This paper contains a study of a simple multirate scheme, consisting of the θ-method with one level of temporal local refinement. Issues of interest are local accuracy, propagation of interpolation errors and stability. The theoretical results are illustrated by numerical experiments, including results for more levels of refinement with automatic partitioning.
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Modelling, Analysis and Simulation [MAS]
Multiscale Dynamics

Hundsdorfer, W, & Savcenco, V. (2006). Analysis of a multirate θ-method for stiff ODEs. Modelling, Analysis and Simulation [MAS]. CWI.