Seven-point difference schemes for hyperbolic equations

Livne, Avishai

doi:10.1090/S0025-5718-1975-0398114-1

Seven-point difference schemes for hyperbolic equations
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Math. Comp. 29 (1975), 425-433 Request permission

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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