Numerical solutions of Duffing’s oscillator problem

In this paper, we approximate the solution of Duffing’s equation by converting it to a system of the first order ordinary differential equations and using Adomian’s decomposition method. This approach shows that for different versions of Duffing’s equation in identical conditions, the order of response polynomial is considerably lower than the polynomial obtained from direct application of Adomian’s decomposition method. Therefore, the order of computations and the running time of applied softwares will reduce.