id	sid	tid	token	lemma	pos
ejpam-4727	1	1	european	european	PROPN
ejpam-4727	1	2	journal	journal	PROPN
ejpam-4727	1	3	of	of	ADP
ejpam-4727	1	4	pure	pure	ADJ
ejpam-4727	1	5	and	and	CCONJ
ejpam-4727	1	6	applied	apply	VERB
ejpam-4727	1	7	mathematics	mathematic	NOUN
ejpam-4727	1	8	vol	vol	NOUN
ejpam-4727	1	9	.	.	PUNCT
ejpam-4727	2	1	16	16	NUM
ejpam-4727	2	2	,	,	PUNCT
ejpam-4727	2	3	no	no	INTJ
ejpam-4727	2	4	.	.	NOUN
ejpam-4727	2	5	2	2	NUM
ejpam-4727	2	6	,	,	PUNCT
ejpam-4727	2	7	2023	2023	NUM
ejpam-4727	2	8	,	,	PUNCT
ejpam-4727	2	9	965	965	NUM
ejpam-4727	2	10	-	-	SYM
ejpam-4727	2	11	974	974	NUM
ejpam-4727	2	12	issn	issn	PROPN
ejpam-4727	2	13	1307	1307	NUM
ejpam-4727	2	14	-	-	SYM
ejpam-4727	2	15	5543	5543	NUM
ejpam-4727	2	16	–	–	PUNCT
ejpam-4727	2	17	ejpam.com	ejpam.com	X
ejpam-4727	2	18	published	publish	VERB
ejpam-4727	2	19	by	by	ADP
ejpam-4727	2	20	new	new	PROPN
ejpam-4727	2	21	york	york	PROPN
ejpam-4727	2	22	business	business	PROPN
ejpam-4727	2	23	global	global	ADJ
ejpam-4727	2	24	solving	solve	VERB
ejpam-4727	2	25	the	the	DET
ejpam-4727	2	26	first	first	ADJ
ejpam-4727	2	27	order	order	NOUN
ejpam-4727	2	28	differential	differential	ADJ
ejpam-4727	2	29	equations	equation	NOUN
ejpam-4727	2	30	using	use	VERB
ejpam-4727	2	31	newton	newton	PROPN
ejpam-4727	2	32	’s	’s	PART
ejpam-4727	2	33	interpolation	interpolation	NOUN
ejpam-4727	2	34	and	and	CCONJ
ejpam-4727	2	35	lagrange	lagrange	PROPN
ejpam-4727	2	36	polynomial	polynomial	ADJ
ejpam-4727	2	37	apichat	apichat	PROPN
ejpam-4727	2	38	neamvonk1,∗	neamvonk1,∗	NOUN
ejpam-4727	2	39	,	,	PUNCT
ejpam-4727	2	40	boonyong	boonyong	NOUN
ejpam-4727	2	41	sriponpaew1	sriponpaew1	PROPN
ejpam-4727	2	42	1	1	NUM
ejpam-4727	2	43	department	department	NOUN
ejpam-4727	2	44	of	of	ADP
ejpam-4727	2	45	mathematics	mathematic	NOUN
ejpam-4727	2	46	,	,	PUNCT
ejpam-4727	2	47	faculty	faculty	NOUN
ejpam-4727	2	48	of	of	ADP
ejpam-4727	2	49	science	science	NOUN
ejpam-4727	2	50	,	,	PUNCT
ejpam-4727	2	51	burapha	burapha	PROPN
ejpam-4727	2	52	university	university	PROPN
ejpam-4727	2	53	,	,	PUNCT
ejpam-4727	2	54	thailand	thailand	PROPN
ejpam-4727	2	55	abstract	abstract	NOUN
ejpam-4727	2	56	.	.	PUNCT
ejpam-4727	3	1	in	in	ADP
ejpam-4727	3	2	this	this	DET
ejpam-4727	3	3	paper	paper	NOUN
ejpam-4727	3	4	,	,	PUNCT
ejpam-4727	3	5	we	we	PRON
ejpam-4727	3	6	use	use	VERB
ejpam-4727	3	7	both	both	DET
ejpam-4727	3	8	newton	newton	PROPN
ejpam-4727	3	9	’s	’s	PART
ejpam-4727	3	10	interpolation	interpolation	NOUN
ejpam-4727	3	11	and	and	CCONJ
ejpam-4727	3	12	lagrange	lagrange	PROPN
ejpam-4727	3	13	polynomial	polynomial	NOUN
ejpam-4727	3	14	to	to	PART
ejpam-4727	3	15	create	create	VERB
ejpam-4727	3	16	cubic	cubic	ADJ
ejpam-4727	3	17	polynomials	polynomial	NOUN
ejpam-4727	3	18	for	for	ADP
ejpam-4727	3	19	solving	solve	VERB
ejpam-4727	3	20	the	the	DET
ejpam-4727	3	21	initial	initial	ADJ
ejpam-4727	3	22	value	value	NOUN
ejpam-4727	3	23	problems	problem	NOUN
ejpam-4727	3	24	.	.	PUNCT
ejpam-4727	4	1	by	by	ADP
ejpam-4727	4	2	this	this	DET
ejpam-4727	4	3	new	new	ADJ
ejpam-4727	4	4	method	method	NOUN
ejpam-4727	4	5	,	,	PUNCT
ejpam-4727	4	6	it	it	PRON
ejpam-4727	4	7	is	be	AUX
ejpam-4727	4	8	simple	simple	ADJ
ejpam-4727	4	9	to	to	PART
ejpam-4727	4	10	solve	solve	VERB
ejpam-4727	4	11	linear	linear	NOUN
ejpam-4727	4	12	and	and	CCONJ
ejpam-4727	4	13	nonlinear	nonlinear	ADJ
ejpam-4727	4	14	first	first	ADJ
ejpam-4727	4	15	order	order	NOUN
ejpam-4727	4	16	ordinary	ordinary	ADJ
ejpam-4727	4	17	differential	differential	ADJ
ejpam-4727	4	18	equations	equation	NOUN
ejpam-4727	4	19	and	and	CCONJ
ejpam-4727	4	20	to	to	PART
ejpam-4727	4	21	yield	yield	VERB
ejpam-4727	4	22	and	and	CCONJ
ejpam-4727	4	23	implement	implement	VERB
ejpam-4727	4	24	actual	actual	ADJ
ejpam-4727	4	25	precise	precise	ADJ
ejpam-4727	4	26	results	result	NOUN
ejpam-4727	4	27	.	.	PUNCT
ejpam-4727	5	1	some	some	DET
ejpam-4727	5	2	numerical	numerical	ADJ
ejpam-4727	5	3	examples	example	NOUN
ejpam-4727	5	4	are	be	AUX
ejpam-4727	5	5	provided	provide	VERB
ejpam-4727	5	6	to	to	PART
ejpam-4727	5	7	test	test	VERB
ejpam-4727	5	8	the	the	DET
ejpam-4727	5	9	performance	performance	NOUN
ejpam-4727	5	10	and	and	CCONJ
ejpam-4727	5	11	illustrate	illustrate	VERB
ejpam-4727	5	12	the	the	DET
ejpam-4727	5	13	efficiency	efficiency	NOUN
ejpam-4727	5	14	of	of	ADP
ejpam-4727	5	15	the	the	DET
ejpam-4727	5	16	method	method	NOUN
ejpam-4727	5	17	.	.	PUNCT
ejpam-4727	6	1	2020	2020	NUM
ejpam-4727	6	2	mathematics	mathematic	NOUN
ejpam-4727	6	3	subject	subject	NOUN
ejpam-4727	6	4	classifications	classification	NOUN
ejpam-4727	6	5	:	:	PUNCT
ejpam-4727	6	6	65l05	65l05	NUM
ejpam-4727	6	7	key	key	ADJ
ejpam-4727	6	8	words	word	NOUN
ejpam-4727	6	9	and	and	CCONJ
ejpam-4727	6	10	phrases	phrase	NOUN
ejpam-4727	6	11	:	:	PUNCT
ejpam-4727	6	12	numerical	numerical	ADJ
ejpam-4727	6	13	method	method	NOUN
ejpam-4727	6	14	,	,	PUNCT
ejpam-4727	6	15	initial	initial	ADJ
ejpam-4727	6	16	value	value	NOUN
ejpam-4727	6	17	problems	problem	NOUN
ejpam-4727	6	18	,	,	PUNCT
ejpam-4727	6	19	newton	newton	PROPN
ejpam-4727	6	20	’s	’s	PART
ejpam-4727	6	21	interpolation	interpolation	NOUN
ejpam-4727	6	22	,	,	PUNCT
ejpam-4727	6	23	lagrange	lagrange	NOUN
ejpam-4727	6	24	polynomial	polynomial	ADJ
ejpam-4727	6	25	1	1	NUM
ejpam-4727	6	26	.	.	PUNCT
ejpam-4727	7	1	introduction	introduction	NOUN
ejpam-4727	7	2	many	many	ADJ
ejpam-4727	7	3	mathematical	mathematical	ADJ
ejpam-4727	7	4	models	model	NOUN
ejpam-4727	7	5	in	in	ADP
ejpam-4727	7	6	science	science	NOUN
ejpam-4727	7	7	and	and	CCONJ
ejpam-4727	7	8	engineering	engineering	NOUN
ejpam-4727	7	9	fields	field	NOUN
ejpam-4727	7	10	(	(	PUNCT
ejpam-4727	7	11	[	[	X
ejpam-4727	7	12	3],[4],[5],[6],[7],[10],[13	3],[4],[5],[6],[7],[10],[13	NOUN
ejpam-4727	7	13	]	]	PUNCT
ejpam-4727	7	14	)	)	PUNCT
ejpam-4727	7	15	can	can	AUX
ejpam-4727	7	16	be	be	AUX
ejpam-4727	7	17	formulated	formulate	VERB
ejpam-4727	7	18	in	in	ADP
ejpam-4727	7	19	the	the	DET
ejpam-4727	7	20	form	form	NOUN
ejpam-4727	7	21	of	of	ADP
ejpam-4727	7	22	linear	linear	PROPN
ejpam-4727	7	23	and	and	CCONJ
ejpam-4727	7	24	nonlinear	nonlinear	ADJ
ejpam-4727	7	25	ordinary	ordinary	ADJ
ejpam-4727	7	26	differential	differential	ADJ
ejpam-4727	7	27	equations	equation	NOUN
ejpam-4727	7	28	(	(	PUNCT
ejpam-4727	7	29	[	[	X
ejpam-4727	7	30	9],[12	9],[12	NOUN
ejpam-4727	7	31	]	]	PUNCT
ejpam-4727	7	32	)	)	PUNCT
ejpam-4727	7	33	which	which	PRON
ejpam-4727	7	34	need	need	VERB
ejpam-4727	7	35	an	an	DET
ejpam-4727	7	36	analytical	analytical	ADJ
ejpam-4727	7	37	method	method	NOUN
ejpam-4727	7	38	(	(	PUNCT
ejpam-4727	7	39	[	[	X
ejpam-4727	7	40	2],[15],[17	2],[15],[17	NUM
ejpam-4727	7	41	]	]	PUNCT
ejpam-4727	7	42	)	)	PUNCT
ejpam-4727	7	43	to	to	PART
ejpam-4727	7	44	solve	solve	VERB
ejpam-4727	7	45	the	the	DET
ejpam-4727	7	46	exact	exact	ADJ
ejpam-4727	7	47	equations	equation	NOUN
ejpam-4727	7	48	.	.	PUNCT
ejpam-4727	8	1	however	however	ADV
ejpam-4727	8	2	in	in	ADP
ejpam-4727	8	3	some	some	DET
ejpam-4727	8	4	problems	problem	NOUN
ejpam-4727	8	5	,	,	PUNCT
ejpam-4727	8	6	we	we	PRON
ejpam-4727	8	7	can	can	AUX
ejpam-4727	8	8	not	not	PART
ejpam-4727	8	9	obtain	obtain	VERB
ejpam-4727	8	10	the	the	DET
ejpam-4727	8	11	exact	exact	ADJ
ejpam-4727	8	12	solutions	solution	NOUN
ejpam-4727	8	13	by	by	ADP
ejpam-4727	8	14	the	the	DET
ejpam-4727	8	15	analytical	analytical	ADJ
ejpam-4727	8	16	method	method	NOUN
ejpam-4727	8	17	in	in	ADP
ejpam-4727	8	18	[	[	X
ejpam-4727	8	19	7	7	NUM
ejpam-4727	8	20	]	]	PUNCT
ejpam-4727	8	21	for	for	ADP
ejpam-4727	8	22	example	example	NOUN
ejpam-4727	8	23	y′	y′	NOUN
ejpam-4727	9	1	=	=	SYM
ejpam-4727	9	2	x2	x2	PROPN
ejpam-4727	10	1	+	+	CCONJ
ejpam-4727	10	2	y2	y2	PROPN
ejpam-4727	10	3	.	.	PUNCT
ejpam-4727	11	1	therefore	therefore	ADV
ejpam-4727	11	2	numerical	numerical	ADJ
ejpam-4727	11	3	method	method	NOUN
ejpam-4727	11	4	is	be	AUX
ejpam-4727	11	5	an	an	DET
ejpam-4727	11	6	important	important	ADJ
ejpam-4727	11	7	tool	tool	NOUN
ejpam-4727	11	8	to	to	PART
ejpam-4727	11	9	solve	solve	VERB
ejpam-4727	11	10	this	this	DET
ejpam-4727	11	11	kind	kind	NOUN
ejpam-4727	11	12	of	of	ADP
ejpam-4727	11	13	problems	problem	NOUN
ejpam-4727	11	14	such	such	ADJ
ejpam-4727	11	15	as	as	ADP
ejpam-4727	11	16	euler	euler	PROPN
ejpam-4727	11	17	’s	’s	PART
ejpam-4727	11	18	method	method	NOUN
ejpam-4727	11	19	,	,	PUNCT
ejpam-4727	11	20	runge	runge	NOUN
ejpam-4727	11	21	-	-	PUNCT
ejpam-4727	11	22	kutta	kutta	NOUN
ejpam-4727	11	23	method	method	NOUN
ejpam-4727	11	24	(	(	PUNCT
ejpam-4727	11	25	[	[	X
ejpam-4727	11	26	11],[14	11],[14	ADJ
ejpam-4727	11	27	]	]	X
ejpam-4727	11	28	)	)	PUNCT
ejpam-4727	11	29	and	and	CCONJ
ejpam-4727	11	30	rungekutta	rungekutta	NOUN
ejpam-4727	11	31	-	-	PUNCT
ejpam-4727	11	32	fehlberg	fehlberg	NOUN
ejpam-4727	11	33	method	method	NOUN
ejpam-4727	11	34	(	(	PUNCT
ejpam-4727	11	35	[	[	X
ejpam-4727	11	36	8],[18	8],[18	NUM
ejpam-4727	11	37	]	]	PUNCT
ejpam-4727	11	38	)	)	PUNCT
ejpam-4727	11	39	.	.	PUNCT
ejpam-4727	12	1	many	many	ADJ
ejpam-4727	12	2	methods	method	NOUN
ejpam-4727	12	3	have	have	AUX
ejpam-4727	12	4	been	be	AUX
ejpam-4727	12	5	widely	widely	ADV
ejpam-4727	12	6	developed	develop	VERB
ejpam-4727	12	7	by	by	ADP
ejpam-4727	12	8	a	a	DET
ejpam-4727	12	9	lot	lot	NOUN
ejpam-4727	12	10	of	of	ADP
ejpam-4727	12	11	researchers	researcher	NOUN
ejpam-4727	12	12	(	(	PUNCT
ejpam-4727	13	1	[	[	X
ejpam-4727	13	2	1],[11	1],[11	X
ejpam-4727	13	3	]	]	PUNCT
ejpam-4727	13	4	,	,	PUNCT
ejpam-4727	14	1	[	[	X
ejpam-4727	14	2	14	14	NUM
ejpam-4727	14	3	]	]	PUNCT
ejpam-4727	14	4	and	and	CCONJ
ejpam-4727	14	5	[	[	X
ejpam-4727	14	6	16	16	NUM
ejpam-4727	14	7	]	]	PUNCT
ejpam-4727	14	8	)	)	PUNCT
ejpam-4727	14	9	to	to	PART
ejpam-4727	14	10	solve	solve	VERB
ejpam-4727	14	11	these	these	DET
ejpam-4727	14	12	problems	problem	NOUN
ejpam-4727	14	13	.	.	PUNCT
ejpam-4727	15	1	some	some	DET
ejpam-4727	15	2	problems	problem	NOUN
ejpam-4727	15	3	in	in	ADP
ejpam-4727	15	4	form	form	NOUN
ejpam-4727	15	5	of	of	ADP
ejpam-4727	15	6	partial	partial	ADJ
ejpam-4727	15	7	differential	differential	NOUN
ejpam-4727	15	8	equations	equation	NOUN
ejpam-4727	15	9	can	can	AUX
ejpam-4727	15	10	be	be	AUX
ejpam-4727	15	11	converted	convert	VERB
ejpam-4727	15	12	to	to	ADP
ejpam-4727	15	13	ordinary	ordinary	ADJ
ejpam-4727	15	14	differential	differential	ADJ
ejpam-4727	15	15	equations	equation	NOUN
ejpam-4727	15	16	form	form	NOUN
ejpam-4727	15	17	(	(	PUNCT
ejpam-4727	15	18	[	[	X
ejpam-4727	15	19	10],[13	10],[13	PROPN
ejpam-4727	15	20	]	]	X
ejpam-4727	15	21	)	)	PUNCT
ejpam-4727	15	22	.	.	PUNCT
ejpam-4727	16	1	in	in	ADP
ejpam-4727	16	2	this	this	DET
ejpam-4727	16	3	article	article	NOUN
ejpam-4727	16	4	,	,	PUNCT
ejpam-4727	16	5	we	we	PRON
ejpam-4727	16	6	consider	consider	VERB
ejpam-4727	16	7	only	only	ADV
ejpam-4727	16	8	the	the	DET
ejpam-4727	16	9	first	first	ADJ
ejpam-4727	16	10	order	order	NOUN
ejpam-4727	16	11	ordinary	ordinary	ADJ
ejpam-4727	16	12	differential	differential	ADJ
ejpam-4727	16	13	equations	equation	NOUN
ejpam-4727	16	14	with	with	ADP
ejpam-4727	16	15	an	an	DET
ejpam-4727	16	16	initial	initial	ADJ
ejpam-4727	16	17	condition	condition	NOUN
ejpam-4727	16	18	(	(	PUNCT
ejpam-4727	16	19	initial	initial	ADJ
ejpam-4727	16	20	value	value	NOUN
ejpam-4727	16	21	problems	problem	NOUN
ejpam-4727	16	22	)	)	PUNCT
ejpam-4727	16	23	in	in	ADP
ejpam-4727	16	24	form	form	NOUN
ejpam-4727	16	25	:	:	PUNCT
ejpam-4727	16	26	dy	dy	PROPN
ejpam-4727	16	27	dx	dx	PROPN
ejpam-4727	16	28	=	=	SYM
ejpam-4727	16	29	f(x	f(x	PROPN
ejpam-4727	16	30	,	,	PUNCT
ejpam-4727	16	31	y	y	PROPN
ejpam-4727	16	32	)	)	PUNCT
ejpam-4727	16	33	,	,	PUNCT
ejpam-4727	16	34	y(x0	y(x0	NOUN
ejpam-4727	16	35	)	)	PUNCT
ejpam-4727	16	36	=	=	SYM
ejpam-4727	16	37	y0	y0	NOUN
ejpam-4727	16	38	,	,	PUNCT
ejpam-4727	16	39	(	(	PUNCT
ejpam-4727	16	40	1	1	X
ejpam-4727	16	41	)	)	PUNCT
ejpam-4727	16	42	where	where	SCONJ
ejpam-4727	16	43	f(x	f(x	PROPN
ejpam-4727	16	44	,	,	PUNCT
ejpam-4727	16	45	y	y	PROPN
ejpam-4727	16	46	)	)	PUNCT
ejpam-4727	16	47	is	be	AUX
ejpam-4727	16	48	a	a	DET
ejpam-4727	16	49	known	know	VERB
ejpam-4727	16	50	function	function	NOUN
ejpam-4727	16	51	and	and	CCONJ
ejpam-4727	16	52	the	the	DET
ejpam-4727	16	53	value	value	NOUN
ejpam-4727	16	54	of	of	ADP
ejpam-4727	16	55	initial	initial	ADJ
ejpam-4727	16	56	conditions	condition	NOUN
ejpam-4727	16	57	x0	x0	PROPN
ejpam-4727	16	58	,	,	PUNCT
ejpam-4727	16	59	y0	y0	PROPN
ejpam-4727	16	60	are	be	AUX
ejpam-4727	16	61	also	also	ADV
ejpam-4727	16	62	known	know	VERB
ejpam-4727	16	63	numbers	number	NOUN
ejpam-4727	16	64	.	.	PUNCT
ejpam-4727	17	1	in	in	ADP
ejpam-4727	17	2	2018	2018	NUM
ejpam-4727	17	3	,	,	PUNCT
ejpam-4727	17	4	to	to	PART
ejpam-4727	17	5	find	find	VERB
ejpam-4727	17	6	solutions	solution	NOUN
ejpam-4727	17	7	of	of	ADP
ejpam-4727	17	8	(	(	PUNCT
ejpam-4727	17	9	1	1	NUM
ejpam-4727	17	10	)	)	PUNCT
ejpam-4727	17	11	,	,	PUNCT
ejpam-4727	18	1	[	[	X
ejpam-4727	18	2	14	14	NUM
ejpam-4727	18	3	]	]	PUNCT
ejpam-4727	18	4	used	use	VERB
ejpam-4727	18	5	newton	newton	PROPN
ejpam-4727	18	6	’s	’s	PART
ejpam-4727	18	7	interpolation	interpolation	NOUN
ejpam-4727	18	8	and	and	CCONJ
ejpam-4727	18	9	three	three	NUM
ejpam-4727	18	10	∗corresponding	∗corresponde	VERB
ejpam-4727	18	11	author	author	NOUN
ejpam-4727	18	12	.	.	PUNCT
ejpam-4727	19	1	doi	doi	NOUN
ejpam-4727	19	2	:	:	PUNCT
ejpam-4727	19	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4727	https://doi.org/10.29020/nybg.ejpam.v16i2.4727	PUNCT
ejpam-4727	19	4	email	email	NOUN
ejpam-4727	19	5	addresses	address	NOUN
ejpam-4727	19	6	:	:	PUNCT
ejpam-4727	20	1	apichat@buu.ac.th	apichat@buu.ac.th	PROPN
ejpam-4727	20	2	(	(	PUNCT
ejpam-4727	20	3	a.	a.	NOUN
ejpam-4727	20	4	neamvonk	neamvonk	ADV
ejpam-4727	20	5	)	)	PUNCT
ejpam-4727	20	6	,	,	PUNCT
ejpam-4727	20	7	boonyong@buu.ac.th	boonyong@buu.ac.th	PROPN
ejpam-4727	20	8	(	(	PUNCT
ejpam-4727	20	9	b.	b.	PROPN
ejpam-4727	20	10	sriponpaew	sriponpaew	PROPN
ejpam-4727	20	11	)	)	PUNCT
ejpam-4727	20	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4727	21	1	965	965	NUM
ejpam-4727	21	2	©	©	PROPN
ejpam-4727	21	3	2023	2023	NUM
ejpam-4727	21	4	ejpam	ejpam	NOUN
ejpam-4727	21	5	all	all	DET
ejpam-4727	21	6	rights	right	NOUN
ejpam-4727	21	7	reserved	reserve	VERB
ejpam-4727	21	8	.	.	PUNCT
ejpam-4727	22	1	a.	a.	PROPN
ejpam-4727	22	2	neamvonk	neamvonk	PROPN
ejpam-4727	22	3	,	,	PUNCT
ejpam-4727	22	4	b.	b.	PROPN
ejpam-4727	22	5	sriponpaew	sriponpaew	PROPN
ejpam-4727	22	6	/	/	SYM
ejpam-4727	22	7	eur	eur	PROPN
ejpam-4727	22	8	.	.	PUNCT
ejpam-4727	23	1	j.	j.	PROPN
ejpam-4727	23	2	pure	pure	PROPN
ejpam-4727	23	3	appl	appl	PROPN
ejpam-4727	23	4	.	.	PROPN
ejpam-4727	23	5	math	math	PROPN
ejpam-4727	23	6	,	,	PUNCT
ejpam-4727	23	7	16	16	NUM
ejpam-4727	23	8	(	(	PUNCT
ejpam-4727	23	9	2	2	NUM
ejpam-4727	23	10	)	)	PUNCT
ejpam-4727	23	11	(	(	PUNCT
ejpam-4727	23	12	2023	2023	NUM
ejpam-4727	23	13	)	)	PUNCT
ejpam-4727	23	14	,	,	PUNCT
ejpam-4727	23	15	965	965	NUM
ejpam-4727	23	16	-	-	SYM
ejpam-4727	23	17	974	974	NUM
ejpam-4727	23	18	966	966	NUM
ejpam-4727	23	19	points	point	NOUN
ejpam-4727	23	20	to	to	PART
ejpam-4727	23	21	build	build	VERB
ejpam-4727	23	22	a	a	DET
ejpam-4727	23	23	quadratic	quadratic	ADJ
ejpam-4727	23	24	equation	equation	NOUN
ejpam-4727	23	25	by	by	ADP
ejpam-4727	23	26	lagrange	lagrange	PROPN
ejpam-4727	23	27	method	method	NOUN
ejpam-4727	23	28	.	.	PUNCT
ejpam-4727	24	1	also	also	ADV
ejpam-4727	24	2	[	[	X
ejpam-4727	24	3	11	11	NUM
ejpam-4727	24	4	]	]	PUNCT
ejpam-4727	24	5	and	and	CCONJ
ejpam-4727	24	6	[	[	X
ejpam-4727	24	7	16	16	NUM
ejpam-4727	24	8	]	]	PUNCT
ejpam-4727	24	9	used	use	VERB
ejpam-4727	24	10	newton	newton	PROPN
ejpam-4727	24	11	’s	’s	PART
ejpam-4727	24	12	interpolation	interpolation	NOUN
ejpam-4727	24	13	and	and	CCONJ
ejpam-4727	24	14	constructed	construct	VERB
ejpam-4727	24	15	a	a	DET
ejpam-4727	24	16	quadratic	quadratic	ADJ
ejpam-4727	24	17	equation	equation	NOUN
ejpam-4727	24	18	by	by	ADP
ejpam-4727	24	19	aitken	aitken	PROPN
ejpam-4727	24	20	’s	’s	PART
ejpam-4727	24	21	method	method	NOUN
ejpam-4727	24	22	to	to	PART
ejpam-4727	24	23	solve	solve	VERB
ejpam-4727	24	24	the	the	DET
ejpam-4727	24	25	same	same	ADJ
ejpam-4727	24	26	problems	problem	NOUN
ejpam-4727	24	27	.	.	PUNCT
ejpam-4727	25	1	moreover	moreover	ADV
ejpam-4727	25	2	[	[	X
ejpam-4727	25	3	20	20	NUM
ejpam-4727	25	4	]	]	PUNCT
ejpam-4727	25	5	gave	give	VERB
ejpam-4727	25	6	an	an	DET
ejpam-4727	25	7	idea	idea	NOUN
ejpam-4727	25	8	to	to	PART
ejpam-4727	25	9	solve	solve	VERB
ejpam-4727	25	10	these	these	DET
ejpam-4727	25	11	problems	problem	NOUN
ejpam-4727	25	12	for	for	ADP
ejpam-4727	25	13	combining	combine	VERB
ejpam-4727	25	14	picard	picard	NOUN
ejpam-4727	25	15	’s	’s	PART
ejpam-4727	25	16	method	method	NOUN
ejpam-4727	25	17	and	and	CCONJ
ejpam-4727	25	18	taylor	taylor	PROPN
ejpam-4727	25	19	’s	’s	PART
ejpam-4727	25	20	series	series	NOUN
ejpam-4727	25	21	.	.	PUNCT
ejpam-4727	26	1	furthermore	furthermore	ADV
ejpam-4727	26	2	[	[	X
ejpam-4727	26	3	21	21	NUM
ejpam-4727	26	4	]	]	PUNCT
ejpam-4727	26	5	proposed	propose	VERB
ejpam-4727	26	6	a	a	DET
ejpam-4727	26	7	new	new	ADJ
ejpam-4727	26	8	solving	solving	NOUN
ejpam-4727	26	9	technique	technique	NOUN
ejpam-4727	26	10	by	by	ADP
ejpam-4727	26	11	improved	improve	VERB
ejpam-4727	26	12	euler	euler	NOUN
ejpam-4727	26	13	’s	’s	PART
ejpam-4727	26	14	method	method	NOUN
ejpam-4727	26	15	.	.	PUNCT
ejpam-4727	27	1	ultimately	ultimately	ADV
ejpam-4727	27	2	[	[	X
ejpam-4727	27	3	1	1	X
ejpam-4727	27	4	]	]	PUNCT
ejpam-4727	27	5	applied	apply	VERB
ejpam-4727	27	6	all	all	DET
ejpam-4727	27	7	techniques	technique	NOUN
ejpam-4727	27	8	from	from	ADP
ejpam-4727	27	9	[	[	X
ejpam-4727	27	10	11	11	NUM
ejpam-4727	27	11	]	]	PUNCT
ejpam-4727	27	12	,	,	PUNCT
ejpam-4727	27	13	[	[	X
ejpam-4727	27	14	14	14	NUM
ejpam-4727	27	15	]	]	PUNCT
ejpam-4727	27	16	,	,	PUNCT
ejpam-4727	27	17	[	[	X
ejpam-4727	27	18	16	16	NUM
ejpam-4727	27	19	]	]	PUNCT
ejpam-4727	27	20	,	,	PUNCT
ejpam-4727	27	21	[	[	X
ejpam-4727	27	22	19	19	NUM
ejpam-4727	27	23	]	]	PUNCT
ejpam-4727	27	24	,	,	PUNCT
ejpam-4727	27	25	[	[	X
ejpam-4727	27	26	20	20	NUM
ejpam-4727	27	27	]	]	PUNCT
ejpam-4727	27	28	and	and	CCONJ
ejpam-4727	27	29	[	[	X
ejpam-4727	27	30	21	21	NUM
ejpam-4727	27	31	]	]	PUNCT
ejpam-4727	27	32	to	to	PART
ejpam-4727	27	33	approximate	approximate	VERB
ejpam-4727	27	34	the	the	DET
ejpam-4727	27	35	solution	solution	NOUN
ejpam-4727	27	36	of	of	ADP
ejpam-4727	27	37	(	(	PUNCT
ejpam-4727	27	38	1	1	NUM
ejpam-4727	27	39	)	)	PUNCT
ejpam-4727	27	40	and	and	CCONJ
ejpam-4727	27	41	other	other	ADJ
ejpam-4727	27	42	systems	system	NOUN
ejpam-4727	27	43	of	of	ADP
ejpam-4727	27	44	first	first	ADJ
ejpam-4727	27	45	order	order	NOUN
ejpam-4727	27	46	ordinary	ordinary	ADJ
ejpam-4727	27	47	differential	differential	ADJ
ejpam-4727	27	48	equations	equation	NOUN
ejpam-4727	27	49	.	.	PUNCT
ejpam-4727	28	1	the	the	DET
ejpam-4727	28	2	goal	goal	NOUN
ejpam-4727	28	3	of	of	ADP
ejpam-4727	28	4	this	this	DET
ejpam-4727	28	5	study	study	NOUN
ejpam-4727	28	6	is	be	AUX
ejpam-4727	28	7	to	to	PART
ejpam-4727	28	8	estimate	estimate	VERB
ejpam-4727	28	9	approximated	approximate	VERB
ejpam-4727	28	10	solutions	solution	NOUN
ejpam-4727	28	11	and	and	CCONJ
ejpam-4727	28	12	relative	relative	ADJ
ejpam-4727	28	13	errors	error	NOUN
ejpam-4727	28	14	by	by	ADP
ejpam-4727	28	15	comparing	compare	VERB
ejpam-4727	28	16	the	the	DET
ejpam-4727	28	17	results	result	NOUN
ejpam-4727	28	18	of	of	ADP
ejpam-4727	28	19	our	our	PRON
ejpam-4727	28	20	new	new	ADJ
ejpam-4727	28	21	method	method	NOUN
ejpam-4727	28	22	with	with	ADP
ejpam-4727	28	23	other	other	ADJ
ejpam-4727	28	24	methods	method	NOUN
ejpam-4727	28	25	such	such	ADJ
ejpam-4727	28	26	as	as	ADP
ejpam-4727	28	27	euler	euler	NOUN
ejpam-4727	28	28	’s	’s	PART
ejpam-4727	28	29	method	method	NOUN
ejpam-4727	28	30	and	and	CCONJ
ejpam-4727	28	31	methods	method	NOUN
ejpam-4727	28	32	in	in	ADP
ejpam-4727	28	33	[	[	X
ejpam-4727	28	34	11	11	NUM
ejpam-4727	28	35	]	]	PUNCT
ejpam-4727	28	36	and	and	CCONJ
ejpam-4727	28	37	[	[	X
ejpam-4727	28	38	14	14	NUM
ejpam-4727	28	39	]	]	SYM
ejpam-4727	28	40	.	.	PUNCT
ejpam-4727	29	1	2	2	X
ejpam-4727	29	2	.	.	X
ejpam-4727	29	3	our	our	PRON
ejpam-4727	29	4	proposed	propose	VERB
ejpam-4727	29	5	method	method	NOUN
ejpam-4727	29	6	to	to	PART
ejpam-4727	29	7	improve	improve	VERB
ejpam-4727	29	8	the	the	DET
ejpam-4727	29	9	accuracy	accuracy	NOUN
ejpam-4727	29	10	of	of	ADP
ejpam-4727	29	11	methods	method	NOUN
ejpam-4727	29	12	in	in	ADP
ejpam-4727	29	13	[	[	X
ejpam-4727	29	14	11	11	NUM
ejpam-4727	29	15	]	]	PUNCT
ejpam-4727	29	16	and	and	CCONJ
ejpam-4727	29	17	[	[	X
ejpam-4727	29	18	14	14	NUM
ejpam-4727	29	19	]	]	PUNCT
ejpam-4727	29	20	which	which	PRON
ejpam-4727	29	21	are	be	AUX
ejpam-4727	29	22	the	the	DET
ejpam-4727	29	23	same	same	ADJ
ejpam-4727	29	24	quadratics	quadratic	NOUN
ejpam-4727	29	25	solutions	solution	NOUN
ejpam-4727	29	26	,	,	PUNCT
ejpam-4727	29	27	we	we	PRON
ejpam-4727	29	28	combine	combine	VERB
ejpam-4727	29	29	newton	newton	PROPN
ejpam-4727	29	30	’s	’s	PART
ejpam-4727	29	31	interpolation	interpolation	NOUN
ejpam-4727	29	32	and	and	CCONJ
ejpam-4727	29	33	lagrange	lagrange	NOUN
ejpam-4727	29	34	’s	’s	PART
ejpam-4727	29	35	method	method	NOUN
ejpam-4727	29	36	for	for	ADP
ejpam-4727	29	37	solving	solve	VERB
ejpam-4727	29	38	(	(	PUNCT
ejpam-4727	29	39	1	1	NUM
ejpam-4727	29	40	)	)	PUNCT
ejpam-4727	29	41	to	to	PART
ejpam-4727	29	42	create	create	VERB
ejpam-4727	29	43	higher	high	ADJ
ejpam-4727	29	44	degree	degree	NOUN
ejpam-4727	29	45	polynomial	polynomial	ADJ
ejpam-4727	29	46	.	.	PUNCT
ejpam-4727	30	1	newton	newton	PROPN
ejpam-4727	30	2	’s	’s	PART
ejpam-4727	30	3	interpolation	interpolation	NOUN
ejpam-4727	30	4	is	be	AUX
ejpam-4727	30	5	applied	apply	VERB
ejpam-4727	30	6	to	to	PART
ejpam-4727	30	7	find	find	VERB
ejpam-4727	30	8	four	four	NUM
ejpam-4727	30	9	values	value	NOUN
ejpam-4727	30	10	yi	yi	NOUN
ejpam-4727	30	11	for	for	ADP
ejpam-4727	30	12	i	i	PROPN
ejpam-4727	30	13	=	=	NOUN
ejpam-4727	30	14	0	0	NUM
ejpam-4727	30	15	,	,	PUNCT
ejpam-4727	30	16	1	1	NUM
ejpam-4727	30	17	,	,	PUNCT
ejpam-4727	30	18	2	2	NUM
ejpam-4727	30	19	,	,	PUNCT
ejpam-4727	30	20	3	3	NUM
ejpam-4727	30	21	to	to	PART
ejpam-4727	30	22	form	form	VERB
ejpam-4727	30	23	a	a	DET
ejpam-4727	30	24	cubic	cubic	ADJ
ejpam-4727	30	25	polynomial	polynomial	ADJ
ejpam-4727	30	26	,	,	PUNCT
ejpam-4727	30	27	p3(x	p3(x	PROPN
ejpam-4727	30	28	)	)	PUNCT
ejpam-4727	30	29	=	=	SYM
ejpam-4727	30	30	c0+c1x+c2x	c0+c1x+c2x	NOUN
ejpam-4727	31	1	2+c3x	2+c3x	NUM
ejpam-4727	31	2	3	3	NUM
ejpam-4727	31	3	.	.	PUNCT
ejpam-4727	32	1	this	this	DET
ejpam-4727	32	2	polynomial	polynomial	ADJ
ejpam-4727	32	3	approximates	approximate	VERB
ejpam-4727	32	4	solutions	solution	NOUN
ejpam-4727	32	5	of	of	ADP
ejpam-4727	32	6	(	(	PUNCT
ejpam-4727	32	7	1	1	NUM
ejpam-4727	32	8	)	)	PUNCT
ejpam-4727	32	9	by	by	ADP
ejpam-4727	32	10	using	use	VERB
ejpam-4727	32	11	lagrange	lagrange	NOUN
ejpam-4727	32	12	’s	’s	PART
ejpam-4727	32	13	method	method	NOUN
ejpam-4727	32	14	as	as	ADP
ejpam-4727	32	15	following	follow	VERB
ejpam-4727	32	16	.	.	PUNCT
ejpam-4727	33	1	2.1	2.1	NUM
ejpam-4727	33	2	.	.	PUNCT
ejpam-4727	34	1	newton	newton	PROPN
ejpam-4727	34	2	’s	’s	PART
ejpam-4727	34	3	interpolation	interpolation	NOUN
ejpam-4727	34	4	method	method	NOUN
ejpam-4727	34	5	this	this	DET
ejpam-4727	34	6	method	method	NOUN
ejpam-4727	34	7	use	use	VERB
ejpam-4727	34	8	the	the	DET
ejpam-4727	34	9	initial	initial	ADJ
ejpam-4727	34	10	point	point	NOUN
ejpam-4727	34	11	(	(	PUNCT
ejpam-4727	34	12	x0	x0	PROPN
ejpam-4727	34	13	,	,	PUNCT
ejpam-4727	34	14	y0	y0	PROPN
ejpam-4727	34	15	)	)	PUNCT
ejpam-4727	34	16	from	from	ADP
ejpam-4727	34	17	(	(	PUNCT
ejpam-4727	34	18	1	1	NUM
ejpam-4727	34	19	)	)	PUNCT
ejpam-4727	34	20	to	to	PART
ejpam-4727	34	21	estimate	estimate	VERB
ejpam-4727	34	22	the	the	DET
ejpam-4727	34	23	values	value	NOUN
ejpam-4727	34	24	of	of	ADP
ejpam-4727	34	25	a	a	DET
ejpam-4727	34	26	function	function	NOUN
ejpam-4727	34	27	from	from	ADP
ejpam-4727	34	28	any	any	DET
ejpam-4727	34	29	intermediate	intermediate	ADJ
ejpam-4727	34	30	values	value	NOUN
ejpam-4727	34	31	of	of	ADP
ejpam-4727	34	32	the	the	DET
ejpam-4727	34	33	independent	independent	ADJ
ejpam-4727	34	34	variables	variable	NOUN
ejpam-4727	34	35	.	.	PUNCT
ejpam-4727	35	1	the	the	DET
ejpam-4727	35	2	general	general	ADJ
ejpam-4727	35	3	form	form	NOUN
ejpam-4727	35	4	of	of	ADP
ejpam-4727	35	5	the	the	DET
ejpam-4727	35	6	nth	nth	NOUN
ejpam-4727	35	7	degree	degree	NOUN
ejpam-4727	35	8	polynomial	polynomial	NOUN
ejpam-4727	35	9	that	that	PRON
ejpam-4727	35	10	goes	go	VERB
ejpam-4727	35	11	through	through	ADP
ejpam-4727	35	12	n+	n+	ADP
ejpam-4727	35	13	1	1	NUM
ejpam-4727	35	14	points	point	NOUN
ejpam-4727	35	15	(	(	PUNCT
ejpam-4727	35	16	(	(	PUNCT
ejpam-4727	35	17	xi	xi	PROPN
ejpam-4727	35	18	,	,	PUNCT
ejpam-4727	35	19	yi	yi	PROPN
ejpam-4727	35	20	)	)	PUNCT
ejpam-4727	35	21	for	for	ADP
ejpam-4727	35	22	i	i	PROPN
ejpam-4727	35	23	=	=	SYM
ejpam-4727	35	24	0	0	NUM
ejpam-4727	35	25	,	,	PUNCT
ejpam-4727	35	26	1	1	NUM
ejpam-4727	35	27	,	,	PUNCT
ejpam-4727	35	28	...	...	PUNCT
ejpam-4727	35	29	,	,	PUNCT
ejpam-4727	35	30	n	n	CCONJ
ejpam-4727	35	31	)	)	PUNCT
ejpam-4727	35	32	is	be	AUX
ejpam-4727	35	33	written	write	VERB
ejpam-4727	35	34	as	as	ADP
ejpam-4727	35	35	fn(x	fn(x	NOUN
ejpam-4727	35	36	)	)	PUNCT
ejpam-4727	35	37	=	=	SYM
ejpam-4727	35	38	a0	a0	PROPN
ejpam-4727	35	39	+	+	CCONJ
ejpam-4727	35	40	a1(x−	a1(x−	X
ejpam-4727	35	41	x0	x0	PROPN
ejpam-4727	35	42	)	)	PUNCT
ejpam-4727	36	1	+	+	CCONJ
ejpam-4727	36	2	a2(x−	a2(x−	X
ejpam-4727	36	3	x0)(x−	x0)(x−	X
ejpam-4727	37	1	x1	x1	NUM
ejpam-4727	37	2	)	)	PUNCT
ejpam-4727	38	1	+	+	CCONJ
ejpam-4727	38	2	...	...	PUNCT
ejpam-4727	39	1	+	+	NUM
ejpam-4727	39	2	an(x−	an(x−	X
ejpam-4727	39	3	x0)(x−	x0)(x−	NOUN
ejpam-4727	39	4	x1)	x1)	PROPN
ejpam-4727	39	5	...	...	PUNCT
ejpam-4727	39	6	(x−	(x−	PUNCT
ejpam-4727	39	7	xn−1	xn−1	PROPN
ejpam-4727	39	8	)	)	PUNCT
ejpam-4727	39	9	,	,	PUNCT
ejpam-4727	39	10	(	(	PUNCT
ejpam-4727	39	11	2	2	X
ejpam-4727	39	12	)	)	PUNCT
ejpam-4727	39	13	where	where	SCONJ
ejpam-4727	39	14	a0	a0	PROPN
ejpam-4727	39	15	,	,	PUNCT
ejpam-4727	39	16	a1	a1	PROPN
ejpam-4727	39	17	,	,	PUNCT
ejpam-4727	39	18	a2	a2	PROPN
ejpam-4727	39	19	,	,	PUNCT
ejpam-4727	39	20	a3	a3	NOUN
ejpam-4727	39	21	,	,	PUNCT
ejpam-4727	39	22	...	...	PUNCT
ejpam-4727	39	23	are	be	AUX
ejpam-4727	39	24	given	give	VERB
ejpam-4727	39	25	by	by	ADP
ejpam-4727	39	26	a0	a0	NOUN
ejpam-4727	39	27	=	=	SYM
ejpam-4727	39	28	y0	y0	PROPN
ejpam-4727	39	29	,	,	PUNCT
ejpam-4727	39	30	(	(	PUNCT
ejpam-4727	39	31	3	3	X
ejpam-4727	39	32	)	)	PUNCT
ejpam-4727	39	33	a1	a1	NOUN
ejpam-4727	39	34	=	=	NOUN
ejpam-4727	39	35	y1	y1	NOUN
ejpam-4727	40	1	−	−	PROPN
ejpam-4727	40	2	y0	y0	NOUN
ejpam-4727	40	3	x1	x1	NOUN
ejpam-4727	41	1	−	−	NOUN
ejpam-4727	41	2	x0	x0	PROPN
ejpam-4727	41	3	,	,	PUNCT
ejpam-4727	41	4	(	(	PUNCT
ejpam-4727	41	5	4	4	X
ejpam-4727	41	6	)	)	PUNCT
ejpam-4727	41	7	a2	a2	NOUN
ejpam-4727	41	8	=	=	SYM
ejpam-4727	41	9	y2−y1	y2−y1	NUM
ejpam-4727	41	10	x2−x1	x2−x1	NUM
ejpam-4727	42	1	−	−	NOUN
ejpam-4727	43	1	y1−y0	y1−y0	NUM
ejpam-4727	43	2	x1−x0	x1−x0	NUM
ejpam-4727	43	3	x2	x2	NUM
ejpam-4727	43	4	−	−	PROPN
ejpam-4727	43	5	x0	x0	PROPN
ejpam-4727	43	6	,	,	PUNCT
ejpam-4727	43	7	(	(	PUNCT
ejpam-4727	43	8	5	5	NUM
ejpam-4727	43	9	)	)	PUNCT
ejpam-4727	43	10	a3	a3	NOUN
ejpam-4727	43	11	=	=	PUNCT
ejpam-4727	43	12	y3−y2	y3−y2	PROPN
ejpam-4727	43	13	x3−x2	x3−x2	PRON
ejpam-4727	43	14	−	−	NUM
ejpam-4727	43	15	y2−y1	y2−y1	NUM
ejpam-4727	43	16	x2−x1	x2−x1	NUM
ejpam-4727	44	1	x3−x1	x3−x1	NUM
ejpam-4727	44	2	−	−	NUM
ejpam-4727	44	3	y2−y1	y2−y1	NUM
ejpam-4727	44	4	x2−x1	x2−x1	NUM
ejpam-4727	44	5	−	−	PROPN
ejpam-4727	44	6	y1−y0	y1−y0	NUM
ejpam-4727	44	7	x1−x0	x1−x0	X
ejpam-4727	44	8	x2−x0	x2−x0	X
ejpam-4727	45	1	x3	x3	ADJ
ejpam-4727	45	2	−	−	PROPN
ejpam-4727	46	1	x0	x0	PROPN
ejpam-4727	46	2	,	,	PUNCT
ejpam-4727	46	3	...	...	PUNCT
ejpam-4727	46	4	.	.	PUNCT
ejpam-4727	47	1	(	(	PUNCT
ejpam-4727	47	2	6	6	NUM
ejpam-4727	47	3	)	)	PUNCT
ejpam-4727	47	4	since	since	SCONJ
ejpam-4727	47	5	y1	y1	NOUN
ejpam-4727	47	6	,	,	PUNCT
ejpam-4727	47	7	y2	y2	PROPN
ejpam-4727	47	8	and	and	CCONJ
ejpam-4727	47	9	y3	y3	NOUN
ejpam-4727	47	10	in	in	ADP
ejpam-4727	47	11	(	(	PUNCT
ejpam-4727	47	12	4)-(6	4)-(6	NUM
ejpam-4727	47	13	)	)	PUNCT
ejpam-4727	47	14	are	be	AUX
ejpam-4727	47	15	unknown	unknown	ADJ
ejpam-4727	47	16	values	value	NOUN
ejpam-4727	47	17	,	,	PUNCT
ejpam-4727	47	18	we	we	PRON
ejpam-4727	47	19	use	use	VERB
ejpam-4727	47	20	differential	differential	ADJ
ejpam-4727	47	21	values	value	NOUN
ejpam-4727	47	22	for	for	ADP
ejpam-4727	47	23	approximation	approximation	NOUN
ejpam-4727	47	24	i.e.	i.e.	X
ejpam-4727	47	25	yi−yi−1	yi−yi−1	NOUN
ejpam-4727	47	26	xi−xi−1	xi−xi−1	X
ejpam-4727	48	1	≈	≈	PROPN
ejpam-4727	48	2	dy	dy	PROPN
ejpam-4727	48	3	dx	dx	PROPN
ejpam-4727	48	4	|(xi−1,yi−1	|(xi−1,yi−1	PROPN
ejpam-4727	48	5	)	)	PUNCT
ejpam-4727	48	6	.	.	PUNCT
ejpam-4727	49	1	for	for	ADP
ejpam-4727	49	2	our	our	PRON
ejpam-4727	49	3	method	method	NOUN
ejpam-4727	49	4	,	,	PUNCT
ejpam-4727	49	5	we	we	PRON
ejpam-4727	49	6	require	require	VERB
ejpam-4727	49	7	three	three	NUM
ejpam-4727	49	8	more	more	ADJ
ejpam-4727	49	9	values	value	NOUN
ejpam-4727	49	10	,	,	PUNCT
ejpam-4727	49	11	y1	y1	NOUN
ejpam-4727	49	12	,	,	PUNCT
ejpam-4727	49	13	y2	y2	PROPN
ejpam-4727	49	14	and	and	CCONJ
ejpam-4727	49	15	y3	y3	NOUN
ejpam-4727	49	16	which	which	PRON
ejpam-4727	49	17	are	be	AUX
ejpam-4727	49	18	given	give	VERB
ejpam-4727	49	19	by	by	ADP
ejpam-4727	49	20	y1	y1	PROPN
ejpam-4727	49	21	=	=	SYM
ejpam-4727	49	22	a0	a0	PROPN
ejpam-4727	49	23	+	+	CCONJ
ejpam-4727	49	24	a1(x1	a1(x1	ADJ
ejpam-4727	49	25	−	−	PROPN
ejpam-4727	49	26	x0	x0	PROPN
ejpam-4727	49	27	)	)	PUNCT
ejpam-4727	49	28	,	,	PUNCT
ejpam-4727	49	29	(	(	PUNCT
ejpam-4727	49	30	7	7	X
ejpam-4727	49	31	)	)	PUNCT
ejpam-4727	49	32	y2	y2	NOUN
ejpam-4727	49	33	=	=	SYM
ejpam-4727	49	34	a0	a0	PROPN
ejpam-4727	49	35	+	+	CCONJ
ejpam-4727	49	36	a1(x2	a1(x2	NOUN
ejpam-4727	49	37	−	−	PROPN
ejpam-4727	49	38	x0	x0	PROPN
ejpam-4727	49	39	)	)	PUNCT
ejpam-4727	50	1	+	+	NUM
ejpam-4727	50	2	a2(x2	a2(x2	NOUN
ejpam-4727	50	3	−	−	NOUN
ejpam-4727	50	4	x0)(x2	x0)(x2	NOUN
ejpam-4727	51	1	−	−	PROPN
ejpam-4727	51	2	x1	x1	PROPN
ejpam-4727	51	3	)	)	PUNCT
ejpam-4727	51	4	,	,	PUNCT
ejpam-4727	51	5	(	(	PUNCT
ejpam-4727	51	6	8)	8)	NUM
ejpam-4727	51	7	y3	y3	NOUN
ejpam-4727	51	8	=	=	SYM
ejpam-4727	51	9	a0	a0	PROPN
ejpam-4727	51	10	+	+	CCONJ
ejpam-4727	51	11	a1(x3	a1(x3	NOUN
ejpam-4727	51	12	−	−	NOUN
ejpam-4727	51	13	x0	x0	PROPN
ejpam-4727	51	14	)	)	PUNCT
ejpam-4727	52	1	+	+	CCONJ
ejpam-4727	52	2	a2(x3	a2(x3	ADV
ejpam-4727	52	3	−	−	NOUN
ejpam-4727	52	4	x0)(x3	x0)(x3	PUNCT
ejpam-4727	53	1	−	−	PROPN
ejpam-4727	54	1	x1	x1	PROPN
ejpam-4727	54	2	)	)	PUNCT
ejpam-4727	55	1	+	+	CCONJ
ejpam-4727	55	2	a3(x3	a3(x3	NUM
ejpam-4727	55	3	−	−	NOUN
ejpam-4727	55	4	x0)(x3	x0)(x3	PUNCT
ejpam-4727	56	1	−	−	PROPN
ejpam-4727	56	2	x1)(x3	x1)(x3	PUNCT
ejpam-4727	57	1	−	−	PROPN
ejpam-4727	57	2	x2	x2	PROPN
ejpam-4727	57	3	)	)	PUNCT
ejpam-4727	57	4	,	,	PUNCT
ejpam-4727	57	5	(	(	PUNCT
ejpam-4727	57	6	9	9	X
ejpam-4727	57	7	)	)	PUNCT
ejpam-4727	58	1	where	where	SCONJ
ejpam-4727	58	2	xi+1	xi+1	NOUN
ejpam-4727	58	3	=	=	SYM
ejpam-4727	58	4	xi	xi	PROPN
ejpam-4727	59	1	+	+	CCONJ
ejpam-4727	59	2	h	h	NOUN
ejpam-4727	59	3	and	and	CCONJ
ejpam-4727	59	4	the	the	DET
ejpam-4727	59	5	step	step	NOUN
ejpam-4727	59	6	size	size	NOUN
ejpam-4727	59	7	h	h	NOUN
ejpam-4727	59	8	is	be	AUX
ejpam-4727	59	9	very	very	ADV
ejpam-4727	59	10	small	small	ADJ
ejpam-4727	59	11	constant	constant	ADJ
ejpam-4727	59	12	.	.	PUNCT
ejpam-4727	60	1	a.	a.	PROPN
ejpam-4727	60	2	neamvonk	neamvonk	PROPN
ejpam-4727	60	3	,	,	PUNCT
ejpam-4727	60	4	b.	b.	PROPN
ejpam-4727	60	5	sriponpaew	sriponpaew	PROPN
ejpam-4727	60	6	/	/	SYM
ejpam-4727	60	7	eur	eur	PROPN
ejpam-4727	60	8	.	.	PUNCT
ejpam-4727	61	1	j.	j.	PROPN
ejpam-4727	61	2	pure	pure	PROPN
ejpam-4727	61	3	appl	appl	PROPN
ejpam-4727	61	4	.	.	PROPN
ejpam-4727	61	5	math	math	PROPN
ejpam-4727	61	6	,	,	PUNCT
ejpam-4727	61	7	16	16	NUM
ejpam-4727	61	8	(	(	PUNCT
ejpam-4727	61	9	2	2	NUM
ejpam-4727	61	10	)	)	PUNCT
ejpam-4727	61	11	(	(	PUNCT
ejpam-4727	61	12	2023	2023	NUM
ejpam-4727	61	13	)	)	PUNCT
ejpam-4727	61	14	,	,	PUNCT
ejpam-4727	61	15	965	965	NUM
ejpam-4727	61	16	-	-	SYM
ejpam-4727	61	17	974	974	NUM
ejpam-4727	61	18	967	967	NUM
ejpam-4727	61	19	2.2	2.2	NUM
ejpam-4727	61	20	.	.	PUNCT
ejpam-4727	62	1	lagrange	lagrange	PROPN
ejpam-4727	62	2	’s	’s	PART
ejpam-4727	62	3	method	method	PROPN
ejpam-4727	62	4	lagrange	lagrange	PROPN
ejpam-4727	62	5	’s	’s	PART
ejpam-4727	62	6	method	method	NOUN
ejpam-4727	62	7	is	be	AUX
ejpam-4727	62	8	a	a	DET
ejpam-4727	62	9	method	method	NOUN
ejpam-4727	62	10	to	to	PART
ejpam-4727	62	11	find	find	VERB
ejpam-4727	62	12	a	a	DET
ejpam-4727	62	13	nth	nth	NOUN
ejpam-4727	62	14	degree	degree	NOUN
ejpam-4727	62	15	polynomial	polynomial	NOUN
ejpam-4727	62	16	that	that	PRON
ejpam-4727	62	17	takes	take	VERB
ejpam-4727	62	18	on	on	ADP
ejpam-4727	62	19	certain	certain	ADJ
ejpam-4727	62	20	values	value	NOUN
ejpam-4727	62	21	at	at	ADP
ejpam-4727	62	22	an	an	DET
ejpam-4727	62	23	arbitrary	arbitrary	ADJ
ejpam-4727	62	24	point	point	NOUN
ejpam-4727	62	25	.	.	PUNCT
ejpam-4727	63	1	we	we	PRON
ejpam-4727	63	2	have	have	VERB
ejpam-4727	63	3	only	only	ADV
ejpam-4727	63	4	(	(	PUNCT
ejpam-4727	63	5	x0	x0	PROPN
ejpam-4727	63	6	,	,	PUNCT
ejpam-4727	63	7	y0	y0	PROPN
ejpam-4727	63	8	)	)	PUNCT
ejpam-4727	63	9	,	,	PUNCT
ejpam-4727	63	10	(	(	PUNCT
ejpam-4727	63	11	x1	x1	PROPN
ejpam-4727	63	12	,	,	PUNCT
ejpam-4727	63	13	y1	y1	PROPN
ejpam-4727	63	14	)	)	PUNCT
ejpam-4727	63	15	,	,	PUNCT
ejpam-4727	63	16	(	(	PUNCT
ejpam-4727	63	17	x2	x2	PROPN
ejpam-4727	63	18	,	,	PUNCT
ejpam-4727	63	19	y2	y2	PROPN
ejpam-4727	63	20	)	)	PUNCT
ejpam-4727	63	21	and	and	CCONJ
ejpam-4727	63	22	(	(	PUNCT
ejpam-4727	63	23	x3	x3	ADJ
ejpam-4727	63	24	,	,	PUNCT
ejpam-4727	63	25	y3	y3	NOUN
ejpam-4727	63	26	)	)	PUNCT
ejpam-4727	63	27	to	to	PART
ejpam-4727	63	28	build	build	VERB
ejpam-4727	63	29	the	the	DET
ejpam-4727	63	30	3rd	3rd	ADJ
ejpam-4727	63	31	degree	degree	NOUN
ejpam-4727	63	32	polynomial	polynomial	ADJ
ejpam-4727	63	33	equation	equation	NOUN
ejpam-4727	63	34	(	(	PUNCT
ejpam-4727	63	35	cubic	cubic	ADJ
ejpam-4727	63	36	function	function	NOUN
ejpam-4727	63	37	)	)	PUNCT
ejpam-4727	63	38	,	,	PUNCT
ejpam-4727	63	39	p3(x	p3(x	PROPN
ejpam-4727	63	40	)	)	PUNCT
ejpam-4727	63	41	=	=	SYM
ejpam-4727	63	42	c0	c0	NOUN
ejpam-4727	63	43	+	+	CCONJ
ejpam-4727	63	44	c1x+	c1x+	X
ejpam-4727	63	45	c2x	c2x	NOUN
ejpam-4727	63	46	2	2	NUM
ejpam-4727	63	47	+	+	CCONJ
ejpam-4727	63	48	c3x	c3x	PROPN
ejpam-4727	63	49	3	3	NUM
ejpam-4727	63	50	,	,	PUNCT
ejpam-4727	63	51	p3(x	p3(x	NOUN
ejpam-4727	63	52	)	)	PUNCT
ejpam-4727	63	53	=	=	SYM
ejpam-4727	63	54	(	(	PUNCT
ejpam-4727	63	55	x−	x−	PROPN
ejpam-4727	63	56	x1)(x−	x1)(x−	PROPN
ejpam-4727	63	57	x2)(x−	x2)(x−	PROPN
ejpam-4727	63	58	x3	x3	ADJ
ejpam-4727	63	59	)	)	PUNCT
ejpam-4727	64	1	(	(	PUNCT
ejpam-4727	64	2	x0	x0	PROPN
ejpam-4727	64	3	−	−	PROPN
ejpam-4727	64	4	x1)(x0	x1)(x0	PUNCT
ejpam-4727	65	1	−	−	PROPN
ejpam-4727	65	2	x2)(x0	x2)(x0	PUNCT
ejpam-4727	66	1	−	−	PROPN
ejpam-4727	66	2	x3	x3	ADJ
ejpam-4727	66	3	)	)	PUNCT
ejpam-4727	66	4	y0	y0	PROPN
ejpam-4727	66	5	+	+	CCONJ
ejpam-4727	66	6	(	(	PUNCT
ejpam-4727	66	7	x−	x−	PROPN
ejpam-4727	66	8	x0)(x−	x0)(x−	PROPN
ejpam-4727	66	9	x2)(x−	x2)(x−	PUNCT
ejpam-4727	67	1	x3	x3	ADJ
ejpam-4727	67	2	)	)	PUNCT
ejpam-4727	68	1	(	(	PUNCT
ejpam-4727	68	2	x1	x1	PROPN
ejpam-4727	68	3	−	−	PROPN
ejpam-4727	68	4	x0)(x1	x0)(x1	PROPN
ejpam-4727	68	5	−	−	PROPN
ejpam-4727	68	6	x2)(x1	x2)(x1	PROPN
ejpam-4727	68	7	−	−	PROPN
ejpam-4727	68	8	x3	x3	ADJ
ejpam-4727	68	9	)	)	PUNCT
ejpam-4727	68	10	y1	y1	NOUN
ejpam-4727	68	11	+	+	CCONJ
ejpam-4727	68	12	(	(	PUNCT
ejpam-4727	68	13	x−	x−	PROPN
ejpam-4727	68	14	x0)(x−	x0)(x−	PROPN
ejpam-4727	68	15	x1)(x−	x1)(x−	PUNCT
ejpam-4727	69	1	x3	x3	ADJ
ejpam-4727	69	2	)	)	PUNCT
ejpam-4727	70	1	(	(	PUNCT
ejpam-4727	70	2	x2	x2	INTJ
ejpam-4727	70	3	−	−	PROPN
ejpam-4727	70	4	x0)(x2	x0)(x2	NOUN
ejpam-4727	70	5	−	−	NOUN
ejpam-4727	70	6	x1)(x2	x1)(x2	PUNCT
ejpam-4727	71	1	−	−	PROPN
ejpam-4727	71	2	x3	x3	ADJ
ejpam-4727	71	3	)	)	PUNCT
ejpam-4727	72	1	y2	y2	NOUN
ejpam-4727	72	2	+	+	CCONJ
ejpam-4727	73	1	(	(	PUNCT
ejpam-4727	73	2	x−	x−	PROPN
ejpam-4727	73	3	x0)(x−	x0)(x−	PROPN
ejpam-4727	73	4	x1)(x−	x1)(x−	PUNCT
ejpam-4727	74	1	x2	x2	PROPN
ejpam-4727	74	2	)	)	PUNCT
ejpam-4727	75	1	(	(	PUNCT
ejpam-4727	75	2	x3	x3	ADV
ejpam-4727	75	3	−	−	PROPN
ejpam-4727	75	4	x0)(x3	x0)(x3	PUNCT
ejpam-4727	76	1	−	−	PROPN
ejpam-4727	76	2	x1)(x3	x1)(x3	PUNCT
ejpam-4727	77	1	−	−	PROPN
ejpam-4727	77	2	x2	x2	SYM
ejpam-4727	77	3	)	)	PUNCT
ejpam-4727	77	4	y3	y3	PROPN
ejpam-4727	77	5	.	.	PUNCT
ejpam-4727	78	1	(	(	PUNCT
ejpam-4727	78	2	10	10	NUM
ejpam-4727	78	3	)	)	PUNCT
ejpam-4727	78	4	then	then	ADV
ejpam-4727	78	5	we	we	PRON
ejpam-4727	78	6	apply	apply	VERB
ejpam-4727	78	7	(	(	PUNCT
ejpam-4727	78	8	10	10	NUM
ejpam-4727	78	9	)	)	PUNCT
ejpam-4727	78	10	to	to	PART
ejpam-4727	78	11	approximate	approximate	VERB
ejpam-4727	78	12	yi	yi	PROPN
ejpam-4727	78	13	=	=	SYM
ejpam-4727	78	14	p3(xi	p3(xi	PROPN
ejpam-4727	78	15	)	)	PUNCT
ejpam-4727	78	16	where	where	SCONJ
ejpam-4727	78	17	i	i	PRON
ejpam-4727	78	18	=	=	NOUN
ejpam-4727	78	19	4	4	NUM
ejpam-4727	78	20	,	,	PUNCT
ejpam-4727	78	21	5	5	NUM
ejpam-4727	78	22	,	,	PUNCT
ejpam-4727	78	23	..	..	PUNCT
ejpam-4727	78	24	,	,	PUNCT
ejpam-4727	78	25	8	8	NUM
ejpam-4727	78	26	which	which	PRON
ejpam-4727	78	27	are	be	AUX
ejpam-4727	78	28	the	the	DET
ejpam-4727	78	29	solutions	solution	NOUN
ejpam-4727	78	30	of	of	ADP
ejpam-4727	78	31	(	(	PUNCT
ejpam-4727	78	32	1	1	NUM
ejpam-4727	78	33	)	)	PUNCT
ejpam-4727	78	34	as	as	SCONJ
ejpam-4727	78	35	shown	show	VERB
ejpam-4727	78	36	in	in	ADP
ejpam-4727	78	37	figure	figure	NOUN
ejpam-4727	78	38	1	1	NUM
ejpam-4727	78	39	.	.	PUNCT
ejpam-4727	78	40	figure	figure	NOUN
ejpam-4727	78	41	1	1	NUM
ejpam-4727	78	42	:	:	PUNCT
ejpam-4727	78	43	showing	show	VERB
ejpam-4727	78	44	an	an	DET
ejpam-4727	78	45	initial	initial	ADJ
ejpam-4727	78	46	point	point	NOUN
ejpam-4727	78	47	,	,	PUNCT
ejpam-4727	78	48	(	(	PUNCT
ejpam-4727	78	49	x0	x0	PROPN
ejpam-4727	78	50	,	,	PUNCT
ejpam-4727	78	51	y0	y0	PROPN
ejpam-4727	78	52	)	)	PUNCT
ejpam-4727	78	53	,	,	PUNCT
ejpam-4727	78	54	the	the	DET
ejpam-4727	78	55	red	red	ADJ
ejpam-4727	78	56	points	point	NOUN
ejpam-4727	78	57	from	from	ADP
ejpam-4727	78	58	the	the	DET
ejpam-4727	78	59	newton	newton	PROPN
ejpam-4727	78	60	’s	’s	PART
ejpam-4727	78	61	interpolation	interpolation	NOUN
ejpam-4727	78	62	,	,	PUNCT
ejpam-4727	78	63	(	(	PUNCT
ejpam-4727	78	64	x1	x1	PROPN
ejpam-4727	78	65	,	,	PUNCT
ejpam-4727	78	66	y1	y1	PROPN
ejpam-4727	78	67	)	)	PUNCT
ejpam-4727	78	68	,	,	PUNCT
ejpam-4727	78	69	(	(	PUNCT
ejpam-4727	78	70	x2	x2	PROPN
ejpam-4727	78	71	,	,	PUNCT
ejpam-4727	78	72	y2	y2	PROPN
ejpam-4727	78	73	)	)	PUNCT
ejpam-4727	78	74	and	and	CCONJ
ejpam-4727	78	75	(	(	PUNCT
ejpam-4727	78	76	x3	x3	ADJ
ejpam-4727	78	77	,	,	PUNCT
ejpam-4727	78	78	y3	y3	NOUN
ejpam-4727	78	79	)	)	PUNCT
ejpam-4727	78	80	and	and	CCONJ
ejpam-4727	78	81	the	the	DET
ejpam-4727	78	82	solution	solution	NOUN
ejpam-4727	78	83	points	point	VERB
ejpam-4727	78	84	by	by	ADP
ejpam-4727	78	85	(	(	PUNCT
ejpam-4727	78	86	10	10	NUM
ejpam-4727	78	87	)	)	PUNCT
ejpam-4727	78	88	.	.	PUNCT
ejpam-4727	79	1	2.3	2.3	NUM
ejpam-4727	79	2	.	.	PUNCT
ejpam-4727	79	3	algorithm	algorithm	NOUN
ejpam-4727	79	4	of	of	ADP
ejpam-4727	79	5	our	our	PRON
ejpam-4727	79	6	method	method	NOUN
ejpam-4727	79	7	#	#	NOUN
ejpam-4727	79	8	consider	consider	VERB
ejpam-4727	79	9	ivp	ivp	ADJ
ejpam-4727	79	10	dy	dy	NOUN
ejpam-4727	79	11	/	/	SYM
ejpam-4727	79	12	dx	dx	PROPN
ejpam-4727	79	13	=	=	SYM
ejpam-4727	79	14	f(x	f(x	PROPN
ejpam-4727	79	15	,	,	PUNCT
ejpam-4727	79	16	y	y	NOUN
ejpam-4727	79	17	)	)	PUNCT
ejpam-4727	79	18	with	with	ADP
ejpam-4727	79	19	initial	initial	ADJ
ejpam-4727	79	20	condition	condition	NOUN
ejpam-4727	79	21	y(x0	y(x0	NOUN
ejpam-4727	79	22	)	)	PUNCT
ejpam-4727	79	23	=	=	PUNCT
ejpam-4727	80	1	y0	y0	NOUN
ejpam-4727	80	2	1	1	NUM
ejpam-4727	80	3	.	.	PUNCT
ejpam-4727	80	4	define	define	VERB
ejpam-4727	80	5	function	function	NOUN
ejpam-4727	80	6	f(x	f(x	PROPN
ejpam-4727	80	7	,	,	PUNCT
ejpam-4727	80	8	y	y	NOUN
ejpam-4727	80	9	)	)	PUNCT
ejpam-4727	80	10	2	2	NUM
ejpam-4727	80	11	.	.	X
ejpam-4727	81	1	set	set	VERB
ejpam-4727	81	2	values	value	NOUN
ejpam-4727	81	3	of	of	ADP
ejpam-4727	81	4	initial	initial	ADJ
ejpam-4727	81	5	condition	condition	NOUN
ejpam-4727	81	6	(	(	PUNCT
ejpam-4727	81	7	x0	x0	PROPN
ejpam-4727	81	8	,	,	PUNCT
ejpam-4727	81	9	y0	y0	PROPN
ejpam-4727	81	10	)	)	PUNCT
ejpam-4727	81	11	,	,	PUNCT
ejpam-4727	81	12	number	number	NOUN
ejpam-4727	81	13	of	of	ADP
ejpam-4727	81	14	steps	step	NOUN
ejpam-4727	81	15	(	(	PUNCT
ejpam-4727	81	16	n	n	CCONJ
ejpam-4727	81	17	)	)	PUNCT
ejpam-4727	81	18	and	and	CCONJ
ejpam-4727	81	19	step	step	NOUN
ejpam-4727	81	20	size	size	NOUN
ejpam-4727	81	21	(	(	PUNCT
ejpam-4727	81	22	h	h	NOUN
ejpam-4727	81	23	)	)	PUNCT
ejpam-4727	81	24	3	3	NUM
ejpam-4727	81	25	.	.	X
ejpam-4727	81	26	use	use	PROPN
ejpam-4727	81	27	newton	newton	PROPN
ejpam-4727	81	28	’s	’s	PART
ejpam-4727	81	29	interpolation	interpolation	NOUN
ejpam-4727	81	30	method	method	NOUN
ejpam-4727	81	31	to	to	PART
ejpam-4727	81	32	find	find	VERB
ejpam-4727	81	33	(	(	PUNCT
ejpam-4727	81	34	x1	x1	PROPN
ejpam-4727	81	35	,	,	PUNCT
ejpam-4727	81	36	y1	y1	PROPN
ejpam-4727	81	37	)	)	PUNCT
ejpam-4727	81	38	,	,	PUNCT
ejpam-4727	81	39	(	(	PUNCT
ejpam-4727	81	40	x2	x2	PROPN
ejpam-4727	81	41	,	,	PUNCT
ejpam-4727	81	42	y2	y2	PROPN
ejpam-4727	81	43	)	)	PUNCT
ejpam-4727	81	44	and	and	CCONJ
ejpam-4727	81	45	(	(	PUNCT
ejpam-4727	81	46	x3	x3	ADJ
ejpam-4727	81	47	,	,	PUNCT
ejpam-4727	81	48	y3	y3	NOUN
ejpam-4727	81	49	)	)	PUNCT
ejpam-4727	81	50	4	4	NUM
ejpam-4727	81	51	.	.	X
ejpam-4727	81	52	use	use	VERB
ejpam-4727	81	53	lagrange	lagrange	PROPN
ejpam-4727	81	54	’s	’s	PART
ejpam-4727	81	55	method	method	NOUN
ejpam-4727	81	56	to	to	PART
ejpam-4727	81	57	find	find	VERB
ejpam-4727	81	58	p3(x	p3(x	PRON
ejpam-4727	81	59	)	)	PUNCT
ejpam-4727	81	60	5	5	NUM
ejpam-4727	81	61	.	.	PUNCT
ejpam-4727	82	1	set	set	VERB
ejpam-4727	82	2	i	i	NOUN
ejpam-4727	82	3	=	=	NOUN
ejpam-4727	82	4	4	4	NUM
ejpam-4727	82	5	6	6	NUM
ejpam-4727	82	6	.	.	PUNCT
ejpam-4727	82	7	loop	loop	NOUN
ejpam-4727	82	8	while	while	SCONJ
ejpam-4727	82	9	i	i	PRON
ejpam-4727	82	10	<	<	X
ejpam-4727	82	11	=	=	X
ejpam-4727	82	12	n	n	PRON
ejpam-4727	82	13	yi	yi	NOUN
ejpam-4727	82	14	=	=	SYM
ejpam-4727	82	15	p3(xi	p3(xi	PROPN
ejpam-4727	82	16	)	)	PUNCT
ejpam-4727	82	17	xi	xi	X
ejpam-4727	83	1	=	=	PUNCT
ejpam-4727	83	2	xi	xi	PROPN
ejpam-4727	84	1	+	+	CCONJ
ejpam-4727	84	2	h	h	NOUN
ejpam-4727	85	1	i	i	PRON
ejpam-4727	85	2	=	=	VERB
ejpam-4727	86	1	i	i	PRON
ejpam-4727	86	2	+	+	NOUN
ejpam-4727	86	3	1	1	NUM
ejpam-4727	86	4	7	7	NUM
ejpam-4727	86	5	.	.	PUNCT
ejpam-4727	86	6	display	display	NOUN
ejpam-4727	86	7	yi	yi	PROPN
ejpam-4727	86	8	as	as	ADP
ejpam-4727	86	9	results	result	NOUN
ejpam-4727	86	10	a.	a.	NOUN
ejpam-4727	86	11	neamvonk	neamvonk	ADV
ejpam-4727	86	12	,	,	PUNCT
ejpam-4727	86	13	b.	b.	PROPN
ejpam-4727	86	14	sriponpaew	sriponpaew	PROPN
ejpam-4727	86	15	/	/	SYM
ejpam-4727	86	16	eur	eur	PROPN
ejpam-4727	86	17	.	.	PUNCT
ejpam-4727	87	1	j.	j.	PROPN
ejpam-4727	87	2	pure	pure	PROPN
ejpam-4727	87	3	appl	appl	PROPN
ejpam-4727	87	4	.	.	PROPN
ejpam-4727	87	5	math	math	PROPN
ejpam-4727	87	6	,	,	PUNCT
ejpam-4727	87	7	16	16	NUM
ejpam-4727	87	8	(	(	PUNCT
ejpam-4727	87	9	2	2	NUM
ejpam-4727	87	10	)	)	PUNCT
ejpam-4727	87	11	(	(	PUNCT
ejpam-4727	87	12	2023	2023	NUM
ejpam-4727	87	13	)	)	PUNCT
ejpam-4727	87	14	,	,	PUNCT
ejpam-4727	87	15	965	965	NUM
ejpam-4727	87	16	-	-	SYM
ejpam-4727	87	17	974	974	NUM
ejpam-4727	87	18	968	968	NUM
ejpam-4727	87	19	3	3	NUM
ejpam-4727	87	20	.	.	PUNCT
ejpam-4727	87	21	numerical	numerical	ADJ
ejpam-4727	87	22	results	result	NOUN
ejpam-4727	87	23	we	we	PRON
ejpam-4727	87	24	will	will	AUX
ejpam-4727	87	25	use	use	VERB
ejpam-4727	87	26	our	our	PRON
ejpam-4727	87	27	method	method	NOUN
ejpam-4727	87	28	to	to	PART
ejpam-4727	87	29	find	find	VERB
ejpam-4727	87	30	the	the	DET
ejpam-4727	87	31	numerical	numerical	ADJ
ejpam-4727	87	32	solutions	solution	NOUN
ejpam-4727	87	33	and	and	CCONJ
ejpam-4727	87	34	relative	relative	ADJ
ejpam-4727	87	35	errors	error	NOUN
ejpam-4727	87	36	and	and	CCONJ
ejpam-4727	87	37	compare	compare	VERB
ejpam-4727	87	38	results	result	NOUN
ejpam-4727	87	39	with	with	ADP
ejpam-4727	87	40	euler	euler	PROPN
ejpam-4727	87	41	’s	’s	PART
ejpam-4727	87	42	method	method	NOUN
ejpam-4727	87	43	,	,	PUNCT
ejpam-4727	87	44	methods	method	NOUN
ejpam-4727	87	45	of	of	ADP
ejpam-4727	87	46	[	[	X
ejpam-4727	87	47	11	11	NUM
ejpam-4727	87	48	]	]	PUNCT
ejpam-4727	87	49	and	and	CCONJ
ejpam-4727	87	50	[	[	X
ejpam-4727	87	51	14	14	NUM
ejpam-4727	87	52	]	]	PUNCT
ejpam-4727	87	53	in	in	ADP
ejpam-4727	87	54	the	the	DET
ejpam-4727	87	55	following	follow	VERB
ejpam-4727	87	56	examples	example	NOUN
ejpam-4727	87	57	.	.	PUNCT
ejpam-4727	88	1	example	example	NOUN
ejpam-4727	89	1	1	1	NUM
ejpam-4727	89	2	.	.	X
ejpam-4727	89	3	consider	consider	VERB
ejpam-4727	89	4	the	the	DET
ejpam-4727	89	5	initial	initial	ADJ
ejpam-4727	89	6	value	value	NOUN
ejpam-4727	89	7	problem	problem	NOUN
ejpam-4727	89	8	dy	dy	NOUN
ejpam-4727	89	9	dx	dx	PROPN
ejpam-4727	90	1	=	=	PROPN
ejpam-4727	91	1	1−	1−	NUM
ejpam-4727	91	2	y	y	PROPN
ejpam-4727	91	3	,	,	PUNCT
ejpam-4727	91	4	y(0	y(0	PROPN
ejpam-4727	91	5	)	)	PUNCT
ejpam-4727	91	6	=	=	SYM
ejpam-4727	92	1	0	0	X
ejpam-4727	92	2	.	.	PUNCT
ejpam-4727	92	3	then	then	ADV
ejpam-4727	92	4	take	take	VERB
ejpam-4727	92	5	the	the	DET
ejpam-4727	92	6	step	step	NOUN
ejpam-4727	92	7	size	size	NOUN
ejpam-4727	92	8	h	h	NOUN
ejpam-4727	92	9	=	=	NOUN
ejpam-4727	92	10	0.1	0.1	NUM
ejpam-4727	92	11	and	and	CCONJ
ejpam-4727	92	12	use	use	VERB
ejpam-4727	92	13	newton	newton	PROPN
ejpam-4727	92	14	’s	’s	PART
ejpam-4727	92	15	interpolation	interpolation	NOUN
ejpam-4727	92	16	a0	a0	NOUN
ejpam-4727	92	17	=	=	SYM
ejpam-4727	92	18	0.0	0.0	NUM
ejpam-4727	92	19	,	,	PUNCT
ejpam-4727	92	20	a1	a1	NOUN
ejpam-4727	92	21	=	=	SYM
ejpam-4727	92	22	1.0	1.0	NUM
ejpam-4727	92	23	,	,	PUNCT
ejpam-4727	92	24	a2	a2	NOUN
ejpam-4727	92	25	=	=	SYM
ejpam-4727	92	26	−0.499999	−0.499999	NOUN
ejpam-4727	92	27	,	,	PUNCT
ejpam-4727	92	28	a3	a3	NOUN
ejpam-4727	92	29	=	=	SYM
ejpam-4727	92	30	0.166667	0.166667	NUM
ejpam-4727	92	31	and	and	CCONJ
ejpam-4727	92	32	y1	y1	NOUN
ejpam-4727	92	33	=	=	SYM
ejpam-4727	92	34	0.1	0.1	NUM
ejpam-4727	92	35	,	,	PUNCT
ejpam-4727	93	1	y2	y2	NOUN
ejpam-4727	93	2	=	=	NOUN
ejpam-4727	93	3	0.19	0.19	NUM
ejpam-4727	93	4	,	,	PUNCT
ejpam-4727	93	5	y3	y3	NOUN
ejpam-4727	93	6	=	=	NUM
ejpam-4727	93	7	0.271	0.271	NUM
ejpam-4727	93	8	.	.	PUNCT
ejpam-4727	94	1	apply	apply	VERB
ejpam-4727	94	2	(	(	PUNCT
ejpam-4727	94	3	0	0	NUM
ejpam-4727	94	4	,	,	PUNCT
ejpam-4727	94	5	0	0	NUM
ejpam-4727	94	6	)	)	PUNCT
ejpam-4727	94	7	,	,	PUNCT
ejpam-4727	94	8	(	(	PUNCT
ejpam-4727	94	9	0.1	0.1	NUM
ejpam-4727	94	10	,	,	PUNCT
ejpam-4727	94	11	0.1	0.1	NUM
ejpam-4727	94	12	)	)	PUNCT
ejpam-4727	94	13	,	,	PUNCT
ejpam-4727	94	14	(	(	PUNCT
ejpam-4727	94	15	0.2	0.2	NUM
ejpam-4727	94	16	,	,	PUNCT
ejpam-4727	94	17	0.19	0.19	NUM
ejpam-4727	94	18	)	)	PUNCT
ejpam-4727	94	19	and	and	CCONJ
ejpam-4727	94	20	(	(	PUNCT
ejpam-4727	94	21	0.3	0.3	NUM
ejpam-4727	94	22	,	,	PUNCT
ejpam-4727	94	23	0.271	0.271	NUM
ejpam-4727	94	24	)	)	PUNCT
ejpam-4727	94	25	to	to	PART
ejpam-4727	94	26	find	find	VERB
ejpam-4727	94	27	cubic	cubic	ADJ
ejpam-4727	94	28	polynomial	polynomial	NOUN
ejpam-4727	94	29	by	by	ADP
ejpam-4727	94	30	(	(	PUNCT
ejpam-4727	94	31	10	10	NUM
ejpam-4727	94	32	)	)	PUNCT
ejpam-4727	94	33	.	.	PUNCT
ejpam-4727	95	1	then	then	ADV
ejpam-4727	95	2	we	we	PRON
ejpam-4727	95	3	obtain	obtain	VERB
ejpam-4727	95	4	p3(x	p3(x	PRON
ejpam-4727	95	5	)	)	PUNCT
ejpam-4727	95	6	=	=	PUNCT
ejpam-4727	96	1	0.166667x3	0.166667x3	PRON
ejpam-4727	96	2	−	−	NOUN
ejpam-4727	96	3	0.549997x2	0.549997x2	NUM
ejpam-4727	96	4	+	+	PUNCT
ejpam-4727	96	5	1.053333x	1.053333x	X
ejpam-4727	96	6	.	.	PUNCT
ejpam-4727	97	1	(	(	PUNCT
ejpam-4727	97	2	11	11	NUM
ejpam-4727	97	3	)	)	PUNCT
ejpam-4727	97	4	in	in	ADP
ejpam-4727	97	5	order	order	NOUN
ejpam-4727	97	6	to	to	PART
ejpam-4727	97	7	approximate	approximate	VERB
ejpam-4727	97	8	the	the	DET
ejpam-4727	97	9	solutions	solution	NOUN
ejpam-4727	97	10	,	,	PUNCT
ejpam-4727	97	11	we	we	PRON
ejpam-4727	97	12	substitute	substitute	VERB
ejpam-4727	97	13	xi	xi	PROPN
ejpam-4727	97	14	in	in	ADP
ejpam-4727	97	15	p3(x	p3(x	PROPN
ejpam-4727	97	16	)	)	PUNCT
ejpam-4727	97	17	to	to	PART
ejpam-4727	97	18	get	get	VERB
ejpam-4727	97	19	yi	yi	NOUN
ejpam-4727	97	20	=	=	SYM
ejpam-4727	97	21	p3(xi	p3(xi	PROPN
ejpam-4727	97	22	)	)	PUNCT
ejpam-4727	97	23	for	for	ADP
ejpam-4727	97	24	i	i	PROPN
ejpam-4727	97	25	=	=	NOUN
ejpam-4727	97	26	4	4	NUM
ejpam-4727	97	27	,	,	PUNCT
ejpam-4727	97	28	5	5	NUM
ejpam-4727	97	29	,	,	PUNCT
ejpam-4727	97	30	...	...	PUNCT
ejpam-4727	97	31	20	20	NUM
ejpam-4727	97	32	and	and	CCONJ
ejpam-4727	97	33	compute	compute	VERB
ejpam-4727	97	34	relative	relative	ADJ
ejpam-4727	97	35	error	error	NOUN
ejpam-4727	97	36	,	,	PUNCT
ejpam-4727	97	37	∣∣∣yxi−yi	∣∣∣yxi−yi	PROPN
ejpam-4727	97	38	yxi	yxi	NOUN
ejpam-4727	97	39	∣∣∣	∣∣∣	ADJ
ejpam-4727	97	40	,	,	PUNCT
ejpam-4727	97	41	where	where	SCONJ
ejpam-4727	97	42	yxi	yxi	NOUN
ejpam-4727	97	43	is	be	AUX
ejpam-4727	97	44	exact	exact	ADJ
ejpam-4727	97	45	solutions	solution	NOUN
ejpam-4727	97	46	at	at	ADP
ejpam-4727	97	47	xi	xi	PROPN
ejpam-4727	97	48	,	,	PUNCT
ejpam-4727	97	49	as	as	SCONJ
ejpam-4727	97	50	shown	show	VERB
ejpam-4727	97	51	in	in	ADP
ejpam-4727	97	52	table	table	NOUN
ejpam-4727	97	53	1	1	NUM
ejpam-4727	97	54	and	and	CCONJ
ejpam-4727	97	55	figure	figure	VERB
ejpam-4727	97	56	2	2	NUM
ejpam-4727	97	57	.	.	PUNCT
ejpam-4727	98	1	the	the	DET
ejpam-4727	98	2	approximate	approximate	ADJ
ejpam-4727	98	3	solutions	solution	NOUN
ejpam-4727	98	4	are	be	AUX
ejpam-4727	98	5	close	close	ADJ
ejpam-4727	98	6	to	to	ADP
ejpam-4727	98	7	exact	exact	ADJ
ejpam-4727	98	8	solution	solution	NOUN
ejpam-4727	98	9	where	where	SCONJ
ejpam-4727	98	10	x	x	PUNCT
ejpam-4727	98	11	∈	∈	PROPN
ejpam-4727	98	12	[	[	X
ejpam-4727	98	13	0	0	NUM
ejpam-4727	98	14	,	,	PUNCT
ejpam-4727	98	15	0.8	0.8	NUM
ejpam-4727	98	16	]	]	PUNCT
ejpam-4727	98	17	and	and	CCONJ
ejpam-4727	98	18	relative	relative	ADJ
ejpam-4727	98	19	errors	error	NOUN
ejpam-4727	98	20	when	when	SCONJ
ejpam-4727	98	21	x	x	X
ejpam-4727	98	22	≥	≥	VERB
ejpam-4727	98	23	0.9	0.9	NUM
ejpam-4727	98	24	highly	highly	ADV
ejpam-4727	98	25	increase	increase	NOUN
ejpam-4727	98	26	as	as	ADP
ejpam-4727	98	27	show	show	NOUN
ejpam-4727	98	28	in	in	ADP
ejpam-4727	98	29	figure	figure	NOUN
ejpam-4727	98	30	2	2	NUM
ejpam-4727	98	31	.	.	PUNCT
ejpam-4727	98	32	table	table	NOUN
ejpam-4727	98	33	1	1	NUM
ejpam-4727	98	34	:	:	PUNCT
ejpam-4727	98	35	showing	show	VERB
ejpam-4727	98	36	results	result	NOUN
ejpam-4727	98	37	of	of	ADP
ejpam-4727	98	38	example	example	NOUN
ejpam-4727	98	39	1	1	NUM
ejpam-4727	98	40	with	with	ADP
ejpam-4727	98	41	h	h	NOUN
ejpam-4727	98	42	=	=	NOUN
ejpam-4727	98	43	0.1	0.1	NUM
ejpam-4727	98	44	on	on	ADP
ejpam-4727	98	45	xi	xi	ADP
ejpam-4727	98	46	∈	∈	PROPN
ejpam-4727	99	1	[	[	X
ejpam-4727	99	2	0	0	NUM
ejpam-4727	99	3	,	,	PUNCT
ejpam-4727	99	4	2	2	NUM
ejpam-4727	99	5	]	]	X
ejpam-4727	99	6	i	i	PRON
ejpam-4727	99	7	xi	xi	PROPN
ejpam-4727	99	8	approx	approx	PROPN
ejpam-4727	99	9	.	.	PUNCT
ejpam-4727	100	1	sol	sol	PROPN
ejpam-4727	100	2	.	.	PUNCT
ejpam-4727	101	1	yi	yi	PROPN
ejpam-4727	101	2	exact	exact	ADJ
ejpam-4727	101	3	relative	relative	ADJ
ejpam-4727	101	4	errors	error	NOUN
ejpam-4727	101	5	euler	euler	NOUN
ejpam-4727	102	1	[	[	X
ejpam-4727	102	2	11],[14	11],[14	X
ejpam-4727	102	3	]	]	X
ejpam-4727	102	4	present	present	ADJ
ejpam-4727	102	5	solution	solution	NOUN
ejpam-4727	102	6	euler	euler	NOUN
ejpam-4727	103	1	[	[	X
ejpam-4727	103	2	11],[14	11],[14	X
ejpam-4727	103	3	]	]	X
ejpam-4727	103	4	present	present	ADJ
ejpam-4727	103	5	0	0	NUM
ejpam-4727	103	6	0.00	0.00	NUM
ejpam-4727	103	7	0.000000	0.000000	NUM
ejpam-4727	103	8	0.000000	0.000000	NUM
ejpam-4727	103	9	0.000000	0.000000	NUM
ejpam-4727	103	10	0.000000	0.000000	NUM
ejpam-4727	103	11	0.000000	0.000000	NUM
ejpam-4727	103	12	0.000000	0.000000	NUM
ejpam-4727	103	13	0.000000	0.000000	NUM
ejpam-4727	103	14	1	1	NUM
ejpam-4727	103	15	0.10	0.10	NUM
ejpam-4727	103	16	0.100000	0.100000	NUM
ejpam-4727	103	17	0.100000	0.100000	NUM
ejpam-4727	103	18	0.100000	0.100000	NUM
ejpam-4727	103	19	0.095163	0.095163	NUM
ejpam-4727	103	20	0.050833	0.050833	NUM
ejpam-4727	103	21	0.050833	0.050833	NUM
ejpam-4727	103	22	0.050833	0.050833	NUM
ejpam-4727	103	23	2	2	NUM
ejpam-4727	103	24	0.20	0.20	NUM
ejpam-4727	103	25	0.190000	0.190000	NUM
ejpam-4727	103	26	0.190000	0.190000	NUM
ejpam-4727	103	27	0.190000	0.190000	NUM
ejpam-4727	103	28	0.181282	0.181282	NUM
ejpam-4727	103	29	0.048090	0.048090	NUM
ejpam-4727	103	30	0.048090	0.048090	NUM
ejpam-4727	103	31	0.048090	0.048090	NUM
ejpam-4727	103	32	3	3	NUM
ejpam-4727	103	33	0.30	0.30	NUM
ejpam-4727	103	34	0.271000	0.271000	NUM
ejpam-4727	103	35	0.270000	0.270000	NUM
ejpam-4727	103	36	0.271000	0.271000	NUM
ejpam-4727	103	37	0.259215	0.259215	NUM
ejpam-4727	103	38	0.045465	0.045465	NUM
ejpam-4727	103	39	0.041608	0.041608	NUM
ejpam-4727	103	40	0.045465	0.045465	NUM
ejpam-4727	103	41	4	4	NUM
ejpam-4727	103	42	0.40	0.40	NUM
ejpam-4727	103	43	0.343900	0.343900	NUM
ejpam-4727	103	44	0.340000	0.340000	NUM
ejpam-4727	103	45	0.344000	0.344000	NUM
ejpam-4727	104	1	0.329717	0.329717	NUM
ejpam-4727	104	2	0.043017	0.043017	NUM
ejpam-4727	104	3	0.031189	0.031189	NUM
ejpam-4727	104	4	0.043320	0.043320	NUM
ejpam-4727	104	5	5	5	NUM
ejpam-4727	104	6	0.50	0.50	NUM
ejpam-4727	104	7	0.409510	0.409510	NUM
ejpam-4727	104	8	0.400000	0.400000	NUM
ejpam-4727	104	9	0.410000	0.410000	NUM
ejpam-4727	104	10	0.393490	0.393490	NUM
ejpam-4727	104	11	0.040712	0.040712	NUM
ejpam-4727	104	12	0.016543	0.016543	NUM
ejpam-4727	104	13	0.041957	0.041957	NUM
ejpam-4727	104	14	6	6	NUM
ejpam-4727	104	15	0.60	0.60	NUM
ejpam-4727	104	16	0.468559	0.468559	NUM
ejpam-4727	104	17	0.450000	0.450000	NUM
ejpam-4727	104	18	0.470000	0.470000	NUM
ejpam-4727	104	19	0.451186	0.451186	NUM
ejpam-4727	104	20	0.038506	0.038506	NUM
ejpam-4727	104	21	0.002628	0.002628	NUM
ejpam-4727	104	22	0.041699	0.041699	NUM
ejpam-4727	104	23	7	7	NUM
ejpam-4727	104	24	0.70	0.70	NUM
ejpam-4727	104	25	0.521703	0.521703	NUM
ejpam-4727	104	26	0.490000	0.490000	NUM
ejpam-4727	104	27	0.525000	0.525000	NUM
ejpam-4727	104	28	0.503399	0.503399	NUM
ejpam-4727	104	29	0.036361	0.036361	NUM
ejpam-4727	104	30	0.026617	0.026617	NUM
ejpam-4727	104	31	0.042910	0.042910	NUM
ejpam-4727	104	32	8	8	NUM
ejpam-4727	104	33	0.80	0.80	NUM
ejpam-4727	104	34	0.569533	0.569533	NUM
ejpam-4727	104	35	0.520000	0.520000	NUM
ejpam-4727	104	36	0.576000	0.576000	NUM
ejpam-4727	104	37	0.550681	0.550681	NUM
ejpam-4727	104	38	0.034234	0.034234	NUM
ejpam-4727	104	39	0.055714	0.055714	NUM
ejpam-4727	104	40	0.045978	0.045978	NUM
ejpam-4727	104	41	9	9	NUM
ejpam-4727	104	42	0.90	0.90	NUM
ejpam-4727	104	43	0.612580	0.612580	NUM
ejpam-4727	104	44	0.540000	0.540000	NUM
ejpam-4727	104	45	0.624000	0.624000	NUM
ejpam-4727	104	46	0.593488	0.593488	NUM
ejpam-4727	104	47	0.032169	0.032169	NUM
ejpam-4727	104	48	0.090124	0.090124	NUM
ejpam-4727	104	49	0.051412	0.051412	NUM
ejpam-4727	104	50	10	10	NUM
ejpam-4727	104	51	1.00	1.00	NUM
ejpam-4727	104	52	0.651322	0.651322	NUM
ejpam-4727	104	53	0.550000	0.550000	NUM
ejpam-4727	104	54	0.670000	0.670000	NUM
ejpam-4727	104	55	0.632211	0.632211	NUM
ejpam-4727	104	56	0.030228	0.030228	NUM
ejpam-4727	104	57	0.130037	0.130037	NUM
ejpam-4727	104	58	0.059773	0.059773	NUM
ejpam-4727	104	59	11	11	NUM
ejpam-4727	104	60	1.10	1.10	NUM
ejpam-4727	104	61	0.686189	0.686189	NUM
ejpam-4727	104	62	0.550000	0.550000	NUM
ejpam-4727	104	63	0.715000	0.715000	NUM
ejpam-4727	104	64	0.667221	0.667221	NUM
ejpam-4727	104	65	0.028429	0.028429	NUM
ejpam-4727	104	66	0.175686	0.175686	NUM
ejpam-4727	104	67	0.071609	0.071609	NUM
ejpam-4727	104	68	12	12	NUM
ejpam-4727	104	69	1.20	1.20	NUM
ejpam-4727	104	70	0.717570	0.717570	NUM
ejpam-4727	104	71	0.540000	0.540000	NUM
ejpam-4727	104	72	0.760000	0.760000	NUM
ejpam-4727	105	1	0.698868	0.698868	NUM
ejpam-4727	105	2	0.026761	0.026761	NUM
ejpam-4727	105	3	0.227322	0.227322	NUM
ejpam-4727	105	4	0.087473	0.087473	NUM
ejpam-4727	105	5	13	13	NUM
ejpam-4727	105	6	1.30	1.30	NUM
ejpam-4727	105	7	0.745813	0.745813	NUM
ejpam-4727	105	8	0.520000	0.520000	NUM
ejpam-4727	105	9	0.806000	0.806000	NUM
ejpam-4727	105	10	0.727479	0.727479	NUM
ejpam-4727	105	11	0.025202	0.025202	NUM
ejpam-4727	105	12	0.285203	0.285203	NUM
ejpam-4727	105	13	0.107935	0.107935	NUM
ejpam-4727	105	14	14	14	NUM
ejpam-4727	105	15	1.40	1.40	NUM
ejpam-4727	105	16	0.771232	0.771232	NUM
ejpam-4727	105	17	0.490000	0.490000	NUM
ejpam-4727	105	18	0.854000	0.854000	NUM
ejpam-4727	105	19	0.753364	0.753364	NUM
ejpam-4727	105	20	0.023718	0.023718	NUM
ejpam-4727	105	21	0.349584	0.349584	NUM
ejpam-4727	105	22	0.133583	0.133583	NUM
ejpam-4727	105	23	15	15	NUM
ejpam-4727	105	24	1.50	1.50	NUM
ejpam-4727	105	25	0.794109	0.794109	NUM
ejpam-4727	105	26	0.450000	0.450000	NUM
ejpam-4727	105	27	0.905000	0.905000	NUM
ejpam-4727	105	28	0.776808	0.776808	NUM
ejpam-4727	105	29	0.022272	0.022272	NUM
ejpam-4727	105	30	0.420706	0.420706	NUM
ejpam-4727	105	31	0.165025	0.165025	NUM
ejpam-4727	105	32	16	16	NUM
ejpam-4727	105	33	1.60	1.60	NUM
ejpam-4727	105	34	0.814698	0.814698	NUM
ejpam-4727	105	35	0.400000	0.400000	NUM
ejpam-4727	105	36	0.960000	0.960000	NUM
ejpam-4727	105	37	0.798069	0.798069	NUM
ejpam-4727	105	38	0.020837	0.020837	NUM
ejpam-4727	105	39	0.498790	0.498790	NUM
ejpam-4727	105	40	0.202904	0.202904	NUM
ejpam-4727	105	41	17	17	NUM
ejpam-4727	105	42	1.70	1.70	NUM
ejpam-4727	105	43	0.833228	0.833228	NUM
ejpam-4727	105	44	0.340000	0.340000	NUM
ejpam-4727	105	45	1.020000	1.020000	NUM
ejpam-4727	105	46	0.817336	0.817336	NUM
ejpam-4727	105	47	0.019444	0.019444	NUM
ejpam-4727	105	48	0.584015	0.584015	NUM
ejpam-4727	105	49	0.247956	0.247956	NUM
ejpam-4727	105	50	18	18	NUM
ejpam-4727	105	51	1.80	1.80	NUM
ejpam-4727	105	52	0.849905	0.849905	NUM
ejpam-4727	105	53	0.270000	0.270000	NUM
ejpam-4727	105	54	1.086000	1.086000	NUM
ejpam-4727	105	55	0.834771	0.834771	NUM
ejpam-4727	105	56	0.018130	0.018130	NUM
ejpam-4727	105	57	0.676558	0.676558	NUM
ejpam-4727	105	58	0.300956	0.300956	NUM
ejpam-4727	105	59	19	19	NUM
ejpam-4727	105	60	1.90	1.90	NUM
ejpam-4727	105	61	0.864915	0.864915	NUM
ejpam-4727	105	62	0.190000	0.190000	NUM
ejpam-4727	105	63	1.159000	1.159000	NUM
ejpam-4727	105	64	0.850528	0.850528	NUM
ejpam-4727	105	65	0.016915	0.016915	NUM
ejpam-4727	105	66	0.776609	0.776609	NUM
ejpam-4727	105	67	0.362683	0.362683	NUM
ejpam-4727	105	68	20	20	NUM
ejpam-4727	105	69	2.00	2.00	NUM
ejpam-4727	105	70	0.878423	0.878423	NUM
ejpam-4727	105	71	0.100000	0.100000	NUM
ejpam-4727	105	72	1.240000	1.240000	NUM
ejpam-4727	105	73	0.864758	0.864758	NUM
ejpam-4727	105	74	0.015803	0.015803	NUM
ejpam-4727	105	75	0.884361	0.884361	NUM
ejpam-4727	105	76	0.433928	0.433928	NUM
ejpam-4727	105	77	a.	a.	NOUN
ejpam-4727	105	78	neamvonk	neamvonk	ADV
ejpam-4727	105	79	,	,	PUNCT
ejpam-4727	105	80	b.	b.	PROPN
ejpam-4727	105	81	sriponpaew	sriponpaew	PROPN
ejpam-4727	105	82	/	/	SYM
ejpam-4727	105	83	eur	eur	PROPN
ejpam-4727	105	84	.	.	PUNCT
ejpam-4727	106	1	j.	j.	PROPN
ejpam-4727	106	2	pure	pure	PROPN
ejpam-4727	106	3	appl	appl	PROPN
ejpam-4727	106	4	.	.	PROPN
ejpam-4727	106	5	math	math	PROPN
ejpam-4727	106	6	,	,	PUNCT
ejpam-4727	106	7	16	16	NUM
ejpam-4727	106	8	(	(	PUNCT
ejpam-4727	106	9	2	2	NUM
ejpam-4727	106	10	)	)	PUNCT
ejpam-4727	106	11	(	(	PUNCT
ejpam-4727	106	12	2023	2023	NUM
ejpam-4727	106	13	)	)	PUNCT
ejpam-4727	106	14	,	,	PUNCT
ejpam-4727	106	15	965	965	NUM
ejpam-4727	106	16	-	-	SYM
ejpam-4727	106	17	974	974	NUM
ejpam-4727	106	18	969	969	NUM
ejpam-4727	106	19	figure	figure	NOUN
ejpam-4727	106	20	2	2	NUM
ejpam-4727	106	21	:	:	PUNCT
ejpam-4727	106	22	comparing	compare	VERB
ejpam-4727	106	23	graph	graph	NOUN
ejpam-4727	106	24	of	of	ADP
ejpam-4727	106	25	approximate	approximate	ADJ
ejpam-4727	106	26	solutions	solution	NOUN
ejpam-4727	106	27	(	(	PUNCT
ejpam-4727	106	28	left	left	ADV
ejpam-4727	106	29	)	)	PUNCT
ejpam-4727	106	30	and	and	CCONJ
ejpam-4727	106	31	relative	relative	ADJ
ejpam-4727	106	32	errors	error	NOUN
ejpam-4727	106	33	(	(	PUNCT
ejpam-4727	106	34	right	right	ADJ
ejpam-4727	106	35	)	)	PUNCT
ejpam-4727	106	36	in	in	ADP
ejpam-4727	106	37	example	example	NOUN
ejpam-4727	106	38	1	1	NUM
ejpam-4727	106	39	with	with	ADP
ejpam-4727	106	40	h	h	NOUN
ejpam-4727	106	41	=	=	NOUN
ejpam-4727	106	42	0.1	0.1	NUM
ejpam-4727	106	43	on	on	ADP
ejpam-4727	106	44	xi	xi	ADP
ejpam-4727	106	45	∈	∈	PROPN
ejpam-4727	107	1	[	[	X
ejpam-4727	107	2	0	0	NUM
ejpam-4727	107	3	,	,	PUNCT
ejpam-4727	107	4	2	2	NUM
ejpam-4727	107	5	]	]	PUNCT
ejpam-4727	107	6	example	example	NOUN
ejpam-4727	107	7	2	2	X
ejpam-4727	107	8	.	.	X
ejpam-4727	107	9	consider	consider	VERB
ejpam-4727	107	10	the	the	DET
ejpam-4727	107	11	initial	initial	ADJ
ejpam-4727	107	12	value	value	NOUN
ejpam-4727	107	13	problem	problem	NOUN
ejpam-4727	107	14	dy	dy	X
ejpam-4727	107	15	dx	dx	PROPN
ejpam-4727	108	1	=	=	SYM
ejpam-4727	108	2	x2	x2	PROPN
ejpam-4727	108	3	−	−	PROPN
ejpam-4727	108	4	y	y	PROPN
ejpam-4727	108	5	,	,	PUNCT
ejpam-4727	108	6	y(0	y(0	PROPN
ejpam-4727	108	7	)	)	PUNCT
ejpam-4727	108	8	=	=	SYM
ejpam-4727	109	1	1	1	X
ejpam-4727	109	2	.	.	PUNCT
ejpam-4727	109	3	then	then	ADV
ejpam-4727	109	4	take	take	VERB
ejpam-4727	109	5	the	the	DET
ejpam-4727	109	6	step	step	NOUN
ejpam-4727	109	7	size	size	NOUN
ejpam-4727	109	8	h	h	NOUN
ejpam-4727	109	9	=	=	NOUN
ejpam-4727	109	10	0.1	0.1	NUM
ejpam-4727	109	11	and	and	CCONJ
ejpam-4727	109	12	use	use	VERB
ejpam-4727	109	13	newton	newton	PROPN
ejpam-4727	109	14	’s	’s	PART
ejpam-4727	109	15	interpolation	interpolation	NOUN
ejpam-4727	109	16	a0	a0	NOUN
ejpam-4727	109	17	=	=	SYM
ejpam-4727	109	18	1.0	1.0	NUM
ejpam-4727	109	19	,	,	PUNCT
ejpam-4727	109	20	a1	a1	NOUN
ejpam-4727	109	21	=	=	SYM
ejpam-4727	109	22	−1.0	−1.0	PROPN
ejpam-4727	109	23	,	,	PUNCT
ejpam-4727	109	24	a2	a2	PROPN
ejpam-4727	109	25	=	=	SYM
ejpam-4727	109	26	0.549999	0.549999	NUM
ejpam-4727	109	27	,	,	PUNCT
ejpam-4727	109	28	a3	a3	NOUN
ejpam-4727	109	29	=	=	NOUN
ejpam-4727	109	30	0.149999	0.149999	NUM
ejpam-4727	109	31	and	and	CCONJ
ejpam-4727	109	32	y1	y1	NOUN
ejpam-4727	109	33	=	=	SYM
ejpam-4727	109	34	0.9	0.9	NUM
ejpam-4727	109	35	,	,	PUNCT
ejpam-4727	109	36	y2	y2	PROPN
ejpam-4727	109	37	=	=	NOUN
ejpam-4727	109	38	0.811	0.811	NUM
ejpam-4727	109	39	,	,	PUNCT
ejpam-4727	109	40	y3	y3	NOUN
ejpam-4727	109	41	=	=	SYM
ejpam-4727	109	42	0.7339	0.7339	NUM
ejpam-4727	109	43	.	.	PUNCT
ejpam-4727	110	1	apply	apply	VERB
ejpam-4727	110	2	(	(	PUNCT
ejpam-4727	110	3	0	0	NUM
ejpam-4727	110	4	,	,	PUNCT
ejpam-4727	110	5	1.0	1.0	NUM
ejpam-4727	110	6	)	)	PUNCT
ejpam-4727	110	7	,	,	PUNCT
ejpam-4727	110	8	(	(	PUNCT
ejpam-4727	110	9	0.1	0.1	NUM
ejpam-4727	110	10	,	,	PUNCT
ejpam-4727	110	11	0.9	0.9	NUM
ejpam-4727	110	12	)	)	PUNCT
ejpam-4727	110	13	,	,	PUNCT
ejpam-4727	110	14	(	(	PUNCT
ejpam-4727	110	15	0.2	0.2	NUM
ejpam-4727	110	16	,	,	PUNCT
ejpam-4727	110	17	0.811	0.811	NUM
ejpam-4727	110	18	)	)	PUNCT
ejpam-4727	110	19	and	and	CCONJ
ejpam-4727	110	20	(	(	PUNCT
ejpam-4727	110	21	0.3	0.3	NUM
ejpam-4727	110	22	,	,	PUNCT
ejpam-4727	110	23	0.7339	0.7339	NUM
ejpam-4727	110	24	)	)	PUNCT
ejpam-4727	110	25	to	to	PART
ejpam-4727	110	26	find	find	VERB
ejpam-4727	110	27	cubic	cubic	ADJ
ejpam-4727	110	28	polynomial	polynomial	NOUN
ejpam-4727	110	29	by	by	ADP
ejpam-4727	110	30	(	(	PUNCT
ejpam-4727	110	31	10	10	NUM
ejpam-4727	110	32	)	)	PUNCT
ejpam-4727	110	33	.	.	PUNCT
ejpam-4727	111	1	then	then	ADV
ejpam-4727	111	2	we	we	PRON
ejpam-4727	111	3	obtain	obtain	VERB
ejpam-4727	111	4	p3(x	p3(x	PRON
ejpam-4727	111	5	)	)	PUNCT
ejpam-4727	111	6	=	=	SYM
ejpam-4727	111	7	0.149999x3	0.149999x3	SYM
ejpam-4727	111	8	+	+	NUM
ejpam-4727	111	9	0.505x2	0.505x2	NOUN
ejpam-4727	111	10	−	−	NUM
ejpam-4727	111	11	1.052x+	1.052x+	NOUN
ejpam-4727	111	12	1	1	NUM
ejpam-4727	111	13	.	.	PUNCT
ejpam-4727	112	1	(	(	PUNCT
ejpam-4727	112	2	12	12	NUM
ejpam-4727	112	3	)	)	PUNCT
ejpam-4727	112	4	in	in	ADP
ejpam-4727	112	5	order	order	NOUN
ejpam-4727	112	6	to	to	PART
ejpam-4727	112	7	approximate	approximate	VERB
ejpam-4727	112	8	the	the	DET
ejpam-4727	112	9	solutions	solution	NOUN
ejpam-4727	112	10	,	,	PUNCT
ejpam-4727	112	11	we	we	PRON
ejpam-4727	112	12	substitute	substitute	VERB
ejpam-4727	112	13	xi	xi	PROPN
ejpam-4727	112	14	in	in	ADP
ejpam-4727	112	15	p3(x	p3(x	PROPN
ejpam-4727	112	16	)	)	PUNCT
ejpam-4727	112	17	to	to	PART
ejpam-4727	112	18	get	get	VERB
ejpam-4727	112	19	yi	yi	NOUN
ejpam-4727	112	20	=	=	SYM
ejpam-4727	112	21	p3(xi	p3(xi	PROPN
ejpam-4727	112	22	)	)	PUNCT
ejpam-4727	112	23	for	for	ADP
ejpam-4727	112	24	i	i	PROPN
ejpam-4727	112	25	=	=	NOUN
ejpam-4727	112	26	4	4	NUM
ejpam-4727	112	27	,	,	PUNCT
ejpam-4727	112	28	5	5	NUM
ejpam-4727	112	29	,	,	PUNCT
ejpam-4727	112	30	...	...	PUNCT
ejpam-4727	112	31	20	20	NUM
ejpam-4727	112	32	in	in	ADP
ejpam-4727	112	33	(	(	PUNCT
ejpam-4727	112	34	12	12	NUM
ejpam-4727	112	35	)	)	PUNCT
ejpam-4727	112	36	and	and	CCONJ
ejpam-4727	112	37	relative	relative	ADJ
ejpam-4727	112	38	error	error	NOUN
ejpam-4727	112	39	as	as	SCONJ
ejpam-4727	112	40	shown	show	VERB
ejpam-4727	112	41	in	in	ADP
ejpam-4727	112	42	table	table	NOUN
ejpam-4727	112	43	2	2	NUM
ejpam-4727	112	44	and	and	CCONJ
ejpam-4727	112	45	figure	figure	VERB
ejpam-4727	112	46	3	3	NUM
ejpam-4727	112	47	.	.	PUNCT
ejpam-4727	113	1	the	the	DET
ejpam-4727	113	2	approximate	approximate	ADJ
ejpam-4727	113	3	solutions	solution	NOUN
ejpam-4727	113	4	are	be	AUX
ejpam-4727	113	5	close	close	ADJ
ejpam-4727	113	6	to	to	ADP
ejpam-4727	113	7	exact	exact	ADJ
ejpam-4727	113	8	solution	solution	NOUN
ejpam-4727	113	9	where	where	SCONJ
ejpam-4727	113	10	x	x	PUNCT
ejpam-4727	113	11	∈	∈	PROPN
ejpam-4727	113	12	[	[	X
ejpam-4727	113	13	0	0	NUM
ejpam-4727	113	14	,	,	PUNCT
ejpam-4727	113	15	0.6	0.6	NUM
ejpam-4727	113	16	]	]	PUNCT
ejpam-4727	113	17	and	and	CCONJ
ejpam-4727	113	18	relative	relative	ADJ
ejpam-4727	113	19	errors	error	NOUN
ejpam-4727	113	20	when	when	SCONJ
ejpam-4727	113	21	x	x	X
ejpam-4727	113	22	≥	≥	VERB
ejpam-4727	113	23	0.7	0.7	NUM
ejpam-4727	113	24	highly	highly	ADV
ejpam-4727	113	25	increase	increase	NOUN
ejpam-4727	113	26	as	as	ADP
ejpam-4727	113	27	show	show	NOUN
ejpam-4727	113	28	in	in	ADP
ejpam-4727	113	29	figure	figure	NOUN
ejpam-4727	113	30	3	3	NUM
ejpam-4727	113	31	.	.	PUNCT
ejpam-4727	113	32	a.	a.	NOUN
ejpam-4727	113	33	neamvonk	neamvonk	PROPN
ejpam-4727	113	34	,	,	PUNCT
ejpam-4727	113	35	b.	b.	PROPN
ejpam-4727	113	36	sriponpaew	sriponpaew	PROPN
ejpam-4727	113	37	/	/	SYM
ejpam-4727	113	38	eur	eur	PROPN
ejpam-4727	113	39	.	.	PUNCT
ejpam-4727	114	1	j.	j.	PROPN
ejpam-4727	114	2	pure	pure	PROPN
ejpam-4727	114	3	appl	appl	PROPN
ejpam-4727	114	4	.	.	PROPN
ejpam-4727	114	5	math	math	PROPN
ejpam-4727	114	6	,	,	PUNCT
ejpam-4727	114	7	16	16	NUM
ejpam-4727	114	8	(	(	PUNCT
ejpam-4727	114	9	2	2	NUM
ejpam-4727	114	10	)	)	PUNCT
ejpam-4727	114	11	(	(	PUNCT
ejpam-4727	114	12	2023	2023	NUM
ejpam-4727	114	13	)	)	PUNCT
ejpam-4727	114	14	,	,	PUNCT
ejpam-4727	114	15	965	965	NUM
ejpam-4727	114	16	-	-	SYM
ejpam-4727	114	17	974	974	NUM
ejpam-4727	114	18	970	970	NUM
ejpam-4727	114	19	table	table	NOUN
ejpam-4727	114	20	2	2	NUM
ejpam-4727	114	21	:	:	PUNCT
ejpam-4727	114	22	showing	show	VERB
ejpam-4727	114	23	results	result	NOUN
ejpam-4727	114	24	of	of	ADP
ejpam-4727	114	25	example	example	NOUN
ejpam-4727	114	26	2	2	NUM
ejpam-4727	114	27	with	with	ADP
ejpam-4727	114	28	h	h	NOUN
ejpam-4727	114	29	=	=	NOUN
ejpam-4727	114	30	0.1	0.1	NUM
ejpam-4727	114	31	on	on	ADP
ejpam-4727	114	32	xi	xi	ADP
ejpam-4727	114	33	∈	∈	PROPN
ejpam-4727	115	1	[	[	X
ejpam-4727	115	2	0	0	NUM
ejpam-4727	115	3	,	,	PUNCT
ejpam-4727	115	4	2	2	NUM
ejpam-4727	115	5	]	]	X
ejpam-4727	115	6	i	i	PRON
ejpam-4727	115	7	xi	xi	PROPN
ejpam-4727	115	8	approx	approx	PROPN
ejpam-4727	115	9	.	.	PUNCT
ejpam-4727	116	1	sol	sol	PROPN
ejpam-4727	116	2	.	.	PUNCT
ejpam-4727	117	1	yi	yi	PROPN
ejpam-4727	117	2	exact	exact	ADJ
ejpam-4727	117	3	relative	relative	ADJ
ejpam-4727	117	4	errors	error	NOUN
ejpam-4727	117	5	euler	euler	NOUN
ejpam-4727	118	1	[	[	X
ejpam-4727	118	2	11],[14	11],[14	X
ejpam-4727	118	3	]	]	X
ejpam-4727	118	4	present	present	ADJ
ejpam-4727	118	5	solution	solution	NOUN
ejpam-4727	118	6	euler	euler	NOUN
ejpam-4727	119	1	[	[	X
ejpam-4727	119	2	11],[14	11],[14	X
ejpam-4727	119	3	]	]	X
ejpam-4727	119	4	present	present	ADJ
ejpam-4727	119	5	0	0	NUM
ejpam-4727	119	6	0.00	0.00	NUM
ejpam-4727	119	7	1.000000	1.000000	NUM
ejpam-4727	119	8	1.000000	1.000000	NUM
ejpam-4727	119	9	1.000000	1.000000	NUM
ejpam-4727	119	10	1.000000	1.000000	NUM
ejpam-4727	119	11	0.000000	0.000000	NUM
ejpam-4727	119	12	0.000000	0.000000	NUM
ejpam-4727	119	13	0.000000	0.000000	NUM
ejpam-4727	119	14	1	1	NUM
ejpam-4727	119	15	0.10	0.10	NUM
ejpam-4727	119	16	0.900000	0.900000	NUM
ejpam-4727	119	17	0.900000	0.900000	NUM
ejpam-4727	119	18	0.900000	0.900000	NUM
ejpam-4727	119	19	0.905163	0.905163	NUM
ejpam-4727	119	20	0.005703	0.005703	NUM
ejpam-4727	119	21	0.005703	0.005703	NUM
ejpam-4727	119	22	0.005703	0.005703	NUM
ejpam-4727	119	23	2	2	NUM
ejpam-4727	119	24	0.20	0.20	NUM
ejpam-4727	119	25	0.811000	0.811000	NUM
ejpam-4727	119	26	0.811000	0.811000	NUM
ejpam-4727	119	27	0.811000	0.811000	NUM
ejpam-4727	119	28	0.821212	0.821212	NUM
ejpam-4727	119	29	0.012435	0.012435	NUM
ejpam-4727	119	30	0.012435	0.012435	NUM
ejpam-4727	119	31	0.012435	0.012435	NUM
ejpam-4727	119	32	3	3	NUM
ejpam-4727	119	33	0.30	0.30	NUM
ejpam-4727	119	34	0.733900	0.733900	NUM
ejpam-4727	119	35	0.733000	0.733000	NUM
ejpam-4727	119	36	0.733900	0.733900	NUM
ejpam-4727	119	37	0.749005	0.749005	NUM
ejpam-4727	119	38	0.020167	0.020167	NUM
ejpam-4727	119	39	0.021368	0.021368	NUM
ejpam-4727	119	40	0.020167	0.020167	NUM
ejpam-4727	119	41	4	4	NUM
ejpam-4727	119	42	0.40	0.40	NUM
ejpam-4727	119	43	0.669510	0.669510	NUM
ejpam-4727	119	44	0.666000	0.666000	NUM
ejpam-4727	119	45	0.669600	0.669600	NUM
ejpam-4727	119	46	0.689391	0.689391	NUM
ejpam-4727	119	47	0.028839	0.028839	NUM
ejpam-4727	119	48	0.033930	0.033930	NUM
ejpam-4727	119	49	0.028708	0.028708	NUM
ejpam-4727	119	50	5	5	NUM
ejpam-4727	119	51	0.50	0.50	NUM
ejpam-4727	119	52	0.618559	0.618559	NUM
ejpam-4727	119	53	0.610000	0.610000	NUM
ejpam-4727	119	54	0.619000	0.619000	NUM
ejpam-4727	120	1	0.643129	0.643129	NUM
ejpam-4727	120	2	0.038204	0.038204	NUM
ejpam-4727	120	3	0.051513	0.051513	NUM
ejpam-4727	120	4	0.037519	0.037519	NUM
ejpam-4727	120	5	6	6	NUM
ejpam-4727	120	6	0.60	0.60	NUM
ejpam-4727	120	7	0.581703	0.581703	NUM
ejpam-4727	120	8	0.565000	0.565000	NUM
ejpam-4727	120	9	0.583000	0.583000	NUM
ejpam-4727	120	10	0.610887	0.610887	NUM
ejpam-4727	121	1	0.047773	0.047773	NUM
ejpam-4727	121	2	0.075115	0.075115	NUM
ejpam-4727	121	3	0.045650	0.045650	NUM
ejpam-4727	121	4	7	7	NUM
ejpam-4727	121	5	0.70	0.70	NUM
ejpam-4727	121	6	0.559533	0.559533	NUM
ejpam-4727	121	7	0.531000	0.531000	NUM
ejpam-4727	121	8	0.562500	0.562500	NUM
ejpam-4727	121	9	0.593241	0.593241	NUM
ejpam-4727	121	10	0.056820	0.056820	NUM
ejpam-4727	121	11	0.104916	0.104916	NUM
ejpam-4727	121	12	0.051818	0.051818	NUM
ejpam-4727	121	13	8	8	NUM
ejpam-4727	121	14	0.80	0.80	NUM
ejpam-4727	121	15	0.552580	0.552580	NUM
ejpam-4727	121	16	0.508000	0.508000	NUM
ejpam-4727	122	1	0.558400	0.558400	NUM
ejpam-4727	122	2	0.590676	0.590676	NUM
ejpam-4727	122	3	0.064496	0.064496	NUM
ejpam-4727	122	4	0.139968	0.139968	NUM
ejpam-4727	122	5	0.054642	0.054642	NUM
ejpam-4727	122	6	9	9	NUM
ejpam-4727	122	7	0.90	0.90	NUM
ejpam-4727	122	8	0.561322	0.561322	NUM
ejpam-4727	122	9	0.496000	0.496000	NUM
ejpam-4727	122	10	0.571600	0.571600	NUM
ejpam-4727	122	11	0.603586	0.603586	NUM
ejpam-4727	122	12	0.070023	0.070023	NUM
ejpam-4727	122	13	0.178245	0.178245	NUM
ejpam-4727	122	14	0.052994	0.052994	NUM
ejpam-4727	122	15	10	10	NUM
ejpam-4727	122	16	1.00	1.00	NUM
ejpam-4727	122	17	0.586189	0.586189	NUM
ejpam-4727	122	18	0.495000	0.495000	NUM
ejpam-4727	122	19	0.603000	0.603000	NUM
ejpam-4727	122	20	0.632280	0.632280	NUM
ejpam-4727	122	21	0.072896	0.072896	NUM
ejpam-4727	122	22	0.217119	0.217119	NUM
ejpam-4727	122	23	0.046308	0.046308	NUM
ejpam-4727	122	24	11	11	NUM
ejpam-4727	122	25	1.10	1.10	NUM
ejpam-4727	122	26	0.627570	0.627570	NUM
ejpam-4727	122	27	0.505000	0.505000	NUM
ejpam-4727	122	28	0.653500	0.653500	NUM
ejpam-4727	122	29	0.677123	0.677123	NUM
ejpam-4727	123	1	0.073181	0.073181	NUM
ejpam-4727	123	2	0.254198	0.254198	NUM
ejpam-4727	123	3	0.034888	0.034888	NUM
ejpam-4727	123	4	12	12	NUM
ejpam-4727	123	5	1.20	1.20	NUM
ejpam-4727	123	6	0.685813	0.685813	NUM
ejpam-4727	123	7	0.526000	0.526000	NUM
ejpam-4727	123	8	0.724000	0.724000	NUM
ejpam-4727	123	9	0.738595	0.738595	NUM
ejpam-4727	123	10	0.071462	0.071462	NUM
ejpam-4727	123	11	0.287837	0.287837	NUM
ejpam-4727	124	1	0.019760	0.019760	NUM
ejpam-4727	124	2	13	13	NUM
ejpam-4727	124	3	1.30	1.30	NUM
ejpam-4727	124	4	0.761232	0.761232	NUM
ejpam-4727	124	5	0.558000	0.558000	NUM
ejpam-4727	124	6	0.815400	0.815400	NUM
ejpam-4727	124	7	0.817114	0.817114	NUM
ejpam-4727	124	8	0.068389	0.068389	NUM
ejpam-4727	124	9	0.317109	0.317109	NUM
ejpam-4727	124	10	0.002097	0.002097	NUM
ejpam-4727	124	11	14	14	NUM
ejpam-4727	124	12	1.40	1.40	NUM
ejpam-4727	124	13	0.854109	0.854109	NUM
ejpam-4727	124	14	0.601000	0.601000	NUM
ejpam-4727	124	15	0.928600	0.928600	NUM
ejpam-4727	124	16	0.913027	0.913027	NUM
ejpam-4727	124	17	0.064531	0.064531	NUM
ejpam-4727	124	18	0.341750	0.341750	NUM
ejpam-4727	124	19	0.017056	0.017056	NUM
ejpam-4727	124	20	15	15	NUM
ejpam-4727	124	21	1.50	1.50	NUM
ejpam-4727	124	22	0.964698	0.964698	NUM
ejpam-4727	124	23	0.655000	0.655000	NUM
ejpam-4727	124	24	1.064500	1.064500	NUM
ejpam-4727	124	25	1.026610	1.026610	NUM
ejpam-4727	124	26	0.060307	0.060307	NUM
ejpam-4727	124	27	0.361978	0.361978	NUM
ejpam-4727	124	28	0.036908	0.036908	NUM
ejpam-4727	124	29	16	16	NUM
ejpam-4727	124	30	1.60	1.60	NUM
ejpam-4727	124	31	1.093228	1.093228	NUM
ejpam-4727	124	32	0.720000	0.720000	NUM
ejpam-4727	124	33	1.224000	1.224000	NUM
ejpam-4727	124	34	1.158067	1.158067	NUM
ejpam-4727	124	35	0.055989	0.055989	NUM
ejpam-4727	124	36	0.378274	0.378274	NUM
ejpam-4727	124	37	0.056934	0.056934	NUM
ejpam-4727	124	38	17	17	NUM
ejpam-4727	124	39	1.70	1.70	NUM
ejpam-4727	124	40	1.239905	1.239905	NUM
ejpam-4727	124	41	0.796000	0.796000	NUM
ejpam-4727	124	42	1.408000	1.408000	NUM
ejpam-4727	124	43	1.307528	1.307528	NUM
ejpam-4727	124	44	0.051718	0.051718	NUM
ejpam-4727	124	45	0.391218	0.391218	NUM
ejpam-4727	124	46	0.076841	0.076841	NUM
ejpam-4727	124	47	18	18	NUM
ejpam-4727	124	48	1.80	1.80	NUM
ejpam-4727	124	49	1.404915	1.404915	NUM
ejpam-4727	124	50	0.883000	0.883000	NUM
ejpam-4727	124	51	1.617400	1.617400	NUM
ejpam-4727	124	52	1.475055	1.475055	NUM
ejpam-4727	124	53	0.047551	0.047551	NUM
ejpam-4727	124	54	0.401378	0.401378	NUM
ejpam-4727	124	55	0.096502	0.096502	NUM
ejpam-4727	124	56	19	19	NUM
ejpam-4727	124	57	1.90	1.90	NUM
ejpam-4727	124	58	1.588423	1.588423	NUM
ejpam-4727	124	59	0.981000	0.981000	NUM
ejpam-4727	124	60	1.853100	1.853100	NUM
ejpam-4727	124	61	1.660676	1.660676	NUM
ejpam-4727	124	62	0.043508	0.043508	NUM
ejpam-4727	124	63	0.409277	0.409277	NUM
ejpam-4727	124	64	0.115871	0.115871	NUM
ejpam-4727	124	65	20	20	NUM
ejpam-4727	124	66	2.00	2.00	NUM
ejpam-4727	124	67	1.790581	1.790581	NUM
ejpam-4727	124	68	1.090000	1.090000	NUM
ejpam-4727	124	69	2.116000	2.116000	NUM
ejpam-4727	124	70	1.864644	1.864644	NUM
ejpam-4727	124	71	0.039720	0.039720	NUM
ejpam-4727	124	72	0.415438	0.415438	NUM
ejpam-4727	124	73	0.134801	0.134801	NUM
ejpam-4727	124	74	figure	figure	NOUN
ejpam-4727	124	75	3	3	NUM
ejpam-4727	124	76	:	:	PUNCT
ejpam-4727	124	77	comparing	compare	VERB
ejpam-4727	124	78	graph	graph	NOUN
ejpam-4727	124	79	of	of	ADP
ejpam-4727	124	80	approximate	approximate	ADJ
ejpam-4727	124	81	solutions	solution	NOUN
ejpam-4727	124	82	(	(	PUNCT
ejpam-4727	124	83	left	left	ADV
ejpam-4727	124	84	)	)	PUNCT
ejpam-4727	124	85	and	and	CCONJ
ejpam-4727	124	86	relative	relative	ADJ
ejpam-4727	124	87	errors	error	NOUN
ejpam-4727	124	88	(	(	PUNCT
ejpam-4727	124	89	right	right	ADJ
ejpam-4727	124	90	)	)	PUNCT
ejpam-4727	124	91	in	in	ADP
ejpam-4727	124	92	example	example	NOUN
ejpam-4727	124	93	2	2	NUM
ejpam-4727	124	94	with	with	ADP
ejpam-4727	124	95	h	h	NOUN
ejpam-4727	124	96	=	=	NOUN
ejpam-4727	124	97	0.1	0.1	NUM
ejpam-4727	124	98	on	on	ADP
ejpam-4727	124	99	xi	xi	ADP
ejpam-4727	124	100	∈	∈	PROPN
ejpam-4727	125	1	[	[	X
ejpam-4727	125	2	0	0	NUM
ejpam-4727	125	3	,	,	PUNCT
ejpam-4727	125	4	2	2	NUM
ejpam-4727	125	5	]	]	PUNCT
ejpam-4727	125	6	example	example	NOUN
ejpam-4727	125	7	3	3	X
ejpam-4727	125	8	.	.	X
ejpam-4727	126	1	consider	consider	VERB
ejpam-4727	126	2	the	the	DET
ejpam-4727	126	3	initial	initial	ADJ
ejpam-4727	126	4	value	value	NOUN
ejpam-4727	126	5	problem	problem	NOUN
ejpam-4727	126	6	dy	dy	NOUN
ejpam-4727	126	7	dx	dx	PROPN
ejpam-4727	126	8	=	=	SYM
ejpam-4727	126	9	x−	x−	PROPN
ejpam-4727	126	10	y	y	PROPN
ejpam-4727	126	11	ex+y	ex+y	PROPN
ejpam-4727	126	12	,	,	PUNCT
ejpam-4727	126	13	y(0	y(0	PROPN
ejpam-4727	126	14	)	)	PUNCT
ejpam-4727	126	15	=	=	SYM
ejpam-4727	127	1	1	1	X
ejpam-4727	127	2	.	.	PUNCT
ejpam-4727	127	3	then	then	ADV
ejpam-4727	127	4	take	take	VERB
ejpam-4727	127	5	the	the	DET
ejpam-4727	127	6	step	step	NOUN
ejpam-4727	127	7	size	size	NOUN
ejpam-4727	127	8	h	h	NOUN
ejpam-4727	127	9	=	=	NOUN
ejpam-4727	127	10	0.1	0.1	NUM
ejpam-4727	127	11	and	and	CCONJ
ejpam-4727	127	12	use	use	VERB
ejpam-4727	127	13	newton	newton	PROPN
ejpam-4727	127	14	’s	’s	PART
ejpam-4727	127	15	interpolation	interpolation	NOUN
ejpam-4727	127	16	a0	a0	NOUN
ejpam-4727	127	17	=	=	SYM
ejpam-4727	127	18	1.0	1.0	NUM
ejpam-4727	127	19	,	,	PUNCT
ejpam-4727	127	20	a1	a1	NOUN
ejpam-4727	127	21	=	=	SYM
ejpam-4727	127	22	−0.367879	−0.367879	NUM
ejpam-4727	127	23	,	,	PUNCT
ejpam-4727	127	24	a2	a2	PROPN
ejpam-4727	127	25	=	=	SYM
ejpam-4727	127	26	0.348868	0.348868	NUM
ejpam-4727	127	27	,	,	PUNCT
ejpam-4727	127	28	a3	a3	NOUN
ejpam-4727	127	29	=	=	SYM
ejpam-4727	127	30	−0.129608	−0.129608	NOUN
ejpam-4727	127	31	and	and	CCONJ
ejpam-4727	127	32	y1	y1	NOUN
ejpam-4727	127	33	=	=	SYM
ejpam-4727	127	34	0.963212	0.963212	NUM
ejpam-4727	127	35	,	,	PUNCT
ejpam-4727	127	36	y2	y2	PROPN
ejpam-4727	127	37	=	=	SYM
ejpam-4727	127	38	0.933401	0.933401	NUM
ejpam-4727	127	39	,	,	PUNCT
ejpam-4727	127	40	y3	y3	NOUN
ejpam-4727	127	41	=	=	NUM
ejpam-4727	127	42	0.909791	0.909791	NUM
ejpam-4727	127	43	.	.	PUNCT
ejpam-4727	128	1	a.	a.	PROPN
ejpam-4727	128	2	neamvonk	neamvonk	PROPN
ejpam-4727	128	3	,	,	PUNCT
ejpam-4727	128	4	b.	b.	PROPN
ejpam-4727	128	5	sriponpaew	sriponpaew	PROPN
ejpam-4727	128	6	/	/	SYM
ejpam-4727	128	7	eur	eur	PROPN
ejpam-4727	128	8	.	.	PUNCT
ejpam-4727	129	1	j.	j.	PROPN
ejpam-4727	129	2	pure	pure	PROPN
ejpam-4727	129	3	appl	appl	PROPN
ejpam-4727	129	4	.	.	PROPN
ejpam-4727	129	5	math	math	PROPN
ejpam-4727	129	6	,	,	PUNCT
ejpam-4727	129	7	16	16	NUM
ejpam-4727	129	8	(	(	PUNCT
ejpam-4727	129	9	2	2	NUM
ejpam-4727	129	10	)	)	PUNCT
ejpam-4727	129	11	(	(	PUNCT
ejpam-4727	129	12	2023	2023	NUM
ejpam-4727	129	13	)	)	PUNCT
ejpam-4727	129	14	,	,	PUNCT
ejpam-4727	129	15	965	965	NUM
ejpam-4727	129	16	-	-	SYM
ejpam-4727	129	17	974	974	NUM
ejpam-4727	129	18	971	971	NUM
ejpam-4727	129	19	apply	apply	NOUN
ejpam-4727	129	20	(	(	PUNCT
ejpam-4727	129	21	0	0	NUM
ejpam-4727	129	22	,	,	PUNCT
ejpam-4727	129	23	1.0	1.0	NUM
ejpam-4727	129	24	)	)	PUNCT
ejpam-4727	129	25	,	,	PUNCT
ejpam-4727	129	26	(	(	PUNCT
ejpam-4727	129	27	0.1	0.1	NUM
ejpam-4727	129	28	,	,	PUNCT
ejpam-4727	129	29	0.963212	0.963212	NUM
ejpam-4727	129	30	)	)	PUNCT
ejpam-4727	129	31	,	,	PUNCT
ejpam-4727	129	32	(	(	PUNCT
ejpam-4727	129	33	0.2	0.2	NUM
ejpam-4727	129	34	,	,	PUNCT
ejpam-4727	129	35	0.933401	0.933401	NUM
ejpam-4727	129	36	)	)	PUNCT
ejpam-4727	129	37	and	and	CCONJ
ejpam-4727	129	38	(	(	PUNCT
ejpam-4727	129	39	0.3	0.3	NUM
ejpam-4727	129	40	,	,	PUNCT
ejpam-4727	129	41	0.909791	0.909791	NUM
ejpam-4727	129	42	)	)	PUNCT
ejpam-4727	129	43	to	to	PART
ejpam-4727	129	44	find	find	VERB
ejpam-4727	129	45	cubic	cubic	ADJ
ejpam-4727	129	46	polynomial	polynomial	NOUN
ejpam-4727	129	47	by	by	ADP
ejpam-4727	129	48	(	(	PUNCT
ejpam-4727	129	49	10	10	NUM
ejpam-4727	129	50	)	)	PUNCT
ejpam-4727	129	51	.	.	PUNCT
ejpam-4727	130	1	then	then	ADV
ejpam-4727	130	2	we	we	PRON
ejpam-4727	130	3	obtain	obtain	VERB
ejpam-4727	130	4	p3(x	p3(x	PRON
ejpam-4727	130	5	)	)	PUNCT
ejpam-4727	130	6	=	=	SYM
ejpam-4727	130	7	−0.129608x3	−0.129608x3	NOUN
ejpam-4727	130	8	+	+	CCONJ
ejpam-4727	130	9	0.387751x2	0.387751x2	NUM
ejpam-4727	131	1	−	−	X
ejpam-4727	131	2	0.405358x+	0.405358x+	NUM
ejpam-4727	131	3	1	1	NUM
ejpam-4727	131	4	.	.	PUNCT
ejpam-4727	131	5	(	(	PUNCT
ejpam-4727	131	6	13	13	NUM
ejpam-4727	131	7	)	)	PUNCT
ejpam-4727	131	8	in	in	ADP
ejpam-4727	131	9	order	order	NOUN
ejpam-4727	131	10	to	to	PART
ejpam-4727	131	11	approximate	approximate	VERB
ejpam-4727	131	12	the	the	DET
ejpam-4727	131	13	solutions	solution	NOUN
ejpam-4727	131	14	,	,	PUNCT
ejpam-4727	131	15	we	we	PRON
ejpam-4727	131	16	substitute	substitute	VERB
ejpam-4727	131	17	xi	xi	PROPN
ejpam-4727	131	18	in	in	ADP
ejpam-4727	131	19	p3(x	p3(x	PROPN
ejpam-4727	131	20	)	)	PUNCT
ejpam-4727	131	21	to	to	PART
ejpam-4727	131	22	get	get	VERB
ejpam-4727	131	23	yi	yi	NOUN
ejpam-4727	131	24	=	=	SYM
ejpam-4727	131	25	p3(xi	p3(xi	PROPN
ejpam-4727	131	26	)	)	PUNCT
ejpam-4727	131	27	for	for	ADP
ejpam-4727	131	28	i	i	PROPN
ejpam-4727	131	29	=	=	NOUN
ejpam-4727	131	30	4	4	NUM
ejpam-4727	131	31	,	,	PUNCT
ejpam-4727	131	32	5	5	NUM
ejpam-4727	131	33	,	,	PUNCT
ejpam-4727	131	34	...	...	PUNCT
ejpam-4727	131	35	20	20	NUM
ejpam-4727	131	36	in	in	ADP
ejpam-4727	131	37	(	(	PUNCT
ejpam-4727	131	38	13	13	NUM
ejpam-4727	131	39	)	)	PUNCT
ejpam-4727	131	40	and	and	CCONJ
ejpam-4727	131	41	relative	relative	ADJ
ejpam-4727	131	42	error	error	NOUN
ejpam-4727	131	43	as	as	SCONJ
ejpam-4727	131	44	shown	show	VERB
ejpam-4727	131	45	in	in	ADP
ejpam-4727	131	46	table	table	NOUN
ejpam-4727	131	47	3	3	NUM
ejpam-4727	131	48	and	and	CCONJ
ejpam-4727	131	49	figure	figure	VERB
ejpam-4727	131	50	4	4	NUM
ejpam-4727	131	51	.	.	PUNCT
ejpam-4727	132	1	the	the	DET
ejpam-4727	132	2	approximate	approximate	ADJ
ejpam-4727	132	3	solutions	solution	NOUN
ejpam-4727	132	4	are	be	AUX
ejpam-4727	132	5	close	close	ADJ
ejpam-4727	132	6	to	to	ADP
ejpam-4727	132	7	exact	exact	ADJ
ejpam-4727	132	8	solution	solution	NOUN
ejpam-4727	132	9	where	where	SCONJ
ejpam-4727	132	10	x	x	PUNCT
ejpam-4727	132	11	∈	∈	PROPN
ejpam-4727	132	12	[	[	X
ejpam-4727	132	13	0	0	NUM
ejpam-4727	132	14	,	,	PUNCT
ejpam-4727	132	15	0.8	0.8	NUM
ejpam-4727	132	16	]	]	PUNCT
ejpam-4727	132	17	and	and	CCONJ
ejpam-4727	132	18	relative	relative	ADJ
ejpam-4727	132	19	errors	error	NOUN
ejpam-4727	132	20	when	when	SCONJ
ejpam-4727	132	21	x	x	X
ejpam-4727	132	22	≥	≥	VERB
ejpam-4727	132	23	0.9	0.9	NUM
ejpam-4727	132	24	highly	highly	ADV
ejpam-4727	132	25	increase	increase	NOUN
ejpam-4727	132	26	as	as	ADP
ejpam-4727	132	27	show	show	NOUN
ejpam-4727	132	28	in	in	ADP
ejpam-4727	132	29	figure	figure	NOUN
ejpam-4727	132	30	4	4	NUM
ejpam-4727	132	31	.	.	PUNCT
ejpam-4727	132	32	table	table	NOUN
ejpam-4727	132	33	3	3	NUM
ejpam-4727	132	34	:	:	PUNCT
ejpam-4727	132	35	showing	show	VERB
ejpam-4727	132	36	results	result	NOUN
ejpam-4727	132	37	of	of	ADP
ejpam-4727	132	38	example	example	NOUN
ejpam-4727	132	39	2	2	NUM
ejpam-4727	132	40	with	with	ADP
ejpam-4727	132	41	h	h	NOUN
ejpam-4727	132	42	=	=	NOUN
ejpam-4727	132	43	0.1	0.1	NUM
ejpam-4727	132	44	on	on	ADP
ejpam-4727	132	45	xi	xi	ADP
ejpam-4727	132	46	∈	∈	PROPN
ejpam-4727	133	1	[	[	X
ejpam-4727	133	2	0	0	NUM
ejpam-4727	133	3	,	,	PUNCT
ejpam-4727	133	4	2	2	NUM
ejpam-4727	133	5	]	]	X
ejpam-4727	133	6	i	i	PRON
ejpam-4727	133	7	xi	xi	PROPN
ejpam-4727	133	8	approx	approx	PROPN
ejpam-4727	133	9	.	.	PUNCT
ejpam-4727	134	1	sol	sol	PROPN
ejpam-4727	134	2	.	.	PUNCT
ejpam-4727	135	1	yi	yi	PROPN
ejpam-4727	135	2	exact	exact	ADJ
ejpam-4727	135	3	relative	relative	ADJ
ejpam-4727	135	4	errors	error	NOUN
ejpam-4727	135	5	euler	euler	NOUN
ejpam-4727	136	1	[	[	X
ejpam-4727	136	2	11],[14	11],[14	X
ejpam-4727	136	3	]	]	X
ejpam-4727	136	4	present	present	ADJ
ejpam-4727	136	5	solution	solution	NOUN
ejpam-4727	136	6	euler	euler	NOUN
ejpam-4727	137	1	[	[	X
ejpam-4727	137	2	11],[14	11],[14	X
ejpam-4727	137	3	]	]	X
ejpam-4727	137	4	present	present	ADJ
ejpam-4727	137	5	0	0	NUM
ejpam-4727	137	6	0.00	0.00	NUM
ejpam-4727	137	7	1.000000	1.000000	NUM
ejpam-4727	137	8	1.000000	1.000000	NUM
ejpam-4727	137	9	1.000000	1.000000	NUM
ejpam-4727	137	10	1.000000	1.000000	NUM
ejpam-4727	137	11	0.000000	0.000000	NUM
ejpam-4727	137	12	0.000000	0.000000	NUM
ejpam-4727	137	13	0.000000	0.000000	NUM
ejpam-4727	137	14	1	1	NUM
ejpam-4727	137	15	0.10	0.10	NUM
ejpam-4727	137	16	0.963212	0.963212	NUM
ejpam-4727	138	1	0.963212	0.963212	NUM
ejpam-4727	138	2	0.963212	0.963212	NUM
ejpam-4727	138	3	0.966759	0.966759	NUM
ejpam-4727	138	4	0.003669	0.003669	NUM
ejpam-4727	138	5	0.003669	0.003669	NUM
ejpam-4727	138	6	0.003669	0.003669	NUM
ejpam-4727	138	7	2	2	NUM
ejpam-4727	138	8	0.20	0.20	NUM
ejpam-4727	138	9	0.933401	0.933401	NUM
ejpam-4727	138	10	0.933401	0.933401	NUM
ejpam-4727	138	11	0.933401	0.933401	NUM
ejpam-4727	138	12	0.940092	0.940092	NUM
ejpam-4727	138	13	0.007117	0.007117	NUM
ejpam-4727	138	14	0.007117	0.007117	NUM
ejpam-4727	138	15	0.007117	0.007117	NUM
ejpam-4727	138	16	3	3	NUM
ejpam-4727	138	17	0.30	0.30	NUM
ejpam-4727	138	18	0.909791	0.909791	NUM
ejpam-4727	138	19	0.910568	0.910568	NUM
ejpam-4727	138	20	0.909791	0.909791	NUM
ejpam-4727	138	21	0.919197	0.919197	NUM
ejpam-4727	138	22	0.010233	0.010233	NUM
ejpam-4727	138	23	0.009387	0.009387	NUM
ejpam-4727	138	24	0.010233	0.010233	NUM
ejpam-4727	138	25	4	4	NUM
ejpam-4727	138	26	0.40	0.40	NUM
ejpam-4727	138	27	0.891603	0.891603	NUM
ejpam-4727	138	28	0.894712	0.894712	NUM
ejpam-4727	138	29	0.891602	0.891602	NUM
ejpam-4727	139	1	0.903288	0.903288	NUM
ejpam-4727	139	2	0.012936	0.012936	NUM
ejpam-4727	139	3	0.009493	0.009493	NUM
ejpam-4727	139	4	0.012937	0.012937	NUM
ejpam-4727	139	5	5	5	NUM
ejpam-4727	139	6	0.50	0.50	NUM
ejpam-4727	139	7	0.878092	0.878092	NUM
ejpam-4727	139	8	0.885834	0.885834	NUM
ejpam-4727	139	9	0.878057	0.878057	NUM
ejpam-4727	139	10	0.891643	0.891643	NUM
ejpam-4727	139	11	0.015198	0.015198	NUM
ejpam-4727	139	12	0.006515	0.006515	NUM
ejpam-4727	139	13	0.015237	0.015237	NUM
ejpam-4727	139	14	6	6	NUM
ejpam-4727	139	15	0.60	0.60	NUM
ejpam-4727	139	16	0.868562	0.868562	NUM
ejpam-4727	139	17	0.883933	0.883933	NUM
ejpam-4727	139	18	0.868380	0.868380	NUM
ejpam-4727	139	19	0.883609	0.883609	NUM
ejpam-4727	139	20	0.017029	0.017029	NUM
ejpam-4727	139	21	0.000366	0.000366	NUM
ejpam-4727	139	22	0.017235	0.017235	NUM
ejpam-4727	139	23	7	7	NUM
ejpam-4727	139	24	0.70	0.70	NUM
ejpam-4727	139	25	0.862378	0.862378	NUM
ejpam-4727	139	26	0.889009	0.889009	NUM
ejpam-4727	139	27	0.861791	0.861791	NUM
ejpam-4727	139	28	0.878595	0.878595	NUM
ejpam-4727	139	29	0.018457	0.018457	NUM
ejpam-4727	139	30	0.011854	0.011854	NUM
ejpam-4727	139	31	0.019125	0.019125	NUM
ejpam-4727	139	32	8	8	NUM
ejpam-4727	139	33	0.80	0.80	NUM
ejpam-4727	139	34	0.858974	0.858974	NUM
ejpam-4727	139	35	0.901063	0.901063	NUM
ejpam-4727	139	36	0.857514	0.857514	NUM
ejpam-4727	139	37	0.876075	0.876075	NUM
ejpam-4727	140	1	0.019520	0.019520	NUM
ejpam-4727	140	2	0.028522	0.028522	NUM
ejpam-4727	140	3	0.021186	0.021186	NUM
ejpam-4727	140	4	9	9	NUM
ejpam-4727	140	5	0.90	0.90	NUM
ejpam-4727	140	6	0.857852	0.857852	NUM
ejpam-4727	140	7	0.920094	0.920094	NUM
ejpam-4727	140	8	0.854771	0.854771	NUM
ejpam-4727	140	9	0.875591	0.875591	NUM
ejpam-4727	140	10	0.020259	0.020259	NUM
ejpam-4727	140	11	0.050826	0.050826	NUM
ejpam-4727	140	12	0.023778	0.023778	NUM
ejpam-4727	140	13	10	10	NUM
ejpam-4727	140	14	1.00	1.00	NUM
ejpam-4727	140	15	0.858579	0.858579	NUM
ejpam-4727	140	16	0.946102	0.946102	NUM
ejpam-4727	140	17	0.852784	0.852784	NUM
ejpam-4727	140	18	0.876747	0.876747	NUM
ejpam-4727	140	19	0.020723	0.020723	NUM
ejpam-4727	140	20	0.079105	0.079105	NUM
ejpam-4727	140	21	0.027332	0.027332	NUM
ejpam-4727	140	22	11	11	NUM
ejpam-4727	140	23	1.10	1.10	NUM
ejpam-4727	140	24	0.860783	0.860783	NUM
ejpam-4727	140	25	0.979088	0.979088	NUM
ejpam-4727	141	1	0.850776	0.850776	NUM
ejpam-4727	141	2	0.879215	0.879215	NUM
ejpam-4727	141	3	0.020964	0.020964	NUM
ejpam-4727	141	4	0.113594	0.113594	NUM
ejpam-4727	141	5	0.032346	0.032346	NUM
ejpam-4727	141	6	12	12	NUM
ejpam-4727	141	7	1.20	1.20	NUM
ejpam-4727	141	8	0.864150	0.864150	NUM
ejpam-4727	141	9	1.019051	1.019051	NUM
ejpam-4727	141	10	0.847968	0.847968	NUM
ejpam-4727	141	11	0.882720	0.882720	NUM
ejpam-4727	141	12	0.021037	0.021037	NUM
ejpam-4727	141	13	0.154444	0.154444	NUM
ejpam-4727	141	14	0.039369	0.039369	NUM
ejpam-4727	141	15	13	13	NUM
ejpam-4727	141	16	1.30	1.30	NUM
ejpam-4727	141	17	0.868413	0.868413	NUM
ejpam-4727	141	18	1.065991	1.065991	NUM
ejpam-4727	141	19	0.843583	0.843583	NUM
ejpam-4727	141	20	0.886895	0.886895	NUM
ejpam-4727	141	21	0.020840	0.020840	NUM
ejpam-4727	141	22	0.201936	0.201936	NUM
ejpam-4727	141	23	0.048835	0.048835	NUM
ejpam-4727	141	24	14	14	NUM
ejpam-4727	141	25	1.40	1.40	NUM
ejpam-4727	141	26	0.873349	0.873349	NUM
ejpam-4727	141	27	1.119909	1.119909	NUM
ejpam-4727	141	28	0.836845	0.836845	NUM
ejpam-4727	141	29	0.891563	0.891563	NUM
ejpam-4727	141	30	0.020430	0.020430	NUM
ejpam-4727	141	31	0.256119	0.256119	NUM
ejpam-4727	141	32	0.061373	0.061373	NUM
ejpam-4727	141	33	15	15	NUM
ejpam-4727	141	34	1.50	1.50	NUM
ejpam-4727	141	35	0.878771	0.878771	NUM
ejpam-4727	141	36	1.180804	1.180804	NUM
ejpam-4727	141	37	0.826974	0.826974	NUM
ejpam-4727	141	38	0.896627	0.896627	NUM
ejpam-4727	141	39	0.019915	0.019915	NUM
ejpam-4727	141	40	0.316940	0.316940	NUM
ejpam-4727	141	41	0.077684	0.077684	NUM
ejpam-4727	141	42	16	16	NUM
ejpam-4727	141	43	1.60	1.60	NUM
ejpam-4727	141	44	0.884528	0.884528	NUM
ejpam-4727	141	45	1.248677	1.248677	NUM
ejpam-4727	141	46	0.813193	0.813193	NUM
ejpam-4727	141	47	0.902001	0.902001	NUM
ejpam-4727	141	48	0.019371	0.019371	NUM
ejpam-4727	141	49	0.384342	0.384342	NUM
ejpam-4727	141	50	0.098456	0.098456	NUM
ejpam-4727	141	51	17	17	NUM
ejpam-4727	141	52	1.70	1.70	NUM
ejpam-4727	141	53	0.890492	0.890492	NUM
ejpam-4727	141	54	1.323527	1.323527	NUM
ejpam-4727	141	55	0.794725	0.794725	NUM
ejpam-4727	141	56	0.907601	0.907601	NUM
ejpam-4727	141	57	0.018850	0.018850	NUM
ejpam-4727	141	58	0.458270	0.458270	NUM
ejpam-4727	141	59	0.124368	0.124368	NUM
ejpam-4727	141	60	18	18	NUM
ejpam-4727	141	61	1.80	1.80	NUM
ejpam-4727	141	62	0.896562	0.896562	NUM
ejpam-4727	141	63	1.405354	1.405354	NUM
ejpam-4727	141	64	0.770792	0.770792	NUM
ejpam-4727	141	65	0.913352	0.913352	NUM
ejpam-4727	141	66	0.018383	0.018383	NUM
ejpam-4727	141	67	0.538677	0.538677	NUM
ejpam-4727	141	68	0.156085	0.156085	NUM
ejpam-4727	141	69	19	19	NUM
ejpam-4727	141	70	1.90	1.90	NUM
ejpam-4727	141	71	0.902655	0.902655	NUM
ejpam-4727	141	72	1.494159	1.494159	NUM
ejpam-4727	141	73	0.740616	0.740616	NUM
ejpam-4727	141	74	0.919185	0.919185	NUM
ejpam-4727	141	75	0.017984	0.017984	NUM
ejpam-4727	141	76	0.625525	0.625525	NUM
ejpam-4727	141	77	0.194269	0.194269	NUM
ejpam-4727	141	78	20	20	NUM
ejpam-4727	141	79	2.00	2.00	NUM
ejpam-4727	141	80	0.908704	0.908704	NUM
ejpam-4727	141	81	1.589941	1.589941	NUM
ejpam-4727	141	82	0.703420	0.703420	NUM
ejpam-4727	141	83	0.925037	0.925037	NUM
ejpam-4727	141	84	0.017657	0.017657	NUM
ejpam-4727	141	85	0.718787	0.718787	NUM
ejpam-4727	141	86	0.239576	0.239576	NUM
ejpam-4727	141	87	figure	figure	NOUN
ejpam-4727	141	88	4	4	NUM
ejpam-4727	141	89	:	:	PUNCT
ejpam-4727	141	90	comparing	compare	VERB
ejpam-4727	141	91	graph	graph	NOUN
ejpam-4727	141	92	of	of	ADP
ejpam-4727	141	93	approximate	approximate	ADJ
ejpam-4727	141	94	solutions	solution	NOUN
ejpam-4727	141	95	(	(	PUNCT
ejpam-4727	141	96	left	left	ADV
ejpam-4727	141	97	)	)	PUNCT
ejpam-4727	141	98	and	and	CCONJ
ejpam-4727	141	99	relative	relative	ADJ
ejpam-4727	141	100	errors	error	NOUN
ejpam-4727	141	101	(	(	PUNCT
ejpam-4727	141	102	right	right	ADJ
ejpam-4727	141	103	)	)	PUNCT
ejpam-4727	141	104	in	in	ADP
ejpam-4727	141	105	example	example	NOUN
ejpam-4727	141	106	3	3	NUM
ejpam-4727	141	107	with	with	ADP
ejpam-4727	141	108	h	h	NOUN
ejpam-4727	141	109	=	=	NOUN
ejpam-4727	141	110	0.1	0.1	NUM
ejpam-4727	141	111	on	on	ADP
ejpam-4727	141	112	xi	xi	ADP
ejpam-4727	141	113	∈	∈	PROPN
ejpam-4727	142	1	[	[	X
ejpam-4727	142	2	0	0	NUM
ejpam-4727	142	3	,	,	PUNCT
ejpam-4727	142	4	2	2	NUM
ejpam-4727	142	5	]	]	PUNCT
ejpam-4727	142	6	references	reference	NOUN
ejpam-4727	142	7	972	972	NUM
ejpam-4727	142	8	4	4	NUM
ejpam-4727	142	9	.	.	PUNCT
ejpam-4727	142	10	conclusions	conclusion	NOUN
ejpam-4727	142	11	in	in	ADP
ejpam-4727	142	12	this	this	DET
ejpam-4727	142	13	article	article	NOUN
ejpam-4727	142	14	,	,	PUNCT
ejpam-4727	142	15	we	we	PRON
ejpam-4727	142	16	studied	study	VERB
ejpam-4727	142	17	many	many	ADJ
ejpam-4727	142	18	numerical	numerical	ADJ
ejpam-4727	142	19	techniques	technique	NOUN
ejpam-4727	142	20	for	for	ADP
ejpam-4727	142	21	solving	solve	VERB
ejpam-4727	142	22	initial	initial	ADJ
ejpam-4727	142	23	value	value	NOUN
ejpam-4727	142	24	problems	problem	NOUN
ejpam-4727	142	25	.	.	PUNCT
ejpam-4727	143	1	then	then	ADV
ejpam-4727	143	2	we	we	PRON
ejpam-4727	143	3	decide	decide	VERB
ejpam-4727	143	4	to	to	PART
ejpam-4727	143	5	combine	combine	VERB
ejpam-4727	143	6	the	the	DET
ejpam-4727	143	7	newton	newton	PROPN
ejpam-4727	143	8	’s	’s	PART
ejpam-4727	143	9	interpolation	interpolation	NOUN
ejpam-4727	143	10	and	and	CCONJ
ejpam-4727	143	11	lagrange	lagrange	NOUN
ejpam-4727	143	12	’s	’s	PART
ejpam-4727	143	13	method	method	NOUN
ejpam-4727	143	14	to	to	PART
ejpam-4727	143	15	construct	construct	VERB
ejpam-4727	143	16	cubic	cubic	ADJ
ejpam-4727	143	17	polynomials	polynomial	NOUN
ejpam-4727	143	18	as	as	ADP
ejpam-4727	143	19	the	the	DET
ejpam-4727	143	20	solutions	solution	NOUN
ejpam-4727	143	21	of	of	ADP
ejpam-4727	143	22	linear	linear	PROPN
ejpam-4727	143	23	and	and	CCONJ
ejpam-4727	143	24	nonlinear	nonlinear	NOUN
ejpam-4727	143	25	of	of	ADP
ejpam-4727	143	26	ordinary	ordinary	ADJ
ejpam-4727	143	27	differential	differential	ADJ
ejpam-4727	143	28	equations	equation	NOUN
ejpam-4727	143	29	.	.	PUNCT
ejpam-4727	144	1	we	we	PRON
ejpam-4727	144	2	compared	compare	VERB
ejpam-4727	144	3	our	our	PRON
ejpam-4727	144	4	numerical	numerical	ADJ
ejpam-4727	144	5	results	result	NOUN
ejpam-4727	144	6	and	and	CCONJ
ejpam-4727	144	7	relative	relative	ADJ
ejpam-4727	144	8	errors	error	NOUN
ejpam-4727	144	9	with	with	ADP
ejpam-4727	144	10	the	the	DET
ejpam-4727	144	11	results	result	NOUN
ejpam-4727	144	12	of	of	ADP
ejpam-4727	144	13	euler	euler	PROPN
ejpam-4727	144	14	’s	’s	PART
ejpam-4727	144	15	method	method	NOUN
ejpam-4727	144	16	,	,	PUNCT
ejpam-4727	144	17	methods	method	NOUN
ejpam-4727	144	18	from	from	ADP
ejpam-4727	144	19	[	[	X
ejpam-4727	144	20	11	11	NUM
ejpam-4727	144	21	]	]	PUNCT
ejpam-4727	144	22	and	and	CCONJ
ejpam-4727	144	23	[	[	X
ejpam-4727	144	24	14	14	NUM
ejpam-4727	144	25	]	]	PUNCT
ejpam-4727	144	26	and	and	CCONJ
ejpam-4727	144	27	exact	exact	ADJ
ejpam-4727	144	28	solutions	solution	NOUN
ejpam-4727	144	29	.	.	PUNCT
ejpam-4727	145	1	from	from	ADP
ejpam-4727	145	2	example	example	NOUN
ejpam-4727	145	3	1	1	NUM
ejpam-4727	145	4	-	-	SYM
ejpam-4727	145	5	3	3	NUM
ejpam-4727	145	6	,	,	PUNCT
ejpam-4727	145	7	when	when	SCONJ
ejpam-4727	145	8	we	we	PRON
ejpam-4727	145	9	compare	compare	VERB
ejpam-4727	145	10	the	the	DET
ejpam-4727	145	11	result	result	NOUN
ejpam-4727	145	12	in	in	ADP
ejpam-4727	145	13	other	other	ADJ
ejpam-4727	145	14	methods	method	NOUN
ejpam-4727	145	15	,	,	PUNCT
ejpam-4727	145	16	our	our	PRON
ejpam-4727	145	17	method	method	NOUN
ejpam-4727	145	18	gives	give	VERB
ejpam-4727	145	19	numerical	numerical	ADJ
ejpam-4727	145	20	approximated	approximate	VERB
ejpam-4727	145	21	solutions	solution	NOUN
ejpam-4727	145	22	which	which	PRON
ejpam-4727	145	23	is	be	AUX
ejpam-4727	145	24	much	much	ADV
ejpam-4727	145	25	closer	close	ADJ
ejpam-4727	145	26	to	to	ADP
ejpam-4727	145	27	the	the	DET
ejpam-4727	145	28	exact	exact	ADJ
ejpam-4727	145	29	solutions	solution	NOUN
ejpam-4727	145	30	as	as	SCONJ
ejpam-4727	145	31	shown	show	VERB
ejpam-4727	145	32	in	in	ADP
ejpam-4727	145	33	table	table	NOUN
ejpam-4727	145	34	1	1	NUM
ejpam-4727	145	35	-	-	SYM
ejpam-4727	145	36	3	3	NUM
ejpam-4727	145	37	.	.	PUNCT
ejpam-4727	146	1	also	also	ADV
ejpam-4727	146	2	our	our	PRON
ejpam-4727	146	3	relative	relative	ADJ
ejpam-4727	146	4	errors	error	NOUN
ejpam-4727	146	5	are	be	AUX
ejpam-4727	146	6	nearly	nearly	ADV
ejpam-4727	146	7	close	close	ADJ
ejpam-4727	146	8	to	to	ADP
ejpam-4727	146	9	zero	zero	NUM
ejpam-4727	146	10	and	and	CCONJ
ejpam-4727	146	11	much	much	ADV
ejpam-4727	146	12	smaller	small	ADJ
ejpam-4727	146	13	than	than	ADP
ejpam-4727	146	14	errors	error	NOUN
ejpam-4727	146	15	from	from	ADP
ejpam-4727	146	16	[	[	X
ejpam-4727	146	17	11	11	NUM
ejpam-4727	146	18	]	]	PUNCT
ejpam-4727	146	19	and	and	CCONJ
ejpam-4727	146	20	[	[	X
ejpam-4727	146	21	14	14	NUM
ejpam-4727	146	22	]	]	X
ejpam-4727	146	23	methods	method	NOUN
ejpam-4727	146	24	as	as	SCONJ
ejpam-4727	146	25	shown	show	VERB
ejpam-4727	146	26	in	in	ADP
ejpam-4727	146	27	figure	figure	NOUN
ejpam-4727	146	28	2	2	NUM
ejpam-4727	146	29	-	-	SYM
ejpam-4727	146	30	4	4	NUM
ejpam-4727	146	31	.	.	PUNCT
ejpam-4727	147	1	notice	notice	VERB
ejpam-4727	147	2	that	that	SCONJ
ejpam-4727	147	3	to	to	PART
ejpam-4727	147	4	compute	compute	VERB
ejpam-4727	147	5	each	each	DET
ejpam-4727	147	6	yi	yi	NOUN
ejpam-4727	147	7	in	in	ADP
ejpam-4727	147	8	each	each	DET
ejpam-4727	147	9	step	step	NOUN
ejpam-4727	147	10	size	size	NOUN
ejpam-4727	147	11	of	of	ADP
ejpam-4727	147	12	euler	euler	PROPN
ejpam-4727	147	13	’s	’s	PART
ejpam-4727	147	14	method	method	NOUN
ejpam-4727	147	15	is	be	AUX
ejpam-4727	147	16	so	so	ADV
ejpam-4727	147	17	much	much	ADJ
ejpam-4727	147	18	time	time	NOUN
ejpam-4727	147	19	-	-	PUNCT
ejpam-4727	147	20	consuming	consume	VERB
ejpam-4727	147	21	.	.	PUNCT
ejpam-4727	148	1	therefore	therefore	ADV
ejpam-4727	148	2	,	,	PUNCT
ejpam-4727	148	3	our	our	PRON
ejpam-4727	148	4	method	method	NOUN
ejpam-4727	148	5	is	be	AUX
ejpam-4727	148	6	much	much	ADV
ejpam-4727	148	7	more	more	ADV
ejpam-4727	148	8	accurate	accurate	ADJ
ejpam-4727	148	9	and	and	CCONJ
ejpam-4727	148	10	simpler	simple	ADJ
ejpam-4727	148	11	to	to	PART
ejpam-4727	148	12	find	find	VERB
ejpam-4727	148	13	approximated	approximated	ADJ
ejpam-4727	148	14	solutions	solution	NOUN
ejpam-4727	148	15	directly	directly	ADV
ejpam-4727	148	16	from	from	ADP
ejpam-4727	148	17	yi	yi	PROPN
ejpam-4727	148	18	=	=	SYM
ejpam-4727	148	19	p3(xi	p3(xi	PROPN
ejpam-4727	148	20	)	)	PUNCT
ejpam-4727	148	21	at	at	ADP
ejpam-4727	148	22	any	any	DET
ejpam-4727	148	23	value	value	NOUN
ejpam-4727	148	24	of	of	ADP
ejpam-4727	148	25	xi	xi	PROPN
ejpam-4727	148	26	.	.	PUNCT
ejpam-4727	149	1	for	for	ADP
ejpam-4727	149	2	the	the	DET
ejpam-4727	149	3	future	future	ADJ
ejpam-4727	149	4	work	work	NOUN
ejpam-4727	149	5	,	,	PUNCT
ejpam-4727	149	6	we	we	PRON
ejpam-4727	149	7	aim	aim	VERB
ejpam-4727	149	8	to	to	PART
ejpam-4727	149	9	apply	apply	VERB
ejpam-4727	149	10	our	our	PRON
ejpam-4727	149	11	method	method	NOUN
ejpam-4727	149	12	to	to	PART
ejpam-4727	149	13	solve	solve	VERB
ejpam-4727	149	14	other	other	ADJ
ejpam-4727	149	15	systems	system	NOUN
ejpam-4727	149	16	of	of	ADP
ejpam-4727	149	17	first	first	ADJ
ejpam-4727	149	18	order	order	NOUN
ejpam-4727	149	19	differential	differential	ADJ
ejpam-4727	149	20	equations	equation	NOUN
ejpam-4727	149	21	or	or	CCONJ
ejpam-4727	149	22	higher	high	ADJ
ejpam-4727	149	23	order	order	NOUN
ejpam-4727	149	24	differential	differential	ADJ
ejpam-4727	149	25	equations	equation	NOUN
ejpam-4727	149	26	.	.	PUNCT
ejpam-4727	150	1	acknowledgements	acknowledgement	NOUN
ejpam-4727	150	2	this	this	DET
ejpam-4727	150	3	research	research	NOUN
ejpam-4727	150	4	is	be	AUX
ejpam-4727	150	5	partially	partially	ADV
ejpam-4727	150	6	supported	support	VERB
ejpam-4727	150	7	by	by	ADP
ejpam-4727	150	8	a	a	DET
ejpam-4727	150	9	research	research	NOUN
ejpam-4727	150	10	grant	grant	NOUN
ejpam-4727	150	11	from	from	ADP
ejpam-4727	150	12	the	the	DET
ejpam-4727	150	13	faculty	faculty	NOUN
ejpam-4727	150	14	of	of	ADP
ejpam-4727	150	15	science	science	NOUN
ejpam-4727	150	16	,	,	PUNCT
ejpam-4727	150	17	burapha	burapha	PROPN
ejpam-4727	150	18	university	university	PROPN
ejpam-4727	150	19	,	,	PUNCT
ejpam-4727	150	20	thailand	thailand	PROPN
ejpam-4727	150	21	.	.	PUNCT
ejpam-4727	151	1	references	reference	NOUN
ejpam-4727	151	2	[	[	X
ejpam-4727	151	3	1	1	X
ejpam-4727	151	4	]	]	PUNCT
ejpam-4727	151	5	j.	j.	PROPN
ejpam-4727	151	6	d.	d.	PROPN
ejpam-4727	151	7	abraha	abraha	PROPN
ejpam-4727	151	8	.	.	PUNCT
ejpam-4727	152	1	comparison	comparison	NOUN
ejpam-4727	152	2	of	of	ADP
ejpam-4727	152	3	numerical	numerical	ADJ
ejpam-4727	152	4	methods	method	NOUN
ejpam-4727	152	5	for	for	ADP
ejpam-4727	152	6	system	system	NOUN
ejpam-4727	152	7	of	of	ADP
ejpam-4727	152	8	first	first	ADJ
ejpam-4727	152	9	order	order	NOUN
ejpam-4727	152	10	ordinary	ordinary	ADJ
ejpam-4727	152	11	differential	differential	ADJ
ejpam-4727	152	12	equations	equation	NOUN
ejpam-4727	152	13	.	.	PUNCT
ejpam-4727	153	1	pure	pure	ADJ
ejpam-4727	153	2	appl	appl	PROPN
ejpam-4727	153	3	.	.	PUNCT
ejpam-4727	153	4	math	math	PROPN
ejpam-4727	153	5	.	.	PUNCT
ejpam-4727	154	1	j.	j.	PROPN
ejpam-4727	154	2	,	,	PUNCT
ejpam-4727	154	3	9:32–36	9:32–36	NUM
ejpam-4727	154	4	,	,	PUNCT
ejpam-4727	154	5	2020	2020	NUM
ejpam-4727	154	6	.	.	PUNCT
ejpam-4727	155	1	[	[	X
ejpam-4727	155	2	2	2	NUM
ejpam-4727	155	3	]	]	PUNCT
ejpam-4727	155	4	f.	f.	PROPN
ejpam-4727	155	5	m.	m.	PROPN
ejpam-4727	155	6	al	al	PROPN
ejpam-4727	155	7	-	-	PUNCT
ejpam-4727	155	8	askar	askar	PROPN
ejpam-4727	155	9	,	,	PUNCT
ejpam-4727	155	10	c.	c.	PROPN
ejpam-4727	155	11	cesarano	cesarano	PROPN
ejpam-4727	155	12	,	,	PUNCT
ejpam-4727	155	13	and	and	CCONJ
ejpam-4727	155	14	w.	w.	PROPN
ejpam-4727	155	15	w.	w.	PROPN
ejpam-4727	155	16	mohammed	mohammed	PROPN
ejpam-4727	155	17	.	.	PUNCT
ejpam-4727	156	1	the	the	DET
ejpam-4727	156	2	analytical	analytical	ADJ
ejpam-4727	156	3	solutions	solution	NOUN
ejpam-4727	156	4	of	of	ADP
ejpam-4727	156	5	stochastic	stochastic	NOUN
ejpam-4727	156	6	-	-	PUNCT
ejpam-4727	156	7	fractional	fractional	ADJ
ejpam-4727	156	8	drinfel’d	drinfel’d	NOUN
ejpam-4727	156	9	-	-	PUNCT
ejpam-4727	156	10	sokolov	sokolov	NOUN
ejpam-4727	156	11	-	-	PUNCT
ejpam-4727	156	12	wilson	wilson	PROPN
ejpam-4727	156	13	equations	equation	NOUN
ejpam-4727	156	14	via	via	ADP
ejpam-4727	156	15	(	(	PUNCT
ejpam-4727	156	16	g’/g)-expansion	g’/g)-expansion	NOUN
ejpam-4727	156	17	method	method	NOUN
ejpam-4727	156	18	.	.	PUNCT
ejpam-4727	157	1	symmetry	symmetry	NOUN
ejpam-4727	157	2	,	,	PUNCT
ejpam-4727	157	3	14(10	14(10	NUM
ejpam-4727	157	4	)	)	PUNCT
ejpam-4727	157	5	,	,	PUNCT
ejpam-4727	157	6	2022	2022	NUM
ejpam-4727	157	7	.	.	PUNCT
ejpam-4727	158	1	[	[	X
ejpam-4727	158	2	3	3	NUM
ejpam-4727	158	3	]	]	X
ejpam-4727	158	4	m.	m.	NOUN
ejpam-4727	158	5	alkasassbeh	alkasassbeh	NOUN
ejpam-4727	158	6	,	,	PUNCT
ejpam-4727	158	7	z.	z.	PROPN
ejpam-4727	158	8	omar	omar	PROPN
ejpam-4727	158	9	,	,	PUNCT
ejpam-4727	158	10	f.	f.	PROPN
ejpam-4727	158	11	mebarek	mebarek	PROPN
ejpam-4727	158	12	-	-	PUNCT
ejpam-4727	158	13	oudina	oudina	PROPN
ejpam-4727	158	14	,	,	PUNCT
ejpam-4727	158	15	j.	j.	PROPN
ejpam-4727	158	16	raza	raza	PROPN
ejpam-4727	158	17	,	,	PUNCT
ejpam-4727	158	18	and	and	CCONJ
ejpam-4727	158	19	a.	a.	NOUN
ejpam-4727	158	20	chamkha	chamkha	PROPN
ejpam-4727	158	21	.	.	PUNCT
ejpam-4727	159	1	heat	heat	NOUN
ejpam-4727	159	2	transfer	transfer	NOUN
ejpam-4727	159	3	study	study	NOUN
ejpam-4727	159	4	of	of	ADP
ejpam-4727	159	5	convective	convective	ADJ
ejpam-4727	159	6	fin	fin	NOUN
ejpam-4727	159	7	with	with	ADP
ejpam-4727	159	8	temperature	temperature	NOUN
ejpam-4727	159	9	-	-	PUNCT
ejpam-4727	159	10	dependent	dependent	ADJ
ejpam-4727	159	11	internal	internal	ADJ
ejpam-4727	159	12	heat	heat	NOUN
ejpam-4727	159	13	generation	generation	NOUN
ejpam-4727	159	14	by	by	ADP
ejpam-4727	159	15	hybrid	hybrid	ADJ
ejpam-4727	159	16	block	block	NOUN
ejpam-4727	159	17	method	method	NOUN
ejpam-4727	159	18	.	.	PUNCT
ejpam-4727	160	1	heat	heat	NOUN
ejpam-4727	160	2	transfer	transfer	NOUN
ejpam-4727	160	3	,	,	PUNCT
ejpam-4727	160	4	48(4):1225–1244	48(4):1225–1244	NUM
ejpam-4727	160	5	,	,	PUNCT
ejpam-4727	160	6	2019	2019	NUM
ejpam-4727	160	7	.	.	PUNCT
ejpam-4727	161	1	[	[	X
ejpam-4727	161	2	4	4	X
ejpam-4727	161	3	]	]	X
ejpam-4727	161	4	o.	o.	ADJ
ejpam-4727	161	5	a.	a.	NOUN
ejpam-4727	161	6	arqub	arqub	NOUN
ejpam-4727	161	7	.	.	PUNCT
ejpam-4727	162	1	the	the	DET
ejpam-4727	162	2	reproducing	reproduce	VERB
ejpam-4727	162	3	kernel	kernel	NOUN
ejpam-4727	162	4	algorithm	algorithm	NOUN
ejpam-4727	162	5	for	for	ADP
ejpam-4727	162	6	handling	handle	VERB
ejpam-4727	162	7	differential	differential	ADJ
ejpam-4727	162	8	algebraic	algebraic	ADJ
ejpam-4727	162	9	systems	system	NOUN
ejpam-4727	162	10	of	of	ADP
ejpam-4727	162	11	ordinary	ordinary	ADJ
ejpam-4727	162	12	differential	differential	ADJ
ejpam-4727	162	13	equations	equation	NOUN
ejpam-4727	162	14	.	.	PUNCT
ejpam-4727	163	1	math	math	NOUN
ejpam-4727	163	2	.	.	PUNCT
ejpam-4727	164	1	methods	method	NOUN
ejpam-4727	164	2	in	in	ADP
ejpam-4727	164	3	the	the	DET
ejpam-4727	164	4	app	app	PROPN
ejpam-4727	164	5	.	.	PUNCT
ejpam-4727	165	1	sci	sci	PROPN
ejpam-4727	165	2	.	.	PROPN
ejpam-4727	165	3	,	,	PUNCT
ejpam-4727	165	4	39(15):4549	39(15):4549	NUM
ejpam-4727	165	5	–	–	PUNCT
ejpam-4727	165	6	4562	4562	NUM
ejpam-4727	165	7	,	,	PUNCT
ejpam-4727	165	8	2016	2016	NUM
ejpam-4727	165	9	.	.	PUNCT
ejpam-4727	166	1	[	[	X
ejpam-4727	166	2	5	5	X
ejpam-4727	166	3	]	]	PUNCT
ejpam-4727	166	4	o.	o.	ADJ
ejpam-4727	166	5	a.	a.	NOUN
ejpam-4727	166	6	arqub	arqub	PROPN
ejpam-4727	166	7	,	,	PUNCT
ejpam-4727	166	8	h.	h.	PROPN
ejpam-4727	166	9	o.	o.	PROPN
ejpam-4727	166	10	alsulami	alsulami	PROPN
ejpam-4727	166	11	,	,	PUNCT
ejpam-4727	166	12	and	and	CCONJ
ejpam-4727	166	13	m.	m.	PROPN
ejpam-4727	166	14	alhodaly	alhodaly	PROPN
ejpam-4727	166	15	.	.	PUNCT
ejpam-4727	167	1	numerical	numerical	PROPN
ejpam-4727	167	2	hilbert	hilbert	PROPN
ejpam-4727	167	3	space	space	NOUN
ejpam-4727	167	4	solution	solution	NOUN
ejpam-4727	167	5	of	of	ADP
ejpam-4727	167	6	fractional	fractional	ADJ
ejpam-4727	167	7	sobolev	sobolev	NOUN
ejpam-4727	167	8	equation	equation	NOUN
ejpam-4727	167	9	in	in	ADP
ejpam-4727	167	10	(	(	PUNCT
ejpam-4727	167	11	1	1	NUM
ejpam-4727	167	12	+	+	NOUN
ejpam-4727	167	13	1)-dimensional	1)-dimensional	ADJ
ejpam-4727	167	14	space	space	NOUN
ejpam-4727	167	15	.	.	PUNCT
ejpam-4727	168	1	math	math	NOUN
ejpam-4727	168	2	.	.	PUNCT
ejpam-4727	169	1	sci	sci	PROPN
ejpam-4727	169	2	.	.	PROPN
ejpam-4727	169	3	,	,	PUNCT
ejpam-4727	169	4	16	16	NUM
ejpam-4727	169	5	,	,	PUNCT
ejpam-4727	169	6	2022	2022	NUM
ejpam-4727	169	7	.	.	PUNCT
ejpam-4727	170	1	[	[	X
ejpam-4727	170	2	6	6	NUM
ejpam-4727	170	3	]	]	PUNCT
ejpam-4727	170	4	o.	o.	NOUN
ejpam-4727	170	5	a.	a.	NOUN
ejpam-4727	170	6	arqub	arqub	NOUN
ejpam-4727	170	7	and	and	CCONJ
ejpam-4727	170	8	b.	b.	PROPN
ejpam-4727	170	9	maayah	maayah	PROPN
ejpam-4727	170	10	.	.	PUNCT
ejpam-4727	171	1	adaptive	adaptive	PROPN
ejpam-4727	171	2	the	the	DET
ejpam-4727	171	3	dirichlet	dirichlet	PROPN
ejpam-4727	171	4	model	model	NOUN
ejpam-4727	171	5	of	of	ADP
ejpam-4727	171	6	mobile	mobile	ADJ
ejpam-4727	171	7	/	/	SYM
ejpam-4727	171	8	immobile	immobile	ADJ
ejpam-4727	171	9	advection	advection	NOUN
ejpam-4727	171	10	/	/	SYM
ejpam-4727	171	11	dispersion	dispersion	NOUN
ejpam-4727	171	12	in	in	ADP
ejpam-4727	171	13	a	a	DET
ejpam-4727	171	14	time	time	NOUN
ejpam-4727	171	15	-	-	PUNCT
ejpam-4727	171	16	fractional	fractional	ADJ
ejpam-4727	171	17	sense	sense	NOUN
ejpam-4727	171	18	with	with	ADP
ejpam-4727	171	19	the	the	DET
ejpam-4727	171	20	reproducing	reproduce	VERB
ejpam-4727	171	21	kernel	kernel	PROPN
ejpam-4727	171	22	computational	computational	ADJ
ejpam-4727	171	23	approach	approach	NOUN
ejpam-4727	171	24	:	:	PUNCT
ejpam-4727	171	25	formulations	formulation	NOUN
ejpam-4727	171	26	and	and	CCONJ
ejpam-4727	171	27	approximations	approximation	NOUN
ejpam-4727	171	28	.	.	PUNCT
ejpam-4727	172	1	int	int	NOUN
ejpam-4727	172	2	.	.	PUNCT
ejpam-4727	173	1	j.	j.	PROPN
ejpam-4727	173	2	modern	modern	PROPN
ejpam-4727	173	3	physics	physics	PROPN
ejpam-4727	173	4	b	b	PROPN
ejpam-4727	173	5	,	,	PUNCT
ejpam-4727	173	6	37	37	NUM
ejpam-4727	173	7	,	,	PUNCT
ejpam-4727	173	8	2022	2022	NUM
ejpam-4727	173	9	.	.	PUNCT
ejpam-4727	174	1	references	reference	NOUN
ejpam-4727	174	2	973	973	NUM
ejpam-4727	175	1	[	[	X
ejpam-4727	175	2	7	7	NUM
ejpam-4727	175	3	]	]	X
ejpam-4727	175	4	h.	h.	PROPN
ejpam-4727	175	5	badawi	badawi	PROPN
ejpam-4727	175	6	,	,	PUNCT
ejpam-4727	175	7	n.	n.	NOUN
ejpam-4727	175	8	shawagfeh	shawagfeh	NOUN
ejpam-4727	175	9	,	,	PUNCT
ejpam-4727	175	10	and	and	CCONJ
ejpam-4727	175	11	o.	o.	NOUN
ejpam-4727	175	12	a.	a.	NOUN
ejpam-4727	175	13	arqub	arqub	NOUN
ejpam-4727	175	14	.	.	PUNCT
ejpam-4727	176	1	fractional	fractional	ADJ
ejpam-4727	176	2	conformable	conformable	ADJ
ejpam-4727	176	3	stochastic	stochastic	ADJ
ejpam-4727	176	4	integrodifferential	integrodifferential	ADJ
ejpam-4727	176	5	equations	equation	NOUN
ejpam-4727	176	6	:	:	PUNCT
ejpam-4727	176	7	existence	existence	NOUN
ejpam-4727	176	8	,	,	PUNCT
ejpam-4727	176	9	uniqueness	uniqueness	NOUN
ejpam-4727	176	10	,	,	PUNCT
ejpam-4727	176	11	and	and	CCONJ
ejpam-4727	176	12	numerical	numerical	ADJ
ejpam-4727	176	13	simulations	simulation	NOUN
ejpam-4727	176	14	utilizing	utilize	VERB
ejpam-4727	176	15	the	the	DET
ejpam-4727	176	16	shifted	shift	VERB
ejpam-4727	176	17	legendre	legendre	PROPN
ejpam-4727	176	18	spectral	spectral	ADJ
ejpam-4727	176	19	collocation	collocation	NOUN
ejpam-4727	176	20	algorithm	algorithm	NOUN
ejpam-4727	176	21	.	.	PUNCT
ejpam-4727	177	1	math	math	NOUN
ejpam-4727	177	2	.	.	PUNCT
ejpam-4727	178	1	problems	problem	NOUN
ejpam-4727	178	2	in	in	ADP
ejpam-4727	178	3	engineering	engineering	NOUN
ejpam-4727	178	4	,	,	PUNCT
ejpam-4727	178	5	2022	2022	NUM
ejpam-4727	178	6	,	,	PUNCT
ejpam-4727	178	7	2022	2022	NUM
ejpam-4727	178	8	.	.	PUNCT
ejpam-4727	179	1	[	[	X
ejpam-4727	179	2	8	8	NUM
ejpam-4727	179	3	]	]	X
ejpam-4727	179	4	r.	r.	PROPN
ejpam-4727	179	5	djebali	djebali	PROPN
ejpam-4727	179	6	,	,	PUNCT
ejpam-4727	179	7	f.	f.	PROPN
ejpam-4727	179	8	mebarek	mebarek	PROPN
ejpam-4727	179	9	-	-	PUNCT
ejpam-4727	179	10	oudina	oudina	PROPN
ejpam-4727	179	11	,	,	PUNCT
ejpam-4727	179	12	and	and	CCONJ
ejpam-4727	179	13	c.	c.	NOUN
ejpam-4727	179	14	rajashekhar	rajashekhar	NOUN
ejpam-4727	179	15	.	.	PUNCT
ejpam-4727	180	1	similarity	similarity	NOUN
ejpam-4727	180	2	solution	solution	NOUN
ejpam-4727	180	3	analysis	analysis	NOUN
ejpam-4727	180	4	of	of	ADP
ejpam-4727	180	5	dynamic	dynamic	ADJ
ejpam-4727	180	6	and	and	CCONJ
ejpam-4727	180	7	thermal	thermal	ADJ
ejpam-4727	180	8	boundary	boundary	ADJ
ejpam-4727	180	9	layers	layer	NOUN
ejpam-4727	180	10	:	:	PUNCT
ejpam-4727	180	11	further	further	ADJ
ejpam-4727	180	12	formulation	formulation	NOUN
ejpam-4727	180	13	along	along	ADP
ejpam-4727	180	14	a	a	DET
ejpam-4727	180	15	vertical	vertical	ADJ
ejpam-4727	180	16	flat	flat	ADJ
ejpam-4727	180	17	plate	plate	NOUN
ejpam-4727	180	18	.	.	PUNCT
ejpam-4727	181	1	physica	physica	PROPN
ejpam-4727	181	2	scripta	scripta	PROPN
ejpam-4727	181	3	,	,	PUNCT
ejpam-4727	181	4	96(8	96(8	NUM
ejpam-4727	181	5	)	)	PUNCT
ejpam-4727	181	6	,	,	PUNCT
ejpam-4727	181	7	2021	2021	NUM
ejpam-4727	181	8	.	.	PUNCT
ejpam-4727	182	1	[	[	X
ejpam-4727	182	2	9	9	NUM
ejpam-4727	182	3	]	]	X
ejpam-4727	182	4	m.	m.	NOUN
ejpam-4727	182	5	farhan	farhan	PROPN
ejpam-4727	182	6	,	,	PUNCT
ejpam-4727	182	7	z.	z.	PROPN
ejpam-4727	182	8	omar	omar	PROPN
ejpam-4727	182	9	,	,	PUNCT
ejpam-4727	182	10	f.	f.	PROPN
ejpam-4727	182	11	mebarek	mebarek	PROPN
ejpam-4727	182	12	-	-	PUNCT
ejpam-4727	182	13	oudina	oudina	PROPN
ejpam-4727	182	14	,	,	PUNCT
ejpam-4727	182	15	z.	z.	PROPN
ejpam-4727	182	16	shah	shah	PROPN
ejpam-4727	182	17	j.	j.	PROPN
ejpam-4727	182	18	raza	raza	PROPN
ejpam-4727	182	19	,	,	PUNCT
ejpam-4727	182	20	r.	r.	PROPN
ejpam-4727	182	21	v	v	ADP
ejpam-4727	182	22	choudhari	choudhari	PROPN
ejpam-4727	182	23	,	,	PUNCT
ejpam-4727	182	24	and	and	CCONJ
ejpam-4727	182	25	o.	o.	PROPN
ejpam-4727	182	26	d.	d.	PROPN
ejpam-4727	182	27	makinde	makinde	PROPN
ejpam-4727	182	28	.	.	PUNCT
ejpam-4727	183	1	implementation	implementation	NOUN
ejpam-4727	183	2	of	of	ADP
ejpam-4727	183	3	the	the	DET
ejpam-4727	183	4	one	one	NUM
ejpam-4727	183	5	-	-	PUNCT
ejpam-4727	183	6	step	step	NOUN
ejpam-4727	183	7	one	one	NUM
ejpam-4727	183	8	-	-	PUNCT
ejpam-4727	183	9	hybrid	hybrid	ADJ
ejpam-4727	183	10	block	block	NOUN
ejpam-4727	183	11	method	method	NOUN
ejpam-4727	183	12	on	on	ADP
ejpam-4727	183	13	the	the	DET
ejpam-4727	183	14	nonlinear	nonlinear	ADJ
ejpam-4727	183	15	equation	equation	NOUN
ejpam-4727	183	16	of	of	ADP
ejpam-4727	183	17	a	a	DET
ejpam-4727	183	18	circular	circular	ADJ
ejpam-4727	183	19	sector	sector	NOUN
ejpam-4727	183	20	oscillator	oscillator	NOUN
ejpam-4727	183	21	.	.	PUNCT
ejpam-4727	184	1	comput	comput	NOUN
ejpam-4727	184	2	.	.	PUNCT
ejpam-4727	185	1	math	math	NOUN
ejpam-4727	185	2	.	.	PUNCT
ejpam-4727	186	1	model	model	PROPN
ejpam-4727	186	2	,	,	PUNCT
ejpam-4727	186	3	31:116–132	31:116–132	PROPN
ejpam-4727	186	4	,	,	PUNCT
ejpam-4727	186	5	2020	2020	NUM
ejpam-4727	186	6	.	.	PUNCT
ejpam-4727	187	1	[	[	X
ejpam-4727	187	2	10	10	NUM
ejpam-4727	187	3	]	]	PUNCT
ejpam-4727	187	4	m.	m.	NOUN
ejpam-4727	187	5	hassan	hassan	PROPN
ejpam-4727	187	6	,	,	PUNCT
ejpam-4727	187	7	f.	f.	PROPN
ejpam-4727	187	8	mebarek	mebarek	PROPN
ejpam-4727	187	9	-	-	PUNCT
ejpam-4727	187	10	oudina	oudina	PROPN
ejpam-4727	187	11	,	,	PUNCT
ejpam-4727	187	12	a.	a.	NOUN
ejpam-4727	187	13	faisal	faisal	PROPN
ejpam-4727	187	14	,	,	PUNCT
ejpam-4727	187	15	a.	a.	NOUN
ejpam-4727	187	16	ghafar	ghafar	ADV
ejpam-4727	187	17	,	,	PUNCT
ejpam-4727	187	18	and	and	CCONJ
ejpam-4727	187	19	a.	a.	PROPN
ejpam-4727	187	20	i.	i.	PROPN
ejpam-4727	187	21	ismail	ismail	PROPN
ejpam-4727	187	22	.	.	PUNCT
ejpam-4727	188	1	thermal	thermal	ADJ
ejpam-4727	188	2	energy	energy	NOUN
ejpam-4727	188	3	and	and	CCONJ
ejpam-4727	188	4	mass	mass	NOUN
ejpam-4727	188	5	transport	transport	NOUN
ejpam-4727	188	6	of	of	ADP
ejpam-4727	188	7	shear	shear	NOUN
ejpam-4727	188	8	thinning	thin	VERB
ejpam-4727	188	9	fluid	fluid	NOUN
ejpam-4727	188	10	under	under	ADP
ejpam-4727	188	11	effects	effect	NOUN
ejpam-4727	188	12	of	of	ADP
ejpam-4727	188	13	low	low	ADJ
ejpam-4727	188	14	to	to	ADP
ejpam-4727	188	15	high	high	ADJ
ejpam-4727	188	16	shear	shear	NOUN
ejpam-4727	188	17	rate	rate	NOUN
ejpam-4727	188	18	viscosity	viscosity	NOUN
ejpam-4727	188	19	.	.	PUNCT
ejpam-4727	189	1	int	int	NOUN
ejpam-4727	189	2	.	.	PUNCT
ejpam-4727	190	1	j.	j.	PROPN
ejpam-4727	190	2	thermofluids	thermofluids	PROPN
ejpam-4727	190	3	,	,	PUNCT
ejpam-4727	190	4	15	15	NUM
ejpam-4727	190	5	,	,	PUNCT
ejpam-4727	190	6	2022	2022	NUM
ejpam-4727	190	7	.	.	PUNCT
ejpam-4727	191	1	[	[	X
ejpam-4727	191	2	11	11	NUM
ejpam-4727	191	3	]	]	X
ejpam-4727	191	4	n.	n.	PROPN
ejpam-4727	191	5	d.	d.	PROPN
ejpam-4727	191	6	ide	ide	PROPN
ejpam-4727	191	7	.	.	PUNCT
ejpam-4727	192	1	using	use	VERB
ejpam-4727	192	2	newton	newton	PROPN
ejpam-4727	192	3	’s	’s	PART
ejpam-4727	192	4	interpolation	interpolation	NOUN
ejpam-4727	192	5	and	and	CCONJ
ejpam-4727	192	6	aitken	aitken	PROPN
ejpam-4727	192	7	’s	’s	PART
ejpam-4727	192	8	method	method	NOUN
ejpam-4727	192	9	for	for	ADP
ejpam-4727	192	10	solving	solve	VERB
ejpam-4727	192	11	first	first	ADJ
ejpam-4727	192	12	order	order	NOUN
ejpam-4727	192	13	differential	differential	ADJ
ejpam-4727	192	14	equation	equation	NOUN
ejpam-4727	192	15	.	.	PUNCT
ejpam-4727	193	1	world	world	NOUN
ejpam-4727	193	2	appl	appl	PROPN
ejpam-4727	193	3	.	.	PUNCT
ejpam-4727	194	1	sci	sci	PROPN
ejpam-4727	194	2	.	.	PUNCT
ejpam-4727	195	1	j.	j.	PROPN
ejpam-4727	195	2	,	,	PUNCT
ejpam-4727	195	3	38:191–194	38:191–194	PROPN
ejpam-4727	195	4	,	,	PUNCT
ejpam-4727	195	5	2022	2022	NUM
ejpam-4727	195	6	.	.	PUNCT
ejpam-4727	196	1	[	[	X
ejpam-4727	196	2	12	12	NUM
ejpam-4727	196	3	]	]	PUNCT
ejpam-4727	196	4	a.	a.	NOUN
ejpam-4727	196	5	ishkhanyan	ishkhanyan	PROPN
ejpam-4727	196	6	and	and	CCONJ
ejpam-4727	196	7	c.	c.	PROPN
ejpam-4727	196	8	cesarano	cesarano	PROPN
ejpam-4727	196	9	.	.	PUNCT
ejpam-4727	197	1	generalized	generalize	VERB
ejpam-4727	197	2	-	-	PUNCT
ejpam-4727	197	3	hypergeometric	hypergeometric	ADJ
ejpam-4727	197	4	solutions	solution	NOUN
ejpam-4727	197	5	of	of	ADP
ejpam-4727	197	6	the	the	DET
ejpam-4727	197	7	general	general	ADJ
ejpam-4727	197	8	fuchsian	fuchsian	ADJ
ejpam-4727	197	9	linear	linear	PROPN
ejpam-4727	197	10	ode	ode	PROPN
ejpam-4727	197	11	having	have	VERB
ejpam-4727	197	12	five	five	NUM
ejpam-4727	197	13	regular	regular	ADJ
ejpam-4727	197	14	singularities	singularity	NOUN
ejpam-4727	197	15	.	.	PUNCT
ejpam-4727	198	1	axioms	axiom	NOUN
ejpam-4727	198	2	,	,	PUNCT
ejpam-4727	198	3	8(3):102	8(3):102	NUM
ejpam-4727	198	4	,	,	PUNCT
ejpam-4727	198	5	2019	2019	NUM
ejpam-4727	198	6	.	.	PUNCT
ejpam-4727	199	1	[	[	X
ejpam-4727	199	2	13	13	NUM
ejpam-4727	199	3	]	]	X
ejpam-4727	199	4	u.	u.	PROPN
ejpam-4727	199	5	khan	khan	PROPN
ejpam-4727	199	6	,	,	PUNCT
ejpam-4727	199	7	f.	f.	PROPN
ejpam-4727	199	8	mebarek	mebarek	PROPN
ejpam-4727	199	9	-	-	PUNCT
ejpam-4727	199	10	oudina	oudina	PROPN
ejpam-4727	199	11	,	,	PUNCT
ejpam-4727	199	12	a.	a.	NOUN
ejpam-4727	199	13	zaib	zaib	PROPN
ejpam-4727	199	14	,	,	PUNCT
ejpam-4727	199	15	a.	a.	NOUN
ejpam-4727	199	16	ishak	ishak	PROPN
ejpam-4727	199	17	,	,	PUNCT
ejpam-4727	199	18	s.	s.	PROPN
ejpam-4727	199	19	a.	a.	PROPN
ejpam-4727	199	20	bakar	bakar	PROPN
ejpam-4727	199	21	,	,	PUNCT
ejpam-4727	199	22	e.	e.	PROPN
ejpam-4727	199	23	m.	m.	PROPN
ejpam-4727	199	24	sherif	sherif	PROPN
ejpam-4727	199	25	,	,	PUNCT
ejpam-4727	199	26	and	and	CCONJ
ejpam-4727	199	27	d.	d.	PROPN
ejpam-4727	199	28	baleanu	baleanu	PROPN
ejpam-4727	199	29	.	.	PUNCT
ejpam-4727	200	1	an	an	DET
ejpam-4727	200	2	exact	exact	ADJ
ejpam-4727	200	3	solution	solution	NOUN
ejpam-4727	200	4	of	of	ADP
ejpam-4727	200	5	a	a	DET
ejpam-4727	200	6	casson	casson	PROPN
ejpam-4727	200	7	fluid	fluid	NOUN
ejpam-4727	200	8	flow	flow	NOUN
ejpam-4727	200	9	induced	induce	VERB
ejpam-4727	200	10	by	by	ADP
ejpam-4727	200	11	dust	dust	NOUN
ejpam-4727	200	12	particles	particle	NOUN
ejpam-4727	200	13	with	with	ADP
ejpam-4727	200	14	hybrid	hybrid	ADJ
ejpam-4727	200	15	nanofluid	nanofluid	NOUN
ejpam-4727	200	16	over	over	ADP
ejpam-4727	200	17	a	a	DET
ejpam-4727	200	18	stretching	stretch	VERB
ejpam-4727	200	19	sheet	sheet	NOUN
ejpam-4727	200	20	subject	subject	NOUN
ejpam-4727	200	21	to	to	ADP
ejpam-4727	200	22	lorentz	lorentz	PROPN
ejpam-4727	200	23	forces	force	NOUN
ejpam-4727	200	24	.	.	PUNCT
ejpam-4727	201	1	waves	wave	NOUN
ejpam-4727	201	2	in	in	ADP
ejpam-4727	201	3	random	random	ADJ
ejpam-4727	201	4	and	and	CCONJ
ejpam-4727	201	5	complex	complex	ADJ
ejpam-4727	201	6	media	medium	NOUN
ejpam-4727	201	7	,	,	PUNCT
ejpam-4727	201	8	32	32	NUM
ejpam-4727	201	9	,	,	PUNCT
ejpam-4727	201	10	2022	2022	NUM
ejpam-4727	201	11	.	.	PUNCT
ejpam-4727	202	1	[	[	X
ejpam-4727	202	2	14	14	NUM
ejpam-4727	202	3	]	]	X
ejpam-4727	202	4	f.	f.	PROPN
ejpam-4727	202	5	c.	c.	PROPN
ejpam-4727	202	6	kosgei	kosgei	PROPN
ejpam-4727	202	7	.	.	PUNCT
ejpam-4727	203	1	solution	solution	NOUN
ejpam-4727	203	2	of	of	ADP
ejpam-4727	203	3	first	first	ADJ
ejpam-4727	203	4	order	order	NOUN
ejpam-4727	203	5	differential	differential	NOUN
ejpam-4727	203	6	equation	equation	NOUN
ejpam-4727	203	7	using	use	VERB
ejpam-4727	203	8	numerical	numerical	PROPN
ejpam-4727	203	9	newton	newton	PROPN
ejpam-4727	203	10	’s	’s	PART
ejpam-4727	203	11	interpolation	interpolation	NOUN
ejpam-4727	203	12	and	and	CCONJ
ejpam-4727	203	13	lagrange	lagrange	NOUN
ejpam-4727	203	14	method	method	NOUN
ejpam-4727	203	15	.	.	PUNCT
ejpam-4727	204	1	int	int	NOUN
ejpam-4727	204	2	.	.	PUNCT
ejpam-4727	205	1	j.	j.	PROPN
ejpam-4727	205	2	dev	dev	PROPN
ejpam-4727	205	3	.	.	PUNCT
ejpam-4727	206	1	res	res	PROPN
ejpam-4727	206	2	.	.	PROPN
ejpam-4727	206	3	,	,	PUNCT
ejpam-4727	206	4	8:18973–18976	8:18973–18976	NUM
ejpam-4727	206	5	,	,	PUNCT
ejpam-4727	206	6	2018	2018	NUM
ejpam-4727	206	7	.	.	PUNCT
ejpam-4727	207	1	[	[	X
ejpam-4727	207	2	15	15	NUM
ejpam-4727	207	3	]	]	X
ejpam-4727	207	4	a.	a.	PROPN
ejpam-4727	207	5	lupica	lupica	PROPN
ejpam-4727	207	6	,	,	PUNCT
ejpam-4727	207	7	c.	c.	PROPN
ejpam-4727	207	8	cesarano	cesarano	PROPN
ejpam-4727	207	9	,	,	PUNCT
ejpam-4727	207	10	f.	f.	PROPN
ejpam-4727	207	11	crisanti	crisanti	PROPN
ejpam-4727	207	12	,	,	PUNCT
ejpam-4727	207	13	and	and	CCONJ
ejpam-4727	207	14	a.	a.	PROPN
ejpam-4727	207	15	ishkhanyan	ishkhanyan	PROPN
ejpam-4727	207	16	.	.	PUNCT
ejpam-4727	208	1	analytical	analytical	ADJ
ejpam-4727	208	2	solution	solution	NOUN
ejpam-4727	208	3	of	of	ADP
ejpam-4727	208	4	the	the	DET
ejpam-4727	208	5	three	three	NUM
ejpam-4727	208	6	-	-	PUNCT
ejpam-4727	208	7	dimensional	dimensional	ADJ
ejpam-4727	208	8	laplace	laplace	NOUN
ejpam-4727	208	9	equation	equation	NOUN
ejpam-4727	208	10	in	in	ADP
ejpam-4727	208	11	terms	term	NOUN
ejpam-4727	208	12	of	of	ADP
ejpam-4727	208	13	linear	linear	ADJ
ejpam-4727	208	14	combinations	combination	NOUN
ejpam-4727	208	15	of	of	ADP
ejpam-4727	208	16	hypergeometric	hypergeometric	ADJ
ejpam-4727	208	17	functions	function	NOUN
ejpam-4727	208	18	.	.	PUNCT
ejpam-4727	209	1	mathematics	mathematic	NOUN
ejpam-4727	209	2	,	,	PUNCT
ejpam-4727	209	3	9(24	9(24	NUM
ejpam-4727	209	4	)	)	PUNCT
ejpam-4727	209	5	,	,	PUNCT
ejpam-4727	209	6	2021	2021	NUM
ejpam-4727	209	7	.	.	PUNCT
ejpam-4727	210	1	[	[	X
ejpam-4727	210	2	16	16	NUM
ejpam-4727	210	3	]	]	X
ejpam-4727	210	4	j.	j.	PROPN
ejpam-4727	210	5	c.	c.	PROPN
ejpam-4727	210	6	mbagwu	mbagwu	PROPN
ejpam-4727	210	7	and	and	CCONJ
ejpam-4727	210	8	n.	n.	PROPN
ejpam-4727	210	9	d.	d.	PROPN
ejpam-4727	210	10	ide	ide	PROPN
ejpam-4727	210	11	.	.	PROPN
ejpam-4727	211	1	comparison	comparison	NOUN
ejpam-4727	211	2	of	of	ADP
ejpam-4727	211	3	newton	newton	PROPN
ejpam-4727	211	4	’s	’s	PART
ejpam-4727	211	5	interpolation	interpolation	NOUN
ejpam-4727	211	6	and	and	CCONJ
ejpam-4727	211	7	aitken	aitken	PROPN
ejpam-4727	211	8	’s	’s	PART
ejpam-4727	211	9	methods	method	NOUN
ejpam-4727	211	10	with	with	ADP
ejpam-4727	211	11	some	some	DET
ejpam-4727	211	12	numerical	numerical	ADJ
ejpam-4727	211	13	methods	method	NOUN
ejpam-4727	211	14	for	for	ADP
ejpam-4727	211	15	solving	solve	VERB
ejpam-4727	211	16	system	system	NOUN
ejpam-4727	211	17	of	of	ADP
ejpam-4727	211	18	first	first	ADJ
ejpam-4727	211	19	and	and	CCONJ
ejpam-4727	211	20	second	second	ADJ
ejpam-4727	211	21	order	order	NOUN
ejpam-4727	211	22	differential	differential	ADJ
ejpam-4727	211	23	equation	equation	NOUN
ejpam-4727	211	24	.	.	PUNCT
ejpam-4727	212	1	world	world	PROPN
ejpam-4727	212	2	sci	sci	PROPN
ejpam-4727	212	3	.	.	PUNCT
ejpam-4727	212	4	news	news	PROPN
ejpam-4727	212	5	,	,	PUNCT
ejpam-4727	212	6	164:108–121	164:108–121	NUM
ejpam-4727	212	7	,	,	PUNCT
ejpam-4727	212	8	2022	2022	NUM
ejpam-4727	212	9	.	.	PUNCT
ejpam-4727	213	1	[	[	X
ejpam-4727	213	2	17	17	NUM
ejpam-4727	213	3	]	]	X
ejpam-4727	213	4	w.	w.	PROPN
ejpam-4727	213	5	w.	w.	PROPN
ejpam-4727	213	6	mohammed	mohammed	PROPN
ejpam-4727	213	7	,	,	PUNCT
ejpam-4727	213	8	f.	f.	PROPN
ejpam-4727	213	9	m.	m.	PROPN
ejpam-4727	213	10	al	al	PROPN
ejpam-4727	213	11	-	-	PUNCT
ejpam-4727	213	12	askar	askar	PROPN
ejpam-4727	213	13	,	,	PUNCT
ejpam-4727	213	14	c.	c.	PROPN
ejpam-4727	213	15	cesarano	cesarano	PROPN
ejpam-4727	213	16	,	,	PUNCT
ejpam-4727	213	17	t.	t.	NOUN
ejpam-4727	213	18	botmart	botmart	NOUN
ejpam-4727	213	19	,	,	PUNCT
ejpam-4727	213	20	and	and	CCONJ
ejpam-4727	213	21	m.	m.	PROPN
ejpam-4727	213	22	el	el	PROPN
ejpam-4727	213	23	-	-	PUNCT
ejpam-4727	213	24	morshedy	morshedy	PROPN
ejpam-4727	213	25	.	.	PUNCT
ejpam-4727	214	1	wiener	wiener	NOUN
ejpam-4727	214	2	process	process	NOUN
ejpam-4727	214	3	effects	effect	NOUN
ejpam-4727	214	4	on	on	ADP
ejpam-4727	214	5	the	the	DET
ejpam-4727	214	6	solutions	solution	NOUN
ejpam-4727	214	7	of	of	ADP
ejpam-4727	214	8	the	the	DET
ejpam-4727	214	9	fractional	fractional	ADJ
ejpam-4727	214	10	(	(	PUNCT
ejpam-4727	214	11	2	2	NUM
ejpam-4727	214	12	+	+	NUM
ejpam-4727	214	13	1)-dimensional	1)-dimensional	PROPN
ejpam-4727	214	14	heisenberg	heisenberg	PROPN
ejpam-4727	214	15	ferromagnetic	ferromagnetic	ADJ
ejpam-4727	214	16	spin	spin	NOUN
ejpam-4727	214	17	chain	chain	NOUN
ejpam-4727	214	18	equation	equation	NOUN
ejpam-4727	214	19	.	.	PUNCT
ejpam-4727	215	1	mathematics	mathematic	NOUN
ejpam-4727	215	2	,	,	PUNCT
ejpam-4727	215	3	10(12	10(12	NUM
ejpam-4727	215	4	)	)	PUNCT
ejpam-4727	215	5	,	,	PUNCT
ejpam-4727	215	6	2022	2022	NUM
ejpam-4727	215	7	.	.	PUNCT
ejpam-4727	216	1	[	[	X
ejpam-4727	216	2	18	18	NUM
ejpam-4727	216	3	]	]	PUNCT
ejpam-4727	216	4	j.	j.	PROPN
ejpam-4727	216	5	raza	raza	PROPN
ejpam-4727	216	6	,	,	PUNCT
ejpam-4727	216	7	f.	f.	PROPN
ejpam-4727	216	8	mebarek	mebarek	PROPN
ejpam-4727	216	9	-	-	PUNCT
ejpam-4727	216	10	oudina	oudina	PROPN
ejpam-4727	216	11	,	,	PUNCT
ejpam-4727	216	12	and	and	CCONJ
ejpam-4727	216	13	l.	l.	PROPN
ejpam-4727	216	14	ali	ali	PROPN
ejpam-4727	216	15	lund	lund	PROPN
ejpam-4727	216	16	.	.	PUNCT
ejpam-4727	217	1	the	the	DET
ejpam-4727	217	2	flow	flow	NOUN
ejpam-4727	217	3	of	of	ADP
ejpam-4727	217	4	magnetised	magnetise	VERB
ejpam-4727	217	5	convective	convective	ADJ
ejpam-4727	217	6	casson	casson	NOUN
ejpam-4727	217	7	liquid	liquid	NOUN
ejpam-4727	217	8	via	via	ADP
ejpam-4727	217	9	a	a	DET
ejpam-4727	217	10	porous	porous	ADJ
ejpam-4727	217	11	channel	channel	NOUN
ejpam-4727	217	12	with	with	ADP
ejpam-4727	217	13	shrinking	shrink	VERB
ejpam-4727	217	14	and	and	CCONJ
ejpam-4727	217	15	stationary	stationary	ADJ
ejpam-4727	217	16	walls	wall	NOUN
ejpam-4727	217	17	.	.	PUNCT
ejpam-4727	218	1	pramana	pramana	PROPN
ejpam-4727	218	2	,	,	PUNCT
ejpam-4727	218	3	96	96	NUM
ejpam-4727	218	4	,	,	PUNCT
ejpam-4727	218	5	2022	2022	NUM
ejpam-4727	218	6	.	.	PUNCT
ejpam-4727	219	1	references	reference	NOUN
ejpam-4727	219	2	974	974	NUM
ejpam-4727	220	1	[	[	SYM
ejpam-4727	220	2	19	19	NUM
ejpam-4727	220	3	]	]	PUNCT
ejpam-4727	220	4	a.	a.	NOUN
ejpam-4727	220	5	setia	setia	PROPN
ejpam-4727	220	6	,	,	PUNCT
ejpam-4727	220	7	y.	y.	PROPN
ejpam-4727	220	8	liu	liu	PROPN
ejpam-4727	220	9	,	,	PUNCT
ejpam-4727	220	10	and	and	CCONJ
ejpam-4727	220	11	a.	a.	PROPN
ejpam-4727	220	12	s.	s.	PROPN
ejpam-4727	220	13	vatsala	vatsala	PROPN
ejpam-4727	220	14	.	.	PUNCT
ejpam-4727	221	1	numerical	numerical	ADJ
ejpam-4727	221	2	solution	solution	NOUN
ejpam-4727	221	3	of	of	ADP
ejpam-4727	221	4	fractional	fractional	ADJ
ejpam-4727	221	5	integro	integro	ADJ
ejpam-4727	221	6	-	-	PUNCT
ejpam-4727	221	7	differential	differential	NOUN
ejpam-4727	221	8	equations	equation	NOUN
ejpam-4727	221	9	with	with	ADP
ejpam-4727	221	10	nonlocal	nonlocal	ADJ
ejpam-4727	221	11	boundary	boundary	ADJ
ejpam-4727	221	12	conditions	condition	NOUN
ejpam-4727	221	13	.	.	PUNCT
ejpam-4727	222	1	j.	j.	PROPN
ejpam-4727	222	2	frac	frac	PROPN
ejpam-4727	222	3	.	.	PROPN
ejpam-4727	223	1	cal	cal	PROPN
ejpam-4727	223	2	.	.	PUNCT
ejpam-4727	224	1	appl	appl	PROPN
ejpam-4727	224	2	.	.	PROPN
ejpam-4727	224	3	,	,	PUNCT
ejpam-4727	224	4	8:155–165	8:155–165	NUM
ejpam-4727	224	5	,	,	PUNCT
ejpam-4727	224	6	2014	2014	NUM
ejpam-4727	224	7	.	.	PUNCT
ejpam-4727	225	1	[	[	X
ejpam-4727	225	2	20	20	NUM
ejpam-4727	225	3	]	]	PUNCT
ejpam-4727	225	4	i.	i.	PROPN
ejpam-4727	225	5	singh	singh	PROPN
ejpam-4727	225	6	and	and	CCONJ
ejpam-4727	225	7	g.	g.	PROPN
ejpam-4727	225	8	singh	singh	PROPN
ejpam-4727	225	9	.	.	PUNCT
ejpam-4727	226	1	numerical	numerical	ADJ
ejpam-4727	226	2	solution	solution	NOUN
ejpam-4727	226	3	of	of	ADP
ejpam-4727	226	4	first	first	ADJ
ejpam-4727	226	5	order	order	NOUN
ejpam-4727	226	6	ordinary	ordinary	ADJ
ejpam-4727	226	7	diffential	diffential	ADJ
ejpam-4727	226	8	equations	equation	NOUN
ejpam-4727	226	9	.	.	PUNCT
ejpam-4727	227	1	int	int	NOUN
ejpam-4727	227	2	.	.	PUNCT
ejpam-4727	228	1	j.	j.	PROPN
ejpam-4727	228	2	sci	sci	PROPN
ejpam-4727	228	3	.	.	PUNCT
ejpam-4727	229	1	res	res	PROPN
ejpam-4727	229	2	.	.	PUNCT
ejpam-4727	230	1	rev	rev	PROPN
ejpam-4727	230	2	.	.	PROPN
ejpam-4727	230	3	,	,	PUNCT
ejpam-4727	230	4	8:593–602	8:593–602	NUM
ejpam-4727	230	5	,	,	PUNCT
ejpam-4727	230	6	2019	2019	NUM
ejpam-4727	230	7	.	.	PUNCT
ejpam-4727	231	1	[	[	X
ejpam-4727	231	2	21	21	NUM
ejpam-4727	231	3	]	]	X
ejpam-4727	231	4	s.	s.	PROPN
ejpam-4727	231	5	tapaswini	tapaswini	PROPN
ejpam-4727	231	6	and	and	CCONJ
ejpam-4727	231	7	s.	s.	PROPN
ejpam-4727	231	8	chakraverty	chakraverty	PROPN
ejpam-4727	231	9	.	.	PUNCT
ejpam-4727	232	1	a	a	DET
ejpam-4727	232	2	new	new	ADJ
ejpam-4727	232	3	approach	approach	NOUN
ejpam-4727	232	4	to	to	ADP
ejpam-4727	232	5	fuzzy	fuzzy	ADJ
ejpam-4727	232	6	initial	initial	ADJ
ejpam-4727	232	7	value	value	NOUN
ejpam-4727	232	8	problem	problem	NOUN
ejpam-4727	232	9	by	by	ADP
ejpam-4727	232	10	improved	improved	ADJ
ejpam-4727	232	11	euler	euler	NOUN
ejpam-4727	232	12	method	method	NOUN
ejpam-4727	232	13	.	.	PUNCT
ejpam-4727	233	1	fuzzy	fuzzy	ADJ
ejpam-4727	233	2	information	information	NOUN
ejpam-4727	233	3	and	and	CCONJ
ejpam-4727	233	4	engineering	engineering	NOUN
ejpam-4727	233	5	,	,	PUNCT
ejpam-4727	233	6	4:293–312	4:293–312	PROPN
ejpam-4727	233	7	,	,	PUNCT
ejpam-4727	233	8	2012	2012	NUM
ejpam-4727	233	9	.	.	PUNCT