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Computation of steady shocks by second-order finite-difference schemes


Author: Lasse K. Karlsen
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
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Abstract: The computational stability of steady shocks which satisfy the entropy condition is considered for the scalar conservation law

$\displaystyle \frac{{\partial u}}{{\partial t}} + \frac{\partial }{{\partial x}}\left( {\frac{1}{2}{u^2}} \right) = 0.$

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 [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1980-0559192-1
Article copyright: © Copyright 1980 American Mathematical Society

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