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Based on the homotopy analysismethod (HAM), an analytic approach is proposed for highlynonlinear periodic oscillating equations with absolute valueterms. The nonsmoothness of absolute value terms is handled bymeans of Fourier expansion, and the convergence is accelerated by usingthe iteration method. Two typical examples which can not be solved by the method of averaging of perturbationtechnique are employed to illustrate the validity and flexibility of this approach. Rather, accurate approximations are obtainedusing the HAM-based approach. The proposed approach has generalmeanings and thus can be used to solve many highly nonlinearperiodic oscillating systems with this type of nonsmoothness of absolute value term.

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