Spectral collocation method for the solution of the generalized Burger–Fisher equation

Abstract

In this paper, we present a new method for solving the generalized Burger–Fisher equation by using the collocation formula for calculating spectral differentiation matrix for Chebyshev–Gauss–Lobatto point. Firstly, theory of application of pseudospectral method on Burger–Fisher equations is presented. This method yields Burger–Fisher equation to a system of ordinary-differential equations (ODEs). Secondly, we use forth-order Runge–Kutta formula for the numerical integration of the system of ODE. The numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method.