Application of modified homotopy perturbation method to nonlinear oscillations

Abstract

The purpose of this paper is to apply a version of homotopy technique to nonlinear problems. The modified version of homotopy perturbation method is applied to derive highly accurate analytical expressions for periodic solutions or for approximate formulas of frequency. In contrast with the traditional perturbation methods, the proposed method does not require any small parameter in the equation. The proposed algorithm avoids the complexity provided by other numerical approaches. The analysis is accompanied by three numerical examples. The results prove that this method is very effective and simple.