同伦分析方法:一种新的求解非线性问题的近似解析方法

廖世俊; 戴世强

同伦分析方法:一种新的求解非线性问题的近似解析方法

上海交通大学船舶及海洋工程学院, 上海200030

详细信息

中图分类号: O174;O173;O175
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出版历程
- 收稿日期: 1997-05-27
- 刊出日期: 1998-10-15

Homotopy Analysis Method: a New Analytic Method for Nonlinear Problems

Liao Shijun,

Shanghai Jiaotong University, Shanghai 200030, P.R.China

摘要

摘要: 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。
- 非线性近似解析方法 /
- 强非线性 /
- 同伦 /
- 拓扑
Abstract: In this paper, the basic ideas of a new analytic technique, namely the Homotopy Analysis Method (HAM), are described. Differem 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.
- nonlinear analytic technique /
- strong nonlinearity /
- homotopy /
- topology

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参考文献(15)

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