Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators

Abstract

In this work, some general forms for forced and damped complex Duffing oscillators (FDCDOs), including two different models, which are known as the forced and damped complex Duffing oscillator (I) (FDCDO (I)) and FDCDO (II), are investigated by using some effective analytical and numerical approaches. For the analytical approximation, the two models of the FDCDOs are reduced to two decoupled standard forced and damped Duffing oscillators (FDDOs). After that, both the ansatz method and Krylov–Bogoliubov–Mitropolsky (KBM) approach are applied in order to derive some accurate analytical approximations in terms of trigonometric functions. For the numerical approximations, the finite difference method is employed to analyze the two coupled models without causing them to be decoupled for the original problems. In addition, all obtained analytical and numerical approximations are compared with the fourth-order Runge–Kutta (RK4) numerical approximations. Moreover, the maximum residual distance error (MRDE) is estimated in order to verify the accuracy of all obtained approximations.