Computation of fluxes of conservation laws.

*(English)*Zbl 1193.65155Author’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.

Reviewer: Qin Mengzhao (Beijing)

##### 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 |

##### Keywords:

conservation laws; direct construction method; multipliers; symbolic software; review paper##### References:

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