A note on stability of pseudospectral methods for wave propagation

In this paper we deal with the e/ects on stability of subtle di/erences in formulations of pseudospectral methods for solution of the acoustic wave equation. We suppose that spatial derivatives are approximated by Chebyshev pseudospectral discretizations. Through reformulation of the equations as 4rst order hyperbolic systems any appropriate ordinary di/erential equation solver can be used to integrate in time. However, the resulting stability, and hence e6ciency, properties of the numerical algorithms are drastically impacted by the manner in which the absorbing boundary conditions are incorporated. Speci4cally, mathematically equivalent well-posed approaches are not equivalent numerically. An analysis of the spectrum of the resultant system operator predicts these properties. c © 2002 Elsevier Science B.V. All rights reserved. MSC: 65M05; 65M10; 35L05