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