A numerical solution of BurgersÕ equation by pseudospectral method and DarvishiÕs preconditioning M.T. Darvishi * , M. Javidi Department of Mathematics, Razi University, Kermanshah 67149, Iran Abstract In this paper, we solve the BurgersÕ equation by pseudospectral method. This equa- tion is one-dimensional quasilinear partial differential equation. To reduce round-off error of pseudospectral method we use DarvishiÕs preconditioning. The numerical results obtained by this method, for different values of viscosity, have been compared with the exact solution. It was seen that they were in good agreement with each other, because norm infinity of error is very small. Ó 2005 Elsevier Inc. All rights reserved. Keywords: BurgersÕ equation; Pseudospectral; Preconditioning 1. Introduction We consider the following initial boundary value problem: u t þ uu x ¼ lu xx ; a < x < b; 0 < t < T ; ð1Þ 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.04.079 * Corresponding author. E-mail address: darvishi@razi.ac.ir (M.T. Darvishi). Applied Mathematics and Computation 173 (2006) 421–429 www.elsevier.com/locate/amc