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Mathematics of Computation

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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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Article copyright: © Copyright 1981 American Mathematical Society