Self adjusting multirate methods for accurate and efficient time discretization of PDEs

After a short general introduction on multirate methods, self adjusting multirate methods based on implicit schemes will be reviewed in greater detail and a general approach for their  linear stability analysis will be presented. Specific examples of these methods employing efficient DIRK solvers such as the TR-BDF2 method will also be introduced.A number of numerical experiments will  demonstrate the efficiency and accuracyof the resulting approach for the time discretization of partial differential equations, with special focus on systems of hyperbolic equations.