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

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Article copyright:
© Copyright 1980
American Mathematical Society