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

Abarbanel, S.; Gottlieb, D.

doi:10.1090/S0025-5718-1973-0334541-4

Higher order accuracy finite difference algorithms for quasi-linear, conservation law hyperbolic systems
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by S. Abarbanel and D. Gottlieb PDF

Math. Comp. 27 (1973), 505-523 Request permission

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 $d\;(d > 2)$ 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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