Homotopy analysis method to obtain numerical solutions of the Painleve equations

被引：9

作者：

Hesameddini, Esmail ^{[1
]}

Latifizadeh, Habibolla ^{[1
]}

机构：

[1] Shiraz Univ Technol, Dept Math, Fac Basic Sci, Shiraz, Iran

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2012年 / 35卷 / 12期

关键词：

Painleve equations; homotopy analysis method; ANALYTIC SOLUTION; APPROXIMATE SOLUTION; SERIES SOLUTION; GRADE FLUID; FLOW; DIFFUSION; MODEL;

D O I：

10.1002/mma.2521

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 presented to obtain the numerical solutions for the two kinds of the Painleve equations with a number of initial conditions. Then, a numerical evaluation and comparison with the results obtained via the HAM are included. It illustrates the validity and the great potential of the HAM in solving Painleve equations. Although the HAM contains the auxiliary parameter, the convergence region of the series solution can be controlled in a simple way. Copyright (c) 2012 John Wiley & Sons, Ltd.

引用

页码：1423 / 1433

页数：11

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