Parameterized families of finite difference schemes for the wave equation

This article is devoted to an analysis of simple families of finite difference schemes for the wave equation. OF These families are dependent on several free parameters, and methods for obtaining stability bounds as a IF function of these parameters are discussed in detail. Access to explicit stability bounds such as those derived here may, it is hoped, lead to optimization techniques for so-called spectral-like methods, which are difference schemes dependent on many free parameters (and for which maximizing the order of accuracy may not be the defining criterion). Though the focus is on schemes for the wave equation in one dimension, the analysis techniques are extended to two dimensions; implicit schemes such as ADI methods are examined in detail. Numerical results are presented. (C) 2004 Wiley Periodicals, Inc.