On the application of Sumudu transform series decomposition method and oscillation equations

Abstract

In this paper, a new method called Sumudu Transform Series Decomposition Method (STSDM) is applied to three different models of Oscillatory problems (Van der Pol, Duffing and Nonlinear Oscillatory equations). The method was developed by Combining the Sumudu Transform, Series Expansion Schemes and Adomian Polynomials. The Sumudu Transform was used to avoid integration of some difficult functions or rigour of reducing order of differential equations to system of differential equations, the Series Expansion was employed to increase the rate of convergence of the solution while Adomian Polynomials were used to decompose the nonlinear terms of the differential equations. The results obtained in all the problems considered showed that the new method was very effective, accurate and reliable.