id	sid	tid	token	lemma	pos
iajs-2654	1	1	special	special	ADJ
iajs-2654	1	2	issue	issue	NOUN
iajs-2654	1	3	1ihicpas	1ihicpas	NUM
iajs-2654	1	4	202	202	NUM
iajs-2654	1	5	ibn	ibn	PROPN
iajs-2654	1	6	al	al	PROPN
iajs-2654	1	7	-	-	PUNCT
iajs-2654	1	8	haitham	haitham	PROPN
iajs-2654	1	9	journal	journal	PROPN
iajs-2654	1	10	for	for	ADP
iajs-2654	1	11	pure	pure	ADJ
iajs-2654	1	12	and	and	CCONJ
iajs-2654	1	13	applied	apply	VERB
iajs-2654	1	14	science	science	NOUN
iajs-2654	1	15	https://doi.org/10.30526/2021.ihicpas.2654	https://doi.org/10.30526/2021.ihicpas.2654	PUNCT
iajs-2654	1	16	for	for	ADP
iajs-2654	1	17	more	more	ADJ
iajs-2654	1	18	information	information	NOUN
iajs-2654	1	19	about	about	ADP
iajs-2654	1	20	the	the	DET
iajs-2654	1	21	conference	conference	NOUN
iajs-2654	1	22	please	please	INTJ
iajs-2654	1	23	visit	visit	VERB
iajs-2654	1	24	the	the	DET
iajs-2654	1	25	websites	website	NOUN
iajs-2654	1	26	:	:	PUNCT
iajs-2654	1	27	http://ihicps.com/	http://ihicps.com/	VERB
iajs-2654	1	28	m	m	PROPN
iajs-2654	1	29	a	a	DET
iajs-2654	1	30	t	t	NOUN
iajs-2654	1	31	h	h	NOUN
iajs-2654	2	1	e	e	NOUN
iajs-2654	2	2	m	m	VERB
iajs-2654	2	3	a	a	DET
iajs-2654	2	4	t	t	X
iajs-2654	3	1	i	i	PRON
iajs-2654	3	2	c	c	NOUN
iajs-2654	3	3	s	s	VERB
iajs-2654	4	1	|	|	ADV
iajs-2654	4	2	76	76	NUM
iajs-2654	4	3	a	a	DET
iajs-2654	4	4	new	new	ADJ
iajs-2654	4	5	approach	approach	NOUN
iajs-2654	4	6	of	of	ADP
iajs-2654	4	7	morgan	morgan	PROPN
iajs-2654	4	8	-	-	PUNCT
iajs-2654	4	9	voyce	voyce	PROPN
iajs-2654	4	10	polynomial	polynomial	NOUN
iajs-2654	4	11	to	to	PART
iajs-2654	4	12	solve	solve	VERB
iajs-2654	4	13	three	three	NUM
iajs-2654	4	14	point	point	NOUN
iajs-2654	4	15	boundary	boundary	ADJ
iajs-2654	4	16	value	value	NOUN
iajs-2654	4	17	problems	problem	NOUN
iajs-2654	4	18	bushra	bushra	PROPN
iajs-2654	4	19	esaa	esaa	PROPN
iajs-2654	4	20	kashem	kashem	PROPN
iajs-2654	4	21	bushra_eesa@yahoo.com	bushra_eesa@yahoo.com	NOUN
iajs-2654	4	22	,	,	PUNCT
iajs-2654	4	23	100047@uotechnology.edu.iq	100047@uotechnology.edu.iq	NUM
iajs-2654	4	24	department	department	NOUN
iajs-2654	4	25	applied	apply	VERB
iajs-2654	4	26	sciences	science	NOUN
iajs-2654	4	27	,	,	PUNCT
iajs-2654	4	28	university	university	NOUN
iajs-2654	4	29	of	of	ADP
iajs-2654	4	30	technology	technology	NOUN
iajs-2654	4	31	,	,	PUNCT
iajs-2654	4	32	baghdad	baghdad	PROPN
iajs-2654	4	33	,	,	PUNCT
iajs-2654	4	34	iraq	iraq	PROPN
iajs-2654	4	35	.	.	PUNCT
iajs-2654	5	1	abstract	abstract	ADJ
iajs-2654	5	2	in	in	ADP
iajs-2654	5	3	this	this	DET
iajs-2654	5	4	paper	paper	NOUN
iajs-2654	5	5	,	,	PUNCT
iajs-2654	5	6	a	a	DET
iajs-2654	5	7	new	new	ADJ
iajs-2654	5	8	procedure	procedure	NOUN
iajs-2654	5	9	is	be	AUX
iajs-2654	5	10	introduced	introduce	VERB
iajs-2654	5	11	to	to	PART
iajs-2654	5	12	estimate	estimate	VERB
iajs-2654	5	13	the	the	DET
iajs-2654	5	14	solution	solution	NOUN
iajs-2654	5	15	for	for	ADP
iajs-2654	5	16	the	the	DET
iajs-2654	5	17	three	three	NUM
iajs-2654	5	18	-	-	PUNCT
iajs-2654	5	19	point	point	NOUN
iajs-2654	5	20	boundary	boundary	ADJ
iajs-2654	5	21	value	value	NOUN
iajs-2654	5	22	problem	problem	NOUN
iajs-2654	5	23	which	which	PRON
iajs-2654	5	24	is	be	AUX
iajs-2654	5	25	instituted	institute	VERB
iajs-2654	5	26	on	on	ADP
iajs-2654	5	27	the	the	DET
iajs-2654	5	28	use	use	NOUN
iajs-2654	5	29	of	of	ADP
iajs-2654	5	30	morgan	morgan	PROPN
iajs-2654	5	31	-	-	PUNCT
iajs-2654	5	32	voyce	voyce	ADJ
iajs-2654	5	33	polynomial	polynomial	NOUN
iajs-2654	5	34	.	.	PUNCT
iajs-2654	6	1	in	in	ADP
iajs-2654	6	2	the	the	DET
iajs-2654	6	3	beginning	beginning	NOUN
iajs-2654	6	4	,	,	PUNCT
iajs-2654	6	5	morgan	morgan	PROPN
iajs-2654	6	6	-	-	PUNCT
iajs-2654	6	7	voyce	voyce	PROPN
iajs-2654	6	8	polynomial	polynomial	NOUN
iajs-2654	6	9	along	along	ADP
iajs-2654	6	10	with	with	ADP
iajs-2654	6	11	their	their	PRON
iajs-2654	6	12	important	important	ADJ
iajs-2654	6	13	properties	property	NOUN
iajs-2654	6	14	is	be	AUX
iajs-2654	6	15	introduced	introduce	VERB
iajs-2654	6	16	.	.	PUNCT
iajs-2654	7	1	next	next	ADV
iajs-2654	7	2	,	,	PUNCT
iajs-2654	7	3	this	this	DET
iajs-2654	7	4	polynomial	polynomial	NOUN
iajs-2654	7	5	with	with	ADP
iajs-2654	7	6	aid	aid	NOUN
iajs-2654	7	7	of	of	ADP
iajs-2654	7	8	the	the	DET
iajs-2654	7	9	collocation	collocation	NOUN
iajs-2654	7	10	method	method	NOUN
iajs-2654	7	11	utilized	utilize	VERB
iajs-2654	7	12	to	to	PART
iajs-2654	7	13	modify	modify	VERB
iajs-2654	7	14	the	the	DET
iajs-2654	7	15	differential	differential	ADJ
iajs-2654	7	16	equation	equation	NOUN
iajs-2654	7	17	with	with	ADP
iajs-2654	7	18	boundary	boundary	ADJ
iajs-2654	7	19	conditions	condition	NOUN
iajs-2654	7	20	to	to	ADP
iajs-2654	7	21	the	the	DET
iajs-2654	7	22	algebraic	algebraic	ADJ
iajs-2654	7	23	system	system	NOUN
iajs-2654	7	24	.	.	PUNCT
iajs-2654	8	1	finally	finally	ADV
iajs-2654	8	2	,	,	PUNCT
iajs-2654	8	3	the	the	DET
iajs-2654	8	4	examples	example	NOUN
iajs-2654	8	5	approve	approve	VERB
iajs-2654	8	6	the	the	DET
iajs-2654	8	7	validity	validity	NOUN
iajs-2654	8	8	and	and	CCONJ
iajs-2654	8	9	accuracy	accuracy	NOUN
iajs-2654	8	10	of	of	ADP
iajs-2654	8	11	the	the	DET
iajs-2654	8	12	proposed	propose	VERB
iajs-2654	8	13	method	method	NOUN
iajs-2654	8	14	.	.	PUNCT
iajs-2654	9	1	keywords	keyword	NOUN
iajs-2654	9	2	:	:	PUNCT
iajs-2654	9	3	morgan	morgan	PROPN
iajs-2654	9	4	-	-	PUNCT
iajs-2654	9	5	voyce	voyce	PROPN
iajs-2654	9	6	,	,	PUNCT
iajs-2654	9	7	three	three	NUM
iajs-2654	9	8	-	-	PUNCT
iajs-2654	9	9	point	point	NOUN
iajs-2654	9	10	boundary	boundary	ADJ
iajs-2654	9	11	value	value	NOUN
iajs-2654	9	12	problem	problem	NOUN
iajs-2654	9	13	,	,	PUNCT
iajs-2654	9	14	collocation	collocation	NOUN
iajs-2654	9	15	method	method	NOUN
iajs-2654	9	16	,	,	PUNCT
iajs-2654	9	17	approximation	approximation	NOUN
iajs-2654	9	18	method	method	NOUN
iajs-2654	9	19	.	.	PUNCT
iajs-2654	10	1	1.introduction	1.introduction	NUM
iajs-2654	10	2	the	the	DET
iajs-2654	10	3	three	three	NUM
iajs-2654	10	4	point	point	NOUN
iajs-2654	10	5	boundary	boundary	ADJ
iajs-2654	10	6	value	value	NOUN
iajs-2654	10	7	problem	problem	NOUN
iajs-2654	10	8	belongs	belong	VERB
iajs-2654	10	9	to	to	ADP
iajs-2654	10	10	the	the	DET
iajs-2654	10	11	seeming	seem	VERB
iajs-2654	10	12	nonlocal	nonlocal	ADJ
iajs-2654	10	13	or	or	CCONJ
iajs-2654	10	14	multipoint	multipoint	NOUN
iajs-2654	10	15	boundary	boundary	ADJ
iajs-2654	10	16	value	value	NOUN
iajs-2654	10	17	problem	problem	NOUN
iajs-2654	10	18	.	.	PUNCT
iajs-2654	11	1	this	this	DET
iajs-2654	11	2	local	local	ADJ
iajs-2654	11	3	boundary	boundary	ADJ
iajs-2654	11	4	value	value	NOUN
iajs-2654	11	5	problem	problem	NOUN
iajs-2654	11	6	has	have	VERB
iajs-2654	11	7	a	a	DET
iajs-2654	11	8	major	major	ADJ
iajs-2654	11	9	role	role	NOUN
iajs-2654	11	10	in	in	ADP
iajs-2654	11	11	physics	physics	NOUN
iajs-2654	11	12	,	,	PUNCT
iajs-2654	11	13	engineering	engineering	NOUN
iajs-2654	11	14	and	and	CCONJ
iajs-2654	11	15	many	many	ADJ
iajs-2654	11	16	phenomena	phenomenon	NOUN
iajs-2654	11	17	in	in	ADP
iajs-2654	11	18	applied	apply	VERB
iajs-2654	11	19	mathematical	mathematical	NOUN
iajs-2654	11	20	.	.	PUNCT
iajs-2654	12	1	an	an	DET
iajs-2654	12	2	amount	amount	NOUN
iajs-2654	12	3	of	of	ADP
iajs-2654	12	4	research	research	NOUN
iajs-2654	12	5	has	have	AUX
iajs-2654	12	6	been	be	AUX
iajs-2654	12	7	studying	study	VERB
iajs-2654	12	8	the	the	DET
iajs-2654	12	9	three	three	NUM
iajs-2654	12	10	-	-	PUNCT
iajs-2654	12	11	point	point	NOUN
iajs-2654	12	12	boundary	boundary	ADJ
iajs-2654	12	13	value	value	NOUN
iajs-2654	12	14	problem	problem	NOUN
iajs-2654	12	15	,	,	PUNCT
iajs-2654	12	16	for	for	ADP
iajs-2654	12	17	example	example	NOUN
iajs-2654	12	18	,	,	PUNCT
iajs-2654	12	19	the	the	DET
iajs-2654	12	20	positive	positive	ADJ
iajs-2654	12	21	solution	solution	NOUN
iajs-2654	12	22	[	[	X
iajs-2654	12	23	1	1	NUM
iajs-2654	12	24	]	]	PUNCT
iajs-2654	12	25	,	,	PUNCT
iajs-2654	12	26	existence	existence	NOUN
iajs-2654	12	27	and	and	CCONJ
iajs-2654	12	28	stability	stability	NOUN
iajs-2654	12	29	[	[	X
iajs-2654	12	30	2	2	NUM
iajs-2654	12	31	]	]	PUNCT
iajs-2654	12	32	,	,	PUNCT
iajs-2654	12	33	discrete	discrete	ADJ
iajs-2654	12	34	first	first	ADJ
iajs-2654	12	35	order	order	NOUN
iajs-2654	13	1	[	[	X
iajs-2654	13	2	3	3	NUM
iajs-2654	13	3	]	]	PUNCT
iajs-2654	13	4	,	,	PUNCT
iajs-2654	13	5	and	and	CCONJ
iajs-2654	13	6	variational	variational	ADJ
iajs-2654	13	7	principle	principle	NOUN
iajs-2654	13	8	[	[	X
iajs-2654	13	9	4	4	NUM
iajs-2654	13	10	]	]	PUNCT
iajs-2654	13	11	.	.	PUNCT
iajs-2654	14	1	in	in	ADP
iajs-2654	14	2	this	this	DET
iajs-2654	14	3	study	study	NOUN
iajs-2654	14	4	,	,	PUNCT
iajs-2654	14	5	we	we	PRON
iajs-2654	14	6	consider	consider	VERB
iajs-2654	14	7	the	the	DET
iajs-2654	14	8	linear	linear	ADJ
iajs-2654	14	9	three	three	NUM
iajs-2654	14	10	point	point	NOUN
iajs-2654	14	11	boundary	boundary	ADJ
iajs-2654	14	12	value	value	NOUN
iajs-2654	14	13	problem	problem	NOUN
iajs-2654	14	14	is	be	AUX
iajs-2654	14	15	:	:	PUNCT
iajs-2654	14	16	�	�	PROPN
iajs-2654	14	17	̈	̈	X
iajs-2654	14	18	�	�	NOUN
iajs-2654	14	19	𝑍(𝑥	𝑍(𝑥	NOUN
iajs-2654	14	20	)	)	PUNCT
iajs-2654	14	21	+	+	NUM
iajs-2654	14	22	𝐹(𝑥)𝑍(𝑥	𝐹(𝑥)𝑍(𝑥	X
iajs-2654	14	23	)	)	PUNCT
iajs-2654	14	24	=	=	SYM
iajs-2654	14	25	𝐺(𝑥	𝐺(𝑥	NUM
iajs-2654	14	26	)	)	PUNCT
iajs-2654	14	27	𝑤𝑖𝑡ℎ	𝑤𝑖𝑡ℎ	NOUN
iajs-2654	14	28	𝑍(𝑎	𝑍(𝑎	NOUN
iajs-2654	14	29	)	)	PUNCT
iajs-2654	14	30	=	=	SYM
iajs-2654	14	31	𝑍(𝑏	𝑍(𝑏	NUM
iajs-2654	14	32	)	)	PUNCT
iajs-2654	14	33	=	=	SYM
iajs-2654	14	34	𝐴	𝐴	PROPN
iajs-2654	14	35	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
iajs-2654	14	36	�	�	PROPN
iajs-2654	14	37	̇	̇	PROPN
iajs-2654	14	38	�	�	PROPN
iajs-2654	14	39	(𝑐	(𝑐	PROPN
iajs-2654	14	40	)	)	PUNCT
iajs-2654	14	41	=	=	SYM
iajs-2654	14	42	𝐵	𝐵	NOUN
iajs-2654	14	43	𝑥	𝑥	X
iajs-2654	14	44	∈	∈	PROPN
iajs-2654	14	45	(	(	PUNCT
iajs-2654	14	46	𝑎	𝑎	NOUN
iajs-2654	14	47	,	,	PUNCT
iajs-2654	14	48	𝑏	𝑏	NOUN
iajs-2654	14	49	)	)	PUNCT
iajs-2654	14	50	(	(	PUNCT
iajs-2654	14	51	1	1	X
iajs-2654	14	52	)	)	PUNCT
iajs-2654	14	53	where	where	SCONJ
iajs-2654	14	54	f	f	X
iajs-2654	14	55	,	,	PUNCT
iajs-2654	14	56	g	g	PROPN
iajs-2654	14	57	is	be	AUX
iajs-2654	14	58	a	a	DET
iajs-2654	14	59	continuous	continuous	ADJ
iajs-2654	14	60	function	function	NOUN
iajs-2654	14	61	.	.	PUNCT
iajs-2654	15	1	a	a	DET
iajs-2654	15	2	,	,	PUNCT
iajs-2654	15	3	b	b	NOUN
iajs-2654	15	4	,	,	PUNCT
iajs-2654	15	5	c	c	PROPN
iajs-2654	15	6	∈	∈	PROPN
iajs-2654	15	7	r.	r.	PROPN
iajs-2654	15	8	a	a	PROPN
iajs-2654	15	9	,	,	PUNCT
iajs-2654	15	10	b	b	PROPN
iajs-2654	15	11	real	real	ADV
iajs-2654	15	12	constant	constant	ADJ
iajs-2654	15	13	.	.	PUNCT
iajs-2654	16	1	the	the	DET
iajs-2654	16	2	main	main	ADJ
iajs-2654	16	3	purpose	purpose	NOUN
iajs-2654	16	4	of	of	ADP
iajs-2654	16	5	this	this	DET
iajs-2654	16	6	work	work	NOUN
iajs-2654	16	7	is	be	AUX
iajs-2654	16	8	to	to	PART
iajs-2654	16	9	modify	modify	VERB
iajs-2654	16	10	a	a	DET
iajs-2654	16	11	new	new	ADJ
iajs-2654	16	12	algorithm	algorithm	NOUN
iajs-2654	16	13	for	for	ADP
iajs-2654	16	14	an	an	DET
iajs-2654	16	15	approximate	approximate	ADJ
iajs-2654	16	16	solution	solution	NOUN
iajs-2654	16	17	to	to	ADP
iajs-2654	16	18	three	three	NUM
iajs-2654	16	19	point	point	NOUN
iajs-2654	16	20	boundary	boundary	ADJ
iajs-2654	16	21	value	value	NOUN
iajs-2654	16	22	problems	problem	NOUN
iajs-2654	16	23	based	base	VERB
iajs-2654	16	24	on	on	ADP
iajs-2654	16	25	the	the	DET
iajs-2654	16	26	special	special	ADJ
iajs-2654	16	27	case	case	NOUN
iajs-2654	16	28	of	of	ADP
iajs-2654	16	29	morgan	morgan	PROPN
iajs-2654	16	30	-	-	PUNCT
iajs-2654	16	31	voyce	voyce	ADJ
iajs-2654	16	32	polynomial	polynomial	NOUN
iajs-2654	16	33	.	.	PUNCT
iajs-2654	17	1	the	the	DET
iajs-2654	17	2	properties	property	NOUN
iajs-2654	17	3	and	and	CCONJ
iajs-2654	17	4	the	the	DET
iajs-2654	17	5	method	method	NOUN
iajs-2654	17	6	for	for	ADP
iajs-2654	17	7	using	use	VERB
iajs-2654	17	8	are	be	AUX
iajs-2654	17	9	explored	explore	VERB
iajs-2654	17	10	.	.	PUNCT
iajs-2654	18	1	this	this	DET
iajs-2654	18	2	method	method	NOUN
iajs-2654	18	3	decreased	decrease	VERB
iajs-2654	18	4	the	the	DET
iajs-2654	18	5	differential	differential	ADJ
iajs-2654	18	6	equation	equation	NOUN
iajs-2654	18	7	with	with	ADP
iajs-2654	18	8	its	its	PRON
iajs-2654	18	9	initial	initial	ADJ
iajs-2654	18	10	and	and	CCONJ
iajs-2654	18	11	boundary	boundary	ADJ
iajs-2654	18	12	conditions	condition	NOUN
iajs-2654	18	13	to	to	ADP
iajs-2654	18	14	a	a	DET
iajs-2654	18	15	system	system	NOUN
iajs-2654	18	16	of	of	ADP
iajs-2654	18	17	algebraic	algebraic	ADJ
iajs-2654	18	18	equations	equation	NOUN
iajs-2654	18	19	in	in	ADP
iajs-2654	18	20	the	the	DET
iajs-2654	18	21	unknown	unknown	ADJ
iajs-2654	18	22	expand	expand	NOUN
iajs-2654	18	23	coefficients	coefficient	NOUN
iajs-2654	18	24	.	.	PUNCT
iajs-2654	19	1	2	2	X
iajs-2654	19	2	.	.	X
iajs-2654	19	3	morgan	morgan	PROPN
iajs-2654	19	4	-	-	PUNCT
iajs-2654	19	5	voyce	voyce	PROPN
iajs-2654	19	6	polynomial	polynomial	ADJ
iajs-2654	19	7	diametrical	diametrical	ADJ
iajs-2654	19	8	polynomial	polynomial	ADJ
iajs-2654	19	9	morgan	morgan	PROPN
iajs-2654	19	10	-	-	PUNCT
iajs-2654	19	11	voyce	voyce	PROPN
iajs-2654	19	12	which	which	PRON
iajs-2654	19	13	is	be	AUX
iajs-2654	19	14	introduced	introduce	VERB
iajs-2654	19	15	recently	recently	ADV
iajs-2654	19	16	in	in	ADP
iajs-2654	19	17	1959	1959	NUM
iajs-2654	19	18	[	[	X
iajs-2654	19	19	5	5	NUM
iajs-2654	19	20	]	]	PUNCT
iajs-2654	19	21	at	at	ADP
iajs-2654	19	22	was	be	AUX
iajs-2654	19	23	used	use	VERB
iajs-2654	19	24	in	in	ADP
iajs-2654	19	25	many	many	ADJ
iajs-2654	19	26	interesting	interesting	ADJ
iajs-2654	19	27	papers	paper	NOUN
iajs-2654	19	28	such	such	ADJ
iajs-2654	19	29	as	as	ADP
iajs-2654	19	30	,	,	PUNCT
iajs-2654	19	31	functional	functional	ADJ
iajs-2654	19	32	integro	integro	NOUN
iajs-2654	20	1	[	[	X
iajs-2654	20	2	6	6	NUM
iajs-2654	20	3	]	]	PUNCT
iajs-2654	20	4	,	,	PUNCT
iajs-2654	20	5	pantograph	pantograph	NOUN
iajs-2654	20	6	equation	equation	NOUN
iajs-2654	20	7	[	[	X
iajs-2654	20	8	7	7	NUM
iajs-2654	20	9	]	]	PUNCT
iajs-2654	20	10	,	,	PUNCT
iajs-2654	20	11	differential	differential	ADJ
iajs-2654	20	12	-	-	PUNCT
iajs-2654	20	13	difference	difference	NOUN
iajs-2654	20	14	equation	equation	NOUN
iajs-2654	20	15	[	[	X
iajs-2654	20	16	8	8	NUM
iajs-2654	20	17	]	]	PUNCT
iajs-2654	20	18	,	,	PUNCT
iajs-2654	20	19	and	and	CCONJ
iajs-2654	20	20	nonlinear	nonlinear	ADJ
iajs-2654	20	21	ordinary	ordinary	ADJ
iajs-2654	20	22	differential	differential	ADJ
iajs-2654	20	23	equation	equation	NOUN
iajs-2654	20	24	[	[	X
iajs-2654	20	25	9	9	NUM
iajs-2654	20	26	]	]	PUNCT
iajs-2654	20	27	.	.	PUNCT
iajs-2654	21	1	http://ihicps.com/	http://ihicps.com/	PROPN
iajs-2654	21	2	mailto:bushra_eesa@yahoo.com	mailto:bushra_eesa@yahoo.com	PUNCT
iajs-2654	21	3	mailto:100047@uotechnology.edu.iq	mailto:100047@uotechnology.edu.iq	PROPN
iajs-2654	21	4	special	special	ADJ
iajs-2654	21	5	issue	issue	NOUN
iajs-2654	21	6	1ihicpas	1ihicpas	NUM
iajs-2654	21	7	202	202	NUM
iajs-2654	21	8	ibn	ibn	PROPN
iajs-2654	21	9	al	al	PROPN
iajs-2654	21	10	-	-	PUNCT
iajs-2654	21	11	haitham	haitham	PROPN
iajs-2654	21	12	journal	journal	PROPN
iajs-2654	21	13	for	for	ADP
iajs-2654	21	14	pure	pure	ADJ
iajs-2654	21	15	and	and	CCONJ
iajs-2654	21	16	applied	apply	VERB
iajs-2654	21	17	science	science	NOUN
iajs-2654	21	18	https://doi.org/10.30526/2021.ihicpas.2654	https://doi.org/10.30526/2021.ihicpas.2654	PUNCT
iajs-2654	21	19	for	for	ADP
iajs-2654	21	20	more	more	ADJ
iajs-2654	21	21	information	information	NOUN
iajs-2654	21	22	about	about	ADP
iajs-2654	21	23	the	the	DET
iajs-2654	21	24	conference	conference	NOUN
iajs-2654	21	25	please	please	INTJ
iajs-2654	21	26	visit	visit	VERB
iajs-2654	21	27	the	the	DET
iajs-2654	21	28	websites	website	NOUN
iajs-2654	21	29	:	:	PUNCT
iajs-2654	21	30	http://ihicps.com/	http://ihicps.com/	VERB
iajs-2654	21	31	m	m	PROPN
iajs-2654	21	32	a	a	DET
iajs-2654	21	33	t	t	NOUN
iajs-2654	21	34	h	h	NOUN
iajs-2654	22	1	e	e	NOUN
iajs-2654	22	2	m	m	VERB
iajs-2654	22	3	a	a	DET
iajs-2654	22	4	t	t	X
iajs-2654	23	1	i	i	PRON
iajs-2654	23	2	c	c	NOUN
iajs-2654	23	3	s	s	VERB
iajs-2654	23	4	|	|	ADV
iajs-2654	23	5	77	77	NUM
iajs-2654	24	1	the	the	DET
iajs-2654	24	2	morgan	morgan	PROPN
iajs-2654	24	3	-	-	PUNCT
iajs-2654	24	4	voyce	voyce	PROPN
iajs-2654	24	5	polynomials	polynomial	NOUN
iajs-2654	24	6	𝑀𝑛(𝑥	𝑀𝑛(𝑥	NOUN
iajs-2654	24	7	)	)	PUNCT
iajs-2654	24	8	defined	define	VERB
iajs-2654	24	9	by:[10	by:[10	NOUN
iajs-2654	24	10	]	]	SYM
iajs-2654	24	11	𝑀𝑛+2(𝑥	𝑀𝑛+2(𝑥	NOUN
iajs-2654	24	12	)	)	PUNCT
iajs-2654	24	13	=	=	SYM
iajs-2654	24	14	𝑀𝑛+1(𝑥	𝑀𝑛+1(𝑥	NOUN
iajs-2654	24	15	)	)	PUNCT
iajs-2654	24	16	−	−	PROPN
iajs-2654	24	17	𝑀𝑛(𝑥	𝑀𝑛(𝑥	PROPN
iajs-2654	24	18	)	)	PUNCT
iajs-2654	24	19	(	(	PUNCT
iajs-2654	24	20	2	2	X
iajs-2654	24	21	)	)	PUNCT
iajs-2654	24	22	with	with	ADP
iajs-2654	24	23	𝑀0(𝑥	𝑀0(𝑥	PROPN
iajs-2654	24	24	)	)	PUNCT
iajs-2654	24	25	=	=	SYM
iajs-2654	24	26	2	2	NUM
iajs-2654	24	27	,	,	PUNCT
iajs-2654	24	28	𝑀1(𝑥	𝑀1(𝑥	NOUN
iajs-2654	24	29	)	)	PUNCT
iajs-2654	25	1	=	=	PUNCT
iajs-2654	26	1	𝑥	𝑥	PROPN
iajs-2654	26	2	+	+	NUM
iajs-2654	26	3	2	2	NUM
iajs-2654	26	4	and	and	CCONJ
iajs-2654	26	5	explicit	explicit	ADJ
iajs-2654	26	6	formulation	formulation	NOUN
iajs-2654	26	7	(	(	PUNCT
iajs-2654	26	8	𝑛	𝑛	DET
iajs-2654	26	9	≥	≥	NUM
iajs-2654	26	10	1	1	NUM
iajs-2654	26	11	,	,	PUNCT
iajs-2654	26	12	𝑛	𝑛	PRON
iajs-2654	26	13	>	>	X
iajs-2654	26	14	𝑘	𝑘	NOUN
iajs-2654	26	15	)	)	PUNCT
iajs-2654	26	16	𝑀𝑛(𝑥	𝑀𝑛(𝑥	PROPN
iajs-2654	26	17	)	)	PUNCT
iajs-2654	26	18	=	=	PUNCT
iajs-2654	27	1	∑	∑	PUNCT
iajs-2654	27	2	2𝑛	2𝑛	PROPN
iajs-2654	27	3	𝑛−𝑘	𝑛−𝑘	X
iajs-2654	27	4	(	(	PUNCT
iajs-2654	27	5	𝑛+𝑘−1	𝑛+𝑘−1	PROPN
iajs-2654	27	6	𝑛−𝑘−1	𝑛−𝑘−1	PROPN
iajs-2654	27	7	)	)	PUNCT
iajs-2654	27	8	𝑥𝑘	𝑥𝑘	PROPN
iajs-2654	28	1	+	+	CCONJ
iajs-2654	28	2	𝑥𝑛𝑛−1	𝑥𝑛𝑛−1	PROPN
iajs-2654	28	3	𝑘=0	𝑘=0	ADP
iajs-2654	28	4	…	…	PUNCT
iajs-2654	28	5	(	(	PUNCT
iajs-2654	28	6	3	3	NUM
iajs-2654	28	7	)	)	PUNCT
iajs-2654	28	8	on	on	ADP
iajs-2654	28	9	other	other	ADJ
iajs-2654	28	10	hand	hand	NOUN
iajs-2654	28	11	,	,	PUNCT
iajs-2654	28	12	by	by	ADP
iajs-2654	28	13	using	use	VERB
iajs-2654	28	14	eq.(2	eq.(2	ADJ
iajs-2654	28	15	)	)	PUNCT
iajs-2654	28	16	&	&	CCONJ
iajs-2654	28	17	eq.(3	eq.(3	NOUN
iajs-2654	28	18	)	)	PUNCT
iajs-2654	28	19	the	the	DET
iajs-2654	28	20	first	first	ADJ
iajs-2654	28	21	seven	seven	NUM
iajs-2654	28	22	morgan	morgan	PROPN
iajs-2654	28	23	-	-	PUNCT
iajs-2654	28	24	voyce	voyce	ADJ
iajs-2654	28	25	polynomials	polynomial	NOUN
iajs-2654	28	26	are	be	AUX
iajs-2654	28	27	given	give	VERB
iajs-2654	28	28	:	:	PUNCT
iajs-2654	28	29	𝑀0(𝑥	𝑀0(𝑥	NUM
iajs-2654	28	30	)	)	PUNCT
iajs-2654	29	1	=	=	SYM
iajs-2654	29	2	2	2	NUM
iajs-2654	29	3	,	,	PUNCT
iajs-2654	29	4	𝑀1(𝑥	𝑀1(𝑥	NOUN
iajs-2654	29	5	)	)	PUNCT
iajs-2654	29	6	=	=	PUNCT
iajs-2654	30	1	𝑥	𝑥	PRON
iajs-2654	30	2	+	+	SYM
iajs-2654	30	3	2	2	NUM
iajs-2654	30	4	𝑀2(𝑥	𝑀2(𝑥	NOUN
iajs-2654	30	5	)	)	PUNCT
iajs-2654	30	6	=	=	SYM
iajs-2654	30	7	𝑥2	𝑥2	NOUN
iajs-2654	30	8	+	+	CCONJ
iajs-2654	30	9	4𝑥	4𝑥	NOUN
iajs-2654	30	10	+	+	CCONJ
iajs-2654	30	11	2	2	NUM
iajs-2654	30	12	𝑀3(𝑥	𝑀3(𝑥	NOUN
iajs-2654	30	13	)	)	PUNCT
iajs-2654	31	1	=	=	SYM
iajs-2654	31	2	𝑥3	𝑥3	NOUN
iajs-2654	31	3	+	+	CCONJ
iajs-2654	31	4	6𝑥2	6𝑥2	NUM
iajs-2654	31	5	+	+	CCONJ
iajs-2654	31	6	9𝑥	9𝑥	NUM
iajs-2654	31	7	+	+	CCONJ
iajs-2654	31	8	2	2	NUM
iajs-2654	31	9	𝑀4(𝑥	𝑀4(𝑥	NOUN
iajs-2654	31	10	)	)	PUNCT
iajs-2654	31	11	=	=	SYM
iajs-2654	31	12	𝑥4	𝑥4	NOUN
iajs-2654	31	13	+	+	CCONJ
iajs-2654	31	14	8𝑥3	8𝑥3	NUM
iajs-2654	32	1	+	+	CCONJ
iajs-2654	32	2	20𝑥2	20𝑥2	NUM
iajs-2654	32	3	+	+	NUM
iajs-2654	32	4	16𝑥	16𝑥	NUM
iajs-2654	32	5	+	+	CCONJ
iajs-2654	32	6	2	2	NUM
iajs-2654	32	7	𝑀5(𝑥	𝑀5(𝑥	NOUN
iajs-2654	32	8	)	)	PUNCT
iajs-2654	33	1	=	=	SYM
iajs-2654	33	2	𝑥5	𝑥5	PROPN
iajs-2654	33	3	+	+	NOUN
iajs-2654	33	4	10𝑥4	10𝑥4	NUM
iajs-2654	33	5	+	+	SYM
iajs-2654	33	6	35𝑥3	35𝑥3	NUM
iajs-2654	33	7	+	+	CCONJ
iajs-2654	33	8	50𝑥2	50𝑥2	NUM
iajs-2654	33	9	+	+	NUM
iajs-2654	33	10	25𝑥	25𝑥	NOUN
iajs-2654	33	11	+	+	CCONJ
iajs-2654	33	12	2	2	NUM
iajs-2654	33	13	𝑀6(𝑥	𝑀6(𝑥	NUM
iajs-2654	33	14	)	)	PUNCT
iajs-2654	34	1	=	=	NOUN
iajs-2654	34	2	𝑥6	𝑥6	PROPN
iajs-2654	34	3	+	+	CCONJ
iajs-2654	35	1	12𝑥5	12𝑥5	NUM
iajs-2654	36	1	+	+	NUM
iajs-2654	36	2	54𝑥4	54𝑥4	NUM
iajs-2654	37	1	+	+	NUM
iajs-2654	37	2	112𝑥3	112𝑥3	NUM
iajs-2654	37	3	+	+	SYM
iajs-2654	37	4	105𝑥2	105𝑥2	NUM
iajs-2654	37	5	+	+	NUM
iajs-2654	37	6	36𝑥	36𝑥	NUM
iajs-2654	37	7	+	+	CCONJ
iajs-2654	37	8	2	2	NUM
iajs-2654	37	9	𝑀7(𝑥	𝑀7(𝑥	NOUN
iajs-2654	37	10	)	)	PUNCT
iajs-2654	37	11	=	=	VERB
iajs-2654	37	12	𝑥7	𝑥7	VERB
iajs-2654	37	13	+	+	PROPN
iajs-2654	37	14	14𝑥6	14𝑥6	NUM
iajs-2654	37	15	+	+	NUM
iajs-2654	37	16	77𝑥5	77𝑥5	NUM
iajs-2654	37	17	+	+	CCONJ
iajs-2654	37	18	210𝑥4	210𝑥4	NUM
iajs-2654	37	19	+	+	CCONJ
iajs-2654	37	20	294𝑥3	294𝑥3	NUM
iajs-2654	37	21	+	+	SYM
iajs-2654	37	22	196𝑥2	196𝑥2	NUM
iajs-2654	37	23	+	+	NUM
iajs-2654	37	24	49𝑥	49𝑥	NOUN
iajs-2654	37	25	+	+	CCONJ
iajs-2654	37	26	2	2	NUM
iajs-2654	37	27	3important	3important	NUM
iajs-2654	37	28	properties	property	NOUN
iajs-2654	37	29	of	of	ADP
iajs-2654	37	30	morgan	morgan	PROPN
iajs-2654	37	31	-	-	PUNCT
iajs-2654	37	32	voyce	voyce	ADJ
iajs-2654	37	33	polynomial	polynomial	NOUN
iajs-2654	37	34	:	:	PUNCT
iajs-2654	38	1	[	[	X
iajs-2654	38	2	11,12	11,12	X
iajs-2654	38	3	]	]	PUNCT
iajs-2654	38	4	1connection	1connection	NUM
iajs-2654	38	5	with	with	ADP
iajs-2654	38	6	chybechev	chybechev	ADJ
iajs-2654	38	7	and	and	CCONJ
iajs-2654	38	8	lucas	lucas	PROPN
iajs-2654	38	9	polynomial	polynomial	ADJ
iajs-2654	38	10	𝑻𝒏(𝒙	𝑻𝒏(𝒙	NUM
iajs-2654	38	11	)	)	PUNCT
iajs-2654	38	12	,	,	PUNCT
iajs-2654	38	13	𝑳𝒏(𝒙	𝑳𝒏(𝒙	NOUN
iajs-2654	38	14	)	)	PUNCT
iajs-2654	38	15	𝑀𝑛(𝑥	𝑀𝑛(𝑥	NOUN
iajs-2654	38	16	)	)	PUNCT
iajs-2654	38	17	=	=	SYM
iajs-2654	38	18	2𝑇𝑛	2𝑇𝑛	NUM
iajs-2654	38	19	(	(	PUNCT
iajs-2654	38	20	𝑥	𝑥	NOUN
iajs-2654	38	21	+	+	NUM
iajs-2654	38	22	2	2	NUM
iajs-2654	38	23	2	2	NUM
iajs-2654	38	24	)	)	PUNCT
iajs-2654	38	25	𝑀𝑛(𝑥2	𝑀𝑛(𝑥2	PROPN
iajs-2654	38	26	)	)	PUNCT
iajs-2654	38	27	=	=	SYM
iajs-2654	38	28	𝐿2𝑛(𝑥	𝐿2𝑛(𝑥	PROPN
iajs-2654	38	29	)	)	PUNCT
iajs-2654	38	30	2orthogonality	2orthogonality	PROPN
iajs-2654	38	31	𝑀𝑛(𝑥	𝑀𝑛(𝑥	NOUN
iajs-2654	38	32	)	)	PUNCT
iajs-2654	38	33	is	be	AUX
iajs-2654	38	34	an	an	DET
iajs-2654	38	35	orthogonal	orthogonal	ADJ
iajs-2654	38	36	polynomial	polynomial	NOUN
iajs-2654	38	37	over	over	ADP
iajs-2654	38	38	[	[	X
iajs-2654	38	39	0,-4	0,-4	NUM
iajs-2654	38	40	]	]	PUNCT
iajs-2654	38	41	with	with	ADP
iajs-2654	38	42	weight	weight	NOUN
iajs-2654	38	43	function	function	NOUN
iajs-2654	38	44	1	1	NUM
iajs-2654	38	45	√4−(𝑥+2)2	√4−(𝑥+2)2	PROPN
iajs-2654	38	46	3	3	NUM
iajs-2654	38	47	.	.	PUNCT
iajs-2654	38	48	integration	integration	NOUN
iajs-2654	38	49	http://ihicps.com/	http://ihicps.com/	PROPN
iajs-2654	38	50	special	special	ADJ
iajs-2654	38	51	issue	issue	NOUN
iajs-2654	38	52	1ihicpas	1ihicpas	NUM
iajs-2654	38	53	202	202	NUM
iajs-2654	38	54	ibn	ibn	PROPN
iajs-2654	38	55	al	al	PROPN
iajs-2654	38	56	-	-	PUNCT
iajs-2654	38	57	haitham	haitham	PROPN
iajs-2654	38	58	journal	journal	PROPN
iajs-2654	38	59	for	for	ADP
iajs-2654	38	60	pure	pure	ADJ
iajs-2654	38	61	and	and	CCONJ
iajs-2654	38	62	applied	apply	VERB
iajs-2654	38	63	science	science	NOUN
iajs-2654	38	64	https://doi.org/10.30526/2021.ihicpas.2654	https://doi.org/10.30526/2021.ihicpas.2654	PUNCT
iajs-2654	38	65	for	for	ADP
iajs-2654	38	66	more	more	ADJ
iajs-2654	38	67	information	information	NOUN
iajs-2654	38	68	about	about	ADP
iajs-2654	38	69	the	the	DET
iajs-2654	38	70	conference	conference	NOUN
iajs-2654	38	71	please	please	INTJ
iajs-2654	38	72	visit	visit	VERB
iajs-2654	38	73	the	the	DET
iajs-2654	38	74	websites	website	NOUN
iajs-2654	38	75	:	:	PUNCT
iajs-2654	38	76	http://ihicps.com/	http://ihicps.com/	VERB
iajs-2654	38	77	m	m	PROPN
iajs-2654	38	78	a	a	DET
iajs-2654	38	79	t	t	NOUN
iajs-2654	38	80	h	h	NOUN
iajs-2654	39	1	e	e	NOUN
iajs-2654	39	2	m	m	VERB
iajs-2654	39	3	a	a	DET
iajs-2654	39	4	t	t	X
iajs-2654	40	1	i	i	PRON
iajs-2654	40	2	c	c	NOUN
iajs-2654	40	3	s	s	VERB
iajs-2654	41	1	|	|	ADV
iajs-2654	41	2	78	78	NUM
iajs-2654	41	3	∫	∫	NOUN
iajs-2654	42	1	𝑀2𝑛+1(𝑥)𝑑𝑥	𝑀2𝑛+1(𝑥)𝑑𝑥	PROPN
iajs-2654	42	2	=	=	SYM
iajs-2654	42	3	0	0	SYM
iajs-2654	42	4	0	0	NUM
iajs-2654	43	1	−4	−4	NOUN
iajs-2654	43	2	∫	∫	PROPN
iajs-2654	43	3	𝑀2𝑛(𝑥)𝑑𝑥	𝑀2𝑛(𝑥)𝑑𝑥	PROPN
iajs-2654	43	4	=	=	SYM
iajs-2654	43	5	8	8	NUM
iajs-2654	43	6	(	(	PUNCT
iajs-2654	43	7	2𝑛	2𝑛	PROPN
iajs-2654	43	8	+	+	CCONJ
iajs-2654	43	9	1)(2𝑛	1)(2𝑛	NUM
iajs-2654	43	10	−	−	NOUN
iajs-2654	43	11	1	1	NUM
iajs-2654	43	12	)	)	PUNCT
iajs-2654	43	13	0	0	NUM
iajs-2654	44	1	−4	−4	PROPN
iajs-2654	44	2	4	4	NUM
iajs-2654	44	3	-	-	PUNCT
iajs-2654	44	4	zeros	zero	NOUN
iajs-2654	44	5	𝑀𝑛(𝑥	𝑀𝑛(𝑥	NOUN
iajs-2654	44	6	):	):	PUNCT
iajs-2654	44	7	𝑥𝑟	𝑥𝑟	PRON
iajs-2654	44	8	=	=	PUNCT
iajs-2654	44	9	−4	−4	X
iajs-2654	44	10	𝑠𝑖𝑛2	𝑠𝑖𝑛2	NOUN
iajs-2654	44	11	[	[	PUNCT
iajs-2654	44	12	2𝑟	2𝑟	NOUN
iajs-2654	44	13	−	−	NUM
iajs-2654	44	14	1	1	NUM
iajs-2654	44	15	2𝑛	2𝑛	PROPN
iajs-2654	44	16	∗	∗	NOUN
iajs-2654	44	17	𝜋	𝜋	VERB
iajs-2654	44	18	2	2	NUM
iajs-2654	44	19	]	]	PUNCT
iajs-2654	44	20	,	,	PUNCT
iajs-2654	44	21	𝑟	𝑟	X
iajs-2654	44	22	=	=	SYM
iajs-2654	44	23	1,2	1,2	NUM
iajs-2654	44	24	,	,	PUNCT
iajs-2654	44	25	…	…	PUNCT
iajs-2654	44	26	,	,	PUNCT
iajs-2654	44	27	𝑛	𝑛	DET
iajs-2654	44	28	3	3	NUM
iajs-2654	44	29	.	.	PUNCT
iajs-2654	44	30	morgan	morgan	PROPN
iajs-2654	44	31	-	-	PUNCT
iajs-2654	44	32	voyce	voyce	PROPN
iajs-2654	44	33	collocation	collocation	NOUN
iajs-2654	44	34	method	method	NOUN
iajs-2654	44	35	in	in	ADP
iajs-2654	44	36	this	this	DET
iajs-2654	44	37	section	section	NOUN
iajs-2654	44	38	,	,	PUNCT
iajs-2654	44	39	the	the	DET
iajs-2654	44	40	solution	solution	NOUN
iajs-2654	44	41	of	of	ADP
iajs-2654	44	42	three	three	NUM
iajs-2654	44	43	-	-	PUNCT
iajs-2654	44	44	point	point	NOUN
iajs-2654	44	45	boundary	boundary	ADJ
iajs-2654	44	46	value	value	NOUN
iajs-2654	44	47	problem	problem	NOUN
iajs-2654	44	48	can	can	AUX
iajs-2654	44	49	be	be	AUX
iajs-2654	44	50	abstracted	abstract	VERB
iajs-2654	44	51	by	by	ADP
iajs-2654	44	52	the	the	DET
iajs-2654	44	53	following	follow	VERB
iajs-2654	44	54	steps	step	NOUN
iajs-2654	44	55	.	.	PUNCT
iajs-2654	45	1	step	step	NOUN
iajs-2654	45	2	1	1	NUM
iajs-2654	45	3	the	the	DET
iajs-2654	45	4	function	function	NOUN
iajs-2654	45	5	�	�	PROPN
iajs-2654	45	6	̈	̈	SYM
iajs-2654	45	7	�	�	NOUN
iajs-2654	45	8	(𝑥	(𝑥	NOUN
iajs-2654	45	9	)	)	PUNCT
iajs-2654	45	10	in	in	ADP
iajs-2654	45	11	eq.(1	eq.(1	ADJ
iajs-2654	45	12	)	)	PUNCT
iajs-2654	45	13	developed	develop	VERB
iajs-2654	45	14	approximately	approximately	ADV
iajs-2654	45	15	using	use	VERB
iajs-2654	45	16	morgan	morgan	PROPN
iajs-2654	45	17	-	-	PUNCT
iajs-2654	45	18	voyce	voyce	ADJ
iajs-2654	45	19	polynomial	polynomial	NOUN
iajs-2654	45	20	:	:	PUNCT
iajs-2654	45	21	�	�	PROPN
iajs-2654	45	22	̈	̈	X
iajs-2654	45	23	�	�	NOUN
iajs-2654	45	24	(𝑥	(𝑥	NOUN
iajs-2654	45	25	)	)	PUNCT
iajs-2654	45	26	=	=	PUNCT
iajs-2654	46	1	∑	∑	PUNCT
iajs-2654	46	2	𝐶𝑖	𝐶𝑖	PROPN
iajs-2654	46	3	𝑀𝑖(𝑥)𝑛	𝑀𝑖(𝑥)𝑛	PROPN
iajs-2654	46	4	𝑖=0	𝑖=0	PROPN
iajs-2654	46	5	(	(	PUNCT
iajs-2654	46	6	4	4	X
iajs-2654	46	7	)	)	PUNCT
iajs-2654	46	8	step	step	NOUN
iajs-2654	46	9	2	2	NUM
iajs-2654	46	10	integrating	integrating	NOUN
iajs-2654	46	11	eq.(4	eq.(4	NOUN
iajs-2654	46	12	)	)	PUNCT
iajs-2654	46	13	twice	twice	ADV
iajs-2654	46	14	from	from	ADP
iajs-2654	46	15	0	0	NUM
iajs-2654	46	16	t0	t0	NUM
iajs-2654	46	17	x	x	PUNCT
iajs-2654	46	18	depending	depend	VERB
iajs-2654	46	19	the	the	DET
iajs-2654	46	20	boundary	boundary	ADJ
iajs-2654	46	21	condition	condition	NOUN
iajs-2654	46	22	to	to	PART
iajs-2654	46	23	get	get	VERB
iajs-2654	46	24	:	:	PUNCT
iajs-2654	46	25	𝑍(𝑥	𝑍(𝑥	NUM
iajs-2654	46	26	)	)	PUNCT
iajs-2654	46	27	=	=	SYM
iajs-2654	46	28	𝑍(0	𝑍(0	X
iajs-2654	46	29	)	)	PUNCT
iajs-2654	46	30	+	+	CCONJ
iajs-2654	46	31	�	�	PROPN
iajs-2654	46	32	̇	̇	PROPN
iajs-2654	46	33	�	�	PROPN
iajs-2654	46	34	(0)𝑥	(0)𝑥	PUNCT
iajs-2654	46	35	+	+	CCONJ
iajs-2654	46	36	∬	∬	ADJ
iajs-2654	46	37	∑	∑	PUNCT
iajs-2654	46	38	𝐶𝑖𝑀𝑖(𝑥)𝑛	𝐶𝑖𝑀𝑖(𝑥)𝑛	PROPN
iajs-2654	46	39	𝑖=0	𝑖=0	PROPN
iajs-2654	47	1	𝑥	𝑥	NOUN
iajs-2654	47	2	0	0	PUNCT
iajs-2654	47	3	(	(	PUNCT
iajs-2654	47	4	5	5	NUM
iajs-2654	47	5	)	)	PUNCT
iajs-2654	47	6	step	step	NOUN
iajs-2654	47	7	3	3	NUM
iajs-2654	47	8	substituting	substitute	VERB
iajs-2654	47	9	the	the	DET
iajs-2654	47	10	boundary	boundary	ADJ
iajs-2654	47	11	condition	condition	NOUN
iajs-2654	47	12	into	into	ADP
iajs-2654	47	13	eq.(5	eq.(5	NOUN
iajs-2654	47	14	)	)	PUNCT
iajs-2654	47	15	to	to	PART
iajs-2654	47	16	reduce	reduce	VERB
iajs-2654	47	17	the	the	DET
iajs-2654	47	18	morgan	morgan	PROPN
iajs-2654	47	19	-	-	PUNCT
iajs-2654	47	20	voyce	voyce	PROPN
iajs-2654	47	21	coefficient	coefficient	NOUN
iajs-2654	47	22	differential	differential	ADJ
iajs-2654	47	23	equation	equation	NOUN
iajs-2654	47	24	.	.	PUNCT
iajs-2654	48	1	step	step	NOUN
iajs-2654	48	2	4	4	NUM
iajs-2654	48	3	rewriting	rewrite	VERB
iajs-2654	48	4	eq.(1	eq.(1	ADJ
iajs-2654	48	5	)	)	PUNCT
iajs-2654	48	6	by	by	ADP
iajs-2654	48	7	substituted	substitute	VERB
iajs-2654	48	8	eq.(5	eq.(5	NOUN
iajs-2654	48	9	)	)	PUNCT
iajs-2654	48	10	&	&	CCONJ
iajs-2654	48	11	(	(	PUNCT
iajs-2654	48	12	4	4	NUM
iajs-2654	48	13	)	)	PUNCT
iajs-2654	48	14	to	to	PART
iajs-2654	48	15	get	get	VERB
iajs-2654	48	16	∑	∑	PUNCT
iajs-2654	48	17	𝐶𝑖	𝐶𝑖	PROPN
iajs-2654	48	18	𝑀𝑖(𝑥)𝑛	𝑀𝑖(𝑥)𝑛	PROPN
iajs-2654	48	19	𝑖=0	𝑖=0	PROPN
iajs-2654	48	20	+	+	CCONJ
iajs-2654	48	21	𝐹(𝑥)[𝑍(0	𝐹(𝑥)[𝑍(0	NUM
iajs-2654	48	22	)	)	PUNCT
iajs-2654	49	1	+	+	CCONJ
iajs-2654	49	2	�	�	PROPN
iajs-2654	49	3	̇	̇	PROPN
iajs-2654	49	4	�	�	PROPN
iajs-2654	49	5	(0)𝑥	(0)𝑥	PUNCT
iajs-2654	49	6	+	+	CCONJ
iajs-2654	49	7	∬	∬	ADJ
iajs-2654	49	8	∑	∑	PUNCT
iajs-2654	49	9	𝐶𝑖𝑀𝑖(𝑥)𝑛	𝐶𝑖𝑀𝑖(𝑥)𝑛	PROPN
iajs-2654	49	10	𝑖=0	𝑖=0	PUNCT
iajs-2654	49	11	𝑥	𝑥	NOUN
iajs-2654	49	12	0	0	NUM
iajs-2654	49	13	]	]	PUNCT
iajs-2654	49	14	=	=	SYM
iajs-2654	49	15	𝐺(𝑥	𝐺(𝑥	NOUN
iajs-2654	49	16	)	)	PUNCT
iajs-2654	49	17	(	(	PUNCT
iajs-2654	49	18	6	6	X
iajs-2654	49	19	)	)	PUNCT
iajs-2654	49	20	step	step	NOUN
iajs-2654	49	21	5	5	NUM
iajs-2654	49	22	by	by	ADP
iajs-2654	49	23	consider	consider	VERB
iajs-2654	49	24	the	the	DET
iajs-2654	49	25	collocation	collocation	NOUN
iajs-2654	49	26	point	point	NOUN
iajs-2654	49	27	𝑥𝑗	𝑥𝑗	NOUN
iajs-2654	49	28	=	=	PROPN
iajs-2654	49	29	𝑗−0.5	𝑗−0.5	NUM
iajs-2654	49	30	2𝑛	2𝑛	PROPN
iajs-2654	49	31	j=1,2,3	j=1,2,3	NUM
iajs-2654	49	32	,	,	PUNCT
iajs-2654	49	33	…	…	PUNCT
iajs-2654	49	34	can	can	AUX
iajs-2654	49	35	be	be	AUX
iajs-2654	49	36	resulting	result	VERB
iajs-2654	49	37	algebraic	algebraic	ADJ
iajs-2654	49	38	system	system	NOUN
iajs-2654	49	39	which	which	PRON
iajs-2654	49	40	is	be	AUX
iajs-2654	49	41	solved	solve	VERB
iajs-2654	49	42	to	to	PART
iajs-2654	49	43	find	find	VERB
iajs-2654	49	44	the	the	DET
iajs-2654	49	45	unknown	unknown	ADJ
iajs-2654	49	46	coefficient	coefficient	NOUN
iajs-2654	49	47	𝑀𝑖.	𝑀𝑖.	PROPN
iajs-2654	49	48	step	step	NOUN
iajs-2654	49	49	7	7	NUM
iajs-2654	49	50	http://ihicps.com/	http://ihicps.com/	ADJ
iajs-2654	49	51	special	special	ADJ
iajs-2654	49	52	issue	issue	NOUN
iajs-2654	49	53	1ihicpas	1ihicpas	NUM
iajs-2654	49	54	202	202	NUM
iajs-2654	49	55	ibn	ibn	PROPN
iajs-2654	49	56	al	al	PROPN
iajs-2654	49	57	-	-	PUNCT
iajs-2654	49	58	haitham	haitham	PROPN
iajs-2654	49	59	journal	journal	PROPN
iajs-2654	49	60	for	for	ADP
iajs-2654	49	61	pure	pure	ADJ
iajs-2654	49	62	and	and	CCONJ
iajs-2654	49	63	applied	apply	VERB
iajs-2654	49	64	science	science	NOUN
iajs-2654	49	65	https://doi.org/10.30526/2021.ihicpas.2654	https://doi.org/10.30526/2021.ihicpas.2654	PUNCT
iajs-2654	49	66	for	for	ADP
iajs-2654	49	67	more	more	ADJ
iajs-2654	49	68	information	information	NOUN
iajs-2654	49	69	about	about	ADP
iajs-2654	49	70	the	the	DET
iajs-2654	49	71	conference	conference	NOUN
iajs-2654	49	72	please	please	INTJ
iajs-2654	49	73	visit	visit	VERB
iajs-2654	49	74	the	the	DET
iajs-2654	49	75	websites	website	NOUN
iajs-2654	49	76	:	:	PUNCT
iajs-2654	49	77	http://ihicps.com/	http://ihicps.com/	VERB
iajs-2654	49	78	m	m	PROPN
iajs-2654	49	79	a	a	DET
iajs-2654	49	80	t	t	NOUN
iajs-2654	49	81	h	h	NOUN
iajs-2654	50	1	e	e	NOUN
iajs-2654	50	2	m	m	VERB
iajs-2654	50	3	a	a	DET
iajs-2654	50	4	t	t	X
iajs-2654	51	1	i	i	PRON
iajs-2654	51	2	c	c	NOUN
iajs-2654	51	3	s	s	VERB
iajs-2654	52	1	|	|	ADV
iajs-2654	52	2	79	79	NUM
iajs-2654	52	3	substituted	substitute	VERB
iajs-2654	52	4	the	the	DET
iajs-2654	52	5	calculated	calculated	ADJ
iajs-2654	52	6	coefficients	coefficient	NOUN
iajs-2654	52	7	into	into	ADP
iajs-2654	52	8	eq.(5	eq.(5	NOUN
iajs-2654	52	9	)	)	PUNCT
iajs-2654	52	10	.	.	PUNCT
iajs-2654	53	1	the	the	DET
iajs-2654	53	2	solution	solution	NOUN
iajs-2654	53	3	for	for	ADP
iajs-2654	53	4	eq.(1	eq.(1	ADJ
iajs-2654	53	5	)	)	PUNCT
iajs-2654	53	6	will	will	AUX
iajs-2654	53	7	be	be	AUX
iajs-2654	53	8	obtained	obtain	VERB
iajs-2654	53	9	.	.	PUNCT
iajs-2654	54	1	4	4	X
iajs-2654	54	2	.	.	X
iajs-2654	54	3	examples	example	NOUN
iajs-2654	54	4	illustrations	illustration	NOUN
iajs-2654	54	5	:	:	PUNCT
iajs-2654	54	6	for	for	ADP
iajs-2654	54	7	showing	show	VERB
iajs-2654	54	8	the	the	DET
iajs-2654	54	9	accuracy	accuracy	NOUN
iajs-2654	54	10	and	and	CCONJ
iajs-2654	54	11	activity	activity	NOUN
iajs-2654	54	12	of	of	ADP
iajs-2654	54	13	our	our	PRON
iajs-2654	54	14	approximate	approximate	ADJ
iajs-2654	54	15	method	method	NOUN
iajs-2654	54	16	,	,	PUNCT
iajs-2654	54	17	we	we	PRON
iajs-2654	54	18	consider	consider	VERB
iajs-2654	54	19	the	the	DET
iajs-2654	54	20	following	follow	VERB
iajs-2654	54	21	examples	example	NOUN
iajs-2654	54	22	.	.	PUNCT
iajs-2654	55	1	example	example	NOUN
iajs-2654	55	2	(	(	PUNCT
iajs-2654	55	3	1	1	NUM
iajs-2654	55	4	):	):	PUNCT
iajs-2654	55	5	�	�	PROPN
iajs-2654	55	6	̈	̈	X
iajs-2654	55	7	�	�	PROPN
iajs-2654	55	8	−	−	PROPN
iajs-2654	55	9	12	12	NUM
iajs-2654	55	10	𝑥−2𝑍	𝑥−2𝑍	NOUN
iajs-2654	55	11	=	=	SYM
iajs-2654	55	12	0	0	NUM
iajs-2654	55	13	𝑍(1	𝑍(1	NUM
iajs-2654	55	14	)	)	PUNCT
iajs-2654	55	15	=	=	SYM
iajs-2654	55	16	𝑍(−1	𝑍(−1	X
iajs-2654	55	17	)	)	PUNCT
iajs-2654	55	18	=	=	SYM
iajs-2654	55	19	1	1	NUM
iajs-2654	55	20	,	,	PUNCT
iajs-2654	55	21	𝑍(0	𝑍(0	X
iajs-2654	55	22	)	)	PUNCT
iajs-2654	55	23	=	=	SYM
iajs-2654	55	24	�	�	PROPN
iajs-2654	55	25	̇	̇	PROPN
iajs-2654	55	26	�	�	PROPN
iajs-2654	55	27	(0	(0	X
iajs-2654	55	28	)	)	PUNCT
iajs-2654	55	29	=	=	SYM
iajs-2654	55	30	0	0	PUNCT
iajs-2654	55	31	(	(	PUNCT
iajs-2654	55	32	7	7	NUM
iajs-2654	55	33	)	)	PUNCT
iajs-2654	55	34	exact	exact	ADJ
iajs-2654	55	35	solution	solution	NOUN
iajs-2654	55	36	x4	x4	PROPN
iajs-2654	55	37	for	for	ADP
iajs-2654	55	38	assume	assume	PROPN
iajs-2654	55	39	�	�	PROPN
iajs-2654	55	40	̈	̈	X
iajs-2654	55	41	�	�	PROPN
iajs-2654	55	42	(𝑥	(𝑥	NOUN
iajs-2654	55	43	)	)	PUNCT
iajs-2654	55	44	≅	≅	PROPN
iajs-2654	55	45	∑	∑	PROPN
iajs-2654	55	46	𝐶𝑖𝑀𝑖(𝑥)4	𝐶𝑖𝑀𝑖(𝑥)4	PROPN
iajs-2654	55	47	𝑖=0	𝑖=0	PROPN
iajs-2654	55	48	(	(	PUNCT
iajs-2654	55	49	8)	8)	NUM
iajs-2654	55	50	by	by	ADP
iajs-2654	55	51	integrating	integrate	VERB
iajs-2654	55	52	eq.(8	eq.(8	ADV
iajs-2654	55	53	)	)	PUNCT
iajs-2654	55	54	twice	twice	ADJ
iajs-2654	55	55	time	time	NOUN
iajs-2654	55	56	and	and	CCONJ
iajs-2654	55	57	applying	apply	VERB
iajs-2654	55	58	the	the	DET
iajs-2654	55	59	steps	step	NOUN
iajs-2654	55	60	studied	study	VERB
iajs-2654	55	61	in	in	ADP
iajs-2654	55	62	section(3	section(3	PROPN
iajs-2654	55	63	)	)	PUNCT
iajs-2654	55	64	,	,	PUNCT
iajs-2654	55	65	the	the	DET
iajs-2654	55	66	approximate	approximate	ADJ
iajs-2654	55	67	coefficient	coefficient	NOUN
iajs-2654	55	68	will	will	AUX
iajs-2654	55	69	be	be	AUX
iajs-2654	55	70	c0=36	c0=36	PROPN
iajs-2654	55	71	,	,	PUNCT
iajs-2654	55	72	c1=-48	c1=-48	PROPN
iajs-2654	55	73	,	,	PUNCT
iajs-2654	55	74	c2=12	c2=12	PROPN
iajs-2654	55	75	,	,	PUNCT
iajs-2654	55	76	c3	c3	PROPN
iajs-2654	55	77	=	=	PROPN
iajs-2654	55	78	c4=0	c4=0	PROPN
iajs-2654	55	79	.	.	PUNCT
iajs-2654	56	1	applying	apply	VERB
iajs-2654	56	2	the	the	DET
iajs-2654	56	3	approximate	approximate	ADJ
iajs-2654	56	4	coefficient	coefficient	NOUN
iajs-2654	56	5	into	into	ADP
iajs-2654	56	6	eq.(8	eq.(8	ADJ
iajs-2654	56	7	)	)	PUNCT
iajs-2654	56	8	,	,	PUNCT
iajs-2654	56	9	we	we	PRON
iajs-2654	56	10	obtain	obtain	VERB
iajs-2654	56	11	the	the	DET
iajs-2654	56	12	exact	exact	ADJ
iajs-2654	56	13	solution	solution	NOUN
iajs-2654	56	14	𝑍(𝑥	𝑍(𝑥	NUM
iajs-2654	56	15	)	)	PUNCT
iajs-2654	56	16	≅	≅	PROPN
iajs-2654	56	17	𝑥4	𝑥4	PROPN
iajs-2654	56	18	example	example	NOUN
iajs-2654	56	19	(	(	PUNCT
iajs-2654	56	20	2	2	NUM
iajs-2654	56	21	):	):	PUNCT
iajs-2654	56	22	�	�	PROPN
iajs-2654	56	23	̈	̈	SYM
iajs-2654	56	24	�	�	PROPN
iajs-2654	56	25	−	−	NOUN
iajs-2654	56	26	𝑍	𝑍	PROPN
iajs-2654	56	27	=	=	SYM
iajs-2654	56	28	(	(	PUNCT
iajs-2654	56	29	4𝑥6	4𝑥6	NUM
iajs-2654	56	30	+	+	CCONJ
iajs-2654	56	31	12	12	NUM
iajs-2654	56	32	𝑥2)𝑒𝑥2	𝑥2)𝑒𝑥2	NOUN
iajs-2654	56	33	𝑍(1	𝑍(1	PUNCT
iajs-2654	56	34	)	)	PUNCT
iajs-2654	56	35	=	=	SYM
iajs-2654	56	36	𝑍(−1	𝑍(−1	X
iajs-2654	56	37	)	)	PUNCT
iajs-2654	57	1	=	=	NOUN
iajs-2654	57	2	𝑒1	𝑒1	NOUN
iajs-2654	57	3	,	,	PUNCT
iajs-2654	57	4	𝑍(0	𝑍(0	X
iajs-2654	57	5	)	)	PUNCT
iajs-2654	57	6	=	=	SYM
iajs-2654	57	7	�	�	PROPN
iajs-2654	57	8	̇	̇	PROPN
iajs-2654	57	9	�	�	PROPN
iajs-2654	57	10	(0	(0	X
iajs-2654	57	11	)	)	PUNCT
iajs-2654	57	12	=	=	SYM
iajs-2654	57	13	0	0	NUM
iajs-2654	57	14	exact	exact	ADJ
iajs-2654	57	15	solution	solution	NOUN
iajs-2654	57	16	𝑥4	𝑥4	NOUN
iajs-2654	57	17	𝑒𝑥2	𝑒𝑥2	AUX
iajs-2654	57	18	assume	assume	VERB
iajs-2654	57	19	that	that	SCONJ
iajs-2654	57	20	�	�	PROPN
iajs-2654	57	21	̈	̈	SYM
iajs-2654	57	22	�	�	PROPN
iajs-2654	57	23	(𝑥	(𝑥	NOUN
iajs-2654	57	24	)	)	PUNCT
iajs-2654	57	25	≅	≅	PROPN
iajs-2654	57	26	∑	∑	PROPN
iajs-2654	57	27	𝐶𝑖𝑀𝑖(𝑥)6	𝐶𝑖𝑀𝑖(𝑥)6	PROPN
iajs-2654	57	28	𝑖=0	𝑖=0	PROPN
iajs-2654	57	29	by	by	ADP
iajs-2654	57	30	applying	apply	VERB
iajs-2654	57	31	the	the	DET
iajs-2654	57	32	same	same	ADJ
iajs-2654	57	33	method	method	NOUN
iajs-2654	57	34	and	and	CCONJ
iajs-2654	57	35	solve	solve	VERB
iajs-2654	57	36	a	a	DET
iajs-2654	57	37	system	system	NOUN
iajs-2654	57	38	of	of	ADP
iajs-2654	57	39	equations	equation	NOUN
iajs-2654	57	40	we	we	PRON
iajs-2654	57	41	approximate	approximate	VERB
iajs-2654	57	42	the	the	DET
iajs-2654	57	43	solution	solution	NOUN
iajs-2654	57	44	.	.	PUNCT
iajs-2654	58	1	table	table	NOUN
iajs-2654	58	2	1	1	NUM
iajs-2654	58	3	reflects	reflect	VERB
iajs-2654	58	4	the	the	DET
iajs-2654	58	5	comparison	comparison	NOUN
iajs-2654	58	6	between	between	ADP
iajs-2654	58	7	the	the	DET
iajs-2654	58	8	approximate	approximate	ADJ
iajs-2654	58	9	solution	solution	NOUN
iajs-2654	58	10	with	with	ADP
iajs-2654	58	11	the	the	DET
iajs-2654	58	12	exact	exact	ADJ
iajs-2654	58	13	solution	solution	NOUN
iajs-2654	58	14	and	and	CCONJ
iajs-2654	58	15	absolute	absolute	ADJ
iajs-2654	58	16	error	error	NOUN
iajs-2654	58	17	.	.	PUNCT
iajs-2654	59	1	table	table	NOUN
iajs-2654	59	2	1	1	NUM
iajs-2654	59	3	x	x	SYM
iajs-2654	59	4	approximate	approximate	ADJ
iajs-2654	59	5	exact	exact	ADJ
iajs-2654	59	6	absolute	absolute	ADJ
iajs-2654	59	7	error	error	NOUN
iajs-2654	59	8	-1	-1	ADP
iajs-2654	59	9	2.718282	2.718282	NUM
iajs-2654	59	10	2.718282	2.718282	NUM
iajs-2654	59	11	0	0	NUM
iajs-2654	59	12	-0.75	-0.75	NUM
iajs-2654	59	13	0.555381	0.555381	NUM
iajs-2654	60	1	0.555310	0.555310	NUM
iajs-2654	60	2	0.000071	0.000071	NUM
iajs-2654	60	3	-0.5	-0.5	NUM
iajs-2654	60	4	0.080242	0.080242	NUM
iajs-2654	60	5	0.080252	0.080252	NUM
iajs-2654	60	6	0.00001	0.00001	NUM
iajs-2654	60	7	-0.25	-0.25	NUM
iajs-2654	60	8	0.004157	0.004157	NUM
iajs-2654	60	9	0.004158	0.004158	NUM
iajs-2654	60	10	0.0000001	0.0000001	NUM
iajs-2654	60	11	http://ihicps.com/	http://ihicps.com/	ADJ
iajs-2654	60	12	special	special	ADJ
iajs-2654	60	13	issue	issue	NOUN
iajs-2654	60	14	1ihicpas	1ihicpas	NUM
iajs-2654	60	15	202	202	NUM
iajs-2654	60	16	ibn	ibn	PROPN
iajs-2654	60	17	al	al	PROPN
iajs-2654	60	18	-	-	PUNCT
iajs-2654	60	19	haitham	haitham	PROPN
iajs-2654	60	20	journal	journal	PROPN
iajs-2654	60	21	for	for	ADP
iajs-2654	60	22	pure	pure	ADJ
iajs-2654	60	23	and	and	CCONJ
iajs-2654	60	24	applied	apply	VERB
iajs-2654	60	25	science	science	NOUN
iajs-2654	60	26	https://doi.org/10.30526/2021.ihicpas.2654	https://doi.org/10.30526/2021.ihicpas.2654	PUNCT
iajs-2654	60	27	for	for	ADP
iajs-2654	60	28	more	more	ADJ
iajs-2654	60	29	information	information	NOUN
iajs-2654	60	30	about	about	ADP
iajs-2654	60	31	the	the	DET
iajs-2654	60	32	conference	conference	NOUN
iajs-2654	60	33	please	please	INTJ
iajs-2654	60	34	visit	visit	VERB
iajs-2654	60	35	the	the	DET
iajs-2654	60	36	websites	website	NOUN
iajs-2654	60	37	:	:	PUNCT
iajs-2654	60	38	http://ihicps.com/	http://ihicps.com/	VERB
iajs-2654	60	39	m	m	PROPN
iajs-2654	60	40	a	a	DET
iajs-2654	60	41	t	t	NOUN
iajs-2654	60	42	h	h	NOUN
iajs-2654	61	1	e	e	NOUN
iajs-2654	61	2	m	m	VERB
iajs-2654	61	3	a	a	DET
iajs-2654	61	4	t	t	X
iajs-2654	62	1	i	i	PRON
iajs-2654	62	2	c	c	NOUN
iajs-2654	62	3	s	s	VERB
iajs-2654	62	4	|	|	ADV
iajs-2654	63	1	80	80	NUM
iajs-2654	63	2	0	0	NUM
iajs-2654	63	3	0	0	NUM
iajs-2654	63	4	0	0	NUM
iajs-2654	63	5	0	0	NUM
iajs-2654	63	6	0.25	0.25	NUM
iajs-2654	63	7	0.004157	0.004157	NUM
iajs-2654	63	8	0.004158	0.004158	NUM
iajs-2654	63	9	0.0000001	0.0000001	NUM
iajs-2654	63	10	0.5	0.5	NUM
iajs-2654	63	11	0.080242	0.080242	NUM
iajs-2654	63	12	0.080252	0.080252	NUM
iajs-2654	63	13	0.00001	0.00001	NUM
iajs-2654	63	14	0.75	0.75	NUM
iajs-2654	63	15	0.555381	0.555381	NUM
iajs-2654	63	16	0.555310	0.555310	NUM
iajs-2654	63	17	0.000071	0.000071	NUM
iajs-2654	63	18	1	1	NUM
iajs-2654	63	19	2.718282	2.718282	NUM
iajs-2654	63	20	2.718282	2.718282	NUM
iajs-2654	63	21	0	0	NUM
iajs-2654	63	22	example	example	NOUN
iajs-2654	63	23	(	(	PUNCT
iajs-2654	63	24	3	3	NUM
iajs-2654	63	25	):	):	PUNCT
iajs-2654	63	26	�	�	PROPN
iajs-2654	63	27	̈	̈	X
iajs-2654	63	28	�	�	PROPN
iajs-2654	63	29	−	−	ADP
iajs-2654	63	30	1	1	NUM
iajs-2654	63	31	𝑥	𝑥	DET
iajs-2654	63	32	�	�	PROPN
iajs-2654	63	33	̇	̇	VERB
iajs-2654	63	34	�	�	PROPN
iajs-2654	63	35	+	+	CCONJ
iajs-2654	63	36	𝑍	𝑍	PROPN
iajs-2654	63	37	=	=	SYM
iajs-2654	63	38	(	(	PUNCT
iajs-2654	63	39	4𝑥	4𝑥	NOUN
iajs-2654	63	40	+	+	CCONJ
iajs-2654	63	41	1)𝑒𝑥2	1)𝑒𝑥2	NUM
iajs-2654	63	42	+	+	CCONJ
iajs-2654	63	43	𝑥2	𝑥2	NOUN
iajs-2654	63	44	𝑍(1	𝑍(1	NUM
iajs-2654	63	45	)	)	PUNCT
iajs-2654	64	1	=	=	SYM
iajs-2654	64	2	𝑍(−1	𝑍(−1	X
iajs-2654	64	3	)	)	PUNCT
iajs-2654	64	4	=	=	SYM
iajs-2654	64	5	1	1	NUM
iajs-2654	64	6	+	+	NUM
iajs-2654	64	7	𝑒1	𝑒1	NOUN
iajs-2654	64	8	,	,	PUNCT
iajs-2654	64	9	𝑍(0	𝑍(0	X
iajs-2654	64	10	)	)	PUNCT
iajs-2654	64	11	=	=	SYM
iajs-2654	64	12	1	1	NUM
iajs-2654	64	13	,	,	PUNCT
iajs-2654	64	14	�	�	PROPN
iajs-2654	64	15	̇	̇	PROPN
iajs-2654	64	16	�	�	PROPN
iajs-2654	64	17	(0	(0	X
iajs-2654	64	18	)	)	PUNCT
iajs-2654	64	19	=	=	SYM
iajs-2654	64	20	0	0	NUM
iajs-2654	64	21	exact	exact	ADJ
iajs-2654	64	22	solution	solution	NOUN
iajs-2654	64	23	𝑥2	𝑥2	NOUN
iajs-2654	64	24	+	+	CCONJ
iajs-2654	64	25	𝑒𝑥2	𝑒𝑥2	AUX
iajs-2654	64	26	let	let	VERB
iajs-2654	64	27	�	�	PRON
iajs-2654	64	28	̈	̈	X
iajs-2654	64	29	�	�	NOUN
iajs-2654	64	30	(𝑥	(𝑥	NOUN
iajs-2654	64	31	)	)	PUNCT
iajs-2654	64	32	≅	≅	PROPN
iajs-2654	64	33	∑	∑	PROPN
iajs-2654	64	34	𝐶𝑖𝑀𝑖(𝑥)8	𝐶𝑖𝑀𝑖(𝑥)8	NUM
iajs-2654	64	35	𝑖=0	𝑖=0	NOUN
iajs-2654	64	36	the	the	DET
iajs-2654	64	37	comparison	comparison	NOUN
iajs-2654	64	38	between	between	ADP
iajs-2654	64	39	the	the	DET
iajs-2654	64	40	approximate	approximate	ADJ
iajs-2654	64	41	and	and	CCONJ
iajs-2654	64	42	exact	exact	ADJ
iajs-2654	64	43	solution	solution	NOUN
iajs-2654	64	44	are	be	AUX
iajs-2654	64	45	showing	show	VERB
iajs-2654	64	46	in	in	ADP
iajs-2654	64	47	table	table	NOUN
iajs-2654	64	48	2	2	NUM
iajs-2654	64	49	.	.	PUNCT
iajs-2654	64	50	table	table	NOUN
iajs-2654	64	51	2	2	NUM
iajs-2654	64	52	x	x	SYM
iajs-2654	64	53	approximate	approximate	ADJ
iajs-2654	64	54	exact	exact	ADJ
iajs-2654	64	55	absolute	absolute	ADJ
iajs-2654	64	56	error	error	NOUN
iajs-2654	64	57	-1	-1	ADP
iajs-2654	64	58	3.718282	3.718282	NUM
iajs-2654	64	59	3.718282	3.718282	NUM
iajs-2654	64	60	0	0	NUM
iajs-2654	64	61	-0.8	-0.8	PROPN
iajs-2654	64	62	2.536470	2.536470	NUM
iajs-2654	64	63	2.536481	2.536481	NUM
iajs-2654	64	64	0.000011	0.000011	NUM
iajs-2654	64	65	-0.6	-0.6	X
iajs-2654	64	66	1.793318	1.793318	NUM
iajs-2654	65	1	1.793329	1.793329	NUM
iajs-2654	65	2	0.000011	0.000011	NUM
iajs-2654	65	3	-0.4	-0.4	NUM
iajs-2654	65	4	1.333511	1.333511	NUM
iajs-2654	65	5	1.333511	1.333511	NUM
iajs-2654	65	6	0.000000	0.000000	NUM
iajs-2654	65	7	-0.2	-0.2	NUM
iajs-2654	65	8	1.080812	1.080812	NUM
iajs-2654	65	9	1.080811	1.080811	NUM
iajs-2654	65	10	0.000001	0.000001	NUM
iajs-2654	65	11	0	0	NUM
iajs-2654	65	12	1	1	NUM
iajs-2654	65	13	1	1	NUM
iajs-2654	65	14	0	0	NUM
iajs-2654	65	15	0.2	0.2	NUM
iajs-2654	65	16	1.080812	1.080812	NUM
iajs-2654	65	17	1.080811	1.080811	NUM
iajs-2654	65	18	0.000001	0.000001	NUM
iajs-2654	65	19	0.4	0.4	NUM
iajs-2654	65	20	1.333511	1.333511	NUM
iajs-2654	65	21	1.333511	1.333511	NUM
iajs-2654	65	22	0.000000	0.000000	NUM
iajs-2654	65	23	0.6	0.6	NUM
iajs-2654	65	24	1.793318	1.793318	NUM
iajs-2654	65	25	1.793329	1.793329	NUM
iajs-2654	65	26	0.000011	0.000011	NUM
iajs-2654	65	27	0.8	0.8	NUM
iajs-2654	65	28	2.536470	2.536470	NUM
iajs-2654	65	29	2.536481	2.536481	NUM
iajs-2654	65	30	0.000011	0.000011	NUM
iajs-2654	65	31	1	1	NUM
iajs-2654	66	1	3.718282	3.718282	NUM
iajs-2654	66	2	3.718282	3.718282	NUM
iajs-2654	66	3	0	0	NUM
iajs-2654	66	4	http://ihicps.com/	http://ihicps.com/	ADJ
iajs-2654	66	5	special	special	ADJ
iajs-2654	66	6	issue	issue	NOUN
iajs-2654	66	7	1ihicpas	1ihicpas	NUM
iajs-2654	66	8	202	202	NUM
iajs-2654	66	9	ibn	ibn	PROPN
iajs-2654	66	10	al	al	PROPN
iajs-2654	66	11	-	-	PUNCT
iajs-2654	66	12	haitham	haitham	PROPN
iajs-2654	66	13	journal	journal	PROPN
iajs-2654	66	14	for	for	ADP
iajs-2654	66	15	pure	pure	ADJ
iajs-2654	66	16	and	and	CCONJ
iajs-2654	66	17	applied	apply	VERB
iajs-2654	66	18	science	science	NOUN
iajs-2654	66	19	https://doi.org/10.30526/2021.ihicpas.2654	https://doi.org/10.30526/2021.ihicpas.2654	PUNCT
iajs-2654	66	20	for	for	ADP
iajs-2654	66	21	more	more	ADJ
iajs-2654	66	22	information	information	NOUN
iajs-2654	66	23	about	about	ADP
iajs-2654	66	24	the	the	DET
iajs-2654	66	25	conference	conference	NOUN
iajs-2654	66	26	please	please	INTJ
iajs-2654	66	27	visit	visit	VERB
iajs-2654	66	28	the	the	DET
iajs-2654	66	29	websites	website	NOUN
iajs-2654	66	30	:	:	PUNCT
iajs-2654	66	31	http://ihicps.com/	http://ihicps.com/	VERB
iajs-2654	66	32	m	m	PROPN
iajs-2654	66	33	a	a	DET
iajs-2654	66	34	t	t	NOUN
iajs-2654	66	35	h	h	NOUN
iajs-2654	67	1	e	e	NOUN
iajs-2654	67	2	m	m	VERB
iajs-2654	67	3	a	a	DET
iajs-2654	67	4	t	t	X
iajs-2654	68	1	i	i	PRON
iajs-2654	68	2	c	c	NOUN
iajs-2654	68	3	s	s	VERB
iajs-2654	69	1	|	|	ADV
iajs-2654	69	2	81	81	NUM
iajs-2654	69	3	4.conclusion	4.conclusion	NUM
iajs-2654	69	4	in	in	ADP
iajs-2654	69	5	this	this	DET
iajs-2654	69	6	article	article	NOUN
iajs-2654	69	7	,	,	PUNCT
iajs-2654	69	8	a	a	DET
iajs-2654	69	9	new	new	ADJ
iajs-2654	69	10	general	general	ADJ
iajs-2654	69	11	formula	formula	NOUN
iajs-2654	69	12	for	for	ADP
iajs-2654	69	13	morgan	morgan	PROPN
iajs-2654	69	14	-	-	PUNCT
iajs-2654	69	15	voyce	voyce	ADJ
iajs-2654	69	16	polynomial	polynomial	ADJ
iajs-2654	69	17	collocation	collocation	NOUN
iajs-2654	69	18	method	method	NOUN
iajs-2654	69	19	is	be	AUX
iajs-2654	69	20	employed	employ	VERB
iajs-2654	69	21	to	to	PART
iajs-2654	69	22	solve	solve	VERB
iajs-2654	69	23	the	the	DET
iajs-2654	69	24	three	three	NUM
iajs-2654	69	25	-	-	PUNCT
iajs-2654	69	26	point	point	NOUN
iajs-2654	69	27	boundary	boundary	ADJ
iajs-2654	69	28	value	value	NOUN
iajs-2654	69	29	problems	problem	NOUN
iajs-2654	69	30	.	.	PUNCT
iajs-2654	70	1	the	the	DET
iajs-2654	70	2	approached	approach	VERB
iajs-2654	70	3	plane	plane	NOUN
iajs-2654	70	4	is	be	AUX
iajs-2654	70	5	tested	test	VERB
iajs-2654	70	6	by	by	ADP
iajs-2654	70	7	some	some	DET
iajs-2654	70	8	examples	example	NOUN
iajs-2654	70	9	and	and	CCONJ
iajs-2654	70	10	the	the	DET
iajs-2654	70	11	results	result	NOUN
iajs-2654	70	12	are	be	AUX
iajs-2654	70	13	satisfied	satisfied	ADJ
iajs-2654	70	14	in	in	ADP
iajs-2654	70	15	comparison	comparison	NOUN
iajs-2654	70	16	with	with	ADP
iajs-2654	70	17	approximate	approximate	ADJ
iajs-2654	70	18	with	with	ADP
iajs-2654	70	19	existing	exist	VERB
iajs-2654	70	20	.	.	PUNCT
iajs-2654	71	1	references	reference	NOUN
iajs-2654	71	2	1	1	NUM
iajs-2654	71	3	.	.	X
iajs-2654	71	4	yang	yang	PROPN
iajs-2654	71	5	,	,	PUNCT
iajs-2654	71	6	c.	c.	PROPN
iajs-2654	71	7	positive	positive	ADJ
iajs-2654	71	8	solutions	solution	NOUN
iajs-2654	71	9	for	for	ADP
iajs-2654	71	10	a	a	DET
iajs-2654	71	11	three	three	NUM
iajs-2654	71	12	-	-	PUNCT
iajs-2654	71	13	point	point	NOUN
iajs-2654	71	14	boundary	boundary	ADJ
iajs-2654	71	15	value	value	NOUN
iajs-2654	71	16	problem	problem	NOUN
iajs-2654	71	17	of	of	ADP
iajs-2654	71	18	fractional	fractional	ADJ
iajs-2654	71	19	qdifference	qdifference	NOUN
iajs-2654	71	20	equations	equation	NOUN
iajs-2654	71	21	.	.	PUNCT
iajs-2654	72	1	symmetry	symmetry	PROPN
iajs-2654	72	2	.	.	PUNCT
iajs-2654	73	1	2018	2018	NUM
iajs-2654	73	2	,	,	PUNCT
iajs-2654	73	3	10(9	10(9	NUM
iajs-2654	73	4	)	)	PUNCT
iajs-2654	73	5	,	,	PUNCT
iajs-2654	73	6	358	358	NUM
iajs-2654	73	7	;	;	PUNCT
iajs-2654	73	8	doi:10.3390	doi:10.3390	NOUN
iajs-2654	73	9	/	/	SYM
iajs-2654	73	10	sym10090358	sym10090358	NOUN
iajs-2654	73	11	.	.	PUNCT
iajs-2654	74	1	2	2	X
iajs-2654	74	2	.	.	X
iajs-2654	74	3	ali	ali	PROPN
iajs-2654	74	4	,	,	PUNCT
iajs-2654	74	5	z.	z.	PROPN
iajs-2654	74	6	;	;	PUNCT
iajs-2654	74	7	zada	zada	PROPN
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iajs-2654	79	8	,	,	PUNCT
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iajs-2654	87	8	-	-	PUNCT
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iajs-2654	87	19	.	.	PUNCT
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iajs-2654	88	7	,	,	PUNCT
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iajs-2654	88	9	,	,	PUNCT
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iajs-2654	88	16	:	:	PUNCT
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iajs-2654	88	18	.	.	PUNCT
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iajs-2654	89	8	,	,	PUNCT
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iajs-2654	90	9	,	,	PUNCT
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iajs-2654	90	15	)	)	PUNCT
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iajs-2654	90	18	-	-	SYM
iajs-2654	90	19	0	0	NUM
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iajs-2654	91	29	-	-	PUNCT
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iajs-2654	92	5	,	,	PUNCT
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iajs-2654	92	9	,	,	PUNCT
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iajs-2654	92	11	-	-	PUNCT
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