Application of Geometric Explicit Runge-Kutta Methods to Pharmacokinetic Models

In an earlier work, the authors proposed a class of geometric explicit Runge- Kutta methods for solving one-dimensional first order Initial Value Problems (IVPs). In this work, some members of this class of schemes which were found to be more accurate are applied to systems of first order ordinary differential equations (ODEs). We present the development of these selected schemes and also study their basic properties vis-a-vis systems of ODEs. We then apply this approach to solve some mathematical models arising in Pharmacokinetics.