The homotopy analysis method to solve the Burgers-Huxley equation

被引:108
作者
Molabahrami, A. [1 ,2 ]
Khani, F. [1 ,3 ]
机构
[1] Ilam Univ, Dept Math, Ilam, Iran
[2] Maragheh Univ, Dept Math, Maragheh, Iran
[3] Bakhtar Inst Higher Educ, Ilam, Iran
关键词
Homotopy analysis method; Burgers-Huxley equation; Burgers-Fisher equation; Power-law nonlinearity; PERTURBATION METHOD; ANALYTIC SOLUTION; TANH METHOD; FLUID; FLOWS;
D O I
10.1016/j.nonrwa.2007.10.014
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, an analytical technique, namely the homotopy analysis method (HAM) is applied to obtain an approximate analytical solution of the Burgers-Huxley equation. This paper introduces the two theorems which provide us with a simple and convenient way to apply the HAM to the nonlinear PDEs with the power-law nonlinearity. The homotopy analysis method contains the auxiliary parameter t, which provides us with a simple way to adjust and control the convergence region of solution series. (C) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码:589 / 600
页数:12
相关论文
共 31 条
[1]   Homotopy analysis method for heat radiation equations [J].
Abbasbandy, S. .
INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER, 2007, 34 (03) :380-387
[2]   The application of homotopy analysis method to nonlinear equations arising in heat transfer [J].
Abbasbandy, S. .
PHYSICS LETTERS A, 2006, 360 (01) :109-113
[3]  
Adomian G., 1994, Solving Frontier Problems of Physics: the Decomposition Method
[4]  
[Anonymous], 1982, Stability of Motion
[5]  
Cole J.D., 1968, Perturbation methods in applied mathematics
[6]   On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder [J].
Hayat, T. ;
Sajid, M. .
PHYSICS LETTERS A, 2007, 361 (4-5) :316-322
[7]   Series solution for the upper-convected Maxwell fluid over a porous stretching plate [J].
Hayat, T. ;
Abbas, Z. ;
Sajid, M. .
PHYSICS LETTERS A, 2006, 358 (5-6) :396-403
[8]   Homotopy perturbation method for solving boundary value problems [J].
He, JH .
PHYSICS LETTERS A, 2006, 350 (1-2) :87-88
[9]   Comparison of homotopy perturbation method and homotopy analysis method [J].
He, JH .
APPLIED MATHEMATICS AND COMPUTATION, 2004, 156 (02) :527-539
[10]   Some asymptotic methods for strongly nonlinear equations [J].
He, Ji-Huan .
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2006, 20 (10) :1141-1199