Analytical approximations to a generalized forced damped complex Duffing oscillator: Multiple scales method and KBM approach


 In this investigation, some different approaches including the hybrid homotopy perturbation method (H-HPM) which sometimes is called Krylov-Bogoliubov-Mitropolsky (KBM) method and the multiple scales method (MSM), are implemented for analyzing a generalized forced damped complex Duffing oscillator. All mentioned methods are applied to obtain some accurate and stable approximations to the proposed problem without decoupling for the original problem. All obtained approximations are discussed graphically using different numerical values to the relevant parameters. Moreover, all obtained approximate solution are compared with the 4^{th}-order Runge-Kutta (RK4) numerical approximation. Also, the maximum residual distance error (MRDE) is estimated in order to verify the high-accuracy to the obtained analytic approximations.