Solutions of non-linear oscillators by the modified differential transform method

Abstract

A numerical method for solving nonlinear oscillators is proposed. The proposed scheme is based on the differential transform method (DTM), Laplace transform and Padé approximants. The modified differential transform method (MDTM) technique introduces an alternative framework designed to overcome the difficulty of capturing the periodic behavior of the solution, which is characteristic of oscillator equations, and give a good approximation to the true solution in a very large region. The numerical results demonstrate the validity and applicability of the new technique and a comparison is made with existing results.