A simple new iterative method for solving strongly nonlinear oscillator systems having a rational and an irrational force

Abstract

In this paper, a new noble modified iterative method is proposed to obtain the approximate solution of strongly nonlinear oscillator systems having a rational and an irrational forces. The approximate frequency and the corresponding periodic solution can easily be determined by the present proposed method. Two examples are considered to illustrate the effectiveness and convenience of this procedure. The results obtained in this paper show good agreement with the corresponding numerical solution (considered to be exact) for both small and large amplitudes of oscillation. Furthermore, the method provides better result than other existing results (those results obtained by several authors). The main advantage of the present method is its simplicity which contains up to third harmonic terms. These harmonic terms make the solution rapidly converge. The method is important and powerful for solving nonlinear oscillator systems arising in nonlinear science and engineering. Keywords: Duffing-harmonic oscillator, Nonlinear oscillator, Iteration method