Numerical simulation of a contractivity based multiscale cancer invasion   model
  We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that describes the macroscopic dynamics of two types of cancer cells coupled with microscopic dynamics of the cells adhesion on the extracellular matrix. The difficulties to overcome arises from the non-constant advection and diffusion coefficients, a time delay term, as well as stiff reaction terms. Our numerical method is a second order finite volume implicit-explicit scheme adjusted to include a) non-constant diffusion coefficients in the implicit part, b) an interpolation technique for the time delay, and c) a restriction on the time increment for the stiff reaction terms. 
Niklas Kolbe and Maria Lukacova-Medvidova and Nikolaos Sfakianakis and   Bettina Wiebe
math.NA