Numerical methods for nonlinear reaction-diffusion equations with traveling wave solutions

In this report, we first introduce operator splitting as a way to solve nonlinear reaction-diffusion PDEs. We then present a flux-limiting technique for anisotropic diffusion problems that allows to recover the discrete maximum principle. Finally, we implement a simple action potential model, which allows us to represent the evolution of the transmembrane potential of a stimulated cell, and investigate the effect of anisotropic diffusion on the positivity of this potential.