Stability Limitations in Simulation of Dynamical Systems with Multiple Time-Scales
Paper i proceeding, 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

Författare

Sadegh Rahrovani

Dynamik

Thomas Abrahamsson

Dynamik

Klas Modin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Conference Proceedings of the Society for Experimental Mechanics Series

2191-5652 (eISSN)

Vol. 1 93-105

Ämneskategorier

Annan maskinteknik

Matematisk analys

Fundament

Grundläggande vetenskaper

Infrastruktur

C3SE (Chalmers Centre for Computational Science and Engineering)

DOI

10.1007/978-3-319-15221-9_7

ISBN

978-3-319-15221-9