document: Operator splitting and approximate factorization for taxis-diffusion-reaction models 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 -LRB- Method of Lines -RRB- . 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
doc_bio_tags: B I O B I O O O O O O O O O B I O O O O O O O O O O B I O O B I O B I O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I I O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: operator splitting numerical solution mathematical biology spatial discretization pde systems nonlinear odes numerical integration approximate matrix factorization approximate factorization
abstractive_keyphrases: runge-kutta methods linearly implicit runge-kutta-rosenbrock methods taxis-diffusion-reaction models