A numerical solution of the generalized Burger’s–Huxley equation by pseudospectral method and Darvishi’s preconditioning

Abstract

In this paper, we present a new method for solving of the generalized Burger’s–Huxley 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 Darvishi’s precondotioning. Firstly, theory of application of spectral collocation method on Burger’s–Huxley equation presented. This method yields Burger’s–Huxley 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.