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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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Stable approximations for hyperbolic systems with moving internal boundary conditions
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by M. Goldberg and S. Abarbanel PDF
Math. Comp. 28 (1974), 413-447 Request permission

Abstract:

The work of Kreiss on the stability theory of difference schemes for the mixed initial boundary value problem for linear hyperbolic systems is extended to deal with the case of the pure initial value problem with an internal boundary. The case of an internal boundary ${X_B}$ that moves with constant speed c is treated, i.e., ${X_B} = {X_0} + ct$. In particular, the stability of "hybrid" schemes is studied by using the Lax-Wendroff scheme at points that are not on the internal boundary, while using a first order accurate scheme at the internal boundary points. Numerical evidence is given that the results of the linear stability analysis describes the qualitative behavior of such schemes for nonlinear cases, when the internal boundary is a shock.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 413-447
  • MSC: Primary 65N10
  • DOI: https://doi.org/10.1090/S0025-5718-1974-0381343-X
  • MathSciNet review: 0381343