An analytical approximate technique for solving cubic–quintic Duffing oscillator

In this paper, an analytical approximate technique combined of homotopy perturbation method and variational formulation is presented to obtain the approximate frequency and the corresponding periodic solution of strongly nonlinear oscillator named as cubic–quintic Duffing oscillator. The first-order approximation is mainly considered in this paper. The solutions (first-order approximation) are valid for both small and large amplitudes of oscillation. The main advantage of the present method is that its simplicity and straightforward. Moreover, the first-order approximate solution gives better result than other existing second, third and fourth-order approximations for all values of amplitude. The present method is more suitable for solving cubic–quintic Duffing oscillator than other existing methods.