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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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Higher order accuracy finite difference algorithms for quasi-linear, conservation law hyperbolic systems
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by S. Abarbanel and D. Gottlieb PDF
Math. Comp. 27 (1973), 505-523 Request permission

Abstract:

An explicit algorithm that yields finite difference schemes of aly desired order of accuracy for solving quasi-linear hyperbolic systems of partial differential equations in several space dimensions is presented. These schemes are shown to be stable under certain conditions. The stability conditions in the one-dimensional case are derived for any order of accuracy. Analytic stability proofs for two and $d\;(d > 2)$ space dimensions are also obtained up to and including third order accuracy. A conjecture is submitted for the highest accuracy schemes in the multi-dimensional cases. Numerical examples show that the above schemes have the stipulated accuracy and stability.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Math. Comp. 27 (1973), 505-523
  • MSC: Primary 65M10
  • DOI: https://doi.org/10.1090/S0025-5718-1973-0334541-4
  • MathSciNet review: 0334541