id	sid	tid	token	lemma	pos
iajs-2963	1	1	ihjpas	ihjpas	PROPN
iajs-2963	1	2	.	.	PUNCT
iajs-2963	2	1	36(1)2023	36(1)2023	NUM
iajs-2963	2	2	345	345	NUM
iajs-2963	2	3	this	this	DET
iajs-2963	2	4	work	work	NOUN
iajs-2963	2	5	is	be	AUX
iajs-2963	2	6	licensed	license	VERB
iajs-2963	2	7	under	under	ADP
iajs-2963	2	8	a	a	DET
iajs-2963	2	9	creative	creative	ADJ
iajs-2963	2	10	commons	common	NOUN
iajs-2963	2	11	attribution	attribution	NOUN
iajs-2963	2	12	4.0	4.0	NUM
iajs-2963	2	13	international	international	ADJ
iajs-2963	2	14	license	license	NOUN
iajs-2963	2	15	improved	improve	VERB
iajs-2963	2	16	runge	runge	NOUN
iajs-2963	2	17	-	-	PUNCT
iajs-2963	2	18	kutta	kutta	NOUN
iajs-2963	2	19	method	method	NOUN
iajs-2963	2	20	for	for	ADP
iajs-2963	2	21	oscillatory	oscillatory	ADJ
iajs-2963	2	22	problem	problem	NOUN
iajs-2963	2	23	solution	solution	NOUN
iajs-2963	2	24	using	use	VERB
iajs-2963	2	25	trigonometric	trigonometric	ADJ
iajs-2963	2	26	fitting	fitting	ADJ
iajs-2963	2	27	approach	approach	NOUN
iajs-2963	2	28	abstract	abstract	NOUN
iajs-2963	2	29	this	this	DET
iajs-2963	2	30	paper	paper	NOUN
iajs-2963	2	31	provides	provide	VERB
iajs-2963	2	32	a	a	DET
iajs-2963	2	33	four	four	NUM
iajs-2963	2	34	-	-	PUNCT
iajs-2963	2	35	stage	stage	NOUN
iajs-2963	2	36	trigonometrically	trigonometrically	ADV
iajs-2963	2	37	fitted	fit	VERB
iajs-2963	2	38	improved	improved	ADJ
iajs-2963	2	39	runge	runge	NOUN
iajs-2963	2	40	-	-	PUNCT
iajs-2963	2	41	kutta	kutta	NOUN
iajs-2963	2	42	(	(	PUNCT
iajs-2963	2	43	tfirk4	tfirk4	NOUN
iajs-2963	2	44	)	)	PUNCT
iajs-2963	2	45	method	method	NOUN
iajs-2963	2	46	of	of	ADP
iajs-2963	2	47	four	four	NUM
iajs-2963	2	48	orders	order	NOUN
iajs-2963	2	49	to	to	PART
iajs-2963	2	50	solve	solve	VERB
iajs-2963	2	51	oscillatory	oscillatory	ADJ
iajs-2963	2	52	problems	problem	NOUN
iajs-2963	2	53	,	,	PUNCT
iajs-2963	2	54	which	which	PRON
iajs-2963	2	55	contains	contain	VERB
iajs-2963	2	56	an	an	DET
iajs-2963	2	57	oscillatory	oscillatory	ADJ
iajs-2963	2	58	character	character	NOUN
iajs-2963	2	59	in	in	ADP
iajs-2963	2	60	the	the	DET
iajs-2963	2	61	solutions	solution	NOUN
iajs-2963	2	62	.	.	PUNCT
iajs-2963	3	1	compared	compare	VERB
iajs-2963	3	2	to	to	ADP
iajs-2963	3	3	the	the	DET
iajs-2963	3	4	traditional	traditional	ADJ
iajs-2963	3	5	runge	runge	NOUN
iajs-2963	3	6	-	-	PUNCT
iajs-2963	3	7	kutta	kutta	NOUN
iajs-2963	3	8	method	method	NOUN
iajs-2963	3	9	,	,	PUNCT
iajs-2963	3	10	the	the	DET
iajs-2963	3	11	improved	improved	ADJ
iajs-2963	3	12	runge	runge	NOUN
iajs-2963	3	13	-	-	PUNCT
iajs-2963	3	14	kutta	kutta	NOUN
iajs-2963	3	15	(	(	PUNCT
iajs-2963	3	16	irk	irk	NOUN
iajs-2963	3	17	)	)	PUNCT
iajs-2963	3	18	method	method	NOUN
iajs-2963	3	19	is	be	AUX
iajs-2963	3	20	a	a	DET
iajs-2963	3	21	natural	natural	ADJ
iajs-2963	3	22	two	two	NUM
iajs-2963	3	23	-	-	PUNCT
iajs-2963	3	24	step	step	NOUN
iajs-2963	3	25	method	method	NOUN
iajs-2963	3	26	requiring	require	VERB
iajs-2963	3	27	fewer	few	ADJ
iajs-2963	3	28	steps	step	NOUN
iajs-2963	3	29	.	.	PUNCT
iajs-2963	4	1	the	the	DET
iajs-2963	4	2	suggested	suggest	VERB
iajs-2963	4	3	method	method	NOUN
iajs-2963	4	4	extends	extend	VERB
iajs-2963	4	5	the	the	DET
iajs-2963	4	6	fourth	fourth	ADJ
iajs-2963	4	7	-	-	PUNCT
iajs-2963	4	8	order	order	NOUN
iajs-2963	4	9	improved	improve	VERB
iajs-2963	4	10	runge	runge	NOUN
iajs-2963	4	11	-	-	PUNCT
iajs-2963	4	12	kutta	kutta	NOUN
iajs-2963	4	13	(	(	PUNCT
iajs-2963	4	14	irk4	irk4	PROPN
iajs-2963	4	15	)	)	PUNCT
iajs-2963	4	16	method	method	NOUN
iajs-2963	4	17	with	with	ADP
iajs-2963	4	18	trigonometric	trigonometric	ADJ
iajs-2963	4	19	calculations	calculation	NOUN
iajs-2963	4	20	.	.	PUNCT
iajs-2963	5	1	this	this	DET
iajs-2963	5	2	approach	approach	NOUN
iajs-2963	5	3	is	be	AUX
iajs-2963	5	4	intended	intend	VERB
iajs-2963	5	5	to	to	PART
iajs-2963	5	6	integrate	integrate	VERB
iajs-2963	5	7	problems	problem	NOUN
iajs-2963	5	8	with	with	ADP
iajs-2963	5	9	particular	particular	ADJ
iajs-2963	5	10	initial	initial	ADJ
iajs-2963	5	11	value	value	NOUN
iajs-2963	5	12	problems	problem	NOUN
iajs-2963	5	13	(	(	PUNCT
iajs-2963	5	14	ivps	ivps	PROPN
iajs-2963	5	15	)	)	PUNCT
iajs-2963	5	16	using	use	VERB
iajs-2963	5	17	the	the	DET
iajs-2963	5	18	set	set	NOUN
iajs-2963	5	19	functions	function	NOUN
iajs-2963	5	20	𝑒𝜔𝑥	𝑒𝜔𝑥	VERB
iajs-2963	5	21	and	and	CCONJ
iajs-2963	5	22	𝑒−𝜔𝑥	𝑒−𝜔𝑥	PROPN
iajs-2963	5	23	for	for	ADP
iajs-2963	5	24	trigonometrically	trigonometrically	ADV
iajs-2963	5	25	fitted	fit	VERB
iajs-2963	5	26	.	.	PUNCT
iajs-2963	6	1	to	to	PART
iajs-2963	6	2	improve	improve	VERB
iajs-2963	6	3	the	the	DET
iajs-2963	6	4	method	method	NOUN
iajs-2963	6	5	's	's	PART
iajs-2963	6	6	accuracy	accuracy	NOUN
iajs-2963	6	7	,	,	PUNCT
iajs-2963	6	8	the	the	DET
iajs-2963	6	9	problem	problem	NOUN
iajs-2963	6	10	primary	primary	ADJ
iajs-2963	6	11	frequency	frequency	NOUN
iajs-2963	6	12	𝜔	𝜔	ADP
iajs-2963	6	13	∈	∈	PROPN
iajs-2963	6	14	𝑅	𝑅	PROPN
iajs-2963	6	15	is	be	AUX
iajs-2963	6	16	used	use	VERB
iajs-2963	6	17	.	.	PUNCT
iajs-2963	7	1	the	the	DET
iajs-2963	7	2	novel	novel	ADJ
iajs-2963	7	3	method	method	NOUN
iajs-2963	7	4	is	be	AUX
iajs-2963	7	5	more	more	ADV
iajs-2963	7	6	accurate	accurate	ADJ
iajs-2963	7	7	than	than	ADP
iajs-2963	7	8	the	the	DET
iajs-2963	7	9	conventional	conventional	ADJ
iajs-2963	7	10	runge	runge	NOUN
iajs-2963	7	11	-	-	PUNCT
iajs-2963	7	12	kutta	kutta	NOUN
iajs-2963	7	13	method	method	NOUN
iajs-2963	7	14	and	and	CCONJ
iajs-2963	7	15	irk4	irk4	PROPN
iajs-2963	7	16	.	.	PUNCT
iajs-2963	8	1	several	several	ADJ
iajs-2963	8	2	test	test	NOUN
iajs-2963	8	3	problems	problem	NOUN
iajs-2963	8	4	for	for	ADP
iajs-2963	8	5	the	the	DET
iajs-2963	8	6	system	system	NOUN
iajs-2963	8	7	of	of	ADP
iajs-2963	8	8	first	first	ADJ
iajs-2963	8	9	-	-	PUNCT
iajs-2963	8	10	order	order	NOUN
iajs-2963	8	11	ordinary	ordinary	ADJ
iajs-2963	8	12	differential	differential	ADJ
iajs-2963	8	13	equations	equation	NOUN
iajs-2963	8	14	carry	carry	VERB
iajs-2963	8	15	out	out	ADP
iajs-2963	8	16	numerically	numerically	ADV
iajs-2963	8	17	to	to	PART
iajs-2963	8	18	demonstrate	demonstrate	VERB
iajs-2963	8	19	the	the	DET
iajs-2963	8	20	effectiveness	effectiveness	NOUN
iajs-2963	8	21	of	of	ADP
iajs-2963	8	22	this	this	DET
iajs-2963	8	23	approach	approach	NOUN
iajs-2963	8	24	.	.	PUNCT
iajs-2963	9	1	the	the	DET
iajs-2963	9	2	computational	computational	ADJ
iajs-2963	9	3	studies	study	NOUN
iajs-2963	9	4	show	show	VERB
iajs-2963	9	5	that	that	SCONJ
iajs-2963	9	6	the	the	DET
iajs-2963	9	7	tfirk4	tfirk4	PROPN
iajs-2963	9	8	approach	approach	NOUN
iajs-2963	9	9	is	be	AUX
iajs-2963	9	10	more	more	ADV
iajs-2963	9	11	efficient	efficient	ADJ
iajs-2963	9	12	than	than	ADP
iajs-2963	9	13	the	the	DET
iajs-2963	9	14	existing	exist	VERB
iajs-2963	9	15	runge	runge	NOUN
iajs-2963	9	16	-	-	PUNCT
iajs-2963	9	17	kutta	kutta	NOUN
iajs-2963	9	18	methods	method	NOUN
iajs-2963	9	19	.	.	PUNCT
iajs-2963	10	1	keywords	keyword	NOUN
iajs-2963	10	2	:	:	PUNCT
iajs-2963	10	3	improved	improved	ADJ
iajs-2963	10	4	runge	runge	NOUN
iajs-2963	10	5	-	-	PUNCT
iajs-2963	10	6	kutta	kutta	NOUN
iajs-2963	10	7	method	method	NOUN
iajs-2963	10	8	,	,	PUNCT
iajs-2963	10	9	trigonometrically	trigonometrically	ADV
iajs-2963	10	10	-	-	PUNCT
iajs-2963	10	11	fitted	fit	VERB
iajs-2963	10	12	,	,	PUNCT
iajs-2963	10	13	initial	initial	ADJ
iajs-2963	10	14	value	value	NOUN
iajs-2963	10	15	problem	problem	NOUN
iajs-2963	10	16	,	,	PUNCT
iajs-2963	10	17	oscillating	oscillate	VERB
iajs-2963	10	18	solution	solution	NOUN
iajs-2963	10	19	.	.	PUNCT
iajs-2963	11	1	1	1	X
iajs-2963	11	2	.	.	X
iajs-2963	11	3	introduction	introduction	NOUN
iajs-2963	11	4	this	this	DET
iajs-2963	11	5	paper	paper	NOUN
iajs-2963	11	6	focuses	focus	VERB
iajs-2963	11	7	on	on	ADP
iajs-2963	11	8	solving	solve	VERB
iajs-2963	11	9	the	the	DET
iajs-2963	11	10	system	system	NOUN
iajs-2963	11	11	of	of	ADP
iajs-2963	11	12	the	the	DET
iajs-2963	11	13	first	first	ADJ
iajs-2963	11	14	-	-	PUNCT
iajs-2963	11	15	order	order	NOUN
iajs-2963	11	16	ordinary	ordinary	ADJ
iajs-2963	11	17	differential	differential	ADJ
iajs-2963	11	18	equations	equation	NOUN
iajs-2963	11	19	(	(	PUNCT
iajs-2963	11	20	odes	ode	NOUN
iajs-2963	11	21	)	)	PUNCT
iajs-2963	11	22	of	of	ADP
iajs-2963	11	23	the	the	DET
iajs-2963	11	24	form	form	NOUN
iajs-2963	11	25	:	:	PUNCT
iajs-2963	11	26	𝑢′(𝑡	𝑢′(𝑡	NUM
iajs-2963	11	27	)	)	PUNCT
iajs-2963	11	28	=	=	PUNCT
iajs-2963	12	1	𝑓(𝑡	𝑓(𝑡	NOUN
iajs-2963	12	2	,	,	PUNCT
iajs-2963	12	3	𝑢	𝑢	NOUN
iajs-2963	12	4	)	)	PUNCT
iajs-2963	12	5	,	,	PUNCT
iajs-2963	12	6	𝑢(𝑡0	𝑢(𝑡0	PROPN
iajs-2963	12	7	)	)	PUNCT
iajs-2963	12	8	=	=	SYM
iajs-2963	12	9	𝑢0	𝑢0	PROPN
iajs-2963	12	10	.	.	PUNCT
iajs-2963	13	1	(	(	PUNCT
iajs-2963	13	2	1	1	X
iajs-2963	13	3	)	)	PUNCT
iajs-2963	13	4	these	these	DET
iajs-2963	13	5	issues	issue	NOUN
iajs-2963	13	6	are	be	AUX
iajs-2963	13	7	frequently	frequently	ADV
iajs-2963	13	8	seen	see	VERB
iajs-2963	13	9	in	in	ADP
iajs-2963	13	10	various	various	ADJ
iajs-2963	13	11	applied	apply	VERB
iajs-2963	13	12	sciences	science	NOUN
iajs-2963	13	13	,	,	PUNCT
iajs-2963	13	14	including	include	VERB
iajs-2963	13	15	quantum	quantum	ADJ
iajs-2963	13	16	mechanics	mechanic	NOUN
iajs-2963	13	17	,	,	PUNCT
iajs-2963	13	18	electronics	electronic	NOUN
iajs-2963	13	19	,	,	PUNCT
iajs-2963	13	20	chemical	chemical	NOUN
iajs-2963	13	21	physics	physics	NOUN
iajs-2963	13	22	,	,	PUNCT
iajs-2963	13	23	and	and	CCONJ
iajs-2963	13	24	astronomy	astronomy	NOUN
iajs-2963	13	25	(	(	PUNCT
iajs-2963	13	26	see	see	VERB
iajs-2963	13	27	[	[	X
iajs-2963	13	28	1	1	X
iajs-2963	13	29	]	]	PUNCT
iajs-2963	13	30	and	and	CCONJ
iajs-2963	13	31	[	[	X
iajs-2963	13	32	2	2	NUM
iajs-2963	13	33	]	]	NUM
iajs-2963	13	34	)	)	PUNCT
iajs-2963	13	35	.	.	PUNCT
iajs-2963	14	1	traditionally	traditionally	ADV
iajs-2963	14	2	,	,	PUNCT
iajs-2963	14	3	runge	runge	NOUN
iajs-2963	14	4	-	-	PUNCT
iajs-2963	14	5	kutta	kutta	NOUN
iajs-2963	14	6	(	(	PUNCT
iajs-2963	14	7	rk	rk	NOUN
iajs-2963	14	8	)	)	PUNCT
iajs-2963	14	9	doi.org/10.30526/36.1.2963	doi.org/10.30526/36.1.2963	VERB
iajs-2963	14	10	article	article	NOUN
iajs-2963	14	11	history	history	NOUN
iajs-2963	14	12	:	:	PUNCT
iajs-2963	14	13	received	receive	VERB
iajs-2963	14	14	29	29	NUM
iajs-2963	14	15	july	july	PROPN
iajs-2963	14	16	2022	2022	NUM
iajs-2963	14	17	,	,	PUNCT
iajs-2963	14	18	accepted	accept	VERB
iajs-2963	14	19	1	1	NUM
iajs-2963	14	20	september	september	PROPN
iajs-2963	14	21	2022	2022	NUM
iajs-2963	14	22	,	,	PUNCT
iajs-2963	14	23	published	publish	VERB
iajs-2963	14	24	in	in	ADP
iajs-2963	14	25	january	january	PROPN
iajs-2963	14	26	2023	2023	NUM
iajs-2963	14	27	.	.	PUNCT
iajs-2963	15	1	ibn	ibn	PROPN
iajs-2963	15	2	al	al	PROPN
iajs-2963	15	3	-	-	PUNCT
iajs-2963	15	4	haitham	haitham	PROPN
iajs-2963	15	5	journal	journal	PROPN
iajs-2963	15	6	for	for	ADP
iajs-2963	15	7	pure	pure	ADJ
iajs-2963	15	8	and	and	CCONJ
iajs-2963	15	9	applied	applied	ADJ
iajs-2963	15	10	sciences	sciences	PROPN
iajs-2963	15	11	journal	journal	PROPN
iajs-2963	15	12	homepage	homepage	NOUN
iajs-2963	15	13	:	:	PUNCT
iajs-2963	15	14	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	PROPN
iajs-2963	15	15	kasim	kasim	PROPN
iajs-2963	15	16	abbas	abbas	PROPN
iajs-2963	15	17	hussain	hussain	PROPN
iajs-2963	15	18	department	department	PROPN
iajs-2963	15	19	of	of	ADP
iajs-2963	15	20	mathematics	mathematics	PROPN
iajs-2963	15	21	,	,	PUNCT
iajs-2963	15	22	college	college	NOUN
iajs-2963	15	23	of	of	ADP
iajs-2963	15	24	sciences	sciences	PROPN
iajs-2963	15	25	,	,	PUNCT
iajs-2963	15	26	mustansiriyah	mustansiriyah	NOUN
iajs-2963	15	27	university	university	NOUN
iajs-2963	15	28	,	,	PUNCT
iajs-2963	15	29	baghdad	baghdad	PROPN
iajs-2963	15	30	,	,	PUNCT
iajs-2963	15	31	iraq	iraq	PROPN
iajs-2963	15	32	kasimabbas@uomustansiriyah.edu.iq	kasimabbas@uomustansiriyah.edu.iq	PROPN
iajs-2963	15	33	waleed	waleed	PROPN
iajs-2963	15	34	jamal	jamal	PROPN
iajs-2963	15	35	hasan	hasan	PROPN
iajs-2963	15	36	department	department	PROPN
iajs-2963	15	37	of	of	ADP
iajs-2963	15	38	mathematics	mathematics	PROPN
iajs-2963	15	39	,	,	PUNCT
iajs-2963	15	40	college	college	NOUN
iajs-2963	15	41	of	of	ADP
iajs-2963	15	42	sciences	sciences	PROPN
iajs-2963	15	43	,	,	PUNCT
iajs-2963	15	44	mustansiriyah	mustansiriyah	NOUN
iajs-2963	15	45	university	university	NOUN
iajs-2963	15	46	,	,	PUNCT
iajs-2963	15	47	baghdad	baghdad	PROPN
iajs-2963	15	48	,	,	PUNCT
iajs-2963	15	49	iraq	iraq	PROPN
iajs-2963	15	50	waleedjamalhasan1979@gmail.com	waleedjamalhasan1979@gmail.com	X
iajs-2963	16	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-2963	16	2	mailto:kasimabbas@uomustansiriyah.edu.iq	mailto:kasimabbas@uomustansiriyah.edu.iq	PROPN
iajs-2963	16	3	mailto:waleedjamalhasan1979@gmail.com	mailto:waleedjamalhasan1979@gmail.com	PROPN
iajs-2963	16	4	ihjpas	ihjpas	PROPN
iajs-2963	16	5	.	.	PUNCT
iajs-2963	17	1	36(1)2023	36(1)2023	NUM
iajs-2963	17	2	346	346	NUM
iajs-2963	17	3	methods	method	NOUN
iajs-2963	17	4	or	or	CCONJ
iajs-2963	17	5	two	two	NUM
iajs-2963	17	6	-	-	PUNCT
iajs-2963	17	7	step	step	NOUN
iajs-2963	17	8	methods	method	NOUN
iajs-2963	17	9	are	be	AUX
iajs-2963	17	10	used	use	VERB
iajs-2963	17	11	to	to	PART
iajs-2963	17	12	solve	solve	VERB
iajs-2963	17	13	equation	equation	NOUN
iajs-2963	17	14	(	(	PUNCT
iajs-2963	17	15	1	1	X
iajs-2963	17	16	)	)	PUNCT
iajs-2963	18	1	[	[	X
iajs-2963	18	2	3	3	NUM
iajs-2963	18	3	]	]	PUNCT
iajs-2963	18	4	.	.	PUNCT
iajs-2963	19	1	in	in	ADP
iajs-2963	19	2	2013	2013	NUM
iajs-2963	19	3	,	,	PUNCT
iajs-2963	19	4	[	[	X
iajs-2963	19	5	4	4	X
iajs-2963	19	6	]	]	PUNCT
iajs-2963	19	7	developed	develop	VERB
iajs-2963	19	8	the	the	DET
iajs-2963	19	9	improved	improve	VERB
iajs-2963	19	10	runge	runge	NOUN
iajs-2963	19	11	-	-	PUNCT
iajs-2963	19	12	kutta	kutta	NOUN
iajs-2963	19	13	technique	technique	NOUN
iajs-2963	19	14	for	for	ADP
iajs-2963	19	15	solving	solve	VERB
iajs-2963	19	16	first	first	ADJ
iajs-2963	19	17	odes	ode	NOUN
iajs-2963	19	18	using	use	VERB
iajs-2963	19	19	new	new	ADJ
iajs-2963	19	20	terms	term	NOUN
iajs-2963	19	21	𝑘−𝑖	𝑘−𝑖	NOUN
iajs-2963	19	22	taking	take	VERB
iajs-2963	19	23	the	the	DET
iajs-2963	19	24	values	value	NOUN
iajs-2963	19	25	of	of	ADP
iajs-2963	19	26	𝑘𝑖	𝑘𝑖	NOUN
iajs-2963	19	27	,	,	PUNCT
iajs-2963	19	28	𝑖	𝑖	X
iajs-2963	19	29	≥	≥	NOUN
iajs-2963	19	30	2	2	NUM
iajs-2963	19	31	from	from	ADP
iajs-2963	19	32	earlier	early	ADJ
iajs-2963	19	33	stages	stage	NOUN
iajs-2963	19	34	..	..	PUNCT
iajs-2963	19	35	another	another	DET
iajs-2963	19	36	choice	choice	NOUN
iajs-2963	19	37	for	for	ADP
iajs-2963	19	38	coming	come	VERB
iajs-2963	19	39	up	up	ADP
iajs-2963	19	40	with	with	ADP
iajs-2963	19	41	approaches	approach	NOUN
iajs-2963	19	42	to	to	PART
iajs-2963	19	43	solve	solve	VERB
iajs-2963	19	44	the	the	DET
iajs-2963	19	45	oscillatory	oscillatory	ADJ
iajs-2963	19	46	odes	ode	NOUN
iajs-2963	19	47	is	be	AUX
iajs-2963	19	48	the	the	DET
iajs-2963	19	49	trigonometrically	trigonometrically	ADV
iajs-2963	19	50	-	-	PUNCT
iajs-2963	19	51	fitted	fit	VERB
iajs-2963	19	52	approach	approach	NOUN
iajs-2963	19	53	.	.	PUNCT
iajs-2963	20	1	these	these	DET
iajs-2963	20	2	techniques	technique	NOUN
iajs-2963	20	3	are	be	AUX
iajs-2963	20	4	an	an	DET
iajs-2963	20	5	improved	improved	ADJ
iajs-2963	20	6	version	version	NOUN
iajs-2963	20	7	of	of	ADP
iajs-2963	20	8	any	any	DET
iajs-2963	20	9	earlier	early	ADJ
iajs-2963	20	10	techniques	technique	NOUN
iajs-2963	20	11	.	.	PUNCT
iajs-2963	21	1	in	in	ADP
iajs-2963	21	2	2019	2019	NUM
iajs-2963	21	3	,	,	PUNCT
iajs-2963	21	4	[	[	X
iajs-2963	21	5	5	5	NUM
iajs-2963	21	6	]	]	PUNCT
iajs-2963	21	7	developed	develop	VERB
iajs-2963	21	8	trigonometrically	trigonometrically	ADV
iajs-2963	21	9	-	-	PUNCT
iajs-2963	21	10	fitted	fit	VERB
iajs-2963	21	11	sixth	sixth	ADJ
iajs-2963	21	12	-	-	PUNCT
iajs-2963	21	13	order	order	NOUN
iajs-2963	21	14	twoderivative	twoderivative	ADJ
iajs-2963	21	15	runge	runge	NOUN
iajs-2963	21	16	-	-	PUNCT
iajs-2963	21	17	kutta	kutta	NOUN
iajs-2963	21	18	method	method	NOUN
iajs-2963	21	19	for	for	ADP
iajs-2963	21	20	solving	solve	VERB
iajs-2963	21	21	oscillatory	oscillatory	ADJ
iajs-2963	21	22	problems	problem	NOUN
iajs-2963	21	23	.	.	PUNCT
iajs-2963	22	1	in	in	ADP
iajs-2963	22	2	2021	2021	NUM
iajs-2963	22	3	,	,	PUNCT
iajs-2963	22	4	[	[	X
iajs-2963	22	5	6	6	NUM
iajs-2963	22	6	]	]	PUNCT
iajs-2963	22	7	derived	derive	VERB
iajs-2963	22	8	the	the	DET
iajs-2963	22	9	fourth	fourth	ADJ
iajs-2963	22	10	and	and	CCONJ
iajs-2963	22	11	fifth	fifth	ADJ
iajs-2963	22	12	-	-	PUNCT
iajs-2963	22	13	order	order	NOUN
iajs-2963	22	14	modified	modify	VERB
iajs-2963	22	15	runge	runge	NOUN
iajs-2963	22	16	-	-	PUNCT
iajs-2963	22	17	kutta	kutta	NOUN
iajs-2963	22	18	method	method	NOUN
iajs-2963	22	19	to	to	PART
iajs-2963	22	20	resolve	resolve	VERB
iajs-2963	22	21	oscillatory	oscillatory	ADJ
iajs-2963	22	22	problems	problem	NOUN
iajs-2963	22	23	using	use	VERB
iajs-2963	22	24	phase	phase	NOUN
iajs-2963	22	25	-	-	PUNCT
iajs-2963	22	26	lag	lag	NOUN
iajs-2963	22	27	properties	property	NOUN
iajs-2963	22	28	.	.	PUNCT
iajs-2963	23	1	recently	recently	ADV
iajs-2963	23	2	,	,	PUNCT
iajs-2963	23	3	[	[	X
iajs-2963	23	4	7	7	X
iajs-2963	23	5	]	]	PUNCT
iajs-2963	23	6	derived	derive	VERB
iajs-2963	23	7	the	the	DET
iajs-2963	23	8	trigonometrically	trigonometrically	ADV
iajs-2963	23	9	-	-	PUNCT
iajs-2963	23	10	fitted	fit	VERB
iajs-2963	23	11	third	third	ADJ
iajs-2963	23	12	-	-	PUNCT
iajs-2963	23	13	order	order	NOUN
iajs-2963	23	14	improved	improve	VERB
iajs-2963	23	15	runge	runge	NOUN
iajs-2963	23	16	-	-	PUNCT
iajs-2963	23	17	kutta	kutta	NOUN
iajs-2963	23	18	method	method	NOUN
iajs-2963	23	19	for	for	ADP
iajs-2963	23	20	solving	solve	VERB
iajs-2963	23	21	oscillatory	oscillatory	ADJ
iajs-2963	23	22	problems	problem	NOUN
iajs-2963	23	23	.	.	PUNCT
iajs-2963	24	1	this	this	DET
iajs-2963	24	2	paper	paper	NOUN
iajs-2963	24	3	aims	aim	VERB
iajs-2963	24	4	to	to	PART
iajs-2963	24	5	develop	develop	VERB
iajs-2963	24	6	the	the	DET
iajs-2963	24	7	fourth	fourth	ADJ
iajs-2963	24	8	-	-	PUNCT
iajs-2963	24	9	order	order	NOUN
iajs-2963	24	10	irk	irk	NOUN
iajs-2963	24	11	method	method	NOUN
iajs-2963	24	12	called	call	VERB
iajs-2963	24	13	trigonometrically	trigonometrically	ADV
iajs-2963	24	14	fitted	fit	VERB
iajs-2963	24	15	improved	improve	VERB
iajs-2963	24	16	runge	runge	NOUN
iajs-2963	24	17	-	-	PUNCT
iajs-2963	24	18	kutta	kutta	NOUN
iajs-2963	24	19	(	(	PUNCT
iajs-2963	24	20	tfirk4	tfirk4	NOUN
iajs-2963	24	21	)	)	PUNCT
iajs-2963	24	22	to	to	PART
iajs-2963	24	23	solve	solve	VERB
iajs-2963	24	24	a	a	DET
iajs-2963	24	25	system	system	NOUN
iajs-2963	24	26	of	of	ADP
iajs-2963	24	27	first	first	ADJ
iajs-2963	24	28	-	-	PUNCT
iajs-2963	24	29	order	order	NOUN
iajs-2963	24	30	odes	ode	NOUN
iajs-2963	24	31	with	with	ADP
iajs-2963	24	32	oscillatory	oscillatory	ADJ
iajs-2963	24	33	solutions	solution	NOUN
iajs-2963	24	34	.	.	PUNCT
iajs-2963	25	1	numerical	numerical	ADJ
iajs-2963	25	2	experiments	experiment	NOUN
iajs-2963	25	3	demonstrate	demonstrate	VERB
iajs-2963	25	4	the	the	DET
iajs-2963	25	5	accuracy	accuracy	NOUN
iajs-2963	25	6	of	of	ADP
iajs-2963	25	7	the	the	DET
iajs-2963	25	8	newly	newly	ADV
iajs-2963	25	9	proposed	propose	VERB
iajs-2963	25	10	method	method	NOUN
iajs-2963	25	11	over	over	ADP
iajs-2963	25	12	other	other	ADJ
iajs-2963	25	13	methods	method	NOUN
iajs-2963	25	14	.	.	PUNCT
iajs-2963	26	1	a	a	DET
iajs-2963	26	2	proposed	propose	VERB
iajs-2963	26	3	tfirk	tfirk	NOUN
iajs-2963	26	4	technique	technique	NOUN
iajs-2963	26	5	derivation	derivation	NOUN
iajs-2963	26	6	is	be	AUX
iajs-2963	26	7	presented	present	VERB
iajs-2963	26	8	in	in	ADP
iajs-2963	26	9	section	section	NOUN
iajs-2963	26	10	2	2	NUM
iajs-2963	26	11	.	.	PUNCT
iajs-2963	27	1	a	a	DET
iajs-2963	27	2	numerical	numerical	ADJ
iajs-2963	27	3	test	test	NOUN
iajs-2963	27	4	and	and	CCONJ
iajs-2963	27	5	comparison	comparison	NOUN
iajs-2963	27	6	with	with	ADP
iajs-2963	27	7	different	different	ADJ
iajs-2963	27	8	approaches	approach	NOUN
iajs-2963	27	9	are	be	AUX
iajs-2963	27	10	discussed	discuss	VERB
iajs-2963	27	11	in	in	ADP
iajs-2963	27	12	section	section	NOUN
iajs-2963	27	13	3	3	NUM
iajs-2963	27	14	to	to	PART
iajs-2963	27	15	show	show	VERB
iajs-2963	27	16	the	the	DET
iajs-2963	27	17	efficiency	efficiency	NOUN
iajs-2963	27	18	of	of	ADP
iajs-2963	27	19	the	the	DET
iajs-2963	27	20	tfirk4	tfirk4	PROPN
iajs-2963	27	21	method	method	NOUN
iajs-2963	27	22	.	.	PUNCT
iajs-2963	28	1	section	section	NOUN
iajs-2963	28	2	4	4	NUM
iajs-2963	28	3	contains	contain	VERB
iajs-2963	28	4	the	the	DET
iajs-2963	28	5	discussion	discussion	NOUN
iajs-2963	28	6	and	and	CCONJ
iajs-2963	28	7	conclusion	conclusion	NOUN
iajs-2963	28	8	of	of	ADP
iajs-2963	28	9	this	this	DET
iajs-2963	28	10	paper	paper	NOUN
iajs-2963	28	11	.	.	PUNCT
iajs-2963	29	1	2	2	X
iajs-2963	29	2	.	.	X
iajs-2963	29	3	the	the	DET
iajs-2963	29	4	derivation	derivation	NOUN
iajs-2963	29	5	of	of	ADP
iajs-2963	29	6	tfirk4	tfirk4	PROPN
iajs-2963	29	7	method	method	NOUN
iajs-2963	29	8	the	the	DET
iajs-2963	29	9	improved	improved	ADJ
iajs-2963	29	10	runge	runge	NOUN
iajs-2963	29	11	-	-	PUNCT
iajs-2963	29	12	kutta	kutta	NOUN
iajs-2963	29	13	(	(	PUNCT
iajs-2963	29	14	irk	irk	NOUN
iajs-2963	29	15	)	)	PUNCT
iajs-2963	29	16	method	method	NOUN
iajs-2963	29	17	for	for	ADP
iajs-2963	29	18	solving	solve	VERB
iajs-2963	29	19	equation	equation	NOUN
iajs-2963	29	20	(	(	PUNCT
iajs-2963	29	21	1	1	X
iajs-2963	29	22	)	)	PUNCT
iajs-2963	29	23	has	have	VERB
iajs-2963	29	24	the	the	DET
iajs-2963	29	25	following	follow	VERB
iajs-2963	29	26	form	form	NOUN
iajs-2963	29	27	:	:	PUNCT
iajs-2963	29	28	[	[	X
iajs-2963	29	29	4	4	X
iajs-2963	29	30	]	]	PUNCT
iajs-2963	29	31	𝑢𝑛+1	𝑢𝑛+1	NUM
iajs-2963	29	32	′	′	NUM
iajs-2963	29	33	=	=	PUNCT
iajs-2963	29	34	𝑢𝑛	𝑢𝑛	NOUN
iajs-2963	29	35	+	+	CCONJ
iajs-2963	29	36	ℎ(𝑏1𝑘1	ℎ(𝑏1𝑘1	ADP
iajs-2963	29	37	−	−	PROPN
iajs-2963	29	38	𝑏−1𝑘−1	𝑏−1𝑘−1	PROPN
iajs-2963	30	1	+	+	CCONJ
iajs-2963	30	2	∑	∑	PROPN
iajs-2963	30	3	𝑏𝑖(𝑘𝑖	𝑏𝑖(𝑘𝑖	NOUN
iajs-2963	30	4	−	−	NOUN
iajs-2963	30	5	𝑘−𝑖),𝑠	𝑘−𝑖),𝑠	NOUN
iajs-2963	30	6	𝑖=2	𝑖=2	X
iajs-2963	30	7	(	(	PUNCT
iajs-2963	30	8	2	2	X
iajs-2963	30	9	)	)	PUNCT
iajs-2963	30	10	𝑘1	𝑘1	NOUN
iajs-2963	30	11	=	=	SYM
iajs-2963	30	12	𝑓(𝑡𝑛	𝑓(𝑡𝑛	NOUN
iajs-2963	30	13	,	,	PUNCT
iajs-2963	30	14	𝑢𝑛	𝑢𝑛	NOUN
iajs-2963	30	15	)	)	PUNCT
iajs-2963	30	16	,	,	PUNCT
iajs-2963	30	17	(	(	PUNCT
iajs-2963	30	18	3	3	X
iajs-2963	30	19	)	)	PUNCT
iajs-2963	30	20	𝑘−1	𝑘−1	PROPN
iajs-2963	30	21	=	=	SYM
iajs-2963	30	22	𝑓(𝑡𝑛−1	𝑓(𝑡𝑛−1	NOUN
iajs-2963	30	23	,	,	PUNCT
iajs-2963	30	24	𝑢𝑛−1	𝑢𝑛−1	NOUN
iajs-2963	30	25	)	)	PUNCT
iajs-2963	30	26	,	,	PUNCT
iajs-2963	30	27	(	(	PUNCT
iajs-2963	30	28	4	4	X
iajs-2963	30	29	)	)	PUNCT
iajs-2963	30	30	𝑘𝑖	𝑘𝑖	NOUN
iajs-2963	30	31	=	=	SYM
iajs-2963	30	32	𝑓(𝑡𝑛	𝑓(𝑡𝑛	ADJ
iajs-2963	30	33	+	+	CCONJ
iajs-2963	30	34	𝑐𝑖ℎ	𝑐𝑖ℎ	NOUN
iajs-2963	30	35	,	,	PUNCT
iajs-2963	30	36	𝑢𝑛	𝑢𝑛	NOUN
iajs-2963	30	37	+	+	CCONJ
iajs-2963	30	38	ℎ	ℎ	PROPN
iajs-2963	30	39	∑	∑	PUNCT
iajs-2963	30	40	𝑎𝑖𝑗𝑘𝑗),𝑖−1	𝑎𝑖𝑗𝑘𝑗),𝑖−1	NOUN
iajs-2963	30	41	𝑗=1	𝑗=1	PROPN
iajs-2963	30	42	(	(	PUNCT
iajs-2963	30	43	5	5	X
iajs-2963	30	44	)	)	PUNCT
iajs-2963	30	45	𝑘−𝑖	𝑘−𝑖	NOUN
iajs-2963	30	46	=	=	PUNCT
iajs-2963	30	47	𝑓(𝑡𝑛−1	𝑓(𝑡𝑛−1	PROPN
iajs-2963	31	1	+	+	CCONJ
iajs-2963	31	2	𝑐𝑖ℎ	𝑐𝑖ℎ	NOUN
iajs-2963	31	3	,	,	PUNCT
iajs-2963	31	4	𝑢𝑛−1	𝑢𝑛−1	NOUN
iajs-2963	31	5	+	+	CCONJ
iajs-2963	31	6	ℎ	ℎ	PROPN
iajs-2963	31	7	∑	∑	PROPN
iajs-2963	31	8	𝑎𝑖𝑗𝑘−𝑗).𝑖−1	𝑎𝑖𝑗𝑘−𝑗).𝑖−1	PROPN
iajs-2963	31	9	𝑗=1	𝑗=1	PROPN
iajs-2963	31	10	(	(	PUNCT
iajs-2963	31	11	6	6	NUM
iajs-2963	31	12	)	)	PUNCT
iajs-2963	31	13	where	where	SCONJ
iajs-2963	31	14	𝑐𝑖	𝑐𝑖	NOUN
iajs-2963	31	15	,	,	PUNCT
iajs-2963	31	16	𝑏𝑖	𝑏𝑖	ADP
iajs-2963	31	17	,	,	PUNCT
iajs-2963	31	18	𝑏−1	𝑏−1	PROPN
iajs-2963	31	19	,	,	PUNCT
iajs-2963	31	20	and	and	CCONJ
iajs-2963	31	21	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-2963	31	22	are	be	AUX
iajs-2963	31	23	real	real	ADJ
iajs-2963	31	24	numbers	number	NOUN
iajs-2963	31	25	and	and	CCONJ
iajs-2963	31	26	𝑖	𝑖	SYM
iajs-2963	31	27	,	,	PUNCT
iajs-2963	31	28	𝑗	𝑗	NOUN
iajs-2963	31	29	=	=	SYM
iajs-2963	31	30	1,2	1,2	NUM
iajs-2963	31	31	,	,	PUNCT
iajs-2963	31	32	…	…	PUNCT
iajs-2963	31	33	,	,	PUNCT
iajs-2963	31	34	𝑠.	𝑠.	PROPN
iajs-2963	31	35	irk	irk	NOUN
iajs-2963	31	36	method	method	NOUN
iajs-2963	31	37	(	(	PUNCT
iajs-2963	31	38	2)-(6	2)-(6	NUM
iajs-2963	31	39	)	)	PUNCT
iajs-2963	31	40	can	can	AUX
iajs-2963	31	41	be	be	AUX
iajs-2963	31	42	expressed	express	VERB
iajs-2963	31	43	using	use	VERB
iajs-2963	31	44	the	the	DET
iajs-2963	31	45	following	follow	VERB
iajs-2963	31	46	butcher	butcher	NOUN
iajs-2963	31	47	tableau	tableau	PROPN
iajs-2963	31	48	(	(	PUNCT
iajs-2963	31	49	see	see	VERB
iajs-2963	31	50	table	table	NOUN
iajs-2963	31	51	1	1	NUM
iajs-2963	31	52	):	):	PUNCT
iajs-2963	31	53	table	table	NOUN
iajs-2963	31	54	1	1	NUM
iajs-2963	31	55	.	.	PUNCT
iajs-2963	32	1	𝑠	𝑠	AUX
iajs-2963	32	2	−	−	PROPN
iajs-2963	32	3	stages	stage	NOUN
iajs-2963	32	4	irk	irk	VERB
iajs-2963	32	5	method	method	NOUN
iajs-2963	32	6	0	0	NUM
iajs-2963	32	7	𝑐2	𝑐2	NOUN
iajs-2963	32	8	𝑎21	𝑎21	NOUN
iajs-2963	32	9	𝑐3	𝑐3	VERB
iajs-2963	32	10	𝑎31	𝑎31	NOUN
iajs-2963	32	11	𝑎32	𝑎32	NOUN
iajs-2963	32	12	.	.	PUNCT
iajs-2963	32	13	.	.	PUNCT
iajs-2963	32	14	.	.	PUNCT
iajs-2963	32	15	.	.	PUNCT
iajs-2963	32	16	.	.	PUNCT
iajs-2963	32	17	.	.	PUNCT
iajs-2963	32	18	.	.	PUNCT
iajs-2963	32	19	.	.	PUNCT
iajs-2963	32	20	.	.	PUNCT
iajs-2963	32	21	.	.	PUNCT
iajs-2963	32	22	.	.	PUNCT
iajs-2963	33	1	.	.	PUNCT
iajs-2963	34	1	𝑐𝑠	𝑐𝑠	VERB
iajs-2963	34	2	𝑎𝑠1	𝑎𝑠1	ADJ
iajs-2963	34	3	𝑎𝑠2	𝑎𝑠2	NOUN
iajs-2963	34	4	…	…	PUNCT
iajs-2963	34	5	𝑎𝑠𝑠−1	𝑎𝑠𝑠−1	NOUN
iajs-2963	34	6	𝑏−1	𝑏−1	PROPN
iajs-2963	34	7	𝑏1	𝑏1	NOUN
iajs-2963	34	8	𝑏2	𝑏2	NOUN
iajs-2963	34	9	…	…	PUNCT
iajs-2963	34	10	𝑏𝑠−1	𝑏𝑠−1	PROPN
iajs-2963	34	11	𝑏𝑠	𝑏𝑠	NOUN
iajs-2963	34	12	ihjpas	ihjpa	VERB
iajs-2963	34	13	.	.	PUNCT
iajs-2963	35	1	36(1)2023	36(1)2023	NUM
iajs-2963	35	2	347	347	NUM
iajs-2963	35	3	following	following	NOUN
iajs-2963	35	4	are	be	AUX
iajs-2963	35	5	the	the	DET
iajs-2963	35	6	four	four	NUM
iajs-2963	35	7	stages	stage	NOUN
iajs-2963	35	8	of	of	ADP
iajs-2963	35	9	the	the	DET
iajs-2963	35	10	irk4	irk4	PROPN
iajs-2963	35	11	method	method	NOUN
iajs-2963	35	12	in	in	ADP
iajs-2963	35	13	its	its	PRON
iajs-2963	35	14	general	general	ADJ
iajs-2963	35	15	form	form	NOUN
iajs-2963	35	16	:	:	PUNCT
iajs-2963	35	17	𝑢𝑛+1	𝑢𝑛+1	NUM
iajs-2963	35	18	′	′	NUM
iajs-2963	35	19	=	=	PUNCT
iajs-2963	35	20	𝑢𝑛	𝑢𝑛	NOUN
iajs-2963	36	1	+	+	CCONJ
iajs-2963	36	2	ℎ(𝑏1𝑘1	ℎ(𝑏1𝑘1	ADP
iajs-2963	36	3	−	−	PROPN
iajs-2963	36	4	𝑏−1𝑘−1	𝑏−1𝑘−1	PROPN
iajs-2963	36	5	+	+	NUM
iajs-2963	36	6	𝑏2(𝑘2	𝑏2(𝑘2	VERB
iajs-2963	36	7	−	−	PROPN
iajs-2963	36	8	𝑘−2	𝑘−2	PROPN
iajs-2963	36	9	)	)	PUNCT
iajs-2963	36	10	+	+	X
iajs-2963	36	11	𝑏3(𝑘3	𝑏3(𝑘3	ADP
iajs-2963	36	12	−	−	PROPN
iajs-2963	36	13	𝑘−3	𝑘−3	PROPN
iajs-2963	36	14	)	)	PUNCT
iajs-2963	36	15	+	+	NUM
iajs-2963	36	16	𝑏4(𝑘4	𝑏4(𝑘4	PROPN
iajs-2963	36	17	−	−	PROPN
iajs-2963	36	18	𝑘−4	𝑘−4	PROPN
iajs-2963	36	19	)	)	PUNCT
iajs-2963	36	20	,	,	PUNCT
iajs-2963	36	21	(	(	PUNCT
iajs-2963	36	22	7	7	X
iajs-2963	36	23	)	)	PUNCT
iajs-2963	36	24	𝑘1	𝑘1	ADJ
iajs-2963	36	25	=	=	PUNCT
iajs-2963	36	26	𝑓(𝑡𝑛	𝑓(𝑡𝑛	NOUN
iajs-2963	36	27	,	,	PUNCT
iajs-2963	36	28	𝑢𝑛	𝑢𝑛	NOUN
iajs-2963	36	29	)	)	PUNCT
iajs-2963	36	30	,	,	PUNCT
iajs-2963	36	31	(	(	PUNCT
iajs-2963	36	32	8)	8)	NUM
iajs-2963	36	33	𝑘−1	𝑘−1	PROPN
iajs-2963	36	34	=	=	SYM
iajs-2963	36	35	𝑓(𝑡𝑛−1	𝑓(𝑡𝑛−1	NOUN
iajs-2963	36	36	,	,	PUNCT
iajs-2963	36	37	𝑢𝑛−1	𝑢𝑛−1	NOUN
iajs-2963	36	38	)	)	PUNCT
iajs-2963	36	39	,	,	PUNCT
iajs-2963	36	40	(	(	PUNCT
iajs-2963	36	41	9	9	X
iajs-2963	36	42	)	)	PUNCT
iajs-2963	36	43	𝑘2	𝑘2	NOUN
iajs-2963	36	44	=	=	NOUN
iajs-2963	36	45	𝑓(𝑡𝑛	𝑓(𝑡𝑛	PROPN
iajs-2963	36	46	+	+	CCONJ
iajs-2963	36	47	𝑐2ℎ	𝑐2ℎ	NOUN
iajs-2963	36	48	,	,	PUNCT
iajs-2963	36	49	𝑢𝑛	𝑢𝑛	NOUN
iajs-2963	36	50	+	+	CCONJ
iajs-2963	36	51	ℎ	ℎ	PROPN
iajs-2963	36	52	𝑎21𝑘1	𝑎21𝑘1	NUM
iajs-2963	36	53	)	)	PUNCT
iajs-2963	36	54	,	,	PUNCT
iajs-2963	36	55	(	(	PUNCT
iajs-2963	36	56	10	10	NUM
iajs-2963	36	57	)	)	PUNCT
iajs-2963	36	58	𝑘−2	𝑘−2	PROPN
iajs-2963	36	59	=	=	SYM
iajs-2963	36	60	𝑓(𝑡𝑛−1	𝑓(𝑡𝑛−1	PROPN
iajs-2963	36	61	+	+	X
iajs-2963	36	62	𝑐2ℎ	𝑐2ℎ	NOUN
iajs-2963	36	63	,	,	PUNCT
iajs-2963	36	64	𝑢𝑛−1	𝑢𝑛−1	NOUN
iajs-2963	36	65	+	+	CCONJ
iajs-2963	36	66	ℎ	ℎ	PROPN
iajs-2963	36	67	𝑎21𝑘−1	𝑎21𝑘−1	NOUN
iajs-2963	36	68	)	)	PUNCT
iajs-2963	36	69	,	,	PUNCT
iajs-2963	36	70	(	(	PUNCT
iajs-2963	36	71	11	11	X
iajs-2963	36	72	)	)	PUNCT
iajs-2963	36	73	𝑘3	𝑘3	NOUN
iajs-2963	36	74	=	=	NOUN
iajs-2963	36	75	𝑓(𝑡𝑛	𝑓(𝑡𝑛	NOUN
iajs-2963	36	76	+	+	CCONJ
iajs-2963	36	77	𝑐3ℎ	𝑐3ℎ	NOUN
iajs-2963	36	78	,	,	PUNCT
iajs-2963	36	79	𝑢𝑛	𝑢𝑛	NOUN
iajs-2963	36	80	+	+	X
iajs-2963	36	81	ℎ	ℎ	PROPN
iajs-2963	36	82	(	(	PUNCT
iajs-2963	36	83	𝑎31𝑘1	𝑎31𝑘1	X
iajs-2963	36	84	+	+	X
iajs-2963	36	85	𝑎32𝑘2	𝑎32𝑘2	NOUN
iajs-2963	36	86	)	)	PUNCT
iajs-2963	36	87	)	)	PUNCT
iajs-2963	36	88	,	,	PUNCT
iajs-2963	36	89	(	(	PUNCT
iajs-2963	36	90	12	12	NUM
iajs-2963	36	91	)	)	PUNCT
iajs-2963	36	92	𝑘−3	𝑘−3	PROPN
iajs-2963	36	93	=	=	SYM
iajs-2963	36	94	𝑓(𝑡𝑛−1	𝑓(𝑡𝑛−1	PROPN
iajs-2963	37	1	+	+	ADP
iajs-2963	37	2	𝑐3ℎ	𝑐3ℎ	NOUN
iajs-2963	37	3	,	,	PUNCT
iajs-2963	37	4	𝑢𝑛−1	𝑢𝑛−1	NOUN
iajs-2963	37	5	+	+	CCONJ
iajs-2963	37	6	ℎ	ℎ	PROPN
iajs-2963	37	7	(	(	PUNCT
iajs-2963	37	8	𝑎31𝑘−1	𝑎31𝑘−1	X
iajs-2963	37	9	+	+	CCONJ
iajs-2963	37	10	𝑎32𝑘−2	𝑎32𝑘−2	NOUN
iajs-2963	37	11	)	)	PUNCT
iajs-2963	37	12	)	)	PUNCT
iajs-2963	37	13	,	,	PUNCT
iajs-2963	37	14	(	(	PUNCT
iajs-2963	37	15	13	13	X
iajs-2963	37	16	)	)	PUNCT
iajs-2963	37	17	𝑘4	𝑘4	NOUN
iajs-2963	37	18	=	=	NOUN
iajs-2963	37	19	𝑓(𝑡𝑛	𝑓(𝑡𝑛	PROPN
iajs-2963	37	20	+	+	X
iajs-2963	37	21	𝑐4ℎ	𝑐4ℎ	NUM
iajs-2963	37	22	,	,	PUNCT
iajs-2963	37	23	𝑢𝑛	𝑢𝑛	NOUN
iajs-2963	37	24	+	+	CCONJ
iajs-2963	37	25	ℎ	ℎ	PROPN
iajs-2963	37	26	(	(	PUNCT
iajs-2963	37	27	𝑎41𝑘1	𝑎41𝑘1	NOUN
iajs-2963	37	28	+	+	CCONJ
iajs-2963	37	29	𝑎42𝑘2	𝑎42𝑘2	NOUN
iajs-2963	37	30	+	+	CCONJ
iajs-2963	37	31	𝑎43𝑘3	𝑎43𝑘3	PROPN
iajs-2963	37	32	)	)	PUNCT
iajs-2963	37	33	)	)	PUNCT
iajs-2963	38	1	,	,	PUNCT
iajs-2963	38	2	(	(	PUNCT
iajs-2963	38	3	14	14	X
iajs-2963	38	4	)	)	PUNCT
iajs-2963	38	5	𝑘−4	𝑘−4	NOUN
iajs-2963	38	6	=	=	NOUN
iajs-2963	38	7	𝑓(𝑡𝑛	𝑓(𝑡𝑛	ADJ
iajs-2963	38	8	+	+	X
iajs-2963	38	9	𝑐4ℎ	𝑐4ℎ	ADJ
iajs-2963	38	10	,	,	PUNCT
iajs-2963	38	11	𝑢𝑛−1	𝑢𝑛−1	NOUN
iajs-2963	38	12	+	+	CCONJ
iajs-2963	38	13	ℎ	ℎ	PROPN
iajs-2963	38	14	(	(	PUNCT
iajs-2963	38	15	𝑎41𝑘−1	𝑎41𝑘−1	X
iajs-2963	38	16	+	+	CCONJ
iajs-2963	38	17	𝑎42𝑘−2	𝑎42𝑘−2	X
iajs-2963	38	18	+	+	NOUN
iajs-2963	38	19	𝑎43𝑘−3	𝑎43𝑘−3	NOUN
iajs-2963	38	20	)	)	PUNCT
iajs-2963	38	21	)	)	PUNCT
iajs-2963	38	22	.	.	PUNCT
iajs-2963	39	1	(	(	PUNCT
iajs-2963	39	2	15	15	X
iajs-2963	39	3	)	)	PUNCT
iajs-2963	39	4	the	the	DET
iajs-2963	39	5	coefficients	coefficient	NOUN
iajs-2963	39	6	of	of	ADP
iajs-2963	39	7	the	the	DET
iajs-2963	39	8	irk4	irk4	PROPN
iajs-2963	39	9	method	method	NOUN
iajs-2963	39	10	in	in	ADP
iajs-2963	39	11	[	[	X
iajs-2963	39	12	4	4	NUM
iajs-2963	39	13	]	]	PUNCT
iajs-2963	39	14	are	be	AUX
iajs-2963	39	15	offered	offer	VERB
iajs-2963	39	16	in	in	ADP
iajs-2963	39	17	table	table	NOUN
iajs-2963	39	18	2	2	NUM
iajs-2963	39	19	:	:	PUNCT
iajs-2963	39	20	table	table	NOUN
iajs-2963	39	21	2	2	NUM
iajs-2963	39	22	.	.	PUNCT
iajs-2963	39	23	irk4	irk4	PROPN
iajs-2963	39	24	method	method	NOUN
iajs-2963	39	25	applying	apply	VERB
iajs-2963	39	26	the	the	DET
iajs-2963	39	27	exponential	exponential	ADJ
iajs-2963	39	28	function	function	NOUN
iajs-2963	39	29	into	into	ADP
iajs-2963	39	30	the	the	DET
iajs-2963	39	31	irk4	irk4	PROPN
iajs-2963	39	32	method	method	NOUN
iajs-2963	39	33	(	(	PUNCT
iajs-2963	39	34	7)-(15	7)-(15	NOUN
iajs-2963	39	35	)	)	PUNCT
iajs-2963	39	36	,	,	PUNCT
iajs-2963	39	37	the	the	DET
iajs-2963	39	38	trigonometrically	trigonometrically	ADV
iajs-2963	39	39	fitting	fitting	ADJ
iajs-2963	39	40	approach	approach	NOUN
iajs-2963	39	41	is	be	AUX
iajs-2963	39	42	implemented	implement	VERB
iajs-2963	39	43	by	by	ADP
iajs-2963	39	44	allow	allow	VERB
iajs-2963	39	45	:	:	PUNCT
iajs-2963	39	46	𝑢n	𝑢n	ADV
iajs-2963	39	47	=	=	SYM
iajs-2963	39	48	𝑢(𝑡n	𝑢(𝑡n	PROPN
iajs-2963	39	49	)	)	PUNCT
iajs-2963	40	1	=	=	SYM
iajs-2963	40	2	eiω𝑡n	eiω𝑡n	NOUN
iajs-2963	40	3	,	,	PUNCT
iajs-2963	40	4	(	(	PUNCT
iajs-2963	40	5	16	16	NUM
iajs-2963	40	6	)	)	PUNCT
iajs-2963	40	7	𝑢n+1	𝑢n+1	X
iajs-2963	40	8	=	=	SYM
iajs-2963	40	9	𝑢(𝑡n+1	𝑢(𝑡n+1	X
iajs-2963	40	10	)	)	PUNCT
iajs-2963	40	11	=	=	SYM
iajs-2963	40	12	eiω(𝑡n+ℎ	eiω(𝑡n+ℎ	NOUN
iajs-2963	40	13	)	)	PUNCT
iajs-2963	40	14	,	,	PUNCT
iajs-2963	40	15	(	(	PUNCT
iajs-2963	40	16	17	17	NUM
iajs-2963	40	17	)	)	PUNCT
iajs-2963	41	1	𝑢n−1	𝑢n−1	PROPN
iajs-2963	41	2	=	=	SYM
iajs-2963	41	3	𝑢(𝑡n−1	𝑢(𝑡n−1	X
iajs-2963	41	4	)	)	PUNCT
iajs-2963	41	5	=	=	SYM
iajs-2963	41	6	eiω(𝑡n−ℎ	eiω(𝑡n−ℎ	PROPN
iajs-2963	41	7	)	)	PUNCT
iajs-2963	41	8	.	.	PUNCT
iajs-2963	42	1	(	(	PUNCT
iajs-2963	42	2	18	18	NUM
iajs-2963	42	3	)	)	PUNCT
iajs-2963	42	4	using	use	VERB
iajs-2963	42	5	euler	euler	NOUN
iajs-2963	42	6	formula	formula	NOUN
iajs-2963	42	7	𝑒𝑖𝑣	𝑒𝑖𝑣	NOUN
iajs-2963	42	8	=	=	SYM
iajs-2963	42	9	cos(𝑣	cos(𝑣	PROPN
iajs-2963	42	10	)	)	PUNCT
iajs-2963	42	11	+	+	PUNCT
iajs-2963	42	12	𝑖𝑠𝑖𝑛(𝑣	𝑖𝑠𝑖𝑛(𝑣	NOUN
iajs-2963	42	13	)	)	PUNCT
iajs-2963	42	14	,	,	PUNCT
iajs-2963	42	15	and	and	CCONJ
iajs-2963	42	16	substituting	substitute	VERB
iajs-2963	42	17	the	the	DET
iajs-2963	42	18	equations	equation	NOUN
iajs-2963	42	19	(	(	PUNCT
iajs-2963	42	20	16)-(18	16)-(18	NOUN
iajs-2963	42	21	)	)	PUNCT
iajs-2963	42	22	into	into	ADP
iajs-2963	42	23	equation	equation	NOUN
iajs-2963	42	24	irk4	irk4	PROPN
iajs-2963	42	25	method	method	NOUN
iajs-2963	42	26	(	(	PUNCT
iajs-2963	42	27	7)-(15	7)-(15	NOUN
iajs-2963	42	28	)	)	PUNCT
iajs-2963	42	29	,	,	PUNCT
iajs-2963	42	30	we	we	PRON
iajs-2963	42	31	get	get	VERB
iajs-2963	42	32	:	:	PUNCT
iajs-2963	42	33	𝑒𝑖𝑣	𝑒𝑖𝑣	ADJ
iajs-2963	42	34	=	=	SYM
iajs-2963	42	35	cos(𝑣	cos(𝑣	PROPN
iajs-2963	42	36	)	)	PUNCT
iajs-2963	42	37	+	+	PUNCT
iajs-2963	43	1	𝑖𝑠𝑖𝑛(𝑣	𝑖𝑠𝑖𝑛(𝑣	NOUN
iajs-2963	43	2	)	)	PUNCT
iajs-2963	43	3	=	=	SYM
iajs-2963	44	1	1	1	NUM
iajs-2963	44	2	−	−	PROPN
iajs-2963	44	3	𝑣𝑏−1	𝑣𝑏−1	PROPN
iajs-2963	44	4	sin(𝑣	sin(𝑣	PROPN
iajs-2963	44	5	)	)	PUNCT
iajs-2963	44	6	−	−	NOUN
iajs-2963	45	1	𝑣2𝑏2	𝑣2𝑏2	X
iajs-2963	45	2	𝑎21	𝑎21	PROPN
iajs-2963	45	3	−	−	PROPN
iajs-2963	45	4	𝑣𝑏2	𝑣𝑏2	PROPN
iajs-2963	45	5	sin(𝑣	sin(𝑣	PROPN
iajs-2963	45	6	)	)	PUNCT
iajs-2963	45	7	−	−	PUNCT
iajs-2963	45	8	𝑣2𝑏3	𝑣2𝑏3	PUNCT
iajs-2963	45	9	𝑎31	𝑎31	NOUN
iajs-2963	45	10	+	+	PROPN
iajs-2963	45	11	𝑣2	𝑣2	PROPN
iajs-2963	45	12	𝑏2𝑎21	𝑏2𝑎21	PROPN
iajs-2963	45	13	cos	cos	PROPN
iajs-2963	45	14	(	(	PUNCT
iajs-2963	45	15	𝑣	𝑣	NOUN
iajs-2963	45	16	)	)	PUNCT
iajs-2963	45	17	−	−	PRON
iajs-2963	45	18	𝑣2𝑏3	𝑣2𝑏3	PUNCT
iajs-2963	45	19	𝑎32	𝑎32	NOUN
iajs-2963	45	20	−	−	PROPN
iajs-2963	45	21	𝑣𝑏3	𝑣𝑏3	NOUN
iajs-2963	45	22	sin(𝑣	sin(𝑣	NOUN
iajs-2963	45	23	)	)	PUNCT
iajs-2963	46	1	+	+	CCONJ
iajs-2963	46	2	𝑣2	𝑣2	PROPN
iajs-2963	46	3	𝑏3𝑎31	𝑏3𝑎31	ADJ
iajs-2963	46	4	cos	cos	PROPN
iajs-2963	46	5	(	(	PUNCT
iajs-2963	46	6	𝑣	𝑣	NOUN
iajs-2963	46	7	)	)	PUNCT
iajs-2963	46	8	−	−	NOUN
iajs-2963	46	9	𝑣2𝑏4	𝑣2𝑏4	SYM
iajs-2963	46	10	𝑎41	𝑎41	NOUN
iajs-2963	46	11	+	+	PROPN
iajs-2963	46	12	𝑣2	𝑣2	PROPN
iajs-2963	46	13	𝑏3𝑎32	𝑏3𝑎32	PUNCT
iajs-2963	46	14	cos(𝑣	cos(𝑣	PROPN
iajs-2963	46	15	)	)	PUNCT
iajs-2963	47	1	+	+	SYM
iajs-2963	47	2	𝑣3	𝑣3	ADJ
iajs-2963	47	3	𝑏3𝑎32𝑎21	𝑏3𝑎32𝑎21	PROPN
iajs-2963	47	4	sin(𝑣	sin(𝑣	PROPN
iajs-2963	47	5	)	)	PUNCT
iajs-2963	47	6	−	−	PROPN
iajs-2963	47	7	𝑣2	𝑣2	PROPN
iajs-2963	47	8	𝑏4𝑎42	𝑏4𝑎42	PROPN
iajs-2963	47	9	−	−	PROPN
iajs-2963	47	10	𝑣2	𝑣2	PROPN
iajs-2963	47	11	𝑏4𝑎43	𝑏4𝑎43	NOUN
iajs-2963	47	12	−	−	PROPN
iajs-2963	47	13	𝑣𝑏4	𝑣𝑏4	ADV
iajs-2963	47	14	sin(𝑣	sin(𝑣	NOUN
iajs-2963	47	15	)	)	PUNCT
iajs-2963	48	1	+	+	NOUN
iajs-2963	48	2	𝑣4	𝑣4	NOUN
iajs-2963	48	3	𝑏4𝑎43𝑎32𝑎21	𝑏4𝑎43𝑎32𝑎21	ADP
iajs-2963	48	4	+	+	NUM
iajs-2963	48	5	𝑣2	𝑣2	PROPN
iajs-2963	48	6	𝑏4𝑎41	𝑏4𝑎41	PROPN
iajs-2963	48	7	cos(𝑣	cos(𝑣	PROPN
iajs-2963	48	8	)	)	PUNCT
iajs-2963	48	9	+	+	CCONJ
iajs-2963	48	10	𝑣2	𝑣2	PROPN
iajs-2963	48	11	𝑏4𝑎42	𝑏4𝑎42	PROPN
iajs-2963	48	12	cos(𝑣	cos(𝑣	PROPN
iajs-2963	48	13	)	)	PUNCT
iajs-2963	49	1	+	+	CCONJ
iajs-2963	49	2	𝑣3	𝑣3	ADJ
iajs-2963	49	3	𝑏4𝑎42𝑎21	𝑏4𝑎42𝑎21	PROPN
iajs-2963	49	4	sin(𝑣	sin(𝑣	PROPN
iajs-2963	49	5	)	)	PUNCT
iajs-2963	49	6	0	0	NUM
iajs-2963	49	7	1	1	NUM
iajs-2963	49	8	5	5	NUM
iajs-2963	49	9	1	1	NUM
iajs-2963	49	10	5	5	NUM
iajs-2963	49	11	3	3	NUM
iajs-2963	49	12	5	5	NUM
iajs-2963	49	13	0	0	NUM
iajs-2963	49	14	3	3	NUM
iajs-2963	49	15	5	5	NUM
iajs-2963	49	16	4	4	NUM
iajs-2963	49	17	5	5	NUM
iajs-2963	49	18	2	2	NUM
iajs-2963	49	19	15	15	NUM
iajs-2963	49	20	4	4	NUM
iajs-2963	49	21	25	25	NUM
iajs-2963	49	22	38	38	NUM
iajs-2963	49	23	75	75	NUM
iajs-2963	49	24	19	19	NUM
iajs-2963	49	25	288	288	NUM
iajs-2963	49	26	307	307	NUM
iajs-2963	49	27	288	288	NUM
iajs-2963	49	28	−	−	NUM
iajs-2963	49	29	25	25	NUM
iajs-2963	49	30	144	144	NUM
iajs-2963	49	31	25	25	NUM
iajs-2963	49	32	144	144	NUM
iajs-2963	49	33	125	125	NUM
iajs-2963	49	34	288	288	NUM
iajs-2963	49	35	ihjpas	ihjpa	NOUN
iajs-2963	49	36	.	.	PUNCT
iajs-2963	50	1	36(1)2023	36(1)2023	NUM
iajs-2963	50	2	348	348	NUM
iajs-2963	50	3	+	+	NOUN
iajs-2963	50	4	𝑣2	𝑣2	PROPN
iajs-2963	50	5	𝑏4𝑎43	𝑏4𝑎43	ADV
iajs-2963	50	6	cos(𝑣	cos(𝑣	PROPN
iajs-2963	50	7	)	)	PUNCT
iajs-2963	51	1	+	+	CCONJ
iajs-2963	51	2	𝑣3	𝑣3	ADJ
iajs-2963	51	3	𝑏4𝑎43𝑎31	𝑏4𝑎43𝑎31	NUM
iajs-2963	51	4	sin(𝑣	sin(𝑣	NUM
iajs-2963	51	5	)	)	PUNCT
iajs-2963	52	1	+	+	CCONJ
iajs-2963	52	2	𝑣3	𝑣3	ADV
iajs-2963	52	3	𝑏4𝑎43𝑎32	𝑏4𝑎43𝑎32	PROPN
iajs-2963	52	4	sin(𝑣	sin(𝑣	PROPN
iajs-2963	52	5	)	)	PUNCT
iajs-2963	52	6	−𝑣3	−𝑣3	PROPN
iajs-2963	52	7	𝑏4𝑎43𝑎32	𝑏4𝑎43𝑎32	VERB
iajs-2963	52	8	𝑎21	𝑎21	PROPN
iajs-2963	52	9	cos(𝑣	cos(𝑣	PROPN
iajs-2963	52	10	)	)	PUNCT
iajs-2963	52	11	+	+	NUM
iajs-2963	52	12	𝑖𝑣𝑏1	𝑖𝑣𝑏1	NOUN
iajs-2963	52	13	−	−	PROPN
iajs-2963	52	14	𝑖𝑣𝑏−1	𝑖𝑣𝑏−1	PUNCT
iajs-2963	52	15	cos(𝑣	cos(𝑣	PROPN
iajs-2963	52	16	)	)	PUNCT
iajs-2963	52	17	+	+	CCONJ
iajs-2963	52	18	𝑖𝑣𝑏2	𝑖𝑣𝑏2	PROPN
iajs-2963	52	19	−	−	PROPN
iajs-2963	52	20	𝑖𝑣𝑏2	𝑖𝑣𝑏2	PROPN
iajs-2963	52	21	cos(𝑣	cos(𝑣	PROPN
iajs-2963	52	22	)	)	PUNCT
iajs-2963	53	1	+	+	NOUN
iajs-2963	53	2	𝑖𝑣𝑏3	𝑖𝑣𝑏3	ADJ
iajs-2963	53	3	−	−	PROPN
iajs-2963	53	4	𝑖𝑣2𝑏2𝑎21	𝑖𝑣2𝑏2𝑎21	PUNCT
iajs-2963	53	5	sin(𝑣	sin(𝑣	PROPN
iajs-2963	53	6	)	)	PUNCT
iajs-2963	53	7	−	−	NOUN
iajs-2963	54	1	𝑖𝑣3	𝑖𝑣3	PROPN
iajs-2963	54	2	𝑏3𝑎32𝑎21	𝑏3𝑎32𝑎21	PROPN
iajs-2963	54	3	−	−	PROPN
iajs-2963	54	4	𝑖𝑣𝑏3	𝑖𝑣𝑏3	PROPN
iajs-2963	54	5	cos(𝑣	cos(𝑣	PROPN
iajs-2963	54	6	)	)	PUNCT
iajs-2963	54	7	−	−	PROPN
iajs-2963	54	8	𝑖𝑣2𝑏3𝑎31	𝑖𝑣2𝑏3𝑎31	PUNCT
iajs-2963	54	9	sin(𝑣	sin(𝑣	NOUN
iajs-2963	54	10	)	)	PUNCT
iajs-2963	55	1	+	+	ADJ
iajs-2963	55	2	𝑖𝑣𝑏4	𝑖𝑣𝑏4	ADJ
iajs-2963	55	3	+	+	CCONJ
iajs-2963	55	4	𝑖𝑣3𝑏3𝑎32𝑎21	𝑖𝑣3𝑏3𝑎32𝑎21	PUNCT
iajs-2963	55	5	cos(𝑣	cos(𝑣	PROPN
iajs-2963	55	6	)	)	PUNCT
iajs-2963	55	7	−	−	PROPN
iajs-2963	55	8	𝑖𝑣3𝑏4𝑎42𝑎21	𝑖𝑣3𝑏4𝑎42𝑎21	NUM
iajs-2963	55	9	−	−	PROPN
iajs-2963	56	1	𝑖𝑣3𝑏4𝑎43𝑎31	𝑖𝑣3𝑏4𝑎43𝑎31	NUM
iajs-2963	56	2	−	−	NOUN
iajs-2963	56	3	𝑖𝑣3𝑏4𝑎43𝑎32	𝑖𝑣3𝑏4𝑎43𝑎32	SYM
iajs-2963	56	4	−𝑖𝑣𝑏4	−𝑖𝑣𝑏4	NOUN
iajs-2963	56	5	cos(𝑣	cos(𝑣	PROPN
iajs-2963	56	6	)	)	PUNCT
iajs-2963	56	7	−	−	PROPN
iajs-2963	56	8	𝑖𝑣2𝑏4𝑎41	𝑖𝑣2𝑏4𝑎41	PROPN
iajs-2963	56	9	sin(𝑣	sin(𝑣	PROPN
iajs-2963	56	10	)	)	PUNCT
iajs-2963	56	11	−	−	PROPN
iajs-2963	56	12	𝑖𝑣2𝑏4𝑎42	𝑖𝑣2𝑏4𝑎42	INTJ
iajs-2963	56	13	sin(𝑣	sin(𝑣	PROPN
iajs-2963	56	14	)	)	PUNCT
iajs-2963	56	15	−	−	PROPN
iajs-2963	56	16	𝑖𝑣2𝑏4𝑎43	𝑖𝑣2𝑏4𝑎43	PROPN
iajs-2963	56	17	sin(𝑣	sin(𝑣	PROPN
iajs-2963	56	18	)	)	PUNCT
iajs-2963	57	1	+	+	NOUN
iajs-2963	57	2	𝑖𝑣3𝑏4𝑎42𝑎21cos	𝑖𝑣3𝑏4𝑎42𝑎21cos	NUM
iajs-2963	57	3	(	(	PUNCT
iajs-2963	57	4	𝑣	𝑣	NOUN
iajs-2963	57	5	)	)	PUNCT
iajs-2963	57	6	+	+	NUM
iajs-2963	57	7	𝑖𝑣3𝑏4𝑎43𝑎31cos	𝑖𝑣3𝑏4𝑎43𝑎31cos	X
iajs-2963	57	8	(	(	PUNCT
iajs-2963	57	9	𝑣	𝑣	NOUN
iajs-2963	57	10	)	)	PUNCT
iajs-2963	57	11	+	+	NUM
iajs-2963	57	12	𝑖𝑣3𝑏4𝑎43𝑎32cos	𝑖𝑣3𝑏4𝑎43𝑎32cos	PUNCT
iajs-2963	57	13	(	(	PUNCT
iajs-2963	57	14	𝑣	𝑣	NOUN
iajs-2963	57	15	)	)	PUNCT
iajs-2963	57	16	+	+	PROPN
iajs-2963	57	17	𝑖𝑣4𝑏4𝑎43𝑎32𝑎21	𝑖𝑣4𝑏4𝑎43𝑎32𝑎21	PROPN
iajs-2963	57	18	sin(𝑣	sin(𝑣	PROPN
iajs-2963	57	19	)	)	PUNCT
iajs-2963	57	20	−	−	PROPN
iajs-2963	57	21	𝑖𝑣2𝑏3𝑎32	𝑖𝑣2𝑏3𝑎32	PUNCT
iajs-2963	57	22	sin(𝑣	sin(𝑣	PROPN
iajs-2963	57	23	)	)	PUNCT
iajs-2963	57	24	.	.	PUNCT
iajs-2963	58	1	(	(	PUNCT
iajs-2963	58	2	19	19	NUM
iajs-2963	58	3	)	)	PUNCT
iajs-2963	58	4	where	where	SCONJ
iajs-2963	58	5	𝑣	𝑣	ADP
iajs-2963	58	6	=	=	SYM
iajs-2963	58	7	𝜔ℎ.	𝜔ℎ.	NOUN
iajs-2963	58	8	we	we	PRON
iajs-2963	58	9	obtain	obtain	VERB
iajs-2963	58	10	the	the	DET
iajs-2963	58	11	trigonometrically	trigonometrically	ADV
iajs-2963	58	12	fitting	fitting	ADJ
iajs-2963	58	13	order	order	NOUN
iajs-2963	58	14	conditions	condition	NOUN
iajs-2963	58	15	by	by	ADP
iajs-2963	58	16	equating	equate	VERB
iajs-2963	58	17	the	the	DET
iajs-2963	58	18	real	real	ADJ
iajs-2963	58	19	and	and	CCONJ
iajs-2963	58	20	imaginary	imaginary	ADJ
iajs-2963	58	21	parts	part	NOUN
iajs-2963	58	22	:	:	PUNCT
iajs-2963	58	23	cos(𝑣	cos(𝑣	NUM
iajs-2963	58	24	)	)	PUNCT
iajs-2963	58	25	=	=	SYM
iajs-2963	59	1	1	1	NUM
iajs-2963	59	2	−	−	PROPN
iajs-2963	59	3	𝑣𝑏−1	𝑣𝑏−1	PROPN
iajs-2963	59	4	sin(𝑣	sin(𝑣	PROPN
iajs-2963	59	5	)	)	PUNCT
iajs-2963	59	6	−	−	NOUN
iajs-2963	60	1	𝑣2𝑏2	𝑣2𝑏2	X
iajs-2963	60	2	𝑎21	𝑎21	PROPN
iajs-2963	60	3	−	−	PROPN
iajs-2963	60	4	𝑣𝑏2	𝑣𝑏2	PROPN
iajs-2963	60	5	sin(𝑣	sin(𝑣	PROPN
iajs-2963	60	6	)	)	PUNCT
iajs-2963	60	7	−	−	PROPN
iajs-2963	60	8	𝑣2𝑏3	𝑣2𝑏3	PUNCT
iajs-2963	60	9	𝑎31+𝑣2	𝑎31+𝑣2	NOUN
iajs-2963	60	10	𝑏2𝑎21	𝑏2𝑎21	PROPN
iajs-2963	60	11	cos	cos	PROPN
iajs-2963	60	12	(	(	PUNCT
iajs-2963	60	13	𝑣	𝑣	NOUN
iajs-2963	60	14	)	)	PUNCT
iajs-2963	60	15	−𝑣2𝑏3	−𝑣2𝑏3	PROPN
iajs-2963	60	16	𝑎32	𝑎32	NOUN
iajs-2963	60	17	−	−	PROPN
iajs-2963	60	18	𝑣𝑏3	𝑣𝑏3	NOUN
iajs-2963	60	19	sin(𝑣	sin(𝑣	NOUN
iajs-2963	60	20	)	)	PUNCT
iajs-2963	60	21	+	+	CCONJ
iajs-2963	60	22	𝑣2	𝑣2	PROPN
iajs-2963	60	23	𝑏3𝑎31	𝑏3𝑎31	ADJ
iajs-2963	60	24	cos	cos	PROPN
iajs-2963	60	25	(	(	PUNCT
iajs-2963	60	26	𝑣	𝑣	NOUN
iajs-2963	60	27	)	)	PUNCT
iajs-2963	60	28	−	−	NOUN
iajs-2963	60	29	𝑣2𝑏4	𝑣2𝑏4	SYM
iajs-2963	60	30	𝑎41	𝑎41	NOUN
iajs-2963	60	31	+	+	CCONJ
iajs-2963	60	32	𝑣2	𝑣2	PROPN
iajs-2963	60	33	𝑏3𝑎32	𝑏3𝑎32	PUNCT
iajs-2963	60	34	cos(𝑣	cos(𝑣	PROPN
iajs-2963	60	35	)	)	PUNCT
iajs-2963	61	1	+	+	NOUN
iajs-2963	61	2	𝑣3	𝑣3	ADJ
iajs-2963	61	3	𝑏3𝑎32𝑎21	𝑏3𝑎32𝑎21	NUM
iajs-2963	61	4	sin(𝑣	sin(𝑣	PROPN
iajs-2963	61	5	)	)	PUNCT
iajs-2963	61	6	−	−	PROPN
iajs-2963	61	7	𝑣2	𝑣2	PROPN
iajs-2963	61	8	𝑏4𝑎42	𝑏4𝑎42	PROPN
iajs-2963	61	9	−	−	PROPN
iajs-2963	61	10	𝑣2	𝑣2	PROPN
iajs-2963	61	11	𝑏4𝑎43	𝑏4𝑎43	NOUN
iajs-2963	61	12	−	−	PROPN
iajs-2963	61	13	𝑣𝑏4	𝑣𝑏4	ADV
iajs-2963	61	14	sin(𝑣	sin(𝑣	NOUN
iajs-2963	61	15	)	)	PUNCT
iajs-2963	61	16	+	+	NUM
iajs-2963	61	17	𝑣4	𝑣4	NOUN
iajs-2963	61	18	𝑏4𝑎43𝑎32𝑎21	𝑏4𝑎43𝑎32𝑎21	ADP
iajs-2963	61	19	+	+	PROPN
iajs-2963	61	20	𝑣2	𝑣2	PROPN
iajs-2963	61	21	𝑏4𝑎41	𝑏4𝑎41	PROPN
iajs-2963	61	22	cos(𝑣	cos(𝑣	PROPN
iajs-2963	61	23	)	)	PUNCT
iajs-2963	61	24	+	+	CCONJ
iajs-2963	61	25	𝑣2	𝑣2	PROPN
iajs-2963	61	26	𝑏4𝑎42	𝑏4𝑎42	PROPN
iajs-2963	61	27	cos(𝑣	cos(𝑣	PROPN
iajs-2963	61	28	)	)	PUNCT
iajs-2963	61	29	+	+	CCONJ
iajs-2963	61	30	𝑣3	𝑣3	ADJ
iajs-2963	61	31	𝑏4𝑎42𝑎21	𝑏4𝑎42𝑎21	PROPN
iajs-2963	61	32	sin(𝑣	sin(𝑣	PROPN
iajs-2963	61	33	)	)	PUNCT
iajs-2963	61	34	+	+	CCONJ
iajs-2963	61	35	𝑣2	𝑣2	PROPN
iajs-2963	61	36	𝑏4𝑎43	𝑏4𝑎43	ADV
iajs-2963	61	37	cos(𝑣	cos(𝑣	PROPN
iajs-2963	61	38	)	)	PUNCT
iajs-2963	61	39	+	+	NOUN
iajs-2963	61	40	𝑣3	𝑣3	ADJ
iajs-2963	61	41	𝑏4𝑎43𝑎31	𝑏4𝑎43𝑎31	NUM
iajs-2963	61	42	sin(𝑣	sin(𝑣	NUM
iajs-2963	61	43	)	)	PUNCT
iajs-2963	62	1	+	+	CCONJ
iajs-2963	62	2	𝑣3	𝑣3	ADV
iajs-2963	62	3	𝑏4𝑎43𝑎32	𝑏4𝑎43𝑎32	PROPN
iajs-2963	62	4	sin(𝑣	sin(𝑣	PROPN
iajs-2963	62	5	)	)	PUNCT
iajs-2963	62	6	−	−	PROPN
iajs-2963	62	7	𝑣3	𝑣3	PROPN
iajs-2963	62	8	𝑏4𝑎43𝑎32	𝑏4𝑎43𝑎32	VERB
iajs-2963	62	9	𝑎21	𝑎21	PROPN
iajs-2963	62	10	cos(𝑣	cos(𝑣	PROPN
iajs-2963	62	11	)	)	PUNCT
iajs-2963	62	12	,	,	PUNCT
iajs-2963	62	13	(	(	PUNCT
iajs-2963	62	14	20	20	NUM
iajs-2963	62	15	)	)	PUNCT
iajs-2963	62	16	sin(𝑣	sin(𝑣	PROPN
iajs-2963	62	17	)	)	PUNCT
iajs-2963	62	18	=	=	PUNCT
iajs-2963	63	1	𝑣𝑏1	𝑣𝑏1	X
iajs-2963	63	2	−	−	PROPN
iajs-2963	63	3	𝑣𝑏−1	𝑣𝑏−1	VERB
iajs-2963	63	4	cos(𝑣	cos(𝑣	PROPN
iajs-2963	63	5	)	)	PUNCT
iajs-2963	64	1	+	+	CCONJ
iajs-2963	64	2	𝑣𝑏2	𝑣𝑏2	NOUN
iajs-2963	64	3	−	−	PROPN
iajs-2963	64	4	𝑣𝑏2	𝑣𝑏2	PROPN
iajs-2963	64	5	cos(𝑣	cos(𝑣	PROPN
iajs-2963	64	6	)	)	PUNCT
iajs-2963	64	7	−	−	PROPN
iajs-2963	64	8	𝑣𝑏3	𝑣𝑏3	PROPN
iajs-2963	64	9	cos(𝑣	cos(𝑣	PROPN
iajs-2963	64	10	)	)	PUNCT
iajs-2963	64	11	−	−	PROPN
iajs-2963	64	12	𝑣2𝑏3𝑎31	𝑣2𝑏3𝑎31	NUM
iajs-2963	64	13	sin(𝑣	sin(𝑣	NOUN
iajs-2963	64	14	)	)	PUNCT
iajs-2963	65	1	+	+	ADP
iajs-2963	65	2	𝑣𝑏3	𝑣𝑏3	ADJ
iajs-2963	65	3	−	−	PROPN
iajs-2963	65	4	𝑣2𝑏2𝑎21	𝑣2𝑏2𝑎21	PROPN
iajs-2963	65	5	sin(𝑣	sin(𝑣	PROPN
iajs-2963	65	6	)	)	PUNCT
iajs-2963	65	7	−	−	PROPN
iajs-2963	66	1	𝑣3	𝑣3	ADJ
iajs-2963	66	2	𝑏3𝑎32𝑎21	𝑏3𝑎32𝑎21	VERB
iajs-2963	66	3	−	−	NOUN
iajs-2963	66	4	𝑣3𝑏4𝑎43𝑎31	𝑣3𝑏4𝑎43𝑎31	ADP
iajs-2963	66	5	−	−	VERB
iajs-2963	66	6	𝑣3𝑏4𝑎43𝑎32	𝑣3𝑏4𝑎43𝑎32	NOUN
iajs-2963	66	7	+	+	NOUN
iajs-2963	66	8	𝑣𝑏4	𝑣𝑏4	NOUN
iajs-2963	66	9	+	+	CCONJ
iajs-2963	66	10	𝑣3𝑏3𝑎32𝑎21	𝑣3𝑏3𝑎32𝑎21	PUNCT
iajs-2963	66	11	cos(𝑣	cos(𝑣	NOUN
iajs-2963	66	12	)	)	PUNCT
iajs-2963	66	13	−	−	PROPN
iajs-2963	66	14	𝑣3𝑏4𝑎42𝑎21	𝑣3𝑏4𝑎42𝑎21	X
iajs-2963	66	15	−	−	NOUN
iajs-2963	66	16	𝑣2𝑏4𝑎42	𝑣2𝑏4𝑎42	ADJ
iajs-2963	66	17	sin(𝑣	sin(𝑣	NOUN
iajs-2963	66	18	)	)	PUNCT
iajs-2963	66	19	−	−	PROPN
iajs-2963	67	1	𝑣2𝑏4𝑎43	𝑣2𝑏4𝑎43	PROPN
iajs-2963	67	2	sin(𝑣	sin(𝑣	PROPN
iajs-2963	67	3	)	)	PUNCT
iajs-2963	67	4	−𝑣𝑏4	−𝑣𝑏4	PRON
iajs-2963	67	5	cos(𝑣	cos(𝑣	PROPN
iajs-2963	67	6	)	)	PUNCT
iajs-2963	67	7	−	−	PROPN
iajs-2963	67	8	𝑣2𝑏4𝑎41	𝑣2𝑏4𝑎41	PROPN
iajs-2963	67	9	sin(𝑣	sin(𝑣	PROPN
iajs-2963	67	10	)	)	PUNCT
iajs-2963	68	1	+	+	CCONJ
iajs-2963	68	2	𝑣3𝑏4𝑎43𝑎31cos	𝑣3𝑏4𝑎43𝑎31co	NOUN
iajs-2963	68	3	(	(	PUNCT
iajs-2963	68	4	𝑣	𝑣	NOUN
iajs-2963	68	5	)	)	PUNCT
iajs-2963	69	1	+	+	NUM
iajs-2963	69	2	𝑣3𝑏4𝑎43𝑎32cos	𝑣3𝑏4𝑎43𝑎32co	NOUN
iajs-2963	69	3	(	(	PUNCT
iajs-2963	69	4	𝑣	𝑣	NOUN
iajs-2963	69	5	)	)	PUNCT
iajs-2963	69	6	+	+	NOUN
iajs-2963	69	7	𝑣3𝑏4𝑎42𝑎21cos	𝑣3𝑏4𝑎42𝑎21co	NOUN
iajs-2963	69	8	(	(	PUNCT
iajs-2963	69	9	𝑣	𝑣	X
iajs-2963	69	10	)	)	PUNCT
iajs-2963	69	11	+	+	NUM
iajs-2963	69	12	𝑣4𝑏4𝑎43𝑎32𝑎21	𝑣4𝑏4𝑎43𝑎32𝑎21	PROPN
iajs-2963	69	13	sin(𝑣	sin(𝑣	PROPN
iajs-2963	69	14	)	)	PUNCT
iajs-2963	69	15	−	−	PROPN
iajs-2963	69	16	𝑣2𝑏3𝑎32	𝑣2𝑏3𝑎32	NUM
iajs-2963	69	17	sin(𝑣	sin(𝑣	NOUN
iajs-2963	69	18	)	)	PUNCT
iajs-2963	69	19	.	.	PUNCT
iajs-2963	70	1	(	(	PUNCT
iajs-2963	70	2	21	21	NUM
iajs-2963	70	3	)	)	PUNCT
iajs-2963	70	4	solving	solve	VERB
iajs-2963	70	5	equations	equation	NOUN
iajs-2963	70	6	(	(	PUNCT
iajs-2963	70	7	20	20	NUM
iajs-2963	70	8	)	)	PUNCT
iajs-2963	70	9	and	and	CCONJ
iajs-2963	70	10	(	(	PUNCT
iajs-2963	70	11	21	21	NUM
iajs-2963	70	12	)	)	PUNCT
iajs-2963	70	13	using	use	VERB
iajs-2963	70	14	the	the	DET
iajs-2963	70	15	coefficients	coefficient	NOUN
iajs-2963	70	16	of	of	ADP
iajs-2963	70	17	the	the	DET
iajs-2963	70	18	irk4	irk4	PROPN
iajs-2963	70	19	method	method	NOUN
iajs-2963	70	20	in	in	ADP
iajs-2963	70	21	table2	table2	PROPN
iajs-2963	70	22	for	for	ADP
iajs-2963	70	23	unknowns	unknown	NOUN
iajs-2963	70	24	parameters	parameter	NOUN
iajs-2963	70	25	𝑎31	𝑎31	ADJ
iajs-2963	70	26	and	and	CCONJ
iajs-2963	70	27	𝑎41	𝑎41	NUM
iajs-2963	70	28	we	we	PRON
iajs-2963	70	29	obtain	obtain	VERB
iajs-2963	70	30	the	the	DET
iajs-2963	70	31	following	follow	VERB
iajs-2963	70	32	solution	solution	NOUN
iajs-2963	70	33	:	:	PUNCT
iajs-2963	70	34	𝑎31	𝑎31	NUM
iajs-2963	70	35	=	=	SYM
iajs-2963	70	36	−72	−72	X
iajs-2963	70	37	95	95	NUM
iajs-2963	70	38	𝑣3(sin2(𝑣	𝑣3(sin2(𝑣	NOUN
iajs-2963	70	39	)	)	PUNCT
iajs-2963	70	40	+	+	NUM
iajs-2963	70	41	cos2(𝑣	cos2(𝑣	NOUN
iajs-2963	70	42	)	)	PUNCT
iajs-2963	70	43	−	−	PROPN
iajs-2963	70	44	2	2	NUM
iajs-2963	70	45	cos(𝑣	cos(𝑣	PROPN
iajs-2963	70	46	)	)	PUNCT
iajs-2963	71	1	+	+	NOUN
iajs-2963	71	2	1	1	X
iajs-2963	71	3	)	)	PUNCT
iajs-2963	71	4	(	(	PUNCT
iajs-2963	71	5	−12	−12	X
iajs-2963	71	6	cos(𝑣	cos(𝑣	PROPN
iajs-2963	71	7	)	)	PUNCT
iajs-2963	71	8	sin(𝑣	sin(𝑣	PROPN
iajs-2963	71	9	)	)	PUNCT
iajs-2963	72	1	+	+	CCONJ
iajs-2963	72	2	12	12	NUM
iajs-2963	72	3	sin	sin	NOUN
iajs-2963	72	4	(	(	PUNCT
iajs-2963	72	5	𝑣	𝑣	NOUN
iajs-2963	72	6	)	)	PUNCT
iajs-2963	72	7	−3	−3	PROPN
iajs-2963	72	8	𝑣	𝑣	PROPN
iajs-2963	72	9	sin2(𝑣	sin2(𝑣	PROPN
iajs-2963	72	10	)	)	PUNCT
iajs-2963	73	1	+	+	CCONJ
iajs-2963	73	2	𝑣3	𝑣3	ADJ
iajs-2963	73	3	sin2(𝑣	sin2(𝑣	NUM
iajs-2963	73	4	)	)	PUNCT
iajs-2963	74	1	+	+	CCONJ
iajs-2963	74	2	12	12	NUM
iajs-2963	74	3	𝑣	𝑣	PRON
iajs-2963	74	4	𝑐𝑜𝑠(𝑣	𝑐𝑜𝑠(𝑣	PROPN
iajs-2963	74	5	)	)	PUNCT
iajs-2963	74	6	−	−	PROPN
iajs-2963	74	7	3	3	NUM
iajs-2963	74	8	𝑣	𝑣	PRON
iajs-2963	74	9	cos2(𝑣	cos2(𝑣	NOUN
iajs-2963	74	10	)	)	PUNCT
iajs-2963	74	11	−	−	PROPN
iajs-2963	74	12	2	2	NUM
iajs-2963	74	13	𝑣3	𝑣3	PROPN
iajs-2963	74	14	cos(𝑣	cos(𝑣	PROPN
iajs-2963	74	15	)	)	PUNCT
iajs-2963	74	16	−9𝑣	−9𝑣	PROPN
iajs-2963	74	17	+	+	CCONJ
iajs-2963	74	18	𝑣3	𝑣3	ADJ
iajs-2963	74	19	cos2(𝑣	cos2(𝑣	NOUN
iajs-2963	74	20	)	)	PUNCT
iajs-2963	75	1	+	+	CCONJ
iajs-2963	75	2	𝑣3	𝑣3	ADJ
iajs-2963	75	3	)	)	PUNCT
iajs-2963	75	4	,	,	PUNCT
iajs-2963	75	5	(	(	PUNCT
iajs-2963	75	6	22	22	X
iajs-2963	75	7	)	)	PUNCT
iajs-2963	75	8	𝑎41	𝑎41	NOUN
iajs-2963	75	9	=	=	SYM
iajs-2963	75	10	2	2	NUM
iajs-2963	75	11	35625	35625	NUM
iajs-2963	75	12	𝑣3(sin2(𝑣)+cos2(𝑣)−2	𝑣3(sin2(𝑣)+cos2(𝑣)−2	PROPN
iajs-2963	75	13	cos(𝑣)+1	cos(𝑣)+1	NOUN
iajs-2963	75	14	)	)	PUNCT
iajs-2963	76	1	(	(	PUNCT
iajs-2963	76	2	−7560	−7560	NOUN
iajs-2963	76	3	𝑣	𝑣	ADP
iajs-2963	76	4	−	−	PROPN
iajs-2963	76	5	9325	9325	NUM
iajs-2963	76	6	𝑣3	𝑣3	PROPN
iajs-2963	76	7	−17280𝑣	−17280𝑣	ADP
iajs-2963	76	8	𝑐𝑜𝑠(𝑣	𝑐𝑜𝑠(𝑣	NOUN
iajs-2963	76	9	)	)	PUNCT
iajs-2963	77	1	+	+	NUM
iajs-2963	77	2	24840	24840	NUM
iajs-2963	77	3	𝑣	𝑣	DET
iajs-2963	77	4	cos2(𝑣	cos2(𝑣	NOUN
iajs-2963	77	5	)	)	PUNCT
iajs-2963	77	6	+	+	CCONJ
iajs-2963	77	7	18650	18650	NUM
iajs-2963	77	8	𝑣3	𝑣3	ADJ
iajs-2963	77	9	cos(𝑣	cos(𝑣	PROPN
iajs-2963	77	10	)	)	PUNCT
iajs-2963	77	11	+1083	+1083	NUM
iajs-2963	77	12	𝑣5	𝑣5	NOUN
iajs-2963	77	13	cos2(𝑣	cos2(𝑣	NOUN
iajs-2963	77	14	)	)	PUNCT
iajs-2963	77	15	+	+	CCONJ
iajs-2963	77	16	64800	64800	NUM
iajs-2963	77	17	sin(𝑣	sin(𝑣	NOUN
iajs-2963	77	18	)	)	PUNCT
iajs-2963	78	1	−	−	PROPN
iajs-2963	78	2	57240	57240	NUM
iajs-2963	78	3	𝑣	𝑣	PRON
iajs-2963	78	4	sin2(𝑣	sin2(𝑣	PROPN
iajs-2963	78	5	)	)	PUNCT
iajs-2963	79	1	+	+	NUM
iajs-2963	79	2	1083	1083	NUM
iajs-2963	79	3	𝑣5	𝑣5	NOUN
iajs-2963	79	4	−64800	−64800	PROPN
iajs-2963	79	5	cos(𝑣	cos(𝑣	PROPN
iajs-2963	79	6	)	)	PUNCT
iajs-2963	79	7	sin(𝑣	sin(𝑣	PROPN
iajs-2963	79	8	)	)	PUNCT
iajs-2963	79	9	−	−	PROPN
iajs-2963	79	10	9325	9325	NUM
iajs-2963	79	11	𝑣3sin2(𝑣	𝑣3sin2(𝑣	NOUN
iajs-2963	79	12	)	)	PUNCT
iajs-2963	79	13	−	−	PROPN
iajs-2963	79	14	2166	2166	NUM
iajs-2963	79	15	𝑣5	𝑣5	PROPN
iajs-2963	79	16	cos(𝑣	cos(𝑣	PROPN
iajs-2963	79	17	)	)	PUNCT
iajs-2963	79	18	−9325	−9325	PROPN
iajs-2963	79	19	𝑣3	𝑣3	PROPN
iajs-2963	79	20	cos2(𝑣	cos2(𝑣	NOUN
iajs-2963	79	21	)	)	PUNCT
iajs-2963	79	22	+	+	SYM
iajs-2963	79	23	41040𝑣2	41040𝑣2	PROPN
iajs-2963	79	24	sin(𝑣	sin(𝑣	PROPN
iajs-2963	79	25	)	)	PUNCT
iajs-2963	80	1	+	+	NUM
iajs-2963	80	2	1083	1083	NUM
iajs-2963	80	3	𝑣5	𝑣5	NOUN
iajs-2963	80	4	sin2(𝑣	sin2(𝑣	NUM
iajs-2963	80	5	)	)	PUNCT
iajs-2963	80	6	)	)	PUNCT
iajs-2963	80	7	.	.	PUNCT
iajs-2963	81	1	(	(	PUNCT
iajs-2963	81	2	23	23	X
iajs-2963	81	3	)	)	PUNCT
iajs-2963	81	4	ihjpas	ihjpa	NOUN
iajs-2963	81	5	.	.	PUNCT
iajs-2963	82	1	36(1)2023	36(1)2023	NUM
iajs-2963	82	2	349	349	NUM
iajs-2963	82	3	it	it	PRON
iajs-2963	82	4	can	can	AUX
iajs-2963	82	5	be	be	AUX
iajs-2963	82	6	noticed	notice	VERB
iajs-2963	82	7	that	that	SCONJ
iajs-2963	82	8	for	for	ADP
iajs-2963	82	9	𝑣	𝑣	PRON
iajs-2963	82	10	→	→	SYM
iajs-2963	82	11	0	0	NUM
iajs-2963	82	12	using	use	VERB
iajs-2963	82	13	maple	maple	NOUN
iajs-2963	82	14	package	package	NOUN
iajs-2963	82	15	,	,	PUNCT
iajs-2963	82	16	the	the	DET
iajs-2963	82	17	series	series	NOUN
iajs-2963	82	18	expansions	expansion	NOUN
iajs-2963	82	19	are	be	AUX
iajs-2963	82	20	given	give	VERB
iajs-2963	82	21	in	in	ADP
iajs-2963	82	22	following	follow	VERB
iajs-2963	82	23	form	form	NOUN
iajs-2963	82	24	:	:	PUNCT
iajs-2963	82	25	𝑎31	𝑎31	NUM
iajs-2963	82	26	=	=	SYM
iajs-2963	82	27	−	−	PROPN
iajs-2963	82	28	18	18	NUM
iajs-2963	82	29	475	475	NUM
iajs-2963	82	30	𝑣2	𝑣2	NOUN
iajs-2963	82	31	+	+	CCONJ
iajs-2963	82	32	3	3	NUM
iajs-2963	82	33	3325	3325	NUM
iajs-2963	82	34	𝑣4	𝑣4	NOUN
iajs-2963	82	35	−	−	PROPN
iajs-2963	82	36	1	1	NUM
iajs-2963	82	37	79800	79800	NUM
iajs-2963	82	38	𝑣6	𝑣6	NOUN
iajs-2963	82	39	+	+	CCONJ
iajs-2963	82	40	1	1	NUM
iajs-2963	82	41	8778000	8778000	NUM
iajs-2963	82	42	𝑣8	𝑣8	NOUN
iajs-2963	82	43	−	−	ADP
iajs-2963	82	44	1	1	NUM
iajs-2963	82	45	1369368000	1369368000	NUM
iajs-2963	82	46	𝑣10	𝑣10	NOUN
iajs-2963	82	47	+	+	CCONJ
iajs-2963	82	48	1	1	NUM
iajs-2963	82	49	28756728000	28756728000	NUM
iajs-2963	82	50	𝑣12	𝑣12	NOUN
iajs-2963	82	51	−	−	PROPN
iajs-2963	82	52	1	1	NUM
iajs-2963	82	53	78218300160000	78218300160000	NUM
iajs-2963	82	54	𝑣14	𝑣14	NUM
iajs-2963	82	55	+	+	CCONJ
iajs-2963	82	56	⋯	⋯	PROPN
iajs-2963	82	57	,	,	PUNCT
iajs-2963	82	58	(	(	PUNCT
iajs-2963	82	59	24	24	NUM
iajs-2963	82	60	)	)	PUNCT
iajs-2963	82	61	𝑎41	𝑎41	NOUN
iajs-2963	82	62	=	=	SYM
iajs-2963	82	63	2	2	NUM
iajs-2963	82	64	15	15	NUM
iajs-2963	82	65	−	−	NOUN
iajs-2963	82	66	276	276	NUM
iajs-2963	82	67	11875	11875	NUM
iajs-2963	82	68	𝑣2	𝑣2	NOUN
iajs-2963	82	69	+	+	CCONJ
iajs-2963	82	70	689	689	NUM
iajs-2963	82	71	249375	249375	NUM
iajs-2963	82	72	𝑣4	𝑣4	NOUN
iajs-2963	82	73	−	−	PROPN
iajs-2963	82	74	77	77	NUM
iajs-2963	82	75	1425000	1425000	NUM
iajs-2963	82	76	𝑣6	𝑣6	NOUN
iajs-2963	82	77	+	+	CCONJ
iajs-2963	82	78	1069	1069	NUM
iajs-2963	82	79	1975050000	1975050000	NUM
iajs-2963	82	80	𝑣8	𝑣8	NOUN
iajs-2963	82	81	−	−	PROPN
iajs-2963	82	82	61849	61849	NUM
iajs-2963	82	83	10783773000000	10783773000000	NUM
iajs-2963	82	84	𝑣10	𝑣10	NOUN
iajs-2963	82	85	−	−	NOUN
iajs-2963	82	86	1	1	NUM
iajs-2963	82	87	172540368000	172540368000	NUM
iajs-2963	82	88	𝑣12	𝑣12	NOUN
iajs-2963	82	89	−	−	PROPN
iajs-2963	82	90	77963	77963	NUM
iajs-2963	82	91	87995587680000000	87995587680000000	NUM
iajs-2963	82	92	𝑣14	𝑣14	NUM
iajs-2963	82	93	+	+	CCONJ
iajs-2963	82	94	⋯	⋯	PROPN
iajs-2963	82	95	,	,	PUNCT
iajs-2963	82	96	(	(	PUNCT
iajs-2963	82	97	25	25	NUM
iajs-2963	82	98	)	)	PUNCT
iajs-2963	82	99	which	which	PRON
iajs-2963	82	100	lead	lead	VERB
iajs-2963	82	101	to	to	ADP
iajs-2963	82	102	the	the	DET
iajs-2963	82	103	new	new	ADJ
iajs-2963	82	104	tfirk4	tfirk4	PROPN
iajs-2963	82	105	method	method	NOUN
iajs-2963	82	106	.	.	PUNCT
iajs-2963	83	1	as	as	ADP
iajs-2963	83	2	𝑣	𝑣	PRON
iajs-2963	83	3	→	→	SYM
iajs-2963	83	4	0	0	NUM
iajs-2963	83	5	,	,	PUNCT
iajs-2963	83	6	the	the	DET
iajs-2963	83	7	newly	newly	ADV
iajs-2963	83	8	obtained	obtain	VERB
iajs-2963	83	9	parameters	parameter	NOUN
iajs-2963	83	10	𝑎31	𝑎31	ADJ
iajs-2963	83	11	and	and	CCONJ
iajs-2963	83	12	𝑎41	𝑎41	ADJ
iajs-2963	83	13	turn	turn	NOUN
iajs-2963	83	14	into	into	ADP
iajs-2963	83	15	the	the	DET
iajs-2963	83	16	parameters	parameter	NOUN
iajs-2963	83	17	of	of	ADP
iajs-2963	83	18	the	the	DET
iajs-2963	83	19	original	original	ADJ
iajs-2963	83	20	method	method	NOUN
iajs-2963	83	21	.	.	PUNCT
iajs-2963	84	1	3	3	X
iajs-2963	84	2	.	.	X
iajs-2963	84	3	numerical	numerical	ADJ
iajs-2963	84	4	results	result	NOUN
iajs-2963	84	5	to	to	PART
iajs-2963	84	6	evaluate	evaluate	VERB
iajs-2963	84	7	the	the	DET
iajs-2963	84	8	efficacy	efficacy	NOUN
iajs-2963	84	9	of	of	ADP
iajs-2963	84	10	the	the	DET
iajs-2963	84	11	tfirk4	tfirk4	PROPN
iajs-2963	84	12	method	method	NOUN
iajs-2963	84	13	proposed	propose	VERB
iajs-2963	84	14	,	,	PUNCT
iajs-2963	84	15	we	we	PRON
iajs-2963	84	16	apply	apply	VERB
iajs-2963	84	17	them	they	PRON
iajs-2963	84	18	to	to	ADP
iajs-2963	84	19	oscillatory	oscillatory	ADJ
iajs-2963	84	20	test	test	NOUN
iajs-2963	84	21	problems	problem	NOUN
iajs-2963	84	22	and	and	CCONJ
iajs-2963	84	23	their	their	PRON
iajs-2963	84	24	numerical	numerical	ADJ
iajs-2963	84	25	results	result	NOUN
iajs-2963	84	26	are	be	AUX
iajs-2963	84	27	compared	compare	VERB
iajs-2963	84	28	with	with	ADP
iajs-2963	84	29	the	the	DET
iajs-2963	84	30	existing	exist	VERB
iajs-2963	84	31	effective	effective	ADJ
iajs-2963	84	32	methods	method	NOUN
iajs-2963	84	33	.	.	PUNCT
iajs-2963	85	1	the	the	DET
iajs-2963	85	2	following	follow	VERB
iajs-2963	85	3	numerical	numerical	ADJ
iajs-2963	85	4	methods	method	NOUN
iajs-2963	85	5	are	be	AUX
iajs-2963	85	6	applied	apply	VERB
iajs-2963	85	7	in	in	ADP
iajs-2963	85	8	the	the	DET
iajs-2963	85	9	comparison	comparison	NOUN
iajs-2963	85	10	:	:	PUNCT
iajs-2963	85	11	▪	▪	ADJ
iajs-2963	85	12	step	step	NOUN
iajs-2963	85	13	size	size	NOUN
iajs-2963	85	14	.	.	PUNCT
iajs-2963	86	1	▪	▪	X
iajs-2963	86	2	tfirk4	tfirk4	NOUN
iajs-2963	86	3	:	:	PUNCT
iajs-2963	86	4	the	the	DET
iajs-2963	86	5	trigonometrically	trigonometrically	ADV
iajs-2963	86	6	fitted	fit	VERB
iajs-2963	86	7	four	four	NUM
iajs-2963	86	8	-	-	PUNCT
iajs-2963	86	9	stage	stage	NOUN
iajs-2963	86	10	fourth	fourth	ADJ
iajs-2963	86	11	-	-	PUNCT
iajs-2963	86	12	order	order	NOUN
iajs-2963	86	13	irk	irk	NOUN
iajs-2963	86	14	method	method	NOUN
iajs-2963	86	15	presented	present	VERB
iajs-2963	86	16	here	here	ADV
iajs-2963	86	17	.	.	PUNCT
iajs-2963	87	1	▪	▪	ADJ
iajs-2963	87	2	irk4	irk4	NOUN
iajs-2963	87	3	:	:	PUNCT
iajs-2963	87	4	fourth	fourth	ADJ
iajs-2963	87	5	-	-	PUNCT
iajs-2963	87	6	order	order	NOUN
iajs-2963	87	7	irk	irk	NOUN
iajs-2963	87	8	method	method	NOUN
iajs-2963	87	9	derive	derive	ADJ
iajs-2963	87	10	in	in	ADP
iajs-2963	87	11	[	[	X
iajs-2963	87	12	4	4	NUM
iajs-2963	87	13	]	]	PUNCT
iajs-2963	87	14	.	.	PUNCT
iajs-2963	88	1	▪	▪	ADJ
iajs-2963	88	2	tfrk4	tfrk4	NOUN
iajs-2963	88	3	:	:	PUNCT
iajs-2963	88	4	trigonometrically	trigonometrically	ADV
iajs-2963	88	5	-	-	PUNCT
iajs-2963	88	6	fitted	fit	VERB
iajs-2963	88	7	rk	rk	NOUN
iajs-2963	88	8	method	method	NOUN
iajs-2963	88	9	developed	develop	VERB
iajs-2963	88	10	in	in	ADP
iajs-2963	88	11	[	[	X
iajs-2963	88	12	8	8	NUM
iajs-2963	88	13	]	]	PUNCT
iajs-2963	88	14	.	.	PUNCT
iajs-2963	89	1	▪	▪	X
iajs-2963	89	2	rk4z	rk4z	ADJ
iajs-2963	89	3	:	:	PUNCT
iajs-2963	89	4	fifth	fifth	ADJ
iajs-2963	89	5	-	-	PUNCT
iajs-2963	89	6	order	order	NOUN
iajs-2963	89	7	rk	rk	NOUN
iajs-2963	89	8	method	method	NOUN
iajs-2963	89	9	given	give	VERB
iajs-2963	89	10	in	in	ADP
iajs-2963	89	11	[	[	X
iajs-2963	89	12	1	1	NUM
iajs-2963	89	13	]	]	PUNCT
iajs-2963	89	14	.	.	PUNCT
iajs-2963	90	1	▪	▪	ADJ
iajs-2963	90	2	mrk4	mrk4	PROPN
iajs-2963	90	3	:	:	PUNCT
iajs-2963	90	4	modified	modify	VERB
iajs-2963	90	5	rk	rk	NOUN
iajs-2963	90	6	method	method	NOUN
iajs-2963	90	7	of	of	ADP
iajs-2963	90	8	order	order	NOUN
iajs-2963	90	9	four	four	NUM
iajs-2963	90	10	proposed	propose	VERB
iajs-2963	90	11	in	in	ADP
iajs-2963	90	12	[	[	X
iajs-2963	90	13	9	9	NUM
iajs-2963	90	14	]	]	PUNCT
iajs-2963	90	15	.	.	PUNCT
iajs-2963	91	1	▪	▪	ADJ
iajs-2963	91	2	max	max	PROPN
iajs-2963	91	3	error	error	NOUN
iajs-2963	91	4	:	:	PUNCT
iajs-2963	91	5	max	max	PROPN
iajs-2963	91	6	(	(	PUNCT
iajs-2963	91	7	|𝑢(𝑥𝑛	|𝑢(𝑥𝑛	PROPN
iajs-2963	91	8	)	)	PUNCT
iajs-2963	91	9	−	−	PROPN
iajs-2963	92	1	𝑢𝑛|	𝑢𝑛|	NOUN
iajs-2963	92	2	)	)	PUNCT
iajs-2963	92	3	this	this	PRON
iajs-2963	92	4	is	be	AUX
iajs-2963	92	5	the	the	DET
iajs-2963	92	6	maximum	maximum	NOUN
iajs-2963	92	7	between	between	ADP
iajs-2963	92	8	absolute	absolute	ADJ
iajs-2963	92	9	errors	error	NOUN
iajs-2963	92	10	of	of	ADP
iajs-2963	92	11	the	the	DET
iajs-2963	92	12	exact	exact	ADJ
iajs-2963	92	13	solutions	solution	NOUN
iajs-2963	92	14	and	and	CCONJ
iajs-2963	92	15	the	the	DET
iajs-2963	92	16	computed	computed	ADJ
iajs-2963	92	17	solutions	solution	NOUN
iajs-2963	92	18	.	.	PUNCT
iajs-2963	93	1	problem	problem	NOUN
iajs-2963	93	2	1	1	NUM
iajs-2963	93	3	:	:	PUNCT
iajs-2963	94	1	[	[	X
iajs-2963	94	2	10	10	NUM
iajs-2963	94	3	]	]	X
iajs-2963	94	4	inhomogeneous	inhomogeneous	ADJ
iajs-2963	94	5	problem	problem	NOUN
iajs-2963	94	6	:	:	PUNCT
iajs-2963	94	7	𝑢1	𝑢1	PROPN
iajs-2963	94	8	′	′	NUM
iajs-2963	94	9	(	(	PUNCT
iajs-2963	94	10	𝑡	𝑡	NOUN
iajs-2963	94	11	)	)	PUNCT
iajs-2963	94	12	=	=	SYM
iajs-2963	94	13	𝑢2(𝑡	𝑢2(𝑡	PROPN
iajs-2963	94	14	)	)	PUNCT
iajs-2963	94	15	,	,	PUNCT
iajs-2963	94	16	𝑢1(0	𝑢1(0	PROPN
iajs-2963	94	17	)	)	PUNCT
iajs-2963	94	18	=	=	SYM
iajs-2963	94	19	1	1	NUM
iajs-2963	94	20	,	,	PUNCT
iajs-2963	94	21	𝑢2	𝑢2	PROPN
iajs-2963	94	22	′	′	NUM
iajs-2963	94	23	(	(	PUNCT
iajs-2963	94	24	𝑡	𝑡	NOUN
iajs-2963	94	25	)	)	PUNCT
iajs-2963	94	26	=	=	SYM
iajs-2963	94	27	−100	−100	ADP
iajs-2963	94	28	𝑢1(𝑡	𝑢1(𝑡	PROPN
iajs-2963	94	29	)	)	PUNCT
iajs-2963	94	30	+	+	CCONJ
iajs-2963	94	31	99	99	NUM
iajs-2963	94	32	sin(𝑡	sin(𝑡	NOUN
iajs-2963	94	33	)	)	PUNCT
iajs-2963	94	34	,	,	PUNCT
iajs-2963	94	35	𝑢2(0	𝑢2(0	PROPN
iajs-2963	94	36	)	)	PUNCT
iajs-2963	94	37	=	=	SYM
iajs-2963	95	1	11	11	NUM
iajs-2963	95	2	.	.	PUNCT
iajs-2963	96	1	exact	exact	ADJ
iajs-2963	96	2	solution	solution	NOUN
iajs-2963	96	3	is	be	AUX
iajs-2963	96	4	:	:	PUNCT
iajs-2963	96	5	𝑢1(𝑡	𝑢1(𝑡	X
iajs-2963	96	6	)	)	PUNCT
iajs-2963	96	7	=	=	SYM
iajs-2963	96	8	cos(10𝑡	cos(10𝑡	X
iajs-2963	96	9	)	)	PUNCT
iajs-2963	96	10	+	+	CCONJ
iajs-2963	96	11	sin(10𝑡	sin(10𝑡	X
iajs-2963	96	12	)	)	PUNCT
iajs-2963	96	13	+	+	CCONJ
iajs-2963	96	14	sin(𝑡	sin(𝑡	PROPN
iajs-2963	96	15	)	)	PUNCT
iajs-2963	96	16	,	,	PUNCT
iajs-2963	96	17	𝑢2(𝑡	𝑢2(𝑡	PROPN
iajs-2963	96	18	)	)	PUNCT
iajs-2963	96	19	=	=	PRON
iajs-2963	96	20	−10	−10	X
iajs-2963	96	21	sin(10𝑡	sin(10𝑡	NOUN
iajs-2963	96	22	)	)	PUNCT
iajs-2963	96	23	+	+	CCONJ
iajs-2963	96	24	10	10	NUM
iajs-2963	96	25	cos(10𝑡	cos(10𝑡	NUM
iajs-2963	96	26	)	)	PUNCT
iajs-2963	96	27	+	+	CCONJ
iajs-2963	96	28	cos(𝑡	cos(𝑡	NOUN
iajs-2963	96	29	)	)	PUNCT
iajs-2963	96	30	.	.	PUNCT
iajs-2963	97	1	problem	problem	NOUN
iajs-2963	97	2	2	2	NUM
iajs-2963	97	3	:	:	PUNCT
iajs-2963	98	1	[	[	X
iajs-2963	98	2	7	7	X
iajs-2963	98	3	]	]	ADJ
iajs-2963	98	4	inhomogeneous	inhomogeneous	ADJ
iajs-2963	98	5	problem	problem	NOUN
iajs-2963	98	6	:	:	PUNCT
iajs-2963	98	7	𝑢1	𝑢1	PROPN
iajs-2963	98	8	′	′	NUM
iajs-2963	98	9	(	(	PUNCT
iajs-2963	98	10	𝑡	𝑡	NOUN
iajs-2963	98	11	)	)	PUNCT
iajs-2963	98	12	=	=	SYM
iajs-2963	98	13	𝑢2(𝑡	𝑢2(𝑡	PROPN
iajs-2963	98	14	)	)	PUNCT
iajs-2963	98	15	,	,	PUNCT
iajs-2963	98	16	𝑢1(0	𝑢1(0	PROPN
iajs-2963	98	17	)	)	PUNCT
iajs-2963	98	18	=	=	SYM
iajs-2963	98	19	1	1	NUM
iajs-2963	98	20	,	,	PUNCT
iajs-2963	98	21	𝑢2	𝑢2	PROPN
iajs-2963	98	22	′	′	NUM
iajs-2963	98	23	(	(	PUNCT
iajs-2963	98	24	𝑡	𝑡	NOUN
iajs-2963	98	25	)	)	PUNCT
iajs-2963	98	26	=	=	SYM
iajs-2963	98	27	−𝑢1(𝑡	−𝑢1(𝑡	PROPN
iajs-2963	98	28	)	)	PUNCT
iajs-2963	99	1	+	+	SYM
iajs-2963	99	2	𝑡	𝑡	PROPN
iajs-2963	99	3	,	,	PUNCT
iajs-2963	99	4	𝑢2(0	𝑢2(0	NOUN
iajs-2963	99	5	)	)	PUNCT
iajs-2963	99	6	=	=	SYM
iajs-2963	99	7	−2	−2	NOUN
iajs-2963	99	8	.	.	PUNCT
iajs-2963	100	1	exact	exact	ADJ
iajs-2963	100	2	solution	solution	NOUN
iajs-2963	100	3	is	be	AUX
iajs-2963	100	4	:	:	PUNCT
iajs-2963	100	5	𝑢1(𝑡	𝑢1(𝑡	X
iajs-2963	100	6	)	)	PUNCT
iajs-2963	100	7	=	=	SYM
iajs-2963	100	8	sin(𝑡	sin(𝑡	PROPN
iajs-2963	100	9	)	)	PUNCT
iajs-2963	100	10	+	+	CCONJ
iajs-2963	100	11	cos(𝑡	cos(𝑡	X
iajs-2963	100	12	)	)	PUNCT
iajs-2963	100	13	+	+	SYM
iajs-2963	100	14	𝑡	𝑡	PROPN
iajs-2963	100	15	,	,	PUNCT
iajs-2963	100	16	𝑢2(𝑡	𝑢2(𝑡	PROPN
iajs-2963	100	17	)	)	PUNCT
iajs-2963	100	18	=	=	SYM
iajs-2963	100	19	cos(𝑡	cos(𝑡	X
iajs-2963	100	20	)	)	PUNCT
iajs-2963	100	21	−	−	PROPN
iajs-2963	100	22	sin(𝑡	sin(𝑡	PROPN
iajs-2963	100	23	)	)	PUNCT
iajs-2963	100	24	+	+	NOUN
iajs-2963	100	25	1	1	NUM
iajs-2963	100	26	problem	problem	NOUN
iajs-2963	100	27	3	3	NUM
iajs-2963	100	28	:	:	PUNCT
iajs-2963	100	29	[	[	X
iajs-2963	100	30	11	11	NUM
iajs-2963	100	31	]	]	X
iajs-2963	100	32	duffing	duffing	NOUN
iajs-2963	100	33	problem	problem	NOUN
iajs-2963	100	34	:	:	PUNCT
iajs-2963	100	35	𝑢1	𝑢1	PROPN
iajs-2963	100	36	′	′	NUM
iajs-2963	100	37	(	(	PUNCT
iajs-2963	100	38	𝑡	𝑡	NOUN
iajs-2963	100	39	)	)	PUNCT
iajs-2963	100	40	=	=	SYM
iajs-2963	100	41	𝑢2(𝑡	𝑢2(𝑡	PROPN
iajs-2963	100	42	)	)	PUNCT
iajs-2963	100	43	,	,	PUNCT
iajs-2963	100	44	𝑢1(0	𝑢1(0	PROPN
iajs-2963	100	45	)	)	PUNCT
iajs-2963	100	46	=	=	SYM
iajs-2963	100	47	0.200426728067	0.200426728067	NUM
iajs-2963	100	48	,	,	PUNCT
iajs-2963	100	49	𝑢3	𝑢3	PROPN
iajs-2963	100	50	′	′	NUM
iajs-2963	100	51	(	(	PUNCT
iajs-2963	100	52	𝑡	𝑡	NOUN
iajs-2963	100	53	)	)	PUNCT
iajs-2963	100	54	=	=	SYM
iajs-2963	100	55	−𝑢1(𝑡	−𝑢1(𝑡	PROPN
iajs-2963	100	56	)	)	PUNCT
iajs-2963	100	57	−	−	PROPN
iajs-2963	100	58	(	(	PUNCT
iajs-2963	100	59	𝑢1(𝑡	𝑢1(𝑡	NOUN
iajs-2963	100	60	)	)	PUNCT
iajs-2963	100	61	)	)	PUNCT
iajs-2963	101	1	3	3	NUM
iajs-2963	101	2	+	+	SYM
iajs-2963	101	3	0.002	0.002	NUM
iajs-2963	101	4	cos(1.01	cos(1.01	ADJ
iajs-2963	101	5	𝑡	𝑡	NOUN
iajs-2963	101	6	)	)	PUNCT
iajs-2963	101	7	,	,	PUNCT
iajs-2963	101	8	𝑢2(0	𝑢2(0	NOUN
iajs-2963	101	9	)	)	PUNCT
iajs-2963	101	10	=	=	SYM
iajs-2963	101	11	0	0	NUM
iajs-2963	101	12	,	,	PUNCT
iajs-2963	101	13	exact	exact	ADJ
iajs-2963	101	14	solution	solution	NOUN
iajs-2963	101	15	is	be	AUX
iajs-2963	101	16	:	:	PUNCT
iajs-2963	101	17	𝑢1(𝑡	𝑢1(𝑡	X
iajs-2963	101	18	)	)	PUNCT
iajs-2963	101	19	=	=	SYM
iajs-2963	101	20	0.200179477536	0.200179477536	NUM
iajs-2963	101	21	cos(1.01	cos(1.01	NOUN
iajs-2963	101	22	𝑡	𝑡	NOUN
iajs-2963	101	23	)	)	PUNCT
iajs-2963	101	24	+	+	NUM
iajs-2963	101	25	2.46946143	2.46946143	NUM
iajs-2963	101	26	×	×	NOUN
iajs-2963	101	27	10−4	10−4	NUM
iajs-2963	101	28	cos(3.03	cos(3.03	ADJ
iajs-2963	101	29	𝑡	𝑡	NOUN
iajs-2963	101	30	)	)	PUNCT
iajs-2963	101	31	ihjpas	ihjpa	NOUN
iajs-2963	101	32	.	.	PUNCT
iajs-2963	102	1	36(1)2023	36(1)2023	NUM
iajs-2963	102	2	350	350	NUM
iajs-2963	102	3	+3.04014	+3.04014	NOUN
iajs-2963	102	4	×	×	PROPN
iajs-2963	102	5	10−7	10−7	NUM
iajs-2963	102	6	cos(5.05	cos(5.05	NOUN
iajs-2963	102	7	𝑡	𝑡	NOUN
iajs-2963	102	8	)	)	PUNCT
iajs-2963	102	9	+	+	NUM
iajs-2963	102	10	3.74	3.74	NUM
iajs-2963	102	11	10−10	10−10	NUM
iajs-2963	102	12	cos(7.07	cos(7.07	NUM
iajs-2963	102	13	𝑡	𝑡	NOUN
iajs-2963	102	14	)	)	PUNCT
iajs-2963	102	15	,	,	PUNCT
iajs-2963	102	16	𝑢2(𝑡	𝑢2(𝑡	PROPN
iajs-2963	102	17	)	)	PUNCT
iajs-2963	102	18	=	=	SYM
iajs-2963	102	19	−0.2021812723	−0.2021812723	PROPN
iajs-2963	102	20	sin(1.01	sin(1.01	NUM
iajs-2963	102	21	𝑡	𝑡	NOUN
iajs-2963	102	22	)	)	PUNCT
iajs-2963	102	23	−	−	PROPN
iajs-2963	102	24	7.482468133	7.482468133	NUM
iajs-2963	102	25	×	×	NOUN
iajs-2963	102	26	10−4	10−4	NUM
iajs-2963	102	27	sin(3.03	sin(3.03	X
iajs-2963	102	28	𝑡	𝑡	NOUN
iajs-2963	102	29	)	)	PUNCT
iajs-2963	102	30	−1.53527070	−1.53527070	X
iajs-2963	102	31	×	×	NOUN
iajs-2963	102	32	10−6	10−6	NUM
iajs-2963	102	33	sin(5.05	sin(5.05	ADJ
iajs-2963	102	34	𝑡	𝑡	NOUN
iajs-2963	102	35	)	)	PUNCT
iajs-2963	102	36	−	−	PROPN
iajs-2963	102	37	2.64418	2.64418	NUM
iajs-2963	102	38	×	×	NOUN
iajs-2963	102	39	10−9	10−9	NUM
iajs-2963	102	40	sin(7.07	sin(7.07	NUM
iajs-2963	102	41	𝑡	𝑡	NOUN
iajs-2963	102	42	)	)	PUNCT
iajs-2963	102	43	.	.	PUNCT
iajs-2963	103	1	problem	problem	NOUN
iajs-2963	103	2	4	4	NUM
iajs-2963	103	3	:	:	PUNCT
iajs-2963	104	1	[	[	X
iajs-2963	104	2	8	8	NUM
iajs-2963	104	3	]	]	PUNCT
iajs-2963	104	4	𝑢1	𝑢1	PROPN
iajs-2963	104	5	′	′	NUM
iajs-2963	104	6	(	(	PUNCT
iajs-2963	104	7	𝑡	𝑡	NOUN
iajs-2963	104	8	)	)	PUNCT
iajs-2963	104	9	=	=	SYM
iajs-2963	104	10	𝑢3(𝑡	𝑢3(𝑡	PROPN
iajs-2963	104	11	)	)	PUNCT
iajs-2963	104	12	,	,	PUNCT
iajs-2963	104	13	𝑢1(0	𝑢1(0	PROPN
iajs-2963	104	14	)	)	PUNCT
iajs-2963	104	15	=	=	SYM
iajs-2963	104	16	1	1	NUM
iajs-2963	104	17	,	,	PUNCT
iajs-2963	104	18	𝑢3	𝑢3	PROPN
iajs-2963	104	19	′	′	NUM
iajs-2963	104	20	(	(	PUNCT
iajs-2963	104	21	𝑡	𝑡	NOUN
iajs-2963	104	22	)	)	PUNCT
iajs-2963	104	23	=	=	SYM
iajs-2963	104	24	−𝑢1(𝑡	−𝑢1(𝑡	PROPN
iajs-2963	104	25	)	)	PUNCT
iajs-2963	104	26	(	(	PUNCT
iajs-2963	104	27	√(𝑢1(𝑡))2+(𝑢2(𝑡))2	√(𝑢1(𝑡))2+(𝑢2(𝑡))2	NOUN
iajs-2963	104	28	)	)	PUNCT
iajs-2963	104	29	3	3	NUM
iajs-2963	104	30	𝑢3(0	𝑢3(0	PROPN
iajs-2963	104	31	)	)	PUNCT
iajs-2963	104	32	=	=	SYM
iajs-2963	104	33	0	0	NUM
iajs-2963	104	34	,	,	PUNCT
iajs-2963	104	35	𝑢2	𝑢2	PROPN
iajs-2963	104	36	′	′	NUM
iajs-2963	104	37	(	(	PUNCT
iajs-2963	104	38	𝑡	𝑡	NOUN
iajs-2963	104	39	)	)	PUNCT
iajs-2963	104	40	=	=	SYM
iajs-2963	104	41	𝑢4(𝑡	𝑢4(𝑡	NOUN
iajs-2963	104	42	)	)	PUNCT
iajs-2963	104	43	,	,	PUNCT
iajs-2963	104	44	𝑢2(0	𝑢2(0	NOUN
iajs-2963	104	45	)	)	PUNCT
iajs-2963	104	46	=	=	SYM
iajs-2963	104	47	0	0	NUM
iajs-2963	104	48	,	,	PUNCT
iajs-2963	104	49	𝑢4	𝑢4	NOUN
iajs-2963	104	50	′	′	NUM
iajs-2963	104	51	(	(	PUNCT
iajs-2963	104	52	𝑡	𝑡	NOUN
iajs-2963	104	53	)	)	PUNCT
iajs-2963	104	54	=	=	SYM
iajs-2963	104	55	−𝑢2(𝑡	−𝑢2(𝑡	NOUN
iajs-2963	104	56	)	)	PUNCT
iajs-2963	104	57	(	(	PUNCT
iajs-2963	104	58	√(𝑢1(𝑡))2+(𝑢2(𝑡))2	√(𝑢1(𝑡))2+(𝑢2(𝑡))2	NOUN
iajs-2963	104	59	)	)	PUNCT
iajs-2963	104	60	3	3	NUM
iajs-2963	104	61	𝑢4(0	𝑢4(0	NOUN
iajs-2963	104	62	)	)	PUNCT
iajs-2963	104	63	=	=	SYM
iajs-2963	105	1	1	1	X
iajs-2963	105	2	.	.	PUNCT
iajs-2963	105	3	exact	exact	ADJ
iajs-2963	105	4	solution	solution	NOUN
iajs-2963	105	5	is	be	AUX
iajs-2963	105	6	:	:	PUNCT
iajs-2963	105	7	𝑢1(𝑡	𝑢1(𝑡	X
iajs-2963	105	8	)	)	PUNCT
iajs-2963	105	9	=	=	SYM
iajs-2963	105	10	cos(𝑡	cos(𝑡	X
iajs-2963	105	11	)	)	PUNCT
iajs-2963	105	12	,	,	PUNCT
iajs-2963	105	13	𝑢1(𝑡	𝑢1(𝑡	PROPN
iajs-2963	105	14	)	)	PUNCT
iajs-2963	105	15	=	=	SYM
iajs-2963	105	16	sin(𝑡	sin(𝑡	PROPN
iajs-2963	105	17	)	)	PUNCT
iajs-2963	105	18	,	,	PUNCT
iajs-2963	105	19	𝑢3(𝑡	𝑢3(𝑡	PROPN
iajs-2963	105	20	)	)	PUNCT
iajs-2963	105	21	=	=	SYM
iajs-2963	105	22	−sin(𝑡	−sin(𝑡	NOUN
iajs-2963	105	23	)	)	PUNCT
iajs-2963	105	24	,	,	PUNCT
iajs-2963	105	25	𝑢4(𝑡	𝑢4(𝑡	NOUN
iajs-2963	105	26	)	)	PUNCT
iajs-2963	105	27	=	=	SYM
iajs-2963	105	28	cos(𝑡	cos(𝑡	X
iajs-2963	105	29	)	)	PUNCT
iajs-2963	105	30	,	,	PUNCT
iajs-2963	105	31	problem	problem	NOUN
iajs-2963	105	32	5	5	NUM
iajs-2963	105	33	:	:	PUNCT
iajs-2963	106	1	[	[	X
iajs-2963	106	2	11	11	NUM
iajs-2963	106	3	]	]	PUNCT
iajs-2963	106	4	𝑢1	𝑢1	PROPN
iajs-2963	106	5	′	′	NUM
iajs-2963	106	6	(	(	PUNCT
iajs-2963	106	7	𝑡	𝑡	NOUN
iajs-2963	106	8	)	)	PUNCT
iajs-2963	106	9	=	=	SYM
iajs-2963	106	10	𝑢3(𝑡	𝑢3(𝑡	PROPN
iajs-2963	106	11	)	)	PUNCT
iajs-2963	106	12	,	,	PUNCT
iajs-2963	106	13	𝑢1(0	𝑢1(0	PROPN
iajs-2963	106	14	)	)	PUNCT
iajs-2963	106	15	=	=	SYM
iajs-2963	106	16	1	1	NUM
iajs-2963	106	17	,	,	PUNCT
iajs-2963	106	18	𝑢3	𝑢3	PROPN
iajs-2963	106	19	′	′	NUM
iajs-2963	106	20	(	(	PUNCT
iajs-2963	106	21	𝑡	𝑡	NOUN
iajs-2963	106	22	)	)	PUNCT
iajs-2963	106	23	=	=	SYM
iajs-2963	106	24	−𝑢1(𝑡	−𝑢1(𝑡	PROPN
iajs-2963	106	25	)	)	PUNCT
iajs-2963	107	1	+	+	CCONJ
iajs-2963	108	1	0.001	0.001	NUM
iajs-2963	108	2	cos(𝑡	cos(𝑡	NOUN
iajs-2963	108	3	)	)	PUNCT
iajs-2963	108	4	,	,	PUNCT
iajs-2963	108	5	𝑢3(0	𝑢3(0	PROPN
iajs-2963	108	6	)	)	PUNCT
iajs-2963	108	7	=	=	SYM
iajs-2963	108	8	0	0	NUM
iajs-2963	108	9	,	,	PUNCT
iajs-2963	108	10	𝑢2	𝑢2	PROPN
iajs-2963	108	11	′	′	NUM
iajs-2963	108	12	(	(	PUNCT
iajs-2963	108	13	𝑡	𝑡	NOUN
iajs-2963	108	14	)	)	PUNCT
iajs-2963	108	15	=	=	SYM
iajs-2963	108	16	𝑢4(𝑡	𝑢4(𝑡	NOUN
iajs-2963	108	17	)	)	PUNCT
iajs-2963	108	18	,	,	PUNCT
iajs-2963	108	19	𝑢2(0	𝑢2(0	NOUN
iajs-2963	108	20	)	)	PUNCT
iajs-2963	108	21	=	=	SYM
iajs-2963	108	22	0	0	NUM
iajs-2963	108	23	,	,	PUNCT
iajs-2963	108	24	𝑢4	𝑢4	NOUN
iajs-2963	108	25	′	′	NUM
iajs-2963	108	26	(	(	PUNCT
iajs-2963	108	27	𝑡	𝑡	NOUN
iajs-2963	108	28	)	)	PUNCT
iajs-2963	108	29	=	=	SYM
iajs-2963	108	30	−𝑢2(𝑡	−𝑢2(𝑡	NOUN
iajs-2963	108	31	)	)	PUNCT
iajs-2963	108	32	+	+	CCONJ
iajs-2963	108	33	0.001	0.001	NUM
iajs-2963	108	34	sin(𝑡	sin(𝑡	NOUN
iajs-2963	108	35	)	)	PUNCT
iajs-2963	108	36	,	,	PUNCT
iajs-2963	108	37	𝑢4(0	𝑢4(0	NOUN
iajs-2963	108	38	)	)	PUNCT
iajs-2963	108	39	=	=	PUNCT
iajs-2963	109	1	0.9995	0.9995	NUM
iajs-2963	109	2	.	.	PUNCT
iajs-2963	110	1	exact	exact	ADJ
iajs-2963	110	2	solution	solution	NOUN
iajs-2963	110	3	is	be	AUX
iajs-2963	110	4	:	:	PUNCT
iajs-2963	110	5	𝑢1(𝑡	𝑢1(𝑡	X
iajs-2963	110	6	)	)	PUNCT
iajs-2963	110	7	=	=	SYM
iajs-2963	110	8	cos(𝑡	cos(𝑡	X
iajs-2963	110	9	)	)	PUNCT
iajs-2963	110	10	+	+	NUM
iajs-2963	111	1	0.0005	0.0005	NUM
iajs-2963	111	2	𝑡	𝑡	PRON
iajs-2963	111	3	sin(𝑡	sin(𝑡	PROPN
iajs-2963	111	4	)	)	PUNCT
iajs-2963	111	5	,	,	PUNCT
iajs-2963	111	6	𝑢2(𝑡	𝑢2(𝑡	PROPN
iajs-2963	111	7	)	)	PUNCT
iajs-2963	111	8	=	=	SYM
iajs-2963	111	9	−0.9995	−0.9995	PROPN
iajs-2963	111	10	sin(𝑡	sin(𝑡	PROPN
iajs-2963	111	11	)	)	PUNCT
iajs-2963	111	12	+	+	NUM
iajs-2963	111	13	0.0005	0.0005	NUM
iajs-2963	111	14	𝑡	𝑡	X
iajs-2963	111	15	cos(𝑡	cos(𝑡	NOUN
iajs-2963	111	16	)	)	PUNCT
iajs-2963	111	17	,	,	PUNCT
iajs-2963	111	18	𝑢3(𝑡	𝑢3(𝑡	PROPN
iajs-2963	111	19	)	)	PUNCT
iajs-2963	111	20	=	=	SYM
iajs-2963	111	21	sin(𝑡	sin(𝑡	PROPN
iajs-2963	111	22	)	)	PUNCT
iajs-2963	111	23	−	−	PROPN
iajs-2963	111	24	0.0005	0.0005	NUM
iajs-2963	111	25	𝑡	𝑡	X
iajs-2963	111	26	cos(𝑡	cos(𝑡	NOUN
iajs-2963	111	27	)	)	PUNCT
iajs-2963	111	28	,	,	PUNCT
iajs-2963	111	29	𝑢4(𝑡	𝑢4(𝑡	NOUN
iajs-2963	111	30	)	)	PUNCT
iajs-2963	111	31	=	=	SYM
iajs-2963	111	32	0.9995	0.9995	NUM
iajs-2963	111	33	cos(𝑡	cos(𝑡	X
iajs-2963	111	34	)	)	PUNCT
iajs-2963	111	35	+	+	NUM
iajs-2963	111	36	0.0005	0.0005	NUM
iajs-2963	111	37	𝑡	𝑡	PRON
iajs-2963	111	38	sin(𝑡	sin(𝑡	PROPN
iajs-2963	111	39	)	)	PUNCT
iajs-2963	111	40	.	.	PUNCT
iajs-2963	112	1	ihjpas	ihjpas	PROPN
iajs-2963	112	2	.	.	PUNCT
iajs-2963	113	1	36(1)2023	36(1)2023	NUM
iajs-2963	113	2	351	351	NUM
iajs-2963	113	3	figure	figure	NOUN
iajs-2963	113	4	1	1	NUM
iajs-2963	113	5	.	.	PUNCT
iajs-2963	114	1	the	the	DET
iajs-2963	114	2	curves	curve	NOUN
iajs-2963	114	3	comparisons	comparison	NOUN
iajs-2963	114	4	for	for	ADP
iajs-2963	114	5	problem	problem	NOUN
iajs-2963	114	6	1	1	NUM
iajs-2963	114	7	with	with	ADP
iajs-2963	114	8	step	step	NOUN
iajs-2963	114	9	size	size	NOUN
iajs-2963	114	10	ℎ	ℎ	PROPN
iajs-2963	114	11	=	=	SYM
iajs-2963	114	12	1	1	NUM
iajs-2963	114	13	2𝑟	2𝑟	NUM
iajs-2963	114	14	,	,	PUNCT
iajs-2963	114	15	𝑟	𝑟	X
iajs-2963	114	16	=	=	SYM
iajs-2963	114	17	0,1,2,4	0,1,2,4	X
iajs-2963	114	18	.	.	PUNCT
iajs-2963	114	19	figure	figure	NOUN
iajs-2963	114	20	2	2	NUM
iajs-2963	114	21	.	.	PUNCT
iajs-2963	115	1	the	the	DET
iajs-2963	115	2	curves	curve	NOUN
iajs-2963	115	3	comparisons	comparison	NOUN
iajs-2963	115	4	for	for	ADP
iajs-2963	115	5	problem	problem	NOUN
iajs-2963	115	6	2	2	NUM
iajs-2963	115	7	with	with	ADP
iajs-2963	115	8	step	step	NOUN
iajs-2963	115	9	size	size	NOUN
iajs-2963	115	10	ℎ	ℎ	PROPN
iajs-2963	115	11	=	=	SYM
iajs-2963	115	12	1	1	NUM
iajs-2963	115	13	2𝑟	2𝑟	NUM
iajs-2963	115	14	,	,	PUNCT
iajs-2963	115	15	𝑟	𝑟	X
iajs-2963	115	16	=	=	SYM
iajs-2963	115	17	0,1,2,4	0,1,2,4	X
iajs-2963	115	18	.	.	PUNCT
iajs-2963	115	19	ihjpas	ihjpas	PROPN
iajs-2963	115	20	.	.	PUNCT
iajs-2963	116	1	36(1)2023	36(1)2023	NUM
iajs-2963	116	2	352	352	NUM
iajs-2963	116	3	figure	figure	NOUN
iajs-2963	116	4	3	3	NUM
iajs-2963	116	5	.	.	PUNCT
iajs-2963	117	1	the	the	DET
iajs-2963	117	2	curves	curve	NOUN
iajs-2963	117	3	comparisons	comparison	NOUN
iajs-2963	117	4	for	for	ADP
iajs-2963	117	5	problem	problem	NOUN
iajs-2963	117	6	3	3	NUM
iajs-2963	117	7	with	with	ADP
iajs-2963	117	8	step	step	NOUN
iajs-2963	117	9	size	size	NOUN
iajs-2963	117	10	ℎ	ℎ	PROPN
iajs-2963	117	11	=	=	SYM
iajs-2963	117	12	1	1	NUM
iajs-2963	117	13	2𝑟	2𝑟	NUM
iajs-2963	117	14	,	,	PUNCT
iajs-2963	117	15	𝑟	𝑟	X
iajs-2963	117	16	=	=	SYM
iajs-2963	117	17	0,1,2,4	0,1,2,4	X
iajs-2963	117	18	.	.	PUNCT
iajs-2963	117	19	figure	figure	NOUN
iajs-2963	117	20	4	4	NUM
iajs-2963	117	21	.	.	PUNCT
iajs-2963	118	1	the	the	DET
iajs-2963	118	2	curves	curve	NOUN
iajs-2963	118	3	comparisons	comparison	NOUN
iajs-2963	118	4	for	for	ADP
iajs-2963	118	5	problem	problem	NOUN
iajs-2963	118	6	4	4	NUM
iajs-2963	118	7	with	with	ADP
iajs-2963	118	8	step	step	NOUN
iajs-2963	118	9	size	size	NOUN
iajs-2963	118	10	ℎ	ℎ	PROPN
iajs-2963	118	11	=	=	SYM
iajs-2963	118	12	1	1	NUM
iajs-2963	118	13	2𝑟	2𝑟	NUM
iajs-2963	118	14	,	,	PUNCT
iajs-2963	118	15	𝑟	𝑟	X
iajs-2963	118	16	=	=	SYM
iajs-2963	118	17	0,1,2,4	0,1,2,4	X
iajs-2963	118	18	.	.	PUNCT
iajs-2963	118	19	ihjpas	ihjpas	PROPN
iajs-2963	118	20	.	.	PUNCT
iajs-2963	119	1	36(1)2023	36(1)2023	NUM
iajs-2963	119	2	353	353	NUM
iajs-2963	119	3	figure	figure	NOUN
iajs-2963	119	4	5	5	NUM
iajs-2963	119	5	.	.	PUNCT
iajs-2963	120	1	the	the	DET
iajs-2963	120	2	curves	curve	NOUN
iajs-2963	120	3	comparisons	comparison	NOUN
iajs-2963	120	4	for	for	ADP
iajs-2963	120	5	problem	problem	NOUN
iajs-2963	120	6	5	5	NUM
iajs-2963	120	7	with	with	ADP
iajs-2963	120	8	step	step	NOUN
iajs-2963	120	9	size	size	NOUN
iajs-2963	120	10	ℎ	ℎ	PROPN
iajs-2963	120	11	=	=	SYM
iajs-2963	120	12	1	1	NUM
iajs-2963	120	13	2𝑟	2𝑟	NUM
iajs-2963	120	14	,	,	PUNCT
iajs-2963	120	15	𝑟	𝑟	X
iajs-2963	120	16	=	=	SYM
iajs-2963	120	17	0,1,2,4	0,1,2,4	NUM
iajs-2963	120	18	.	.	PUNCT
iajs-2963	120	19	to	to	PART
iajs-2963	120	20	assess	assess	VERB
iajs-2963	120	21	the	the	DET
iajs-2963	120	22	method	method	NOUN
iajs-2963	120	23	's	's	PART
iajs-2963	120	24	accuracy	accuracy	NOUN
iajs-2963	120	25	,	,	PUNCT
iajs-2963	120	26	we	we	PRON
iajs-2963	120	27	utilize	utilize	VERB
iajs-2963	120	28	the	the	DET
iajs-2963	120	29	absolute	absolute	ADJ
iajs-2963	120	30	error	error	NOUN
iajs-2963	120	31	criterion	criterion	NOUN
iajs-2963	120	32	.	.	PUNCT
iajs-2963	121	1	the	the	DET
iajs-2963	121	2	step	step	NOUN
iajs-2963	121	3	size	size	NOUN
iajs-2963	121	4	is	be	AUX
iajs-2963	121	5	ℎ	ℎ	PROPN
iajs-2963	121	6	=	=	SYM
iajs-2963	121	7	1	1	NUM
iajs-2963	121	8	2𝑟	2𝑟	NUM
iajs-2963	121	9	,	,	PUNCT
iajs-2963	121	10	𝑟	𝑟	X
iajs-2963	121	11	=	=	SYM
iajs-2963	121	12	0,1,2,4	0,1,2,4	NUM
iajs-2963	121	13	.	.	PUNCT
iajs-2963	122	1	and	and	CCONJ
iajs-2963	122	2	integration	integration	NOUN
iajs-2963	122	3	interval	interval	NOUN
iajs-2963	122	4	is	be	AUX
iajs-2963	122	5	[	[	X
iajs-2963	122	6	0	0	NUM
iajs-2963	122	7	,	,	PUNCT
iajs-2963	122	8	1000	1000	NUM
iajs-2963	122	9	]	]	PUNCT
iajs-2963	122	10	for	for	ADP
iajs-2963	122	11	all	all	DET
iajs-2963	122	12	problems	problem	NOUN
iajs-2963	122	13	.	.	PUNCT
iajs-2963	123	1	the	the	DET
iajs-2963	123	2	accuracy	accuracy	NOUN
iajs-2963	123	3	of	of	ADP
iajs-2963	123	4	the	the	DET
iajs-2963	123	5	new	new	ADJ
iajs-2963	123	6	tfirk4	tfirk4	PROPN
iajs-2963	123	7	approach	approach	NOUN
iajs-2963	123	8	is	be	AUX
iajs-2963	123	9	depicted	depict	VERB
iajs-2963	123	10	in	in	ADP
iajs-2963	123	11	figures	figure	NOUN
iajs-2963	123	12	1–5	1–5	NUM
iajs-2963	123	13	in	in	ADP
iajs-2963	123	14	terms	term	NOUN
iajs-2963	123	15	of	of	ADP
iajs-2963	123	16	the	the	DET
iajs-2963	123	17	greatest	great	ADJ
iajs-2963	123	18	global	global	ADJ
iajs-2963	123	19	absolute	absolute	ADJ
iajs-2963	123	20	error	error	NOUN
iajs-2963	123	21	versus	versus	ADP
iajs-2963	123	22	the	the	DET
iajs-2963	123	23	step	step	NOUN
iajs-2963	123	24	sizes	size	NOUN
iajs-2963	123	25	required	require	VERB
iajs-2963	123	26	by	by	ADP
iajs-2963	123	27	each	each	DET
iajs-2963	123	28	method	method	NOUN
iajs-2963	123	29	.	.	PUNCT
iajs-2963	124	1	compared	compare	VERB
iajs-2963	124	2	to	to	ADP
iajs-2963	124	3	other	other	ADJ
iajs-2963	124	4	rk	rk	NOUN
iajs-2963	124	5	methods	method	NOUN
iajs-2963	124	6	of	of	ADP
iajs-2963	124	7	the	the	DET
iajs-2963	124	8	same	same	ADJ
iajs-2963	124	9	order	order	NOUN
iajs-2963	124	10	,	,	PUNCT
iajs-2963	124	11	the	the	DET
iajs-2963	124	12	tfirk4	tfirk4	PROPN
iajs-2963	124	13	approaches	approach	VERB
iajs-2963	124	14	,	,	PUNCT
iajs-2963	124	15	as	as	SCONJ
iajs-2963	124	16	shown	show	VERB
iajs-2963	124	17	in	in	ADP
iajs-2963	124	18	figures	figure	NOUN
iajs-2963	124	19	1–5	1–5	NUM
iajs-2963	124	20	,	,	PUNCT
iajs-2963	124	21	have	have	VERB
iajs-2963	124	22	the	the	DET
iajs-2963	124	23	smallest	small	ADJ
iajs-2963	124	24	maximum	maximum	ADJ
iajs-2963	124	25	global	global	ADJ
iajs-2963	124	26	error	error	NOUN
iajs-2963	124	27	per	per	ADP
iajs-2963	124	28	step	step	NOUN
iajs-2963	124	29	.	.	PUNCT
iajs-2963	125	1	the	the	DET
iajs-2963	125	2	tfirk4	tfirk4	NOUN
iajs-2963	125	3	produces	produce	VERB
iajs-2963	125	4	results	result	NOUN
iajs-2963	125	5	that	that	PRON
iajs-2963	125	6	are	be	AUX
iajs-2963	125	7	more	more	ADV
iajs-2963	125	8	accurate	accurate	ADJ
iajs-2963	125	9	than	than	ADP
iajs-2963	125	10	those	those	PRON
iajs-2963	125	11	of	of	ADP
iajs-2963	125	12	other	other	ADJ
iajs-2963	125	13	research	research	NOUN
iajs-2963	125	14	in	in	ADP
iajs-2963	125	15	the	the	DET
iajs-2963	125	16	literature	literature	NOUN
iajs-2963	125	17	,	,	PUNCT
iajs-2963	125	18	as	as	SCONJ
iajs-2963	125	19	seen	see	VERB
iajs-2963	125	20	in	in	ADP
iajs-2963	125	21	figures	figure	NOUN
iajs-2963	125	22	1–5	1–5	NUM
iajs-2963	125	23	.	.	NOUN
iajs-2963	125	24	4	4	NUM
iajs-2963	125	25	.	.	PUNCT
iajs-2963	126	1	conclusions	conclusion	NOUN
iajs-2963	126	2	we	we	PRON
iajs-2963	126	3	derived	derive	VERB
iajs-2963	126	4	the	the	DET
iajs-2963	126	5	conditions	condition	NOUN
iajs-2963	126	6	of	of	ADP
iajs-2963	126	7	the	the	DET
iajs-2963	126	8	trigonometrically	trigonometrically	ADV
iajs-2963	126	9	-	-	PUNCT
iajs-2963	126	10	fitted	fit	VERB
iajs-2963	126	11	irk	irk	NOUN
iajs-2963	126	12	approach	approach	NOUN
iajs-2963	126	13	to	to	ADP
iajs-2963	126	14	solving	solve	VERB
iajs-2963	126	15	oscillatory	oscillatory	ADJ
iajs-2963	126	16	problems	problem	NOUN
iajs-2963	126	17	in	in	ADP
iajs-2963	126	18	this	this	DET
iajs-2963	126	19	paper	paper	NOUN
iajs-2963	126	20	.	.	PUNCT
iajs-2963	127	1	as	as	ADP
iajs-2963	127	2	a	a	DET
iajs-2963	127	3	result	result	NOUN
iajs-2963	127	4	,	,	PUNCT
iajs-2963	127	5	we	we	PRON
iajs-2963	127	6	developed	develop	VERB
iajs-2963	127	7	the	the	DET
iajs-2963	127	8	tfirk4	tfirk4	PROPN
iajs-2963	127	9	method	method	NOUN
iajs-2963	127	10	,	,	PUNCT
iajs-2963	127	11	a	a	DET
iajs-2963	127	12	four	four	NUM
iajs-2963	127	13	-	-	PUNCT
iajs-2963	127	14	stage	stage	NOUN
iajs-2963	127	15	,	,	PUNCT
iajs-2963	127	16	fourth	fourth	ADJ
iajs-2963	127	17	-	-	PUNCT
iajs-2963	127	18	order	order	NOUN
iajs-2963	127	19	irk	irk	NOUN
iajs-2963	127	20	method	method	NOUN
iajs-2963	127	21	that	that	PRON
iajs-2963	127	22	is	be	AUX
iajs-2963	127	23	trigonometrically	trigonometrically	ADV
iajs-2963	127	24	fitted	fit	VERB
iajs-2963	127	25	.	.	PUNCT
iajs-2963	128	1	the	the	DET
iajs-2963	128	2	figures	figure	NOUN
iajs-2963	128	3	show	show	VERB
iajs-2963	128	4	how	how	SCONJ
iajs-2963	128	5	the	the	DET
iajs-2963	128	6	step	step	NOUN
iajs-2963	128	7	size	size	NOUN
iajs-2963	128	8	was	be	AUX
iajs-2963	128	9	used	use	VERB
iajs-2963	128	10	to	to	PART
iajs-2963	128	11	calculate	calculate	VERB
iajs-2963	128	12	the	the	DET
iajs-2963	128	13	common	common	ADJ
iajs-2963	128	14	logarithm	logarithm	NOUN
iajs-2963	128	15	of	of	ADP
iajs-2963	128	16	the	the	DET
iajs-2963	128	17	most	most	ADV
iajs-2963	128	18	significant	significant	ADJ
iajs-2963	128	19	global	global	ADJ
iajs-2963	128	20	error	error	NOUN
iajs-2963	128	21	during	during	ADP
iajs-2963	128	22	integration	integration	NOUN
iajs-2963	128	23	and	and	CCONJ
iajs-2963	128	24	computing	computing	NOUN
iajs-2963	128	25	cost	cost	NOUN
iajs-2963	128	26	.	.	PUNCT
iajs-2963	129	1	the	the	DET
iajs-2963	129	2	numerical	numerical	ADJ
iajs-2963	129	3	results	result	NOUN
iajs-2963	129	4	made	make	VERB
iajs-2963	129	5	it	it	PRON
iajs-2963	129	6	clear	clear	ADJ
iajs-2963	129	7	that	that	SCONJ
iajs-2963	129	8	the	the	DET
iajs-2963	129	9	tfirk4	tfirk4	PROPN
iajs-2963	129	10	approach	approach	NOUN
iajs-2963	129	11	using	use	VERB
iajs-2963	129	12	a	a	DET
iajs-2963	129	13	trigonometrically	trigonometrically	ADV
iajs-2963	129	14	fitted	fit	VERB
iajs-2963	129	15	strategy	strategy	NOUN
iajs-2963	129	16	,	,	PUNCT
iajs-2963	129	17	had	have	VERB
iajs-2963	129	18	less	less	ADJ
iajs-2963	129	19	global	global	ADJ
iajs-2963	129	20	error	error	NOUN
iajs-2963	129	21	than	than	ADP
iajs-2963	129	22	the	the	DET
iajs-2963	129	23	existing	exist	VERB
iajs-2963	129	24	methods	method	NOUN
iajs-2963	129	25	used	use	VERB
iajs-2963	129	26	to	to	PART
iajs-2963	129	27	solve	solve	VERB
iajs-2963	129	28	oscillatory	oscillatory	ADJ
iajs-2963	129	29	problems	problem	NOUN
iajs-2963	129	30	.	.	PUNCT
iajs-2963	130	1	references	reference	NOUN
iajs-2963	130	2	1	1	NUM
iajs-2963	130	3	.	.	PUNCT
iajs-2963	130	4	hairer	hairer	PROPN
iajs-2963	130	5	,	,	PUNCT
iajs-2963	130	6	e.	e.	PROPN
iajs-2963	130	7	;	;	PUNCT
iajs-2963	130	8	nrsett	nrsett	PROPN
iajs-2963	130	9	,	,	PUNCT
iajs-2963	130	10	s.p	s.p	PROPN
iajs-2963	130	11	.	.	PROPN
iajs-2963	130	12	;	;	PUNCT
iajs-2963	130	13	and	and	CCONJ
iajs-2963	130	14	wanner	wanner	NOUN
iajs-2963	130	15	,	,	PUNCT
iajs-2963	130	16	g.	g.	PROPN
iajs-2963	130	17	solving	solve	VERB
iajs-2963	130	18	ordinary	ordinary	ADJ
iajs-2963	130	19	differential	differential	ADJ
iajs-2963	130	20	equations	equation	NOUN
iajs-2963	131	1	i	i	PRON
iajs-2963	131	2	:	:	PUNCT
iajs-2963	131	3	nonstiff	nonstiff	PROPN
iajs-2963	131	4	problems	problem	NOUN
iajs-2963	131	5	.	.	PUNCT
iajs-2963	132	1	springer	springer	NOUN
iajs-2963	132	2	;	;	PUNCT
iajs-2963	132	3	berlin	berlin	PROPN
iajs-2963	132	4	;	;	PUNCT
iajs-2963	132	5	1993	1993	NUM
iajs-2963	132	6	.	.	PUNCT
iajs-2963	133	1	isbn	isbn	ADJ
iajs-2963	133	2	:	:	PUNCT
iajs-2963	133	3	978	978	NUM
iajs-2963	133	4	-	-	SYM
iajs-2963	133	5	3	3	NUM
iajs-2963	133	6	-	-	PUNCT
iajs-2963	133	7	540	540	NUM
iajs-2963	133	8	-	-	PUNCT
iajs-2963	133	9	78862	78862	NUM
iajs-2963	133	10	-	-	SYM
iajs-2963	133	11	1	1	NUM
iajs-2963	133	12	.	.	NOUN
iajs-2963	133	13	2	2	NUM
iajs-2963	133	14	.	.	X
iajs-2963	133	15	butcher	butcher	NOUN
iajs-2963	133	16	,	,	PUNCT
iajs-2963	133	17	j.c	j.c	PROPN
iajs-2963	133	18	.	.	PROPN
iajs-2963	133	19	numerical	numerical	PROPN
iajs-2963	133	20	methods	method	NOUN
iajs-2963	133	21	for	for	ADP
iajs-2963	133	22	ordinary	ordinary	ADJ
iajs-2963	133	23	differential	differential	ADJ
iajs-2963	133	24	equations	equation	NOUN
iajs-2963	133	25	.	.	PUNCT
iajs-2963	134	1	2nd	2nd	ADJ
iajs-2963	134	2	ed	ed	NOUN
iajs-2963	134	3	.	.	PROPN
iajs-2963	134	4	,	,	PUNCT
iajs-2963	134	5	john	john	PROPN
iajs-2963	134	6	wiley	wiley	PROPN
iajs-2963	134	7	&	&	CCONJ
iajs-2963	134	8	son	son	PROPN
iajs-2963	134	9	;	;	PUNCT
iajs-2963	134	10	new	new	PROPN
iajs-2963	134	11	york	york	PROPN
iajs-2963	134	12	;	;	PUNCT
iajs-2963	134	13	2016	2016	NUM
iajs-2963	134	14	,	,	PUNCT
iajs-2963	134	15	isbn	isbn	ADJ
iajs-2963	134	16	:	:	PUNCT
iajs-2963	134	17	978	978	NUM
iajs-2963	134	18	-	-	SYM
iajs-2963	134	19	0	0	NUM
iajs-2963	134	20	-	-	PUNCT
iajs-2963	134	21	470	470	NUM
iajs-2963	134	22	-	-	PUNCT
iajs-2963	134	23	72335	72335	NUM
iajs-2963	134	24	-	-	PUNCT
iajs-2963	134	25	7	7	NUM
iajs-2963	134	26	.	.	NOUN
iajs-2963	134	27	3	3	NUM
iajs-2963	134	28	.	.	X
iajs-2963	135	1	salih	salih	PROPN
iajs-2963	135	2	,	,	PUNCT
iajs-2963	135	3	m.	m.	NOUN
iajs-2963	135	4	;	;	PUNCT
iajs-2963	135	5	ismail	ismail	PROPN
iajs-2963	135	6	,	,	PUNCT
iajs-2963	135	7	f.	f.	PROPN
iajs-2963	135	8	;	;	PUNCT
iajs-2963	135	9	senu	senu	X
iajs-2963	135	10	,	,	PUNCT
iajs-2963	135	11	n.	n.	NOUN
iajs-2963	135	12	phase	phase	NOUN
iajs-2963	135	13	fitted	fit	VERB
iajs-2963	135	14	and	and	CCONJ
iajs-2963	135	15	amplification	amplification	NOUN
iajs-2963	135	16	fitted	fit	VERB
iajs-2963	135	17	of	of	ADP
iajs-2963	135	18	runge	runge	NOUN
iajs-2963	135	19	-	-	PUNCT
iajs-2963	135	20	kutta	kutta	NOUN
iajs-2963	135	21	fehlberg	fehlberg	NOUN
iajs-2963	135	22	method	method	NOUN
iajs-2963	135	23	of	of	ADP
iajs-2963	135	24	order	order	NOUN
iajs-2963	135	25	4	4	NUM
iajs-2963	135	26	(	(	PUNCT
iajs-2963	135	27	5	5	NUM
iajs-2963	135	28	)	)	PUNCT
iajs-2963	135	29	for	for	ADP
iajs-2963	135	30	solving	solve	VERB
iajs-2963	135	31	oscillatory	oscillatory	ADJ
iajs-2963	135	32	problems	problem	NOUN
iajs-2963	135	33	.	.	PUNCT
iajs-2963	136	1	baghdad	baghdad	PROPN
iajs-2963	136	2	science	science	PROPN
iajs-2963	136	3	journal	journal	PROPN
iajs-2963	136	4	.	.	PUNCT
iajs-2963	137	1	2020	2020	NUM
iajs-2963	137	2	,	,	PUNCT
iajs-2963	137	3	17(2	17(2	NUM
iajs-2963	137	4	)	)	PUNCT
iajs-2963	137	5	,	,	PUNCT
iajs-2963	137	6	689	689	NUM
iajs-2963	137	7	-	-	SYM
iajs-2963	137	8	689	689	NUM
iajs-2963	137	9	.	.	PUNCT
iajs-2963	137	10	ihjpas	ihjpas	PROPN
iajs-2963	137	11	.	.	PUNCT
iajs-2963	138	1	36(1)2023	36(1)2023	NUM
iajs-2963	138	2	354	354	NUM
iajs-2963	138	3	4.rabiei	4.rabiei	NUM
iajs-2963	138	4	,	,	PUNCT
iajs-2963	138	5	f.	f.	PROPN
iajs-2963	138	6	;	;	PUNCT
iajs-2963	138	7	ismail	ismail	PROPN
iajs-2963	138	8	,	,	PUNCT
iajs-2963	138	9	f.	f.	PROPN
iajs-2963	138	10	improved	improve	VERB
iajs-2963	138	11	runge	runge	NOUN
iajs-2963	138	12	-	-	PUNCT
iajs-2963	138	13	kutta	kutta	NOUN
iajs-2963	138	14	methods	method	NOUN
iajs-2963	138	15	for	for	ADP
iajs-2963	138	16	solving	solve	VERB
iajs-2963	138	17	ordinary	ordinary	ADJ
iajs-2963	138	18	differential	differential	ADJ
iajs-2963	138	19	equations	equation	NOUN
iajs-2963	138	20	.	.	PUNCT
iajs-2963	139	1	sains	sain	NOUN
iajs-2963	139	2	malaysiana	malaysiana	PROPN
iajs-2963	139	3	.	.	PUNCT
iajs-2963	140	1	2013	2013	NUM
iajs-2963	140	2	,	,	PUNCT
iajs-2963	140	3	42(11	42(11	NUM
iajs-2963	140	4	)	)	PUNCT
iajs-2963	140	5	,	,	PUNCT
iajs-2963	140	6	1679–1687	1679–1687	NOUN
iajs-2963	140	7	.	.	PUNCT
iajs-2963	141	1	5	5	NUM
iajs-2963	141	2	.	.	X
iajs-2963	141	3	ahmad	ahmad	PROPN
iajs-2963	141	4	,	,	PUNCT
iajs-2963	141	5	n.a	n.a	PROPN
iajs-2963	141	6	.	.	PROPN
iajs-2963	141	7	;	;	PUNCT
iajs-2963	141	8	senu	senu	NOUN
iajs-2963	141	9	,	,	PUNCT
iajs-2963	141	10	n.	n.	NOUN
iajs-2963	141	11	;	;	PUNCT
iajs-2963	141	12	and	and	CCONJ
iajs-2963	141	13	ismail	ismail	PROPN
iajs-2963	141	14	,	,	PUNCT
iajs-2963	141	15	f.	f.	PROPN
iajs-2963	141	16	trigonometrically	trigonometrically	ADV
iajs-2963	141	17	-	-	PUNCT
iajs-2963	141	18	fitted	fit	VERB
iajs-2963	141	19	higher	high	ADJ
iajs-2963	141	20	order	order	NOUN
iajs-2963	141	21	two	two	NUM
iajs-2963	141	22	derivative	derivative	ADJ
iajs-2963	141	23	runge	runge	NOUN
iajs-2963	141	24	-	-	PUNCT
iajs-2963	141	25	kutta	kutta	NOUN
iajs-2963	141	26	method	method	NOUN
iajs-2963	141	27	for	for	ADP
iajs-2963	141	28	solving	solve	VERB
iajs-2963	141	29	orbital	orbital	ADJ
iajs-2963	141	30	and	and	CCONJ
iajs-2963	141	31	related	relate	VERB
iajs-2963	141	32	periodical	periodical	ADJ
iajs-2963	141	33	ivps	ivps	PROPN
iajs-2963	141	34	.	.	PUNCT
iajs-2963	142	1	hacettepe	hacettepe	PROPN
iajs-2963	142	2	journal	journal	PROPN
iajs-2963	142	3	of	of	ADP
iajs-2963	142	4	mathematics	mathematic	NOUN
iajs-2963	142	5	and	and	CCONJ
iajs-2963	142	6	statistics	statistic	NOUN
iajs-2963	142	7	,	,	PUNCT
iajs-2963	142	8	2019	2019	NUM
iajs-2963	142	9	,	,	PUNCT
iajs-2963	142	10	48(5),1312	48(5),1312	NUM
iajs-2963	142	11	-	-	SYM
iajs-2963	142	12	1323	1323	NUM
iajs-2963	142	13	.	.	PUNCT
iajs-2963	143	1	6.ghazal	6.ghazal	NUM
iajs-2963	143	2	,	,	PUNCT
iajs-2963	143	3	z.k	z.k	PROPN
iajs-2963	143	4	.	.	PROPN
iajs-2963	143	5	;	;	PUNCT
iajs-2963	144	1	hussain	hussain	AUX
iajs-2963	144	2	,	,	PUNCT
iajs-2963	144	3	k.a	k.a	PROPN
iajs-2963	144	4	.	.	PUNCT
iajs-2963	144	5	solving	solve	VERB
iajs-2963	144	6	oscillating	oscillating	NOUN
iajs-2963	144	7	problems	problem	NOUN
iajs-2963	144	8	using	use	VERB
iajs-2963	144	9	modifying	modify	VERB
iajs-2963	144	10	runge	runge	NOUN
iajs-2963	144	11	-	-	PUNCT
iajs-2963	144	12	kutta	kutta	NOUN
iajs-2963	144	13	methods	method	NOUN
iajs-2963	144	14	.	.	PUNCT
iajs-2963	145	1	ibn	ibn	PROPN
iajs-2963	145	2	al	al	PROPN
iajs-2963	145	3	-	-	PUNCT
iajs-2963	145	4	haitham	haitham	PROPN
iajs-2963	145	5	journal	journal	PROPN
iajs-2963	145	6	for	for	ADP
iajs-2963	145	7	pure	pure	ADJ
iajs-2963	145	8	and	and	CCONJ
iajs-2963	145	9	applied	applied	ADJ
iajs-2963	145	10	sciences	science	NOUN
iajs-2963	145	11	,	,	PUNCT
iajs-2963	145	12	2021	2021	NUM
iajs-2963	145	13	,	,	PUNCT
iajs-2963	145	14	34(4	34(4	NUM
iajs-2963	145	15	)	)	PUNCT
iajs-2963	145	16	,	,	PUNCT
iajs-2963	145	17	58	58	NUM
iajs-2963	145	18	-	-	SYM
iajs-2963	145	19	67	67	NUM
iajs-2963	145	20	.	.	PUNCT
iajs-2963	146	1	7	7	NUM
iajs-2963	146	2	.	.	X
iajs-2963	146	3	senu	senu	NOUN
iajs-2963	146	4	,	,	PUNCT
iajs-2963	146	5	n.	n.	PROPN
iajs-2963	146	6	;	;	PUNCT
iajs-2963	146	7	lee	lee	PROPN
iajs-2963	146	8	,	,	PUNCT
iajs-2963	146	9	k.c	k.c	PROPN
iajs-2963	146	10	.	.	PROPN
iajs-2963	146	11	;	;	PUNCT
iajs-2963	146	12	wan	wan	PROPN
iajs-2963	146	13	ismail	ismail	PROPN
iajs-2963	146	14	,	,	PUNCT
iajs-2963	146	15	w.f	w.f	PROPN
iajs-2963	146	16	.	.	PROPN
iajs-2963	146	17	;	;	PUNCT
iajs-2963	147	1	ahmadian	ahmadian	ADJ
iajs-2963	147	2	,	,	PUNCT
iajs-2963	147	3	a.	a.	NOUN
iajs-2963	147	4	;	;	PUNCT
iajs-2963	147	5	ibrahim	ibrahim	PROPN
iajs-2963	147	6	s.n	s.n	PROPN
iajs-2963	147	7	.	.	PROPN
iajs-2963	147	8	;	;	PUNCT
iajs-2963	147	9	laham	laham	PROPN
iajs-2963	147	10	,	,	PUNCT
iajs-2963	147	11	m.	m.	NOUN
iajs-2963	147	12	improved	improve	VERB
iajs-2963	147	13	runge	runge	NOUN
iajs-2963	147	14	-	-	PUNCT
iajs-2963	147	15	kutta	kutta	NOUN
iajs-2963	147	16	method	method	NOUN
iajs-2963	147	17	with	with	ADP
iajs-2963	147	18	trigonometrically	trigonometrically	ADV
iajs-2963	147	19	-	-	PUNCT
iajs-2963	147	20	fitting	fit	VERB
iajs-2963	147	21	technique	technique	NOUN
iajs-2963	147	22	for	for	ADP
iajs-2963	147	23	solving	solve	VERB
iajs-2963	147	24	oscillatory	oscillatory	ADJ
iajs-2963	147	25	problem	problem	NOUN
iajs-2963	147	26	.	.	PUNCT
iajs-2963	148	1	malaysian	malaysian	ADJ
iajs-2963	148	2	journal	journal	PROPN
iajs-2963	148	3	of	of	ADP
iajs-2963	148	4	mathematical	mathematical	ADJ
iajs-2963	148	5	sciences	sciences	PROPN
iajs-2963	148	6	.	.	PUNCT
iajs-2963	149	1	2021,15(2	2021,15(2	PROPN
iajs-2963	149	2	)	)	PUNCT
iajs-2963	149	3	,	,	PUNCT
iajs-2963	149	4	253	253	NUM
iajs-2963	149	5	-	-	SYM
iajs-2963	149	6	266	266	NUM
iajs-2963	149	7	.	.	PUNCT
iajs-2963	150	1	8.fawzi	8.fawzi	NUM
iajs-2963	150	2	,	,	PUNCT
iajs-2963	150	3	f.a	f.a	PROPN
iajs-2963	150	4	.	.	PROPN
iajs-2963	150	5	;	;	PUNCT
iajs-2963	151	1	senu	senu	X
iajs-2963	151	2	,	,	PUNCT
iajs-2963	151	3	n.	n.	NOUN
iajs-2963	151	4	;	;	PUNCT
iajs-2963	151	5	ismail	ismail	PROPN
iajs-2963	151	6	,	,	PUNCT
iajs-2963	151	7	f.;majid	f.;majid	PROPN
iajs-2963	151	8	,	,	PUNCT
iajs-2963	151	9	z.a	z.a	PROPN
iajs-2963	151	10	.	.	PUNCT
iajs-2963	151	11	explicit	explicit	ADJ
iajs-2963	151	12	runge	runge	NOUN
iajs-2963	151	13	-	-	PUNCT
iajs-2963	151	14	kutta	kutta	NOUN
iajs-2963	151	15	method	method	NOUN
iajs-2963	151	16	with	with	ADP
iajs-2963	151	17	trigonometrically	trigonometrically	ADV
iajs-2963	151	18	-	-	PUNCT
iajs-2963	151	19	fitted	fit	VERB
iajs-2963	151	20	for	for	ADP
iajs-2963	151	21	solving	solve	VERB
iajs-2963	151	22	first	first	ADJ
iajs-2963	151	23	order	order	NOUN
iajs-2963	151	24	odes	ode	NOUN
iajs-2963	151	25	.	.	PUNCT
iajs-2963	152	1	in	in	ADP
iajs-2963	152	2	aip	aip	PROPN
iajs-2963	152	3	conference	conference	NOUN
iajs-2963	152	4	proceedings	proceeding	NOUN
iajs-2963	152	5	.	.	PUNCT
iajs-2963	153	1	2016	2016	NUM
iajs-2963	153	2	,	,	PUNCT
iajs-2963	153	3	1739(1),1	1739(1),1	NUM
iajs-2963	153	4	-	-	SYM
iajs-2963	153	5	7	7	NUM
iajs-2963	153	6	.	.	PUNCT
iajs-2963	154	1	9.simos	9.simos	NUM
iajs-2963	154	2	,	,	PUNCT
iajs-2963	154	3	t.e	t.e	PROPN
iajs-2963	154	4	.	.	PROPN
iajs-2963	154	5	;	;	PUNCT
iajs-2963	154	6	aguiar	aguiar	PROPN
iajs-2963	154	7	,	,	PUNCT
iajs-2963	154	8	j.v	j.v	PROPN
iajs-2963	154	9	.	.	PUNCT
iajs-2963	155	1	a	a	DET
iajs-2963	155	2	modified	modify	VERB
iajs-2963	155	3	runge	runge	NOUN
iajs-2963	155	4	–	–	PUNCT
iajs-2963	155	5	kutta	kutta	NOUN
iajs-2963	155	6	method	method	NOUN
iajs-2963	155	7	with	with	ADP
iajs-2963	155	8	phase	phase	NOUN
iajs-2963	155	9	-	-	PUNCT
iajs-2963	155	10	lag	lag	NOUN
iajs-2963	155	11	of	of	ADP
iajs-2963	155	12	order	order	NOUN
iajs-2963	155	13	infinity	infinity	NOUN
iajs-2963	155	14	for	for	ADP
iajs-2963	155	15	the	the	DET
iajs-2963	155	16	numerical	numerical	ADJ
iajs-2963	155	17	solution	solution	NOUN
iajs-2963	155	18	of	of	ADP
iajs-2963	155	19	the	the	DET
iajs-2963	155	20	schrodinger	schrodinger	ADJ
iajs-2963	155	21	equation	equation	NOUN
iajs-2963	155	22	and	and	CCONJ
iajs-2963	155	23	related	related	ADJ
iajs-2963	155	24	problems	problem	NOUN
iajs-2963	155	25	.	.	PUNCT
iajs-2963	156	1	computers	computer	NOUN
iajs-2963	156	2	&	&	CCONJ
iajs-2963	156	3	chemistry	chemistry	NOUN
iajs-2963	156	4	,	,	PUNCT
iajs-2963	156	5	2001	2001	NUM
iajs-2963	156	6	,	,	PUNCT
iajs-2963	156	7	25(3	25(3	NUM
iajs-2963	156	8	)	)	PUNCT
iajs-2963	156	9	,	,	PUNCT
iajs-2963	156	10	275	275	NUM
iajs-2963	156	11	-	-	SYM
iajs-2963	156	12	281	281	NUM
iajs-2963	156	13	.	.	PUNCT
iajs-2963	157	1	10.hussain	10.hussain	NUM
iajs-2963	157	2	,	,	PUNCT
iajs-2963	157	3	k.a	k.a	PROPN
iajs-2963	157	4	.	.	PUNCT
iajs-2963	158	1	solving	solve	VERB
iajs-2963	158	2	oscillation	oscillation	NOUN
iajs-2963	158	3	problems	problem	NOUN
iajs-2963	158	4	using	use	VERB
iajs-2963	158	5	optimized	optimize	VERB
iajs-2963	158	6	integrator	integrator	NOUN
iajs-2963	158	7	method	method	NOUN
iajs-2963	158	8	.	.	PUNCT
iajs-2963	159	1	italian	italian	ADJ
iajs-2963	159	2	journal	journal	NOUN
iajs-2963	159	3	of	of	ADP
iajs-2963	159	4	pure	pure	ADJ
iajs-2963	159	5	and	and	CCONJ
iajs-2963	159	6	applied	applied	ADJ
iajs-2963	159	7	mathematics	mathematic	NOUN
iajs-2963	159	8	.	.	PUNCT
iajs-2963	160	1	2022	2022	NUM
iajs-2963	160	2	,	,	PUNCT
iajs-2963	160	3	47	47	NUM
iajs-2963	160	4	,	,	PUNCT
iajs-2963	160	5	578	578	NUM
iajs-2963	160	6	-	-	SYM
iajs-2963	160	7	587	587	NUM
iajs-2963	160	8	.	.	PUNCT
iajs-2963	161	1	11.senu	11.senu	NUM
iajs-2963	161	2	,	,	PUNCT
iajs-2963	161	3	n.	n.	NOUN
iajs-2963	161	4	;	;	PUNCT
iajs-2963	161	5	ahmed	ahmed	PROPN
iajs-2963	161	6	,	,	PUNCT
iajs-2963	161	7	n.a	n.a	PROPN
iajs-2963	161	8	.	.	PROPN
iajs-2963	161	9	,	,	PUNCT
iajs-2963	161	10	ibrahim	ibrahim	PROPN
iajs-2963	161	11	,	,	PUNCT
iajs-2963	161	12	z.b	z.b	PROPN
iajs-2963	161	13	.	.	PROPN
iajs-2963	161	14	;	;	PUNCT
iajs-2963	162	1	othman	othman	PROPN
iajs-2963	162	2	,	,	PUNCT
iajs-2963	162	3	m.	m.	PROPN
iajs-2963	162	4	numerical	numerical	PROPN
iajs-2963	162	5	study	study	PROPN
iajs-2963	162	6	on	on	ADP
iajs-2963	162	7	phase	phase	NOUN
iajs-2963	162	8	-	-	PUNCT
iajs-2963	162	9	fitted	fit	VERB
iajs-2963	162	10	and	and	CCONJ
iajs-2963	162	11	amplification	amplification	NOUN
iajs-2963	162	12	-	-	PUNCT
iajs-2963	162	13	fitted	fit	VERB
iajs-2963	162	14	diagonally	diagonally	ADV
iajs-2963	162	15	implicit	implicit	ADJ
iajs-2963	162	16	two	two	NUM
iajs-2963	162	17	derivative	derivative	ADJ
iajs-2963	162	18	runge	runge	NOUN
iajs-2963	162	19	-	-	PUNCT
iajs-2963	162	20	kutta	kutta	NOUN
iajs-2963	162	21	method	method	NOUN
iajs-2963	162	22	for	for	ADP
iajs-2963	162	23	periodic	periodic	ADJ
iajs-2963	162	24	ivps	ivps	PROPN
iajs-2963	162	25	.	.	PUNCT
iajs-2963	163	1	sains	sain	NOUN
iajs-2963	163	2	malaysiana	malaysiana	PROPN
iajs-2963	163	3	,	,	PUNCT
iajs-2963	163	4	2021	2021	NUM
iajs-2963	163	5	,	,	PUNCT
iajs-2963	163	6	50(6	50(6	NUM
iajs-2963	163	7	)	)	PUNCT
iajs-2963	163	8	,	,	PUNCT
iajs-2963	163	9	1799	1799	NUM
iajs-2963	163	10	-	-	SYM
iajs-2963	163	11	1814	1814	NUM
iajs-2963	163	12	.	.	PUNCT