id	sid	tid	token	lemma	pos
iajs-3292	1	1	358	358	NUM
iajs-3292	1	2	ihjpas	ihjpa	NOUN
iajs-3292	1	3	.	.	PUNCT
iajs-3292	2	1	37	37	NUM
iajs-3292	2	2	(	(	PUNCT
iajs-3292	2	3	1	1	NUM
iajs-3292	2	4	)	)	PUNCT
iajs-3292	2	5	2024	2024	NUM
iajs-3292	2	6	ibn	ibn	PROPN
iajs-3292	2	7	al	al	PROPN
iajs-3292	2	8	-	-	PUNCT
iajs-3292	2	9	haitham	haitham	PROPN
iajs-3292	2	10	journal	journal	PROPN
iajs-3292	2	11	for	for	ADP
iajs-3292	2	12	pure	pure	ADJ
iajs-3292	2	13	and	and	CCONJ
iajs-3292	2	14	applied	applied	ADJ
iajs-3292	2	15	sciences	sciences	PROPN
iajs-3292	2	16	journal	journal	PROPN
iajs-3292	2	17	homepage	homepage	NOUN
iajs-3292	2	18	:	:	PUNCT
iajs-3292	2	19	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	NOUN
iajs-3292	2	20	pissn	pissn	ADJ
iajs-3292	2	21	:	:	PUNCT
iajs-3292	2	22	1609	1609	NUM
iajs-3292	2	23	-	-	SYM
iajs-3292	2	24	4042	4042	NUM
iajs-3292	2	25	,	,	PUNCT
iajs-3292	2	26	eissn	eissn	NOUN
iajs-3292	2	27	:	:	PUNCT
iajs-3292	2	28	2521	2521	NUM
iajs-3292	2	29	-	-	SYM
iajs-3292	2	30	3407	3407	NUM
iajs-3292	2	31	1amna	1amna	NUM
iajs-3292	2	32	m.	m.	NOUN
iajs-3292	2	33	mahdi	mahdi	PROPN
iajs-3292	2	34	*	*	PROPN
iajs-3292	2	35	2majeed	2majeed	NUM
iajs-3292	2	36	a.	a.	NOUN
iajs-3292	2	37	al	al	PROPN
iajs-3292	2	38	-	-	PUNCT
iajs-3292	2	39	jawary	jawary	PROPN
iajs-3292	2	40	3mustafa	3mustafa	NUM
iajs-3292	2	41	turkyilmazoglu	turkyilmazoglu	NOUN
iajs-3292	2	42	university	university	NOUN
iajs-3292	2	43	of	of	ADP
iajs-3292	2	44	haitham	haitham	PROPN
iajs-3292	2	45	,	,	PUNCT
iajs-3292	2	46	-r	-r	PUNCT
iajs-3292	2	47	pure	pure	ADJ
iajs-3292	2	48	sciences	sciences	PROPN
iajs-3292	2	49	ibn	ibn	PROPN
iajs-3292	2	50	aldepartment	aldepartment	NOUN
iajs-3292	2	51	of	of	ADP
iajs-3292	2	52	mathematics	mathematic	NOUN
iajs-3292	2	53	,	,	PUNCT
iajs-3292	2	54	college	college	NOUN
iajs-3292	2	55	of	of	ADP
iajs-3292	2	56	education	education	NOUN
iajs-3292	2	57	fo	fo	ADP
iajs-3292	2	58	1,2	1,2	NUM
iajs-3292	2	59	baghdad	baghdad	PROPN
iajs-3292	2	60	,	,	PUNCT
iajs-3292	2	61	baghdad	baghdad	PROPN
iajs-3292	2	62	,	,	PUNCT
iajs-3292	2	63	iraq	iraq	PROPN
iajs-3292	2	64	.	.	PUNCT
iajs-3292	3	1	3department	3department	NUM
iajs-3292	3	2	of	of	ADP
iajs-3292	3	3	mathematics	mathematic	NOUN
iajs-3292	3	4	,	,	PUNCT
iajs-3292	3	5	hacettepe	hacettepe	PROPN
iajs-3292	3	6	university	university	NOUN
iajs-3292	3	7	,	,	PUNCT
iajs-3292	3	8	ankara	ankara	PROPN
iajs-3292	3	9	,	,	PUNCT
iajs-3292	3	10	turkey	turkey	PROPN
iajs-3292	3	11	.	.	PUNCT
iajs-3292	4	1	china	china	PROPN
iajs-3292	4	2	medical	medical	PROPN
iajs-3292	4	3	university	university	PROPN
iajs-3292	4	4	,	,	PUNCT
iajs-3292	4	5	department	department	NOUN
iajs-3292	4	6	of	of	ADP
iajs-3292	4	7	medical	medical	ADJ
iajs-3292	4	8	research	research	NOUN
iajs-3292	4	9	,	,	PUNCT
iajs-3292	4	10	china	china	PROPN
iajs-3292	4	11	medical	medical	PROPN
iajs-3292	4	12	university	university	PROPN
iajs-3292	4	13	hospital	hospital	NOUN
iajs-3292	4	14	,	,	PUNCT
iajs-3292	4	15	3	3	NUM
iajs-3292	4	16	.taichung	.taichung	ADJ
iajs-3292	4	17	,	,	PUNCT
iajs-3292	4	18	taiwan	taiwan	PROPN
iajs-3292	4	19	*	*	PUNCT
iajs-3292	4	20	corresponding	correspond	VERB
iajs-3292	4	21	author	author	NOUN
iajs-3292	4	22	:	:	PUNCT
iajs-3292	4	23	amna.meqdad1203a@ihcoedu.uobaghdad.edu.iq	amna.meqdad1203a@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-3292	4	24	abstract	abstract	VERB
iajs-3292	4	25	the	the	DET
iajs-3292	4	26	method	method	NOUN
iajs-3292	4	27	of	of	ADP
iajs-3292	4	28	operational	operational	ADJ
iajs-3292	4	29	matrices	matrix	NOUN
iajs-3292	4	30	based	base	VERB
iajs-3292	4	31	on	on	ADP
iajs-3292	4	32	different	different	ADJ
iajs-3292	4	33	types	type	NOUN
iajs-3292	4	34	of	of	ADP
iajs-3292	4	35	polynomials	polynomial	NOUN
iajs-3292	4	36	such	such	ADJ
iajs-3292	4	37	as	as	ADP
iajs-3292	4	38	bernstein	bernstein	PROPN
iajs-3292	4	39	,	,	PUNCT
iajs-3292	4	40	shifted	shift	VERB
iajs-3292	4	41	legendre	legendre	PROPN
iajs-3292	4	42	and	and	CCONJ
iajs-3292	4	43	bernoulli	bernoulli	NOUN
iajs-3292	4	44	polynomials	polynomial	NOUN
iajs-3292	4	45	is	be	AUX
iajs-3292	4	46	introduced	introduce	VERB
iajs-3292	4	47	and	and	CCONJ
iajs-3292	4	48	implemented	implement	VERB
iajs-3292	4	49	to	to	PART
iajs-3292	4	50	solve	solve	VERB
iajs-3292	4	51	the	the	DET
iajs-3292	4	52	nonlinear	nonlinear	ADJ
iajs-3292	4	53	blasius	blasius	ADJ
iajs-3292	4	54	equations	equation	NOUN
iajs-3292	4	55	approximately	approximately	ADV
iajs-3292	4	56	.	.	PUNCT
iajs-3292	5	1	the	the	DET
iajs-3292	5	2	nonlinear	nonlinear	ADJ
iajs-3292	5	3	differential	differential	ADJ
iajs-3292	5	4	equation	equation	NOUN
iajs-3292	5	5	is	be	AUX
iajs-3292	5	6	converted	convert	VERB
iajs-3292	5	7	into	into	ADP
iajs-3292	5	8	a	a	DET
iajs-3292	5	9	system	system	NOUN
iajs-3292	5	10	of	of	ADP
iajs-3292	5	11	nonlinear	nonlinear	ADJ
iajs-3292	5	12	algebraic	algebraic	ADJ
iajs-3292	5	13	equations	equation	NOUN
iajs-3292	5	14	that	that	PRON
iajs-3292	5	15	can	can	AUX
iajs-3292	5	16	be	be	AUX
iajs-3292	5	17	solved	solve	VERB
iajs-3292	5	18	using	use	VERB
iajs-3292	5	19	mathematica	mathematica	PROPN
iajs-3292	5	20	®	®	PROPN
iajs-3292	5	21	12	12	NUM
iajs-3292	5	22	.	.	PUNCT
iajs-3292	6	1	the	the	DET
iajs-3292	6	2	efficiency	efficiency	NOUN
iajs-3292	6	3	of	of	ADP
iajs-3292	6	4	these	these	DET
iajs-3292	6	5	methods	method	NOUN
iajs-3292	6	6	has	have	AUX
iajs-3292	6	7	been	be	AUX
iajs-3292	6	8	studied	study	VERB
iajs-3292	6	9	by	by	ADP
iajs-3292	6	10	calculating	calculate	VERB
iajs-3292	6	11	the	the	DET
iajs-3292	6	12	maximum	maximum	ADJ
iajs-3292	6	13	error	error	NOUN
iajs-3292	6	14	remainder	remainder	NOUN
iajs-3292	6	15	(	(	PUNCT
iajs-3292	6	16	,	,	PUNCT
iajs-3292	6	17	𝑀𝐸𝑅-𝑛.	𝑀𝐸𝑅-𝑛.	ADJ
iajs-3292	6	18	)	)	PUNCT
iajs-3292	6	19	,	,	PUNCT
iajs-3292	6	20	and	and	CCONJ
iajs-3292	6	21	it	it	PRON
iajs-3292	6	22	was	be	AUX
iajs-3292	6	23	found	find	VERB
iajs-3292	6	24	that	that	SCONJ
iajs-3292	6	25	their	their	PRON
iajs-3292	6	26	efficiency	efficiency	NOUN
iajs-3292	6	27	increases	increase	VERB
iajs-3292	6	28	with	with	ADP
iajs-3292	6	29	increasing	increase	VERB
iajs-3292	6	30	polynomial	polynomial	ADJ
iajs-3292	6	31	degree	degree	NOUN
iajs-3292	6	32	(	(	PUNCT
iajs-3292	6	33	n	n	CCONJ
iajs-3292	6	34	)	)	PUNCT
iajs-3292	6	35	as	as	SCONJ
iajs-3292	6	36	the	the	DET
iajs-3292	6	37	errors	error	NOUN
iajs-3292	6	38	decrease	decrease	VERB
iajs-3292	6	39	.	.	PUNCT
iajs-3292	7	1	moreover	moreover	ADV
iajs-3292	7	2	,	,	PUNCT
iajs-3292	7	3	the	the	DET
iajs-3292	7	4	approximate	approximate	ADJ
iajs-3292	7	5	solutions	solution	NOUN
iajs-3292	7	6	obtained	obtain	VERB
iajs-3292	7	7	by	by	ADP
iajs-3292	7	8	the	the	DET
iajs-3292	7	9	proposed	propose	VERB
iajs-3292	7	10	methods	method	NOUN
iajs-3292	7	11	are	be	AUX
iajs-3292	7	12	compared	compare	VERB
iajs-3292	7	13	with	with	ADP
iajs-3292	7	14	the	the	DET
iajs-3292	7	15	solution	solution	NOUN
iajs-3292	7	16	of	of	ADP
iajs-3292	7	17	the	the	DET
iajs-3292	7	18	fourth	fourth	ADJ
iajs-3292	7	19	-	-	PUNCT
iajs-3292	7	20	order	order	NOUN
iajs-3292	7	21	runge	runge	NOUN
iajs-3292	7	22	-	-	PUNCT
iajs-3292	7	23	kutta	kutta	NOUN
iajs-3292	7	24	method	method	NOUN
iajs-3292	7	25	(	(	PUNCT
iajs-3292	7	26	rk4	rk4	NOUN
iajs-3292	7	27	)	)	PUNCT
iajs-3292	7	28	,	,	PUNCT
iajs-3292	7	29	which	which	PRON
iajs-3292	7	30	gives	give	VERB
iajs-3292	7	31	a	a	DET
iajs-3292	7	32	very	very	ADV
iajs-3292	7	33	good	good	ADJ
iajs-3292	7	34	agreement	agreement	NOUN
iajs-3292	7	35	.	.	PUNCT
iajs-3292	8	1	in	in	ADP
iajs-3292	8	2	addition	addition	NOUN
iajs-3292	8	3	,	,	PUNCT
iajs-3292	8	4	the	the	DET
iajs-3292	8	5	convergence	convergence	NOUN
iajs-3292	8	6	of	of	ADP
iajs-3292	8	7	the	the	DET
iajs-3292	8	8	proposed	propose	VERB
iajs-3292	8	9	approximation	approximation	NOUN
iajs-3292	8	10	methods	method	NOUN
iajs-3292	8	11	is	be	AUX
iajs-3292	8	12	given	give	VERB
iajs-3292	8	13	based	base	VERB
iajs-3292	8	14	on	on	ADP
iajs-3292	8	15	one	one	NUM
iajs-3292	8	16	of	of	ADP
iajs-3292	8	17	the	the	DET
iajs-3292	8	18	results	result	NOUN
iajs-3292	8	19	of	of	ADP
iajs-3292	8	20	the	the	DET
iajs-3292	8	21	banach	banach	ADV
iajs-3292	8	22	fixed	fix	VERB
iajs-3292	8	23	point	point	NOUN
iajs-3292	8	24	theorem	theorem	ADJ
iajs-3292	8	25	.	.	PUNCT
iajs-3292	9	1	keywords	keyword	NOUN
iajs-3292	9	2	:	:	PUNCT
iajs-3292	9	3	blasius	blasius	ADJ
iajs-3292	9	4	equations	equation	NOUN
iajs-3292	9	5	;	;	PUNCT
iajs-3292	9	6	bernstein	bernstein	PROPN
iajs-3292	9	7	polynomial	polynomial	PROPN
iajs-3292	9	8	;	;	PUNCT
iajs-3292	9	9	legendre	legendre	PROPN
iajs-3292	9	10	polynomial	polynomial	PROPN
iajs-3292	9	11	;	;	PUNCT
iajs-3292	9	12	bernoulli	bernoulli	NOUN
iajs-3292	9	13	polynomial	polynomial	NOUN
iajs-3292	9	14	;	;	PUNCT
iajs-3292	9	15	operational	operational	ADJ
iajs-3292	9	16	matrices	matrix	NOUN
iajs-3292	9	17	.	.	PUNCT
iajs-3292	10	1	1	1	X
iajs-3292	10	2	.	.	X
iajs-3292	10	3	introduction	introduction	NOUN
iajs-3292	10	4	the	the	DET
iajs-3292	10	5	nonlinear	nonlinear	ADJ
iajs-3292	10	6	ordinary	ordinary	ADJ
iajs-3292	10	7	differential	differential	ADJ
iajs-3292	10	8	equations	equation	NOUN
iajs-3292	10	9	(	(	PUNCT
iajs-3292	10	10	node	node	NOUN
iajs-3292	10	11	)	)	PUNCT
iajs-3292	10	12	have	have	VERB
iajs-3292	10	13	many	many	ADJ
iajs-3292	10	14	practical	practical	ADJ
iajs-3292	10	15	applications	application	NOUN
iajs-3292	10	16	in	in	ADP
iajs-3292	10	17	engineering	engineering	NOUN
iajs-3292	10	18	and	and	CCONJ
iajs-3292	10	19	applied	apply	VERB
iajs-3292	10	20	sciences	science	NOUN
iajs-3292	10	21	,	,	PUNCT
iajs-3292	10	22	such	such	ADJ
iajs-3292	10	23	as	as	ADP
iajs-3292	10	24	fluid	fluid	ADJ
iajs-3292	10	25	flow	flow	NOUN
iajs-3292	10	26	,	,	PUNCT
iajs-3292	10	27	current	current	ADJ
iajs-3292	10	28	flow	flow	NOUN
iajs-3292	10	29	in	in	ADP
iajs-3292	10	30	electric	electric	ADJ
iajs-3292	10	31	circuits	circuit	NOUN
iajs-3292	10	32	,	,	PUNCT
iajs-3292	10	33	heat	heat	NOUN
iajs-3292	10	34	dissipation	dissipation	NOUN
iajs-3292	10	35	in	in	ADP
iajs-3292	10	36	solid	solid	ADJ
iajs-3292	10	37	bodies	body	NOUN
iajs-3292	10	38	,	,	PUNCT
iajs-3292	10	39	seismic	seismic	ADJ
iajs-3292	10	40	wave	wave	NOUN
iajs-3292	10	41	propagation	propagation	NOUN
iajs-3292	10	42	,	,	PUNCT
iajs-3292	10	43	population	population	NOUN
iajs-3292	10	44	increase	increase	NOUN
iajs-3292	10	45	or	or	CCONJ
iajs-3292	10	46	decrease	decrease	NOUN
iajs-3292	10	47	,	,	PUNCT
iajs-3292	10	48	and	and	CCONJ
iajs-3292	10	49	many	many	ADJ
iajs-3292	10	50	other	other	ADJ
iajs-3292	10	51	topics	topic	NOUN
iajs-3292	10	52	[	[	X
iajs-3292	10	53	1,2	1,2	NUM
iajs-3292	10	54	]	]	PUNCT
iajs-3292	10	55	.	.	PUNCT
iajs-3292	11	1	in	in	ADP
iajs-3292	11	2	approximation	approximation	NOUN
iajs-3292	11	3	theory	theory	NOUN
iajs-3292	11	4	and	and	CCONJ
iajs-3292	11	5	numerical	numerical	ADJ
iajs-3292	11	6	analysis	analysis	NOUN
iajs-3292	11	7	,	,	PUNCT
iajs-3292	11	8	polynomials	polynomial	NOUN
iajs-3292	11	9	are	be	AUX
iajs-3292	11	10	particularly	particularly	ADV
iajs-3292	11	11	useful	useful	ADJ
iajs-3292	11	12	tools	tool	NOUN
iajs-3292	11	13	[	[	X
iajs-3292	11	14	3	3	NUM
iajs-3292	11	15	]	]	PUNCT
iajs-3292	11	16	.	.	PUNCT
iajs-3292	12	1	consequently	consequently	ADV
iajs-3292	12	2	,	,	PUNCT
iajs-3292	12	3	the	the	DET
iajs-3292	12	4	polynomial	polynomial	ADJ
iajs-3292	12	5	series	series	NOUN
iajs-3292	12	6	then	then	ADV
iajs-3292	12	7	the	the	DET
iajs-3292	12	8	operational	operational	ADJ
iajs-3292	12	9	matrices	matrix	NOUN
iajs-3292	12	10	(	(	PUNCT
iajs-3292	12	11	om	om	NOUN
iajs-3292	12	12	)	)	PUNCT
iajs-3292	12	13	are	be	AUX
iajs-3292	12	14	used	use	VERB
iajs-3292	12	15	to	to	PART
iajs-3292	12	16	simplify	simplify	VERB
iajs-3292	12	17	the	the	DET
iajs-3292	12	18	unknown	unknown	ADJ
iajs-3292	12	19	function	function	NOUN
iajs-3292	12	20	by	by	ADP
iajs-3292	12	21	transforming	transform	VERB
iajs-3292	12	22	it	it	PRON
iajs-3292	12	23	into	into	ADP
iajs-3292	12	24	a	a	DET
iajs-3292	12	25	system	system	NOUN
iajs-3292	12	26	of	of	ADP
iajs-3292	12	27	algebraic	algebraic	ADJ
iajs-3292	12	28	equations	equation	NOUN
iajs-3292	12	29	that	that	PRON
iajs-3292	12	30	can	can	AUX
iajs-3292	12	31	be	be	AUX
iajs-3292	12	32	easily	easily	ADV
iajs-3292	12	33	solved	solve	VERB
iajs-3292	12	34	without	without	ADP
iajs-3292	12	35	integration	integration	NOUN
iajs-3292	12	36	and	and	CCONJ
iajs-3292	12	37	differentiation	differentiation	NOUN
iajs-3292	12	38	.	.	PUNCT
iajs-3292	13	1	several	several	ADJ
iajs-3292	13	2	studies	study	NOUN
iajs-3292	13	3	have	have	AUX
iajs-3292	13	4	been	be	AUX
iajs-3292	13	5	conducted	conduct	VERB
iajs-3292	13	6	on	on	ADP
iajs-3292	13	7	this	this	DET
iajs-3292	13	8	technique	technique	NOUN
iajs-3292	13	9	,	,	PUNCT
iajs-3292	13	10	which	which	PRON
iajs-3292	13	11	uses	use	VERB
iajs-3292	13	12	om	om	PROPN
iajs-3292	13	13	methods	method	NOUN
iajs-3292	13	14	to	to	PART
iajs-3292	13	15	solve	solve	VERB
iajs-3292	13	16	many	many	ADJ
iajs-3292	13	17	problems	problem	NOUN
iajs-3292	13	18	based	base	VERB
iajs-3292	13	19	on	on	ADP
iajs-3292	13	20	various	various	ADJ
iajs-3292	13	21	polynomials	polynomial	NOUN
iajs-3292	13	22	.	.	PUNCT
iajs-3292	14	1	many	many	ADJ
iajs-3292	14	2	researchers	researcher	NOUN
iajs-3292	14	3	have	have	AUX
iajs-3292	14	4	solved	solve	VERB
iajs-3292	14	5	various	various	ADJ
iajs-3292	14	6	problems	problem	NOUN
iajs-3292	14	7	using	use	VERB
iajs-3292	14	8	om	om	PROPN
iajs-3292	14	9	based	base	VERB
iajs-3292	14	10	on	on	ADP
iajs-3292	14	11	the	the	DET
iajs-3292	14	12	bernstein	bernstein	PROPN
iajs-3292	14	13	polynomial	polynomial	PROPN
iajs-3292	14	14	(	(	PUNCT
iajs-3292	14	15	bom	bom	PROPN
iajs-3292	14	16	)	)	PUNCT
iajs-3292	14	17	,	,	PUNCT
iajs-3292	14	18	such	such	ADJ
iajs-3292	14	19	as	as	ADP
iajs-3292	14	20	:	:	PUNCT
iajs-3292	14	21	[	[	X
iajs-3292	14	22	4	4	X
iajs-3292	14	23	]	]	PUNCT
iajs-3292	14	24	solved	solve	VERB
iajs-3292	14	25	odd	odd	ADJ
iajs-3292	14	26	boundary	boundary	ADJ
iajs-3292	14	27	value	value	NOUN
iajs-3292	14	28	problems	problem	NOUN
iajs-3292	14	29	,	,	PUNCT
iajs-3292	14	30	[	[	X
iajs-3292	14	31	5	5	NUM
iajs-3292	14	32	]	]	PUNCT
iajs-3292	14	33	studied	study	VERB
iajs-3292	14	34	third	third	ADJ
iajs-3292	14	35	order	order	NOUN
iajs-3292	14	36	equations	equation	NOUN
iajs-3292	14	37	ode	ode	VERB
iajs-3292	14	38	,	,	PUNCT
iajs-3292	14	39	[	[	X
iajs-3292	14	40	6	6	NUM
iajs-3292	14	41	]	]	PUNCT
iajs-3292	14	42	solved	solve	VERB
iajs-3292	14	43	fractional	fractional	ADJ
iajs-3292	14	44	integral	integral	ADJ
iajs-3292	14	45	equations	equation	NOUN
iajs-3292	14	46	.	.	PUNCT
iajs-3292	15	1	moreover	moreover	ADV
iajs-3292	15	2	,	,	PUNCT
iajs-3292	15	3	there	there	PRON
iajs-3292	15	4	are	be	VERB
iajs-3292	15	5	many	many	ADJ
iajs-3292	15	6	researchers	researcher	NOUN
iajs-3292	15	7	who	who	PRON
iajs-3292	15	8	have	have	AUX
iajs-3292	15	9	used	use	VERB
iajs-3292	15	10	operational	operational	ADJ
iajs-3292	15	11	matrices	matrix	NOUN
iajs-3292	15	12	based	base	VERB
iajs-3292	15	13	on	on	ADP
iajs-3292	15	14	different	different	ADJ
iajs-3292	15	15	polynomials	polynomial	NOUN
iajs-3292	15	16	,	,	PUNCT
iajs-3292	15	17	such	such	ADJ
iajs-3292	15	18	as	as	ADP
iajs-3292	15	19	[	[	X
iajs-3292	15	20	7	7	NUM
iajs-3292	15	21	]	]	PUNCT
iajs-3292	15	22	used	use	VERB
iajs-3292	15	23	the	the	DET
iajs-3292	15	24	legendre	legendre	PROPN
iajs-3292	15	25	operational	operational	ADJ
iajs-3292	15	26	novel	novel	ADJ
iajs-3292	15	27	approximate	approximate	ADJ
iajs-3292	15	28	solutions	solution	NOUN
iajs-3292	15	29	for	for	ADP
iajs-3292	15	30	nonlinear	nonlinear	ADJ
iajs-3292	15	31	blasius	blasius	ADJ
iajs-3292	15	32	equations	equation	NOUN
iajs-3292	15	33	received	receive	VERB
iajs-3292	15	34	24	24	NUM
iajs-3292	15	35	february	february	NOUN
iajs-3292	15	36	2023	2023	NUM
iajs-3292	15	37	,	,	PUNCT
iajs-3292	15	38	received	receive	VERB
iajs-3292	15	39	2	2	NUM
iajs-3292	15	40	may	may	PROPN
iajs-3292	15	41	2023	2023	NUM
iajs-3292	15	42	,	,	PUNCT
iajs-3292	15	43	accepted	accept	VERB
iajs-3292	15	44	8	8	NUM
iajs-3292	15	45	may	may	PROPN
iajs-3292	15	46	2023	2023	NUM
iajs-3292	15	47	,	,	PUNCT
iajs-3292	15	48	published	publish	VERB
iajs-3292	15	49	20	20	NUM
iajs-3292	15	50	january	january	NOUN
iajs-3292	15	51	2024	2024	NUM
iajs-3292	15	52	doi.org/10.30526/37.1.3292	doi.org/10.30526/37.1.3292	NOUN
iajs-3292	15	53	https://jih.uobaghdad.edu.iq/index.php/j/index#1609-4042	https://jih.uobaghdad.edu.iq/index.php/j/index#1609-4042	NOUN
iajs-3292	15	54	https://jih.uobaghdad.edu.iq/index.php/j/index#2521-3407	https://jih.uobaghdad.edu.iq/index.php/j/index#2521-3407	VERB
iajs-3292	15	55	mailto:amna.meqdad1203a@ihcoedu.uobaghdad.edu.iq	mailto:amna.meqdad1203a@ihcoedu.uobaghdad.edu.iq	VERB
iajs-3292	15	56	https://orcid.org/0000-0001-7140-2144	https://orcid.org/0000-0001-7140-2144	PROPN
iajs-3292	15	57	mailto:amna.meqdad1203a@ihcoedu.uobaghdad.edu.iq	mailto:amna.meqdad1203a@ihcoedu.uobaghdad.edu.iq	ADJ
iajs-3292	15	58	https://orcid.org/0000-0003-3967-0012	https://orcid.org/0000-0003-3967-0012	PROPN
iajs-3292	15	59	mailto:majeed.a.w@ihcoedu.uobaghdad.edu.iq	mailto:majeed.a.w@ihcoedu.uobaghdad.edu.iq	VERB
iajs-3292	15	60	https://orcid.org/0000-0003-0412-4580	https://orcid.org/0000-0003-0412-4580	NOUN
iajs-3292	15	61	mailto:turkyilm@hacettepe.edu.tr	mailto:turkyilm@hacettepe.edu.tr	PROPN
iajs-3292	15	62	ihjpas	ihjpas	PROPN
iajs-3292	15	63	.	.	PUNCT
iajs-3292	16	1	37	37	NUM
iajs-3292	16	2	(	(	PUNCT
iajs-3292	16	3	1	1	NUM
iajs-3292	16	4	)	)	SYM
iajs-3292	16	5	2024	2024	NUM
iajs-3292	16	6	359	359	NUM
iajs-3292	16	7	matrix	matrix	NOUN
iajs-3292	16	8	(	(	PUNCT
iajs-3292	16	9	lom	lom	NOUN
iajs-3292	16	10	)	)	PUNCT
iajs-3292	16	11	method	method	NOUN
iajs-3292	16	12	to	to	PART
iajs-3292	16	13	solve	solve	VERB
iajs-3292	16	14	the	the	DET
iajs-3292	16	15	fractional	fractional	ADJ
iajs-3292	16	16	-	-	PUNCT
iajs-3292	16	17	order	order	NOUN
iajs-3292	16	18	two	two	NUM
iajs-3292	16	19	-	-	PUNCT
iajs-3292	16	20	dimensional	dimensional	ADJ
iajs-3292	16	21	integral	integral	ADJ
iajs-3292	16	22	equations	equation	NOUN
iajs-3292	16	23	.	.	PUNCT
iajs-3292	17	1	in	in	ADP
iajs-3292	17	2	[	[	X
iajs-3292	17	3	8	8	NUM
iajs-3292	17	4	]	]	X
iajs-3292	17	5	sharma	sharma	PROPN
iajs-3292	17	6	et	et	PROPN
iajs-3292	17	7	al	al	PROPN
iajs-3292	17	8	.	.	PROPN
iajs-3292	17	9	solved	solve	VERB
iajs-3292	17	10	the	the	DET
iajs-3292	17	11	lane	lane	NOUN
iajs-3292	17	12	-	-	PUNCT
iajs-3292	17	13	emden	emden	NOUN
iajs-3292	17	14	equations	equation	NOUN
iajs-3292	17	15	using	use	VERB
iajs-3292	17	16	the	the	DET
iajs-3292	17	17	chebyshev	chebyshev	NOUN
iajs-3292	17	18	operational	operational	ADJ
iajs-3292	17	19	matrix	matrix	NOUN
iajs-3292	17	20	(	(	PUNCT
iajs-3292	17	21	chom	chom	NOUN
iajs-3292	17	22	)	)	PUNCT
iajs-3292	17	23	method	method	NOUN
iajs-3292	17	24	.	.	PUNCT
iajs-3292	18	1	also	also	ADV
iajs-3292	18	2	,	,	PUNCT
iajs-3292	18	3	om	om	PROPN
iajs-3292	18	4	with	with	ADP
iajs-3292	18	5	bernoulli	bernoulli	NOUN
iajs-3292	18	6	polynomials	polynomial	NOUN
iajs-3292	18	7	(	(	PUNCT
iajs-3292	18	8	brom	brom	NOUN
iajs-3292	18	9	)	)	PUNCT
iajs-3292	18	10	was	be	AUX
iajs-3292	18	11	used	use	VERB
iajs-3292	18	12	by	by	ADP
iajs-3292	18	13	bazm	bazm	PROPN
iajs-3292	19	1	[	[	X
iajs-3292	19	2	9	9	NUM
iajs-3292	19	3	]	]	PUNCT
iajs-3292	19	4	to	to	PART
iajs-3292	19	5	solve	solve	VERB
iajs-3292	19	6	some	some	DET
iajs-3292	19	7	types	type	NOUN
iajs-3292	19	8	of	of	ADP
iajs-3292	19	9	integral	integral	ADJ
iajs-3292	19	10	equations	equation	NOUN
iajs-3292	19	11	.	.	PUNCT
iajs-3292	20	1	[	[	X
iajs-3292	20	2	10	10	NUM
iajs-3292	20	3	]	]	PUNCT
iajs-3292	20	4	studied	study	VERB
iajs-3292	20	5	the	the	DET
iajs-3292	20	6	magnetohydrodynamic	magnetohydrodynamic	ADJ
iajs-3292	20	7	squeezing	squeeze	VERB
iajs-3292	20	8	fluid	fluid	NOUN
iajs-3292	20	9	,	,	PUNCT
iajs-3292	20	10	straight	straight	ADJ
iajs-3292	20	11	fin	fin	NOUN
iajs-3292	20	12	problem	problem	NOUN
iajs-3292	20	13	,	,	PUNCT
iajs-3292	20	14	jeffery	jeffery	PROPN
iajs-3292	20	15	-	-	PUNCT
iajs-3292	20	16	hamel	hamel	PROPN
iajs-3292	20	17	flow	flow	NOUN
iajs-3292	20	18	,	,	PUNCT
iajs-3292	20	19	and	and	CCONJ
iajs-3292	20	20	falkner	falkner	PROPN
iajs-3292	20	21	-	-	PUNCT
iajs-3292	20	22	skan	skan	VERB
iajs-3292	20	23	equation	equation	NOUN
iajs-3292	20	24	using	use	VERB
iajs-3292	20	25	bom	bom	PROPN
iajs-3292	20	26	and	and	CCONJ
iajs-3292	20	27	chom	chom	NOUN
iajs-3292	20	28	.	.	PUNCT
iajs-3292	21	1	they	they	PRON
iajs-3292	21	2	also	also	ADV
iajs-3292	21	3	studied	study	VERB
iajs-3292	21	4	the	the	DET
iajs-3292	21	5	solution	solution	NOUN
iajs-3292	21	6	of	of	ADP
iajs-3292	21	7	nonlinear	nonlinear	ADJ
iajs-3292	21	8	thinfilm	thinfilm	NOUN
iajs-3292	21	9	flow	flow	NOUN
iajs-3292	21	10	of	of	ADP
iajs-3292	21	11	3rd	3rd	ADJ
iajs-3292	21	12	-	-	PUNCT
iajs-3292	21	13	grade	grade	NOUN
iajs-3292	21	14	fluid	fluid	NOUN
iajs-3292	21	15	problems	problem	NOUN
iajs-3292	21	16	with	with	ADP
iajs-3292	21	17	lom	lom	PROPN
iajs-3292	22	1	[	[	X
iajs-3292	22	2	11	11	NUM
iajs-3292	22	3	]	]	PUNCT
iajs-3292	22	4	.	.	PUNCT
iajs-3292	23	1	in	in	ADP
iajs-3292	23	2	[	[	PUNCT
iajs-3292	23	3	12	12	NUM
iajs-3292	23	4	-	-	SYM
iajs-3292	23	5	20	20	NUM
iajs-3292	23	6	]	]	PUNCT
iajs-3292	23	7	,	,	PUNCT
iajs-3292	23	8	other	other	ADJ
iajs-3292	23	9	types	type	NOUN
iajs-3292	23	10	of	of	ADP
iajs-3292	23	11	polynomials	polynomial	NOUN
iajs-3292	23	12	were	be	AUX
iajs-3292	23	13	used	use	VERB
iajs-3292	23	14	to	to	PART
iajs-3292	23	15	solve	solve	VERB
iajs-3292	23	16	different	different	ADJ
iajs-3292	23	17	types	type	NOUN
iajs-3292	23	18	of	of	ADP
iajs-3292	23	19	problems	problem	NOUN
iajs-3292	23	20	.	.	PUNCT
iajs-3292	24	1	there	there	PRON
iajs-3292	24	2	is	be	VERB
iajs-3292	24	3	an	an	DET
iajs-3292	24	4	application	application	NOUN
iajs-3292	24	5	for	for	ADP
iajs-3292	24	6	third	third	ADJ
iajs-3292	24	7	-	-	PUNCT
iajs-3292	24	8	order	order	NOUN
iajs-3292	24	9	nodes	node	NOUN
iajs-3292	24	10	that	that	PRON
iajs-3292	24	11	occurs	occur	VERB
iajs-3292	24	12	in	in	ADP
iajs-3292	24	13	fluid	fluid	ADJ
iajs-3292	24	14	mechanics	mechanic	NOUN
iajs-3292	24	15	with	with	ADP
iajs-3292	24	16	the	the	DET
iajs-3292	24	17	laminar	laminar	ADJ
iajs-3292	24	18	viscous	viscous	ADJ
iajs-3292	24	19	flow	flow	NOUN
iajs-3292	24	20	and	and	CCONJ
iajs-3292	24	21	the	the	DET
iajs-3292	24	22	various	various	ADJ
iajs-3292	24	23	aspects	aspect	NOUN
iajs-3292	24	24	of	of	ADP
iajs-3292	24	25	the	the	DET
iajs-3292	24	26	hydrodynamic	hydrodynamic	ADJ
iajs-3292	24	27	boundary	boundary	ADJ
iajs-3292	24	28	layer	layer	NOUN
iajs-3292	24	29	problem	problem	NOUN
iajs-3292	24	30	is	be	AUX
iajs-3292	24	31	the	the	DET
iajs-3292	24	32	nonlinear	nonlinear	ADJ
iajs-3292	24	33	blasius	blasius	ADJ
iajs-3292	24	34	equation	equation	NOUN
iajs-3292	25	1	[	[	X
iajs-3292	25	2	21,22	21,22	X
iajs-3292	25	3	]	]	X
iajs-3292	25	4	.	.	PUNCT
iajs-3292	26	1	several	several	ADJ
iajs-3292	26	2	researchers	researcher	NOUN
iajs-3292	26	3	have	have	AUX
iajs-3292	26	4	worked	work	VERB
iajs-3292	26	5	on	on	ADP
iajs-3292	26	6	the	the	DET
iajs-3292	26	7	solution	solution	NOUN
iajs-3292	26	8	of	of	ADP
iajs-3292	26	9	this	this	DET
iajs-3292	26	10	equation	equation	NOUN
iajs-3292	26	11	:	:	PUNCT
iajs-3292	27	1	[	[	X
iajs-3292	27	2	23	23	NUM
iajs-3292	27	3	]	]	PUNCT
iajs-3292	27	4	obtained	obtain	VERB
iajs-3292	27	5	a	a	DET
iajs-3292	27	6	numerical	numerical	ADJ
iajs-3292	27	7	solution	solution	NOUN
iajs-3292	27	8	by	by	ADP
iajs-3292	27	9	the	the	DET
iajs-3292	27	10	runge	runge	NOUN
iajs-3292	27	11	-	-	PUNCT
iajs-3292	27	12	kutta	kutta	NOUN
iajs-3292	27	13	method	method	NOUN
iajs-3292	27	14	.	.	PUNCT
iajs-3292	28	1	[	[	X
iajs-3292	28	2	21	21	NUM
iajs-3292	28	3	]	]	PUNCT
iajs-3292	28	4	solved	solve	VERB
iajs-3292	28	5	the	the	DET
iajs-3292	28	6	blasius	blasius	ADJ
iajs-3292	28	7	equation	equation	NOUN
iajs-3292	28	8	,	,	PUNCT
iajs-3292	28	9	the	the	DET
iajs-3292	28	10	duffing	duffing	NOUN
iajs-3292	28	11	equation	equation	NOUN
iajs-3292	28	12	,	,	PUNCT
iajs-3292	28	13	the	the	DET
iajs-3292	28	14	van	van	PROPN
iajs-3292	28	15	der	der	ADJ
iajs-3292	28	16	pol	pol	NOUN
iajs-3292	28	17	equation	equation	NOUN
iajs-3292	28	18	,	,	PUNCT
iajs-3292	28	19	and	and	CCONJ
iajs-3292	28	20	the	the	DET
iajs-3292	28	21	jerk	jerk	NOUN
iajs-3292	28	22	equation	equation	NOUN
iajs-3292	28	23	using	use	VERB
iajs-3292	28	24	the	the	DET
iajs-3292	28	25	numerical	numerical	ADJ
iajs-3292	28	26	approach	approach	NOUN
iajs-3292	28	27	of	of	ADP
iajs-3292	28	28	the	the	DET
iajs-3292	28	29	inverse	inverse	NOUN
iajs-3292	28	30	laplace	laplace	NOUN
iajs-3292	28	31	transform	transform	NOUN
iajs-3292	28	32	based	base	VERB
iajs-3292	28	33	on	on	ADP
iajs-3292	28	34	the	the	DET
iajs-3292	28	35	brom	brom	NOUN
iajs-3292	28	36	integration	integration	NOUN
iajs-3292	28	37	technique	technique	NOUN
iajs-3292	28	38	.	.	PUNCT
iajs-3292	29	1	also	also	ADV
iajs-3292	29	2	,	,	PUNCT
iajs-3292	29	3	he	he	PRON
iajs-3292	30	1	[	[	X
iajs-3292	30	2	24	24	NUM
iajs-3292	30	3	]	]	PUNCT
iajs-3292	30	4	used	use	VERB
iajs-3292	30	5	the	the	DET
iajs-3292	30	6	variational	variational	ADJ
iajs-3292	30	7	iteration	iteration	NOUN
iajs-3292	30	8	method	method	NOUN
iajs-3292	30	9	to	to	PART
iajs-3292	30	10	obtain	obtain	VERB
iajs-3292	30	11	an	an	DET
iajs-3292	30	12	analytic	analytic	ADJ
iajs-3292	30	13	approximate	approximate	ADJ
iajs-3292	30	14	solution	solution	NOUN
iajs-3292	30	15	for	for	ADP
iajs-3292	30	16	the	the	DET
iajs-3292	30	17	blasius	blasius	ADJ
iajs-3292	30	18	equation	equation	NOUN
iajs-3292	30	19	.	.	PUNCT
iajs-3292	31	1	[	[	X
iajs-3292	31	2	25	25	NUM
iajs-3292	31	3	]	]	PUNCT
iajs-3292	31	4	solved	solve	VERB
iajs-3292	31	5	it	it	PRON
iajs-3292	31	6	using	use	VERB
iajs-3292	31	7	adomian	adomian	NOUN
iajs-3292	31	8	’s	’s	PART
iajs-3292	31	9	decomposition	decomposition	NOUN
iajs-3292	31	10	method	method	NOUN
iajs-3292	31	11	.	.	PUNCT
iajs-3292	32	1	moreover	moreover	ADV
iajs-3292	32	2	,	,	PUNCT
iajs-3292	32	3	[	[	X
iajs-3292	32	4	26	26	NUM
iajs-3292	32	5	]	]	PUNCT
iajs-3292	32	6	studied	study	VERB
iajs-3292	32	7	it	it	PRON
iajs-3292	32	8	with	with	ADP
iajs-3292	32	9	the	the	DET
iajs-3292	32	10	new	new	ADJ
iajs-3292	32	11	homotopy	homotopy	NOUN
iajs-3292	32	12	perturbation	perturbation	NOUN
iajs-3292	32	13	method	method	NOUN
iajs-3292	32	14	.	.	PUNCT
iajs-3292	33	1	the	the	DET
iajs-3292	33	2	aim	aim	NOUN
iajs-3292	33	3	of	of	ADP
iajs-3292	33	4	this	this	DET
iajs-3292	33	5	paper	paper	NOUN
iajs-3292	33	6	is	be	AUX
iajs-3292	33	7	to	to	PART
iajs-3292	33	8	use	use	VERB
iajs-3292	33	9	the	the	DET
iajs-3292	33	10	method	method	NOUN
iajs-3292	33	11	of	of	ADP
iajs-3292	33	12	operational	operational	ADJ
iajs-3292	33	13	matrices	matrix	NOUN
iajs-3292	33	14	based	base	VERB
iajs-3292	33	15	on	on	ADP
iajs-3292	33	16	different	different	ADJ
iajs-3292	33	17	types	type	NOUN
iajs-3292	33	18	of	of	ADP
iajs-3292	33	19	polynomials	polynomial	NOUN
iajs-3292	33	20	such	such	ADJ
iajs-3292	33	21	as	as	ADP
iajs-3292	33	22	bernstein	bernstein	PROPN
iajs-3292	33	23	,	,	PUNCT
iajs-3292	33	24	shifted	shift	VERB
iajs-3292	33	25	legendre	legendre	PROPN
iajs-3292	33	26	and	and	CCONJ
iajs-3292	33	27	bernoulli	bernoulli	NOUN
iajs-3292	33	28	polynomials	polynomial	NOUN
iajs-3292	33	29	will	will	AUX
iajs-3292	33	30	be	be	AUX
iajs-3292	33	31	used	use	VERB
iajs-3292	33	32	to	to	PART
iajs-3292	33	33	solve	solve	VERB
iajs-3292	33	34	the	the	DET
iajs-3292	33	35	nonlinear	nonlinear	ADJ
iajs-3292	33	36	blasius	blasius	ADJ
iajs-3292	33	37	equations	equation	NOUN
iajs-3292	33	38	and	and	CCONJ
iajs-3292	33	39	novel	novel	ADJ
iajs-3292	33	40	approximate	approximate	ADJ
iajs-3292	33	41	solutions	solution	NOUN
iajs-3292	33	42	will	will	AUX
iajs-3292	33	43	be	be	AUX
iajs-3292	33	44	obtained	obtain	VERB
iajs-3292	33	45	.	.	PUNCT
iajs-3292	34	1	the	the	DET
iajs-3292	34	2	structure	structure	NOUN
iajs-3292	34	3	of	of	ADP
iajs-3292	34	4	this	this	DET
iajs-3292	34	5	paper	paper	NOUN
iajs-3292	34	6	is	be	AUX
iajs-3292	34	7	as	as	SCONJ
iajs-3292	34	8	follows	follow	VERB
iajs-3292	34	9	:	:	PUNCT
iajs-3292	34	10	in	in	ADP
iajs-3292	34	11	section	section	NOUN
iajs-3292	34	12	two	two	NUM
iajs-3292	34	13	,	,	PUNCT
iajs-3292	34	14	the	the	DET
iajs-3292	34	15	blasius	blasius	ADJ
iajs-3292	34	16	equation	equation	NOUN
iajs-3292	34	17	is	be	AUX
iajs-3292	34	18	introduced	introduce	VERB
iajs-3292	34	19	.	.	PUNCT
iajs-3292	35	1	section	section	NOUN
iajs-3292	35	2	three	three	NUM
iajs-3292	35	3	gives	give	VERB
iajs-3292	35	4	the	the	DET
iajs-3292	35	5	orthogonal	orthogonal	ADJ
iajs-3292	35	6	polynomials	polynomial	NOUN
iajs-3292	35	7	on	on	ADP
iajs-3292	35	8	which	which	PRON
iajs-3292	35	9	the	the	DET
iajs-3292	35	10	operational	operational	ADJ
iajs-3292	35	11	matrices	matrix	NOUN
iajs-3292	35	12	depend	depend	VERB
iajs-3292	35	13	,	,	PUNCT
iajs-3292	35	14	namely	namely	ADV
iajs-3292	35	15	the	the	DET
iajs-3292	35	16	bernstein	bernstein	PROPN
iajs-3292	35	17	polynomial	polynomial	PROPN
iajs-3292	35	18	,	,	PUNCT
iajs-3292	35	19	the	the	DET
iajs-3292	35	20	shifted	shift	VERB
iajs-3292	35	21	legendre	legendre	PROPN
iajs-3292	35	22	polynomial	polynomial	PROPN
iajs-3292	35	23	,	,	PUNCT
iajs-3292	35	24	and	and	CCONJ
iajs-3292	35	25	the	the	DET
iajs-3292	35	26	bernoulli	bernoulli	NOUN
iajs-3292	35	27	polynomial	polynomial	NOUN
iajs-3292	35	28	.	.	PUNCT
iajs-3292	36	1	in	in	ADP
iajs-3292	36	2	section	section	NOUN
iajs-3292	36	3	four	four	NUM
iajs-3292	36	4	,	,	PUNCT
iajs-3292	36	5	the	the	DET
iajs-3292	36	6	convergence	convergence	NOUN
iajs-3292	36	7	of	of	ADP
iajs-3292	36	8	the	the	DET
iajs-3292	36	9	proposed	propose	VERB
iajs-3292	36	10	methods	method	NOUN
iajs-3292	36	11	is	be	AUX
iajs-3292	36	12	explained	explain	VERB
iajs-3292	36	13	.	.	PUNCT
iajs-3292	37	1	in	in	ADP
iajs-3292	37	2	section	section	NOUN
iajs-3292	37	3	five	five	NUM
iajs-3292	37	4	,	,	PUNCT
iajs-3292	37	5	the	the	DET
iajs-3292	37	6	problem	problem	NOUN
iajs-3292	37	7	will	will	AUX
iajs-3292	37	8	be	be	AUX
iajs-3292	37	9	solved	solve	VERB
iajs-3292	37	10	using	use	VERB
iajs-3292	37	11	the	the	DET
iajs-3292	37	12	proposed	propose	VERB
iajs-3292	37	13	methods	method	NOUN
iajs-3292	37	14	.	.	PUNCT
iajs-3292	38	1	finally	finally	ADV
iajs-3292	38	2	,	,	PUNCT
iajs-3292	38	3	section	section	NOUN
iajs-3292	38	4	six	six	NUM
iajs-3292	38	5	presents	present	VERB
iajs-3292	38	6	the	the	DET
iajs-3292	38	7	conclusions	conclusion	NOUN
iajs-3292	38	8	.	.	PUNCT
iajs-3292	39	1	2	2	X
iajs-3292	39	2	.	.	X
iajs-3292	39	3	the	the	DET
iajs-3292	39	4	blasius	blasius	ADJ
iajs-3292	39	5	equation	equation	NOUN
iajs-3292	39	6	this	this	DET
iajs-3292	39	7	equation	equation	NOUN
iajs-3292	39	8	is	be	AUX
iajs-3292	39	9	important	important	ADJ
iajs-3292	39	10	because	because	SCONJ
iajs-3292	39	11	it	it	PRON
iajs-3292	39	12	appears	appear	VERB
iajs-3292	39	13	in	in	ADP
iajs-3292	39	14	many	many	ADJ
iajs-3292	39	15	hydrodynamic	hydrodynamic	ADJ
iajs-3292	39	16	boundary	boundary	ADJ
iajs-3292	39	17	layer	layer	NOUN
iajs-3292	39	18	problems	problem	NOUN
iajs-3292	39	19	as	as	ADV
iajs-3292	39	20	well	well	ADV
iajs-3292	39	21	as	as	ADP
iajs-3292	39	22	in	in	ADP
iajs-3292	39	23	the	the	DET
iajs-3292	39	24	fluid	fluid	ADJ
iajs-3292	39	25	mechanics	mechanic	NOUN
iajs-3292	39	26	of	of	ADP
iajs-3292	39	27	laminar	laminar	ADJ
iajs-3292	39	28	viscous	viscous	ADJ
iajs-3292	39	29	flows	flow	NOUN
iajs-3292	39	30	and	and	CCONJ
iajs-3292	39	31	its	its	PRON
iajs-3292	39	32	formula	formula	NOUN
iajs-3292	39	33	is	be	AUX
iajs-3292	39	34	given	give	VERB
iajs-3292	39	35	by	by	ADP
iajs-3292	39	36	[	[	PUNCT
iajs-3292	39	37	22	22	NUM
iajs-3292	39	38	]	]	X
iajs-3292	39	39	:	:	PUNCT
iajs-3292	39	40	𝑓′′′(𝑥	𝑓′′′(𝑥	NUM
iajs-3292	39	41	)	)	PUNCT
iajs-3292	40	1	+	+	CCONJ
iajs-3292	40	2	1	1	NUM
iajs-3292	40	3	2	2	NUM
iajs-3292	40	4	𝑓(𝑥)𝑓′′(𝑥	𝑓(𝑥)𝑓′′(𝑥	VERB
iajs-3292	40	5	)	)	PUNCT
iajs-3292	40	6	=	=	SYM
iajs-3292	40	7	0	0	NUM
iajs-3292	40	8	,	,	PUNCT
iajs-3292	40	9	(	(	PUNCT
iajs-3292	40	10	1	1	X
iajs-3292	40	11	)	)	PUNCT
iajs-3292	40	12	with	with	ADP
iajs-3292	40	13	boundary	boundary	ADJ
iajs-3292	40	14	conditions	condition	NOUN
iajs-3292	40	15	:	:	PUNCT
iajs-3292	40	16	𝑓(0	𝑓(0	NOUN
iajs-3292	40	17	)	)	PUNCT
iajs-3292	40	18	=	=	PUNCT
iajs-3292	40	19	𝑓′(0	𝑓′(0	ADJ
iajs-3292	40	20	)	)	PUNCT
iajs-3292	40	21	=	=	SYM
iajs-3292	40	22	0	0	NUM
iajs-3292	40	23	,	,	PUNCT
iajs-3292	40	24	𝑓′(∞	𝑓′(∞	ADJ
iajs-3292	40	25	)	)	PUNCT
iajs-3292	40	26	=	=	SYM
iajs-3292	41	1	1	1	X
iajs-3292	41	2	.	.	PUNCT
iajs-3292	41	3	(	(	PUNCT
iajs-3292	41	4	2	2	X
iajs-3292	41	5	)	)	PUNCT
iajs-3292	41	6	to	to	PART
iajs-3292	41	7	solve	solve	VERB
iajs-3292	41	8	this	this	DET
iajs-3292	41	9	equation	equation	NOUN
iajs-3292	41	10	,	,	PUNCT
iajs-3292	41	11	the	the	DET
iajs-3292	41	12	boundary	boundary	ADJ
iajs-3292	41	13	conditions	condition	NOUN
iajs-3292	41	14	were	be	AUX
iajs-3292	41	15	converted	convert	VERB
iajs-3292	41	16	to	to	ADP
iajs-3292	41	17	initial	initial	ADJ
iajs-3292	41	18	conditions	condition	NOUN
iajs-3292	41	19	by	by	ADP
iajs-3292	41	20	computing	compute	VERB
iajs-3292	41	21	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	41	22	)	)	PUNCT
iajs-3292	41	23	instead	instead	ADV
iajs-3292	41	24	of	of	ADP
iajs-3292	41	25	𝑓′(∞	𝑓′(∞	ADV
iajs-3292	41	26	)	)	PUNCT
iajs-3292	41	27	,	,	PUNCT
iajs-3292	41	28	as	as	SCONJ
iajs-3292	41	29	liao	liao	PROPN
iajs-3292	41	30	[	[	X
iajs-3292	41	31	27	27	NUM
iajs-3292	41	32	]	]	X
iajs-3292	41	33	did	do	VERB
iajs-3292	41	34	and	and	CCONJ
iajs-3292	41	35	found	find	VERB
iajs-3292	41	36	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	41	37	)	)	PUNCT
iajs-3292	42	1	=	=	SYM
iajs-3292	42	2	0.3320573	0.3320573	NUM
iajs-3292	42	3	,	,	PUNCT
iajs-3292	42	4	followed	follow	VERB
iajs-3292	42	5	by	by	ADP
iajs-3292	42	6	khataybeh	khataybeh	PROPN
iajs-3292	42	7	et	et	PROPN
iajs-3292	42	8	al	al	PROPN
iajs-3292	42	9	.	.	PUNCT
iajs-3292	43	1	[	[	X
iajs-3292	43	2	5	5	NUM
iajs-3292	43	3	]	]	PUNCT
iajs-3292	43	4	used	use	VERB
iajs-3292	43	5	the	the	DET
iajs-3292	43	6	value	value	NOUN
iajs-3292	43	7	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	43	8	)	)	PUNCT
iajs-3292	43	9	=	=	SYM
iajs-3292	44	1	1	1	X
iajs-3292	44	2	.	.	X
iajs-3292	45	1	in	in	ADP
iajs-3292	45	2	general	general	ADJ
iajs-3292	45	3	,	,	PUNCT
iajs-3292	45	4	the	the	DET
iajs-3292	45	5	blasius	blasius	ADJ
iajs-3292	45	6	equation	equation	NOUN
iajs-3292	45	7	represents	represent	VERB
iajs-3292	45	8	a	a	DET
iajs-3292	45	9	model	model	NOUN
iajs-3292	45	10	of	of	ADP
iajs-3292	45	11	the	the	DET
iajs-3292	45	12	attitude	attitude	NOUN
iajs-3292	45	13	of	of	ADP
iajs-3292	45	14	a	a	DET
iajs-3292	45	15	two	two	NUM
iajs-3292	45	16	-	-	PUNCT
iajs-3292	45	17	dimensional	dimensional	ADJ
iajs-3292	45	18	stable	stable	ADJ
iajs-3292	45	19	laminar	laminar	ADJ
iajs-3292	45	20	viscous	viscous	ADJ
iajs-3292	45	21	flow	flow	NOUN
iajs-3292	45	22	on	on	ADP
iajs-3292	45	23	a	a	DET
iajs-3292	45	24	semi	semi	ADJ
iajs-3292	45	25	-	-	ADJ
iajs-3292	45	26	infinite	infinite	ADJ
iajs-3292	45	27	flat	flat	ADJ
iajs-3292	45	28	plate	plate	NOUN
iajs-3292	45	29	in	in	ADP
iajs-3292	45	30	which	which	PRON
iajs-3292	45	31	the	the	DET
iajs-3292	45	32	flowing	flow	VERB
iajs-3292	45	33	fluid	fluid	NOUN
iajs-3292	45	34	is	be	AUX
iajs-3292	45	35	incompressible	incompressible	ADJ
iajs-3292	45	36	,	,	PUNCT
iajs-3292	45	37	but	but	CCONJ
iajs-3292	45	38	the	the	DET
iajs-3292	45	39	boundary	boundary	ADJ
iajs-3292	45	40	layer	layer	NOUN
iajs-3292	45	41	assumption	assumption	NOUN
iajs-3292	45	42	must	must	AUX
iajs-3292	45	43	be	be	AUX
iajs-3292	45	44	governed	govern	VERB
iajs-3292	45	45	by	by	ADP
iajs-3292	45	46	the	the	DET
iajs-3292	45	47	continuity	continuity	NOUN
iajs-3292	45	48	and	and	CCONJ
iajs-3292	45	49	navier	navier	NOUN
iajs-3292	45	50	-	-	PUNCT
iajs-3292	45	51	stokes	stoke	NOUN
iajs-3292	45	52	equations	equation	NOUN
iajs-3292	45	53	of	of	ADP
iajs-3292	45	54	motion	motion	NOUN
iajs-3292	45	55	,	,	PUNCT
iajs-3292	45	56	but	but	CCONJ
iajs-3292	45	57	it	it	PRON
iajs-3292	45	58	should	should	AUX
iajs-3292	45	59	be	be	AUX
iajs-3292	45	60	noted	note	VERB
iajs-3292	45	61	that	that	SCONJ
iajs-3292	45	62	the	the	DET
iajs-3292	45	63	fluid	fluid	ADJ
iajs-3292	45	64	flow	flow	NOUN
iajs-3292	45	65	velocity	velocity	NOUN
iajs-3292	45	66	decreases	decrease	VERB
iajs-3292	45	67	sharply	sharply	ADV
iajs-3292	45	68	from	from	ADP
iajs-3292	45	69	𝑈	𝑈	PROPN
iajs-3292	45	70	to	to	ADP
iajs-3292	45	71	0	0	NUM
iajs-3292	45	72	at	at	ADP
iajs-3292	45	73	𝑦	𝑦	NOUN
iajs-3292	45	74	=	=	SYM
iajs-3292	45	75	0	0	PUNCT
iajs-3292	45	76	as	as	ADP
iajs-3292	45	77	𝑥	𝑥	PRON
iajs-3292	45	78	changes	change	NOUN
iajs-3292	45	79	from	from	ADP
iajs-3292	45	80	−0	−0	NOUN
iajs-3292	45	81	to	to	ADP
iajs-3292	45	82	+	+	NOUN
iajs-3292	45	83	0	0	X
iajs-3292	45	84	.	.	NUM
iajs-3292	46	1	ihjpas	ihjpas	PROPN
iajs-3292	46	2	.	.	PUNCT
iajs-3292	47	1	37	37	NUM
iajs-3292	47	2	(	(	PUNCT
iajs-3292	47	3	1	1	NUM
iajs-3292	47	4	)	)	PUNCT
iajs-3292	47	5	2024	2024	NUM
iajs-3292	47	6	360	360	NUM
iajs-3292	47	7	3	3	NUM
iajs-3292	47	8	.	.	PUNCT
iajs-3292	48	1	the	the	DET
iajs-3292	48	2	operational	operational	ADJ
iajs-3292	48	3	matrices	matrix	NOUN
iajs-3292	48	4	of	of	ADP
iajs-3292	48	5	the	the	DET
iajs-3292	48	6	orthogonal	orthogonal	ADJ
iajs-3292	48	7	polynomials	polynomial	NOUN
iajs-3292	48	8	orthogonal	orthogonal	ADJ
iajs-3292	48	9	polynomials	polynomial	NOUN
iajs-3292	48	10	play	play	VERB
iajs-3292	48	11	an	an	DET
iajs-3292	48	12	important	important	ADJ
iajs-3292	48	13	role	role	NOUN
iajs-3292	48	14	in	in	ADP
iajs-3292	48	15	pure	pure	ADJ
iajs-3292	48	16	and	and	CCONJ
iajs-3292	48	17	applied	applied	ADJ
iajs-3292	48	18	mathematics	mathematic	NOUN
iajs-3292	48	19	as	as	ADV
iajs-3292	48	20	well	well	ADV
iajs-3292	48	21	as	as	ADP
iajs-3292	48	22	in	in	ADP
iajs-3292	48	23	numerical	numerical	ADJ
iajs-3292	48	24	computation	computation	NOUN
iajs-3292	48	25	[	[	X
iajs-3292	48	26	28	28	NUM
iajs-3292	48	27	]	]	PUNCT
iajs-3292	48	28	.	.	PUNCT
iajs-3292	49	1	three	three	NUM
iajs-3292	49	2	types	type	NOUN
iajs-3292	49	3	of	of	ADP
iajs-3292	49	4	these	these	DET
iajs-3292	49	5	polynomials	polynomial	NOUN
iajs-3292	49	6	will	will	AUX
iajs-3292	49	7	be	be	AUX
iajs-3292	49	8	used	use	VERB
iajs-3292	49	9	:	:	PUNCT
iajs-3292	49	10	bernstein	bernstein	PROPN
iajs-3292	49	11	,	,	PUNCT
iajs-3292	49	12	shifted	shift	VERB
iajs-3292	49	13	legendre	legendre	PROPN
iajs-3292	49	14	,	,	PUNCT
iajs-3292	49	15	and	and	CCONJ
iajs-3292	49	16	bernoulli	bernoulli	PROPN
iajs-3292	49	17	to	to	PART
iajs-3292	49	18	solve	solve	VERB
iajs-3292	49	19	the	the	DET
iajs-3292	49	20	blasius	blasius	ADJ
iajs-3292	49	21	equation	equation	NOUN
iajs-3292	49	22	.	.	PUNCT
iajs-3292	50	1	3.1	3.1	NUM
iajs-3292	50	2	the	the	DET
iajs-3292	50	3	bernstein	bernstein	PROPN
iajs-3292	50	4	polynomials	polynomial	VERB
iajs-3292	50	5	the	the	DET
iajs-3292	50	6	bernstein	bernstein	PROPN
iajs-3292	50	7	polynomials	polynomial	NOUN
iajs-3292	50	8	of	of	ADP
iajs-3292	50	9	𝑛𝑡ℎ	𝑛𝑡ℎ	PRON
iajs-3292	50	10	degree	degree	VERB
iajs-3292	50	11	in	in	ADP
iajs-3292	50	12	[	[	X
iajs-3292	50	13	0,1	0,1	NUM
iajs-3292	50	14	]	]	PUNCT
iajs-3292	50	15	are	be	AUX
iajs-3292	50	16	defined	define	VERB
iajs-3292	50	17	by	by	ADP
iajs-3292	50	18	[	[	X
iajs-3292	50	19	4,10,29	4,10,29	NUM
iajs-3292	50	20	]	]	SYM
iajs-3292	50	21	:	:	PUNCT
iajs-3292	50	22	𝐵𝑖,𝑛(𝑥	𝐵𝑖,𝑛(𝑥	NOUN
iajs-3292	50	23	)	)	PUNCT
iajs-3292	51	1	=	=	PRON
iajs-3292	51	2	(	(	PUNCT
iajs-3292	51	3	𝑛	𝑛	PROPN
iajs-3292	51	4	𝑖	𝑖	SYM
iajs-3292	51	5	)	)	PUNCT
iajs-3292	51	6	𝑥𝑖	𝑥𝑖	PROPN
iajs-3292	51	7	(	(	PUNCT
iajs-3292	51	8	1	1	NUM
iajs-3292	51	9	−	−	NOUN
iajs-3292	51	10	𝑥)𝑛−𝑖	𝑥)𝑛−𝑖	ADP
iajs-3292	51	11	,	,	PUNCT
iajs-3292	51	12	𝑖	𝑖	NOUN
iajs-3292	51	13	=	=	NOUN
iajs-3292	51	14	0,1,2	0,1,2	NUM
iajs-3292	51	15	,	,	PUNCT
iajs-3292	51	16	…	…	PUNCT
iajs-3292	51	17	,	,	PUNCT
iajs-3292	51	18	𝑛	𝑛	PROPN
iajs-3292	51	19	,	,	PUNCT
iajs-3292	51	20	(	(	PUNCT
iajs-3292	51	21	3	3	X
iajs-3292	51	22	)	)	PUNCT
iajs-3292	51	23	where	where	SCONJ
iajs-3292	51	24	(	(	PUNCT
iajs-3292	51	25	𝑛	𝑛	NOUN
iajs-3292	51	26	𝑖	𝑖	PROPN
iajs-3292	51	27	)	)	PUNCT
iajs-3292	52	1	=	=	SYM
iajs-3292	52	2	𝑛	𝑛	PROPN
iajs-3292	52	3	!	!	PUNCT
iajs-3292	52	4	𝑖	𝑖	X
iajs-3292	52	5	!	!	PUNCT
iajs-3292	52	6	(	(	PUNCT
iajs-3292	52	7	𝑛−𝑖	𝑛−𝑖	PROPN
iajs-3292	52	8	)	)	PUNCT
iajs-3292	52	9	!	!	PUNCT
iajs-3292	52	10	.	.	PUNCT
iajs-3292	53	1	or	or	CCONJ
iajs-3292	53	2	the	the	DET
iajs-3292	53	3	recursive	recursive	ADJ
iajs-3292	53	4	definition	definition	NOUN
iajs-3292	53	5	over	over	ADP
iajs-3292	53	6	[	[	X
iajs-3292	53	7	0,1	0,1	NUM
iajs-3292	53	8	]	]	PUNCT
iajs-3292	53	9	is	be	AUX
iajs-3292	53	10	used	use	VERB
iajs-3292	53	11	to	to	PART
iajs-3292	53	12	generate	generate	VERB
iajs-3292	53	13	these	these	DET
iajs-3292	53	14	polynomials	polynomial	NOUN
iajs-3292	53	15	,	,	PUNCT
iajs-3292	53	16	resulting	result	VERB
iajs-3292	53	17	in	in	ADP
iajs-3292	53	18	bernstein	bernstein	PROPN
iajs-3292	53	19	polynomial	polynomial	PROPN
iajs-3292	53	20	being	be	AUX
iajs-3292	53	21	represented	represent	VERB
iajs-3292	53	22	as	as	SCONJ
iajs-3292	53	23	follows	follow	VERB
iajs-3292	53	24	:	:	PUNCT
iajs-3292	53	25	𝐵𝑖,𝑛(𝑥	𝐵𝑖,𝑛(𝑥	NOUN
iajs-3292	53	26	)	)	PUNCT
iajs-3292	54	1	=	=	PUNCT
iajs-3292	54	2	(	(	PUNCT
iajs-3292	54	3	1	1	NUM
iajs-3292	54	4	−	−	DET
iajs-3292	54	5	𝑥	𝑥	NOUN
iajs-3292	54	6	)	)	PUNCT
iajs-3292	54	7	𝐵𝑖,𝑛−1(𝑥	𝐵𝑖,𝑛−1(𝑥	NOUN
iajs-3292	54	8	)	)	PUNCT
iajs-3292	55	1	+	+	CCONJ
iajs-3292	55	2	𝑥	𝑥	X
iajs-3292	55	3	𝐵𝑖−1,𝑛−1(𝑥	𝐵𝑖−1,𝑛−1(𝑥	NOUN
iajs-3292	55	4	)	)	PUNCT
iajs-3292	55	5	.	.	PUNCT
iajs-3292	56	1	(	(	PUNCT
iajs-3292	56	2	4	4	X
iajs-3292	56	3	)	)	PUNCT
iajs-3292	56	4	practically	practically	ADV
iajs-3292	56	5	only	only	ADV
iajs-3292	56	6	the	the	DET
iajs-3292	56	7	first	first	ADJ
iajs-3292	56	8	(	(	PUNCT
iajs-3292	56	9	𝑛	𝑛	PROPN
iajs-3292	56	10	+	+	NOUN
iajs-3292	56	11	1	1	NUM
iajs-3292	56	12	)	)	PUNCT
iajs-3292	56	13	terms	term	NOUN
iajs-3292	56	14	of	of	ADP
iajs-3292	56	15	the	the	DET
iajs-3292	56	16	bernstein	bernstein	PROPN
iajs-3292	56	17	polynomials	polynomial	NOUN
iajs-3292	56	18	of	of	ADP
iajs-3292	56	19	degree	degree	NOUN
iajs-3292	56	20	𝑛	𝑛	PROPN
iajs-3292	56	21	are	be	AUX
iajs-3292	56	22	satisfied	satisfied	ADJ
iajs-3292	56	23	,	,	PUNCT
iajs-3292	56	24	because	because	SCONJ
iajs-3292	56	25	𝐵𝑖,𝑛(𝑥	𝐵𝑖,𝑛(𝑥	NOUN
iajs-3292	56	26	)	)	PUNCT
iajs-3292	57	1	=	=	SYM
iajs-3292	57	2	0	0	PUNCT
iajs-3292	58	1	if	if	SCONJ
iajs-3292	58	2	𝑖	𝑖	X
iajs-3292	58	3	<	<	X
iajs-3292	58	4	0	0	NUM
iajs-3292	58	5	or	or	CCONJ
iajs-3292	58	6	𝑛	𝑛	ADJ
iajs-3292	58	7	<	<	X
iajs-3292	58	8	𝑖.	𝑖.	ADV
iajs-3292	58	9	there	there	PRON
iajs-3292	58	10	are	be	VERB
iajs-3292	58	11	many	many	ADJ
iajs-3292	58	12	properties	property	NOUN
iajs-3292	58	13	make	make	VERB
iajs-3292	58	14	bernstein	bernstein	PROPN
iajs-3292	58	15	polynomial	polynomial	PROPN
iajs-3292	58	16	important	important	ADJ
iajs-3292	58	17	,	,	PUNCT
iajs-3292	58	18	some	some	PRON
iajs-3292	58	19	of	of	ADP
iajs-3292	58	20	them	they	PRON
iajs-3292	58	21	are	be	AUX
iajs-3292	58	22	:	:	PUNCT
iajs-3292	58	23	i.	i.	NOUN
iajs-3292	58	24	property	property	NOUN
iajs-3292	58	25	of	of	ADP
iajs-3292	58	26	positivity	positivity	NOUN
iajs-3292	58	27	:	:	PUNCT
iajs-3292	58	28	𝐵𝑖,𝑛(𝑥	𝐵𝑖,𝑛(𝑥	NOUN
iajs-3292	58	29	)	)	PUNCT
iajs-3292	58	30	>	>	X
iajs-3292	58	31	0	0	PUNCT
iajs-3292	59	1	for	for	ADP
iajs-3292	59	2	all	all	PRON
iajs-3292	59	3	0	0	NUM
iajs-3292	59	4	<	<	X
iajs-3292	59	5	𝑖	𝑖	X
iajs-3292	59	6	<	<	X
iajs-3292	59	7	𝑛	𝑛	NOUN
iajs-3292	59	8	and	and	CCONJ
iajs-3292	59	9	all	all	PRON
iajs-3292	59	10	𝑥𝜖[0,1	𝑥𝜖[0,1	NOUN
iajs-3292	59	11	]	]	PUNCT
iajs-3292	59	12	.	.	PUNCT
iajs-3292	59	13	ii	ii	PROPN
iajs-3292	59	14	.	.	PUNCT
iajs-3292	59	15	unity	unity	NOUN
iajs-3292	59	16	partition	partition	NOUN
iajs-3292	59	17	property	property	NOUN
iajs-3292	59	18	:	:	PUNCT
iajs-3292	59	19	∑	∑	PUNCT
iajs-3292	59	20	𝐵𝑖,𝑛(𝑥	𝐵𝑖,𝑛(𝑥	NOUN
iajs-3292	59	21	)	)	PUNCT
iajs-3292	59	22	=	=	SYM
iajs-3292	59	23	∑	∑	NOUN
iajs-3292	59	24	𝐵𝑖,𝑛−1(𝑥	𝐵𝑖,𝑛−1(𝑥	NOUN
iajs-3292	59	25	)	)	PUNCT
iajs-3292	59	26	=	=	NOUN
iajs-3292	59	27	.	.	PUNCT
iajs-3292	59	28	.	.	PUNCT
iajs-3292	59	29	.	.	PUNCT
iajs-3292	60	1	=	=	PUNCT
iajs-3292	60	2	∑	∑	PUNCT
iajs-3292	60	3	𝐵𝑖,1(𝑥	𝐵𝑖,1(𝑥	NOUN
iajs-3292	60	4	)	)	PUNCT
iajs-3292	60	5	=	=	PUNCT
iajs-3292	61	1	1	1	NUM
iajs-3292	61	2	.	.	NOUN
iajs-3292	61	3	1	1	NUM
iajs-3292	61	4	𝑖=0	𝑖=0	SYM
iajs-3292	61	5	𝑛−1	𝑛−1	NUM
iajs-3292	61	6	𝑖=0	𝑖=0	PROPN
iajs-3292	61	7	𝑛	𝑛	DET
iajs-3292	61	8	𝑖=0	𝑖=0	PROPN
iajs-3292	61	9	moreover	moreover	ADV
iajs-3292	61	10	,	,	PUNCT
iajs-3292	61	11	the	the	DET
iajs-3292	61	12	type	type	NOUN
iajs-3292	61	13	of	of	ADP
iajs-3292	61	14	linear	linear	ADJ
iajs-3292	61	15	combination	combination	NOUN
iajs-3292	61	16	shown	show	VERB
iajs-3292	61	17	below	below	ADV
iajs-3292	61	18	can	can	AUX
iajs-3292	61	19	be	be	AUX
iajs-3292	61	20	used	use	VERB
iajs-3292	61	21	to	to	PART
iajs-3292	61	22	approximate	approximate	VERB
iajs-3292	61	23	any	any	DET
iajs-3292	61	24	polynomial	polynomial	NOUN
iajs-3292	61	25	of	of	ADP
iajs-3292	61	26	𝑛𝑡ℎdegree	𝑛𝑡ℎdegree	NOUN
iajs-3292	61	27	in	in	ADP
iajs-3292	61	28	𝐿2[0,1	𝐿2[0,1	NOUN
iajs-3292	61	29	]	]	PUNCT
iajs-3292	61	30	:	:	PUNCT
iajs-3292	61	31	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	61	32	)	)	PUNCT
iajs-3292	62	1	=	=	SYM
iajs-3292	62	2	∑	∑	PUNCT
iajs-3292	62	3	𝑐𝑖	𝑐𝑖	NOUN
iajs-3292	62	4	𝐵𝑖,𝑛(𝑥	𝐵𝑖,𝑛(𝑥	PROPN
iajs-3292	62	5	)	)	PUNCT
iajs-3292	62	6	𝑛	𝑛	DET
iajs-3292	62	7	𝑖=0	𝑖=0	PROPN
iajs-3292	62	8	=	=	PUNCT
iajs-3292	62	9	𝐶𝑇𝜙(𝑥	𝐶𝑇𝜙(𝑥	PROPN
iajs-3292	62	10	)	)	PUNCT
iajs-3292	62	11	,	,	PUNCT
iajs-3292	62	12	(	(	PUNCT
iajs-3292	62	13	5	5	X
iajs-3292	62	14	)	)	PUNCT
iajs-3292	62	15	where	where	SCONJ
iajs-3292	62	16	𝐶𝑇	𝐶𝑇	PROPN
iajs-3292	63	1	=	=	PUNCT
iajs-3292	63	2	[	[	X
iajs-3292	63	3	𝑐0	𝑐0	NOUN
iajs-3292	63	4	,	,	PUNCT
iajs-3292	63	5	𝑐1	𝑐1	NOUN
iajs-3292	63	6	,	,	PUNCT
iajs-3292	63	7	𝑐2	𝑐2	NOUN
iajs-3292	63	8	,	,	PUNCT
iajs-3292	63	9	…	…	PUNCT
iajs-3292	63	10	,	,	PUNCT
iajs-3292	63	11	𝑐𝑛	𝑐𝑛	ADP
iajs-3292	63	12	]	]	PUNCT
iajs-3292	63	13	,	,	PUNCT
iajs-3292	63	14	and	and	CCONJ
iajs-3292	63	15	𝜙(𝑥	𝜙(𝑥	NUM
iajs-3292	63	16	)	)	PUNCT
iajs-3292	63	17	=	=	PUNCT
iajs-3292	64	1	[	[	X
iajs-3292	64	2	𝐵0,𝑛	𝐵0,𝑛	PROPN
iajs-3292	64	3	,	,	PUNCT
iajs-3292	64	4	𝐵1,𝑛	𝐵1,𝑛	PROPN
iajs-3292	64	5	,	,	PUNCT
iajs-3292	64	6	𝐵2,𝑛	𝐵2,𝑛	NUM
iajs-3292	64	7	,	,	PUNCT
iajs-3292	64	8	…	…	PUNCT
iajs-3292	64	9	,	,	PUNCT
iajs-3292	64	10	,	,	PUNCT
iajs-3292	64	11	𝐵𝑛,𝑛	𝐵𝑛,𝑛	PROPN
iajs-3292	64	12	]	]	X
iajs-3292	64	13	𝑇	𝑇	PROPN
iajs-3292	64	14	.	.	PUNCT
iajs-3292	65	1	in	in	ADP
iajs-3292	65	2	addition	addition	NOUN
iajs-3292	65	3	,	,	PUNCT
iajs-3292	65	4	𝜙(𝑥	𝜙(𝑥	PROPN
iajs-3292	65	5	)	)	PUNCT
iajs-3292	65	6	can	can	AUX
iajs-3292	65	7	be	be	AUX
iajs-3292	65	8	decomposed	decompose	VERB
iajs-3292	65	9	as	as	ADP
iajs-3292	65	10	the	the	DET
iajs-3292	65	11	product	product	NOUN
iajs-3292	65	12	of	of	ADP
iajs-3292	65	13	a	a	PRON
iajs-3292	65	14	(	(	PUNCT
iajs-3292	65	15	𝑛	𝑛	PROPN
iajs-3292	65	16	+	+	NOUN
iajs-3292	65	17	1	1	NUM
iajs-3292	65	18	)	)	PUNCT
iajs-3292	65	19	×	×	NOUN
iajs-3292	65	20	(	(	PUNCT
iajs-3292	65	21	𝑛	𝑛	PROPN
iajs-3292	65	22	+	+	ADJ
iajs-3292	65	23	1	1	NUM
iajs-3292	65	24	)	)	PUNCT
iajs-3292	65	25	matrix	matrix	NOUN
iajs-3292	65	26	𝐴	𝐴	PROPN
iajs-3292	65	27	and	and	CCONJ
iajs-3292	65	28	a	a	DET
iajs-3292	65	29	(	(	PUNCT
iajs-3292	65	30	𝑛	𝑛	PROPN
iajs-3292	65	31	+	+	NOUN
iajs-3292	65	32	1	1	X
iajs-3292	65	33	)	)	PUNCT
iajs-3292	65	34	×	×	NOUN
iajs-3292	65	35	1	1	NUM
iajs-3292	65	36	vector	vector	NOUN
iajs-3292	65	37	𝑋	𝑋	PROPN
iajs-3292	65	38	,	,	PUNCT
iajs-3292	65	39	i.e.	i.e.	X
iajs-3292	65	40	:	:	PUNCT
iajs-3292	65	41	𝜙(𝑥	𝜙(𝑥	NUM
iajs-3292	65	42	)	)	PUNCT
iajs-3292	66	1	=	=	SYM
iajs-3292	66	2	𝐴	𝐴	PROPN
iajs-3292	66	3	𝑋	𝑋	PROPN
iajs-3292	66	4	,	,	PUNCT
iajs-3292	66	5	(	(	PUNCT
iajs-3292	66	6	6	6	NUM
iajs-3292	66	7	)	)	PUNCT
iajs-3292	66	8	where	where	SCONJ
iajs-3292	66	9	:	:	PUNCT
iajs-3292	66	10	𝐴	𝐴	PROPN
iajs-3292	66	11	=	=	PUNCT
iajs-3292	66	12	[	[	PUNCT
iajs-3292	66	13	(	(	PUNCT
iajs-3292	66	14	−1)0	−1)0	NOUN
iajs-3292	66	15	(	(	PUNCT
iajs-3292	66	16	𝑛	𝑛	PROPN
iajs-3292	66	17	0	0	NUM
iajs-3292	66	18	)	)	PUNCT
iajs-3292	66	19	(	(	PUNCT
iajs-3292	66	20	−1)1	−1)1	X
iajs-3292	66	21	(	(	PUNCT
iajs-3292	66	22	𝑛	𝑛	PROPN
iajs-3292	66	23	0	0	NUM
iajs-3292	66	24	)	)	PUNCT
iajs-3292	66	25	(	(	PUNCT
iajs-3292	66	26	𝑛−0	𝑛−0	PROPN
iajs-3292	66	27	1	1	NUM
iajs-3292	66	28	)	)	PUNCT
iajs-3292	66	29	.	.	PUNCT
iajs-3292	66	30	.	.	PUNCT
iajs-3292	66	31	.	.	PUNCT
iajs-3292	67	1	(	(	PUNCT
iajs-3292	67	2	−1)𝑛−0	−1)𝑛−0	INTJ
iajs-3292	67	3	(	(	PUNCT
iajs-3292	67	4	𝑛	𝑛	PROPN
iajs-3292	67	5	0	0	NUM
iajs-3292	67	6	)	)	PUNCT
iajs-3292	67	7	(	(	PUNCT
iajs-3292	67	8	𝑛−0	𝑛−0	PROPN
iajs-3292	67	9	𝑛−0	𝑛−0	PROPN
iajs-3292	67	10	)	)	PUNCT
iajs-3292	67	11	0	0	PUNCT
iajs-3292	68	1	(	(	PUNCT
iajs-3292	68	2	−1)0	−1)0	X
iajs-3292	68	3	(	(	PUNCT
iajs-3292	68	4	𝑛	𝑛	PROPN
iajs-3292	68	5	𝑖	𝑖	NUM
iajs-3292	68	6	)	)	PUNCT
iajs-3292	68	7	.	.	PUNCT
iajs-3292	68	8	.	.	PUNCT
iajs-3292	68	9	.	.	PUNCT
iajs-3292	69	1	(	(	PUNCT
iajs-3292	69	2	−1)𝑛−𝑖	−1)𝑛−𝑖	X
iajs-3292	69	3	(	(	PUNCT
iajs-3292	69	4	𝑛	𝑛	PROPN
iajs-3292	69	5	𝑖	𝑖	PROPN
iajs-3292	69	6	)	)	PUNCT
iajs-3292	69	7	(	(	PUNCT
iajs-3292	69	8	𝑛−𝑖	𝑛−𝑖	ADP
iajs-3292	69	9	𝑛−𝑖	𝑛−𝑖	NUM
iajs-3292	69	10	)	)	PUNCT
iajs-3292	69	11	⋮	⋮	NOUN
iajs-3292	69	12	0	0	PUNCT
iajs-3292	69	13	⋮	⋮	NOUN
iajs-3292	69	14	0	0	NUM
iajs-3292	69	15	⋱	⋱	PUNCT
iajs-3292	69	16	.	.	PUNCT
iajs-3292	69	17	.	.	PUNCT
iajs-3292	70	1	.	.	PUNCT
iajs-3292	71	1	⋮	⋮	NOUN
iajs-3292	71	2	(	(	PUNCT
iajs-3292	71	3	−1)0	−1)0	NOUN
iajs-3292	71	4	(	(	PUNCT
iajs-3292	71	5	𝑛	𝑛	PROPN
iajs-3292	71	6	𝑛	𝑛	PROPN
iajs-3292	71	7	)	)	PUNCT
iajs-3292	71	8	]	]	PUNCT
iajs-3292	71	9	,	,	PUNCT
iajs-3292	71	10	x=	x=	X
iajs-3292	72	1	[	[	PUNCT
iajs-3292	72	2	1	1	NUM
iajs-3292	72	3	𝑥	𝑥	PRON
iajs-3292	72	4	𝑥2	𝑥2	NOUN
iajs-3292	72	5	⋮	⋮	NOUN
iajs-3292	72	6	𝑥𝑛	𝑥𝑛	PROPN
iajs-3292	72	7	]	]	PUNCT
iajs-3292	72	8	.	.	PUNCT
iajs-3292	73	1	(	(	PUNCT
iajs-3292	73	2	7	7	X
iajs-3292	73	3	)	)	PUNCT
iajs-3292	73	4	the	the	DET
iajs-3292	73	5	determinant	determinant	NOUN
iajs-3292	73	6	of	of	ADP
iajs-3292	73	7	the	the	DET
iajs-3292	73	8	matrix	matrix	NOUN
iajs-3292	73	9	𝐴	𝐴	PROPN
iajs-3292	73	10	is	be	AUX
iajs-3292	73	11	|𝐴|	|𝐴|	NOUN
iajs-3292	73	12	=	=	SYM
iajs-3292	73	13	∏	∏	PROPN
iajs-3292	73	14	(	(	PUNCT
iajs-3292	73	15	𝑛	𝑛	NOUN
iajs-3292	73	16	𝑖	𝑖	NOUN
iajs-3292	73	17	)	)	PUNCT
iajs-3292	73	18	𝑛	𝑛	DET
iajs-3292	73	19	𝑖=0	𝑖=0	PROPN
iajs-3292	73	20	.	.	PUNCT
iajs-3292	74	1	as	as	ADP
iajs-3292	74	2	a	a	DET
iajs-3292	74	3	result	result	NOUN
iajs-3292	74	4	,	,	PUNCT
iajs-3292	74	5	𝐴	𝐴	PROPN
iajs-3292	74	6	is	be	AUX
iajs-3292	74	7	an	an	DET
iajs-3292	74	8	invertible	invertible	ADJ
iajs-3292	74	9	matrix	matrix	NOUN
iajs-3292	74	10	.	.	PUNCT
iajs-3292	75	1	let	let	VERB
iajs-3292	75	2	us	we	PRON
iajs-3292	75	3	introduce	introduce	VERB
iajs-3292	75	4	the	the	DET
iajs-3292	75	5	bom	bom	NOUN
iajs-3292	75	6	.	.	PUNCT
iajs-3292	76	1	if	if	SCONJ
iajs-3292	76	2	𝐷𝐵	𝐷𝐵	PROPN
iajs-3292	76	3	is	be	AUX
iajs-3292	76	4	the	the	DET
iajs-3292	76	5	om	om	NOUN
iajs-3292	76	6	of	of	ADP
iajs-3292	76	7	derivative	derivative	NOUN
iajs-3292	76	8	of	of	ADP
iajs-3292	76	9	size	size	NOUN
iajs-3292	76	10	(	(	PUNCT
iajs-3292	76	11	𝑛	𝑛	PROPN
iajs-3292	76	12	+	+	NOUN
iajs-3292	76	13	1	1	NUM
iajs-3292	76	14	)	)	PUNCT
iajs-3292	76	15	×	×	NOUN
iajs-3292	76	16	(	(	PUNCT
iajs-3292	76	17	𝑛	𝑛	PROPN
iajs-3292	76	18	+	+	NOUN
iajs-3292	76	19	1	1	NUM
iajs-3292	76	20	)	)	PUNCT
iajs-3292	76	21	,	,	PUNCT
iajs-3292	76	22	then	then	ADV
iajs-3292	76	23	the	the	DET
iajs-3292	76	24	derivative	derivative	NOUN
iajs-3292	76	25	of	of	ADP
iajs-3292	76	26	𝜙(𝑥	𝜙(𝑥	PROPN
iajs-3292	76	27	)	)	PUNCT
iajs-3292	76	28	is	be	AUX
iajs-3292	76	29	:	:	PUNCT
iajs-3292	76	30	𝑑𝜙(𝑥	𝑑𝜙(𝑥	X
iajs-3292	76	31	)	)	PUNCT
iajs-3292	76	32	𝑑𝑥	𝑑𝑥	VERB
iajs-3292	76	33	=	=	SYM
iajs-3292	76	34	𝐷𝐵𝜙(𝑥	𝐷𝐵𝜙(𝑥	NOUN
iajs-3292	76	35	)	)	PUNCT
iajs-3292	76	36	;	;	PUNCT
iajs-3292	77	1	𝑥𝜖[0,1	𝑥𝜖[0,1	PROPN
iajs-3292	77	2	]	]	PUNCT
iajs-3292	77	3	,	,	PUNCT
iajs-3292	77	4	(	(	PUNCT
iajs-3292	77	5	8)	8)	NUM
iajs-3292	77	6	ihjpas	ihjpa	NOUN
iajs-3292	77	7	.	.	PUNCT
iajs-3292	78	1	37	37	NUM
iajs-3292	78	2	(	(	PUNCT
iajs-3292	78	3	1	1	NUM
iajs-3292	78	4	)	)	PUNCT
iajs-3292	78	5	2024	2024	NUM
iajs-3292	78	6	361	361	NUM
iajs-3292	78	7	where	where	SCONJ
iajs-3292	78	8	𝐷𝐵	𝐷𝐵	PROPN
iajs-3292	78	9	is	be	AUX
iajs-3292	78	10	given	give	VERB
iajs-3292	78	11	as	as	ADP
iajs-3292	78	12	𝐷𝐵	𝐷𝐵	PROPN
iajs-3292	78	13	=	=	SYM
iajs-3292	78	14	𝐴	𝐴	PROPN
iajs-3292	78	15	𝑉	𝑉	PROPN
iajs-3292	78	16	𝐵	𝐵	PROPN
iajs-3292	78	17	∗	∗	NOUN
iajs-3292	78	18	,	,	PUNCT
iajs-3292	78	19	where	where	SCONJ
iajs-3292	78	20	:	:	PUNCT
iajs-3292	78	21	𝑉	𝑉	PROPN
iajs-3292	78	22	=	=	X
iajs-3292	78	23	[	[	PUNCT
iajs-3292	78	24	0	0	NUM
iajs-3292	78	25	0	0	NUM
iajs-3292	78	26	0	0	NUM
iajs-3292	79	1	⋯	⋯	VERB
iajs-3292	79	2	0	0	NUM
iajs-3292	79	3	1	1	NUM
iajs-3292	79	4	0	0	NUM
iajs-3292	79	5	0	0	NUM
iajs-3292	79	6	⋯	⋯	ADP
iajs-3292	79	7	0	0	NOUN
iajs-3292	79	8	0	0	NUM
iajs-3292	79	9	⋮	⋮	NOUN
iajs-3292	79	10	0	0	NUM
iajs-3292	79	11	2	2	NUM
iajs-3292	79	12	⋮	⋮	NOUN
iajs-3292	79	13	0	0	NUM
iajs-3292	79	14	0	0	NUM
iajs-3292	79	15	⋮	⋮	NOUN
iajs-3292	79	16	0	0	NUM
iajs-3292	80	1	⋯	⋯	NOUN
iajs-3292	80	2	⋱	⋱	PUNCT
iajs-3292	80	3	⋯	⋯	NOUN
iajs-3292	80	4	0	0	NUM
iajs-3292	80	5	⋮	⋮	NOUN
iajs-3292	80	6	𝑛	𝑛	PROPN
iajs-3292	80	7	]	]	X
iajs-3292	80	8	(	(	PUNCT
iajs-3292	80	9	𝑛+1)×𝑛	𝑛+1)×𝑛	ADV
iajs-3292	80	10	,	,	PUNCT
iajs-3292	80	11	𝐵∗	𝐵∗	X
iajs-3292	80	12	=	=	PUNCT
iajs-3292	81	1	[	[	PUNCT
iajs-3292	81	2	𝐴1	𝐴1	PROPN
iajs-3292	81	3	−1	−1	NOUN
iajs-3292	81	4	𝐴2	𝐴2	PROPN
iajs-3292	81	5	−1	−1	NOUN
iajs-3292	81	6	𝐴3	𝐴3	PROPN
iajs-3292	81	7	−1	−1	NOUN
iajs-3292	81	8	⋮	⋮	NOUN
iajs-3292	81	9	𝐴𝑛	𝐴𝑛	PROPN
iajs-3292	81	10	−1	−1	NOUN
iajs-3292	81	11	]	]	PUNCT
iajs-3292	81	12	𝑛×(𝑛+1	𝑛×(𝑛+1	PROPN
iajs-3292	81	13	)	)	PUNCT
iajs-3292	81	14	,	,	PUNCT
iajs-3292	81	15	(	(	PUNCT
iajs-3292	81	16	9	9	X
iajs-3292	81	17	)	)	PUNCT
iajs-3292	81	18	where	where	SCONJ
iajs-3292	81	19	𝐵∗	𝐵∗	PROPN
iajs-3292	81	20	represents	represent	VERB
iajs-3292	81	21	the	the	DET
iajs-3292	81	22	𝛼𝑡ℎ	𝛼𝑡ℎ	PROPN
iajs-3292	81	23	rows	row	NOUN
iajs-3292	81	24	of	of	ADP
iajs-3292	81	25	𝐴−1for	𝐴−1for	ADP
iajs-3292	81	26	𝛼=1	𝛼=1	PROPN
iajs-3292	81	27	,	,	PUNCT
iajs-3292	81	28	2	2	NUM
iajs-3292	81	29	,	,	PUNCT
iajs-3292	81	30	…	…	PUNCT
iajs-3292	81	31	,	,	PUNCT
iajs-3292	81	32	n.	n.	PROPN
iajs-3292	81	33	furthermore	furthermore	ADV
iajs-3292	81	34	,	,	PUNCT
iajs-3292	81	35	the	the	DET
iajs-3292	81	36	generalization	generalization	NOUN
iajs-3292	81	37	of	of	ADP
iajs-3292	81	38	(	(	PUNCT
iajs-3292	81	39	8)	8)	NUM
iajs-3292	81	40	can	can	AUX
iajs-3292	81	41	be	be	AUX
iajs-3292	81	42	written	write	VERB
iajs-3292	81	43	as	as	SCONJ
iajs-3292	81	44	follows	follow	VERB
iajs-3292	81	45	:	:	PUNCT
iajs-3292	81	46	𝑑𝑛𝜙(𝑥	𝑑𝑛𝜙(𝑥	NOUN
iajs-3292	81	47	)	)	PUNCT
iajs-3292	81	48	𝑑𝑥𝑛	𝑑𝑥𝑛	VERB
iajs-3292	81	49	=	=	PUNCT
iajs-3292	81	50	(	(	PUNCT
iajs-3292	81	51	𝐷𝐵	𝐷𝐵	PROPN
iajs-3292	81	52	)	)	PUNCT
iajs-3292	81	53	𝑛	𝑛	DET
iajs-3292	81	54	𝜙(𝑥	𝜙(𝑥	PROPN
iajs-3292	81	55	)	)	PUNCT
iajs-3292	81	56	;	;	PUNCT
iajs-3292	81	57	𝑛	𝑛	PROPN
iajs-3292	81	58	=	=	SYM
iajs-3292	81	59	1	1	NUM
iajs-3292	81	60	,	,	PUNCT
iajs-3292	81	61	2	2	NUM
iajs-3292	81	62	,	,	PUNCT
iajs-3292	81	63	.	.	PUNCT
iajs-3292	81	64	..	..	PUNCT
iajs-3292	81	65	.	.	PUNCT
iajs-3292	82	1	(	(	PUNCT
iajs-3292	82	2	10	10	NUM
iajs-3292	82	3	)	)	PUNCT
iajs-3292	82	4	thus	thus	ADV
iajs-3292	82	5	,	,	PUNCT
iajs-3292	82	6	it	it	PRON
iajs-3292	82	7	will	will	AUX
iajs-3292	82	8	be	be	AUX
iajs-3292	82	9	able	able	ADJ
iajs-3292	82	10	to	to	PART
iajs-3292	82	11	approximate	approximate	VERB
iajs-3292	82	12	the	the	DET
iajs-3292	82	13	derivatives	derivative	NOUN
iajs-3292	82	14	of	of	ADP
iajs-3292	82	15	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	82	16	)	)	PUNCT
iajs-3292	82	17	in	in	ADP
iajs-3292	82	18	terms	term	NOUN
iajs-3292	82	19	of	of	ADP
iajs-3292	82	20	om	om	PROPN
iajs-3292	82	21	as	as	SCONJ
iajs-3292	82	22	follows	follow	VERB
iajs-3292	82	23	:	:	PUNCT
iajs-3292	82	24	𝑓′(𝑥	𝑓′(𝑥	PROPN
iajs-3292	82	25	)	)	PUNCT
iajs-3292	82	26	=	=	PUNCT
iajs-3292	83	1	𝐶𝑇𝐷𝐵	𝐶𝑇𝐷𝐵	PROPN
iajs-3292	83	2	𝜙(𝑥	𝜙(𝑥	PROPN
iajs-3292	83	3	)	)	PUNCT
iajs-3292	83	4	,	,	PUNCT
iajs-3292	83	5	𝑓′′(𝑥	𝑓′′(𝑥	NOUN
iajs-3292	83	6	)	)	PUNCT
iajs-3292	83	7	=	=	SYM
iajs-3292	83	8	𝐶	𝐶	PROPN
iajs-3292	83	9	𝑇(𝐷𝐵	𝑇(𝐷𝐵	PROPN
iajs-3292	83	10	)	)	PUNCT
iajs-3292	83	11	2	2	NUM
iajs-3292	83	12	𝜙(𝑥	𝜙(𝑥	NOUN
iajs-3292	83	13	)	)	PUNCT
iajs-3292	83	14	,	,	PUNCT
iajs-3292	83	15	.	.	PUNCT
iajs-3292	83	16	.	.	PUNCT
iajs-3292	84	1	.	.	PUNCT
iajs-3292	85	1	,	,	PUNCT
iajs-3292	85	2	𝑓(𝑛)(𝑥	𝑓(𝑛)(𝑥	X
iajs-3292	85	3	)	)	PUNCT
iajs-3292	85	4	=	=	SYM
iajs-3292	85	5	𝐶𝑇(𝐷𝐵	𝐶𝑇(𝐷𝐵	PROPN
iajs-3292	85	6	)	)	PUNCT
iajs-3292	85	7	𝑛	𝑛	DET
iajs-3292	85	8	𝜙(𝑥	𝜙(𝑥	PROPN
iajs-3292	85	9	)	)	PUNCT
iajs-3292	85	10	.	.	PUNCT
iajs-3292	86	1	(	(	PUNCT
iajs-3292	86	2	11	11	NUM
iajs-3292	86	3	)	)	PUNCT
iajs-3292	86	4	this	this	DET
iajs-3292	86	5	approximation	approximation	NOUN
iajs-3292	86	6	and	and	CCONJ
iajs-3292	86	7	eq.(5	eq.(5	NOUN
iajs-3292	86	8	)	)	PUNCT
iajs-3292	86	9	are	be	AUX
iajs-3292	86	10	also	also	ADV
iajs-3292	86	11	applied	apply	VERB
iajs-3292	86	12	to	to	ADP
iajs-3292	86	13	all	all	DET
iajs-3292	86	14	conditions	condition	NOUN
iajs-3292	86	15	of	of	ADP
iajs-3292	86	16	the	the	DET
iajs-3292	86	17	equation	equation	NOUN
iajs-3292	86	18	.	.	PUNCT
iajs-3292	87	1	to	to	PART
iajs-3292	87	2	solve	solve	VERB
iajs-3292	87	3	the	the	DET
iajs-3292	87	4	equation	equation	NOUN
iajs-3292	87	5	,	,	PUNCT
iajs-3292	87	6	we	we	PRON
iajs-3292	87	7	replace	replace	VERB
iajs-3292	87	8	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	87	9	)	)	PUNCT
iajs-3292	87	10	and	and	CCONJ
iajs-3292	87	11	its	its	PRON
iajs-3292	87	12	derivatives	derivative	NOUN
iajs-3292	87	13	by	by	ADP
iajs-3292	87	14	eqs.(5	eqs.(5	PROPN
iajs-3292	87	15	)	)	PUNCT
iajs-3292	87	16	and	and	CCONJ
iajs-3292	87	17	(	(	PUNCT
iajs-3292	87	18	11	11	NUM
iajs-3292	87	19	)	)	PUNCT
iajs-3292	87	20	,	,	PUNCT
iajs-3292	87	21	then	then	ADV
iajs-3292	87	22	modify	modify	VERB
iajs-3292	87	23	𝑥	𝑥	PRON
iajs-3292	87	24	by	by	ADP
iajs-3292	87	25	appropriate	appropriate	ADJ
iajs-3292	87	26	points	point	NOUN
iajs-3292	87	27	from	from	ADP
iajs-3292	87	28	chebyshev	chebyshev	NOUN
iajs-3292	87	29	roots	root	NOUN
iajs-3292	87	30	,	,	PUNCT
iajs-3292	87	31	called	call	VERB
iajs-3292	87	32	collocation	collocation	NOUN
iajs-3292	87	33	nodes	nod	VERB
iajs-3292	87	34	,	,	PUNCT
iajs-3292	87	35	as	as	SCONJ
iajs-3292	87	36	follows	follow	VERB
iajs-3292	87	37	:	:	PUNCT
iajs-3292	87	38	𝑥𝑟	𝑥𝑟	X
iajs-3292	87	39	=	=	NOUN
iajs-3292	87	40	1	1	NUM
iajs-3292	87	41	2	2	NUM
iajs-3292	87	42	(	(	PUNCT
iajs-3292	87	43	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3292	88	1	𝑟	𝑟	X
iajs-3292	88	2	𝜋	𝜋	NOUN
iajs-3292	88	3	𝑛	𝑛	ADJ
iajs-3292	88	4	+	+	NOUN
iajs-3292	88	5	1	1	NUM
iajs-3292	88	6	)	)	PUNCT
iajs-3292	88	7	,	,	PUNCT
iajs-3292	88	8	𝑟	𝑟	NOUN
iajs-3292	88	9	=	=	SYM
iajs-3292	88	10	1	1	NUM
iajs-3292	88	11	,	,	PUNCT
iajs-3292	88	12	.	.	PUNCT
iajs-3292	88	13	.	.	PUNCT
iajs-3292	89	1	.	.	PUNCT
iajs-3292	90	1	,	,	PUNCT
iajs-3292	90	2	𝑛	𝑛	DET
iajs-3292	90	3	−	−	NOUN
iajs-3292	90	4	1	1	NUM
iajs-3292	90	5	.	.	PUNCT
iajs-3292	91	1	(	(	PUNCT
iajs-3292	91	2	12	12	NUM
iajs-3292	91	3	)	)	PUNCT
iajs-3292	91	4	this	this	PRON
iajs-3292	91	5	results	result	VERB
iajs-3292	91	6	in	in	ADP
iajs-3292	91	7	a	a	DET
iajs-3292	91	8	system	system	NOUN
iajs-3292	91	9	of	of	ADP
iajs-3292	91	10	algebraic	algebraic	ADJ
iajs-3292	91	11	equations	equation	NOUN
iajs-3292	91	12	that	that	PRON
iajs-3292	91	13	can	can	AUX
iajs-3292	91	14	be	be	AUX
iajs-3292	91	15	solved	solve	VERB
iajs-3292	91	16	using	use	VERB
iajs-3292	91	17	software	software	NOUN
iajs-3292	91	18	such	such	ADJ
iajs-3292	91	19	as	as	ADP
iajs-3292	91	20	mathematica	mathematica	PROPN
iajs-3292	91	21	or	or	CCONJ
iajs-3292	91	22	matlab	matlab	PROPN
iajs-3292	91	23	to	to	PART
iajs-3292	91	24	obtain	obtain	VERB
iajs-3292	91	25	the	the	DET
iajs-3292	91	26	value	value	NOUN
iajs-3292	91	27	of	of	ADP
iajs-3292	91	28	the	the	DET
iajs-3292	91	29	vector	vector	NOUN
iajs-3292	91	30	𝐶𝑇	𝐶𝑇	PROPN
iajs-3292	91	31	in	in	ADP
iajs-3292	91	32	eq.(5	eq.(5	NOUN
iajs-3292	91	33	)	)	PUNCT
iajs-3292	91	34	.	.	PUNCT
iajs-3292	92	1	3.2	3.2	NUM
iajs-3292	92	2	the	the	DET
iajs-3292	92	3	shifted	shift	VERB
iajs-3292	92	4	legendre	legendre	PROPN
iajs-3292	92	5	polynomials	polynomial	VERB
iajs-3292	92	6	the	the	DET
iajs-3292	92	7	legendre	legendre	PROPN
iajs-3292	92	8	polynomials	polynomial	NOUN
iajs-3292	92	9	of	of	ADP
iajs-3292	92	10	𝑛𝑡ℎ	𝑛𝑡ℎ	NUM
iajs-3292	92	11	order	order	NOUN
iajs-3292	92	12	are	be	AUX
iajs-3292	92	13	defined	define	VERB
iajs-3292	92	14	on	on	ADP
iajs-3292	92	15	[	[	X
iajs-3292	92	16	-1,1	-1,1	X
iajs-3292	92	17	]	]	X
iajs-3292	92	18	as	as	ADP
iajs-3292	92	19	[	[	X
iajs-3292	92	20	11,13	11,13	NUM
iajs-3292	92	21	]	]	PUNCT
iajs-3292	92	22	:	:	PUNCT
iajs-3292	92	23	𝐿0(𝑡	𝐿0(𝑡	PUNCT
iajs-3292	92	24	)	)	PUNCT
iajs-3292	92	25	=	=	SYM
iajs-3292	92	26	1	1	NUM
iajs-3292	92	27	,	,	PUNCT
iajs-3292	92	28	𝐿1(𝑡	𝐿1(𝑡	NUM
iajs-3292	92	29	)	)	PUNCT
iajs-3292	92	30	=	=	SYM
iajs-3292	92	31	𝑡	𝑡	NOUN
iajs-3292	92	32	,	,	PUNCT
iajs-3292	92	33	.	.	PUNCT
iajs-3292	92	34	.	.	PUNCT
iajs-3292	93	1	.	.	PUNCT
iajs-3292	93	2	,	,	PUNCT
iajs-3292	93	3	𝐿𝑛+1(𝑡	𝐿𝑛+1(𝑡	NOUN
iajs-3292	93	4	)	)	PUNCT
iajs-3292	93	5	=	=	SYM
iajs-3292	93	6	2	2	NUM
iajs-3292	93	7	𝑛+1	𝑛+1	PROPN
iajs-3292	93	8	𝑛+1	𝑛+1	PROPN
iajs-3292	93	9	𝑡	𝑡	PROPN
iajs-3292	93	10	𝐿𝑛(𝑡	𝐿𝑛(𝑡	VERB
iajs-3292	93	11	)	)	PUNCT
iajs-3292	93	12	−	−	PROPN
iajs-3292	93	13	𝑛	𝑛	PROPN
iajs-3292	93	14	𝑛+1	𝑛+1	PROPN
iajs-3292	93	15	𝐿𝑛−1(𝑡	𝐿𝑛−1(𝑡	PROPN
iajs-3292	93	16	)	)	PUNCT
iajs-3292	93	17	,	,	PUNCT
iajs-3292	93	18	𝑛	𝑛	PROPN
iajs-3292	93	19	=	=	SYM
iajs-3292	93	20	1,2	1,2	NUM
iajs-3292	93	21	,	,	PUNCT
iajs-3292	93	22	.	.	PUNCT
iajs-3292	93	23	..	..	PUNCT
iajs-3292	93	24	.	.	PUNCT
iajs-3292	94	1	(	(	PUNCT
iajs-3292	94	2	13	13	NUM
iajs-3292	94	3	)	)	PUNCT
iajs-3292	94	4	legendre	legendre	NOUN
iajs-3292	94	5	polynomials	polynomial	NOUN
iajs-3292	94	6	can	can	AUX
iajs-3292	94	7	be	be	AUX
iajs-3292	94	8	defined	define	VERB
iajs-3292	94	9	on	on	ADP
iajs-3292	94	10	[	[	X
iajs-3292	94	11	0,1	0,1	NUM
iajs-3292	94	12	]	]	PUNCT
iajs-3292	94	13	by	by	ADP
iajs-3292	94	14	changing	change	VERB
iajs-3292	94	15	the	the	DET
iajs-3292	94	16	variable	variable	ADJ
iajs-3292	94	17	𝑡	𝑡	NOUN
iajs-3292	94	18	=	=	NOUN
iajs-3292	94	19	2𝑥	2𝑥	NUM
iajs-3292	94	20	−	−	NOUN
iajs-3292	94	21	1	1	NUM
iajs-3292	94	22	and	and	CCONJ
iajs-3292	94	23	denoting	denote	VERB
iajs-3292	94	24	it	it	PRON
iajs-3292	94	25	as	as	ADP
iajs-3292	94	26	a	a	DET
iajs-3292	94	27	shifted	shift	VERB
iajs-3292	94	28	legendre	legendre	PROPN
iajs-3292	94	29	polynomial	polynomial	PROPN
iajs-3292	94	30	denoted	denote	VERB
iajs-3292	94	31	by	by	ADP
iajs-3292	94	32	𝑃𝑛(𝑥	𝑃𝑛(𝑥	NOUN
iajs-3292	94	33	)	)	PUNCT
iajs-3292	94	34	,	,	PUNCT
iajs-3292	94	35	and	and	CCONJ
iajs-3292	94	36	then	then	ADV
iajs-3292	94	37	calculated	calculate	VERB
iajs-3292	94	38	as	as	SCONJ
iajs-3292	94	39	follows	follow	VERB
iajs-3292	94	40	:	:	PUNCT
iajs-3292	94	41	𝑃0(𝑥	𝑃0(𝑥	NUM
iajs-3292	94	42	)	)	PUNCT
iajs-3292	94	43	=	=	SYM
iajs-3292	95	1	1	1	NUM
iajs-3292	95	2	,	,	PUNCT
iajs-3292	95	3	𝑃1(𝑥	𝑃1(𝑥	NOUN
iajs-3292	95	4	)	)	PUNCT
iajs-3292	95	5	=	=	SYM
iajs-3292	95	6	2𝑥	2𝑥	NOUN
iajs-3292	95	7	−	−	NOUN
iajs-3292	95	8	1	1	NUM
iajs-3292	95	9	,	,	PUNCT
iajs-3292	95	10	.	.	PUNCT
iajs-3292	95	11	.	.	PUNCT
iajs-3292	96	1	.	.	PUNCT
iajs-3292	96	2	,	,	PUNCT
iajs-3292	96	3	𝑃𝑛+1(𝑥	𝑃𝑛+1(𝑥	NOUN
iajs-3292	96	4	)	)	PUNCT
iajs-3292	97	1	=	=	SYM
iajs-3292	97	2	(	(	PUNCT
iajs-3292	97	3	2𝑛+1)(2𝑥−1	2𝑛+1)(2𝑥−1	PROPN
iajs-3292	97	4	)	)	PUNCT
iajs-3292	97	5	𝑛+1	𝑛+1	X
iajs-3292	97	6	𝑃𝑛(𝑥	𝑃𝑛(𝑥	PROPN
iajs-3292	97	7	)	)	PUNCT
iajs-3292	97	8	−	−	PROPN
iajs-3292	97	9	𝑛	𝑛	PRON
iajs-3292	97	10	𝑛+1	𝑛+1	PROPN
iajs-3292	97	11	𝑃𝑛−1(𝑥	𝑃𝑛−1(𝑥	PROPN
iajs-3292	97	12	)	)	PUNCT
iajs-3292	97	13	,	,	PUNCT
iajs-3292	97	14	𝑛	𝑛	NOUN
iajs-3292	97	15	=	=	SYM
iajs-3292	97	16	1,2	1,2	NUM
iajs-3292	97	17	,	,	PUNCT
iajs-3292	97	18	.	.	PUNCT
iajs-3292	97	19	..	..	PUNCT
iajs-3292	97	20	.	.	PUNCT
iajs-3292	98	1	(	(	PUNCT
iajs-3292	98	2	14	14	NUM
iajs-3292	98	3	)	)	PUNCT
iajs-3292	98	4	also	also	ADV
iajs-3292	98	5	,	,	PUNCT
iajs-3292	98	6	𝑃𝑛(𝑥	𝑃𝑛(𝑥	NOUN
iajs-3292	98	7	)	)	PUNCT
iajs-3292	98	8	can	can	AUX
iajs-3292	98	9	be	be	AUX
iajs-3292	98	10	written	write	VERB
iajs-3292	98	11	as	as	SCONJ
iajs-3292	98	12	shown	show	VERB
iajs-3292	98	13	:	:	PUNCT
iajs-3292	98	14	𝑃𝑛(𝑥	𝑃𝑛(𝑥	NOUN
iajs-3292	98	15	)	)	PUNCT
iajs-3292	98	16	=	=	PUNCT
iajs-3292	99	1	∑	∑	PUNCT
iajs-3292	99	2	(	(	PUNCT
iajs-3292	99	3	−1)𝑛+𝑖	−1)𝑛+𝑖	PROPN
iajs-3292	99	4	(	(	PUNCT
iajs-3292	99	5	𝑛+𝑖	𝑛+𝑖	NUM
iajs-3292	99	6	)	)	PUNCT
iajs-3292	99	7	(	(	PUNCT
iajs-3292	99	8	𝑛−𝑖	𝑛−𝑖	NOUN
iajs-3292	99	9	)	)	PUNCT
iajs-3292	99	10	!	!	PUNCT
iajs-3292	100	1	(	(	PUNCT
iajs-3292	100	2	𝑖!)2	𝑖!)2	X
iajs-3292	100	3	𝑥𝑖	𝑥𝑖	NUM
iajs-3292	100	4	.𝑛	.𝑛	PUNCT
iajs-3292	101	1	𝑖=0	𝑖=0	PUNCT
iajs-3292	101	2	(	(	PUNCT
iajs-3292	101	3	15	15	NUM
iajs-3292	101	4	)	)	PUNCT
iajs-3292	101	5	any	any	DET
iajs-3292	101	6	function	function	NOUN
iajs-3292	101	7	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	101	8	)	)	PUNCT
iajs-3292	101	9	∈	∈	PROPN
iajs-3292	101	10	𝐿2[0,1	𝐿2[0,1	PROPN
iajs-3292	101	11	]	]	PUNCT
iajs-3292	101	12	,	,	PUNCT
iajs-3292	101	13	could	could	AUX
iajs-3292	101	14	be	be	AUX
iajs-3292	101	15	characterized	characterize	VERB
iajs-3292	101	16	by	by	ADP
iajs-3292	101	17	a	a	DET
iajs-3292	101	18	shifted	shift	VERB
iajs-3292	101	19	legendre	legendre	NOUN
iajs-3292	101	20	polynomial	polynomial	PROPN
iajs-3292	101	21	as	as	SCONJ
iajs-3292	101	22	follows	follow	VERB
iajs-3292	101	23	:	:	PUNCT
iajs-3292	101	24	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	101	25	)	)	PUNCT
iajs-3292	102	1	=	=	SYM
iajs-3292	102	2	∑	∑	PROPN
iajs-3292	102	3	𝑐𝑖	𝑐𝑖	PROPN
iajs-3292	102	4	𝑃𝑖(𝑥	𝑃𝑖(𝑥	PROPN
iajs-3292	102	5	)	)	PUNCT
iajs-3292	102	6	∞	∞	PROPN
iajs-3292	102	7	𝑖=0	𝑖=0	PROPN
iajs-3292	102	8	,	,	PUNCT
iajs-3292	102	9	(	(	PUNCT
iajs-3292	102	10	16	16	NUM
iajs-3292	102	11	)	)	PUNCT
iajs-3292	102	12	where	where	SCONJ
iajs-3292	102	13	𝑐𝑖	𝑐𝑖	NOUN
iajs-3292	102	14	=	=	PUNCT
iajs-3292	102	15	(	(	PUNCT
iajs-3292	102	16	2	2	NUM
iajs-3292	102	17	𝑖	𝑖	NOUN
iajs-3292	102	18	+	+	NOUN
iajs-3292	102	19	1	1	X
iajs-3292	102	20	)	)	PUNCT
iajs-3292	102	21	∫	∫	PROPN
iajs-3292	102	22	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	102	23	)	)	PUNCT
iajs-3292	102	24	1	1	NUM
iajs-3292	102	25	0	0	NUM
iajs-3292	102	26	𝑃𝑖(𝑥	𝑃𝑖(𝑥	PROPN
iajs-3292	102	27	)	)	PUNCT
iajs-3292	102	28	𝑑𝑥	𝑑𝑥	VERB
iajs-3292	102	29	;	;	PUNCT
iajs-3292	102	30	𝑖	𝑖	SYM
iajs-3292	102	31	=	=	SYM
iajs-3292	102	32	0	0	NUM
iajs-3292	102	33	,	,	PUNCT
iajs-3292	102	34	1	1	NUM
iajs-3292	102	35	,	,	PUNCT
iajs-3292	102	36	2	2	NUM
iajs-3292	102	37	,	,	PUNCT
iajs-3292	102	38	.	.	PUNCT
iajs-3292	102	39	..	..	PUNCT
iajs-3292	102	40	.	.	PUNCT
iajs-3292	103	1	in	in	ADP
iajs-3292	103	2	practice	practice	NOUN
iajs-3292	103	3	,	,	PUNCT
iajs-3292	103	4	only	only	ADV
iajs-3292	103	5	the	the	DET
iajs-3292	103	6	first	first	ADJ
iajs-3292	103	7	(	(	PUNCT
iajs-3292	103	8	𝑛	𝑛	PROPN
iajs-3292	103	9	+	+	NOUN
iajs-3292	103	10	1	1	NUM
iajs-3292	103	11	)	)	PUNCT
iajs-3292	103	12	terms	term	NOUN
iajs-3292	103	13	of	of	ADP
iajs-3292	103	14	eq.(16	eq.(16	NOUN
iajs-3292	103	15	)	)	PUNCT
iajs-3292	103	16	will	will	AUX
iajs-3292	103	17	be	be	AUX
iajs-3292	103	18	considered	consider	VERB
iajs-3292	103	19	:	:	PUNCT
iajs-3292	103	20	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	103	21	)	)	PUNCT
iajs-3292	104	1	=	=	SYM
iajs-3292	104	2	∑	∑	PROPN
iajs-3292	104	3	𝑐𝑖	𝑐𝑖	PROPN
iajs-3292	104	4	𝑃𝑖(𝑥	𝑃𝑖(𝑥	PROPN
iajs-3292	104	5	)	)	PUNCT
iajs-3292	104	6	𝑛	𝑛	DET
iajs-3292	104	7	𝑖=0	𝑖=0	PROPN
iajs-3292	104	8	=	=	PUNCT
iajs-3292	104	9	𝐶𝑇𝜙(𝑥	𝐶𝑇𝜙(𝑥	PROPN
iajs-3292	104	10	)	)	PUNCT
iajs-3292	104	11	,	,	PUNCT
iajs-3292	104	12	(	(	PUNCT
iajs-3292	104	13	17	17	NUM
iajs-3292	104	14	)	)	PUNCT
iajs-3292	104	15	ihjpas	ihjpa	NOUN
iajs-3292	104	16	.	.	PUNCT
iajs-3292	105	1	37	37	NUM
iajs-3292	105	2	(	(	PUNCT
iajs-3292	105	3	1	1	NUM
iajs-3292	105	4	)	)	PUNCT
iajs-3292	105	5	2024	2024	NUM
iajs-3292	105	6	362	362	NUM
iajs-3292	105	7	where	where	SCONJ
iajs-3292	105	8	𝐶𝑇	𝐶𝑇	PROPN
iajs-3292	105	9	=	=	PUNCT
iajs-3292	106	1	[	[	X
iajs-3292	106	2	𝑐0	𝑐0	NOUN
iajs-3292	106	3	,	,	PUNCT
iajs-3292	106	4	𝑐1	𝑐1	NOUN
iajs-3292	106	5	,	,	PUNCT
iajs-3292	106	6	.	.	PUNCT
iajs-3292	106	7	.	.	PUNCT
iajs-3292	107	1	.	.	PUNCT
iajs-3292	108	1	,	,	PUNCT
iajs-3292	108	2	𝑐𝑛	𝑐𝑛	ADP
iajs-3292	108	3	]	]	PUNCT
iajs-3292	108	4	,	,	PUNCT
iajs-3292	108	5	and	and	CCONJ
iajs-3292	108	6	𝜙(𝑥	𝜙(𝑥	NUM
iajs-3292	108	7	)	)	PUNCT
iajs-3292	108	8	=	=	PUNCT
iajs-3292	109	1	[	[	X
iajs-3292	109	2	𝑃0(𝑥	𝑃0(𝑥	NUM
iajs-3292	109	3	)	)	PUNCT
iajs-3292	109	4	,	,	PUNCT
iajs-3292	109	5	𝑃1(𝑥	𝑃1(𝑥	NOUN
iajs-3292	109	6	)	)	PUNCT
iajs-3292	109	7	,	,	PUNCT
iajs-3292	109	8	.	.	PUNCT
iajs-3292	109	9	.	.	PUNCT
iajs-3292	110	1	.	.	PUNCT
iajs-3292	111	1	,	,	PUNCT
iajs-3292	111	2	𝑃𝑛(𝑥	𝑃𝑛(𝑥	PROPN
iajs-3292	111	3	)	)	PUNCT
iajs-3292	111	4	]	]	PUNCT
iajs-3292	111	5	𝑇	𝑇	PROPN
iajs-3292	111	6	.	.	PUNCT
iajs-3292	112	1	the	the	DET
iajs-3292	112	2	derivatives	derivative	NOUN
iajs-3292	112	3	of	of	ADP
iajs-3292	112	4	𝜙(𝑥)can	𝜙(𝑥)can	PROPN
iajs-3292	112	5	be	be	AUX
iajs-3292	112	6	defined	define	VERB
iajs-3292	112	7	as	as	ADP
iajs-3292	112	8	:	:	PUNCT
iajs-3292	112	9	𝑑𝜙(𝑥	𝑑𝜙(𝑥	NUM
iajs-3292	112	10	)	)	PUNCT
iajs-3292	112	11	𝑑𝑥	𝑑𝑥	VERB
iajs-3292	112	12	=	=	SYM
iajs-3292	112	13	𝐷𝐿𝜙(𝑥	𝐷𝐿𝜙(𝑥	NOUN
iajs-3292	112	14	)	)	PUNCT
iajs-3292	112	15	,	,	PUNCT
iajs-3292	112	16	𝑑2𝜙(𝑥	𝑑2𝜙(𝑥	PROPN
iajs-3292	112	17	)	)	PUNCT
iajs-3292	112	18	𝑑𝑥2	𝑑𝑥2	NOUN
iajs-3292	112	19	=	=	SYM
iajs-3292	112	20	(	(	PUNCT
iajs-3292	112	21	𝐷𝐿	𝐷𝐿	PROPN
iajs-3292	112	22	)	)	PUNCT
iajs-3292	112	23	2𝜙(𝑥	2𝜙(𝑥	NUM
iajs-3292	112	24	)	)	PUNCT
iajs-3292	112	25	,	,	PUNCT
iajs-3292	112	26	.	.	PUNCT
iajs-3292	112	27	.	.	PUNCT
iajs-3292	113	1	.	.	PUNCT
iajs-3292	113	2	,	,	PUNCT
iajs-3292	113	3	𝑑𝑛𝜙(𝑥	𝑑𝑛𝜙(𝑥	PROPN
iajs-3292	113	4	)	)	PUNCT
iajs-3292	113	5	𝑑𝑥𝑛	𝑑𝑥𝑛	VERB
iajs-3292	113	6	=	=	PUNCT
iajs-3292	113	7	(	(	PUNCT
iajs-3292	113	8	𝐷𝐿	𝐷𝐿	PROPN
iajs-3292	113	9	)	)	PUNCT
iajs-3292	113	10	𝑛𝜙(𝑥	𝑛𝜙(𝑥	PUNCT
iajs-3292	114	1	(	(	PUNCT
iajs-3292	114	2	18	18	NUM
iajs-3292	114	3	)	)	PUNCT
iajs-3292	114	4	where	where	SCONJ
iajs-3292	114	5	𝐷𝐿	𝐷𝐿	PROPN
iajs-3292	114	6	is	be	AUX
iajs-3292	114	7	the	the	DET
iajs-3292	114	8	(	(	PUNCT
iajs-3292	114	9	𝑛	𝑛	PROPN
iajs-3292	114	10	+	+	NOUN
iajs-3292	114	11	1	1	NUM
iajs-3292	114	12	)	)	PUNCT
iajs-3292	114	13	×	×	NOUN
iajs-3292	114	14	(	(	PUNCT
iajs-3292	114	15	𝑛	𝑛	PROPN
iajs-3292	114	16	+	+	NOUN
iajs-3292	114	17	1	1	X
iajs-3292	114	18	)	)	PUNCT
iajs-3292	114	19	om	om	NOUN
iajs-3292	114	20	of	of	ADP
iajs-3292	114	21	derivative	derivative	NOUN
iajs-3292	114	22	,	,	PUNCT
iajs-3292	114	23	given	give	VERB
iajs-3292	114	24	as	as	ADP
iajs-3292	114	25	:	:	PUNCT
iajs-3292	114	26	𝐷𝐿	𝐷𝐿	PROPN
iajs-3292	114	27	=	=	SYM
iajs-3292	114	28	(	(	PUNCT
iajs-3292	114	29	𝑑𝑖𝑗	𝑑𝑖𝑗	PROPN
iajs-3292	114	30	)	)	PUNCT
iajs-3292	114	31	{	{	PUNCT
iajs-3292	114	32	2	2	NUM
iajs-3292	114	33	(	(	PUNCT
iajs-3292	114	34	2𝑗	2𝑗	NOUN
iajs-3292	114	35	+	+	NOUN
iajs-3292	114	36	1	1	NUM
iajs-3292	114	37	)	)	PUNCT
iajs-3292	114	38	,	,	PUNCT
iajs-3292	114	39	𝑗	𝑗	X
iajs-3292	114	40	=	=	SYM
iajs-3292	114	41	𝑖	𝑖	SYM
iajs-3292	114	42	−	−	PROPN
iajs-3292	114	43	𝑘	𝑘	INTJ
iajs-3292	114	44	,	,	PUNCT
iajs-3292	114	45	{	{	PUNCT
iajs-3292	114	46	𝑘	𝑘	X
iajs-3292	114	47	=	=	SYM
iajs-3292	114	48	1,3	1,3	NUM
iajs-3292	114	49	,	,	PUNCT
iajs-3292	114	50	.	.	PUNCT
iajs-3292	114	51	.	.	PUNCT
iajs-3292	115	1	.	.	PUNCT
iajs-3292	116	1	,	,	PUNCT
iajs-3292	116	2	𝑛	𝑛	X
iajs-3292	116	3	,	,	PUNCT
iajs-3292	116	4	if	if	SCONJ
iajs-3292	116	5	𝑛	𝑛	PROPN
iajs-3292	116	6	odd	odd	ADJ
iajs-3292	116	7	,	,	PUNCT
iajs-3292	116	8	𝑘	𝑘	NOUN
iajs-3292	116	9	=	=	SYM
iajs-3292	116	10	1,3	1,3	NUM
iajs-3292	116	11	,	,	PUNCT
iajs-3292	116	12	.	.	PUNCT
iajs-3292	116	13	.	.	PUNCT
iajs-3292	117	1	.	.	PUNCT
iajs-3292	118	1	,	,	PUNCT
iajs-3292	118	2	𝑛	𝑛	DET
iajs-3292	118	3	−	−	NOUN
iajs-3292	118	4	1	1	NUM
iajs-3292	118	5	,	,	PUNCT
iajs-3292	118	6	if	if	SCONJ
iajs-3292	118	7	𝑛	𝑛	ADP
iajs-3292	118	8	even	even	ADV
iajs-3292	118	9	,	,	PUNCT
iajs-3292	118	10	0	0	NUM
iajs-3292	118	11	otherwise	otherwise	ADV
iajs-3292	118	12	.	.	PUNCT
iajs-3292	119	1	(	(	PUNCT
iajs-3292	119	2	19	19	NUM
iajs-3292	119	3	)	)	PUNCT
iajs-3292	119	4	then	then	ADV
iajs-3292	119	5	write	write	VERB
iajs-3292	119	6	the	the	DET
iajs-3292	119	7	derivatives	derivative	NOUN
iajs-3292	119	8	of	of	ADP
iajs-3292	119	9	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	119	10	)	)	PUNCT
iajs-3292	119	11	with	with	ADP
iajs-3292	119	12	respect	respect	NOUN
iajs-3292	119	13	to	to	ADP
iajs-3292	119	14	the	the	DET
iajs-3292	119	15	om	om	PROPN
iajs-3292	119	16	as	as	SCONJ
iajs-3292	119	17	follows	follow	VERB
iajs-3292	119	18	:	:	PUNCT
iajs-3292	119	19	𝑓′(𝑥	𝑓′(𝑥	PROPN
iajs-3292	119	20	)	)	PUNCT
iajs-3292	119	21	=	=	SYM
iajs-3292	119	22	𝐶𝑇𝐷𝐿𝜙(𝑥	𝐶𝑇𝐷𝐿𝜙(𝑥	NOUN
iajs-3292	119	23	)	)	PUNCT
iajs-3292	119	24	,	,	PUNCT
iajs-3292	119	25	𝑓′′(𝑥	𝑓′′(𝑥	NOUN
iajs-3292	119	26	)	)	PUNCT
iajs-3292	119	27	=	=	SYM
iajs-3292	119	28	𝐶	𝐶	PROPN
iajs-3292	119	29	𝑇(𝐷𝐿	𝑇(𝐷𝐿	PROPN
iajs-3292	119	30	)	)	PUNCT
iajs-3292	119	31	2	2	NUM
iajs-3292	119	32	𝜙(𝑥	𝜙(𝑥	NOUN
iajs-3292	119	33	)	)	PUNCT
iajs-3292	119	34	,	,	PUNCT
iajs-3292	119	35	.	.	PUNCT
iajs-3292	119	36	.	.	PUNCT
iajs-3292	120	1	.	.	PUNCT
iajs-3292	121	1	,	,	PUNCT
iajs-3292	121	2	𝑓(𝑛)(𝑥	𝑓(𝑛)(𝑥	X
iajs-3292	121	3	)	)	PUNCT
iajs-3292	121	4	=	=	SYM
iajs-3292	121	5	𝐶𝑇(𝐷𝐿	𝐶𝑇(𝐷𝐿	PROPN
iajs-3292	121	6	)	)	PUNCT
iajs-3292	121	7	𝑛	𝑛	DET
iajs-3292	121	8	𝜙(𝑥	𝜙(𝑥	PROPN
iajs-3292	121	9	)	)	PUNCT
iajs-3292	121	10	.	.	PUNCT
iajs-3292	122	1	(	(	PUNCT
iajs-3292	122	2	20	20	NUM
iajs-3292	122	3	)	)	PUNCT
iajs-3292	122	4	this	this	PRON
iajs-3292	122	5	helps	help	VERB
iajs-3292	122	6	to	to	PART
iajs-3292	122	7	solve	solve	VERB
iajs-3292	122	8	the	the	DET
iajs-3292	122	9	node	node	NOUN
iajs-3292	122	10	by	by	ADP
iajs-3292	122	11	substituting	substitute	VERB
iajs-3292	122	12	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	122	13	)	)	PUNCT
iajs-3292	122	14	and	and	CCONJ
iajs-3292	122	15	its	its	PRON
iajs-3292	122	16	derivatives	derivative	NOUN
iajs-3292	122	17	as	as	ADP
iajs-3292	122	18	in	in	ADP
iajs-3292	122	19	eqs.(17	eqs.(17	NOUN
iajs-3292	122	20	)	)	PUNCT
iajs-3292	122	21	and	and	CCONJ
iajs-3292	122	22	(	(	PUNCT
iajs-3292	122	23	20	20	NUM
iajs-3292	122	24	)	)	PUNCT
iajs-3292	122	25	.	.	PUNCT
iajs-3292	123	1	also	also	ADV
iajs-3292	123	2	,	,	PUNCT
iajs-3292	123	3	compensated	compensate	VERB
iajs-3292	123	4	in	in	ADP
iajs-3292	123	5	the	the	DET
iajs-3292	123	6	conditions	condition	NOUN
iajs-3292	123	7	with	with	ADP
iajs-3292	123	8	the	the	DET
iajs-3292	123	9	node	node	NOUN
iajs-3292	123	10	.	.	PUNCT
iajs-3292	124	1	then	then	ADV
iajs-3292	124	2	the	the	DET
iajs-3292	124	3	collocation	collocation	NOUN
iajs-3292	124	4	nodes	node	NOUN
iajs-3292	124	5	are	be	AUX
iajs-3292	124	6	inserted	insert	VERB
iajs-3292	124	7	into	into	ADP
iajs-3292	124	8	these	these	DET
iajs-3292	124	9	equations	equation	NOUN
iajs-3292	124	10	to	to	PART
iajs-3292	124	11	produce	produce	VERB
iajs-3292	124	12	a	a	DET
iajs-3292	124	13	system	system	NOUN
iajs-3292	124	14	of	of	ADP
iajs-3292	124	15	algebraic	algebraic	ADJ
iajs-3292	124	16	equations	equation	NOUN
iajs-3292	124	17	(	(	PUNCT
iajs-3292	124	18	𝑛	𝑛	PROPN
iajs-3292	124	19	+	+	NOUN
iajs-3292	124	20	1	1	NUM
iajs-3292	124	21	)	)	PUNCT
iajs-3292	124	22	that	that	PRON
iajs-3292	124	23	can	can	AUX
iajs-3292	124	24	be	be	AUX
iajs-3292	124	25	solved	solve	VERB
iajs-3292	124	26	with	with	ADP
iajs-3292	124	27	software	software	NOUN
iajs-3292	124	28	such	such	ADJ
iajs-3292	124	29	as	as	ADP
iajs-3292	124	30	matlab	matlab	PROPN
iajs-3292	124	31	or	or	CCONJ
iajs-3292	124	32	mathematica	mathematica	PROPN
iajs-3292	124	33	to	to	PART
iajs-3292	124	34	obtain	obtain	VERB
iajs-3292	124	35	the	the	DET
iajs-3292	124	36	coefficients	coefficient	NOUN
iajs-3292	124	37	of	of	ADP
iajs-3292	124	38	the	the	DET
iajs-3292	124	39	vector	vector	NOUN
iajs-3292	124	40	𝐶𝑇	𝐶𝑇	PROPN
iajs-3292	124	41	.	.	PUNCT
iajs-3292	125	1	3.3	3.3	NUM
iajs-3292	125	2	the	the	DET
iajs-3292	125	3	bernoulli	bernoulli	NOUN
iajs-3292	125	4	polynomials	polynomial	VERB
iajs-3292	125	5	the	the	DET
iajs-3292	125	6	𝑛𝑡ℎbernoulli	𝑛𝑡ℎbernoulli	NOUN
iajs-3292	125	7	polynomials	polynomial	VERB
iajs-3292	125	8	on	on	ADP
iajs-3292	125	9	[	[	X
iajs-3292	125	10	0,1	0,1	NUM
iajs-3292	125	11	]	]	PUNCT
iajs-3292	125	12	are	be	AUX
iajs-3292	125	13	defined	define	VERB
iajs-3292	125	14	as	as	SCONJ
iajs-3292	125	15	follows	follow	VERB
iajs-3292	125	16	[	[	X
iajs-3292	125	17	9,21	9,21	NUM
iajs-3292	125	18	]	]	X
iajs-3292	125	19	:	:	PUNCT
iajs-3292	125	20	𝐵𝑟𝑛(𝑥	𝐵𝑟𝑛(𝑥	PROPN
iajs-3292	125	21	)	)	PUNCT
iajs-3292	125	22	=	=	PUNCT
iajs-3292	126	1	∑	∑	PUNCT
iajs-3292	126	2	(	(	PUNCT
iajs-3292	126	3	𝑛	𝑛	PROPN
iajs-3292	126	4	𝑖	𝑖	SYM
iajs-3292	126	5	)	)	PUNCT
iajs-3292	126	6	𝐵𝑟𝑖	𝐵𝑟𝑖	PROPN
iajs-3292	126	7	𝑥	𝑥	NOUN
iajs-3292	126	8	𝑛−𝑖𝑛	𝑛−𝑖𝑛	ADJ
iajs-3292	126	9	𝑖=0	𝑖=0	PROPN
iajs-3292	126	10	,	,	PUNCT
iajs-3292	126	11	(	(	PUNCT
iajs-3292	126	12	21	21	NUM
iajs-3292	126	13	)	)	PUNCT
iajs-3292	126	14	where	where	SCONJ
iajs-3292	126	15	𝐵𝑟𝑖	𝐵𝑟𝑖	PROPN
iajs-3292	126	16	=	=	SYM
iajs-3292	126	17	𝐵𝑟𝑖(0	𝐵𝑟𝑖(0	NUM
iajs-3292	126	18	)	)	PUNCT
iajs-3292	126	19	is	be	AUX
iajs-3292	126	20	the	the	DET
iajs-3292	126	21	bernoulli	bernoulli	NOUN
iajs-3292	126	22	number	number	NOUN
iajs-3292	126	23	for	for	ADP
iajs-3292	126	24	all	all	DET
iajs-3292	126	25	𝑖	𝑖	NOUN
iajs-3292	126	26	=	=	NOUN
iajs-3292	126	27	0,1	0,1	NUM
iajs-3292	126	28	,	,	PUNCT
iajs-3292	126	29	.	.	PUNCT
iajs-3292	126	30	.	.	PUNCT
iajs-3292	126	31	.	.	PUNCT
iajs-3292	127	1	,	,	PUNCT
iajs-3292	127	2	𝑛.	𝑛.	NOUN
iajs-3292	127	3	these	these	DET
iajs-3292	127	4	numbers	number	NOUN
iajs-3292	127	5	are	be	AUX
iajs-3292	127	6	calculated	calculate	VERB
iajs-3292	127	7	by	by	ADP
iajs-3292	127	8	:	:	PUNCT
iajs-3292	127	9	𝐵𝑟𝑛	𝐵𝑟𝑛	PROPN
iajs-3292	127	10	=	=	SYM
iajs-3292	127	11	−∑	−∑	PROPN
iajs-3292	127	12	(	(	PUNCT
iajs-3292	127	13	−1)𝑖	−1)𝑖	NOUN
iajs-3292	127	14	𝑖	𝑖	X
iajs-3292	127	15	𝑛+1	𝑛+1	PROPN
iajs-3292	127	16	𝑖=1	𝑖=1	PROPN
iajs-3292	127	17	(	(	PUNCT
iajs-3292	127	18	𝑛+1	𝑛+1	PROPN
iajs-3292	127	19	𝑖	𝑖	NUM
iajs-3292	127	20	)	)	PUNCT
iajs-3292	127	21	∑	∑	PROPN
iajs-3292	127	22	𝑗𝑛𝑖	𝑗𝑛𝑖	PROPN
iajs-3292	127	23	𝑗=1	𝑗=1	PROPN
iajs-3292	127	24	,	,	PUNCT
iajs-3292	127	25	(	(	PUNCT
iajs-3292	127	26	22	22	NUM
iajs-3292	127	27	)	)	PUNCT
iajs-3292	127	28	for	for	ADP
iajs-3292	127	29	𝑛	𝑛	PRON
iajs-3292	127	30	≥	≥	NUM
iajs-3292	127	31	0	0	NUM
iajs-3292	127	32	,	,	PUNCT
iajs-3292	127	33	𝑛	𝑛	DET
iajs-3292	127	34	≠	≠	PROPN
iajs-3292	127	35	1	1	NUM
iajs-3292	127	36	.	.	PUNCT
iajs-3292	128	1	if	if	SCONJ
iajs-3292	128	2	𝑛	𝑛	PROPN
iajs-3292	128	3	=	=	SYM
iajs-3292	128	4	1	1	NUM
iajs-3292	128	5	,	,	PUNCT
iajs-3292	128	6	then	then	ADV
iajs-3292	128	7	𝐵𝑟1	𝐵𝑟1	NOUN
iajs-3292	129	1	=	=	PUNCT
iajs-3292	129	2	−	−	PROPN
iajs-3292	129	3	1	1	NUM
iajs-3292	129	4	2	2	NUM
iajs-3292	129	5	.	.	PUNCT
iajs-3292	130	1	therefore	therefore	ADV
iajs-3292	130	2	,	,	PUNCT
iajs-3292	130	3	some	some	DET
iajs-3292	130	4	bernoulli	bernoulli	NOUN
iajs-3292	130	5	polynomials	polynomial	NOUN
iajs-3292	130	6	can	can	AUX
iajs-3292	130	7	be	be	AUX
iajs-3292	130	8	represented	represent	VERB
iajs-3292	130	9	as	as	SCONJ
iajs-3292	130	10	follows	follow	VERB
iajs-3292	130	11	:	:	PUNCT
iajs-3292	130	12	𝐵𝑟0(𝑥	𝐵𝑟0(𝑥	NUM
iajs-3292	130	13	)	)	PUNCT
iajs-3292	130	14	=	=	SYM
iajs-3292	130	15	1	1	NUM
iajs-3292	130	16	,	,	PUNCT
iajs-3292	130	17	𝐵𝑟1(𝑥	𝐵𝑟1(𝑥	NOUN
iajs-3292	130	18	)	)	PUNCT
iajs-3292	130	19	=	=	SYM
iajs-3292	131	1	𝑥	𝑥	PRON
iajs-3292	131	2	−	−	NUM
iajs-3292	131	3	1	1	NUM
iajs-3292	131	4	2	2	NUM
iajs-3292	131	5	,	,	PUNCT
iajs-3292	131	6	𝐵𝑟2(𝑥	𝐵𝑟2(𝑥	NOUN
iajs-3292	131	7	)	)	PUNCT
iajs-3292	132	1	=	=	PUNCT
iajs-3292	133	1	𝑥	𝑥	DET
iajs-3292	133	2	2	2	NUM
iajs-3292	133	3	−	−	NOUN
iajs-3292	133	4	𝑥	𝑥	NOUN
iajs-3292	133	5	+	+	NOUN
iajs-3292	133	6	1	1	NUM
iajs-3292	133	7	6	6	NUM
iajs-3292	133	8	,	,	PUNCT
iajs-3292	133	9	𝐵𝑟3(𝑥	𝐵𝑟3(𝑥	NUM
iajs-3292	133	10	)	)	PUNCT
iajs-3292	133	11	=	=	PUNCT
iajs-3292	134	1	𝑥	𝑥	DET
iajs-3292	134	2	3	3	NUM
iajs-3292	134	3	−	−	NOUN
iajs-3292	134	4	3	3	NUM
iajs-3292	134	5	2	2	NUM
iajs-3292	134	6	𝑥2	𝑥2	NOUN
iajs-3292	134	7	+	+	CCONJ
iajs-3292	134	8	1	1	NUM
iajs-3292	134	9	2	2	NUM
iajs-3292	134	10	x	x	NOUN
iajs-3292	134	11	,	,	PUNCT
iajs-3292	134	12	𝐵𝑟4(𝑥	𝐵𝑟4(𝑥	NOUN
iajs-3292	134	13	)	)	PUNCT
iajs-3292	135	1	=	=	PUNCT
iajs-3292	136	1	𝑥	𝑥	DET
iajs-3292	136	2	4	4	NUM
iajs-3292	136	3	−	−	NOUN
iajs-3292	136	4	2𝑥3	2𝑥3	NUM
iajs-3292	136	5	+	+	NUM
iajs-3292	136	6	𝑥2	𝑥2	NOUN
iajs-3292	136	7	−	−	PROPN
iajs-3292	136	8	1	1	NUM
iajs-3292	136	9	30	30	NUM
iajs-3292	136	10	.	.	PUNCT
iajs-3292	137	1	bernoulli	bernoulli	NOUN
iajs-3292	137	2	polynomials	polynomial	NOUN
iajs-3292	137	3	are	be	AUX
iajs-3292	137	4	used	use	VERB
iajs-3292	137	5	in	in	ADP
iajs-3292	137	6	many	many	ADJ
iajs-3292	137	7	fields	field	NOUN
iajs-3292	137	8	of	of	ADP
iajs-3292	137	9	mathematics	mathematic	NOUN
iajs-3292	137	10	,	,	PUNCT
iajs-3292	137	11	which	which	PRON
iajs-3292	137	12	led	lead	VERB
iajs-3292	137	13	to	to	ADP
iajs-3292	137	14	the	the	DET
iajs-3292	137	15	discovery	discovery	NOUN
iajs-3292	137	16	of	of	ADP
iajs-3292	137	17	important	important	ADJ
iajs-3292	137	18	properties	property	NOUN
iajs-3292	137	19	for	for	ADP
iajs-3292	137	20	them	they	PRON
iajs-3292	137	21	,	,	PUNCT
iajs-3292	137	22	some	some	PRON
iajs-3292	137	23	of	of	ADP
iajs-3292	137	24	which	which	PRON
iajs-3292	137	25	we	we	PRON
iajs-3292	137	26	mention	mention	VERB
iajs-3292	137	27	below	below	ADV
iajs-3292	137	28	:	:	PUNCT
iajs-3292	137	29	i.	i.	NOUN
iajs-3292	137	30	𝑑𝐵𝑟𝑛(𝑥	𝑑𝐵𝑟𝑛(𝑥	PROPN
iajs-3292	137	31	)	)	PUNCT
iajs-3292	137	32	𝑑𝑥	𝑑𝑥	VERB
iajs-3292	137	33	=	=	PUNCT
iajs-3292	137	34	𝑛	𝑛	DET
iajs-3292	137	35	𝐵𝑟𝑛−1(𝑥	𝐵𝑟𝑛−1(𝑥	NUM
iajs-3292	137	36	)	)	PUNCT
iajs-3292	137	37	,	,	PUNCT
iajs-3292	138	1	𝑛	𝑛	PRON
iajs-3292	138	2	≥	≥	NOUN
iajs-3292	138	3	1	1	NUM
iajs-3292	138	4	.	.	X
iajs-3292	138	5	ii	ii	PROPN
iajs-3292	138	6	.	.	PUNCT
iajs-3292	139	1	∫	∫	PROPN
iajs-3292	139	2	𝐵𝑟𝑛(𝑥	𝐵𝑟𝑛(𝑥	PROPN
iajs-3292	139	3	)	)	PUNCT
iajs-3292	139	4	𝑑𝑥	𝑑𝑥	VERB
iajs-3292	139	5	=	=	SYM
iajs-3292	139	6	𝐵𝑟𝑛+1(𝑧)−𝐵𝑟𝑛+1(𝑎	𝐵𝑟𝑛+1(𝑧)−𝐵𝑟𝑛+1(𝑎	PROPN
iajs-3292	139	7	)	)	PUNCT
iajs-3292	140	1	𝑛+1	𝑛+1	ADP
iajs-3292	140	2	𝑧	𝑧	PROPN
iajs-3292	140	3	𝑎	𝑎	X
iajs-3292	140	4	.	.	PUNCT
iajs-3292	140	5	iii	iii	PROPN
iajs-3292	140	6	.	.	PUNCT
iajs-3292	140	7	∫	∫	PROPN
iajs-3292	140	8	𝐵𝑟𝑛(𝑥	𝐵𝑟𝑛(𝑥	PROPN
iajs-3292	140	9	)	)	PUNCT
iajs-3292	140	10	𝑑𝑥	𝑑𝑥	VERB
iajs-3292	140	11	=	=	SYM
iajs-3292	140	12	0	0	NUM
iajs-3292	140	13	,	,	PUNCT
iajs-3292	140	14	1	1	NUM
iajs-3292	140	15	0	0	NUM
iajs-3292	140	16	𝑛	𝑛	PRON
iajs-3292	140	17	≥	≥	NUM
iajs-3292	140	18	1	1	NUM
iajs-3292	140	19	.	.	NUM
iajs-3292	140	20	iv	iv	PROPN
iajs-3292	140	21	.	.	PUNCT
iajs-3292	140	22	∫	∫	PROPN
iajs-3292	140	23	𝐵𝑟𝑛(𝑥	𝐵𝑟𝑛(𝑥	PROPN
iajs-3292	140	24	)	)	PUNCT
iajs-3292	140	25	𝐵𝑟𝑚(𝑥	𝐵𝑟𝑚(𝑥	NOUN
iajs-3292	140	26	)	)	PUNCT
iajs-3292	140	27	𝑑𝑥	𝑑𝑥	ADP
iajs-3292	140	28	=	=	SYM
iajs-3292	140	29	(	(	PUNCT
iajs-3292	140	30	−1	−1	NOUN
iajs-3292	140	31	)	)	PUNCT
iajs-3292	140	32	𝑛−11	𝑛−11	X
iajs-3292	140	33	0	0	NUM
iajs-3292	140	34	𝑛	𝑛	NOUN
iajs-3292	140	35	!	!	PUNCT
iajs-3292	141	1	𝑚	𝑚	X
iajs-3292	141	2	!	!	PUNCT
iajs-3292	141	3	(	(	PUNCT
iajs-3292	141	4	𝑛+𝑚	𝑛+𝑚	ADJ
iajs-3292	141	5	)	)	PUNCT
iajs-3292	141	6	!	!	PUNCT
iajs-3292	142	1	𝐵𝑟𝑛+𝑚.	𝐵𝑟𝑛+𝑚.	PROPN
iajs-3292	143	1	v.	v.	ADP
iajs-3292	143	2	𝐵𝑟𝑛(1	𝐵𝑟𝑛(1	NUM
iajs-3292	143	3	−	−	PROPN
iajs-3292	143	4	𝑥	𝑥	NOUN
iajs-3292	143	5	)	)	PUNCT
iajs-3292	143	6	=	=	SYM
iajs-3292	143	7	(	(	PUNCT
iajs-3292	143	8	−1	−1	NOUN
iajs-3292	143	9	)	)	PUNCT
iajs-3292	143	10	𝑛𝐵𝑟𝑛(𝑥	𝑛𝐵𝑟𝑛(𝑥	NUM
iajs-3292	143	11	)	)	PUNCT
iajs-3292	143	12	.	.	PUNCT
iajs-3292	144	1	vi	vi	X
iajs-3292	144	2	.	.	PUNCT
iajs-3292	145	1	𝐵𝑟(𝑥	𝐵𝑟(𝑥	NOUN
iajs-3292	145	2	+	+	CCONJ
iajs-3292	145	3	1)−𝐵𝑟𝑛(𝑥	1)−𝐵𝑟𝑛(𝑥	NUM
iajs-3292	145	4	)	)	PUNCT
iajs-3292	146	1	=	=	SYM
iajs-3292	147	1	𝑛	𝑛	DET
iajs-3292	147	2	𝑥	𝑥	PRON
iajs-3292	147	3	𝑛−1	𝑛−1	PROPN
iajs-3292	147	4	.	.	PUNCT
iajs-3292	147	5	ihjpas	ihjpas	PROPN
iajs-3292	147	6	.	.	PUNCT
iajs-3292	148	1	37	37	NUM
iajs-3292	148	2	(	(	PUNCT
iajs-3292	148	3	1	1	NUM
iajs-3292	148	4	)	)	PUNCT
iajs-3292	148	5	2024	2024	NUM
iajs-3292	148	6	363	363	NUM
iajs-3292	148	7	therefore	therefore	ADV
iajs-3292	148	8	,	,	PUNCT
iajs-3292	148	9	it	it	PRON
iajs-3292	148	10	is	be	AUX
iajs-3292	148	11	now	now	ADV
iajs-3292	148	12	easy	easy	ADJ
iajs-3292	148	13	to	to	PART
iajs-3292	148	14	express	express	VERB
iajs-3292	148	15	any	any	DET
iajs-3292	148	16	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	148	17	)	)	PUNCT
iajs-3292	148	18	∈	∈	PROPN
iajs-3292	148	19	𝐿2[0,1	𝐿2[0,1	NOUN
iajs-3292	148	20	]	]	PUNCT
iajs-3292	148	21	by	by	ADP
iajs-3292	148	22	the	the	DET
iajs-3292	148	23	linear	linear	ADJ
iajs-3292	148	24	combination	combination	NOUN
iajs-3292	148	25	of	of	ADP
iajs-3292	148	26	the	the	DET
iajs-3292	148	27	bernoulli	bernoulli	NOUN
iajs-3292	148	28	polynomial	polynomial	ADJ
iajs-3292	148	29	as	as	ADP
iajs-3292	148	30	:	:	PUNCT
iajs-3292	148	31	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	148	32	)	)	PUNCT
iajs-3292	149	1	=	=	PUNCT
iajs-3292	149	2	∑	∑	PUNCT
iajs-3292	149	3	𝑐𝑖	𝑐𝑖	NOUN
iajs-3292	149	4	𝑛	𝑛	DET
iajs-3292	149	5	𝑖=0	𝑖=0	PROPN
iajs-3292	149	6	𝐵𝑟𝑖(𝑥	𝐵𝑟𝑖(𝑥	PROPN
iajs-3292	149	7	)	)	PUNCT
iajs-3292	149	8	=	=	SYM
iajs-3292	149	9	𝐶	𝐶	PROPN
iajs-3292	149	10	𝑇	𝑇	PROPN
iajs-3292	149	11	𝐵𝑟(𝑥	𝐵𝑟(𝑥	NOUN
iajs-3292	149	12	)	)	PUNCT
iajs-3292	149	13	,	,	PUNCT
iajs-3292	149	14	(	(	PUNCT
iajs-3292	149	15	23	23	NUM
iajs-3292	149	16	)	)	PUNCT
iajs-3292	149	17	where	where	SCONJ
iajs-3292	149	18	𝐶𝑇	𝐶𝑇	PROPN
iajs-3292	149	19	=	=	PUNCT
iajs-3292	150	1	[	[	X
iajs-3292	150	2	𝑐0	𝑐0	NOUN
iajs-3292	150	3	,	,	PUNCT
iajs-3292	150	4	𝑐1	𝑐1	NOUN
iajs-3292	150	5	,	,	PUNCT
iajs-3292	150	6	…	…	PUNCT
iajs-3292	150	7	,	,	PUNCT
iajs-3292	150	8	𝑐𝑛	𝑐𝑛	ADP
iajs-3292	150	9	]	]	PUNCT
iajs-3292	150	10	,	,	PUNCT
iajs-3292	150	11	and	and	CCONJ
iajs-3292	150	12	𝐵𝑟(𝑥	𝐵𝑟(𝑥	NOUN
iajs-3292	150	13	)	)	PUNCT
iajs-3292	150	14	=	=	NOUN
iajs-3292	150	15	[	[	PUNCT
iajs-3292	150	16	𝐵𝑟0(𝑥	𝐵𝑟0(𝑥	NUM
iajs-3292	150	17	)	)	PUNCT
iajs-3292	150	18	,	,	PUNCT
iajs-3292	150	19	𝐵𝑟1(𝑥	𝐵𝑟1(𝑥	NOUN
iajs-3292	150	20	)	)	PUNCT
iajs-3292	150	21	,	,	PUNCT
iajs-3292	150	22	.	.	PUNCT
iajs-3292	150	23	.	.	PUNCT
iajs-3292	151	1	.	.	PUNCT
iajs-3292	152	1	,	,	PUNCT
iajs-3292	152	2	𝐵𝑟𝑛(𝑥	𝐵𝑟𝑛(𝑥	PROPN
iajs-3292	152	3	)	)	PUNCT
iajs-3292	152	4	]	]	PUNCT
iajs-3292	153	1	𝑇.	𝑇.	PROPN
iajs-3292	153	2	for	for	ADP
iajs-3292	153	3	all	all	PRON
iajs-3292	153	4	𝑖	𝑖	NOUN
iajs-3292	153	5	=	=	SYM
iajs-3292	153	6	0,1	0,1	NUM
iajs-3292	153	7	,	,	PUNCT
iajs-3292	153	8	…	…	PUNCT
iajs-3292	153	9	,	,	PUNCT
iajs-3292	153	10	𝑛	𝑛	PROPN
iajs-3292	153	11	,	,	PUNCT
iajs-3292	153	12	the	the	DET
iajs-3292	153	13	matrix	matrix	NOUN
iajs-3292	153	14	form	form	NOUN
iajs-3292	153	15	of	of	ADP
iajs-3292	153	16	𝐵𝑟𝑖(𝑥	𝐵𝑟𝑖(𝑥	PROPN
iajs-3292	153	17	)	)	PUNCT
iajs-3292	153	18	can	can	AUX
iajs-3292	153	19	be	be	AUX
iajs-3292	153	20	obtained	obtain	VERB
iajs-3292	153	21	as	as	ADP
iajs-3292	153	22	follows	follow	VERB
iajs-3292	153	23	:	:	PUNCT
iajs-3292	153	24	𝐵𝑟𝑖(𝑥	𝐵𝑟𝑖(𝑥	ADJ
iajs-3292	153	25	)	)	PUNCT
iajs-3292	153	26	=	=	NOUN
iajs-3292	153	27	∑	∑	PROPN
iajs-3292	153	28	(	(	PUNCT
iajs-3292	153	29	𝑖	𝑖	NOUN
iajs-3292	153	30	𝑗	𝑗	NOUN
iajs-3292	153	31	)	)	PUNCT
iajs-3292	153	32	𝐵𝑟𝑗	𝐵𝑟𝑗	NOUN
iajs-3292	153	33	𝑥	𝑥	NOUN
iajs-3292	153	34	𝑖−𝑗	𝑖−𝑗	PUNCT
iajs-3292	153	35	𝑖	𝑖	SYM
iajs-3292	154	1	𝑗=0	𝑗=0	NOUN
iajs-3292	154	2	,	,	PUNCT
iajs-3292	154	3	=	=	PUNCT
iajs-3292	154	4	(	(	PUNCT
iajs-3292	154	5	𝑖	𝑖	SYM
iajs-3292	154	6	𝑖	𝑖	NOUN
iajs-3292	154	7	)	)	PUNCT
iajs-3292	155	1	𝐵𝑟𝑖	𝐵𝑟𝑖	PROPN
iajs-3292	155	2	𝑥	𝑥	NOUN
iajs-3292	155	3	0	0	PUNCT
iajs-3292	156	1	+	+	CCONJ
iajs-3292	156	2	(	(	PUNCT
iajs-3292	156	3	𝑖	𝑖	SYM
iajs-3292	156	4	𝑖	𝑖	NOUN
iajs-3292	156	5	−	−	PROPN
iajs-3292	156	6	1	1	NUM
iajs-3292	156	7	)	)	PUNCT
iajs-3292	156	8	𝐵𝑟𝑖−1	𝐵𝑟𝑖−1	NOUN
iajs-3292	156	9	𝑥	𝑥	PROPN
iajs-3292	157	1	+	+	NUM
iajs-3292	157	2	⋯+	⋯+	NOUN
iajs-3292	157	3	(	(	PUNCT
iajs-3292	157	4	𝑖	𝑖	SYM
iajs-3292	157	5	1	1	NUM
iajs-3292	157	6	)	)	PUNCT
iajs-3292	157	7	𝐵𝑟1	𝐵𝑟1	NOUN
iajs-3292	158	1	𝑥	𝑥	X
iajs-3292	158	2	𝑖−1	𝑖−1	PROPN
iajs-3292	159	1	+	+	CCONJ
iajs-3292	159	2	(	(	PUNCT
iajs-3292	159	3	𝑖	𝑖	SYM
iajs-3292	159	4	0	0	NUM
iajs-3292	159	5	)	)	PUNCT
iajs-3292	159	6	𝐵𝑟0	𝐵𝑟0	NOUN
iajs-3292	160	1	𝑥	𝑥	NOUN
iajs-3292	160	2	𝑖	𝑖	X
iajs-3292	160	3	,	,	PUNCT
iajs-3292	160	4	=	=	PUNCT
iajs-3292	161	1	[	[	X
iajs-3292	161	2	(	(	PUNCT
iajs-3292	161	3	𝑖	𝑖	SYM
iajs-3292	161	4	𝑖	𝑖	NOUN
iajs-3292	161	5	)	)	PUNCT
iajs-3292	161	6	𝐵𝑟𝑖	𝐵𝑟𝑖	PROPN
iajs-3292	161	7	(	(	PUNCT
iajs-3292	161	8	𝑖	𝑖	SYM
iajs-3292	161	9	𝑖	𝑖	SYM
iajs-3292	161	10	−	−	PROPN
iajs-3292	161	11	1	1	NUM
iajs-3292	161	12	)	)	PUNCT
iajs-3292	161	13	𝐵𝑟𝑖−1	𝐵𝑟𝑖−1	PROPN
iajs-3292	161	14	⋯	⋯	PROPN
iajs-3292	161	15	(	(	PUNCT
iajs-3292	161	16	𝑖	𝑖	NOUN
iajs-3292	161	17	1	1	NUM
iajs-3292	161	18	)	)	PUNCT
iajs-3292	161	19	𝐵𝑟1	𝐵𝑟1	NOUN
iajs-3292	161	20	(	(	PUNCT
iajs-3292	161	21	𝑖	𝑖	NOUN
iajs-3292	161	22	0	0	NUM
iajs-3292	161	23	)	)	PUNCT
iajs-3292	161	24	𝐵𝑟0	𝐵𝑟0	NOUN
iajs-3292	161	25	0	0	NUM
iajs-3292	161	26	0	0	NUM
iajs-3292	161	27	.	.	PUNCT
iajs-3292	161	28	.	.	PUNCT
iajs-3292	161	29	.	.	PUNCT
iajs-3292	162	1	0⏞	0⏞	VERB
iajs-3292	162	2	𝑛−𝑖	𝑛−𝑖	NOUN
iajs-3292	162	3	]	]	PUNCT
iajs-3292	162	4	[	[	PUNCT
iajs-3292	162	5	1	1	NUM
iajs-3292	162	6	…	…	SYM
iajs-3292	162	7	⋮	⋮	NOUN
iajs-3292	162	8	𝑥𝑖	𝑥𝑖	PRON
iajs-3292	162	9	𝑥𝑖+1	𝑥𝑖+1	PROPN
iajs-3292	162	10	⋮	⋮	NOUN
iajs-3292	162	11	𝑥𝑛	𝑥𝑛	PROPN
iajs-3292	162	12	]	]	PUNCT
iajs-3292	162	13	,	,	PUNCT
iajs-3292	162	14	=	=	PUNCT
iajs-3292	162	15	𝑀𝑖	𝑀𝑖	PROPN
iajs-3292	162	16	𝐻(𝑥	𝐻(𝑥	NUM
iajs-3292	162	17	)	)	PUNCT
iajs-3292	162	18	.	.	PUNCT
iajs-3292	163	1	(	(	PUNCT
iajs-3292	163	2	24	24	NUM
iajs-3292	163	3	)	)	PUNCT
iajs-3292	163	4	where	where	SCONJ
iajs-3292	163	5	𝐻(𝑥	𝐻(𝑥	VERB
iajs-3292	163	6	)	)	PUNCT
iajs-3292	163	7	=	=	PUNCT
iajs-3292	164	1	[	[	X
iajs-3292	164	2	1	1	NUM
iajs-3292	164	3	,	,	PUNCT
iajs-3292	164	4	𝑥	𝑥	NOUN
iajs-3292	164	5	,	,	PUNCT
iajs-3292	164	6	.	.	PUNCT
iajs-3292	164	7	.	.	PUNCT
iajs-3292	165	1	.	.	PUNCT
iajs-3292	166	1	,	,	PUNCT
iajs-3292	166	2	𝑥𝑛]𝑇and	𝑥𝑛]𝑇and	PROPN
iajs-3292	167	1	𝑀𝑖	𝑀𝑖	PROPN
iajs-3292	167	2	=	=	PUNCT
iajs-3292	168	1	[	[	X
iajs-3292	168	2	(	(	PUNCT
iajs-3292	168	3	𝑖	𝑖	NOUN
iajs-3292	168	4	𝑖	𝑖	NOUN
iajs-3292	168	5	)	)	PUNCT
iajs-3292	168	6	𝐵𝑟𝑖	𝐵𝑟𝑖	PROPN
iajs-3292	168	7	(	(	PUNCT
iajs-3292	168	8	𝑖	𝑖	NOUN
iajs-3292	168	9	𝑖−1	𝑖−1	PROPN
iajs-3292	168	10	)	)	PUNCT
iajs-3292	168	11	𝐵𝑟𝑖−1	𝐵𝑟𝑖−1	PROPN
iajs-3292	168	12	⋯	⋯	PROPN
iajs-3292	168	13	(	(	PUNCT
iajs-3292	168	14	𝑖	𝑖	NOUN
iajs-3292	168	15	1	1	NUM
iajs-3292	168	16	)	)	PUNCT
iajs-3292	168	17	𝐵𝑟1	𝐵𝑟1	NOUN
iajs-3292	168	18	(	(	PUNCT
iajs-3292	168	19	𝑖	𝑖	NOUN
iajs-3292	168	20	0	0	NUM
iajs-3292	168	21	)	)	PUNCT
iajs-3292	168	22	𝐵𝑟0	𝐵𝑟0	NOUN
iajs-3292	168	23	0	0	NUM
iajs-3292	168	24	0	0	NUM
iajs-3292	168	25	.	.	PUNCT
iajs-3292	168	26	.	.	PUNCT
iajs-3292	168	27	.	.	PUNCT
iajs-3292	169	1	0⏞	0⏞	VERB
iajs-3292	169	2	𝑛−𝑖	𝑛−𝑖	NOUN
iajs-3292	169	3	]	]	PUNCT
iajs-3292	169	4	.	.	PUNCT
iajs-3292	170	1	as	as	ADP
iajs-3292	170	2	a	a	DET
iajs-3292	170	3	result	result	NOUN
iajs-3292	170	4	,	,	PUNCT
iajs-3292	170	5	𝐵𝑟(𝑥	𝐵𝑟(𝑥	NOUN
iajs-3292	170	6	)	)	PUNCT
iajs-3292	170	7	in	in	ADP
iajs-3292	170	8	eq.(23	eq.(23	NOUN
iajs-3292	170	9	)	)	PUNCT
iajs-3292	170	10	can	can	AUX
iajs-3292	170	11	be	be	AUX
iajs-3292	170	12	written	write	VERB
iajs-3292	170	13	as	as	SCONJ
iajs-3292	170	14	follows	follow	VERB
iajs-3292	170	15	:	:	PUNCT
iajs-3292	170	16	𝐵𝑟(𝑥	𝐵𝑟(𝑥	VERB
iajs-3292	170	17	)	)	PUNCT
iajs-3292	170	18	=	=	PUNCT
iajs-3292	171	1	[	[	X
iajs-3292	171	2	𝐵𝑟0(𝑥	𝐵𝑟0(𝑥	NUM
iajs-3292	171	3	)	)	PUNCT
iajs-3292	171	4	,	,	PUNCT
iajs-3292	171	5	𝐵𝑟1(𝑥	𝐵𝑟1(𝑥	NOUN
iajs-3292	171	6	)	)	PUNCT
iajs-3292	171	7	,	,	PUNCT
iajs-3292	171	8	…	…	PUNCT
iajs-3292	171	9	,	,	PUNCT
iajs-3292	171	10	𝐵𝑟𝑛(𝑥	𝐵𝑟𝑛(𝑥	PROPN
iajs-3292	171	11	)	)	PUNCT
iajs-3292	171	12	]	]	PUNCT
iajs-3292	171	13	𝑇	𝑇	PROPN
iajs-3292	171	14	,	,	PUNCT
iajs-3292	171	15	=	=	PUNCT
iajs-3292	172	1	[	[	X
iajs-3292	172	2	𝑀0𝐻(𝑥),𝑀1𝐻(𝑥	𝑀0𝐻(𝑥),𝑀1𝐻(𝑥	NOUN
iajs-3292	172	3	)	)	PUNCT
iajs-3292	172	4	,	,	PUNCT
iajs-3292	172	5	…	…	PUNCT
iajs-3292	172	6	,	,	PUNCT
iajs-3292	172	7	𝑀𝑛𝐻(𝑥	𝑀𝑛𝐻(𝑥	PROPN
iajs-3292	172	8	)	)	PUNCT
iajs-3292	172	9	]	]	PUNCT
iajs-3292	172	10	𝑇	𝑇	PROPN
iajs-3292	172	11	,	,	PUNCT
iajs-3292	172	12	=	=	PUNCT
iajs-3292	173	1	[	[	X
iajs-3292	173	2	𝑀0	𝑀0	PROPN
iajs-3292	173	3	,	,	PUNCT
iajs-3292	173	4	𝑀1	𝑀1	PROPN
iajs-3292	173	5	,	,	PUNCT
iajs-3292	173	6	…	…	PUNCT
iajs-3292	173	7	,	,	PUNCT
iajs-3292	173	8	𝑀𝑛	𝑀𝑛	PROPN
iajs-3292	173	9	]	]	PUNCT
iajs-3292	173	10	𝑇𝐻(𝑥	𝑇𝐻(𝑥	PROPN
iajs-3292	173	11	)	)	PUNCT
iajs-3292	173	12	,	,	PUNCT
iajs-3292	173	13	=	=	PUNCT
iajs-3292	173	14	[	[	PUNCT
iajs-3292	173	15	(	(	PUNCT
iajs-3292	173	16	0	0	NUM
iajs-3292	173	17	0	0	NUM
iajs-3292	173	18	)	)	PUNCT
iajs-3292	173	19	𝐵𝑟0	𝐵𝑟0	NOUN
iajs-3292	173	20	0	0	NUM
iajs-3292	173	21	0	0	SYM
iajs-3292	174	1	⋯	⋯	NOUN
iajs-3292	174	2	0	0	NUM
iajs-3292	174	3	(	(	PUNCT
iajs-3292	174	4	1	1	NUM
iajs-3292	174	5	1	1	NUM
iajs-3292	174	6	)	)	PUNCT
iajs-3292	174	7	𝐵𝑟1	𝐵𝑟1	NOUN
iajs-3292	174	8	(	(	PUNCT
iajs-3292	174	9	1	1	NUM
iajs-3292	174	10	0	0	NUM
iajs-3292	174	11	)	)	PUNCT
iajs-3292	174	12	𝐵𝑟0	𝐵𝑟0	NOUN
iajs-3292	174	13	0	0	NUM
iajs-3292	175	1	⋯	⋯	NOUN
iajs-3292	175	2	0	0	NUM
iajs-3292	175	3	⋮	⋮	NOUN
iajs-3292	175	4	(	(	PUNCT
iajs-3292	175	5	𝑛	𝑛	DET
iajs-3292	175	6	𝑛	𝑛	ADJ
iajs-3292	175	7	)	)	PUNCT
iajs-3292	175	8	𝐵𝑟𝑛	𝐵𝑟𝑛	NOUN
iajs-3292	175	9	⋮	⋮	NOUN
iajs-3292	175	10	(	(	PUNCT
iajs-3292	175	11	𝑛	𝑛	PROPN
iajs-3292	175	12	𝑛−1	𝑛−1	PROPN
iajs-3292	175	13	)	)	PUNCT
iajs-3292	175	14	𝐵𝑟𝑛−1	𝐵𝑟𝑛−1	PROPN
iajs-3292	175	15	⋮	⋮	NOUN
iajs-3292	175	16	(	(	PUNCT
iajs-3292	175	17	𝑛	𝑛	DET
iajs-3292	175	18	𝑛−2	𝑛−2	PROPN
iajs-3292	175	19	)	)	PUNCT
iajs-3292	175	20	𝐵𝑟𝑛−2	𝐵𝑟𝑛−2	PROPN
iajs-3292	175	21	⋯	⋯	NOUN
iajs-3292	175	22	⋯	⋯	NOUN
iajs-3292	175	23	⋮	⋮	NOUN
iajs-3292	175	24	(	(	PUNCT
iajs-3292	175	25	𝑛	𝑛	PROPN
iajs-3292	175	26	0	0	NUM
iajs-3292	175	27	)	)	PUNCT
iajs-3292	175	28	𝐵𝑟0	𝐵𝑟0	X
iajs-3292	175	29	]	]	PUNCT
iajs-3292	176	1	𝐻(𝑥	𝐻(𝑥	NUM
iajs-3292	176	2	)	)	PUNCT
iajs-3292	176	3	,	,	PUNCT
iajs-3292	176	4	=	=	SYM
iajs-3292	176	5	𝑀	𝑀	PROPN
iajs-3292	176	6	𝐻(𝑥	𝐻(𝑥	PROPN
iajs-3292	176	7	)	)	PUNCT
iajs-3292	176	8	.	.	PUNCT
iajs-3292	177	1	(	(	PUNCT
iajs-3292	177	2	25	25	NUM
iajs-3292	177	3	)	)	PUNCT
iajs-3292	177	4	while	while	SCONJ
iajs-3292	177	5	the	the	DET
iajs-3292	177	6	derivative	derivative	NOUN
iajs-3292	177	7	of	of	ADP
iajs-3292	177	8	it	it	PRON
iajs-3292	177	9	will	will	AUX
iajs-3292	177	10	be	be	AUX
iajs-3292	177	11	:	:	PUNCT
iajs-3292	177	12	𝑑𝐵𝑟(𝑥	𝑑𝐵𝑟(𝑥	NOUN
iajs-3292	177	13	)	)	PUNCT
iajs-3292	177	14	𝑑𝑥	𝑑𝑥	VERB
iajs-3292	177	15	=	=	VERB
iajs-3292	177	16	𝐷𝐵𝑟	𝐷𝐵𝑟	NOUN
iajs-3292	177	17	𝐵𝑟(𝑥	𝐵𝑟(𝑥	NOUN
iajs-3292	177	18	)	)	PUNCT
iajs-3292	177	19	,	,	PUNCT
iajs-3292	177	20	(	(	PUNCT
iajs-3292	177	21	26	26	NUM
iajs-3292	177	22	)	)	PUNCT
iajs-3292	177	23	where	where	SCONJ
iajs-3292	177	24	𝐷𝐵𝑟	𝐷𝐵𝑟	NOUN
iajs-3292	177	25	=	=	PUNCT
iajs-3292	178	1	[	[	PUNCT
iajs-3292	178	2	0	0	NUM
iajs-3292	178	3	0	0	NUM
iajs-3292	178	4	0	0	NUM
iajs-3292	178	5	.	.	PUNCT
iajs-3292	178	6	.	.	PUNCT
iajs-3292	178	7	.	.	PUNCT
iajs-3292	179	1	0	0	NUM
iajs-3292	180	1	0	0	NUM
iajs-3292	180	2	1	1	NUM
iajs-3292	180	3	0	0	NUM
iajs-3292	180	4	0	0	NUM
iajs-3292	180	5	.	.	PUNCT
iajs-3292	180	6	.	.	PUNCT
iajs-3292	180	7	.	.	PUNCT
iajs-3292	181	1	0	0	NUM
iajs-3292	181	2	0	0	NUM
iajs-3292	181	3	0	0	NUM
iajs-3292	181	4	⋮	⋮	NOUN
iajs-3292	181	5	0	0	NUM
iajs-3292	181	6	2	2	NUM
iajs-3292	181	7	⋮	⋮	NOUN
iajs-3292	181	8	0	0	NUM
iajs-3292	181	9	0	0	NUM
iajs-3292	181	10	⋮	⋮	NOUN
iajs-3292	181	11	0	0	NUM
iajs-3292	181	12	⋯	⋯	NOUN
iajs-3292	181	13	⋱	⋱	PUNCT
iajs-3292	181	14	.	.	PUNCT
iajs-3292	181	15	.	.	PUNCT
iajs-3292	181	16	.	.	PUNCT
iajs-3292	182	1	0	0	NUM
iajs-3292	182	2	0	0	NUM
iajs-3292	182	3	⋮	⋮	NOUN
iajs-3292	182	4	⋮	⋮	NOUN
iajs-3292	182	5	𝑛	𝑛	PROPN
iajs-3292	182	6	0	0	NUM
iajs-3292	182	7	]	]	PUNCT
iajs-3292	182	8	is	be	AUX
iajs-3292	182	9	the	the	DET
iajs-3292	182	10	(	(	PUNCT
iajs-3292	182	11	𝑛	𝑛	PROPN
iajs-3292	182	12	+	+	NOUN
iajs-3292	182	13	1	1	NUM
iajs-3292	182	14	)	)	PUNCT
iajs-3292	182	15	×	×	NOUN
iajs-3292	182	16	(	(	PUNCT
iajs-3292	182	17	𝑛	𝑛	PROPN
iajs-3292	182	18	+	+	NOUN
iajs-3292	182	19	1	1	X
iajs-3292	182	20	)	)	PUNCT
iajs-3292	182	21	om	om	PROPN
iajs-3292	182	22	.	.	PUNCT
iajs-3292	182	23	ihjpas	ihjpas	PROPN
iajs-3292	182	24	.	.	PUNCT
iajs-3292	183	1	37	37	NUM
iajs-3292	183	2	(	(	PUNCT
iajs-3292	183	3	1	1	NUM
iajs-3292	183	4	)	)	PUNCT
iajs-3292	183	5	2024	2024	NUM
iajs-3292	183	6	364	364	NUM
iajs-3292	183	7	moreover	moreover	ADV
iajs-3292	183	8	,	,	PUNCT
iajs-3292	183	9	the	the	DET
iajs-3292	183	10	𝑛𝑡ℎderivative	𝑛𝑡ℎderivative	NOUN
iajs-3292	183	11	:	:	PUNCT
iajs-3292	183	12	𝑑𝑛𝐵𝑟(𝑥	𝑑𝑛𝐵𝑟(𝑥	NOUN
iajs-3292	183	13	)	)	PUNCT
iajs-3292	183	14	𝑑𝑥𝑛	𝑑𝑥𝑛	VERB
iajs-3292	183	15	=	=	PUNCT
iajs-3292	183	16	(	(	PUNCT
iajs-3292	183	17	𝐷𝐵𝑟	𝐷𝐵𝑟	PROPN
iajs-3292	183	18	)	)	PUNCT
iajs-3292	183	19	𝑛	𝑛	DET
iajs-3292	183	20	𝐵𝑟(𝑥	𝐵𝑟(𝑥	NOUN
iajs-3292	183	21	)	)	PUNCT
iajs-3292	183	22	.	.	PUNCT
iajs-3292	184	1	(	(	PUNCT
iajs-3292	184	2	27	27	NUM
iajs-3292	184	3	)	)	PUNCT
iajs-3292	184	4	to	to	PART
iajs-3292	184	5	complete	complete	VERB
iajs-3292	184	6	the	the	DET
iajs-3292	184	7	solution	solution	NOUN
iajs-3292	184	8	,	,	PUNCT
iajs-3292	184	9	we	we	PRON
iajs-3292	184	10	must	must	AUX
iajs-3292	184	11	find	find	VERB
iajs-3292	184	12	the	the	DET
iajs-3292	184	13	value	value	NOUN
iajs-3292	184	14	of	of	ADP
iajs-3292	184	15	the	the	DET
iajs-3292	184	16	vector	vector	NOUN
iajs-3292	184	17	𝐶𝑇	𝐶𝑇	PROPN
iajs-3292	184	18	in	in	ADP
iajs-3292	184	19	eq.(23	eq.(23	NOUN
iajs-3292	184	20	)	)	PUNCT
iajs-3292	184	21	,	,	PUNCT
iajs-3292	184	22	using	use	VERB
iajs-3292	184	23	the	the	DET
iajs-3292	184	24	same	same	ADJ
iajs-3292	184	25	procedures	procedure	NOUN
iajs-3292	184	26	as	as	ADP
iajs-3292	184	27	the	the	DET
iajs-3292	184	28	previous	previous	ADJ
iajs-3292	184	29	methods	method	NOUN
iajs-3292	184	30	.	.	PUNCT
iajs-3292	185	1	4	4	X
iajs-3292	185	2	.	.	X
iajs-3292	185	3	the	the	DET
iajs-3292	185	4	convergence	convergence	NOUN
iajs-3292	185	5	of	of	ADP
iajs-3292	185	6	the	the	DET
iajs-3292	185	7	proposed	propose	VERB
iajs-3292	185	8	methods	method	NOUN
iajs-3292	185	9	in	in	ADP
iajs-3292	185	10	this	this	DET
iajs-3292	185	11	section	section	NOUN
iajs-3292	185	12	,	,	PUNCT
iajs-3292	185	13	the	the	DET
iajs-3292	185	14	convergence	convergence	NOUN
iajs-3292	185	15	analysis	analysis	NOUN
iajs-3292	185	16	for	for	ADP
iajs-3292	185	17	the	the	DET
iajs-3292	185	18	proposed	propose	VERB
iajs-3292	185	19	methods	method	NOUN
iajs-3292	185	20	and	and	CCONJ
iajs-3292	185	21	fundamental	fundamental	ADJ
iajs-3292	185	22	theorem	theorem	NOUN
iajs-3292	185	23	are	be	AUX
iajs-3292	185	24	discussed	discuss	VERB
iajs-3292	185	25	.	.	PUNCT
iajs-3292	186	1	theorem	theorem	VERB
iajs-3292	186	2	4.1	4.1	NUM
iajs-3292	186	3	.	.	PUNCT
iajs-3292	187	1	let	let	VERB
iajs-3292	187	2	a	a	DET
iajs-3292	187	3	banach	banach	NOUN
iajs-3292	187	4	space	space	NOUN
iajs-3292	187	5	𝐴	𝐴	PROPN
iajs-3292	187	6	⊂	⊂	PROPN
iajs-3292	187	7	𝑅	𝑅	PROPN
iajs-3292	187	8	be	be	AUX
iajs-3292	187	9	given	give	VERB
iajs-3292	187	10	with	with	ADP
iajs-3292	187	11	a	a	DET
iajs-3292	187	12	norm	norm	NOUN
iajs-3292	187	13	‖	‖	ADJ
iajs-3292	187	14	‖	‖	PROPN
iajs-3292	187	15	defined	define	VERB
iajs-3292	187	16	on	on	ADP
iajs-3292	187	17	it	it	PRON
iajs-3292	187	18	.	.	PUNCT
iajs-3292	188	1	taking	take	VERB
iajs-3292	188	2	𝑓1(𝑥	𝑓1(𝑥	NOUN
iajs-3292	188	3	)	)	PUNCT
iajs-3292	188	4	as	as	ADP
iajs-3292	188	5	an	an	DET
iajs-3292	188	6	approximate	approximate	ADJ
iajs-3292	188	7	solution	solution	NOUN
iajs-3292	188	8	obtain	obtain	VERB
iajs-3292	188	9	from	from	ADP
iajs-3292	188	10	the	the	DET
iajs-3292	188	11	first	first	ADJ
iajs-3292	188	12	iteration	iteration	NOUN
iajs-3292	188	13	n	n	CCONJ
iajs-3292	188	14	,	,	PUNCT
iajs-3292	188	15	we	we	PRON
iajs-3292	188	16	construct	construct	VERB
iajs-3292	188	17	the	the	DET
iajs-3292	188	18	following	follow	VERB
iajs-3292	188	19	sequence	sequence	NOUN
iajs-3292	188	20	regarding	regard	VERB
iajs-3292	188	21	the	the	DET
iajs-3292	188	22	solution	solution	NOUN
iajs-3292	188	23	of	of	ADP
iajs-3292	188	24	eq.(1	eq.(1	ADJ
iajs-3292	188	25	):	):	PUNCT
iajs-3292	188	26	𝑣1(𝑥	𝑣1(𝑥	NUM
iajs-3292	188	27	)	)	PUNCT
iajs-3292	188	28	=	=	SYM
iajs-3292	188	29	𝑓1(𝑥	𝑓1(𝑥	NOUN
iajs-3292	188	30	)	)	PUNCT
iajs-3292	188	31	,	,	PUNCT
iajs-3292	188	32	𝑣𝑖(𝑥	𝑣𝑖(𝑥	PUNCT
iajs-3292	188	33	)	)	PUNCT
iajs-3292	188	34	=	=	SYM
iajs-3292	188	35	𝑓𝑖(𝑥	𝑓𝑖(𝑥	X
iajs-3292	188	36	)	)	PUNCT
iajs-3292	188	37	−	−	PROPN
iajs-3292	188	38	𝑓𝑖−1(𝑥	𝑓𝑖−1(𝑥	NOUN
iajs-3292	188	39	)	)	PUNCT
iajs-3292	188	40	,	,	PUNCT
iajs-3292	188	41	(	(	PUNCT
iajs-3292	188	42	𝑖	𝑖	X
iajs-3292	188	43	≥	≥	NOUN
iajs-3292	188	44	2	2	NUM
iajs-3292	188	45	)	)	PUNCT
iajs-3292	188	46	.	.	PUNCT
iajs-3292	189	1	then	then	ADV
iajs-3292	189	2	,	,	PUNCT
iajs-3292	189	3	the	the	DET
iajs-3292	189	4	assertions	assertion	NOUN
iajs-3292	189	5	are	be	AUX
iajs-3292	189	6	:	:	PUNCT
iajs-3292	189	7	(	(	PUNCT
iajs-3292	189	8	i	i	NOUN
iajs-3292	189	9	)	)	PUNCT
iajs-3292	189	10	provided	provide	VERB
iajs-3292	189	11	that	that	SCONJ
iajs-3292	189	12	for	for	ADP
iajs-3292	189	13	all	all	DET
iajs-3292	189	14	𝑖	𝑖	PRON
iajs-3292	189	15	there	there	PRON
iajs-3292	189	16	exist	exist	VERB
iajs-3292	189	17	0	0	NUM
iajs-3292	189	18	<	<	X
iajs-3292	189	19	𝛽𝑖	𝛽𝑖	VERB
iajs-3292	189	20	<	<	X
iajs-3292	189	21	1	1	NUM
iajs-3292	189	22	such	such	ADJ
iajs-3292	189	23	that	that	SCONJ
iajs-3292	189	24	‖𝑣𝑖+1(𝑥)‖	‖𝑣𝑖+1(𝑥)‖	PROPN
iajs-3292	189	25	≤	≤	NUM
iajs-3292	189	26	𝛽𝑖‖𝑣𝑖(𝑥)‖	𝛽𝑖‖𝑣𝑖(𝑥)‖	PROPN
iajs-3292	189	27	,	,	PUNCT
iajs-3292	189	28	the	the	DET
iajs-3292	189	29	series	series	NOUN
iajs-3292	189	30	∑	∑	PROPN
iajs-3292	189	31	𝑣𝑖(𝑥	𝑣𝑖(𝑥	PUNCT
iajs-3292	189	32	)	)	PUNCT
iajs-3292	189	33	∞	∞	PROPN
iajs-3292	190	1	𝑖=1	𝑖=1	PROPN
iajs-3292	190	2	is	be	AUX
iajs-3292	190	3	than	than	ADP
iajs-3292	190	4	convergent	convergent	ADJ
iajs-3292	190	5	and	and	CCONJ
iajs-3292	190	6	so	so	ADV
iajs-3292	190	7	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	190	8	)	)	PUNCT
iajs-3292	190	9	=	=	SYM
iajs-3292	190	10	∑	∑	PUNCT
iajs-3292	190	11	𝑣𝑖(𝑥	𝑣𝑖(𝑥	PUNCT
iajs-3292	190	12	)	)	PUNCT
iajs-3292	190	13	∞	∞	NUM
iajs-3292	191	1	𝑖=1	𝑖=1	PUNCT
iajs-3292	192	1	in	in	ADP
iajs-3292	192	2	the	the	DET
iajs-3292	192	3	interval	interval	NOUN
iajs-3292	192	4	of	of	ADP
iajs-3292	192	5	interest	interest	NOUN
iajs-3292	192	6	𝑥	𝑥	PRON
iajs-3292	192	7	∈	∈	PROPN
iajs-3292	192	8	γ	γ	X
iajs-3292	192	9	.	.	PROPN
iajs-3292	192	10	(	(	PUNCT
iajs-3292	192	11	ii	ii	NOUN
iajs-3292	192	12	)	)	PUNCT
iajs-3292	192	13	otherwise	otherwise	ADV
iajs-3292	192	14	,	,	PUNCT
iajs-3292	192	15	for	for	ADP
iajs-3292	192	16	all	all	DET
iajs-3292	192	17	𝑖	𝑖	SYM
iajs-3292	192	18	there	there	PRON
iajs-3292	192	19	exist	exist	VERB
iajs-3292	192	20	𝛽𝑖	𝛽𝑖	VERB
iajs-3292	192	21	>	>	X
iajs-3292	192	22	1	1	NUM
iajs-3292	192	23	leading	lead	VERB
iajs-3292	192	24	to	to	ADP
iajs-3292	192	25	‖𝑣𝑖+1(𝑥)‖	‖𝑣𝑖+1(𝑥)‖	PROPN
iajs-3292	192	26	≥	≥	PROPN
iajs-3292	192	27	𝛽𝑖‖𝑣𝑖(𝑥)‖	𝛽𝑖‖𝑣𝑖(𝑥)‖	PROPN
iajs-3292	192	28	,	,	PUNCT
iajs-3292	192	29	the	the	DET
iajs-3292	192	30	series	series	NOUN
iajs-3292	192	31	∑	∑	PROPN
iajs-3292	192	32	𝑣𝑖(𝑥	𝑣𝑖(𝑥	PUNCT
iajs-3292	192	33	)	)	PUNCT
iajs-3292	193	1	∞	∞	NUM
iajs-3292	193	2	𝑖=1	𝑖=1	PUNCT
iajs-3292	193	3	and	and	CCONJ
iajs-3292	193	4	thus	thus	ADV
iajs-3292	193	5	,	,	PUNCT
iajs-3292	193	6	the	the	DET
iajs-3292	193	7	proposed	propose	VERB
iajs-3292	193	8	method	method	NOUN
iajs-3292	193	9	diverges	diverge	VERB
iajs-3292	193	10	in	in	ADP
iajs-3292	193	11	the	the	DET
iajs-3292	193	12	interval	interval	NOUN
iajs-3292	193	13	of	of	ADP
iajs-3292	193	14	interest	interest	NOUN
iajs-3292	193	15	𝑥	𝑥	PRON
iajs-3292	193	16	∈	∈	PROPN
iajs-3292	193	17	γ	γ	X
iajs-3292	193	18	.	.	PUNCT
iajs-3292	193	19	proof	proof	NOUN
iajs-3292	193	20	:	:	PUNCT
iajs-3292	193	21	see	see	VERB
iajs-3292	193	22	[	[	X
iajs-3292	193	23	30	30	NUM
iajs-3292	193	24	]	]	PUNCT
iajs-3292	193	25	.	.	PUNCT
iajs-3292	194	1	remark	remark	PROPN
iajs-3292	194	2	1	1	NUM
iajs-3292	194	3	.	.	PUNCT
iajs-3292	195	1	defining	define	VERB
iajs-3292	195	2	a	a	DET
iajs-3292	195	3	ratio	ratio	NOUN
iajs-3292	195	4	𝛽𝑖	𝛽𝑖	NOUN
iajs-3292	195	5	via	via	ADP
iajs-3292	195	6	:	:	PUNCT
iajs-3292	195	7	𝛽𝑖	𝛽𝑖	ADJ
iajs-3292	195	8	=	=	PUNCT
iajs-3292	195	9	‖𝑣𝑖+1(𝑥)‖	‖𝑣𝑖+1(𝑥)‖	PROPN
iajs-3292	195	10	‖𝑣𝑖(𝑥)‖	‖𝑣𝑖(𝑥)‖	PROPN
iajs-3292	195	11	,	,	PUNCT
iajs-3292	195	12	(	(	PUNCT
iajs-3292	195	13	28	28	NUM
iajs-3292	195	14	)	)	PUNCT
iajs-3292	195	15	if	if	SCONJ
iajs-3292	195	16	this	this	DET
iajs-3292	195	17	ratio	ratio	NOUN
iajs-3292	195	18	stays	stay	VERB
iajs-3292	195	19	less	less	ADJ
iajs-3292	195	20	than	than	ADP
iajs-3292	195	21	one	one	NUM
iajs-3292	195	22	for	for	ADP
iajs-3292	195	23	all	all	DET
iajs-3292	195	24	𝑖	𝑖	ADP
iajs-3292	195	25	,	,	PUNCT
iajs-3292	195	26	the	the	DET
iajs-3292	195	27	approximate	approximate	ADJ
iajs-3292	195	28	solution	solution	NOUN
iajs-3292	195	29	converges	converge	VERB
iajs-3292	195	30	to	to	ADP
iajs-3292	195	31	the	the	DET
iajs-3292	195	32	exact	exact	ADJ
iajs-3292	195	33	solution	solution	NOUN
iajs-3292	195	34	.	.	PUNCT
iajs-3292	196	1	5	5	X
iajs-3292	196	2	.	.	X
iajs-3292	196	3	numerical	numerical	ADJ
iajs-3292	196	4	results	result	NOUN
iajs-3292	196	5	and	and	CCONJ
iajs-3292	196	6	discussions	discussion	NOUN
iajs-3292	196	7	in	in	ADP
iajs-3292	196	8	this	this	DET
iajs-3292	196	9	section	section	NOUN
iajs-3292	196	10	,	,	PUNCT
iajs-3292	196	11	the	the	DET
iajs-3292	196	12	methods	method	NOUN
iajs-3292	196	13	presented	present	VERB
iajs-3292	196	14	in	in	ADP
iajs-3292	196	15	section	section	NOUN
iajs-3292	196	16	three	three	NUM
iajs-3292	196	17	:	:	PUNCT
iajs-3292	196	18	the	the	DET
iajs-3292	196	19	bom	bom	NOUN
iajs-3292	196	20	,	,	PUNCT
iajs-3292	196	21	the	the	DET
iajs-3292	196	22	shifted	shift	VERB
iajs-3292	196	23	lom	lom	NOUN
iajs-3292	196	24	,	,	PUNCT
iajs-3292	196	25	and	and	CCONJ
iajs-3292	196	26	the	the	DET
iajs-3292	196	27	brom	brom	NOUN
iajs-3292	196	28	are	be	AUX
iajs-3292	196	29	applied	apply	VERB
iajs-3292	196	30	to	to	PART
iajs-3292	196	31	solve	solve	VERB
iajs-3292	196	32	the	the	DET
iajs-3292	196	33	nonlinear	nonlinear	ADJ
iajs-3292	196	34	blasius	blasius	ADJ
iajs-3292	196	35	equation	equation	NOUN
iajs-3292	196	36	.	.	PUNCT
iajs-3292	197	1	however	however	ADV
iajs-3292	197	2	,	,	PUNCT
iajs-3292	197	3	first	first	ADV
iajs-3292	197	4	,	,	PUNCT
iajs-3292	197	5	the	the	DET
iajs-3292	197	6	boundary	boundary	ADJ
iajs-3292	197	7	conditions	condition	NOUN
iajs-3292	197	8	must	must	AUX
iajs-3292	197	9	be	be	AUX
iajs-3292	197	10	converted	convert	VERB
iajs-3292	197	11	to	to	ADP
iajs-3292	197	12	initial	initial	ADJ
iajs-3292	197	13	conditions	condition	NOUN
iajs-3292	197	14	,	,	PUNCT
iajs-3292	197	15	i.e.	i.e.	X
iajs-3292	197	16	,	,	PUNCT
iajs-3292	197	17	the	the	DET
iajs-3292	197	18	value	value	NOUN
iajs-3292	197	19	of	of	ADP
iajs-3292	197	20	the	the	DET
iajs-3292	197	21	second	second	ADJ
iajs-3292	197	22	derivative	derivative	NOUN
iajs-3292	197	23	at	at	ADP
iajs-3292	197	24	zero	zero	NUM
iajs-3292	197	25	must	must	AUX
iajs-3292	197	26	be	be	AUX
iajs-3292	197	27	found	find	VERB
iajs-3292	197	28	.	.	PUNCT
iajs-3292	198	1	this	this	PRON
iajs-3292	198	2	was	be	AUX
iajs-3292	198	3	done	do	VERB
iajs-3292	198	4	in	in	ADP
iajs-3292	198	5	[	[	X
iajs-3292	198	6	27	27	NUM
iajs-3292	198	7	]	]	PUNCT
iajs-3292	198	8	using	use	VERB
iajs-3292	198	9	the	the	DET
iajs-3292	198	10	homotopy	homotopy	NOUN
iajs-3292	198	11	-	-	PUNCT
iajs-3292	198	12	padé	padé	NOUN
iajs-3292	198	13	method	method	NOUN
iajs-3292	198	14	for	for	ADP
iajs-3292	198	15	approximate	approximate	ADJ
iajs-3292	198	16	and	and	CCONJ
iajs-3292	198	17	finding	find	VERB
iajs-3292	198	18	that	that	SCONJ
iajs-3292	198	19	the	the	DET
iajs-3292	198	20	best	good	ADJ
iajs-3292	198	21	result	result	NOUN
iajs-3292	198	22	is	be	AUX
iajs-3292	198	23	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	198	24	)	)	PUNCT
iajs-3292	199	1	=	=	SYM
iajs-3292	199	2	0.3320573	0.3320573	NUM
iajs-3292	199	3	.	.	PUNCT
iajs-3292	200	1	to	to	PART
iajs-3292	200	2	solve	solve	VERB
iajs-3292	200	3	this	this	DET
iajs-3292	200	4	equation	equation	NOUN
iajs-3292	200	5	using	use	VERB
iajs-3292	200	6	the	the	DET
iajs-3292	200	7	bom	bom	PROPN
iajs-3292	200	8	method	method	NOUN
iajs-3292	200	9	,	,	PUNCT
iajs-3292	200	10	we	we	PRON
iajs-3292	200	11	apply	apply	VERB
iajs-3292	200	12	the	the	DET
iajs-3292	200	13	technique	technique	NOUN
iajs-3292	200	14	from	from	ADP
iajs-3292	200	15	section	section	NOUN
iajs-3292	200	16	3.1	3.1	NUM
iajs-3292	200	17	with	with	ADP
iajs-3292	200	18	𝑛	𝑛	PROPN
iajs-3292	200	19	=	=	SYM
iajs-3292	200	20	3	3	X
iajs-3292	200	21	.	.	PUNCT
iajs-3292	201	1	let	let	VERB
iajs-3292	201	2	us	we	PRON
iajs-3292	201	3	first	first	ADV
iajs-3292	201	4	assume	assume	VERB
iajs-3292	201	5	the	the	DET
iajs-3292	201	6	approximate	approximate	ADJ
iajs-3292	201	7	solution	solution	NOUN
iajs-3292	201	8	as	as	ADP
iajs-3292	201	9	:	:	PUNCT
iajs-3292	201	10	ihjpas	ihjpas	PROPN
iajs-3292	201	11	.	.	PUNCT
iajs-3292	202	1	37	37	NUM
iajs-3292	202	2	(	(	PUNCT
iajs-3292	202	3	1	1	NUM
iajs-3292	202	4	)	)	PUNCT
iajs-3292	202	5	2024	2024	NUM
iajs-3292	202	6	365	365	NUM
iajs-3292	202	7	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	202	8	)	)	PUNCT
iajs-3292	202	9	=	=	SYM
iajs-3292	202	10	𝑐0	𝑐0	PROPN
iajs-3292	202	11	𝐵0,3(𝑥	𝐵0,3(𝑥	NUM
iajs-3292	202	12	)	)	PUNCT
iajs-3292	202	13	+	+	CCONJ
iajs-3292	202	14	𝑐1	𝑐1	NOUN
iajs-3292	202	15	𝐵1,3(𝑥	𝐵1,3(𝑥	NUM
iajs-3292	202	16	)	)	PUNCT
iajs-3292	202	17	+	+	NUM
iajs-3292	202	18	𝑐2	𝑐2	NOUN
iajs-3292	202	19	𝐵2,3(𝑥	𝐵2,3(𝑥	NOUN
iajs-3292	202	20	)	)	PUNCT
iajs-3292	202	21	+	+	NUM
iajs-3292	202	22	𝑐3	𝑐3	NOUN
iajs-3292	202	23	𝐵3,3(𝑥	𝐵3,3(𝑥	NUM
iajs-3292	202	24	)	)	PUNCT
iajs-3292	202	25	=	=	SYM
iajs-3292	202	26	𝐶	𝐶	PROPN
iajs-3292	202	27	𝑇𝜙(𝑥	𝑇𝜙(𝑥	NUM
iajs-3292	202	28	)	)	PUNCT
iajs-3292	202	29	,	,	PUNCT
iajs-3292	202	30	(	(	PUNCT
iajs-3292	202	31	29	29	NUM
iajs-3292	202	32	)	)	PUNCT
iajs-3292	202	33	where	where	SCONJ
iajs-3292	202	34	𝐵0,3(𝑥	𝐵0,3(𝑥	NOUN
iajs-3292	202	35	)	)	PUNCT
iajs-3292	202	36	=	=	SYM
iajs-3292	202	37	1	1	NUM
iajs-3292	202	38	−	−	NOUN
iajs-3292	202	39	3𝑥	3𝑥	NUM
iajs-3292	202	40	+	+	CCONJ
iajs-3292	202	41	3𝑥	3𝑥	NUM
iajs-3292	202	42	2	2	NUM
iajs-3292	202	43	−	−	PROPN
iajs-3292	202	44	𝑥3	𝑥3	NOUN
iajs-3292	202	45	,	,	PUNCT
iajs-3292	202	46	𝐵1,3(𝑥	𝐵1,3(𝑥	PROPN
iajs-3292	202	47	)	)	PUNCT
iajs-3292	202	48	=	=	SYM
iajs-3292	202	49	3𝑥	3𝑥	NUM
iajs-3292	202	50	−	−	NOUN
iajs-3292	202	51	6𝑥	6𝑥	NOUN
iajs-3292	202	52	2	2	NUM
iajs-3292	202	53	+	+	CCONJ
iajs-3292	202	54	3𝑥3	3𝑥3	NUM
iajs-3292	202	55	,	,	PUNCT
iajs-3292	202	56	𝐵2,3(𝑥	𝐵2,3(𝑥	NOUN
iajs-3292	202	57	)	)	PUNCT
iajs-3292	202	58	=	=	SYM
iajs-3292	202	59	3𝑥	3𝑥	NUM
iajs-3292	202	60	2	2	NUM
iajs-3292	202	61	−	−	PROPN
iajs-3292	202	62	3𝑥3	3𝑥3	NUM
iajs-3292	202	63	,	,	PUNCT
iajs-3292	202	64	𝐵3,3(𝑥	𝐵3,3(𝑥	NUM
iajs-3292	202	65	)	)	PUNCT
iajs-3292	202	66	=	=	SYM
iajs-3292	203	1	𝑥	𝑥	DET
iajs-3292	203	2	3	3	X
iajs-3292	203	3	.	.	PUNCT
iajs-3292	203	4	from	from	ADP
iajs-3292	203	5	eq.(8	eq.(8	ADJ
iajs-3292	203	6	)	)	PUNCT
iajs-3292	203	7	we	we	PRON
iajs-3292	203	8	obtain	obtain	VERB
iajs-3292	203	9	the	the	DET
iajs-3292	203	10	om	om	NOUN
iajs-3292	203	11	:	:	PUNCT
iajs-3292	203	12	𝐷𝐵	𝐷𝐵	X
iajs-3292	204	1	=	=	PUNCT
iajs-3292	205	1	[	[	PUNCT
iajs-3292	205	2	−3	−3	NOUN
iajs-3292	205	3	−1	−1	NOUN
iajs-3292	205	4	0	0	NUM
iajs-3292	205	5	0	0	NUM
iajs-3292	205	6	3	3	NUM
iajs-3292	205	7	−1	−1	NOUN
iajs-3292	205	8	−2	−2	NOUN
iajs-3292	205	9	0	0	NUM
iajs-3292	205	10	0	0	NUM
iajs-3292	205	11	2	2	NUM
iajs-3292	205	12	1	1	NUM
iajs-3292	205	13	−3	−3	NOUN
iajs-3292	205	14	0	0	NUM
iajs-3292	205	15	0	0	NUM
iajs-3292	205	16	1	1	NUM
iajs-3292	205	17	3	3	NUM
iajs-3292	205	18	]	]	PUNCT
iajs-3292	205	19	,	,	PUNCT
iajs-3292	205	20	(	(	PUNCT
iajs-3292	205	21	𝐷𝐵	𝐷𝐵	NOUN
iajs-3292	205	22	)	)	PUNCT
iajs-3292	205	23	2	2	NUM
iajs-3292	205	24	=	=	PUNCT
iajs-3292	205	25	[	[	PUNCT
iajs-3292	205	26	6	6	NUM
iajs-3292	205	27	4	4	NUM
iajs-3292	205	28	2	2	NUM
iajs-3292	205	29	0	0	NUM
iajs-3292	205	30	−12	−12	NUM
iajs-3292	206	1	−6	−6	NOUN
iajs-3292	206	2	0	0	NUM
iajs-3292	206	3	6	6	NUM
iajs-3292	206	4	6	6	NUM
iajs-3292	206	5	0	0	NUM
iajs-3292	206	6	−6	−6	NOUN
iajs-3292	206	7	−12	−12	NOUN
iajs-3292	206	8	0	0	NUM
iajs-3292	206	9	2	2	NUM
iajs-3292	206	10	4	4	NUM
iajs-3292	206	11	6	6	NUM
iajs-3292	206	12	]	]	PUNCT
iajs-3292	206	13	,	,	PUNCT
iajs-3292	206	14	(	(	PUNCT
iajs-3292	206	15	𝐷𝐵	𝐷𝐵	PROPN
iajs-3292	206	16	)	)	PUNCT
iajs-3292	206	17	3	3	NUM
iajs-3292	207	1	=	=	PUNCT
iajs-3292	207	2	[	[	PUNCT
iajs-3292	207	3	−6	−6	NOUN
iajs-3292	207	4	−6	−6	NOUN
iajs-3292	207	5	−6	−6	NOUN
iajs-3292	207	6	−6	−6	NOUN
iajs-3292	207	7	18	18	NUM
iajs-3292	207	8	18	18	NUM
iajs-3292	207	9	18	18	NUM
iajs-3292	207	10	18	18	NUM
iajs-3292	207	11	−18	−18	NUM
iajs-3292	208	1	−18	−18	NUM
iajs-3292	209	1	−18	−18	NUM
iajs-3292	210	1	−18	−18	NUM
iajs-3292	210	2	6	6	NUM
iajs-3292	210	3	6	6	NUM
iajs-3292	210	4	6	6	NUM
iajs-3292	210	5	6	6	NUM
iajs-3292	210	6	]	]	PUNCT
iajs-3292	210	7	.	.	PUNCT
iajs-3292	211	1	after	after	ADP
iajs-3292	211	2	converting	convert	VERB
iajs-3292	211	3	each	each	DET
iajs-3292	211	4	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	211	5	)	)	PUNCT
iajs-3292	211	6	and	and	CCONJ
iajs-3292	211	7	its	its	PRON
iajs-3292	211	8	derivatives	derivative	NOUN
iajs-3292	211	9	in	in	ADP
iajs-3292	211	10	the	the	DET
iajs-3292	211	11	nonlinear	nonlinear	ADJ
iajs-3292	211	12	blasius	blasius	ADJ
iajs-3292	211	13	equation	equation	NOUN
iajs-3292	211	14	and	and	CCONJ
iajs-3292	211	15	its	its	PRON
iajs-3292	211	16	initial	initial	ADJ
iajs-3292	211	17	conditions	condition	NOUN
iajs-3292	211	18	into	into	ADP
iajs-3292	211	19	terms	term	NOUN
iajs-3292	211	20	of	of	ADP
iajs-3292	211	21	operational	operational	ADJ
iajs-3292	211	22	matrices	matrix	NOUN
iajs-3292	211	23	,	,	PUNCT
iajs-3292	211	24	we	we	PRON
iajs-3292	211	25	substitute	substitute	VERB
iajs-3292	211	26	the	the	DET
iajs-3292	211	27	collocation	collocation	NOUN
iajs-3292	211	28	nodes	node	NOUN
iajs-3292	211	29	eq.(12	eq.(12	NOUN
iajs-3292	211	30	)	)	PUNCT
iajs-3292	211	31	instead	instead	ADV
iajs-3292	211	32	of	of	ADP
iajs-3292	211	33	each	each	DET
iajs-3292	211	34	x	x	NOUN
iajs-3292	211	35	,	,	PUNCT
iajs-3292	211	36	which	which	PRON
iajs-3292	211	37	gives	give	VERB
iajs-3292	211	38	us	we	PRON
iajs-3292	211	39	the	the	DET
iajs-3292	211	40	following	follow	VERB
iajs-3292	211	41	system	system	NOUN
iajs-3292	211	42	of	of	ADP
iajs-3292	211	43	nonlinear	nonlinear	ADJ
iajs-3292	211	44	algebraic	algebraic	ADJ
iajs-3292	211	45	equations	equation	NOUN
iajs-3292	211	46	:	:	PUNCT
iajs-3292	211	47	−6𝑐0	−6𝑐0	PUNCT
iajs-3292	212	1	+	+	CCONJ
iajs-3292	212	2	18𝑐1	18𝑐1	NUM
iajs-3292	212	3	−	−	NUM
iajs-3292	212	4	18𝑐2	18𝑐2	NUM
iajs-3292	212	5	+	+	NUM
iajs-3292	212	6	6𝑐3	6𝑐3	NUM
iajs-3292	212	7	+	+	CCONJ
iajs-3292	212	8	1	1	NUM
iajs-3292	212	9	2	2	NUM
iajs-3292	212	10	(	(	PUNCT
iajs-3292	212	11	0.015625𝑐0	0.015625𝑐0	NUM
iajs-3292	212	12	+	+	CCONJ
iajs-3292	212	13	0.140625𝑐1	0.140625𝑐1	NUM
iajs-3292	212	14	+	+	NUM
iajs-3292	212	15	0.421875𝑐2	0.421875𝑐2	NUM
iajs-3292	212	16	+	+	CCONJ
iajs-3292	212	17	0.421875𝑐3)(1.5𝑐0	0.421875𝑐3)(1.5𝑐0	ADJ
iajs-3292	212	18	+	+	CCONJ
iajs-3292	212	19	1.5𝑐1	1.5𝑐1	NUM
iajs-3292	212	20	−	−	NUM
iajs-3292	212	21	7.5𝑐2	7.5𝑐2	NUM
iajs-3292	212	22	+	+	CCONJ
iajs-3292	212	23	4.5𝑐3	4.5𝑐3	NUM
iajs-3292	212	24	)	)	PUNCT
iajs-3292	212	25	=	=	SYM
iajs-3292	212	26	0	0	NUM
iajs-3292	212	27	,	,	PUNCT
iajs-3292	212	28	−3𝑐0	−3𝑐0	PUNCT
iajs-3292	212	29	+	+	CCONJ
iajs-3292	212	30	3𝑐1	3𝑐1	NUM
iajs-3292	212	31	=	=	SYM
iajs-3292	212	32	0	0	NUM
iajs-3292	212	33	,	,	PUNCT
iajs-3292	212	34	𝑐0	𝑐0	NOUN
iajs-3292	212	35	=	=	SYM
iajs-3292	212	36	0	0	NUM
iajs-3292	212	37	,	,	PUNCT
iajs-3292	212	38	6𝑐0	6𝑐0	NUM
iajs-3292	212	39	−	−	PROPN
iajs-3292	212	40	12𝑐1	12𝑐1	NUM
iajs-3292	212	41	+	+	CCONJ
iajs-3292	212	42	6𝑐2	6𝑐2	NUM
iajs-3292	212	43	=	=	SYM
iajs-3292	212	44	0.3320573	0.3320573	NUM
iajs-3292	212	45	.	.	PUNCT
iajs-3292	213	1	(	(	PUNCT
iajs-3292	213	2	30	30	NUM
iajs-3292	213	3	)	)	PUNCT
iajs-3292	213	4	finally	finally	ADV
iajs-3292	213	5	,	,	PUNCT
iajs-3292	213	6	by	by	ADP
iajs-3292	213	7	solving	solve	VERB
iajs-3292	213	8	(	(	PUNCT
iajs-3292	213	9	30	30	NUM
iajs-3292	213	10	)	)	PUNCT
iajs-3292	213	11	we	we	PRON
iajs-3292	213	12	obtain	obtain	VERB
iajs-3292	213	13	:	:	PUNCT
iajs-3292	213	14	𝑐0	𝑐0	X
iajs-3292	213	15	=	=	SYM
iajs-3292	213	16	0	0	NUM
iajs-3292	213	17	,	,	PUNCT
iajs-3292	213	18	𝑐1	𝑐1	NOUN
iajs-3292	213	19	=	=	SYM
iajs-3292	213	20	0	0	NUM
iajs-3292	213	21	,	,	PUNCT
iajs-3292	213	22	𝑐2	𝑐2	NOUN
iajs-3292	213	23	=	=	SYM
iajs-3292	213	24	0.055342883	0.055342883	NUM
iajs-3292	213	25	,	,	PUNCT
iajs-3292	213	26	𝑐3	𝑐3	NOUN
iajs-3292	213	27	=	=	PUNCT
iajs-3292	213	28	0.1635587513832345	0.1635587513832345	NUM
iajs-3292	213	29	.	.	PUNCT
iajs-3292	214	1	so	so	ADV
iajs-3292	214	2	,	,	PUNCT
iajs-3292	214	3	the	the	DET
iajs-3292	214	4	approximate	approximate	ADJ
iajs-3292	214	5	solution	solution	NOUN
iajs-3292	214	6	will	will	AUX
iajs-3292	214	7	be	be	AUX
iajs-3292	214	8	as	as	SCONJ
iajs-3292	214	9	follows	follow	VERB
iajs-3292	214	10	:	:	PUNCT
iajs-3292	214	11	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	214	12	)	)	PUNCT
iajs-3292	214	13	=	=	PUNCT
iajs-3292	215	1	[	[	X
iajs-3292	215	2	0	0	NUM
iajs-3292	215	3	,	,	PUNCT
iajs-3292	215	4	0	0	NUM
iajs-3292	215	5	,	,	PUNCT
iajs-3292	215	6	0.055342883	0.055342883	NUM
iajs-3292	215	7	,	,	PUNCT
iajs-3292	215	8	0.1635587513832345	0.1635587513832345	NUM
iajs-3292	215	9	]	]	PUNCT
iajs-3292	215	10	[	[	PUNCT
iajs-3292	215	11	1	1	NUM
iajs-3292	215	12	−	−	NUM
iajs-3292	215	13	3𝑥	3𝑥	NUM
iajs-3292	215	14	+	+	CCONJ
iajs-3292	215	15	3𝑥2	3𝑥2	NUM
iajs-3292	215	16	−	−	NOUN
iajs-3292	215	17	𝑥3	𝑥3	ADJ
iajs-3292	215	18	3𝑥	3𝑥	NUM
iajs-3292	215	19	−	−	NOUN
iajs-3292	215	20	6𝑥2	6𝑥2	NUM
iajs-3292	216	1	+	+	CCONJ
iajs-3292	216	2	3𝑥3	3𝑥3	NUM
iajs-3292	216	3	3𝑥2	3𝑥2	NUM
iajs-3292	216	4	−	−	NOUN
iajs-3292	216	5	3𝑥3	3𝑥3	NUM
iajs-3292	216	6	𝑥3	𝑥3	NOUN
iajs-3292	216	7	]	]	PUNCT
iajs-3292	216	8	,	,	PUNCT
iajs-3292	216	9	=	=	SYM
iajs-3292	216	10	0.16602865𝑥2	0.16602865𝑥2	NUM
iajs-3292	216	11	−	−	PROPN
iajs-3292	216	12	0.002469898616765498𝑥3	0.002469898616765498𝑥3	NUM
iajs-3292	216	13	.	.	PUNCT
iajs-3292	217	1	thus	thus	ADV
iajs-3292	217	2	,	,	PUNCT
iajs-3292	217	3	until	until	ADP
iajs-3292	217	4	𝑛	𝑛	PROPN
iajs-3292	217	5	=	=	SYM
iajs-3292	217	6	11	11	NUM
iajs-3292	217	7	,	,	PUNCT
iajs-3292	217	8	the	the	DET
iajs-3292	217	9	approximate	approximate	ADJ
iajs-3292	217	10	solution	solution	NOUN
iajs-3292	217	11	will	will	AUX
iajs-3292	217	12	be	be	AUX
iajs-3292	217	13	:	:	PUNCT
iajs-3292	217	14	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	217	15	)	)	PUNCT
iajs-3292	217	16	=	=	SYM
iajs-3292	217	17	0.16602865𝑥2	0.16602865𝑥2	NUM
iajs-3292	217	18	+	+	CCONJ
iajs-3292	217	19	2.491375994395639	2.491375994395639	NUM
iajs-3292	217	20	×	×	NOUN
iajs-3292	217	21	10−10𝑥3	10−10𝑥3	NOUN
iajs-3292	217	22	−	−	PROPN
iajs-3292	217	23	1.878031063995422	1.878031063995422	NUM
iajs-3292	217	24	×	×	NOUN
iajs-3292	217	25	10−9𝑥4	10−9𝑥4	NUM
iajs-3292	217	26	−	−	NOUN
iajs-3292	217	27	0.000459416599124296𝑥5	0.000459416599124296𝑥5	NUM
iajs-3292	217	28	−	−	NUM
iajs-3292	217	29	2.537478849262697	2.537478849262697	NUM
iajs-3292	217	30	×	×	NOUN
iajs-3292	217	31	10−8𝑥6	10−8𝑥6	NUM
iajs-3292	217	32	+	+	NUM
iajs-3292	217	33	4.931977670707965	4.931977670707965	NUM
iajs-3292	217	34	×	×	NOUN
iajs-3292	217	35	10−8𝑥7	10−8𝑥7	NUM
iajs-3292	217	36	+	+	CCONJ
iajs-3292	217	37	0.000002433876389318357𝑥8	0.000002433876389318357𝑥8	NUM
iajs-3292	218	1	+	+	CCONJ
iajs-3292	218	2	5.216138276864513	5.216138276864513	NUM
iajs-3292	218	3	×	×	NOUN
iajs-3292	218	4	10−8𝑥9	10−8𝑥9	NUM
iajs-3292	218	5	−	−	PROPN
iajs-3292	218	6	2.538929066986384	2.538929066986384	NUM
iajs-3292	218	7	×	×	NOUN
iajs-3292	218	8	10−8𝑥10	10−8𝑥10	NUM
iajs-3292	218	9	−	−	PROPN
iajs-3292	218	10	8.5669178417902	8.5669178417902	NUM
iajs-3292	218	11	×	×	NOUN
iajs-3292	218	12	10−9𝑥11	10−9𝑥11	NUM
iajs-3292	218	13	.	.	PUNCT
iajs-3292	219	1	(	(	PUNCT
iajs-3292	219	2	31	31	NUM
iajs-3292	219	3	)	)	PUNCT
iajs-3292	219	4	ihjpas	ihjpa	NOUN
iajs-3292	219	5	.	.	PUNCT
iajs-3292	220	1	37	37	NUM
iajs-3292	220	2	(	(	PUNCT
iajs-3292	220	3	1	1	NUM
iajs-3292	220	4	)	)	PUNCT
iajs-3292	220	5	2024	2024	NUM
iajs-3292	220	6	366	366	NUM
iajs-3292	220	7	also	also	ADV
iajs-3292	220	8	,	,	PUNCT
iajs-3292	220	9	this	this	DET
iajs-3292	220	10	equation	equation	NOUN
iajs-3292	220	11	is	be	AUX
iajs-3292	220	12	solved	solve	VERB
iajs-3292	220	13	by	by	ADP
iajs-3292	220	14	using	use	VERB
iajs-3292	220	15	the	the	DET
iajs-3292	220	16	shifted	shift	VERB
iajs-3292	220	17	lom	lom	PROPN
iajs-3292	220	18	method	method	NOUN
iajs-3292	220	19	,	,	PUNCT
iajs-3292	220	20	and	and	CCONJ
iajs-3292	220	21	the	the	DET
iajs-3292	220	22	description	description	NOUN
iajs-3292	220	23	in	in	ADP
iajs-3292	220	24	section	section	NOUN
iajs-3292	220	25	3.2	3.2	NUM
iajs-3292	220	26	is	be	AUX
iajs-3292	220	27	followed	follow	VERB
iajs-3292	220	28	when	when	SCONJ
iajs-3292	220	29	𝑛	𝑛	PROPN
iajs-3292	220	30	=	=	SYM
iajs-3292	220	31	3	3	NUM
iajs-3292	220	32	,	,	PUNCT
iajs-3292	220	33	the	the	DET
iajs-3292	220	34	approximate	approximate	ADJ
iajs-3292	220	35	solution	solution	NOUN
iajs-3292	220	36	is	be	AUX
iajs-3292	220	37	assumed	assume	VERB
iajs-3292	220	38	to	to	PART
iajs-3292	220	39	be	be	AUX
iajs-3292	220	40	as	as	SCONJ
iajs-3292	220	41	follows	follow	VERB
iajs-3292	220	42	:	:	PUNCT
iajs-3292	220	43	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	220	44	)	)	PUNCT
iajs-3292	220	45	=	=	PUNCT
iajs-3292	221	1	𝑐0𝑃0(𝑥	𝑐0𝑃0(𝑥	X
iajs-3292	221	2	)	)	PUNCT
iajs-3292	221	3	+	+	NUM
iajs-3292	221	4	𝑐1𝑃1(𝑥	𝑐1𝑃1(𝑥	X
iajs-3292	221	5	)	)	PUNCT
iajs-3292	222	1	+	+	CCONJ
iajs-3292	222	2	𝑐2𝑃2(𝑥	𝑐2𝑃2(𝑥	X
iajs-3292	222	3	)	)	PUNCT
iajs-3292	222	4	+	+	PUNCT
iajs-3292	222	5	𝑐3𝑃3(𝑥	𝑐3𝑃3(𝑥	X
iajs-3292	222	6	)	)	PUNCT
iajs-3292	222	7	=	=	SYM
iajs-3292	222	8	𝐶	𝐶	PROPN
iajs-3292	222	9	𝑇	𝑇	PROPN
iajs-3292	222	10	𝜙(𝑥	𝜙(𝑥	PROPN
iajs-3292	222	11	)	)	PUNCT
iajs-3292	222	12	,	,	PUNCT
iajs-3292	222	13	(	(	PUNCT
iajs-3292	222	14	32	32	NUM
iajs-3292	222	15	)	)	PUNCT
iajs-3292	222	16	where	where	SCONJ
iajs-3292	222	17	𝑃0(𝑥	𝑃0(𝑥	NUM
iajs-3292	222	18	)	)	PUNCT
iajs-3292	222	19	=	=	SYM
iajs-3292	222	20	1	1	NUM
iajs-3292	222	21	,	,	PUNCT
iajs-3292	222	22	𝑃1(𝑥	𝑃1(𝑥	NOUN
iajs-3292	222	23	)	)	PUNCT
iajs-3292	222	24	=	=	SYM
iajs-3292	222	25	2𝑥	2𝑥	NOUN
iajs-3292	222	26	−	−	NOUN
iajs-3292	222	27	1	1	NUM
iajs-3292	222	28	,	,	PUNCT
iajs-3292	222	29	𝑃2(𝑥	𝑃2(𝑥	NOUN
iajs-3292	222	30	)	)	PUNCT
iajs-3292	222	31	=	=	NOUN
iajs-3292	223	1	6𝑥	6𝑥	NUM
iajs-3292	223	2	2	2	NUM
iajs-3292	223	3	−	−	NOUN
iajs-3292	223	4	6𝑥	6𝑥	NOUN
iajs-3292	223	5	+	+	CCONJ
iajs-3292	223	6	1	1	NUM
iajs-3292	223	7	,	,	PUNCT
iajs-3292	223	8	𝑃3(𝑥	𝑃3(𝑥	NOUN
iajs-3292	223	9	)	)	PUNCT
iajs-3292	223	10	=	=	SYM
iajs-3292	223	11	20𝑥	20𝑥	NUM
iajs-3292	223	12	3	3	NUM
iajs-3292	223	13	−	−	PROPN
iajs-3292	223	14	30𝑥2	30𝑥2	NUM
iajs-3292	224	1	+	+	NUM
iajs-3292	224	2	12𝑥	12𝑥	NOUN
iajs-3292	224	3	−	−	PROPN
iajs-3292	224	4	1	1	X
iajs-3292	224	5	.	.	PUNCT
iajs-3292	224	6	from	from	ADP
iajs-3292	224	7	eq.(19	eq.(19	NOUN
iajs-3292	224	8	)	)	PUNCT
iajs-3292	224	9	we	we	PRON
iajs-3292	224	10	have	have	VERB
iajs-3292	224	11	the	the	DET
iajs-3292	224	12	om	om	NOUN
iajs-3292	224	13	:	:	PUNCT
iajs-3292	224	14	𝐷𝐿	𝐷𝐿	PROPN
iajs-3292	224	15	=	=	PUNCT
iajs-3292	225	1	[	[	PUNCT
iajs-3292	225	2	0	0	NUM
iajs-3292	225	3	0	0	NUM
iajs-3292	225	4	0	0	NUM
iajs-3292	225	5	0	0	NUM
iajs-3292	225	6	2	2	NUM
iajs-3292	225	7	0	0	NUM
iajs-3292	225	8	0	0	NUM
iajs-3292	225	9	0	0	NUM
iajs-3292	225	10	0	0	NUM
iajs-3292	225	11	6	6	NUM
iajs-3292	225	12	0	0	NUM
iajs-3292	225	13	0	0	NUM
iajs-3292	225	14	2	2	NUM
iajs-3292	225	15	0	0	NUM
iajs-3292	225	16	10	10	NUM
iajs-3292	225	17	0	0	NUM
iajs-3292	225	18	]	]	PUNCT
iajs-3292	225	19	,	,	PUNCT
iajs-3292	225	20	(	(	PUNCT
iajs-3292	225	21	𝐷𝐿	𝐷𝐿	PROPN
iajs-3292	225	22	)	)	PUNCT
iajs-3292	225	23	2	2	NUM
iajs-3292	225	24	=	=	PUNCT
iajs-3292	225	25	[	[	PUNCT
iajs-3292	225	26	0	0	NUM
iajs-3292	225	27	0	0	NUM
iajs-3292	225	28	0	0	NUM
iajs-3292	225	29	0	0	NUM
iajs-3292	225	30	0	0	NUM
iajs-3292	225	31	0	0	NUM
iajs-3292	225	32	0	0	NUM
iajs-3292	225	33	0	0	NUM
iajs-3292	225	34	12	12	NUM
iajs-3292	225	35	0	0	NUM
iajs-3292	225	36	0	0	NUM
iajs-3292	225	37	0	0	NUM
iajs-3292	225	38	0	0	NUM
iajs-3292	225	39	60	60	NUM
iajs-3292	225	40	0	0	NUM
iajs-3292	225	41	0	0	NUM
iajs-3292	225	42	]	]	PUNCT
iajs-3292	225	43	,	,	PUNCT
iajs-3292	225	44	(	(	PUNCT
iajs-3292	225	45	𝐷𝐿	𝐷𝐿	PROPN
iajs-3292	225	46	)	)	PUNCT
iajs-3292	225	47	3	3	NUM
iajs-3292	225	48	=	=	PUNCT
iajs-3292	225	49	[	[	PUNCT
iajs-3292	225	50	0	0	NUM
iajs-3292	225	51	0	0	NUM
iajs-3292	225	52	0	0	NUM
iajs-3292	225	53	0	0	NUM
iajs-3292	225	54	0	0	NUM
iajs-3292	225	55	0	0	NUM
iajs-3292	225	56	0	0	NUM
iajs-3292	225	57	0	0	NUM
iajs-3292	225	58	0	0	NUM
iajs-3292	225	59	0	0	NUM
iajs-3292	225	60	0	0	NUM
iajs-3292	225	61	0	0	NUM
iajs-3292	225	62	120	120	NUM
iajs-3292	225	63	0	0	NUM
iajs-3292	225	64	0	0	NUM
iajs-3292	225	65	0	0	NUM
iajs-3292	225	66	]	]	PUNCT
iajs-3292	225	67	.	.	PUNCT
iajs-3292	226	1	after	after	ADP
iajs-3292	226	2	writing	write	VERB
iajs-3292	226	3	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	226	4	)	)	PUNCT
iajs-3292	226	5	and	and	CCONJ
iajs-3292	226	6	its	its	PRON
iajs-3292	226	7	derivatives	derivative	NOUN
iajs-3292	226	8	in	in	ADP
iajs-3292	226	9	node	node	NOUN
iajs-3292	226	10	and	and	CCONJ
iajs-3292	226	11	its	its	PRON
iajs-3292	226	12	initial	initial	ADJ
iajs-3292	226	13	conditions	condition	NOUN
iajs-3292	226	14	in	in	ADP
iajs-3292	226	15	terms	term	NOUN
iajs-3292	226	16	of	of	ADP
iajs-3292	226	17	operational	operational	ADJ
iajs-3292	226	18	matrices	matrix	NOUN
iajs-3292	226	19	,	,	PUNCT
iajs-3292	226	20	the	the	DET
iajs-3292	226	21	collocation	collocation	NOUN
iajs-3292	226	22	nodes	node	NOUN
iajs-3292	226	23	eq.(12	eq.(12	NOUN
iajs-3292	226	24	)	)	PUNCT
iajs-3292	226	25	are	be	AUX
iajs-3292	226	26	substituted	substitute	VERB
iajs-3292	226	27	in	in	ADP
iajs-3292	226	28	place	place	NOUN
iajs-3292	226	29	of	of	ADP
iajs-3292	226	30	each	each	PRON
iajs-3292	226	31	x	x	PUNCT
iajs-3292	226	32	to	to	PART
iajs-3292	226	33	obtain	obtain	VERB
iajs-3292	226	34	the	the	DET
iajs-3292	226	35	system	system	NOUN
iajs-3292	226	36	of	of	ADP
iajs-3292	226	37	nonlinear	nonlinear	ADJ
iajs-3292	226	38	algebraic	algebraic	ADJ
iajs-3292	226	39	equations	equation	NOUN
iajs-3292	226	40	:	:	PUNCT
iajs-3292	227	1	6𝑐0𝑐2	6𝑐0𝑐2	NUM
iajs-3292	227	2	+	+	NUM
iajs-3292	227	3	3	3	X
iajs-3292	227	4	.	.	PUNCT
iajs-3292	228	1	𝑐1𝑐2	𝑐1𝑐2	VERB
iajs-3292	228	2	−	−	NOUN
iajs-3292	228	3	0.75𝑐2	0.75𝑐2	NUM
iajs-3292	228	4	2	2	NUM
iajs-3292	228	5	+	+	NUM
iajs-3292	228	6	120𝑐3	120𝑐3	NUM
iajs-3292	228	7	+	+	SYM
iajs-3292	228	8	15	15	NUM
iajs-3292	228	9	.	.	PUNCT
iajs-3292	229	1	𝑐0𝑐3	𝑐0𝑐3	PUNCT
iajs-3292	230	1	+	+	NOUN
iajs-3292	231	1	7.5𝑐1𝑐3	7.5𝑐1𝑐3	NUM
iajs-3292	231	2	−	−	NOUN
iajs-3292	231	3	4.5𝑐2𝑐3	4.5𝑐2𝑐3	NUM
iajs-3292	231	4	−	−	NOUN
iajs-3292	232	1	6.5625𝑐3	6.5625𝑐3	NUM
iajs-3292	232	2	2	2	NUM
iajs-3292	232	3	=	=	SYM
iajs-3292	232	4	0	0	NUM
iajs-3292	232	5	,	,	PUNCT
iajs-3292	232	6	2𝑐1	2𝑐1	NUM
iajs-3292	233	1	−	−	NUM
iajs-3292	233	2	6𝑐2	6𝑐2	NUM
iajs-3292	234	1	+	+	CCONJ
iajs-3292	234	2	12𝑐3	12𝑐3	NUM
iajs-3292	234	3	=	=	SYM
iajs-3292	234	4	0	0	NUM
iajs-3292	234	5	,	,	PUNCT
iajs-3292	234	6	𝑐0	𝑐0	VERB
iajs-3292	234	7	−	−	NOUN
iajs-3292	234	8	𝑐1	𝑐1	NOUN
iajs-3292	234	9	+	+	NOUN
iajs-3292	234	10	𝑐2	𝑐2	NOUN
iajs-3292	234	11	−	−	NOUN
iajs-3292	234	12	𝑐3	𝑐3	NOUN
iajs-3292	234	13	=	=	SYM
iajs-3292	234	14	0	0	NUM
iajs-3292	234	15	,	,	PUNCT
iajs-3292	234	16	12𝑐2	12𝑐2	NUM
iajs-3292	234	17	−	−	NUM
iajs-3292	234	18	60𝑐3	60𝑐3	NUM
iajs-3292	234	19	=	=	SYM
iajs-3292	234	20	0.3320573	0.3320573	NUM
iajs-3292	234	21	.	.	PUNCT
iajs-3292	235	1	(	(	PUNCT
iajs-3292	235	2	33	33	NUM
iajs-3292	235	3	)	)	PUNCT
iajs-3292	235	4	solving	solve	VERB
iajs-3292	235	5	this	this	DET
iajs-3292	235	6	system	system	NOUN
iajs-3292	235	7	and	and	CCONJ
iajs-3292	235	8	substituting	substitute	VERB
iajs-3292	235	9	the	the	DET
iajs-3292	235	10	value	value	NOUN
iajs-3292	235	11	of	of	ADP
iajs-3292	235	12	𝐶𝑇	𝐶𝑇	PROPN
iajs-3292	235	13	into	into	ADP
iajs-3292	235	14	eq.(32	eq.(32	PROPN
iajs-3292	235	15	)	)	PUNCT
iajs-3292	235	16	yields	yield	VERB
iajs-3292	235	17	the	the	DET
iajs-3292	235	18	approximate	approximate	ADJ
iajs-3292	235	19	solution	solution	NOUN
iajs-3292	235	20	:	:	PUNCT
iajs-3292	235	21	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	235	22	)	)	PUNCT
iajs-3292	236	1	=	=	NOUN
iajs-3292	236	2	−3.469446951953614	−3.469446951953614	NUM
iajs-3292	237	1	×	×	NOUN
iajs-3292	237	2	10−18	10−18	NOUN
iajs-3292	237	3	+	+	CCONJ
iajs-3292	237	4	0.16602865𝑥2	0.16602865𝑥2	NUM
iajs-3292	237	5	−	−	NOUN
iajs-3292	237	6	0.002469898616765488𝑥3	0.002469898616765488𝑥3	NUM
iajs-3292	237	7	.	.	PUNCT
iajs-3292	238	1	consequently	consequently	ADV
iajs-3292	238	2	,	,	PUNCT
iajs-3292	238	3	until	until	ADP
iajs-3292	238	4	𝑛	𝑛	PROPN
iajs-3292	238	5	=	=	SYM
iajs-3292	238	6	11	11	NUM
iajs-3292	238	7	,	,	PUNCT
iajs-3292	238	8	we	we	PRON
iajs-3292	238	9	obtain	obtain	VERB
iajs-3292	238	10	the	the	DET
iajs-3292	238	11	following	follow	VERB
iajs-3292	238	12	approximate	approximate	ADJ
iajs-3292	238	13	solution	solution	NOUN
iajs-3292	238	14	:	:	PUNCT
iajs-3292	238	15	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	238	16	)	)	PUNCT
iajs-3292	238	17	=	=	PUNCT
iajs-3292	239	1	−3.696547211931118	−3.696547211931118	X
iajs-3292	239	2	×	×	NOUN
iajs-3292	239	3	10−12	10−12	NOUN
iajs-3292	239	4	+	+	CCONJ
iajs-3292	239	5	3.253866343033706	3.253866343033706	NUM
iajs-3292	239	6	×	×	NOUN
iajs-3292	239	7	10−10𝑥	10−10𝑥	NUM
iajs-3292	239	8	+	+	CCONJ
iajs-3292	239	9	0.16602864303933304𝑥2	0.16602864303933304𝑥2	NUM
iajs-3292	239	10	+	+	CCONJ
iajs-3292	240	1	6.283554605411232	6.283554605411232	NUM
iajs-3292	240	2	×	×	NOUN
iajs-3292	240	3	10−8𝑥3	10−8𝑥3	NUM
iajs-3292	240	4	−	−	PROPN
iajs-3292	240	5	2.920702954934285	2.920702954934285	NUM
iajs-3292	240	6	×	×	NOUN
iajs-3292	240	7	10−7𝑥4	10−7𝑥4	NUM
iajs-3292	240	8	−	−	NOUN
iajs-3292	240	9	0.00045866085596424073𝑥5	0.00045866085596424073𝑥5	NUM
iajs-3292	241	1	−	−	NOUN
iajs-3292	241	2	0.000001148562469835698𝑥6	0.000001148562469835698𝑥6	NOUN
iajs-3292	241	3	+	+	NOUN
iajs-3292	241	4	9.397408390670055	9.397408390670055	NUM
iajs-3292	241	5	×	×	NOUN
iajs-3292	241	6	10−7𝑥7	10−7𝑥7	NUM
iajs-3292	241	7	+	+	CCONJ
iajs-3292	241	8	0.000002163350548329646𝑥8	0.000002163350548329646𝑥8	NOUN
iajs-3292	241	9	.	.	PUNCT
iajs-3292	242	1	(	(	PUNCT
iajs-3292	242	2	34	34	NUM
iajs-3292	242	3	)	)	PUNCT
iajs-3292	242	4	moreover	moreover	ADV
iajs-3292	242	5	,	,	PUNCT
iajs-3292	242	6	if	if	SCONJ
iajs-3292	242	7	we	we	PRON
iajs-3292	242	8	use	use	VERB
iajs-3292	242	9	the	the	DET
iajs-3292	242	10	brom	brom	NOUN
iajs-3292	242	11	method	method	NOUN
iajs-3292	242	12	,	,	PUNCT
iajs-3292	242	13	then	then	ADV
iajs-3292	242	14	the	the	DET
iajs-3292	242	15	explanation	explanation	NOUN
iajs-3292	242	16	in	in	ADP
iajs-3292	242	17	section	section	NOUN
iajs-3292	242	18	3.3	3.3	NUM
iajs-3292	242	19	is	be	AUX
iajs-3292	242	20	followed	follow	VERB
iajs-3292	242	21	and	and	CCONJ
iajs-3292	242	22	the	the	DET
iajs-3292	242	23	approximate	approximate	ADJ
iajs-3292	242	24	solution	solution	NOUN
iajs-3292	242	25	is	be	AUX
iajs-3292	242	26	taken	take	VERB
iajs-3292	242	27	as	as	SCONJ
iajs-3292	242	28	assumed	assume	VERB
iajs-3292	242	29	:	:	PUNCT
iajs-3292	242	30	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	242	31	)	)	PUNCT
iajs-3292	242	32	=	=	SYM
iajs-3292	242	33	𝑐0𝐵𝑟0(𝑥	𝑐0𝐵𝑟0(𝑥	PROPN
iajs-3292	242	34	)	)	PUNCT
iajs-3292	242	35	+	+	NOUN
iajs-3292	242	36	𝑐1𝐵𝑟1(𝑥	𝑐1𝐵𝑟1(𝑥	NUM
iajs-3292	242	37	)	)	PUNCT
iajs-3292	242	38	+	+	ADJ
iajs-3292	243	1	𝑐2𝐵𝑟2(𝑥	𝑐2𝐵𝑟2(𝑥	NUM
iajs-3292	243	2	)	)	PUNCT
iajs-3292	243	3	+	+	PUNCT
iajs-3292	243	4	𝑐3𝐵𝑟3(𝑥	𝑐3𝐵𝑟3(𝑥	PROPN
iajs-3292	243	5	)	)	PUNCT
iajs-3292	243	6	=	=	SYM
iajs-3292	243	7	𝐶	𝐶	PROPN
iajs-3292	243	8	𝑇	𝑇	PROPN
iajs-3292	243	9	𝐵𝑟(𝑥	𝐵𝑟(𝑥	NOUN
iajs-3292	243	10	)	)	PUNCT
iajs-3292	243	11	,	,	PUNCT
iajs-3292	243	12	(	(	PUNCT
iajs-3292	243	13	35	35	NUM
iajs-3292	243	14	)	)	PUNCT
iajs-3292	243	15	where	where	SCONJ
iajs-3292	243	16	𝐵𝑟0(𝑥	𝐵𝑟0(𝑥	NUM
iajs-3292	243	17	)	)	PUNCT
iajs-3292	243	18	=	=	SYM
iajs-3292	243	19	1	1	NUM
iajs-3292	243	20	,	,	PUNCT
iajs-3292	243	21	𝐵𝑟1(𝑥	𝐵𝑟1(𝑥	NOUN
iajs-3292	243	22	)	)	PUNCT
iajs-3292	243	23	=	=	SYM
iajs-3292	244	1	𝑥	𝑥	PRON
iajs-3292	244	2	−	−	NUM
iajs-3292	244	3	1	1	NUM
iajs-3292	244	4	2	2	NUM
iajs-3292	244	5	,	,	PUNCT
iajs-3292	244	6	𝐵𝑟2(𝑥	𝐵𝑟2(𝑥	NOUN
iajs-3292	244	7	)	)	PUNCT
iajs-3292	245	1	=	=	PUNCT
iajs-3292	246	1	𝑥	𝑥	DET
iajs-3292	246	2	2	2	NUM
iajs-3292	246	3	−	−	NOUN
iajs-3292	246	4	𝑥	𝑥	NOUN
iajs-3292	246	5	+	+	NOUN
iajs-3292	246	6	1	1	NUM
iajs-3292	246	7	6	6	NUM
iajs-3292	246	8	,	,	PUNCT
iajs-3292	246	9	𝐵𝑟3(𝑥	𝐵𝑟3(𝑥	NUM
iajs-3292	246	10	)	)	PUNCT
iajs-3292	246	11	=	=	PUNCT
iajs-3292	247	1	𝑥	𝑥	DET
iajs-3292	247	2	3	3	NUM
iajs-3292	247	3	−	−	NOUN
iajs-3292	247	4	3	3	NUM
iajs-3292	247	5	2	2	NUM
iajs-3292	247	6	𝑥2	𝑥2	NOUN
iajs-3292	247	7	+	+	CCONJ
iajs-3292	247	8	1	1	NUM
iajs-3292	247	9	2	2	NUM
iajs-3292	247	10	𝑥.	𝑥.	ADV
iajs-3292	247	11	here	here	ADV
iajs-3292	247	12	,	,	PUNCT
iajs-3292	247	13	from	from	ADP
iajs-3292	247	14	eq.(26	eq.(26	ADV
iajs-3292	247	15	)	)	PUNCT
iajs-3292	247	16	we	we	PRON
iajs-3292	247	17	have	have	VERB
iajs-3292	247	18	the	the	DET
iajs-3292	247	19	om	om	NOUN
iajs-3292	247	20	:	:	PUNCT
iajs-3292	247	21	𝐷𝐵𝑟	𝐷𝐵𝑟	X
iajs-3292	247	22	=	=	PUNCT
iajs-3292	248	1	[	[	PUNCT
iajs-3292	248	2	0	0	NUM
iajs-3292	248	3	0	0	NUM
iajs-3292	248	4	0	0	NUM
iajs-3292	248	5	0	0	NUM
iajs-3292	248	6	1	1	NUM
iajs-3292	248	7	0	0	NUM
iajs-3292	248	8	0	0	NUM
iajs-3292	248	9	0	0	NUM
iajs-3292	248	10	0	0	NUM
iajs-3292	248	11	2	2	NUM
iajs-3292	248	12	0	0	NUM
iajs-3292	248	13	0	0	NUM
iajs-3292	248	14	0	0	NUM
iajs-3292	248	15	0	0	NUM
iajs-3292	248	16	3	3	NUM
iajs-3292	248	17	0	0	NUM
iajs-3292	248	18	]	]	PUNCT
iajs-3292	248	19	,	,	PUNCT
iajs-3292	248	20	(	(	PUNCT
iajs-3292	248	21	𝐷𝐵𝑟	𝐷𝐵𝑟	NOUN
iajs-3292	248	22	)	)	PUNCT
iajs-3292	248	23	2	2	NUM
iajs-3292	248	24	=	=	PUNCT
iajs-3292	248	25	[	[	PUNCT
iajs-3292	248	26	0	0	NUM
iajs-3292	248	27	0	0	NUM
iajs-3292	248	28	0	0	NUM
iajs-3292	248	29	0	0	NUM
iajs-3292	248	30	0	0	NUM
iajs-3292	248	31	0	0	NUM
iajs-3292	248	32	0	0	NUM
iajs-3292	248	33	0	0	NUM
iajs-3292	248	34	2	2	NUM
iajs-3292	248	35	0	0	NUM
iajs-3292	248	36	0	0	NUM
iajs-3292	248	37	0	0	NUM
iajs-3292	248	38	0	0	NUM
iajs-3292	248	39	6	6	NUM
iajs-3292	248	40	0	0	NUM
iajs-3292	248	41	0	0	NUM
iajs-3292	248	42	]	]	PUNCT
iajs-3292	248	43	,	,	PUNCT
iajs-3292	248	44	(	(	PUNCT
iajs-3292	248	45	𝐷𝐵𝑟	𝐷𝐵𝑟	NOUN
iajs-3292	248	46	)	)	PUNCT
iajs-3292	248	47	3	3	NUM
iajs-3292	248	48	=	=	PUNCT
iajs-3292	248	49	[	[	PUNCT
iajs-3292	248	50	0	0	NUM
iajs-3292	248	51	0	0	NUM
iajs-3292	248	52	0	0	NUM
iajs-3292	248	53	0	0	NUM
iajs-3292	248	54	0	0	NUM
iajs-3292	248	55	0	0	NUM
iajs-3292	248	56	0	0	NUM
iajs-3292	248	57	0	0	NUM
iajs-3292	248	58	0	0	NUM
iajs-3292	248	59	0	0	NUM
iajs-3292	248	60	0	0	NUM
iajs-3292	248	61	0	0	NUM
iajs-3292	248	62	6	6	NUM
iajs-3292	248	63	0	0	NUM
iajs-3292	248	64	0	0	NUM
iajs-3292	248	65	0	0	NUM
iajs-3292	248	66	]	]	PUNCT
iajs-3292	248	67	.	.	PUNCT
iajs-3292	249	1	ihjpas	ihjpas	PROPN
iajs-3292	249	2	.	.	PUNCT
iajs-3292	250	1	37	37	NUM
iajs-3292	250	2	(	(	PUNCT
iajs-3292	250	3	1	1	NUM
iajs-3292	250	4	)	)	PUNCT
iajs-3292	250	5	2024	2024	NUM
iajs-3292	250	6	367	367	NUM
iajs-3292	250	7	after	after	ADP
iajs-3292	250	8	writing	write	VERB
iajs-3292	250	9	the	the	DET
iajs-3292	250	10	nonlinear	nonlinear	ADJ
iajs-3292	250	11	blasius	blasius	ADJ
iajs-3292	250	12	equation	equation	NOUN
iajs-3292	250	13	and	and	CCONJ
iajs-3292	250	14	its	its	PRON
iajs-3292	250	15	initial	initial	ADJ
iajs-3292	250	16	conditions	condition	NOUN
iajs-3292	250	17	in	in	ADP
iajs-3292	250	18	the	the	DET
iajs-3292	250	19	form	form	NOUN
iajs-3292	250	20	of	of	ADP
iajs-3292	250	21	operational	operational	ADJ
iajs-3292	250	22	matrices	matrix	NOUN
iajs-3292	250	23	and	and	CCONJ
iajs-3292	250	24	putting	put	VERB
iajs-3292	250	25	the	the	DET
iajs-3292	250	26	collocation	collocation	NOUN
iajs-3292	250	27	nodes	node	NOUN
iajs-3292	250	28	instead	instead	ADV
iajs-3292	250	29	of	of	ADP
iajs-3292	250	30	each	each	DET
iajs-3292	250	31	x	x	NOUN
iajs-3292	250	32	,	,	PUNCT
iajs-3292	250	33	we	we	PRON
iajs-3292	250	34	obtain	obtain	VERB
iajs-3292	250	35	the	the	DET
iajs-3292	250	36	following	follow	VERB
iajs-3292	250	37	system	system	NOUN
iajs-3292	250	38	:	:	PUNCT
iajs-3292	250	39	𝑐0𝑐2	𝑐0𝑐2	X
iajs-3292	251	1	+	+	PUNCT
iajs-3292	251	2	0.25𝑐1𝑐2	0.25𝑐1𝑐2	VERB
iajs-3292	251	3	−	−	NOUN
iajs-3292	251	4	0.02083333333333337𝑐2	0.02083333333333337𝑐2	NUM
iajs-3292	251	5	2	2	NUM
iajs-3292	251	6	+	+	NUM
iajs-3292	251	7	6𝑐3	6𝑐3	NUM
iajs-3292	251	8	+	+	CCONJ
iajs-3292	251	9	0.75𝑐0𝑐3	0.75𝑐0𝑐3	NUM
iajs-3292	251	10	+	+	NUM
iajs-3292	251	11	0.1875𝑐1𝑐3	0.1875𝑐1𝑐3	NUM
iajs-3292	251	12	−	−	NOUN
iajs-3292	251	13	0.06250000000000003𝑐2𝑐3	0.06250000000000003𝑐2𝑐3	NUM
iajs-3292	252	1	−	−	NOUN
iajs-3292	253	1	0.03515625𝑐3	0.03515625𝑐3	NUM
iajs-3292	253	2	2	2	NUM
iajs-3292	253	3	=	=	SYM
iajs-3292	253	4	0	0	NUM
iajs-3292	253	5	,	,	PUNCT
iajs-3292	253	6	𝑐1	𝑐1	NOUN
iajs-3292	253	7	−	−	NOUN
iajs-3292	253	8	𝑐2	𝑐2	NOUN
iajs-3292	253	9	+	+	NUM
iajs-3292	253	10	𝑐3	𝑐3	NOUN
iajs-3292	253	11	2	2	NUM
iajs-3292	253	12	=	=	SYM
iajs-3292	253	13	0	0	NUM
iajs-3292	253	14	,	,	PUNCT
iajs-3292	253	15	𝑐0	𝑐0	VERB
iajs-3292	253	16	−	−	NOUN
iajs-3292	253	17	𝑐1	𝑐1	NOUN
iajs-3292	253	18	2	2	NUM
iajs-3292	253	19	+	+	NUM
iajs-3292	253	20	𝑐2	𝑐2	NOUN
iajs-3292	253	21	6	6	NUM
iajs-3292	253	22	=	=	SYM
iajs-3292	253	23	0	0	NUM
iajs-3292	253	24	,	,	PUNCT
iajs-3292	253	25	2𝑐2	2𝑐2	NUM
iajs-3292	253	26	−	−	NOUN
iajs-3292	253	27	3𝑐3	3𝑐3	NUM
iajs-3292	253	28	=	=	SYM
iajs-3292	253	29	0.3320573	0.3320573	NUM
iajs-3292	253	30	.	.	PUNCT
iajs-3292	254	1	(	(	PUNCT
iajs-3292	254	2	36	36	NUM
iajs-3292	254	3	)	)	PUNCT
iajs-3292	254	4	once	once	SCONJ
iajs-3292	254	5	this	this	DET
iajs-3292	254	6	system	system	NOUN
iajs-3292	254	7	is	be	AUX
iajs-3292	254	8	solved	solve	VERB
iajs-3292	254	9	,	,	PUNCT
iajs-3292	254	10	the	the	DET
iajs-3292	254	11	roots	root	NOUN
iajs-3292	254	12	are	be	AUX
iajs-3292	254	13	substituted	substitute	VERB
iajs-3292	254	14	into	into	ADP
iajs-3292	254	15	eq.(35	eq.(35	NOUN
iajs-3292	254	16	)	)	PUNCT
iajs-3292	254	17	,	,	PUNCT
iajs-3292	254	18	and	and	CCONJ
iajs-3292	254	19	we	we	PRON
iajs-3292	254	20	obtain	obtain	VERB
iajs-3292	254	21	the	the	DET
iajs-3292	254	22	approximate	approximate	ADJ
iajs-3292	254	23	solution	solution	NOUN
iajs-3292	254	24	as	as	SCONJ
iajs-3292	254	25	follows	follow	VERB
iajs-3292	254	26	:	:	PUNCT
iajs-3292	254	27	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	254	28	)	)	PUNCT
iajs-3292	255	1	=	=	SYM
iajs-3292	255	2	−6.93889390391	−6.93889390391	NUM
iajs-3292	255	3	×	×	NOUN
iajs-3292	255	4	10−18	10−18	NOUN
iajs-3292	255	5	+	+	CCONJ
iajs-3292	255	6	0.1660286500000003𝑥2	0.1660286500000003𝑥2	NOUN
iajs-3292	255	7	−	−	NOUN
iajs-3292	255	8	0.00246989861677𝑥3	0.00246989861677𝑥3	NUM
iajs-3292	255	9	.	.	PUNCT
iajs-3292	256	1	thus	thus	ADV
iajs-3292	256	2	,	,	PUNCT
iajs-3292	256	3	up	up	ADP
iajs-3292	256	4	to	to	PART
iajs-3292	256	5	𝑛	𝑛	NOUN
iajs-3292	256	6	=	=	SYM
iajs-3292	256	7	11	11	NUM
iajs-3292	256	8	,	,	PUNCT
iajs-3292	256	9	the	the	DET
iajs-3292	256	10	approximate	approximate	ADJ
iajs-3292	256	11	solution	solution	NOUN
iajs-3292	256	12	will	will	AUX
iajs-3292	256	13	be	be	AUX
iajs-3292	256	14	:	:	PUNCT
iajs-3292	256	15	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	256	16	)	)	PUNCT
iajs-3292	256	17	=	=	SYM
iajs-3292	257	1	−3.529427472531059	−3.529427472531059	NUM
iajs-3292	257	2	×	×	NOUN
iajs-3292	257	3	10−18	10−18	NOUN
iajs-3292	257	4	−	−	PROPN
iajs-3292	257	5	3.962758940434519	3.962758940434519	NUM
iajs-3292	257	6	×	×	NOUN
iajs-3292	257	7	10−17𝑥	10−17𝑥	NUM
iajs-3292	257	8	+	+	NOUN
iajs-3292	257	9	0.16602865000000003𝑥2	0.16602865000000003𝑥2	NUM
iajs-3292	258	1	+	+	CCONJ
iajs-3292	258	2	1.979266592913857	1.979266592913857	NUM
iajs-3292	258	3	×	×	NOUN
iajs-3292	258	4	10−10𝑥3	10−10𝑥3	NOUN
iajs-3292	258	5	−	−	ADP
iajs-3292	258	6	1.499749921060817	1.499749921060817	NUM
iajs-3292	258	7	×	×	NOUN
iajs-3292	258	8	10−9𝑥4	10−9𝑥4	NUM
iajs-3292	258	9	−	−	NOUN
iajs-3292	258	10	0.000459418278828476𝑥5	0.000459418278828476𝑥5	NUM
iajs-3292	258	11	−	−	PROPN
iajs-3292	258	12	2.065013702012278	2.065013702012278	NUM
iajs-3292	258	13	×	×	NOUN
iajs-3292	258	14	10−8𝑥6	10−8𝑥6	NUM
iajs-3292	258	15	+	+	SYM
iajs-3292	258	16	4.070826065187125	4.070826065187125	NUM
iajs-3292	258	17	×	×	NOUN
iajs-3292	258	18	10−8𝑥7	10−8𝑥7	NUM
iajs-3292	258	19	+	+	CCONJ
iajs-3292	258	20	0.000002444007699522198𝑥8	0.000002444007699522198𝑥8	PRON
iajs-3292	258	21	+	+	CCONJ
iajs-3292	258	22	4.474523682223838	4.474523682223838	NUM
iajs-3292	258	23	×	×	NOUN
iajs-3292	258	24	10−8𝑥9	10−8𝑥9	NUM
iajs-3292	258	25	−	−	NOUN
iajs-3292	258	26	2.232041556339086	2.232041556339086	NUM
iajs-3292	258	27	×	×	NOUN
iajs-3292	258	28	10−8𝑥10	10−8𝑥10	NUM
iajs-3292	258	29	−	−	PROPN
iajs-3292	258	30	9.11508105682988	9.11508105682988	NUM
iajs-3292	258	31	×	×	PROPN
iajs-3292	258	32	10−9𝑥11	10−9𝑥11	NUM
iajs-3292	258	33	.	.	PUNCT
iajs-3292	259	1	(	(	PUNCT
iajs-3292	259	2	37	37	NUM
iajs-3292	259	3	)	)	PUNCT
iajs-3292	259	4	the	the	DET
iajs-3292	259	5	exact	exact	ADJ
iajs-3292	259	6	solution	solution	NOUN
iajs-3292	259	7	of	of	ADP
iajs-3292	259	8	the	the	DET
iajs-3292	259	9	blasius	blasius	ADJ
iajs-3292	259	10	equation	equation	NOUN
iajs-3292	259	11	is	be	AUX
iajs-3292	259	12	unknown	unknown	ADJ
iajs-3292	259	13	.	.	PUNCT
iajs-3292	260	1	therefore	therefore	ADV
iajs-3292	260	2	,	,	PUNCT
iajs-3292	260	3	the	the	DET
iajs-3292	260	4	maximum	maximum	ADJ
iajs-3292	260	5	error	error	NOUN
iajs-3292	260	6	remainder	remainder	NOUN
iajs-3292	260	7	(	(	PUNCT
iajs-3292	260	8	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	PROPN
iajs-3292	260	9	)	)	PUNCT
iajs-3292	260	10	is	be	AUX
iajs-3292	260	11	calculated	calculate	VERB
iajs-3292	260	12	to	to	PART
iajs-3292	260	13	determine	determine	VERB
iajs-3292	260	14	the	the	DET
iajs-3292	260	15	accuracy	accuracy	NOUN
iajs-3292	260	16	of	of	ADP
iajs-3292	260	17	the	the	DET
iajs-3292	260	18	proposed	propose	VERB
iajs-3292	260	19	methods	method	NOUN
iajs-3292	260	20	.	.	PUNCT
iajs-3292	261	1	the	the	DET
iajs-3292	261	2	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	PROPN
iajs-3292	261	3	is	be	AUX
iajs-3292	261	4	given	give	VERB
iajs-3292	261	5	by	by	ADP
iajs-3292	261	6	:	:	PUNCT
iajs-3292	261	7	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3292	261	8	=	=	SYM
iajs-3292	261	9	max	max	PROPN
iajs-3292	261	10	0≤𝑥≤1	0≤𝑥≤1	ADJ
iajs-3292	261	11	|𝑓′′′(𝑥	|𝑓′′′(𝑥	NOUN
iajs-3292	261	12	)	)	PUNCT
iajs-3292	262	1	+	+	CCONJ
iajs-3292	262	2	1	1	NUM
iajs-3292	262	3	2	2	NUM
iajs-3292	262	4	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	262	5	)	)	PUNCT
iajs-3292	262	6	𝑓′′(𝑥)|	𝑓′′(𝑥)|	SYM
iajs-3292	262	7	.	.	PUNCT
iajs-3292	263	1	(	(	PUNCT
iajs-3292	263	2	38	38	NUM
iajs-3292	263	3	)	)	PUNCT
iajs-3292	263	4	figure	figure	NOUN
iajs-3292	263	5	1	1	NUM
iajs-3292	263	6	shows	show	VERB
iajs-3292	263	7	the	the	DET
iajs-3292	263	8	logarithmic	logarithmic	ADJ
iajs-3292	263	9	plots	plot	NOUN
iajs-3292	263	10	for	for	ADP
iajs-3292	263	11	𝑀𝐸𝑅𝑛of	𝑀𝐸𝑅𝑛of	PROPN
iajs-3292	263	12	the	the	DET
iajs-3292	263	13	approximate	approximate	ADJ
iajs-3292	263	14	solutions	solution	NOUN
iajs-3292	263	15	obtained	obtain	VERB
iajs-3292	263	16	by	by	ADP
iajs-3292	263	17	the	the	DET
iajs-3292	263	18	three	three	NUM
iajs-3292	263	19	proposed	propose	VERB
iajs-3292	263	20	methods	method	NOUN
iajs-3292	263	21	at	at	ADP
iajs-3292	263	22	all	all	ADV
iajs-3292	263	23	𝑛	𝑛	DET
iajs-3292	263	24	iterations	iteration	NOUN
iajs-3292	263	25	(	(	PUNCT
iajs-3292	263	26	𝑛	𝑛	NOUN
iajs-3292	263	27	=	=	SYM
iajs-3292	263	28	3	3	NUM
iajs-3292	263	29	to	to	PART
iajs-3292	263	30	11	11	NUM
iajs-3292	263	31	)	)	PUNCT
iajs-3292	263	32	.	.	PUNCT
iajs-3292	264	1	figure	figure	VERB
iajs-3292	264	2	1.logarithmic	1.logarithmic	NUM
iajs-3292	264	3	plots	plot	NOUN
iajs-3292	264	4	for	for	ADP
iajs-3292	264	5	the	the	DET
iajs-3292	264	6	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3292	264	7	of	of	ADP
iajs-3292	264	8	bom	bom	PROPN
iajs-3292	264	9	,	,	PUNCT
iajs-3292	264	10	lom	lom	PROPN
iajs-3292	264	11	,	,	PUNCT
iajs-3292	264	12	and	and	CCONJ
iajs-3292	264	13	brom	brom	NOUN
iajs-3292	264	14	.	.	PUNCT
iajs-3292	265	1	ihjpas	ihjpas	PROPN
iajs-3292	265	2	.	.	PUNCT
iajs-3292	266	1	37	37	NUM
iajs-3292	266	2	(	(	PUNCT
iajs-3292	266	3	1	1	NUM
iajs-3292	266	4	)	)	PUNCT
iajs-3292	266	5	2024	2024	NUM
iajs-3292	266	6	368	368	NUM
iajs-3292	266	7	in	in	ADP
iajs-3292	266	8	addition	addition	NOUN
iajs-3292	266	9	,	,	PUNCT
iajs-3292	266	10	table	table	NOUN
iajs-3292	266	11	1	1	NUM
iajs-3292	266	12	shows	show	VERB
iajs-3292	266	13	the	the	DET
iajs-3292	266	14	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3292	266	15	value	value	NOUN
iajs-3292	266	16	for	for	ADP
iajs-3292	266	17	all	all	PRON
iajs-3292	266	18	𝑛	𝑛	ADP
iajs-3292	266	19	studied	study	VERB
iajs-3292	266	20	in	in	ADP
iajs-3292	266	21	solving	solve	VERB
iajs-3292	266	22	the	the	DET
iajs-3292	266	23	nonlinear	nonlinear	ADJ
iajs-3292	266	24	blasius	blasius	ADJ
iajs-3292	266	25	equation	equation	NOUN
iajs-3292	266	26	by	by	ADP
iajs-3292	266	27	using	use	VERB
iajs-3292	266	28	the	the	DET
iajs-3292	266	29	proposed	propose	VERB
iajs-3292	266	30	methods	method	NOUN
iajs-3292	266	31	.	.	PUNCT
iajs-3292	267	1	table	table	NOUN
iajs-3292	267	2	1	1	NUM
iajs-3292	267	3	:	:	PUNCT
iajs-3292	267	4	the	the	DET
iajs-3292	267	5	comparison	comparison	NOUN
iajs-3292	267	6	of	of	ADP
iajs-3292	267	7	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3292	267	8	between	between	ADP
iajs-3292	267	9	the	the	DET
iajs-3292	267	10	bom	bom	PROPN
iajs-3292	267	11	,	,	PUNCT
iajs-3292	267	12	lom	lom	PROPN
iajs-3292	267	13	,	,	PUNCT
iajs-3292	267	14	and	and	CCONJ
iajs-3292	267	15	brom	brom	NOUN
iajs-3292	267	16	methods	method	NOUN
iajs-3292	267	17	for	for	ADP
iajs-3292	267	18	𝑛	𝑛	NOUN
iajs-3292	267	19	=	=	SYM
iajs-3292	267	20	3	3	NUM
iajs-3292	267	21	to	to	PART
iajs-3292	267	22	11	11	NUM
iajs-3292	267	23	.	.	PUNCT
iajs-3292	268	1	𝑛	𝑛	DET
iajs-3292	268	2	bom	bom	PROPN
iajs-3292	268	3	lom	lom	PROPN
iajs-3292	268	4	brom	brom	PROPN
iajs-3292	268	5	3	3	NUM
iajs-3292	268	6	0.014819391700592988	0.014819391700592988	NUM
iajs-3292	268	7	0.014819391700592925	0.014819391700592925	NUM
iajs-3292	268	8	0.014819391700593073	0.014819391700593073	NUM
iajs-3292	268	9	4	4	NUM
iajs-3292	268	10	0.011427015738563973	0.011427015738563973	NUM
iajs-3292	268	11	0.011427015738558465	0.011427015738558465	NUM
iajs-3292	268	12	0.011427015738558968	0.011427015738558968	NUM
iajs-3292	268	13	5	5	NUM
iajs-3292	268	14	0.0004197059747635956	0.0004197059747635956	NUM
iajs-3292	268	15	0.00041970597546251153	0.00041970597546251153	NUM
iajs-3292	268	16	0.0004197059754639646	0.0004197059754639646	NUM
iajs-3292	268	17	6	6	NUM
iajs-3292	268	18	0.00017127579193321196	0.00017127579193321196	NUM
iajs-3292	268	19	0.00017127579194381904	0.00017127579194381904	NUM
iajs-3292	268	20	0.00017127579189292255	0.00017127579189292255	NUM
iajs-3292	268	21	7	7	NUM
iajs-3292	268	22	0.000025137988745926876	0.000025137988745926876	NUM
iajs-3292	268	23	0.00002513798831121161	0.00002513798831121161	NUM
iajs-3292	268	24	0.00002513798889495492	0.00002513798889495492	NUM
iajs-3292	268	25	8	8	NUM
iajs-3292	268	26	0.000001263005001916894	0.000001263005001916894	NUM
iajs-3292	268	27	0.000001263003365650816	0.000001263003365650816	NUM
iajs-3292	268	28	0.000001263003561146565	0.000001263003561146565	NUM
iajs-3292	268	29	9	9	NUM
iajs-3292	268	30	2.347967527072114	2.347967527072114	NUM
iajs-3292	268	31	×	×	NOUN
iajs-3292	268	32	10−7	10−7	NUM
iajs-3292	268	33	5.772589885717771	5.772589885717771	NUM
iajs-3292	268	34	×	×	NOUN
iajs-3292	268	35	10−7	10−7	NUM
iajs-3292	268	36	2.34800920268644	2.34800920268644	NUM
iajs-3292	268	37	×	×	NOUN
iajs-3292	268	38	10−7	10−7	NUM
iajs-3292	268	39	10	10	NUM
iajs-3292	268	40	1.588884090963915	1.588884090963915	NUM
iajs-3292	268	41	×	×	NOUN
iajs-3292	268	42	10−8	10−8	NUM
iajs-3292	268	43	5.387294752107197	5.387294752107197	NUM
iajs-3292	268	44	×	×	NOUN
iajs-3292	268	45	10−7	10−7	NUM
iajs-3292	268	46	1.59061837140361	1.59061837140361	NUM
iajs-3292	268	47	×	×	NOUN
iajs-3292	268	48	10−8	10−8	NUM
iajs-3292	268	49	11	11	NUM
iajs-3292	268	50	1.494825596637383	1.494825596637383	NUM
iajs-3292	268	51	×	×	NOUN
iajs-3292	268	52	10−9	10−9	NUM
iajs-3292	268	53	5.385043960887126	5.385043960887126	NUM
iajs-3292	268	54	×	×	NOUN
iajs-3292	268	55	10−7	10−7	NUM
iajs-3292	268	56	1.187559955162328	1.187559955162328	NUM
iajs-3292	268	57	×	×	NOUN
iajs-3292	268	58	10−9	10−9	NUM
iajs-3292	268	59	from	from	ADP
iajs-3292	268	60	figure	figure	NOUN
iajs-3292	268	61	1	1	NUM
iajs-3292	268	62	and	and	CCONJ
iajs-3292	268	63	table	table	NOUN
iajs-3292	268	64	1	1	NUM
iajs-3292	268	65	,	,	PUNCT
iajs-3292	268	66	we	we	PRON
iajs-3292	268	67	can	can	AUX
iajs-3292	268	68	conclude	conclude	VERB
iajs-3292	268	69	that	that	SCONJ
iajs-3292	268	70	the	the	DET
iajs-3292	268	71	value	value	NOUN
iajs-3292	268	72	of	of	ADP
iajs-3292	268	73	the	the	DET
iajs-3292	268	74	error	error	NOUN
iajs-3292	268	75	decreases	decrease	VERB
iajs-3292	268	76	as	as	ADP
iajs-3292	268	77	𝑛	𝑛	DET
iajs-3292	268	78	increases	increase	NOUN
iajs-3292	268	79	.	.	PUNCT
iajs-3292	269	1	thus	thus	ADV
iajs-3292	269	2	,	,	PUNCT
iajs-3292	269	3	the	the	DET
iajs-3292	269	4	brom	brom	NOUN
iajs-3292	269	5	method	method	NOUN
iajs-3292	269	6	is	be	AUX
iajs-3292	269	7	better	well	ADJ
iajs-3292	269	8	than	than	ADP
iajs-3292	269	9	the	the	DET
iajs-3292	269	10	lom	lom	NOUN
iajs-3292	269	11	method	method	NOUN
iajs-3292	269	12	and	and	CCONJ
iajs-3292	269	13	slightly	slightly	ADV
iajs-3292	269	14	better	well	ADJ
iajs-3292	269	15	than	than	ADP
iajs-3292	269	16	the	the	DET
iajs-3292	269	17	bom	bom	PROPN
iajs-3292	269	18	method	method	NOUN
iajs-3292	269	19	.	.	PUNCT
iajs-3292	270	1	moreover	moreover	ADV
iajs-3292	270	2	,	,	PUNCT
iajs-3292	270	3	a	a	DET
iajs-3292	270	4	comparison	comparison	NOUN
iajs-3292	270	5	was	be	AUX
iajs-3292	270	6	made	make	VERB
iajs-3292	270	7	between	between	ADP
iajs-3292	270	8	the	the	DET
iajs-3292	270	9	approximate	approximate	ADJ
iajs-3292	270	10	solutions	solution	NOUN
iajs-3292	270	11	found	find	VERB
iajs-3292	270	12	by	by	ADP
iajs-3292	270	13	the	the	DET
iajs-3292	270	14	proposed	propose	VERB
iajs-3292	270	15	methods	method	NOUN
iajs-3292	270	16	at	at	ADP
iajs-3292	270	17	𝑛	𝑛	PROPN
iajs-3292	270	18	=	=	SYM
iajs-3292	270	19	11	11	NUM
iajs-3292	270	20	,	,	PUNCT
iajs-3292	270	21	and	and	CCONJ
iajs-3292	270	22	the	the	DET
iajs-3292	270	23	numerical	numerical	ADJ
iajs-3292	270	24	solution	solution	NOUN
iajs-3292	270	25	obtained	obtain	VERB
iajs-3292	270	26	by	by	ADP
iajs-3292	270	27	the	the	DET
iajs-3292	270	28	range	range	NOUN
iajs-3292	270	29	-	-	PUNCT
iajs-3292	270	30	kutta	kutta	NOUN
iajs-3292	270	31	method	method	NOUN
iajs-3292	270	32	(	(	PUNCT
iajs-3292	270	33	rk4	rk4	NOUN
iajs-3292	270	34	)	)	PUNCT
iajs-3292	270	35	.	.	PUNCT
iajs-3292	271	1	this	this	PRON
iajs-3292	271	2	is	be	AUX
iajs-3292	271	3	shown	show	VERB
iajs-3292	271	4	in	in	ADP
iajs-3292	271	5	figure	figure	NOUN
iajs-3292	271	6	2	2	NUM
iajs-3292	271	7	,	,	PUNCT
iajs-3292	271	8	which	which	PRON
iajs-3292	271	9	shows	show	VERB
iajs-3292	271	10	a	a	DET
iajs-3292	271	11	good	good	ADJ
iajs-3292	271	12	agreement	agreement	NOUN
iajs-3292	271	13	between	between	ADP
iajs-3292	271	14	them	they	PRON
iajs-3292	271	15	.	.	PUNCT
iajs-3292	272	1	figure	figure	VERB
iajs-3292	272	2	2	2	NUM
iajs-3292	272	3	.	.	PUNCT
iajs-3292	273	1	the	the	DET
iajs-3292	273	2	comparison	comparison	NOUN
iajs-3292	273	3	of	of	ADP
iajs-3292	273	4	the	the	DET
iajs-3292	273	5	solutions	solution	NOUN
iajs-3292	273	6	of	of	ADP
iajs-3292	273	7	proposed	propose	VERB
iajs-3292	273	8	methods	method	NOUN
iajs-3292	273	9	and	and	CCONJ
iajs-3292	273	10	rk4	rk4	NOUN
iajs-3292	273	11	at	at	ADP
iajs-3292	273	12	𝑛	𝑛	PROPN
iajs-3292	273	13	=	=	SYM
iajs-3292	273	14	11	11	NUM
iajs-3292	273	15	.	.	PUNCT
iajs-3292	273	16	to	to	PART
iajs-3292	273	17	investigate	investigate	VERB
iajs-3292	273	18	the	the	DET
iajs-3292	273	19	convergence	convergence	NOUN
iajs-3292	273	20	of	of	ADP
iajs-3292	273	21	the	the	DET
iajs-3292	273	22	solutions	solution	NOUN
iajs-3292	273	23	of	of	ADP
iajs-3292	273	24	the	the	DET
iajs-3292	273	25	nonlinear	nonlinear	ADJ
iajs-3292	273	26	blasius	blasius	ADJ
iajs-3292	273	27	equation	equation	NOUN
iajs-3292	273	28	,	,	PUNCT
iajs-3292	273	29	the	the	DET
iajs-3292	273	30	convergence	convergence	NOUN
iajs-3292	273	31	condition	condition	NOUN
iajs-3292	273	32	described	describe	VERB
iajs-3292	273	33	in	in	ADP
iajs-3292	273	34	section	section	NOUN
iajs-3292	273	35	4	4	NUM
iajs-3292	273	36	is	be	AUX
iajs-3292	273	37	applied	apply	VERB
iajs-3292	273	38	to	to	ADP
iajs-3292	273	39	the	the	DET
iajs-3292	273	40	solutions	solution	NOUN
iajs-3292	273	41	of	of	ADP
iajs-3292	273	42	the	the	DET
iajs-3292	273	43	proposed	propose	VERB
iajs-3292	273	44	methods	method	NOUN
iajs-3292	273	45	for	for	ADP
iajs-3292	273	46	all	all	DET
iajs-3292	273	47	iterations	iteration	NOUN
iajs-3292	273	48	n	n	PRON
iajs-3292	273	49	(	(	PUNCT
iajs-3292	273	50	n=3	n=3	PUNCT
iajs-3292	273	51	to	to	ADP
iajs-3292	273	52	11	11	NUM
iajs-3292	273	53	)	)	PUNCT
iajs-3292	273	54	by	by	ADP
iajs-3292	273	55	calculating	calculate	VERB
iajs-3292	273	56	the	the	DET
iajs-3292	273	57	values	value	NOUN
iajs-3292	273	58	of	of	ADP
iajs-3292	273	59	𝛽𝑖	𝛽𝑖	NOUN
iajs-3292	273	60	=	=	SYM
iajs-3292	273	61	‖𝑣𝑖+1(𝑥)‖	‖𝑣𝑖+1(𝑥)‖	PROPN
iajs-3292	273	62	‖𝑣𝑖(𝑥)‖	‖𝑣𝑖(𝑥)‖	PROPN
iajs-3292	273	63	,	,	PUNCT
iajs-3292	273	64	as	as	SCONJ
iajs-3292	273	65	shown	show	VERB
iajs-3292	273	66	in	in	ADP
iajs-3292	273	67	ihjpas	ihjpas	PROPN
iajs-3292	273	68	.	.	PUNCT
iajs-3292	274	1	37	37	NUM
iajs-3292	274	2	(	(	PUNCT
iajs-3292	274	3	1	1	NUM
iajs-3292	274	4	)	)	PUNCT
iajs-3292	274	5	2024	2024	NUM
iajs-3292	274	6	369	369	NUM
iajs-3292	274	7	table	table	NOUN
iajs-3292	274	8	2	2	NUM
iajs-3292	274	9	,	,	PUNCT
iajs-3292	274	10	the	the	DET
iajs-3292	274	11	values	value	NOUN
iajs-3292	274	12	of	of	ADP
iajs-3292	274	13	𝛽𝑖	𝛽𝑖	VERB
iajs-3292	274	14	for	for	ADP
iajs-3292	274	15	all	all	PRON
iajs-3292	274	16	𝑖	𝑖	PRON
iajs-3292	274	17	≥	≥	NOUN
iajs-3292	274	18	3	3	NUM
iajs-3292	274	19	are	be	AUX
iajs-3292	274	20	less	less	ADJ
iajs-3292	274	21	than	than	ADP
iajs-3292	274	22	1	1	NUM
iajs-3292	274	23	,	,	PUNCT
iajs-3292	274	24	so	so	SCONJ
iajs-3292	274	25	these	these	DET
iajs-3292	274	26	solutions	solution	NOUN
iajs-3292	274	27	converge	converge	VERB
iajs-3292	274	28	to	to	ADP
iajs-3292	274	29	the	the	DET
iajs-3292	274	30	exact	exact	ADJ
iajs-3292	274	31	solution	solution	NOUN
iajs-3292	274	32	.	.	PUNCT
iajs-3292	275	1	table	table	NOUN
iajs-3292	275	2	2	2	NUM
iajs-3292	275	3	.	.	PUNCT
iajs-3292	276	1	the	the	DET
iajs-3292	276	2	value	value	NOUN
iajs-3292	276	3	of	of	ADP
iajs-3292	276	4	𝛽𝑖	𝛽𝑖	NOUN
iajs-3292	276	5	to	to	ADP
iajs-3292	276	6	the	the	DET
iajs-3292	276	7	solutions	solution	NOUN
iajs-3292	276	8	of	of	ADP
iajs-3292	276	9	the	the	DET
iajs-3292	276	10	proposed	propose	VERB
iajs-3292	276	11	methods	method	NOUN
iajs-3292	276	12	for	for	ADP
iajs-3292	276	13	𝑛	𝑛	NOUN
iajs-3292	276	14	=	=	SYM
iajs-3292	276	15	3	3	NUM
iajs-3292	276	16	to	to	PART
iajs-3292	276	17	11	11	NUM
iajs-3292	276	18	when	when	SCONJ
iajs-3292	276	19	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	276	20	)	)	PUNCT
iajs-3292	276	21	=	=	SYM
iajs-3292	276	22	0.3320573	0.3320573	NUM
iajs-3292	276	23	.	.	PUNCT
iajs-3292	276	24	𝛽𝑖	𝛽𝑖	VERB
iajs-3292	276	25	bom	bom	PROPN
iajs-3292	276	26	lom	lom	PROPN
iajs-3292	276	27	brom	brom	PROPN
iajs-3292	276	28	𝛽3	𝛽3	PROPN
iajs-3292	276	29	0.016073750074326664	0.016073750074326664	NUM
iajs-3292	276	30	0.01607375007432271	0.01607375007432271	NUM
iajs-3292	276	31	0.016073750074321977	0.016073750074321977	NUM
iajs-3292	276	32	𝛽4	𝛽4	PROPN
iajs-3292	276	33	0.29293061768966266	0.29293061768966266	NUM
iajs-3292	276	34	0.29293061766935835	0.29293061766935835	NUM
iajs-3292	276	35	0.2929306176693013	0.2929306176693013	NUM
iajs-3292	276	36	𝛽5	𝛽5	NOUN
iajs-3292	276	37	0.03639714771755241	0.03639714771755241	NUM
iajs-3292	276	38	0.03639714778922806	0.03639714778922806	NUM
iajs-3292	276	39	0.03639714778673125	0.03639714778673125	NUM
iajs-3292	276	40	𝛽6	𝛽6	NOUN
iajs-3292	276	41	0.24728635030717735	0.24728635030717735	NUM
iajs-3292	276	42	0.24728634929502963	0.24728634929502963	NUM
iajs-3292	276	43	0.24728634997162285	0.24728634997162285	NUM
iajs-3292	276	44	𝛽7	𝛽7	NOUN
iajs-3292	276	45	0.09393295721721101	0.09393295721721101	NUM
iajs-3292	276	46	0.09393296065173386	0.09393296065173386	NUM
iajs-3292	276	47	0.09393296261024817	0.09393296261024817	NUM
iajs-3292	276	48	𝛽8	𝛽8	NOUN
iajs-3292	276	49	0.0477950301697603	0.0477950301697603	NUM
iajs-3292	276	50	0.04779170199698017	0.04779170199698017	NUM
iajs-3292	276	51	0.047795085567504614	0.047795085567504614	NUM
iajs-3292	276	52	𝛽9	𝛽9	VERB
iajs-3292	276	53	0.13563608954043813	0.13563608954043813	NUM
iajs-3292	276	54	0.1356410881800995	0.1356410881800995	NUM
iajs-3292	276	55	0.1356460394028394	0.1356460394028394	NUM
iajs-3292	276	56	𝛽10	𝛽10	NOUN
iajs-3292	276	57	0.047883452366514034	0.047883452366514034	NUM
iajs-3292	276	58	0.04874842641203115	0.04874842641203115	NUM
iajs-3292	276	59	0.04878982655985626	0.04878982655985626	NUM
iajs-3292	276	60	on	on	ADP
iajs-3292	276	61	the	the	DET
iajs-3292	276	62	other	other	ADJ
iajs-3292	276	63	hand	hand	NOUN
iajs-3292	276	64	,	,	PUNCT
iajs-3292	276	65	in	in	ADP
iajs-3292	276	66	[	[	X
iajs-3292	276	67	5	5	X
iajs-3292	276	68	]	]	PUNCT
iajs-3292	276	69	the	the	DET
iajs-3292	276	70	blasius	blasius	ADJ
iajs-3292	276	71	equation	equation	NOUN
iajs-3292	276	72	for	for	ADP
iajs-3292	276	73	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	276	74	)	)	PUNCT
iajs-3292	276	75	=	=	SYM
iajs-3292	276	76	1	1	NUM
iajs-3292	276	77	was	be	AUX
iajs-3292	276	78	solved	solve	VERB
iajs-3292	276	79	with	with	ADP
iajs-3292	276	80	bom	bom	PROPN
iajs-3292	276	81	at	at	ADP
iajs-3292	276	82	𝑛	𝑛	PROPN
iajs-3292	276	83	=	=	SYM
iajs-3292	276	84	11	11	NUM
iajs-3292	276	85	,	,	PUNCT
iajs-3292	276	86	so	so	ADV
iajs-3292	276	87	figure	figure	NOUN
iajs-3292	276	88	3	3	NUM
iajs-3292	276	89	shows	show	VERB
iajs-3292	276	90	the	the	DET
iajs-3292	276	91	difference	difference	NOUN
iajs-3292	276	92	between	between	ADP
iajs-3292	276	93	the	the	DET
iajs-3292	276	94	approximate	approximate	ADJ
iajs-3292	276	95	solution	solution	NOUN
iajs-3292	276	96	at	at	ADP
iajs-3292	276	97	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	276	98	)	)	PUNCT
iajs-3292	277	1	=	=	SYM
iajs-3292	277	2	0.3320573	0.3320573	NUM
iajs-3292	277	3	and	and	CCONJ
iajs-3292	277	4	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	277	5	)	)	PUNCT
iajs-3292	278	1	=	=	SYM
iajs-3292	278	2	1	1	X
iajs-3292	278	3	.	.	X
iajs-3292	278	4	figure	figure	NOUN
iajs-3292	278	5	3	3	NUM
iajs-3292	278	6	.	.	PUNCT
iajs-3292	278	7	comparing	compare	VERB
iajs-3292	278	8	the	the	DET
iajs-3292	278	9	solution	solution	NOUN
iajs-3292	278	10	to	to	ADP
iajs-3292	278	11	the	the	DET
iajs-3292	278	12	blasius	blasius	ADJ
iajs-3292	278	13	equation	equation	NOUN
iajs-3292	278	14	by	by	ADP
iajs-3292	278	15	bom	bom	NOUN
iajs-3292	278	16	for	for	ADP
iajs-3292	278	17	two	two	NUM
iajs-3292	278	18	different	different	ADJ
iajs-3292	278	19	values	value	NOUN
iajs-3292	278	20	of	of	ADP
iajs-3292	278	21	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	278	22	)	)	PUNCT
iajs-3292	278	23	at	at	ADP
iajs-3292	278	24	𝑛	𝑛	PROPN
iajs-3292	278	25	=	=	SYM
iajs-3292	278	26	11	11	NUM
iajs-3292	278	27	.	.	PUNCT
iajs-3292	279	1	from	from	ADP
iajs-3292	279	2	the	the	DET
iajs-3292	279	3	above	above	ADJ
iajs-3292	279	4	figure	figure	NOUN
iajs-3292	279	5	,	,	PUNCT
iajs-3292	279	6	it	it	PRON
iajs-3292	279	7	can	can	AUX
iajs-3292	279	8	be	be	AUX
iajs-3292	279	9	seen	see	VERB
iajs-3292	279	10	that	that	SCONJ
iajs-3292	279	11	the	the	DET
iajs-3292	279	12	solution	solution	NOUN
iajs-3292	279	13	is	be	AUX
iajs-3292	279	14	better	well	ADJ
iajs-3292	279	15	at	at	ADP
iajs-3292	279	16	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	279	17	)	)	PUNCT
iajs-3292	280	1	=	=	SYM
iajs-3292	280	2	0.3320573	0.3320573	NUM
iajs-3292	280	3	.	.	PUNCT
iajs-3292	281	1	to	to	PART
iajs-3292	281	2	illustrate	illustrate	VERB
iajs-3292	281	3	this	this	PRON
iajs-3292	281	4	,	,	PUNCT
iajs-3292	281	5	the	the	DET
iajs-3292	281	6	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3292	281	7	for	for	ADP
iajs-3292	281	8	both	both	DET
iajs-3292	281	9	values	value	NOUN
iajs-3292	281	10	of	of	ADP
iajs-3292	281	11	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	281	12	)	)	PUNCT
iajs-3292	281	13	was	be	AUX
iajs-3292	281	14	calculated	calculate	VERB
iajs-3292	281	15	for	for	ADP
iajs-3292	281	16	all	all	DET
iajs-3292	281	17	𝑛	𝑛	PROPN
iajs-3292	281	18	(	(	PUNCT
iajs-3292	281	19	𝑛	𝑛	NOUN
iajs-3292	281	20	=	=	SYM
iajs-3292	281	21	3	3	NUM
iajs-3292	281	22	to	to	PART
iajs-3292	281	23	11	11	NUM
iajs-3292	281	24	)	)	PUNCT
iajs-3292	281	25	as	as	ADP
iajs-3292	281	26	in	in	ADP
iajs-3292	281	27	table	table	NOUN
iajs-3292	281	28	3	3	NUM
iajs-3292	281	29	.	.	PUNCT
iajs-3292	281	30	ihjpas	ihjpas	PROPN
iajs-3292	281	31	.	.	PUNCT
iajs-3292	282	1	37	37	NUM
iajs-3292	282	2	(	(	PUNCT
iajs-3292	282	3	1	1	NUM
iajs-3292	282	4	)	)	PUNCT
iajs-3292	282	5	2024	2024	NUM
iajs-3292	282	6	370	370	NUM
iajs-3292	282	7	table	table	NOUN
iajs-3292	282	8	3	3	NUM
iajs-3292	282	9	.	.	PUNCT
iajs-3292	283	1	the	the	DET
iajs-3292	283	2	comparison	comparison	NOUN
iajs-3292	283	3	of	of	ADP
iajs-3292	283	4	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3292	283	5	of	of	ADP
iajs-3292	283	6	the	the	DET
iajs-3292	283	7	solutions	solution	NOUN
iajs-3292	283	8	of	of	ADP
iajs-3292	283	9	the	the	DET
iajs-3292	283	10	blasius	blasius	ADJ
iajs-3292	283	11	equation	equation	NOUN
iajs-3292	283	12	by	by	ADP
iajs-3292	283	13	bom	bom	PROPN
iajs-3292	283	14	at	at	ADP
iajs-3292	283	15	n=3	n=3	PUNCT
iajs-3292	283	16	to	to	ADP
iajs-3292	283	17	11	11	NUM
iajs-3292	283	18	at	at	ADP
iajs-3292	283	19	two	two	NUM
iajs-3292	283	20	different	different	ADJ
iajs-3292	283	21	values	value	NOUN
iajs-3292	283	22	of	of	ADP
iajs-3292	283	23	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	283	24	)	)	PUNCT
iajs-3292	283	25	𝑛	𝑛	ADP
iajs-3292	283	26	when	when	SCONJ
iajs-3292	283	27	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	283	28	)	)	PUNCT
iajs-3292	283	29	=	=	PUNCT
iajs-3292	283	30	0.3320573	0.3320573	NUM
iajs-3292	283	31	when	when	SCONJ
iajs-3292	283	32	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	283	33	)	)	PUNCT
iajs-3292	283	34	=	=	SYM
iajs-3292	283	35	1	1	NUM
iajs-3292	283	36	3	3	NUM
iajs-3292	283	37	0.014819391700592988	0.014819391700592988	NUM
iajs-3292	283	38	0.12364105477870169	0.12364105477870169	NUM
iajs-3292	283	39	4	4	NUM
iajs-3292	283	40	0.011427015738563973	0.011427015738563973	NUM
iajs-3292	283	41	0.09719389597650396	0.09719389597650396	NUM
iajs-3292	283	42	5	5	NUM
iajs-3292	283	43	0.0004197059747635956	0.0004197059747635956	NUM
iajs-3292	283	44	0.011027011129465247	0.011027011129465247	NUM
iajs-3292	283	45	6	6	NUM
iajs-3292	283	46	0.00017127579193321196	0.00017127579193321196	NUM
iajs-3292	283	47	0.004293535161145279	0.004293535161145279	NUM
iajs-3292	283	48	7	7	NUM
iajs-3292	283	49	0.000025137988745926876	0.000025137988745926876	NUM
iajs-3292	283	50	0.0004907797800370872	0.0004907797800370872	NUM
iajs-3292	283	51	8	8	NUM
iajs-3292	283	52	0.000001263005001916894	0.000001263005001916894	NUM
iajs-3292	283	53	0.00009600784941188323	0.00009600784941188323	NUM
iajs-3292	283	54	9	9	NUM
iajs-3292	283	55	2.347967527072114	2.347967527072114	NUM
iajs-3292	283	56	×	×	NOUN
iajs-3292	283	57	10−7	10−7	NUM
iajs-3292	283	58	0.00001612130638850573	0.00001612130638850573	NUM
iajs-3292	283	59	10	10	NUM
iajs-3292	283	60	1.588884090963915	1.588884090963915	NUM
iajs-3292	283	61	×	×	NOUN
iajs-3292	283	62	10−8	10−8	NUM
iajs-3292	283	63	4.033942939685175	4.033942939685175	NUM
iajs-3292	283	64	×	×	NOUN
iajs-3292	283	65	10−7	10−7	NUM
iajs-3292	283	66	11	11	NUM
iajs-3292	283	67	1.494825596637383	1.494825596637383	NUM
iajs-3292	283	68	×	×	NOUN
iajs-3292	283	69	10−9	10−9	NUM
iajs-3292	283	70	2.636242850684311	2.636242850684311	NUM
iajs-3292	283	71	×	×	NOUN
iajs-3292	283	72	10−7	10−7	NUM
iajs-3292	283	73	thus	thus	ADV
iajs-3292	283	74	,	,	PUNCT
iajs-3292	283	75	it	it	PRON
iajs-3292	283	76	can	can	AUX
iajs-3292	283	77	be	be	AUX
iajs-3292	283	78	clearly	clearly	ADV
iajs-3292	283	79	seen	see	VERB
iajs-3292	283	80	that	that	SCONJ
iajs-3292	283	81	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3292	283	82	converges	converge	VERB
iajs-3292	283	83	to	to	ADP
iajs-3292	283	84	zero	zero	NUM
iajs-3292	283	85	faster	fast	ADV
iajs-3292	283	86	in	in	ADP
iajs-3292	283	87	the	the	DET
iajs-3292	283	88	case	case	NOUN
iajs-3292	283	89	of	of	ADP
iajs-3292	283	90	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	283	91	)	)	PUNCT
iajs-3292	283	92	=	=	SYM
iajs-3292	284	1	0.3320573	0.3320573	NUM
iajs-3292	284	2	than	than	ADP
iajs-3292	284	3	in	in	ADP
iajs-3292	284	4	the	the	DET
iajs-3292	284	5	case	case	NOUN
iajs-3292	284	6	of	of	ADP
iajs-3292	284	7	at	at	ADP
iajs-3292	284	8	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	284	9	)	)	PUNCT
iajs-3292	284	10	=	=	SYM
iajs-3292	285	1	1	1	NUM
iajs-3292	285	2	,	,	PUNCT
iajs-3292	285	3	as	as	ADP
iajs-3292	285	4	𝑛	𝑛	DET
iajs-3292	285	5	increases	increase	NOUN
iajs-3292	285	6	.	.	PUNCT
iajs-3292	286	1	moreover	moreover	ADV
iajs-3292	286	2	,	,	PUNCT
iajs-3292	286	3	we	we	PRON
iajs-3292	286	4	will	will	AUX
iajs-3292	286	5	solve	solve	VERB
iajs-3292	286	6	this	this	DET
iajs-3292	286	7	problem	problem	NOUN
iajs-3292	286	8	with	with	ADP
iajs-3292	286	9	the	the	DET
iajs-3292	286	10	initial	initial	ADJ
iajs-3292	286	11	condition	condition	NOUN
iajs-3292	286	12	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	286	13	)	)	PUNCT
iajs-3292	286	14	=	=	PUNCT
iajs-3292	287	1	1	1	NUM
iajs-3292	287	2	using	use	VERB
iajs-3292	287	3	the	the	DET
iajs-3292	287	4	shifted	shift	VERB
iajs-3292	287	5	lom	lom	NOUN
iajs-3292	287	6	and	and	CCONJ
iajs-3292	287	7	the	the	DET
iajs-3292	287	8	brom	brom	NOUN
iajs-3292	287	9	.	.	PUNCT
iajs-3292	288	1	the	the	DET
iajs-3292	288	2	solution	solution	NOUN
iajs-3292	288	3	with	with	ADP
iajs-3292	288	4	the	the	DET
iajs-3292	288	5	shifted	shift	VERB
iajs-3292	288	6	lom	lom	NOUN
iajs-3292	288	7	when	when	SCONJ
iajs-3292	288	8	𝑛	𝑛	PROPN
iajs-3292	288	9	=	=	SYM
iajs-3292	288	10	11	11	NUM
iajs-3292	288	11	is	be	AUX
iajs-3292	288	12	as	as	SCONJ
iajs-3292	288	13	follows	follow	VERB
iajs-3292	288	14	:	:	PUNCT
iajs-3292	288	15	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	288	16	)	)	PUNCT
iajs-3292	288	17	=	=	PUNCT
iajs-3292	288	18	2.717523012968703	2.717523012968703	NUM
iajs-3292	288	19	×	×	NOUN
iajs-3292	288	20	10−11	10−11	NUM
iajs-3292	288	21	−	−	PROPN
iajs-3292	288	22	2.989454184199047	2.989454184199047	NUM
iajs-3292	288	23	×	×	NOUN
iajs-3292	288	24	10−9𝑥	10−9𝑥	NUM
iajs-3292	288	25	+	+	CCONJ
iajs-3292	288	26	0.5000000807212571𝑥2	0.5000000807212571𝑥2	NUM
iajs-3292	288	27	−	−	PROPN
iajs-3292	288	28	8.890725537863409	8.890725537863409	NUM
iajs-3292	288	29	×	×	NOUN
iajs-3292	288	30	10−7𝑥3	10−7𝑥3	NUM
iajs-3292	288	31	+	+	CCONJ
iajs-3292	288	32	0.00000538235410165247𝑥4	0.00000538235410165247𝑥4	NUM
iajs-3292	288	33	−	−	PROPN
iajs-3292	288	34	0.00418570492658484𝑥5	0.00418570492658484𝑥5	NOUN
iajs-3292	289	1	+	+	CCONJ
iajs-3292	289	2	0.000041144785309415706𝑥6	0.000041144785309415706𝑥6	NUM
iajs-3292	289	3	−	−	NUM
iajs-3292	289	4	0.000054417856055302455𝑥7	0.000054417856055302455𝑥7	NUM
iajs-3292	290	1	+	+	CCONJ
iajs-3292	291	1	0.00010990985811043829𝑥8	0.00010990985811043829𝑥8	NUM
iajs-3292	291	2	−	−	NUM
iajs-3292	292	1	0.000015116787731315758𝑥9	0.000015116787731315758𝑥9	NUM
iajs-3292	292	2	.	.	PUNCT
iajs-3292	293	1	(	(	PUNCT
iajs-3292	293	2	39	39	NUM
iajs-3292	293	3	)	)	PUNCT
iajs-3292	293	4	if	if	SCONJ
iajs-3292	293	5	the	the	DET
iajs-3292	293	6	brom	brom	NOUN
iajs-3292	293	7	apply	apply	VERB
iajs-3292	293	8	,	,	PUNCT
iajs-3292	293	9	the	the	DET
iajs-3292	293	10	approximate	approximate	ADJ
iajs-3292	293	11	solution	solution	NOUN
iajs-3292	293	12	is	be	AUX
iajs-3292	293	13	as	as	SCONJ
iajs-3292	293	14	follows	follow	VERB
iajs-3292	293	15	:	:	PUNCT
iajs-3292	293	16	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3292	293	17	)	)	PUNCT
iajs-3292	294	1	=	=	PUNCT
iajs-3292	295	1	4.28022688906543	4.28022688906543	NUM
iajs-3292	295	2	×	×	NOUN
iajs-3292	295	3	10−17	10−17	NUM
iajs-3292	295	4	+	+	NOUN
iajs-3292	295	5	4.126066892665148	4.126066892665148	NUM
iajs-3292	295	6	×	×	NOUN
iajs-3292	295	7	10−17𝑥	10−17𝑥	NUM
iajs-3292	295	8	+	+	CCONJ
iajs-3292	295	9	0.5𝑥2	0.5𝑥2	NUM
iajs-3292	295	10	+	+	CCONJ
iajs-3292	295	11	4.379568419265968	4.379568419265968	NUM
iajs-3292	295	12	×	×	NOUN
iajs-3292	295	13	10−8𝑥3	10−8𝑥3	NUM
iajs-3292	295	14	−	−	PROPN
iajs-3292	295	15	3.321493629909657	3.321493629909657	NUM
iajs-3292	295	16	×	×	NOUN
iajs-3292	295	17	10−7𝑥4	10−7𝑥4	NUM
iajs-3292	295	18	−	−	NOUN
iajs-3292	295	19	0.0041651294231496725𝑥5	0.0041651294231496725𝑥5	NUM
iajs-3292	295	20	−	−	NUM
iajs-3292	295	21	0.000004588795148760594𝑥6	0.000004588795148760594𝑥6	NUM
iajs-3292	295	22	+	+	CCONJ
iajs-3292	295	23	0.000009070467696073757𝑥7	0.000009070467696073757𝑥7	NUM
iajs-3292	295	24	+	+	CCONJ
iajs-3292	295	25	0.000056311613028286645𝑥8	0.000056311613028286645𝑥8	NUM
iajs-3292	295	26	+	+	CCONJ
iajs-3292	295	27	0.000010056188911186578𝑥9	0.000010056188911186578𝑥9	ADV
iajs-3292	295	28	−	−	NOUN
iajs-3292	295	29	0.000005051467149564113𝑥10	0.000005051467149564113𝑥10	NOUN
iajs-3292	295	30	+	+	CCONJ
iajs-3292	295	31	5.856448890320508	5.856448890320508	NUM
iajs-3292	295	32	×	×	NOUN
iajs-3292	295	33	10−9𝑥11	10−9𝑥11	NUM
iajs-3292	295	34	.	.	PUNCT
iajs-3292	296	1	(	(	PUNCT
iajs-3292	296	2	40	40	NUM
iajs-3292	296	3	)	)	PUNCT
iajs-3292	296	4	table	table	NOUN
iajs-3292	296	5	4	4	NUM
iajs-3292	296	6	shows	show	VERB
iajs-3292	296	7	a	a	DET
iajs-3292	296	8	comparison	comparison	NOUN
iajs-3292	296	9	between	between	ADP
iajs-3292	296	10	the	the	DET
iajs-3292	296	11	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3292	296	12	of	of	ADP
iajs-3292	296	13	the	the	DET
iajs-3292	296	14	three	three	NUM
iajs-3292	296	15	proposed	propose	VERB
iajs-3292	296	16	methods	method	NOUN
iajs-3292	296	17	for	for	ADP
iajs-3292	296	18	this	this	DET
iajs-3292	296	19	problem	problem	NOUN
iajs-3292	296	20	for	for	ADP
iajs-3292	296	21	all	all	DET
iajs-3292	296	22	iterations	iteration	NOUN
iajs-3292	296	23	n	n	PRON
iajs-3292	296	24	(	(	PUNCT
iajs-3292	296	25	n=3	n=3	PUNCT
iajs-3292	296	26	to	to	ADP
iajs-3292	296	27	11	11	NUM
iajs-3292	296	28	)	)	PUNCT
iajs-3292	296	29	.	.	PUNCT
iajs-3292	297	1	it	it	PRON
iajs-3292	297	2	can	can	AUX
iajs-3292	297	3	be	be	AUX
iajs-3292	297	4	seen	see	VERB
iajs-3292	297	5	that	that	SCONJ
iajs-3292	297	6	the	the	DET
iajs-3292	297	7	accuracy	accuracy	NOUN
iajs-3292	297	8	increases	increase	VERB
iajs-3292	297	9	as	as	ADP
iajs-3292	297	10	n	n	DET
iajs-3292	297	11	increases	increase	NOUN
iajs-3292	297	12	.	.	PUNCT
iajs-3292	298	1	also	also	ADV
iajs-3292	298	2	,	,	PUNCT
iajs-3292	298	3	the	the	DET
iajs-3292	298	4	brom	brom	NOUN
iajs-3292	298	5	and	and	CCONJ
iajs-3292	298	6	the	the	DET
iajs-3292	298	7	bom	bom	PROPN
iajs-3292	298	8	methods	method	NOUN
iajs-3292	298	9	are	be	AUX
iajs-3292	298	10	better	well	ADJ
iajs-3292	298	11	than	than	ADP
iajs-3292	298	12	the	the	DET
iajs-3292	298	13	lom	lom	NOUN
iajs-3292	298	14	method	method	NOUN
iajs-3292	298	15	,	,	PUNCT
iajs-3292	298	16	and	and	CCONJ
iajs-3292	298	17	the	the	DET
iajs-3292	298	18	brom	brom	NOUN
iajs-3292	298	19	method	method	NOUN
iajs-3292	298	20	is	be	AUX
iajs-3292	298	21	slightly	slightly	ADV
iajs-3292	298	22	better	well	ADJ
iajs-3292	298	23	than	than	ADP
iajs-3292	298	24	the	the	DET
iajs-3292	298	25	bom	bom	PROPN
iajs-3292	298	26	method	method	NOUN
iajs-3292	298	27	.	.	PUNCT
iajs-3292	299	1	ihjpas	ihjpas	PROPN
iajs-3292	299	2	.	.	PUNCT
iajs-3292	300	1	37	37	NUM
iajs-3292	300	2	(	(	PUNCT
iajs-3292	300	3	1	1	NUM
iajs-3292	300	4	)	)	PUNCT
iajs-3292	300	5	2024	2024	NUM
iajs-3292	300	6	371	371	NUM
iajs-3292	300	7	table	table	NOUN
iajs-3292	300	8	4	4	NUM
iajs-3292	300	9	.	.	PUNCT
iajs-3292	301	1	the	the	DET
iajs-3292	301	2	comparison	comparison	NOUN
iajs-3292	301	3	of	of	ADP
iajs-3292	301	4	𝑀𝐸𝑅𝑛	𝑀𝐸𝑅𝑛	NOUN
iajs-3292	301	5	between	between	ADP
iajs-3292	301	6	the	the	DET
iajs-3292	301	7	bom	bom	PROPN
iajs-3292	301	8	,	,	PUNCT
iajs-3292	301	9	lom	lom	PROPN
iajs-3292	301	10	,	,	PUNCT
iajs-3292	301	11	and	and	CCONJ
iajs-3292	301	12	brom	brom	NOUN
iajs-3292	301	13	methods	method	NOUN
iajs-3292	301	14	for	for	ADP
iajs-3292	301	15	𝑛	𝑛	NOUN
iajs-3292	301	16	=	=	SYM
iajs-3292	301	17	3	3	NUM
iajs-3292	301	18	to	to	PART
iajs-3292	301	19	11	11	NUM
iajs-3292	301	20	at	at	ADP
iajs-3292	301	21	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	301	22	)	)	PUNCT
iajs-3292	301	23	=	=	SYM
iajs-3292	302	1	1	1	X
iajs-3292	302	2	.	.	X
iajs-3292	302	3	𝑛	𝑛	PRON
iajs-3292	302	4	bom	bom	PROPN
iajs-3292	302	5	lom	lom	PROPN
iajs-3292	302	6	brom	brom	PROPN
iajs-3292	303	1	3	3	NUM
iajs-3292	303	2	0.12364105477870169	0.12364105477870169	NUM
iajs-3292	303	3	0.12364105477870149	0.12364105477870149	NUM
iajs-3292	303	4	0.12364105477870134	0.12364105477870134	NUM
iajs-3292	303	5	4	4	NUM
iajs-3292	303	6	0.09719389597650396	0.09719389597650396	NUM
iajs-3292	303	7	0.09719389597647592	0.09719389597647592	NUM
iajs-3292	303	8	0.09719389597650352	0.09719389597650352	NUM
iajs-3292	303	9	5	5	NUM
iajs-3292	303	10	0.011027011129465247	0.011027011129465247	NUM
iajs-3292	303	11	0.011027011129505574	0.011027011129505574	NUM
iajs-3292	303	12	0.011027011129506844	0.011027011129506844	NUM
iajs-3292	303	13	6	6	NUM
iajs-3292	303	14	0.004293535161145279	0.004293535161145279	NUM
iajs-3292	303	15	0.004293535161116567	0.004293535161116567	NUM
iajs-3292	303	16	0.00429353516106645	0.00429353516106645	NUM
iajs-3292	303	17	7	7	NUM
iajs-3292	303	18	0.0004907797800370872	0.0004907797800370872	NUM
iajs-3292	303	19	0.0004907797800190347	0.0004907797800190347	NUM
iajs-3292	303	20	0.0004907797804556991	0.0004907797804556991	NUM
iajs-3292	303	21	8	8	NUM
iajs-3292	303	22	0.00009600784941188323	0.00009600784941188323	NUM
iajs-3292	303	23	0.00009600784484897892	0.00009600784484897892	NUM
iajs-3292	303	24	0.00009600784504393617	0.00009600784504393617	NUM
iajs-3292	303	25	9	9	NUM
iajs-3292	303	26	0.00001612130638850573	0.00001612130638850573	NUM
iajs-3292	303	27	0.000016121319056666043	0.000016121319056666043	NUM
iajs-3292	303	28	0.000016121340651173055	0.000016121340651173055	NUM
iajs-3292	303	29	1	1	NUM
iajs-3292	303	30	0	0	NUM
iajs-3292	303	31	4.033942939685175	4.033942939685175	NUM
iajs-3292	303	32	×	×	NOUN
iajs-3292	303	33	10−7	10−7	NUM
iajs-3292	303	34	0.000005672419462032785	0.000005672419462032785	NUM
iajs-3292	303	35	4.034414582290297	4.034414582290297	NUM
iajs-3292	303	36	×	×	NOUN
iajs-3292	303	37	10−7	10−7	NUM
iajs-3292	303	38	1	1	NUM
iajs-3292	303	39	1	1	NUM
iajs-3292	303	40	2.636242850684311	2.636242850684311	NUM
iajs-3292	303	41	×	×	NOUN
iajs-3292	303	42	10−7	10−7	NUM
iajs-3292	303	43	0.000005624000721099476	0.000005624000721099476	NUM
iajs-3292	303	44	2.627741051773592	2.627741051773592	NUM
iajs-3292	303	45	×	×	NOUN
iajs-3292	303	46	10−7	10−7	NUM
iajs-3292	303	47	moreover	moreover	ADV
iajs-3292	303	48	,	,	PUNCT
iajs-3292	303	49	the	the	DET
iajs-3292	303	50	convergence	convergence	NOUN
iajs-3292	303	51	condition	condition	NOUN
iajs-3292	303	52	given	give	VERB
iajs-3292	303	53	in	in	ADP
iajs-3292	303	54	section	section	NOUN
iajs-3292	303	55	4	4	NUM
iajs-3292	303	56	is	be	AUX
iajs-3292	303	57	applied	apply	VERB
iajs-3292	303	58	to	to	ADP
iajs-3292	303	59	the	the	DET
iajs-3292	303	60	solutions	solution	NOUN
iajs-3292	303	61	of	of	ADP
iajs-3292	303	62	the	the	DET
iajs-3292	303	63	proposed	propose	VERB
iajs-3292	303	64	methods	method	NOUN
iajs-3292	303	65	for	for	ADP
iajs-3292	303	66	all	all	DET
iajs-3292	303	67	iterations	iteration	NOUN
iajs-3292	303	68	n	n	PRON
iajs-3292	303	69	(	(	PUNCT
iajs-3292	303	70	n=3	n=3	PUNCT
iajs-3292	303	71	to	to	ADP
iajs-3292	303	72	11	11	NUM
iajs-3292	303	73	)	)	PUNCT
iajs-3292	303	74	when	when	SCONJ
iajs-3292	303	75	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	303	76	)	)	PUNCT
iajs-3292	303	77	=	=	SYM
iajs-3292	303	78	1	1	NUM
iajs-3292	303	79	by	by	ADP
iajs-3292	303	80	calculating	calculate	VERB
iajs-3292	303	81	the	the	DET
iajs-3292	303	82	values	value	NOUN
iajs-3292	303	83	of	of	ADP
iajs-3292	303	84	𝛽𝑖	𝛽𝑖	NOUN
iajs-3292	303	85	=	=	SYM
iajs-3292	303	86	‖𝑣𝑖+1(𝑥)‖	‖𝑣𝑖+1(𝑥)‖	PROPN
iajs-3292	303	87	‖𝑣𝑖(𝑥)‖	‖𝑣𝑖(𝑥)‖	PROPN
iajs-3292	303	88	,	,	PUNCT
iajs-3292	303	89	as	as	SCONJ
iajs-3292	303	90	shown	show	VERB
iajs-3292	303	91	in	in	ADP
iajs-3292	303	92	table	table	NOUN
iajs-3292	303	93	5	5	NUM
iajs-3292	303	94	,	,	PUNCT
iajs-3292	303	95	the	the	DET
iajs-3292	303	96	values	value	NOUN
iajs-3292	303	97	of	of	ADP
iajs-3292	303	98	𝛽𝑖	𝛽𝑖	VERB
iajs-3292	303	99	for	for	ADP
iajs-3292	303	100	all	all	PRON
iajs-3292	303	101	𝑖	𝑖	PRON
iajs-3292	303	102	≥	≥	NOUN
iajs-3292	303	103	3	3	NUM
iajs-3292	303	104	are	be	AUX
iajs-3292	303	105	less	less	ADJ
iajs-3292	303	106	than	than	ADP
iajs-3292	303	107	1	1	NUM
iajs-3292	303	108	.	.	PUNCT
iajs-3292	304	1	consequently	consequently	ADV
iajs-3292	304	2	,	,	PUNCT
iajs-3292	304	3	the	the	DET
iajs-3292	304	4	convergence	convergence	NOUN
iajs-3292	304	5	condition	condition	NOUN
iajs-3292	304	6	is	be	AUX
iajs-3292	304	7	satisfied	satisfied	ADJ
iajs-3292	304	8	.	.	PUNCT
iajs-3292	305	1	table	table	NOUN
iajs-3292	305	2	5	5	NUM
iajs-3292	305	3	.	.	PUNCT
iajs-3292	306	1	the	the	DET
iajs-3292	306	2	value	value	NOUN
iajs-3292	306	3	of	of	ADP
iajs-3292	306	4	𝛽𝑖	𝛽𝑖	NOUN
iajs-3292	306	5	to	to	ADP
iajs-3292	306	6	the	the	DET
iajs-3292	306	7	solutions	solution	NOUN
iajs-3292	306	8	of	of	ADP
iajs-3292	306	9	the	the	DET
iajs-3292	306	10	proposed	propose	VERB
iajs-3292	306	11	methods	method	NOUN
iajs-3292	306	12	for	for	ADP
iajs-3292	306	13	𝑛	𝑛	NOUN
iajs-3292	306	14	=	=	SYM
iajs-3292	306	15	3	3	NUM
iajs-3292	306	16	to	to	PART
iajs-3292	306	17	11	11	NUM
iajs-3292	306	18	when	when	SCONJ
iajs-3292	306	19	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	306	20	)	)	PUNCT
iajs-3292	306	21	=	=	SYM
iajs-3292	306	22	1	1	X
iajs-3292	306	23	.	.	PUNCT
iajs-3292	306	24	𝛽𝑖	𝛽𝑖	VERB
iajs-3292	306	25	bom	bom	PROPN
iajs-3292	306	26	lom	lom	PROPN
iajs-3292	306	27	brom	brom	PROPN
iajs-3292	306	28	𝛽3	𝛽3	PROPN
iajs-3292	306	29	0.04510659083967248	0.04510659083967248	NUM
iajs-3292	306	30	0.04510659083966797	0.04510659083966797	NUM
iajs-3292	306	31	0.04510659083967211	0.04510659083967211	NUM
iajs-3292	306	32	𝛽4	𝛽4	PROPN
iajs-3292	306	33	0.277633864539339	0.277633864539339	NUM
iajs-3292	306	34	0.27763386453933614	0.27763386453933614	NUM
iajs-3292	306	35	0.04510659083967211	0.04510659083967211	NUM
iajs-3292	306	36	𝛽5	𝛽5	NOUN
iajs-3292	306	37	0.11985758340437944	0.11985758340437944	NUM
iajs-3292	306	38	0.11985758340397297	0.11985758340397297	NUM
iajs-3292	306	39	0.1198575834036301	0.1198575834036301	NUM
iajs-3292	306	40	𝛽6	𝛽6	NOUN
iajs-3292	307	1	0.23281227458321288	0.23281227458321288	NUM
iajs-3292	307	2	0.23281227457927967	0.23281227457927967	NUM
iajs-3292	307	3	0.23281227459976303	0.23281227459976303	NUM
iajs-3292	307	4	𝛽7	𝛽7	NOUN
iajs-3292	307	5	0.06500373117417597	0.06500373117417597	NUM
iajs-3292	307	6	0.06500373174199665	0.06500373174199665	NUM
iajs-3292	307	7	0.0650037318024709	0.0650037318024709	NUM
iajs-3292	307	8	𝛽8	𝛽8	NOUN
iajs-3292	307	9	0.21189027133781216	0.21189027133781216	NUM
iajs-3292	307	10	0.21189028400881857	0.21189028400881857	NUM
iajs-3292	307	11	0.21189031026366478	0.21189031026366478	NUM
iajs-3292	307	12	𝛽9	𝛽9	VERB
iajs-3292	307	13	0.1197929121542225	0.1197929121542225	NUM
iajs-3292	307	14	0.11979856224759194	0.11979856224759194	NUM
iajs-3292	307	15	0.11979340082544765	0.11979340082544765	NUM
iajs-3292	307	16	𝛽10	𝛽10	VERB
iajs-3292	307	17	0.008393018377721006	0.008393018377721006	NUM
iajs-3292	307	18	0.008431707509080347	0.008431707509080347	NUM
iajs-3292	307	19	0.008431055448947825	0.008431055448947825	NUM
iajs-3292	307	20	6	6	NUM
iajs-3292	307	21	.	.	PUNCT
iajs-3292	307	22	conclusions	conclusion	NOUN
iajs-3292	307	23	in	in	ADP
iajs-3292	307	24	this	this	DET
iajs-3292	307	25	work	work	NOUN
iajs-3292	307	26	,	,	PUNCT
iajs-3292	307	27	the	the	DET
iajs-3292	307	28	operational	operational	ADJ
iajs-3292	307	29	matrices	matrix	NOUN
iajs-3292	307	30	of	of	ADP
iajs-3292	307	31	differentiation	differentiation	NOUN
iajs-3292	307	32	were	be	AUX
iajs-3292	307	33	used	use	VERB
iajs-3292	307	34	based	base	VERB
iajs-3292	307	35	on	on	ADP
iajs-3292	307	36	:	:	PUNCT
iajs-3292	307	37	bernstein	bernstein	PROPN
iajs-3292	307	38	,	,	PUNCT
iajs-3292	307	39	shifted	shift	VERB
iajs-3292	307	40	legendre	legendre	PROPN
iajs-3292	307	41	,	,	PUNCT
iajs-3292	307	42	and	and	CCONJ
iajs-3292	307	43	bernoulli	bernoulli	NOUN
iajs-3292	307	44	polynomials	polynomial	NOUN
iajs-3292	307	45	to	to	PART
iajs-3292	307	46	solve	solve	VERB
iajs-3292	307	47	the	the	DET
iajs-3292	307	48	nonlinear	nonlinear	ADJ
iajs-3292	307	49	blasius	blasius	ADJ
iajs-3292	307	50	equation	equation	NOUN
iajs-3292	307	51	.	.	PUNCT
iajs-3292	308	1	we	we	PRON
iajs-3292	308	2	concluded	conclude	VERB
iajs-3292	308	3	that	that	SCONJ
iajs-3292	308	4	the	the	DET
iajs-3292	308	5	bernoulli	bernoulli	PROPN
iajs-3292	308	6	operational	operational	ADJ
iajs-3292	308	7	matrix	matrix	NOUN
iajs-3292	308	8	method	method	NOUN
iajs-3292	308	9	is	be	AUX
iajs-3292	308	10	better	well	ADJ
iajs-3292	308	11	than	than	ADP
iajs-3292	308	12	the	the	DET
iajs-3292	308	13	bernstein	bernstein	PROPN
iajs-3292	308	14	operational	operational	PROPN
iajs-3292	308	15	matrix	matrix	NOUN
iajs-3292	308	16	method	method	NOUN
iajs-3292	308	17	and	and	CCONJ
iajs-3292	308	18	the	the	DET
iajs-3292	308	19	shifted	shift	VERB
iajs-3292	308	20	legendre	legendre	PROPN
iajs-3292	308	21	operational	operational	ADJ
iajs-3292	308	22	matrix	matrix	NOUN
iajs-3292	308	23	method	method	NOUN
iajs-3292	308	24	.	.	PUNCT
iajs-3292	309	1	we	we	PRON
iajs-3292	309	2	also	also	ADV
iajs-3292	309	3	compared	compare	VERB
iajs-3292	309	4	the	the	DET
iajs-3292	309	5	results	result	NOUN
iajs-3292	309	6	numerically	numerically	ADV
iajs-3292	309	7	with	with	ADP
iajs-3292	309	8	the	the	DET
iajs-3292	309	9	runge	runge	NOUN
iajs-3292	309	10	-	-	PUNCT
iajs-3292	309	11	kutta	kutta	NOUN
iajs-3292	309	12	method	method	NOUN
iajs-3292	309	13	and	and	CCONJ
iajs-3292	309	14	found	find	VERB
iajs-3292	309	15	good	good	ADJ
iajs-3292	309	16	agreement	agreement	NOUN
iajs-3292	309	17	between	between	ADP
iajs-3292	309	18	them	they	PRON
iajs-3292	309	19	.	.	PUNCT
iajs-3292	310	1	the	the	DET
iajs-3292	310	2	calculations	calculation	NOUN
iajs-3292	310	3	in	in	ADP
iajs-3292	310	4	this	this	DET
iajs-3292	310	5	study	study	NOUN
iajs-3292	310	6	were	be	AUX
iajs-3292	310	7	performed	perform	VERB
iajs-3292	310	8	using	use	VERB
iajs-3292	310	9	the	the	DET
iajs-3292	310	10	mathematica	mathematica	PROPN
iajs-3292	310	11	®	®	PROPN
iajs-3292	310	12	12	12	NUM
iajs-3292	310	13	program	program	NOUN
iajs-3292	310	14	.	.	PUNCT
iajs-3292	311	1	also	also	ADV
iajs-3292	311	2	,	,	PUNCT
iajs-3292	311	3	the	the	DET
iajs-3292	311	4	maximal	maximal	ADJ
iajs-3292	311	5	error	error	NOUN
iajs-3292	311	6	remainder	remainder	NOUN
iajs-3292	311	7	value	value	NOUN
iajs-3292	311	8	for	for	ADP
iajs-3292	311	9	the	the	DET
iajs-3292	311	10	proposed	propose	VERB
iajs-3292	311	11	approximation	approximation	NOUN
iajs-3292	311	12	methods	method	NOUN
iajs-3292	311	13	was	be	AUX
iajs-3292	311	14	calculated	calculate	VERB
iajs-3292	311	15	.	.	PUNCT
iajs-3292	312	1	ihjpas	ihjpas	PROPN
iajs-3292	312	2	.	.	PUNCT
iajs-3292	313	1	37	37	NUM
iajs-3292	313	2	(	(	PUNCT
iajs-3292	313	3	1	1	NUM
iajs-3292	313	4	)	)	PUNCT
iajs-3292	313	5	2024	2024	NUM
iajs-3292	313	6	372	372	NUM
iajs-3292	313	7	moreover	moreover	ADV
iajs-3292	313	8	,	,	PUNCT
iajs-3292	313	9	after	after	ADP
iajs-3292	313	10	examining	examine	VERB
iajs-3292	313	11	a	a	DET
iajs-3292	313	12	certain	certain	ADJ
iajs-3292	313	13	value	value	NOUN
iajs-3292	313	14	of	of	ADP
iajs-3292	313	15	the	the	DET
iajs-3292	313	16	second	second	ADJ
iajs-3292	313	17	derivative	derivative	ADJ
iajs-3292	313	18	(	(	PUNCT
iajs-3292	313	19	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	313	20	)	)	PUNCT
iajs-3292	313	21	=	=	SYM
iajs-3292	313	22	0.3320573	0.3320573	NUM
iajs-3292	313	23	)	)	PUNCT
iajs-3292	313	24	calculated	calculate	VERB
iajs-3292	313	25	in	in	ADP
iajs-3292	313	26	[	[	X
iajs-3292	313	27	27	27	NUM
iajs-3292	313	28	]	]	PUNCT
iajs-3292	313	29	,	,	PUNCT
iajs-3292	313	30	the	the	DET
iajs-3292	313	31	result	result	NOUN
iajs-3292	313	32	was	be	AUX
iajs-3292	313	33	compared	compare	VERB
iajs-3292	313	34	with	with	ADP
iajs-3292	313	35	the	the	DET
iajs-3292	313	36	value	value	NOUN
iajs-3292	313	37	obtained	obtain	VERB
iajs-3292	313	38	in	in	ADP
iajs-3292	313	39	[	[	X
iajs-3292	313	40	5	5	NUM
iajs-3292	313	41	]	]	PUNCT
iajs-3292	313	42	(	(	PUNCT
iajs-3292	313	43	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	313	44	)	)	PUNCT
iajs-3292	313	45	=	=	SYM
iajs-3292	314	1	1	1	NUM
iajs-3292	314	2	)	)	PUNCT
iajs-3292	314	3	.	.	PUNCT
iajs-3292	315	1	it	it	PRON
iajs-3292	315	2	was	be	AUX
iajs-3292	315	3	found	find	VERB
iajs-3292	315	4	that	that	SCONJ
iajs-3292	315	5	the	the	DET
iajs-3292	315	6	solution	solution	NOUN
iajs-3292	315	7	is	be	AUX
iajs-3292	315	8	more	more	ADV
iajs-3292	315	9	accurate	accurate	ADJ
iajs-3292	315	10	at	at	ADP
iajs-3292	315	11	𝑓′′(0	𝑓′′(0	NOUN
iajs-3292	315	12	)	)	PUNCT
iajs-3292	316	1	=	=	SYM
iajs-3292	316	2	0.3320573	0.3320573	NUM
iajs-3292	316	3	.	.	PUNCT
iajs-3292	317	1	acknowledgment	acknowledgment	NOUN
iajs-3292	317	2	the	the	DET
iajs-3292	317	3	authors	author	NOUN
iajs-3292	317	4	are	be	AUX
iajs-3292	317	5	greatly	greatly	ADV
iajs-3292	317	6	appreciated	appreciate	VERB
iajs-3292	317	7	the	the	DET
iajs-3292	317	8	referees	referee	NOUN
iajs-3292	317	9	for	for	ADP
iajs-3292	317	10	their	their	PRON
iajs-3292	317	11	valuable	valuable	ADJ
iajs-3292	317	12	comments	comment	NOUN
iajs-3292	317	13	and	and	CCONJ
iajs-3292	317	14	suggestions	suggestion	NOUN
iajs-3292	317	15	for	for	ADP
iajs-3292	317	16	improving	improve	VERB
iajs-3292	317	17	the	the	DET
iajs-3292	317	18	paper	paper	NOUN
iajs-3292	317	19	conflict	conflict	NOUN
iajs-3292	317	20	of	of	ADP
iajs-3292	317	21	interest	interest	NOUN
iajs-3292	317	22	the	the	DET
iajs-3292	317	23	authors	author	NOUN
iajs-3292	317	24	declare	declare	VERB
iajs-3292	317	25	that	that	SCONJ
iajs-3292	317	26	they	they	PRON
iajs-3292	317	27	have	have	VERB
iajs-3292	317	28	no	no	DET
iajs-3292	317	29	conflicts	conflict	NOUN
iajs-3292	317	30	of	of	ADP
iajs-3292	317	31	interest	interest	NOUN
iajs-3292	317	32	.	.	PUNCT
iajs-3292	318	1	funding	funding	NOUN
iajs-3292	318	2	there	there	PRON
iajs-3292	318	3	is	be	VERB
iajs-3292	318	4	no	no	DET
iajs-3292	318	5	financial	financial	ADJ
iajs-3292	318	6	support	support	NOUN
iajs-3292	318	7	in	in	ADP
iajs-3292	318	8	preparation	preparation	NOUN
iajs-3292	318	9	for	for	ADP
iajs-3292	318	10	the	the	DET
iajs-3292	318	11	publication	publication	NOUN
iajs-3292	318	12	.	.	PUNCT
iajs-3292	319	1	references	reference	NOUN
iajs-3292	319	2	1	1	NUM
iajs-3292	319	3	.	.	PUNCT
iajs-3292	320	1	murphy	murphy	PROPN
iajs-3292	320	2	,	,	PUNCT
iajs-3292	320	3	g.m	g.m	PROPN
iajs-3292	320	4	.	.	PUNCT
iajs-3292	321	1	ordinary	ordinary	ADJ
iajs-3292	321	2	differential	differential	ADJ
iajs-3292	321	3	equations	equation	NOUN
iajs-3292	321	4	and	and	CCONJ
iajs-3292	321	5	their	their	PRON
iajs-3292	321	6	solutions	solution	NOUN
iajs-3292	321	7	;	;	PUNCT
iajs-3292	321	8	dover	dover	PROPN
iajs-3292	321	9	publications	publications	PROPN
iajs-3292	321	10	,	,	PUNCT
iajs-3292	321	11	inc	inc	PROPN
iajs-3292	321	12	.	.	PROPN
iajs-3292	321	13	,	,	PUNCT
iajs-3292	321	14	new	new	PROPN
iajs-3292	321	15	york	york	PROPN
iajs-3292	321	16	,	,	PUNCT
iajs-3292	321	17	1960	1960	NUM
iajs-3292	321	18	.	.	PUNCT
iajs-3292	322	1	2	2	X
iajs-3292	322	2	.	.	X
iajs-3292	322	3	boyce	boyce	PROPN
iajs-3292	322	4	,	,	PUNCT
iajs-3292	322	5	w.e	w.e	PROPN
iajs-3292	322	6	.	.	PROPN
iajs-3292	322	7	;	;	PUNCT
iajs-3292	322	8	diprima	diprima	PROPN
iajs-3292	322	9	,	,	PUNCT
iajs-3292	322	10	r.c	r.c	PROPN
iajs-3292	322	11	.	.	PROPN
iajs-3292	322	12	elementary	elementary	PROPN
iajs-3292	322	13	differential	differential	PROPN
iajs-3292	322	14	equations	equation	NOUN
iajs-3292	322	15	and	and	CCONJ
iajs-3292	322	16	boundary	boundary	ADJ
iajs-3292	322	17	value	value	NOUN
iajs-3292	322	18	problems	problem	NOUN
iajs-3292	322	19	,	,	PUNCT
iajs-3292	322	20	ed.;9th	ed.;9th	ADJ
iajs-3292	322	21	ed	ed	NOUN
iajs-3292	322	22	.	.	PROPN
iajs-3292	322	23	2009	2009	NUM
iajs-3292	322	24	;	;	PUNCT
iajs-3292	322	25	john	john	PROPN
iajs-3292	322	26	wiley	wiley	PROPN
iajs-3292	322	27	&	&	CCONJ
iajs-3292	322	28	sons	sons	PROPN
iajs-3292	322	29	,	,	PUNCT
iajs-3292	322	30	inc	inc	PROPN
iajs-3292	322	31	.	.	PROPN
iajs-3292	322	32	,	,	PUNCT
iajs-3292	322	33	united	united	PROPN
iajs-3292	322	34	states	states	PROPN
iajs-3292	322	35	of	of	ADP
iajs-3292	322	36	america	america	PROPN
iajs-3292	322	37	,	,	PUNCT
iajs-3292	322	38	2009	2009	NUM
iajs-3292	322	39	;	;	PUNCT
iajs-3292	322	40	isbn	isbn	PROPN
iajs-3292	322	41	9780470383346	9780470383346	NUM
iajs-3292	322	42	.	.	PUNCT
iajs-3292	323	1	3	3	X
iajs-3292	323	2	.	.	X
iajs-3292	323	3	yousefi	yousefi	PROPN
iajs-3292	323	4	,	,	PUNCT
iajs-3292	323	5	s.a	s.a	PROPN
iajs-3292	323	6	.	.	PROPN
iajs-3292	323	7	;	;	PUNCT
iajs-3292	323	8	behroozifar	behroozifar	ADV
iajs-3292	323	9	,	,	PUNCT
iajs-3292	323	10	m.	m.	NOUN
iajs-3292	323	11	;	;	PUNCT
iajs-3292	323	12	operational	operational	ADJ
iajs-3292	323	13	matrices	matrix	NOUN
iajs-3292	323	14	of	of	ADP
iajs-3292	323	15	bernstein	bernstein	PROPN
iajs-3292	323	16	polynomials	polynomial	NOUN
iajs-3292	323	17	and	and	CCONJ
iajs-3292	323	18	their	their	PRON
iajs-3292	323	19	applications	application	NOUN
iajs-3292	323	20	,	,	PUNCT
iajs-3292	323	21	international	international	ADJ
iajs-3292	323	22	journal	journal	NOUN
iajs-3292	323	23	of	of	ADP
iajs-3292	323	24	systems	system	NOUN
iajs-3292	323	25	science	science	NOUN
iajs-3292	323	26	2010	2010	NUM
iajs-3292	323	27	,	,	PUNCT
iajs-3292	323	28	41(6	41(6	NOUN
iajs-3292	323	29	)	)	PUNCT
iajs-3292	323	30	,	,	PUNCT
iajs-3292	323	31	709	709	NUM
iajs-3292	323	32	-	-	SYM
iajs-3292	323	33	716	716	NUM
iajs-3292	323	34	.	.	PUNCT
iajs-3292	324	1	doi	doi	NOUN
iajs-3292	324	2	:	:	PUNCT
iajs-3292	324	3	https://doi.org/10.1080/00207720903154783	https://doi.org/10.1080/00207720903154783	NOUN
iajs-3292	324	4	4	4	NUM
iajs-3292	324	5	.	.	PUNCT
iajs-3292	325	1	pirabaharan	pirabaharan	NOUN
iajs-3292	325	2	,	,	PUNCT
iajs-3292	325	3	p.	p.	NOUN
iajs-3292	325	4	;	;	PUNCT
iajs-3292	325	5	chandrakumar	chandrakumar	PROPN
iajs-3292	325	6	,	,	PUNCT
iajs-3292	325	7	r.d	r.d	PROPN
iajs-3292	325	8	.	.	PROPN
iajs-3292	325	9	;	;	PUNCT
iajs-3292	325	10	a	a	DET
iajs-3292	325	11	computational	computational	ADJ
iajs-3292	325	12	method	method	NOUN
iajs-3292	325	13	for	for	ADP
iajs-3292	325	14	solving	solve	VERB
iajs-3292	325	15	a	a	DET
iajs-3292	325	16	class	class	NOUN
iajs-3292	325	17	of	of	ADP
iajs-3292	325	18	singular	singular	ADJ
iajs-3292	325	19	boundary	boundary	ADJ
iajs-3292	325	20	value	value	NOUN
iajs-3292	325	21	problems	problem	NOUN
iajs-3292	325	22	arising	arise	VERB
iajs-3292	325	23	in	in	ADP
iajs-3292	325	24	science	science	NOUN
iajs-3292	325	25	and	and	CCONJ
iajs-3292	325	26	engineering	engineering	NOUN
iajs-3292	325	27	,	,	PUNCT
iajs-3292	325	28	egyptian	egyptian	ADJ
iajs-3292	325	29	journal	journal	NOUN
iajs-3292	325	30	of	of	ADP
iajs-3292	325	31	basic	basic	ADJ
iajs-3292	325	32	and	and	CCONJ
iajs-3292	325	33	applied	apply	VERB
iajs-3292	325	34	sciences	science	NOUN
iajs-3292	325	35	2016	2016	NUM
iajs-3292	325	36	,	,	PUNCT
iajs-3292	325	37	3(4	3(4	NUM
iajs-3292	325	38	)	)	PUNCT
iajs-3292	325	39	,	,	PUNCT
iajs-3292	325	40	383	383	NUM
iajs-3292	325	41	-	-	SYM
iajs-3292	325	42	391	391	NUM
iajs-3292	325	43	.	.	PUNCT
iajs-3292	326	1	doi	doi	NOUN
iajs-3292	326	2	:	:	PUNCT
iajs-3292	326	3	https://doi.org/10.1016/j.ejbas.2016.09.004	https://doi.org/10.1016/j.ejbas.2016.09.004	PROPN
iajs-3292	326	4	5	5	NUM
iajs-3292	326	5	.	.	PUNCT
iajs-3292	326	6	khataybeh	khataybeh	PROPN
iajs-3292	326	7	,	,	PUNCT
iajs-3292	326	8	s.	s.	PROPN
iajs-3292	326	9	;	;	PUNCT
iajs-3292	326	10	hashim	hashim	PROPN
iajs-3292	326	11	,	,	PUNCT
iajs-3292	326	12	i.	i.	PROPN
iajs-3292	326	13	;	;	PUNCT
iajs-3292	326	14	alshbool	alshbool	NOUN
iajs-3292	326	15	,	,	PUNCT
iajs-3292	326	16	m.	m.	NOUN
iajs-3292	326	17	;	;	PUNCT
iajs-3292	326	18	solving	solve	VERB
iajs-3292	326	19	directly	directly	ADV
iajs-3292	326	20	third	third	ADJ
iajs-3292	326	21	-	-	PUNCT
iajs-3292	326	22	order	order	NOUN
iajs-3292	326	23	odes	ode	NOUN
iajs-3292	326	24	using	use	VERB
iajs-3292	326	25	operational	operational	ADJ
iajs-3292	326	26	matrices	matrix	NOUN
iajs-3292	326	27	of	of	ADP
iajs-3292	326	28	bernstein	bernstein	PROPN
iajs-3292	326	29	polynomials	polynomials	PROPN
iajs-3292	326	30	method	method	VERB
iajs-3292	326	31	with	with	ADP
iajs-3292	326	32	applications	application	NOUN
iajs-3292	326	33	to	to	ADP
iajs-3292	326	34	fluid	fluid	ADJ
iajs-3292	326	35	flow	flow	NOUN
iajs-3292	326	36	equations	equation	NOUN
iajs-3292	326	37	,	,	PUNCT
iajs-3292	326	38	journal	journal	NOUN
iajs-3292	326	39	of	of	ADP
iajs-3292	326	40	king	king	PROPN
iajs-3292	326	41	saud	saud	PROPN
iajs-3292	326	42	university	university	PROPN
iajs-3292	326	43	-	-	PUNCT
iajs-3292	326	44	science	science	NOUN
iajs-3292	326	45	2019	2019	NUM
iajs-3292	326	46	,	,	PUNCT
iajs-3292	326	47	31(4	31(4	NUM
iajs-3292	326	48	)	)	PUNCT
iajs-3292	326	49	,	,	PUNCT
iajs-3292	326	50	822	822	NUM
iajs-3292	326	51	-	-	SYM
iajs-3292	326	52	826	826	NUM
iajs-3292	326	53	.	.	PUNCT
iajs-3292	327	1	doi	doi	NOUN
iajs-3292	327	2	:	:	PUNCT
iajs-3292	327	3	https://doi.org/10.1016/j.jksus.2018.05.002	https://doi.org/10.1016/j.jksus.2018.05.002	NOUN
iajs-3292	327	4	6	6	NUM
iajs-3292	327	5	.	.	PUNCT
iajs-3292	328	1	asgari	asgari	PROPN
iajs-3292	328	2	,	,	PUNCT
iajs-3292	328	3	m.	m.	NOUN
iajs-3292	328	4	;	;	PUNCT
iajs-3292	328	5	ezzati	ezzati	PROPN
iajs-3292	328	6	,	,	PUNCT
iajs-3292	328	7	r.	r.	PROPN
iajs-3292	328	8	;	;	PUNCT
iajs-3292	328	9	using	use	VERB
iajs-3292	328	10	operational	operational	ADJ
iajs-3292	328	11	matrix	matrix	NOUN
iajs-3292	328	12	of	of	ADP
iajs-3292	328	13	two	two	NUM
iajs-3292	328	14	-	-	PUNCT
iajs-3292	328	15	dimensional	dimensional	ADJ
iajs-3292	328	16	bernstein	bernstein	NOUN
iajs-3292	328	17	polynomials	polynomial	NOUN
iajs-3292	328	18	for	for	ADP
iajs-3292	328	19	solving	solve	VERB
iajs-3292	328	20	two	two	NUM
iajs-3292	328	21	-	-	PUNCT
iajs-3292	328	22	dimensional	dimensional	ADJ
iajs-3292	328	23	integral	integral	ADJ
iajs-3292	328	24	equations	equation	NOUN
iajs-3292	328	25	of	of	ADP
iajs-3292	328	26	fractional	fractional	ADJ
iajs-3292	328	27	order	order	NOUN
iajs-3292	328	28	,	,	PUNCT
iajs-3292	328	29	applied	apply	VERB
iajs-3292	328	30	mathematics	mathematic	NOUN
iajs-3292	328	31	and	and	CCONJ
iajs-3292	328	32	computation	computation	NOUN
iajs-3292	328	33	2017	2017	NUM
iajs-3292	328	34	,	,	PUNCT
iajs-3292	328	35	307(c	307(c	NOUN
iajs-3292	328	36	)	)	PUNCT
iajs-3292	328	37	,	,	PUNCT
iajs-3292	328	38	290	290	NUM
iajs-3292	328	39	-	-	SYM
iajs-3292	328	40	298	298	NUM
iajs-3292	328	41	.	.	PUNCT
iajs-3292	329	1	doi	doi	NOUN
iajs-3292	329	2	:	:	PUNCT
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iajs-3292	329	5	.	.	PUNCT
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iajs-3292	329	7	,	,	PUNCT
iajs-3292	329	8	e.	e.	PROPN
iajs-3292	329	9	;	;	PUNCT
iajs-3292	329	10	shahbazi	shahbazi	NOUN
iajs-3292	329	11	,	,	PUNCT
iajs-3292	329	12	m.	m.	NOUN
iajs-3292	329	13	;	;	PUNCT
iajs-3292	329	14	two	two	NUM
iajs-3292	329	15	-	-	PUNCT
iajs-3292	329	16	dimensional	dimensional	ADJ
iajs-3292	329	17	shifted	shift	VERB
iajs-3292	329	18	legendre	legendre	PROPN
iajs-3292	329	19	polynomials	polynomial	NOUN
iajs-3292	329	20	operational	operational	ADJ
iajs-3292	329	21	matrix	matrix	NOUN
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iajs-3292	329	23	for	for	ADP
iajs-3292	329	24	solving	solve	VERB
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iajs-3292	329	27	integral	integral	ADJ
iajs-3292	329	28	equations	equation	NOUN
iajs-3292	329	29	of	of	ADP
iajs-3292	329	30	fractional	fractional	ADJ
iajs-3292	329	31	order	order	NOUN
iajs-3292	329	32	,	,	PUNCT
iajs-3292	329	33	applied	apply	VERB
iajs-3292	329	34	mathematics	mathematic	NOUN
iajs-3292	329	35	and	and	CCONJ
iajs-3292	329	36	computation	computation	NOUN
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iajs-3292	329	38	,	,	PUNCT
iajs-3292	329	39	322(c	322(c	PROPN
iajs-3292	329	40	)	)	PUNCT
iajs-3292	329	41	,	,	PUNCT
iajs-3292	329	42	40	40	NUM
iajs-3292	329	43	-	-	SYM
iajs-3292	329	44	54	54	NUM
iajs-3292	329	45	.	.	PUNCT
iajs-3292	330	1	doi	doi	NOUN
iajs-3292	330	2	:	:	PUNCT
iajs-3292	330	3	https://doi.org/10.1016/j.amc.2017.11.024	https://doi.org/10.1016/j.amc.2017.11.024	NUM
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iajs-3292	330	5	.	.	PUNCT
iajs-3292	331	1	sharma	sharma	PROPN
iajs-3292	331	2	,	,	PUNCT
iajs-3292	331	3	b.	b.	PROPN
iajs-3292	331	4	;	;	PUNCT
iajs-3292	331	5	kumar	kumar	PROPN
iajs-3292	331	6	,	,	PUNCT
iajs-3292	331	7	s.	s.	PROPN
iajs-3292	331	8	;	;	PUNCT
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iajs-3292	331	13	;	;	PUNCT
iajs-3292	331	14	mahato	mahato	PROPN
iajs-3292	331	15	,	,	PUNCT
iajs-3292	331	16	d.	d.	PROPN
iajs-3292	331	17	;	;	PUNCT
iajs-3292	331	18	chebyshev	chebyshev	PROPN
iajs-3292	331	19	operational	operational	ADJ
iajs-3292	331	20	matrix	matrix	NOUN
iajs-3292	331	21	method	method	NOUN
iajs-3292	331	22	for	for	ADP
iajs-3292	331	23	lane	lane	NOUN
iajs-3292	331	24	-	-	PUNCT
iajs-3292	331	25	emden	emden	NOUN
iajs-3292	331	26	problem	problem	NOUN
iajs-3292	331	27	,	,	PUNCT
iajs-3292	331	28	nonlinear	nonlinear	ADJ
iajs-3292	331	29	engineering	engineering	NOUN
iajs-3292	331	30	2019	2019	NUM
iajs-3292	331	31	,	,	PUNCT
iajs-3292	331	32	8(1	8(1	NOUN
iajs-3292	331	33	)	)	PUNCT
iajs-3292	331	34	,	,	PUNCT
iajs-3292	331	35	1	1	NUM
iajs-3292	331	36	-	-	SYM
iajs-3292	331	37	9	9	NUM
iajs-3292	331	38	.	.	PUNCT
iajs-3292	331	39	doi	doi	NOUN
iajs-3292	331	40	:	:	PUNCT
iajs-3292	331	41	https://doi.org/10.1515/nleng-2017-0157	https://doi.org/10.1515/nleng-2017-0157	PROPN
iajs-3292	331	42	9	9	X
iajs-3292	331	43	.	.	X
iajs-3292	331	44	bazm	bazm	PROPN
iajs-3292	331	45	,	,	PUNCT
iajs-3292	331	46	s.	s.	PROPN
iajs-3292	331	47	;	;	PUNCT
iajs-3292	331	48	bernoulli	bernoulli	NOUN
iajs-3292	331	49	polynomials	polynomial	VERB
iajs-3292	331	50	for	for	ADP
iajs-3292	331	51	the	the	DET
iajs-3292	331	52	numerical	numerical	ADJ
iajs-3292	331	53	solution	solution	NOUN
iajs-3292	331	54	of	of	ADP
iajs-3292	331	55	some	some	DET
iajs-3292	331	56	classes	class	NOUN
iajs-3292	331	57	of	of	ADP
iajs-3292	331	58	linear	linear	PROPN
iajs-3292	331	59	and	and	CCONJ
iajs-3292	331	60	nonlinear	nonlinear	ADJ
iajs-3292	331	61	integral	integral	ADJ
iajs-3292	331	62	equations	equation	NOUN
iajs-3292	331	63	,	,	PUNCT
iajs-3292	331	64	journal	journal	NOUN
iajs-3292	331	65	of	of	ADP
iajs-3292	331	66	computational	computational	ADJ
iajs-3292	331	67	and	and	CCONJ
iajs-3292	331	68	applied	applied	ADJ
iajs-3292	331	69	mathematics	mathematic	NOUN
iajs-3292	331	70	2015	2015	NUM
iajs-3292	331	71	,	,	PUNCT
iajs-3292	331	72	275(c	275(c	PROPN
iajs-3292	331	73	)	)	PUNCT
iajs-3292	331	74	,	,	PUNCT
iajs-3292	331	75	44	44	NUM
iajs-3292	331	76	-	-	SYM
iajs-3292	331	77	60	60	NUM
iajs-3292	331	78	.	.	PUNCT
iajs-3292	332	1	doi	doi	NOUN
iajs-3292	332	2	:	:	PUNCT
iajs-3292	332	3	https://doi.org/10.1016/j.cam.2014.07.018	https://doi.org/10.1016/j.cam.2014.07.018	PROPN
iajs-3292	332	4	https://doi.org/10.1080/00207720903154783	https://doi.org/10.1080/00207720903154783	NOUN
iajs-3292	332	5	https://doi.org/10.1016/j.ejbas.2016.09.004	https://doi.org/10.1016/j.ejbas.2016.09.004	PROPN
iajs-3292	332	6	https://doi.org/10.1016/j.jksus.2018.05.002	https://doi.org/10.1016/j.jksus.2018.05.002	NOUN
iajs-3292	333	1	https://doi.org/10.1016/j.amc.2017.03.012	https://doi.org/10.1016/j.amc.2017.03.012	ADV
iajs-3292	333	2	https://doi.org/10.1016/j.amc.2017.11.024	https://doi.org/10.1016/j.amc.2017.11.024	NOUN
iajs-3292	333	3	https://doi.org/10.1515/nleng-2017-0157	https://doi.org/10.1515/nleng-2017-0157	PROPN
iajs-3292	333	4	https://doi.org/10.1016/j.cam.2014.07.018	https://doi.org/10.1016/j.cam.2014.07.018	NOUN
iajs-3292	333	5	ihjpas	ihjpa	VERB
iajs-3292	333	6	.	.	PUNCT
iajs-3292	334	1	37	37	NUM
iajs-3292	334	2	(	(	PUNCT
iajs-3292	334	3	1	1	NUM
iajs-3292	334	4	)	)	PUNCT
iajs-3292	334	5	2024	2024	NUM
iajs-3292	334	6	373	373	NUM
iajs-3292	334	7	10	10	NUM
iajs-3292	334	8	.	.	PUNCT
iajs-3292	335	1	al	al	PROPN
iajs-3292	335	2	-	-	PUNCT
iajs-3292	335	3	jawary	jawary	PROPN
iajs-3292	335	4	,	,	PUNCT
iajs-3292	335	5	m.a	m.a	PROPN
iajs-3292	335	6	.	.	PROPN
iajs-3292	335	7	;	;	PUNCT
iajs-3292	335	8	ibraheem	ibraheem	PROPN
iajs-3292	335	9	,	,	PUNCT
iajs-3292	335	10	g.h	g.h	PROPN
iajs-3292	335	11	.	.	PROPN
iajs-3292	335	12	;	;	PUNCT
iajs-3292	335	13	tow	tow	VERB
iajs-3292	335	14	meshless	meshless	ADJ
iajs-3292	335	15	methods	method	NOUN
iajs-3292	335	16	for	for	ADP
iajs-3292	335	17	solving	solve	VERB
iajs-3292	335	18	nonlinear	nonlinear	ADJ
iajs-3292	335	19	ordinary	ordinary	ADJ
iajs-3292	335	20	differential	differential	ADJ
iajs-3292	335	21	equations	equation	NOUN
iajs-3292	335	22	in	in	ADP
iajs-3292	335	23	engineering	engineering	NOUN
iajs-3292	335	24	and	and	CCONJ
iajs-3292	335	25	applied	apply	VERB
iajs-3292	335	26	sciences	science	NOUN
iajs-3292	335	27	,	,	PUNCT
iajs-3292	335	28	nonlinear	nonlinear	ADJ
iajs-3292	335	29	engineering	engineering	NOUN
iajs-3292	335	30	2020	2020	NUM
iajs-3292	335	31	,	,	PUNCT
iajs-3292	335	32	9(1	9(1	NUM
iajs-3292	335	33	)	)	PUNCT
iajs-3292	335	34	,	,	PUNCT
iajs-3292	335	35	244	244	NUM
iajs-3292	335	36	-	-	SYM
iajs-3292	335	37	255	255	NUM
iajs-3292	335	38	.	.	PUNCT
iajs-3292	336	1	doi	doi	NOUN
iajs-3292	336	2	:	:	PUNCT
iajs-3292	336	3	https://doi.org/10.1515/nleng-2020-0012	https://doi.org/10.1515/nleng-2020-0012	PROPN
iajs-3292	336	4	11	11	NUM
iajs-3292	336	5	.	.	PUNCT
iajs-3292	337	1	ibraheem	ibraheem	PROPN
iajs-3292	337	2	,	,	PUNCT
iajs-3292	337	3	g.h	g.h	PROPN
iajs-3292	337	4	.	.	PROPN
iajs-3292	337	5	;	;	PUNCT
iajs-3292	338	1	al	al	PROPN
iajs-3292	338	2	-	-	PUNCT
iajs-3292	338	3	jawary	jawary	PROPN
iajs-3292	338	4	,	,	PUNCT
iajs-3292	338	5	m.a	m.a	PROPN
iajs-3292	338	6	.	.	PROPN
iajs-3292	338	7	;	;	PUNCT
iajs-3292	338	8	the	the	DET
iajs-3292	338	9	operational	operational	ADJ
iajs-3292	338	10	matrix	matrix	NOUN
iajs-3292	338	11	of	of	ADP
iajs-3292	338	12	legendre	legendre	PROPN
iajs-3292	338	13	polynomials	polynomial	NOUN
iajs-3292	338	14	for	for	ADP
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iajs-3292	338	16	nonlinear	nonlinear	ADJ
iajs-3292	338	17	thin	thin	ADJ
iajs-3292	338	18	film	film	NOUN
iajs-3292	338	19	flow	flow	NOUN
iajs-3292	338	20	problems	problem	NOUN
iajs-3292	338	21	,	,	PUNCT
iajs-3292	338	22	alexandria	alexandria	PROPN
iajs-3292	338	23	engineering	engineering	PROPN
iajs-3292	338	24	journal	journal	PROPN
iajs-3292	338	25	,	,	PUNCT
iajs-3292	338	26	2020	2020	NUM
iajs-3292	338	27	,	,	PUNCT
iajs-3292	338	28	59(5	59(5	NUM
iajs-3292	338	29	)	)	PUNCT
iajs-3292	338	30	,	,	PUNCT
iajs-3292	338	31	4027	4027	NUM
iajs-3292	338	32	-	-	SYM
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iajs-3292	338	34	.	.	PUNCT
iajs-3292	339	1	doi	doi	NOUN
iajs-3292	339	2	:	:	PUNCT
iajs-3292	339	3	https://doi.org/10.1016/j.aej.2020.07.008	https://doi.org/10.1016/j.aej.2020.07.008	NOUN
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iajs-3292	339	5	.	.	PUNCT
iajs-3292	340	1	talib	talib	PROPN
iajs-3292	340	2	,	,	PUNCT
iajs-3292	340	3	i.	i.	NOUN
iajs-3292	340	4	;	;	PUNCT
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iajs-3292	340	6	,	,	PUNCT
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iajs-3292	340	8	;	;	PUNCT
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iajs-3292	340	18	orthogonal	orthogonal	ADJ
iajs-3292	340	19	legendre	legendre	PROPN
iajs-3292	340	20	polynomials	polynomial	NOUN
iajs-3292	340	21	and	and	CCONJ
iajs-3292	340	22	their	their	PRON
iajs-3292	340	23	operational	operational	ADJ
iajs-3292	340	24	,	,	PUNCT
iajs-3292	340	25	journal	journal	NOUN
iajs-3292	340	26	of	of	ADP
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iajs-3292	340	31	2019	2019	NUM
iajs-3292	340	32	,	,	PUNCT
iajs-3292	340	33	13(1	13(1	NUM
iajs-3292	340	34	)	)	PUNCT
iajs-3292	340	35	,	,	PUNCT
iajs-3292	340	36	377	377	NUM
iajs-3292	340	37	-	-	SYM
iajs-3292	340	38	389	389	NUM
iajs-3292	340	39	.	.	PUNCT
iajs-3292	341	1	doi	doi	NOUN
iajs-3292	341	2	:	:	PUNCT
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iajs-3292	341	4	13	13	NUM
iajs-3292	341	5	.	.	X
iajs-3292	342	1	bani	bani	PROPN
iajs-3292	342	2	-	-	PUNCT
iajs-3292	342	3	ahmad	ahmad	PROPN
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iajs-3292	342	6	;	;	PUNCT
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iajs-3292	342	34	legendre	legendre	PROPN
iajs-3292	342	35	operational	operational	ADJ
iajs-3292	342	36	matrix	matrix	NOUN
iajs-3292	342	37	of	of	ADP
iajs-3292	342	38	differentiation	differentiation	NOUN
iajs-3292	342	39	,	,	PUNCT
iajs-3292	342	40	italian	italian	ADJ
iajs-3292	342	41	journal	journal	NOUN
iajs-3292	342	42	of	of	ADP
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iajs-3292	342	44	and	and	CCONJ
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iajs-3292	342	46	mathematics	mathematic	NOUN
iajs-3292	342	47	2016	2016	NUM
iajs-3292	342	48	,	,	PUNCT
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iajs-3292	342	50	,	,	PUNCT
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iajs-3292	342	53	.	.	PUNCT
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iajs-3292	343	2	,	,	PUNCT
iajs-3292	343	3	s.	s.	PROPN
iajs-3292	343	4	;	;	PUNCT
iajs-3292	343	5	pandey	pandey	PROPN
iajs-3292	343	6	,	,	PUNCT
iajs-3292	343	7	p.	p.	PROPN
iajs-3292	343	8	;	;	PUNCT
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iajs-3292	343	10	,	,	PUNCT
iajs-3292	343	11	s.	s.	PROPN
iajs-3292	343	12	;	;	PUNCT
iajs-3292	343	13	craciun	craciun	PROPN
iajs-3292	343	14	,	,	PUNCT
iajs-3292	343	15	e.-m	e.-m	PROPN
iajs-3292	343	16	.	.	PUNCT
iajs-3292	343	17	;	;	PUNCT
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iajs-3292	343	19	solution	solution	NOUN
iajs-3292	343	20	of	of	ADP
iajs-3292	343	21	two	two	NUM
iajs-3292	343	22	dimensional	dimensional	ADJ
iajs-3292	343	23	reaction	reaction	NOUN
iajs-3292	343	24	-	-	PUNCT
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iajs-3292	343	26	equation	equation	NOUN
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iajs-3292	343	35	-	-	PUNCT
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iajs-3292	343	38	:	:	PUNCT
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iajs-3292	343	41	and	and	CCONJ
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iajs-3292	343	44	,	,	PUNCT
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iajs-3292	343	60	399	399	NUM
iajs-3292	343	61	.	.	PUNCT
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iajs-3292	345	5	;	;	PUNCT
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iajs-3292	345	7	,	,	PUNCT
iajs-3292	345	8	c.	c.	PROPN
iajs-3292	345	9	;	;	PUNCT
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iajs-3292	345	11	solution	solution	NOUN
iajs-3292	345	12	of	of	ADP
iajs-3292	345	13	fredholm	fredholm	ADJ
iajs-3292	345	14	fractional	fractional	ADJ
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iajs-3292	345	16	-	-	PUNCT
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iajs-3292	345	18	equation	equation	NOUN
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iajs-3292	345	20	right	right	ADV
iajs-3292	345	21	-	-	PUNCT
iajs-3292	345	22	sided	side	VERB
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iajs-3292	345	29	operational	operational	ADJ
iajs-3292	345	30	matrix	matrix	NOUN
iajs-3292	345	31	of	of	ADP
iajs-3292	345	32	fractional	fractional	ADJ
iajs-3292	345	33	derivative	derivative	ADJ
iajs-3292	345	34	,	,	PUNCT
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iajs-3292	345	39	2019	2019	NUM
iajs-3292	345	40	,	,	PUNCT
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iajs-3292	345	42	)	)	PUNCT
iajs-3292	345	43	,	,	PUNCT
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iajs-3292	345	45	-	-	SYM
iajs-3292	345	46	25	25	NUM
iajs-3292	345	47	.	.	PUNCT
iajs-3292	345	48	doi	doi	NOUN
iajs-3292	345	49	:	:	PUNCT
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iajs-3292	345	52	.	.	PUNCT
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iajs-3292	346	2	,	,	PUNCT
iajs-3292	346	3	r.	r.	PROPN
iajs-3292	346	4	;	;	PUNCT
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iajs-3292	346	6	solution	solution	NOUN
iajs-3292	346	7	of	of	ADP
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iajs-3292	346	12	using	use	VERB
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iajs-3292	346	15	matrix	matrix	NOUN
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iajs-3292	346	19	computers	computer	NOUN
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iajs-3292	346	23	,	,	PUNCT
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iajs-3292	346	25	)	)	PUNCT
iajs-3292	346	26	,	,	PUNCT
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iajs-3292	346	28	-	-	SYM
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iajs-3292	346	30	.	.	PUNCT
iajs-3292	347	1	doi	doi	NOUN
iajs-3292	347	2	:	:	PUNCT
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iajs-3292	347	4	17	17	NUM
iajs-3292	347	5	.	.	PUNCT
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iajs-3292	348	2	,	,	PUNCT
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iajs-3292	348	4	.	.	PUNCT
iajs-3292	348	5	;	;	PUNCT
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iajs-3292	348	7	,	,	PUNCT
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iajs-3292	348	10	;	;	PUNCT
iajs-3292	348	11	fractional	fractional	ADJ
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iajs-3292	348	16	by	by	ADP
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iajs-3292	348	19	methods	method	NOUN
iajs-3292	348	20	,	,	PUNCT
iajs-3292	348	21	ibn	ibn	PROPN
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iajs-3292	348	23	-	-	PUNCT
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iajs-3292	348	29	applied	applied	ADJ
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iajs-3292	348	31	2023	2023	NUM
iajs-3292	348	32	,	,	PUNCT
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iajs-3292	348	34	,	,	PUNCT
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iajs-3292	348	36	.	.	PUNCT
iajs-3292	349	1	doi	doi	NOUN
iajs-3292	349	2	:	:	PUNCT
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iajs-3292	349	5	.	.	PUNCT
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iajs-3292	350	4	.	.	PUNCT
iajs-3292	350	5	;	;	PUNCT
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iajs-3292	351	2	,	,	PUNCT
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iajs-3292	351	4	;	;	PUNCT
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iajs-3292	351	6	,	,	PUNCT
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iajs-3292	351	8	;	;	PUNCT
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iajs-3292	351	10	,	,	PUNCT
iajs-3292	351	11	i.	i.	PROPN
iajs-3292	351	12	;	;	PUNCT
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iajs-3292	351	16	matrices	matrix	NOUN
iajs-3292	351	17	for	for	ADP
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iajs-3292	351	19	integro	integro	ADJ
iajs-3292	351	20	-	-	PUNCT
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iajs-3292	351	30	in	in	ADP
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iajs-3292	351	34	,	,	PUNCT
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iajs-3292	351	36	,	,	PUNCT
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iajs-3292	351	38	.	.	PUNCT
iajs-3292	352	1	doi	doi	NOUN
iajs-3292	352	2	:	:	PUNCT
iajs-3292	352	3	https://doi.org/10.1016/j.rinam.2022.100258	https://doi.org/10.1016/j.rinam.2022.100258	PROPN
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iajs-3292	352	5	.	.	PUNCT
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iajs-3292	353	2	,	,	PUNCT
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iajs-3292	353	5	;	;	PUNCT
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iajs-3292	353	12	matrices	matrix	NOUN
iajs-3292	353	13	approach	approach	VERB
iajs-3292	353	14	for	for	ADP
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iajs-3292	353	21	polynomials	polynomial	NOUN
iajs-3292	353	22	,	,	PUNCT
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iajs-3292	353	25	of	of	ADP
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iajs-3292	353	28	applied	apply	VERB
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iajs-3292	353	31	,	,	PUNCT
iajs-3292	353	32	2(2	2(2	NUM
iajs-3292	353	33	)	)	PUNCT
iajs-3292	353	34	,	,	PUNCT
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iajs-3292	353	36	.	.	PUNCT
iajs-3292	354	1	doi	doi	PROPN
iajs-3292	354	2	:	:	PUNCT
iajs-3292	354	3	http://dx.doi.org/10.54153/sjpas.2020.v2i2.115	http://dx.doi.org/10.54153/sjpas.2020.v2i2.115	PROPN
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iajs-3292	354	5	.	.	PUNCT
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iajs-3292	355	2	,	,	PUNCT
iajs-3292	355	3	r.	r.	PROPN
iajs-3292	355	4	;	;	PUNCT
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iajs-3292	355	6	,	,	PUNCT
iajs-3292	355	7	s.	s.	PROPN
iajs-3292	355	8	;	;	PUNCT
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iajs-3292	355	12	m.	m.	NOUN
iajs-3292	355	13	;	;	PUNCT
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iajs-3292	355	15	,	,	PUNCT
iajs-3292	355	16	m.	m.	NOUN
iajs-3292	355	17	;	;	PUNCT
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iajs-3292	355	21	for	for	ADP
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iajs-3292	355	27	-	-	PUNCT
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iajs-3292	355	30	matrices	matrix	NOUN
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iajs-3292	355	33	of	of	ADP
iajs-3292	355	34	physics	physics	PROPN
iajs-3292	355	35	:	:	PUNCT
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iajs-3292	355	42	,	,	PUNCT
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iajs-3292	355	45	,	,	PUNCT
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iajs-3292	355	47	.	.	PUNCT
iajs-3292	356	1	doi	doi	NOUN
iajs-3292	356	2	:	:	PUNCT
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iajs-3292	356	5	.	.	PUNCT
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iajs-3292	358	5	.	.	PUNCT
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iajs-3292	362	2	(	(	PUNCT
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iajs-3292	362	20	.	.	PUNCT
iajs-3292	363	1	doi	doi	NOUN
iajs-3292	363	2	:	:	PUNCT
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iajs-3292	363	4	23	23	NUM
iajs-3292	363	5	.	.	PUNCT
iajs-3292	364	1	cortell	cortell	PROPN
iajs-3292	364	2	,	,	PUNCT
iajs-3292	364	3	r.	r.	PROPN
iajs-3292	364	4	;	;	PUNCT
iajs-3292	364	5	numerical	numerical	ADJ
iajs-3292	364	6	solutions	solution	NOUN
iajs-3292	364	7	of	of	ADP
iajs-3292	364	8	the	the	DET
iajs-3292	364	9	classical	classical	ADJ
iajs-3292	364	10	blasius	blasius	ADJ
iajs-3292	364	11	flat	flat	ADJ
iajs-3292	364	12	-	-	PUNCT
iajs-3292	364	13	plate	plate	NOUN
iajs-3292	364	14	problem	problem	NOUN
iajs-3292	364	15	,	,	PUNCT
iajs-3292	364	16	applied	apply	VERB
iajs-3292	364	17	mathematics	mathematic	NOUN
iajs-3292	364	18	and	and	CCONJ
iajs-3292	364	19	computation	computation	NOUN
iajs-3292	364	20	2005	2005	NUM
iajs-3292	364	21	,	,	PUNCT
iajs-3292	364	22	170(1	170(1	NUM
iajs-3292	364	23	)	)	PUNCT
iajs-3292	364	24	,	,	PUNCT
iajs-3292	364	25	706	706	NUM
iajs-3292	364	26	-	-	SYM
iajs-3292	364	27	710	710	NUM
iajs-3292	364	28	.	.	PUNCT
iajs-3292	365	1	doi	doi	NOUN
iajs-3292	365	2	:	:	PUNCT
iajs-3292	365	3	https://doi.org/10.1016/j.amc.2004.12.037	https://doi.org/10.1016/j.amc.2004.12.037	NOUN
iajs-3292	365	4	24	24	NUM
iajs-3292	365	5	.	.	PUNCT
iajs-3292	366	1	[	[	X
iajs-3292	366	2	24	24	NUM
iajs-3292	366	3	]	]	PUNCT
iajs-3292	366	4	he	he	PRON
iajs-3292	366	5	,	,	PUNCT
iajs-3292	366	6	j.	j.	PROPN
iajs-3292	366	7	;	;	PUNCT
iajs-3292	366	8	approximate	approximate	ADJ
iajs-3292	366	9	analytical	analytical	ADJ
iajs-3292	366	10	solution	solution	NOUN
iajs-3292	366	11	of	of	ADP
iajs-3292	366	12	blasius	blasius	NOUN
iajs-3292	366	13	’	'	PUNCT
iajs-3292	366	14	equation	equation	NOUN
iajs-3292	366	15	,	,	PUNCT
iajs-3292	366	16	communications	communication	NOUN
iajs-3292	366	17	in	in	ADP
iajs-3292	366	18	nonlinear	nonlinear	ADJ
iajs-3292	366	19	science	science	NOUN
iajs-3292	366	20	and	and	CCONJ
iajs-3292	366	21	numerical	numerical	PROPN
iajs-3292	366	22	simulation	simulation	PROPN
iajs-3292	366	23	1999	1999	NUM
iajs-3292	366	24	,	,	PUNCT
iajs-3292	366	25	4(1	4(1	NOUN
iajs-3292	366	26	)	)	PUNCT
iajs-3292	366	27	,	,	PUNCT
iajs-3292	366	28	75	75	NUM
iajs-3292	366	29	-	-	SYM
iajs-3292	366	30	78	78	NUM
iajs-3292	366	31	.	.	PUNCT
iajs-3292	367	1	doi	doi	NOUN
iajs-3292	367	2	:	:	PUNCT
iajs-3292	367	3	https://doi.org/10.1016/s1007-5704(99)90063-1	https://doi.org/10.1016/s1007-5704(99)90063-1	NOUN
iajs-3292	367	4	25	25	NUM
iajs-3292	367	5	.	.	PUNCT
iajs-3292	368	1	abbasbandy	abbasbandy	PROPN
iajs-3292	368	2	,	,	PUNCT
iajs-3292	368	3	s.	s.	PROPN
iajs-3292	368	4	;	;	PUNCT
iajs-3292	368	5	a	a	DET
iajs-3292	368	6	numerical	numerical	ADJ
iajs-3292	368	7	solution	solution	NOUN
iajs-3292	368	8	of	of	ADP
iajs-3292	368	9	blasius	blasius	ADJ
iajs-3292	368	10	equation	equation	NOUN
iajs-3292	368	11	by	by	ADP
iajs-3292	368	12	adomian	adomian	NOUN
iajs-3292	368	13	’s	’s	PART
iajs-3292	368	14	decomposition	decomposition	NOUN
iajs-3292	368	15	method	method	NOUN
iajs-3292	368	16	and	and	CCONJ
iajs-3292	368	17	comparison	comparison	NOUN
iajs-3292	368	18	with	with	ADP
iajs-3292	368	19	homotopy	homotopy	NOUN
iajs-3292	368	20	perturbation	perturbation	NOUN
iajs-3292	368	21	method	method	NOUN
iajs-3292	368	22	,	,	PUNCT
iajs-3292	368	23	chaos	chaos	NOUN
iajs-3292	368	24	,	,	PUNCT
iajs-3292	368	25	solitons	soliton	NOUN
iajs-3292	368	26	&	&	CCONJ
iajs-3292	368	27	fractals	fractal	NOUN
iajs-3292	368	28	2007	2007	NUM
iajs-3292	368	29	,	,	PUNCT
iajs-3292	368	30	31(1	31(1	NUM
iajs-3292	368	31	)	)	PUNCT
iajs-3292	368	32	,	,	PUNCT
iajs-3292	368	33	257	257	NUM
iajs-3292	368	34	-	-	SYM
iajs-3292	368	35	260	260	NUM
iajs-3292	368	36	.	.	PUNCT
iajs-3292	369	1	doi	doi	NOUN
iajs-3292	369	2	:	:	PUNCT
iajs-3292	369	3	https://doi.org/10.1016/j.chaos.2005.10.071	https://doi.org/10.1016/j.chaos.2005.10.071	ADJ
iajs-3292	369	4	26	26	NUM
iajs-3292	369	5	.	.	PUNCT
iajs-3292	370	1	aminikhah	aminikhah	PROPN
iajs-3292	370	2	,	,	PUNCT
iajs-3292	370	3	h.	h.	PROPN
iajs-3292	370	4	;	;	PUNCT
iajs-3292	370	5	an	an	DET
iajs-3292	370	6	analytical	analytical	ADJ
iajs-3292	370	7	approximation	approximation	NOUN
iajs-3292	370	8	for	for	ADP
iajs-3292	370	9	solving	solve	VERB
iajs-3292	370	10	nonlinear	nonlinear	ADJ
iajs-3292	370	11	blasius	blasius	ADJ
iajs-3292	370	12	equation	equation	NOUN
iajs-3292	370	13	by	by	ADP
iajs-3292	370	14	nhpm	nhpm	ADJ
iajs-3292	370	15	,	,	PUNCT
iajs-3292	370	16	numerical	numerical	ADJ
iajs-3292	370	17	methods	method	NOUN
iajs-3292	370	18	for	for	ADP
iajs-3292	370	19	partial	partial	ADJ
iajs-3292	370	20	differential	differential	ADJ
iajs-3292	370	21	equations	equation	NOUN
iajs-3292	370	22	2010	2010	NUM
iajs-3292	370	23	,	,	PUNCT
iajs-3292	370	24	26(6	26(6	NUM
iajs-3292	370	25	)	)	PUNCT
iajs-3292	370	26	,	,	PUNCT
iajs-3292	370	27	1291	1291	NUM
iajs-3292	370	28	-	-	SYM
iajs-3292	370	29	1299	1299	NUM
iajs-3292	370	30	.	.	PUNCT
iajs-3292	371	1	doi	doi	NOUN
iajs-3292	371	2	:	:	PUNCT
iajs-3292	371	3	https://doi.org/10.1002/num.20490	https://doi.org/10.1002/num.20490	PROPN
iajs-3292	371	4	27	27	NUM
iajs-3292	371	5	.	.	PUNCT
iajs-3292	372	1	liao	liao	PROPN
iajs-3292	372	2	,	,	PUNCT
iajs-3292	372	3	s.	s.	PROPN
iajs-3292	372	4	;	;	PUNCT
iajs-3292	372	5	an	an	DET
iajs-3292	372	6	optimal	optimal	ADJ
iajs-3292	372	7	homotopy	homotopy	NOUN
iajs-3292	372	8	-	-	PUNCT
iajs-3292	372	9	analysis	analysis	NOUN
iajs-3292	372	10	approach	approach	NOUN
iajs-3292	372	11	for	for	ADP
iajs-3292	372	12	strongly	strongly	ADV
iajs-3292	372	13	nonlinear	nonlinear	ADJ
iajs-3292	372	14	differential	differential	ADJ
iajs-3292	372	15	equations	equation	NOUN
iajs-3292	372	16	,	,	PUNCT
iajs-3292	372	17	communications	communication	NOUN
iajs-3292	372	18	in	in	ADP
iajs-3292	372	19	nonlinear	nonlinear	ADJ
iajs-3292	372	20	science	science	NOUN
iajs-3292	372	21	and	and	CCONJ
iajs-3292	372	22	numerical	numerical	PROPN
iajs-3292	372	23	simulation	simulation	PROPN
iajs-3292	372	24	2010	2010	NUM
iajs-3292	372	25	,	,	PUNCT
iajs-3292	372	26	15(8	15(8	NUM
iajs-3292	372	27	)	)	PUNCT
iajs-3292	372	28	,	,	PUNCT
iajs-3292	372	29	2003	2003	NUM
iajs-3292	372	30	-	-	SYM
iajs-3292	372	31	2016	2016	NUM
iajs-3292	372	32	.	.	PUNCT
iajs-3292	373	1	doi	doi	NOUN
iajs-3292	373	2	:	:	PUNCT
iajs-3292	373	3	https://doi.org/10.1016/j.cnsns.2009.09.002	https://doi.org/10.1016/j.cnsns.2009.09.002	PROPN
iajs-3292	373	4	28	28	NUM
iajs-3292	373	5	.	.	PUNCT
iajs-3292	374	1	mohammed	mohammed	PROPN
iajs-3292	374	2	ali	ali	PROPN
iajs-3292	374	3	,	,	PUNCT
iajs-3292	374	4	m.n	m.n	PROPN
iajs-3292	374	5	.	.	PROPN
iajs-3292	374	6	;	;	PUNCT
iajs-3292	374	7	a	a	DET
iajs-3292	374	8	new	new	ADJ
iajs-3292	374	9	operational	operational	ADJ
iajs-3292	374	10	matrix	matrix	NOUN
iajs-3292	374	11	of	of	ADP
iajs-3292	374	12	derivative	derivative	NOUN
iajs-3292	374	13	for	for	ADP
iajs-3292	374	14	orthonormal	orthonormal	ADJ
iajs-3292	374	15	bernstein	bernstein	PROPN
iajs-3292	374	16	polynomial	polynomial	PROPN
iajs-3292	374	17	’s	’s	PROPN
iajs-3292	374	18	,	,	PUNCT
iajs-3292	374	19	baghdad	baghdad	PROPN
iajs-3292	374	20	science	science	PROPN
iajs-3292	374	21	journal	journal	PROPN
iajs-3292	374	22	2014	2014	NUM
iajs-3292	374	23	,	,	PUNCT
iajs-3292	374	24	11(3	11(3	NUM
iajs-3292	374	25	)	)	PUNCT
iajs-3292	374	26	,	,	PUNCT
iajs-3292	374	27	1295	1295	NUM
iajs-3292	374	28	-	-	SYM
iajs-3292	374	29	1300	1300	NUM
iajs-3292	374	30	.	.	PUNCT
iajs-3292	375	1	doi	doi	NOUN
iajs-3292	375	2	:	:	PUNCT
iajs-3292	375	3	https://doi.org/10.21123	https://doi.org/10.21123	NOUN
iajs-3292	375	4	/	/	SYM
iajs-3292	375	5	bsj.2014.11.3.1295	bsj.2014.11.3.1295	NOUN
iajs-3292	375	6	-	-	PUNCT
iajs-3292	375	7	1300	1300	NUM
iajs-3292	375	8	29	29	NUM
iajs-3292	375	9	.	.	PUNCT
iajs-3292	376	1	al	al	PROPN
iajs-3292	376	2	-	-	PUNCT
iajs-3292	376	3	a’asam	a’asam	PROPN
iajs-3292	376	4	,	,	PUNCT
iajs-3292	376	5	j.a	j.a	PROPN
iajs-3292	376	6	.	.	PROPN
iajs-3292	376	7	;	;	PUNCT
iajs-3292	376	8	deriving	derive	VERB
iajs-3292	376	9	the	the	DET
iajs-3292	376	10	composite	composite	ADJ
iajs-3292	376	11	simpson	simpson	NOUN
iajs-3292	376	12	rule	rule	NOUN
iajs-3292	376	13	by	by	ADP
iajs-3292	376	14	using	use	VERB
iajs-3292	376	15	bernstein	bernstein	PROPN
iajs-3292	376	16	polynomials	polynomial	NOUN
iajs-3292	376	17	for	for	ADP
iajs-3292	376	18	solving	solve	VERB
iajs-3292	376	19	volterra	volterra	NOUN
iajs-3292	376	20	integral	integral	ADJ
iajs-3292	376	21	equations	equation	NOUN
iajs-3292	376	22	,	,	PUNCT
iajs-3292	376	23	baghdad	baghdad	PROPN
iajs-3292	376	24	science	science	PROPN
iajs-3292	376	25	journal	journal	PROPN
iajs-3292	376	26	2014	2014	NUM
iajs-3292	376	27	,	,	PUNCT
iajs-3292	376	28	11(3	11(3	NUM
iajs-3292	376	29	)	)	PUNCT
iajs-3292	376	30	,	,	PUNCT
iajs-3292	376	31	1274	1274	NUM
iajs-3292	376	32	-	-	SYM
iajs-3292	376	33	1281	1281	NUM
iajs-3292	376	34	.	.	PUNCT
iajs-3292	377	1	doi	doi	NOUN
iajs-3292	377	2	:	:	PUNCT
iajs-3292	377	3	https://doi.org/10.21123/bsj.2014.11.3.1274-1281	https://doi.org/10.21123/bsj.2014.11.3.1274-1281	PROPN
iajs-3292	377	4	30	30	NUM
iajs-3292	377	5	.	.	PUNCT
iajs-3292	378	1	turkyilmazoglu	turkyilmazoglu	NOUN
iajs-3292	378	2	,	,	PUNCT
iajs-3292	378	3	m.	m.	NOUN
iajs-3292	378	4	;	;	PUNCT
iajs-3292	378	5	convergent	convergent	NOUN
iajs-3292	378	6	optimal	optimal	ADJ
iajs-3292	378	7	variational	variational	ADJ
iajs-3292	378	8	iteration	iteration	NOUN
iajs-3292	378	9	method	method	NOUN
iajs-3292	378	10	and	and	CCONJ
iajs-3292	378	11	applications	application	NOUN
iajs-3292	378	12	to	to	PART
iajs-3292	378	13	heat	heat	VERB
iajs-3292	378	14	and	and	CCONJ
iajs-3292	378	15	fluid	fluid	ADJ
iajs-3292	378	16	flow	flow	NOUN
iajs-3292	378	17	problems	problem	NOUN
iajs-3292	378	18	,	,	PUNCT
iajs-3292	378	19	international	international	ADJ
iajs-3292	378	20	journal	journal	NOUN
iajs-3292	378	21	of	of	ADP
iajs-3292	378	22	numerical	numerical	ADJ
iajs-3292	378	23	methods	method	NOUN
iajs-3292	378	24	for	for	ADP
iajs-3292	378	25	heat	heat	NOUN
iajs-3292	378	26	&	&	CCONJ
iajs-3292	378	27	fluid	fluid	ADJ
iajs-3292	378	28	flow	flow	NOUN
iajs-3292	378	29	2016	2016	NUM
iajs-3292	378	30	,	,	PUNCT
iajs-3292	378	31	26(3/4	26(3/4	NOUN
iajs-3292	378	32	)	)	PUNCT
iajs-3292	378	33	,	,	PUNCT
iajs-3292	378	34	790–804	790–804	NUM
iajs-3292	378	35	.	.	PUNCT
iajs-3292	379	1	doi	doi	NOUN
iajs-3292	379	2	:	:	PUNCT
iajs-3292	379	3	https://doi.org/10.1108/hff-09-2015-0353	https://doi.org/10.1108/hff-09-2015-0353	NUM
iajs-3292	379	4	http://dx.doi.org/10.5281/zenodo.1087368	http://dx.doi.org/10.5281/zenodo.1087368	SYM
iajs-3292	379	5	https://doi.org/10.1016/j.amc.2004.12.037	https://doi.org/10.1016/j.amc.2004.12.037	NOUN
iajs-3292	379	6	https://doi.org/10.1016/s1007-5704(99)90063-1	https://doi.org/10.1016/s1007-5704(99)90063-1	NOUN
iajs-3292	379	7	https://doi.org/10.1016/j.chaos.2005.10.071	https://doi.org/10.1016/j.chaos.2005.10.071	ADJ
iajs-3292	379	8	https://doi.org/10.1002/num.20490	https://doi.org/10.1002/num.20490	PROPN
iajs-3292	379	9	https://doi.org/10.1016/j.cnsns.2009.09.002	https://doi.org/10.1016/j.cnsns.2009.09.002	PROPN
iajs-3292	379	10	https://doi.org/10.21123/bsj.2014.11.3.1295-1300	https://doi.org/10.21123/bsj.2014.11.3.1295-1300	NOUN
iajs-3292	379	11	https://doi.org/10.21123/bsj.2014.11.3.1274-1281	https://doi.org/10.21123/bsj.2014.11.3.1274-1281	VERB
iajs-3292	379	12	https://doi.org/10.1108/hff-09-2015-0353	https://doi.org/10.1108/hff-09-2015-0353	NUM