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

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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.

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