Stability analysis of the BDF Slowest-first multirate methods

Stability analysis of the BDF slowest first multirate methods This paper deals with the stability analysis of the BDF Slowest first multirate time-integration methods which are applied to the transient analysis of circuit models. From an asymptotic analysis it appears that these methods are indeed stable if the subsystems are stable and weakly coupled. Index 1. Introduction 1.1. Partition of the system 1.2. Relaxation 1.3. General types of multirate 1.4. Dynamical properties of the active part 1.5. Overview of the paper 2. Stability analysis of multirate schemes 2.1. Stability of multirate scheme 2.2. Two-dimensional test equations 3. Stability analysis of Euler Backward multirate algorithm 3.1. Derivation of the recurrence relation 3.2. Stability conditions 3.3. Asymptotic stability conditions 3.4. Remarks 4. Stability analysis of multistep BDF multirate algorithm 4.1. Derivation of the recurrence relation 4.2. Stability conditions 4.3. Asymptotic stability conditions 4.4. Remarks 5. Conclusions