同伦分析方法：一种新的求解非线性问题的近似解析方法

本文描述了一种称为“同伦分析方法”（ＨＡＭ）的新的求解非线性问题的近似解析方法之基本思想·不同于摄动展开方法，“同伦分析方法”的有效性不依赖于所研究的非线性方程中是否含有小参数·因此，该方法提供了一个强有力的分析非线性问题的新工具·作为示例，我们应用一个典型的非线性问题来说明该方法的有效性及其巨大潜力·

Homotopy Analysis Method: a New Analytic Method for Nonlinear Problems

In this paper, the basic ideas of a new analytic technique, namely the Homotopy Analysis Mehtod(HAM), are described. Different from perturbation methods, the validity of the HAM is independent on whether or not there exist small parameters in considered nonlinear equations. Therefore, it provides us with a powerful analytic tool for strongly nonlinear problems. A typical nonlinear problem is used as an example to verify the validity and the great potential of the HAM.