Convergence of the homotopy perturbation method for partial differential equations

被引：104

作者：

Biazar, J. ^{[1
]}

Ghazvini, H. ^{[1
,2
]}

机构：

[1] Univ Guilan, Fac Sci, Dept Math, Rasht, Iran

[2] Shahrood Univ Technol, Sch Math Sci, Dept Math, Shahrood, Iran

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2009年 / 10卷 / 05期

关键词：

Homotopy perturbation method; Partial differential equations; Burgers' equations; Schrodinger equations; Fourth order parabolic equations; Convergence sequence; DECOMPOSITION METHOD; NONLINEAR PROBLEMS;

D O I：

10.1016/j.nonrwa.2008.07.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a homotopy perturbation method to obtain exact solutions to some linear and nonlinear partial differential equations. This method is a powerful device for solving a wide variety of problems. Using the homotopy perturbation method, it is possible to find the exact solution or an approximate solution of the problem. Convergence of the method is proved. Some examples such as Burgers', Schrodinger and fourth order parabolic partial differential equations are presented, to verify convergence hypothesis, and illustrating the efficiency and simplicity of the method. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：2633 / 2640

页数：8

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