Modified pseudospectral method for generalized Burger's-Fisher equation

Abstract

We consider solitary-wave solutions of the generalized Burger’s-Fisher equation ∂Ψ ∂t + αΨ δ ∂Ψ ∂x − ∂ 2 Ψ ∂x2 = βΨ(1 − Ψ δ ). In this paper, we present a new method for solving of the generalized Burger’s-Fisher equation by using the collocation formula for calculating spectral differentiation matrix for Chebyshev-Gauss-Lobatto point. To reduce round-off error in spectral collocation method we use a new precondotioning. Firstly, theory of application of spectral collocation method on Burger’s-Fisher equation presented. This method yields Burger’s-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.