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Stability Limitations in Simulation of Dynamical Systems with Multiple Time-Scales

Conference paper
Authors Sadegh Rahrovani
Thomas Abrahamsson
Klas Modin
Published in Conference Proceedings of the Society for Experimental Mechanics Series
Volume 1
Pages 93-105
ISBN 978-3-319-15221-9
ISSN 2191-5644
Publication year 2016
Published at Department of Mathematical Sciences, Mathematics
Pages 93-105
Language en
Links dx.doi.org/10.1007/978-3-319-15221-...
Keywords Algorithmic instability; Numerical resonance; Multiple time-scale; Exponential integrator; Linear stability
Subject categories Mathematical Analysis, Other Mechanical Engineering

Abstract

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.

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