Approximate Analytic Solutions of the Inverse Cubic Truly Nonlinear Oscillator by Iterative Method

Abstract

An analytical technique has been developed based on an iteration method to determine higher-order approximate periodic solutions for nonlinear oscillatory differential equations. Usually, a set of nonlinear algebraic equations is solved with this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of large oscillations. A new technique based on the Mickens iterative method has been presented to obtain approximate analytic solutions of the Inverse Cubic Truly Nonlinear Oscillator. In this thesis, we have adopted the method of Fourier series and utilized truncated terms in each steps of iteration. The solutions obtained by this method nicely matched with the exact frequency. Also the obtained solutions are much more accurate than other existing results and the method is convergent and consistent.