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.
CITATION STYLE
Rahrovani, S., Abrahamsson, T., & Modin, K. (2016). Stability limitations in simulation of dynamical systems with multiple time-scales. In Conference Proceedings of the Society for Experimental Mechanics Series (Vol. 1, pp. 93–105). Springer New York LLC. https://doi.org/10.1007/978-3-319-15221-9_7
Mendeley helps you to discover research relevant for your work.