id	sid	tid	token	lemma	pos
ejpam-3073	1	1	european	european	PROPN
ejpam-3073	1	2	journal	journal	PROPN
ejpam-3073	1	3	of	of	ADP
ejpam-3073	1	4	pure	pure	ADJ
ejpam-3073	1	5	and	and	CCONJ
ejpam-3073	1	6	applied	apply	VERB
ejpam-3073	1	7	mathematics	mathematic	NOUN
ejpam-3073	1	8	vol	vol	NOUN
ejpam-3073	1	9	.	.	PROPN
ejpam-3073	2	1	10	10	NUM
ejpam-3073	2	2	,	,	PUNCT
ejpam-3073	2	3	no	no	INTJ
ejpam-3073	2	4	.	.	NOUN
ejpam-3073	2	5	5	5	NUM
ejpam-3073	2	6	,	,	PUNCT
ejpam-3073	2	7	2017	2017	NUM
ejpam-3073	2	8	,	,	PUNCT
ejpam-3073	2	9	1092	1092	NUM
ejpam-3073	2	10	-	-	SYM
ejpam-3073	2	11	1098	1098	NUM
ejpam-3073	2	12	issn	issn	PROPN
ejpam-3073	2	13	1307	1307	NUM
ejpam-3073	2	14	-	-	SYM
ejpam-3073	2	15	5543	5543	NUM
ejpam-3073	2	16	–	–	PUNCT
ejpam-3073	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3073	2	18	published	publish	VERB
ejpam-3073	2	19	by	by	ADP
ejpam-3073	2	20	new	new	PROPN
ejpam-3073	2	21	york	york	PROPN
ejpam-3073	2	22	business	business	PROPN
ejpam-3073	2	23	global	global	PROPN
ejpam-3073	2	24	on	on	ADP
ejpam-3073	2	25	the	the	DET
ejpam-3073	2	26	error	error	NOUN
ejpam-3073	2	27	analysis	analysis	NOUN
ejpam-3073	2	28	of	of	ADP
ejpam-3073	2	29	a	a	DET
ejpam-3073	2	30	continuous	continuous	ADJ
ejpam-3073	2	31	implicit	implicit	ADJ
ejpam-3073	2	32	hybrid	hybrid	NOUN
ejpam-3073	2	33	one	one	NUM
ejpam-3073	2	34	step	step	NOUN
ejpam-3073	2	35	method	method	NOUN
ejpam-3073	2	36	t.	t.	PROPN
ejpam-3073	2	37	a.	a.	PROPN
ejpam-3073	2	38	anake1,∗	anake1,∗	PROPN
ejpam-3073	2	39	,	,	PUNCT
ejpam-3073	3	1	s.	s.	PROPN
ejpam-3073	3	2	o.	o.	PROPN
ejpam-3073	3	3	edeki1	edeki1	PROPN
ejpam-3073	4	1	1	1	NUM
ejpam-3073	4	2	department	department	NOUN
ejpam-3073	4	3	of	of	ADP
ejpam-3073	4	4	mathematics	mathematic	NOUN
ejpam-3073	4	5	,	,	PUNCT
ejpam-3073	4	6	covenant	covenant	ADJ
ejpam-3073	4	7	university	university	NOUN
ejpam-3073	4	8	,	,	PUNCT
ejpam-3073	4	9	canaanland	canaanland	PROPN
ejpam-3073	4	10	,	,	PUNCT
ejpam-3073	4	11	ota	ota	PROPN
ejpam-3073	4	12	,	,	PUNCT
ejpam-3073	4	13	nigeria	nigeria	PROPN
ejpam-3073	4	14	abstract	abstract	ADJ
ejpam-3073	4	15	.	.	PUNCT
ejpam-3073	5	1	it	it	PRON
ejpam-3073	5	2	is	be	AUX
ejpam-3073	5	3	a	a	DET
ejpam-3073	5	4	known	known	ADJ
ejpam-3073	5	5	fact	fact	NOUN
ejpam-3073	5	6	that	that	SCONJ
ejpam-3073	5	7	in	in	ADP
ejpam-3073	5	8	the	the	DET
ejpam-3073	5	9	application	application	NOUN
ejpam-3073	5	10	of	of	ADP
ejpam-3073	5	11	a	a	DET
ejpam-3073	5	12	continuous	continuous	ADJ
ejpam-3073	5	13	linear	linear	ADJ
ejpam-3073	5	14	multistep	multistep	ADJ
ejpam-3073	5	15	method	method	NOUN
ejpam-3073	5	16	,	,	PUNCT
ejpam-3073	5	17	the	the	DET
ejpam-3073	5	18	global	global	ADJ
ejpam-3073	5	19	error	error	NOUN
ejpam-3073	5	20	at	at	ADP
ejpam-3073	5	21	a	a	DET
ejpam-3073	5	22	particular	particular	ADJ
ejpam-3073	5	23	point	point	NOUN
ejpam-3073	5	24	is	be	AUX
ejpam-3073	5	25	influenced	influence	VERB
ejpam-3073	5	26	by	by	ADP
ejpam-3073	5	27	the	the	DET
ejpam-3073	5	28	accumulation	accumulation	NOUN
ejpam-3073	5	29	of	of	ADP
ejpam-3073	5	30	local	local	ADJ
ejpam-3073	5	31	truncation	truncation	NOUN
ejpam-3073	5	32	errors	error	NOUN
ejpam-3073	5	33	at	at	ADP
ejpam-3073	5	34	each	each	DET
ejpam-3073	5	35	step	step	NOUN
ejpam-3073	5	36	from	from	ADP
ejpam-3073	5	37	the	the	DET
ejpam-3073	5	38	initial	initial	ADJ
ejpam-3073	5	39	point	point	NOUN
ejpam-3073	5	40	and	and	CCONJ
ejpam-3073	5	41	thereby	thereby	ADV
ejpam-3073	5	42	reduces	reduce	VERB
ejpam-3073	5	43	the	the	DET
ejpam-3073	5	44	accuracy	accuracy	NOUN
ejpam-3073	5	45	of	of	ADP
ejpam-3073	5	46	the	the	DET
ejpam-3073	5	47	approximated	approximate	VERB
ejpam-3073	5	48	result	result	NOUN
ejpam-3073	5	49	.	.	PUNCT
ejpam-3073	6	1	hence	hence	ADV
ejpam-3073	6	2	,	,	PUNCT
ejpam-3073	6	3	by	by	ADP
ejpam-3073	6	4	controlling	control	VERB
ejpam-3073	6	5	the	the	DET
ejpam-3073	6	6	growth	growth	NOUN
ejpam-3073	6	7	of	of	ADP
ejpam-3073	6	8	local	local	ADJ
ejpam-3073	6	9	errors	error	NOUN
ejpam-3073	6	10	it	it	PRON
ejpam-3073	6	11	is	be	AUX
ejpam-3073	6	12	expected	expect	VERB
ejpam-3073	6	13	that	that	SCONJ
ejpam-3073	6	14	the	the	DET
ejpam-3073	6	15	accuracy	accuracy	NOUN
ejpam-3073	6	16	of	of	ADP
ejpam-3073	6	17	the	the	DET
ejpam-3073	6	18	approximations	approximation	NOUN
ejpam-3073	6	19	should	should	AUX
ejpam-3073	6	20	improve	improve	VERB
ejpam-3073	6	21	.	.	PUNCT
ejpam-3073	7	1	in	in	ADP
ejpam-3073	7	2	this	this	DET
ejpam-3073	7	3	paper	paper	NOUN
ejpam-3073	7	4	therefore	therefore	ADV
ejpam-3073	7	5	,	,	PUNCT
ejpam-3073	7	6	a	a	DET
ejpam-3073	7	7	method	method	NOUN
ejpam-3073	7	8	is	be	AUX
ejpam-3073	7	9	derived	derive	VERB
ejpam-3073	7	10	for	for	ADP
ejpam-3073	7	11	the	the	DET
ejpam-3073	7	12	bound	bind	VERB
ejpam-3073	7	13	on	on	ADP
ejpam-3073	7	14	the	the	DET
ejpam-3073	7	15	local	local	ADJ
ejpam-3073	7	16	truncation	truncation	NOUN
ejpam-3073	7	17	error	error	NOUN
ejpam-3073	7	18	of	of	ADP
ejpam-3073	7	19	continuous	continuous	ADJ
ejpam-3073	7	20	implicit	implicit	ADJ
ejpam-3073	7	21	hybrid	hybrid	NOUN
ejpam-3073	7	22	one	one	NUM
ejpam-3073	7	23	step	step	NOUN
ejpam-3073	7	24	method	method	NOUN
ejpam-3073	7	25	for	for	ADP
ejpam-3073	7	26	the	the	DET
ejpam-3073	7	27	solution	solution	NOUN
ejpam-3073	7	28	of	of	ADP
ejpam-3073	7	29	initial	initial	ADJ
ejpam-3073	7	30	value	value	NOUN
ejpam-3073	7	31	problems	problem	NOUN
ejpam-3073	7	32	of	of	ADP
ejpam-3073	7	33	second	second	ADJ
ejpam-3073	7	34	order	order	NOUN
ejpam-3073	7	35	ordinary	ordinary	ADJ
ejpam-3073	7	36	differential	differential	ADJ
ejpam-3073	7	37	equations	equation	NOUN
ejpam-3073	7	38	by	by	ADP
ejpam-3073	7	39	means	mean	NOUN
ejpam-3073	7	40	of	of	ADP
ejpam-3073	7	41	the	the	DET
ejpam-3073	7	42	generalized	generalize	VERB
ejpam-3073	7	43	lagrange	lagrange	NOUN
ejpam-3073	7	44	form	form	NOUN
ejpam-3073	7	45	of	of	ADP
ejpam-3073	7	46	the	the	DET
ejpam-3073	7	47	taylor	taylor	PROPN
ejpam-3073	7	48	’s	’s	PART
ejpam-3073	7	49	remainder	remainder	NOUN
ejpam-3073	7	50	and	and	CCONJ
ejpam-3073	7	51	the	the	DET
ejpam-3073	7	52	mean	mean	ADJ
ejpam-3073	7	53	value	value	NOUN
ejpam-3073	7	54	theorem	theorem	NOUN
ejpam-3073	7	55	.	.	PROPN
ejpam-3073	7	56	2010	2010	NUM
ejpam-3073	7	57	mathematics	mathematic	NOUN
ejpam-3073	7	58	subject	subject	NOUN
ejpam-3073	7	59	classifications	classification	NOUN
ejpam-3073	7	60	:	:	PUNCT
ejpam-3073	7	61	34k34	34k34	NUM
ejpam-3073	7	62	,	,	PUNCT
ejpam-3073	7	63	65l70	65l70	NUM
ejpam-3073	7	64	,	,	PUNCT
ejpam-3073	7	65	34a45	34a45	NUM
ejpam-3073	7	66	key	key	ADJ
ejpam-3073	7	67	words	word	NOUN
ejpam-3073	7	68	and	and	CCONJ
ejpam-3073	7	69	phrases	phrase	NOUN
ejpam-3073	7	70	:	:	PUNCT
ejpam-3073	7	71	truncation	truncation	NOUN
ejpam-3073	7	72	error	error	NOUN
ejpam-3073	7	73	,	,	PUNCT
ejpam-3073	7	74	global	global	ADJ
ejpam-3073	7	75	error	error	NOUN
ejpam-3073	7	76	,	,	PUNCT
ejpam-3073	7	77	mean	mean	ADJ
ejpam-3073	7	78	value	value	NOUN
ejpam-3073	7	79	theorem	theorem	NOUN
ejpam-3073	7	80	,	,	PUNCT
ejpam-3073	7	81	remainder	remainder	NOUN
ejpam-3073	7	82	theorem	theorem	NOUN
ejpam-3073	7	83	,	,	PUNCT
ejpam-3073	7	84	one	one	NUM
ejpam-3073	7	85	step	step	NOUN
ejpam-3073	7	86	method	method	NOUN
ejpam-3073	7	87	,	,	PUNCT
ejpam-3073	7	88	hybrid	hybrid	ADJ
ejpam-3073	7	89	multistep	multistep	ADJ
ejpam-3073	7	90	method	method	NOUN
ejpam-3073	7	91	1	1	NUM
ejpam-3073	7	92	.	.	PUNCT
ejpam-3073	7	93	introduction	introduction	NOUN
ejpam-3073	7	94	an	an	DET
ejpam-3073	7	95	important	important	ADJ
ejpam-3073	7	96	property	property	NOUN
ejpam-3073	7	97	associated	associate	VERB
ejpam-3073	7	98	with	with	ADP
ejpam-3073	7	99	the	the	DET
ejpam-3073	7	100	numerical	numerical	ADJ
ejpam-3073	7	101	solutions	solution	NOUN
ejpam-3073	7	102	of	of	ADP
ejpam-3073	7	103	the	the	DET
ejpam-3073	7	104	initial	initial	ADJ
ejpam-3073	7	105	value	value	NOUN
ejpam-3073	7	106	problems	problem	NOUN
ejpam-3073	7	107	of	of	ADP
ejpam-3073	7	108	ordinary	ordinary	ADJ
ejpam-3073	7	109	differential	differential	ADJ
ejpam-3073	7	110	equations	equation	NOUN
ejpam-3073	7	111	(	(	PUNCT
ejpam-3073	7	112	odes	ode	NOUN
ejpam-3073	7	113	)	)	PUNCT
ejpam-3073	7	114	,	,	PUNCT
ejpam-3073	7	115	is	be	AUX
ejpam-3073	7	116	the	the	DET
ejpam-3073	7	117	global	global	ADJ
ejpam-3073	7	118	error	error	NOUN
ejpam-3073	7	119	of	of	ADP
ejpam-3073	7	120	computation	computation	NOUN
ejpam-3073	7	121	.	.	PUNCT
ejpam-3073	8	1	the	the	DET
ejpam-3073	8	2	size	size	NOUN
ejpam-3073	8	3	of	of	ADP
ejpam-3073	8	4	this	this	DET
ejpam-3073	8	5	error	error	NOUN
ejpam-3073	8	6	on	on	ADP
ejpam-3073	8	7	the	the	DET
ejpam-3073	8	8	interval	interval	NOUN
ejpam-3073	8	9	of	of	ADP
ejpam-3073	8	10	interest	interest	NOUN
ejpam-3073	8	11	makes	make	VERB
ejpam-3073	8	12	the	the	DET
ejpam-3073	8	13	effort	effort	NOUN
ejpam-3073	8	14	put	put	VERB
ejpam-3073	8	15	into	into	ADP
ejpam-3073	8	16	developing	develop	VERB
ejpam-3073	8	17	the	the	DET
ejpam-3073	8	18	numerical	numerical	ADJ
ejpam-3073	8	19	method	method	NOUN
ejpam-3073	8	20	worthwhile	worthwhile	ADJ
ejpam-3073	8	21	or	or	CCONJ
ejpam-3073	8	22	futile	futile	ADJ
ejpam-3073	8	23	.	.	PUNCT
ejpam-3073	9	1	if	if	SCONJ
ejpam-3073	9	2	the	the	DET
ejpam-3073	9	3	global	global	ADJ
ejpam-3073	9	4	error	error	NOUN
ejpam-3073	9	5	is	be	AUX
ejpam-3073	9	6	small	small	ADJ
ejpam-3073	9	7	,	,	PUNCT
ejpam-3073	9	8	the	the	DET
ejpam-3073	9	9	numerical	numerical	ADJ
ejpam-3073	9	10	solution	solution	NOUN
ejpam-3073	9	11	is	be	AUX
ejpam-3073	9	12	considered	consider	VERB
ejpam-3073	9	13	to	to	PART
ejpam-3073	9	14	be	be	AUX
ejpam-3073	9	15	accurate	accurate	ADJ
ejpam-3073	9	16	,	,	PUNCT
ejpam-3073	9	17	and	and	CCONJ
ejpam-3073	9	18	other	other	ADJ
ejpam-3073	9	19	properties	property	NOUN
ejpam-3073	9	20	of	of	ADP
ejpam-3073	9	21	the	the	DET
ejpam-3073	9	22	solution	solution	NOUN
ejpam-3073	9	23	become	become	VERB
ejpam-3073	9	24	less	less	ADV
ejpam-3073	9	25	important	important	ADJ
ejpam-3073	9	26	.	.	PUNCT
ejpam-3073	10	1	the	the	DET
ejpam-3073	10	2	requirement	requirement	NOUN
ejpam-3073	10	3	of	of	ADP
ejpam-3073	10	4	a	a	DET
ejpam-3073	10	5	small	small	ADJ
ejpam-3073	10	6	global	global	ADJ
ejpam-3073	10	7	error	error	NOUN
ejpam-3073	10	8	will	will	AUX
ejpam-3073	10	9	guarantee	guarantee	VERB
ejpam-3073	10	10	that	that	SCONJ
ejpam-3073	10	11	the	the	DET
ejpam-3073	10	12	dynamics	dynamic	NOUN
ejpam-3073	10	13	of	of	ADP
ejpam-3073	10	14	the	the	DET
ejpam-3073	10	15	approximate	approximate	ADJ
ejpam-3073	10	16	solution	solution	NOUN
ejpam-3073	10	17	is	be	AUX
ejpam-3073	10	18	similar	similar	ADJ
ejpam-3073	10	19	to	to	ADP
ejpam-3073	10	20	that	that	PRON
ejpam-3073	10	21	of	of	ADP
ejpam-3073	10	22	the	the	DET
ejpam-3073	10	23	exact	exact	ADJ
ejpam-3073	10	24	solution	solution	NOUN
ejpam-3073	10	25	and	and	CCONJ
ejpam-3073	10	26	facilitate	facilitate	NOUN
ejpam-3073	10	27	step	step	NOUN
ejpam-3073	10	28	size	size	NOUN
ejpam-3073	10	29	control	control	NOUN
ejpam-3073	10	30	using	use	VERB
ejpam-3073	10	31	the	the	DET
ejpam-3073	10	32	global	global	ADJ
ejpam-3073	10	33	error	error	NOUN
ejpam-3073	10	34	estimate	estimate	NOUN
ejpam-3073	10	35	,	,	PUNCT
ejpam-3073	10	36	(	(	PUNCT
ejpam-3073	10	37	orel,2010	orel,2010	NOUN
ejpam-3073	10	38	)	)	PUNCT
ejpam-3073	10	39	.	.	PUNCT
ejpam-3073	11	1	the	the	DET
ejpam-3073	11	2	relationship	relationship	NOUN
ejpam-3073	11	3	between	between	ADP
ejpam-3073	11	4	the	the	DET
ejpam-3073	11	5	local	local	ADJ
ejpam-3073	11	6	and	and	CCONJ
ejpam-3073	11	7	the	the	DET
ejpam-3073	11	8	global	global	ADJ
ejpam-3073	11	9	errors	error	NOUN
ejpam-3073	11	10	and	and	CCONJ
ejpam-3073	11	11	possible	possible	ADJ
ejpam-3073	11	12	ways	way	NOUN
ejpam-3073	11	13	of	of	ADP
ejpam-3073	11	14	controlling	control	VERB
ejpam-3073	11	15	the	the	DET
ejpam-3073	11	16	global	global	ADJ
ejpam-3073	11	17	error	error	NOUN
ejpam-3073	11	18	directly	directly	ADV
ejpam-3073	11	19	has	have	AUX
ejpam-3073	11	20	attracted	attract	VERB
ejpam-3073	11	21	a	a	DET
ejpam-3073	11	22	lot	lot	NOUN
ejpam-3073	11	23	of	of	ADP
ejpam-3073	11	24	interest	interest	NOUN
ejpam-3073	11	25	.	.	PUNCT
ejpam-3073	12	1	a	a	DET
ejpam-3073	12	2	number	number	NOUN
ejpam-3073	12	3	of	of	ADP
ejpam-3073	12	4	researchers	researcher	NOUN
ejpam-3073	12	5	have	have	AUX
ejpam-3073	12	6	studied	study	VERB
ejpam-3073	12	7	this	this	DET
ejpam-3073	12	8	situation	situation	NOUN
ejpam-3073	12	9	for	for	ADP
ejpam-3073	12	10	different	different	ADJ
ejpam-3073	12	11	numerical	numerical	ADJ
ejpam-3073	12	12	methods	method	NOUN
ejpam-3073	12	13	;	;	PUNCT
ejpam-3073	12	14	for	for	ADP
ejpam-3073	12	15	instance	instance	NOUN
ejpam-3073	12	16	,	,	PUNCT
ejpam-3073	12	17	highhman(1993	highhman(1993	PRON
ejpam-3073	12	18	)	)	PUNCT
ejpam-3073	12	19	,	,	PUNCT
ejpam-3073	12	20	dormund	dormund	NOUN
ejpam-3073	12	21	et	et	NOUN
ejpam-3073	12	22	al.(1994	al.(1994	PROPN
ejpam-3073	12	23	)	)	PUNCT
ejpam-3073	12	24	,	,	PUNCT
ejpam-3073	12	25	calvo	calvo	PROPN
ejpam-3073	12	26	et	et	NOUN
ejpam-3073	12	27	al.(1996	al.(1996	PROPN
ejpam-3073	12	28	)	)	PUNCT
ejpam-3073	12	29	and	and	CCONJ
ejpam-3073	12	30	stuart(1997	stuart(1997	NOUN
ejpam-3073	12	31	)	)	PUNCT
ejpam-3073	12	32	all	all	PRON
ejpam-3073	12	33	studied	study	VERB
ejpam-3073	12	34	the	the	DET
ejpam-3073	12	35	connection	connection	NOUN
ejpam-3073	12	36	between	between	ADP
ejpam-3073	12	37	local	local	ADJ
ejpam-3073	12	38	truncation	truncation	NOUN
ejpam-3073	12	39	error	error	NOUN
ejpam-3073	12	40	and	and	CCONJ
ejpam-3073	12	41	global	global	ADJ
ejpam-3073	12	42	error	error	NOUN
ejpam-3073	12	43	for	for	ADP
ejpam-3073	12	44	runge	runge	NOUN
ejpam-3073	12	45	-	-	PUNCT
ejpam-3073	12	46	kutta	kutta	NOUN
ejpam-3073	12	47	methods	method	NOUN
ejpam-3073	12	48	while	while	SCONJ
ejpam-3073	12	49	lambert(1979	lambert(1979	NOUN
ejpam-3073	12	50	)	)	PUNCT
ejpam-3073	12	51	,	,	PUNCT
ejpam-3073	12	52	∗corresponding	∗corresponde	VERB
ejpam-3073	12	53	author	author	NOUN
ejpam-3073	12	54	.	.	PUNCT
ejpam-3073	13	1	email	email	NOUN
ejpam-3073	13	2	addresses	address	NOUN
ejpam-3073	13	3	:	:	PUNCT
ejpam-3073	13	4	timothy.anake@covenantuniversity.edu.ng	timothy.anake@covenantuniversity.edu.ng	INTJ
ejpam-3073	13	5	(	(	PUNCT
ejpam-3073	13	6	t.	t.	NOUN
ejpam-3073	13	7	a.	a.	PROPN
ejpam-3073	13	8	anake	anake	PROPN
ejpam-3073	13	9	)	)	PUNCT
ejpam-3073	13	10	,	,	PUNCT
ejpam-3073	13	11	soedeki@yahoo.com	soedeki@yahoo.com	X
ejpam-3073	13	12	(	(	PUNCT
ejpam-3073	13	13	s.	s.	PROPN
ejpam-3073	13	14	o.	o.	PROPN
ejpam-3073	13	15	edeki	edeki	PROPN
ejpam-3073	13	16	)	)	PUNCT
ejpam-3073	13	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3073	13	18	1092	1092	NUM
ejpam-3073	14	1	c	c	X
ejpam-3073	14	2	©	©	PROPN
ejpam-3073	14	3	2017	2017	NUM
ejpam-3073	14	4	ejpam	ejpam	VERB
ejpam-3073	14	5	all	all	DET
ejpam-3073	14	6	rights	right	NOUN
ejpam-3073	14	7	reserved	reserve	VERB
ejpam-3073	14	8	.	.	PUNCT
ejpam-3073	15	1	t.	t.	PROPN
ejpam-3073	15	2	a.	a.	PROPN
ejpam-3073	15	3	anake	anake	PROPN
ejpam-3073	15	4	,	,	PUNCT
ejpam-3073	15	5	s.	s.	PROPN
ejpam-3073	15	6	o.	o.	PROPN
ejpam-3073	15	7	edeki	edeki	PROPN
ejpam-3073	15	8	/	/	SYM
ejpam-3073	15	9	eur	eur	PROPN
ejpam-3073	15	10	.	.	PUNCT
ejpam-3073	16	1	j.	j.	PROPN
ejpam-3073	16	2	pure	pure	PROPN
ejpam-3073	16	3	appl	appl	PROPN
ejpam-3073	16	4	.	.	PROPN
ejpam-3073	16	5	math	math	PROPN
ejpam-3073	16	6	,	,	PUNCT
ejpam-3073	16	7	10	10	NUM
ejpam-3073	16	8	(	(	PUNCT
ejpam-3073	16	9	5	5	NUM
ejpam-3073	16	10	)	)	PUNCT
ejpam-3073	16	11	(	(	PUNCT
ejpam-3073	16	12	2017	2017	NUM
ejpam-3073	16	13	)	)	PUNCT
ejpam-3073	16	14	,	,	PUNCT
ejpam-3073	16	15	1092	1092	NUM
ejpam-3073	16	16	-	-	SYM
ejpam-3073	16	17	1098	1098	NUM
ejpam-3073	16	18	1093	1093	NUM
ejpam-3073	16	19	onumayi	onumayi	PROPN
ejpam-3073	16	20	et	et	PROPN
ejpam-3073	16	21	al.(1999	al.(1999	PROPN
ejpam-3073	16	22	)	)	PUNCT
ejpam-3073	16	23	as	as	ADV
ejpam-3073	16	24	well	well	ADV
ejpam-3073	16	25	as	as	ADP
ejpam-3073	16	26	kulikov	kulikov	NOUN
ejpam-3073	16	27	and	and	CCONJ
ejpam-3073	16	28	shindin(2004	shindin(2004	NOUN
ejpam-3073	16	29	)	)	PUNCT
ejpam-3073	16	30	were	be	AUX
ejpam-3073	16	31	concerned	concern	VERB
ejpam-3073	16	32	with	with	ADP
ejpam-3073	16	33	estimates	estimate	NOUN
ejpam-3073	16	34	of	of	ADP
ejpam-3073	16	35	these	these	DET
ejpam-3073	16	36	errors	error	NOUN
ejpam-3073	16	37	for	for	ADP
ejpam-3073	16	38	multistep	multistep	ADJ
ejpam-3073	16	39	methods	method	NOUN
ejpam-3073	16	40	.	.	PUNCT
ejpam-3073	17	1	it	it	PRON
ejpam-3073	17	2	is	be	AUX
ejpam-3073	17	3	a	a	DET
ejpam-3073	17	4	well	well	ADV
ejpam-3073	17	5	known	know	VERB
ejpam-3073	17	6	that	that	SCONJ
ejpam-3073	17	7	in	in	ADP
ejpam-3073	17	8	the	the	DET
ejpam-3073	17	9	application	application	NOUN
ejpam-3073	17	10	of	of	ADP
ejpam-3073	17	11	a	a	DET
ejpam-3073	17	12	linear	linear	ADJ
ejpam-3073	17	13	multistep	multistep	ADJ
ejpam-3073	17	14	method	method	NOUN
ejpam-3073	17	15	at	at	ADP
ejpam-3073	17	16	any	any	DET
ejpam-3073	17	17	given	give	VERB
ejpam-3073	17	18	point	point	NOUN
ejpam-3073	17	19	,	,	PUNCT
ejpam-3073	17	20	say	say	VERB
ejpam-3073	17	21	xi	xi	PROPN
ejpam-3073	17	22	,	,	PUNCT
ejpam-3073	17	23	the	the	DET
ejpam-3073	17	24	global	global	ADJ
ejpam-3073	17	25	error	error	NOUN
ejpam-3073	17	26	would	would	AUX
ejpam-3073	17	27	usually	usually	ADV
ejpam-3073	17	28	be	be	AUX
ejpam-3073	17	29	an	an	DET
ejpam-3073	17	30	accumulation	accumulation	NOUN
ejpam-3073	17	31	of	of	ADP
ejpam-3073	17	32	the	the	DET
ejpam-3073	17	33	local	local	ADJ
ejpam-3073	17	34	errors	error	NOUN
ejpam-3073	17	35	committed	commit	VERB
ejpam-3073	17	36	at	at	ADP
ejpam-3073	17	37	each	each	DET
ejpam-3073	17	38	step	step	NOUN
ejpam-3073	17	39	from	from	ADP
ejpam-3073	17	40	the	the	DET
ejpam-3073	17	41	initial	initial	ADJ
ejpam-3073	17	42	point	point	NOUN
ejpam-3073	17	43	up	up	ADP
ejpam-3073	17	44	to	to	ADP
ejpam-3073	17	45	the	the	DET
ejpam-3073	17	46	reference	reference	NOUN
ejpam-3073	17	47	point	point	NOUN
ejpam-3073	17	48	.	.	PUNCT
ejpam-3073	18	1	this	this	PRON
ejpam-3073	18	2	is	be	AUX
ejpam-3073	18	3	usually	usually	ADV
ejpam-3073	18	4	a	a	DET
ejpam-3073	18	5	function	function	NOUN
ejpam-3073	18	6	of	of	ADP
ejpam-3073	18	7	the	the	DET
ejpam-3073	18	8	problem	problem	NOUN
ejpam-3073	18	9	to	to	PART
ejpam-3073	18	10	be	be	AUX
ejpam-3073	18	11	solved	solve	VERB
ejpam-3073	18	12	,	,	PUNCT
ejpam-3073	18	13	the	the	DET
ejpam-3073	18	14	numerical	numerical	ADJ
ejpam-3073	18	15	method	method	NOUN
ejpam-3073	18	16	adopted	adopt	VERB
ejpam-3073	18	17	and	and	CCONJ
ejpam-3073	18	18	step	step	NOUN
ejpam-3073	18	19	size	size	NOUN
ejpam-3073	18	20	selected	select	VERB
ejpam-3073	18	21	,	,	PUNCT
ejpam-3073	18	22	(	(	PUNCT
ejpam-3073	18	23	orel,2010	orel,2010	NOUN
ejpam-3073	18	24	)	)	PUNCT
ejpam-3073	18	25	.	.	PUNCT
ejpam-3073	19	1	however	however	ADV
ejpam-3073	19	2	,	,	PUNCT
ejpam-3073	19	3	while	while	SCONJ
ejpam-3073	19	4	it	it	PRON
ejpam-3073	19	5	may	may	AUX
ejpam-3073	19	6	be	be	AUX
ejpam-3073	19	7	possible	possible	ADJ
ejpam-3073	19	8	to	to	PART
ejpam-3073	19	9	control	control	VERB
ejpam-3073	19	10	the	the	DET
ejpam-3073	19	11	local	local	ADJ
ejpam-3073	19	12	errors	error	NOUN
ejpam-3073	19	13	and	and	CCONJ
ejpam-3073	19	14	step	step	NOUN
ejpam-3073	19	15	size	size	NOUN
ejpam-3073	19	16	during	during	ADP
ejpam-3073	19	17	the	the	DET
ejpam-3073	19	18	implementation	implementation	NOUN
ejpam-3073	19	19	of	of	ADP
ejpam-3073	19	20	the	the	DET
ejpam-3073	19	21	linear	linear	ADJ
ejpam-3073	19	22	multistep	multistep	ADJ
ejpam-3073	19	23	method	method	NOUN
ejpam-3073	19	24	,	,	PUNCT
ejpam-3073	19	25	it	it	PRON
ejpam-3073	19	26	may	may	AUX
ejpam-3073	19	27	not	not	PART
ejpam-3073	19	28	be	be	AUX
ejpam-3073	19	29	possible	possible	ADJ
ejpam-3073	19	30	to	to	PART
ejpam-3073	19	31	do	do	VERB
ejpam-3073	19	32	the	the	DET
ejpam-3073	19	33	same	same	ADJ
ejpam-3073	19	34	for	for	ADP
ejpam-3073	19	35	the	the	DET
ejpam-3073	19	36	global	global	ADJ
ejpam-3073	19	37	error	error	NOUN
ejpam-3073	19	38	directly	directly	ADV
ejpam-3073	19	39	.	.	PUNCT
ejpam-3073	20	1	the	the	DET
ejpam-3073	20	2	aim	aim	NOUN
ejpam-3073	20	3	of	of	ADP
ejpam-3073	20	4	this	this	DET
ejpam-3073	20	5	paper	paper	NOUN
ejpam-3073	20	6	is	be	AUX
ejpam-3073	20	7	to	to	PART
ejpam-3073	20	8	derive	derive	VERB
ejpam-3073	20	9	a	a	DET
ejpam-3073	20	10	method	method	NOUN
ejpam-3073	20	11	for	for	ADP
ejpam-3073	20	12	a	a	DET
ejpam-3073	20	13	bound	bind	VERB
ejpam-3073	20	14	on	on	ADP
ejpam-3073	20	15	the	the	DET
ejpam-3073	20	16	local	local	ADJ
ejpam-3073	20	17	truncation	truncation	NOUN
ejpam-3073	20	18	error	error	NOUN
ejpam-3073	20	19	,	,	PUNCT
ejpam-3073	20	20	at	at	ADP
ejpam-3073	20	21	each	each	DET
ejpam-3073	20	22	step	step	NOUN
ejpam-3073	20	23	of	of	ADP
ejpam-3073	20	24	application	application	NOUN
ejpam-3073	20	25	,	,	PUNCT
ejpam-3073	20	26	of	of	ADP
ejpam-3073	20	27	a	a	DET
ejpam-3073	20	28	continuous	continuous	ADJ
ejpam-3073	20	29	implicit	implicit	ADJ
ejpam-3073	20	30	hybrid	hybrid	NOUN
ejpam-3073	20	31	one	one	NUM
ejpam-3073	20	32	step	step	NOUN
ejpam-3073	20	33	method(cihosm	method(cihosm	NOUN
ejpam-3073	20	34	)	)	PUNCT
ejpam-3073	20	35	as	as	ADP
ejpam-3073	20	36	a	a	DET
ejpam-3073	20	37	means	means	NOUN
ejpam-3073	20	38	of	of	ADP
ejpam-3073	20	39	managing	manage	VERB
ejpam-3073	20	40	the	the	DET
ejpam-3073	20	41	magnitude	magnitude	NOUN
ejpam-3073	20	42	of	of	ADP
ejpam-3073	20	43	the	the	DET
ejpam-3073	20	44	global	global	ADJ
ejpam-3073	20	45	error	error	NOUN
ejpam-3073	20	46	of	of	ADP
ejpam-3073	20	47	computation	computation	NOUN
ejpam-3073	20	48	.	.	PUNCT
ejpam-3073	21	1	the	the	DET
ejpam-3073	21	2	result	result	NOUN
ejpam-3073	21	3	presented	present	VERB
ejpam-3073	21	4	in	in	ADP
ejpam-3073	21	5	this	this	DET
ejpam-3073	21	6	paper	paper	NOUN
ejpam-3073	21	7	,	,	PUNCT
ejpam-3073	21	8	extends	extend	VERB
ejpam-3073	21	9	an	an	DET
ejpam-3073	21	10	earlier	early	ADJ
ejpam-3073	21	11	result	result	NOUN
ejpam-3073	21	12	by	by	ADP
ejpam-3073	21	13	lambert(1979	lambert(1979	NOUN
ejpam-3073	21	14	)	)	PUNCT
ejpam-3073	21	15	for	for	ADP
ejpam-3073	21	16	special	special	ADJ
ejpam-3073	21	17	second	second	ADJ
ejpam-3073	21	18	order	order	NOUN
ejpam-3073	21	19	initial	initial	ADJ
ejpam-3073	21	20	value	value	NOUN
ejpam-3073	21	21	problems	problem	NOUN
ejpam-3073	21	22	to	to	ADP
ejpam-3073	21	23	the	the	DET
ejpam-3073	21	24	general	general	ADJ
ejpam-3073	21	25	case	case	NOUN
ejpam-3073	21	26	.	.	PUNCT
ejpam-3073	22	1	the	the	DET
ejpam-3073	22	2	paper	paper	NOUN
ejpam-3073	22	3	is	be	AUX
ejpam-3073	22	4	organized	organize	VERB
ejpam-3073	22	5	as	as	SCONJ
ejpam-3073	22	6	follows	follow	VERB
ejpam-3073	22	7	:	:	PUNCT
ejpam-3073	22	8	in	in	ADP
ejpam-3073	22	9	section	section	NOUN
ejpam-3073	22	10	2	2	NUM
ejpam-3073	22	11	the	the	DET
ejpam-3073	22	12	cihosm	cihosm	NOUN
ejpam-3073	22	13	is	be	AUX
ejpam-3073	22	14	introduced	introduce	VERB
ejpam-3073	22	15	.	.	PUNCT
ejpam-3073	23	1	the	the	DET
ejpam-3073	23	2	main	main	ADJ
ejpam-3073	23	3	result	result	NOUN
ejpam-3073	23	4	is	be	AUX
ejpam-3073	23	5	presented	present	VERB
ejpam-3073	23	6	in	in	ADP
ejpam-3073	23	7	section	section	NOUN
ejpam-3073	23	8	3	3	NUM
ejpam-3073	23	9	.	.	PUNCT
ejpam-3073	24	1	the	the	DET
ejpam-3073	24	2	error	error	NOUN
ejpam-3073	24	3	bound	bind	VERB
ejpam-3073	24	4	method	method	NOUN
ejpam-3073	24	5	derived	derive	VERB
ejpam-3073	24	6	in	in	ADP
ejpam-3073	24	7	section	section	NOUN
ejpam-3073	24	8	3	3	NUM
ejpam-3073	24	9	is	be	AUX
ejpam-3073	24	10	applied	apply	VERB
ejpam-3073	24	11	on	on	ADP
ejpam-3073	24	12	the	the	DET
ejpam-3073	24	13	cihosm	cihosm	NOUN
ejpam-3073	24	14	proposed	propose	VERB
ejpam-3073	24	15	in	in	ADP
ejpam-3073	24	16	anake	anake	NOUN
ejpam-3073	24	17	and	and	CCONJ
ejpam-3073	24	18	adoghe(2013	adoghe(2013	NUM
ejpam-3073	24	19	)	)	PUNCT
ejpam-3073	24	20	for	for	ADP
ejpam-3073	24	21	the	the	DET
ejpam-3073	24	22	solution	solution	NOUN
ejpam-3073	24	23	of	of	ADP
ejpam-3073	24	24	a	a	DET
ejpam-3073	24	25	simple	simple	ADJ
ejpam-3073	24	26	electric	electric	ADJ
ejpam-3073	24	27	circuit	circuit	NOUN
ejpam-3073	24	28	problem	problem	NOUN
ejpam-3073	24	29	using	use	VERB
ejpam-3073	24	30	different	different	ADJ
ejpam-3073	24	31	step	step	NOUN
ejpam-3073	24	32	sizes	size	NOUN
ejpam-3073	24	33	in	in	ADP
ejpam-3073	24	34	section	section	NOUN
ejpam-3073	24	35	4	4	NUM
ejpam-3073	24	36	.	.	PUNCT
ejpam-3073	25	1	finally	finally	ADV
ejpam-3073	25	2	in	in	ADP
ejpam-3073	25	3	section	section	NOUN
ejpam-3073	25	4	5	5	NUM
ejpam-3073	25	5	,	,	PUNCT
ejpam-3073	25	6	conclusions	conclusion	NOUN
ejpam-3073	25	7	are	be	AUX
ejpam-3073	25	8	presented	present	VERB
ejpam-3073	25	9	.	.	PUNCT
ejpam-3073	26	1	2	2	X
ejpam-3073	26	2	.	.	X
ejpam-3073	26	3	the	the	DET
ejpam-3073	26	4	continuous	continuous	ADJ
ejpam-3073	26	5	implicit	implicit	ADJ
ejpam-3073	26	6	hybrid	hybrid	NOUN
ejpam-3073	26	7	one	one	NUM
ejpam-3073	26	8	step	step	NOUN
ejpam-3073	26	9	method	method	NOUN
ejpam-3073	26	10	consider	consider	VERB
ejpam-3073	26	11	the	the	DET
ejpam-3073	26	12	general	general	ADJ
ejpam-3073	26	13	form	form	NOUN
ejpam-3073	26	14	of	of	ADP
ejpam-3073	26	15	the	the	DET
ejpam-3073	26	16	continuous	continuous	ADJ
ejpam-3073	26	17	implicit	implicit	ADJ
ejpam-3073	26	18	hybrid	hybrid	NOUN
ejpam-3073	26	19	one	one	NUM
ejpam-3073	26	20	step	step	NOUN
ejpam-3073	26	21	method	method	NOUN
ejpam-3073	26	22	proposed	propose	VERB
ejpam-3073	26	23	by	by	ADP
ejpam-3073	26	24	anake	anake	NOUN
ejpam-3073	26	25	and	and	CCONJ
ejpam-3073	26	26	adoghe(2013	adoghe(2013	NUM
ejpam-3073	26	27	):	):	PUNCT
ejpam-3073	26	28	y(x	y(x	NOUN
ejpam-3073	26	29	)	)	PUNCT
ejpam-3073	26	30	=	=	PUNCT
ejpam-3073	27	1	∑	∑	PUNCT
ejpam-3073	27	2	j′=r−1,r	j′=r−1,r	VERB
ejpam-3073	27	3	ανj′	ανj′	NOUN
ejpam-3073	27	4	(	(	PUNCT
ejpam-3073	27	5	t)yn+νj′	t)yn+νj′	NOUN
ejpam-3073	27	6	+	+	CCONJ
ejpam-3073	27	7	h2	h2	PROPN
ejpam-3073	27	8			PROPN
ejpam-3073	27	9	1∑	1∑	PROPN
ejpam-3073	27	10	j=0	j=0	PROPN
ejpam-3073	27	11	βj(t)fn+j	βj(t)fn+j	PROPN
ejpam-3073	27	12	+	+	CCONJ
ejpam-3073	27	13	r∑	r∑	NOUN
ejpam-3073	27	14	j′=1	j′=1	PROPN
ejpam-3073	27	15	βνj′	βνj′	NOUN
ejpam-3073	27	16	(	(	PUNCT
ejpam-3073	27	17	t)fn+νj′	t)fn+νj′	NOUN
ejpam-3073	27	18			NOUN
ejpam-3073	27	19	,	,	PUNCT
ejpam-3073	27	20	(	(	PUNCT
ejpam-3073	27	21	1	1	X
ejpam-3073	27	22	)	)	PUNCT
ejpam-3073	27	23	where	where	SCONJ
ejpam-3073	27	24	αν′j	αν′j	ADJ
ejpam-3073	27	25	βν′j	βν′j	VERB
ejpam-3073	27	26	and	and	CCONJ
ejpam-3073	27	27	βj	βj	PRON
ejpam-3073	27	28	are	be	AUX
ejpam-3073	27	29	continuous	continuous	ADJ
ejpam-3073	27	30	in	in	ADP
ejpam-3073	27	31	t	t	PROPN
ejpam-3073	27	32	∈	∈	PROPN
ejpam-3073	27	33	;	;	PUNCT
ejpam-3073	27	34	yn+j	yn+j	PROPN
ejpam-3073	27	35	is	be	AUX
ejpam-3073	27	36	the	the	DET
ejpam-3073	27	37	numerical	numerical	ADJ
ejpam-3073	27	38	approximation	approximation	NOUN
ejpam-3073	27	39	of	of	ADP
ejpam-3073	27	40	the	the	DET
ejpam-3073	27	41	exact	exact	ADJ
ejpam-3073	27	42	solution	solution	NOUN
ejpam-3073	27	43	at	at	ADP
ejpam-3073	27	44	the	the	DET
ejpam-3073	27	45	grid	grid	NOUN
ejpam-3073	27	46	point	point	NOUN
ejpam-3073	27	47	xn+j	xn+j	PROPN
ejpam-3073	27	48	,	,	PUNCT
ejpam-3073	27	49	and	and	CCONJ
ejpam-3073	27	50	fn+j	fn+j	PROPN
ejpam-3073	27	51	=	=	SYM
ejpam-3073	27	52	f(xn+j	f(xn+j	PROPN
ejpam-3073	27	53	,	,	PUNCT
ejpam-3073	27	54	yn+j	yn+j	PROPN
ejpam-3073	27	55	,	,	PUNCT
ejpam-3073	27	56	y	y	PROPN
ejpam-3073	27	57	′	′	NUM
ejpam-3073	27	58	n+j	n+j	PROPN
ejpam-3073	27	59	)	)	PUNCT
ejpam-3073	27	60	.	.	PUNCT
ejpam-3073	28	1	the	the	DET
ejpam-3073	28	2	subscript	subscript	NOUN
ejpam-3073	28	3	,	,	PUNCT
ejpam-3073	28	4	νj′	νj′	PROPN
ejpam-3073	28	5	∈	∈	PROPN
ejpam-3073	28	6	(	(	PUNCT
ejpam-3073	28	7	0	0	NUM
ejpam-3073	28	8	,	,	PUNCT
ejpam-3073	28	9	1	1	NUM
ejpam-3073	28	10	)	)	PUNCT
ejpam-3073	28	11	,	,	PUNCT
ejpam-3073	28	12	∀	∀	PUNCT
ejpam-3073	28	13	j′	j′	X
ejpam-3073	28	14	is	be	AUX
ejpam-3073	28	15	a	a	DET
ejpam-3073	28	16	rational	rational	ADJ
ejpam-3073	28	17	number	number	NOUN
ejpam-3073	28	18	representing	represent	VERB
ejpam-3073	28	19	the	the	DET
ejpam-3073	28	20	j′th	j′th	NOUN
ejpam-3073	28	21	off	off	ADP
ejpam-3073	28	22	-	-	PUNCT
ejpam-3073	28	23	grid	grid	NOUN
ejpam-3073	28	24	point	point	NOUN
ejpam-3073	28	25	.	.	PUNCT
ejpam-3073	29	1	we	we	PRON
ejpam-3073	29	2	note	note	VERB
ejpam-3073	29	3	that	that	SCONJ
ejpam-3073	29	4	by	by	ADP
ejpam-3073	29	5	using	use	VERB
ejpam-3073	29	6	off	off	ADP
ejpam-3073	29	7	-	-	PUNCT
ejpam-3073	29	8	grid	grid	NOUN
ejpam-3073	29	9	points	point	NOUN
ejpam-3073	29	10	,	,	PUNCT
ejpam-3073	29	11	the	the	DET
ejpam-3073	29	12	method	method	NOUN
ejpam-3073	29	13	mimics	mimic	VERB
ejpam-3073	29	14	a	a	DET
ejpam-3073	29	15	continuous	continuous	ADJ
ejpam-3073	29	16	implicit	implicit	ADJ
ejpam-3073	29	17	multistep	multistep	ADJ
ejpam-3073	29	18	method	method	NOUN
ejpam-3073	29	19	and	and	CCONJ
ejpam-3073	29	20	solves	solve	VERB
ejpam-3073	29	21	directly	directly	ADV
ejpam-3073	29	22	ordinary	ordinary	ADJ
ejpam-3073	29	23	differential	differential	ADJ
ejpam-3073	29	24	equations	equation	NOUN
ejpam-3073	29	25	of	of	ADP
ejpam-3073	29	26	the	the	DET
ejpam-3073	29	27	form:	form:	PROPN
ejpam-3073	29	28	y′′	y′′	PROPN
ejpam-3073	30	1	=	=	SYM
ejpam-3073	30	2	f(x	f(x	PROPN
ejpam-3073	30	3	,	,	PUNCT
ejpam-3073	30	4	y	y	PROPN
ejpam-3073	30	5	,	,	PUNCT
ejpam-3073	30	6	y′	y′	NUM
ejpam-3073	30	7	)	)	PUNCT
ejpam-3073	30	8	y(a	y(a	X
ejpam-3073	30	9	)	)	PUNCT
ejpam-3073	30	10	=	=	SYM
ejpam-3073	30	11	η0	η0	NOUN
ejpam-3073	30	12	,	,	PUNCT
ejpam-3073	30	13	y′(a	y′(a	NUM
ejpam-3073	30	14	)	)	PUNCT
ejpam-3073	30	15	=	=	NOUN
ejpam-3073	30	16	η1	η1	NOUN
ejpam-3073	30	17	(	(	PUNCT
ejpam-3073	30	18	2	2	NUM
ejpam-3073	30	19	)	)	PUNCT
ejpam-3073	30	20	where	where	SCONJ
ejpam-3073	30	21	x	x	SYM
ejpam-3073	30	22	∈	∈	PROPN
ejpam-3073	31	1	[	[	X
ejpam-3073	31	2	a	a	X
ejpam-3073	31	3	,	,	PUNCT
ejpam-3073	31	4	b	b	NOUN
ejpam-3073	31	5	]	]	X
ejpam-3073	31	6	,	,	PUNCT
ejpam-3073	31	7	a	a	PRON
ejpam-3073	31	8	,	,	PUNCT
ejpam-3073	31	9	b	b	PROPN
ejpam-3073	31	10	∈	∈	PROPN
ejpam-3073	31	11	and	and	CCONJ
ejpam-3073	31	12	f	f	PROPN
ejpam-3073	31	13	is	be	AUX
ejpam-3073	31	14	continuously	continuously	ADV
ejpam-3073	31	15	differentiable	differentiable	ADJ
ejpam-3073	31	16	with	with	ADP
ejpam-3073	31	17	respect	respect	NOUN
ejpam-3073	31	18	to	to	ADP
ejpam-3073	31	19	its	its	PRON
ejpam-3073	31	20	arguments	argument	NOUN
ejpam-3073	31	21	.	.	PUNCT
ejpam-3073	32	1	ordinary	ordinary	ADJ
ejpam-3073	32	2	differential	differential	ADJ
ejpam-3073	32	3	equations	equation	NOUN
ejpam-3073	32	4	such	such	ADJ
ejpam-3073	32	5	as	as	ADP
ejpam-3073	32	6	(	(	PUNCT
ejpam-3073	32	7	2	2	NUM
ejpam-3073	32	8	)	)	PUNCT
ejpam-3073	32	9	are	be	AUX
ejpam-3073	32	10	important	important	ADJ
ejpam-3073	32	11	in	in	ADP
ejpam-3073	32	12	many	many	ADJ
ejpam-3073	32	13	application	application	NOUN
ejpam-3073	32	14	areas	area	NOUN
ejpam-3073	32	15	(	(	PUNCT
ejpam-3073	32	16	see	see	VERB
ejpam-3073	32	17	,	,	PUNCT
ejpam-3073	32	18	chapra	chapra	NOUN
ejpam-3073	32	19	and	and	CCONJ
ejpam-3073	32	20	canale(2010	canale(2010	NOUN
ejpam-3073	32	21	)	)	PUNCT
ejpam-3073	32	22	,	,	PUNCT
ejpam-3073	32	23	anake(2011	anake(2011	NOUN
ejpam-3073	32	24	)	)	PUNCT
ejpam-3073	32	25	)	)	PUNCT
ejpam-3073	32	26	.	.	PUNCT
ejpam-3073	33	1	the	the	DET
ejpam-3073	33	2	following	follow	VERB
ejpam-3073	33	3	definition	definition	NOUN
ejpam-3073	33	4	and	and	CCONJ
ejpam-3073	33	5	theorem	theorem	NOUN
ejpam-3073	33	6	are	be	AUX
ejpam-3073	33	7	useful	useful	ADJ
ejpam-3073	33	8	results	result	NOUN
ejpam-3073	33	9	needed	need	VERB
ejpam-3073	33	10	for	for	ADP
ejpam-3073	33	11	the	the	DET
ejpam-3073	33	12	derivation	derivation	NOUN
ejpam-3073	33	13	in	in	ADP
ejpam-3073	33	14	the	the	DET
ejpam-3073	33	15	next	next	ADJ
ejpam-3073	33	16	section	section	NOUN
ejpam-3073	33	17	.	.	PUNCT
ejpam-3073	34	1	t.	t.	PROPN
ejpam-3073	34	2	a.	a.	PROPN
ejpam-3073	34	3	anake	anake	PROPN
ejpam-3073	34	4	,	,	PUNCT
ejpam-3073	34	5	s.	s.	PROPN
ejpam-3073	34	6	o.	o.	PROPN
ejpam-3073	34	7	edeki	edeki	PROPN
ejpam-3073	34	8	/	/	SYM
ejpam-3073	34	9	eur	eur	PROPN
ejpam-3073	34	10	.	.	PUNCT
ejpam-3073	35	1	j.	j.	PROPN
ejpam-3073	35	2	pure	pure	PROPN
ejpam-3073	35	3	appl	appl	PROPN
ejpam-3073	35	4	.	.	PROPN
ejpam-3073	35	5	math	math	PROPN
ejpam-3073	35	6	,	,	PUNCT
ejpam-3073	35	7	10	10	NUM
ejpam-3073	35	8	(	(	PUNCT
ejpam-3073	35	9	5	5	NUM
ejpam-3073	35	10	)	)	PUNCT
ejpam-3073	35	11	(	(	PUNCT
ejpam-3073	35	12	2017	2017	NUM
ejpam-3073	35	13	)	)	PUNCT
ejpam-3073	35	14	,	,	PUNCT
ejpam-3073	35	15	1092	1092	NUM
ejpam-3073	35	16	-	-	SYM
ejpam-3073	35	17	1098	1098	NUM
ejpam-3073	35	18	1094	1094	NUM
ejpam-3073	35	19	definition	definition	NOUN
ejpam-3073	35	20	1	1	NUM
ejpam-3073	35	21	(	(	PUNCT
ejpam-3073	35	22	[	[	X
ejpam-3073	35	23	anake	anake	NOUN
ejpam-3073	35	24	,	,	PUNCT
ejpam-3073	35	25	2011	2011	NUM
ejpam-3073	35	26	,	,	PUNCT
ejpam-3073	35	27	p.61	p.61	NOUN
ejpam-3073	35	28	]	]	PUNCT
ejpam-3073	35	29	local	local	ADJ
ejpam-3073	35	30	truncation	truncation	NOUN
ejpam-3073	35	31	error	error	NOUN
ejpam-3073	35	32	)	)	PUNCT
ejpam-3073	35	33	.	.	PUNCT
ejpam-3073	36	1	the	the	DET
ejpam-3073	36	2	local	local	ADJ
ejpam-3073	36	3	truncation	truncation	NOUN
ejpam-3073	36	4	error	error	NOUN
ejpam-3073	36	5	at	at	ADP
ejpam-3073	36	6	xn+k	xn+k	PROPN
ejpam-3073	36	7	of	of	ADP
ejpam-3073	36	8	the	the	DET
ejpam-3073	36	9	numerical	numerical	ADJ
ejpam-3073	36	10	method	method	NOUN
ejpam-3073	36	11	(	(	PUNCT
ejpam-3073	36	12	2	2	X
ejpam-3073	36	13	)	)	PUNCT
ejpam-3073	36	14	is	be	AUX
ejpam-3073	36	15	defined	define	VERB
ejpam-3073	36	16	to	to	PART
ejpam-3073	36	17	be	be	AUX
ejpam-3073	36	18	the	the	DET
ejpam-3073	36	19	operator	operator	NOUN
ejpam-3073	36	20	l[y(xn);h	l[y(xn);h	PROPN
ejpam-3073	36	21	]	]	PUNCT
ejpam-3073	36	22	given	give	VERB
ejpam-3073	36	23	by	by	ADP
ejpam-3073	36	24	:	:	PUNCT
ejpam-3073	36	25	l[y(xn);h	l[y(xn);h	PROPN
ejpam-3073	36	26	]	]	X
ejpam-3073	36	27	=	=	SYM
ejpam-3073	36	28	k∑	k∑	VERB
ejpam-3073	36	29	j=0	j=0	PROPN
ejpam-3073	36	30	[	[	PUNCT
ejpam-3073	36	31	αjy(xn	αjy(xn	X
ejpam-3073	36	32	+	+	CCONJ
ejpam-3073	36	33	jh)−	jh)−	PROPN
ejpam-3073	36	34	h2βjy′′(xn	h2βjy′′(xn	PROPN
ejpam-3073	37	1	+	+	CCONJ
ejpam-3073	37	2	jh	jh	PROPN
ejpam-3073	37	3	)	)	PUNCT
ejpam-3073	37	4	]	]	PUNCT
ejpam-3073	38	1	(	(	PUNCT
ejpam-3073	38	2	3	3	X
ejpam-3073	38	3	)	)	PUNCT
ejpam-3073	38	4	when	when	SCONJ
ejpam-3073	38	5	y(xn	y(xn	NOUN
ejpam-3073	38	6	)	)	PUNCT
ejpam-3073	38	7	is	be	AUX
ejpam-3073	38	8	the	the	DET
ejpam-3073	38	9	theoretical	theoretical	ADJ
ejpam-3073	38	10	solution	solution	NOUN
ejpam-3073	38	11	of	of	ADP
ejpam-3073	38	12	the	the	DET
ejpam-3073	38	13	initial	initial	ADJ
ejpam-3073	38	14	value	value	NOUN
ejpam-3073	38	15	problem	problem	NOUN
ejpam-3073	38	16	(	(	PUNCT
ejpam-3073	38	17	2	2	NUM
ejpam-3073	38	18	)	)	PUNCT
ejpam-3073	38	19	at	at	ADP
ejpam-3073	38	20	xn	xn	PROPN
ejpam-3073	38	21	.	.	PUNCT
ejpam-3073	39	1	in	in	ADP
ejpam-3073	39	2	what	what	PRON
ejpam-3073	39	3	follows	follow	VERB
ejpam-3073	39	4	,	,	PUNCT
ejpam-3073	39	5	we	we	PRON
ejpam-3073	39	6	shall	shall	AUX
ejpam-3073	39	7	assume	assume	VERB
ejpam-3073	39	8	that	that	SCONJ
ejpam-3073	39	9	in	in	ADP
ejpam-3073	39	10	the	the	DET
ejpam-3073	39	11	application	application	NOUN
ejpam-3073	39	12	of	of	ADP
ejpam-3073	39	13	the	the	DET
ejpam-3073	39	14	method	method	NOUN
ejpam-3073	39	15	(	(	PUNCT
ejpam-3073	39	16	1	1	NUM
ejpam-3073	39	17	)	)	PUNCT
ejpam-3073	39	18	to	to	PART
ejpam-3073	39	19	yield	yield	VERB
ejpam-3073	39	20	yn+k	yn+k	PROPN
ejpam-3073	39	21	,	,	PUNCT
ejpam-3073	39	22	no	no	DET
ejpam-3073	39	23	previous	previous	ADJ
ejpam-3073	39	24	truncation	truncation	NOUN
ejpam-3073	39	25	errors	error	NOUN
ejpam-3073	39	26	have	have	AUX
ejpam-3073	39	27	been	be	AUX
ejpam-3073	39	28	made	make	VERB
ejpam-3073	39	29	.	.	PUNCT
ejpam-3073	40	1	furthermore	furthermore	ADV
ejpam-3073	40	2	,	,	PUNCT
ejpam-3073	40	3	we	we	PRON
ejpam-3073	40	4	shall	shall	AUX
ejpam-3073	40	5	assume	assume	VERB
ejpam-3073	40	6	the	the	DET
ejpam-3073	40	7	theoretical	theoretical	ADJ
ejpam-3073	40	8	solution	solution	NOUN
ejpam-3073	40	9	y(x	y(x	NOUN
ejpam-3073	40	10	)	)	PUNCT
ejpam-3073	40	11	possesses	possess	VERB
ejpam-3073	40	12	p+2	p+2	DET
ejpam-3073	40	13	continuous	continuous	ADJ
ejpam-3073	40	14	derivatives	derivative	NOUN
ejpam-3073	40	15	,	,	PUNCT
ejpam-3073	40	16	so	so	SCONJ
ejpam-3073	40	17	that	that	SCONJ
ejpam-3073	40	18	the	the	DET
ejpam-3073	40	19	local	local	ADJ
ejpam-3073	40	20	truncation	truncation	NOUN
ejpam-3073	40	21	error	error	NOUN
ejpam-3073	40	22	has	have	VERB
ejpam-3073	40	23	the	the	DET
ejpam-3073	40	24	value	value	NOUN
ejpam-3073	40	25	;	;	PUNCT
ejpam-3073	40	26	l[y(xn);h	l[y(xn);h	PROPN
ejpam-3073	40	27	]	]	PUNCT
ejpam-3073	40	28	=	=	SYM
ejpam-3073	40	29	cp+2h	cp+2h	PROPN
ejpam-3073	40	30	p+2yp+2(xn	p+2yp+2(xn	PUNCT
ejpam-3073	40	31	)	)	PUNCT
ejpam-3073	41	1	+	+	NOUN
ejpam-3073	41	2	o(hp+3	o(hp+3	NOUN
ejpam-3073	41	3	)	)	PUNCT
ejpam-3073	41	4	(	(	PUNCT
ejpam-3073	41	5	4	4	X
ejpam-3073	41	6	)	)	PUNCT
ejpam-3073	41	7	where	where	SCONJ
ejpam-3073	41	8	p	p	NOUN
ejpam-3073	41	9	and	and	CCONJ
ejpam-3073	41	10	cp+2	cp+2	PROPN
ejpam-3073	41	11	are	be	AUX
ejpam-3073	41	12	taken	take	VERB
ejpam-3073	41	13	to	to	PART
ejpam-3073	41	14	be	be	AUX
ejpam-3073	41	15	the	the	DET
ejpam-3073	41	16	order	order	NOUN
ejpam-3073	41	17	and	and	CCONJ
ejpam-3073	41	18	error	error	NOUN
ejpam-3073	41	19	constant	constant	ADJ
ejpam-3073	41	20	of	of	ADP
ejpam-3073	41	21	method	method	NOUN
ejpam-3073	41	22	(	(	PUNCT
ejpam-3073	41	23	1	1	NUM
ejpam-3073	41	24	)	)	PUNCT
ejpam-3073	41	25	respectively	respectively	ADV
ejpam-3073	41	26	.	.	PUNCT
ejpam-3073	42	1	theorem	theorem	ADJ
ejpam-3073	42	2	1	1	NUM
ejpam-3073	42	3	(	(	PUNCT
ejpam-3073	42	4	[	[	X
ejpam-3073	42	5	huang	huang	PROPN
ejpam-3073	42	6	,	,	PUNCT
ejpam-3073	42	7	2001	2001	NUM
ejpam-3073	42	8	,	,	PUNCT
ejpam-3073	42	9	p.2	p.2	NUM
ejpam-3073	42	10	]	]	X
ejpam-3073	42	11	generalized	generalized	ADJ
ejpam-3073	42	12	mean	mean	NOUN
ejpam-3073	42	13	value	value	NOUN
ejpam-3073	42	14	theorem	theorem	NOUN
ejpam-3073	42	15	)	)	PUNCT
ejpam-3073	42	16	.	.	PUNCT
ejpam-3073	43	1	if	if	SCONJ
ejpam-3073	43	2	ϕ	ϕ	NOUN
ejpam-3073	43	3	is	be	AUX
ejpam-3073	43	4	continuous	continuous	ADJ
ejpam-3073	43	5	and	and	CCONJ
ejpam-3073	43	6	ϑ	ϑ	NOUN
ejpam-3073	43	7	is	be	AUX
ejpam-3073	43	8	integrable	integrable	ADJ
ejpam-3073	43	9	on	on	ADP
ejpam-3073	43	10	an	an	DET
ejpam-3073	43	11	interval	interval	NOUN
ejpam-3073	43	12	containing	contain	VERB
ejpam-3073	43	13	a	a	PRON
ejpam-3073	43	14	and	and	CCONJ
ejpam-3073	43	15	x	x	NOUN
ejpam-3073	43	16	,	,	PUNCT
ejpam-3073	43	17	and	and	CCONJ
ejpam-3073	43	18	ϑ	ϑ	X
ejpam-3073	43	19	does	do	AUX
ejpam-3073	43	20	not	not	PART
ejpam-3073	43	21	change	change	VERB
ejpam-3073	43	22	sign	sign	NOUN
ejpam-3073	43	23	in	in	ADP
ejpam-3073	43	24	the	the	DET
ejpam-3073	43	25	interval	interval	NOUN
ejpam-3073	43	26	[	[	X
ejpam-3073	43	27	a	a	X
ejpam-3073	43	28	,	,	PUNCT
ejpam-3073	43	29	x	x	X
ejpam-3073	43	30	]	]	X
ejpam-3073	43	31	,	,	PUNCT
ejpam-3073	43	32	then	then	ADV
ejpam-3073	43	33	there	there	PRON
ejpam-3073	43	34	exists	exist	VERB
ejpam-3073	43	35	a	a	DET
ejpam-3073	43	36	point	point	NOUN
ejpam-3073	43	37	ζ	ζ	NOUN
ejpam-3073	43	38	between	between	ADP
ejpam-3073	43	39	a	a	PRON
ejpam-3073	43	40	and	and	CCONJ
ejpam-3073	43	41	x	x	ADP
ejpam-3073	43	42	such	such	ADJ
ejpam-3073	43	43	that∫	that∫	NOUN
ejpam-3073	43	44	x	x	PUNCT
ejpam-3073	43	45	a	a	DET
ejpam-3073	43	46	ϕ(t)ϑ(t	ϕ(t)ϑ(t	NOUN
ejpam-3073	43	47	)	)	PUNCT
ejpam-3073	43	48	dt	dt	NOUN
ejpam-3073	44	1	=	=	SYM
ejpam-3073	44	2	ϕ(ζ	ϕ(ζ	PROPN
ejpam-3073	44	3	)	)	PUNCT
ejpam-3073	44	4	∫	∫	PROPN
ejpam-3073	44	5	x	x	X
ejpam-3073	44	6	a	a	DET
ejpam-3073	44	7	ϑ(t	ϑ(t	NOUN
ejpam-3073	44	8	)	)	PUNCT
ejpam-3073	44	9	dt	dt	PROPN
ejpam-3073	44	10	.	.	PUNCT
ejpam-3073	45	1	(	(	PUNCT
ejpam-3073	45	2	5	5	X
ejpam-3073	45	3	)	)	PUNCT
ejpam-3073	45	4	we	we	PRON
ejpam-3073	45	5	note	note	VERB
ejpam-3073	45	6	that	that	SCONJ
ejpam-3073	45	7	the	the	DET
ejpam-3073	45	8	asymptotic	asymptotic	ADJ
ejpam-3073	45	9	method	method	NOUN
ejpam-3073	45	10	(	(	PUNCT
ejpam-3073	45	11	4	4	NUM
ejpam-3073	45	12	)	)	PUNCT
ejpam-3073	45	13	can	can	AUX
ejpam-3073	45	14	only	only	ADV
ejpam-3073	45	15	predict	predict	VERB
ejpam-3073	45	16	the	the	DET
ejpam-3073	45	17	behaviour	behaviour	NOUN
ejpam-3073	45	18	of	of	ADP
ejpam-3073	45	19	the	the	DET
ejpam-3073	45	20	error	error	NOUN
ejpam-3073	45	21	in	in	ADP
ejpam-3073	45	22	the	the	DET
ejpam-3073	45	23	limit	limit	NOUN
ejpam-3073	45	24	as	as	ADP
ejpam-3073	45	25	h→	h→	NOUN
ejpam-3073	45	26	0	0	NUM
ejpam-3073	45	27	.	.	PUNCT
ejpam-3073	46	1	furthermore	furthermore	ADV
ejpam-3073	46	2	,	,	PUNCT
ejpam-3073	46	3	our	our	PRON
ejpam-3073	46	4	knowledge	knowledge	NOUN
ejpam-3073	46	5	of	of	ADP
ejpam-3073	46	6	the	the	DET
ejpam-3073	46	7	order	order	NOUN
ejpam-3073	46	8	p	p	NOUN
ejpam-3073	46	9	and	and	CCONJ
ejpam-3073	46	10	error	error	NOUN
ejpam-3073	46	11	constant	constant	ADJ
ejpam-3073	46	12	cp+2	cp+2	NOUN
ejpam-3073	46	13	of	of	ADP
ejpam-3073	46	14	the	the	DET
ejpam-3073	46	15	method	method	NOUN
ejpam-3073	46	16	is	be	AUX
ejpam-3073	46	17	not	not	PART
ejpam-3073	46	18	sufficient	sufficient	ADJ
ejpam-3073	46	19	to	to	PART
ejpam-3073	46	20	deduce	deduce	VERB
ejpam-3073	46	21	a	a	DET
ejpam-3073	46	22	bound	bind	VERB
ejpam-3073	46	23	for	for	ADP
ejpam-3073	46	24	the	the	DET
ejpam-3073	46	25	magnitude	magnitude	NOUN
ejpam-3073	46	26	of	of	ADP
ejpam-3073	46	27	the	the	DET
ejpam-3073	46	28	local	local	ADJ
ejpam-3073	46	29	truncation	truncation	NOUN
ejpam-3073	46	30	error	error	NOUN
ejpam-3073	46	31	when	when	SCONJ
ejpam-3073	46	32	h	h	NOUN
ejpam-3073	46	33	is	be	AUX
ejpam-3073	46	34	fixed	fix	VERB
ejpam-3073	46	35	,	,	PUNCT
ejpam-3073	46	36	since	since	SCONJ
ejpam-3073	46	37	the	the	DET
ejpam-3073	46	38	magnitude	magnitude	NOUN
ejpam-3073	46	39	of	of	ADP
ejpam-3073	46	40	the	the	DET
ejpam-3073	46	41	term	term	NOUN
ejpam-3073	46	42	o(hp+3	o(hp+3	ADV
ejpam-3073	46	43	)	)	PUNCT
ejpam-3073	46	44	is	be	AUX
ejpam-3073	46	45	unknown	unknown	ADJ
ejpam-3073	46	46	.	.	PUNCT
ejpam-3073	47	1	3	3	X
ejpam-3073	47	2	.	.	X
ejpam-3073	47	3	main	main	ADJ
ejpam-3073	47	4	result	result	NOUN
ejpam-3073	47	5	we	we	PRON
ejpam-3073	47	6	present	present	VERB
ejpam-3073	47	7	the	the	DET
ejpam-3073	47	8	main	main	ADJ
ejpam-3073	47	9	result	result	NOUN
ejpam-3073	47	10	as	as	ADP
ejpam-3073	47	11	a	a	DET
ejpam-3073	47	12	proposition	proposition	NOUN
ejpam-3073	47	13	as	as	SCONJ
ejpam-3073	47	14	follows	follow	VERB
ejpam-3073	47	15	.	.	PUNCT
ejpam-3073	48	1	proposition	proposition	NOUN
ejpam-3073	48	2	1	1	NUM
ejpam-3073	48	3	.	.	PUNCT
ejpam-3073	48	4	given	give	VERB
ejpam-3073	48	5	the	the	DET
ejpam-3073	48	6	operator	operator	NOUN
ejpam-3073	48	7	l	l	NOUN
ejpam-3073	48	8	,	,	PUNCT
ejpam-3073	48	9	of	of	ADP
ejpam-3073	48	10	order	order	NOUN
ejpam-3073	48	11	p	p	NOUN
ejpam-3073	48	12	and	and	CCONJ
ejpam-3073	48	13	error	error	NOUN
ejpam-3073	48	14	constant	constant	ADJ
ejpam-3073	48	15	cp+2	cp+2	PROPN
ejpam-3073	48	16	,	,	PUNCT
ejpam-3073	48	17	for	for	ADP
ejpam-3073	48	18	h	h	NOUN
ejpam-3073	48	19	fixed	fix	VERB
ejpam-3073	48	20	,	,	PUNCT
ejpam-3073	48	21	the	the	DET
ejpam-3073	48	22	local	local	ADJ
ejpam-3073	48	23	truncation	truncation	NOUN
ejpam-3073	48	24	error	error	NOUN
ejpam-3073	48	25	takes	take	VERB
ejpam-3073	48	26	the	the	DET
ejpam-3073	48	27	form	form	NOUN
ejpam-3073	48	28	:	:	PUNCT
ejpam-3073	48	29	l[y(xn);h	l[y(xn);h	PROPN
ejpam-3073	48	30	]	]	PUNCT
ejpam-3073	48	31	=	=	SYM
ejpam-3073	48	32	cp+2h	cp+2h	ADJ
ejpam-3073	48	33	p+2yp+2(xn	p+2yp+2(xn	X
ejpam-3073	48	34	+	+	CCONJ
ejpam-3073	48	35	ξh	ξh	NOUN
ejpam-3073	48	36	)	)	PUNCT
ejpam-3073	48	37	,	,	PUNCT
ejpam-3073	49	1	0	0	PUNCT
ejpam-3073	49	2	<	<	X
ejpam-3073	49	3	ξ	ξ	X
ejpam-3073	49	4	<	<	X
ejpam-3073	49	5	k	k	X
ejpam-3073	49	6	(	(	PUNCT
ejpam-3073	49	7	6	6	NUM
ejpam-3073	49	8	)	)	PUNCT
ejpam-3073	49	9	and	and	CCONJ
ejpam-3073	49	10	|l[y(xn);h]|	|l[y(xn);h]|	VERB
ejpam-3073	49	11	≤	≤	ADJ
ejpam-3073	49	12	hp+2qy	hp+2qy	X
ejpam-3073	49	13	(	(	PUNCT
ejpam-3073	49	14	7	7	NUM
ejpam-3073	49	15	)	)	PUNCT
ejpam-3073	49	16	where	where	SCONJ
ejpam-3073	49	17	q	q	NOUN
ejpam-3073	49	18	=	=	SYM
ejpam-3073	49	19	|cp+2|	|cp+2|	NOUN
ejpam-3073	49	20	=	=	SYM
ejpam-3073	49	21	1	1	NUM
ejpam-3073	49	22	p	p	NOUN
ejpam-3073	49	23	!	!	PUNCT
ejpam-3073	49	24	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-3073	50	1	k	k	NOUN
ejpam-3073	50	2	0	0	NUM
ejpam-3073	50	3	g(t	g(t	PROPN
ejpam-3073	50	4	)	)	PUNCT
ejpam-3073	50	5	dt	dt	PROPN
ejpam-3073	51	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3073	51	2	(	(	PUNCT
ejpam-3073	51	3	8a	8a	NUM
ejpam-3073	51	4	)	)	PUNCT
ejpam-3073	51	5	and	and	CCONJ
ejpam-3073	51	6	y	y	PROPN
ejpam-3073	51	7	=	=	PROPN
ejpam-3073	51	8	max	max	PROPN
ejpam-3073	51	9	x∈[a	x∈[a	PROPN
ejpam-3073	51	10	,	,	PUNCT
ejpam-3073	51	11	b	b	X
ejpam-3073	51	12	]	]	PUNCT
ejpam-3073	51	13	|y(p+2)(x)|	|y(p+2)(x)|	X
ejpam-3073	51	14	.	.	PUNCT
ejpam-3073	51	15	(	(	PUNCT
ejpam-3073	51	16	8b	8b	NUM
ejpam-3073	51	17	)	)	PUNCT
ejpam-3073	51	18	t.	t.	PROPN
ejpam-3073	51	19	a.	a.	PROPN
ejpam-3073	51	20	anake	anake	PROPN
ejpam-3073	51	21	,	,	PUNCT
ejpam-3073	51	22	s.	s.	PROPN
ejpam-3073	51	23	o.	o.	PROPN
ejpam-3073	51	24	edeki	edeki	PROPN
ejpam-3073	51	25	/	/	SYM
ejpam-3073	51	26	eur	eur	PROPN
ejpam-3073	51	27	.	.	PUNCT
ejpam-3073	52	1	j.	j.	PROPN
ejpam-3073	52	2	pure	pure	PROPN
ejpam-3073	52	3	appl	appl	PROPN
ejpam-3073	52	4	.	.	PROPN
ejpam-3073	52	5	math	math	PROPN
ejpam-3073	52	6	,	,	PUNCT
ejpam-3073	52	7	10	10	NUM
ejpam-3073	52	8	(	(	PUNCT
ejpam-3073	52	9	5	5	NUM
ejpam-3073	52	10	)	)	PUNCT
ejpam-3073	52	11	(	(	PUNCT
ejpam-3073	52	12	2017	2017	NUM
ejpam-3073	52	13	)	)	PUNCT
ejpam-3073	52	14	,	,	PUNCT
ejpam-3073	52	15	1092	1092	NUM
ejpam-3073	52	16	-	-	SYM
ejpam-3073	52	17	1098	1098	NUM
ejpam-3073	52	18	1095	1095	NUM
ejpam-3073	52	19	proof	proof	NOUN
ejpam-3073	52	20	.	.	PUNCT
ejpam-3073	53	1	define	define	VERB
ejpam-3073	53	2	the	the	DET
ejpam-3073	53	3	generalized	generalized	ADJ
ejpam-3073	53	4	form	form	NOUN
ejpam-3073	53	5	of	of	ADP
ejpam-3073	53	6	the	the	DET
ejpam-3073	53	7	lagrange	lagrange	NOUN
ejpam-3073	53	8	remainder	remainder	NOUN
ejpam-3073	53	9	rp+1	rp+1	NOUN
ejpam-3073	54	1	after	after	ADP
ejpam-3073	54	2	p+	p+	NOUN
ejpam-3073	54	3	2	2	NUM
ejpam-3073	54	4	terms	term	NOUN
ejpam-3073	54	5	in	in	ADP
ejpam-3073	54	6	a	a	DET
ejpam-3073	54	7	taylor	taylor	NOUN
ejpam-3073	54	8	expansion	expansion	NOUN
ejpam-3073	54	9	of	of	ADP
ejpam-3073	54	10	a	a	DET
ejpam-3073	54	11	sufficiently	sufficiently	ADV
ejpam-3073	54	12	differentiable	differentiable	ADJ
ejpam-3073	54	13	function	function	NOUN
ejpam-3073	54	14	g(x	g(x	NOUN
ejpam-3073	54	15	)	)	PUNCT
ejpam-3073	54	16	about	about	ADP
ejpam-3073	54	17	x	x	X
ejpam-3073	54	18	=	=	NOUN
ejpam-3073	54	19	a	a	DET
ejpam-3073	54	20	as	as	ADP
ejpam-3073	54	21	;	;	PUNCT
ejpam-3073	54	22	rp+1	rp+1	X
ejpam-3073	54	23	=	=	SYM
ejpam-3073	54	24	1	1	NUM
ejpam-3073	54	25	(	(	PUNCT
ejpam-3073	54	26	p+	p+	NOUN
ejpam-3073	54	27	1	1	NUM
ejpam-3073	54	28	)	)	PUNCT
ejpam-3073	54	29	!	!	PUNCT
ejpam-3073	55	1	∫	∫	PROPN
ejpam-3073	56	1	h	h	NOUN
ejpam-3073	56	2	0	0	PUNCT
ejpam-3073	57	1	(	(	PUNCT
ejpam-3073	57	2	h−	h−	PROPN
ejpam-3073	57	3	z)p+1g(p+2)(a+	z)p+1g(p+2)(a+	PROPN
ejpam-3073	57	4	z	z	X
ejpam-3073	57	5	)	)	PUNCT
ejpam-3073	57	6	dz	dz	PROPN
ejpam-3073	57	7	.	.	PUNCT
ejpam-3073	58	1	(	(	PUNCT
ejpam-3073	58	2	9	9	NUM
ejpam-3073	58	3	)	)	PUNCT
ejpam-3073	58	4	then	then	ADV
ejpam-3073	58	5	we	we	PRON
ejpam-3073	58	6	can	can	AUX
ejpam-3073	58	7	now	now	ADV
ejpam-3073	58	8	write	write	VERB
ejpam-3073	58	9	the	the	DET
ejpam-3073	58	10	taylor	taylor	PROPN
ejpam-3073	58	11	expansions	expansion	NOUN
ejpam-3073	58	12	of	of	ADP
ejpam-3073	58	13	y(xn	y(xn	PROPN
ejpam-3073	58	14	+	+	CCONJ
ejpam-3073	58	15	jh	jh	PROPN
ejpam-3073	58	16	)	)	PUNCT
ejpam-3073	58	17	about	about	ADV
ejpam-3073	58	18	xn	xn	PROPN
ejpam-3073	58	19	truncated	truncate	VERB
ejpam-3073	58	20	after	after	ADP
ejpam-3073	58	21	p+	p+	NOUN
ejpam-3073	58	22	2	2	NUM
ejpam-3073	58	23	terms	term	NOUN
ejpam-3073	58	24	as	as	ADP
ejpam-3073	58	25	y(xn	y(xn	PROPN
ejpam-3073	58	26	+	+	PROPN
ejpam-3073	58	27	jh	jh	PROPN
ejpam-3073	58	28	)	)	PUNCT
ejpam-3073	59	1	=	=	SYM
ejpam-3073	59	2	y(xn	y(xn	NOUN
ejpam-3073	59	3	)	)	PUNCT
ejpam-3073	59	4	+	+	NUM
ejpam-3073	59	5	jhy(1	jhy(1	ADJ
ejpam-3073	59	6	)	)	PUNCT
ejpam-3073	60	1	+	+	CCONJ
ejpam-3073	60	2	(	(	PUNCT
ejpam-3073	60	3	jh)2	jh)2	PROPN
ejpam-3073	60	4	2	2	NUM
ejpam-3073	60	5	!	!	PUNCT
ejpam-3073	60	6	y(2)(xn	y(2)(xn	NOUN
ejpam-3073	60	7	)	)	PUNCT
ejpam-3073	61	1	+	+	CCONJ
ejpam-3073	61	2	·	·	PUNCT
ejpam-3073	61	3	·	·	PUNCT
ejpam-3073	61	4	·	·	PUNCT
ejpam-3073	61	5	+	+	CCONJ
ejpam-3073	61	6	(	(	PUNCT
ejpam-3073	61	7	jh)p+1	jh)p+1	X
ejpam-3073	61	8	(	(	PUNCT
ejpam-3073	61	9	p+	p+	NOUN
ejpam-3073	61	10	1	1	NUM
ejpam-3073	61	11	)	)	PUNCT
ejpam-3073	61	12	!	!	PUNCT
ejpam-3073	61	13	y(p+1	y(p+1	PUNCT
ejpam-3073	61	14	)	)	PUNCT
ejpam-3073	62	1	+	+	CCONJ
ejpam-3073	62	2	1	1	NUM
ejpam-3073	62	3	(	(	PUNCT
ejpam-3073	62	4	p+	p+	NOUN
ejpam-3073	62	5	1	1	NUM
ejpam-3073	62	6	)	)	PUNCT
ejpam-3073	62	7	!	!	PUNCT
ejpam-3073	63	1	∫	∫	PROPN
ejpam-3073	64	1	jh	jh	PROPN
ejpam-3073	64	2	0	0	NUM
ejpam-3073	65	1	(	(	PUNCT
ejpam-3073	65	2	jh−	jh−	X
ejpam-3073	65	3	z)p+1y(p+2)(xn	z)p+1y(p+2)(xn	NUM
ejpam-3073	65	4	+	+	CCONJ
ejpam-3073	65	5	z)dz	z)dz	PROPN
ejpam-3073	65	6	(	(	PUNCT
ejpam-3073	65	7	10	10	NUM
ejpam-3073	65	8	)	)	PUNCT
ejpam-3073	65	9	and	and	CCONJ
ejpam-3073	65	10	in	in	ADP
ejpam-3073	65	11	the	the	DET
ejpam-3073	65	12	same	same	ADJ
ejpam-3073	65	13	manner	manner	NOUN
ejpam-3073	65	14	,	,	PUNCT
ejpam-3073	65	15	the	the	DET
ejpam-3073	65	16	taylor	taylor	PROPN
ejpam-3073	65	17	expansion	expansion	NOUN
ejpam-3073	65	18	of	of	ADP
ejpam-3073	65	19	y′′(xn	y′′(xn	PROPN
ejpam-3073	65	20	+	+	X
ejpam-3073	65	21	jh	jh	PROPN
ejpam-3073	65	22	)	)	PUNCT
ejpam-3073	65	23	about	about	ADV
ejpam-3073	65	24	xn	xn	PROPN
ejpam-3073	65	25	truncated	truncate	VERB
ejpam-3073	65	26	after	after	SCONJ
ejpam-3073	65	27	p	p	NOUN
ejpam-3073	65	28	terms	term	NOUN
ejpam-3073	65	29	may	may	AUX
ejpam-3073	65	30	now	now	ADV
ejpam-3073	65	31	be	be	AUX
ejpam-3073	65	32	written	write	VERB
ejpam-3073	65	33	as	as	ADP
ejpam-3073	65	34	y(2)(xn	y(2)(xn	PROPN
ejpam-3073	65	35	+	+	PROPN
ejpam-3073	65	36	jh	jh	PROPN
ejpam-3073	65	37	)	)	PUNCT
ejpam-3073	65	38	=	=	SYM
ejpam-3073	65	39	y(2)(xn	y(2)(xn	PROPN
ejpam-3073	65	40	)	)	PUNCT
ejpam-3073	66	1	+	+	NUM
ejpam-3073	66	2	jhy(3	jhy(3	ADJ
ejpam-3073	66	3	)	)	PUNCT
ejpam-3073	67	1	+	+	CCONJ
ejpam-3073	67	2	(	(	PUNCT
ejpam-3073	67	3	jh)2	jh)2	PROPN
ejpam-3073	67	4	2	2	NUM
ejpam-3073	67	5	!	!	PUNCT
ejpam-3073	67	6	y(4)(xn	y(4)(xn	PROPN
ejpam-3073	67	7	)	)	PUNCT
ejpam-3073	67	8	+	+	CCONJ
ejpam-3073	67	9	·	·	PUNCT
ejpam-3073	67	10	·	·	PUNCT
ejpam-3073	67	11	·	·	PUNCT
ejpam-3073	67	12	+	+	CCONJ
ejpam-3073	67	13	(	(	PUNCT
ejpam-3073	67	14	jh)p−1	jh)p−1	PROPN
ejpam-3073	67	15	(	(	PUNCT
ejpam-3073	67	16	p−	p−	NOUN
ejpam-3073	67	17	1	1	NUM
ejpam-3073	67	18	)	)	PUNCT
ejpam-3073	67	19	!	!	PUNCT
ejpam-3073	67	20	y(p+1	y(p+1	PUNCT
ejpam-3073	67	21	)	)	PUNCT
ejpam-3073	68	1	+	+	CCONJ
ejpam-3073	68	2	1	1	NUM
ejpam-3073	68	3	(	(	PUNCT
ejpam-3073	68	4	p−	p−	NOUN
ejpam-3073	68	5	1	1	NUM
ejpam-3073	68	6	)	)	PUNCT
ejpam-3073	68	7	!	!	PUNCT
ejpam-3073	69	1	∫	∫	PROPN
ejpam-3073	70	1	jh	jh	PROPN
ejpam-3073	70	2	0	0	NUM
ejpam-3073	71	1	(	(	PUNCT
ejpam-3073	71	2	jh−	jh−	PROPN
ejpam-3073	71	3	z)p−1y(p+2)(xn	z)p−1y(p+2)(xn	X
ejpam-3073	71	4	+	+	CCONJ
ejpam-3073	71	5	z)dz	z)dz	PROPN
ejpam-3073	71	6	.	.	PUNCT
ejpam-3073	72	1	(	(	PUNCT
ejpam-3073	72	2	11	11	X
ejpam-3073	72	3	)	)	PUNCT
ejpam-3073	72	4	making	make	VERB
ejpam-3073	72	5	z	z	NOUN
ejpam-3073	72	6	=	=	SYM
ejpam-3073	72	7	th	th	NOUN
ejpam-3073	72	8	,	,	PUNCT
ejpam-3073	72	9	(	(	PUNCT
ejpam-3073	72	10	10	10	NUM
ejpam-3073	72	11	)	)	PUNCT
ejpam-3073	72	12	and	and	CCONJ
ejpam-3073	72	13	(	(	PUNCT
ejpam-3073	72	14	11	11	NUM
ejpam-3073	72	15	)	)	PUNCT
ejpam-3073	72	16	respectively	respectively	ADV
ejpam-3073	72	17	become	become	VERB
ejpam-3073	72	18	y(xn	y(xn	NOUN
ejpam-3073	72	19	+	+	CCONJ
ejpam-3073	72	20	jh	jh	PROPN
ejpam-3073	72	21	)	)	PUNCT
ejpam-3073	73	1	=	=	SYM
ejpam-3073	73	2	y(xn	y(xn	NOUN
ejpam-3073	73	3	)	)	PUNCT
ejpam-3073	73	4	+	+	NUM
ejpam-3073	73	5	jhy(1	jhy(1	ADJ
ejpam-3073	73	6	)	)	PUNCT
ejpam-3073	74	1	+	+	CCONJ
ejpam-3073	74	2	(	(	PUNCT
ejpam-3073	74	3	jh)2	jh)2	PROPN
ejpam-3073	74	4	2	2	NUM
ejpam-3073	74	5	!	!	PUNCT
ejpam-3073	74	6	y(2)(xn	y(2)(xn	NOUN
ejpam-3073	74	7	)	)	PUNCT
ejpam-3073	75	1	+	+	CCONJ
ejpam-3073	75	2	·	·	PUNCT
ejpam-3073	75	3	·	·	PUNCT
ejpam-3073	75	4	·	·	PUNCT
ejpam-3073	75	5	+	+	CCONJ
ejpam-3073	75	6	(	(	PUNCT
ejpam-3073	75	7	jh)p+1	jh)p+1	X
ejpam-3073	75	8	(	(	PUNCT
ejpam-3073	75	9	p+	p+	NOUN
ejpam-3073	75	10	1	1	NUM
ejpam-3073	75	11	)	)	PUNCT
ejpam-3073	75	12	!	!	PUNCT
ejpam-3073	75	13	y(p+1	y(p+1	PUNCT
ejpam-3073	75	14	)	)	PUNCT
ejpam-3073	76	1	+	+	CCONJ
ejpam-3073	76	2	hp+1	hp+1	NOUN
ejpam-3073	76	3	(	(	PUNCT
ejpam-3073	76	4	p+	p+	NOUN
ejpam-3073	76	5	1	1	NUM
ejpam-3073	76	6	)	)	PUNCT
ejpam-3073	76	7	!	!	PUNCT
ejpam-3073	77	1	∫	∫	PROPN
ejpam-3073	78	1	j	j	PROPN
ejpam-3073	78	2	0	0	PUNCT
ejpam-3073	79	1	(	(	PUNCT
ejpam-3073	79	2	j	j	PROPN
ejpam-3073	79	3	−	−	PROPN
ejpam-3073	79	4	t)p+1y(p+2)(xn	t)p+1y(p+2)(xn	PRON
ejpam-3073	80	1	+	+	CCONJ
ejpam-3073	80	2	th)dt	th)dt	SYM
ejpam-3073	80	3	(	(	PUNCT
ejpam-3073	80	4	12	12	NUM
ejpam-3073	80	5	)	)	PUNCT
ejpam-3073	80	6	and	and	CCONJ
ejpam-3073	80	7	y(2)(xn	y(2)(xn	PROPN
ejpam-3073	80	8	+	+	CCONJ
ejpam-3073	80	9	jh	jh	PROPN
ejpam-3073	80	10	)	)	PUNCT
ejpam-3073	80	11	=	=	SYM
ejpam-3073	80	12	y(2)(xn	y(2)(xn	PROPN
ejpam-3073	80	13	)	)	PUNCT
ejpam-3073	81	1	+	+	NUM
ejpam-3073	81	2	jhy(3	jhy(3	ADJ
ejpam-3073	81	3	)	)	PUNCT
ejpam-3073	82	1	+	+	CCONJ
ejpam-3073	82	2	(	(	PUNCT
ejpam-3073	82	3	jh)2	jh)2	PROPN
ejpam-3073	82	4	2	2	NUM
ejpam-3073	82	5	!	!	PUNCT
ejpam-3073	82	6	y(4)(xn	y(4)(xn	PROPN
ejpam-3073	82	7	)	)	PUNCT
ejpam-3073	82	8	+	+	CCONJ
ejpam-3073	82	9	·	·	PUNCT
ejpam-3073	82	10	·	·	PUNCT
ejpam-3073	82	11	·	·	PUNCT
ejpam-3073	82	12	+	+	CCONJ
ejpam-3073	82	13	(	(	PUNCT
ejpam-3073	82	14	jh)p−1	jh)p−1	PROPN
ejpam-3073	82	15	(	(	PUNCT
ejpam-3073	82	16	p−	p−	NOUN
ejpam-3073	82	17	1	1	NUM
ejpam-3073	82	18	)	)	PUNCT
ejpam-3073	82	19	!	!	PUNCT
ejpam-3073	82	20	y(p+1	y(p+1	PUNCT
ejpam-3073	82	21	)	)	PUNCT
ejpam-3073	83	1	+	+	CCONJ
ejpam-3073	83	2	hp−1	hp−1	PROPN
ejpam-3073	83	3	(	(	PUNCT
ejpam-3073	83	4	p−	p−	NOUN
ejpam-3073	83	5	1	1	NUM
ejpam-3073	83	6	)	)	PUNCT
ejpam-3073	83	7	!	!	PUNCT
ejpam-3073	84	1	∫	∫	PROPN
ejpam-3073	85	1	j	j	PROPN
ejpam-3073	85	2	0	0	PUNCT
ejpam-3073	86	1	(	(	PUNCT
ejpam-3073	86	2	j	j	PROPN
ejpam-3073	86	3	−	−	PROPN
ejpam-3073	87	1	t)p−1y(p+2)(xn	t)p−1y(p+2)(xn	PROPN
ejpam-3073	87	2	+	+	NOUN
ejpam-3073	87	3	th)dt	th)dt	X
ejpam-3073	87	4	.	.	PUNCT
ejpam-3073	88	1	(	(	PUNCT
ejpam-3073	88	2	13	13	NUM
ejpam-3073	88	3	)	)	PUNCT
ejpam-3073	88	4	then	then	ADV
ejpam-3073	88	5	,	,	PUNCT
ejpam-3073	88	6	using	use	VERB
ejpam-3073	88	7	(	(	PUNCT
ejpam-3073	88	8	12	12	NUM
ejpam-3073	88	9	)	)	PUNCT
ejpam-3073	88	10	and	and	CCONJ
ejpam-3073	88	11	(	(	PUNCT
ejpam-3073	88	12	13	13	NUM
ejpam-3073	88	13	)	)	PUNCT
ejpam-3073	88	14	in	in	ADP
ejpam-3073	88	15	(	(	PUNCT
ejpam-3073	88	16	3	3	X
ejpam-3073	88	17	)	)	PUNCT
ejpam-3073	88	18	yields	yield	NOUN
ejpam-3073	88	19	after	after	ADP
ejpam-3073	88	20	a	a	DET
ejpam-3073	88	21	little	little	ADJ
ejpam-3073	88	22	algebraic	algebraic	ADJ
ejpam-3073	88	23	computation	computation	NOUN
ejpam-3073	88	24	l[y(xn);h	l[y(xn);h	PROPN
ejpam-3073	88	25	]	]	PUNCT
ejpam-3073	88	26	=	=	SYM
ejpam-3073	88	27	hp+2	hp+2	VERB
ejpam-3073	88	28	p	p	X
ejpam-3073	88	29	!	!	PUNCT
ejpam-3073	89	1	∫	∫	PROPN
ejpam-3073	89	2	k	k	PROPN
ejpam-3073	89	3	0	0	PROPN
ejpam-3073	89	4	k∑	k∑	PROPN
ejpam-3073	89	5	j=0	j=0	PROPN
ejpam-3073	89	6	[	[	PUNCT
ejpam-3073	89	7	(	(	PUNCT
ejpam-3073	89	8	p+	p+	PROPN
ejpam-3073	89	9	1)−1αj(j	1)−1αj(j	NUM
ejpam-3073	89	10	−	−	NOUN
ejpam-3073	89	11	t)p+1	t)p+1	NOUN
ejpam-3073	89	12	+	+	CCONJ
ejpam-3073	90	1	−	−	PROPN
ejpam-3073	90	2	pβj(j	pβj(j	NOUN
ejpam-3073	90	3	−	−	NOUN
ejpam-3073	90	4	t)p−1	t)p−1	PROPN
ejpam-3073	90	5	+	+	X
ejpam-3073	90	6	]	]	PUNCT
ejpam-3073	90	7	y(p+2)(xn	y(p+2)(xn	PROPN
ejpam-3073	91	1	+	+	CCONJ
ejpam-3073	91	2	th	th	NOUN
ejpam-3073	91	3	)	)	PUNCT
ejpam-3073	91	4	dt	dt	X
ejpam-3073	91	5	(	(	PUNCT
ejpam-3073	91	6	14	14	NUM
ejpam-3073	91	7	)	)	PUNCT
ejpam-3073	91	8	where	where	SCONJ
ejpam-3073	91	9	s+	s+	ADV
ejpam-3073	91	10	=	=	PRON
ejpam-3073	91	11	{	{	PUNCT
ejpam-3073	91	12	s	s	X
ejpam-3073	91	13	,	,	PUNCT
ejpam-3073	91	14	if	if	SCONJ
ejpam-3073	91	15	s	s	VERB
ejpam-3073	91	16	≥	≥	NOUN
ejpam-3073	91	17	0	0	NUM
ejpam-3073	91	18	,	,	PUNCT
ejpam-3073	91	19	0	0	NUM
ejpam-3073	91	20	,	,	PUNCT
ejpam-3073	91	21	if	if	SCONJ
ejpam-3073	91	22	s	s	VERB
ejpam-3073	91	23	<	<	X
ejpam-3073	91	24	0	0	NUM
ejpam-3073	91	25	.	.	PUNCT
ejpam-3073	92	1	(	(	PUNCT
ejpam-3073	92	2	15	15	NUM
ejpam-3073	92	3	)	)	PUNCT
ejpam-3073	92	4	t.	t.	NOUN
ejpam-3073	92	5	a.	a.	PROPN
ejpam-3073	92	6	anake	anake	PROPN
ejpam-3073	92	7	,	,	PUNCT
ejpam-3073	92	8	s.	s.	PROPN
ejpam-3073	92	9	o.	o.	PROPN
ejpam-3073	92	10	edeki	edeki	PROPN
ejpam-3073	92	11	/	/	SYM
ejpam-3073	92	12	eur	eur	PROPN
ejpam-3073	92	13	.	.	PUNCT
ejpam-3073	93	1	j.	j.	PROPN
ejpam-3073	93	2	pure	pure	PROPN
ejpam-3073	93	3	appl	appl	PROPN
ejpam-3073	93	4	.	.	PROPN
ejpam-3073	93	5	math	math	PROPN
ejpam-3073	93	6	,	,	PUNCT
ejpam-3073	93	7	10	10	NUM
ejpam-3073	93	8	(	(	PUNCT
ejpam-3073	93	9	5	5	NUM
ejpam-3073	93	10	)	)	PUNCT
ejpam-3073	93	11	(	(	PUNCT
ejpam-3073	93	12	2017	2017	NUM
ejpam-3073	93	13	)	)	PUNCT
ejpam-3073	93	14	,	,	PUNCT
ejpam-3073	93	15	1092	1092	NUM
ejpam-3073	93	16	-	-	SYM
ejpam-3073	93	17	1098	1098	NUM
ejpam-3073	93	18	1096	1096	NUM
ejpam-3073	93	19	suppose	suppose	VERB
ejpam-3073	93	20	the	the	DET
ejpam-3073	93	21	method	method	NOUN
ejpam-3073	93	22	is	be	AUX
ejpam-3073	93	23	consistent	consistent	ADJ
ejpam-3073	93	24	,	,	PUNCT
ejpam-3073	93	25	that	that	ADV
ejpam-3073	93	26	is	is	ADV
ejpam-3073	93	27	p	p	PRON
ejpam-3073	93	28	≥	≥	NUM
ejpam-3073	93	29	1	1	NUM
ejpam-3073	93	30	,	,	PUNCT
ejpam-3073	93	31	also	also	ADV
ejpam-3073	93	32	define	define	VERB
ejpam-3073	93	33	the	the	DET
ejpam-3073	93	34	function	function	NOUN
ejpam-3073	93	35	f	f	PROPN
ejpam-3073	93	36	(	(	PUNCT
ejpam-3073	93	37	t	t	PROPN
ejpam-3073	93	38	):	):	PUNCT
ejpam-3073	93	39	f	f	PROPN
ejpam-3073	93	40	(	(	PUNCT
ejpam-3073	93	41	t	t	PROPN
ejpam-3073	93	42	)	)	PUNCT
ejpam-3073	93	43	=	=	SYM
ejpam-3073	94	1	k∑	k∑	PROPN
ejpam-3073	94	2	j=0	j=0	PROPN
ejpam-3073	94	3	[	[	PUNCT
ejpam-3073	94	4	(	(	PUNCT
ejpam-3073	94	5	p+	p+	PROPN
ejpam-3073	94	6	1)−1αj(j	1)−1αj(j	NUM
ejpam-3073	94	7	−	−	NOUN
ejpam-3073	94	8	t)p+1	t)p+1	NOUN
ejpam-3073	94	9	+	+	CCONJ
ejpam-3073	95	1	−	−	PROPN
ejpam-3073	95	2	pβj(j	pβj(j	NOUN
ejpam-3073	95	3	−	−	NOUN
ejpam-3073	95	4	t)p−1	t)p−1	PROPN
ejpam-3073	95	5	+	+	X
ejpam-3073	95	6	]	]	PUNCT
ejpam-3073	95	7	(	(	PUNCT
ejpam-3073	95	8	16	16	NUM
ejpam-3073	95	9	)	)	PUNCT
ejpam-3073	95	10	such	such	ADJ
ejpam-3073	95	11	that	that	SCONJ
ejpam-3073	95	12	f	f	PROPN
ejpam-3073	95	13	(	(	PUNCT
ejpam-3073	95	14	t	t	PROPN
ejpam-3073	95	15	)	)	PUNCT
ejpam-3073	95	16	is	be	AUX
ejpam-3073	95	17	a	a	DET
ejpam-3073	95	18	polynomial	polynomial	NOUN
ejpam-3073	95	19	in	in	ADP
ejpam-3073	95	20	each	each	DET
ejpam-3073	95	21	partition	partition	NOUN
ejpam-3073	95	22	of	of	ADP
ejpam-3073	95	23	the	the	DET
ejpam-3073	95	24	interval	interval	NOUN
ejpam-3073	95	25	[	[	X
ejpam-3073	95	26	0	0	NUM
ejpam-3073	95	27	,	,	PUNCT
ejpam-3073	95	28	k	k	X
ejpam-3073	95	29	]	]	X
ejpam-3073	95	30	and	and	CCONJ
ejpam-3073	95	31	independent	independent	ADJ
ejpam-3073	95	32	of	of	ADP
ejpam-3073	95	33	the	the	DET
ejpam-3073	95	34	theoretical	theoretical	ADJ
ejpam-3073	95	35	solution	solution	NOUN
ejpam-3073	95	36	y(x	y(x	NOUN
ejpam-3073	95	37	)	)	PUNCT
ejpam-3073	95	38	.	.	PUNCT
ejpam-3073	96	1	then	then	ADV
ejpam-3073	96	2	,	,	PUNCT
ejpam-3073	96	3	(	(	PUNCT
ejpam-3073	96	4	14	14	NUM
ejpam-3073	96	5	)	)	PUNCT
ejpam-3073	96	6	can	can	AUX
ejpam-3073	96	7	be	be	AUX
ejpam-3073	96	8	written	write	VERB
ejpam-3073	96	9	in	in	ADP
ejpam-3073	96	10	terms	term	NOUN
ejpam-3073	96	11	of	of	ADP
ejpam-3073	96	12	f	f	PROPN
ejpam-3073	96	13	(	(	PUNCT
ejpam-3073	96	14	t	t	PROPN
ejpam-3073	96	15	)	)	PUNCT
ejpam-3073	96	16	as	as	SCONJ
ejpam-3073	96	17	follows	follow	VERB
ejpam-3073	96	18	:	:	PUNCT
ejpam-3073	96	19	l[y(xn);h	l[y(xn);h	PROPN
ejpam-3073	96	20	]	]	PUNCT
ejpam-3073	96	21	=	=	SYM
ejpam-3073	96	22	hp+2	hp+2	VERB
ejpam-3073	96	23	p	p	X
ejpam-3073	96	24	!	!	PUNCT
ejpam-3073	96	25	∫	∫	PROPN
ejpam-3073	97	1	k	k	NOUN
ejpam-3073	97	2	0	0	PUNCT
ejpam-3073	97	3	f	f	PROPN
ejpam-3073	97	4	(	(	PUNCT
ejpam-3073	97	5	t)y(p+2)(xn	t)y(p+2)(xn	X
ejpam-3073	97	6	+	+	NUM
ejpam-3073	97	7	th	th	NOUN
ejpam-3073	97	8	)	)	PUNCT
ejpam-3073	97	9	dt	dt	PROPN
ejpam-3073	97	10	.	.	PUNCT
ejpam-3073	98	1	(	(	PUNCT
ejpam-3073	98	2	17	17	NUM
ejpam-3073	98	3	)	)	PUNCT
ejpam-3073	98	4	furthermore	furthermore	ADV
ejpam-3073	98	5	,	,	PUNCT
ejpam-3073	98	6	assume	assume	VERB
ejpam-3073	98	7	that	that	SCONJ
ejpam-3073	98	8	f	f	PROPN
ejpam-3073	98	9	(	(	PUNCT
ejpam-3073	98	10	t	t	PROPN
ejpam-3073	98	11	)	)	PUNCT
ejpam-3073	98	12	does	do	AUX
ejpam-3073	98	13	not	not	PART
ejpam-3073	98	14	change	change	VERB
ejpam-3073	98	15	sign	sign	NOUN
ejpam-3073	98	16	in	in	ADP
ejpam-3073	98	17	the	the	DET
ejpam-3073	98	18	interval	interval	NOUN
ejpam-3073	98	19	[	[	X
ejpam-3073	98	20	0	0	NUM
ejpam-3073	98	21	,	,	PUNCT
ejpam-3073	98	22	k	k	NOUN
ejpam-3073	98	23	]	]	X
ejpam-3073	98	24	,	,	PUNCT
ejpam-3073	98	25	then	then	ADV
ejpam-3073	98	26	by	by	ADP
ejpam-3073	98	27	theorem	theorem	NOUN
ejpam-3073	98	28	3.2	3.2	NUM
ejpam-3073	98	29	,	,	PUNCT
ejpam-3073	98	30	(	(	PUNCT
ejpam-3073	98	31	17	17	NUM
ejpam-3073	98	32	)	)	PUNCT
ejpam-3073	98	33	becomes	become	VERB
ejpam-3073	98	34	l[y(xn);h	l[y(xn);h	PROPN
ejpam-3073	98	35	]	]	PUNCT
ejpam-3073	98	36	=	=	SYM
ejpam-3073	98	37	hp+2	hp+2	VERB
ejpam-3073	98	38	1	1	NUM
ejpam-3073	98	39	p	p	NOUN
ejpam-3073	98	40	!	!	PUNCT
ejpam-3073	99	1	(	(	PUNCT
ejpam-3073	99	2	∫	∫	PROPN
ejpam-3073	99	3	k	k	PROPN
ejpam-3073	99	4	0	0	PROPN
ejpam-3073	99	5	f	f	PROPN
ejpam-3073	99	6	(	(	PUNCT
ejpam-3073	99	7	t	t	PROPN
ejpam-3073	99	8	)	)	PUNCT
ejpam-3073	99	9	dt	dt	NOUN
ejpam-3073	99	10	)	)	PUNCT
ejpam-3073	100	1	y(p+2)(xn	y(p+2)(xn	PROPN
ejpam-3073	101	1	+	+	CCONJ
ejpam-3073	102	1	ξh	ξh	NOUN
ejpam-3073	102	2	)	)	PUNCT
ejpam-3073	102	3	,	,	PUNCT
ejpam-3073	102	4	0	0	PUNCT
ejpam-3073	102	5	<	<	X
ejpam-3073	102	6	ξ	ξ	X
ejpam-3073	102	7	<	<	X
ejpam-3073	102	8	k.	k.	PROPN
ejpam-3073	102	9	(	(	PUNCT
ejpam-3073	102	10	18	18	NUM
ejpam-3073	102	11	)	)	PUNCT
ejpam-3073	102	12	assume	assume	VERB
ejpam-3073	102	13	y(x	y(x	X
ejpam-3073	102	14	)	)	PUNCT
ejpam-3073	102	15	=	=	SYM
ejpam-3073	102	16	xp+2	xp+2	PROPN
ejpam-3073	102	17	,	,	PUNCT
ejpam-3073	102	18	such	such	ADJ
ejpam-3073	102	19	that	that	SCONJ
ejpam-3073	102	20	all	all	DET
ejpam-3073	102	21	derivatives	derivative	NOUN
ejpam-3073	102	22	of	of	ADP
ejpam-3073	102	23	xp+2	xp+2	NUM
ejpam-3073	102	24	of	of	ADP
ejpam-3073	102	25	order	order	NOUN
ejpam-3073	102	26	greater	great	ADJ
ejpam-3073	102	27	than	than	ADP
ejpam-3073	102	28	p	p	NOUN
ejpam-3073	102	29	+	+	CCONJ
ejpam-3073	102	30	2	2	NUM
ejpam-3073	102	31	vanish	vanish	VERB
ejpam-3073	102	32	identically	identically	ADV
ejpam-3073	102	33	.	.	PUNCT
ejpam-3073	103	1	then	then	ADV
ejpam-3073	103	2	,	,	PUNCT
ejpam-3073	103	3	by	by	ADP
ejpam-3073	103	4	(	(	PUNCT
ejpam-3073	103	5	18	18	NUM
ejpam-3073	103	6	)	)	PUNCT
ejpam-3073	103	7	and	and	CCONJ
ejpam-3073	103	8	the	the	DET
ejpam-3073	103	9	expansion	expansion	NOUN
ejpam-3073	103	10	of	of	ADP
ejpam-3073	103	11	the	the	DET
ejpam-3073	103	12	operator	operator	NOUN
ejpam-3073	103	13	l	l	NOUN
ejpam-3073	103	14	we	we	PRON
ejpam-3073	103	15	have	have	VERB
ejpam-3073	103	16	;	;	PUNCT
ejpam-3073	103	17	cp+2	cp+2	PROPN
ejpam-3073	103	18	=	=	SYM
ejpam-3073	103	19	1	1	NUM
ejpam-3073	103	20	p	p	NOUN
ejpam-3073	103	21	!	!	PUNCT
ejpam-3073	103	22	∫	∫	PROPN
ejpam-3073	104	1	k	k	NOUN
ejpam-3073	104	2	0	0	PUNCT
ejpam-3073	104	3	f	f	PROPN
ejpam-3073	104	4	(	(	PUNCT
ejpam-3073	104	5	t	t	PROPN
ejpam-3073	104	6	)	)	PUNCT
ejpam-3073	104	7	dt	dt	PROPN
ejpam-3073	104	8	.	.	PUNCT
ejpam-3073	105	1	(	(	PUNCT
ejpam-3073	105	2	19	19	NUM
ejpam-3073	105	3	)	)	PUNCT
ejpam-3073	105	4	thus	thus	ADV
ejpam-3073	105	5	,	,	PUNCT
ejpam-3073	105	6	(	(	PUNCT
ejpam-3073	105	7	19	19	NUM
ejpam-3073	105	8	)	)	PUNCT
ejpam-3073	105	9	becomes	become	VERB
ejpam-3073	105	10	l[y(xn);h	l[y(xn);h	PROPN
ejpam-3073	105	11	]	]	PUNCT
ejpam-3073	105	12	=	=	PUNCT
ejpam-3073	105	13	hp+2cp+2y	hp+2cp+2y	NOUN
ejpam-3073	105	14	(	(	PUNCT
ejpam-3073	105	15	p+2)(xn	p+2)(xn	PROPN
ejpam-3073	105	16	+	+	CCONJ
ejpam-3073	105	17	ξh	ξh	NOUN
ejpam-3073	105	18	)	)	PUNCT
ejpam-3073	105	19	,	,	PUNCT
ejpam-3073	106	1	0	0	PUNCT
ejpam-3073	106	2	<	<	X
ejpam-3073	106	3	ξ	ξ	X
ejpam-3073	106	4	<	<	X
ejpam-3073	106	5	k	k	X
ejpam-3073	106	6	(	(	PUNCT
ejpam-3073	106	7	20	20	NUM
ejpam-3073	106	8	)	)	PUNCT
ejpam-3073	106	9	which	which	PRON
ejpam-3073	106	10	is	be	AUX
ejpam-3073	106	11	the	the	DET
ejpam-3073	106	12	desired	desire	VERB
ejpam-3073	106	13	form	form	NOUN
ejpam-3073	106	14	.	.	PUNCT
ejpam-3073	107	1	hence	hence	ADV
ejpam-3073	107	2	,	,	PUNCT
ejpam-3073	107	3	|l[y(xn);h]|	|l[y(xn);h]|	PROPN
ejpam-3073	107	4	=	=	SYM
ejpam-3073	107	5	|hp+2cp+2y	|hp+2cp+2y	PROPN
ejpam-3073	107	6	(	(	PUNCT
ejpam-3073	107	7	p+2)(xn	p+2)(xn	NOUN
ejpam-3073	107	8	+	+	CCONJ
ejpam-3073	107	9	ξh)|	ξh)|	PROPN
ejpam-3073	107	10	≤	≤	ADJ
ejpam-3073	107	11	|hp+2||cp+2|	|hp+2||cp+2|	NOUN
ejpam-3073	107	12	max	max	PROPN
ejpam-3073	107	13	x∈[a	x∈[a	PROPN
ejpam-3073	107	14	,	,	PUNCT
ejpam-3073	107	15	b	b	AUX
ejpam-3073	107	16	]	]	PUNCT
ejpam-3073	107	17	|y(p+2)(x)|	|y(p+2)(x)|	PUNCT
ejpam-3073	107	18	∴	∴	PROPN
ejpam-3073	107	19	|l[y(xn);h]|	|l[y(xn);h]|	PROPN
ejpam-3073	107	20	≤	≤	NUM
ejpam-3073	107	21	hp+2qy	hp+2qy	X
ejpam-3073	107	22	.	.	PUNCT
ejpam-3073	108	1	(	(	PUNCT
ejpam-3073	108	2	21	21	NUM
ejpam-3073	108	3	)	)	PUNCT
ejpam-3073	108	4	4	4	NUM
ejpam-3073	108	5	.	.	PUNCT
ejpam-3073	109	1	application	application	NOUN
ejpam-3073	109	2	of	of	ADP
ejpam-3073	109	3	the	the	DET
ejpam-3073	109	4	bound	bind	VERB
ejpam-3073	109	5	suppose	suppose	VERB
ejpam-3073	109	6	the	the	DET
ejpam-3073	109	7	continuous	continuous	ADJ
ejpam-3073	109	8	implicit	implicit	ADJ
ejpam-3073	109	9	hybrid	hybrid	NOUN
ejpam-3073	109	10	one	one	NUM
ejpam-3073	109	11	step	step	NOUN
ejpam-3073	109	12	method	method	NOUN
ejpam-3073	109	13	proposed	propose	VERB
ejpam-3073	109	14	in	in	ADP
ejpam-3073	109	15	anake	anake	NOUN
ejpam-3073	109	16	and	and	CCONJ
ejpam-3073	109	17	adoghe	adoghe	ADJ
ejpam-3073	109	18	(	(	PUNCT
ejpam-3073	109	19	2013	2013	NUM
ejpam-3073	109	20	)	)	PUNCT
ejpam-3073	109	21	,	,	PUNCT
ejpam-3073	109	22	by	by	ADP
ejpam-3073	109	23	evaluating	evaluate	VERB
ejpam-3073	109	24	(	(	PUNCT
ejpam-3073	109	25	1	1	NUM
ejpam-3073	109	26	)	)	PUNCT
ejpam-3073	109	27	at	at	ADP
ejpam-3073	109	28	the	the	DET
ejpam-3073	109	29	point	point	NOUN
ejpam-3073	109	30	xn+1	xn+1	ADV
ejpam-3073	109	31	,	,	PUNCT
ejpam-3073	109	32	given	give	VERB
ejpam-3073	109	33	as	as	SCONJ
ejpam-3073	109	34	follows	follow	VERB
ejpam-3073	109	35	:	:	PUNCT
ejpam-3073	109	36	yn+1	yn+1	PROPN
ejpam-3073	109	37	=	=	SYM
ejpam-3073	109	38	2yn+	2yn+	NUM
ejpam-3073	109	39	4	4	NUM
ejpam-3073	109	40	5	5	NUM
ejpam-3073	109	41	−yn+	−yn+	NOUN
ejpam-3073	109	42	3	3	NUM
ejpam-3073	109	43	5	5	NUM
ejpam-3073	109	44	+	+	CCONJ
ejpam-3073	109	45	h2	h2	NOUN
ejpam-3073	109	46	6000	6000	NUM
ejpam-3073	109	47	[	[	PUNCT
ejpam-3073	109	48	18fn+1	18fn+1	NUM
ejpam-3073	109	49	+	+	CCONJ
ejpam-3073	109	50	209fn+	209fn+	NUM
ejpam-3073	109	51	4	4	NUM
ejpam-3073	109	52	5	5	NUM
ejpam-3073	109	53	+	+	SYM
ejpam-3073	109	54	4fn+	4fn+	NUM
ejpam-3073	109	55	3	3	NUM
ejpam-3073	109	56	5	5	NUM
ejpam-3073	109	57	+	+	CCONJ
ejpam-3073	109	58	14fn+	14fn+	NUM
ejpam-3073	109	59	2	2	NUM
ejpam-3073	109	60	5	5	NUM
ejpam-3073	109	61	−	−	NOUN
ejpam-3073	109	62	6fn+	6fn+	NUM
ejpam-3073	109	63	1	1	NUM
ejpam-3073	109	64	5	5	NUM
ejpam-3073	109	65	+	+	SYM
ejpam-3073	109	66	fn	fn	NOUN
ejpam-3073	109	67	]	]	PUNCT
ejpam-3073	109	68	,	,	PUNCT
ejpam-3073	109	69	(	(	PUNCT
ejpam-3073	109	70	22	22	NUM
ejpam-3073	109	71	)	)	PUNCT
ejpam-3073	109	72	is	be	AUX
ejpam-3073	109	73	implemented	implement	VERB
ejpam-3073	109	74	for	for	ADP
ejpam-3073	109	75	the	the	DET
ejpam-3073	109	76	solution	solution	NOUN
ejpam-3073	109	77	of	of	ADP
ejpam-3073	109	78	the	the	DET
ejpam-3073	109	79	initial	initial	ADJ
ejpam-3073	109	80	value	value	NOUN
ejpam-3073	109	81	problem	problem	NOUN
ejpam-3073	109	82	:	:	PUNCT
ejpam-3073	109	83	lq′′	lq′′	PROPN
ejpam-3073	109	84	+	+	ADJ
ejpam-3073	109	85	rq′	rq′	ADJ
ejpam-3073	109	86	+	+	CCONJ
ejpam-3073	109	87	1	1	NUM
ejpam-3073	109	88	c	c	NOUN
ejpam-3073	109	89	q	q	NOUN
ejpam-3073	110	1	=	=	NOUN
ejpam-3073	111	1	e(t	e(t	NOUN
ejpam-3073	111	2	)	)	PUNCT
ejpam-3073	111	3	,	,	PUNCT
ejpam-3073	111	4	q(0	q(0	PROPN
ejpam-3073	111	5	)	)	PUNCT
ejpam-3073	111	6	=	=	SYM
ejpam-3073	112	1	0	0	NUM
ejpam-3073	112	2	,	,	PUNCT
ejpam-3073	112	3	q′(0	q′(0	PROPN
ejpam-3073	112	4	)	)	PUNCT
ejpam-3073	112	5	=	=	SYM
ejpam-3073	112	6	0	0	NUM
ejpam-3073	112	7	t.	t.	PROPN
ejpam-3073	112	8	a.	a.	PROPN
ejpam-3073	112	9	anake	anake	PROPN
ejpam-3073	112	10	,	,	PUNCT
ejpam-3073	112	11	s.	s.	PROPN
ejpam-3073	112	12	o.	o.	PROPN
ejpam-3073	112	13	edeki	edeki	PROPN
ejpam-3073	112	14	/	/	SYM
ejpam-3073	112	15	eur	eur	PROPN
ejpam-3073	112	16	.	.	PUNCT
ejpam-3073	113	1	j.	j.	PROPN
ejpam-3073	113	2	pure	pure	PROPN
ejpam-3073	113	3	appl	appl	PROPN
ejpam-3073	113	4	.	.	PROPN
ejpam-3073	113	5	math	math	PROPN
ejpam-3073	113	6	,	,	PUNCT
ejpam-3073	113	7	10	10	NUM
ejpam-3073	113	8	(	(	PUNCT
ejpam-3073	113	9	5	5	NUM
ejpam-3073	113	10	)	)	PUNCT
ejpam-3073	113	11	(	(	PUNCT
ejpam-3073	113	12	2017	2017	NUM
ejpam-3073	113	13	)	)	PUNCT
ejpam-3073	113	14	,	,	PUNCT
ejpam-3073	113	15	1092	1092	NUM
ejpam-3073	113	16	-	-	SYM
ejpam-3073	113	17	1098	1098	NUM
ejpam-3073	113	18	1097	1097	NUM
ejpam-3073	113	19	with	with	ADP
ejpam-3073	113	20	exact	exact	ADJ
ejpam-3073	113	21	solution	solution	NOUN
ejpam-3073	113	22	:	:	PUNCT
ejpam-3073	113	23	q(t	q(t	X
ejpam-3073	113	24	)	)	PUNCT
ejpam-3073	113	25	=	=	SYM
ejpam-3073	113	26	3	3	NUM
ejpam-3073	113	27	4	4	NUM
ejpam-3073	113	28	−	−	NOUN
ejpam-3073	113	29	3	3	NUM
ejpam-3073	113	30	4	4	NUM
ejpam-3073	113	31	e−10t(cos	e−10t(co	NOUN
ejpam-3073	113	32	10t+	10t+	NUM
ejpam-3073	113	33	sin	sin	NOUN
ejpam-3073	113	34	10	10	NUM
ejpam-3073	113	35	t	t	NOUN
ejpam-3073	113	36	)	)	PUNCT
ejpam-3073	113	37	,	,	PUNCT
ejpam-3073	113	38	where	where	SCONJ
ejpam-3073	113	39	l	l	NOUN
ejpam-3073	113	40	=	=	SYM
ejpam-3073	113	41	1	1	NUM
ejpam-3073	113	42	,	,	PUNCT
ejpam-3073	113	43	c	c	NOUN
ejpam-3073	113	44	=	=	SYM
ejpam-3073	113	45	0.005	0.005	NUM
ejpam-3073	113	46	,	,	PUNCT
ejpam-3073	113	47	e(t	e(t	NOUN
ejpam-3073	113	48	)	)	PUNCT
ejpam-3073	113	49	=	=	SYM
ejpam-3073	113	50	150	150	NUM
ejpam-3073	113	51	and	and	CCONJ
ejpam-3073	113	52	r	r	NOUN
ejpam-3073	113	53	=	=	SYM
ejpam-3073	113	54	20	20	NUM
ejpam-3073	113	55	.	.	PUNCT
ejpam-3073	114	1	according	accord	VERB
ejpam-3073	114	2	to	to	ADP
ejpam-3073	114	3	anake	anake	NOUN
ejpam-3073	114	4	and	and	CCONJ
ejpam-3073	114	5	adoghe(2013	adoghe(2013	NUM
ejpam-3073	114	6	)	)	PUNCT
ejpam-3073	114	7	,	,	PUNCT
ejpam-3073	114	8	application	application	NOUN
ejpam-3073	114	9	of	of	ADP
ejpam-3073	114	10	the	the	DET
ejpam-3073	114	11	convergent	convergent	NOUN
ejpam-3073	114	12	method	method	NOUN
ejpam-3073	114	13	,	,	PUNCT
ejpam-3073	114	14	of	of	ADP
ejpam-3073	114	15	order	order	NOUN
ejpam-3073	114	16	p	p	X
ejpam-3073	114	17	=	=	NOUN
ejpam-3073	114	18	6	6	NUM
ejpam-3073	114	19	,	,	PUNCT
ejpam-3073	114	20	at	at	ADP
ejpam-3073	114	21	the	the	DET
ejpam-3073	114	22	first	first	ADJ
ejpam-3073	114	23	grid	grid	NOUN
ejpam-3073	114	24	point	point	NOUN
ejpam-3073	114	25	xn+1	xn+1	PROPN
ejpam-3073	114	26	yields	yield	VERB
ejpam-3073	114	27	the	the	DET
ejpam-3073	114	28	local	local	ADJ
ejpam-3073	114	29	error	error	NOUN
ejpam-3073	114	30	constant	constant	ADJ
ejpam-3073	114	31	cp+2	cp+2	NOUN
ejpam-3073	114	32	=	=	PUNCT
ejpam-3073	114	33	−	−	PROPN
ejpam-3073	114	34	221	221	NUM
ejpam-3073	114	35	23625000000	23625000000	NUM
ejpam-3073	114	36	.	.	PUNCT
ejpam-3073	115	1	to	to	PART
ejpam-3073	115	2	apply	apply	VERB
ejpam-3073	115	3	(	(	PUNCT
ejpam-3073	115	4	21	21	NUM
ejpam-3073	115	5	)	)	PUNCT
ejpam-3073	115	6	,	,	PUNCT
ejpam-3073	115	7	we	we	PRON
ejpam-3073	115	8	will	will	AUX
ejpam-3073	115	9	need	need	VERB
ejpam-3073	115	10	to	to	PART
ejpam-3073	115	11	find	find	VERB
ejpam-3073	115	12	q	q	NOUN
ejpam-3073	115	13	,	,	PUNCT
ejpam-3073	115	14	y	y	PROPN
ejpam-3073	115	15	and	and	CCONJ
ejpam-3073	115	16	choose	choose	VERB
ejpam-3073	115	17	a	a	DET
ejpam-3073	115	18	suitable	suitable	ADJ
ejpam-3073	115	19	step	step	NOUN
ejpam-3073	115	20	size	size	NOUN
ejpam-3073	115	21	.	.	PUNCT
ejpam-3073	116	1	thus	thus	ADV
ejpam-3073	116	2	,	,	PUNCT
ejpam-3073	116	3	we	we	PRON
ejpam-3073	116	4	checked	check	VERB
ejpam-3073	116	5	that	that	SCONJ
ejpam-3073	116	6	(	(	PUNCT
ejpam-3073	116	7	19	19	NUM
ejpam-3073	116	8	)	)	PUNCT
ejpam-3073	116	9	is	be	AUX
ejpam-3073	116	10	satisfied	satisfied	ADJ
ejpam-3073	116	11	and	and	CCONJ
ejpam-3073	116	12	the	the	DET
ejpam-3073	116	13	result	result	NOUN
ejpam-3073	116	14	of	of	ADP
ejpam-3073	116	15	our	our	PRON
ejpam-3073	116	16	computation	computation	NOUN
ejpam-3073	116	17	agrees	agree	VERB
ejpam-3073	116	18	with	with	SCONJ
ejpam-3073	116	19	the	the	DET
ejpam-3073	116	20	error	error	NOUN
ejpam-3073	116	21	constant	constant	NOUN
ejpam-3073	116	22	reported	report	VERB
ejpam-3073	116	23	by	by	ADP
ejpam-3073	116	24	anake	anake	NOUN
ejpam-3073	116	25	and	and	CCONJ
ejpam-3073	116	26	adoghe	adoghe	ADJ
ejpam-3073	116	27	(	(	PUNCT
ejpam-3073	116	28	2013	2013	NUM
ejpam-3073	116	29	)	)	PUNCT
ejpam-3073	116	30	as	as	SCONJ
ejpam-3073	116	31	follows	follow	VERB
ejpam-3073	116	32	:	:	PUNCT
ejpam-3073	116	33	q	q	NOUN
ejpam-3073	116	34	=	=	SYM
ejpam-3073	116	35	|cp+2|	|cp+2|	NOUN
ejpam-3073	116	36	=	=	SYM
ejpam-3073	116	37	∣∣	∣∣	X
ejpam-3073	117	1	1	1	NUM
ejpam-3073	117	2	p	p	NOUN
ejpam-3073	117	3	!	!	PUNCT
ejpam-3073	117	4	∫	∫	PROPN
ejpam-3073	118	1	1	1	NUM
ejpam-3073	118	2	0	0	NUM
ejpam-3073	118	3	f	f	PROPN
ejpam-3073	118	4	(	(	PUNCT
ejpam-3073	118	5	t	t	PROPN
ejpam-3073	118	6	)	)	PUNCT
ejpam-3073	118	7	dt	dt	PUNCT
ejpam-3073	118	8	∣∣	∣∣	X
ejpam-3073	118	9	=	=	PUNCT
ejpam-3073	118	10	221	221	NUM
ejpam-3073	118	11	23625000000	23625000000	NUM
ejpam-3073	118	12	,	,	PUNCT
ejpam-3073	118	13	where	where	SCONJ
ejpam-3073	118	14	f	f	PROPN
ejpam-3073	118	15	(	(	PUNCT
ejpam-3073	118	16	t	t	PROPN
ejpam-3073	118	17	)	)	PUNCT
ejpam-3073	118	18	=	=	SYM
ejpam-3073	118	19	1	1	NUM
ejpam-3073	118	20	7	7	NUM
ejpam-3073	118	21	(	(	PUNCT
ejpam-3073	118	22	(	(	PUNCT
ejpam-3073	118	23	3	3	NUM
ejpam-3073	118	24	5	5	NUM
ejpam-3073	118	25	−	−	PROPN
ejpam-3073	118	26	t	t	NOUN
ejpam-3073	118	27	)	)	PUNCT
ejpam-3073	118	28	7	7	NUM
ejpam-3073	119	1	+	+	CCONJ
ejpam-3073	119	2	−	−	NUM
ejpam-3073	119	3	2	2	NUM
ejpam-3073	119	4	(	(	PUNCT
ejpam-3073	119	5	4	4	NUM
ejpam-3073	119	6	5	5	NUM
ejpam-3073	119	7	−	−	PROPN
ejpam-3073	119	8	t	t	NOUN
ejpam-3073	119	9	)	)	PUNCT
ejpam-3073	119	10	7	7	NUM
ejpam-3073	120	1	+	+	CCONJ
ejpam-3073	120	2	+	+	CCONJ
ejpam-3073	120	3	(	(	PUNCT
ejpam-3073	120	4	1−	1−	NUM
ejpam-3073	120	5	t)7	t)7	NOUN
ejpam-3073	120	6	+	+	NUM
ejpam-3073	120	7	)	)	PUNCT
ejpam-3073	121	1	−	−	PROPN
ejpam-3073	121	2	1	1	NUM
ejpam-3073	121	3	1000	1000	NUM
ejpam-3073	121	4	(	(	PUNCT
ejpam-3073	121	5	18(1−	18(1−	NUM
ejpam-3073	121	6	t)5	t)5	NOUN
ejpam-3073	121	7	+	+	CCONJ
ejpam-3073	121	8	+	+	NUM
ejpam-3073	121	9	209	209	NUM
ejpam-3073	121	10	(	(	PUNCT
ejpam-3073	121	11	4	4	NUM
ejpam-3073	121	12	5	5	NUM
ejpam-3073	121	13	−	−	PROPN
ejpam-3073	121	14	t	t	NOUN
ejpam-3073	121	15	)	)	PUNCT
ejpam-3073	121	16	5	5	NUM
ejpam-3073	122	1	+	+	CCONJ
ejpam-3073	122	2	+4	+4	PROPN
ejpam-3073	122	3	(	(	PUNCT
ejpam-3073	122	4	3	3	NUM
ejpam-3073	122	5	5	5	NUM
ejpam-3073	122	6	−	−	PROPN
ejpam-3073	122	7	t	t	NOUN
ejpam-3073	122	8	)	)	PUNCT
ejpam-3073	122	9	5	5	NUM
ejpam-3073	123	1	+	+	CCONJ
ejpam-3073	123	2	+	+	NUM
ejpam-3073	123	3	14	14	NUM
ejpam-3073	123	4	(	(	PUNCT
ejpam-3073	123	5	2	2	NUM
ejpam-3073	123	6	5	5	NUM
ejpam-3073	123	7	−	−	PROPN
ejpam-3073	123	8	t	t	NOUN
ejpam-3073	123	9	)	)	PUNCT
ejpam-3073	123	10	5	5	NUM
ejpam-3073	124	1	+	+	CCONJ
ejpam-3073	124	2	−	−	NUM
ejpam-3073	124	3	6	6	NUM
ejpam-3073	124	4	(	(	PUNCT
ejpam-3073	124	5	1	1	NUM
ejpam-3073	124	6	5	5	NUM
ejpam-3073	124	7	−	−	PROPN
ejpam-3073	124	8	t	t	NOUN
ejpam-3073	124	9	)	)	PUNCT
ejpam-3073	124	10	5	5	NUM
ejpam-3073	125	1	+	+	CCONJ
ejpam-3073	125	2	+	+	CCONJ
ejpam-3073	125	3	(	(	PUNCT
ejpam-3073	125	4	0−	0−	NUM
ejpam-3073	125	5	t)5	t)5	NOUN
ejpam-3073	125	6	+	+	NUM
ejpam-3073	125	7	)	)	PUNCT
ejpam-3073	125	8	.	.	PUNCT
ejpam-3073	126	1	by	by	ADP
ejpam-3073	126	2	(	(	PUNCT
ejpam-3073	126	3	17	17	NUM
ejpam-3073	126	4	)	)	PUNCT
ejpam-3073	126	5	given	give	VERB
ejpam-3073	126	6	that	that	DET
ejpam-3073	126	7	p	p	NOUN
ejpam-3073	126	8	=	=	SYM
ejpam-3073	126	9	6	6	NUM
ejpam-3073	126	10	,	,	PUNCT
ejpam-3073	126	11	y	y	PROPN
ejpam-3073	126	12	is	be	AUX
ejpam-3073	126	13	obtained	obtain	VERB
ejpam-3073	126	14	as	as	ADP
ejpam-3073	126	15	follows	follow	VERB
ejpam-3073	126	16	:	:	PUNCT
ejpam-3073	126	17	y(p+2	y(p+2	NUM
ejpam-3073	126	18	)	)	PUNCT
ejpam-3073	126	19	=	=	SYM
ejpam-3073	127	1	q(8)(t	q(8)(t	X
ejpam-3073	127	2	)	)	PUNCT
ejpam-3073	127	3	=	=	SYM
ejpam-3073	127	4	1200000000e−10t(cos	1200000000e−10t(cos	NUM
ejpam-3073	127	5	10t+	10t+	NUM
ejpam-3073	127	6	sin	sin	NOUN
ejpam-3073	127	7	10	10	NUM
ejpam-3073	127	8	t	t	NOUN
ejpam-3073	127	9	)	)	PUNCT
ejpam-3073	127	10	.	.	PUNCT
ejpam-3073	128	1	(	(	PUNCT
ejpam-3073	128	2	23	23	NUM
ejpam-3073	128	3	)	)	PUNCT
ejpam-3073	128	4	hence	hence	ADV
ejpam-3073	128	5	,	,	PUNCT
ejpam-3073	128	6	y	y	PROPN
ejpam-3073	128	7	=	=	PUNCT
ejpam-3073	128	8	max	max	PROPN
ejpam-3073	128	9	x∈[0,1	x∈[0,1	PROPN
ejpam-3073	128	10	]	]	PUNCT
ejpam-3073	128	11	|y(p+2)(x)|	|y(p+2)(x)|	PUNCT
ejpam-3073	128	12	=	=	SYM
ejpam-3073	128	13	75351	75351	NUM
ejpam-3073	128	14	.	.	PUNCT
ejpam-3073	129	1	(	(	PUNCT
ejpam-3073	129	2	24	24	NUM
ejpam-3073	129	3	)	)	PUNCT
ejpam-3073	129	4	the	the	DET
ejpam-3073	129	5	bound	bind	VERB
ejpam-3073	129	6	on	on	ADP
ejpam-3073	129	7	the	the	DET
ejpam-3073	129	8	application	application	NOUN
ejpam-3073	129	9	of	of	ADP
ejpam-3073	129	10	the	the	DET
ejpam-3073	129	11	method	method	NOUN
ejpam-3073	129	12	(	(	PUNCT
ejpam-3073	129	13	22	22	NUM
ejpam-3073	129	14	)	)	PUNCT
ejpam-3073	129	15	at	at	ADP
ejpam-3073	129	16	the	the	DET
ejpam-3073	129	17	point	point	NOUN
ejpam-3073	129	18	xn+1	xn+1	NUM
ejpam-3073	129	19	obtained	obtain	VERB
ejpam-3073	129	20	for	for	ADP
ejpam-3073	129	21	different	different	ADJ
ejpam-3073	129	22	values	value	NOUN
ejpam-3073	129	23	of	of	ADP
ejpam-3073	129	24	the	the	DET
ejpam-3073	129	25	step	step	NOUN
ejpam-3073	129	26	size	size	NOUN
ejpam-3073	129	27	h	h	NOUN
ejpam-3073	129	28	is	be	AUX
ejpam-3073	129	29	shown	show	VERB
ejpam-3073	129	30	in	in	ADP
ejpam-3073	129	31	the	the	DET
ejpam-3073	129	32	table	table	NOUN
ejpam-3073	129	33	below	below	ADV
ejpam-3073	129	34	:	:	PUNCT
ejpam-3073	129	35	table	table	NOUN
ejpam-3073	129	36	1	1	NUM
ejpam-3073	129	37	:	:	PUNCT
ejpam-3073	129	38	different	different	ADJ
ejpam-3073	129	39	values	value	NOUN
ejpam-3073	129	40	of	of	ADP
ejpam-3073	129	41	h	h	NOUN
ejpam-3073	129	42	and	and	CCONJ
ejpam-3073	129	43	the	the	DET
ejpam-3073	129	44	corresponding	corresponding	ADJ
ejpam-3073	129	45	bound	bind	VERB
ejpam-3073	129	46	h	h	NOUN
ejpam-3073	129	47	hp+2qy	hp+2qy	NOUN
ejpam-3073	129	48	0.003125	0.003125	NUM
ejpam-3073	129	49	6.4108×10−24	6.4108×10−24	NUM
ejpam-3073	129	50	0.01	0.01	NUM
ejpam-3073	129	51	7.0487×10−20	7.0487×10−20	NUM
ejpam-3073	129	52	0.03	0.03	NUM
ejpam-3073	129	53	4.6247×10−16	4.6247×10−16	PROPN
ejpam-3073	129	54	0.05	0.05	NUM
ejpam-3073	129	55	2.7534×10−14	2.7534×10−14	NUM
ejpam-3073	129	56	0.10	0.10	NUM
ejpam-3073	129	57	7.0487×10−12	7.0487×10−12	NUM
ejpam-3073	129	58	5	5	NUM
ejpam-3073	129	59	.	.	PUNCT
ejpam-3073	130	1	conclusion	conclusion	VERB
ejpam-3073	130	2	a	a	DET
ejpam-3073	130	3	method	method	NOUN
ejpam-3073	130	4	for	for	ADP
ejpam-3073	130	5	the	the	DET
ejpam-3073	130	6	bound	bind	VERB
ejpam-3073	130	7	on	on	ADP
ejpam-3073	130	8	the	the	DET
ejpam-3073	130	9	local	local	ADJ
ejpam-3073	130	10	truncation	truncation	NOUN
ejpam-3073	130	11	error	error	NOUN
ejpam-3073	130	12	has	have	AUX
ejpam-3073	130	13	been	be	AUX
ejpam-3073	130	14	derived	derive	VERB
ejpam-3073	130	15	in	in	ADP
ejpam-3073	130	16	this	this	DET
ejpam-3073	130	17	paper	paper	NOUN
ejpam-3073	130	18	.	.	PUNCT
ejpam-3073	131	1	the	the	DET
ejpam-3073	131	2	method	method	NOUN
ejpam-3073	131	3	has	have	AUX
ejpam-3073	131	4	been	be	AUX
ejpam-3073	131	5	applied	apply	VERB
ejpam-3073	131	6	to	to	ADP
ejpam-3073	131	7	the	the	DET
ejpam-3073	131	8	continuous	continuous	ADJ
ejpam-3073	131	9	implicit	implicit	ADJ
ejpam-3073	131	10	hybrid	hybrid	NOUN
ejpam-3073	131	11	one	one	NUM
ejpam-3073	131	12	step	step	NOUN
ejpam-3073	131	13	method	method	NOUN
ejpam-3073	131	14	proposed	propose	VERB
ejpam-3073	131	15	by	by	ADP
ejpam-3073	131	16	anake	anake	NOUN
ejpam-3073	131	17	and	and	CCONJ
ejpam-3073	131	18	adoghe	adoghe	ADJ
ejpam-3073	131	19	(	(	PUNCT
ejpam-3073	131	20	2013	2013	NUM
ejpam-3073	131	21	)	)	PUNCT
ejpam-3073	131	22	and	and	CCONJ
ejpam-3073	131	23	bounds	bound	NOUN
ejpam-3073	131	24	were	be	AUX
ejpam-3073	131	25	obtained	obtain	VERB
ejpam-3073	131	26	,	,	PUNCT
ejpam-3073	131	27	in	in	ADP
ejpam-3073	131	28	the	the	DET
ejpam-3073	131	29	application	application	NOUN
ejpam-3073	131	30	of	of	ADP
ejpam-3073	131	31	the	the	DET
ejpam-3073	131	32	method	method	NOUN
ejpam-3073	131	33	at	at	ADP
ejpam-3073	131	34	the	the	DET
ejpam-3073	131	35	point	point	NOUN
ejpam-3073	131	36	xn+1	xn+1	ADV
ejpam-3073	131	37	,	,	PUNCT
ejpam-3073	131	38	on	on	ADP
ejpam-3073	131	39	the	the	DET
ejpam-3073	131	40	local	local	ADJ
ejpam-3073	131	41	truncation	truncation	NOUN
ejpam-3073	131	42	error	error	NOUN
ejpam-3073	131	43	for	for	ADP
ejpam-3073	131	44	different	different	ADJ
ejpam-3073	131	45	values	value	NOUN
ejpam-3073	131	46	of	of	ADP
ejpam-3073	131	47	h.	h.	PROPN
ejpam-3073	132	1	it	it	PRON
ejpam-3073	132	2	is	be	AUX
ejpam-3073	132	3	observed	observe	VERB
ejpam-3073	132	4	references	reference	NOUN
ejpam-3073	132	5	1098	1098	NUM
ejpam-3073	132	6	that	that	SCONJ
ejpam-3073	132	7	the	the	DET
ejpam-3073	132	8	magnitude	magnitude	NOUN
ejpam-3073	132	9	of	of	ADP
ejpam-3073	132	10	the	the	DET
ejpam-3073	132	11	bound	bind	VERB
ejpam-3073	132	12	computed	compute	VERB
ejpam-3073	132	13	reduces	reduce	VERB
ejpam-3073	132	14	as	as	ADP
ejpam-3073	132	15	h→	h→	NOUN
ejpam-3073	132	16	0	0	NUM
ejpam-3073	132	17	.	.	PUNCT
ejpam-3073	133	1	this	this	PRON
ejpam-3073	133	2	indicates	indicate	VERB
ejpam-3073	133	3	that	that	SCONJ
ejpam-3073	133	4	the	the	DET
ejpam-3073	133	5	size	size	NOUN
ejpam-3073	133	6	of	of	ADP
ejpam-3073	133	7	the	the	DET
ejpam-3073	133	8	global	global	ADJ
ejpam-3073	133	9	error	error	NOUN
ejpam-3073	133	10	reduces	reduce	VERB
ejpam-3073	133	11	with	with	ADP
ejpam-3073	133	12	decrease	decrease	NOUN
ejpam-3073	133	13	in	in	ADP
ejpam-3073	133	14	the	the	DET
ejpam-3073	133	15	step	step	NOUN
ejpam-3073	133	16	size	size	NOUN
ejpam-3073	133	17	and	and	CCONJ
ejpam-3073	133	18	consequently	consequently	ADV
ejpam-3073	133	19	,	,	PUNCT
ejpam-3073	133	20	the	the	DET
ejpam-3073	133	21	accuracy	accuracy	NOUN
ejpam-3073	133	22	of	of	ADP
ejpam-3073	133	23	the	the	DET
ejpam-3073	133	24	approximation	approximation	NOUN
ejpam-3073	133	25	theoretically	theoretically	ADV
ejpam-3073	133	26	improves	improve	VERB
ejpam-3073	133	27	.	.	PUNCT
ejpam-3073	134	1	acknowledgements	acknowledgement	NOUN
ejpam-3073	134	2	the	the	DET
ejpam-3073	134	3	authors	author	NOUN
ejpam-3073	134	4	are	be	AUX
ejpam-3073	134	5	sincerely	sincerely	ADV
ejpam-3073	134	6	grateful	grateful	ADJ
ejpam-3073	134	7	to	to	ADP
ejpam-3073	134	8	covenant	covenant	ADJ
ejpam-3073	134	9	university	university	NOUN
ejpam-3073	134	10	for	for	ADP
ejpam-3073	134	11	financial	financial	ADJ
ejpam-3073	134	12	support	support	NOUN
ejpam-3073	134	13	and	and	CCONJ
ejpam-3073	134	14	provision	provision	NOUN
ejpam-3073	134	15	of	of	ADP
ejpam-3073	134	16	good	good	ADJ
ejpam-3073	134	17	working	working	NOUN
ejpam-3073	134	18	environment	environment	NOUN
ejpam-3073	134	19	.	.	PUNCT
ejpam-3073	135	1	the	the	DET
ejpam-3073	135	2	referees	referee	NOUN
ejpam-3073	135	3	’	’	PART
ejpam-3073	135	4	helpful	helpful	ADJ
ejpam-3073	135	5	comments	comment	NOUN
ejpam-3073	135	6	are	be	AUX
ejpam-3073	135	7	highly	highly	ADV
ejpam-3073	135	8	appreciated	appreciated	ADJ
ejpam-3073	135	9	.	.	PUNCT
ejpam-3073	136	1	references	reference	NOUN
ejpam-3073	136	2	[	[	X
ejpam-3073	136	3	1	1	NUM
ejpam-3073	136	4	]	]	PUNCT
ejpam-3073	136	5	anake	anake	NOUN
ejpam-3073	136	6	,	,	PUNCT
ejpam-3073	136	7	t.a	t.a	PROPN
ejpam-3073	136	8	.	.	PROPN
ejpam-3073	136	9	,	,	PUNCT
ejpam-3073	136	10	continuous	continuous	ADJ
ejpam-3073	136	11	implicit	implicit	ADJ
ejpam-3073	136	12	hybrid	hybrid	ADJ
ejpam-3073	136	13	one	one	NUM
ejpam-3073	136	14	step	step	NOUN
ejpam-3073	136	15	methods	method	NOUN
ejpam-3073	136	16	for	for	ADP
ejpam-3073	136	17	the	the	DET
ejpam-3073	136	18	solutions	solution	NOUN
ejpam-3073	136	19	of	of	ADP
ejpam-3073	136	20	initial	initial	ADJ
ejpam-3073	136	21	value	value	NOUN
ejpam-3073	136	22	problems	problem	NOUN
ejpam-3073	136	23	of	of	ADP
ejpam-3073	136	24	general	general	ADJ
ejpam-3073	136	25	second	second	ADJ
ejpam-3073	136	26	order	order	NOUN
ejpam-3073	136	27	ordinary	ordinary	ADJ
ejpam-3073	136	28	differential	differential	ADJ
ejpam-3073	136	29	equations	equation	NOUN
ejpam-3073	136	30	,	,	PUNCT
ejpam-3073	136	31	ph.d	ph.d	PROPN
ejpam-3073	136	32	thesis	thesis	NOUN
ejpam-3073	136	33	,	,	PUNCT
ejpam-3073	136	34	covenant	covenant	ADJ
ejpam-3073	136	35	university	university	NOUN
ejpam-3073	136	36	,	,	PUNCT
ejpam-3073	136	37	canaanland	canaanland	PROPN
ejpam-3073	136	38	,	,	PUNCT
ejpam-3073	136	39	ota	ota	PROPN
ejpam-3073	136	40	,	,	PUNCT
ejpam-3073	136	41	ogun	ogun	PROPN
ejpam-3073	136	42	state	state	PROPN
ejpam-3073	136	43	,	,	PUNCT
ejpam-3073	136	44	nigeria	nigeria	PROPN
ejpam-3073	136	45	.	.	PUNCT
ejpam-3073	137	1	2011	2011	NUM
ejpam-3073	137	2	.	.	PUNCT
ejpam-3073	138	1	[	[	X
ejpam-3073	138	2	2	2	NUM
ejpam-3073	138	3	]	]	PUNCT
ejpam-3073	138	4	anake	anake	NOUN
ejpam-3073	138	5	,	,	PUNCT
ejpam-3073	138	6	t.a	t.a	PROPN
ejpam-3073	138	7	.	.	PROPN
ejpam-3073	138	8	and	and	CCONJ
ejpam-3073	138	9	l.	l.	PROPN
ejpam-3073	138	10	adoghe	adoghe	PROPN
ejpam-3073	138	11	.	.	PUNCT
ejpam-3073	139	1	a	a	DET
ejpam-3073	139	2	four	four	NUM
ejpam-3073	139	3	point	point	NOUN
ejpam-3073	139	4	integration	integration	NOUN
ejpam-3073	139	5	method	method	NOUN
ejpam-3073	139	6	for	for	ADP
ejpam-3073	139	7	the	the	DET
ejpam-3073	139	8	solutions	solution	NOUN
ejpam-3073	139	9	of	of	ADP
ejpam-3073	139	10	ivp	ivp	NOUN
ejpam-3073	139	11	in	in	ADP
ejpam-3073	139	12	ode	ode	PROPN
ejpam-3073	139	13	.	.	PUNCT
ejpam-3073	140	1	australian	australian	ADJ
ejpam-3073	140	2	journal	journal	NOUN
ejpam-3073	140	3	of	of	ADP
ejpam-3073	140	4	basic	basic	ADJ
ejpam-3073	140	5	and	and	CCONJ
ejpam-3073	140	6	applied	applied	ADJ
ejpam-3073	140	7	sciences	science	NOUN
ejpam-3073	140	8	,	,	PUNCT
ejpam-3073	140	9	7(10	7(10	NUM
ejpam-3073	140	10	)	)	PUNCT
ejpam-3073	140	11	,	,	PUNCT
ejpam-3073	140	12	467	467	NUM
ejpam-3073	140	13	-	-	SYM
ejpam-3073	140	14	473	473	NUM
ejpam-3073	140	15	.	.	PUNCT
ejpam-3073	140	16	2013	2013	NUM
ejpam-3073	140	17	.	.	PUNCT
ejpam-3073	141	1	[	[	X
ejpam-3073	141	2	3	3	NUM
ejpam-3073	141	3	]	]	X
ejpam-3073	141	4	calvo	calvo	NOUN
ejpam-3073	141	5	,	,	PUNCT
ejpam-3073	141	6	m.	m.	NOUN
ejpam-3073	141	7	,	,	PUNCT
ejpam-3073	141	8	d.j	d.j	PROPN
ejpam-3073	141	9	.	.	PROPN
ejpam-3073	141	10	higham	higham	PROPN
ejpam-3073	141	11	,	,	PUNCT
ejpam-3073	141	12	j.i	j.i	PROPN
ejpam-3073	141	13	.	.	PROPN
ejpam-3073	141	14	monijano	monijano	PROPN
ejpam-3073	141	15	and	and	CCONJ
ejpam-3073	141	16	l.	l.	PROPN
ejpam-3073	141	17	randez	randez	PROPN
ejpam-3073	141	18	.	.	PUNCT
ejpam-3073	142	1	global	global	ADJ
ejpam-3073	142	2	error	error	NOUN
ejpam-3073	142	3	estimation	estimation	NOUN
ejpam-3073	142	4	with	with	ADP
ejpam-3073	142	5	adaptive	adaptive	ADJ
ejpam-3073	142	6	explicit	explicit	ADJ
ejpam-3073	142	7	runge	runge	NOUN
ejpam-3073	142	8	-	-	PUNCT
ejpam-3073	142	9	kutta	kutta	NOUN
ejpam-3073	142	10	methods	method	NOUN
ejpam-3073	142	11	.	.	PUNCT
ejpam-3073	143	1	i	i	PRON
ejpam-3073	143	2	m	m	VERB
ejpam-3073	143	3	a	a	PROPN
ejpam-3073	143	4	j.	j.	PROPN
ejpam-3073	143	5	numer	numer	PROPN
ejpam-3073	143	6	anal	anal	PROPN
ejpam-3073	143	7	.	.	PROPN
ejpam-3073	143	8	,	,	PUNCT
ejpam-3073	143	9	16	16	NUM
ejpam-3073	143	10	,	,	PUNCT
ejpam-3073	143	11	47	47	NUM
ejpam-3073	143	12	-	-	SYM
ejpam-3073	143	13	63	63	NUM
ejpam-3073	143	14	.	.	PUNCT
ejpam-3073	143	15	1996	1996	NUM
ejpam-3073	143	16	.	.	PUNCT
ejpam-3073	144	1	[	[	X
ejpam-3073	144	2	4	4	NUM
ejpam-3073	144	3	]	]	X
ejpam-3073	144	4	chapra	chapra	PROPN
ejpam-3073	144	5	,	,	PUNCT
ejpam-3073	144	6	s.c	s.c	PROPN
ejpam-3073	144	7	.	.	PROPN
ejpam-3073	144	8	and	and	CCONJ
ejpam-3073	144	9	r.p	r.p	PROPN
ejpam-3073	144	10	.	.	PROPN
ejpam-3073	144	11	canale	canale	PROPN
ejpam-3073	144	12	,	,	PUNCT
ejpam-3073	144	13	numerical	numerical	ADJ
ejpam-3073	144	14	methods	method	NOUN
ejpam-3073	144	15	for	for	ADP
ejpam-3073	144	16	engineers(6th	engineers(6th	ADJ
ejpam-3073	144	17	ed	ed	NOUN
ejpam-3073	144	18	)	)	PUNCT
ejpam-3073	144	19	.	.	PUNCT
ejpam-3073	145	1	mcgrawhill	mcgrawhill	NOUN
ejpam-3073	145	2	:	:	PUNCT
ejpam-3073	145	3	new	new	PROPN
ejpam-3073	145	4	york	york	PROPN
ejpam-3073	145	5	.	.	PUNCT
ejpam-3073	146	1	2010	2010	NUM
ejpam-3073	146	2	.	.	PUNCT
ejpam-3073	147	1	[	[	X
ejpam-3073	147	2	5	5	NUM
ejpam-3073	147	3	]	]	X
ejpam-3073	147	4	dormund	dormund	PROPN
ejpam-3073	147	5	,	,	PUNCT
ejpam-3073	147	6	j.r	j.r	PROPN
ejpam-3073	147	7	.	.	PROPN
ejpam-3073	147	8	,	,	PUNCT
ejpam-3073	147	9	j.p	j.p	PROPN
ejpam-3073	147	10	.	.	PROPN
ejpam-3073	147	11	gilmore	gilmore	PROPN
ejpam-3073	147	12	and	and	CCONJ
ejpam-3073	147	13	p.j	p.j	PROPN
ejpam-3073	147	14	.	.	PROPN
ejpam-3073	147	15	prince	prince	PROPN
ejpam-3073	147	16	.	.	PUNCT
ejpam-3073	148	1	globally	globally	ADV
ejpam-3073	148	2	embedded	embed	VERB
ejpam-3073	148	3	runge	runge	NOUN
ejpam-3073	148	4	-	-	PUNCT
ejpam-3073	148	5	kutta	kutta	NOUN
ejpam-3073	148	6	schemes	scheme	NOUN
ejpam-3073	148	7	.	.	PUNCT
ejpam-3073	149	1	ann	ann	PROPN
ejpam-3073	149	2	.	.	PUNCT
ejpam-3073	149	3	numer	numer	PROPN
ejpam-3073	149	4	,	,	PUNCT
ejpam-3073	149	5	math	math	NOUN
ejpam-3073	149	6	.	.	PUNCT
ejpam-3073	149	7	,	,	PUNCT
ejpam-3073	149	8	1	1	NUM
ejpam-3073	149	9	,	,	PUNCT
ejpam-3073	149	10	97	97	NUM
ejpam-3073	149	11	-	-	SYM
ejpam-3073	149	12	106	106	NUM
ejpam-3073	149	13	.	.	PUNCT
ejpam-3073	149	14	1994	1994	NUM
ejpam-3073	149	15	.	.	PUNCT
ejpam-3073	150	1	[	[	X
ejpam-3073	150	2	6	6	NUM
ejpam-3073	150	3	]	]	X
ejpam-3073	150	4	higham	higham	PROPN
ejpam-3073	150	5	,	,	PUNCT
ejpam-3073	150	6	d.j	d.j	PROPN
ejpam-3073	150	7	.	.	PROPN
ejpam-3073	151	1	the	the	DET
ejpam-3073	151	2	tolerance	tolerance	NOUN
ejpam-3073	151	3	proportionality	proportionality	NOUN
ejpam-3073	151	4	of	of	ADP
ejpam-3073	151	5	adaptive	adaptive	ADJ
ejpam-3073	151	6	ode	ode	ADJ
ejpam-3073	151	7	solvers	solver	NOUN
ejpam-3073	151	8	.	.	PUNCT
ejpam-3073	152	1	j.	j.	PROPN
ejpam-3073	152	2	comput	comput	PROPN
ejpam-3073	152	3	.	.	PUNCT
ejpam-3073	153	1	appl	appl	PROPN
ejpam-3073	153	2	.	.	PROPN
ejpam-3073	153	3	math	math	PROPN
ejpam-3073	153	4	.	.	PUNCT
ejpam-3073	154	1	,	,	PUNCT
ejpam-3073	154	2	45	45	NUM
ejpam-3073	154	3	,	,	PUNCT
ejpam-3073	154	4	227	227	NUM
ejpam-3073	154	5	-	-	SYM
ejpam-3073	154	6	236	236	NUM
ejpam-3073	154	7	.	.	PUNCT
ejpam-3073	155	1	1993	1993	NUM
ejpam-3073	155	2	.	.	PUNCT
ejpam-3073	156	1	[	[	X
ejpam-3073	156	2	7	7	NUM
ejpam-3073	156	3	]	]	X
ejpam-3073	156	4	huang	huang	PROPN
ejpam-3073	156	5	,	,	PUNCT
ejpam-3073	156	6	gb	gb	PROPN
ejpam-3073	156	7	.	.	PUNCT
ejpam-3073	156	8	topics	topic	NOUN
ejpam-3073	156	9	on	on	ADP
ejpam-3073	156	10	mean	mean	ADJ
ejpam-3073	156	11	value	value	NOUN
ejpam-3073	156	12	theorem	theorem	VERB
ejpam-3073	156	13	.	.	PROPN
ejpam-3073	156	14	available	available	ADJ
ejpam-3073	156	15	at	at	ADP
ejpam-3073	156	16	www.nsysu.edu.tw	www.nsysu.edu.tw	NOUN
ejpam-3073	156	17	.	.	PUNCT
ejpam-3073	156	18	2001	2001	NUM
ejpam-3073	156	19	.	.	PUNCT
ejpam-3073	157	1	[	[	X
ejpam-3073	157	2	8	8	NUM
ejpam-3073	157	3	]	]	X
ejpam-3073	157	4	kulikov	kulikov	PROPN
ejpam-3073	157	5	,	,	PUNCT
ejpam-3073	157	6	g.	g.	PROPN
ejpam-3073	157	7	y.	y.	PROPN
ejpam-3073	157	8	and	and	CCONJ
ejpam-3073	157	9	s.k	s.k	PROPN
ejpam-3073	157	10	.	.	PROPN
ejpam-3073	157	11	shindin	shindin	PROPN
ejpam-3073	157	12	.	.	PUNCT
ejpam-3073	158	1	on	on	ADP
ejpam-3073	158	2	the	the	DET
ejpam-3073	158	3	efficient	efficient	ADJ
ejpam-3073	158	4	computation	computation	NOUN
ejpam-3073	158	5	of	of	ADP
ejpam-3073	158	6	asymptotically	asymptotically	ADV
ejpam-3073	158	7	sharp	sharp	ADJ
ejpam-3073	158	8	estimates	estimate	NOUN
ejpam-3073	158	9	for	for	ADP
ejpam-3073	158	10	local	local	ADJ
ejpam-3073	158	11	and	and	CCONJ
ejpam-3073	158	12	global	global	ADJ
ejpam-3073	158	13	errors	error	NOUN
ejpam-3073	158	14	in	in	ADP
ejpam-3073	158	15	multistep	multistep	ADJ
ejpam-3073	158	16	methods	method	NOUN
ejpam-3073	158	17	with	with	ADP
ejpam-3073	158	18	constant	constant	ADJ
ejpam-3073	158	19	coefficients	coefficient	NOUN
ejpam-3073	158	20	.	.	PUNCT
ejpam-3073	159	1	zh	zh	X
ejpam-3073	159	2	.	.	PUNCT
ejpam-3073	159	3	vychisl	vychisl	PROPN
ejpam-3073	159	4	.	.	PUNCT
ejpam-3073	160	1	mat	mat	PROPN
ejpam-3073	160	2	.	.	PUNCT
ejpam-3073	160	3	fiz	fiz	PROPN
ejpam-3073	160	4	.	.	PROPN
ejpam-3073	160	5	,	,	PUNCT
ejpam-3073	160	6	44	44	NUM
ejpam-3073	160	7	,	,	PUNCT
ejpam-3073	160	8	840	840	NUM
ejpam-3073	160	9	-	-	SYM
ejpam-3073	160	10	861	861	NUM
ejpam-3073	160	11	.	.	NUM
ejpam-3073	160	12	2004	2004	NUM
ejpam-3073	160	13	.	.	PUNCT
ejpam-3073	161	1	[	[	X
ejpam-3073	161	2	9	9	NUM
ejpam-3073	161	3	]	]	X
ejpam-3073	161	4	lambert	lambert	PROPN
ejpam-3073	161	5	,	,	PUNCT
ejpam-3073	161	6	j.d	j.d	PROPN
ejpam-3073	161	7	.	.	PROPN
ejpam-3073	161	8	,	,	PUNCT
ejpam-3073	161	9	numerical	numerical	ADJ
ejpam-3073	161	10	methods	method	NOUN
ejpam-3073	161	11	for	for	ADP
ejpam-3073	161	12	ordinary	ordinary	ADJ
ejpam-3073	161	13	differential	differential	ADJ
ejpam-3073	161	14	systems	system	NOUN
ejpam-3073	161	15	:	:	PUNCT
ejpam-3073	161	16	the	the	DET
ejpam-3073	161	17	initial	initial	ADJ
ejpam-3073	161	18	value	value	NOUN
ejpam-3073	161	19	problem	problem	NOUN
ejpam-3073	161	20	.	.	PUNCT
ejpam-3073	162	1	john	john	PROPN
ejpam-3073	162	2	wiley	wiley	PROPN
ejpam-3073	162	3	and	and	CCONJ
ejpam-3073	162	4	sons	son	NOUN
ejpam-3073	162	5	:	:	PUNCT
ejpam-3073	162	6	new	new	PROPN
ejpam-3073	162	7	york	york	PROPN
ejpam-3073	162	8	.	.	PUNCT
ejpam-3073	162	9	1991	1991	NUM
ejpam-3073	162	10	.	.	PUNCT
ejpam-3073	163	1	[	[	X
ejpam-3073	163	2	10	10	NUM
ejpam-3073	163	3	]	]	X
ejpam-3073	163	4	onumanyi	onumanyi	PROPN
ejpam-3073	163	5	,	,	PUNCT
ejpam-3073	163	6	p.	p.	PROPN
ejpam-3073	163	7	,	,	PUNCT
ejpam-3073	163	8	u.w	u.w	PROPN
ejpam-3073	163	9	.	.	PROPN
ejpam-3073	163	10	sirisena	sirisena	PROPN
ejpam-3073	163	11	and	and	CCONJ
ejpam-3073	163	12	s.	s.	PROPN
ejpam-3073	163	13	n.	n.	PROPN
ejpam-3073	163	14	jator	jator	PROPN
ejpam-3073	163	15	.	.	PUNCT
ejpam-3073	164	1	continuous	continuous	ADJ
ejpam-3073	164	2	finite	finite	ADJ
ejpam-3073	164	3	difference	difference	NOUN
ejpam-3073	164	4	approximations	approximation	NOUN
ejpam-3073	164	5	for	for	ADP
ejpam-3073	164	6	solving	solve	VERB
ejpam-3073	164	7	differential	differential	NOUN
ejpam-3073	164	8	equations.int	equations.int	PROPN
ejpam-3073	164	9	.	.	PUNCT
ejpam-3073	165	1	j.	j.	PROPN
ejpam-3073	165	2	comput	comput	PROPN
ejpam-3073	165	3	.	.	PUNCT
ejpam-3073	166	1	math	math	NOUN
ejpam-3073	166	2	.	.	PUNCT
ejpam-3073	166	3	,	,	PUNCT
ejpam-3073	166	4	72	72	NUM
ejpam-3073	166	5	,	,	PUNCT
ejpam-3073	166	6	15	15	NUM
ejpam-3073	166	7	-	-	SYM
ejpam-3073	166	8	27	27	NUM
ejpam-3073	166	9	.	.	PUNCT
ejpam-3073	166	10	1999	1999	NUM
ejpam-3073	166	11	.	.	PUNCT
ejpam-3073	167	1	[	[	X
ejpam-3073	167	2	11	11	NUM
ejpam-3073	167	3	]	]	X
ejpam-3073	167	4	orel	orel	PROPN
ejpam-3073	167	5	,	,	PUNCT
ejpam-3073	167	6	b.	b.	PROPN
ejpam-3073	167	7	accumulation	accumulation	NOUN
ejpam-3073	167	8	of	of	ADP
ejpam-3073	167	9	global	global	ADJ
ejpam-3073	167	10	error	error	NOUN
ejpam-3073	167	11	in	in	ADP
ejpam-3073	167	12	lie	lie	NOUN
ejpam-3073	167	13	group	group	NOUN
ejpam-3073	167	14	methods	method	NOUN
ejpam-3073	167	15	for	for	ADP
ejpam-3073	167	16	linear	linear	ADJ
ejpam-3073	167	17	ordinary	ordinary	ADJ
ejpam-3073	167	18	differential	differential	ADJ
ejpam-3073	167	19	equations	equation	NOUN
ejpam-3073	167	20	.	.	PUNCT
ejpam-3073	168	1	electron	electron	PROPN
ejpam-3073	168	2	.	.	PUNCT
ejpam-3073	169	1	trans	trans	PROPN
ejpam-3073	169	2	.	.	PUNCT
ejpam-3073	170	1	numer	numer	PROPN
ejpam-3073	170	2	anal	anal	PROPN
ejpam-3073	170	3	.	.	PROPN
ejpam-3073	170	4	,	,	PUNCT
ejpam-3073	170	5	37	37	NUM
ejpam-3073	170	6	,	,	PUNCT
ejpam-3073	170	7	252	252	NUM
ejpam-3073	170	8	-	-	SYM
ejpam-3073	170	9	262	262	NUM
ejpam-3073	170	10	.	.	PUNCT
ejpam-3073	171	1	2010	2010	NUM
ejpam-3073	171	2	.	.	PUNCT
ejpam-3073	172	1	[	[	X
ejpam-3073	172	2	12	12	NUM
ejpam-3073	172	3	]	]	X
ejpam-3073	172	4	stuart	stuart	PROPN
ejpam-3073	172	5	,	,	PUNCT
ejpam-3073	172	6	a.m.	a.m.	PROPN
ejpam-3073	172	7	probabilistic	probabilistic	ADJ
ejpam-3073	172	8	and	and	CCONJ
ejpam-3073	172	9	deterministic	deterministic	ADJ
ejpam-3073	172	10	convergence	convergence	NOUN
ejpam-3073	172	11	proofs	proof	NOUN
ejpam-3073	172	12	for	for	ADP
ejpam-3073	172	13	software	software	NOUN
ejpam-3073	172	14	for	for	ADP
ejpam-3073	172	15	initial	initial	ADJ
ejpam-3073	172	16	value	value	NOUN
ejpam-3073	172	17	problems	problem	NOUN
ejpam-3073	172	18	.	.	PUNCT
ejpam-3073	173	1	numer	numer	PROPN
ejpam-3073	173	2	.	.	PUNCT
ejpam-3073	174	1	algorithms	algorithms	PROPN
ejpam-3073	174	2	,	,	PUNCT
ejpam-3073	174	3	14	14	NUM
ejpam-3073	174	4	,	,	PUNCT
ejpam-3073	174	5	227	227	NUM
ejpam-3073	174	6	-	-	SYM
ejpam-3073	174	7	260	260	NUM
ejpam-3073	174	8	.	.	PUNCT
ejpam-3073	174	9	1997	1997	NUM
ejpam-3073	174	10	.	.	PUNCT