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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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Computation of steady shocks by second-order finite-difference schemes
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by Lasse K. Karlsen PDF
Math. Comp. 34 (1980), 391-400 Request permission

Abstract:

The computational stability of steady shocks which satisfy the entropy condition is considered for the scalar conservation law \[ \frac {{\partial u}}{{\partial t}} + \frac {\partial }{{\partial x}}\left ( {\frac {1}{2}{u^2}} \right ) = 0.\] It is shown that the computation of the pure initial value problem by Lax-Wendroff type schemes approaches a steady state if the initial data satisfies a specified condition, and that this condition is always satisfied for the corresponding initial-boundary value problem with a finite number of grid points. The effect of machine accuracy on the influence of the boundaries on the error near the shock is also discussed.
References
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 34 (1980), 391-400
  • MSC: Primary 65M10; Secondary 76L05
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0559192-1
  • MathSciNet review: 559192