUN
iajs-2883	94	16	)	)	PUNCT
iajs-2883	94	17	=	=	SYM
iajs-2883	95	1	1	1	NUM
iajs-2883	95	2	+	+	CCONJ
iajs-2883	95	3	𝑣	𝑣	PART
iajs-2883	95	4	∑	∑	VERB
iajs-2883	95	5	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	95	6	′′	′′	PROPN
iajs-2883	95	7	𝑚	𝑚	ADP
iajs-2883	95	8	𝑖=1	𝑖=1	PROPN
iajs-2883	95	9	sinh(𝑣𝑐𝑖	sinh(𝑣𝑐𝑖	NOUN
iajs-2883	95	10	)	)	PUNCT
iajs-2883	95	11	,	,	PUNCT
iajs-2883	95	12	(	(	PUNCT
iajs-2883	95	13	20	20	X
iajs-2883	95	14	)	)	PUNCT
iajs-2883	95	15	𝑠𝑖𝑛ℎ(𝑣	𝑠𝑖𝑛ℎ(𝑣	PROPN
iajs-2883	95	16	)	)	PUNCT
iajs-2883	95	17	=	=	SYM
iajs-2883	96	1	𝑣	𝑣	X
iajs-2883	96	2	∑	∑	ADP
iajs-2883	96	3	𝑏𝑖	𝑏𝑖	ADP
iajs-2883	96	4	′′	′′	PROPN
iajs-2883	96	5	𝑚	𝑚	ADP
iajs-2883	96	6	𝑖=1	𝑖=1	PROPN
iajs-2883	96	7	𝑐𝑜𝑠ℎ(𝑣𝑐𝑖	𝑐𝑜𝑠ℎ(𝑣𝑐𝑖	PROPN
iajs-2883	96	8	)	)	PUNCT
iajs-2883	96	9	.	.	PUNCT
iajs-2883	97	1	(	(	PUNCT
iajs-2883	97	2	21	21	NUM
iajs-2883	97	3	)	)	PUNCT
iajs-2883	97	4	in	in	ADP
iajs-2883	97	5	[	[	X
iajs-2883	97	6	12	12	NUM
iajs-2883	97	7	]	]	PUNCT
iajs-2883	97	8	,	,	PUNCT
iajs-2883	97	9	devised	devise	VERB
iajs-2883	97	10	the	the	DET
iajs-2883	97	11	following	follow	VERB
iajs-2883	97	12	3	3	NUM
iajs-2883	97	13	-	-	PUNCT
iajs-2883	97	14	stage	stage	NOUN
iajs-2883	97	15	4𝑡ℎ-order	4𝑡ℎ-order	NUM
iajs-2883	97	16	diagonally	diagonally	ADV
iajs-2883	97	17	implicit	implicit	ADJ
iajs-2883	97	18	approach	approach	NOUN
iajs-2883	97	19	.	.	PUNCT
iajs-2883	98	1	𝑐1	𝑐1	NOUN
iajs-2883	98	2	=	=	NOUN
iajs-2883	98	3	4	4	NUM
iajs-2883	98	4	5	5	NUM
iajs-2883	98	5	,	,	PUNCT
iajs-2883	98	6	𝑐2	𝑐2	NOUN
iajs-2883	98	7	=	=	SYM
iajs-2883	98	8	2	2	NUM
iajs-2883	98	9	5	5	NUM
iajs-2883	98	10	,	,	PUNCT
iajs-2883	98	11	𝑐3	𝑐3	NOUN
iajs-2883	98	12	=	=	SYM
iajs-2883	98	13	7	7	NUM
iajs-2883	98	14	10	10	NUM
iajs-2883	98	15	,	,	PUNCT
iajs-2883	98	16	𝑎11	𝑎11	VERB
iajs-2883	98	17	=	=	NOUN
iajs-2883	98	18	1	1	NUM
iajs-2883	98	19	600	600	NUM
iajs-2883	98	20	,	,	PUNCT
iajs-2883	98	21	𝑎21	𝑎21	NOUN
iajs-2883	98	22	=	=	SYM
iajs-2883	98	23	0	0	NUM
iajs-2883	98	24	,	,	PUNCT
iajs-2883	98	25	𝑎22	𝑎22	NOUN
iajs-2883	98	26	=	=	SYM
iajs-2883	98	27	1	1	NUM
iajs-2883	98	28	600	600	NUM
iajs-2883	98	29	,	,	PUNCT
iajs-2883	98	30	𝑎31	𝑎31	NUM
iajs-2883	98	31	=	=	SYM
iajs-2883	98	32	0	0	NUM
iajs-2883	98	33	,	,	PUNCT
iajs-2883	98	34	𝑎32	𝑎32	NOUN
iajs-2883	98	35	=	=	SYM
iajs-2883	98	36	2	2	NUM
iajs-2883	98	37	25	25	NUM
iajs-2883	98	38	,	,	PUNCT
iajs-2883	98	39	𝑎33	𝑎33	VERB
iajs-2883	98	40	=	=	SYM
iajs-2883	98	41	1	1	NUM
iajs-2883	98	42	600	600	NUM
iajs-2883	98	43	,	,	PUNCT
iajs-2883	98	44	𝑏1	𝑏1	ADJ
iajs-2883	98	45	=	=	SYM
iajs-2883	98	46	0	0	NUM
iajs-2883	98	47	,	,	PUNCT
iajs-2883	98	48	𝑏2	𝑏2	NOUN
iajs-2883	98	49	=	=	NOUN
iajs-2883	98	50	1	1	NUM
iajs-2883	98	51	10	10	NUM
iajs-2883	98	52	,	,	PUNCT
iajs-2883	98	53	𝑏3	𝑏3	NOUN
iajs-2883	98	54	=	=	SYM
iajs-2883	98	55	1	1	NUM
iajs-2883	98	56	100	100	NUM
iajs-2883	98	57	,	,	PUNCT
iajs-2883	98	58	𝑏1	𝑏1	VERB
iajs-2883	98	59	′	′	NUM
iajs-2883	98	60	=	=	SYM
iajs-2883	98	61	0	0	NUM
iajs-2883	98	62	,	,	PUNCT
iajs-2883	98	63	𝑏2	𝑏2	PROPN
iajs-2883	98	64	′	′	NOUN
iajs-2883	99	1	=	=	NOUN
iajs-2883	99	2	3	3	NUM
iajs-2883	99	3	10	10	NUM
iajs-2883	99	4	,	,	PUNCT
iajs-2883	99	5	𝑏3	𝑏3	NOUN
iajs-2883	99	6	′	′	NOUN
iajs-2883	99	7	=	=	NOUN
iajs-2883	99	8	1	1	NUM
iajs-2883	99	9	10	10	NUM
iajs-2883	99	10	,	,	PUNCT
iajs-2883	99	11	𝑏1	𝑏1	VERB
iajs-2883	99	12	′′	′′	NOUN
iajs-2883	99	13	=	=	SYM
iajs-2883	99	14	0	0	NUM
iajs-2883	99	15	,	,	PUNCT
iajs-2883	99	16	𝑏2	𝑏2	PROPN
iajs-2883	99	17	′′	′′	PROPN
iajs-2883	99	18	=	=	NOUN
iajs-2883	99	19	1	1	NUM
iajs-2883	99	20	2	2	NUM
iajs-2883	99	21	,	,	PUNCT
iajs-2883	99	22	𝑏3	𝑏3	NOUN
iajs-2883	99	23	′′	′′	NOUN
iajs-2883	99	24	=	=	NOUN
iajs-2883	99	25	1	1	NUM
iajs-2883	99	26	2	2	NUM
iajs-2883	99	27	.	.	PUNCT
iajs-2883	100	1	next	next	ADV
iajs-2883	100	2	,	,	PUNCT
iajs-2883	100	3	we	we	PRON
iajs-2883	100	4	solve	solve	VERB
iajs-2883	100	5	(	(	PUNCT
iajs-2883	100	6	16	16	NUM
iajs-2883	100	7	)	)	PUNCT
iajs-2883	100	8	–	–	PUNCT
iajs-2883	100	9	(	(	PUNCT
iajs-2883	100	10	21	21	NUM
iajs-2883	100	11	)	)	PUNCT
iajs-2883	100	12	and	and	CCONJ
iajs-2883	100	13	use	use	NOUN
iajs-2883	100	14	of	of	ADP
iajs-2883	100	15	the	the	DET
iajs-2883	100	16	coefficients	coefficient	NOUN
iajs-2883	100	17	listed	list	VERB
iajs-2883	100	18	above	above	ADV
iajs-2883	100	19	to	to	PART
iajs-2883	100	20	find	find	VERB
iajs-2883	100	21	𝑏1	𝑏1	NOUN
iajs-2883	100	22	,	,	PUNCT
iajs-2883	100	23	𝑏2	𝑏2	NOUN
iajs-2883	100	24	,	,	PUNCT
iajs-2883	100	25	𝑏1	𝑏1	ADJ
iajs-2883	100	26	′	′	NOUN
iajs-2883	100	27	,	,	PUNCT
iajs-2883	100	28	𝑏2	𝑏2	PROPN
iajs-2883	100	29	′	′	NOUN
iajs-2883	100	30	,	,	PUNCT
iajs-2883	100	31	𝑏1	𝑏1	ADJ
iajs-2883	100	32	′′	′′	PROPN
iajs-2883	100	33	and	and	CCONJ
iajs-2883	100	34	𝑏2	𝑏2	PROPN
iajs-2883	100	35	′′.	′′.	PROPN
iajs-2883	100	36	ihjpas	ihjpa	VERB
iajs-2883	100	37	.	.	PUNCT
iajs-2883	101	1	36(1)2023	36(1)2023	NUM
iajs-2883	101	2	394	394	NUM
iajs-2883	101	3	𝑏1	𝑏1	NOUN
iajs-2883	101	4	=	=	SYM
iajs-2883	101	5	(	(	PUNCT
iajs-2883	101	6	cosh	cosh	PROPN
iajs-2883	101	7	(	(	PUNCT
iajs-2883	101	8	𝑣	𝑣	NOUN
iajs-2883	101	9	3	3	NUM
iajs-2883	101	10	)	)	PUNCT
iajs-2883	101	11	sinh	sinh	NOUN
iajs-2883	101	12	(	(	PUNCT
iajs-2883	101	13	7𝑣	7𝑣	NOUN
iajs-2883	101	14	10	10	NUM
iajs-2883	101	15	)	)	PUNCT
iajs-2883	101	16	−	−	PROPN
iajs-2883	102	1	cosh	cosh	PROPN
iajs-2883	102	2	(	(	PUNCT
iajs-2883	102	3	7𝑣	7𝑣	NOUN
iajs-2883	102	4	10	10	NUM
iajs-2883	102	5	)	)	PUNCT
iajs-2883	102	6	sinh	sinh	PROPN
iajs-2883	102	7	(	(	PUNCT
iajs-2883	102	8	𝑣	𝑣	PROPN
iajs-2883	102	9	3	3	NUM
iajs-2883	102	10	)	)	PUNCT
iajs-2883	102	11	100	100	NUM
iajs-2883	102	12	cosh	cosh	NOUN
iajs-2883	102	13	(	(	PUNCT
iajs-2883	102	14	4	4	NUM
iajs-2883	102	15	5	5	NUM
iajs-2883	102	16	𝑣	𝑣	NOUN
iajs-2883	102	17	)	)	PUNCT
iajs-2883	102	18	sinh	sinh	NOUN
iajs-2883	102	19	(	(	PUNCT
iajs-2883	102	20	𝑣	𝑣	ADP
iajs-2883	102	21	5	5	NUM
iajs-2883	102	22	)	)	PUNCT
iajs-2883	102	23	−	−	PROPN
iajs-2883	102	24	100	100	NUM
iajs-2883	102	25	cosh	cosh	NOUN
iajs-2883	102	26	(	(	PUNCT
iajs-2883	102	27	𝑣	𝑣	PART
iajs-2883	102	28	5	5	NUM
iajs-2883	102	29	)	)	PUNCT
iajs-2883	102	30	sinh	sinh	NOUN
iajs-2883	102	31	(	(	PUNCT
iajs-2883	102	32	4	4	NUM
iajs-2883	102	33	5	5	NUM
iajs-2883	102	34	𝑣	𝑣	NOUN
iajs-2883	102	35	)	)	PUNCT
iajs-2883	102	36	+	+	CCONJ
iajs-2883	102	37	1	1	NUM
iajs-2883	102	38	2⁄	2⁄	NUM
iajs-2883	102	39	cosh	cosh	NOUN
iajs-2883	102	40	(	(	PUNCT
iajs-2883	102	41	𝑣	𝑣	NOUN
iajs-2883	102	42	5	5	NUM
iajs-2883	102	43	)	)	PUNCT
iajs-2883	102	44	𝑣2	𝑣2	NOUN
iajs-2883	102	45	+	+	CCONJ
iajs-2883	102	46	2	2	NUM
iajs-2883	102	47	sinh(𝑣	sinh(𝑣	NOUN
iajs-2883	102	48	)	)	PUNCT
iajs-2883	102	49	sinh	sinh	NOUN
iajs-2883	102	50	(	(	PUNCT
iajs-2883	102	51	𝑣	𝑣	NOUN
iajs-2883	102	52	5	5	NUM
iajs-2883	102	53	)	)	PUNCT
iajs-2883	102	54	−	−	PROPN
iajs-2883	102	55	2	2	NUM
iajs-2883	102	56	cosh	cosh	NOUN
iajs-2883	102	57	(	(	PUNCT
iajs-2883	102	58	𝑣	𝑣	PART
iajs-2883	102	59	5	5	NUM
iajs-2883	102	60	)	)	PUNCT
iajs-2883	102	61	cosh(𝑣	cosh(𝑣	NOUN
iajs-2883	102	62	)	)	PUNCT
iajs-2883	102	63	−	−	PROPN
iajs-2883	102	64	2	2	NUM
iajs-2883	102	65	sinh	sinh	NOUN
iajs-2883	102	66	(	(	PUNCT
iajs-2883	102	67	𝑣	𝑣	PROPN
iajs-2883	102	68	5	5	NUM
iajs-2883	102	69	)	)	PUNCT
iajs-2883	102	70	𝑣	𝑣	ADP
iajs-2883	102	71	+	+	ADJ
iajs-2883	102	72	2	2	NUM
iajs-2883	102	73	cosh	cosh	NOUN
iajs-2883	102	74	(	(	PUNCT
iajs-2883	102	75	𝑣	𝑣	PART
iajs-2883	102	76	5	5	NUM
iajs-2883	102	77	)	)	PUNCT
iajs-2883	102	78	𝑣3(cosh	𝑣3(cosh	NOUN
iajs-2883	102	79	(	(	PUNCT
iajs-2883	102	80	4	4	NUM
iajs-2883	102	81	5	5	NUM
iajs-2883	102	82	𝑣	𝑣	NOUN
iajs-2883	102	83	)	)	PUNCT
iajs-2883	102	84	sinh	sinh	NOUN
iajs-2883	102	85	(	(	PUNCT
iajs-2883	102	86	𝑣	𝑣	ADP
iajs-2883	102	87	5	5	NUM
iajs-2883	102	88	)	)	PUNCT
iajs-2883	102	89	−	−	NOUN
iajs-2883	103	1	cosh	cosh	PROPN
iajs-2883	103	2	(	(	PUNCT
iajs-2883	103	3	𝑣	𝑣	PART
iajs-2883	103	4	5	5	NUM
iajs-2883	103	5	)	)	PUNCT
iajs-2883	103	6	sinh	sinh	NOUN
iajs-2883	103	7	(	(	PUNCT
iajs-2883	103	8	4	4	NUM
iajs-2883	103	9	5	5	NUM
iajs-2883	103	10	𝑣	𝑣	NOUN
iajs-2883	103	11	)	)	PUNCT
iajs-2883	103	12	)	)	PUNCT
iajs-2883	103	13	𝑏2	𝑏2	NOUN
iajs-2883	103	14	=	=	SYM
iajs-2883	103	15	−	−	PROPN
iajs-2883	103	16	(	(	PUNCT
iajs-2883	103	17	cosh	cosh	PROPN
iajs-2883	103	18	(	(	PUNCT
iajs-2883	103	19	4	4	NUM
iajs-2883	103	20	5	5	NUM
iajs-2883	103	21	𝑣	𝑣	NOUN
iajs-2883	103	22	)	)	PUNCT
iajs-2883	103	23	sinh	sinh	NOUN
iajs-2883	103	24	(	(	PUNCT
iajs-2883	103	25	7𝑣	7𝑣	NOUN
iajs-2883	103	26	10	10	NUM
iajs-2883	103	27	)	)	PUNCT
iajs-2883	103	28	−	−	PROPN
iajs-2883	104	1	cosh	cosh	NOUN
iajs-2883	104	2	(	(	PUNCT
iajs-2883	104	3	7𝑣	7𝑣	NOUN
iajs-2883	104	4	10	10	NUM
iajs-2883	104	5	)	)	PUNCT
iajs-2883	104	6	sinh	sinh	NOUN
iajs-2883	104	7	(	(	PUNCT
iajs-2883	104	8	4	4	NUM
iajs-2883	104	9	5	5	NUM
iajs-2883	104	10	𝑣	𝑣	NOUN
iajs-2883	104	11	)	)	PUNCT
iajs-2883	104	12	100	100	NUM
iajs-2883	104	13	cosh	cosh	NOUN
iajs-2883	104	14	(	(	PUNCT
iajs-2883	104	15	4	4	NUM
iajs-2883	104	16	5	5	NUM
iajs-2883	104	17	𝑣	𝑣	NOUN
iajs-2883	104	18	)	)	PUNCT
iajs-2883	104	19	sinh	sinh	NOUN
iajs-2883	104	20	(	(	PUNCT
iajs-2883	104	21	𝑣	𝑣	ADP
iajs-2883	104	22	5	5	NUM
iajs-2883	104	23	)	)	PUNCT
iajs-2883	104	24	−	−	PROPN
iajs-2883	104	25	100	100	NUM
iajs-2883	104	26	cosh	cosh	NOUN
iajs-2883	104	27	(	(	PUNCT
iajs-2883	104	28	𝑣	𝑣	PART
iajs-2883	104	29	5	5	NUM
iajs-2883	104	30	)	)	PUNCT
iajs-2883	104	31	sinh	sinh	NOUN
iajs-2883	104	32	(	(	PUNCT
iajs-2883	104	33	4	4	NUM
iajs-2883	104	34	5	5	NUM
iajs-2883	104	35	𝑣	𝑣	NOUN
iajs-2883	104	36	)	)	PUNCT
iajs-2883	104	37	−	−	PROPN
iajs-2883	104	38	1	1	NUM
iajs-2883	104	39	2⁄	2⁄	NUM
iajs-2883	104	40	cosh	cosh	NOUN
iajs-2883	104	41	(	(	PUNCT
iajs-2883	104	42	4	4	NUM
iajs-2883	104	43	5	5	NUM
iajs-2883	104	44	𝑣	𝑣	NOUN
iajs-2883	104	45	)	)	PUNCT
iajs-2883	104	46	𝑣2	𝑣2	NOUN
iajs-2883	104	47	+	+	CCONJ
iajs-2883	104	48	2	2	NUM
iajs-2883	104	49	sinh	sinh	NOUN
iajs-2883	104	50	(	(	PUNCT
iajs-2883	104	51	4	4	NUM
iajs-2883	104	52	5	5	NUM
iajs-2883	104	53	𝑣	𝑣	NOUN
iajs-2883	104	54	)	)	PUNCT
iajs-2883	104	55	sinh(𝑣	sinh(𝑣	NOUN
iajs-2883	104	56	)	)	PUNCT
iajs-2883	104	57	−	−	PROPN
iajs-2883	104	58	2	2	NUM
iajs-2883	104	59	cosh(𝑣	cosh(𝑣	NOUN
iajs-2883	104	60	)	)	PUNCT
iajs-2883	104	61	cosh	cosh	NOUN
iajs-2883	104	62	(	(	PUNCT
iajs-2883	104	63	4	4	NUM
iajs-2883	104	64	5	5	NUM
iajs-2883	104	65	𝑣	𝑣	NOUN
iajs-2883	104	66	)	)	PUNCT
iajs-2883	104	67	−	−	PROPN
iajs-2883	104	68	2	2	NUM
iajs-2883	104	69	sinh	sinh	NOUN
iajs-2883	104	70	(	(	PUNCT
iajs-2883	104	71	4	4	NUM
iajs-2883	104	72	5	5	NUM
iajs-2883	104	73	𝑣	𝑣	NOUN
iajs-2883	104	74	)	)	PUNCT
iajs-2883	104	75	𝑣	𝑣	ADP
iajs-2883	104	76	+	+	ADJ
iajs-2883	104	77	2	2	NUM
iajs-2883	104	78	cosh	cosh	NOUN
iajs-2883	104	79	(	(	PUNCT
iajs-2883	104	80	4	4	NUM
iajs-2883	104	81	5	5	NUM
iajs-2883	104	82	𝑣	𝑣	NOUN
iajs-2883	104	83	)	)	PUNCT
iajs-2883	104	84	𝑣3(cosh	𝑣3(cosh	NOUN
iajs-2883	104	85	(	(	PUNCT
iajs-2883	104	86	4	4	NUM
iajs-2883	104	87	5	5	NUM
iajs-2883	104	88	𝑣	𝑣	NOUN
iajs-2883	104	89	)	)	PUNCT
iajs-2883	104	90	sinh	sinh	NOUN
iajs-2883	104	91	(	(	PUNCT
iajs-2883	104	92	𝑣	𝑣	ADP
iajs-2883	104	93	5	5	NUM
iajs-2883	104	94	)	)	PUNCT
iajs-2883	104	95	−	−	NOUN
iajs-2883	105	1	cosh	cosh	PROPN
iajs-2883	105	2	(	(	PUNCT
iajs-2883	105	3	𝑣	𝑣	PART
iajs-2883	105	4	5	5	NUM
iajs-2883	105	5	)	)	PUNCT
iajs-2883	105	6	sinh	sinh	NOUN
iajs-2883	105	7	(	(	PUNCT
iajs-2883	105	8	4	4	NUM
iajs-2883	105	9	5	5	NUM
iajs-2883	105	10	𝑣	𝑣	NOUN
iajs-2883	105	11	)	)	PUNCT
iajs-2883	105	12	)	)	PUNCT
iajs-2883	105	13	𝑏1	𝑏1	NOUN
iajs-2883	105	14	′	′	NUM
iajs-2883	105	15	=	=	SYM
iajs-2883	105	16	1	1	NUM
iajs-2883	105	17	10	10	NUM
iajs-2883	105	18	(	(	PUNCT
iajs-2883	105	19	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
iajs-2883	105	20	(	(	PUNCT
iajs-2883	105	21	𝑣	𝑣	PART
iajs-2883	105	22	5	5	NUM
iajs-2883	105	23	)	)	PUNCT
iajs-2883	105	24	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	NOUN
iajs-2883	105	25	(	(	PUNCT
iajs-2883	105	26	7𝑣	7𝑣	PROPN
iajs-2883	105	27	10	10	NUM
iajs-2883	105	28	)	)	PUNCT
iajs-2883	105	29	−	−	PROPN
iajs-2883	106	1	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
iajs-2883	106	2	(	(	PUNCT
iajs-2883	106	3	7𝑣	7𝑣	NOUN
iajs-2883	106	4	10	10	NUM
iajs-2883	106	5	)	)	PUNCT
iajs-2883	106	6	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	NOUN
iajs-2883	106	7	(	(	PUNCT
iajs-2883	106	8	𝑣	𝑣	PRON
iajs-2883	106	9	5	5	NUM
iajs-2883	106	10	)	)	PUNCT
iajs-2883	106	11	)	)	PUNCT
iajs-2883	106	12	cosh	cosh	NOUN
iajs-2883	106	13	(	(	PUNCT
iajs-2883	106	14	4	4	NUM
iajs-2883	106	15	5	5	NUM
iajs-2883	106	16	𝑣	𝑣	NOUN
iajs-2883	106	17	)	)	PUNCT
iajs-2883	106	18	sinh	sinh	NOUN
iajs-2883	106	19	(	(	PUNCT
iajs-2883	106	20	𝑣	𝑣	NOUN
iajs-2883	106	21	5	5	NUM
iajs-2883	106	22	)	)	PUNCT
iajs-2883	106	23	−	−	PROPN
iajs-2883	107	1	cosh	cosh	NOUN
iajs-2883	107	2	(	(	PUNCT
iajs-2883	107	3	𝑣	𝑣	PART
iajs-2883	107	4	5	5	NUM
iajs-2883	107	5	)	)	PUNCT
iajs-2883	107	6	sinh	sinh	NOUN
iajs-2883	107	7	(	(	PUNCT
iajs-2883	107	8	4	4	NUM
iajs-2883	107	9	5	5	NUM
iajs-2883	107	10	𝑣	𝑣	NOUN
iajs-2883	107	11	)	)	PUNCT
iajs-2883	107	12	−	−	PROPN
iajs-2883	108	1	cosh	cosh	NOUN
iajs-2883	108	2	(	(	PUNCT
iajs-2883	108	3	𝑣	𝑣	PART
iajs-2883	108	4	5	5	NUM
iajs-2883	108	5	)	)	PUNCT
iajs-2883	108	6	sinh(𝑣	sinh(𝑣	NOUN
iajs-2883	108	7	)	)	PUNCT
iajs-2883	108	8	−	−	PROPN
iajs-2883	109	1	cosh	cosh	NOUN
iajs-2883	109	2	(	(	PUNCT
iajs-2883	109	3	𝑣	𝑣	PART
iajs-2883	109	4	5	5	NUM
iajs-2883	109	5	)	)	PUNCT
iajs-2883	109	6	𝑣	𝑣	PRON
iajs-2883	109	7	−	−	PROPN
iajs-2883	109	8	sinh	sinh	NOUN
iajs-2883	109	9	(	(	PUNCT
iajs-2883	109	10	𝑣	𝑣	ADP
iajs-2883	109	11	5	5	NUM
iajs-2883	109	12	)	)	PUNCT
iajs-2883	109	13	+	+	CCONJ
iajs-2883	109	14	sinh	sinh	PROPN
iajs-2883	109	15	(	(	PUNCT
iajs-2883	109	16	𝑣	𝑣	PROPN
iajs-2883	109	17	5	5	NUM
iajs-2883	109	18	)	)	PUNCT
iajs-2883	109	19	𝑣2(cosh	𝑣2(cosh	ADV
iajs-2883	109	20	(	(	PUNCT
iajs-2883	109	21	4	4	NUM
iajs-2883	109	22	5	5	NUM
iajs-2883	109	23	𝑣	𝑣	NOUN
iajs-2883	109	24	)	)	PUNCT
iajs-2883	109	25	sinh	sinh	NOUN
iajs-2883	109	26	(	(	PUNCT
iajs-2883	109	27	𝑣	𝑣	ADP
iajs-2883	109	28	5	5	NUM
iajs-2883	109	29	)	)	PUNCT
iajs-2883	109	30	−	−	NOUN
iajs-2883	110	1	cosh	cosh	PROPN
iajs-2883	110	2	(	(	PUNCT
iajs-2883	110	3	𝑣	𝑣	PART
iajs-2883	110	4	5	5	NUM
iajs-2883	110	5	)	)	PUNCT
iajs-2883	110	6	sinh	sinh	NOUN
iajs-2883	110	7	(	(	PUNCT
iajs-2883	110	8	4	4	NUM
iajs-2883	110	9	5	5	NUM
iajs-2883	110	10	𝑣	𝑣	NOUN
iajs-2883	110	11	)	)	PUNCT
iajs-2883	110	12	)	)	PUNCT
iajs-2883	110	13	𝑏1	𝑏1	NOUN
iajs-2883	110	14	′′	′′	NOUN
iajs-2883	110	15	=	=	PUNCT
iajs-2883	110	16	(	(	PUNCT
iajs-2883	110	17	1	1	NUM
iajs-2883	110	18	2	2	NUM
iajs-2883	110	19	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
iajs-2883	110	20	(	(	PUNCT
iajs-2883	110	21	𝑣	𝑣	ADP
iajs-2883	110	22	5	5	NUM
iajs-2883	110	23	)	)	PUNCT
iajs-2883	110	24	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	NOUN
iajs-2883	110	25	(	(	PUNCT
iajs-2883	110	26	7𝑣	7𝑣	PROPN
iajs-2883	110	27	10	10	NUM
iajs-2883	110	28	)	)	PUNCT
iajs-2883	111	1	𝑣	𝑣	DET
iajs-2883	111	2	−	−	PROPN
iajs-2883	111	3	1	1	NUM
iajs-2883	111	4	2	2	NUM
iajs-2883	111	5	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
iajs-2883	111	6	(	(	PUNCT
iajs-2883	111	7	7𝑣	7𝑣	NOUN
iajs-2883	111	8	10	10	NUM
iajs-2883	111	9	)	)	PUNCT
iajs-2883	111	10	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	NOUN
iajs-2883	111	11	(	(	PUNCT
iajs-2883	111	12	𝑣	𝑣	DET
iajs-2883	111	13	5	5	NUM
iajs-2883	111	14	)	)	PUNCT
iajs-2883	111	15	𝑣	𝑣	PRON
iajs-2883	111	16	−	−	PROPN
iajs-2883	111	17	cosh	cosh	NOUN
iajs-2883	111	18	(	(	PUNCT
iajs-2883	111	19	𝑣	𝑣	PART
iajs-2883	111	20	5	5	NUM
iajs-2883	111	21	)	)	PUNCT
iajs-2883	111	22	cosh(𝑣	cosh(𝑣	PROPN
iajs-2883	111	23	)	)	PUNCT
iajs-2883	112	1	+	+	CCONJ
iajs-2883	112	2	sinh(𝑣	sinh(𝑣	NOUN
iajs-2883	112	3	)	)	PUNCT
iajs-2883	112	4	sinh	sinh	NOUN
iajs-2883	112	5	(	(	PUNCT
iajs-2883	112	6	𝑣	𝑣	ADP
iajs-2883	112	7	5	5	NUM
iajs-2883	112	8	)	)	PUNCT
iajs-2883	113	1	+	+	CCONJ
iajs-2883	113	2	cosh	cosh	PROPN
iajs-2883	113	3	(	(	PUNCT
iajs-2883	113	4	𝑣	𝑣	ADP
iajs-2883	113	5	5	5	NUM
iajs-2883	113	6	)	)	PUNCT
iajs-2883	113	7	)	)	PUNCT
iajs-2883	114	1	𝑣	𝑣	X
iajs-2883	114	2	(	(	PUNCT
iajs-2883	114	3	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
iajs-2883	114	4	(	(	PUNCT
iajs-2883	114	5	4	4	NUM
iajs-2883	114	6	5	5	NUM
iajs-2883	114	7	𝑣	𝑣	NOUN
iajs-2883	114	8	)	)	PUNCT
iajs-2883	114	9	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	NOUN
iajs-2883	114	10	(	(	PUNCT
iajs-2883	114	11	𝑣	𝑣	PRON
iajs-2883	114	12	5	5	NUM
iajs-2883	114	13	)	)	PUNCT
iajs-2883	114	14	−	−	PROPN
iajs-2883	114	15	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
iajs-2883	114	16	(	(	PUNCT
iajs-2883	114	17	𝑣	𝑣	PART
iajs-2883	114	18	5	5	NUM
iajs-2883	114	19	)	)	PUNCT
iajs-2883	114	20	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	NOUN
iajs-2883	114	21	(	(	PUNCT
iajs-2883	114	22	4	4	NUM
iajs-2883	114	23	5	5	NUM
iajs-2883	114	24	𝑣	𝑣	NOUN
iajs-2883	114	25	)	)	PUNCT
iajs-2883	114	26	)	)	PUNCT
iajs-2883	114	27	𝑏2	𝑏2	PROPN
iajs-2883	114	28	′′	′′	PROPN
iajs-2883	114	29	=	=	PRON
iajs-2883	114	30	(	(	PUNCT
iajs-2883	114	31	1	1	NUM
iajs-2883	114	32	2	2	NUM
iajs-2883	114	33	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
iajs-2883	114	34	(	(	PUNCT
iajs-2883	114	35	4	4	NUM
iajs-2883	114	36	5	5	NUM
iajs-2883	114	37	𝑣	𝑣	NOUN
iajs-2883	114	38	)	)	PUNCT
iajs-2883	114	39	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	NOUN
iajs-2883	114	40	(	(	PUNCT
iajs-2883	114	41	7𝑣	7𝑣	PROPN
iajs-2883	114	42	10	10	NUM
iajs-2883	114	43	)	)	PUNCT
iajs-2883	115	1	𝑣	𝑣	DET
iajs-2883	115	2	−	−	PROPN
iajs-2883	115	3	1	1	NUM
iajs-2883	115	4	2	2	NUM
iajs-2883	115	5	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
iajs-2883	115	6	(	(	PUNCT
iajs-2883	115	7	7𝑣	7𝑣	NOUN
iajs-2883	115	8	10	10	NUM
iajs-2883	115	9	)	)	PUNCT
iajs-2883	115	10	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	NOUN
iajs-2883	115	11	(	(	PUNCT
iajs-2883	115	12	4	4	NUM
iajs-2883	115	13	5	5	NUM
iajs-2883	115	14	𝑣	𝑣	NOUN
iajs-2883	115	15	)	)	PUNCT
iajs-2883	115	16	𝑣	𝑣	ADP
iajs-2883	115	17	−	−	NOUN
iajs-2883	115	18	cosh(𝑣	cosh(𝑣	NOUN
iajs-2883	115	19	)	)	PUNCT
iajs-2883	115	20	cosh	cosh	NOUN
iajs-2883	115	21	(	(	PUNCT
iajs-2883	115	22	4	4	NUM
iajs-2883	115	23	5	5	NUM
iajs-2883	115	24	𝑣	𝑣	NOUN
iajs-2883	115	25	)	)	PUNCT
iajs-2883	115	26	+	+	CCONJ
iajs-2883	115	27	sinh	sinh	NOUN
iajs-2883	115	28	(	(	PUNCT
iajs-2883	115	29	4	4	NUM
iajs-2883	115	30	5	5	NUM
iajs-2883	115	31	𝑣	𝑣	NOUN
iajs-2883	115	32	)	)	PUNCT
iajs-2883	115	33	sinh(𝑣	sinh(𝑣	NOUN
iajs-2883	115	34	)	)	PUNCT
iajs-2883	115	35	+	+	CCONJ
iajs-2883	115	36	cosh	cosh	PROPN
iajs-2883	115	37	(	(	PUNCT
iajs-2883	115	38	4	4	NUM
iajs-2883	115	39	5	5	NUM
iajs-2883	115	40	𝑣	𝑣	NOUN
iajs-2883	115	41	)	)	PUNCT
iajs-2883	115	42	)	)	PUNCT
iajs-2883	116	1	𝑣	𝑣	ADP
iajs-2883	116	2	(	(	PUNCT
iajs-2883	116	3	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
iajs-2883	116	4	(	(	PUNCT
iajs-2883	116	5	4	4	NUM
iajs-2883	116	6	5	5	NUM
iajs-2883	116	7	𝑣	𝑣	NOUN
iajs-2883	116	8	)	)	PUNCT
iajs-2883	116	9	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	NOUN
iajs-2883	116	10	(	(	PUNCT
iajs-2883	116	11	𝑣	𝑣	PRON
iajs-2883	116	12	5	5	NUM
iajs-2883	116	13	)	)	PUNCT
iajs-2883	116	14	−	−	PROPN
iajs-2883	116	15	𝑐𝑜𝑠ℎ	𝑐𝑜𝑠ℎ	NOUN
iajs-2883	116	16	(	(	PUNCT
iajs-2883	116	17	𝑣	𝑣	PART
iajs-2883	116	18	5	5	NUM
iajs-2883	116	19	)	)	PUNCT
iajs-2883	116	20	𝑠𝑖𝑛ℎ	𝑠𝑖𝑛ℎ	NOUN
iajs-2883	116	21	(	(	PUNCT
iajs-2883	116	22	4	4	NUM
iajs-2883	116	23	5	5	NUM
iajs-2883	116	24	𝑣	𝑣	NOUN
iajs-2883	116	25	)	)	PUNCT
iajs-2883	116	26	)	)	PUNCT
iajs-2883	116	27	as	as	ADP
iajs-2883	116	28	a	a	DET
iajs-2883	116	29	result	result	NOUN
iajs-2883	116	30	,	,	PUNCT
iajs-2883	116	31	we	we	PRON
iajs-2883	116	32	developed	develop	VERB
iajs-2883	116	33	editrk4	editrk4	PROPN
iajs-2883	116	34	,	,	PUNCT
iajs-2883	116	35	a	a	DET
iajs-2883	116	36	3	3	NUM
iajs-2883	116	37	-	-	PUNCT
iajs-2883	116	38	stage	stage	NOUN
iajs-2883	116	39	4th	4th	ADJ
iajs-2883	116	40	-	-	PUNCT
iajs-2883	116	41	order	order	NOUN
iajs-2883	116	42	diagonally	diagonally	ADV
iajs-2883	116	43	implicit	implicit	ADJ
iajs-2883	116	44	exponentially	exponentially	ADV
iajs-2883	116	45	fitted	fit	VERB
iajs-2883	116	46	rk	rk	NOUN
iajs-2883	116	47	type	type	NOUN
iajs-2883	116	48	approach	approach	NOUN
iajs-2883	116	49	.	.	PUNCT
iajs-2883	117	1	the	the	DET
iajs-2883	117	2	solution	solution	NOUN
iajs-2883	117	3	's	's	PART
iajs-2883	117	4	matching	matching	PROPN
iajs-2883	117	5	taylor	taylor	PROPN
iajs-2883	117	6	series	series	PROPN
iajs-2883	117	7	expansion	expansion	NOUN
iajs-2883	117	8	is	be	AUX
iajs-2883	117	9	given	give	VERB
iajs-2883	117	10	by	by	ADP
iajs-2883	117	11	:	:	PUNCT
iajs-2883	117	12	𝑏1	𝑏1	ADJ
iajs-2883	117	13	=	=	SYM
iajs-2883	117	14	1	1	NUM
iajs-2883	117	15	180	180	NUM
iajs-2883	117	16	−	−	NOUN
iajs-2883	117	17	𝑣2	𝑣2	PROPN
iajs-2883	117	18	8000	8000	NUM
iajs-2883	117	19	+	+	CCONJ
iajs-2883	117	20	4057𝑣4	4057𝑣4	NOUN
iajs-2883	117	21	1008000000	1008000000	NUM
iajs-2883	117	22	−	−	NUM
iajs-2883	117	23	732037𝑣6	732037𝑣6	NOUN
iajs-2883	117	24	5443200000000	5443200000000	NUM
iajs-2883	117	25	+	+	CCONJ
iajs-2883	117	26	380948723𝑣8	380948723𝑣8	NUM
iajs-2883	117	27	79833600000000000	79833600000000000	NUM
iajs-2883	117	28	−	−	PROPN
iajs-2883	117	29	150590645851𝑣10	150590645851𝑣10	PROPN
iajs-2883	117	30	871782912000000000000	871782912000000000000	NUM
iajs-2883	117	31	𝑏2	𝑏2	NOUN
iajs-2883	117	32	=	=	NOUN
iajs-2883	118	1	34	34	NUM
iajs-2883	118	2	225	225	NUM
iajs-2883	119	1	+	+	CCONJ
iajs-2883	119	2	29𝑣2	29𝑣2	NUM
iajs-2883	119	3	24000	24000	NUM
iajs-2883	119	4	+	+	CCONJ
iajs-2883	119	5	5333𝑣4	5333𝑣4	NUM
iajs-2883	119	6	1008000000	1008000000	NUM
iajs-2883	119	7	−	−	NOUN
iajs-2883	119	8	658169𝑣6	658169𝑣6	NOUN
iajs-2883	119	9	5443200000000	5443200000000	NUM
iajs-2883	119	10	+	+	CCONJ
iajs-2883	120	1	41437183𝑣8	41437183𝑣8	NUM
iajs-2883	120	2	8870400000000000	8870400000000000	NUM
iajs-2883	120	3	−	−	PROPN
iajs-2883	120	4	149781459959𝑣10	149781459959𝑣10	NUM
iajs-2883	120	5	871782912000000000000	871782912000000000000	NUM
iajs-2883	120	6	𝑏1	𝑏1	NOUN
iajs-2883	120	7	′	′	NUM
iajs-2883	121	1	=	=	SYM
iajs-2883	121	2	1	1	NUM
iajs-2883	121	3	36	36	NUM
iajs-2883	121	4	−	−	NOUN
iajs-2883	121	5	𝑣2	𝑣2	PROPN
iajs-2883	121	6	1440	1440	NUM
iajs-2883	121	7	+	+	CCONJ
iajs-2883	121	8	1259𝑣4	1259𝑣4	NUM
iajs-2883	121	9	33600000	33600000	NUM
iajs-2883	121	10	−	−	NOUN
iajs-2883	121	11	108659𝑣6	108659𝑣6	NOUN
iajs-2883	121	12	77760000000	77760000000	NUM
iajs-2883	121	13	+	+	CCONJ
iajs-2883	121	14	1226395609𝑣8	1226395609𝑣8	NUM
iajs-2883	121	15	23950080000000000	23950080000000000	NUM
iajs-2883	121	16	−	−	PROPN
iajs-2883	122	1	90543546703𝑣10	90543546703𝑣10	NUM
iajs-2883	122	2	484323840000000000000	484323840000000000000	NUM
iajs-2883	122	3	𝑏2	𝑏2	NOUN
iajs-2883	122	4	′	′	NUM
iajs-2883	123	1	=	=	NOUN
iajs-2883	124	1	67	67	NUM
iajs-2883	124	2	180	180	NUM
iajs-2883	124	3	+	+	NUM
iajs-2883	124	4	11𝑣2	11𝑣2	NUM
iajs-2883	124	5	7200	7200	NUM
iajs-2883	124	6	+	+	CCONJ
iajs-2883	124	7	1471𝑣4	1471𝑣4	NUM
iajs-2883	124	8	33600000	33600000	NUM
iajs-2883	124	9	−	−	NOUN
iajs-2883	124	10	152837𝑣6	152837𝑣6	NOUN
iajs-2883	124	11	108864000000	108864000000	NUM
iajs-2883	124	12	+	+	CCONJ
iajs-2883	124	13	1228905701𝑣8	1228905701𝑣8	PROPN
iajs-2883	124	14	23950080000000000	23950080000000000	NUM
iajs-2883	124	15	−	−	PROPN
iajs-2883	124	16	10065377507𝑣10	10065377507𝑣10	NUM
iajs-2883	124	17	5381376000000000000	5381376000000000000	NUM
iajs-2883	124	18	ihjpas	ihjpa	NOUN
iajs-2883	124	19	.	.	PUNCT
iajs-2883	125	1	36(1)2023	36(1)2023	NUM
iajs-2883	125	2	395	395	NUM
iajs-2883	125	3	𝑏1	𝑏1	NOUN
iajs-2883	125	4	′′	′′	NOUN
iajs-2883	125	5	=	=	NOUN
iajs-2883	125	6	1	1	NUM
iajs-2883	125	7	12	12	NUM
iajs-2883	125	8	+	+	CCONJ
iajs-2883	125	9	43𝑣2	43𝑣2	NUM
iajs-2883	125	10	7200	7200	NUM
iajs-2883	125	11	−	−	PROPN
iajs-2883	125	12	169𝑣4	169𝑣4	NUM
iajs-2883	125	13	2880000	2880000	NUM
iajs-2883	125	14	+	+	CCONJ
iajs-2883	125	15	117487𝑣6	117487𝑣6	NUM
iajs-2883	125	16	60480000000	60480000000	NUM
iajs-2883	125	17	−	−	NOUN
iajs-2883	125	18	29389781𝑣8	29389781𝑣8	NUM
iajs-2883	125	19	435456000000000	435456000000000	NUM
iajs-2883	125	20	+	+	CCONJ
iajs-2883	125	21	1665975073𝑣10	1665975073𝑣10	NUM
iajs-2883	125	22	68428800000000000	68428800000000000	NUM
iajs-2883	125	23	−	−	PUNCT
iajs-2883	126	1	6617676448637𝑣12	6617676448637𝑣12	NOUN
iajs-2883	126	2	74724249600000000000000	74724249600000000000000	NUM
iajs-2883	126	3	𝑏2	𝑏2	NOUN
iajs-2883	126	4	′′	′′	PROPN
iajs-2883	126	5	=	=	NOUN
iajs-2883	126	6	5	5	NUM
iajs-2883	126	7	12	12	NUM
iajs-2883	126	8	+	+	CCONJ
iajs-2883	126	9	23𝑣2	23𝑣2	NUM
iajs-2883	126	10	7200	7200	NUM
iajs-2883	126	11	−	−	PROPN
iajs-2883	126	12	101𝑣4	101𝑣4	NUM
iajs-2883	126	13	2880000	2880000	NUM
iajs-2883	126	14	+	+	CCONJ
iajs-2883	126	15	104747𝑣6	104747𝑣6	NUM
iajs-2883	126	16	60480000000	60480000000	NUM
iajs-2883	126	17	−	−	NOUN
iajs-2883	127	1	28558129𝑣8	28558129𝑣8	PROPN
iajs-2883	127	2	435456000000000	435456000000000	NUM
iajs-2883	127	3	−	−	NOUN
iajs-2883	128	1	11578525811𝑣10	11578525811𝑣10	NOUN
iajs-2883	128	2	4790016000000000000	4790016000000000000	NUM
iajs-2883	129	1	+	+	CCONJ
iajs-2883	129	2	6605830989193𝑣12	6605830989193𝑣12	NUM
iajs-2883	129	3	74724249600000000000000	74724249600000000000000	NUM
iajs-2883	129	4	3.numerical	3.numerical	NUM
iajs-2883	129	5	experiments	experiment	NOUN
iajs-2883	129	6	problem	problem	VERB
iajs-2883	129	7	1	1	NUM
iajs-2883	129	8	:	:	PUNCT
iajs-2883	129	9	(	(	PUNCT
iajs-2883	129	10	non	non	ADJ
iajs-2883	129	11	-	-	ADJ
iajs-2883	129	12	homogeneous	homogeneous	ADJ
iajs-2883	129	13	linear	linear	NOUN
iajs-2883	129	14	problem	problem	NOUN
iajs-2883	129	15	)	)	PUNCT
iajs-2883	129	16	.	.	PUNCT
iajs-2883	130	1	𝑣′′′(𝑡	𝑣′′′(𝑡	NUM
iajs-2883	130	2	)	)	PUNCT
iajs-2883	130	3	=	=	PUNCT
iajs-2883	130	4	𝑣(𝑡	𝑣(𝑡	NOUN
iajs-2883	130	5	)	)	PUNCT
iajs-2883	131	1	+	+	PUNCT
iajs-2883	131	2	𝑐𝑜𝑠(𝑣	𝑐𝑜𝑠(𝑣	PROPN
iajs-2883	131	3	)	)	PUNCT
iajs-2883	131	4	,	,	PUNCT
iajs-2883	131	5	𝑣(0	𝑣(0	NUM
iajs-2883	131	6	)	)	PUNCT
iajs-2883	131	7	=	=	SYM
iajs-2883	132	1	0	0	NUM
iajs-2883	132	2	,	,	PUNCT
iajs-2883	132	3	𝑣	𝑣	X
iajs-2883	132	4	′(0	′(0	NOUN
iajs-2883	132	5	)	)	PUNCT
iajs-2883	132	6	=	=	SYM
iajs-2883	132	7	0	0	NUM
iajs-2883	132	8	,	,	PUNCT
iajs-2883	132	9	𝑣′′(0	𝑣′′(0	NOUN
iajs-2883	132	10	)	)	PUNCT
iajs-2883	132	11	=	=	SYM
iajs-2883	132	12	1	1	X
iajs-2883	132	13	.	.	PUNCT
iajs-2883	132	14	theoretical	theoretical	ADJ
iajs-2883	132	15	solution	solution	NOUN
iajs-2883	132	16	:	:	PUNCT
iajs-2883	132	17	𝑣(𝑡	𝑣(𝑡	NOUN
iajs-2883	132	18	)	)	PUNCT
iajs-2883	132	19	=	=	SYM
iajs-2883	132	20	(	(	PUNCT
iajs-2883	132	21	𝑒𝑡	𝑒𝑡	NOUN
iajs-2883	132	22	−	−	PROPN
iajs-2883	132	23	cos(𝑡	cos(𝑡	PROPN
iajs-2883	132	24	)	)	PUNCT
iajs-2883	132	25	−	−	PROPN
iajs-2883	132	26	sin(𝑡	sin(𝑡	PROPN
iajs-2883	132	27	)	)	PUNCT
iajs-2883	132	28	)	)	PUNCT
iajs-2883	132	29	.	.	PUNCT
iajs-2883	133	1	problem	problem	NOUN
iajs-2883	133	2	2	2	NUM
iajs-2883	133	3	:	:	PUNCT
iajs-2883	133	4	(	(	PUNCT
iajs-2883	133	5	non	non	ADJ
iajs-2883	133	6	-	-	ADJ
iajs-2883	133	7	homogeneous	homogeneous	ADJ
iajs-2883	133	8	nonlinear	nonlinear	ADJ
iajs-2883	133	9	problem	problem	NOUN
iajs-2883	133	10	)	)	PUNCT
iajs-2883	133	11	.	.	PUNCT
iajs-2883	134	1	𝑣′′′(𝑡	𝑣′′′(𝑡	NUM
iajs-2883	134	2	)	)	PUNCT
iajs-2883	134	3	=	=	SYM
iajs-2883	134	4	(	(	PUNCT
iajs-2883	134	5	𝑣(𝑡))2	𝑣(𝑡))2	X
iajs-2883	134	6	+	+	CCONJ
iajs-2883	134	7	𝑐𝑜𝑠2(𝑣	𝑐𝑜𝑠2(𝑣	NOUN
iajs-2883	134	8	)	)	PUNCT
iajs-2883	135	1	−	−	PROPN
iajs-2883	135	2	𝑐𝑜𝑠(𝑡	𝑐𝑜𝑠(𝑡	NOUN
iajs-2883	135	3	)	)	PUNCT
iajs-2883	135	4	−	−	NUM
iajs-2883	135	5	1	1	NUM
iajs-2883	135	6	,	,	PUNCT
iajs-2883	135	7	𝑣(0	𝑣(0	NUM
iajs-2883	135	8	)	)	PUNCT
iajs-2883	135	9	=	=	SYM
iajs-2883	135	10	0	0	NUM
iajs-2883	135	11	,	,	PUNCT
iajs-2883	135	12	𝑣′(0	𝑣′(0	ADJ
iajs-2883	135	13	)	)	PUNCT
iajs-2883	135	14	=	=	SYM
iajs-2883	135	15	1	1	NUM
iajs-2883	135	16	,	,	PUNCT
iajs-2883	135	17	𝑣′′(0	𝑣′′(0	NOUN
iajs-2883	135	18	)	)	PUNCT
iajs-2883	135	19	=	=	SYM
iajs-2883	135	20	1	1	X
iajs-2883	135	21	.	.	PUNCT
iajs-2883	135	22	theoretical	theoretical	ADJ
iajs-2883	135	23	solution	solution	NOUN
iajs-2883	135	24	:	:	PUNCT
iajs-2883	135	25	𝑣(𝑡	𝑣(𝑡	NOUN
iajs-2883	135	26	)	)	PUNCT
iajs-2883	135	27	=	=	PUNCT
iajs-2883	135	28	𝑠𝑖𝑛(𝑡	𝑠𝑖𝑛(𝑡	PROPN
iajs-2883	135	29	)	)	PUNCT
iajs-2883	135	30	.	.	PUNCT
iajs-2883	136	1	problem	problem	NOUN
iajs-2883	136	2	3	3	NUM
iajs-2883	136	3	:	:	PUNCT
iajs-2883	136	4	(	(	PUNCT
iajs-2883	136	5	non	non	ADJ
iajs-2883	136	6	-	-	ADJ
iajs-2883	136	7	homogeneous	homogeneous	ADJ
iajs-2883	136	8	nonlinear	nonlinear	ADJ
iajs-2883	136	9	problem	problem	NOUN
iajs-2883	136	10	)	)	PUNCT
iajs-2883	136	11	.	.	PUNCT
iajs-2883	137	1	𝑣′′′(t	𝑣′′′(t	VERB
iajs-2883	137	2	)	)	PUNCT
iajs-2883	137	3	=	=	SYM
iajs-2883	137	4	8	8	NUM
iajs-2883	137	5	(	(	PUNCT
iajs-2883	137	6	𝑣2(𝑡	𝑣2(𝑡	PROPN
iajs-2883	137	7	)	)	PUNCT
iajs-2883	137	8	𝑒2𝑡	𝑒2𝑡	NOUN
iajs-2883	137	9	)	)	PUNCT
iajs-2883	137	10	,	,	PUNCT
iajs-2883	137	11	𝑣(0	𝑣(0	NUM
iajs-2883	137	12	)	)	PUNCT
iajs-2883	137	13	=	=	SYM
iajs-2883	137	14	1	1	NUM
iajs-2883	137	15	,	,	PUNCT
iajs-2883	137	16	𝑣′(0	𝑣′(0	PROPN
iajs-2883	137	17	)	)	PUNCT
iajs-2883	137	18	=	=	SYM
iajs-2883	137	19	2	2	NUM
iajs-2883	137	20	,	,	PUNCT
iajs-2883	137	21	𝑣′′(0	𝑣′′(0	NOUN
iajs-2883	137	22	)	)	PUNCT
iajs-2883	137	23	=	=	SYM
iajs-2883	138	1	4	4	X
iajs-2883	138	2	.	.	PUNCT
iajs-2883	139	1	theoretical	theoretical	ADJ
iajs-2883	139	2	solution	solution	NOUN
iajs-2883	139	3	:	:	PUNCT
iajs-2883	139	4	𝑣(𝑡	𝑣(𝑡	NOUN
iajs-2883	139	5	)	)	PUNCT
iajs-2883	139	6	=	=	PUNCT
iajs-2883	139	7	𝑒2𝑡.	𝑒2𝑡.	NOUN
iajs-2883	139	8	problem	problem	NOUN
iajs-2883	139	9	4	4	NUM
iajs-2883	139	10	:	:	PUNCT
iajs-2883	139	11	(	(	PUNCT
iajs-2883	139	12	non	non	ADJ
iajs-2883	139	13	-	-	ADJ
iajs-2883	139	14	linear	linear	ADJ
iajs-2883	139	15	system	system	NOUN
iajs-2883	139	16	)	)	PUNCT
iajs-2883	139	17	.	.	PUNCT
iajs-2883	140	1	𝑦1	𝑦1	PROPN
iajs-2883	140	2	′′′(t	′′′(t	PROPN
iajs-2883	140	3	)	)	PUNCT
iajs-2883	140	4	=	=	SYM
iajs-2883	140	5	𝑦2(t	𝑦2(t	NUM
iajs-2883	140	6	)	)	PUNCT
iajs-2883	140	7	,	,	PUNCT
iajs-2883	140	8	𝑦1(0	𝑦1(0	PROPN
iajs-2883	140	9	)	)	PUNCT
iajs-2883	140	10	=	=	SYM
iajs-2883	140	11	1	1	NUM
iajs-2883	140	12	,	,	PUNCT
iajs-2883	140	13	𝑦1	𝑦1	NOUN
iajs-2883	140	14	′	′	NUM
iajs-2883	140	15	(	(	PUNCT
iajs-2883	140	16	0	0	NUM
iajs-2883	140	17	)	)	PUNCT
iajs-2883	140	18	=	=	SYM
iajs-2883	140	19	0	0	NUM
iajs-2883	140	20	,	,	PUNCT
iajs-2883	140	21	𝑦1	𝑦1	NOUN
iajs-2883	140	22	′′(0	′′(0	NOUN
iajs-2883	140	23	)	)	PUNCT
iajs-2883	140	24	=	=	SYM
iajs-2883	140	25	1	1	NUM
iajs-2883	140	26	,	,	PUNCT
iajs-2883	140	27	𝑦2	𝑦2	PROPN
iajs-2883	140	28	′′′(t	′′′(t	PROPN
iajs-2883	140	29	)	)	PUNCT
iajs-2883	140	30	=	=	SYM
iajs-2883	140	31	−𝑦1(𝑡	−𝑦1(𝑡	NOUN
iajs-2883	140	32	)	)	PUNCT
iajs-2883	140	33	−	−	PROPN
iajs-2883	140	34	2𝑦2(𝑡	2𝑦2(𝑡	NUM
iajs-2883	140	35	)	)	PUNCT
iajs-2883	140	36	+	+	NUM
iajs-2883	140	37	2𝑦3(𝑡	2𝑦3(𝑡	NUM
iajs-2883	140	38	)	)	PUNCT
iajs-2883	140	39	,	,	PUNCT
iajs-2883	140	40	𝑦2(0	𝑦2(0	PROPN
iajs-2883	140	41	)	)	PUNCT
iajs-2883	140	42	=	=	SYM
iajs-2883	140	43	0	0	NUM
iajs-2883	140	44	,	,	PUNCT
iajs-2883	141	1	𝑦2	𝑦2	PROPN
iajs-2883	141	2	′	′	NUM
iajs-2883	141	3	(	(	PUNCT
iajs-2883	141	4	0	0	NUM
iajs-2883	141	5	)	)	PUNCT
iajs-2883	141	6	=	=	SYM
iajs-2883	141	7	1	1	NUM
iajs-2883	141	8	,	,	PUNCT
iajs-2883	141	9	𝑦2	𝑦2	NOUN
iajs-2883	141	10	′′(0	′′(0	NOUN
iajs-2883	141	11	)	)	PUNCT
iajs-2883	141	12	=	=	SYM
iajs-2883	141	13	0	0	NUM
iajs-2883	141	14	,	,	PUNCT
iajs-2883	141	15	𝑦3	𝑦3	PROPN
iajs-2883	141	16	′′′(t	′′′(t	PROPN
iajs-2883	141	17	)	)	PUNCT
iajs-2883	141	18	=	=	SYM
iajs-2883	141	19	𝑦1(𝑡	𝑦1(𝑡	PROPN
iajs-2883	141	20	)	)	PUNCT
iajs-2883	141	21	+	+	NUM
iajs-2883	141	22	𝑦2(𝑡	𝑦2(𝑡	NOUN
iajs-2883	141	23	)	)	PUNCT
iajs-2883	141	24	𝑦3(0	𝑦3(0	PROPN
iajs-2883	141	25	)	)	PUNCT
iajs-2883	141	26	=	=	SYM
iajs-2883	141	27	1	1	NUM
iajs-2883	141	28	,	,	PUNCT
iajs-2883	141	29	𝑦3	𝑦3	PROPN
iajs-2883	141	30	′	′	PROPN
iajs-2883	142	1	(	(	PUNCT
iajs-2883	142	2	0	0	NUM
iajs-2883	142	3	)	)	PUNCT
iajs-2883	142	4	=	=	SYM
iajs-2883	142	5	1	1	NUM
iajs-2883	142	6	,	,	PUNCT
iajs-2883	142	7	𝑦3	𝑦3	PROPN
iajs-2883	142	8	′′(0	′′(0	PRON
iajs-2883	142	9	)	)	PUNCT
iajs-2883	142	10	=	=	SYM
iajs-2883	143	1	1	1	X
iajs-2883	143	2	.	.	PUNCT
iajs-2883	144	1	the	the	DET
iajs-2883	144	2	precise	precise	ADJ
iajs-2883	144	3	solution	solution	NOUN
iajs-2883	144	4	is	be	AUX
iajs-2883	144	5	provided	provide	VERB
iajs-2883	144	6	by	by	ADP
iajs-2883	144	7	𝑦1(𝑡	𝑦1(𝑡	NOUN
iajs-2883	144	8	)	)	PUNCT
iajs-2883	144	9	=	=	SYM
iajs-2883	144	10	𝑐𝑜𝑠ℎ(𝑡	𝑐𝑜𝑠ℎ(𝑡	NOUN
iajs-2883	144	11	)	)	PUNCT
iajs-2883	144	12	,	,	PUNCT
iajs-2883	144	13	𝑦2(𝑡	𝑦2(𝑡	NOUN
iajs-2883	144	14	)	)	PUNCT
iajs-2883	144	15	=	=	SYM
iajs-2883	144	16	𝑠𝑖𝑛ℎ(𝑡	𝑠𝑖𝑛ℎ(𝑡	NUM
iajs-2883	144	17	)	)	PUNCT
iajs-2883	144	18	,	,	PUNCT
iajs-2883	144	19	ihjpas	ihjpa	VERB
iajs-2883	144	20	.	.	PUNCT
iajs-2883	145	1	36(1)2023	36(1)2023	NUM
iajs-2883	145	2	396	396	NUM
iajs-2883	145	3	𝑦3(𝑡	𝑦3(𝑡	PROPN
iajs-2883	145	4	)	)	PUNCT
iajs-2883	145	5	=	=	SYM
iajs-2883	145	6	𝑒𝑡	𝑒𝑡	NOUN
iajs-2883	145	7	.	.	PUNCT
iajs-2883	146	1	problem	problem	NOUN
iajs-2883	146	2	5	5	NUM
iajs-2883	146	3	:	:	PUNCT
iajs-2883	146	4	(	(	PUNCT
iajs-2883	146	5	non	non	ADJ
iajs-2883	146	6	-	-	ADJ
iajs-2883	146	7	linear	linear	ADJ
iajs-2883	146	8	system	system	NOUN
iajs-2883	146	9	)	)	PUNCT
iajs-2883	146	10	.	.	PUNCT
iajs-2883	147	1	𝑦1	𝑦1	PROPN
iajs-2883	147	2	′′′(t	′′′(t	PROPN
iajs-2883	147	3	)	)	PUNCT
iajs-2883	147	4	=	=	SYM
iajs-2883	147	5	𝑦2(t	𝑦2(t	NUM
iajs-2883	147	6	)	)	PUNCT
iajs-2883	147	7	,	,	PUNCT
iajs-2883	147	8	𝑦1(0	𝑦1(0	PROPN
iajs-2883	147	9	)	)	PUNCT
iajs-2883	147	10	=	=	SYM
iajs-2883	147	11	1	1	NUM
iajs-2883	147	12	,	,	PUNCT
iajs-2883	147	13	𝑦1	𝑦1	NOUN
iajs-2883	147	14	′	′	NUM
iajs-2883	147	15	(	(	PUNCT
iajs-2883	147	16	0	0	NUM
iajs-2883	147	17	)	)	PUNCT
iajs-2883	147	18	=	=	SYM
iajs-2883	147	19	0	0	NUM
iajs-2883	147	20	,	,	PUNCT
iajs-2883	147	21	𝑦1	𝑦1	NOUN
iajs-2883	147	22	′′(0	′′(0	NOUN
iajs-2883	147	23	)	)	PUNCT
iajs-2883	147	24	=	=	SYM
iajs-2883	147	25	1	1	NUM
iajs-2883	147	26	,	,	PUNCT
iajs-2883	147	27	𝑦2	𝑦2	PROPN
iajs-2883	147	28	′′′(t	′′′(t	PROPN
iajs-2883	147	29	)	)	PUNCT
iajs-2883	147	30	=	=	SYM
iajs-2883	147	31	𝑦1(t	𝑦1(t	PROPN
iajs-2883	147	32	)	)	PUNCT
iajs-2883	147	33	,	,	PUNCT
iajs-2883	147	34	𝑦2(0	𝑦2(0	PROPN
iajs-2883	147	35	)	)	PUNCT
iajs-2883	147	36	=	=	SYM
iajs-2883	147	37	0	0	NUM
iajs-2883	147	38	,	,	PUNCT
iajs-2883	147	39	𝑦2	𝑦2	PROPN
iajs-2883	147	40	′	′	NUM
iajs-2883	147	41	(	(	PUNCT
iajs-2883	147	42	0	0	NUM
iajs-2883	147	43	)	)	PUNCT
iajs-2883	147	44	=	=	SYM
iajs-2883	147	45	1	1	NUM
iajs-2883	147	46	,	,	PUNCT
iajs-2883	147	47	𝑦2	𝑦2	NOUN
iajs-2883	147	48	′′(0	′′(0	NOUN
iajs-2883	147	49	)	)	PUNCT
iajs-2883	147	50	=	=	SYM
iajs-2883	147	51	0	0	NUM
iajs-2883	147	52	,	,	PUNCT
iajs-2883	147	53	𝑦3	𝑦3	PROPN
iajs-2883	148	1	′′′(t	′′′(t	PROPN
iajs-2883	148	2	)	)	PUNCT
iajs-2883	148	3	=	=	SYM
iajs-2883	148	4	𝑦1(𝑡	𝑦1(𝑡	PROPN
iajs-2883	148	5	)	)	PUNCT
iajs-2883	148	6	+	+	NUM
iajs-2883	148	7	𝑦2(𝑡	𝑦2(𝑡	NUM
iajs-2883	148	8	)	)	PUNCT
iajs-2883	148	9	−	−	ADP
iajs-2883	148	10	sinh(𝑡	sinh(𝑡	NOUN
iajs-2883	148	11	)	)	PUNCT
iajs-2883	148	12	𝑦3(0	𝑦3(0	PROPN
iajs-2883	148	13	)	)	PUNCT
iajs-2883	148	14	=	=	SYM
iajs-2883	148	15	1	1	NUM
iajs-2883	148	16	,	,	PUNCT
iajs-2883	148	17	𝑦3	𝑦3	PROPN
iajs-2883	148	18	′	′	PROPN
iajs-2883	148	19	(	(	PUNCT
iajs-2883	148	20	0	0	NUM
iajs-2883	148	21	)	)	PUNCT
iajs-2883	148	22	=	=	SYM
iajs-2883	148	23	0	0	NUM
iajs-2883	148	24	,	,	PUNCT
iajs-2883	148	25	𝑦3	𝑦3	PROPN
iajs-2883	148	26	′′(0	′′(0	PRON
iajs-2883	148	27	)	)	PUNCT
iajs-2883	148	28	=	=	SYM
iajs-2883	149	1	1	1	X
iajs-2883	149	2	.	.	PUNCT
iajs-2883	150	1	the	the	DET
iajs-2883	150	2	precise	precise	ADJ
iajs-2883	150	3	solution	solution	NOUN
iajs-2883	150	4	is	be	AUX
iajs-2883	150	5	provided	provide	VERB
iajs-2883	150	6	by	by	ADP
iajs-2883	150	7	𝑦1(𝑡	𝑦1(𝑡	NOUN
iajs-2883	150	8	)	)	PUNCT
iajs-2883	150	9	=	=	PUNCT
iajs-2883	150	10	cosh(𝑡	cosh(𝑡	NOUN
iajs-2883	150	11	)	)	PUNCT
iajs-2883	150	12	,	,	PUNCT
iajs-2883	150	13	𝑦2(𝑡	𝑦2(𝑡	NUM
iajs-2883	150	14	)	)	PUNCT
iajs-2883	150	15	=	=	SYM
iajs-2883	150	16	sinh(𝑡	sinh(𝑡	NOUN
iajs-2883	150	17	)	)	PUNCT
iajs-2883	150	18	,	,	PUNCT
iajs-2883	150	19	𝑦3(𝑡	𝑦3(𝑡	PROPN
iajs-2883	150	20	)	)	PUNCT
iajs-2883	150	21	=	=	SYM
iajs-2883	150	22	𝑒𝑡	𝑒𝑡	NOUN
iajs-2883	150	23	+	+	CCONJ
iajs-2883	150	24	1	1	NUM
iajs-2883	150	25	−	−	NOUN
iajs-2883	150	26	cosh(𝑡	cosh(𝑡	NOUN
iajs-2883	150	27	)	)	PUNCT
iajs-2883	151	1	+	+	CCONJ
iajs-2883	151	2	𝑡2	𝑡2	ADJ
iajs-2883	151	3	2	2	NUM
iajs-2883	151	4	−	−	NOUN
iajs-2883	151	5	𝑡.	𝑡.	NOUN
iajs-2883	151	6	figures	figure	VERB
iajs-2883	151	7	1–5	1–5	PRON
iajs-2883	151	8	show	show	VERB
iajs-2883	151	9	the	the	DET
iajs-2883	151	10	decimal	decimal	ADJ
iajs-2883	151	11	logarithm	logarithm	NOUN
iajs-2883	151	12	of	of	ADP
iajs-2883	151	13	the	the	DET
iajs-2883	151	14	largest	large	ADJ
iajs-2883	151	15	global	global	ADJ
iajs-2883	151	16	error	error	NOUN
iajs-2883	151	17	and	and	CCONJ
iajs-2883	151	18	the	the	DET
iajs-2883	151	19	logarithm	logarithm	NOUN
iajs-2883	151	20	function	function	NOUN
iajs-2883	151	21	valuations	valuation	NOUN
iajs-2883	151	22	,	,	PUNCT
iajs-2883	151	23	which	which	PRON
iajs-2883	151	24	illustrate	illustrate	VERB
iajs-2883	151	25	how	how	SCONJ
iajs-2883	151	26	effective	effective	ADJ
iajs-2883	151	27	the	the	DET
iajs-2883	151	28	editrk4	editrk4	PROPN
iajs-2883	151	29	techniques	technique	NOUN
iajs-2883	151	30	.	.	PUNCT
iajs-2883	152	1	the	the	DET
iajs-2883	152	2	editrk4	editrk4	PROPN
iajs-2883	152	3	approach	approach	NOUN
iajs-2883	152	4	requires	require	VERB
iajs-2883	152	5	fewer	few	ADJ
iajs-2883	152	6	function	function	NOUN
iajs-2883	152	7	evaluations	evaluation	NOUN
iajs-2883	152	8	than	than	ADP
iajs-2883	152	9	other	other	ADJ
iajs-2883	152	10	implicit	implicit	ADJ
iajs-2883	152	11	rk	rk	NOUN
iajs-2883	152	12	approaches	approach	NOUN
iajs-2883	152	13	of	of	ADP
iajs-2883	152	14	the	the	DET
iajs-2883	152	15	same	same	ADJ
iajs-2883	152	16	order	order	NOUN
iajs-2883	152	17	.	.	PUNCT
iajs-2883	153	1	this	this	PRON
iajs-2883	153	2	is	be	AUX
iajs-2883	153	3	because	because	SCONJ
iajs-2883	153	4	the	the	DET
iajs-2883	153	5	number	number	NOUN
iajs-2883	153	6	of	of	ADP
iajs-2883	153	7	equations	equation	NOUN
iajs-2883	153	8	tripled	triple	VERB
iajs-2883	153	9	when	when	SCONJ
iajs-2883	153	10	the	the	DET
iajs-2883	153	11	problems	problem	NOUN
iajs-2883	153	12	were	be	AUX
iajs-2883	153	13	converted	convert	VERB
iajs-2883	153	14	into	into	ADP
iajs-2883	153	15	a	a	DET
iajs-2883	153	16	system	system	NOUN
iajs-2883	153	17	of	of	ADP
iajs-2883	153	18	1𝑠𝑡order	1𝑠𝑡order	NUM
iajs-2883	153	19	odes	ode	NOUN
iajs-2883	153	20	.	.	PUNCT
iajs-2883	154	1	furthermore	furthermore	ADV
iajs-2883	154	2	,	,	PUNCT
iajs-2883	154	3	as	as	SCONJ
iajs-2883	154	4	shown	show	VERB
iajs-2883	154	5	in	in	ADP
iajs-2883	154	6	figures	figure	NOUN
iajs-2883	154	7	1–5	1–5	NUM
iajs-2883	154	8	,	,	PUNCT
iajs-2883	154	9	the	the	DET
iajs-2883	154	10	editrk4	editrk4	PROPN
iajs-2883	154	11	approaches	approach	NOUN
iajs-2883	154	12	have	have	VERB
iajs-2883	154	13	the	the	DET
iajs-2883	154	14	smallest	small	ADJ
iajs-2883	154	15	maximum	maximum	ADJ
iajs-2883	154	16	global	global	ADJ
iajs-2883	154	17	error	error	NOUN
iajs-2883	154	18	and	and	CCONJ
iajs-2883	154	19	the	the	DET
iajs-2883	154	20	fewest	few	ADJ
iajs-2883	154	21	number	number	NOUN
iajs-2883	154	22	of	of	ADP
iajs-2883	154	23	function	function	NOUN
iajs-2883	154	24	evaluations	evaluation	NOUN
iajs-2883	154	25	for	for	ADP
iajs-2883	154	26	each	each	DET
iajs-2883	154	27	step	step	NOUN
iajs-2883	154	28	.	.	PUNCT
iajs-2883	155	1	the	the	DET
iajs-2883	155	2	editrk4	editrk4	PROPN
iajs-2883	155	3	produces	produce	VERB
iajs-2883	155	4	more	more	ADV
iajs-2883	155	5	accurate	accurate	ADJ
iajs-2883	155	6	findings	finding	NOUN
iajs-2883	155	7	than	than	ADP
iajs-2883	155	8	the	the	DET
iajs-2883	155	9	other	other	ADJ
iajs-2883	155	10	results	result	NOUN
iajs-2883	155	11	in	in	ADP
iajs-2883	155	12	the	the	DET
iajs-2883	155	13	literature	literature	NOUN
iajs-2883	155	14	,	,	PUNCT
iajs-2883	155	15	as	as	SCONJ
iajs-2883	155	16	seen	see	VERB
iajs-2883	155	17	in	in	ADP
iajs-2883	155	18	figures	figure	NOUN
iajs-2883	155	19	1	1	NUM
iajs-2883	155	20	-	-	SYM
iajs-2883	155	21	5	5	NUM
iajs-2883	155	22	(	(	PUNCT
iajs-2883	155	23	ditrkm4	ditrkm4	ADJ
iajs-2883	155	24	,	,	PUNCT
iajs-2883	155	25	rkliiib4	rkliiib4	NOUN
iajs-2883	155	26	,	,	PUNCT
iajs-2883	155	27	and	and	CCONJ
iajs-2883	155	28	dirkn4	dirkn4	PROPN
iajs-2883	155	29	)	)	PUNCT
iajs-2883	155	30	.	.	PUNCT
iajs-2883	156	1	the	the	DET
iajs-2883	156	2	logarithm	logarithm	NOUN
iajs-2883	156	3	of	of	ADP
iajs-2883	156	4	function	function	NOUN
iajs-2883	156	5	evaluations	evaluation	NOUN
iajs-2883	156	6	with	with	ADP
iajs-2883	156	7	different	different	ADJ
iajs-2883	156	8	step	step	NOUN
iajs-2883	156	9	sizes	size	NOUN
iajs-2883	156	10	ℎ	ℎ	PROPN
iajs-2883	156	11	=	=	SYM
iajs-2883	156	12	0.1	0.1	NUM
iajs-2883	156	13	,	,	PUNCT
iajs-2883	156	14	0.05	0.05	NUM
iajs-2883	156	15	,	,	PUNCT
iajs-2883	156	16	0.025	0.025	NUM
iajs-2883	156	17	,	,	PUNCT
iajs-2883	156	18	0.00125	0.00125	NUM
iajs-2883	156	19	,	,	PUNCT
iajs-2883	156	20	and	and	CCONJ
iajs-2883	156	21	0.00625	0.00625	NUM
iajs-2883	156	22	in	in	ADP
iajs-2883	156	23	this	this	DET
iajs-2883	156	24	study	study	NOUN
iajs-2883	156	25	is	be	AUX
iajs-2883	156	26	a	a	DET
iajs-2883	156	27	function	function	NOUN
iajs-2883	156	28	of	of	ADP
iajs-2883	156	29	the	the	DET
iajs-2883	156	30	decimal	decimal	ADJ
iajs-2883	156	31	logarithm	logarithm	NOUN
iajs-2883	156	32	of	of	ADP
iajs-2883	156	33	the	the	DET
iajs-2883	156	34	greatest	great	ADJ
iajs-2883	156	35	global	global	ADJ
iajs-2883	156	36	fault	fault	NOUN
iajs-2883	156	37	for	for	ADP
iajs-2883	156	38	5	5	NUM
iajs-2883	156	39	test	test	NOUN
iajs-2883	156	40	problems	problem	NOUN
iajs-2883	156	41	.	.	PUNCT
iajs-2883	157	1	figure	figure	VERB
iajs-2883	157	2	1	1	NUM
iajs-2883	157	3	.	.	PUNCT
iajs-2883	157	4	accuracy	accuracy	NOUN
iajs-2883	157	5	curve	curve	NOUN
iajs-2883	157	6	for	for	ADP
iajs-2883	157	7	editrk4	editrk4	PROPN
iajs-2883	157	8	,	,	PUNCT
iajs-2883	157	9	ditrkm4	ditrkm4	PROPN
iajs-2883	157	10	,	,	PUNCT
iajs-2883	157	11	rkliiib4	rkliiib4	NOUN
iajs-2883	157	12	,	,	PUNCT
iajs-2883	157	13	and	and	CCONJ
iajs-2883	157	14	dirkn4	dirkn4	X
iajs-2883	157	15	with	with	ADP
iajs-2883	157	16	ℎ	ℎ	PROPN
iajs-2883	157	17	=	=	SYM
iajs-2883	157	18	0.1	0.1	NUM
iajs-2883	157	19	,	,	PUNCT
iajs-2883	157	20	0.05	0.05	NUM
iajs-2883	157	21	0.025	0.025	NUM
iajs-2883	157	22	,	,	PUNCT
iajs-2883	157	23	0.00125	0.00125	NUM
iajs-2883	157	24	,	,	PUNCT
iajs-2883	157	25	and	and	CCONJ
iajs-2883	157	26	0.00625	0.00625	NUM
iajs-2883	157	27	for	for	ADP
iajs-2883	157	28	the	the	DET
iajs-2883	157	29	problem	problem	NOUN
iajs-2883	157	30	1	1	NUM
iajs-2883	157	31	.	.	PUNCT
iajs-2883	157	32	ihjpas	ihjpas	PROPN
iajs-2883	157	33	.	.	PUNCT
iajs-2883	158	1	36(1)2023	36(1)2023	NUM
iajs-2883	158	2	397	397	NUM
iajs-2883	158	3	figure	figure	NOUN
iajs-2883	158	4	2	2	NUM
iajs-2883	158	5	.	.	PUNCT
iajs-2883	158	6	accuracy	accuracy	NOUN
iajs-2883	158	7	curve	curve	NOUN
iajs-2883	158	8	for	for	ADP
iajs-2883	158	9	editrk4	editrk4	PROPN
iajs-2883	158	10	,	,	PUNCT
iajs-2883	158	11	ditrkm4	ditrkm4	PROPN
iajs-2883	158	12	,	,	PUNCT
iajs-2883	158	13	rkliiib4	rkliiib4	NOUN
iajs-2883	158	14	,	,	PUNCT
iajs-2883	158	15	and	and	CCONJ
iajs-2883	158	16	dirkn4	dirkn4	X
iajs-2883	158	17	with	with	ADP
iajs-2883	158	18	ℎ	ℎ	PROPN
iajs-2883	158	19	=	=	SYM
iajs-2883	158	20	0.1	0.1	NUM
iajs-2883	158	21	,	,	PUNCT
iajs-2883	158	22	0.05	0.05	NUM
iajs-2883	158	23	0.025	0.025	NUM
iajs-2883	158	24	,	,	PUNCT
iajs-2883	158	25	0.00125	0.00125	NUM
iajs-2883	158	26	,	,	PUNCT
iajs-2883	158	27	and	and	CCONJ
iajs-2883	158	28	0.00625	0.00625	NUM
iajs-2883	158	29	for	for	ADP
iajs-2883	158	30	the	the	DET
iajs-2883	158	31	problem	problem	NOUN
iajs-2883	158	32	2	2	X
iajs-2883	158	33	.	.	X
iajs-2883	158	34	figure	figure	NOUN
iajs-2883	158	35	3	3	NUM
iajs-2883	158	36	.	.	PUNCT
iajs-2883	158	37	accuracy	accuracy	NOUN
iajs-2883	158	38	curve	curve	NOUN
iajs-2883	158	39	for	for	ADP
iajs-2883	158	40	editrk4	editrk4	PROPN
iajs-2883	158	41	,	,	PUNCT
iajs-2883	158	42	ditrkm4	ditrkm4	PROPN
iajs-2883	158	43	,	,	PUNCT
iajs-2883	158	44	rkliiib4	rkliiib4	NOUN
iajs-2883	158	45	,	,	PUNCT
iajs-2883	158	46	and	and	CCONJ
iajs-2883	158	47	dirkn4	dirkn4	X
iajs-2883	158	48	with	with	ADP
iajs-2883	158	49	ℎ	ℎ	PROPN
iajs-2883	158	50	=	=	SYM
iajs-2883	158	51	0.1	0.1	NUM
iajs-2883	158	52	,	,	PUNCT
iajs-2883	158	53	0.05	0.05	NUM
iajs-2883	158	54	0.025	0.025	NUM
iajs-2883	158	55	,	,	PUNCT
iajs-2883	158	56	0.00125	0.00125	NUM
iajs-2883	158	57	,	,	PUNCT
iajs-2883	158	58	and	and	CCONJ
iajs-2883	158	59	0.00625	0.00625	NUM
iajs-2883	158	60	for	for	ADP
iajs-2883	158	61	the	the	DET
iajs-2883	158	62	problem	problem	NOUN
iajs-2883	159	1	3	3	X
iajs-2883	159	2	.	.	X
iajs-2883	159	3	figure	figure	NOUN
iajs-2883	159	4	4	4	NUM
iajs-2883	159	5	.	.	PUNCT
iajs-2883	159	6	accuracy	accuracy	NOUN
iajs-2883	159	7	curve	curve	NOUN
iajs-2883	159	8	for	for	ADP
iajs-2883	159	9	editrk4	editrk4	PROPN
iajs-2883	159	10	,	,	PUNCT
iajs-2883	159	11	ditrkm4	ditrkm4	PROPN
iajs-2883	159	12	,	,	PUNCT
iajs-2883	159	13	rkliiib4	rkliiib4	NOUN
iajs-2883	159	14	,	,	PUNCT
iajs-2883	159	15	and	and	CCONJ
iajs-2883	159	16	dirkn4	dirkn4	X
iajs-2883	159	17	with	with	ADP
iajs-2883	159	18	ℎ	ℎ	PROPN
iajs-2883	159	19	=	=	SYM
iajs-2883	159	20	0.1	0.1	NUM
iajs-2883	159	21	,	,	PUNCT
iajs-2883	159	22	0.05	0.05	NUM
iajs-2883	159	23	0.025	0.025	NUM
iajs-2883	159	24	,	,	PUNCT
iajs-2883	159	25	0.00125	0.00125	NUM
iajs-2883	159	26	,	,	PUNCT
iajs-2883	159	27	and	and	CCONJ
iajs-2883	159	28	0.00625	0.00625	NUM
iajs-2883	159	29	for	for	ADP
iajs-2883	159	30	the	the	DET
iajs-2883	159	31	problem	problem	NOUN
iajs-2883	159	32	4	4	NUM
iajs-2883	159	33	.	.	PUNCT
iajs-2883	159	34	ihjpas	ihjpas	PROPN
iajs-2883	159	35	.	.	PUNCT
iajs-2883	160	1	36(1)2023	36(1)2023	NUM
iajs-2883	160	2	398	398	NUM
iajs-2883	160	3	figure	figure	NOUN
iajs-2883	160	4	5	5	NUM
iajs-2883	160	5	.	.	PUNCT
iajs-2883	160	6	accuracy	accuracy	NOUN
iajs-2883	160	7	curve	curve	NOUN
iajs-2883	160	8	for	for	ADP
iajs-2883	160	9	editrk4	editrk4	PROPN
iajs-2883	160	10	,	,	PUNCT
iajs-2883	160	11	ditrkm4	ditrkm4	PROPN
iajs-2883	160	12	,	,	PUNCT
iajs-2883	160	13	rkliiib4	rkliiib4	NOUN
iajs-2883	160	14	,	,	PUNCT
iajs-2883	160	15	and	and	CCONJ
iajs-2883	160	16	dirkn4	dirkn4	X
iajs-2883	160	17	with	with	ADP
iajs-2883	160	18	ℎ	ℎ	PROPN
iajs-2883	160	19	=	=	SYM
iajs-2883	160	20	0.1	0.1	NUM
iajs-2883	160	21	,	,	PUNCT
iajs-2883	160	22	0.05	0.05	NUM
iajs-2883	160	23	0.025	0.025	NUM
iajs-2883	160	24	,	,	PUNCT
iajs-2883	160	25	0.00125	0.00125	NUM
iajs-2883	160	26	,	,	PUNCT
iajs-2883	160	27	and	and	CCONJ
iajs-2883	160	28	0.00625	0.00625	NUM
iajs-2883	160	29	for	for	ADP
iajs-2883	160	30	the	the	DET
iajs-2883	160	31	problem	problem	NOUN
iajs-2883	160	32	5	5	NUM
iajs-2883	160	33	.	.	PUNCT
iajs-2883	161	1	4.conclusion	4.conclusion	NUM
iajs-2883	161	2	in	in	ADP
iajs-2883	161	3	this	this	DET
iajs-2883	161	4	paper	paper	NOUN
iajs-2883	161	5	,	,	PUNCT
iajs-2883	161	6	we	we	PRON
iajs-2883	161	7	devise	devise	VERB
iajs-2883	161	8	an	an	DET
iajs-2883	161	9	exponentially	exponentially	ADV
iajs-2883	161	10	fitted	fit	VERB
iajs-2883	161	11	diagonally	diagonally	ADV
iajs-2883	161	12	implicit	implicit	ADJ
iajs-2883	161	13	rk	rk	NOUN
iajs-2883	161	14	type	type	NOUN
iajs-2883	161	15	technique	technique	NOUN
iajs-2883	161	16	to	to	PART
iajs-2883	161	17	address	address	VERB
iajs-2883	161	18	the	the	DET
iajs-2883	161	19	𝑦′′′(𝑥	𝑦′′′(𝑥	PROPN
iajs-2883	161	20	)	)	PUNCT
iajs-2883	161	21	=	=	SYM
iajs-2883	161	22	𝑓	𝑓	PROPN
iajs-2883	161	23	(	(	PUNCT
iajs-2883	161	24	𝑥	𝑥	PROPN
iajs-2883	161	25	,	,	PUNCT
iajs-2883	161	26	𝑦	𝑦	NOUN
iajs-2883	161	27	)	)	PUNCT
iajs-2883	161	28	problem	problem	NOUN
iajs-2883	161	29	.	.	PUNCT
iajs-2883	162	1	as	as	ADP
iajs-2883	162	2	a	a	DET
iajs-2883	162	3	result	result	NOUN
iajs-2883	162	4	,	,	PUNCT
iajs-2883	162	5	the	the	DET
iajs-2883	162	6	editrk4	editrk4	PROPN
iajs-2883	162	7	method	method	NOUN
iajs-2883	162	8	,	,	PUNCT
iajs-2883	162	9	a	a	DET
iajs-2883	162	10	diagonally	diagonally	ADV
iajs-2883	162	11	implicit	implicit	ADJ
iajs-2883	162	12	three	three	NUM
iajs-2883	162	13	-	-	PUNCT
iajs-2883	162	14	stage	stage	NOUN
iajs-2883	162	15	fourth	fourth	ADJ
iajs-2883	162	16	-	-	PUNCT
iajs-2883	162	17	order	order	NOUN
iajs-2883	162	18	exponentially	exponentially	ADV
iajs-2883	162	19	-	-	PUNCT
iajs-2883	162	20	fitted	fit	VERB
iajs-2883	162	21	technique	technique	NOUN
iajs-2883	162	22	based	base	VERB
iajs-2883	162	23	on	on	ADP
iajs-2883	162	24	computing	compute	VERB
iajs-2883	162	25	the	the	DET
iajs-2883	162	26	solution	solution	NOUN
iajs-2883	162	27	's	's	PART
iajs-2883	162	28	greatest	great	ADJ
iajs-2883	162	29	error	error	NOUN
iajs-2883	162	30	(	(	PUNCT
iajs-2883	162	31	𝑚𝑎𝑥(|	𝑚𝑎𝑥(|	NOUN
iajs-2883	162	32	𝑦(𝑡𝑛	𝑦(𝑡𝑛	PROPN
iajs-2883	162	33	)	)	PUNCT
iajs-2883	162	34	−	−	PROPN
iajs-2883	162	35	𝑦𝑛|	𝑦𝑛|	PROPN
iajs-2883	162	36	)	)	PUNCT
iajs-2883	162	37	)	)	PUNCT
iajs-2883	162	38	.	.	PUNCT
iajs-2883	163	1	this	this	PRON
iajs-2883	163	2	is	be	AUX
iajs-2883	163	3	the	the	DET
iajs-2883	163	4	greatest	great	ADJ
iajs-2883	163	5	difference	difference	NOUN
iajs-2883	163	6	between	between	ADP
iajs-2883	163	7	actual	actual	ADJ
iajs-2883	163	8	and	and	CCONJ
iajs-2883	163	9	computed	computed	ADJ
iajs-2883	163	10	solution	solution	NOUN
iajs-2883	163	11	absolute	absolute	ADJ
iajs-2883	163	12	errors	error	NOUN
iajs-2883	163	13	,	,	PUNCT
iajs-2883	163	14	was	be	AUX
iajs-2883	163	15	developed	develop	VERB
iajs-2883	163	16	and	and	CCONJ
iajs-2883	163	17	used	use	VERB
iajs-2883	163	18	in	in	ADP
iajs-2883	163	19	the	the	DET
iajs-2883	163	20	numerical	numerical	ADJ
iajs-2883	163	21	comparison	comparison	NOUN
iajs-2883	163	22	of	of	ADP
iajs-2883	163	23	criteria	criterion	NOUN
iajs-2883	163	24	.	.	PUNCT
iajs-2883	164	1	the	the	DET
iajs-2883	164	2	numerical	numerical	ADJ
iajs-2883	164	3	results	result	NOUN
iajs-2883	164	4	are	be	AUX
iajs-2883	164	5	shown	show	VERB
iajs-2883	164	6	in	in	ADP
iajs-2883	164	7	figures	figure	NOUN
iajs-2883	164	8	1–5	1–5	NUM
iajs-2883	164	9	.	.	PUNCT
iajs-2883	165	1	then	then	ADV
iajs-2883	165	2	,	,	PUNCT
iajs-2883	165	3	the	the	DET
iajs-2883	165	4	editrk4	editrk4	PROPN
iajs-2883	165	5	method	method	NOUN
iajs-2883	165	6	requires	require	VERB
iajs-2883	165	7	fewer	few	ADJ
iajs-2883	165	8	capacity	capacity	NOUN
iajs-2883	165	9	assessments	assessment	NOUN
iajs-2883	165	10	than	than	ADP
iajs-2883	165	11	the	the	DET
iajs-2883	165	12	ditrk4	ditrk4	PROPN
iajs-2883	165	13	,	,	PUNCT
iajs-2883	165	14	rkliiib4	rkliiib4	NOUN
iajs-2883	165	15	,	,	PUNCT
iajs-2883	165	16	and	and	CCONJ
iajs-2883	165	17	dirkn4	dirkn4	NOUN
iajs-2883	165	18	procedures	procedure	NOUN
iajs-2883	165	19	.	.	PUNCT
iajs-2883	166	1	the	the	DET
iajs-2883	166	2	common	common	ADJ
iajs-2883	166	3	logarithm	logarithm	NOUN
iajs-2883	166	4	of	of	ADP
iajs-2883	166	5	the	the	DET
iajs-2883	166	6	greatest	great	ADJ
iajs-2883	166	7	global	global	ADJ
iajs-2883	166	8	error	error	NOUN
iajs-2883	166	9	during	during	ADP
iajs-2883	166	10	integration	integration	NOUN
iajs-2883	166	11	and	and	CCONJ
iajs-2883	166	12	computing	computing	NOUN
iajs-2883	166	13	cost	cost	NOUN
iajs-2883	166	14	was	be	AUX
iajs-2883	166	15	calculated	calculate	VERB
iajs-2883	166	16	using	use	VERB
iajs-2883	166	17	the	the	DET
iajs-2883	166	18	number	number	NOUN
iajs-2883	166	19	of	of	ADP
iajs-2883	166	20	function	function	NOUN
iajs-2883	166	21	evaluations	evaluation	NOUN
iajs-2883	166	22	,	,	PUNCT
iajs-2883	166	23	as	as	SCONJ
iajs-2883	166	24	indicated	indicate	VERB
iajs-2883	166	25	in	in	ADP
iajs-2883	166	26	the	the	DET
iajs-2883	166	27	figures	figure	NOUN
iajs-2883	166	28	.	.	PUNCT
iajs-2883	167	1	the	the	DET
iajs-2883	167	2	numerical	numerical	ADJ
iajs-2883	167	3	results	result	NOUN
iajs-2883	167	4	showed	show	VERB
iajs-2883	167	5	that	that	SCONJ
iajs-2883	167	6	over	over	ADP
iajs-2883	167	7	a	a	DET
iajs-2883	167	8	brief	brief	ADJ
iajs-2883	167	9	duration	duration	NOUN
iajs-2883	167	10	of	of	ADP
iajs-2883	167	11	integration	integration	NOUN
iajs-2883	167	12	,	,	PUNCT
iajs-2883	167	13	the	the	DET
iajs-2883	167	14	unique	unique	ADJ
iajs-2883	167	15	exponentially	exponentially	ADV
iajs-2883	167	16	fitted	fit	VERB
iajs-2883	167	17	methodology	methodology	NOUN
iajs-2883	167	18	rk	rk	NOUN
iajs-2883	167	19	type	type	NOUN
iajs-2883	167	20	approach	approach	NOUN
iajs-2883	167	21	has	have	VERB
iajs-2883	167	22	a	a	DET
iajs-2883	167	23	lower	low	ADJ
iajs-2883	167	24	global	global	ADJ
iajs-2883	167	25	error	error	NOUN
iajs-2883	167	26	than	than	ADP
iajs-2883	167	27	the	the	DET
iajs-2883	167	28	other	other	ADJ
iajs-2883	167	29	current	current	ADJ
iajs-2883	167	30	approaches	approach	NOUN
iajs-2883	167	31	.	.	PUNCT
iajs-2883	168	1	the	the	DET
iajs-2883	168	2	innovative	innovative	ADJ
iajs-2883	168	3	editrk4	editrk4	PROPN
iajs-2883	168	4	methodology	methodology	NOUN
iajs-2883	168	5	is	be	AUX
iajs-2883	168	6	significantly	significantly	ADV
iajs-2883	168	7	more	more	ADV
iajs-2883	168	8	effective	effective	ADJ
iajs-2883	168	9	than	than	ADP
iajs-2883	168	10	the	the	DET
iajs-2883	168	11	competition	competition	NOUN
iajs-2883	168	12	present	present	ADJ
iajs-2883	168	13	approaches	approach	NOUN
iajs-2883	168	14	when	when	SCONJ
iajs-2883	168	15	solving	solve	VERB
iajs-2883	168	16	third	third	ADJ
iajs-2883	168	17	-	-	PUNCT
iajs-2883	168	18	order	order	NOUN
iajs-2883	168	19	odes	ode	NOUN
iajs-2883	168	20	of	of	ADP
iajs-2883	168	21	the	the	DET
iajs-2883	168	22	kind	kind	NOUN
iajs-2883	168	23	𝑦′′′	𝑦′′′	PROPN
iajs-2883	168	24	=	=	SYM
iajs-2883	168	25	𝑓	𝑓	PROPN
iajs-2883	168	26	(	(	PUNCT
iajs-2883	168	27	𝑥	𝑥	PROPN
iajs-2883	168	28	,	,	PUNCT
iajs-2883	168	29	𝑦	𝑦	NOUN
iajs-2883	168	30	)	)	PUNCT
iajs-2883	168	31	directly	directly	ADV
iajs-2883	168	32	.	.	PUNCT
iajs-2883	169	1	references	reference	NOUN
iajs-2883	169	2	1	1	NUM
iajs-2883	169	3	.	.	PUNCT
iajs-2883	170	1	myers	myers	PROPN
iajs-2883	170	2	,	,	PUNCT
iajs-2883	170	3	g.	g.	PROPN
iajs-2883	170	4	thin	thin	ADJ
iajs-2883	170	5	films	film	NOUN
iajs-2883	170	6	with	with	ADP
iajs-2883	170	7	high	high	ADJ
iajs-2883	170	8	surface	surface	NOUN
iajs-2883	170	9	tension	tension	NOUN
iajs-2883	170	10	,	,	PUNCT
iajs-2883	170	11	siam	siam	PROPN
iajs-2883	170	12	rev	rev	PROPN
iajs-2883	170	13	.	.	PROPN
iajs-2883	170	14	1998	1998	NUM
iajs-2883	170	15	,	,	PUNCT
iajs-2883	170	16	40,441–462	40,441–462	NUM
iajs-2883	170	17	.	.	PUNCT
iajs-2883	171	1	2	2	NUM
iajs-2883	171	2	..	..	PUNCT
iajs-2883	171	3	momoniat	momoniat	NOUN
iajs-2883	171	4	,	,	PUNCT
iajs-2883	171	5	e.	e.	PROPN
iajs-2883	171	6	symmetries	symmetries	PROPN
iajs-2883	171	7	,	,	PUNCT
iajs-2883	171	8	first	first	ADJ
iajs-2883	171	9	integrals	integral	NOUN
iajs-2883	171	10	and	and	CCONJ
iajs-2883	171	11	phase	phase	NOUN
iajs-2883	171	12	planes	plane	NOUN
iajs-2883	171	13	of	of	ADP
iajs-2883	171	14	a	a	DET
iajs-2883	171	15	third	third	ADJ
iajs-2883	171	16	-	-	PUNCT
iajs-2883	171	17	order	order	NOUN
iajs-2883	171	18	ordinary	ordinary	ADJ
iajs-2883	171	19	differential	differential	ADJ
iajs-2883	171	20	equation	equation	NOUN
iajs-2883	171	21	from	from	ADP
iajs-2883	171	22	thin	thin	ADJ
iajs-2883	171	23	film	film	NOUN
iajs-2883	171	24	flow	flow	NOUN
iajs-2883	171	25	,	,	PUNCT
iajs-2883	171	26	math	math	NOUN
iajs-2883	171	27	.	.	PUNCT
iajs-2883	172	1	comput	comput	PROPN
iajs-2883	172	2	.	.	PUNCT
iajs-2883	173	1	model	model	NOUN
iajs-2883	173	2	.	.	PUNCT
iajs-2883	174	1	2009,49	2009,49	NUM
iajs-2883	174	2	,	,	PUNCT
iajs-2883	174	3	1	1	NUM
iajs-2883	174	4	-	-	SYM
iajs-2883	174	5	2	2	NUM
iajs-2883	174	6	,	,	PUNCT
iajs-2883	174	7	215–225	215–225	NUM
iajs-2883	174	8	.	.	PUNCT
iajs-2883	175	1	3	3	X
iajs-2883	175	2	.	.	X
iajs-2883	175	3	duffy	duffy	PROPN
iajs-2883	175	4	,	,	PUNCT
iajs-2883	175	5	b.r	b.r	PROPN
iajs-2883	175	6	.	.	PROPN
iajs-2883	175	7	;	;	PUNCT
iajs-2883	175	8	wilson	wilson	PROPN
iajs-2883	175	9	,	,	PUNCT
iajs-2883	175	10	s.k	s.k	PROPN
iajs-2883	175	11	.	.	PROPN
iajs-2883	176	1	a	a	DET
iajs-2883	176	2	third	third	ADJ
iajs-2883	176	3	-	-	PUNCT
iajs-2883	176	4	order	order	NOUN
iajs-2883	176	5	differential	differential	ADJ
iajs-2883	176	6	equation	equation	NOUN
iajs-2883	176	7	arising	arise	VERB
iajs-2883	176	8	in	in	ADP
iajs-2883	176	9	thin	thin	ADJ
iajs-2883	176	10	-	-	PUNCT
iajs-2883	176	11	film	film	NOUN
iajs-2883	176	12	flows	flow	NOUN
iajs-2883	176	13	and	and	CCONJ
iajs-2883	176	14	relevant	relevant	ADJ
iajs-2883	176	15	to	to	ADP
iajs-2883	176	16	tanner	tanner	NOUN
iajs-2883	176	17	’s	’s	PART
iajs-2883	176	18	law	law	NOUN
iajs-2883	176	19	,	,	PUNCT
iajs-2883	176	20	math	math	NOUN
iajs-2883	176	21	.	.	PUNCT
iajs-2883	177	1	lett	lett	PROPN
iajs-2883	177	2	..	..	PUNCT
iajs-2883	177	3	1997	1997	NUM
iajs-2883	177	4	,	,	PUNCT
iajs-2883	177	5	10	10	NUM
iajs-2883	177	6	,	,	PUNCT
iajs-2883	177	7	63–68	63–68	NUM
iajs-2883	177	8	.	.	PUNCT
iajs-2883	178	1	4.paternoster	4.paternoster	NUM
iajs-2883	178	2	,	,	PUNCT
iajs-2883	178	3	b	b	NOUN
iajs-2883	178	4	,	,	PUNCT
iajs-2883	178	5	runge	runge	NOUN
iajs-2883	178	6	-	-	PUNCT
iajs-2883	178	7	kutta	kutta	NOUN
iajs-2883	178	8	(	(	PUNCT
iajs-2883	178	9	-nyström	-nyström	NOUN
iajs-2883	178	10	)	)	PUNCT
iajs-2883	178	11	methods	method	NOUN
iajs-2883	178	12	for	for	ADP
iajs-2883	178	13	odes	ode	NOUN
iajs-2883	178	14	with	with	ADP
iajs-2883	178	15	periodic	periodic	ADJ
iajs-2883	178	16	solutions	solution	NOUN
iajs-2883	178	17	based	base	VERB
iajs-2883	178	18	on	on	ADP
iajs-2883	178	19	trigonometric	trigonometric	ADJ
iajs-2883	178	20	polynomials	polynomial	NOUN
iajs-2883	178	21	,	,	PUNCT
iajs-2883	178	22	applied	apply	VERB
iajs-2883	178	23	numerical	numerical	ADJ
iajs-2883	178	24	mathematics	mathematic	NOUN
iajs-2883	178	25	.	.	PUNCT
iajs-2883	179	1	1998	1998	NUM
iajs-2883	179	2	,	,	PUNCT
iajs-2883	179	3	28	28	NUM
iajs-2883	179	4	,	,	PUNCT
iajs-2883	179	5	2	2	NUM
iajs-2883	179	6	–	–	PUNCT
iajs-2883	179	7	4	4	NUM
iajs-2883	179	8	,	,	PUNCT
iajs-2883	179	9	401	401	NUM
iajs-2883	179	10	–	–	PUNCT
iajs-2883	179	11	412	412	NUM
iajs-2883	179	12	.	.	PUNCT
iajs-2883	180	1	5.berghe	5.berghe	NUM
iajs-2883	180	2	,	,	PUNCT
iajs-2883	180	3	g	g	PROPN
iajs-2883	180	4	vanden	vanden	PROPN
iajs-2883	180	5	;	;	PUNCT
iajs-2883	180	6	de	de	X
iajs-2883	180	7	meyer	meyer	PROPN
iajs-2883	180	8	,	,	PUNCT
iajs-2883	180	9	h	h	NOUN
iajs-2883	180	10	;	;	PUNCT
iajs-2883	180	11	van	van	PROPN
iajs-2883	180	12	daele	daele	PROPN
iajs-2883	180	13	,	,	PUNCT
iajs-2883	180	14	m	m	PROPN
iajs-2883	180	15	and	and	CCONJ
iajs-2883	180	16	van	van	PROPN
iajs-2883	180	17	hecke	hecke	PROPN
iajs-2883	180	18	,	,	PUNCT
iajs-2883	180	19	t	t	PROPN
iajs-2883	180	20	,	,	PUNCT
iajs-2883	180	21	exponentially	exponentially	ADV
iajs-2883	180	22	fitted	fit	VERB
iajs-2883	180	23	runge	runge	NOUN
iajs-2883	180	24	–	–	PUNCT
iajs-2883	180	25	kutta	kutta	NOUN
iajs-2883	180	26	methods	method	NOUN
iajs-2883	180	27	,	,	PUNCT
iajs-2883	180	28	journal	journal	NOUN
iajs-2883	180	29	of	of	ADP
iajs-2883	180	30	computational	computational	ADJ
iajs-2883	180	31	and	and	CCONJ
iajs-2883	180	32	applied	applied	ADJ
iajs-2883	180	33	mathematics	mathematic	NOUN
iajs-2883	180	34	.	.	PUNCT
iajs-2883	181	1	2000,125	2000,125	NUM
iajs-2883	181	2	,	,	PUNCT
iajs-2883	181	3	1	1	NUM
iajs-2883	181	4	–	–	PUNCT
iajs-2883	181	5	2	2	NUM
iajs-2883	181	6	,	,	PUNCT
iajs-2883	181	7	107–115	107–115	NUM
iajs-2883	181	8	.	.	PUNCT
iajs-2883	182	1	6.simos	6.simos	NUM
iajs-2883	182	2	,	,	PUNCT
iajs-2883	182	3	te	te	INTJ
iajs-2883	182	4	.	.	PUNCT
iajs-2883	183	1	exponentially	exponentially	ADV
iajs-2883	183	2	fitted	fit	VERB
iajs-2883	183	3	runge	runge	NOUN
iajs-2883	183	4	–	–	PUNCT
iajs-2883	183	5	kutta	kutta	NOUN
iajs-2883	183	6	methods	method	NOUN
iajs-2883	183	7	for	for	ADP
iajs-2883	183	8	the	the	DET
iajs-2883	183	9	numerical	numerical	ADJ
iajs-2883	183	10	solution	solution	NOUN
iajs-2883	183	11	of	of	ADP
iajs-2883	183	12	the	the	DET
iajs-2883	183	13	schrödinger	schrödinger	ADJ
iajs-2883	183	14	equation	equation	NOUN
iajs-2883	183	15	and	and	CCONJ
iajs-2883	183	16	related	related	ADJ
iajs-2883	183	17	problems	problem	NOUN
iajs-2883	183	18	,	,	PUNCT
iajs-2883	183	19	computational	computational	ADJ
iajs-2883	183	20	materials	material	NOUN
iajs-2883	183	21	science	science	NOUN
iajs-2883	183	22	.	.	PUNCT
iajs-2883	184	1	2000	2000	NUM
iajs-2883	184	2	,	,	PUNCT
iajs-2883	184	3	18	18	NUM
iajs-2883	184	4	,	,	PUNCT
iajs-2883	184	5	3	3	NUM
iajs-2883	184	6	–	–	PUNCT
iajs-2883	184	7	4	4	NUM
iajs-2883	184	8	,	,	PUNCT
iajs-2883	184	9	315–332	315–332	NUM
iajs-2883	184	10	.	.	PUNCT
iajs-2883	184	11	ihjpas	ihjpas	PROPN
iajs-2883	184	12	.	.	PUNCT
iajs-2883	185	1	36(1)2023	36(1)2023	NUM
iajs-2883	185	2	399	399	NUM
iajs-2883	185	3	7.alshareeda	7.alshareeda	NUM
iajs-2883	185	4	,	,	PUNCT
iajs-2883	185	5	firas	firas	PROPN
iajs-2883	185	6	adel	adel	PROPN
iajs-2883	185	7	fawzi	fawzi	PROPN
iajs-2883	185	8	,	,	PUNCT
iajs-2883	185	9	runge	runge	NOUN
iajs-2883	185	10	-	-	PUNCT
iajs-2883	185	11	kutta	kutta	NOUN
iajs-2883	185	12	type	type	NOUN
iajs-2883	185	13	methods	method	NOUN
iajs-2883	185	14	for	for	ADP
iajs-2883	185	15	solving	solve	VERB
iajs-2883	185	16	third	third	ADJ
iajs-2883	185	17	-	-	PUNCT
iajs-2883	185	18	order	order	NOUN
iajs-2883	185	19	ordinary	ordinary	ADJ
iajs-2883	185	20	differential	differential	ADJ
iajs-2883	185	21	equations	equation	NOUN
iajs-2883	185	22	and	and	CCONJ
iajs-2883	185	23	first	first	ADJ
iajs-2883	185	24	-	-	PUNCT
iajs-2883	185	25	order	order	NOUN
iajs-2883	185	26	oscillatory	oscillatory	ADJ
iajs-2883	185	27	problems	problem	NOUN
iajs-2883	185	28	,	,	PUNCT
iajs-2883	185	29	(	(	PUNCT
iajs-2883	185	30	ph.d	ph.d	PROPN
iajs-2883	185	31	.	.	PUNCT
iajs-2883	186	1	thesis	thesis	NOUN
iajs-2883	186	2	)	)	PUNCT
iajs-2883	186	3	,	,	PUNCT
iajs-2883	186	4	universiti	universiti	PROPN
iajs-2883	186	5	putra	putra	PROPN
iajs-2883	186	6	malaysia	malaysia	PROPN
iajs-2883	186	7	,	,	PUNCT
iajs-2883	186	8	2017	2017	NUM
iajs-2883	186	9	.	.	PUNCT
iajs-2883	187	1	8.fawzi	8.fawzi	NUM
iajs-2883	187	2	,	,	PUNCT
iajs-2883	187	3	fa	fa	PROPN
iajs-2883	187	4	and	and	CCONJ
iajs-2883	187	5	senu	senu	VERB
iajs-2883	187	6	,	,	PUNCT
iajs-2883	187	7	n	n	NOUN
iajs-2883	187	8	and	and	CCONJ
iajs-2883	187	9	ismail	ismail	PROPN
iajs-2883	187	10	,	,	PUNCT
iajs-2883	187	11	f	f	PROPN
iajs-2883	187	12	,	,	PUNCT
iajs-2883	187	13	an	an	DET
iajs-2883	187	14	efficient	efficient	ADJ
iajs-2883	187	15	of	of	ADP
iajs-2883	187	16	direct	direct	ADJ
iajs-2883	187	17	integrator	integrator	NOUN
iajs-2883	187	18	of	of	ADP
iajs-2883	187	19	runge	runge	NOUN
iajs-2883	187	20	-	-	PUNCT
iajs-2883	187	21	kutta	kutta	NOUN
iajs-2883	187	22	type	type	NOUN
iajs-2883	187	23	method	method	NOUN
iajs-2883	187	24	for	for	ADP
iajs-2883	187	25	solving	solve	VERB
iajs-2883	187	26	y	y	NOUN
iajs-2883	187	27	''	''	PUNCT
iajs-2883	187	28	'	'	PUNCT
iajs-2883	188	1	=	=	SYM
iajs-2883	188	2	f	f	X
iajs-2883	188	3	(	(	PUNCT
iajs-2883	188	4	x	x	PROPN
iajs-2883	188	5	,	,	PUNCT
iajs-2883	188	6	y	y	PROPN
iajs-2883	188	7	,	,	PUNCT
iajs-2883	188	8	y	y	NOUN
iajs-2883	188	9	''	''	PUNCT
iajs-2883	188	10	)	)	PUNCT
iajs-2883	188	11	with	with	ADP
iajs-2883	188	12	application	application	NOUN
iajs-2883	188	13	to	to	ADP
iajs-2883	188	14	thin	thin	ADJ
iajs-2883	188	15	film	film	NOUN
iajs-2883	188	16	flow	flow	NOUN
iajs-2883	188	17	problem	problem	NOUN
iajs-2883	188	18	,	,	PUNCT
iajs-2883	188	19	international	international	ADJ
iajs-2883	188	20	journal	journal	NOUN
iajs-2883	188	21	of	of	ADP
iajs-2883	188	22	pure	pure	ADJ
iajs-2883	188	23	and	and	CCONJ
iajs-2883	188	24	applied	applied	ADJ
iajs-2883	188	25	mathematics	mathematic	NOUN
iajs-2883	188	26	,	,	PUNCT
iajs-2883	188	27	2018	2018	NUM
iajs-2883	188	28	,	,	PUNCT
iajs-2883	188	29	120	120	NUM
iajs-2883	188	30	,	,	PUNCT
iajs-2883	188	31	27–50	27–50	NUM
iajs-2883	188	32	.	.	PUNCT
iajs-2883	189	1	9.mechee	9.mechee	NUM
iajs-2883	189	2	,	,	PUNCT
iajs-2883	189	3	m	m	PRON
iajs-2883	189	4	;	;	PUNCT
iajs-2883	189	5	senu	senu	X
iajs-2883	189	6	,	,	PUNCT
iajs-2883	189	7	n	n	CCONJ
iajs-2883	189	8	;	;	PUNCT
iajs-2883	189	9	ismail	ismail	PROPN
iajs-2883	189	10	,	,	PUNCT
iajs-2883	189	11	f	f	PROPN
iajs-2883	189	12	;	;	PUNCT
iajs-2883	189	13	nikouravan	nikouravan	PROPN
iajs-2883	189	14	,	,	PUNCT
iajs-2883	189	15	bijan	bijan	PROPN
iajs-2883	189	16	;	;	PUNCT
iajs-2883	189	17	siri	siri	NOUN
iajs-2883	189	18	,	,	PUNCT
iajs-2883	189	19	z	z	PROPN
iajs-2883	189	20	,	,	PUNCT
iajs-2883	189	21	a	a	DET
iajs-2883	189	22	three	three	NUM
iajs-2883	189	23	-	-	PUNCT
iajs-2883	189	24	stage	stage	NOUN
iajs-2883	189	25	fifth	fifth	ADJ
iajs-2883	189	26	-	-	PUNCT
iajs-2883	189	27	order	order	NOUN
iajs-2883	189	28	rungekutta	rungekutta	NOUN
iajs-2883	189	29	method	method	NOUN
iajs-2883	189	30	for	for	ADP
iajs-2883	189	31	directly	directly	ADV
iajs-2883	189	32	solving	solve	VERB
iajs-2883	189	33	special	special	ADJ
iajs-2883	189	34	third	third	ADJ
iajs-2883	189	35	-	-	PUNCT
iajs-2883	189	36	order	order	NOUN
iajs-2883	189	37	differential	differential	ADJ
iajs-2883	189	38	equation	equation	NOUN
iajs-2883	189	39	with	with	ADP
iajs-2883	189	40	application	application	NOUN
iajs-2883	189	41	to	to	ADP
iajs-2883	189	42	thin	thin	ADJ
iajs-2883	189	43	film	film	NOUN
iajs-2883	189	44	flow	flow	NOUN
iajs-2883	189	45	problem	problem	NOUN
iajs-2883	189	46	mathematical	mathematical	ADJ
iajs-2883	189	47	problems	problem	NOUN
iajs-2883	189	48	in	in	ADP
iajs-2883	189	49	engineering	engineering	NOUN
iajs-2883	189	50	,	,	PUNCT
iajs-2883	189	51	vol	vol	NOUN
iajs-2883	189	52	.	.	PROPN
iajs-2883	189	53	2013	2013	NUM
iajs-2883	189	54	,	,	PUNCT
iajs-2883	189	55	2013	2013	NUM
iajs-2883	189	56	.	.	PUNCT
iajs-2883	190	1	10.mechee	10.mechee	NUM
iajs-2883	190	2	,	,	PUNCT
iajs-2883	190	3	m	m	NOUN
iajs-2883	190	4	;	;	PUNCT
iajs-2883	190	5	senu	senu	X
iajs-2883	190	6	,	,	PUNCT
iajs-2883	190	7	n	n	CCONJ
iajs-2883	190	8	;	;	PUNCT
iajs-2883	190	9	ismail	ismail	NOUN
iajs-2883	190	10	,	,	PUNCT
iajs-2883	190	11	f	f	X
iajs-2883	190	12	;	;	PUNCT
iajs-2883	190	13	nikouravan	nikouravan	PROPN
iajs-2883	190	14	,	,	PUNCT
iajs-2883	190	15	bijan	bijan	PROPN
iajs-2883	190	16	;	;	PUNCT
iajs-2883	190	17	siri	siri	NOUN
iajs-2883	190	18	,	,	PUNCT
iajs-2883	190	19	z	z	NOUN
iajs-2883	190	20	,	,	PUNCT
iajs-2883	190	21	exponentially	exponentially	ADV
iajs-2883	190	22	fitted	fit	VERB
iajs-2883	190	23	and	and	CCONJ
iajs-2883	190	24	trigonometrically	trigonometrically	ADV
iajs-2883	190	25	fitted	fit	VERB
iajs-2883	190	26	two	two	NUM
iajs-2883	190	27	-	-	PUNCT
iajs-2883	190	28	derivative	derivative	NOUN
iajs-2883	190	29	runge	runge	NOUN
iajs-2883	190	30	-	-	PUNCT
iajs-2883	190	31	kutta	kutta	NOUN
iajs-2883	190	32	-	-	PUNCT
iajs-2883	190	33	nyström	nyström	NOUN
iajs-2883	190	34	methods	method	NOUN
iajs-2883	190	35	for	for	ADP
iajs-2883	190	36	solving	solve	VERB
iajs-2883	190	37	,	,	PUNCT
iajs-2883	190	38	mathematical	mathematical	ADJ
iajs-2883	190	39	problems	problem	NOUN
iajs-2883	190	40	in	in	ADP
iajs-2883	190	41	engineering	engineering	NOUN
iajs-2883	190	42	,	,	PUNCT
iajs-2883	190	43	vol	vol	NOUN
iajs-2883	190	44	.	.	PROPN
iajs-2883	190	45	2018	2018	NUM
iajs-2883	190	46	,	,	PUNCT
iajs-2883	190	47	2018	2018	NUM
iajs-2883	190	48	.	.	PUNCT
iajs-2883	191	1	11.demba	11.demba	NUM
iajs-2883	191	2	,	,	PUNCT
iajs-2883	191	3	ma	ma	PROPN
iajs-2883	191	4	;	;	PUNCT
iajs-2883	191	5	senu	senu	X
iajs-2883	191	6	,	,	PUNCT
iajs-2883	191	7	n	n	PROPN
iajs-2883	191	8	and	and	CCONJ
iajs-2883	191	9	ismail	ismail	PROPN
iajs-2883	191	10	,	,	PUNCT
iajs-2883	191	11	f	f	X
iajs-2883	191	12	,	,	PUNCT
iajs-2883	191	13	trigonometrically	trigonometrically	ADV
iajs-2883	191	14	-	-	PUNCT
iajs-2883	191	15	fitted	fit	VERB
iajs-2883	191	16	explicit	explicit	ADJ
iajs-2883	191	17	four	four	NUM
iajs-2883	191	18	-	-	PUNCT
iajs-2883	191	19	stage	stage	NOUN
iajs-2883	191	20	fourthorder	fourthorder	NOUN
iajs-2883	191	21	runge	runge	NOUN
iajs-2883	191	22	–	–	PUNCT
iajs-2883	191	23	kutta	kutta	NOUN
iajs-2883	191	24	–	–	PUNCT
iajs-2883	191	25	nyström	nyström	NOUN
iajs-2883	191	26	method	method	NOUN
iajs-2883	191	27	for	for	ADP
iajs-2883	191	28	the	the	DET
iajs-2883	191	29	solution	solution	NOUN
iajs-2883	191	30	of	of	ADP
iajs-2883	191	31	initial	initial	ADJ
iajs-2883	191	32	value	value	NOUN
iajs-2883	191	33	problems	problem	NOUN
iajs-2883	191	34	with	with	ADP
iajs-2883	191	35	oscillatory	oscillatory	ADJ
iajs-2883	191	36	behavior	behavior	NOUN
iajs-2883	191	37	,	,	PUNCT
iajs-2883	191	38	global	global	ADJ
iajs-2883	191	39	journal	journal	NOUN
iajs-2883	191	40	of	of	ADP
iajs-2883	191	41	pure	pure	ADJ
iajs-2883	191	42	and	and	CCONJ
iajs-2883	191	43	applied	applied	ADJ
iajs-2883	191	44	mathematics	mathematic	NOUN
iajs-2883	191	45	.	.	PUNCT
iajs-2883	192	1	2016	2016	NUM
iajs-2883	192	2	,	,	PUNCT
iajs-2883	192	3	12	12	NUM
iajs-2883	192	4	,	,	PUNCT
iajs-2883	192	5	1	1	NUM
iajs-2883	192	6	,	,	PUNCT
iajs-2883	192	7	67–80	67–80	NOUN
iajs-2883	192	8	.	.	PUNCT
iajs-2883	193	1	12.fawzi	12.fawzi	NUM
iajs-2883	193	2	,	,	PUNCT
iajs-2883	193	3	firas	firas	PROPN
iajs-2883	193	4	a	a	PRON
iajs-2883	193	5	;	;	PUNCT
iajs-2883	193	6	jumaa	jumaa	PROPN
iajs-2883	193	7	,	,	PUNCT
iajs-2883	193	8	mustafa	mustafa	PROPN
iajs-2883	193	9	h	h	PROPN
iajs-2883	193	10	,	,	PUNCT
iajs-2883	193	11	the	the	DET
iajs-2883	193	12	implementations	implementation	NOUN
iajs-2883	193	13	special	special	ADJ
iajs-2883	193	14	third	third	ADJ
iajs-2883	193	15	-	-	PUNCT
iajs-2883	193	16	order	order	NOUN
iajs-2883	193	17	ordinary	ordinary	ADJ
iajs-2883	193	18	differential	differential	ADJ
iajs-2883	193	19	equations	equation	NOUN
iajs-2883	193	20	(	(	PUNCT
iajs-2883	193	21	ode	ode	PROPN
iajs-2883	193	22	)	)	PUNCT
iajs-2883	193	23	for	for	ADP
iajs-2883	193	24	5th	5th	ADJ
iajs-2883	193	25	-	-	PUNCT
iajs-2883	193	26	order	order	NOUN
iajs-2883	193	27	3rdstage	3rdstage	NUM
iajs-2883	193	28	diagonally	diagonally	ADV
iajs-2883	193	29	implicit	implicit	ADJ
iajs-2883	193	30	type	type	NOUN
iajs-2883	193	31	runge	runge	NOUN
iajs-2883	193	32	-	-	PUNCT
iajs-2883	193	33	kutta	kutta	NOUN
iajs-2883	193	34	method	method	NOUN
iajs-2883	193	35	(	(	PUNCT
iajs-2883	193	36	ditrkm	ditrkm	NOUN
iajs-2883	193	37	)	)	PUNCT
iajs-2883	193	38	,	,	PUNCT
iajs-2883	193	39	ibn	ibn	PROPN
iajs-2883	193	40	al	al	PROPN
iajs-2883	193	41	-	-	PUNCT
iajs-2883	193	42	haitham	haitham	PROPN
iajs-2883	193	43	journal	journal	PROPN
iajs-2883	193	44	for	for	ADP
iajs-2883	193	45	pure	pure	ADJ
iajs-2883	193	46	and	and	CCONJ
iajs-2883	193	47	applied	applied	ADJ
iajs-2883	193	48	sciences	science	NOUN
iajs-2883	193	49	.	.	PUNCT
iajs-2883	194	1	2022	2022	NUM
iajs-2883	194	2	,	,	PUNCT
iajs-2883	194	3	35	35	NUM
iajs-2883	194	4	,	,	PUNCT
iajs-2883	194	5	1	1	NUM
iajs-2883	194	6	,	,	PUNCT
iajs-2883	194	7	92	92	NUM
iajs-2883	194	8	–	–	PUNCT
iajs-2883	194	9	101	101	NUM
iajs-2883	194	10	.	.	PUNCT
iajs-2883	195	1	13.ghawadri	13.ghawadri	NUM
iajs-2883	195	2	,	,	PUNCT
iajs-2883	195	3	nizam	nizam	PROPN
iajs-2883	195	4	;	;	PUNCT
iajs-2883	195	5	senu	senu	NOUN
iajs-2883	195	6	,	,	PUNCT
iajs-2883	195	7	norazak	norazak	NOUN
iajs-2883	195	8	;	;	PUNCT
iajs-2883	195	9	adel	adel	PROPN
iajs-2883	195	10	fawzi	fawzi	PROPN
iajs-2883	195	11	,	,	PUNCT
iajs-2883	195	12	firas	firas	PROPN
iajs-2883	195	13	;	;	PUNCT
iajs-2883	195	14	ismail	ismail	PROPN
iajs-2883	195	15	,	,	PUNCT
iajs-2883	195	16	fudziah	fudziah	NOUN
iajs-2883	195	17	and	and	CCONJ
iajs-2883	195	18	ibrahim	ibrahim	PROPN
iajs-2883	195	19	,	,	PUNCT
iajs-2883	195	20	zarina	zarina	PROPN
iajs-2883	195	21	bibi	bibi	PROPN
iajs-2883	195	22	,	,	PUNCT
iajs-2883	195	23	diagonally	diagonally	ADV
iajs-2883	195	24	implicit	implicit	ADJ
iajs-2883	195	25	runge	runge	NOUN
iajs-2883	195	26	–	–	PUNCT
iajs-2883	195	27	kutta	kutta	NOUN
iajs-2883	195	28	type	type	NOUN
iajs-2883	195	29	method	method	NOUN
iajs-2883	195	30	for	for	ADP
iajs-2883	195	31	directly	directly	ADV
iajs-2883	195	32	solving	solve	VERB
iajs-2883	195	33	special	special	ADJ
iajs-2883	195	34	fourth	fourth	ADJ
iajs-2883	195	35	-	-	PUNCT
iajs-2883	195	36	order	order	NOUN
iajs-2883	195	37	ordinary	ordinary	ADJ
iajs-2883	195	38	differential	differential	ADJ
iajs-2883	195	39	equations	equation	NOUN
iajs-2883	195	40	with	with	ADP
iajs-2883	195	41	ill	ill	ADV
iajs-2883	195	42	-	-	PUNCT
iajs-2883	195	43	posed	pose	VERB
iajs-2883	195	44	problem	problem	NOUN
iajs-2883	195	45	of	of	ADP
iajs-2883	195	46	a	a	DET
iajs-2883	195	47	beam	beam	NOUN
iajs-2883	195	48	on	on	ADP
iajs-2883	195	49	elastic	elastic	ADJ
iajs-2883	195	50	foundation	foundation	NOUN
iajs-2883	195	51	,	,	PUNCT
iajs-2883	195	52	algorithms	algorithm	NOUN
iajs-2883	195	53	.	.	PUNCT
iajs-2883	196	1	2018	2018	NUM
iajs-2883	196	2	,	,	PUNCT
iajs-2883	196	3	12	12	NUM
iajs-2883	196	4	,	,	PUNCT
iajs-2883	196	5	1	1	NUM
iajs-2883	196	6	,	,	PUNCT
iajs-2883	196	7	10	10	NUM
iajs-2883	196	8	.	.	PUNCT
iajs-2883	197	1	14	14	NUM
iajs-2883	197	2	.	.	PUNCT
iajs-2883	198	1	gander	gander	NOUN
iajs-2883	198	2	,	,	PUNCT
iajs-2883	198	3	w.	w.	NOUN
iajs-2883	198	4	;	;	PUNCT
iajs-2883	198	5	gruntz	gruntz	PROPN
iajs-2883	198	6	,	,	PUNCT
iajs-2883	198	7	d.	d.	PROPN
iajs-2883	198	8	derivation	derivation	NOUN
iajs-2883	198	9	of	of	ADP
iajs-2883	198	10	numerical	numerical	ADJ
iajs-2883	198	11	methods	method	NOUN
iajs-2883	198	12	using	use	VERB
iajs-2883	198	13	computer	computer	NOUN
iajs-2883	198	14	algebra	algebra	NOUN
iajs-2883	198	15	,	,	PUNCT
iajs-2883	198	16	siam	siam	PROPN
iajs-2883	198	17	review	review	NOUN
iajs-2883	198	18	.	.	PUNCT
iajs-2883	199	1	1999	1999	NUM
iajs-2883	199	2	,	,	PUNCT
iajs-2883	199	3	41	41	NUM
iajs-2883	199	4	,	,	PUNCT
iajs-2883	199	5	3	3	NUM
iajs-2883	199	6	,	,	PUNCT
iajs-2883	199	7	577–593	577–593	NUM
iajs-2883	199	8	.	.	PUNCT
iajs-2883	200	1	15	15	NUM
iajs-2883	200	2	.	.	X
iajs-2883	200	3	dormand	dormand	NOUN
iajs-2883	200	4	,	,	PUNCT
iajs-2883	200	5	j.	j.	PROPN
iajs-2883	200	6	r.	r.	PROPN
iajs-2883	200	7	numerical	numerical	PROPN
iajs-2883	200	8	methods	method	NOUN
iajs-2883	200	9	for	for	ADP
iajs-2883	200	10	differential	differential	ADJ
iajs-2883	200	11	equations	equation	NOUN
iajs-2883	200	12	,	,	PUNCT
iajs-2883	200	13	a	a	DET
iajs-2883	200	14	computational	computational	ADJ
iajs-2883	200	15	approach	approach	NOUN
iajs-2883	200	16	,	,	PUNCT
iajs-2883	200	17	crc	crc	NOUN
iajs-2883	200	18	press	press	PROPN
iajs-2883	200	19	,	,	PUNCT
iajs-2883	200	20	boca	boca	PROPN
iajs-2883	200	21	raton	raton	PROPN
iajs-2883	200	22	,	,	PUNCT
iajs-2883	200	23	fla	fla	PROPN
iajs-2883	200	24	,	,	PUNCT
iajs-2883	200	25	usa	usa	PROPN
iajs-2883	200	26	,	,	PUNCT
iajs-2883	200	27	1996	1996	NUM
iajs-2883	200	28	.	.	PUNCT
iajs-2883	201	1	16.sommeijer	16.sommeijer	NUM
iajs-2883	201	2	,	,	PUNCT
iajs-2883	201	3	ben	ben	PROPN
iajs-2883	201	4	p	p	PROPN
iajs-2883	201	5	,	,	PUNCT
iajs-2883	201	6	a	a	DET
iajs-2883	201	7	note	note	NOUN
iajs-2883	201	8	on	on	ADP
iajs-2883	201	9	a	a	DET
iajs-2883	201	10	diagonally	diagonally	ADV
iajs-2883	201	11	implicit	implicit	ADJ
iajs-2883	201	12	runge	runge	NOUN
iajs-2883	201	13	-	-	PUNCT
iajs-2883	201	14	kutta	kutta	NOUN
iajs-2883	201	15	-	-	PUNCT
iajs-2883	201	16	nyström	nyström	NOUN
iajs-2883	201	17	method	method	NOUN
iajs-2883	201	18	,	,	PUNCT
iajs-2883	201	19	journal	journal	NOUN
iajs-2883	201	20	of	of	ADP
iajs-2883	201	21	computational	computational	ADJ
iajs-2883	201	22	and	and	CCONJ
iajs-2883	201	23	applied	applied	ADJ
iajs-2883	201	24	mathematics	mathematic	NOUN
iajs-2883	201	25	.	.	PUNCT
iajs-2883	202	1	1987	1987	NUM
iajs-2883	202	2	,	,	PUNCT
iajs-2883	202	3	19	19	NUM
iajs-2883	202	4	,	,	PUNCT
iajs-2883	202	5	3	3	NUM
iajs-2883	202	6	,	,	PUNCT
iajs-2883	202	7	395–399	395–399	NUM
iajs-2883	202	8	.	.	PUNCT
iajs-2883	203	1	17.moo	17.moo	PROPN
iajs-2883	203	2	,	,	PUNCT
iajs-2883	203	3	kw	kw	NOUN
iajs-2883	203	4	;	;	PUNCT
iajs-2883	203	5	senu	senu	NOUN
iajs-2883	203	6	,	,	PUNCT
iajs-2883	203	7	n	n	CCONJ
iajs-2883	203	8	;	;	PUNCT
iajs-2883	203	9	ismail	ismail	PROPN
iajs-2883	203	10	,	,	PUNCT
iajs-2883	203	11	f	f	PROPN
iajs-2883	203	12	;	;	PUNCT
iajs-2883	203	13	suleiman	suleiman	PROPN
iajs-2883	203	14	,	,	PUNCT
iajs-2883	203	15	m	m	PROPN
iajs-2883	203	16	,	,	PUNCT
iajs-2883	203	17	a	a	DET
iajs-2883	203	18	zero	zero	NUM
iajs-2883	203	19	-	-	PUNCT
iajs-2883	203	20	dissipative	dissipative	NOUN
iajs-2883	203	21	phase	phase	NOUN
iajs-2883	203	22	-	-	PUNCT
iajs-2883	203	23	fitted	fit	VERB
iajs-2883	203	24	fourth	fourth	ADJ
iajs-2883	203	25	order	order	NOUN
iajs-2883	203	26	diagonally	diagonally	ADV
iajs-2883	203	27	implicit	implicit	ADJ
iajs-2883	203	28	runge	runge	NOUN
iajs-2883	203	29	-	-	PUNCT
iajs-2883	203	30	kutta	kutta	NOUN
iajs-2883	203	31	-	-	PUNCT
iajs-2883	203	32	nyström	nyström	NOUN
iajs-2883	203	33	method	method	NOUN
iajs-2883	203	34	for	for	ADP
iajs-2883	203	35	solving	solve	VERB
iajs-2883	203	36	oscillatory	oscillatory	ADJ
iajs-2883	203	37	problems	problem	NOUN
iajs-2883	203	38	,	,	PUNCT
iajs-2883	203	39	mathematical	mathematical	ADJ
iajs-2883	203	40	problems	problem	NOUN
iajs-2883	203	41	in	in	ADP
iajs-2883	203	42	engineering	engineering	NOUN
iajs-2883	203	43	,	,	PUNCT
iajs-2883	203	44	vol	vol	NOUN
iajs-2883	203	45	.	.	PROPN
iajs-2883	203	46	2014	2014	NUM
iajs-2883	203	47	,	,	PUNCT
iajs-2883	203	48	2014	2014	NUM
iajs-2883	203	49	.	.	PUNCT