On the numerical stability in dynamical distributed simulations

Abstract

This work takes aim at studying numerical stability in distributed simulations through dynamic stabilityand stability criteria for explicit solvers. This is done by studying outer stability limits, for example stabilityconditions when handling unstable subsystems or marginally stable solvers. To conclude global stability of adistributed system simulation both dynamic stability and solver stability must hold, and this work combinesthese stability criteria into one unified criterion for distributed linear dynamical systems. Some examples aregiven in order to both highlight numerical stability issues and to prove stability in different case studies. Thederived stability criterion is also extended to include distributed systems containing non-linear dynamics.