Journal of Engineering Mathematics

, Volume 66, Issue 1, pp 153–173

Computation of fluxes of conservation laws


DOI: 10.1007/s10665-009-9307-x

Cite this article as:
Cheviakov, A.F. J Eng Math (2010) 66: 153. doi:10.1007/s10665-009-9307-x


The direct method for the construction of local conservation laws of partial differential equations (PDE) is a systematic method applicable to a wide class of PDE systems (S. Anco and G. Bluman, Eur J Appl Math 13:567–585, 2002). 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.


Conservation lawsDirect construction methodMultipliersSymbolic software

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of SaskatchewanSaskatoonCanada