Approximate Analytic Solutions of the Nonlinear Cubic Oscillator by Iterative Method

Abstract

A modified approximate analytic solution of the cubic nonlinear oscillator “ẍ + x3 = 0" has been obtained based on an iteration method. Here we have used the truncated Fourier series in each iterative step. The approximate frequencies obtained by this technique show a good agreement with the exact frequency. The percentage of error between exact frequency and our fifth approximate frequency is as low as 0.009%. The calculation with this technique is very easy. The modified technique accelerates the rapid convergence of the solution, reduces the error solution and increases the validity range.