A third-order accurate variation nonexpansive difference scheme for single nonlinear conservation laws

Author:
Richard Sanders

Journal:
Math. Comp. **51** (1988), 535-558

MSC:
Primary 65M10; Secondary 35L65

DOI:
https://doi.org/10.1090/S0025-5718-1988-0935073-3

MathSciNet review:
935073

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Abstract: It was widely believed that all variation nonexpansive finite difference schemes for single conservation laws must reduce to first-order at extreme points of the approximation. It is shown here that this belief is in fact false. A third-order scheme, which at worst may reduce to second order at extreme points, is developed and analyzed. Moreover, extensive numerical experiments indicate that the third-order scheme introduced here yields superior approximations when compared with other variation nonexpansive difference schemes.

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DOI:
https://doi.org/10.1090/S0025-5718-1988-0935073-3

Article copyright:
© Copyright 1988
American Mathematical Society