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Computation of fluxes of conservation laws. (English) Zbl 1193.65155
Author’s abstract: The direct method for the construction of local conservation laws of partial differential equations (PDEs) is a systematic method applicable to a wide class of PDE systems [S. Anco and G. Bluman, Eur. J. Appl. Math. 13, No. 5, 567–585 (2002; Zbl 1034.35071)]. According to the direct method one seeks multipliers, such that the linear combination of PDEs of a given system with these multipliers yields a divergence expression. Once local-conservation-law multipliers have been found, one needs to reconstruct the fluxes of the conservation law. In this review paper, common methods of flux computation are discussed, compared, and illustrated by examples. An implementation of these methods in symbolic software is also presented.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35B06 Symmetries, invariants, etc. in context of PDEs
68W30 Symbolic computation and algebraic computation
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
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