A numerical conception of entropy for quasilinear equations
Author:
A. Y. le Roux
Journal:
Math. Comp. 31 (1977), 848872
MSC:
Primary 65M10; Secondary 35F25
MathSciNet review:
0478651
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Abstract: A family of difference schemes solving the Cauchy problem for quasilinear equations is studied. This family contains wellknown schemes such as the decentered, Lax, Godounov or LaxWendroff schemes. Two conditions are given, the first assures the convergence to a weak solution and the second, more restrictive, implies the convergence to the solution in Kružkov's sense, which satisfies an entropy condition that guarantees uniqueness. Some counterexamples are proposed to show the necessity of such conditions.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197704786513
PII:
S 00255718(1977)04786513
Article copyright:
© Copyright 1977 American Mathematical Society
