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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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Existence and uniqueness of traveling waves and error estimates for Godunov schemes of conservation laws
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by Haitao Fan PDF
Math. Comp. 67 (1998), 87-109 Request permission


The existence and uniqueness of the Lipschitz continuous traveling wave of Godunov’s scheme for scalar conservation laws are proved. The structure of the traveling waves is studied. The approximation error of Godunov’s scheme on single shock solutions is shown to be $O(1)\Delta x$.
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Additional Information
  • Haitao Fan
  • Affiliation: Department of Mathematics, Georgetown University, Washington, DC 20057
  • Email:
  • Received by editor(s): February 9, 1996
  • Received by editor(s) in revised form: August 19, 1996
  • Additional Notes: Research supported by NSF Fellowship under Grant DMS-9306064.
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 87-109
  • MSC (1991): Primary 65M10, 35L65
  • DOI:
  • MathSciNet review: 1451320