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Application of the Exp‐function method for solving a partial differential equation arising in biology and population genetics

Mehdi Dehghan (Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran)
Jalil Manafian Heris (Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran)
Abbas Saadatmandi (Department of Mathematics, Faculty of Science, University of Kashan, Kashan, Iran)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 9 August 2011

Abstract

Purpose

The purpose of this paper is to use He's Exp‐function method (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation.

Design/methodology/approach

This technique is straightforward and simple to use and is a powerful method to overcome some difficulties in the nonlinear problems.

Findings

This method is developed for searching exact traveling wave solutions of the nonlinear partial differential equations. The EFM presents a wider applicability for handling nonlinear wave equations.

Originality/value

The paper shows that EFM, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations. Application of EFM to Fitzhugh‐Nagumo equation illustrates its effectiveness.

Keywords

Citation

Dehghan, M., Manafian Heris, J. and Saadatmandi, A. (2011), "Application of the Exp‐function method for solving a partial differential equation arising in biology and population genetics", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 No. 6, pp. 736-753. https://doi.org/10.1108/09615531111148482

Publisher

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Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited