A Coupled Homotopy-Variational Method and Variational Formulation Applied to Nonlinear Oscillators With and Without Discontinuities

Abstract

In this paper, two novel and different methods are applied to nonlinear oscillators. It has been found that the coupled method of homotopy perturbation method and variational formulation and amplitude-frequency formulation work very well for the whole range of initial amplitudes. The analytical approximate frequency and the corresponding periodic solution are valid for small as well as large amplitudes of oscillation. Contrary to the conventional methods, only one iteration leads to high accuracy of the solutions. Some examples are given to illustrate the accuracy and effectiveness of these methods.