Exact solutions for non-linear Duffing’s equations by He’s homotopy perturbation method

In this paper, the homotopy perturbation method (HPM) is proposed to solve Duffing’s equation, which yields a series solution. Then, Padé approximation yielding the analytic approximate solution with fast convergence rate and high accuracy is applied for the series solution derived from the HPM. To illustrate the ability and the reliability of the method, two examples are provided. The results reveal that the method is very effective and simple.