A large-time-stepping scheme for balance equations

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. KHK has been supported in part by an Outstanding Young Investigators Award from the Research Council of Norway.