id	sid	tid	token	lemma	pos
ma-226	1	1	2024	2024	NUM
ma-226	1	2	ada	ada	PROPN
ma-226	1	3	academica	academica	PROPN
ma-226	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-226	1	5	.	.	PUNCT
ma-226	2	1	j.	j.	PROPN
ma-226	2	2	math	math	PROPN
ma-226	2	3	.	.	PUNCT
ma-226	3	1	anal	anal	ADJ
ma-226	3	2	.	.	PUNCT
ma-226	4	1	4	4	NUM
ma-226	4	2	(	(	PUNCT
ma-226	4	3	2024	2024	NUM
ma-226	4	4	)	)	PUNCT
ma-226	4	5	10doi	10doi	NUM
ma-226	4	6	:	:	PUNCT
ma-226	4	7	10.28924	10.28924	NUM
ma-226	4	8	/	/	SYM
ma-226	4	9	ada	ada	NOUN
ma-226	4	10	/	/	SYM
ma-226	4	11	ma.4.10	ma.4.10	ADJ
ma-226	4	12	finite	finite	ADJ
ma-226	4	13	difference	difference	NOUN
ma-226	4	14	method	method	NOUN
ma-226	4	15	for	for	ADP
ma-226	4	16	solving	solve	VERB
ma-226	4	17	second	second	ADJ
ma-226	4	18	-	-	PUNCT
ma-226	4	19	order	order	NOUN
ma-226	4	20	boundary	boundary	ADJ
ma-226	4	21	value	value	NOUN
ma-226	4	22	problems	problem	NOUN
ma-226	4	23	with	with	ADP
ma-226	4	24	high	high	ADJ
ma-226	4	25	-	-	PUNCT
ma-226	4	26	order	order	NOUN
ma-226	4	27	accuracy	accuracy	NOUN
ma-226	4	28	nguyen	nguyen	PROPN
ma-226	4	29	dinh	dinh	PROPN
ma-226	4	30	dung∗	dung∗	NOUN
ma-226	4	31	,	,	PUNCT
ma-226	4	32	vu	vu	PROPN
ma-226	4	33	vinh	vinh	PROPN
ma-226	4	34	quang	quang	PROPN
ma-226	4	35	thai	thai	PROPN
ma-226	4	36	nguyen	nguyen	PROPN
ma-226	4	37	university	university	PROPN
ma-226	4	38	of	of	ADP
ma-226	4	39	information	information	NOUN
ma-226	4	40	and	and	CCONJ
ma-226	4	41	communication	communication	NOUN
ma-226	4	42	technology	technology	NOUN
ma-226	4	43	,	,	PUNCT
ma-226	4	44	thai	thai	PROPN
ma-226	4	45	nguyen	nguyen	NOUN
ma-226	4	46	,	,	PUNCT
ma-226	4	47	vietnam	vietnam	PROPN
ma-226	4	48	∗correspondence	∗correspondence	NOUN
ma-226	4	49	:	:	PUNCT
ma-226	4	50	nddung@ictu.edu.vn	nddung@ictu.edu.vn	ADJ
ma-226	4	51	abstract	abstract	NOUN
ma-226	4	52	.	.	PUNCT
ma-226	5	1	when	when	SCONJ
ma-226	5	2	researching	research	VERB
ma-226	5	3	and	and	CCONJ
ma-226	5	4	solving	solve	VERB
ma-226	5	5	practical	practical	ADJ
ma-226	5	6	problems	problem	NOUN
ma-226	5	7	in	in	ADP
ma-226	5	8	continuous	continuous	ADJ
ma-226	5	9	environments	environment	NOUN
ma-226	5	10	,	,	PUNCT
ma-226	5	11	throughmodeling	throughmodeling	NOUN
ma-226	5	12	methods	method	NOUN
ma-226	5	13	,	,	PUNCT
ma-226	5	14	the	the	DET
ma-226	5	15	vast	vast	ADJ
ma-226	5	16	majority	majority	NOUN
ma-226	5	17	of	of	ADP
ma-226	5	18	problems	problem	NOUN
ma-226	5	19	lead	lead	VERB
ma-226	5	20	to	to	ADP
ma-226	5	21	models	model	NOUN
ma-226	5	22	described	describe	VERB
ma-226	5	23	by	by	ADP
ma-226	5	24	equations	equation	NOUN
ma-226	5	25	containingdifferential	containingdifferential	ADJ
ma-226	5	26	operators	operator	NOUN
ma-226	5	27	.	.	PUNCT
ma-226	6	1	in	in	ADP
ma-226	6	2	case	case	NOUN
ma-226	6	3	the	the	DET
ma-226	6	4	problem	problem	NOUN
ma-226	6	5	model	model	NOUN
ma-226	6	6	is	be	AUX
ma-226	6	7	not	not	PART
ma-226	6	8	complicated	complicated	ADJ
ma-226	6	9	,	,	PUNCT
ma-226	6	10	we	we	PRON
ma-226	6	11	often	often	ADV
ma-226	6	12	obtain	obtain	VERB
ma-226	6	13	simple	simple	ADJ
ma-226	6	14	partialdifferential	partialdifferential	ADJ
ma-226	6	15	equations	equation	NOUN
ma-226	6	16	,	,	PUNCT
ma-226	6	17	then	then	ADV
ma-226	6	18	the	the	DET
ma-226	6	19	solution	solution	NOUN
ma-226	6	20	of	of	ADP
ma-226	6	21	the	the	DET
ma-226	6	22	problem	problem	NOUN
ma-226	6	23	can	can	AUX
ma-226	6	24	be	be	AUX
ma-226	6	25	obtained	obtain	VERB
ma-226	6	26	directly	directly	ADV
ma-226	6	27	through	through	ADP
ma-226	6	28	analyti	analyti	ADJ
ma-226	6	29	-	-	PUNCT
ma-226	6	30	cal	cal	NUM
ma-226	6	31	methods	method	NOUN
ma-226	6	32	.	.	PUNCT
ma-226	7	1	most	most	ADJ
ma-226	7	2	complex	complex	ADJ
ma-226	7	3	problems	problem	NOUN
ma-226	7	4	,	,	PUNCT
ma-226	7	5	through	through	ADP
ma-226	7	6	the	the	DET
ma-226	7	7	method	method	NOUN
ma-226	7	8	of	of	ADP
ma-226	7	9	approximating	approximate	VERB
ma-226	7	10	differential	differential	NOUN
ma-226	7	11	operatorsby	operatorsby	ADJ
ma-226	7	12	difference	difference	NOUN
ma-226	7	13	operators	operator	NOUN
ma-226	7	14	,	,	PUNCT
ma-226	7	15	from	from	ADP
ma-226	7	16	which	which	PRON
ma-226	7	17	differential	differential	NOUN
ma-226	7	18	problems	problem	NOUN
ma-226	7	19	are	be	AUX
ma-226	7	20	approximated	approximate	VERB
ma-226	7	21	by	by	ADP
ma-226	7	22	corresponding	correspond	VERB
ma-226	7	23	differ	differ	NOUN
ma-226	7	24	-	-	PUNCT
ma-226	7	25	ence	ence	NOUN
ma-226	7	26	schemes	scheme	NOUN
ma-226	7	27	and	and	CCONJ
ma-226	7	28	approximate	approximate	ADJ
ma-226	7	29	solutions	solution	NOUN
ma-226	7	30	will	will	AUX
ma-226	7	31	be	be	AUX
ma-226	7	32	obtained	obtain	VERB
ma-226	7	33	.	.	PUNCT
ma-226	8	1	is	be	AUX
ma-226	8	2	achieved	achieve	VERB
ma-226	8	3	through	through	ADP
ma-226	8	4	solving	solve	VERB
ma-226	8	5	systems	system	NOUN
ma-226	8	6	ofdifference	ofdifference	NOUN
ma-226	8	7	equations	equation	NOUN
ma-226	8	8	based	base	VERB
ma-226	8	9	on	on	ADP
ma-226	8	10	the	the	DET
ma-226	8	11	tools	tool	NOUN
ma-226	8	12	of	of	ADP
ma-226	8	13	electronic	electronic	ADJ
ma-226	8	14	computers	computer	NOUN
ma-226	8	15	.	.	PUNCT
ma-226	9	1	then	then	ADV
ma-226	9	2	,	,	PUNCT
ma-226	9	3	building	building	NOUN
ma-226	9	4	difference	difference	NOUN
ma-226	9	5	schemesto	schemesto	PROPN
ma-226	9	6	approximate	approximate	VERB
ma-226	9	7	the	the	DET
ma-226	9	8	differential	differential	ADJ
ma-226	9	9	problem	problem	NOUN
ma-226	9	10	with	with	ADP
ma-226	9	11	high	high	ADJ
ma-226	9	12	-	-	PUNCT
ma-226	9	13	order	order	NOUN
ma-226	9	14	accuracy	accuracy	NOUN
ma-226	9	15	will	will	AUX
ma-226	9	16	play	play	VERB
ma-226	9	17	an	an	DET
ma-226	9	18	important	important	ADJ
ma-226	9	19	role	role	NOUN
ma-226	9	20	in	in	ADP
ma-226	9	21	theaccuracy	theaccuracy	NOUN
ma-226	9	22	of	of	ADP
ma-226	9	23	the	the	DET
ma-226	9	24	obtained	obtain	VERB
ma-226	9	25	approximate	approximate	ADJ
ma-226	9	26	solution	solution	NOUN
ma-226	9	27	.	.	PUNCT
ma-226	10	1	in	in	ADP
ma-226	10	2	this	this	DET
ma-226	10	3	paper	paper	NOUN
ma-226	10	4	,	,	PUNCT
ma-226	10	5	we	we	PRON
ma-226	10	6	propose	propose	VERB
ma-226	10	7	two	two	NUM
ma-226	10	8	difference	difference	NOUN
ma-226	10	9	schemes	scheme	NOUN
ma-226	10	10	withhigh	withhigh	NOUN
ma-226	10	11	-	-	PUNCT
ma-226	10	12	order	order	NOUN
ma-226	10	13	accuracy	accuracy	NOUN
ma-226	10	14	to	to	PART
ma-226	10	15	solve	solve	VERB
ma-226	10	16	second	second	ADJ
ma-226	10	17	-	-	PUNCT
ma-226	10	18	order	order	NOUN
ma-226	10	19	differential	differential	NOUN
ma-226	10	20	problems	problem	NOUN
ma-226	10	21	with	with	ADP
ma-226	10	22	dirichlet	dirichlet	PROPN
ma-226	10	23	and	and	CCONJ
ma-226	10	24	mixed	mixed	ADJ
ma-226	10	25	boundaryconditions	boundarycondition	NOUN
ma-226	10	26	.	.	PUNCT
ma-226	11	1	theoretical	theoretical	ADJ
ma-226	11	2	results	result	NOUN
ma-226	11	3	and	and	CCONJ
ma-226	11	4	experimental	experimental	ADJ
ma-226	11	5	calculations	calculation	NOUN
ma-226	11	6	have	have	AUX
ma-226	11	7	confirmed	confirm	VERB
ma-226	11	8	the	the	DET
ma-226	11	9	accuracy	accuracy	NOUN
ma-226	11	10	of	of	ADP
ma-226	11	11	theproposed	thepropose	VERB
ma-226	11	12	schemes	scheme	NOUN
ma-226	11	13	.	.	PUNCT
ma-226	12	1	1	1	X
ma-226	12	2	.	.	X
ma-226	12	3	introduction	introduction	NOUN
ma-226	12	4	in	in	ADP
ma-226	12	5	this	this	DET
ma-226	12	6	paper	paper	NOUN
ma-226	12	7	,	,	PUNCT
ma-226	12	8	we	we	PRON
ma-226	12	9	consider	consider	VERB
ma-226	12	10	the	the	DET
ma-226	12	11	second	second	ADJ
ma-226	12	12	-	-	PUNCT
ma-226	12	13	order	order	NOUN
ma-226	12	14	boundary	boundary	ADJ
ma-226	12	15	problem	problem	NOUN
ma-226	12	16	with	with	ADP
ma-226	12	17	mixed	mixed	ADJ
ma-226	12	18	boundary	boundary	ADJ
ma-226	12	19	conditions	conditions	NOUN
ma-226	12	20	u′′(x	u′′(x	PROPN
ma-226	12	21	)	)	PUNCT
ma-226	12	22	=	=	SYM
ma-226	12	23	f	f	PROPN
ma-226	12	24	(	(	PUNCT
ma-226	12	25	x	x	NOUN
ma-226	12	26	)	)	PUNCT
ma-226	12	27	,	,	PUNCT
ma-226	12	28	x	x	PUNCT
ma-226	12	29	∈	∈	PROPN
ma-226	12	30	(	(	PUNCT
ma-226	12	31	a	a	DET
ma-226	12	32	,	,	PUNCT
ma-226	12	33	b	b	NOUN
ma-226	12	34	)	)	PUNCT
ma-226	12	35	c0u(a)−	c0u(a)−	NOUN
ma-226	12	36	c1u′(a	c1u′(a	PROPN
ma-226	12	37	)	)	PUNCT
ma-226	12	38	=	=	PUNCT
ma-226	12	39	c	c	NOUN
ma-226	12	40	d0u(b	d0u(b	PROPN
ma-226	12	41	)	)	PUNCT
ma-226	13	1	+	+	CCONJ
ma-226	14	1	d1u	d1u	PROPN
ma-226	14	2	′(b	′(b	NOUN
ma-226	14	3	)	)	PUNCT
ma-226	14	4	=	=	SYM
ma-226	15	1	d	d	PROPN
ma-226	15	2	c0	c0	PROPN
ma-226	15	3	,	,	PUNCT
ma-226	15	4	c1	c1	PROPN
ma-226	15	5	,	,	PUNCT
ma-226	15	6	d0	d0	NOUN
ma-226	15	7	,	,	PUNCT
ma-226	15	8	d1	d1	PROPN
ma-226	15	9	≥	≥	NOUN
ma-226	15	10	0	0	NUM
ma-226	15	11	(	(	PUNCT
ma-226	15	12	1	1	NUM
ma-226	15	13	)	)	PUNCT
ma-226	15	14	in	in	ADP
ma-226	15	15	some	some	DET
ma-226	15	16	cases	case	NOUN
ma-226	15	17	when	when	SCONJ
ma-226	15	18	the	the	DET
ma-226	15	19	function	function	NOUN
ma-226	15	20	f	f	X
ma-226	15	21	(	(	PUNCT
ma-226	15	22	x	x	X
ma-226	15	23	)	)	PUNCT
ma-226	15	24	is	be	AUX
ma-226	15	25	a	a	DET
ma-226	15	26	polynomial	polynomial	ADJ
ma-226	15	27	function	function	NOUN
ma-226	15	28	,	,	PUNCT
ma-226	15	29	trigonometric	trigonometric	ADJ
ma-226	15	30	function	function	NOUN
ma-226	15	31	,	,	PUNCT
ma-226	15	32	exponentialfunction	exponentialfunction	NOUN
ma-226	15	33	or	or	CCONJ
ma-226	15	34	product	product	NOUN
ma-226	15	35	of	of	ADP
ma-226	15	36	the	the	DET
ma-226	15	37	above	above	ADJ
ma-226	15	38	functional	functional	ADJ
ma-226	15	39	forms	form	NOUN
ma-226	15	40	,	,	PUNCT
ma-226	15	41	the	the	DET
ma-226	15	42	solution	solution	NOUN
ma-226	15	43	to	to	ADP
ma-226	15	44	problem	problem	NOUN
ma-226	15	45	(	(	PUNCT
ma-226	15	46	1	1	X
ma-226	15	47	)	)	PUNCT
ma-226	15	48	can	can	AUX
ma-226	15	49	be	be	AUX
ma-226	15	50	found	find	VERB
ma-226	15	51	byanalytical	byanalytical	ADJ
ma-226	15	52	methods	method	NOUN
ma-226	15	53	or	or	CCONJ
ma-226	15	54	using	use	VERB
ma-226	15	55	using	use	VERB
ma-226	15	56	green	green	PROPN
ma-226	15	57	’s	’s	PART
ma-226	15	58	function	function	NOUN
ma-226	15	59	method	method	NOUN
ma-226	15	60	,	,	PUNCT
ma-226	15	61	we	we	PRON
ma-226	15	62	must	must	AUX
ma-226	15	63	find	find	VERB
ma-226	15	64	the	the	DET
ma-226	15	65	approximate	approximate	ADJ
ma-226	15	66	solutionof	solutionof	NOUN
ma-226	15	67	problem	problem	NOUN
ma-226	15	68	(	(	PUNCT
ma-226	15	69	1	1	NUM
ma-226	15	70	)	)	PUNCT
ma-226	15	71	by	by	ADP
ma-226	15	72	numerical	numerical	ADJ
ma-226	15	73	methods	method	NOUN
ma-226	15	74	using	use	VERB
ma-226	15	75	electronic	electronic	ADJ
ma-226	15	76	computers.in	computers.in	NOUN
ma-226	15	77	order	order	NOUN
ma-226	15	78	to	to	PART
ma-226	15	79	find	find	VERB
ma-226	15	80	approximate	approximate	ADJ
ma-226	15	81	solutions	solution	NOUN
ma-226	15	82	using	use	VERB
ma-226	15	83	numerical	numerical	ADJ
ma-226	15	84	methods	method	NOUN
ma-226	15	85	,	,	PUNCT
ma-226	15	86	we	we	PRON
ma-226	15	87	need	need	VERB
ma-226	15	88	to	to	PART
ma-226	15	89	build	build	VERB
ma-226	15	90	systems	system	NOUN
ma-226	15	91	ofdifference	ofdifference	NOUN
ma-226	15	92	equations	equation	NOUN
ma-226	15	93	that	that	PRON
ma-226	15	94	approximate	approximate	VERB
ma-226	15	95	the	the	DET
ma-226	15	96	differential	differential	ADJ
ma-226	15	97	problem	problem	NOUN
ma-226	15	98	and	and	CCONJ
ma-226	15	99	then	then	ADV
ma-226	15	100	find	find	VERB
ma-226	15	101	numerical	numerical	ADJ
ma-226	15	102	solutions	solution	NOUN
ma-226	15	103	received	receive	VERB
ma-226	15	104	:	:	PUNCT
ma-226	15	105	11	11	NUM
ma-226	15	106	feb	feb	NOUN
ma-226	15	107	2024	2024	NUM
ma-226	15	108	.	.	PUNCT
ma-226	16	1	key	key	ADJ
ma-226	16	2	words	word	NOUN
ma-226	16	3	and	and	CCONJ
ma-226	16	4	phrases	phrase	NOUN
ma-226	16	5	.	.	PUNCT
ma-226	17	1	derivative	derivative	ADJ
ma-226	17	2	;	;	PUNCT
ma-226	17	3	grid	grid	NOUN
ma-226	17	4	space	space	NOUN
ma-226	17	5	;	;	PUNCT
ma-226	17	6	mesh	mesh	NOUN
ma-226	17	7	function	function	NOUN
ma-226	17	8	;	;	PUNCT
ma-226	17	9	partial	partial	ADJ
ma-226	17	10	differential	differential	NOUN
ma-226	17	11	equations	equation	NOUN
ma-226	17	12	;	;	PUNCT
ma-226	17	13	difference	difference	NOUN
ma-226	17	14	schemes.1	schemes.1	NOUN
ma-226	17	15	https://adac.ee	https://adac.ee	PROPN
ma-226	17	16	https://doi.org/10.28924/ada/ma.4.10	https://doi.org/10.28924/ada/ma.4.10	NOUN
ma-226	17	17	eur	eur	NOUN
ma-226	17	18	.	.	PUNCT
ma-226	18	1	j.	j.	PROPN
ma-226	18	2	math	math	PROPN
ma-226	18	3	.	.	PUNCT
ma-226	19	1	anal	anal	PROPN
ma-226	19	2	.	.	PUNCT
ma-226	20	1	10.28924	10.28924	NUM
ma-226	20	2	/	/	SYM
ma-226	20	3	ada	ada	NOUN
ma-226	20	4	/	/	NOUN
ma-226	20	5	ma.4.10	ma.4.10	NOUN
ma-226	20	6	2using	2use	VERB
ma-226	20	7	algebraic	algebraic	ADJ
ma-226	20	8	methods	method	NOUN
ma-226	20	9	.	.	PUNCT
ma-226	21	1	then	then	ADV
ma-226	21	2	the	the	DET
ma-226	21	3	accuracy	accuracy	NOUN
ma-226	21	4	order	order	NOUN
ma-226	21	5	of	of	ADP
ma-226	21	6	approximating	approximate	VERB
ma-226	21	7	differential	differential	ADJ
ma-226	21	8	operators	operator	NOUN
ma-226	21	9	usingdifference	usingdifference	NOUN
ma-226	21	10	operators	operator	NOUN
ma-226	21	11	will	will	AUX
ma-226	21	12	determine	determine	VERB
ma-226	21	13	the	the	DET
ma-226	21	14	accuracy	accuracy	NOUN
ma-226	21	15	order	order	NOUN
ma-226	21	16	of	of	ADP
ma-226	21	17	the	the	DET
ma-226	21	18	obtained	obtain	VERB
ma-226	21	19	approximated	approximate	VERB
ma-226	21	20	solution.in	solution.in	PRON
ma-226	22	1	[	[	X
ma-226	22	2	1	1	NUM
ma-226	22	3	]	]	PUNCT
ma-226	22	4	,	,	PUNCT
ma-226	22	5	a	a	DET
ma-226	22	6	method	method	NOUN
ma-226	22	7	for	for	ADP
ma-226	22	8	building	build	VERB
ma-226	22	9	a	a	DET
ma-226	22	10	difference	difference	NOUN
ma-226	22	11	scheme	scheme	NOUN
ma-226	22	12	for	for	ADP
ma-226	22	13	problem	problem	NOUN
ma-226	22	14	(	(	PUNCT
ma-226	22	15	1	1	X
ma-226	22	16	)	)	PUNCT
ma-226	22	17	was	be	AUX
ma-226	22	18	introduced	introduce	VERB
ma-226	22	19	by	by	ADP
ma-226	22	20	approximatingthe	approximatingthe	DET
ma-226	22	21	first	first	ADJ
ma-226	22	22	and	and	CCONJ
ma-226	22	23	second	second	ADJ
ma-226	22	24	derivatives	derivative	NOUN
ma-226	22	25	of	of	ADP
ma-226	22	26	the	the	DET
ma-226	22	27	function	function	NOUN
ma-226	22	28	u(x	u(x	VERB
ma-226	22	29	)	)	PUNCT
ma-226	22	30	with	with	ADP
ma-226	22	31	accuracy	accuracy	NOUN
ma-226	22	32	o(h	o(h	PROPN
ma-226	22	33	)	)	PUNCT
ma-226	22	34	,	,	PUNCT
ma-226	22	35	where	where	SCONJ
ma-226	22	36	h	h	NOUN
ma-226	22	37	is	be	AUX
ma-226	22	38	the	the	DET
ma-226	22	39	grid	grid	NOUN
ma-226	22	40	stepin	stepin	NOUN
ma-226	22	41	grid	grid	NOUN
ma-226	22	42	space	space	NOUN
ma-226	22	43	,	,	PUNCT
ma-226	22	44	in	in	ADP
ma-226	22	45	[	[	X
ma-226	22	46	2	2	X
ma-226	22	47	]	]	PUNCT
ma-226	22	48	a	a	DET
ma-226	22	49	method	method	NOUN
ma-226	22	50	of	of	ADP
ma-226	22	51	building	build	VERB
ma-226	22	52	a	a	DET
ma-226	22	53	difference	difference	NOUN
ma-226	22	54	scheme	scheme	NOUN
ma-226	22	55	with	with	ADP
ma-226	22	56	accuracy	accuracy	NOUN
ma-226	22	57	o(h2	o(h2	NOUN
ma-226	22	58	)	)	PUNCT
ma-226	22	59	.	.	PUNCT
ma-226	23	1	in	in	ADP
ma-226	23	2	addition	addition	NOUN
ma-226	23	3	,	,	PUNCT
ma-226	23	4	some	some	DET
ma-226	23	5	authors	author	NOUN
ma-226	23	6	[	[	X
ma-226	23	7	3][5	3][5	NOUN
ma-226	23	8	]	]	PUNCT
ma-226	23	9	have	have	AUX
ma-226	23	10	proposed	propose	VERB
ma-226	23	11	difference	difference	NOUN
ma-226	23	12	methods	method	NOUN
ma-226	23	13	with	with	ADP
ma-226	23	14	order	order	NOUN
ma-226	23	15	of	of	ADP
ma-226	23	16	accuracy	accuracy	NOUN
ma-226	23	17	from	from	ADP
ma-226	23	18	o(h4	o(h4	NOUN
ma-226	23	19	)	)	PUNCT
ma-226	23	20	to	to	ADP
ma-226	23	21	o(h8).however	o(h8).however	PROPN
ma-226	23	22	,	,	PUNCT
ma-226	23	23	these	these	DET
ma-226	23	24	methods	method	NOUN
ma-226	23	25	lead	lead	VERB
ma-226	23	26	to	to	ADP
ma-226	23	27	very	very	ADV
ma-226	23	28	complicated	complicated	ADJ
ma-226	23	29	systems	system	NOUN
ma-226	23	30	of	of	ADP
ma-226	23	31	difference	difference	NOUN
ma-226	23	32	equations	equation	NOUN
ma-226	23	33	that	that	PRON
ma-226	23	34	requiringthe	requiringthe	ADJ
ma-226	23	35	use	use	NOUN
ma-226	23	36	of	of	ADP
ma-226	23	37	intermediate	intermediate	ADJ
ma-226	23	38	grid	grid	NOUN
ma-226	23	39	points	point	NOUN
ma-226	23	40	.	.	PUNCT
ma-226	24	1	this	this	PRON
ma-226	24	2	makes	make	VERB
ma-226	24	3	solving	solve	VERB
ma-226	24	4	these	these	DET
ma-226	24	5	systems	system	NOUN
ma-226	24	6	of	of	ADP
ma-226	24	7	difference	difference	NOUN
ma-226	24	8	equationsvery	equationsvery	NOUN
ma-226	24	9	complicated	complicate	VERB
ma-226	24	10	.	.	PUNCT
ma-226	25	1	therefore	therefore	ADV
ma-226	25	2	,	,	PUNCT
ma-226	25	3	it	it	PRON
ma-226	25	4	is	be	AUX
ma-226	25	5	required	require	VERB
ma-226	25	6	to	to	PART
ma-226	25	7	build	build	VERB
ma-226	25	8	a	a	DET
ma-226	25	9	difference	difference	NOUN
ma-226	25	10	scheme	scheme	NOUN
ma-226	25	11	with	with	ADP
ma-226	25	12	order	order	NOUN
ma-226	25	13	of	of	ADP
ma-226	25	14	accuracy	accuracy	NOUN
ma-226	25	15	forproblem	forproblem	NOUN
ma-226	25	16	(	(	PUNCT
ma-226	25	17	1	1	NUM
ma-226	25	18	)	)	PUNCT
ma-226	25	19	so	so	SCONJ
ma-226	25	20	that	that	SCONJ
ma-226	25	21	the	the	DET
ma-226	25	22	resulting	result	VERB
ma-226	25	23	system	system	NOUN
ma-226	25	24	of	of	ADP
ma-226	25	25	difference	difference	NOUN
ma-226	25	26	equations	equation	NOUN
ma-226	25	27	is	be	AUX
ma-226	25	28	simple	simple	ADJ
ma-226	25	29	and	and	CCONJ
ma-226	25	30	can	can	AUX
ma-226	25	31	be	be	AUX
ma-226	25	32	solved	solve	VERB
ma-226	25	33	withan	withan	ADP
ma-226	25	34	algorithm	algorithm	NOUN
ma-226	25	35	of	of	ADP
ma-226	25	36	linear	linear	PROPN
ma-226	25	37	complexity.studying	complexity.studye	VERB
ma-226	25	38	methods	method	NOUN
ma-226	25	39	to	to	PART
ma-226	25	40	approximate	approximate	VERB
ma-226	25	41	the	the	DET
ma-226	25	42	derivative	derivative	ADJ
ma-226	25	43	value	value	NOUN
ma-226	25	44	at	at	ADP
ma-226	25	45	a	a	DET
ma-226	25	46	point	point	NOUN
ma-226	25	47	of	of	ADP
ma-226	25	48	a	a	DET
ma-226	25	49	function	function	NOUN
ma-226	25	50	is	be	AUX
ma-226	25	51	an	an	DET
ma-226	25	52	importantresearch	importantresearch	NOUN
ma-226	25	53	direction	direction	NOUN
ma-226	25	54	that	that	PRON
ma-226	25	55	mathematicians	mathematician	NOUN
ma-226	25	56	are	be	AUX
ma-226	25	57	especially	especially	ADV
ma-226	25	58	interested	interested	ADJ
ma-226	25	59	in	in	ADP
ma-226	25	60	.	.	PUNCT
ma-226	26	1	in	in	ADP
ma-226	26	2	the	the	DET
ma-226	26	3	literature	literature	NOUN
ma-226	26	4	on	on	ADP
ma-226	26	5	numericalmethods	numericalmethods	PROPN
ma-226	26	6	[	[	X
ma-226	26	7	1	1	NUM
ma-226	26	8	]	]	PUNCT
ma-226	26	9	,	,	PUNCT
ma-226	26	10	formulas	formula	NOUN
ma-226	26	11	for	for	ADP
ma-226	26	12	approximating	approximate	VERB
ma-226	26	13	the	the	DET
ma-226	26	14	first	first	ADJ
ma-226	26	15	and	and	CCONJ
ma-226	26	16	second	second	ADJ
ma-226	26	17	derivatives	derivative	NOUN
ma-226	26	18	of	of	ADP
ma-226	26	19	the	the	DET
ma-226	26	20	function	function	NOUN
ma-226	26	21	u(x	u(x	NOUN
ma-226	26	22	)	)	PUNCT
ma-226	26	23	withaccuracy	withaccuracy	NOUN
ma-226	26	24	order	order	NOUN
ma-226	26	25	o(h2	o(h2	NOUN
ma-226	26	26	)	)	PUNCT
ma-226	26	27	have	have	AUX
ma-226	26	28	been	be	AUX
ma-226	26	29	given	give	VERB
ma-226	26	30	,	,	PUNCT
ma-226	26	31	which	which	PRON
ma-226	26	32	uses	use	VERB
ma-226	26	33	the	the	DET
ma-226	26	34	value	value	NOUN
ma-226	26	35	of	of	ADP
ma-226	26	36	the	the	DET
ma-226	26	37	function	function	NOUN
ma-226	26	38	at	at	ADP
ma-226	26	39	3	3	NUM
ma-226	26	40	neighboring	neighboring	NOUN
ma-226	26	41	pointsof	pointsof	NOUN
ma-226	26	42	point	point	NOUN
ma-226	26	43	x	x	PUNCT
ma-226	26	44	and	and	CCONJ
ma-226	26	45	h	h	NOUN
ma-226	26	46	is	be	AUX
ma-226	26	47	denoted	denote	VERB
ma-226	26	48	as	as	ADP
ma-226	26	49	the	the	DET
ma-226	26	50	grid	grid	NOUN
ma-226	26	51	step	step	NOUN
ma-226	26	52	on	on	ADP
ma-226	26	53	the	the	DET
ma-226	26	54	grid	grid	NOUN
ma-226	26	55	space	space	NOUN
ma-226	26	56	.	.	PUNCT
ma-226	27	1	based	base	VERB
ma-226	27	2	on	on	ADP
ma-226	27	3	the	the	DET
ma-226	27	4	interpolation	interpolation	NOUN
ma-226	27	5	polynomialapproximation	polynomialapproximation	NOUN
ma-226	27	6	method	method	NOUN
ma-226	27	7	,	,	PUNCT
ma-226	27	8	in	in	ADP
ma-226	27	9	the	the	DET
ma-226	27	10	document	document	NOUN
ma-226	27	11	[	[	X
ma-226	27	12	6	6	NUM
ma-226	27	13	]	]	PUNCT
ma-226	27	14	,	,	PUNCT
ma-226	27	15	the	the	DET
ma-226	27	16	m	m	NOUN
ma-226	27	17	-	-	PUNCT
ma-226	27	18	order	order	NOUN
ma-226	27	19	derivative	derivative	ADJ
ma-226	27	20	approximation	approximation	NOUN
ma-226	27	21	formulas	formula	NOUN
ma-226	27	22	withaccuracy	withaccuracy	NOUN
ma-226	27	23	order	order	NOUN
ma-226	27	24	o(h5−m	o(h5−m	NOUN
ma-226	27	25	)	)	PUNCT
ma-226	27	26	are	be	AUX
ma-226	27	27	given	give	VERB
ma-226	27	28	,	,	PUNCT
ma-226	27	29	which	which	PRON
ma-226	27	30	uses	use	VERB
ma-226	27	31	value	value	NOUN
ma-226	27	32	of	of	ADP
ma-226	27	33	the	the	DET
ma-226	27	34	function	function	NOUN
ma-226	27	35	at	at	ADP
ma-226	27	36	5	5	NUM
ma-226	27	37	neighboring	neighboring	NOUN
ma-226	27	38	points	point	NOUN
ma-226	27	39	ofpoint	ofpoint	NOUN
ma-226	27	40	x	x	X
ma-226	27	41	.	.	PUNCT
ma-226	28	1	recently	recently	ADV
ma-226	28	2	,	,	PUNCT
ma-226	28	3	in	in	ADP
ma-226	28	4	the	the	DET
ma-226	28	5	document	document	NOUN
ma-226	28	6	[	[	X
ma-226	28	7	7	7	NUM
ma-226	28	8	]	]	PUNCT
ma-226	28	9	,	,	PUNCT
ma-226	28	10	a	a	DET
ma-226	28	11	set	set	NOUN
ma-226	28	12	of	of	ADP
ma-226	28	13	formulas	formula	NOUN
ma-226	28	14	for	for	ADP
ma-226	28	15	approximating	approximate	VERB
ma-226	28	16	derivatives	derivative	NOUN
ma-226	28	17	of	of	ADP
ma-226	28	18	allorder	allorder	NOUN
ma-226	28	19	with	with	ADP
ma-226	28	20	accuracy	accuracy	NOUN
ma-226	28	21	order	order	NOUN
ma-226	28	22	o(hn−m	o(hn−m	NOUN
ma-226	28	23	)	)	PUNCT
ma-226	28	24	has	have	AUX
ma-226	28	25	been	be	AUX
ma-226	28	26	introduced	introduce	VERB
ma-226	28	27	,	,	PUNCT
ma-226	28	28	which	which	PRON
ma-226	28	29	uses	use	VERB
ma-226	28	30	the	the	DET
ma-226	28	31	value	value	NOUN
ma-226	28	32	of	of	ADP
ma-226	28	33	the	the	DET
ma-226	28	34	function	function	NOUN
ma-226	28	35	at	at	ADP
ma-226	28	36	n	n	PROPN
ma-226	28	37	+	+	CCONJ
ma-226	28	38	1	1	NUM
ma-226	28	39	neighboring	neighboring	NOUN
ma-226	28	40	points	point	NOUN
ma-226	28	41	of	of	ADP
ma-226	28	42	point	point	NOUN
ma-226	28	43	x	x	INTJ
ma-226	28	44	.	.	PUNCT
ma-226	29	1	based	base	VERB
ma-226	29	2	on	on	ADP
ma-226	29	3	the	the	DET
ma-226	29	4	published	publish	VERB
ma-226	29	5	formulas	formula	NOUN
ma-226	29	6	,	,	PUNCT
ma-226	29	7	numerical	numerical	ADJ
ma-226	29	8	solutions	solution	NOUN
ma-226	29	9	fordifferential	fordifferential	ADJ
ma-226	29	10	problems	problem	NOUN
ma-226	29	11	with	with	ADP
ma-226	29	12	nonlinear	nonlinear	ADJ
ma-226	29	13	differential	differential	ADJ
ma-226	29	14	equations	equation	NOUN
ma-226	29	15	of	of	ADP
ma-226	29	16	all	all	DET
ma-226	29	17	order	order	NOUN
ma-226	29	18	have	have	AUX
ma-226	29	19	been	be	AUX
ma-226	29	20	improved	improve	VERB
ma-226	29	21	.	.	PUNCT
ma-226	30	1	in	in	ADP
ma-226	30	2	[	[	X
ma-226	30	3	8]-[12	8]-[12	NUM
ma-226	30	4	]	]	PUNCT
ma-226	30	5	,	,	PUNCT
ma-226	30	6	published	publish	VERB
ma-226	30	7	algorithms	algorithm	NOUN
ma-226	30	8	for	for	ADP
ma-226	30	9	numerically	numerically	ADV
ma-226	30	10	solving	solve	VERB
ma-226	30	11	3rd	3rd	ADJ
ma-226	30	12	and	and	CCONJ
ma-226	30	13	4th	4th	ADJ
ma-226	30	14	order	order	NOUN
ma-226	30	15	nonlinear	nonlinear	ADJ
ma-226	30	16	differential	differential	NOUN
ma-226	30	17	equationswith	equationswith	PROPN
ma-226	30	18	accuracy	accuracy	NOUN
ma-226	30	19	order	order	NOUN
ma-226	30	20	o(h6	o(h6	ADJ
ma-226	30	21	)	)	PUNCT
ma-226	30	22	.	.	PUNCT
ma-226	31	1	however	however	ADV
ma-226	31	2	,	,	PUNCT
ma-226	31	3	the	the	DET
ma-226	31	4	published	publish	VERB
ma-226	31	5	results	result	NOUN
ma-226	31	6	of	of	ADP
ma-226	31	7	the	the	DET
ma-226	31	8	above	above	ADJ
ma-226	31	9	derivative	derivative	ADJ
ma-226	31	10	approximationformulas	approximationformula	NOUN
ma-226	31	11	are	be	AUX
ma-226	31	12	all	all	PRON
ma-226	31	13	results	result	NOUN
ma-226	31	14	obtained	obtain	VERB
ma-226	31	15	by	by	ADP
ma-226	31	16	the	the	DET
ma-226	31	17	direct	direct	ADJ
ma-226	31	18	method	method	NOUN
ma-226	31	19	,	,	PUNCT
ma-226	31	20	results	result	NOUN
ma-226	31	21	obtained	obtain	VERB
ma-226	31	22	by	by	ADP
ma-226	31	23	direct	direct	ADJ
ma-226	31	24	calculation	calculation	NOUN
ma-226	31	25	ofanalytical	ofanalytical	ADJ
ma-226	31	26	expressions	expression	NOUN
ma-226	31	27	,	,	PUNCT
ma-226	31	28	not	not	PART
ma-226	31	29	general	general	ADJ
ma-226	31	30	.	.	PUNCT
ma-226	32	1	thus	thus	ADV
ma-226	32	2	,	,	PUNCT
ma-226	32	3	to	to	PART
ma-226	32	4	improve	improve	VERB
ma-226	32	5	the	the	DET
ma-226	32	6	accuracy	accuracy	NOUN
ma-226	32	7	of	of	ADP
ma-226	32	8	derivative	derivative	ADJ
ma-226	32	9	approximation	approximation	NOUN
ma-226	32	10	,	,	PUNCT
ma-226	32	11	itis	itis	NOUN
ma-226	32	12	necessary	necessary	ADJ
ma-226	32	13	to	to	PART
ma-226	32	14	build	build	VERB
ma-226	32	15	a	a	DET
ma-226	32	16	general	general	ADJ
ma-226	32	17	algorithm	algorithm	NOUN
ma-226	32	18	to	to	PART
ma-226	32	19	provide	provide	VERB
ma-226	32	20	formulas	formula	NOUN
ma-226	32	21	for	for	ADP
ma-226	32	22	approximating	approximate	VERB
ma-226	32	23	derivatives	derivative	NOUN
ma-226	32	24	of	of	ADP
ma-226	32	25	anydegree	anydegree	NOUN
ma-226	32	26	with	with	ADP
ma-226	32	27	arbitrary	arbitrary	ADJ
ma-226	32	28	order	order	NOUN
ma-226	32	29	of	of	ADP
ma-226	32	30	accuracy	accuracy	NOUN
ma-226	32	31	based	base	VERB
ma-226	32	32	on	on	ADP
ma-226	32	33	the	the	DET
ma-226	32	34	support	support	NOUN
ma-226	32	35	of	of	ADP
ma-226	32	36	the	the	DET
ma-226	32	37	computer.the	computer.the	DET
ma-226	32	38	main	main	ADJ
ma-226	32	39	content	content	NOUN
ma-226	32	40	of	of	ADP
ma-226	32	41	the	the	DET
ma-226	32	42	article	article	NOUN
ma-226	32	43	presents	present	VERB
ma-226	32	44	research	research	NOUN
ma-226	32	45	results	result	NOUN
ma-226	32	46	based	base	VERB
ma-226	32	47	on	on	ADP
ma-226	32	48	the	the	DET
ma-226	32	49	taylo	taylo	ADJ
ma-226	32	50	expansion	expansion	NOUN
ma-226	32	51	formula	formula	NOUN
ma-226	33	1	[	[	X
ma-226	33	2	1]and	1]and	NUM
ma-226	33	3	the	the	DET
ma-226	33	4	algorithm	algorithm	NOUN
ma-226	33	5	for	for	ADP
ma-226	33	6	determining	determine	VERB
ma-226	33	7	numerical	numerical	ADJ
ma-226	33	8	derivatives	derivative	NOUN
ma-226	33	9	with	with	ADP
ma-226	33	10	high	high	ADJ
ma-226	33	11	order	order	NOUN
ma-226	33	12	accuracy	accuracy	NOUN
ma-226	33	13	,	,	PUNCT
ma-226	33	14	thereby	thereby	ADV
ma-226	33	15	proposinga	proposinga	ADV
ma-226	33	16	method	method	VERB
ma-226	33	17	to	to	PART
ma-226	33	18	build	build	VERB
ma-226	33	19	two	two	NUM
ma-226	33	20	difference	difference	NOUN
ma-226	33	21	scheme	scheme	NOUN
ma-226	33	22	for	for	ADP
ma-226	33	23	problem	problem	NOUN
ma-226	33	24	(	(	PUNCT
ma-226	33	25	1	1	NUM
ma-226	33	26	)	)	PUNCT
ma-226	33	27	in	in	ADP
ma-226	33	28	the	the	DET
ma-226	33	29	case	case	NOUN
ma-226	33	30	of	of	ADP
ma-226	33	31	dirichlet	dirichlet	PROPN
ma-226	33	32	boundary	boundary	PROPN
ma-226	33	33	conditionsand	conditionsand	NOUN
ma-226	33	34	mixed	mix	VERB
ma-226	33	35	boundary	boundary	ADJ
ma-226	33	36	conditions	condition	NOUN
ma-226	33	37	with	with	ADP
ma-226	33	38	arbitrary	arbitrary	ADJ
ma-226	33	39	high	high	ADJ
ma-226	33	40	-	-	PUNCT
ma-226	33	41	order	order	NOUN
ma-226	33	42	precision	precision	NOUN
ma-226	33	43	.	.	PUNCT
ma-226	34	1	difference	difference	NOUN
ma-226	34	2	schemes	scheme	NOUN
ma-226	34	3	are	be	AUX
ma-226	34	4	verysimple	verysimple	ADJ
ma-226	34	5	and	and	CCONJ
ma-226	34	6	can	can	AUX
ma-226	34	7	be	be	AUX
ma-226	34	8	solved	solve	VERB
ma-226	34	9	with	with	ADP
ma-226	34	10	the	the	DET
ma-226	34	11	algorithm	algorithm	NOUN
ma-226	34	12	has	have	VERB
ma-226	34	13	o(n	o(n	NUM
ma-226	34	14	)	)	PUNCT
ma-226	34	15	complexity	complexity	NOUN
ma-226	34	16	where	where	SCONJ
ma-226	34	17	n	n	PRON
ma-226	34	18	is	be	AUX
ma-226	34	19	the	the	DET
ma-226	34	20	number	number	NOUN
ma-226	34	21	of	of	ADP
ma-226	34	22	pointsin	pointsin	VERB
ma-226	34	23	the	the	DET
ma-226	34	24	grid	grid	NOUN
ma-226	34	25	space	space	NOUN
ma-226	34	26	.	.	PUNCT
ma-226	35	1	the	the	DET
ma-226	35	2	experimental	experimental	ADJ
ma-226	35	3	results	result	NOUN
ma-226	35	4	we	we	PRON
ma-226	35	5	calculated	calculate	VERB
ma-226	35	6	confirm	confirm	VERB
ma-226	35	7	the	the	DET
ma-226	35	8	accuracy	accuracy	NOUN
ma-226	35	9	of	of	ADP
ma-226	35	10	the	the	DET
ma-226	35	11	proposedschemes	proposedscheme	NOUN
ma-226	35	12	.	.	PUNCT
ma-226	36	1	https://doi.org/10.28924/ada/ma.4.10	https://doi.org/10.28924/ada/ma.4.10	PROPN
ma-226	36	2	eur	eur	PROPN
ma-226	36	3	.	.	PUNCT
ma-226	37	1	j.	j.	PROPN
ma-226	37	2	math	math	PROPN
ma-226	37	3	.	.	PUNCT
ma-226	38	1	anal	anal	PROPN
ma-226	38	2	.	.	PUNCT
ma-226	39	1	10.28924	10.28924	NUM
ma-226	39	2	/	/	SYM
ma-226	39	3	ada	ada	NOUN
ma-226	39	4	/	/	SYM
ma-226	39	5	ma.4.10	ma.4.10	NOUN
ma-226	39	6	3the	3the	ADJ
ma-226	39	7	structure	structure	NOUN
ma-226	39	8	of	of	ADP
ma-226	39	9	the	the	DET
ma-226	39	10	article	article	NOUN
ma-226	39	11	consists	consist	VERB
ma-226	39	12	of	of	ADP
ma-226	39	13	four	four	NUM
ma-226	39	14	parts	part	NOUN
ma-226	39	15	:	:	PUNCT
ma-226	39	16	in	in	ADP
ma-226	39	17	section	section	NOUN
ma-226	39	18	1	1	NUM
ma-226	39	19	,	,	PUNCT
ma-226	39	20	we	we	PRON
ma-226	39	21	introduce	introduce	VERB
ma-226	39	22	some	some	DET
ma-226	39	23	publishedresults	publishedresult	NOUN
ma-226	39	24	on	on	ADP
ma-226	39	25	based	base	VERB
ma-226	39	26	on	on	ADP
ma-226	39	27	the	the	DET
ma-226	39	28	difference	difference	NOUN
ma-226	39	29	method	method	NOUN
ma-226	39	30	.	.	PUNCT
ma-226	40	1	section	section	NOUN
ma-226	40	2	2	2	NUM
ma-226	40	3	,	,	PUNCT
ma-226	40	4	we	we	PRON
ma-226	40	5	present	present	VERB
ma-226	40	6	the	the	DET
ma-226	40	7	theoretical	theoretical	ADJ
ma-226	40	8	basis	basis	NOUN
ma-226	40	9	of	of	ADP
ma-226	40	10	thederivative	thederivative	ADJ
ma-226	40	11	approximation	approximation	NOUN
ma-226	40	12	method	method	NOUN
ma-226	40	13	based	base	VERB
ma-226	40	14	on	on	ADP
ma-226	40	15	the	the	DET
ma-226	40	16	taylor	taylor	PROPN
ma-226	40	17	formula	formula	NOUN
ma-226	40	18	,	,	PUNCT
ma-226	40	19	then	then	ADV
ma-226	40	20	we	we	PRON
ma-226	40	21	propose	propose	VERB
ma-226	40	22	a	a	DET
ma-226	40	23	method	method	NOUN
ma-226	40	24	to	to	PART
ma-226	40	25	build	build	VERB
ma-226	40	26	adifference	adifference	NOUN
ma-226	40	27	scheme	scheme	NOUN
ma-226	40	28	with	with	ADP
ma-226	40	29	high	high	ADJ
ma-226	40	30	-	-	PUNCT
ma-226	40	31	order	order	NOUN
ma-226	40	32	accuracy	accuracy	NOUN
ma-226	40	33	based	base	VERB
ma-226	40	34	on	on	ADP
ma-226	40	35	the	the	DET
ma-226	40	36	high	high	ADJ
ma-226	40	37	-	-	PUNCT
ma-226	40	38	order	order	NOUN
ma-226	40	39	derivative	derivative	ADJ
ma-226	40	40	approximation	approximation	NOUN
ma-226	40	41	andevaluate	andevaluate	NOUN
ma-226	40	42	schema	schema	NOUN
ma-226	40	43	accuracy	accuracy	NOUN
ma-226	40	44	.	.	PUNCT
ma-226	41	1	section	section	NOUN
ma-226	41	2	3	3	NUM
ma-226	41	3	,	,	PUNCT
ma-226	41	4	we	we	PRON
ma-226	41	5	present	present	VERB
ma-226	41	6	some	some	DET
ma-226	41	7	experimental	experimental	ADJ
ma-226	41	8	calculation	calculation	NOUN
ma-226	41	9	results	result	NOUN
ma-226	41	10	to	to	ADP
ma-226	41	11	evaluatethe	evaluatethe	DET
ma-226	41	12	accuracy	accuracy	NOUN
ma-226	41	13	of	of	ADP
ma-226	41	14	the	the	DET
ma-226	41	15	proposed	propose	VERB
ma-226	41	16	algorithm	algorithm	NOUN
ma-226	41	17	.	.	PUNCT
ma-226	42	1	finally	finally	ADV
ma-226	42	2	,	,	PUNCT
ma-226	42	3	there	there	PRON
ma-226	42	4	are	be	VERB
ma-226	42	5	conclusions	conclusion	NOUN
ma-226	42	6	and	and	CCONJ
ma-226	42	7	references	reference	NOUN
ma-226	42	8	.	.	PUNCT
ma-226	43	1	2	2	X
ma-226	43	2	.	.	NUM
ma-226	43	3	proposed	propose	VERB
ma-226	43	4	method	method	NOUN
ma-226	43	5	2.1	2.1	NUM
ma-226	43	6	.	.	PUNCT
ma-226	44	1	derivative	derivative	ADJ
ma-226	44	2	approximation	approximation	NOUN
ma-226	44	3	formulas	formula	NOUN
ma-226	44	4	consider	consider	VERB
ma-226	44	5	the	the	DET
ma-226	44	6	function	function	NOUN
ma-226	44	7	u(x	u(x	NOUN
ma-226	44	8	)	)	PUNCT
ma-226	44	9	∈	∈	PROPN
ma-226	44	10	cn+1[a	cn+1[a	NOUN
ma-226	44	11	,	,	PUNCT
ma-226	44	12	b	b	NOUN
ma-226	44	13	]	]	PUNCT
ma-226	44	14	,	,	PUNCT
ma-226	44	15	expanding	expand	VERB
ma-226	44	16	the	the	DET
ma-226	44	17	taylor	taylor	PROPN
ma-226	44	18	series	series	NOUN
ma-226	44	19	[	[	X
ma-226	44	20	3	3	NUM
ma-226	44	21	]	]	PUNCT
ma-226	44	22	,	,	PUNCT
ma-226	44	23	we	we	PRON
ma-226	44	24	have	have	VERB
ma-226	44	25	the	the	DET
ma-226	44	26	formula	formula	NOUN
ma-226	44	27	u(x	u(x	NOUN
ma-226	45	1	+	+	CCONJ
ma-226	45	2	∆x	∆x	PROPN
ma-226	45	3	)	)	PUNCT
ma-226	45	4	=	=	SYM
ma-226	45	5	u(x	u(x	PROPN
ma-226	45	6	)	)	PUNCT
ma-226	46	1	+	+	CCONJ
ma-226	46	2	u′(x)∆x	u′(x)∆x	ADV
ma-226	46	3	+	+	NUM
ma-226	46	4	u′′(x	u′′(x	NOUN
ma-226	46	5	)	)	PUNCT
ma-226	46	6	2	2	NUM
ma-226	46	7	!	!	PUNCT
ma-226	47	1	(	(	PUNCT
ma-226	47	2	∆x)2	∆x)2	VERB
ma-226	47	3	+	+	CCONJ
ma-226	47	4	...	...	PUNCT
ma-226	48	1	+	+	CCONJ
ma-226	48	2	u(n)(x	u(n)(x	NUM
ma-226	48	3	)	)	PUNCT
ma-226	48	4	n	n	CCONJ
ma-226	48	5	!	!	PUNCT
ma-226	49	1	(	(	PUNCT
ma-226	49	2	∆x)n	∆x)n	VERB
ma-226	49	3	+	+	X
ma-226	49	4	rn(x	rn(x	NUM
ma-226	49	5	)	)	PUNCT
ma-226	49	6	(	(	PUNCT
ma-226	49	7	2	2	X
ma-226	49	8	)	)	PUNCT
ma-226	49	9	where	where	SCONJ
ma-226	49	10	rn(x	rn(x	X
ma-226	49	11	)	)	PUNCT
ma-226	49	12	=	=	SYM
ma-226	49	13	u(n+1)(θ	u(n+1)(θ	PROPN
ma-226	49	14	)	)	PUNCT
ma-226	49	15	(	(	PUNCT
ma-226	49	16	n+1	n+1	NOUN
ma-226	49	17	)	)	PUNCT
ma-226	49	18	!	!	PUNCT
ma-226	50	1	(	(	PUNCT
ma-226	50	2	∆x)n+1	∆x)n+1	VERB
ma-226	50	3	,	,	PUNCT
ma-226	50	4	θ	θ	PROPN
ma-226	50	5	∈	∈	PROPN
ma-226	50	6	(	(	PUNCT
ma-226	50	7	x	x	X
ma-226	50	8	,	,	PUNCT
ma-226	50	9	x	x	PROPN
ma-226	50	10	+	+	NUM
ma-226	50	11	∆x	∆x	PROPN
ma-226	50	12	)	)	PUNCT
ma-226	50	13	since	since	SCONJ
ma-226	50	14	formula	formula	NOUN
ma-226	50	15	(	(	PUNCT
ma-226	50	16	2	2	NUM
ma-226	50	17	)	)	PUNCT
ma-226	50	18	,	,	PUNCT
ma-226	50	19	we	we	PRON
ma-226	50	20	can	can	AUX
ma-226	50	21	approximate	approximate	VERB
ma-226	50	22	thederivative	thederivative	NOUN
ma-226	50	23	of	of	ADP
ma-226	50	24	the	the	DET
ma-226	50	25	function	function	NOUN
ma-226	50	26	u(x	u(x	VERB
ma-226	50	27	)	)	PUNCT
ma-226	50	28	in	in	ADP
ma-226	50	29	the	the	DET
ma-226	50	30	neighborhood	neighborhood	NOUN
ma-226	50	31	x	x	PUNCT
ma-226	50	32	as	as	SCONJ
ma-226	50	33	follows	follow	VERB
ma-226	50	34	:	:	PUNCT
ma-226	50	35	u(x	u(x	PROPN
ma-226	50	36	+	+	CCONJ
ma-226	50	37	∆x	∆x	PROPN
ma-226	50	38	)	)	PUNCT
ma-226	50	39	≈	≈	PROPN
ma-226	50	40	u(x	u(x	PROPN
ma-226	50	41	)	)	PUNCT
ma-226	51	1	+	+	CCONJ
ma-226	51	2	u′(x)∆x	u′(x)∆x	ADV
ma-226	51	3	+	+	NUM
ma-226	51	4	u′′(x	u′′(x	NOUN
ma-226	51	5	)	)	PUNCT
ma-226	51	6	2	2	NUM
ma-226	51	7	!	!	PUNCT
ma-226	52	1	(	(	PUNCT
ma-226	52	2	∆x)2	∆x)2	VERB
ma-226	52	3	+	+	CCONJ
ma-226	52	4	...	...	PUNCT
ma-226	53	1	+	+	CCONJ
ma-226	53	2	u(n)(x	u(n)(x	NUM
ma-226	53	3	)	)	PUNCT
ma-226	53	4	n	n	CCONJ
ma-226	53	5	!	!	PUNCT
ma-226	54	1	(	(	PUNCT
ma-226	54	2	∆x)n	∆x)n	INTJ
ma-226	54	3	(	(	PUNCT
ma-226	54	4	3	3	NUM
ma-226	54	5	)	)	PUNCT
ma-226	54	6	divide	divide	VERB
ma-226	54	7	the	the	DET
ma-226	54	8	interval	interval	NOUN
ma-226	54	9	[	[	X
ma-226	54	10	a	a	X
ma-226	54	11	,	,	PUNCT
ma-226	54	12	b	b	NOUN
ma-226	54	13	]	]	PUNCT
ma-226	54	14	by	by	ADP
ma-226	54	15	(	(	PUNCT
ma-226	54	16	n+	n+	NOUN
ma-226	54	17	1	1	NUM
ma-226	54	18	)	)	PUNCT
ma-226	54	19	grid	grid	NOUN
ma-226	54	20	points	point	NOUN
ma-226	54	21	xi	xi	X
ma-226	54	22	=	=	SYM
ma-226	54	23	a+	a+	PUNCT
ma-226	54	24	ih	ih	NOUN
ma-226	54	25	,	,	PUNCT
ma-226	54	26	i	i	PRON
ma-226	54	27	=	=	NOUN
ma-226	54	28	0	0	NUM
ma-226	54	29	,	,	PUNCT
ma-226	54	30	1	1	NUM
ma-226	54	31	,	,	PUNCT
ma-226	54	32	...	...	PUNCT
ma-226	54	33	,	,	PUNCT
ma-226	54	34	n	n	CCONJ
ma-226	54	35	,	,	PUNCT
ma-226	54	36	grid	grid	NOUN
ma-226	54	37	step	step	NOUN
ma-226	54	38	h	h	NOUN
ma-226	54	39	=	=	NOUN
ma-226	54	40	b−a	b−a	PROPN
ma-226	54	41	n	n	PROPN
ma-226	54	42	,	,	PUNCT
ma-226	54	43	sinceformula	sinceformula	X
ma-226	54	44	(	(	PUNCT
ma-226	54	45	3	3	NUM
ma-226	54	46	)	)	PUNCT
ma-226	54	47	,	,	PUNCT
ma-226	54	48	we	we	PRON
ma-226	54	49	get	get	VERB
ma-226	54	50	the	the	DET
ma-226	54	51	following	follow	VERB
ma-226	54	52	formulas	formula	NOUN
ma-226	54	53	u(xi	u(xi	PROPN
ma-226	54	54	+	+	X
ma-226	55	1	h	h	NOUN
ma-226	55	2	)	)	PUNCT
ma-226	55	3	=	=	SYM
ma-226	55	4	u(xi	u(xi	X
ma-226	55	5	)	)	PUNCT
ma-226	56	1	+	+	CCONJ
ma-226	56	2	u′(xi)h	u′(xi)h	ADJ
ma-226	56	3	+	+	CCONJ
ma-226	56	4	u′′(xi	u′′(xi	ADJ
ma-226	56	5	)	)	PUNCT
ma-226	56	6	2	2	NUM
ma-226	56	7	!	!	X
ma-226	56	8	h2	h2	NOUN
ma-226	56	9	+	+	CCONJ
ma-226	56	10	...	...	PUNCT
ma-226	56	11	+	+	CCONJ
ma-226	56	12	u(n)(xi	u(n)(xi	NUM
ma-226	56	13	)	)	PUNCT
ma-226	56	14	n	n	CCONJ
ma-226	56	15	!	!	PUNCT
ma-226	57	1	hn	hn	PRON
ma-226	57	2	+	+	NOUN
ma-226	57	3	o(hn+1	o(hn+1	NOUN
ma-226	57	4	)	)	PUNCT
ma-226	57	5	,	,	PUNCT
ma-226	57	6	i	i	PRON
ma-226	57	7	=	=	NOUN
ma-226	57	8	0	0	NUM
ma-226	57	9	,	,	PUNCT
ma-226	57	10	n	n	CCONJ
ma-226	57	11	−	−	PROPN
ma-226	57	12	1	1	NUM
ma-226	57	13	(	(	PUNCT
ma-226	57	14	4	4	NUM
ma-226	57	15	)	)	PUNCT
ma-226	57	16	u(xi	u(xi	VERB
ma-226	57	17	−	−	PROPN
ma-226	57	18	h	h	NOUN
ma-226	57	19	)	)	PUNCT
ma-226	57	20	=	=	SYM
ma-226	57	21	u(xi)−	u(xi)−	NOUN
ma-226	57	22	u′(xi)h	u′(xi)h	PROPN
ma-226	57	23	+	+	CCONJ
ma-226	57	24	u′′(xi	u′′(xi	ADJ
ma-226	57	25	)	)	PUNCT
ma-226	57	26	2	2	NUM
ma-226	57	27	!	!	X
ma-226	57	28	h2	h2	NOUN
ma-226	58	1	+	+	CCONJ
ma-226	58	2	...	...	PUNCT
ma-226	59	1	+	+	CCONJ
ma-226	59	2	(	(	PUNCT
ma-226	59	3	−1)n	−1)n	PROPN
ma-226	59	4	u(n)(xi	u(n)(xi	PROPN
ma-226	59	5	)	)	PUNCT
ma-226	59	6	n	n	CCONJ
ma-226	59	7	!	!	PUNCT
ma-226	60	1	hn	hn	PRON
ma-226	60	2	+	+	NOUN
ma-226	60	3	o(hn+1	o(hn+1	NOUN
ma-226	60	4	)	)	PUNCT
ma-226	60	5	,	,	PUNCT
ma-226	60	6	i	i	PRON
ma-226	60	7	=	=	NOUN
ma-226	60	8	0	0	NUM
ma-226	60	9	,	,	PUNCT
ma-226	60	10	n	n	CCONJ
ma-226	60	11	−	−	PROPN
ma-226	60	12	1	1	NUM
ma-226	60	13	(	(	PUNCT
ma-226	60	14	5	5	NUM
ma-226	60	15	)	)	PUNCT
ma-226	60	16	using	use	VERB
ma-226	60	17	(	(	PUNCT
ma-226	60	18	4	4	NUM
ma-226	60	19	)	)	PUNCT
ma-226	60	20	,	,	PUNCT
ma-226	60	21	we	we	PRON
ma-226	60	22	obtain	obtain	VERB
ma-226	60	23	u′(xi	u′(xi	PROPN
ma-226	60	24	)	)	PUNCT
ma-226	60	25	=	=	PUNCT
ma-226	61	1	u(xi	u(xi	PROPN
ma-226	61	2	+	+	X
ma-226	61	3	h)−	h)−	PROPN
ma-226	61	4	u(xi	u(xi	PROPN
ma-226	61	5	)	)	PUNCT
ma-226	61	6	h	h	NOUN
ma-226	62	1	−	−	NOUN
ma-226	62	2	u′′(xi	u′′(xi	ADJ
ma-226	62	3	)	)	PUNCT
ma-226	63	1	2	2	NUM
ma-226	63	2	!	!	PUNCT
ma-226	63	3	h	h	NOUN
ma-226	63	4	−	−	PROPN
ma-226	63	5	...	...	PUNCT
ma-226	64	1	−	−	PROPN
ma-226	64	2	u(n)(xi	u(n)(xi	NUM
ma-226	64	3	)	)	PUNCT
ma-226	64	4	n	n	CCONJ
ma-226	64	5	!	!	PUNCT
ma-226	65	1	hn−1	hn−1	ADJ
ma-226	65	2	+	+	NOUN
ma-226	65	3	o(hn	o(hn	X
ma-226	65	4	)	)	PUNCT
ma-226	65	5	(	(	PUNCT
ma-226	65	6	6	6	NUM
ma-226	65	7	)	)	PUNCT
ma-226	65	8	formula	formula	NOUN
ma-226	65	9	(	(	PUNCT
ma-226	65	10	6	6	NUM
ma-226	65	11	)	)	PUNCT
ma-226	65	12	is	be	AUX
ma-226	65	13	a	a	DET
ma-226	65	14	formula	formula	NOUN
ma-226	65	15	that	that	PRON
ma-226	65	16	supports	support	VERB
ma-226	65	17	approximating	approximate	VERB
ma-226	65	18	the	the	DET
ma-226	65	19	first	first	ADJ
ma-226	65	20	derivative	derivative	NOUN
ma-226	65	21	on	on	ADP
ma-226	65	22	a	a	DET
ma-226	65	23	uniform	uniform	ADJ
ma-226	65	24	grid	grid	NOUN
ma-226	65	25	witherror	witherror	NOUN
ma-226	65	26	o(hn).since	o(hn).since	NOUN
ma-226	65	27	(	(	PUNCT
ma-226	65	28	4	4	NUM
ma-226	65	29	)	)	PUNCT
ma-226	65	30	and	and	CCONJ
ma-226	65	31	(	(	PUNCT
ma-226	65	32	5	5	NUM
ma-226	65	33	)	)	PUNCT
ma-226	65	34	,	,	PUNCT
ma-226	65	35	we	we	PRON
ma-226	65	36	have	have	VERB
ma-226	65	37	u′′(xi	u′′(xi	ADJ
ma-226	65	38	)	)	PUNCT
ma-226	66	1	=	=	VERB
ma-226	66	2	u(xi	u(xi	PROPN
ma-226	66	3	+	+	X
ma-226	66	4	h)−	h)−	PROPN
ma-226	66	5	2u(xi	2u(xi	NUM
ma-226	66	6	)	)	PUNCT
ma-226	67	1	+	+	CCONJ
ma-226	67	2	u(xi	u(xi	ADJ
ma-226	67	3	−	−	PROPN
ma-226	67	4	h	h	NOUN
ma-226	67	5	)	)	PUNCT
ma-226	67	6	h2	h2	NOUN
ma-226	67	7	−	−	PROPN
ma-226	67	8	u(4)(xi	u(4)(xi	PROPN
ma-226	67	9	)	)	PUNCT
ma-226	67	10	4	4	NUM
ma-226	67	11	!	!	PUNCT
ma-226	67	12	h2	h2	NOUN
ma-226	67	13	−	−	PROPN
ma-226	67	14	...	...	PUNCT
ma-226	68	1	−	−	PROPN
ma-226	68	2	u(2m)(xi	u(2m)(xi	PROPN
ma-226	68	3	)	)	PUNCT
ma-226	68	4	(	(	PUNCT
ma-226	68	5	2	2	NUM
ma-226	68	6	m	m	NOUN
ma-226	68	7	)	)	PUNCT
ma-226	69	1	!	!	PUNCT
ma-226	70	1	h2m−2	h2m−2	X
ma-226	71	1	+	+	NOUN
ma-226	71	2	o(hn−1	o(hn−1	X
ma-226	71	3	)	)	PUNCT
ma-226	71	4	(	(	PUNCT
ma-226	71	5	7	7	X
ma-226	71	6	)	)	PUNCT
ma-226	71	7	let	let	VERB
ma-226	71	8	v(x	v(x	NOUN
ma-226	71	9	)	)	PUNCT
ma-226	71	10	be	be	AUX
ma-226	71	11	a	a	DET
ma-226	71	12	function	function	NOUN
ma-226	71	13	defined	define	VERB
ma-226	71	14	on	on	ADP
ma-226	71	15	[	[	X
ma-226	71	16	a	a	X
ma-226	71	17	,	,	PUNCT
ma-226	71	18	b	b	NOUN
ma-226	71	19	]	]	X
ma-226	71	20	,	,	PUNCT
ma-226	71	21	ωh	ωh	PART
ma-226	71	22	be	be	AUX
ma-226	71	23	the	the	DET
ma-226	71	24	grid	grid	NOUN
ma-226	71	25	space	space	NOUN
ma-226	71	26	with	with	ADP
ma-226	71	27	grid	grid	NOUN
ma-226	71	28	step	step	NOUN
ma-226	71	29	h	h	NOUN
ma-226	72	1	=	=	PUNCT
ma-226	72	2	(	(	PUNCT
ma-226	72	3	b	b	X
ma-226	72	4	−	−	PROPN
ma-226	72	5	a)/n	a)/n	PROPN
ma-226	72	6	,	,	PUNCT
ma-226	72	7	xi	xi	X
ma-226	72	8	=	=	PUNCT
ma-226	72	9	a	a	PROPN
ma-226	72	10	+	+	X
ma-226	72	11	ih	ih	NOUN
ma-226	72	12	,	,	PUNCT
ma-226	72	13	(	(	PUNCT
ma-226	72	14	i	i	NOUN
ma-226	72	15	=	=	NOUN
ma-226	72	16	0	0	NUM
ma-226	72	17	,	,	PUNCT
ma-226	72	18	1	1	NUM
ma-226	72	19	,	,	PUNCT
ma-226	72	20	2	2	NUM
ma-226	72	21	,	,	PUNCT
ma-226	72	22	.	.	PUNCT
ma-226	72	23	.	.	PUNCT
ma-226	73	1	.	.	PUNCT
ma-226	73	2	,	,	PUNCT
ma-226	73	3	n	n	CCONJ
ma-226	73	4	)	)	PUNCT
ma-226	73	5	,	,	PUNCT
ma-226	73	6	v	v	NOUN
ma-226	73	7	=	=	SYM
ma-226	73	8	(	(	PUNCT
ma-226	73	9	v	v	NOUN
ma-226	73	10	(	(	PUNCT
ma-226	73	11	x0	x0	PROPN
ma-226	73	12	)	)	PUNCT
ma-226	73	13	,	,	PUNCT
ma-226	73	14	v	v	X
ma-226	73	15	(	(	PUNCT
ma-226	73	16	x1	x1	PROPN
ma-226	73	17	)	)	PUNCT
ma-226	73	18	,	,	PUNCT
ma-226	73	19	.	.	PUNCT
ma-226	73	20	.	.	PUNCT
ma-226	74	1	.	.	PUNCT
ma-226	75	1	,	,	PUNCT
ma-226	75	2	v	v	X
ma-226	75	3	(	(	PUNCT
ma-226	75	4	xn	xn	PROPN
ma-226	75	5	)	)	PUNCT
ma-226	75	6	)	)	PUNCT
ma-226	75	7	is	be	AUX
ma-226	75	8	the	the	DET
ma-226	75	9	approximated	approximate	VERB
ma-226	75	10	value	value	NOUN
ma-226	75	11	of	of	ADP
ma-226	75	12	the	the	DET
ma-226	75	13	vd	vd	NOUN
ma-226	75	14	on	on	ADP
ma-226	75	15	ωh	ωh	INTJ
ma-226	75	16	,	,	PUNCT
ma-226	75	17	where	where	SCONJ
ma-226	75	18	vd	vd	NOUN
ma-226	75	19	=	=	SYM
ma-226	75	20	(	(	PUNCT
ma-226	75	21	v(x0	v(x0	NOUN
ma-226	75	22	)	)	PUNCT
ma-226	75	23	,	,	PUNCT
ma-226	75	24	v(x1	v(x1	NOUN
ma-226	75	25	)	)	PUNCT
ma-226	75	26	,	,	PUNCT
ma-226	75	27	.	.	PUNCT
ma-226	75	28	.	.	PUNCT
ma-226	76	1	.	.	PUNCT
ma-226	77	1	,	,	PUNCT
ma-226	77	2	v(xn	v(xn	PROPN
ma-226	77	3	)	)	PUNCT
ma-226	77	4	)	)	PUNCT
ma-226	77	5	.	.	PUNCT
ma-226	78	1	definition	definition	NOUN
ma-226	78	2	1	1	NUM
ma-226	78	3	:	:	PUNCT
ma-226	78	4	on	on	ADP
ma-226	78	5	grid	grid	NOUN
ma-226	78	6	ωh	ωh	PROPN
ma-226	78	7	,	,	PUNCT
ma-226	78	8	a	a	DET
ma-226	78	9	method	method	NOUN
ma-226	78	10	for	for	ADP
ma-226	78	11	approximating	approximate	VERB
ma-226	78	12	the	the	DET
ma-226	78	13	function	function	NOUN
ma-226	78	14	v(x	v(x	PROPN
ma-226	78	15	)	)	PUNCT
ma-226	78	16	that	that	PRON
ma-226	78	17	is	be	AUX
ma-226	78	18	said	say	VERB
ma-226	78	19	to	to	PART
ma-226	78	20	have	have	VERB
ma-226	78	21	n	n	NUM
ma-226	78	22	-	-	PUNCT
ma-226	78	23	order	order	NOUN
ma-226	78	24	accuracy	accuracy	NOUN
ma-226	78	25	if	if	SCONJ
ma-226	78	26	‖v	‖v	ADJ
ma-226	78	27	−	−	NOUN
ma-226	78	28	vd‖ωh	vd‖ωh	NUM
ma-226	78	29	=	=	SYM
ma-226	78	30	o(hn	o(hn	NUM
ma-226	78	31	)	)	PUNCT
ma-226	78	32	.	.	PUNCT
ma-226	79	1	https://doi.org/10.28924/ada/ma.4.10	https://doi.org/10.28924/ada/ma.4.10	PROPN
ma-226	79	2	eur	eur	PROPN
ma-226	79	3	.	.	PUNCT
ma-226	80	1	j.	j.	PROPN
ma-226	80	2	math	math	PROPN
ma-226	80	3	.	.	PUNCT
ma-226	81	1	anal	anal	PROPN
ma-226	81	2	.	.	PUNCT
ma-226	82	1	10.28924	10.28924	NUM
ma-226	82	2	/	/	SYM
ma-226	82	3	ada	ada	NOUN
ma-226	82	4	/	/	SYM
ma-226	82	5	ma.4.10	ma.4.10	NOUN
ma-226	82	6	4since	4since	NUM
ma-226	82	7	(	(	PUNCT
ma-226	82	8	3	3	NUM
ma-226	82	9	)	)	PUNCT
ma-226	82	10	,	,	PUNCT
ma-226	82	11	(	(	PUNCT
ma-226	82	12	6	6	NUM
ma-226	82	13	)	)	PUNCT
ma-226	82	14	,	,	PUNCT
ma-226	82	15	(	(	PUNCT
ma-226	82	16	7	7	NUM
ma-226	82	17	)	)	PUNCT
ma-226	82	18	,	,	PUNCT
ma-226	82	19	we	we	PRON
ma-226	82	20	can	can	AUX
ma-226	82	21	build	build	VERB
ma-226	82	22	derivative	derivative	ADJ
ma-226	82	23	approximation	approximation	NOUN
ma-226	82	24	formulas	formula	NOUN
ma-226	82	25	with	with	ADP
ma-226	82	26	(	(	PUNCT
ma-226	82	27	n+1)order	n+1)order	NUM
ma-226	82	28	accuracy	accuracy	VERB
ma-226	82	29	forthe	forthe	PRON
ma-226	82	30	grid	grid	NOUN
ma-226	82	31	function	function	NOUN
ma-226	82	32	,	,	PUNCT
ma-226	82	33	and	and	CCONJ
ma-226	82	34	n	n	CCONJ
ma-226	82	35	-	-	PUNCT
ma-226	82	36	order	order	NOUN
ma-226	82	37	accuracy	accuracy	NOUN
ma-226	82	38	for	for	ADP
ma-226	82	39	first	first	ADJ
ma-226	82	40	-	-	PUNCT
ma-226	82	41	order	order	NOUN
ma-226	82	42	derivative	derivative	NOUN
ma-226	82	43	,	,	PUNCT
ma-226	82	44	(	(	PUNCT
ma-226	82	45	n-1)order	n-1)order	NOUN
ma-226	82	46	accuracy	accuracy	NOUN
ma-226	82	47	for	for	ADP
ma-226	82	48	second	second	ADJ
ma-226	82	49	-	-	PUNCT
ma-226	82	50	order	order	NOUN
ma-226	82	51	derivative	derivative	NOUN
ma-226	82	52	.	.	PUNCT
ma-226	83	1	lemma	lemma	PROPN
ma-226	83	2	1	1	NUM
ma-226	83	3	:	:	PUNCT
ma-226	83	4	if	if	SCONJ
ma-226	83	5	the	the	DET
ma-226	83	6	accuracy	accuracy	NOUN
ma-226	83	7	of	of	ADP
ma-226	83	8	the	the	DET
ma-226	83	9	second	second	ADJ
ma-226	83	10	derivative	derivative	ADJ
ma-226	83	11	approximation	approximation	NOUN
ma-226	83	12	is	be	AUX
ma-226	83	13	of	of	ADP
ma-226	83	14	order	order	NOUN
ma-226	83	15	(	(	PUNCT
ma-226	83	16	n	n	CCONJ
ma-226	83	17	−	−	PROPN
ma-226	83	18	2	2	NUM
ma-226	83	19	)	)	PUNCT
ma-226	83	20	,	,	PUNCT
ma-226	83	21	then	then	ADV
ma-226	83	22	the	the	DET
ma-226	83	23	accuracy	accuracy	NOUN
ma-226	83	24	of	of	ADP
ma-226	83	25	the	the	DET
ma-226	83	26	function	function	NOUN
ma-226	83	27	approximation	approximation	NOUN
ma-226	83	28	will	will	AUX
ma-226	83	29	be	be	AUX
ma-226	83	30	of	of	ADP
ma-226	83	31	order	order	NOUN
ma-226	83	32	n	n	NOUN
ma-226	83	33	and	and	CCONJ
ma-226	83	34	vice	vice	NOUN
ma-226	83	35	versa.let	versa.let	X
ma-226	83	36	ti(x	ti(x	NUM
ma-226	83	37	)	)	PUNCT
ma-226	83	38	=	=	SYM
ma-226	84	1	(	(	PUNCT
ma-226	84	2	x	x	X
ma-226	84	3	−	−	PROPN
ma-226	84	4	z0)(x	z0)(x	NUM
ma-226	84	5	−	−	PROPN
ma-226	84	6	z1)	z1)	PROPN
ma-226	84	7	...	...	PUNCT
ma-226	85	1	(x	(x	PROPN
ma-226	85	2	−	−	PROPN
ma-226	85	3	zi−1)(x	zi−1)(x	PROPN
ma-226	85	4	−	−	PROPN
ma-226	85	5	zi+1)	zi+1)	PROPN
ma-226	85	6	...	...	PUNCT
ma-226	86	1	(x	(x	PROPN
ma-226	86	2	−	−	PROPN
ma-226	87	1	zn	zn	NUM
ma-226	87	2	)	)	PUNCT
ma-226	87	3	,	,	PUNCT
ma-226	87	4	mi(x	mi(x	X
ma-226	87	5	)	)	PUNCT
ma-226	88	1	=	=	PRON
ma-226	88	2	(	(	PUNCT
ma-226	88	3	zi	zi	NOUN
ma-226	88	4	−	−	PROPN
ma-226	88	5	z0)(zi	z0)(zi	PROPN
ma-226	88	6	−	−	PROPN
ma-226	88	7	z1)	z1)	NOUN
ma-226	88	8	...	...	PUNCT
ma-226	88	9	(zi	(zi	PUNCT
ma-226	88	10	−	−	PROPN
ma-226	88	11	zi−1)(zi	zi−1)(zi	PROPN
ma-226	88	12	−	−	PROPN
ma-226	88	13	zi+1)	zi+1)	PROPN
ma-226	88	14	...	...	PUNCT
ma-226	88	15	(zi	(zi	PUNCT
ma-226	88	16	−	−	PROPN
ma-226	88	17	zn).let	zn).let	PROPN
ma-226	88	18	b(n(m	b(n(m	PROPN
ma-226	88	19	)	)	PUNCT
ma-226	88	20	)	)	PUNCT
ma-226	88	21	be	be	AUX
ma-226	88	22	the	the	DET
ma-226	88	23	coefficient	coefficient	NOUN
ma-226	88	24	matrix	matrix	NOUN
ma-226	88	25	in	in	ADP
ma-226	88	26	the	the	DET
ma-226	88	27	morder	morder	NOUN
ma-226	88	28	derivative	derivative	ADJ
ma-226	88	29	approximation	approximation	NOUN
ma-226	88	30	formula	formula	NOUN
ma-226	88	31	using	use	VERB
ma-226	88	32	(	(	PUNCT
ma-226	88	33	n	n	X
ma-226	88	34	+	+	NOUN
ma-226	88	35	1	1	X
ma-226	88	36	)	)	PUNCT
ma-226	88	37	neighboring	neighboring	NOUN
ma-226	88	38	points	point	NOUN
ma-226	88	39	,	,	PUNCT
ma-226	88	40	then	then	ADV
ma-226	88	41	the	the	DET
ma-226	88	42	grid	grid	NOUN
ma-226	88	43	derivative	derivative	NOUN
ma-226	88	44	of	of	ADP
ma-226	88	45	orders	order	NOUN
ma-226	88	46	will	will	AUX
ma-226	88	47	be	be	AUX
ma-226	88	48	determined	determine	VERB
ma-226	88	49	by	by	ADP
ma-226	88	50	the	the	DET
ma-226	88	51	formula:	formula:	PROPN
ma-226	88	52	u(m)(xi	u(m)(xi	PROPN
ma-226	88	53	)	)	PUNCT
ma-226	88	54	=	=	SYM
ma-226	89	1	1	1	NUM
ma-226	89	2	hm	hm	INTJ
ma-226	89	3	n∑	n∑	PROPN
ma-226	89	4	k=0	k=0	PROPN
ma-226	89	5	b	b	PROPN
ma-226	89	6	(	(	PUNCT
ma-226	89	7	m	m	NOUN
ma-226	89	8	)	)	PUNCT
ma-226	89	9	n	n	CCONJ
ma-226	89	10	(	(	PUNCT
ma-226	89	11	i	i	INTJ
ma-226	89	12	,	,	PUNCT
ma-226	90	1	k)uk	k)uk	PROPN
ma-226	90	2	,	,	PUNCT
ma-226	90	3	i	i	PRON
ma-226	90	4	<	<	X
ma-226	90	5	n/2	n/2	PROPN
ma-226	90	6	u(m)(xi	u(m)(xi	NUM
ma-226	90	7	)	)	PUNCT
ma-226	90	8	=	=	SYM
ma-226	91	1	1	1	NUM
ma-226	91	2	hm	hm	INTJ
ma-226	91	3	n∑	n∑	PROPN
ma-226	91	4	k=0	k=0	PROPN
ma-226	91	5	b	b	PROPN
ma-226	91	6	(	(	PUNCT
ma-226	91	7	m	m	NOUN
ma-226	91	8	)	)	PUNCT
ma-226	91	9	n	n	CCONJ
ma-226	91	10	(	(	PUNCT
ma-226	91	11	i	i	NOUN
ma-226	91	12	,	,	PUNCT
ma-226	91	13	k)ui+k−n/2	k)ui+k−n/2	PROPN
ma-226	91	14	,	,	PUNCT
ma-226	91	15	n/2	n/2	NOUN
ma-226	91	16	≤	≤	PUNCT
ma-226	91	17	i	i	PRON
ma-226	91	18	≤	≤	NOUN
ma-226	91	19	n	n	CCONJ
ma-226	91	20	−	−	PROPN
ma-226	91	21	n/2	n/2	NOUN
ma-226	91	22	u(m)(xi	u(m)(xi	NUM
ma-226	91	23	)	)	PUNCT
ma-226	91	24	=	=	SYM
ma-226	92	1	1	1	NUM
ma-226	92	2	hm	hm	INTJ
ma-226	92	3	n∑	n∑	PROPN
ma-226	92	4	k=0	k=0	PROPN
ma-226	92	5	b	b	PROPN
ma-226	92	6	(	(	PUNCT
ma-226	92	7	m	m	NOUN
ma-226	92	8	)	)	PUNCT
ma-226	92	9	n	n	CCONJ
ma-226	92	10	(	(	PUNCT
ma-226	92	11	i	i	INTJ
ma-226	92	12	,	,	PUNCT
ma-226	92	13	k)un−n+k	k)un−n+k	PROPN
ma-226	92	14	,	,	PUNCT
ma-226	92	15	i	i	PRON
ma-226	92	16	>	>	X
ma-226	92	17	n	n	CCONJ
ma-226	92	18	−	−	PROPN
ma-226	92	19	n/2	n/2	NOUN
ma-226	92	20	(	(	PUNCT
ma-226	92	21	8)	8)	NUM
ma-226	92	22	where	where	SCONJ
ma-226	92	23	,	,	PUNCT
ma-226	92	24	l(m)i	l(m)i	PROPN
ma-226	92	25	(	(	PUNCT
ma-226	92	26	x	x	NOUN
ma-226	92	27	)	)	PUNCT
ma-226	92	28	=	=	SYM
ma-226	93	1	m	m	PROPN
ma-226	93	2	!	!	PUNCT
ma-226	94	1	t	t	PROPN
ma-226	94	2	(	(	PUNCT
ma-226	94	3	m	m	NOUN
ma-226	94	4	)	)	PUNCT
ma-226	94	5	i	i	PRON
ma-226	94	6	(	(	PUNCT
ma-226	94	7	x	x	X
ma-226	94	8	)	)	PUNCT
ma-226	94	9	mi	mi	PROPN
ma-226	94	10	;	;	PUNCT
ma-226	94	11	t	t	PROPN
ma-226	94	12	(	(	PUNCT
ma-226	94	13	m)i	m)i	X
ma-226	94	14	(	(	PUNCT
ma-226	94	15	x	x	NOUN
ma-226	94	16	)	)	PUNCT
ma-226	94	17	=	=	SYM
ma-226	94	18	(	(	PUNCT
ma-226	94	19	x	x	X
ma-226	94	20	−	−	PROPN
ma-226	94	21	zm)(x	zm)(x	PROPN
ma-226	94	22	−	−	PROPN
ma-226	94	23	zm+1)	zm+1)	PROPN
ma-226	94	24	...	...	PUNCT
ma-226	94	25	(x	(x	PROPN
ma-226	94	26	−	−	PROPN
ma-226	94	27	zn	zn	X
ma-226	94	28	)	)	PUNCT
ma-226	95	1	+	+	CCONJ
ma-226	95	2	(	(	PUNCT
ma-226	95	3	x	x	SYM
ma-226	95	4	−	−	PROPN
ma-226	95	5	z0)(x	z0)(x	NUM
ma-226	95	6	−	−	PROPN
ma-226	95	7	zm+1)	zm+1)	PROPN
ma-226	95	8	...	...	PUNCT
ma-226	96	1	(x	(x	PROPN
ma-226	96	2	−	−	PROPN
ma-226	96	3	zn	zn	X
ma-226	96	4	)	)	PUNCT
ma-226	97	1	+	+	CCONJ
ma-226	97	2	(	(	PUNCT
ma-226	97	3	x	x	SYM
ma-226	97	4	−	−	PROPN
ma-226	97	5	z0)(x	z0)(x	NUM
ma-226	97	6	−	−	PROPN
ma-226	97	7	z1)(x	z1)(x	NOUN
ma-226	97	8	−	−	PROPN
ma-226	98	1	zm+2)	zm+2)	NOUN
ma-226	98	2	...	...	PUNCT
ma-226	98	3	(x	(x	PROPN
ma-226	98	4	−	−	PROPN
ma-226	98	5	zn	zn	X
ma-226	98	6	)	)	PUNCT
ma-226	99	1	+	+	CCONJ
ma-226	99	2	...	...	PUNCT
ma-226	100	1	+	+	CCONJ
ma-226	100	2	(	(	PUNCT
ma-226	100	3	x	x	SYM
ma-226	100	4	−	−	PROPN
ma-226	100	5	z0)(x	z0)(x	NUM
ma-226	100	6	−	−	PROPN
ma-226	100	7	z1)(x	z1)(x	PROPN
ma-226	100	8	−	−	PROPN
ma-226	100	9	z2)	z2)	NUM
ma-226	100	10	...	...	PUNCT
ma-226	101	1	(x	(x	PROPN
ma-226	101	2	−	−	PROPN
ma-226	101	3	zn−m	zn−m	PROPN
ma-226	101	4	)	)	PUNCT
ma-226	101	5	.	.	PUNCT
ma-226	102	1	theorem	theorem	VERB
ma-226	102	2	1	1	NUM
ma-226	102	3	:	:	PUNCT
ma-226	102	4	the	the	DET
ma-226	102	5	accuracy	accuracy	NOUN
ma-226	102	6	of	of	ADP
ma-226	102	7	approximating	approximate	VERB
ma-226	102	8	the	the	DET
ma-226	102	9	grid	grid	NOUN
ma-226	102	10	derivative	derivative	NOUN
ma-226	102	11	of	of	ADP
ma-226	102	12	order	order	NOUN
ma-226	102	13	m	m	AUX
ma-226	102	14	using	use	VERB
ma-226	102	15	(	(	PUNCT
ma-226	102	16	n	n	X
ma-226	102	17	+	+	NOUN
ma-226	102	18	1	1	X
ma-226	102	19	)	)	PUNCT
ma-226	102	20	neighboring	neighboring	NOUN
ma-226	102	21	points	point	NOUN
ma-226	102	22	on	on	ADP
ma-226	102	23	the	the	DET
ma-226	102	24	regular	regular	ADJ
ma-226	102	25	grid	grid	NOUN
ma-226	102	26	is	be	AUX
ma-226	102	27	of	of	ADP
ma-226	102	28	order	order	NOUN
ma-226	102	29	(	(	PUNCT
ma-226	102	30	n	n	CCONJ
ma-226	102	31	−m	−m	NOUN
ma-226	102	32	+	+	CCONJ
ma-226	102	33	1).formulas	1).formulas	NUM
ma-226	102	34	(	(	PUNCT
ma-226	102	35	6	6	NUM
ma-226	102	36	)	)	PUNCT
ma-226	102	37	,	,	PUNCT
ma-226	102	38	(	(	PUNCT
ma-226	102	39	7	7	NUM
ma-226	102	40	)	)	PUNCT
ma-226	102	41	,	,	PUNCT
ma-226	102	42	(	(	PUNCT
ma-226	102	43	8)	8)	NUM
ma-226	102	44	will	will	AUX
ma-226	102	45	be	be	AUX
ma-226	102	46	used	use	VERB
ma-226	102	47	to	to	PART
ma-226	102	48	propose	propose	VERB
ma-226	102	49	the	the	DET
ma-226	102	50	difference	difference	NOUN
ma-226	102	51	scheme	scheme	NOUN
ma-226	102	52	given	give	VERB
ma-226	102	53	in	in	ADP
ma-226	102	54	section	section	NOUN
ma-226	102	55	2.2	2.2	NUM
ma-226	102	56	2.2	2.2	NUM
ma-226	102	57	.	.	PUNCT
ma-226	102	58	difference	difference	NOUN
ma-226	102	59	scheme	scheme	NOUN
ma-226	102	60	with	with	ADP
ma-226	102	61	high	high	ADJ
ma-226	102	62	order	order	NOUN
ma-226	102	63	accuracyconsider	accuracyconsider	ADP
ma-226	102	64	the	the	DET
ma-226	102	65	differential	differential	ADJ
ma-226	102	66	problem	problem	NOUN
ma-226	102	67	lnu(x	lnu(x	VERB
ma-226	102	68	)	)	PUNCT
ma-226	103	1	=	=	SYM
ma-226	103	2	f	f	X
ma-226	103	3	(	(	PUNCT
ma-226	103	4	x	x	NOUN
ma-226	103	5	)	)	PUNCT
ma-226	103	6	,	,	PUNCT
ma-226	103	7	bau(a	bau(a	PROPN
ma-226	103	8	)	)	PUNCT
ma-226	103	9	=	=	SYM
ma-226	103	10	ga	ga	PROPN
ma-226	103	11	,	,	PUNCT
ma-226	103	12	bbu(b	bbu(b	NUM
ma-226	103	13	)	)	PUNCT
ma-226	103	14	=	=	SYM
ma-226	103	15	gb	gb	NOUN
ma-226	103	16	,	,	PUNCT
ma-226	103	17	x	x	SYM
ma-226	103	18	∈	∈	PROPN
ma-226	104	1	[	[	X
ma-226	104	2	a	a	X
ma-226	104	3	,	,	PUNCT
ma-226	104	4	b	b	NOUN
ma-226	104	5	]	]	X
ma-226	104	6	,	,	PUNCT
ma-226	104	7	(	(	PUNCT
ma-226	104	8	9	9	X
ma-226	104	9	)	)	PUNCT
ma-226	104	10	where	where	SCONJ
ma-226	104	11	ln	ln	ADV
ma-226	104	12	is	be	AUX
ma-226	104	13	the	the	DET
ma-226	104	14	linear	linear	ADJ
ma-226	104	15	differential	differential	NOUN
ma-226	104	16	operator	operator	NOUN
ma-226	104	17	,	,	PUNCT
ma-226	104	18	ba	ba	PROPN
ma-226	104	19	,	,	PUNCT
ma-226	104	20	bb	bb	PROPN
ma-226	104	21	are	be	AUX
ma-226	104	22	the	the	DET
ma-226	104	23	boundary	boundary	ADJ
ma-226	104	24	condition	condition	NOUN
ma-226	104	25	operators.let	operators.let	X
ma-226	104	26	λnu	λnu	NOUN
ma-226	105	1	=	=	SYM
ma-226	105	2	φ	φ	PROPN
ma-226	105	3	,	,	PUNCT
ma-226	105	4	λau	λau	PROPN
ma-226	105	5	=	=	SYM
ma-226	105	6	φa	φa	PROPN
ma-226	105	7	,	,	PUNCT
ma-226	105	8	λbu	λbu	PROPN
ma-226	106	1	=	=	SYM
ma-226	106	2	φb	φb	X
ma-226	106	3	(	(	PUNCT
ma-226	106	4	10)be	10)be	NUM
ma-226	106	5	the	the	DET
ma-226	106	6	difference	difference	NOUN
ma-226	106	7	scheme	scheme	NOUN
ma-226	106	8	for	for	ADP
ma-226	106	9	the	the	DET
ma-226	106	10	differential	differential	ADJ
ma-226	106	11	problem	problem	NOUN
ma-226	106	12	(	(	PUNCT
ma-226	106	13	9	9	NUM
ma-226	106	14	)	)	PUNCT
ma-226	106	15	,	,	PUNCT
ma-226	106	16	where	where	SCONJ
ma-226	106	17	λn	λn	PROPN
ma-226	106	18	is	be	AUX
ma-226	106	19	the	the	DET
ma-226	106	20	linear	linear	ADJ
ma-226	106	21	difference	difference	NOUN
ma-226	106	22	operator	operator	NOUN
ma-226	106	23	,	,	PUNCT
ma-226	106	24	λa	λa	ADP
ma-226	106	25	,	,	PUNCT
ma-226	106	26	λb	λb	PROPN
ma-226	106	27	are	be	AUX
ma-226	106	28	the	the	DET
ma-226	106	29	boundary	boundary	ADJ
ma-226	106	30	condition	condition	NOUN
ma-226	106	31	difference	difference	NOUN
ma-226	106	32	operators	operator	NOUN
ma-226	106	33	.	.	PUNCT
ma-226	107	1	let	let	VERB
ma-226	107	2	u	u	PRON
ma-226	107	3	be	be	AUX
ma-226	107	4	the	the	DET
ma-226	107	5	grid	grid	NOUN
ma-226	107	6	function	function	NOUN
ma-226	107	7	determinedbased	determinedbase	VERB
ma-226	107	8	on	on	ADP
ma-226	107	9	the	the	DET
ma-226	107	10	difference	difference	NOUN
ma-226	107	11	scheme	scheme	NOUN
ma-226	107	12	,	,	PUNCT
ma-226	107	13	let	let	VERB
ma-226	107	14	ud	ud	INTJ
ma-226	107	15	be	be	AUX
ma-226	107	16	the	the	DET
ma-226	107	17	value	value	NOUN
ma-226	107	18	of	of	ADP
ma-226	107	19	u(x	u(x	NOUN
ma-226	107	20	)	)	PUNCT
ma-226	107	21	on	on	ADP
ma-226	107	22	the	the	DET
ma-226	107	23	grid	grid	NOUN
ma-226	107	24	ωh	ωh	PROPN
ma-226	107	25	.	.	PUNCT
ma-226	107	26	below	below	ADV
ma-226	107	27	we	we	PRON
ma-226	107	28	give	give	VERB
ma-226	107	29	twodifference	twodifference	NOUN
ma-226	107	30	schemes	scheme	NOUN
ma-226	107	31	corresponding	correspond	VERB
ma-226	107	32	to	to	ADP
ma-226	107	33	two	two	NUM
ma-226	107	34	differential	differential	ADJ
ma-226	107	35	problems	problem	NOUN
ma-226	107	36	.	.	PUNCT
ma-226	108	1	2.2.1	2.2.1	NUM
ma-226	108	2	.	.	PUNCT
ma-226	108	3	differential	differential	ADJ
ma-226	108	4	scheme	scheme	NOUN
ma-226	108	5	1consider	1consider	NUM
ma-226	108	6	the	the	DET
ma-226	108	7	second	second	ADJ
ma-226	108	8	-	-	PUNCT
ma-226	108	9	order	order	NOUN
ma-226	108	10	boundary	boundary	ADJ
ma-226	108	11	problem	problem	NOUN
ma-226	108	12	with	with	ADP
ma-226	108	13	dirichlet	dirichlet	PROPN
ma-226	108	14	boundary	boundary	PROPN
ma-226	108	15	conditions	condition	NOUN
ma-226	108	16	{	{	PUNCT
ma-226	108	17	u′′(x	u′′(x	NOUN
ma-226	108	18	)	)	PUNCT
ma-226	108	19	=	=	SYM
ma-226	108	20	f	f	X
ma-226	108	21	(	(	PUNCT
ma-226	108	22	x	x	NOUN
ma-226	108	23	)	)	PUNCT
ma-226	108	24	,	,	PUNCT
ma-226	108	25	x	x	PUNCT
ma-226	108	26	∈	∈	PROPN
ma-226	108	27	(	(	PUNCT
ma-226	108	28	a	a	PRON
ma-226	108	29	,	,	PUNCT
ma-226	108	30	b	b	NOUN
ma-226	108	31	)	)	PUNCT
ma-226	108	32	u(a	u(a	PROPN
ma-226	108	33	)	)	PUNCT
ma-226	108	34	=	=	SYM
ma-226	108	35	c	c	X
ma-226	108	36	;	;	PUNCT
ma-226	108	37	u(b	u(b	NOUN
ma-226	108	38	)	)	PUNCT
ma-226	108	39	=	=	SYM
ma-226	108	40	d.	d.	NOUN
ma-226	108	41	(	(	PUNCT
ma-226	108	42	11	11	NUM
ma-226	108	43	)	)	PUNCT
ma-226	108	44	https://doi.org/10.28924/ada/ma.4.10	https://doi.org/10.28924/ada/ma.4.10	NOUN
ma-226	108	45	eur	eur	PROPN
ma-226	108	46	.	.	PUNCT
ma-226	109	1	j.	j.	PROPN
ma-226	109	2	math	math	PROPN
ma-226	109	3	.	.	PUNCT
ma-226	110	1	anal	anal	PROPN
ma-226	110	2	.	.	PUNCT
ma-226	111	1	10.28924	10.28924	NUM
ma-226	111	2	/	/	SYM
ma-226	111	3	ada	ada	NOUN
ma-226	111	4	/	/	NOUN
ma-226	111	5	ma.4.10	ma.4.10	NOUN
ma-226	111	6	5considering	5considere	VERB
ma-226	111	7	the	the	DET
ma-226	111	8	grid	grid	NOUN
ma-226	111	9	space	space	NOUN
ma-226	111	10	ωh	ωh	PROPN
ma-226	111	11	,	,	PUNCT
ma-226	111	12	let	let	VERB
ma-226	111	13	ui	ui	PROPN
ma-226	111	14	=	=	PUNCT
ma-226	111	15	u(xi	u(xi	PROPN
ma-226	111	16	)	)	PUNCT
ma-226	111	17	,	,	PUNCT
ma-226	111	18	u	u	NOUN
ma-226	111	19	=	=	PUNCT
ma-226	111	20	(	(	PUNCT
ma-226	111	21	u0	u0	ADJ
ma-226	111	22	,	,	PUNCT
ma-226	111	23	u1	u1	NOUN
ma-226	111	24	,	,	PUNCT
ma-226	111	25	.	.	PUNCT
ma-226	111	26	.	.	PUNCT
ma-226	112	1	.	.	PUNCT
ma-226	113	1	,	,	PUNCT
ma-226	113	2	un	un	PROPN
ma-226	113	3	)	)	PUNCT
ma-226	113	4	be	be	VERB
ma-226	113	5	the	the	DET
ma-226	113	6	grid	grid	NOUN
ma-226	113	7	function	function	NOUN
ma-226	113	8	,	,	PUNCT
ma-226	113	9	f	f	PROPN
ma-226	113	10	=	=	PRON
ma-226	113	11	(	(	PUNCT
ma-226	113	12	f0	f0	PROPN
ma-226	113	13	,	,	PUNCT
ma-226	113	14	f1	f1	NOUN
ma-226	113	15	,	,	PUNCT
ma-226	113	16	.	.	PUNCT
ma-226	113	17	.	.	PUNCT
ma-226	114	1	.	.	PUNCT
ma-226	115	1	,	,	PUNCT
ma-226	115	2	fn	fn	X
ma-226	115	3	)	)	PUNCT
ma-226	115	4	is	be	AUX
ma-226	115	5	the	the	DET
ma-226	115	6	right	right	ADJ
ma-226	115	7	-	-	PUNCT
ma-226	115	8	hand	hand	NOUN
ma-226	115	9	grid	grid	NOUN
ma-226	115	10	function	function	NOUN
ma-226	115	11	,	,	PUNCT
ma-226	115	12	d(m)f	d(m)f	NOUN
ma-226	115	13	is	be	AUX
ma-226	115	14	the	the	DET
ma-226	115	15	m	m	NOUN
ma-226	115	16	-	-	PUNCT
ma-226	115	17	order	order	NOUN
ma-226	115	18	derivative	derivative	NOUN
ma-226	115	19	of	of	ADP
ma-226	115	20	the	the	DET
ma-226	115	21	grid	grid	NOUN
ma-226	115	22	function	function	NOUN
ma-226	115	23	f	f	PROPN
ma-226	115	24	.	.	PUNCT
ma-226	116	1	since	since	SCONJ
ma-226	116	2	f	f	PROPN
ma-226	116	3	(	(	PUNCT
ma-226	116	4	x	x	X
ma-226	116	5	)	)	PUNCT
ma-226	116	6	satisfies	satisfy	VERB
ma-226	116	7	the	the	DET
ma-226	116	8	differential	differential	ADJ
ma-226	116	9	equation	equation	NOUN
ma-226	116	10	(	(	PUNCT
ma-226	116	11	11	11	NUM
ma-226	116	12	)	)	PUNCT
ma-226	116	13	,	,	PUNCT
ma-226	116	14	we	we	PRON
ma-226	116	15	have	have	VERB
ma-226	116	16	f	f	PROPN
ma-226	116	17	(	(	PUNCT
ma-226	116	18	xi	xi	PROPN
ma-226	116	19	)	)	PUNCT
ma-226	116	20	=	=	SYM
ma-226	116	21	u′′(xi	u′′(xi	ADJ
ma-226	116	22	)	)	PUNCT
ma-226	116	23	,	,	PUNCT
ma-226	116	24	i	i	PRON
ma-226	116	25	=	=	NOUN
ma-226	116	26	0	0	NUM
ma-226	116	27	,	,	PUNCT
ma-226	116	28	1	1	NUM
ma-226	116	29	,	,	PUNCT
ma-226	116	30	2	2	NUM
ma-226	116	31	,	,	PUNCT
ma-226	116	32	.	.	PUNCT
ma-226	116	33	.	.	PUNCT
ma-226	117	1	.	.	PUNCT
ma-226	118	1	,	,	PUNCT
ma-226	118	2	n	n	X
ma-226	118	3	.using	.use	VERB
ma-226	118	4	(	(	PUNCT
ma-226	118	5	7	7	X
ma-226	118	6	)	)	PUNCT
ma-226	118	7	we	we	PRON
ma-226	118	8	obtain	obtain	VERB
ma-226	118	9	the	the	DET
ma-226	118	10	approximated	approximate	VERB
ma-226	118	11	formula	formula	NOUN
ma-226	118	12	u′′(xi	u′′(xi	ADJ
ma-226	118	13	)	)	PUNCT
ma-226	119	1	=	=	PUNCT
ma-226	119	2	ui−1	ui−1	PROPN
ma-226	119	3	−	−	PROPN
ma-226	119	4	2ui	2ui	ADJ
ma-226	119	5	+	+	CCONJ
ma-226	119	6	ui+1	ui+1	NUM
ma-226	119	7	h2	h2	NOUN
ma-226	119	8	−	−	PROPN
ma-226	119	9	h2	h2	PROPN
ma-226	119	10	4	4	NUM
ma-226	119	11	!	!	NOUN
ma-226	119	12	d(2)fi	d(2)fi	NOUN
ma-226	119	13	−	−	PROPN
ma-226	119	14	h4	h4	PROPN
ma-226	119	15	6	6	NUM
ma-226	119	16	!	!	PUNCT
ma-226	119	17	d(4)fi	d(4)fi	PROPN
ma-226	119	18	−	−	PROPN
ma-226	119	19	...	...	PUNCT
ma-226	120	1	−	−	PROPN
ma-226	121	1	h2m−2	h2m−2	PROPN
ma-226	121	2	(	(	PUNCT
ma-226	121	3	2	2	NUM
ma-226	121	4	m	m	NOUN
ma-226	121	5	)	)	PUNCT
ma-226	121	6	!	!	PUNCT
ma-226	122	1	d(2m−2)fi	d(2m−2)fi	VERB
ma-226	122	2	+	+	ADJ
ma-226	122	3	o(hn−1	o(hn−1	X
ma-226	122	4	)	)	PUNCT
ma-226	122	5	(	(	PUNCT
ma-226	122	6	12	12	NUM
ma-226	122	7	)	)	PUNCT
ma-226	122	8	set	set	NOUN
ma-226	122	9	φi	φi	ADV
ma-226	122	10	=	=	PUNCT
ma-226	122	11	h2fi	h2fi	PUNCT
ma-226	123	1	+	+	CCONJ
ma-226	123	2	h4	h4	PROPN
ma-226	123	3	4!d	4!d	PROPN
ma-226	123	4	(	(	PUNCT
ma-226	123	5	2)fi	2)fi	PROPN
ma-226	123	6	+	+	CCONJ
ma-226	123	7	h6	h6	PROPN
ma-226	123	8	6!d	6!d	PUNCT
ma-226	123	9	(	(	PUNCT
ma-226	123	10	4)fi	4)fi	NUM
ma-226	123	11	+	+	CCONJ
ma-226	123	12	...	...	PUNCT
ma-226	123	13	+	+	NUM
ma-226	123	14	h2	h2	NOUN
ma-226	123	15	m	m	PROPN
ma-226	123	16	(	(	PUNCT
ma-226	123	17	2m)!d	2m)!d	NUM
ma-226	123	18	(	(	PUNCT
ma-226	123	19	2m−2)fi	2m−2)fi	NUM
ma-226	123	20	,	,	PUNCT
ma-226	123	21	1	1	NUM
ma-226	123	22	≤	≤	NUM
ma-226	123	23	i	i	PRON
ma-226	123	24	≤	≤	NOUN
ma-226	123	25	n	n	CCONJ
ma-226	123	26	−	−	PROPN
ma-226	123	27	1	1	NUM
ma-226	123	28	,	,	PUNCT
ma-226	123	29	we	we	PRON
ma-226	123	30	obtain	obtain	VERB
ma-226	123	31	the	the	DET
ma-226	123	32	systemof	systemof	ADJ
ma-226	123	33	difference	difference	NOUN
ma-226	123	34	equations	equation	NOUN
ma-226	123	35	{	{	PUNCT
ma-226	123	36	ui−1	ui−1	PROPN
ma-226	123	37	−	−	PROPN
ma-226	123	38	2ui	2ui	ADJ
ma-226	124	1	+	+	CCONJ
ma-226	124	2	ui+1	ui+1	ADJ
ma-226	124	3	=	=	PUNCT
ma-226	124	4	φi	φi	ADV
ma-226	124	5	,	,	PUNCT
ma-226	124	6	i	i	PRON
ma-226	124	7	=	=	NOUN
ma-226	124	8	1	1	NUM
ma-226	124	9	,	,	PUNCT
ma-226	124	10	2	2	NUM
ma-226	124	11	,	,	PUNCT
ma-226	124	12	...	...	PUNCT
ma-226	124	13	,	,	PUNCT
ma-226	124	14	n	n	CCONJ
ma-226	124	15	−	−	PROPN
ma-226	124	16	1	1	NUM
ma-226	124	17	u0	u0	NOUN
ma-226	124	18	=	=	ADJ
ma-226	124	19	c	c	NOUN
ma-226	124	20	;	;	PUNCT
ma-226	124	21	un	un	PROPN
ma-226	124	22	=	=	PROPN
ma-226	124	23	d	d	PROPN
ma-226	124	24	(	(	PUNCT
ma-226	124	25	13	13	NUM
ma-226	124	26	)	)	PUNCT
ma-226	124	27	(	(	PUNCT
ma-226	124	28	13	13	NUM
ma-226	124	29	)	)	PUNCT
ma-226	124	30	is	be	AUX
ma-226	124	31	is	be	AUX
ma-226	124	32	called	call	VERB
ma-226	124	33	a	a	DET
ma-226	124	34	three	three	NUM
ma-226	124	35	-	-	PUNCT
ma-226	124	36	diagonal	diagonal	ADJ
ma-226	124	37	system	system	NOUN
ma-226	124	38	because	because	SCONJ
ma-226	124	39	the	the	DET
ma-226	124	40	matrix	matrix	NOUN
ma-226	124	41	of	of	ADP
ma-226	124	42	the	the	DET
ma-226	124	43	system	system	NOUN
ma-226	124	44	has	have	VERB
ma-226	124	45	a	a	DET
ma-226	124	46	three	three	NUM
ma-226	124	47	-	-	PUNCT
ma-226	124	48	diagonal	diagonal	ADJ
ma-226	124	49	form.solving	form.solve	VERB
ma-226	124	50	system	system	NOUN
ma-226	124	51	(	(	PUNCT
ma-226	124	52	13	13	NUM
ma-226	124	53	)	)	PUNCT
ma-226	124	54	is	be	AUX
ma-226	124	55	performed	perform	VERB
ma-226	124	56	using	use	VERB
ma-226	124	57	the	the	DET
ma-226	124	58	following	following	ADJ
ma-226	124	59	pursuit	pursuit	NOUN
ma-226	124	60	algorithm	algorithm	NOUN
ma-226	124	61	.	.	PUNCT
ma-226	125	1	in	in	ADP
ma-226	125	2	the	the	DET
ma-226	125	3	case	case	NOUN
ma-226	125	4	of	of	ADP
ma-226	125	5	constructingscheme	constructingscheme	NOUN
ma-226	125	6	(	(	PUNCT
ma-226	125	7	13	13	NUM
ma-226	125	8	)	)	PUNCT
ma-226	125	9	,	,	PUNCT
ma-226	125	10	we	we	PRON
ma-226	125	11	used	use	VERB
ma-226	125	12	formula	formula	NOUN
ma-226	125	13	(	(	PUNCT
ma-226	125	14	7	7	X
ma-226	125	15	)	)	PUNCT
ma-226	125	16	which	which	PRON
ma-226	125	17	is	be	AUX
ma-226	125	18	used	use	VERB
ma-226	125	19	to	to	PART
ma-226	125	20	approximate	approximate	VERB
ma-226	125	21	the	the	DET
ma-226	125	22	2nd	2nd	ADJ
ma-226	125	23	derivative	derivative	NOUN
ma-226	125	24	with	with	ADP
ma-226	125	25	(	(	PUNCT
ma-226	125	26	n−2)-orderaccuracy	n−2)-orderaccuracy	NOUN
ma-226	125	27	,	,	PUNCT
ma-226	125	28	therefore	therefore	ADV
ma-226	125	29	,	,	PUNCT
ma-226	125	30	since	since	SCONJ
ma-226	125	31	lemma	lemma	PROPN
ma-226	125	32	1	1	NUM
ma-226	125	33	,	,	PUNCT
ma-226	125	34	it	it	PRON
ma-226	125	35	is	be	AUX
ma-226	125	36	implies	imply	VERB
ma-226	125	37	solution	solution	NOUN
ma-226	125	38	of	of	ADP
ma-226	125	39	system	system	NOUN
ma-226	125	40	(	(	PUNCT
ma-226	125	41	13	13	NUM
ma-226	125	42	)	)	PUNCT
ma-226	125	43	is	be	AUX
ma-226	125	44	the	the	DET
ma-226	125	45	approximation	approximation	NOUN
ma-226	125	46	of	of	ADP
ma-226	125	47	thefunction	thefunction	NOUN
ma-226	125	48	with	with	ADP
ma-226	125	49	n	n	CCONJ
ma-226	125	50	-	-	PUNCT
ma-226	125	51	order	order	NOUN
ma-226	125	52	accuracy	accuracy	NOUN
ma-226	125	53	.	.	PUNCT
ma-226	126	1	since	since	SCONJ
ma-226	126	2	there	there	ADV
ma-226	126	3	we	we	PRON
ma-226	126	4	have	have	VERB
ma-226	126	5	the	the	DET
ma-226	126	6	following	follow	VERB
ma-226	126	7	theorem	theorem	NOUN
ma-226	126	8	:	:	PUNCT
ma-226	126	9	theorem	theorem	NOUN
ma-226	126	10	2	2	NUM
ma-226	126	11	:	:	PUNCT
ma-226	126	12	the	the	DET
ma-226	126	13	system	system	NOUN
ma-226	126	14	of	of	ADP
ma-226	126	15	difference	difference	NOUN
ma-226	126	16	equations	equation	NOUN
ma-226	126	17	(	(	PUNCT
ma-226	126	18	13	13	NUM
ma-226	126	19	)	)	PUNCT
ma-226	126	20	is	be	AUX
ma-226	126	21	stable	stable	ADJ
ma-226	126	22	and	and	CCONJ
ma-226	126	23	its	its	PRON
ma-226	126	24	solution	solution	NOUN
ma-226	126	25	approximates	approximate	VERB
ma-226	126	26	to	to	ADP
ma-226	126	27	solution	solution	NOUN
ma-226	126	28	of	of	ADP
ma-226	126	29	problem	problem	NOUN
ma-226	126	30	(	(	PUNCT
ma-226	126	31	11	11	NUM
ma-226	126	32	)	)	PUNCT
ma-226	126	33	with	with	ADP
ma-226	126	34	n	n	NOUN
ma-226	126	35	-	-	PUNCT
ma-226	126	36	order	order	NOUN
ma-226	126	37	accuracy.the	accuracy.the	DET
ma-226	126	38	solution	solution	NOUN
ma-226	126	39	of	of	ADP
ma-226	126	40	the	the	DET
ma-226	126	41	system	system	NOUN
ma-226	126	42	is	be	AUX
ma-226	126	43	obtained	obtain	VERB
ma-226	126	44	from	from	ADP
ma-226	126	45	the	the	DET
ma-226	126	46	pursuit	pursuit	ADJ
ma-226	126	47	algorithm	algorithm	NOUN
ma-226	126	48	which	which	PRON
ma-226	126	49	has	have	VERB
ma-226	126	50	complexity	complexity	NOUN
ma-226	126	51	o(n	o(n	PROPN
ma-226	126	52	)	)	PUNCT
ma-226	126	53	.	.	PUNCT
ma-226	127	1	2.2.2	2.2.2	X
ma-226	127	2	.	.	PUNCT
ma-226	127	3	differential	differential	ADJ
ma-226	127	4	scheme	scheme	NOUN
ma-226	127	5	2consider	2consider	NUM
ma-226	127	6	the	the	DET
ma-226	127	7	second	second	ADJ
ma-226	127	8	-	-	PUNCT
ma-226	127	9	order	order	NOUN
ma-226	127	10	boundary	boundary	ADJ
ma-226	127	11	problem	problem	NOUN
ma-226	127	12	with	with	ADP
ma-226	127	13	mixed	mixed	ADJ
ma-226	127	14	boundary	boundary	ADJ
ma-226	127	15	conditions	condition	NOUN
ma-226	127	16	{	{	PUNCT
ma-226	127	17	u′′(x	u′′(x	NOUN
ma-226	127	18	)	)	PUNCT
ma-226	127	19	=	=	SYM
ma-226	127	20	f	f	X
ma-226	127	21	(	(	PUNCT
ma-226	127	22	x	x	NOUN
ma-226	127	23	)	)	PUNCT
ma-226	127	24	,	,	PUNCT
ma-226	127	25	x	x	PUNCT
ma-226	127	26	∈	∈	PROPN
ma-226	127	27	(	(	PUNCT
ma-226	127	28	a	a	DET
ma-226	127	29	,	,	PUNCT
ma-226	127	30	b	b	NOUN
ma-226	127	31	)	)	PUNCT
ma-226	127	32	c0u(a)−	c0u(a)−	NOUN
ma-226	127	33	c1u′(a	c1u′(a	PROPN
ma-226	127	34	)	)	PUNCT
ma-226	127	35	=	=	SYM
ma-226	128	1	c	c	X
ma-226	128	2	;	;	PUNCT
ma-226	128	3	d0u(b	d0u(b	PROPN
ma-226	128	4	)	)	PUNCT
ma-226	129	1	+	+	CCONJ
ma-226	130	1	d1u	d1u	PROPN
ma-226	130	2	′(b	′(b	NOUN
ma-226	130	3	)	)	PUNCT
ma-226	131	1	=	=	SYM
ma-226	131	2	d	d	X
ma-226	131	3	(	(	PUNCT
ma-226	131	4	14	14	NUM
ma-226	131	5	)	)	PUNCT
ma-226	131	6	consider	consider	VERB
ma-226	131	7	the	the	DET
ma-226	131	8	grid	grid	NOUN
ma-226	131	9	space	space	NOUN
ma-226	131	10	ωh	ωh	PROPN
ma-226	131	11	,	,	PUNCT
ma-226	131	12	set	set	VERB
ma-226	131	13	ui	ui	NOUN
ma-226	131	14	=	=	PUNCT
ma-226	131	15	u(xi	u(xi	PROPN
ma-226	131	16	)	)	PUNCT
ma-226	131	17	,	,	PUNCT
ma-226	131	18	fi	fi	NOUN
ma-226	132	1	=	=	SYM
ma-226	132	2	f	f	PROPN
ma-226	132	3	(	(	PUNCT
ma-226	132	4	xi	xi	PROPN
ma-226	132	5	)	)	PUNCT
ma-226	132	6	,	,	PUNCT
ma-226	132	7	u	u	NOUN
ma-226	132	8	=	=	PUNCT
ma-226	132	9	(	(	PUNCT
ma-226	132	10	u0	u0	ADJ
ma-226	132	11	,	,	PUNCT
ma-226	132	12	u1	u1	NOUN
ma-226	132	13	,	,	PUNCT
ma-226	132	14	.	.	PUNCT
ma-226	132	15	.	.	PUNCT
ma-226	132	16	.	.	PUNCT
ma-226	133	1	,	,	PUNCT
ma-226	133	2	un	un	AUX
ma-226	133	3	)	)	PUNCT
ma-226	133	4	be	be	AUX
ma-226	133	5	grid	grid	NOUN
ma-226	133	6	function	function	NOUN
ma-226	133	7	.	.	PUNCT
ma-226	134	1	f	f	X
ma-226	135	1	=	=	PRON
ma-226	135	2	(	(	PUNCT
ma-226	135	3	f0	f0	PROPN
ma-226	135	4	,	,	PUNCT
ma-226	135	5	f1	f1	NOUN
ma-226	135	6	,	,	PUNCT
ma-226	135	7	.	.	PUNCT
ma-226	135	8	.	.	PUNCT
ma-226	135	9	.	.	PUNCT
ma-226	136	1	,	,	PUNCT
ma-226	136	2	fn	fn	X
ma-226	136	3	)	)	PUNCT
ma-226	136	4	is	be	AUX
ma-226	136	5	the	the	DET
ma-226	136	6	right	right	ADJ
ma-226	136	7	-	-	PUNCT
ma-226	136	8	hand	hand	NOUN
ma-226	136	9	grid	grid	NOUN
ma-226	136	10	function	function	NOUN
ma-226	136	11	,	,	PUNCT
ma-226	136	12	d(m)n	d(m)n	PROPN
ma-226	136	13	f	f	PROPN
ma-226	136	14	is	be	AUX
ma-226	136	15	the	the	DET
ma-226	136	16	m	m	NOUN
ma-226	136	17	-	-	PUNCT
ma-226	136	18	order	order	NOUN
ma-226	136	19	derivative	derivative	NOUN
ma-226	136	20	of	of	ADP
ma-226	136	21	the	the	DET
ma-226	136	22	gridfunction	gridfunction	NOUN
ma-226	136	23	f	f	X
ma-226	136	24	with	with	ADP
ma-226	136	25	n	n	CCONJ
ma-226	136	26	-	-	PUNCT
ma-226	136	27	order	order	NOUN
ma-226	136	28	accuracy	accuracy	NOUN
ma-226	136	29	.	.	PUNCT
ma-226	137	1	since	since	SCONJ
ma-226	137	2	(	(	PUNCT
ma-226	137	3	6	6	NUM
ma-226	137	4	)	)	PUNCT
ma-226	137	5	,	,	PUNCT
ma-226	137	6	we	we	PRON
ma-226	137	7	obtain	obtain	VERB
ma-226	137	8	the	the	DET
ma-226	137	9	difference	difference	NOUN
ma-226	137	10	formula	formula	NOUN
ma-226	137	11	u′(xi	u′(xi	PROPN
ma-226	137	12	)	)	PUNCT
ma-226	137	13	=	=	SYM
ma-226	138	1	ui+1	ui+1	PROPN
ma-226	138	2	−	−	NOUN
ma-226	138	3	ui	ui	PROPN
ma-226	139	1	h	h	NOUN
ma-226	139	2	−	−	PROPN
ma-226	139	3	h	h	NOUN
ma-226	140	1	2	2	NUM
ma-226	140	2	!	!	NOUN
ma-226	140	3	fi	fi	NOUN
ma-226	141	1	−	−	PROPN
ma-226	141	2	h2	h2	PROPN
ma-226	141	3	3	3	NUM
ma-226	141	4	!	!	PUNCT
ma-226	141	5	d(1)fi	d(1)fi	NOUN
ma-226	141	6	−	−	NOUN
ma-226	141	7	...	...	PUNCT
ma-226	141	8	−	−	PROPN
ma-226	141	9	hn−1	hn−1	ADJ
ma-226	141	10	n	n	X
ma-226	141	11	!	!	PUNCT
ma-226	141	12	d(n−2)fi	d(n−2)fi	NOUN
ma-226	141	13	+	+	ADJ
ma-226	141	14	o(hn	o(hn	X
ma-226	141	15	)	)	PUNCT
ma-226	141	16	(	(	PUNCT
ma-226	141	17	15	15	X
ma-226	141	18	)	)	PUNCT
ma-226	141	19	consider	consider	VERB
ma-226	141	20	two	two	NUM
ma-226	141	21	points	point	NOUN
ma-226	141	22	x0	x0	PROPN
ma-226	141	23	=	=	PUNCT
ma-226	142	1	a	a	X
ma-226	142	2	,	,	PUNCT
ma-226	142	3	xn	xn	PUNCT
ma-226	143	1	=	=	SYM
ma-226	143	2	b	b	PROPN
ma-226	143	3	,	,	PUNCT
ma-226	143	4	we	we	PRON
ma-226	143	5	obtain	obtain	VERB
ma-226	143	6	u′(a	u′(a	PUNCT
ma-226	143	7	)	)	PUNCT
ma-226	143	8	=	=	SYM
ma-226	143	9	u1	u1	NOUN
ma-226	143	10	−	−	PROPN
ma-226	143	11	u0	u0	ADJ
ma-226	143	12	h	h	NOUN
ma-226	144	1	−	−	PROPN
ma-226	144	2	h	h	NOUN
ma-226	144	3	2	2	NUM
ma-226	144	4	!	!	PUNCT
ma-226	145	1	f0	f0	PROPN
ma-226	145	2	−	−	PROPN
ma-226	145	3	h2	h2	PROPN
ma-226	145	4	3	3	NUM
ma-226	145	5	!	!	PUNCT
ma-226	145	6	d(1)f0	d(1)f0	NOUN
ma-226	145	7	−	−	PROPN
ma-226	145	8	...	...	PUNCT
ma-226	145	9	−	−	PROPN
ma-226	145	10	hn−1	hn−1	ADJ
ma-226	145	11	n	n	X
ma-226	145	12	!	!	PUNCT
ma-226	145	13	d(n−2)f0	d(n−2)f0	NOUN
ma-226	145	14	+	+	ADJ
ma-226	145	15	o(hn	o(hn	X
ma-226	145	16	)	)	PUNCT
ma-226	145	17	(	(	PUNCT
ma-226	145	18	16	16	NUM
ma-226	145	19	)	)	PUNCT
ma-226	145	20	u′(b	u′(b	PROPN
ma-226	145	21	)	)	PUNCT
ma-226	146	1	=	=	SYM
ma-226	146	2	un	un	PROPN
ma-226	146	3	−	−	PROPN
ma-226	146	4	un−1	un−1	PROPN
ma-226	146	5	h	h	NOUN
ma-226	146	6	+	+	CCONJ
ma-226	146	7	h	h	NOUN
ma-226	146	8	2	2	NUM
ma-226	146	9	!	!	PUNCT
ma-226	146	10	fn	fn	NOUN
ma-226	147	1	−	−	PROPN
ma-226	147	2	h2	h2	PROPN
ma-226	147	3	3	3	NUM
ma-226	147	4	!	!	PUNCT
ma-226	147	5	d(1)fn	d(1)fn	PROPN
ma-226	147	6	+	+	CCONJ
ma-226	147	7	...	...	PUNCT
ma-226	148	1	+	+	CCONJ
ma-226	148	2	(	(	PUNCT
ma-226	148	3	−1)n	−1)n	X
ma-226	148	4	hn−1	hn−1	PROPN
ma-226	148	5	n	n	CCONJ
ma-226	148	6	!	!	PUNCT
ma-226	149	1	d(n−2)fn	d(n−2)fn	PROPN
ma-226	149	2	+	+	ADV
ma-226	149	3	o(hn	o(hn	X
ma-226	149	4	)	)	PUNCT
ma-226	149	5	(	(	PUNCT
ma-226	149	6	17	17	NUM
ma-226	149	7	)	)	PUNCT
ma-226	149	8	https://doi.org/10.28924/ada/ma.4.10	https://doi.org/10.28924/ada/ma.4.10	NOUN
ma-226	149	9	eur	eur	PROPN
ma-226	149	10	.	.	PUNCT
ma-226	150	1	j.	j.	PROPN
ma-226	150	2	math	math	PROPN
ma-226	150	3	.	.	PUNCT
ma-226	151	1	anal	anal	PROPN
ma-226	151	2	.	.	PUNCT
ma-226	152	1	10.28924	10.28924	NUM
ma-226	152	2	/	/	SYM
ma-226	152	3	ada	ada	NOUN
ma-226	152	4	/	/	NOUN
ma-226	152	5	ma.4.10	ma.4.10	NOUN
ma-226	152	6	6substituting	6substituting	NUM
ma-226	152	7	formulas	formula	NOUN
ma-226	152	8	(	(	PUNCT
ma-226	152	9	16	16	NUM
ma-226	152	10	)	)	PUNCT
ma-226	152	11	and	and	CCONJ
ma-226	152	12	(	(	PUNCT
ma-226	152	13	17	17	NUM
ma-226	152	14	)	)	PUNCT
ma-226	152	15	into	into	ADP
ma-226	152	16	the	the	DET
ma-226	152	17	boundary	boundary	ADJ
ma-226	152	18	condition	condition	NOUN
ma-226	152	19	system	system	NOUN
ma-226	152	20	,	,	PUNCT
ma-226	152	21	combined	combine	VERB
ma-226	152	22	with	with	ADP
ma-226	152	23	schemenumber	schemenumber	NOUN
ma-226	152	24	1	1	NUM
ma-226	152	25	,	,	PUNCT
ma-226	152	26	we	we	PRON
ma-226	152	27	obtain	obtain	VERB
ma-226	152	28	the	the	DET
ma-226	152	29	difference	difference	NOUN
ma-226	152	30	scheme	scheme	PROPN
ma-226	152	31	c0u0	c0u0	PROPN
ma-226	152	32	−	−	PROPN
ma-226	152	33	c1	c1	PROPN
ma-226	152	34	(	(	PUNCT
ma-226	152	35	u1−u0	u1−u0	PROPN
ma-226	152	36	h	h	NOUN
ma-226	152	37	−	−	PROPN
ma-226	152	38	h	h	NOUN
ma-226	153	1	2!f0	2!f0	NUM
ma-226	153	2	−	−	PROPN
ma-226	153	3	h2	h2	NOUN
ma-226	153	4	3!d	3!d	NUM
ma-226	153	5	(	(	PUNCT
ma-226	153	6	1	1	NUM
ma-226	153	7	)	)	PUNCT
ma-226	153	8	n−2f0	n−2f0	NOUN
ma-226	153	9	−	−	PROPN
ma-226	153	10	...	...	PUNCT
ma-226	153	11	−	−	PROPN
ma-226	153	12	hn−1	hn−1	ADJ
ma-226	153	13	n	n	X
ma-226	153	14	!	!	PUNCT
ma-226	154	1	d	d	X
ma-226	154	2	(	(	PUNCT
ma-226	154	3	n−2	n−2	PROPN
ma-226	154	4	)	)	PUNCT
ma-226	154	5	1	1	NUM
ma-226	154	6	f0	f0	PROPN
ma-226	154	7	)	)	PUNCT
ma-226	155	1	=	=	PUNCT
ma-226	156	1	c	c	PROPN
ma-226	156	2	ui−1	ui−1	PROPN
ma-226	156	3	−	−	PROPN
ma-226	156	4	2ui	2ui	ADJ
ma-226	157	1	+	+	CCONJ
ma-226	157	2	ui+1	ui+1	ADJ
ma-226	157	3	=	=	PUNCT
ma-226	157	4	φi	φi	ADV
ma-226	157	5	,	,	PUNCT
ma-226	157	6	i	i	PRON
ma-226	157	7	=	=	NOUN
ma-226	157	8	1	1	NUM
ma-226	157	9	,	,	PUNCT
ma-226	157	10	2	2	NUM
ma-226	157	11	,	,	PUNCT
ma-226	157	12	...	...	PUNCT
ma-226	157	13	,	,	PUNCT
ma-226	157	14	n	n	CCONJ
ma-226	157	15	−	−	PROPN
ma-226	157	16	1	1	NUM
ma-226	157	17	d0un	d0un	NOUN
ma-226	157	18	+	+	CCONJ
ma-226	157	19	d1	d1	PROPN
ma-226	157	20	(	(	PUNCT
ma-226	157	21	un−un−1	un−un−1	ADJ
ma-226	157	22	h	h	NOUN
ma-226	158	1	+	+	CCONJ
ma-226	158	2	h	h	PROPN
ma-226	158	3	2!fn	2!fn	PROPN
ma-226	158	4	−	−	PROPN
ma-226	158	5	h2	h2	PROPN
ma-226	159	1	3!d	3!d	NUM
ma-226	159	2	(	(	PUNCT
ma-226	159	3	1	1	NUM
ma-226	159	4	)	)	PUNCT
ma-226	159	5	n−2fn	n−2fn	NOUN
ma-226	159	6	+	+	CCONJ
ma-226	159	7	...	...	PUNCT
ma-226	160	1	+	+	CCONJ
ma-226	160	2	(	(	PUNCT
ma-226	160	3	−1)n	−1)n	PROPN
ma-226	160	4	h	h	NOUN
ma-226	160	5	n−1	n−1	PROPN
ma-226	160	6	n	n	CCONJ
ma-226	160	7	!	!	PUNCT
ma-226	161	1	d	d	X
ma-226	161	2	(	(	PUNCT
ma-226	161	3	n−2	n−2	PROPN
ma-226	161	4	)	)	PUNCT
ma-226	161	5	1	1	NUM
ma-226	161	6	fn	fn	NOUN
ma-226	161	7	)	)	PUNCT
ma-226	162	1	=	=	SYM
ma-226	162	2	d	d	X
ma-226	162	3	(	(	PUNCT
ma-226	162	4	18	18	NUM
ma-226	162	5	)	)	PUNCT
ma-226	162	6	the	the	DET
ma-226	162	7	solution	solution	NOUN
ma-226	162	8	of	of	ADP
ma-226	162	9	the	the	DET
ma-226	162	10	system	system	NOUN
ma-226	162	11	is	be	AUX
ma-226	162	12	obtained	obtain	VERB
ma-226	162	13	from	from	ADP
ma-226	162	14	the	the	DET
ma-226	162	15	pursuit	pursuit	ADJ
ma-226	162	16	algorithm	algorithm	NOUN
ma-226	162	17	which	which	PRON
ma-226	162	18	has	have	VERB
ma-226	162	19	complexity	complexity	NOUN
ma-226	162	20	o(n).since	o(n).since	NOUN
ma-226	162	21	there	there	ADV
ma-226	162	22	we	we	PRON
ma-226	162	23	have	have	VERB
ma-226	162	24	the	the	DET
ma-226	162	25	following	follow	VERB
ma-226	162	26	theorem	theorem	NOUN
ma-226	162	27	:	:	PUNCT
ma-226	162	28	theorem	theorem	NOUN
ma-226	162	29	3	3	NUM
ma-226	162	30	:	:	PUNCT
ma-226	162	31	the	the	DET
ma-226	162	32	system	system	NOUN
ma-226	162	33	of	of	ADP
ma-226	162	34	difference	difference	NOUN
ma-226	162	35	equations	equation	NOUN
ma-226	162	36	(	(	PUNCT
ma-226	162	37	18	18	NUM
ma-226	162	38	)	)	PUNCT
ma-226	162	39	is	be	AUX
ma-226	162	40	stable	stable	ADJ
ma-226	162	41	and	and	CCONJ
ma-226	162	42	the	the	DET
ma-226	162	43	solution	solution	NOUN
ma-226	162	44	approximates	approximate	VERB
ma-226	162	45	the	the	DET
ma-226	162	46	solution	solution	NOUN
ma-226	162	47	of	of	ADP
ma-226	162	48	problem	problem	NOUN
ma-226	162	49	(	(	PUNCT
ma-226	162	50	14	14	NUM
ma-226	162	51	)	)	PUNCT
ma-226	162	52	with	with	ADP
ma-226	162	53	n	n	NOUN
ma-226	162	54	-	-	PUNCT
ma-226	162	55	order	order	NOUN
ma-226	162	56	accuracy.the	accuracy.the	DET
ma-226	162	57	following	follow	VERB
ma-226	162	58	are	be	AUX
ma-226	162	59	some	some	DET
ma-226	162	60	experimental	experimental	ADJ
ma-226	162	61	calculation	calculation	NOUN
ma-226	162	62	results	result	NOUN
ma-226	162	63	for	for	ADP
ma-226	162	64	the	the	DET
ma-226	162	65	proposed	propose	VERB
ma-226	162	66	theory	theory	NOUN
ma-226	162	67	.	.	PUNCT
ma-226	163	1	3	3	X
ma-226	163	2	.	.	X
ma-226	163	3	experimental	experimental	ADJ
ma-226	163	4	results	result	NOUN
ma-226	163	5	and	and	CCONJ
ma-226	163	6	discussions	discussion	NOUN
ma-226	163	7	in	in	ADP
ma-226	163	8	this	this	DET
ma-226	163	9	section	section	NOUN
ma-226	163	10	,	,	PUNCT
ma-226	163	11	we	we	PRON
ma-226	163	12	verify	verify	VERB
ma-226	163	13	the	the	DET
ma-226	163	14	accuracy	accuracy	NOUN
ma-226	163	15	of	of	ADP
ma-226	163	16	the	the	DET
ma-226	163	17	proposed	propose	VERB
ma-226	163	18	schemes	scheme	NOUN
ma-226	163	19	,	,	PUNCT
ma-226	163	20	we	we	PRON
ma-226	163	21	let	let	VERB
ma-226	163	22	the	the	DET
ma-226	163	23	function	function	NOUN
ma-226	163	24	ud(x)that	ud(x)that	PRON
ma-226	163	25	satisfies	satisfy	VERB
ma-226	163	26	the	the	DET
ma-226	163	27	boundary	boundary	ADJ
ma-226	163	28	problem	problem	NOUN
ma-226	163	29	,	,	PUNCT
ma-226	163	30	from	from	ADP
ma-226	163	31	there	there	ADV
ma-226	163	32	,	,	PUNCT
ma-226	163	33	we	we	PRON
ma-226	163	34	determine	determine	VERB
ma-226	163	35	the	the	DET
ma-226	163	36	right	right	ADJ
ma-226	163	37	-	-	PUNCT
ma-226	163	38	hand	hand	NOUN
ma-226	163	39	side	side	NOUN
ma-226	163	40	function	function	NOUN
ma-226	163	41	f	f	PROPN
ma-226	163	42	(	(	PUNCT
ma-226	163	43	x	x	NOUN
ma-226	163	44	)	)	PUNCT
ma-226	163	45	,	,	PUNCT
ma-226	164	1	x	x	PUNCT
ma-226	164	2	∈	∈	PROPN
ma-226	164	3	[	[	X
ma-226	164	4	a	a	X
ma-226	164	5	,	,	PUNCT
ma-226	164	6	b	b	NOUN
ma-226	164	7	]	]	PUNCT
ma-226	164	8	and	and	CCONJ
ma-226	164	9	boundary	boundary	ADJ
ma-226	164	10	conditions	condition	NOUN
ma-226	164	11	.	.	PUNCT
ma-226	165	1	on	on	ADP
ma-226	165	2	grid	grid	NOUN
ma-226	165	3	space	space	NOUN
ma-226	165	4	ωh	ωh	PROPN
ma-226	165	5	,	,	PUNCT
ma-226	165	6	we	we	PRON
ma-226	165	7	define	define	VERB
ma-226	165	8	the	the	DET
ma-226	165	9	grid	grid	NOUN
ma-226	165	10	function	function	NOUN
ma-226	165	11	value	value	NOUN
ma-226	165	12	ud	ud	INTJ
ma-226	165	13	=	=	SYM
ma-226	165	14	(	(	PUNCT
ma-226	165	15	ud(x0	ud(x0	NOUN
ma-226	165	16	)	)	PUNCT
ma-226	165	17	,	,	PUNCT
ma-226	165	18	ud(x1	ud(x1	NOUN
ma-226	165	19	)	)	PUNCT
ma-226	165	20	,	,	PUNCT
ma-226	165	21	.	.	PUNCT
ma-226	165	22	.	.	PUNCT
ma-226	166	1	.	.	PUNCT
ma-226	167	1	,	,	PUNCT
ma-226	167	2	ud(xn	ud(xn	PROPN
ma-226	167	3	)	)	PUNCT
ma-226	167	4	)	)	PUNCT
ma-226	167	5	is	be	AUX
ma-226	167	6	the	the	DET
ma-226	167	7	exact	exact	ADJ
ma-226	167	8	solution	solution	NOUN
ma-226	167	9	value	value	NOUN
ma-226	167	10	on	on	ADP
ma-226	167	11	the	the	DET
ma-226	167	12	grid	grid	NOUN
ma-226	167	13	ωh	ωh	PROPN
ma-226	167	14	.	.	PUNCT
ma-226	168	1	then	then	ADV
ma-226	168	2	,	,	PUNCT
ma-226	168	3	we	we	PRON
ma-226	168	4	use	use	VERB
ma-226	168	5	the	the	DET
ma-226	168	6	proposedschemes	proposedscheme	NOUN
ma-226	168	7	to	to	PART
ma-226	168	8	find	find	VERB
ma-226	168	9	approximate	approximate	ADJ
ma-226	168	10	solutions	solution	NOUN
ma-226	168	11	u	u	NOUN
ma-226	168	12	=	=	PUNCT
ma-226	168	13	(	(	PUNCT
ma-226	168	14	u0	u0	ADJ
ma-226	168	15	,	,	PUNCT
ma-226	168	16	u1	u1	NOUN
ma-226	168	17	,	,	PUNCT
ma-226	168	18	.	.	PUNCT
ma-226	168	19	.	.	PUNCT
ma-226	168	20	.	.	PUNCT
ma-226	169	1	,	,	PUNCT
ma-226	169	2	un	un	PROPN
ma-226	169	3	)	)	PUNCT
ma-226	169	4	,	,	PUNCT
ma-226	169	5	from	from	ADP
ma-226	169	6	there	there	ADV
ma-226	169	7	,	,	PUNCT
ma-226	169	8	we	we	PRON
ma-226	169	9	evaluate	evaluate	VERB
ma-226	169	10	the	the	DET
ma-226	169	11	accuracyof	accuracyof	NOUN
ma-226	169	12	the	the	DET
ma-226	169	13	scheme	scheme	NOUN
ma-226	169	14	through	through	ADP
ma-226	169	15	error	error	NOUN
ma-226	169	16	ε	ε	PROPN
ma-226	169	17	=	=	SYM
ma-226	169	18	‖u	‖u	PROPN
ma-226	169	19	−	−	PROPN
ma-226	169	20	ud‖ωh	ud‖ωh	NOUN
ma-226	169	21	.	.	PUNCT
ma-226	170	1	3.1	3.1	NUM
ma-226	170	2	.	.	X
ma-226	170	3	evaluate	evaluate	VERB
ma-226	170	4	the	the	DET
ma-226	170	5	accuracy	accuracy	NOUN
ma-226	170	6	of	of	ADP
ma-226	170	7	scheme	scheme	NOUN
ma-226	170	8	1example	1example	NUM
ma-226	170	9	1	1	NUM
ma-226	170	10	:	:	PUNCT
ma-226	170	11	consider	consider	VERB
ma-226	170	12	the	the	DET
ma-226	170	13	problem	problem	NOUN
ma-226	170	14	{	{	PUNCT
ma-226	170	15	u′′(x	u′′(x	NOUN
ma-226	170	16	)	)	PUNCT
ma-226	171	1	=	=	SYM
ma-226	171	2	−sinx	−sinx	NOUN
ma-226	171	3	,	,	PUNCT
ma-226	171	4	x	x	X
ma-226	171	5	∈	∈	PROPN
ma-226	171	6	(	(	PUNCT
ma-226	171	7	0	0	NUM
ma-226	171	8	,	,	PUNCT
ma-226	171	9	1	1	X
ma-226	171	10	)	)	PUNCT
ma-226	171	11	u(0	u(0	NOUN
ma-226	171	12	)	)	PUNCT
ma-226	171	13	=	=	SYM
ma-226	171	14	0	0	NUM
ma-226	171	15	;	;	PUNCT
ma-226	171	16	u(1	u(1	PROPN
ma-226	171	17	)	)	PUNCT
ma-226	171	18	=	=	SYM
ma-226	171	19	sin(1)exact	sin(1)exact	ADJ
ma-226	171	20	solution	solution	NOUN
ma-226	171	21	of	of	ADP
ma-226	171	22	the	the	DET
ma-226	171	23	problem	problem	NOUN
ma-226	171	24	is	be	AUX
ma-226	171	25	u(x	u(x	NOUN
ma-226	171	26	)	)	PUNCT
ma-226	171	27	=	=	SYM
ma-226	171	28	sinx	sinx	NOUN
ma-226	171	29	.using	.use	VERB
ma-226	171	30	scheme	scheme	NOUN
ma-226	171	31	1	1	NUM
ma-226	171	32	combined	combine	VERB
ma-226	171	33	with	with	ADP
ma-226	171	34	the	the	DET
ma-226	171	35	pursuit	pursuit	ADJ
ma-226	171	36	algorithm	algorithm	NOUN
ma-226	171	37	,	,	PUNCT
ma-226	171	38	we	we	PRON
ma-226	171	39	obtain	obtain	VERB
ma-226	171	40	the	the	DET
ma-226	171	41	grid	grid	NOUN
ma-226	171	42	solution	solution	NOUN
ma-226	171	43	u	u	PROPN
ma-226	171	44	.	.	PUNCT
ma-226	172	1	the	the	DET
ma-226	172	2	resultsof	resultsof	NOUN
ma-226	172	3	evaluating	evaluate	VERB
ma-226	172	4	the	the	DET
ma-226	172	5	accuracy	accuracy	NOUN
ma-226	172	6	of	of	ADP
ma-226	172	7	scheme	scheme	NOUN
ma-226	172	8	1	1	NUM
ma-226	172	9	are	be	AUX
ma-226	172	10	given	give	VERB
ma-226	172	11	in	in	ADP
ma-226	172	12	table	table	NOUN
ma-226	172	13	1	1	NUM
ma-226	172	14	table	table	NOUN
ma-226	172	15	1	1	NUM
ma-226	172	16	.	.	PUNCT
ma-226	172	17	results	result	NOUN
ma-226	172	18	of	of	ADP
ma-226	172	19	evaluating	evaluate	VERB
ma-226	172	20	the	the	DET
ma-226	172	21	accuracy	accuracy	NOUN
ma-226	172	22	of	of	ADP
ma-226	172	23	scheme	scheme	NOUN
ma-226	172	24	1	1	NUM
ma-226	172	25	example	example	NOUN
ma-226	172	26	1	1	NUM
ma-226	172	27	n	n	NOUN
ma-226	172	28	h8	h8	PROPN
ma-226	172	29	‖u	‖u	PROPN
ma-226	172	30	−	−	PROPN
ma-226	172	31	ud‖ωh	ud‖ωh	PROPN
ma-226	172	32	h10	h10	PROPN
ma-226	172	33	‖u	‖u	PROPN
ma-226	173	1	−	−	PROPN
ma-226	173	2	ud‖ωh10	ud‖ωh10	NOUN
ma-226	174	1	1.0000e-008	1.0000e-008	PROPN
ma-226	174	2	2.9675e-012	2.9675e-012	PROPN
ma-226	174	3	1.0000e-010	1.0000e-010	PROPN
ma-226	174	4	1.6467e-01420	1.6467e-01420	NUM
ma-226	174	5	3.9063e-011	3.9063e-011	PROPN
ma-226	175	1	4.6426e-014	4.6426e-014	PROPN
ma-226	175	2	9.7656e-014	9.7656e-014	PROPN
ma-226	175	3	1.1343e-01730	1.1343e-01730	NUM
ma-226	175	4	1.5242e-012	1.5242e-012	PROPN
ma-226	175	5	4.0825e-015	4.0825e-015	PROPN
ma-226	175	6	1.6935e-015	1.6935e-015	NUM
ma-226	175	7	3.6987e-01940	3.6987e-01940	NUM
ma-226	175	8	1.5259e-013	1.5259e-013	PROPN
ma-226	175	9	7.2653e-016	7.2653e-016	PROPN
ma-226	175	10	9.5367e-017	9.5367e-017	NUM
ma-226	175	11	2.9933e-02050	2.9933e-02050	NUM
ma-226	176	1	2.5600e-014	2.5600e-014	PROPN
ma-226	176	2	1.9039e-016	1.9039e-016	PROPN
ma-226	176	3	1.0240e-017	1.0240e-017	NUM
ma-226	176	4	4.1543e-02160	4.1543e-02160	NUM
ma-226	176	5	5.9537e-015	5.9537e-015	PROPN
ma-226	176	6	6.3781e-017	6.3781e-017	NUM
ma-226	176	7	1.6538e-018	1.6538e-018	PROPN
ma-226	176	8	8.1987e-02270	8.1987e-02270	NUM
ma-226	177	1	1.7347e-015	1.7347e-015	PROPN
ma-226	177	2	2.5295e-017	2.5295e-017	PROPN
ma-226	177	3	3.5401e-019	3.5401e-019	PROPN
ma-226	177	4	2.0679e-022	2.0679e-022	PROPN
ma-226	177	5	https://doi.org/10.28924/ada/ma.4.10	https://doi.org/10.28924/ada/ma.4.10	NOUN
ma-226	177	6	eur	eur	PROPN
ma-226	177	7	.	.	PUNCT
ma-226	178	1	j.	j.	PROPN
ma-226	178	2	math	math	PROPN
ma-226	178	3	.	.	PUNCT
ma-226	179	1	anal	anal	PROPN
ma-226	179	2	.	.	PUNCT
ma-226	180	1	10.28924	10.28924	NUM
ma-226	180	2	/	/	SYM
ma-226	180	3	ada	ada	NOUN
ma-226	180	4	/	/	NOUN
ma-226	180	5	ma.4.10	ma.4.10	NOUN
ma-226	180	6	7	7	NUM
ma-226	180	7	n	n	NUM
ma-226	180	8	h8	h8	PROPN
ma-226	180	9	‖u	‖u	PROPN
ma-226	180	10	−	−	PROPN
ma-226	180	11	ud‖ωh	ud‖ωh	ADJ
ma-226	180	12	h10	h10	PROPN
ma-226	180	13	‖u	‖u	NOUN
ma-226	181	1	−	−	ADP
ma-226	181	2	ud‖ωh80	ud‖ωh80	NOUN
ma-226	181	3	5.9605e-016	5.9605e-016	PROPN
ma-226	181	4	1.1351e-017	1.1351e-017	PROPN
ma-226	182	1	9.3132e-020	9.3132e-020	PROPN
ma-226	182	2	6.2629e-02390	6.2629e-02390	NUM
ma-226	183	1	2.3231e-016	2.3231e-016	PROPN
ma-226	183	2	5.5993e-018	5.5993e-018	PROPN
ma-226	183	3	2.8680e-020	2.8680e-020	PROPN
ma-226	183	4	2.1680e-023100	2.1680e-023100	NUM
ma-226	183	5	1.0000e-016	1.0000e-016	PROPN
ma-226	183	6	2.9759e-018	2.9759e-018	PROPN
ma-226	183	7	1.0000e-020	1.0000e-020	PROPN
ma-226	183	8	8.4722e-024	8.4722e-024	NUM
ma-226	183	9	figure	figure	NOUN
ma-226	183	10	1	1	NUM
ma-226	183	11	.	.	NOUN
ma-226	183	12	error	error	NOUN
ma-226	183	13	at	at	ADP
ma-226	183	14	each	each	DET
ma-226	183	15	point	point	NOUN
ma-226	183	16	between	between	ADP
ma-226	183	17	exact	exact	ADJ
ma-226	183	18	solution	solution	NOUN
ma-226	183	19	and	and	CCONJ
ma-226	183	20	approximated	approximate	VERB
ma-226	183	21	solution	solution	NOUN
ma-226	183	22	example	example	NOUN
ma-226	184	1	1example	1example	NUM
ma-226	184	2	2	2	NUM
ma-226	184	3	:	:	PUNCT
ma-226	184	4	consider	consider	VERB
ma-226	184	5	the	the	DET
ma-226	184	6	problem	problem	NOUN
ma-226	184	7	{	{	PUNCT
ma-226	184	8	u′′(x	u′′(x	NOUN
ma-226	184	9	)	)	PUNCT
ma-226	184	10	=	=	SYM
ma-226	184	11	−sinh(x	−sinh(x	PROPN
ma-226	184	12	)	)	PUNCT
ma-226	185	1	+	+	CCONJ
ma-226	185	2	1	1	NUM
ma-226	185	3	9e	9e	NUM
ma-226	185	4	−x/3	−x/3	PROPN
ma-226	185	5	,	,	PUNCT
ma-226	185	6	x	x	SYM
ma-226	185	7	∈	∈	PROPN
ma-226	185	8	(	(	PUNCT
ma-226	185	9	0	0	NUM
ma-226	185	10	,	,	PUNCT
ma-226	185	11	1	1	X
ma-226	185	12	)	)	PUNCT
ma-226	185	13	u(0	u(0	NOUN
ma-226	185	14	)	)	PUNCT
ma-226	185	15	=	=	SYM
ma-226	186	1	1	1	NUM
ma-226	186	2	;	;	PUNCT
ma-226	186	3	u(1	u(1	PROPN
ma-226	186	4	)	)	PUNCT
ma-226	186	5	=	=	PUNCT
ma-226	186	6	sinh(1	sinh(1	NOUN
ma-226	186	7	)	)	PUNCT
ma-226	187	1	+	+	CCONJ
ma-226	187	2	e−1/3	e−1/3	ADJ
ma-226	187	3	exact	exact	ADJ
ma-226	187	4	solution	solution	NOUN
ma-226	187	5	of	of	ADP
ma-226	187	6	the	the	DET
ma-226	187	7	problem	problem	NOUN
ma-226	187	8	is	be	AUX
ma-226	187	9	u(x	u(x	NOUN
ma-226	187	10	)	)	PUNCT
ma-226	187	11	=	=	SYM
ma-226	187	12	sinh(x	sinh(x	PROPN
ma-226	187	13	)	)	PUNCT
ma-226	187	14	+	+	CCONJ
ma-226	187	15	e−x/3	e−x/3	NOUN
ma-226	187	16	.	.	PUNCT
ma-226	187	17	table	table	NOUN
ma-226	188	1	2	2	NUM
ma-226	188	2	.	.	PUNCT
ma-226	188	3	results	result	NOUN
ma-226	188	4	of	of	ADP
ma-226	188	5	evaluating	evaluate	VERB
ma-226	188	6	the	the	DET
ma-226	188	7	accuracy	accuracy	NOUN
ma-226	188	8	of	of	ADP
ma-226	188	9	scheme	scheme	NOUN
ma-226	188	10	1	1	NUM
ma-226	188	11	example	example	NOUN
ma-226	188	12	2	2	NUM
ma-226	188	13	n	n	NOUN
ma-226	188	14	h8	h8	PROPN
ma-226	188	15	‖u	‖u	PROPN
ma-226	188	16	−	−	PROPN
ma-226	188	17	ud‖ωh	ud‖ωh	PROPN
ma-226	188	18	h10	h10	PROPN
ma-226	188	19	‖u	‖u	PROPN
ma-226	189	1	−	−	PROPN
ma-226	190	1	ud‖ωh10	ud‖ωh10	PRON
ma-226	191	1	1.0000e-008	1.0000e-008	PROPN
ma-226	191	2	3.3899e-012	3.3899e-012	PROPN
ma-226	191	3	1.0000e-010	1.0000e-010	PROPN
ma-226	191	4	2.0506e-01420	2.0506e-01420	VERB
ma-226	191	5	3.9063e-011	3.9063e-011	NUM
ma-226	191	6	5.3052e-014	5.3052e-014	PROPN
ma-226	192	1	9.7656e-014	9.7656e-014	PROPN
ma-226	192	2	1.7488e-01730	1.7488e-01730	NUM
ma-226	192	3	1.5242e-012	1.5242e-012	PROPN
ma-226	192	4	4.6589e-015	4.6589e-015	PROPN
ma-226	193	1	1.6935e-015	1.6935e-015	PROPN
ma-226	193	2	5.2038e-01940	5.2038e-01940	NUM
ma-226	193	3	1.5259e-013	1.5259e-013	PROPN
ma-226	193	4	8.3000e-016	8.3000e-016	PROPN
ma-226	193	5	9.5367e-017	9.5367e-017	NUM
ma-226	193	6	4.0990e-02050	4.0990e-02050	NOUN
ma-226	193	7	2.5600e-014	2.5600e-014	PROPN
ma-226	193	8	2.1765e-016	2.1765e-016	PROPN
ma-226	194	1	1.0240e-017	1.0240e-017	NUM
ma-226	194	2	5.6274e-021	5.6274e-021	NUM
ma-226	194	3	https://doi.org/10.28924/ada/ma.4.10	https://doi.org/10.28924/ada/ma.4.10	NOUN
ma-226	194	4	eur	eur	NOUN
ma-226	194	5	.	.	PUNCT
ma-226	195	1	j.	j.	PROPN
ma-226	195	2	math	math	PROPN
ma-226	195	3	.	.	PUNCT
ma-226	196	1	anal	anal	PROPN
ma-226	196	2	.	.	PUNCT
ma-226	197	1	10.28924	10.28924	NUM
ma-226	197	2	/	/	SYM
ma-226	197	3	ada	ada	NOUN
ma-226	197	4	/	/	NOUN
ma-226	197	5	ma.4.10	ma.4.10	ADJ
ma-226	197	6	8	8	NUM
ma-226	197	7	n	n	NUM
ma-226	197	8	h8	h8	PROPN
ma-226	197	9	‖u	‖u	PROPN
ma-226	197	10	−	−	PROPN
ma-226	197	11	ud‖ωh	ud‖ωh	PROPN
ma-226	197	12	h10	h10	PROPN
ma-226	197	13	‖u	‖u	PROPN
ma-226	197	14	−	−	PROPN
ma-226	197	15	ud‖ωh60	ud‖ωh60	ADV
ma-226	197	16	5.9537e-015	5.9537e-015	PROPN
ma-226	197	17	7.2895e-017	7.2895e-017	PROPN
ma-226	197	18	1.6538e-018	1.6538e-018	PROPN
ma-226	198	1	1.1046e-02170	1.1046e-02170	NUM
ma-226	198	2	1.7347e-015	1.7347e-015	NUM
ma-226	198	3	2.8908e-017	2.8908e-017	NUM
ma-226	198	4	3.5401e-019	3.5401e-019	NUM
ma-226	198	5	2.7774e-02280	2.7774e-02280	NUM
ma-226	198	6	5.9605e-016	5.9605e-016	PROPN
ma-226	198	7	1.2973e-017	1.2973e-017	NUM
ma-226	198	8	9.3132e-020	9.3132e-020	PROPN
ma-226	198	9	8.3970e-02390	8.3970e-02390	NUM
ma-226	198	10	2.3231e-016	2.3231e-016	PROPN
ma-226	198	11	6.3989e-018	6.3989e-018	PROPN
ma-226	198	12	2.8680e-020	2.8680e-020	PROPN
ma-226	199	1	2.9033e-023100	2.9033e-023100	NUM
ma-226	199	2	1.0000e-016	1.0000e-016	PROPN
ma-226	199	3	3.4009e-018	3.4009e-018	PROPN
ma-226	199	4	1.0000e-020	1.0000e-020	PROPN
ma-226	199	5	1.1337e-023	1.1337e-023	PROPN
ma-226	199	6	the	the	DET
ma-226	199	7	results	result	NOUN
ma-226	199	8	in	in	ADP
ma-226	199	9	table	table	NOUN
ma-226	199	10	1	1	NUM
ma-226	199	11	and	and	CCONJ
ma-226	199	12	table	table	NOUN
ma-226	199	13	2	2	NUM
ma-226	199	14	confirm	confirm	VERB
ma-226	199	15	that	that	SCONJ
ma-226	199	16	our	our	PRON
ma-226	199	17	proposed	propose	VERB
ma-226	199	18	scheme	scheme	NOUN
ma-226	199	19	1	1	NUM
ma-226	199	20	has	have	AUX
ma-226	199	21	determined	determine	VERB
ma-226	199	22	theapproximated	theapproximated	ADJ
ma-226	199	23	solution	solution	NOUN
ma-226	199	24	of	of	ADP
ma-226	199	25	the	the	DET
ma-226	199	26	second	second	ADJ
ma-226	199	27	-	-	PUNCT
ma-226	199	28	order	order	NOUN
ma-226	199	29	boundary	boundary	ADJ
ma-226	199	30	problem	problem	NOUN
ma-226	199	31	with	with	ADP
ma-226	199	32	dirichlet	dirichlet	PROPN
ma-226	199	33	boundary	boundary	PROPN
ma-226	199	34	conditionswith	conditionswith	PROPN
ma-226	199	35	n	n	CCONJ
ma-226	199	36	-	-	PUNCT
ma-226	199	37	order	order	NOUN
ma-226	199	38	accuracy	accuracy	NOUN
ma-226	199	39	,	,	PUNCT
ma-226	199	40	where	where	SCONJ
ma-226	199	41	n	n	PRON
ma-226	199	42	is	be	AUX
ma-226	199	43	the	the	DET
ma-226	199	44	number	number	NOUN
ma-226	199	45	of	of	ADP
ma-226	199	46	neighboring	neighboring	NOUN
ma-226	199	47	points	point	NOUN
ma-226	199	48	.	.	PUNCT
ma-226	200	1	3.2	3.2	NUM
ma-226	200	2	.	.	PUNCT
ma-226	200	3	evaluate	evaluate	VERB
ma-226	200	4	the	the	DET
ma-226	200	5	accuracy	accuracy	NOUN
ma-226	200	6	of	of	ADP
ma-226	200	7	scheme	scheme	NOUN
ma-226	200	8	2example	2example	NUM
ma-226	200	9	3	3	NUM
ma-226	200	10	:	:	PUNCT
ma-226	200	11	consider	consider	VERB
ma-226	200	12	the	the	DET
ma-226	200	13	problem	problem	NOUN
ma-226	200	14	{	{	PUNCT
ma-226	200	15	u′′(x	u′′(x	NOUN
ma-226	200	16	)	)	PUNCT
ma-226	200	17	=	=	SYM
ma-226	201	1	6x	6x	NOUN
ma-226	201	2	+	+	NOUN
ma-226	201	3	1	1	NUM
ma-226	201	4	8sinh(1	8sinh(1	NUM
ma-226	201	5	+	+	CCONJ
ma-226	201	6	x/2	x/2	NUM
ma-226	201	7	)	)	PUNCT
ma-226	201	8	,	,	PUNCT
ma-226	201	9	x	x	PUNCT
ma-226	201	10	∈	∈	PROPN
ma-226	201	11	(	(	PUNCT
ma-226	201	12	0	0	NUM
ma-226	201	13	,	,	PUNCT
ma-226	201	14	1	1	X
ma-226	201	15	)	)	PUNCT
ma-226	201	16	u(0)−	u(0)−	PROPN
ma-226	201	17	u′(0	u′(0	PROPN
ma-226	201	18	)	)	PUNCT
ma-226	201	19	=	=	SYM
ma-226	201	20	sinh(1)−	sinh(1)−	NOUN
ma-226	201	21	12cosh(1	12cosh(1	NUM
ma-226	201	22	)	)	PUNCT
ma-226	201	23	;	;	PUNCT
ma-226	201	24	u(1	u(1	PROPN
ma-226	201	25	)	)	PUNCT
ma-226	201	26	+	+	SYM
ma-226	201	27	u′(1	u′(1	ADJ
ma-226	201	28	)	)	PUNCT
ma-226	201	29	=	=	SYM
ma-226	201	30	4	4	NUM
ma-226	201	31	+	+	CCONJ
ma-226	201	32	sinh(3/2	sinh(3/2	PROPN
ma-226	201	33	)	)	PUNCT
ma-226	202	1	+	+	CCONJ
ma-226	202	2	1	1	NUM
ma-226	202	3	2cosh(3/2)exact	2cosh(3/2)exact	NUM
ma-226	202	4	solution	solution	NOUN
ma-226	202	5	of	of	ADP
ma-226	202	6	the	the	DET
ma-226	202	7	problem	problem	NOUN
ma-226	202	8	is	be	AUX
ma-226	202	9	u(x	u(x	NOUN
ma-226	202	10	)	)	PUNCT
ma-226	202	11	=	=	SYM
ma-226	203	1	x3	x3	ADJ
ma-226	203	2	+	+	CCONJ
ma-226	203	3	sinh(1	sinh(1	PROPN
ma-226	203	4	+	+	CCONJ
ma-226	203	5	x/2)using	x/2)using	PROPN
ma-226	203	6	scheme	scheme	NOUN
ma-226	203	7	2	2	NUM
ma-226	203	8	combined	combine	VERB
ma-226	203	9	with	with	ADP
ma-226	203	10	the	the	DET
ma-226	203	11	pursuit	pursuit	ADJ
ma-226	203	12	algorithm	algorithm	NOUN
ma-226	203	13	,	,	PUNCT
ma-226	203	14	we	we	PRON
ma-226	203	15	obtain	obtain	VERB
ma-226	203	16	the	the	DET
ma-226	203	17	grid	grid	NOUN
ma-226	203	18	solution	solution	NOUN
ma-226	203	19	u	u	PROPN
ma-226	203	20	.	.	PUNCT
ma-226	204	1	the	the	DET
ma-226	204	2	resultsof	resultsof	NOUN
ma-226	204	3	evaluating	evaluate	VERB
ma-226	204	4	the	the	DET
ma-226	204	5	accuracy	accuracy	NOUN
ma-226	204	6	of	of	ADP
ma-226	204	7	scheme	scheme	NOUN
ma-226	204	8	2	2	NUM
ma-226	204	9	are	be	AUX
ma-226	204	10	given	give	VERB
ma-226	204	11	in	in	ADP
ma-226	204	12	table	table	NOUN
ma-226	204	13	3	3	NUM
ma-226	204	14	table	table	NOUN
ma-226	204	15	3	3	NUM
ma-226	204	16	.	.	PUNCT
ma-226	204	17	results	result	NOUN
ma-226	204	18	of	of	ADP
ma-226	204	19	evaluating	evaluate	VERB
ma-226	204	20	the	the	DET
ma-226	204	21	accuracy	accuracy	NOUN
ma-226	204	22	of	of	ADP
ma-226	204	23	scheme	scheme	NOUN
ma-226	204	24	2	2	NUM
ma-226	204	25	example	example	NOUN
ma-226	205	1	3	3	NUM
ma-226	205	2	n	n	NOUN
ma-226	205	3	h8	h8	PROPN
ma-226	205	4	‖u	‖u	PROPN
ma-226	205	5	−	−	PROPN
ma-226	205	6	ud‖ωh	ud‖ωh	PROPN
ma-226	205	7	h10	h10	PROPN
ma-226	205	8	‖u	‖u	PROPN
ma-226	205	9	−	−	PROPN
ma-226	206	1	ud‖ωh10	ud‖ωh10	NOUN
ma-226	207	1	1.0000e-008	1.0000e-008	PROPN
ma-226	207	2	2.0382e-013	2.0382e-013	PROPN
ma-226	207	3	1.0000e-010	1.0000e-010	PROPN
ma-226	207	4	5.3121e-01620	5.3121e-01620	NUM
ma-226	208	1	3.9063e-011	3.9063e-011	NUM
ma-226	208	2	3.3597e-015	3.3597e-015	PROPN
ma-226	208	3	9.7656e-014	9.7656e-014	PROPN
ma-226	209	1	9.1360e-01930	9.1360e-01930	NUM
ma-226	210	1	1.5242e-012	1.5242e-012	PROPN
ma-226	210	2	2.9998e-016	2.9998e-016	NUM
ma-226	210	3	1.6935e-015	1.6935e-015	NUM
ma-226	210	4	2.5005e-02040	2.5005e-02040	NUM
ma-226	210	5	1.5259e-013	1.5259e-013	PROPN
ma-226	210	6	5.3835e-017	5.3835e-017	PROPN
ma-226	210	7	9.5367e-017	9.5367e-017	NUM
ma-226	210	8	2.0884e-02150	2.0884e-02150	NUM
ma-226	211	1	2.5600e-014	2.5600e-014	PROPN
ma-226	211	2	1.4183e-017	1.4183e-017	PROPN
ma-226	211	3	1.0240e-017	1.0240e-017	PROPN
ma-226	211	4	3.1494e-02260	3.1494e-02260	NUM
ma-226	212	1	5.9537e-015	5.9537e-015	PROPN
ma-226	212	2	4.7654e-018	4.7654e-018	PROPN
ma-226	213	1	1.6538e-018	1.6538e-018	PROPN
ma-226	213	2	7.0444e-02370	7.0444e-02370	NUM
ma-226	213	3	1.7347e-015	1.7347e-015	PROPN
ma-226	213	4	1.8943e-018	1.8943e-018	NUM
ma-226	213	5	3.5401e-019	3.5401e-019	PROPN
ma-226	213	6	1.6852e-02380	1.6852e-02380	NUM
ma-226	213	7	5.9605e-016	5.9605e-016	PROPN
ma-226	213	8	8.5167e-019	8.5167e-019	PROPN
ma-226	213	9	9.3132e-020	9.3132e-020	PROPN
ma-226	213	10	5.3577e-02490	5.3577e-02490	NUM
ma-226	213	11	2.3231e-016	2.3231e-016	PROPN
ma-226	213	12	4.2068e-019	4.2068e-019	PROPN
ma-226	213	13	2.8680e-020	2.8680e-020	PROPN
ma-226	213	14	1.8066e-024100	1.8066e-024100	NUM
ma-226	213	15	1.0000e-016	1.0000e-016	PROPN
ma-226	213	16	2.2381e-019	2.2381e-019	NUM
ma-226	213	17	1.0000e-020	1.0000e-020	NUM
ma-226	213	18	3.0015e-025	3.0015e-025	PROPN
ma-226	213	19	https://doi.org/10.28924/ada/ma.4.10	https://doi.org/10.28924/ada/ma.4.10	NOUN
ma-226	213	20	eur	eur	PROPN
ma-226	213	21	.	.	PUNCT
ma-226	214	1	j.	j.	PROPN
ma-226	214	2	math	math	PROPN
ma-226	214	3	.	.	PUNCT
ma-226	215	1	anal	anal	PROPN
ma-226	215	2	.	.	PUNCT
ma-226	216	1	10.28924	10.28924	NUM
ma-226	216	2	/	/	SYM
ma-226	216	3	ada	ada	NOUN
ma-226	216	4	/	/	SYM
ma-226	216	5	ma.4.10	ma.4.10	ADJ
ma-226	216	6	9	9	NUM
ma-226	216	7	figure	figure	NOUN
ma-226	216	8	2	2	NUM
ma-226	216	9	.	.	NOUN
ma-226	216	10	error	error	NOUN
ma-226	216	11	at	at	ADP
ma-226	216	12	each	each	DET
ma-226	216	13	point	point	NOUN
ma-226	216	14	between	between	ADP
ma-226	216	15	exact	exact	ADJ
ma-226	216	16	solution	solution	NOUN
ma-226	216	17	and	and	CCONJ
ma-226	216	18	approximated	approximate	VERB
ma-226	216	19	solution	solution	NOUN
ma-226	216	20	example	example	NOUN
ma-226	217	1	3example	3example	NUM
ma-226	217	2	4	4	NUM
ma-226	217	3	:	:	PUNCT
ma-226	217	4	consider	consider	VERB
ma-226	217	5	the	the	DET
ma-226	217	6	problem	problem	NOUN
ma-226	217	7	{	{	PUNCT
ma-226	217	8	u′′(x	u′′(x	NOUN
ma-226	217	9	)	)	PUNCT
ma-226	217	10	=	=	SYM
ma-226	217	11	cosh(x	cosh(x	NOUN
ma-226	217	12	)	)	PUNCT
ma-226	218	1	+	+	CCONJ
ma-226	218	2	1	1	NUM
ma-226	218	3	9e	9e	NUM
ma-226	218	4	x/3	x/3	NUM
ma-226	218	5	,	,	PUNCT
ma-226	218	6	x	x	PROPN
ma-226	218	7	∈	∈	PROPN
ma-226	218	8	(	(	PUNCT
ma-226	218	9	0	0	NUM
ma-226	218	10	,	,	PUNCT
ma-226	218	11	1	1	X
ma-226	218	12	)	)	PUNCT
ma-226	218	13	u(0)−	u(0)−	PROPN
ma-226	218	14	12u	12u	NUM
ma-226	218	15	′(0	′(0	X
ma-226	218	16	)	)	PUNCT
ma-226	218	17	=	=	SYM
ma-226	218	18	1	1	NUM
ma-226	218	19	2	2	NUM
ma-226	218	20	;	;	PUNCT
ma-226	218	21	13u(1	13u(1	NUM
ma-226	218	22	)	)	PUNCT
ma-226	219	1	+	+	SYM
ma-226	219	2	u′(1	u′(1	ADJ
ma-226	219	3	)	)	PUNCT
ma-226	219	4	=	=	SYM
ma-226	219	5	1	1	NUM
ma-226	219	6	3	3	NUM
ma-226	219	7	(	(	PUNCT
ma-226	219	8	cosh(1	cosh(1	PROPN
ma-226	219	9	)	)	PUNCT
ma-226	220	1	+	+	CCONJ
ma-226	220	2	e1/3	e1/3	ADJ
ma-226	220	3	)	)	PUNCT
ma-226	220	4	−	−	PROPN
ma-226	220	5	(	(	PUNCT
ma-226	220	6	sinh(1	sinh(1	PROPN
ma-226	220	7	)	)	PUNCT
ma-226	221	1	+	+	CCONJ
ma-226	221	2	1	1	NUM
ma-226	221	3	3e	3e	NUM
ma-226	221	4	1/3	1/3	NUM
ma-226	221	5	)	)	PUNCT
ma-226	221	6	exact	exact	ADJ
ma-226	221	7	solution	solution	NOUN
ma-226	221	8	of	of	ADP
ma-226	221	9	the	the	DET
ma-226	221	10	problem	problem	NOUN
ma-226	221	11	is	be	AUX
ma-226	221	12	u(x	u(x	NOUN
ma-226	221	13	)	)	PUNCT
ma-226	221	14	=	=	SYM
ma-226	221	15	cosh(x	cosh(x	NOUN
ma-226	221	16	)	)	PUNCT
ma-226	222	1	+	+	CCONJ
ma-226	222	2	ex/3using	ex/3use	VERB
ma-226	222	3	scheme	scheme	NOUN
ma-226	222	4	2	2	NUM
ma-226	222	5	combined	combine	VERB
ma-226	222	6	with	with	ADP
ma-226	222	7	the	the	DET
ma-226	222	8	pursuit	pursuit	ADJ
ma-226	222	9	algorithm	algorithm	NOUN
ma-226	222	10	,	,	PUNCT
ma-226	222	11	we	we	PRON
ma-226	222	12	obtain	obtain	VERB
ma-226	222	13	the	the	DET
ma-226	222	14	grid	grid	NOUN
ma-226	222	15	solution	solution	NOUN
ma-226	222	16	u	u	PROPN
ma-226	222	17	.	.	PUNCT
ma-226	223	1	the	the	DET
ma-226	223	2	resultsof	resultsof	NOUN
ma-226	223	3	evaluating	evaluate	VERB
ma-226	223	4	the	the	DET
ma-226	223	5	accuracy	accuracy	NOUN
ma-226	223	6	of	of	ADP
ma-226	223	7	scheme	scheme	NOUN
ma-226	223	8	2	2	NUM
ma-226	223	9	are	be	AUX
ma-226	223	10	given	give	VERB
ma-226	223	11	in	in	ADP
ma-226	223	12	table	table	NOUN
ma-226	223	13	4	4	NUM
ma-226	223	14	.	.	PUNCT
ma-226	223	15	table	table	NOUN
ma-226	223	16	4	4	NUM
ma-226	223	17	.	.	PUNCT
ma-226	223	18	results	result	NOUN
ma-226	223	19	of	of	ADP
ma-226	223	20	evaluating	evaluate	VERB
ma-226	223	21	the	the	DET
ma-226	223	22	accuracy	accuracy	NOUN
ma-226	223	23	of	of	ADP
ma-226	223	24	scheme	scheme	NOUN
ma-226	223	25	2	2	NUM
ma-226	223	26	example	example	NOUN
ma-226	224	1	4	4	NUM
ma-226	224	2	n	n	NOUN
ma-226	224	3	h8	h8	PROPN
ma-226	224	4	‖u	‖u	PROPN
ma-226	224	5	−	−	PROPN
ma-226	224	6	ud‖ωh	ud‖ωh	PROPN
ma-226	224	7	h10	h10	PROPN
ma-226	224	8	‖u	‖u	PROPN
ma-226	224	9	−	−	PROPN
ma-226	225	1	ud‖ωh10	ud‖ωh10	PRON
ma-226	226	1	1.0000e-008	1.0000e-008	PROPN
ma-226	226	2	3.7083e-011	3.7083e-011	PROPN
ma-226	226	3	1.0000e-010	1.0000e-010	PROPN
ma-226	226	4	3.5960e-01320	3.5960e-01320	NUM
ma-226	226	5	3.9063e-011	3.9063e-011	PROPN
ma-226	226	6	6.1634e-013	6.1634e-013	PROPN
ma-226	226	7	9.7656e-014	9.7656e-014	PROPN
ma-226	226	8	5.6152e-01630	5.6152e-01630	NOUN
ma-226	226	9	1.5242e-012	1.5242e-012	PROPN
ma-226	226	10	5.5099e-014	5.5099e-014	PROPN
ma-226	226	11	1.6935e-015	1.6935e-015	NUM
ma-226	226	12	1.1085e-01740	1.1085e-01740	NOUN
ma-226	226	13	1.5259e-013	1.5259e-013	NUM
ma-226	226	14	9.8929e-015	9.8929e-015	PROPN
ma-226	226	15	9.5367e-017	9.5367e-017	NUM
ma-226	226	16	6.5992e-01950	6.5992e-01950	NOUN
ma-226	227	1	2.5600e-014	2.5600e-014	PROPN
ma-226	227	2	2.6068e-015	2.6068e-015	PROPN
ma-226	228	1	1.0240e-017	1.0240e-017	NUM
ma-226	228	2	7.2379e-02060	7.2379e-02060	NOUN
ma-226	229	1	5.9537e-015	5.9537e-015	NUM
ma-226	229	2	8.7603e-016	8.7603e-016	PROPN
ma-226	229	3	1.6538e-018	1.6538e-018	PROPN
ma-226	230	1	1.1673e-020	1.1673e-020	NUM
ma-226	230	2	https://doi.org/10.28924/ada/ma.4.10	https://doi.org/10.28924/ada/ma.4.10	NOUN
ma-226	230	3	eur	eur	PROPN
ma-226	230	4	.	.	PUNCT
ma-226	231	1	j.	j.	PROPN
ma-226	231	2	math	math	PROPN
ma-226	231	3	.	.	PUNCT
ma-226	232	1	anal	anal	PROPN
ma-226	232	2	.	.	PUNCT
ma-226	233	1	10.28924	10.28924	NUM
ma-226	233	2	/	/	SYM
ma-226	233	3	ada	ada	NOUN
ma-226	233	4	/	/	NOUN
ma-226	233	5	ma.4.10	ma.4.10	NOUN
ma-226	233	6	10	10	NUM
ma-226	233	7	n	n	NUM
ma-226	233	8	h8	h8	PROPN
ma-226	233	9	‖u	‖u	PROPN
ma-226	233	10	−	−	PROPN
ma-226	233	11	ud‖ωh	ud‖ωh	PROPN
ma-226	233	12	h10	h10	PROPN
ma-226	233	13	‖u	‖u	NOUN
ma-226	233	14	−	−	PUNCT
ma-226	233	15	ud‖ωh70	ud‖ωh70	NUM
ma-226	234	1	1.7347e-015	1.7347e-015	PROPN
ma-226	234	2	3.4826e-016	3.4826e-016	PROPN
ma-226	234	3	3.5401e-019	3.5401e-019	PROPN
ma-226	234	4	2.4481e-02180	2.4481e-02180	NUM
ma-226	235	1	5.9605e-016	5.9605e-016	NUM
ma-226	235	2	1.5659e-016	1.5659e-016	PROPN
ma-226	235	3	9.3132e-020	9.3132e-020	PROPN
ma-226	235	4	6.1971e-02290	6.1971e-02290	NUM
ma-226	235	5	2.3231e-016	2.3231e-016	PROPN
ma-226	235	6	7.7351e-017	7.7351e-017	PROPN
ma-226	235	7	2.8680e-020	2.8680e-020	PROPN
ma-226	235	8	1.7954e-022100	1.7954e-022100	NUM
ma-226	235	9	1.0000e-016	1.0000e-016	PROPN
ma-226	235	10	4.1155e-017	4.1155e-017	PROPN
ma-226	235	11	1.0000e-020	1.0000e-020	PROPN
ma-226	235	12	5.7442e-023	5.7442e-023	PROPN
ma-226	235	13	the	the	DET
ma-226	235	14	results	result	NOUN
ma-226	235	15	in	in	ADP
ma-226	235	16	table	table	NOUN
ma-226	235	17	3	3	NUM
ma-226	235	18	and	and	CCONJ
ma-226	235	19	table	table	NOUN
ma-226	235	20	4	4	NUM
ma-226	235	21	also	also	ADV
ma-226	235	22	confirm	confirm	VERB
ma-226	235	23	that	that	SCONJ
ma-226	235	24	our	our	PRON
ma-226	235	25	proposed	propose	VERB
ma-226	235	26	scheme	scheme	NOUN
ma-226	235	27	2	2	NUM
ma-226	235	28	has	have	AUX
ma-226	235	29	determined	determine	VERB
ma-226	235	30	theapproximate	theapproximate	ADJ
ma-226	235	31	solution	solution	NOUN
ma-226	235	32	of	of	ADP
ma-226	235	33	the	the	DET
ma-226	235	34	second	second	ADJ
ma-226	235	35	-	-	PUNCT
ma-226	235	36	order	order	NOUN
ma-226	235	37	boundary	boundary	ADJ
ma-226	235	38	problem	problem	NOUN
ma-226	235	39	with	with	ADP
ma-226	235	40	mixed	mixed	ADJ
ma-226	235	41	boundary	boundary	ADJ
ma-226	235	42	conditions	condition	NOUN
ma-226	235	43	with	with	ADP
ma-226	235	44	n	n	CCONJ
ma-226	235	45	-	-	PUNCT
ma-226	235	46	order	order	NOUN
ma-226	235	47	accuracy	accuracy	NOUN
ma-226	235	48	,	,	PUNCT
ma-226	235	49	where	where	SCONJ
ma-226	235	50	n	n	PRON
ma-226	235	51	is	be	AUX
ma-226	235	52	the	the	DET
ma-226	235	53	number	number	NOUN
ma-226	235	54	of	of	ADP
ma-226	235	55	neighboring	neighboring	NOUN
ma-226	235	56	points	point	NOUN
ma-226	235	57	.	.	PUNCT
ma-226	236	1	4	4	X
ma-226	236	2	.	.	X
ma-226	236	3	conclusion	conclusion	VERB
ma-226	236	4	the	the	DET
ma-226	236	5	main	main	ADJ
ma-226	236	6	content	content	NOUN
ma-226	236	7	of	of	ADP
ma-226	236	8	article	article	NOUN
ma-226	236	9	has	have	AUX
ma-226	236	10	proposed	propose	VERB
ma-226	236	11	two	two	NUM
ma-226	236	12	difference	difference	NOUN
ma-226	236	13	schemes	scheme	NOUN
ma-226	236	14	with	with	ADP
ma-226	236	15	high	high	ADJ
ma-226	236	16	-	-	PUNCT
ma-226	236	17	order	order	NOUN
ma-226	236	18	accuracy	accuracy	NOUN
ma-226	236	19	tosolve	tosolve	VERB
ma-226	236	20	second	second	ADJ
ma-226	236	21	-	-	PUNCT
ma-226	236	22	order	order	NOUN
ma-226	236	23	boundary	boundary	ADJ
ma-226	236	24	problems	problem	NOUN
ma-226	236	25	with	with	ADP
ma-226	236	26	the	the	DET
ma-226	236	27	dirichlet	dirichlet	PROPN
ma-226	236	28	boundary	boundary	ADJ
ma-226	236	29	condition	condition	NOUN
ma-226	236	30	system	system	NOUN
ma-226	236	31	and	and	CCONJ
ma-226	236	32	the	the	DET
ma-226	236	33	mixedboundary	mixedboundary	ADJ
ma-226	236	34	condition	condition	NOUN
ma-226	236	35	system	system	NOUN
ma-226	236	36	.	.	PUNCT
ma-226	237	1	the	the	DET
ma-226	237	2	highlight	highlight	NOUN
ma-226	237	3	of	of	ADP
ma-226	237	4	these	these	DET
ma-226	237	5	two	two	NUM
ma-226	237	6	schemes	scheme	NOUN
ma-226	237	7	compared	compare	VERB
ma-226	237	8	to	to	ADP
ma-226	237	9	other	other	ADJ
ma-226	237	10	schemes	scheme	NOUN
ma-226	238	1	[	[	X
ma-226	238	2	3][5]is	3][5]is	NUM
ma-226	238	3	that	that	SCONJ
ma-226	238	4	the	the	DET
ma-226	238	5	two	two	NUM
ma-226	238	6	proposed	propose	VERB
ma-226	238	7	schemes	scheme	NOUN
ma-226	238	8	have	have	VERB
ma-226	238	9	a	a	DET
ma-226	238	10	simple	simple	ADJ
ma-226	238	11	structure	structure	NOUN
ma-226	238	12	,	,	PUNCT
ma-226	238	13	high	high	ADJ
ma-226	238	14	accuracy	accuracy	NOUN
ma-226	238	15	and	and	CCONJ
ma-226	238	16	finding	find	VERB
ma-226	238	17	solutions	solution	NOUN
ma-226	238	18	isdone	isdone	NOUN
ma-226	238	19	using	use	VERB
ma-226	238	20	a	a	DET
ma-226	238	21	pursuit	pursuit	ADJ
ma-226	238	22	algorithm	algorithm	NOUN
ma-226	238	23	with	with	ADP
ma-226	238	24	the	the	DET
ma-226	238	25	computational	computational	ADJ
ma-226	238	26	complexity	complexity	NOUN
ma-226	238	27	is	be	AUX
ma-226	238	28	o(n	o(n	NUM
ma-226	238	29	)	)	PUNCT
ma-226	238	30	,	,	PUNCT
ma-226	238	31	where	where	SCONJ
ma-226	238	32	n	n	PRON
ma-226	238	33	is	be	AUX
ma-226	238	34	the	the	DET
ma-226	238	35	numberof	numberof	ADJ
ma-226	238	36	grid	grid	NOUN
ma-226	238	37	points	point	NOUN
ma-226	238	38	.	.	PUNCT
ma-226	239	1	through	through	ADP
ma-226	239	2	the	the	DET
ma-226	239	3	calculation	calculation	NOUN
ma-226	239	4	results	result	NOUN
ma-226	239	5	,	,	PUNCT
ma-226	239	6	it	it	PRON
ma-226	239	7	has	have	AUX
ma-226	239	8	been	be	AUX
ma-226	239	9	confirmed	confirm	VERB
ma-226	239	10	that	that	SCONJ
ma-226	239	11	the	the	DET
ma-226	239	12	two	two	NUM
ma-226	239	13	schemes	scheme	NOUN
ma-226	239	14	bothprovide	bothprovide	VERB
ma-226	239	15	approximated	approximate	VERB
ma-226	239	16	solutions	solution	NOUN
ma-226	239	17	with	with	ADP
ma-226	239	18	n	n	CCONJ
ma-226	239	19	-	-	PUNCT
ma-226	239	20	level	level	NOUN
ma-226	239	21	accuracy	accuracy	NOUN
ma-226	239	22	compared	compare	VERB
ma-226	239	23	to	to	ADP
ma-226	239	24	the	the	DET
ma-226	239	25	grid	grid	NOUN
ma-226	239	26	step	step	NOUN
ma-226	239	27	with	with	ADP
ma-226	239	28	n+1	n+1	NUM
ma-226	239	29	being	be	AUX
ma-226	239	30	thenumber	thenumber	NOUN
ma-226	239	31	of	of	ADP
ma-226	239	32	neighboring	neighboring	NOUN
ma-226	239	33	points	point	NOUN
ma-226	239	34	used	use	VERB
ma-226	239	35	to	to	PART
ma-226	239	36	determine	determine	VERB
ma-226	239	37	approximate	approximate	ADJ
ma-226	239	38	derivatives	derivative	NOUN
ma-226	239	39	of	of	ADP
ma-226	239	40	levels	level	NOUN
ma-226	239	41	.	.	PUNCT
ma-226	240	1	these	these	DET
ma-226	240	2	differenceschemes	differencescheme	NOUN
ma-226	240	3	will	will	AUX
ma-226	240	4	allow	allow	VERB
ma-226	240	5	to	to	PART
ma-226	240	6	improve	improve	VERB
ma-226	240	7	the	the	DET
ma-226	240	8	accuracy	accuracy	NOUN
ma-226	240	9	of	of	ADP
ma-226	240	10	the	the	DET
ma-226	240	11	solution	solution	NOUN
ma-226	240	12	for	for	ADP
ma-226	240	13	the	the	DET
ma-226	240	14	class	class	NOUN
ma-226	240	15	of	of	ADP
ma-226	240	16	nonlinear	nonlinear	ADJ
ma-226	240	17	boundarieswith	boundarieswith	ADJ
ma-226	240	18	mixed	mixed	ADJ
ma-226	240	19	boundary	boundary	ADJ
ma-226	240	20	conditions	condition	NOUN
ma-226	240	21	.	.	PUNCT
ma-226	241	1	references	reference	NOUN
ma-226	241	2	[	[	X
ma-226	241	3	1	1	NUM
ma-226	241	4	]	]	X
ma-226	241	5	r.b.srivastava	r.b.srivastava	NOUN
ma-226	241	6	and	and	CCONJ
ma-226	241	7	s.shukla	s.shukla	NOUN
ma-226	241	8	,	,	PUNCT
ma-226	241	9	numerical	numerical	ADJ
ma-226	241	10	accuracies	accuracy	NOUN
ma-226	241	11	of	of	ADP
ma-226	241	12	lagrange	lagrange	PROPN
ma-226	241	13	’s	’s	PART
ma-226	241	14	and	and	CCONJ
ma-226	241	15	newton	newton	PROPN
ma-226	241	16	polynomial	polynomial	ADJ
ma-226	241	17	interpolation	interpolation	NOUN
ma-226	241	18	:	:	PUNCT
ma-226	241	19	numericalaccuracies	numericalaccuracie	NOUN
ma-226	241	20	of	of	ADP
ma-226	241	21	interpolation	interpolation	NOUN
ma-226	241	22	formulas	formula	NOUN
ma-226	241	23	,	,	PUNCT
ma-226	241	24	lap	lap	NOUN
ma-226	241	25	lambert	lambert	PROPN
ma-226	241	26	academic	academic	PROPN
ma-226	241	27	publishing	publishing	NOUN
ma-226	241	28	,	,	PUNCT
ma-226	241	29	2012.[2	2012.[2	NUM
ma-226	241	30	]	]	X
ma-226	241	31	q.v	q.v	PROPN
ma-226	241	32	.	.	PROPN
ma-226	241	33	vinh	vinh	PROPN
ma-226	241	34	,	,	PUNCT
ma-226	241	35	t.h	t.h	PROPN
ma-226	241	36	.	.	PROPN
ma-226	241	37	nguyen	nguyen	PROPN
ma-226	241	38	,	,	PUNCT
ma-226	241	39	difference	difference	NOUN
ma-226	241	40	scheme	scheme	NOUN
ma-226	241	41	for	for	ADP
ma-226	241	42	solving	solve	VERB
ma-226	241	43	boundary	boundary	ADJ
ma-226	241	44	problems	problem	NOUN
ma-226	241	45	for	for	ADP
ma-226	241	46	high	high	ADJ
ma-226	241	47	-	-	PUNCT
ma-226	241	48	order	order	NOUN
ma-226	241	49	linear	linear	ADJ
ma-226	241	50	and	and	CCONJ
ma-226	241	51	non	non	ADJ
ma-226	241	52	-	-	ADJ
ma-226	241	53	lineardifferential	lineardifferential	ADJ
ma-226	241	54	equations	equation	NOUN
ma-226	241	55	,	,	PUNCT
ma-226	241	56	fair	fair	ADJ
ma-226	241	57	10	10	NUM
ma-226	241	58	national	national	ADJ
ma-226	241	59	scientific	scientific	ADJ
ma-226	241	60	conference	conference	NOUN
ma-226	241	61	,	,	PUNCT
ma-226	241	62	natural	natural	ADJ
ma-226	241	63	science	science	NOUN
ma-226	241	64	and	and	CCONJ
ma-226	241	65	technology	technology	NOUN
ma-226	241	66	publishing	publishing	NOUN
ma-226	241	67	house,(2017	house,(2017	NOUN
ma-226	241	68	)	)	PUNCT
ma-226	241	69	,	,	PUNCT
ma-226	241	70	358	358	NUM
ma-226	241	71	-	-	SYM
ma-226	241	72	365.[3	365.[3	NUM
ma-226	241	73	]	]	X
ma-226	241	74	n.	n.	PROPN
ma-226	241	75	setia	setia	PROPN
ma-226	241	76	,	,	PUNCT
ma-226	241	77	r.k	r.k	PROPN
ma-226	241	78	.	.	PROPN
ma-226	241	79	mohanty	mohanty	PROPN
ma-226	241	80	,	,	PUNCT
ma-226	241	81	a	a	DET
ma-226	241	82	high	high	ADJ
ma-226	241	83	accuracy	accuracy	NOUN
ma-226	241	84	variable	variable	ADJ
ma-226	241	85	mesh	mesh	PROPN
ma-226	241	86	numerical	numerical	ADJ
ma-226	241	87	approximation	approximation	NOUN
ma-226	241	88	for	for	ADP
ma-226	241	89	two	two	NUM
ma-226	241	90	point	point	NOUN
ma-226	241	91	nonlinear	nonlinear	PROPN
ma-226	241	92	bvps	bvps	PROPN
ma-226	241	93	withmixed	withmixe	VERB
ma-226	241	94	boundary	boundary	ADJ
ma-226	241	95	conditions	condition	NOUN
ma-226	241	96	,	,	PUNCT
ma-226	241	97	soft	soft	ADJ
ma-226	241	98	computing	compute	VERB
ma-226	241	99	a	a	DET
ma-226	241	100	fusion	fusion	NOUN
ma-226	241	101	of	of	ADP
ma-226	241	102	foundations	foundation	NOUN
ma-226	241	103	,	,	PUNCT
ma-226	241	104	methodol	methodol	NOUN
ma-226	241	105	.	.	PUNCT
ma-226	242	1	appl	appl	PROPN
ma-226	242	2	.	.	PROPN
ma-226	243	1	26	26	NUM
ma-226	243	2	(	(	PUNCT
ma-226	243	3	2022	2022	NUM
ma-226	243	4	)	)	PUNCT
ma-226	243	5	,	,	PUNCT
ma-226	243	6	9805	9805	NUM
ma-226	243	7	-	-	SYM
ma-226	243	8	9821.[4	9821.[4	NUM
ma-226	243	9	]	]	PUNCT
ma-226	243	10	m.	m.	NOUN
ma-226	243	11	baccouch	baccouch	NOUN
ma-226	243	12	,	,	PUNCT
ma-226	243	13	analysis	analysis	NOUN
ma-226	243	14	of	of	ADP
ma-226	243	15	optimal	optimal	ADJ
ma-226	243	16	superconvergence	superconvergence	NOUN
ma-226	243	17	of	of	ADP
ma-226	243	18	a	a	DET
ma-226	243	19	local	local	ADJ
ma-226	243	20	discontinuous	discontinuous	ADJ
ma-226	243	21	galerkin	galerkin	ADJ
ma-226	243	22	method	method	NOUN
ma-226	243	23	for	for	ADP
ma-226	243	24	nonlinear	nonlinear	ADJ
ma-226	243	25	second	second	ADJ
ma-226	243	26	-	-	PUNCT
ma-226	243	27	order	order	NOUN
ma-226	243	28	two	two	NUM
ma-226	243	29	-	-	PUNCT
ma-226	243	30	point	point	NOUN
ma-226	243	31	boundary	boundary	ADJ
ma-226	243	32	-	-	PUNCT
ma-226	243	33	value	value	NOUN
ma-226	243	34	problems	problem	NOUN
ma-226	243	35	,	,	PUNCT
ma-226	243	36	appl	appl	PROPN
ma-226	243	37	.	.	PUNCT
ma-226	244	1	numer	numer	PROPN
ma-226	244	2	.	.	PUNCT
ma-226	244	3	math	math	NOUN
ma-226	244	4	.	.	PUNCT
ma-226	245	1	145	145	NUM
ma-226	245	2	(	(	PUNCT
ma-226	245	3	2019	2019	NUM
ma-226	245	4	)	)	PUNCT
ma-226	245	5	,	,	PUNCT
ma-226	245	6	361	361	NUM
ma-226	245	7	-	-	SYM
ma-226	245	8	383.[5	383.[5	NUM
ma-226	245	9	]	]	X
ma-226	245	10	h.	h.	PROPN
ma-226	245	11	ramos	ramos	PROPN
ma-226	245	12	,	,	PUNCT
ma-226	245	13	m.a	m.a	PROPN
ma-226	245	14	.	.	PROPN
ma-226	245	15	rufai	rufai	PROPN
ma-226	245	16	,	,	PUNCT
ma-226	245	17	numerical	numerical	ADJ
ma-226	245	18	solution	solution	NOUN
ma-226	245	19	of	of	ADP
ma-226	245	20	boundary	boundary	ADJ
ma-226	245	21	value	value	NOUN
ma-226	245	22	problems	problem	NOUN
ma-226	245	23	by	by	ADP
ma-226	245	24	using	use	VERB
ma-226	245	25	an	an	DET
ma-226	245	26	optimized	optimize	VERB
ma-226	245	27	two	two	NUM
ma-226	245	28	-	-	PUNCT
ma-226	245	29	step	step	NOUN
ma-226	245	30	blockmethod	blockmethod	NOUN
ma-226	245	31	,	,	PUNCT
ma-226	245	32	numer	numer	NOUN
ma-226	245	33	.	.	PROPN
ma-226	245	34	algorithms	algorithms	PROPN
ma-226	245	35	,	,	PUNCT
ma-226	245	36	84	84	NUM
ma-226	245	37	(	(	PUNCT
ma-226	245	38	2020	2020	NUM
ma-226	245	39	)	)	PUNCT
ma-226	245	40	,	,	PUNCT
ma-226	245	41	229	229	NUM
ma-226	245	42	-	-	SYM
ma-226	245	43	251.[6	251.[6	NUM
ma-226	245	44	]	]	PUNCT
ma-226	245	45	j.	j.	PROPN
ma-226	245	46	li	li	PROPN
ma-226	245	47	,	,	PUNCT
ma-226	245	48	general	general	ADJ
ma-226	245	49	explicit	explicit	ADJ
ma-226	245	50	difference	difference	NOUN
ma-226	245	51	formulas	formula	NOUN
ma-226	245	52	for	for	ADP
ma-226	245	53	numerical	numerical	ADJ
ma-226	245	54	differentiation	differentiation	NOUN
ma-226	245	55	,	,	PUNCT
ma-226	245	56	j.	j.	PROPN
ma-226	245	57	comput	comput	PROPN
ma-226	245	58	.	.	PUNCT
ma-226	246	1	appl	appl	PROPN
ma-226	246	2	.	.	PROPN
ma-226	246	3	math	math	NOUN
ma-226	246	4	.	.	PUNCT
ma-226	247	1	183	183	NUM
ma-226	247	2	(	(	PUNCT
ma-226	247	3	2005	2005	NUM
ma-226	247	4	)	)	PUNCT
ma-226	247	5	,	,	PUNCT
ma-226	247	6	29	29	NUM
ma-226	247	7	-	-	SYM
ma-226	247	8	52.[7	52.[7	NUM
ma-226	247	9	]	]	PUNCT
ma-226	247	10	m.	m.	NOUN
ma-226	247	11	kaur1	kaur1	PROPN
ma-226	247	12	,	,	PUNCT
ma-226	247	13	s.	s.	PROPN
ma-226	247	14	kumar	kumar	PROPN
ma-226	247	15	,	,	PUNCT
ma-226	247	16	j.	j.	PROPN
ma-226	247	17	bhatti	bhatti	PROPN
ma-226	247	18	,	,	PUNCT
ma-226	247	19	numerical	numerical	ADJ
ma-226	247	20	solution	solution	NOUN
ma-226	247	21	to	to	ADP
ma-226	247	22	sixth	sixth	ADJ
ma-226	247	23	order	order	NOUN
ma-226	247	24	ordinary	ordinary	ADJ
ma-226	247	25	differential	differential	ADJ
ma-226	247	26	equation	equation	NOUN
ma-226	247	27	using	use	VERB
ma-226	247	28	three	three	NUM
ma-226	247	29	stageeighth	stageeighth	ADJ
ma-226	247	30	order	order	NOUN
ma-226	247	31	runge	runge	NOUN
ma-226	247	32	-	-	PUNCT
ma-226	247	33	kutta	kutta	NOUN
ma-226	247	34	type	type	NOUN
ma-226	247	35	method	method	NOUN
ma-226	247	36	,	,	PUNCT
ma-226	247	37	the	the	DET
ma-226	247	38	electrochemical	electrochemical	ADJ
ma-226	247	39	society	society	NOUN
ma-226	247	40	,	,	PUNCT
ma-226	247	41	107	107	NUM
ma-226	247	42	(	(	PUNCT
ma-226	247	43	2022	2022	NUM
ma-226	247	44	)	)	PUNCT
ma-226	247	45	,	,	PUNCT
ma-226	247	46	86	86	NUM
ma-226	247	47	-	-	SYM
ma-226	247	48	97	97	NUM
ma-226	247	49	.	.	PUNCT
ma-226	248	1	https://doi.org/10	https://doi.org/10	PROPN
ma-226	248	2	.	.	PUNCT
ma-226	249	1	28924	28924	NUM
ma-226	249	2	/	/	SYM
ma-226	249	3	ada	ada	PROPN
ma-226	249	4	/	/	SYM
ma-226	249	5	ma.1.1	ma.1.1	PROPN
ma-226	249	6	.	.	PUNCT
ma-226	250	1	https://doi.org/10.28924/ada/ma.4.10	https://doi.org/10.28924/ada/ma.4.10	NOUN
ma-226	250	2	https://doi.org/10.28924/ada/ma.1.1	https://doi.org/10.28924/ada/ma.1.1	PROPN
ma-226	250	3	https://doi.org/10.28924/ada/ma.1.1	https://doi.org/10.28924/ada/ma.1.1	PROPN
ma-226	250	4	eur	eur	PROPN
ma-226	250	5	.	.	PUNCT
ma-226	251	1	j.	j.	PROPN
ma-226	251	2	math	math	PROPN
ma-226	251	3	.	.	PUNCT
ma-226	252	1	anal	anal	PROPN
ma-226	252	2	.	.	PUNCT
ma-226	253	1	10.28924	10.28924	NUM
ma-226	253	2	/	/	SYM
ma-226	253	3	ada	ada	NOUN
ma-226	253	4	/	/	NOUN
ma-226	253	5	ma.4.10	ma.4.10	NOUN
ma-226	253	6	11	11	NUM
ma-226	253	7	[	[	NOUN
ma-226	253	8	8	8	NUM
ma-226	253	9	]	]	X
ma-226	253	10	q.a	q.a	PROPN
ma-226	253	11	.	.	PROPN
ma-226	253	12	dang	dang	PROPN
ma-226	253	13	,	,	PUNCT
ma-226	253	14	q.l	q.l	PROPN
ma-226	253	15	.	.	PROPN
ma-226	253	16	dang	dang	PROPN
ma-226	253	17	,	,	PUNCT
ma-226	253	18	a	a	DET
ma-226	253	19	unified	unified	ADJ
ma-226	253	20	approach	approach	NOUN
ma-226	253	21	to	to	ADP
ma-226	253	22	fully	fully	ADV
ma-226	253	23	third	third	ADJ
ma-226	253	24	order	order	NOUN
ma-226	253	25	nonlinear	nonlinear	ADJ
ma-226	253	26	boundary	boundary	ADJ
ma-226	253	27	value	value	NOUN
ma-226	253	28	problems	problem	NOUN
ma-226	253	29	,	,	PUNCT
ma-226	253	30	j.	j.	PROPN
ma-226	253	31	nonlinearfunct	nonlinearfunct	PROPN
ma-226	253	32	.	.	PUNCT
ma-226	254	1	anal	anal	PROPN
ma-226	254	2	.	.	PUNCT
ma-226	255	1	2020	2020	NUM
ma-226	255	2	(	(	PUNCT
ma-226	255	3	2020	2020	NUM
ma-226	255	4	)	)	PUNCT
ma-226	255	5	,	,	PUNCT
ma-226	255	6	9	9	X
ma-226	255	7	.	.	PUNCT
ma-226	255	8	https://doi.org/10.23952/jnfa.2020.9.[9	https://doi.org/10.23952/jnfa.2020.9.[9	VERB
ma-226	255	9	]	]	X
ma-226	255	10	q.a	q.a	PROPN
ma-226	255	11	.	.	PROPN
ma-226	255	12	dang	dang	PROPN
ma-226	255	13	,	,	PUNCT
ma-226	255	14	q.l	q.l	PROPN
ma-226	255	15	.	.	PROPN
ma-226	255	16	dang	dang	PROPN
ma-226	255	17	,	,	PUNCT
ma-226	255	18	simple	simple	ADJ
ma-226	255	19	numerical	numerical	ADJ
ma-226	255	20	methods	method	NOUN
ma-226	255	21	of	of	ADP
ma-226	255	22	second	second	ADJ
ma-226	255	23	and	and	CCONJ
ma-226	255	24	third	third	ADJ
ma-226	255	25	-	-	PUNCT
ma-226	255	26	order	order	NOUN
ma-226	255	27	convergence	convergence	NOUN
ma-226	255	28	for	for	ADP
ma-226	255	29	solving	solve	VERB
ma-226	255	30	a	a	DET
ma-226	255	31	fullythird	fullythird	ADJ
ma-226	255	32	-	-	PUNCT
ma-226	255	33	order	order	NOUN
ma-226	255	34	nonlinear	nonlinear	ADJ
ma-226	255	35	boundary	boundary	ADJ
ma-226	255	36	value	value	NOUN
ma-226	255	37	problem	problem	NOUN
ma-226	255	38	,	,	PUNCT
ma-226	255	39	numer	numer	PROPN
ma-226	255	40	.	.	PROPN
ma-226	255	41	algor	algor	PROPN
ma-226	255	42	.	.	PUNCT
ma-226	256	1	87	87	NUM
ma-226	256	2	(	(	PUNCT
ma-226	256	3	2021	2021	NUM
ma-226	256	4	)	)	PUNCT
ma-226	256	5	,	,	PUNCT
ma-226	256	6	1479–1499	1479–1499	NUM
ma-226	256	7	.	.	PUNCT
ma-226	257	1	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-226	257	2	s11075	s11075	PROPN
ma-226	257	3	-	-	PUNCT
ma-226	257	4	020	020	NUM
ma-226	257	5	-	-	PUNCT
ma-226	257	6	01016	01016	NUM
ma-226	257	7	-	-	SYM
ma-226	257	8	2.[10	2.[10	NUM
ma-226	257	9	]	]	X
ma-226	257	10	q.a	q.a	PROPN
ma-226	257	11	.	.	PROPN
ma-226	257	12	dang	dang	PROPN
ma-226	257	13	,	,	PUNCT
ma-226	257	14	t.h	t.h	PROPN
ma-226	257	15	.	.	PROPN
ma-226	257	16	nguyen	nguyen	PROPN
ma-226	257	17	,	,	PUNCT
ma-226	257	18	solving	solve	VERB
ma-226	257	19	the	the	DET
ma-226	257	20	dirichlet	dirichlet	PROPN
ma-226	257	21	problem	problem	NOUN
ma-226	257	22	for	for	ADP
ma-226	257	23	fully	fully	ADV
ma-226	257	24	fourth	fourth	ADJ
ma-226	257	25	order	order	NOUN
ma-226	257	26	nonlinear	nonlinear	ADJ
ma-226	257	27	differential	differential	ADJ
ma-226	257	28	equation	equation	NOUN
ma-226	257	29	,	,	PUNCT
ma-226	257	30	afr.mat	afr.mat	NOUN
ma-226	257	31	.	.	NOUN
ma-226	258	1	30	30	NUM
ma-226	258	2	(	(	PUNCT
ma-226	258	3	2019	2019	NUM
ma-226	258	4	)	)	PUNCT
ma-226	258	5	,	,	PUNCT
ma-226	259	1	623–641	623–641	NUM
ma-226	259	2	,	,	PUNCT
ma-226	259	3	https://doi.org/10.1007/s13370-019-00671-6.[11	https://doi.org/10.1007/s13370-019-00671-6.[11	NOUN
ma-226	259	4	]	]	PUNCT
ma-226	259	5	j.	j.	PROPN
ma-226	259	6	alzabut	alzabut	PROPN
ma-226	259	7	,	,	PUNCT
ma-226	259	8	s.r	s.r	PROPN
ma-226	259	9	.	.	PROPN
ma-226	259	10	grace	grace	PROPN
ma-226	259	11	,	,	PUNCT
ma-226	259	12	g.n	g.n	PROPN
ma-226	259	13	.	.	PROPN
ma-226	259	14	chhatria	chhatria	PROPN
ma-226	259	15	,	,	PUNCT
ma-226	259	16	new	new	ADJ
ma-226	259	17	oscillation	oscillation	NOUN
ma-226	259	18	results	result	NOUN
ma-226	259	19	for	for	ADP
ma-226	259	20	higher	high	ADJ
ma-226	259	21	order	order	NOUN
ma-226	259	22	nonlinear	nonlinear	ADJ
ma-226	259	23	differential	differential	ADJ
ma-226	259	24	equations	equation	NOUN
ma-226	259	25	witha	witha	VERB
ma-226	259	26	nonlinear	nonlinear	ADJ
ma-226	259	27	neutral	neutral	ADJ
ma-226	259	28	terms	term	NOUN
ma-226	259	29	,	,	PUNCT
ma-226	259	30	j.	j.	PROPN
ma-226	259	31	math	math	PROPN
ma-226	259	32	.	.	PUNCT
ma-226	260	1	comp	comp	PROPN
ma-226	260	2	.	.	PUNCT
ma-226	261	1	sci	sci	PROPN
ma-226	261	2	.	.	PROPN
ma-226	261	3	28	28	NUM
ma-226	261	4	(	(	PUNCT
ma-226	261	5	2022	2022	NUM
ma-226	261	6	)	)	PUNCT
ma-226	261	7	,	,	PUNCT
ma-226	261	8	294	294	NUM
ma-226	261	9	-	-	SYM
ma-226	261	10	305.[12	305.[12	NUM
ma-226	261	11	]	]	PUNCT
ma-226	261	12	s.	s.	PROPN
ma-226	261	13	baraket	baraket	PROPN
ma-226	261	14	,	,	PUNCT
ma-226	261	15	s.	s.	PROPN
ma-226	261	16	mahdaoui	mahdaoui	PROPN
ma-226	261	17	,	,	PUNCT
ma-226	261	18	t.	t.	PROPN
ma-226	261	19	ouni	ouni	PROPN
ma-226	261	20	,	,	PUNCT
ma-226	261	21	limiting	limit	VERB
ma-226	261	22	profile	profile	NOUN
ma-226	261	23	of	of	ADP
ma-226	261	24	the	the	DET
ma-226	261	25	blow	blow	NOUN
ma-226	261	26	-	-	PUNCT
ma-226	261	27	up	up	ADP
ma-226	261	28	solutions	solution	NOUN
ma-226	261	29	for	for	ADP
ma-226	261	30	the	the	DET
ma-226	261	31	fourth	fourth	ADJ
ma-226	261	32	-	-	PUNCT
ma-226	261	33	order	order	NOUN
ma-226	261	34	nonlinear	nonlinear	ADJ
ma-226	261	35	emden	emden	ADJ
ma-226	261	36	-	-	PUNCT
ma-226	261	37	fowler	fowler	NOUN
ma-226	261	38	equation	equation	NOUN
ma-226	261	39	with	with	ADP
ma-226	261	40	a	a	DET
ma-226	261	41	singular	singular	ADJ
ma-226	261	42	source	source	NOUN
ma-226	261	43	,	,	PUNCT
ma-226	261	44	discr	discr	PROPN
ma-226	261	45	.	.	PUNCT
ma-226	262	1	contin	contin	NOUN
ma-226	262	2	.	.	PUNCT
ma-226	263	1	dyn	dyn	PROPN
ma-226	263	2	.	.	PUNCT
ma-226	264	1	syst	syst	PROPN
ma-226	264	2	.	.	PUNCT
ma-226	265	1	s	s	PROPN
ma-226	265	2	,	,	PUNCT
ma-226	265	3	16	16	NUM
ma-226	265	4	(	(	PUNCT
ma-226	265	5	2023	2023	NUM
ma-226	265	6	)	)	PUNCT
ma-226	265	7	,	,	PUNCT
ma-226	265	8	1181	1181	NUM
ma-226	265	9	-	-	SYM
ma-226	265	10	1200	1200	NUM
ma-226	265	11	.	.	PUNCT
ma-226	266	1	https://doi.org/10.28924/ada/ma.4.10	https://doi.org/10.28924/ada/ma.4.10	PROPN
ma-226	266	2	https://doi.org/10.23952/jnfa.2020.9	https://doi.org/10.23952/jnfa.2020.9	PROPN
ma-226	266	3	https://doi.org/10.1007/s11075-020-01016-2	https://doi.org/10.1007/s11075-020-01016-2	X
ma-226	266	4	https://doi.org/10.1007/s11075-020-01016-2	https://doi.org/10.1007/s11075-020-01016-2	PROPN
ma-226	266	5	https://doi.org/10.1007/s13370-019-00671-6	https://doi.org/10.1007/s13370-019-00671-6	NUM
ma-226	266	6	1	1	NUM
ma-226	266	7	.	.	PUNCT
ma-226	266	8	introduction	introduction	NOUN
ma-226	266	9	2	2	NUM
ma-226	266	10	.	.	PUNCT
ma-226	266	11	proposed	propose	VERB
ma-226	266	12	method	method	NOUN
ma-226	266	13	3	3	NUM
ma-226	266	14	.	.	PUNCT
ma-226	266	15	experimental	experimental	ADJ
ma-226	266	16	results	result	NOUN
ma-226	266	17	and	and	CCONJ
ma-226	266	18	discussions	discussion	NOUN
ma-226	266	19	4	4	NUM
ma-226	266	20	.	.	PUNCT
ma-226	267	1	conclusion	conclusion	NOUN
ma-226	267	2	references	reference	NOUN