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High resolution schemes and the entropy condition. (English) Zbl 0556.65074
Semidiscrete, second order accurate, variation diminishing, five-point band width approximations to scalar conservation laws are constructed. These schemes satisfy a single discrete entropy inequality and converge to the unique physically correct solution. For hyperbolic systems of conservation laws a first accurate scheme of the first author is extended, and it is shown that limit solutions satisfy an entropy inequality. Results concerning discrete shocks, a maximum principle and maximum order of accuracy are obtained and numerical applications are presented.
Reviewer: L.Vulkov

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
76L05 Shock waves and blast waves in fluid mechanics
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