Notes on the homotopy analysis method: Some definitions and theorems
Notes on the homotopy analysis method: Some definitions and theorems
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同伦分析方法注意事项：一些定义和定理
DOI：
10.1016/j.cnsns.2008.04.013
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发表时间：
2009-04-01
影响因子：
3.9
通讯作者：
Liao, Shijun
中科院分区：
文献类型：
--
作者：
Liao, Shijun
本文简要介绍了同伦分析方法的基本思想和发展现状。同伦分析方法是一种求解强非线性问题的收敛级数解的解析方法，近年来引起了越来越多的研究者的兴趣。定义了同伦导数、收敛控制参数等新概念，使算法的描述更加严格。证明了关于同伦导数和形变方程的一些引理和定理。此外，还讨论了几个有待解决的问题，并提出了一个假设，为今后的研究。(c)2008 Elsevier B.V.保留所有权利。
We describe, very briefly, the basic ideas and current developments of the homotopy analysis method, an analytic approach to get convergent series solutions of strongly nonlinear problems, which recently attracts interests of more and more researchers. Definitions of some new concepts such as the homotopy-derivative, the convergence-control parameter and so on, are given to redescribe the method more rigorously. Some lemmas and theorems about the homotopy-derivative and the deformation equation are proved. Besides, a few open questions are discussed, and a hypothesis is put forward for future studies. (c) 2008 Elsevier B.V. All rights reserved.