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 (%) |
| 0 | 1.000000000 | 1.000000000 | 0.000000000 | 1.000000000 | 0.000000000 | 1.000000000 | 0.000000000 | 0.5 | 0.939545503 | 0.945169971 | 0.598637105 | 0.944189348 | 0.494265045 | 0.945834709 | 0.669388122 | 1 | 0.769687769 | 0.786692549 | 2.20930885 | 0.782987048 | 1.727879737 | 0.789206596 | 2.535940908 | 1.5 | 0.520367974 | 0.541946378 | 4.146758655 | 0.534386712 | 2.694004762 | 0.547083274 | 5.13392471 | 2 | 0.226896964 | 0.237770336 | 4.792206916 | 0.226137434 | 0.334746656 | 0.245694103 | 8.284438306 | 2.5 | −0.082424976 | −0.092479615 | 12.19853434 | −0.107353589 | 30.24400395 | −0.082311253 | 0.137971529 | 3 | −0.386261801 | −0.412588246 | 6.815699852 | −0.428861683 | 11.0287587 | −0.401399783 | 3.919098902 | 3.5 | −0.660436345 | −0.687452426 | 4.090641165 | −0.702499667 | 6.369019864 | −0.677004442 | 2.50865918 | 4 | −0.871990011 | −0.886930535 | 1.713382471 | −0.897723721 | 2.951147338 | −0.879268816 | 0.834734906 | 4.5 | −0.986529936 | −0.989147789 | 0.265359712 | −0.992742682 | 0.629757473 | −0.986281489 | 0.025183929 | 5 | −0.982752773 | −0.982895042 | 0.014476581 | −0.970950401 | 1.200950262 | −0.986449715 | 0.376182302 | 5.5 | −0.861382758 | −0.868857967 | 0.867815025 | −0.852109657 | 1.07653664 | −0.879755271 | 2.132909305 | 6 | −0.644890958 | −0.659541879 | 2.271844692 | −0.632155313 | 1.974852468 | −0.677756428 | 5.09628327 | 6.5 | −0.368002797 | −0.377900390 | 2.689542873 | −0.341638967 | 7.164029789 | −0.402335838 | 9.329559797 | 7 | −0.063204827 | −0.054818323 | 13.26877139 | −0.012988435 | 79.45024832 | −0.083329972 | 31.84115194 | 7.5 | 0.245785975 | 0.274275125 | 11.59103972 | 0.317111883 | 29.01951912 | 0.244703077 | 0.440585758 | 8 | 0.537446333 | 0.573291546 | 6.669542762 | 0.611815759 | 13.8375539 | 0.546227301 | 1.633831596 | 8.5 | 0.78289188 | 0.809440784 | 3.391132885 | 0.838227903 | 7.068156461 | 0.788578403 | 0.726348445 | 9 | 0.946701653 | 0.956826699 | 1.069507586 | 0.971676667 | 2.638108207 | 0.945502349 | 0.12668236 | 9.5 | 0.999764591 | 0.999286944 | 0.047775947 | 0.995531392 | 0.423419577 | 0.999999478 | 0.023494231 | 10 | 0.931963943 | 0.932165326 | 0.021608454 | 0.908764206 | 2.489338474 | 0.946166081 | 1.523893505 |
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