Operator splitting and approximate factorization for taxis-diffusion-reaction models

Authors:
A. Gerisch;J. G. Verwer
Affiliations:
Institut für Numerische Mathematik, Fachbereich Mathematik und Informatick, Martin-Luther-Universität Halle-Wittenberg, Postfach, 06099 Halle, Germany;CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Venue:
Applied Numerical Mathematics
Year:
2002

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Abstract

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.