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This work focuses on the construction of a new class of fourth-order accuratemethods for multirate time evolution of systems of ordinary differentialequations. We base our work on the Recursive Flux Splitting Multirate (RFSMR)version of the Multirate Infinitesimal Step (MIS) methods and use recenttheoretical developments for Generalized Additive Runge-Kutta methods topropose our higher-order Relaxed Multirate Infinitesimal Step extensions. Theresulting framework supports a range of attractive properties for multiratemethods, including telescopic extensions, subcycling, embeddings for temporalerror estimation, and support for changes to the fast/slow time-scaleseparation between steps, without requiring any sacrifices in linear stability.In addition to providing rigorous theoretical developments for these newmethods, we provide numerical tests demonstrating convergence and efficiency ona suite of multirate test problems.

Relaxed Multirate Infinitesimal Step Methods for Initial-Value Problems