Stability of pseudospectral and finite-difference methods for variable coefficient problems

Authors:
David Gottlieb, Steven A. Orszag and Eli Turkel

Journal:
Math. Comp. **37** (1981), 293-305

MSC:
Primary 65M10

MathSciNet review:
628696

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Abstract: It is shown that pseudospectral approximation to a special class of variable coefficient one-dimensional wave equations is stable and convergent even though the wave speed changes sign within the domain. Computer experiments indicate similar results are valid for more general problems. Similarly, computer results indicate that the leapfrog finite-difference scheme is stable even though the wave speed changes sign within the domain. However, both schemes can be asymptotically unstable in time when a fixed spatial mesh is used.

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DOI:
https://doi.org/10.1090/S0025-5718-1981-0628696-6

Article copyright:
© Copyright 1981
American Mathematical Society