An explicit numerical scheme for the modified Burgers' equation

An explicit finite difference scheme based on second-order rational approximants to the matrix-exponential term is proposed for the numerical solution of the modified Burgers' equation already known in the bibliography. The method, which is analyzed for local truncation error and stability, is tested to various wave packets and the results arising from the experiments are compared with the relevant known ones. Copyright (C) 2009 John Wiley & Sons, Ltd.