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Mathematics of Computation

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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
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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Article copyright: © Copyright 1988 American Mathematical Society

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