Higher order accuracy finite difference algorithms for quasi-linear, conservation law hyperbolic systems

Authors:
S. Abarbanel and D. Gottlieb

Journal:
Math. Comp. **27** (1973), 505-523

MSC:
Primary 65M10

DOI:
https://doi.org/10.1090/S0025-5718-1973-0334541-4

MathSciNet review:
0334541

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Abstract: An explicit algorithm that yields finite difference schemes of aly desired order of accuracy for solving quasi-linear hyperbolic systems of partial differential equations in several space dimensions is presented. These schemes are shown to be stable under certain conditions. The stability conditions in the one-dimensional case are derived for any order of accuracy. Analytic stability proofs for two and space dimensions are also obtained up to and including third order accuracy. A conjecture is submitted for the highest accuracy schemes in the multi-dimensional cases. Numerical examples show that the above schemes have the stipulated accuracy and stability.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0334541-4

Keywords:
Finite difference schemes,
stability,
accuracy,
convergence,
quasi-linear hyperbolic systems,
conservation law forms,
the Lax-Wendroff schemes,
Richtmyer scheme,
von Neumann condition

Article copyright:
© Copyright 1973
American Mathematical Society