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On discreteness of the Hopf equation. (English) Zbl 1149.65071
Summary: The principle aim of this essay is to illustrate how different phenomena is captured by different discretizations of the Hopf equation and general hyperbolic conservation laws. This includes dispersive schemes, shock capturing schemes as well as schemes for computing multi-valued solutions of the underlying equation. We introduce some model equations which describe the behavior of the discrete equation more accurate than the original equation. These model equations can either be conveniently discretized for producing novel numerical schemes or further analyzed to enrich the theory of nonlinear partial differential equations.

MSC:
65M06Finite difference methods (IVP of PDE)
35L65Conservation laws
Software:
HLLE
References:
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