### Operator Splitting, Fast Methods, and Applications

Holge Holden

University of Science and Technology, Norway

Several important problems can be modeled using nonlinear partial differential
equations of convection-diffusion type, the simplest being the Burgers equation.
However, in many cases the diffusion may be degenerate. Furthermore, the equation
can include a source term. The idea of the operator splitting method is to break
the equation into simpler parts, apply fast methods for each of them, and finally
combine the individual computations into an approximate solution of the full
set of equations. We discuss a general mathematical framework for this. Among
the fast methods, we will discuss front tracking in detail.

Applications include two-phase flow in porous media, sedimentation, and gas
dynamics.

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