An analytic approach to solve multiple solutions of a strongly nonlinear problem

被引：97

作者：

Li, SC ^{[1
]}

Liao, SJ ^{[1
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Naval Architecture Ocean & Civil Engn, Shanghai 200030, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2005年 / 169卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Gelfand problem; multiple solutions; strong nonlinearity; bifurcation; heat transfer; homotopy analysis method;

D O I：

10.1016/j.amc.2004.09.066

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on a new kind of analytic method, namely the homotopy analysis method, an analytic approach to solve multiple solutions of strongly nonlinear problems is described by using Gelfand equation as an example. Its validity is verified by comparing the approximation series with the known exact solution. And different from perturbation techniques, this approach is independent upon any small/large perturbation quantities. So, the basic ideas of this approach can be employed to search for multiple solutions of strongly nonlinear problems in science and engineering. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：854 / 865

页数：12

共 22 条

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