Multirate partitioned Runge-Kutta methods

The coupling of subsystems in a hierarchical modelling approach leads to different time constants in the dynamical simulation of technical systems. Multirate schemes exploit the different time scales by using different time steps for the subsystems. The stiffness of the system or at least of some subsystems in chemical reaction kinetics or network analysis, for example, forbids the use of explicit integration schemes. To cope with stiff problems, we introduce multirate schemes based on partitioned Runge-Kutta methods which avoid the coupling between active and latent components based on interpolating and extrapolating state variables. Order conditions and test results for such a lower order MPRK method are presented.