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Mathematics of Computation

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Seven-point difference schemes for hyperbolic equations

Author: Avishai Livne
Journal: Math. Comp. 29 (1975), 425-433
MSC: Primary 65M05
MathSciNet review: 0398114
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Abstract: A necessary and sufficient condition is given for all hyperbolic difference schemes that use up to nine mesh points to be of second-order accuracy. We also construct a new difference scheme for two-dimensional hyperbolic systems of conservation laws. The scheme is of second-order accuracy and requires knowledge of only seven mesh points. A stability condition is obtained and is utilized in numerical computations.

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Keywords: Quasi-linear hyperbolic equations, finite-difference schemes, Lax-Wendroff, seven points, consistency, stability conservation laws
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society