Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition

Abstract

In this work the combined finite difference and spectral methods have been proposed for the numerical solution of the one-dimensional wave equation with an integral condition. The time variable is approximated using a finite difference scheme. But the spectral method is employed for discretizing the space variable. The main idea behind this approach is that we can get high-order results. The new method is used for two test problems and the numerical results are obtained to support our theoretical expectations. © 2007 Wiley Periodicals, Inc.