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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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:
  • MathSciNet review: 0334541