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
计量
- 文章访问数: 3165
- HTML全文浏览量: 183
- PDF下载量: 1629
- 被引次数: 0
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

HTML全文

参考文献(15)

[1]	S. J. Liao, The homotopy analysis method and its applications in mechanics, Ph. D.Dissertation, Shanghai Jiaotong University (1992).
[2]	S. J. Liao, A kind of linear invariance under homotopy and some simple applications of it in mechanics, Bericht Nr. 520. Institut fuer Schiffbau der Universitaet Hamburg (1992).
[3]	S. J. Liao. A second-order approximate analytical solution of a simple pendulum by the process analysis method, J. Applied Mechanics, 1(1992), 1173-1191.
[4]	S. J. Liao, Application of process analysis method to the solution of 2D non-linear progressive gravity waves, J. Ship, Rasearch, 3(1992), 30-37.
[5]	S. J. Liao, A kind of approximate solution technique which does not depend upon small parameters: a special example, Int. J. Non-Linear Mechanics. 30 (1905), 371-380.
[6]	S. J. Liao. A kind of approximate solution technique which does not depend upon small parameters (2): an application in fluid mechanics, Int. J. Non-Linear Mechanics, 32, 5(1997), 815-822.
[7]	S. J. Liao, Boundary Elements, X Ⅶ, Computational Mechanics Publications,Southampton (1995), 67-74.
[8]	S. J. Liao, High-order BEM formulations for strongly nonlinear problems governed by quite general nonlinear differential operators, Int. J. Numerical Methods in Fluide, 23 (1996), 739-751.
[9]	S. J. Liao and A. T. Chwang, The general BEM for strongly non-linear problems, Int. J.Numerical Methods in Fluids, 23 (1996), 467-483.
[10]	S. J. Liao, Homotopy analysis method and its applications in mathematics, Journal of Bosic Science and Engineering, 5, 2 (1997). 111-125.
[11]	H. Blasius, Grenzschichten in Fluessigkeiten mit kleiner Reibung, Z. Math. u. Phys., 5(1908). 1-37.
[12]	L. Howarth. On the calculation of steady now in the boundary layer near the surface of a cylinder in a stream. ARC RM, 1632 (1935).
[13]	L. Howarth. On the solution of tile laminar boundary layer equations. Proc. Roy. Soc.London A, 16(1938), 547-579.
[14]	M.L.Abell and J.P.Braselton,The Mathe matica Handbook,Academic Press,Inc.,Boston (1992).
[15]	S.L.L iao,The common ground of all numerical and analytical techniques for solving nonlinear problems,Communications of Nonlinear Science and Nonlinear Simulations,1(4)(1996),26-30.