The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators

Table 3

The results of present, approximate obtained by Jouybari & Ramzani, and numerical solution for when and , Example 2.

	Numerical solution [2]	MMA solution; [6]	. error; (%)	EBM solution; [14]	. error; (%)	Present solution	. error; (%)
0	1.000000000	1.000000000	0.000000000	1.000000000	0.000000000	1.000000000	0.000000000
0.5	0.953968489	0.963119576	0.959265123	0.961786066	0.819479583	0.964200044	1.072525468
1	0.825442672	0.855198634	3.604849011	0.850064873	2.982908666	0.859363450	4.109404463
1.5	0.638888746	0.684197515	7.091808908	0.673375035	5.397855138	0.692996509	8.469043059
2	0.422287711	0.462729406	9.576810773	0.445220578	5.430626183	0.477011079	12.95878771
2.5	0.195637881	0.207129984	5.874170657	0.183038862	6.439969057	0.226871698	15.96511721
3	−0.032545617	−0.063747522	95.87129659	−0.093132124	186.1587291	−0.039511677	21.40398813
3.5	−0.260619945	−0.329922957	26.5915995	−0.362185221	38.97064593	−0.303066019	16.28657929
4	−0.485739543	−0.571762994	17.70978959	−0.603557273	24.25533019	−0.544920861	12.18375544
4.5	−0.696309233	−0.771429307	10.78832083	−0.79880073	14.71925003	−0.747759417	7.388984888
5	−0.869266232	−0.914194339	5.16850941	−0.93299355	7.331162267	−0.897058465	3.197206101
5.5	−0.976272484	−0.989527622	1.357729345	−0.995879662	2.008371466	−0.982128207	0.599804163
6	−0.996192580	−0.991872507	0.43365842	−0.982652815	1.35915136	−0.996877655	0.068769334
6.5	−0.924854298	−0.921056034	0.410687825	−0.894323908	3.301102678	−0.940250751	1.664743629
7	−0.776876524	−0.782301685	0.698329893	−0.737643731	5.050068034	−0.816301976	5.074867213
7.5	−0.579081909	−0.585844101	1.167743612	−0.524587017	9.410567167	−0.633906052	9.467424582
8	−0.358097172	−0.346174158	3.329547098	−0.271437236	24.20011739	−0.406122511	13.41125894
8.5	−0.130576292	−0.080970115	37.99018661	0.002457915	101.8823593	−0.149260634	14.30913814
9	0.097635936	0.190206352	94.8118283	0.276165213	182.8520157	0.118288292	21.15241257
9.5	0.325420035	0.447353037	37.46942071	0.528765792	62.48716586	0.377367786	15.96329218
10	0.548087739	0.671502582	22.51735155	0.740953929	35.1889262	0.609427780	11.19164627