本文一篇综述类文章，综述了同伦摄动方法及它在非线性微积分方程中的某些应用。
The paper reviews Some applications of the homotopy perturbation method to nonlinear differential and integral equations.
利用精细积分技术对同伦摄动方法进行了改进，构造了一种求解非线性动力学方程的新的渐近数值方法。
A new asymptotic numerical method for nonlinear dynamic equations was proposed. In this method, the homotopy perturbation method was improved by using the precise integration technique.
在第4章，同伦摄动的方法被成功应用到求解带有一个可动边条件的时间分数阶扩散方程并且得到了一个近似解。
In chapter 4, Homotopy perturbation method is successfully extended to solve time-fractional diffusion equation with a moving boundary condition and an approximate solution is obtained.
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