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 solutionof a nonlinear duffing oscillator with a damping effect under different initial conditions. moreover, thesolutions of the nonlinear duffing oscillator with the damping effect are obtained using the fourth-orderrungekutta numerical solution. a comparison of the results show that for the same number of termsthe differential transform method (dtm) can only predict the solutions of a duffing oscillator in a smallrange of time domains, whereas the mdtm can predict the results in a whole range of time domainsaccurately.