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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.

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Monotone difference approximations for scalar conservation laws
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by Michael G. Crandall and Andrew Majda PDF
Math. Comp. 34 (1980), 1-21 Request permission


A complete self-contained treatment of the stability and convergence properties of conservation-form, monotone difference approximations to scalar conservation laws in several space variables is developed. In particular, the authors prove that general monotone difference schemes always converge and that they converge to the physical weak solution satisfying the entropy condition. Rigorous convergence results follow for dimensional splitting algorithms when each step is approximated by a monotone difference scheme. The results are general enough to include, for instance, Godunov’s scheme, the upwind scheme (differenced through stagnation points), and the Lax-Friedrichs scheme together with appropriate multi-dimensional generalizations.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 34 (1980), 1-21
  • MSC: Primary 65M05
  • DOI:
  • MathSciNet review: 551288