id	sid	tid	token	lemma	pos
iajs-3265	1	1	ihjpas	ihjpas	PROPN
iajs-3265	1	2	.	.	PUNCT
iajs-3265	2	1	36	36	NUM
iajs-3265	2	2	(	(	PUNCT
iajs-3265	2	3	4	4	NUM
iajs-3265	2	4	)	)	PUNCT
iajs-3265	2	5	2023	2023	NUM
iajs-3265	2	6	338	338	NUM
iajs-3265	2	7	this	this	DET
iajs-3265	2	8	work	work	NOUN
iajs-3265	2	9	is	be	AUX
iajs-3265	2	10	licensed	license	VERB
iajs-3265	2	11	under	under	ADP
iajs-3265	2	12	a	a	DET
iajs-3265	2	13	creative	creative	ADJ
iajs-3265	2	14	commons	common	NOUN
iajs-3265	2	15	attribution	attribution	NOUN
iajs-3265	2	16	4.0	4.0	NUM
iajs-3265	2	17	international	international	ADJ
iajs-3265	2	18	license	license	NOUN
iajs-3265	2	19	*	*	PUNCT
iajs-3265	2	20	corresponding	correspond	VERB
iajs-3265	2	21	author	author	NOUN
iajs-3265	2	22	:	:	PUNCT
iajs-3265	2	23	othman.m.s@ihcoedu.uobaghdad.edu.iq	othman.m.s@ihcoedu.uobaghdad.edu.iq	ADJ
iajs-3265	2	24	abctract	abctract	NOUN
iajs-3265	2	25	this	this	DET
iajs-3265	2	26	paper	paper	NOUN
iajs-3265	2	27	investigates	investigate	VERB
iajs-3265	2	28	an	an	DET
iajs-3265	2	29	effective	effective	ADJ
iajs-3265	2	30	computational	computational	ADJ
iajs-3265	2	31	method	method	NOUN
iajs-3265	2	32	(	(	PUNCT
iajs-3265	2	33	ecm	ecm	PROPN
iajs-3265	2	34	)	)	PUNCT
iajs-3265	2	35	based	base	VERB
iajs-3265	2	36	on	on	ADP
iajs-3265	2	37	the	the	DET
iajs-3265	2	38	standard	standard	ADJ
iajs-3265	2	39	polynomials	polynomial	NOUN
iajs-3265	2	40	used	use	VERB
iajs-3265	2	41	to	to	PART
iajs-3265	2	42	solve	solve	VERB
iajs-3265	2	43	some	some	DET
iajs-3265	2	44	nonlinear	nonlinear	ADJ
iajs-3265	2	45	initial	initial	ADJ
iajs-3265	2	46	and	and	CCONJ
iajs-3265	2	47	boundary	boundary	ADJ
iajs-3265	2	48	value	value	NOUN
iajs-3265	2	49	problems	problem	NOUN
iajs-3265	2	50	in	in	ADP
iajs-3265	2	51	engineering	engineering	NOUN
iajs-3265	2	52	and	and	CCONJ
iajs-3265	2	53	applied	apply	VERB
iajs-3265	2	54	sciences	science	NOUN
iajs-3265	2	55	.	.	PUNCT
iajs-3265	3	1	moreover	moreover	ADV
iajs-3265	3	2	,	,	PUNCT
iajs-3265	3	3	the	the	DET
iajs-3265	3	4	effective	effective	ADJ
iajs-3265	3	5	computational	computational	ADJ
iajs-3265	3	6	methods	method	NOUN
iajs-3265	3	7	in	in	ADP
iajs-3265	3	8	this	this	DET
iajs-3265	3	9	paper	paper	NOUN
iajs-3265	3	10	were	be	AUX
iajs-3265	3	11	improved	improve	VERB
iajs-3265	3	12	by	by	ADP
iajs-3265	3	13	suitable	suitable	ADJ
iajs-3265	3	14	orthogonal	orthogonal	ADJ
iajs-3265	3	15	base	base	NOUN
iajs-3265	3	16	functions	function	NOUN
iajs-3265	3	17	,	,	PUNCT
iajs-3265	3	18	especially	especially	ADV
iajs-3265	3	19	the	the	DET
iajs-3265	3	20	chebyshev	chebyshev	NOUN
iajs-3265	3	21	,	,	PUNCT
iajs-3265	3	22	bernoulli	bernoulli	PROPN
iajs-3265	3	23	,	,	PUNCT
iajs-3265	3	24	and	and	CCONJ
iajs-3265	3	25	laguerre	laguerre	NOUN
iajs-3265	3	26	polynomials	polynomial	NOUN
iajs-3265	3	27	,	,	PUNCT
iajs-3265	3	28	to	to	PART
iajs-3265	3	29	obtain	obtain	VERB
iajs-3265	3	30	novel	novel	ADJ
iajs-3265	3	31	approximate	approximate	ADJ
iajs-3265	3	32	solutions	solution	NOUN
iajs-3265	3	33	for	for	ADP
iajs-3265	3	34	some	some	DET
iajs-3265	3	35	nonlinear	nonlinear	ADJ
iajs-3265	3	36	problems	problem	NOUN
iajs-3265	3	37	.	.	PUNCT
iajs-3265	4	1	these	these	DET
iajs-3265	4	2	base	base	NOUN
iajs-3265	4	3	functions	function	NOUN
iajs-3265	4	4	enable	enable	VERB
iajs-3265	4	5	the	the	DET
iajs-3265	4	6	nonlinear	nonlinear	ADJ
iajs-3265	4	7	problem	problem	NOUN
iajs-3265	4	8	to	to	PART
iajs-3265	4	9	be	be	AUX
iajs-3265	4	10	effectively	effectively	ADV
iajs-3265	4	11	converted	convert	VERB
iajs-3265	4	12	into	into	ADP
iajs-3265	4	13	a	a	DET
iajs-3265	4	14	nonlinear	nonlinear	ADJ
iajs-3265	4	15	algebraic	algebraic	ADJ
iajs-3265	4	16	system	system	NOUN
iajs-3265	4	17	of	of	ADP
iajs-3265	4	18	equations	equation	NOUN
iajs-3265	4	19	,	,	PUNCT
iajs-3265	4	20	which	which	PRON
iajs-3265	4	21	are	be	AUX
iajs-3265	4	22	then	then	ADV
iajs-3265	4	23	solved	solve	VERB
iajs-3265	4	24	using	use	VERB
iajs-3265	4	25	mathematica	mathematica	PROPN
iajs-3265	4	26	®	®	PROPN
iajs-3265	4	27	12	12	NUM
iajs-3265	4	28	.	.	PUNCT
iajs-3265	5	1	the	the	DET
iajs-3265	5	2	improved	improved	ADJ
iajs-3265	5	3	effective	effective	ADJ
iajs-3265	5	4	computational	computational	ADJ
iajs-3265	5	5	methods	method	NOUN
iajs-3265	5	6	(	(	PUNCT
iajs-3265	5	7	i	i	NOUN
iajs-3265	5	8	-	-	PUNCT
iajs-3265	5	9	ecms	ecms	NOUN
iajs-3265	5	10	)	)	PUNCT
iajs-3265	5	11	have	have	AUX
iajs-3265	5	12	been	be	AUX
iajs-3265	5	13	implemented	implement	VERB
iajs-3265	5	14	to	to	PART
iajs-3265	5	15	solve	solve	VERB
iajs-3265	5	16	three	three	NUM
iajs-3265	5	17	applications	application	NOUN
iajs-3265	5	18	involving	involve	VERB
iajs-3265	5	19	nonlinear	nonlinear	ADJ
iajs-3265	5	20	initial	initial	ADJ
iajs-3265	5	21	and	and	CCONJ
iajs-3265	5	22	boundary	boundary	ADJ
iajs-3265	5	23	value	value	NOUN
iajs-3265	5	24	problems	problem	NOUN
iajs-3265	5	25	:	:	PUNCT
iajs-3265	5	26	the	the	DET
iajs-3265	5	27	darcy	darcy	PROPN
iajs-3265	5	28	-	-	PUNCT
iajs-3265	5	29	brinkman	brinkman	PROPN
iajs-3265	5	30	-	-	PUNCT
iajs-3265	5	31	forchheimer	forchheimer	PROPN
iajs-3265	5	32	equation	equation	NOUN
iajs-3265	5	33	,	,	PUNCT
iajs-3265	5	34	the	the	DET
iajs-3265	5	35	blasius	blasius	ADJ
iajs-3265	5	36	equation	equation	NOUN
iajs-3265	5	37	,	,	PUNCT
iajs-3265	5	38	and	and	CCONJ
iajs-3265	5	39	the	the	DET
iajs-3265	5	40	falkner	falkner	PROPN
iajs-3265	5	41	-	-	PUNCT
iajs-3265	5	42	skan	skan	VERB
iajs-3265	5	43	equation	equation	NOUN
iajs-3265	5	44	,	,	PUNCT
iajs-3265	5	45	and	and	CCONJ
iajs-3265	5	46	a	a	DET
iajs-3265	5	47	comparison	comparison	NOUN
iajs-3265	5	48	between	between	ADP
iajs-3265	5	49	the	the	DET
iajs-3265	5	50	proposed	propose	VERB
iajs-3265	5	51	methods	method	NOUN
iajs-3265	5	52	has	have	AUX
iajs-3265	5	53	been	be	AUX
iajs-3265	5	54	presented	present	VERB
iajs-3265	5	55	.	.	PUNCT
iajs-3265	6	1	furthermore	furthermore	ADV
iajs-3265	6	2	,	,	PUNCT
iajs-3265	6	3	the	the	DET
iajs-3265	6	4	maximum	maximum	ADJ
iajs-3265	6	5	error	error	NOUN
iajs-3265	6	6	remainder	remainder	NOUN
iajs-3265	6	7	(	(	PUNCT
iajs-3265	6	8	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	PROPN
iajs-3265	6	9	)	)	PUNCT
iajs-3265	6	10	has	have	AUX
iajs-3265	6	11	been	be	AUX
iajs-3265	6	12	computed	compute	VERB
iajs-3265	6	13	to	to	PART
iajs-3265	6	14	prove	prove	VERB
iajs-3265	6	15	the	the	DET
iajs-3265	6	16	proposed	propose	VERB
iajs-3265	6	17	methods	method	NOUN
iajs-3265	6	18	'	'	PART
iajs-3265	6	19	accuracy	accuracy	NOUN
iajs-3265	6	20	.	.	PUNCT
iajs-3265	7	1	the	the	DET
iajs-3265	7	2	results	result	NOUN
iajs-3265	7	3	convincingly	convincingly	ADV
iajs-3265	7	4	prove	prove	VERB
iajs-3265	7	5	that	that	SCONJ
iajs-3265	7	6	ecm	ecm	NOUN
iajs-3265	7	7	and	and	CCONJ
iajs-3265	7	8	i	i	PROPN
iajs-3265	7	9	-	-	PUNCT
iajs-3265	7	10	ecms	ecms	PROPN
iajs-3265	7	11	are	be	AUX
iajs-3265	7	12	effective	effective	ADJ
iajs-3265	7	13	and	and	CCONJ
iajs-3265	7	14	accurate	accurate	ADJ
iajs-3265	7	15	in	in	ADP
iajs-3265	7	16	obtaining	obtain	VERB
iajs-3265	7	17	novel	novel	ADJ
iajs-3265	7	18	approximate	approximate	ADJ
iajs-3265	7	19	solutions	solution	NOUN
iajs-3265	7	20	to	to	ADP
iajs-3265	7	21	the	the	DET
iajs-3265	7	22	problems	problem	NOUN
iajs-3265	7	23	.	.	PUNCT
iajs-3265	8	1	keywords	keyword	NOUN
iajs-3265	8	2	:	:	PUNCT
iajs-3265	8	3	darcy	darcy	PROPN
iajs-3265	8	4	-	-	PUNCT
iajs-3265	8	5	brinkman	brinkman	PROPN
iajs-3265	8	6	-	-	PUNCT
iajs-3265	8	7	forchheimer	forchheimer	PROPN
iajs-3265	8	8	equation	equation	NOUN
iajs-3265	8	9	;	;	PUNCT
iajs-3265	8	10	blasius	blasius	ADJ
iajs-3265	8	11	equation	equation	NOUN
iajs-3265	8	12	;	;	PUNCT
iajs-3265	8	13	falkner	falkner	PROPN
iajs-3265	8	14	-	-	PUNCT
iajs-3265	8	15	skan	skan	PROPN
iajs-3265	8	16	equation	equation	NOUN
iajs-3265	8	17	;	;	PUNCT
iajs-3265	8	18	chebyshev	chebyshev	NOUN
iajs-3265	8	19	polynomials	polynomial	NOUN
iajs-3265	8	20	;	;	PUNCT
iajs-3265	8	21	bernoulli	bernoulli	NOUN
iajs-3265	8	22	polynomials	polynomial	NOUN
iajs-3265	8	23	;	;	PUNCT
iajs-3265	8	24	laguerre	laguerre	NOUN
iajs-3265	8	25	polynomials	polynomial	NOUN
iajs-3265	8	26	.	.	PUNCT
iajs-3265	9	1	doi.org/10.30526/36.4.3265	doi.org/10.30526/36.4.3265	AUX
iajs-3265	9	2	article	article	NOUN
iajs-3265	9	3	history	history	NOUN
iajs-3265	9	4	:	:	PUNCT
iajs-3265	9	5	received	receive	VERB
iajs-3265	9	6	03	03	NUM
iajs-3265	9	7	februray	februray	ADJ
iajs-3265	9	8	2022	2022	NUM
iajs-3265	9	9	,	,	PUNCT
iajs-3265	9	10	accepted	accept	VERB
iajs-3265	9	11	14	14	NUM
iajs-3265	9	12	march	march	NOUN
iajs-3265	9	13	2023	2023	NUM
iajs-3265	9	14	,	,	PUNCT
iajs-3265	9	15	published	publish	VERB
iajs-3265	9	16	in	in	ADP
iajs-3265	9	17	october	october	PROPN
iajs-3265	9	18	2023	2023	NUM
iajs-3265	9	19	ibn	ibn	PROPN
iajs-3265	9	20	al	al	PROPN
iajs-3265	9	21	-	-	PUNCT
iajs-3265	9	22	haitham	haitham	PROPN
iajs-3265	9	23	journal	journal	PROPN
iajs-3265	9	24	for	for	ADP
iajs-3265	9	25	pure	pure	ADJ
iajs-3265	9	26	and	and	CCONJ
iajs-3265	9	27	applied	applied	ADJ
iajs-3265	9	28	sciences	sciences	PROPN
iajs-3265	9	29	journal	journal	PROPN
iajs-3265	9	30	homepage	homepage	NOUN
iajs-3265	9	31	:	:	PUNCT
iajs-3265	9	32	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	NOUN
iajs-3265	9	33	novel	novel	ADJ
iajs-3265	9	34	approximate	approximate	ADJ
iajs-3265	9	35	solutions	solution	NOUN
iajs-3265	9	36	for	for	ADP
iajs-3265	9	37	nonlinear	nonlinear	ADJ
iajs-3265	9	38	initial	initial	ADJ
iajs-3265	9	39	and	and	CCONJ
iajs-3265	9	40	boundary	boundary	ADJ
iajs-3265	9	41	value	value	NOUN
iajs-3265	9	42	problems	problem	NOUN
iajs-3265	9	43	othman	othman	PROPN
iajs-3265	9	44	mahdi	mahdi	PROPN
iajs-3265	9	45	salih	salih	PROPN
iajs-3265	9	46	*	*	PROPN
iajs-3265	9	47	department	department	PROPN
iajs-3265	9	48	of	of	ADP
iajs-3265	9	49	mathematics	mathematics	PROPN
iajs-3265	9	50	,	,	PUNCT
iajs-3265	9	51	college	college	NOUN
iajs-3265	9	52	of	of	ADP
iajs-3265	9	53	education	education	NOUN
iajs-3265	9	54	for	for	ADP
iajs-3265	9	55	pure	pure	ADJ
iajs-3265	9	56	sciences	science	NOUN
iajs-3265	9	57	ibn	ibn	PROPN
iajs-3265	9	58	al	al	PROPN
iajs-3265	9	59	-	-	PUNCT
iajs-3265	9	60	haitham	haitham	PROPN
iajs-3265	9	61	,	,	PUNCT
iajs-3265	9	62	university	university	PROPN
iajs-3265	9	63	of	of	ADP
iajs-3265	9	64	baghdad	baghdad	PROPN
iajs-3265	9	65	,	,	PUNCT
iajs-3265	9	66	baghdad	baghdad	PROPN
iajs-3265	9	67	,	,	PUNCT
iajs-3265	9	68	iraq	iraq	PROPN
iajs-3265	9	69	.	.	PUNCT
iajs-3265	10	1	majeed	majeed	PROPN
iajs-3265	10	2	a.	a.	PROPN
iajs-3265	10	3	al	al	PROPN
iajs-3265	10	4	-	-	PUNCT
iajs-3265	10	5	jawary	jawary	PROPN
iajs-3265	10	6	department	department	PROPN
iajs-3265	10	7	of	of	ADP
iajs-3265	10	8	mathematics	mathematics	PROPN
iajs-3265	10	9	,	,	PUNCT
iajs-3265	10	10	college	college	NOUN
iajs-3265	10	11	of	of	ADP
iajs-3265	10	12	education	education	NOUN
iajs-3265	10	13	for	for	ADP
iajs-3265	10	14	pure	pure	ADJ
iajs-3265	10	15	sciences	science	NOUN
iajs-3265	10	16	ibn	ibn	PROPN
iajs-3265	10	17	al	al	PROPN
iajs-3265	10	18	-	-	PUNCT
iajs-3265	10	19	haitham	haitham	PROPN
iajs-3265	10	20	,	,	PUNCT
iajs-3265	10	21	university	university	PROPN
iajs-3265	10	22	of	of	ADP
iajs-3265	10	23	baghdad	baghdad	PROPN
iajs-3265	10	24	,	,	PUNCT
iajs-3265	10	25	baghdad	baghdad	PROPN
iajs-3265	10	26	,	,	PUNCT
iajs-3265	10	27	iraq	iraq	PROPN
iajs-3265	10	28	.	.	PUNCT
iajs-3265	11	1	mustafa	mustafa	PROPN
iajs-3265	11	2	turkyilmazoglu	turkyilmazoglu	NOUN
iajs-3265	11	3	-department	-department	NOUN
iajs-3265	11	4	of	of	ADP
iajs-3265	11	5	mathematics	mathematic	NOUN
iajs-3265	11	6	,	,	PUNCT
iajs-3265	11	7	hacettepe	hacettepe	PROPN
iajs-3265	11	8	university	university	NOUN
iajs-3265	11	9	,	,	PUNCT
iajs-3265	11	10	ankara	ankara	PROPN
iajs-3265	11	11	,	,	PUNCT
iajs-3265	11	12	turkey	turkey	PROPN
iajs-3265	11	13	.	.	PUNCT
iajs-3265	12	1	-department	-department	NOUN
iajs-3265	12	2	of	of	ADP
iajs-3265	12	3	medical	medical	ADJ
iajs-3265	12	4	research	research	NOUN
iajs-3265	12	5	,	,	PUNCT
iajs-3265	12	6	china	china	PROPN
iajs-3265	12	7	medical	medical	PROPN
iajs-3265	12	8	university	university	PROPN
iajs-3265	12	9	hospital	hospital	NOUN
iajs-3265	12	10	,	,	PUNCT
iajs-3265	12	11	china	china	PROPN
iajs-3265	12	12	medical	medical	PROPN
iajs-3265	12	13	university	university	PROPN
iajs-3265	12	14	,	,	PUNCT
iajs-3265	12	15	taichung	taichung	PROPN
iajs-3265	12	16	,	,	PUNCT
iajs-3265	12	17	taiwan	taiwan	PROPN
iajs-3265	12	18	.	.	PUNCT
iajs-3265	13	1	turkyilm@hacettepe.edu.tr	turkyilm@hacettepe.edu.tr	PROPN
iajs-3265	13	2	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3265	13	3	mailto:othman.m.s@ihcoedu.uobaghdad.edu.iq	mailto:othman.m.s@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-3265	13	4	mailto:othman.m.s@ihcoedu.uobaghdad.edu.iq	mailto:othman.m.s@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-3265	13	5	mailto:majeed.a.w@ihcoedu.uobaghdad.edu.iq	mailto:majeed.a.w@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-3265	13	6	mailto:turkyilm@hacettepe.edu.tr	mailto:turkyilm@hacettepe.edu.tr	PROPN
iajs-3265	13	7	mailto:turkyilm@hacettepe.edu.tr	mailto:turkyilm@hacettepe.edu.tr	PROPN
iajs-3265	13	8	ihjpas	ihjpas	PROPN
iajs-3265	13	9	.	.	PUNCT
iajs-3265	14	1	36	36	NUM
iajs-3265	14	2	(	(	PUNCT
iajs-3265	14	3	4	4	NUM
iajs-3265	14	4	)	)	PUNCT
iajs-3265	14	5	2023	2023	NUM
iajs-3265	14	6	339	339	NUM
iajs-3265	14	7	1	1	NUM
iajs-3265	14	8	.	.	PUNCT
iajs-3265	14	9	introduction	introduction	NOUN
iajs-3265	14	10	there	there	PRON
iajs-3265	14	11	are	be	VERB
iajs-3265	14	12	many	many	ADJ
iajs-3265	14	13	problems	problem	NOUN
iajs-3265	14	14	in	in	ADP
iajs-3265	14	15	engineering	engineering	NOUN
iajs-3265	14	16	and	and	CCONJ
iajs-3265	14	17	applied	apply	VERB
iajs-3265	14	18	sciences	science	NOUN
iajs-3265	14	19	,	,	PUNCT
iajs-3265	14	20	such	such	ADJ
iajs-3265	14	21	as	as	ADP
iajs-3265	14	22	fluid	fluid	ADJ
iajs-3265	14	23	flow	flow	NOUN
iajs-3265	14	24	models	model	NOUN
iajs-3265	14	25	,	,	PUNCT
iajs-3265	14	26	mechanical	mechanical	ADJ
iajs-3265	14	27	engineering	engineering	NOUN
iajs-3265	14	28	,	,	PUNCT
iajs-3265	14	29	and	and	CCONJ
iajs-3265	14	30	mathematical	mathematical	ADJ
iajs-3265	14	31	physics	physics	NOUN
iajs-3265	14	32	,	,	PUNCT
iajs-3265	14	33	which	which	PRON
iajs-3265	14	34	can	can	AUX
iajs-3265	14	35	be	be	AUX
iajs-3265	14	36	described	describe	VERB
iajs-3265	14	37	by	by	ADP
iajs-3265	14	38	nonlinear	nonlinear	ADJ
iajs-3265	14	39	ordinary	ordinary	ADJ
iajs-3265	14	40	differential	differential	ADJ
iajs-3265	14	41	equations	equation	NOUN
iajs-3265	15	1	[	[	X
iajs-3265	15	2	1	1	NUM
iajs-3265	15	3	]	]	PUNCT
iajs-3265	15	4	.	.	PUNCT
iajs-3265	16	1	this	this	PRON
iajs-3265	16	2	leads	lead	VERB
iajs-3265	16	3	to	to	ADP
iajs-3265	16	4	significant	significant	ADJ
iajs-3265	16	5	computational	computational	ADJ
iajs-3265	16	6	difficulties	difficulty	NOUN
iajs-3265	16	7	for	for	ADP
iajs-3265	16	8	nonlinear	nonlinear	ADJ
iajs-3265	16	9	boundary	boundary	ADJ
iajs-3265	16	10	conditions	condition	NOUN
iajs-3265	16	11	,	,	PUNCT
iajs-3265	16	12	particularly	particularly	ADV
iajs-3265	16	13	for	for	ADP
iajs-3265	16	14	nonlinear	nonlinear	ADJ
iajs-3265	16	15	initial	initial	ADJ
iajs-3265	16	16	value	value	NOUN
iajs-3265	16	17	problems	problem	NOUN
iajs-3265	16	18	[	[	X
iajs-3265	16	19	2	2	NUM
iajs-3265	16	20	]	]	PUNCT
iajs-3265	16	21	.	.	PUNCT
iajs-3265	17	1	since	since	SCONJ
iajs-3265	17	2	the	the	DET
iajs-3265	17	3	exact	exact	ADJ
iajs-3265	17	4	solutions	solution	NOUN
iajs-3265	17	5	to	to	ADP
iajs-3265	17	6	these	these	DET
iajs-3265	17	7	problems	problem	NOUN
iajs-3265	17	8	are	be	AUX
iajs-3265	17	9	often	often	ADV
iajs-3265	17	10	complicated	complicated	ADJ
iajs-3265	17	11	or	or	CCONJ
iajs-3265	17	12	occasionally	occasionally	ADV
iajs-3265	17	13	may	may	AUX
iajs-3265	17	14	not	not	PART
iajs-3265	17	15	be	be	AUX
iajs-3265	17	16	available	available	ADJ
iajs-3265	17	17	.	.	PUNCT
iajs-3265	18	1	therefore	therefore	ADV
iajs-3265	18	2	,	,	PUNCT
iajs-3265	18	3	there	there	PRON
iajs-3265	18	4	is	be	VERB
iajs-3265	18	5	a	a	DET
iajs-3265	18	6	great	great	ADJ
iajs-3265	18	7	need	need	NOUN
iajs-3265	18	8	to	to	PART
iajs-3265	18	9	develop	develop	VERB
iajs-3265	18	10	efficient	efficient	ADJ
iajs-3265	18	11	,	,	PUNCT
iajs-3265	18	12	novel	novel	ADJ
iajs-3265	18	13	approximate	approximate	NOUN
iajs-3265	18	14	,	,	PUNCT
iajs-3265	18	15	and	and	CCONJ
iajs-3265	18	16	numerical	numerical	ADJ
iajs-3265	18	17	methods	method	NOUN
iajs-3265	18	18	to	to	PART
iajs-3265	18	19	solve	solve	VERB
iajs-3265	18	20	these	these	DET
iajs-3265	18	21	problems	problem	NOUN
iajs-3265	18	22	[	[	X
iajs-3265	18	23	3	3	NUM
iajs-3265	18	24	and	and	CCONJ
iajs-3265	18	25	4	4	NUM
iajs-3265	18	26	]	]	PUNCT
iajs-3265	18	27	.	.	PUNCT
iajs-3265	19	1	numerous	numerous	ADJ
iajs-3265	19	2	analytical	analytical	ADJ
iajs-3265	19	3	and	and	CCONJ
iajs-3265	19	4	approximate	approximate	ADJ
iajs-3265	19	5	methods	method	NOUN
iajs-3265	19	6	for	for	ADP
iajs-3265	19	7	solving	solve	VERB
iajs-3265	19	8	nonlinear	nonlinear	ADJ
iajs-3265	19	9	differential	differential	ADJ
iajs-3265	19	10	equations	equation	NOUN
iajs-3265	19	11	have	have	AUX
iajs-3265	19	12	been	be	AUX
iajs-3265	19	13	introduced	introduce	VERB
iajs-3265	19	14	and	and	CCONJ
iajs-3265	19	15	developed	develop	VERB
iajs-3265	19	16	by	by	ADP
iajs-3265	19	17	authors	author	NOUN
iajs-3265	19	18	around	around	ADP
iajs-3265	19	19	the	the	DET
iajs-3265	19	20	world	world	NOUN
iajs-3265	19	21	,	,	PUNCT
iajs-3265	19	22	such	such	ADJ
iajs-3265	19	23	as	as	ADP
iajs-3265	19	24	the	the	DET
iajs-3265	19	25	advanced	advanced	ADJ
iajs-3265	19	26	adomian	adomian	NOUN
iajs-3265	19	27	decomposition	decomposition	NOUN
iajs-3265	19	28	method	method	NOUN
iajs-3265	19	29	[	[	X
iajs-3265	19	30	5	5	NUM
iajs-3265	19	31	]	]	PUNCT
iajs-3265	19	32	,	,	PUNCT
iajs-3265	19	33	the	the	DET
iajs-3265	19	34	variational	variational	ADJ
iajs-3265	19	35	iteration	iteration	NOUN
iajs-3265	19	36	method	method	NOUN
iajs-3265	19	37	(	(	PUNCT
iajs-3265	19	38	vim	vim	NOUN
iajs-3265	19	39	)	)	PUNCT
iajs-3265	19	40	,	,	PUNCT
iajs-3265	19	41	the	the	DET
iajs-3265	19	42	differential	differential	ADJ
iajs-3265	19	43	transformation	transformation	NOUN
iajs-3265	19	44	method	method	NOUN
iajs-3265	19	45	(	(	PUNCT
iajs-3265	19	46	dtm	dtm	PROPN
iajs-3265	19	47	)	)	PUNCT
iajs-3265	20	1	[	[	X
iajs-3265	20	2	6	6	NUM
iajs-3265	20	3	]	]	PUNCT
iajs-3265	20	4	,	,	PUNCT
iajs-3265	20	5	the	the	DET
iajs-3265	20	6	finite	finite	ADJ
iajs-3265	20	7	difference	difference	NOUN
iajs-3265	20	8	methods	method	NOUN
iajs-3265	20	9	[	[	X
iajs-3265	20	10	7	7	NUM
iajs-3265	20	11	]	]	PUNCT
iajs-3265	20	12	,	,	PUNCT
iajs-3265	20	13	the	the	DET
iajs-3265	20	14	optimal	optimal	ADJ
iajs-3265	20	15	quartic	quartic	ADJ
iajs-3265	20	16	bspline	bspline	NOUN
iajs-3265	20	17	collocation	collocation	NOUN
iajs-3265	20	18	method	method	NOUN
iajs-3265	20	19	[	[	X
iajs-3265	20	20	8	8	NUM
iajs-3265	20	21	]	]	PUNCT
iajs-3265	20	22	,	,	PUNCT
iajs-3265	20	23	the	the	DET
iajs-3265	20	24	homotopy	homotopy	NOUN
iajs-3265	20	25	analysis	analysis	NOUN
iajs-3265	20	26	method	method	NOUN
iajs-3265	20	27	with	with	ADP
iajs-3265	20	28	padé	padé	NOUN
iajs-3265	20	29	approximations	approximation	NOUN
iajs-3265	20	30	[	[	X
iajs-3265	20	31	9	9	NUM
iajs-3265	20	32	]	]	PUNCT
iajs-3265	20	33	,	,	PUNCT
iajs-3265	20	34	the	the	DET
iajs-3265	20	35	chebyshev	chebyshev	PROPN
iajs-3265	20	36	operational	operational	ADJ
iajs-3265	20	37	matrix	matrix	NOUN
iajs-3265	20	38	method	method	NOUN
iajs-3265	20	39	[	[	X
iajs-3265	20	40	10	10	NUM
iajs-3265	20	41	]	]	PUNCT
iajs-3265	20	42	,	,	PUNCT
iajs-3265	20	43	the	the	DET
iajs-3265	20	44	bernoulli	bernoulli	PROPN
iajs-3265	20	45	matrix	matrix	NOUN
iajs-3265	20	46	method	method	NOUN
iajs-3265	20	47	[	[	X
iajs-3265	20	48	11	11	NUM
iajs-3265	20	49	]	]	PUNCT
iajs-3265	20	50	,	,	PUNCT
iajs-3265	20	51	the	the	DET
iajs-3265	20	52	laguerre	laguerre	NOUN
iajs-3265	20	53	collocation	collocation	NOUN
iajs-3265	20	54	method	method	NOUN
iajs-3265	20	55	[	[	X
iajs-3265	20	56	12	12	NUM
iajs-3265	20	57	]	]	PUNCT
iajs-3265	20	58	.	.	PUNCT
iajs-3265	21	1	in	in	ADP
iajs-3265	21	2	particular	particular	ADJ
iajs-3265	21	3	,	,	PUNCT
iajs-3265	21	4	al	al	PROPN
iajs-3265	21	5	-	-	PUNCT
iajs-3265	21	6	jawary	jawary	PROPN
iajs-3265	21	7	et	et	PROPN
iajs-3265	21	8	al	al	PROPN
iajs-3265	21	9	.	.	PUNCT
iajs-3265	22	1	[	[	X
iajs-3265	22	2	13	13	NUM
iajs-3265	22	3	]	]	PUNCT
iajs-3265	22	4	have	have	AUX
iajs-3265	22	5	applied	apply	VERB
iajs-3265	22	6	the	the	DET
iajs-3265	22	7	daftardar	daftardar	ADV
iajs-3265	22	8	-	-	PUNCT
iajs-3265	22	9	jafari	jafari	ADJ
iajs-3265	22	10	method	method	NOUN
iajs-3265	22	11	(	(	PUNCT
iajs-3265	22	12	djm	djm	PROPN
iajs-3265	22	13	)	)	PUNCT
iajs-3265	22	14	,	,	PUNCT
iajs-3265	22	15	the	the	DET
iajs-3265	22	16	temimi	temimi	NOUN
iajs-3265	22	17	-	-	PUNCT
iajs-3265	22	18	ansari	ansari	ADJ
iajs-3265	22	19	method	method	NOUN
iajs-3265	22	20	(	(	PUNCT
iajs-3265	22	21	tam	tam	NOUN
iajs-3265	22	22	)	)	PUNCT
iajs-3265	22	23	,	,	PUNCT
iajs-3265	22	24	and	and	CCONJ
iajs-3265	22	25	the	the	DET
iajs-3265	22	26	banach	banach	NOUN
iajs-3265	22	27	contraction	contraction	NOUN
iajs-3265	22	28	method	method	NOUN
iajs-3265	22	29	(	(	PUNCT
iajs-3265	22	30	bcm	bcm	NOUN
iajs-3265	22	31	)	)	PUNCT
iajs-3265	22	32	to	to	PART
iajs-3265	22	33	obtain	obtain	VERB
iajs-3265	22	34	the	the	DET
iajs-3265	22	35	solution	solution	NOUN
iajs-3265	22	36	for	for	ADP
iajs-3265	22	37	the	the	DET
iajs-3265	22	38	jeffery	jeffery	PROPN
iajs-3265	22	39	-	-	PUNCT
iajs-3265	22	40	hamel	hamel	PROPN
iajs-3265	22	41	flow	flow	NOUN
iajs-3265	22	42	problem	problem	NOUN
iajs-3265	22	43	.	.	PUNCT
iajs-3265	23	1	agom	agom	PROPN
iajs-3265	23	2	et	et	PROPN
iajs-3265	23	3	al	al	PROPN
iajs-3265	23	4	.	.	PUNCT
iajs-3265	24	1	[	[	X
iajs-3265	24	2	14	14	NUM
iajs-3265	24	3	]	]	PUNCT
iajs-3265	24	4	have	have	AUX
iajs-3265	24	5	implemented	implement	VERB
iajs-3265	24	6	the	the	DET
iajs-3265	24	7	homotopy	homotopy	NOUN
iajs-3265	24	8	perturbation	perturbation	NOUN
iajs-3265	24	9	method	method	NOUN
iajs-3265	24	10	(	(	PUNCT
iajs-3265	24	11	hpm	hpm	NOUN
iajs-3265	24	12	)	)	PUNCT
iajs-3265	24	13	and	and	CCONJ
iajs-3265	24	14	the	the	DET
iajs-3265	24	15	adomian	adomian	NOUN
iajs-3265	24	16	decomposition	decomposition	NOUN
iajs-3265	24	17	method	method	NOUN
iajs-3265	24	18	(	(	PUNCT
iajs-3265	24	19	adm	adm	PROPN
iajs-3265	24	20	)	)	PUNCT
iajs-3265	24	21	for	for	ADP
iajs-3265	24	22	solving	solve	VERB
iajs-3265	24	23	the	the	DET
iajs-3265	24	24	12𝑡ℎ-order	12𝑡ℎ-order	NUM
iajs-3265	24	25	boundary	boundary	ADJ
iajs-3265	24	26	value	value	NOUN
iajs-3265	24	27	problems	problem	NOUN
iajs-3265	24	28	in	in	ADP
iajs-3265	24	29	finite	finite	ADJ
iajs-3265	24	30	domains	domain	NOUN
iajs-3265	24	31	.	.	PUNCT
iajs-3265	25	1	also	also	ADV
iajs-3265	25	2	,	,	PUNCT
iajs-3265	25	3	singh	singh	PROPN
iajs-3265	26	1	[	[	X
iajs-3265	26	2	15	15	NUM
iajs-3265	26	3	]	]	PUNCT
iajs-3265	26	4	used	use	VERB
iajs-3265	26	5	the	the	DET
iajs-3265	26	6	modified	modify	VERB
iajs-3265	26	7	homotopy	homotopy	NOUN
iajs-3265	26	8	perturbation	perturbation	NOUN
iajs-3265	26	9	approach	approach	NOUN
iajs-3265	26	10	to	to	PART
iajs-3265	26	11	solve	solve	VERB
iajs-3265	26	12	a	a	DET
iajs-3265	26	13	set	set	NOUN
iajs-3265	26	14	of	of	ADP
iajs-3265	26	15	nonlinear	nonlinear	ADJ
iajs-3265	26	16	lane	lane	NOUN
iajs-3265	26	17	-	-	PUNCT
iajs-3265	26	18	emden	emden	NOUN
iajs-3265	26	19	equations	equation	NOUN
iajs-3265	26	20	.	.	PUNCT
iajs-3265	27	1	ibraheem	ibraheem	PROPN
iajs-3265	27	2	et	et	PROPN
iajs-3265	27	3	al	al	PROPN
iajs-3265	27	4	.	.	PUNCT
iajs-3265	28	1	[	[	X
iajs-3265	28	2	16	16	NUM
iajs-3265	28	3	]	]	PUNCT
iajs-3265	28	4	have	have	AUX
iajs-3265	28	5	recently	recently	ADV
iajs-3265	28	6	implemented	implement	VERB
iajs-3265	28	7	the	the	DET
iajs-3265	28	8	operational	operational	ADJ
iajs-3265	28	9	matrix	matrix	NOUN
iajs-3265	28	10	of	of	ADP
iajs-3265	28	11	legendre	legendre	PROPN
iajs-3265	28	12	polynomials	polynomial	NOUN
iajs-3265	28	13	to	to	PART
iajs-3265	28	14	solve	solve	VERB
iajs-3265	28	15	nonlinear	nonlinear	ADJ
iajs-3265	28	16	thin	thin	ADJ
iajs-3265	28	17	-	-	PUNCT
iajs-3265	28	18	film	film	NOUN
iajs-3265	28	19	flow	flow	NOUN
iajs-3265	28	20	problems	problem	NOUN
iajs-3265	28	21	.	.	PUNCT
iajs-3265	29	1	gürbüz	gürbüz	PROPN
iajs-3265	29	2	et	et	PROPN
iajs-3265	29	3	al	al	PROPN
iajs-3265	29	4	.	.	PUNCT
iajs-3265	30	1	[	[	X
iajs-3265	30	2	17	17	NUM
iajs-3265	30	3	]	]	PUNCT
iajs-3265	30	4	used	use	VERB
iajs-3265	30	5	the	the	DET
iajs-3265	30	6	matrix	matrix	NOUN
iajs-3265	30	7	relations	relation	NOUN
iajs-3265	30	8	between	between	ADP
iajs-3265	30	9	the	the	DET
iajs-3265	30	10	laguerre	laguerre	NOUN
iajs-3265	30	11	polynomials	polynomial	NOUN
iajs-3265	30	12	and	and	CCONJ
iajs-3265	30	13	their	their	PRON
iajs-3265	30	14	derivatives	derivative	NOUN
iajs-3265	30	15	to	to	PART
iajs-3265	30	16	study	study	VERB
iajs-3265	30	17	second	second	ADJ
iajs-3265	30	18	-	-	PUNCT
iajs-3265	30	19	order	order	NOUN
iajs-3265	30	20	nonlinear	nonlinear	ADJ
iajs-3265	30	21	ordinary	ordinary	ADJ
iajs-3265	30	22	differential	differential	ADJ
iajs-3265	30	23	equations	equation	NOUN
iajs-3265	30	24	with	with	ADP
iajs-3265	30	25	quadratic	quadratic	ADJ
iajs-3265	30	26	and	and	CCONJ
iajs-3265	30	27	cubic	cubic	ADJ
iajs-3265	30	28	terms	term	NOUN
iajs-3265	30	29	and	and	CCONJ
iajs-3265	30	30	several	several	ADJ
iajs-3265	30	31	other	other	ADJ
iajs-3265	30	32	approximation	approximation	NOUN
iajs-3265	30	33	methods	method	NOUN
iajs-3265	30	34	for	for	ADP
iajs-3265	30	35	instance	instance	NOUN
iajs-3265	30	36	,	,	PUNCT
iajs-3265	30	37	see	see	VERB
iajs-3265	30	38	[	[	X
iajs-3265	30	39	18	18	NUM
iajs-3265	30	40	-	-	SYM
iajs-3265	30	41	23	23	NUM
iajs-3265	30	42	]	]	PUNCT
iajs-3265	30	43	.	.	PUNCT
iajs-3265	31	1	in	in	ADP
iajs-3265	31	2	recent	recent	ADJ
iajs-3265	31	3	years	year	NOUN
iajs-3265	31	4	,	,	PUNCT
iajs-3265	31	5	approximation	approximation	NOUN
iajs-3265	31	6	methods	method	NOUN
iajs-3265	31	7	for	for	ADP
iajs-3265	31	8	analyzing	analyze	VERB
iajs-3265	31	9	linear	linear	ADJ
iajs-3265	31	10	systems	system	NOUN
iajs-3265	31	11	of	of	ADP
iajs-3265	31	12	ordinary	ordinary	ADJ
iajs-3265	31	13	differential	differential	ADJ
iajs-3265	31	14	equations	equation	NOUN
iajs-3265	31	15	using	use	VERB
iajs-3265	31	16	orthogonal	orthogonal	ADJ
iajs-3265	31	17	series	series	NOUN
iajs-3265	31	18	have	have	AUX
iajs-3265	31	19	been	be	AUX
iajs-3265	31	20	widely	widely	ADV
iajs-3265	31	21	developed	develop	VERB
iajs-3265	31	22	.	.	PUNCT
iajs-3265	32	1	these	these	PRON
iajs-3265	32	2	are	be	AUX
iajs-3265	32	3	known	know	VERB
iajs-3265	32	4	as	as	ADP
iajs-3265	32	5	spectral	spectral	ADJ
iajs-3265	32	6	methods	method	NOUN
iajs-3265	32	7	,	,	PUNCT
iajs-3265	32	8	assuming	assume	VERB
iajs-3265	32	9	that	that	SCONJ
iajs-3265	32	10	a	a	DET
iajs-3265	32	11	truncated	truncate	VERB
iajs-3265	32	12	orthogonal	orthogonal	ADJ
iajs-3265	32	13	series	series	NOUN
iajs-3265	32	14	expansion	expansion	NOUN
iajs-3265	32	15	can	can	AUX
iajs-3265	32	16	reasonably	reasonably	ADV
iajs-3265	32	17	approximate	approximate	VERB
iajs-3265	32	18	the	the	DET
iajs-3265	32	19	solution	solution	NOUN
iajs-3265	32	20	.	.	PUNCT
iajs-3265	33	1	depending	depend	VERB
iajs-3265	33	2	on	on	ADP
iajs-3265	33	3	the	the	DET
iajs-3265	33	4	nature	nature	NOUN
iajs-3265	33	5	of	of	ADP
iajs-3265	33	6	the	the	DET
iajs-3265	33	7	problem	problem	NOUN
iajs-3265	33	8	,	,	PUNCT
iajs-3265	33	9	a	a	DET
iajs-3265	33	10	variety	variety	NOUN
iajs-3265	33	11	of	of	ADP
iajs-3265	33	12	orthogonal	orthogonal	ADJ
iajs-3265	33	13	series	series	NOUN
iajs-3265	33	14	have	have	AUX
iajs-3265	33	15	been	be	AUX
iajs-3265	33	16	used	use	VERB
iajs-3265	33	17	,	,	PUNCT
iajs-3265	33	18	such	such	ADJ
iajs-3265	33	19	as	as	ADP
iajs-3265	33	20	the	the	DET
iajs-3265	33	21	walsh	walsh	PROPN
iajs-3265	33	22	series	series	PROPN
iajs-3265	33	23	,	,	PUNCT
iajs-3265	33	24	block	block	NOUN
iajs-3265	33	25	-	-	PUNCT
iajs-3265	33	26	pulse	pulse	NOUN
iajs-3265	33	27	,	,	PUNCT
iajs-3265	33	28	laguerre	laguerre	NOUN
iajs-3265	33	29	,	,	PUNCT
iajs-3265	33	30	chebyshev	chebyshev	PROPN
iajs-3265	33	31	,	,	PUNCT
iajs-3265	33	32	fourier	fourier	NOUN
iajs-3265	33	33	series	series	NOUN
iajs-3265	33	34	,	,	PUNCT
iajs-3265	33	35	and	and	CCONJ
iajs-3265	33	36	others	other	NOUN
iajs-3265	34	1	[	[	X
iajs-3265	34	2	24	24	NUM
iajs-3265	34	3	]	]	PUNCT
iajs-3265	34	4	.	.	PUNCT
iajs-3265	35	1	furthermore	furthermore	ADV
iajs-3265	35	2	,	,	PUNCT
iajs-3265	35	3	orthogonal	orthogonal	ADJ
iajs-3265	35	4	functions	function	NOUN
iajs-3265	35	5	and	and	CCONJ
iajs-3265	35	6	polynomial	polynomial	ADJ
iajs-3265	35	7	series	series	NOUN
iajs-3265	35	8	have	have	AUX
iajs-3265	35	9	attracted	attract	VERB
iajs-3265	35	10	significant	significant	ADJ
iajs-3265	35	11	attention	attention	NOUN
iajs-3265	35	12	because	because	SCONJ
iajs-3265	35	13	they	they	PRON
iajs-3265	35	14	have	have	AUX
iajs-3265	35	15	been	be	AUX
iajs-3265	35	16	instrumental	instrumental	ADJ
iajs-3265	35	17	in	in	ADP
iajs-3265	35	18	treating	treat	VERB
iajs-3265	35	19	various	various	ADJ
iajs-3265	35	20	dynamical	dynamical	ADJ
iajs-3265	35	21	system	system	NOUN
iajs-3265	35	22	problems	problem	NOUN
iajs-3265	35	23	.	.	PUNCT
iajs-3265	36	1	the	the	DET
iajs-3265	36	2	main	main	ADJ
iajs-3265	36	3	feature	feature	NOUN
iajs-3265	36	4	of	of	ADP
iajs-3265	36	5	this	this	DET
iajs-3265	36	6	technique	technique	NOUN
iajs-3265	36	7	is	be	AUX
iajs-3265	36	8	that	that	SCONJ
iajs-3265	36	9	it	it	PRON
iajs-3265	36	10	reduces	reduce	VERB
iajs-3265	36	11	these	these	DET
iajs-3265	36	12	problems	problem	NOUN
iajs-3265	36	13	to	to	ADP
iajs-3265	36	14	the	the	DET
iajs-3265	36	15	solution	solution	NOUN
iajs-3265	36	16	of	of	ADP
iajs-3265	36	17	a	a	DET
iajs-3265	36	18	system	system	NOUN
iajs-3265	36	19	of	of	ADP
iajs-3265	36	20	algebraic	algebraic	ADJ
iajs-3265	36	21	equations	equation	NOUN
iajs-3265	36	22	by	by	ADP
iajs-3265	36	23	using	use	VERB
iajs-3265	36	24	the	the	DET
iajs-3265	36	25	method	method	NOUN
iajs-3265	36	26	of	of	ADP
iajs-3265	36	27	operational	operational	ADJ
iajs-3265	36	28	matrices	matrix	NOUN
iajs-3265	36	29	based	base	VERB
iajs-3265	36	30	on	on	ADP
iajs-3265	36	31	orthogonal	orthogonal	ADJ
iajs-3265	36	32	polynomials	polynomial	NOUN
iajs-3265	36	33	[	[	X
iajs-3265	36	34	25	25	NUM
iajs-3265	36	35	]	]	X
iajs-3265	36	36	,	,	PUNCT
iajs-3265	36	37	such	such	ADJ
iajs-3265	36	38	as	as	ADP
iajs-3265	36	39	chebyshev	chebyshev	NOUN
iajs-3265	36	40	polynomials	polynomial	NOUN
iajs-3265	36	41	[	[	X
iajs-3265	36	42	26	26	NUM
iajs-3265	36	43	]	]	PUNCT
iajs-3265	36	44	,	,	PUNCT
iajs-3265	36	45	bernoulli	bernoulli	NOUN
iajs-3265	36	46	polynomials	polynomial	VERB
iajs-3265	36	47	[	[	X
iajs-3265	36	48	27	27	NUM
iajs-3265	36	49	]	]	PUNCT
iajs-3265	36	50	,	,	PUNCT
iajs-3265	36	51	and	and	CCONJ
iajs-3265	36	52	laguerre	laguerre	NOUN
iajs-3265	36	53	polynomials	polynomial	VERB
iajs-3265	36	54	[	[	X
iajs-3265	36	55	28	28	NUM
iajs-3265	36	56	]	]	PUNCT
iajs-3265	36	57	,	,	PUNCT
iajs-3265	36	58	which	which	PRON
iajs-3265	36	59	significantly	significantly	ADV
iajs-3265	36	60	simplifies	simplify	VERB
iajs-3265	36	61	the	the	DET
iajs-3265	36	62	problems	problem	NOUN
iajs-3265	36	63	and	and	CCONJ
iajs-3265	36	64	allows	allow	VERB
iajs-3265	36	65	them	they	PRON
iajs-3265	36	66	to	to	PART
iajs-3265	36	67	be	be	AUX
iajs-3265	36	68	solved	solve	VERB
iajs-3265	36	69	by	by	ADP
iajs-3265	36	70	any	any	DET
iajs-3265	36	71	computational	computational	ADJ
iajs-3265	36	72	program	program	NOUN
iajs-3265	36	73	.	.	PUNCT
iajs-3265	37	1	more	more	ADV
iajs-3265	37	2	recently	recently	ADV
iajs-3265	37	3	,	,	PUNCT
iajs-3265	37	4	turkyilmazoglu	turkyilmazoglu	NOUN
iajs-3265	37	5	[	[	X
iajs-3265	37	6	29	29	NUM
iajs-3265	37	7	]	]	PUNCT
iajs-3265	37	8	has	have	AUX
iajs-3265	37	9	proposed	propose	VERB
iajs-3265	37	10	and	and	CCONJ
iajs-3265	37	11	used	use	VERB
iajs-3265	37	12	an	an	DET
iajs-3265	37	13	analytical	analytical	ADJ
iajs-3265	37	14	approximation	approximation	NOUN
iajs-3265	37	15	method	method	NOUN
iajs-3265	37	16	,	,	PUNCT
iajs-3265	37	17	namely	namely	ADV
iajs-3265	37	18	the	the	DET
iajs-3265	37	19	ecm	ecm	NOUN
iajs-3265	37	20	,	,	PUNCT
iajs-3265	37	21	to	to	PART
iajs-3265	37	22	solve	solve	VERB
iajs-3265	37	23	various	various	ADJ
iajs-3265	37	24	types	type	NOUN
iajs-3265	37	25	of	of	ADP
iajs-3265	37	26	problems	problem	NOUN
iajs-3265	37	27	,	,	PUNCT
iajs-3265	37	28	such	such	ADJ
iajs-3265	37	29	as	as	ADP
iajs-3265	37	30	nonlinear	nonlinear	ADJ
iajs-3265	37	31	lane	lane	NOUN
iajs-3265	37	32	-	-	PUNCT
iajs-3265	37	33	emdenfowler	emdenfowler	NOUN
iajs-3265	37	34	equations	equation	NOUN
iajs-3265	37	35	[	[	X
iajs-3265	37	36	29	29	NUM
iajs-3265	37	37	]	]	PUNCT
iajs-3265	37	38	,	,	PUNCT
iajs-3265	37	39	fredholm	fredholm	NOUN
iajs-3265	37	40	integro	integro	ADJ
iajs-3265	37	41	-	-	PUNCT
iajs-3265	37	42	differential	differential	NOUN
iajs-3265	37	43	equations	equation	NOUN
iajs-3265	37	44	[	[	X
iajs-3265	37	45	30	30	NUM
iajs-3265	37	46	]	]	PUNCT
iajs-3265	37	47	,	,	PUNCT
iajs-3265	37	48	volterra	volterra	PROPN
iajs-3265	37	49	-	-	PUNCT
iajs-3265	37	50	fredholmhammerstein	fredholmhammerstein	PROPN
iajs-3265	37	51	integro	integro	PROPN
iajs-3265	37	52	-	-	PUNCT
iajs-3265	37	53	differential	differential	NOUN
iajs-3265	37	54	equations	equation	NOUN
iajs-3265	37	55	[	[	X
iajs-3265	37	56	31	31	NUM
iajs-3265	37	57	]	]	PUNCT
iajs-3265	37	58	,	,	PUNCT
iajs-3265	37	59	heat	heat	NOUN
iajs-3265	37	60	transfer	transfer	NOUN
iajs-3265	37	61	of	of	ADP
iajs-3265	37	62	fin	fin	NOUN
iajs-3265	37	63	problems	problem	NOUN
iajs-3265	37	64	[	[	X
iajs-3265	37	65	32	32	NUM
iajs-3265	37	66	]	]	PUNCT
iajs-3265	37	67	,	,	PUNCT
iajs-3265	37	68	and	and	CCONJ
iajs-3265	37	69	initial	initial	ADJ
iajs-3265	37	70	and	and	CCONJ
iajs-3265	37	71	boundary	boundary	ADJ
iajs-3265	37	72	value	value	NOUN
iajs-3265	37	73	problems	problem	NOUN
iajs-3265	37	74	with	with	ADP
iajs-3265	37	75	difficult	difficult	ADJ
iajs-3265	37	76	exact	exact	ADJ
iajs-3265	37	77	solutions	solution	NOUN
iajs-3265	37	78	[	[	X
iajs-3265	37	79	33	33	NUM
iajs-3265	37	80	]	]	PUNCT
iajs-3265	37	81	.	.	PUNCT
iajs-3265	38	1	moreover	moreover	ADV
iajs-3265	38	2	,	,	PUNCT
iajs-3265	38	3	the	the	DET
iajs-3265	38	4	approach	approach	NOUN
iajs-3265	38	5	depends	depend	VERB
iajs-3265	38	6	on	on	ADP
iajs-3265	38	7	appropriate	appropriate	ADJ
iajs-3265	38	8	base	base	NOUN
iajs-3265	38	9	functions	function	NOUN
iajs-3265	38	10	,	,	PUNCT
iajs-3265	38	11	such	such	ADJ
iajs-3265	38	12	as	as	ADP
iajs-3265	38	13	the	the	DET
iajs-3265	38	14	standard	standard	ADJ
iajs-3265	38	15	polynomials	polynomial	NOUN
iajs-3265	38	16	.	.	PUNCT
iajs-3265	39	1	in	in	ADP
iajs-3265	39	2	addition	addition	NOUN
iajs-3265	39	3	,	,	PUNCT
iajs-3265	39	4	the	the	DET
iajs-3265	39	5	solution	solution	NOUN
iajs-3265	39	6	of	of	ADP
iajs-3265	39	7	the	the	DET
iajs-3265	39	8	nonlinear	nonlinear	ADJ
iajs-3265	39	9	equations	equation	NOUN
iajs-3265	39	10	is	be	AUX
iajs-3265	39	11	transformed	transform	VERB
iajs-3265	39	12	into	into	ADP
iajs-3265	39	13	a	a	DET
iajs-3265	39	14	nonlinear	nonlinear	ADJ
iajs-3265	39	15	algebraic	algebraic	ADJ
iajs-3265	39	16	system	system	NOUN
iajs-3265	39	17	with	with	ADP
iajs-3265	39	18	unknown	unknown	ADJ
iajs-3265	39	19	standard	standard	ADJ
iajs-3265	39	20	polynomial	polynomial	ADJ
iajs-3265	39	21	coefficients	coefficient	NOUN
iajs-3265	39	22	,	,	PUNCT
iajs-3265	39	23	which	which	PRON
iajs-3265	39	24	can	can	AUX
iajs-3265	39	25	be	be	AUX
iajs-3265	39	26	solved	solve	VERB
iajs-3265	39	27	numerically	numerically	ADV
iajs-3265	39	28	or	or	CCONJ
iajs-3265	39	29	analytically	analytically	ADV
iajs-3265	39	30	with	with	ADP
iajs-3265	39	31	modern	modern	ADJ
iajs-3265	39	32	software	software	NOUN
iajs-3265	39	33	.	.	PUNCT
iajs-3265	40	1	ihjpas	ihjpas	PROPN
iajs-3265	40	2	.	.	PUNCT
iajs-3265	41	1	36	36	NUM
iajs-3265	41	2	(	(	PUNCT
iajs-3265	41	3	4	4	NUM
iajs-3265	41	4	)	)	PUNCT
iajs-3265	41	5	2023	2023	NUM
iajs-3265	41	6	340	340	NUM
iajs-3265	41	7	the	the	DET
iajs-3265	41	8	current	current	ADJ
iajs-3265	41	9	paper	paper	NOUN
iajs-3265	41	10	aims	aim	VERB
iajs-3265	41	11	to	to	PART
iajs-3265	41	12	use	use	VERB
iajs-3265	41	13	the	the	DET
iajs-3265	41	14	ecm	ecm	NOUN
iajs-3265	41	15	based	base	VERB
iajs-3265	41	16	on	on	ADP
iajs-3265	41	17	the	the	DET
iajs-3265	41	18	standard	standard	ADJ
iajs-3265	41	19	polynomials	polynomial	NOUN
iajs-3265	41	20	to	to	PART
iajs-3265	41	21	solve	solve	VERB
iajs-3265	41	22	three	three	NUM
iajs-3265	41	23	applications	application	NOUN
iajs-3265	41	24	involving	involve	VERB
iajs-3265	41	25	nonlinear	nonlinear	ADJ
iajs-3265	41	26	initial	initial	ADJ
iajs-3265	41	27	and	and	CCONJ
iajs-3265	41	28	boundary	boundary	ADJ
iajs-3265	41	29	value	value	NOUN
iajs-3265	41	30	problems	problem	NOUN
iajs-3265	41	31	:	:	PUNCT
iajs-3265	41	32	the	the	DET
iajs-3265	41	33	darcy	darcy	PROPN
iajs-3265	41	34	-	-	PUNCT
iajs-3265	41	35	brinkmanforchheimer	brinkmanforchheimer	NOUN
iajs-3265	41	36	equation	equation	NOUN
iajs-3265	41	37	,	,	PUNCT
iajs-3265	41	38	the	the	DET
iajs-3265	41	39	blasius	blasius	ADJ
iajs-3265	41	40	equation	equation	NOUN
iajs-3265	41	41	,	,	PUNCT
iajs-3265	41	42	and	and	CCONJ
iajs-3265	41	43	the	the	DET
iajs-3265	41	44	falkner	falkner	PROPN
iajs-3265	41	45	-	-	PUNCT
iajs-3265	41	46	skan	skan	VERB
iajs-3265	41	47	equation	equation	NOUN
iajs-3265	41	48	,	,	PUNCT
iajs-3265	41	49	which	which	PRON
iajs-3265	41	50	are	be	AUX
iajs-3265	41	51	found	find	VERB
iajs-3265	41	52	in	in	ADP
iajs-3265	41	53	engineering	engineering	NOUN
iajs-3265	41	54	and	and	CCONJ
iajs-3265	41	55	applied	apply	VERB
iajs-3265	41	56	sciences	science	NOUN
iajs-3265	41	57	.	.	PUNCT
iajs-3265	42	1	the	the	DET
iajs-3265	42	2	main	main	ADJ
iajs-3265	42	3	goals	goal	NOUN
iajs-3265	42	4	are	be	AUX
iajs-3265	42	5	to	to	PART
iajs-3265	42	6	develop	develop	VERB
iajs-3265	42	7	the	the	DET
iajs-3265	42	8	ecm	ecm	NOUN
iajs-3265	42	9	by	by	ADP
iajs-3265	42	10	introducing	introduce	VERB
iajs-3265	42	11	various	various	ADJ
iajs-3265	42	12	orthogonal	orthogonal	ADJ
iajs-3265	42	13	polynomials	polynomial	NOUN
iajs-3265	42	14	,	,	PUNCT
iajs-3265	42	15	such	such	ADJ
iajs-3265	42	16	as	as	ADP
iajs-3265	42	17	chebyshev	chebyshev	PROPN
iajs-3265	42	18	,	,	PUNCT
iajs-3265	42	19	bernoulli	bernoulli	PROPN
iajs-3265	42	20	,	,	PUNCT
iajs-3265	42	21	and	and	CCONJ
iajs-3265	42	22	laguerre	laguerre	NOUN
iajs-3265	42	23	polynomials	polynomial	NOUN
iajs-3265	42	24	,	,	PUNCT
iajs-3265	42	25	and	and	CCONJ
iajs-3265	42	26	to	to	PART
iajs-3265	42	27	form	form	VERB
iajs-3265	42	28	a	a	DET
iajs-3265	42	29	novel	novel	ADJ
iajs-3265	42	30	collection	collection	NOUN
iajs-3265	42	31	of	of	ADP
iajs-3265	42	32	the	the	DET
iajs-3265	42	33	i	i	PROPN
iajs-3265	42	34	-	-	PUNCT
iajs-3265	42	35	ecms	ecms	NOUN
iajs-3265	42	36	.	.	PUNCT
iajs-3265	43	1	the	the	DET
iajs-3265	43	2	final	final	ADJ
iajs-3265	43	3	goal	goal	NOUN
iajs-3265	43	4	is	be	AUX
iajs-3265	43	5	to	to	PART
iajs-3265	43	6	implement	implement	VERB
iajs-3265	43	7	the	the	DET
iajs-3265	43	8	i	i	PROPN
iajs-3265	43	9	-	-	PUNCT
iajs-3265	43	10	ecms	ecms	PROPN
iajs-3265	43	11	to	to	PART
iajs-3265	43	12	solve	solve	VERB
iajs-3265	43	13	these	these	DET
iajs-3265	43	14	problems	problem	NOUN
iajs-3265	43	15	.	.	PUNCT
iajs-3265	44	1	the	the	DET
iajs-3265	44	2	paper	paper	NOUN
iajs-3265	44	3	is	be	AUX
iajs-3265	44	4	organized	organize	VERB
iajs-3265	44	5	as	as	SCONJ
iajs-3265	44	6	follows	follow	VERB
iajs-3265	44	7	:	:	PUNCT
iajs-3265	44	8	section	section	NOUN
iajs-3265	44	9	two	two	NUM
iajs-3265	44	10	presents	present	VERB
iajs-3265	44	11	the	the	DET
iajs-3265	44	12	mathematical	mathematical	ADJ
iajs-3265	44	13	formulations	formulation	NOUN
iajs-3265	44	14	of	of	ADP
iajs-3265	44	15	three	three	NUM
iajs-3265	44	16	nonlinear	nonlinear	ADJ
iajs-3265	44	17	models	model	NOUN
iajs-3265	44	18	.	.	PUNCT
iajs-3265	45	1	section	section	NOUN
iajs-3265	45	2	three	three	NUM
iajs-3265	45	3	introduces	introduce	NOUN
iajs-3265	45	4	the	the	DET
iajs-3265	45	5	basic	basic	ADJ
iajs-3265	45	6	concepts	concept	NOUN
iajs-3265	45	7	of	of	ADP
iajs-3265	45	8	the	the	DET
iajs-3265	45	9	proposed	propose	VERB
iajs-3265	45	10	methods	method	NOUN
iajs-3265	45	11	.	.	PUNCT
iajs-3265	46	1	section	section	NOUN
iajs-3265	46	2	four	four	NUM
iajs-3265	46	3	displays	display	VERB
iajs-3265	46	4	the	the	DET
iajs-3265	46	5	implementation	implementation	NOUN
iajs-3265	46	6	of	of	ADP
iajs-3265	46	7	the	the	DET
iajs-3265	46	8	ecm	ecm	PROPN
iajs-3265	46	9	and	and	CCONJ
iajs-3265	46	10	i	i	PROPN
iajs-3265	46	11	-	-	PUNCT
iajs-3265	46	12	ecms	ecms	PROPN
iajs-3265	46	13	to	to	PART
iajs-3265	46	14	solve	solve	VERB
iajs-3265	46	15	three	three	NUM
iajs-3265	46	16	nonlinear	nonlinear	ADJ
iajs-3265	46	17	problems	problem	NOUN
iajs-3265	46	18	and	and	CCONJ
iajs-3265	46	19	discusses	discuss	VERB
iajs-3265	46	20	the	the	DET
iajs-3265	46	21	results	result	NOUN
iajs-3265	46	22	.	.	PUNCT
iajs-3265	47	1	finally	finally	ADV
iajs-3265	47	2	,	,	PUNCT
iajs-3265	47	3	section	section	NOUN
iajs-3265	47	4	five	five	NUM
iajs-3265	47	5	presents	present	VERB
iajs-3265	47	6	the	the	DET
iajs-3265	47	7	conclusions	conclusion	NOUN
iajs-3265	47	8	.	.	PUNCT
iajs-3265	48	1	2	2	X
iajs-3265	48	2	.	.	X
iajs-3265	48	3	the	the	DET
iajs-3265	48	4	mathematical	mathematical	ADJ
iajs-3265	48	5	formulations	formulation	NOUN
iajs-3265	48	6	of	of	ADP
iajs-3265	48	7	nonlinear	nonlinear	ADJ
iajs-3265	48	8	models	model	NOUN
iajs-3265	48	9	2.1	2.1	NUM
iajs-3265	48	10	the	the	DET
iajs-3265	48	11	darcy	darcy	PROPN
iajs-3265	48	12	-	-	PUNCT
iajs-3265	48	13	brinkman	brinkman	PROPN
iajs-3265	48	14	-	-	PUNCT
iajs-3265	48	15	forchheimer	forchheimer	PROPN
iajs-3265	48	16	equation	equation	NOUN
iajs-3265	48	17	consider	consider	VERB
iajs-3265	48	18	the	the	DET
iajs-3265	48	19	following	follow	VERB
iajs-3265	48	20	steady	steady	ADJ
iajs-3265	48	21	-	-	PUNCT
iajs-3265	48	22	state	state	NOUN
iajs-3265	48	23	,	,	PUNCT
iajs-3265	48	24	pressure	pressure	NOUN
iajs-3265	48	25	-	-	PUNCT
iajs-3265	48	26	driven	drive	VERB
iajs-3265	48	27	,	,	PUNCT
iajs-3265	48	28	fully	fully	ADV
iajs-3265	48	29	developed	develop	VERB
iajs-3265	48	30	parallel	parallel	ADJ
iajs-3265	48	31	flow	flow	NOUN
iajs-3265	48	32	over	over	ADP
iajs-3265	48	33	a	a	DET
iajs-3265	48	34	horizontal	horizontal	ADJ
iajs-3265	48	35	channel	channel	NOUN
iajs-3265	48	36	filled	fill	VERB
iajs-3265	48	37	with	with	ADP
iajs-3265	48	38	a	a	DET
iajs-3265	48	39	porous	porous	ADJ
iajs-3265	48	40	medium	medium	NOUN
iajs-3265	48	41	[	[	X
iajs-3265	48	42	34	34	NUM
iajs-3265	48	43	]	]	PUNCT
iajs-3265	48	44	,	,	PUNCT
iajs-3265	48	45	as	as	SCONJ
iajs-3265	48	46	demonstrated	demonstrate	VERB
iajs-3265	48	47	in	in	ADP
iajs-3265	48	48	figure	figure	NOUN
iajs-3265	48	49	1	1	NUM
iajs-3265	48	50	:	:	PUNCT
iajs-3265	48	51	figure	figure	NOUN
iajs-3265	48	52	1	1	NUM
iajs-3265	48	53	.	.	PUNCT
iajs-3265	48	54	parallel	parallel	ADJ
iajs-3265	48	55	flow	flow	NOUN
iajs-3265	48	56	in	in	ADP
iajs-3265	48	57	a	a	DET
iajs-3265	48	58	fluid	fluid	NOUN
iajs-3265	48	59	-	-	PUNCT
iajs-3265	48	60	saturated	saturate	VERB
iajs-3265	48	61	porous	porous	ADJ
iajs-3265	48	62	channel	channel	NOUN
iajs-3265	48	63	[	[	X
iajs-3265	48	64	35	35	NUM
iajs-3265	48	65	]	]	PUNCT
iajs-3265	48	66	.	.	PUNCT
iajs-3265	49	1	the	the	DET
iajs-3265	49	2	positions	position	NOUN
iajs-3265	49	3	of	of	ADP
iajs-3265	49	4	the	the	DET
iajs-3265	49	5	bottom	bottom	NOUN
iajs-3265	49	6	and	and	CCONJ
iajs-3265	49	7	top	top	ADJ
iajs-3265	49	8	plates	plate	NOUN
iajs-3265	49	9	are	be	AUX
iajs-3265	49	10	𝑦	𝑦	NOUN
iajs-3265	49	11	=	=	SYM
iajs-3265	49	12	ℎ	ℎ	NOUN
iajs-3265	49	13	and	and	CCONJ
iajs-3265	49	14	𝑦	𝑦	NOUN
iajs-3265	49	15	=	=	SYM
iajs-3265	49	16	−	−	ADP
iajs-3265	49	17	ℎ	ℎ	PROPN
iajs-3265	49	18	,	,	PUNCT
iajs-3265	49	19	respectively	respectively	ADV
iajs-3265	49	20	.	.	PUNCT
iajs-3265	50	1	the	the	DET
iajs-3265	50	2	velocity	velocity	NOUN
iajs-3265	50	3	takes	take	VERB
iajs-3265	50	4	the	the	DET
iajs-3265	50	5	form	form	NOUN
iajs-3265	50	6	𝑢	𝑢	X
iajs-3265	50	7	=	=	SYM
iajs-3265	50	8	(	(	PUNCT
iajs-3265	50	9	𝑦(𝑥	𝑦(𝑥	PROPN
iajs-3265	50	10	)	)	PUNCT
iajs-3265	50	11	,	,	PUNCT
iajs-3265	50	12	0	0	NUM
iajs-3265	50	13	,	,	PUNCT
iajs-3265	50	14	0	0	NUM
iajs-3265	50	15	)	)	PUNCT
iajs-3265	50	16	and	and	CCONJ
iajs-3265	50	17	the	the	DET
iajs-3265	50	18	flow	flow	NOUN
iajs-3265	50	19	is	be	AUX
iajs-3265	50	20	in	in	ADP
iajs-3265	50	21	the	the	DET
iajs-3265	50	22	𝑥-axis	𝑥-axis	NOUN
iajs-3265	50	23	direction	direction	NOUN
iajs-3265	50	24	.	.	PUNCT
iajs-3265	51	1	the	the	DET
iajs-3265	51	2	darcy	darcy	PROPN
iajs-3265	51	3	-	-	PUNCT
iajs-3265	51	4	brinkmanforchheimer	brinkmanforchheimer	NOUN
iajs-3265	51	5	equation	equation	NOUN
iajs-3265	51	6	,	,	PUNCT
iajs-3265	51	7	which	which	PRON
iajs-3265	51	8	has	have	VERB
iajs-3265	51	9	the	the	DET
iajs-3265	51	10	following	follow	VERB
iajs-3265	51	11	form	form	NOUN
iajs-3265	51	12	[	[	X
iajs-3265	51	13	36	36	NUM
iajs-3265	51	14	]	]	PUNCT
iajs-3265	51	15	,	,	PUNCT
iajs-3265	51	16	is	be	AUX
iajs-3265	51	17	known	know	VERB
iajs-3265	51	18	to	to	PART
iajs-3265	51	19	determine	determine	VERB
iajs-3265	51	20	the	the	DET
iajs-3265	51	21	flow	flow	NOUN
iajs-3265	51	22	in	in	ADP
iajs-3265	51	23	the	the	DET
iajs-3265	51	24	channel	channel	NOUN
iajs-3265	51	25	.	.	PUNCT
iajs-3265	52	1	𝑦′′(𝑥	𝑦′′(𝑥	NUM
iajs-3265	52	2	)	)	PUNCT
iajs-3265	52	3	−	−	ADP
iajs-3265	52	4	𝑠2	𝑠2	NOUN
iajs-3265	52	5	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	52	6	)	)	PUNCT
iajs-3265	52	7	−	−	PROPN
iajs-3265	53	1	𝐹	𝐹	PROPN
iajs-3265	53	2	𝑠	𝑠	PROPN
iajs-3265	53	3	𝑦2(𝑥	𝑦2(𝑥	NOUN
iajs-3265	53	4	)	)	PUNCT
iajs-3265	54	1	+	+	CCONJ
iajs-3265	54	2	1	1	NUM
iajs-3265	54	3	𝑀	𝑀	NOUN
iajs-3265	54	4	=	=	SYM
iajs-3265	54	5	0	0	PROPN
iajs-3265	54	6	,	,	PUNCT
iajs-3265	54	7	(	(	PUNCT
iajs-3265	54	8	1	1	X
iajs-3265	54	9	)	)	PUNCT
iajs-3265	54	10	subjected	subject	VERB
iajs-3265	54	11	to	to	ADP
iajs-3265	54	12	the	the	DET
iajs-3265	54	13	boundary	boundary	ADJ
iajs-3265	54	14	conditions	condition	NOUN
iajs-3265	54	15	:	:	PUNCT
iajs-3265	54	16	𝑦′(0	𝑦′(0	NOUN
iajs-3265	54	17	)	)	PUNCT
iajs-3265	54	18	=	=	SYM
iajs-3265	54	19	0	0	NUM
iajs-3265	54	20	,	,	PUNCT
iajs-3265	54	21	𝑦(1	𝑦(1	PROPN
iajs-3265	54	22	)	)	PUNCT
iajs-3265	54	23	=	=	SYM
iajs-3265	55	1	0	0	X
iajs-3265	55	2	.	.	PUNCT
iajs-3265	56	1	(	(	PUNCT
iajs-3265	56	2	2	2	X
iajs-3265	56	3	)	)	PUNCT
iajs-3265	56	4	where	where	SCONJ
iajs-3265	56	5	𝐹	𝐹	PROPN
iajs-3265	56	6	stands	stand	VERB
iajs-3265	56	7	for	for	ADP
iajs-3265	56	8	the	the	DET
iajs-3265	56	9	forchheimer	forchheimer	ADJ
iajs-3265	56	10	number	number	NOUN
iajs-3265	56	11	,	,	PUNCT
iajs-3265	56	12	𝑠	𝑠	PROPN
iajs-3265	56	13	for	for	ADP
iajs-3265	56	14	the	the	DET
iajs-3265	56	15	shape	shape	NOUN
iajs-3265	56	16	parameter	parameter	NOUN
iajs-3265	56	17	of	of	ADP
iajs-3265	56	18	the	the	DET
iajs-3265	56	19	porous	porous	ADJ
iajs-3265	56	20	medium	medium	NOUN
iajs-3265	56	21	,	,	PUNCT
iajs-3265	56	22	and	and	CCONJ
iajs-3265	56	23	𝑀	𝑀	PROPN
iajs-3265	56	24	for	for	ADP
iajs-3265	56	25	the	the	DET
iajs-3265	56	26	viscosity	viscosity	NOUN
iajs-3265	56	27	ratio	ratio	NOUN
iajs-3265	56	28	.	.	PUNCT
iajs-3265	57	1	the	the	DET
iajs-3265	57	2	darcy	darcy	PROPN
iajs-3265	57	3	-	-	PUNCT
iajs-3265	57	4	brinkman	brinkman	PROPN
iajs-3265	57	5	-	-	PUNCT
iajs-3265	57	6	forchheimer	forchheimer	PROPN
iajs-3265	57	7	equation	equation	NOUN
iajs-3265	57	8	has	have	AUX
iajs-3265	57	9	been	be	AUX
iajs-3265	57	10	solved	solve	VERB
iajs-3265	57	11	analytically	analytically	ADV
iajs-3265	57	12	and	and	CCONJ
iajs-3265	57	13	approximately	approximately	ADV
iajs-3265	57	14	using	use	VERB
iajs-3265	57	15	a	a	DET
iajs-3265	57	16	variety	variety	NOUN
iajs-3265	57	17	of	of	ADP
iajs-3265	57	18	methods	method	NOUN
iajs-3265	57	19	,	,	PUNCT
iajs-3265	57	20	such	such	ADJ
iajs-3265	57	21	as	as	ADP
iajs-3265	57	22	the	the	DET
iajs-3265	57	23	homotopy	homotopy	NOUN
iajs-3265	57	24	analysis	analysis	NOUN
iajs-3265	57	25	method	method	NOUN
iajs-3265	57	26	[	[	X
iajs-3265	57	27	37	37	NUM
iajs-3265	57	28	]	]	PUNCT
iajs-3265	57	29	,	,	PUNCT
iajs-3265	57	30	the	the	DET
iajs-3265	57	31	finite	finite	ADJ
iajs-3265	57	32	difference	difference	NOUN
iajs-3265	57	33	method	method	NOUN
iajs-3265	58	1	[	[	X
iajs-3265	58	2	38	38	NUM
iajs-3265	58	3	]	]	PUNCT
iajs-3265	58	4	,	,	PUNCT
iajs-3265	58	5	the	the	DET
iajs-3265	58	6	optimal	optimal	ADJ
iajs-3265	58	7	asymptotic	asymptotic	ADJ
iajs-3265	58	8	galerkin	galerkin	PROPN
iajs-3265	58	9	homotopy	homotopy	NOUN
iajs-3265	58	10	method	method	NOUN
iajs-3265	58	11	[	[	X
iajs-3265	58	12	36	36	NUM
iajs-3265	58	13	]	]	PUNCT
iajs-3265	58	14	,	,	PUNCT
iajs-3265	58	15	and	and	CCONJ
iajs-3265	58	16	the	the	DET
iajs-3265	58	17	tau	tau	PROPN
iajs-3265	58	18	homotopy	homotopy	NOUN
iajs-3265	58	19	analysis	analysis	NOUN
iajs-3265	58	20	method	method	NOUN
iajs-3265	58	21	[	[	X
iajs-3265	58	22	34	34	NUM
iajs-3265	58	23	]	]	PUNCT
iajs-3265	58	24	.	.	PUNCT
iajs-3265	59	1	in	in	ADP
iajs-3265	59	2	particular	particular	ADJ
iajs-3265	59	3	,	,	PUNCT
iajs-3265	59	4	adewumi	adewumi	PROPN
iajs-3265	59	5	et	et	PROPN
iajs-3265	59	6	al	al	PROPN
iajs-3265	59	7	.	.	PUNCT
iajs-3265	60	1	[	[	X
iajs-3265	60	2	39	39	NUM
iajs-3265	60	3	]	]	PUNCT
iajs-3265	60	4	obtained	obtain	VERB
iajs-3265	60	5	the	the	DET
iajs-3265	60	6	approximate	approximate	ADJ
iajs-3265	60	7	solutions	solution	NOUN
iajs-3265	60	8	for	for	ADP
iajs-3265	60	9	the	the	DET
iajs-3265	60	10	model	model	NOUN
iajs-3265	60	11	by	by	ADP
iajs-3265	60	12	using	use	VERB
iajs-3265	60	13	the	the	DET
iajs-3265	60	14	hybrid	hybrid	ADJ
iajs-3265	60	15	method	method	NOUN
iajs-3265	60	16	in	in	ADP
iajs-3265	60	17	combination	combination	NOUN
iajs-3265	60	18	with	with	ADP
iajs-3265	60	19	the	the	DET
iajs-3265	60	20	chebyshev	chebyshev	NOUN
iajs-3265	60	21	collocation	collocation	NOUN
iajs-3265	60	22	method	method	NOUN
iajs-3265	60	23	with	with	ADP
iajs-3265	60	24	laplace	laplace	NOUN
iajs-3265	60	25	and	and	CCONJ
iajs-3265	60	26	differential	differential	ADJ
iajs-3265	60	27	transform	transform	NOUN
iajs-3265	60	28	methods	method	NOUN
iajs-3265	60	29	.	.	PUNCT
iajs-3265	61	1	motsa	motsa	PROPN
iajs-3265	61	2	et	et	PROPN
iajs-3265	61	3	al	al	PROPN
iajs-3265	61	4	.	.	PUNCT
iajs-3265	62	1	[	[	X
iajs-3265	62	2	35	35	NUM
iajs-3265	62	3	]	]	PUNCT
iajs-3265	62	4	implemented	implement	VERB
iajs-3265	62	5	the	the	DET
iajs-3265	62	6	spectral	spectral	PROPN
iajs-3265	62	7	homotopy	homotopy	NOUN
iajs-3265	62	8	analysis	analysis	NOUN
iajs-3265	62	9	approach	approach	NOUN
iajs-3265	62	10	to	to	PART
iajs-3265	62	11	obtain	obtain	VERB
iajs-3265	62	12	an	an	DET
iajs-3265	62	13	accurate	accurate	ADJ
iajs-3265	62	14	result	result	NOUN
iajs-3265	62	15	for	for	ADP
iajs-3265	62	16	the	the	DET
iajs-3265	62	17	model	model	NOUN
iajs-3265	62	18	.	.	PUNCT
iajs-3265	63	1	in	in	ADP
iajs-3265	63	2	addition	addition	NOUN
iajs-3265	63	3	,	,	PUNCT
iajs-3265	63	4	abbasbandy	abbasbandy	PROPN
iajs-3265	63	5	et	et	PROPN
iajs-3265	63	6	al	al	PROPN
iajs-3265	63	7	.	.	PUNCT
iajs-3265	64	1	[	[	X
iajs-3265	64	2	40	40	NUM
iajs-3265	64	3	]	]	PUNCT
iajs-3265	64	4	obtained	obtain	VERB
iajs-3265	64	5	a	a	DET
iajs-3265	64	6	closed	closed	ADJ
iajs-3265	64	7	-	-	PUNCT
iajs-3265	64	8	form	form	NOUN
iajs-3265	64	9	solution	solution	NOUN
iajs-3265	64	10	of	of	ADP
iajs-3265	64	11	forced	force	VERB
iajs-3265	64	12	convection	convection	NOUN
iajs-3265	64	13	in	in	ADP
iajs-3265	64	14	a	a	DET
iajs-3265	64	15	porous	porous	ADJ
iajs-3265	64	16	saturated	saturated	ADJ
iajs-3265	64	17	channel	channel	NOUN
iajs-3265	64	18	.	.	PUNCT
iajs-3265	65	1	ihjpas	ihjpas	PROPN
iajs-3265	65	2	.	.	PUNCT
iajs-3265	66	1	36	36	NUM
iajs-3265	66	2	(	(	PUNCT
iajs-3265	66	3	4	4	NUM
iajs-3265	66	4	)	)	PUNCT
iajs-3265	66	5	2023	2023	NUM
iajs-3265	66	6	341	341	NUM
iajs-3265	66	7	2.2	2.2	NUM
iajs-3265	66	8	the	the	DET
iajs-3265	66	9	blasius	blasius	ADJ
iajs-3265	66	10	equation	equation	NOUN
iajs-3265	66	11	the	the	DET
iajs-3265	66	12	blasius	blasius	ADJ
iajs-3265	66	13	equation	equation	NOUN
iajs-3265	66	14	is	be	AUX
iajs-3265	66	15	the	the	DET
iajs-3265	66	16	well	well	ADV
iajs-3265	66	17	-	-	PUNCT
iajs-3265	66	18	known	know	VERB
iajs-3265	66	19	third	third	ADJ
iajs-3265	66	20	-	-	PUNCT
iajs-3265	66	21	order	order	NOUN
iajs-3265	66	22	nonlinear	nonlinear	ADJ
iajs-3265	66	23	ordinary	ordinary	ADJ
iajs-3265	66	24	differential	differential	ADJ
iajs-3265	66	25	equation	equation	NOUN
iajs-3265	66	26	that	that	PRON
iajs-3265	66	27	appeared	appear	VERB
iajs-3265	66	28	in	in	ADP
iajs-3265	66	29	several	several	ADJ
iajs-3265	66	30	boundary	boundary	ADJ
iajs-3265	66	31	layer	layer	NOUN
iajs-3265	66	32	problems	problem	NOUN
iajs-3265	66	33	involving	involve	VERB
iajs-3265	66	34	a	a	DET
iajs-3265	66	35	fluid	fluid	NOUN
iajs-3265	66	36	's	's	PART
iajs-3265	66	37	two	two	NUM
iajs-3265	66	38	-	-	PUNCT
iajs-3265	66	39	dimensional	dimensional	ADJ
iajs-3265	66	40	laminar	laminar	ADJ
iajs-3265	66	41	viscous	viscous	ADJ
iajs-3265	66	42	flow	flow	NOUN
iajs-3265	66	43	through	through	ADP
iajs-3265	66	44	a	a	DET
iajs-3265	66	45	flat	flat	ADJ
iajs-3265	66	46	plate	plate	NOUN
iajs-3265	66	47	.	.	PUNCT
iajs-3265	67	1	the	the	DET
iajs-3265	67	2	following	follow	VERB
iajs-3265	67	3	equation	equation	NOUN
iajs-3265	67	4	presents	present	VERB
iajs-3265	67	5	it	it	PRON
iajs-3265	67	6	as	as	ADP
iajs-3265	67	7	a	a	DET
iajs-3265	67	8	governing	govern	VERB
iajs-3265	67	9	equation	equation	NOUN
iajs-3265	67	10	for	for	ADP
iajs-3265	67	11	fluid	fluid	ADJ
iajs-3265	67	12	dynamics	dynamic	NOUN
iajs-3265	67	13	[	[	X
iajs-3265	67	14	41	41	NUM
iajs-3265	67	15	]	]	X
iajs-3265	67	16	:	:	PUNCT
iajs-3265	67	17	𝑦′′′(𝑥	𝑦′′′(𝑥	NUM
iajs-3265	67	18	)	)	PUNCT
iajs-3265	67	19	+	+	CCONJ
iajs-3265	67	20	1	1	NUM
iajs-3265	67	21	2	2	NUM
iajs-3265	67	22	𝑦(𝑥	𝑦(𝑥	PROPN
iajs-3265	67	23	)	)	PUNCT
iajs-3265	67	24	𝑦′′(𝑥	𝑦′′(𝑥	NOUN
iajs-3265	67	25	)	)	PUNCT
iajs-3265	67	26	=	=	SYM
iajs-3265	67	27	0	0	NUM
iajs-3265	67	28	,	,	PUNCT
iajs-3265	67	29	(	(	PUNCT
iajs-3265	67	30	3	3	X
iajs-3265	67	31	)	)	PUNCT
iajs-3265	67	32	subjected	subject	VERB
iajs-3265	67	33	to	to	ADP
iajs-3265	67	34	the	the	DET
iajs-3265	67	35	boundary	boundary	ADJ
iajs-3265	67	36	conditions	condition	NOUN
iajs-3265	67	37	:	:	PUNCT
iajs-3265	67	38	𝑦(0	𝑦(0	PROPN
iajs-3265	67	39	)	)	PUNCT
iajs-3265	67	40	=	=	SYM
iajs-3265	67	41	0	0	NUM
iajs-3265	67	42	,	,	PUNCT
iajs-3265	67	43	𝑦′(0	𝑦′(0	NOUN
iajs-3265	67	44	)	)	PUNCT
iajs-3265	67	45	=	=	SYM
iajs-3265	67	46	0	0	NUM
iajs-3265	67	47	,	,	PUNCT
iajs-3265	67	48	𝑦′(∞	𝑦′(∞	NOUN
iajs-3265	67	49	)	)	PUNCT
iajs-3265	67	50	=	=	SYM
iajs-3265	67	51	1	1	X
iajs-3265	67	52	.	.	PUNCT
iajs-3265	67	53	(	(	PUNCT
iajs-3265	67	54	4	4	X
iajs-3265	67	55	)	)	PUNCT
iajs-3265	67	56	the	the	DET
iajs-3265	67	57	second	second	ADJ
iajs-3265	67	58	derivative	derivative	NOUN
iajs-3265	67	59	of	of	ADP
iajs-3265	67	60	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	67	61	)	)	PUNCT
iajs-3265	67	62	at	at	ADP
iajs-3265	67	63	zero	zero	NUM
iajs-3265	67	64	is	be	AUX
iajs-3265	67	65	important	important	ADJ
iajs-3265	67	66	in	in	ADP
iajs-3265	67	67	the	the	DET
iajs-3265	67	68	blasius	blasius	ADJ
iajs-3265	67	69	equation	equation	NOUN
iajs-3265	67	70	to	to	PART
iajs-3265	67	71	evaluate	evaluate	VERB
iajs-3265	67	72	the	the	DET
iajs-3265	67	73	shear	shear	NOUN
iajs-3265	67	74	stress	stress	NOUN
iajs-3265	67	75	on	on	ADP
iajs-3265	67	76	the	the	DET
iajs-3265	67	77	plate	plate	NOUN
iajs-3265	67	78	.	.	PUNCT
iajs-3265	68	1	numerous	numerous	ADJ
iajs-3265	68	2	authors	author	NOUN
iajs-3265	68	3	have	have	AUX
iajs-3265	68	4	tried	try	VERB
iajs-3265	68	5	to	to	PART
iajs-3265	68	6	solve	solve	VERB
iajs-3265	68	7	this	this	DET
iajs-3265	68	8	problem	problem	NOUN
iajs-3265	68	9	and	and	CCONJ
iajs-3265	68	10	obtained	obtain	VERB
iajs-3265	68	11	various	various	ADJ
iajs-3265	68	12	numbers	number	NOUN
iajs-3265	68	13	for	for	ADP
iajs-3265	68	14	this	this	DET
iajs-3265	68	15	value	value	NOUN
iajs-3265	68	16	.	.	PUNCT
iajs-3265	69	1	for	for	ADP
iajs-3265	69	2	more	more	ADJ
iajs-3265	69	3	details	detail	NOUN
iajs-3265	69	4	,	,	PUNCT
iajs-3265	69	5	see	see	VERB
iajs-3265	69	6	[	[	X
iajs-3265	69	7	42	42	NUM
iajs-3265	69	8	-	-	SYM
iajs-3265	69	9	44	44	NUM
iajs-3265	69	10	]	]	PUNCT
iajs-3265	69	11	.	.	PUNCT
iajs-3265	70	1	therefore	therefore	ADV
iajs-3265	70	2	,	,	PUNCT
iajs-3265	70	3	the	the	DET
iajs-3265	70	4	boundary	boundary	ADJ
iajs-3265	70	5	conditions	condition	NOUN
iajs-3265	70	6	of	of	ADP
iajs-3265	70	7	the	the	DET
iajs-3265	70	8	blasius	blasius	ADJ
iajs-3265	70	9	equation	equation	NOUN
iajs-3265	70	10	become	become	VERB
iajs-3265	70	11	:	:	PUNCT
iajs-3265	70	12	𝑦(0	𝑦(0	PROPN
iajs-3265	70	13	)	)	PUNCT
iajs-3265	70	14	=	=	SYM
iajs-3265	70	15	0	0	NUM
iajs-3265	70	16	,	,	PUNCT
iajs-3265	70	17	𝑦′(0	𝑦′(0	NOUN
iajs-3265	70	18	)	)	PUNCT
iajs-3265	70	19	=	=	SYM
iajs-3265	70	20	0	0	NUM
iajs-3265	70	21	,	,	PUNCT
iajs-3265	70	22	𝑦′′(0	𝑦′′(0	NOUN
iajs-3265	70	23	)	)	PUNCT
iajs-3265	71	1	=	=	SYM
iajs-3265	71	2	𝛼.	𝛼.	NOUN
iajs-3265	71	3	(	(	PUNCT
iajs-3265	71	4	5	5	X
iajs-3265	71	5	)	)	PUNCT
iajs-3265	71	6	the	the	DET
iajs-3265	71	7	value	value	NOUN
iajs-3265	71	8	of	of	ADP
iajs-3265	71	9	𝛼	𝛼	NOUN
iajs-3265	71	10	=	=	NOUN
iajs-3265	71	11	0.3320573	0.3320573	NUM
iajs-3265	71	12	will	will	AUX
iajs-3265	71	13	be	be	AUX
iajs-3265	71	14	utilized	utilize	VERB
iajs-3265	71	15	in	in	ADP
iajs-3265	71	16	the	the	DET
iajs-3265	71	17	present	present	ADJ
iajs-3265	71	18	work	work	NOUN
iajs-3265	71	19	,	,	PUNCT
iajs-3265	71	20	as	as	SCONJ
iajs-3265	71	21	stated	state	VERB
iajs-3265	71	22	in	in	ADP
iajs-3265	71	23	[	[	X
iajs-3265	71	24	43	43	NUM
iajs-3265	71	25	]	]	PUNCT
iajs-3265	71	26	.	.	PUNCT
iajs-3265	72	1	several	several	ADJ
iajs-3265	72	2	numerical	numerical	ADJ
iajs-3265	72	3	and	and	CCONJ
iajs-3265	72	4	analytical	analytical	ADJ
iajs-3265	72	5	techniques	technique	NOUN
iajs-3265	72	6	have	have	AUX
iajs-3265	72	7	been	be	AUX
iajs-3265	72	8	used	use	VERB
iajs-3265	72	9	to	to	PART
iajs-3265	72	10	solve	solve	VERB
iajs-3265	72	11	the	the	DET
iajs-3265	72	12	blasius	blasius	ADJ
iajs-3265	72	13	equation	equation	NOUN
iajs-3265	72	14	,	,	PUNCT
iajs-3265	72	15	such	such	ADJ
iajs-3265	72	16	as	as	ADP
iajs-3265	72	17	the	the	DET
iajs-3265	72	18	homotopy	homotopy	NOUN
iajs-3265	72	19	analysis	analysis	NOUN
iajs-3265	72	20	method	method	NOUN
iajs-3265	72	21	[	[	X
iajs-3265	72	22	45	45	NUM
iajs-3265	72	23	]	]	PUNCT
iajs-3265	72	24	,	,	PUNCT
iajs-3265	72	25	the	the	DET
iajs-3265	72	26	optimal	optimal	ADJ
iajs-3265	72	27	homotopy	homotopy	NOUN
iajs-3265	72	28	asymptotic	asymptotic	ADJ
iajs-3265	72	29	method	method	NOUN
iajs-3265	72	30	[	[	X
iajs-3265	72	31	46	46	NUM
iajs-3265	72	32	]	]	PUNCT
iajs-3265	72	33	,	,	PUNCT
iajs-3265	72	34	the	the	DET
iajs-3265	72	35	variational	variational	ADJ
iajs-3265	72	36	iteration	iteration	NOUN
iajs-3265	72	37	method	method	NOUN
iajs-3265	72	38	[	[	X
iajs-3265	72	39	47	47	NUM
iajs-3265	72	40	]	]	PUNCT
iajs-3265	72	41	,	,	PUNCT
iajs-3265	72	42	and	and	CCONJ
iajs-3265	72	43	the	the	DET
iajs-3265	72	44	adomian	adomian	NOUN
iajs-3265	72	45	decomposition	decomposition	NOUN
iajs-3265	72	46	method	method	NOUN
iajs-3265	72	47	[	[	X
iajs-3265	72	48	48	48	NUM
iajs-3265	72	49	]	]	PUNCT
iajs-3265	72	50	.	.	PUNCT
iajs-3265	73	1	in	in	ADP
iajs-3265	73	2	addition	addition	NOUN
iajs-3265	73	3	,	,	PUNCT
iajs-3265	73	4	khataybeh	khataybeh	NOUN
iajs-3265	73	5	et	et	PROPN
iajs-3265	73	6	al	al	PROPN
iajs-3265	73	7	.	.	PUNCT
iajs-3265	74	1	[	[	X
iajs-3265	74	2	42	42	NUM
iajs-3265	74	3	]	]	PUNCT
iajs-3265	74	4	applied	apply	VERB
iajs-3265	74	5	the	the	DET
iajs-3265	74	6	classical	classical	ADJ
iajs-3265	74	7	operational	operational	ADJ
iajs-3265	74	8	matrices	matrix	NOUN
iajs-3265	74	9	of	of	ADP
iajs-3265	74	10	the	the	DET
iajs-3265	74	11	bernstein	bernstein	PROPN
iajs-3265	74	12	polynomial	polynomial	PROPN
iajs-3265	74	13	to	to	PART
iajs-3265	74	14	solve	solve	VERB
iajs-3265	74	15	the	the	DET
iajs-3265	74	16	equation	equation	NOUN
iajs-3265	74	17	.	.	PUNCT
iajs-3265	75	1	also	also	ADV
iajs-3265	75	2	,	,	PUNCT
iajs-3265	75	3	parand	parand	NOUN
iajs-3265	75	4	and	and	CCONJ
iajs-3265	75	5	taghavi	taghavi	VERB
iajs-3265	75	6	[	[	X
iajs-3265	75	7	49	49	NUM
iajs-3265	75	8	]	]	PUNCT
iajs-3265	75	9	implemented	implement	VERB
iajs-3265	75	10	a	a	DET
iajs-3265	75	11	collocation	collocation	NOUN
iajs-3265	75	12	method	method	NOUN
iajs-3265	75	13	based	base	VERB
iajs-3265	75	14	on	on	ADP
iajs-3265	75	15	a	a	DET
iajs-3265	75	16	rationally	rationally	ADV
iajs-3265	75	17	scaled	scale	VERB
iajs-3265	75	18	generalized	generalized	ADJ
iajs-3265	75	19	laguerre	laguerre	NOUN
iajs-3265	75	20	function	function	VERB
iajs-3265	75	21	to	to	PART
iajs-3265	75	22	solve	solve	VERB
iajs-3265	75	23	the	the	DET
iajs-3265	75	24	blasius	blasius	ADJ
iajs-3265	75	25	equation	equation	NOUN
iajs-3265	75	26	.	.	PUNCT
iajs-3265	76	1	2.3	2.3	NUM
iajs-3265	76	2	the	the	DET
iajs-3265	76	3	falkner	falkner	PROPN
iajs-3265	76	4	-	-	PUNCT
iajs-3265	76	5	skan	skan	VERB
iajs-3265	76	6	equation	equation	NOUN
iajs-3265	76	7	the	the	DET
iajs-3265	76	8	boundary	boundary	ADJ
iajs-3265	76	9	layer	layer	NOUN
iajs-3265	76	10	equations	equation	NOUN
iajs-3265	76	11	are	be	AUX
iajs-3265	76	12	a	a	DET
iajs-3265	76	13	significant	significant	ADJ
iajs-3265	76	14	class	class	NOUN
iajs-3265	76	15	of	of	ADP
iajs-3265	76	16	nonlinear	nonlinear	ADJ
iajs-3265	76	17	ordinary	ordinary	ADJ
iajs-3265	76	18	differential	differential	ADJ
iajs-3265	76	19	equations	equation	NOUN
iajs-3265	76	20	with	with	ADP
iajs-3265	76	21	several	several	ADJ
iajs-3265	76	22	uses	use	NOUN
iajs-3265	76	23	in	in	ADP
iajs-3265	76	24	fluid	fluid	ADJ
iajs-3265	76	25	dynamics	dynamic	NOUN
iajs-3265	76	26	and	and	CCONJ
iajs-3265	76	27	physics	physic	NOUN
iajs-3265	76	28	[	[	X
iajs-3265	76	29	50	50	NUM
iajs-3265	76	30	]	]	PUNCT
iajs-3265	76	31	.	.	PUNCT
iajs-3265	77	1	one	one	NUM
iajs-3265	77	2	of	of	ADP
iajs-3265	77	3	these	these	DET
iajs-3265	77	4	equations	equation	NOUN
iajs-3265	77	5	is	be	AUX
iajs-3265	77	6	the	the	DET
iajs-3265	77	7	stationary	stationary	ADJ
iajs-3265	77	8	falkner	falkner	PROPN
iajs-3265	77	9	-	-	PUNCT
iajs-3265	77	10	skan	skan	VERB
iajs-3265	77	11	boundary	boundary	ADJ
iajs-3265	77	12	layer	layer	NOUN
iajs-3265	77	13	equation	equation	NOUN
iajs-3265	77	14	.	.	PUNCT
iajs-3265	78	1	the	the	DET
iajs-3265	78	2	falkner	falkner	PROPN
iajs-3265	78	3	-	-	PUNCT
iajs-3265	78	4	skan	skan	VERB
iajs-3265	78	5	equation	equation	NOUN
iajs-3265	78	6	was	be	AUX
iajs-3265	78	7	initially	initially	ADV
iajs-3265	78	8	put	put	VERB
iajs-3265	78	9	out	out	ADP
iajs-3265	78	10	by	by	ADP
iajs-3265	78	11	falkner	falkner	PROPN
iajs-3265	78	12	and	and	CCONJ
iajs-3265	78	13	skan	skan	VERB
iajs-3265	78	14	in	in	ADP
iajs-3265	78	15	1931[51	1931[51	NUM
iajs-3265	78	16	]	]	PUNCT
iajs-3265	78	17	.	.	PUNCT
iajs-3265	79	1	this	this	DET
iajs-3265	79	2	equation	equation	NOUN
iajs-3265	79	3	is	be	AUX
iajs-3265	79	4	essential	essential	ADJ
iajs-3265	79	5	for	for	ADP
iajs-3265	79	6	numerous	numerous	ADJ
iajs-3265	79	7	applications	application	NOUN
iajs-3265	79	8	,	,	PUNCT
iajs-3265	79	9	including	include	VERB
iajs-3265	79	10	fluid	fluid	ADJ
iajs-3265	79	11	mechanics	mechanic	NOUN
iajs-3265	79	12	,	,	PUNCT
iajs-3265	79	13	aerospace	aerospace	NOUN
iajs-3265	79	14	,	,	PUNCT
iajs-3265	79	15	heat	heat	NOUN
iajs-3265	79	16	transfer	transfer	NOUN
iajs-3265	79	17	,	,	PUNCT
iajs-3265	79	18	glass	glass	NOUN
iajs-3265	79	19	applications	application	NOUN
iajs-3265	79	20	,	,	PUNCT
iajs-3265	79	21	and	and	CCONJ
iajs-3265	79	22	polymer	polymer	NOUN
iajs-3265	79	23	investigations	investigation	NOUN
iajs-3265	79	24	[	[	X
iajs-3265	79	25	20	20	NUM
iajs-3265	79	26	]	]	PUNCT
iajs-3265	79	27	.	.	PUNCT
iajs-3265	80	1	the	the	DET
iajs-3265	80	2	third	third	ADJ
iajs-3265	80	3	-	-	PUNCT
iajs-3265	80	4	order	order	NOUN
iajs-3265	80	5	ordinary	ordinary	ADJ
iajs-3265	80	6	differential	differential	ADJ
iajs-3265	80	7	equation	equation	NOUN
iajs-3265	80	8	of	of	ADP
iajs-3265	80	9	the	the	DET
iajs-3265	80	10	falkner	falkner	PROPN
iajs-3265	80	11	-	-	PUNCT
iajs-3265	80	12	skan	skan	VERB
iajs-3265	80	13	equation	equation	NOUN
iajs-3265	80	14	over	over	ADP
iajs-3265	80	15	a	a	DET
iajs-3265	80	16	semiinfinite	semiinfinite	ADJ
iajs-3265	80	17	domain	domain	NOUN
iajs-3265	80	18	is	be	AUX
iajs-3265	80	19	given	give	VERB
iajs-3265	80	20	by	by	ADP
iajs-3265	80	21	[	[	X
iajs-3265	80	22	52	52	NUM
iajs-3265	80	23	]	]	SYM
iajs-3265	80	24	:	:	PUNCT
iajs-3265	80	25	𝑦′′′(𝑥	𝑦′′′(𝑥	NUM
iajs-3265	80	26	)	)	PUNCT
iajs-3265	80	27	+	+	NUM
iajs-3265	80	28	𝑘𝑦(𝑥	𝑘𝑦(𝑥	X
iajs-3265	80	29	)	)	PUNCT
iajs-3265	80	30	𝑦′′(𝑥	𝑦′′(𝑥	NUM
iajs-3265	80	31	)	)	PUNCT
iajs-3265	81	1	+	+	NUM
iajs-3265	81	2	𝛽	𝛽	X
iajs-3265	81	3	[	[	X
iajs-3265	81	4	𝜖2	𝜖2	ADJ
iajs-3265	81	5	−	−	PROPN
iajs-3265	81	6	(	(	PUNCT
iajs-3265	81	7	𝑦′(𝑥))2	𝑦′(𝑥))2	ADP
iajs-3265	81	8	]	]	PUNCT
iajs-3265	81	9	=	=	SYM
iajs-3265	81	10	0	0	NUM
iajs-3265	81	11	,	,	PUNCT
iajs-3265	81	12	(	(	PUNCT
iajs-3265	81	13	6	6	NUM
iajs-3265	81	14	)	)	PUNCT
iajs-3265	81	15	subjected	subject	VERB
iajs-3265	81	16	to	to	ADP
iajs-3265	81	17	the	the	DET
iajs-3265	81	18	boundary	boundary	ADJ
iajs-3265	81	19	conditions	condition	NOUN
iajs-3265	81	20	:	:	PUNCT
iajs-3265	81	21	𝑦(0	𝑦(0	PROPN
iajs-3265	81	22	)	)	PUNCT
iajs-3265	81	23	=	=	SYM
iajs-3265	81	24	0	0	NUM
iajs-3265	81	25	,	,	PUNCT
iajs-3265	81	26	𝑦′(0	𝑦′(0	NOUN
iajs-3265	81	27	)	)	PUNCT
iajs-3265	81	28	=	=	SYM
iajs-3265	82	1	1	1	NUM
iajs-3265	82	2	−	−	PROPN
iajs-3265	82	3	𝜖	𝜖	PROPN
iajs-3265	82	4	,	,	PUNCT
iajs-3265	82	5	𝑦′(∞	𝑦′(∞	NOUN
iajs-3265	82	6	)	)	PUNCT
iajs-3265	82	7	=	=	SYM
iajs-3265	82	8	𝜖	𝜖	PROPN
iajs-3265	82	9	,	,	PUNCT
iajs-3265	82	10	(	(	PUNCT
iajs-3265	82	11	7	7	NUM
iajs-3265	82	12	)	)	PUNCT
iajs-3265	82	13	where	where	SCONJ
iajs-3265	82	14	𝑘	𝑘	NOUN
iajs-3265	82	15	=	=	SYM
iajs-3265	82	16	1	1	NUM
iajs-3265	82	17	is	be	AUX
iajs-3265	82	18	constant	constant	ADJ
iajs-3265	82	19	.	.	PUNCT
iajs-3265	83	1	the	the	DET
iajs-3265	83	2	velocity	velocity	NOUN
iajs-3265	83	3	ratio	ratio	NOUN
iajs-3265	83	4	parameter	parameter	NOUN
iajs-3265	83	5	is	be	AUX
iajs-3265	83	6	denoted	denote	VERB
iajs-3265	83	7	by	by	ADP
iajs-3265	83	8	𝜖	𝜖	PROPN
iajs-3265	83	9	,	,	PUNCT
iajs-3265	83	10	and	and	CCONJ
iajs-3265	83	11	the	the	DET
iajs-3265	83	12	pressure	pressure	NOUN
iajs-3265	83	13	gradient	gradient	NOUN
iajs-3265	83	14	parameter	parameter	NOUN
iajs-3265	83	15	by	by	ADP
iajs-3265	83	16	𝛽.	𝛽.	VERB
iajs-3265	83	17	the	the	DET
iajs-3265	83	18	equation	equation	NOUN
iajs-3265	83	19	(	(	PUNCT
iajs-3265	83	20	6	6	NUM
iajs-3265	83	21	)	)	PUNCT
iajs-3265	83	22	is	be	AUX
iajs-3265	83	23	known	know	VERB
iajs-3265	83	24	as	as	ADP
iajs-3265	83	25	the	the	DET
iajs-3265	83	26	blasius	blasius	ADJ
iajs-3265	83	27	equation	equation	NOUN
iajs-3265	83	28	when	when	SCONJ
iajs-3265	83	29	𝛽	𝛽	NOUN
iajs-3265	83	30	=	=	SYM
iajs-3265	83	31	0	0	NUM
iajs-3265	83	32	and	and	CCONJ
iajs-3265	83	33	𝑘	𝑘	X
iajs-3265	83	34	=	=	NOUN
iajs-3265	83	35	1	1	NUM
iajs-3265	83	36	2	2	NUM
iajs-3265	83	37	,	,	PUNCT
iajs-3265	83	38	the	the	DET
iajs-3265	83	39	homann	homann	PROPN
iajs-3265	83	40	flow	flow	NOUN
iajs-3265	83	41	issue	issue	NOUN
iajs-3265	83	42	when	when	SCONJ
iajs-3265	83	43	𝛽	𝛽	NOUN
iajs-3265	83	44	=	=	SYM
iajs-3265	83	45	1	1	NUM
iajs-3265	83	46	2	2	NUM
iajs-3265	83	47	and	and	CCONJ
iajs-3265	83	48	𝑘	𝑘	X
iajs-3265	83	49	=	=	ADJ
iajs-3265	83	50	1	1	NUM
iajs-3265	83	51	,	,	PUNCT
iajs-3265	83	52	and	and	CCONJ
iajs-3265	83	53	the	the	DET
iajs-3265	83	54	hiemenz	hiemenz	PROPN
iajs-3265	83	55	flow	flow	NOUN
iajs-3265	83	56	problem	problem	NOUN
iajs-3265	83	57	when	when	SCONJ
iajs-3265	83	58	𝛽	𝛽	NOUN
iajs-3265	83	59	=	=	SYM
iajs-3265	83	60	1	1	NUM
iajs-3265	83	61	and	and	CCONJ
iajs-3265	83	62	𝑘	𝑘	X
iajs-3265	83	63	=	=	ADJ
iajs-3265	83	64	1	1	NUM
iajs-3265	83	65	,	,	PUNCT
iajs-3265	83	66	see	see	VERB
iajs-3265	83	67	[	[	X
iajs-3265	83	68	20	20	NUM
iajs-3265	83	69	]	]	PUNCT
iajs-3265	83	70	.	.	PUNCT
iajs-3265	84	1	the	the	DET
iajs-3265	84	2	initial	initial	ADJ
iajs-3265	84	3	condition	condition	NOUN
iajs-3265	84	4	𝑦′′(0	𝑦′′(0	NOUN
iajs-3265	84	5	)	)	PUNCT
iajs-3265	85	1	=	=	PUNCT
iajs-3265	85	2	−0.832666	−0.832666	PROPN
iajs-3265	85	3	has	have	AUX
iajs-3265	85	4	been	be	AUX
iajs-3265	85	5	derived	derive	VERB
iajs-3265	85	6	by	by	ADP
iajs-3265	85	7	the	the	DET
iajs-3265	85	8	authors	author	NOUN
iajs-3265	85	9	from	from	ADP
iajs-3265	85	10	the	the	DET
iajs-3265	85	11	boundary	boundary	ADJ
iajs-3265	85	12	condition	condition	NOUN
iajs-3265	85	13	𝑦′(∞	𝑦′(∞	NOUN
iajs-3265	85	14	)	)	PUNCT
iajs-3265	85	15	=	=	SYM
iajs-3265	85	16	𝜖	𝜖	PROPN
iajs-3265	85	17	,	,	PUNCT
iajs-3265	85	18	using	use	VERB
iajs-3265	85	19	the	the	DET
iajs-3265	85	20	padé	padé	NOUN
iajs-3265	85	21	approximation	approximation	NOUN
iajs-3265	85	22	method	method	NOUN
iajs-3265	85	23	[	[	X
iajs-3265	85	24	53	53	NUM
iajs-3265	85	25	]	]	PUNCT
iajs-3265	85	26	,	,	PUNCT
iajs-3265	85	27	and	and	CCONJ
iajs-3265	85	28	this	this	DET
iajs-3265	85	29	value	value	NOUN
iajs-3265	85	30	will	will	AUX
iajs-3265	85	31	be	be	AUX
iajs-3265	85	32	utilized	utilize	VERB
iajs-3265	85	33	in	in	ADP
iajs-3265	85	34	the	the	DET
iajs-3265	85	35	current	current	ADJ
iajs-3265	85	36	paper	paper	NOUN
iajs-3265	85	37	.	.	PUNCT
iajs-3265	86	1	as	as	ADP
iajs-3265	86	2	a	a	DET
iajs-3265	86	3	result	result	NOUN
iajs-3265	86	4	,	,	PUNCT
iajs-3265	86	5	the	the	DET
iajs-3265	86	6	following	follow	VERB
iajs-3265	86	7	are	be	AUX
iajs-3265	86	8	the	the	DET
iajs-3265	86	9	initial	initial	ADJ
iajs-3265	86	10	conditions	condition	NOUN
iajs-3265	86	11	for	for	ADP
iajs-3265	86	12	the	the	DET
iajs-3265	86	13	falkner	falkner	PROPN
iajs-3265	86	14	-	-	PUNCT
iajs-3265	86	15	skan	skan	VERB
iajs-3265	86	16	equation	equation	NOUN
iajs-3265	86	17	:	:	PUNCT
iajs-3265	86	18	𝑦(0	𝑦(0	PROPN
iajs-3265	86	19	)	)	PUNCT
iajs-3265	86	20	=	=	SYM
iajs-3265	86	21	0	0	NUM
iajs-3265	86	22	,	,	PUNCT
iajs-3265	86	23	𝑦′(0	𝑦′(0	NOUN
iajs-3265	86	24	)	)	PUNCT
iajs-3265	86	25	=	=	SYM
iajs-3265	87	1	1	1	NUM
iajs-3265	87	2	−	−	PROPN
iajs-3265	87	3	𝜖	𝜖	PROPN
iajs-3265	87	4	,	,	PUNCT
iajs-3265	87	5	𝑦′′(0	𝑦′′(0	NOUN
iajs-3265	87	6	)	)	PUNCT
iajs-3265	87	7	=	=	PUNCT
iajs-3265	88	1	−0.832666	−0.832666	PROPN
iajs-3265	88	2	.	.	PUNCT
iajs-3265	89	1	(	(	PUNCT
iajs-3265	89	2	8)	8)	NUM
iajs-3265	89	3	ihjpas	ihjpa	NOUN
iajs-3265	89	4	.	.	PUNCT
iajs-3265	90	1	36	36	NUM
iajs-3265	90	2	(	(	PUNCT
iajs-3265	90	3	4	4	NUM
iajs-3265	90	4	)	)	PUNCT
iajs-3265	90	5	2023	2023	NUM
iajs-3265	90	6	342	342	NUM
iajs-3265	90	7	the	the	DET
iajs-3265	90	8	falkner	falkner	PROPN
iajs-3265	90	9	-	-	PUNCT
iajs-3265	90	10	skan	skan	VERB
iajs-3265	90	11	equation	equation	NOUN
iajs-3265	90	12	has	have	AUX
iajs-3265	90	13	been	be	AUX
iajs-3265	90	14	solved	solve	VERB
iajs-3265	90	15	by	by	ADP
iajs-3265	90	16	using	use	VERB
iajs-3265	90	17	a	a	DET
iajs-3265	90	18	variety	variety	NOUN
iajs-3265	90	19	of	of	ADP
iajs-3265	90	20	techniques	technique	NOUN
iajs-3265	90	21	,	,	PUNCT
iajs-3265	90	22	like	like	ADP
iajs-3265	90	23	the	the	DET
iajs-3265	90	24	homotopy	homotopy	NOUN
iajs-3265	90	25	perturbation	perturbation	NOUN
iajs-3265	90	26	method	method	NOUN
iajs-3265	90	27	[	[	X
iajs-3265	90	28	54	54	NUM
iajs-3265	90	29	]	]	PUNCT
iajs-3265	90	30	,	,	PUNCT
iajs-3265	90	31	the	the	DET
iajs-3265	90	32	homotopy	homotopy	NOUN
iajs-3265	90	33	analysis	analysis	NOUN
iajs-3265	90	34	method	method	NOUN
iajs-3265	90	35	[	[	X
iajs-3265	90	36	55	55	NUM
iajs-3265	90	37	]	]	PUNCT
iajs-3265	90	38	,	,	PUNCT
iajs-3265	90	39	the	the	DET
iajs-3265	90	40	adomian	adomian	NOUN
iajs-3265	90	41	decomposition	decomposition	NOUN
iajs-3265	90	42	method	method	NOUN
iajs-3265	90	43	[	[	X
iajs-3265	90	44	56	56	NUM
iajs-3265	90	45	]	]	PUNCT
iajs-3265	90	46	,	,	PUNCT
iajs-3265	90	47	the	the	DET
iajs-3265	90	48	differential	differential	ADJ
iajs-3265	90	49	transformation	transformation	NOUN
iajs-3265	90	50	method	method	NOUN
iajs-3265	90	51	[	[	X
iajs-3265	90	52	57	57	NUM
iajs-3265	90	53	]	]	PUNCT
iajs-3265	90	54	,	,	PUNCT
iajs-3265	90	55	the	the	DET
iajs-3265	90	56	iterative	iterative	NOUN
iajs-3265	90	57	transformation	transformation	NOUN
iajs-3265	90	58	method	method	NOUN
iajs-3265	90	59	[	[	X
iajs-3265	90	60	58	58	NUM
iajs-3265	90	61	]	]	PUNCT
iajs-3265	90	62	,	,	PUNCT
iajs-3265	90	63	the	the	DET
iajs-3265	90	64	legendre	legendre	PROPN
iajs-3265	90	65	rational	rational	ADJ
iajs-3265	90	66	polynomials	polynomial	NOUN
iajs-3265	90	67	method	method	VERB
iajs-3265	90	68	[	[	X
iajs-3265	90	69	59	59	NUM
iajs-3265	90	70	]	]	PUNCT
iajs-3265	90	71	,	,	PUNCT
iajs-3265	90	72	the	the	DET
iajs-3265	90	73	shifted	shift	VERB
iajs-3265	90	74	chebyshev	chebyshev	NOUN
iajs-3265	90	75	collocation	collocation	NOUN
iajs-3265	90	76	method	method	NOUN
iajs-3265	90	77	[	[	X
iajs-3265	90	78	60	60	NUM
iajs-3265	90	79	]	]	PUNCT
iajs-3265	90	80	,	,	PUNCT
iajs-3265	90	81	and	and	CCONJ
iajs-3265	90	82	the	the	DET
iajs-3265	90	83	modified	modify	VERB
iajs-3265	90	84	rational	rational	ADJ
iajs-3265	90	85	bernoulli	bernoulli	NOUN
iajs-3265	90	86	functions	function	NOUN
iajs-3265	90	87	[	[	X
iajs-3265	90	88	61	61	NUM
iajs-3265	90	89	]	]	PUNCT
iajs-3265	90	90	.	.	PUNCT
iajs-3265	91	1	3	3	X
iajs-3265	91	2	.	.	X
iajs-3265	91	3	the	the	DET
iajs-3265	91	4	basic	basic	ADJ
iajs-3265	91	5	concepts	concept	NOUN
iajs-3265	91	6	of	of	ADP
iajs-3265	91	7	the	the	DET
iajs-3265	91	8	proposed	propose	VERB
iajs-3265	91	9	methods	method	NOUN
iajs-3265	91	10	the	the	DET
iajs-3265	91	11	fundamental	fundamental	ADJ
iajs-3265	91	12	ideas	idea	NOUN
iajs-3265	91	13	of	of	ADP
iajs-3265	91	14	the	the	DET
iajs-3265	91	15	suggested	suggest	VERB
iajs-3265	91	16	methods	method	NOUN
iajs-3265	91	17	are	be	AUX
iajs-3265	91	18	presented	present	VERB
iajs-3265	91	19	in	in	ADP
iajs-3265	91	20	this	this	DET
iajs-3265	91	21	section	section	NOUN
iajs-3265	91	22	.	.	PUNCT
iajs-3265	92	1	in	in	ADP
iajs-3265	92	2	addition	addition	NOUN
iajs-3265	92	3	,	,	PUNCT
iajs-3265	92	4	the	the	DET
iajs-3265	92	5	orthogonal	orthogonal	ADJ
iajs-3265	92	6	polynomials	polynomial	NOUN
iajs-3265	92	7	and	and	CCONJ
iajs-3265	92	8	operational	operational	ADJ
iajs-3265	92	9	matrices	matrix	NOUN
iajs-3265	92	10	will	will	AUX
iajs-3265	92	11	be	be	AUX
iajs-3265	92	12	introduced	introduce	VERB
iajs-3265	92	13	as	as	ADP
iajs-3265	92	14	instruments	instrument	NOUN
iajs-3265	92	15	for	for	ADP
iajs-3265	92	16	improving	improve	VERB
iajs-3265	92	17	the	the	DET
iajs-3265	92	18	ecm	ecm	NOUN
iajs-3265	92	19	approach	approach	NOUN
iajs-3265	92	20	to	to	PART
iajs-3265	92	21	obtain	obtain	VERB
iajs-3265	92	22	novel	novel	ADJ
iajs-3265	92	23	approximate	approximate	ADJ
iajs-3265	92	24	solutions	solution	NOUN
iajs-3265	92	25	to	to	ADP
iajs-3265	92	26	specific	specific	ADJ
iajs-3265	92	27	nonlinear	nonlinear	ADJ
iajs-3265	92	28	initial	initial	ADJ
iajs-3265	92	29	and	and	CCONJ
iajs-3265	92	30	boundary	boundary	ADJ
iajs-3265	92	31	value	value	NOUN
iajs-3265	92	32	problems	problem	NOUN
iajs-3265	92	33	described	describe	VERB
iajs-3265	92	34	in	in	ADP
iajs-3265	92	35	section	section	NOUN
iajs-3265	92	36	two	two	NUM
iajs-3265	92	37	.	.	PUNCT
iajs-3265	93	1	3.1	3.1	NUM
iajs-3265	93	2	the	the	DET
iajs-3265	93	3	basic	basic	ADJ
iajs-3265	93	4	concepts	concept	NOUN
iajs-3265	93	5	of	of	ADP
iajs-3265	93	6	the	the	DET
iajs-3265	93	7	ecm	ecm	NOUN
iajs-3265	93	8	and	and	CCONJ
iajs-3265	93	9	their	their	PRON
iajs-3265	93	10	operational	operational	ADJ
iajs-3265	93	11	matrices	matrix	NOUN
iajs-3265	93	12	consider	consider	VERB
iajs-3265	93	13	the	the	DET
iajs-3265	93	14	following	follow	VERB
iajs-3265	93	15	𝑛𝑡ℎorder	𝑛𝑡ℎorder	ADJ
iajs-3265	93	16	ordinary	ordinary	ADJ
iajs-3265	93	17	differential	differential	ADJ
iajs-3265	93	18	equation	equation	NOUN
iajs-3265	93	19	[	[	X
iajs-3265	93	20	29	29	NUM
iajs-3265	93	21	]	]	SYM
iajs-3265	93	22	:	:	PUNCT
iajs-3265	93	23	𝐺(𝑥	𝐺(𝑥	NUM
iajs-3265	93	24	,	,	PUNCT
iajs-3265	93	25	𝑦	𝑦	NOUN
iajs-3265	93	26	,	,	PUNCT
iajs-3265	93	27	𝑦′	𝑦′	NOUN
iajs-3265	93	28	,	,	PUNCT
iajs-3265	93	29	𝑦′′	𝑦′′	ADJ
iajs-3265	93	30	,	,	PUNCT
iajs-3265	93	31	…	…	PUNCT
iajs-3265	93	32	,	,	PUNCT
iajs-3265	93	33	𝑦(𝑛	𝑦(𝑛	PROPN
iajs-3265	93	34	)	)	PUNCT
iajs-3265	93	35	)	)	PUNCT
iajs-3265	94	1	=	=	SYM
iajs-3265	94	2	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3265	94	3	)	)	PUNCT
iajs-3265	94	4	,	,	PUNCT
iajs-3265	94	5	𝑎	𝑎	PROPN
iajs-3265	94	6	≤	≤	NUM
iajs-3265	94	7	𝑥	𝑥	DET
iajs-3265	94	8	≤	≤	NUM
iajs-3265	94	9	𝑏	𝑏	NOUN
iajs-3265	94	10	,	,	PUNCT
iajs-3265	94	11	(	(	PUNCT
iajs-3265	94	12	9	9	X
iajs-3265	94	13	)	)	PUNCT
iajs-3265	94	14	subjected	subject	VERB
iajs-3265	94	15	to	to	ADP
iajs-3265	94	16	the	the	DET
iajs-3265	94	17	initial	initial	ADJ
iajs-3265	94	18	condition	condition	NOUN
iajs-3265	94	19	:	:	PUNCT
iajs-3265	94	20	𝑦(𝑘)(𝑎	𝑦(𝑘)(𝑎	NUM
iajs-3265	94	21	)	)	PUNCT
iajs-3265	95	1	=	=	NOUN
iajs-3265	95	2	𝜇𝑘	𝜇𝑘	NOUN
iajs-3265	95	3	,	,	PUNCT
iajs-3265	95	4	0	0	NUM
iajs-3265	95	5	≤	≤	NOUN
iajs-3265	95	6	𝑘	𝑘	DET
iajs-3265	95	7	≤	≤	NOUN
iajs-3265	95	8	𝑛	𝑛	PRON
iajs-3265	95	9	−	−	PROPN
iajs-3265	95	10	1	1	NUM
iajs-3265	95	11	,	,	PUNCT
iajs-3265	95	12	(	(	PUNCT
iajs-3265	95	13	10	10	NUM
iajs-3265	95	14	)	)	PUNCT
iajs-3265	95	15	or	or	CCONJ
iajs-3265	95	16	with	with	ADP
iajs-3265	95	17	the	the	DET
iajs-3265	95	18	boundary	boundary	ADJ
iajs-3265	95	19	conditions	condition	NOUN
iajs-3265	95	20	:	:	PUNCT
iajs-3265	95	21	𝑦(𝑘)(𝑎	𝑦(𝑘)(𝑎	NUM
iajs-3265	95	22	)	)	PUNCT
iajs-3265	95	23	=	=	PUNCT
iajs-3265	95	24	𝜔𝑘	𝜔𝑘	PROPN
iajs-3265	95	25	,	,	PUNCT
iajs-3265	95	26	𝑦	𝑦	NOUN
iajs-3265	95	27	(	(	PUNCT
iajs-3265	95	28	𝑘)(𝑏	𝑘)(𝑏	NOUN
iajs-3265	95	29	)	)	PUNCT
iajs-3265	95	30	=	=	SYM
iajs-3265	95	31	𝛾𝑘	𝛾𝑘	NOUN
iajs-3265	95	32	,	,	PUNCT
iajs-3265	95	33	0	0	NUM
iajs-3265	95	34	≤	≤	NOUN
iajs-3265	96	1	𝑘	𝑘	PRON
iajs-3265	96	2	≤	≤	NUM
iajs-3265	96	3	𝑛	𝑛	DET
iajs-3265	96	4	2	2	NUM
iajs-3265	96	5	−	−	NOUN
iajs-3265	96	6	1	1	NUM
iajs-3265	96	7	.	.	PUNCT
iajs-3265	97	1	(	(	PUNCT
iajs-3265	97	2	11	11	NUM
iajs-3265	97	3	)	)	PUNCT
iajs-3265	97	4	where	where	SCONJ
iajs-3265	97	5	𝜇𝑘	𝜇𝑘	NOUN
iajs-3265	97	6	,	,	PUNCT
iajs-3265	97	7	𝜔𝑘	𝜔𝑘	ADP
iajs-3265	97	8	,	,	PUNCT
iajs-3265	97	9	and	and	CCONJ
iajs-3265	97	10	𝛾𝑘	𝛾𝑘	PROPN
iajs-3265	97	11	are	be	AUX
iajs-3265	97	12	constants	constant	NOUN
iajs-3265	97	13	and	and	CCONJ
iajs-3265	97	14	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3265	97	15	)	)	PUNCT
iajs-3265	97	16	is	be	AUX
iajs-3265	97	17	a	a	DET
iajs-3265	97	18	known	know	VERB
iajs-3265	97	19	function	function	NOUN
iajs-3265	97	20	.	.	PUNCT
iajs-3265	98	1	the	the	DET
iajs-3265	98	2	essential	essential	ADJ
iajs-3265	98	3	assumption	assumption	NOUN
iajs-3265	98	4	is	be	AUX
iajs-3265	98	5	that	that	SCONJ
iajs-3265	98	6	the	the	DET
iajs-3265	98	7	equation	equation	NOUN
iajs-3265	98	8	(	(	PUNCT
iajs-3265	98	9	9	9	NUM
iajs-3265	98	10	)	)	PUNCT
iajs-3265	98	11	has	have	VERB
iajs-3265	98	12	a	a	DET
iajs-3265	98	13	unique	unique	ADJ
iajs-3265	98	14	solution	solution	NOUN
iajs-3265	98	15	when	when	SCONJ
iajs-3265	98	16	the	the	DET
iajs-3265	98	17	initial	initial	ADJ
iajs-3265	98	18	or	or	CCONJ
iajs-3265	98	19	boundary	boundary	ADJ
iajs-3265	98	20	conditions	condition	NOUN
iajs-3265	98	21	are	be	AUX
iajs-3265	98	22	determined	determine	VERB
iajs-3265	98	23	in	in	ADP
iajs-3265	98	24	the	the	DET
iajs-3265	98	25	equations	equation	NOUN
iajs-3265	98	26	(	(	PUNCT
iajs-3265	98	27	10	10	NUM
iajs-3265	98	28	)	)	PUNCT
iajs-3265	98	29	or	or	CCONJ
iajs-3265	98	30	(	(	PUNCT
iajs-3265	98	31	11	11	NUM
iajs-3265	98	32	)	)	PUNCT
iajs-3265	98	33	.	.	PUNCT
iajs-3265	99	1	moreover	moreover	ADV
iajs-3265	99	2	,	,	PUNCT
iajs-3265	99	3	a	a	DET
iajs-3265	99	4	linear	linear	ADJ
iajs-3265	99	5	combination	combination	NOUN
iajs-3265	99	6	of	of	ADP
iajs-3265	99	7	𝑛𝑡ℎ-order	𝑛𝑡ℎ-order	NOUN
iajs-3265	99	8	functional	functional	ADJ
iajs-3265	99	9	series	series	NOUN
iajs-3265	99	10	based	base	VERB
iajs-3265	99	11	on	on	ADP
iajs-3265	99	12	standard	standard	ADJ
iajs-3265	99	13	polynomials	polynomial	NOUN
iajs-3265	99	14	may	may	AUX
iajs-3265	99	15	be	be	AUX
iajs-3265	99	16	used	use	VERB
iajs-3265	99	17	to	to	PART
iajs-3265	99	18	represent	represent	VERB
iajs-3265	99	19	the	the	DET
iajs-3265	99	20	unknown	unknown	ADJ
iajs-3265	99	21	function	function	NOUN
iajs-3265	99	22	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	99	23	)	)	PUNCT
iajs-3265	99	24	as	as	SCONJ
iajs-3265	99	25	follows	follow	VERB
iajs-3265	99	26	:	:	PUNCT
iajs-3265	99	27	𝑦(𝑥	𝑦(𝑥	NUM
iajs-3265	99	28	)	)	PUNCT
iajs-3265	99	29	=	=	PUNCT
iajs-3265	99	30	∑	∑	PUNCT
iajs-3265	99	31	𝑎𝑘	𝑎𝑘	NOUN
iajs-3265	99	32	𝜓𝑘(𝑥	𝜓𝑘(𝑥	PUNCT
iajs-3265	99	33	)	)	PUNCT
iajs-3265	99	34	=	=	SYM
iajs-3265	100	1	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	100	2	)	)	PUNCT
iajs-3265	100	3	𝑨	𝑨	PROPN
iajs-3265	100	4	,	,	PUNCT
iajs-3265	100	5	(	(	PUNCT
iajs-3265	100	6	12	12	NUM
iajs-3265	100	7	)	)	PUNCT
iajs-3265	100	8	𝑛	𝑛	NOUN
iajs-3265	100	9	𝑘=0	𝑘=0	ADP
iajs-3265	100	10	where	where	SCONJ
iajs-3265	100	11	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	100	12	)	)	PUNCT
iajs-3265	100	13	=	=	NOUN
iajs-3265	101	1	[	[	PUNCT
iajs-3265	101	2	1	1	NUM
iajs-3265	101	3	𝑥	𝑥	PRON
iajs-3265	101	4	𝑥2	𝑥2	NOUN
iajs-3265	101	5	𝑥3	𝑥3	NOUN
iajs-3265	101	6	…	…	PUNCT
iajs-3265	101	7	𝑥𝑛	𝑥𝑛	X
iajs-3265	101	8	]	]	X
iajs-3265	101	9	and	and	CCONJ
iajs-3265	101	10	𝑨	𝑨	PROPN
iajs-3265	101	11	=	=	PUNCT
iajs-3265	102	1	[	[	X
iajs-3265	102	2	𝑎0	𝑎0	ADV
iajs-3265	102	3	𝑎1	𝑎1	VERB
iajs-3265	102	4	𝑎2	𝑎2	NOUN
iajs-3265	102	5	…	…	PUNCT
iajs-3265	102	6	𝑎𝑛]𝑇	𝑎𝑛]𝑇	NOUN
iajs-3265	102	7	,	,	PUNCT
iajs-3265	102	8	such	such	ADJ
iajs-3265	102	9	that	that	DET
iajs-3265	102	10	𝑎𝑘	𝑎𝑘	NOUN
iajs-3265	102	11	,	,	PUNCT
iajs-3265	102	12	𝑘	𝑘	X
iajs-3265	102	13	=	=	SYM
iajs-3265	102	14	0	0	NUM
iajs-3265	102	15	,	,	PUNCT
iajs-3265	102	16	…	…	PUNCT
iajs-3265	102	17	,	,	PUNCT
iajs-3265	102	18	𝑛	𝑛	PROPN
iajs-3265	102	19	,	,	PUNCT
iajs-3265	102	20	are	be	AUX
iajs-3265	102	21	the	the	DET
iajs-3265	102	22	coefficients	coefficient	NOUN
iajs-3265	102	23	,	,	PUNCT
iajs-3265	102	24	whose	whose	DET
iajs-3265	102	25	values	value	NOUN
iajs-3265	102	26	will	will	AUX
iajs-3265	102	27	be	be	AUX
iajs-3265	102	28	specified	specify	VERB
iajs-3265	102	29	later	later	ADV
iajs-3265	102	30	.	.	PUNCT
iajs-3265	103	1	assume	assume	VERB
iajs-3265	103	2	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	103	3	)	)	PUNCT
iajs-3265	103	4	has	have	VERB
iajs-3265	103	5	the	the	DET
iajs-3265	103	6	following	follow	VERB
iajs-3265	103	7	derivatives	derivative	NOUN
iajs-3265	103	8	:	:	PUNCT
iajs-3265	103	9	𝜳′(𝑥	𝜳′(𝑥	NUM
iajs-3265	103	10	)	)	PUNCT
iajs-3265	103	11	=	=	PUNCT
iajs-3265	104	1	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	104	2	)	)	PUNCT
iajs-3265	104	3	𝑩∗	𝑩∗	ADJ
iajs-3265	104	4	,	,	PUNCT
iajs-3265	104	5	𝜳′′(𝑥	𝜳′′(𝑥	NOUN
iajs-3265	104	6	)	)	PUNCT
iajs-3265	104	7	=	=	PUNCT
iajs-3265	105	1	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	105	2	)	)	PUNCT
iajs-3265	105	3	(	(	PUNCT
iajs-3265	105	4	𝑩∗)2	𝑩∗)2	PROPN
iajs-3265	105	5	,	,	PUNCT
iajs-3265	105	6	…	…	PUNCT
iajs-3265	105	7	,	,	PUNCT
iajs-3265	105	8	𝜳(𝑛)(𝑥	𝜳(𝑛)(𝑥	NOUN
iajs-3265	105	9	)	)	PUNCT
iajs-3265	105	10	=	=	PUNCT
iajs-3265	106	1	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	106	2	)	)	PUNCT
iajs-3265	106	3	(	(	PUNCT
iajs-3265	106	4	𝑩∗)𝑛	𝑩∗)𝑛	PROPN
iajs-3265	106	5	,	,	PUNCT
iajs-3265	106	6	where	where	SCONJ
iajs-3265	106	7	𝑩∗	𝑩∗	PROPN
iajs-3265	106	8	(	(	PUNCT
iajs-3265	106	9	𝑛+1)×(𝑛+1	𝑛+1)×(𝑛+1	NOUN
iajs-3265	106	10	)	)	PUNCT
iajs-3265	106	11	,	,	PUNCT
iajs-3265	106	12	is	be	AUX
iajs-3265	106	13	the	the	DET
iajs-3265	106	14	operational	operational	ADJ
iajs-3265	106	15	matrix	matrix	NOUN
iajs-3265	106	16	and	and	CCONJ
iajs-3265	106	17	its	its	PRON
iajs-3265	106	18	entry	entry	NOUN
iajs-3265	106	19	values	value	NOUN
iajs-3265	106	20	are	be	AUX
iajs-3265	106	21	from	from	ADP
iajs-3265	106	22	the	the	DET
iajs-3265	106	23	following	following	NOUN
iajs-3265	106	24	in	in	ADP
iajs-3265	106	25	the	the	DET
iajs-3265	106	26	standard	standard	ADJ
iajs-3265	106	27	polynomials	polynomial	NOUN
iajs-3265	106	28	:	:	PUNCT
iajs-3265	106	29	𝑩∗	𝑩∗	X
iajs-3265	107	1	=	=	PUNCT
iajs-3265	107	2	[	[	PUNCT
iajs-3265	107	3	0	0	NUM
iajs-3265	107	4	1	1	NUM
iajs-3265	107	5	0	0	NUM
iajs-3265	107	6	0	0	NUM
iajs-3265	107	7	0	0	NUM
iajs-3265	107	8	2	2	NUM
iajs-3265	107	9	0	0	NUM
iajs-3265	107	10	0	0	NUM
iajs-3265	107	11	0	0	NUM
iajs-3265	107	12	⋯	⋯	ADP
iajs-3265	107	13	0	0	NUM
iajs-3265	107	14	0	0	NUM
iajs-3265	107	15	0	0	NUM
iajs-3265	107	16	⋮	⋮	NOUN
iajs-3265	107	17	⋱	⋱	PUNCT
iajs-3265	107	18	⋮	⋮	NOUN
iajs-3265	107	19	0	0	NOUN
iajs-3265	107	20	0	0	NUM
iajs-3265	107	21	0	0	NUM
iajs-3265	107	22	0	0	NUM
iajs-3265	107	23	0	0	NUM
iajs-3265	107	24	0	0	NUM
iajs-3265	107	25	⋯	⋯	NOUN
iajs-3265	107	26	𝑛	𝑛	ADP
iajs-3265	107	27	0	0	NUM
iajs-3265	107	28	]	]	X
iajs-3265	107	29	(	(	PUNCT
iajs-3265	107	30	𝑛+1)×(𝑛+1	𝑛+1)×(𝑛+1	NOUN
iajs-3265	107	31	)	)	PUNCT
iajs-3265	107	32	thus	thus	ADV
iajs-3265	107	33	,	,	PUNCT
iajs-3265	107	34	the	the	DET
iajs-3265	107	35	forms	form	NOUN
iajs-3265	107	36	presented	present	VERB
iajs-3265	107	37	below	below	ADV
iajs-3265	107	38	can	can	AUX
iajs-3265	107	39	be	be	AUX
iajs-3265	107	40	used	use	VERB
iajs-3265	107	41	to	to	PART
iajs-3265	107	42	define	define	VERB
iajs-3265	107	43	the	the	DET
iajs-3265	107	44	derivatives	derivative	NOUN
iajs-3265	107	45	of	of	ADP
iajs-3265	107	46	the	the	DET
iajs-3265	107	47	function	function	NOUN
iajs-3265	107	48	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	107	49	):	):	PUNCT
iajs-3265	107	50	𝑦(𝑛)(𝑥	𝑦(𝑛)(𝑥	NUM
iajs-3265	107	51	)	)	PUNCT
iajs-3265	107	52	=	=	SYM
iajs-3265	108	1	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	108	2	)	)	PUNCT
iajs-3265	108	3	(	(	PUNCT
iajs-3265	108	4	𝑩∗)𝑛	𝑩∗)𝑛	PROPN
iajs-3265	108	5	𝑨	𝑨	PROPN
iajs-3265	108	6	,	,	PUNCT
iajs-3265	108	7	where	where	SCONJ
iajs-3265	108	8	,	,	PUNCT
iajs-3265	108	9	𝑛	𝑛	PRON
iajs-3265	108	10	≥	≥	NOUN
iajs-3265	108	11	1	1	NUM
iajs-3265	108	12	.	.	PUNCT
iajs-3265	109	1	(	(	PUNCT
iajs-3265	109	2	13	13	NUM
iajs-3265	109	3	)	)	PUNCT
iajs-3265	109	4	then	then	ADV
iajs-3265	109	5	,	,	PUNCT
iajs-3265	109	6	the	the	DET
iajs-3265	109	7	equations	equation	NOUN
iajs-3265	109	8	(	(	PUNCT
iajs-3265	109	9	12	12	NUM
iajs-3265	109	10	)	)	PUNCT
iajs-3265	109	11	and	and	CCONJ
iajs-3265	109	12	(	(	PUNCT
iajs-3265	109	13	13	13	NUM
iajs-3265	109	14	)	)	PUNCT
iajs-3265	109	15	are	be	AUX
iajs-3265	109	16	substituted	substitute	VERB
iajs-3265	109	17	into	into	ADP
iajs-3265	109	18	the	the	DET
iajs-3265	109	19	equations	equation	NOUN
iajs-3265	109	20	(	(	PUNCT
iajs-3265	109	21	9	9	NUM
iajs-3265	109	22	)	)	PUNCT
iajs-3265	109	23	,	,	PUNCT
iajs-3265	109	24	(	(	PUNCT
iajs-3265	109	25	10	10	NUM
iajs-3265	109	26	)	)	PUNCT
iajs-3265	109	27	,	,	PUNCT
iajs-3265	109	28	and	and	CCONJ
iajs-3265	109	29	(	(	PUNCT
iajs-3265	109	30	11	11	NUM
iajs-3265	109	31	)	)	PUNCT
iajs-3265	109	32	,	,	PUNCT
iajs-3265	109	33	to	to	PART
iajs-3265	109	34	provide	provide	VERB
iajs-3265	109	35	the	the	DET
iajs-3265	109	36	following	follow	VERB
iajs-3265	109	37	result	result	NOUN
iajs-3265	109	38	:	:	PUNCT
iajs-3265	109	39	𝐺(𝑥	𝐺(𝑥	NOUN
iajs-3265	109	40	,	,	PUNCT
iajs-3265	109	41	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	109	42	)	)	PUNCT
iajs-3265	109	43	𝑨	𝑨	PROPN
iajs-3265	109	44	,	,	PUNCT
iajs-3265	109	45	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	109	46	)	)	PUNCT
iajs-3265	109	47	𝑩∗	𝑩∗	NOUN
iajs-3265	109	48	𝑨	𝑨	PROPN
iajs-3265	109	49	,	,	PUNCT
iajs-3265	109	50	𝜳(𝑥	𝜳(𝑥	PROPN
iajs-3265	109	51	)	)	PUNCT
iajs-3265	109	52	(	(	PUNCT
iajs-3265	109	53	𝑩∗)2	𝑩∗)2	ADV
iajs-3265	109	54	𝑨	𝑨	PROPN
iajs-3265	109	55	,	,	PUNCT
iajs-3265	109	56	…	…	PUNCT
iajs-3265	109	57	,	,	PUNCT
iajs-3265	109	58	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	109	59	)	)	PUNCT
iajs-3265	109	60	(	(	PUNCT
iajs-3265	109	61	𝑩∗)𝑛	𝑩∗)𝑛	PROPN
iajs-3265	109	62	𝑨	𝑨	PROPN
iajs-3265	109	63	)	)	PUNCT
iajs-3265	109	64	=	=	SYM
iajs-3265	109	65	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3265	109	66	)	)	PUNCT
iajs-3265	109	67	,	,	PUNCT
iajs-3265	109	68	(	(	PUNCT
iajs-3265	109	69	14	14	NUM
iajs-3265	109	70	)	)	PUNCT
iajs-3265	109	71	with	with	ADP
iajs-3265	109	72	,	,	PUNCT
iajs-3265	109	73	𝜳(𝑎	𝜳(𝑎	NOUN
iajs-3265	109	74	)	)	PUNCT
iajs-3265	109	75	(	(	PUNCT
iajs-3265	109	76	𝑩∗)𝑘	𝑩∗)𝑘	NOUN
iajs-3265	109	77	𝑨	𝑨	NOUN
iajs-3265	109	78	=	=	PUNCT
iajs-3265	109	79	𝜇𝑘	𝜇𝑘	NOUN
iajs-3265	109	80	,	,	PUNCT
iajs-3265	109	81	0	0	NUM
iajs-3265	109	82	≤	≤	NOUN
iajs-3265	109	83	𝑘	𝑘	DET
iajs-3265	109	84	≤	≤	NOUN
iajs-3265	109	85	𝑛	𝑛	PRON
iajs-3265	109	86	−	−	PROPN
iajs-3265	109	87	1	1	NUM
iajs-3265	109	88	,	,	PUNCT
iajs-3265	109	89	(	(	PUNCT
iajs-3265	109	90	15	15	NUM
iajs-3265	109	91	)	)	PUNCT
iajs-3265	109	92	and	and	CCONJ
iajs-3265	109	93	,	,	PUNCT
iajs-3265	109	94	𝜳(𝑎	𝜳(𝑎	NOUN
iajs-3265	109	95	)	)	PUNCT
iajs-3265	109	96	(	(	PUNCT
iajs-3265	109	97	𝑩∗)𝑘	𝑩∗)𝑘	NOUN
iajs-3265	109	98	𝑨	𝑨	NOUN
iajs-3265	109	99	=	=	SYM
iajs-3265	109	100	𝜔𝑘	𝜔𝑘	PROPN
iajs-3265	109	101	,	,	PUNCT
iajs-3265	109	102	𝜳(𝑏	𝜳(𝑏	X
iajs-3265	109	103	)	)	PUNCT
iajs-3265	109	104	(	(	PUNCT
iajs-3265	109	105	𝑩∗)𝑘	𝑩∗)𝑘	NOUN
iajs-3265	109	106	𝑨	𝑨	NOUN
iajs-3265	109	107	=	=	SYM
iajs-3265	109	108	𝛾𝑘	𝛾𝑘	PROPN
iajs-3265	109	109	,	,	PUNCT
iajs-3265	109	110	0	0	NUM
iajs-3265	109	111	≤	≤	NOUN
iajs-3265	110	1	𝑘	𝑘	PRON
iajs-3265	110	2	≤	≤	NUM
iajs-3265	110	3	𝑛	𝑛	DET
iajs-3265	110	4	2	2	NUM
iajs-3265	110	5	−	−	NOUN
iajs-3265	110	6	1	1	NUM
iajs-3265	110	7	.	.	PUNCT
iajs-3265	111	1	(	(	PUNCT
iajs-3265	111	2	16	16	NUM
iajs-3265	111	3	)	)	PUNCT
iajs-3265	111	4	moreover	moreover	ADV
iajs-3265	111	5	,	,	PUNCT
iajs-3265	111	6	the	the	DET
iajs-3265	111	7	inner	inner	ADJ
iajs-3265	111	8	product	product	NOUN
iajs-3265	111	9	in	in	ADP
iajs-3265	111	10	the	the	DET
iajs-3265	111	11	hilbert	hilbert	NOUN
iajs-3265	111	12	space	space	NOUN
iajs-3265	111	13	𝐻	𝐻	PROPN
iajs-3265	111	14	=	=	SYM
iajs-3265	111	15	𝐿2[0,1	𝐿2[0,1	PROPN
iajs-3265	111	16	]	]	PUNCT
iajs-3265	111	17	,	,	PUNCT
iajs-3265	111	18	is	be	AUX
iajs-3265	111	19	defined	define	VERB
iajs-3265	111	20	as	as	ADP
iajs-3265	111	21	follows	follow	VERB
iajs-3265	111	22	:	:	PUNCT
iajs-3265	111	23	ihjpas	ihjpas	PROPN
iajs-3265	111	24	.	.	PUNCT
iajs-3265	112	1	36	36	NUM
iajs-3265	112	2	(	(	PUNCT
iajs-3265	112	3	4	4	NUM
iajs-3265	112	4	)	)	PUNCT
iajs-3265	112	5	2023	2023	NUM
iajs-3265	112	6	343	343	NUM
iajs-3265	112	7	〈	〈	PROPN
iajs-3265	112	8	𝑔1	𝑔1	PROPN
iajs-3265	112	9	,	,	PUNCT
iajs-3265	112	10	𝑔2	𝑔2	VERB
iajs-3265	112	11	〉	〉	NOUN
iajs-3265	112	12	=	=	SYM
iajs-3265	112	13	∫𝑔1(𝑥	∫𝑔1(𝑥	NOUN
iajs-3265	112	14	)	)	PUNCT
iajs-3265	112	15	𝑔2(𝑥	𝑔2(𝑥	NUM
iajs-3265	112	16	)	)	PUNCT
iajs-3265	112	17	𝑑𝑥	𝑑𝑥	VERB
iajs-3265	112	18	1	1	NUM
iajs-3265	112	19	0	0	NUM
iajs-3265	112	20	.	.	PUNCT
iajs-3265	113	1	(	(	PUNCT
iajs-3265	113	2	17	17	NUM
iajs-3265	113	3	)	)	PUNCT
iajs-3265	113	4	also	also	ADV
iajs-3265	113	5	,	,	PUNCT
iajs-3265	113	6	the	the	DET
iajs-3265	113	7	set	set	NOUN
iajs-3265	113	8	of	of	ADP
iajs-3265	113	9	functions	function	NOUN
iajs-3265	113	10	𝜴	𝜴	X
iajs-3265	113	11	=	=	SYM
iajs-3265	113	12	{	{	PUNCT
iajs-3265	113	13	𝛺0	𝛺0	PROPN
iajs-3265	113	14	,	,	PUNCT
iajs-3265	113	15	𝛺1	𝛺1	PROPN
iajs-3265	113	16	…	…	PUNCT
iajs-3265	113	17	,	,	PUNCT
iajs-3265	113	18	𝛺𝑘	𝛺𝑘	ADP
iajs-3265	113	19	}	}	PUNCT
iajs-3265	113	20	,	,	PUNCT
iajs-3265	113	21	are	be	AUX
iajs-3265	113	22	linearly	linearly	ADV
iajs-3265	113	23	independent	independent	ADJ
iajs-3265	113	24	in	in	ADP
iajs-3265	113	25	𝐻	𝐻	PROPN
iajs-3265	113	26	,	,	PUNCT
iajs-3265	113	27	where	where	SCONJ
iajs-3265	113	28	𝛺𝑘	𝛺𝑘	ADP
iajs-3265	113	29	=	=	PUNCT
iajs-3265	113	30	𝑥𝑘	𝑥𝑘	X
iajs-3265	113	31	,	,	PUNCT
iajs-3265	113	32	0	0	NUM
iajs-3265	113	33	≤	≤	NOUN
iajs-3265	113	34	𝑘	𝑘	DET
iajs-3265	113	35	≤	≤	NUM
iajs-3265	113	36	𝑛	𝑛	NOUN
iajs-3265	113	37	,	,	PUNCT
iajs-3265	113	38	is	be	AUX
iajs-3265	113	39	the	the	DET
iajs-3265	113	40	base	base	ADJ
iajs-3265	113	41	function	function	NOUN
iajs-3265	113	42	of	of	ADP
iajs-3265	113	43	the	the	DET
iajs-3265	113	44	standard	standard	ADJ
iajs-3265	113	45	polynomials	polynomial	NOUN
iajs-3265	113	46	[	[	X
iajs-3265	113	47	29	29	NUM
iajs-3265	113	48	]	]	PUNCT
iajs-3265	113	49	.	.	PUNCT
iajs-3265	114	1	therefore	therefore	ADV
iajs-3265	114	2	,	,	PUNCT
iajs-3265	114	3	applying	apply	VERB
iajs-3265	114	4	the	the	DET
iajs-3265	114	5	inner	inner	ADJ
iajs-3265	114	6	product	product	NOUN
iajs-3265	114	7	of	of	ADP
iajs-3265	114	8	the	the	DET
iajs-3265	114	9	set	set	NOUN
iajs-3265	114	10	of	of	ADP
iajs-3265	114	11	base	base	NOUN
iajs-3265	114	12	functions	function	NOUN
iajs-3265	114	13	𝜴	𝜴	PROPN
iajs-3265	114	14	with	with	ADP
iajs-3265	114	15	the	the	DET
iajs-3265	114	16	left	left	ADJ
iajs-3265	114	17	and	and	CCONJ
iajs-3265	114	18	right	right	ADJ
iajs-3265	114	19	sides	side	NOUN
iajs-3265	114	20	of	of	ADP
iajs-3265	114	21	the	the	DET
iajs-3265	114	22	equation	equation	NOUN
iajs-3265	114	23	(	(	PUNCT
iajs-3265	114	24	14	14	NUM
iajs-3265	114	25	)	)	PUNCT
iajs-3265	114	26	,	,	PUNCT
iajs-3265	114	27	as	as	SCONJ
iajs-3265	114	28	given	give	VERB
iajs-3265	114	29	in	in	ADP
iajs-3265	114	30	the	the	DET
iajs-3265	114	31	equation	equation	NOUN
iajs-3265	114	32	(	(	PUNCT
iajs-3265	114	33	17	17	NUM
iajs-3265	114	34	)	)	PUNCT
iajs-3265	114	35	,	,	PUNCT
iajs-3265	114	36	yields	yield	VERB
iajs-3265	114	37	the	the	DET
iajs-3265	114	38	matrix	matrix	NOUN
iajs-3265	114	39	equation	equation	NOUN
iajs-3265	114	40	shown	show	VERB
iajs-3265	114	41	below	below	ADP
iajs-3265	114	42	[	[	X
iajs-3265	114	43	31	31	NUM
iajs-3265	114	44	]	]	SYM
iajs-3265	114	45	:	:	PUNCT
iajs-3265	114	46	𝑭	𝑭	NOUN
iajs-3265	114	47	=	=	SYM
iajs-3265	114	48	𝑮	𝑮	PROPN
iajs-3265	114	49	,	,	PUNCT
iajs-3265	114	50	(	(	PUNCT
iajs-3265	114	51	18	18	NUM
iajs-3265	114	52	)	)	PUNCT
iajs-3265	114	53	where	where	SCONJ
iajs-3265	114	54	the	the	DET
iajs-3265	114	55	𝑖𝑡ℎ	𝑖𝑡ℎ	NOUN
iajs-3265	114	56	row	row	NOUN
iajs-3265	114	57	of	of	ADP
iajs-3265	114	58	𝑭	𝑭	PROPN
iajs-3265	114	59	and	and	CCONJ
iajs-3265	114	60	𝑮	𝑮	PROPN
iajs-3265	114	61	in	in	ADP
iajs-3265	114	62	the	the	DET
iajs-3265	114	63	matrix	matrix	NOUN
iajs-3265	114	64	equation	equation	NOUN
iajs-3265	114	65	given	give	VERB
iajs-3265	114	66	in	in	ADP
iajs-3265	114	67	the	the	DET
iajs-3265	114	68	equation	equation	NOUN
iajs-3265	114	69	(	(	PUNCT
iajs-3265	114	70	18	18	NUM
iajs-3265	114	71	)	)	PUNCT
iajs-3265	114	72	includes	include	VERB
iajs-3265	114	73	the	the	DET
iajs-3265	114	74	following	follow	VERB
iajs-3265	114	75	:	:	PUNCT
iajs-3265	114	76	〈	〈	PROPN
iajs-3265	114	77	𝛺𝑖	𝛺𝑖	PROPN
iajs-3265	114	78	,	,	PUNCT
iajs-3265	114	79	𝐺(𝑥	𝐺(𝑥	NOUN
iajs-3265	114	80	,	,	PUNCT
iajs-3265	114	81	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	114	82	)	)	PUNCT
iajs-3265	114	83	𝑨	𝑨	PROPN
iajs-3265	114	84	,	,	PUNCT
iajs-3265	114	85	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	114	86	)	)	PUNCT
iajs-3265	114	87	𝑩∗	𝑩∗	NOUN
iajs-3265	114	88	𝑨	𝑨	PROPN
iajs-3265	114	89	,	,	PUNCT
iajs-3265	114	90	𝜳(𝑥	𝜳(𝑥	PROPN
iajs-3265	114	91	)	)	PUNCT
iajs-3265	114	92	(	(	PUNCT
iajs-3265	114	93	𝑩∗)2	𝑩∗)2	ADV
iajs-3265	114	94	𝑨	𝑨	PROPN
iajs-3265	114	95	,	,	PUNCT
iajs-3265	114	96	…	…	PUNCT
iajs-3265	114	97	,	,	PUNCT
iajs-3265	114	98	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	114	99	)	)	PUNCT
iajs-3265	114	100	(	(	PUNCT
iajs-3265	114	101	𝑩∗)𝑛	𝑩∗)𝑛	PROPN
iajs-3265	114	102	𝑨	𝑨	PROPN
iajs-3265	114	103	)	)	PUNCT
iajs-3265	114	104	〉	〉	NOUN
iajs-3265	114	105	,	,	PUNCT
iajs-3265	114	106	〈	〈	PROPN
iajs-3265	114	107	𝛺𝑖	𝛺𝑖	PROPN
iajs-3265	114	108	,	,	PUNCT
iajs-3265	114	109	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3265	114	110	)	)	PUNCT
iajs-3265	114	111	〉	〉	NOUN
iajs-3265	114	112	,	,	PUNCT
iajs-3265	114	113	0	0	NUM
iajs-3265	114	114	≤	≤	NUM
iajs-3265	114	115	𝑖	𝑖	SYM
iajs-3265	114	116	≤	≤	NOUN
iajs-3265	114	117	𝑛.	𝑛.	NOUN
iajs-3265	114	118	(	(	PUNCT
iajs-3265	114	119	19	19	NUM
iajs-3265	114	120	)	)	PUNCT
iajs-3265	114	121	finally	finally	ADV
iajs-3265	114	122	,	,	PUNCT
iajs-3265	114	123	some	some	PRON
iajs-3265	114	124	of	of	ADP
iajs-3265	114	125	the	the	DET
iajs-3265	114	126	entries	entry	NOUN
iajs-3265	114	127	in	in	ADP
iajs-3265	114	128	the	the	DET
iajs-3265	114	129	matrix	matrix	NOUN
iajs-3265	114	130	equation	equation	NOUN
iajs-3265	114	131	(	(	PUNCT
iajs-3265	114	132	equation(18	equation(18	NOUN
iajs-3265	114	133	)	)	PUNCT
iajs-3265	114	134	)	)	PUNCT
iajs-3265	114	135	will	will	AUX
iajs-3265	114	136	be	be	AUX
iajs-3265	114	137	modified	modify	VERB
iajs-3265	114	138	when	when	SCONJ
iajs-3265	114	139	the	the	DET
iajs-3265	114	140	initial	initial	ADJ
iajs-3265	114	141	or	or	CCONJ
iajs-3265	114	142	boundary	boundary	ADJ
iajs-3265	114	143	conditions	condition	NOUN
iajs-3265	114	144	from	from	ADP
iajs-3265	114	145	the	the	DET
iajs-3265	114	146	equations	equation	NOUN
iajs-3265	114	147	(	(	PUNCT
iajs-3265	114	148	15	15	NUM
iajs-3265	114	149	)	)	PUNCT
iajs-3265	114	150	and	and	CCONJ
iajs-3265	114	151	(	(	PUNCT
iajs-3265	114	152	16	16	NUM
iajs-3265	114	153	)	)	PUNCT
iajs-3265	114	154	are	be	AUX
iajs-3265	114	155	substituted	substitute	VERB
iajs-3265	114	156	.	.	PUNCT
iajs-3265	115	1	as	as	ADP
iajs-3265	115	2	a	a	DET
iajs-3265	115	3	result	result	NOUN
iajs-3265	115	4	,	,	PUNCT
iajs-3265	115	5	a	a	DET
iajs-3265	115	6	system	system	NOUN
iajs-3265	115	7	of	of	ADP
iajs-3265	115	8	(	(	PUNCT
iajs-3265	115	9	𝑛	𝑛	PROPN
iajs-3265	115	10	+	+	NOUN
iajs-3265	115	11	1	1	NUM
iajs-3265	115	12	)	)	PUNCT
iajs-3265	115	13	non	non	ADJ
iajs-3265	115	14	-	-	ADJ
iajs-3265	115	15	linear	linear	ADJ
iajs-3265	115	16	algebraic	algebraic	ADJ
iajs-3265	115	17	equations	equation	NOUN
iajs-3265	115	18	are	be	AUX
iajs-3265	115	19	produced	produce	VERB
iajs-3265	115	20	,	,	PUNCT
iajs-3265	115	21	with	with	ADP
iajs-3265	115	22	unknown	unknown	ADJ
iajs-3265	115	23	coefficients	coefficient	NOUN
iajs-3265	115	24	𝑨.	𝑨.	ADJ
iajs-3265	115	25	then	then	ADV
iajs-3265	115	26	,	,	PUNCT
iajs-3265	115	27	solve	solve	VERB
iajs-3265	115	28	these	these	DET
iajs-3265	115	29	algebraic	algebraic	ADJ
iajs-3265	115	30	equations	equation	NOUN
iajs-3265	115	31	numerically	numerically	ADV
iajs-3265	115	32	with	with	ADP
iajs-3265	115	33	applicable	applicable	ADJ
iajs-3265	115	34	programs	program	NOUN
iajs-3265	115	35	or	or	CCONJ
iajs-3265	115	36	sometimes	sometimes	ADV
iajs-3265	115	37	analytically	analytically	ADV
iajs-3265	115	38	.	.	PUNCT
iajs-3265	116	1	unique	unique	ADJ
iajs-3265	116	2	values	value	NOUN
iajs-3265	116	3	for	for	ADP
iajs-3265	116	4	the	the	DET
iajs-3265	116	5	unknown	unknown	ADJ
iajs-3265	116	6	coefficients	coefficient	NOUN
iajs-3265	116	7	𝑨	𝑨	NOUN
iajs-3265	117	1	=	=	PUNCT
iajs-3265	118	1	[	[	PUNCT
iajs-3265	118	2	𝑎0	𝑎0	ADV
iajs-3265	118	3	𝑎1	𝑎1	VERB
iajs-3265	118	4	𝑎2	𝑎2	NOUN
iajs-3265	118	5	…	…	PUNCT
iajs-3265	118	6	𝑎𝑛	𝑎𝑛	PROPN
iajs-3265	118	7	]	]	X
iajs-3265	118	8	can	can	AUX
iajs-3265	118	9	be	be	AUX
iajs-3265	118	10	acquired	acquire	VERB
iajs-3265	118	11	,	,	PUNCT
iajs-3265	118	12	which	which	PRON
iajs-3265	118	13	are	be	AUX
iajs-3265	118	14	substituted	substitute	VERB
iajs-3265	118	15	into	into	ADP
iajs-3265	118	16	the	the	DET
iajs-3265	118	17	equation	equation	NOUN
iajs-3265	118	18	(	(	PUNCT
iajs-3265	118	19	12	12	NUM
iajs-3265	118	20	)	)	PUNCT
iajs-3265	118	21	to	to	PART
iajs-3265	118	22	obtain	obtain	VERB
iajs-3265	118	23	the	the	DET
iajs-3265	118	24	approximate	approximate	ADJ
iajs-3265	118	25	solution	solution	NOUN
iajs-3265	118	26	of	of	ADP
iajs-3265	118	27	the	the	DET
iajs-3265	118	28	equation	equation	NOUN
iajs-3265	118	29	(	(	PUNCT
iajs-3265	118	30	9	9	NUM
iajs-3265	118	31	)	)	PUNCT
iajs-3265	118	32	.	.	PUNCT
iajs-3265	119	1	3.2	3.2	NUM
iajs-3265	119	2	the	the	DET
iajs-3265	119	3	chebyshev	chebyshev	NOUN
iajs-3265	119	4	polynomials	polynomial	NOUN
iajs-3265	119	5	and	and	CCONJ
iajs-3265	119	6	their	their	PRON
iajs-3265	119	7	operational	operational	ADJ
iajs-3265	119	8	matrices	matrix	NOUN
iajs-3265	119	9	the	the	DET
iajs-3265	119	10	following	follow	VERB
iajs-3265	119	11	is	be	AUX
iajs-3265	119	12	the	the	DET
iajs-3265	119	13	definition	definition	NOUN
iajs-3265	119	14	of	of	ADP
iajs-3265	119	15	the	the	DET
iajs-3265	119	16	first	first	ADJ
iajs-3265	119	17	kind	kind	NOUN
iajs-3265	119	18	of	of	ADP
iajs-3265	119	19	the	the	DET
iajs-3265	119	20	chebyshev	chebyshev	NOUN
iajs-3265	119	21	polynomials	polynomial	NOUN
iajs-3265	119	22	𝑻𝑛(𝑥	𝑻𝑛(𝑥	NOUN
iajs-3265	119	23	)	)	PUNCT
iajs-3265	119	24	of	of	ADP
iajs-3265	119	25	degree	degree	NOUN
iajs-3265	119	26	𝑛	𝑛	NOUN
iajs-3265	119	27	:	:	PUNCT
iajs-3265	119	28	𝑻𝑛(𝑥	𝑻𝑛(𝑥	ADJ
iajs-3265	119	29	)	)	PUNCT
iajs-3265	119	30	=	=	SYM
iajs-3265	119	31	∑(−1)𝑛−𝑘	∑(−1)𝑛−𝑘	PROPN
iajs-3265	120	1	2𝑘	2𝑘	NUM
iajs-3265	120	2	(	(	PUNCT
iajs-3265	120	3	𝑛	𝑛	PROPN
iajs-3265	120	4	+	+	X
iajs-3265	120	5	𝑘	𝑘	DET
iajs-3265	120	6	−	−	NOUN
iajs-3265	120	7	1	1	NUM
iajs-3265	120	8	)	)	PUNCT
iajs-3265	120	9	!	!	PUNCT
iajs-3265	121	1	(	(	PUNCT
iajs-3265	121	2	𝑛	𝑛	PRON
iajs-3265	121	3	−	−	NOUN
iajs-3265	121	4	𝑘	𝑘	NOUN
iajs-3265	121	5	)	)	PUNCT
iajs-3265	121	6	!	!	PUNCT
iajs-3265	122	1	(	(	PUNCT
iajs-3265	122	2	2𝑘	2𝑘	NUM
iajs-3265	122	3	)	)	PUNCT
iajs-3265	122	4	!	!	PUNCT
iajs-3265	123	1	(	(	PUNCT
iajs-3265	123	2	𝑥	𝑥	X
iajs-3265	123	3	+	+	PUNCT
iajs-3265	123	4	1)𝑘.	1)𝑘.	PROPN
iajs-3265	123	5	(	(	PUNCT
iajs-3265	123	6	20	20	NUM
iajs-3265	123	7	)	)	PUNCT
iajs-3265	123	8	𝑛	𝑛	NOUN
iajs-3265	123	9	𝑘=0	𝑘=0	ADP
iajs-3265	123	10	the	the	DET
iajs-3265	123	11	function	function	NOUN
iajs-3265	123	12	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	123	13	)	)	PUNCT
iajs-3265	123	14	can	can	AUX
iajs-3265	123	15	be	be	AUX
iajs-3265	123	16	represented	represent	VERB
iajs-3265	123	17	by	by	ADP
iajs-3265	123	18	the	the	DET
iajs-3265	123	19	(	(	PUNCT
iajs-3265	123	20	𝑛	𝑛	PROPN
iajs-3265	123	21	+	+	PROPN
iajs-3265	123	22	1)-terms	1)-terms	NUM
iajs-3265	123	23	of	of	ADP
iajs-3265	123	24	the	the	DET
iajs-3265	123	25	chebyshev	chebyshev	NOUN
iajs-3265	123	26	polynomials	polynomial	NOUN
iajs-3265	123	27	of	of	ADP
iajs-3265	123	28	the	the	DET
iajs-3265	123	29	first	first	ADJ
iajs-3265	123	30	kind	kind	NOUN
iajs-3265	123	31	as	as	ADV
iajs-3265	123	32	below	below	ADP
iajs-3265	123	33	[	[	X
iajs-3265	123	34	10	10	NUM
iajs-3265	123	35	]	]	NOUN
iajs-3265	123	36	:	:	PUNCT
iajs-3265	123	37	𝑦(𝑥	𝑦(𝑥	NUM
iajs-3265	123	38	)	)	PUNCT
iajs-3265	123	39	=	=	PUNCT
iajs-3265	123	40	∑	∑	PROPN
iajs-3265	123	41	𝑎𝑘	𝑎𝑘	NOUN
iajs-3265	123	42	𝑻𝑘(𝑥	𝑻𝑘(𝑥	NOUN
iajs-3265	123	43	)	)	PUNCT
iajs-3265	123	44	=	=	SYM
iajs-3265	123	45	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	123	46	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	123	47	)	)	PUNCT
iajs-3265	123	48	,	,	PUNCT
iajs-3265	123	49	(	(	PUNCT
iajs-3265	123	50	21	21	NUM
iajs-3265	123	51	)	)	PUNCT
iajs-3265	123	52	𝑛	𝑛	NOUN
iajs-3265	123	53	𝑘=0	𝑘=0	PROPN
iajs-3265	123	54	where	where	SCONJ
iajs-3265	123	55	,	,	PUNCT
iajs-3265	123	56	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	123	57	)	)	PUNCT
iajs-3265	123	58	=	=	PUNCT
iajs-3265	124	1	[	[	X
iajs-3265	124	2	𝑻0(𝑥	𝑻0(𝑥	NUM
iajs-3265	124	3	)	)	PUNCT
iajs-3265	124	4	,	,	PUNCT
iajs-3265	124	5	𝑻1(𝑥	𝑻1(𝑥	NOUN
iajs-3265	124	6	)	)	PUNCT
iajs-3265	124	7	,	,	PUNCT
iajs-3265	124	8	𝑻2(𝑥	𝑻2(𝑥	NUM
iajs-3265	124	9	)	)	PUNCT
iajs-3265	124	10	,	,	PUNCT
iajs-3265	124	11	…	…	PUNCT
iajs-3265	124	12	,	,	PUNCT
iajs-3265	124	13	𝑻𝑛(𝑥)]𝑇	𝑻𝑛(𝑥)]𝑇	NOUN
iajs-3265	124	14	and	and	CCONJ
iajs-3265	124	15	𝑨	𝑨	PROPN
iajs-3265	125	1	=	=	PUNCT
iajs-3265	126	1	[	[	X
iajs-3265	126	2	𝑎0	𝑎0	ADV
iajs-3265	126	3	𝑎1	𝑎1	VERB
iajs-3265	126	4	𝑎2	𝑎2	NOUN
iajs-3265	126	5	…	…	SYM
iajs-3265	126	6	𝑎𝑛]𝑇	𝑎𝑛]𝑇	PROPN
iajs-3265	126	7	,	,	PUNCT
iajs-3265	126	8	such	such	ADJ
iajs-3265	126	9	that	that	DET
iajs-3265	126	10	𝑎𝑘	𝑎𝑘	NOUN
iajs-3265	126	11	,	,	PUNCT
iajs-3265	126	12	𝑘	𝑘	X
iajs-3265	126	13	=	=	SYM
iajs-3265	126	14	0	0	NUM
iajs-3265	126	15	,	,	PUNCT
iajs-3265	126	16	…	…	PUNCT
iajs-3265	126	17	,	,	PUNCT
iajs-3265	126	18	𝑛	𝑛	PROPN
iajs-3265	126	19	,	,	PUNCT
iajs-3265	126	20	are	be	AUX
iajs-3265	126	21	the	the	DET
iajs-3265	126	22	unknown	unknown	ADJ
iajs-3265	126	23	chebyshev	chebyshev	NOUN
iajs-3265	126	24	polynomials	polynomial	NOUN
iajs-3265	126	25	coefficients	coefficient	NOUN
iajs-3265	126	26	of	of	ADP
iajs-3265	126	27	the	the	DET
iajs-3265	126	28	first	first	ADJ
iajs-3265	126	29	kind	kind	NOUN
iajs-3265	126	30	,	,	PUNCT
iajs-3265	126	31	whose	whose	DET
iajs-3265	126	32	values	value	NOUN
iajs-3265	126	33	will	will	AUX
iajs-3265	126	34	be	be	AUX
iajs-3265	126	35	determined	determine	VERB
iajs-3265	126	36	later	later	ADV
iajs-3265	126	37	.	.	PUNCT
iajs-3265	127	1	moreover	moreover	ADV
iajs-3265	127	2	,	,	PUNCT
iajs-3265	127	3	the	the	DET
iajs-3265	127	4	derivatives	derivative	NOUN
iajs-3265	127	5	of	of	ADP
iajs-3265	127	6	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	127	7	)	)	PUNCT
iajs-3265	127	8	can	can	AUX
iajs-3265	127	9	be	be	AUX
iajs-3265	127	10	regarded	regard	VERB
iajs-3265	127	11	as	as	ADP
iajs-3265	127	12	:	:	PUNCT
iajs-3265	127	13	𝜳′(𝑥	𝜳′(𝑥	NUM
iajs-3265	127	14	)	)	PUNCT
iajs-3265	128	1	=	=	SYM
iajs-3265	128	2	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	128	3	∗	∗	NOUN
iajs-3265	128	4	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	128	5	)	)	PUNCT
iajs-3265	128	6	,	,	PUNCT
iajs-3265	128	7	𝜳′′(𝑥	𝜳′′(𝑥	NOUN
iajs-3265	128	8	)	)	PUNCT
iajs-3265	128	9	=	=	PUNCT
iajs-3265	129	1	(	(	PUNCT
iajs-3265	129	2	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	129	3	∗	∗	NOUN
iajs-3265	129	4	)	)	PUNCT
iajs-3265	129	5	2	2	NUM
iajs-3265	129	6	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	129	7	)	)	PUNCT
iajs-3265	129	8	,	,	PUNCT
iajs-3265	129	9	…	…	PUNCT
iajs-3265	129	10	,	,	PUNCT
iajs-3265	129	11	𝜳(𝑛)(𝑥	𝜳(𝑛)(𝑥	NOUN
iajs-3265	129	12	)	)	PUNCT
iajs-3265	129	13	=	=	PUNCT
iajs-3265	129	14	(	(	PUNCT
iajs-3265	129	15	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	129	16	∗	∗	NOUN
iajs-3265	129	17	)	)	PUNCT
iajs-3265	129	18	𝑛	𝑛	PRON
iajs-3265	130	1	𝜳(𝑥	𝜳(𝑥	PROPN
iajs-3265	130	2	)	)	PUNCT
iajs-3265	130	3	,	,	PUNCT
iajs-3265	130	4	where	where	SCONJ
iajs-3265	130	5	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	130	6	∗	∗	NOUN
iajs-3265	130	7	(	(	PUNCT
iajs-3265	130	8	𝑛	𝑛	PROPN
iajs-3265	130	9	+	+	NUM
iajs-3265	130	10	1)×	1)×	NUM
iajs-3265	130	11	(	(	PUNCT
iajs-3265	130	12	𝑛	𝑛	PROPN
iajs-3265	130	13	+	+	NOUN
iajs-3265	130	14	1	1	NUM
iajs-3265	130	15	)	)	PUNCT
iajs-3265	130	16	,	,	PUNCT
iajs-3265	130	17	is	be	AUX
iajs-3265	130	18	the	the	DET
iajs-3265	130	19	specified	specify	VERB
iajs-3265	130	20	derivative	derivative	NOUN
iajs-3265	130	21	's	's	PART
iajs-3265	130	22	operational	operational	ADJ
iajs-3265	130	23	matrix	matrix	NOUN
iajs-3265	130	24	,	,	PUNCT
iajs-3265	130	25	which	which	PRON
iajs-3265	130	26	is	be	AUX
iajs-3265	130	27	defined	define	VERB
iajs-3265	130	28	as	as	SCONJ
iajs-3265	130	29	follows	follow	VERB
iajs-3265	130	30	:	:	PUNCT
iajs-3265	130	31	𝑩𝑻	𝑩𝑻	NOUN
iajs-3265	130	32	∗	∗	NOUN
iajs-3265	130	33	=	=	SYM
iajs-3265	130	34	(	(	PUNCT
iajs-3265	130	35	𝑑𝑖,𝑗	𝑑𝑖,𝑗	NOUN
iajs-3265	130	36	)	)	PUNCT
iajs-3265	130	37	=	=	PRON
iajs-3265	130	38	{	{	PUNCT
iajs-3265	130	39	2𝑖	2𝑖	NOUN
iajs-3265	130	40	𝜇𝑗	𝜇𝑗	VERB
iajs-3265	130	41	,	,	PUNCT
iajs-3265	130	42	for	for	ADP
iajs-3265	130	43	𝑗	𝑗	NOUN
iajs-3265	130	44	=	=	SYM
iajs-3265	130	45	𝑖	𝑖	SYM
iajs-3265	130	46	−	−	PROPN
iajs-3265	130	47	𝑘	𝑘	PROPN
iajs-3265	130	48	,	,	PUNCT
iajs-3265	130	49	0	0	NUM
iajs-3265	130	50	otherwise	otherwise	ADV
iajs-3265	130	51	,	,	PUNCT
iajs-3265	130	52	where	where	SCONJ
iajs-3265	130	53	𝑘	𝑘	PRON
iajs-3265	130	54	=	=	SYM
iajs-3265	130	55	1	1	NUM
iajs-3265	130	56	,	,	PUNCT
iajs-3265	130	57	3	3	NUM
iajs-3265	130	58	,	,	PUNCT
iajs-3265	130	59	5	5	NUM
iajs-3265	130	60	,	,	PUNCT
iajs-3265	130	61	…	…	PUNCT
iajs-3265	130	62	,	,	PUNCT
iajs-3265	130	63	𝑛	𝑛	DET
iajs-3265	130	64	−	−	NUM
iajs-3265	130	65	1	1	NUM
iajs-3265	130	66	if	if	SCONJ
iajs-3265	130	67	𝑛	𝑛	PRON
iajs-3265	130	68	is	be	AUX
iajs-3265	130	69	even	even	ADV
iajs-3265	130	70	,	,	PUNCT
iajs-3265	130	71	or	or	CCONJ
iajs-3265	130	72	𝑘	𝑘	X
iajs-3265	130	73	=	=	SYM
iajs-3265	130	74	1	1	NUM
iajs-3265	130	75	,	,	PUNCT
iajs-3265	130	76	3	3	NUM
iajs-3265	130	77	,	,	PUNCT
iajs-3265	130	78	5	5	NUM
iajs-3265	130	79	,	,	PUNCT
iajs-3265	130	80	…	…	PUNCT
iajs-3265	130	81	,	,	PUNCT
iajs-3265	130	82	𝑛	𝑛	X
iajs-3265	130	83	if	if	SCONJ
iajs-3265	130	84	𝑛	𝑛	PROPN
iajs-3265	130	85	is	be	AUX
iajs-3265	130	86	odd	odd	ADJ
iajs-3265	130	87	,	,	PUNCT
iajs-3265	130	88	𝜇0	𝜇0	NOUN
iajs-3265	130	89	=	=	SYM
iajs-3265	130	90	2	2	NUM
iajs-3265	130	91	,	,	PUNCT
iajs-3265	130	92	and	and	CCONJ
iajs-3265	130	93	𝜇𝑘	𝜇𝑘	NOUN
iajs-3265	130	94	=	=	SYM
iajs-3265	130	95	1	1	NUM
iajs-3265	130	96	for	for	ADP
iajs-3265	130	97	all	all	DET
iajs-3265	130	98	𝑘	𝑘	DET
iajs-3265	130	99	≥	≥	NOUN
iajs-3265	130	100	1	1	NUM
iajs-3265	130	101	.	.	X
iajs-3265	131	1	for	for	ADP
iajs-3265	131	2	instance	instance	NOUN
iajs-3265	131	3	,	,	PUNCT
iajs-3265	131	4	if	if	SCONJ
iajs-3265	131	5	𝑛	𝑛	PRON
iajs-3265	131	6	is	be	AUX
iajs-3265	131	7	even	even	ADV
iajs-3265	131	8	,	,	PUNCT
iajs-3265	131	9	the	the	DET
iajs-3265	131	10	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	131	11	∗	∗	NOUN
iajs-3265	131	12	is	be	AUX
iajs-3265	131	13	written	write	VERB
iajs-3265	131	14	as	as	SCONJ
iajs-3265	131	15	follows	follow	VERB
iajs-3265	131	16	:	:	PUNCT
iajs-3265	131	17	ihjpas	ihjpas	PROPN
iajs-3265	131	18	.	.	PUNCT
iajs-3265	132	1	36	36	NUM
iajs-3265	132	2	(	(	PUNCT
iajs-3265	132	3	4	4	NUM
iajs-3265	132	4	)	)	PUNCT
iajs-3265	132	5	2023	2023	NUM
iajs-3265	132	6	344	344	NUM
iajs-3265	132	7	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	132	8	∗	∗	NOUN
iajs-3265	132	9	=	=	SYM
iajs-3265	132	10	(	(	PUNCT
iajs-3265	132	11	0	0	NUM
iajs-3265	132	12	0	0	NUM
iajs-3265	132	13	0	0	NUM
iajs-3265	132	14	0	0	NUM
iajs-3265	132	15	0	0	NUM
iajs-3265	132	16	…	…	PUNCT
iajs-3265	132	17	0	0	NUM
iajs-3265	132	18	0	0	NUM
iajs-3265	132	19	0	0	NUM
iajs-3265	132	20	1	1	NUM
iajs-3265	132	21	0	0	NUM
iajs-3265	132	22	0	0	NUM
iajs-3265	132	23	0	0	NUM
iajs-3265	132	24	0	0	NUM
iajs-3265	132	25	…	…	PUNCT
iajs-3265	132	26	0	0	NUM
iajs-3265	132	27	0	0	NUM
iajs-3265	132	28	0	0	NUM
iajs-3265	132	29	0	0	NUM
iajs-3265	132	30	4	4	NUM
iajs-3265	132	31	0	0	NUM
iajs-3265	132	32	0	0	NUM
iajs-3265	132	33	0	0	NUM
iajs-3265	132	34	…	…	PUNCT
iajs-3265	132	35	0	0	NUM
iajs-3265	132	36	0	0	NUM
iajs-3265	132	37	0	0	NUM
iajs-3265	132	38	3	3	NUM
iajs-3265	132	39	0	0	NUM
iajs-3265	132	40	6	6	NUM
iajs-3265	132	41	0	0	NUM
iajs-3265	132	42	0	0	NUM
iajs-3265	132	43	…	…	PUNCT
iajs-3265	132	44	0	0	NUM
iajs-3265	132	45	0	0	NUM
iajs-3265	132	46	0	0	NUM
iajs-3265	132	47	0	0	NUM
iajs-3265	132	48	8	8	NUM
iajs-3265	132	49	0	0	NUM
iajs-3265	132	50	8	8	NUM
iajs-3265	132	51	0	0	NUM
iajs-3265	132	52	…	…	SYM
iajs-3265	132	53	0	0	NUM
iajs-3265	132	54	0	0	NUM
iajs-3265	132	55	0	0	NUM
iajs-3265	132	56	5	5	NUM
iajs-3265	132	57	0	0	NUM
iajs-3265	132	58	10	10	NUM
iajs-3265	132	59	0	0	NUM
iajs-3265	132	60	10	10	NUM
iajs-3265	132	61	…	…	PUNCT
iajs-3265	132	62	0	0	NUM
iajs-3265	132	63	0	0	NUM
iajs-3265	132	64	0	0	NUM
iajs-3265	132	65	⋮	⋮	NOUN
iajs-3265	132	66	⋮	⋮	ADJ
iajs-3265	132	67	⋮	⋮	ADJ
iajs-3265	132	68	⋮	⋮	ADJ
iajs-3265	132	69	⋮	⋮	NOUN
iajs-3265	132	70	⋱	⋱	PUNCT
iajs-3265	132	71	0	0	NUM
iajs-3265	132	72	0	0	NUM
iajs-3265	132	73	0	0	NUM
iajs-3265	133	1	𝑛	𝑛	PRON
iajs-3265	134	1	−	−	NUM
iajs-3265	134	2	1	1	NUM
iajs-3265	134	3	0	0	NUM
iajs-3265	134	4	2(𝑛	2(𝑛	NUM
iajs-3265	134	5	−	−	NUM
iajs-3265	134	6	1	1	NUM
iajs-3265	134	7	)	)	PUNCT
iajs-3265	134	8	0	0	NUM
iajs-3265	134	9	2(𝑛	2(𝑛	NUM
iajs-3265	134	10	−	−	NUM
iajs-3265	134	11	1	1	NUM
iajs-3265	134	12	)	)	PUNCT
iajs-3265	134	13	…	…	PUNCT
iajs-3265	134	14	2(𝑛	2(𝑛	NUM
iajs-3265	134	15	−	−	NOUN
iajs-3265	134	16	1	1	NUM
iajs-3265	134	17	)	)	PUNCT
iajs-3265	134	18	0	0	NUM
iajs-3265	134	19	0	0	NUM
iajs-3265	134	20	0	0	NUM
iajs-3265	134	21	2𝑛	2𝑛	NUM
iajs-3265	134	22	0	0	NUM
iajs-3265	135	1	2𝑛	2𝑛	NOUN
iajs-3265	135	2	0	0	NUM
iajs-3265	135	3	…	…	SYM
iajs-3265	135	4	0	0	NUM
iajs-3265	135	5	2𝑛	2𝑛	NOUN
iajs-3265	135	6	0	0	NUM
iajs-3265	135	7	)	)	PUNCT
iajs-3265	135	8	.	.	PUNCT
iajs-3265	136	1	the	the	DET
iajs-3265	136	2	matrix	matrix	NOUN
iajs-3265	136	3	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	136	4	∗	∗	NOUN
iajs-3265	136	5	is	be	AUX
iajs-3265	136	6	also	also	ADV
iajs-3265	136	7	defined	define	VERB
iajs-3265	136	8	as	as	SCONJ
iajs-3265	136	9	follows	follow	VERB
iajs-3265	136	10	if	if	SCONJ
iajs-3265	136	11	𝑛	𝑛	PRON
iajs-3265	136	12	is	be	AUX
iajs-3265	136	13	odd	odd	ADJ
iajs-3265	136	14	:	:	PUNCT
iajs-3265	136	15	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	136	16	∗	∗	NOUN
iajs-3265	136	17	=	=	SYM
iajs-3265	136	18	(	(	PUNCT
iajs-3265	136	19	0	0	NUM
iajs-3265	136	20	0	0	NUM
iajs-3265	136	21	0	0	NUM
iajs-3265	136	22	0	0	NUM
iajs-3265	136	23	…	…	PUNCT
iajs-3265	136	24	0	0	NUM
iajs-3265	136	25	0	0	NUM
iajs-3265	136	26	0	0	NUM
iajs-3265	136	27	1	1	NUM
iajs-3265	136	28	0	0	NUM
iajs-3265	136	29	0	0	NUM
iajs-3265	136	30	0	0	NUM
iajs-3265	136	31	…	…	PUNCT
iajs-3265	136	32	0	0	NUM
iajs-3265	136	33	0	0	NUM
iajs-3265	136	34	0	0	NUM
iajs-3265	136	35	0	0	NUM
iajs-3265	136	36	4	4	NUM
iajs-3265	136	37	0	0	NUM
iajs-3265	136	38	0	0	NUM
iajs-3265	136	39	…	…	PUNCT
iajs-3265	136	40	0	0	NUM
iajs-3265	136	41	0	0	NUM
iajs-3265	136	42	0	0	NUM
iajs-3265	136	43	3	3	NUM
iajs-3265	136	44	0	0	NUM
iajs-3265	136	45	6	6	NUM
iajs-3265	136	46	0	0	NUM
iajs-3265	136	47	…	…	SYM
iajs-3265	136	48	0	0	NUM
iajs-3265	136	49	0	0	NUM
iajs-3265	136	50	0	0	NUM
iajs-3265	136	51	0	0	NUM
iajs-3265	136	52	8	8	NUM
iajs-3265	136	53	0	0	NUM
iajs-3265	136	54	8	8	NUM
iajs-3265	136	55	…	…	SYM
iajs-3265	136	56	0	0	NUM
iajs-3265	136	57	0	0	NUM
iajs-3265	136	58	0	0	NUM
iajs-3265	136	59	⋮	⋮	NOUN
iajs-3265	136	60	⋮	⋮	ADJ
iajs-3265	136	61	⋮	⋮	ADJ
iajs-3265	136	62	⋮	⋮	NOUN
iajs-3265	136	63	⋱	⋱	PUNCT
iajs-3265	136	64	0	0	NUM
iajs-3265	136	65	0	0	NUM
iajs-3265	136	66	0	0	NUM
iajs-3265	136	67	0	0	NUM
iajs-3265	136	68	2(𝑛	2(𝑛	NUM
iajs-3265	136	69	−	−	NUM
iajs-3265	136	70	1	1	NUM
iajs-3265	136	71	)	)	PUNCT
iajs-3265	136	72	0	0	NUM
iajs-3265	136	73	2(𝑛	2(𝑛	NUM
iajs-3265	136	74	−	−	NUM
iajs-3265	136	75	1	1	NUM
iajs-3265	136	76	)	)	PUNCT
iajs-3265	136	77	…	…	PUNCT
iajs-3265	136	78	2(𝑛	2(𝑛	NUM
iajs-3265	136	79	−	−	NOUN
iajs-3265	136	80	1	1	NUM
iajs-3265	136	81	)	)	PUNCT
iajs-3265	136	82	0	0	NUM
iajs-3265	136	83	0	0	NUM
iajs-3265	137	1	𝑛	𝑛	DET
iajs-3265	137	2	0	0	NUM
iajs-3265	137	3	2𝑛	2𝑛	NOUN
iajs-3265	137	4	0	0	NUM
iajs-3265	137	5	…	…	SYM
iajs-3265	137	6	0	0	NUM
iajs-3265	137	7	2𝑛	2𝑛	NOUN
iajs-3265	137	8	0	0	NUM
iajs-3265	137	9	)	)	PUNCT
iajs-3265	137	10	.	.	PUNCT
iajs-3265	138	1	consequently	consequently	ADV
iajs-3265	138	2	,	,	PUNCT
iajs-3265	138	3	the	the	DET
iajs-3265	138	4	derivatives	derivative	NOUN
iajs-3265	138	5	of	of	ADP
iajs-3265	138	6	the	the	DET
iajs-3265	138	7	function	function	NOUN
iajs-3265	138	8	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	138	9	)	)	PUNCT
iajs-3265	138	10	have	have	VERB
iajs-3265	138	11	the	the	DET
iajs-3265	138	12	following	follow	VERB
iajs-3265	138	13	form	form	NOUN
iajs-3265	138	14	:	:	PUNCT
iajs-3265	138	15	𝑦(𝑛)(𝑥	𝑦(𝑛)(𝑥	NUM
iajs-3265	138	16	)	)	PUNCT
iajs-3265	138	17	=	=	SYM
iajs-3265	138	18	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	138	19	(	(	PUNCT
iajs-3265	138	20	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	138	21	∗	∗	NOUN
iajs-3265	138	22	)	)	PUNCT
iajs-3265	138	23	𝑛	𝑛	DET
iajs-3265	138	24	𝜳(𝑥	𝜳(𝑥	PROPN
iajs-3265	138	25	)	)	PUNCT
iajs-3265	138	26	,	,	PUNCT
iajs-3265	138	27	where	where	SCONJ
iajs-3265	138	28	,	,	PUNCT
iajs-3265	138	29	𝑛	𝑛	PRON
iajs-3265	138	30	≥	≥	NOUN
iajs-3265	138	31	1	1	NUM
iajs-3265	138	32	.	.	PUNCT
iajs-3265	139	1	(	(	PUNCT
iajs-3265	139	2	22	22	NUM
iajs-3265	139	3	)	)	PUNCT
iajs-3265	139	4	3.3	3.3	NUM
iajs-3265	139	5	the	the	DET
iajs-3265	139	6	bernoulli	bernoulli	NOUN
iajs-3265	139	7	polynomials	polynomial	NOUN
iajs-3265	139	8	and	and	CCONJ
iajs-3265	139	9	their	their	PRON
iajs-3265	139	10	operational	operational	ADJ
iajs-3265	139	11	matrices	matrix	NOUN
iajs-3265	139	12	the	the	DET
iajs-3265	139	13	definition	definition	NOUN
iajs-3265	139	14	of	of	ADP
iajs-3265	139	15	the	the	DET
iajs-3265	139	16	bernoulli	bernoulli	PROPN
iajs-3265	139	17	polynomials	polynomial	VERB
iajs-3265	139	18	𝑩𝑛(𝑥	𝑩𝑛(𝑥	PROPN
iajs-3265	139	19	)	)	PUNCT
iajs-3265	139	20	of	of	ADP
iajs-3265	139	21	degree	degree	NOUN
iajs-3265	139	22	𝑛	𝑛	NOUN
iajs-3265	139	23	is	be	AUX
iajs-3265	139	24	as	as	SCONJ
iajs-3265	139	25	follows	follow	VERB
iajs-3265	139	26	:	:	PUNCT
iajs-3265	139	27	𝑩𝑛(𝑥	𝑩𝑛(𝑥	NOUN
iajs-3265	139	28	)	)	PUNCT
iajs-3265	140	1	=	=	PUNCT
iajs-3265	140	2	∑	∑	PUNCT
iajs-3265	140	3	𝑛	𝑛	PROPN
iajs-3265	140	4	!	!	PUNCT
iajs-3265	140	5	𝒃𝑖	𝒃𝑖	PROPN
iajs-3265	140	6	𝑖	𝑖	X
iajs-3265	140	7	!	!	PUNCT
iajs-3265	141	1	(	(	PUNCT
iajs-3265	141	2	𝑛	𝑛	DET
iajs-3265	141	3	−	−	NOUN
iajs-3265	141	4	𝑖	𝑖	SYM
iajs-3265	141	5	)	)	PUNCT
iajs-3265	141	6	!	!	PUNCT
iajs-3265	142	1	2𝑛−𝑖	2𝑛−𝑖	NUM
iajs-3265	142	2	(	(	PUNCT
iajs-3265	142	3	𝑥	𝑥	PROPN
iajs-3265	142	4	+	+	NUM
iajs-3265	142	5	1)𝑛−𝑖	1)𝑛−𝑖	NUM
iajs-3265	142	6	𝑛	𝑛	DET
iajs-3265	142	7	𝑖=0	𝑖=0	PROPN
iajs-3265	142	8	,	,	PUNCT
iajs-3265	142	9	(	(	PUNCT
iajs-3265	142	10	23	23	NUM
iajs-3265	142	11	)	)	PUNCT
iajs-3265	142	12	where	where	SCONJ
iajs-3265	142	13	𝒃𝑖	𝒃𝑖	X
iajs-3265	142	14	=	=	PUNCT
iajs-3265	142	15	𝑩𝑖(0	𝑩𝑖(0	PROPN
iajs-3265	142	16	)	)	PUNCT
iajs-3265	142	17	is	be	AUX
iajs-3265	142	18	called	call	VERB
iajs-3265	142	19	the	the	DET
iajs-3265	142	20	bernoulli	bernoulli	NOUN
iajs-3265	142	21	number	number	NOUN
iajs-3265	142	22	for	for	ADP
iajs-3265	142	23	each	each	DET
iajs-3265	142	24	𝑖	𝑖	NOUN
iajs-3265	142	25	=	=	SYM
iajs-3265	142	26	0,1	0,1	NUM
iajs-3265	142	27	,	,	PUNCT
iajs-3265	142	28	…	…	PUNCT
iajs-3265	142	29	.	.	PUNCT
iajs-3265	143	1	these	these	DET
iajs-3265	143	2	numbers	number	NOUN
iajs-3265	143	3	are	be	AUX
iajs-3265	143	4	calculated	calculate	VERB
iajs-3265	143	5	by	by	ADP
iajs-3265	143	6	the	the	DET
iajs-3265	143	7	following	follow	VERB
iajs-3265	143	8	identity	identity	NOUN
iajs-3265	143	9	[	[	X
iajs-3265	143	10	62	62	NUM
iajs-3265	143	11	]	]	PUNCT
iajs-3265	143	12	:	:	PUNCT
iajs-3265	143	13	𝑥	𝑥	DET
iajs-3265	143	14	𝑒𝑥	𝑒𝑥	NOUN
iajs-3265	143	15	−	−	PROPN
iajs-3265	143	16	1	1	NUM
iajs-3265	143	17	=	=	SYM
iajs-3265	143	18	∑𝒃𝑖	∑𝒃𝑖	NOUN
iajs-3265	143	19	∞	∞	NUM
iajs-3265	143	20	𝑖=0	𝑖=0	PROPN
iajs-3265	143	21	𝑥𝑖	𝑥𝑖	ADJ
iajs-3265	143	22	𝑖	𝑖	PROPN
iajs-3265	143	23	!	!	PROPN
iajs-3265	143	24	,	,	PUNCT
iajs-3265	143	25	the	the	DET
iajs-3265	143	26	first	first	ADJ
iajs-3265	143	27	few	few	ADJ
iajs-3265	143	28	of	of	ADP
iajs-3265	143	29	the	the	DET
iajs-3265	143	30	bernoulli	bernoulli	NOUN
iajs-3265	143	31	numbers	number	NOUN
iajs-3265	143	32	are	be	AUX
iajs-3265	143	33	:	:	PUNCT
iajs-3265	143	34	𝒃0	𝒃0	PROPN
iajs-3265	143	35	=	=	SYM
iajs-3265	143	36	1	1	NUM
iajs-3265	143	37	,	,	PUNCT
iajs-3265	143	38	𝒃1	𝒃1	NOUN
iajs-3265	143	39	=	=	SYM
iajs-3265	143	40	−	−	PROPN
iajs-3265	143	41	1	1	NUM
iajs-3265	143	42	2	2	NUM
iajs-3265	143	43	,	,	PUNCT
iajs-3265	143	44	𝒃2	𝒃2	VERB
iajs-3265	143	45	=	=	SYM
iajs-3265	143	46	1	1	NUM
iajs-3265	143	47	6	6	NUM
iajs-3265	143	48	,	,	PUNCT
iajs-3265	143	49	𝒃4	𝒃4	NOUN
iajs-3265	143	50	=	=	SYM
iajs-3265	143	51	−	−	PROPN
iajs-3265	143	52	1	1	NUM
iajs-3265	143	53	30	30	NUM
iajs-3265	143	54	,	,	PUNCT
iajs-3265	143	55	…	…	PUNCT
iajs-3265	143	56	,	,	PUNCT
iajs-3265	143	57	and	and	CCONJ
iajs-3265	143	58	𝒃2𝑖+1	𝒃2𝑖+1	PROPN
iajs-3265	143	59	=	=	NOUN
iajs-3265	143	60	0	0	NUM
iajs-3265	143	61	for	for	ADP
iajs-3265	143	62	𝑖	𝑖	PRON
iajs-3265	143	63	≥	≥	NOUN
iajs-3265	143	64	1	1	NUM
iajs-3265	143	65	.	.	PUNCT
iajs-3265	144	1	we	we	PRON
iajs-3265	144	2	intend	intend	VERB
iajs-3265	144	3	to	to	PART
iajs-3265	144	4	approximate	approximate	VERB
iajs-3265	144	5	the	the	DET
iajs-3265	144	6	solution	solution	NOUN
iajs-3265	144	7	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	144	8	)	)	PUNCT
iajs-3265	144	9	of	of	ADP
iajs-3265	144	10	the	the	DET
iajs-3265	144	11	problem	problem	NOUN
iajs-3265	144	12	with	with	ADP
iajs-3265	144	13	the	the	DET
iajs-3265	144	14	initial	initial	ADJ
iajs-3265	144	15	or	or	CCONJ
iajs-3265	144	16	boundary	boundary	ADJ
iajs-3265	144	17	conditions	condition	NOUN
iajs-3265	144	18	in	in	ADP
iajs-3265	144	19	the	the	DET
iajs-3265	144	20	form	form	NOUN
iajs-3265	144	21	[	[	X
iajs-3265	144	22	44	44	NUM
iajs-3265	144	23	]	]	X
iajs-3265	144	24	:	:	PUNCT
iajs-3265	144	25	𝑦(𝑥	𝑦(𝑥	NUM
iajs-3265	144	26	)	)	PUNCT
iajs-3265	144	27	=	=	PUNCT
iajs-3265	145	1	∑	∑	PROPN
iajs-3265	145	2	𝑎𝑘	𝑎𝑘	PROPN
iajs-3265	145	3	𝑩𝑘(𝑥	𝑩𝑘(𝑥	NOUN
iajs-3265	145	4	)	)	PUNCT
iajs-3265	145	5	=	=	SYM
iajs-3265	145	6	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	145	7	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	145	8	)	)	PUNCT
iajs-3265	145	9	,	,	PUNCT
iajs-3265	145	10	(	(	PUNCT
iajs-3265	145	11	24	24	NUM
iajs-3265	145	12	)	)	PUNCT
iajs-3265	145	13	𝑛	𝑛	NOUN
iajs-3265	145	14	𝑘=0	𝑘=0	ADP
iajs-3265	145	15	where	where	SCONJ
iajs-3265	145	16	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	145	17	)	)	PUNCT
iajs-3265	145	18	=	=	NOUN
iajs-3265	146	1	[	[	X
iajs-3265	146	2	𝑩0(𝑥),𝑩1(𝑥	𝑩0(𝑥),𝑩1(𝑥	NOUN
iajs-3265	146	3	)	)	PUNCT
iajs-3265	146	4	,	,	PUNCT
iajs-3265	146	5	𝑩2(𝑥	𝑩2(𝑥	PROPN
iajs-3265	146	6	)	)	PUNCT
iajs-3265	146	7	,	,	PUNCT
iajs-3265	146	8	…	…	PUNCT
iajs-3265	146	9	,	,	PUNCT
iajs-3265	146	10	,	,	PUNCT
iajs-3265	146	11	𝑩𝑛(𝑥)]𝑇	𝑩𝑛(𝑥)]𝑇	NOUN
iajs-3265	146	12	and	and	CCONJ
iajs-3265	146	13	𝑨	𝑨	PROPN
iajs-3265	146	14	=	=	PUNCT
iajs-3265	147	1	[	[	X
iajs-3265	147	2	𝑎0	𝑎0	ADV
iajs-3265	147	3	𝑎1	𝑎1	VERB
iajs-3265	147	4	𝑎2	𝑎2	NOUN
iajs-3265	147	5	…	…	PUNCT
iajs-3265	147	6	𝑎𝑛]𝑇	𝑎𝑛]𝑇	NOUN
iajs-3265	147	7	,	,	PUNCT
iajs-3265	147	8	such	such	ADJ
iajs-3265	147	9	that	that	DET
iajs-3265	147	10	𝑎𝑘	𝑎𝑘	NOUN
iajs-3265	147	11	,	,	PUNCT
iajs-3265	147	12	𝑘	𝑘	X
iajs-3265	147	13	=	=	SYM
iajs-3265	147	14	0	0	NUM
iajs-3265	147	15	,	,	PUNCT
iajs-3265	147	16	…	…	PUNCT
iajs-3265	147	17	,	,	PUNCT
iajs-3265	147	18	𝑛	𝑛	PROPN
iajs-3265	147	19	,	,	PUNCT
iajs-3265	147	20	are	be	AUX
iajs-3265	147	21	the	the	DET
iajs-3265	147	22	unknown	unknown	ADJ
iajs-3265	147	23	bernoulli	bernoulli	NOUN
iajs-3265	147	24	coefficients	coefficient	NOUN
iajs-3265	147	25	,	,	PUNCT
iajs-3265	147	26	whose	whose	DET
iajs-3265	147	27	values	value	NOUN
iajs-3265	147	28	will	will	AUX
iajs-3265	147	29	be	be	AUX
iajs-3265	147	30	identified	identify	VERB
iajs-3265	147	31	later	later	ADV
iajs-3265	147	32	.	.	PUNCT
iajs-3265	148	1	furthermore	furthermore	ADV
iajs-3265	148	2	,	,	PUNCT
iajs-3265	148	3	the	the	DET
iajs-3265	148	4	derivatives	derivative	NOUN
iajs-3265	148	5	of	of	ADP
iajs-3265	148	6	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	148	7	)	)	PUNCT
iajs-3265	148	8	can	can	AUX
iajs-3265	148	9	be	be	AUX
iajs-3265	148	10	expressed	express	VERB
iajs-3265	148	11	as	as	ADP
iajs-3265	148	12	:	:	PUNCT
iajs-3265	148	13	𝜳′(𝑥	𝜳′(𝑥	NUM
iajs-3265	148	14	)	)	PUNCT
iajs-3265	149	1	=	=	SYM
iajs-3265	149	2	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	149	3	∗	∗	NOUN
iajs-3265	149	4	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	149	5	)	)	PUNCT
iajs-3265	149	6	,	,	PUNCT
iajs-3265	149	7	𝜳′′(𝑥	𝜳′′(𝑥	NOUN
iajs-3265	149	8	)	)	PUNCT
iajs-3265	149	9	=	=	PUNCT
iajs-3265	150	1	(	(	PUNCT
iajs-3265	150	2	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	150	3	∗	∗	NOUN
iajs-3265	150	4	)	)	PUNCT
iajs-3265	150	5	2	2	NUM
iajs-3265	150	6	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	150	7	)	)	PUNCT
iajs-3265	150	8	,	,	PUNCT
iajs-3265	150	9	…	…	PUNCT
iajs-3265	150	10	,	,	PUNCT
iajs-3265	150	11	𝜳(𝑛)(𝑥	𝜳(𝑛)(𝑥	NOUN
iajs-3265	150	12	)	)	PUNCT
iajs-3265	150	13	=	=	PUNCT
iajs-3265	150	14	(	(	PUNCT
iajs-3265	150	15	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	150	16	∗	∗	NOUN
iajs-3265	150	17	)	)	PUNCT
iajs-3265	150	18	𝑛	𝑛	PRON
iajs-3265	151	1	𝜳(𝑥	𝜳(𝑥	PROPN
iajs-3265	151	2	)	)	PUNCT
iajs-3265	151	3	,	,	PUNCT
iajs-3265	151	4	where	where	SCONJ
iajs-3265	151	5	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	151	6	∗	∗	NOUN
iajs-3265	151	7	(	(	PUNCT
iajs-3265	151	8	𝑛	𝑛	PROPN
iajs-3265	151	9	+	+	NUM
iajs-3265	151	10	1)×	1)×	NUM
iajs-3265	151	11	(	(	PUNCT
iajs-3265	151	12	𝑛	𝑛	PROPN
iajs-3265	151	13	+	+	NOUN
iajs-3265	151	14	1	1	NUM
iajs-3265	151	15	)	)	PUNCT
iajs-3265	151	16	,	,	PUNCT
iajs-3265	151	17	is	be	AUX
iajs-3265	151	18	the	the	DET
iajs-3265	151	19	differentiation	differentiation	NOUN
iajs-3265	151	20	operational	operational	ADJ
iajs-3265	151	21	bernoulli	bernoulli	NOUN
iajs-3265	151	22	matrix	matrix	NOUN
iajs-3265	151	23	,	,	PUNCT
iajs-3265	151	24	which	which	PRON
iajs-3265	151	25	is	be	AUX
iajs-3265	151	26	defined	define	VERB
iajs-3265	151	27	as	as	SCONJ
iajs-3265	151	28	follows	follow	VERB
iajs-3265	151	29	[	[	X
iajs-3265	151	30	11	11	NUM
iajs-3265	151	31	]	]	SYM
iajs-3265	151	32	:	:	PUNCT
iajs-3265	151	33	ihjpas	ihjpas	PROPN
iajs-3265	151	34	.	.	PUNCT
iajs-3265	152	1	36	36	NUM
iajs-3265	152	2	(	(	PUNCT
iajs-3265	152	3	4	4	NUM
iajs-3265	152	4	)	)	PUNCT
iajs-3265	152	5	2023	2023	NUM
iajs-3265	152	6	345	345	NUM
iajs-3265	152	7	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	152	8	∗	∗	NOUN
iajs-3265	152	9	=	=	PUNCT
iajs-3265	152	10	[	[	PUNCT
iajs-3265	152	11	0	0	NUM
iajs-3265	152	12	0	0	NUM
iajs-3265	152	13	0	0	NUM
iajs-3265	152	14	.	.	PUNCT
iajs-3265	152	15	.	.	PUNCT
iajs-3265	152	16	.	.	PUNCT
iajs-3265	153	1	0	0	NUM
iajs-3265	154	1	0	0	NUM
iajs-3265	154	2	1	1	NUM
iajs-3265	154	3	0	0	NUM
iajs-3265	154	4	0	0	NUM
iajs-3265	154	5	.	.	PUNCT
iajs-3265	154	6	.	.	PUNCT
iajs-3265	154	7	.	.	PUNCT
iajs-3265	155	1	0	0	NUM
iajs-3265	155	2	0	0	NUM
iajs-3265	155	3	0	0	NUM
iajs-3265	155	4	⋮	⋮	NOUN
iajs-3265	155	5	0	0	NUM
iajs-3265	155	6	2	2	NUM
iajs-3265	155	7	⋮	⋮	NOUN
iajs-3265	155	8	0	0	NUM
iajs-3265	155	9	0	0	NUM
iajs-3265	155	10	⋮	⋮	NOUN
iajs-3265	155	11	0	0	NUM
iajs-3265	155	12	⋯	⋯	NOUN
iajs-3265	155	13	⋱	⋱	PUNCT
iajs-3265	155	14	.	.	PUNCT
iajs-3265	155	15	.	.	PUNCT
iajs-3265	155	16	.	.	PUNCT
iajs-3265	156	1	0	0	NUM
iajs-3265	156	2	0	0	NUM
iajs-3265	156	3	⋮	⋮	NOUN
iajs-3265	156	4	⋮	⋮	NOUN
iajs-3265	156	5	𝑛	𝑛	PROPN
iajs-3265	156	6	0	0	NUM
iajs-3265	156	7	]	]	X
iajs-3265	156	8	(	(	PUNCT
iajs-3265	156	9	𝑛+1)×(𝑛+1	𝑛+1)×(𝑛+1	NOUN
iajs-3265	156	10	)	)	PUNCT
iajs-3265	156	11	then	then	ADV
iajs-3265	156	12	,	,	PUNCT
iajs-3265	156	13	the	the	DET
iajs-3265	156	14	derivatives	derivative	NOUN
iajs-3265	156	15	of	of	ADP
iajs-3265	156	16	the	the	DET
iajs-3265	156	17	function	function	NOUN
iajs-3265	156	18	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	156	19	)	)	PUNCT
iajs-3265	156	20	can	can	AUX
iajs-3265	156	21	be	be	AUX
iajs-3265	156	22	defined	define	VERB
iajs-3265	156	23	by	by	ADP
iajs-3265	156	24	:	:	PUNCT
iajs-3265	156	25	𝑦(𝑛)(𝑥	𝑦(𝑛)(𝑥	NUM
iajs-3265	156	26	)	)	PUNCT
iajs-3265	156	27	=	=	SYM
iajs-3265	156	28	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	156	29	(	(	PUNCT
iajs-3265	156	30	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	156	31	∗	∗	NOUN
iajs-3265	156	32	)	)	PUNCT
iajs-3265	156	33	𝑛	𝑛	DET
iajs-3265	156	34	𝜳(𝑥	𝜳(𝑥	PROPN
iajs-3265	156	35	)	)	PUNCT
iajs-3265	156	36	,	,	PUNCT
iajs-3265	156	37	where	where	SCONJ
iajs-3265	156	38	,	,	PUNCT
iajs-3265	156	39	𝑛	𝑛	PRON
iajs-3265	156	40	≥	≥	NOUN
iajs-3265	156	41	1	1	NUM
iajs-3265	156	42	.	.	PUNCT
iajs-3265	156	43	(	(	PUNCT
iajs-3265	156	44	25	25	NUM
iajs-3265	156	45	)	)	PUNCT
iajs-3265	156	46	3.4	3.4	NUM
iajs-3265	156	47	the	the	DET
iajs-3265	156	48	laguerre	laguerre	NOUN
iajs-3265	156	49	polynomials	polynomial	NOUN
iajs-3265	156	50	and	and	CCONJ
iajs-3265	156	51	their	their	PRON
iajs-3265	156	52	operational	operational	ADJ
iajs-3265	156	53	matrices	matrix	NOUN
iajs-3265	156	54	the	the	DET
iajs-3265	156	55	laguerre	laguerre	NOUN
iajs-3265	156	56	polynomials	polynomial	VERB
iajs-3265	156	57	𝑳𝑛(𝑥	𝑳𝑛(𝑥	NOUN
iajs-3265	156	58	)	)	PUNCT
iajs-3265	156	59	of	of	ADP
iajs-3265	156	60	degree	degree	NOUN
iajs-3265	156	61	𝑛	𝑛	PROPN
iajs-3265	156	62	are	be	AUX
iajs-3265	156	63	defined	define	VERB
iajs-3265	156	64	as	as	SCONJ
iajs-3265	156	65	follows	follow	VERB
iajs-3265	156	66	[	[	X
iajs-3265	156	67	12	12	NUM
iajs-3265	156	68	]	]	NOUN
iajs-3265	156	69	:	:	PUNCT
iajs-3265	156	70	𝑳𝑛(𝑥	𝑳𝑛(𝑥	PROPN
iajs-3265	156	71	)	)	PUNCT
iajs-3265	156	72	=	=	NOUN
iajs-3265	156	73	∑(−1)𝑘	∑(−1)𝑘	NOUN
iajs-3265	156	74	𝑛	𝑛	PROPN
iajs-3265	156	75	!	!	PUNCT
iajs-3265	156	76	(	(	PUNCT
iajs-3265	156	77	𝑛	𝑛	PRON
iajs-3265	156	78	−	−	NOUN
iajs-3265	156	79	𝑘	𝑘	NOUN
iajs-3265	156	80	)	)	PUNCT
iajs-3265	156	81	!	!	PUNCT
iajs-3265	157	1	(	(	PUNCT
iajs-3265	157	2	𝑘!)2	𝑘!)2	NOUN
iajs-3265	157	3	𝑥𝑘	𝑥𝑘	X
iajs-3265	157	4	𝑛	𝑛	PROPN
iajs-3265	157	5	𝑘=0	𝑘=0	PROPN
iajs-3265	157	6	,	,	PUNCT
iajs-3265	157	7	𝑛	𝑛	DET
iajs-3265	157	8	≥	≥	NOUN
iajs-3265	157	9	0	0	NUM
iajs-3265	157	10	(	(	PUNCT
iajs-3265	157	11	26	26	NUM
iajs-3265	157	12	)	)	PUNCT
iajs-3265	157	13	with	with	ADP
iajs-3265	157	14	𝑳𝑛(0	𝑳𝑛(0	ADJ
iajs-3265	157	15	)	)	PUNCT
iajs-3265	157	16	=	=	SYM
iajs-3265	157	17	1	1	X
iajs-3265	157	18	.	.	PUNCT
iajs-3265	158	1	moreover	moreover	ADV
iajs-3265	158	2	,	,	PUNCT
iajs-3265	158	3	the	the	DET
iajs-3265	158	4	first	first	ADJ
iajs-3265	158	5	few	few	ADJ
iajs-3265	158	6	laguerre	laguerre	NOUN
iajs-3265	158	7	polynomials	polynomial	NOUN
iajs-3265	158	8	𝑳𝑛(𝑥	𝑳𝑛(𝑥	NOUN
iajs-3265	158	9	)	)	PUNCT
iajs-3265	158	10	are	be	AUX
iajs-3265	158	11	as	as	SCONJ
iajs-3265	158	12	follows	follow	VERB
iajs-3265	158	13	:	:	PUNCT
iajs-3265	158	14	𝑳0(𝑥	𝑳0(𝑥	ADV
iajs-3265	158	15	)	)	PUNCT
iajs-3265	159	1	=	=	SYM
iajs-3265	159	2	1	1	NUM
iajs-3265	159	3	,	,	PUNCT
iajs-3265	159	4	𝑳1(𝑥	𝑳1(𝑥	NOUN
iajs-3265	159	5	)	)	PUNCT
iajs-3265	159	6	=	=	SYM
iajs-3265	160	1	1	1	NUM
iajs-3265	160	2	−	−	PROPN
iajs-3265	160	3	𝑥	𝑥	PROPN
iajs-3265	160	4	,	,	PUNCT
iajs-3265	160	5	𝑳2(𝑥	𝑳2(𝑥	PROPN
iajs-3265	160	6	)	)	PUNCT
iajs-3265	160	7	=	=	SYM
iajs-3265	161	1	1	1	NUM
iajs-3265	161	2	−	−	NUM
iajs-3265	161	3	2	2	NUM
iajs-3265	161	4	𝑥	𝑥	NOUN
iajs-3265	161	5	+	+	NUM
iajs-3265	161	6	𝑥2	𝑥2	NOUN
iajs-3265	161	7	2	2	NUM
iajs-3265	161	8	,	,	PUNCT
iajs-3265	161	9	𝑳3(𝑥	𝑳3(𝑥	PROPN
iajs-3265	161	10	)	)	PUNCT
iajs-3265	161	11	=	=	SYM
iajs-3265	162	1	1	1	NUM
iajs-3265	162	2	−	−	NUM
iajs-3265	162	3	3	3	NUM
iajs-3265	163	1	𝑥	𝑥	NOUN
iajs-3265	164	1	+	+	NUM
iajs-3265	164	2	3	3	NUM
iajs-3265	164	3	𝑥2	𝑥2	NOUN
iajs-3265	164	4	2	2	NUM
iajs-3265	164	5	−	−	NOUN
iajs-3265	164	6	𝑥3	𝑥3	NOUN
iajs-3265	164	7	6	6	NUM
iajs-3265	164	8	,	,	PUNCT
iajs-3265	164	9	…	…	PUNCT
iajs-3265	164	10	the	the	DET
iajs-3265	164	11	unknown	unknown	ADJ
iajs-3265	164	12	function	function	NOUN
iajs-3265	164	13	𝑦(𝑥	𝑦(𝑥	PROPN
iajs-3265	164	14	)	)	PUNCT
iajs-3265	164	15	can	can	AUX
iajs-3265	164	16	be	be	AUX
iajs-3265	164	17	approximated	approximate	VERB
iajs-3265	164	18	by	by	ADP
iajs-3265	164	19	the	the	DET
iajs-3265	164	20	(	(	PUNCT
iajs-3265	164	21	𝑛	𝑛	PROPN
iajs-3265	164	22	+	+	PROPN
iajs-3265	164	23	1)-terms	1)-terms	NUM
iajs-3265	164	24	of	of	ADP
iajs-3265	164	25	the	the	DET
iajs-3265	164	26	laguerre	laguerre	NOUN
iajs-3265	164	27	polynomials	polynomial	VERB
iajs-3265	164	28	as	as	ADP
iajs-3265	164	29	[	[	X
iajs-3265	164	30	17	17	NUM
iajs-3265	164	31	]	]	SYM
iajs-3265	164	32	:	:	PUNCT
iajs-3265	164	33	𝑦(𝑥	𝑦(𝑥	X
iajs-3265	164	34	)	)	PUNCT
iajs-3265	164	35	=	=	PUNCT
iajs-3265	164	36	∑	∑	PUNCT
iajs-3265	164	37	𝑎𝑘	𝑎𝑘	PROPN
iajs-3265	164	38	𝑳𝑘(𝑥	𝑳𝑘(𝑥	PROPN
iajs-3265	164	39	)	)	PUNCT
iajs-3265	164	40	=	=	PUNCT
iajs-3265	165	1	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	165	2	)	)	PUNCT
iajs-3265	165	3	𝑨	𝑨	PROPN
iajs-3265	165	4	,	,	PUNCT
iajs-3265	165	5	(	(	PUNCT
iajs-3265	165	6	27	27	NUM
iajs-3265	165	7	)	)	PUNCT
iajs-3265	165	8	𝑛	𝑛	NOUN
iajs-3265	165	9	𝑘=0	𝑘=0	ADJ
iajs-3265	166	1	where	where	SCONJ
iajs-3265	166	2	,	,	PUNCT
iajs-3265	166	3	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	166	4	)	)	PUNCT
iajs-3265	166	5	=	=	PUNCT
iajs-3265	167	1	[	[	X
iajs-3265	167	2	𝑳0(𝑥	𝑳0(𝑥	NOUN
iajs-3265	167	3	)	)	PUNCT
iajs-3265	167	4	,	,	PUNCT
iajs-3265	167	5	𝑳1(𝑥	𝑳1(𝑥	NOUN
iajs-3265	167	6	)	)	PUNCT
iajs-3265	167	7	,	,	PUNCT
iajs-3265	167	8	𝑳2(𝑥	𝑳2(𝑥	PROPN
iajs-3265	167	9	)	)	PUNCT
iajs-3265	167	10	,	,	PUNCT
iajs-3265	167	11	…	…	PUNCT
iajs-3265	167	12	,	,	PUNCT
iajs-3265	167	13	𝑳𝑛(𝑥	𝑳𝑛(𝑥	PROPN
iajs-3265	167	14	)	)	PUNCT
iajs-3265	167	15	]	]	PUNCT
iajs-3265	167	16	and	and	CCONJ
iajs-3265	167	17	𝑨	𝑨	PROPN
iajs-3265	167	18	=	=	PUNCT
iajs-3265	168	1	[	[	X
iajs-3265	168	2	𝑎0	𝑎0	ADV
iajs-3265	168	3	𝑎1	𝑎1	VERB
iajs-3265	168	4	𝑎2	𝑎2	NOUN
iajs-3265	168	5	…	…	PUNCT
iajs-3265	168	6	𝑎𝑛]𝑇	𝑎𝑛]𝑇	NOUN
iajs-3265	168	7	,	,	PUNCT
iajs-3265	168	8	such	such	ADJ
iajs-3265	168	9	that	that	DET
iajs-3265	168	10	𝑎𝑘	𝑎𝑘	NOUN
iajs-3265	168	11	,	,	PUNCT
iajs-3265	168	12	𝑘	𝑘	X
iajs-3265	168	13	=	=	SYM
iajs-3265	168	14	0	0	NUM
iajs-3265	168	15	,	,	PUNCT
iajs-3265	168	16	…	…	PUNCT
iajs-3265	168	17	,	,	PUNCT
iajs-3265	168	18	𝑛	𝑛	PROPN
iajs-3265	168	19	,	,	PUNCT
iajs-3265	168	20	are	be	AUX
iajs-3265	168	21	the	the	DET
iajs-3265	168	22	unknown	unknown	ADJ
iajs-3265	168	23	laguerre	laguerre	NOUN
iajs-3265	168	24	coefficients	coefficient	NOUN
iajs-3265	168	25	,	,	PUNCT
iajs-3265	168	26	whose	whose	DET
iajs-3265	168	27	values	value	NOUN
iajs-3265	168	28	will	will	AUX
iajs-3265	168	29	be	be	AUX
iajs-3265	168	30	determined	determine	VERB
iajs-3265	168	31	later	later	ADV
iajs-3265	168	32	.	.	PUNCT
iajs-3265	169	1	in	in	ADP
iajs-3265	169	2	addition	addition	NOUN
iajs-3265	169	3	,	,	PUNCT
iajs-3265	169	4	the	the	DET
iajs-3265	169	5	relation	relation	NOUN
iajs-3265	169	6	between	between	ADP
iajs-3265	169	7	the	the	DET
iajs-3265	169	8	laguerre	laguerre	NOUN
iajs-3265	169	9	polynomials	polynomial	VERB
iajs-3265	169	10	𝑳𝑛(𝑥	𝑳𝑛(𝑥	NOUN
iajs-3265	169	11	)	)	PUNCT
iajs-3265	169	12	and	and	CCONJ
iajs-3265	169	13	its	its	PRON
iajs-3265	169	14	integer	integer	NOUN
iajs-3265	169	15	order	order	NOUN
iajs-3265	169	16	derivatives	derivative	NOUN
iajs-3265	169	17	is	be	AUX
iajs-3265	169	18	defined	define	VERB
iajs-3265	169	19	by	by	ADP
iajs-3265	169	20	[	[	X
iajs-3265	169	21	17	17	NUM
iajs-3265	169	22	]	]	SYM
iajs-3265	169	23	:	:	PUNCT
iajs-3265	169	24	𝜳′(𝑥	𝜳′(𝑥	NUM
iajs-3265	169	25	)	)	PUNCT
iajs-3265	170	1	=	=	PUNCT
iajs-3265	170	2	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	170	3	)	)	PUNCT
iajs-3265	170	4	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	170	5	∗	∗	NOUN
iajs-3265	170	6	,	,	PUNCT
iajs-3265	170	7	𝜳′′(𝑥	𝜳′′(𝑥	NOUN
iajs-3265	170	8	)	)	PUNCT
iajs-3265	170	9	=	=	PUNCT
iajs-3265	171	1	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	171	2	)	)	PUNCT
iajs-3265	171	3	(	(	PUNCT
iajs-3265	171	4	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	171	5	∗)2	∗)2	PROPN
iajs-3265	171	6	,	,	PUNCT
iajs-3265	171	7	…	…	PUNCT
iajs-3265	171	8	,	,	PUNCT
iajs-3265	171	9	𝜳(𝑛)(𝑥	𝜳(𝑛)(𝑥	NOUN
iajs-3265	171	10	)	)	PUNCT
iajs-3265	171	11	=	=	PUNCT
iajs-3265	172	1	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	172	2	)	)	PUNCT
iajs-3265	172	3	(	(	PUNCT
iajs-3265	172	4	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	172	5	∗)𝑛	∗)𝑛	PROPN
iajs-3265	172	6	,	,	PUNCT
iajs-3265	172	7	where	where	SCONJ
iajs-3265	172	8	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	172	9	∗	∗	NOUN
iajs-3265	172	10	(	(	PUNCT
iajs-3265	172	11	𝑛	𝑛	PROPN
iajs-3265	172	12	+	+	NUM
iajs-3265	172	13	1)×	1)×	NUM
iajs-3265	172	14	(	(	PUNCT
iajs-3265	172	15	𝑛	𝑛	PROPN
iajs-3265	172	16	+	+	NOUN
iajs-3265	172	17	1	1	NUM
iajs-3265	172	18	)	)	PUNCT
iajs-3265	172	19	,	,	PUNCT
iajs-3265	172	20	is	be	AUX
iajs-3265	172	21	the	the	DET
iajs-3265	172	22	operational	operational	ADJ
iajs-3265	172	23	matrix	matrix	NOUN
iajs-3265	172	24	of	of	ADP
iajs-3265	172	25	the	the	DET
iajs-3265	172	26	provided	provide	VERB
iajs-3265	172	27	derivative	derivative	NOUN
iajs-3265	172	28	of	of	ADP
iajs-3265	172	29	the	the	DET
iajs-3265	172	30	laguerre	laguerre	NOUN
iajs-3265	172	31	polynomials	polynomial	NOUN
iajs-3265	172	32	,	,	PUNCT
iajs-3265	172	33	which	which	PRON
iajs-3265	172	34	is	be	AUX
iajs-3265	172	35	defined	define	VERB
iajs-3265	172	36	by	by	ADP
iajs-3265	172	37	[	[	X
iajs-3265	172	38	17	17	NUM
iajs-3265	172	39	]	]	X
iajs-3265	172	40	:	:	PUNCT
iajs-3265	172	41	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	172	42	∗	∗	NOUN
iajs-3265	172	43	=	=	PUNCT
iajs-3265	172	44	[	[	PUNCT
iajs-3265	172	45	0	0	NUM
iajs-3265	172	46	−1	−1	NOUN
iajs-3265	172	47	−1	−1	NOUN
iajs-3265	172	48	0	0	NUM
iajs-3265	172	49	0	0	NUM
iajs-3265	172	50	−1	−1	NOUN
iajs-3265	172	51	0	0	NUM
iajs-3265	172	52	0	0	NUM
iajs-3265	172	53	0	0	NUM
iajs-3265	172	54	⋯	⋯	NOUN
iajs-3265	172	55	−1	−1	NOUN
iajs-3265	172	56	−1	−1	NOUN
iajs-3265	172	57	−1	−1	NOUN
iajs-3265	172	58	⋮	⋮	NOUN
iajs-3265	172	59	⋱	⋱	PUNCT
iajs-3265	172	60	⋮	⋮	NOUN
iajs-3265	172	61	0	0	NOUN
iajs-3265	172	62	0	0	NUM
iajs-3265	172	63	0	0	NUM
iajs-3265	172	64	0	0	NUM
iajs-3265	172	65	0	0	NUM
iajs-3265	172	66	0	0	NUM
iajs-3265	172	67	⋯	⋯	NOUN
iajs-3265	172	68	−1	−1	NOUN
iajs-3265	172	69	0	0	NUM
iajs-3265	172	70	]	]	PUNCT
iajs-3265	172	71	(	(	PUNCT
iajs-3265	172	72	𝑛+1)×(𝑛+1	𝑛+1)×(𝑛+1	NOUN
iajs-3265	172	73	)	)	PUNCT
iajs-3265	172	74	.	.	PUNCT
iajs-3265	173	1	accordingly	accordingly	ADV
iajs-3265	173	2	,	,	PUNCT
iajs-3265	173	3	the	the	DET
iajs-3265	173	4	derivatives	derivative	NOUN
iajs-3265	173	5	of	of	ADP
iajs-3265	173	6	the	the	DET
iajs-3265	173	7	function	function	NOUN
iajs-3265	173	8	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	173	9	)	)	PUNCT
iajs-3265	173	10	can	can	AUX
iajs-3265	173	11	be	be	AUX
iajs-3265	173	12	expressed	express	VERB
iajs-3265	173	13	by	by	ADP
iajs-3265	173	14	:	:	PUNCT
iajs-3265	173	15	𝑦(𝑛)(𝑥	𝑦(𝑛)(𝑥	NUM
iajs-3265	173	16	)	)	PUNCT
iajs-3265	173	17	=	=	SYM
iajs-3265	174	1	𝜳(𝑥	𝜳(𝑥	VERB
iajs-3265	174	2	)	)	PUNCT
iajs-3265	174	3	(	(	PUNCT
iajs-3265	174	4	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	174	5	∗)𝑛	∗)𝑛	PROPN
iajs-3265	174	6	𝑨	𝑨	PROPN
iajs-3265	174	7	,	,	PUNCT
iajs-3265	174	8	where	where	SCONJ
iajs-3265	174	9	,	,	PUNCT
iajs-3265	174	10	𝑛	𝑛	PRON
iajs-3265	174	11	≥	≥	NOUN
iajs-3265	174	12	1	1	NUM
iajs-3265	174	13	.	.	PUNCT
iajs-3265	175	1	(	(	PUNCT
iajs-3265	175	2	28	28	NUM
iajs-3265	175	3	)	)	PUNCT
iajs-3265	175	4	4	4	NUM
iajs-3265	175	5	.	.	PUNCT
iajs-3265	176	1	the	the	DET
iajs-3265	176	2	implementation	implementation	NOUN
iajs-3265	176	3	of	of	ADP
iajs-3265	176	4	the	the	DET
iajs-3265	176	5	ecm	ecm	PROPN
iajs-3265	176	6	and	and	CCONJ
iajs-3265	176	7	i	i	PROPN
iajs-3265	176	8	-	-	PUNCT
iajs-3265	176	9	ecms	ecms	PROPN
iajs-3265	176	10	and	and	CCONJ
iajs-3265	176	11	numerical	numerical	ADJ
iajs-3265	176	12	results	result	NOUN
iajs-3265	176	13	the	the	DET
iajs-3265	176	14	proposed	propose	VERB
iajs-3265	176	15	methods	method	NOUN
iajs-3265	176	16	of	of	ADP
iajs-3265	176	17	the	the	DET
iajs-3265	176	18	ecm	ecm	NOUN
iajs-3265	176	19	and	and	CCONJ
iajs-3265	176	20	the	the	DET
iajs-3265	176	21	i	i	PROPN
iajs-3265	176	22	-	-	PUNCT
iajs-3265	176	23	ecms	ecms	PROPN
iajs-3265	176	24	will	will	AUX
iajs-3265	176	25	be	be	AUX
iajs-3265	176	26	applied	apply	VERB
iajs-3265	176	27	in	in	ADP
iajs-3265	176	28	this	this	DET
iajs-3265	176	29	section	section	NOUN
iajs-3265	176	30	to	to	PART
iajs-3265	176	31	find	find	VERB
iajs-3265	176	32	novel	novel	ADJ
iajs-3265	176	33	approximate	approximate	ADJ
iajs-3265	176	34	solutions	solution	NOUN
iajs-3265	176	35	,	,	PUNCT
iajs-3265	176	36	and	and	CCONJ
iajs-3265	176	37	the	the	DET
iajs-3265	176	38	numerical	numerical	ADJ
iajs-3265	176	39	results	result	NOUN
iajs-3265	176	40	will	will	AUX
iajs-3265	176	41	be	be	AUX
iajs-3265	176	42	presented	present	VERB
iajs-3265	176	43	for	for	ADP
iajs-3265	176	44	three	three	NUM
iajs-3265	176	45	nonlinear	nonlinear	ADJ
iajs-3265	176	46	problems	problem	NOUN
iajs-3265	176	47	:	:	PUNCT
iajs-3265	176	48	the	the	DET
iajs-3265	176	49	darcy	darcy	PROPN
iajs-3265	176	50	-	-	PUNCT
iajs-3265	176	51	brinkman	brinkman	PROPN
iajs-3265	176	52	-	-	PUNCT
iajs-3265	176	53	forchheimer	forchheimer	PROPN
iajs-3265	176	54	equation	equation	NOUN
iajs-3265	176	55	,	,	PUNCT
iajs-3265	176	56	the	the	DET
iajs-3265	176	57	blasius	blasius	ADJ
iajs-3265	176	58	equation	equation	NOUN
iajs-3265	176	59	,	,	PUNCT
iajs-3265	176	60	and	and	CCONJ
iajs-3265	176	61	the	the	DET
iajs-3265	176	62	falkner	falkner	PROPN
iajs-3265	176	63	-	-	PUNCT
iajs-3265	176	64	skan	skan	VERB
iajs-3265	176	65	equation	equation	NOUN
iajs-3265	176	66	.	.	PUNCT
iajs-3265	177	1	the	the	DET
iajs-3265	177	2	i	i	PROPN
iajs-3265	177	3	-	-	PUNCT
iajs-3265	177	4	ecms	ecms	PROPN
iajs-3265	177	5	are	be	AUX
iajs-3265	177	6	based	base	VERB
iajs-3265	177	7	on	on	ADP
iajs-3265	177	8	the	the	DET
iajs-3265	177	9	base	base	NOUN
iajs-3265	177	10	functions	function	NOUN
iajs-3265	177	11	of	of	ADP
iajs-3265	177	12	diverse	diverse	ADJ
iajs-3265	177	13	polynomials	polynomial	NOUN
iajs-3265	177	14	such	such	ADJ
iajs-3265	177	15	as	as	ADP
iajs-3265	177	16	chebyshev	chebyshev	NOUN
iajs-3265	177	17	,	,	PUNCT
iajs-3265	177	18	bernoulli	bernoulli	PROPN
iajs-3265	177	19	,	,	PUNCT
iajs-3265	177	20	and	and	CCONJ
iajs-3265	177	21	laguerre	laguerre	NOUN
iajs-3265	177	22	polynomials	polynomial	NOUN
iajs-3265	177	23	,	,	PUNCT
iajs-3265	177	24	introduced	introduce	VERB
iajs-3265	177	25	in	in	ADP
iajs-3265	177	26	equations	equation	NOUN
iajs-3265	177	27	(	(	PUNCT
iajs-3265	177	28	20	20	NUM
iajs-3265	177	29	)	)	PUNCT
iajs-3265	177	30	,	,	PUNCT
iajs-3265	177	31	(	(	PUNCT
iajs-3265	177	32	23	23	NUM
iajs-3265	177	33	)	)	PUNCT
iajs-3265	177	34	,	,	PUNCT
iajs-3265	177	35	and	and	CCONJ
iajs-3265	177	36	(	(	PUNCT
iajs-3265	177	37	26	26	NUM
iajs-3265	177	38	)	)	PUNCT
iajs-3265	177	39	,	,	PUNCT
iajs-3265	177	40	respectively	respectively	ADV
iajs-3265	177	41	,	,	PUNCT
iajs-3265	177	42	with	with	ADP
iajs-3265	177	43	relevant	relevant	ADJ
iajs-3265	177	44	operational	operational	ADJ
iajs-3265	177	45	matrices	matrix	NOUN
iajs-3265	177	46	.	.	PUNCT
iajs-3265	178	1	these	these	DET
iajs-3265	178	2	polynomials	polynomial	NOUN
iajs-3265	178	3	are	be	AUX
iajs-3265	178	4	performed	perform	VERB
iajs-3265	178	5	in	in	ADP
iajs-3265	178	6	two	two	NUM
iajs-3265	178	7	steps	step	NOUN
iajs-3265	178	8	of	of	ADP
iajs-3265	178	9	the	the	DET
iajs-3265	178	10	proposed	propose	VERB
iajs-3265	178	11	method	method	NOUN
iajs-3265	178	12	's	's	PART
iajs-3265	178	13	procedures	procedure	NOUN
iajs-3265	178	14	to	to	PART
iajs-3265	178	15	improve	improve	VERB
iajs-3265	178	16	the	the	DET
iajs-3265	178	17	ecm	ecm	NOUN
iajs-3265	178	18	's	's	PART
iajs-3265	178	19	accuracy	accuracy	NOUN
iajs-3265	178	20	and	and	CCONJ
iajs-3265	178	21	reliability	reliability	NOUN
iajs-3265	178	22	.	.	PUNCT
iajs-3265	179	1	first	first	ADV
iajs-3265	179	2	,	,	PUNCT
iajs-3265	179	3	describe	describe	VERB
iajs-3265	179	4	the	the	DET
iajs-3265	179	5	unknown	unknown	ADJ
iajs-3265	179	6	function	function	NOUN
iajs-3265	179	7	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	179	8	)	)	PUNCT
iajs-3265	179	9	and	and	CCONJ
iajs-3265	179	10	its	its	PRON
iajs-3265	179	11	derivatives	derivative	NOUN
iajs-3265	179	12	;	;	PUNCT
iajs-3265	179	13	and	and	CCONJ
iajs-3265	179	14	second	second	ADV
iajs-3265	179	15	,	,	PUNCT
iajs-3265	179	16	calculate	calculate	VERB
iajs-3265	179	17	the	the	DET
iajs-3265	179	18	inner	inner	ADJ
iajs-3265	179	19	product	product	NOUN
iajs-3265	179	20	to	to	PART
iajs-3265	179	21	solve	solve	VERB
iajs-3265	179	22	the	the	DET
iajs-3265	179	23	left	left	ADJ
iajs-3265	179	24	and	and	CCONJ
iajs-3265	179	25	right	right	ADJ
iajs-3265	179	26	sides	side	NOUN
iajs-3265	179	27	of	of	ADP
iajs-3265	179	28	the	the	DET
iajs-3265	179	29	matrix	matrix	NOUN
iajs-3265	179	30	equation	equation	NOUN
iajs-3265	179	31	explained	explain	VERB
iajs-3265	179	32	in	in	ADP
iajs-3265	179	33	equation	equation	NOUN
iajs-3265	179	34	(	(	PUNCT
iajs-3265	179	35	18	18	NUM
iajs-3265	179	36	)	)	PUNCT
iajs-3265	179	37	.	.	PUNCT
iajs-3265	180	1	ihjpas	ihjpas	PROPN
iajs-3265	180	2	.	.	PUNCT
iajs-3265	181	1	36	36	NUM
iajs-3265	181	2	(	(	PUNCT
iajs-3265	181	3	4	4	NUM
iajs-3265	181	4	)	)	PUNCT
iajs-3265	181	5	2023	2023	NUM
iajs-3265	181	6	346	346	NUM
iajs-3265	181	7	furthermore	furthermore	ADV
iajs-3265	181	8	,	,	PUNCT
iajs-3265	181	9	the	the	DET
iajs-3265	181	10	initial	initial	ADJ
iajs-3265	181	11	or	or	CCONJ
iajs-3265	181	12	boundary	boundary	ADJ
iajs-3265	181	13	conditions	condition	NOUN
iajs-3265	181	14	are	be	AUX
iajs-3265	181	15	substituted	substitute	VERB
iajs-3265	181	16	,	,	PUNCT
iajs-3265	181	17	as	as	SCONJ
iajs-3265	181	18	specified	specify	VERB
iajs-3265	181	19	in	in	ADP
iajs-3265	181	20	equations	equation	NOUN
iajs-3265	181	21	(	(	PUNCT
iajs-3265	181	22	15	15	NUM
iajs-3265	181	23	)	)	PUNCT
iajs-3265	181	24	and	and	CCONJ
iajs-3265	181	25	(	(	PUNCT
iajs-3265	181	26	16	16	NUM
iajs-3265	181	27	)	)	PUNCT
iajs-3265	181	28	,	,	PUNCT
iajs-3265	181	29	and	and	CCONJ
iajs-3265	181	30	some	some	DET
iajs-3265	181	31	entries	entry	NOUN
iajs-3265	181	32	of	of	ADP
iajs-3265	181	33	equation	equation	NOUN
iajs-3265	181	34	(	(	PUNCT
iajs-3265	181	35	18	18	NUM
iajs-3265	181	36	)	)	PUNCT
iajs-3265	181	37	are	be	AUX
iajs-3265	181	38	modified	modify	VERB
iajs-3265	181	39	.	.	PUNCT
iajs-3265	182	1	therefore	therefore	ADV
iajs-3265	182	2	,	,	PUNCT
iajs-3265	182	3	we	we	PRON
iajs-3265	182	4	obtain	obtain	VERB
iajs-3265	182	5	(	(	PUNCT
iajs-3265	182	6	𝑛	𝑛	PROPN
iajs-3265	182	7	+	+	NUM
iajs-3265	182	8	1	1	X
iajs-3265	182	9	)	)	PUNCT
iajs-3265	182	10	nonlinear	nonlinear	ADJ
iajs-3265	182	11	algebraic	algebraic	ADJ
iajs-3265	182	12	equations	equation	NOUN
iajs-3265	182	13	for	for	ADP
iajs-3265	182	14	the	the	DET
iajs-3265	182	15	unknown	unknown	ADJ
iajs-3265	182	16	coefficients𝑨.	coefficients𝑨.	NOUN
iajs-3265	182	17	by	by	ADP
iajs-3265	182	18	solving	solve	VERB
iajs-3265	182	19	this	this	DET
iajs-3265	182	20	system	system	NOUN
iajs-3265	182	21	numerically	numerically	ADV
iajs-3265	182	22	using	use	VERB
iajs-3265	182	23	mathematica	mathematica	PROPN
iajs-3265	182	24	®	®	PROPN
iajs-3265	182	25	12	12	NUM
iajs-3265	182	26	,	,	PUNCT
iajs-3265	182	27	we	we	PRON
iajs-3265	182	28	get	get	VERB
iajs-3265	182	29	the	the	DET
iajs-3265	182	30	values	value	NOUN
iajs-3265	182	31	for	for	ADP
iajs-3265	182	32	the	the	DET
iajs-3265	182	33	unknown	unknown	ADJ
iajs-3265	182	34	coefficients	coefficient	NOUN
iajs-3265	182	35	𝑎0	𝑎0	PROPN
iajs-3265	182	36	,	,	PUNCT
iajs-3265	182	37	𝑎1	𝑎1	PROPN
iajs-3265	182	38	,	,	PUNCT
iajs-3265	182	39	𝑎2	𝑎2	PROPN
iajs-3265	182	40	,	,	PUNCT
iajs-3265	182	41	…	…	PUNCT
iajs-3265	182	42	,	,	PUNCT
iajs-3265	182	43	𝑎𝑛	𝑎𝑛	VERB
iajs-3265	182	44	to	to	PART
iajs-3265	182	45	obtain	obtain	VERB
iajs-3265	182	46	a	a	DET
iajs-3265	182	47	novel	novel	ADJ
iajs-3265	182	48	approximate	approximate	ADJ
iajs-3265	182	49	solution	solution	NOUN
iajs-3265	182	50	to	to	ADP
iajs-3265	182	51	the	the	DET
iajs-3265	182	52	nonlinear	nonlinear	ADJ
iajs-3265	182	53	initial	initial	ADJ
iajs-3265	182	54	and	and	CCONJ
iajs-3265	182	55	boundary	boundary	ADJ
iajs-3265	182	56	value	value	NOUN
iajs-3265	182	57	problems	problem	NOUN
iajs-3265	182	58	.	.	PUNCT
iajs-3265	183	1	4.1	4.1	NUM
iajs-3265	183	2	solving	solve	VERB
iajs-3265	183	3	the	the	DET
iajs-3265	183	4	darcy	darcy	PROPN
iajs-3265	183	5	-	-	PUNCT
iajs-3265	183	6	brinkman	brinkman	PROPN
iajs-3265	183	7	-	-	PUNCT
iajs-3265	183	8	forchheimer	forchheimer	PROPN
iajs-3265	183	9	equation	equation	NOUN
iajs-3265	183	10	by	by	ADP
iajs-3265	183	11	the	the	DET
iajs-3265	183	12	ecm	ecm	PROPN
iajs-3265	183	13	and	and	CCONJ
iajs-3265	183	14	i	i	PROPN
iajs-3265	183	15	-	-	PUNCT
iajs-3265	183	16	ecms	ecms	PROPN
iajs-3265	183	17	the	the	DET
iajs-3265	183	18	ecm	ecm	NOUN
iajs-3265	183	19	and	and	CCONJ
iajs-3265	183	20	the	the	DET
iajs-3265	183	21	i	i	PROPN
iajs-3265	183	22	-	-	PUNCT
iajs-3265	183	23	ecms	ecms	NOUN
iajs-3265	183	24	techniques	technique	NOUN
iajs-3265	183	25	are	be	AUX
iajs-3265	183	26	used	use	VERB
iajs-3265	183	27	to	to	PART
iajs-3265	183	28	solve	solve	VERB
iajs-3265	183	29	the	the	DET
iajs-3265	183	30	first	first	ADJ
iajs-3265	183	31	problem	problem	NOUN
iajs-3265	183	32	presented	present	VERB
iajs-3265	183	33	in	in	ADP
iajs-3265	183	34	the	the	DET
iajs-3265	183	35	equation	equation	NOUN
iajs-3265	183	36	(	(	PUNCT
iajs-3265	183	37	1	1	NUM
iajs-3265	183	38	)	)	PUNCT
iajs-3265	183	39	with	with	ADP
iajs-3265	183	40	boundary	boundary	ADJ
iajs-3265	183	41	conditions	condition	NOUN
iajs-3265	183	42	in	in	ADP
iajs-3265	183	43	equation	equation	NOUN
iajs-3265	183	44	(	(	PUNCT
iajs-3265	183	45	2	2	NUM
iajs-3265	183	46	)	)	PUNCT
iajs-3265	183	47	.	.	PUNCT
iajs-3265	184	1	more	more	ADV
iajs-3265	184	2	precisely	precisely	ADV
iajs-3265	184	3	,	,	PUNCT
iajs-3265	184	4	for	for	ADP
iajs-3265	184	5	the	the	DET
iajs-3265	184	6	ecm	ecm	PROPN
iajs-3265	184	7	technique	technique	NOUN
iajs-3265	184	8	,	,	PUNCT
iajs-3265	184	9	we	we	PRON
iajs-3265	184	10	transform	transform	VERB
iajs-3265	184	11	the	the	DET
iajs-3265	184	12	function	function	NOUN
iajs-3265	184	13	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	184	14	)	)	PUNCT
iajs-3265	184	15	and	and	CCONJ
iajs-3265	184	16	its	its	PRON
iajs-3265	184	17	derivatives	derivative	NOUN
iajs-3265	184	18	into	into	ADP
iajs-3265	184	19	matrices	matrix	NOUN
iajs-3265	184	20	by	by	ADP
iajs-3265	184	21	substituting	substitute	VERB
iajs-3265	184	22	equations	equation	NOUN
iajs-3265	184	23	(	(	PUNCT
iajs-3265	184	24	12	12	NUM
iajs-3265	184	25	)	)	PUNCT
iajs-3265	184	26	and	and	CCONJ
iajs-3265	184	27	(	(	PUNCT
iajs-3265	184	28	13	13	NUM
iajs-3265	184	29	)	)	PUNCT
iajs-3265	184	30	into	into	ADP
iajs-3265	184	31	equations	equation	NOUN
iajs-3265	184	32	(	(	PUNCT
iajs-3265	184	33	1	1	NUM
iajs-3265	184	34	)	)	PUNCT
iajs-3265	184	35	and	and	CCONJ
iajs-3265	184	36	(	(	PUNCT
iajs-3265	184	37	2	2	NUM
iajs-3265	184	38	)	)	PUNCT
iajs-3265	184	39	.	.	PUNCT
iajs-3265	185	1	thus	thus	ADV
iajs-3265	185	2	,	,	PUNCT
iajs-3265	185	3	we	we	PRON
iajs-3265	185	4	get	get	VERB
iajs-3265	185	5	the	the	DET
iajs-3265	185	6	following	follow	VERB
iajs-3265	185	7	result	result	NOUN
iajs-3265	185	8	:	:	PUNCT
iajs-3265	185	9	𝜳(𝑥	𝜳(𝑥	X
iajs-3265	185	10	)	)	PUNCT
iajs-3265	185	11	(	(	PUNCT
iajs-3265	185	12	𝑩∗)2	𝑩∗)2	ADV
iajs-3265	185	13	𝑨	𝑨	NOUN
iajs-3265	185	14	−	−	NOUN
iajs-3265	185	15	𝑠2	𝑠2	NOUN
iajs-3265	185	16	(	(	PUNCT
iajs-3265	185	17	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	185	18	)	)	PUNCT
iajs-3265	185	19	𝑨	𝑨	NOUN
iajs-3265	185	20	)	)	PUNCT
iajs-3265	185	21	−	−	PROPN
iajs-3265	185	22	𝐹𝑠(𝜳(𝑥	𝐹𝑠(𝜳(𝑥	ADJ
iajs-3265	185	23	)	)	PUNCT
iajs-3265	185	24	𝑨)2	𝑨)2	PUNCT
iajs-3265	186	1	+	+	SYM
iajs-3265	186	2	1	1	NUM
iajs-3265	186	3	𝑀	𝑀	NOUN
iajs-3265	186	4	=	=	SYM
iajs-3265	186	5	0	0	NUM
iajs-3265	186	6	,	,	PUNCT
iajs-3265	186	7	𝜳(0	𝜳(0	PUNCT
iajs-3265	186	8	)	)	PUNCT
iajs-3265	186	9	𝑩∗	𝑩∗	NOUN
iajs-3265	186	10	𝑨	𝑨	NOUN
iajs-3265	186	11	=	=	SYM
iajs-3265	186	12	0	0	NUM
iajs-3265	186	13	,	,	PUNCT
iajs-3265	186	14	𝜳(1	𝜳(1	NUM
iajs-3265	186	15	)	)	PUNCT
iajs-3265	186	16	𝑨	𝑨	NOUN
iajs-3265	186	17	=	=	SYM
iajs-3265	186	18	0	0	PROPN
iajs-3265	186	19	.	.	PUNCT
iajs-3265	187	1	(	(	PUNCT
iajs-3265	187	2	29	29	NUM
iajs-3265	187	3	)	)	PUNCT
iajs-3265	187	4	then	then	ADV
iajs-3265	187	5	,	,	PUNCT
iajs-3265	187	6	the	the	DET
iajs-3265	187	7	procedures	procedure	NOUN
iajs-3265	187	8	have	have	AUX
iajs-3265	187	9	been	be	AUX
iajs-3265	187	10	applied	apply	VERB
iajs-3265	187	11	,	,	PUNCT
iajs-3265	187	12	as	as	SCONJ
iajs-3265	187	13	shown	show	VERB
iajs-3265	187	14	in	in	ADP
iajs-3265	187	15	equations	equation	NOUN
iajs-3265	187	16	(	(	PUNCT
iajs-3265	187	17	18	18	NUM
iajs-3265	187	18	)	)	PUNCT
iajs-3265	187	19	and	and	CCONJ
iajs-3265	187	20	(	(	PUNCT
iajs-3265	187	21	19	19	NUM
iajs-3265	187	22	)	)	PUNCT
iajs-3265	187	23	,	,	PUNCT
iajs-3265	187	24	leading	lead	VERB
iajs-3265	187	25	to	to	ADP
iajs-3265	187	26	:	:	PUNCT
iajs-3265	187	27	〈	〈	PROPN
iajs-3265	187	28	𝑥𝑖	𝑥𝑖	PROPN
iajs-3265	187	29	,	,	PUNCT
iajs-3265	187	30	𝜳(𝑥	𝜳(𝑥	PROPN
iajs-3265	187	31	)	)	PUNCT
iajs-3265	187	32	(	(	PUNCT
iajs-3265	187	33	𝑩∗)2	𝑩∗)2	ADV
iajs-3265	187	34	𝑨	𝑨	NOUN
iajs-3265	187	35	−	−	NOUN
iajs-3265	187	36	𝑠2	𝑠2	NOUN
iajs-3265	187	37	(	(	PUNCT
iajs-3265	187	38	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	187	39	)	)	PUNCT
iajs-3265	187	40	𝑨	𝑨	NOUN
iajs-3265	187	41	)	)	PUNCT
iajs-3265	187	42	−	−	PROPN
iajs-3265	188	1	𝐹𝑠(𝜳(𝑥	𝐹𝑠(𝜳(𝑥	ADJ
iajs-3265	188	2	)	)	PUNCT
iajs-3265	188	3	𝑨)2	𝑨)2	NUM
iajs-3265	188	4	〉	〉	NOUN
iajs-3265	188	5	=	=	SYM
iajs-3265	188	6	〈	〈	PROPN
iajs-3265	188	7	𝑥𝑖	𝑥𝑖	PROPN
iajs-3265	188	8	,	,	PUNCT
iajs-3265	188	9	−	−	PROPN
iajs-3265	188	10	1	1	NUM
iajs-3265	188	11	𝑀	𝑀	PROPN
iajs-3265	188	12	〉	〉	NOUN
iajs-3265	188	13	,	,	PUNCT
iajs-3265	188	14	∀	∀	NOUN
iajs-3265	188	15	0	0	NUM
iajs-3265	188	16	≤	≤	NUM
iajs-3265	188	17	𝑖	𝑖	SYM
iajs-3265	188	18	≤	≤	NOUN
iajs-3265	188	19	𝑛.	𝑛.	NOUN
iajs-3265	188	20	(	(	PUNCT
iajs-3265	188	21	30	30	NUM
iajs-3265	188	22	)	)	PUNCT
iajs-3265	188	23	substituting	substitute	VERB
iajs-3265	188	24	equations	equation	NOUN
iajs-3265	188	25	(	(	PUNCT
iajs-3265	188	26	21	21	NUM
iajs-3265	188	27	)	)	PUNCT
iajs-3265	188	28	and	and	CCONJ
iajs-3265	188	29	(	(	PUNCT
iajs-3265	188	30	22	22	NUM
iajs-3265	188	31	)	)	PUNCT
iajs-3265	188	32	into	into	ADP
iajs-3265	188	33	equations	equation	NOUN
iajs-3265	188	34	(	(	PUNCT
iajs-3265	188	35	1	1	NUM
iajs-3265	188	36	)	)	PUNCT
iajs-3265	188	37	and	and	CCONJ
iajs-3265	188	38	(	(	PUNCT
iajs-3265	188	39	2	2	X
iajs-3265	188	40	)	)	PUNCT
iajs-3265	188	41	for	for	ADP
iajs-3265	188	42	the	the	DET
iajs-3265	188	43	i	i	PROPN
iajs-3265	188	44	-	-	PUNCT
iajs-3265	188	45	ecms	ecms	PROPN
iajs-3265	188	46	based	base	VERB
iajs-3265	188	47	on	on	ADP
iajs-3265	188	48	the	the	DET
iajs-3265	188	49	first	first	ADJ
iajs-3265	188	50	kind	kind	NOUN
iajs-3265	188	51	of	of	ADP
iajs-3265	188	52	the	the	DET
iajs-3265	188	53	chebyshev	chebyshev	NOUN
iajs-3265	188	54	polynomials	polynomial	NOUN
iajs-3265	188	55	,	,	PUNCT
iajs-3265	188	56	the	the	DET
iajs-3265	188	57	following	following	ADJ
iajs-3265	188	58	result	result	NOUN
iajs-3265	188	59	is	be	AUX
iajs-3265	188	60	obtained	obtain	VERB
iajs-3265	188	61	:	:	PUNCT
iajs-3265	188	62	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	188	63	(	(	PUNCT
iajs-3265	188	64	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	188	65	∗	∗	NOUN
iajs-3265	188	66	)	)	PUNCT
iajs-3265	188	67	2	2	NUM
iajs-3265	188	68	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	188	69	)	)	PUNCT
iajs-3265	188	70	−	−	NOUN
iajs-3265	189	1	𝑠2	𝑠2	NOUN
iajs-3265	189	2	(	(	PUNCT
iajs-3265	189	3	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	189	4	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	189	5	)	)	PUNCT
iajs-3265	189	6	)	)	PUNCT
iajs-3265	190	1	−	−	ADP
iajs-3265	190	2	𝐹𝑠(𝑨𝑇	𝐹𝑠(𝑨𝑇	NOUN
iajs-3265	190	3	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	190	4	)	)	PUNCT
iajs-3265	190	5	)	)	PUNCT
iajs-3265	190	6	2	2	NUM
iajs-3265	191	1	+	+	SYM
iajs-3265	191	2	1	1	NUM
iajs-3265	191	3	𝑀	𝑀	NOUN
iajs-3265	191	4	=	=	SYM
iajs-3265	191	5	0	0	NUM
iajs-3265	191	6	,	,	PUNCT
iajs-3265	191	7	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	191	8	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	191	9	∗	∗	NOUN
iajs-3265	191	10	𝜳(0	𝜳(0	NUM
iajs-3265	191	11	)	)	PUNCT
iajs-3265	191	12	=	=	SYM
iajs-3265	191	13	0	0	NUM
iajs-3265	191	14	,	,	PUNCT
iajs-3265	191	15	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	191	16	𝜳(1	𝜳(1	NUM
iajs-3265	191	17	)	)	PUNCT
iajs-3265	191	18	=	=	SYM
iajs-3265	191	19	0	0	X
iajs-3265	191	20	.	.	PUNCT
iajs-3265	192	1	(	(	PUNCT
iajs-3265	192	2	31	31	NUM
iajs-3265	192	3	)	)	PUNCT
iajs-3265	192	4	additionally	additionally	ADV
iajs-3265	192	5	,	,	PUNCT
iajs-3265	192	6	the	the	DET
iajs-3265	192	7	results	result	NOUN
iajs-3265	192	8	of	of	ADP
iajs-3265	192	9	applying	apply	VERB
iajs-3265	192	10	equations	equation	NOUN
iajs-3265	192	11	(	(	PUNCT
iajs-3265	192	12	18	18	NUM
iajs-3265	192	13	)	)	PUNCT
iajs-3265	192	14	and	and	CCONJ
iajs-3265	192	15	(	(	PUNCT
iajs-3265	192	16	19	19	NUM
iajs-3265	192	17	)	)	PUNCT
iajs-3265	192	18	are	be	AUX
iajs-3265	192	19	as	as	SCONJ
iajs-3265	192	20	follows	follow	VERB
iajs-3265	192	21	:	:	PUNCT
iajs-3265	192	22	〈	〈	NOUN
iajs-3265	192	23	𝑻𝑖(𝑥	𝑻𝑖(𝑥	NOUN
iajs-3265	192	24	)	)	PUNCT
iajs-3265	192	25	,	,	PUNCT
iajs-3265	192	26	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	192	27	(	(	PUNCT
iajs-3265	192	28	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	192	29	∗	∗	NOUN
iajs-3265	192	30	)	)	PUNCT
iajs-3265	192	31	2	2	NUM
iajs-3265	192	32	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	192	33	)	)	PUNCT
iajs-3265	192	34	−	−	NOUN
iajs-3265	193	1	𝑠2	𝑠2	NOUN
iajs-3265	193	2	(	(	PUNCT
iajs-3265	193	3	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	193	4	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	193	5	)	)	PUNCT
iajs-3265	193	6	)	)	PUNCT
iajs-3265	194	1	−	−	ADP
iajs-3265	194	2	𝐹𝑠(𝑨𝑇	𝐹𝑠(𝑨𝑇	NOUN
iajs-3265	194	3	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	194	4	)	)	PUNCT
iajs-3265	194	5	)	)	PUNCT
iajs-3265	194	6	2	2	NUM
iajs-3265	194	7	〉	〉	NOUN
iajs-3265	194	8	=	=	SYM
iajs-3265	194	9	〈	〈	NOUN
iajs-3265	194	10	𝑻𝑖(𝑥),−	𝑻𝑖(𝑥),−	NOUN
iajs-3265	194	11	1	1	NUM
iajs-3265	194	12	𝑀	𝑀	PROPN
iajs-3265	194	13	〉	〉	NOUN
iajs-3265	194	14	,	,	PUNCT
iajs-3265	194	15	∀	∀	NOUN
iajs-3265	194	16	0	0	NUM
iajs-3265	194	17	≤	≤	NUM
iajs-3265	194	18	𝑖	𝑖	SYM
iajs-3265	194	19	≤	≤	NOUN
iajs-3265	194	20	𝑛.	𝑛.	NOUN
iajs-3265	194	21	(	(	PUNCT
iajs-3265	194	22	32	32	NUM
iajs-3265	194	23	)	)	PUNCT
iajs-3265	194	24	implementing	implement	VERB
iajs-3265	194	25	the	the	DET
iajs-3265	194	26	i	i	PROPN
iajs-3265	194	27	-	-	PUNCT
iajs-3265	194	28	ecms	ecms	PROPN
iajs-3265	194	29	based	base	VERB
iajs-3265	194	30	on	on	ADP
iajs-3265	194	31	the	the	DET
iajs-3265	194	32	bernoulli	bernoulli	NOUN
iajs-3265	194	33	polynomials	polynomial	NOUN
iajs-3265	194	34	by	by	ADP
iajs-3265	194	35	substituting	substitute	VERB
iajs-3265	194	36	equations	equation	NOUN
iajs-3265	194	37	(	(	PUNCT
iajs-3265	194	38	24	24	NUM
iajs-3265	194	39	)	)	PUNCT
iajs-3265	194	40	and	and	CCONJ
iajs-3265	194	41	(	(	PUNCT
iajs-3265	194	42	25	25	NUM
iajs-3265	194	43	)	)	PUNCT
iajs-3265	194	44	into	into	ADP
iajs-3265	194	45	equations	equation	NOUN
iajs-3265	194	46	(	(	PUNCT
iajs-3265	194	47	1	1	NUM
iajs-3265	194	48	)	)	PUNCT
iajs-3265	194	49	and	and	CCONJ
iajs-3265	194	50	(	(	PUNCT
iajs-3265	194	51	2	2	NUM
iajs-3265	194	52	)	)	PUNCT
iajs-3265	194	53	,	,	PUNCT
iajs-3265	194	54	it	it	PRON
iajs-3265	194	55	follows	follow	VERB
iajs-3265	194	56	:	:	PUNCT
iajs-3265	194	57	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	194	58	(	(	PUNCT
iajs-3265	194	59	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	194	60	∗	∗	NOUN
iajs-3265	194	61	)	)	PUNCT
iajs-3265	194	62	2	2	NUM
iajs-3265	194	63	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	194	64	)	)	PUNCT
iajs-3265	194	65	−	−	NOUN
iajs-3265	195	1	𝑠2	𝑠2	NOUN
iajs-3265	195	2	(	(	PUNCT
iajs-3265	195	3	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	195	4	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	195	5	)	)	PUNCT
iajs-3265	195	6	)	)	PUNCT
iajs-3265	196	1	−	−	ADP
iajs-3265	196	2	𝐹𝑠(𝑨𝑇	𝐹𝑠(𝑨𝑇	NOUN
iajs-3265	196	3	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	196	4	)	)	PUNCT
iajs-3265	196	5	)	)	PUNCT
iajs-3265	196	6	2	2	NUM
iajs-3265	197	1	+	+	SYM
iajs-3265	197	2	1	1	NUM
iajs-3265	197	3	𝑀	𝑀	NOUN
iajs-3265	197	4	=	=	SYM
iajs-3265	197	5	0	0	NUM
iajs-3265	197	6	,	,	PUNCT
iajs-3265	197	7	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	197	8	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	197	9	∗	∗	NOUN
iajs-3265	197	10	𝜳(0	𝜳(0	NUM
iajs-3265	197	11	)	)	PUNCT
iajs-3265	197	12	=	=	SYM
iajs-3265	197	13	0	0	NUM
iajs-3265	197	14	,	,	PUNCT
iajs-3265	197	15	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	197	16	𝜳(1	𝜳(1	NUM
iajs-3265	197	17	)	)	PUNCT
iajs-3265	197	18	=	=	SYM
iajs-3265	197	19	0	0	X
iajs-3265	197	20	.	.	PUNCT
iajs-3265	198	1	(	(	PUNCT
iajs-3265	198	2	33	33	NUM
iajs-3265	198	3	)	)	PUNCT
iajs-3265	198	4	using	use	VERB
iajs-3265	198	5	the	the	DET
iajs-3265	198	6	technique	technique	NOUN
iajs-3265	198	7	described	describe	VERB
iajs-3265	198	8	in	in	ADP
iajs-3265	198	9	equations	equation	NOUN
iajs-3265	198	10	(	(	PUNCT
iajs-3265	198	11	18	18	NUM
iajs-3265	198	12	)	)	PUNCT
iajs-3265	198	13	and	and	CCONJ
iajs-3265	198	14	(	(	PUNCT
iajs-3265	198	15	19	19	NUM
iajs-3265	198	16	)	)	PUNCT
iajs-3265	198	17	,	,	PUNCT
iajs-3265	198	18	the	the	DET
iajs-3265	198	19	following	follow	VERB
iajs-3265	198	20	equation	equation	NOUN
iajs-3265	198	21	will	will	AUX
iajs-3265	198	22	be	be	AUX
iajs-3265	198	23	given	give	VERB
iajs-3265	198	24	:	:	PUNCT
iajs-3265	198	25	〈	〈	NOUN
iajs-3265	198	26	𝑩𝑖(𝑥	𝑩𝑖(𝑥	NOUN
iajs-3265	198	27	)	)	PUNCT
iajs-3265	198	28	,	,	PUNCT
iajs-3265	198	29	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	198	30	(	(	PUNCT
iajs-3265	198	31	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	198	32	∗	∗	NOUN
iajs-3265	198	33	)	)	PUNCT
iajs-3265	198	34	2	2	NUM
iajs-3265	198	35	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	198	36	)	)	PUNCT
iajs-3265	198	37	−	−	NOUN
iajs-3265	199	1	𝑠2	𝑠2	NOUN
iajs-3265	199	2	(	(	PUNCT
iajs-3265	199	3	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	199	4	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	199	5	)	)	PUNCT
iajs-3265	199	6	)	)	PUNCT
iajs-3265	200	1	−	−	ADP
iajs-3265	200	2	𝐹𝑠(𝑨𝑇	𝐹𝑠(𝑨𝑇	NOUN
iajs-3265	200	3	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	200	4	)	)	PUNCT
iajs-3265	200	5	)	)	PUNCT
iajs-3265	200	6	2	2	NUM
iajs-3265	200	7	〉	〉	NOUN
iajs-3265	200	8	=	=	PUNCT
iajs-3265	200	9	〈	〈	NOUN
iajs-3265	200	10	𝑩𝑖(𝑥),−	𝑩𝑖(𝑥),−	VERB
iajs-3265	200	11	1	1	NUM
iajs-3265	200	12	𝑀	𝑀	PROPN
iajs-3265	200	13	〉	〉	NOUN
iajs-3265	200	14	,	,	PUNCT
iajs-3265	200	15	∀	∀	NOUN
iajs-3265	200	16	0	0	NUM
iajs-3265	200	17	≤	≤	NUM
iajs-3265	200	18	𝑖	𝑖	SYM
iajs-3265	200	19	≤	≤	NOUN
iajs-3265	200	20	𝑛.	𝑛.	NOUN
iajs-3265	200	21	(	(	PUNCT
iajs-3265	200	22	34	34	NUM
iajs-3265	200	23	)	)	PUNCT
iajs-3265	200	24	moreover	moreover	ADV
iajs-3265	200	25	,	,	PUNCT
iajs-3265	200	26	applying	apply	VERB
iajs-3265	200	27	the	the	DET
iajs-3265	200	28	i	i	PROPN
iajs-3265	200	29	-	-	PUNCT
iajs-3265	200	30	ecms	ecms	PROPN
iajs-3265	200	31	based	base	VERB
iajs-3265	200	32	on	on	ADP
iajs-3265	200	33	the	the	DET
iajs-3265	200	34	laguerre	laguerre	NOUN
iajs-3265	200	35	polynomials	polynomial	NOUN
iajs-3265	200	36	by	by	ADP
iajs-3265	200	37	substituting	substitute	VERB
iajs-3265	200	38	the	the	DET
iajs-3265	200	39	equations	equation	NOUN
iajs-3265	200	40	(	(	PUNCT
iajs-3265	200	41	27	27	NUM
iajs-3265	200	42	)	)	PUNCT
iajs-3265	200	43	and	and	CCONJ
iajs-3265	200	44	(	(	PUNCT
iajs-3265	200	45	28	28	NUM
iajs-3265	200	46	)	)	PUNCT
iajs-3265	200	47	into	into	ADP
iajs-3265	200	48	the	the	DET
iajs-3265	200	49	equations	equation	NOUN
iajs-3265	200	50	(	(	PUNCT
iajs-3265	200	51	1	1	NUM
iajs-3265	200	52	)	)	PUNCT
iajs-3265	200	53	and	and	CCONJ
iajs-3265	200	54	(	(	PUNCT
iajs-3265	200	55	2	2	NUM
iajs-3265	200	56	)	)	PUNCT
iajs-3265	200	57	,	,	PUNCT
iajs-3265	200	58	we	we	PRON
iajs-3265	200	59	obtain	obtain	VERB
iajs-3265	200	60	:	:	PUNCT
iajs-3265	200	61	𝜳(𝑥	𝜳(𝑥	ADJ
iajs-3265	200	62	)	)	PUNCT
iajs-3265	200	63	(	(	PUNCT
iajs-3265	200	64	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	200	65	∗)2	∗)2	PROPN
iajs-3265	200	66	𝑨	𝑨	NOUN
iajs-3265	200	67	−	−	NOUN
iajs-3265	200	68	𝑠2	𝑠2	NOUN
iajs-3265	200	69	(	(	PUNCT
iajs-3265	200	70	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	200	71	)	)	PUNCT
iajs-3265	200	72	𝑨	𝑨	NOUN
iajs-3265	200	73	)	)	PUNCT
iajs-3265	200	74	−	−	PROPN
iajs-3265	200	75	𝐹𝑠(𝜳(𝑥	𝐹𝑠(𝜳(𝑥	ADJ
iajs-3265	200	76	)	)	PUNCT
iajs-3265	200	77	𝑨)2	𝑨)2	PUNCT
iajs-3265	201	1	+	+	SYM
iajs-3265	201	2	1	1	NUM
iajs-3265	201	3	𝑀	𝑀	NOUN
iajs-3265	201	4	=	=	SYM
iajs-3265	201	5	0	0	NUM
iajs-3265	201	6	,	,	PUNCT
iajs-3265	201	7	𝜳(0	𝜳(0	NUM
iajs-3265	201	8	)	)	PUNCT
iajs-3265	201	9	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	201	10	∗	∗	NOUN
iajs-3265	201	11	𝑨	𝑨	NOUN
iajs-3265	201	12	=	=	SYM
iajs-3265	201	13	0	0	NUM
iajs-3265	201	14	,	,	PUNCT
iajs-3265	201	15	𝜳(1	𝜳(1	NUM
iajs-3265	201	16	)	)	PUNCT
iajs-3265	201	17	𝑨	𝑨	NOUN
iajs-3265	201	18	=	=	SYM
iajs-3265	201	19	0	0	PROPN
iajs-3265	201	20	.	.	PUNCT
iajs-3265	201	21	(	(	PUNCT
iajs-3265	201	22	35	35	NUM
iajs-3265	201	23	)	)	PUNCT
iajs-3265	201	24	subsequently	subsequently	ADV
iajs-3265	201	25	,	,	PUNCT
iajs-3265	201	26	the	the	DET
iajs-3265	201	27	procedures	procedure	NOUN
iajs-3265	201	28	as	as	SCONJ
iajs-3265	201	29	specified	specify	VERB
iajs-3265	201	30	in	in	ADP
iajs-3265	201	31	equations	equation	NOUN
iajs-3265	201	32	(	(	PUNCT
iajs-3265	201	33	18	18	NUM
iajs-3265	201	34	)	)	PUNCT
iajs-3265	201	35	and	and	CCONJ
iajs-3265	201	36	(	(	PUNCT
iajs-3265	201	37	19	19	NUM
iajs-3265	201	38	)	)	PUNCT
iajs-3265	201	39	have	have	AUX
iajs-3265	201	40	been	be	AUX
iajs-3265	201	41	utilized	utilize	VERB
iajs-3265	201	42	,	,	PUNCT
iajs-3265	201	43	as	as	SCONJ
iajs-3265	201	44	will	will	AUX
iajs-3265	201	45	be	be	AUX
iajs-3265	201	46	illustrated	illustrate	VERB
iajs-3265	201	47	:	:	PUNCT
iajs-3265	201	48	〈	〈	NOUN
iajs-3265	201	49	𝑳𝑖(𝑥),𝜳(𝑥	𝑳𝑖(𝑥),𝜳(𝑥	ADJ
iajs-3265	201	50	)	)	PUNCT
iajs-3265	201	51	(	(	PUNCT
iajs-3265	201	52	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	201	53	∗)2	∗)2	PROPN
iajs-3265	201	54	𝑨	𝑨	NOUN
iajs-3265	201	55	−	−	NOUN
iajs-3265	201	56	𝑠2	𝑠2	NOUN
iajs-3265	201	57	(	(	PUNCT
iajs-3265	201	58	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	201	59	)	)	PUNCT
iajs-3265	201	60	𝑨	𝑨	NOUN
iajs-3265	201	61	)	)	PUNCT
iajs-3265	201	62	−	−	PROPN
iajs-3265	201	63	𝐹𝑠(𝜳(𝑥	𝐹𝑠(𝜳(𝑥	ADJ
iajs-3265	201	64	)	)	PUNCT
iajs-3265	201	65	𝑨)2	𝑨)2	NUM
iajs-3265	201	66	〉	〉	NOUN
iajs-3265	201	67	=	=	SYM
iajs-3265	201	68	〈	〈	NOUN
iajs-3265	201	69	𝑳𝑖(𝑥),−	𝑳𝑖(𝑥),−	ADP
iajs-3265	201	70	1	1	NUM
iajs-3265	201	71	𝑀	𝑀	PROPN
iajs-3265	201	72	〉	〉	NOUN
iajs-3265	201	73	,	,	PUNCT
iajs-3265	201	74	∀	∀	NOUN
iajs-3265	201	75	0	0	NUM
iajs-3265	201	76	≤	≤	NUM
iajs-3265	201	77	𝑖	𝑖	SYM
iajs-3265	201	78	≤	≤	NOUN
iajs-3265	201	79	𝑛.	𝑛.	NOUN
iajs-3265	201	80	(	(	PUNCT
iajs-3265	201	81	36	36	NUM
iajs-3265	201	82	)	)	PUNCT
iajs-3265	201	83	additionally	additionally	ADV
iajs-3265	201	84	,	,	PUNCT
iajs-3265	201	85	the	the	DET
iajs-3265	201	86	inner	inner	ADJ
iajs-3265	201	87	product	product	NOUN
iajs-3265	201	88	for	for	ADP
iajs-3265	201	89	the	the	DET
iajs-3265	201	90	left	left	ADJ
iajs-3265	201	91	and	and	CCONJ
iajs-3265	201	92	right	right	ADJ
iajs-3265	201	93	sides	side	NOUN
iajs-3265	201	94	of	of	ADP
iajs-3265	201	95	equations	equation	NOUN
iajs-3265	201	96	(	(	PUNCT
iajs-3265	201	97	30	30	NUM
iajs-3265	201	98	)	)	PUNCT
iajs-3265	201	99	,	,	PUNCT
iajs-3265	201	100	(	(	PUNCT
iajs-3265	201	101	32	32	NUM
iajs-3265	201	102	)	)	PUNCT
iajs-3265	201	103	,	,	PUNCT
iajs-3265	201	104	(	(	PUNCT
iajs-3265	201	105	34	34	NUM
iajs-3265	201	106	)	)	PUNCT
iajs-3265	201	107	,	,	PUNCT
iajs-3265	201	108	and	and	CCONJ
iajs-3265	201	109	(	(	PUNCT
iajs-3265	201	110	36	36	NUM
iajs-3265	201	111	)	)	PUNCT
iajs-3265	201	112	,	,	PUNCT
iajs-3265	201	113	respectively	respectively	ADV
iajs-3265	201	114	,	,	PUNCT
iajs-3265	201	115	is	be	AUX
iajs-3265	201	116	used	use	VERB
iajs-3265	201	117	to	to	PART
iajs-3265	201	118	get	get	VERB
iajs-3265	201	119	the	the	DET
iajs-3265	201	120	values	value	NOUN
iajs-3265	201	121	of	of	ADP
iajs-3265	201	122	𝑨	𝑨	NOUN
iajs-3265	201	123	=	=	PUNCT
iajs-3265	202	1	[	[	X
iajs-3265	202	2	𝑎0	𝑎0	ADV
iajs-3265	202	3	𝑎1	𝑎1	VERB
iajs-3265	202	4	𝑎2	𝑎2	NOUN
iajs-3265	202	5	…	…	PUNCT
iajs-3265	202	6	𝑎𝑛]𝑇	𝑎𝑛]𝑇	NOUN
iajs-3265	202	7	by	by	ADP
iajs-3265	202	8	solving	solve	VERB
iajs-3265	202	9	the	the	DET
iajs-3265	202	10	algebraic	algebraic	ADJ
iajs-3265	202	11	system	system	NOUN
iajs-3265	202	12	of	of	ADP
iajs-3265	202	13	equations	equation	NOUN
iajs-3265	202	14	.	.	PUNCT
iajs-3265	203	1	once	once	ADV
iajs-3265	203	2	the	the	DET
iajs-3265	203	3	boundary	boundary	ADJ
iajs-3265	203	4	conditions	condition	NOUN
iajs-3265	203	5	have	have	AUX
iajs-3265	203	6	been	be	AUX
iajs-3265	203	7	applied	apply	VERB
iajs-3265	203	8	to	to	ADP
iajs-3265	203	9	equations	equation	NOUN
iajs-3265	203	10	(	(	PUNCT
iajs-3265	203	11	29	29	NUM
iajs-3265	203	12	)	)	PUNCT
iajs-3265	203	13	,	,	PUNCT
iajs-3265	203	14	(	(	PUNCT
iajs-3265	203	15	31	31	NUM
iajs-3265	203	16	)	)	PUNCT
iajs-3265	203	17	,	,	PUNCT
iajs-3265	203	18	(	(	PUNCT
iajs-3265	203	19	33	33	NUM
iajs-3265	203	20	)	)	PUNCT
iajs-3265	203	21	,	,	PUNCT
iajs-3265	203	22	and	and	CCONJ
iajs-3265	203	23	(	(	PUNCT
iajs-3265	203	24	35	35	NUM
iajs-3265	203	25	)	)	PUNCT
iajs-3265	203	26	,	,	PUNCT
iajs-3265	203	27	respectively	respectively	ADV
iajs-3265	203	28	,	,	PUNCT
iajs-3265	203	29	the	the	DET
iajs-3265	203	30	desired	desire	VERB
iajs-3265	203	31	novel	novel	ADJ
iajs-3265	203	32	approximate	approximate	ADJ
iajs-3265	203	33	solutions	solution	NOUN
iajs-3265	203	34	are	be	AUX
iajs-3265	203	35	obtained	obtain	VERB
iajs-3265	203	36	.	.	PUNCT
iajs-3265	204	1	ihjpas	ihjpas	PROPN
iajs-3265	204	2	.	.	PUNCT
iajs-3265	205	1	36	36	NUM
iajs-3265	205	2	(	(	PUNCT
iajs-3265	205	3	4	4	NUM
iajs-3265	205	4	)	)	PUNCT
iajs-3265	205	5	2023	2023	NUM
iajs-3265	205	6	347	347	NUM
iajs-3265	205	7	if	if	SCONJ
iajs-3265	205	8	the	the	DET
iajs-3265	205	9	parameter	parameter	NOUN
iajs-3265	205	10	values	value	NOUN
iajs-3265	205	11	are	be	AUX
iajs-3265	205	12	𝑠	𝑠	PROPN
iajs-3265	205	13	=	=	SYM
iajs-3265	205	14	1	1	NUM
iajs-3265	205	15	,	,	PUNCT
iajs-3265	205	16	𝐹	𝐹	PROPN
iajs-3265	205	17	=	=	NOUN
iajs-3265	205	18	1	1	NUM
iajs-3265	205	19	,	,	PUNCT
iajs-3265	205	20	and	and	CCONJ
iajs-3265	205	21	𝑀	𝑀	PROPN
iajs-3265	205	22	=	=	SYM
iajs-3265	205	23	1	1	NUM
iajs-3265	205	24	,	,	PUNCT
iajs-3265	205	25	as	as	ADP
iajs-3265	205	26	in	in	ADP
iajs-3265	205	27	[	[	X
iajs-3265	205	28	36	36	NUM
iajs-3265	205	29	]	]	PUNCT
iajs-3265	205	30	,	,	PUNCT
iajs-3265	205	31	with	with	ADP
iajs-3265	205	32	𝑛	𝑛	PROPN
iajs-3265	205	33	=	=	SYM
iajs-3265	205	34	10	10	NUM
iajs-3265	205	35	,	,	PUNCT
iajs-3265	205	36	then	then	ADV
iajs-3265	205	37	the	the	DET
iajs-3265	205	38	novel	novel	ADJ
iajs-3265	205	39	approximate	approximate	ADJ
iajs-3265	205	40	solutions	solution	NOUN
iajs-3265	205	41	for	for	ADP
iajs-3265	205	42	the	the	DET
iajs-3265	205	43	darcy	darcy	PROPN
iajs-3265	205	44	-	-	PUNCT
iajs-3265	205	45	brinkman	brinkman	PROPN
iajs-3265	205	46	-	-	PUNCT
iajs-3265	205	47	forchheimer	forchheimer	PROPN
iajs-3265	205	48	equation	equation	NOUN
iajs-3265	205	49	will	will	AUX
iajs-3265	205	50	be	be	AUX
iajs-3265	205	51	:	:	PUNCT
iajs-3265	205	52	by	by	ADP
iajs-3265	205	53	applying	apply	VERB
iajs-3265	205	54	the	the	DET
iajs-3265	205	55	ecm	ecm	NOUN
iajs-3265	205	56	based	base	VERB
iajs-3265	205	57	on	on	ADP
iajs-3265	205	58	the	the	DET
iajs-3265	205	59	standard	standard	ADJ
iajs-3265	205	60	polynomials	polynomial	NOUN
iajs-3265	205	61	:	:	PUNCT
iajs-3265	205	62	𝑦(𝑥	𝑦(𝑥	NUM
iajs-3265	205	63	)	)	PUNCT
iajs-3265	206	1	≈	≈	PROPN
iajs-3265	206	2	0.323852	0.323852	NUM
iajs-3265	206	3	−	−	PROPN
iajs-3265	206	4	0.285634	0.285634	NUM
iajs-3265	206	5	𝑥2	𝑥2	NOUN
iajs-3265	206	6	+	+	CCONJ
iajs-3265	206	7	2.29576	2.29576	NUM
iajs-3265	206	8	×	×	NOUN
iajs-3265	206	9	10−6𝑥3	10−6𝑥3	NUM
iajs-3265	206	10	−	−	NOUN
iajs-3265	206	11	0.0392379	0.0392379	NUM
iajs-3265	206	12	𝑥4	𝑥4	NOUN
iajs-3265	206	13	+	+	CCONJ
iajs-3265	206	14	0.0000786079	0.0000786079	NUM
iajs-3265	206	15	𝑥5	𝑥5	PROPN
iajs-3265	206	16	+	+	NOUN
iajs-3265	206	17	0.000355229	0.000355229	NUM
iajs-3265	206	18	𝑥6	𝑥6	NOUN
iajs-3265	206	19	+	+	CCONJ
iajs-3265	206	20	0.000352023	0.000352023	NUM
iajs-3265	206	21	𝑥7	𝑥7	VERB
iajs-3265	206	22	+	+	CCONJ
iajs-3265	206	23	0.0000516179	0.0000516179	NUM
iajs-3265	206	24	𝑥8	𝑥8	NOUN
iajs-3265	206	25	+	+	CCONJ
iajs-3265	206	26	0.00021914	0.00021914	NUM
iajs-3265	206	27	𝑥9	𝑥9	NOUN
iajs-3265	206	28	−	−	NOUN
iajs-3265	206	29	0.0000397161	0.0000397161	NUM
iajs-3265	206	30	𝑥10	𝑥10	NOUN
iajs-3265	206	31	.	.	PUNCT
iajs-3265	207	1	also	also	ADV
iajs-3265	207	2	,	,	PUNCT
iajs-3265	207	3	by	by	ADP
iajs-3265	207	4	implementing	implement	VERB
iajs-3265	207	5	the	the	DET
iajs-3265	207	6	i	i	PROPN
iajs-3265	207	7	-	-	PUNCT
iajs-3265	207	8	ecms	ecms	PROPN
iajs-3265	207	9	based	base	VERB
iajs-3265	207	10	on	on	ADP
iajs-3265	207	11	the	the	DET
iajs-3265	207	12	first	first	ADJ
iajs-3265	207	13	kind	kind	NOUN
iajs-3265	207	14	of	of	ADP
iajs-3265	207	15	the	the	DET
iajs-3265	207	16	chebyshev	chebyshev	NOUN
iajs-3265	207	17	polynomials	polynomial	NOUN
iajs-3265	207	18	,	,	PUNCT
iajs-3265	207	19	we	we	PRON
iajs-3265	207	20	obtain	obtain	VERB
iajs-3265	207	21	:	:	PUNCT
iajs-3265	207	22	𝑦(𝑥	𝑦(𝑥	X
iajs-3265	207	23	)	)	PUNCT
iajs-3265	208	1	≈	≈	PROPN
iajs-3265	208	2	0.323852	0.323852	NUM
iajs-3265	208	3	−	−	PROPN
iajs-3265	208	4	0.285634	0.285634	NUM
iajs-3265	208	5	𝑥2	𝑥2	NOUN
iajs-3265	208	6	+	+	CCONJ
iajs-3265	208	7	8.64572	8.64572	NUM
iajs-3265	208	8	×	×	NOUN
iajs-3265	208	9	10−7𝑥3	10−7𝑥3	NUM
iajs-3265	208	10	−	−	NUM
iajs-3265	208	11	0.039229	0.039229	NUM
iajs-3265	208	12	𝑥4	𝑥4	NOUN
iajs-3265	208	13	+	+	CCONJ
iajs-3265	208	14	0.0000472476	0.0000472476	NUM
iajs-3265	208	15	𝑥5	𝑥5	ADJ
iajs-3265	208	16	+	+	CCONJ
iajs-3265	208	17	0.000421857	0.000421857	NUM
iajs-3265	208	18	𝑥6	𝑥6	NOUN
iajs-3265	208	19	+	+	CCONJ
iajs-3265	208	20	0.000264638	0.000264638	NUM
iajs-3265	208	21	𝑥7	𝑥7	VERB
iajs-3265	208	22	+	+	CCONJ
iajs-3265	208	23	0.000120859	0.000120859	NUM
iajs-3265	208	24	𝑥8	𝑥8	NOUN
iajs-3265	208	25	+	+	CCONJ
iajs-3265	208	26	0.000188736	0.000188736	NUM
iajs-3265	208	27	𝑥9	𝑥9	NOUN
iajs-3265	208	28	−	−	PROPN
iajs-3265	208	29	0.0000340335	0.0000340335	NUM
iajs-3265	208	30	𝑥10	𝑥10	NOUN
iajs-3265	208	31	.	.	PUNCT
iajs-3265	209	1	moreover	moreover	ADV
iajs-3265	209	2	,	,	PUNCT
iajs-3265	209	3	by	by	ADP
iajs-3265	209	4	using	use	VERB
iajs-3265	209	5	the	the	DET
iajs-3265	209	6	i	i	PROPN
iajs-3265	209	7	-	-	PUNCT
iajs-3265	209	8	ecms	ecms	PROPN
iajs-3265	209	9	based	base	VERB
iajs-3265	209	10	on	on	ADP
iajs-3265	209	11	the	the	DET
iajs-3265	209	12	bernoulli	bernoulli	NOUN
iajs-3265	209	13	polynomials	polynomial	NOUN
iajs-3265	209	14	,	,	PUNCT
iajs-3265	209	15	we	we	PRON
iajs-3265	209	16	achieve	achieve	VERB
iajs-3265	209	17	:	:	PUNCT
iajs-3265	209	18	𝑦(𝑥	𝑦(𝑥	X
iajs-3265	209	19	)	)	PUNCT
iajs-3265	210	1	≈	≈	PROPN
iajs-3265	210	2	0.323852	0.323852	NUM
iajs-3265	210	3	−	−	PROPN
iajs-3265	210	4	0.285634	0.285634	NUM
iajs-3265	210	5	𝑥2	𝑥2	NOUN
iajs-3265	210	6	+	+	CCONJ
iajs-3265	210	7	8.72335	8.72335	NUM
iajs-3265	210	8	×	×	NOUN
iajs-3265	210	9	10−7𝑥3	10−7𝑥3	NUM
iajs-3265	210	10	−	−	NUM
iajs-3265	210	11	0.039229	0.039229	NUM
iajs-3265	210	12	𝑥4	𝑥4	NOUN
iajs-3265	210	13	+	+	CCONJ
iajs-3265	210	14	0.0000475082	0.0000475082	NUM
iajs-3265	210	15	𝑥5	𝑥5	ADJ
iajs-3265	210	16	+	+	CCONJ
iajs-3265	210	17	0.000421236	0.000421236	NUM
iajs-3265	210	18	𝑥6	𝑥6	PROPN
iajs-3265	210	19	+	+	CCONJ
iajs-3265	210	20	0.000265524	0.000265524	NUM
iajs-3265	210	21	𝑥7	𝑥7	VERB
iajs-3265	210	22	+	+	CCONJ
iajs-3265	210	23	0.000120109	0.000120109	NUM
iajs-3265	210	24	𝑥8	𝑥8	NOUN
iajs-3265	210	25	+	+	CCONJ
iajs-3265	210	26	0.000189083	0.000189083	NUM
iajs-3265	210	27	𝑥9	𝑥9	NOUN
iajs-3265	210	28	−	−	PROPN
iajs-3265	210	29	0.0000341013	0.0000341013	NUM
iajs-3265	210	30	𝑥10	𝑥10	NOUN
iajs-3265	210	31	.	.	PUNCT
iajs-3265	211	1	in	in	ADP
iajs-3265	211	2	addition	addition	NOUN
iajs-3265	211	3	,	,	PUNCT
iajs-3265	211	4	by	by	ADP
iajs-3265	211	5	utilizing	utilize	VERB
iajs-3265	211	6	the	the	DET
iajs-3265	211	7	i	i	PROPN
iajs-3265	211	8	-	-	PUNCT
iajs-3265	211	9	ecms	ecms	PROPN
iajs-3265	211	10	based	base	VERB
iajs-3265	211	11	on	on	ADP
iajs-3265	211	12	the	the	DET
iajs-3265	211	13	laguerre	laguerre	NOUN
iajs-3265	211	14	polynomials	polynomial	NOUN
iajs-3265	211	15	,	,	PUNCT
iajs-3265	211	16	we	we	PRON
iajs-3265	211	17	get	get	VERB
iajs-3265	211	18	:	:	PUNCT
iajs-3265	211	19	𝑦(𝑥	𝑦(𝑥	X
iajs-3265	211	20	)	)	PUNCT
iajs-3265	212	1	≈	≈	PROPN
iajs-3265	212	2	0.323852	0.323852	NUM
iajs-3265	212	3	−	−	PROPN
iajs-3265	212	4	0.285634	0.285634	NUM
iajs-3265	212	5	𝑥2	𝑥2	NOUN
iajs-3265	212	6	+	+	CCONJ
iajs-3265	212	7	7.16738	7.16738	NUM
iajs-3265	212	8	×	×	NOUN
iajs-3265	212	9	10−7𝑥3	10−7𝑥3	NUM
iajs-3265	212	10	−	−	NUM
iajs-3265	212	11	0.0392277	0.0392277	NUM
iajs-3265	212	12	𝑥4	𝑥4	NOUN
iajs-3265	212	13	+	+	CCONJ
iajs-3265	212	14	0.0000418568	0.0000418568	NUM
iajs-3265	212	15	𝑥5	𝑥5	ADJ
iajs-3265	212	16	+	+	CCONJ
iajs-3265	212	17	0.000435078	0.000435078	NUM
iajs-3265	212	18	𝑥6	𝑥6	NOUN
iajs-3265	212	19	+	+	CCONJ
iajs-3265	212	20	0.0002453	0.0002453	NUM
iajs-3265	212	21	𝑥7	𝑥7	VERB
iajs-3265	212	22	+	+	CCONJ
iajs-3265	212	23	0.000137559	0.000137559	NUM
iajs-3265	212	24	𝑥8	𝑥8	NOUN
iajs-3265	212	25	+	+	CCONJ
iajs-3265	212	26	0.000180872	0.000180872	NUM
iajs-3265	212	27	𝑥9	𝑥9	NOUN
iajs-3265	212	28	−	−	PROPN
iajs-3265	212	29	0.0000324758	0.0000324758	NUM
iajs-3265	212	30	𝑥10	𝑥10	NOUN
iajs-3265	212	31	.	.	PUNCT
iajs-3265	213	1	furthermore	furthermore	ADV
iajs-3265	213	2	,	,	PUNCT
iajs-3265	213	3	since	since	SCONJ
iajs-3265	213	4	the	the	DET
iajs-3265	213	5	exact	exact	ADJ
iajs-3265	213	6	solution	solution	NOUN
iajs-3265	213	7	to	to	ADP
iajs-3265	213	8	the	the	DET
iajs-3265	213	9	darcy	darcy	PROPN
iajs-3265	213	10	-	-	PUNCT
iajs-3265	213	11	brinkman	brinkman	PROPN
iajs-3265	213	12	-	-	PUNCT
iajs-3265	213	13	forchheimer	forchheimer	PROPN
iajs-3265	213	14	equation	equation	NOUN
iajs-3265	213	15	is	be	AUX
iajs-3265	213	16	unknown	unknown	ADJ
iajs-3265	213	17	,	,	PUNCT
iajs-3265	213	18	the	the	DET
iajs-3265	213	19	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	213	20	has	have	AUX
iajs-3265	213	21	been	be	AUX
iajs-3265	213	22	calculated	calculate	VERB
iajs-3265	213	23	to	to	PART
iajs-3265	213	24	determine	determine	VERB
iajs-3265	213	25	the	the	DET
iajs-3265	213	26	accuracy	accuracy	NOUN
iajs-3265	213	27	and	and	CCONJ
iajs-3265	213	28	reliability	reliability	NOUN
iajs-3265	213	29	of	of	ADP
iajs-3265	213	30	the	the	DET
iajs-3265	213	31	novel	novel	ADJ
iajs-3265	213	32	approximate	approximate	ADJ
iajs-3265	213	33	solution	solution	NOUN
iajs-3265	213	34	produced	produce	VERB
iajs-3265	213	35	by	by	ADP
iajs-3265	213	36	the	the	DET
iajs-3265	213	37	proposed	propose	VERB
iajs-3265	213	38	approaches	approach	NOUN
iajs-3265	213	39	.	.	PUNCT
iajs-3265	214	1	the	the	DET
iajs-3265	214	2	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	214	3	is	be	AUX
iajs-3265	214	4	calculated	calculate	VERB
iajs-3265	214	5	by	by	ADP
iajs-3265	214	6	:	:	PUNCT
iajs-3265	214	7	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	214	8	=	=	SYM
iajs-3265	214	9	𝑚𝑎𝑥	𝑚𝑎𝑥	ADV
iajs-3265	214	10	0≤𝑥≤1	0≤𝑥≤1	ADJ
iajs-3265	214	11	|𝑦′′(𝑥	|𝑦′′(𝑥	NOUN
iajs-3265	214	12	)	)	PUNCT
iajs-3265	214	13	−	−	PROPN
iajs-3265	214	14	𝑠2𝑦(𝑥	𝑠2𝑦(𝑥	NOUN
iajs-3265	214	15	)	)	PUNCT
iajs-3265	214	16	−	−	PROPN
iajs-3265	215	1	𝐹𝑠𝑦2(𝑥	𝐹𝑠𝑦2(𝑥	NOUN
iajs-3265	215	2	)	)	PUNCT
iajs-3265	215	3	+	+	CCONJ
iajs-3265	215	4	1	1	NUM
iajs-3265	215	5	𝑀	𝑀	PROPN
iajs-3265	215	6	|	|	ADV
iajs-3265	215	7	.	.	PUNCT
iajs-3265	216	1	figure	figure	VERB
iajs-3265	216	2	2	2	NUM
iajs-3265	216	3	presents	present	VERB
iajs-3265	216	4	the	the	DET
iajs-3265	216	5	logarithmic	logarithmic	ADJ
iajs-3265	216	6	plots	plot	NOUN
iajs-3265	216	7	for	for	ADP
iajs-3265	216	8	the	the	DET
iajs-3265	216	9	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	216	10	values	value	NOUN
iajs-3265	216	11	obtained	obtain	VERB
iajs-3265	216	12	by	by	ADP
iajs-3265	216	13	the	the	DET
iajs-3265	216	14	ecm	ecm	NOUN
iajs-3265	216	15	based	base	VERB
iajs-3265	216	16	on	on	ADP
iajs-3265	216	17	the	the	DET
iajs-3265	216	18	standard	standard	ADJ
iajs-3265	216	19	polynomials	polynomial	NOUN
iajs-3265	216	20	and	and	CCONJ
iajs-3265	216	21	by	by	ADP
iajs-3265	216	22	the	the	DET
iajs-3265	216	23	i	i	PROPN
iajs-3265	216	24	-	-	PUNCT
iajs-3265	216	25	ecms	ecms	PROPN
iajs-3265	216	26	based	base	VERB
iajs-3265	216	27	on	on	ADP
iajs-3265	216	28	the	the	DET
iajs-3265	216	29	chebyshev	chebyshev	NOUN
iajs-3265	216	30	,	,	PUNCT
iajs-3265	216	31	bernoulli	bernoulli	PROPN
iajs-3265	216	32	,	,	PUNCT
iajs-3265	216	33	and	and	CCONJ
iajs-3265	216	34	laguerre	laguerre	NOUN
iajs-3265	216	35	polynomials	polynomial	NOUN
iajs-3265	216	36	,	,	PUNCT
iajs-3265	216	37	which	which	PRON
iajs-3265	216	38	prove	prove	VERB
iajs-3265	216	39	the	the	DET
iajs-3265	216	40	efficiency	efficiency	NOUN
iajs-3265	216	41	and	and	CCONJ
iajs-3265	216	42	accuracy	accuracy	NOUN
iajs-3265	216	43	of	of	ADP
iajs-3265	216	44	these	these	DET
iajs-3265	216	45	techniques	technique	NOUN
iajs-3265	216	46	by	by	ADP
iajs-3265	216	47	observation	observation	NOUN
iajs-3265	216	48	of	of	ADP
iajs-3265	216	49	the	the	DET
iajs-3265	216	50	error	error	NOUN
iajs-3265	216	51	values	value	NOUN
iajs-3265	216	52	for	for	ADP
iajs-3265	216	53	𝑛	𝑛	NOUN
iajs-3265	216	54	=	=	SYM
iajs-3265	216	55	2	2	NUM
iajs-3265	216	56	to	to	ADP
iajs-3265	216	57	10	10	NUM
iajs-3265	216	58	,	,	PUNCT
iajs-3265	216	59	as	as	SCONJ
iajs-3265	216	60	we	we	PRON
iajs-3265	216	61	found	find	VERB
iajs-3265	216	62	that	that	SCONJ
iajs-3265	216	63	the	the	DET
iajs-3265	216	64	error	error	NOUN
iajs-3265	216	65	decreases	decrease	VERB
iajs-3265	216	66	with	with	ADP
iajs-3265	216	67	increasing	increase	VERB
iajs-3265	216	68	the	the	DET
iajs-3265	216	69	values	value	NOUN
iajs-3265	216	70	of	of	ADP
iajs-3265	216	71	𝑛.	𝑛.	NOUN
iajs-3265	216	72	figure	figure	NOUN
iajs-3265	216	73	2	2	NUM
iajs-3265	216	74	.	.	PUNCT
iajs-3265	217	1	logarithmic	logarithmic	ADJ
iajs-3265	217	2	plots	plot	NOUN
iajs-3265	217	3	of	of	ADP
iajs-3265	217	4	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	217	5	to	to	ADP
iajs-3265	217	6	the	the	DET
iajs-3265	217	7	darcy	darcy	PROPN
iajs-3265	217	8	-	-	PUNCT
iajs-3265	217	9	brinkman	brinkman	PROPN
iajs-3265	217	10	-	-	PUNCT
iajs-3265	217	11	forchheimer	forchheimer	PROPN
iajs-3265	217	12	equation	equation	NOUN
iajs-3265	217	13	.	.	PUNCT
iajs-3265	218	1	ihjpas	ihjpas	PROPN
iajs-3265	218	2	.	.	PUNCT
iajs-3265	219	1	36	36	NUM
iajs-3265	219	2	(	(	PUNCT
iajs-3265	219	3	4	4	NUM
iajs-3265	219	4	)	)	PUNCT
iajs-3265	219	5	2023	2023	NUM
iajs-3265	219	6	348	348	NUM
iajs-3265	219	7	also	also	ADV
iajs-3265	219	8	,	,	PUNCT
iajs-3265	219	9	figure	figure	VERB
iajs-3265	219	10	3	3	NUM
iajs-3265	219	11	presents	present	VERB
iajs-3265	219	12	the	the	DET
iajs-3265	219	13	comparison	comparison	NOUN
iajs-3265	219	14	between	between	ADP
iajs-3265	219	15	the	the	DET
iajs-3265	219	16	novel	novel	ADJ
iajs-3265	219	17	approximate	approximate	ADJ
iajs-3265	219	18	solutions	solution	NOUN
iajs-3265	219	19	calculated	calculate	VERB
iajs-3265	219	20	by	by	ADP
iajs-3265	219	21	the	the	DET
iajs-3265	219	22	proposed	propose	VERB
iajs-3265	219	23	techniques	technique	NOUN
iajs-3265	219	24	for	for	ADP
iajs-3265	219	25	𝑛	𝑛	NOUN
iajs-3265	219	26	=	=	SYM
iajs-3265	219	27	10	10	NUM
iajs-3265	219	28	,	,	PUNCT
iajs-3265	219	29	𝑠	𝑠	PROPN
iajs-3265	219	30	=	=	SYM
iajs-3265	219	31	1	1	NUM
iajs-3265	219	32	,	,	PUNCT
iajs-3265	219	33	𝐹	𝐹	PROPN
iajs-3265	219	34	=	=	NOUN
iajs-3265	219	35	1	1	NUM
iajs-3265	219	36	,	,	PUNCT
iajs-3265	219	37	and	and	CCONJ
iajs-3265	219	38	𝑀	𝑀	PROPN
iajs-3265	219	39	=	=	PUNCT
iajs-3265	220	1	1	1	X
iajs-3265	220	2	.	.	PUNCT
iajs-3265	221	1	it	it	PRON
iajs-3265	221	2	is	be	AUX
iajs-3265	221	3	evident	evident	ADJ
iajs-3265	221	4	that	that	SCONJ
iajs-3265	221	5	impressive	impressive	ADJ
iajs-3265	221	6	agreements	agreement	NOUN
iajs-3265	221	7	have	have	AUX
iajs-3265	221	8	been	be	AUX
iajs-3265	221	9	achieved	achieve	VERB
iajs-3265	221	10	for	for	ADP
iajs-3265	221	11	all	all	DET
iajs-3265	221	12	the	the	DET
iajs-3265	221	13	suggested	suggest	VERB
iajs-3265	221	14	methods	method	NOUN
iajs-3265	221	15	.	.	PUNCT
iajs-3265	222	1	figure	figure	NOUN
iajs-3265	222	2	3	3	NUM
iajs-3265	222	3	.	.	PUNCT
iajs-3265	223	1	the	the	DET
iajs-3265	223	2	comparison	comparison	NOUN
iajs-3265	223	3	of	of	ADP
iajs-3265	223	4	the	the	DET
iajs-3265	223	5	solutions	solution	NOUN
iajs-3265	223	6	to	to	ADP
iajs-3265	223	7	the	the	DET
iajs-3265	223	8	darcy	darcy	PROPN
iajs-3265	223	9	-	-	PUNCT
iajs-3265	223	10	brinkman	brinkman	PROPN
iajs-3265	223	11	-	-	PUNCT
iajs-3265	223	12	forchheimer	forchheimer	PROPN
iajs-3265	223	13	equation	equation	NOUN
iajs-3265	223	14	by	by	ADP
iajs-3265	223	15	proposed	propose	VERB
iajs-3265	223	16	methods	method	NOUN
iajs-3265	223	17	.	.	PUNCT
iajs-3265	224	1	moreover	moreover	ADV
iajs-3265	224	2	,	,	PUNCT
iajs-3265	224	3	the	the	DET
iajs-3265	224	4	values	value	NOUN
iajs-3265	224	5	of	of	ADP
iajs-3265	224	6	the	the	DET
iajs-3265	224	7	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	224	8	for	for	ADP
iajs-3265	224	9	the	the	DET
iajs-3265	224	10	novel	novel	ADJ
iajs-3265	224	11	approximate	approximate	ADJ
iajs-3265	224	12	solutions	solution	NOUN
iajs-3265	224	13	utilizing	utilize	VERB
iajs-3265	224	14	ecm	ecm	NOUN
iajs-3265	224	15	and	and	CCONJ
iajs-3265	224	16	iecms	iecms	NOUN
iajs-3265	224	17	are	be	AUX
iajs-3265	224	18	also	also	ADV
iajs-3265	224	19	shown	show	VERB
iajs-3265	224	20	in	in	ADP
iajs-3265	224	21	table	table	NOUN
iajs-3265	224	22	1	1	NUM
iajs-3265	224	23	with	with	ADP
iajs-3265	224	24	𝑛	𝑛	NOUN
iajs-3265	224	25	=	=	SYM
iajs-3265	224	26	10	10	NUM
iajs-3265	224	27	and	and	CCONJ
iajs-3265	224	28	parameters	parameter	NOUN
iajs-3265	224	29	𝑠	𝑠	PROPN
iajs-3265	224	30	=	=	SYM
iajs-3265	224	31	𝑀	𝑀	PROPN
iajs-3265	224	32	=	=	SYM
iajs-3265	224	33	1	1	NUM
iajs-3265	224	34	,	,	PUNCT
iajs-3265	224	35	versus	versus	ADP
iajs-3265	224	36	the	the	DET
iajs-3265	224	37	value	value	NOUN
iajs-3265	224	38	of	of	ADP
iajs-3265	224	39	𝐹	𝐹	PROPN
iajs-3265	224	40	,	,	PUNCT
iajs-3265	224	41	which	which	PRON
iajs-3265	224	42	offers	offer	VERB
iajs-3265	224	43	the	the	DET
iajs-3265	224	44	accuracy	accuracy	NOUN
iajs-3265	224	45	of	of	ADP
iajs-3265	224	46	these	these	DET
iajs-3265	224	47	techniques	technique	NOUN
iajs-3265	224	48	.	.	PUNCT
iajs-3265	225	1	in	in	ADP
iajs-3265	225	2	addition	addition	NOUN
iajs-3265	225	3	,	,	PUNCT
iajs-3265	225	4	it	it	PRON
iajs-3265	225	5	can	can	AUX
iajs-3265	225	6	be	be	AUX
iajs-3265	225	7	observed	observe	VERB
iajs-3265	225	8	that	that	SCONJ
iajs-3265	225	9	the	the	DET
iajs-3265	225	10	i	i	PROPN
iajs-3265	225	11	-	-	PUNCT
iajs-3265	225	12	ecms	ecms	PROPN
iajs-3265	225	13	based	base	VERB
iajs-3265	225	14	on	on	ADP
iajs-3265	225	15	the	the	DET
iajs-3265	225	16	chebyshev	chebyshev	PROPN
iajs-3265	225	17	polynomial	polynomial	ADJ
iajs-3265	225	18	method	method	NOUN
iajs-3265	225	19	provide	provide	VERB
iajs-3265	225	20	slightly	slightly	ADV
iajs-3265	225	21	better	well	ADJ
iajs-3265	225	22	accuracy	accuracy	NOUN
iajs-3265	225	23	with	with	ADP
iajs-3265	225	24	the	the	DET
iajs-3265	225	25	lowest	low	ADJ
iajs-3265	225	26	number	number	NOUN
iajs-3265	225	27	of	of	ADP
iajs-3265	225	28	errors	error	NOUN
iajs-3265	225	29	compared	compare	VERB
iajs-3265	225	30	to	to	ADP
iajs-3265	225	31	other	other	ADJ
iajs-3265	225	32	techniques	technique	NOUN
iajs-3265	225	33	.	.	PUNCT
iajs-3265	226	1	table	table	NOUN
iajs-3265	226	2	1	1	NUM
iajs-3265	226	3	.	.	PUNCT
iajs-3265	227	1	the	the	DET
iajs-3265	227	2	comparison	comparison	NOUN
iajs-3265	227	3	between	between	ADP
iajs-3265	227	4	the	the	DET
iajs-3265	227	5	𝑀𝐸𝑅10	𝑀𝐸𝑅10	PROPN
iajs-3265	227	6	when	when	SCONJ
iajs-3265	227	7	𝑠	𝑠	PROPN
iajs-3265	227	8	=	=	SYM
iajs-3265	227	9	𝑀	𝑀	PROPN
iajs-3265	227	10	=	=	SYM
iajs-3265	227	11	1	1	NUM
iajs-3265	227	12	,	,	PUNCT
iajs-3265	227	13	and	and	CCONJ
iajs-3265	227	14	versus	versus	ADP
iajs-3265	227	15	the	the	DET
iajs-3265	227	16	value	value	NOUN
iajs-3265	227	17	of	of	ADP
iajs-3265	227	18	𝐹	𝐹	PROPN
iajs-3265	227	19	for	for	ADP
iajs-3265	227	20	the	the	DET
iajs-3265	227	21	darcybrinkman	darcybrinkman	ADJ
iajs-3265	227	22	-	-	PUNCT
iajs-3265	227	23	forchheimer	forchheimer	NOUN
iajs-3265	227	24	equation	equation	NOUN
iajs-3265	227	25	.	.	PUNCT
iajs-3265	228	1	4.2	4.2	NUM
iajs-3265	228	2	solving	solve	VERB
iajs-3265	228	3	the	the	DET
iajs-3265	228	4	blasius	blasius	ADJ
iajs-3265	228	5	equation	equation	NOUN
iajs-3265	228	6	by	by	ADP
iajs-3265	228	7	the	the	DET
iajs-3265	228	8	ecm	ecm	PROPN
iajs-3265	228	9	and	and	CCONJ
iajs-3265	228	10	i	i	PROPN
iajs-3265	228	11	-	-	PUNCT
iajs-3265	228	12	ecms	ecms	PROPN
iajs-3265	228	13	the	the	DET
iajs-3265	228	14	ecm	ecm	NOUN
iajs-3265	228	15	and	and	CCONJ
iajs-3265	228	16	the	the	DET
iajs-3265	228	17	i	i	PROPN
iajs-3265	228	18	-	-	PUNCT
iajs-3265	228	19	ecms	ecms	NOUN
iajs-3265	228	20	techniques	technique	NOUN
iajs-3265	228	21	are	be	AUX
iajs-3265	228	22	utilized	utilize	VERB
iajs-3265	228	23	to	to	PART
iajs-3265	228	24	solve	solve	VERB
iajs-3265	228	25	the	the	DET
iajs-3265	228	26	second	second	ADJ
iajs-3265	228	27	problem	problem	NOUN
iajs-3265	228	28	shown	show	VERB
iajs-3265	228	29	in	in	ADP
iajs-3265	228	30	the	the	DET
iajs-3265	228	31	equations	equation	NOUN
iajs-3265	228	32	(	(	PUNCT
iajs-3265	228	33	3	3	NUM
iajs-3265	228	34	)	)	PUNCT
iajs-3265	228	35	and	and	CCONJ
iajs-3265	228	36	(	(	PUNCT
iajs-3265	228	37	5	5	NUM
iajs-3265	228	38	)	)	PUNCT
iajs-3265	228	39	.	.	PUNCT
iajs-3265	229	1	more	more	ADV
iajs-3265	229	2	precisely	precisely	ADV
iajs-3265	229	3	,	,	PUNCT
iajs-3265	229	4	we	we	PRON
iajs-3265	229	5	substitute	substitute	VERB
iajs-3265	229	6	equations	equation	NOUN
iajs-3265	229	7	(	(	PUNCT
iajs-3265	229	8	12	12	NUM
iajs-3265	229	9	)	)	PUNCT
iajs-3265	229	10	and	and	CCONJ
iajs-3265	229	11	(	(	PUNCT
iajs-3265	229	12	13	13	NUM
iajs-3265	229	13	)	)	PUNCT
iajs-3265	229	14	into	into	ADP
iajs-3265	229	15	equations	equation	NOUN
iajs-3265	229	16	(	(	PUNCT
iajs-3265	229	17	3	3	NUM
iajs-3265	229	18	)	)	PUNCT
iajs-3265	229	19	and	and	CCONJ
iajs-3265	229	20	(	(	PUNCT
iajs-3265	229	21	5	5	NUM
iajs-3265	229	22	)	)	PUNCT
iajs-3265	229	23	for	for	ADP
iajs-3265	229	24	the	the	DET
iajs-3265	229	25	technique	technique	NOUN
iajs-3265	229	26	ecm	ecm	NOUN
iajs-3265	229	27	,	,	PUNCT
iajs-3265	229	28	converting	convert	VERB
iajs-3265	229	29	the	the	DET
iajs-3265	229	30	function	function	NOUN
iajs-3265	229	31	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	229	32	)	)	PUNCT
iajs-3265	229	33	and	and	CCONJ
iajs-3265	229	34	its	its	PRON
iajs-3265	229	35	derivatives	derivative	NOUN
iajs-3265	229	36	as	as	ADP
iajs-3265	229	37	matrices	matrix	NOUN
iajs-3265	229	38	.	.	PUNCT
iajs-3265	230	1	thus	thus	ADV
iajs-3265	230	2	,	,	PUNCT
iajs-3265	230	3	we	we	PRON
iajs-3265	230	4	obtain	obtain	VERB
iajs-3265	230	5	the	the	DET
iajs-3265	230	6	following	follow	VERB
iajs-3265	230	7	result	result	NOUN
iajs-3265	230	8	:	:	PUNCT
iajs-3265	230	9	𝜳(𝑥	𝜳(𝑥	X
iajs-3265	230	10	)	)	PUNCT
iajs-3265	230	11	(	(	PUNCT
iajs-3265	230	12	𝑩∗)3	𝑩∗)3	ADV
iajs-3265	230	13	𝑨	𝑨	PROPN
iajs-3265	230	14	+	+	CCONJ
iajs-3265	230	15	1	1	NUM
iajs-3265	230	16	2	2	NUM
iajs-3265	230	17	(	(	PUNCT
iajs-3265	230	18	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	230	19	)	)	PUNCT
iajs-3265	230	20	𝑨)(𝜳(𝑥	𝑨)(𝜳(𝑥	NOUN
iajs-3265	230	21	)	)	PUNCT
iajs-3265	230	22	(	(	PUNCT
iajs-3265	230	23	𝑩∗)2	𝑩∗)2	ADV
iajs-3265	230	24	𝑨	𝑨	NOUN
iajs-3265	230	25	)	)	PUNCT
iajs-3265	230	26	=	=	SYM
iajs-3265	230	27	0	0	NUM
iajs-3265	230	28	,	,	PUNCT
iajs-3265	230	29	𝜳(0	𝜳(0	NUM
iajs-3265	230	30	)	)	PUNCT
iajs-3265	230	31	𝑨	𝑨	NOUN
iajs-3265	230	32	=	=	SYM
iajs-3265	230	33	0	0	NUM
iajs-3265	230	34	,	,	PUNCT
iajs-3265	230	35	𝜳(0	𝜳(0	PUNCT
iajs-3265	230	36	)	)	PUNCT
iajs-3265	230	37	𝑩∗	𝑩∗	NOUN
iajs-3265	230	38	𝑨	𝑨	NOUN
iajs-3265	230	39	=	=	SYM
iajs-3265	230	40	0	0	NUM
iajs-3265	230	41	,	,	PUNCT
iajs-3265	230	42	𝜳(0	𝜳(0	NUM
iajs-3265	230	43	)	)	PUNCT
iajs-3265	230	44	(	(	PUNCT
iajs-3265	230	45	𝑩∗)2	𝑩∗)2	ADV
iajs-3265	230	46	𝑨	𝑨	NOUN
iajs-3265	230	47	=	=	SYM
iajs-3265	230	48	𝛼.	𝛼.	NOUN
iajs-3265	230	49	(	(	PUNCT
iajs-3265	230	50	37	37	NUM
iajs-3265	230	51	)	)	PUNCT
iajs-3265	230	52	then	then	ADV
iajs-3265	230	53	,	,	PUNCT
iajs-3265	230	54	the	the	DET
iajs-3265	230	55	processes	process	NOUN
iajs-3265	230	56	have	have	AUX
iajs-3265	230	57	been	be	AUX
iajs-3265	230	58	applied	apply	VERB
iajs-3265	230	59	,	,	PUNCT
iajs-3265	230	60	as	as	SCONJ
iajs-3265	230	61	shown	show	VERB
iajs-3265	230	62	in	in	ADP
iajs-3265	230	63	the	the	DET
iajs-3265	230	64	equations	equation	NOUN
iajs-3265	230	65	(	(	PUNCT
iajs-3265	230	66	18	18	NUM
iajs-3265	230	67	)	)	PUNCT
iajs-3265	230	68	and	and	CCONJ
iajs-3265	230	69	(	(	PUNCT
iajs-3265	230	70	19	19	NUM
iajs-3265	230	71	)	)	PUNCT
iajs-3265	230	72	,	,	PUNCT
iajs-3265	230	73	so	so	ADV
iajs-3265	230	74	:	:	PUNCT
iajs-3265	230	75	〈	〈	PROPN
iajs-3265	230	76	𝑥𝑖	𝑥𝑖	PRON
iajs-3265	230	77	,	,	PUNCT
iajs-3265	230	78	𝜳(𝑥	𝜳(𝑥	PROPN
iajs-3265	230	79	)	)	PUNCT
iajs-3265	230	80	(	(	PUNCT
iajs-3265	230	81	𝑩∗)3	𝑩∗)3	ADV
iajs-3265	230	82	𝑨	𝑨	PROPN
iajs-3265	230	83	+	+	CCONJ
iajs-3265	230	84	1	1	NUM
iajs-3265	230	85	2	2	NUM
iajs-3265	230	86	(	(	PUNCT
iajs-3265	230	87	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	230	88	)	)	PUNCT
iajs-3265	230	89	𝑨)(𝜳(𝑥	𝑨)(𝜳(𝑥	NOUN
iajs-3265	230	90	)	)	PUNCT
iajs-3265	230	91	(	(	PUNCT
iajs-3265	230	92	𝑩∗)2	𝑩∗)2	ADV
iajs-3265	230	93	𝑨	𝑨	NOUN
iajs-3265	230	94	)	)	PUNCT
iajs-3265	230	95	〉	〉	NOUN
iajs-3265	230	96	=	=	SYM
iajs-3265	230	97	〈	〈	PROPN
iajs-3265	230	98	𝑥𝑖	𝑥𝑖	PROPN
iajs-3265	230	99	,	,	PUNCT
iajs-3265	230	100	0	0	NUM
iajs-3265	230	101	〉	〉	NOUN
iajs-3265	230	102	,	,	PUNCT
iajs-3265	230	103	∀	∀	NOUN
iajs-3265	230	104	0	0	NUM
iajs-3265	230	105	≤	≤	NUM
iajs-3265	230	106	𝑖	𝑖	SYM
iajs-3265	230	107	≤	≤	NOUN
iajs-3265	230	108	𝑛.	𝑛.	NOUN
iajs-3265	230	109	(	(	PUNCT
iajs-3265	230	110	38	38	NUM
iajs-3265	230	111	)	)	PUNCT
iajs-3265	230	112	substituting	substitute	VERB
iajs-3265	230	113	equations	equation	NOUN
iajs-3265	230	114	(	(	PUNCT
iajs-3265	230	115	21	21	NUM
iajs-3265	230	116	)	)	PUNCT
iajs-3265	230	117	and	and	CCONJ
iajs-3265	230	118	(	(	PUNCT
iajs-3265	230	119	22	22	NUM
iajs-3265	230	120	)	)	PUNCT
iajs-3265	230	121	into	into	ADP
iajs-3265	230	122	equations	equation	NOUN
iajs-3265	230	123	(	(	PUNCT
iajs-3265	230	124	3	3	NUM
iajs-3265	230	125	)	)	PUNCT
iajs-3265	230	126	and	and	CCONJ
iajs-3265	230	127	(	(	PUNCT
iajs-3265	230	128	5	5	NUM
iajs-3265	230	129	)	)	PUNCT
iajs-3265	230	130	for	for	ADP
iajs-3265	230	131	the	the	DET
iajs-3265	230	132	i	i	PROPN
iajs-3265	230	133	-	-	PUNCT
iajs-3265	230	134	ecms	ecms	PROPN
iajs-3265	230	135	based	base	VERB
iajs-3265	230	136	on	on	ADP
iajs-3265	230	137	the	the	DET
iajs-3265	230	138	first	first	ADJ
iajs-3265	230	139	kind	kind	NOUN
iajs-3265	230	140	of	of	ADP
iajs-3265	230	141	chebyshev	chebyshev	NOUN
iajs-3265	230	142	polynomials	polynomial	NOUN
iajs-3265	230	143	,	,	PUNCT
iajs-3265	230	144	it	it	PRON
iajs-3265	230	145	follows	follow	VERB
iajs-3265	230	146	:	:	PUNCT
iajs-3265	230	147	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	230	148	(	(	PUNCT
iajs-3265	230	149	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	230	150	∗	∗	NOUN
iajs-3265	230	151	)	)	PUNCT
iajs-3265	230	152	3	3	NUM
iajs-3265	230	153	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	230	154	)	)	PUNCT
iajs-3265	231	1	+	+	CCONJ
iajs-3265	231	2	1	1	NUM
iajs-3265	231	3	2	2	NUM
iajs-3265	231	4	(	(	PUNCT
iajs-3265	231	5	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	231	6	𝜳(𝑥))(𝑨𝑇	𝜳(𝑥))(𝑨𝑇	NOUN
iajs-3265	231	7	(	(	PUNCT
iajs-3265	231	8	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	231	9	∗	∗	NOUN
iajs-3265	231	10	)	)	PUNCT
iajs-3265	231	11	2	2	NUM
iajs-3265	231	12	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	231	13	)	)	PUNCT
iajs-3265	231	14	)	)	PUNCT
iajs-3265	232	1	=	=	SYM
iajs-3265	232	2	0	0	NUM
iajs-3265	232	3	,	,	PUNCT
iajs-3265	232	4	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	232	5	𝜳(0	𝜳(0	PUNCT
iajs-3265	232	6	)	)	PUNCT
iajs-3265	232	7	=	=	SYM
iajs-3265	232	8	0	0	NUM
iajs-3265	232	9	,	,	PUNCT
iajs-3265	232	10	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	232	11	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	232	12	∗	∗	NOUN
iajs-3265	232	13	𝜳(0	𝜳(0	NUM
iajs-3265	232	14	)	)	PUNCT
iajs-3265	232	15	=	=	SYM
iajs-3265	232	16	0	0	NUM
iajs-3265	232	17	,	,	PUNCT
iajs-3265	232	18	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	232	19	(	(	PUNCT
iajs-3265	232	20	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	232	21	∗	∗	NOUN
iajs-3265	232	22	)	)	PUNCT
iajs-3265	232	23	2	2	NUM
iajs-3265	232	24	𝜳(0	𝜳(0	NUM
iajs-3265	232	25	)	)	PUNCT
iajs-3265	232	26	=	=	SYM
iajs-3265	232	27	𝛼.	𝛼.	NOUN
iajs-3265	232	28	(	(	PUNCT
iajs-3265	232	29	39	39	NUM
iajs-3265	232	30	)	)	PUNCT
iajs-3265	232	31	and	and	CCONJ
iajs-3265	232	32	,	,	PUNCT
iajs-3265	232	33	the	the	DET
iajs-3265	232	34	results	result	NOUN
iajs-3265	232	35	of	of	ADP
iajs-3265	232	36	implementing	implement	VERB
iajs-3265	232	37	equations	equation	NOUN
iajs-3265	232	38	(	(	PUNCT
iajs-3265	232	39	18	18	NUM
iajs-3265	232	40	)	)	PUNCT
iajs-3265	232	41	and	and	CCONJ
iajs-3265	232	42	(	(	PUNCT
iajs-3265	232	43	19	19	NUM
iajs-3265	232	44	)	)	PUNCT
iajs-3265	232	45	are	be	AUX
iajs-3265	232	46	as	as	SCONJ
iajs-3265	232	47	follows	follow	VERB
iajs-3265	232	48	:	:	PUNCT
iajs-3265	232	49	〈	〈	NOUN
iajs-3265	232	50	𝑻𝑖(𝑥	𝑻𝑖(𝑥	NOUN
iajs-3265	232	51	)	)	PUNCT
iajs-3265	232	52	,	,	PUNCT
iajs-3265	232	53	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	232	54	(	(	PUNCT
iajs-3265	232	55	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	232	56	∗	∗	NOUN
iajs-3265	232	57	)	)	PUNCT
iajs-3265	232	58	3	3	NUM
iajs-3265	232	59	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	232	60	)	)	PUNCT
iajs-3265	233	1	+	+	CCONJ
iajs-3265	233	2	1	1	NUM
iajs-3265	233	3	2	2	NUM
iajs-3265	233	4	(	(	PUNCT
iajs-3265	233	5	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	233	6	𝜳(𝑥))(𝑨𝑇	𝜳(𝑥))(𝑨𝑇	NOUN
iajs-3265	233	7	(	(	PUNCT
iajs-3265	233	8	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	233	9	∗	∗	NOUN
iajs-3265	233	10	)	)	PUNCT
iajs-3265	233	11	2	2	NUM
iajs-3265	233	12	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	233	13	)	)	PUNCT
iajs-3265	233	14	)	)	PUNCT
iajs-3265	233	15	〉	〉	NOUN
iajs-3265	233	16	=	=	PUNCT
iajs-3265	233	17	〈	〈	NOUN
iajs-3265	233	18	𝑻𝑖(𝑥	𝑻𝑖(𝑥	NOUN
iajs-3265	233	19	)	)	PUNCT
iajs-3265	233	20	,	,	PUNCT
iajs-3265	233	21	0	0	NUM
iajs-3265	233	22	〉	〉	NOUN
iajs-3265	233	23	,	,	PUNCT
iajs-3265	233	24	∀	∀	NOUN
iajs-3265	233	25	0	0	NUM
iajs-3265	233	26	≤	≤	NUM
iajs-3265	233	27	𝑖	𝑖	SYM
iajs-3265	233	28	≤	≤	NOUN
iajs-3265	233	29	𝑛.	𝑛.	NOUN
iajs-3265	233	30	(	(	PUNCT
iajs-3265	233	31	40	40	NUM
iajs-3265	233	32	)	)	PUNCT
iajs-3265	233	33	𝑭	𝑭	PROPN
iajs-3265	233	34	ecm	ecm	NOUN
iajs-3265	233	35	standard	standard	NOUN
iajs-3265	233	36	i	i	PROPN
iajs-3265	233	37	-	-	PUNCT
iajs-3265	233	38	ecms	ecms	PROPN
iajs-3265	233	39	chebyshev	chebyshev	NOUN
iajs-3265	233	40	i	i	PROPN
iajs-3265	233	41	-	-	PUNCT
iajs-3265	233	42	ecms	ecms	NOUN
iajs-3265	233	43	bernoulli	bernoulli	PROPN
iajs-3265	233	44	i	i	PROPN
iajs-3265	233	45	-	-	PUNCT
iajs-3265	233	46	ecms	ecms	PROPN
iajs-3265	233	47	laguerre	laguerre	NOUN
iajs-3265	233	48	2	2	NUM
iajs-3265	233	49	1.27523	1.27523	NUM
iajs-3265	233	50	×	×	NOUN
iajs-3265	233	51	10−6	10−6	NUM
iajs-3265	233	52	2.75302	2.75302	NUM
iajs-3265	233	53	×	×	NOUN
iajs-3265	233	54	10−7	10−7	NUM
iajs-3265	233	55	2.7852	2.7852	NUM
iajs-3265	233	56	×	×	NOUN
iajs-3265	233	57	10−7	10−7	NUM
iajs-3265	233	58	2.77819	2.77819	NUM
iajs-3265	233	59	×	×	NOUN
iajs-3265	233	60	10−7	10−7	NUM
iajs-3265	233	61	4	4	NUM
iajs-3265	233	62	5.33771	5.33771	NUM
iajs-3265	233	63	×	×	NOUN
iajs-3265	233	64	10−6	10−6	NUM
iajs-3265	233	65	1.14476	1.14476	NUM
iajs-3265	233	66	×	×	NOUN
iajs-3265	233	67	10−6	10−6	NUM
iajs-3265	233	68	1.15826	1.15826	NUM
iajs-3265	233	69	×	×	NOUN
iajs-3265	233	70	10−6	10−6	NUM
iajs-3265	233	71	1.17427	1.17427	NUM
iajs-3265	233	72	×	×	NOUN
iajs-3265	233	73	10−6	10−6	NUM
iajs-3265	233	74	6	6	NUM
iajs-3265	233	75	0.0000118871	0.0000118871	NUM
iajs-3265	233	76	2.52936	2.52936	NUM
iajs-3265	233	77	×	×	NOUN
iajs-3265	233	78	10−6	10−6	NUM
iajs-3265	233	79	2.5595	2.5595	NUM
iajs-3265	233	80	×	×	NOUN
iajs-3265	233	81	10−6	10−6	NUM
iajs-3265	233	82	2.65222	2.65222	NUM
iajs-3265	233	83	×	×	NOUN
iajs-3265	233	84	10−6	10−6	NUM
iajs-3265	233	85	ihjpas	ihjpa	NOUN
iajs-3265	233	86	.	.	PUNCT
iajs-3265	234	1	36	36	NUM
iajs-3265	234	2	(	(	PUNCT
iajs-3265	234	3	4	4	NUM
iajs-3265	234	4	)	)	PUNCT
iajs-3265	234	5	2023	2023	NUM
iajs-3265	234	6	349	349	NUM
iajs-3265	234	7	applying	apply	VERB
iajs-3265	234	8	the	the	DET
iajs-3265	234	9	i	i	PROPN
iajs-3265	234	10	-	-	PUNCT
iajs-3265	234	11	ecms	ecms	PROPN
iajs-3265	234	12	based	base	VERB
iajs-3265	234	13	on	on	ADP
iajs-3265	234	14	the	the	DET
iajs-3265	234	15	bernoulli	bernoulli	NOUN
iajs-3265	234	16	polynomials	polynomial	NOUN
iajs-3265	234	17	by	by	ADP
iajs-3265	234	18	substituting	substitute	VERB
iajs-3265	234	19	equations	equation	NOUN
iajs-3265	234	20	(	(	PUNCT
iajs-3265	234	21	24	24	NUM
iajs-3265	234	22	)	)	PUNCT
iajs-3265	234	23	and	and	CCONJ
iajs-3265	234	24	(	(	PUNCT
iajs-3265	234	25	25	25	NUM
iajs-3265	234	26	)	)	PUNCT
iajs-3265	234	27	into	into	ADP
iajs-3265	234	28	equations	equation	NOUN
iajs-3265	234	29	(	(	PUNCT
iajs-3265	234	30	3	3	NUM
iajs-3265	234	31	)	)	PUNCT
iajs-3265	234	32	and	and	CCONJ
iajs-3265	234	33	(	(	PUNCT
iajs-3265	234	34	5	5	NUM
iajs-3265	234	35	)	)	PUNCT
iajs-3265	234	36	,	,	PUNCT
iajs-3265	234	37	the	the	DET
iajs-3265	234	38	following	follow	VERB
iajs-3265	234	39	is	be	AUX
iajs-3265	234	40	obtained	obtain	VERB
iajs-3265	234	41	:	:	PUNCT
iajs-3265	234	42	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	234	43	(	(	PUNCT
iajs-3265	234	44	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	234	45	∗	∗	NOUN
iajs-3265	234	46	)	)	PUNCT
iajs-3265	234	47	3	3	NUM
iajs-3265	234	48	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	234	49	)	)	PUNCT
iajs-3265	235	1	+	+	CCONJ
iajs-3265	235	2	1	1	NUM
iajs-3265	235	3	2	2	NUM
iajs-3265	235	4	(	(	PUNCT
iajs-3265	235	5	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	235	6	𝜳(𝑥))(𝑨𝑇	𝜳(𝑥))(𝑨𝑇	NOUN
iajs-3265	235	7	(	(	PUNCT
iajs-3265	235	8	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	235	9	∗	∗	NOUN
iajs-3265	235	10	)	)	PUNCT
iajs-3265	235	11	2	2	NUM
iajs-3265	235	12	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	235	13	)	)	PUNCT
iajs-3265	235	14	)	)	PUNCT
iajs-3265	236	1	=	=	SYM
iajs-3265	236	2	0	0	NUM
iajs-3265	236	3	,	,	PUNCT
iajs-3265	236	4	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	236	5	𝜳(0	𝜳(0	PUNCT
iajs-3265	236	6	)	)	PUNCT
iajs-3265	236	7	=	=	SYM
iajs-3265	236	8	0	0	NUM
iajs-3265	236	9	,	,	PUNCT
iajs-3265	236	10	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	236	11	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	236	12	∗	∗	NOUN
iajs-3265	236	13	𝜳(0	𝜳(0	NUM
iajs-3265	236	14	)	)	PUNCT
iajs-3265	236	15	=	=	SYM
iajs-3265	236	16	0	0	NUM
iajs-3265	236	17	,	,	PUNCT
iajs-3265	236	18	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	236	19	(	(	PUNCT
iajs-3265	236	20	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	236	21	∗	∗	NOUN
iajs-3265	236	22	)	)	PUNCT
iajs-3265	236	23	2	2	NUM
iajs-3265	236	24	𝜳(0	𝜳(0	NUM
iajs-3265	236	25	)	)	PUNCT
iajs-3265	236	26	=	=	SYM
iajs-3265	236	27	𝛼.	𝛼.	NOUN
iajs-3265	236	28	(	(	PUNCT
iajs-3265	236	29	41	41	NUM
iajs-3265	236	30	)	)	PUNCT
iajs-3265	236	31	using	use	VERB
iajs-3265	236	32	the	the	DET
iajs-3265	236	33	procedures	procedure	NOUN
iajs-3265	236	34	described	describe	VERB
iajs-3265	236	35	in	in	ADP
iajs-3265	236	36	equations	equation	NOUN
iajs-3265	236	37	(	(	PUNCT
iajs-3265	236	38	18	18	NUM
iajs-3265	236	39	)	)	PUNCT
iajs-3265	236	40	and	and	CCONJ
iajs-3265	236	41	(	(	PUNCT
iajs-3265	236	42	19	19	NUM
iajs-3265	236	43	)	)	PUNCT
iajs-3265	236	44	,	,	PUNCT
iajs-3265	236	45	as	as	ADP
iajs-3265	236	46	a	a	DET
iajs-3265	236	47	result	result	NOUN
iajs-3265	236	48	,	,	PUNCT
iajs-3265	236	49	the	the	DET
iajs-3265	236	50	following	follow	VERB
iajs-3265	236	51	equation	equation	NOUN
iajs-3265	236	52	will	will	AUX
iajs-3265	236	53	be	be	AUX
iajs-3265	236	54	offered	offer	VERB
iajs-3265	236	55	:	:	PUNCT
iajs-3265	236	56	〈	〈	NOUN
iajs-3265	236	57	𝑩𝑖(𝑥	𝑩𝑖(𝑥	NOUN
iajs-3265	236	58	)	)	PUNCT
iajs-3265	236	59	,	,	PUNCT
iajs-3265	236	60	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	236	61	(	(	PUNCT
iajs-3265	236	62	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	236	63	∗	∗	NOUN
iajs-3265	236	64	)	)	PUNCT
iajs-3265	236	65	3	3	NUM
iajs-3265	236	66	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	236	67	)	)	PUNCT
iajs-3265	236	68	+	+	CCONJ
iajs-3265	236	69	1	1	NUM
iajs-3265	236	70	2	2	NUM
iajs-3265	236	71	(	(	PUNCT
iajs-3265	236	72	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	236	73	𝜳(𝑥))(𝑨𝑇	𝜳(𝑥))(𝑨𝑇	NOUN
iajs-3265	236	74	(	(	PUNCT
iajs-3265	236	75	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	236	76	∗	∗	NOUN
iajs-3265	236	77	)	)	PUNCT
iajs-3265	236	78	2	2	NUM
iajs-3265	236	79	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	236	80	)	)	PUNCT
iajs-3265	236	81	)	)	PUNCT
iajs-3265	236	82	〉	〉	NOUN
iajs-3265	236	83	=	=	PUNCT
iajs-3265	236	84	〈	〈	NOUN
iajs-3265	236	85	𝑩𝑖(𝑥	𝑩𝑖(𝑥	NOUN
iajs-3265	236	86	)	)	PUNCT
iajs-3265	236	87	,	,	PUNCT
iajs-3265	236	88	0	0	NUM
iajs-3265	236	89	〉	〉	NOUN
iajs-3265	236	90	,	,	PUNCT
iajs-3265	236	91	∀	∀	NOUN
iajs-3265	236	92	0	0	NUM
iajs-3265	236	93	≤	≤	NUM
iajs-3265	236	94	𝑖	𝑖	SYM
iajs-3265	236	95	≤	≤	NOUN
iajs-3265	236	96	𝑛.	𝑛.	NOUN
iajs-3265	236	97	(	(	PUNCT
iajs-3265	236	98	42	42	NUM
iajs-3265	236	99	)	)	PUNCT
iajs-3265	236	100	moreover	moreover	ADV
iajs-3265	236	101	,	,	PUNCT
iajs-3265	236	102	implementing	implement	VERB
iajs-3265	236	103	the	the	DET
iajs-3265	236	104	i	i	PROPN
iajs-3265	236	105	-	-	PUNCT
iajs-3265	236	106	ecms	ecms	PROPN
iajs-3265	236	107	based	base	VERB
iajs-3265	236	108	on	on	ADP
iajs-3265	236	109	the	the	DET
iajs-3265	236	110	laguerre	laguerre	NOUN
iajs-3265	236	111	polynomials	polynomial	NOUN
iajs-3265	236	112	by	by	ADP
iajs-3265	236	113	substituting	substitute	VERB
iajs-3265	236	114	equations	equation	NOUN
iajs-3265	236	115	(	(	PUNCT
iajs-3265	236	116	27	27	NUM
iajs-3265	236	117	)	)	PUNCT
iajs-3265	236	118	and	and	CCONJ
iajs-3265	236	119	(	(	PUNCT
iajs-3265	236	120	28	28	NUM
iajs-3265	236	121	)	)	PUNCT
iajs-3265	236	122	into	into	ADP
iajs-3265	236	123	equations	equation	NOUN
iajs-3265	236	124	(	(	PUNCT
iajs-3265	236	125	3	3	NUM
iajs-3265	236	126	)	)	PUNCT
iajs-3265	236	127	and	and	CCONJ
iajs-3265	236	128	(	(	PUNCT
iajs-3265	236	129	5	5	NUM
iajs-3265	236	130	)	)	PUNCT
iajs-3265	236	131	,	,	PUNCT
iajs-3265	236	132	it	it	PRON
iajs-3265	236	133	follows	follow	VERB
iajs-3265	236	134	that	that	SCONJ
iajs-3265	236	135	:	:	PUNCT
iajs-3265	236	136	𝜳(𝑥	𝜳(𝑥	NUM
iajs-3265	236	137	)	)	PUNCT
iajs-3265	236	138	(	(	PUNCT
iajs-3265	236	139	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	236	140	∗)3	∗)3	PUNCT
iajs-3265	236	141	𝑨	𝑨	NOUN
iajs-3265	236	142	+	+	CCONJ
iajs-3265	236	143	1	1	NUM
iajs-3265	236	144	2	2	NUM
iajs-3265	236	145	(	(	PUNCT
iajs-3265	236	146	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	236	147	)	)	PUNCT
iajs-3265	236	148	𝑨)(𝜳(𝑥	𝑨)(𝜳(𝑥	NOUN
iajs-3265	236	149	)	)	PUNCT
iajs-3265	236	150	(	(	PUNCT
iajs-3265	236	151	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	236	152	∗)2	∗)2	PROPN
iajs-3265	236	153	𝑨	𝑨	PROPN
iajs-3265	236	154	)	)	PUNCT
iajs-3265	236	155	=	=	SYM
iajs-3265	236	156	0	0	NUM
iajs-3265	236	157	,	,	PUNCT
iajs-3265	236	158	𝜳(0	𝜳(0	NUM
iajs-3265	236	159	)	)	PUNCT
iajs-3265	236	160	𝑨	𝑨	NOUN
iajs-3265	236	161	=	=	SYM
iajs-3265	236	162	0	0	NUM
iajs-3265	236	163	,	,	PUNCT
iajs-3265	236	164	𝜳(0	𝜳(0	NUM
iajs-3265	236	165	)	)	PUNCT
iajs-3265	236	166	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	236	167	∗	∗	NOUN
iajs-3265	236	168	𝑨	𝑨	NOUN
iajs-3265	236	169	=	=	SYM
iajs-3265	236	170	0	0	NUM
iajs-3265	236	171	,	,	PUNCT
iajs-3265	236	172	𝜳(0	𝜳(0	NUM
iajs-3265	236	173	)	)	PUNCT
iajs-3265	236	174	(	(	PUNCT
iajs-3265	236	175	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	236	176	∗)2	∗)2	PROPN
iajs-3265	236	177	𝑨	𝑨	NOUN
iajs-3265	236	178	=	=	SYM
iajs-3265	236	179	𝛼.	𝛼.	NOUN
iajs-3265	236	180	(	(	PUNCT
iajs-3265	236	181	43	43	NUM
iajs-3265	236	182	)	)	PUNCT
iajs-3265	236	183	then	then	ADV
iajs-3265	236	184	,	,	PUNCT
iajs-3265	236	185	the	the	DET
iajs-3265	236	186	processes	process	NOUN
iajs-3265	236	187	have	have	AUX
iajs-3265	236	188	been	be	AUX
iajs-3265	236	189	utilized	utilize	VERB
iajs-3265	236	190	as	as	ADP
iajs-3265	236	191	given	give	VERB
iajs-3265	236	192	in	in	ADP
iajs-3265	236	193	equations	equation	NOUN
iajs-3265	236	194	(	(	PUNCT
iajs-3265	236	195	18	18	NUM
iajs-3265	236	196	)	)	PUNCT
iajs-3265	236	197	and	and	CCONJ
iajs-3265	236	198	(	(	PUNCT
iajs-3265	236	199	19	19	NUM
iajs-3265	236	200	)	)	PUNCT
iajs-3265	236	201	,	,	PUNCT
iajs-3265	236	202	which	which	PRON
iajs-3265	236	203	will	will	AUX
iajs-3265	236	204	be	be	AUX
iajs-3265	236	205	presented	present	VERB
iajs-3265	236	206	:	:	PUNCT
iajs-3265	236	207	〈	〈	NOUN
iajs-3265	236	208	𝑳𝑖(𝑥),𝜳(𝑥	𝑳𝑖(𝑥),𝜳(𝑥	ADJ
iajs-3265	236	209	)	)	PUNCT
iajs-3265	236	210	(	(	PUNCT
iajs-3265	236	211	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	236	212	∗)3	∗)3	PUNCT
iajs-3265	236	213	𝑨	𝑨	NOUN
iajs-3265	236	214	+	+	CCONJ
iajs-3265	236	215	1	1	NUM
iajs-3265	236	216	2	2	NUM
iajs-3265	236	217	(	(	PUNCT
iajs-3265	236	218	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	236	219	)	)	PUNCT
iajs-3265	236	220	𝑨)(𝜳(𝑥	𝑨)(𝜳(𝑥	NOUN
iajs-3265	236	221	)	)	PUNCT
iajs-3265	236	222	(	(	PUNCT
iajs-3265	236	223	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	236	224	∗)2	∗)2	PROPN
iajs-3265	236	225	𝑨	𝑨	NOUN
iajs-3265	236	226	)	)	PUNCT
iajs-3265	236	227	〉	〉	NOUN
iajs-3265	236	228	=	=	PUNCT
iajs-3265	237	1	〈	〈	PROPN
iajs-3265	237	2	𝑳𝑖(𝑥	𝑳𝑖(𝑥	NOUN
iajs-3265	237	3	)	)	PUNCT
iajs-3265	237	4	,	,	PUNCT
iajs-3265	237	5	0	0	NUM
iajs-3265	237	6	〉	〉	NOUN
iajs-3265	237	7	,	,	PUNCT
iajs-3265	237	8	∀	∀	NOUN
iajs-3265	237	9	0	0	NUM
iajs-3265	237	10	≤	≤	NUM
iajs-3265	237	11	𝑖	𝑖	SYM
iajs-3265	237	12	≤	≤	NOUN
iajs-3265	237	13	𝑛.	𝑛.	NOUN
iajs-3265	237	14	(	(	PUNCT
iajs-3265	237	15	44	44	NUM
iajs-3265	237	16	)	)	PUNCT
iajs-3265	237	17	furthermore	furthermore	ADV
iajs-3265	237	18	,	,	PUNCT
iajs-3265	237	19	the	the	DET
iajs-3265	237	20	inner	inner	ADJ
iajs-3265	237	21	product	product	NOUN
iajs-3265	237	22	for	for	ADP
iajs-3265	237	23	the	the	DET
iajs-3265	237	24	left	left	ADJ
iajs-3265	237	25	and	and	CCONJ
iajs-3265	237	26	right	right	ADJ
iajs-3265	237	27	sides	side	NOUN
iajs-3265	237	28	of	of	ADP
iajs-3265	237	29	the	the	DET
iajs-3265	237	30	equations	equation	NOUN
iajs-3265	237	31	(	(	PUNCT
iajs-3265	237	32	38	38	NUM
iajs-3265	237	33	)	)	PUNCT
iajs-3265	237	34	,	,	PUNCT
iajs-3265	237	35	(	(	PUNCT
iajs-3265	237	36	40	40	NUM
iajs-3265	237	37	)	)	PUNCT
iajs-3265	237	38	,	,	PUNCT
iajs-3265	237	39	(	(	PUNCT
iajs-3265	237	40	42	42	NUM
iajs-3265	237	41	)	)	PUNCT
iajs-3265	237	42	,	,	PUNCT
iajs-3265	237	43	and	and	CCONJ
iajs-3265	237	44	(	(	PUNCT
iajs-3265	237	45	44	44	NUM
iajs-3265	237	46	)	)	PUNCT
iajs-3265	237	47	,	,	PUNCT
iajs-3265	237	48	respectively	respectively	ADV
iajs-3265	237	49	,	,	PUNCT
iajs-3265	237	50	is	be	AUX
iajs-3265	237	51	implemented	implement	VERB
iajs-3265	237	52	to	to	PART
iajs-3265	237	53	obtain	obtain	VERB
iajs-3265	237	54	the	the	DET
iajs-3265	237	55	values	value	NOUN
iajs-3265	237	56	of	of	ADP
iajs-3265	237	57	𝑨	𝑨	NOUN
iajs-3265	237	58	=	=	PUNCT
iajs-3265	238	1	[	[	X
iajs-3265	238	2	𝑎0	𝑎0	ADV
iajs-3265	238	3	𝑎1	𝑎1	VERB
iajs-3265	238	4	𝑎2	𝑎2	NOUN
iajs-3265	238	5	…	…	PUNCT
iajs-3265	238	6	𝑎𝑛]𝑇by	𝑎𝑛]𝑇by	NOUN
iajs-3265	238	7	solving	solve	VERB
iajs-3265	238	8	the	the	DET
iajs-3265	238	9	algebraic	algebraic	ADJ
iajs-3265	238	10	system	system	NOUN
iajs-3265	238	11	of	of	ADP
iajs-3265	238	12	equations	equation	NOUN
iajs-3265	238	13	.	.	PUNCT
iajs-3265	239	1	then	then	ADV
iajs-3265	239	2	,	,	PUNCT
iajs-3265	239	3	the	the	DET
iajs-3265	239	4	desired	desire	VERB
iajs-3265	239	5	novel	novel	ADJ
iajs-3265	239	6	approximate	approximate	ADJ
iajs-3265	239	7	solutions	solution	NOUN
iajs-3265	239	8	are	be	AUX
iajs-3265	239	9	achieved	achieve	VERB
iajs-3265	239	10	by	by	ADP
iajs-3265	239	11	applying	apply	VERB
iajs-3265	239	12	the	the	DET
iajs-3265	239	13	initial	initial	ADJ
iajs-3265	239	14	conditions	condition	NOUN
iajs-3265	239	15	to	to	ADP
iajs-3265	239	16	equations	equation	NOUN
iajs-3265	239	17	(	(	PUNCT
iajs-3265	239	18	37	37	NUM
iajs-3265	239	19	)	)	PUNCT
iajs-3265	239	20	,	,	PUNCT
iajs-3265	239	21	(	(	PUNCT
iajs-3265	239	22	39	39	NUM
iajs-3265	239	23	)	)	PUNCT
iajs-3265	239	24	,	,	PUNCT
iajs-3265	239	25	(	(	PUNCT
iajs-3265	239	26	41	41	NUM
iajs-3265	239	27	)	)	PUNCT
iajs-3265	239	28	,	,	PUNCT
iajs-3265	239	29	and	and	CCONJ
iajs-3265	239	30	(	(	PUNCT
iajs-3265	239	31	43	43	NUM
iajs-3265	239	32	)	)	PUNCT
iajs-3265	239	33	,	,	PUNCT
iajs-3265	239	34	respectively	respectively	ADV
iajs-3265	239	35	.	.	PUNCT
iajs-3265	240	1	in	in	ADP
iajs-3265	240	2	this	this	DET
iajs-3265	240	3	problem	problem	NOUN
iajs-3265	240	4	,	,	PUNCT
iajs-3265	240	5	we	we	PRON
iajs-3265	240	6	consider	consider	VERB
iajs-3265	240	7	the	the	DET
iajs-3265	240	8	value	value	NOUN
iajs-3265	240	9	of	of	ADP
iajs-3265	240	10	𝛼	𝛼	NOUN
iajs-3265	240	11	=	=	SYM
iajs-3265	240	12	0.3320573	0.3320573	NUM
iajs-3265	240	13	,	,	PUNCT
iajs-3265	240	14	as	as	ADP
iajs-3265	240	15	in	in	ADP
iajs-3265	240	16	[	[	X
iajs-3265	240	17	43	43	NUM
iajs-3265	240	18	]	]	PUNCT
iajs-3265	240	19	with	with	ADP
iajs-3265	240	20	𝑛	𝑛	PROPN
iajs-3265	240	21	=	=	SYM
iajs-3265	240	22	10	10	NUM
iajs-3265	240	23	.	.	PUNCT
iajs-3265	241	1	the	the	DET
iajs-3265	241	2	novel	novel	ADJ
iajs-3265	241	3	approximate	approximate	ADJ
iajs-3265	241	4	polynomials	polynomial	NOUN
iajs-3265	241	5	for	for	ADP
iajs-3265	241	6	the	the	DET
iajs-3265	241	7	blasius	blasius	ADJ
iajs-3265	241	8	equation	equation	NOUN
iajs-3265	241	9	are	be	AUX
iajs-3265	241	10	:	:	PUNCT
iajs-3265	241	11	by	by	ADP
iajs-3265	241	12	using	use	VERB
iajs-3265	241	13	the	the	DET
iajs-3265	241	14	ecm	ecm	NOUN
iajs-3265	241	15	based	base	VERB
iajs-3265	241	16	on	on	ADP
iajs-3265	241	17	the	the	DET
iajs-3265	241	18	standard	standard	ADJ
iajs-3265	241	19	polynomials	polynomial	NOUN
iajs-3265	241	20	:	:	PUNCT
iajs-3265	241	21	𝑦(𝑥	𝑦(𝑥	NUM
iajs-3265	241	22	)	)	PUNCT
iajs-3265	241	23	≈	≈	PROPN
iajs-3265	241	24	0.166029	0.166029	NUM
iajs-3265	241	25	𝑥2	𝑥2	NOUN
iajs-3265	241	26	+	+	CCONJ
iajs-3265	241	27	3.40035	3.40035	NUM
iajs-3265	241	28	×	×	NOUN
iajs-3265	241	29	10−9𝑥3	10−9𝑥3	NOUN
iajs-3265	241	30	−	−	PROPN
iajs-3265	242	1	2.07849	2.07849	NUM
iajs-3265	242	2	×	×	NOUN
iajs-3265	242	3	10−8𝑥4	10−8𝑥4	NUM
iajs-3265	242	4	−	−	PROPN
iajs-3265	242	5	0.000459348	0.000459348	NUM
iajs-3265	242	6	𝑥5	𝑥5	ADV
iajs-3265	242	7	−	−	PROPN
iajs-3265	242	8	1.85524	1.85524	NUM
iajs-3265	242	9	×	×	NOUN
iajs-3265	242	10	10−7𝑥6	10−7𝑥6	NUM
iajs-3265	242	11	+	+	CCONJ
iajs-3265	242	12	2.93847	2.93847	NUM
iajs-3265	242	13	×	×	NOUN
iajs-3265	242	14	10−7𝑥7	10−7𝑥7	NUM
iajs-3265	242	15	+	+	CCONJ
iajs-3265	242	16	2.1901	2.1901	NUM
iajs-3265	242	17	×	×	NOUN
iajs-3265	242	18	10−6𝑥8	10−6𝑥8	NUM
iajs-3265	242	19	+	+	CCONJ
iajs-3265	242	20	2.05083	2.05083	NUM
iajs-3265	242	21	×	×	NOUN
iajs-3265	242	22	10−7𝑥9	10−7𝑥9	NUM
iajs-3265	242	23	−	−	NUM
iajs-3265	242	24	8.02077	8.02077	NUM
iajs-3265	242	25	×	×	NOUN
iajs-3265	242	26	10−8𝑥10	10−8𝑥10	NUM
iajs-3265	242	27	.	.	PUNCT
iajs-3265	243	1	also	also	ADV
iajs-3265	243	2	,	,	PUNCT
iajs-3265	243	3	by	by	ADP
iajs-3265	243	4	applying	apply	VERB
iajs-3265	243	5	the	the	DET
iajs-3265	243	6	i	i	PROPN
iajs-3265	243	7	-	-	PUNCT
iajs-3265	243	8	ecms	ecms	PROPN
iajs-3265	243	9	based	base	VERB
iajs-3265	243	10	on	on	ADP
iajs-3265	243	11	the	the	DET
iajs-3265	243	12	first	first	ADJ
iajs-3265	243	13	kind	kind	NOUN
iajs-3265	243	14	of	of	ADP
iajs-3265	243	15	the	the	DET
iajs-3265	243	16	chebyshev	chebyshev	NOUN
iajs-3265	243	17	polynomials	polynomial	NOUN
iajs-3265	243	18	,	,	PUNCT
iajs-3265	243	19	we	we	PRON
iajs-3265	243	20	obtain	obtain	VERB
iajs-3265	243	21	:	:	PUNCT
iajs-3265	243	22	𝑦(𝑥	𝑦(𝑥	X
iajs-3265	243	23	)	)	PUNCT
iajs-3265	243	24	≈	≈	PROPN
iajs-3265	243	25	0.166029	0.166029	NUM
iajs-3265	243	26	𝑥2	𝑥2	NOUN
iajs-3265	243	27	+	+	CCONJ
iajs-3265	243	28	2.73849	2.73849	NUM
iajs-3265	243	29	×	×	NOUN
iajs-3265	243	30	10−10𝑥3	10−10𝑥3	NOUN
iajs-3265	243	31	−	−	ADP
iajs-3265	243	32	4.13564	4.13564	NUM
iajs-3265	243	33	×	×	NOUN
iajs-3265	243	34	10−9𝑥4	10−9𝑥4	NUM
iajs-3265	243	35	−	−	PROPN
iajs-3265	243	36	0.000459399	0.000459399	NUM
iajs-3265	243	37	𝑥5	𝑥5	PROPN
iajs-3265	243	38	−	−	PROPN
iajs-3265	243	39	8.68423	8.68423	NUM
iajs-3265	243	40	×	×	NOUN
iajs-3265	243	41	10−8𝑥6	10−8𝑥6	NUM
iajs-3265	243	42	+	+	CCONJ
iajs-3265	244	1	1.75903	1.75903	NUM
iajs-3265	244	2	×	×	NOUN
iajs-3265	244	3	10−7𝑥7	10−7𝑥7	NUM
iajs-3265	244	4	+	+	CCONJ
iajs-3265	244	5	2.2761	2.2761	NUM
iajs-3265	244	6	×	×	NOUN
iajs-3265	244	7	10−6𝑥8	10−6𝑥8	NUM
iajs-3265	244	8	+	+	CCONJ
iajs-3265	244	9	1.70069	1.70069	NUM
iajs-3265	244	10	×	×	NOUN
iajs-3265	244	11	10−7𝑥9	10−7𝑥9	NUM
iajs-3265	244	12	−	−	PROPN
iajs-3265	244	13	7.41017	7.41017	NUM
iajs-3265	244	14	×	×	NOUN
iajs-3265	244	15	10−8𝑥10	10−8𝑥10	NUM
iajs-3265	244	16	.	.	PUNCT
iajs-3265	245	1	moreover	moreover	ADV
iajs-3265	245	2	,	,	PUNCT
iajs-3265	245	3	by	by	ADP
iajs-3265	245	4	implementing	implement	VERB
iajs-3265	245	5	the	the	DET
iajs-3265	245	6	i	i	PROPN
iajs-3265	245	7	-	-	PUNCT
iajs-3265	245	8	ecms	ecms	PROPN
iajs-3265	245	9	based	base	VERB
iajs-3265	245	10	on	on	ADP
iajs-3265	245	11	the	the	DET
iajs-3265	245	12	bernoulli	bernoulli	NOUN
iajs-3265	245	13	polynomials	polynomial	NOUN
iajs-3265	245	14	,	,	PUNCT
iajs-3265	245	15	we	we	PRON
iajs-3265	245	16	achieve	achieve	VERB
iajs-3265	245	17	:	:	PUNCT
iajs-3265	245	18	𝑦(𝑥	𝑦(𝑥	X
iajs-3265	245	19	)	)	PUNCT
iajs-3265	245	20	≈	≈	PROPN
iajs-3265	245	21	0.166029	0.166029	NUM
iajs-3265	245	22	𝑥2	𝑥2	NOUN
iajs-3265	245	23	+	+	CCONJ
iajs-3265	245	24	2.44299	2.44299	NUM
iajs-3265	245	25	×	×	NOUN
iajs-3265	245	26	10−10𝑥3	10−10𝑥3	NOUN
iajs-3265	245	27	−	−	PROPN
iajs-3265	245	28	3.8326	3.8326	NUM
iajs-3265	245	29	×	×	NOUN
iajs-3265	245	30	10−9𝑥4	10−9𝑥4	NUM
iajs-3265	245	31	−	−	PROPN
iajs-3265	245	32	0.000459401	0.000459401	NUM
iajs-3265	245	33	𝑥5	𝑥5	PROPN
iajs-3265	245	34	−	−	PROPN
iajs-3265	245	35	8.36908	8.36908	NUM
iajs-3265	245	36	×	×	NOUN
iajs-3265	245	37	10−8𝑥6	10−8𝑥6	NUM
iajs-3265	245	38	+	+	NOUN
iajs-3265	245	39	1.71538	1.71538	NUM
iajs-3265	245	40	×	×	NOUN
iajs-3265	245	41	10−7𝑥7	10−7𝑥7	NUM
iajs-3265	245	42	+	+	CCONJ
iajs-3265	245	43	2.27964	2.27964	NUM
iajs-3265	245	44	×	×	NOUN
iajs-3265	245	45	10−6𝑥8	10−6𝑥8	NUM
iajs-3265	245	46	+	+	CCONJ
iajs-3265	245	47	1.68511	1.68511	NUM
iajs-3265	245	48	×	×	NOUN
iajs-3265	245	49	10−7𝑥9	10−7𝑥9	NUM
iajs-3265	245	50	−	−	PROPN
iajs-3265	245	51	7.38136	7.38136	NUM
iajs-3265	245	52	×	×	NOUN
iajs-3265	245	53	10−8𝑥10	10−8𝑥10	NUM
iajs-3265	245	54	.	.	PUNCT
iajs-3265	246	1	in	in	ADP
iajs-3265	246	2	addition	addition	NOUN
iajs-3265	246	3	,	,	PUNCT
iajs-3265	246	4	by	by	ADP
iajs-3265	246	5	utilizing	utilize	VERB
iajs-3265	246	6	the	the	DET
iajs-3265	246	7	i	i	PROPN
iajs-3265	246	8	-	-	PUNCT
iajs-3265	246	9	ecms	ecms	PROPN
iajs-3265	246	10	based	base	VERB
iajs-3265	246	11	on	on	ADP
iajs-3265	246	12	the	the	DET
iajs-3265	246	13	laguerre	laguerre	NOUN
iajs-3265	246	14	polynomials	polynomial	NOUN
iajs-3265	246	15	,	,	PUNCT
iajs-3265	246	16	we	we	PRON
iajs-3265	246	17	get	get	VERB
iajs-3265	246	18	:	:	PUNCT
iajs-3265	246	19	𝑦(𝑥	𝑦(𝑥	X
iajs-3265	246	20	)	)	PUNCT
iajs-3265	247	1	≈	≈	PROPN
iajs-3265	247	2	0.166029	0.166029	NUM
iajs-3265	247	3	𝑥2	𝑥2	NOUN
iajs-3265	247	4	+	+	CCONJ
iajs-3265	247	5	1.27153	1.27153	NUM
iajs-3265	247	6	×	×	NOUN
iajs-3265	247	7	10−10𝑥3	10−10𝑥3	NOUN
iajs-3265	247	8	−	−	PROPN
iajs-3265	247	9	2.35939	2.35939	NUM
iajs-3265	247	10	×	×	NOUN
iajs-3265	247	11	10−9𝑥4	10−9𝑥4	NUM
iajs-3265	247	12	−	−	PROPN
iajs-3265	247	13	0.000459408	0.000459408	NUM
iajs-3265	247	14	𝑥5	𝑥5	ADV
iajs-3265	247	15	−	−	PROPN
iajs-3265	247	16	6.42605	6.42605	NUM
iajs-3265	247	17	×	×	NOUN
iajs-3265	247	18	10−8𝑥6	10−8𝑥6	NUM
iajs-3265	247	19	+	+	NUM
iajs-3265	247	20	1.42272	1.42272	NUM
iajs-3265	247	21	×	×	NOUN
iajs-3265	247	22	10−7𝑥7	10−7𝑥7	NUM
iajs-3265	247	23	+	+	CCONJ
iajs-3265	247	24	2.3051	2.3051	NUM
iajs-3265	247	25	×	×	NOUN
iajs-3265	247	26	10−6𝑥8	10−6𝑥8	NUM
iajs-3265	247	27	+	+	CCONJ
iajs-3265	247	28	1.56588	1.56588	NUM
iajs-3265	247	29	×	×	NOUN
iajs-3265	247	30	10−7𝑥9	10−7𝑥9	NUM
iajs-3265	247	31	−	−	PROPN
iajs-3265	247	32	7.14836	7.14836	NUM
iajs-3265	247	33	×	×	NOUN
iajs-3265	247	34	10−8𝑥10	10−8𝑥10	NUM
iajs-3265	247	35	.	.	PUNCT
iajs-3265	248	1	the	the	DET
iajs-3265	248	2	exact	exact	ADJ
iajs-3265	248	3	solution	solution	NOUN
iajs-3265	248	4	to	to	ADP
iajs-3265	248	5	the	the	DET
iajs-3265	248	6	blasius	blasius	ADJ
iajs-3265	248	7	equation	equation	NOUN
iajs-3265	248	8	is	be	AUX
iajs-3265	248	9	not	not	PART
iajs-3265	248	10	available	available	ADJ
iajs-3265	248	11	.	.	PUNCT
iajs-3265	249	1	hence	hence	ADV
iajs-3265	249	2	,	,	PUNCT
iajs-3265	249	3	the	the	DET
iajs-3265	249	4	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	249	5	has	have	AUX
iajs-3265	249	6	been	be	AUX
iajs-3265	249	7	calculated	calculate	VERB
iajs-3265	249	8	to	to	PART
iajs-3265	249	9	demonstrate	demonstrate	VERB
iajs-3265	249	10	the	the	DET
iajs-3265	249	11	accuracy	accuracy	NOUN
iajs-3265	249	12	of	of	ADP
iajs-3265	249	13	the	the	DET
iajs-3265	249	14	novel	novel	ADJ
iajs-3265	249	15	approximate	approximate	ADJ
iajs-3265	249	16	solutions	solution	NOUN
iajs-3265	249	17	obtained	obtain	VERB
iajs-3265	249	18	by	by	ADP
iajs-3265	249	19	the	the	DET
iajs-3265	249	20	proposed	propose	VERB
iajs-3265	249	21	techniques	technique	NOUN
iajs-3265	249	22	.	.	PUNCT
iajs-3265	250	1	the	the	DET
iajs-3265	250	2	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	250	3	is	be	AUX
iajs-3265	250	4	calculated	calculate	VERB
iajs-3265	250	5	by	by	ADP
iajs-3265	250	6	:	:	PUNCT
iajs-3265	250	7	ihjpas	ihjpas	PROPN
iajs-3265	250	8	.	.	PUNCT
iajs-3265	251	1	36	36	NUM
iajs-3265	251	2	(	(	PUNCT
iajs-3265	251	3	4	4	NUM
iajs-3265	251	4	)	)	PUNCT
iajs-3265	251	5	2023	2023	NUM
iajs-3265	251	6	350	350	NUM
iajs-3265	251	7	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	251	8	=	=	PUNCT
iajs-3265	251	9	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
iajs-3265	251	10	0≤𝑥≤1	0≤𝑥≤1	ADJ
iajs-3265	251	11	|𝑦′′′(𝑥	|𝑦′′′(𝑥	PUNCT
iajs-3265	251	12	)	)	PUNCT
iajs-3265	252	1	+	+	CCONJ
iajs-3265	252	2	1	1	NUM
iajs-3265	252	3	2	2	NUM
iajs-3265	252	4	𝑦(𝑥	𝑦(𝑥	PROPN
iajs-3265	252	5	)	)	PUNCT
iajs-3265	252	6	𝑦′′(𝑥)|	𝑦′′(𝑥)|	NUM
iajs-3265	252	7	.	.	PUNCT
iajs-3265	253	1	figure	figure	VERB
iajs-3265	253	2	4	4	NUM
iajs-3265	253	3	shows	show	VERB
iajs-3265	253	4	the	the	DET
iajs-3265	253	5	logarithmic	logarithmic	ADJ
iajs-3265	253	6	plots	plot	NOUN
iajs-3265	253	7	for	for	ADP
iajs-3265	253	8	the	the	DET
iajs-3265	253	9	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	253	10	values	value	NOUN
iajs-3265	253	11	obtained	obtain	VERB
iajs-3265	253	12	by	by	ADP
iajs-3265	253	13	the	the	DET
iajs-3265	253	14	ecm	ecm	NOUN
iajs-3265	253	15	based	base	VERB
iajs-3265	253	16	on	on	ADP
iajs-3265	253	17	the	the	DET
iajs-3265	253	18	standard	standard	ADJ
iajs-3265	253	19	polynomials	polynomial	NOUN
iajs-3265	253	20	and	and	CCONJ
iajs-3265	253	21	by	by	ADP
iajs-3265	253	22	the	the	DET
iajs-3265	253	23	i	i	PROPN
iajs-3265	253	24	-	-	PUNCT
iajs-3265	253	25	ecms	ecms	PROPN
iajs-3265	253	26	based	base	VERB
iajs-3265	253	27	on	on	ADP
iajs-3265	253	28	the	the	DET
iajs-3265	253	29	chebyshev	chebyshev	NOUN
iajs-3265	253	30	,	,	PUNCT
iajs-3265	253	31	bernoulli	bernoulli	PROPN
iajs-3265	253	32	,	,	PUNCT
iajs-3265	253	33	and	and	CCONJ
iajs-3265	253	34	laguerre	laguerre	NOUN
iajs-3265	253	35	polynomials	polynomial	NOUN
iajs-3265	253	36	,	,	PUNCT
iajs-3265	253	37	for	for	ADP
iajs-3265	253	38	𝑛	𝑛	PRON
iajs-3265	253	39	=	=	SYM
iajs-3265	253	40	3	3	NUM
iajs-3265	253	41	to	to	PART
iajs-3265	253	42	10	10	NUM
iajs-3265	253	43	,	,	PUNCT
iajs-3265	253	44	with	with	ADP
iajs-3265	253	45	a	a	DET
iajs-3265	253	46	value	value	NOUN
iajs-3265	253	47	of	of	ADP
iajs-3265	253	48	𝛼	𝛼	NOUN
iajs-3265	253	49	=	=	SYM
iajs-3265	253	50	0.3320573	0.3320573	NUM
iajs-3265	253	51	,	,	PUNCT
iajs-3265	253	52	according	accord	VERB
iajs-3265	253	53	to	to	ADP
iajs-3265	253	54	previous	previous	ADJ
iajs-3265	253	55	studies	study	NOUN
iajs-3265	253	56	[	[	X
iajs-3265	253	57	43	43	NUM
iajs-3265	253	58	]	]	PUNCT
iajs-3265	253	59	.	.	PUNCT
iajs-3265	254	1	the	the	DET
iajs-3265	254	2	accuracy	accuracy	NOUN
iajs-3265	254	3	and	and	CCONJ
iajs-3265	254	4	efficiency	efficiency	NOUN
iajs-3265	254	5	of	of	ADP
iajs-3265	254	6	these	these	DET
iajs-3265	254	7	methods	method	NOUN
iajs-3265	254	8	can	can	AUX
iajs-3265	254	9	be	be	AUX
iajs-3265	254	10	demonstrated	demonstrate	VERB
iajs-3265	254	11	by	by	ADP
iajs-3265	254	12	observing	observe	VERB
iajs-3265	254	13	the	the	DET
iajs-3265	254	14	error	error	NOUN
iajs-3265	254	15	values	value	NOUN
iajs-3265	254	16	for	for	ADP
iajs-3265	254	17	𝑛	𝑛	NOUN
iajs-3265	254	18	,	,	PUNCT
iajs-3265	254	19	as	as	SCONJ
iajs-3265	254	20	we	we	PRON
iajs-3265	254	21	observed	observe	VERB
iajs-3265	254	22	that	that	SCONJ
iajs-3265	254	23	the	the	DET
iajs-3265	254	24	error	error	NOUN
iajs-3265	254	25	decreases	decrease	VERB
iajs-3265	254	26	as	as	ADP
iajs-3265	254	27	the	the	DET
iajs-3265	254	28	value	value	NOUN
iajs-3265	254	29	of	of	ADP
iajs-3265	254	30	𝑛	𝑛	DET
iajs-3265	254	31	increases	increase	NOUN
iajs-3265	254	32	.	.	PUNCT
iajs-3265	255	1	figure	figure	VERB
iajs-3265	255	2	4	4	NUM
iajs-3265	255	3	.	.	PUNCT
iajs-3265	256	1	logarithmic	logarithmic	ADJ
iajs-3265	256	2	plots	plot	NOUN
iajs-3265	256	3	of	of	ADP
iajs-3265	256	4	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	256	5	for	for	ADP
iajs-3265	256	6	the	the	DET
iajs-3265	256	7	blasius	blasius	ADJ
iajs-3265	256	8	equation	equation	NOUN
iajs-3265	256	9	.	.	PUNCT
iajs-3265	257	1	figure	figure	NOUN
iajs-3265	257	2	5	5	NUM
iajs-3265	257	3	also	also	ADV
iajs-3265	257	4	illustrates	illustrate	VERB
iajs-3265	257	5	the	the	DET
iajs-3265	257	6	comparison	comparison	NOUN
iajs-3265	257	7	between	between	ADP
iajs-3265	257	8	the	the	DET
iajs-3265	257	9	novel	novel	ADJ
iajs-3265	257	10	approximate	approximate	ADJ
iajs-3265	257	11	solutions	solution	NOUN
iajs-3265	257	12	calculated	calculate	VERB
iajs-3265	257	13	by	by	ADP
iajs-3265	257	14	the	the	DET
iajs-3265	257	15	proposed	propose	VERB
iajs-3265	257	16	techniques	technique	NOUN
iajs-3265	257	17	for	for	ADP
iajs-3265	257	18	𝑛	𝑛	NOUN
iajs-3265	257	19	=	=	SYM
iajs-3265	257	20	10	10	NUM
iajs-3265	257	21	and	and	CCONJ
iajs-3265	257	22	𝛼	𝛼	ADJ
iajs-3265	257	23	=	=	ADJ
iajs-3265	257	24	0.3320573	0.3320573	NUM
iajs-3265	257	25	.	.	PUNCT
iajs-3265	258	1	the	the	DET
iajs-3265	258	2	figure	figure	NOUN
iajs-3265	258	3	shows	show	VERB
iajs-3265	258	4	that	that	SCONJ
iajs-3265	258	5	all	all	PRON
iajs-3265	258	6	of	of	ADP
iajs-3265	258	7	the	the	DET
iajs-3265	258	8	suggested	suggest	VERB
iajs-3265	258	9	methods	method	NOUN
iajs-3265	258	10	have	have	AUX
iajs-3265	258	11	obtained	obtain	VERB
iajs-3265	258	12	good	good	ADJ
iajs-3265	258	13	agreement	agreement	NOUN
iajs-3265	258	14	.	.	PUNCT
iajs-3265	259	1	figure	figure	NOUN
iajs-3265	259	2	5	5	NUM
iajs-3265	259	3	.	.	PUNCT
iajs-3265	260	1	the	the	DET
iajs-3265	260	2	comparison	comparison	NOUN
iajs-3265	260	3	of	of	ADP
iajs-3265	260	4	the	the	DET
iajs-3265	260	5	solutions	solution	NOUN
iajs-3265	260	6	for	for	ADP
iajs-3265	260	7	the	the	DET
iajs-3265	260	8	blasius	blasius	ADJ
iajs-3265	260	9	equation	equation	NOUN
iajs-3265	260	10	.	.	PUNCT
iajs-3265	261	1	table	table	NOUN
iajs-3265	261	2	2	2	NUM
iajs-3265	261	3	also	also	ADV
iajs-3265	261	4	presents	present	VERB
iajs-3265	261	5	the	the	DET
iajs-3265	261	6	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	261	7	values	value	NOUN
iajs-3265	261	8	for	for	ADP
iajs-3265	261	9	the	the	DET
iajs-3265	261	10	novel	novel	ADJ
iajs-3265	261	11	approximate	approximate	ADJ
iajs-3265	261	12	solutions	solution	NOUN
iajs-3265	261	13	obtained	obtain	VERB
iajs-3265	261	14	with	with	ADP
iajs-3265	261	15	the	the	DET
iajs-3265	261	16	ecm	ecm	NOUN
iajs-3265	261	17	and	and	CCONJ
iajs-3265	261	18	the	the	DET
iajs-3265	261	19	i	i	PROPN
iajs-3265	261	20	-	-	PUNCT
iajs-3265	261	21	ecms	ecms	PROPN
iajs-3265	261	22	with	with	ADP
iajs-3265	261	23	𝑛	𝑛	PROPN
iajs-3265	261	24	=	=	SYM
iajs-3265	261	25	10	10	NUM
iajs-3265	261	26	,	,	PUNCT
iajs-3265	261	27	illustrating	illustrate	VERB
iajs-3265	261	28	the	the	DET
iajs-3265	261	29	efficacy	efficacy	NOUN
iajs-3265	261	30	of	of	ADP
iajs-3265	261	31	these	these	DET
iajs-3265	261	32	methods	method	NOUN
iajs-3265	261	33	.	.	PUNCT
iajs-3265	262	1	furthermore	furthermore	ADV
iajs-3265	262	2	,	,	PUNCT
iajs-3265	262	3	it	it	PRON
iajs-3265	262	4	can	can	AUX
iajs-3265	262	5	be	be	AUX
iajs-3265	262	6	seen	see	VERB
iajs-3265	262	7	that	that	SCONJ
iajs-3265	262	8	the	the	DET
iajs-3265	262	9	i	i	PROPN
iajs-3265	262	10	-	-	PUNCT
iajs-3265	262	11	ecms	ecms	PROPN
iajs-3265	262	12	based	base	VERB
iajs-3265	262	13	on	on	ADP
iajs-3265	262	14	the	the	DET
iajs-3265	262	15	laguerre	laguerre	NOUN
iajs-3265	262	16	polynomials	polynomial	NOUN
iajs-3265	262	17	technique	technique	NOUN
iajs-3265	262	18	give	give	VERB
iajs-3265	262	19	good	good	ADJ
iajs-3265	262	20	accuracy	accuracy	NOUN
iajs-3265	262	21	with	with	ADP
iajs-3265	262	22	fewer	few	ADJ
iajs-3265	262	23	errors	error	NOUN
iajs-3265	262	24	compared	compare	VERB
iajs-3265	262	25	to	to	ADP
iajs-3265	262	26	the	the	DET
iajs-3265	262	27	other	other	ADJ
iajs-3265	262	28	methods	method	NOUN
iajs-3265	262	29	.	.	PUNCT
iajs-3265	263	1	table	table	NOUN
iajs-3265	263	2	2	2	NUM
iajs-3265	263	3	.	.	PUNCT
iajs-3265	264	1	the	the	DET
iajs-3265	264	2	comparison	comparison	NOUN
iajs-3265	264	3	between	between	ADP
iajs-3265	264	4	the	the	DET
iajs-3265	264	5	𝑀𝐸𝑅10	𝑀𝐸𝑅10	PROPN
iajs-3265	264	6	for	for	ADP
iajs-3265	264	7	the	the	DET
iajs-3265	264	8	blasius	blasius	ADJ
iajs-3265	264	9	equation	equation	NOUN
iajs-3265	264	10	by	by	ADP
iajs-3265	264	11	proposed	propose	VERB
iajs-3265	264	12	methods	method	NOUN
iajs-3265	264	13	.	.	PUNCT
iajs-3265	265	1	𝒏	𝒏	PROPN
iajs-3265	265	2	ecm	ecm	PROPN
iajs-3265	265	3	standard	standard	PROPN
iajs-3265	265	4	i	i	PROPN
iajs-3265	265	5	-	-	PUNCT
iajs-3265	265	6	ecms	ecms	PROPN
iajs-3265	265	7	chebyshev	chebyshev	NOUN
iajs-3265	265	8	i	i	PROPN
iajs-3265	265	9	-	-	PUNCT
iajs-3265	265	10	ecms	ecms	NOUN
iajs-3265	265	11	bernoulli	bernoulli	PROPN
iajs-3265	265	12	i	i	PROPN
iajs-3265	265	13	-	-	PUNCT
iajs-3265	265	14	ecms	ecms	PROPN
iajs-3265	265	15	laguerre	laguerre	NOUN
iajs-3265	265	16	10	10	NUM
iajs-3265	265	17	2.04021	2.04021	NUM
iajs-3265	265	18	×	×	NOUN
iajs-3265	265	19	10−8	10−8	NUM
iajs-3265	265	20	1.64309	1.64309	NUM
iajs-3265	265	21	×	×	NOUN
iajs-3265	265	22	10−9	10−9	NUM
iajs-3265	265	23	1.46579	1.46579	NUM
iajs-3265	265	24	×	×	NOUN
iajs-3265	265	25	10−9	10−9	NUM
iajs-3265	265	26	8.05404	8.05404	NUM
iajs-3265	265	27	×	×	NOUN
iajs-3265	265	28	10−10	10−10	NUM
iajs-3265	265	29	ihjpas	ihjpa	NOUN
iajs-3265	265	30	.	.	PUNCT
iajs-3265	266	1	36	36	NUM
iajs-3265	266	2	(	(	PUNCT
iajs-3265	266	3	4	4	NUM
iajs-3265	266	4	)	)	PUNCT
iajs-3265	266	5	2023	2023	NUM
iajs-3265	266	6	351	351	NUM
iajs-3265	266	7	4.3	4.3	NUM
iajs-3265	266	8	solving	solve	VERB
iajs-3265	266	9	the	the	DET
iajs-3265	266	10	falkner	falkner	PROPN
iajs-3265	266	11	-	-	PUNCT
iajs-3265	266	12	skan	skan	VERB
iajs-3265	266	13	equation	equation	NOUN
iajs-3265	266	14	by	by	ADP
iajs-3265	266	15	the	the	DET
iajs-3265	266	16	ecm	ecm	PROPN
iajs-3265	266	17	and	and	CCONJ
iajs-3265	266	18	i	i	PROPN
iajs-3265	266	19	-	-	PUNCT
iajs-3265	266	20	ecms	ecms	NOUN
iajs-3265	266	21	the	the	DET
iajs-3265	266	22	procedures	procedure	NOUN
iajs-3265	266	23	of	of	ADP
iajs-3265	266	24	the	the	DET
iajs-3265	266	25	ecm	ecm	NOUN
iajs-3265	266	26	and	and	CCONJ
iajs-3265	266	27	the	the	DET
iajs-3265	266	28	i	i	PROPN
iajs-3265	266	29	-	-	PUNCT
iajs-3265	266	30	ecms	ecms	NOUN
iajs-3265	266	31	techniques	technique	NOUN
iajs-3265	266	32	can	can	AUX
iajs-3265	266	33	be	be	AUX
iajs-3265	266	34	implemented	implement	VERB
iajs-3265	266	35	to	to	PART
iajs-3265	266	36	solve	solve	VERB
iajs-3265	266	37	the	the	DET
iajs-3265	266	38	third	third	ADJ
iajs-3265	266	39	problem	problem	NOUN
iajs-3265	266	40	introduced	introduce	VERB
iajs-3265	266	41	in	in	ADP
iajs-3265	266	42	equations	equation	NOUN
iajs-3265	266	43	(	(	PUNCT
iajs-3265	266	44	6	6	NUM
iajs-3265	266	45	)	)	PUNCT
iajs-3265	266	46	and	and	CCONJ
iajs-3265	266	47	(	(	PUNCT
iajs-3265	266	48	8)	8)	NUM
iajs-3265	266	49	.	.	PUNCT
iajs-3265	266	50	to	to	PART
iajs-3265	266	51	be	be	AUX
iajs-3265	266	52	more	more	ADV
iajs-3265	266	53	specific	specific	ADJ
iajs-3265	266	54	,	,	PUNCT
iajs-3265	266	55	for	for	ADP
iajs-3265	266	56	the	the	DET
iajs-3265	266	57	ecm	ecm	PROPN
iajs-3265	266	58	technique	technique	NOUN
iajs-3265	266	59	,	,	PUNCT
iajs-3265	266	60	we	we	PRON
iajs-3265	266	61	transform	transform	VERB
iajs-3265	266	62	the	the	DET
iajs-3265	266	63	unknown	unknown	ADJ
iajs-3265	266	64	function	function	NOUN
iajs-3265	266	65	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	266	66	)	)	PUNCT
iajs-3265	266	67	with	with	ADP
iajs-3265	266	68	its	its	PRON
iajs-3265	266	69	derivatives	derivative	NOUN
iajs-3265	266	70	as	as	ADP
iajs-3265	266	71	matrices	matrix	NOUN
iajs-3265	266	72	by	by	ADP
iajs-3265	266	73	substituting	substitute	VERB
iajs-3265	266	74	the	the	DET
iajs-3265	266	75	equations	equation	NOUN
iajs-3265	266	76	(	(	PUNCT
iajs-3265	266	77	12	12	NUM
iajs-3265	266	78	)	)	PUNCT
iajs-3265	266	79	and	and	CCONJ
iajs-3265	266	80	(	(	PUNCT
iajs-3265	266	81	13	13	NUM
iajs-3265	266	82	)	)	PUNCT
iajs-3265	266	83	into	into	ADP
iajs-3265	266	84	equations	equation	NOUN
iajs-3265	266	85	(	(	PUNCT
iajs-3265	266	86	6	6	NUM
iajs-3265	266	87	)	)	PUNCT
iajs-3265	266	88	and	and	CCONJ
iajs-3265	266	89	(	(	PUNCT
iajs-3265	266	90	8)	8)	NUM
iajs-3265	266	91	.	.	PUNCT
iajs-3265	267	1	thus	thus	ADV
iajs-3265	267	2	,	,	PUNCT
iajs-3265	267	3	we	we	PRON
iajs-3265	267	4	get	get	VERB
iajs-3265	267	5	the	the	DET
iajs-3265	267	6	following	follow	VERB
iajs-3265	267	7	result	result	NOUN
iajs-3265	267	8	:	:	PUNCT
iajs-3265	267	9	𝜳(𝑥	𝜳(𝑥	X
iajs-3265	267	10	)	)	PUNCT
iajs-3265	267	11	(	(	PUNCT
iajs-3265	267	12	𝑩∗)3	𝑩∗)3	ADV
iajs-3265	267	13	𝑨	𝑨	PROPN
iajs-3265	267	14	+	+	CCONJ
iajs-3265	267	15	(	(	PUNCT
iajs-3265	267	16	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	267	17	)	)	PUNCT
iajs-3265	267	18	𝑨)(𝜳(𝑥	𝑨)(𝜳(𝑥	NOUN
iajs-3265	267	19	)	)	PUNCT
iajs-3265	267	20	(	(	PUNCT
iajs-3265	267	21	𝑩∗)2	𝑩∗)2	ADV
iajs-3265	267	22	𝑨	𝑨	NOUN
iajs-3265	267	23	)	)	PUNCT
iajs-3265	267	24	+	+	NUM
iajs-3265	267	25	𝛽	𝛽	X
iajs-3265	267	26	[	[	X
iajs-3265	267	27	𝜖2	𝜖2	ADJ
iajs-3265	267	28	−	−	PROPN
iajs-3265	267	29	(	(	PUNCT
iajs-3265	267	30	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	267	31	)	)	PUNCT
iajs-3265	267	32	𝑩∗	𝑩∗	NOUN
iajs-3265	267	33	𝑨)2	𝑨)2	NUM
iajs-3265	267	34	]	]	PUNCT
iajs-3265	267	35	=	=	SYM
iajs-3265	267	36	0	0	NUM
iajs-3265	267	37	,	,	PUNCT
iajs-3265	267	38	𝜳(0	𝜳(0	NUM
iajs-3265	267	39	)	)	PUNCT
iajs-3265	267	40	𝑨	𝑨	NOUN
iajs-3265	267	41	=	=	SYM
iajs-3265	267	42	0	0	NUM
iajs-3265	267	43	,	,	PUNCT
iajs-3265	267	44	𝜳(0	𝜳(0	PUNCT
iajs-3265	267	45	)	)	PUNCT
iajs-3265	267	46	𝑩∗	𝑩∗	NOUN
iajs-3265	268	1	𝑨	𝑨	NOUN
iajs-3265	268	2	=	=	SYM
iajs-3265	268	3	1	1	NUM
iajs-3265	268	4	−	−	PROPN
iajs-3265	268	5	𝜖	𝜖	PROPN
iajs-3265	268	6	,	,	PUNCT
iajs-3265	268	7	𝜳(0	𝜳(0	NUM
iajs-3265	268	8	)	)	PUNCT
iajs-3265	268	9	(	(	PUNCT
iajs-3265	268	10	𝑩∗)2	𝑩∗)2	ADV
iajs-3265	268	11	𝑨	𝑨	NOUN
iajs-3265	268	12	=	=	SYM
iajs-3265	268	13	−0.832666	−0.832666	PROPN
iajs-3265	268	14	.	.	PUNCT
iajs-3265	269	1	(	(	PUNCT
iajs-3265	269	2	45	45	NUM
iajs-3265	269	3	)	)	PUNCT
iajs-3265	269	4	then	then	ADV
iajs-3265	269	5	,	,	PUNCT
iajs-3265	269	6	the	the	DET
iajs-3265	269	7	processes	process	NOUN
iajs-3265	269	8	have	have	AUX
iajs-3265	269	9	been	be	AUX
iajs-3265	269	10	used	use	VERB
iajs-3265	269	11	as	as	SCONJ
iajs-3265	269	12	presented	present	VERB
iajs-3265	269	13	in	in	ADP
iajs-3265	269	14	the	the	DET
iajs-3265	269	15	equations	equation	NOUN
iajs-3265	269	16	(	(	PUNCT
iajs-3265	269	17	18	18	NUM
iajs-3265	269	18	)	)	PUNCT
iajs-3265	269	19	and	and	CCONJ
iajs-3265	269	20	(	(	PUNCT
iajs-3265	269	21	19	19	NUM
iajs-3265	269	22	)	)	PUNCT
iajs-3265	269	23	,	,	PUNCT
iajs-3265	269	24	so	so	ADV
iajs-3265	269	25	:	:	PUNCT
iajs-3265	269	26	〈	〈	PROPN
iajs-3265	269	27	𝑥𝑖	𝑥𝑖	PRON
iajs-3265	269	28	,	,	PUNCT
iajs-3265	269	29	𝜳(𝑥	𝜳(𝑥	PROPN
iajs-3265	269	30	)	)	PUNCT
iajs-3265	269	31	(	(	PUNCT
iajs-3265	269	32	𝑩∗)3	𝑩∗)3	ADV
iajs-3265	269	33	𝑨	𝑨	PROPN
iajs-3265	269	34	+	+	CCONJ
iajs-3265	269	35	(	(	PUNCT
iajs-3265	269	36	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	269	37	)	)	PUNCT
iajs-3265	269	38	𝑨)(𝜳(𝑥	𝑨)(𝜳(𝑥	NOUN
iajs-3265	269	39	)	)	PUNCT
iajs-3265	269	40	(	(	PUNCT
iajs-3265	269	41	𝑩∗)2	𝑩∗)2	ADV
iajs-3265	269	42	𝑨	𝑨	NOUN
iajs-3265	269	43	)	)	PUNCT
iajs-3265	270	1	+	+	NUM
iajs-3265	270	2	𝛽	𝛽	NOUN
iajs-3265	270	3	[	[	X
iajs-3265	270	4	−(𝜳(𝑥	−(𝜳(𝑥	NOUN
iajs-3265	270	5	)	)	PUNCT
iajs-3265	270	6	𝑩∗	𝑩∗	NOUN
iajs-3265	270	7	𝑨)2	𝑨)2	NUM
iajs-3265	270	8	]	]	PUNCT
iajs-3265	270	9	〉	〉	NOUN
iajs-3265	270	10	=	=	SYM
iajs-3265	270	11	〈	〈	PROPN
iajs-3265	270	12	𝑥𝑖	𝑥𝑖	PROPN
iajs-3265	270	13	,	,	PUNCT
iajs-3265	270	14	−	−	PROPN
iajs-3265	270	15	𝛽	𝛽	NOUN
iajs-3265	270	16	𝜖2	𝜖2	NOUN
iajs-3265	270	17	〉	〉	NOUN
iajs-3265	270	18	,	,	PUNCT
iajs-3265	270	19	∀	∀	NOUN
iajs-3265	270	20	0	0	NUM
iajs-3265	270	21	≤	≤	NUM
iajs-3265	270	22	𝑖	𝑖	SYM
iajs-3265	270	23	≤	≤	NOUN
iajs-3265	270	24	𝑛.	𝑛.	NOUN
iajs-3265	270	25	(	(	PUNCT
iajs-3265	270	26	46	46	NUM
iajs-3265	270	27	)	)	PUNCT
iajs-3265	270	28	substituting	substitute	VERB
iajs-3265	270	29	equations	equation	NOUN
iajs-3265	270	30	(	(	PUNCT
iajs-3265	270	31	21	21	NUM
iajs-3265	270	32	)	)	PUNCT
iajs-3265	270	33	and	and	CCONJ
iajs-3265	270	34	(	(	PUNCT
iajs-3265	270	35	22	22	NUM
iajs-3265	270	36	)	)	PUNCT
iajs-3265	270	37	into	into	ADP
iajs-3265	270	38	equations	equation	NOUN
iajs-3265	270	39	(	(	PUNCT
iajs-3265	270	40	6	6	NUM
iajs-3265	270	41	)	)	PUNCT
iajs-3265	270	42	and	and	CCONJ
iajs-3265	270	43	(	(	PUNCT
iajs-3265	270	44	8)	8)	NUM
iajs-3265	270	45	for	for	ADP
iajs-3265	270	46	the	the	DET
iajs-3265	270	47	i	i	PROPN
iajs-3265	270	48	-	-	PUNCT
iajs-3265	270	49	ecms	ecms	PROPN
iajs-3265	270	50	based	base	VERB
iajs-3265	270	51	on	on	ADP
iajs-3265	270	52	the	the	DET
iajs-3265	270	53	first	first	ADJ
iajs-3265	270	54	kind	kind	NOUN
iajs-3265	270	55	of	of	ADP
iajs-3265	270	56	the	the	DET
iajs-3265	270	57	chebyshev	chebyshev	NOUN
iajs-3265	270	58	polynomials	polynomial	NOUN
iajs-3265	270	59	yields	yield	VERB
iajs-3265	270	60	the	the	DET
iajs-3265	270	61	following	follow	VERB
iajs-3265	270	62	:	:	PUNCT
iajs-3265	270	63	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	270	64	(	(	PUNCT
iajs-3265	270	65	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	270	66	∗	∗	NOUN
iajs-3265	270	67	)	)	PUNCT
iajs-3265	270	68	3	3	NUM
iajs-3265	270	69	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	270	70	)	)	PUNCT
iajs-3265	270	71	+	+	CCONJ
iajs-3265	270	72	(	(	PUNCT
iajs-3265	270	73	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	270	74	𝜳(𝑥))(𝑨𝑇	𝜳(𝑥))(𝑨𝑇	NOUN
iajs-3265	270	75	(	(	PUNCT
iajs-3265	270	76	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	270	77	∗	∗	NOUN
iajs-3265	270	78	)	)	PUNCT
iajs-3265	270	79	2	2	NUM
iajs-3265	270	80	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	270	81	)	)	PUNCT
iajs-3265	270	82	)	)	PUNCT
iajs-3265	271	1	+	+	PUNCT
iajs-3265	271	2	𝛽	𝛽	X
iajs-3265	271	3	[	[	X
iajs-3265	271	4	𝜖2	𝜖2	ADJ
iajs-3265	271	5	−	−	PROPN
iajs-3265	271	6	(	(	PUNCT
iajs-3265	271	7	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	271	8	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	271	9	∗	∗	NOUN
iajs-3265	271	10	𝜳(𝑥))2	𝜳(𝑥))2	NOUN
iajs-3265	271	11	]	]	PUNCT
iajs-3265	271	12	=	=	SYM
iajs-3265	271	13	0	0	NUM
iajs-3265	271	14	,	,	PUNCT
iajs-3265	271	15	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	271	16	𝜳(0	𝜳(0	PUNCT
iajs-3265	271	17	)	)	PUNCT
iajs-3265	271	18	=	=	SYM
iajs-3265	271	19	0	0	NUM
iajs-3265	271	20	,	,	PUNCT
iajs-3265	271	21	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	271	22	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	271	23	∗	∗	NOUN
iajs-3265	271	24	𝜳(0	𝜳(0	NUM
iajs-3265	271	25	)	)	PUNCT
iajs-3265	271	26	=	=	SYM
iajs-3265	272	1	1	1	NUM
iajs-3265	272	2	−	−	PROPN
iajs-3265	272	3	𝜖	𝜖	PROPN
iajs-3265	272	4	,	,	PUNCT
iajs-3265	272	5	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	272	6	(	(	PUNCT
iajs-3265	272	7	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	272	8	∗	∗	NOUN
iajs-3265	272	9	)	)	PUNCT
iajs-3265	272	10	2	2	NUM
iajs-3265	272	11	𝜳(0	𝜳(0	NUM
iajs-3265	272	12	)	)	PUNCT
iajs-3265	272	13	=	=	SYM
iajs-3265	272	14	−0.832666	−0.832666	PROPN
iajs-3265	272	15	.	.	PUNCT
iajs-3265	273	1	(	(	PUNCT
iajs-3265	273	2	47	47	NUM
iajs-3265	273	3	)	)	PUNCT
iajs-3265	273	4	and	and	CCONJ
iajs-3265	273	5	,	,	PUNCT
iajs-3265	273	6	by	by	ADP
iajs-3265	273	7	applying	apply	VERB
iajs-3265	273	8	the	the	DET
iajs-3265	273	9	processes	process	NOUN
iajs-3265	273	10	shown	show	VERB
iajs-3265	273	11	in	in	ADP
iajs-3265	273	12	the	the	DET
iajs-3265	273	13	equations	equation	NOUN
iajs-3265	273	14	(	(	PUNCT
iajs-3265	273	15	18	18	NUM
iajs-3265	273	16	)	)	PUNCT
iajs-3265	273	17	and	and	CCONJ
iajs-3265	273	18	(	(	PUNCT
iajs-3265	273	19	19	19	NUM
iajs-3265	273	20	)	)	PUNCT
iajs-3265	273	21	,	,	PUNCT
iajs-3265	273	22	the	the	DET
iajs-3265	273	23	following	follow	VERB
iajs-3265	273	24	results	result	NOUN
iajs-3265	273	25	:	:	PUNCT
iajs-3265	273	26	〈	〈	NOUN
iajs-3265	273	27	𝑻𝑖(𝑥	𝑻𝑖(𝑥	NOUN
iajs-3265	273	28	)	)	PUNCT
iajs-3265	273	29	,	,	PUNCT
iajs-3265	273	30	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	273	31	(	(	PUNCT
iajs-3265	273	32	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	273	33	∗	∗	NOUN
iajs-3265	273	34	)	)	PUNCT
iajs-3265	273	35	3	3	NUM
iajs-3265	273	36	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	273	37	)	)	PUNCT
iajs-3265	273	38	+	+	CCONJ
iajs-3265	273	39	(	(	PUNCT
iajs-3265	273	40	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	273	41	𝜳(𝑥))(𝑨𝑇	𝜳(𝑥))(𝑨𝑇	NOUN
iajs-3265	273	42	(	(	PUNCT
iajs-3265	273	43	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	273	44	∗	∗	NOUN
iajs-3265	273	45	)	)	PUNCT
iajs-3265	273	46	2	2	NUM
iajs-3265	273	47	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	273	48	)	)	PUNCT
iajs-3265	273	49	)	)	PUNCT
iajs-3265	274	1	+	+	PUNCT
iajs-3265	274	2	𝛽	𝛽	NOUN
iajs-3265	274	3	[	[	X
iajs-3265	274	4	−(𝑨𝑇	−(𝑨𝑇	PROPN
iajs-3265	274	5	𝑩𝑻	𝑩𝑻	PROPN
iajs-3265	274	6	∗	∗	NOUN
iajs-3265	274	7	𝜳(𝑥))2	𝜳(𝑥))2	NOUN
iajs-3265	274	8	]	]	PUNCT
iajs-3265	274	9	〉	〉	NOUN
iajs-3265	274	10	=	=	SYM
iajs-3265	274	11	〈	〈	PROPN
iajs-3265	274	12	𝑻𝑖(𝑥),−	𝑻𝑖(𝑥),−	PROPN
iajs-3265	274	13	𝛽	𝛽	PROPN
iajs-3265	274	14	𝜖2	𝜖2	NOUN
iajs-3265	274	15	〉	〉	NOUN
iajs-3265	274	16	,	,	PUNCT
iajs-3265	274	17	∀	∀	NOUN
iajs-3265	274	18	0	0	NUM
iajs-3265	274	19	≤	≤	NUM
iajs-3265	274	20	𝑖	𝑖	SYM
iajs-3265	274	21	≤	≤	NOUN
iajs-3265	274	22	𝑛.	𝑛.	NOUN
iajs-3265	274	23	(	(	PUNCT
iajs-3265	274	24	48	48	NUM
iajs-3265	274	25	)	)	PUNCT
iajs-3265	274	26	implementing	implement	VERB
iajs-3265	274	27	the	the	DET
iajs-3265	274	28	i	i	PROPN
iajs-3265	274	29	-	-	PUNCT
iajs-3265	274	30	ecms	ecms	PROPN
iajs-3265	274	31	based	base	VERB
iajs-3265	274	32	on	on	ADP
iajs-3265	274	33	the	the	DET
iajs-3265	274	34	bernoulli	bernoulli	NOUN
iajs-3265	274	35	polynomials	polynomial	NOUN
iajs-3265	274	36	by	by	ADP
iajs-3265	274	37	substituting	substitute	VERB
iajs-3265	274	38	equations	equation	NOUN
iajs-3265	274	39	(	(	PUNCT
iajs-3265	274	40	24	24	NUM
iajs-3265	274	41	)	)	PUNCT
iajs-3265	274	42	and	and	CCONJ
iajs-3265	274	43	(	(	PUNCT
iajs-3265	274	44	25	25	NUM
iajs-3265	274	45	)	)	PUNCT
iajs-3265	274	46	into	into	ADP
iajs-3265	274	47	equations	equation	NOUN
iajs-3265	274	48	(	(	PUNCT
iajs-3265	274	49	6	6	NUM
iajs-3265	274	50	)	)	PUNCT
iajs-3265	274	51	and	and	CCONJ
iajs-3265	274	52	(	(	PUNCT
iajs-3265	274	53	8)	8)	NUM
iajs-3265	274	54	,	,	PUNCT
iajs-3265	274	55	the	the	DET
iajs-3265	274	56	following	follow	VERB
iajs-3265	274	57	is	be	AUX
iajs-3265	274	58	achieved	achieve	VERB
iajs-3265	274	59	:	:	PUNCT
iajs-3265	274	60	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	274	61	(	(	PUNCT
iajs-3265	274	62	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	274	63	∗	∗	NOUN
iajs-3265	274	64	)	)	PUNCT
iajs-3265	274	65	3	3	NUM
iajs-3265	274	66	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	274	67	)	)	PUNCT
iajs-3265	274	68	+	+	CCONJ
iajs-3265	274	69	(	(	PUNCT
iajs-3265	274	70	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	274	71	𝜳(𝑥))(𝑨𝑇	𝜳(𝑥))(𝑨𝑇	NOUN
iajs-3265	274	72	(	(	PUNCT
iajs-3265	274	73	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	274	74	∗	∗	NOUN
iajs-3265	274	75	)	)	PUNCT
iajs-3265	274	76	2	2	NUM
iajs-3265	274	77	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	274	78	)	)	PUNCT
iajs-3265	274	79	)	)	PUNCT
iajs-3265	275	1	+	+	PUNCT
iajs-3265	275	2	𝛽	𝛽	X
iajs-3265	275	3	[	[	X
iajs-3265	275	4	𝜖2	𝜖2	ADJ
iajs-3265	275	5	−	−	PROPN
iajs-3265	275	6	(	(	PUNCT
iajs-3265	275	7	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	275	8	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	275	9	∗	∗	NOUN
iajs-3265	275	10	𝜳(𝑥))2	𝜳(𝑥))2	NOUN
iajs-3265	275	11	]	]	PUNCT
iajs-3265	275	12	=	=	SYM
iajs-3265	275	13	0	0	NUM
iajs-3265	275	14	,	,	PUNCT
iajs-3265	275	15	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	275	16	𝜳(0	𝜳(0	PUNCT
iajs-3265	275	17	)	)	PUNCT
iajs-3265	275	18	=	=	SYM
iajs-3265	275	19	0	0	NUM
iajs-3265	275	20	,	,	PUNCT
iajs-3265	275	21	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	275	22	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	275	23	∗	∗	NOUN
iajs-3265	275	24	𝜳(0	𝜳(0	NUM
iajs-3265	275	25	)	)	PUNCT
iajs-3265	275	26	=	=	SYM
iajs-3265	275	27	1	1	NUM
iajs-3265	275	28	−	−	PROPN
iajs-3265	275	29	𝜖	𝜖	PROPN
iajs-3265	275	30	,	,	PUNCT
iajs-3265	275	31	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	275	32	(	(	PUNCT
iajs-3265	275	33	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	275	34	∗	∗	NOUN
iajs-3265	275	35	)	)	PUNCT
iajs-3265	275	36	2	2	NUM
iajs-3265	275	37	𝜳(0	𝜳(0	NUM
iajs-3265	275	38	)	)	PUNCT
iajs-3265	275	39	=	=	SYM
iajs-3265	276	1	−0.832666	−0.832666	PROPN
iajs-3265	276	2	.	.	PUNCT
iajs-3265	277	1	(	(	PUNCT
iajs-3265	277	2	49	49	NUM
iajs-3265	277	3	)	)	PUNCT
iajs-3265	277	4	also	also	ADV
iajs-3265	277	5	,	,	PUNCT
iajs-3265	277	6	by	by	ADP
iajs-3265	277	7	using	use	VERB
iajs-3265	277	8	the	the	DET
iajs-3265	277	9	techniques	technique	NOUN
iajs-3265	277	10	as	as	SCONJ
iajs-3265	277	11	specified	specify	VERB
iajs-3265	277	12	in	in	ADP
iajs-3265	277	13	equations	equation	NOUN
iajs-3265	277	14	(	(	PUNCT
iajs-3265	277	15	18	18	NUM
iajs-3265	277	16	)	)	PUNCT
iajs-3265	277	17	and	and	CCONJ
iajs-3265	277	18	(	(	PUNCT
iajs-3265	277	19	19	19	NUM
iajs-3265	277	20	)	)	PUNCT
iajs-3265	277	21	,	,	PUNCT
iajs-3265	277	22	it	it	PRON
iajs-3265	277	23	follows	follow	VERB
iajs-3265	277	24	that	that	PRON
iajs-3265	277	25	:	:	PUNCT
iajs-3265	278	1	〈	〈	NOUN
iajs-3265	278	2	𝑩𝑖(𝑥	𝑩𝑖(𝑥	NOUN
iajs-3265	278	3	)	)	PUNCT
iajs-3265	278	4	,	,	PUNCT
iajs-3265	278	5	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	278	6	(	(	PUNCT
iajs-3265	278	7	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	278	8	∗	∗	NOUN
iajs-3265	278	9	)	)	PUNCT
iajs-3265	278	10	3	3	NUM
iajs-3265	278	11	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	278	12	)	)	PUNCT
iajs-3265	278	13	+	+	CCONJ
iajs-3265	278	14	(	(	PUNCT
iajs-3265	278	15	𝑨𝑇	𝑨𝑇	PROPN
iajs-3265	278	16	𝜳(𝑥))(𝑨𝑇	𝜳(𝑥))(𝑨𝑇	NOUN
iajs-3265	278	17	(	(	PUNCT
iajs-3265	278	18	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	278	19	∗	∗	NOUN
iajs-3265	278	20	)	)	PUNCT
iajs-3265	278	21	2	2	NUM
iajs-3265	278	22	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	278	23	)	)	PUNCT
iajs-3265	278	24	)	)	PUNCT
iajs-3265	279	1	+	+	PUNCT
iajs-3265	280	1	𝛽	𝛽	NOUN
iajs-3265	280	2	[	[	X
iajs-3265	280	3	−(𝑨𝑇	−(𝑨𝑇	PROPN
iajs-3265	280	4	𝑩𝓑	𝑩𝓑	PROPN
iajs-3265	280	5	∗	∗	NOUN
iajs-3265	280	6	𝜳(𝑥))2	𝜳(𝑥))2	NOUN
iajs-3265	280	7	]	]	PUNCT
iajs-3265	280	8	〉	〉	NOUN
iajs-3265	280	9	=	=	PUNCT
iajs-3265	280	10	〈	〈	NOUN
iajs-3265	280	11	𝑩𝑖(𝑥	𝑩𝑖(𝑥	NOUN
iajs-3265	280	12	)	)	PUNCT
iajs-3265	280	13	,	,	PUNCT
iajs-3265	280	14	−	−	PROPN
iajs-3265	280	15	𝛽	𝛽	NOUN
iajs-3265	280	16	𝜖2	𝜖2	NOUN
iajs-3265	280	17	〉	〉	NOUN
iajs-3265	280	18	,	,	PUNCT
iajs-3265	280	19	∀	∀	NOUN
iajs-3265	280	20	0	0	NUM
iajs-3265	280	21	≤	≤	NUM
iajs-3265	280	22	𝑖	𝑖	SYM
iajs-3265	280	23	≤	≤	NOUN
iajs-3265	280	24	𝑛.	𝑛.	NOUN
iajs-3265	280	25	(	(	PUNCT
iajs-3265	280	26	50	50	NUM
iajs-3265	280	27	)	)	PUNCT
iajs-3265	280	28	moreover	moreover	ADV
iajs-3265	280	29	,	,	PUNCT
iajs-3265	280	30	applying	apply	VERB
iajs-3265	280	31	the	the	DET
iajs-3265	280	32	i	i	PROPN
iajs-3265	280	33	-	-	PUNCT
iajs-3265	280	34	ecms	ecms	PROPN
iajs-3265	280	35	based	base	VERB
iajs-3265	280	36	on	on	ADP
iajs-3265	280	37	the	the	DET
iajs-3265	280	38	laguerre	laguerre	NOUN
iajs-3265	280	39	polynomials	polynomial	NOUN
iajs-3265	280	40	by	by	ADP
iajs-3265	280	41	substituting	substitute	VERB
iajs-3265	280	42	equations	equation	NOUN
iajs-3265	280	43	(	(	PUNCT
iajs-3265	280	44	27	27	NUM
iajs-3265	280	45	)	)	PUNCT
iajs-3265	280	46	and	and	CCONJ
iajs-3265	280	47	(	(	PUNCT
iajs-3265	280	48	28	28	NUM
iajs-3265	280	49	)	)	PUNCT
iajs-3265	280	50	into	into	ADP
iajs-3265	280	51	equations	equation	NOUN
iajs-3265	280	52	(	(	PUNCT
iajs-3265	280	53	6	6	NUM
iajs-3265	280	54	)	)	PUNCT
iajs-3265	280	55	and	and	CCONJ
iajs-3265	280	56	(	(	PUNCT
iajs-3265	280	57	8)	8)	NUM
iajs-3265	280	58	,	,	PUNCT
iajs-3265	280	59	we	we	PRON
iajs-3265	280	60	get	get	VERB
iajs-3265	280	61	:	:	PUNCT
iajs-3265	280	62	𝜳(𝑥	𝜳(𝑥	ADJ
iajs-3265	280	63	)	)	PUNCT
iajs-3265	280	64	(	(	PUNCT
iajs-3265	280	65	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	280	66	∗)3	∗)3	PUNCT
iajs-3265	280	67	𝑨	𝑨	PROPN
iajs-3265	280	68	+	+	CCONJ
iajs-3265	280	69	(	(	PUNCT
iajs-3265	280	70	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	280	71	)	)	PUNCT
iajs-3265	280	72	𝑨)(𝜳(𝑥	𝑨)(𝜳(𝑥	NOUN
iajs-3265	280	73	)	)	PUNCT
iajs-3265	280	74	(	(	PUNCT
iajs-3265	280	75	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	280	76	∗)2	∗)2	PROPN
iajs-3265	280	77	𝑨	𝑨	PROPN
iajs-3265	280	78	)	)	PUNCT
iajs-3265	280	79	+	+	NUM
iajs-3265	281	1	𝛽	𝛽	X
iajs-3265	281	2	[	[	X
iajs-3265	281	3	𝜖2	𝜖2	ADJ
iajs-3265	281	4	−	−	PROPN
iajs-3265	281	5	(	(	PUNCT
iajs-3265	281	6	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	281	7	)	)	PUNCT
iajs-3265	281	8	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	281	9	∗	∗	NOUN
iajs-3265	281	10	𝑨)2	𝑨)2	NUM
iajs-3265	281	11	]	]	PUNCT
iajs-3265	281	12	=	=	SYM
iajs-3265	281	13	0	0	NUM
iajs-3265	281	14	,	,	PUNCT
iajs-3265	281	15	𝜳(0	𝜳(0	NUM
iajs-3265	281	16	)	)	PUNCT
iajs-3265	281	17	𝑨	𝑨	NOUN
iajs-3265	281	18	=	=	SYM
iajs-3265	281	19	0	0	NUM
iajs-3265	281	20	,	,	PUNCT
iajs-3265	281	21	𝜳(0	𝜳(0	NUM
iajs-3265	281	22	)	)	PUNCT
iajs-3265	281	23	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	281	24	∗	∗	NOUN
iajs-3265	281	25	𝑨	𝑨	NOUN
iajs-3265	281	26	=	=	SYM
iajs-3265	281	27	1	1	NUM
iajs-3265	281	28	−	−	PROPN
iajs-3265	281	29	𝜖	𝜖	PROPN
iajs-3265	281	30	,	,	PUNCT
iajs-3265	281	31	𝜳(0	𝜳(0	NUM
iajs-3265	281	32	)	)	PUNCT
iajs-3265	281	33	(	(	PUNCT
iajs-3265	281	34	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	281	35	∗)2	∗)2	PROPN
iajs-3265	281	36	𝑨	𝑨	NOUN
iajs-3265	281	37	=	=	SYM
iajs-3265	281	38	−0.832666	−0.832666	PROPN
iajs-3265	281	39	.	.	PUNCT
iajs-3265	282	1	(	(	PUNCT
iajs-3265	282	2	51	51	NUM
iajs-3265	282	3	)	)	PUNCT
iajs-3265	282	4	then	then	ADV
iajs-3265	282	5	,	,	PUNCT
iajs-3265	282	6	the	the	DET
iajs-3265	282	7	processes	process	NOUN
iajs-3265	282	8	have	have	AUX
iajs-3265	282	9	been	be	AUX
iajs-3265	282	10	utilized	utilize	VERB
iajs-3265	282	11	as	as	SCONJ
iajs-3265	282	12	provided	provide	VERB
iajs-3265	282	13	in	in	ADP
iajs-3265	282	14	equations	equation	NOUN
iajs-3265	282	15	(	(	PUNCT
iajs-3265	282	16	18	18	NUM
iajs-3265	282	17	)	)	PUNCT
iajs-3265	282	18	and	and	CCONJ
iajs-3265	282	19	(	(	PUNCT
iajs-3265	282	20	19	19	NUM
iajs-3265	282	21	)	)	PUNCT
iajs-3265	282	22	,	,	PUNCT
iajs-3265	282	23	which	which	PRON
iajs-3265	282	24	will	will	AUX
iajs-3265	282	25	be	be	AUX
iajs-3265	282	26	shown	show	VERB
iajs-3265	282	27	:	:	PUNCT
iajs-3265	282	28	〈	〈	PROPN
iajs-3265	282	29	𝑳𝑖(𝑥	𝑳𝑖(𝑥	PROPN
iajs-3265	282	30	)	)	PUNCT
iajs-3265	282	31	,	,	PUNCT
iajs-3265	282	32	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	282	33	)	)	PUNCT
iajs-3265	282	34	(	(	PUNCT
iajs-3265	282	35	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	282	36	∗)3	∗)3	PUNCT
iajs-3265	282	37	𝑨	𝑨	PROPN
iajs-3265	282	38	+	+	CCONJ
iajs-3265	282	39	(	(	PUNCT
iajs-3265	282	40	𝜳(𝑥	𝜳(𝑥	NOUN
iajs-3265	282	41	)	)	PUNCT
iajs-3265	282	42	𝑨)(𝜳(𝑥	𝑨)(𝜳(𝑥	NOUN
iajs-3265	282	43	)	)	PUNCT
iajs-3265	282	44	(	(	PUNCT
iajs-3265	282	45	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	282	46	∗)2	∗)2	PROPN
iajs-3265	282	47	𝑨	𝑨	PROPN
iajs-3265	282	48	)	)	PUNCT
iajs-3265	283	1	+	+	NUM
iajs-3265	283	2	𝛽	𝛽	NOUN
iajs-3265	283	3	[	[	X
iajs-3265	283	4	−(𝜳(𝑥	−(𝜳(𝑥	ADJ
iajs-3265	283	5	)	)	PUNCT
iajs-3265	283	6	𝑩𝑳	𝑩𝑳	PROPN
iajs-3265	283	7	∗	∗	NOUN
iajs-3265	283	8	𝑨)2	𝑨)2	NUM
iajs-3265	283	9	]	]	SYM
iajs-3265	283	10	〉	〉	NOUN
iajs-3265	283	11	=	=	PUNCT
iajs-3265	283	12	〈	〈	PROPN
iajs-3265	283	13	𝑳𝑖(𝑥	𝑳𝑖(𝑥	PROPN
iajs-3265	283	14	)	)	PUNCT
iajs-3265	283	15	,	,	PUNCT
iajs-3265	283	16	−	−	PROPN
iajs-3265	283	17	𝛽	𝛽	NOUN
iajs-3265	283	18	𝜖2	𝜖2	NOUN
iajs-3265	283	19	〉	〉	NOUN
iajs-3265	283	20	,	,	PUNCT
iajs-3265	283	21	∀	∀	NOUN
iajs-3265	283	22	0	0	NUM
iajs-3265	283	23	≤	≤	NUM
iajs-3265	283	24	𝑖	𝑖	SYM
iajs-3265	283	25	≤	≤	NOUN
iajs-3265	283	26	𝑛.	𝑛.	NOUN
iajs-3265	283	27	(	(	PUNCT
iajs-3265	283	28	52	52	NUM
iajs-3265	283	29	)	)	PUNCT
iajs-3265	283	30	furthermore	furthermore	ADV
iajs-3265	283	31	,	,	PUNCT
iajs-3265	283	32	the	the	DET
iajs-3265	283	33	values	value	NOUN
iajs-3265	283	34	of	of	ADP
iajs-3265	283	35	𝑨	𝑨	NOUN
iajs-3265	283	36	=	=	PUNCT
iajs-3265	284	1	[	[	X
iajs-3265	284	2	𝑎0	𝑎0	ADV
iajs-3265	284	3	𝑎1	𝑎1	VERB
iajs-3265	284	4	𝑎2	𝑎2	NOUN
iajs-3265	284	5	…	…	PUNCT
iajs-3265	284	6	𝑎𝑛]𝑇	𝑎𝑛]𝑇	NOUN
iajs-3265	284	7	are	be	AUX
iajs-3265	284	8	calculated	calculate	VERB
iajs-3265	284	9	by	by	ADP
iajs-3265	284	10	solving	solve	VERB
iajs-3265	284	11	the	the	DET
iajs-3265	284	12	algebraic	algebraic	ADJ
iajs-3265	284	13	system	system	NOUN
iajs-3265	284	14	of	of	ADP
iajs-3265	284	15	equations	equation	NOUN
iajs-3265	284	16	obtained	obtain	VERB
iajs-3265	284	17	by	by	ADP
iajs-3265	284	18	the	the	DET
iajs-3265	284	19	inner	inner	ADJ
iajs-3265	284	20	product	product	NOUN
iajs-3265	284	21	for	for	ADP
iajs-3265	284	22	the	the	DET
iajs-3265	284	23	left	left	ADJ
iajs-3265	284	24	and	and	CCONJ
iajs-3265	284	25	right	right	ADJ
iajs-3265	284	26	sides	side	NOUN
iajs-3265	284	27	of	of	ADP
iajs-3265	284	28	equations	equation	NOUN
iajs-3265	284	29	(	(	PUNCT
iajs-3265	284	30	46	46	NUM
iajs-3265	284	31	)	)	PUNCT
iajs-3265	284	32	,	,	PUNCT
iajs-3265	284	33	(	(	PUNCT
iajs-3265	284	34	48	48	NUM
iajs-3265	284	35	)	)	PUNCT
iajs-3265	284	36	,	,	PUNCT
iajs-3265	284	37	(	(	PUNCT
iajs-3265	284	38	50	50	NUM
iajs-3265	284	39	)	)	PUNCT
iajs-3265	284	40	,	,	PUNCT
iajs-3265	284	41	and	and	CCONJ
iajs-3265	284	42	(	(	PUNCT
iajs-3265	284	43	52	52	NUM
iajs-3265	284	44	)	)	PUNCT
iajs-3265	284	45	,	,	PUNCT
iajs-3265	284	46	respectively	respectively	ADV
iajs-3265	284	47	.	.	PUNCT
iajs-3265	285	1	then	then	ADV
iajs-3265	285	2	,	,	PUNCT
iajs-3265	285	3	we	we	PRON
iajs-3265	285	4	utilize	utilize	VERB
iajs-3265	285	5	the	the	DET
iajs-3265	285	6	initial	initial	ADJ
iajs-3265	285	7	conditions	condition	NOUN
iajs-3265	285	8	to	to	ADP
iajs-3265	285	9	equations	equation	NOUN
iajs-3265	285	10	(	(	PUNCT
iajs-3265	285	11	45	45	NUM
iajs-3265	285	12	)	)	PUNCT
iajs-3265	285	13	,	,	PUNCT
iajs-3265	285	14	(	(	PUNCT
iajs-3265	285	15	47	47	NUM
iajs-3265	285	16	)	)	PUNCT
iajs-3265	285	17	,	,	PUNCT
iajs-3265	285	18	(	(	PUNCT
iajs-3265	285	19	49	49	NUM
iajs-3265	285	20	)	)	PUNCT
iajs-3265	285	21	,	,	PUNCT
iajs-3265	285	22	and	and	CCONJ
iajs-3265	285	23	(	(	PUNCT
iajs-3265	285	24	51	51	NUM
iajs-3265	285	25	)	)	PUNCT
iajs-3265	285	26	,	,	PUNCT
iajs-3265	285	27	respectively	respectively	ADV
iajs-3265	285	28	,	,	PUNCT
iajs-3265	285	29	the	the	DET
iajs-3265	285	30	desired	desire	VERB
iajs-3265	285	31	novel	novel	ADJ
iajs-3265	285	32	approximate	approximate	ADJ
iajs-3265	285	33	solutions	solution	NOUN
iajs-3265	285	34	are	be	AUX
iajs-3265	285	35	obtained	obtain	VERB
iajs-3265	285	36	.	.	PUNCT
iajs-3265	286	1	the	the	DET
iajs-3265	286	2	novel	novel	ADJ
iajs-3265	286	3	approximate	approximate	ADJ
iajs-3265	286	4	polynomials	polynomial	NOUN
iajs-3265	286	5	for	for	ADP
iajs-3265	286	6	the	the	DET
iajs-3265	286	7	falkner	falkner	PROPN
iajs-3265	286	8	-	-	PUNCT
iajs-3265	286	9	skan	skan	VERB
iajs-3265	286	10	equation	equation	NOUN
iajs-3265	286	11	when	when	SCONJ
iajs-3265	286	12	the	the	DET
iajs-3265	286	13	parameter	parameter	NOUN
iajs-3265	286	14	values	value	NOUN
iajs-3265	286	15	are	be	AUX
iajs-3265	286	16	as	as	SCONJ
iajs-3265	286	17	follows	follow	VERB
iajs-3265	286	18	:	:	PUNCT
iajs-3265	286	19	𝜖	𝜖	X
iajs-3265	286	20	=	=	SYM
iajs-3265	286	21	0.1	0.1	NUM
iajs-3265	286	22	,	,	PUNCT
iajs-3265	286	23	β	β	X
iajs-3265	286	24	=	=	SYM
iajs-3265	286	25	0.5	0.5	NUM
iajs-3265	286	26	,	,	PUNCT
iajs-3265	286	27	as	as	ADP
iajs-3265	286	28	in	in	ADP
iajs-3265	286	29	[	[	X
iajs-3265	286	30	53	53	NUM
iajs-3265	286	31	]	]	PUNCT
iajs-3265	286	32	,	,	PUNCT
iajs-3265	286	33	with	with	ADP
iajs-3265	286	34	𝑛=8	𝑛=8	NOUN
iajs-3265	286	35	,	,	PUNCT
iajs-3265	286	36	will	will	AUX
iajs-3265	286	37	be	be	AUX
iajs-3265	286	38	:	:	PUNCT
iajs-3265	286	39	by	by	ADP
iajs-3265	286	40	implementing	implement	VERB
iajs-3265	286	41	the	the	DET
iajs-3265	286	42	ecm	ecm	NOUN
iajs-3265	286	43	based	base	VERB
iajs-3265	286	44	on	on	ADP
iajs-3265	286	45	the	the	DET
iajs-3265	286	46	standard	standard	ADJ
iajs-3265	286	47	polynomials	polynomial	NOUN
iajs-3265	286	48	:	:	PUNCT
iajs-3265	286	49	𝑦(𝑥	𝑦(𝑥	NUM
iajs-3265	286	50	)	)	PUNCT
iajs-3265	287	1	≈	≈	PROPN
iajs-3265	287	2	0.9	0.9	NUM
iajs-3265	287	3	𝑥	𝑥	NOUN
iajs-3265	287	4	−	−	PROPN
iajs-3265	287	5	0.416333	0.416333	NUM
iajs-3265	287	6	𝑥2	𝑥2	NOUN
iajs-3265	287	7	+	+	CCONJ
iajs-3265	287	8	0.0666511	0.0666511	NUM
iajs-3265	287	9	𝑥3	𝑥3	NOUN
iajs-3265	287	10	+	+	CCONJ
iajs-3265	287	11	0.0000592155	0.0000592155	NUM
iajs-3265	287	12	𝑥4	𝑥4	NOUN
iajs-3265	287	13	−	−	PROPN
iajs-3265	287	14	0.00313186	0.00313186	NUM
iajs-3265	287	15	𝑥5	𝑥5	PROPN
iajs-3265	287	16	+	+	CCONJ
iajs-3265	287	17	0.000639976	0.000639976	NUM
iajs-3265	287	18	𝑥6	𝑥6	NOUN
iajs-3265	287	19	+	+	CCONJ
iajs-3265	287	20	0.0000210854	0.0000210854	NUM
iajs-3265	287	21	𝑥7	𝑥7	VERB
iajs-3265	287	22	−	−	PROPN
iajs-3265	287	23	0.0000188788	0.0000188788	NUM
iajs-3265	287	24	𝑥8	𝑥8	NOUN
iajs-3265	287	25	.	.	PUNCT
iajs-3265	288	1	also	also	ADV
iajs-3265	288	2	,	,	PUNCT
iajs-3265	288	3	by	by	ADP
iajs-3265	288	4	applying	apply	VERB
iajs-3265	288	5	the	the	DET
iajs-3265	288	6	i	i	PROPN
iajs-3265	288	7	-	-	PUNCT
iajs-3265	288	8	ecms	ecms	PROPN
iajs-3265	288	9	based	base	VERB
iajs-3265	288	10	on	on	ADP
iajs-3265	288	11	the	the	DET
iajs-3265	288	12	first	first	ADJ
iajs-3265	288	13	kind	kind	NOUN
iajs-3265	288	14	of	of	ADP
iajs-3265	288	15	the	the	DET
iajs-3265	288	16	chebyshev	chebyshev	NOUN
iajs-3265	288	17	polynomials	polynomial	NOUN
iajs-3265	288	18	,	,	PUNCT
iajs-3265	288	19	we	we	PRON
iajs-3265	288	20	obtain	obtain	VERB
iajs-3265	288	21	:	:	PUNCT
iajs-3265	288	22	ihjpas	ihjpas	PROPN
iajs-3265	288	23	.	.	PUNCT
iajs-3265	289	1	36	36	NUM
iajs-3265	289	2	(	(	PUNCT
iajs-3265	289	3	4	4	NUM
iajs-3265	289	4	)	)	PUNCT
iajs-3265	289	5	2023	2023	NUM
iajs-3265	289	6	352	352	NUM
iajs-3265	289	7	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	289	8	)	)	PUNCT
iajs-3265	290	1	≈	≈	PROPN
iajs-3265	290	2	0.9	0.9	NUM
iajs-3265	290	3	𝑥	𝑥	NOUN
iajs-3265	290	4	−	−	PROPN
iajs-3265	290	5	0.416333	0.416333	NUM
iajs-3265	290	6	𝑥2	𝑥2	NOUN
iajs-3265	290	7	+	+	CCONJ
iajs-3265	290	8	0.0666646	0.0666646	NUM
iajs-3265	290	9	𝑥3	𝑥3	NOUN
iajs-3265	290	10	+	+	CCONJ
iajs-3265	290	11	0.0000169313	0.0000169313	NUM
iajs-3265	290	12	𝑥4	𝑥4	NOUN
iajs-3265	290	13	−	−	PROPN
iajs-3265	291	1	0.00305864	0.00305864	NUM
iajs-3265	291	2	𝑥5	𝑥5	PROPN
iajs-3265	291	3	+	+	CCONJ
iajs-3265	291	4	0.00056836	0.00056836	NUM
iajs-3265	291	5	𝑥6	𝑥6	NOUN
iajs-3265	291	6	+	+	CCONJ
iajs-3265	291	7	0.0000581686	0.0000581686	NUM
iajs-3265	291	8	𝑥7	𝑥7	VERB
iajs-3265	291	9	−	−	PROPN
iajs-3265	291	10	0.0000267944	0.0000267944	NUM
iajs-3265	291	11	𝑥8	𝑥8	NOUN
iajs-3265	291	12	.	.	PUNCT
iajs-3265	292	1	in	in	ADP
iajs-3265	292	2	addition	addition	NOUN
iajs-3265	292	3	,	,	PUNCT
iajs-3265	292	4	by	by	ADP
iajs-3265	292	5	utilizing	utilize	VERB
iajs-3265	292	6	the	the	DET
iajs-3265	292	7	i	i	PROPN
iajs-3265	292	8	-	-	PUNCT
iajs-3265	292	9	ecms	ecms	PROPN
iajs-3265	292	10	based	base	VERB
iajs-3265	292	11	on	on	ADP
iajs-3265	292	12	the	the	DET
iajs-3265	292	13	bernoulli	bernoulli	NOUN
iajs-3265	292	14	polynomials	polynomial	NOUN
iajs-3265	292	15	,	,	PUNCT
iajs-3265	292	16	we	we	PRON
iajs-3265	292	17	get	get	VERB
iajs-3265	292	18	:	:	PUNCT
iajs-3265	292	19	𝑦(𝑥	𝑦(𝑥	X
iajs-3265	292	20	)	)	PUNCT
iajs-3265	293	1	≈	≈	PROPN
iajs-3265	293	2	0.9	0.9	NUM
iajs-3265	293	3	𝑥	𝑥	NOUN
iajs-3265	293	4	−	−	PROPN
iajs-3265	293	5	0.416333	0.416333	NUM
iajs-3265	293	6	𝑥2	𝑥2	NOUN
iajs-3265	293	7	+	+	CCONJ
iajs-3265	293	8	0.0666648	0.0666648	NUM
iajs-3265	293	9	𝑥3	𝑥3	NOUN
iajs-3265	293	10	+	+	CCONJ
iajs-3265	293	11	0.0000164756	0.0000164756	NUM
iajs-3265	293	12	𝑥4	𝑥4	NOUN
iajs-3265	293	13	−	−	PROPN
iajs-3265	294	1	0.00305823	0.00305823	NUM
iajs-3265	294	2	𝑥5	𝑥5	PROPN
iajs-3265	294	3	+	+	NOUN
iajs-3265	294	4	0.000568589	0.000568589	NUM
iajs-3265	294	5	𝑥6	𝑥6	NOUN
iajs-3265	294	6	+	+	CCONJ
iajs-3265	294	7	0.000057627	0.000057627	NUM
iajs-3265	294	8	𝑥7	𝑥7	VERB
iajs-3265	294	9	−	−	PROPN
iajs-3265	294	10	0.0000265718	0.0000265718	NUM
iajs-3265	294	11	𝑥8	𝑥8	NOUN
iajs-3265	294	12	.	.	PUNCT
iajs-3265	295	1	moreover	moreover	ADV
iajs-3265	295	2	,	,	PUNCT
iajs-3265	295	3	by	by	ADP
iajs-3265	295	4	using	use	VERB
iajs-3265	295	5	the	the	DET
iajs-3265	295	6	i	i	PROPN
iajs-3265	295	7	-	-	PUNCT
iajs-3265	295	8	ecms	ecms	PROPN
iajs-3265	295	9	based	base	VERB
iajs-3265	295	10	on	on	ADP
iajs-3265	295	11	the	the	DET
iajs-3265	295	12	laguerre	laguerre	NOUN
iajs-3265	295	13	polynomials	polynomial	NOUN
iajs-3265	295	14	,	,	PUNCT
iajs-3265	295	15	we	we	PRON
iajs-3265	295	16	achieve	achieve	VERB
iajs-3265	295	17	:	:	PUNCT
iajs-3265	295	18	𝑦(𝑥	𝑦(𝑥	X
iajs-3265	295	19	)	)	PUNCT
iajs-3265	296	1	≈	≈	NUM
iajs-3265	296	2	−8.72066	−8.72066	NUM
iajs-3265	296	3	×	×	NOUN
iajs-3265	296	4	10−14	10−14	NOUN
iajs-3265	297	1	+	+	CCONJ
iajs-3265	298	1	0.9	0.9	NUM
iajs-3265	298	2	𝑥	𝑥	NOUN
iajs-3265	298	3	−	−	NUM
iajs-3265	298	4	0.416333	0.416333	NUM
iajs-3265	298	5	𝑥2	𝑥2	NOUN
iajs-3265	298	6	+	+	CCONJ
iajs-3265	298	7	0.0666602	0.0666602	NUM
iajs-3265	299	1	𝑥3	𝑥3	NOUN
iajs-3265	299	2	+	+	CCONJ
iajs-3265	299	3	0.0000532904	0.0000532904	NUM
iajs-3265	299	4	𝑥4	𝑥4	NOUN
iajs-3265	299	5	−	−	PROPN
iajs-3265	299	6	0.00316698	0.00316698	NUM
iajs-3265	299	7	𝑥5	𝑥5	PROPN
iajs-3265	299	8	+	+	CCONJ
iajs-3265	299	9	0.00071942	0.00071942	NUM
iajs-3265	299	10	𝑥6	𝑥6	NOUN
iajs-3265	299	11	−	−	PROPN
iajs-3265	299	12	0.0000423225	0.0000423225	NUM
iajs-3265	299	13	𝑥7	𝑥7	VERB
iajs-3265	299	14	−	−	PROPN
iajs-3265	299	15	9.73011	9.73011	NUM
iajs-3265	299	16	×	×	NOUN
iajs-3265	299	17	10−7𝑥8	10−7𝑥8	NUM
iajs-3265	299	18	.	.	PUNCT
iajs-3265	300	1	since	since	SCONJ
iajs-3265	300	2	there	there	PRON
iajs-3265	300	3	is	be	VERB
iajs-3265	300	4	no	no	DET
iajs-3265	300	5	exact	exact	ADJ
iajs-3265	300	6	solution	solution	NOUN
iajs-3265	300	7	to	to	ADP
iajs-3265	300	8	the	the	DET
iajs-3265	300	9	falkner	falkner	PROPN
iajs-3265	300	10	-	-	PUNCT
iajs-3265	300	11	skan	skan	VERB
iajs-3265	300	12	equation	equation	NOUN
iajs-3265	300	13	,	,	PUNCT
iajs-3265	300	14	the	the	DET
iajs-3265	300	15	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	300	16	is	be	AUX
iajs-3265	300	17	computed	compute	VERB
iajs-3265	300	18	in	in	ADP
iajs-3265	300	19	order	order	NOUN
iajs-3265	300	20	to	to	PART
iajs-3265	300	21	verify	verify	VERB
iajs-3265	300	22	the	the	DET
iajs-3265	300	23	efficiency	efficiency	NOUN
iajs-3265	300	24	and	and	CCONJ
iajs-3265	300	25	accuracy	accuracy	NOUN
iajs-3265	300	26	of	of	ADP
iajs-3265	300	27	the	the	DET
iajs-3265	300	28	novel	novel	ADJ
iajs-3265	300	29	approximate	approximate	ADJ
iajs-3265	300	30	solutions	solution	NOUN
iajs-3265	300	31	found	find	VERB
iajs-3265	300	32	by	by	ADP
iajs-3265	300	33	the	the	DET
iajs-3265	300	34	ecm	ecm	PROPN
iajs-3265	300	35	and	and	CCONJ
iajs-3265	300	36	the	the	DET
iajs-3265	300	37	i	i	PROPN
iajs-3265	300	38	-	-	PUNCT
iajs-3265	300	39	ecms	ecms	NOUN
iajs-3265	300	40	.	.	PUNCT
iajs-3265	301	1	the	the	DET
iajs-3265	301	2	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	PROPN
iajs-3265	301	3	is	be	AUX
iajs-3265	301	4	calculated	calculate	VERB
iajs-3265	301	5	by	by	ADP
iajs-3265	301	6	:	:	PUNCT
iajs-3265	301	7	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	301	8	=	=	SYM
iajs-3265	301	9	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
iajs-3265	301	10	0≤𝑥≤1	0≤𝑥≤1	ADJ
iajs-3265	301	11	|𝑦′′′(𝑥	|𝑦′′′(𝑥	PUNCT
iajs-3265	301	12	)	)	PUNCT
iajs-3265	302	1	+	+	CCONJ
iajs-3265	302	2	𝑦(𝑥	𝑦(𝑥	NOUN
iajs-3265	302	3	)	)	PUNCT
iajs-3265	302	4	𝑦′′(𝑥	𝑦′′(𝑥	NUM
iajs-3265	302	5	)	)	PUNCT
iajs-3265	303	1	+	+	NUM
iajs-3265	303	2	𝛽	𝛽	X
iajs-3265	303	3	[	[	X
iajs-3265	303	4	𝜖2	𝜖2	ADJ
iajs-3265	303	5	−	−	PROPN
iajs-3265	303	6	(	(	PUNCT
iajs-3265	303	7	𝑦′(𝑥))2]|	𝑦′(𝑥))2]|	PROPN
iajs-3265	303	8	.	.	PUNCT
iajs-3265	304	1	figure	figure	NOUN
iajs-3265	304	2	6	6	NUM
iajs-3265	304	3	exhibits	exhibit	VERB
iajs-3265	304	4	the	the	DET
iajs-3265	304	5	logarithmic	logarithmic	ADJ
iajs-3265	304	6	plots	plot	NOUN
iajs-3265	304	7	for	for	ADP
iajs-3265	304	8	the	the	DET
iajs-3265	304	9	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	304	10	values	value	NOUN
iajs-3265	304	11	obtained	obtain	VERB
iajs-3265	304	12	for	for	ADP
iajs-3265	304	13	the	the	DET
iajs-3265	304	14	parameters	parameter	NOUN
iajs-3265	304	15	𝜖	𝜖	X
iajs-3265	304	16	=	=	SYM
iajs-3265	304	17	0.1	0.1	NUM
iajs-3265	304	18	,	,	PUNCT
iajs-3265	304	19	and	and	CCONJ
iajs-3265	304	20	𝛽	𝛽	NOUN
iajs-3265	304	21	=	=	SYM
iajs-3265	304	22	0.5	0.5	NUM
iajs-3265	304	23	,	,	PUNCT
iajs-3265	304	24	according	accord	VERB
iajs-3265	304	25	to	to	ADP
iajs-3265	304	26	studies	study	NOUN
iajs-3265	304	27	[	[	X
iajs-3265	304	28	53	53	NUM
iajs-3265	304	29	]	]	PUNCT
iajs-3265	304	30	,	,	PUNCT
iajs-3265	304	31	by	by	ADP
iajs-3265	304	32	the	the	DET
iajs-3265	304	33	ecm	ecm	NOUN
iajs-3265	304	34	based	base	VERB
iajs-3265	304	35	on	on	ADP
iajs-3265	304	36	the	the	DET
iajs-3265	304	37	standard	standard	ADJ
iajs-3265	304	38	polynomials	polynomial	NOUN
iajs-3265	304	39	and	and	CCONJ
iajs-3265	304	40	by	by	ADP
iajs-3265	304	41	the	the	DET
iajs-3265	304	42	i	i	PROPN
iajs-3265	304	43	-	-	PUNCT
iajs-3265	304	44	ecms	ecms	PROPN
iajs-3265	304	45	based	base	VERB
iajs-3265	304	46	on	on	ADP
iajs-3265	304	47	the	the	DET
iajs-3265	304	48	chebyshev	chebyshev	NOUN
iajs-3265	304	49	,	,	PUNCT
iajs-3265	304	50	bernoulli	bernoulli	PROPN
iajs-3265	304	51	,	,	PUNCT
iajs-3265	304	52	and	and	CCONJ
iajs-3265	304	53	laguerre	laguerre	NOUN
iajs-3265	304	54	polynomials	polynomial	NOUN
iajs-3265	304	55	,	,	PUNCT
iajs-3265	304	56	which	which	PRON
iajs-3265	304	57	demonstrate	demonstrate	VERB
iajs-3265	304	58	the	the	DET
iajs-3265	304	59	accuracy	accuracy	NOUN
iajs-3265	304	60	and	and	CCONJ
iajs-3265	304	61	efficiency	efficiency	NOUN
iajs-3265	304	62	of	of	ADP
iajs-3265	304	63	these	these	DET
iajs-3265	304	64	techniques	technique	NOUN
iajs-3265	304	65	by	by	ADP
iajs-3265	304	66	observing	observe	VERB
iajs-3265	304	67	the	the	DET
iajs-3265	304	68	error	error	NOUN
iajs-3265	304	69	values	value	NOUN
iajs-3265	304	70	for	for	ADP
iajs-3265	304	71	𝑛	𝑛	NOUN
iajs-3265	304	72	=	=	SYM
iajs-3265	304	73	2	2	NUM
iajs-3265	304	74	to	to	PART
iajs-3265	304	75	8	8	NUM
iajs-3265	304	76	.	.	PUNCT
iajs-3265	305	1	we	we	PRON
iajs-3265	305	2	observe	observe	VERB
iajs-3265	305	3	that	that	SCONJ
iajs-3265	305	4	when	when	SCONJ
iajs-3265	305	5	𝑛	𝑛	PROPN
iajs-3265	305	6	is	be	AUX
iajs-3265	305	7	increased	increase	VERB
iajs-3265	305	8	,	,	PUNCT
iajs-3265	305	9	the	the	DET
iajs-3265	305	10	error	error	NOUN
iajs-3265	305	11	decreased	decrease	VERB
iajs-3265	305	12	.	.	PUNCT
iajs-3265	306	1	figure	figure	NOUN
iajs-3265	306	2	6	6	NUM
iajs-3265	306	3	.	.	PUNCT
iajs-3265	307	1	logarithmic	logarithmic	ADJ
iajs-3265	307	2	plots	plot	NOUN
iajs-3265	307	3	of	of	ADP
iajs-3265	307	4	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	307	5	for	for	ADP
iajs-3265	307	6	the	the	DET
iajs-3265	307	7	falkner	falkner	PROPN
iajs-3265	307	8	-	-	PUNCT
iajs-3265	307	9	skan	skan	VERB
iajs-3265	307	10	equation	equation	NOUN
iajs-3265	307	11	by	by	ADP
iajs-3265	307	12	proposed	propose	VERB
iajs-3265	307	13	methods	method	NOUN
iajs-3265	307	14	.	.	PUNCT
iajs-3265	308	1	also	also	ADV
iajs-3265	308	2	,	,	PUNCT
iajs-3265	308	3	table	table	NOUN
iajs-3265	308	4	3	3	NUM
iajs-3265	308	5	shows	show	VERB
iajs-3265	308	6	the	the	DET
iajs-3265	308	7	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	PROPN
iajs-3265	308	8	values	value	NOUN
iajs-3265	308	9	for	for	ADP
iajs-3265	308	10	the	the	DET
iajs-3265	308	11	novel	novel	ADJ
iajs-3265	308	12	approximate	approximate	ADJ
iajs-3265	308	13	solutions	solution	NOUN
iajs-3265	308	14	achieved	achieve	VERB
iajs-3265	308	15	with	with	ADP
iajs-3265	308	16	the	the	DET
iajs-3265	308	17	ecm	ecm	NOUN
iajs-3265	308	18	and	and	CCONJ
iajs-3265	308	19	the	the	DET
iajs-3265	308	20	i	i	PROPN
iajs-3265	308	21	-	-	PUNCT
iajs-3265	308	22	ecms	ecms	PROPN
iajs-3265	308	23	with	with	ADP
iajs-3265	308	24	𝑛	𝑛	PROPN
iajs-3265	308	25	=	=	SYM
iajs-3265	308	26	8	8	NUM
iajs-3265	308	27	,	,	PUNCT
iajs-3265	308	28	explaining	explain	VERB
iajs-3265	308	29	the	the	DET
iajs-3265	308	30	accuracy	accuracy	NOUN
iajs-3265	308	31	of	of	ADP
iajs-3265	308	32	these	these	DET
iajs-3265	308	33	methods	method	NOUN
iajs-3265	308	34	.	.	PUNCT
iajs-3265	309	1	moreover	moreover	ADV
iajs-3265	309	2	,	,	PUNCT
iajs-3265	309	3	the	the	DET
iajs-3265	309	4	iecms	iecms	NOUN
iajs-3265	309	5	based	base	VERB
iajs-3265	309	6	on	on	ADP
iajs-3265	309	7	the	the	DET
iajs-3265	309	8	bernoulli	bernoulli	PROPN
iajs-3265	309	9	polynomials	polynomial	NOUN
iajs-3265	309	10	method	method	VERB
iajs-3265	309	11	,	,	PUNCT
iajs-3265	309	12	offer	offer	VERB
iajs-3265	309	13	slightly	slightly	ADV
iajs-3265	309	14	better	well	ADJ
iajs-3265	309	15	accuracy	accuracy	NOUN
iajs-3265	309	16	and	and	CCONJ
iajs-3265	309	17	fewer	few	ADJ
iajs-3265	309	18	errors	error	NOUN
iajs-3265	309	19	than	than	ADP
iajs-3265	309	20	the	the	DET
iajs-3265	309	21	other	other	ADJ
iajs-3265	309	22	methods	method	NOUN
iajs-3265	309	23	.	.	PUNCT
iajs-3265	310	1	table	table	NOUN
iajs-3265	310	2	3	3	NUM
iajs-3265	310	3	.	.	PUNCT
iajs-3265	311	1	the	the	DET
iajs-3265	311	2	comparison	comparison	NOUN
iajs-3265	311	3	between	between	ADP
iajs-3265	311	4	the	the	DET
iajs-3265	311	5	𝑀𝐸𝑅8	𝑀𝐸𝑅8	PROPN
iajs-3265	311	6	for	for	ADP
iajs-3265	311	7	the	the	DET
iajs-3265	311	8	falkner	falkner	PROPN
iajs-3265	311	9	-	-	PUNCT
iajs-3265	311	10	skan	skan	VERB
iajs-3265	311	11	equation	equation	NOUN
iajs-3265	311	12	by	by	ADP
iajs-3265	311	13	proposed	propose	VERB
iajs-3265	311	14	methods	method	NOUN
iajs-3265	311	15	.	.	PUNCT
iajs-3265	312	1	moreover	moreover	ADV
iajs-3265	312	2	,	,	PUNCT
iajs-3265	312	3	figure	figure	VERB
iajs-3265	312	4	7	7	NUM
iajs-3265	312	5	shows	show	VERB
iajs-3265	312	6	the	the	DET
iajs-3265	312	7	comparison	comparison	NOUN
iajs-3265	312	8	between	between	ADP
iajs-3265	312	9	the	the	DET
iajs-3265	312	10	novel	novel	ADJ
iajs-3265	312	11	approximate	approximate	ADJ
iajs-3265	312	12	solutions	solution	NOUN
iajs-3265	312	13	calculated	calculate	VERB
iajs-3265	312	14	by	by	ADP
iajs-3265	312	15	the	the	DET
iajs-3265	312	16	proposed	propose	VERB
iajs-3265	312	17	techniques	technique	NOUN
iajs-3265	312	18	for	for	ADP
iajs-3265	312	19	𝑛	𝑛	NOUN
iajs-3265	312	20	=	=	SYM
iajs-3265	312	21	8	8	NUM
iajs-3265	312	22	,	,	PUNCT
iajs-3265	312	23	𝜖	𝜖	X
iajs-3265	312	24	=	=	NOUN
iajs-3265	312	25	0.1	0.1	NUM
iajs-3265	312	26	,	,	PUNCT
iajs-3265	312	27	and	and	CCONJ
iajs-3265	312	28	𝛽	𝛽	NOUN
iajs-3265	312	29	=	=	SYM
iajs-3265	312	30	0.5	0.5	NUM
iajs-3265	312	31	.	.	PUNCT
iajs-3265	313	1	the	the	DET
iajs-3265	313	2	figure	figure	NOUN
iajs-3265	313	3	shows	show	VERB
iajs-3265	313	4	that	that	SCONJ
iajs-3265	313	5	all	all	PRON
iajs-3265	313	6	of	of	ADP
iajs-3265	313	7	the	the	DET
iajs-3265	313	8	suggested	suggest	VERB
iajs-3265	313	9	approaches	approach	NOUN
iajs-3265	313	10	exhibited	exhibit	VERB
iajs-3265	313	11	good	good	ADJ
iajs-3265	313	12	agreement	agreement	NOUN
iajs-3265	313	13	.	.	PUNCT
iajs-3265	314	1	𝒏	𝒏	PROPN
iajs-3265	314	2	ecm	ecm	PROPN
iajs-3265	314	3	standard	standard	PROPN
iajs-3265	314	4	i	i	PROPN
iajs-3265	314	5	-	-	PUNCT
iajs-3265	314	6	ecms	ecms	PROPN
iajs-3265	314	7	chebyshev	chebyshev	NOUN
iajs-3265	314	8	i	i	PROPN
iajs-3265	314	9	-	-	PUNCT
iajs-3265	314	10	ecms	ecms	NOUN
iajs-3265	314	11	bernoulli	bernoulli	PROPN
iajs-3265	314	12	i	i	PROPN
iajs-3265	314	13	-	-	PUNCT
iajs-3265	314	14	ecms	ecms	PROPN
iajs-3265	314	15	laguerre	laguerre	NOUN
iajs-3265	314	16	8	8	NUM
iajs-3265	314	17	0.0000935074	0.0000935074	NUM
iajs-3265	314	18	0.0000123869	0.0000123869	NUM
iajs-3265	314	19	0.0000113839	0.0000113839	NUM
iajs-3265	314	20	0.0000385485	0.0000385485	NUM
iajs-3265	314	21	ihjpas	ihjpa	NOUN
iajs-3265	314	22	.	.	PUNCT
iajs-3265	315	1	36	36	NUM
iajs-3265	315	2	(	(	PUNCT
iajs-3265	315	3	4	4	NUM
iajs-3265	315	4	)	)	PUNCT
iajs-3265	315	5	2023	2023	NUM
iajs-3265	315	6	353	353	NUM
iajs-3265	315	7	figure	figure	NOUN
iajs-3265	315	8	7	7	NUM
iajs-3265	315	9	.	.	PUNCT
iajs-3265	316	1	the	the	DET
iajs-3265	316	2	comparison	comparison	NOUN
iajs-3265	316	3	of	of	ADP
iajs-3265	316	4	the	the	DET
iajs-3265	316	5	solutions	solution	NOUN
iajs-3265	316	6	to	to	ADP
iajs-3265	316	7	the	the	DET
iajs-3265	316	8	falkner	falkner	PROPN
iajs-3265	316	9	-	-	PUNCT
iajs-3265	316	10	skan	skan	VERB
iajs-3265	316	11	equation	equation	NOUN
iajs-3265	316	12	by	by	ADP
iajs-3265	316	13	proposed	propose	VERB
iajs-3265	316	14	methods	method	NOUN
iajs-3265	316	15	.	.	PUNCT
iajs-3265	317	1	figure	figure	NOUN
iajs-3265	317	2	8	8	NUM
iajs-3265	317	3	.	.	PUNCT
iajs-3265	318	1	logarithmic	logarithmic	ADJ
iajs-3265	318	2	plots	plot	NOUN
iajs-3265	318	3	of	of	ADP
iajs-3265	318	4	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	318	5	for	for	ADP
iajs-3265	318	6	the	the	DET
iajs-3265	318	7	falkner	falkner	PROPN
iajs-3265	318	8	-	-	PUNCT
iajs-3265	318	9	skan	skan	VERB
iajs-3265	318	10	equation	equation	NOUN
iajs-3265	318	11	by	by	ADP
iajs-3265	318	12	(	(	PUNCT
iajs-3265	318	13	a	a	PRON
iajs-3265	318	14	)	)	PUNCT
iajs-3265	318	15	ecm	ecm	NOUN
iajs-3265	318	16	based	base	VERB
iajs-3265	318	17	on	on	ADP
iajs-3265	318	18	the	the	DET
iajs-3265	318	19	standard	standard	ADJ
iajs-3265	318	20	polynomials	polynomial	NOUN
iajs-3265	318	21	and	and	CCONJ
iajs-3265	318	22	(	(	PUNCT
iajs-3265	318	23	b	b	X
iajs-3265	318	24	)	)	PUNCT
iajs-3265	318	25	i	i	PROPN
iajs-3265	318	26	-	-	PUNCT
iajs-3265	318	27	ecms	ecms	PROPN
iajs-3265	318	28	based	base	VERB
iajs-3265	318	29	on	on	ADP
iajs-3265	318	30	the	the	DET
iajs-3265	318	31	chebyshev	chebyshev	NOUN
iajs-3265	318	32	polynomials	polynomial	NOUN
iajs-3265	318	33	.	.	PUNCT
iajs-3265	319	1	in	in	ADP
iajs-3265	319	2	addition	addition	NOUN
iajs-3265	319	3	,	,	PUNCT
iajs-3265	319	4	figures	figure	NOUN
iajs-3265	319	5	(	(	PUNCT
iajs-3265	319	6	8	8	NUM
iajs-3265	319	7	and	and	CCONJ
iajs-3265	319	8	9	9	NUM
iajs-3265	319	9	)	)	PUNCT
iajs-3265	319	10	explain	explain	VERB
iajs-3265	319	11	the	the	DET
iajs-3265	319	12	logarithmic	logarithmic	ADJ
iajs-3265	319	13	plots	plot	NOUN
iajs-3265	319	14	of	of	ADP
iajs-3265	319	15	the	the	DET
iajs-3265	319	16	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	319	17	for	for	ADP
iajs-3265	319	18	the	the	DET
iajs-3265	319	19	novel	novel	ADJ
iajs-3265	319	20	approximate	approximate	ADJ
iajs-3265	319	21	solutions	solution	NOUN
iajs-3265	319	22	of	of	ADP
iajs-3265	319	23	the	the	DET
iajs-3265	319	24	falkner	falkner	PROPN
iajs-3265	319	25	-	-	PUNCT
iajs-3265	319	26	skan	skan	VERB
iajs-3265	319	27	equation	equation	NOUN
iajs-3265	319	28	with	with	ADP
iajs-3265	319	29	𝑛	𝑛	PROPN
iajs-3265	319	30	=	=	SYM
iajs-3265	319	31	2	2	NUM
iajs-3265	319	32	to	to	ADP
iajs-3265	319	33	8	8	NUM
iajs-3265	319	34	,	,	PUNCT
iajs-3265	319	35	using	use	VERB
iajs-3265	319	36	the	the	DET
iajs-3265	319	37	ecm	ecm	NOUN
iajs-3265	319	38	and	and	CCONJ
iajs-3265	319	39	the	the	DET
iajs-3265	319	40	iecms	iecms	NOUN
iajs-3265	319	41	when	when	SCONJ
iajs-3265	319	42	fixed	fix	VERB
iajs-3265	319	43	the	the	DET
iajs-3265	319	44	pressure	pressure	NOUN
iajs-3265	319	45	gradient	gradient	NOUN
iajs-3265	319	46	parameter	parameter	NOUN
iajs-3265	319	47	𝛽	𝛽	NOUN
iajs-3265	319	48	=	=	PROPN
iajs-3265	319	49	0.5	0.5	NUM
iajs-3265	319	50	,	,	PUNCT
iajs-3265	319	51	and	and	CCONJ
iajs-3265	319	52	increasing	increase	VERB
iajs-3265	319	53	the	the	DET
iajs-3265	319	54	values	value	NOUN
iajs-3265	319	55	of	of	ADP
iajs-3265	319	56	the	the	DET
iajs-3265	319	57	velocity	velocity	NOUN
iajs-3265	319	58	ratio	ratio	NOUN
iajs-3265	319	59	parameter	parameter	NOUN
iajs-3265	319	60	as	as	ADP
iajs-3265	319	61	𝜖	𝜖	PROPN
iajs-3265	319	62	=	=	SYM
iajs-3265	319	63	0.1	0.1	NUM
iajs-3265	319	64	,	,	PUNCT
iajs-3265	319	65	0.2	0.2	NUM
iajs-3265	319	66	,	,	PUNCT
iajs-3265	319	67	0.3	0.3	NUM
iajs-3265	319	68	,	,	PUNCT
iajs-3265	319	69	and	and	CCONJ
iajs-3265	319	70	0.4	0.4	NUM
iajs-3265	319	71	,	,	PUNCT
iajs-3265	319	72	as	as	SCONJ
iajs-3265	319	73	chosen	choose	VERB
iajs-3265	319	74	in	in	ADP
iajs-3265	319	75	[	[	X
iajs-3265	319	76	53	53	NUM
iajs-3265	319	77	]	]	PUNCT
iajs-3265	319	78	.	.	PUNCT
iajs-3265	320	1	in	in	ADP
iajs-3265	320	2	figures	figure	NOUN
iajs-3265	320	3	(	(	PUNCT
iajs-3265	320	4	8	8	NUM
iajs-3265	320	5	and	and	CCONJ
iajs-3265	320	6	9	9	NUM
iajs-3265	320	7	)	)	PUNCT
iajs-3265	320	8	,	,	PUNCT
iajs-3265	320	9	the	the	DET
iajs-3265	320	10	errors	error	NOUN
iajs-3265	320	11	decrease	decrease	VERB
iajs-3265	320	12	when	when	SCONJ
iajs-3265	320	13	the	the	DET
iajs-3265	320	14	value	value	NOUN
iajs-3265	320	15	of	of	ADP
iajs-3265	320	16	𝜖	𝜖	PROPN
iajs-3265	320	17	is	be	AUX
iajs-3265	320	18	increased	increase	VERB
iajs-3265	320	19	.	.	PUNCT
iajs-3265	321	1	(	(	PUNCT
iajs-3265	321	2	a	a	X
iajs-3265	321	3	)	)	PUNCT
iajs-3265	321	4	(	(	PUNCT
iajs-3265	321	5	b	b	X
iajs-3265	321	6	)	)	PUNCT
iajs-3265	321	7	figure	figure	NOUN
iajs-3265	321	8	9	9	NUM
iajs-3265	321	9	.	.	PUNCT
iajs-3265	322	1	logarithmic	logarithmic	ADJ
iajs-3265	322	2	plots	plot	NOUN
iajs-3265	322	3	of	of	ADP
iajs-3265	322	4	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	322	5	for	for	ADP
iajs-3265	322	6	the	the	DET
iajs-3265	322	7	falkner	falkner	PROPN
iajs-3265	322	8	-	-	PUNCT
iajs-3265	322	9	skan	skan	VERB
iajs-3265	322	10	equation	equation	NOUN
iajs-3265	322	11	by	by	ADP
iajs-3265	322	12	(	(	PUNCT
iajs-3265	322	13	a	a	X
iajs-3265	322	14	)	)	PUNCT
iajs-3265	322	15	i	i	PROPN
iajs-3265	322	16	-	-	PUNCT
iajs-3265	322	17	ecms	ecms	PROPN
iajs-3265	322	18	based	base	VERB
iajs-3265	322	19	on	on	ADP
iajs-3265	322	20	the	the	DET
iajs-3265	322	21	bernoulli	bernoulli	NOUN
iajs-3265	322	22	polynomials	polynomial	NOUN
iajs-3265	322	23	and	and	CCONJ
iajs-3265	322	24	(	(	PUNCT
iajs-3265	322	25	b	b	X
iajs-3265	322	26	)	)	PUNCT
iajs-3265	322	27	i	i	PROPN
iajs-3265	322	28	-	-	PUNCT
iajs-3265	322	29	ecms	ecms	PROPN
iajs-3265	322	30	based	base	VERB
iajs-3265	322	31	on	on	ADP
iajs-3265	322	32	the	the	DET
iajs-3265	322	33	laguerre	laguerre	NOUN
iajs-3265	322	34	polynomials	polynomial	NOUN
iajs-3265	322	35	.	.	PUNCT
iajs-3265	323	1	(	(	PUNCT
iajs-3265	323	2	a	a	X
iajs-3265	323	3	)	)	PUNCT
iajs-3265	323	4	(	(	PUNCT
iajs-3265	323	5	b	b	NOUN
iajs-3265	323	6	)	)	PUNCT
iajs-3265	323	7	ihjpas	ihjpa	NOUN
iajs-3265	323	8	.	.	PUNCT
iajs-3265	324	1	36	36	NUM
iajs-3265	324	2	(	(	PUNCT
iajs-3265	324	3	4	4	NUM
iajs-3265	324	4	)	)	PUNCT
iajs-3265	324	5	2023	2023	NUM
iajs-3265	324	6	354	354	NUM
iajs-3265	324	7	furthermore	furthermore	ADV
iajs-3265	324	8	,	,	PUNCT
iajs-3265	324	9	figures	figure	NOUN
iajs-3265	324	10	(	(	PUNCT
iajs-3265	324	11	10	10	NUM
iajs-3265	324	12	and	and	CCONJ
iajs-3265	324	13	11	11	NUM
iajs-3265	324	14	)	)	PUNCT
iajs-3265	324	15	illustrate	illustrate	VERB
iajs-3265	324	16	the	the	DET
iajs-3265	324	17	logarithmic	logarithmic	ADJ
iajs-3265	324	18	plots	plot	NOUN
iajs-3265	324	19	of	of	ADP
iajs-3265	324	20	the	the	DET
iajs-3265	324	21	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	324	22	for	for	ADP
iajs-3265	324	23	the	the	DET
iajs-3265	324	24	novel	novel	ADJ
iajs-3265	324	25	approximate	approximate	ADJ
iajs-3265	324	26	solutions	solution	NOUN
iajs-3265	324	27	of	of	ADP
iajs-3265	324	28	the	the	DET
iajs-3265	324	29	falkner	falkner	PROPN
iajs-3265	324	30	-	-	PUNCT
iajs-3265	324	31	skan	skan	VERB
iajs-3265	324	32	equation	equation	NOUN
iajs-3265	324	33	with	with	ADP
iajs-3265	324	34	𝑛	𝑛	PROPN
iajs-3265	324	35	=	=	SYM
iajs-3265	324	36	2	2	NUM
iajs-3265	324	37	to	to	ADP
iajs-3265	324	38	8	8	NUM
iajs-3265	324	39	,	,	PUNCT
iajs-3265	324	40	by	by	ADP
iajs-3265	324	41	using	use	VERB
iajs-3265	324	42	the	the	DET
iajs-3265	324	43	ecm	ecm	NOUN
iajs-3265	324	44	and	and	CCONJ
iajs-3265	324	45	the	the	DET
iajs-3265	324	46	i	i	PROPN
iajs-3265	324	47	-	-	PUNCT
iajs-3265	324	48	ecms	ecms	PROPN
iajs-3265	324	49	for	for	ADP
iajs-3265	324	50	different	different	ADJ
iajs-3265	324	51	values	value	NOUN
iajs-3265	324	52	of	of	ADP
iajs-3265	324	53	𝛽	𝛽	NOUN
iajs-3265	324	54	when	when	SCONJ
iajs-3265	324	55	fixed	fix	VERB
iajs-3265	324	56	the	the	DET
iajs-3265	324	57	parameter	parameter	NOUN
iajs-3265	324	58	𝜖	𝜖	PROPN
iajs-3265	324	59	=	=	NOUN
iajs-3265	324	60	0.1	0.1	NUM
iajs-3265	324	61	.	.	PUNCT
iajs-3265	325	1	in	in	ADP
iajs-3265	325	2	figures	figure	NOUN
iajs-3265	325	3	(	(	PUNCT
iajs-3265	325	4	10	10	NUM
iajs-3265	325	5	and	and	CCONJ
iajs-3265	325	6	11	11	NUM
iajs-3265	325	7	)	)	PUNCT
iajs-3265	325	8	,	,	PUNCT
iajs-3265	325	9	it	it	PRON
iajs-3265	325	10	is	be	AUX
iajs-3265	325	11	evident	evident	ADJ
iajs-3265	325	12	that	that	SCONJ
iajs-3265	325	13	the	the	DET
iajs-3265	325	14	errors	error	NOUN
iajs-3265	325	15	increase	increase	VERB
iajs-3265	325	16	as	as	ADP
iajs-3265	325	17	the	the	DET
iajs-3265	325	18	values	value	NOUN
iajs-3265	325	19	of	of	ADP
iajs-3265	325	20	𝛽	𝛽	NOUN
iajs-3265	325	21	increase	increase	NOUN
iajs-3265	325	22	.	.	PUNCT
iajs-3265	326	1	(	(	PUNCT
iajs-3265	326	2	a	a	X
iajs-3265	326	3	)	)	PUNCT
iajs-3265	326	4	(	(	PUNCT
iajs-3265	326	5	b	b	X
iajs-3265	326	6	)	)	PUNCT
iajs-3265	326	7	figure	figure	NOUN
iajs-3265	326	8	10	10	NUM
iajs-3265	326	9	.	.	PUNCT
iajs-3265	327	1	logarithmic	logarithmic	ADJ
iajs-3265	327	2	plots	plot	NOUN
iajs-3265	327	3	of	of	ADP
iajs-3265	327	4	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	327	5	for	for	ADP
iajs-3265	327	6	the	the	DET
iajs-3265	327	7	falkner	falkner	PROPN
iajs-3265	327	8	-	-	PUNCT
iajs-3265	327	9	skan	skan	VERB
iajs-3265	327	10	equation	equation	NOUN
iajs-3265	327	11	by	by	ADP
iajs-3265	327	12	(	(	PUNCT
iajs-3265	327	13	a	a	PRON
iajs-3265	327	14	)	)	PUNCT
iajs-3265	327	15	ecm	ecm	NOUN
iajs-3265	327	16	based	base	VERB
iajs-3265	327	17	on	on	ADP
iajs-3265	327	18	the	the	DET
iajs-3265	327	19	standard	standard	ADJ
iajs-3265	327	20	polynomials	polynomial	NOUN
iajs-3265	327	21	and	and	CCONJ
iajs-3265	327	22	(	(	PUNCT
iajs-3265	327	23	b	b	X
iajs-3265	327	24	)	)	PUNCT
iajs-3265	327	25	i	i	PROPN
iajs-3265	327	26	-	-	PUNCT
iajs-3265	327	27	ecms	ecms	PROPN
iajs-3265	327	28	based	base	VERB
iajs-3265	327	29	on	on	ADP
iajs-3265	327	30	the	the	DET
iajs-3265	327	31	chebyshev	chebyshev	NOUN
iajs-3265	327	32	polynomials	polynomial	NOUN
iajs-3265	327	33	.	.	PUNCT
iajs-3265	328	1	(	(	PUNCT
iajs-3265	328	2	a	a	X
iajs-3265	328	3	)	)	PUNCT
iajs-3265	328	4	(	(	PUNCT
iajs-3265	328	5	b	b	X
iajs-3265	328	6	)	)	PUNCT
iajs-3265	328	7	figure	figure	NOUN
iajs-3265	328	8	11	11	NUM
iajs-3265	328	9	.	.	PUNCT
iajs-3265	329	1	logarithmic	logarithmic	ADJ
iajs-3265	329	2	plots	plot	NOUN
iajs-3265	329	3	of	of	ADP
iajs-3265	329	4	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	329	5	for	for	ADP
iajs-3265	329	6	the	the	DET
iajs-3265	329	7	falkner	falkner	PROPN
iajs-3265	329	8	-	-	PUNCT
iajs-3265	329	9	skan	skan	VERB
iajs-3265	329	10	equation	equation	NOUN
iajs-3265	329	11	by	by	ADP
iajs-3265	329	12	(	(	PUNCT
iajs-3265	329	13	a	a	X
iajs-3265	329	14	)	)	PUNCT
iajs-3265	329	15	i	i	PROPN
iajs-3265	329	16	-	-	PUNCT
iajs-3265	329	17	ecms	ecms	PROPN
iajs-3265	329	18	based	base	VERB
iajs-3265	329	19	on	on	ADP
iajs-3265	329	20	the	the	DET
iajs-3265	329	21	bernoulli	bernoulli	NOUN
iajs-3265	329	22	polynomials	polynomial	NOUN
iajs-3265	329	23	and	and	CCONJ
iajs-3265	329	24	(	(	PUNCT
iajs-3265	329	25	b	b	X
iajs-3265	329	26	)	)	PUNCT
iajs-3265	329	27	i	i	PROPN
iajs-3265	329	28	-	-	PUNCT
iajs-3265	329	29	ecms	ecms	PROPN
iajs-3265	329	30	based	base	VERB
iajs-3265	329	31	on	on	ADP
iajs-3265	329	32	the	the	DET
iajs-3265	329	33	laguerre	laguerre	NOUN
iajs-3265	329	34	polynomials	polynomial	NOUN
iajs-3265	329	35	.	.	PUNCT
iajs-3265	330	1	5	5	X
iajs-3265	330	2	.	.	X
iajs-3265	330	3	conclusions	conclusion	NOUN
iajs-3265	330	4	in	in	ADP
iajs-3265	330	5	this	this	DET
iajs-3265	330	6	paper	paper	NOUN
iajs-3265	330	7	,	,	PUNCT
iajs-3265	330	8	the	the	DET
iajs-3265	330	9	effective	effective	ADJ
iajs-3265	330	10	computational	computational	ADJ
iajs-3265	330	11	method	method	NOUN
iajs-3265	330	12	based	base	VERB
iajs-3265	330	13	on	on	ADP
iajs-3265	330	14	standard	standard	ADJ
iajs-3265	330	15	polynomials	polynomial	NOUN
iajs-3265	330	16	and	and	CCONJ
iajs-3265	330	17	the	the	DET
iajs-3265	330	18	novel	novel	ADJ
iajs-3265	330	19	effective	effective	ADJ
iajs-3265	330	20	computational	computational	ADJ
iajs-3265	330	21	methods	method	NOUN
iajs-3265	330	22	based	base	VERB
iajs-3265	330	23	on	on	ADP
iajs-3265	330	24	the	the	DET
iajs-3265	330	25	three	three	NUM
iajs-3265	330	26	different	different	ADJ
iajs-3265	330	27	types	type	NOUN
iajs-3265	330	28	of	of	ADP
iajs-3265	330	29	chebyshev	chebyshev	NOUN
iajs-3265	330	30	,	,	PUNCT
iajs-3265	330	31	bernoulli	bernoulli	PROPN
iajs-3265	330	32	,	,	PUNCT
iajs-3265	330	33	and	and	CCONJ
iajs-3265	330	34	laguerre	laguerre	NOUN
iajs-3265	330	35	polynomials	polynomial	NOUN
iajs-3265	330	36	have	have	AUX
iajs-3265	330	37	been	be	AUX
iajs-3265	330	38	implemented	implement	VERB
iajs-3265	330	39	to	to	PART
iajs-3265	330	40	solve	solve	VERB
iajs-3265	330	41	three	three	NUM
iajs-3265	330	42	nonlinear	nonlinear	ADJ
iajs-3265	330	43	models	model	NOUN
iajs-3265	330	44	involving	involve	VERB
iajs-3265	330	45	initial	initial	ADJ
iajs-3265	330	46	and	and	CCONJ
iajs-3265	330	47	boundary	boundary	ADJ
iajs-3265	330	48	value	value	NOUN
iajs-3265	330	49	problems	problem	NOUN
iajs-3265	330	50	.	.	PUNCT
iajs-3265	331	1	three	three	NUM
iajs-3265	331	2	models	model	NOUN
iajs-3265	331	3	,	,	PUNCT
iajs-3265	331	4	which	which	PRON
iajs-3265	331	5	are	be	AUX
iajs-3265	331	6	well	well	ADV
iajs-3265	331	7	-	-	PUNCT
iajs-3265	331	8	known	know	VERB
iajs-3265	331	9	nonlinear	nonlinear	ADJ
iajs-3265	331	10	problems	problem	NOUN
iajs-3265	331	11	:	:	PUNCT
iajs-3265	331	12	the	the	DET
iajs-3265	331	13	darcy	darcy	PROPN
iajs-3265	331	14	-	-	PUNCT
iajs-3265	331	15	brinkman	brinkman	PROPN
iajs-3265	331	16	-	-	PUNCT
iajs-3265	331	17	forchheimer	forchheimer	PROPN
iajs-3265	331	18	model	model	NOUN
iajs-3265	331	19	,	,	PUNCT
iajs-3265	331	20	the	the	DET
iajs-3265	331	21	blasius	blasius	ADJ
iajs-3265	331	22	model	model	NOUN
iajs-3265	331	23	,	,	PUNCT
iajs-3265	331	24	and	and	CCONJ
iajs-3265	331	25	the	the	DET
iajs-3265	331	26	falkner	falkner	PROPN
iajs-3265	331	27	-	-	PUNCT
iajs-3265	331	28	skan	skan	VERB
iajs-3265	331	29	model	model	NOUN
iajs-3265	331	30	,	,	PUNCT
iajs-3265	331	31	have	have	AUX
iajs-3265	331	32	been	be	AUX
iajs-3265	331	33	presented	present	VERB
iajs-3265	331	34	and	and	CCONJ
iajs-3265	331	35	solved	solve	VERB
iajs-3265	331	36	by	by	ADP
iajs-3265	331	37	using	use	VERB
iajs-3265	331	38	our	our	PRON
iajs-3265	331	39	suggested	suggest	VERB
iajs-3265	331	40	methods	method	NOUN
iajs-3265	331	41	.	.	PUNCT
iajs-3265	332	1	the	the	DET
iajs-3265	332	2	nonlinear	nonlinear	ADJ
iajs-3265	332	3	problems	problem	NOUN
iajs-3265	332	4	are	be	AUX
iajs-3265	332	5	reduced	reduce	VERB
iajs-3265	332	6	to	to	ADP
iajs-3265	332	7	a	a	DET
iajs-3265	332	8	nonlinear	nonlinear	ADJ
iajs-3265	332	9	algebraic	algebraic	ADJ
iajs-3265	332	10	system	system	NOUN
iajs-3265	332	11	of	of	ADP
iajs-3265	332	12	equations	equation	NOUN
iajs-3265	332	13	solved	solve	VERB
iajs-3265	332	14	with	with	ADP
iajs-3265	332	15	mathematica	mathematica	PROPN
iajs-3265	332	16	®	®	PROPN
iajs-3265	332	17	12	12	NUM
iajs-3265	332	18	.	.	PUNCT
iajs-3265	333	1	the	the	DET
iajs-3265	333	2	novel	novel	ADJ
iajs-3265	333	3	approximate	approximate	ADJ
iajs-3265	333	4	ihjpas	ihjpa	NOUN
iajs-3265	333	5	.	.	PUNCT
iajs-3265	334	1	36	36	NUM
iajs-3265	334	2	(	(	PUNCT
iajs-3265	334	3	4	4	NUM
iajs-3265	334	4	)	)	PUNCT
iajs-3265	334	5	2023	2023	NUM
iajs-3265	334	6	355	355	NUM
iajs-3265	334	7	solutions	solution	NOUN
iajs-3265	334	8	were	be	AUX
iajs-3265	334	9	obtained	obtain	VERB
iajs-3265	334	10	and	and	CCONJ
iajs-3265	334	11	proved	prove	VERB
iajs-3265	334	12	accurate	accurate	ADJ
iajs-3265	334	13	and	and	CCONJ
iajs-3265	334	14	reliable	reliable	ADJ
iajs-3265	334	15	,	,	PUNCT
iajs-3265	334	16	even	even	ADV
iajs-3265	334	17	within	within	ADP
iajs-3265	334	18	a	a	DET
iajs-3265	334	19	few	few	ADJ
iajs-3265	334	20	polynomial	polynomial	ADJ
iajs-3265	334	21	orders	order	NOUN
iajs-3265	334	22	.	.	PUNCT
iajs-3265	335	1	moreover	moreover	ADV
iajs-3265	335	2	,	,	PUNCT
iajs-3265	335	3	the	the	DET
iajs-3265	335	4	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	335	5	for	for	ADP
iajs-3265	335	6	the	the	DET
iajs-3265	335	7	proposed	propose	VERB
iajs-3265	335	8	methods	method	NOUN
iajs-3265	335	9	were	be	AUX
iajs-3265	335	10	calculated	calculate	VERB
iajs-3265	335	11	.	.	PUNCT
iajs-3265	336	1	the	the	DET
iajs-3265	336	2	results	result	NOUN
iajs-3265	336	3	show	show	VERB
iajs-3265	336	4	that	that	SCONJ
iajs-3265	336	5	the	the	DET
iajs-3265	336	6	proposed	propose	VERB
iajs-3265	336	7	approaches	approach	NOUN
iajs-3265	336	8	have	have	VERB
iajs-3265	336	9	higher	high	ADJ
iajs-3265	336	10	accuracy	accuracy	NOUN
iajs-3265	336	11	and	and	CCONJ
iajs-3265	336	12	less	less	ADJ
iajs-3265	336	13	error	error	NOUN
iajs-3265	336	14	.	.	PUNCT
iajs-3265	337	1	it	it	PRON
iajs-3265	337	2	is	be	AUX
iajs-3265	337	3	also	also	ADV
iajs-3265	337	4	observed	observe	VERB
iajs-3265	337	5	that	that	SCONJ
iajs-3265	337	6	the	the	DET
iajs-3265	337	7	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3265	337	8	results	result	NOUN
iajs-3265	337	9	of	of	ADP
iajs-3265	337	10	the	the	DET
iajs-3265	337	11	proposed	propose	VERB
iajs-3265	337	12	methods	method	NOUN
iajs-3265	337	13	i	i	PROPN
iajs-3265	337	14	-	-	PUNCT
iajs-3265	337	15	ecms	ecms	NOUN
iajs-3265	337	16	decrease	decrease	NOUN
iajs-3265	337	17	vastly	vastly	ADV
iajs-3265	337	18	compared	compare	VERB
iajs-3265	337	19	to	to	ADP
iajs-3265	337	20	the	the	DET
iajs-3265	337	21	ecm	ecm	NOUN
iajs-3265	337	22	.	.	PUNCT
iajs-3265	338	1	therefore	therefore	ADV
iajs-3265	338	2	,	,	PUNCT
iajs-3265	338	3	the	the	DET
iajs-3265	338	4	proposed	propose	VERB
iajs-3265	338	5	novel	novel	NOUN
iajs-3265	338	6	methods	method	NOUN
iajs-3265	338	7	i	i	PRON
iajs-3265	338	8	-	-	PUNCT
iajs-3265	338	9	ecms	ecms	PROPN
iajs-3265	338	10	have	have	VERB
iajs-3265	338	11	better	well	ADJ
iajs-3265	338	12	accuracy	accuracy	NOUN
iajs-3265	338	13	than	than	ADP
iajs-3265	338	14	the	the	DET
iajs-3265	338	15	ecm	ecm	NOUN
iajs-3265	338	16	.	.	PUNCT
iajs-3265	339	1	the	the	DET
iajs-3265	339	2	main	main	ADJ
iajs-3265	339	3	conclusion	conclusion	NOUN
iajs-3265	339	4	from	from	ADP
iajs-3265	339	5	the	the	DET
iajs-3265	339	6	results	result	NOUN
iajs-3265	339	7	is	be	AUX
iajs-3265	339	8	that	that	SCONJ
iajs-3265	339	9	the	the	DET
iajs-3265	339	10	chebyshev	chebyshev	NOUN
iajs-3265	339	11	polynomials	polynomial	NOUN
iajs-3265	339	12	-	-	PUNCT
iajs-3265	339	13	based	base	VERB
iajs-3265	339	14	i	i	PROPN
iajs-3265	339	15	-	-	PUNCT
iajs-3265	339	16	ecms	ecms	PROPN
iajs-3265	339	17	have	have	VERB
iajs-3265	339	18	slightly	slightly	ADV
iajs-3265	339	19	better	well	ADJ
iajs-3265	339	20	accuracy	accuracy	NOUN
iajs-3265	339	21	than	than	ADP
iajs-3265	339	22	the	the	DET
iajs-3265	339	23	other	other	ADJ
iajs-3265	339	24	methods	method	NOUN
iajs-3265	339	25	for	for	ADP
iajs-3265	339	26	solving	solve	VERB
iajs-3265	339	27	the	the	DET
iajs-3265	339	28	darcy	darcy	PROPN
iajs-3265	339	29	-	-	PUNCT
iajs-3265	339	30	brinkman	brinkman	PROPN
iajs-3265	339	31	-	-	PUNCT
iajs-3265	339	32	forchheimer	forchheimer	PROPN
iajs-3265	339	33	equation	equation	NOUN
iajs-3265	339	34	.	.	PUNCT
iajs-3265	340	1	moreover	moreover	ADV
iajs-3265	340	2	,	,	PUNCT
iajs-3265	340	3	the	the	DET
iajs-3265	340	4	i	i	PROPN
iajs-3265	340	5	-	-	PUNCT
iajs-3265	340	6	ecms	ecms	PROPN
iajs-3265	340	7	based	base	VERB
iajs-3265	340	8	on	on	ADP
iajs-3265	340	9	the	the	DET
iajs-3265	340	10	laguerre	laguerre	NOUN
iajs-3265	340	11	polynomials	polynomial	NOUN
iajs-3265	340	12	are	be	AUX
iajs-3265	340	13	more	more	ADV
iajs-3265	340	14	accurate	accurate	ADJ
iajs-3265	340	15	than	than	ADP
iajs-3265	340	16	the	the	DET
iajs-3265	340	17	other	other	ADJ
iajs-3265	340	18	methods	method	NOUN
iajs-3265	340	19	in	in	ADP
iajs-3265	340	20	solving	solve	VERB
iajs-3265	340	21	the	the	DET
iajs-3265	340	22	blasius	blasius	ADJ
iajs-3265	340	23	equation	equation	NOUN
iajs-3265	340	24	.	.	PUNCT
iajs-3265	341	1	in	in	ADP
iajs-3265	341	2	addition	addition	NOUN
iajs-3265	341	3	,	,	PUNCT
iajs-3265	341	4	the	the	DET
iajs-3265	341	5	i	i	PROPN
iajs-3265	341	6	-	-	PUNCT
iajs-3265	341	7	ecms	ecms	PROPN
iajs-3265	341	8	based	base	VERB
iajs-3265	341	9	on	on	ADP
iajs-3265	341	10	the	the	DET
iajs-3265	341	11	bernoulli	bernoulli	NOUN
iajs-3265	341	12	polynomials	polynomial	NOUN
iajs-3265	341	13	are	be	AUX
iajs-3265	341	14	slightly	slightly	ADV
iajs-3265	341	15	more	more	ADV
iajs-3265	341	16	accurate	accurate	ADJ
iajs-3265	341	17	than	than	ADP
iajs-3265	341	18	the	the	DET
iajs-3265	341	19	other	other	ADJ
iajs-3265	341	20	methods	method	NOUN
iajs-3265	341	21	in	in	ADP
iajs-3265	341	22	solving	solve	VERB
iajs-3265	341	23	the	the	DET
iajs-3265	341	24	falkner	falkner	PROPN
iajs-3265	341	25	-	-	PUNCT
iajs-3265	341	26	skan	skan	VERB
iajs-3265	341	27	equation	equation	NOUN
iajs-3265	341	28	.	.	PUNCT
iajs-3265	342	1	references	reference	NOUN
iajs-3265	342	2	1	1	NUM
iajs-3265	342	3	.	.	PUNCT
iajs-3265	343	1	hermann	hermann	PROPN
iajs-3265	343	2	,	,	PUNCT
iajs-3265	343	3	m.	m.	NOUN
iajs-3265	343	4	;	;	PUNCT
iajs-3265	343	5	saravi	saravi	NOUN
iajs-3265	343	6	,	,	PUNCT
iajs-3265	343	7	m.	m.	NOUN
iajs-3265	343	8	nonlinear	nonlinear	ADJ
iajs-3265	343	9	ordinary	ordinary	ADJ
iajs-3265	343	10	differential	differential	ADJ
iajs-3265	343	11	equations	equation	NOUN
iajs-3265	343	12	:	:	PUNCT
iajs-3265	343	13	analytical	analytical	ADJ
iajs-3265	343	14	approximation	approximation	NOUN
iajs-3265	343	15	and	and	CCONJ
iajs-3265	343	16	numerical	numerical	ADJ
iajs-3265	343	17	methods	method	NOUN
iajs-3265	343	18	.	.	PUNCT
iajs-3265	344	1	springer	springer	PROPN
iajs-3265	344	2	india	india	PROPN
iajs-3265	344	3	,	,	PUNCT
iajs-3265	344	4	2016	2016	NUM
iajs-3265	344	5	.	.	PUNCT
iajs-3265	345	1	2	2	X
iajs-3265	345	2	.	.	X
iajs-3265	345	3	kounadis	kounadis	PROPN
iajs-3265	345	4	,	,	PUNCT
iajs-3265	345	5	a.	a.	PROPN
iajs-3265	345	6	n.	n.	PROPN
iajs-3265	345	7	an	an	DET
iajs-3265	345	8	efficient	efficient	ADJ
iajs-3265	345	9	and	and	CCONJ
iajs-3265	345	10	simple	simple	ADJ
iajs-3265	345	11	approximate	approximate	ADJ
iajs-3265	345	12	technique	technique	NOUN
iajs-3265	345	13	for	for	ADP
iajs-3265	345	14	solving	solve	VERB
iajs-3265	345	15	nonlinear	nonlinear	ADJ
iajs-3265	345	16	initial	initial	ADJ
iajs-3265	345	17	and	and	CCONJ
iajs-3265	345	18	boundary	boundary	ADJ
iajs-3265	345	19	-	-	PUNCT
iajs-3265	345	20	value	value	NOUN
iajs-3265	345	21	problems	problem	NOUN
iajs-3265	345	22	.	.	PUNCT
iajs-3265	346	1	computational	computational	ADJ
iajs-3265	346	2	mechanics	mechanic	NOUN
iajs-3265	346	3	,	,	PUNCT
iajs-3265	346	4	1992	1992	NUM
iajs-3265	346	5	,	,	PUNCT
iajs-3265	346	6	9(3	9(3	NUM
iajs-3265	346	7	)	)	PUNCT
iajs-3265	346	8	,	,	PUNCT
iajs-3265	346	9	221	221	NUM
iajs-3265	346	10	-	-	SYM
iajs-3265	346	11	231	231	NUM
iajs-3265	346	12	.	.	PUNCT
iajs-3265	347	1	3	3	NUM
iajs-3265	347	2	.	.	X
iajs-3265	347	3	talib	talib	PROPN
iajs-3265	347	4	,	,	PUNCT
iajs-3265	347	5	i.	i.	NOUN
iajs-3265	347	6	;	;	PUNCT
iajs-3265	347	7	tunc	tunc	PROPN
iajs-3265	347	8	,	,	PUNCT
iajs-3265	347	9	c.	c.	PROPN
iajs-3265	347	10	;	;	PUNCT
iajs-3265	347	11	noor	noor	PROPN
iajs-3265	347	12	,	,	PUNCT
iajs-3265	347	13	z.	z.	PROPN
iajs-3265	347	14	a.	a.	PROPN
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iajs-3265	347	16	operational	operational	ADJ
iajs-3265	347	17	matrices	matrix	NOUN
iajs-3265	347	18	of	of	ADP
iajs-3265	347	19	orthogonal	orthogonal	ADJ
iajs-3265	347	20	legendre	legendre	PROPN
iajs-3265	347	21	polynomials	polynomial	NOUN
iajs-3265	347	22	and	and	CCONJ
iajs-3265	348	1	their	their	PRON
iajs-3265	348	2	operational	operational	ADJ
iajs-3265	348	3	.	.	PUNCT
iajs-3265	348	4	journal	journal	PROPN
iajs-3265	348	5	of	of	ADP
iajs-3265	348	6	taibah	taibah	PROPN
iajs-3265	348	7	university	university	PROPN
iajs-3265	348	8	for	for	ADP
iajs-3265	348	9	science	science	NOUN
iajs-3265	348	10	,	,	PUNCT
iajs-3265	348	11	2019	2019	NUM
iajs-3265	348	12	,	,	PUNCT
iajs-3265	348	13	13(1	13(1	NUM
iajs-3265	348	14	)	)	PUNCT
iajs-3265	348	15	,	,	PUNCT
iajs-3265	348	16	377	377	NUM
iajs-3265	348	17	-	-	SYM
iajs-3265	348	18	389	389	NUM
iajs-3265	348	19	.	.	PUNCT
iajs-3265	349	1	4	4	NUM
iajs-3265	349	2	.	.	X
iajs-3265	349	3	al	al	PROPN
iajs-3265	349	4	-	-	PUNCT
iajs-3265	349	5	jawary	jawary	PROPN
iajs-3265	349	6	,	,	PUNCT
iajs-3265	349	7	m.	m.	NOUN
iajs-3265	349	8	a.	a.	PROPN
iajs-3265	349	9	;	;	PUNCT
iajs-3265	349	10	salih	salih	PROPN
iajs-3265	349	11	,	,	PUNCT
iajs-3265	349	12	o.	o.	PROPN
iajs-3265	349	13	m.	m.	NOUN
iajs-3265	349	14	reliable	reliable	ADJ
iajs-3265	349	15	iterative	iterative	NOUN
iajs-3265	349	16	methods	method	NOUN
iajs-3265	349	17	for	for	ADP
iajs-3265	349	18	1d	1d	NUM
iajs-3265	349	19	swift	swift	ADJ
iajs-3265	349	20	–	–	PUNCT
iajs-3265	349	21	hohenberg	hohenberg	NOUN
iajs-3265	349	22	equation	equation	NOUN
iajs-3265	349	23	.	.	PUNCT
iajs-3265	350	1	arab	arab	PROPN
iajs-3265	350	2	journal	journal	PROPN
iajs-3265	350	3	of	of	ADP
iajs-3265	350	4	basic	basic	ADJ
iajs-3265	350	5	and	and	CCONJ
iajs-3265	350	6	applied	applied	ADJ
iajs-3265	350	7	sciences	science	NOUN
iajs-3265	350	8	,	,	PUNCT
iajs-3265	350	9	2020	2020	NUM
iajs-3265	350	10	,	,	PUNCT
iajs-3265	350	11	27(1	27(1	NUM
iajs-3265	350	12	)	)	PUNCT
iajs-3265	350	13	,	,	PUNCT
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iajs-3265	350	15	-	-	SYM
iajs-3265	350	16	66	66	NUM
iajs-3265	350	17	.	.	PUNCT
iajs-3265	351	1	5	5	X
iajs-3265	351	2	.	.	X
iajs-3265	351	3	umesh	umesh	PROPN
iajs-3265	351	4	;	;	PUNCT
iajs-3265	352	1	kumar	kumar	PROPN
iajs-3265	352	2	,	,	PUNCT
iajs-3265	352	3	m.	m.	NOUN
iajs-3265	352	4	numerical	numerical	PROPN
iajs-3265	352	5	solution	solution	NOUN
iajs-3265	352	6	of	of	ADP
iajs-3265	352	7	singular	singular	ADJ
iajs-3265	352	8	boundary	boundary	ADJ
iajs-3265	352	9	value	value	NOUN
iajs-3265	352	10	problems	problem	NOUN
iajs-3265	352	11	using	use	VERB
iajs-3265	352	12	advanced	advanced	ADJ
iajs-3265	352	13	adomian	adomian	NOUN
iajs-3265	352	14	decomposition	decomposition	NOUN
iajs-3265	352	15	method	method	NOUN
iajs-3265	352	16	.	.	PUNCT
iajs-3265	353	1	engineering	engineering	NOUN
iajs-3265	353	2	with	with	ADP
iajs-3265	353	3	computers	computer	NOUN
iajs-3265	353	4	,	,	PUNCT
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iajs-3265	353	6	,	,	PUNCT
iajs-3265	353	7	37(4	37(4	NUM
iajs-3265	353	8	)	)	PUNCT
iajs-3265	353	9	,	,	PUNCT
iajs-3265	353	10	2853	2853	NUM
iajs-3265	353	11	-	-	SYM
iajs-3265	353	12	2863	2863	NUM
iajs-3265	353	13	.	.	PUNCT
iajs-3265	354	1	6	6	NUM
iajs-3265	354	2	.	.	PUNCT
iajs-3265	354	3	harir	harir	NOUN
iajs-3265	354	4	,	,	PUNCT
iajs-3265	354	5	a.	a.	NOUN
iajs-3265	354	6	;	;	PUNCT
iajs-3265	354	7	melliani	melliani	PROPN
iajs-3265	354	8	,	,	PUNCT
iajs-3265	354	9	s.	s.	PROPN
iajs-3265	354	10	;	;	PUNCT
iajs-3265	354	11	el	el	PROPN
iajs-3265	354	12	harfi	harfi	PROPN
iajs-3265	354	13	,	,	PUNCT
iajs-3265	354	14	h.	h.	PROPN
iajs-3265	354	15	;	;	PUNCT
iajs-3265	354	16	chadli	chadli	PROPN
iajs-3265	354	17	,	,	PUNCT
iajs-3265	354	18	l.	l.	PROPN
iajs-3265	354	19	s.	s.	PROPN
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iajs-3265	354	21	iteration	iteration	PROPN
iajs-3265	354	22	method	method	NOUN
iajs-3265	354	23	and	and	CCONJ
iajs-3265	354	24	differential	differential	ADJ
iajs-3265	354	25	transformation	transformation	NOUN
iajs-3265	354	26	method	method	NOUN
iajs-3265	354	27	for	for	ADP
iajs-3265	354	28	solving	solve	VERB
iajs-3265	354	29	the	the	DET
iajs-3265	354	30	seir	seir	ADJ
iajs-3265	354	31	epidemic	epidemic	NOUN
iajs-3265	354	32	model	model	NOUN
iajs-3265	354	33	.	.	PUNCT
iajs-3265	355	1	international	international	ADJ
iajs-3265	355	2	journal	journal	PROPN
iajs-3265	355	3	of	of	ADP
iajs-3265	355	4	differential	differential	ADJ
iajs-3265	355	5	equations	equation	NOUN
iajs-3265	355	6	,	,	PUNCT
iajs-3265	355	7	2020	2020	NUM
iajs-3265	355	8	,	,	PUNCT
iajs-3265	355	9	2020	2020	NUM
iajs-3265	355	10	,	,	PUNCT
iajs-3265	355	11	1	1	NUM
iajs-3265	355	12	-	-	SYM
iajs-3265	355	13	7	7	NUM
iajs-3265	355	14	.	.	NOUN
iajs-3265	355	15	7	7	NUM
iajs-3265	355	16	.	.	X
iajs-3265	356	1	gohar	gohar	PROPN
iajs-3265	356	2	,	,	PUNCT
iajs-3265	356	3	m.	m.	NOUN
iajs-3265	356	4	;	;	PUNCT
iajs-3265	356	5	li	li	PROPN
iajs-3265	356	6	,	,	PUNCT
iajs-3265	356	7	c.	c.	PROPN
iajs-3265	356	8	;	;	PUNCT
iajs-3265	356	9	li	li	PROPN
iajs-3265	356	10	,	,	PUNCT
iajs-3265	356	11	z.	z.	PROPN
iajs-3265	356	12	finite	finite	PROPN
iajs-3265	356	13	difference	difference	NOUN
iajs-3265	356	14	methods	method	NOUN
iajs-3265	356	15	for	for	ADP
iajs-3265	356	16	caputo	caputo	PROPN
iajs-3265	356	17	–	–	PUNCT
iajs-3265	356	18	hadamard	hadamard	ADJ
iajs-3265	356	19	fractional	fractional	ADJ
iajs-3265	356	20	differential	differential	ADJ
iajs-3265	356	21	equations	equation	NOUN
iajs-3265	356	22	.	.	PUNCT
iajs-3265	357	1	mediterranean	mediterranean	PROPN
iajs-3265	357	2	journal	journal	PROPN
iajs-3265	357	3	of	of	ADP
iajs-3265	357	4	mathematics	mathematic	NOUN
iajs-3265	357	5	,	,	PUNCT
iajs-3265	357	6	2020	2020	NUM
iajs-3265	357	7	,	,	PUNCT
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iajs-3265	357	9	)	)	PUNCT
iajs-3265	357	10	,	,	PUNCT
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iajs-3265	357	12	-	-	SYM
iajs-3265	357	13	26	26	NUM
iajs-3265	357	14	.	.	NOUN
iajs-3265	357	15	8	8	NUM
iajs-3265	357	16	.	.	X
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iajs-3265	357	20	;	;	PUNCT
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iajs-3265	357	22	,	,	PUNCT
iajs-3265	357	23	k.	k.	PROPN
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iajs-3265	358	3	high	high	ADJ
iajs-3265	358	4	-	-	PUNCT
iajs-3265	358	5	order	order	NOUN
iajs-3265	358	6	numerical	numerical	ADJ
iajs-3265	358	7	method	method	NOUN
iajs-3265	358	8	for	for	ADP
iajs-3265	358	9	solving	solve	VERB
iajs-3265	358	10	singular	singular	ADJ
iajs-3265	358	11	two	two	NUM
iajs-3265	358	12	-	-	PUNCT
iajs-3265	358	13	point	point	NOUN
iajs-3265	358	14	boundary	boundary	ADJ
iajs-3265	358	15	value	value	NOUN
iajs-3265	358	16	problems	problem	NOUN
iajs-3265	358	17	.	.	PUNCT
iajs-3265	359	1	journal	journal	NOUN
iajs-3265	359	2	of	of	ADP
iajs-3265	359	3	computational	computational	ADJ
iajs-3265	359	4	and	and	CCONJ
iajs-3265	359	5	applied	applied	ADJ
iajs-3265	359	6	mathematics	mathematic	NOUN
iajs-3265	359	7	,	,	PUNCT
iajs-3265	359	8	2018	2018	NUM
iajs-3265	359	9	,	,	PUNCT
iajs-3265	359	10	343	343	NUM
iajs-3265	359	11	,	,	PUNCT
iajs-3265	359	12	556	556	NUM
iajs-3265	359	13	-	-	SYM
iajs-3265	359	14	574	574	NUM
iajs-3265	359	15	.	.	PUNCT
iajs-3265	360	1	9	9	X
iajs-3265	360	2	.	.	X
iajs-3265	360	3	ibraheem	ibraheem	PROPN
iajs-3265	360	4	,	,	PUNCT
iajs-3265	360	5	k.	k.	PROPN
iajs-3265	360	6	i.	i.	PROPN
iajs-3265	360	7	;	;	PUNCT
iajs-3265	360	8	mahmmood	mahmmood	PROPN
iajs-3265	360	9	,	,	PUNCT
iajs-3265	360	10	h.	h.	PROPN
iajs-3265	360	11	s.	s.	PROPN
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iajs-3265	360	13	for	for	ADP
iajs-3265	360	14	solving	solve	VERB
iajs-3265	360	15	fractional	fractional	ADJ
iajs-3265	360	16	partial	partial	ADJ
iajs-3265	360	17	differential	differential	NOUN
iajs-3265	360	18	equations	equation	NOUN
iajs-3265	360	19	using	use	VERB
iajs-3265	360	20	homotopy	homotopy	NOUN
iajs-3265	360	21	analysis	analysis	NOUN
iajs-3265	360	22	method	method	NOUN
iajs-3265	360	23	with	with	ADP
iajs-3265	360	24	pade	pade	NOUN
iajs-3265	360	25	approximation	approximation	NOUN
iajs-3265	360	26	.	.	PUNCT
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iajs-3265	361	2	journal	journal	NOUN
iajs-3265	361	3	of	of	ADP
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iajs-3265	361	5	and	and	CCONJ
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iajs-3265	361	7	engineering	engineering	NOUN
iajs-3265	361	8	,	,	PUNCT
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iajs-3265	361	10	,	,	PUNCT
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iajs-3265	361	12	)	)	PUNCT
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iajs-3265	361	15	-	-	SYM
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iajs-3265	362	17	,	,	PUNCT
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iajs-3265	362	21	matrix	matrix	NOUN
iajs-3265	362	22	method	method	NOUN
iajs-3265	362	23	for	for	ADP
iajs-3265	362	24	lane	lane	NOUN
iajs-3265	362	25	-	-	PUNCT
iajs-3265	362	26	emden	emden	NOUN
iajs-3265	362	27	problem	problem	NOUN
iajs-3265	362	28	.	.	PUNCT
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iajs-3265	363	2	engineering	engineering	NOUN
iajs-3265	363	3	,	,	PUNCT
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iajs-3265	363	5	,	,	PUNCT
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iajs-3265	363	7	)	)	PUNCT
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iajs-3265	363	11	9	9	NUM
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iajs-3265	363	13	11	11	NUM
iajs-3265	363	14	.	.	X
iajs-3265	364	1	singh	singh	PROPN
iajs-3265	364	2	,	,	PUNCT
iajs-3265	364	3	s.	s.	PROPN
iajs-3265	364	4	;	;	PUNCT
iajs-3265	364	5	patel	patel	PROPN
iajs-3265	364	6	,	,	PUNCT
iajs-3265	364	7	v.	v.	PROPN
iajs-3265	364	8	k.	k.	PROPN
iajs-3265	364	9	;	;	PUNCT
iajs-3265	364	10	singh	singh	PROPN
iajs-3265	364	11	,	,	PUNCT
iajs-3265	364	12	v.	v.	PROPN
iajs-3265	364	13	k.	k.	PROPN
iajs-3265	364	14	;	;	PUNCT
iajs-3265	364	15	tohidi	tohidi	PROPN
iajs-3265	364	16	,	,	PUNCT
iajs-3265	364	17	e.	e.	PROPN
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iajs-3265	364	19	of	of	ADP
iajs-3265	364	20	bernoulli	bernoulli	PROPN
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iajs-3265	364	29	telegraph	telegraph	NOUN
iajs-3265	364	30	equations	equation	NOUN
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iajs-3265	364	32	dirichlet	dirichlet	PROPN
iajs-3265	364	33	boundary	boundary	PROPN
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iajs-3265	365	3	mathematics	mathematic	NOUN
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iajs-3265	365	5	applications	application	NOUN
iajs-3265	365	6	,	,	PUNCT
iajs-3265	365	7	2018	2018	NUM
iajs-3265	365	8	,	,	PUNCT
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iajs-3265	365	10	)	)	PUNCT
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iajs-3265	365	13	-	-	SYM
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iajs-3265	366	2	.	.	PUNCT
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iajs-3265	366	4	,	,	PUNCT
iajs-3265	366	5	a.	a.	PROPN
iajs-3265	366	6	h.	h.	PROPN
iajs-3265	366	7	;	;	PUNCT
iajs-3265	366	8	taha	taha	PROPN
iajs-3265	366	9	,	,	PUNCT
iajs-3265	366	10	t.	t.	PROPN
iajs-3265	366	11	m.	m.	NOUN
iajs-3265	366	12	an	an	DET
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iajs-3265	366	14	matrix	matrix	NOUN
iajs-3265	366	15	of	of	ADP
iajs-3265	366	16	fractional	fractional	ADJ
iajs-3265	366	17	integration	integration	NOUN
iajs-3265	366	18	of	of	ADP
iajs-3265	366	19	the	the	DET
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iajs-3265	366	22	and	and	CCONJ
iajs-3265	366	23	its	its	PRON
iajs-3265	366	24	application	application	NOUN
iajs-3265	366	25	on	on	ADP
iajs-3265	366	26	a	a	DET
iajs-3265	366	27	semi	semi	ADJ
iajs-3265	366	28	-	-	ADJ
iajs-3265	366	29	infinite	infinite	ADJ
iajs-3265	366	30	interval	interval	NOUN
iajs-3265	366	31	.	.	PUNCT
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iajs-3265	367	2	sciences	sciences	PROPN
iajs-3265	367	3	,	,	PUNCT
iajs-3265	367	4	2012	2012	NUM
iajs-3265	367	5	,	,	PUNCT
iajs-3265	367	6	6(1	6(1	NUM
iajs-3265	367	7	)	)	PUNCT
iajs-3265	367	8	,	,	PUNCT
iajs-3265	367	9	1	1	NUM
iajs-3265	367	10	-	-	SYM
iajs-3265	367	11	7	7	NUM
iajs-3265	367	12	.	.	NOUN
iajs-3265	367	13	13	13	NUM
iajs-3265	367	14	.	.	PUNCT
iajs-3265	368	1	al	al	PROPN
iajs-3265	368	2	-	-	PUNCT
iajs-3265	368	3	jawary	jawary	PROPN
iajs-3265	368	4	,	,	PUNCT
iajs-3265	368	5	m.	m.	NOUN
iajs-3265	368	6	a.	a.	PROPN
iajs-3265	368	7	;	;	PUNCT
iajs-3265	368	8	abdul	abdul	PROPN
iajs-3265	368	9	nabi	nabi	PROPN
iajs-3265	368	10	,	,	PUNCT
iajs-3265	368	11	a.	a.	PROPN
iajs-3265	368	12	j.	j.	PROPN
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iajs-3265	368	16	for	for	ADP
iajs-3265	368	17	solving	solve	VERB
iajs-3265	368	18	jeffery	jeffery	PROPN
iajs-3265	368	19	-	-	PUNCT
iajs-3265	368	20	hamel	hamel	PROPN
iajs-3265	368	21	flow	flow	NOUN
iajs-3265	368	22	problem	problem	NOUN
iajs-3265	368	23	.	.	PUNCT
iajs-3265	369	1	kuwait	kuwait	PROPN
iajs-3265	369	2	journal	journal	PROPN
iajs-3265	369	3	of	of	ADP
iajs-3265	369	4	science	science	NOUN
iajs-3265	369	5	,	,	PUNCT
iajs-3265	369	6	2020	2020	NUM
iajs-3265	369	7	,	,	PUNCT
iajs-3265	369	8	47(1	47(1	NUM
iajs-3265	369	9	)	)	PUNCT
iajs-3265	369	10	,	,	PUNCT
iajs-3265	369	11	1	1	NUM
iajs-3265	369	12	-	-	SYM
iajs-3265	369	13	13	13	NUM
iajs-3265	369	14	.	.	PUNCT
iajs-3265	369	15	14	14	NUM
iajs-3265	369	16	.	.	PUNCT
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iajs-3265	370	2	,	,	PUNCT
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iajs-3265	370	7	,	,	PUNCT
iajs-3265	370	8	f.	f.	PROPN
iajs-3265	370	9	o.	o.	PROPN
iajs-3265	370	10	;	;	PUNCT
iajs-3265	370	11	bassey	bassey	PROPN
iajs-3265	370	12	,	,	PUNCT
iajs-3265	370	13	e.	e.	PROPN
iajs-3265	370	14	v.	v.	PROPN
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iajs-3265	370	17	and	and	CCONJ
iajs-3265	370	18	adomian	adomian	NOUN
iajs-3265	370	19	decomposition	decomposition	NOUN
iajs-3265	370	20	methods	method	NOUN
iajs-3265	370	21	on	on	ADP
iajs-3265	370	22	12th	12th	ADJ
iajs-3265	370	23	-	-	PUNCT
iajs-3265	370	24	order	order	NOUN
iajs-3265	370	25	boundary	boundary	ADJ
iajs-3265	370	26	value	value	NOUN
iajs-3265	370	27	problems	problem	NOUN
iajs-3265	370	28	.	.	PUNCT
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iajs-3265	371	2	in	in	ADP
iajs-3265	371	3	mathematics	mathematic	NOUN
iajs-3265	371	4	:	:	PUNCT
iajs-3265	371	5	scientific	scientific	ADJ
iajs-3265	371	6	journal	journal	NOUN
iajs-3265	371	7	,	,	PUNCT
iajs-3265	371	8	2020	2020	NUM
iajs-3265	371	9	,	,	PUNCT
iajs-3265	371	10	9(12	9(12	NUM
iajs-3265	371	11	)	)	PUNCT
iajs-3265	371	12	,	,	PUNCT
iajs-3265	371	13	10671	10671	NUM
iajs-3265	371	14	-	-	SYM
iajs-3265	371	15	10683	10683	NUM
iajs-3265	371	16	.	.	PUNCT
iajs-3265	372	1	ihjpas	ihjpas	PROPN
iajs-3265	372	2	.	.	PUNCT
iajs-3265	373	1	36	36	NUM
iajs-3265	373	2	(	(	PUNCT
iajs-3265	373	3	4	4	NUM
iajs-3265	373	4	)	)	PUNCT
iajs-3265	373	5	2023	2023	NUM
iajs-3265	373	6	356	356	NUM
iajs-3265	373	7	15	15	NUM
iajs-3265	373	8	.	.	PUNCT
iajs-3265	374	1	singh	singh	PROPN
iajs-3265	374	2	,	,	PUNCT
iajs-3265	374	3	r.	r.	PROPN
iajs-3265	374	4	a	a	DET
iajs-3265	374	5	modified	modify	VERB
iajs-3265	374	6	homotopy	homotopy	NOUN
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iajs-3265	374	8	method	method	NOUN
iajs-3265	374	9	for	for	ADP
iajs-3265	374	10	nonlinear	nonlinear	ADJ
iajs-3265	374	11	singular	singular	PROPN
iajs-3265	374	12	lane	lane	PROPN
iajs-3265	374	13	–	–	PUNCT
iajs-3265	374	14	emden	emden	ADJ
iajs-3265	374	15	equations	equation	NOUN
iajs-3265	374	16	arising	arise	VERB
iajs-3265	374	17	in	in	ADP
iajs-3265	374	18	various	various	ADJ
iajs-3265	374	19	physical	physical	ADJ
iajs-3265	374	20	models	model	NOUN
iajs-3265	374	21	.	.	PUNCT
iajs-3265	375	1	international	international	ADJ
iajs-3265	375	2	journal	journal	PROPN
iajs-3265	375	3	of	of	ADP
iajs-3265	375	4	applied	applied	ADJ
iajs-3265	375	5	and	and	CCONJ
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iajs-3265	375	7	mathematics	mathematic	NOUN
iajs-3265	375	8	,	,	PUNCT
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iajs-3265	375	10	,	,	PUNCT
iajs-3265	375	11	5(3	5(3	NUM
iajs-3265	375	12	)	)	PUNCT
iajs-3265	375	13	,	,	PUNCT
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iajs-3265	375	16	15	15	NUM
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iajs-3265	375	19	.	.	PUNCT
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iajs-3265	376	7	-	-	PUNCT
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iajs-3265	376	9	,	,	PUNCT
iajs-3265	376	10	m.	m.	NOUN
iajs-3265	376	11	a.	a.	NOUN
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iajs-3265	376	13	operational	operational	ADJ
iajs-3265	376	14	matrix	matrix	NOUN
iajs-3265	376	15	of	of	ADP
iajs-3265	376	16	legendre	legendre	PROPN
iajs-3265	376	17	polynomials	polynomial	NOUN
iajs-3265	376	18	for	for	ADP
iajs-3265	376	19	solving	solve	VERB
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iajs-3265	376	25	.	.	PUNCT
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iajs-3265	377	3	journal	journal	PROPN
iajs-3265	377	4	,	,	PUNCT
iajs-3265	377	5	2020	2020	NUM
iajs-3265	377	6	,	,	PUNCT
iajs-3265	377	7	59(5	59(5	NUM
iajs-3265	377	8	)	)	PUNCT
iajs-3265	377	9	,	,	PUNCT
iajs-3265	377	10	4027	4027	NUM
iajs-3265	377	11	-	-	SYM
iajs-3265	377	12	4033	4033	NUM
iajs-3265	377	13	.	.	PUNCT
iajs-3265	378	1	17	17	NUM
iajs-3265	378	2	.	.	PUNCT
iajs-3265	379	1	gürbüz	gürbüz	PROPN
iajs-3265	379	2	,	,	PUNCT
iajs-3265	379	3	b.	b.	PROPN
iajs-3265	379	4	;	;	PUNCT
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iajs-3265	379	6	,	,	PUNCT
iajs-3265	379	7	m.	m.	NOUN
iajs-3265	379	8	modified	modify	VERB
iajs-3265	379	9	operational	operational	ADJ
iajs-3265	379	10	matrix	matrix	NOUN
iajs-3265	379	11	method	method	NOUN
iajs-3265	379	12	for	for	ADP
iajs-3265	379	13	second	second	ADJ
iajs-3265	379	14	-	-	PUNCT
iajs-3265	379	15	order	order	NOUN
iajs-3265	379	16	nonlinear	nonlinear	ADJ
iajs-3265	379	17	ordinary	ordinary	ADJ
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iajs-3265	379	25	.	.	PUNCT
iajs-3265	380	1	an	an	DET
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iajs-3265	380	3	journal	journal	NOUN
iajs-3265	380	4	of	of	ADP
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iajs-3265	380	8	:	:	PUNCT
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iajs-3265	380	10	&	&	CCONJ
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iajs-3265	380	14	,	,	PUNCT
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iajs-3265	380	16	)	)	PUNCT
iajs-3265	380	17	,	,	PUNCT
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iajs-3265	380	19	-	-	SYM
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iajs-3265	380	23	.	.	PUNCT
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iajs-3265	381	6	o.	o.	PROPN
iajs-3265	381	7	;	;	PUNCT
iajs-3265	381	8	al	al	PROPN
iajs-3265	381	9	-	-	PUNCT
iajs-3265	381	10	saadawi	saadawi	PROPN
iajs-3265	381	11	,	,	PUNCT
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iajs-3265	381	13	a.	a.	PROPN
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iajs-3265	382	2	numerical	numerical	ADJ
iajs-3265	382	3	technique	technique	NOUN
iajs-3265	382	4	based	base	VERB
iajs-3265	382	5	on	on	ADP
iajs-3265	382	6	shifted	shift	VERB
iajs-3265	382	7	jacobigauss	jacobigauss	ADJ
iajs-3265	382	8	-	-	PUNCT
iajs-3265	382	9	lobatto	lobatto	NOUN
iajs-3265	382	10	polynomials	polynomial	NOUN
iajs-3265	382	11	for	for	ADP
iajs-3265	382	12	solving	solve	VERB
iajs-3265	382	13	two	two	NUM
iajs-3265	382	14	dimensional	dimensional	ADJ
iajs-3265	382	15	multi	multi	ADJ
iajs-3265	382	16	-	-	ADJ
iajs-3265	382	17	space	space	ADJ
iajs-3265	382	18	fractional	fractional	ADJ
iajs-3265	382	19	bioheat	bioheat	NOUN
iajs-3265	382	20	equations	equation	NOUN
iajs-3265	382	21	.	.	PUNCT
iajs-3265	383	1	baghdad	baghdad	PROPN
iajs-3265	383	2	science	science	PROPN
iajs-3265	383	3	journal	journal	PROPN
iajs-3265	383	4	,	,	PUNCT
iajs-3265	383	5	2020	2020	NUM
iajs-3265	383	6	,	,	PUNCT
iajs-3265	383	7	17(4	17(4	NUM
iajs-3265	383	8	)	)	PUNCT
iajs-3265	383	9	,	,	PUNCT
iajs-3265	383	10	1271	1271	NUM
iajs-3265	383	11	-	-	SYM
iajs-3265	383	12	1282	1282	NUM
iajs-3265	383	13	.	.	PUNCT
iajs-3265	384	1	19	19	NUM
iajs-3265	384	2	.	.	PUNCT
iajs-3265	385	1	al	al	PROPN
iajs-3265	385	2	-	-	PUNCT
iajs-3265	385	3	a’asam	a’asam	PROPN
iajs-3265	385	4	,	,	PUNCT
iajs-3265	385	5	j.	j.	PROPN
iajs-3265	385	6	a.	a.	PROPN
iajs-3265	385	7	deriving	derive	VERB
iajs-3265	385	8	the	the	DET
iajs-3265	385	9	composite	composite	ADJ
iajs-3265	385	10	simpson	simpson	NOUN
iajs-3265	385	11	rule	rule	NOUN
iajs-3265	385	12	by	by	ADP
iajs-3265	385	13	using	use	VERB
iajs-3265	385	14	bernstein	bernstein	PROPN
iajs-3265	385	15	polynomials	polynomial	NOUN
iajs-3265	385	16	for	for	ADP
iajs-3265	385	17	solving	solve	VERB
iajs-3265	385	18	volterra	volterra	NOUN
iajs-3265	385	19	integral	integral	ADJ
iajs-3265	385	20	equations	equation	NOUN
iajs-3265	385	21	.	.	PUNCT
iajs-3265	386	1	baghdad	baghdad	PROPN
iajs-3265	386	2	science	science	PROPN
iajs-3265	386	3	journal	journal	PROPN
iajs-3265	386	4	,	,	PUNCT
iajs-3265	386	5	2014	2014	NUM
iajs-3265	386	6	,	,	PUNCT
iajs-3265	386	7	11(3	11(3	NUM
iajs-3265	386	8	)	)	PUNCT
iajs-3265	386	9	,	,	PUNCT
iajs-3265	386	10	1274	1274	NUM
iajs-3265	386	11	-	-	SYM
iajs-3265	386	12	1282	1282	NUM
iajs-3265	386	13	.	.	PUNCT
iajs-3265	387	1	20	20	NUM
iajs-3265	387	2	.	.	PUNCT
iajs-3265	388	1	al	al	PROPN
iajs-3265	388	2	-	-	PUNCT
iajs-3265	388	3	jawary	jawary	PROPN
iajs-3265	388	4	,	,	PUNCT
iajs-3265	388	5	m.	m.	NOUN
iajs-3265	388	6	a.	a.	NOUN
iajs-3265	388	7	;	;	PUNCT
iajs-3265	388	8	ibraheem	ibraheem	ADJ
iajs-3265	388	9	,	,	PUNCT
iajs-3265	388	10	g.	g.	PROPN
iajs-3265	388	11	h.	h.	PROPN
iajs-3265	389	1	two	two	NUM
iajs-3265	389	2	meshless	meshless	ADJ
iajs-3265	389	3	methods	method	NOUN
iajs-3265	389	4	for	for	ADP
iajs-3265	389	5	solving	solve	VERB
iajs-3265	389	6	nonlinear	nonlinear	ADJ
iajs-3265	389	7	ordinary	ordinary	ADJ
iajs-3265	389	8	differential	differential	ADJ
iajs-3265	389	9	equations	equation	NOUN
iajs-3265	389	10	in	in	ADP
iajs-3265	389	11	engineering	engineering	NOUN
iajs-3265	389	12	and	and	CCONJ
iajs-3265	389	13	applied	apply	VERB
iajs-3265	389	14	sciences	science	NOUN
iajs-3265	389	15	.	.	PUNCT
iajs-3265	390	1	nonlinear	nonlinear	ADJ
iajs-3265	390	2	engineering	engineering	NOUN
iajs-3265	390	3	,	,	PUNCT
iajs-3265	390	4	2020	2020	NUM
iajs-3265	390	5	,	,	PUNCT
iajs-3265	390	6	9(1	9(1	NUM
iajs-3265	390	7	)	)	PUNCT
iajs-3265	390	8	,	,	PUNCT
iajs-3265	390	9	244	244	NUM
iajs-3265	390	10	-	-	SYM
iajs-3265	390	11	255	255	NUM
iajs-3265	390	12	.	.	PUNCT
iajs-3265	391	1	21	21	NUM
iajs-3265	391	2	.	.	PUNCT
iajs-3265	392	1	hasan	hasan	PROPN
iajs-3265	392	2	,	,	PUNCT
iajs-3265	392	3	p.	p.	NOUN
iajs-3265	392	4	m.	m.	NOUN
iajs-3265	392	5	;	;	PUNCT
iajs-3265	392	6	sulaiman	sulaiman	PROPN
iajs-3265	392	7	,	,	PUNCT
iajs-3265	392	8	n.	n.	NOUN
iajs-3265	392	9	a.	a.	NOUN
iajs-3265	392	10	convergence	convergence	NOUN
iajs-3265	392	11	analysis	analysis	NOUN
iajs-3265	392	12	for	for	ADP
iajs-3265	392	13	the	the	DET
iajs-3265	392	14	homotopy	homotopy	NOUN
iajs-3265	392	15	perturbation	perturbation	NOUN
iajs-3265	392	16	method	method	NOUN
iajs-3265	392	17	for	for	ADP
iajs-3265	392	18	a	a	DET
iajs-3265	392	19	linear	linear	ADJ
iajs-3265	392	20	system	system	NOUN
iajs-3265	392	21	of	of	ADP
iajs-3265	392	22	mixed	mixed	ADJ
iajs-3265	392	23	volterra	volterra	NOUN
iajs-3265	392	24	-	-	PUNCT
iajs-3265	392	25	fredholm	fredholm	NOUN
iajs-3265	392	26	integral	integral	ADJ
iajs-3265	392	27	equations	equation	NOUN
iajs-3265	392	28	.	.	PUNCT
iajs-3265	393	1	baghdad	baghdad	PROPN
iajs-3265	393	2	science	science	PROPN
iajs-3265	393	3	journal	journal	PROPN
iajs-3265	393	4	,	,	PUNCT
iajs-3265	393	5	2020	2020	NUM
iajs-3265	393	6	,	,	PUNCT
iajs-3265	393	7	17(3	17(3	NUM
iajs-3265	393	8	(	(	PUNCT
iajs-3265	393	9	suppl	suppl	PROPN
iajs-3265	393	10	.	.	PUNCT
iajs-3265	393	11	)	)	PUNCT
iajs-3265	393	12	)	)	PUNCT
iajs-3265	393	13	,	,	PUNCT
iajs-3265	393	14	1010	1010	NUM
iajs-3265	393	15	-	-	SYM
iajs-3265	393	16	1018	1018	NUM
iajs-3265	393	17	.	.	PUNCT
iajs-3265	394	1	22	22	NUM
iajs-3265	394	2	.	.	PUNCT
iajs-3265	394	3	ateeah	ateeah	NOUN
iajs-3265	394	4	,	,	PUNCT
iajs-3265	394	5	a.	a.	PROPN
iajs-3265	394	6	k.	k.	PROPN
iajs-3265	394	7	approximate	approximate	PROPN
iajs-3265	394	8	solution	solution	NOUN
iajs-3265	394	9	for	for	ADP
iajs-3265	394	10	fuzzy	fuzzy	ADJ
iajs-3265	394	11	differential	differential	ADJ
iajs-3265	394	12	algebraic	algebraic	ADJ
iajs-3265	394	13	equations	equation	NOUN
iajs-3265	394	14	of	of	ADP
iajs-3265	394	15	fractional	fractional	ADJ
iajs-3265	394	16	order	order	NOUN
iajs-3265	394	17	using	use	VERB
iajs-3265	394	18	adomian	adomian	NOUN
iajs-3265	394	19	decomposition	decomposition	NOUN
iajs-3265	394	20	method	method	NOUN
iajs-3265	394	21	.	.	PUNCT
iajs-3265	395	1	ibn	ibn	PROPN
iajs-3265	395	2	al	al	PROPN
iajs-3265	395	3	-	-	PUNCT
iajs-3265	395	4	haitham	haitham	PROPN
iajs-3265	395	5	journal	journal	PROPN
iajs-3265	395	6	for	for	ADP
iajs-3265	395	7	pure	pure	ADJ
iajs-3265	395	8	and	and	CCONJ
iajs-3265	395	9	applied	applied	ADJ
iajs-3265	395	10	science	science	NOUN
iajs-3265	395	11	,	,	PUNCT
iajs-3265	395	12	2017	2017	NUM
iajs-3265	395	13	,	,	PUNCT
iajs-3265	395	14	30(2	30(2	NUM
iajs-3265	395	15	)	)	PUNCT
iajs-3265	395	16	,	,	PUNCT
iajs-3265	395	17	202	202	NUM
iajs-3265	395	18	-	-	SYM
iajs-3265	395	19	213	213	NUM
iajs-3265	395	20	.	.	PUNCT
iajs-3265	395	21	23	23	NUM
iajs-3265	395	22	.	.	PUNCT
iajs-3265	396	1	abed	abe	VERB
iajs-3265	396	2	,	,	PUNCT
iajs-3265	396	3	s.	s.	PROPN
iajs-3265	396	4	m.	m.	PROPN
iajs-3265	396	5	;	;	PUNCT
iajs-3265	396	6	al	al	PROPN
iajs-3265	396	7	-	-	PUNCT
iajs-3265	396	8	jawary	jawary	PROPN
iajs-3265	396	9	,	,	PUNCT
iajs-3265	396	10	m.	m.	NOUN
iajs-3265	396	11	a.	a.	NOUN
iajs-3265	396	12	efficient	efficient	ADJ
iajs-3265	396	13	iterative	iterative	NOUN
iajs-3265	396	14	methods	method	NOUN
iajs-3265	396	15	for	for	ADP
iajs-3265	396	16	solving	solve	VERB
iajs-3265	396	17	the	the	DET
iajs-3265	396	18	sir	sir	NOUN
iajs-3265	396	19	epidemic	epidemic	NOUN
iajs-3265	396	20	model	model	NOUN
iajs-3265	396	21	.	.	PUNCT
iajs-3265	397	1	iraqi	iraqi	ADJ
iajs-3265	397	2	journal	journal	PROPN
iajs-3265	397	3	of	of	ADP
iajs-3265	397	4	science	science	NOUN
iajs-3265	397	5	,	,	PUNCT
iajs-3265	397	6	2021	2021	NUM
iajs-3265	397	7	,	,	PUNCT
iajs-3265	397	8	62(2	62(2	NUM
iajs-3265	397	9	)	)	PUNCT
iajs-3265	397	10	,	,	PUNCT
iajs-3265	397	11	613	613	NUM
iajs-3265	397	12	-	-	SYM
iajs-3265	397	13	622	622	NUM
iajs-3265	397	14	.	.	PUNCT
iajs-3265	398	1	24	24	NUM
iajs-3265	398	2	.	.	X
iajs-3265	398	3	sparis	sparis	PROPN
iajs-3265	398	4	,	,	PUNCT
iajs-3265	398	5	p.	p.	PROPN
iajs-3265	398	6	d.	d.	PROPN
iajs-3265	398	7	;	;	PUNCT
iajs-3265	398	8	mouroutsos	mouroutsos	PROPN
iajs-3265	398	9	,	,	PUNCT
iajs-3265	398	10	s.	s.	PROPN
iajs-3265	398	11	g.	g.	PROPN
iajs-3265	398	12	the	the	DET
iajs-3265	398	13	operational	operational	ADJ
iajs-3265	398	14	matrix	matrix	NOUN
iajs-3265	398	15	of	of	ADP
iajs-3265	398	16	differentiation	differentiation	NOUN
iajs-3265	398	17	for	for	ADP
iajs-3265	398	18	orthogonal	orthogonal	ADJ
iajs-3265	398	19	polynomial	polynomial	ADJ
iajs-3265	398	20	series	series	NOUN
iajs-3265	398	21	.	.	PUNCT
iajs-3265	399	1	international	international	ADJ
iajs-3265	399	2	journal	journal	PROPN
iajs-3265	399	3	of	of	ADP
iajs-3265	399	4	control	control	NOUN
iajs-3265	399	5	,	,	PUNCT
iajs-3265	399	6	1986	1986	NUM
iajs-3265	399	7	,	,	PUNCT
iajs-3265	399	8	44(1	44(1	PROPN
iajs-3265	399	9	)	)	PUNCT
iajs-3265	399	10	,	,	PUNCT
iajs-3265	399	11	1	1	NUM
iajs-3265	399	12	-	-	SYM
iajs-3265	399	13	15	15	NUM
iajs-3265	399	14	.	.	X
iajs-3265	400	1	25	25	NUM
iajs-3265	400	2	.	.	PUNCT
iajs-3265	400	3	yousefi	yousefi	PROPN
iajs-3265	400	4	,	,	PUNCT
iajs-3265	400	5	s.	s.	PROPN
iajs-3265	400	6	a.	a.	PROPN
iajs-3265	400	7	;	;	PUNCT
iajs-3265	400	8	behroozifar	behroozifar	ADV
iajs-3265	400	9	,	,	PUNCT
iajs-3265	400	10	m.	m.	NOUN
iajs-3265	400	11	operational	operational	ADJ
iajs-3265	400	12	matrices	matrix	NOUN
iajs-3265	400	13	of	of	ADP
iajs-3265	400	14	bernstein	bernstein	PROPN
iajs-3265	400	15	polynomials	polynomial	NOUN
iajs-3265	400	16	and	and	CCONJ
iajs-3265	400	17	their	their	PRON
iajs-3265	400	18	applications	application	NOUN
iajs-3265	400	19	.	.	PUNCT
iajs-3265	401	1	international	international	ADJ
iajs-3265	401	2	journal	journal	PROPN
iajs-3265	401	3	of	of	ADP
iajs-3265	401	4	systems	system	NOUN
iajs-3265	401	5	science	science	NOUN
iajs-3265	401	6	,	,	PUNCT
iajs-3265	401	7	2010	2010	NUM
iajs-3265	401	8	,	,	PUNCT
iajs-3265	401	9	41(6	41(6	NOUN
iajs-3265	401	10	)	)	PUNCT
iajs-3265	401	11	,	,	PUNCT
iajs-3265	401	12	709	709	NUM
iajs-3265	401	13	-	-	SYM
iajs-3265	401	14	716	716	NUM
iajs-3265	401	15	.	.	X
iajs-3265	401	16	26	26	NUM
iajs-3265	401	17	.	.	X
iajs-3265	401	18	öztürk	öztürk	NOUN
iajs-3265	401	19	,	,	PUNCT
iajs-3265	401	20	y.	y.	PROPN
iajs-3265	401	21	numerical	numerical	PROPN
iajs-3265	401	22	solution	solution	NOUN
iajs-3265	401	23	of	of	ADP
iajs-3265	401	24	systems	system	NOUN
iajs-3265	401	25	of	of	ADP
iajs-3265	401	26	differential	differential	ADJ
iajs-3265	401	27	equations	equation	NOUN
iajs-3265	401	28	using	use	VERB
iajs-3265	401	29	operational	operational	ADJ
iajs-3265	401	30	matrix	matrix	NOUN
iajs-3265	401	31	method	method	NOUN
iajs-3265	401	32	with	with	ADP
iajs-3265	401	33	chebyshev	chebyshev	NOUN
iajs-3265	401	34	polynomials	polynomial	NOUN
iajs-3265	401	35	.	.	PUNCT
iajs-3265	402	1	journal	journal	PROPN
iajs-3265	402	2	of	of	ADP
iajs-3265	402	3	taibah	taibah	PROPN
iajs-3265	402	4	university	university	PROPN
iajs-3265	402	5	for	for	ADP
iajs-3265	402	6	science	science	NOUN
iajs-3265	402	7	,	,	PUNCT
iajs-3265	402	8	2018	2018	NUM
iajs-3265	402	9	,	,	PUNCT
iajs-3265	402	10	12(2	12(2	NUM
iajs-3265	402	11	)	)	PUNCT
iajs-3265	402	12	,	,	PUNCT
iajs-3265	402	13	155	155	NUM
iajs-3265	402	14	-	-	SYM
iajs-3265	402	15	162	162	NUM
iajs-3265	402	16	.	.	PUNCT
iajs-3265	402	17	27	27	NUM
iajs-3265	402	18	.	.	PUNCT
iajs-3265	403	1	bazm	bazm	PROPN
iajs-3265	403	2	,	,	PUNCT
iajs-3265	403	3	s.	s.	PROPN
iajs-3265	403	4	;	;	PUNCT
iajs-3265	403	5	hosseini	hosseini	PROPN
iajs-3265	403	6	,	,	PUNCT
iajs-3265	403	7	a.	a.	NOUN
iajs-3265	403	8	bernoulli	bernoulli	PROPN
iajs-3265	403	9	operational	operational	ADJ
iajs-3265	403	10	matrix	matrix	NOUN
iajs-3265	403	11	method	method	NOUN
iajs-3265	403	12	for	for	ADP
iajs-3265	403	13	the	the	DET
iajs-3265	403	14	numerical	numerical	ADJ
iajs-3265	403	15	solution	solution	NOUN
iajs-3265	403	16	of	of	ADP
iajs-3265	403	17	nonlinear	nonlinear	ADJ
iajs-3265	403	18	two	two	NUM
iajs-3265	403	19	-	-	PUNCT
iajs-3265	403	20	dimensional	dimensional	ADJ
iajs-3265	403	21	volterra	volterra	NOUN
iajs-3265	403	22	–	–	PUNCT
iajs-3265	403	23	fredholm	fredholm	ADJ
iajs-3265	403	24	integral	integral	ADJ
iajs-3265	403	25	equations	equation	NOUN
iajs-3265	403	26	of	of	ADP
iajs-3265	403	27	hammerstein	hammerstein	PROPN
iajs-3265	403	28	type	type	PROPN
iajs-3265	403	29	.	.	PUNCT
iajs-3265	404	1	computational	computational	ADJ
iajs-3265	404	2	and	and	CCONJ
iajs-3265	404	3	applied	applied	ADJ
iajs-3265	404	4	mathematics	mathematic	NOUN
iajs-3265	404	5	,	,	PUNCT
iajs-3265	404	6	2020	2020	NUM
iajs-3265	404	7	,	,	PUNCT
iajs-3265	404	8	39(2	39(2	NUM
iajs-3265	404	9	)	)	PUNCT
iajs-3265	404	10	,	,	PUNCT
iajs-3265	404	11	1	1	NUM
iajs-3265	404	12	-	-	SYM
iajs-3265	404	13	20	20	NUM
iajs-3265	404	14	.	.	PUNCT
iajs-3265	404	15	28	28	NUM
iajs-3265	404	16	.	.	PUNCT
iajs-3265	405	1	abdelkawy	abdelkawy	PROPN
iajs-3265	405	2	,	,	PUNCT
iajs-3265	405	3	m.	m.	NOUN
iajs-3265	405	4	a.	a.	PROPN
iajs-3265	405	5	;	;	PUNCT
iajs-3265	405	6	taha	taha	PROPN
iajs-3265	405	7	,	,	PUNCT
iajs-3265	405	8	t.	t.	PROPN
iajs-3265	405	9	m.	m.	NOUN
iajs-3265	405	10	an	an	DET
iajs-3265	405	11	operational	operational	ADJ
iajs-3265	405	12	matrix	matrix	NOUN
iajs-3265	405	13	of	of	ADP
iajs-3265	405	14	fractional	fractional	ADJ
iajs-3265	405	15	derivatives	derivative	NOUN
iajs-3265	405	16	of	of	ADP
iajs-3265	405	17	laguerre	laguerre	NOUN
iajs-3265	405	18	polynomials	polynomial	NOUN
iajs-3265	405	19	.	.	PUNCT
iajs-3265	406	1	walailak	walailak	ADJ
iajs-3265	406	2	journal	journal	NOUN
iajs-3265	406	3	of	of	ADP
iajs-3265	406	4	science	science	NOUN
iajs-3265	406	5	and	and	CCONJ
iajs-3265	406	6	technology	technology	NOUN
iajs-3265	406	7	,	,	PUNCT
iajs-3265	406	8	2014	2014	NUM
iajs-3265	406	9	,	,	PUNCT
iajs-3265	406	10	11(12	11(12	NUM
iajs-3265	406	11	)	)	PUNCT
iajs-3265	406	12	,	,	PUNCT
iajs-3265	406	13	1041	1041	NUM
iajs-3265	406	14	-	-	SYM
iajs-3265	406	15	1055	1055	NUM
iajs-3265	406	16	.	.	PUNCT
iajs-3265	407	1	29	29	NUM
iajs-3265	407	2	.	.	X
iajs-3265	407	3	turkyilmazoglu	turkyilmazoglu	NOUN
iajs-3265	407	4	,	,	PUNCT
iajs-3265	407	5	m.	m.	NOUN
iajs-3265	407	6	effective	effective	ADJ
iajs-3265	407	7	computation	computation	NOUN
iajs-3265	407	8	of	of	ADP
iajs-3265	407	9	exact	exact	ADJ
iajs-3265	407	10	and	and	CCONJ
iajs-3265	407	11	analytic	analytic	ADJ
iajs-3265	407	12	approximate	approximate	ADJ
iajs-3265	407	13	solutions	solution	NOUN
iajs-3265	407	14	to	to	PART
iajs-3265	407	15	singular	singular	VERB
iajs-3265	407	16	nonlinear	nonlinear	ADJ
iajs-3265	407	17	equations	equation	NOUN
iajs-3265	407	18	of	of	ADP
iajs-3265	407	19	lane	lane	NOUN
iajs-3265	407	20	–	–	PUNCT
iajs-3265	407	21	emden	emden	ADJ
iajs-3265	407	22	–	–	PUNCT
iajs-3265	407	23	fowler	fowler	PROPN
iajs-3265	407	24	type	type	NOUN
iajs-3265	407	25	.	.	PUNCT
iajs-3265	408	1	applied	apply	VERB
iajs-3265	408	2	mathematical	mathematical	ADJ
iajs-3265	408	3	modelling	modelling	NOUN
iajs-3265	408	4	,	,	PUNCT
iajs-3265	408	5	2013	2013	NUM
iajs-3265	408	6	,	,	PUNCT
iajs-3265	408	7	37(14	37(14	NUM
iajs-3265	408	8	-	-	SYM
iajs-3265	408	9	15	15	NUM
iajs-3265	408	10	)	)	PUNCT
iajs-3265	408	11	,	,	PUNCT
iajs-3265	408	12	7539	7539	NUM
iajs-3265	408	13	-	-	SYM
iajs-3265	408	14	7548	7548	NUM
iajs-3265	408	15	.	.	PUNCT
iajs-3265	409	1	30	30	NUM
iajs-3265	409	2	.	.	PUNCT
iajs-3265	409	3	turkyilmazoglu	turkyilmazoglu	NOUN
iajs-3265	409	4	,	,	PUNCT
iajs-3265	409	5	m.	m.	NOUN
iajs-3265	409	6	an	an	DET
iajs-3265	409	7	effective	effective	ADJ
iajs-3265	409	8	approach	approach	NOUN
iajs-3265	409	9	for	for	ADP
iajs-3265	409	10	numerical	numerical	ADJ
iajs-3265	409	11	solutions	solution	NOUN
iajs-3265	409	12	of	of	ADP
iajs-3265	409	13	high	high	ADJ
iajs-3265	409	14	-	-	PUNCT
iajs-3265	409	15	order	order	NOUN
iajs-3265	409	16	fredholm	fredholm	NOUN
iajs-3265	409	17	integro	integro	ADJ
iajs-3265	409	18	-	-	PUNCT
iajs-3265	409	19	differential	differential	NOUN
iajs-3265	409	20	equations	equation	NOUN
iajs-3265	409	21	.	.	PUNCT
iajs-3265	410	1	applied	apply	VERB
iajs-3265	410	2	mathematics	mathematic	NOUN
iajs-3265	410	3	and	and	CCONJ
iajs-3265	410	4	computation	computation	NOUN
iajs-3265	410	5	,	,	PUNCT
iajs-3265	410	6	2014	2014	NUM
iajs-3265	410	7	,	,	PUNCT
iajs-3265	410	8	227(15	227(15	NUM
iajs-3265	410	9	)	)	PUNCT
iajs-3265	410	10	,	,	PUNCT
iajs-3265	410	11	384398	384398	NUM
iajs-3265	410	12	.	.	PUNCT
iajs-3265	411	1	31	31	NUM
iajs-3265	411	2	.	.	PUNCT
iajs-3265	411	3	turkyilmazoglu	turkyilmazoglu	NOUN
iajs-3265	411	4	,	,	PUNCT
iajs-3265	411	5	m.	m.	NOUN
iajs-3265	411	6	high	high	ADJ
iajs-3265	411	7	-	-	PUNCT
iajs-3265	411	8	order	order	NOUN
iajs-3265	411	9	nonlinear	nonlinear	PROPN
iajs-3265	411	10	volterra	volterra	PROPN
iajs-3265	411	11	–	–	PUNCT
iajs-3265	411	12	fredholm	fredholm	NOUN
iajs-3265	411	13	-	-	PUNCT
iajs-3265	411	14	hammerstein	hammerstein	NOUN
iajs-3265	411	15	integrodifferential	integrodifferential	ADJ
iajs-3265	411	16	equations	equation	NOUN
iajs-3265	411	17	and	and	CCONJ
iajs-3265	411	18	their	their	PRON
iajs-3265	411	19	effective	effective	ADJ
iajs-3265	411	20	computation	computation	NOUN
iajs-3265	411	21	.	.	PUNCT
iajs-3265	412	1	applied	apply	VERB
iajs-3265	412	2	mathematics	mathematic	NOUN
iajs-3265	412	3	and	and	CCONJ
iajs-3265	412	4	computation	computation	NOUN
iajs-3265	412	5	,	,	PUNCT
iajs-3265	412	6	2014	2014	NUM
iajs-3265	412	7	,	,	PUNCT
iajs-3265	412	8	247	247	NUM
iajs-3265	412	9	,	,	PUNCT
iajs-3265	412	10	410	410	NUM
iajs-3265	412	11	-	-	SYM
iajs-3265	412	12	416	416	NUM
iajs-3265	412	13	.	.	PUNCT
iajs-3265	413	1	32	32	NUM
iajs-3265	413	2	.	.	X
iajs-3265	414	1	turkyilmazoglu	turkyilmazoglu	NOUN
iajs-3265	414	2	,	,	PUNCT
iajs-3265	414	3	m.	m.	NOUN
iajs-3265	414	4	effective	effective	ADJ
iajs-3265	414	5	computation	computation	NOUN
iajs-3265	414	6	of	of	ADP
iajs-3265	414	7	solutions	solution	NOUN
iajs-3265	414	8	for	for	ADP
iajs-3265	414	9	nonlinear	nonlinear	ADJ
iajs-3265	414	10	heat	heat	NOUN
iajs-3265	414	11	transfer	transfer	NOUN
iajs-3265	414	12	problems	problem	NOUN
iajs-3265	414	13	in	in	ADP
iajs-3265	414	14	fins	fin	NOUN
iajs-3265	414	15	.	.	PUNCT
iajs-3265	415	1	journal	journal	PROPN
iajs-3265	415	2	of	of	ADP
iajs-3265	415	3	heat	heat	NOUN
iajs-3265	415	4	transfer	transfer	NOUN
iajs-3265	415	5	,	,	PUNCT
iajs-3265	415	6	2014	2014	NUM
iajs-3265	415	7	,	,	PUNCT
iajs-3265	415	8	136(9	136(9	NUM
iajs-3265	415	9	)	)	PUNCT
iajs-3265	415	10	,	,	PUNCT
iajs-3265	415	11	091901	091901	NUM
iajs-3265	415	12	.	.	PUNCT
iajs-3265	416	1	33	33	NUM
iajs-3265	416	2	.	.	PUNCT
iajs-3265	416	3	turkyilmazoglu	turkyilmazoglu	NOUN
iajs-3265	416	4	,	,	PUNCT
iajs-3265	416	5	m.	m.	NOUN
iajs-3265	416	6	solution	solution	NOUN
iajs-3265	416	7	of	of	ADP
iajs-3265	416	8	initial	initial	ADJ
iajs-3265	416	9	and	and	CCONJ
iajs-3265	416	10	boundary	boundary	ADJ
iajs-3265	416	11	value	value	NOUN
iajs-3265	416	12	problems	problem	NOUN
iajs-3265	416	13	by	by	ADP
iajs-3265	416	14	an	an	DET
iajs-3265	416	15	effective	effective	ADJ
iajs-3265	416	16	accurate	accurate	ADJ
iajs-3265	416	17	method	method	NOUN
iajs-3265	416	18	.	.	PUNCT
iajs-3265	417	1	international	international	ADJ
iajs-3265	417	2	journal	journal	NOUN
iajs-3265	417	3	of	of	ADP
iajs-3265	417	4	computational	computational	ADJ
iajs-3265	417	5	methods	method	NOUN
iajs-3265	417	6	,	,	PUNCT
iajs-3265	417	7	2017	2017	NUM
iajs-3265	417	8	,	,	PUNCT
iajs-3265	417	9	14(06	14(06	NUM
iajs-3265	417	10	)	)	PUNCT
iajs-3265	417	11	,	,	PUNCT
iajs-3265	417	12	1750069	1750069	NUM
iajs-3265	417	13	.	.	PUNCT
iajs-3265	418	1	ihjpas	ihjpas	PROPN
iajs-3265	418	2	.	.	PUNCT
iajs-3265	419	1	36	36	NUM
iajs-3265	419	2	(	(	PUNCT
iajs-3265	419	3	4	4	NUM
iajs-3265	419	4	)	)	PUNCT
iajs-3265	419	5	2023	2023	NUM
iajs-3265	419	6	357	357	NUM
iajs-3265	419	7	34	34	NUM
iajs-3265	419	8	.	.	PUNCT
iajs-3265	420	1	shaban	shaban	PROPN
iajs-3265	420	2	,	,	PUNCT
iajs-3265	420	3	m.	m.	NOUN
iajs-3265	420	4	;	;	PUNCT
iajs-3265	420	5	kazem	kazem	PROPN
iajs-3265	420	6	,	,	PUNCT
iajs-3265	420	7	s.	s.	PROPN
iajs-3265	420	8	;	;	PUNCT
iajs-3265	420	9	rad	rad	PROPN
iajs-3265	420	10	,	,	PUNCT
iajs-3265	420	11	j.	j.	PROPN
iajs-3265	420	12	a.	a.	PROPN
iajs-3265	420	13	a	a	DET
iajs-3265	420	14	modification	modification	NOUN
iajs-3265	420	15	of	of	ADP
iajs-3265	420	16	the	the	DET
iajs-3265	420	17	homotopy	homotopy	NOUN
iajs-3265	420	18	analysis	analysis	NOUN
iajs-3265	420	19	method	method	NOUN
iajs-3265	420	20	based	base	VERB
iajs-3265	420	21	on	on	ADP
iajs-3265	420	22	chebyshev	chebyshev	PROPN
iajs-3265	420	23	operational	operational	ADJ
iajs-3265	420	24	matrices	matrix	NOUN
iajs-3265	420	25	.	.	PUNCT
iajs-3265	421	1	mathematical	mathematical	ADJ
iajs-3265	421	2	and	and	CCONJ
iajs-3265	421	3	computer	computer	NOUN
iajs-3265	421	4	modelling	modelling	NOUN
iajs-3265	421	5	,	,	PUNCT
iajs-3265	421	6	2013	2013	NUM
iajs-3265	421	7	,	,	PUNCT
iajs-3265	421	8	57(5	57(5	PROPN
iajs-3265	421	9	-	-	SYM
iajs-3265	421	10	6	6	NUM
iajs-3265	421	11	)	)	PUNCT
iajs-3265	421	12	,	,	PUNCT
iajs-3265	421	13	1227	1227	NUM
iajs-3265	421	14	-	-	SYM
iajs-3265	421	15	1239	1239	NUM
iajs-3265	421	16	.	.	PUNCT
iajs-3265	421	17	35	35	NUM
iajs-3265	421	18	.	.	PUNCT
iajs-3265	422	1	motsa	motsa	PROPN
iajs-3265	422	2	,	,	PUNCT
iajs-3265	422	3	s.	s.	PROPN
iajs-3265	422	4	s.	s.	PROPN
iajs-3265	422	5	;	;	PUNCT
iajs-3265	422	6	sibanda	sibanda	NOUN
iajs-3265	422	7	,	,	PUNCT
iajs-3265	422	8	p.	p.	NOUN
iajs-3265	422	9	;	;	PUNCT
iajs-3265	422	10	shateyi	shateyi	PROPN
iajs-3265	422	11	,	,	PUNCT
iajs-3265	422	12	s.	s.	PROPN
iajs-3265	422	13	a	a	DET
iajs-3265	422	14	new	new	ADJ
iajs-3265	422	15	spectral	spectral	ADJ
iajs-3265	422	16	-	-	PUNCT
iajs-3265	422	17	homotopy	homotopy	NOUN
iajs-3265	422	18	analysis	analysis	NOUN
iajs-3265	422	19	method	method	NOUN
iajs-3265	422	20	for	for	ADP
iajs-3265	422	21	solving	solve	VERB
iajs-3265	422	22	a	a	DET
iajs-3265	422	23	nonlinear	nonlinear	ADJ
iajs-3265	422	24	second	second	ADJ
iajs-3265	422	25	order	order	NOUN
iajs-3265	422	26	bvp	bvp	NOUN
iajs-3265	422	27	.	.	PUNCT
iajs-3265	423	1	communications	communication	NOUN
iajs-3265	423	2	in	in	ADP
iajs-3265	423	3	nonlinear	nonlinear	ADJ
iajs-3265	423	4	science	science	NOUN
iajs-3265	423	5	and	and	CCONJ
iajs-3265	423	6	numerical	numerical	PROPN
iajs-3265	423	7	simulation	simulation	PROPN
iajs-3265	423	8	,	,	PUNCT
iajs-3265	423	9	2010	2010	NUM
iajs-3265	423	10	,	,	PUNCT
iajs-3265	423	11	15(9	15(9	NUM
iajs-3265	423	12	)	)	PUNCT
iajs-3265	423	13	,	,	PUNCT
iajs-3265	423	14	2293	2293	NUM
iajs-3265	423	15	-	-	SYM
iajs-3265	423	16	2302	2302	NUM
iajs-3265	423	17	.	.	PUNCT
iajs-3265	424	1	36	36	NUM
iajs-3265	424	2	.	.	PUNCT
iajs-3265	424	3	manafian	manafian	PROPN
iajs-3265	424	4	,	,	PUNCT
iajs-3265	424	5	j.	j.	PROPN
iajs-3265	424	6	an	an	DET
iajs-3265	424	7	optimal	optimal	ADJ
iajs-3265	424	8	galerkin	galerkin	ADJ
iajs-3265	424	9	-	-	PUNCT
iajs-3265	424	10	homotopy	homotopy	NOUN
iajs-3265	424	11	asymptotic	asymptotic	ADJ
iajs-3265	424	12	method	method	NOUN
iajs-3265	424	13	applied	apply	VERB
iajs-3265	424	14	to	to	ADP
iajs-3265	424	15	the	the	DET
iajs-3265	424	16	nonlinear	nonlinear	ADJ
iajs-3265	424	17	second	second	ADJ
iajs-3265	424	18	-	-	PUNCT
iajs-3265	424	19	order	order	NOUN
iajs-3265	424	20	bvps	bvps	NOUN
iajs-3265	424	21	.	.	PUNCT
iajs-3265	425	1	proceedings	proceeding	NOUN
iajs-3265	425	2	of	of	ADP
iajs-3265	425	3	the	the	DET
iajs-3265	425	4	institute	institute	NOUN
iajs-3265	425	5	of	of	ADP
iajs-3265	425	6	mathematics	mathematics	PROPN
iajs-3265	425	7	and	and	CCONJ
iajs-3265	425	8	mechanics	mechanic	NOUN
iajs-3265	425	9	,	,	PUNCT
iajs-3265	425	10	2021	2021	NUM
iajs-3265	425	11	,	,	PUNCT
iajs-3265	425	12	47(1	47(1	NUM
iajs-3265	425	13	)	)	PUNCT
iajs-3265	425	14	,	,	PUNCT
iajs-3265	425	15	156	156	NUM
iajs-3265	425	16	-	-	SYM
iajs-3265	425	17	182	182	NUM
iajs-3265	425	18	.	.	PUNCT
iajs-3265	426	1	37	37	NUM
iajs-3265	426	2	.	.	PUNCT
iajs-3265	427	1	waqas	waqas	PROPN
iajs-3265	427	2	,	,	PUNCT
iajs-3265	427	3	m.	m.	NOUN
iajs-3265	427	4	;	;	PUNCT
iajs-3265	427	5	gulzar	gulzar	PROPN
iajs-3265	427	6	,	,	PUNCT
iajs-3265	427	7	m.	m.	NOUN
iajs-3265	427	8	m.	m.	NOUN
iajs-3265	427	9	;	;	PUNCT
iajs-3265	427	10	dogonchi	dogonchi	PROPN
iajs-3265	427	11	,	,	PUNCT
iajs-3265	427	12	a.	a.	PROPN
iajs-3265	427	13	s.	s.	PROPN
iajs-3265	427	14	;	;	PUNCT
iajs-3265	427	15	javed	javed	ADJ
iajs-3265	427	16	,	,	PUNCT
iajs-3265	427	17	m.	m.	NOUN
iajs-3265	427	18	a.	a.	PROPN
iajs-3265	427	19	;	;	PUNCT
iajs-3265	427	20	khan	khan	PROPN
iajs-3265	427	21	,	,	PUNCT
iajs-3265	427	22	w.	w.	PROPN
iajs-3265	427	23	a.	a.	PROPN
iajs-3265	427	24	darcy	darcy	PROPN
iajs-3265	427	25	–	–	PUNCT
iajs-3265	427	26	forchheimer	forchheimer	PROPN
iajs-3265	427	27	stratified	stratified	ADJ
iajs-3265	427	28	flow	flow	NOUN
iajs-3265	427	29	of	of	ADP
iajs-3265	427	30	viscoelastic	viscoelastic	ADJ
iajs-3265	427	31	nanofluid	nanofluid	PROPN
iajs-3265	427	32	subjected	subject	VERB
iajs-3265	427	33	to	to	ADP
iajs-3265	427	34	convective	convective	ADJ
iajs-3265	427	35	conditions	condition	NOUN
iajs-3265	427	36	.	.	PUNCT
iajs-3265	428	1	applied	apply	VERB
iajs-3265	428	2	nanoscience	nanoscience	NOUN
iajs-3265	428	3	,	,	PUNCT
iajs-3265	428	4	2019	2019	NUM
iajs-3265	428	5	,	,	PUNCT
iajs-3265	428	6	9(8	9(8	NUM
iajs-3265	428	7	)	)	PUNCT
iajs-3265	428	8	,	,	PUNCT
iajs-3265	428	9	2031	2031	NUM
iajs-3265	428	10	-	-	SYM
iajs-3265	428	11	2037	2037	NUM
iajs-3265	428	12	.	.	PUNCT
iajs-3265	429	1	38	38	NUM
iajs-3265	429	2	.	.	PUNCT
iajs-3265	429	3	awartani	awartani	PROPN
iajs-3265	429	4	,	,	PUNCT
iajs-3265	429	5	m.	m.	NOUN
iajs-3265	429	6	m.	m.	NOUN
iajs-3265	429	7	;	;	PUNCT
iajs-3265	429	8	hamdan	hamdan	PROPN
iajs-3265	429	9	,	,	PUNCT
iajs-3265	429	10	m.	m.	PROPN
iajs-3265	429	11	h.	h.	PROPN
iajs-3265	429	12	fully	fully	ADV
iajs-3265	429	13	developed	develop	VERB
iajs-3265	429	14	flow	flow	NOUN
iajs-3265	429	15	through	through	ADP
iajs-3265	429	16	a	a	DET
iajs-3265	429	17	porous	porous	ADJ
iajs-3265	429	18	channel	channel	NOUN
iajs-3265	429	19	bounded	bound	VERB
iajs-3265	429	20	by	by	ADP
iajs-3265	429	21	flat	flat	ADJ
iajs-3265	429	22	plates	plate	NOUN
iajs-3265	429	23	.	.	PUNCT
iajs-3265	430	1	applied	apply	VERB
iajs-3265	430	2	mathematics	mathematic	NOUN
iajs-3265	430	3	and	and	CCONJ
iajs-3265	430	4	computation	computation	NOUN
iajs-3265	430	5	,	,	PUNCT
iajs-3265	430	6	2005	2005	NUM
iajs-3265	430	7	,	,	PUNCT
iajs-3265	430	8	169(2	169(2	NUM
iajs-3265	430	9	)	)	PUNCT
iajs-3265	430	10	,	,	PUNCT
iajs-3265	430	11	749	749	NUM
iajs-3265	430	12	-	-	SYM
iajs-3265	430	13	757	757	NOUN
iajs-3265	430	14	.	.	PUNCT
iajs-3265	430	15	39	39	NUM
iajs-3265	430	16	.	.	PUNCT
iajs-3265	431	1	adewumi	adewumi	PROPN
iajs-3265	431	2	,	,	PUNCT
iajs-3265	431	3	a.	a.	NOUN
iajs-3265	431	4	o.	o.	PROPN
iajs-3265	431	5	;	;	PUNCT
iajs-3265	431	6	akindeinde	akindeinde	PROPN
iajs-3265	431	7	,	,	PUNCT
iajs-3265	431	8	s.	s.	PROPN
iajs-3265	431	9	o.	o.	PROPN
iajs-3265	431	10	;	;	PUNCT
iajs-3265	431	11	aderogba	aderogba	PROPN
iajs-3265	431	12	,	,	PUNCT
iajs-3265	431	13	a.	a.	NOUN
iajs-3265	431	14	a.	a.	PROPN
iajs-3265	431	15	;	;	PUNCT
iajs-3265	431	16	ogundare	ogundare	PROPN
iajs-3265	431	17	,	,	PUNCT
iajs-3265	431	18	b.	b.	PROPN
iajs-3265	431	19	s.	s.	PROPN
iajs-3265	431	20	a	a	DET
iajs-3265	431	21	hybrid	hybrid	ADJ
iajs-3265	431	22	collocation	collocation	NOUN
iajs-3265	431	23	method	method	NOUN
iajs-3265	431	24	for	for	ADP
iajs-3265	431	25	solving	solve	VERB
iajs-3265	431	26	highly	highly	ADV
iajs-3265	431	27	nonlinear	nonlinear	ADJ
iajs-3265	431	28	boundary	boundary	ADJ
iajs-3265	431	29	value	value	NOUN
iajs-3265	431	30	problems	problem	NOUN
iajs-3265	431	31	.	.	PUNCT
iajs-3265	432	1	heliyon	heliyon	NOUN
iajs-3265	432	2	,	,	PUNCT
iajs-3265	432	3	2020	2020	NUM
iajs-3265	432	4	,	,	PUNCT
iajs-3265	432	5	6(3	6(3	NUM
iajs-3265	432	6	)	)	PUNCT
iajs-3265	432	7	,	,	PUNCT
iajs-3265	432	8	1	1	NUM
iajs-3265	432	9	-	-	SYM
iajs-3265	432	10	10	10	NUM
iajs-3265	432	11	.	.	PUNCT
iajs-3265	432	12	40	40	NUM
iajs-3265	432	13	.	.	PUNCT
iajs-3265	433	1	abbasbandy	abbasbandy	PROPN
iajs-3265	433	2	,	,	PUNCT
iajs-3265	433	3	s.	s.	PROPN
iajs-3265	433	4	;	;	PUNCT
iajs-3265	433	5	shivanian	shivanian	PROPN
iajs-3265	433	6	,	,	PUNCT
iajs-3265	433	7	e.	e.	PROPN
iajs-3265	433	8	;	;	PUNCT
iajs-3265	433	9	hashim	hashim	PROPN
iajs-3265	433	10	,	,	PUNCT
iajs-3265	433	11	i.	i.	PROPN
iajs-3265	433	12	exact	exact	ADJ
iajs-3265	433	13	analytical	analytical	ADJ
iajs-3265	433	14	solution	solution	NOUN
iajs-3265	433	15	of	of	ADP
iajs-3265	433	16	forced	force	VERB
iajs-3265	433	17	convection	convection	NOUN
iajs-3265	433	18	in	in	ADP
iajs-3265	433	19	a	a	DET
iajs-3265	433	20	porous	porous	ADJ
iajs-3265	433	21	-	-	PUNCT
iajs-3265	433	22	saturated	saturate	VERB
iajs-3265	433	23	duct	duct	NOUN
iajs-3265	433	24	.	.	PUNCT
iajs-3265	434	1	communications	communication	NOUN
iajs-3265	434	2	in	in	ADP
iajs-3265	434	3	nonlinear	nonlinear	ADJ
iajs-3265	434	4	science	science	NOUN
iajs-3265	434	5	and	and	CCONJ
iajs-3265	434	6	numerical	numerical	PROPN
iajs-3265	434	7	simulation	simulation	PROPN
iajs-3265	434	8	,	,	PUNCT
iajs-3265	434	9	2011	2011	NUM
iajs-3265	434	10	,	,	PUNCT
iajs-3265	434	11	16(10	16(10	NOUN
iajs-3265	434	12	)	)	PUNCT
iajs-3265	434	13	,	,	PUNCT
iajs-3265	434	14	3981	3981	NUM
iajs-3265	434	15	-	-	SYM
iajs-3265	434	16	3989	3989	NUM
iajs-3265	434	17	.	.	PUNCT
iajs-3265	435	1	41	41	NUM
iajs-3265	435	2	.	.	PUNCT
iajs-3265	436	1	el	el	PROPN
iajs-3265	436	2	-	-	PUNCT
iajs-3265	436	3	gamel	gamel	PROPN
iajs-3265	436	4	,	,	PUNCT
iajs-3265	436	5	m.	m.	NOUN
iajs-3265	436	6	;	;	PUNCT
iajs-3265	436	7	el	el	PROPN
iajs-3265	436	8	-	-	PUNCT
iajs-3265	436	9	shenawy	shenawy	PROPN
iajs-3265	436	10	,	,	PUNCT
iajs-3265	436	11	a.	a.	NOUN
iajs-3265	436	12	a	a	DET
iajs-3265	436	13	numerical	numerical	ADJ
iajs-3265	436	14	solution	solution	NOUN
iajs-3265	436	15	of	of	ADP
iajs-3265	436	16	blasius	blasius	ADJ
iajs-3265	436	17	equation	equation	NOUN
iajs-3265	436	18	on	on	ADP
iajs-3265	436	19	a	a	DET
iajs-3265	436	20	semi	semi	ADJ
iajs-3265	436	21	-	-	ADJ
iajs-3265	436	22	infinity	infinity	ADJ
iajs-3265	436	23	flat	flat	ADJ
iajs-3265	436	24	plate	plate	NOUN
iajs-3265	436	25	.	.	PUNCT
iajs-3265	437	1	sema	sema	PROPN
iajs-3265	437	2	journal	journal	PROPN
iajs-3265	437	3	,	,	PUNCT
iajs-3265	437	4	2018	2018	NUM
iajs-3265	437	5	,	,	PUNCT
iajs-3265	437	6	75(3	75(3	NUM
iajs-3265	437	7	)	)	PUNCT
iajs-3265	437	8	,	,	PUNCT
iajs-3265	437	9	475	475	NUM
iajs-3265	437	10	-	-	SYM
iajs-3265	437	11	484	484	NUM
iajs-3265	437	12	.	.	PUNCT
iajs-3265	438	1	42	42	NUM
iajs-3265	438	2	.	.	PUNCT
iajs-3265	438	3	khataybeh	khataybeh	PROPN
iajs-3265	438	4	,	,	PUNCT
iajs-3265	438	5	s.	s.	PROPN
iajs-3265	438	6	n.	n.	PROPN
iajs-3265	438	7	;	;	PUNCT
iajs-3265	438	8	hashim	hashim	PROPN
iajs-3265	438	9	,	,	PUNCT
iajs-3265	438	10	i.	i.	PROPN
iajs-3265	438	11	;	;	PUNCT
iajs-3265	438	12	alshbool	alshbool	NOUN
iajs-3265	438	13	,	,	PUNCT
iajs-3265	438	14	m.	m.	NOUN
iajs-3265	438	15	solving	solve	VERB
iajs-3265	438	16	directly	directly	ADV
iajs-3265	438	17	third	third	ADJ
iajs-3265	438	18	-	-	PUNCT
iajs-3265	438	19	order	order	NOUN
iajs-3265	438	20	odes	ode	NOUN
iajs-3265	438	21	using	use	VERB
iajs-3265	438	22	operational	operational	ADJ
iajs-3265	438	23	matrices	matrix	NOUN
iajs-3265	438	24	of	of	ADP
iajs-3265	438	25	bernstein	bernstein	PROPN
iajs-3265	438	26	polynomials	polynomials	PROPN
iajs-3265	438	27	method	method	VERB
iajs-3265	438	28	with	with	ADP
iajs-3265	438	29	applications	application	NOUN
iajs-3265	438	30	to	to	ADP
iajs-3265	438	31	fluid	fluid	ADJ
iajs-3265	438	32	flow	flow	NOUN
iajs-3265	438	33	equations	equation	NOUN
iajs-3265	438	34	.	.	PUNCT
iajs-3265	439	1	journal	journal	PROPN
iajs-3265	439	2	of	of	ADP
iajs-3265	439	3	king	king	PROPN
iajs-3265	439	4	saud	saud	PROPN
iajs-3265	439	5	university	university	PROPN
iajs-3265	439	6	-	-	PUNCT
iajs-3265	439	7	science	science	NOUN
iajs-3265	439	8	,	,	PUNCT
iajs-3265	439	9	2019	2019	NUM
iajs-3265	439	10	,	,	PUNCT
iajs-3265	439	11	31(4	31(4	NUM
iajs-3265	439	12	)	)	PUNCT
iajs-3265	439	13	,	,	PUNCT
iajs-3265	439	14	822	822	NUM
iajs-3265	439	15	-	-	SYM
iajs-3265	439	16	826	826	NUM
iajs-3265	439	17	.	.	PUNCT
iajs-3265	440	1	43	43	NUM
iajs-3265	440	2	.	.	PUNCT
iajs-3265	441	1	liao	liao	PROPN
iajs-3265	441	2	,	,	PUNCT
iajs-3265	441	3	s.	s.	PROPN
iajs-3265	441	4	an	an	DET
iajs-3265	441	5	optimal	optimal	ADJ
iajs-3265	441	6	homotopy	homotopy	NOUN
iajs-3265	441	7	-	-	PUNCT
iajs-3265	441	8	analysis	analysis	NOUN
iajs-3265	441	9	approach	approach	NOUN
iajs-3265	441	10	for	for	ADP
iajs-3265	441	11	strongly	strongly	ADV
iajs-3265	441	12	nonlinear	nonlinear	ADJ
iajs-3265	441	13	differential	differential	ADJ
iajs-3265	441	14	equations	equation	NOUN
iajs-3265	441	15	.	.	PUNCT
iajs-3265	442	1	communications	communication	NOUN
iajs-3265	442	2	in	in	ADP
iajs-3265	442	3	nonlinear	nonlinear	ADJ
iajs-3265	442	4	science	science	NOUN
iajs-3265	442	5	and	and	CCONJ
iajs-3265	442	6	numerical	numerical	PROPN
iajs-3265	442	7	simulation	simulation	PROPN
iajs-3265	442	8	,	,	PUNCT
iajs-3265	442	9	2010	2010	NUM
iajs-3265	442	10	,	,	PUNCT
iajs-3265	442	11	15(8	15(8	NUM
iajs-3265	442	12	)	)	PUNCT
iajs-3265	442	13	,	,	PUNCT
iajs-3265	442	14	2003	2003	NUM
iajs-3265	442	15	-	-	SYM
iajs-3265	442	16	2016	2016	NUM
iajs-3265	442	17	.	.	PUNCT
iajs-3265	443	1	44	44	NUM
iajs-3265	443	2	.	.	PUNCT
iajs-3265	443	3	rani	rani	PROPN
iajs-3265	443	4	,	,	PUNCT
iajs-3265	443	5	d.	d.	PROPN
iajs-3265	443	6	;	;	PUNCT
iajs-3265	443	7	mishra	mishra	PROPN
iajs-3265	443	8	,	,	PUNCT
iajs-3265	443	9	v.	v.	ADP
iajs-3265	443	10	numerical	numerical	ADJ
iajs-3265	443	11	inverse	inverse	NOUN
iajs-3265	443	12	laplace	laplace	NOUN
iajs-3265	443	13	transform	transform	NOUN
iajs-3265	443	14	based	base	VERB
iajs-3265	443	15	on	on	ADP
iajs-3265	443	16	bernoulli	bernoulli	PROPN
iajs-3265	443	17	polynomials	polynomial	NOUN
iajs-3265	443	18	operational	operational	ADJ
iajs-3265	443	19	matrix	matrix	NOUN
iajs-3265	443	20	for	for	ADP
iajs-3265	443	21	solving	solve	VERB
iajs-3265	443	22	nonlinear	nonlinear	ADJ
iajs-3265	443	23	differential	differential	ADJ
iajs-3265	443	24	equations	equation	NOUN
iajs-3265	443	25	.	.	PUNCT
iajs-3265	444	1	results	result	NOUN
iajs-3265	444	2	in	in	ADP
iajs-3265	444	3	physics	physics	NOUN
iajs-3265	444	4	,	,	PUNCT
iajs-3265	444	5	2020	2020	NUM
iajs-3265	444	6	,	,	PUNCT
iajs-3265	444	7	16	16	NUM
iajs-3265	444	8	,	,	PUNCT
iajs-3265	444	9	102836	102836	NUM
iajs-3265	444	10	.	.	PUNCT
iajs-3265	445	1	45	45	NUM
iajs-3265	445	2	.	.	X
iajs-3265	445	3	yao	yao	PROPN
iajs-3265	445	4	,	,	PUNCT
iajs-3265	445	5	b.	b.	PROPN
iajs-3265	445	6	;	;	PUNCT
iajs-3265	445	7	chen	chen	PROPN
iajs-3265	445	8	,	,	PUNCT
iajs-3265	445	9	j.	j.	PROPN
iajs-3265	445	10	a	a	DET
iajs-3265	445	11	new	new	ADJ
iajs-3265	445	12	analytical	analytical	ADJ
iajs-3265	445	13	solution	solution	NOUN
iajs-3265	445	14	branch	branch	NOUN
iajs-3265	445	15	for	for	ADP
iajs-3265	445	16	the	the	DET
iajs-3265	445	17	blasius	blasius	ADJ
iajs-3265	445	18	equation	equation	NOUN
iajs-3265	445	19	with	with	ADP
iajs-3265	445	20	a	a	DET
iajs-3265	445	21	shrinking	shrink	VERB
iajs-3265	445	22	sheet	sheet	NOUN
iajs-3265	445	23	.	.	PUNCT
iajs-3265	446	1	applied	apply	VERB
iajs-3265	446	2	mathematics	mathematic	NOUN
iajs-3265	446	3	and	and	CCONJ
iajs-3265	446	4	computation	computation	NOUN
iajs-3265	446	5	,	,	PUNCT
iajs-3265	446	6	2009	2009	NUM
iajs-3265	446	7	,	,	PUNCT
iajs-3265	446	8	215(3	215(3	NUM
iajs-3265	446	9	)	)	PUNCT
iajs-3265	446	10	,	,	PUNCT
iajs-3265	446	11	1146	1146	NUM
iajs-3265	446	12	-	-	SYM
iajs-3265	446	13	1153	1153	NUM
iajs-3265	446	14	.	.	PUNCT
iajs-3265	447	1	46	46	NUM
iajs-3265	447	2	.	.	PUNCT
iajs-3265	447	3	marinca	marinca	VERB
iajs-3265	447	4	,	,	PUNCT
iajs-3265	447	5	v.	v.	CCONJ
iajs-3265	447	6	;	;	PUNCT
iajs-3265	447	7	herişanu	herişanu	NOUN
iajs-3265	447	8	,	,	PUNCT
iajs-3265	447	9	n.	n.	VERB
iajs-3265	447	10	the	the	DET
iajs-3265	447	11	optimal	optimal	ADJ
iajs-3265	447	12	homotopy	homotopy	NOUN
iajs-3265	447	13	asymptotic	asymptotic	ADJ
iajs-3265	447	14	method	method	NOUN
iajs-3265	447	15	for	for	ADP
iajs-3265	447	16	solving	solve	VERB
iajs-3265	447	17	blasius	blasius	ADJ
iajs-3265	447	18	equation	equation	NOUN
iajs-3265	447	19	.	.	PUNCT
iajs-3265	448	1	applied	apply	VERB
iajs-3265	448	2	mathematics	mathematic	NOUN
iajs-3265	448	3	and	and	CCONJ
iajs-3265	448	4	computation	computation	NOUN
iajs-3265	448	5	,	,	PUNCT
iajs-3265	448	6	2014	2014	NUM
iajs-3265	448	7	,	,	PUNCT
iajs-3265	448	8	231	231	NUM
iajs-3265	448	9	,	,	PUNCT
iajs-3265	448	10	134	134	NUM
iajs-3265	448	11	-	-	SYM
iajs-3265	448	12	139	139	NUM
iajs-3265	448	13	.	.	PUNCT
iajs-3265	449	1	47	47	NUM
iajs-3265	449	2	.	.	PUNCT
iajs-3265	450	1	wazwaz	wazwaz	NOUN
iajs-3265	450	2	,	,	PUNCT
iajs-3265	450	3	a.	a.	NOUN
iajs-3265	450	4	m.	m.	NOUN
iajs-3265	450	5	the	the	DET
iajs-3265	450	6	variational	variational	ADJ
iajs-3265	450	7	iteration	iteration	NOUN
iajs-3265	450	8	method	method	NOUN
iajs-3265	450	9	for	for	ADP
iajs-3265	450	10	solving	solve	VERB
iajs-3265	450	11	two	two	NUM
iajs-3265	450	12	forms	form	NOUN
iajs-3265	450	13	of	of	ADP
iajs-3265	450	14	blasius	blasius	ADJ
iajs-3265	450	15	equation	equation	NOUN
iajs-3265	450	16	on	on	ADP
iajs-3265	450	17	a	a	DET
iajs-3265	450	18	half	half	ADJ
iajs-3265	450	19	-	-	PUNCT
iajs-3265	450	20	infinite	infinite	ADJ
iajs-3265	450	21	domain	domain	NOUN
iajs-3265	450	22	.	.	PUNCT
iajs-3265	451	1	applied	apply	VERB
iajs-3265	451	2	mathematics	mathematic	NOUN
iajs-3265	451	3	and	and	CCONJ
iajs-3265	451	4	computation	computation	NOUN
iajs-3265	451	5	,	,	PUNCT
iajs-3265	451	6	2007	2007	NUM
iajs-3265	451	7	,	,	PUNCT
iajs-3265	451	8	188(1	188(1	NUM
iajs-3265	451	9	)	)	PUNCT
iajs-3265	451	10	,	,	PUNCT
iajs-3265	451	11	485	485	NUM
iajs-3265	451	12	-	-	SYM
iajs-3265	451	13	491	491	NUM
iajs-3265	451	14	.	.	PUNCT
iajs-3265	452	1	48	48	NUM
iajs-3265	452	2	.	.	PUNCT
iajs-3265	453	1	abbasbandy	abbasbandy	PROPN
iajs-3265	453	2	,	,	PUNCT
iajs-3265	453	3	s.	s.	PROPN
iajs-3265	453	4	a	a	DET
iajs-3265	453	5	numerical	numerical	ADJ
iajs-3265	453	6	solution	solution	NOUN
iajs-3265	453	7	of	of	ADP
iajs-3265	453	8	blasius	blasius	ADJ
iajs-3265	453	9	equation	equation	NOUN
iajs-3265	453	10	by	by	ADP
iajs-3265	453	11	adomian	adomian	NOUN
iajs-3265	453	12	’s	’s	PART
iajs-3265	453	13	decomposition	decomposition	NOUN
iajs-3265	453	14	method	method	NOUN
iajs-3265	453	15	and	and	CCONJ
iajs-3265	453	16	comparison	comparison	NOUN
iajs-3265	453	17	with	with	ADP
iajs-3265	453	18	homotopy	homotopy	NOUN
iajs-3265	453	19	perturbation	perturbation	NOUN
iajs-3265	453	20	method	method	NOUN
iajs-3265	453	21	.	.	PUNCT
iajs-3265	454	1	chaos	chaos	NOUN
iajs-3265	454	2	,	,	PUNCT
iajs-3265	454	3	solitons	soliton	NOUN
iajs-3265	454	4	&	&	CCONJ
iajs-3265	454	5	fractals	fractal	NOUN
iajs-3265	454	6	,	,	PUNCT
iajs-3265	454	7	2007	2007	NUM
iajs-3265	454	8	,	,	PUNCT
iajs-3265	454	9	31(1	31(1	NUM
iajs-3265	454	10	)	)	PUNCT
iajs-3265	454	11	,	,	PUNCT
iajs-3265	454	12	257	257	NUM
iajs-3265	454	13	-	-	SYM
iajs-3265	454	14	260	260	NUM
iajs-3265	454	15	.	.	PUNCT
iajs-3265	454	16	49	49	NUM
iajs-3265	454	17	.	.	PUNCT
iajs-3265	455	1	parand	parand	NOUN
iajs-3265	455	2	,	,	PUNCT
iajs-3265	455	3	k.	k.	PROPN
iajs-3265	455	4	;	;	PUNCT
iajs-3265	455	5	taghavi	taghavi	VERB
iajs-3265	455	6	,	,	PUNCT
iajs-3265	455	7	a.	a.	NOUN
iajs-3265	455	8	rational	rational	ADV
iajs-3265	455	9	scaled	scale	VERB
iajs-3265	455	10	generalized	generalize	VERB
iajs-3265	455	11	laguerre	laguerre	NOUN
iajs-3265	455	12	function	function	NOUN
iajs-3265	455	13	collocation	collocation	NOUN
iajs-3265	455	14	method	method	NOUN
iajs-3265	455	15	for	for	ADP
iajs-3265	455	16	solving	solve	VERB
iajs-3265	455	17	the	the	DET
iajs-3265	455	18	blasius	blasius	ADJ
iajs-3265	455	19	equation	equation	NOUN
iajs-3265	455	20	.	.	PUNCT
iajs-3265	456	1	journal	journal	PROPN
iajs-3265	456	2	of	of	ADP
iajs-3265	456	3	computational	computational	ADJ
iajs-3265	456	4	and	and	CCONJ
iajs-3265	456	5	applied	applied	ADJ
iajs-3265	456	6	mathematics	mathematic	NOUN
iajs-3265	456	7	,	,	PUNCT
iajs-3265	456	8	2009	2009	NUM
iajs-3265	456	9	,	,	PUNCT
iajs-3265	456	10	233(4	233(4	NUM
iajs-3265	456	11	)	)	PUNCT
iajs-3265	456	12	,	,	PUNCT
iajs-3265	456	13	980	980	NUM
iajs-3265	456	14	-	-	SYM
iajs-3265	456	15	989	989	NUM
iajs-3265	456	16	.	.	PUNCT
iajs-3265	457	1	50	50	NUM
iajs-3265	457	2	.	.	PUNCT
iajs-3265	458	1	abbasbandy	abbasbandy	PROPN
iajs-3265	458	2	,	,	PUNCT
iajs-3265	458	3	s.	s.	PROPN
iajs-3265	458	4	;	;	PUNCT
iajs-3265	458	5	hajishafieiha	hajishafieiha	PROPN
iajs-3265	458	6	,	,	PUNCT
iajs-3265	458	7	j.	j.	PROPN
iajs-3265	458	8	numerical	numerical	PROPN
iajs-3265	458	9	solution	solution	NOUN
iajs-3265	458	10	to	to	ADP
iajs-3265	458	11	the	the	DET
iajs-3265	458	12	falkner	falkner	PROPN
iajs-3265	458	13	-	-	PUNCT
iajs-3265	458	14	skan	skan	VERB
iajs-3265	458	15	equation	equation	NOUN
iajs-3265	458	16	:	:	PUNCT
iajs-3265	458	17	a	a	DET
iajs-3265	458	18	novel	novel	ADJ
iajs-3265	458	19	numerical	numerical	ADJ
iajs-3265	458	20	approach	approach	NOUN
iajs-3265	458	21	through	through	ADP
iajs-3265	458	22	the	the	DET
iajs-3265	458	23	new	new	ADJ
iajs-3265	458	24	rational	rational	ADJ
iajs-3265	458	25	a	a	PRON
iajs-3265	458	26	-	-	PUNCT
iajs-3265	458	27	polynomials	polynomial	NOUN
iajs-3265	458	28	.	.	PUNCT
iajs-3265	459	1	applied	apply	VERB
iajs-3265	459	2	mathematics	mathematic	NOUN
iajs-3265	459	3	and	and	CCONJ
iajs-3265	459	4	mechanics	mechanic	NOUN
iajs-3265	459	5	,	,	PUNCT
iajs-3265	459	6	2021	2021	NUM
iajs-3265	459	7	,	,	PUNCT
iajs-3265	459	8	42(10	42(10	PROPN
iajs-3265	459	9	)	)	PUNCT
iajs-3265	459	10	,	,	PUNCT
iajs-3265	459	11	1449	1449	NUM
iajs-3265	459	12	-	-	SYM
iajs-3265	459	13	1460	1460	NUM
iajs-3265	459	14	.	.	PUNCT
iajs-3265	460	1	51	51	NUM
iajs-3265	460	2	.	.	PUNCT
iajs-3265	461	1	falkner	falkner	PROPN
iajs-3265	461	2	,	,	PUNCT
iajs-3265	461	3	v.	v.	ADP
iajs-3265	461	4	m.	m.	NOUN
iajs-3265	461	5	;	;	PUNCT
iajs-3265	461	6	skan	skan	PROPN
iajs-3265	461	7	,	,	PUNCT
iajs-3265	461	8	s.	s.	PROPN
iajs-3265	461	9	w.	w.	PROPN
iajs-3265	461	10	solutions	solution	NOUN
iajs-3265	461	11	of	of	ADP
iajs-3265	461	12	the	the	DET
iajs-3265	461	13	boundary	boundary	ADJ
iajs-3265	461	14	-	-	PUNCT
iajs-3265	461	15	layer	layer	NOUN
iajs-3265	461	16	equations	equation	NOUN
iajs-3265	461	17	.	.	PUNCT
iajs-3265	462	1	the	the	DET
iajs-3265	462	2	london	london	PROPN
iajs-3265	462	3	,	,	PUNCT
iajs-3265	462	4	edinburgh	edinburgh	PROPN
iajs-3265	462	5	,	,	PUNCT
iajs-3265	462	6	and	and	CCONJ
iajs-3265	462	7	dublin	dublin	PROPN
iajs-3265	462	8	philosophical	philosophical	PROPN
iajs-3265	462	9	magazine	magazine	NOUN
iajs-3265	462	10	and	and	CCONJ
iajs-3265	462	11	journal	journal	NOUN
iajs-3265	462	12	of	of	ADP
iajs-3265	462	13	science	science	NOUN
iajs-3265	462	14	,	,	PUNCT
iajs-3265	462	15	1931	1931	NUM
iajs-3265	462	16	,	,	PUNCT
iajs-3265	462	17	12(80	12(80	NUM
iajs-3265	462	18	)	)	PUNCT
iajs-3265	462	19	,	,	PUNCT
iajs-3265	462	20	865896	865896	NUM
iajs-3265	462	21	.	.	PUNCT
iajs-3265	463	1	52	52	NUM
iajs-3265	463	2	.	.	PUNCT
iajs-3265	463	3	bakodah	bakodah	NOUN
iajs-3265	463	4	,	,	PUNCT
iajs-3265	463	5	h.	h.	PROPN
iajs-3265	463	6	o.	o.	PROPN
iajs-3265	463	7	;	;	PUNCT
iajs-3265	463	8	ebaid	ebaid	PROPN
iajs-3265	463	9	,	,	PUNCT
iajs-3265	463	10	a.	a.	NOUN
iajs-3265	463	11	;	;	PUNCT
iajs-3265	463	12	wazwaz	wazwaz	NOUN
iajs-3265	463	13	,	,	PUNCT
iajs-3265	463	14	a.	a.	NOUN
iajs-3265	463	15	m.	m.	NOUN
iajs-3265	463	16	analytical	analytical	ADJ
iajs-3265	463	17	and	and	CCONJ
iajs-3265	463	18	numerical	numerical	ADJ
iajs-3265	463	19	treatment	treatment	NOUN
iajs-3265	463	20	of	of	ADP
iajs-3265	463	21	falknerskan	falknerskan	ADJ
iajs-3265	463	22	equation	equation	NOUN
iajs-3265	463	23	via	via	ADP
iajs-3265	463	24	a	a	DET
iajs-3265	463	25	transformation	transformation	NOUN
iajs-3265	463	26	and	and	CCONJ
iajs-3265	463	27	adomian	adomian	NOUN
iajs-3265	463	28	’s	’s	PART
iajs-3265	463	29	method	method	NOUN
iajs-3265	463	30	.	.	PUNCT
iajs-3265	464	1	romanian	romanian	ADJ
iajs-3265	464	2	reports	report	NOUN
iajs-3265	464	3	in	in	ADP
iajs-3265	464	4	physics	physics	NOUN
iajs-3265	464	5	,	,	PUNCT
iajs-3265	464	6	2018	2018	NUM
iajs-3265	464	7	,	,	PUNCT
iajs-3265	464	8	70(2	70(2	NUM
iajs-3265	464	9	)	)	PUNCT
iajs-3265	464	10	,	,	PUNCT
iajs-3265	464	11	1	1	NUM
iajs-3265	464	12	-	-	SYM
iajs-3265	464	13	17	17	NUM
iajs-3265	464	14	.	.	PUNCT
iajs-3265	464	15	ihjpas	ihjpas	PROPN
iajs-3265	464	16	.	.	PUNCT
iajs-3265	465	1	36	36	NUM
iajs-3265	465	2	(	(	PUNCT
iajs-3265	465	3	4	4	NUM
iajs-3265	465	4	)	)	PUNCT
iajs-3265	465	5	2023	2023	NUM
iajs-3265	465	6	358	358	NUM
iajs-3265	465	7	53	53	NUM
iajs-3265	465	8	.	.	PUNCT
iajs-3265	466	1	al	al	PROPN
iajs-3265	466	2	-	-	PUNCT
iajs-3265	466	3	jawary	jawary	PROPN
iajs-3265	466	4	,	,	PUNCT
iajs-3265	466	5	m.	m.	NOUN
iajs-3265	466	6	a.	a.	NOUN
iajs-3265	466	7	;	;	PUNCT
iajs-3265	466	8	adwan	adwan	PROPN
iajs-3265	466	9	,	,	PUNCT
iajs-3265	466	10	m.	m.	NOUN
iajs-3265	466	11	i.	i.	PROPN
iajs-3265	466	12	reliable	reliable	ADJ
iajs-3265	466	13	iterative	iterative	NOUN
iajs-3265	466	14	methods	method	NOUN
iajs-3265	466	15	for	for	ADP
iajs-3265	466	16	solving	solve	VERB
iajs-3265	466	17	the	the	DET
iajs-3265	466	18	falkner	falkner	PROPN
iajs-3265	466	19	-	-	PUNCT
iajs-3265	466	20	skan	skan	VERB
iajs-3265	466	21	equation	equation	NOUN
iajs-3265	466	22	.	.	PUNCT
iajs-3265	467	1	gazi	gazi	PROPN
iajs-3265	467	2	university	university	PROPN
iajs-3265	467	3	journal	journal	PROPN
iajs-3265	467	4	of	of	ADP
iajs-3265	467	5	science	science	NOUN
iajs-3265	467	6	,	,	PUNCT
iajs-3265	467	7	2020	2020	NUM
iajs-3265	467	8	,	,	PUNCT
iajs-3265	467	9	33(1	33(1	NUM
iajs-3265	467	10	)	)	PUNCT
iajs-3265	467	11	,	,	PUNCT
iajs-3265	467	12	168	168	NUM
iajs-3265	467	13	-	-	SYM
iajs-3265	467	14	186	186	NUM
iajs-3265	467	15	.	.	PUNCT
iajs-3265	468	1	54	54	NUM
iajs-3265	468	2	.	.	PUNCT
iajs-3265	469	1	moallemi	moallemi	PROPN
iajs-3265	469	2	,	,	PUNCT
iajs-3265	469	3	n.	n.	NOUN
iajs-3265	469	4	;	;	PUNCT
iajs-3265	469	5	shafieenejad	shafieenejad	PROPN
iajs-3265	469	6	,	,	PUNCT
iajs-3265	469	7	i.	i.	PROPN
iajs-3265	469	8	;	;	PUNCT
iajs-3265	469	9	hashemi	hashemi	PROPN
iajs-3265	469	10	,	,	PUNCT
iajs-3265	469	11	s.	s.	PROPN
iajs-3265	469	12	f.	f.	PROPN
iajs-3265	469	13	;	;	PUNCT
iajs-3265	469	14	fata	fata	PROPN
iajs-3265	469	15	,	,	PUNCT
iajs-3265	469	16	a.	a.	NOUN
iajs-3265	469	17	approximate	approximate	ADJ
iajs-3265	469	18	explicit	explicit	ADJ
iajs-3265	469	19	solution	solution	NOUN
iajs-3265	469	20	of	of	ADP
iajs-3265	469	21	falkner	falkner	PROPN
iajs-3265	469	22	-	-	PUNCT
iajs-3265	469	23	skan	skan	VERB
iajs-3265	469	24	equation	equation	NOUN
iajs-3265	469	25	by	by	ADP
iajs-3265	469	26	homotopy	homotopy	NOUN
iajs-3265	469	27	perturbation	perturbation	NOUN
iajs-3265	469	28	method	method	NOUN
iajs-3265	469	29	.	.	PUNCT
iajs-3265	470	1	research	research	NOUN
iajs-3265	470	2	journal	journal	NOUN
iajs-3265	470	3	of	of	ADP
iajs-3265	470	4	applied	apply	VERB
iajs-3265	470	5	sciences	science	NOUN
iajs-3265	470	6	,	,	PUNCT
iajs-3265	470	7	engineering	engineering	NOUN
iajs-3265	470	8	and	and	CCONJ
iajs-3265	470	9	technology	technology	NOUN
iajs-3265	470	10	,	,	PUNCT
iajs-3265	470	11	2012	2012	NUM
iajs-3265	470	12	,	,	PUNCT
iajs-3265	470	13	4(17	4(17	NUM
iajs-3265	470	14	)	)	PUNCT
iajs-3265	470	15	,	,	PUNCT
iajs-3265	470	16	2893	2893	NUM
iajs-3265	470	17	-	-	SYM
iajs-3265	470	18	2897	2897	NUM
iajs-3265	470	19	.	.	PUNCT
iajs-3265	471	1	55	55	NUM
iajs-3265	471	2	.	.	PUNCT
iajs-3265	472	1	abbasbandy	abbasbandy	PROPN
iajs-3265	472	2	,	,	PUNCT
iajs-3265	472	3	s.	s.	PROPN
iajs-3265	472	4	;	;	PUNCT
iajs-3265	472	5	hayat	hayat	PROPN
iajs-3265	472	6	,	,	PUNCT
iajs-3265	472	7	t.	t.	NOUN
iajs-3265	472	8	solution	solution	NOUN
iajs-3265	472	9	of	of	ADP
iajs-3265	472	10	the	the	DET
iajs-3265	472	11	mhd	mhd	PROPN
iajs-3265	472	12	falkner	falkner	PROPN
iajs-3265	472	13	-	-	PUNCT
iajs-3265	472	14	skan	skan	VERB
iajs-3265	472	15	flow	flow	NOUN
iajs-3265	472	16	by	by	ADP
iajs-3265	472	17	homotopy	homotopy	NOUN
iajs-3265	472	18	analysis	analysis	NOUN
iajs-3265	472	19	method	method	NOUN
iajs-3265	472	20	.	.	PUNCT
iajs-3265	473	1	communications	communication	NOUN
iajs-3265	473	2	in	in	ADP
iajs-3265	473	3	nonlinear	nonlinear	ADJ
iajs-3265	473	4	science	science	NOUN
iajs-3265	473	5	and	and	CCONJ
iajs-3265	473	6	numerical	numerical	PROPN
iajs-3265	473	7	simulation	simulation	PROPN
iajs-3265	473	8	,	,	PUNCT
iajs-3265	473	9	2009	2009	NUM
iajs-3265	473	10	,	,	PUNCT
iajs-3265	473	11	14(9	14(9	NUM
iajs-3265	473	12	-	-	SYM
iajs-3265	473	13	10	10	NUM
iajs-3265	473	14	)	)	PUNCT
iajs-3265	473	15	,	,	PUNCT
iajs-3265	473	16	3591	3591	NUM
iajs-3265	473	17	-	-	SYM
iajs-3265	473	18	3598	3598	NUM
iajs-3265	473	19	.	.	PUNCT
iajs-3265	474	1	56	56	NUM
iajs-3265	474	2	.	.	X
iajs-3265	474	3	elgazery	elgazery	PROPN
iajs-3265	474	4	,	,	PUNCT
iajs-3265	474	5	n.	n.	PROPN
iajs-3265	474	6	s.	s.	PROPN
iajs-3265	474	7	numerical	numerical	PROPN
iajs-3265	474	8	solution	solution	NOUN
iajs-3265	474	9	for	for	ADP
iajs-3265	474	10	the	the	DET
iajs-3265	474	11	falkner	falkner	PROPN
iajs-3265	474	12	-	-	PUNCT
iajs-3265	474	13	skan	skan	VERB
iajs-3265	474	14	equation	equation	NOUN
iajs-3265	474	15	.	.	PUNCT
iajs-3265	475	1	chaos	chaos	NOUN
iajs-3265	475	2	,	,	PUNCT
iajs-3265	475	3	solitons	soliton	NOUN
iajs-3265	475	4	&	&	CCONJ
iajs-3265	475	5	fractals	fractal	NOUN
iajs-3265	475	6	,	,	PUNCT
iajs-3265	475	7	2008	2008	NUM
iajs-3265	475	8	,	,	PUNCT
iajs-3265	475	9	35(4	35(4	NUM
iajs-3265	475	10	)	)	PUNCT
iajs-3265	475	11	,	,	PUNCT
iajs-3265	475	12	738	738	NUM
iajs-3265	475	13	-	-	SYM
iajs-3265	475	14	746	746	NUM
iajs-3265	475	15	.	.	PUNCT
iajs-3265	476	1	57	57	NUM
iajs-3265	476	2	.	.	PUNCT
iajs-3265	477	1	kuo	kuo	PROPN
iajs-3265	477	2	,	,	PUNCT
iajs-3265	477	3	b.	b.	PROPN
iajs-3265	477	4	l.	l.	PROPN
iajs-3265	477	5	application	application	PROPN
iajs-3265	477	6	of	of	ADP
iajs-3265	477	7	the	the	DET
iajs-3265	477	8	differential	differential	ADJ
iajs-3265	477	9	transformation	transformation	NOUN
iajs-3265	477	10	method	method	NOUN
iajs-3265	477	11	to	to	ADP
iajs-3265	477	12	the	the	DET
iajs-3265	477	13	solutions	solution	NOUN
iajs-3265	477	14	of	of	ADP
iajs-3265	477	15	falknerskan	falknerskan	ADJ
iajs-3265	477	16	wedge	wedge	NOUN
iajs-3265	477	17	flow	flow	NOUN
iajs-3265	477	18	.	.	PUNCT
iajs-3265	478	1	acta	acta	PROPN
iajs-3265	478	2	mechanica	mechanica	PROPN
iajs-3265	478	3	,	,	PUNCT
iajs-3265	478	4	2003	2003	NUM
iajs-3265	478	5	,	,	PUNCT
iajs-3265	478	6	164(3	164(3	NUM
iajs-3265	478	7	)	)	PUNCT
iajs-3265	478	8	,	,	PUNCT
iajs-3265	478	9	161	161	NUM
iajs-3265	478	10	-	-	SYM
iajs-3265	478	11	174	174	NUM
iajs-3265	478	12	.	.	PUNCT
iajs-3265	479	1	58	58	NUM
iajs-3265	479	2	.	.	PUNCT
iajs-3265	480	1	temimi	temimi	PROPN
iajs-3265	480	2	,	,	PUNCT
iajs-3265	480	3	h.	h.	PROPN
iajs-3265	480	4	;	;	PUNCT
iajs-3265	480	5	ben	ben	PROPN
iajs-3265	480	6	-	-	PUNCT
iajs-3265	480	7	romdhane	romdhane	PROPN
iajs-3265	480	8	,	,	PUNCT
iajs-3265	480	9	m.	m.	NOUN
iajs-3265	480	10	numerical	numerical	PROPN
iajs-3265	480	11	solution	solution	NOUN
iajs-3265	480	12	of	of	ADP
iajs-3265	480	13	falkner	falkner	PROPN
iajs-3265	480	14	-	-	PUNCT
iajs-3265	480	15	skan	skan	VERB
iajs-3265	480	16	equation	equation	NOUN
iajs-3265	480	17	by	by	ADP
iajs-3265	480	18	iterative	iterative	NOUN
iajs-3265	480	19	transformation	transformation	NOUN
iajs-3265	480	20	method	method	NOUN
iajs-3265	480	21	.	.	PUNCT
iajs-3265	481	1	mathematical	mathematical	ADJ
iajs-3265	481	2	modelling	modelling	NOUN
iajs-3265	481	3	and	and	CCONJ
iajs-3265	481	4	analysis	analysis	NOUN
iajs-3265	481	5	,	,	PUNCT
iajs-3265	481	6	2018	2018	NUM
iajs-3265	481	7	,	,	PUNCT
iajs-3265	481	8	23(1	23(1	NUM
iajs-3265	481	9	)	)	PUNCT
iajs-3265	481	10	,	,	PUNCT
iajs-3265	481	11	139	139	NUM
iajs-3265	481	12	-	-	SYM
iajs-3265	481	13	151	151	NUM
iajs-3265	481	14	.	.	PUNCT
iajs-3265	481	15	59	59	NUM
iajs-3265	481	16	.	.	PUNCT
iajs-3265	482	1	guo	guo	PROPN
iajs-3265	482	2	,	,	PUNCT
iajs-3265	482	3	b.	b.	PROPN
iajs-3265	482	4	y.	y.	PROPN
iajs-3265	482	5	;	;	PUNCT
iajs-3265	482	6	shen	shen	PROPN
iajs-3265	482	7	,	,	PUNCT
iajs-3265	482	8	j.	j.	PROPN
iajs-3265	482	9	;	;	PUNCT
iajs-3265	482	10	wang	wang	PROPN
iajs-3265	482	11	,	,	PUNCT
iajs-3265	482	12	z.	z.	PROPN
iajs-3265	482	13	q.	q.	PROPN
iajs-3265	482	14	a	a	DET
iajs-3265	482	15	rational	rational	ADJ
iajs-3265	482	16	approximation	approximation	NOUN
iajs-3265	482	17	and	and	CCONJ
iajs-3265	482	18	its	its	PRON
iajs-3265	482	19	applications	application	NOUN
iajs-3265	482	20	to	to	PART
iajs-3265	482	21	differential	differential	VERB
iajs-3265	482	22	equations	equation	NOUN
iajs-3265	482	23	on	on	ADP
iajs-3265	482	24	the	the	DET
iajs-3265	482	25	half	half	ADJ
iajs-3265	482	26	line	line	NOUN
iajs-3265	482	27	.	.	PUNCT
iajs-3265	483	1	journal	journal	NOUN
iajs-3265	483	2	of	of	ADP
iajs-3265	483	3	scientific	scientific	ADJ
iajs-3265	483	4	computing	computing	NOUN
iajs-3265	483	5	,	,	PUNCT
iajs-3265	483	6	2000	2000	NUM
iajs-3265	483	7	,	,	PUNCT
iajs-3265	483	8	15(2	15(2	NUM
iajs-3265	483	9	)	)	PUNCT
iajs-3265	483	10	,	,	PUNCT
iajs-3265	483	11	117	117	NUM
iajs-3265	483	12	-	-	SYM
iajs-3265	483	13	147	147	NUM
iajs-3265	483	14	.	.	PUNCT
iajs-3265	483	15	60	60	NUM
iajs-3265	483	16	.	.	PUNCT
iajs-3265	484	1	kajani	kajani	NOUN
iajs-3265	484	2	,	,	PUNCT
iajs-3265	484	3	m.	m.	NOUN
iajs-3265	484	4	t.	t.	PROPN
iajs-3265	484	5	;	;	PUNCT
iajs-3265	484	6	maleki	maleki	NOUN
iajs-3265	484	7	,	,	PUNCT
iajs-3265	484	8	m.	m.	NOUN
iajs-3265	484	9	;	;	PUNCT
iajs-3265	484	10	allame	allame	PROPN
iajs-3265	484	11	,	,	PUNCT
iajs-3265	484	12	m.	m.	NOUN
iajs-3265	484	13	a	a	DET
iajs-3265	484	14	numerical	numerical	ADJ
iajs-3265	484	15	solution	solution	NOUN
iajs-3265	484	16	of	of	ADP
iajs-3265	484	17	falkner	falkner	PROPN
iajs-3265	484	18	-	-	PUNCT
iajs-3265	484	19	skan	skan	VERB
iajs-3265	484	20	equation	equation	NOUN
iajs-3265	484	21	via	via	ADP
iajs-3265	484	22	a	a	DET
iajs-3265	484	23	shifted	shift	VERB
iajs-3265	484	24	chebyshev	chebyshev	NOUN
iajs-3265	484	25	collocation	collocation	NOUN
iajs-3265	484	26	method	method	NOUN
iajs-3265	484	27	.	.	PUNCT
iajs-3265	485	1	aip	aip	PROPN
iajs-3265	485	2	conference	conference	NOUN
iajs-3265	485	3	proceedings	proceeding	NOUN
iajs-3265	485	4	,	,	PUNCT
iajs-3265	485	5	2014	2014	NUM
iajs-3265	485	6	,	,	PUNCT
iajs-3265	485	7	1629(1	1629(1	NUM
iajs-3265	485	8	)	)	PUNCT
iajs-3265	485	9	,	,	PUNCT
iajs-3265	485	10	381386	381386	NUM
iajs-3265	485	11	.	.	PUNCT
iajs-3265	486	1	61	61	NUM
iajs-3265	486	2	.	.	PUNCT
iajs-3265	487	1	calvert	calvert	NOUN
iajs-3265	487	2	,	,	PUNCT
iajs-3265	487	3	v.	v.	PROPN
iajs-3265	487	4	;	;	PUNCT
iajs-3265	487	5	razzaghi	razzaghi	PROPN
iajs-3265	487	6	,	,	PUNCT
iajs-3265	487	7	m.	m.	NOUN
iajs-3265	487	8	solutions	solution	NOUN
iajs-3265	487	9	of	of	ADP
iajs-3265	487	10	the	the	DET
iajs-3265	487	11	blasius	blasius	NOUN
iajs-3265	487	12	and	and	CCONJ
iajs-3265	487	13	mhd	mhd	PROPN
iajs-3265	487	14	falkner	falkner	PROPN
iajs-3265	487	15	-	-	PUNCT
iajs-3265	487	16	skan	skan	VERB
iajs-3265	487	17	boundary	boundary	ADJ
iajs-3265	487	18	-	-	PUNCT
iajs-3265	487	19	layer	layer	NOUN
iajs-3265	487	20	equations	equation	NOUN
iajs-3265	487	21	by	by	ADP
iajs-3265	487	22	modified	modify	VERB
iajs-3265	487	23	rational	rational	ADJ
iajs-3265	487	24	bernoulli	bernoulli	NOUN
iajs-3265	487	25	functions	function	NOUN
iajs-3265	487	26	.	.	PUNCT
iajs-3265	488	1	international	international	ADJ
iajs-3265	488	2	journal	journal	PROPN
iajs-3265	488	3	of	of	ADP
iajs-3265	488	4	numerical	numerical	ADJ
iajs-3265	488	5	methods	method	NOUN
iajs-3265	488	6	for	for	ADP
iajs-3265	488	7	heat	heat	NOUN
iajs-3265	488	8	&	&	CCONJ
iajs-3265	488	9	fluid	fluid	ADJ
iajs-3265	488	10	flow	flow	NOUN
iajs-3265	488	11	,	,	PUNCT
iajs-3265	488	12	2017	2017	NUM
iajs-3265	488	13	,	,	PUNCT
iajs-3265	488	14	27(8	27(8	NUM
iajs-3265	488	15	)	)	PUNCT
iajs-3265	488	16	,	,	PUNCT
iajs-3265	488	17	1687	1687	NUM
iajs-3265	488	18	-	-	SYM
iajs-3265	488	19	1705	1705	NUM
iajs-3265	488	20	.	.	PUNCT
iajs-3265	489	1	62	62	NUM
iajs-3265	489	2	.	.	PUNCT
iajs-3265	490	1	azodi	azodi	PROPN
iajs-3265	490	2	,	,	PUNCT
iajs-3265	490	3	h.	h.	PROPN
iajs-3265	490	4	d.	d.	PROPN
iajs-3265	490	5	;	;	PUNCT
iajs-3265	490	6	yaghouti	yaghouti	PROPN
iajs-3265	490	7	,	,	PUNCT
iajs-3265	490	8	m.	m.	PROPN
iajs-3265	490	9	r.	r.	PROPN
iajs-3265	490	10	bernoulli	bernoulli	PROPN
iajs-3265	490	11	polynomials	polynomial	VERB
iajs-3265	490	12	collocation	collocation	NOUN
iajs-3265	490	13	for	for	ADP
iajs-3265	490	14	weakly	weakly	ADJ
iajs-3265	490	15	singular	singular	PROPN
iajs-3265	490	16	volterra	volterra	PROPN
iajs-3265	490	17	integro	integro	PROPN
iajs-3265	490	18	-	-	PUNCT
iajs-3265	490	19	differential	differential	NOUN
iajs-3265	490	20	equations	equation	NOUN
iajs-3265	490	21	of	of	ADP
iajs-3265	490	22	fractional	fractional	ADJ
iajs-3265	490	23	order	order	NOUN
iajs-3265	490	24	.	.	PUNCT
iajs-3265	491	1	filomat	filomat	NOUN
iajs-3265	491	2	,	,	PUNCT
iajs-3265	491	3	2018	2018	NUM
iajs-3265	491	4	,	,	PUNCT
iajs-3265	491	5	32(10	32(10	NUM
iajs-3265	491	6	)	)	PUNCT
iajs-3265	491	7	,	,	PUNCT
iajs-3265	491	8	36233635	36233635	NUM
iajs-3265	491	9	.	.	PUNCT