Improvement of Analytic Solution to the Inverse Truly Nonlinear Oscillator by Extended Iterative Method

Abstract

A new approach of the Mickens extended iterative method has been presented to obtain approximate analytic solutions for nonlinear oscillatory differential equation. To get modified approximate solution of the inverse nonlinear oscillator “x+x-1=0” we have used the Fourier series and utilized indispensable truncated terms in each iterative step. In this thesis the solution gives more accurate result than other existing methods and shows a good agreement with its exact solution. The percentage of error between exact frequency and our third approximate frequency is as low as 0.0029%. We have compared our results with exact results and other existing results and the solution is convergent as well as consistent.