<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, numerical solutions of the generalized Burgers-Huxley equation are obtained using a new technique of forming improved exponential finite difference method. The technique is called implicit exponential finite difference method for the solution of the equation. Firstly, the implicit exponential finite difference method is applied to the generalized Burgers-Huxley equation. Since the generalized Burgers-Huxley equation is nonlinear the scheme leads to a system of nonlinear equations. Secondly, at each time-step Newton’s method is used to solve this nonlinear system then linear equations system is obtained. Finally, linear equations system is solved using Gauss elimination method at each time-step. The numerical solutions obtained by this way are compared with the exact solutions and obtained by other methods to show the efficiency of the method.</p></abstract>

In this paper, numerical solutions of the generalized Burgers-Huxley equation are obtained using a new technique of forming improved exponential finite difference method. The technique is called implicit exponential finite difference method for the solution of the equation. Firstly, the implicit exponential finite difference method is applied to the generalized Burgers-Huxley equation. Since the generalized Burgers-Huxley equation is nonlinear the scheme leads to a system of nonlinear equations. Secondly, at each time-step Newton’s method is used to solve this nonlinear system then linear equations system is obtained. Finally, linear equations system is solved using Gauss elimination method at each time-step. The numerical solutions obtained by this way are compared with the exact solutions and obtained by other methods to show the efficiency of the method.

Numerical solutions of the generalized Burgers-Huxley equation by implicit exponential finite difference method

Department of Mathematics, Faculty of Muallim Rıfat Education, Kilis 7 Aralık University, Kilis, Turkey

Department of Mathematics, Faculty of Arts and Science, İnönü University, Malatya, Turkey

Journal of Applied Mathematics, Statistics and Informatics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, numerical solutions of the generalized Burgers-Huxley equation are obtained using a new technique of forming improved exponential finite...

Numerical solutions of the generalized Burgers-Huxley equation by implicit exponential finite difference method

Published Online: Dec 30, 2015

Page range: 57 - 67

DOI: https://doi.org/10.1515/jamsi-2015-0012

© 2015 Faculty of Natural Sciences, University of Saint Cyril and Metodius

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.