Abstract

The mathematical modeling of various real life applications leads to systems of ordinary differential equations which include crucial properties like the positivity of the solution as well as the conservation of mass or energy. Based on the fundamental work of Burchard et al. (2003), unconditionally positive and conservative modified Patankar-Runge-Kutta schemes (MPRK) are available. These methods are highly stable and often outperform standard Runge-Kutta schemes.