Stability Limitations in Simulation of Dynamical Systems with Multiple Time-Scales
Paper in proceedings, 2016

This paper focuses on the stability properties of a recently proposed exponential integrator particularly in simulation of highly oscillatory systems with multiple time-scales. The linear and nonlinear stability properties of the presented exponential integrator have been studied. We illustrate this with the Fermi–Pasta–Ulam (FPU) problem, a highly oscillatory nonlinear system known as a test benchmark for multi-scale time integrators. This example is also illustrative when studying the numerical resonance and algorithmic instability in the multi-time-stepping (MTS) methods, such as in exponential and/or trigonometric integration schemes, since it has no external input force and therefore no real physical resonance.

Algorithmic instability

Linear stability

Numerical resonance

Multiple time-scale

Exponential integrator


Sadegh Rahrovani

Chalmers, Applied Mechanics, Dynamics

Thomas Abrahamsson

Chalmers, Applied Mechanics, Dynamics

Klas Modin

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Conference Proceedings of the Society for Experimental Mechanics Series

2191-5652 (eISSN)

Vol. 1 93-105

Subject Categories

Other Mechanical Engineering

Mathematical Analysis


Basic sciences


C3SE (Chalmers Centre for Computational Science and Engineering)