  We present an approach for the efficient implementation of self-adjusting
multi-rate Runge-Kutta methods and we extend the previously available stability
analyses of these methods to the case of an arbitrary number of sub-steps for
the active components. We propose a physically motivated model problem that can
be used to assess the stability of different multi-rate versions of standard
Runge-Kutta methods and the impact of different interpolation methods for the
latent variables. Finally, we present the results of several numerical
experiments, performed with implementations of the proposed methods in the
framework of the \textit{OpenModelica} open-source modelling and simulation
software, which demonstrate the efficiency gains deriving from the use of the
proposed multi-rate approach for physical modelling problems with multiple time
scales.
