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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.


The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme
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by Eitan Tadmor PDF
Math. Comp. 43 (1984), 353-368 Request permission


We study the Lax-Friedrichs scheme, approximating the scalar, genuinely nonlinear conservation law ${u_t} + {f_x}(u) = 0$, where $f(u)$ is, say, strictly convex, $\ddot f \geqslant {\dot a_ \ast } > 0$. We show that the divided differences of the numerical solution at time t do not exceed $2{(t{\dot a_ \ast })^{ - 1}}$. This one-sided Lipschitz boundedness is in complete agreement with the corresponding estimate one has in the differential case; in particular, it is independent of the initial amplitude, in sharp contrast to linear problems. It guarantees the entropy compactness of the scheme in this case, as well as providing a quantitative insight into the large-time behavior of the numerical computation.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Math. Comp. 43 (1984), 353-368
  • MSC: Primary 65M05; Secondary 35L65
  • DOI:
  • MathSciNet review: 758188