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

S. Abarbanel, D. Gottlieb

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

An explicit algorithm that yields finite difference schemes of any 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.

Original languageEnglish
Pages (from-to)505-523
Number of pages19
JournalMathematics of Computation
Volume27
Issue number123
DOIs
StatePublished - Jul 1973
Externally publishedYes

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