Journal of Engineering Mathematics

, Volume 60, Issue 3–4, pp 351–363 | Cite as

A large-time-stepping scheme for balance equations

  • Kenneth Hvistendahl Karlsen
  • Siddhartha MishraEmail author
  • Nils Henrik Risebro


A well-balanced, large-time-stepping method for conservation laws with source terms is presented. The numerical method is based on a local reformulation of the balance law as a conservation law with a discontinuous flux function, and the approximate solution of this equation by a front tracking method. This yields an unconditionally stable method which is particularly well suited to calculate stationary states. The viability of this approach is demonstrated by several numerical examples.


Conservation law Discontinuous solution Finite-volume scheme Front tracking Source term Well-balanced scheme 


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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  • Kenneth Hvistendahl Karlsen
    • 1
  • Siddhartha Mishra
    • 1
    Email author
  • Nils Henrik Risebro
    • 1
  1. 1.Centre of Mathematics for Applications (CMA)University of OsloOsloNorway

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