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

机译：具有绝对值项的非线性周期振动方程的同伦分析方法

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摘要

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.
机译：基于同伦分析法（HAM），提出了一种具有绝对值项的高度非线性周期振动方程的解析方法。绝对值项的不光滑度通过傅立叶展开来处理，并且通过使用迭代方法来加速收敛。以扰动平均法无法解决的两个典型例子为例，说明了该方法的有效性和灵活性。相反，使用基于HAM的方法可以获得准确的近似值。所提出的方法具有一般意义，因此可以用于解决具有这种类型的绝对值项非光滑性的高度非线性周期振荡系统。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第12期|132651.1-132651.7|共7页
  • 作者

    Cui Jifeng; Xu Hang; Lin Zhiliang;

  • 作者单位

    Shanghai Jiao Tong Univ, Sch Naval Architecture Ocean & Civil Engn, State Key Lab Ocean Engn, Shanghai 200240, Peoples R China;

    Shanghai Jiao Tong Univ, Sch Naval Architecture Ocean & Civil Engn, State Key Lab Ocean Engn, Shanghai 200240, Peoples R China;

    Shanghai Jiao Tong Univ, Sch Naval Architecture Ocean & Civil Engn, State Key Lab Ocean Engn, Shanghai 200240, Peoples R China;

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