Semi-analytical solution of non-homogeneous Duffing oscillator equation by the Padé differential transformation algorithm

Abstract

The Duffing oscillator equation is one of important equations that model several nonlinear phenomena in science and engineering. The differential transform method (DTM) is applied to obtain the solutions of homogeneous and non-homogeneous Duffing oscillator equations under the influence of different initial conditions. In fact, the DTM can only find the solutions of the Duffing oscillator equation in a small domain, therefore the method has been improved using Padé approximation. We obtain the solutions by the Padé-DTM (PDTM) in long domain. This article proves the validity, simplicity and applicability of the PDTM method. In addition, the accuracy of the PDTM and the instability of the solution are discussed.