  We propose a self adjusting multirate method based on the TR-BDF2 solver. The
potential advantages of using TR-BDF2 as the key component of a multirate
framework are highlighted. A linear stability analysis of the resulting
approach is presented and the stability features of the resulting algorithm are
analysed. The analysis framework is completely general and allows to study
along the same lines the stability of self adjusting multirate methods based on
a generic one step solver. A number of numerical experiments demonstrate the
efficiency and accuracy of the resulting approach also the time discretization
of hyperbolic partial differential equations.
