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

Abstract

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