id	sid	eid	entity	type
ma-226	1	1	2024	CARDINAL
ma-226	2	1	j. math	PERSON
ma-226	4	1	4 (2024	CARDINAL
ma-226	4	2	10doi	CARDINAL
ma-226	4	3	10.28924	CARDINAL
ma-226	4	4	second	ORDINAL
ma-226	4	5	nguyen dinh dung∗	PERSON
ma-226	4	6	thai nguyen university of information and communication technology	ORG
ma-226	4	7	thai	NORP
ma-226	10	1	two	CARDINAL
ma-226	10	2	second	ORDINAL
ma-226	12	1	1	CARDINAL
ma-226	12	2	second	ORDINAL
ma-226	12	3	∈	ORG
ma-226	15	1	0	CARDINAL
ma-226	15	2	1	CARDINAL
ma-226	15	3	1	CARDINAL
ma-226	15	4	1	CARDINAL
ma-226	15	5	11 feb 2024	DATE
ma-226	18	1	j. math	PERSON
ma-226	20	1	10.28924	CARDINAL
ma-226	20	2	2using	CARDINAL
ma-226	22	1	1	CARDINAL
ma-226	22	2	1	CARDINAL
ma-226	22	3	first	ORDINAL
ma-226	22	4	second	ORDINAL
ma-226	22	5	o(h	PERSON
ma-226	22	6	2	CARDINAL
ma-226	23	1	3][5	CARDINAL
ma-226	25	1	1	CARDINAL
ma-226	25	2	linear	ORG
ma-226	26	1	1	CARDINAL
ma-226	26	2	first	ORDINAL
ma-226	26	3	second	ORDINAL
ma-226	26	4	u(x	ORG
ma-226	26	5	3	CARDINAL
ma-226	27	1	6	CARDINAL
ma-226	27	2	5	CARDINAL
ma-226	30	1	8]-[12	CARDINAL
ma-226	30	2	3rd	ORDINAL
ma-226	30	3	4th	ORDINAL
ma-226	33	1	1]and	ORDINAL
ma-226	33	2	two	CARDINAL
ma-226	33	3	1	CARDINAL
ma-226	34	1	pointsin	GPE
ma-226	37	1	j. math	PERSON
ma-226	39	1	10.28924	CARDINAL
ma-226	39	2	3the	CARDINAL
ma-226	39	3	four	CARDINAL
ma-226	39	4	section 1	LAW
ma-226	40	1	section 2	LAW
ma-226	40	2	taylor	PERSON
ma-226	41	1	section 3	LAW
ma-226	43	1	2.	CARDINAL
ma-226	43	2	2.1	CARDINAL
ma-226	44	1	u(x	ORG
ma-226	44	2	taylor	PERSON
ma-226	44	3	3	CARDINAL
ma-226	46	1	2	CARDINAL
ma-226	49	1	2	CARDINAL
ma-226	50	1	∆x)n+1	ORG
ma-226	50	2	2	CARDINAL
ma-226	50	3	u(x	ORG
ma-226	51	1	2	CARDINAL
ma-226	54	1	∆x)n	ORG
ma-226	54	2	3	CARDINAL
ma-226	54	3	1	CARDINAL
ma-226	54	4	0	CARDINAL
ma-226	54	5	1	DATE
ma-226	54	6	3	CARDINAL
ma-226	56	1	2	CARDINAL
ma-226	57	1	2	CARDINAL
ma-226	60	1	4	CARDINAL
ma-226	63	1	2	CARDINAL
ma-226	65	1	6	CARDINAL
ma-226	65	2	6	CARDINAL
ma-226	65	3	first	ORDINAL
ma-226	65	4	4	CARDINAL
ma-226	65	5	5	CARDINAL
ma-226	67	1	4	CARDINAL
ma-226	68	1	2	CARDINAL
ma-226	71	1	7	CARDINAL
ma-226	72	1	0	CARDINAL
ma-226	72	2	1	DATE
ma-226	72	3	2	CARDINAL
ma-226	73	1	x0	ORG
ma-226	75	1	v(x1	ORG
ma-226	78	1	1	CARDINAL
ma-226	80	1	j. math	PERSON
ma-226	82	1	10.28924	CARDINAL
ma-226	82	2	ma.4.10 4since	PERSON
ma-226	82	3	3	CARDINAL
ma-226	82	4	6	CARDINAL
ma-226	82	5	7	CARDINAL
ma-226	82	6	first	ORDINAL
ma-226	82	7	second	ORDINAL
ma-226	83	1	1	CARDINAL
ma-226	83	2	second	ORDINAL
ma-226	88	1	zi − z0)(zi	PERSON
ma-226	89	1	n∑ k=0	PERSON
ma-226	91	1	n∑ k=0	PERSON
ma-226	91	2	k)ui+k−n/2	PERSON
ma-226	91	3	n/2 ≤	MONEY
ma-226	92	1	n∑ k=0	PERSON
ma-226	92	2	k)un−n+k	GPE
ma-226	94	1	− zn	PERSON
ma-226	96	1	− zn	PERSON
ma-226	98	1	− zn	PERSON
ma-226	102	1	1	CARDINAL
ma-226	102	2	6	CARDINAL
ma-226	102	3	7	CARDINAL
ma-226	102	4	2.2 2.2	CARDINAL
ma-226	103	1	ga	ORG
ma-226	104	1	9	CARDINAL
ma-226	106	1	10)be	CARDINAL
ma-226	106	2	9	CARDINAL
ma-226	107	1	u(x	ORG
ma-226	107	2	two	CARDINAL
ma-226	108	1	2.2.1	CARDINAL
ma-226	108	2	1consider	CARDINAL
ma-226	108	3	second	ORDINAL
ma-226	108	4	∈	ORG
ma-226	108	5	11	CARDINAL
ma-226	109	1	j. math	PERSON
ma-226	111	1	10.28924	CARDINAL
ma-226	113	1	un	ORG
ma-226	113	2	f1	PERSON
ma-226	115	1	d(m)f	NORP
ma-226	116	1	11	CARDINAL
ma-226	116	2	0	CARDINAL
ma-226	116	3	1	DATE
ma-226	116	4	2	CARDINAL
ma-226	119	1	4	CARDINAL
ma-226	119	2	6	CARDINAL
ma-226	121	1	2	CARDINAL
ma-226	122	1	12	CARDINAL
ma-226	123	1	2)fi	ORG
ma-226	123	2	2m)!d	CARDINAL
ma-226	123	3	2m−2)fi	CARDINAL
ma-226	123	4	1 ≤	QUANTITY
ma-226	124	1	1	CARDINAL
ma-226	124	2	2	DATE
ma-226	124	3	un	ORG
ma-226	124	4	13	CARDINAL
ma-226	124	5	13	CARDINAL
ma-226	124	6	three	CARDINAL
ma-226	124	7	three	CARDINAL
ma-226	124	8	13	CARDINAL
ma-226	125	1	13	CARDINAL
ma-226	125	2	7	CARDINAL
ma-226	125	3	2nd	ORDINAL
ma-226	125	4	1	CARDINAL
ma-226	125	5	13	CARDINAL
ma-226	126	1	2	CARDINAL
ma-226	126	2	13	CARDINAL
ma-226	126	3	11	CARDINAL
ma-226	127	1	2.2.2	CARDINAL
ma-226	127	2	2consider	CARDINAL
ma-226	127	3	second	ORDINAL
ma-226	127	4	∈	ORG
ma-226	131	1	14	CARDINAL
ma-226	133	1	un	ORG
ma-226	135	1	f1	PERSON
ma-226	136	1	d(m)n	ORG
ma-226	137	1	6	CARDINAL
ma-226	140	1	2	CARDINAL
ma-226	141	1	3	CARDINAL
ma-226	141	2	− hn−1 n	PERSON
ma-226	141	3	15	CARDINAL
ma-226	141	4	two	CARDINAL
ma-226	143	1	− u0 h	ORG
ma-226	144	1	2	CARDINAL
ma-226	145	1	3	CARDINAL
ma-226	145	2	− hn−1 n!	PERSON
ma-226	145	3	16	CARDINAL
ma-226	146	1	2	CARDINAL
ma-226	147	1	3	CARDINAL
ma-226	149	1	17	CARDINAL
ma-226	150	1	j. math	PERSON
ma-226	152	1	10.28924	CARDINAL
ma-226	152	2	16	CARDINAL
ma-226	152	3	17	CARDINAL
ma-226	152	4	schemenumber 1	DATE
ma-226	152	5	u1−u0	ORG
ma-226	153	1	1	CARDINAL
ma-226	153	2	− hn−1 n	PERSON
ma-226	157	1	1	CARDINAL
ma-226	157	2	2	DATE
ma-226	157	3	1	CARDINAL
ma-226	159	1	1	CARDINAL
ma-226	161	1	1	CARDINAL
ma-226	162	1	18	CARDINAL
ma-226	162	2	3	CARDINAL
ma-226	162	3	18	CARDINAL
ma-226	162	4	14	CARDINAL
ma-226	163	1	3	CARDINAL
ma-226	169	1	un	ORG
ma-226	170	1	3.1	CARDINAL
ma-226	170	2	1example 1	DATE
ma-226	171	1	0	CARDINAL
ma-226	171	2	1	CARDINAL
ma-226	171	3	0	CARDINAL
ma-226	171	4	u(1	ORG
ma-226	171	5	1	CARDINAL
ma-226	172	1	1	CARDINAL
ma-226	172	2	1	CARDINAL
ma-226	172	3	1	CARDINAL
ma-226	172	4	1	CARDINAL
ma-226	174	1	1.0000e-008 2.9675e-012	QUANTITY
ma-226	174	2	3.9063e-011	CARDINAL
ma-226	175	1	4.6426e-014	CARDINAL
ma-226	175	2	4.0825e-015	CARDINAL
ma-226	175	3	7.2653e-016 9.5367e-017	TIME
ma-226	176	1	2.5600e-014	CARDINAL
ma-226	176	2	1.0240e-017	CARDINAL
ma-226	176	3	5.9537e-015 6.3781e-017	CARDINAL
ma-226	178	1	j. math	PERSON
ma-226	180	1	10.28924	CARDINAL
ma-226	181	1	5.9605e-016	CARDINAL
ma-226	183	1	2.3231e-016	CARDINAL
ma-226	183	2	2.8680e-020	CARDINAL
ma-226	183	3	2.1680e-023100 1.0000e-016	TIME
ma-226	183	4	2.9759e-018	PERSON
ma-226	183	5	8.4722e-024	DATE
ma-226	183	6	1	CARDINAL
ma-226	184	1	1example 2	CARDINAL
ma-226	185	1	0	CARDINAL
ma-226	185	2	1	CARDINAL
ma-226	186	1	1	CARDINAL
ma-226	186	2	u(1	ORG
ma-226	186	3	= sinh(1	PERSON
ma-226	188	1	2	CARDINAL
ma-226	188	2	1	CARDINAL
ma-226	191	1	1.0000e-008 3.3899e-012	CARDINAL
ma-226	191	2	5.3052e-014	CARDINAL
ma-226	192	1	4.6589e-015	CARDINAL
ma-226	193	1	8.3000e-016 9.5367e-017	CARDINAL
ma-226	193	2	2.5600e-014	CARDINAL
ma-226	195	1	j. math	PERSON
ma-226	197	1	10.28924	CARDINAL
ma-226	197	2	5.9537e-015 7.2895e-017	DATE
ma-226	198	1	1.1046e-02170 1.7347e-015 2.8908e-017	DATE
ma-226	198	2	2.7774e-02280 5.9605e-016 1.2973e-017	DATE
ma-226	198	3	2.3231e-016	TIME
ma-226	198	4	2.8680e-020	CARDINAL
ma-226	199	1	1.0000e-016	TIME
ma-226	199	2	1	CARDINAL
ma-226	199	3	2	CARDINAL
ma-226	199	4	1	CARDINAL
ma-226	199	5	second	ORDINAL
ma-226	200	1	3.2	CARDINAL
ma-226	200	2	2example 3	CARDINAL
ma-226	201	1	6x	CARDINAL
ma-226	201	2	+ x/2	GPE
ma-226	201	3	0	CARDINAL
ma-226	201	4	1	CARDINAL
ma-226	201	5	u(0)−	NORP
ma-226	201	6	u(1	ORG
ma-226	201	7	4 + sinh(3/2	QUANTITY
ma-226	202	1	+ 1 2cosh(3/2)exact	DATE
ma-226	203	1	2	CARDINAL
ma-226	204	1	2	CARDINAL
ma-226	204	2	3	CARDINAL
ma-226	204	3	3	CARDINAL
ma-226	204	4	2	CARDINAL
ma-226	207	1	1.0000e-010	CARDINAL
ma-226	208	1	3.9063e-011	CARDINAL
ma-226	208	2	3.3597e-015	CARDINAL
ma-226	210	1	2.9998e-016	CARDINAL
ma-226	213	1	7.0444e-02370 1.7347e-015 1.8943e-018	DATE
ma-226	213	2	5.9605e-016	CARDINAL
ma-226	213	3	2.3231e-016 4.2068e-019	TIME
ma-226	213	4	2.8680e-020 1.8066e-024100	TIME
ma-226	213	5	2.2381e-019	PERSON
ma-226	213	6	3.0015e-025	CARDINAL
ma-226	214	1	j. math	PERSON
ma-226	216	1	10.28924	CARDINAL
ma-226	216	2	9	CARDINAL
ma-226	216	3	2	CARDINAL
ma-226	217	1	3example 4	DATE
ma-226	218	1	+ 1 9e	DATE
ma-226	218	2	0	CARDINAL
ma-226	218	3	1	CARDINAL
ma-226	218	4	1 2	CARDINAL
ma-226	219	1	1 3	DATE
ma-226	222	1	2	CARDINAL
ma-226	223	1	2	CARDINAL
ma-226	223	2	4	CARDINAL
ma-226	223	3	4	CARDINAL
ma-226	223	4	2	CARDINAL
ma-226	226	1	1.0000e-008 3.7083e-011	CARDINAL
ma-226	226	2	5.5099e-014	CARDINAL
ma-226	226	3	6.5992e-01950	CARDINAL
ma-226	229	1	8.7603e-016	TIME
ma-226	230	1	1.1673e-020	CARDINAL
ma-226	231	1	j. math	PERSON
ma-226	233	1	10.28924	CARDINAL
ma-226	233	2	10	CARDINAL
ma-226	234	1	1.7347e-015 3.4826e-016	DATE
ma-226	235	1	6.1971e-02290 2.3231e-016	DATE
ma-226	235	2	2.8680e-020	CARDINAL
ma-226	235	3	4.1155e-017 1.0000e-020	EVENT
ma-226	235	4	3	CARDINAL
ma-226	235	5	4	CARDINAL
ma-226	235	6	2	CARDINAL
ma-226	235	7	second	ORDINAL
ma-226	236	1	4.	CARDINAL
ma-226	236	2	two	CARDINAL
ma-226	236	3	second	ORDINAL
ma-226	237	1	two	CARDINAL
ma-226	238	1	3][5]is	ORDINAL
ma-226	238	2	two	CARDINAL
ma-226	239	1	two	CARDINAL
ma-226	241	1	1	CARDINAL
ma-226	241	2	lagrange	GPE
ma-226	241	3	newton	GPE
ma-226	241	4	lap lambert academic publishing	ORG
ma-226	241	5	2012.[2	CARDINAL
ma-226	241	6	t.h. nguyen	PERSON
ma-226	241	7	10	CARDINAL
ma-226	241	8	358	CARDINAL
ma-226	241	9	n. setia	PERSON
ma-226	241	10	r.k. mohanty	GPE
ma-226	241	11	two	CARDINAL
ma-226	243	1	26	CARDINAL
ma-226	243	2	2022	CARDINAL
ma-226	243	3	9805	CARDINAL
ma-226	243	4	second	ORDINAL
ma-226	243	5	two	CARDINAL
ma-226	245	1	145	CARDINAL
ma-226	245	2	2019	CARDINAL
ma-226	245	3	361	CARDINAL
ma-226	245	4	h. ramos	PERSON
ma-226	245	5	m.a. rufai	PERSON
ma-226	245	6	two	CARDINAL
ma-226	245	7	numer	ORG
ma-226	245	8	84	CARDINAL
ma-226	245	9	2020	DATE
ma-226	245	10	229	CARDINAL
ma-226	245	11	j. li	PERSON
ma-226	245	12	j. comput	PERSON
ma-226	247	1	183	CARDINAL
ma-226	247	2	29-52.[7	CARDINAL
ma-226	247	3	m. kaur1	PERSON
ma-226	247	4	s. kumar	PERSON
ma-226	247	5	j. bhatti	PERSON
ma-226	247	6	sixth	ORDINAL
ma-226	247	7	three	CARDINAL
ma-226	247	8	runge-kutta	PERSON
ma-226	247	9	107	CARDINAL
ma-226	247	10	2022	CARDINAL
ma-226	247	11	86	CARDINAL
ma-226	249	1	28924	DATE
ma-226	251	1	j. math	PERSON
ma-226	253	1	10.28924	CARDINAL
ma-226	253	2	11	CARDINAL
ma-226	253	3	8	CARDINAL
ma-226	253	4	q.a. dang	GPE
ma-226	253	5	q.l. dang	GPE
ma-226	253	6	third	ORDINAL
ma-226	253	7	j. nonlinearfunct	PERSON
ma-226	255	1	2020	DATE
ma-226	255	2	2020	DATE
ma-226	255	3	9	CARDINAL
ma-226	255	4	q.a. dang	GPE
ma-226	255	5	q.l. dang	GPE
ma-226	255	6	second	ORDINAL
ma-226	255	7	third	ORDINAL
ma-226	255	8	fullythird	ORDINAL
ma-226	255	9	algor	PERSON
ma-226	256	1	87	CARDINAL
ma-226	256	2	2021	CARDINAL
ma-226	256	3	1479–1499	CARDINAL
ma-226	257	1	q.a. dang	GPE
ma-226	257	2	t.h. nguyen	PERSON
ma-226	257	3	fourth	ORDINAL
ma-226	258	1	30 (2019	CARDINAL
ma-226	259	1	623–641	CARDINAL
ma-226	259	2	j. alzabut	PERSON
ma-226	259	3	s.r. grace	PERSON
ma-226	259	4	g.n. chhatria	PERSON
ma-226	259	5	j. math	PERSON
ma-226	261	1	sci	ORG
ma-226	261	2	28	CARDINAL
ma-226	261	3	2022	CARDINAL
ma-226	261	4	294	CARDINAL
ma-226	261	5	s. baraket	PERSON
ma-226	261	6	s. mahdaoui	PERSON
ma-226	261	7	t. ouni	GPE
ma-226	261	8	fourth	ORDINAL
ma-226	261	9	discr	PERSON
ma-226	262	1	contin	PERSON
ma-226	263	1	dyn.	ORG
ma-226	264	1	syst	ORG
ma-226	265	1	16	CARDINAL
ma-226	265	2	2023	CARDINAL
ma-226	265	3	1181-1200	DATE
ma-226	266	1	2	CARDINAL
ma-226	266	2	3	CARDINAL
ma-226	266	3	4	CARDINAL