Approximate solution for nonlinear Duffing oscillator with damping effect using the modified differential transform method

The Duffing oscillator is a common model for nonlinear phenomena in science and engineering. In this paper, we use the modified differential transform method to obtain the approximate solution of a nonlinear Duffing oscillator with a damping effect under different initial conditions. Moreover, the solutions of the nonlinear Duffing oscillator with the damping effect are obtained using the fourth-order Runge–Kutta numerical solution. A comparison of the results show that for the same number of terms the differential transform method (DTM) can only predict the solutions of a Duffing oscillator in a small range of time domains, whereas the MDTM can predict the results in a whole range of time domains accurately.