In this paper we consider the numerical solution of 2D systems of certain types of taxis-diffusion-reaction equations from mathematical biology. By spatial discretization these PDE systems are approximated by systems of positive, nonlinear ODEs (Method of Lines). The aim of this paper is to examine the numerical integration of these ODE systems for low to moderate accuracy by means of splitting techniques. An important consideration is maintenance of positivity. We apply operator splitting and approximate matrix factorization using low order explicit Runge-Kutta methods and linearly implicit Runge-Kutta-Rosenbrock methods. As a reference method the general purpose solver VODPK is applied.

Ordinary Differential Equations (acm G.1.7), Partial Differential Equations (acm G.1.8)
Method of lines (msc 65M20), General biology and biomathematics (msc 92B05), None of the above, but in MSC2010 section 92Cxx (msc 92C99)
Modelling, Analysis and Simulation [MAS]
Modelling, Analysis and Computation

Gerisch, A, & Verwer, J.G. (2000). Operator splitting and approximate factorization for taxis-diffusion-reaction models. Modelling, Analysis and Simulation [MAS]. CWI.