id	sid	tid	token	lemma	pos
iajs-2150	1	1	321	321	NUM
iajs-2150	1	2	ibn	ibn	PROPN
iajs-2150	1	3	al	al	PROPN
iajs-2150	1	4	-	-	PUNCT
iajs-2150	1	5	haitham	haitham	PROPN
iajs-2150	1	6	jour	jour	X
iajs-2150	1	7	.	.	PROPN
iajs-2150	1	8	for	for	ADP
iajs-2150	1	9	pure	pure	ADJ
iajs-2150	1	10	&	&	CCONJ
iajs-2150	1	11	appl	appl	PROPN
iajs-2150	1	12	.	.	PUNCT
iajs-2150	2	1	sci	sci	PROPN
iajs-2150	2	2	.	.	PROPN
iajs-2150	2	3	32	32	NUM
iajs-2150	2	4	(	(	PUNCT
iajs-2150	2	5	2	2	NUM
iajs-2150	2	6	)	)	PUNCT
iajs-2150	2	7	2019	2019	NUM
iajs-2150	2	8	abstract	abstract	NOUN
iajs-2150	2	9	this	this	DET
iajs-2150	2	10	paper	paper	NOUN
iajs-2150	2	11	demonstrates	demonstrate	VERB
iajs-2150	2	12	a	a	DET
iajs-2150	2	13	new	new	ADJ
iajs-2150	2	14	technique	technique	NOUN
iajs-2150	2	15	based	base	VERB
iajs-2150	2	16	on	on	ADP
iajs-2150	2	17	a	a	DET
iajs-2150	2	18	combined	combine	VERB
iajs-2150	2	19	form	form	NOUN
iajs-2150	2	20	of	of	ADP
iajs-2150	2	21	the	the	DET
iajs-2150	2	22	new	new	ADJ
iajs-2150	2	23	transform	transform	NOUN
iajs-2150	2	24	method	method	NOUN
iajs-2150	2	25	with	with	ADP
iajs-2150	2	26	homotopy	homotopy	NOUN
iajs-2150	2	27	perturbation	perturbation	NOUN
iajs-2150	2	28	method	method	NOUN
iajs-2150	2	29	to	to	PART
iajs-2150	2	30	find	find	VERB
iajs-2150	2	31	the	the	DET
iajs-2150	2	32	suitable	suitable	ADJ
iajs-2150	2	33	accurate	accurate	ADJ
iajs-2150	2	34	solution	solution	NOUN
iajs-2150	2	35	of	of	ADP
iajs-2150	2	36	autonomous	autonomous	ADJ
iajs-2150	2	37	equations	equation	NOUN
iajs-2150	2	38	with	with	ADP
iajs-2150	2	39	initial	initial	ADJ
iajs-2150	2	40	condition	condition	NOUN
iajs-2150	2	41	.	.	PUNCT
iajs-2150	3	1	this	this	DET
iajs-2150	3	2	technique	technique	NOUN
iajs-2150	3	3	is	be	AUX
iajs-2150	3	4	called	call	VERB
iajs-2150	3	5	the	the	DET
iajs-2150	3	6	transform	transform	NOUN
iajs-2150	3	7	homotopy	homotopy	NOUN
iajs-2150	3	8	perturbation	perturbation	NOUN
iajs-2150	3	9	method	method	NOUN
iajs-2150	3	10	(	(	PUNCT
iajs-2150	3	11	thpm	thpm	NOUN
iajs-2150	3	12	)	)	PUNCT
iajs-2150	3	13	.	.	PUNCT
iajs-2150	4	1	it	it	PRON
iajs-2150	4	2	can	can	AUX
iajs-2150	4	3	be	be	AUX
iajs-2150	4	4	used	use	VERB
iajs-2150	4	5	to	to	PART
iajs-2150	4	6	solve	solve	VERB
iajs-2150	4	7	the	the	DET
iajs-2150	4	8	problems	problem	NOUN
iajs-2150	4	9	without	without	ADP
iajs-2150	4	10	resorting	resort	VERB
iajs-2150	4	11	to	to	ADP
iajs-2150	4	12	the	the	DET
iajs-2150	4	13	frequency	frequency	NOUN
iajs-2150	4	14	domain	domain	NOUN
iajs-2150	4	15	.	.	PUNCT
iajs-2150	5	1	the	the	DET
iajs-2150	5	2	implementation	implementation	NOUN
iajs-2150	5	3	of	of	ADP
iajs-2150	5	4	the	the	DET
iajs-2150	5	5	suggested	suggest	VERB
iajs-2150	5	6	method	method	NOUN
iajs-2150	5	7	demonstrates	demonstrate	VERB
iajs-2150	5	8	the	the	DET
iajs-2150	5	9	usefulness	usefulness	NOUN
iajs-2150	5	10	in	in	ADP
iajs-2150	5	11	finding	find	VERB
iajs-2150	5	12	exact	exact	ADJ
iajs-2150	5	13	solution	solution	NOUN
iajs-2150	5	14	for	for	ADP
iajs-2150	5	15	linear	linear	ADJ
iajs-2150	5	16	and	and	CCONJ
iajs-2150	5	17	nonlinear	nonlinear	ADJ
iajs-2150	5	18	problems	problem	NOUN
iajs-2150	5	19	.	.	PUNCT
iajs-2150	6	1	the	the	DET
iajs-2150	6	2	practical	practical	ADJ
iajs-2150	6	3	results	result	NOUN
iajs-2150	6	4	show	show	VERB
iajs-2150	6	5	the	the	DET
iajs-2150	6	6	efficiency	efficiency	NOUN
iajs-2150	6	7	and	and	CCONJ
iajs-2150	6	8	reliability	reliability	NOUN
iajs-2150	6	9	of	of	ADP
iajs-2150	6	10	technique	technique	NOUN
iajs-2150	6	11	and	and	CCONJ
iajs-2150	6	12	easier	easy	ADJ
iajs-2150	6	13	implemented	implement	VERB
iajs-2150	6	14	than	than	ADP
iajs-2150	6	15	hpm	hpm	NOUN
iajs-2150	6	16	in	in	ADP
iajs-2150	6	17	finding	find	VERB
iajs-2150	6	18	exact	exact	ADJ
iajs-2150	6	19	solutions	solution	NOUN
iajs-2150	6	20	.	.	PUNCT
iajs-2150	7	1	finally	finally	ADV
iajs-2150	7	2	,	,	PUNCT
iajs-2150	7	3	all	all	DET
iajs-2150	7	4	algorithms	algorithm	NOUN
iajs-2150	7	5	in	in	ADP
iajs-2150	7	6	this	this	DET
iajs-2150	7	7	paper	paper	NOUN
iajs-2150	7	8	implemented	implement	VERB
iajs-2150	7	9	in	in	ADP
iajs-2150	7	10	matlab	matlab	PROPN
iajs-2150	7	11	version	version	NOUN
iajs-2150	7	12	7.12	7.12	NUM
iajs-2150	7	13	.	.	PUNCT
iajs-2150	8	1	keywords	keyword	NOUN
iajs-2150	8	2	:	:	PUNCT
iajs-2150	8	3	initial	initial	ADJ
iajs-2150	8	4	value	value	NOUN
iajs-2150	8	5	problem	problem	NOUN
iajs-2150	8	6	,	,	PUNCT
iajs-2150	8	7	autonomous	autonomous	ADJ
iajs-2150	8	8	equation	equation	NOUN
iajs-2150	8	9	,	,	PUNCT
iajs-2150	8	10	homotopy	homotopy	VERB
iajs-2150	8	11	perturbation	perturbation	NOUN
iajs-2150	8	12	method	method	NOUN
iajs-2150	8	13	,	,	PUNCT
iajs-2150	8	14	transformation	transformation	NOUN
iajs-2150	8	15	.	.	PUNCT
iajs-2150	9	1	1	1	X
iajs-2150	9	2	.	.	X
iajs-2150	9	3	introduction	introduction	NOUN
iajs-2150	9	4	the	the	DET
iajs-2150	9	5	most	most	ADJ
iajs-2150	9	6	of	of	ADP
iajs-2150	9	7	the	the	DET
iajs-2150	9	8	phenomena	phenomenon	NOUN
iajs-2150	9	9	that	that	PRON
iajs-2150	9	10	arise	arise	VERB
iajs-2150	9	11	in	in	ADP
iajs-2150	9	12	mathematical	mathematical	ADJ
iajs-2150	9	13	physics	physics	NOUN
iajs-2150	9	14	and	and	CCONJ
iajs-2150	9	15	engineering	engineering	NOUN
iajs-2150	9	16	fields	field	NOUN
iajs-2150	9	17	can	can	AUX
iajs-2150	9	18	be	be	AUX
iajs-2150	9	19	described	describe	VERB
iajs-2150	9	20	by	by	ADP
iajs-2150	9	21	partial	partial	ADJ
iajs-2150	9	22	differential	differential	ADJ
iajs-2150	9	23	equations	equation	NOUN
iajs-2150	9	24	(	(	PUNCT
iajs-2150	9	25	pdes	pde	NOUN
iajs-2150	9	26	)	)	PUNCT
iajs-2150	9	27	,	,	PUNCT
iajs-2150	9	28	for	for	ADP
iajs-2150	9	29	example	example	NOUN
iajs-2150	9	30	,	,	PUNCT
iajs-2150	9	31	in	in	ADP
iajs-2150	9	32	chemical	chemical	NOUN
iajs-2150	9	33	diffusion	diffusion	NOUN
iajs-2150	9	34	,	,	PUNCT
iajs-2150	9	35	the	the	DET
iajs-2150	9	36	heat	heat	NOUN
iajs-2150	9	37	flow	flow	NOUN
iajs-2150	9	38	,	,	PUNCT
iajs-2150	9	39	thermo	thermo	NOUN
iajs-2150	9	40	elasticity	elasticity	NOUN
iajs-2150	9	41	and	and	CCONJ
iajs-2150	9	42	the	the	DET
iajs-2150	9	43	wave	wave	NOUN
iajs-2150	9	44	propagation	propagation	NOUN
iajs-2150	9	45	phenomena	phenomenon	NOUN
iajs-2150	9	46	are	be	AUX
iajs-2150	9	47	well	well	ADV
iajs-2150	9	48	described	describe	VERB
iajs-2150	9	49	by	by	ADP
iajs-2150	9	50	pdes	pde	NOUN
iajs-2150	9	51	[	[	X
iajs-2150	9	52	1–4	1–4	NOUN
iajs-2150	9	53	]	]	X
iajs-2150	9	54	.	.	PUNCT
iajs-2150	10	1	so	so	ADV
iajs-2150	10	2	,	,	PUNCT
iajs-2150	10	3	it	it	PRON
iajs-2150	10	4	's	be	AUX
iajs-2150	10	5	important	important	ADJ
iajs-2150	10	6	tool	tool	NOUN
iajs-2150	10	7	for	for	ADP
iajs-2150	10	8	describing	describe	VERB
iajs-2150	10	9	natural	natural	ADJ
iajs-2150	10	10	phenomena	phenomenon	NOUN
iajs-2150	10	11	of	of	ADP
iajs-2150	10	12	science	science	NOUN
iajs-2150	10	13	and	and	CCONJ
iajs-2150	10	14	engineering	engineering	NOUN
iajs-2150	10	15	models	model	NOUN
iajs-2150	10	16	.	.	PUNCT
iajs-2150	11	1	most	most	ADJ
iajs-2150	11	2	of	of	ADP
iajs-2150	11	3	these	these	DET
iajs-2150	11	4	problems	problem	NOUN
iajs-2150	11	5	are	be	AUX
iajs-2150	11	6	difficult	difficult	ADJ
iajs-2150	11	7	to	to	PART
iajs-2150	11	8	solve	solve	VERB
iajs-2150	11	9	them	they	PRON
iajs-2150	11	10	analytically	analytically	ADV
iajs-2150	11	11	.	.	PUNCT
iajs-2150	12	1	so	so	ADV
iajs-2150	12	2	,	,	PUNCT
iajs-2150	12	3	the	the	DET
iajs-2150	12	4	researchers	researcher	NOUN
iajs-2150	12	5	due	due	ADJ
iajs-2150	12	6	to	to	ADP
iajs-2150	12	7	the	the	DET
iajs-2150	12	8	get	get	NOUN
iajs-2150	12	9	approximate	approximate	ADJ
iajs-2150	12	10	solution	solution	NOUN
iajs-2150	12	11	.	.	PUNCT
iajs-2150	13	1	the	the	DET
iajs-2150	13	2	importance	importance	NOUN
iajs-2150	13	3	of	of	ADP
iajs-2150	13	4	obtaining	obtain	VERB
iajs-2150	13	5	the	the	DET
iajs-2150	13	6	exact	exact	ADJ
iajs-2150	13	7	or	or	CCONJ
iajs-2150	13	8	approximate	approximate	ADJ
iajs-2150	13	9	solution	solution	NOUN
iajs-2150	13	10	of	of	ADP
iajs-2150	13	11	nonlinear	nonlinear	ADJ
iajs-2150	13	12	pdes	pde	NOUN
iajs-2150	13	13	is	be	AUX
iajs-2150	13	14	still	still	ADV
iajs-2150	13	15	a	a	DET
iajs-2150	13	16	significant	significant	ADJ
iajs-2150	13	17	problem	problem	NOUN
iajs-2150	13	18	that	that	PRON
iajs-2150	13	19	needs	need	VERB
iajs-2150	13	20	new	new	ADJ
iajs-2150	13	21	methods	method	NOUN
iajs-2150	13	22	to	to	PART
iajs-2150	13	23	get	get	VERB
iajs-2150	13	24	exact	exact	ADJ
iajs-2150	13	25	or	or	CCONJ
iajs-2150	13	26	approximate	approximate	ADJ
iajs-2150	13	27	solutions	solution	NOUN
iajs-2150	13	28	.	.	PUNCT
iajs-2150	14	1	in	in	ADP
iajs-2150	14	2	the	the	DET
iajs-2150	14	3	last	last	ADJ
iajs-2150	14	4	two	two	NUM
iajs-2150	14	5	decades	decade	NOUN
iajs-2150	14	6	,	,	PUNCT
iajs-2150	14	7	various	various	ADJ
iajs-2150	14	8	powerful	powerful	ADJ
iajs-2150	14	9	methods	method	NOUN
iajs-2150	14	10	have	have	AUX
iajs-2150	14	11	been	be	AUX
iajs-2150	14	12	proposed	propose	VERB
iajs-2150	14	13	for	for	ADP
iajs-2150	14	14	obtaining	obtain	VERB
iajs-2150	14	15	exact	exact	ADJ
iajs-2150	14	16	and	and	CCONJ
iajs-2150	14	17	approximate	approximate	ADJ
iajs-2150	14	18	analytic	analytic	ADJ
iajs-2150	14	19	solutions	solution	NOUN
iajs-2150	14	20	.	.	PUNCT
iajs-2150	15	1	among	among	ADP
iajs-2150	15	2	these	these	PRON
iajs-2150	15	3	are	be	AUX
iajs-2150	15	4	the	the	DET
iajs-2150	15	5	adomian	adomian	ADJ
iajs-2150	15	6	decomposition	decomposition	NOUN
iajs-2150	15	7	method	method	NOUN
iajs-2150	15	8	(	(	PUNCT
iajs-2150	15	9	adm	adm	PROPN
iajs-2150	15	10	)	)	PUNCT
iajs-2150	16	1	[	[	X
iajs-2150	16	2	5,6	5,6	NUM
iajs-2150	16	3	]	]	X
iajs-2150	16	4	.	.	PUNCT
iajs-2150	17	1	the	the	DET
iajs-2150	17	2	homotopy	homotopy	NOUN
iajs-2150	17	3	perturbation	perturbation	NOUN
iajs-2150	17	4	method	method	NOUN
iajs-2150	17	5	(	(	PUNCT
iajs-2150	17	6	hpm	hpm	NOUN
iajs-2150	17	7	)	)	PUNCT
iajs-2150	18	1	[	[	X
iajs-2150	18	2	7	7	NUM
iajs-2150	18	3	,	,	PUNCT
iajs-2150	18	4	8	8	NUM
iajs-2150	18	5	]	]	PUNCT
iajs-2150	18	6	.	.	PUNCT
iajs-2150	19	1	the	the	DET
iajs-2150	19	2	homotopy	homotopy	NOUN
iajs-2150	19	3	analysis	analysis	NOUN
iajs-2150	19	4	method	method	NOUN
iajs-2150	19	5	(	(	PUNCT
iajs-2150	19	6	ham	ham	PROPN
iajs-2150	19	7	)	)	PUNCT
iajs-2150	19	8	,	,	PUNCT
iajs-2150	19	9	the	the	DET
iajs-2150	19	10	differential	differential	ADJ
iajs-2150	19	11	transform	transform	NOUN
iajs-2150	19	12	method	method	NOUN
iajs-2150	19	13	,	,	PUNCT
iajs-2150	19	14	laplace	laplace	NOUN
iajs-2150	19	15	decomposition	decomposition	NOUN
iajs-2150	19	16	method	method	NOUN
iajs-2150	19	17	[	[	X
iajs-2150	19	18	9	9	NUM
iajs-2150	19	19	]	]	PUNCT
iajs-2150	19	20	.	.	PUNCT
iajs-2150	20	1	and	and	CCONJ
iajs-2150	20	2	the	the	DET
iajs-2150	20	3	variational	variational	ADJ
iajs-2150	20	4	iteration	iteration	NOUN
iajs-2150	20	5	method	method	NOUN
iajs-2150	20	6	(	(	PUNCT
iajs-2150	20	7	vim	vim	NOUN
iajs-2150	20	8	)	)	PUNCT
iajs-2150	20	9	[	[	X
iajs-2150	20	10	10,11	10,11	NOUN
iajs-2150	20	11	]	]	PUNCT
iajs-2150	20	12	.	.	PUNCT
iajs-2150	21	1	in	in	ADP
iajs-2150	21	2	this	this	DET
iajs-2150	21	3	research	research	NOUN
iajs-2150	21	4	we	we	PRON
iajs-2150	21	5	suggest	suggest	VERB
iajs-2150	21	6	new	new	ADJ
iajs-2150	21	7	technique	technique	NOUN
iajs-2150	21	8	to	to	PART
iajs-2150	21	9	solve	solve	VERB
iajs-2150	21	10	one	one	NUM
iajs-2150	21	11	of	of	ADP
iajs-2150	21	12	the	the	DET
iajs-2150	21	13	most	most	ADV
iajs-2150	21	14	important	important	ADJ
iajs-2150	21	15	of	of	ADP
iajs-2150	21	16	amplitude	amplitude	NOUN
iajs-2150	21	17	equations	equation	NOUN
iajs-2150	21	18	is	be	AUX
iajs-2150	21	19	the	the	DET
iajs-2150	21	20	autonomous	autonomous	ADJ
iajs-2150	21	21	equation	equation	NOUN
iajs-2150	21	22	which	which	PRON
iajs-2150	21	23	describes	describe	VERB
iajs-2150	21	24	the	the	DET
iajs-2150	21	25	appearance	appearance	NOUN
iajs-2150	21	26	of	of	ADP
iajs-2150	21	27	the	the	DET
iajs-2150	21	28	stripe	stripe	NOUN
iajs-2150	21	29	pattern	pattern	NOUN
iajs-2150	21	30	in	in	ADP
iajs-2150	21	31	two	two	NUM
iajs-2150	21	32	dimensional	dimensional	ADJ
iajs-2150	21	33	systems	system	NOUN
iajs-2150	21	34	.	.	PUNCT
iajs-2150	22	1	moreover	moreover	ADV
iajs-2150	22	2	,	,	PUNCT
iajs-2150	22	3	this	this	DET
iajs-2150	22	4	equation	equation	NOUN
iajs-2150	22	5	was	be	AUX
iajs-2150	22	6	applied	apply	VERB
iajs-2150	22	7	to	to	ADP
iajs-2150	22	8	a	a	DET
iajs-2150	22	9	number	number	NOUN
iajs-2150	22	10	of	of	ADP
iajs-2150	22	11	problems	problem	NOUN
iajs-2150	22	12	in	in	ADP
iajs-2150	22	13	variety	variety	NOUN
iajs-2150	22	14	systems	system	NOUN
iajs-2150	22	15	,	,	PUNCT
iajs-2150	22	16	e.g.	e.g.	ADV
iajs-2150	22	17	,	,	PUNCT
iajs-2150	22	18	rayleigh	rayleigh	PROPN
iajs-2150	22	19	-	-	PUNCT
iajs-2150	22	20	benard	benard	NOUN
iajs-2150	22	21	convection	convection	NOUN
iajs-2150	22	22	,	,	PUNCT
iajs-2150	22	23	faraday	faraday	PROPN
iajs-2150	22	24	instability	instability	PROPN
iajs-2150	22	25	,	,	PUNCT
iajs-2150	22	26	nonlinear	nonlinear	ADJ
iajs-2150	22	27	optics	optic	NOUN
iajs-2150	22	28	,	,	PUNCT
iajs-2150	22	29	chemical	chemical	ADJ
iajs-2150	22	30	reactions	reaction	NOUN
iajs-2150	22	31	and	and	CCONJ
iajs-2150	22	32	biological	biological	ADJ
iajs-2150	22	33	systems	system	NOUN
iajs-2150	22	34	.	.	PUNCT
iajs-2150	23	1	the	the	DET
iajs-2150	23	2	approximate	approximate	ADJ
iajs-2150	23	3	solutions	solution	NOUN
iajs-2150	23	4	of	of	ADP
iajs-2150	23	5	the	the	DET
iajs-2150	23	6	autonomous	autonomous	ADJ
iajs-2150	23	7	ibn	ibn	PROPN
iajs-2150	23	8	al	al	PROPN
iajs-2150	23	9	haitham	haitham	PROPN
iajs-2150	23	10	journal	journal	PROPN
iajs-2150	23	11	for	for	ADP
iajs-2150	23	12	pure	pure	ADJ
iajs-2150	23	13	and	and	CCONJ
iajs-2150	23	14	applied	apply	VERB
iajs-2150	23	15	science	science	NOUN
iajs-2150	23	16	journal	journal	PROPN
iajs-2150	23	17	homepage	homepage	NOUN
iajs-2150	23	18	:	:	PUNCT
iajs-2150	23	19	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2150	23	20	new	new	ADJ
iajs-2150	23	21	technique	technique	NOUN
iajs-2150	23	22	for	for	ADP
iajs-2150	23	23	solving	solve	VERB
iajs-2150	23	24	autonomous	autonomous	ADJ
iajs-2150	23	25	equations	equation	NOUN
iajs-2150	23	26	enadi	enadi	VERB
iajs-2150	23	27	m.	m.	NOUN
iajs-2150	23	28	o.	o.	PROPN
iajs-2150	23	29	tawfiq	tawfiq	PROPN
iajs-2150	23	30	l.n	l.n	PROPN
iajs-2150	23	31	.	.	PROPN
iajs-2150	23	32	m.	m.	PROPN
iajs-2150	23	33	luma.n.m@ihcoedu.uobaghdad.edu.iq	luma.n.m@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-2150	23	34	doi	doi	PROPN
iajs-2150	23	35	:	:	PUNCT
iajs-2150	23	36	10.30526/32.2.2150	10.30526/32.2.2150	PROPN
iajs-2150	23	37	department	department	NOUN
iajs-2150	23	38	of	of	ADP
iajs-2150	23	39	mathematics	mathematics	PROPN
iajs-2150	23	40	,	,	PUNCT
iajs-2150	23	41	college	college	NOUN
iajs-2150	23	42	of	of	ADP
iajs-2150	23	43	education	education	NOUN
iajs-2150	23	44	for	for	ADP
iajs-2150	23	45	pure	pure	ADJ
iajs-2150	23	46	science	science	NOUN
iajs-2150	23	47	ibn	ibn	PROPN
iajs-2150	23	48	al	al	PROPN
iajs-2150	23	49	-	-	PUNCT
iajs-2150	23	50	haitham	haitham	PROPN
iajs-2150	23	51	,	,	PUNCT
iajs-2150	23	52	university	university	PROPN
iajs-2150	23	53	of	of	ADP
iajs-2150	23	54	baghdad	baghdad	PROPN
iajs-2150	23	55	,	,	PUNCT
iajs-2150	23	56	baghdad	baghdad	PROPN
iajs-2150	23	57	,	,	PUNCT
iajs-2150	23	58	iraq	iraq	PROPN
iajs-2150	23	59	.	.	PUNCT
iajs-2150	24	1	myasarobaid@gmail.com	myasarobaid@gmail.com	X
iajs-2150	24	2	article	article	NOUN
iajs-2150	24	3	history	history	NOUN
iajs-2150	24	4	:	:	PUNCT
iajs-2150	24	5	received	receive	VERB
iajs-2150	24	6	9	9	NUM
iajs-2150	24	7	january	january	PROPN
iajs-2150	24	8	2019	2019	NUM
iajs-2150	24	9	,	,	PUNCT
iajs-2150	24	10	accepted	accept	VERB
iajs-2150	24	11	18	18	NUM
iajs-2150	24	12	february	february	NOUN
iajs-2150	24	13	2019	2019	NUM
iajs-2150	24	14	,	,	PUNCT
iajs-2150	24	15	publish	publish	VERB
iajs-2150	24	16	may2019	may2019	ADJ
iajs-2150	24	17	mailto:luma.n.m@ihcoedu.uobaghdad.edu.iq	mailto:luma.n.m@ihcoedu.uobaghdad.edu.iq	NOUN
iajs-2150	24	18	mailto:tibataiee92@gmail.com	mailto:tibataiee92@gmail.com	X
iajs-2150	24	19	mailto:tibataiee92@gmail.com	mailto:tibataiee92@gmail.com	PROPN
iajs-2150	24	20	mailto:tibataiee92@gmail.com	mailto:tibataiee92@gmail.com	PROPN
iajs-2150	24	21	mailto:myasarobaid@gmail.com	mailto:myasarobaid@gmail.com	PROPN
iajs-2150	24	22	mailto:tibataiee92@gmail.com	mailto:tibataiee92@gmail.com	PROPN
iajs-2150	24	23	mailto:tibataiee92@gmail.com	mailto:tibataiee92@gmail.com	PROPN
iajs-2150	24	24	mailto:tibataiee92@gmail.com	mailto:tibataiee92@gmail.com	PROPN
iajs-2150	24	25	321	321	NUM
iajs-2150	24	26	ibn	ibn	PROPN
iajs-2150	24	27	al	al	PROPN
iajs-2150	24	28	-	-	PUNCT
iajs-2150	24	29	haitham	haitham	PROPN
iajs-2150	24	30	jour	jour	X
iajs-2150	24	31	.	.	PROPN
iajs-2150	25	1	for	for	ADP
iajs-2150	25	2	pure	pure	ADJ
iajs-2150	25	3	&	&	CCONJ
iajs-2150	25	4	appl	appl	PROPN
iajs-2150	25	5	.	.	PUNCT
iajs-2150	26	1	sci	sci	PROPN
iajs-2150	26	2	.	.	PROPN
iajs-2150	26	3	32	32	NUM
iajs-2150	26	4	(	(	PUNCT
iajs-2150	26	5	2	2	NUM
iajs-2150	26	6	)	)	PUNCT
iajs-2150	26	7	2019	2019	NUM
iajs-2150	26	8	equation	equation	NOUN
iajs-2150	26	9	were	be	AUX
iajs-2150	26	10	presented	present	VERB
iajs-2150	26	11	by	by	ADP
iajs-2150	26	12	differential	differential	ADJ
iajs-2150	26	13	transformation	transformation	NOUN
iajs-2150	26	14	method	method	NOUN
iajs-2150	26	15	[	[	X
iajs-2150	26	16	12	12	NUM
iajs-2150	26	17	]	]	PUNCT
iajs-2150	26	18	.	.	PUNCT
iajs-2150	27	1	reduce	reduce	VERB
iajs-2150	27	2	differential	differential	ADJ
iajs-2150	27	3	transformation	transformation	NOUN
iajs-2150	27	4	[	[	X
iajs-2150	27	5	13	13	NUM
iajs-2150	27	6	]	]	PUNCT
iajs-2150	27	7	.	.	PUNCT
iajs-2150	28	1	in	in	ADP
iajs-2150	28	2	this	this	DET
iajs-2150	28	3	paper	paper	NOUN
iajs-2150	28	4	a	a	DET
iajs-2150	28	5	reliable	reliable	ADJ
iajs-2150	28	6	transform	transform	NOUN
iajs-2150	28	7	homotopy	homotopy	NOUN
iajs-2150	28	8	perturbation	perturbation	NOUN
iajs-2150	28	9	method	method	NOUN
iajs-2150	28	10	is	be	AUX
iajs-2150	28	11	proposed	propose	VERB
iajs-2150	28	12	and	and	CCONJ
iajs-2150	28	13	applied	apply	VERB
iajs-2150	28	14	for	for	ADP
iajs-2150	28	15	solving	solve	VERB
iajs-2150	28	16	autonomous	autonomous	ADJ
iajs-2150	28	17	equation	equation	NOUN
iajs-2150	28	18	.	.	PUNCT
iajs-2150	29	1	the	the	DET
iajs-2150	29	2	technique	technique	NOUN
iajs-2150	29	3	can	can	AUX
iajs-2150	29	4	be	be	AUX
iajs-2150	29	5	employed	employ	VERB
iajs-2150	29	6	to	to	AUX
iajs-2150	29	7	linear	linear	ADJ
iajs-2150	29	8	and	and	CCONJ
iajs-2150	29	9	nonlinear	nonlinear	ADJ
iajs-2150	29	10	problems	problem	NOUN
iajs-2150	29	11	.	.	PUNCT
iajs-2150	30	1	moreover	moreover	ADV
iajs-2150	30	2	,	,	PUNCT
iajs-2150	30	3	some	some	DET
iajs-2150	30	4	examples	example	NOUN
iajs-2150	30	5	are	be	AUX
iajs-2150	30	6	illustrative	illustrative	ADJ
iajs-2150	30	7	for	for	ADP
iajs-2150	30	8	demonstrating	demonstrate	VERB
iajs-2150	30	9	the	the	DET
iajs-2150	30	10	advantage	advantage	NOUN
iajs-2150	30	11	of	of	ADP
iajs-2150	30	12	the	the	DET
iajs-2150	30	13	technique	technique	NOUN
iajs-2150	30	14	.	.	PUNCT
iajs-2150	31	1	2	2	X
iajs-2150	31	2	.	.	X
iajs-2150	31	3	partial	partial	ADJ
iajs-2150	31	4	differential	differential	ADJ
iajs-2150	31	5	equations	equation	NOUN
iajs-2150	31	6	partial	partial	ADJ
iajs-2150	31	7	differential	differential	NOUN
iajs-2150	31	8	equations	equation	NOUN
iajs-2150	31	9	are	be	AUX
iajs-2150	31	10	a	a	DET
iajs-2150	31	11	type	type	NOUN
iajs-2150	31	12	of	of	ADP
iajs-2150	31	13	differential	differential	ADJ
iajs-2150	31	14	equation	equation	NOUN
iajs-2150	31	15	,	,	PUNCT
iajs-2150	31	16	i.e	i.e	PRON
iajs-2150	31	17	,	,	PUNCT
iajs-2150	31	18	a	a	DET
iajs-2150	31	19	relation	relation	NOUN
iajs-2150	31	20	involving	involve	VERB
iajs-2150	31	21	an	an	DET
iajs-2150	31	22	unknown	unknown	ADJ
iajs-2150	31	23	function	function	NOUN
iajs-2150	31	24	(	(	PUNCT
iajs-2150	31	25	or	or	CCONJ
iajs-2150	31	26	functions	function	NOUN
iajs-2150	31	27	say	say	VERB
iajs-2150	31	28	dependent	dependent	ADJ
iajs-2150	31	29	variables	variable	NOUN
iajs-2150	31	30	)	)	PUNCT
iajs-2150	31	31	of	of	ADP
iajs-2150	31	32	several	several	ADJ
iajs-2150	31	33	independent	independent	ADJ
iajs-2150	31	34	variables	variable	NOUN
iajs-2150	31	35	and	and	CCONJ
iajs-2150	31	36	their	their	PRON
iajs-2150	31	37	partial	partial	ADJ
iajs-2150	31	38	derivatives	derivative	NOUN
iajs-2150	31	39	with	with	ADP
iajs-2150	31	40	respect	respect	NOUN
iajs-2150	31	41	to	to	ADP
iajs-2150	31	42	those	those	DET
iajs-2150	31	43	variables	variable	NOUN
iajs-2150	31	44	.	.	PUNCT
iajs-2150	32	1	partial	partial	ADJ
iajs-2150	32	2	differential	differential	ADJ
iajs-2150	32	3	equations	equation	NOUN
iajs-2150	32	4	appear	appear	VERB
iajs-2150	32	5	frequently	frequently	ADV
iajs-2150	32	6	in	in	ADP
iajs-2150	32	7	all	all	DET
iajs-2150	32	8	areas	area	NOUN
iajs-2150	32	9	of	of	ADP
iajs-2150	32	10	physics	physics	NOUN
iajs-2150	32	11	and	and	CCONJ
iajs-2150	32	12	engineering	engineering	NOUN
iajs-2150	32	13	.	.	PUNCT
iajs-2150	33	1	in	in	ADP
iajs-2150	33	2	recent	recent	ADJ
iajs-2150	33	3	years	year	NOUN
iajs-2150	33	4	,	,	PUNCT
iajs-2150	33	5	we	we	PRON
iajs-2150	33	6	have	have	AUX
iajs-2150	33	7	seen	see	VERB
iajs-2150	33	8	a	a	DET
iajs-2150	33	9	dramatic	dramatic	ADJ
iajs-2150	33	10	increase	increase	NOUN
iajs-2150	33	11	in	in	ADP
iajs-2150	33	12	the	the	DET
iajs-2150	33	13	use	use	NOUN
iajs-2150	33	14	of	of	ADP
iajs-2150	33	15	these	these	DET
iajs-2150	33	16	equations	equation	NOUN
iajs-2150	33	17	in	in	ADP
iajs-2150	33	18	areas	area	NOUN
iajs-2150	33	19	such	such	ADJ
iajs-2150	33	20	biology	biology	NOUN
iajs-2150	33	21	,	,	PUNCT
iajs-2150	33	22	chemistry	chemistry	NOUN
iajs-2150	33	23	,	,	PUNCT
iajs-2150	33	24	chemical	chemical	NOUN
iajs-2150	33	25	engineering	engineering	NOUN
iajs-2150	33	26	,	,	PUNCT
iajs-2150	33	27	computer	computer	NOUN
iajs-2150	33	28	science	science	NOUN
iajs-2150	33	29	(	(	PUNCT
iajs-2150	33	30	partially	partially	ADV
iajs-2150	33	31	in	in	ADP
iajs-2150	33	32	relation	relation	NOUN
iajs-2150	33	33	to	to	ADP
iajs-2150	33	34	image	image	NOUN
iajs-2150	33	35	processing	processing	NOUN
iajs-2150	33	36	and	and	CCONJ
iajs-2150	33	37	graphics	graphic	NOUN
iajs-2150	33	38	)	)	PUNCT
iajs-2150	33	39	and	and	CCONJ
iajs-2150	33	40	economics	economic	NOUN
iajs-2150	33	41	.	.	PUNCT
iajs-2150	34	1	a	a	DET
iajs-2150	34	2	pde	pde	NOUN
iajs-2150	34	3	is	be	AUX
iajs-2150	34	4	called	call	VERB
iajs-2150	34	5	linear	linear	PROPN
iajs-2150	34	6	if	if	SCONJ
iajs-2150	34	7	the	the	DET
iajs-2150	34	8	power	power	NOUN
iajs-2150	34	9	of	of	ADP
iajs-2150	34	10	the	the	DET
iajs-2150	34	11	dependent	dependent	ADJ
iajs-2150	34	12	variable	variable	NOUN
iajs-2150	34	13	and	and	CCONJ
iajs-2150	34	14	each	each	DET
iajs-2150	34	15	partial	partial	ADJ
iajs-2150	34	16	derivative	derivative	NOUN
iajs-2150	34	17	contained	contain	VERB
iajs-2150	34	18	in	in	ADP
iajs-2150	34	19	the	the	DET
iajs-2150	34	20	equation	equation	NOUN
iajs-2150	34	21	is	be	AUX
iajs-2150	34	22	one	one	NUM
iajs-2150	34	23	and	and	CCONJ
iajs-2150	34	24	the	the	DET
iajs-2150	34	25	coefficients	coefficient	NOUN
iajs-2150	34	26	of	of	ADP
iajs-2150	34	27	the	the	DET
iajs-2150	34	28	dependent	dependent	ADJ
iajs-2150	34	29	variable	variable	NOUN
iajs-2150	34	30	and	and	CCONJ
iajs-2150	34	31	the	the	DET
iajs-2150	34	32	coefficients	coefficient	NOUN
iajs-2150	34	33	of	of	ADP
iajs-2150	34	34	each	each	DET
iajs-2150	34	35	partial	partial	ADJ
iajs-2150	34	36	derivative	derivative	NOUN
iajs-2150	34	37	are	be	AUX
iajs-2150	34	38	constants	constant	NOUN
iajs-2150	34	39	or	or	CCONJ
iajs-2150	34	40	independent	independent	ADJ
iajs-2150	34	41	variables	variable	NOUN
iajs-2150	34	42	.	.	PUNCT
iajs-2150	35	1	however	however	ADV
iajs-2150	35	2	,	,	PUNCT
iajs-2150	35	3	if	if	SCONJ
iajs-2150	35	4	any	any	PRON
iajs-2150	35	5	of	of	ADP
iajs-2150	35	6	these	these	DET
iajs-2150	35	7	conditions	condition	NOUN
iajs-2150	35	8	is	be	AUX
iajs-2150	35	9	not	not	PART
iajs-2150	35	10	satisfied	satisfied	ADJ
iajs-2150	35	11	,	,	PUNCT
iajs-2150	35	12	the	the	DET
iajs-2150	35	13	equation	equation	NOUN
iajs-2150	35	14	is	be	AUX
iajs-2150	35	15	called	call	VERB
iajs-2150	35	16	nonlinear	nonlinear	ADJ
iajs-2150	35	17	[	[	X
iajs-2150	35	18	4	4	NUM
iajs-2150	35	19	]	]	PUNCT
iajs-2150	35	20	.	.	PUNCT
iajs-2150	36	1	3	3	X
iajs-2150	36	2	.	.	X
iajs-2150	36	3	new	new	ADJ
iajs-2150	36	4	transform	transform	VERB
iajs-2150	36	5	new	new	ADJ
iajs-2150	36	6	transform	transform	NOUN
iajs-2150	36	7	was	be	AUX
iajs-2150	36	8	introduced	introduce	VERB
iajs-2150	36	9	by	by	ADP
iajs-2150	36	10	luma	luma	PROPN
iajs-2150	36	11	and	and	CCONJ
iajs-2150	36	12	alaa	alaa	PROPN
iajs-2150	37	1	[	[	X
iajs-2150	37	2	14	14	NUM
iajs-2150	37	3	]	]	PUNCT
iajs-2150	37	4	.	.	PUNCT
iajs-2150	38	1	to	to	PART
iajs-2150	38	2	solve	solve	VERB
iajs-2150	38	3	differential	differential	ADJ
iajs-2150	38	4	equations	equation	NOUN
iajs-2150	38	5	and	and	CCONJ
iajs-2150	38	6	engineering	engineering	NOUN
iajs-2150	38	7	problems	problem	NOUN
iajs-2150	38	8	.	.	PUNCT
iajs-2150	39	1	apart	apart	ADV
iajs-2150	39	2	from	from	ADP
iajs-2150	39	3	other	other	ADJ
iajs-2150	39	4	advantages	advantage	NOUN
iajs-2150	39	5	of	of	ADP
iajs-2150	39	6	new	new	ADJ
iajs-2150	39	7	transform	transform	NOUN
iajs-2150	39	8	(	(	PUNCT
iajs-2150	39	9	nt	not	PART
iajs-2150	39	10	)	)	PUNCT
iajs-2150	39	11	over	over	ADP
iajs-2150	39	12	other	other	ADJ
iajs-2150	39	13	integral	integral	ADJ
iajs-2150	39	14	transforms	transform	NOUN
iajs-2150	39	15	such	such	ADJ
iajs-2150	39	16	as	as	ADP
iajs-2150	39	17	accuracy	accuracy	NOUN
iajs-2150	39	18	and	and	CCONJ
iajs-2150	39	19	simplicity	simplicity	NOUN
iajs-2150	39	20	,	,	PUNCT
iajs-2150	39	21	in	in	ADP
iajs-2150	39	22	[	[	PUNCT
iajs-2150	39	23	15	15	NUM
iajs-2150	39	24	]	]	PUNCT
iajs-2150	39	25	.	.	PUNCT
iajs-2150	39	26	consist	consist	VERB
iajs-2150	39	27	a	a	DET
iajs-2150	39	28	very	very	ADV
iajs-2150	39	29	interesting	interesting	ADJ
iajs-2150	39	30	fact	fact	NOUN
iajs-2150	39	31	about	about	ADP
iajs-2150	39	32	this	this	DET
iajs-2150	39	33	transform	transform	NOUN
iajs-2150	39	34	.	.	PUNCT
iajs-2150	40	1	the	the	DET
iajs-2150	40	2	new	new	ADJ
iajs-2150	40	3	transform	transform	NOUN
iajs-2150	40	4	of	of	ADP
iajs-2150	40	5	a	a	DET
iajs-2150	40	6	function	function	NOUN
iajs-2150	40	7	f(t	f(t	PROPN
iajs-2150	40	8	)	)	PUNCT
iajs-2150	40	9	,	,	PUNCT
iajs-2150	40	10	defined	define	VERB
iajs-2150	40	11	by	by	ADP
iajs-2150	40	12	:	:	PUNCT
iajs-2150	40	13	(	(	PUNCT
iajs-2150	40	14	̅	̅	NOUN
iajs-2150	40	15	)	)	PUNCT
iajs-2150	40	16	*	*	PUNCT
iajs-2150	40	17	(	(	PUNCT
iajs-2150	40	18	)	)	PUNCT
iajs-2150	40	19	+	+	CCONJ
iajs-2150	40	20	∫	∫	PROPN
iajs-2150	40	21	.	.	PUNCT
iajs-2150	40	22	/	/	PUNCT
iajs-2150	41	1	(	(	PUNCT
iajs-2150	41	2	)	)	PUNCT
iajs-2150	41	3	here	here	ADV
iajs-2150	41	4	some	some	DET
iajs-2150	41	5	basic	basic	ADJ
iajs-2150	41	6	properties	property	NOUN
iajs-2150	41	7	of	of	ADP
iajs-2150	41	8	the	the	DET
iajs-2150	41	9	nt	not	PART
iajs-2150	41	10	are	be	AUX
iajs-2150	41	11	introduced	introduce	VERB
iajs-2150	41	12	:	:	PUNCT
iajs-2150	41	13	if	if	SCONJ
iajs-2150	41	14	a	a	DET
iajs-2150	41	15	,	,	PUNCT
iajs-2150	41	16	b	b	NOUN
iajs-2150	41	17	are	be	AUX
iajs-2150	41	18	constants	constant	NOUN
iajs-2150	41	19	,	,	PUNCT
iajs-2150	41	20	f(t	f(t	PROPN
iajs-2150	41	21	)	)	PUNCT
iajs-2150	41	22	and	and	CCONJ
iajs-2150	41	23	g(t	g(t	PROPN
iajs-2150	41	24	)	)	PUNCT
iajs-2150	41	25	are	be	AUX
iajs-2150	41	26	functions	function	NOUN
iajs-2150	41	27	having	have	VERB
iajs-2150	41	28	nt	not	PART
iajs-2150	41	29	,	,	PUNCT
iajs-2150	41	30	then	then	ADV
iajs-2150	41	31	:	:	PUNCT
iajs-2150	41	32	1	1	X
iajs-2150	41	33	.	.	X
iajs-2150	41	34	linearity	linearity	NOUN
iajs-2150	41	35	property	property	NOUN
iajs-2150	41	36	:	:	PUNCT
iajs-2150	41	37	*	*	PUNCT
iajs-2150	41	38	(	(	PUNCT
iajs-2150	41	39	)	)	PUNCT
iajs-2150	41	40	(	(	PUNCT
iajs-2150	41	41	)	)	PUNCT
iajs-2150	42	1	+	+	NUM
iajs-2150	42	2	*	*	PUNCT
iajs-2150	42	3	(	(	PUNCT
iajs-2150	42	4	)	)	PUNCT
iajs-2150	42	5	+	+	NUM
iajs-2150	42	6	*	*	PUNCT
iajs-2150	42	7	(	(	PUNCT
iajs-2150	42	8	)	)	PUNCT
iajs-2150	42	9	+	+	CCONJ
iajs-2150	42	10	;	;	PUNCT
iajs-2150	42	11	a	a	DET
iajs-2150	42	12	,	,	PUNCT
iajs-2150	42	13	b	b	NOUN
iajs-2150	42	14	ϵ	ϵ	X
iajs-2150	42	15	r	r	NOUN
iajs-2150	42	16	2	2	NUM
iajs-2150	42	17	.	.	PUNCT
iajs-2150	42	18	convolution	convolution	NOUN
iajs-2150	42	19	property	property	NOUN
iajs-2150	42	20	:	:	PUNCT
iajs-2150	42	21	(	(	PUNCT
iajs-2150	42	22	)	)	PUNCT
iajs-2150	42	23	(	(	PUNCT
iajs-2150	42	24	)	)	PUNCT
iajs-2150	42	25	∫	∫	PROPN
iajs-2150	42	26	(	(	PUNCT
iajs-2150	42	27	)	)	PUNCT
iajs-2150	42	28	(	(	PUNCT
iajs-2150	42	29	)	)	PUNCT
iajs-2150	42	30	(	(	PUNCT
iajs-2150	42	31	)	)	PUNCT
iajs-2150	42	32	3	3	X
iajs-2150	42	33	.	.	X
iajs-2150	42	34	*	*	PUNCT
iajs-2150	43	1	+	+	NOUN
iajs-2150	43	2	4	4	X
iajs-2150	43	3	.	.	X
iajs-2150	43	4	differentiation	differentiation	NOUN
iajs-2150	43	5	property	property	NOUN
iajs-2150	43	6	:	:	PUNCT
iajs-2150	44	1	*	*	PUNCT
iajs-2150	45	1	+	+	PUNCT
iajs-2150	45	2	(	(	PUNCT
iajs-2150	45	3	*	*	PUNCT
iajs-2150	45	4	+	+	PUNCT
iajs-2150	45	5	(	(	PUNCT
iajs-2150	45	6	)	)	PUNCT
iajs-2150	45	7	)	)	PUNCT
iajs-2150	45	8	for	for	SCONJ
iajs-2150	45	9	more	more	ADJ
iajs-2150	45	10	details	detail	NOUN
iajs-2150	45	11	see	see	VERB
iajs-2150	45	12	[	[	X
iajs-2150	45	13	14,15	14,15	NUM
iajs-2150	45	14	]	]	PUNCT
iajs-2150	45	15	.	.	PUNCT
iajs-2150	46	1	4	4	X
iajs-2150	46	2	.	.	X
iajs-2150	46	3	basic	basic	ADJ
iajs-2150	46	4	idea	idea	NOUN
iajs-2150	46	5	of	of	ADP
iajs-2150	46	6	suggested	suggest	VERB
iajs-2150	46	7	method	method	NOUN
iajs-2150	46	8	to	to	PART
iajs-2150	46	9	illustrate	illustrate	VERB
iajs-2150	46	10	the	the	DET
iajs-2150	46	11	ideas	idea	NOUN
iajs-2150	46	12	of	of	ADP
iajs-2150	46	13	new	new	ADJ
iajs-2150	46	14	transform	transform	NOUN
iajs-2150	46	15	homotopy	homotopy	NOUN
iajs-2150	46	16	perturbation	perturbation	NOUN
iajs-2150	46	17	method	method	NOUN
iajs-2150	46	18	(	(	PUNCT
iajs-2150	46	19	nthpm	nthpm	NOUN
iajs-2150	46	20	)	)	PUNCT
iajs-2150	46	21	firstly	firstly	ADV
iajs-2150	46	22	rewrite	rewrite	VERB
iajs-2150	46	23	the	the	DET
iajs-2150	46	24	initial	initial	ADJ
iajs-2150	46	25	value	value	NOUN
iajs-2150	46	26	problem	problem	NOUN
iajs-2150	46	27	in	in	ADP
iajs-2150	46	28	autonomous	autonomous	ADJ
iajs-2150	46	29	equation	equation	NOUN
iajs-2150	46	30	in	in	ADP
iajs-2150	46	31	the	the	DET
iajs-2150	46	32	form	form	NOUN
iajs-2150	46	33	:	:	PUNCT
iajs-2150	46	34	(	(	PUNCT
iajs-2150	46	35	)	)	PUNCT
iajs-2150	46	36	(	(	PUNCT
iajs-2150	46	37	)	)	PUNCT
iajs-2150	46	38	(	(	PUNCT
iajs-2150	46	39	)	)	PUNCT
iajs-2150	46	40	(	(	PUNCT
iajs-2150	46	41	)	)	PUNCT
iajs-2150	46	42	(	(	PUNCT
iajs-2150	46	43	)	)	PUNCT
iajs-2150	46	44	with	with	ADP
iajs-2150	46	45	the	the	DET
iajs-2150	46	46	initial	initial	ADJ
iajs-2150	46	47	condition	condition	NOUN
iajs-2150	46	48	:	:	PUNCT
iajs-2150	46	49	(	(	PUNCT
iajs-2150	46	50	)	)	PUNCT
iajs-2150	46	51	(	(	PUNCT
iajs-2150	46	52	)	)	PUNCT
iajs-2150	46	53	(	(	PUNCT
iajs-2150	46	54	)	)	PUNCT
iajs-2150	46	55	where	where	SCONJ
iajs-2150	46	56	and	and	CCONJ
iajs-2150	46	57	are	be	AUX
iajs-2150	46	58	real	real	ADJ
iajs-2150	46	59	numbers	number	NOUN
iajs-2150	46	60	and	and	CCONJ
iajs-2150	46	61	c	c	PROPN
iajs-2150	46	62	and	and	CCONJ
iajs-2150	46	63	n	n	PROPN
iajs-2150	46	64	are	be	AUX
iajs-2150	46	65	positive	positive	ADJ
iajs-2150	46	66	integers	integer	NOUN
iajs-2150	46	67	.	.	PUNCT
iajs-2150	47	1	taking	take	VERB
iajs-2150	47	2	new	new	ADJ
iajs-2150	47	3	transformation	transformation	NOUN
iajs-2150	47	4	on	on	ADP
iajs-2150	47	5	both	both	DET
iajs-2150	47	6	sides	side	NOUN
iajs-2150	47	7	of	of	ADP
iajs-2150	47	8	the	the	DET
iajs-2150	47	9	equation	equation	NOUN
iajs-2150	47	10	(	(	PUNCT
iajs-2150	47	11	3	3	NUM
iajs-2150	47	12	)	)	PUNCT
iajs-2150	47	13	and	and	CCONJ
iajs-2150	47	14	using	use	VERB
iajs-2150	47	15	the	the	DET
iajs-2150	47	16	linearity	linearity	NOUN
iajs-2150	47	17	property	property	NOUN
iajs-2150	47	18	of	of	ADP
iajs-2150	47	19	the	the	DET
iajs-2150	47	20	new	new	ADJ
iajs-2150	47	21	transform	transform	NOUN
iajs-2150	47	22	gives	give	VERB
iajs-2150	47	23	:	:	PUNCT
iajs-2150	47	24	*	*	PUNCT
iajs-2150	47	25	(	(	PUNCT
iajs-2150	47	26	)	)	PUNCT
iajs-2150	47	27	+	+	NUM
iajs-2150	47	28	*	*	PUNCT
iajs-2150	47	29	(	(	PUNCT
iajs-2150	47	30	)	)	PUNCT
iajs-2150	47	31	+	+	NUM
iajs-2150	47	32	*	*	PUNCT
iajs-2150	47	33	(	(	PUNCT
iajs-2150	47	34	)	)	PUNCT
iajs-2150	47	35	+	+	NUM
iajs-2150	47	36	*	*	PUNCT
iajs-2150	47	37	(	(	PUNCT
iajs-2150	47	38	)	)	PUNCT
iajs-2150	47	39	+	+	CCONJ
iajs-2150	47	40	(	(	PUNCT
iajs-2150	47	41	)	)	PUNCT
iajs-2150	47	42	by	by	ADP
iajs-2150	47	43	applying	apply	VERB
iajs-2150	47	44	the	the	DET
iajs-2150	47	45	differentiation	differentiation	NOUN
iajs-2150	47	46	property	property	NOUN
iajs-2150	47	47	of	of	ADP
iajs-2150	47	48	new	new	ADJ
iajs-2150	47	49	transform	transform	NOUN
iajs-2150	47	50	,	,	PUNCT
iajs-2150	47	51	we	we	PRON
iajs-2150	47	52	have	have	AUX
iajs-2150	47	53	:	:	PUNCT
iajs-2150	47	54	321	321	NUM
iajs-2150	47	55	ibn	ibn	PROPN
iajs-2150	47	56	al	al	PROPN
iajs-2150	47	57	-	-	PUNCT
iajs-2150	47	58	haitham	haitham	PROPN
iajs-2150	47	59	jour	jour	X
iajs-2150	47	60	.	.	PROPN
iajs-2150	48	1	for	for	ADP
iajs-2150	48	2	pure	pure	ADJ
iajs-2150	48	3	&	&	CCONJ
iajs-2150	48	4	appl	appl	PROPN
iajs-2150	48	5	.	.	PUNCT
iajs-2150	49	1	sci	sci	PROPN
iajs-2150	49	2	.	.	PROPN
iajs-2150	49	3	32	32	NUM
iajs-2150	49	4	(	(	PUNCT
iajs-2150	49	5	2	2	NUM
iajs-2150	49	6	)	)	PUNCT
iajs-2150	49	7	2019	2019	NUM
iajs-2150	49	8	*	*	PUNCT
iajs-2150	49	9	(	(	PUNCT
iajs-2150	49	10	)	)	PUNCT
iajs-2150	49	11	+	+	CCONJ
iajs-2150	49	12	(	(	PUNCT
iajs-2150	49	13	)	)	PUNCT
iajs-2150	49	14	*	*	PUNCT
iajs-2150	49	15	(	(	PUNCT
iajs-2150	49	16	)	)	PUNCT
iajs-2150	49	17	+	+	NUM
iajs-2150	49	18	*	*	PUNCT
iajs-2150	49	19	(	(	PUNCT
iajs-2150	49	20	)	)	PUNCT
iajs-2150	49	21	+	+	NUM
iajs-2150	49	22	*	*	PUNCT
iajs-2150	49	23	(	(	PUNCT
iajs-2150	49	24	)	)	PUNCT
iajs-2150	49	25	+	+	CCONJ
iajs-2150	49	26	(	(	PUNCT
iajs-2150	49	27	)	)	PUNCT
iajs-2150	49	28	thus	thus	ADV
iajs-2150	49	29	,	,	PUNCT
iajs-2150	49	30	we	we	PRON
iajs-2150	49	31	get	get	VERB
iajs-2150	49	32	:	:	PUNCT
iajs-2150	49	33	(	(	PUNCT
iajs-2150	49	34	)	)	PUNCT
iajs-2150	49	35	*	*	PUNCT
iajs-2150	49	36	(	(	PUNCT
iajs-2150	49	37	)	)	PUNCT
iajs-2150	49	38	+	+	NUM
iajs-2150	49	39	(	(	PUNCT
iajs-2150	49	40	)	)	PUNCT
iajs-2150	49	41	*	*	PUNCT
iajs-2150	49	42	(	(	PUNCT
iajs-2150	49	43	)	)	PUNCT
iajs-2150	49	44	+	+	NUM
iajs-2150	49	45	*	*	PUNCT
iajs-2150	49	46	(	(	PUNCT
iajs-2150	49	47	)	)	PUNCT
iajs-2150	49	48	+	+	CCONJ
iajs-2150	49	49	(	(	PUNCT
iajs-2150	49	50	)	)	PUNCT
iajs-2150	49	51	*	*	PUNCT
iajs-2150	49	52	(	(	PUNCT
iajs-2150	49	53	)	)	PUNCT
iajs-2150	49	54	+	+	NUM
iajs-2150	49	55	(	(	PUNCT
iajs-2150	49	56	)	)	PUNCT
iajs-2150	49	57	*	*	PUNCT
iajs-2150	49	58	(	(	PUNCT
iajs-2150	49	59	)	)	PUNCT
iajs-2150	49	60	+	+	NUM
iajs-2150	49	61	*	*	PUNCT
iajs-2150	49	62	(	(	PUNCT
iajs-2150	49	63	)	)	PUNCT
iajs-2150	49	64	+	+	CCONJ
iajs-2150	49	65	(	(	PUNCT
iajs-2150	49	66	)	)	PUNCT
iajs-2150	49	67	taking	take	VERB
iajs-2150	49	68	the	the	DET
iajs-2150	49	69	inverse	inverse	NOUN
iajs-2150	49	70	of	of	ADP
iajs-2150	49	71	new	new	ADJ
iajs-2150	49	72	transform	transform	NOUN
iajs-2150	49	73	on	on	ADP
iajs-2150	49	74	equation	equation	NOUN
iajs-2150	49	75	(	(	PUNCT
iajs-2150	49	76	6	6	NUM
iajs-2150	49	77	)	)	PUNCT
iajs-2150	49	78	,	,	PUNCT
iajs-2150	49	79	we	we	PRON
iajs-2150	49	80	obtain	obtain	VERB
iajs-2150	49	81	:	:	PUNCT
iajs-2150	49	82	(	(	PUNCT
iajs-2150	49	83	)	)	PUNCT
iajs-2150	49	84	2	2	NUM
iajs-2150	49	85	(	(	PUNCT
iajs-2150	49	86	)	)	PUNCT
iajs-2150	49	87	3	3	NUM
iajs-2150	49	88	.	.	PUNCT
iajs-2150	50	1	*	*	PUNCT
iajs-2150	50	2	(	(	PUNCT
iajs-2150	50	3	)	)	PUNCT
iajs-2150	50	4	+	+	NUM
iajs-2150	50	5	*	*	PUNCT
iajs-2150	50	6	(	(	PUNCT
iajs-2150	50	7	)	)	PUNCT
iajs-2150	50	8	+	+	X
iajs-2150	50	9	/	/	SYM
iajs-2150	50	10	(	(	PUNCT
iajs-2150	50	11	)	)	PUNCT
iajs-2150	50	12	in	in	ADP
iajs-2150	50	13	the	the	DET
iajs-2150	50	14	hpm	hpm	NOUN
iajs-2150	50	15	,	,	PUNCT
iajs-2150	50	16	the	the	DET
iajs-2150	50	17	basic	basic	ADJ
iajs-2150	50	18	assumption	assumption	NOUN
iajs-2150	50	19	is	be	AUX
iajs-2150	50	20	that	that	SCONJ
iajs-2150	50	21	the	the	DET
iajs-2150	50	22	solutions	solution	NOUN
iajs-2150	50	23	can	can	AUX
iajs-2150	50	24	be	be	AUX
iajs-2150	50	25	written	write	VERB
iajs-2150	50	26	as	as	ADP
iajs-2150	50	27	a	a	DET
iajs-2150	50	28	power	power	NOUN
iajs-2150	50	29	series	series	NOUN
iajs-2150	50	30	in	in	ADP
iajs-2150	50	31	p	p	PROPN
iajs-2150	50	32	as	as	ADP
iajs-2150	50	33	:	:	PUNCT
iajs-2150	50	34	(	(	PUNCT
iajs-2150	50	35	)	)	PUNCT
iajs-2150	50	36	∑	∑	PUNCT
iajs-2150	50	37	(	(	PUNCT
iajs-2150	50	38	)	)	PUNCT
iajs-2150	50	39	(	(	PUNCT
iajs-2150	50	40	)	)	PUNCT
iajs-2150	50	41	and	and	CCONJ
iajs-2150	50	42	the	the	DET
iajs-2150	50	43	nonlinear	nonlinear	ADJ
iajs-2150	50	44	term	term	NOUN
iajs-2150	50	45	n(u	n(u	PROPN
iajs-2150	50	46	)	)	PUNCT
iajs-2150	51	1	=	=	PRON
iajs-2150	51	2	,	,	PUNCT
iajs-2150	51	3	can	can	AUX
iajs-2150	51	4	be	be	AUX
iajs-2150	51	5	presented	present	VERB
iajs-2150	51	6	by	by	ADP
iajs-2150	51	7	an	an	DET
iajs-2150	51	8	infinite	infinite	ADJ
iajs-2150	51	9	series	series	NOUN
iajs-2150	51	10	as	as	ADP
iajs-2150	51	11	:	:	PUNCT
iajs-2150	51	12	(	(	PUNCT
iajs-2150	51	13	)	)	PUNCT
iajs-2150	51	14	∑	∑	PUNCT
iajs-2150	51	15	(	(	PUNCT
iajs-2150	51	16	)	)	PUNCT
iajs-2150	51	17	(	(	PUNCT
iajs-2150	51	18	)	)	PUNCT
iajs-2150	51	19	where	where	SCONJ
iajs-2150	51	20	p	p	X
iajs-2150	51	21	[	[	X
iajs-2150	51	22	0,1	0,1	NUM
iajs-2150	51	23	]	]	PUNCT
iajs-2150	51	24	is	be	AUX
iajs-2150	51	25	an	an	DET
iajs-2150	51	26	embedding	embed	VERB
iajs-2150	51	27	parameter	parameter	NOUN
iajs-2150	51	28	.	.	PUNCT
iajs-2150	52	1	hn	hn	PROPN
iajs-2150	52	2	(	(	PUNCT
iajs-2150	52	3	u	u	NOUN
iajs-2150	52	4	)	)	PUNCT
iajs-2150	52	5	is	be	AUX
iajs-2150	52	6	he	he	PRON
iajs-2150	52	7	polynomials	polynomial	VERB
iajs-2150	52	8	[	[	X
iajs-2150	52	9	16,17	16,17	NUM
iajs-2150	52	10	]	]	PUNCT
iajs-2150	52	11	.	.	PUNCT
iajs-2150	53	1	that	that	PRON
iajs-2150	53	2	can	can	AUX
iajs-2150	53	3	be	be	AUX
iajs-2150	53	4	generated	generate	VERB
iajs-2150	53	5	by	by	ADP
iajs-2150	53	6	formula	formula	NOUN
iajs-2150	53	7	given	give	VERB
iajs-2150	53	8	below	below	ADV
iajs-2150	53	9	:	:	PUNCT
iajs-2150	53	10	(	(	PUNCT
iajs-2150	53	11	)	)	PUNCT
iajs-2150	54	1	0	0	NUM
iajs-2150	54	2	.(∑	.(∑	PROPN
iajs-2150	54	3	(	(	PUNCT
iajs-2150	54	4	)	)	PUNCT
iajs-2150	54	5	)	)	PUNCT
iajs-2150	54	6	/1	/1	PROPN
iajs-2150	54	7	(	(	PUNCT
iajs-2150	54	8	)	)	PUNCT
iajs-2150	54	9	substituting	substitute	VERB
iajs-2150	54	10	(	(	PUNCT
iajs-2150	54	11	10	10	NUM
iajs-2150	54	12	)	)	PUNCT
iajs-2150	54	13	and	and	CCONJ
iajs-2150	54	14	(	(	PUNCT
iajs-2150	54	15	11	11	NUM
iajs-2150	54	16	)	)	PUNCT
iajs-2150	54	17	in	in	ADP
iajs-2150	54	18	(	(	PUNCT
iajs-2150	54	19	9	9	NUM
iajs-2150	54	20	)	)	PUNCT
iajs-2150	54	21	,	,	PUNCT
iajs-2150	54	22	we	we	PRON
iajs-2150	54	23	get	get	VERB
iajs-2150	54	24	:	:	PUNCT
iajs-2150	54	25	∑	∑	PUNCT
iajs-2150	54	26	(	(	PUNCT
iajs-2150	54	27	)	)	PUNCT
iajs-2150	54	28	2	2	NUM
iajs-2150	54	29	(	(	PUNCT
iajs-2150	54	30	)	)	PUNCT
iajs-2150	54	31	3	3	X
iajs-2150	54	32	.	.	PUNCT
iajs-2150	55	1	*	*	PUNCT
iajs-2150	55	2	∑	∑	PROPN
iajs-2150	55	3	(	(	PUNCT
iajs-2150	55	4	)	)	PUNCT
iajs-2150	55	5	+	+	CCONJ
iajs-2150	55	6	*	*	PUNCT
iajs-2150	55	7	∑	∑	PUNCT
iajs-2150	55	8	+	+	ADJ
iajs-2150	55	9	/	/	SYM
iajs-2150	55	10	(	(	PUNCT
iajs-2150	55	11	)	)	PUNCT
iajs-2150	55	12	which	which	PRON
iajs-2150	55	13	is	be	AUX
iajs-2150	55	14	the	the	DET
iajs-2150	55	15	coupling	coupling	NOUN
iajs-2150	55	16	of	of	ADP
iajs-2150	55	17	the	the	DET
iajs-2150	55	18	new	new	ADJ
iajs-2150	55	19	transform	transform	NOUN
iajs-2150	55	20	and	and	CCONJ
iajs-2150	55	21	the	the	DET
iajs-2150	55	22	hpm	hpm	NOUN
iajs-2150	55	23	using	use	VERB
iajs-2150	55	24	he	he	PRON
iajs-2150	55	25	’s	’s	PART
iajs-2150	55	26	polynomials	polynomial	NOUN
iajs-2150	55	27	.	.	PUNCT
iajs-2150	56	1	comparing	compare	VERB
iajs-2150	56	2	the	the	DET
iajs-2150	56	3	coefficient	coefficient	NOUN
iajs-2150	56	4	of	of	ADP
iajs-2150	56	5	like	like	ADP
iajs-2150	56	6	powers	power	NOUN
iajs-2150	56	7	of	of	ADP
iajs-2150	56	8	p	p	NOUN
iajs-2150	56	9	,	,	PUNCT
iajs-2150	56	10	the	the	DET
iajs-2150	56	11	following	follow	VERB
iajs-2150	56	12	approximations	approximation	NOUN
iajs-2150	56	13	are	be	AUX
iajs-2150	56	14	obtained	obtain	VERB
iajs-2150	56	15	:	:	PUNCT
iajs-2150	56	16	(	(	PUNCT
iajs-2150	56	17	)	)	PUNCT
iajs-2150	56	18	{	{	PUNCT
iajs-2150	56	19	(	(	PUNCT
iajs-2150	56	20	)	)	PUNCT
iajs-2150	56	21	}	}	PUNCT
iajs-2150	56	22	(	(	PUNCT
iajs-2150	56	23	)	)	PUNCT
iajs-2150	56	24	.	.	PUNCT
iajs-2150	57	1	{	{	PUNCT
iajs-2150	57	2	(	(	PUNCT
iajs-2150	57	3	)	)	PUNCT
iajs-2150	57	4	}	}	PUNCT
iajs-2150	57	5	*	*	PUNCT
iajs-2150	58	1	+	+	PUNCT
iajs-2150	58	2	/	/	SYM
iajs-2150	58	3	(	(	PUNCT
iajs-2150	58	4	)	)	PUNCT
iajs-2150	58	5	.	.	PUNCT
iajs-2150	59	1	{	{	PUNCT
iajs-2150	59	2	(	(	PUNCT
iajs-2150	59	3	)	)	PUNCT
iajs-2150	59	4	}	}	PUNCT
iajs-2150	59	5	*	*	PUNCT
iajs-2150	60	1	+	+	PUNCT
iajs-2150	60	2	/	/	SYM
iajs-2150	60	3	(	(	PUNCT
iajs-2150	60	4	)	)	PUNCT
iajs-2150	60	5	.	.	PUNCT
iajs-2150	61	1	{	{	PUNCT
iajs-2150	61	2	(	(	PUNCT
iajs-2150	61	3	)	)	PUNCT
iajs-2150	61	4	}	}	PUNCT
iajs-2150	61	5	*	*	PUNCT
iajs-2150	62	1	+	+	PUNCT
iajs-2150	62	2	/	/	SYM
iajs-2150	62	3	(	(	PUNCT
iajs-2150	62	4	)	)	PUNCT
iajs-2150	62	5	proceeding	proceed	VERB
iajs-2150	62	6	in	in	ADP
iajs-2150	62	7	this	this	DET
iajs-2150	62	8	same	same	ADJ
iajs-2150	62	9	manner	manner	NOUN
iajs-2150	62	10	,	,	PUNCT
iajs-2150	62	11	the	the	DET
iajs-2150	62	12	rest	rest	NOUN
iajs-2150	62	13	of	of	ADP
iajs-2150	62	14	the	the	DET
iajs-2150	62	15	components	component	NOUN
iajs-2150	62	16	un(x	un(x	PROPN
iajs-2150	62	17	,	,	PUNCT
iajs-2150	62	18	t	t	PROPN
iajs-2150	62	19	)	)	PUNCT
iajs-2150	62	20	can	can	AUX
iajs-2150	62	21	be	be	AUX
iajs-2150	62	22	completely	completely	ADV
iajs-2150	62	23	obtained	obtain	VERB
iajs-2150	62	24	and	and	CCONJ
iajs-2150	62	25	the	the	DET
iajs-2150	62	26	series	series	NOUN
iajs-2150	62	27	solution	solution	NOUN
iajs-2150	62	28	is	be	AUX
iajs-2150	62	29	thus	thus	ADV
iajs-2150	62	30	entirely	entirely	ADV
iajs-2150	62	31	determined	determine	VERB
iajs-2150	62	32	.	.	PUNCT
iajs-2150	63	1	finally	finally	ADV
iajs-2150	63	2	,	,	PUNCT
iajs-2150	63	3	we	we	PRON
iajs-2150	63	4	approximate	approximate	VERB
iajs-2150	63	5	the	the	DET
iajs-2150	63	6	analytical	analytical	ADJ
iajs-2150	63	7	solution	solution	NOUN
iajs-2150	63	8	(	(	PUNCT
iajs-2150	63	9	)	)	PUNCT
iajs-2150	63	10	by	by	ADP
iajs-2150	63	11	truncated	truncated	ADJ
iajs-2150	63	12	series	series	NOUN
iajs-2150	63	13	:	:	PUNCT
iajs-2150	63	14	(	(	PUNCT
iajs-2150	63	15	)	)	PUNCT
iajs-2150	63	16	(	(	PUNCT
iajs-2150	63	17	∑	∑	PUNCT
iajs-2150	63	18	(	(	PUNCT
iajs-2150	63	19	)	)	PUNCT
iajs-2150	63	20	)	)	PUNCT
iajs-2150	64	1	(	(	PUNCT
iajs-2150	64	2	)	)	PUNCT
iajs-2150	64	3	the	the	DET
iajs-2150	64	4	above	above	ADJ
iajs-2150	64	5	series	series	NOUN
iajs-2150	64	6	solutions	solution	NOUN
iajs-2150	64	7	generally	generally	ADV
iajs-2150	64	8	converge	converge	VERB
iajs-2150	64	9	very	very	ADV
iajs-2150	64	10	rapidly	rapidly	ADV
iajs-2150	64	11	.	.	PUNCT
iajs-2150	65	1	321	321	NUM
iajs-2150	65	2	ibn	ibn	PROPN
iajs-2150	65	3	al	al	PROPN
iajs-2150	65	4	-	-	PUNCT
iajs-2150	65	5	haitham	haitham	PROPN
iajs-2150	65	6	jour	jour	X
iajs-2150	65	7	.	.	PROPN
iajs-2150	65	8	for	for	ADP
iajs-2150	65	9	pure	pure	ADJ
iajs-2150	65	10	&	&	CCONJ
iajs-2150	65	11	appl	appl	PROPN
iajs-2150	65	12	.	.	PUNCT
iajs-2150	66	1	sci	sci	PROPN
iajs-2150	66	2	.	.	PROPN
iajs-2150	66	3	32	32	NUM
iajs-2150	66	4	(	(	PUNCT
iajs-2150	66	5	2	2	NUM
iajs-2150	66	6	)	)	PUNCT
iajs-2150	66	7	2019	2019	NUM
iajs-2150	66	8	5	5	NUM
iajs-2150	66	9	.	.	PUNCT
iajs-2150	66	10	illustrative	illustrative	ADJ
iajs-2150	66	11	examples	example	NOUN
iajs-2150	66	12	in	in	ADP
iajs-2150	66	13	this	this	DET
iajs-2150	66	14	section	section	NOUN
iajs-2150	66	15	,	,	PUNCT
iajs-2150	66	16	some	some	DET
iajs-2150	66	17	initial	initial	ADJ
iajs-2150	66	18	value	value	NOUN
iajs-2150	66	19	problems	problem	NOUN
iajs-2150	66	20	are	be	AUX
iajs-2150	66	21	presented	present	VERB
iajs-2150	66	22	to	to	PART
iajs-2150	66	23	show	show	VERB
iajs-2150	66	24	the	the	DET
iajs-2150	66	25	advantages	advantage	NOUN
iajs-2150	66	26	of	of	ADP
iajs-2150	66	27	the	the	DET
iajs-2150	66	28	proposed	propose	VERB
iajs-2150	66	29	method	method	NOUN
iajs-2150	66	30	which	which	PRON
iajs-2150	66	31	can	can	AUX
iajs-2150	66	32	be	be	AUX
iajs-2150	66	33	applied	apply	VERB
iajs-2150	66	34	to	to	ADP
iajs-2150	66	35	non	non	ADJ
iajs-2150	66	36	-	-	ADJ
iajs-2150	66	37	linear	linear	ADJ
iajs-2150	66	38	problem	problem	NOUN
iajs-2150	66	39	.	.	PUNCT
iajs-2150	67	1	example	example	NOUN
iajs-2150	67	2	1	1	NUM
iajs-2150	67	3	consider	consider	VERB
iajs-2150	67	4	linear	linear	ADJ
iajs-2150	67	5	2	2	NUM
iajs-2150	67	6	nd	nd	NOUN
iajs-2150	67	7	order	order	NOUN
iajs-2150	67	8	autonomous	autonomous	ADJ
iajs-2150	67	9	equation	equation	NOUN
iajs-2150	67	10	:	:	PUNCT
iajs-2150	67	11	(	(	PUNCT
iajs-2150	67	12	)	)	PUNCT
iajs-2150	67	13	(	(	PUNCT
iajs-2150	67	14	)	)	PUNCT
iajs-2150	67	15	(	(	PUNCT
iajs-2150	67	16	)	)	PUNCT
iajs-2150	67	17	(	(	PUNCT
iajs-2150	67	18	)	)	PUNCT
iajs-2150	67	19	with	with	ADP
iajs-2150	67	20	the	the	DET
iajs-2150	67	21	initial	initial	ADJ
iajs-2150	67	22	condition	condition	NOUN
iajs-2150	67	23	:	:	PUNCT
iajs-2150	67	24	(	(	PUNCT
iajs-2150	67	25	)	)	PUNCT
iajs-2150	67	26	(	(	PUNCT
iajs-2150	67	27	)	)	PUNCT
iajs-2150	67	28	taking	take	VERB
iajs-2150	67	29	the	the	DET
iajs-2150	67	30	new	new	ADJ
iajs-2150	67	31	transform	transform	NOUN
iajs-2150	67	32	on	on	ADP
iajs-2150	67	33	both	both	DET
iajs-2150	67	34	sides	side	NOUN
iajs-2150	67	35	of	of	ADP
iajs-2150	67	36	equation	equation	NOUN
iajs-2150	67	37	(	(	PUNCT
iajs-2150	67	38	16	16	NUM
iajs-2150	67	39	)	)	PUNCT
iajs-2150	67	40	subject	subject	NOUN
iajs-2150	67	41	to	to	ADP
iajs-2150	67	42	the	the	DET
iajs-2150	67	43	initial	initial	ADJ
iajs-2150	67	44	condition	condition	NOUN
iajs-2150	67	45	(	(	PUNCT
iajs-2150	67	46	17	17	NUM
iajs-2150	67	47	)	)	PUNCT
iajs-2150	67	48	,	,	PUNCT
iajs-2150	67	49	we	we	PRON
iajs-2150	67	50	have	have	VERB
iajs-2150	67	51	:	:	PUNCT
iajs-2150	67	52	*	*	PUNCT
iajs-2150	67	53	(	(	PUNCT
iajs-2150	67	54	)	)	PUNCT
iajs-2150	68	1	+	+	NUM
iajs-2150	68	2	*	*	PUNCT
iajs-2150	68	3	(	(	PUNCT
iajs-2150	68	4	)	)	PUNCT
iajs-2150	68	5	+	+	NUM
iajs-2150	68	6	*	*	PUNCT
iajs-2150	68	7	(	(	PUNCT
iajs-2150	68	8	)	)	PUNCT
iajs-2150	68	9	+	+	CCONJ
iajs-2150	68	10	(	(	PUNCT
iajs-2150	68	11	)	)	PUNCT
iajs-2150	68	12	by	by	ADP
iajs-2150	68	13	applying	apply	VERB
iajs-2150	68	14	the	the	DET
iajs-2150	68	15	differentiation	differentiation	NOUN
iajs-2150	68	16	property	property	NOUN
iajs-2150	68	17	of	of	ADP
iajs-2150	68	18	new	new	ADJ
iajs-2150	68	19	transform	transform	NOUN
iajs-2150	68	20	,	,	PUNCT
iajs-2150	68	21	we	we	PRON
iajs-2150	68	22	get	get	VERB
iajs-2150	68	23	:	:	PUNCT
iajs-2150	68	24	*	*	PUNCT
iajs-2150	68	25	(	(	PUNCT
iajs-2150	68	26	)	)	PUNCT
iajs-2150	68	27	+	+	NUM
iajs-2150	68	28	(	(	PUNCT
iajs-2150	68	29	)	)	PUNCT
iajs-2150	68	30	*	*	PUNCT
iajs-2150	68	31	(	(	PUNCT
iajs-2150	68	32	)	)	PUNCT
iajs-2150	68	33	+	+	NUM
iajs-2150	68	34	*	*	PUNCT
iajs-2150	68	35	(	(	PUNCT
iajs-2150	68	36	)	)	PUNCT
iajs-2150	68	37	+	+	CCONJ
iajs-2150	68	38	(	(	PUNCT
iajs-2150	68	39	)	)	PUNCT
iajs-2150	68	40	thus	thus	ADV
iajs-2150	68	41	,	,	PUNCT
iajs-2150	68	42	we	we	PRON
iajs-2150	68	43	have	have	AUX
iajs-2150	68	44	(	(	PUNCT
iajs-2150	68	45	)	)	PUNCT
iajs-2150	68	46	*	*	PUNCT
iajs-2150	68	47	(	(	PUNCT
iajs-2150	68	48	)	)	PUNCT
iajs-2150	68	49	+	+	NUM
iajs-2150	68	50	*	*	PUNCT
iajs-2150	68	51	(	(	PUNCT
iajs-2150	68	52	)	)	PUNCT
iajs-2150	68	53	+	+	CCONJ
iajs-2150	68	54	(	(	PUNCT
iajs-2150	68	55	)	)	PUNCT
iajs-2150	68	56	*	*	PUNCT
iajs-2150	68	57	(	(	PUNCT
iajs-2150	68	58	)	)	PUNCT
iajs-2150	68	59	+	+	NUM
iajs-2150	68	60	*	*	PUNCT
iajs-2150	68	61	(	(	PUNCT
iajs-2150	68	62	)	)	PUNCT
iajs-2150	68	63	+	+	CCONJ
iajs-2150	68	64	(	(	PUNCT
iajs-2150	68	65	)	)	PUNCT
iajs-2150	68	66	taking	take	VERB
iajs-2150	68	67	the	the	DET
iajs-2150	68	68	inverse	inverse	NOUN
iajs-2150	68	69	new	new	ADJ
iajs-2150	68	70	transform	transform	NOUN
iajs-2150	68	71	on	on	ADP
iajs-2150	68	72	equation	equation	NOUN
iajs-2150	68	73	(	(	PUNCT
iajs-2150	68	74	21	21	NUM
iajs-2150	68	75	)	)	PUNCT
iajs-2150	68	76	,	,	PUNCT
iajs-2150	68	77	we	we	PRON
iajs-2150	68	78	get	get	VERB
iajs-2150	68	79	:	:	PUNCT
iajs-2150	68	80	(	(	PUNCT
iajs-2150	68	81	)	)	PUNCT
iajs-2150	68	82	2	2	NUM
iajs-2150	68	83	3	3	NUM
iajs-2150	68	84	.	.	PUNCT
iajs-2150	69	1	*	*	PUNCT
iajs-2150	69	2	(	(	PUNCT
iajs-2150	69	3	)	)	PUNCT
iajs-2150	69	4	+	+	X
iajs-2150	69	5	/	/	SYM
iajs-2150	69	6	(	(	PUNCT
iajs-2150	69	7	)	)	PUNCT
iajs-2150	69	8	now	now	ADV
iajs-2150	69	9	,	,	PUNCT
iajs-2150	69	10	applying	apply	VERB
iajs-2150	69	11	the	the	DET
iajs-2150	69	12	hpm	hpm	NOUN
iajs-2150	69	13	,	,	PUNCT
iajs-2150	69	14	we	we	PRON
iajs-2150	69	15	get	get	VERB
iajs-2150	69	16	∑	∑	PUNCT
iajs-2150	69	17	(	(	PUNCT
iajs-2150	69	18	)	)	PUNCT
iajs-2150	69	19	.	.	PUNCT
iajs-2150	70	1	*	*	PUNCT
iajs-2150	70	2	∑	∑	PROPN
iajs-2150	70	3	(	(	PUNCT
iajs-2150	70	4	)	)	PUNCT
iajs-2150	70	5	+	+	X
iajs-2150	70	6	/	/	SYM
iajs-2150	70	7	(	(	PUNCT
iajs-2150	70	8	)	)	PUNCT
iajs-2150	70	9	comparing	compare	VERB
iajs-2150	70	10	the	the	DET
iajs-2150	70	11	coefficients	coefficient	NOUN
iajs-2150	70	12	of	of	ADP
iajs-2150	70	13	like	like	ADP
iajs-2150	70	14	powers	power	NOUN
iajs-2150	70	15	of	of	ADP
iajs-2150	70	16	p	p	NOUN
iajs-2150	70	17	,	,	PUNCT
iajs-2150	70	18	we	we	PRON
iajs-2150	70	19	have	have	VERB
iajs-2150	70	20	:	:	PUNCT
iajs-2150	70	21	(	(	PUNCT
iajs-2150	70	22	)	)	PUNCT
iajs-2150	70	23	(	(	PUNCT
iajs-2150	70	24	)	)	PUNCT
iajs-2150	70	25	.	.	PUNCT
iajs-2150	71	1	{	{	PUNCT
iajs-2150	71	2	(	(	PUNCT
iajs-2150	71	3	)	)	PUNCT
iajs-2150	71	4	}	}	PUNCT
iajs-2150	71	5	/	/	PUNCT
iajs-2150	71	6	.	.	PUNCT
iajs-2150	72	1	*	*	PUNCT
iajs-2150	72	2	+	+	ADJ
iajs-2150	72	3	/	/	SYM
iajs-2150	72	4	.	.	PUNCT
iajs-2150	73	1	(	(	PUNCT
iajs-2150	73	2	)	)	PUNCT
iajs-2150	73	3	/	/	SYM
iajs-2150	73	4	(	(	PUNCT
iajs-2150	73	5	)	)	PUNCT
iajs-2150	73	6	.	.	PUNCT
iajs-2150	74	1	{	{	PUNCT
iajs-2150	74	2	(	(	PUNCT
iajs-2150	74	3	)	)	PUNCT
iajs-2150	74	4	}	}	PUNCT
iajs-2150	74	5	/	/	PUNCT
iajs-2150	74	6	.	.	PUNCT
iajs-2150	75	1	*	*	PUNCT
iajs-2150	75	2	+	+	ADJ
iajs-2150	75	3	/	/	SYM
iajs-2150	75	4	.	.	PUNCT
iajs-2150	76	1	(	(	PUNCT
iajs-2150	76	2	)	)	PUNCT
iajs-2150	76	3	/	/	SYM
iajs-2150	76	4	(	(	PUNCT
iajs-2150	76	5	)	)	PUNCT
iajs-2150	76	6	.	.	PUNCT
iajs-2150	77	1	(	(	PUNCT
iajs-2150	77	2	)	)	PUNCT
iajs-2150	77	3	/	/	SYM
iajs-2150	77	4	(	(	PUNCT
iajs-2150	77	5	)	)	PUNCT
iajs-2150	77	6	(	(	PUNCT
iajs-2150	77	7	{	{	PUNCT
iajs-2150	77	8	(	(	PUNCT
iajs-2150	77	9	)	)	PUNCT
iajs-2150	77	10	}	}	PUNCT
iajs-2150	77	11	)	)	PUNCT
iajs-2150	78	1	(	(	PUNCT
iajs-2150	78	2	*	*	PUNCT
iajs-2150	78	3	+	+	X
iajs-2150	78	4	)	)	PUNCT
iajs-2150	78	5	(	(	PUNCT
iajs-2150	78	6	(	(	PUNCT
iajs-2150	78	7	)	)	PUNCT
iajs-2150	78	8	)	)	PUNCT
iajs-2150	78	9	.	.	PUNCT
iajs-2150	79	1	(	(	PUNCT
iajs-2150	79	2	)	)	PUNCT
iajs-2150	79	3	/	/	PUNCT
iajs-2150	79	4	.	.	PUNCT
iajs-2150	80	1	(	(	PUNCT
iajs-2150	80	2	)	)	PUNCT
iajs-2150	80	3	/	/	SYM
iajs-2150	80	4	and	and	CCONJ
iajs-2150	80	5	so	so	ADV
iajs-2150	80	6	on	on	ADV
iajs-2150	80	7	,	,	PUNCT
iajs-2150	80	8	therefore	therefore	ADV
iajs-2150	80	9	the	the	DET
iajs-2150	80	10	solution	solution	NOUN
iajs-2150	80	11	u(x	u(x	VERB
iajs-2150	80	12	,	,	PUNCT
iajs-2150	80	13	t	t	NOUN
iajs-2150	80	14	)	)	PUNCT
iajs-2150	80	15	is	be	AUX
iajs-2150	80	16	given	give	VERB
iajs-2150	80	17	by	by	ADP
iajs-2150	80	18	:	:	PUNCT
iajs-2150	80	19	321	321	NUM
iajs-2150	80	20	ibn	ibn	PROPN
iajs-2150	80	21	al	al	PROPN
iajs-2150	80	22	-	-	PUNCT
iajs-2150	80	23	haitham	haitham	PROPN
iajs-2150	80	24	jour	jour	X
iajs-2150	80	25	.	.	PROPN
iajs-2150	80	26	for	for	ADP
iajs-2150	80	27	pure	pure	ADJ
iajs-2150	80	28	&	&	CCONJ
iajs-2150	80	29	appl	appl	PROPN
iajs-2150	80	30	.	.	PUNCT
iajs-2150	81	1	sci	sci	PROPN
iajs-2150	81	2	.	.	PROPN
iajs-2150	81	3	32	32	NUM
iajs-2150	81	4	(	(	PUNCT
iajs-2150	81	5	2	2	NUM
iajs-2150	81	6	)	)	PUNCT
iajs-2150	81	7	2019	2019	NUM
iajs-2150	81	8	(	(	PUNCT
iajs-2150	81	9	)	)	PUNCT
iajs-2150	81	10	.	.	PUNCT
iajs-2150	81	11	/	/	PUNCT
iajs-2150	81	12	.	.	PUNCT
iajs-2150	82	1	(	(	PUNCT
iajs-2150	82	2	)	)	PUNCT
iajs-2150	82	3	(	(	PUNCT
iajs-2150	82	4	)	)	PUNCT
iajs-2150	82	5	(	(	PUNCT
iajs-2150	82	6	)	)	PUNCT
iajs-2150	82	7	/	/	SYM
iajs-2150	82	8	(	(	PUNCT
iajs-2150	82	9	25	25	NUM
iajs-2150	82	10	)	)	PUNCT
iajs-2150	82	11	example	example	NOUN
iajs-2150	82	12	2	2	NUM
iajs-2150	82	13	consider	consider	VERB
iajs-2150	82	14	nonlinear	nonlinear	ADJ
iajs-2150	82	15	2	2	NUM
iajs-2150	82	16	nd	nd	NOUN
iajs-2150	82	17	order	order	NOUN
iajs-2150	82	18	autonomous	autonomous	ADJ
iajs-2150	82	19	equation	equation	NOUN
iajs-2150	82	20	:	:	PUNCT
iajs-2150	82	21	(	(	PUNCT
iajs-2150	82	22	)	)	PUNCT
iajs-2150	82	23	(	(	PUNCT
iajs-2150	82	24	)	)	PUNCT
iajs-2150	82	25	(	(	PUNCT
iajs-2150	82	26	)	)	PUNCT
iajs-2150	82	27	(	(	PUNCT
iajs-2150	82	28	)	)	PUNCT
iajs-2150	82	29	(	(	PUNCT
iajs-2150	82	30	)	)	PUNCT
iajs-2150	82	31	with	with	ADP
iajs-2150	82	32	the	the	DET
iajs-2150	82	33	initial	initial	ADJ
iajs-2150	82	34	condition	condition	NOUN
iajs-2150	82	35	:	:	PUNCT
iajs-2150	82	36	(	(	PUNCT
iajs-2150	82	37	)	)	PUNCT
iajs-2150	82	38	(	(	PUNCT
iajs-2150	82	39	)	)	PUNCT
iajs-2150	82	40	where	where	SCONJ
iajs-2150	82	41	is	be	AUX
iajs-2150	82	42	arbitrary	arbitrary	ADJ
iajs-2150	82	43	constant	constant	ADJ
iajs-2150	82	44	.	.	PUNCT
iajs-2150	83	1	taking	take	VERB
iajs-2150	83	2	the	the	DET
iajs-2150	83	3	new	new	ADJ
iajs-2150	83	4	transform	transform	NOUN
iajs-2150	83	5	on	on	ADP
iajs-2150	83	6	both	both	DET
iajs-2150	83	7	sides	side	NOUN
iajs-2150	83	8	of	of	ADP
iajs-2150	83	9	equation	equation	NOUN
iajs-2150	83	10	(	(	PUNCT
iajs-2150	83	11	23	23	NUM
iajs-2150	83	12	)	)	PUNCT
iajs-2150	83	13	subject	subject	NOUN
iajs-2150	83	14	to	to	ADP
iajs-2150	83	15	the	the	DET
iajs-2150	83	16	initial	initial	ADJ
iajs-2150	83	17	condition	condition	NOUN
iajs-2150	83	18	(	(	PUNCT
iajs-2150	83	19	24	24	NUM
iajs-2150	83	20	)	)	PUNCT
iajs-2150	83	21	,	,	PUNCT
iajs-2150	83	22	we	we	PRON
iajs-2150	83	23	have	have	VERB
iajs-2150	83	24	:	:	PUNCT
iajs-2150	83	25	*	*	PUNCT
iajs-2150	83	26	(	(	PUNCT
iajs-2150	83	27	)	)	PUNCT
iajs-2150	84	1	+	+	NUM
iajs-2150	84	2	*	*	PUNCT
iajs-2150	84	3	(	(	PUNCT
iajs-2150	84	4	)	)	PUNCT
iajs-2150	84	5	+	+	NUM
iajs-2150	84	6	*	*	PUNCT
iajs-2150	84	7	(	(	PUNCT
iajs-2150	84	8	)	)	PUNCT
iajs-2150	84	9	+	+	NUM
iajs-2150	84	10	*	*	PUNCT
iajs-2150	84	11	(	(	PUNCT
iajs-2150	84	12	)	)	PUNCT
iajs-2150	84	13	+	+	CCONJ
iajs-2150	84	14	(	(	PUNCT
iajs-2150	84	15	)	)	PUNCT
iajs-2150	84	16	*	*	PUNCT
iajs-2150	84	17	(	(	PUNCT
iajs-2150	84	18	)	)	PUNCT
iajs-2150	84	19	+	+	NUM
iajs-2150	84	20	(	(	PUNCT
iajs-2150	84	21	)	)	PUNCT
iajs-2150	84	22	*	*	PUNCT
iajs-2150	84	23	(	(	PUNCT
iajs-2150	84	24	)	)	PUNCT
iajs-2150	84	25	+	+	NUM
iajs-2150	84	26	*	*	PUNCT
iajs-2150	84	27	(	(	PUNCT
iajs-2150	84	28	)	)	PUNCT
iajs-2150	84	29	+	+	NUM
iajs-2150	84	30	*	*	PUNCT
iajs-2150	84	31	(	(	PUNCT
iajs-2150	84	32	)	)	PUNCT
iajs-2150	84	33	+	+	CCONJ
iajs-2150	84	34	(	(	PUNCT
iajs-2150	84	35	)	)	PUNCT
iajs-2150	84	36	(	(	PUNCT
iajs-2150	84	37	)	)	PUNCT
iajs-2150	84	38	*	*	PUNCT
iajs-2150	84	39	(	(	PUNCT
iajs-2150	84	40	)	)	PUNCT
iajs-2150	84	41	+	+	NUM
iajs-2150	84	42	*	*	PUNCT
iajs-2150	84	43	(	(	PUNCT
iajs-2150	84	44	)	)	PUNCT
iajs-2150	84	45	+	+	NUM
iajs-2150	84	46	*	*	PUNCT
iajs-2150	84	47	(	(	PUNCT
iajs-2150	84	48	)	)	PUNCT
iajs-2150	84	49	+	+	CCONJ
iajs-2150	84	50	(	(	PUNCT
iajs-2150	84	51	)	)	PUNCT
iajs-2150	84	52	*	*	PUNCT
iajs-2150	84	53	(	(	PUNCT
iajs-2150	84	54	)	)	PUNCT
iajs-2150	84	55	+	+	NUM
iajs-2150	84	56	*	*	PUNCT
iajs-2150	84	57	(	(	PUNCT
iajs-2150	84	58	)	)	PUNCT
iajs-2150	84	59	+	+	NUM
iajs-2150	84	60	*	*	PUNCT
iajs-2150	84	61	(	(	PUNCT
iajs-2150	84	62	)	)	PUNCT
iajs-2150	84	63	+	+	CCONJ
iajs-2150	84	64	(	(	PUNCT
iajs-2150	84	65	)	)	PUNCT
iajs-2150	84	66	taking	take	VERB
iajs-2150	84	67	the	the	DET
iajs-2150	84	68	inverse	inverse	NOUN
iajs-2150	84	69	new	new	ADJ
iajs-2150	84	70	transform	transform	NOUN
iajs-2150	84	71	on	on	ADP
iajs-2150	84	72	equation	equation	NOUN
iajs-2150	84	73	(	(	PUNCT
iajs-2150	84	74	28	28	NUM
iajs-2150	84	75	)	)	PUNCT
iajs-2150	84	76	,	,	PUNCT
iajs-2150	84	77	we	we	PRON
iajs-2150	84	78	obtain	obtain	VERB
iajs-2150	84	79	:	:	PUNCT
iajs-2150	84	80	(	(	PUNCT
iajs-2150	84	81	)	)	PUNCT
iajs-2150	84	82	2	2	NUM
iajs-2150	84	83	3	3	NUM
iajs-2150	84	84	.	.	PUNCT
iajs-2150	85	1	*	*	PUNCT
iajs-2150	85	2	(	(	PUNCT
iajs-2150	85	3	)	)	PUNCT
iajs-2150	85	4	+	+	NUM
iajs-2150	85	5	*	*	PUNCT
iajs-2150	85	6	(	(	PUNCT
iajs-2150	85	7	)	)	PUNCT
iajs-2150	85	8	+	+	X
iajs-2150	85	9	/	/	SYM
iajs-2150	85	10	(	(	PUNCT
iajs-2150	85	11	)	)	PUNCT
iajs-2150	85	12	now	now	ADV
iajs-2150	85	13	,	,	PUNCT
iajs-2150	85	14	applying	apply	VERB
iajs-2150	85	15	the	the	DET
iajs-2150	85	16	hpm	hpm	NOUN
iajs-2150	85	17	,	,	PUNCT
iajs-2150	85	18	we	we	PRON
iajs-2150	85	19	get	get	VERB
iajs-2150	85	20	:	:	PUNCT
iajs-2150	85	21	∑	∑	PUNCT
iajs-2150	85	22	(	(	PUNCT
iajs-2150	85	23	)	)	PUNCT
iajs-2150	85	24	.	.	PUNCT
iajs-2150	86	1	*	*	PUNCT
iajs-2150	86	2	∑	∑	PROPN
iajs-2150	86	3	(	(	PUNCT
iajs-2150	86	4	)	)	PUNCT
iajs-2150	86	5	+	+	CCONJ
iajs-2150	86	6	*	*	PUNCT
iajs-2150	86	7	∑	∑	PUNCT
iajs-2150	86	8	+	+	ADJ
iajs-2150	86	9	/	/	SYM
iajs-2150	86	10	(	(	PUNCT
iajs-2150	86	11	)	)	PUNCT
iajs-2150	86	12	comparing	compare	VERB
iajs-2150	86	13	the	the	DET
iajs-2150	86	14	coefficients	coefficient	NOUN
iajs-2150	86	15	of	of	ADP
iajs-2150	86	16	like	like	ADP
iajs-2150	86	17	powers	power	NOUN
iajs-2150	86	18	of	of	ADP
iajs-2150	86	19	p	p	NOUN
iajs-2150	86	20	,	,	PUNCT
iajs-2150	86	21	we	we	PRON
iajs-2150	86	22	have	have	VERB
iajs-2150	86	23	:	:	PUNCT
iajs-2150	86	24	(	(	PUNCT
iajs-2150	86	25	)	)	PUNCT
iajs-2150	86	26	(	(	PUNCT
iajs-2150	86	27	)	)	PUNCT
iajs-2150	86	28	.	.	PUNCT
iajs-2150	87	1	{	{	PUNCT
iajs-2150	87	2	(	(	PUNCT
iajs-2150	87	3	)	)	PUNCT
iajs-2150	87	4	}	}	PUNCT
iajs-2150	87	5	*	*	PUNCT
iajs-2150	87	6	(	(	PUNCT
iajs-2150	87	7	)	)	PUNCT
iajs-2150	87	8	+	+	X
iajs-2150	87	9	/	/	SYM
iajs-2150	87	10	(	(	PUNCT
iajs-2150	87	11	)	)	PUNCT
iajs-2150	87	12	.	.	PUNCT
iajs-2150	88	1	{	{	PUNCT
iajs-2150	88	2	(	(	PUNCT
iajs-2150	88	3	)	)	PUNCT
iajs-2150	88	4	}	}	PUNCT
iajs-2150	88	5	*	*	PUNCT
iajs-2150	88	6	(	(	PUNCT
iajs-2150	88	7	)	)	PUNCT
iajs-2150	88	8	+	+	X
iajs-2150	88	9	/	/	SYM
iajs-2150	88	10	(	(	PUNCT
iajs-2150	88	11	)	)	PUNCT
iajs-2150	88	12	(	(	PUNCT
iajs-2150	88	13	)	)	PUNCT
iajs-2150	88	14	.	.	PUNCT
iajs-2150	89	1	{	{	PUNCT
iajs-2150	89	2	(	(	PUNCT
iajs-2150	89	3	)	)	PUNCT
iajs-2150	89	4	}	}	PUNCT
iajs-2150	89	5	*	*	PUNCT
iajs-2150	89	6	(	(	PUNCT
iajs-2150	89	7	)	)	PUNCT
iajs-2150	89	8	+	+	X
iajs-2150	89	9	/	/	SYM
iajs-2150	89	10	therefore	therefore	ADV
iajs-2150	89	11	the	the	DET
iajs-2150	89	12	solution	solution	NOUN
iajs-2150	89	13	u(x	u(x	NOUN
iajs-2150	89	14	,	,	PUNCT
iajs-2150	89	15	t	t	PROPN
iajs-2150	89	16	)	)	PUNCT
iajs-2150	89	17	is	be	AUX
iajs-2150	89	18	given	give	VERB
iajs-2150	89	19	by	by	ADP
iajs-2150	89	20	:	:	PUNCT
iajs-2150	89	21	(	(	PUNCT
iajs-2150	89	22	)	)	PUNCT
iajs-2150	89	23	(	(	PUNCT
iajs-2150	89	24	(	(	PUNCT
iajs-2150	89	25	)	)	PUNCT
iajs-2150	89	26	(	(	PUNCT
iajs-2150	89	27	)	)	PUNCT
iajs-2150	89	28	(	(	PUNCT
iajs-2150	89	29	)	)	PUNCT
iajs-2150	89	30	=	=	SYM
iajs-2150	89	31	(	(	PUNCT
iajs-2150	89	32	)	)	PUNCT
iajs-2150	89	33	there	there	PRON
iajs-2150	89	34	is	be	VERB
iajs-2150	89	35	many	many	ADJ
iajs-2150	89	36	research	research	NOUN
iajs-2150	89	37	study	study	NOUN
iajs-2150	89	38	the	the	DET
iajs-2150	89	39	convergence	convergence	NOUN
iajs-2150	89	40	of	of	ADP
iajs-2150	89	41	methods	method	NOUN
iajs-2150	90	1	such	such	ADJ
iajs-2150	90	2	[	[	X
iajs-2150	90	3	18	18	NUM
iajs-2150	90	4	-	-	SYM
iajs-2150	90	5	25	25	NUM
iajs-2150	90	6	]	]	PUNCT
iajs-2150	90	7	.	.	PUNCT
iajs-2150	91	1	but	but	CCONJ
iajs-2150	91	2	here	here	ADV
iajs-2150	91	3	we	we	PRON
iajs-2150	91	4	introduce	introduce	VERB
iajs-2150	91	5	other	other	ADJ
iajs-2150	91	6	manner	manner	NOUN
iajs-2150	91	7	illustrated	illustrate	VERB
iajs-2150	91	8	in	in	ADP
iajs-2150	91	9	the	the	DET
iajs-2150	91	10	following	follow	VERB
iajs-2150	91	11	section	section	NOUN
iajs-2150	91	12	.	.	PUNCT
iajs-2150	92	1	6	6	X
iajs-2150	92	2	.	.	X
iajs-2150	92	3	the	the	DET
iajs-2150	92	4	convergence	convergence	NOUN
iajs-2150	92	5	of	of	ADP
iajs-2150	92	6	the	the	DET
iajs-2150	92	7	solution	solution	NOUN
iajs-2150	92	8	now	now	ADV
iajs-2150	92	9	,	,	PUNCT
iajs-2150	92	10	we	we	PRON
iajs-2150	92	11	need	need	VERB
iajs-2150	92	12	to	to	PART
iajs-2150	92	13	show	show	VERB
iajs-2150	92	14	the	the	DET
iajs-2150	92	15	convergence	convergence	NOUN
iajs-2150	92	16	of	of	ADP
iajs-2150	92	17	series	series	NOUN
iajs-2150	92	18	form	form	NOUN
iajs-2150	92	19	to	to	ADP
iajs-2150	92	20	the	the	DET
iajs-2150	92	21	exact	exact	ADJ
iajs-2150	92	22	form	form	NOUN
iajs-2150	92	23	as	as	ADP
iajs-2150	92	24	the	the	DET
iajs-2150	92	25	following	following	NOUN
iajs-2150	92	26	.	.	PUNCT
iajs-2150	93	1	321	321	NUM
iajs-2150	93	2	ibn	ibn	PROPN
iajs-2150	93	3	al	al	PROPN
iajs-2150	93	4	-	-	PUNCT
iajs-2150	93	5	haitham	haitham	PROPN
iajs-2150	93	6	jour	jour	X
iajs-2150	93	7	.	.	PROPN
iajs-2150	93	8	for	for	ADP
iajs-2150	93	9	pure	pure	ADJ
iajs-2150	93	10	&	&	CCONJ
iajs-2150	93	11	appl	appl	PROPN
iajs-2150	93	12	.	.	PUNCT
iajs-2150	94	1	sci	sci	PROPN
iajs-2150	94	2	.	.	PROPN
iajs-2150	94	3	32	32	NUM
iajs-2150	94	4	(	(	PUNCT
iajs-2150	94	5	2	2	NUM
iajs-2150	94	6	)	)	PUNCT
iajs-2150	94	7	2019	2019	NUM
iajs-2150	94	8	lemma	lemma	PROPN
iajs-2150	94	9	1	1	NUM
iajs-2150	94	10	if	if	SCONJ
iajs-2150	94	11	f	f	PRON
iajs-2150	94	12	be	be	VERB
iajs-2150	94	13	continues	continue	VERB
iajs-2150	94	14	function	function	NOUN
iajs-2150	94	15	then	then	ADV
iajs-2150	94	16	:	:	PUNCT
iajs-2150	94	17	∫	∫	PROPN
iajs-2150	94	18	(	(	PUNCT
iajs-2150	94	19	)	)	PUNCT
iajs-2150	94	20	(	(	PUNCT
iajs-2150	94	21	)	)	PUNCT
iajs-2150	94	22	proof	proof	NOUN
iajs-2150	94	23	suppose	suppose	VERB
iajs-2150	94	24	that	that	SCONJ
iajs-2150	94	25	:	:	PUNCT
iajs-2150	94	26	∫	∫	PROPN
iajs-2150	94	27	(	(	PUNCT
iajs-2150	94	28	)	)	PUNCT
iajs-2150	94	29	(	(	PUNCT
iajs-2150	94	30	)	)	PUNCT
iajs-2150	94	31	assume	assume	VERB
iajs-2150	94	32	that	that	SCONJ
iajs-2150	94	33	then	then	ADV
iajs-2150	94	34	then	then	ADV
iajs-2150	94	35	:	:	PUNCT
iajs-2150	94	36	∫	∫	PROPN
iajs-2150	94	37	(	(	PUNCT
iajs-2150	94	38	)	)	PUNCT
iajs-2150	94	39	∫	∫	PROPN
iajs-2150	94	40	(	(	PUNCT
iajs-2150	94	41	)	)	PUNCT
iajs-2150	94	42	∫	∫	PROPN
iajs-2150	94	43	(	(	PUNCT
iajs-2150	94	44	)	)	PUNCT
iajs-2150	94	45	,	,	PUNCT
iajs-2150	94	46	(	(	PUNCT
iajs-2150	94	47	)	)	PUNCT
iajs-2150	94	48	|	|	ADV
iajs-2150	94	49	,	,	PUNCT
iajs-2150	94	50	(	(	PUNCT
iajs-2150	94	51	)	)	PUNCT
iajs-2150	94	52	(	(	PUNCT
iajs-2150	94	53	)	)	PUNCT
iajs-2150	94	54	(	(	PUNCT
iajs-2150	94	55	)	)	PUNCT
iajs-2150	94	56	(	(	PUNCT
iajs-2150	94	57	)	)	PUNCT
iajs-2150	94	58	(	(	PUNCT
iajs-2150	94	59	)	)	PUNCT
iajs-2150	94	60	∫	∫	PROPN
iajs-2150	94	61	(	(	PUNCT
iajs-2150	94	62	)	)	PUNCT
iajs-2150	94	63	(	(	PUNCT
iajs-2150	94	64	)	)	PUNCT
iajs-2150	94	65	lemma	lemma	PROPN
iajs-2150	94	66	2	2	NUM
iajs-2150	94	67	let	let	VERB
iajs-2150	94	68	is	be	AUX
iajs-2150	94	69	new	new	ADJ
iajs-2150	94	70	transform	transform	NOUN
iajs-2150	94	71	.	.	PUNCT
iajs-2150	95	1	then	then	ADV
iajs-2150	95	2	:	:	PUNCT
iajs-2150	95	3	.	.	PUNCT
iajs-2150	96	1	{	{	PUNCT
iajs-2150	96	2	*	*	PUNCT
iajs-2150	96	3	(	(	PUNCT
iajs-2150	96	4	)	)	PUNCT
iajs-2150	96	5	+	+	ADJ
iajs-2150	96	6	}	}	PUNCT
iajs-2150	96	7	/	/	SYM
iajs-2150	96	8	(	(	PUNCT
iajs-2150	96	9	)	)	PUNCT
iajs-2150	96	10	proof	proof	NOUN
iajs-2150	96	11	using	use	VERB
iajs-2150	96	12	property	property	NOUN
iajs-2150	96	13	2	2	NUM
iajs-2150	96	14	and	and	CCONJ
iajs-2150	96	15	3	3	NUM
iajs-2150	96	16	of	of	ADP
iajs-2150	96	17	nt	not	PART
iajs-2150	96	18	,	,	PUNCT
iajs-2150	96	19	and	and	CCONJ
iajs-2150	96	20	lemma	lemma	PROPN
iajs-2150	96	21	(	(	PUNCT
iajs-2150	96	22	1	1	NUM
iajs-2150	96	23	)	)	PUNCT
iajs-2150	96	24	,	,	PUNCT
iajs-2150	96	25	we	we	PRON
iajs-2150	96	26	have	have	VERB
iajs-2150	96	27	4	4	NUM
iajs-2150	96	28	{	{	PUNCT
iajs-2150	96	29	*	*	PUNCT
iajs-2150	96	30	(	(	PUNCT
iajs-2150	96	31	)	)	PUNCT
iajs-2150	96	32	+	+	ADJ
iajs-2150	96	33	}	}	SYM
iajs-2150	96	34	5	5	NUM
iajs-2150	96	35	4	4	NUM
iajs-2150	96	36	{	{	PUNCT
iajs-2150	96	37	*	*	PUNCT
iajs-2150	97	1	+	+	PUNCT
iajs-2150	97	2	*	*	PUNCT
iajs-2150	97	3	(	(	PUNCT
iajs-2150	97	4	)	)	PUNCT
iajs-2150	97	5	+	+	ADJ
iajs-2150	97	6	}	}	SYM
iajs-2150	97	7	5	5	NUM
iajs-2150	97	8	(	(	PUNCT
iajs-2150	97	9	{	{	PUNCT
iajs-2150	97	10	*	*	PUNCT
iajs-2150	97	11	(	(	PUNCT
iajs-2150	97	12	)	)	PUNCT
iajs-2150	97	13	+	+	ADJ
iajs-2150	97	14	}	}	PUNCT
iajs-2150	97	15	)	)	PUNCT
iajs-2150	97	16	(	(	PUNCT
iajs-2150	97	17	(	(	PUNCT
iajs-2150	97	18	)	)	PUNCT
iajs-2150	97	19	)	)	PUNCT
iajs-2150	97	20	(	(	PUNCT
iajs-2150	97	21	∫	∫	PROPN
iajs-2150	97	22	(	(	PUNCT
iajs-2150	97	23	)	)	PUNCT
iajs-2150	97	24	)	)	PUNCT
iajs-2150	97	25	(	(	PUNCT
iajs-2150	97	26	)	)	PUNCT
iajs-2150	97	27	theorem	theorem	NOUN
iajs-2150	97	28	1	1	NUM
iajs-2150	97	29	(	(	PUNCT
iajs-2150	97	30	convergence	convergence	NOUN
iajs-2150	97	31	theorem	theorem	VERB
iajs-2150	97	32	)	)	PUNCT
iajs-2150	97	33	if	if	SCONJ
iajs-2150	97	34	the	the	DET
iajs-2150	97	35	series	series	NOUN
iajs-2150	97	36	form	form	NOUN
iajs-2150	97	37	given	give	VERB
iajs-2150	97	38	in	in	ADP
iajs-2150	97	39	equation	equation	NOUN
iajs-2150	97	40	(	(	PUNCT
iajs-2150	97	41	10	10	NUM
iajs-2150	97	42	)	)	PUNCT
iajs-2150	97	43	with	with	ADP
iajs-2150	97	44	p	p	NOUN
iajs-2150	97	45	=	=	SYM
iajs-2150	97	46	1	1	NUM
iajs-2150	97	47	,	,	PUNCT
iajs-2150	97	48	i.e.	i.e.	X
iajs-2150	97	49	,	,	PUNCT
iajs-2150	97	50	(	(	PUNCT
iajs-2150	97	51	)	)	PUNCT
iajs-2150	97	52	∑	∑	PUNCT
iajs-2150	97	53	(	(	PUNCT
iajs-2150	97	54	)	)	PUNCT
iajs-2150	97	55	(	(	PUNCT
iajs-2150	97	56	)	)	PUNCT
iajs-2150	97	57	is	be	AUX
iajs-2150	97	58	convergent	convergent	ADJ
iajs-2150	97	59	.	.	PUNCT
iajs-2150	98	1	then	then	ADV
iajs-2150	98	2	the	the	DET
iajs-2150	98	3	limit	limit	NOUN
iajs-2150	98	4	point	point	NOUN
iajs-2150	98	5	converges	converge	NOUN
iajs-2150	98	6	to	to	ADP
iajs-2150	98	7	the	the	DET
iajs-2150	98	8	exact	exact	ADJ
iajs-2150	98	9	solution	solution	NOUN
iajs-2150	98	10	of	of	ADP
iajs-2150	98	11	equation	equation	NOUN
iajs-2150	98	12	(	(	PUNCT
iajs-2150	98	13	3	3	NUM
iajs-2150	98	14	)	)	PUNCT
iajs-2150	98	15	,	,	PUNCT
iajs-2150	98	16	where	where	SCONJ
iajs-2150	98	17	un	un	PROPN
iajs-2150	98	18	(	(	PUNCT
iajs-2150	98	19	n	n	NOUN
iajs-2150	98	20	=	=	SYM
iajs-2150	98	21	0	0	NUM
iajs-2150	98	22	,	,	PUNCT
iajs-2150	98	23	1	1	NUM
iajs-2150	98	24	,	,	PUNCT
iajs-2150	98	25	…	…	PUNCT
iajs-2150	98	26	)	)	PUNCT
iajs-2150	98	27	are	be	AUX
iajs-2150	98	28	calculated	calculate	VERB
iajs-2150	98	29	by	by	ADP
iajs-2150	98	30	nthpm	nthpm	NOUN
iajs-2150	98	31	,	,	PUNCT
iajs-2150	98	32	i.e.	i.e.	X
iajs-2150	98	33	,	,	PUNCT
iajs-2150	98	34	(	(	PUNCT
iajs-2150	98	35	)	)	PUNCT
iajs-2150	98	36	(	(	PUNCT
iajs-2150	98	37	)	)	PUNCT
iajs-2150	98	38	{	{	PUNCT
iajs-2150	98	39	*	*	PUNCT
iajs-2150	98	40	,	,	PUNCT
iajs-2150	98	41	-+	-+	PROPN
iajs-2150	98	42	}	}	PUNCT
iajs-2150	98	43	(	(	PUNCT
iajs-2150	98	44	)	)	PUNCT
iajs-2150	98	45	{	{	PUNCT
iajs-2150	98	46	*	*	PUNCT
iajs-2150	98	47	,	,	PUNCT
iajs-2150	98	48	-+	-+	PROPN
iajs-2150	98	49	}	}	PUNCT
iajs-2150	98	50	}	}	PUNCT
iajs-2150	98	51	(	(	PUNCT
iajs-2150	98	52	)	)	PUNCT
iajs-2150	98	53	proof	proof	NOUN
iajs-2150	98	54	suppose	suppose	VERB
iajs-2150	98	55	that	that	SCONJ
iajs-2150	98	56	equation	equation	NOUN
iajs-2150	98	57	(	(	PUNCT
iajs-2150	98	58	32	32	NUM
iajs-2150	98	59	)	)	PUNCT
iajs-2150	98	60	converge	converge	VERB
iajs-2150	98	61	to	to	ADP
iajs-2150	98	62	the	the	DET
iajs-2150	98	63	limit	limit	NOUN
iajs-2150	98	64	point	point	NOUN
iajs-2150	98	65	say	say	VERB
iajs-2150	98	66	as	as	ADP
iajs-2150	98	67	:	:	PUNCT
iajs-2150	98	68	(	(	PUNCT
iajs-2150	98	69	)	)	PUNCT
iajs-2150	98	70	∑	∑	PUNCT
iajs-2150	98	71	(	(	PUNCT
iajs-2150	98	72	)	)	PUNCT
iajs-2150	98	73	(	(	PUNCT
iajs-2150	98	74	)	)	PUNCT
iajs-2150	98	75	now	now	ADV
iajs-2150	98	76	,	,	PUNCT
iajs-2150	98	77	from	from	ADP
iajs-2150	98	78	right	right	ADJ
iajs-2150	98	79	hand	hand	NOUN
iajs-2150	98	80	side	side	NOUN
iajs-2150	98	81	of	of	ADP
iajs-2150	98	82	equation	equation	NOUN
iajs-2150	98	83	(	(	PUNCT
iajs-2150	98	84	3	3	X
iajs-2150	98	85	)	)	PUNCT
iajs-2150	98	86	we	we	PRON
iajs-2150	98	87	have	have	VERB
iajs-2150	98	88	:	:	PUNCT
iajs-2150	98	89	(	(	PUNCT
iajs-2150	98	90	)	)	PUNCT
iajs-2150	98	91	(	(	PUNCT
iajs-2150	98	92	)	)	PUNCT
iajs-2150	98	93	(	(	PUNCT
iajs-2150	98	94	)	)	PUNCT
iajs-2150	98	95	(	(	PUNCT
iajs-2150	98	96	)	)	PUNCT
iajs-2150	98	97	321	321	NUM
iajs-2150	98	98	ibn	ibn	PROPN
iajs-2150	98	99	al	al	PROPN
iajs-2150	98	100	-	-	PUNCT
iajs-2150	98	101	haitham	haitham	PROPN
iajs-2150	98	102	jour	jour	X
iajs-2150	98	103	.	.	PROPN
iajs-2150	98	104	for	for	ADP
iajs-2150	98	105	pure	pure	ADJ
iajs-2150	98	106	&	&	CCONJ
iajs-2150	98	107	appl	appl	PROPN
iajs-2150	98	108	.	.	PUNCT
iajs-2150	99	1	sci	sci	PROPN
iajs-2150	99	2	.	.	PROPN
iajs-2150	99	3	32	32	NUM
iajs-2150	99	4	(	(	PUNCT
iajs-2150	99	5	2	2	NUM
iajs-2150	99	6	)	)	PUNCT
iajs-2150	99	7	2019	2019	NUM
iajs-2150	99	8	∑	∑	PUNCT
iajs-2150	99	9	(	(	PUNCT
iajs-2150	99	10	)	)	PUNCT
iajs-2150	99	11	[	[	PUNCT
iajs-2150	99	12	∑	∑	PUNCT
iajs-2150	99	13	(	(	PUNCT
iajs-2150	99	14	)	)	PUNCT
iajs-2150	99	15	]	]	PUNCT
iajs-2150	99	16	0	0	PUNCT
iajs-2150	100	1	{	{	PUNCT
iajs-2150	100	2	*	*	PUNCT
iajs-2150	100	3	,	,	PUNCT
iajs-2150	100	4	-+	-+	PROPN
iajs-2150	100	5	}	}	PUNCT
iajs-2150	100	6	∑	∑	ADP
iajs-2150	100	7	2	2	NUM
iajs-2150	100	8	,	,	PUNCT
iajs-2150	100	9	*	*	PUNCT
iajs-2150	100	10	,	,	PUNCT
iajs-2150	100	11	-+-3	-+-3	NOUN
iajs-2150	100	12	1	1	NUM
iajs-2150	100	13	,	,	PUNCT
iajs-2150	100	14	.∑	.∑	X
iajs-2150	100	15	2	2	NUM
iajs-2150	100	16	,	,	PUNCT
iajs-2150	100	17	*	*	PUNCT
iajs-2150	100	18	,	,	PUNCT
iajs-2150	100	19	-+-3	-+-3	NOUN
iajs-2150	100	20	/	/	SYM
iajs-2150	100	21	,	,	PUNCT
iajs-2150	100	22	∑	∑	PROPN
iajs-2150	100	23	.	.	PROPN
iajs-2150	100	24	2	2	NUM
iajs-2150	100	25	,	,	PUNCT
iajs-2150	100	26	*	*	PUNCT
iajs-2150	100	27	,	,	PUNCT
iajs-2150	100	28	-+-3/	-+-3/	PROPN
iajs-2150	100	29	(	(	PUNCT
iajs-2150	100	30	)	)	PUNCT
iajs-2150	100	31	by	by	ADP
iajs-2150	100	32	lemma	lemma	PROPN
iajs-2150	100	33	(	(	PUNCT
iajs-2150	100	34	2	2	NUM
iajs-2150	100	35	)	)	PUNCT
iajs-2150	100	36	,	,	PUNCT
iajs-2150	100	37	equation	equation	NOUN
iajs-2150	100	38	(	(	PUNCT
iajs-2150	100	39	35	35	NUM
iajs-2150	100	40	)	)	PUNCT
iajs-2150	100	41	becomes	become	VERB
iajs-2150	100	42	∑	∑	PROPN
iajs-2150	100	43	,	,	PUNCT
iajs-2150	100	44	[	[	X
iajs-2150	100	45	∑	∑	X
iajs-2150	100	46	]	]	PUNCT
iajs-2150	100	47	then	then	ADV
iajs-2150	100	48	w(x	w(x	PROPN
iajs-2150	100	49	,	,	PUNCT
iajs-2150	100	50	t	t	PROPN
iajs-2150	100	51	)	)	PUNCT
iajs-2150	100	52	is	be	AUX
iajs-2150	100	53	satisfying	satisfy	VERB
iajs-2150	100	54	equation	equation	NOUN
iajs-2150	100	55	(	(	PUNCT
iajs-2150	100	56	3	3	NUM
iajs-2150	100	57	)	)	PUNCT
iajs-2150	100	58	.	.	PUNCT
iajs-2150	101	1	so	so	ADV
iajs-2150	101	2	,	,	PUNCT
iajs-2150	101	3	its	its	PRON
iajs-2150	101	4	exact	exact	ADJ
iajs-2150	101	5	solution	solution	NOUN
iajs-2150	101	6	.	.	PUNCT
iajs-2150	102	1	7	7	X
iajs-2150	102	2	.	.	X
iajs-2150	102	3	conclusion	conclusion	NOUN
iajs-2150	102	4	we	we	PRON
iajs-2150	102	5	employed	employ	VERB
iajs-2150	102	6	the	the	DET
iajs-2150	102	7	combination	combination	NOUN
iajs-2150	102	8	of	of	ADP
iajs-2150	102	9	new	new	ADJ
iajs-2150	102	10	transform	transform	NOUN
iajs-2150	102	11	suggested	suggest	VERB
iajs-2150	102	12	by	by	ADP
iajs-2150	102	13	luma	luma	PROPN
iajs-2150	102	14	and	and	CCONJ
iajs-2150	102	15	alaa	alaa	PROPN
iajs-2150	102	16	with	with	ADP
iajs-2150	102	17	hpm	hpm	NOUN
iajs-2150	102	18	method	method	NOUN
iajs-2150	102	19	to	to	PART
iajs-2150	102	20	get	get	VERB
iajs-2150	102	21	a	a	DET
iajs-2150	102	22	closed	closed	ADJ
iajs-2150	102	23	form	form	NOUN
iajs-2150	102	24	solution	solution	NOUN
iajs-2150	102	25	of	of	ADP
iajs-2150	102	26	the	the	DET
iajs-2150	102	27	2	2	NUM
iajs-2150	102	28	nd	nd	NOUN
iajs-2150	102	29	order	order	NOUN
iajs-2150	102	30	autonomous	autonomous	ADJ
iajs-2150	102	31	equation	equation	NOUN
iajs-2150	102	32	pde	pde	NOUN
iajs-2150	102	33	linear	linear	PROPN
iajs-2150	102	34	and	and	CCONJ
iajs-2150	102	35	nonlinear	nonlinear	ADJ
iajs-2150	102	36	.	.	PUNCT
iajs-2150	103	1	the	the	DET
iajs-2150	103	2	new	new	ADJ
iajs-2150	103	3	method	method	NOUN
iajs-2150	103	4	is	be	AUX
iajs-2150	103	5	free	free	ADJ
iajs-2150	103	6	of	of	ADP
iajs-2150	103	7	unnecessary	unnecessary	ADJ
iajs-2150	103	8	mathematical	mathematical	ADJ
iajs-2150	103	9	complexities	complexity	NOUN
iajs-2150	103	10	.	.	PUNCT
iajs-2150	104	1	although	although	SCONJ
iajs-2150	104	2	the	the	DET
iajs-2150	104	3	problem	problem	NOUN
iajs-2150	104	4	considered	consider	VERB
iajs-2150	104	5	has	have	VERB
iajs-2150	104	6	no	no	DET
iajs-2150	104	7	exact	exact	ADJ
iajs-2150	104	8	solution	solution	NOUN
iajs-2150	104	9	,	,	PUNCT
iajs-2150	104	10	the	the	DET
iajs-2150	104	11	accuracy	accuracy	NOUN
iajs-2150	104	12	,	,	PUNCT
iajs-2150	104	13	efficiency	efficiency	NOUN
iajs-2150	104	14	and	and	CCONJ
iajs-2150	104	15	reliability	reliability	NOUN
iajs-2150	104	16	of	of	ADP
iajs-2150	104	17	the	the	DET
iajs-2150	104	18	new	new	ADJ
iajs-2150	104	19	method	method	NOUN
iajs-2150	104	20	are	be	AUX
iajs-2150	104	21	guaranteed	guarantee	VERB
iajs-2150	104	22	.	.	PUNCT
iajs-2150	105	1	the	the	DET
iajs-2150	105	2	convergence	convergence	NOUN
iajs-2150	105	3	of	of	ADP
iajs-2150	105	4	obtained	obtain	VERB
iajs-2150	105	5	solution	solution	NOUN
iajs-2150	105	6	to	to	ADP
iajs-2150	105	7	the	the	DET
iajs-2150	105	8	exact	exact	ADJ
iajs-2150	105	9	solution	solution	NOUN
iajs-2150	105	10	by	by	ADP
iajs-2150	105	11	using	use	VERB
iajs-2150	105	12	nthpm	nthpm	NOUN
iajs-2150	105	13	is	be	AUX
iajs-2150	105	14	proved	prove	VERB
iajs-2150	105	15	.	.	PUNCT
iajs-2150	106	1	this	this	DET
iajs-2150	106	2	method	method	NOUN
iajs-2150	106	3	provides	provide	VERB
iajs-2150	106	4	an	an	DET
iajs-2150	106	5	effective	effective	ADJ
iajs-2150	106	6	and	and	CCONJ
iajs-2150	106	7	efficient	efficient	ADJ
iajs-2150	106	8	way	way	NOUN
iajs-2150	106	9	of	of	ADP
iajs-2150	106	10	solving	solve	VERB
iajs-2150	106	11	a	a	DET
iajs-2150	106	12	wide	wide	ADJ
iajs-2150	106	13	range	range	NOUN
iajs-2150	106	14	of	of	ADP
iajs-2150	106	15	non	non	ADJ
iajs-2150	106	16	-	-	ADJ
iajs-2150	106	17	linear	linear	ADJ
iajs-2150	106	18	pdes	pde	NOUN
iajs-2150	106	19	.	.	PUNCT
iajs-2150	107	1	the	the	DET
iajs-2150	107	2	advantage	advantage	NOUN
iajs-2150	107	3	of	of	ADP
iajs-2150	107	4	this	this	DET
iajs-2150	107	5	method	method	NOUN
iajs-2150	107	6	is	be	AUX
iajs-2150	107	7	its	its	PRON
iajs-2150	107	8	capability	capability	NOUN
iajs-2150	107	9	of	of	ADP
iajs-2150	107	10	combining	combine	VERB
iajs-2150	107	11	two	two	NUM
iajs-2150	107	12	powerful	powerful	ADJ
iajs-2150	107	13	methods	method	NOUN
iajs-2150	107	14	for	for	ADP
iajs-2150	107	15	obtaining	obtain	VERB
iajs-2150	107	16	exact	exact	ADJ
iajs-2150	107	17	solutions	solution	NOUN
iajs-2150	107	18	for	for	ADP
iajs-2150	107	19	non	non	ADJ
iajs-2150	107	20	-	-	ADJ
iajs-2150	107	21	linear	linear	ADJ
iajs-2150	107	22	pdes	pde	NOUN
iajs-2150	107	23	.	.	PUNCT
iajs-2150	108	1	this	this	DET
iajs-2150	108	2	research	research	NOUN
iajs-2150	108	3	considers	consider	VERB
iajs-2150	108	4	the	the	DET
iajs-2150	108	5	effectiveness	effectiveness	NOUN
iajs-2150	108	6	of	of	ADP
iajs-2150	108	7	the	the	DET
iajs-2150	108	8	suggested	suggest	VERB
iajs-2150	108	9	method	method	NOUN
iajs-2150	108	10	in	in	ADP
iajs-2150	108	11	solving	solve	VERB
iajs-2150	108	12	non	non	ADJ
iajs-2150	108	13	-	-	ADJ
iajs-2150	108	14	linear	linear	ADJ
iajs-2150	108	15	2	2	NUM
iajs-2150	108	16	nd	nd	NOUN
iajs-2150	108	17	order	order	NOUN
iajs-2150	108	18	autonomous	autonomous	ADJ
iajs-2150	108	19	equation	equation	NOUN
iajs-2150	108	20	references	reference	NOUN
iajs-2150	108	21	1	1	NUM
iajs-2150	109	1	.	.	PUNCT
iajs-2150	109	2	salih	salih	PROPN
iajs-2150	109	3	,	,	PUNCT
iajs-2150	109	4	h.	h.	PROPN
iajs-2150	109	5	;	;	PUNCT
iajs-2150	109	6	tawfiq	tawfiq	PROPN
iajs-2150	109	7	,	,	PUNCT
iajs-2150	109	8	l.n.m	l.n.m	NOUN
iajs-2150	109	9	.	.	PUNCT
iajs-2150	109	10	;	;	PUNCT
iajs-2150	109	11	yahya	yahya	PROPN
iajs-2150	109	12	,	,	PUNCT
iajs-2150	109	13	z.r	z.r	PROPN
iajs-2150	109	14	.	.	PROPN
iajs-2150	109	15	;	;	PUNCT
iajs-2150	109	16	zin	zin	PROPN
iajs-2150	109	17	,	,	PUNCT
iajs-2150	109	18	s.m	s.m	PROPN
iajs-2150	109	19	.	.	PUNCT
iajs-2150	109	20	solving	solve	VERB
iajs-2150	109	21	modified	modify	VERB
iajs-2150	109	22	regularized	regularize	VERB
iajs-2150	109	23	long	long	ADJ
iajs-2150	109	24	wave	wave	NOUN
iajs-2150	109	25	equation	equation	NOUN
iajs-2150	109	26	using	use	VERB
iajs-2150	109	27	collocation	collocation	NOUN
iajs-2150	109	28	method	method	NOUN
iajs-2150	109	29	.	.	PUNCT
iajs-2150	110	1	journal	journal	PROPN
iajs-2150	110	2	of	of	ADP
iajs-2150	110	3	physics	physics	PROPN
iajs-2150	110	4	:	:	PUNCT
iajs-2150	110	5	conference	conference	NOUN
iajs-2150	110	6	series.2018,1003,012062,1–10	series.2018,1003,012062,1–10	NOUN
iajs-2150	110	7	,	,	PUNCT
iajs-2150	110	8	doi:10.1088/1742	doi:10.1088/1742	NOUN
iajs-2150	110	9	-	-	PUNCT
iajs-2150	110	10	6596/1003/1/012062	6596/1003/1/012062	NUM
iajs-2150	110	11	2	2	NUM
iajs-2150	110	12	.	.	X
iajs-2150	111	1	tawfiq	tawfiq	NOUN
iajs-2150	111	2	,	,	PUNCT
iajs-2150	111	3	l.n.m	l.n.m	NOUN
iajs-2150	111	4	.	.	PUNCT
iajs-2150	111	5	;	;	PUNCT
iajs-2150	112	1	jabber	jabber	PROPN
iajs-2150	112	2	,	,	PUNCT
iajs-2150	112	3	a.k	a.k	PROPN
iajs-2150	112	4	.	.	PROPN
iajs-2150	112	5	steady	steady	ADJ
iajs-2150	112	6	state	state	NOUN
iajs-2150	112	7	radial	radial	ADJ
iajs-2150	112	8	flow	flow	NOUN
iajs-2150	112	9	in	in	ADP
iajs-2150	112	10	anisotropic	anisotropic	NOUN
iajs-2150	112	11	and	and	CCONJ
iajs-2150	112	12	homogenous	homogenous	ADJ
iajs-2150	112	13	in	in	ADP
iajs-2150	112	14	confined	confine	VERB
iajs-2150	112	15	aquifers	aquifer	NOUN
iajs-2150	112	16	.	.	PUNCT
iajs-2150	113	1	journal	journal	PROPN
iajs-2150	113	2	of	of	ADP
iajs-2150	113	3	physics	physics	PROPN
iajs-2150	113	4	:	:	PUNCT
iajs-2150	113	5	conference	conference	NOUN
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iajs-2150	113	7	,	,	PUNCT
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iajs-2150	113	9	-	-	SYM
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iajs-2150	113	11	,	,	PUNCT
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iajs-2150	113	13	-	-	PUNCT
iajs-2150	113	14	6596/1003/1/012056	6596/1003/1/012056	NUM
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iajs-2150	113	16	.	.	PUNCT
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iajs-2150	114	2	,	,	PUNCT
iajs-2150	114	3	h.	h.	PROPN
iajs-2150	114	4	;	;	PUNCT
iajs-2150	114	5	tawfiq	tawfiq	PROPN
iajs-2150	114	6	,	,	PUNCT
iajs-2150	114	7	l.n.m	l.n.m	NOUN
iajs-2150	114	8	.	.	PUNCT
iajs-2150	114	9	;	;	PUNCT
iajs-2150	114	10	yahya	yahya	PROPN
iajs-2150	114	11	,	,	PUNCT
iajs-2150	114	12	z.r	z.r	PROPN
iajs-2150	114	13	.	.	PROPN
iajs-2150	114	14	;	;	PUNCT
iajs-2150	114	15	zin	zin	PROPN
iajs-2150	114	16	,	,	PUNCT
iajs-2150	114	17	s.m	s.m	PROPN
iajs-2150	114	18	.	.	PROPN
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iajs-2150	114	21	of	of	ADP
iajs-2150	114	22	the	the	DET
iajs-2150	114	23	equation	equation	NOUN
iajs-2150	114	24	modified	modify	VERB
iajs-2150	114	25	equal	equal	ADJ
iajs-2150	114	26	width	width	ADJ
iajs-2150	114	27	equation	equation	NOUN
iajs-2150	114	28	by	by	ADP
iajs-2150	114	29	using	use	VERB
iajs-2150	114	30	cubic	cubic	ADJ
iajs-2150	114	31	trigonometric	trigonometric	ADJ
iajs-2150	114	32	b	b	X
iajs-2150	114	33	-	-	PUNCT
iajs-2150	114	34	spline	spline	NOUN
iajs-2150	114	35	method	method	NOUN
iajs-2150	114	36	.	.	PUNCT
iajs-2150	115	1	international	international	ADJ
iajs-2150	115	2	journal	journal	PROPN
iajs-2150	115	3	of	of	ADP
iajs-2150	115	4	engineering	engineering	PROPN
iajs-2150	115	5	&	&	CCONJ
iajs-2150	115	6	technology.2018	technology.2018	PROPN
iajs-2150	115	7	,	,	PUNCT
iajs-2150	115	8	7	7	NUM
iajs-2150	115	9	,	,	PUNCT
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iajs-2150	115	11	,	,	PUNCT
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iajs-2150	115	13	-	-	SYM
iajs-2150	115	14	344	344	NUM
iajs-2150	115	15	.	.	NOUN
iajs-2150	116	1	4	4	NUM
iajs-2150	116	2	.	.	X
iajs-2150	116	3	wazwaz	wazwaz	NOUN
iajs-2150	116	4	,	,	PUNCT
iajs-2150	116	5	a.m.	a.m.	NOUN
iajs-2150	117	1	partial	partial	ADJ
iajs-2150	117	2	differential	differential	NOUN
iajs-2150	117	3	equations	equation	NOUN
iajs-2150	117	4	and	and	CCONJ
iajs-2150	117	5	solitary	solitary	ADJ
iajs-2150	117	6	waves	wave	NOUN
iajs-2150	117	7	theory	theory	NOUN
iajs-2150	117	8	,	,	PUNCT
iajs-2150	117	9	springer	springer	NOUN
iajs-2150	117	10	,	,	PUNCT
iajs-2150	117	11	beijing	beijing	PROPN
iajs-2150	117	12	and	and	CCONJ
iajs-2150	117	13	berlin.2009	berlin.2009	PROPN
iajs-2150	117	14	,	,	PUNCT
iajs-2150	117	15	isbn	isbn	ADJ
iajs-2150	117	16	978	978	NUM
iajs-2150	117	17	-	-	SYM
iajs-2150	117	18	3	3	NUM
iajs-2150	117	19	-	-	PUNCT
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iajs-2150	117	21	-	-	PUNCT
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iajs-2150	117	23	-	-	SYM
iajs-2150	117	24	2	2	NUM
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iajs-2150	117	26	.	.	PUNCT
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iajs-2150	117	28	,	,	PUNCT
iajs-2150	117	29	g.	g.	PROPN
iajs-2150	117	30	solving	solve	VERB
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iajs-2150	117	34	physics	physics	NOUN
iajs-2150	117	35	:	:	PUNCT
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iajs-2150	117	39	,	,	PUNCT
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iajs-2150	117	41	academic	academic	ADJ
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iajs-2150	117	43	,	,	PUNCT
iajs-2150	117	44	boston	boston	PROPN
iajs-2150	117	45	,	,	PUNCT
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iajs-2150	118	2	.	.	X
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iajs-2150	118	4	,	,	PUNCT
iajs-2150	118	5	l.n.m	l.n.m	NOUN
iajs-2150	118	6	.	.	PUNCT
iajs-2150	118	7	;	;	PUNCT
iajs-2150	118	8	jasim	jasim	PROPN
iajs-2150	118	9	,	,	PUNCT
iajs-2150	118	10	k.a	k.a	PROPN
iajs-2150	118	11	.	.	PROPN
iajs-2150	118	12	;	;	PUNCT
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iajs-2150	118	14	,	,	PUNCT
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iajs-2150	118	21	the	the	DET
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iajs-2150	118	23	of	of	ADP
iajs-2150	118	24	heavy	heavy	ADJ
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iajs-2150	118	26	in	in	ADP
iajs-2150	118	27	soil	soil	NOUN
iajs-2150	118	28	and	and	CCONJ
iajs-2150	118	29	its	its	PRON
iajs-2150	118	30	application	application	NOUN
iajs-2150	118	31	in	in	ADP
iajs-2150	118	32	iraq	iraq	PROPN
iajs-2150	118	33	.	.	PUNCT
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iajs-2150	119	2	journal	journal	PROPN
iajs-2150	119	3	of	of	ADP
iajs-2150	119	4	engineering	engineering	NOUN
iajs-2150	119	5	science	science	NOUN
iajs-2150	119	6	and	and	CCONJ
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iajs-2150	119	8	,	,	PUNCT
iajs-2150	119	9	3	3	NUM
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iajs-2150	119	12	,	,	PUNCT
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iajs-2150	119	14	-	-	SYM
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iajs-2150	119	16	.	.	PUNCT
iajs-2150	120	1	7	7	X
iajs-2150	120	2	.	.	X
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iajs-2150	120	4	,	,	PUNCT
iajs-2150	120	5	l.n.m	l.n.m	NOUN
iajs-2150	120	6	.	.	PUNCT
iajs-2150	120	7	;	;	PUNCT
iajs-2150	121	1	jabber	jabber	PROPN
iajs-2150	121	2	,	,	PUNCT
iajs-2150	121	3	a.k	a.k	PROPN
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iajs-2150	121	7	of	of	ADP
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iajs-2150	121	10	.	.	PUNCT
iajs-2150	122	1	global	global	ADJ
iajs-2150	122	2	journal	journal	PROPN
iajs-2150	122	3	of	of	ADP
iajs-2150	122	4	engineering	engineering	NOUN
iajs-2150	122	5	science	science	NOUN
iajs-2150	122	6	and	and	CCONJ
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iajs-2150	122	8	-	-	PUNCT
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iajs-2150	122	10	.	.	PUNCT
iajs-2150	123	1	8	8	NUM
iajs-2150	123	2	.	.	PUNCT
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iajs-2150	124	2	,	,	PUNCT
iajs-2150	124	3	j.h	j.h	PROPN
iajs-2150	124	4	.	.	PROPN
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iajs-2150	124	8	.	.	PUNCT
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iajs-2150	125	3	in	in	ADP
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iajs-2150	125	6	and	and	CCONJ
iajs-2150	125	7	engineering.1999	engineering.1999	PROPN
iajs-2150	125	8	,	,	PUNCT
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iajs-2150	125	19	doi:10.1016	doi:10.1016	PROPN
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iajs-2150	125	22	-	-	PUNCT
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iajs-2150	125	24	-	-	PUNCT
iajs-2150	125	25	3	3	NUM
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iajs-2150	125	30	-	-	PUNCT
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iajs-2150	125	33	.	.	PROPN
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iajs-2150	125	36	&	&	CCONJ
iajs-2150	125	37	appl	appl	PROPN
iajs-2150	125	38	.	.	PUNCT
iajs-2150	126	1	sci	sci	PROPN
iajs-2150	126	2	.	.	PROPN
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iajs-2150	126	6	)	)	PUNCT
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iajs-2150	126	9	.	.	PUNCT
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iajs-2150	127	2	,	,	PUNCT
iajs-2150	127	3	n.h	n.h	PROPN
iajs-2150	127	4	.	.	PROPN
iajs-2150	127	5	;	;	PUNCT
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iajs-2150	127	7	,	,	PUNCT
iajs-2150	127	8	m.m	m.m	PROPN
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iajs-2150	127	13	some	some	DET
iajs-2150	127	14	coupled	couple	VERB
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iajs-2150	127	16	partial	partial	ADJ
iajs-2150	127	17	differential	differential	NOUN
iajs-2150	127	18	equations	equation	NOUN
iajs-2150	127	19	using	use	VERB
iajs-2150	127	20	the	the	DET
iajs-2150	127	21	homotopy	homotopy	NOUN
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iajs-2150	127	24	.	.	PUNCT
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iajs-2150	128	4	with	with	ADP
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iajs-2150	128	6	,	,	PUNCT
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iajs-2150	128	8	,	,	PUNCT
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iajs-2150	128	10	.	.	PUNCT
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iajs-2150	129	2	.	.	PUNCT
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iajs-2150	130	2	,	,	PUNCT
iajs-2150	130	3	j.h	j.h	PROPN
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iajs-2150	130	5	;	;	PUNCT
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iajs-2150	130	7	,	,	PUNCT
iajs-2150	130	8	g.c	g.c	PROPN
iajs-2150	130	9	.	.	PROPN
iajs-2150	130	10	;	;	PUNCT
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iajs-2150	130	13	f.	f.	PROPN
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iajs-2150	130	16	iteration	iteration	NOUN
iajs-2150	130	17	method	method	NOUN
iajs-2150	130	18	which	which	PRON
iajs-2150	130	19	should	should	AUX
iajs-2150	130	20	be	be	AUX
iajs-2150	130	21	followed	follow	VERB
iajs-2150	130	22	.	.	PUNCT
iajs-2150	131	1	nonlinear	nonlinear	ADJ
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iajs-2150	131	3	letters	letter	NOUN
iajs-2150	131	4	a1.2010	a1.2010	PROPN
iajs-2150	131	5	,	,	PUNCT
iajs-2150	131	6	1–30	1–30	NOUN
iajs-2150	131	7	.	.	PUNCT
iajs-2150	132	1	11	11	NUM
iajs-2150	132	2	.	.	PUNCT
iajs-2150	133	1	he	he	PRON
iajs-2150	133	2	,	,	PUNCT
iajs-2150	133	3	j.h	j.h	PROPN
iajs-2150	133	4	.	.	PROPN
iajs-2150	133	5	;	;	PUNCT
iajs-2150	133	6	wu	wu	PROPN
iajs-2150	133	7	,	,	PUNCT
iajs-2150	133	8	x.h	x.h	PROPN
iajs-2150	133	9	.	.	PROPN
iajs-2150	133	10	variational	variational	ADJ
iajs-2150	133	11	iteration	iteration	NOUN
iajs-2150	133	12	method	method	NOUN
iajs-2150	133	13	:	:	PUNCT
iajs-2150	133	14	new	new	ADJ
iajs-2150	133	15	development	development	NOUN
iajs-2150	133	16	and	and	CCONJ
iajs-2150	133	17	applications	application	NOUN
iajs-2150	133	18	.	.	PUNCT
iajs-2150	134	1	computers	computer	NOUN
iajs-2150	134	2	&	&	CCONJ
iajs-2150	134	3	mathematics	mathematic	NOUN
iajs-2150	134	4	with	with	ADP
iajs-2150	134	5	applications.2007	applications.2007	PROPN
iajs-2150	134	6	,	,	PUNCT
iajs-2150	134	7	54	54	NUM
iajs-2150	134	8	,	,	PUNCT
iajs-2150	134	9	881–894	881–894	NUM
iajs-2150	134	10	.	.	PROPN
iajs-2150	134	11	12	12	NUM
iajs-2150	134	12	.	.	PUNCT
iajs-2150	135	1	aasaraai	aasaraai	NOUN
iajs-2150	135	2	,	,	PUNCT
iajs-2150	135	3	a.	a.	NOUN
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iajs-2150	135	8	-	-	PUNCT
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iajs-2150	135	10	-	-	PUNCT
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iajs-2150	135	13	by	by	ADP
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iajs-2150	135	17	.	.	PUNCT
iajs-2150	136	1	middle	middle	PROPN
iajs-2150	136	2	east	east	PROPN
iajs-2150	136	3	j.	j.	PROPN
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iajs-2150	136	5	.	.	PUNCT
iajs-2150	137	1	res.2011	res.2011	NOUN
iajs-2150	137	2	,	,	PUNCT
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iajs-2150	137	4	,	,	PUNCT
iajs-2150	137	5	2	2	NUM
iajs-2150	137	6	,	,	PUNCT
iajs-2150	137	7	270–273	270–273	NUM
iajs-2150	137	8	.	.	NOUN
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iajs-2150	137	10	.	.	X
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iajs-2150	138	3	a.	a.	PROPN
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iajs-2150	138	6	,	,	PUNCT
iajs-2150	138	7	n.	n.	NOUN
iajs-2150	138	8	a	a	DET
iajs-2150	138	9	comparison	comparison	NOUN
iajs-2150	138	10	between	between	ADP
iajs-2150	138	11	the	the	DET
iajs-2150	138	12	reduced	reduce	VERB
iajs-2150	138	13	differential	differential	NOUN
iajs-2150	138	14	transform	transform	NOUN
iajs-2150	138	15	method	method	NOUN
iajs-2150	138	16	and	and	CCONJ
iajs-2150	138	17	the	the	DET
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iajs-2150	138	21	for	for	ADP
iajs-2150	138	22	the	the	DET
iajs-2150	138	23	newell	newell	PROPN
iajs-2150	138	24	-	-	PUNCT
iajs-2150	138	25	whitehead	whitehead	PROPN
iajs-2150	138	26	-	-	PUNCT
iajs-2150	138	27	segel	segel	NOUN
iajs-2150	138	28	.	.	PUNCT
iajs-2150	139	1	egyptian	egyptian	ADJ
iajs-2150	139	2	math	math	PROPN
iajs-2150	139	3	.	.	PUNCT
iajs-2150	140	1	soc.2013	soc.2013	PROPN
iajs-2150	140	2	,	,	PUNCT
iajs-2150	140	3	21	21	NUM
iajs-2150	140	4	,	,	PUNCT
iajs-2150	140	5	259–265	259–265	NUM
iajs-2150	140	6	.	.	PUNCT
iajs-2150	141	1	14	14	NUM
iajs-2150	141	2	.	.	PUNCT
iajs-2150	142	1	tawfiq	tawfiq	PROPN
iajs-2150	142	2	,	,	PUNCT
iajs-2150	142	3	l.n.m	l.n.m	NOUN
iajs-2150	142	4	.	.	PUNCT
iajs-2150	142	5	;	;	PUNCT
iajs-2150	143	1	jabber	jabber	PROPN
iajs-2150	143	2	,	,	PUNCT
iajs-2150	143	3	a.k	a.k	PROPN
iajs-2150	143	4	.	.	PROPN
iajs-2150	143	5	new	new	ADJ
iajs-2150	143	6	transform	transform	VERB
iajs-2150	143	7	fundamental	fundamental	ADJ
iajs-2150	143	8	properties	property	NOUN
iajs-2150	143	9	and	and	CCONJ
iajs-2150	143	10	its	its	PRON
iajs-2150	143	11	applications	application	NOUN
iajs-2150	143	12	.	.	PUNCT
iajs-2150	144	1	ibn	ibn	PROPN
iajs-2150	144	2	alhaitham	alhaitham	PROPN
iajs-2150	144	3	journal	journal	NOUN
iajs-2150	144	4	for	for	ADP
iajs-2150	144	5	pure	pure	ADJ
iajs-2150	144	6	and	and	CCONJ
iajs-2150	144	7	applied	apply	VERB
iajs-2150	144	8	science.2018	science.2018	PROPN
iajs-2150	144	9	,	,	PUNCT
iajs-2150	144	10	31	31	NUM
iajs-2150	144	11	,	,	PUNCT
iajs-2150	144	12	1,151	1,151	NUM
iajs-2150	144	13	-	-	SYM
iajs-2150	144	14	163	163	NUM
iajs-2150	144	15	,	,	PUNCT
iajs-2150	144	16	doi	doi	NOUN
iajs-2150	144	17	:	:	PUNCT
iajs-2150	144	18	http://dx.doi.org/10.30526/31.2.1954	http://dx.doi.org/10.30526/31.2.1954	VERB
iajs-2150	144	19	15	15	NUM
iajs-2150	144	20	.	.	PUNCT
iajs-2150	145	1	jabber	jabber	PROPN
iajs-2150	145	2	,	,	PUNCT
iajs-2150	145	3	a.k	a.k	PROPN
iajs-2150	145	4	.	.	PROPN
iajs-2150	145	5	design	design	PROPN
iajs-2150	145	6	mathematical	mathematical	ADJ
iajs-2150	145	7	model	model	NOUN
iajs-2150	145	8	for	for	ADP
iajs-2150	145	9	groundwater	groundwater	NOUN
iajs-2150	145	10	and	and	CCONJ
iajs-2150	145	11	its	its	PRON
iajs-2150	145	12	application	application	NOUN
iajs-2150	145	13	in	in	ADP
iajs-2150	145	14	iraq	iraq	PROPN
iajs-2150	145	15	,	,	PUNCT
iajs-2150	145	16	ph.d	ph.d	PROPN
iajs-2150	145	17	.	.	PUNCT
iajs-2150	146	1	thesis	thesis	NOUN
iajs-2150	146	2	,	,	PUNCT
iajs-2150	146	3	department	department	NOUN
iajs-2150	146	4	of	of	ADP
iajs-2150	146	5	mathematics	mathematics	PROPN
iajs-2150	146	6	,	,	PUNCT
iajs-2150	146	7	college	college	NOUN
iajs-2150	146	8	of	of	ADP
iajs-2150	146	9	education	education	NOUN
iajs-2150	146	10	for	for	ADP
iajs-2150	146	11	pure	pure	ADJ
iajs-2150	146	12	science	science	NOUN
iajs-2150	146	13	ibn	ibn	PROPN
iajs-2150	146	14	alhaitham	alhaitham	NOUN
iajs-2150	146	15	,	,	PUNCT
iajs-2150	146	16	university	university	NOUN
iajs-2150	146	17	of	of	ADP
iajs-2150	146	18	bagdad	bagdad	PROPN
iajs-2150	146	19	,	,	PUNCT
iajs-2150	146	20	bagdad	bagdad	PROPN
iajs-2150	146	21	,	,	PUNCT
iajs-2150	146	22	iraq	iraq	PROPN
iajs-2150	146	23	,	,	PUNCT
iajs-2150	146	24	2018	2018	NUM
iajs-2150	146	25	.	.	PUNCT
iajs-2150	147	1	16	16	NUM
iajs-2150	147	2	.	.	PUNCT
iajs-2150	148	1	yusufoglu	yusufoglu	PROPN
iajs-2150	148	2	,	,	PUNCT
iajs-2150	148	3	e.	e.	PROPN
iajs-2150	148	4	numerical	numerical	PROPN
iajs-2150	148	5	solution	solution	NOUN
iajs-2150	148	6	of	of	ADP
iajs-2150	148	7	diffusing	diffuse	VERB
iajs-2150	148	8	equation	equation	NOUN
iajs-2150	148	9	by	by	ADP
iajs-2150	148	10	the	the	DET
iajs-2150	148	11	laplace	laplace	NOUN
iajs-2150	148	12	decomposition	decomposition	NOUN
iajs-2150	148	13	algorithm	algorithm	NOUN
iajs-2150	148	14	.	.	PUNCT
iajs-2150	149	1	applied	apply	VERB
iajs-2150	149	2	mathematics	mathematic	NOUN
iajs-2150	149	3	and	and	CCONJ
iajs-2150	149	4	computation.2006	computation.2006	NOUN
iajs-2150	149	5	,	,	PUNCT
iajs-2150	149	6	177	177	NUM
iajs-2150	149	7	,	,	PUNCT
iajs-2150	149	8	572–580	572–580	NUM
iajs-2150	149	9	.	.	PUNCT
iajs-2150	150	1	17	17	NUM
iajs-2150	150	2	.	.	PUNCT
iajs-2150	150	3	khan	khan	PROPN
iajs-2150	150	4	,	,	PUNCT
iajs-2150	150	5	y.	y.	NOUN
iajs-2150	150	6	an	an	DET
iajs-2150	150	7	effective	effective	ADJ
iajs-2150	150	8	modification	modification	NOUN
iajs-2150	150	9	of	of	ADP
iajs-2150	150	10	the	the	DET
iajs-2150	150	11	laplace	laplace	NOUN
iajs-2150	150	12	decomposition	decomposition	NOUN
iajs-2150	150	13	method	method	NOUN
iajs-2150	150	14	for	for	ADP
iajs-2150	150	15	nonlinear	nonlinear	ADJ
iajs-2150	150	16	equations	equation	NOUN
iajs-2150	150	17	.	.	PUNCT
iajs-2150	151	1	journal	journal	PROPN
iajs-2150	151	2	of	of	ADP
iajs-2150	151	3	nonlinear	nonlinear	PROPN
iajs-2150	151	4	sciences	sciences	PROPN
iajs-2150	151	5	and	and	CCONJ
iajs-2150	151	6	numer	numer	NOUN
iajs-2150	151	7	.	.	PROPN
iajs-2150	151	8	simulation	simulation	PROPN
iajs-2150	151	9	.	.	PUNCT
iajs-2150	152	1	2009	2009	NUM
iajs-2150	152	2	,	,	PUNCT
iajs-2150	152	3	10	10	NUM
iajs-2150	152	4	,	,	PUNCT
iajs-2150	152	5	1373–1376	1373–1376	NUM
iajs-2150	152	6	.	.	NOUN
iajs-2150	153	1	18	18	NUM
iajs-2150	153	2	.	.	X
iajs-2150	153	3	tawfiq	tawfiq	PROPN
iajs-2150	153	4	,	,	PUNCT
iajs-2150	153	5	l.n.m	l.n.m	NOUN
iajs-2150	153	6	.	.	PUNCT
iajs-2150	153	7	;	;	PUNCT
iajs-2150	153	8	rasheed	rasheed	NOUN
iajs-2150	153	9	,	,	PUNCT
iajs-2150	153	10	h.w	h.w	PROPN
iajs-2150	153	11	.	.	PROPN
iajs-2150	154	1	on	on	ADP
iajs-2150	154	2	solution	solution	NOUN
iajs-2150	154	3	of	of	ADP
iajs-2150	154	4	non	non	ADJ
iajs-2150	154	5	linear	linear	ADJ
iajs-2150	154	6	singular	singular	ADJ
iajs-2150	154	7	boundary	boundary	ADJ
iajs-2150	154	8	value	value	NOUN
iajs-2150	154	9	problem	problem	NOUN
iajs-2150	154	10	.	.	PUNCT
iajs-2150	155	1	ibn	ibn	PROPN
iajs-2150	155	2	al	al	PROPN
iajs-2150	155	3	-	-	PUNCT
iajs-2150	155	4	haitham	haitham	PROPN
iajs-2150	155	5	journal	journal	PROPN
iajs-2150	155	6	for	for	ADP
iajs-2150	155	7	pure	pure	ADJ
iajs-2150	155	8	&	&	CCONJ
iajs-2150	155	9	applied	applied	ADJ
iajs-2150	155	10	sciences	science	NOUN
iajs-2150	155	11	.	.	PUNCT
iajs-2150	156	1	2013	2013	NUM
iajs-2150	156	2	,	,	PUNCT
iajs-2150	156	3	26	26	NUM
iajs-2150	156	4	,	,	PUNCT
iajs-2150	156	5	3	3	NUM
iajs-2150	156	6	,	,	PUNCT
iajs-2150	156	7	320328	320328	NUM
iajs-2150	156	8	.	.	PUNCT
iajs-2150	157	1	19	19	NUM
iajs-2150	157	2	.	.	X
iajs-2150	157	3	tawfiq	tawfiq	PROPN
iajs-2150	157	4	,	,	PUNCT
iajs-2150	157	5	l.n.m	l.n.m	NOUN
iajs-2150	157	6	.	.	PUNCT
iajs-2150	157	7	;	;	PUNCT
iajs-2150	157	8	hussein	hussein	PROPN
iajs-2150	157	9	,	,	PUNCT
iajs-2150	157	10	r.w	r.w	PROPN
iajs-2150	157	11	.	.	PROPN
iajs-2150	157	12	efficient	efficient	ADJ
iajs-2150	157	13	semi	semi	ADJ
iajs-2150	157	14	-	-	ADJ
iajs-2150	157	15	analytic	analytic	ADJ
iajs-2150	157	16	technique	technique	NOUN
iajs-2150	157	17	for	for	ADP
iajs-2150	157	18	solving	solve	VERB
iajs-2150	157	19	nonlinear	nonlinear	ADJ
iajs-2150	157	20	singular	singular	ADJ
iajs-2150	157	21	initial	initial	ADJ
iajs-2150	157	22	value	value	NOUN
iajs-2150	157	23	problems	problem	NOUN
iajs-2150	157	24	.	.	PUNCT
iajs-2150	158	1	ibn	ibn	PROPN
iajs-2150	158	2	al	al	PROPN
iajs-2150	158	3	-	-	PUNCT
iajs-2150	158	4	haitham	haitham	PROPN
iajs-2150	158	5	journal	journal	PROPN
iajs-2150	158	6	for	for	ADP
iajs-2150	158	7	pure	pure	ADJ
iajs-2150	158	8	&	&	CCONJ
iajs-2150	158	9	applied	apply	VERB
iajs-2150	158	10	sciences.2014	sciences.2014	PROPN
iajs-2150	158	11	,	,	PUNCT
iajs-2150	158	12	27	27	NUM
iajs-2150	158	13	,	,	PUNCT
iajs-2150	158	14	3	3	NUM
iajs-2150	158	15	,	,	PUNCT
iajs-2150	158	16	513	513	NUM
iajs-2150	158	17	-	-	SYM
iajs-2150	158	18	522	522	NUM
iajs-2150	158	19	.	.	PUNCT
iajs-2150	159	1	20	20	NUM
iajs-2150	159	2	.	.	X
iajs-2150	160	1	tawfiq	tawfiq	PROPN
iajs-2150	160	2	,	,	PUNCT
iajs-2150	160	3	l.n.m	l.n.m	NOUN
iajs-2150	160	4	.	.	PUNCT
iajs-2150	160	5	;	;	PUNCT
iajs-2150	161	1	hilal	hilal	PROPN
iajs-2150	161	2	,	,	PUNCT
iajs-2150	161	3	m.m	m.m	PROPN
iajs-2150	161	4	.	.	PROPN
iajs-2150	161	5	solution	solution	NOUN
iajs-2150	161	6	of	of	ADP
iajs-2150	161	7	2nd	2nd	ADJ
iajs-2150	161	8	order	order	NOUN
iajs-2150	161	9	nonlinear	nonlinear	ADJ
iajs-2150	161	10	three	three	NUM
iajs-2150	161	11	-	-	PUNCT
iajs-2150	161	12	point	point	NOUN
iajs-2150	161	13	boundary	boundary	ADJ
iajs-2150	161	14	value	value	NOUN
iajs-2150	161	15	problems	problem	NOUN
iajs-2150	161	16	by	by	ADP
iajs-2150	161	17	semi	semi	ADJ
iajs-2150	161	18	-	-	ADJ
iajs-2150	161	19	analytic	analytic	ADJ
iajs-2150	161	20	technique	technique	NOUN
iajs-2150	161	21	.	.	PUNCT
iajs-2150	162	1	ibn	ibn	PROPN
iajs-2150	162	2	al	al	PROPN
iajs-2150	162	3	-	-	PUNCT
iajs-2150	162	4	haitham	haitham	PROPN
iajs-2150	162	5	journal	journal	PROPN
iajs-2150	162	6	for	for	ADP
iajs-2150	162	7	pure	pure	ADJ
iajs-2150	162	8	&	&	CCONJ
iajs-2150	162	9	applied	applied	ADJ
iajs-2150	162	10	sciences	science	NOUN
iajs-2150	162	11	.	.	PUNCT
iajs-2150	162	12	2014	2014	NUM
iajs-2150	162	13	,	,	PUNCT
iajs-2150	162	14	27	27	NUM
iajs-2150	162	15	,	,	PUNCT
iajs-2150	162	16	3	3	NUM
iajs-2150	162	17	,	,	PUNCT
iajs-2150	162	18	501	501	NUM
iajs-2150	162	19	-	-	SYM
iajs-2150	162	20	512	512	NUM
iajs-2150	162	21	.	.	PUNCT
iajs-2150	163	1	21	21	NUM
iajs-2150	163	2	.	.	X
iajs-2150	164	1	tawfiq	tawfiq	PROPN
iajs-2150	164	2	,	,	PUNCT
iajs-2150	164	3	l.n.m	l.n.m	NOUN
iajs-2150	164	4	.	.	PUNCT
iajs-2150	164	5	;	;	PUNCT
iajs-2150	164	6	rasheed	rasheed	NOUN
iajs-2150	164	7	,	,	PUNCT
iajs-2150	164	8	h.w	h.w	PROPN
iajs-2150	164	9	.	.	PROPN
iajs-2150	165	1	on	on	ADP
iajs-2150	165	2	solution	solution	NOUN
iajs-2150	165	3	of	of	ADP
iajs-2150	165	4	regular	regular	ADJ
iajs-2150	165	5	singular	singular	ADJ
iajs-2150	165	6	ordinary	ordinary	ADJ
iajs-2150	165	7	boundary	boundary	ADJ
iajs-2150	165	8	value	value	NOUN
iajs-2150	165	9	problem	problem	NOUN
iajs-2150	165	10	.	.	PUNCT
iajs-2150	166	1	ibn	ibn	PROPN
iajs-2150	166	2	al	al	PROPN
iajs-2150	166	3	-	-	PUNCT
iajs-2150	166	4	haitham	haitham	PROPN
iajs-2150	166	5	journal	journal	PROPN
iajs-2150	166	6	for	for	ADP
iajs-2150	166	7	pure	pure	ADJ
iajs-2150	166	8	&	&	CCONJ
iajs-2150	166	9	applied	apply	VERB
iajs-2150	166	10	sciences.2013	sciences.2013	PROPN
iajs-2150	166	11	,	,	PUNCT
iajs-2150	166	12	26	26	NUM
iajs-2150	166	13	,	,	PUNCT
iajs-2150	166	14	2	2	NUM
iajs-2150	166	15	,	,	PUNCT
iajs-2150	166	16	249256	249256	NUM
iajs-2150	166	17	.	.	PUNCT
iajs-2150	167	1	22	22	NUM
iajs-2150	167	2	.	.	PUNCT
iajs-2150	168	1	tawfiq	tawfiq	PROPN
iajs-2150	168	2	,	,	PUNCT
iajs-2150	168	3	l.n.m	l.n.m	NOUN
iajs-2150	168	4	.	.	PUNCT
iajs-2150	168	5	;	;	PUNCT
iajs-2150	168	6	yassien	yassien	PROPN
iajs-2150	168	7	,	,	PUNCT
iajs-2150	168	8	s.m	s.m	PROPN
iajs-2150	168	9	.	.	PROPN
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iajs-2150	168	11	of	of	ADP
iajs-2150	168	12	high	high	ADJ
iajs-2150	168	13	order	order	NOUN
iajs-2150	168	14	ordinary	ordinary	ADJ
iajs-2150	168	15	boundary	boundary	ADJ
iajs-2150	168	16	value	value	NOUN
iajs-2150	168	17	problems	problem	NOUN
iajs-2150	168	18	using	use	VERB
iajs-2150	168	19	semi	semi	ADJ
iajs-2150	168	20	-	-	ADJ
iajs-2150	168	21	analytic	analytic	ADJ
iajs-2150	168	22	technique	technique	NOUN
iajs-2150	168	23	.	.	PUNCT
iajs-2150	169	1	ibn	ibn	PROPN
iajs-2150	169	2	al	al	PROPN
iajs-2150	169	3	-	-	PUNCT
iajs-2150	169	4	haitham	haitham	PROPN
iajs-2150	169	5	journal	journal	PROPN
iajs-2150	169	6	for	for	ADP
iajs-2150	169	7	pure	pure	ADJ
iajs-2150	169	8	&	&	CCONJ
iajs-2150	169	9	applied	apply	VERB
iajs-2150	169	10	sciences.2013	sciences.2013	PROPN
iajs-2150	169	11	,	,	PUNCT
iajs-2150	169	12	26	26	NUM
iajs-2150	169	13	,	,	PUNCT
iajs-2150	169	14	1	1	NUM
iajs-2150	169	15	,	,	PUNCT
iajs-2150	169	16	281	281	NUM
iajs-2150	169	17	-	-	SYM
iajs-2150	169	18	291	291	NUM
iajs-2150	169	19	.	.	PUNCT
iajs-2150	170	1	23	23	NUM
iajs-2150	170	2	.	.	PUNCT
iajs-2150	171	1	tawfiq	tawfiq	PROPN
iajs-2150	171	2	,	,	PUNCT
iajs-2150	171	3	l.n.m	l.n.m	NOUN
iajs-2150	171	4	.	.	PUNCT
iajs-2150	171	5	;	;	PUNCT
iajs-2150	171	6	hussein	hussein	PROPN
iajs-2150	171	7	,	,	PUNCT
iajs-2150	171	8	r.w	r.w	PROPN
iajs-2150	171	9	.	.	PROPN
iajs-2150	171	10	on	on	ADP
iajs-2150	171	11	solution	solution	NOUN
iajs-2150	171	12	of	of	ADP
iajs-2150	171	13	regular	regular	ADJ
iajs-2150	171	14	singular	singular	ADJ
iajs-2150	171	15	initial	initial	ADJ
iajs-2150	171	16	value	value	NOUN
iajs-2150	171	17	problems	problem	NOUN
iajs-2150	171	18	.	.	PUNCT
iajs-2150	172	1	ibn	ibn	PROPN
iajs-2150	172	2	al	al	PROPN
iajs-2150	172	3	-	-	PUNCT
iajs-2150	172	4	haitham	haitham	PROPN
iajs-2150	172	5	journal	journal	PROPN
iajs-2150	172	6	for	for	ADP
iajs-2150	172	7	pure	pure	ADJ
iajs-2150	172	8	&	&	CCONJ
iajs-2150	172	9	applied	applied	ADJ
iajs-2150	172	10	sciences	science	NOUN
iajs-2150	172	11	.	.	PUNCT
iajs-2150	173	1	2013	2013	NUM
iajs-2150	173	2	,	,	PUNCT
iajs-2150	173	3	26	26	NUM
iajs-2150	173	4	,	,	PUNCT
iajs-2150	173	5	1	1	NUM
iajs-2150	173	6	,	,	PUNCT
iajs-2150	173	7	257264	257264	NUM
iajs-2150	173	8	.	.	PUNCT
iajs-2150	174	1	24	24	NUM
iajs-2150	174	2	.	.	X
iajs-2150	174	3	tawfiq	tawfiq	PROPN
iajs-2150	174	4	,	,	PUNCT
iajs-2150	174	5	l.n.m	l.n.m	NOUN
iajs-2150	174	6	.	.	PUNCT
iajs-2150	174	7	;	;	PUNCT
iajs-2150	174	8	hussein	hussein	PROPN
iajs-2150	174	9	,	,	PUNCT
iajs-2150	174	10	a.a.t	a.a.t	NOUN
iajs-2150	174	11	.	.	PUNCT
iajs-2150	175	1	design	design	NOUN
iajs-2150	175	2	feed	feed	VERB
iajs-2150	175	3	forward	forward	ADV
iajs-2150	175	4	neural	neural	ADJ
iajs-2150	175	5	network	network	NOUN
iajs-2150	175	6	to	to	PART
iajs-2150	175	7	solve	solve	VERB
iajs-2150	175	8	singular	singular	ADJ
iajs-2150	175	9	boundary	boundary	ADJ
iajs-2150	175	10	value	value	NOUN
iajs-2150	175	11	problems	problem	NOUN
iajs-2150	175	12	.	.	PUNCT
iajs-2150	176	1	isrn	isrn	NOUN
iajs-2150	176	2	applied	apply	VERB
iajs-2150	176	3	mathematics	mathematic	NOUN
iajs-2150	176	4	.	.	PUNCT
iajs-2150	177	1	2013	2013	NUM
iajs-2150	177	2	,	,	PUNCT
iajs-2150	177	3	2013	2013	NUM
iajs-2150	177	4	,	,	PUNCT
iajs-2150	177	5	1	1	NUM
iajs-2150	177	6	-	-	SYM
iajs-2150	177	7	8	8	NUM
iajs-2150	177	8	,	,	PUNCT
iajs-2150	177	9	http://dx.doi.org/10.1155/2013/650467	http://dx.doi.org/10.1155/2013/650467	ADJ
iajs-2150	177	10	25	25	NUM
iajs-2150	177	11	.	.	PUNCT
iajs-2150	178	1	tawfiq	tawfiq	PROPN
iajs-2150	178	2	,	,	PUNCT
iajs-2150	178	3	l.n.m	l.n.m	NOUN
iajs-2150	178	4	.	.	PUNCT
iajs-2150	179	1	using	use	VERB
iajs-2150	179	2	collocation	collocation	NOUN
iajs-2150	179	3	neural	neural	ADJ
iajs-2150	179	4	network	network	NOUN
iajs-2150	179	5	to	to	PART
iajs-2150	179	6	solve	solve	VERB
iajs-2150	179	7	eigenvalue	eigenvalue	NOUN
iajs-2150	179	8	problems	problem	NOUN
iajs-2150	179	9	.	.	PUNCT
iajs-2150	180	1	mj	mj	PROPN
iajs-2150	180	2	journal	journal	PROPN
iajs-2150	180	3	on	on	ADP
iajs-2150	180	4	applied	apply	VERB
iajs-2150	180	5	mathematics.2016	mathematics.2016	PROPN
iajs-2150	180	6	,	,	PUNCT
iajs-2150	180	7	1	1	NUM
iajs-2150	180	8	,	,	PUNCT
iajs-2150	180	9	1	1	NUM
iajs-2150	180	10	,	,	PUNCT
iajs-2150	180	11	1	1	NUM
iajs-2150	180	12	-	-	SYM
iajs-2150	180	13	8	8	NUM
iajs-2150	180	14	.	.	PUNCT
iajs-2150	180	15	http://dx.doi.org/10.30526/31.2.1954	http://dx.doi.org/10.30526/31.2.1954	VERB