Homotopy Analysis Method for Nonlinear Periodic Oscillating Equations with Absolute Value Term

Abstract

Based on the homotopy analysis method (HAM), an analytic approach is proposed for highly nonlinear periodic oscillating equations with absolute value terms. The nonsmoothness of absolute value terms is handled by means of Fourier expansion, and the convergence is accelerated by using the iteration method. Two typical examples which can not be solved by the method of averaging of perturbation technique are employed to illustrate the validity and flexibility of this approach. Rather, accurate approximations are obtained using the HAM-based approach. The proposed approach has general meanings and thus can be used to solve many highly nonlinear periodic oscillating systems with this type of nonsmoothness of absolute value term.