Analytical treatment of generalized burgers-huxley equation by homotopy analysis method

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4 Citations (Scopus)

Abstract

In this paper, the homotopy analysis method (HAM) is applied to obtain approximate analytical solutions of the generalized Burgers-Huxley and Huxley equations. The series solution is developed and given explicitly. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. The comparison of the HAM results with the variational iteration method (VIM) results is made. It is shown, in particular, that the VIM solutions are only special cases of the HAM solutions.

Original languageEnglish
Pages (from-to)233-243
Number of pages11
JournalBulletin of the Malaysian Mathematical Sciences Society
Volume32
Issue number2
Publication statusPublished - 2009

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Homotopy Analysis Method
Burgers Equation
Generalized Equation
Variational Iteration Method
Series Solution
Analytical Solution
Initial conditions
Boundary conditions
Unknown
Approximation

Keywords

  • Burgers-Huxley equation
  • Homotopy analysis method
  • Huxley equation
  • Nonlinear PDEs

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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abstract = "In this paper, the homotopy analysis method (HAM) is applied to obtain approximate analytical solutions of the generalized Burgers-Huxley and Huxley equations. The series solution is developed and given explicitly. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. The comparison of the HAM results with the variational iteration method (VIM) results is made. It is shown, in particular, that the VIM solutions are only special cases of the HAM solutions.",
keywords = "Burgers-Huxley equation, Homotopy analysis method, Huxley equation, Nonlinear PDEs",
author = "{Sami Bataineh}, A. and {Md. Noorani}, {Mohd. Salmi} and Ishak Hashim",
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journal = "Bulletin of the Malaysian Mathematical Sciences Society",
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T1 - Analytical treatment of generalized burgers-huxley equation by homotopy analysis method

AU - Sami Bataineh, A.

AU - Md. Noorani, Mohd. Salmi

AU - Hashim, Ishak

PY - 2009

Y1 - 2009

N2 - In this paper, the homotopy analysis method (HAM) is applied to obtain approximate analytical solutions of the generalized Burgers-Huxley and Huxley equations. The series solution is developed and given explicitly. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. The comparison of the HAM results with the variational iteration method (VIM) results is made. It is shown, in particular, that the VIM solutions are only special cases of the HAM solutions.

AB - In this paper, the homotopy analysis method (HAM) is applied to obtain approximate analytical solutions of the generalized Burgers-Huxley and Huxley equations. The series solution is developed and given explicitly. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. The comparison of the HAM results with the variational iteration method (VIM) results is made. It is shown, in particular, that the VIM solutions are only special cases of the HAM solutions.

KW - Burgers-Huxley equation

KW - Homotopy analysis method

KW - Huxley equation

KW - Nonlinear PDEs

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VL - 32

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JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

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