id	sid	tid	token	lemma	pos
iajs-316	1	1	microsoft	microsoft	PROPN
iajs-316	1	2	word	word	NOUN
iajs-316	1	3	22	22	NUM
iajs-316	1	4	513	513	NUM
iajs-316	1	5	|	|	ADV
iajs-316	1	6	mathematics	mathematic	NOUN
iajs-316	1	7	2014	2014	NUM
iajs-316	1	8	)	)	PUNCT
iajs-316	1	9	عام	عام	ADP
iajs-316	1	10	3العدد	3العدد	NUM
iajs-316	1	11	(	(	PUNCT
iajs-316	1	12	27مجلة	27مجلة	NUM
iajs-316	1	13	إبن	إبن	VERB
iajs-316	1	14	الھيثم	الھيثم	NOUN
iajs-316	1	15	للعلوم	للعلوم	NOUN
iajs-316	1	16	الصرفة	الصرفة	NOUN
iajs-316	2	1	و	و	PRON
iajs-316	2	2	التطبيقية	التطبيقية	ADV
iajs-316	2	3	المجلد	المجلد	VERB
iajs-316	2	4	ibn	ibn	PROPN
iajs-316	2	5	al	al	PROPN
iajs-316	2	6	-	-	PUNCT
iajs-316	2	7	haitham	haitham	PROPN
iajs-316	2	8	jour	jour	X
iajs-316	2	9	.	.	PROPN
iajs-316	3	1	for	for	ADP
iajs-316	3	2	pure	pure	ADJ
iajs-316	3	3	&	&	CCONJ
iajs-316	3	4	appl	appl	PROPN
iajs-316	3	5	.	.	PUNCT
iajs-316	4	1	sci	sci	PROPN
iajs-316	4	2	.	.	PUNCT
iajs-316	4	3	vol	vol	NOUN
iajs-316	4	4	.	.	PROPN
iajs-316	5	1	27	27	NUM
iajs-316	5	2	(	(	PUNCT
iajs-316	5	3	3	3	NUM
iajs-316	5	4	)	)	PUNCT
iajs-316	5	5	2014	2014	NUM
iajs-316	5	6	efficient	efficient	ADJ
iajs-316	5	7	semi	semi	ADJ
iajs-316	5	8	-	-	ADJ
iajs-316	5	9	analytic	analytic	ADJ
iajs-316	5	10	technique	technique	NOUN
iajs-316	5	11	for	for	ADP
iajs-316	5	12	solving	solve	VERB
iajs-316	5	13	nonlinear	nonlinear	ADJ
iajs-316	5	14	singular	singular	ADJ
iajs-316	5	15	initial	initial	ADJ
iajs-316	5	16	value	value	NOUN
iajs-316	5	17	problems	problem	NOUN
iajs-316	5	18	luma	luma	PROPN
iajs-316	5	19	n.	n.	PROPN
iajs-316	5	20	m.	m.	PROPN
iajs-316	6	1	tawfiq	tawfiq	PROPN
iajs-316	6	2	reem	reem	PROPN
iajs-316	6	3	w.	w.	PROPN
iajs-316	6	4	hussein	hussein	PROPN
iajs-316	6	5	dept	dept	PROPN
iajs-316	6	6	.of	.of	PROPN
iajs-316	6	7	mathematics	mathematics	PROPN
iajs-316	6	8	\	\	PROPN
iajs-316	6	9	college	college	NOUN
iajs-316	6	10	of	of	ADP
iajs-316	6	11	education	education	NOUN
iajs-316	6	12	for	for	ADP
iajs-316	6	13	pure	pure	ADJ
iajs-316	6	14	scince	scince	NOUN
iajs-316	6	15	(	(	PUNCT
iajs-316	6	16	ibn	ibn	PROPN
iajs-316	6	17	al	al	PROPN
iajs-316	6	18	-	-	PUNCT
iajs-316	6	19	haitham)/	haitham)/	PROPN
iajs-316	6	20	university	university	NOUN
iajs-316	6	21	of	of	ADP
iajs-316	6	22	bagdad	bagdad	PROPN
iajs-316	6	23	received	receive	VERB
iajs-316	6	24	in	in	ADP
iajs-316	6	25	:	:	PUNCT
iajs-316	6	26	23	23	NUM
iajs-316	6	27	september	september	PROPN
iajs-316	6	28	2012	2012	NUM
iajs-316	6	29	,	,	PUNCT
iajs-316	6	30	accepted	accept	VERB
iajs-316	6	31	in	in	ADP
iajs-316	6	32	:	:	PUNCT
iajs-316	6	33	9	9	NUM
iajs-316	6	34	december	december	PROPN
iajs-316	6	35	2012	2012	NUM
iajs-316	6	36	abstract	abstract	NOUN
iajs-316	6	37	the	the	DET
iajs-316	6	38	aim	aim	NOUN
iajs-316	6	39	of	of	ADP
iajs-316	6	40	this	this	DET
iajs-316	6	41	paper	paper	NOUN
iajs-316	6	42	is	be	AUX
iajs-316	6	43	to	to	PART
iajs-316	6	44	present	present	VERB
iajs-316	6	45	a	a	DET
iajs-316	6	46	semi	semi	ADJ
iajs-316	6	47	analytic	analytic	ADJ
iajs-316	6	48	technique	technique	NOUN
iajs-316	6	49	for	for	ADP
iajs-316	6	50	solving	solve	VERB
iajs-316	6	51	singular	singular	ADJ
iajs-316	6	52	initial	initial	ADJ
iajs-316	6	53	value	value	NOUN
iajs-316	6	54	problems	problem	NOUN
iajs-316	6	55	of	of	ADP
iajs-316	6	56	ordinary	ordinary	ADJ
iajs-316	6	57	differential	differential	ADJ
iajs-316	6	58	equations	equation	NOUN
iajs-316	6	59	with	with	ADP
iajs-316	6	60	a	a	DET
iajs-316	6	61	singularity	singularity	NOUN
iajs-316	6	62	of	of	ADP
iajs-316	6	63	different	different	ADJ
iajs-316	6	64	kinds	kind	NOUN
iajs-316	6	65	to	to	PART
iajs-316	6	66	construct	construct	VERB
iajs-316	6	67	polynomial	polynomial	ADJ
iajs-316	6	68	solution	solution	NOUN
iajs-316	6	69	using	use	VERB
iajs-316	6	70	two	two	NUM
iajs-316	6	71	point	point	NOUN
iajs-316	6	72	osculatory	osculatory	NOUN
iajs-316	6	73	interpolation	interpolation	NOUN
iajs-316	6	74	.	.	PUNCT
iajs-316	7	1	the	the	DET
iajs-316	7	2	efficiency	efficiency	NOUN
iajs-316	7	3	and	and	CCONJ
iajs-316	7	4	accuracy	accuracy	NOUN
iajs-316	7	5	of	of	ADP
iajs-316	7	6	suggested	suggest	VERB
iajs-316	7	7	method	method	NOUN
iajs-316	7	8	is	be	AUX
iajs-316	7	9	assessed	assess	VERB
iajs-316	7	10	by	by	ADP
iajs-316	7	11	comparisons	comparison	NOUN
iajs-316	7	12	with	with	ADP
iajs-316	7	13	exact	exact	ADJ
iajs-316	7	14	and	and	CCONJ
iajs-316	7	15	other	other	ADJ
iajs-316	7	16	approximate	approximate	ADJ
iajs-316	7	17	solutions	solution	NOUN
iajs-316	7	18	for	for	ADP
iajs-316	7	19	a	a	DET
iajs-316	7	20	wide	wide	ADJ
iajs-316	7	21	classes	class	NOUN
iajs-316	7	22	of	of	ADP
iajs-316	7	23	non	non	ADJ
iajs-316	7	24	–	–	NOUN
iajs-316	7	25	homogeneous	homogeneous	ADJ
iajs-316	7	26	,	,	PUNCT
iajs-316	7	27	non	non	ADJ
iajs-316	7	28	–	–	ADJ
iajs-316	7	29	linear	linear	ADJ
iajs-316	7	30	singular	singular	ADJ
iajs-316	7	31	initial	initial	ADJ
iajs-316	7	32	value	value	NOUN
iajs-316	7	33	problems	problem	NOUN
iajs-316	7	34	.	.	PUNCT
iajs-316	8	1	a	a	DET
iajs-316	8	2	new	new	ADJ
iajs-316	8	3	,	,	PUNCT
iajs-316	8	4	efficient	efficient	ADJ
iajs-316	8	5	estimate	estimate	NOUN
iajs-316	8	6	of	of	ADP
iajs-316	8	7	the	the	DET
iajs-316	8	8	global	global	ADJ
iajs-316	8	9	error	error	NOUN
iajs-316	8	10	is	be	AUX
iajs-316	8	11	used	use	VERB
iajs-316	8	12	for	for	ADP
iajs-316	8	13	adaptive	adaptive	ADJ
iajs-316	8	14	mesh	mesh	NOUN
iajs-316	8	15	selection	selection	NOUN
iajs-316	8	16	.	.	PUNCT
iajs-316	9	1	also	also	ADV
iajs-316	9	2	,	,	PUNCT
iajs-316	9	3	analyze	analyze	VERB
iajs-316	9	4	some	some	PRON
iajs-316	9	5	of	of	ADP
iajs-316	9	6	the	the	DET
iajs-316	9	7	numerical	numerical	ADJ
iajs-316	9	8	aspects	aspect	NOUN
iajs-316	9	9	relevant	relevant	ADJ
iajs-316	9	10	for	for	ADP
iajs-316	9	11	the	the	DET
iajs-316	9	12	implementation	implementation	NOUN
iajs-316	9	13	,	,	PUNCT
iajs-316	9	14	describe	describe	VERB
iajs-316	9	15	measures	measure	NOUN
iajs-316	9	16	to	to	PART
iajs-316	9	17	increase	increase	VERB
iajs-316	9	18	the	the	DET
iajs-316	9	19	efficiency	efficiency	NOUN
iajs-316	9	20	of	of	ADP
iajs-316	9	21	the	the	DET
iajs-316	9	22	code	code	NOUN
iajs-316	9	23	and	and	CCONJ
iajs-316	9	24	compare	compare	VERB
iajs-316	9	25	its	its	PRON
iajs-316	9	26	performance	performance	NOUN
iajs-316	9	27	with	with	ADP
iajs-316	9	28	the	the	DET
iajs-316	9	29	performance	performance	NOUN
iajs-316	9	30	of	of	ADP
iajs-316	9	31	established	establish	VERB
iajs-316	9	32	standard	standard	ADJ
iajs-316	9	33	codes	code	NOUN
iajs-316	9	34	for	for	ADP
iajs-316	9	35	singular	singular	ADJ
iajs-316	9	36	initial	initial	ADJ
iajs-316	9	37	value	value	NOUN
iajs-316	9	38	problems	problem	NOUN
iajs-316	9	39	.	.	PUNCT
iajs-316	10	1	many	many	ADJ
iajs-316	10	2	examples	example	NOUN
iajs-316	10	3	are	be	AUX
iajs-316	10	4	presented	present	VERB
iajs-316	10	5	to	to	PART
iajs-316	10	6	demonstrate	demonstrate	VERB
iajs-316	10	7	the	the	DET
iajs-316	10	8	applicability	applicability	NOUN
iajs-316	10	9	and	and	CCONJ
iajs-316	10	10	efficiency	efficiency	NOUN
iajs-316	10	11	of	of	ADP
iajs-316	10	12	the	the	DET
iajs-316	10	13	suggested	suggest	VERB
iajs-316	10	14	method	method	NOUN
iajs-316	10	15	on	on	ADP
iajs-316	10	16	one	one	NUM
iajs-316	10	17	hand	hand	NOUN
iajs-316	10	18	and	and	CCONJ
iajs-316	10	19	to	to	PART
iajs-316	10	20	confirm	confirm	VERB
iajs-316	10	21	the	the	DET
iajs-316	10	22	convergence	convergence	NOUN
iajs-316	10	23	order	order	NOUN
iajs-316	10	24	on	on	ADP
iajs-316	10	25	the	the	DET
iajs-316	10	26	other	other	ADJ
iajs-316	10	27	hand	hand	NOUN
iajs-316	10	28	.	.	PUNCT
iajs-316	11	1	kay	kay	PROPN
iajs-316	11	2	ward	ward	PROPN
iajs-316	11	3	:	:	PUNCT
iajs-316	11	4	ode	ode	ADJ
iajs-316	11	5	,	,	PUNCT
iajs-316	11	6	singular	singular	ADJ
iajs-316	11	7	initial	initial	ADJ
iajs-316	11	8	value	value	NOUN
iajs-316	11	9	problems	problem	NOUN
iajs-316	11	10	.	.	PUNCT
iajs-316	12	1	514	514	NUM
iajs-316	12	2	|	|	ADV
iajs-316	12	3	mathematics	mathematic	NOUN
iajs-316	12	4	2014	2014	NUM
iajs-316	12	5	)	)	PUNCT
iajs-316	12	6	عام	عام	ADP
iajs-316	12	7	3العدد	3العدد	NUM
iajs-316	12	8	(	(	PUNCT
iajs-316	12	9	27مجلة	27مجلة	NUM
iajs-316	12	10	إبن	إبن	VERB
iajs-316	12	11	الھيثم	الھيثم	NOUN
iajs-316	12	12	للعلوم	للعلوم	NOUN
iajs-316	12	13	الصرفة	الصرفة	NOUN
iajs-316	13	1	و	و	PRON
iajs-316	13	2	التطبيقية	التطبيقية	ADV
iajs-316	13	3	المجلد	المجلد	VERB
iajs-316	13	4	ibn	ibn	PROPN
iajs-316	13	5	al	al	PROPN
iajs-316	13	6	-	-	PUNCT
iajs-316	13	7	haitham	haitham	PROPN
iajs-316	13	8	jour	jour	X
iajs-316	13	9	.	.	PROPN
iajs-316	14	1	for	for	ADP
iajs-316	14	2	pure	pure	ADJ
iajs-316	14	3	&	&	CCONJ
iajs-316	14	4	appl	appl	PROPN
iajs-316	14	5	.	.	PUNCT
iajs-316	15	1	sci	sci	PROPN
iajs-316	15	2	.	.	PUNCT
iajs-316	15	3	vol	vol	NOUN
iajs-316	15	4	.	.	PROPN
iajs-316	16	1	27	27	NUM
iajs-316	16	2	(	(	PUNCT
iajs-316	16	3	3	3	NUM
iajs-316	16	4	)	)	PUNCT
iajs-316	16	5	2014	2014	NUM
iajs-316	16	6	1	1	NUM
iajs-316	16	7	.	.	PUNCT
iajs-316	17	1	introduction	introduction	NOUN
iajs-316	17	2	the	the	DET
iajs-316	17	3	modeliy	modeliy	ADJ
iajs-316	17	4	of	of	ADP
iajs-316	17	5	nonlinear	nonlinear	ADJ
iajs-316	17	6	phenomena	phenomenon	NOUN
iajs-316	17	7	in	in	ADP
iajs-316	17	8	physics	physics	NOUN
iajs-316	17	9	,	,	PUNCT
iajs-316	17	10	engineering	engineering	NOUN
iajs-316	17	11	and	and	CCONJ
iajs-316	17	12	other	other	ADJ
iajs-316	17	13	sciences	science	NOUN
iajs-316	17	14	,	,	PUNCT
iajs-316	17	15	leads	lead	VERB
iajs-316	17	16	to	to	ADP
iajs-316	17	17	singular	singular	PROPN
iajs-316	17	18	initial	initial	ADJ
iajs-316	17	19	value	value	NOUN
iajs-316	17	20	problems	problem	NOUN
iajs-316	17	21	(	(	PUNCT
iajs-316	17	22	sivp	sivp	NOUN
iajs-316	17	23	)	)	PUNCT
iajs-316	17	24	associated	associate	VERB
iajs-316	17	25	with	with	ADP
iajs-316	17	26	nonlinear	nonlinear	ADJ
iajs-316	17	27	second	second	ADJ
iajs-316	17	28	order	order	NOUN
iajs-316	17	29	ordinary	ordinary	ADJ
iajs-316	17	30	differential	differential	ADJ
iajs-316	17	31	equations	equation	NOUN
iajs-316	17	32	(	(	PUNCT
iajs-316	17	33	ode	ode	PROPN
iajs-316	17	34	)	)	PUNCT
iajs-316	18	1	[	[	X
iajs-316	18	2	1	1	NUM
iajs-316	18	3	]	]	PUNCT
iajs-316	18	4	.	.	PUNCT
iajs-316	19	1	the	the	DET
iajs-316	19	2	general	general	ADJ
iajs-316	19	3	form	form	NOUN
iajs-316	19	4	of	of	ADP
iajs-316	19	5	the	the	DET
iajs-316	19	6	sivp	sivp	NOUN
iajs-316	19	7	is	be	AUX
iajs-316	19	8	:	:	PUNCT
iajs-316	19	9	xm	xm	PROPN
iajs-316	19	10	y	y	PROPN
iajs-316	19	11	"	"	PUNCT
iajs-316	19	12	+	+	CCONJ
iajs-316	19	13	f(x	f(x	PROPN
iajs-316	19	14	,	,	PUNCT
iajs-316	19	15	y	y	PROPN
iajs-316	19	16	,	,	PUNCT
iajs-316	19	17	y	y	PROPN
iajs-316	19	18	'	'	PUNCT
iajs-316	19	19	)	)	PUNCT
iajs-316	20	1	=	=	SYM
iajs-316	20	2	0	0	NUM
iajs-316	20	3	,	,	PUNCT
iajs-316	20	4	0	0	PUNCT
iajs-316	20	5	<	<	X
iajs-316	20	6	x	x	X
iajs-316	20	7	<	<	X
iajs-316	20	8	1	1	NUM
iajs-316	20	9	,	,	PUNCT
iajs-316	20	10	(	(	PUNCT
iajs-316	20	11	1	1	X
iajs-316	20	12	)	)	PUNCT
iajs-316	20	13	with	with	ADP
iajs-316	20	14	some	some	DET
iajs-316	20	15	initial	initial	ADJ
iajs-316	20	16	conditions	condition	NOUN
iajs-316	20	17	.	.	PUNCT
iajs-316	21	1	the	the	DET
iajs-316	21	2	object	object	NOUN
iajs-316	21	3	is	be	AUX
iajs-316	21	4	to	to	PART
iajs-316	21	5	find	find	VERB
iajs-316	21	6	a	a	DET
iajs-316	21	7	function	function	NOUN
iajs-316	21	8	y	y	PROPN
iajs-316	21	9	that	that	PRON
iajs-316	21	10	satisfies	satisfy	VERB
iajs-316	21	11	the	the	DET
iajs-316	21	12	differential	differential	ADJ
iajs-316	21	13	equation	equation	NOUN
iajs-316	21	14	together	together	ADV
iajs-316	21	15	with	with	ADP
iajs-316	21	16	ic	ic	PROPN
iajs-316	21	17	.	.	PUNCT
iajs-316	22	1	we	we	PRON
iajs-316	22	2	view	view	VERB
iajs-316	22	3	f	f	PROPN
iajs-316	22	4	as	as	ADP
iajs-316	22	5	a	a	DET
iajs-316	22	6	generally	generally	ADV
iajs-316	22	7	nonlinear	nonlinear	ADJ
iajs-316	22	8	function	function	NOUN
iajs-316	22	9	of	of	ADP
iajs-316	22	10	y	y	PROPN
iajs-316	22	11	and	and	CCONJ
iajs-316	22	12	y	y	PROPN
iajs-316	22	13	'	'	PROPN
iajs-316	22	14	,	,	PUNCT
iajs-316	22	15	but	but	CCONJ
iajs-316	22	16	here	here	ADV
iajs-316	22	17	it	it	PRON
iajs-316	22	18	wins	win	VERB
iajs-316	22	19	,	,	PUNCT
iajs-316	22	20	we	we	PRON
iajs-316	22	21	as	as	SCONJ
iajs-316	22	22	look	look	VERB
iajs-316	22	23	f	f	NOUN
iajs-316	22	24	=	=	SYM
iajs-316	22	25	f(x	f(x	PROPN
iajs-316	22	26	)	)	PUNCT
iajs-316	22	27	only	only	ADV
iajs-316	22	28	.	.	PUNCT
iajs-316	23	1	for	for	ADP
iajs-316	23	2	such	such	DET
iajs-316	23	3	a	a	DET
iajs-316	23	4	problem	problem	NOUN
iajs-316	23	5	to	to	PART
iajs-316	23	6	have	have	AUX
iajs-316	23	7	a	a	DET
iajs-316	23	8	solution	solution	NOUN
iajs-316	23	9	,	,	PUNCT
iajs-316	23	10	it	it	PRON
iajs-316	23	11	is	be	AUX
iajs-316	23	12	generally	generally	ADV
iajs-316	23	13	necessary	necessary	ADJ
iajs-316	23	14	either	either	CCONJ
iajs-316	23	15	that	that	SCONJ
iajs-316	23	16	f(x	f(x	PROPN
iajs-316	23	17	)	)	PUNCT
iajs-316	23	18	≠	≠	PROPN
iajs-316	23	19	0	0	NUM
iajs-316	23	20	hold	hold	NOUN
iajs-316	23	21	.	.	PUNCT
iajs-316	24	1	when	when	SCONJ
iajs-316	24	2	f(x	f(x	PROPN
iajs-316	24	3	)	)	PUNCT
iajs-316	24	4	≡	≡	PROPN
iajs-316	24	5	0	0	NUM
iajs-316	24	6	,	,	PUNCT
iajs-316	24	7	and/or	and/or	CCONJ
iajs-316	24	8	a	a	PRON
iajs-316	24	9	=	=	NOUN
iajs-316	24	10	0	0	NUM
iajs-316	24	11	,	,	PUNCT
iajs-316	24	12	b	b	X
iajs-316	24	13	=	=	SYM
iajs-316	24	14	0	0	NOUN
iajs-316	25	1	the	the	DET
iajs-316	25	2	ivp	ivp	NOUN
iajs-316	25	3	is	be	AUX
iajs-316	25	4	said	say	VERB
iajs-316	25	5	to	to	PART
iajs-316	25	6	be	be	AUX
iajs-316	25	7	homogeneous	homogeneous	ADJ
iajs-316	25	8	and	and	CCONJ
iajs-316	25	9	will	will	AUX
iajs-316	25	10	in	in	ADP
iajs-316	25	11	general	general	ADJ
iajs-316	25	12	have	have	VERB
iajs-316	25	13	only	only	ADV
iajs-316	25	14	the	the	DET
iajs-316	25	15	trivial	trivial	ADJ
iajs-316	25	16	solution	solution	NOUN
iajs-316	25	17	,	,	PUNCT
iajs-316	25	18	y(x	y(x	PROPN
iajs-316	25	19	)	)	PUNCT
iajs-316	25	20	≡	≡	PROPN
iajs-316	25	21	0	0	PUNCT
iajs-316	26	1	[	[	X
iajs-316	26	2	2	2	NUM
iajs-316	26	3	]	]	PUNCT
iajs-316	26	4	.	.	PUNCT
iajs-316	27	1	2	2	X
iajs-316	27	2	.	.	X
iajs-316	27	3	solution	solution	NOUN
iajs-316	27	4	of	of	ADP
iajs-316	27	5	second	second	ADJ
iajs-316	27	6	order	order	NOUN
iajs-316	27	7	sivp	sivp	NOUN
iajs-316	27	8	in	in	ADP
iajs-316	27	9	this	this	DET
iajs-316	27	10	section	section	NOUN
iajs-316	27	11	,	,	PUNCT
iajs-316	27	12	we	we	PRON
iajs-316	27	13	suggest	suggest	VERB
iajs-316	27	14	a	a	DET
iajs-316	27	15	semi	semi	ADJ
iajs-316	27	16	analytic	analytic	ADJ
iajs-316	27	17	technique	technique	NOUN
iajs-316	27	18	which	which	PRON
iajs-316	27	19	is	be	AUX
iajs-316	27	20	based	base	VERB
iajs-316	27	21	on	on	ADP
iajs-316	27	22	osculatory	osculatory	NOUN
iajs-316	27	23	interpolating	interpolate	VERB
iajs-316	27	24	polynomials	polynomial	NOUN
iajs-316	27	25	p2n+1	p2n+1	VERB
iajs-316	27	26	and	and	CCONJ
iajs-316	27	27	taylor	taylor	PROPN
iajs-316	27	28	series	series	PROPN
iajs-316	27	29	expansion	expansion	NOUN
iajs-316	27	30	to	to	PART
iajs-316	27	31	solve	solve	VERB
iajs-316	27	32	second	second	ADJ
iajs-316	27	33	order	order	NOUN
iajs-316	27	34	sivp	sivp	NOUN
iajs-316	27	35	,	,	PUNCT
iajs-316	27	36	we	we	PRON
iajs-316	27	37	consider	consider	VERB
iajs-316	27	38	the	the	DET
iajs-316	27	39	problem	problem	NOUN
iajs-316	27	40	(	(	PUNCT
iajs-316	27	41	1	1	NUM
iajs-316	27	42	)	)	PUNCT
iajs-316	27	43	,	,	PUNCT
iajs-316	27	44	where	where	SCONJ
iajs-316	27	45	f	f	PROPN
iajs-316	27	46	are	be	AUX
iajs-316	27	47	in	in	ADP
iajs-316	27	48	general	general	ADJ
iajs-316	27	49	nonlinear	nonlinear	ADJ
iajs-316	27	50	functions	function	NOUN
iajs-316	27	51	of	of	ADP
iajs-316	27	52	their	their	PRON
iajs-316	27	53	arguments	argument	NOUN
iajs-316	27	54	.	.	PUNCT
iajs-316	28	1	now	now	ADV
iajs-316	28	2	,	,	PUNCT
iajs-316	28	3	to	to	PART
iajs-316	28	4	solve	solve	VERB
iajs-316	28	5	the	the	DET
iajs-316	28	6	problem	problem	NOUN
iajs-316	28	7	by	by	ADP
iajs-316	28	8	suggested	suggest	VERB
iajs-316	28	9	method	method	NOUN
iajs-316	28	10	we	we	PRON
iajs-316	28	11	do	do	VERB
iajs-316	28	12	the	the	DET
iajs-316	28	13	following	follow	VERB
iajs-316	28	14	steps	step	NOUN
iajs-316	28	15	:	:	PUNCT
iajs-316	28	16	step	step	VERB
iajs-316	28	17	one	one	NUM
iajs-316	28	18	:	:	PUNCT
iajs-316	28	19	evaluate	evaluate	VERB
iajs-316	28	20	taylor	taylor	PROPN
iajs-316	28	21	series	series	PROPN
iajs-316	28	22	of	of	ADP
iajs-316	28	23	y(x	y(x	PROPN
iajs-316	28	24	)	)	PUNCT
iajs-316	28	25	abut	abut	PROPN
iajs-316	28	26	x	x	PUNCT
iajs-316	29	1	=	=	SYM
iajs-316	29	2	0	0	NUM
iajs-316	29	3	:	:	PUNCT
iajs-316	29	4	y	y	PROPN
iajs-316	29	5	=	=	PUNCT
iajs-316	29	6	a	a	PRON
iajs-316	29	7	0	0	NUM
iajs-316	30	1	+	+	CCONJ
iajs-316	30	2	a1	a1	NOUN
iajs-316	30	3	x	x	SYM
iajs-316	30	4	+	+	CCONJ
iajs-316	30	5			X
iajs-316	30	6			VERB
iajs-316	30	7	2i	2i	PROPN
iajs-316	30	8	a	a	DET
iajs-316	30	9	i	i	NOUN
iajs-316	30	10	x	x	PROPN
iajs-316	30	11	i	i	NOUN
iajs-316	30	12	(	(	PUNCT
iajs-316	30	13	2	2	NUM
iajs-316	30	14	)	)	PUNCT
iajs-316	30	15	where	where	SCONJ
iajs-316	30	16	y(0	y(0	NOUN
iajs-316	30	17	)	)	PUNCT
iajs-316	30	18	=	=	PROPN
iajs-316	30	19	a0	a0	PROPN
iajs-316	30	20	,	,	PUNCT
iajs-316	30	21	y'(0	y'(0	PROPN
iajs-316	30	22	)	)	PUNCT
iajs-316	30	23	=	=	NOUN
iajs-316	30	24	a1	a1	NOUN
iajs-316	30	25	,	,	PUNCT
iajs-316	30	26	y"(0	y"(0	NOUN
iajs-316	30	27	)	)	PUNCT
iajs-316	30	28	/	/	SYM
iajs-316	30	29	2	2	NUM
iajs-316	30	30	!	!	PUNCT
iajs-316	30	31	=	=	SYM
iajs-316	30	32	a2	a2	PROPN
iajs-316	30	33	,	,	PUNCT
iajs-316	30	34	…	…	PUNCT
iajs-316	30	35	,	,	PUNCT
iajs-316	30	36	y(i)(0	y(i)(0	NUM
iajs-316	30	37	)	)	PUNCT
iajs-316	30	38	/	/	SYM
iajs-316	31	1	i	i	INTJ
iajs-316	31	2	!	!	PUNCT
iajs-316	32	1	=	=	PUNCT
iajs-316	32	2	ai	ai	VERB
iajs-316	32	3	,	,	PUNCT
iajs-316	32	4	i=	i=	PROPN
iajs-316	32	5	3	3	NUM
iajs-316	32	6	,	,	PUNCT
iajs-316	32	7	4	4	NUM
iajs-316	32	8	,	,	PUNCT
iajs-316	32	9	…	…	PUNCT
iajs-316	32	10	and	and	CCONJ
iajs-316	32	11	evaluate	evaluate	VERB
iajs-316	32	12	taylor	taylor	PROPN
iajs-316	32	13	series	series	NOUN
iajs-316	32	14	of	of	ADP
iajs-316	32	15	y(x	y(x	PROPN
iajs-316	32	16	)	)	PUNCT
iajs-316	32	17	about	about	ADP
iajs-316	32	18	x	x	X
iajs-316	32	19	=	=	SYM
iajs-316	32	20	1	1	NUM
iajs-316	32	21	:	:	PUNCT
iajs-316	33	1	y	y	PROPN
iajs-316	33	2	=	=	SYM
iajs-316	33	3	b	b	PROPN
iajs-316	33	4	0	0	PUNCT
iajs-316	33	5	+	+	NUM
iajs-316	33	6	b1	b1	NOUN
iajs-316	33	7	(	(	PUNCT
iajs-316	33	8	x-1	x-1	NOUN
iajs-316	33	9	)	)	PUNCT
iajs-316	34	1	+	+	CCONJ
iajs-316	34	2			X
iajs-316	34	3			VERB
iajs-316	34	4	2i	2i	PROPN
iajs-316	34	5	b	b	PROPN
iajs-316	35	1	i	i	PROPN
iajs-316	35	2	(	(	PUNCT
iajs-316	35	3	x-1	x-1	PROPN
iajs-316	35	4	)	)	PUNCT
iajs-316	35	5	i	i	PRON
iajs-316	35	6	(	(	PUNCT
iajs-316	35	7	3	3	X
iajs-316	35	8	)	)	PUNCT
iajs-316	35	9	where	where	SCONJ
iajs-316	35	10	y(1	y(1	PROPN
iajs-316	35	11	)	)	PUNCT
iajs-316	35	12	=	=	PROPN
iajs-316	35	13	b0	b0	PROPN
iajs-316	35	14	,	,	PUNCT
iajs-316	35	15	y'(1	y'(1	PROPN
iajs-316	35	16	)	)	PUNCT
iajs-316	35	17	=	=	SYM
iajs-316	35	18	b1	b1	NOUN
iajs-316	35	19	,	,	PUNCT
iajs-316	35	20	y"(1	y"(1	NOUN
iajs-316	35	21	)	)	PUNCT
iajs-316	35	22	/	/	SYM
iajs-316	35	23	2	2	NUM
iajs-316	35	24	!	!	PUNCT
iajs-316	35	25	=	=	NOUN
iajs-316	35	26	b2	b2	PROPN
iajs-316	35	27	,	,	PUNCT
iajs-316	35	28	…	…	PUNCT
iajs-316	35	29	,	,	PUNCT
iajs-316	35	30	y(i)(1	y(i)(1	NUM
iajs-316	35	31	)	)	PUNCT
iajs-316	35	32	/	/	PUNCT
iajs-316	35	33	i	i	NOUN
iajs-316	35	34	!	!	PUNCT
iajs-316	36	1	=	=	NOUN
iajs-316	36	2	bi	bi	INTJ
iajs-316	36	3	,	,	PUNCT
iajs-316	36	4	i	i	NOUN
iajs-316	36	5	=	=	NOUN
iajs-316	36	6	3,4	3,4	NUM
iajs-316	36	7	,	,	PUNCT
iajs-316	36	8	…	…	PUNCT
iajs-316	36	9	step	step	NOUN
iajs-316	36	10	two	two	NUM
iajs-316	36	11	:	:	PUNCT
iajs-316	36	12	insert	insert	VERB
iajs-316	36	13	the	the	DET
iajs-316	36	14	series	series	NOUN
iajs-316	36	15	form	form	NOUN
iajs-316	36	16	(	(	PUNCT
iajs-316	36	17	3	3	NUM
iajs-316	36	18	)	)	PUNCT
iajs-316	36	19	into	into	ADP
iajs-316	36	20	equation	equation	NOUN
iajs-316	36	21	(	(	PUNCT
iajs-316	36	22	1	1	NUM
iajs-316	36	23	)	)	PUNCT
iajs-316	36	24	and	and	CCONJ
iajs-316	36	25	put	put	VERB
iajs-316	36	26	x	x	SYM
iajs-316	36	27	=	=	SYM
iajs-316	36	28	1	1	NUM
iajs-316	36	29	,	,	PUNCT
iajs-316	36	30	then	then	ADV
iajs-316	36	31	equate	equate	VERB
iajs-316	36	32	the	the	DET
iajs-316	36	33	coefficients	coefficient	NOUN
iajs-316	36	34	of	of	ADP
iajs-316	36	35	powers	power	NOUN
iajs-316	36	36	of	of	ADP
iajs-316	36	37	(	(	PUNCT
iajs-316	36	38	x-1	x-1	NOUN
iajs-316	36	39	)	)	PUNCT
iajs-316	36	40	to	to	PART
iajs-316	36	41	obtain	obtain	VERB
iajs-316	36	42	b2	b2	NOUN
iajs-316	36	43	.	.	PUNCT
iajs-316	37	1	step	step	NOUN
iajs-316	37	2	three	three	NUM
iajs-316	37	3	 	 	SPACE
iajs-316	37	4	:	:	PUNCT
iajs-316	37	5	derive	derive	ADJ
iajs-316	37	6	equation(1	equation(1	NOUN
iajs-316	37	7	)	)	PUNCT
iajs-316	37	8	with	with	ADP
iajs-316	37	9	respect	respect	NOUN
iajs-316	37	10	to	to	ADP
iajs-316	37	11	x	x	PRON
iajs-316	37	12	,	,	PUNCT
iajs-316	37	13	to	to	PART
iajs-316	37	14	get	get	VERB
iajs-316	37	15	new	new	ADJ
iajs-316	37	16	form	form	NOUN
iajs-316	37	17	of	of	ADP
iajs-316	37	18	equation	equation	NOUN
iajs-316	37	19	say	say	VERB
iajs-316	37	20	(	(	PUNCT
iajs-316	37	21	4	4	NUM
iajs-316	37	22	)	)	PUNCT
iajs-316	37	23	xm	xm	PROPN
iajs-316	37	24	y	y	PROPN
iajs-316	37	25	''	''	PUNCT
iajs-316	37	26	'	'	PUNCT
iajs-316	38	1	+	+	NUM
iajs-316	38	2	m	m	VERB
iajs-316	38	3	xm-1	xm-1	NUM
iajs-316	38	4	y	y	NOUN
iajs-316	38	5	''	''	PUNCT
iajs-316	38	6	+	+	PROPN
iajs-316	38	7	df(x	df(x	NOUN
iajs-316	38	8	,	,	PUNCT
iajs-316	38	9	y	y	PROPN
iajs-316	38	10	,	,	PUNCT
iajs-316	38	11	y	y	PROPN
iajs-316	38	12	'	'	PUNCT
iajs-316	38	13	)	)	PUNCT
iajs-316	38	14	/	/	SYM
iajs-316	38	15	dx	dx	PROPN
iajs-316	39	1	=	=	SYM
iajs-316	39	2	0	0	NUM
iajs-316	40	1	(	(	PUNCT
iajs-316	40	2	4	4	NUM
iajs-316	40	3	)	)	PUNCT
iajs-316	40	4	then	then	ADV
iajs-316	40	5	,	,	PUNCT
iajs-316	40	6	insert	insert	VERB
iajs-316	40	7	the	the	DET
iajs-316	40	8	series	series	NOUN
iajs-316	40	9	form	form	NOUN
iajs-316	40	10	(	(	PUNCT
iajs-316	40	11	2	2	NUM
iajs-316	40	12	)	)	PUNCT
iajs-316	40	13	into	into	ADP
iajs-316	40	14	equation	equation	NOUN
iajs-316	40	15	(	(	PUNCT
iajs-316	40	16	4	4	NUM
iajs-316	40	17	)	)	PUNCT
iajs-316	40	18	and	and	CCONJ
iajs-316	40	19	put	put	VERB
iajs-316	40	20	x	x	X
iajs-316	40	21	=	=	SYM
iajs-316	40	22	0	0	NUM
iajs-316	40	23	and	and	CCONJ
iajs-316	40	24	equate	equate	VERB
iajs-316	40	25	the	the	DET
iajs-316	40	26	coefficients	coefficient	NOUN
iajs-316	40	27	of	of	ADP
iajs-316	40	28	powers	power	NOUN
iajs-316	40	29	of	of	ADP
iajs-316	40	30	x	x	PART
iajs-316	40	31	to	to	PART
iajs-316	40	32	obtain	obtain	VERB
iajs-316	40	33	a2	a2	NOUN
iajs-316	40	34	,	,	PUNCT
iajs-316	40	35	again	again	ADV
iajs-316	40	36	insert	insert	VERB
iajs-316	40	37	the	the	DET
iajs-316	40	38	series	series	NOUN
iajs-316	40	39	form	form	NOUN
iajs-316	40	40	(	(	PUNCT
iajs-316	40	41	3	3	NUM
iajs-316	40	42	)	)	PUNCT
iajs-316	40	43	into	into	ADP
iajs-316	40	44	equation(4	equation(4	PROPN
iajs-316	40	45	)	)	PUNCT
iajs-316	40	46	and	and	CCONJ
iajs-316	40	47	put	put	VERB
iajs-316	40	48	x	x	SYM
iajs-316	40	49	=	=	SYM
iajs-316	40	50	1	1	NUM
iajs-316	40	51	,	,	PUNCT
iajs-316	40	52	then	then	ADV
iajs-316	40	53	equate	equate	VERB
iajs-316	40	54	the	the	DET
iajs-316	40	55	coefficients	coefficient	NOUN
iajs-316	40	56	of	of	ADP
iajs-316	40	57	powers	power	NOUN
iajs-316	40	58	of	of	ADP
iajs-316	40	59	(	(	PUNCT
iajs-316	40	60	x-1	x-1	NOUN
iajs-316	40	61	)	)	PUNCT
iajs-316	40	62	to	to	PART
iajs-316	40	63	obtain	obtain	VERB
iajs-316	40	64	b3	b3	PROPN
iajs-316	40	65	.	.	PUNCT
iajs-316	41	1	step	step	VERB
iajs-316	41	2	four	four	NUM
iajs-316	41	3	:	:	PUNCT
iajs-316	41	4	iterate	iterate	VERB
iajs-316	41	5	the	the	DET
iajs-316	41	6	above	above	ADJ
iajs-316	41	7	process	process	NOUN
iajs-316	41	8	many	many	ADJ
iajs-316	41	9	times	time	NOUN
iajs-316	41	10	to	to	PART
iajs-316	41	11	obtain	obtain	VERB
iajs-316	41	12	a3	a3	NOUN
iajs-316	41	13	,	,	PUNCT
iajs-316	41	14	b4	b4	NOUN
iajs-316	41	15	,	,	PUNCT
iajs-316	41	16	then	then	ADV
iajs-316	41	17	a4	a4	INTJ
iajs-316	41	18	,	,	PUNCT
iajs-316	41	19	b5	b5	PROPN
iajs-316	41	20	and	and	CCONJ
iajs-316	41	21	so	so	ADV
iajs-316	41	22	on	on	ADV
iajs-316	41	23	,	,	PUNCT
iajs-316	41	24	that	that	ADV
iajs-316	41	25	is	is	ADV
iajs-316	41	26	,	,	PUNCT
iajs-316	41	27	to	to	PART
iajs-316	41	28	get	get	VERB
iajs-316	41	29	ai	ai	INTJ
iajs-316	41	30	and	and	CCONJ
iajs-316	41	31	bi	bi	NOUN
iajs-316	41	32	for	for	ADP
iajs-316	41	33	all	all	PRON
iajs-316	41	34	i	i	PRON
iajs-316	41	35	≥	≥	VERB
iajs-316	41	36	2	2	NUM
iajs-316	41	37	,	,	PUNCT
iajs-316	41	38	the	the	DET
iajs-316	41	39	resulting	result	VERB
iajs-316	41	40	equations	equation	NOUN
iajs-316	41	41	can	can	AUX
iajs-316	41	42	be	be	AUX
iajs-316	41	43	solved	solve	VERB
iajs-316	41	44	using	use	VERB
iajs-316	41	45	matlab	matlab	PROPN
iajs-316	41	46	version	version	NOUN
iajs-316	41	47	7.10	7.10	NUM
iajs-316	41	48	,	,	PUNCT
iajs-316	41	49	to	to	PART
iajs-316	41	50	obtain	obtain	VERB
iajs-316	41	51	ai	ai	NOUN
iajs-316	41	52	and	and	CCONJ
iajs-316	41	53	bi	bi	NOUN
iajs-316	41	54	for	for	ADP
iajs-316	41	55	all	all	PRON
iajs-316	41	56	i	i	PROPN
iajs-316	41	57	2	2	NUM
iajs-316	41	58	.	.	PUNCT
iajs-316	42	1	step	step	NOUN
iajs-316	42	2	five	five	NUM
iajs-316	43	1	:	:	PUNCT
iajs-316	43	2	the	the	DET
iajs-316	43	3	notation	notation	NOUN
iajs-316	43	4	implies	imply	VERB
iajs-316	43	5	that	that	SCONJ
iajs-316	43	6	the	the	DET
iajs-316	43	7	coefficients	coefficient	NOUN
iajs-316	43	8	depend	depend	VERB
iajs-316	43	9	only	only	ADV
iajs-316	43	10	on	on	ADP
iajs-316	43	11	the	the	DET
iajs-316	43	12	indicated	indicate	VERB
iajs-316	43	13	unknowns	unknown	NOUN
iajs-316	43	14	a0	a0	PROPN
iajs-316	43	15	,	,	PUNCT
iajs-316	43	16	a1	a1	PROPN
iajs-316	43	17	,	,	PUNCT
iajs-316	43	18	b0	b0	NOUN
iajs-316	43	19	,	,	PUNCT
iajs-316	43	20	b1	b1	NOUN
iajs-316	43	21	,	,	PUNCT
iajs-316	43	22	and	and	CCONJ
iajs-316	43	23	use	use	VERB
iajs-316	43	24	the	the	DET
iajs-316	43	25	ic	ic	PROPN
iajs-316	43	26	to	to	PART
iajs-316	43	27	get	get	VERB
iajs-316	43	28	a0	a0	PROPN
iajs-316	43	29	,	,	PUNCT
iajs-316	43	30	a1	a1	PROPN
iajs-316	43	31	,	,	PUNCT
iajs-316	43	32	therefore	therefore	ADV
iajs-316	43	33	we	we	PRON
iajs-316	43	34	have	have	VERB
iajs-316	43	35	only	only	ADV
iajs-316	43	36	two	two	NUM
iajs-316	43	37	unknown	unknown	ADJ
iajs-316	43	38	coefficients	coefficient	NOUN
iajs-316	43	39	b0	b0	NOUN
iajs-316	43	40	and	and	CCONJ
iajs-316	43	41	b1	b1	NOUN
iajs-316	43	42	.	.	PUNCT
iajs-316	44	1	now	now	ADV
iajs-316	44	2	,	,	PUNCT
iajs-316	44	3	we	we	PRON
iajs-316	44	4	can	can	AUX
iajs-316	44	5	construct	construct	VERB
iajs-316	44	6	two	two	NUM
iajs-316	44	7	point	point	NOUN
iajs-316	44	8	osculatory	osculatory	NOUN
iajs-316	44	9	interpolating	interpolate	VERB
iajs-316	44	10	polynomials	polynomial	NOUN
iajs-316	44	11	p2n+1(x	p2n+1(x	VERB
iajs-316	44	12	)	)	PUNCT
iajs-316	44	13	from	from	ADP
iajs-316	44	14	these	these	DET
iajs-316	44	15	coefficients	coefficient	NOUN
iajs-316	44	16	(	(	PUNCT
iajs-316	44	17	aisۥ	aisۥ	ADJ
iajs-316	44	18	and	and	CCONJ
iajs-316	44	19	bisۥ	bisۥ	NOUN
iajs-316	44	20	)	)	PUNCT
iajs-316	44	21	by	by	ADP
iajs-316	44	22	the	the	DET
iajs-316	44	23	following	follow	VERB
iajs-316	44	24	:	:	PUNCT
iajs-316	44	25	515	515	NUM
iajs-316	44	26	|	|	NOUN
iajs-316	44	27	mathematics	mathematic	NOUN
iajs-316	44	28	2014	2014	NUM
iajs-316	44	29	)	)	PUNCT
iajs-316	44	30	عام	عام	ADP
iajs-316	44	31	3العدد	3العدد	NUM
iajs-316	44	32	(	(	PUNCT
iajs-316	44	33	27مجلة	27مجلة	NUM
iajs-316	44	34	إبن	إبن	VERB
iajs-316	44	35	الھيثم	الھيثم	NOUN
iajs-316	44	36	للعلوم	للعلوم	NOUN
iajs-316	44	37	الصرفة	الصرفة	NOUN
iajs-316	45	1	و	و	PRON
iajs-316	45	2	التطبيقية	التطبيقية	ADV
iajs-316	45	3	المجلد	المجلد	VERB
iajs-316	45	4	ibn	ibn	PROPN
iajs-316	45	5	al	al	PROPN
iajs-316	45	6	-	-	PUNCT
iajs-316	45	7	haitham	haitham	PROPN
iajs-316	45	8	jour	jour	X
iajs-316	45	9	.	.	PROPN
iajs-316	46	1	for	for	ADP
iajs-316	46	2	pure	pure	ADJ
iajs-316	46	3	&	&	CCONJ
iajs-316	46	4	appl	appl	PROPN
iajs-316	46	5	.	.	PUNCT
iajs-316	47	1	sci	sci	PROPN
iajs-316	47	2	.	.	PUNCT
iajs-316	47	3	vol	vol	NOUN
iajs-316	47	4	.	.	PROPN
iajs-316	48	1	27	27	NUM
iajs-316	48	2	(	(	PUNCT
iajs-316	48	3	3	3	NUM
iajs-316	48	4	)	)	PUNCT
iajs-316	48	5	2014	2014	NUM
iajs-316	48	6	p2n+1	p2n+1	NOUN
iajs-316	48	7	=	=	SYM
iajs-316	48	8			X
iajs-316	49	1			NUM
iajs-316	49	2	n	n	INTJ
iajs-316	49	3	i	i	PRON
iajs-316	49	4	0	0	PUNCT
iajs-316	49	5	{	{	PUNCT
iajs-316	49	6	ai	ai	PROPN
iajs-316	49	7	qi(x	qi(x	NUM
iajs-316	49	8	)	)	PUNCT
iajs-316	50	1	+	+	CCONJ
iajs-316	50	2	(	(	PUNCT
iajs-316	50	3	–	–	PUNCT
iajs-316	50	4	1)i	1)i	NUM
iajs-316	50	5	bi	bi	PROPN
iajs-316	50	6	qi(1	qi(1	PROPN
iajs-316	50	7	–	–	PUNCT
iajs-316	50	8	x	x	X
iajs-316	50	9	)	)	PUNCT
iajs-316	50	10	}	}	PUNCT
iajs-316	50	11	(	(	PUNCT
iajs-316	50	12	5	5	X
iajs-316	50	13	)	)	PUNCT
iajs-316	50	14	where	where	SCONJ
iajs-316	51	1	q	q	PROPN
iajs-316	51	2	j	j	PROPN
iajs-316	51	3	(	(	PUNCT
iajs-316	51	4	x	x	PROPN
iajs-316	51	5	)	)	PUNCT
iajs-316	51	6	/	/	SYM
iajs-316	51	7	j	j	PROPN
iajs-316	51	8	!	!	PUNCT
iajs-316	51	9	=	=	PUNCT
iajs-316	52	1	(	(	PUNCT
iajs-316	52	2	x	x	PUNCT
iajs-316	52	3	j	j	PROPN
iajs-316	52	4	/	/	SYM
iajs-316	52	5	j	j	PROPN
iajs-316	52	6	!	!	PUNCT
iajs-316	52	7	)	)	PUNCT
iajs-316	53	1	(	(	PUNCT
iajs-316	53	2	1	1	NUM
iajs-316	53	3	–	–	PUNCT
iajs-316	53	4	x	x	NOUN
iajs-316	53	5	)	)	PUNCT
iajs-316	53	6	1n	1n	NUM
iajs-316	53	7			X
iajs-316	53	8			PROPN
iajs-316	53	9			PROPN
iajs-316	53	10	jn	jn	PROPN
iajs-316	53	11	s	s	PROPN
iajs-316	53	12	0	0	NUM
iajs-316	53	13			NOUN
iajs-316	53	14			NOUN
iajs-316	53	15			PROPN
iajs-316	53	16			PROPN
iajs-316	53	17			PROPN
iajs-316	53	18			NOUN
iajs-316	53	19			PROPN
iajs-316	53	20	s	s	PART
iajs-316	53	21	sn	sn	PROPN
iajs-316	53	22	xs	xs	PROPN
iajs-316	53	23	step	step	NOUN
iajs-316	53	24	six	six	NUM
iajs-316	53	25	:	:	PUNCT
iajs-316	53	26	to	to	PART
iajs-316	53	27	find	find	VERB
iajs-316	53	28	the	the	DET
iajs-316	53	29	unknowns	unknown	NOUN
iajs-316	53	30	coefficients	coefficient	NOUN
iajs-316	53	31	b0	b0	NOUN
iajs-316	53	32	and	and	CCONJ
iajs-316	53	33	b1	b1	NOUN
iajs-316	53	34	,	,	PUNCT
iajs-316	53	35	integrate	integrate	VERB
iajs-316	53	36	equation	equation	NOUN
iajs-316	53	37	(	(	PUNCT
iajs-316	53	38	1	1	NUM
iajs-316	53	39	)	)	PUNCT
iajs-316	53	40	on	on	ADP
iajs-316	53	41	[	[	X
iajs-316	53	42	0	0	NUM
iajs-316	53	43	,	,	PUNCT
iajs-316	53	44	x	x	X
iajs-316	53	45	]	]	X
iajs-316	53	46	to	to	PART
iajs-316	53	47	obtain	obtain	VERB
iajs-316	53	48	:	:	PUNCT
iajs-316	53	49	xm	xm	PROPN
iajs-316	53	50	y'(x	y'(x	NOUN
iajs-316	53	51	)	)	PUNCT
iajs-316	53	52	–	–	PUNCT
iajs-316	53	53	mxm-1y(x	mxm-1y(x	NOUN
iajs-316	53	54	)	)	PUNCT
iajs-316	53	55	+	+	NUM
iajs-316	53	56	m(m–1	m(m–1	NOUN
iajs-316	53	57	)	)	PUNCT
iajs-316	53	58			PUNCT
iajs-316	54	1	x	x	SYM
iajs-316	54	2	0	0	NUM
iajs-316	54	3	xm-2	xm-2	NUM
iajs-316	54	4	y(x	y(x	PROPN
iajs-316	54	5	)	)	PUNCT
iajs-316	54	6	dx	dx	PROPN
iajs-316	55	1	+	+	X
iajs-316	55	2			X
iajs-316	55	3	x	x	SYM
iajs-316	55	4	0	0	NUM
iajs-316	55	5	f(x	f(x	PROPN
iajs-316	55	6	,	,	PUNCT
iajs-316	55	7	y	y	PROPN
iajs-316	55	8	,	,	PUNCT
iajs-316	55	9	y	y	PROPN
iajs-316	55	10	'	'	PUNCT
iajs-316	55	11	)	)	PUNCT
iajs-316	55	12	dx	dx	PROPN
iajs-316	56	1	=	=	SYM
iajs-316	56	2	0	0	PROPN
iajs-316	56	3	(	(	PUNCT
iajs-316	56	4	6a	6a	NOUN
iajs-316	56	5	)	)	PUNCT
iajs-316	56	6	and	and	CCONJ
iajs-316	56	7	again	again	ADV
iajs-316	56	8	integrate	integrate	VERB
iajs-316	56	9	equation	equation	NOUN
iajs-316	56	10	(	(	PUNCT
iajs-316	56	11	6a	6a	NOUN
iajs-316	56	12	)	)	PUNCT
iajs-316	56	13	on	on	ADP
iajs-316	56	14	[	[	X
iajs-316	56	15	0	0	NUM
iajs-316	56	16	,	,	PUNCT
iajs-316	56	17	x	x	X
iajs-316	56	18	]	]	X
iajs-316	56	19	to	to	PART
iajs-316	56	20	obtain	obtain	VERB
iajs-316	56	21	:	:	PUNCT
iajs-316	56	22	xmy(x	xmy(x	NUM
iajs-316	56	23	)	)	PUNCT
iajs-316	56	24	–	–	PUNCT
iajs-316	56	25	2m	2m	NUM
iajs-316	56	26	x	x	SYM
iajs-316	56	27	0	0	NUM
iajs-316	56	28	xm-1y(x	xm-1y(x	NOUN
iajs-316	56	29	)	)	PUNCT
iajs-316	56	30	dx	dx	PROPN
iajs-316	57	1	+	+	PROPN
iajs-316	57	2	m(m–1)	m(m–1)	PROPN
iajs-316	57	3	x	x	SYM
iajs-316	57	4	0	0	NUM
iajs-316	57	5	(	(	PUNCT
iajs-316	57	6	1	1	NUM
iajs-316	57	7	–	–	PUNCT
iajs-316	57	8	x)xm-2y(x)dx+	x)xm-2y(x)dx+	NOUN
iajs-316	57	9	x	x	SYM
iajs-316	57	10	0	0	PUNCT
iajs-316	57	11	(	(	PUNCT
iajs-316	57	12	1	1	NUM
iajs-316	57	13	–	–	PUNCT
iajs-316	57	14	x)f(x	x)f(x	PROPN
iajs-316	57	15	,	,	PUNCT
iajs-316	57	16	y	y	PROPN
iajs-316	57	17	,	,	PUNCT
iajs-316	57	18	y	y	PROPN
iajs-316	57	19	'	'	PUNCT
iajs-316	57	20	)	)	PUNCT
iajs-316	57	21	=	=	SYM
iajs-316	57	22	0	0	NUM
iajs-316	57	23	(	(	PUNCT
iajs-316	57	24	6b	6b	NOUN
iajs-316	57	25	)	)	PUNCT
iajs-316	57	26	step	step	NOUN
iajs-316	57	27	seven	seven	NUM
iajs-316	57	28	:	:	PUNCT
iajs-316	57	29	putting	put	VERB
iajs-316	57	30	x	x	X
iajs-316	57	31	=	=	SYM
iajs-316	57	32	1	1	NUM
iajs-316	57	33	in	in	ADP
iajs-316	57	34	equations	equation	NOUN
iajs-316	57	35	(	(	PUNCT
iajs-316	57	36	6	6	NUM
iajs-316	57	37	)	)	PUNCT
iajs-316	57	38	to	to	PART
iajs-316	57	39	get	get	VERB
iajs-316	57	40	:	:	PUNCT
iajs-316	57	41	b1	b1	NOUN
iajs-316	57	42	–	–	PUNCT
iajs-316	57	43	mb0	mb0	PROPN
iajs-316	57	44	+	+	CCONJ
iajs-316	57	45	m(m-1	m(m-1	NOUN
iajs-316	57	46	)	)	PUNCT
iajs-316	57	47			PUNCT
iajs-316	57	48	1	1	NUM
iajs-316	57	49	0	0	NUM
iajs-316	57	50	xm-2	xm-2	NUM
iajs-316	57	51	y(x	y(x	PROPN
iajs-316	57	52	)	)	PUNCT
iajs-316	57	53	dx	dx	PROPN
iajs-316	58	1	+	+	CCONJ
iajs-316	58	2			SYM
iajs-316	58	3	1	1	NUM
iajs-316	58	4	0	0	NUM
iajs-316	58	5	f(x	f(x	PROPN
iajs-316	58	6	,	,	PUNCT
iajs-316	58	7	y	y	PROPN
iajs-316	58	8	,	,	PUNCT
iajs-316	58	9	y	y	PROPN
iajs-316	58	10	'	'	PUNCT
iajs-316	58	11	)	)	PUNCT
iajs-316	58	12	dx	dx	PROPN
iajs-316	59	1	=	=	SYM
iajs-316	59	2	0	0	PROPN
iajs-316	59	3	(	(	PUNCT
iajs-316	59	4	7a	7a	NUM
iajs-316	59	5	)	)	PUNCT
iajs-316	59	6	and	and	CCONJ
iajs-316	59	7	b0–2m	b0–2m	PROPN
iajs-316	59	8	1	1	NUM
iajs-316	59	9	0	0	NUM
iajs-316	59	10	xm-1y(x)dx	xm-1y(x)dx	VERB
iajs-316	60	1	+	+	NOUN
iajs-316	60	2	m(m–1)	m(m–1)	NOUN
iajs-316	60	3	1	1	NUM
iajs-316	60	4	0	0	NUM
iajs-316	60	5	(	(	PUNCT
iajs-316	60	6	1	1	NUM
iajs-316	60	7	–	–	PUNCT
iajs-316	60	8	x)xm-2	x)xm-2	NOUN
iajs-316	60	9	y(x)dx	y(x)dx	NOUN
iajs-316	61	1	+	+	NUM
iajs-316	61	2			SYM
iajs-316	61	3	1	1	NUM
iajs-316	61	4	0	0	NUM
iajs-316	61	5	(	(	PUNCT
iajs-316	61	6	1	1	NUM
iajs-316	61	7	–	–	PUNCT
iajs-316	61	8	x)f(x	x)f(x	PROPN
iajs-316	61	9	,	,	PUNCT
iajs-316	61	10	y	y	PROPN
iajs-316	61	11	,	,	PUNCT
iajs-316	61	12	y')dx	y')dx	NOUN
iajs-316	61	13	=	=	SYM
iajs-316	61	14	0	0	NUM
iajs-316	61	15	(	(	PUNCT
iajs-316	61	16	7b	7b	NOUN
iajs-316	61	17	)	)	PUNCT
iajs-316	61	18	step	step	NOUN
iajs-316	61	19	eight	eight	NUM
iajs-316	61	20	:	:	PUNCT
iajs-316	61	21	use	use	VERB
iajs-316	61	22	p2n+1(x	p2n+1(x	NOUN
iajs-316	61	23	)	)	PUNCT
iajs-316	61	24	which	which	PRON
iajs-316	61	25	defined	define	VERB
iajs-316	61	26	in	in	ADP
iajs-316	61	27	equation	equation	NOUN
iajs-316	61	28	(	(	PUNCT
iajs-316	61	29	5	5	NUM
iajs-316	61	30	)	)	PUNCT
iajs-316	61	31	as	as	ADP
iajs-316	61	32	a	a	DET
iajs-316	61	33	replacement	replacement	NOUN
iajs-316	61	34	of	of	ADP
iajs-316	61	35	y(x	y(x	PROPN
iajs-316	61	36	)	)	PUNCT
iajs-316	61	37	,	,	PUNCT
iajs-316	61	38	we	we	PRON
iajs-316	61	39	see	see	VERB
iajs-316	61	40	that	that	SCONJ
iajs-316	61	41	equations	equation	NOUN
iajs-316	61	42	(	(	PUNCT
iajs-316	61	43	7	7	X
iajs-316	61	44	)	)	PUNCT
iajs-316	61	45	have	have	VERB
iajs-316	61	46	only	only	ADV
iajs-316	61	47	two	two	NUM
iajs-316	61	48	unknown	unknown	ADJ
iajs-316	61	49	coefficients	coefficient	NOUN
iajs-316	61	50	b0	b0	NOUN
iajs-316	61	51	and	and	CCONJ
iajs-316	61	52	b1	b1	NOUN
iajs-316	61	53	.	.	PUNCT
iajs-316	62	1	so	so	ADV
iajs-316	62	2	,	,	PUNCT
iajs-316	62	3	we	we	PRON
iajs-316	62	4	can	can	AUX
iajs-316	62	5	find	find	VERB
iajs-316	62	6	b0	b0	NOUN
iajs-316	62	7	and	and	CCONJ
iajs-316	62	8	b1	b1	NOUN
iajs-316	62	9	by	by	ADP
iajs-316	62	10	solving	solve	VERB
iajs-316	62	11	the	the	DET
iajs-316	62	12	system	system	NOUN
iajs-316	62	13	of	of	ADP
iajs-316	62	14	algebraic	algebraic	ADJ
iajs-316	62	15	equations	equation	NOUN
iajs-316	62	16	(	(	PUNCT
iajs-316	62	17	7	7	X
iajs-316	62	18	)	)	PUNCT
iajs-316	62	19	using	use	VERB
iajs-316	62	20	matlab	matlab	PROPN
iajs-316	62	21	,	,	PUNCT
iajs-316	62	22	so	so	ADV
iajs-316	62	23	insert	insert	VERB
iajs-316	62	24	the	the	DET
iajs-316	62	25	value	value	NOUN
iajs-316	62	26	of	of	ADP
iajs-316	62	27	b0	b0	NOUN
iajs-316	62	28	and	and	CCONJ
iajs-316	62	29	b1	b1	NOUN
iajs-316	62	30	into	into	ADP
iajs-316	62	31	equation	equation	NOUN
iajs-316	62	32	(	(	PUNCT
iajs-316	62	33	5	5	NUM
iajs-316	62	34	)	)	PUNCT
iajs-316	62	35	,	,	PUNCT
iajs-316	62	36	thus	thus	ADV
iajs-316	62	37	equation	equation	NOUN
iajs-316	62	38	(	(	PUNCT
iajs-316	62	39	5	5	NUM
iajs-316	62	40	)	)	PUNCT
iajs-316	62	41	represents	represent	VERB
iajs-316	62	42	the	the	DET
iajs-316	62	43	solution	solution	NOUN
iajs-316	62	44	of	of	ADP
iajs-316	62	45	the	the	DET
iajs-316	62	46	problem	problem	NOUN
iajs-316	62	47	.	.	PUNCT
iajs-316	63	1	note	note	VERB
iajs-316	63	2	extensive	extensive	ADJ
iajs-316	63	3	computations	computation	NOUN
iajs-316	63	4	have	have	AUX
iajs-316	63	5	shown	show	VERB
iajs-316	63	6	that	that	SCONJ
iajs-316	63	7	this	this	PRON
iajs-316	63	8	generally	generally	ADV
iajs-316	63	9	provides	provide	VERB
iajs-316	63	10	a	a	DET
iajs-316	63	11	more	more	ADV
iajs-316	63	12	accurate	accurate	ADJ
iajs-316	63	13	polynomial	polynomial	ADJ
iajs-316	63	14	representation	representation	NOUN
iajs-316	63	15	for	for	ADP
iajs-316	63	16	a	a	DET
iajs-316	63	17	given	give	VERB
iajs-316	63	18	n	n	NOUN
iajs-316	63	19	.	.	PUNCT
iajs-316	64	1	3	3	X
iajs-316	64	2	.	.	X
iajs-316	64	3	examples	example	NOUN
iajs-316	64	4	in	in	ADP
iajs-316	64	5	this	this	DET
iajs-316	64	6	section	section	NOUN
iajs-316	64	7	,	,	PUNCT
iajs-316	64	8	many	many	ADJ
iajs-316	64	9	examples	example	NOUN
iajs-316	64	10	will	will	AUX
iajs-316	64	11	be	be	AUX
iajs-316	64	12	given	give	VERB
iajs-316	64	13	to	to	PART
iajs-316	64	14	illustrate	illustrate	VERB
iajs-316	64	15	the	the	DET
iajs-316	64	16	efficiency	efficiency	NOUN
iajs-316	64	17	,	,	PUNCT
iajs-316	64	18	accuracy	accuracy	NOUN
iajs-316	64	19	,	,	PUNCT
iajs-316	64	20	implementation	implementation	NOUN
iajs-316	64	21	and	and	CCONJ
iajs-316	64	22	utility	utility	NOUN
iajs-316	64	23	of	of	ADP
iajs-316	64	24	the	the	DET
iajs-316	64	25	suggested	suggest	VERB
iajs-316	64	26	method	method	NOUN
iajs-316	64	27	.	.	PUNCT
iajs-316	65	1	the	the	DET
iajs-316	65	2	bvp4c	bvp4c	PROPN
iajs-316	65	3	solver	solver	NOUN
iajs-316	65	4	of	of	ADP
iajs-316	65	5	matlab	matlab	PROPN
iajs-316	65	6	has	have	AUX
iajs-316	65	7	been	be	AUX
iajs-316	65	8	modified	modify	VERB
iajs-316	65	9	accordingly	accordingly	ADV
iajs-316	65	10	so	so	SCONJ
iajs-316	65	11	that	that	SCONJ
iajs-316	65	12	it	it	PRON
iajs-316	65	13	can	can	AUX
iajs-316	65	14	solve	solve	VERB
iajs-316	65	15	some	some	DET
iajs-316	65	16	class	class	NOUN
iajs-316	65	17	of	of	ADP
iajs-316	65	18	sivp	sivp	NOUN
iajs-316	65	19	as	as	ADV
iajs-316	65	20	effectively	effectively	ADV
iajs-316	65	21	as	as	SCONJ
iajs-316	65	22	it	it	PRON
iajs-316	65	23	previously	previously	ADV
iajs-316	65	24	solved	solve	VERB
iajs-316	65	25	nonsingular	nonsingular	ADJ
iajs-316	65	26	ivp	ivp	NOUN
iajs-316	65	27	.	.	PUNCT
iajs-316	66	1	516	516	NUM
iajs-316	66	2	|	|	NOUN
iajs-316	66	3	mathematics	mathematic	NOUN
iajs-316	66	4	2014	2014	NUM
iajs-316	66	5	)	)	PUNCT
iajs-316	66	6	عام	عام	ADP
iajs-316	66	7	3العدد	3العدد	NUM
iajs-316	66	8	(	(	PUNCT
iajs-316	66	9	27مجلة	27مجلة	NUM
iajs-316	66	10	إبن	إبن	VERB
iajs-316	66	11	الھيثم	الھيثم	NOUN
iajs-316	66	12	للعلوم	للعلوم	NOUN
iajs-316	66	13	الصرفة	الصرفة	NOUN
iajs-316	67	1	و	و	PRON
iajs-316	67	2	التطبيقية	التطبيقية	ADV
iajs-316	67	3	المجلد	المجلد	VERB
iajs-316	67	4	ibn	ibn	PROPN
iajs-316	67	5	al	al	PROPN
iajs-316	67	6	-	-	PUNCT
iajs-316	67	7	haitham	haitham	PROPN
iajs-316	67	8	jour	jour	X
iajs-316	67	9	.	.	PROPN
iajs-316	68	1	for	for	ADP
iajs-316	68	2	pure	pure	ADJ
iajs-316	68	3	&	&	CCONJ
iajs-316	68	4	appl	appl	PROPN
iajs-316	68	5	.	.	PUNCT
iajs-316	69	1	sci	sci	PROPN
iajs-316	69	2	.	.	PUNCT
iajs-316	69	3	vol	vol	NOUN
iajs-316	69	4	.	.	PROPN
iajs-316	70	1	27	27	NUM
iajs-316	70	2	(	(	PUNCT
iajs-316	70	3	3	3	NUM
iajs-316	70	4	)	)	PUNCT
iajs-316	70	5	2014	2014	NUM
iajs-316	70	6	example	example	NOUN
iajs-316	70	7	1	1	NUM
iajs-316	70	8	order	order	NOUN
iajs-316	70	9	nonlinear	nonlinear	ADJ
iajs-316	70	10	sivp	sivp	NOUN
iajs-316	70	11	:	:	PUNCT
iajs-316	70	12	ndconsider	ndconsider	NOUN
iajs-316	70	13	the	the	DET
iajs-316	70	14	following	follow	VERB
iajs-316	70	15	2	2	NUM
iajs-316	70	16	+18x	+18x	PUNCT
iajs-316	70	17	+	+	NUM
iajs-316	70	18	4	4	NUM
iajs-316	70	19	3	3	NUM
iajs-316	70	20	+	+	NUM
iajs-316	70	21	4x	4x	NUM
iajs-316	70	22	6=	6=	ADP
iajs-316	70	23	x	x	SYM
iajs-316	70	24	2y	2y	NUM
iajs-316	70	25	"	"	PUNCT
iajs-316	70	26	+	+	CCONJ
iajs-316	70	27	(	(	PUNCT
iajs-316	70	28	4	4	NUM
iajs-316	70	29	/	/	SYM
iajs-316	70	30	x	x	NOUN
iajs-316	70	31	)	)	PUNCT
iajs-316	70	32	y	y	NOUN
iajs-316	70	33	'	'	PUNCT
iajs-316	70	34	+	+	NOUN
iajs-316	70	35	y	y	PROPN
iajs-316	70	36	with	with	ADP
iajs-316	70	37	ic	ic	PROPN
iajs-316	70	38	:	:	PUNCT
iajs-316	70	39	y(0	y(0	PROPN
iajs-316	70	40	)	)	PUNCT
iajs-316	70	41	=	=	SYM
iajs-316	70	42	2	2	NUM
iajs-316	70	43	,	,	PUNCT
iajs-316	70	44	y'(0	y'(0	PROPN
iajs-316	70	45	)	)	PUNCT
iajs-316	70	46	=	=	SYM
iajs-316	71	1	0	0	NUM
iajs-316	72	1	it	it	PRON
iajs-316	72	2	is	be	AUX
iajs-316	72	3	clear	clear	ADJ
iajs-316	72	4	that	that	SCONJ
iajs-316	72	5	x	x	PUNCT
iajs-316	72	6	=	=	SYM
iajs-316	72	7	0	0	NUM
iajs-316	72	8	,	,	PUNCT
iajs-316	72	9	is	be	AUX
iajs-316	72	10	singular	singular	ADJ
iajs-316	72	11	point	point	NOUN
iajs-316	72	12	and	and	CCONJ
iajs-316	72	13	it	it	PRON
iajs-316	72	14	is	be	AUX
iajs-316	72	15	singularity	singularity	NOUN
iajs-316	72	16	of	of	ADP
iajs-316	72	17	first	first	ADJ
iajs-316	72	18	kind	kind	NOUN
iajs-316	72	19	and	and	CCONJ
iajs-316	72	20	the	the	DET
iajs-316	72	21	exact	exact	ADJ
iajs-316	72	22	solution	solution	NOUN
iajs-316	72	23	is	be	AUX
iajs-316	72	24	y(x	y(x	NOUN
iajs-316	72	25	)	)	PUNCT
iajs-316	72	26	=	=	PUNCT
iajs-316	73	1	x3	x3	ADJ
iajs-316	73	2	+	+	NOUN
iajs-316	74	1	2	2	X
iajs-316	74	2	.	.	PUNCT
iajs-316	74	3	now	now	ADV
iajs-316	74	4	,	,	PUNCT
iajs-316	74	5	this	this	DET
iajs-316	74	6	example	example	NOUN
iajs-316	74	7	is	be	AUX
iajs-316	74	8	solved	solve	VERB
iajs-316	74	9	by	by	ADP
iajs-316	74	10	using	use	VERB
iajs-316	74	11	semi	semi	ADJ
iajs-316	74	12	-	-	ADJ
iajs-316	74	13	analytic	analytic	ADJ
iajs-316	74	14	technique	technique	NOUN
iajs-316	74	15	,	,	PUNCT
iajs-316	74	16	from	from	ADP
iajs-316	74	17	equation	equation	NOUN
iajs-316	74	18	(	(	PUNCT
iajs-316	74	19	5	5	X
iajs-316	74	20	)	)	PUNCT
iajs-316	74	21	we	we	PRON
iajs-316	74	22	have	have	VERB
iajs-316	74	23	:	:	PUNCT
iajs-316	74	24	p3	p3	PROPN
iajs-316	74	25	=	=	PUNCT
iajs-316	75	1	x3	x3	VERB
iajs-316	75	2	+2	+2	DET
iajs-316	75	3	example	example	NOUN
iajs-316	75	4	2	2	NUM
iajs-316	75	5	order	order	NOUN
iajs-316	75	6	nonlinear	nonlinear	ADJ
iajs-316	75	7	sivp	sivp	NOUN
iajs-316	75	8	:	:	PUNCT
iajs-316	75	9	ndconsider	ndconsider	NOUN
iajs-316	75	10	the	the	DET
iajs-316	75	11	following	follow	VERB
iajs-316	75	12	2	2	NUM
iajs-316	75	13	y	y	NOUN
iajs-316	75	14	"	"	PUNCT
iajs-316	75	15	+	+	CCONJ
iajs-316	75	16	(	(	PUNCT
iajs-316	75	17	6	6	NUM
iajs-316	75	18	/	/	SYM
iajs-316	75	19	x	x	NOUN
iajs-316	75	20	)	)	PUNCT
iajs-316	75	21	y	y	NOUN
iajs-316	75	22	'	'	PUNCT
iajs-316	75	23	+	+	CCONJ
iajs-316	75	24	(	(	PUNCT
iajs-316	75	25	6	6	NUM
iajs-316	75	26	/	/	SYM
iajs-316	75	27	x2	x2	ADJ
iajs-316	75	28	)	)	PUNCT
iajs-316	75	29	y	y	PROPN
iajs-316	76	1	+	+	CCONJ
iajs-316	76	2	y2	y2	NOUN
iajs-316	76	3	=	=	SYM
iajs-316	76	4	20	20	NUM
iajs-316	76	5	+	+	CCONJ
iajs-316	76	6	x4	x4	PROPN
iajs-316	76	7	with	with	ADP
iajs-316	76	8	ic	ic	PROPN
iajs-316	76	9	:	:	PUNCT
iajs-316	76	10	y(0	y(0	PROPN
iajs-316	76	11	)	)	PUNCT
iajs-316	76	12	=	=	SYM
iajs-316	76	13	0	0	NUM
iajs-316	76	14	,	,	PUNCT
iajs-316	76	15	y'(0	y'(0	PROPN
iajs-316	76	16	)	)	PUNCT
iajs-316	77	1	=	=	SYM
iajs-316	77	2	0	0	NUM
iajs-316	78	1	it	it	PRON
iajs-316	78	2	is	be	AUX
iajs-316	78	3	clear	clear	ADJ
iajs-316	78	4	that	that	SCONJ
iajs-316	78	5	x	x	PUNCT
iajs-316	78	6	=	=	SYM
iajs-316	78	7	0	0	NUM
iajs-316	78	8	,	,	PUNCT
iajs-316	78	9	is	be	AUX
iajs-316	78	10	singular	singular	ADJ
iajs-316	78	11	point	point	NOUN
iajs-316	78	12	and	and	CCONJ
iajs-316	78	13	the	the	DET
iajs-316	78	14	exact	exact	ADJ
iajs-316	78	15	solution	solution	NOUN
iajs-316	78	16	is	be	AUX
iajs-316	78	17	y(x	y(x	NOUN
iajs-316	78	18	)	)	PUNCT
iajs-316	79	1	=	=	SYM
iajs-316	79	2	x2	x2	PROPN
iajs-316	79	3	.	.	PUNCT
iajs-316	80	1	now	now	ADV
iajs-316	80	2	,	,	PUNCT
iajs-316	80	3	this	this	DET
iajs-316	80	4	example	example	NOUN
iajs-316	80	5	is	be	AUX
iajs-316	80	6	solved	solve	VERB
iajs-316	80	7	by	by	ADP
iajs-316	80	8	using	use	VERB
iajs-316	80	9	semi	semi	ADJ
iajs-316	80	10	–	–	PUNCT
iajs-316	80	11	analytic	analytic	ADJ
iajs-316	80	12	technique	technique	NOUN
iajs-316	80	13	,	,	PUNCT
iajs-316	80	14	from	from	ADP
iajs-316	80	15	equation(5	equation(5	PROPN
iajs-316	80	16	)	)	PUNCT
iajs-316	80	17	we	we	PRON
iajs-316	80	18	have	have	VERB
iajs-316	80	19	:	:	PUNCT
iajs-316	80	20	p3	p3	PROPN
iajs-316	80	21	=	=	PUNCT
iajs-316	81	1	x2	x2	ADV
iajs-316	81	2	now	now	ADV
iajs-316	81	3	,	,	PUNCT
iajs-316	81	4	the	the	DET
iajs-316	81	5	suggested	suggest	VERB
iajs-316	81	6	method	method	NOUN
iajs-316	81	7	is	be	AUX
iajs-316	81	8	used	use	VERB
iajs-316	81	9	to	to	PART
iajs-316	81	10	investigate	investigate	VERB
iajs-316	81	11	the	the	DET
iajs-316	81	12	solution	solution	NOUN
iajs-316	81	13	of	of	ADP
iajs-316	81	14	emden	emden	ADJ
iajs-316	81	15	–	–	PUNCT
iajs-316	81	16	fowler	fowler	PROPN
iajs-316	81	17	equations	equation	NOUN
iajs-316	81	18	as	as	ADP
iajs-316	81	19	a	a	DET
iajs-316	81	20	class	class	NOUN
iajs-316	81	21	of	of	ADP
iajs-316	81	22	nonlinear	nonlinear	ADJ
iajs-316	81	23	sivp	sivp	NOUN
iajs-316	81	24	,	,	PUNCT
iajs-316	81	25	which	which	PRON
iajs-316	81	26	plays	play	VERB
iajs-316	81	27	very	very	ADV
iajs-316	81	28	important	important	ADJ
iajs-316	81	29	role	role	NOUN
iajs-316	81	30	because	because	SCONJ
iajs-316	81	31	of	of	ADP
iajs-316	81	32	the	the	DET
iajs-316	81	33	singularity	singularity	NOUN
iajs-316	81	34	behaviour	behaviour	NOUN
iajs-316	81	35	at	at	ADP
iajs-316	81	36	the	the	DET
iajs-316	81	37	origin	origin	NOUN
iajs-316	81	38	.	.	PUNCT
iajs-316	82	1	we	we	PRON
iajs-316	82	2	study	study	VERB
iajs-316	82	3	the	the	DET
iajs-316	82	4	emden	emden	ADJ
iajs-316	82	5	–	–	PUNCT
iajs-316	82	6	fowler	fowler	PROPN
iajs-316	82	7	equations	equation	NOUN
iajs-316	82	8	of	of	ADP
iajs-316	82	9	the	the	DET
iajs-316	82	10	form	form	NOUN
iajs-316	82	11	:	:	PUNCT
iajs-316	82	12	,	,	PUNCT
iajs-316	82	13	b	b	X
iajs-316	82	14	ϵ	ϵ	X
iajs-316	82	15	r	r	NOUN
iajs-316	82	16	(	(	PUNCT
iajs-316	82	17	8)	8)	NUM
iajs-316	82	18	0	0	NUM
iajs-316	82	19			NUM
iajs-316	82	20	;	;	PUNCT
iajs-316	82	21	0	0	NUM
iajs-316	82	22	≤	≤	NUM
iajs-316	82	23	x	x	SYM
iajs-316	82	24	≤	≤	NUM
iajs-316	82	25	1	1	NUM
iajs-316	82	26	,	,	PUNCT
iajs-316	82	27	a	a	DET
iajs-316	82	28	=	=	SYM
iajs-316	82	29	g(x	g(x	NOUN
iajs-316	82	30	)	)	PUNCT
iajs-316	82	31	n	n	CCONJ
iajs-316	82	32	y	y	PROPN
iajs-316	82	33	1	1	NUM
iajs-316	82	34	-	-	PUNCT
iajs-316	82	35	my	my	PRON
iajs-316	82	36	"	"	PUNCT
iajs-316	82	37	+	+	PROPN
iajs-316	82	38	(	(	PUNCT
iajs-316	82	39	a	a	X
iajs-316	82	40	/	/	SYM
iajs-316	82	41	x	x	NOUN
iajs-316	82	42	)	)	PUNCT
iajs-316	82	43	y	y	NOUN
iajs-316	82	44	'	'	PUNCT
iajs-316	82	45	+	+	NUM
iajs-316	82	46	b	b	X
iajs-316	82	47	x	x	X
iajs-316	82	48	under	under	ADP
iajs-316	82	49	the	the	DET
iajs-316	82	50	following	follow	VERB
iajs-316	82	51	initial	initial	ADJ
iajs-316	82	52	conditions	condition	NOUN
iajs-316	82	53	:	:	PUNCT
iajs-316	82	54	y(0	y(0	PROPN
iajs-316	82	55	)	)	PUNCT
iajs-316	82	56	=	=	SYM
iajs-316	82	57	a	a	PRON
iajs-316	82	58	,	,	PUNCT
iajs-316	82	59	y'(0	y'(0	NOUN
iajs-316	82	60	)	)	PUNCT
iajs-316	82	61	=	=	SYM
iajs-316	82	62	0	0	NUM
iajs-316	82	63	where	where	SCONJ
iajs-316	82	64	a	a	DET
iajs-316	82	65	,	,	PUNCT
iajs-316	82	66	a	a	DET
iajs-316	82	67	,	,	PUNCT
iajs-316	82	68	b	b	NOUN
iajs-316	82	69	,	,	PUNCT
iajs-316	82	70	m	m	VERB
iajs-316	82	71	are	be	AUX
iajs-316	82	72	constants	constant	NOUN
iajs-316	82	73	,	,	PUNCT
iajs-316	82	74	n	n	CCONJ
iajs-316	82	75	≠	≠	PROPN
iajs-316	82	76	0	0	NUM
iajs-316	82	77	,	,	PUNCT
iajs-316	82	78	n	n	PRON
iajs-316	82	79	≠	≠	PROPN
iajs-316	82	80	1	1	NUM
iajs-316	82	81	.	.	PUNCT
iajs-316	83	1	when	when	SCONJ
iajs-316	83	2	m	m	VERB
iajs-316	83	3	=	=	SYM
iajs-316	83	4	1	1	NUM
iajs-316	83	5	,	,	PUNCT
iajs-316	83	6	a	a	DET
iajs-316	83	7	=	=	SYM
iajs-316	83	8	2	2	NUM
iajs-316	83	9	and	and	CCONJ
iajs-316	83	10	b	b	NOUN
iajs-316	83	11	=	=	SYM
iajs-316	83	12	1	1	NUM
iajs-316	83	13	equation	equation	NOUN
iajs-316	83	14	(	(	PUNCT
iajs-316	83	15	8)	8)	NUM
iajs-316	83	16	reduces	reduce	VERB
iajs-316	83	17	to	to	ADP
iajs-316	83	18	the	the	DET
iajs-316	83	19	lane	lane	NOUN
iajs-316	83	20	–	–	PUNCT
iajs-316	83	21	emden	emden	ADJ
iajs-316	83	22	equation	equation	NOUN
iajs-316	83	23	[	[	X
iajs-316	83	24	3	3	NUM
iajs-316	83	25	]	]	PUNCT
iajs-316	83	26	.	.	PUNCT
iajs-316	84	1	example	example	NOUN
iajs-316	85	1	3	3	NUM
iajs-316	85	2	consider	consider	VERB
iajs-316	85	3	the	the	DET
iajs-316	85	4	following	follow	VERB
iajs-316	85	5	emden	emden	ADJ
iajs-316	85	6	–	–	PUNCT
iajs-316	85	7	fowler	fowler	NOUN
iajs-316	85	8	equation	equation	NOUN
iajs-316	85	9	as	as	ADP
iajs-316	85	10	a	a	DET
iajs-316	85	11	sivp	sivp	NOUN
iajs-316	85	12	:	:	PUNCT
iajs-316	85	13	;	;	PUNCT
iajs-316	85	14	0	0	NUM
iajs-316	85	15	≤	≤	NUM
iajs-316	85	16	x	x	SYM
iajs-316	85	17	≤	≤	NUM
iajs-316	85	18	1	1	NUM
iajs-316	85	19	4	4	NUM
iajs-316	85	20	+	+	NUM
iajs-316	85	21	x	x	SYM
iajs-316	85	22	5=	5=	NUM
iajs-316	85	23	x	x	NOUN
iajs-316	85	24	2y	2y	NUM
iajs-316	85	25	"	"	PUNCT
iajs-316	85	26	+	+	CCONJ
iajs-316	85	27	(	(	PUNCT
iajs-316	85	28	8	8	NUM
iajs-316	85	29	/	/	SYM
iajs-316	85	30	x	x	X
iajs-316	85	31	)	)	PUNCT
iajs-316	85	32	y	y	NOUN
iajs-316	85	33	'	'	PUNCT
iajs-316	85	34	+	+	NOUN
iajs-316	85	35	x	x	SYM
iajs-316	85	36	y	y	NOUN
iajs-316	85	37	with	with	ADP
iajs-316	85	38	ic	ic	PROPN
iajs-316	85	39	:	:	PUNCT
iajs-316	85	40	y(0	y(0	PROPN
iajs-316	85	41	)	)	PUNCT
iajs-316	85	42	=	=	SYM
iajs-316	85	43	1	1	NUM
iajs-316	85	44	,	,	PUNCT
iajs-316	85	45	y'(0	y'(0	PROPN
iajs-316	85	46	)	)	PUNCT
iajs-316	85	47	=	=	SYM
iajs-316	85	48	0	0	NUM
iajs-316	86	1	it	it	PRON
iajs-316	86	2	is	be	AUX
iajs-316	86	3	clear	clear	ADJ
iajs-316	86	4	that	that	SCONJ
iajs-316	86	5	x=	x=	PROPN
iajs-316	86	6	0	0	NUM
iajs-316	86	7	,	,	PUNCT
iajs-316	86	8	is	be	AUX
iajs-316	86	9	nonlinear	nonlinear	ADJ
iajs-316	86	10	singular	singular	ADJ
iajs-316	86	11	point	point	NOUN
iajs-316	86	12	of	of	ADP
iajs-316	86	13	the	the	DET
iajs-316	86	14	first	first	ADJ
iajs-316	86	15	kind	kind	NOUN
iajs-316	86	16	,	,	PUNCT
iajs-316	86	17	we	we	PRON
iajs-316	86	18	solve	solve	VERB
iajs-316	86	19	this	this	DET
iajs-316	86	20	example	example	NOUN
iajs-316	86	21	by	by	ADP
iajs-316	86	22	using	use	VERB
iajs-316	86	23	semi	semi	ADJ
iajs-316	86	24	-	-	ADJ
iajs-316	86	25	analytic	analytic	ADJ
iajs-316	86	26	technique	technique	NOUN
iajs-316	86	27	,	,	PUNCT
iajs-316	86	28	from	from	ADP
iajs-316	86	29	equation	equation	NOUN
iajs-316	86	30	(	(	PUNCT
iajs-316	86	31	5	5	NUM
iajs-316	86	32	)	)	PUNCT
iajs-316	86	33	,	,	PUNCT
iajs-316	86	34	we	we	PRON
iajs-316	86	35	have	have	VERB
iajs-316	86	36	:	:	PUNCT
iajs-316	86	37	p9	p9	PROPN
iajs-316	86	38	=	=	PROPN
iajs-316	86	39	–	–	PUNCT
iajs-316	86	40	0.00078826882	0.00078826882	NUM
iajs-316	86	41	x9	x9	NOUN
iajs-316	86	42	+	+	CCONJ
iajs-316	86	43	0.0012952791	0.0012952791	NUM
iajs-316	86	44	x8	x8	NOUN
iajs-316	86	45	+	+	CCONJ
iajs-316	86	46	0.00879760172	0.00879760172	NUM
iajs-316	86	47	x7	x7	NOUN
iajs-316	86	48	+	+	CCONJ
iajs-316	86	49	0.014414828109	0.014414828109	NUM
iajs-316	86	50	x6	x6	NOUN
iajs-316	86	51	–	–	PUNCT
iajs-316	86	52	0.000150192x5	0.000150192x5	NUM
iajs-316	86	53	–	–	PUNCT
iajs-316	86	54	0.0333333333337578	0.0333333333337578	NUM
iajs-316	86	55	x3	x3	ADJ
iajs-316	86	56	+	+	CCONJ
iajs-316	86	57	1.0	1.0	NUM
iajs-316	86	58	higher	high	ADJ
iajs-316	86	59	accuracy	accuracy	NOUN
iajs-316	86	60	can	can	AUX
iajs-316	86	61	be	be	AUX
iajs-316	86	62	obtained	obtain	VERB
iajs-316	86	63	by	by	ADP
iajs-316	86	64	evaluating	evaluate	VERB
iajs-316	86	65	higher	high	ADJ
iajs-316	86	66	n	n	CCONJ
iajs-316	86	67	,	,	PUNCT
iajs-316	86	68	now	now	ADV
iajs-316	86	69	,	,	PUNCT
iajs-316	86	70	take	take	VERB
iajs-316	86	71	n=	n=	ADJ
iajs-316	86	72	5	5	NUM
iajs-316	86	73	,	,	PUNCT
iajs-316	86	74	i.e.	i.e.	X
iajs-316	86	75	,	,	PUNCT
iajs-316	86	76	+	+	X
iajs-316	87	1	7	7	NUM
iajs-316	87	2	+	+	NUM
iajs-316	87	3	0.0014538812	0.0014538812	NUM
iajs-316	87	4	x	x	SYM
iajs-316	87	5	+0.009581210401	+0.009581210401	NOUN
iajs-316	87	6	x90.00189361335x	x90.00189361335x	PROPN
iajs-316	87	7	-10	-10	PUNCT
iajs-316	87	8	+	+	CCONJ
iajs-316	87	9	0.00086427359x110.00021822695x	0.00086427359x110.00021822695x	ADJ
iajs-316	87	10	–	–	PUNCT
iajs-316	87	11	11	11	NUM
iajs-316	87	12	=	=	SYM
iajs-316	87	13	p	p	X
iajs-316	87	14	+	+	NOUN
iajs-316	87	15	1.0	1.0	NUM
iajs-316	87	16	30.033333333333758	30.033333333333758	NUM
iajs-316	87	17	x	x	NOUN
iajs-316	88	1	-6	-6	NOUN
iajs-316	88	2	x	x	SYM
iajs-316	88	3	0.0137816833	0.0137816833	NUM
iajs-316	88	4	now	now	ADV
iajs-316	88	5	,	,	PUNCT
iajs-316	88	6	increase	increase	VERB
iajs-316	88	7	n	n	CCONJ
iajs-316	88	8	,	,	PUNCT
iajs-316	88	9	to	to	PART
iajs-316	88	10	get	get	VERB
iajs-316	88	11	higher	high	ADJ
iajs-316	88	12	accuracy	accuracy	NOUN
iajs-316	88	13	,	,	PUNCT
iajs-316	88	14	let	let	VERB
iajs-316	88	15	n	n	X
iajs-316	88	16	=	=	SYM
iajs-316	88	17	6	6	NUM
iajs-316	88	18	,	,	PUNCT
iajs-316	88	19	i.e.	i.e.	X
iajs-316	88	20	,	,	PUNCT
iajs-316	88	21	517	517	NUM
iajs-316	88	22	|	|	ADV
iajs-316	88	23	mathematics	mathematic	NOUN
iajs-316	88	24	2014	2014	NUM
iajs-316	88	25	)	)	PUNCT
iajs-316	88	26	عام	عام	ADP
iajs-316	88	27	3العدد	3العدد	NUM
iajs-316	88	28	(	(	PUNCT
iajs-316	88	29	27مجلة	27مجلة	NUM
iajs-316	88	30	إبن	إبن	VERB
iajs-316	88	31	الھيثم	الھيثم	NOUN
iajs-316	88	32	للعلوم	للعلوم	NOUN
iajs-316	88	33	الصرفة	الصرفة	NOUN
iajs-316	89	1	و	و	PRON
iajs-316	89	2	التطبيقية	التطبيقية	ADV
iajs-316	89	3	المجلد	المجلد	VERB
iajs-316	89	4	ibn	ibn	PROPN
iajs-316	89	5	al	al	PROPN
iajs-316	89	6	-	-	PUNCT
iajs-316	89	7	haitham	haitham	PROPN
iajs-316	89	8	jour	jour	X
iajs-316	89	9	.	.	PROPN
iajs-316	90	1	for	for	ADP
iajs-316	90	2	pure	pure	ADJ
iajs-316	90	3	&	&	CCONJ
iajs-316	90	4	appl	appl	PROPN
iajs-316	90	5	.	.	PUNCT
iajs-316	91	1	sci	sci	PROPN
iajs-316	91	2	.	.	PUNCT
iajs-316	91	3	vol	vol	NOUN
iajs-316	91	4	.	.	PROPN
iajs-316	92	1	27	27	NUM
iajs-316	92	2	(	(	PUNCT
iajs-316	92	3	3	3	NUM
iajs-316	92	4	)	)	PUNCT
iajs-316	92	5	2014	2014	NUM
iajs-316	93	1	p13=	p13=	NUM
iajs-316	93	2	0.0000996316x13	0.0000996316x13	PUNCT
iajs-316	94	1	+	+	CCONJ
iajs-316	94	2	0.0004488478x12	0.0004488478x12	NUM
iajs-316	94	3	0.000849659317x11	0.000849659317x11	NOUN
iajs-316	95	1	+	+	CCONJ
iajs-316	95	2	0.0007848859x10	0.0007848859x10	NUM
iajs-316	95	3	0.0007538654	0.0007538654	NUM
iajs-316	95	4	x9	x9	NOUN
iajs-316	95	5	+	+	CCONJ
iajs-316	95	6	0.0001852901x8	0.0001852901x8	PRON
iajs-316	95	7	+	+	NUM
iajs-316	95	8	0.01017813169x7	0.01017813169x7	X
iajs-316	95	9	+	+	CCONJ
iajs-316	95	10	0.01367521368x6	0.01367521368x6	NUM
iajs-316	95	11	0.03333333333375776x3	0.03333333333375776x3	NUM
iajs-316	95	12	+	+	CCONJ
iajs-316	95	13	1.0	1.0	NUM
iajs-316	95	14	demir[3	demir[3	NOUN
iajs-316	95	15	]	]	PUNCT
iajs-316	95	16	solved	solve	VERB
iajs-316	95	17	this	this	DET
iajs-316	95	18	example	example	NOUN
iajs-316	95	19	by	by	ADP
iajs-316	95	20	dtm	dtm	PROPN
iajs-316	95	21	and	and	CCONJ
iajs-316	95	22	gave	give	VERB
iajs-316	95	23	the	the	DET
iajs-316	95	24	following	follow	VERB
iajs-316	95	25	solution	solution	NOUN
iajs-316	95	26	:	:	PUNCT
iajs-316	95	27	also	also	ADV
iajs-316	95	28	,	,	PUNCT
iajs-316	95	29	this	this	DET
iajs-316	95	30	example	example	NOUN
iajs-316	95	31	is	be	AUX
iajs-316	95	32	solved	solve	VERB
iajs-316	95	33	by	by	ADP
iajs-316	95	34	numerical	numerical	ADJ
iajs-316	95	35	method	method	NOUN
iajs-316	95	36	by	by	ADP
iajs-316	95	37	using	use	VERB
iajs-316	95	38	the	the	DET
iajs-316	95	39	maple11	maple11	NOUN
iajs-316	95	40	as	as	SCONJ
iajs-316	95	41	given	give	VERB
iajs-316	95	42	in	in	ADP
iajs-316	95	43	[	[	X
iajs-316	95	44	3	3	NUM
iajs-316	95	45	]	]	PUNCT
iajs-316	95	46	and	and	CCONJ
iajs-316	95	47	the	the	DET
iajs-316	95	48	results	result	NOUN
iajs-316	95	49	are	be	AUX
iajs-316	95	50	compared	compare	VERB
iajs-316	95	51	with	with	ADP
iajs-316	95	52	the	the	DET
iajs-316	95	53	suggested	suggest	VERB
iajs-316	95	54	method	method	NOUN
iajs-316	95	55	and	and	CCONJ
iajs-316	95	56	its	its	PRON
iajs-316	95	57	results	result	NOUN
iajs-316	95	58	are	be	AUX
iajs-316	95	59	given	give	VERB
iajs-316	95	60	in	in	ADP
iajs-316	95	61	table	table	NOUN
iajs-316	95	62	(	(	PUNCT
iajs-316	95	63	1a	1a	X
iajs-316	95	64	)	)	PUNCT
iajs-316	95	65	and	and	CCONJ
iajs-316	95	66	(	(	PUNCT
iajs-316	95	67	1b	1b	NUM
iajs-316	95	68	)	)	PUNCT
iajs-316	95	69	.	.	PUNCT
iajs-316	96	1	figure	figure	NOUN
iajs-316	96	2	(	(	PUNCT
iajs-316	96	3	1	1	X
iajs-316	96	4	)	)	PUNCT
iajs-316	96	5	give	give	VERB
iajs-316	96	6	a	a	DET
iajs-316	96	7	comparison	comparison	NOUN
iajs-316	96	8	between	between	ADP
iajs-316	96	9	the	the	DET
iajs-316	96	10	numerical	numerical	ADJ
iajs-316	96	11	solution	solution	NOUN
iajs-316	96	12	in[3	in[3	X
iajs-316	96	13	]	]	PUNCT
iajs-316	96	14	and	and	CCONJ
iajs-316	96	15	p13	p13	NOUN
iajs-316	96	16	;	;	PUNCT
iajs-316	96	17	table	table	NOUN
iajs-316	96	18	(	(	PUNCT
iajs-316	96	19	2	2	X
iajs-316	96	20	)	)	PUNCT
iajs-316	96	21	gave	give	VERB
iajs-316	96	22	the	the	DET
iajs-316	96	23	results	result	NOUN
iajs-316	96	24	obtained	obtain	VERB
iajs-316	96	25	with	with	ADP
iajs-316	96	26	dtm	dtm	PROPN
iajs-316	96	27	for	for	ADP
iajs-316	96	28	different	different	ADJ
iajs-316	96	29	values	value	NOUN
iajs-316	96	30	of	of	ADP
iajs-316	96	31	n	n	PRON
iajs-316	96	32	which	which	PRON
iajs-316	96	33	are	be	AUX
iajs-316	96	34	given	give	VERB
iajs-316	96	35	[	[	X
iajs-316	96	36	3	3	NUM
iajs-316	96	37	]	]	PUNCT
iajs-316	96	38	.	.	PUNCT
iajs-316	97	1	4	4	X
iajs-316	97	2	.	.	X
iajs-316	97	3	error	error	NOUN
iajs-316	97	4	/	/	SYM
iajs-316	97	5	defect	defect	NOUN
iajs-316	97	6	weights	weight	NOUN
iajs-316	97	7	every	every	DET
iajs-316	97	8	known	know	VERB
iajs-316	97	9	ivp	ivp	NOUN
iajs-316	97	10	software	software	NOUN
iajs-316	97	11	package	package	NOUN
iajs-316	97	12	reports	report	VERB
iajs-316	97	13	an	an	DET
iajs-316	97	14	estimate	estimate	NOUN
iajs-316	97	15	of	of	ADP
iajs-316	97	16	either	either	CCONJ
iajs-316	97	17	the	the	DET
iajs-316	97	18	relative	relative	ADJ
iajs-316	97	19	error	error	NOUN
iajs-316	97	20	or	or	CCONJ
iajs-316	97	21	the	the	DET
iajs-316	97	22	maximum	maximum	ADJ
iajs-316	97	23	relative	relative	ADJ
iajs-316	97	24	defect	defect	NOUN
iajs-316	97	25	.	.	PUNCT
iajs-316	98	1	the	the	DET
iajs-316	98	2	weights	weight	NOUN
iajs-316	98	3	used	use	VERB
iajs-316	98	4	to	to	PART
iajs-316	98	5	scale	scale	VERB
iajs-316	98	6	either	either	CCONJ
iajs-316	98	7	the	the	DET
iajs-316	98	8	error	error	NOUN
iajs-316	98	9	or	or	CCONJ
iajs-316	98	10	the	the	DET
iajs-316	98	11	maximum	maximum	ADJ
iajs-316	98	12	defect	defect	NOUN
iajs-316	98	13	differ	differ	VERB
iajs-316	98	14	among	among	ADP
iajs-316	98	15	ivp	ivp	ADJ
iajs-316	98	16	software	software	NOUN
iajs-316	98	17	.	.	PUNCT
iajs-316	99	1	therefore	therefore	ADV
iajs-316	99	2	,	,	PUNCT
iajs-316	99	3	the	the	DET
iajs-316	99	4	ivp	ivp	ADJ
iajs-316	99	5	component	component	NOUN
iajs-316	99	6	of	of	ADP
iajs-316	99	7	pythode	pythode	PROPN
iajs-316	99	8	[	[	X
iajs-316	99	9	4	4	X
iajs-316	99	10	]	]	PUNCT
iajs-316	99	11	allows	allow	VERB
iajs-316	99	12	users	user	NOUN
iajs-316	99	13	to	to	PART
iajs-316	99	14	select	select	VERB
iajs-316	99	15	the	the	DET
iajs-316	99	16	weights	weight	NOUN
iajs-316	99	17	they	they	PRON
iajs-316	99	18	wish	wish	VERB
iajs-316	99	19	to	to	PART
iajs-316	99	20	use	use	VERB
iajs-316	99	21	.	.	PUNCT
iajs-316	100	1	the	the	DET
iajs-316	100	2	default	default	NOUN
iajs-316	100	3	weights	weight	NOUN
iajs-316	100	4	depend	depend	VERB
iajs-316	100	5	on	on	ADP
iajs-316	100	6	whether	whether	SCONJ
iajs-316	100	7	an	an	DET
iajs-316	100	8	estimate	estimate	NOUN
iajs-316	100	9	of	of	ADP
iajs-316	100	10	the	the	DET
iajs-316	100	11	error	error	NOUN
iajs-316	100	12	or	or	CCONJ
iajs-316	100	13	maximum	maximum	ADJ
iajs-316	100	14	defect	defect	NOUN
iajs-316	100	15	is	be	AUX
iajs-316	100	16	being	be	AUX
iajs-316	100	17	used	use	VERB
iajs-316	100	18	.	.	PUNCT
iajs-316	101	1	if	if	SCONJ
iajs-316	101	2	the	the	DET
iajs-316	101	3	error	error	NOUN
iajs-316	101	4	is	be	AUX
iajs-316	101	5	being	be	AUX
iajs-316	101	6	estimated	estimate	VERB
iajs-316	101	7	,	,	PUNCT
iajs-316	101	8	then	then	ADV
iajs-316	101	9	the	the	DET
iajs-316	101	10	ivp	ivp	ADJ
iajs-316	101	11	component	component	NOUN
iajs-316	101	12	of	of	ADP
iajs-316	101	13	pythode	pythode	ADJ
iajs-316	101	14	uses	use	NOUN
iajs-316	101	15	,	,	PUNCT
iajs-316	101	16	in	in	ADP
iajs-316	101	17	this	this	DET
iajs-316	101	18	thesis	thesis	NOUN
iajs-316	101	19	we	we	PRON
iajs-316	101	20	modify	modify	VERB
iajs-316	101	21	this	this	DET
iajs-316	101	22	package	package	NOUN
iajs-316	101	23	to	to	PART
iajs-316	101	24	consist	consist	VERB
iajs-316	101	25	sivp	sivp	NOUN
iajs-316	101	26	and	and	CCONJ
iajs-316	101	27	named	name	VERB
iajs-316	101	28	"	"	PUNCT
iajs-316	101	29	pythsode	pythsode	NOUN
iajs-316	101	30	"	"	PUNCT
iajs-316	101	31	,	,	PUNCT
iajs-316	101	32	defined	define	VERB
iajs-316	101	33	as	as	ADP
iajs-316	101	34	:	:	PUNCT
iajs-316	101	35	║	║	NOUN
iajs-316	101	36	y(x	y(x	NOUN
iajs-316	101	37	)	)	PUNCT
iajs-316	101	38	−	−	PROPN
iajs-316	101	39	p(x)	p(x)	PROPN
iajs-316	101	40	║	║	VERB
iajs-316	101	41	∞	∞	PROPN
iajs-316	101	42	/	/	SYM
iajs-316	101	43	(	(	PUNCT
iajs-316	101	44	1	1	NUM
iajs-316	101	45	+	+	CCONJ
iajs-316	101	46	║	║	VERB
iajs-316	101	47	p(x)	p(x)	NOUN
iajs-316	101	48	║	║	VERB
iajs-316	101	49	∞	∞	PROPN
iajs-316	101	50	)	)	PUNCT
iajs-316	101	51	;	;	PUNCT
iajs-316	101	52	0	0	NUM
iajs-316	101	53	≤	≤	NUM
iajs-316	101	54	x	x	SYM
iajs-316	101	55	≤	≤	NUM
iajs-316	101	56	1	1	NUM
iajs-316	101	57	,	,	PUNCT
iajs-316	101	58	(	(	PUNCT
iajs-316	101	59	9	9	NUM
iajs-316	101	60	)	)	PUNCT
iajs-316	101	61	where	where	SCONJ
iajs-316	101	62	y(x	y(x	NOUN
iajs-316	101	63	)	)	PUNCT
iajs-316	101	64	is	be	AUX
iajs-316	101	65	exact	exact	ADJ
iajs-316	101	66	solution	solution	NOUN
iajs-316	101	67	and	and	CCONJ
iajs-316	101	68	p(x	p(x	PROPN
iajs-316	101	69	)	)	PUNCT
iajs-316	101	70	is	be	AUX
iajs-316	101	71	suggested	suggest	VERB
iajs-316	101	72	solution	solution	NOUN
iajs-316	101	73	of	of	ADP
iajs-316	101	74	sivp	sivp	NOUN
iajs-316	101	75	(	(	PUNCT
iajs-316	101	76	1	1	NUM
iajs-316	101	77	)	)	PUNCT
iajs-316	101	78	.	.	PUNCT
iajs-316	102	1	if	if	SCONJ
iajs-316	102	2	the	the	DET
iajs-316	102	3	maximum	maximum	ADJ
iajs-316	102	4	defect	defect	NOUN
iajs-316	102	5	is	be	AUX
iajs-316	102	6	being	be	AUX
iajs-316	102	7	estimated	estimate	VERB
iajs-316	102	8	,	,	PUNCT
iajs-316	102	9	then	then	ADV
iajs-316	102	10	the	the	DET
iajs-316	102	11	sivp	sivp	NOUN
iajs-316	102	12	component	component	NOUN
iajs-316	102	13	of	of	ADP
iajs-316	102	14	pythsode	pythsode	PROPN
iajs-316	102	15	uses	use	NOUN
iajs-316	102	16	:	:	PUNCT
iajs-316	102	17	║	║	NOUN
iajs-316	102	18	p(x)−f(x	p(x)−f(x	NOUN
iajs-316	102	19	,	,	PUNCT
iajs-316	102	20	p(x	p(x	PROPN
iajs-316	102	21	)	)	PUNCT
iajs-316	102	22	,	,	PUNCT
iajs-316	102	23	p(x))	p(x))	PROPN
iajs-316	102	24	║	║	X
iajs-316	102	25	∞	∞	NUM
iajs-316	102	26	/(1	/(1	PUNCT
iajs-316	103	1	+	+	PROPN
iajs-316	103	2	║	║	NOUN
iajs-316	103	3	f(x	f(x	PROPN
iajs-316	103	4	,	,	PUNCT
iajs-316	103	5	p(x	p(x	PROPN
iajs-316	103	6	)	)	PUNCT
iajs-316	103	7	,	,	PUNCT
iajs-316	103	8	p(x	p(x	PROPN
iajs-316	103	9	)	)	PUNCT
iajs-316	103	10	)	)	PUNCT
iajs-316	103	11	║	║	VERB
iajs-316	103	12	∞	∞	NOUN
iajs-316	103	13	)	)	PUNCT
iajs-316	103	14	;	;	PUNCT
iajs-316	103	15	0	0	NUM
iajs-316	103	16	≤	≤	NUM
iajs-316	103	17	x	x	SYM
iajs-316	103	18	≤	≤	NUM
iajs-316	103	19	1	1	NUM
iajs-316	103	20	,	,	PUNCT
iajs-316	103	21	(	(	PUNCT
iajs-316	103	22	10	10	NUM
iajs-316	103	23	)	)	PUNCT
iajs-316	103	24	the	the	DET
iajs-316	103	25	relative	relative	ADJ
iajs-316	103	26	estimate	estimate	NOUN
iajs-316	103	27	of	of	ADP
iajs-316	103	28	both	both	CCONJ
iajs-316	103	29	the	the	DET
iajs-316	103	30	error	error	NOUN
iajs-316	103	31	and	and	CCONJ
iajs-316	103	32	the	the	DET
iajs-316	103	33	maximum	maximum	ADJ
iajs-316	103	34	defect	defect	NOUN
iajs-316	103	35	are	be	AUX
iajs-316	103	36	slightly	slightly	ADV
iajs-316	103	37	modified	modify	VERB
iajs-316	103	38	from	from	ADP
iajs-316	103	39	the	the	DET
iajs-316	103	40	one	one	NOUN
iajs-316	103	41	used	use	VERB
iajs-316	103	42	in	in	ADP
iajs-316	103	43	sivp	sivp	NOUN
iajs-316	103	44	solver	solver	PROPN
iajs-316	103	45	.	.	PUNCT
iajs-316	104	1	again	again	ADV
iajs-316	104	2	applied	apply	VERB
iajs-316	104	3	equation	equation	NOUN
iajs-316	104	4	(	(	PUNCT
iajs-316	104	5	10	10	NUM
iajs-316	104	6	)	)	PUNCT
iajs-316	104	7	for	for	ADP
iajs-316	104	8	example	example	NOUN
iajs-316	104	9	3	3	NUM
iajs-316	104	10	is	be	AUX
iajs-316	104	11	as	as	ADP
iajs-316	104	12	following	follow	VERB
iajs-316	104	13	:	:	PUNCT
iajs-316	104	14	4	4	NUM
iajs-316	104	15	+	+	SYM
iajs-316	104	16	x	x	SYM
iajs-316	104	17	5x=	5x=	NUM
iajs-316	104	18	2consider	2consider	NUM
iajs-316	104	19	the	the	DET
iajs-316	104	20	nonlinear	nonlinear	ADJ
iajs-316	104	21	sivp	sivp	NOUN
iajs-316	104	22	:	:	PUNCT
iajs-316	104	23	y	y	X
iajs-316	104	24	"	"	PUNCT
iajs-316	104	25	+	+	CCONJ
iajs-316	104	26	(	(	PUNCT
iajs-316	104	27	8	8	NUM
iajs-316	104	28	/	/	SYM
iajs-316	104	29	x	x	NOUN
iajs-316	104	30	)	)	PUNCT
iajs-316	104	31	y	y	NOUN
iajs-316	104	32	'	'	PUNCT
iajs-316	104	33	+	+	NOUN
iajs-316	104	34	x	x	SYM
iajs-316	104	35	y	y	NOUN
iajs-316	104	36	with	with	ADP
iajs-316	104	37	ic	ic	PROPN
iajs-316	104	38	:	:	PUNCT
iajs-316	104	39	y(0	y(0	PROPN
iajs-316	104	40	)	)	PUNCT
iajs-316	105	1	=	=	NOUN
iajs-316	105	2	1	1	NUM
iajs-316	105	3	,	,	PUNCT
iajs-316	105	4	y'(0	y'(0	PROPN
iajs-316	105	5	)	)	PUNCT
iajs-316	105	6	=	=	SYM
iajs-316	105	7	0	0	NUM
iajs-316	105	8	,	,	PUNCT
iajs-316	105	9	apply	apply	VERB
iajs-316	105	10	equation	equation	NOUN
iajs-316	105	11	(	(	PUNCT
iajs-316	105	12	10	10	NUM
iajs-316	105	13	)	)	PUNCT
iajs-316	105	14	as	as	ADP
iajs-316	105	15	the	the	DET
iajs-316	105	16	following	following	NOUN
iajs-316	105	17	:	:	PUNCT
iajs-316	105	18	then	then	ADV
iajs-316	105	19	equation	equation	NOUN
iajs-316	105	20	(	(	PUNCT
iajs-316	105	21	10	10	NUM
iajs-316	105	22	)	)	PUNCT
iajs-316	105	23	became	become	VERB
iajs-316	105	24	:	:	PUNCT
iajs-316	105	25	(	(	PUNCT
iajs-316	105	26	for	for	SCONJ
iajs-316	105	27	more	more	ADJ
iajs-316	105	28	detail	detail	NOUN
iajs-316	105	29	see	see	VERB
iajs-316	105	30	table	table	NOUN
iajs-316	105	31	3	3	NUM
iajs-316	105	32	)	)	PUNCT
iajs-316	105	33	║	║	NOUN
iajs-316	105	34	p13	p13	NOUN
iajs-316	105	35	(x	(x	NOUN
iajs-316	105	36	)	)	PUNCT
iajs-316	105	37	f(x	f(x	PROPN
iajs-316	105	38	,	,	PUNCT
iajs-316	105	39	p13(x	p13(x	PROPN
iajs-316	105	40	)	)	PUNCT
iajs-316	105	41	,	,	PUNCT
iajs-316	105	42	p13	p13	NOUN
iajs-316	105	43	(x))	(x))	NOUN
iajs-316	105	44	║	║	VERB
iajs-316	105	45	∞	∞	NUM
iajs-316	105	46	/	/	SYM
iajs-316	105	47	(	(	PUNCT
iajs-316	105	48	1	1	NUM
iajs-316	105	49	+	+	CCONJ
iajs-316	105	50	║	║	PROPN
iajs-316	105	51	f(x	f(x	PROPN
iajs-316	105	52	,	,	PUNCT
iajs-316	105	53	p13(x	p13(x	PROPN
iajs-316	105	54	)	)	PUNCT
iajs-316	105	55	,	,	PUNCT
iajs-316	105	56	p13	p13	PROPN
iajs-316	105	57	(x	(x	PROPN
iajs-316	105	58	)	)	PUNCT
iajs-316	105	59	)	)	PUNCT
iajs-316	106	1	║	║	X
iajs-316	106	2	∞	∞	NUM
iajs-316	106	3	)	)	PUNCT
iajs-316	106	4	=	=	SYM
iajs-316	107	1	e-007	e-007	CCONJ
iajs-316	107	2	/	/	SYM
iajs-316	107	3	1.999966681360863	1.999966681360863	NUM
iajs-316	107	4	=	=	SYM
iajs-316	107	5	8.419941391601780e-0081.683960224221478	8.419941391601780e-0081.683960224221478	NUM
iajs-316	107	6	5	5	NUM
iajs-316	107	7	.	.	PUNCT
iajs-316	107	8	accuracy	accuracy	NOUN
iajs-316	107	9	of	of	ADP
iajs-316	107	10	the	the	DET
iajs-316	107	11	computed	computed	ADJ
iajs-316	107	12	values	value	NOUN
iajs-316	107	13	the	the	DET
iajs-316	107	14	convergence	convergence	NOUN
iajs-316	107	15	orders	order	NOUN
iajs-316	107	16	of	of	ADP
iajs-316	107	17	the	the	DET
iajs-316	107	18	approximations	approximation	NOUN
iajs-316	107	19	appear	appear	VERB
iajs-316	107	20	to	to	PART
iajs-316	107	21	be	be	AUX
iajs-316	107	22	very	very	ADV
iajs-316	107	23	stable	stable	ADJ
iajs-316	107	24	,	,	PUNCT
iajs-316	107	25	indicating	indicate	VERB
iajs-316	107	26	that	that	SCONJ
iajs-316	107	27	our	our	PRON
iajs-316	107	28	results	result	NOUN
iajs-316	107	29	are	be	AUX
iajs-316	107	30	reliable	reliable	ADJ
iajs-316	107	31	and	and	CCONJ
iajs-316	107	32	accurate	accurate	ADJ
iajs-316	107	33	.	.	PUNCT
iajs-316	108	1	in	in	ADP
iajs-316	108	2	this	this	DET
iajs-316	108	3	section	section	NOUN
iajs-316	108	4	,	,	PUNCT
iajs-316	108	5	we	we	PRON
iajs-316	108	6	try	try	VERB
iajs-316	108	7	to	to	PART
iajs-316	108	8	quantify	quantify	VERB
iajs-316	108	9	the	the	DET
iajs-316	108	10	accuracy	accuracy	NOUN
iajs-316	108	11	we	we	PRON
iajs-316	108	12	can	can	AUX
iajs-316	108	13	obtain	obtain	VERB
iajs-316	108	14	.	.	PUNCT
iajs-316	109	1	to	to	PART
iajs-316	109	2	examine	examine	VERB
iajs-316	109	3	the	the	DET
iajs-316	109	4	error	error	NOUN
iajs-316	109	5	of	of	ADP
iajs-316	109	6	the	the	DET
iajs-316	109	7	approximation	approximation	NOUN
iajs-316	109	8	,	,	PUNCT
iajs-316	109	9	let	let	VERB
iajs-316	109	10	e(n	e(n	PRON
iajs-316	109	11	)	)	PUNCT
iajs-316	109	12	=	=	SYM
iajs-316	109	13	max	max	PROPN
iajs-316	109	14	|	|	ADV
iajs-316	109	15	y(xi	y(xi	PROPN
iajs-316	109	16	)	)	PUNCT
iajs-316	109	17	−	−	PROPN
iajs-316	109	18	yi	yi	NOUN
iajs-316	110	1	|	|	ADV
iajs-316	110	2	(	(	PUNCT
iajs-316	110	3	11	11	NUM
iajs-316	110	4	)	)	PUNCT
iajs-316	110	5	518	518	NUM
iajs-316	110	6	|	|	NOUN
iajs-316	110	7	mathematics	mathematic	NOUN
iajs-316	110	8	2014	2014	NUM
iajs-316	110	9	)	)	PUNCT
iajs-316	110	10	عام	عام	ADP
iajs-316	110	11	3العدد	3العدد	NUM
iajs-316	110	12	(	(	PUNCT
iajs-316	110	13	27مجلة	27مجلة	NUM
iajs-316	110	14	إبن	إبن	VERB
iajs-316	110	15	الھيثم	الھيثم	NOUN
iajs-316	110	16	للعلوم	للعلوم	NOUN
iajs-316	110	17	الصرفة	الصرفة	NOUN
iajs-316	111	1	و	و	PRON
iajs-316	111	2	التطبيقية	التطبيقية	ADV
iajs-316	111	3	المجلد	المجلد	VERB
iajs-316	111	4	ibn	ibn	PROPN
iajs-316	111	5	al	al	PROPN
iajs-316	111	6	-	-	PUNCT
iajs-316	111	7	haitham	haitham	PROPN
iajs-316	111	8	jour	jour	X
iajs-316	111	9	.	.	PROPN
iajs-316	112	1	for	for	ADP
iajs-316	112	2	pure	pure	ADJ
iajs-316	112	3	&	&	CCONJ
iajs-316	112	4	appl	appl	PROPN
iajs-316	112	5	.	.	PUNCT
iajs-316	113	1	sci	sci	PROPN
iajs-316	113	2	.	.	PUNCT
iajs-316	113	3	vol	vol	NOUN
iajs-316	113	4	.	.	PROPN
iajs-316	114	1	27	27	NUM
iajs-316	114	2	(	(	PUNCT
iajs-316	114	3	3	3	NUM
iajs-316	114	4	)	)	PUNCT
iajs-316	114	5	2014	2014	NUM
iajs-316	115	1	where	where	SCONJ
iajs-316	115	2	y(xi	y(xi	X
iajs-316	115	3	)	)	PUNCT
iajs-316	115	4	is	be	AUX
iajs-316	115	5	the	the	DET
iajs-316	115	6	exact	exact	ADJ
iajs-316	115	7	solution	solution	NOUN
iajs-316	115	8	at	at	ADP
iajs-316	115	9	the	the	DET
iajs-316	115	10	xi	xi	PROPN
iajs-316	115	11	and	and	CCONJ
iajs-316	115	12	yi	yi	PROPN
iajs-316	115	13	suggested	suggest	VERB
iajs-316	115	14	solution	solution	NOUN
iajs-316	115	15	at	at	ADP
iajs-316	115	16	xi	xi	PROPN
iajs-316	115	17	.	.	PUNCT
iajs-316	116	1	it	it	PRON
iajs-316	116	2	is	be	AUX
iajs-316	116	3	known	know	VERB
iajs-316	116	4	that	that	SCONJ
iajs-316	116	5	for	for	ADP
iajs-316	116	6	a	a	DET
iajs-316	116	7	large	large	ADJ
iajs-316	116	8	n	n	CCONJ
iajs-316	116	9	,	,	PUNCT
iajs-316	116	10	if	if	SCONJ
iajs-316	116	11	m	m	ADV
iajs-316	116	12	is	be	AUX
iajs-316	116	13	the	the	DET
iajs-316	116	14	order	order	NOUN
iajs-316	116	15	of	of	ADP
iajs-316	116	16	convergence	convergence	NOUN
iajs-316	116	17	of	of	ADP
iajs-316	116	18	the	the	DET
iajs-316	116	19	method	method	NOUN
iajs-316	116	20	,	,	PUNCT
iajs-316	116	21	then	then	ADV
iajs-316	116	22	:	:	PUNCT
iajs-316	116	23	e(n	e(n	ADJ
iajs-316	116	24	)	)	PUNCT
iajs-316	116	25			PUNCT
iajs-316	117	1	k	k	X
iajs-316	117	2	|n|m	|n|m	PROPN
iajs-316	117	3	(	(	PUNCT
iajs-316	117	4	12	12	NUM
iajs-316	117	5	)	)	PUNCT
iajs-316	117	6	where	where	SCONJ
iajs-316	117	7	k	k	PROPN
iajs-316	117	8	is	be	AUX
iajs-316	117	9	the	the	DET
iajs-316	117	10	error	error	NOUN
iajs-316	117	11	constant	constant	ADJ
iajs-316	117	12	and	and	CCONJ
iajs-316	117	13	e(n	e(n	NOUN
iajs-316	117	14	)	)	PUNCT
iajs-316	117	15	is	be	AUX
iajs-316	117	16	the	the	DET
iajs-316	117	17	max	max	PROPN
iajs-316	117	18	error	error	NOUN
iajs-316	117	19	.	.	PUNCT
iajs-316	118	1	following	follow	VERB
iajs-316	118	2	the	the	DET
iajs-316	118	3	generalized	generalized	ADJ
iajs-316	118	4	algorithm	algorithm	NOUN
iajs-316	118	5	for	for	ADP
iajs-316	118	6	the	the	DET
iajs-316	118	7	order	order	NOUN
iajs-316	118	8	verification	verification	NOUN
iajs-316	118	9	of	of	ADP
iajs-316	118	10	methods	method	NOUN
iajs-316	118	11	given	give	VERB
iajs-316	118	12	in	in	ADP
iajs-316	118	13	[	[	X
iajs-316	118	14	5	5	NUM
iajs-316	118	15	]	]	PUNCT
iajs-316	118	16	,	,	PUNCT
iajs-316	118	17	we	we	PRON
iajs-316	118	18	can	can	AUX
iajs-316	118	19	find	find	VERB
iajs-316	118	20	m	m	PRON
iajs-316	118	21	and	and	CCONJ
iajs-316	118	22	k	k	X
iajs-316	118	23	from	from	ADP
iajs-316	118	24	the	the	DET
iajs-316	118	25	line	line	NOUN
iajs-316	118	26	:	:	PUNCT
iajs-316	119	1	y	y	X
iajs-316	119	2	=	=	PUNCT
iajs-316	119	3	m	m	VERB
iajs-316	119	4	x	x	PUNCT
iajs-316	119	5	+	+	CCONJ
iajs-316	119	6	log	log	VERB
iajs-316	119	7	k	k	X
iajs-316	119	8	(	(	PUNCT
iajs-316	119	9	13	13	NUM
iajs-316	119	10	)	)	PUNCT
iajs-316	119	11	that	that	PRON
iajs-316	119	12	best	well	ADV
iajs-316	119	13	fits	fit	VERB
iajs-316	119	14	the	the	DET
iajs-316	119	15	equation	equation	NOUN
iajs-316	119	16	:	:	PUNCT
iajs-316	119	17	log	log	VERB
iajs-316	119	18	e(n	e(n	PROPN
iajs-316	119	19	)	)	PUNCT
iajs-316	119	20	=	=	SYM
iajs-316	120	1	log	log	NOUN
iajs-316	120	2	k	k	NOUN
iajs-316	121	1	+	+	CCONJ
iajs-316	121	2	m	m	VERB
iajs-316	121	3	log	log	NOUN
iajs-316	121	4	n	n	INTJ
iajs-316	121	5	(	(	PUNCT
iajs-316	121	6	14	14	NUM
iajs-316	121	7	)	)	PUNCT
iajs-316	121	8	where	where	SCONJ
iajs-316	121	9	y	y	PRON
iajs-316	121	10	represent	represent	VERB
iajs-316	121	11	log	log	PROPN
iajs-316	121	12	e(n	e(n	PROPN
iajs-316	121	13	)	)	PUNCT
iajs-316	121	14	and	and	CCONJ
iajs-316	121	15	x	x	PART
iajs-316	121	16	represent	represent	VERB
iajs-316	121	17	log	log	NOUN
iajs-316	121	18	n	n	INTJ
iajs-316	121	19	.	.	PUNCT
iajs-316	122	1	applying	apply	VERB
iajs-316	122	2	this	this	DET
iajs-316	122	3	algorithm	algorithm	NOUN
iajs-316	122	4	for	for	ADP
iajs-316	122	5	the	the	DET
iajs-316	122	6	following	follow	VERB
iajs-316	122	7	example	example	NOUN
iajs-316	122	8	:	:	PUNCT
iajs-316	122	9	y	y	X
iajs-316	122	10	"	"	PUNCT
iajs-316	122	11	+	+	CCONJ
iajs-316	122	12	(	(	PUNCT
iajs-316	122	13	2	2	NUM
iajs-316	122	14	/	/	SYM
iajs-316	122	15	x	x	NOUN
iajs-316	122	16	)	)	PUNCT
iajs-316	122	17	y	y	PROPN
iajs-316	122	18	'	'	PUNCT
iajs-316	122	19	−	−	NOUN
iajs-316	122	20	6y	6y	NOUN
iajs-316	122	21	=	=	PUNCT
iajs-316	122	22	−	−	PROPN
iajs-316	122	23	4ylny	4ylny	NUM
iajs-316	122	24	,	,	PUNCT
iajs-316	122	25	with	with	ADP
iajs-316	122	26	the	the	DET
iajs-316	122	27	ic	ic	X
iajs-316	122	28	:	:	PUNCT
iajs-316	122	29	y(0	y(0	PROPN
iajs-316	122	30	)	)	PUNCT
iajs-316	122	31	=	=	NOUN
iajs-316	122	32	1	1	NUM
iajs-316	122	33	,	,	PUNCT
iajs-316	122	34	y'(0	y'(0	PROPN
iajs-316	122	35	)	)	PUNCT
iajs-316	122	36	=	=	SYM
iajs-316	123	1	0	0	NUM
iajs-316	124	1	the	the	DET
iajs-316	124	2	exact	exact	ADJ
iajs-316	124	3	solution	solution	NOUN
iajs-316	124	4	is	be	AUX
iajs-316	124	5	y(x	y(x	NOUN
iajs-316	124	6	)	)	PUNCT
iajs-316	124	7	=	=	SYM
iajs-316	124	8	exp	exp	NOUN
iajs-316	124	9	(	(	PUNCT
iajs-316	124	10	x−	x−	PROPN
iajs-316	124	11	2	2	NUM
iajs-316	124	12	)	)	PUNCT
iajs-316	124	13	,	,	PUNCT
iajs-316	124	14	we	we	PRON
iajs-316	124	15	have	have	VERB
iajs-316	124	16	from	from	ADP
iajs-316	124	17	table	table	NOUN
iajs-316	124	18	(	(	PUNCT
iajs-316	124	19	4	4	NUM
iajs-316	124	20	)	)	PUNCT
iajs-316	124	21	the	the	DET
iajs-316	124	22	best	well	ADV
iajs-316	124	23	fit	fit	ADJ
iajs-316	124	24	line	line	NOUN
iajs-316	124	25	whose	whose	DET
iajs-316	124	26	graph	graph	NOUN
iajs-316	124	27	is	be	AUX
iajs-316	124	28	shown	show	VERB
iajs-316	124	29	in	in	ADP
iajs-316	124	30	figure	figure	NOUN
iajs-316	124	31	(	(	PUNCT
iajs-316	124	32	2	2	NUM
iajs-316	124	33	)	)	PUNCT
iajs-316	124	34	,	,	PUNCT
iajs-316	124	35	i.e.	i.e.	X
iajs-316	124	36	,	,	PUNCT
iajs-316	124	37	y	y	PROPN
iajs-316	124	38	=	=	PUNCT
iajs-316	124	39	−	−	PROPN
iajs-316	125	1	6.6214	6.6214	NUM
iajs-316	125	2	x	x	SYM
iajs-316	125	3	−	−	ADP
iajs-316	125	4	1.3330	1.3330	NUM
iajs-316	125	5	from	from	ADP
iajs-316	125	6	equation	equation	NOUN
iajs-316	125	7	(	(	PUNCT
iajs-316	125	8	13	13	NUM
iajs-316	125	9	)	)	PUNCT
iajs-316	125	10	,	,	PUNCT
iajs-316	125	11	we	we	PRON
iajs-316	125	12	conclude	conclude	VERB
iajs-316	125	13	that	that	SCONJ
iajs-316	125	14	the	the	DET
iajs-316	125	15	order	order	NOUN
iajs-316	125	16	of	of	ADP
iajs-316	125	17	convergence	convergence	NOUN
iajs-316	125	18	|m|	|m|	VERB
iajs-316	125	19			X
iajs-316	125	20	6	6	NUM
iajs-316	125	21	with	with	ADP
iajs-316	125	22	error	error	NOUN
iajs-316	125	23	constant	constant	ADJ
iajs-316	125	24	:	:	PUNCT
iajs-316	125	25	k	k	X
iajs-316	125	26	=	=	SYM
iajs-316	125	27	101.3330	101.3330	NUM
iajs-316	125	28	.	.	NOUN
iajs-316	125	29	6	6	NUM
iajs-316	125	30	.	.	PUNCT
iajs-316	126	1	conclusions	conclusion	NOUN
iajs-316	126	2	our	our	PRON
iajs-316	126	3	decision	decision	NOUN
iajs-316	126	4	to	to	PART
iajs-316	126	5	use	use	VERB
iajs-316	126	6	semi	semi	ADJ
iajs-316	126	7	-	-	ADJ
iajs-316	126	8	analytic	analytic	ADJ
iajs-316	126	9	technique	technique	NOUN
iajs-316	126	10	for	for	ADP
iajs-316	126	11	the	the	DET
iajs-316	126	12	solution	solution	NOUN
iajs-316	126	13	of	of	ADP
iajs-316	126	14	the	the	DET
iajs-316	126	15	underlying	underlying	ADJ
iajs-316	126	16	initial	initial	ADJ
iajs-316	126	17	value	value	NOUN
iajs-316	126	18	problem	problem	NOUN
iajs-316	126	19	was	be	AUX
iajs-316	126	20	motivated	motivate	VERB
iajs-316	126	21	by	by	ADP
iajs-316	126	22	its	its	PRON
iajs-316	126	23	advantageous	advantageous	ADJ
iajs-316	126	24	convergence	convergence	NOUN
iajs-316	126	25	properties	property	NOUN
iajs-316	126	26	,	,	PUNCT
iajs-316	126	27	whereas	whereas	SCONJ
iajs-316	126	28	in	in	ADP
iajs-316	126	29	presence	presence	NOUN
iajs-316	126	30	of	of	ADP
iajs-316	126	31	a	a	DET
iajs-316	126	32	singularity	singularity	NOUN
iajs-316	126	33	other	other	ADJ
iajs-316	126	34	direct	direct	ADJ
iajs-316	126	35	higher	high	ADJ
iajs-316	126	36	order	order	NOUN
iajs-316	126	37	methods	method	NOUN
iajs-316	126	38	(	(	PUNCT
iajs-316	126	39	finite	finite	ADJ
iajs-316	126	40	difference	difference	NOUN
iajs-316	126	41	)	)	PUNCT
iajs-316	126	42	show	show	VERB
iajs-316	126	43	order	order	NOUN
iajs-316	126	44	reductions	reduction	NOUN
iajs-316	126	45	and	and	CCONJ
iajs-316	126	46	become	become	VERB
iajs-316	126	47	inefficient	inefficient	ADJ
iajs-316	126	48	.	.	PUNCT
iajs-316	127	1	moreover	moreover	ADV
iajs-316	127	2	,	,	PUNCT
iajs-316	127	3	the	the	DET
iajs-316	127	4	standard	standard	ADJ
iajs-316	127	5	acceleration	acceleration	NOUN
iajs-316	127	6	techniques	technique	NOUN
iajs-316	127	7	like	like	ADP
iajs-316	127	8	iterated	iterate	VERB
iajs-316	127	9	.	.	PUNCT
iajs-316	128	1	our	our	PRON
iajs-316	128	2	reason	reason	NOUN
iajs-316	128	3	for	for	ADP
iajs-316	128	4	choosing	choose	VERB
iajs-316	128	5	the	the	DET
iajs-316	128	6	global	global	ADJ
iajs-316	128	7	error	error	NOUN
iajs-316	128	8	estimate	estimate	NOUN
iajs-316	128	9	instead	instead	ADV
iajs-316	128	10	of	of	ADP
iajs-316	128	11	monitoring	monitor	VERB
iajs-316	128	12	the	the	DET
iajs-316	128	13	local	local	ADJ
iajs-316	128	14	error	error	NOUN
iajs-316	128	15	is	be	AUX
iajs-316	128	16	the	the	DET
iajs-316	128	17	non	non	ADJ
iajs-316	128	18	-	-	ADJ
iajs-316	128	19	smoothness	smoothness	ADJ
iajs-316	128	20	of	of	ADP
iajs-316	128	21	the	the	DET
iajs-316	128	22	latter	latter	ADJ
iajs-316	128	23	near	near	ADP
iajs-316	128	24	the	the	DET
iajs-316	128	25	singular	singular	ADJ
iajs-316	128	26	point	point	NOUN
iajs-316	128	27	and	and	CCONJ
iajs-316	128	28	the	the	DET
iajs-316	128	29	order	order	NOUN
iajs-316	128	30	reductions	reduction	VERB
iajs-316	128	31	it	it	PRON
iajs-316	128	32	suffers	suffer	VERB
iajs-316	128	33	from	from	ADP
iajs-316	128	34	.	.	PUNCT
iajs-316	129	1	the	the	DET
iajs-316	129	2	results	result	NOUN
iajs-316	129	3	show	show	VERB
iajs-316	129	4	that	that	SCONJ
iajs-316	129	5	the	the	DET
iajs-316	129	6	convergence	convergence	NOUN
iajs-316	129	7	order	order	NOUN
iajs-316	129	8	estimates	estimate	NOUN
iajs-316	129	9	are	be	AUX
iajs-316	129	10	increased	increase	VERB
iajs-316	129	11	,	,	PUNCT
iajs-316	129	12	if	if	SCONJ
iajs-316	129	13	we	we	PRON
iajs-316	129	14	increase	increase	VERB
iajs-316	129	15	n	n	ADV
iajs-316	129	16	.	.	PUNCT
iajs-316	130	1	this	this	PRON
iajs-316	130	2	is	be	AUX
iajs-316	130	3	not	not	PART
iajs-316	130	4	surprising	surprising	ADJ
iajs-316	130	5	.	.	PUNCT
iajs-316	131	1	references	reference	NOUN
iajs-316	131	2	1karakostas	1karakostas	NUM
iajs-316	131	3	(	(	PUNCT
iajs-316	131	4	2010	2010	NUM
iajs-316	131	5	)	)	PUNCT
iajs-316	131	6	c1	c1	NOUN
iajs-316	131	7	-	-	PUNCT
iajs-316	131	8	approximate	approximate	ADJ
iajs-316	131	9	solutions	solution	NOUN
iajs-316	131	10	of	of	ADP
iajs-316	131	11	second	second	ADJ
iajs-316	131	12	-	-	PUNCT
iajs-316	131	13	order	order	NOUN
iajs-316	131	14	singular	singular	ADJ
iajs-316	131	15	ordinary	ordinary	ADJ
iajs-316	131	16	differential	differential	ADJ
iajs-316	131	17	equations	equation	NOUN
iajs-316	131	18	,	,	PUNCT
iajs-316	131	19	electronic	electronic	ADJ
iajs-316	131	20	journal	journal	NOUN
iajs-316	131	21	of	of	ADP
iajs-316	131	22	differential	differential	ADJ
iajs-316	131	23	equations	equation	NOUN
iajs-316	131	24	.	.	PUNCT
iajs-316	131	25	,	,	PUNCT
iajs-316	131	26	125	125	NUM
iajs-316	131	27	:	:	SYM
iajs-316	131	28	147	147	NUM
iajs-316	131	29	.	.	PUNCT
iajs-316	132	1	2robert	2robert	NUM
iajs-316	132	2	and	and	CCONJ
iajs-316	132	3	courtney	courtney	PROPN
iajs-316	132	4	(	(	PUNCT
iajs-316	132	5	1996	1996	NUM
iajs-316	132	6	)	)	PUNCT
iajs-316	132	7	"	"	PUNCT
iajs-316	132	8	differential	differential	ADJ
iajs-316	132	9	equations	equation	NOUN
iajs-316	132	10	a	a	DET
iajs-316	132	11	modeling	modeling	NOUN
iajs-316	132	12	perspective	perspective	NOUN
iajs-316	132	13	"	"	PUNCT
iajs-316	132	14	,	,	PUNCT
iajs-316	132	15	united	united	PROPN
iajs-316	132	16	states	states	PROPN
iajs-316	132	17	of	of	ADP
iajs-316	132	18	america	america	PROPN
iajs-316	132	19	.	.	PUNCT
iajs-316	133	1	3demir	3demir	NUM
iajs-316	133	2	and	and	CCONJ
iajs-316	133	3	süngü	süngü	ADJ
iajs-316	133	4	(	(	PUNCT
iajs-316	133	5	2009	2009	NUM
iajs-316	133	6	)	)	PUNCT
iajs-316	133	7	numerical	numerical	ADJ
iajs-316	133	8	solution	solution	NOUN
iajs-316	133	9	of	of	ADP
iajs-316	133	10	a	a	DET
iajs-316	133	11	class	class	NOUN
iajs-316	133	12	of	of	ADP
iajs-316	133	13	nonlinear	nonlinear	ADJ
iajs-316	133	14	emden	emden	ADJ
iajs-316	133	15	-	-	PUNCT
iajs-316	133	16	fowler	fowler	PROPN
iajs-316	133	17	equations	equation	NOUN
iajs-316	133	18	by	by	ADP
iajs-316	133	19	using	use	VERB
iajs-316	133	20	differential	differential	ADJ
iajs-316	133	21	transform	transform	NOUN
iajs-316	133	22	method	method	NOUN
iajs-316	133	23	,	,	PUNCT
iajs-316	133	24	journal	journal	NOUN
iajs-316	133	25	of	of	ADP
iajs-316	133	26	arts	art	NOUN
iajs-316	133	27	and	and	CCONJ
iajs-316	133	28	sciences	science	NOUN
iajs-316	133	29	,	,	PUNCT
iajs-316	133	30	.	.	PUNCT
iajs-316	134	1	75	75	NUM
iajs-316	134	2	-	-	SYM
iajs-316	134	3	82	82	NUM
iajs-316	134	4	.	.	PUNCT
iajs-316	135	1	4shampine	4shampine	NUM
iajs-316	135	2	(	(	PUNCT
iajs-316	135	3	2002	2002	NUM
iajs-316	135	4	)	)	PUNCT
iajs-316	135	5	"	"	PUNCT
iajs-316	135	6	singular	singular	PROPN
iajs-316	135	7	boundary	boundary	ADJ
iajs-316	135	8	value	value	NOUN
iajs-316	135	9	problems	problem	NOUN
iajs-316	135	10	for	for	ADP
iajs-316	135	11	odes	ode	NOUN
iajs-316	135	12	"	"	PUNCT
iajs-316	135	13	,	,	PUNCT
iajs-316	135	14	southern	southern	PROPN
iajs-316	135	15	methodist	methodist	PROPN
iajs-316	135	16	university	university	PROPN
iajs-316	135	17	j.	j.	PROPN
iajs-316	135	18	,	,	PUNCT
iajs-316	135	19	.	.	PUNCT
iajs-316	136	1	1	1	X
iajs-316	136	2	.	.	X
iajs-316	137	1	5rasheed	5rasheed	NUM
iajs-316	137	2	(	(	PUNCT
iajs-316	137	3	2011	2011	NUM
iajs-316	137	4	)	)	PUNCT
iajs-316	137	5	"	"	PUNCT
iajs-316	137	6	efficient	efficient	ADJ
iajs-316	137	7	semi	semi	ADJ
iajs-316	137	8	-	-	ADJ
iajs-316	137	9	analytic	analytic	ADJ
iajs-316	137	10	technique	technique	NOUN
iajs-316	137	11	for	for	ADP
iajs-316	137	12	solving	solve	VERB
iajs-316	137	13	second	second	ADJ
iajs-316	137	14	order	order	NOUN
iajs-316	137	15	singular	singular	ADJ
iajs-316	137	16	ordinary	ordinary	ADJ
iajs-316	137	17	boundary	boundary	ADJ
iajs-316	137	18	value	value	NOUN
iajs-316	137	19	problems	problem	NOUN
iajs-316	137	20	"	"	PUNCT
iajs-316	137	21	,	,	PUNCT
iajs-316	138	1	msc	msc	PROPN
iajs-316	138	2	.	.	PROPN
iajs-316	138	3	thesis	thesis	PROPN
iajs-316	138	4	,	,	PUNCT
iajs-316	138	5	university	university	NOUN
iajs-316	138	6	of	of	ADP
iajs-316	138	7	baghdad	baghdad	PROPN
iajs-316	138	8	,	,	PUNCT
iajs-316	138	9	college	college	NOUN
iajs-316	138	10	of	of	ADP
iajs-316	138	11	education	education	NOUN
iajs-316	138	12	–	–	PUNCT
iajs-316	138	13	ibn	ibn	NOUN
iajs-316	138	14	–	–	PUNCT
iajs-316	138	15	alhaitham	alhaitham	NOUN
iajs-316	138	16	.	.	PUNCT
iajs-316	139	1	519	519	NUM
iajs-316	139	2	|	|	NOUN
iajs-316	139	3	mathematics	mathematic	NOUN
iajs-316	139	4	2014	2014	NUM
iajs-316	139	5	)	)	PUNCT
iajs-316	139	6	عام	عام	ADP
iajs-316	139	7	3العدد	3العدد	NUM
iajs-316	139	8	(	(	PUNCT
iajs-316	139	9	27مجلة	27مجلة	NUM
iajs-316	139	10	إبن	إبن	VERB
iajs-316	139	11	الھيثم	الھيثم	NOUN
iajs-316	139	12	للعلوم	للعلوم	NOUN
iajs-316	139	13	الصرفة	الصرفة	NOUN
iajs-316	140	1	و	و	PRON
iajs-316	140	2	التطبيقية	التطبيقية	ADV
iajs-316	140	3	المجلد	المجلد	VERB
iajs-316	140	4	ibn	ibn	PROPN
iajs-316	140	5	al	al	PROPN
iajs-316	140	6	-	-	PUNCT
iajs-316	140	7	haitham	haitham	PROPN
iajs-316	140	8	jour	jour	X
iajs-316	140	9	.	.	PROPN
iajs-316	141	1	for	for	ADP
iajs-316	141	2	pure	pure	ADJ
iajs-316	141	3	&	&	CCONJ
iajs-316	141	4	appl	appl	PROPN
iajs-316	141	5	.	.	PUNCT
iajs-316	142	1	sci	sci	PROPN
iajs-316	142	2	.	.	PUNCT
iajs-316	142	3	vol	vol	NOUN
iajs-316	142	4	.	.	PROPN
iajs-316	143	1	27	27	NUM
iajs-316	143	2	(	(	PUNCT
iajs-316	143	3	3	3	NUM
iajs-316	143	4	)	)	PUNCT
iajs-316	143	5	2014	2014	NUM
iajs-316	143	6	table	table	NOUN
iajs-316	143	7	no.(1a):the	no.(1a):the	NOUN
iajs-316	143	8	result	result	NOUN
iajs-316	143	9	of	of	ADP
iajs-316	143	10	suggested	suggest	VERB
iajs-316	143	11	method	method	NOUN
iajs-316	143	12	for	for	ADP
iajs-316	143	13	n	n	PRON
iajs-316	143	14	=	=	SYM
iajs-316	143	15	2	2	NUM
iajs-316	143	16	,	,	PUNCT
iajs-316	143	17	3	3	NUM
iajs-316	143	18	,	,	PUNCT
iajs-316	143	19	4	4	NUM
iajs-316	143	20	&	&	CCONJ
iajs-316	143	21	method	method	PROPN
iajs-316	143	22	in[3	in[3	PROPN
iajs-316	143	23	]	]	PUNCT
iajs-316	143	24	for	for	ADP
iajs-316	143	25	example	example	NOUN
iajs-316	143	26	3	3	NUM
iajs-316	143	27	0.990235879509409	0.990235879509409	NUM
iajs-316	143	28	0.9902358748522030.990235914910346	0.9902358748522030.990235914910346	NUM
iajs-316	143	29	0b	0b	NOUN
iajs-316	143	30	0.050589305215627	0.050589305215627	NUM
iajs-316	143	31	0.0505893414767570.0505890348752984	0.0505893414767570.0505890348752984	PROPN
iajs-316	143	32	1b	1b	PROPN
iajs-316	143	33	13p	13p	PROPN
iajs-316	143	34	11p	11p	PROPN
iajs-316	143	35	9p	9p	NUM
iajs-316	143	36	numerical	numerical	ADJ
iajs-316	143	37	solution	solution	NOUN
iajs-316	143	38	(	(	PUNCT
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iajs-316	143	40	)	)	PUNCT
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iajs-316	143	42	1	1	NUM
iajs-316	143	43	1	1	NUM
iajs-316	143	44	1	1	NUM
iajs-316	143	45	1	1	NUM
iajs-316	143	46	0	0	NUM
iajs-316	143	47	.0.999966681360863	.0.999966681360863	PUNCT
iajs-316	143	48	..	..	PUNCT
iajs-316	143	49	999966681419201	999966681419201	NUM
iajs-316	144	1	0.999966680471501	0.999966680471501	NUM
iajs-316	144	2	0.99996668000000	0.99996668000000	NUM
iajs-316	144	3	0.1	0.1	NUM
iajs-316	144	4	0.999734338980186	0.999734338980186	NUM
iajs-316	144	5	0.999734340836996	0.999734340836996	NUM
iajs-316	144	6	0.999734323342549	0.999734323342549	NUM
iajs-316	144	7	0.999734330000000	0.999734330000000	NUM
iajs-316	144	8	0.2	0.2	NUM
iajs-316	144	9	0.999112195858900	0.999112195858900	NUM
iajs-316	144	10	0.999112205091858	0.999112205091858	NUM
iajs-316	144	11	0.999112136946651	0.999112136946651	NUM
iajs-316	144	12	0.999112190000000	0.999112190000000	NUM
iajs-316	144	13	0.3	0.3	NUM
iajs-316	144	14	0.997939333529043	0.997939333529043	NUM
iajs-316	144	15	0.997939352185325	0.997939352185325	NUM
iajs-316	144	16	0.997939228062444	0.997939228062444	NUM
iajs-316	144	17	0.997939330000000	0.997939330000000	NUM
iajs-316	144	18	0.4	0.4	NUM
iajs-316	145	1	0.996126225634366	0.996126225634366	NUM
iajs-316	145	2	0.996126243561995	0.996126243561995	NUM
iajs-316	145	3	0.996126122885822	0.996126122885822	NUM
iajs-316	145	4	0.996126220000000	0.996126220000000	NUM
iajs-316	145	5	0.5	0.5	NUM
iajs-316	145	6	0.993720978536793	0.993720978536793	NUM
iajs-316	145	7	0.993720981359821	0.993720981359821	NUM
iajs-316	145	8	0.993720947623996	0.993720947623996	NUM
iajs-316	145	9	0.993720970000000	0.993720970000000	NUM
iajs-316	145	10	0.6	0.6	NUM
iajs-316	145	11	0.991004633063186	0.991004633063186	NUM
iajs-316	145	12	0.991004619559273	0.991004619559273	NUM
iajs-316	145	13	0.991004695132483	0.991004695132483	NUM
iajs-316	145	14	0.9910046300000000	0.9910046300000000	NUM
iajs-316	146	1	0.7	0.7	NUM
iajs-316	146	2	0.988619280474356	0.988619280474356	NUM
iajs-316	146	3	0.988619263799973	0.988619263799973	NUM
iajs-316	146	4	0.988619382084590	0.988619382084590	NUM
iajs-316	146	5	0.988619280000000	0.988619280000000	NUM
iajs-316	146	6	0.8	0.8	NUM
iajs-316	146	7	0.987731920033536	0.987731920033536	NUM
iajs-316	146	8	0.987731909996439	0.987731909996439	NUM
iajs-316	146	9	0.987731993184585	0.987731993184585	NUM
iajs-316	146	10	0.987723192000000	0.987723192000000	NUM
iajs-316	146	11	0.9	0.9	NUM
iajs-316	146	12	0.990235879509409	0.990235879509409	NUM
iajs-316	146	13	0.990235874852203	0.990235874852203	NUM
iajs-316	146	14	0.990235914910346	0.990235914910346	NUM
iajs-316	146	15	0.990235880000000	0.990235880000000	NUM
iajs-316	146	16	1	1	NUM
iajs-316	146	17	table	table	NOUN
iajs-316	146	18	no.(1b):comparison	no.(1b):comparison	NOUN
iajs-316	146	19	between	between	ADP
iajs-316	146	20	suggested	suggest	VERB
iajs-316	146	21	method	method	NOUN
iajs-316	146	22	with	with	ADP
iajs-316	146	23	method	method	NOUN
iajs-316	146	24	in[3	in[3	PROPN
iajs-316	146	25	]	]	PUNCT
iajs-316	146	26	for	for	ADP
iajs-316	146	27	example	example	NOUN
iajs-316	146	28	3	3	NUM
iajs-316	146	29	|13p	|13p	NUM
iajs-316	146	30	-	-	PUNCT
iajs-316	146	31	error	error	NOUN
iajs-316	146	32	|y	|y	NOUN
iajs-316	146	33	|11p	|11p	NOUN
iajs-316	146	34	-	-	PUNCT
iajs-316	146	35	error	error	NOUN
iajs-316	146	36	|y	|y	NOUN
iajs-316	146	37	|9p	|9p	NOUN
iajs-316	146	38	-	-	PUNCT
iajs-316	146	39	error	error	NOUN
iajs-316	146	40	|y	|y	NOUN
iajs-316	146	41	ix	ix	ADP
iajs-316	146	42	0	0	NUM
iajs-316	146	43	0	0	NUM
iajs-316	146	44	0	0	NUM
iajs-316	146	45	0	0	NUM
iajs-316	147	1	1.360863421950850e-009	1.360863421950850e-009	NUM
iajs-316	147	2	1.419200645891300e-009	1.419200645891300e-009	NUM
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iajs-316	176	34	n=6	n=6	PROPN
iajs-316	176	35	numerical	numerical	ADJ
iajs-316	176	36	solution	solution	NOUN
iajs-316	176	37	p13	p13	VERB
iajs-316	176	38	0.35	0.35	NUM
iajs-316	176	39	0.4	0.4	NUM
iajs-316	176	40	0.45	0.45	NUM
iajs-316	176	41	0.5	0.5	NUM
iajs-316	176	42	0.55	0.55	NUM
iajs-316	176	43	0.6	0.6	NUM
iajs-316	176	44	0.65	0.65	NUM
iajs-316	176	45	0.7	0.7	NUM
iajs-316	176	46	-5.5	-5.5	NOUN
iajs-316	176	47	-5	-5	INTJ
iajs-316	176	48	-4.5	-4.5	INTJ
iajs-316	176	49	-4	-4	INTJ
iajs-316	176	50	-3.5	-3.5	INTJ
iajs-316	176	51	-3	-3	PUNCT
iajs-316	176	52	the	the	DET
iajs-316	176	53	best	good	ADJ
iajs-316	176	54	fit	fit	ADJ
iajs-316	176	55	line	line	NOUN
iajs-316	176	56	for	for	ADP
iajs-316	176	57	the	the	DET
iajs-316	176	58	order	order	NOUN
iajs-316	176	59	of	of	ADP
iajs-316	176	60	convergent	convergent	NOUN
iajs-316	176	61	log	log	NOUN
iajs-316	177	1	n	n	INTJ
iajs-316	178	1	lo	lo	NOUN
iajs-316	178	2	g	g	NOUN
iajs-316	178	3	m	m	NOUN
iajs-316	178	4	ax	ax	NOUN
iajs-316	178	5	e	e	X
iajs-316	178	6	rr	rr	NOUN
iajs-316	179	1	er	er	INTJ
iajs-316	179	2	522	522	NUM
iajs-316	179	3	|	|	NOUN
iajs-316	179	4	mathematics	mathematic	NOUN
iajs-316	179	5	2014	2014	NUM
iajs-316	179	6	)	)	PUNCT
iajs-316	179	7	عام	عام	ADP
iajs-316	179	8	3العدد	3العدد	NUM
iajs-316	179	9	(	(	PUNCT
iajs-316	179	10	27مجلة	27مجلة	NUM
iajs-316	179	11	إبن	إبن	VERB
iajs-316	179	12	الھيثم	الھيثم	NOUN
iajs-316	179	13	للعلوم	للعلوم	NOUN
iajs-316	179	14	الصرفة	الصرفة	NOUN
iajs-316	180	1	و	و	PRON
iajs-316	180	2	التطبيقية	التطبيقية	ADV
iajs-316	180	3	المجلد	المجلد	VERB
iajs-316	180	4	ibn	ibn	PROPN
iajs-316	180	5	al	al	PROPN
iajs-316	180	6	-	-	PUNCT
iajs-316	180	7	haitham	haitham	PROPN
iajs-316	180	8	jour	jour	X
iajs-316	180	9	.	.	PROPN
iajs-316	181	1	for	for	ADP
iajs-316	181	2	pure	pure	ADJ
iajs-316	181	3	&	&	CCONJ
iajs-316	181	4	appl	appl	PROPN
iajs-316	181	5	.	.	PUNCT
iajs-316	182	1	sci	sci	PROPN
iajs-316	182	2	.	.	PUNCT
iajs-316	182	3	vol	vol	NOUN
iajs-316	182	4	.	.	PROPN
iajs-316	183	1	27	27	NUM
iajs-316	183	2	(	(	PUNCT
iajs-316	183	3	3	3	NUM
iajs-316	183	4	)	)	PUNCT
iajs-316	183	5	2014	2014	NUM
iajs-316	183	6	خطيةالر	خطيةالر	NOUN
iajs-316	183	7	كفاءة	كفاءة	NOUN
iajs-316	183	8	التقـنيـة	التقـنيـة	PROPN
iajs-316	183	9	شبـه	شبـه	PROPN
iajs-316	183	10	التحـليليـة	التحـليليـة	PROPN
iajs-316	183	11	في	في	DET
iajs-316	183	12	حـل	حـل	NOUN
iajs-316	183	13	مسائل	مسائل	PROPN
iajs-316	183	14	القيم	القيم	NOUN
iajs-316	183	15	االبتدائية	االبتدائية	NOUN
iajs-316	183	16	غي	غي	NUM
iajs-316	183	17	الشاذة	الشاذة	ADJ
iajs-316	183	18	لمى	لمى	NOUN
iajs-316	183	19	ناجي	ناجي	ADJ
iajs-316	183	20	محمد	محمد	PROPN
iajs-316	183	21	توفيق	توفيق	NOUN
iajs-316	183	22	حسين	حسين	PROPN
iajs-316	183	23	ريم	ريم	PROPN
iajs-316	183	24	وليد	وليد	PROPN
iajs-316	183	25	جامعة	جامعة	PROPN
iajs-316	183	26	بغداد	بغداد	PROPN
iajs-316	183	27	/)ابن	/)ابن	SYM
iajs-316	183	28	الھيثم	الھيثم	PROPN
iajs-316	183	29	للعلوم	للعلوم	PROPN
iajs-316	183	30	الصرفة	الصرفة	NOUN
iajs-316	183	31	(	(	PUNCT
iajs-316	183	32	كلية	كلية	NOUN
iajs-316	183	33	التربية	التربية	NOUN
iajs-316	183	34	/قسم	/قسم	PROPN
iajs-316	183	35	الرياضيات	الرياضيات	PROPN
iajs-316	183	36	2012كانون	2012كانون	NUM
iajs-316	183	37	االول	االول	NOUN
iajs-316	183	38	9	9	NUM
iajs-316	183	39	،	،	NOUN
iajs-316	183	40	قبل	قبل	NOUN
iajs-316	184	1	في	في	X
iajs-316	184	2	:	:	PUNCT
iajs-316	184	3	2012ايلول	2012ايلول	NUM
iajs-316	184	4	23استلم	23استلم	NUM
iajs-316	184	5	في	في	NOUN
iajs-316	184	6	:	:	PUNCT
iajs-316	184	7	الخالصة	الخالصة	NOUN
iajs-316	184	8	للمعــادالت	للمعــادالت	INTJ
iajs-316	184	9	التفاضــلية	التفاضــلية	VERB
iajs-316	184	10	االعتياديــة	االعتياديــة	PROPN
iajs-316	184	11	اقتــراح	اقتــراح	VERB
iajs-316	184	12	تقنيــة	تقنيــة	PROPN
iajs-316	184	13	شــبه	شــبه	PROPN
iajs-316	184	14	التحليليــة	التحليليــة	PROPN
iajs-316	184	15	لحــل	لحــل	PROPN
iajs-316	184	16	مســائل	مســائل	PROPN
iajs-316	184	17	القــيم	القــيم	PROPN
iajs-316	184	18	االبتدائيــة	االبتدائيــة	PROPN
iajs-316	184	19	الشــاذة	الشــاذة	PROPN
iajs-316	184	20	الهــدف	الهــدف	AUX
iajs-316	184	21	مــن	مــن	VERB
iajs-316	184	22	هــذا	هــذا	PROPN
iajs-316	184	23	البحــث	البحــث	PROPN
iajs-316	184	24	النقطتــين	النقطتــين	PROPN
iajs-316	184	25	أوجــدنا	أوجــدنا	PROPN
iajs-316	184	26	كفــاءة	كفــاءة	NOUN
iajs-316	184	27	الطريقــة	الطريقــة	NOUN
iajs-316	184	28	يباســتخدام	يباســتخدام	ADV
iajs-316	184	29	االنــدراج	االنــدراج	PROPN
iajs-316	184	30	التماســي	التماســي	VERB
iajs-316	184	31	ذمتعــددة	ذمتعــددة	NOUN
iajs-316	184	32	حــدود	حــدود	VERB
iajs-316	184	33	بوصــفها	بوصــفها	NOUN
iajs-316	184	34	وبأنواع	وبأنواع	NOUN
iajs-316	185	1	مختلفة	مختلفة	PROPN
iajs-316	185	2	للحصول	للحصول	PROPN
iajs-316	185	3	على	على	PROPN
iajs-316	185	4	الحل	الحل	NOUN
iajs-316	185	5	من	من	PRON
iajs-316	185	6	خالل	خالل	PROPN
iajs-316	185	7	المقارنــات	المقارنــات	PROPN
iajs-316	185	8	مــع	مــع	PROPN
iajs-316	185	9	الحــل	الحــل	PROPN
iajs-316	185	10	المضــبوط	المضــبوط	PROPN
iajs-316	185	11	و	و	PRON
iajs-316	185	12	حلــول	حلــول	PROPN
iajs-316	185	13	تقريبيــة	تقريبيــة	ADJ
iajs-316	185	14	أخــرى	أخــرى	PROPN
iajs-316	185	15	ألصــناف	ألصــناف	PROPN
iajs-316	185	16	واســعة	واســعة	PROPN
iajs-316	185	17	متجانســة	متجانســة	PROPN
iajs-316	185	18	وغيــر	وغيــر	NOUN
iajs-316	185	19	متجانســة	متجانســة	PROPN
iajs-316	185	20	ودقتها	ودقتها	PROPN
iajs-316	186	1	المقترحة	المقترحة	PROPN
iajs-316	186	2	خطية	خطية	PROPN
iajs-316	186	3	و	و	PROPN
iajs-316	186	4	غير	غير	ADV
iajs-316	186	5	خطية	خطية	VERB
iajs-316	186	6	لمسائل	لمسائل	ADV
iajs-316	186	7	القيم	القيم	PROPN
iajs-316	186	8	االبتدائية	االبتدائية	PROPN
iajs-316	186	9	الشاذة	الشاذة	PROPN
iajs-316	186	10	.	.	PUNCT
iajs-316	187	1	العالقـــة	العالقـــة	PROPN
iajs-316	187	2	ذييـــار	ذييـــار	PROPN
iajs-316	187	3	الشـــبكة	الشـــبكة	PROPN
iajs-316	187	4	المناســـبة	المناســـبة	PROPN
iajs-316	187	5	أيضـــا	أيضـــا	PROPN
iajs-316	187	6	ناقشـــنا	ناقشـــنا	PROPN
iajs-316	187	7	بعـــض	بعـــض	PROPN
iajs-316	187	8	الصـــفات	الصـــفات	VERB
iajs-316	187	9	العدديـــة	العدديـــة	NOUN
iajs-316	187	10	اســـتخدم	اســـتخدم	PROPN
iajs-316	187	11	تخمـــين	تخمـــين	NOUN
iajs-316	187	12	جديـــد	جديـــد	NOUN
iajs-316	187	13	و	و	PRON
iajs-316	187	14	كفـــوء	كفـــوء	VERB
iajs-316	187	15	للخطـــأ	للخطـــأ	PROPN
iajs-316	187	16	الـــرئيس	الـــرئيس	PROPN
iajs-316	187	17	الخت	الخت	PROPN
iajs-316	187	18	لمســائل	لمســائل	PROPN
iajs-316	187	19	القــيم	القــيم	PROPN
iajs-316	187	20	االبتدائيــة	االبتدائيــة	PROPN
iajs-316	187	21	الشــاذة	الشــاذة	PROPN
iajs-316	187	22	.	.	PUNCT
iajs-316	188	1	كــذلك	كــذلك	PROPN
iajs-316	188	2	عــدد	عــدد	PROPN
iajs-316	188	3	مــن	مــن	PROPN
iajs-316	188	4	األمثلــة	األمثلــة	PROPN
iajs-316	188	5	نوقشــت	نوقشــت	PROPN
iajs-316	188	6	)	)	PUNCT
iajs-316	188	7	codeو	codeو	PROPN
iajs-316	188	8	لزيــادة	لزيــادة	PROPN
iajs-316	188	9	كفــاءة	كفــاءة	NOUN
iajs-316	188	10	الشــفرة	الشــفرة	PROPN
iajs-316	188	11	(	(	PUNCT
iajs-316	188	12	ومناقشــتهالتطبيــق	ومناقشــتهالتطبيــق	AUX
iajs-316	188	13	المقــاييس	المقــاييس	VERB
iajs-316	188	14	لتقارب	لتقارب	PROPN
iajs-316	189	1	من	من	PROPN
iajs-316	189	2	جهة	جهة	PROPN
iajs-316	189	3	أخرى.لتوضيح	أخرى.لتوضيح	PROPN
iajs-316	189	4	الدقة	الدقة	VERB
iajs-316	189	5	و	و	PRON
iajs-316	189	6	الكفاءة	الكفاءة	NOUN
iajs-316	189	7	وسهولة	وسهولة	PROPN
iajs-316	189	8	أداء	أداء	PROPN
iajs-316	189	9	الطريقة	الطريقة	VERB
iajs-316	189	10	المقترحة	المقترحة	PROPN
iajs-316	189	11	من	من	PRON
iajs-316	189	12	جهة	جهة	NOUN
iajs-316	189	13	ولتعزيز	ولتعزيز	NOUN
iajs-316	189	14	و	و	PRON
iajs-316	189	15	تأكيد	تأكيد	VERB
iajs-316	189	16	رتبة	رتبة	NOUN
iajs-316	189	17	ا	ا	ADP
iajs-316	189	18	معادالت	معادالت	ADJ
iajs-316	189	19	تفاضلية	تفاضلية	NOUN
iajs-316	189	20	اعتيادية	اعتيادية	ADJ
iajs-316	189	21	,	,	PUNCT
iajs-316	189	22	مسائل	مسائل	PROPN
iajs-316	189	23	القيم	القيم	NOUN
iajs-316	189	24	االبتدائية	االبتدائية	NOUN
iajs-316	189	25	الشاذةالكلمات	الشاذةالكلمات	VERB
iajs-316	189	26	المفتاحية	المفتاحية	NOUN
iajs-316	189	27	:	:	PUNCT