Stability properties of backward euler multirate formulas

Abstract

Stability properties of multirate formulas cannot be analyzed by a scalar test equation but require at least one equation for each different steplength. This paper generalizes the concept of absolute stability and A-stability for backward Euler multirate formulas. Stability theorems for multirate methods with two and three different steplengths are given, while a general result for an arbitrary number of different steplengths is the topic of future research.