id	sid	tid	token	lemma	pos
iajs-2776	1	1	ihjpas	ihjpas	PROPN
iajs-2776	1	2	.	.	PUNCT
iajs-2776	2	1	53	53	NUM
iajs-2776	2	2	(	(	PUNCT
iajs-2776	2	3	3)2022	3)2022	NOUN
iajs-2776	2	4	206	206	NUM
iajs-2776	2	5	this	this	DET
iajs-2776	2	6	work	work	NOUN
iajs-2776	2	7	is	be	AUX
iajs-2776	2	8	licensed	license	VERB
iajs-2776	2	9	under	under	ADP
iajs-2776	2	10	a	a	DET
iajs-2776	2	11	creative	creative	ADJ
iajs-2776	2	12	commons	common	NOUN
iajs-2776	2	13	attribution	attribution	NOUN
iajs-2776	2	14	4.0	4.0	NUM
iajs-2776	2	15	international	international	ADJ
iajs-2776	2	16	license	license	NOUN
iajs-2776	2	17	.	.	PUNCT
iajs-2776	3	1	iterative	iterative	NOUN
iajs-2776	3	2	method	method	NOUN
iajs-2776	3	3	for	for	ADP
iajs-2776	3	4	solving	solve	VERB
iajs-2776	3	5	a	a	DET
iajs-2776	3	6	nonlinear	nonlinear	ADJ
iajs-2776	3	7	fourth	fourth	ADJ
iajs-2776	3	8	order	order	NOUN
iajs-2776	3	9	integro	integro	ADJ
iajs-2776	3	10	-	-	PUNCT
iajs-2776	3	11	differential	differential	NOUN
iajs-2776	3	12	equation	equation	NOUN
iajs-2776	3	13	areej	areej	PROPN
iajs-2776	3	14	salah	salah	PROPN
iajs-2776	3	15	mohammed	mohammed	PROPN
iajs-2776	3	16	department	department	PROPN
iajs-2776	3	17	of	of	ADP
iajs-2776	3	18	mathematics	mathematics	PROPN
iajs-2776	3	19	,	,	PUNCT
iajs-2776	3	20	college	college	NOUN
iajs-2776	3	21	of	of	ADP
iajs-2776	3	22	education	education	NOUN
iajs-2776	3	23	for	for	ADP
iajs-2776	3	24	pure	pure	ADJ
iajs-2776	3	25	science	science	NOUN
iajs-2776	3	26	,	,	PUNCT
iajs-2776	3	27	ibn	ibn	PROPN
iajs-2776	3	28	al	al	PROPN
iajs-2776	3	29	haitham	haitham	PROPN
iajs-2776	3	30	,	,	PUNCT
iajs-2776	3	31	university	university	PROPN
iajs-2776	3	32	of	of	ADP
iajs-2776	3	33	baghdad	baghdad	PROPN
iajs-2776	3	34	,	,	PUNCT
iajs-2776	3	35	iraq	iraq	PROPN
iajs-2776	3	36	.	.	PUNCT
iajs-2776	4	1	areej.s.m@ihcoedu.uobaghdad.edu.iq	areej.s.m@ihcoedu.uobaghdad.edu.iq	ADJ
iajs-2776	4	2	abstract	abstract	ADJ
iajs-2776	4	3	this	this	DET
iajs-2776	4	4	study	study	NOUN
iajs-2776	4	5	presents	present	VERB
iajs-2776	4	6	the	the	DET
iajs-2776	4	7	execution	execution	NOUN
iajs-2776	4	8	of	of	ADP
iajs-2776	4	9	an	an	DET
iajs-2776	4	10	iterative	iterative	NOUN
iajs-2776	4	11	technique	technique	NOUN
iajs-2776	4	12	suggested	suggest	VERB
iajs-2776	4	13	by	by	ADP
iajs-2776	4	14	temimi	temimi	NOUN
iajs-2776	4	15	and	and	CCONJ
iajs-2776	4	16	ansari	ansari	ADJ
iajs-2776	4	17	(	(	PUNCT
iajs-2776	4	18	ta	ta	NOUN
iajs-2776	4	19	)	)	PUNCT
iajs-2776	4	20	method	method	NOUN
iajs-2776	4	21	to	to	PART
iajs-2776	4	22	approximate	approximate	VERB
iajs-2776	4	23	solutions	solution	NOUN
iajs-2776	4	24	to	to	ADP
iajs-2776	4	25	a	a	DET
iajs-2776	4	26	boundary	boundary	ADJ
iajs-2776	4	27	value	value	NOUN
iajs-2776	4	28	problem	problem	NOUN
iajs-2776	4	29	of	of	ADP
iajs-2776	4	30	a	a	DET
iajs-2776	4	31	4th	4th	ADJ
iajs-2776	4	32	-	-	PUNCT
iajs-2776	4	33	order	order	NOUN
iajs-2776	4	34	nonlinear	nonlinear	ADJ
iajs-2776	4	35	integro	integro	ADJ
iajs-2776	4	36	-	-	PUNCT
iajs-2776	4	37	differential	differential	NOUN
iajs-2776	4	38	equation	equation	NOUN
iajs-2776	4	39	(	(	PUNCT
iajs-2776	4	40	4th	4th	ADJ
iajs-2776	4	41	-	-	PUNCT
iajs-2776	4	42	onide	onide	ADJ
iajs-2776	4	43	)	)	PUNCT
iajs-2776	4	44	of	of	ADP
iajs-2776	4	45	the	the	DET
iajs-2776	4	46	type	type	NOUN
iajs-2776	4	47	kirchhoff	kirchhoff	NOUN
iajs-2776	4	48	which	which	PRON
iajs-2776	4	49	appears	appear	VERB
iajs-2776	4	50	in	in	ADP
iajs-2776	4	51	the	the	DET
iajs-2776	4	52	study	study	NOUN
iajs-2776	4	53	of	of	ADP
iajs-2776	4	54	transverse	transverse	NOUN
iajs-2776	4	55	vibration	vibration	NOUN
iajs-2776	4	56	of	of	ADP
iajs-2776	4	57	hinged	hinge	VERB
iajs-2776	4	58	shafts	shafts	ADJ
iajs-2776	4	59	.	.	PUNCT
iajs-2776	5	1	this	this	DET
iajs-2776	5	2	problem	problem	NOUN
iajs-2776	5	3	is	be	AUX
iajs-2776	5	4	difficult	difficult	ADJ
iajs-2776	5	5	to	to	PART
iajs-2776	5	6	solve	solve	VERB
iajs-2776	5	7	because	because	SCONJ
iajs-2776	5	8	there	there	PRON
iajs-2776	5	9	is	be	VERB
iajs-2776	5	10	a	a	DET
iajs-2776	5	11	nonlinear	nonlinear	ADJ
iajs-2776	5	12	term	term	NOUN
iajs-2776	5	13	under	under	ADP
iajs-2776	5	14	the	the	DET
iajs-2776	5	15	integral	integral	ADJ
iajs-2776	5	16	sign	sign	NOUN
iajs-2776	5	17	,	,	PUNCT
iajs-2776	5	18	however	however	ADV
iajs-2776	5	19	,	,	PUNCT
iajs-2776	5	20	a	a	DET
iajs-2776	5	21	number	number	NOUN
iajs-2776	5	22	of	of	ADP
iajs-2776	5	23	authors	author	NOUN
iajs-2776	5	24	have	have	AUX
iajs-2776	5	25	suggested	suggest	VERB
iajs-2776	5	26	iterative	iterative	NOUN
iajs-2776	5	27	methods	method	NOUN
iajs-2776	5	28	for	for	ADP
iajs-2776	5	29	solving	solve	VERB
iajs-2776	5	30	this	this	DET
iajs-2776	5	31	type	type	NOUN
iajs-2776	5	32	of	of	ADP
iajs-2776	5	33	equation	equation	NOUN
iajs-2776	5	34	.	.	PUNCT
iajs-2776	6	1	the	the	DET
iajs-2776	6	2	solution	solution	NOUN
iajs-2776	6	3	is	be	AUX
iajs-2776	6	4	obtained	obtain	VERB
iajs-2776	6	5	as	as	ADP
iajs-2776	6	6	a	a	DET
iajs-2776	6	7	series	series	NOUN
iajs-2776	6	8	that	that	PRON
iajs-2776	6	9	merges	merge	VERB
iajs-2776	6	10	with	with	ADP
iajs-2776	6	11	the	the	DET
iajs-2776	6	12	exact	exact	ADJ
iajs-2776	6	13	solution	solution	NOUN
iajs-2776	6	14	.	.	PUNCT
iajs-2776	7	1	two	two	NUM
iajs-2776	7	2	examples	example	NOUN
iajs-2776	7	3	are	be	AUX
iajs-2776	7	4	solved	solve	VERB
iajs-2776	7	5	by	by	ADP
iajs-2776	7	6	ta	ta	PROPN
iajs-2776	7	7	method	method	NOUN
iajs-2776	7	8	,	,	PUNCT
iajs-2776	7	9	the	the	DET
iajs-2776	7	10	results	result	NOUN
iajs-2776	7	11	showed	show	VERB
iajs-2776	7	12	that	that	SCONJ
iajs-2776	7	13	the	the	DET
iajs-2776	7	14	proposed	propose	VERB
iajs-2776	7	15	technique	technique	NOUN
iajs-2776	7	16	was	be	AUX
iajs-2776	7	17	effective	effective	ADJ
iajs-2776	7	18	,	,	PUNCT
iajs-2776	7	19	accurate	accurate	ADJ
iajs-2776	7	20	,	,	PUNCT
iajs-2776	7	21	and	and	CCONJ
iajs-2776	7	22	reliable	reliable	ADJ
iajs-2776	7	23	.	.	PUNCT
iajs-2776	8	1	also	also	ADV
iajs-2776	8	2	,	,	PUNCT
iajs-2776	8	3	for	for	ADP
iajs-2776	8	4	greater	great	ADJ
iajs-2776	8	5	reliability	reliability	NOUN
iajs-2776	8	6	,	,	PUNCT
iajs-2776	8	7	the	the	DET
iajs-2776	8	8	approximate	approximate	ADJ
iajs-2776	8	9	solutions	solution	NOUN
iajs-2776	8	10	were	be	AUX
iajs-2776	8	11	compared	compare	VERB
iajs-2776	8	12	with	with	ADP
iajs-2776	8	13	the	the	DET
iajs-2776	8	14	classic	classic	ADJ
iajs-2776	8	15	runge	runge	NOUN
iajs-2776	8	16	-	-	PUNCT
iajs-2776	8	17	kutta	kutta	NOUN
iajs-2776	8	18	method	method	NOUN
iajs-2776	8	19	(	(	PUNCT
iajs-2776	8	20	rk4	rk4	NOUN
iajs-2776	8	21	m	m	NOUN
iajs-2776	8	22	)	)	PUNCT
iajs-2776	8	23	where	where	SCONJ
iajs-2776	8	24	good	good	ADJ
iajs-2776	8	25	agreements	agreement	NOUN
iajs-2776	8	26	were	be	AUX
iajs-2776	8	27	observed	observe	VERB
iajs-2776	8	28	.	.	PUNCT
iajs-2776	9	1	for	for	ADP
iajs-2776	9	2	more	more	ADJ
iajs-2776	9	3	accuracy	accuracy	NOUN
iajs-2776	9	4	the	the	DET
iajs-2776	9	5	maximum	maximum	ADJ
iajs-2776	9	6	error	error	NOUN
iajs-2776	9	7	remainder	remainder	NOUN
iajs-2776	9	8	was	be	AUX
iajs-2776	9	9	found	find	VERB
iajs-2776	9	10	,	,	PUNCT
iajs-2776	9	11	and	and	CCONJ
iajs-2776	9	12	the	the	DET
iajs-2776	9	13	absolute	absolute	ADJ
iajs-2776	9	14	error	error	NOUN
iajs-2776	9	15	was	be	AUX
iajs-2776	9	16	computed	compute	VERB
iajs-2776	9	17	between	between	ADP
iajs-2776	9	18	the	the	DET
iajs-2776	9	19	semi	semi	ADJ
iajs-2776	9	20	-	-	ADJ
iajs-2776	9	21	analytical	analytical	ADJ
iajs-2776	9	22	method	method	NOUN
iajs-2776	9	23	and	and	CCONJ
iajs-2776	9	24	the	the	DET
iajs-2776	9	25	numerical	numerical	PROPN
iajs-2776	9	26	method	method	PROPN
iajs-2776	9	27	rk4	rk4	PROPN
iajs-2776	9	28	m.	m.	PROPN
iajs-2776	9	29	mathematica	mathematica	PROPN
iajs-2776	9	30	®	®	PROPN
iajs-2776	9	31	11	11	NUM
iajs-2776	9	32	was	be	AUX
iajs-2776	9	33	used	use	VERB
iajs-2776	9	34	as	as	ADP
iajs-2776	9	35	a	a	DET
iajs-2776	9	36	program	program	NOUN
iajs-2776	9	37	for	for	ADP
iajs-2776	9	38	calculations	calculation	NOUN
iajs-2776	9	39	.	.	PUNCT
iajs-2776	10	1	keywords	keyword	VERB
iajs-2776	10	2	an	an	DET
iajs-2776	10	3	iterative	iterative	NOUN
iajs-2776	10	4	technique	technique	NOUN
iajs-2776	10	5	,	,	PUNCT
iajs-2776	10	6	approximate	approximate	ADJ
iajs-2776	10	7	solutions	solution	NOUN
iajs-2776	10	8	,	,	PUNCT
iajs-2776	10	9	fourth	fourth	ADJ
iajs-2776	10	10	order	order	NOUN
iajs-2776	10	11	integro	integro	ADJ
iajs-2776	10	12	-	-	PUNCT
iajs-2776	10	13	differential	differential	NOUN
iajs-2776	10	14	equation	equation	NOUN
iajs-2776	10	15	,	,	PUNCT
iajs-2776	10	16	maximum	maximum	ADJ
iajs-2776	10	17	error	error	NOUN
iajs-2776	10	18	remainder	remainder	NOUN
iajs-2776	10	19	.	.	PUNCT
iajs-2776	11	1	1.introduction	1.introduction	NUM
iajs-2776	11	2	many	many	ADJ
iajs-2776	11	3	real	real	ADJ
iajs-2776	11	4	-	-	PUNCT
iajs-2776	11	5	life	life	NOUN
iajs-2776	11	6	phenomena	phenomena	NOUN
iajs-2776	11	7	engineering	engineering	NOUN
iajs-2776	11	8	and	and	CCONJ
iajs-2776	11	9	physics	physics	NOUN
iajs-2776	11	10	are	be	AUX
iajs-2776	11	11	mathematically	mathematically	ADV
iajs-2776	11	12	modeled	model	VERB
iajs-2776	11	13	into	into	ADP
iajs-2776	11	14	functional	functional	ADJ
iajs-2776	11	15	equations	equation	NOUN
iajs-2776	11	16	.	.	PUNCT
iajs-2776	12	1	many	many	ADJ
iajs-2776	12	2	mathematical	mathematical	ADJ
iajs-2776	12	3	formulas	formula	NOUN
iajs-2776	12	4	for	for	ADP
iajs-2776	12	5	physical	physical	ADJ
iajs-2776	12	6	phenomena	phenomenon	NOUN
iajs-2776	12	7	and	and	CCONJ
iajs-2776	12	8	fluid	fluid	ADJ
iajs-2776	12	9	dynamics	dynamic	NOUN
iajs-2776	12	10	contain	contain	VERB
iajs-2776	12	11	differential	differential	ADJ
iajs-2776	12	12	and	and	CCONJ
iajs-2776	12	13	integral	integral	ADJ
iajs-2776	12	14	equations	equation	NOUN
iajs-2776	12	15	[	[	X
iajs-2776	12	16	1	1	NUM
iajs-2776	12	17	]	]	PUNCT
iajs-2776	12	18	.	.	PUNCT
iajs-2776	13	1	[	[	X
iajs-2776	13	2	2	2	NUM
iajs-2776	13	3	]	]	PUNCT
iajs-2776	13	4	.	.	PUNCT
iajs-2776	14	1	in	in	ADP
iajs-2776	14	2	this	this	DET
iajs-2776	14	3	paper	paper	NOUN
iajs-2776	14	4	,	,	PUNCT
iajs-2776	14	5	the	the	DET
iajs-2776	14	6	integro	integro	ADJ
iajs-2776	14	7	-	-	PUNCT
iajs-2776	14	8	differential	differential	NOUN
iajs-2776	14	9	equation	equation	NOUN
iajs-2776	14	10	of	of	ADP
iajs-2776	14	11	the	the	DET
iajs-2776	14	12	fourth	fourth	ADJ
iajs-2776	14	13	order	order	NOUN
iajs-2776	14	14	of	of	ADP
iajs-2776	14	15	kirchhoff	kirchhoff	NOUN
iajs-2776	14	16	type	type	NOUN
iajs-2776	14	17	is	be	AUX
iajs-2776	14	18	considered	consider	VERB
iajs-2776	14	19	as	as	ADP
iajs-2776	14	20	ibn	ibn	PROPN
iajs-2776	14	21	al	al	PROPN
iajs-2776	14	22	haitham	haitham	PROPN
iajs-2776	14	23	journal	journal	PROPN
iajs-2776	14	24	for	for	ADP
iajs-2776	14	25	pure	pure	ADJ
iajs-2776	14	26	and	and	CCONJ
iajs-2776	14	27	applied	applied	ADJ
iajs-2776	14	28	sciences	sciences	PROPN
iajs-2776	14	29	journal	journal	PROPN
iajs-2776	14	30	homepage	homepage	NOUN
iajs-2776	14	31	:	:	PUNCT
iajs-2776	14	32	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2776	14	33	doi	doi	NOUN
iajs-2776	14	34	:	:	PUNCT
iajs-2776	14	35	10.30526/35.4.2776	10.30526/35.4.2776	PROPN
iajs-2776	14	36	article	article	NOUN
iajs-2776	14	37	history	history	NOUN
iajs-2776	14	38	:	:	PUNCT
iajs-2776	14	39	received	receive	VERB
iajs-2776	14	40	16	16	NUM
iajs-2776	14	41	january	january	PROPN
iajs-2776	14	42	2022	2022	NUM
iajs-2776	14	43	,	,	PUNCT
iajs-2776	14	44	accepted	accept	VERB
iajs-2776	14	45	3	3	NUM
iajs-2776	14	46	february	february	NOUN
iajs-2776	14	47	2022	2022	NUM
iajs-2776	14	48	,	,	PUNCT
iajs-2776	14	49	published	publish	VERB
iajs-2776	14	50	in	in	ADP
iajs-2776	14	51	october	october	PROPN
iajs-2776	14	52	2022	2022	NUM
iajs-2776	14	53	.	.	PUNCT
iajs-2776	15	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-2776	15	2	mailto:areej.s.m@ihcoedu.uobaghdad.edu.iq	mailto:areej.s.m@ihcoedu.uobaghdad.edu.iq	NOUN
iajs-2776	15	3	ihjpas	ihjpa	VERB
iajs-2776	15	4	.	.	PUNCT
iajs-2776	16	1	53	53	NUM
iajs-2776	16	2	(	(	PUNCT
iajs-2776	16	3	3)2022	3)2022	NOUN
iajs-2776	16	4	207	207	NUM
iajs-2776	16	5	𝜐(4)(𝑡)−𝛿𝜐′′(𝑡)−	𝜐(4)(𝑡)−𝛿𝜐′′(𝑡)−	PROPN
iajs-2776	16	6	2	2	NUM
iajs-2776	16	7	𝐵	𝐵	NOUN
iajs-2776	16	8	∫	∫	PROPN
iajs-2776	17	1	[	[	X
iajs-2776	17	2	𝜐′(𝑡	𝜐′(𝑡	NOUN
iajs-2776	17	3	)	)	PUNCT
iajs-2776	17	4	]	]	PUNCT
iajs-2776	17	5	2	2	NUM
iajs-2776	17	6	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	17	7	𝐵	𝐵	NOUN
iajs-2776	17	8	0	0	NUM
iajs-2776	17	9	𝜐′′(𝑡)=𝑘(𝑡	𝜐′′(𝑡)=𝑘(𝑡	VERB
iajs-2776	17	10	)	)	PUNCT
iajs-2776	17	11	,	,	PUNCT
iajs-2776	17	12	0<𝑡<𝐵	0<𝑡<𝐵	NOUN
iajs-2776	17	13	,	,	PUNCT
iajs-2776	17	14	𝜐(0)=𝜐(𝐵)=𝜐′′(0)=𝜐′′(𝐵)=0	𝜐(0)=𝜐(𝐵)=𝜐′′(0)=𝜐′′(𝐵)=0	PROPN
iajs-2776	17	15	,	,	PUNCT
iajs-2776	17	16	]	]	PUNCT
iajs-2776	17	17	(	(	PUNCT
iajs-2776	17	18	1	1	X
iajs-2776	17	19	)	)	PUNCT
iajs-2776	17	20	where	where	SCONJ
iajs-2776	17	21	𝜐(𝑡	𝜐(𝑡	NOUN
iajs-2776	17	22	)	)	PUNCT
iajs-2776	17	23	represents	represent	VERB
iajs-2776	17	24	the	the	DET
iajs-2776	17	25	constant	constant	ADJ
iajs-2776	17	26	deviation	deviation	NOUN
iajs-2776	17	27	of	of	ADP
iajs-2776	17	28	the	the	DET
iajs-2776	17	29	shafts	shafts	ADJ
iajs-2776	17	30	,	,	PUNCT
iajs-2776	17	31	𝑘(𝑡	𝑘(𝑡	PROPN
iajs-2776	17	32	)	)	PUNCT
iajs-2776	17	33	is	be	AUX
iajs-2776	17	34	a	a	DET
iajs-2776	17	35	continuous	continuous	ADJ
iajs-2776	17	36	function	function	NOUN
iajs-2776	17	37	defined	define	VERB
iajs-2776	17	38	over	over	ADP
iajs-2776	17	39	[	[	X
iajs-2776	17	40	0	0	NUM
iajs-2776	17	41	,	,	PUNCT
iajs-2776	17	42	𝐵]and	𝐵]and	NOUN
iajs-2776	17	43	𝛿	𝛿	NOUN
iajs-2776	17	44	and	and	CCONJ
iajs-2776	17	45	𝐵	𝐵	NOUN
iajs-2776	17	46	are	be	AUX
iajs-2776	17	47	positive	positive	ADJ
iajs-2776	17	48	constants	constant	NOUN
iajs-2776	17	49	.	.	PUNCT
iajs-2776	18	1	this	this	DET
iajs-2776	18	2	type	type	NOUN
iajs-2776	18	3	of	of	ADP
iajs-2776	18	4	problem	problem	NOUN
iajs-2776	18	5	represents	represent	VERB
iajs-2776	18	6	a	a	DET
iajs-2776	18	7	bending	bend	VERB
iajs-2776	18	8	equilibrium	equilibrium	NOUN
iajs-2776	18	9	model	model	NOUN
iajs-2776	18	10	for	for	ADP
iajs-2776	18	11	expandable	expandable	ADJ
iajs-2776	18	12	shafts	shafts	ADJ
iajs-2776	18	13	that	that	PRON
iajs-2776	18	14	are	be	AUX
iajs-2776	18	15	simply	simply	ADV
iajs-2776	18	16	supported	support	VERB
iajs-2776	18	17	on	on	ADP
iajs-2776	18	18	nonlinear	nonlinear	ADJ
iajs-2776	18	19	bases	basis	NOUN
iajs-2776	18	20	.	.	PUNCT
iajs-2776	19	1	the	the	DET
iajs-2776	19	2	force	force	NOUN
iajs-2776	19	3	that	that	SCONJ
iajs-2776	19	4	the	the	DET
iajs-2776	19	5	foundation	foundation	NOUN
iajs-2776	19	6	applies	apply	VERB
iajs-2776	19	7	to	to	ADP
iajs-2776	19	8	the	the	DET
iajs-2776	19	9	shafts	shaft	NOUN
iajs-2776	19	10	is	be	AUX
iajs-2776	19	11	represented	represent	VERB
iajs-2776	19	12	by	by	ADP
iajs-2776	19	13	the	the	DET
iajs-2776	19	14	function	function	NOUN
iajs-2776	19	15	,	,	PUNCT
iajs-2776	19	16	𝑘(𝑡	𝑘(𝑡	PROPN
iajs-2776	19	17	)	)	PUNCT
iajs-2776	19	18	.	.	PUNCT
iajs-2776	20	1	small	small	ADJ
iajs-2776	20	2	changes	change	NOUN
iajs-2776	20	3	in	in	ADP
iajs-2776	20	4	shafts	shafts	ADJ
iajs-2776	20	5	length	length	NOUN
iajs-2776	20	6	and	and	CCONJ
iajs-2776	20	7	their	their	PRON
iajs-2776	20	8	effects	effect	NOUN
iajs-2776	20	9	are	be	AUX
iajs-2776	20	10	represented	represent	VERB
iajs-2776	20	11	by	by	ADP
iajs-2776	20	12	:	:	PUNCT
iajs-2776	20	13	2	2	NUM
iajs-2776	20	14	𝐵	𝐵	NOUN
iajs-2776	20	15	∫	∫	NOUN
iajs-2776	21	1	[	[	X
iajs-2776	21	2	𝜐′(𝑡)]2𝑑𝑡	𝜐′(𝑡)]2𝑑𝑡	ADJ
iajs-2776	21	3	𝐵	𝐵	NOUN
iajs-2776	21	4	0	0	PUNCT
iajs-2776	22	1	[	[	X
iajs-2776	22	2	3	3	NUM
iajs-2776	22	3	]	]	PUNCT
iajs-2776	22	4	.	.	PUNCT
iajs-2776	23	1	it	it	PRON
iajs-2776	23	2	is	be	AUX
iajs-2776	23	3	obvious	obvious	ADJ
iajs-2776	23	4	that	that	SCONJ
iajs-2776	23	5	it	it	PRON
iajs-2776	23	6	is	be	AUX
iajs-2776	23	7	difficult	difficult	ADJ
iajs-2776	23	8	to	to	PART
iajs-2776	23	9	find	find	VERB
iajs-2776	23	10	the	the	DET
iajs-2776	23	11	exact	exact	ADJ
iajs-2776	23	12	solution	solution	NOUN
iajs-2776	23	13	to	to	ADP
iajs-2776	23	14	equation	equation	NOUN
iajs-2776	23	15	(	(	PUNCT
iajs-2776	23	16	1	1	NUM
iajs-2776	23	17	)	)	PUNCT
iajs-2776	23	18	,	,	PUNCT
iajs-2776	23	19	so	so	ADV
iajs-2776	23	20	many	many	ADJ
iajs-2776	23	21	numerical	numerical	ADJ
iajs-2776	23	22	and	and	CCONJ
iajs-2776	23	23	semi	semi	ADJ
iajs-2776	23	24	-	-	ADJ
iajs-2776	23	25	analytical	analytical	ADJ
iajs-2776	23	26	methods	method	NOUN
iajs-2776	23	27	have	have	AUX
iajs-2776	23	28	been	be	AUX
iajs-2776	23	29	developed	develop	VERB
iajs-2776	23	30	,	,	PUNCT
iajs-2776	23	31	such	such	ADJ
iajs-2776	23	32	as	as	ADP
iajs-2776	23	33	[	[	X
iajs-2776	23	34	4	4	NUM
iajs-2776	23	35	]	]	PUNCT
iajs-2776	23	36	reduced	reduce	VERB
iajs-2776	23	37	the	the	DET
iajs-2776	23	38	order	order	NOUN
iajs-2776	23	39	of	of	ADP
iajs-2776	23	40	the	the	DET
iajs-2776	23	41	equation	equation	NOUN
iajs-2776	23	42	to	to	PART
iajs-2776	23	43	find	find	VERB
iajs-2776	23	44	the	the	DET
iajs-2776	23	45	root	root	NOUN
iajs-2776	23	46	of	of	ADP
iajs-2776	23	47	a	a	DET
iajs-2776	23	48	nonlinear	nonlinear	ADJ
iajs-2776	23	49	equation	equation	NOUN
iajs-2776	23	50	and	and	CCONJ
iajs-2776	23	51	solve	solve	VERB
iajs-2776	23	52	it	it	PRON
iajs-2776	23	53	by	by	ADP
iajs-2776	23	54	newton	newton	PROPN
iajs-2776	23	55	's	's	PART
iajs-2776	23	56	method	method	NOUN
iajs-2776	23	57	.	.	PUNCT
iajs-2776	24	1	[	[	X
iajs-2776	24	2	5	5	NUM
iajs-2776	24	3	]	]	PUNCT
iajs-2776	24	4	used	use	VERB
iajs-2776	24	5	the	the	DET
iajs-2776	24	6	optimal	optimal	ADJ
iajs-2776	24	7	homotopy	homotopy	NOUN
iajs-2776	24	8	asymptotic	asymptotic	ADJ
iajs-2776	24	9	strategy	strategy	NOUN
iajs-2776	24	10	to	to	PART
iajs-2776	24	11	solve	solve	VERB
iajs-2776	24	12	equation	equation	NOUN
iajs-2776	24	13	(	(	PUNCT
iajs-2776	24	14	1	1	NUM
iajs-2776	24	15	)	)	PUNCT
iajs-2776	24	16	and	and	CCONJ
iajs-2776	24	17	proved	prove	VERB
iajs-2776	24	18	the	the	DET
iajs-2776	24	19	efficacy	efficacy	NOUN
iajs-2776	24	20	of	of	ADP
iajs-2776	24	21	the	the	DET
iajs-2776	24	22	procedure	procedure	NOUN
iajs-2776	24	23	by	by	ADP
iajs-2776	24	24	comparing	compare	VERB
iajs-2776	24	25	it	it	PRON
iajs-2776	24	26	with	with	ADP
iajs-2776	24	27	a	a	DET
iajs-2776	24	28	finite	finite	ADJ
iajs-2776	24	29	element	element	NOUN
iajs-2776	24	30	technique	technique	NOUN
iajs-2776	24	31	.	.	PUNCT
iajs-2776	25	1	[	[	X
iajs-2776	25	2	6	6	NUM
iajs-2776	25	3	]	]	PUNCT
iajs-2776	25	4	proposed	propose	VERB
iajs-2776	25	5	a	a	DET
iajs-2776	25	6	numerical	numerical	ADJ
iajs-2776	25	7	scheme	scheme	NOUN
iajs-2776	25	8	for	for	ADP
iajs-2776	25	9	solving	solve	VERB
iajs-2776	25	10	equation	equation	NOUN
iajs-2776	25	11	(	(	PUNCT
iajs-2776	25	12	1	1	NUM
iajs-2776	25	13	)	)	PUNCT
iajs-2776	25	14	by	by	ADP
iajs-2776	25	15	transforming	transform	VERB
iajs-2776	25	16	the	the	DET
iajs-2776	25	17	problem	problem	NOUN
iajs-2776	25	18	into	into	ADP
iajs-2776	25	19	a	a	DET
iajs-2776	25	20	nonlinear	nonlinear	ADJ
iajs-2776	25	21	algebraic	algebraic	ADJ
iajs-2776	25	22	system	system	NOUN
iajs-2776	25	23	and	and	CCONJ
iajs-2776	25	24	then	then	ADV
iajs-2776	25	25	solving	solve	VERB
iajs-2776	25	26	it	it	PRON
iajs-2776	25	27	in	in	ADP
iajs-2776	25	28	an	an	DET
iajs-2776	25	29	iterative	iterative	NOUN
iajs-2776	25	30	method	method	NOUN
iajs-2776	25	31	with	with	ADP
iajs-2776	25	32	the	the	DET
iajs-2776	25	33	collocation	collocation	NOUN
iajs-2776	25	34	technique	technique	NOUN
iajs-2776	25	35	.	.	PUNCT
iajs-2776	26	1	[	[	X
iajs-2776	26	2	7	7	X
iajs-2776	26	3	]	]	PUNCT
iajs-2776	26	4	suggested	suggest	VERB
iajs-2776	26	5	an	an	DET
iajs-2776	26	6	iterative	iterative	NOUN
iajs-2776	26	7	method	method	NOUN
iajs-2776	26	8	namely	namely	ADV
iajs-2776	26	9	tamimi	tamimi	NOUN
iajs-2776	26	10	and	and	CCONJ
iajs-2776	26	11	ansari	ansari	ADJ
iajs-2776	26	12	(	(	PUNCT
iajs-2776	26	13	ta	ta	NOUN
iajs-2776	26	14	)	)	PUNCT
iajs-2776	26	15	method	method	NOUN
iajs-2776	26	16	for	for	ADP
iajs-2776	26	17	solving	solve	VERB
iajs-2776	26	18	nonlinear	nonlinear	ADJ
iajs-2776	26	19	equations	equation	NOUN
iajs-2776	26	20	,	,	PUNCT
iajs-2776	26	21	and	and	CCONJ
iajs-2776	26	22	this	this	DET
iajs-2776	26	23	technique	technique	NOUN
iajs-2776	26	24	was	be	AUX
iajs-2776	26	25	applied	apply	VERB
iajs-2776	26	26	to	to	PART
iajs-2776	26	27	solve	solve	VERB
iajs-2776	26	28	numerous	numerous	ADJ
iajs-2776	26	29	differential	differential	ADJ
iajs-2776	26	30	equations	equation	NOUN
iajs-2776	26	31	,	,	PUNCT
iajs-2776	26	32	for	for	ADP
iajs-2776	26	33	example	example	NOUN
iajs-2776	26	34	,	,	PUNCT
iajs-2776	26	35	korteweg	korteweg	NOUN
iajs-2776	26	36	-	-	PUNCT
iajs-2776	26	37	de	de	NOUN
iajs-2776	26	38	vries	vries	PROPN
iajs-2776	26	39	equations	equation	NOUN
iajs-2776	27	1	[	[	X
iajs-2776	27	2	8	8	NUM
iajs-2776	27	3	]	]	PUNCT
iajs-2776	27	4	,	,	PUNCT
iajs-2776	27	5	thin	thin	ADJ
iajs-2776	27	6	-	-	PUNCT
iajs-2776	27	7	film	film	NOUN
iajs-2776	27	8	flow	flow	NOUN
iajs-2776	27	9	problems	problem	NOUN
iajs-2776	28	1	[	[	X
iajs-2776	28	2	9	9	NUM
iajs-2776	28	3	]	]	PUNCT
iajs-2776	28	4	,	,	PUNCT
iajs-2776	28	5	falkner	falkner	PROPN
iajs-2776	28	6	-	-	PUNCT
iajs-2776	28	7	skan	skan	VERB
iajs-2776	28	8	problem	problem	NOUN
iajs-2776	28	9	[	[	X
iajs-2776	28	10	10	10	NUM
iajs-2776	28	11	]	]	PUNCT
iajs-2776	28	12	.	.	PUNCT
iajs-2776	29	1	in	in	ADP
iajs-2776	29	2	this	this	DET
iajs-2776	29	3	work	work	NOUN
iajs-2776	29	4	,	,	PUNCT
iajs-2776	29	5	the	the	DET
iajs-2776	29	6	ta	ta	PROPN
iajs-2776	29	7	method	method	NOUN
iajs-2776	29	8	is	be	AUX
iajs-2776	29	9	used	use	VERB
iajs-2776	29	10	to	to	PART
iajs-2776	29	11	solve	solve	VERB
iajs-2776	29	12	the	the	DET
iajs-2776	29	13	4th	4th	ADJ
iajs-2776	29	14	-	-	PUNCT
iajs-2776	29	15	onide	onide	NOUN
iajs-2776	29	16	of	of	ADP
iajs-2776	29	17	the	the	DET
iajs-2776	29	18	type	type	NOUN
iajs-2776	29	19	kirchhoff	kirchhoff	NOUN
iajs-2776	29	20	which	which	PRON
iajs-2776	29	21	appears	appear	VERB
iajs-2776	29	22	in	in	ADP
iajs-2776	29	23	the	the	DET
iajs-2776	29	24	study	study	NOUN
iajs-2776	29	25	of	of	ADP
iajs-2776	29	26	transverse	transverse	NOUN
iajs-2776	29	27	vibration	vibration	NOUN
iajs-2776	29	28	of	of	ADP
iajs-2776	29	29	hinged	hinge	VERB
iajs-2776	29	30	shafts	shafts	ADJ
iajs-2776	29	31	.	.	PUNCT
iajs-2776	30	1	the	the	DET
iajs-2776	30	2	results	result	NOUN
iajs-2776	30	3	acquired	acquire	VERB
iajs-2776	30	4	from	from	ADP
iajs-2776	30	5	the	the	DET
iajs-2776	30	6	method	method	NOUN
iajs-2776	30	7	showed	show	VERB
iajs-2776	30	8	that	that	SCONJ
iajs-2776	30	9	ta	ta	PROPN
iajs-2776	30	10	method	method	NOUN
iajs-2776	30	11	is	be	AUX
iajs-2776	30	12	accurate	accurate	ADJ
iajs-2776	30	13	,	,	PUNCT
iajs-2776	30	14	fast	fast	ADJ
iajs-2776	30	15	,	,	PUNCT
iajs-2776	30	16	and	and	CCONJ
iajs-2776	30	17	convenient	convenient	ADJ
iajs-2776	30	18	.	.	PUNCT
iajs-2776	31	1	two	two	NUM
iajs-2776	31	2	examples	example	NOUN
iajs-2776	31	3	are	be	AUX
iajs-2776	31	4	solved	solve	VERB
iajs-2776	31	5	and	and	CCONJ
iajs-2776	31	6	the	the	DET
iajs-2776	31	7	results	result	NOUN
iajs-2776	31	8	obtained	obtain	VERB
iajs-2776	31	9	are	be	AUX
iajs-2776	31	10	compared	compare	VERB
iajs-2776	31	11	with	with	ADP
iajs-2776	31	12	the	the	DET
iajs-2776	31	13	rk4	rk4	NOUN
iajs-2776	31	14	m	m	NOUN
iajs-2776	31	15	method	method	NOUN
iajs-2776	31	16	,	,	PUNCT
iajs-2776	31	17	and	and	CCONJ
iajs-2776	31	18	the	the	DET
iajs-2776	31	19	maximum	maximum	ADJ
iajs-2776	31	20	error	error	NOUN
iajs-2776	31	21	reminder	reminder	NOUN
iajs-2776	31	22	is	be	AUX
iajs-2776	31	23	calculated	calculate	VERB
iajs-2776	31	24	.	.	PUNCT
iajs-2776	32	1	this	this	DET
iajs-2776	32	2	article	article	NOUN
iajs-2776	32	3	is	be	AUX
iajs-2776	32	4	arranged	arrange	VERB
iajs-2776	32	5	as	as	SCONJ
iajs-2776	32	6	follows	follow	VERB
iajs-2776	32	7	:	:	PUNCT
iajs-2776	32	8	section	section	NOUN
iajs-2776	32	9	2	2	NUM
iajs-2776	32	10	provides	provide	VERB
iajs-2776	32	11	a	a	DET
iajs-2776	32	12	clear	clear	ADJ
iajs-2776	32	13	formulation	formulation	NOUN
iajs-2776	32	14	of	of	ADP
iajs-2776	32	15	the	the	DET
iajs-2776	32	16	iterative	iterative	NOUN
iajs-2776	32	17	method	method	NOUN
iajs-2776	32	18	in	in	ADP
iajs-2776	32	19	general	general	ADJ
iajs-2776	32	20	and	and	CCONJ
iajs-2776	32	21	specifically	specifically	ADV
iajs-2776	32	22	on	on	ADP
iajs-2776	32	23	equation	equation	NOUN
iajs-2776	32	24	(	(	PUNCT
iajs-2776	32	25	1	1	NUM
iajs-2776	32	26	)	)	PUNCT
iajs-2776	32	27	;	;	PUNCT
iajs-2776	32	28	section	section	NOUN
iajs-2776	32	29	3	3	NUM
iajs-2776	32	30	illustrates	illustrate	VERB
iajs-2776	32	31	the	the	DET
iajs-2776	32	32	effectiveness	effectiveness	NOUN
iajs-2776	32	33	of	of	ADP
iajs-2776	32	34	the	the	DET
iajs-2776	32	35	method	method	NOUN
iajs-2776	32	36	with	with	ADP
iajs-2776	32	37	various	various	ADJ
iajs-2776	32	38	examples	example	NOUN
iajs-2776	32	39	before	before	ADP
iajs-2776	32	40	giving	give	VERB
iajs-2776	32	41	a	a	DET
iajs-2776	32	42	brief	brief	ADJ
iajs-2776	32	43	conclusion	conclusion	NOUN
iajs-2776	32	44	in	in	ADP
iajs-2776	32	45	section	section	NOUN
iajs-2776	32	46	4	4	NUM
iajs-2776	32	47	.	.	NOUN
iajs-2776	32	48	1	1	NUM
iajs-2776	32	49	.	.	PUNCT
iajs-2776	33	1	the	the	DET
iajs-2776	33	2	proposed	propose	VERB
iajs-2776	33	3	method	method	NOUN
iajs-2776	33	4	to	to	PART
iajs-2776	33	5	clarify	clarify	VERB
iajs-2776	33	6	the	the	DET
iajs-2776	33	7	fundamental	fundamental	ADJ
iajs-2776	33	8	thought	thought	NOUN
iajs-2776	33	9	of	of	ADP
iajs-2776	33	10	ta	ta	PART
iajs-2776	33	11	method	method	NOUN
iajs-2776	33	12	.	.	PUNCT
iajs-2776	34	1	let	let	VERB
iajs-2776	34	2	us	we	PRON
iajs-2776	34	3	consider	consider	VERB
iajs-2776	34	4	the	the	DET
iajs-2776	34	5	general	general	ADJ
iajs-2776	34	6	equation	equation	NOUN
iajs-2776	34	7	ℒ(υ(t	ℒ(υ(t	NOUN
iajs-2776	34	8	)	)	PUNCT
iajs-2776	34	9	)	)	PUNCT
iajs-2776	35	1	+	+	CCONJ
iajs-2776	35	2	ℵ(υ(t	ℵ(υ(t	NOUN
iajs-2776	35	3	)	)	PUNCT
iajs-2776	35	4	)	)	PUNCT
iajs-2776	36	1	+	+	CCONJ
iajs-2776	36	2	g(t	g(t	NOUN
iajs-2776	36	3	)	)	PUNCT
iajs-2776	36	4	=	=	SYM
iajs-2776	36	5	0	0	NUM
iajs-2776	36	6	,	,	PUNCT
iajs-2776	36	7	(	(	PUNCT
iajs-2776	36	8	2	2	NUM
iajs-2776	36	9	)	)	PUNCT
iajs-2776	36	10	with	with	ADP
iajs-2776	36	11	boundary	boundary	ADJ
iajs-2776	36	12	conditions	condition	NOUN
iajs-2776	36	13	ℬ	ℬ	NOUN
iajs-2776	36	14	(	(	PUNCT
iajs-2776	36	15	υ	υ	NOUN
iajs-2776	36	16	,	,	PUNCT
iajs-2776	36	17	d𝜐	d𝜐	VERB
iajs-2776	36	18	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	36	19	)	)	PUNCT
iajs-2776	36	20	=	=	SYM
iajs-2776	36	21	0	0	NUM
iajs-2776	36	22	,	,	PUNCT
iajs-2776	36	23	where	where	SCONJ
iajs-2776	36	24	υ	υ	NOUN
iajs-2776	36	25	is	be	AUX
iajs-2776	36	26	unknown	unknown	ADJ
iajs-2776	36	27	function	function	NOUN
iajs-2776	36	28	,	,	PUNCT
iajs-2776	36	29	ℒ	ℒ	PROPN
iajs-2776	36	30	is	be	AUX
iajs-2776	36	31	the	the	DET
iajs-2776	36	32	linear	linear	ADJ
iajs-2776	36	33	operator	operator	NOUN
iajs-2776	36	34	,	,	PUNCT
iajs-2776	36	35	ℵ	ℵ	X
iajs-2776	36	36	is	be	AUX
iajs-2776	36	37	the	the	DET
iajs-2776	36	38	nonlinear	nonlinear	ADJ
iajs-2776	36	39	operator	operator	NOUN
iajs-2776	36	40	and	and	CCONJ
iajs-2776	36	41	g	g	NOUN
iajs-2776	36	42	is	be	AUX
iajs-2776	36	43	a	a	DET
iajs-2776	36	44	known	know	VERB
iajs-2776	36	45	function	function	NOUN
iajs-2776	36	46	.	.	PUNCT
iajs-2776	37	1	assuming	assume	VERB
iajs-2776	37	2	that	that	SCONJ
iajs-2776	37	3	υ0(𝑡	υ0(𝑡	NOUN
iajs-2776	37	4	)	)	PUNCT
iajs-2776	37	5	is	be	AUX
iajs-2776	37	6	a	a	DET
iajs-2776	37	7	solution	solution	NOUN
iajs-2776	37	8	of	of	ADP
iajs-2776	37	9	equation	equation	NOUN
iajs-2776	37	10	(	(	PUNCT
iajs-2776	37	11	3	3	NUM
iajs-2776	37	12	)	)	PUNCT
iajs-2776	37	13	of	of	ADP
iajs-2776	37	14	the	the	DET
iajs-2776	37	15	initial	initial	ADJ
iajs-2776	37	16	condition	condition	NOUN
iajs-2776	37	17	ℒ(υ0(𝑡	ℒ(υ0(𝑡	PROPN
iajs-2776	37	18	)	)	PUNCT
iajs-2776	37	19	)	)	PUNCT
iajs-2776	38	1	+	+	CCONJ
iajs-2776	38	2	g(t	g(t	NOUN
iajs-2776	38	3	)	)	PUNCT
iajs-2776	38	4	=	=	SYM
iajs-2776	38	5	0	0	NUM
iajs-2776	38	6	,	,	PUNCT
iajs-2776	38	7	with	with	ADP
iajs-2776	38	8	ℬ	ℬ	PROPN
iajs-2776	38	9	(	(	PUNCT
iajs-2776	38	10	υ0	υ0	PROPN
iajs-2776	38	11	,	,	PUNCT
iajs-2776	38	12	d𝜐0	d𝜐0	NOUN
iajs-2776	38	13	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	38	14	)	)	PUNCT
iajs-2776	38	15	=	=	SYM
iajs-2776	38	16	0	0	NUM
iajs-2776	38	17	.	.	PUNCT
iajs-2776	39	1	(	(	PUNCT
iajs-2776	39	2	3	3	X
iajs-2776	39	3	)	)	PUNCT
iajs-2776	39	4	to	to	PART
iajs-2776	39	5	find	find	VERB
iajs-2776	39	6	the	the	DET
iajs-2776	39	7	next	next	ADJ
iajs-2776	39	8	iteration	iteration	NOUN
iajs-2776	39	9	,	,	PUNCT
iajs-2776	39	10	we	we	PRON
iajs-2776	39	11	resolve	resolve	VERB
iajs-2776	39	12	the	the	DET
iajs-2776	39	13	following	follow	VERB
iajs-2776	39	14	equation	equation	NOUN
iajs-2776	39	15	:	:	PUNCT
iajs-2776	39	16	ℒ(υ1(𝑡	ℒ(υ1(𝑡	NOUN
iajs-2776	39	17	)	)	PUNCT
iajs-2776	39	18	)	)	PUNCT
iajs-2776	39	19	+	+	CCONJ
iajs-2776	40	1	ℵ(υ0(𝑡	ℵ(υ0(𝑡	VERB
iajs-2776	40	2	)	)	PUNCT
iajs-2776	40	3	)	)	PUNCT
iajs-2776	41	1	+	+	CCONJ
iajs-2776	41	2	g(t	g(t	NOUN
iajs-2776	41	3	)	)	PUNCT
iajs-2776	41	4	=	=	SYM
iajs-2776	41	5	0	0	NUM
iajs-2776	41	6	,	,	PUNCT
iajs-2776	41	7	ℬ	ℬ	PROPN
iajs-2776	41	8	(	(	PUNCT
iajs-2776	41	9	υ1	υ1	PROPN
iajs-2776	41	10	,	,	PUNCT
iajs-2776	41	11	d𝜐1	d𝜐1	NOUN
iajs-2776	41	12	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	41	13	)	)	PUNCT
iajs-2776	41	14	=	=	SYM
iajs-2776	42	1	0	0	X
iajs-2776	42	2	.	.	PUNCT
iajs-2776	42	3	ihjpas	ihjpas	PROPN
iajs-2776	42	4	.	.	PUNCT
iajs-2776	43	1	53	53	NUM
iajs-2776	43	2	(	(	PUNCT
iajs-2776	43	3	3)2022	3)2022	NOUN
iajs-2776	43	4	208	208	NUM
iajs-2776	43	5	thus	thus	ADV
iajs-2776	43	6	,	,	PUNCT
iajs-2776	43	7	an	an	DET
iajs-2776	43	8	iterative	iterative	NOUN
iajs-2776	43	9	procedure	procedure	NOUN
iajs-2776	43	10	can	can	AUX
iajs-2776	43	11	be	be	AUX
iajs-2776	43	12	an	an	DET
iajs-2776	43	13	effective	effective	ADJ
iajs-2776	43	14	solution	solution	NOUN
iajs-2776	43	15	to	to	ADP
iajs-2776	43	16	the	the	DET
iajs-2776	43	17	following	following	ADJ
iajs-2776	43	18	problem	problem	NOUN
iajs-2776	43	19	,	,	PUNCT
iajs-2776	43	20	ℒ(υ𝑛+1(𝑡	ℒ(υ𝑛+1(𝑡	NOUN
iajs-2776	43	21	)	)	PUNCT
iajs-2776	43	22	)	)	PUNCT
iajs-2776	44	1	+	+	CCONJ
iajs-2776	44	2	ℵ(υ𝑛(𝑡	ℵ(υ𝑛(𝑡	NOUN
iajs-2776	44	3	)	)	PUNCT
iajs-2776	44	4	)	)	PUNCT
iajs-2776	45	1	+	+	CCONJ
iajs-2776	45	2	g(t	g(t	NOUN
iajs-2776	45	3	)	)	PUNCT
iajs-2776	45	4	=	=	SYM
iajs-2776	45	5	0	0	NUM
iajs-2776	45	6	,	,	PUNCT
iajs-2776	45	7	ℬ	ℬ	PROPN
iajs-2776	45	8	(	(	PUNCT
iajs-2776	45	9	υ𝑛+1	υ𝑛+1	PROPN
iajs-2776	45	10	,	,	PUNCT
iajs-2776	45	11	d𝜐𝑛+1	d𝜐𝑛+1	ADJ
iajs-2776	45	12	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	45	13	)	)	PUNCT
iajs-2776	45	14	=	=	SYM
iajs-2776	45	15	0	0	X
iajs-2776	45	16	.	.	PUNCT
iajs-2776	45	17	(	(	PUNCT
iajs-2776	45	18	4	4	X
iajs-2776	45	19	)	)	PUNCT
iajs-2776	45	20	each	each	PRON
iajs-2776	45	21	of	of	ADP
iajs-2776	45	22	𝜐𝑖	𝜐𝑖	NOUN
iajs-2776	45	23	are	be	AUX
iajs-2776	45	24	solutions	solution	NOUN
iajs-2776	45	25	to	to	ADP
iajs-2776	45	26	equation	equation	NOUN
iajs-2776	45	27	(	(	PUNCT
iajs-2776	45	28	1	1	X
iajs-2776	45	29	)	)	PUNCT
iajs-2776	46	1	[	[	X
iajs-2776	46	2	7	7	NUM
iajs-2776	46	3	]	]	PUNCT
iajs-2776	46	4	.	.	PUNCT
iajs-2776	47	1	we	we	PRON
iajs-2776	47	2	will	will	AUX
iajs-2776	47	3	apply	apply	VERB
iajs-2776	47	4	the	the	DET
iajs-2776	47	5	steps	step	NOUN
iajs-2776	47	6	of	of	ADP
iajs-2776	47	7	the	the	DET
iajs-2776	47	8	method	method	NOUN
iajs-2776	47	9	in	in	ADP
iajs-2776	47	10	solving	solve	VERB
iajs-2776	47	11	equation	equation	NOUN
iajs-2776	47	12	(	(	PUNCT
iajs-2776	47	13	1	1	NUM
iajs-2776	47	14	)	)	PUNCT
iajs-2776	47	15	,	,	PUNCT
iajs-2776	47	16	so	so	SCONJ
iajs-2776	47	17	it	it	PRON
iajs-2776	47	18	can	can	AUX
iajs-2776	47	19	be	be	AUX
iajs-2776	47	20	formulated	formulate	VERB
iajs-2776	47	21	as	as	ADP
iajs-2776	47	22	:	:	PUNCT
iajs-2776	47	23	ℒ(υ(t))−δr(υ(t))−	ℒ(υ(t))−δr(υ(t))−	ADJ
iajs-2776	47	24	2	2	NUM
iajs-2776	47	25	b	b	X
iajs-2776	47	26	(	(	PUNCT
iajs-2776	47	27	∫	∫	PROPN
iajs-2776	47	28	ℵ(υ(t))dt	ℵ(υ(t))dt	PROPN
iajs-2776	47	29	)	)	PUNCT
iajs-2776	47	30	b	b	NOUN
iajs-2776	47	31	0	0	NUM
iajs-2776	47	32	r(υ(t))=k(t	r(υ(t))=k(t	NOUN
iajs-2776	47	33	)	)	PUNCT
iajs-2776	47	34	,	,	PUNCT
iajs-2776	47	35	0	0	NUM
iajs-2776	47	36	<	<	X
iajs-2776	47	37	t	t	PROPN
iajs-2776	47	38	<	<	X
iajs-2776	47	39	b	b	PROPN
iajs-2776	47	40	,	,	PUNCT
iajs-2776	47	41	υ(0)=υ(b)=υ′′(0)=υ′′(b)=0	υ(0)=υ(b)=υ′′(0)=υ′′(b)=0	PROPN
iajs-2776	47	42	,	,	PUNCT
iajs-2776	47	43	]	]	PUNCT
iajs-2776	47	44	(	(	PUNCT
iajs-2776	47	45	5	5	NUM
iajs-2776	47	46	)	)	PUNCT
iajs-2776	47	47	where	where	SCONJ
iajs-2776	47	48	ℒ	ℒ	PROPN
iajs-2776	47	49	is	be	AUX
iajs-2776	47	50	the	the	DET
iajs-2776	47	51	fourth	fourth	ADJ
iajs-2776	47	52	derivative	derivative	NOUN
iajs-2776	47	53	,	,	PUNCT
iajs-2776	47	54	r	r	NOUN
iajs-2776	47	55	is	be	AUX
iajs-2776	47	56	the	the	DET
iajs-2776	47	57	second	second	ADJ
iajs-2776	47	58	derivative	derivative	NOUN
iajs-2776	47	59	and	and	CCONJ
iajs-2776	47	60	ℵ	ℵ	ADP
iajs-2776	47	61	the	the	DET
iajs-2776	47	62	nonlinear	nonlinear	ADJ
iajs-2776	47	63	term	term	NOUN
iajs-2776	47	64	.	.	PUNCT
iajs-2776	48	1	υ0(𝑡	υ0(𝑡	VERB
iajs-2776	48	2	)	)	PUNCT
iajs-2776	48	3	can	can	AUX
iajs-2776	48	4	be	be	AUX
iajs-2776	48	5	considered	consider	VERB
iajs-2776	48	6	as	as	ADP
iajs-2776	48	7	a	a	DET
iajs-2776	48	8	solution	solution	NOUN
iajs-2776	48	9	to	to	ADP
iajs-2776	48	10	the	the	DET
iajs-2776	48	11	initial	initial	ADJ
iajs-2776	48	12	problem	problem	NOUN
iajs-2776	48	13	:	:	PUNCT
iajs-2776	48	14	ℒ(υ0(𝑡	ℒ(υ0(𝑡	PROPN
iajs-2776	48	15	)	)	PUNCT
iajs-2776	48	16	)	)	PUNCT
iajs-2776	49	1	=	=	PUNCT
iajs-2776	49	2	k(t	k(t	NOUN
iajs-2776	49	3	)	)	PUNCT
iajs-2776	49	4	,	,	PUNCT
iajs-2776	49	5	with	with	ADP
iajs-2776	49	6	𝜐0(0	𝜐0(0	PROPN
iajs-2776	49	7	)	)	PUNCT
iajs-2776	49	8	=	=	SYM
iajs-2776	49	9	𝜐0(𝐵	𝜐0(𝐵	NOUN
iajs-2776	49	10	)	)	PUNCT
iajs-2776	49	11	=	=	NOUN
iajs-2776	49	12	𝜐0	𝜐0	NOUN
iajs-2776	49	13	′′(0	′′(0	NOUN
iajs-2776	49	14	)	)	PUNCT
iajs-2776	49	15	=	=	VERB
iajs-2776	49	16	𝜐0	𝜐0	NOUN
iajs-2776	49	17	′′(𝐵	′′(𝐵	NOUN
iajs-2776	49	18	)	)	PUNCT
iajs-2776	49	19	=	=	SYM
iajs-2776	49	20	0	0	NUM
iajs-2776	49	21	,	,	PUNCT
iajs-2776	49	22	(	(	PUNCT
iajs-2776	49	23	6	6	NUM
iajs-2776	49	24	)	)	PUNCT
iajs-2776	49	25	υ1(𝑡	υ1(𝑡	NOUN
iajs-2776	49	26	)	)	PUNCT
iajs-2776	49	27	can	can	AUX
iajs-2776	49	28	be	be	AUX
iajs-2776	49	29	found	find	VERB
iajs-2776	49	30	by	by	ADP
iajs-2776	49	31	solving	solve	VERB
iajs-2776	49	32	equation	equation	NOUN
iajs-2776	49	33	(	(	PUNCT
iajs-2776	49	34	8)	8)	NUM
iajs-2776	49	35	:	:	PUNCT
iajs-2776	49	36	ℒ(υ1(𝑡))=δr(υ0(𝑡))+	ℒ(υ1(𝑡))=δr(υ0(𝑡))+	VERB
iajs-2776	49	37	2	2	NUM
iajs-2776	49	38	b	b	PROPN
iajs-2776	49	39	(	(	PUNCT
iajs-2776	49	40	∫	∫	PROPN
iajs-2776	49	41	ℵ(υ0(𝑡))dt	ℵ(υ0(𝑡))dt	PROPN
iajs-2776	49	42	)	)	PUNCT
iajs-2776	49	43	b	b	PROPN
iajs-2776	49	44	0	0	NUM
iajs-2776	49	45	r(υ0(𝑡))+k(t	r(υ0(𝑡))+k(t	NOUN
iajs-2776	49	46	)	)	PUNCT
iajs-2776	49	47	,	,	PUNCT
iajs-2776	49	48	υ1(0)=υ1(b)=υ1	υ1(0)=υ1(b)=υ1	VERB
iajs-2776	49	49	′′(0)=υ1	′′(0)=υ1	NOUN
iajs-2776	49	50	′′(b)=0	′′(b)=0	NOUN
iajs-2776	49	51	,	,	PUNCT
iajs-2776	49	52	]	]	PUNCT
iajs-2776	49	53	(	(	PUNCT
iajs-2776	49	54	7	7	X
iajs-2776	49	55	)	)	PUNCT
iajs-2776	49	56	likewise	likewise	ADV
iajs-2776	49	57	,	,	PUNCT
iajs-2776	49	58	more	more	ADJ
iajs-2776	49	59	solutions	solution	NOUN
iajs-2776	49	60	can	can	AUX
iajs-2776	49	61	be	be	AUX
iajs-2776	49	62	gained	gain	VERB
iajs-2776	49	63	for	for	ADP
iajs-2776	49	64	the	the	DET
iajs-2776	49	65	problems	problem	NOUN
iajs-2776	49	66	created	create	VERB
iajs-2776	49	67	by	by	ADP
iajs-2776	49	68	:	:	PUNCT
iajs-2776	49	69	ℒ(υ𝑛+1(𝑡))=δr(υ𝑛(𝑡))+	ℒ(υ𝑛+1(𝑡))=δr(υ𝑛(𝑡))+	NOUN
iajs-2776	49	70	2	2	PROPN
iajs-2776	49	71	b	b	PROPN
iajs-2776	49	72	(	(	PUNCT
iajs-2776	49	73	∫	∫	PROPN
iajs-2776	49	74	ℵ(υ𝑛(𝑡))dt	ℵ(υ𝑛(𝑡))dt	PROPN
iajs-2776	49	75	)	)	PUNCT
iajs-2776	49	76	b	b	NOUN
iajs-2776	49	77	0	0	PUNCT
iajs-2776	49	78	r(υ𝑛(𝑡))+k(t	r(υ𝑛(𝑡))+k(t	NOUN
iajs-2776	49	79	)	)	PUNCT
iajs-2776	49	80	,	,	PUNCT
iajs-2776	49	81	υ𝑛+1(0)=υ𝑛+1(b)=υ𝑛+1	υ𝑛+1(0)=υ𝑛+1(b)=υ𝑛+1	X
iajs-2776	49	82	′′(0)=υ𝑛+1	′′(0)=υ𝑛+1	NOUN
iajs-2776	49	83	′′(b)=0	′′(b)=0	NOUN
iajs-2776	49	84	,	,	PUNCT
iajs-2776	49	85	]	]	PUNCT
iajs-2776	49	86	(	(	PUNCT
iajs-2776	49	87	8)	8)	NUM
iajs-2776	49	88	2	2	NUM
iajs-2776	49	89	.	.	PUNCT
iajs-2776	49	90	solution	solution	NOUN
iajs-2776	49	91	of	of	ADP
iajs-2776	49	92	the	the	DET
iajs-2776	49	93	problem	problem	NOUN
iajs-2776	49	94	in	in	ADP
iajs-2776	49	95	this	this	DET
iajs-2776	49	96	section	section	NOUN
iajs-2776	49	97	,	,	PUNCT
iajs-2776	49	98	we	we	PRON
iajs-2776	49	99	will	will	AUX
iajs-2776	49	100	solve	solve	VERB
iajs-2776	49	101	two	two	NUM
iajs-2776	49	102	problems	problem	NOUN
iajs-2776	49	103	using	use	VERB
iajs-2776	49	104	the	the	DET
iajs-2776	49	105	method	method	NOUN
iajs-2776	49	106	defined	define	VERB
iajs-2776	49	107	above	above	ADP
iajs-2776	49	108	example	example	NOUN
iajs-2776	49	109	1	1	NUM
iajs-2776	49	110	.	.	X
iajs-2776	49	111	consider	consider	VERB
iajs-2776	49	112	the	the	DET
iajs-2776	49	113	4th	4th	ADJ
iajs-2776	49	114	-	-	PUNCT
iajs-2776	49	115	onide	onide	ADJ
iajs-2776	50	1	[	[	X
iajs-2776	50	2	6	6	NUM
iajs-2776	50	3	]	]	SYM
iajs-2776	50	4	𝜐(4)(𝑡	𝜐(4)(𝑡	NUM
iajs-2776	50	5	)	)	PUNCT
iajs-2776	50	6	−	−	NOUN
iajs-2776	50	7	𝜐′′(𝑡	𝜐′′(𝑡	NOUN
iajs-2776	50	8	)	)	PUNCT
iajs-2776	50	9	−	−	PROPN
iajs-2776	51	1	∫	∫	PROPN
iajs-2776	51	2	(	(	PUNCT
iajs-2776	51	3	𝜐′(𝑡	𝜐′(𝑡	NOUN
iajs-2776	51	4	)	)	PUNCT
iajs-2776	51	5	)	)	PUNCT
iajs-2776	51	6	21	21	NUM
iajs-2776	51	7	0	0	NUM
iajs-2776	51	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	51	9	𝜐′′(𝑡	𝜐′′(𝑡	ADJ
iajs-2776	51	10	)	)	PUNCT
iajs-2776	51	11	=	=	SYM
iajs-2776	51	12	1	1	NUM
iajs-2776	51	13	,	,	PUNCT
iajs-2776	51	14	0	0	NUM
iajs-2776	51	15	<	<	X
iajs-2776	51	16	𝑡	𝑡	X
iajs-2776	51	17	<	<	X
iajs-2776	51	18	1	1	NUM
iajs-2776	51	19	,	,	PUNCT
iajs-2776	51	20	𝜐(0	𝜐(0	NOUN
iajs-2776	51	21	)	)	PUNCT
iajs-2776	51	22	=	=	SYM
iajs-2776	52	1	𝜐(1	𝜐(1	ADJ
iajs-2776	52	2	)	)	PUNCT
iajs-2776	52	3	=	=	SYM
iajs-2776	52	4	𝜐′′(0	𝜐′′(0	PROPN
iajs-2776	52	5	)	)	PUNCT
iajs-2776	52	6	=	=	SYM
iajs-2776	52	7	𝜐′′(1	𝜐′′(1	ADJ
iajs-2776	52	8	)	)	PUNCT
iajs-2776	52	9	=	=	SYM
iajs-2776	53	1	0	0	NUM
iajs-2776	53	2	,	,	PUNCT
iajs-2776	53	3	(	(	PUNCT
iajs-2776	53	4	9	9	X
iajs-2776	53	5	)	)	PUNCT
iajs-2776	53	6	we	we	PRON
iajs-2776	53	7	start	start	VERB
iajs-2776	53	8	with	with	ADP
iajs-2776	53	9	the	the	DET
iajs-2776	53	10	assumption	assumption	NOUN
iajs-2776	53	11	that	that	SCONJ
iajs-2776	53	12	ℒ(𝜐(t	ℒ(𝜐(t	NOUN
iajs-2776	53	13	)	)	PUNCT
iajs-2776	53	14	)	)	PUNCT
iajs-2776	54	1	=	=	PUNCT
iajs-2776	54	2	𝜐(4)(𝑡	𝜐(4)(𝑡	X
iajs-2776	54	3	)	)	PUNCT
iajs-2776	54	4	,	,	PUNCT
iajs-2776	54	5	ℵ(𝜐	ℵ(𝜐	X
iajs-2776	54	6	)	)	PUNCT
iajs-2776	54	7	=	=	SYM
iajs-2776	54	8	−𝜐′′(𝑡	−𝜐′′(𝑡	NOUN
iajs-2776	54	9	)	)	PUNCT
iajs-2776	54	10	−	−	PROPN
iajs-2776	54	11	∫	∫	PROPN
iajs-2776	54	12	(	(	PUNCT
iajs-2776	54	13	𝜐′(𝑡	𝜐′(𝑡	NOUN
iajs-2776	54	14	)	)	PUNCT
iajs-2776	54	15	)	)	PUNCT
iajs-2776	54	16	21	21	NUM
iajs-2776	54	17	0	0	NUM
iajs-2776	54	18	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	54	19	𝜐′′(𝑡	𝜐′′(𝑡	NOUN
iajs-2776	54	20	)	)	PUNCT
iajs-2776	54	21	,	,	PUNCT
iajs-2776	54	22	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2776	54	23	)	)	PUNCT
iajs-2776	55	1	=	=	SYM
iajs-2776	55	2	−1	−1	NOUN
iajs-2776	55	3	(	(	PUNCT
iajs-2776	55	4	10	10	NUM
iajs-2776	55	5	)	)	PUNCT
iajs-2776	55	6	with	with	ADP
iajs-2776	55	7	𝑢(0	𝑢(0	PROPN
iajs-2776	55	8	)	)	PUNCT
iajs-2776	55	9	=	=	PUNCT
iajs-2776	55	10	𝑢(1	𝑢(1	NOUN
iajs-2776	55	11	)	)	PUNCT
iajs-2776	55	12	=	=	SYM
iajs-2776	55	13	𝑢′′(0	𝑢′′(0	NOUN
iajs-2776	55	14	)	)	PUNCT
iajs-2776	55	15	=	=	SYM
iajs-2776	55	16	𝑢′′(1	𝑢′′(1	PROPN
iajs-2776	55	17	)	)	PUNCT
iajs-2776	55	18	=	=	SYM
iajs-2776	55	19	0	0	NUM
iajs-2776	55	20	,	,	PUNCT
iajs-2776	55	21	(	(	PUNCT
iajs-2776	55	22	11	11	NUM
iajs-2776	55	23	)	)	PUNCT
iajs-2776	55	24	let	let	VERB
iajs-2776	55	25	us	we	PRON
iajs-2776	55	26	start	start	VERB
iajs-2776	55	27	with	with	ADP
iajs-2776	55	28	the	the	DET
iajs-2776	55	29	first	first	ADJ
iajs-2776	55	30	iteration	iteration	NOUN
iajs-2776	55	31	𝜐0	𝜐0	NOUN
iajs-2776	55	32	(	(	PUNCT
iajs-2776	55	33	4)(𝑡	4)(𝑡	NUM
iajs-2776	55	34	)	)	PUNCT
iajs-2776	56	1	=	=	SYM
iajs-2776	56	2	1	1	NUM
iajs-2776	56	3	,	,	PUNCT
iajs-2776	56	4	(	(	PUNCT
iajs-2776	56	5	12	12	NUM
iajs-2776	56	6	)	)	PUNCT
iajs-2776	56	7	with	with	ADP
iajs-2776	56	8	𝜐0(0	𝜐0(0	PROPN
iajs-2776	56	9	)	)	PUNCT
iajs-2776	56	10	=	=	SYM
iajs-2776	56	11	𝜐0(1	𝜐0(1	ADJ
iajs-2776	56	12	)	)	PUNCT
iajs-2776	56	13	=	=	SYM
iajs-2776	56	14	𝜐0	𝜐0	NOUN
iajs-2776	56	15	′′(0	′′(0	NOUN
iajs-2776	56	16	)	)	PUNCT
iajs-2776	56	17	=	=	NOUN
iajs-2776	56	18	𝜐0	𝜐0	NOUN
iajs-2776	56	19	′′(1	′′(1	PROPN
iajs-2776	56	20	)	)	PUNCT
iajs-2776	56	21	=	=	SYM
iajs-2776	56	22	0	0	NUM
iajs-2776	56	23	,	,	PUNCT
iajs-2776	56	24	(	(	PUNCT
iajs-2776	56	25	13	13	NUM
iajs-2776	56	26	)	)	PUNCT
iajs-2776	56	27	then	then	ADV
iajs-2776	56	28	,	,	PUNCT
iajs-2776	56	29	we	we	PRON
iajs-2776	56	30	get	get	VERB
iajs-2776	56	31	ihjpas	ihjpa	NOUN
iajs-2776	56	32	.	.	PUNCT
iajs-2776	57	1	53	53	NUM
iajs-2776	57	2	(	(	PUNCT
iajs-2776	57	3	3)2022	3)2022	NOUN
iajs-2776	57	4	209	209	NUM
iajs-2776	57	5	𝜐0(𝑡	𝜐0(𝑡	NUM
iajs-2776	57	6	)	)	PUNCT
iajs-2776	57	7	=	=	SYM
iajs-2776	58	1	0.04166(𝑡	0.04166(𝑡	NOUN
iajs-2776	58	2	−	−	NUM
iajs-2776	58	3	2𝑡3	2𝑡3	NUM
iajs-2776	58	4	+	+	NUM
iajs-2776	58	5	𝑡4	𝑡4	NOUN
iajs-2776	58	6	)	)	PUNCT
iajs-2776	58	7	,	,	PUNCT
iajs-2776	58	8	(	(	PUNCT
iajs-2776	58	9	14	14	NUM
iajs-2776	58	10	)	)	PUNCT
iajs-2776	58	11	the	the	DET
iajs-2776	58	12	second	second	ADJ
iajs-2776	58	13	repetition	repetition	NOUN
iajs-2776	58	14	can	can	AUX
iajs-2776	58	15	be	be	AUX
iajs-2776	58	16	performed	perform	VERB
iajs-2776	58	17	as	as	ADP
iajs-2776	58	18	𝜐1	𝜐1	NOUN
iajs-2776	58	19	(	(	PUNCT
iajs-2776	58	20	4)(𝑡	4)(𝑡	NUM
iajs-2776	58	21	)	)	PUNCT
iajs-2776	58	22	=	=	SYM
iajs-2776	58	23	1	1	NUM
iajs-2776	58	24	+	+	NUM
iajs-2776	58	25	𝜐0	𝜐0	NOUN
iajs-2776	58	26	′′(𝑡	′′(𝑡	NOUN
iajs-2776	58	27	)	)	PUNCT
iajs-2776	59	1	+	+	NUM
iajs-2776	59	2	∫	∫	PROPN
iajs-2776	59	3	(	(	PUNCT
iajs-2776	59	4	𝜐0	𝜐0	NOUN
iajs-2776	59	5	′(𝑡	′(𝑡	NOUN
iajs-2776	59	6	)	)	PUNCT
iajs-2776	59	7	)	)	PUNCT
iajs-2776	59	8	21	21	NUM
iajs-2776	59	9	0	0	NUM
iajs-2776	59	10	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	59	11	𝜐0	𝜐0	NOUN
iajs-2776	59	12	′′(𝑡	′′(𝑡	NOUN
iajs-2776	59	13	)	)	PUNCT
iajs-2776	59	14	,	,	PUNCT
iajs-2776	59	15	(	(	PUNCT
iajs-2776	59	16	15	15	NUM
iajs-2776	59	17	)	)	PUNCT
iajs-2776	59	18	with	with	ADP
iajs-2776	59	19	𝜐1(0	𝜐1(0	PROPN
iajs-2776	59	20	)	)	PUNCT
iajs-2776	59	21	=	=	SYM
iajs-2776	59	22	𝜐1(1	𝜐1(1	NOUN
iajs-2776	59	23	)	)	PUNCT
iajs-2776	59	24	=	=	SYM
iajs-2776	59	25	𝜐1	𝜐1	NOUN
iajs-2776	59	26	′′(0	′′(0	NOUN
iajs-2776	59	27	)	)	PUNCT
iajs-2776	59	28	=	=	SYM
iajs-2776	59	29	𝜐1	𝜐1	NOUN
iajs-2776	59	30	′′(1	′′(1	NOUN
iajs-2776	59	31	)	)	PUNCT
iajs-2776	59	32	=	=	SYM
iajs-2776	59	33	0	0	NUM
iajs-2776	59	34	,	,	PUNCT
iajs-2776	59	35	(	(	PUNCT
iajs-2776	59	36	16	16	NUM
iajs-2776	59	37	)	)	PUNCT
iajs-2776	59	38	thus	thus	ADV
iajs-2776	59	39	,	,	PUNCT
iajs-2776	59	40	we	we	PRON
iajs-2776	59	41	get	get	VERB
iajs-2776	59	42	𝜐1(𝑡	𝜐1(𝑡	PRON
iajs-2776	59	43	)	)	PUNCT
iajs-2776	59	44	=	=	PUNCT
iajs-2776	60	1	6.889329	6.889329	NUM
iajs-2776	60	2	×	×	NOUN
iajs-2776	60	3	10−8(544269𝑡	10−8(544269𝑡	NUM
iajs-2776	60	4	−	−	PROPN
iajs-2776	60	5	1108715𝑡3	1108715𝑡3	PROPN
iajs-2776	60	6	+	+	CCONJ
iajs-2776	60	7	604800𝑡4	604800𝑡4	NUM
iajs-2776	60	8	−	−	NUM
iajs-2776	60	9	60531𝑡5	60531𝑡5	NUM
iajs-2776	60	10	+	+	NUM
iajs-2776	60	11	20177𝑡6	20177𝑡6	NOUN
iajs-2776	60	12	)	)	PUNCT
iajs-2776	60	13	(	(	PUNCT
iajs-2776	60	14	17	17	NUM
iajs-2776	60	15	)	)	PUNCT
iajs-2776	60	16	in	in	ADP
iajs-2776	60	17	the	the	DET
iajs-2776	60	18	third	third	ADJ
iajs-2776	60	19	repetition	repetition	NOUN
iajs-2776	60	20	,	,	PUNCT
iajs-2776	60	21	the	the	DET
iajs-2776	60	22	following	follow	VERB
iajs-2776	60	23	equation	equation	NOUN
iajs-2776	60	24	must	must	AUX
iajs-2776	60	25	be	be	AUX
iajs-2776	60	26	solved	solve	VERB
iajs-2776	60	27	:	:	PUNCT
iajs-2776	60	28	𝜐2	𝜐2	NOUN
iajs-2776	60	29	(	(	PUNCT
iajs-2776	60	30	4)(𝑡	4)(𝑡	NUM
iajs-2776	60	31	)	)	PUNCT
iajs-2776	60	32	=	=	SYM
iajs-2776	61	1	1	1	NUM
iajs-2776	61	2	+	+	NUM
iajs-2776	61	3	𝜐1	𝜐1	NOUN
iajs-2776	61	4	′′(𝑡	′′(𝑡	PROPN
iajs-2776	61	5	)	)	PUNCT
iajs-2776	62	1	+	+	NUM
iajs-2776	62	2	∫	∫	PROPN
iajs-2776	62	3	(	(	PUNCT
iajs-2776	62	4	𝜐1	𝜐1	NOUN
iajs-2776	62	5	′(𝑡	′(𝑡	NOUN
iajs-2776	62	6	)	)	PUNCT
iajs-2776	62	7	)	)	PUNCT
iajs-2776	62	8	21	21	NUM
iajs-2776	62	9	0	0	NUM
iajs-2776	62	10	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	62	11	𝜐1	𝜐1	NOUN
iajs-2776	62	12	′′(𝑡	′′(𝑡	PROPN
iajs-2776	62	13	)	)	PUNCT
iajs-2776	62	14	,	,	PUNCT
iajs-2776	62	15	(	(	PUNCT
iajs-2776	62	16	18	18	NUM
iajs-2776	62	17	)	)	PUNCT
iajs-2776	62	18	then	then	ADV
iajs-2776	62	19	,	,	PUNCT
iajs-2776	62	20	we	we	PRON
iajs-2776	62	21	get	get	VERB
iajs-2776	62	22	𝜐2(𝑡	𝜐2(𝑡	NOUN
iajs-2776	62	23	)	)	PUNCT
iajs-2776	62	24	=	=	PUNCT
iajs-2776	63	1	3.7916	3.7916	NUM
iajs-2776	63	2	×	×	NOUN
iajs-2776	63	3	10−26(1.00009	10−26(1.00009	NUM
iajs-2776	63	4	×	×	NOUN
iajs-2776	63	5	1024𝑡	1024𝑡	NUM
iajs-2776	63	6	−	−	PROPN
iajs-2776	63	7	2.032907	2.032907	NUM
iajs-2776	63	8	×	×	NOUN
iajs-2776	63	9	1024𝑡3	1024𝑡3	NOUN
iajs-2776	64	1	+	+	CCONJ
iajs-2776	64	2	1.0989	1.0989	NUM
iajs-2776	64	3	×	×	NOUN
iajs-2776	64	4	1024𝑡4	1024𝑡4	NUM
iajs-2776	64	5	−	−	PROPN
iajs-2776	64	6	1.00795	1.00795	NUM
iajs-2776	64	7	×	×	NOUN
iajs-2776	64	8	1023𝑡5	1023𝑡5	NUM
iajs-2776	64	9	+	+	CCONJ
iajs-2776	64	10	3.6655	3.6655	NUM
iajs-2776	64	11	×	×	NOUN
iajs-2776	64	12	1022𝑡6	1022𝑡6	NUM
iajs-2776	64	13	−	−	PROPN
iajs-2776	64	14	2.6204	2.6204	NUM
iajs-2776	64	15	×	×	NOUN
iajs-2776	64	16	1021𝑡7	1021𝑡7	NUM
iajs-2776	64	17	+	+	CCONJ
iajs-2776	64	18	6.5511	6.5511	NUM
iajs-2776	64	19	×	×	NOUN
iajs-2776	64	20	1020𝑡8	1020𝑡8	NUM
iajs-2776	64	21	)	)	PUNCT
iajs-2776	64	22	(	(	PUNCT
iajs-2776	64	23	19	19	NUM
iajs-2776	64	24	)	)	PUNCT
iajs-2776	64	25	we	we	PRON
iajs-2776	64	26	showed	show	VERB
iajs-2776	64	27	the	the	DET
iajs-2776	64	28	first	first	ADJ
iajs-2776	64	29	three	three	NUM
iajs-2776	64	30	solutions	solution	NOUN
iajs-2776	64	31	but	but	CCONJ
iajs-2776	64	32	we	we	PRON
iajs-2776	64	33	did	do	AUX
iajs-2776	64	34	not	not	PART
iajs-2776	64	35	show	show	VERB
iajs-2776	64	36	the	the	DET
iajs-2776	64	37	later	late	ADJ
iajs-2776	64	38	ones	one	NOUN
iajs-2776	64	39	because	because	SCONJ
iajs-2776	64	40	they	they	PRON
iajs-2776	64	41	get	get	VERB
iajs-2776	64	42	longer	long	ADV
iajs-2776	64	43	.	.	PUNCT
iajs-2776	65	1	by	by	ADP
iajs-2776	65	2	applying	apply	VERB
iajs-2776	65	3	the	the	DET
iajs-2776	65	4	(	(	PUNCT
iajs-2776	65	5	rk4	rk4	NOUN
iajs-2776	65	6	m	m	NOUN
iajs-2776	65	7	)	)	PUNCT
iajs-2776	65	8	using	use	VERB
iajs-2776	65	9	mathematica	mathematica	PROPN
iajs-2776	65	10	®	®	PROPN
iajs-2776	65	11	as	as	ADP
iajs-2776	65	12	a	a	DET
iajs-2776	65	13	standard	standard	NOUN
iajs-2776	65	14	for	for	ADP
iajs-2776	65	15	evaluating	evaluate	VERB
iajs-2776	65	16	ta	ta	ADP
iajs-2776	65	17	method	method	NOUN
iajs-2776	65	18	performance	performance	NOUN
iajs-2776	65	19	.	.	PUNCT
iajs-2776	66	1	in	in	ADP
iajs-2776	66	2	figure	figure	NOUN
iajs-2776	66	3	1	1	NUM
iajs-2776	66	4	,	,	PUNCT
iajs-2776	66	5	good	good	ADJ
iajs-2776	66	6	agreement	agreement	NOUN
iajs-2776	66	7	was	be	AUX
iajs-2776	66	8	observed	observe	VERB
iajs-2776	66	9	between	between	ADP
iajs-2776	66	10	rk4	rk4	NOUN
iajs-2776	66	11	m	m	NOUN
iajs-2776	66	12	and	and	CCONJ
iajs-2776	66	13	ta	ta	PART
iajs-2776	66	14	method	method	PROPN
iajs-2776	66	15	.	.	PUNCT
iajs-2776	67	1	figure	figure	NOUN
iajs-2776	67	2	1	1	NUM
iajs-2776	67	3	.	.	PUNCT
iajs-2776	68	1	the	the	DET
iajs-2776	68	2	ta	ta	PROPN
iajs-2776	68	3	method	method	NOUN
iajs-2776	68	4	and	and	CCONJ
iajs-2776	68	5	rk4	rk4	NOUN
iajs-2776	68	6	m	m	NOUN
iajs-2776	68	7	solutions	solution	NOUN
iajs-2776	68	8	for	for	ADP
iajs-2776	68	9	the	the	DET
iajs-2776	68	10	problem	problem	NOUN
iajs-2776	68	11	the	the	DET
iajs-2776	68	12	logarithmic	logarithmic	ADJ
iajs-2776	68	13	plots	plot	NOUN
iajs-2776	68	14	for	for	ADP
iajs-2776	68	15	mer	mer	NOUN
iajs-2776	68	16	will	will	AUX
iajs-2776	68	17	be	be	AUX
iajs-2776	68	18	presented	present	VERB
iajs-2776	68	19	in	in	ADP
iajs-2776	68	20	figure	figure	NOUN
iajs-2776	68	21	2	2	NUM
iajs-2776	68	22	for	for	ADP
iajs-2776	68	23	the	the	DET
iajs-2776	68	24	approximate	approximate	ADJ
iajs-2776	68	25	solution	solution	NOUN
iajs-2776	68	26	obtained	obtain	VERB
iajs-2776	68	27	by	by	ADP
iajs-2776	68	28	ta	ta	PROPN
iajs-2776	68	29	method	method	NOUN
iajs-2776	68	30	for	for	ADP
iajs-2776	68	31	solving	solve	VERB
iajs-2776	68	32	4th	4th	ADJ
iajs-2776	68	33	-	-	PUNCT
iajs-2776	68	34	onide	onide	ADJ
iajs-2776	68	35	for	for	ADP
iajs-2776	68	36	different	different	ADJ
iajs-2776	68	37	values	value	NOUN
iajs-2776	68	38	of	of	ADP
iajs-2776	68	39	n=1	n=1	PROPN
iajs-2776	68	40	to	to	ADP
iajs-2776	68	41	5	5	NUM
iajs-2776	68	42	.	.	PUNCT
iajs-2776	69	1	figure	figure	NOUN
iajs-2776	69	2	2	2	NUM
iajs-2776	69	3	.	.	PUNCT
iajs-2776	69	4	maximum	maximum	ADJ
iajs-2776	69	5	error	error	NOUN
iajs-2776	69	6	reminder	reminder	NOUN
iajs-2776	69	7	for	for	ADP
iajs-2776	69	8	solution	solution	NOUN
iajs-2776	69	9	by	by	ADP
iajs-2776	69	10	ta	ta	PROPN
iajs-2776	69	11	method	method	PROPN
iajs-2776	69	12	ihjpas	ihjpas	PROPN
iajs-2776	69	13	.	.	PUNCT
iajs-2776	70	1	53	53	NUM
iajs-2776	70	2	(	(	PUNCT
iajs-2776	70	3	3)2022	3)2022	NOUN
iajs-2776	70	4	210	210	NUM
iajs-2776	70	5	example	example	NOUN
iajs-2776	70	6	2	2	NUM
iajs-2776	70	7	:	:	PUNCT
iajs-2776	70	8	consider	consider	VERB
iajs-2776	70	9	the	the	DET
iajs-2776	70	10	4th	4th	ADJ
iajs-2776	70	11	-	-	PUNCT
iajs-2776	70	12	onide	onide	ADJ
iajs-2776	71	1	[	[	X
iajs-2776	71	2	6	6	NUM
iajs-2776	71	3	]	]	SYM
iajs-2776	71	4	𝜐(4)(𝑡	𝜐(4)(𝑡	NUM
iajs-2776	71	5	)	)	PUNCT
iajs-2776	71	6	−	−	NOUN
iajs-2776	71	7	𝜐′′(𝑡	𝜐′′(𝑡	NOUN
iajs-2776	71	8	)	)	PUNCT
iajs-2776	71	9	−	−	PROPN
iajs-2776	71	10	2	2	NUM
iajs-2776	71	11	∫	∫	NOUN
iajs-2776	71	12	(	(	PUNCT
iajs-2776	71	13	𝜐′(𝑡	𝜐′(𝑡	NOUN
iajs-2776	71	14	)	)	PUNCT
iajs-2776	71	15	)	)	PUNCT
iajs-2776	71	16	21	21	NUM
iajs-2776	71	17	0	0	NUM
iajs-2776	71	18	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	71	19	𝜐′′(𝑡	𝜐′′(𝑡	ADJ
iajs-2776	71	20	)	)	PUNCT
iajs-2776	71	21	=	=	SYM
iajs-2776	72	1	−𝑡	−𝑡	NOUN
iajs-2776	72	2	,	,	PUNCT
iajs-2776	72	3	0	0	PUNCT
iajs-2776	72	4	<	<	X
iajs-2776	72	5	𝑡	𝑡	X
iajs-2776	72	6	<	<	X
iajs-2776	72	7	1	1	NUM
iajs-2776	72	8	,	,	PUNCT
iajs-2776	72	9	(	(	PUNCT
iajs-2776	72	10	20	20	NUM
iajs-2776	72	11	)	)	PUNCT
iajs-2776	72	12	𝜐(0	𝜐(0	NOUN
iajs-2776	72	13	)	)	PUNCT
iajs-2776	72	14	=	=	SYM
iajs-2776	73	1	𝜐(1	𝜐(1	PROPN
iajs-2776	73	2	)	)	PUNCT
iajs-2776	73	3	=	=	SYM
iajs-2776	73	4	𝑣′′(0	𝑣′′(0	NOUN
iajs-2776	73	5	)	)	PUNCT
iajs-2776	73	6	=	=	SYM
iajs-2776	73	7	𝜐′′(1	𝜐′′(1	ADJ
iajs-2776	73	8	)	)	PUNCT
iajs-2776	73	9	=	=	SYM
iajs-2776	74	1	0	0	NUM
iajs-2776	74	2	,	,	PUNCT
iajs-2776	74	3	(	(	PUNCT
iajs-2776	74	4	21	21	NUM
iajs-2776	74	5	)	)	PUNCT
iajs-2776	74	6	we	we	PRON
iajs-2776	74	7	start	start	VERB
iajs-2776	74	8	with	with	ADP
iajs-2776	74	9	the	the	DET
iajs-2776	74	10	assumption	assumption	NOUN
iajs-2776	74	11	that	that	SCONJ
iajs-2776	74	12	ℒ(υ(t	ℒ(υ(t	NOUN
iajs-2776	74	13	)	)	PUNCT
iajs-2776	74	14	)	)	PUNCT
iajs-2776	75	1	=	=	PUNCT
iajs-2776	75	2	𝜐(4)(𝑡	𝜐(4)(𝑡	X
iajs-2776	75	3	)	)	PUNCT
iajs-2776	75	4	,	,	PUNCT
iajs-2776	75	5	ℵ(𝜐	ℵ(𝜐	X
iajs-2776	75	6	)	)	PUNCT
iajs-2776	75	7	=	=	SYM
iajs-2776	75	8	−𝜐′′(𝑡	−𝜐′′(𝑡	X
iajs-2776	75	9	)	)	PUNCT
iajs-2776	75	10	−	−	PROPN
iajs-2776	75	11	2	2	NUM
iajs-2776	75	12	∫	∫	NOUN
iajs-2776	75	13	(	(	PUNCT
iajs-2776	75	14	𝜐′(𝑡	𝜐′(𝑡	NOUN
iajs-2776	75	15	)	)	PUNCT
iajs-2776	75	16	)	)	PUNCT
iajs-2776	75	17	21	21	NUM
iajs-2776	75	18	0	0	NUM
iajs-2776	75	19	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	75	20	𝜐′′(𝑡	𝜐′′(𝑡	NOUN
iajs-2776	75	21	)	)	PUNCT
iajs-2776	75	22	,	,	PUNCT
iajs-2776	75	23	𝑔(𝑡	𝑔(𝑡	PROPN
iajs-2776	75	24	)	)	PUNCT
iajs-2776	75	25	=	=	SYM
iajs-2776	75	26	𝑡	𝑡	PROPN
iajs-2776	75	27	(	(	PUNCT
iajs-2776	75	28	22	22	NUM
iajs-2776	75	29	)	)	PUNCT
iajs-2776	75	30	with	with	ADP
iajs-2776	75	31	𝜐(0	𝜐(0	NOUN
iajs-2776	75	32	)	)	PUNCT
iajs-2776	75	33	=	=	SYM
iajs-2776	76	1	𝜐(1	𝜐(1	ADJ
iajs-2776	76	2	)	)	PUNCT
iajs-2776	76	3	=	=	SYM
iajs-2776	76	4	𝜐′′(0	𝜐′′(0	PROPN
iajs-2776	76	5	)	)	PUNCT
iajs-2776	76	6	=	=	SYM
iajs-2776	76	7	𝜐′′(1	𝜐′′(1	ADJ
iajs-2776	76	8	)	)	PUNCT
iajs-2776	76	9	=	=	SYM
iajs-2776	77	1	0	0	NUM
iajs-2776	77	2	,	,	PUNCT
iajs-2776	77	3	(	(	PUNCT
iajs-2776	77	4	23	23	NUM
iajs-2776	77	5	)	)	PUNCT
iajs-2776	77	6	let	let	VERB
iajs-2776	77	7	us	we	PRON
iajs-2776	77	8	start	start	VERB
iajs-2776	77	9	with	with	ADP
iajs-2776	77	10	the	the	DET
iajs-2776	77	11	first	first	ADJ
iajs-2776	77	12	iteration	iteration	NOUN
iajs-2776	77	13	𝜐0	𝜐0	NOUN
iajs-2776	77	14	(	(	PUNCT
iajs-2776	77	15	4)(𝑡	4)(𝑡	NUM
iajs-2776	77	16	)	)	PUNCT
iajs-2776	78	1	=	=	SYM
iajs-2776	79	1	−𝑡	−𝑡	NOUN
iajs-2776	79	2	,	,	PUNCT
iajs-2776	79	3	(	(	PUNCT
iajs-2776	79	4	24	24	NUM
iajs-2776	79	5	)	)	PUNCT
iajs-2776	79	6	with	with	ADP
iajs-2776	79	7	𝜐0(0	𝜐0(0	PROPN
iajs-2776	79	8	)	)	PUNCT
iajs-2776	79	9	=	=	SYM
iajs-2776	79	10	𝜐0(1	𝜐0(1	ADJ
iajs-2776	79	11	)	)	PUNCT
iajs-2776	79	12	=	=	SYM
iajs-2776	79	13	𝜐0	𝜐0	NOUN
iajs-2776	79	14	′′(0	′′(0	NOUN
iajs-2776	79	15	)	)	PUNCT
iajs-2776	79	16	=	=	NOUN
iajs-2776	79	17	𝜐0	𝜐0	NOUN
iajs-2776	79	18	′′(1	′′(1	PROPN
iajs-2776	79	19	)	)	PUNCT
iajs-2776	79	20	=	=	SYM
iajs-2776	79	21	0	0	NUM
iajs-2776	79	22	,	,	PUNCT
iajs-2776	79	23	(	(	PUNCT
iajs-2776	79	24	25	25	NUM
iajs-2776	79	25	)	)	PUNCT
iajs-2776	79	26	then	then	ADV
iajs-2776	79	27	,	,	PUNCT
iajs-2776	79	28	we	we	PRON
iajs-2776	79	29	get	get	VERB
iajs-2776	79	30	𝜐0(𝑡	𝜐0(𝑡	PRON
iajs-2776	79	31	)	)	PUNCT
iajs-2776	79	32	=	=	PUNCT
iajs-2776	79	33	0.0027(−7𝑡	0.0027(−7𝑡	NUM
iajs-2776	80	1	+	+	CCONJ
iajs-2776	80	2	10𝑡3	10𝑡3	NUM
iajs-2776	80	3	−	−	NOUN
iajs-2776	80	4	3𝑡5	3𝑡5	NUM
iajs-2776	80	5	)	)	PUNCT
iajs-2776	80	6	(	(	PUNCT
iajs-2776	80	7	26	26	NUM
iajs-2776	80	8	)	)	PUNCT
iajs-2776	80	9	the	the	DET
iajs-2776	80	10	second	second	ADJ
iajs-2776	80	11	repetition	repetition	NOUN
iajs-2776	80	12	can	can	AUX
iajs-2776	80	13	be	be	AUX
iajs-2776	80	14	performed	perform	VERB
iajs-2776	80	15	as	as	ADP
iajs-2776	80	16	𝜐1	𝜐1	NOUN
iajs-2776	80	17	(	(	PUNCT
iajs-2776	80	18	4)(𝑡	4)(𝑡	NUM
iajs-2776	80	19	)	)	PUNCT
iajs-2776	80	20	=	=	SYM
iajs-2776	81	1	−𝑡	−𝑡	NOUN
iajs-2776	82	1	+	+	CCONJ
iajs-2776	82	2	𝑣0	𝑣0	PROPN
iajs-2776	82	3	′′(𝑡	′′(𝑡	PROPN
iajs-2776	82	4	)	)	PUNCT
iajs-2776	83	1	+	+	CCONJ
iajs-2776	83	2	2	2	NUM
iajs-2776	83	3	∫	∫	NOUN
iajs-2776	83	4	(	(	PUNCT
iajs-2776	83	5	𝜐0	𝜐0	NOUN
iajs-2776	83	6	′(𝑡	′(𝑡	NOUN
iajs-2776	83	7	)	)	PUNCT
iajs-2776	83	8	)	)	PUNCT
iajs-2776	83	9	21	21	NUM
iajs-2776	83	10	0	0	NUM
iajs-2776	83	11	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	83	12	𝜐0	𝜐0	NOUN
iajs-2776	83	13	′′(𝑡	′′(𝑡	NOUN
iajs-2776	83	14	)	)	PUNCT
iajs-2776	83	15	,	,	PUNCT
iajs-2776	83	16	(	(	PUNCT
iajs-2776	83	17	27	27	NUM
iajs-2776	83	18	)	)	PUNCT
iajs-2776	83	19	with	with	ADP
iajs-2776	83	20	𝜐1(0	𝜐1(0	PROPN
iajs-2776	83	21	)	)	PUNCT
iajs-2776	83	22	=	=	SYM
iajs-2776	83	23	𝜐1(1	𝜐1(1	NOUN
iajs-2776	83	24	)	)	PUNCT
iajs-2776	83	25	=	=	SYM
iajs-2776	83	26	𝜐1	𝜐1	NOUN
iajs-2776	83	27	′′(0	′′(0	NOUN
iajs-2776	83	28	)	)	PUNCT
iajs-2776	83	29	=	=	SYM
iajs-2776	83	30	𝜐1	𝜐1	NOUN
iajs-2776	83	31	′′(1	′′(1	NOUN
iajs-2776	83	32	)	)	PUNCT
iajs-2776	83	33	=	=	SYM
iajs-2776	83	34	0	0	NUM
iajs-2776	83	35	,	,	PUNCT
iajs-2776	83	36	(	(	PUNCT
iajs-2776	83	37	28	28	NUM
iajs-2776	83	38	)	)	PUNCT
iajs-2776	83	39	thus	thus	ADV
iajs-2776	83	40	,	,	PUNCT
iajs-2776	83	41	we	we	PRON
iajs-2776	83	42	get	get	VERB
iajs-2776	83	43	𝜐1(𝑡	𝜐1(𝑡	PRON
iajs-2776	83	44	)	)	PUNCT
iajs-2776	83	45	=	=	PUNCT
iajs-2776	84	1	1.3997	1.3997	NUM
iajs-2776	84	2	×	×	NOUN
iajs-2776	84	3	10−8(−1242613𝑡	10−8(−1242613𝑡	NUM
iajs-2776	84	4	+	+	CCONJ
iajs-2776	84	5	1752877𝑡3	1752877𝑡3	NUM
iajs-2776	84	6	−	−	PROPN
iajs-2776	84	7	496083𝑡5	496083𝑡5	PROPN
iajs-2776	84	8	−	−	PROPN
iajs-2776	84	9	14181𝑡7	14181𝑡7	NUM
iajs-2776	84	10	)	)	PUNCT
iajs-2776	84	11	(	(	PUNCT
iajs-2776	84	12	29	29	NUM
iajs-2776	84	13	)	)	PUNCT
iajs-2776	84	14	in	in	ADP
iajs-2776	84	15	the	the	DET
iajs-2776	84	16	third	third	ADJ
iajs-2776	84	17	repetition	repetition	NOUN
iajs-2776	84	18	,	,	PUNCT
iajs-2776	84	19	the	the	DET
iajs-2776	84	20	following	follow	VERB
iajs-2776	84	21	equation	equation	NOUN
iajs-2776	84	22	must	must	AUX
iajs-2776	84	23	be	be	AUX
iajs-2776	84	24	solved	solve	VERB
iajs-2776	84	25	:	:	PUNCT
iajs-2776	84	26	𝜐2	𝜐2	NOUN
iajs-2776	84	27	(	(	PUNCT
iajs-2776	84	28	4)(𝑡	4)(𝑡	NUM
iajs-2776	84	29	)	)	PUNCT
iajs-2776	85	1	=	=	SYM
iajs-2776	85	2	−𝑡	−𝑡	NOUN
iajs-2776	85	3	+	+	CCONJ
iajs-2776	85	4	𝜐1	𝜐1	NOUN
iajs-2776	85	5	′′(𝑡	′′(𝑡	PROPN
iajs-2776	85	6	)	)	PUNCT
iajs-2776	86	1	+	+	CCONJ
iajs-2776	86	2	2	2	NUM
iajs-2776	86	3	∫	∫	NOUN
iajs-2776	86	4	(	(	PUNCT
iajs-2776	86	5	𝜐1	𝜐1	NOUN
iajs-2776	86	6	′(𝑡	′(𝑡	NOUN
iajs-2776	86	7	)	)	PUNCT
iajs-2776	86	8	)	)	PUNCT
iajs-2776	86	9	21	21	NUM
iajs-2776	86	10	0	0	NUM
iajs-2776	86	11	𝑑𝑡	𝑑𝑡	ADP
iajs-2776	86	12	𝜐1	𝜐1	NOUN
iajs-2776	86	13	′′(𝑡	′′(𝑡	PROPN
iajs-2776	86	14	)	)	PUNCT
iajs-2776	86	15	,	,	PUNCT
iajs-2776	86	16	(	(	PUNCT
iajs-2776	86	17	30	30	NUM
iajs-2776	86	18	)	)	PUNCT
iajs-2776	86	19	then	then	ADV
iajs-2776	86	20	,	,	PUNCT
iajs-2776	86	21	we	we	PRON
iajs-2776	86	22	get	get	VERB
iajs-2776	86	23	𝜐2(𝑡	𝜐2(𝑡	NOUN
iajs-2776	86	24	)	)	PUNCT
iajs-2776	86	25	=	=	SYM
iajs-2776	87	1	8.1826	8.1826	NUM
iajs-2776	87	2	×	×	NOUN
iajs-2776	87	3	10−27(−2.1513	10−27(−2.1513	NUM
iajs-2776	87	4	×	×	NOUN
iajs-2776	87	5	1024𝑡	1024𝑡	NUM
iajs-2776	87	6	+	+	CCONJ
iajs-2776	87	7	3.0403	3.0403	NUM
iajs-2776	87	8	×	×	NOUN
iajs-2776	87	9	1024𝑡3	1024𝑡3	NUM
iajs-2776	87	10	−	−	PROPN
iajs-2776	87	11	8.6844	8.6844	NUM
iajs-2776	87	12	×	×	NOUN
iajs-2776	87	13	1023𝑡5	1023𝑡5	NUM
iajs-2776	87	14	−	−	PROPN
iajs-2776	87	15	2.0212	2.0212	NUM
iajs-2776	87	16	×	×	NOUN
iajs-2776	87	17	1022𝑡7	1022𝑡7	NUM
iajs-2776	87	18	−	−	PROPN
iajs-2776	87	19	3.3703	3.3703	NUM
iajs-2776	87	20	×	×	NOUN
iajs-2776	87	21	1020𝑡9	1020𝑡9	NUM
iajs-2776	87	22	)	)	PUNCT
iajs-2776	87	23	)	)	PUNCT
iajs-2776	87	24	(	(	PUNCT
iajs-2776	87	25	31	31	NUM
iajs-2776	87	26	)	)	PUNCT
iajs-2776	87	27	we	we	PRON
iajs-2776	87	28	showed	show	VERB
iajs-2776	87	29	the	the	DET
iajs-2776	87	30	first	first	ADJ
iajs-2776	87	31	three	three	NUM
iajs-2776	87	32	solutions	solution	NOUN
iajs-2776	87	33	but	but	CCONJ
iajs-2776	87	34	we	we	PRON
iajs-2776	87	35	did	do	AUX
iajs-2776	87	36	not	not	PART
iajs-2776	87	37	show	show	VERB
iajs-2776	87	38	the	the	DET
iajs-2776	87	39	later	late	ADJ
iajs-2776	87	40	ones	one	NOUN
iajs-2776	87	41	because	because	SCONJ
iajs-2776	87	42	they	they	PRON
iajs-2776	87	43	get	get	VERB
iajs-2776	87	44	longer	long	ADV
iajs-2776	87	45	.	.	PUNCT
iajs-2776	88	1	by	by	ADP
iajs-2776	88	2	applying	apply	VERB
iajs-2776	88	3	the	the	DET
iajs-2776	88	4	(	(	PUNCT
iajs-2776	88	5	rk4	rk4	NOUN
iajs-2776	88	6	m	m	NOUN
iajs-2776	88	7	)	)	PUNCT
iajs-2776	88	8	using	use	VERB
iajs-2776	88	9	mathematica	mathematica	PROPN
iajs-2776	88	10	as	as	ADP
iajs-2776	88	11	a	a	DET
iajs-2776	88	12	standard	standard	NOUN
iajs-2776	88	13	for	for	ADP
iajs-2776	88	14	evaluating	evaluate	VERB
iajs-2776	88	15	ta	ta	ADP
iajs-2776	88	16	method	method	NOUN
iajs-2776	88	17	performance	performance	NOUN
iajs-2776	88	18	.	.	PUNCT
iajs-2776	89	1	in	in	ADP
iajs-2776	89	2	figure	figure	NOUN
iajs-2776	89	3	3	3	NUM
iajs-2776	89	4	,	,	PUNCT
iajs-2776	89	5	good	good	ADJ
iajs-2776	89	6	agreement	agreement	NOUN
iajs-2776	89	7	was	be	AUX
iajs-2776	89	8	observed	observe	VERB
iajs-2776	89	9	between	between	ADP
iajs-2776	89	10	rk4	rk4	NOUN
iajs-2776	89	11	m	m	NOUN
iajs-2776	89	12	and	and	CCONJ
iajs-2776	89	13	ta	ta	AUX
iajs-2776	89	14	method	method	PROPN
iajs-2776	89	15	.	.	PUNCT
iajs-2776	90	1	ihjpas	ihjpas	PROPN
iajs-2776	90	2	.	.	PUNCT
iajs-2776	91	1	53	53	NUM
iajs-2776	91	2	(	(	PUNCT
iajs-2776	91	3	3)2022	3)2022	NOUN
iajs-2776	91	4	211	211	NUM
iajs-2776	91	5	figure	figure	NOUN
iajs-2776	91	6	3	3	NUM
iajs-2776	91	7	.	.	PUNCT
iajs-2776	92	1	the	the	DET
iajs-2776	92	2	ta	ta	PROPN
iajs-2776	92	3	method	method	NOUN
iajs-2776	92	4	and	and	CCONJ
iajs-2776	92	5	rk4	rk4	NOUN
iajs-2776	92	6	m	m	NOUN
iajs-2776	92	7	solutions	solution	NOUN
iajs-2776	92	8	for	for	ADP
iajs-2776	92	9	the	the	DET
iajs-2776	92	10	problem	problem	NOUN
iajs-2776	92	11	the	the	DET
iajs-2776	92	12	logarithmic	logarithmic	ADJ
iajs-2776	92	13	plots	plot	NOUN
iajs-2776	92	14	for	for	ADP
iajs-2776	92	15	mer	mer	NOUN
iajs-2776	92	16	will	will	AUX
iajs-2776	92	17	be	be	AUX
iajs-2776	92	18	presented	present	VERB
iajs-2776	92	19	in	in	ADP
iajs-2776	92	20	figure	figure	NOUN
iajs-2776	92	21	2	2	NUM
iajs-2776	92	22	for	for	ADP
iajs-2776	92	23	the	the	DET
iajs-2776	92	24	approximate	approximate	ADJ
iajs-2776	92	25	solution	solution	NOUN
iajs-2776	92	26	obtained	obtain	VERB
iajs-2776	92	27	by	by	ADP
iajs-2776	92	28	ta	ta	PROPN
iajs-2776	92	29	method	method	NOUN
iajs-2776	92	30	for	for	ADP
iajs-2776	92	31	solving	solve	VERB
iajs-2776	92	32	4th	4th	ADJ
iajs-2776	92	33	-	-	PUNCT
iajs-2776	92	34	onide	onide	ADJ
iajs-2776	92	35	for	for	ADP
iajs-2776	92	36	different	different	ADJ
iajs-2776	92	37	values	value	NOUN
iajs-2776	92	38	of	of	ADP
iajs-2776	92	39	n=1	n=1	PROPN
iajs-2776	92	40	to	to	ADP
iajs-2776	92	41	5	5	NUM
iajs-2776	92	42	.	.	PUNCT
iajs-2776	92	43	figure	figure	VERB
iajs-2776	92	44	4	4	NUM
iajs-2776	92	45	.	.	PUNCT
iajs-2776	92	46	maximum	maximum	ADJ
iajs-2776	92	47	error	error	NOUN
iajs-2776	92	48	reminder	reminder	NOUN
iajs-2776	92	49	for	for	ADP
iajs-2776	92	50	solution	solution	NOUN
iajs-2776	92	51	by	by	ADP
iajs-2776	92	52	ta	ta	AUX
iajs-2776	92	53	method	method	VERB
iajs-2776	92	54	the	the	DET
iajs-2776	92	55	absolute	absolute	ADJ
iajs-2776	92	56	error	error	NOUN
iajs-2776	92	57	was	be	AUX
iajs-2776	92	58	calculated	calculate	VERB
iajs-2776	92	59	by	by	ADP
iajs-2776	92	60	rk4	rk4	NOUN
iajs-2776	92	61	m	m	NOUN
iajs-2776	92	62	and	and	CCONJ
iajs-2776	92	63	ta	ta	PROPN
iajs-2776	92	64	method	method	NOUN
iajs-2776	92	65	,	,	PUNCT
iajs-2776	92	66	we	we	PRON
iajs-2776	92	67	note	note	VERB
iajs-2776	92	68	a	a	DET
iajs-2776	92	69	good	good	ADJ
iajs-2776	92	70	approximation	approximation	NOUN
iajs-2776	92	71	as	as	SCONJ
iajs-2776	92	72	shown	show	VERB
iajs-2776	92	73	in	in	ADP
iajs-2776	92	74	table	table	NOUN
iajs-2776	92	75	1	1	NUM
iajs-2776	92	76	for	for	ADP
iajs-2776	92	77	both	both	DET
iajs-2776	92	78	examples	example	NOUN
iajs-2776	92	79	.	.	PUNCT
iajs-2776	93	1	table	table	NOUN
iajs-2776	93	2	1	1	NUM
iajs-2776	93	3	.	.	PUNCT
iajs-2776	94	1	the	the	DET
iajs-2776	94	2	absolute	absolute	ADJ
iajs-2776	94	3	error	error	NOUN
iajs-2776	94	4	for	for	ADP
iajs-2776	94	5	rk4	rk4	NOUN
iajs-2776	94	6	m	m	NOUN
iajs-2776	94	7	and	and	CCONJ
iajs-2776	94	8	ta	ta	PART
iajs-2776	94	9	method	method	VERB
iajs-2776	94	10	x	x	PUNCT
iajs-2776	94	11	absolute	absolute	ADJ
iajs-2776	94	12	error	error	NOUN
iajs-2776	94	13	for	for	ADP
iajs-2776	94	14	example	example	NOUN
iajs-2776	94	15	1	1	NUM
iajs-2776	94	16	absolute	absolute	ADJ
iajs-2776	94	17	error	error	NOUN
iajs-2776	94	18	for	for	ADP
iajs-2776	94	19	example	example	NOUN
iajs-2776	94	20	2	2	NUM
iajs-2776	94	21	|𝜐𝑇𝐴𝑀(𝑡	|𝜐𝑇𝐴𝑀(𝑡	PROPN
iajs-2776	94	22	)	)	PUNCT
iajs-2776	94	23	−	−	PROPN
iajs-2776	94	24	𝜐𝑅𝐾4(𝑡)|	𝜐𝑅𝐾4(𝑡)|	SYM
iajs-2776	94	25	|𝜐𝑇𝐴𝑀(𝑡	|𝜐𝑇𝐴𝑀(𝑡	PROPN
iajs-2776	94	26	)	)	PUNCT
iajs-2776	94	27	−	−	PROPN
iajs-2776	94	28	𝜐𝑅𝐾4(𝑡)|	𝜐𝑅𝐾4(𝑡)|	NUM
iajs-2776	94	29	0	0	NUM
iajs-2776	94	30	1.796565911	1.796565911	NUM
iajs-2776	94	31	×	×	NOUN
iajs-2776	94	32	10−7	10−7	NUM
iajs-2776	94	33	2.506032872×10	2.506032872×10	NUM
iajs-2776	94	34	-	-	SYM
iajs-2776	94	35	8	8	NUM
iajs-2776	94	36	0.1	0.1	NUM
iajs-2776	94	37	3.351539886	3.351539886	NUM
iajs-2776	94	38	×	×	NOUN
iajs-2776	94	39	10−7	10−7	NUM
iajs-2776	94	40	4.987247103	4.987247103	NUM
iajs-2776	94	41	×	×	NOUN
iajs-2776	94	42	10−8	10−8	NUM
iajs-2776	94	43	0.2	0.2	NUM
iajs-2776	94	44	4.575623109	4.575623109	NUM
iajs-2776	94	45	×	×	NOUN
iajs-2776	94	46	10−7	10−7	NUM
iajs-2776	94	47	7.253721456	7.253721456	NUM
iajs-2776	94	48	×	×	NOUN
iajs-2776	94	49	10−8	10−8	NUM
iajs-2776	94	50	0.3	0.3	NUM
iajs-2776	94	51	5.365609015	5.365609015	NUM
iajs-2776	94	52	×	×	NOUN
iajs-2776	94	53	10−7	10−7	NUM
iajs-2776	94	54	9.058700125	9.058700125	NUM
iajs-2776	94	55	"	"	PUNCT
iajs-2776	94	56	×	×	NOUN
iajs-2776	94	57	10−8	10−8	NUM
iajs-2776	94	58	0.4	0.4	NUM
iajs-2776	94	59	5.636405136	5.636405136	NUM
iajs-2776	94	60	×	×	NOUN
iajs-2776	94	61	10−7	10−7	NUM
iajs-2776	94	62	1.013928555	1.013928555	NUM
iajs-2776	94	63	×	×	NOUN
iajs-2776	94	64	10−7	10−7	NUM
iajs-2776	94	65	0.5	0.5	NUM
iajs-2776	94	66	5.35561508	5.35561508	NUM
iajs-2776	94	67	×	×	NOUN
iajs-2776	94	68	10−7	10−7	NUM
iajs-2776	94	69	1.028496388	1.028496388	NUM
iajs-2776	94	70	×	×	NOUN
iajs-2776	94	71	10−7	10−7	NUM
iajs-2776	94	72	0.6	0.6	NUM
iajs-2776	94	73	4.558146015	4.558146015	NUM
iajs-2776	94	74	×	×	NOUN
iajs-2776	94	75	10−7	10−7	NUM
iajs-2776	94	76	9.384872716	9.384872716	NUM
iajs-2776	94	77	×	×	NOUN
iajs-2776	94	78	10−8	10−8	NUM
iajs-2776	94	79	0.7	0.7	NUM
iajs-2776	94	80	3.331583074	3.331583074	NUM
iajs-2776	94	81	×	×	NOUN
iajs-2776	94	82	10−7	10−7	NUM
iajs-2776	94	83	7.409719157	7.409719157	NUM
iajs-2776	94	84	×	×	NOUN
iajs-2776	94	85	10−8	10−8	NUM
iajs-2776	94	86	0.8	0.8	NUM
iajs-2776	94	87	1.781605395	1.781605395	NUM
iajs-2776	94	88	×	×	NOUN
iajs-2776	94	89	10−7	10−7	NUM
iajs-2776	94	90	4.326019289	4.326019289	NUM
iajs-2776	94	91	×	×	NOUN
iajs-2776	94	92	10−8	10−8	NUM
iajs-2776	94	93	0.9	0.9	NUM
iajs-2776	94	94	0	0	NUM
iajs-2776	95	1	1.734723476	1.734723476	NUM
iajs-2776	95	2	×	×	NOUN
iajs-2776	95	3	10−18	10−18	NUM
iajs-2776	95	4	ihjpas	ihjpa	VERB
iajs-2776	95	5	.	.	PUNCT
iajs-2776	96	1	53	53	NUM
iajs-2776	96	2	(	(	PUNCT
iajs-2776	96	3	3)2022	3)2022	NOUN
iajs-2776	96	4	212	212	NUM
iajs-2776	96	5	3	3	NUM
iajs-2776	96	6	.	.	PUNCT
iajs-2776	96	7	conclusion	conclusion	NOUN
iajs-2776	96	8	in	in	ADP
iajs-2776	96	9	this	this	DET
iajs-2776	96	10	work	work	NOUN
iajs-2776	96	11	,	,	PUNCT
iajs-2776	96	12	a	a	DET
iajs-2776	96	13	proposed	propose	VERB
iajs-2776	96	14	iterative	iterative	NOUN
iajs-2776	96	15	technique	technique	NOUN
iajs-2776	96	16	is	be	AUX
iajs-2776	96	17	presented	present	VERB
iajs-2776	96	18	for	for	ADP
iajs-2776	96	19	solving	solve	VERB
iajs-2776	96	20	a	a	DET
iajs-2776	96	21	class	class	NOUN
iajs-2776	96	22	of	of	ADP
iajs-2776	96	23	4th	4th	ADJ
iajs-2776	96	24	-	-	PUNCT
iajs-2776	96	25	onide	onide	ADJ
iajs-2776	96	26	kirchhoff	kirchhoff	NOUN
iajs-2776	96	27	type	type	NOUN
iajs-2776	96	28	that	that	PRON
iajs-2776	96	29	emerges	emerge	VERB
iajs-2776	96	30	in	in	ADP
iajs-2776	96	31	the	the	DET
iajs-2776	96	32	investigation	investigation	NOUN
iajs-2776	96	33	of	of	ADP
iajs-2776	96	34	transversal	transversal	ADJ
iajs-2776	96	35	vibrations	vibration	NOUN
iajs-2776	96	36	of	of	ADP
iajs-2776	96	37	hinge	hinge	NOUN
iajs-2776	96	38	shafts	shafts	ADJ
iajs-2776	96	39	.	.	PUNCT
iajs-2776	97	1	the	the	DET
iajs-2776	97	2	ta	ta	PROPN
iajs-2776	97	3	method	method	NOUN
iajs-2776	97	4	is	be	AUX
iajs-2776	97	5	an	an	DET
iajs-2776	97	6	effective	effective	ADJ
iajs-2776	97	7	method	method	NOUN
iajs-2776	97	8	for	for	ADP
iajs-2776	97	9	solving	solve	VERB
iajs-2776	97	10	various	various	ADJ
iajs-2776	97	11	kinds	kind	NOUN
iajs-2776	97	12	of	of	ADP
iajs-2776	97	13	linear	linear	ADJ
iajs-2776	97	14	and	and	CCONJ
iajs-2776	97	15	non	non	ADJ
iajs-2776	97	16	-	-	ADJ
iajs-2776	97	17	linear	linear	ADJ
iajs-2776	97	18	problems	problem	NOUN
iajs-2776	97	19	accurately	accurately	ADV
iajs-2776	97	20	.	.	PUNCT
iajs-2776	98	1	the	the	DET
iajs-2776	98	2	fundamental	fundamental	ADJ
iajs-2776	98	3	benefit	benefit	NOUN
iajs-2776	98	4	of	of	ADP
iajs-2776	98	5	this	this	DET
iajs-2776	98	6	technique	technique	NOUN
iajs-2776	98	7	is	be	AUX
iajs-2776	98	8	that	that	SCONJ
iajs-2776	98	9	it	it	PRON
iajs-2776	98	10	does	do	AUX
iajs-2776	98	11	not	not	PART
iajs-2776	98	12	require	require	VERB
iajs-2776	98	13	the	the	DET
iajs-2776	98	14	estimation	estimation	NOUN
iajs-2776	98	15	of	of	ADP
iajs-2776	98	16	variables	variable	NOUN
iajs-2776	98	17	.	.	PUNCT
iajs-2776	99	1	it	it	PRON
iajs-2776	99	2	very	very	ADV
iajs-2776	99	3	well	well	ADV
iajs-2776	99	4	may	may	AUX
iajs-2776	99	5	be	be	AUX
iajs-2776	99	6	seen	see	VERB
iajs-2776	99	7	that	that	SCONJ
iajs-2776	99	8	when	when	SCONJ
iajs-2776	99	9	the	the	DET
iajs-2776	99	10	number	number	NOUN
iajs-2776	99	11	of	of	ADP
iajs-2776	99	12	repetition	repetition	NOUN
iajs-2776	99	13	increases	increase	NOUN
iajs-2776	99	14	,	,	PUNCT
iajs-2776	99	15	the	the	DET
iajs-2776	99	16	maximum	maximum	ADJ
iajs-2776	99	17	error	error	NOUN
iajs-2776	99	18	reminder	reminder	NOUN
iajs-2776	99	19	have	have	AUX
iajs-2776	99	20	decreased	decrease	VERB
iajs-2776	99	21	.	.	PUNCT
iajs-2776	100	1	in	in	ADP
iajs-2776	100	2	comparison	comparison	NOUN
iajs-2776	100	3	with	with	ADP
iajs-2776	100	4	the	the	DET
iajs-2776	100	5	rk4	rk4	NOUN
iajs-2776	100	6	m	m	NOUN
iajs-2776	100	7	,	,	PUNCT
iajs-2776	100	8	we	we	PRON
iajs-2776	100	9	find	find	VERB
iajs-2776	100	10	a	a	DET
iajs-2776	100	11	great	great	ADJ
iajs-2776	100	12	agreement	agreement	NOUN
iajs-2776	100	13	in	in	ADP
iajs-2776	100	14	the	the	DET
iajs-2776	100	15	results	result	NOUN
iajs-2776	100	16	through	through	ADP
iajs-2776	100	17	the	the	DET
iajs-2776	100	18	above	above	ADJ
iajs-2776	100	19	figures	figure	NOUN
iajs-2776	100	20	and	and	CCONJ
iajs-2776	100	21	table	table	NOUN
iajs-2776	100	22	.	.	PUNCT
iajs-2776	101	1	references	reference	NOUN
iajs-2776	101	2	1	1	NUM
iajs-2776	101	3	.	.	X
iajs-2776	101	4	sabaa	sabaa	PROPN
iajs-2776	101	5	,	,	PUNCT
iajs-2776	101	6	m.	m.	NOUN
iajs-2776	101	7	a.	a.	PROPN
iajs-2776	101	8	;	;	PUNCT
iajs-2776	101	9	mohammed	mohammed	PROPN
iajs-2776	101	10	,	,	PUNCT
iajs-2776	101	11	m.	m.	NOUN
iajs-2776	101	12	a.	a.	PROPN
iajs-2776	101	13	;	;	PUNCT
iajs-2776	101	14	abd	abd	PROPN
iajs-2776	101	15	almjeed	almjeed	NOUN
iajs-2776	101	16	,	,	PUNCT
iajs-2776	101	17	s.	s.	PROPN
iajs-2776	101	18	h.	h.	PROPN
iajs-2776	101	19	approximate	approximate	PROPN
iajs-2776	101	20	solutions	solution	NOUN
iajs-2776	101	21	for	for	ADP
iajs-2776	101	22	alcohol	alcohol	NOUN
iajs-2776	101	23	consumption	consumption	NOUN
iajs-2776	101	24	model	model	NOUN
iajs-2776	101	25	in	in	ADP
iajs-2776	101	26	spain	spain	PROPN
iajs-2776	101	27	.	.	PUNCT
iajs-2776	102	1	ibn	ibn	PROPN
iajs-2776	102	2	al	al	PROPN
iajs-2776	102	3	haitham	haitham	PROPN
iajs-2776	102	4	journal	journal	PROPN
iajs-2776	102	5	for	for	ADP
iajs-2776	102	6	pure	pure	ADJ
iajs-2776	102	7	and	and	CCONJ
iajs-2776	102	8	applied	applied	ADJ
iajs-2776	102	9	science	science	NOUN
iajs-2776	102	10	,	,	PUNCT
iajs-2776	102	11	2019	2019	NUM
iajs-2776	102	12	,	,	PUNCT
iajs-2776	102	13	32	32	NUM
iajs-2776	102	14	,	,	PUNCT
iajs-2776	102	15	3	3	NUM
iajs-2776	102	16	,	,	PUNCT
iajs-2776	102	17	153	153	NUM
iajs-2776	102	18	-	-	SYM
iajs-2776	102	19	164	164	NUM
iajs-2776	102	20	.	.	PUNCT
iajs-2776	103	1	2	2	X
iajs-2776	103	2	.	.	X
iajs-2776	103	3	tawfiq	tawfiq	PROPN
iajs-2776	103	4	,	,	PUNCT
iajs-2776	103	5	l.	l.	PROPN
iajs-2776	103	6	n.	n.	PROPN
iajs-2776	103	7	m.	m.	PROPN
iajs-2776	103	8	;	;	PUNCT
iajs-2776	103	9	hasan	hasan	PROPN
iajs-2776	103	10	,	,	PUNCT
iajs-2776	103	11	m.	m.	NOUN
iajs-2776	103	12	a.	a.	NOUN
iajs-2776	103	13	evaluate	evaluate	VERB
iajs-2776	103	14	therate	therate	NOUN
iajs-2776	103	15	of	of	ADP
iajs-2776	103	16	pollution	pollution	NOUN
iajs-2776	103	17	in	in	ADP
iajs-2776	103	18	soil	soil	NOUN
iajs-2776	103	19	using	use	VERB
iajs-2776	103	20	simulinkenvironment	simulinkenvironment	NOUN
iajs-2776	103	21	.	.	PUNCT
iajs-2776	104	1	ibn	ibn	PROPN
iajs-2776	104	2	al	al	PROPN
iajs-2776	104	3	haitham	haitham	PROPN
iajs-2776	104	4	journal	journal	PROPN
iajs-2776	104	5	for	for	ADP
iajs-2776	104	6	pure	pure	ADJ
iajs-2776	104	7	and	and	CCONJ
iajs-2776	104	8	applied	applied	ADJ
iajs-2776	104	9	science	science	NOUN
iajs-2776	104	10	,	,	PUNCT
iajs-2776	104	11	2019	2019	NUM
iajs-2776	104	12	,	,	PUNCT
iajs-2776	104	13	32	32	NUM
iajs-2776	104	14	,	,	PUNCT
iajs-2776	104	15	1	1	NUM
iajs-2776	104	16	,	,	PUNCT
iajs-2776	104	17	132138	132138	NUM
iajs-2776	104	18	.	.	PUNCT
iajs-2776	105	1	3	3	X
iajs-2776	105	2	.	.	X
iajs-2776	105	3	to	to	ADP
iajs-2776	105	4	fu	fu	PROPN
iajs-2776	105	5	ma	ma	PROPN
iajs-2776	105	6	,	,	PUNCT
iajs-2776	105	7	positive	positive	ADJ
iajs-2776	105	8	solutions	solution	NOUN
iajs-2776	105	9	for	for	ADP
iajs-2776	105	10	a	a	DET
iajs-2776	105	11	nonlocal	nonlocal	ADJ
iajs-2776	105	12	fourth	fourth	ADJ
iajs-2776	105	13	order	order	NOUN
iajs-2776	105	14	equation	equation	NOUN
iajs-2776	105	15	of	of	ADP
iajs-2776	105	16	kirchhoff	kirchhoff	NOUN
iajs-2776	105	17	type	type	NOUN
iajs-2776	105	18	,	,	PUNCT
iajs-2776	105	19	discrete	discrete	ADJ
iajs-2776	105	20	and	and	CCONJ
iajs-2776	105	21	continuous	continuous	ADJ
iajs-2776	105	22	dynamical	dynamical	ADJ
iajs-2776	105	23	systems	system	NOUN
iajs-2776	105	24	.	.	PUNCT
iajs-2776	106	1	discrete	discrete	ADJ
iajs-2776	106	2	and	and	CCONJ
iajs-2776	106	3	continuous	continuous	ADJ
iajs-2776	106	4	dynamical	dynamical	ADJ
iajs-2776	106	5	systems	system	NOUN
iajs-2776	106	6	supplement	supplement	NOUN
iajs-2776	106	7	,	,	PUNCT
iajs-2776	106	8	2007	2007	NUM
iajs-2776	106	9	,	,	PUNCT
iajs-2776	106	10	(	(	PUNCT
iajs-2776	106	11	special	special	ADJ
iajs-2776	106	12	)	)	PUNCT
iajs-2776	106	13	694–703	694–703	NUM
iajs-2776	106	14	,	,	PUNCT
iajs-2776	106	15	doi	doi	NOUN
iajs-2776	106	16	:	:	PUNCT
iajs-2776	106	17	10.3934	10.3934	NUM
iajs-2776	106	18	/	/	SYM
iajs-2776	106	19	proc.2007.2007.694	proc.2007.2007.694	PROPN
iajs-2776	106	20	.	.	PUNCT
iajs-2776	107	1	4	4	X
iajs-2776	107	2	.	.	X
iajs-2776	107	3	dang	dang	PROPN
iajs-2776	107	4	,	,	PUNCT
iajs-2776	107	5	o.	o.	PROPN
iajs-2776	107	6	a.	a.	PROPN
iajs-2776	107	7	;	;	PUNCT
iajs-2776	107	8	luan	luan	PROPN
iajs-2776	107	9	,	,	PUNCT
iajs-2776	107	10	v.	v.	ADP
iajs-2776	107	11	t.	t.	PROPN
iajs-2776	107	12	iterative	iterative	NOUN
iajs-2776	107	13	method	method	NOUN
iajs-2776	107	14	for	for	ADP
iajs-2776	107	15	solving	solve	VERB
iajs-2776	107	16	a	a	DET
iajs-2776	107	17	nonlinear	nonlinear	ADJ
iajs-2776	107	18	fourth	fourth	ADJ
iajs-2776	107	19	order	order	NOUN
iajs-2776	107	20	boundary	boundary	ADJ
iajs-2776	107	21	value	value	NOUN
iajs-2776	107	22	problem	problem	NOUN
iajs-2776	107	23	,	,	PUNCT
iajs-2776	107	24	computers	computer	NOUN
iajs-2776	107	25	and	and	CCONJ
iajs-2776	107	26	mathematics	mathematic	NOUN
iajs-2776	107	27	with	with	ADP
iajs-2776	107	28	applications	application	NOUN
iajs-2776	107	29	,	,	PUNCT
iajs-2776	107	30	2010	2010	NUM
iajs-2776	107	31	,	,	PUNCT
iajs-2776	107	32	60	60	NUM
iajs-2776	107	33	,	,	PUNCT
iajs-2776	107	34	1	1	NUM
iajs-2776	107	35	,	,	PUNCT
iajs-2776	107	36	112_121	112_121	NUM
iajs-2776	107	37	.	.	PUNCT
iajs-2776	108	1	5	5	X
iajs-2776	108	2	.	.	X
iajs-2776	108	3	temimia	temimia	NOUN
iajs-2776	108	4	,	,	PUNCT
iajs-2776	108	5	h	h	NOUN
iajs-2776	108	6	;	;	PUNCT
iajs-2776	108	7	ansari	ansari	X
iajs-2776	108	8	,	,	PUNCT
iajs-2776	108	9	a.r	a.r	PROPN
iajs-2776	108	10	.	.	PROPN
iajs-2776	108	11	;	;	PUNCT
iajs-2776	109	1	siddiqui	siddiqui	NOUN
iajs-2776	109	2	,	,	PUNCT
iajs-2776	109	3	a.	a.	NOUN
iajs-2776	109	4	m.	m.	NOUN
iajs-2776	109	5	an	an	DET
iajs-2776	109	6	approximate	approximate	ADJ
iajs-2776	109	7	solution	solution	NOUN
iajs-2776	109	8	for	for	ADP
iajs-2776	109	9	the	the	DET
iajs-2776	109	10	static	static	ADJ
iajs-2776	109	11	beam	beam	NOUN
iajs-2776	109	12	problem	problem	NOUN
iajs-2776	109	13	and	and	CCONJ
iajs-2776	109	14	nonlinear	nonlinear	ADJ
iajs-2776	109	15	integro	integro	ADJ
iajs-2776	109	16	-	-	PUNCT
iajs-2776	109	17	differential	differential	NOUN
iajs-2776	109	18	equations	equation	NOUN
iajs-2776	109	19	.	.	PUNCT
iajs-2776	110	1	computers	computer	NOUN
iajs-2776	110	2	and	and	CCONJ
iajs-2776	110	3	mathematics	mathematic	NOUN
iajs-2776	110	4	with	with	ADP
iajs-2776	110	5	applications	application	NOUN
iajs-2776	110	6	,	,	PUNCT
iajs-2776	110	7	2011	2011	NUM
iajs-2776	110	8	,	,	PUNCT
iajs-2776	110	9	62	62	NUM
iajs-2776	110	10	,	,	PUNCT
iajs-2776	110	11	8	8	NUM
iajs-2776	110	12	,	,	PUNCT
iajs-2776	110	13	3132–3139	3132–3139	NUM
iajs-2776	110	14	.	.	PUNCT
iajs-2776	111	1	6	6	NUM
iajs-2776	111	2	.	.	X
iajs-2776	112	1	ren	ren	PROPN
iajs-2776	112	2	,	,	PUNCT
iajs-2776	112	3	q.	q.	PROPN
iajs-2776	112	4	;	;	PUNCT
iajs-2776	112	5	tian	tian	PROPN
iajs-2776	112	6	,	,	PUNCT
iajs-2776	112	7	h.	h.	PROPN
iajs-2776	112	8	numerical	numerical	PROPN
iajs-2776	112	9	solution	solution	NOUN
iajs-2776	112	10	of	of	ADP
iajs-2776	112	11	the	the	DET
iajs-2776	112	12	static	static	ADJ
iajs-2776	112	13	beam	beam	NOUN
iajs-2776	112	14	problem	problem	NOUN
iajs-2776	112	15	by	by	ADP
iajs-2776	112	16	bernoulli	bernoulli	NOUN
iajs-2776	112	17	collocation	collocation	NOUN
iajs-2776	112	18	method	method	NOUN
iajs-2776	112	19	.	.	PUNCT
iajs-2776	113	1	applied	apply	VERB
iajs-2776	113	2	mathematical	mathematical	ADJ
iajs-2776	113	3	modelling	modelling	NOUN
iajs-2776	113	4	,	,	PUNCT
iajs-2776	113	5	2016	2016	NUM
iajs-2776	113	6	,	,	PUNCT
iajs-2776	113	7	40	40	NUM
iajs-2776	113	8	,	,	PUNCT
iajs-2776	113	9	21	21	NUM
iajs-2776	113	10	-	-	SYM
iajs-2776	113	11	22	22	NUM
iajs-2776	113	12	,	,	PUNCT
iajs-2776	113	13	8886–8897	8886–8897	NUM
iajs-2776	113	14	.	.	PUNCT
iajs-2776	114	1	7	7	X
iajs-2776	114	2	.	.	X
iajs-2776	114	3	temimia	temimia	NOUN
iajs-2776	114	4	,	,	PUNCT
iajs-2776	114	5	h	h	NOUN
iajs-2776	114	6	;	;	PUNCT
iajs-2776	114	7	ansari	ansari	X
iajs-2776	114	8	,	,	PUNCT
iajs-2776	114	9	a.r	a.r	PROPN
iajs-2776	114	10	a	a	DET
iajs-2776	114	11	semi	semi	ADJ
iajs-2776	114	12	-	-	ADJ
iajs-2776	114	13	analytical	analytical	ADJ
iajs-2776	114	14	iterative	iterative	NOUN
iajs-2776	114	15	technique	technique	NOUN
iajs-2776	114	16	for	for	ADP
iajs-2776	114	17	solving	solve	VERB
iajs-2776	114	18	nonlinear	nonlinear	ADJ
iajs-2776	114	19	problems	problem	NOUN
iajs-2776	114	20	.	.	PUNCT
iajs-2776	115	1	computers	computer	NOUN
iajs-2776	115	2	and	and	CCONJ
iajs-2776	115	3	mathematics	mathematic	NOUN
iajs-2776	115	4	with	with	ADP
iajs-2776	115	5	applications	application	NOUN
iajs-2776	115	6	,	,	PUNCT
iajs-2776	115	7	2011	2011	NUM
iajs-2776	115	8	,	,	PUNCT
iajs-2776	115	9	61	61	NUM
iajs-2776	115	10	,	,	PUNCT
iajs-2776	115	11	2	2	NUM
iajs-2776	115	12	,	,	PUNCT
iajs-2776	115	13	203–210	203–210	NUM
iajs-2776	115	14	.	.	NOUN
iajs-2776	115	15	8	8	NUM
iajs-2776	115	16	.	.	PUNCT
iajs-2776	115	17	ehsani	ehsani	PROPN
iajs-2776	115	18	,	,	PUNCT
iajs-2776	115	19	f.	f.	PROPN
iajs-2776	115	20	;	;	PUNCT
iajs-2776	115	21	hadi	hadi	PROPN
iajs-2776	115	22	,	,	PUNCT
iajs-2776	115	23	a.	a.	NOUN
iajs-2776	115	24	;	;	PUNCT
iajs-2776	115	25	ehsani	ehsani	PROPN
iajs-2776	115	26	,	,	PUNCT
iajs-2776	115	27	f.	f.	PROPN
iajs-2776	115	28	;	;	PUNCT
iajs-2776	115	29	mahdavi	mahdavi	PROPN
iajs-2776	115	30	,	,	PUNCT
iajs-2776	115	31	r.	r.	PROPN
iajs-2776	115	32	an	an	DET
iajs-2776	115	33	iterative	iterative	NOUN
iajs-2776	115	34	method	method	NOUN
iajs-2776	115	35	for	for	ADP
iajs-2776	115	36	solving	solve	VERB
iajs-2776	115	37	partial	partial	ADJ
iajs-2776	115	38	differential	differential	ADJ
iajs-2776	115	39	equations	equation	NOUN
iajs-2776	115	40	and	and	CCONJ
iajs-2776	115	41	solution	solution	NOUN
iajs-2776	115	42	of	of	ADP
iajs-2776	115	43	korteweg	korteweg	NOUN
iajs-2776	115	44	-	-	PUNCT
iajs-2776	115	45	de	de	NOUN
iajs-2776	115	46	vries	vries	PROPN
iajs-2776	115	47	equations	equation	NOUN
iajs-2776	115	48	for	for	ADP
iajs-2776	115	49	showing	show	VERB
iajs-2776	115	50	the	the	DET
iajs-2776	115	51	capability	capability	NOUN
iajs-2776	115	52	of	of	ADP
iajs-2776	115	53	the	the	DET
iajs-2776	115	54	iterative	iterative	NOUN
iajs-2776	115	55	method	method	NOUN
iajs-2776	115	56	.	.	PUNCT
iajs-2776	116	1	world	world	NOUN
iajs-2776	116	2	applied	apply	VERB
iajs-2776	116	3	programming	programming	NOUN
iajs-2776	116	4	,	,	PUNCT
iajs-2776	116	5	2013	2013	NUM
iajs-2776	116	6	,	,	PUNCT
iajs-2776	116	7	3	3	NUM
iajs-2776	116	8	,	,	PUNCT
iajs-2776	116	9	8	8	NUM
iajs-2776	116	10	,	,	PUNCT
iajs-2776	116	11	320	320	NUM
iajs-2776	116	12	-	-	SYM
iajs-2776	116	13	327	327	NUM
iajs-2776	116	14	.	.	NOUN
iajs-2776	117	1	9	9	NUM
iajs-2776	117	2	.	.	X
iajs-2776	118	1	al	al	PROPN
iajs-2776	118	2	-	-	PUNCT
iajs-2776	118	3	jawary	jawary	PROPN
iajs-2776	118	4	,	,	PUNCT
iajs-2776	118	5	m.a	m.a	PROPN
iajs-2776	118	6	.	.	PROPN
iajs-2776	118	7	a	a	DET
iajs-2776	118	8	semi	semi	ADJ
iajs-2776	118	9	-	-	ADJ
iajs-2776	118	10	analytical	analytical	ADJ
iajs-2776	118	11	iterative	iterative	NOUN
iajs-2776	118	12	method	method	NOUN
iajs-2776	118	13	for	for	ADP
iajs-2776	118	14	solving	solve	VERB
iajs-2776	118	15	nonlinear	nonlinear	ADJ
iajs-2776	118	16	thin	thin	ADJ
iajs-2776	118	17	film	film	NOUN
iajs-2776	118	18	flow	flow	NOUN
iajs-2776	118	19	problems	problem	NOUN
iajs-2776	118	20	,	,	PUNCT
iajs-2776	118	21	chaos	chaos	NOUN
iajs-2776	118	22	,	,	PUNCT
iajs-2776	118	23	solitons	soliton	NOUN
iajs-2776	118	24	and	and	CCONJ
iajs-2776	118	25	fractals,2017	fractals,2017	NOUN
iajs-2776	118	26	,	,	PUNCT
iajs-2776	118	27	99	99	NUM
iajs-2776	118	28	,	,	PUNCT
iajs-2776	118	29	52–56	52–56	NUM
iajs-2776	118	30	.	.	PUNCT
iajs-2776	118	31	10	10	NUM
iajs-2776	118	32	.	.	PUNCT
iajs-2776	119	1	al	al	PROPN
iajs-2776	119	2	-	-	PUNCT
iajs-2776	119	3	jawary	jawary	PROPN
iajs-2776	119	4	,	,	PUNCT
iajs-2776	119	5	m.	m.	NOUN
iajs-2776	119	6	a.	a.	NOUN
iajs-2776	119	7	;	;	PUNCT
iajs-2776	119	8	adwan	adwan	PROPN
iajs-2776	119	9	,	,	PUNCT
iajs-2776	119	10	m.	m.	NOUN
iajs-2776	119	11	i.	i.	PROPN
iajs-2776	119	12	reliable	reliable	ADJ
iajs-2776	119	13	iterative	iterative	NOUN
iajs-2776	119	14	methods	method	NOUN
iajs-2776	119	15	for	for	ADP
iajs-2776	119	16	solving	solve	VERB
iajs-2776	119	17	the	the	DET
iajs-2776	119	18	falknerskan	falknerskan	PROPN
iajs-2776	119	19	equation	equation	NOUN
iajs-2776	119	20	,	,	PUNCT
iajs-2776	119	21	gazi	gazi	PROPN
iajs-2776	119	22	university	university	PROPN
iajs-2776	119	23	journal	journal	NOUN
iajs-2776	119	24	of	of	ADP
iajs-2776	119	25	science	science	NOUN
iajs-2776	119	26	,	,	PUNCT
iajs-2776	119	27	2020	2020	NUM
iajs-2776	119	28	,	,	PUNCT
iajs-2776	119	29	l33	l33	PROPN
iajs-2776	119	30	,	,	PUNCT
iajs-2776	119	31	1	1	NUM
iajs-2776	119	32	,	,	PUNCT
iajs-2776	119	33	168	168	NUM
iajs-2776	119	34	-	-	SYM
iajs-2776	119	35	186	186	NUM
iajs-2776	119	36	.	.	PUNCT
iajs-2776	120	1	https://www.aimsciences.org/article/doi/10.3934/proc.2007.2007.694	https://www.aimsciences.org/article/doi/10.3934/proc.2007.2007.694	PROPN