Research Article

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

Table 2

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

Numerical solution [12]MMA solution [6]. error
(%)
EBM solution
[14]
. error
(%)
Present solution. error
(%)

01.0000000001.0000000000.0000000001.0000000000.0000000001.0000000000.000000000
0.50.9395455030.9451699710.5986371050.9441893480.4942650450.9458347090.669388122
10.7696877690.7866925492.209308850.7829870481.7278797370.7892065962.535940908
1.50.5203679740.5419463784.1467586550.5343867122.6940047620.5470832745.13392471
20.2268969640.2377703364.7922069160.2261374340.3347466560.2456941038.284438306
2.5−0.082424976−0.09247961512.19853434−0.10735358930.24400395−0.0823112530.137971529
3−0.386261801−0.4125882466.815699852−0.42886168311.0287587−0.4013997833.919098902
3.5−0.660436345−0.6874524264.090641165−0.7024996676.369019864−0.6770044422.50865918
4−0.871990011−0.8869305351.713382471−0.8977237212.951147338−0.8792688160.834734906
4.5−0.986529936−0.9891477890.265359712−0.9927426820.629757473−0.9862814890.025183929
5−0.982752773−0.9828950420.014476581−0.9709504011.200950262−0.9864497150.376182302
5.5−0.861382758−0.8688579670.867815025−0.8521096571.07653664−0.8797552712.132909305
6−0.644890958−0.6595418792.271844692−0.6321553131.974852468−0.6777564285.09628327
6.5−0.368002797−0.3779003902.689542873−0.3416389677.164029789−0.4023358389.329559797
7−0.063204827−0.05481832313.26877139−0.01298843579.45024832−0.08332997231.84115194
7.50.2457859750.27427512511.591039720.31711188329.019519120.2447030770.440585758
80.5374463330.5732915466.6695427620.61181575913.83755390.5462273011.633831596
8.50.782891880.8094407843.3911328850.8382279037.0681564610.7885784030.726348445
90.9467016530.9568266991.0695075860.9716766672.6381082070.9455023490.12668236
9.50.9997645910.9992869440.0477759470.9955313920.4234195770.9999994780.023494231
100.9319639430.9321653260.0216084540.9087642062.4893384740.9461660811.523893505