id	sid	tid	token	lemma	pos
ap-1870	1	1	acta	acta	PROPN
ap-1870	1	2	polytechnica	polytechnica	PROPN
ap-1870	1	3	doi:10.14311	doi:10.14311	PROPN
ap-1870	1	4	/	/	SYM
ap-1870	1	5	ap.2013.53.0438	ap.2013.53.0438	PROPN
ap-1870	1	6	acta	acta	PROPN
ap-1870	1	7	polytechnica	polytechnica	PROPN
ap-1870	1	8	53(5):438–443	53(5):438–443	PROPN
ap-1870	1	9	,	,	PUNCT
ap-1870	1	10	2013	2013	NUM
ap-1870	1	11	©	©	PROPN
ap-1870	1	12	czech	czech	PROPN
ap-1870	1	13	technical	technical	PROPN
ap-1870	1	14	university	university	PROPN
ap-1870	1	15	in	in	ADP
ap-1870	1	16	prague	prague	PROPN
ap-1870	1	17	,	,	PUNCT
ap-1870	1	18	2013	2013	NUM
ap-1870	1	19	available	available	ADJ
ap-1870	1	20	online	online	ADV
ap-1870	1	21	at	at	ADP
ap-1870	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1870	1	23	lie	lie	NOUN
ap-1870	1	24	groups	group	NOUN
ap-1870	1	25	and	and	CCONJ
ap-1870	1	26	numerical	numerical	ADJ
ap-1870	1	27	solutions	solution	NOUN
ap-1870	1	28	of	of	ADP
ap-1870	1	29	differential	differential	ADJ
ap-1870	1	30	equations	equation	NOUN
ap-1870	1	31	:	:	PUNCT
ap-1870	1	32	invariant	invariant	ADJ
ap-1870	1	33	discretization	discretization	NOUN
ap-1870	1	34	versus	versus	ADP
ap-1870	1	35	differential	differential	ADJ
ap-1870	1	36	approximation	approximation	NOUN
ap-1870	1	37	decio	decio	NOUN
ap-1870	1	38	levia	levia	PROPN
ap-1870	1	39	,	,	PUNCT
ap-1870	1	40	pavel	pavel	PROPN
ap-1870	1	41	winternitzb,∗	winternitzb,∗	PROPN
ap-1870	1	42	a	a	DET
ap-1870	1	43	dipartimento	dipartimento	NOUN
ap-1870	1	44	di	di	X
ap-1870	1	45	matematica	matematica	PROPN
ap-1870	1	46	e	e	PROPN
ap-1870	1	47	fisica	fisica	PROPN
ap-1870	1	48	,	,	PUNCT
ap-1870	1	49	universitá	universitá	PROPN
ap-1870	1	50	degli	degli	NOUN
ap-1870	1	51	studi	studi	PROPN
ap-1870	1	52	roma	roma	PROPN
ap-1870	1	53	tre	tre	PROPN
ap-1870	1	54	and	and	CCONJ
ap-1870	1	55	infn	infn	PROPN
ap-1870	1	56	,	,	PUNCT
ap-1870	1	57	sezione	sezione	PROPN
ap-1870	1	58	roma	roma	PROPN
ap-1870	1	59	tre	tre	PROPN
ap-1870	1	60	,	,	PUNCT
ap-1870	1	61	via	via	ADP
ap-1870	1	62	della	della	PROPN
ap-1870	1	63	vasca	vasca	PROPN
ap-1870	1	64	navale	navale	PROPN
ap-1870	1	65	84	84	NUM
ap-1870	1	66	,	,	PUNCT
ap-1870	1	67	00184	00184	NUM
ap-1870	1	68	roma	roma	PROPN
ap-1870	1	69	,	,	PUNCT
ap-1870	1	70	italy	italy	PROPN
ap-1870	1	71	b	b	PROPN
ap-1870	1	72	centre	centre	PROPN
ap-1870	1	73	de	de	X
ap-1870	1	74	recherches	recherche	NOUN
ap-1870	1	75	mathématiques	mathématique	NOUN
ap-1870	1	76	,	,	PUNCT
ap-1870	1	77	université	université	PROPN
ap-1870	1	78	de	de	PROPN
ap-1870	1	79	montréal	montréal	PROPN
ap-1870	1	80	,	,	PUNCT
ap-1870	1	81	c.p	c.p	PROPN
ap-1870	1	82	.	.	PROPN
ap-1870	1	83	6128	6128	NUM
ap-1870	1	84	,	,	PUNCT
ap-1870	1	85	succ	succ	PROPN
ap-1870	1	86	.	.	PUNCT
ap-1870	1	87	centre	centre	PROPN
ap-1870	1	88	-	-	PUNCT
ap-1870	1	89	ville	ville	PROPN
ap-1870	1	90	,	,	PUNCT
ap-1870	1	91	montréal	montréal	PROPN
ap-1870	1	92	,	,	PUNCT
ap-1870	1	93	qc	qc	PROPN
ap-1870	1	94	,	,	PUNCT
ap-1870	1	95	h3c	h3c	PROPN
ap-1870	1	96	3j7	3j7	NUM
ap-1870	1	97	,	,	PUNCT
ap-1870	1	98	canada	canada	PROPN
ap-1870	1	99	∗	∗	VERB
ap-1870	1	100	corresponding	correspond	VERB
ap-1870	1	101	author	author	NOUN
ap-1870	1	102	:	:	PUNCT
ap-1870	1	103	wintern@crm.umontreal.ca	wintern@crm.umontreal.ca	NOUN
ap-1870	1	104	abstract	abstract	NOUN
ap-1870	1	105	.	.	PUNCT
ap-1870	2	1	we	we	PRON
ap-1870	2	2	briefly	briefly	ADV
ap-1870	2	3	review	review	VERB
ap-1870	2	4	two	two	NUM
ap-1870	2	5	different	different	ADJ
ap-1870	2	6	methods	method	NOUN
ap-1870	2	7	of	of	ADP
ap-1870	2	8	applying	apply	VERB
ap-1870	2	9	lie	lie	NOUN
ap-1870	2	10	group	group	NOUN
ap-1870	2	11	theory	theory	NOUN
ap-1870	2	12	in	in	ADP
ap-1870	2	13	the	the	DET
ap-1870	2	14	numerical	numerical	ADJ
ap-1870	2	15	solution	solution	NOUN
ap-1870	2	16	of	of	ADP
ap-1870	2	17	ordinary	ordinary	ADJ
ap-1870	2	18	differential	differential	ADJ
ap-1870	2	19	equations	equation	NOUN
ap-1870	2	20	.	.	PUNCT
ap-1870	3	1	on	on	ADP
ap-1870	3	2	specific	specific	ADJ
ap-1870	3	3	examples	example	NOUN
ap-1870	3	4	we	we	PRON
ap-1870	3	5	show	show	VERB
ap-1870	3	6	how	how	SCONJ
ap-1870	3	7	the	the	DET
ap-1870	3	8	symmetry	symmetry	NOUN
ap-1870	3	9	preserving	preserve	VERB
ap-1870	3	10	discretization	discretization	NOUN
ap-1870	3	11	provides	provide	VERB
ap-1870	3	12	difference	difference	NOUN
ap-1870	3	13	schemes	scheme	NOUN
ap-1870	3	14	for	for	ADP
ap-1870	3	15	which	which	PRON
ap-1870	3	16	the	the	DET
ap-1870	3	17	“	"	PUNCT
ap-1870	3	18	first	first	ADJ
ap-1870	3	19	differential	differential	ADJ
ap-1870	3	20	approximation	approximation	NOUN
ap-1870	3	21	”	"	PUNCT
ap-1870	3	22	is	be	AUX
ap-1870	3	23	invariant	invariant	ADJ
ap-1870	3	24	under	under	ADP
ap-1870	3	25	the	the	DET
ap-1870	3	26	same	same	ADJ
ap-1870	3	27	lie	lie	NOUN
ap-1870	3	28	group	group	NOUN
ap-1870	3	29	as	as	ADP
ap-1870	3	30	the	the	DET
ap-1870	3	31	original	original	ADJ
ap-1870	3	32	ordinary	ordinary	ADJ
ap-1870	3	33	differential	differential	ADJ
ap-1870	3	34	equation	equation	NOUN
ap-1870	3	35	.	.	PUNCT
ap-1870	4	1	keywords	keyword	NOUN
ap-1870	4	2	:	:	PUNCT
ap-1870	4	3	ordinary	ordinary	ADJ
ap-1870	4	4	difference	difference	NOUN
ap-1870	4	5	equations	equation	NOUN
ap-1870	4	6	,	,	PUNCT
ap-1870	4	7	numerical	numerical	ADJ
ap-1870	4	8	solution	solution	NOUN
ap-1870	4	9	,	,	PUNCT
ap-1870	4	10	lie	lie	NOUN
ap-1870	4	11	group	group	NOUN
ap-1870	4	12	theory	theory	NOUN
ap-1870	4	13	,	,	PUNCT
ap-1870	4	14	invariant	invariant	ADJ
ap-1870	4	15	discretization	discretization	NOUN
ap-1870	4	16	.	.	PUNCT
ap-1870	5	1	submitted	submit	VERB
ap-1870	5	2	:	:	PUNCT
ap-1870	5	3	25	25	NUM
ap-1870	5	4	april	april	PROPN
ap-1870	5	5	2013	2013	NUM
ap-1870	5	6	.	.	PUNCT
ap-1870	6	1	accepted	accept	VERB
ap-1870	6	2	:	:	PUNCT
ap-1870	6	3	5	5	NUM
ap-1870	6	4	may	may	PROPN
ap-1870	6	5	2013	2013	NUM
ap-1870	6	6	.	.	PUNCT
ap-1870	7	1	1	1	X
ap-1870	7	2	.	.	X
ap-1870	7	3	introduction	introduction	NOUN
ap-1870	7	4	lie	lie	NOUN
ap-1870	7	5	group	group	NOUN
ap-1870	7	6	theory	theory	NOUN
ap-1870	7	7	provides	provide	VERB
ap-1870	7	8	powerful	powerful	ADJ
ap-1870	7	9	tools	tool	NOUN
ap-1870	7	10	for	for	ADP
ap-1870	7	11	solving	solve	VERB
ap-1870	7	12	ordinary	ordinary	ADJ
ap-1870	7	13	and	and	CCONJ
ap-1870	7	14	partial	partial	ADJ
ap-1870	7	15	differential	differential	NOUN
ap-1870	7	16	equations	equation	NOUN
ap-1870	7	17	,	,	PUNCT
ap-1870	7	18	specially	specially	ADV
ap-1870	7	19	nonlinear	nonlinear	ADJ
ap-1870	7	20	ones	one	NOUN
ap-1870	7	21	[	[	X
ap-1870	7	22	1–3	1–3	NOUN
ap-1870	7	23	]	]	X
ap-1870	7	24	.	.	PUNCT
ap-1870	8	1	the	the	DET
ap-1870	8	2	standard	standard	ADJ
ap-1870	8	3	approach	approach	NOUN
ap-1870	8	4	is	be	AUX
ap-1870	8	5	to	to	PART
ap-1870	8	6	find	find	VERB
ap-1870	8	7	the	the	DET
ap-1870	8	8	lie	lie	NOUN
ap-1870	8	9	point	point	NOUN
ap-1870	8	10	symmetry	symmetry	NOUN
ap-1870	8	11	group	group	NOUN
ap-1870	8	12	g	g	PROPN
ap-1870	8	13	of	of	ADP
ap-1870	8	14	the	the	DET
ap-1870	8	15	equation	equation	NOUN
ap-1870	8	16	and	and	CCONJ
ap-1870	8	17	then	then	ADV
ap-1870	8	18	look	look	VERB
ap-1870	8	19	for	for	ADP
ap-1870	8	20	invariant	invariant	ADJ
ap-1870	8	21	solutions	solution	NOUN
ap-1870	8	22	,	,	PUNCT
ap-1870	8	23	i.e.	i.e.	X
ap-1870	8	24	solutions	solution	NOUN
ap-1870	8	25	that	that	PRON
ap-1870	8	26	are	be	AUX
ap-1870	8	27	invariant	invariant	ADJ
ap-1870	8	28	under	under	ADP
ap-1870	8	29	some	some	DET
ap-1870	8	30	subgroup	subgroup	NOUN
ap-1870	8	31	g0	g0	PROPN
ap-1870	8	32	⊂	⊂	PROPN
ap-1870	8	33	g.	g.	PROPN
ap-1870	8	34	for	for	ADP
ap-1870	8	35	ordinary	ordinary	ADJ
ap-1870	8	36	differential	differential	ADJ
ap-1870	8	37	equations	equation	NOUN
ap-1870	8	38	(	(	PUNCT
ap-1870	8	39	odes	ode	VERB
ap-1870	8	40	)	)	PUNCT
ap-1870	8	41	this	this	PRON
ap-1870	8	42	leads	lead	VERB
ap-1870	8	43	to	to	ADP
ap-1870	8	44	a	a	DET
ap-1870	8	45	reduction	reduction	NOUN
ap-1870	8	46	of	of	ADP
ap-1870	8	47	the	the	DET
ap-1870	8	48	order	order	NOUN
ap-1870	8	49	of	of	ADP
ap-1870	8	50	the	the	DET
ap-1870	8	51	equation	equation	NOUN
ap-1870	8	52	(	(	PUNCT
ap-1870	8	53	without	without	ADP
ap-1870	8	54	any	any	DET
ap-1870	8	55	loss	loss	NOUN
ap-1870	8	56	of	of	ADP
ap-1870	8	57	information	information	NOUN
ap-1870	8	58	)	)	PUNCT
ap-1870	8	59	.	.	PUNCT
ap-1870	9	1	if	if	SCONJ
ap-1870	9	2	the	the	DET
ap-1870	9	3	dimension	dimension	NOUN
ap-1870	9	4	of	of	ADP
ap-1870	9	5	the	the	DET
ap-1870	9	6	symmetry	symmetry	NOUN
ap-1870	9	7	group	group	NOUN
ap-1870	9	8	is	be	AUX
ap-1870	9	9	large	large	ADJ
ap-1870	9	10	enough	enough	ADV
ap-1870	9	11	(	(	PUNCT
ap-1870	9	12	at	at	ADP
ap-1870	9	13	least	least	ADJ
ap-1870	9	14	equal	equal	ADJ
ap-1870	9	15	to	to	ADP
ap-1870	9	16	the	the	DET
ap-1870	9	17	order	order	NOUN
ap-1870	9	18	of	of	ADP
ap-1870	9	19	the	the	DET
ap-1870	9	20	equation	equation	NOUN
ap-1870	9	21	)	)	PUNCT
ap-1870	9	22	and	and	CCONJ
ap-1870	9	23	the	the	DET
ap-1870	9	24	group	group	NOUN
ap-1870	9	25	is	be	AUX
ap-1870	9	26	solvable	solvable	ADJ
ap-1870	9	27	,	,	PUNCT
ap-1870	9	28	then	then	ADV
ap-1870	9	29	the	the	DET
ap-1870	9	30	order	order	NOUN
ap-1870	9	31	of	of	ADP
ap-1870	9	32	the	the	DET
ap-1870	9	33	equation	equation	NOUN
ap-1870	9	34	can	can	AUX
ap-1870	9	35	be	be	AUX
ap-1870	9	36	reduced	reduce	VERB
ap-1870	9	37	to	to	ADP
ap-1870	9	38	zero	zero	NUM
ap-1870	9	39	.	.	PUNCT
ap-1870	10	1	this	this	PRON
ap-1870	10	2	can	can	AUX
ap-1870	10	3	be	be	AUX
ap-1870	10	4	viewed	view	VERB
ap-1870	10	5	as	as	ADP
ap-1870	10	6	obtaining	obtain	VERB
ap-1870	10	7	the	the	DET
ap-1870	10	8	general	general	ADJ
ap-1870	10	9	solution	solution	NOUN
ap-1870	10	10	of	of	ADP
ap-1870	10	11	the	the	DET
ap-1870	10	12	equation	equation	NOUN
ap-1870	10	13	,	,	PUNCT
ap-1870	10	14	explicitly	explicitly	ADV
ap-1870	10	15	or	or	CCONJ
ap-1870	10	16	implicitly	implicitly	ADV
ap-1870	10	17	.	.	PUNCT
ap-1870	11	1	however	however	ADV
ap-1870	11	2	,	,	PUNCT
ap-1870	11	3	for	for	ADP
ap-1870	11	4	an	an	DET
ap-1870	11	5	ode	ode	ADJ
ap-1870	11	6	obtaining	obtain	VERB
ap-1870	11	7	an	an	DET
ap-1870	11	8	implicit	implicit	ADJ
ap-1870	11	9	solution	solution	NOUN
ap-1870	11	10	is	be	AUX
ap-1870	11	11	essentially	essentially	ADV
ap-1870	11	12	equivalent	equivalent	ADJ
ap-1870	11	13	to	to	ADP
ap-1870	11	14	replacing	replace	VERB
ap-1870	11	15	the	the	DET
ap-1870	11	16	differential	differential	ADJ
ap-1870	11	17	equation	equation	NOUN
ap-1870	11	18	by	by	ADP
ap-1870	11	19	an	an	DET
ap-1870	11	20	algebraic	algebraic	ADJ
ap-1870	11	21	or	or	CCONJ
ap-1870	11	22	a	a	DET
ap-1870	11	23	functional	functional	ADJ
ap-1870	11	24	one	one	NOUN
ap-1870	11	25	.	.	PUNCT
ap-1870	12	1	from	from	ADP
ap-1870	12	2	the	the	DET
ap-1870	12	3	point	point	NOUN
ap-1870	12	4	of	of	ADP
ap-1870	12	5	view	view	NOUN
ap-1870	12	6	of	of	ADP
ap-1870	12	7	visualizing	visualize	VERB
ap-1870	12	8	the	the	DET
ap-1870	12	9	solution	solution	NOUN
ap-1870	12	10	,	,	PUNCT
ap-1870	12	11	or	or	CCONJ
ap-1870	12	12	presenting	present	VERB
ap-1870	12	13	a	a	DET
ap-1870	12	14	graph	graph	NOUN
ap-1870	12	15	of	of	ADP
ap-1870	12	16	the	the	DET
ap-1870	12	17	solution	solution	NOUN
ap-1870	12	18	,	,	PUNCT
ap-1870	12	19	it	it	PRON
ap-1870	12	20	maybe	maybe	ADV
ap-1870	12	21	easier	easy	ADJ
ap-1870	12	22	to	to	PART
ap-1870	12	23	solve	solve	VERB
ap-1870	12	24	the	the	DET
ap-1870	12	25	ode	ode	NOUN
ap-1870	12	26	numerically	numerically	ADV
ap-1870	12	27	than	than	SCONJ
ap-1870	12	28	to	to	PART
ap-1870	12	29	do	do	VERB
ap-1870	12	30	the	the	DET
ap-1870	12	31	same	same	ADJ
ap-1870	12	32	for	for	ADP
ap-1870	12	33	the	the	DET
ap-1870	12	34	functional	functional	ADJ
ap-1870	12	35	equation	equation	NOUN
ap-1870	12	36	.	.	PUNCT
ap-1870	13	1	for	for	ADP
ap-1870	13	2	partial	partial	ADJ
ap-1870	13	3	differential	differential	ADJ
ap-1870	13	4	equations	equation	NOUN
ap-1870	13	5	(	(	PUNCT
ap-1870	13	6	pdes	pde	NOUN
ap-1870	13	7	)	)	PUNCT
ap-1870	13	8	symmetry	symmetry	NOUN
ap-1870	13	9	reduction	reduction	NOUN
ap-1870	13	10	reduces	reduce	VERB
ap-1870	13	11	the	the	DET
ap-1870	13	12	number	number	NOUN
ap-1870	13	13	of	of	ADP
ap-1870	13	14	independent	independent	ADJ
ap-1870	13	15	variables	variable	NOUN
ap-1870	13	16	in	in	ADP
ap-1870	13	17	the	the	DET
ap-1870	13	18	equation	equation	NOUN
ap-1870	13	19	and	and	CCONJ
ap-1870	13	20	leads	lead	VERB
ap-1870	13	21	to	to	ADP
ap-1870	13	22	particular	particular	ADJ
ap-1870	13	23	solutions	solution	NOUN
ap-1870	13	24	,	,	PUNCT
ap-1870	13	25	rather	rather	ADV
ap-1870	13	26	than	than	ADP
ap-1870	13	27	the	the	DET
ap-1870	13	28	general	general	ADJ
ap-1870	13	29	solution	solution	NOUN
ap-1870	13	30	.	.	PUNCT
ap-1870	14	1	both	both	PRON
ap-1870	14	2	for	for	ADP
ap-1870	14	3	odes	ode	NOUN
ap-1870	14	4	and	and	CCONJ
ap-1870	14	5	pdes	pde	NOUN
ap-1870	14	6	with	with	ADP
ap-1870	14	7	nontrivial	nontrivial	ADJ
ap-1870	14	8	symmetry	symmetry	NOUN
ap-1870	14	9	groups	group	NOUN
ap-1870	14	10	it	it	PRON
ap-1870	14	11	may	may	AUX
ap-1870	14	12	still	still	ADV
ap-1870	14	13	be	be	AUX
ap-1870	14	14	necessary	necessary	ADJ
ap-1870	14	15	to	to	PART
ap-1870	14	16	resort	resort	VERB
ap-1870	14	17	to	to	ADP
ap-1870	14	18	numerical	numerical	ADJ
ap-1870	14	19	solutions	solution	NOUN
ap-1870	14	20	.	.	PUNCT
ap-1870	15	1	the	the	DET
ap-1870	15	2	question	question	NOUN
ap-1870	15	3	then	then	ADV
ap-1870	15	4	arises	arise	VERB
ap-1870	15	5	of	of	ADP
ap-1870	15	6	making	make	VERB
ap-1870	15	7	good	good	ADJ
ap-1870	15	8	use	use	NOUN
ap-1870	15	9	of	of	ADP
ap-1870	15	10	the	the	DET
ap-1870	15	11	group	group	NOUN
ap-1870	15	12	g.	g.	PROPN
ap-1870	15	13	any	any	DET
ap-1870	15	14	numerical	numerical	ADJ
ap-1870	15	15	method	method	NOUN
ap-1870	15	16	involves	involve	VERB
ap-1870	15	17	replacing	replace	VERB
ap-1870	15	18	the	the	DET
ap-1870	15	19	differential	differential	ADJ
ap-1870	15	20	equation	equation	NOUN
ap-1870	15	21	by	by	ADP
ap-1870	15	22	a	a	DET
ap-1870	15	23	difference	difference	NOUN
ap-1870	15	24	one	one	NUM
ap-1870	15	25	.	.	PUNCT
ap-1870	16	1	in	in	ADP
ap-1870	16	2	standard	standard	ADJ
ap-1870	16	3	discretizations	discretization	NOUN
ap-1870	16	4	no	no	DET
ap-1870	16	5	heed	heed	NOUN
ap-1870	16	6	is	be	AUX
ap-1870	16	7	paid	pay	VERB
ap-1870	16	8	to	to	ADP
ap-1870	16	9	the	the	DET
ap-1870	16	10	symmetry	symmetry	NOUN
ap-1870	16	11	group	group	NOUN
ap-1870	16	12	g	g	PROPN
ap-1870	16	13	and	and	CCONJ
ap-1870	16	14	some	some	PRON
ap-1870	16	15	,	,	PUNCT
ap-1870	16	16	or	or	CCONJ
ap-1870	16	17	all	all	PRON
ap-1870	16	18	of	of	ADP
ap-1870	16	19	the	the	DET
ap-1870	16	20	symmetries	symmetry	NOUN
ap-1870	16	21	are	be	AUX
ap-1870	16	22	lost	lose	VERB
ap-1870	16	23	.	.	PUNCT
ap-1870	17	1	since	since	SCONJ
ap-1870	17	2	the	the	DET
ap-1870	17	3	lie	lie	NOUN
ap-1870	17	4	point	point	NOUN
ap-1870	17	5	symmetry	symmetry	NOUN
ap-1870	17	6	group	group	NOUN
ap-1870	17	7	encodes	encode	VERB
ap-1870	17	8	many	many	ADJ
ap-1870	17	9	of	of	ADP
ap-1870	17	10	the	the	DET
ap-1870	17	11	properties	property	NOUN
ap-1870	17	12	of	of	ADP
ap-1870	17	13	the	the	DET
ap-1870	17	14	solution	solution	NOUN
ap-1870	17	15	space	space	NOUN
ap-1870	17	16	of	of	ADP
ap-1870	17	17	a	a	DET
ap-1870	17	18	differential	differential	ADJ
ap-1870	17	19	equation	equation	NOUN
ap-1870	17	20	,	,	PUNCT
ap-1870	17	21	it	it	PRON
ap-1870	17	22	seems	seem	VERB
ap-1870	17	23	desirable	desirable	ADJ
ap-1870	17	24	to	to	PART
ap-1870	17	25	preserve	preserve	VERB
ap-1870	17	26	it	it	PRON
ap-1870	17	27	,	,	PUNCT
ap-1870	17	28	or	or	CCONJ
ap-1870	17	29	at	at	ADP
ap-1870	17	30	least	least	ADJ
ap-1870	17	31	some	some	PRON
ap-1870	17	32	of	of	ADP
ap-1870	17	33	its	its	PRON
ap-1870	17	34	features	feature	NOUN
ap-1870	17	35	in	in	ADP
ap-1870	17	36	the	the	DET
ap-1870	17	37	discretization	discretization	NOUN
ap-1870	17	38	process	process	NOUN
ap-1870	17	39	.	.	PUNCT
ap-1870	18	1	two	two	NUM
ap-1870	18	2	different	different	ADJ
ap-1870	18	3	methods	method	NOUN
ap-1870	18	4	for	for	ADP
ap-1870	18	5	incorporating	incorporate	VERB
ap-1870	18	6	symmetry	symmetry	NOUN
ap-1870	18	7	concepts	concept	NOUN
ap-1870	18	8	into	into	ADP
ap-1870	18	9	the	the	DET
ap-1870	18	10	discretization	discretization	NOUN
ap-1870	18	11	of	of	ADP
ap-1870	18	12	differential	differential	ADJ
ap-1870	18	13	equations	equation	NOUN
ap-1870	18	14	exist	exist	VERB
ap-1870	18	15	in	in	ADP
ap-1870	18	16	the	the	DET
ap-1870	18	17	literature	literature	NOUN
ap-1870	18	18	.	.	PUNCT
ap-1870	19	1	one	one	NUM
ap-1870	19	2	was	be	AUX
ap-1870	19	3	proposed	propose	VERB
ap-1870	19	4	and	and	CCONJ
ap-1870	19	5	explored	explore	VERB
ap-1870	19	6	by	by	ADP
ap-1870	19	7	shokin	shokin	NOUN
ap-1870	19	8	and	and	CCONJ
ap-1870	19	9	yanenko	yanenko	ADJ
ap-1870	20	1	[	[	X
ap-1870	20	2	4–8	4–8	X
ap-1870	20	3	]	]	X
ap-1870	20	4	for	for	ADP
ap-1870	20	5	pdes	pde	NOUN
ap-1870	20	6	and	and	CCONJ
ap-1870	20	7	has	have	AUX
ap-1870	20	8	been	be	AUX
ap-1870	20	9	implemented	implement	VERB
ap-1870	20	10	in	in	ADP
ap-1870	20	11	several	several	ADJ
ap-1870	20	12	recent	recent	ADJ
ap-1870	20	13	studies	study	NOUN
ap-1870	20	14	[	[	X
ap-1870	20	15	9	9	NUM
ap-1870	20	16	,	,	PUNCT
ap-1870	20	17	10	10	NUM
ap-1870	20	18	]	]	PUNCT
ap-1870	20	19	.	.	PUNCT
ap-1870	21	1	it	it	PRON
ap-1870	21	2	is	be	AUX
ap-1870	21	3	called	call	VERB
ap-1870	21	4	the	the	DET
ap-1870	21	5	differential	differential	ADJ
ap-1870	21	6	approximation	approximation	NOUN
ap-1870	21	7	method	method	NOUN
ap-1870	21	8	and	and	CCONJ
ap-1870	21	9	the	the	DET
ap-1870	21	10	basic	basic	ADJ
ap-1870	21	11	idea	idea	NOUN
ap-1870	21	12	is	be	AUX
ap-1870	21	13	the	the	DET
ap-1870	21	14	following	following	NOUN
ap-1870	21	15	.	.	PUNCT
ap-1870	22	1	a	a	DET
ap-1870	22	2	uniform	uniform	ADJ
ap-1870	22	3	orthogonal	orthogonal	ADJ
ap-1870	22	4	lattice	lattice	NOUN
ap-1870	22	5	in	in	ADP
ap-1870	22	6	xi	xi	PROPN
ap-1870	22	7	is	be	AUX
ap-1870	22	8	introduced	introduce	VERB
ap-1870	22	9	and	and	CCONJ
ap-1870	22	10	the	the	DET
ap-1870	22	11	considered	consider	VERB
ap-1870	22	12	differential	differential	ADJ
ap-1870	22	13	equation	equation	NOUN
ap-1870	22	14	e(~x	e(~x	PROPN
ap-1870	22	15	,	,	PUNCT
ap-1870	22	16	u	u	NOUN
ap-1870	22	17	,	,	PUNCT
ap-1870	22	18	uxi	uxi	NOUN
ap-1870	22	19	,	,	PUNCT
ap-1870	22	20	uxi	uxi	NOUN
ap-1870	22	21	,	,	PUNCT
ap-1870	22	22	xj	xj	PROPN
ap-1870	22	23	,	,	PUNCT
ap-1870	22	24	·	·	PUNCT
ap-1870	22	25	·	·	PUNCT
ap-1870	22	26	·	·	PUNCT
ap-1870	22	27	)	)	PUNCT
ap-1870	23	1	=	=	PUNCT
ap-1870	23	2	0	0	NUM
ap-1870	23	3	,	,	PUNCT
ap-1870	23	4	(	(	PUNCT
ap-1870	23	5	1	1	X
ap-1870	23	6	)	)	PUNCT
ap-1870	23	7	is	be	AUX
ap-1870	23	8	approximated	approximate	VERB
ap-1870	23	9	by	by	ADP
ap-1870	23	10	some	some	DET
ap-1870	23	11	difference	difference	NOUN
ap-1870	23	12	equation	equation	NOUN
ap-1870	23	13	e∆	e∆	ADV
ap-1870	23	14	=	=	SYM
ap-1870	24	1	0	0	X
ap-1870	24	2	.	.	PUNCT
ap-1870	25	1	the	the	DET
ap-1870	25	2	derivatives	derivative	NOUN
ap-1870	25	3	are	be	AUX
ap-1870	25	4	replaced	replace	VERB
ap-1870	25	5	by	by	ADP
ap-1870	25	6	discrete	discrete	ADJ
ap-1870	25	7	derivatives	derivative	NOUN
ap-1870	25	8	.	.	PUNCT
ap-1870	26	1	all	all	DET
ap-1870	26	2	known	known	ADJ
ap-1870	26	3	and	and	CCONJ
ap-1870	26	4	unknown	unknown	ADJ
ap-1870	26	5	functions	function	NOUN
ap-1870	26	6	in	in	ADP
ap-1870	26	7	(	(	PUNCT
ap-1870	26	8	1	1	X
ap-1870	26	9	)	)	PUNCT
ap-1870	26	10	are	be	AUX
ap-1870	26	11	then	then	ADV
ap-1870	26	12	expanded	expand	VERB
ap-1870	26	13	in	in	ADP
ap-1870	26	14	taylor	taylor	PROPN
ap-1870	26	15	series	series	PROPN
ap-1870	26	16	about	about	ADP
ap-1870	26	17	some	some	DET
ap-1870	26	18	reference	reference	NOUN
ap-1870	26	19	point	point	NOUN
ap-1870	26	20	(	(	PUNCT
ap-1870	26	21	~x	~x	NUM
ap-1870	26	22	)	)	PUNCT
ap-1870	26	23	,	,	PUNCT
ap-1870	26	24	in	in	ADP
ap-1870	26	25	terms	term	NOUN
ap-1870	26	26	of	of	ADP
ap-1870	26	27	the	the	DET
ap-1870	26	28	lattice	lattice	NOUN
ap-1870	26	29	spacings	spacing	NOUN
ap-1870	26	30	.	.	PUNCT
ap-1870	27	1	in	in	ADP
ap-1870	27	2	the	the	DET
ap-1870	27	3	simplest	simple	ADJ
ap-1870	27	4	case	case	NOUN
ap-1870	27	5	of	of	ADP
ap-1870	27	6	2	2	NUM
ap-1870	27	7	variables	variable	NOUN
ap-1870	27	8	,	,	PUNCT
ap-1870	27	9	x	x	PUNCT
ap-1870	27	10	and	and	CCONJ
ap-1870	27	11	t	t	PROPN
ap-1870	27	12	,	,	PUNCT
ap-1870	27	13	we	we	PRON
ap-1870	27	14	have	have	VERB
ap-1870	27	15	σ	σ	NOUN
ap-1870	27	16	=	=	SYM
ap-1870	27	17	xn+1	xn+1	PROPN
ap-1870	28	1	−	−	PROPN
ap-1870	29	1	xn	xn	PROPN
ap-1870	29	2	,	,	PUNCT
ap-1870	29	3	τ	τ	PROPN
ap-1870	29	4	=	=	SYM
ap-1870	29	5	tn+1	tn+1	PROPN
ap-1870	29	6	−	−	PROPN
ap-1870	29	7	tn	tn	PROPN
ap-1870	29	8	e∆(x	e∆(x	PROPN
ap-1870	29	9	,	,	PUNCT
ap-1870	29	10	t	t	PROPN
ap-1870	29	11	,	,	PUNCT
ap-1870	29	12	u,∆xu,∆tu,∆xxu,∆ttu,∆xtu	u,∆xu,∆tu,∆xxu,∆ttu,∆xtu	PROPN
ap-1870	29	13	,	,	PUNCT
ap-1870	29	14	·	·	PUNCT
ap-1870	29	15	·	·	PUNCT
ap-1870	29	16	·	·	PUNCT
ap-1870	29	17	)	)	PUNCT
ap-1870	30	1	=	=	PUNCT
ap-1870	30	2	e	e	NOUN
ap-1870	30	3	+	+	NOUN
ap-1870	30	4	σe1	σe1	NOUN
ap-1870	30	5	+	+	CCONJ
ap-1870	30	6	τe2	τe2	ADJ
ap-1870	30	7	+	+	CCONJ
ap-1870	30	8	σ2e3	σ2e3	NOUN
ap-1870	31	1	+	+	CCONJ
ap-1870	31	2	2στe4	2στe4	NUM
ap-1870	31	3	+	+	CCONJ
ap-1870	31	4	τ2e5	τ2e5	X
ap-1870	31	5	+	+	X
ap-1870	31	6	·	·	PUNCT
ap-1870	31	7	·	·	PUNCT
ap-1870	31	8	·	·	PUNCT
ap-1870	31	9	.	.	PUNCT
ap-1870	32	1	(	(	PUNCT
ap-1870	32	2	2	2	X
ap-1870	32	3	)	)	PUNCT
ap-1870	32	4	the	the	DET
ap-1870	32	5	expansion	expansion	NOUN
ap-1870	32	6	on	on	ADP
ap-1870	32	7	the	the	DET
ap-1870	32	8	right	right	ADJ
ap-1870	32	9	hand	hand	NOUN
ap-1870	32	10	side	side	NOUN
ap-1870	32	11	of	of	ADP
ap-1870	32	12	(	(	PUNCT
ap-1870	32	13	2	2	NUM
ap-1870	32	14	)	)	PUNCT
ap-1870	32	15	is	be	AUX
ap-1870	32	16	a	a	DET
ap-1870	32	17	“	"	PUNCT
ap-1870	32	18	differential	differential	ADJ
ap-1870	32	19	approximation	approximation	NOUN
ap-1870	32	20	”	"	PUNCT
ap-1870	32	21	of	of	ADP
ap-1870	32	22	the	the	DET
ap-1870	32	23	difference	difference	NOUN
ap-1870	32	24	equation	equation	NOUN
ap-1870	32	25	e∆	e∆	ADV
ap-1870	32	26	=	=	SYM
ap-1870	32	27	0	0	X
ap-1870	32	28	.	.	PUNCT
ap-1870	33	1	(	(	PUNCT
ap-1870	33	2	3	3	X
ap-1870	33	3	)	)	PUNCT
ap-1870	33	4	the	the	DET
ap-1870	33	5	“	"	PUNCT
ap-1870	33	6	zero	zero	NUM
ap-1870	33	7	order	order	NOUN
ap-1870	33	8	differential	differential	ADJ
ap-1870	33	9	approximation	approximation	NOUN
ap-1870	33	10	”	"	PUNCT
ap-1870	33	11	of	of	ADP
ap-1870	33	12	(	(	PUNCT
ap-1870	33	13	3	3	X
ap-1870	33	14	)	)	PUNCT
ap-1870	33	15	is	be	AUX
ap-1870	33	16	the	the	DET
ap-1870	33	17	original	original	ADJ
ap-1870	33	18	differential	differential	NOUN
ap-1870	33	19	equation	equation	NOUN
ap-1870	33	20	(	(	PUNCT
ap-1870	33	21	1	1	NUM
ap-1870	33	22	)	)	PUNCT
ap-1870	33	23	and	and	CCONJ
ap-1870	33	24	hence	hence	ADV
ap-1870	33	25	is	be	AUX
ap-1870	33	26	invariant	invariant	ADJ
ap-1870	33	27	under	under	ADP
ap-1870	33	28	the	the	DET
ap-1870	33	29	symmetry	symmetry	NOUN
ap-1870	33	30	groupg	groupg	NOUN
ap-1870	33	31	.	.	PUNCT
ap-1870	34	1	keeping	keep	VERB
ap-1870	34	2	terms	term	NOUN
ap-1870	34	3	of	of	ADP
ap-1870	34	4	order	order	NOUN
ap-1870	34	5	σ	σ	NOUN
ap-1870	34	6	or	or	CCONJ
ap-1870	34	7	τ	τ	PROPN
ap-1870	34	8	in	in	ADP
ap-1870	34	9	(	(	PUNCT
ap-1870	34	10	2	2	X
ap-1870	34	11	)	)	PUNCT
ap-1870	34	12	we	we	PRON
ap-1870	34	13	obtain	obtain	VERB
ap-1870	34	14	the	the	DET
ap-1870	34	15	first	first	ADJ
ap-1870	34	16	differential	differential	ADJ
ap-1870	34	17	approximation	approximation	NOUN
ap-1870	34	18	,	,	PUNCT
ap-1870	34	19	etc	etc	X
ap-1870	34	20	.	.	X
ap-1870	35	1	the	the	DET
ap-1870	35	2	idea	idea	NOUN
ap-1870	35	3	is	be	AUX
ap-1870	35	4	to	to	PART
ap-1870	35	5	take	take	VERB
ap-1870	35	6	a	a	DET
ap-1870	35	7	higher	high	ADJ
ap-1870	35	8	438	438	NUM
ap-1870	35	9	http://dx.doi.org/10.14311/ap.2013.53.0438	http://dx.doi.org/10.14311/ap.2013.53.0438	NOUN
ap-1870	35	10	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1870	35	11	vol	vol	NOUN
ap-1870	35	12	.	.	PUNCT
ap-1870	36	1	53	53	NUM
ap-1870	36	2	no	no	NOUN
ap-1870	36	3	.	.	PUNCT
ap-1870	37	1	5/2013	5/2013	NUM
ap-1870	37	2	lie	lie	NOUN
ap-1870	37	3	groups	group	NOUN
ap-1870	37	4	and	and	CCONJ
ap-1870	37	5	numerical	numerical	ADJ
ap-1870	37	6	solutions	solution	NOUN
ap-1870	37	7	of	of	ADP
ap-1870	37	8	differential	differential	ADJ
ap-1870	37	9	equations	equation	NOUN
ap-1870	37	10	order	order	VERB
ap-1870	37	11	differential	differential	ADJ
ap-1870	37	12	approximation	approximation	NOUN
ap-1870	37	13	,	,	PUNCT
ap-1870	37	14	at	at	ADP
ap-1870	37	15	least	least	ADJ
ap-1870	37	16	the	the	DET
ap-1870	37	17	first	first	ADJ
ap-1870	37	18	order	order	NOUN
ap-1870	37	19	one	one	NUM
ap-1870	37	20	,	,	PUNCT
ap-1870	37	21	and	and	CCONJ
ap-1870	37	22	require	require	VERB
ap-1870	37	23	that	that	PRON
ap-1870	37	24	is	be	AUX
ap-1870	37	25	also	also	ADV
ap-1870	37	26	invariant	invariant	ADJ
ap-1870	37	27	under	under	ADP
ap-1870	37	28	g	g	NOUN
ap-1870	37	29	,	,	PUNCT
ap-1870	37	30	or	or	CCONJ
ap-1870	37	31	at	at	ADP
ap-1870	37	32	least	least	ADJ
ap-1870	37	33	under	under	ADP
ap-1870	37	34	a	a	DET
ap-1870	37	35	subgroup	subgroup	NOUN
ap-1870	37	36	g0	g0	PROPN
ap-1870	37	37	⊂	⊂	PROPN
ap-1870	37	38	g.	g.	PROPN
ap-1870	37	39	this	this	PRON
ap-1870	37	40	is	be	AUX
ap-1870	37	41	done	do	VERB
ap-1870	37	42	by	by	ADP
ap-1870	37	43	constructing	construct	VERB
ap-1870	37	44	different	different	ADJ
ap-1870	37	45	possible	possible	ADJ
ap-1870	37	46	difference	difference	NOUN
ap-1870	37	47	schemes	scheme	NOUN
ap-1870	37	48	approximating	approximate	VERB
ap-1870	37	49	eq	eq	ADP
ap-1870	37	50	.	.	PUNCT
ap-1870	38	1	(	(	PUNCT
ap-1870	38	2	1	1	NUM
ap-1870	38	3	)	)	PUNCT
ap-1870	38	4	and	and	CCONJ
ap-1870	38	5	choosing	choose	VERB
ap-1870	38	6	among	among	ADP
ap-1870	38	7	them	they	PRON
ap-1870	38	8	the	the	DET
ap-1870	38	9	one	one	NOUN
ap-1870	38	10	for	for	ADP
ap-1870	38	11	which	which	PRON
ap-1870	38	12	the	the	DET
ap-1870	38	13	first	first	ADJ
ap-1870	38	14	(	(	PUNCT
ap-1870	38	15	or	or	CCONJ
ap-1870	38	16	higher	high	ADJ
ap-1870	38	17	)	)	PUNCT
ap-1870	38	18	differential	differential	NOUN
ap-1870	38	19	approximation	approximation	NOUN
ap-1870	38	20	has	have	VERB
ap-1870	38	21	the	the	DET
ap-1870	38	22	“	"	PUNCT
ap-1870	38	23	best	good	ADJ
ap-1870	38	24	”	"	PUNCT
ap-1870	38	25	symmetry	symmetry	NOUN
ap-1870	38	26	properties	property	NOUN
ap-1870	38	27	.	.	PUNCT
ap-1870	39	1	the	the	DET
ap-1870	39	2	second	second	ADJ
ap-1870	39	3	approach	approach	NOUN
ap-1870	39	4	,	,	PUNCT
ap-1870	39	5	the	the	DET
ap-1870	39	6	invariant	invariant	ADJ
ap-1870	39	7	discretization	discretization	NOUN
ap-1870	39	8	method	method	NOUN
ap-1870	39	9	is	be	AUX
ap-1870	39	10	part	part	NOUN
ap-1870	39	11	of	of	ADP
ap-1870	39	12	a	a	DET
ap-1870	39	13	program	program	NOUN
ap-1870	39	14	devoted	devote	VERB
ap-1870	39	15	to	to	ADP
ap-1870	39	16	the	the	DET
ap-1870	39	17	study	study	NOUN
ap-1870	39	18	of	of	ADP
ap-1870	39	19	continuous	continuous	ADJ
ap-1870	39	20	symmetries	symmetry	NOUN
ap-1870	39	21	of	of	ADP
ap-1870	39	22	discrete	discrete	ADJ
ap-1870	39	23	equations	equation	NOUN
ap-1870	39	24	,	,	PUNCT
ap-1870	39	25	i.e.	i.e.	X
ap-1870	39	26	the	the	DET
ap-1870	39	27	application	application	NOUN
ap-1870	39	28	of	of	ADP
ap-1870	39	29	lie	lie	NOUN
ap-1870	39	30	groups	group	NOUN
ap-1870	39	31	to	to	ADP
ap-1870	39	32	difference	difference	NOUN
ap-1870	39	33	equations	equation	NOUN
ap-1870	39	34	[	[	X
ap-1870	39	35	11–24	11–24	NUM
ap-1870	39	36	]	]	PUNCT
ap-1870	39	37	.	.	PUNCT
ap-1870	40	1	as	as	ADV
ap-1870	40	2	far	far	ADV
ap-1870	40	3	as	as	SCONJ
ap-1870	40	4	applications	application	NOUN
ap-1870	40	5	to	to	ADP
ap-1870	40	6	the	the	DET
ap-1870	40	7	numerical	numerical	ADJ
ap-1870	40	8	solutions	solution	NOUN
ap-1870	40	9	of	of	ADP
ap-1870	40	10	differential	differential	ADJ
ap-1870	40	11	equations	equation	NOUN
ap-1870	40	12	are	be	AUX
ap-1870	40	13	concerned	concern	VERB
ap-1870	40	14	,	,	PUNCT
ap-1870	40	15	the	the	DET
ap-1870	40	16	idea	idea	NOUN
ap-1870	40	17	,	,	PUNCT
ap-1870	40	18	originally	originally	ADV
ap-1870	40	19	due	due	ADJ
ap-1870	40	20	to	to	ADP
ap-1870	40	21	dorodnitsyn	dorodnitsyn	PROPN
ap-1870	40	22	[	[	X
ap-1870	40	23	12	12	NUM
ap-1870	40	24	,	,	PUNCT
ap-1870	40	25	13	13	NUM
ap-1870	40	26	]	]	PUNCT
ap-1870	40	27	,	,	PUNCT
ap-1870	40	28	is	be	AUX
ap-1870	40	29	to	to	PART
ap-1870	40	30	start	start	VERB
ap-1870	40	31	from	from	ADP
ap-1870	40	32	the	the	DET
ap-1870	40	33	differential	differential	ADJ
ap-1870	40	34	equation	equation	NOUN
ap-1870	40	35	,	,	PUNCT
ap-1870	40	36	its	its	PRON
ap-1870	40	37	symmetry	symmetry	NOUN
ap-1870	40	38	group	group	NOUN
ap-1870	40	39	g	g	PROPN
ap-1870	40	40	and	and	CCONJ
ap-1870	40	41	the	the	DET
ap-1870	40	42	lie	lie	NOUN
ap-1870	40	43	algebra	algebra	PROPN
ap-1870	40	44	l	l	NOUN
ap-1870	40	45	of	of	ADP
ap-1870	40	46	g	g	NOUN
ap-1870	40	47	,	,	PUNCT
ap-1870	40	48	realized	realize	VERB
ap-1870	40	49	by	by	ADP
ap-1870	40	50	vector	vector	NOUN
ap-1870	40	51	fields	field	NOUN
ap-1870	40	52	.	.	PUNCT
ap-1870	41	1	the	the	DET
ap-1870	41	2	differential	differential	ADJ
ap-1870	41	3	equation	equation	NOUN
ap-1870	41	4	can	can	AUX
ap-1870	41	5	then	then	ADV
ap-1870	41	6	be	be	AUX
ap-1870	41	7	expressed	express	VERB
ap-1870	41	8	in	in	ADP
ap-1870	41	9	terms	term	NOUN
ap-1870	41	10	of	of	ADP
ap-1870	41	11	differential	differential	ADJ
ap-1870	41	12	invariants	invariant	NOUN
ap-1870	41	13	of	of	ADP
ap-1870	41	14	g.	g.	PROPN
ap-1870	41	15	the	the	DET
ap-1870	41	16	differential	differential	ADJ
ap-1870	41	17	equation	equation	NOUN
ap-1870	41	18	is	be	AUX
ap-1870	41	19	then	then	ADV
ap-1870	41	20	approximated	approximate	VERB
ap-1870	41	21	by	by	ADP
ap-1870	41	22	a	a	DET
ap-1870	41	23	finite	finite	ADJ
ap-1870	41	24	difference	difference	NOUN
ap-1870	41	25	scheme	scheme	NOUN
ap-1870	41	26	that	that	PRON
ap-1870	41	27	is	be	AUX
ap-1870	41	28	constructed	construct	VERB
ap-1870	41	29	so	so	SCONJ
ap-1870	41	30	as	as	SCONJ
ap-1870	41	31	to	to	PART
ap-1870	41	32	be	be	AUX
ap-1870	41	33	invariant	invariant	ADJ
ap-1870	41	34	under	under	ADP
ap-1870	41	35	the	the	DET
ap-1870	41	36	same	same	ADJ
ap-1870	41	37	group	group	NOUN
ap-1870	41	38	g	g	NOUN
ap-1870	41	39	as	as	ADP
ap-1870	41	40	the	the	DET
ap-1870	41	41	differential	differential	ADJ
ap-1870	41	42	equation	equation	NOUN
ap-1870	41	43	.	.	PUNCT
ap-1870	42	1	the	the	DET
ap-1870	42	2	difference	difference	NOUN
ap-1870	42	3	scheme	scheme	NOUN
ap-1870	42	4	will	will	AUX
ap-1870	42	5	consist	consist	VERB
ap-1870	42	6	of	of	ADP
ap-1870	42	7	several	several	ADJ
ap-1870	42	8	equations	equation	NOUN
ap-1870	42	9	establishing	establish	VERB
ap-1870	42	10	relations	relation	NOUN
ap-1870	42	11	between	between	ADP
ap-1870	42	12	points	point	NOUN
ap-1870	42	13	in	in	ADP
ap-1870	42	14	the	the	DET
ap-1870	42	15	space	space	NOUN
ap-1870	42	16	of	of	ADP
ap-1870	42	17	independent	independent	ADJ
ap-1870	42	18	and	and	CCONJ
ap-1870	42	19	dependent	dependent	ADJ
ap-1870	42	20	variables	variable	NOUN
ap-1870	42	21	.	.	PUNCT
ap-1870	43	1	these	these	DET
ap-1870	43	2	equations	equation	NOUN
ap-1870	43	3	determine	determine	VERB
ap-1870	43	4	both	both	CCONJ
ap-1870	43	5	the	the	DET
ap-1870	43	6	evolution	evolution	NOUN
ap-1870	43	7	of	of	ADP
ap-1870	43	8	the	the	DET
ap-1870	43	9	dependent	dependent	ADJ
ap-1870	43	10	variables	variable	NOUN
ap-1870	43	11	and	and	CCONJ
ap-1870	43	12	the	the	DET
ap-1870	43	13	form	form	NOUN
ap-1870	43	14	of	of	ADP
ap-1870	43	15	the	the	DET
ap-1870	43	16	lattice	lattice	NOUN
ap-1870	43	17	.	.	PUNCT
ap-1870	44	1	the	the	DET
ap-1870	44	2	equations	equation	NOUN
ap-1870	44	3	are	be	AUX
ap-1870	44	4	written	write	VERB
ap-1870	44	5	in	in	ADP
ap-1870	44	6	terms	term	NOUN
ap-1870	44	7	of	of	ADP
ap-1870	44	8	group	group	NOUN
ap-1870	44	9	invariants	invariant	NOUN
ap-1870	44	10	of	of	ADP
ap-1870	44	11	the	the	DET
ap-1870	44	12	group	group	NOUN
ap-1870	44	13	g	g	NOUN
ap-1870	44	14	acting	act	VERB
ap-1870	44	15	via	via	ADP
ap-1870	44	16	its	its	PRON
ap-1870	44	17	prolongation	prolongation	NOUN
ap-1870	44	18	to	to	ADP
ap-1870	44	19	all	all	DET
ap-1870	44	20	points	point	NOUN
ap-1870	44	21	on	on	ADP
ap-1870	44	22	the	the	DET
ap-1870	44	23	lattice	lattice	NOUN
ap-1870	44	24	(	(	PUNCT
ap-1870	44	25	rather	rather	ADV
ap-1870	44	26	than	than	ADP
ap-1870	44	27	to	to	ADP
ap-1870	44	28	derivatives	derivative	NOUN
ap-1870	44	29	of	of	ADP
ap-1870	44	30	the	the	DET
ap-1870	44	31	dependent	dependent	ADJ
ap-1870	44	32	functions	function	NOUN
ap-1870	44	33	)	)	PUNCT
ap-1870	44	34	.	.	PUNCT
ap-1870	45	1	as	as	SCONJ
ap-1870	45	2	pointed	point	VERB
ap-1870	45	3	out	out	ADP
ap-1870	45	4	by	by	ADP
ap-1870	45	5	p.	p.	PROPN
ap-1870	45	6	olver	olver	PROPN
ap-1870	45	7	,	,	PUNCT
ap-1870	45	8	this	this	PRON
ap-1870	45	9	amounts	amount	VERB
ap-1870	45	10	to	to	ADP
ap-1870	45	11	prolonging	prolong	VERB
ap-1870	45	12	the	the	DET
ap-1870	45	13	group	group	NOUN
ap-1870	45	14	action	action	NOUN
ap-1870	45	15	to	to	ADP
ap-1870	45	16	“	"	PUNCT
ap-1870	45	17	multi	multi	ADJ
ap-1870	45	18	-	-	NOUN
ap-1870	45	19	space	space	NOUN
ap-1870	45	20	”	"	PUNCT
ap-1870	45	21	for	for	ADP
ap-1870	45	22	difference	difference	NOUN
ap-1870	45	23	equations	equation	NOUN
ap-1870	45	24	[	[	X
ap-1870	45	25	24	24	NUM
ap-1870	45	26	]	]	PUNCT
ap-1870	45	27	rather	rather	ADV
ap-1870	45	28	than	than	ADP
ap-1870	45	29	to	to	ADP
ap-1870	45	30	“	"	PUNCT
ap-1870	45	31	jet	jet	NOUN
ap-1870	45	32	space	space	NOUN
ap-1870	45	33	”	"	PUNCT
ap-1870	45	34	as	as	ADP
ap-1870	45	35	for	for	ADP
ap-1870	45	36	differential	differential	ADJ
ap-1870	45	37	equations	equation	NOUN
ap-1870	45	38	[	[	X
ap-1870	45	39	25	25	NUM
ap-1870	45	40	]	]	PUNCT
ap-1870	45	41	.	.	PUNCT
ap-1870	46	1	the	the	DET
ap-1870	46	2	purpose	purpose	NOUN
ap-1870	46	3	of	of	ADP
ap-1870	46	4	this	this	DET
ap-1870	46	5	paper	paper	NOUN
ap-1870	46	6	is	be	AUX
ap-1870	46	7	to	to	PART
ap-1870	46	8	compare	compare	VERB
ap-1870	46	9	the	the	DET
ap-1870	46	10	two	two	NUM
ap-1870	46	11	different	different	ADJ
ap-1870	46	12	methods	method	NOUN
ap-1870	46	13	of	of	ADP
ap-1870	46	14	incorporating	incorporate	VERB
ap-1870	46	15	lie	lie	NOUN
ap-1870	46	16	symmetries	symmetry	NOUN
ap-1870	46	17	into	into	ADP
ap-1870	46	18	the	the	DET
ap-1870	46	19	numerical	numerical	ADJ
ap-1870	46	20	analysis	analysis	NOUN
ap-1870	46	21	of	of	ADP
ap-1870	46	22	differential	differential	ADJ
ap-1870	46	23	equations	equation	NOUN
ap-1870	46	24	.	.	PUNCT
ap-1870	47	1	for	for	ADP
ap-1870	47	2	simplicity	simplicity	NOUN
ap-1870	47	3	we	we	PRON
ap-1870	47	4	restrict	restrict	VERB
ap-1870	47	5	ourselves	ourselves	PRON
ap-1870	47	6	to	to	ADP
ap-1870	47	7	the	the	DET
ap-1870	47	8	case	case	NOUN
ap-1870	47	9	of	of	ADP
ap-1870	47	10	odes	ode	NOUN
ap-1870	47	11	and	and	CCONJ
ap-1870	47	12	analyze	analyze	VERB
ap-1870	47	13	difference	difference	NOUN
ap-1870	47	14	schemes	scheme	NOUN
ap-1870	47	15	that	that	PRON
ap-1870	47	16	were	be	AUX
ap-1870	47	17	used	use	VERB
ap-1870	47	18	in	in	ADP
ap-1870	47	19	recent	recent	ADJ
ap-1870	47	20	articles	article	NOUN
ap-1870	47	21	[	[	X
ap-1870	47	22	26–28	26–28	X
ap-1870	47	23	]	]	PUNCT
ap-1870	47	24	to	to	PART
ap-1870	47	25	solve	solve	VERB
ap-1870	47	26	numerically	numerically	ADV
ap-1870	47	27	some	some	DET
ap-1870	47	28	third	third	ADJ
ap-1870	47	29	order	order	NOUN
ap-1870	47	30	nonlinear	nonlinear	ADJ
ap-1870	47	31	odes	ode	NOUN
ap-1870	47	32	with	with	ADP
ap-1870	47	33	three	three	NUM
ap-1870	47	34	or	or	CCONJ
ap-1870	47	35	four	four	NUM
ap-1870	47	36	dimensional	dimensional	ADJ
ap-1870	47	37	symmetry	symmetry	NOUN
ap-1870	47	38	algebras	algebra	NOUN
ap-1870	47	39	.	.	PUNCT
ap-1870	48	1	in	in	ADP
ap-1870	48	2	this	this	DET
ap-1870	48	3	article	article	NOUN
ap-1870	48	4	we	we	PRON
ap-1870	48	5	take	take	VERB
ap-1870	48	6	invariant	invariant	ADJ
ap-1870	48	7	difference	difference	NOUN
ap-1870	48	8	schemes	scheme	NOUN
ap-1870	48	9	(	(	PUNCT
ap-1870	48	10	on	on	ADP
ap-1870	48	11	symmetry	symmetry	NOUN
ap-1870	48	12	adapted	adapt	VERB
ap-1870	48	13	lattices	lattice	NOUN
ap-1870	48	14	)	)	PUNCT
ap-1870	48	15	and	and	CCONJ
ap-1870	48	16	construct	construct	VERB
ap-1870	48	17	its	its	PRON
ap-1870	48	18	first	first	ADJ
ap-1870	48	19	differential	differential	ADJ
ap-1870	48	20	approximation	approximation	NOUN
ap-1870	48	21	.	.	PUNCT
ap-1870	49	1	we	we	PRON
ap-1870	49	2	then	then	ADV
ap-1870	49	3	verify	verify	VERB
ap-1870	49	4	that	that	SCONJ
ap-1870	49	5	in	in	ADP
ap-1870	49	6	all	all	DET
ap-1870	49	7	examples	example	NOUN
ap-1870	49	8	this	this	DET
ap-1870	49	9	first	first	ADJ
ap-1870	49	10	differential	differential	ADJ
ap-1870	49	11	approximation	approximation	NOUN
ap-1870	49	12	is	be	AUX
ap-1870	49	13	invariant	invariant	ADJ
ap-1870	49	14	under	under	ADP
ap-1870	49	15	the	the	DET
ap-1870	49	16	entire	entire	ADJ
ap-1870	49	17	symmetry	symmetry	NOUN
ap-1870	49	18	group	group	NOUN
ap-1870	49	19	g.	g.	PROPN
ap-1870	49	20	2	2	NUM
ap-1870	49	21	.	.	PUNCT
ap-1870	49	22	differential	differential	ADJ
ap-1870	49	23	approximations	approximation	NOUN
ap-1870	49	24	of	of	ADP
ap-1870	49	25	ordinary	ordinary	ADJ
ap-1870	49	26	difference	difference	NOUN
ap-1870	49	27	equations	equation	NOUN
ap-1870	49	28	and	and	CCONJ
ap-1870	49	29	invariant	invariant	ADJ
ap-1870	49	30	discretization	discretization	NOUN
ap-1870	49	31	of	of	ADP
ap-1870	49	32	odes	ode	NOUN
ap-1870	49	33	.	.	PUNCT
ap-1870	50	1	let	let	VERB
ap-1870	50	2	us	we	PRON
ap-1870	50	3	consider	consider	VERB
ap-1870	50	4	the	the	DET
ap-1870	50	5	case	case	NOUN
ap-1870	50	6	of	of	ADP
ap-1870	50	7	a	a	DET
ap-1870	50	8	third	third	ADJ
ap-1870	50	9	order	order	NOUN
ap-1870	50	10	ode	ode	PROPN
ap-1870	50	11	e	e	PROPN
ap-1870	50	12	≡	≡	PROPN
ap-1870	50	13	e(x	e(x	PROPN
ap-1870	50	14	,	,	PUNCT
ap-1870	50	15	y	y	PROPN
ap-1870	50	16	,	,	PUNCT
ap-1870	50	17	y′	y′	NUM
ap-1870	50	18	,	,	PUNCT
ap-1870	50	19	y′′	y′′	PROPN
ap-1870	50	20	,	,	PUNCT
ap-1870	50	21	y′′′	y′′′	PROPN
ap-1870	50	22	)	)	PUNCT
ap-1870	50	23	=	=	SYM
ap-1870	50	24	0	0	NUM
ap-1870	50	25	,	,	PUNCT
ap-1870	50	26	(	(	PUNCT
ap-1870	50	27	4	4	NUM
ap-1870	50	28	)	)	PUNCT
ap-1870	50	29	(	(	PUNCT
ap-1870	50	30	the	the	DET
ap-1870	50	31	generalization	generalization	NOUN
ap-1870	50	32	to	to	PART
ap-1870	50	33	order	order	VERB
ap-1870	50	34	n	n	PRON
ap-1870	50	35	≥	≥	NOUN
ap-1870	50	36	3	3	NUM
ap-1870	50	37	is	be	AUX
ap-1870	50	38	straightforward	straightforward	ADJ
ap-1870	50	39	)	)	PUNCT
ap-1870	50	40	.	.	PUNCT
ap-1870	51	1	we	we	PRON
ap-1870	51	2	can	can	AUX
ap-1870	51	3	approximate	approximate	VERB
ap-1870	51	4	(	(	PUNCT
ap-1870	51	5	4	4	NUM
ap-1870	51	6	)	)	PUNCT
ap-1870	51	7	on	on	ADP
ap-1870	51	8	a	a	DET
ap-1870	51	9	4	4	NUM
ap-1870	51	10	point	point	NOUN
ap-1870	51	11	stencil	stencil	NOUN
ap-1870	51	12	with	with	ADP
ap-1870	51	13	points	point	NOUN
ap-1870	51	14	(	(	PUNCT
ap-1870	51	15	xk	xk	PROPN
ap-1870	51	16	,	,	PUNCT
ap-1870	51	17	yk	yk	PROPN
ap-1870	51	18	)	)	PUNCT
ap-1870	51	19	,	,	PUNCT
ap-1870	51	20	(	(	PUNCT
ap-1870	51	21	k	k	X
ap-1870	51	22	=	=	SYM
ap-1870	51	23	n−1	n−1	PROPN
ap-1870	51	24	,	,	PUNCT
ap-1870	51	25	n	n	CCONJ
ap-1870	51	26	,	,	PUNCT
ap-1870	51	27	n+1	n+1	PROPN
ap-1870	51	28	,	,	PUNCT
ap-1870	51	29	n+2	n+2	PRON
ap-1870	51	30	)	)	PUNCT
ap-1870	51	31	.	.	PUNCT
ap-1870	52	1	alternative	alternative	ADJ
ap-1870	52	2	coordinates	coordinate	NOUN
ap-1870	52	3	on	on	ADP
ap-1870	52	4	the	the	DET
ap-1870	52	5	stencil	stencil	PROPN
ap-1870	52	6	are	be	AUX
ap-1870	52	7	the	the	DET
ap-1870	52	8	coordinates	coordinate	NOUN
ap-1870	52	9	of	of	ADP
ap-1870	52	10	one	one	NUM
ap-1870	52	11	reference	reference	NOUN
ap-1870	52	12	point	point	NOUN
ap-1870	52	13	,	,	PUNCT
ap-1870	52	14	say	say	VERB
ap-1870	52	15	(	(	PUNCT
ap-1870	52	16	xn	xn	PROPN
ap-1870	52	17	,	,	PUNCT
ap-1870	52	18	yn	yn	PROPN
ap-1870	52	19	)	)	PUNCT
ap-1870	52	20	,	,	PUNCT
ap-1870	52	21	the	the	DET
ap-1870	52	22	distances	distance	NOUN
ap-1870	52	23	between	between	ADP
ap-1870	52	24	the	the	DET
ap-1870	52	25	points	point	NOUN
ap-1870	52	26	,	,	PUNCT
ap-1870	52	27	and	and	CCONJ
ap-1870	52	28	the	the	DET
ap-1870	52	29	discrete	discrete	ADJ
ap-1870	52	30	derivatives	derivative	NOUN
ap-1870	52	31	up	up	ADP
ap-1870	52	32	to	to	PART
ap-1870	52	33	order	order	VERB
ap-1870	52	34	3	3	NUM
ap-1870	52	35	,	,	PUNCT
ap-1870	52	36	{	{	PUNCT
ap-1870	52	37	xn	xn	PROPN
ap-1870	52	38	,	,	PUNCT
ap-1870	52	39	yn	yn	PROPN
ap-1870	52	40	,	,	PUNCT
ap-1870	52	41	hn+k	hn+k	PROPN
ap-1870	53	1	=	=	PUNCT
ap-1870	53	2	xn+k	xn+k	PROPN
ap-1870	53	3	−	−	PROPN
ap-1870	53	4	xn+k−1	xn+k−1	PROPN
ap-1870	53	5	,	,	PUNCT
ap-1870	53	6	p	p	X
ap-1870	53	7	(	(	PUNCT
ap-1870	53	8	1	1	NUM
ap-1870	53	9	)	)	PUNCT
ap-1870	53	10	n+1	n+1	PROPN
ap-1870	54	1	=	=	SYM
ap-1870	54	2	yn+1	yn+1	PROPN
ap-1870	54	3	−	−	PROPN
ap-1870	54	4	yn	yn	INTJ
ap-1870	54	5	xn+1	xn+1	PROPN
ap-1870	55	1	−	−	PROPN
ap-1870	55	2	xn	xn	PROPN
ap-1870	55	3	,	,	PUNCT
ap-1870	55	4	p	p	X
ap-1870	55	5	(	(	PUNCT
ap-1870	55	6	2	2	NUM
ap-1870	55	7	)	)	PUNCT
ap-1870	55	8	n+2	n+2	NUM
ap-1870	56	1	=	=	SYM
ap-1870	56	2	2	2	NUM
ap-1870	56	3	p	p	NOUN
ap-1870	56	4	(	(	PUNCT
ap-1870	56	5	1	1	NUM
ap-1870	56	6	)	)	PUNCT
ap-1870	56	7	n+2	n+2	NOUN
ap-1870	57	1	−	−	PROPN
ap-1870	57	2	p	p	X
ap-1870	57	3	(	(	PUNCT
ap-1870	57	4	1	1	NUM
ap-1870	57	5	)	)	PUNCT
ap-1870	57	6	n+1	n+1	PROPN
ap-1870	57	7	xn+2	xn+2	NUM
ap-1870	57	8	−	−	NOUN
ap-1870	58	1	xn	xn	INTJ
ap-1870	58	2	,	,	PUNCT
ap-1870	58	3	p	p	X
ap-1870	58	4	(	(	PUNCT
ap-1870	58	5	3	3	NUM
ap-1870	58	6	)	)	PUNCT
ap-1870	58	7	n+3	n+3	PROPN
ap-1870	58	8	=	=	SYM
ap-1870	58	9	3	3	NUM
ap-1870	58	10	p	p	NOUN
ap-1870	58	11	(	(	PUNCT
ap-1870	58	12	2	2	NUM
ap-1870	58	13	)	)	PUNCT
ap-1870	58	14	n+3	n+3	PROPN
ap-1870	58	15	−	−	PROPN
ap-1870	59	1	p	p	NOUN
ap-1870	59	2	(	(	PUNCT
ap-1870	59	3	2	2	NUM
ap-1870	59	4	)	)	PUNCT
ap-1870	59	5	n+2	n+2	PRON
ap-1870	59	6	xn+3	xn+3	PROPN
ap-1870	60	1	−	−	PROPN
ap-1870	60	2	xn	xn	PROPN
ap-1870	60	3	}	}	PUNCT
ap-1870	60	4	.	.	PUNCT
ap-1870	61	1	(	(	PUNCT
ap-1870	61	2	5	5	X
ap-1870	61	3	)	)	PUNCT
ap-1870	61	4	the	the	DET
ap-1870	61	5	one	one	NUM
ap-1870	61	6	-	-	PUNCT
ap-1870	61	7	dimensional	dimensional	ADJ
ap-1870	61	8	lattice	lattice	NOUN
ap-1870	61	9	can	can	AUX
ap-1870	61	10	be	be	AUX
ap-1870	61	11	chosen	choose	VERB
ap-1870	61	12	to	to	PART
ap-1870	61	13	be	be	AUX
ap-1870	61	14	uniform	uniform	ADJ
ap-1870	61	15	and	and	CCONJ
ap-1870	61	16	then	then	ADV
ap-1870	61	17	hn+1	hn+1	PROPN
ap-1870	62	1	=	=	SYM
ap-1870	62	2	hn	hn	PROPN
ap-1870	62	3	≡	≡	PROPN
ap-1870	62	4	h	h	PROPN
ap-1870	62	5	,	,	PUNCT
ap-1870	62	6	(	(	PUNCT
ap-1870	62	7	6	6	NUM
ap-1870	62	8	)	)	PUNCT
ap-1870	62	9	or	or	CCONJ
ap-1870	62	10	some	some	DET
ap-1870	62	11	other	other	ADJ
ap-1870	62	12	distribution	distribution	NOUN
ap-1870	62	13	of	of	ADP
ap-1870	62	14	points	point	NOUN
ap-1870	62	15	can	can	AUX
ap-1870	62	16	be	be	AUX
ap-1870	62	17	chosen	choose	VERB
ap-1870	62	18	.	.	PUNCT
ap-1870	63	1	the	the	DET
ap-1870	63	2	lie	lie	NOUN
ap-1870	63	3	point	point	NOUN
ap-1870	63	4	symmetry	symmetry	NOUN
ap-1870	63	5	group	group	NOUN
ap-1870	63	6	g	g	PROPN
ap-1870	63	7	transforms	transform	VERB
ap-1870	63	8	the	the	DET
ap-1870	63	9	variables	variable	NOUN
ap-1870	63	10	(	(	PUNCT
ap-1870	63	11	x	x	X
ap-1870	63	12	,	,	PUNCT
ap-1870	63	13	y	y	NOUN
ap-1870	63	14	)	)	PUNCT
ap-1870	63	15	into	into	ADP
ap-1870	63	16	(	(	PUNCT
ap-1870	63	17	x̃	x̃	PROPN
ap-1870	63	18	,	,	PUNCT
ap-1870	63	19	ỹ	ỹ	PROPN
ap-1870	63	20	)	)	PUNCT
ap-1870	64	1	=	=	NOUN
ap-1870	64	2	(	(	PUNCT
ap-1870	64	3	λ(x	λ(x	X
ap-1870	64	4	,	,	PUNCT
ap-1870	64	5	y),ω(x	y),ω(x	X
ap-1870	64	6	,	,	PUNCT
ap-1870	64	7	y	y	NOUN
ap-1870	64	8	)	)	PUNCT
ap-1870	64	9	)	)	PUNCT
ap-1870	64	10	and	and	CCONJ
ap-1870	64	11	its	its	PRON
ap-1870	64	12	lie	lie	NOUN
ap-1870	64	13	point	point	NOUN
ap-1870	64	14	symmetry	symmetry	NOUN
ap-1870	64	15	algebra	algebra	NOUN
ap-1870	64	16	l	l	NOUN
ap-1870	64	17	is	be	AUX
ap-1870	64	18	represented	represent	VERB
ap-1870	64	19	by	by	ADP
ap-1870	64	20	vector	vector	NOUN
ap-1870	64	21	fields	field	NOUN
ap-1870	64	22	of	of	ADP
ap-1870	64	23	the	the	DET
ap-1870	64	24	form	form	NOUN
ap-1870	64	25	x̂µ	x̂µ	PROPN
ap-1870	64	26	=	=	PUNCT
ap-1870	64	27	ξµ(x	ξµ(x	X
ap-1870	64	28	,	,	PUNCT
ap-1870	64	29	y)∂x	y)∂x	PROPN
ap-1870	64	30	+	+	CCONJ
ap-1870	64	31	φµ(x	φµ(x	NUM
ap-1870	64	32	,	,	PUNCT
ap-1870	64	33	y)∂y	y)∂y	PROPN
ap-1870	64	34	,	,	PUNCT
ap-1870	64	35	1	1	NUM
ap-1870	64	36	≤	≤	NUM
ap-1870	64	37	µ	µ	PRON
ap-1870	64	38	≤	≤	NUM
ap-1870	64	39	diml	diml	NOUN
ap-1870	64	40	.	.	PUNCT
ap-1870	65	1	(	(	PUNCT
ap-1870	65	2	7	7	X
ap-1870	65	3	)	)	PUNCT
ap-1870	65	4	the	the	DET
ap-1870	65	5	vector	vector	NOUN
ap-1870	65	6	fields	field	NOUN
ap-1870	65	7	must	must	AUX
ap-1870	65	8	be	be	AUX
ap-1870	65	9	prolonged	prolong	VERB
ap-1870	65	10	in	in	ADP
ap-1870	65	11	the	the	DET
ap-1870	65	12	standard	standard	ADJ
ap-1870	65	13	manner	manner	NOUN
ap-1870	65	14	[	[	X
ap-1870	65	15	1	1	NUM
ap-1870	65	16	]	]	PUNCT
ap-1870	65	17	to	to	ADP
ap-1870	65	18	derivatives	derivative	NOUN
ap-1870	66	1	prx̂µ	prx̂µ	NOUN
ap-1870	66	2	=	=	PUNCT
ap-1870	66	3	x̂µ	x̂µ	PROPN
ap-1870	67	1	+	+	CCONJ
ap-1870	67	2	φx(x	φx(x	NUM
ap-1870	67	3	,	,	PUNCT
ap-1870	67	4	y	y	PROPN
ap-1870	67	5	,	,	PUNCT
ap-1870	67	6	yx)∂yx	yx)∂yx	PROPN
ap-1870	67	7	+	+	CCONJ
ap-1870	67	8	φxx(x	φxx(x	PROPN
ap-1870	67	9	,	,	PUNCT
ap-1870	67	10	y	y	PROPN
ap-1870	67	11	,	,	PUNCT
ap-1870	67	12	yx	yx	NOUN
ap-1870	67	13	,	,	PUNCT
ap-1870	67	14	yxx)∂yxx	yxx)∂yxx	PROPN
ap-1870	67	15	+	+	NUM
ap-1870	67	16	·	·	PUNCT
ap-1870	67	17	·	·	PUNCT
ap-1870	67	18	·	·	PUNCT
ap-1870	67	19	,	,	PUNCT
ap-1870	67	20	(	(	PUNCT
ap-1870	67	21	8)	8)	NUM
ap-1870	67	22	when	when	SCONJ
ap-1870	67	23	acting	act	VERB
ap-1870	67	24	on	on	ADP
ap-1870	67	25	a	a	DET
ap-1870	67	26	differential	differential	ADJ
ap-1870	67	27	equation	equation	NOUN
ap-1870	67	28	,	,	PUNCT
ap-1870	67	29	or	or	CCONJ
ap-1870	67	30	to	to	ADP
ap-1870	67	31	all	all	DET
ap-1870	67	32	points	point	NOUN
ap-1870	67	33	when	when	SCONJ
ap-1870	67	34	acting	act	VERB
ap-1870	67	35	on	on	ADP
ap-1870	67	36	a	a	DET
ap-1870	67	37	difference	difference	NOUN
ap-1870	67	38	scheme	scheme	NOUN
ap-1870	68	1	[	[	X
ap-1870	68	2	15	15	NUM
ap-1870	68	3	,	,	PUNCT
ap-1870	68	4	18	18	NUM
ap-1870	68	5	,	,	PUNCT
ap-1870	68	6	20	20	NUM
ap-1870	68	7	]	]	PUNCT
ap-1870	68	8	pr∆x̂µ	pr∆x̂µ	PROPN
ap-1870	69	1	=	=	PUNCT
ap-1870	69	2	∑	∑	PUNCT
ap-1870	69	3	i	i	PRON
ap-1870	69	4	[	[	PUNCT
ap-1870	69	5	ξµ(xi	ξµ(xi	PROPN
ap-1870	69	6	,	,	PUNCT
ap-1870	69	7	yi)∂xi	yi)∂xi	PROPN
ap-1870	69	8	+	+	CCONJ
ap-1870	69	9	φµ(xi	φµ(xi	PROPN
ap-1870	69	10	,	,	PUNCT
ap-1870	69	11	yi)∂yi	yi)∂yi	NOUN
ap-1870	69	12	]	]	PUNCT
ap-1870	69	13	.	.	PUNCT
ap-1870	70	1	(	(	PUNCT
ap-1870	70	2	9	9	X
ap-1870	70	3	)	)	PUNCT
ap-1870	70	4	in	in	ADP
ap-1870	70	5	the	the	DET
ap-1870	70	6	differential	differential	ADJ
ap-1870	70	7	approximation	approximation	NOUN
ap-1870	70	8	method	method	NOUN
ap-1870	70	9	we	we	PRON
ap-1870	70	10	start	start	VERB
ap-1870	70	11	with	with	ADP
ap-1870	70	12	a	a	DET
ap-1870	70	13	difference	difference	NOUN
ap-1870	70	14	equation	equation	NOUN
ap-1870	70	15	,	,	PUNCT
ap-1870	70	16	usually	usually	ADV
ap-1870	70	17	on	on	ADP
ap-1870	70	18	a	a	DET
ap-1870	70	19	uniform	uniform	ADJ
ap-1870	70	20	lattice	lattice	NOUN
ap-1870	70	21	(	(	PUNCT
ap-1870	70	22	6	6	NUM
ap-1870	70	23	)	)	PUNCT
ap-1870	70	24	e∆(xn	e∆(xn	NOUN
ap-1870	70	25	,	,	PUNCT
ap-1870	70	26	hn+1	hn+1	PROPN
ap-1870	70	27	,	,	PUNCT
ap-1870	70	28	hn+2	hn+2	NOUN
ap-1870	70	29	,	,	PUNCT
ap-1870	70	30	yn	yn	PROPN
ap-1870	70	31	,	,	PUNCT
ap-1870	70	32	p	p	X
ap-1870	70	33	(	(	PUNCT
ap-1870	70	34	1	1	NUM
ap-1870	70	35	)	)	PUNCT
ap-1870	70	36	n+1	n+1	PROPN
ap-1870	70	37	,	,	PUNCT
ap-1870	70	38	p	p	X
ap-1870	70	39	(	(	PUNCT
ap-1870	70	40	2	2	NUM
ap-1870	70	41	)	)	PUNCT
ap-1870	70	42	n+2	n+2	NUM
ap-1870	70	43	,	,	PUNCT
ap-1870	70	44	p	p	X
ap-1870	70	45	(	(	PUNCT
ap-1870	70	46	3	3	NUM
ap-1870	70	47	)	)	PUNCT
ap-1870	70	48	n+3	n+3	NUM
ap-1870	70	49	)	)	PUNCT
ap-1870	70	50	=	=	SYM
ap-1870	71	1	0	0	NUM
ap-1870	71	2	,	,	PUNCT
ap-1870	71	3	(	(	PUNCT
ap-1870	71	4	10	10	NUM
ap-1870	71	5	)	)	PUNCT
ap-1870	72	1	and	and	CCONJ
ap-1870	72	2	expand	expand	VERB
ap-1870	72	3	it	it	PRON
ap-1870	72	4	into	into	ADP
ap-1870	72	5	a	a	DET
ap-1870	72	6	taylor	taylor	PROPN
ap-1870	72	7	series	series	NOUN
ap-1870	72	8	in	in	ADP
ap-1870	72	9	the	the	DET
ap-1870	72	10	spacing	spacing	ADJ
ap-1870	72	11	h	h	NOUN
ap-1870	72	12	:	:	PUNCT
ap-1870	72	13	e∆	e∆	PROPN
ap-1870	72	14	=	=	SYM
ap-1870	72	15	e0	e0	PROPN
ap-1870	72	16	+	+	CCONJ
ap-1870	72	17	he1	he1	PROPN
ap-1870	73	1	+	+	CCONJ
ap-1870	73	2	h2e2	h2e2	PROPN
ap-1870	73	3	+	+	X
ap-1870	74	1	·	·	PUNCT
ap-1870	74	2	·	·	PUNCT
ap-1870	74	3	·	·	PUNCT
ap-1870	74	4	=	=	SYM
ap-1870	74	5	0	0	X
ap-1870	74	6	.	.	PUNCT
ap-1870	75	1	(	(	PUNCT
ap-1870	75	2	11	11	NUM
ap-1870	75	3	)	)	PUNCT
ap-1870	75	4	for	for	ADP
ap-1870	75	5	any	any	DET
ap-1870	75	6	difference	difference	NOUN
ap-1870	75	7	equation	equation	NOUN
ap-1870	75	8	approximating	approximate	VERB
ap-1870	75	9	the	the	DET
ap-1870	75	10	differential	differential	ADJ
ap-1870	75	11	equation	equation	NOUN
ap-1870	75	12	e0	e0	NOUN
ap-1870	75	13	=	=	PUNCT
ap-1870	75	14	0	0	NUM
ap-1870	75	15	the	the	DET
ap-1870	75	16	lowest	low	ADJ
ap-1870	75	17	order	order	NOUN
ap-1870	75	18	term	term	NOUN
ap-1870	75	19	will	will	AUX
ap-1870	75	20	be	be	AUX
ap-1870	75	21	invariant	invariant	ADJ
ap-1870	75	22	under	under	ADP
ap-1870	75	23	the	the	DET
ap-1870	75	24	group	group	NOUN
ap-1870	75	25	g.	g.	PROPN
ap-1870	75	26	different	different	ADJ
ap-1870	75	27	schemes	scheme	NOUN
ap-1870	75	28	(	(	PUNCT
ap-1870	75	29	10	10	NUM
ap-1870	75	30	)	)	PUNCT
ap-1870	75	31	can	can	AUX
ap-1870	75	32	then	then	ADV
ap-1870	75	33	be	be	AUX
ap-1870	75	34	compared	compare	VERB
ap-1870	75	35	with	with	ADP
ap-1870	75	36	respect	respect	NOUN
ap-1870	75	37	to	to	ADP
ap-1870	75	38	the	the	DET
ap-1870	75	39	invariance	invariance	NOUN
ap-1870	75	40	of	of	ADP
ap-1870	75	41	the	the	DET
ap-1870	75	42	first	first	ADJ
ap-1870	75	43	differential	differential	ADJ
ap-1870	75	44	approximation	approximation	NOUN
ap-1870	75	45	e0	e0	PROPN
ap-1870	75	46	+	+	CCONJ
ap-1870	75	47	he1	he1	PROPN
ap-1870	75	48	=	=	SYM
ap-1870	75	49	0	0	PROPN
ap-1870	75	50	,	,	PUNCT
ap-1870	75	51	(	(	PUNCT
ap-1870	75	52	12	12	NUM
ap-1870	75	53	)	)	PUNCT
ap-1870	75	54	or	or	CCONJ
ap-1870	75	55	of	of	ADP
ap-1870	75	56	some	some	DET
ap-1870	75	57	higher	high	ADJ
ap-1870	75	58	order	order	NOUN
ap-1870	75	59	differential	differential	ADJ
ap-1870	75	60	approximations	approximation	NOUN
ap-1870	75	61	.	.	PUNCT
ap-1870	76	1	better	well	ADJ
ap-1870	76	2	results	result	NOUN
ap-1870	76	3	can	can	AUX
ap-1870	76	4	be	be	AUX
ap-1870	76	5	expected	expect	VERB
ap-1870	76	6	for	for	ADP
ap-1870	76	7	schemes	scheme	NOUN
ap-1870	76	8	for	for	ADP
ap-1870	76	9	which	which	PRON
ap-1870	76	10	(	(	PUNCT
ap-1870	76	11	12	12	NUM
ap-1870	76	12	)	)	PUNCT
ap-1870	76	13	is	be	AUX
ap-1870	76	14	invariant	invariant	ADJ
ap-1870	76	15	under	under	ADP
ap-1870	76	16	all	all	PRON
ap-1870	76	17	of	of	ADP
ap-1870	76	18	g	g	NOUN
ap-1870	76	19	or	or	CCONJ
ap-1870	76	20	under	under	ADP
ap-1870	76	21	some	some	DET
ap-1870	76	22	subgroup	subgroup	NOUN
ap-1870	76	23	g0	g0	PROPN
ap-1870	76	24	⊂	⊂	PROPN
ap-1870	76	25	g	g	PROPN
ap-1870	76	26	that	that	PRON
ap-1870	76	27	is	be	AUX
ap-1870	76	28	relevant	relevant	ADJ
ap-1870	76	29	for	for	ADP
ap-1870	76	30	the	the	DET
ap-1870	76	31	problem	problem	NOUN
ap-1870	76	32	.	.	PUNCT
ap-1870	77	1	when	when	SCONJ
ap-1870	77	2	studying	study	VERB
ap-1870	77	3	the	the	DET
ap-1870	77	4	invariance	invariance	NOUN
ap-1870	77	5	of	of	ADP
ap-1870	77	6	(	(	PUNCT
ap-1870	77	7	12	12	NUM
ap-1870	77	8	)	)	PUNCT
ap-1870	77	9	it	it	PRON
ap-1870	77	10	must	must	AUX
ap-1870	77	11	be	be	AUX
ap-1870	77	12	remembered	remember	VERB
ap-1870	77	13	that	that	SCONJ
ap-1870	77	14	the	the	DET
ap-1870	77	15	prolongations	prolongation	NOUN
ap-1870	77	16	of	of	ADP
ap-1870	77	17	x̂µ	x̂µ	PRON
ap-1870	77	18	also	also	ADV
ap-1870	77	19	act	act	VERB
ap-1870	77	20	on	on	ADP
ap-1870	77	21	the	the	DET
ap-1870	77	22	lattice	lattice	PROPN
ap-1870	77	23	parameters	parameter	NOUN
ap-1870	77	24	h.	h.	PROPN
ap-1870	77	25	439	439	NUM
ap-1870	77	26	d.	d.	PROPN
ap-1870	77	27	levi	levi	PROPN
ap-1870	77	28	,	,	PUNCT
ap-1870	77	29	p.	p.	PROPN
ap-1870	77	30	winternitz	winternitz	PROPN
ap-1870	77	31	acta	acta	PROPN
ap-1870	77	32	polytechnica	polytechnica	PROPN
ap-1870	77	33	in	in	ADP
ap-1870	77	34	the	the	DET
ap-1870	77	35	invariant	invariant	ADJ
ap-1870	77	36	discretization	discretization	NOUN
ap-1870	77	37	method	method	NOUN
ap-1870	77	38	one	one	NUM
ap-1870	77	39	constructs	construct	VERB
ap-1870	77	40	an	an	DET
ap-1870	77	41	invariant	invariant	ADJ
ap-1870	77	42	difference	difference	NOUN
ap-1870	77	43	scheme	scheme	NOUN
ap-1870	77	44	e∆	e∆	PROPN
ap-1870	77	45	a	a	DET
ap-1870	77	46	(	(	PUNCT
ap-1870	77	47	xn	xn	PROPN
ap-1870	77	48	,	,	PUNCT
ap-1870	77	49	yn	yn	PROPN
ap-1870	77	50	,	,	PUNCT
ap-1870	77	51	hn	hn	PROPN
ap-1870	77	52	,	,	PUNCT
ap-1870	77	53	hn+1	hn+1	PROPN
ap-1870	77	54	,	,	PUNCT
ap-1870	77	55	hn+2	hn+2	NOUN
ap-1870	77	56	,	,	PUNCT
ap-1870	77	57	yn	yn	PROPN
ap-1870	77	58	,	,	PUNCT
ap-1870	77	59	p	p	X
ap-1870	77	60	(	(	PUNCT
ap-1870	77	61	1	1	NUM
ap-1870	77	62	)	)	PUNCT
ap-1870	77	63	n+1	n+1	PROPN
ap-1870	77	64	,	,	PUNCT
ap-1870	77	65	p	p	X
ap-1870	77	66	(	(	PUNCT
ap-1870	77	67	2	2	NUM
ap-1870	77	68	)	)	PUNCT
ap-1870	77	69	n+2	n+2	NUM
ap-1870	77	70	,	,	PUNCT
ap-1870	77	71	p	p	X
ap-1870	77	72	(	(	PUNCT
ap-1870	77	73	3	3	NUM
ap-1870	77	74	)	)	PUNCT
ap-1870	77	75	n+3	n+3	PROPN
ap-1870	77	76	)	)	PUNCT
ap-1870	78	1	=	=	SYM
ap-1870	78	2	0	0	NUM
ap-1870	78	3	,	,	PUNCT
ap-1870	78	4	a	a	DET
ap-1870	78	5	=	=	SYM
ap-1870	78	6	1	1	NUM
ap-1870	78	7	,	,	PUNCT
ap-1870	78	8	2	2	NUM
ap-1870	78	9	(	(	PUNCT
ap-1870	78	10	13	13	NUM
ap-1870	78	11	)	)	PUNCT
ap-1870	78	12	prx̂µe	prx̂µe	PROPN
ap-1870	78	13	∆	∆	PROPN
ap-1870	78	14	a	a	PRON
ap-1870	78	15	∣∣	∣∣	NUM
ap-1870	78	16	e∆	e∆	ADV
ap-1870	78	17	1	1	NUM
ap-1870	78	18	=	=	NOUN
ap-1870	78	19	0,e∆	0,e∆	NOUN
ap-1870	78	20	2	2	NUM
ap-1870	78	21	=	=	SYM
ap-1870	78	22	0	0	NUM
ap-1870	78	23	=	=	SYM
ap-1870	78	24	0	0	PROPN
ap-1870	78	25	.	.	PUNCT
ap-1870	79	1	(	(	PUNCT
ap-1870	79	2	14	14	NUM
ap-1870	79	3	)	)	PUNCT
ap-1870	79	4	the	the	DET
ap-1870	79	5	two	two	NUM
ap-1870	79	6	equations	equation	NOUN
ap-1870	79	7	(	(	PUNCT
ap-1870	79	8	13	13	NUM
ap-1870	79	9	)	)	PUNCT
ap-1870	79	10	determine	determine	VERB
ap-1870	79	11	both	both	CCONJ
ap-1870	79	12	the	the	DET
ap-1870	79	13	lattice	lattice	NOUN
ap-1870	79	14	and	and	CCONJ
ap-1870	79	15	the	the	DET
ap-1870	79	16	difference	difference	NOUN
ap-1870	79	17	equation	equation	NOUN
ap-1870	79	18	.	.	PUNCT
ap-1870	80	1	both	both	PRON
ap-1870	80	2	are	be	AUX
ap-1870	80	3	constructed	construct	VERB
ap-1870	80	4	out	out	ADP
ap-1870	80	5	of	of	ADP
ap-1870	80	6	the	the	DET
ap-1870	80	7	invariants	invariant	NOUN
ap-1870	80	8	of	of	ADP
ap-1870	80	9	the	the	DET
ap-1870	80	10	group	group	NOUN
ap-1870	80	11	g	g	PROPN
ap-1870	80	12	prolonged	prolong	VERB
ap-1870	80	13	to	to	ADP
ap-1870	80	14	the	the	DET
ap-1870	80	15	lattice	lattice	NOUN
ap-1870	80	16	as	as	SCONJ
ap-1870	80	17	indicated	indicate	VERB
ap-1870	80	18	in	in	ADP
ap-1870	80	19	eq	eq	ADP
ap-1870	80	20	.	.	PUNCT
ap-1870	81	1	(	(	PUNCT
ap-1870	81	2	14	14	NUM
ap-1870	81	3	)	)	PUNCT
ap-1870	81	4	.	.	PUNCT
ap-1870	82	1	thus	thus	ADV
ap-1870	82	2	,	,	PUNCT
ap-1870	82	3	the	the	DET
ap-1870	82	4	difference	difference	NOUN
ap-1870	82	5	scheme	scheme	NOUN
ap-1870	82	6	is	be	AUX
ap-1870	82	7	by	by	ADP
ap-1870	82	8	construction	construction	NOUN
ap-1870	82	9	invariant	invariant	ADJ
ap-1870	82	10	under	under	ADP
ap-1870	82	11	the	the	DET
ap-1870	82	12	entire	entire	ADJ
ap-1870	82	13	group	group	NOUN
ap-1870	82	14	g	g	NOUN
ap-1870	82	15	acting	act	VERB
ap-1870	82	16	on	on	ADP
ap-1870	82	17	the	the	DET
ap-1870	82	18	equation	equation	NOUN
ap-1870	82	19	and	and	CCONJ
ap-1870	82	20	lattice	lattice	NOUN
ap-1870	82	21	.	.	PUNCT
ap-1870	83	1	in	in	ADP
ap-1870	83	2	the	the	DET
ap-1870	83	3	continuous	continuous	ADJ
ap-1870	83	4	limit	limit	NOUN
ap-1870	83	5	we	we	PRON
ap-1870	83	6	have	have	VERB
ap-1870	83	7	e∆	e∆	ADP
ap-1870	83	8	1	1	NUM
ap-1870	83	9	=	=	SYM
ap-1870	83	10	e	e	PROPN
ap-1870	83	11	+	+	PROPN
ap-1870	83	12	hne	hne	X
ap-1870	83	13	(	(	PUNCT
ap-1870	83	14	1	1	NUM
ap-1870	83	15	)	)	PUNCT
ap-1870	83	16	1	1	NUM
ap-1870	83	17	+	+	NUM
ap-1870	83	18	hn+1e	hn+1e	NOUN
ap-1870	83	19	(	(	PUNCT
ap-1870	83	20	2	2	NUM
ap-1870	83	21	)	)	SYM
ap-1870	83	22	1	1	NUM
ap-1870	83	23	+	+	NUM
ap-1870	83	24	hn+2e	hn+2e	NOUN
ap-1870	83	25	(	(	PUNCT
ap-1870	83	26	3	3	NUM
ap-1870	83	27	)	)	PUNCT
ap-1870	83	28	1	1	NUM
ap-1870	84	1	+	+	CCONJ
ap-1870	84	2	h.o.t	h.o.t	ADJ
ap-1870	84	3	.	.	PROPN
ap-1870	84	4	,	,	PUNCT
ap-1870	84	5	(	(	PUNCT
ap-1870	84	6	15	15	NUM
ap-1870	84	7	)	)	PUNCT
ap-1870	84	8	e∆	e∆	ADV
ap-1870	84	9	2	2	NUM
ap-1870	84	10	=	=	SYM
ap-1870	84	11	0	0	PUNCT
ap-1870	85	1	+	+	CCONJ
ap-1870	85	2	hne	hne	PROPN
ap-1870	85	3	(	(	PUNCT
ap-1870	85	4	1	1	NUM
ap-1870	85	5	)	)	SYM
ap-1870	85	6	2	2	NUM
ap-1870	85	7	+	+	NUM
ap-1870	85	8	hn+1e	hn+1e	NOUN
ap-1870	85	9	(	(	PUNCT
ap-1870	85	10	2	2	NUM
ap-1870	85	11	)	)	SYM
ap-1870	85	12	2	2	NUM
ap-1870	86	1	+	+	SYM
ap-1870	86	2	hn+2e	hn+2e	NOUN
ap-1870	86	3	(	(	PUNCT
ap-1870	86	4	3	3	NUM
ap-1870	86	5	)	)	SYM
ap-1870	86	6	2	2	NUM
ap-1870	86	7	+	+	CCONJ
ap-1870	86	8	h.o.t	h.o.t	ADJ
ap-1870	86	9	..	..	PUNCT
ap-1870	86	10	(	(	PUNCT
ap-1870	86	11	16	16	NUM
ap-1870	86	12	)	)	PUNCT
ap-1870	86	13	the	the	DET
ap-1870	86	14	terms	term	NOUN
ap-1870	86	15	spelled	spell	VERB
ap-1870	86	16	out	out	ADP
ap-1870	86	17	in	in	ADP
ap-1870	86	18	(	(	PUNCT
ap-1870	86	19	15	15	NUM
ap-1870	86	20	)	)	PUNCT
ap-1870	86	21	correspond	correspond	VERB
ap-1870	86	22	to	to	ADP
ap-1870	86	23	the	the	DET
ap-1870	86	24	first	first	ADJ
ap-1870	86	25	differential	differential	ADJ
ap-1870	86	26	approximation	approximation	NOUN
ap-1870	86	27	.	.	PUNCT
ap-1870	87	1	since	since	SCONJ
ap-1870	87	2	the	the	DET
ap-1870	87	3	left	left	ADJ
ap-1870	87	4	hand	hand	NOUN
ap-1870	87	5	side	side	NOUN
ap-1870	87	6	of	of	ADP
ap-1870	87	7	(	(	PUNCT
ap-1870	87	8	15	15	NUM
ap-1870	87	9	)	)	PUNCT
ap-1870	87	10	,	,	PUNCT
ap-1870	87	11	(	(	PUNCT
ap-1870	87	12	16	16	NUM
ap-1870	87	13	)	)	PUNCT
ap-1870	87	14	is	be	AUX
ap-1870	87	15	invariant	invariant	ADJ
ap-1870	87	16	under	under	ADP
ap-1870	87	17	g	g	PROPN
ap-1870	87	18	,	,	PUNCT
ap-1870	87	19	the	the	DET
ap-1870	87	20	series	series	NOUN
ap-1870	87	21	on	on	ADP
ap-1870	87	22	the	the	DET
ap-1870	87	23	right	right	ADJ
ap-1870	87	24	hand	hand	NOUN
ap-1870	87	25	side	side	NOUN
ap-1870	87	26	must	must	AUX
ap-1870	87	27	also	also	ADV
ap-1870	87	28	be	be	AUX
ap-1870	87	29	invariant	invariant	ADJ
ap-1870	87	30	.	.	PUNCT
ap-1870	88	1	this	this	PRON
ap-1870	88	2	does	do	AUX
ap-1870	88	3	not	not	PART
ap-1870	88	4	guarantee	guarantee	VERB
ap-1870	88	5	that	that	SCONJ
ap-1870	88	6	the	the	DET
ap-1870	88	7	first	first	ADJ
ap-1870	88	8	(	(	PUNCT
ap-1870	88	9	or	or	CCONJ
ap-1870	88	10	n	n	CCONJ
ap-1870	88	11	-	-	PUNCT
ap-1870	88	12	th	th	NOUN
ap-1870	88	13	)	)	PUNCT
ap-1870	88	14	differential	differential	NOUN
ap-1870	88	15	approximation	approximation	NOUN
ap-1870	88	16	will	will	AUX
ap-1870	88	17	be	be	AUX
ap-1870	88	18	invariant	invariant	ADJ
ap-1870	88	19	.	.	PUNCT
ap-1870	89	1	in	in	ADP
ap-1870	89	2	the	the	DET
ap-1870	89	3	next	next	ADJ
ap-1870	89	4	three	three	NUM
ap-1870	89	5	sections	section	NOUN
ap-1870	89	6	we	we	PRON
ap-1870	89	7	will	will	AUX
ap-1870	89	8	show	show	VERB
ap-1870	89	9	on	on	ADP
ap-1870	89	10	examples	example	NOUN
ap-1870	89	11	that	that	SCONJ
ap-1870	89	12	the	the	DET
ap-1870	89	13	first	first	ADJ
ap-1870	89	14	differential	differential	ADJ
ap-1870	89	15	approximation	approximation	NOUN
ap-1870	89	16	is	be	AUX
ap-1870	89	17	indeed	indeed	ADV
ap-1870	89	18	invariant	invariant	ADJ
ap-1870	89	19	.	.	PUNCT
ap-1870	90	1	thus	thus	ADV
ap-1870	90	2	,	,	PUNCT
ap-1870	90	3	choosing	choose	VERB
ap-1870	90	4	an	an	DET
ap-1870	90	5	invariant	invariant	ADJ
ap-1870	90	6	difference	difference	NOUN
ap-1870	90	7	scheme	scheme	NOUN
ap-1870	90	8	guarantees	guarantee	NOUN
ap-1870	90	9	,	,	PUNCT
ap-1870	90	10	at	at	ADP
ap-1870	90	11	least	least	ADJ
ap-1870	90	12	in	in	ADP
ap-1870	90	13	the	the	DET
ap-1870	90	14	considered	consider	VERB
ap-1870	90	15	cases	case	NOUN
ap-1870	90	16	,	,	PUNCT
ap-1870	90	17	that	that	SCONJ
ap-1870	90	18	the	the	DET
ap-1870	90	19	aims	aim	NOUN
ap-1870	90	20	of	of	ADP
ap-1870	90	21	the	the	DET
ap-1870	90	22	differential	differential	ADJ
ap-1870	90	23	approximation	approximation	NOUN
ap-1870	90	24	method	method	NOUN
ap-1870	90	25	are	be	AUX
ap-1870	90	26	fully	fully	ADV
ap-1870	90	27	achieved	achieve	VERB
ap-1870	90	28	.	.	PUNCT
ap-1870	91	1	the	the	DET
ap-1870	91	2	examples	example	NOUN
ap-1870	91	3	are	be	AUX
ap-1870	91	4	all	all	PRON
ap-1870	91	5	third	third	ADJ
ap-1870	91	6	order	order	NOUN
ap-1870	91	7	odes	ode	VERB
ap-1870	91	8	with	with	ADP
ap-1870	91	9	3	3	NUM
ap-1870	91	10	or	or	CCONJ
ap-1870	91	11	4	4	NUM
ap-1870	91	12	dimensional	dimensional	ADJ
ap-1870	91	13	symmetry	symmetry	NOUN
ap-1870	91	14	groups	group	NOUN
ap-1870	91	15	.	.	PUNCT
ap-1870	92	1	in	in	ADP
ap-1870	92	2	each	each	DET
ap-1870	92	3	case	case	NOUN
ap-1870	92	4	we	we	PRON
ap-1870	92	5	write	write	VERB
ap-1870	92	6	an	an	DET
ap-1870	92	7	invariant	invariant	ADJ
ap-1870	92	8	difference	difference	NOUN
ap-1870	92	9	scheme	scheme	NOUN
ap-1870	92	10	of	of	ADP
ap-1870	92	11	the	the	DET
ap-1870	92	12	form	form	NOUN
ap-1870	92	13	(	(	PUNCT
ap-1870	92	14	13	13	NUM
ap-1870	92	15	)	)	PUNCT
ap-1870	92	16	and	and	CCONJ
ap-1870	92	17	its	its	PRON
ap-1870	92	18	first	first	ADJ
ap-1870	92	19	differential	differential	ADJ
ap-1870	92	20	approximation	approximation	NOUN
ap-1870	92	21	(	(	PUNCT
ap-1870	92	22	15	15	NUM
ap-1870	92	23	)	)	PUNCT
ap-1870	92	24	.	.	PUNCT
ap-1870	93	1	the	the	DET
ap-1870	93	2	terms	term	NOUN
ap-1870	93	3	e	e	X
ap-1870	93	4	(	(	PUNCT
ap-1870	93	5	k	k	NOUN
ap-1870	93	6	)	)	PUNCT
ap-1870	93	7	1	1	NUM
ap-1870	93	8	,	,	PUNCT
ap-1870	93	9	(	(	PUNCT
ap-1870	93	10	k	k	NOUN
ap-1870	93	11	=	=	SYM
ap-1870	93	12	1	1	NUM
ap-1870	93	13	,	,	PUNCT
ap-1870	93	14	2	2	NUM
ap-1870	93	15	,	,	PUNCT
ap-1870	93	16	3	3	NUM
ap-1870	93	17	)	)	PUNCT
ap-1870	93	18	in	in	ADP
ap-1870	93	19	(	(	PUNCT
ap-1870	93	20	15	15	NUM
ap-1870	93	21	)	)	PUNCT
ap-1870	93	22	are	be	AUX
ap-1870	93	23	differential	differential	ADJ
ap-1870	93	24	expressions	expression	NOUN
ap-1870	93	25	containing	contain	VERB
ap-1870	93	26	y′′′	y′′′	PROPN
ap-1870	93	27	and	and	CCONJ
ap-1870	93	28	y′′′′.	y′′′′.	NUM
ap-1870	93	29	these	these	DET
ap-1870	93	30	expressions	expression	NOUN
ap-1870	93	31	will	will	AUX
ap-1870	93	32	be	be	AUX
ap-1870	93	33	simplified	simplify	VERB
ap-1870	93	34	by	by	ADP
ap-1870	93	35	removing	remove	VERB
ap-1870	93	36	y′′′	y′′′	PROPN
ap-1870	93	37	and	and	CCONJ
ap-1870	93	38	y′′′′	y′′′′	PROPN
ap-1870	93	39	,	,	PUNCT
ap-1870	93	40	using	use	VERB
ap-1870	93	41	the	the	DET
ap-1870	93	42	ode	ode	PROPN
ap-1870	93	43	(	(	PUNCT
ap-1870	93	44	4	4	NUM
ap-1870	93	45	)	)	PUNCT
ap-1870	93	46	and	and	CCONJ
ap-1870	93	47	its	its	PRON
ap-1870	93	48	first	first	ADJ
ap-1870	93	49	differential	differential	ADJ
ap-1870	93	50	consequence	consequence	NOUN
ap-1870	93	51	.	.	PUNCT
ap-1870	94	1	3	3	X
ap-1870	94	2	.	.	X
ap-1870	94	3	equations	equation	NOUN
ap-1870	94	4	invariant	invariant	VERB
ap-1870	94	5	under	under	ADP
ap-1870	94	6	the	the	DET
ap-1870	94	7	similitude	similitude	NOUN
ap-1870	94	8	group	group	NOUN
ap-1870	94	9	sim(2	sim(2	PROPN
ap-1870	94	10	)	)	PUNCT
ap-1870	94	11	.	.	PUNCT
ap-1870	95	1	let	let	VERB
ap-1870	95	2	us	we	PRON
ap-1870	95	3	consider	consider	VERB
ap-1870	95	4	the	the	DET
ap-1870	95	5	group	group	NOUN
ap-1870	95	6	of	of	ADP
ap-1870	95	7	translations	translation	NOUN
ap-1870	95	8	,	,	PUNCT
ap-1870	95	9	rotations	rotation	NOUN
ap-1870	95	10	and	and	CCONJ
ap-1870	95	11	uniform	uniform	ADJ
ap-1870	95	12	dilations	dilation	NOUN
ap-1870	95	13	of	of	ADP
ap-1870	95	14	an	an	DET
ap-1870	95	15	euclidean	euclidean	ADJ
ap-1870	95	16	plane	plane	NOUN
ap-1870	95	17	.	.	PUNCT
ap-1870	96	1	its	its	PRON
ap-1870	96	2	lie	lie	NOUN
ap-1870	96	3	algebra	algebra	NOUN
ap-1870	96	4	sim(2	sim(2	PROPN
ap-1870	96	5	)	)	PUNCT
ap-1870	96	6	is	be	AUX
ap-1870	96	7	realized	realize	VERB
ap-1870	96	8	by	by	ADP
ap-1870	96	9	the	the	DET
ap-1870	96	10	vector	vector	NOUN
ap-1870	96	11	fields	field	NOUN
ap-1870	96	12	x̂1	x̂1	PUNCT
ap-1870	97	1	=	=	SYM
ap-1870	97	2	∂	∂	NUM
ap-1870	97	3	∂x	∂x	PROPN
ap-1870	97	4	,	,	PUNCT
ap-1870	97	5	x̂3	x̂3	PUNCT
ap-1870	97	6	=	=	SYM
ap-1870	97	7	y	y	PROPN
ap-1870	97	8	∂	∂	NOUN
ap-1870	98	1	∂x	∂x	PROPN
ap-1870	98	2	−	−	NOUN
ap-1870	98	3	x	x	SYM
ap-1870	98	4	∂	∂	NUM
ap-1870	98	5	∂y	∂y	NOUN
ap-1870	98	6	,	,	PUNCT
ap-1870	98	7	x̂2	x̂2	NOUN
ap-1870	98	8	=	=	SYM
ap-1870	98	9	∂	∂	NUM
ap-1870	98	10	∂y	∂y	PROPN
ap-1870	98	11	,	,	PUNCT
ap-1870	98	12	x̂4	x̂4	PUNCT
ap-1870	98	13	=	=	PUNCT
ap-1870	98	14	x	x	SYM
ap-1870	98	15	∂	∂	NUM
ap-1870	98	16	∂x	∂x	PROPN
ap-1870	99	1	+	+	CCONJ
ap-1870	99	2	y	y	PROPN
ap-1870	99	3	∂	∂	NOUN
ap-1870	99	4	∂y	∂y	NOUN
ap-1870	99	5	,	,	PUNCT
ap-1870	99	6	(	(	PUNCT
ap-1870	99	7	17	17	NUM
ap-1870	99	8	)	)	PUNCT
ap-1870	99	9	this	this	DET
ap-1870	99	10	group	group	NOUN
ap-1870	99	11	has	have	VERB
ap-1870	99	12	no	no	DET
ap-1870	99	13	second	second	ADJ
ap-1870	99	14	order	order	NOUN
ap-1870	99	15	differential	differential	ADJ
ap-1870	99	16	invariant	invariant	ADJ
ap-1870	99	17	and	and	CCONJ
ap-1870	99	18	precisely	precisely	ADV
ap-1870	99	19	one	one	NUM
ap-1870	99	20	third	third	ADJ
ap-1870	99	21	order	order	NOUN
ap-1870	99	22	one	one	NUM
ap-1870	99	23	,	,	PUNCT
ap-1870	99	24	namely[26	namely[26	ADJ
ap-1870	99	25	]	]	X
ap-1870	100	1	i	i	PRON
ap-1870	100	2	=	=	PUNCT
ap-1870	100	3	(	(	PUNCT
ap-1870	100	4	1	1	NUM
ap-1870	101	1	+	+	NUM
ap-1870	101	2	y	y	PROPN
ap-1870	101	3	′2)y′′′	′2)y′′′	PROPN
ap-1870	101	4	−	−	PROPN
ap-1870	101	5	3y′y′′2	3y′y′′2	NUM
ap-1870	102	1	y′′2	y′′2	PROPN
ap-1870	102	2	.	.	PUNCT
ap-1870	103	1	(	(	PUNCT
ap-1870	103	2	18	18	NUM
ap-1870	103	3	)	)	PUNCT
ap-1870	103	4	the	the	DET
ap-1870	103	5	expressions	expression	NOUN
ap-1870	103	6	i1	i1	PROPN
ap-1870	103	7	=	=	PROPN
ap-1870	103	8	y′′	y′′	PROPN
ap-1870	103	9	(	(	PUNCT
ap-1870	103	10	1	1	NUM
ap-1870	103	11	+	+	CCONJ
ap-1870	103	12	y′2)3/2	y′2)3/2	PROPN
ap-1870	103	13	,	,	PUNCT
ap-1870	103	14	i2	i2	PROPN
ap-1870	103	15	=	=	PUNCT
ap-1870	103	16	(	(	PUNCT
ap-1870	103	17	1	1	NUM
ap-1870	103	18	+	+	NUM
ap-1870	103	19	y	y	PROPN
ap-1870	103	20	′2)y′′′	′2)y′′′	PROPN
ap-1870	104	1	−	−	PROPN
ap-1870	104	2	3y′y′′2	3y′y′′2	NUM
ap-1870	104	3	(	(	PUNCT
ap-1870	104	4	1	1	NUM
ap-1870	104	5	+	+	CCONJ
ap-1870	104	6	y′2)3	y′2)3	NUM
ap-1870	104	7	are	be	AUX
ap-1870	104	8	invariant	invariant	ADJ
ap-1870	104	9	under	under	ADP
ap-1870	104	10	the	the	DET
ap-1870	104	11	euclidean	euclidean	ADJ
ap-1870	104	12	group	group	NOUN
ap-1870	104	13	,	,	PUNCT
ap-1870	104	14	with	with	ADP
ap-1870	104	15	lie	lie	NOUN
ap-1870	104	16	algebra	algebra	NOUN
ap-1870	104	17	{	{	PUNCT
ap-1870	104	18	x̂1	x̂1	PROPN
ap-1870	104	19	,	,	PUNCT
ap-1870	104	20	x̂2	x̂2	NOUN
ap-1870	104	21	,	,	PUNCT
ap-1870	104	22	x̂3	x̂3	PROPN
ap-1870	104	23	}	}	PUNCT
ap-1870	104	24	,	,	PUNCT
ap-1870	104	25	but	but	CCONJ
ap-1870	104	26	only	only	ADV
ap-1870	104	27	the	the	DET
ap-1870	104	28	ratio	ratio	NOUN
ap-1870	104	29	i2	i2	PROPN
ap-1870	104	30	/	/	SYM
ap-1870	104	31	i2	i2	PROPN
ap-1870	104	32	1	1	NUM
ap-1870	105	1	=	=	SYM
ap-1870	106	1	i	i	PRON
ap-1870	106	2	is	be	AUX
ap-1870	106	3	invariant	invariant	ADJ
ap-1870	106	4	under	under	ADP
ap-1870	106	5	dilations	dilation	NOUN
ap-1870	106	6	.	.	PUNCT
ap-1870	107	1	thus	thus	ADV
ap-1870	107	2	the	the	DET
ap-1870	107	3	lowest	low	ADJ
ap-1870	107	4	order	order	NOUN
ap-1870	107	5	ode	ode	PROPN
ap-1870	107	6	invariant	invariant	NOUN
ap-1870	107	7	under	under	ADP
ap-1870	107	8	sim(2	sim(2	PROPN
ap-1870	107	9	)	)	PUNCT
ap-1870	107	10	is	be	AUX
ap-1870	107	11	(	(	PUNCT
ap-1870	107	12	1	1	NUM
ap-1870	107	13	+	+	CCONJ
ap-1870	107	14	y′2)y′′′	y′2)y′′′	PROPN
ap-1870	107	15	−	−	PROPN
ap-1870	108	1	3y′y′′2	3y′y′′2	NUM
ap-1870	109	1	=	=	SYM
ap-1870	109	2	ky′′2	ky′′2	PROPN
ap-1870	109	3	(	(	PUNCT
ap-1870	109	4	19	19	NUM
ap-1870	109	5	)	)	PUNCT
ap-1870	109	6	where	where	SCONJ
ap-1870	109	7	k	k	PROPN
ap-1870	109	8	is	be	AUX
ap-1870	109	9	an	an	DET
ap-1870	109	10	arbitrary	arbitrary	ADJ
ap-1870	109	11	constant	constant	ADJ
ap-1870	109	12	.	.	PUNCT
ap-1870	110	1	to	to	PART
ap-1870	110	2	discretize	discretize	VERB
ap-1870	110	3	(	(	PUNCT
ap-1870	110	4	19	19	NUM
ap-1870	110	5	)	)	PUNCT
ap-1870	110	6	(	(	PUNCT
ap-1870	110	7	or	or	CCONJ
ap-1870	110	8	any	any	DET
ap-1870	110	9	third	third	ADJ
ap-1870	110	10	order	order	NOUN
ap-1870	110	11	ode	ode	NOUN
ap-1870	110	12	)	)	PUNCT
ap-1870	110	13	we	we	PRON
ap-1870	110	14	need	need	VERB
ap-1870	110	15	(	(	PUNCT
ap-1870	110	16	at	at	ADP
ap-1870	110	17	least	least	ADJ
ap-1870	110	18	)	)	PUNCT
ap-1870	110	19	a	a	DET
ap-1870	110	20	four	four	NUM
ap-1870	110	21	-	-	PUNCT
ap-1870	110	22	point	point	NOUN
ap-1870	110	23	stencil	stencil	NOUN
ap-1870	110	24	.	.	PUNCT
ap-1870	111	1	the	the	DET
ap-1870	111	2	euclidean	euclidean	ADJ
ap-1870	111	3	group	group	NOUN
ap-1870	111	4	has	have	VERB
ap-1870	111	5	5	5	NUM
ap-1870	111	6	independent	independent	ADJ
ap-1870	111	7	invariants	invariant	NOUN
ap-1870	111	8	depending	depend	VERB
ap-1870	111	9	on	on	ADP
ap-1870	111	10	4	4	NUM
ap-1870	111	11	points	point	NOUN
ap-1870	111	12	(	(	PUNCT
ap-1870	111	13	xn+k	xn+k	PROPN
ap-1870	111	14	,	,	PUNCT
ap-1870	111	15	yn+k	yn+k	PROPN
ap-1870	111	16	)	)	PUNCT
ap-1870	111	17	,	,	PUNCT
ap-1870	111	18	k	k	PROPN
ap-1870	111	19	=	=	PUNCT
ap-1870	111	20	−1	−1	PROPN
ap-1870	111	21	,	,	PUNCT
ap-1870	111	22	0	0	NUM
ap-1870	111	23	,	,	PUNCT
ap-1870	111	24	1	1	NUM
ap-1870	111	25	,	,	PUNCT
ap-1870	111	26	2	2	NUM
ap-1870	111	27	namely	namely	ADV
ap-1870	111	28	[	[	X
ap-1870	111	29	26	26	NUM
ap-1870	111	30	]	]	X
ap-1870	111	31	ξ1	ξ1	NOUN
ap-1870	111	32	=	=	SYM
ap-1870	111	33	hn+2	hn+2	PROPN
ap-1870	111	34	[	[	PUNCT
ap-1870	111	35	1	1	NUM
ap-1870	111	36	+	+	CCONJ
ap-1870	111	37	(	(	PUNCT
ap-1870	111	38	yn+2	yn+2	NUM
ap-1870	111	39	−	−	PROPN
ap-1870	111	40	yn+1	yn+1	PROPN
ap-1870	111	41	hn+2	hn+2	NUM
ap-1870	111	42	)	)	PUNCT
ap-1870	111	43	2]1/2	2]1/2	NUM
ap-1870	111	44	,	,	PUNCT
ap-1870	111	45	ξ2	ξ2	NOUN
ap-1870	111	46	=	=	SYM
ap-1870	111	47	hn+1	hn+1	PROPN
ap-1870	111	48	[	[	PUNCT
ap-1870	111	49	1	1	NUM
ap-1870	111	50	+	+	CCONJ
ap-1870	111	51	(	(	PUNCT
ap-1870	111	52	yn+1	yn+1	PROPN
ap-1870	111	53	−	−	PROPN
ap-1870	111	54	yn	yn	PROPN
ap-1870	111	55	hn+1	hn+1	PROPN
ap-1870	111	56	)	)	PUNCT
ap-1870	111	57	2]1/2	2]1/2	NUM
ap-1870	111	58	,	,	PUNCT
ap-1870	111	59	ξ3	ξ3	NOUN
ap-1870	111	60	=	=	NOUN
ap-1870	111	61	hn	hn	PROPN
ap-1870	111	62	[	[	PUNCT
ap-1870	111	63	1	1	NUM
ap-1870	111	64	+	+	CCONJ
ap-1870	111	65	(	(	PUNCT
ap-1870	111	66	yn	yn	INTJ
ap-1870	111	67	−	−	PROPN
ap-1870	111	68	yn−1	yn−1	PROPN
ap-1870	111	69	hn	hn	PROPN
ap-1870	111	70	)	)	PUNCT
ap-1870	111	71	2]1/2	2]1/2	NUM
ap-1870	111	72	,	,	PUNCT
ap-1870	111	73	ξ4	ξ4	NOUN
ap-1870	111	74	=	=	SYM
ap-1870	111	75	(	(	PUNCT
ap-1870	111	76	yn+2	yn+2	NUM
ap-1870	111	77	−	−	PROPN
ap-1870	111	78	yn+1)hn+1	yn+1)hn+1	ADJ
ap-1870	111	79	−	−	PROPN
ap-1870	111	80	(	(	PUNCT
ap-1870	111	81	yn+1	yn+1	PROPN
ap-1870	111	82	−	−	PROPN
ap-1870	111	83	yn)hn+2	yn)hn+2	NOUN
ap-1870	111	84	,	,	PUNCT
ap-1870	111	85	ξ5	ξ5	NOUN
ap-1870	111	86	=	=	SYM
ap-1870	111	87	(	(	PUNCT
ap-1870	111	88	yn+1	yn+1	PROPN
ap-1870	111	89	−	−	PROPN
ap-1870	111	90	yn)hn	yn)hn	PROPN
ap-1870	112	1	−	−	PROPN
ap-1870	112	2	(	(	PUNCT
ap-1870	112	3	yn	yn	PROPN
ap-1870	112	4	−	−	PROPN
ap-1870	112	5	yn−1)hn+1	yn−1)hn+1	PROPN
ap-1870	112	6	.	.	PUNCT
ap-1870	113	1	(	(	PUNCT
ap-1870	113	2	20	20	NUM
ap-1870	113	3	)	)	PUNCT
ap-1870	113	4	out	out	ADP
ap-1870	113	5	of	of	ADP
ap-1870	113	6	them	they	PRON
ap-1870	113	7	we	we	PRON
ap-1870	113	8	can	can	AUX
ap-1870	113	9	construct	construct	VERB
ap-1870	113	10	4	4	NUM
ap-1870	113	11	independent	independent	ADJ
ap-1870	113	12	sim(2	sim(2	NOUN
ap-1870	113	13	)	)	PUNCT
ap-1870	113	14	invariants	invariant	NOUN
ap-1870	113	15	,	,	PUNCT
ap-1870	113	16	for	for	ADP
ap-1870	113	17	instance	instance	NOUN
ap-1870	113	18	j1	j1	NOUN
ap-1870	113	19	=	=	SYM
ap-1870	113	20	2αξ4	2αξ4	NUM
ap-1870	113	21	ξ1ξ2(ξ1	ξ1ξ2(ξ1	NOUN
ap-1870	113	22	+	+	CCONJ
ap-1870	113	23	ξ2	ξ2	ADJ
ap-1870	113	24	)	)	PUNCT
ap-1870	114	1	+	+	NUM
ap-1870	114	2	2βξ5	2βξ5	NUM
ap-1870	114	3	(	(	PUNCT
ap-1870	114	4	ξ2ξ3)(ξ2	ξ2ξ3)(ξ2	NUM
ap-1870	114	5	+	+	NUM
ap-1870	114	6	ξ3	ξ3	NOUN
ap-1870	114	7	)	)	PUNCT
ap-1870	114	8	,	,	PUNCT
ap-1870	114	9	α+	α+	X
ap-1870	114	10	β	β	X
ap-1870	114	11	=	=	SYM
ap-1870	114	12	1	1	NUM
ap-1870	114	13	,	,	PUNCT
ap-1870	114	14	j2	j2	NOUN
ap-1870	114	15	=	=	SYM
ap-1870	114	16	6	6	NUM
ap-1870	114	17	ξ1	ξ1	NOUN
ap-1870	114	18	+	+	CCONJ
ap-1870	114	19	ξ2	ξ2	NOUN
ap-1870	114	20	+	+	CCONJ
ap-1870	114	21	ξ3	ξ3	NOUN
ap-1870	114	22	[	[	PUNCT
ap-1870	114	23	ξ4	ξ4	NOUN
ap-1870	114	24	ξ1ξ2(ξ1	ξ1ξ2(ξ1	NOUN
ap-1870	114	25	+	+	CCONJ
ap-1870	114	26	ξ2	ξ2	ADJ
ap-1870	114	27	)	)	PUNCT
ap-1870	115	1	−	−	PROPN
ap-1870	115	2	ξ5	ξ5	NOUN
ap-1870	115	3	ξ2ξ3(ξ2	ξ2ξ3(ξ2	NOUN
ap-1870	115	4	+	+	X
ap-1870	115	5	ξ3	ξ3	NOUN
ap-1870	115	6	)	)	PUNCT
ap-1870	115	7	]	]	PUNCT
ap-1870	115	8	,	,	PUNCT
ap-1870	115	9	(	(	PUNCT
ap-1870	115	10	21	21	NUM
ap-1870	115	11	)	)	PUNCT
ap-1870	115	12	and	and	CCONJ
ap-1870	115	13	the	the	DET
ap-1870	115	14	two	two	NUM
ap-1870	115	15	ratios	ratio	NOUN
ap-1870	115	16	ξ1	ξ1	NOUN
ap-1870	115	17	/	/	SYM
ap-1870	115	18	ξ2	ξ2	ADJ
ap-1870	115	19	,	,	PUNCT
ap-1870	115	20	ξ2	ξ2	ADJ
ap-1870	115	21	/	/	SYM
ap-1870	115	22	ξ3	ξ3	NOUN
ap-1870	115	23	.	.	PUNCT
ap-1870	116	1	to	to	PART
ap-1870	116	2	obtain	obtain	VERB
ap-1870	116	3	the	the	DET
ap-1870	116	4	continuous	continuous	ADJ
ap-1870	116	5	limit	limit	NOUN
ap-1870	116	6	we	we	PRON
ap-1870	116	7	put	put	VERB
ap-1870	116	8	xn−1	xn−1	PROPN
ap-1870	117	1	=	=	PUNCT
ap-1870	117	2	xn	xn	PROPN
ap-1870	118	1	−	−	PROPN
ap-1870	118	2	hn	hn	PROPN
ap-1870	118	3	,	,	PUNCT
ap-1870	118	4	xn+1	xn+1	PROPN
ap-1870	118	5	=	=	SYM
ap-1870	118	6	xn	xn	PROPN
ap-1870	119	1	+	+	NUM
ap-1870	119	2	hn+1	hn+1	PROPN
ap-1870	119	3	,	,	PUNCT
ap-1870	120	1	xn+2	xn+2	PUNCT
ap-1870	120	2	=	=	SYM
ap-1870	120	3	xn	xn	PROPN
ap-1870	121	1	+	+	NUM
ap-1870	121	2	hn+1	hn+1	PROPN
ap-1870	121	3	+	+	CCONJ
ap-1870	121	4	hn+2	hn+2	NOUN
ap-1870	121	5	,	,	PUNCT
ap-1870	121	6	yn+k	yn+k	PROPN
ap-1870	121	7	=	=	SYM
ap-1870	121	8	y(xn+k	y(xn+k	PROPN
ap-1870	121	9	)	)	PUNCT
ap-1870	121	10	,	,	PUNCT
ap-1870	121	11	hn+k	hn+k	PROPN
ap-1870	121	12	=	=	SYM
ap-1870	121	13	αkε	αkε	PROPN
ap-1870	121	14	,	,	PUNCT
ap-1870	121	15	αk	αk	ADP
ap-1870	121	16	∼	∼	NOUN
ap-1870	121	17	1	1	NUM
ap-1870	121	18	,	,	PUNCT
ap-1870	121	19	(	(	PUNCT
ap-1870	121	20	22	22	NUM
ap-1870	121	21	)	)	PUNCT
ap-1870	121	22	and	and	CCONJ
ap-1870	121	23	expand	expand	VERB
ap-1870	121	24	yn+k	yn+k	PROPN
ap-1870	121	25	into	into	ADP
ap-1870	121	26	a	a	DET
ap-1870	121	27	taylor	taylor	PROPN
ap-1870	121	28	series	series	NOUN
ap-1870	121	29	about	about	ADP
ap-1870	121	30	xn	xn	PROPN
ap-1870	121	31	≡	≡	PROPN
ap-1870	121	32	x.	x.	NOUN
ap-1870	122	1	the	the	DET
ap-1870	122	2	invariants	invariants	PROPN
ap-1870	122	3	j1	j1	PROPN
ap-1870	122	4	,	,	PUNCT
ap-1870	122	5	j2	j2	NOUN
ap-1870	122	6	where	where	SCONJ
ap-1870	122	7	so	so	ADV
ap-1870	122	8	chosen	choose	VERB
ap-1870	122	9	that	that	SCONJ
ap-1870	122	10	their	their	PRON
ap-1870	122	11	continuous	continuous	ADJ
ap-1870	122	12	limits	limit	NOUN
ap-1870	122	13	are	be	AUX
ap-1870	122	14	i1	i1	NOUN
ap-1870	122	15	and	and	CCONJ
ap-1870	122	16	i2	i2	PROPN
ap-1870	122	17	respectively	respectively	ADV
ap-1870	122	18	.	.	PUNCT
ap-1870	123	1	the	the	DET
ap-1870	123	2	invariant	invariant	ADJ
ap-1870	123	3	scheme	scheme	NOUN
ap-1870	123	4	used	use	VERB
ap-1870	123	5	in	in	ADP
ap-1870	123	6	[	[	X
ap-1870	123	7	26	26	NUM
ap-1870	123	8	]	]	PUNCT
ap-1870	123	9	to	to	PART
ap-1870	123	10	solve	solve	VERB
ap-1870	123	11	the	the	DET
ap-1870	123	12	ode	ode	PROPN
ap-1870	123	13	(	(	PUNCT
ap-1870	123	14	19	19	NUM
ap-1870	123	15	)	)	PUNCT
ap-1870	123	16	numerically	numerically	ADV
ap-1870	123	17	was	be	AUX
ap-1870	123	18	e∆	e∆	ADV
ap-1870	123	19	2	2	NUM
ap-1870	123	20	=	=	SYM
ap-1870	123	21	ξ1ξ3	ξ1ξ3	NOUN
ap-1870	123	22	−	−	NOUN
ap-1870	123	23	ξ2	ξ2	NOUN
ap-1870	123	24	2	2	NUM
ap-1870	123	25	=	=	SYM
ap-1870	123	26	0	0	NUM
ap-1870	123	27	,	,	PUNCT
ap-1870	123	28	(	(	PUNCT
ap-1870	123	29	23	23	NUM
ap-1870	123	30	)	)	PUNCT
ap-1870	123	31	e∆	e∆	ADV
ap-1870	123	32	1	1	NUM
ap-1870	123	33	=	=	SYM
ap-1870	123	34	j2	j2	PROPN
ap-1870	123	35	−kj2	−kj2	PROPN
ap-1870	123	36	1	1	NUM
ap-1870	123	37	=	=	SYM
ap-1870	123	38	0	0	PROPN
ap-1870	123	39	.	.	PUNCT
ap-1870	124	1	(	(	PUNCT
ap-1870	124	2	24	24	NUM
ap-1870	124	3	)	)	PUNCT
ap-1870	124	4	the	the	DET
ap-1870	124	5	first	first	ADJ
ap-1870	124	6	differential	differential	ADJ
ap-1870	124	7	approximation	approximation	NOUN
ap-1870	124	8	of	of	ADP
ap-1870	124	9	(	(	PUNCT
ap-1870	124	10	23	23	NUM
ap-1870	124	11	)	)	PUNCT
ap-1870	124	12	is	be	AUX
ap-1870	124	13	e∆	e∆	SYM
ap-1870	124	14	2	2	NUM
ap-1870	124	15	≈	≈	NUM
ap-1870	124	16	2(−h2	2(−h2	NUM
ap-1870	125	1	n+1	n+1	PROPN
ap-1870	125	2	+	+	NUM
ap-1870	125	3	hnhn+2)(y′2	hnhn+2)(y′2	PROPN
ap-1870	125	4	+	+	PROPN
ap-1870	125	5	1	1	NUM
ap-1870	125	6	)	)	PUNCT
ap-1870	125	7	+	+	CCONJ
ap-1870	125	8	(	(	PUNCT
ap-1870	125	9	2hnhn+1hn+2	2hnhn+1hn+2	NUM
ap-1870	125	10	−	−	NUM
ap-1870	125	11	2h3	2h3	NUM
ap-1870	126	1	n+1	n+1	PROPN
ap-1870	126	2	−	−	PROPN
ap-1870	126	3	h2	h2	NOUN
ap-1870	126	4	nhn+2	nhn+2	PROPN
ap-1870	126	5	+	+	CCONJ
ap-1870	126	6	hnh	hnh	NOUN
ap-1870	126	7	2	2	NUM
ap-1870	126	8	n+2)y′y′′	n+2)y′y′′	NOUN
ap-1870	126	9	=	=	SYM
ap-1870	126	10	0	0	PUNCT
ap-1870	127	1	(	(	PUNCT
ap-1870	127	2	25	25	NUM
ap-1870	127	3	)	)	PUNCT
ap-1870	127	4	440	440	NUM
ap-1870	127	5	vol	vol	NOUN
ap-1870	127	6	.	.	PUNCT
ap-1870	128	1	53	53	NUM
ap-1870	128	2	no	no	NOUN
ap-1870	128	3	.	.	PUNCT
ap-1870	129	1	5/2013	5/2013	NUM
ap-1870	129	2	lie	lie	NOUN
ap-1870	129	3	groups	group	NOUN
ap-1870	129	4	and	and	CCONJ
ap-1870	129	5	numerical	numerical	ADJ
ap-1870	129	6	solutions	solution	NOUN
ap-1870	129	7	of	of	ADP
ap-1870	129	8	differential	differential	ADJ
ap-1870	129	9	equations	equation	NOUN
ap-1870	129	10	applying	apply	VERB
ap-1870	129	11	prdx̂i	prdx̂i	VERB
ap-1870	129	12	to	to	ADP
ap-1870	129	13	eq	eq	PROPN
ap-1870	129	14	.	.	PUNCT
ap-1870	130	1	(	(	PUNCT
ap-1870	130	2	25	25	NUM
ap-1870	130	3	)	)	PUNCT
ap-1870	130	4	we	we	PRON
ap-1870	130	5	find	find	VERB
ap-1870	130	6	that	that	SCONJ
ap-1870	130	7	the	the	DET
ap-1870	130	8	equation	equation	NOUN
ap-1870	130	9	is	be	AUX
ap-1870	130	10	invariant	invariant	ADJ
ap-1870	130	11	under	under	ADP
ap-1870	130	12	the	the	DET
ap-1870	130	13	entire	entire	ADJ
ap-1870	130	14	group	group	NOUN
ap-1870	130	15	sim(2	sim(2	PROPN
ap-1870	130	16	)	)	PUNCT
ap-1870	130	17	,	,	PUNCT
ap-1870	130	18	as	as	SCONJ
ap-1870	130	19	are	be	AUX
ap-1870	130	20	the	the	DET
ap-1870	130	21	terms	term	NOUN
ap-1870	130	22	of	of	ADP
ap-1870	130	23	order	order	NOUN
ap-1870	130	24	ε2	ε2	ADJ
ap-1870	130	25	and	and	CCONJ
ap-1870	130	26	ε3	ε3	VERB
ap-1870	130	27	separately	separately	ADV
ap-1870	130	28	.	.	PUNCT
ap-1870	131	1	the	the	DET
ap-1870	131	2	first	first	ADJ
ap-1870	131	3	order	order	NOUN
ap-1870	131	4	differential	differential	ADJ
ap-1870	131	5	approximation	approximation	NOUN
ap-1870	131	6	of	of	ADP
ap-1870	131	7	the	the	DET
ap-1870	131	8	difference	difference	NOUN
ap-1870	131	9	equation	equation	NOUN
ap-1870	131	10	(	(	PUNCT
ap-1870	131	11	24	24	NUM
ap-1870	131	12	)	)	PUNCT
ap-1870	131	13	is	be	AUX
ap-1870	131	14	quite	quite	ADV
ap-1870	131	15	complicated	complicated	ADJ
ap-1870	131	16	.	.	PUNCT
ap-1870	132	1	however	however	ADV
ap-1870	132	2	,	,	PUNCT
ap-1870	132	3	if	if	SCONJ
ap-1870	132	4	we	we	PRON
ap-1870	132	5	substitute	substitute	VERB
ap-1870	132	6	the	the	DET
ap-1870	132	7	ode	ode	PROPN
ap-1870	132	8	(	(	PUNCT
ap-1870	132	9	19	19	NUM
ap-1870	132	10	)	)	PUNCT
ap-1870	132	11	and	and	CCONJ
ap-1870	132	12	its	its	PRON
ap-1870	132	13	differential	differential	ADJ
ap-1870	132	14	consequences	consequence	NOUN
ap-1870	132	15	into	into	ADP
ap-1870	132	16	the	the	DET
ap-1870	132	17	first	first	ADJ
ap-1870	132	18	nonvanishing	nonvanishing	ADJ
ap-1870	132	19	term	term	NOUN
ap-1870	132	20	of	of	ADP
ap-1870	132	21	the	the	DET
ap-1870	132	22	approximation	approximation	NOUN
ap-1870	132	23	,	,	PUNCT
ap-1870	132	24	we	we	PRON
ap-1870	132	25	obtain	obtain	VERB
ap-1870	132	26	a	a	DET
ap-1870	132	27	manageable	manageable	ADJ
ap-1870	132	28	expression	expression	NOUN
ap-1870	133	1	e∆	e∆	ADP
ap-1870	133	2	1	1	NUM
ap-1870	133	3	≈	≈	PROPN
ap-1870	133	4	(	(	PUNCT
ap-1870	133	5	1	1	NUM
ap-1870	133	6	+	+	CCONJ
ap-1870	133	7	y′2)y′′′	y′2)y′′′	PROPN
ap-1870	133	8	−	−	PROPN
ap-1870	133	9	3y′y′′2	3y′y′′2	NUM
ap-1870	134	1	−ky′′2	−ky′′2	NOUN
ap-1870	134	2	−	−	NOUN
ap-1870	134	3	1	1	NUM
ap-1870	134	4	24	24	NUM
ap-1870	134	5	y′′3	y′′3	NOUN
ap-1870	134	6	[	[	X
ap-1870	134	7	1	1	NUM
ap-1870	134	8	+	+	NUM
ap-1870	134	9	y′4](hn	y′4](hn	PRON
ap-1870	134	10	+	+	CCONJ
ap-1870	134	11	hn+1	hn+1	PROPN
ap-1870	134	12	+	+	NUM
ap-1870	134	13	hn+2	hn+2	NOUN
ap-1870	134	14	)	)	PUNCT
ap-1870	134	15	×	×	NOUN
ap-1870	134	16	{	{	PUNCT
ap-1870	134	17	k2[16α(hn	k2[16α(hn	PROPN
ap-1870	134	18	+	+	CCONJ
ap-1870	134	19	hn+1	hn+1	PROPN
ap-1870	134	20	+	+	CCONJ
ap-1870	134	21	hn+2)2	hn+2)2	NUM
ap-1870	134	22	−	−	PROPN
ap-1870	134	23	4h2	4h2	NUM
ap-1870	134	24	n	n	CCONJ
ap-1870	134	25	−	−	PROPN
ap-1870	135	1	12h2	12h2	NUM
ap-1870	136	1	n+2	n+2	NUM
ap-1870	136	2	−	−	PROPN
ap-1870	136	3	8h2	8h2	NUM
ap-1870	136	4	n+1	n+1	NUM
ap-1870	137	1	−	−	PROPN
ap-1870	137	2	16hnhn+2	16hnhn+2	PROPN
ap-1870	137	3	−	−	PROPN
ap-1870	137	4	20hn+1hn+2	20hn+1hn+2	PROPN
ap-1870	137	5	+	+	CCONJ
ap-1870	137	6	12hnhn+1	12hnhn+1	NUM
ap-1870	137	7	]	]	X
ap-1870	138	1	+	+	NUM
ap-1870	138	2	9hn+1(hn+2	9hn+1(hn+2	NUM
ap-1870	138	3	−	−	NOUN
ap-1870	138	4	hn	hn	PROPN
ap-1870	138	5	)	)	PUNCT
ap-1870	138	6	}	}	PUNCT
ap-1870	139	1	=	=	PUNCT
ap-1870	139	2	0	0	X
ap-1870	139	3	.	.	PUNCT
ap-1870	140	1	(	(	PUNCT
ap-1870	140	2	26	26	NUM
ap-1870	140	3	)	)	PUNCT
ap-1870	140	4	expression	expression	NOUN
ap-1870	140	5	(	(	PUNCT
ap-1870	140	6	26	26	NUM
ap-1870	140	7	)	)	PUNCT
ap-1870	140	8	also	also	ADV
ap-1870	140	9	satisfies	satisfy	VERB
ap-1870	140	10	pr∆x̂ie	pr∆x̂ie	NOUN
ap-1870	140	11	∆	∆	X
ap-1870	140	12	1	1	NUM
ap-1870	140	13	∣∣∣	∣∣∣	NOUN
ap-1870	140	14	e∆	e∆	ADV
ap-1870	140	15	1	1	NUM
ap-1870	140	16	=	=	NOUN
ap-1870	140	17	e∆	e∆	PROPN
ap-1870	140	18	2	2	NUM
ap-1870	140	19	=	=	SYM
ap-1870	140	20	0	0	NUM
ap-1870	140	21	=	=	SYM
ap-1870	140	22	0	0	NUM
ap-1870	140	23	,	,	PUNCT
ap-1870	140	24	i	i	PRON
ap-1870	140	25	=	=	NOUN
ap-1870	140	26	1	1	NUM
ap-1870	140	27	,	,	PUNCT
ap-1870	140	28	·	·	PUNCT
ap-1870	140	29	·	·	PUNCT
ap-1870	140	30	·	·	PUNCT
ap-1870	140	31	,	,	PUNCT
ap-1870	140	32	4	4	NUM
ap-1870	140	33	(	(	PUNCT
ap-1870	140	34	27	27	NUM
ap-1870	140	35	)	)	PUNCT
ap-1870	140	36	so	so	SCONJ
ap-1870	140	37	the	the	DET
ap-1870	140	38	first	first	ADJ
ap-1870	140	39	differential	differential	ADJ
ap-1870	140	40	approximation	approximation	NOUN
ap-1870	140	41	of	of	ADP
ap-1870	140	42	the	the	DET
ap-1870	140	43	entire	entire	ADJ
ap-1870	140	44	scheme	scheme	NOUN
ap-1870	140	45	(	(	PUNCT
ap-1870	140	46	23	23	NUM
ap-1870	140	47	)	)	PUNCT
ap-1870	140	48	,	,	PUNCT
ap-1870	140	49	(	(	PUNCT
ap-1870	140	50	24	24	NUM
ap-1870	140	51	)	)	PUNCT
ap-1870	140	52	is	be	AUX
ap-1870	140	53	invariant	invariant	ADJ
ap-1870	140	54	under	under	ADP
ap-1870	140	55	sim(2	sim(2	PROPN
ap-1870	140	56	)	)	PUNCT
ap-1870	140	57	.	.	PUNCT
ap-1870	141	1	4	4	X
ap-1870	141	2	.	.	X
ap-1870	141	3	equations	equation	NOUN
ap-1870	141	4	invariant	invariant	VERB
ap-1870	141	5	under	under	ADP
ap-1870	141	6	a	a	DET
ap-1870	141	7	one	one	NUM
ap-1870	141	8	-	-	PUNCT
ap-1870	141	9	dimensional	dimensional	ADJ
ap-1870	141	10	realization	realization	NOUN
ap-1870	141	11	of	of	ADP
ap-1870	141	12	sl(2,r	sl(2,r	NOUN
ap-1870	141	13	)	)	PUNCT
ap-1870	141	14	.	.	PUNCT
ap-1870	142	1	four	four	NUM
ap-1870	142	2	non	non	ADJ
ap-1870	142	3	-	-	ADJ
ap-1870	142	4	equivalent	equivalent	ADJ
ap-1870	142	5	realizations	realization	NOUN
ap-1870	142	6	of	of	ADP
ap-1870	142	7	sl(2,r	sl(2,r	NOUN
ap-1870	142	8	)	)	PUNCT
ap-1870	142	9	by	by	ADP
ap-1870	142	10	vector	vector	NOUN
ap-1870	142	11	fields	field	NOUN
ap-1870	142	12	in	in	ADP
ap-1870	142	13	two	two	NUM
ap-1870	142	14	variables	variable	NOUN
ap-1870	142	15	exist	exist	VERB
ap-1870	142	16	[	[	X
ap-1870	142	17	29	29	NUM
ap-1870	142	18	]	]	SYM
ap-1870	142	19	.	.	PUNCT
ap-1870	143	1	invariant	invariant	ADJ
ap-1870	143	2	difference	difference	NOUN
ap-1870	143	3	schemes	scheme	NOUN
ap-1870	143	4	for	for	ADP
ap-1870	143	5	second	second	ADJ
ap-1870	143	6	and	and	CCONJ
ap-1870	143	7	third	third	ADJ
ap-1870	143	8	order	order	NOUN
ap-1870	143	9	odes	ode	NOUN
ap-1870	143	10	have	have	AUX
ap-1870	143	11	been	be	AUX
ap-1870	143	12	constructed	construct	VERB
ap-1870	143	13	and	and	CCONJ
ap-1870	143	14	tested	test	VERB
ap-1870	143	15	for	for	ADP
ap-1870	143	16	all	all	PRON
ap-1870	143	17	of	of	ADP
ap-1870	143	18	them	they	PRON
ap-1870	143	19	[	[	X
ap-1870	143	20	26–28	26–28	NOUN
ap-1870	143	21	]	]	PUNCT
ap-1870	143	22	.	.	PUNCT
ap-1870	144	1	in	in	ADP
ap-1870	144	2	this	this	DET
ap-1870	144	3	section	section	NOUN
ap-1870	144	4	we	we	PRON
ap-1870	144	5	will	will	AUX
ap-1870	144	6	consider	consider	VERB
ap-1870	144	7	the	the	DET
ap-1870	144	8	first	first	ADJ
ap-1870	144	9	one	one	NUM
ap-1870	144	10	,	,	PUNCT
ap-1870	144	11	called	call	VERB
ap-1870	144	12	sl1(2,r	sl1(2,r	PROPN
ap-1870	144	13	)	)	PUNCT
ap-1870	144	14	,	,	PUNCT
ap-1870	144	15	or	or	CCONJ
ap-1870	144	16	alternatively	alternatively	ADV
ap-1870	144	17	sly(2,r	sly(2,r	PROPN
ap-1870	144	18	)	)	PUNCT
ap-1870	144	19	,	,	PUNCT
ap-1870	144	20	which	which	PRON
ap-1870	144	21	actually	actually	ADV
ap-1870	144	22	involves	involve	VERB
ap-1870	144	23	one	one	NUM
ap-1870	144	24	variable	variable	NOUN
ap-1870	144	25	only	only	ADV
ap-1870	144	26	:	:	PUNCT
ap-1870	144	27	x̂1	x̂1	X
ap-1870	144	28	=	=	SYM
ap-1870	144	29	∂	∂	NUM
ap-1870	144	30	∂y	∂y	NOUN
ap-1870	144	31	,	,	PUNCT
ap-1870	144	32	x̂2	x̂2	PUNCT
ap-1870	145	1	=	=	SYM
ap-1870	145	2	y	y	PROPN
ap-1870	145	3	∂	∂	NOUN
ap-1870	145	4	∂y	∂y	PROPN
ap-1870	145	5	,	,	PUNCT
ap-1870	145	6	x̂3	x̂3	PUNCT
ap-1870	145	7	=	=	PUNCT
ap-1870	146	1	y2	y2	PROPN
ap-1870	146	2	∂	∂	NUM
ap-1870	146	3	∂y	∂y	X
ap-1870	146	4	.	.	PUNCT
ap-1870	147	1	(	(	PUNCT
ap-1870	147	2	28	28	NUM
ap-1870	147	3	)	)	PUNCT
ap-1870	147	4	the	the	DET
ap-1870	147	5	corresponding	correspond	VERB
ap-1870	147	6	lie	lie	NOUN
ap-1870	147	7	group	group	NOUN
ap-1870	147	8	acts	act	VERB
ap-1870	147	9	by	by	ADP
ap-1870	147	10	mobius	mobius	NOUN
ap-1870	147	11	transformations	transformation	NOUN
ap-1870	147	12	(	(	PUNCT
ap-1870	147	13	fractional	fractional	ADJ
ap-1870	147	14	linear	linear	ADJ
ap-1870	147	15	transformations	transformation	NOUN
ap-1870	147	16	)	)	PUNCT
ap-1870	147	17	on	on	ADP
ap-1870	147	18	y.	y.	NOUN
ap-1870	147	19	the	the	DET
ap-1870	147	20	third	third	ADJ
ap-1870	147	21	order	order	NOUN
ap-1870	147	22	differential	differential	NOUN
ap-1870	147	23	invariants	invariant	NOUN
ap-1870	147	24	of	of	ADP
ap-1870	147	25	this	this	DET
ap-1870	147	26	action	action	NOUN
ap-1870	147	27	are	be	AUX
ap-1870	147	28	the	the	DET
ap-1870	147	29	schwarzian	schwarzian	ADJ
ap-1870	147	30	derivatives	derivative	NOUN
ap-1870	147	31	of	of	ADP
ap-1870	147	32	y	y	PROPN
ap-1870	147	33	and	and	CCONJ
ap-1870	147	34	the	the	DET
ap-1870	147	35	independent	independent	ADJ
ap-1870	147	36	variable	variable	NOUN
ap-1870	147	37	x.	x.	NOUN
ap-1870	148	1	the	the	DET
ap-1870	148	2	most	most	ADV
ap-1870	148	3	general	general	ADJ
ap-1870	148	4	third	third	ADJ
ap-1870	148	5	order	order	NOUN
ap-1870	148	6	invariant	invariant	ADJ
ap-1870	148	7	ode	ode	NOUN
ap-1870	148	8	is	be	AUX
ap-1870	148	9	1	1	NUM
ap-1870	148	10	y′2	y′2	NOUN
ap-1870	148	11	(	(	PUNCT
ap-1870	148	12	y′y′′′	y′y′′′	PROPN
ap-1870	148	13	−	−	PROPN
ap-1870	148	14	3	3	NUM
ap-1870	148	15	2y	2y	NUM
ap-1870	148	16	′′2	′′2	NOUN
ap-1870	148	17	)	)	PUNCT
ap-1870	149	1	=	=	PUNCT
ap-1870	149	2	f	f	X
ap-1870	149	3	(	(	PUNCT
ap-1870	149	4	x	x	NOUN
ap-1870	149	5	)	)	PUNCT
ap-1870	149	6	.	.	PUNCT
ap-1870	150	1	(	(	PUNCT
ap-1870	150	2	29	29	NUM
ap-1870	150	3	)	)	PUNCT
ap-1870	150	4	where	where	SCONJ
ap-1870	150	5	f	f	PROPN
ap-1870	150	6	(	(	PUNCT
ap-1870	150	7	x	x	X
ap-1870	150	8	)	)	PUNCT
ap-1870	150	9	is	be	AUX
ap-1870	150	10	arbitrary	arbitrary	ADJ
ap-1870	150	11	.	.	PUNCT
ap-1870	151	1	for	for	ADP
ap-1870	151	2	f	f	PROPN
ap-1870	151	3	(	(	PUNCT
ap-1870	151	4	x	x	NOUN
ap-1870	151	5	)	)	PUNCT
ap-1870	151	6	=	=	SYM
ap-1870	151	7	k	k	X
ap-1870	151	8	=	=	PRON
ap-1870	151	9	const	const	ADP
ap-1870	151	10	the	the	DET
ap-1870	151	11	group	group	NOUN
ap-1870	151	12	is	be	AUX
ap-1870	151	13	gl(2,r	gl(2,r	NOUN
ap-1870	151	14	)	)	PUNCT
ap-1870	151	15	and	and	CCONJ
ap-1870	151	16	(	(	PUNCT
ap-1870	151	17	28	28	NUM
ap-1870	151	18	)	)	PUNCT
ap-1870	151	19	is	be	AUX
ap-1870	151	20	extended	extend	VERB
ap-1870	151	21	by	by	ADP
ap-1870	151	22	the	the	DET
ap-1870	151	23	vector	vector	NOUN
ap-1870	151	24	field	field	NOUN
ap-1870	151	25	x̂4	x̂4	PUNCT
ap-1870	151	26	=	=	PUNCT
ap-1870	151	27	∂x	∂x	PROPN
ap-1870	151	28	.	.	PUNCT
ap-1870	152	1	for	for	ADP
ap-1870	152	2	f	f	PROPN
ap-1870	152	3	(	(	PUNCT
ap-1870	152	4	x	x	NOUN
ap-1870	152	5	)	)	PUNCT
ap-1870	152	6	=	=	SYM
ap-1870	152	7	0	0	NUM
ap-1870	153	1	the	the	DET
ap-1870	153	2	symmetry	symmetry	NOUN
ap-1870	153	3	group	group	NOUN
ap-1870	153	4	is	be	AUX
ap-1870	153	5	sly(2,r)⊗	sly(2,r)⊗	PROPN
ap-1870	153	6	slx(2,r	slx(2,r	PROPN
ap-1870	153	7	)	)	PUNCT
ap-1870	153	8	.	.	PUNCT
ap-1870	154	1	the	the	DET
ap-1870	154	2	difference	difference	NOUN
ap-1870	154	3	invariants	invariant	NOUN
ap-1870	154	4	on	on	ADP
ap-1870	154	5	a	a	DET
ap-1870	154	6	four	four	NUM
ap-1870	154	7	point	point	NOUN
ap-1870	154	8	stencil	stencil	NOUN
ap-1870	154	9	are	be	AUX
ap-1870	154	10	r	r	NOUN
ap-1870	154	11	=	=	PUNCT
ap-1870	154	12	(	(	PUNCT
ap-1870	154	13	yn+2	yn+2	NUM
ap-1870	154	14	−	−	NOUN
ap-1870	154	15	yn)(yn+1	yn)(yn+1	NOUN
ap-1870	154	16	−	−	PROPN
ap-1870	154	17	yn−1	yn−1	NOUN
ap-1870	154	18	)	)	PUNCT
ap-1870	154	19	(	(	PUNCT
ap-1870	154	20	yn+2	yn+2	NUM
ap-1870	154	21	−	−	NOUN
ap-1870	155	1	yn+1)(yn	yn+1)(yn	PRON
ap-1870	156	1	−	−	PROPN
ap-1870	156	2	yn−1	yn−1	PROPN
ap-1870	156	3	)	)	PUNCT
ap-1870	156	4	,	,	PUNCT
ap-1870	156	5	xn	xn	PROPN
ap-1870	156	6	,	,	PUNCT
ap-1870	156	7	hn+2	hn+2	NUM
ap-1870	156	8	,	,	PUNCT
ap-1870	156	9	hn+1	hn+1	PROPN
ap-1870	156	10	,	,	PUNCT
ap-1870	156	11	hn	hn	PROPN
ap-1870	156	12	.	.	PUNCT
ap-1870	157	1	(	(	PUNCT
ap-1870	157	2	30	30	NUM
ap-1870	157	3	)	)	PUNCT
ap-1870	157	4	the	the	DET
ap-1870	157	5	discrete	discrete	ADJ
ap-1870	157	6	invariant	invariant	ADJ
ap-1870	157	7	approximating	approximate	VERB
ap-1870	157	8	the	the	DET
ap-1870	157	9	left	left	ADJ
ap-1870	157	10	hand	hand	NOUN
ap-1870	157	11	side	side	NOUN
ap-1870	157	12	of	of	ADP
ap-1870	157	13	(	(	PUNCT
ap-1870	157	14	29	29	NUM
ap-1870	157	15	)	)	PUNCT
ap-1870	157	16	is	be	AUX
ap-1870	157	17	j1	j1	PROPN
ap-1870	157	18	=	=	SYM
ap-1870	157	19	6hn+2hn	6hn+2hn	NUM
ap-1870	157	20	hn+1(hn+1+hn+2)(hn+hn+1)(hn+2+hn+1+hn	hn+1(hn+1+hn+2)(hn+hn+1)(hn+2+hn+1+hn	NOUN
ap-1870	157	21	)	)	PUNCT
ap-1870	157	22	×	×	NOUN
ap-1870	157	23	[	[	PUNCT
ap-1870	157	24	(	(	PUNCT
ap-1870	157	25	hn+2+hn+1)(hn+1+hn	hn+2+hn+1)(hn+1+hn	PROPN
ap-1870	157	26	)	)	PUNCT
ap-1870	158	1	hnhn+2	hnhn+2	VERB
ap-1870	158	2	−r	−r	ADJ
ap-1870	158	3	]	]	PUNCT
ap-1870	158	4	.	.	PUNCT
ap-1870	159	1	(	(	PUNCT
ap-1870	159	2	31	31	NUM
ap-1870	159	3	)	)	PUNCT
ap-1870	159	4	any	any	DET
ap-1870	159	5	lattice	lattice	NOUN
ap-1870	159	6	depending	depend	VERB
ap-1870	159	7	only	only	ADV
ap-1870	159	8	on	on	ADP
ap-1870	159	9	xk	xk	PROPN
ap-1870	159	10	will	will	AUX
ap-1870	159	11	be	be	AUX
ap-1870	159	12	invariant	invariant	ADJ
ap-1870	159	13	,	,	PUNCT
ap-1870	159	14	in	in	ADP
ap-1870	159	15	particular	particular	ADJ
ap-1870	159	16	the	the	DET
ap-1870	159	17	lattice	lattice	NOUN
ap-1870	159	18	equation	equation	NOUN
ap-1870	159	19	can	can	AUX
ap-1870	159	20	be	be	AUX
ap-1870	159	21	chosen	choose	VERB
ap-1870	159	22	to	to	PART
ap-1870	159	23	be	be	AUX
ap-1870	159	24	xn+1	xn+1	NUM
ap-1870	160	1	−	−	NOUN
ap-1870	160	2	2xn	2xn	ADJ
ap-1870	161	1	+	+	CCONJ
ap-1870	161	2	xn−1	xn−1	PROPN
ap-1870	161	3	=	=	PUNCT
ap-1870	161	4	0	0	PROPN
ap-1870	161	5	.	.	PUNCT
ap-1870	162	1	(	(	PUNCT
ap-1870	162	2	32	32	NUM
ap-1870	162	3	)	)	PUNCT
ap-1870	162	4	the	the	DET
ap-1870	162	5	general	general	ADJ
ap-1870	162	6	solution	solution	NOUN
ap-1870	162	7	of	of	ADP
ap-1870	162	8	(	(	PUNCT
ap-1870	162	9	32	32	NUM
ap-1870	162	10	)	)	PUNCT
ap-1870	162	11	is	be	AUX
ap-1870	162	12	xn	xn	NOUN
ap-1870	162	13	=	=	SYM
ap-1870	162	14	nh+	nh+	NOUN
ap-1870	162	15	c0	c0	NOUN
ap-1870	162	16	,	,	PUNCT
ap-1870	162	17	(	(	PUNCT
ap-1870	162	18	33	33	NUM
ap-1870	162	19	)	)	PUNCT
ap-1870	162	20	i.e.	i.e.	X
ap-1870	162	21	a	a	DET
ap-1870	162	22	uniform	uniform	ADJ
ap-1870	162	23	lattice	lattice	NOUN
ap-1870	162	24	with	with	ADP
ap-1870	162	25	origin	origin	NOUN
ap-1870	162	26	x0	x0	PROPN
ap-1870	162	27	and	and	CCONJ
ap-1870	162	28	spacing	space	VERB
ap-1870	162	29	xn+1	xn+1	PROPN
ap-1870	162	30	−	−	PROPN
ap-1870	162	31	xn	xn	PUNCT
ap-1870	163	1	=	=	SYM
ap-1870	163	2	h.	h.	PROPN
ap-1870	163	3	let	let	VERB
ap-1870	163	4	us	we	PRON
ap-1870	163	5	consider	consider	VERB
ap-1870	163	6	the	the	DET
ap-1870	163	7	invariant	invariant	ADJ
ap-1870	163	8	ode	ode	ADJ
ap-1870	163	9	1	1	NUM
ap-1870	163	10	y′2	y′2	NOUN
ap-1870	163	11	(	(	PUNCT
ap-1870	163	12	y′y′′′	y′y′′′	PROPN
ap-1870	163	13	−	−	PROPN
ap-1870	163	14	3	3	NUM
ap-1870	163	15	2y	2y	NUM
ap-1870	163	16	′′2	′′2	NOUN
ap-1870	163	17	)	)	PUNCT
ap-1870	163	18	=	=	SYM
ap-1870	163	19	sin(x	sin(x	PROPN
ap-1870	163	20	)	)	PUNCT
ap-1870	163	21	.	.	PUNCT
ap-1870	164	1	(	(	PUNCT
ap-1870	164	2	34	34	NUM
ap-1870	164	3	)	)	PUNCT
ap-1870	164	4	and	and	CCONJ
ap-1870	164	5	approximate	approximate	VERB
ap-1870	164	6	it	it	PRON
ap-1870	164	7	on	on	ADP
ap-1870	164	8	an	an	DET
ap-1870	164	9	a	a	DET
ap-1870	164	10	priori	priori	ADV
ap-1870	164	11	arbitrary	arbitrary	ADJ
ap-1870	164	12	lattice	lattice	NOUN
ap-1870	164	13	.	.	PUNCT
ap-1870	165	1	such	such	DET
ap-1870	165	2	a	a	DET
ap-1870	165	3	scheme	scheme	NOUN
ap-1870	165	4	is	be	AUX
ap-1870	165	5	given	give	VERB
ap-1870	165	6	by	by	ADP
ap-1870	165	7	e∆	e∆	ADJ
ap-1870	165	8	=	=	SYM
ap-1870	165	9	j1	j1	PROPN
ap-1870	165	10	−	−	PROPN
ap-1870	165	11	sin(ξ	sin(ξ	PROPN
ap-1870	165	12	)	)	PUNCT
ap-1870	165	13	=	=	SYM
ap-1870	165	14	0	0	NUM
ap-1870	165	15	,	,	PUNCT
ap-1870	165	16	(	(	PUNCT
ap-1870	165	17	35	35	NUM
ap-1870	165	18	)	)	PUNCT
ap-1870	166	1	ξ	ξ	NOUN
ap-1870	166	2	=	=	SYM
ap-1870	166	3	xn	xn	PROPN
ap-1870	167	1	+	+	NUM
ap-1870	167	2	ahn	ahn	PROPN
ap-1870	167	3	+	+	NUM
ap-1870	167	4	bhn+1	bhn+1	NOUN
ap-1870	167	5	+	+	X
ap-1870	167	6	chn+2	chn+2	PROPN
ap-1870	167	7	,	,	PUNCT
ap-1870	167	8	φ(xn	φ(xn	PROPN
ap-1870	167	9	,	,	PUNCT
ap-1870	167	10	hn	hn	PROPN
ap-1870	167	11	,	,	PUNCT
ap-1870	167	12	hn+1	hn+1	PROPN
ap-1870	167	13	,	,	PUNCT
ap-1870	167	14	hn+2	hn+2	NOUN
ap-1870	167	15	)	)	PUNCT
ap-1870	167	16	=	=	SYM
ap-1870	167	17	0	0	NUM
ap-1870	167	18	,	,	PUNCT
ap-1870	167	19	(	(	PUNCT
ap-1870	167	20	36	36	NUM
ap-1870	167	21	)	)	PUNCT
ap-1870	167	22	where	where	SCONJ
ap-1870	167	23	a	a	DET
ap-1870	167	24	,	,	PUNCT
ap-1870	167	25	b	b	NOUN
ap-1870	167	26	,	,	PUNCT
ap-1870	167	27	c	c	PROPN
ap-1870	167	28	are	be	AUX
ap-1870	167	29	constants	constant	NOUN
ap-1870	167	30	and	and	CCONJ
ap-1870	167	31	φ	φ	NOUN
ap-1870	167	32	satisfies	satisfy	VERB
ap-1870	167	33	the	the	DET
ap-1870	167	34	condition	condition	NOUN
ap-1870	167	35	φ(xn	φ(xn	NOUN
ap-1870	167	36	,	,	PUNCT
ap-1870	167	37	0	0	NUM
ap-1870	167	38	,	,	PUNCT
ap-1870	167	39	0	0	NUM
ap-1870	167	40	,	,	PUNCT
ap-1870	167	41	0	0	NUM
ap-1870	167	42	)	)	PUNCT
ap-1870	167	43	≡	≡	PROPN
ap-1870	167	44	0	0	NUM
ap-1870	167	45	,	,	PUNCT
ap-1870	167	46	(	(	PUNCT
ap-1870	167	47	37	37	NUM
ap-1870	167	48	)	)	PUNCT
ap-1870	167	49	(	(	PUNCT
ap-1870	167	50	for	for	ADP
ap-1870	167	51	instance	instance	NOUN
ap-1870	167	52	φ	φ	PROPN
ap-1870	167	53	can	can	AUX
ap-1870	167	54	be	be	AUX
ap-1870	167	55	linear	linear	ADJ
ap-1870	167	56	as	as	ADP
ap-1870	167	57	in	in	ADP
ap-1870	167	58	(	(	PUNCT
ap-1870	167	59	32	32	NUM
ap-1870	167	60	)	)	PUNCT
ap-1870	167	61	.	.	PUNCT
ap-1870	168	1	the	the	DET
ap-1870	168	2	first	first	ADJ
ap-1870	168	3	differential	differential	ADJ
ap-1870	168	4	approximation	approximation	NOUN
ap-1870	168	5	of	of	ADP
ap-1870	168	6	(	(	PUNCT
ap-1870	168	7	35	35	NUM
ap-1870	168	8	)	)	PUNCT
ap-1870	168	9	,	,	PUNCT
ap-1870	168	10	after	after	ADP
ap-1870	168	11	the	the	DET
ap-1870	168	12	usual	usual	ADJ
ap-1870	168	13	simplifications	simplification	NOUN
ap-1870	168	14	,	,	PUNCT
ap-1870	168	15	is	be	AUX
ap-1870	168	16	e0	e0	PROPN
ap-1870	169	1	≈	≈	PROPN
ap-1870	169	2	1	1	NUM
ap-1870	169	3	y′2	y′2	NOUN
ap-1870	169	4	(	(	PUNCT
ap-1870	169	5	y′y′′′	y′y′′′	PROPN
ap-1870	169	6	−	−	PROPN
ap-1870	169	7	3	3	NUM
ap-1870	169	8	2y	2y	NUM
ap-1870	169	9	′′2	′′2	NOUN
ap-1870	169	10	)	)	PUNCT
ap-1870	169	11	−	−	ADP
ap-1870	169	12	sin(x	sin(x	PROPN
ap-1870	169	13	)	)	PUNCT
ap-1870	169	14	+	+	NUM
ap-1870	169	15	cos(x	cos(x	PROPN
ap-1870	169	16	)	)	PUNCT
ap-1870	169	17	{	{	PUNCT
ap-1870	170	1	hn(1	hn(1	NOUN
ap-1870	170	2	+	+	CCONJ
ap-1870	170	3	4a)−	4a)−	X
ap-1870	170	4	2hn+1(1−	2hn+1(1−	NUM
ap-1870	170	5	2b	2b	NUM
ap-1870	170	6	)	)	PUNCT
ap-1870	170	7	−	−	PROPN
ap-1870	170	8	hn+2(1−	hn+2(1−	X
ap-1870	170	9	4c	4c	NOUN
ap-1870	170	10	)	)	PUNCT
ap-1870	170	11	}	}	PUNCT
ap-1870	170	12	.	.	PUNCT
ap-1870	171	1	(	(	PUNCT
ap-1870	171	2	38	38	NUM
ap-1870	171	3	)	)	PUNCT
ap-1870	171	4	eq	eq	NOUN
ap-1870	171	5	.	.	PUNCT
ap-1870	172	1	(	(	PUNCT
ap-1870	172	2	38	38	NUM
ap-1870	172	3	)	)	PUNCT
ap-1870	172	4	is	be	AUX
ap-1870	172	5	invariant	invariant	ADJ
ap-1870	172	6	under	under	ADP
ap-1870	172	7	sly(2,r	sly(2,r	PROPN
ap-1870	172	8	)	)	PUNCT
ap-1870	172	9	.	.	PUNCT
ap-1870	173	1	moreover	moreover	ADV
ap-1870	173	2	,	,	PUNCT
ap-1870	173	3	if	if	SCONJ
ap-1870	173	4	we	we	PRON
ap-1870	173	5	choose	choose	VERB
ap-1870	173	6	a	a	DET
ap-1870	173	7	=	=	NOUN
ap-1870	173	8	−1	−1	NOUN
ap-1870	173	9	4	4	NUM
ap-1870	173	10	,	,	PUNCT
ap-1870	173	11	b	b	X
ap-1870	173	12	=	=	SYM
ap-1870	173	13	1	1	NUM
ap-1870	173	14	2	2	NUM
ap-1870	173	15	,	,	PUNCT
ap-1870	173	16	c	c	NOUN
ap-1870	173	17	=	=	SYM
ap-1870	173	18	1	1	NUM
ap-1870	173	19	4	4	NUM
ap-1870	173	20	,	,	PUNCT
ap-1870	173	21	(	(	PUNCT
ap-1870	173	22	39	39	NUM
ap-1870	173	23	)	)	PUNCT
ap-1870	173	24	the	the	DET
ap-1870	173	25	second	second	ADJ
ap-1870	173	26	term	term	NOUN
ap-1870	173	27	in	in	ADP
ap-1870	173	28	(	(	PUNCT
ap-1870	173	29	38	38	NUM
ap-1870	173	30	)	)	PUNCT
ap-1870	173	31	vanishes	vanish	VERB
ap-1870	173	32	completely	completely	ADV
ap-1870	173	33	and	and	CCONJ
ap-1870	173	34	e0	e0	PROPN
ap-1870	174	1	=	=	SYM
ap-1870	174	2	0	0	PUNCT
ap-1870	174	3	is	be	AUX
ap-1870	174	4	a	a	DET
ap-1870	174	5	second	second	ADJ
ap-1870	174	6	order	order	NOUN
ap-1870	174	7	approximation	approximation	NOUN
ap-1870	174	8	of	of	ADP
ap-1870	174	9	the	the	DET
ap-1870	174	10	ode	ode	PROPN
ap-1870	174	11	(	(	PUNCT
ap-1870	174	12	34	34	NUM
ap-1870	174	13	)	)	PUNCT
ap-1870	174	14	.	.	PUNCT
ap-1870	175	1	we	we	PRON
ap-1870	175	2	mention	mention	VERB
ap-1870	175	3	that	that	SCONJ
ap-1870	175	4	the	the	DET
ap-1870	175	5	uniform	uniform	ADJ
ap-1870	175	6	lattice	lattice	PROPN
ap-1870	175	7	(	(	PUNCT
ap-1870	175	8	33	33	NUM
ap-1870	175	9	)	)	PUNCT
ap-1870	175	10	,	,	PUNCT
ap-1870	175	11	used	use	VERB
ap-1870	175	12	in	in	ADP
ap-1870	175	13	[	[	X
ap-1870	175	14	26	26	NUM
ap-1870	175	15	]	]	X
ap-1870	175	16	satisfies	satisfie	NOUN
ap-1870	175	17	(	(	PUNCT
ap-1870	175	18	39	39	NUM
ap-1870	175	19	)	)	PUNCT
ap-1870	175	20	.	.	PUNCT
ap-1870	176	1	5	5	X
ap-1870	176	2	.	.	X
ap-1870	176	3	equations	equation	NOUN
ap-1870	176	4	invariant	invariant	VERB
ap-1870	176	5	under	under	ADP
ap-1870	176	6	a	a	DET
ap-1870	176	7	two	two	NUM
ap-1870	176	8	-	-	PUNCT
ap-1870	176	9	dimensional	dimensional	ADJ
ap-1870	176	10	realization	realization	NOUN
ap-1870	176	11	of	of	ADP
ap-1870	176	12	gl(2,r	gl(2,r	NOUN
ap-1870	176	13	)	)	PUNCT
ap-1870	176	14	.	.	PUNCT
ap-1870	177	1	a	a	DET
ap-1870	177	2	genuinely	genuinely	ADV
ap-1870	177	3	two	two	NUM
ap-1870	177	4	-	-	PUNCT
ap-1870	177	5	dimensional	dimensional	ADJ
ap-1870	177	6	realization	realization	NOUN
ap-1870	177	7	of	of	ADP
ap-1870	177	8	the	the	DET
ap-1870	177	9	algebra	algebra	NOUN
ap-1870	177	10	gl(2,r	gl(2,r	NOUN
ap-1870	177	11	)	)	PUNCT
ap-1870	177	12	is	be	AUX
ap-1870	177	13	given	give	VERB
ap-1870	177	14	by	by	ADP
ap-1870	177	15	the	the	DET
ap-1870	177	16	vector	vector	NOUN
ap-1870	177	17	fields	field	NOUN
ap-1870	177	18	x̂1	x̂1	PUNCT
ap-1870	178	1	=	=	SYM
ap-1870	178	2	∂	∂	NUM
ap-1870	178	3	∂y	∂y	NOUN
ap-1870	178	4	,	,	PUNCT
ap-1870	178	5	x̂2	x̂2	PUNCT
ap-1870	178	6	=	=	SYM
ap-1870	178	7	x	x	SYM
ap-1870	178	8	∂	∂	NUM
ap-1870	178	9	∂x	∂x	PROPN
ap-1870	179	1	+	+	CCONJ
ap-1870	179	2	y	y	PROPN
ap-1870	179	3	∂	∂	NOUN
ap-1870	179	4	∂y	∂y	PROPN
ap-1870	179	5	,	,	PUNCT
ap-1870	179	6	x̂3	x̂3	PUNCT
ap-1870	179	7	=	=	SYM
ap-1870	180	1	2xy	2xy	ADJ
ap-1870	180	2	∂	∂	NUM
ap-1870	180	3	∂x	∂x	NOUN
ap-1870	180	4	+	+	CCONJ
ap-1870	181	1	y2	y2	PROPN
ap-1870	181	2	∂	∂	NOUN
ap-1870	181	3	∂y	∂y	NOUN
ap-1870	181	4	,	,	PUNCT
ap-1870	181	5	x̂4	x̂4	PUNCT
ap-1870	181	6	=	=	PUNCT
ap-1870	181	7	x	x	SYM
ap-1870	181	8	∂	∂	NUM
ap-1870	181	9	∂x	∂x	PROPN
ap-1870	181	10	.	.	PUNCT
ap-1870	182	1	(	(	PUNCT
ap-1870	182	2	40	40	NUM
ap-1870	182	3	)	)	PUNCT
ap-1870	182	4	441	441	NUM
ap-1870	182	5	d.	d.	PROPN
ap-1870	182	6	levi	levi	PROPN
ap-1870	182	7	,	,	PUNCT
ap-1870	182	8	p.	p.	PROPN
ap-1870	182	9	winternitz	winternitz	PROPN
ap-1870	182	10	acta	acta	PROPN
ap-1870	182	11	polytechnica	polytechnica	PROPN
ap-1870	182	12	the	the	DET
ap-1870	182	13	sl(2,r	sl(2,r	NOUN
ap-1870	182	14	)	)	PUNCT
ap-1870	182	15	group	group	NOUN
ap-1870	182	16	corresponding	correspond	VERB
ap-1870	182	17	to	to	ADP
ap-1870	182	18	{	{	PUNCT
ap-1870	182	19	x̂1	x̂1	PROPN
ap-1870	182	20	,	,	PUNCT
ap-1870	182	21	x̂2	x̂2	NOUN
ap-1870	182	22	,	,	PUNCT
ap-1870	182	23	x̂3	x̂3	PROPN
ap-1870	182	24	}	}	PUNCT
ap-1870	182	25	has	have	VERB
ap-1870	182	26	two	two	NUM
ap-1870	182	27	differential	differential	ADJ
ap-1870	182	28	invariants	invariant	NOUN
ap-1870	182	29	of	of	ADP
ap-1870	182	30	order	order	NOUN
ap-1870	182	31	m	m	VERB
ap-1870	182	32	≤	≤	ADJ
ap-1870	182	33	3	3	NUM
ap-1870	182	34	:	:	PUNCT
ap-1870	182	35	i1	i1	PROPN
ap-1870	182	36	=	=	PUNCT
ap-1870	182	37	2xy′′	2xy′′	PROPN
ap-1870	183	1	+	+	CCONJ
ap-1870	183	2	y′	y′	NUM
ap-1870	183	3	y′3	y′3	NOUN
ap-1870	183	4	,	,	PUNCT
ap-1870	183	5	i2	i2	PROPN
ap-1870	183	6	=	=	PUNCT
ap-1870	183	7	x2(y′y′′′	x2(y′y′′′	PROPN
ap-1870	184	1	−	−	PROPN
ap-1870	184	2	3y′′2	3y′′2	NUM
ap-1870	184	3	)	)	PUNCT
ap-1870	184	4	y′5	y′5	NOUN
ap-1870	184	5	.	.	PUNCT
ap-1870	185	1	(	(	PUNCT
ap-1870	185	2	41	41	NUM
ap-1870	185	3	)	)	PUNCT
ap-1870	185	4	the	the	DET
ap-1870	185	5	expression	expression	NOUN
ap-1870	185	6	i2	i2	PROPN
ap-1870	185	7	/	/	SYM
ap-1870	185	8	i	i	PROPN
ap-1870	185	9	3	3	NUM
ap-1870	185	10	2	2	NUM
ap-1870	185	11	1	1	NUM
ap-1870	185	12	is	be	AUX
ap-1870	185	13	also	also	ADV
ap-1870	185	14	invariant	invariant	ADJ
ap-1870	185	15	under	under	ADP
ap-1870	185	16	the	the	DET
ap-1870	185	17	dilations	dilation	NOUN
ap-1870	185	18	generated	generate	VERB
ap-1870	185	19	by	by	ADP
ap-1870	185	20	x̂4	x̂4	PROPN
ap-1870	185	21	and	and	CCONJ
ap-1870	185	22	hence	hence	ADV
ap-1870	185	23	under	under	ADP
ap-1870	185	24	gl(2,r	gl(2,r	NOUN
ap-1870	185	25	)	)	PUNCT
ap-1870	185	26	.	.	PUNCT
ap-1870	186	1	the	the	DET
ap-1870	186	2	corresponding	corresponding	ADJ
ap-1870	186	3	ode	ode	PROPN
ap-1870	186	4	invariant	invariant	NOUN
ap-1870	186	5	under	under	ADP
ap-1870	186	6	gl(2,r	gl(2,r	NOUN
ap-1870	186	7	)	)	PUNCT
ap-1870	186	8	is	be	AUX
ap-1870	186	9	i2	i2	PROPN
ap-1870	186	10	2	2	NUM
ap-1870	186	11	=	=	SYM
ap-1870	186	12	a2i3	a2i3	PUNCT
ap-1870	186	13	1	1	NUM
ap-1870	186	14	(	(	PUNCT
ap-1870	186	15	42	42	NUM
ap-1870	186	16	)	)	PUNCT
ap-1870	186	17	which	which	PRON
ap-1870	186	18	is	be	AUX
ap-1870	186	19	equivalent	equivalent	ADJ
ap-1870	186	20	to	to	ADP
ap-1870	186	21	e	e	X
ap-1870	186	22	=	=	PUNCT
ap-1870	186	23	x4(y′y′′′	x4(y′y′′′	PROPN
ap-1870	187	1	−	−	PROPN
ap-1870	187	2	3y′′2)2	3y′′2)2	NUM
ap-1870	187	3	−a2y′(2xy′′	−a2y′(2xy′′	NOUN
ap-1870	187	4	+	+	CCONJ
ap-1870	187	5	y′)3	y′)3	PROPN
ap-1870	187	6	=	=	NOUN
ap-1870	187	7	0	0	PROPN
ap-1870	187	8	.	.	PUNCT
ap-1870	188	1	(	(	PUNCT
ap-1870	188	2	43	43	NUM
ap-1870	188	3	)	)	PUNCT
ap-1870	188	4	five	five	NUM
ap-1870	188	5	independent	independent	ADJ
ap-1870	188	6	sl(2,r	sl(2,r	NOUN
ap-1870	188	7	)	)	PUNCT
ap-1870	188	8	difference	difference	NOUN
ap-1870	188	9	invariants	invariant	NOUN
ap-1870	188	10	are	be	AUX
ap-1870	188	11	ξ1	ξ1	NOUN
ap-1870	188	12	=	=	SYM
ap-1870	188	13	1	1	NUM
ap-1870	188	14	√	√	NUM
ap-1870	188	15	xn+1xn+2	xn+1xn+2	PUNCT
ap-1870	189	1	(	(	PUNCT
ap-1870	189	2	yn+2	yn+2	NUM
ap-1870	189	3	−	−	NOUN
ap-1870	189	4	yn+1	yn+1	NUM
ap-1870	189	5	)	)	PUNCT
ap-1870	189	6	,	,	PUNCT
ap-1870	189	7	ξ2	ξ2	NOUN
ap-1870	189	8	=	=	NOUN
ap-1870	189	9	1	1	NUM
ap-1870	189	10	√	√	NUM
ap-1870	189	11	xnxn+1	xnxn+1	PROPN
ap-1870	189	12	(	(	PUNCT
ap-1870	189	13	yn+1	yn+1	PROPN
ap-1870	189	14	−	−	PROPN
ap-1870	189	15	yn	yn	PROPN
ap-1870	189	16	)	)	PUNCT
ap-1870	189	17	,	,	PUNCT
ap-1870	189	18	ξ3	ξ3	NOUN
ap-1870	189	19	=	=	NOUN
ap-1870	189	20	1	1	NUM
ap-1870	189	21	√	√	NUM
ap-1870	189	22	xn−1xn	xn−1xn	PROPN
ap-1870	189	23	(	(	PUNCT
ap-1870	189	24	yn	yn	PROPN
ap-1870	189	25	−	−	PROPN
ap-1870	189	26	yn−1	yn−1	PROPN
ap-1870	189	27	)	)	PUNCT
ap-1870	189	28	,	,	PUNCT
ap-1870	189	29	ξ4	ξ4	NOUN
ap-1870	189	30	=	=	NOUN
ap-1870	189	31	1	1	NUM
ap-1870	189	32	√	√	NUM
ap-1870	189	33	xnxn+2	xnxn+2	PUNCT
ap-1870	190	1	(	(	PUNCT
ap-1870	190	2	yn+2	yn+2	NUM
ap-1870	190	3	−	−	PROPN
ap-1870	190	4	yn	yn	PROPN
ap-1870	190	5	)	)	PUNCT
ap-1870	190	6	,	,	PUNCT
ap-1870	190	7	ξ5	ξ5	NOUN
ap-1870	190	8	=	=	SYM
ap-1870	190	9	1	1	NUM
ap-1870	190	10	√	√	NUM
ap-1870	190	11	xn+1xn−1	xn+1xn−1	PROPN
ap-1870	190	12	(	(	PUNCT
ap-1870	190	13	yn+1	yn+1	PROPN
ap-1870	190	14	−	−	PROPN
ap-1870	190	15	yn−1	yn−1	PROPN
ap-1870	190	16	)	)	PUNCT
ap-1870	190	17	.	.	PUNCT
ap-1870	191	1	(	(	PUNCT
ap-1870	191	2	44	44	NUM
ap-1870	191	3	)	)	PUNCT
ap-1870	191	4	any	any	DET
ap-1870	191	5	4	4	NUM
ap-1870	191	6	ratios	ratio	NOUN
ap-1870	191	7	ξi	ξi	NOUN
ap-1870	191	8	/	/	SYM
ap-1870	191	9	ξk	ξk	PROPN
ap-1870	191	10	will	will	AUX
ap-1870	191	11	be	be	AUX
ap-1870	191	12	gl(2,r	gl(2,r	NOUN
ap-1870	191	13	)	)	PUNCT
ap-1870	191	14	invariants	invariant	NOUN
ap-1870	191	15	.	.	PUNCT
ap-1870	192	1	the	the	DET
ap-1870	192	2	sl(2,r	sl(2,r	NOUN
ap-1870	192	3	)	)	PUNCT
ap-1870	192	4	invariants	invariant	NOUN
ap-1870	192	5	that	that	PRON
ap-1870	192	6	have	have	VERB
ap-1870	192	7	the	the	DET
ap-1870	192	8	correct	correct	ADJ
ap-1870	192	9	continuous	continuous	ADJ
ap-1870	192	10	limits	limit	NOUN
ap-1870	192	11	are	be	AUX
ap-1870	192	12	j2	j2	NOUN
ap-1870	192	13	=	=	NOUN
ap-1870	192	14	12	12	NUM
ap-1870	192	15	ξ2(ξ1	ξ2(ξ1	NUM
ap-1870	192	16	+	+	CCONJ
ap-1870	192	17	ξ2	ξ2	ADJ
ap-1870	192	18	+	+	CCONJ
ap-1870	192	19	ξ3	ξ3	NOUN
ap-1870	192	20	)	)	PUNCT
ap-1870	193	1	[	[	X
ap-1870	193	2	ξ4	ξ4	ADJ
ap-1870	193	3	−	−	PROPN
ap-1870	193	4	ξ1	ξ1	NOUN
ap-1870	193	5	−	−	PROPN
ap-1870	193	6	ξ2	ξ2	NOUN
ap-1870	193	7	ξ1(ξ1	ξ1(ξ1	CCONJ
ap-1870	193	8	+	+	CCONJ
ap-1870	193	9	ξ2	ξ2	ADJ
ap-1870	193	10	)	)	PUNCT
ap-1870	193	11	−	−	PROPN
ap-1870	193	12	ξ5	ξ5	NOUN
ap-1870	193	13	−	−	PROPN
ap-1870	193	14	ξ2	ξ2	NOUN
ap-1870	193	15	−	−	PROPN
ap-1870	193	16	ξ3	ξ3	PROPN
ap-1870	193	17	ξ3(ξ2	ξ3(ξ2	PROPN
ap-1870	193	18	+	+	CCONJ
ap-1870	193	19	ξ3	ξ3	NOUN
ap-1870	193	20	)	)	PUNCT
ap-1870	193	21	]	]	PUNCT
ap-1870	194	1	j1	j1	PROPN
ap-1870	194	2	=	=	SYM
ap-1870	194	3	8	8	NUM
ap-1870	194	4	[	[	PUNCT
ap-1870	194	5	α	α	NOUN
ap-1870	194	6	ξ4	ξ4	NOUN
ap-1870	194	7	−	−	PROPN
ap-1870	194	8	ξ1	ξ1	PROPN
ap-1870	194	9	−	−	PROPN
ap-1870	194	10	ξ2	ξ2	PROPN
ap-1870	194	11	ξ1ξ2(ξ1	ξ1ξ2(ξ1	ADJ
ap-1870	194	12	+	+	CCONJ
ap-1870	194	13	ξ2	ξ2	ADJ
ap-1870	194	14	)	)	PUNCT
ap-1870	195	1	+	+	CCONJ
ap-1870	195	2	(	(	PUNCT
ap-1870	195	3	1−	1−	NUM
ap-1870	195	4	α	α	NOUN
ap-1870	195	5	)	)	PUNCT
ap-1870	195	6	ξ5	ξ5	NOUN
ap-1870	195	7	−	−	PROPN
ap-1870	196	1	ξ2	ξ2	NOUN
ap-1870	196	2	−	−	PROPN
ap-1870	196	3	ξ3	ξ3	PROPN
ap-1870	196	4	ξ2ξ3(ξ2	ξ2ξ3(ξ2	NOUN
ap-1870	196	5	+	+	X
ap-1870	196	6	ξ3	ξ3	NOUN
ap-1870	196	7	)	)	PUNCT
ap-1870	196	8	]	]	PUNCT
ap-1870	196	9	.	.	PUNCT
ap-1870	197	1	(	(	PUNCT
ap-1870	197	2	45	45	NUM
ap-1870	197	3	)	)	PUNCT
ap-1870	197	4	the	the	DET
ap-1870	197	5	difference	difference	NOUN
ap-1870	197	6	scheme	scheme	NOUN
ap-1870	197	7	for	for	ADP
ap-1870	197	8	the	the	DET
ap-1870	197	9	ode	ode	PROPN
ap-1870	197	10	(	(	PUNCT
ap-1870	197	11	43	43	NUM
ap-1870	197	12	)	)	PUNCT
ap-1870	197	13	with	with	ADP
ap-1870	197	14	a	a	DET
ap-1870	197	15	=	=	NOUN
ap-1870	197	16	−1	−1	NOUN
ap-1870	197	17	used	use	VERB
ap-1870	197	18	in	in	ADP
ap-1870	197	19	ref	ref	NOUN
ap-1870	197	20	.	.	PUNCT
ap-1870	198	1	[	[	X
ap-1870	198	2	26	26	NUM
ap-1870	198	3	]	]	PUNCT
ap-1870	198	4	was	be	AUX
ap-1870	198	5	actually	actually	ADV
ap-1870	198	6	the	the	DET
ap-1870	198	7	square	square	ADJ
ap-1870	198	8	root	root	NOUN
ap-1870	198	9	of	of	ADP
ap-1870	198	10	(	(	PUNCT
ap-1870	198	11	42	42	NUM
ap-1870	198	12	)	)	PUNCT
ap-1870	198	13	,	,	PUNCT
ap-1870	198	14	equivalent	equivalent	ADJ
ap-1870	198	15	to	to	ADP
ap-1870	198	16	e∆	e∆	SYM
ap-1870	198	17	1	1	NUM
ap-1870	198	18	=	=	SYM
ap-1870	198	19	j2	j2	PROPN
ap-1870	198	20	+	+	CCONJ
ap-1870	198	21	j	j	PROPN
ap-1870	198	22	3	3	NUM
ap-1870	198	23	2	2	NUM
ap-1870	198	24	1	1	NUM
ap-1870	198	25	=	=	SYM
ap-1870	198	26	0	0	NUM
ap-1870	198	27	,	,	PUNCT
ap-1870	198	28	(	(	PUNCT
ap-1870	198	29	46	46	NUM
ap-1870	198	30	)	)	PUNCT
ap-1870	198	31	e∆	e∆	ADV
ap-1870	198	32	2	2	NUM
ap-1870	198	33	=	=	SYM
ap-1870	198	34	ξ1	ξ1	NOUN
ap-1870	198	35	ξ2	ξ2	NOUN
ap-1870	198	36	=	=	PUNCT
ap-1870	198	37	γ	γ	X
ap-1870	198	38	=	=	PUNCT
ap-1870	198	39	const	const	PROPN
ap-1870	198	40	.	.	PUNCT
ap-1870	199	1	(	(	PUNCT
ap-1870	199	2	47	47	NUM
ap-1870	199	3	)	)	PUNCT
ap-1870	199	4	the	the	DET
ap-1870	199	5	first	first	ADJ
ap-1870	199	6	differential	differential	ADJ
ap-1870	199	7	approximation	approximation	NOUN
ap-1870	199	8	of	of	ADP
ap-1870	199	9	the	the	DET
ap-1870	199	10	lattice	lattice	NOUN
ap-1870	199	11	equation	equation	NOUN
ap-1870	199	12	(	(	PUNCT
ap-1870	199	13	47	47	NUM
ap-1870	199	14	)	)	PUNCT
ap-1870	199	15	is	be	AUX
ap-1870	199	16	e	e	NOUN
ap-1870	199	17	(	(	PUNCT
ap-1870	199	18	∆	∆	X
ap-1870	199	19	)	)	PUNCT
ap-1870	199	20	1	1	NUM
ap-1870	199	21	≈	≈	PROPN
ap-1870	199	22	(	(	PUNCT
ap-1870	199	23	γhn+1	γhn+1	PROPN
ap-1870	199	24	−	−	PROPN
ap-1870	199	25	hn+2)y′	hn+2)y′	PROPN
ap-1870	200	1	+	+	CCONJ
ap-1870	200	2	1	1	NUM
ap-1870	200	3	2x2	2x2	NUM
ap-1870	200	4	{	{	PUNCT
ap-1870	200	5	[	[	PUNCT
ap-1870	200	6	−γh2	−γh2	NOUN
ap-1870	200	7	n+1	n+1	PROPN
ap-1870	200	8	+	+	CCONJ
ap-1870	200	9	hn+2(hn+2	hn+2(hn+2	PROPN
ap-1870	200	10	+	+	NOUN
ap-1870	200	11	2hn+1	2hn+1	NUM
ap-1870	200	12	)	)	PUNCT
ap-1870	200	13	]	]	PUNCT
ap-1870	200	14	y′	y′	PUNCT
ap-1870	201	1	+	+	CCONJ
ap-1870	201	2	xy′′	xy′′	PROPN
ap-1870	202	1	[	[	PUNCT
ap-1870	202	2	γh2	γh2	NOUN
ap-1870	202	3	n+1	n+1	ADV
ap-1870	202	4	−	−	NOUN
ap-1870	202	5	hn+1hn+2	hn+1hn+2	ADP
ap-1870	202	6	−	−	PROPN
ap-1870	202	7	h2	h2	PROPN
ap-1870	202	8	n+2	n+2	PRON
ap-1870	202	9	]	]	X
ap-1870	202	10	}	}	PUNCT
ap-1870	202	11	=	=	SYM
ap-1870	202	12	0	0	X
ap-1870	202	13	.	.	PUNCT
ap-1870	203	1	(	(	PUNCT
ap-1870	203	2	48	48	NUM
ap-1870	203	3	)	)	PUNCT
ap-1870	203	4	both	both	DET
ap-1870	203	5	terms	term	NOUN
ap-1870	203	6	in	in	ADP
ap-1870	203	7	(	(	PUNCT
ap-1870	203	8	48	48	NUM
ap-1870	203	9	)	)	PUNCT
ap-1870	203	10	are	be	AUX
ap-1870	203	11	invariant	invariant	ADJ
ap-1870	203	12	under	under	ADP
ap-1870	203	13	gl(2,r	gl(2,r	NOUN
ap-1870	203	14	)	)	PUNCT
ap-1870	203	15	.	.	PUNCT
ap-1870	204	1	the	the	DET
ap-1870	204	2	first	first	ADJ
ap-1870	204	3	differential	differential	ADJ
ap-1870	204	4	approximation	approximation	NOUN
ap-1870	204	5	to	to	ADP
ap-1870	204	6	the	the	DET
ap-1870	204	7	difference	difference	NOUN
ap-1870	204	8	equation	equation	NOUN
ap-1870	204	9	(	(	PUNCT
ap-1870	204	10	46	46	NUM
ap-1870	204	11	)	)	PUNCT
ap-1870	204	12	is	be	AUX
ap-1870	204	13	e	e	NOUN
ap-1870	204	14	(	(	PUNCT
ap-1870	204	15	∆	∆	X
ap-1870	204	16	)	)	PUNCT
ap-1870	204	17	1	1	NUM
ap-1870	205	1	≈	≈	NOUN
ap-1870	205	2	e	e	NOUN
ap-1870	205	3	y′10	y′10	NOUN
ap-1870	205	4	−	−	NOUN
ap-1870	205	5	√	√	NOUN
ap-1870	205	6	y′(y′	y′(y′	NOUN
ap-1870	205	7	+	+	CCONJ
ap-1870	205	8	2xy′′	2xy′′	NUM
ap-1870	205	9	)	)	PUNCT
ap-1870	205	10	7	7	NUM
ap-1870	205	11	2	2	NUM
ap-1870	205	12	16xy′10(hn	16xy′10(hn	NUM
ap-1870	205	13	+	+	NUM
ap-1870	205	14	hn+1	hn+1	NOUN
ap-1870	205	15	+	+	CCONJ
ap-1870	205	16	hn+2	hn+2	NOUN
ap-1870	205	17	)	)	PUNCT
ap-1870	205	18	×	×	NOUN
ap-1870	205	19	[	[	PUNCT
ap-1870	205	20	h2	h2	NOUN
ap-1870	205	21	n(32α−	n(32α−	VERB
ap-1870	205	22	11	11	NUM
ap-1870	205	23	)	)	PUNCT
ap-1870	205	24	+	+	CCONJ
ap-1870	205	25	16h2	16h2	NUM
ap-1870	205	26	n+1(2α−	n+1(2α−	PROPN
ap-1870	205	27	1	1	NUM
ap-1870	205	28	)	)	PUNCT
ap-1870	205	29	+	+	NUM
ap-1870	205	30	h2	h2	NOUN
ap-1870	205	31	n+2(32α−	n+2(32α−	ADP
ap-1870	205	32	21	21	NUM
ap-1870	205	33	)	)	PUNCT
ap-1870	206	1	+	+	NUM
ap-1870	206	2	hnhn+1(64α−	hnhn+1(64α−	NOUN
ap-1870	206	3	21	21	NUM
ap-1870	206	4	)	)	PUNCT
ap-1870	206	5	+	+	CCONJ
ap-1870	206	6	32hnhn+2(2α−	32hnhn+2(2α−	NUM
ap-1870	206	7	1	1	NUM
ap-1870	206	8	)	)	PUNCT
ap-1870	206	9	+	+	NUM
ap-1870	206	10	hn+1hn+2(64α−	hn+1hn+2(64α−	PROPN
ap-1870	206	11	43	43	NUM
ap-1870	206	12	)	)	PUNCT
ap-1870	206	13	]	]	PUNCT
ap-1870	206	14	.	.	PUNCT
ap-1870	207	1	(	(	PUNCT
ap-1870	207	2	49	49	NUM
ap-1870	207	3	)	)	PUNCT
ap-1870	207	4	the	the	DET
ap-1870	207	5	second	second	ADJ
ap-1870	207	6	term	term	NOUN
ap-1870	207	7	of	of	ADP
ap-1870	207	8	expression	expression	NOUN
ap-1870	207	9	(	(	PUNCT
ap-1870	207	10	49	49	NUM
ap-1870	207	11	)	)	PUNCT
ap-1870	207	12	has	have	AUX
ap-1870	207	13	been	be	AUX
ap-1870	207	14	simplified	simplify	VERB
ap-1870	207	15	using	use	VERB
ap-1870	207	16	(	(	PUNCT
ap-1870	207	17	43	43	NUM
ap-1870	207	18	)	)	PUNCT
ap-1870	207	19	and	and	CCONJ
ap-1870	207	20	its	its	PRON
ap-1870	207	21	differential	differential	ADJ
ap-1870	207	22	consequences	consequence	NOUN
ap-1870	207	23	.	.	PUNCT
ap-1870	208	1	again	again	ADV
ap-1870	208	2	,	,	PUNCT
ap-1870	208	3	(	(	PUNCT
ap-1870	208	4	49	49	NUM
ap-1870	208	5	)	)	PUNCT
ap-1870	208	6	is	be	AUX
ap-1870	208	7	invariant	invariant	ADJ
ap-1870	208	8	under	under	ADP
ap-1870	208	9	the	the	DET
ap-1870	208	10	entire	entire	ADJ
ap-1870	208	11	gl(2,r	gl(2,r	NOUN
ap-1870	208	12	)	)	PUNCT
ap-1870	208	13	group	group	NOUN
ap-1870	208	14	.	.	PUNCT
ap-1870	209	1	6	6	NUM
ap-1870	209	2	.	.	PUNCT
ap-1870	209	3	conclusions	conclusion	NOUN
ap-1870	209	4	the	the	DET
ap-1870	209	5	three	three	NUM
ap-1870	209	6	examples	example	NOUN
ap-1870	209	7	considered	consider	VERB
ap-1870	209	8	above	above	ADV
ap-1870	209	9	in	in	ADP
ap-1870	209	10	sections	section	NOUN
ap-1870	209	11	3	3	NUM
ap-1870	209	12	,	,	PUNCT
ap-1870	209	13	4	4	NUM
ap-1870	209	14	and	and	CCONJ
ap-1870	209	15	5	5	NUM
ap-1870	209	16	confirm	confirm	VERB
ap-1870	209	17	that	that	SCONJ
ap-1870	209	18	the	the	DET
ap-1870	209	19	method	method	NOUN
ap-1870	209	20	of	of	ADP
ap-1870	209	21	invariant	invariant	ADJ
ap-1870	209	22	discretization	discretization	NOUN
ap-1870	209	23	provides	provide	VERB
ap-1870	209	24	a	a	DET
ap-1870	209	25	systematic	systematic	ADJ
ap-1870	209	26	way	way	NOUN
ap-1870	209	27	of	of	ADP
ap-1870	209	28	constructing	construct	VERB
ap-1870	209	29	difference	difference	NOUN
ap-1870	209	30	schemes	scheme	NOUN
ap-1870	209	31	for	for	ADP
ap-1870	209	32	which	which	PRON
ap-1870	209	33	the	the	DET
ap-1870	209	34	first	first	ADJ
ap-1870	209	35	differential	differential	ADJ
ap-1870	209	36	approximation	approximation	NOUN
ap-1870	209	37	is	be	AUX
ap-1870	209	38	invariant	invariant	ADJ
ap-1870	209	39	under	under	ADP
ap-1870	209	40	the	the	DET
ap-1870	209	41	entire	entire	ADJ
ap-1870	209	42	symmetry	symmetry	NOUN
ap-1870	209	43	group	group	NOUN
ap-1870	209	44	of	of	ADP
ap-1870	209	45	the	the	DET
ap-1870	209	46	original	original	ADJ
ap-1870	209	47	ode	ode	NOUN
ap-1870	209	48	.	.	PUNCT
ap-1870	210	1	the	the	DET
ap-1870	210	2	two	two	NUM
ap-1870	210	3	equations	equation	NOUN
ap-1870	210	4	(	(	PUNCT
ap-1870	210	5	13	13	NUM
ap-1870	210	6	)	)	PUNCT
ap-1870	210	7	determining	determine	VERB
ap-1870	210	8	the	the	DET
ap-1870	210	9	invariant	invariant	ADJ
ap-1870	210	10	difference	difference	NOUN
ap-1870	210	11	scheme	scheme	NOUN
ap-1870	210	12	for	for	ADP
ap-1870	210	13	an	an	DET
ap-1870	210	14	ode	ode	NOUN
ap-1870	210	15	are	be	AUX
ap-1870	210	16	not	not	PART
ap-1870	210	17	unique	unique	ADJ
ap-1870	210	18	since	since	SCONJ
ap-1870	210	19	there	there	PRON
ap-1870	210	20	are	be	VERB
ap-1870	210	21	more	more	ADJ
ap-1870	210	22	difference	difference	NOUN
ap-1870	210	23	invariants	invariant	NOUN
ap-1870	210	24	than	than	ADP
ap-1870	210	25	differential	differential	ADJ
ap-1870	210	26	ones	one	NOUN
ap-1870	210	27	.	.	PUNCT
ap-1870	211	1	the	the	DET
ap-1870	211	2	differential	differential	ADJ
ap-1870	211	3	approximation	approximation	NOUN
ap-1870	211	4	of	of	ADP
ap-1870	211	5	an	an	DET
ap-1870	211	6	invariant	invariant	ADJ
ap-1870	211	7	scheme	scheme	NOUN
ap-1870	211	8	can	can	AUX
ap-1870	211	9	be	be	AUX
ap-1870	211	10	used	use	VERB
ap-1870	211	11	to	to	PART
ap-1870	211	12	benefit	benefit	VERB
ap-1870	211	13	from	from	ADP
ap-1870	211	14	this	this	DET
ap-1870	211	15	freedom	freedom	NOUN
ap-1870	211	16	and	and	CCONJ
ap-1870	211	17	to	to	PART
ap-1870	211	18	choose	choose	VERB
ap-1870	211	19	an	an	DET
ap-1870	211	20	invariant	invariant	ADJ
ap-1870	211	21	scheme	scheme	NOUN
ap-1870	211	22	with	with	ADP
ap-1870	211	23	a	a	DET
ap-1870	211	24	higher	high	ADJ
ap-1870	211	25	degree	degree	NOUN
ap-1870	211	26	of	of	ADP
ap-1870	211	27	accuracy	accuracy	NOUN
ap-1870	211	28	.	.	PUNCT
ap-1870	212	1	an	an	DET
ap-1870	212	2	example	example	NOUN
ap-1870	212	3	of	of	ADP
ap-1870	212	4	this	this	PRON
ap-1870	212	5	is	be	AUX
ap-1870	212	6	given	give	VERB
ap-1870	212	7	in	in	ADP
ap-1870	212	8	section	section	NOUN
ap-1870	212	9	3	3	NUM
ap-1870	212	10	,	,	PUNCT
ap-1870	212	11	eq	eq	NOUN
ap-1870	212	12	.	.	PUNCT
ap-1870	213	1	(	(	PUNCT
ap-1870	213	2	38	38	NUM
ap-1870	213	3	)	)	PUNCT
ap-1870	213	4	where	where	SCONJ
ap-1870	213	5	the	the	DET
ap-1870	213	6	choice	choice	NOUN
ap-1870	213	7	of	of	ADP
ap-1870	213	8	the	the	DET
ap-1870	213	9	parameters	parameter	NOUN
ap-1870	213	10	(	(	PUNCT
ap-1870	213	11	39	39	NUM
ap-1870	213	12	)	)	PUNCT
ap-1870	213	13	assures	assure	VERB
ap-1870	213	14	that	that	SCONJ
ap-1870	213	15	the	the	DET
ap-1870	213	16	terms	term	NOUN
ap-1870	213	17	of	of	ADP
ap-1870	213	18	order	order	NOUN
ap-1870	213	19	ε	ε	PROPN
ap-1870	213	20	in	in	ADP
ap-1870	213	21	(	(	PUNCT
ap-1870	213	22	38	38	NUM
ap-1870	213	23	)	)	PUNCT
ap-1870	213	24	vanish	vanish	VERB
ap-1870	213	25	identically	identically	ADV
ap-1870	213	26	.	.	PUNCT
ap-1870	214	1	previous	previous	ADJ
ap-1870	214	2	numerical	numerical	ADJ
ap-1870	214	3	comparisons	comparison	NOUN
ap-1870	214	4	between	between	ADP
ap-1870	214	5	invariant	invariant	ADJ
ap-1870	214	6	discretization	discretization	NOUN
ap-1870	214	7	and	and	CCONJ
ap-1870	214	8	standard	standard	ADJ
ap-1870	214	9	noninvariant	noninvariant	ADJ
ap-1870	214	10	numerical	numerical	ADJ
ap-1870	214	11	methods	method	NOUN
ap-1870	214	12	for	for	ADP
ap-1870	214	13	odes	ode	NOUN
ap-1870	214	14	[	[	X
ap-1870	214	15	26–28	26–28	X
ap-1870	214	16	]	]	PUNCT
ap-1870	214	17	have	have	AUX
ap-1870	214	18	shown	show	VERB
ap-1870	214	19	two	two	NUM
ap-1870	214	20	features	feature	NOUN
ap-1870	214	21	.	.	PUNCT
ap-1870	215	1	the	the	DET
ap-1870	215	2	first	first	ADJ
ap-1870	215	3	is	be	AUX
ap-1870	215	4	that	that	SCONJ
ap-1870	215	5	the	the	DET
ap-1870	215	6	discretization	discretization	NOUN
ap-1870	215	7	errors	error	NOUN
ap-1870	215	8	for	for	ADP
ap-1870	215	9	invariant	invariant	ADJ
ap-1870	215	10	schemes	scheme	NOUN
ap-1870	215	11	are	be	AUX
ap-1870	215	12	significantly	significantly	ADV
ap-1870	215	13	smaller	small	ADJ
ap-1870	215	14	[	[	X
ap-1870	215	15	26	26	NUM
ap-1870	215	16	]	]	PUNCT
ap-1870	215	17	(	(	PUNCT
ap-1870	215	18	by	by	ADP
ap-1870	215	19	3	3	NUM
ap-1870	215	20	orders	order	NOUN
ap-1870	215	21	of	of	ADP
ap-1870	215	22	magnitude	magnitude	NOUN
ap-1870	215	23	for	for	ADP
ap-1870	215	24	eq	eq	PROPN
ap-1870	215	25	.	.	PUNCT
ap-1870	216	1	(	(	PUNCT
ap-1870	216	2	18	18	NUM
ap-1870	216	3	)	)	PUNCT
ap-1870	216	4	,	,	PUNCT
ap-1870	216	5	1	1	NUM
ap-1870	216	6	order	order	NOUN
ap-1870	216	7	of	of	ADP
ap-1870	216	8	magnitude	magnitude	NOUN
ap-1870	216	9	for	for	ADP
ap-1870	216	10	eq	eq	NOUN
ap-1870	216	11	.	.	PUNCT
ap-1870	217	1	(	(	PUNCT
ap-1870	217	2	43	43	NUM
ap-1870	217	3	)	)	PUNCT
ap-1870	217	4	)	)	PUNCT
ap-1870	217	5	.	.	PUNCT
ap-1870	218	1	the	the	DET
ap-1870	218	2	second	second	ADJ
ap-1870	218	3	feature	feature	NOUN
ap-1870	218	4	is	be	AUX
ap-1870	218	5	that	that	SCONJ
ap-1870	218	6	the	the	DET
ap-1870	218	7	qualitative	qualitative	ADJ
ap-1870	218	8	behaviour	behaviour	NOUN
ap-1870	218	9	of	of	ADP
ap-1870	218	10	solutions	solution	NOUN
ap-1870	218	11	close	close	ADJ
ap-1870	218	12	to	to	ADP
ap-1870	218	13	singularities	singularity	NOUN
ap-1870	218	14	is	be	AUX
ap-1870	218	15	described	describe	VERB
ap-1870	218	16	much	much	ADV
ap-1870	218	17	more	more	ADV
ap-1870	218	18	accurately	accurately	ADV
ap-1870	218	19	by	by	ADP
ap-1870	218	20	the	the	DET
ap-1870	218	21	invariant	invariant	ADJ
ap-1870	218	22	schemes	scheme	NOUN
ap-1870	218	23	[	[	X
ap-1870	218	24	26	26	NUM
ap-1870	218	25	–	–	SYM
ap-1870	218	26	28	28	NUM
ap-1870	218	27	]	]	PUNCT
ap-1870	218	28	.	.	PUNCT
ap-1870	219	1	an	an	DET
ap-1870	219	2	analysis	analysis	NOUN
ap-1870	219	3	of	of	ADP
ap-1870	219	4	the	the	DET
ap-1870	219	5	relation	relation	NOUN
ap-1870	219	6	between	between	ADP
ap-1870	219	7	invariant	invariant	ADJ
ap-1870	219	8	discretization	discretization	NOUN
ap-1870	219	9	and	and	CCONJ
ap-1870	219	10	the	the	DET
ap-1870	219	11	differential	differential	ADJ
ap-1870	219	12	approximation	approximation	NOUN
ap-1870	219	13	method	method	NOUN
ap-1870	219	14	for	for	ADP
ap-1870	219	15	pdes	pde	NOUN
ap-1870	219	16	is	be	AUX
ap-1870	219	17	in	in	ADP
ap-1870	219	18	progress	progress	NOUN
ap-1870	219	19	.	.	PUNCT
ap-1870	220	1	acknowledgements	acknowledgement	NOUN
ap-1870	220	2	we	we	PRON
ap-1870	220	3	thank	thank	VERB
ap-1870	220	4	alex	alex	PROPN
ap-1870	220	5	bihlo	bihlo	PROPN
ap-1870	220	6	for	for	ADP
ap-1870	220	7	interesting	interesting	ADJ
ap-1870	220	8	discussions	discussion	NOUN
ap-1870	220	9	.	.	PUNCT
ap-1870	221	1	the	the	DET
ap-1870	221	2	research	research	NOUN
ap-1870	221	3	of	of	ADP
ap-1870	221	4	p.w	p.w	PROPN
ap-1870	221	5	.	.	PROPN
ap-1870	221	6	was	be	AUX
ap-1870	221	7	partially	partially	ADV
ap-1870	221	8	supported	support	VERB
ap-1870	221	9	by	by	ADP
ap-1870	221	10	a	a	DET
ap-1870	221	11	grant	grant	NOUN
ap-1870	221	12	from	from	ADP
ap-1870	221	13	nserc	nserc	NOUN
ap-1870	221	14	of	of	ADP
ap-1870	221	15	canada	canada	PROPN
ap-1870	221	16	.	.	PUNCT
ap-1870	222	1	d.l	d.l	PROPN
ap-1870	222	2	.	.	PROPN
ap-1870	223	1	thanks	thank	NOUN
ap-1870	223	2	the	the	DET
ap-1870	223	3	crm	crm	PROPN
ap-1870	223	4	for	for	ADP
ap-1870	223	5	its	its	PRON
ap-1870	223	6	hospitality	hospitality	NOUN
ap-1870	223	7	.	.	PUNCT
ap-1870	224	1	the	the	DET
ap-1870	224	2	research	research	NOUN
ap-1870	224	3	of	of	ADP
ap-1870	224	4	d.l	d.l	PROPN
ap-1870	224	5	.	.	PROPN
ap-1870	224	6	has	have	AUX
ap-1870	224	7	been	be	AUX
ap-1870	224	8	partly	partly	ADV
ap-1870	224	9	supported	support	VERB
ap-1870	224	10	by	by	ADP
ap-1870	224	11	the	the	DET
ap-1870	224	12	italian	italian	PROPN
ap-1870	224	13	ministry	ministry	PROPN
ap-1870	224	14	of	of	ADP
ap-1870	224	15	education	education	PROPN
ap-1870	224	16	and	and	CCONJ
ap-1870	224	17	research	research	NOUN
ap-1870	224	18	,	,	PUNCT
ap-1870	224	19	2010	2010	NUM
ap-1870	224	20	prin	prin	NOUN
ap-1870	224	21	“	"	PUNCT
ap-1870	224	22	teorie	teorie	X
ap-1870	224	23	geometriche	geometriche	PROPN
ap-1870	224	24	e	e	PROPN
ap-1870	224	25	analitiche	analitiche	PROPN
ap-1870	224	26	dei	dei	X
ap-1870	224	27	sistemi	sistemi	X
ap-1870	224	28	hamiltoniani	hamiltoniani	PROPN
ap-1870	224	29	in	in	ADP
ap-1870	224	30	dimensioni	dimensioni	PROPN
ap-1870	224	31	finite	finite	PROPN
ap-1870	224	32	e	e	X
ap-1870	224	33	infinite	infinite	NOUN
ap-1870	224	34	”	"	PUNCT
ap-1870	224	35	.	.	PUNCT
ap-1870	225	1	references	reference	NOUN
ap-1870	225	2	[	[	X
ap-1870	225	3	1	1	NUM
ap-1870	225	4	]	]	X
ap-1870	225	5	peter	peter	PROPN
ap-1870	225	6	j.	j.	PROPN
ap-1870	225	7	olver	olver	PROPN
ap-1870	225	8	.	.	PUNCT
ap-1870	226	1	applications	application	NOUN
ap-1870	226	2	of	of	ADP
ap-1870	226	3	lie	lie	NOUN
ap-1870	226	4	groups	group	NOUN
ap-1870	226	5	to	to	PART
ap-1870	226	6	differential	differential	VERB
ap-1870	226	7	equations	equation	NOUN
ap-1870	226	8	second	second	PROPN
ap-1870	226	9	edition	edition	NOUN
ap-1870	226	10	,	,	PUNCT
ap-1870	226	11	springer	springer	NOUN
ap-1870	226	12	-	-	PUNCT
ap-1870	226	13	verlag	verlag	PROPN
ap-1870	226	14	,	,	PUNCT
ap-1870	226	15	new	new	PROPN
ap-1870	226	16	york	york	PROPN
ap-1870	226	17	,	,	PUNCT
ap-1870	226	18	1993	1993	NUM
ap-1870	226	19	.	.	PUNCT
ap-1870	227	1	442	442	NUM
ap-1870	227	2	vol	vol	NOUN
ap-1870	227	3	.	.	PUNCT
ap-1870	228	1	53	53	NUM
ap-1870	228	2	no	no	NOUN
ap-1870	228	3	.	.	PUNCT
ap-1870	229	1	5/2013	5/2013	NUM
ap-1870	229	2	lie	lie	NOUN
ap-1870	229	3	groups	group	NOUN
ap-1870	229	4	and	and	CCONJ
ap-1870	229	5	numerical	numerical	ADJ
ap-1870	229	6	solutions	solution	NOUN
ap-1870	229	7	of	of	ADP
ap-1870	229	8	differential	differential	ADJ
ap-1870	229	9	equations	equation	NOUN
ap-1870	229	10	[	[	X
ap-1870	229	11	2	2	NUM
ap-1870	229	12	]	]	PUNCT
ap-1870	229	13	george	george	PROPN
ap-1870	229	14	w.	w.	PROPN
ap-1870	229	15	bluman	bluman	PROPN
ap-1870	229	16	,	,	PUNCT
ap-1870	229	17	sukeyuki	sukeyuki	PROPN
ap-1870	229	18	kumei	kumei	PROPN
ap-1870	229	19	,	,	PUNCT
ap-1870	229	20	symmetries	symmetry	NOUN
ap-1870	229	21	and	and	CCONJ
ap-1870	229	22	differential	differential	ADJ
ap-1870	229	23	equations	equation	NOUN
ap-1870	229	24	springer	springer	NOUN
ap-1870	229	25	-	-	PUNCT
ap-1870	229	26	verlag	verlag	PROPN
ap-1870	229	27	new	new	PROPN
ap-1870	229	28	york	york	PROPN
ap-1870	229	29	,	,	PUNCT
ap-1870	229	30	heidelberg	heidelberg	PROPN
ap-1870	229	31	,	,	PUNCT
ap-1870	229	32	berlin	berlin	PROPN
ap-1870	229	33	,	,	PUNCT
ap-1870	229	34	1989	1989	NUM
ap-1870	229	35	,	,	PUNCT
ap-1870	229	36	(	(	PUNCT
ap-1870	229	37	reprinted	reprint	VERB
ap-1870	229	38	with	with	ADP
ap-1870	229	39	corrections	correction	NOUN
ap-1870	229	40	,	,	PUNCT
ap-1870	229	41	1996	1996	NUM
ap-1870	229	42	)	)	PUNCT
ap-1870	229	43	.	.	PUNCT
ap-1870	230	1	[	[	X
ap-1870	230	2	3	3	X
ap-1870	230	3	]	]	X
ap-1870	230	4	nail	nail	NOUN
ap-1870	230	5	h.	h.	NOUN
ap-1870	230	6	ibragimov	ibragimov	NOUN
ap-1870	230	7	,	,	PUNCT
ap-1870	230	8	transformation	transformation	NOUN
ap-1870	230	9	groups	group	NOUN
ap-1870	230	10	applied	apply	VERB
ap-1870	230	11	to	to	ADP
ap-1870	230	12	mathematical	mathematical	ADJ
ap-1870	230	13	physics	physics	NOUN
ap-1870	230	14	translated	translate	VERB
ap-1870	230	15	from	from	ADP
ap-1870	230	16	the	the	DET
ap-1870	230	17	russian	russian	PROPN
ap-1870	230	18	.	.	PUNCT
ap-1870	231	1	d.	d.	PROPN
ap-1870	231	2	reidel	reidel	PROPN
ap-1870	231	3	publishing	publishing	PROPN
ap-1870	231	4	co.	co.	PROPN
ap-1870	231	5	,	,	PUNCT
ap-1870	231	6	dordrecht	dordrecht	PROPN
ap-1870	231	7	,	,	PUNCT
ap-1870	231	8	1985	1985	NUM
ap-1870	231	9	.	.	PUNCT
ap-1870	232	1	[	[	X
ap-1870	232	2	4	4	X
ap-1870	232	3	]	]	PUNCT
ap-1870	232	4	yurii	yurii	PROPN
ap-1870	232	5	i.	i.	PROPN
ap-1870	232	6	shokin	shokin	PROPN
ap-1870	232	7	,	,	PUNCT
ap-1870	232	8	the	the	DET
ap-1870	232	9	method	method	NOUN
ap-1870	232	10	of	of	ADP
ap-1870	232	11	differential	differential	ADJ
ap-1870	232	12	approximation	approximation	NOUN
ap-1870	232	13	translated	translate	VERB
ap-1870	232	14	from	from	ADP
ap-1870	232	15	the	the	DET
ap-1870	232	16	russian	russian	NOUN
ap-1870	232	17	by	by	ADP
ap-1870	232	18	k.	k.	PROPN
ap-1870	232	19	g.	g.	PROPN
ap-1870	232	20	roesner	roesner	PROPN
ap-1870	232	21	.	.	PUNCT
ap-1870	233	1	springer	springer	NOUN
ap-1870	233	2	-	-	PUNCT
ap-1870	233	3	verlag	verlag	PROPN
ap-1870	233	4	,	,	PUNCT
ap-1870	233	5	new	new	PROPN
ap-1870	233	6	york	york	PROPN
ap-1870	233	7	-	-	PUNCT
ap-1870	233	8	berlin	berlin	PROPN
ap-1870	233	9	,	,	PUNCT
ap-1870	233	10	1983	1983	NUM
ap-1870	234	1	[	[	X
ap-1870	234	2	5	5	NUM
ap-1870	234	3	]	]	X
ap-1870	234	4	n.	n.	NOUN
ap-1870	234	5	n.	n.	PROPN
ap-1870	234	6	yanenko	yanenko	PROPN
ap-1870	234	7	and	and	CCONJ
ap-1870	234	8	yu	yu	PROPN
ap-1870	234	9	.	.	PROPN
ap-1870	234	10	i.	i.	PROPN
ap-1870	234	11	shokin	shokin	PROPN
ap-1870	235	1	first	first	ADJ
ap-1870	235	2	differential	differential	ADJ
ap-1870	235	3	approximation	approximation	NOUN
ap-1870	235	4	method	method	NOUN
ap-1870	235	5	and	and	CCONJ
ap-1870	235	6	approximate	approximate	ADJ
ap-1870	235	7	viscosity	viscosity	NOUN
ap-1870	235	8	of	of	ADP
ap-1870	235	9	difference	difference	NOUN
ap-1870	235	10	schemes	scheme	NOUN
ap-1870	235	11	,	,	PUNCT
ap-1870	235	12	phys	phy	NOUN
ap-1870	235	13	.	.	PUNCT
ap-1870	236	1	fluids	fluid	NOUN
ap-1870	236	2	12(ii):28–33,1969	12(ii):28–33,1969	NUM
ap-1870	236	3	.	.	PUNCT
ap-1870	237	1	[	[	X
ap-1870	237	2	6	6	NUM
ap-1870	237	3	]	]	X
ap-1870	237	4	n.	n.	PROPN
ap-1870	237	5	n.	n.	PROPN
ap-1870	237	6	yanenko	yanenko	PROPN
ap-1870	237	7	,	,	PUNCT
ap-1870	237	8	z.i	z.i	PROPN
ap-1870	237	9	.	.	PROPN
ap-1870	237	10	fedotova	fedotova	PROPN
ap-1870	237	11	,	,	PUNCT
ap-1870	237	12	l.a	l.a	PROPN
ap-1870	237	13	.	.	PROPN
ap-1870	237	14	tusheva	tusheva	PROPN
ap-1870	237	15	,	,	PUNCT
ap-1870	237	16	yu	yu	PROPN
ap-1870	237	17	.	.	PROPN
ap-1870	237	18	i.	i.	PROPN
ap-1870	237	19	shokin	shokin	PROPN
ap-1870	237	20	,	,	PUNCT
ap-1870	237	21	classification	classification	NOUN
ap-1870	237	22	of	of	ADP
ap-1870	237	23	difference	difference	NOUN
ap-1870	237	24	schemes	scheme	NOUN
ap-1870	237	25	of	of	ADP
ap-1870	237	26	gas	gas	NOUN
ap-1870	237	27	dynamics	dynamic	NOUN
ap-1870	237	28	by	by	ADP
ap-1870	237	29	the	the	DET
ap-1870	237	30	method	method	NOUN
ap-1870	237	31	of	of	ADP
ap-1870	237	32	differential	differential	ADJ
ap-1870	237	33	approximation	approximation	NOUN
ap-1870	237	34	.	.	PUNCT
ap-1870	238	1	i.	i.	PROPN
ap-1870	238	2	one	one	NUM
ap-1870	238	3	-	-	PUNCT
ap-1870	238	4	dimensional	dimensional	ADJ
ap-1870	238	5	case	case	NOUN
ap-1870	238	6	.	.	PUNCT
ap-1870	239	1	comput	comput	NOUN
ap-1870	239	2	.	.	PUNCT
ap-1870	240	1	&	&	CCONJ
ap-1870	240	2	fluids	fluid	NOUN
ap-1870	240	3	11	11	NUM
ap-1870	240	4	(	(	PUNCT
ap-1870	240	5	3):187–206	3):187–206	NUM
ap-1870	240	6	,	,	PUNCT
ap-1870	240	7	1983	1983	NUM
ap-1870	240	8	.	.	PUNCT
ap-1870	241	1	[	[	X
ap-1870	241	2	7	7	X
ap-1870	241	3	]	]	X
ap-1870	241	4	n.n	n.n	PROPN
ap-1870	241	5	.	.	PROPN
ap-1870	241	6	yanenko	yanenko	PROPN
ap-1870	241	7	and	and	CCONJ
ap-1870	241	8	yu	yu	PROPN
ap-1870	241	9	.	.	PROPN
ap-1870	241	10	i.	i.	PROPN
ap-1870	241	11	shokin	shokin	PROPN
ap-1870	241	12	,	,	PUNCT
ap-1870	241	13	group	group	NOUN
ap-1870	241	14	classification	classification	NOUN
ap-1870	241	15	of	of	ADP
ap-1870	241	16	difference	difference	NOUN
ap-1870	241	17	schemes	scheme	NOUN
ap-1870	241	18	for	for	ADP
ap-1870	241	19	a	a	DET
ap-1870	241	20	system	system	NOUN
ap-1870	241	21	of	of	ADP
ap-1870	241	22	one	one	NUM
ap-1870	241	23	dimensional	dimensional	ADJ
ap-1870	241	24	equations	equation	NOUN
ap-1870	241	25	of	of	ADP
ap-1870	241	26	gas	gas	NOUN
ap-1870	241	27	dynamics	dynamic	NOUN
ap-1870	241	28	,	,	PUNCT
ap-1870	241	29	some	some	DET
ap-1870	241	30	problems	problem	NOUN
ap-1870	241	31	of	of	ADP
ap-1870	241	32	mathematics	mathematic	NOUN
ap-1870	241	33	and	and	CCONJ
ap-1870	241	34	mechanics	mechanic	NOUN
ap-1870	241	35	american	american	PROPN
ap-1870	241	36	mathematical	mathematical	ADJ
ap-1870	241	37	society	society	NOUN
ap-1870	241	38	translations	translation	NOUN
ap-1870	241	39	series	series	NOUN
ap-1870	241	40	2	2	NUM
ap-1870	241	41	volume	volume	NOUN
ap-1870	241	42	:	:	PUNCT
ap-1870	241	43	104	104	NUM
ap-1870	241	44	pp	pp	NOUN
ap-1870	241	45	.	.	PUNCT
ap-1870	242	1	259–265	259–265	NUM
ap-1870	242	2	,	,	PUNCT
ap-1870	242	3	1976	1976	NUM
ap-1870	242	4	[	[	X
ap-1870	242	5	8	8	NUM
ap-1870	242	6	]	]	SYM
ap-1870	242	7	yu.i	yu.i	X
ap-1870	242	8	.	.	PUNCT
ap-1870	242	9	shokin	shokin	PROPN
ap-1870	242	10	,	,	PUNCT
ap-1870	242	11	n.n	n.n	PROPN
ap-1870	242	12	.	.	PROPN
ap-1870	242	13	yanenko	yanenko	PROPN
ap-1870	242	14	,	,	PUNCT
ap-1870	242	15	the	the	DET
ap-1870	242	16	connection	connection	NOUN
ap-1870	242	17	between	between	ADP
ap-1870	242	18	the	the	DET
ap-1870	242	19	proper	proper	ADJ
ap-1870	242	20	formulation	formulation	NOUN
ap-1870	242	21	of	of	ADP
ap-1870	242	22	first	first	ADJ
ap-1870	242	23	differential	differential	ADJ
ap-1870	242	24	approximations	approximation	NOUN
ap-1870	242	25	and	and	CCONJ
ap-1870	242	26	the	the	DET
ap-1870	242	27	stability	stability	NOUN
ap-1870	242	28	of	of	ADP
ap-1870	242	29	difference	difference	NOUN
ap-1870	242	30	schemes	scheme	NOUN
ap-1870	242	31	for	for	ADP
ap-1870	242	32	hyperbolic	hyperbolic	ADJ
ap-1870	242	33	systems	system	NOUN
ap-1870	242	34	of	of	ADP
ap-1870	242	35	equations	equation	NOUN
ap-1870	242	36	.	.	PUNCT
ap-1870	243	1	(	(	PUNCT
ap-1870	243	2	russian	russian	ADJ
ap-1870	243	3	)	)	PUNCT
ap-1870	243	4	mat	mat	NOUN
ap-1870	243	5	.	.	PUNCT
ap-1870	243	6	zametki	zametki	NOUN
ap-1870	243	7	4	4	NUM
ap-1870	243	8	493–502	493–502	NUM
ap-1870	243	9	,	,	PUNCT
ap-1870	243	10	1968	1968	NUM
ap-1870	243	11	.	.	PUNCT
ap-1870	244	1	[	[	X
ap-1870	244	2	9	9	NUM
ap-1870	244	3	]	]	X
ap-1870	244	4	e.	e.	PROPN
ap-1870	244	5	hoarau	hoarau	PROPN
ap-1870	244	6	,	,	PUNCT
ap-1870	244	7	c.	c.	PROPN
ap-1870	244	8	david	david	PROPN
ap-1870	244	9	,	,	PUNCT
ap-1870	244	10	p.	p.	PROPN
ap-1870	244	11	sagaut	sagaut	PROPN
ap-1870	244	12	,	,	PUNCT
ap-1870	244	13	t.-h	t.-h	PROPN
ap-1870	244	14	.	.	PUNCT
ap-1870	245	1	lê	lê	PROPN
ap-1870	245	2	,	,	PUNCT
ap-1870	245	3	lie	lie	NOUN
ap-1870	245	4	group	group	NOUN
ap-1870	245	5	study	study	NOUN
ap-1870	245	6	of	of	ADP
ap-1870	245	7	finite	finite	ADJ
ap-1870	245	8	difference	difference	NOUN
ap-1870	245	9	schemes	scheme	NOUN
ap-1870	245	10	.	.	PUNCT
ap-1870	246	1	discrete	discrete	ADJ
ap-1870	246	2	contin	contin	NOUN
ap-1870	246	3	.	.	PUNCT
ap-1870	247	1	dyn	dyn	NOUN
ap-1870	247	2	.	.	PUNCT
ap-1870	248	1	syst	syst	PROPN
ap-1870	248	2	.	.	PUNCT
ap-1870	248	3	,	,	PUNCT
ap-1870	248	4	dynamical	dynamical	ADJ
ap-1870	248	5	systems	system	NOUN
ap-1870	248	6	and	and	CCONJ
ap-1870	248	7	differential	differential	ADJ
ap-1870	248	8	equations	equation	NOUN
ap-1870	248	9	.	.	PUNCT
ap-1870	249	1	proceedings	proceeding	NOUN
ap-1870	249	2	of	of	ADP
ap-1870	249	3	the	the	DET
ap-1870	249	4	6th	6th	NOUN
ap-1870	249	5	aims	aim	VERB
ap-1870	249	6	international	international	ADJ
ap-1870	249	7	conference	conference	NOUN
ap-1870	249	8	,	,	PUNCT
ap-1870	249	9	suppl	suppl	PROPN
ap-1870	249	10	.	.	PROPN
ap-1870	249	11	,	,	PUNCT
ap-1870	249	12	495–505	495–505	NUM
ap-1870	249	13	,	,	PUNCT
ap-1870	249	14	2007	2007	NUM
ap-1870	249	15	.	.	PUNCT
ap-1870	250	1	[	[	X
ap-1870	250	2	10	10	NUM
ap-1870	250	3	]	]	PUNCT
ap-1870	250	4	m.	m.	NOUN
ap-1870	250	5	chhay	chhay	PROPN
ap-1870	250	6	,	,	PUNCT
ap-1870	250	7	e.	e.	PROPN
ap-1870	250	8	hoarau	hoarau	PROPN
ap-1870	250	9	,	,	PUNCT
ap-1870	250	10	a.	a.	PROPN
ap-1870	250	11	hamdouni	hamdouni	PROPN
ap-1870	250	12	,	,	PUNCT
ap-1870	250	13	p.	p.	PROPN
ap-1870	250	14	sagaut	sagaut	PROPN
ap-1870	250	15	,	,	PUNCT
ap-1870	250	16	comparison	comparison	NOUN
ap-1870	250	17	of	of	ADP
ap-1870	250	18	some	some	DET
ap-1870	250	19	lie	lie	NOUN
ap-1870	250	20	-	-	PUNCT
ap-1870	250	21	symmetry	symmetry	NOUN
ap-1870	250	22	-	-	PUNCT
ap-1870	250	23	based	base	VERB
ap-1870	250	24	integrators	integrator	NOUN
ap-1870	250	25	.	.	PUNCT
ap-1870	251	1	j.	j.	PROPN
ap-1870	251	2	comput	comput	PROPN
ap-1870	251	3	.	.	PUNCT
ap-1870	252	1	phys	phy	NOUN
ap-1870	252	2	.	.	PUNCT
ap-1870	253	1	230	230	NUM
ap-1870	253	2	(	(	PUNCT
ap-1870	253	3	5	5	NUM
ap-1870	253	4	):	):	PUNCT
ap-1870	253	5	2174–2188	2174–2188	NUM
ap-1870	253	6	,	,	PUNCT
ap-1870	253	7	2011	2011	NUM
ap-1870	253	8	.	.	PUNCT
ap-1870	254	1	[	[	X
ap-1870	254	2	11	11	NUM
ap-1870	254	3	]	]	PUNCT
ap-1870	254	4	shigeru	shigeru	PROPN
ap-1870	254	5	maeda	maeda	PROPN
ap-1870	254	6	,	,	PUNCT
ap-1870	254	7	canonical	canonical	ADJ
ap-1870	254	8	structure	structure	NOUN
ap-1870	254	9	and	and	CCONJ
ap-1870	254	10	symmetries	symmetry	NOUN
ap-1870	254	11	for	for	ADP
ap-1870	254	12	discrete	discrete	ADJ
ap-1870	254	13	systems	system	NOUN
ap-1870	254	14	.	.	PUNCT
ap-1870	255	1	math	math	NOUN
ap-1870	255	2	.	.	PUNCT
ap-1870	256	1	japon	japon	PROPN
ap-1870	256	2	.	.	PUNCT
ap-1870	257	1	25	25	NUM
ap-1870	257	2	(	(	PUNCT
ap-1870	257	3	4	4	NUM
ap-1870	257	4	):	):	PUNCT
ap-1870	257	5	405–420	405–420	NUM
ap-1870	257	6	,	,	PUNCT
ap-1870	257	7	1980	1980	NUM
ap-1870	257	8	.	.	PUNCT
ap-1870	258	1	[	[	X
ap-1870	258	2	12	12	NUM
ap-1870	258	3	]	]	X
ap-1870	258	4	v.a	v.a	PROPN
ap-1870	258	5	.	.	PROPN
ap-1870	258	6	dorodnitsyn	dorodnitsyn	PROPN
ap-1870	258	7	,	,	PUNCT
ap-1870	258	8	transformation	transformation	NOUN
ap-1870	258	9	groups	group	NOUN
ap-1870	258	10	in	in	ADP
ap-1870	258	11	difference	difference	NOUN
ap-1870	258	12	spaces	space	NOUN
ap-1870	258	13	.	.	PUNCT
ap-1870	259	1	(	(	PUNCT
ap-1870	259	2	russian	russian	ADJ
ap-1870	259	3	)	)	PUNCT
ap-1870	259	4	translated	translate	VERB
ap-1870	259	5	in	in	ADP
ap-1870	259	6	j.	j.	PROPN
ap-1870	259	7	soviet	soviet	PROPN
ap-1870	259	8	math	math	PROPN
ap-1870	259	9	.	.	PUNCT
ap-1870	260	1	55	55	NUM
ap-1870	260	2	(	(	PUNCT
ap-1870	260	3	1	1	NUM
ap-1870	260	4	):	):	PUNCT
ap-1870	260	5	1490–1517	1490–1517	NUM
ap-1870	260	6	,	,	PUNCT
ap-1870	260	7	1991	1991	NUM
ap-1870	260	8	.	.	PUNCT
ap-1870	261	1	[	[	X
ap-1870	261	2	13	13	NUM
ap-1870	261	3	]	]	X
ap-1870	261	4	v.a	v.a	PROPN
ap-1870	261	5	.	.	PROPN
ap-1870	261	6	dorodnitsyn	dorodnitsyn	PROPN
ap-1870	261	7	,	,	PUNCT
ap-1870	261	8	finite	finite	ADJ
ap-1870	261	9	difference	difference	NOUN
ap-1870	261	10	models	model	NOUN
ap-1870	261	11	entirely	entirely	ADV
ap-1870	261	12	inheriting	inherit	VERB
ap-1870	261	13	continuous	continuous	ADJ
ap-1870	261	14	symmetry	symmetry	NOUN
ap-1870	261	15	of	of	ADP
ap-1870	261	16	original	original	ADJ
ap-1870	261	17	differential	differential	ADJ
ap-1870	261	18	equations	equation	NOUN
ap-1870	261	19	.	.	PUNCT
ap-1870	262	1	internat	internat	PROPN
ap-1870	262	2	.	.	PUNCT
ap-1870	263	1	j.	j.	PROPN
ap-1870	263	2	modern	modern	ADJ
ap-1870	263	3	phys	phys	PROPN
ap-1870	263	4	.	.	PUNCT
ap-1870	264	1	c	c	NOUN
ap-1870	264	2	5	5	NUM
ap-1870	264	3	(	(	PUNCT
ap-1870	264	4	4	4	NUM
ap-1870	264	5	):	):	PUNCT
ap-1870	264	6	723–734	723–734	NUM
ap-1870	264	7	,	,	PUNCT
ap-1870	264	8	1994	1994	NUM
ap-1870	264	9	.	.	PUNCT
ap-1870	265	1	[	[	X
ap-1870	265	2	14	14	NUM
ap-1870	265	3	]	]	X
ap-1870	265	4	v.a	v.a	PROPN
ap-1870	265	5	.	.	PROPN
ap-1870	265	6	dorodnitsyn	dorodnitsyn	PROPN
ap-1870	265	7	,	,	PUNCT
ap-1870	265	8	r.	r.	PROPN
ap-1870	265	9	kozlov	kozlov	PROPN
ap-1870	265	10	,	,	PUNCT
ap-1870	265	11	p.	p.	PROPN
ap-1870	265	12	winternitz	winternitz	PROPN
ap-1870	265	13	,	,	PUNCT
ap-1870	265	14	lie	lie	NOUN
ap-1870	265	15	group	group	NOUN
ap-1870	265	16	classification	classification	NOUN
ap-1870	265	17	of	of	ADP
ap-1870	265	18	second	second	ADJ
ap-1870	265	19	-	-	PUNCT
ap-1870	265	20	order	order	NOUN
ap-1870	265	21	ordinary	ordinary	ADJ
ap-1870	265	22	difference	difference	NOUN
ap-1870	265	23	equations	equation	NOUN
ap-1870	265	24	.	.	PUNCT
ap-1870	266	1	j.	j.	PROPN
ap-1870	266	2	math	math	PROPN
ap-1870	266	3	.	.	PUNCT
ap-1870	267	1	phys	phy	NOUN
ap-1870	267	2	.	.	PUNCT
ap-1870	268	1	41	41	NUM
ap-1870	268	2	(	(	PUNCT
ap-1870	268	3	1	1	NUM
ap-1870	268	4	):	):	PUNCT
ap-1870	268	5	480–504	480–504	NUM
ap-1870	268	6	,	,	PUNCT
ap-1870	268	7	2000	2000	NUM
ap-1870	268	8	.	.	PUNCT
ap-1870	269	1	[	[	X
ap-1870	269	2	15	15	NUM
ap-1870	269	3	]	]	X
ap-1870	269	4	vladimir	vladimir	PROPN
ap-1870	269	5	dorodnitsyn	dorodnitsyn	PROPN
ap-1870	269	6	,	,	PUNCT
ap-1870	269	7	applications	application	NOUN
ap-1870	269	8	of	of	ADP
ap-1870	269	9	lie	lie	NOUN
ap-1870	269	10	groups	group	NOUN
ap-1870	269	11	to	to	ADP
ap-1870	269	12	difference	difference	NOUN
ap-1870	269	13	equations	equation	NOUN
ap-1870	269	14	.	.	PUNCT
ap-1870	270	1	differential	differential	ADJ
ap-1870	270	2	and	and	CCONJ
ap-1870	270	3	integral	integral	ADJ
ap-1870	270	4	equations	equation	NOUN
ap-1870	270	5	and	and	CCONJ
ap-1870	270	6	their	their	PRON
ap-1870	270	7	applications	application	NOUN
ap-1870	270	8	,	,	PUNCT
ap-1870	270	9	crc	crc	NOUN
ap-1870	270	10	press	press	PROPN
ap-1870	270	11	,	,	PUNCT
ap-1870	270	12	boca	boca	PROPN
ap-1870	270	13	raton	raton	PROPN
ap-1870	270	14	,	,	PUNCT
ap-1870	270	15	fl	fl	PROPN
ap-1870	270	16	,	,	PUNCT
ap-1870	270	17	2011	2011	NUM
ap-1870	270	18	.	.	PUNCT
ap-1870	271	1	[	[	X
ap-1870	271	2	16	16	NUM
ap-1870	271	3	]	]	X
ap-1870	271	4	d.	d.	PROPN
ap-1870	271	5	levi	levi	PROPN
ap-1870	271	6	,	,	PUNCT
ap-1870	271	7	p.	p.	PROPN
ap-1870	271	8	winternitz	winternitz	PROPN
ap-1870	271	9	,	,	PUNCT
ap-1870	271	10	continuous	continuous	ADJ
ap-1870	271	11	symmetries	symmetry	NOUN
ap-1870	271	12	of	of	ADP
ap-1870	271	13	discrete	discrete	ADJ
ap-1870	271	14	equations	equation	NOUN
ap-1870	271	15	.	.	PUNCT
ap-1870	272	1	phys	phy	NOUN
ap-1870	272	2	.	.	PUNCT
ap-1870	273	1	lett	lett	PROPN
ap-1870	273	2	.	.	PUNCT
ap-1870	274	1	a	a	DET
ap-1870	274	2	152	152	NUM
ap-1870	274	3	(	(	PUNCT
ap-1870	274	4	7	7	NUM
ap-1870	274	5	):	):	PUNCT
ap-1870	274	6	335–338	335–338	NUM
ap-1870	274	7	,	,	PUNCT
ap-1870	274	8	1991	1991	NUM
ap-1870	274	9	.	.	PUNCT
ap-1870	275	1	[	[	X
ap-1870	275	2	17	17	NUM
ap-1870	275	3	]	]	X
ap-1870	275	4	d.	d.	PROPN
ap-1870	275	5	levi	levi	PROPN
ap-1870	275	6	,	,	PUNCT
ap-1870	275	7	p.	p.	PROPN
ap-1870	275	8	winternitz	winternitz	PROPN
ap-1870	275	9	,	,	PUNCT
ap-1870	275	10	symmetries	symmetry	NOUN
ap-1870	275	11	and	and	CCONJ
ap-1870	275	12	conditional	conditional	ADJ
ap-1870	275	13	symmetries	symmetry	NOUN
ap-1870	275	14	of	of	ADP
ap-1870	275	15	differential	differential	ADJ
ap-1870	275	16	-	-	PUNCT
ap-1870	275	17	difference	difference	NOUN
ap-1870	275	18	equations	equation	NOUN
ap-1870	275	19	.	.	PUNCT
ap-1870	276	1	j.	j.	PROPN
ap-1870	276	2	math	math	PROPN
ap-1870	276	3	.	.	PUNCT
ap-1870	277	1	phys	phy	NOUN
ap-1870	277	2	.	.	PUNCT
ap-1870	278	1	34	34	NUM
ap-1870	278	2	(	(	PUNCT
ap-1870	278	3	8)	8)	NUM
ap-1870	278	4	:	:	PUNCT
ap-1870	278	5	3713–3730	3713–3730	NUM
ap-1870	278	6	,	,	PUNCT
ap-1870	278	7	1993	1993	NUM
ap-1870	278	8	.	.	PUNCT
ap-1870	279	1	[	[	X
ap-1870	279	2	18	18	NUM
ap-1870	279	3	]	]	X
ap-1870	279	4	d.	d.	PROPN
ap-1870	279	5	levi	levi	PROPN
ap-1870	279	6	,	,	PUNCT
ap-1870	279	7	p.	p.	PROPN
ap-1870	279	8	winternitz	winternitz	PROPN
ap-1870	279	9	,	,	PUNCT
ap-1870	279	10	continuous	continuous	ADJ
ap-1870	279	11	symmetries	symmetry	NOUN
ap-1870	279	12	of	of	ADP
ap-1870	279	13	difference	difference	NOUN
ap-1870	279	14	equations	equation	NOUN
ap-1870	279	15	.	.	PUNCT
ap-1870	280	1	j.	j.	PROPN
ap-1870	280	2	phys	phys	PROPN
ap-1870	280	3	.	.	PUNCT
ap-1870	281	1	a	a	DET
ap-1870	281	2	39	39	NUM
ap-1870	281	3	(	(	PUNCT
ap-1870	281	4	2	2	NUM
ap-1870	281	5	):	):	PUNCT
ap-1870	281	6	r1	r1	PROPN
ap-1870	281	7	–	–	PUNCT
ap-1870	281	8	r63	r63	NOUN
ap-1870	281	9	,	,	PUNCT
ap-1870	281	10	2006	2006	NUM
ap-1870	281	11	.	.	PUNCT
ap-1870	282	1	[	[	X
ap-1870	282	2	19	19	NUM
ap-1870	282	3	]	]	X
ap-1870	282	4	d.	d.	PROPN
ap-1870	282	5	levi	levi	PROPN
ap-1870	282	6	,	,	PUNCT
ap-1870	282	7	p.	p.	PROPN
ap-1870	282	8	winternitz	winternitz	PROPN
ap-1870	282	9	,	,	PUNCT
ap-1870	282	10	r.i	r.i	PROPN
ap-1870	282	11	.	.	PROPN
ap-1870	282	12	yamilov	yamilov	PROPN
ap-1870	282	13	,	,	PUNCT
ap-1870	282	14	lie	lie	VERB
ap-1870	282	15	point	point	NOUN
ap-1870	282	16	symmetries	symmetry	NOUN
ap-1870	282	17	of	of	ADP
ap-1870	282	18	differential	differential	ADJ
ap-1870	282	19	-	-	PUNCT
ap-1870	282	20	difference	difference	NOUN
ap-1870	282	21	equations	equation	NOUN
ap-1870	282	22	.	.	PUNCT
ap-1870	283	1	j.	j.	PROPN
ap-1870	283	2	phys	phys	PROPN
ap-1870	283	3	.	.	PUNCT
ap-1870	284	1	a	a	DET
ap-1870	284	2	43	43	NUM
ap-1870	284	3	(	(	PUNCT
ap-1870	284	4	29	29	NUM
ap-1870	284	5	):	):	PUNCT
ap-1870	284	6	292002	292002	NUM
ap-1870	284	7	,	,	PUNCT
ap-1870	284	8	14	14	NUM
ap-1870	284	9	pp	pp	NOUN
ap-1870	284	10	.	.	PUNCT
ap-1870	284	11	,	,	PUNCT
ap-1870	284	12	2010	2010	NUM
ap-1870	284	13	.	.	PUNCT
ap-1870	285	1	[	[	X
ap-1870	285	2	20	20	NUM
ap-1870	285	3	]	]	PUNCT
ap-1870	285	4	p.	p.	NOUN
ap-1870	285	5	winternitz	winternitz	PROPN
ap-1870	285	6	,	,	PUNCT
ap-1870	285	7	symmetry	symmetry	NOUN
ap-1870	285	8	preserving	preserve	VERB
ap-1870	285	9	discretization	discretization	NOUN
ap-1870	285	10	of	of	ADP
ap-1870	285	11	differential	differential	ADJ
ap-1870	285	12	equations	equation	NOUN
ap-1870	285	13	and	and	CCONJ
ap-1870	285	14	lie	lie	VERB
ap-1870	285	15	point	point	NOUN
ap-1870	285	16	symmetries	symmetry	NOUN
ap-1870	285	17	of	of	ADP
ap-1870	285	18	differential	differential	ADJ
ap-1870	285	19	-	-	PUNCT
ap-1870	285	20	difference	difference	NOUN
ap-1870	285	21	equations	equation	NOUN
ap-1870	285	22	.	.	PUNCT
ap-1870	286	1	symmetries	symmetry	NOUN
ap-1870	286	2	and	and	CCONJ
ap-1870	286	3	integrability	integrability	NOUN
ap-1870	286	4	of	of	ADP
ap-1870	286	5	difference	difference	NOUN
ap-1870	286	6	equations	equation	NOUN
ap-1870	286	7	.	.	PUNCT
ap-1870	287	1	edited	edit	VERB
ap-1870	287	2	by	by	ADP
ap-1870	287	3	d.	d.	PROPN
ap-1870	287	4	levi	levi	PROPN
ap-1870	287	5	,	,	PUNCT
ap-1870	287	6	p.	p.	PROPN
ap-1870	287	7	olver	olver	PROPN
ap-1870	287	8	,	,	PUNCT
ap-1870	287	9	z.	z.	PROPN
ap-1870	287	10	thomova	thomova	PROPN
ap-1870	287	11	and	and	CCONJ
ap-1870	287	12	p.	p.	PROPN
ap-1870	287	13	winternitz	winternitz	PROPN
ap-1870	287	14	.	.	PUNCT
ap-1870	288	1	cambridge	cambridge	PROPN
ap-1870	288	2	university	university	PROPN
ap-1870	288	3	press	press	PROPN
ap-1870	288	4	,	,	PUNCT
ap-1870	288	5	cambridge	cambridge	PROPN
ap-1870	288	6	,	,	PUNCT
ap-1870	288	7	pp	pp	ADJ
ap-1870	288	8	.	.	PUNCT
ap-1870	289	1	292	292	NUM
ap-1870	289	2	-	-	SYM
ap-1870	289	3	336	336	NUM
ap-1870	289	4	,	,	PUNCT
ap-1870	289	5	2011	2011	NUM
ap-1870	289	6	.	.	PUNCT
ap-1870	290	1	[	[	X
ap-1870	290	2	21	21	NUM
ap-1870	290	3	]	]	X
ap-1870	290	4	g.	g.	PROPN
ap-1870	290	5	r.	r.	PROPN
ap-1870	290	6	w.	w.	PROPN
ap-1870	290	7	quispel	quispel	PROPN
ap-1870	290	8	,	,	PUNCT
ap-1870	290	9	h.	h.	PROPN
ap-1870	290	10	w.	w.	PROPN
ap-1870	290	11	capel	capel	PROPN
ap-1870	290	12	,	,	PUNCT
ap-1870	290	13	r.	r.	PROPN
ap-1870	290	14	sahadevan	sahadevan	PROPN
ap-1870	290	15	,	,	PUNCT
ap-1870	290	16	continuous	continuous	ADJ
ap-1870	290	17	symmetries	symmetry	NOUN
ap-1870	290	18	of	of	ADP
ap-1870	290	19	differential	differential	ADJ
ap-1870	290	20	-	-	PUNCT
ap-1870	290	21	difference	difference	NOUN
ap-1870	290	22	equations	equation	NOUN
ap-1870	290	23	:	:	PUNCT
ap-1870	290	24	the	the	DET
ap-1870	290	25	kac	kac	PROPN
ap-1870	290	26	-	-	PUNCT
ap-1870	290	27	van	van	PROPN
ap-1870	290	28	moerbeke	moerbeke	ADJ
ap-1870	290	29	equation	equation	NOUN
ap-1870	290	30	and	and	CCONJ
ap-1870	290	31	painlevé	painlevé	NOUN
ap-1870	290	32	reduction	reduction	NOUN
ap-1870	290	33	.	.	PUNCT
ap-1870	291	1	phys	phy	NOUN
ap-1870	291	2	.	.	PUNCT
ap-1870	292	1	lett	lett	PROPN
ap-1870	292	2	.	.	PUNCT
ap-1870	293	1	a	a	DET
ap-1870	293	2	170	170	NUM
ap-1870	293	3	(	(	PUNCT
ap-1870	293	4	5	5	NUM
ap-1870	293	5	):	):	PUNCT
ap-1870	293	6	379–383	379–383	NUM
ap-1870	293	7	,	,	PUNCT
ap-1870	293	8	1992	1992	NUM
ap-1870	293	9	.	.	PUNCT
ap-1870	294	1	[	[	X
ap-1870	294	2	22	22	NUM
ap-1870	294	3	]	]	X
ap-1870	294	4	g.	g.	PROPN
ap-1870	294	5	r.	r.	PROPN
ap-1870	294	6	w.	w.	PROPN
ap-1870	294	7	quispel	quispel	PROPN
ap-1870	294	8	,	,	PUNCT
ap-1870	294	9	r.	r.	PROPN
ap-1870	294	10	sahadevan	sahadevan	PROPN
ap-1870	294	11	,	,	PUNCT
ap-1870	294	12	lie	lie	NOUN
ap-1870	294	13	symmetries	symmetry	NOUN
ap-1870	294	14	and	and	CCONJ
ap-1870	294	15	the	the	DET
ap-1870	294	16	integration	integration	NOUN
ap-1870	294	17	of	of	ADP
ap-1870	294	18	difference	difference	NOUN
ap-1870	294	19	equations	equation	NOUN
ap-1870	294	20	.	.	PUNCT
ap-1870	295	1	phys	phy	NOUN
ap-1870	295	2	.	.	PUNCT
ap-1870	296	1	lett	lett	PROPN
ap-1870	296	2	.	.	PUNCT
ap-1870	297	1	a	a	DET
ap-1870	297	2	184	184	NUM
ap-1870	297	3	(	(	PUNCT
ap-1870	297	4	1	1	NUM
ap-1870	297	5	):	):	PUNCT
ap-1870	297	6	64–70	64–70	NUM
ap-1870	297	7	,	,	PUNCT
ap-1870	297	8	1993	1993	NUM
ap-1870	297	9	.	.	PUNCT
ap-1870	298	1	[	[	X
ap-1870	298	2	23	23	NUM
ap-1870	298	3	]	]	X
ap-1870	298	4	p.e	p.e	PROPN
ap-1870	298	5	.	.	PROPN
ap-1870	298	6	hydon	hydon	PROPN
ap-1870	298	7	,	,	PUNCT
ap-1870	298	8	symmetries	symmetry	NOUN
ap-1870	298	9	and	and	CCONJ
ap-1870	298	10	first	first	ADJ
ap-1870	298	11	integrals	integral	NOUN
ap-1870	298	12	of	of	ADP
ap-1870	298	13	ordinary	ordinary	ADJ
ap-1870	298	14	difference	difference	NOUN
ap-1870	298	15	equations	equation	NOUN
ap-1870	298	16	.	.	PUNCT
ap-1870	299	1	r.	r.	PROPN
ap-1870	299	2	soc	soc	PROPN
ap-1870	299	3	.	.	PUNCT
ap-1870	300	1	lond	lond	PROPN
ap-1870	300	2	.	.	PUNCT
ap-1870	301	1	proc	proc	PROPN
ap-1870	301	2	.	.	PUNCT
ap-1870	302	1	ser	ser	PROPN
ap-1870	302	2	.	.	PUNCT
ap-1870	303	1	a	a	DET
ap-1870	303	2	math	math	NOUN
ap-1870	303	3	.	.	PUNCT
ap-1870	304	1	phys	phy	NOUN
ap-1870	304	2	.	.	PUNCT
ap-1870	305	1	eng	eng	PROPN
ap-1870	305	2	.	.	PUNCT
ap-1870	306	1	sci	sci	PROPN
ap-1870	306	2	.	.	PROPN
ap-1870	307	1	456	456	NUM
ap-1870	307	2	(	(	PUNCT
ap-1870	307	3	2004	2004	NUM
ap-1870	307	4	):	):	PUNCT
ap-1870	307	5	2835–2855	2835–2855	NUM
ap-1870	307	6	,	,	PUNCT
ap-1870	307	7	2000	2000	NUM
ap-1870	307	8	.	.	PUNCT
ap-1870	308	1	[	[	X
ap-1870	308	2	24	24	NUM
ap-1870	308	3	]	]	X
ap-1870	308	4	p.j	p.j	PROPN
ap-1870	308	5	.	.	PROPN
ap-1870	308	6	olver	olver	PROPN
ap-1870	308	7	,	,	PUNCT
ap-1870	308	8	geometric	geometric	ADJ
ap-1870	308	9	foundations	foundation	NOUN
ap-1870	308	10	of	of	ADP
ap-1870	308	11	numerical	numerical	ADJ
ap-1870	308	12	algorithms	algorithm	NOUN
ap-1870	308	13	and	and	CCONJ
ap-1870	308	14	symmetry	symmetry	NOUN
ap-1870	308	15	.	.	PUNCT
ap-1870	309	1	special	special	ADJ
ap-1870	309	2	issue	issue	NOUN
ap-1870	309	3	“	"	PUNCT
ap-1870	309	4	computational	computational	ADJ
ap-1870	309	5	geometry	geometry	NOUN
ap-1870	309	6	for	for	ADP
ap-1870	309	7	differential	differential	ADJ
ap-1870	309	8	equations	equation	NOUN
ap-1870	309	9	”	"	PUNCT
ap-1870	309	10	.	.	PUNCT
ap-1870	310	1	appl	appl	PROPN
ap-1870	310	2	.	.	PUNCT
ap-1870	311	1	algebra	algebra	PROPN
ap-1870	311	2	engrg	engrg	PROPN
ap-1870	311	3	.	.	PROPN
ap-1870	311	4	comm	comm	NOUN
ap-1870	311	5	.	.	PUNCT
ap-1870	312	1	comput	comput	NOUN
ap-1870	312	2	.	.	PUNCT
ap-1870	313	1	11	11	NUM
ap-1870	313	2	(	(	PUNCT
ap-1870	313	3	2001	2001	NUM
ap-1870	313	4	)	)	PUNCT
ap-1870	313	5	,	,	PUNCT
ap-1870	313	6	no	no	INTJ
ap-1870	313	7	.	.	NOUN
ap-1870	313	8	5	5	NUM
ap-1870	313	9	,	,	PUNCT
ap-1870	313	10	417–436	417–436	NUM
ap-1870	313	11	.	.	PUNCT
ap-1870	314	1	[	[	X
ap-1870	314	2	25	25	NUM
ap-1870	314	3	]	]	X
ap-1870	314	4	c.	c.	PROPN
ap-1870	314	5	ehresmann	ehresmann	PROPN
ap-1870	314	6	,	,	PUNCT
ap-1870	314	7	les	les	X
ap-1870	314	8	prolongements	prolongement	NOUN
ap-1870	314	9	d’une	d’une	VERB
ap-1870	314	10	variété	variété	PROPN
ap-1870	314	11	différentiable	différentiable	PROPN
ap-1870	314	12	.	.	PUNCT
ap-1870	315	1	i.	i.	PROPN
ap-1870	315	2	calcul	calcul	PROPN
ap-1870	315	3	des	des	PROPN
ap-1870	315	4	jets	jet	NOUN
ap-1870	315	5	,	,	PUNCT
ap-1870	315	6	prolongement	prolongement	NOUN
ap-1870	315	7	principal	principal	NOUN
ap-1870	315	8	.	.	PUNCT
ap-1870	316	1	c.	c.	PROPN
ap-1870	316	2	r.	r.	PROPN
ap-1870	316	3	acad	acad	PROPN
ap-1870	316	4	.	.	PUNCT
ap-1870	317	1	sci	sci	PROPN
ap-1870	317	2	.	.	PUNCT
ap-1870	317	3	paris	paris	PROPN
ap-1870	317	4	233	233	NUM
ap-1870	317	5	598–600	598–600	NUM
ap-1870	317	6	,	,	PUNCT
ap-1870	317	7	1951	1951	NUM
ap-1870	317	8	;	;	PUNCT
ap-1870	317	9	les	les	X
ap-1870	317	10	prolongements	prolongement	NOUN
ap-1870	317	11	d’une	d’une	VERB
ap-1870	317	12	variété	variété	PROPN
ap-1870	317	13	différentiable	différentiable	PROPN
ap-1870	317	14	.	.	PUNCT
ap-1870	318	1	ii	ii	PROPN
ap-1870	318	2	.	.	PUNCT
ap-1870	318	3	l’espace	l’espace	PROPN
ap-1870	318	4	des	des	PROPN
ap-1870	318	5	jets	jets	PROPN
ap-1870	318	6	d’ordre	d’ordre	PROPN
ap-1870	318	7	r	r	PROPN
ap-1870	318	8	de	de	PROPN
ap-1870	318	9	vn	vn	PROPN
ap-1870	318	10	dans	dans	PROPN
ap-1870	318	11	vm	vm	PROPN
ap-1870	318	12	.	.	PROPN
ap-1870	318	13	c.	c.	PROPN
ap-1870	318	14	r.	r.	PROPN
ap-1870	318	15	acad	acad	PROPN
ap-1870	318	16	.	.	PUNCT
ap-1870	319	1	sci	sci	PROPN
ap-1870	319	2	.	.	PUNCT
ap-1870	320	1	paris	paris	PROPN
ap-1870	320	2	233	233	NUM
ap-1870	320	3	777–779	777–779	NUM
ap-1870	320	4	,	,	PUNCT
ap-1870	320	5	1951	1951	NUM
ap-1870	320	6	;	;	PUNCT
ap-1870	320	7	les	les	X
ap-1870	320	8	prolongements	prolongement	NOUN
ap-1870	320	9	d’une	d’une	VERB
ap-1870	320	10	variété	variété	PROPN
ap-1870	320	11	différentiable	différentiable	PROPN
ap-1870	320	12	.	.	PUNCT
ap-1870	321	1	iii	iii	X
ap-1870	321	2	.	.	PROPN
ap-1870	321	3	transitivité	transitivité	PROPN
ap-1870	321	4	des	des	PROPN
ap-1870	321	5	prolongements	prolongement	NOUN
ap-1870	321	6	.	.	PUNCT
ap-1870	322	1	c.	c.	PROPN
ap-1870	322	2	r.	r.	PROPN
ap-1870	322	3	acad	acad	PROPN
ap-1870	322	4	.	.	PUNCT
ap-1870	323	1	sci	sci	PROPN
ap-1870	323	2	.	.	PUNCT
ap-1870	324	1	paris	paris	PROPN
ap-1870	324	2	233	233	NUM
ap-1870	324	3	1081–1083	1081–1083	NUM
ap-1870	324	4	,	,	PUNCT
ap-1870	324	5	1951	1951	NUM
ap-1870	324	6	;	;	PUNCT
ap-1870	324	7	les	les	X
ap-1870	324	8	prolongements	prolongement	NOUN
ap-1870	324	9	d’une	d’une	VERB
ap-1870	324	10	variété	variété	PROPN
ap-1870	324	11	différentiable	différentiable	PROPN
ap-1870	324	12	.	.	PUNCT
ap-1870	325	1	iv	iv	X
ap-1870	325	2	.	.	PUNCT
ap-1870	325	3	éléments	éléments	PROPN
ap-1870	325	4	de	de	PROPN
ap-1870	325	5	contact	contact	PROPN
ap-1870	325	6	et	et	PROPN
ap-1870	325	7	éléments	éléments	PROPN
ap-1870	325	8	d’enveloppe	d’enveloppe	PROPN
ap-1870	325	9	.	.	PUNCT
ap-1870	326	1	c.	c.	PROPN
ap-1870	326	2	r.	r.	PROPN
ap-1870	326	3	acad	acad	PROPN
ap-1870	326	4	.	.	PUNCT
ap-1870	327	1	sci	sci	PROPN
ap-1870	327	2	.	.	PUNCT
ap-1870	327	3	paris	paris	PROPN
ap-1870	327	4	234	234	NUM
ap-1870	327	5	1028–1030	1028–1030	NUM
ap-1870	327	6	,	,	PUNCT
ap-1870	327	7	1952	1952	NUM
ap-1870	327	8	;	;	PUNCT
ap-1870	327	9	les	les	X
ap-1870	327	10	prolongements	prolongement	NOUN
ap-1870	327	11	d’une	d’une	VERB
ap-1870	327	12	variété	variété	PROPN
ap-1870	327	13	différentiable	différentiable	PROPN
ap-1870	327	14	.	.	PUNCT
ap-1870	328	1	v.	v.	ADP
ap-1870	328	2	covariants	covariant	NOUN
ap-1870	328	3	différentiels	différentiels	VERB
ap-1870	328	4	et	et	NOUN
ap-1870	328	5	prolongements	prolongement	NOUN
ap-1870	328	6	d’une	d’une	VERB
ap-1870	328	7	structure	structure	NOUN
ap-1870	328	8	infinitésimale	infinitésimale	NOUN
ap-1870	328	9	.	.	PUNCT
ap-1870	329	1	c.	c.	PROPN
ap-1870	329	2	r.	r.	PROPN
ap-1870	329	3	acad	acad	PROPN
ap-1870	329	4	.	.	PUNCT
ap-1870	330	1	sci	sci	PROPN
ap-1870	330	2	.	.	PROPN
ap-1870	330	3	paris	paris	PROPN
ap-1870	330	4	234	234	NUM
ap-1870	330	5	1424–1425	1424–1425	NUM
ap-1870	330	6	,	,	PUNCT
ap-1870	330	7	1952	1952	NUM
ap-1870	330	8	.	.	PUNCT
ap-1870	331	1	[	[	X
ap-1870	331	2	26	26	NUM
ap-1870	331	3	]	]	PUNCT
ap-1870	331	4	a.	a.	NOUN
ap-1870	331	5	bourlioux	bourlioux	PROPN
ap-1870	331	6	,	,	PUNCT
ap-1870	331	7	c.	c.	PROPN
ap-1870	331	8	cyr	cyr	PROPN
ap-1870	331	9	-	-	PUNCT
ap-1870	331	10	gagnon	gagnon	PROPN
ap-1870	331	11	,	,	PUNCT
ap-1870	331	12	p.	p.	PROPN
ap-1870	331	13	winternitz	winternitz	PROPN
ap-1870	331	14	,	,	PUNCT
ap-1870	331	15	difference	difference	NOUN
ap-1870	331	16	schemes	scheme	NOUN
ap-1870	331	17	with	with	ADP
ap-1870	331	18	point	point	NOUN
ap-1870	331	19	symmetries	symmetry	NOUN
ap-1870	331	20	and	and	CCONJ
ap-1870	331	21	their	their	PRON
ap-1870	331	22	numerical	numerical	ADJ
ap-1870	331	23	tests	test	NOUN
ap-1870	331	24	.	.	PUNCT
ap-1870	332	1	j.	j.	PROPN
ap-1870	332	2	phys	phys	PROPN
ap-1870	332	3	.	.	PUNCT
ap-1870	333	1	a	a	DET
ap-1870	333	2	39	39	NUM
ap-1870	333	3	(	(	PUNCT
ap-1870	333	4	22	22	NUM
ap-1870	333	5	):	):	PUNCT
ap-1870	333	6	6877–6896	6877–6896	NUM
ap-1870	333	7	,	,	PUNCT
ap-1870	333	8	2006	2006	NUM
ap-1870	333	9	.	.	PUNCT
ap-1870	334	1	[	[	X
ap-1870	334	2	27	27	NUM
ap-1870	334	3	]	]	X
ap-1870	334	4	r.	r.	PROPN
ap-1870	334	5	rebelo	rebelo	PROPN
ap-1870	334	6	,	,	PUNCT
ap-1870	334	7	p.	p.	NOUN
ap-1870	334	8	winternitz	winternitz	PROPN
ap-1870	334	9	,	,	PUNCT
ap-1870	334	10	invariant	invariant	ADJ
ap-1870	334	11	difference	difference	NOUN
ap-1870	334	12	schemes	scheme	NOUN
ap-1870	334	13	and	and	CCONJ
ap-1870	334	14	their	their	PRON
ap-1870	334	15	application	application	NOUN
ap-1870	334	16	to	to	ADP
ap-1870	334	17	sl(2,r	sl(2,r	NOUN
ap-1870	334	18	)	)	PUNCT
ap-1870	334	19	invariant	invariant	ADJ
ap-1870	334	20	ordinary	ordinary	ADJ
ap-1870	334	21	differential	differential	ADJ
ap-1870	334	22	equations	equation	NOUN
ap-1870	334	23	.	.	PUNCT
ap-1870	335	1	j.	j.	PROPN
ap-1870	335	2	phys	phys	PROPN
ap-1870	335	3	.	.	PUNCT
ap-1870	336	1	a	a	DET
ap-1870	336	2	42	42	NUM
ap-1870	336	3	(	(	PUNCT
ap-1870	336	4	45	45	NUM
ap-1870	336	5	):	):	SYM
ap-1870	336	6	454016	454016	NUM
ap-1870	336	7	,	,	PUNCT
ap-1870	336	8	10	10	NUM
ap-1870	336	9	pp	pp	NOUN
ap-1870	336	10	.	.	PUNCT
ap-1870	336	11	,	,	PUNCT
ap-1870	336	12	2009	2009	NUM
ap-1870	336	13	.	.	PUNCT
ap-1870	337	1	[	[	X
ap-1870	337	2	28	28	NUM
ap-1870	337	3	]	]	X
ap-1870	337	4	a.	a.	NOUN
ap-1870	337	5	bourlioux	bourlioux	PROPN
ap-1870	337	6	,	,	PUNCT
ap-1870	337	7	r.	r.	PROPN
ap-1870	337	8	rebelo	rebelo	PROPN
ap-1870	337	9	,	,	PUNCT
ap-1870	337	10	p.	p.	PROPN
ap-1870	337	11	winternitz	winternitz	PROPN
ap-1870	337	12	,	,	PUNCT
ap-1870	337	13	symmetry	symmetry	NOUN
ap-1870	337	14	preserving	preserve	VERB
ap-1870	337	15	discretization	discretization	NOUN
ap-1870	337	16	of	of	ADP
ap-1870	337	17	sl(2,r	sl(2,r	NOUN
ap-1870	337	18	)	)	PUNCT
ap-1870	337	19	invariant	invariant	ADJ
ap-1870	337	20	equations	equation	NOUN
ap-1870	337	21	.	.	PUNCT
ap-1870	338	1	j.	j.	PROPN
ap-1870	338	2	nonlinear	nonlinear	PROPN
ap-1870	338	3	math	math	PROPN
ap-1870	338	4	.	.	PUNCT
ap-1870	339	1	phys	phy	NOUN
ap-1870	339	2	.	.	PUNCT
ap-1870	340	1	15(suppl	15(suppl	NUM
ap-1870	340	2	.	.	X
ap-1870	341	1	3	3	NUM
ap-1870	341	2	):	):	PUNCT
ap-1870	341	3	362–372	362–372	NUM
ap-1870	341	4	,	,	PUNCT
ap-1870	341	5	2008	2008	NUM
ap-1870	341	6	.	.	PUNCT
ap-1870	342	1	[	[	X
ap-1870	342	2	29	29	NUM
ap-1870	342	3	]	]	PUNCT
ap-1870	342	4	a.	a.	PROPN
ap-1870	342	5	gonzález	gonzález	PROPN
ap-1870	342	6	-	-	PUNCT
ap-1870	342	7	lópez	lópez	PROPN
ap-1870	342	8	,	,	PUNCT
ap-1870	342	9	n.	n.	PROPN
ap-1870	342	10	kamran	kamran	PROPN
ap-1870	342	11	,	,	PUNCT
ap-1870	342	12	p.j	p.j	PROPN
ap-1870	342	13	.	.	PROPN
ap-1870	342	14	olver	olver	PROPN
ap-1870	342	15	,	,	PUNCT
ap-1870	342	16	lie	lie	VERB
ap-1870	342	17	algebras	algebra	NOUN
ap-1870	342	18	of	of	ADP
ap-1870	342	19	vector	vector	NOUN
ap-1870	342	20	fields	field	NOUN
ap-1870	342	21	in	in	ADP
ap-1870	342	22	the	the	DET
ap-1870	342	23	real	real	ADJ
ap-1870	342	24	plane	plane	NOUN
ap-1870	342	25	.	.	PUNCT
ap-1870	343	1	proc	proc	PROPN
ap-1870	343	2	.	.	PUNCT
ap-1870	344	1	london	london	PROPN
ap-1870	344	2	math	math	PROPN
ap-1870	344	3	.	.	PUNCT
ap-1870	345	1	soc	soc	PROPN
ap-1870	345	2	.	.	PUNCT
ap-1870	346	1	(	(	PUNCT
ap-1870	346	2	3	3	X
ap-1870	346	3	)	)	PUNCT
ap-1870	346	4	64	64	NUM
ap-1870	346	5	(	(	PUNCT
ap-1870	346	6	2	2	NUM
ap-1870	346	7	):	):	PUNCT
ap-1870	346	8	339–368	339–368	NUM
ap-1870	346	9	,	,	PUNCT
ap-1870	346	10	1992	1992	NUM
ap-1870	346	11	.	.	PUNCT
ap-1870	347	1	443	443	NUM
ap-1870	347	2	acta	acta	PROPN
ap-1870	347	3	polytechnica	polytechnica	PROPN
ap-1870	347	4	53(5):438–443	53(5):438–443	PROPN
ap-1870	347	5	,	,	PUNCT
ap-1870	347	6	2013	2013	NUM
ap-1870	347	7	1	1	NUM
ap-1870	347	8	introduction	introduction	NOUN
ap-1870	347	9	2	2	NUM
ap-1870	347	10	differential	differential	NOUN
ap-1870	347	11	approximations	approximation	NOUN
ap-1870	347	12	of	of	ADP
ap-1870	347	13	ordinary	ordinary	ADJ
ap-1870	347	14	difference	difference	NOUN
ap-1870	347	15	equations	equation	NOUN
ap-1870	347	16	and	and	CCONJ
ap-1870	347	17	invariant	invariant	ADJ
ap-1870	347	18	discretization	discretization	NOUN
ap-1870	347	19	of	of	ADP
ap-1870	347	20	odes	ode	NOUN
ap-1870	347	21	.	.	PUNCT
ap-1870	348	1	3	3	NUM
ap-1870	348	2	equations	equation	NOUN
ap-1870	348	3	invariant	invariant	VERB
ap-1870	348	4	under	under	ADP
ap-1870	348	5	the	the	DET
ap-1870	348	6	similitude	similitude	NOUN
ap-1870	348	7	group	group	NOUN
ap-1870	348	8	sim(2	sim(2	PROPN
ap-1870	348	9	)	)	PUNCT
ap-1870	348	10	.	.	PUNCT
ap-1870	349	1	4	4	NUM
ap-1870	349	2	equations	equation	NOUN
ap-1870	349	3	invariant	invariant	VERB
ap-1870	349	4	under	under	ADP
ap-1870	349	5	a	a	DET
ap-1870	349	6	one	one	NUM
ap-1870	349	7	-	-	PUNCT
ap-1870	349	8	dimensional	dimensional	ADJ
ap-1870	349	9	realization	realization	NOUN
ap-1870	349	10	of	of	ADP
ap-1870	349	11	sl(2,r	sl(2,r	NOUN
ap-1870	349	12	)	)	PUNCT
ap-1870	349	13	.	.	PUNCT
ap-1870	350	1	5	5	NUM
ap-1870	350	2	equations	equation	NOUN
ap-1870	350	3	invariant	invariant	VERB
ap-1870	350	4	under	under	ADP
ap-1870	350	5	a	a	DET
ap-1870	350	6	two	two	NUM
ap-1870	350	7	-	-	PUNCT
ap-1870	350	8	dimensional	dimensional	ADJ
ap-1870	350	9	realization	realization	NOUN
ap-1870	350	10	of	of	ADP
ap-1870	350	11	gl(2,r	gl(2,r	NOUN
ap-1870	350	12	)	)	PUNCT
ap-1870	350	13	.	.	PUNCT
ap-1870	351	1	6	6	NUM
ap-1870	351	2	conclusions	conclusion	NOUN
ap-1870	351	3	acknowledgements	acknowledgement	NOUN
ap-1870	351	4	references	reference	NOUN