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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
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 $d\;(d > 2)$ 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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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