Computational Modeling of Dynamical Systems
Numerical Analysis
2012-05-15 v1
Abstract
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be very costly. By resolving the fast time scales in a short time simulation, a model for the effect of the small time scale variation on large time scales can be determined, making solution possible on a long time interval. This process of computational modeling can be completely automated. Two examples are presented, including a simple model problem oscillating at a time scale of 1e-9 computed over the time interval [0,100], and a lattice consisting of large and small point masses.
Cite
@article{arxiv.1205.2809,
title = {Computational Modeling of Dynamical Systems},
author = {Johan Jansson and Claes Johnson and Anders Logg},
journal= {arXiv preprint arXiv:1205.2809},
year = {2012}
}