A new application of the homotopy analysis method: Solving the Sturm-Liouville problems

被引：88

作者：

Abbasbandy, S. ^{[1
]}

Shirzadi, A. ^{[1
]}

机构：

[1] Imam Khomeini Int Univ, Dept Math, Ghazvin 3414916818, Iran

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2011年 / 16卷 / 01期

关键词：

Homotopy analysis method; Multiple solutions; Two point Sturm-Liouville problems; Four point Sturm-Liouville problems; COMPUTING EIGENELEMENTS; DIFFERENTIAL-EQUATIONS; SERIES SOLUTION; FLOWS; 4TH;

D O I：

10.1016/j.cnsns.2010.04.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the homotopy analysis method (HAM) is applied to numerically approximate the eigenvalues of the second and fourth-order Sturm-Liouville problems. These eigenvalues are calculated by starting the HAM algorithm with one initial guess. In this paper, it can be observed that the auxiliary parameter h, which controls the convergence of the HAM approximate series solutions, also can be used in predicting and calculating multiple solutions. This is a basic and more important qualitative difference in analysis between HAM and other methods. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：112 / 126

页数：15

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