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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Stability of pseudospectral and finite-difference methods for variable coefficient problems
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by David Gottlieb, Steven A. Orszag and Eli Turkel PDF
Math. Comp. 37 (1981), 293-305 Request permission

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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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 293-305
  • MSC: Primary 65M10
  • DOI: https://doi.org/10.1090/S0025-5718-1981-0628696-6
  • MathSciNet review: 628696