COMPUTATIONAL MODELING OF DYNAMICAL SYSTEMS
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 10–9 computed over the time interval [0,100], and a lattice consisting of large and small point masses.
References
- Acta Numer. 4, 105 (1995). Crossref, Google Scholar
-
K. Eriksson , Computational Differential Equations ( Cambridge Univ. Press , 1996 ) . Google Scholar - J. Hoffman, Computational modeling of complex flows, PhD thesis, Chalmers Univ. of Technology, 2002 . Google Scholar
- J. Hoffman, J. Jansson and A. Logg, DOLFIN, http://www.fenics.org/dolfin/ . Google Scholar
- Encyclopedia of Computational Mechanics (2004). Google Scholar
- Acta Numer. 1 (1991). Google Scholar
- A. Logg, Automation of computational mathematical modeling, PhD thesis, Chalmers Univ. of Technology, 2004 . Google Scholar
- , Applied Parallel Computing — Large Scale Scientific and Industrial Problems,
Lecture Notes in Computer Science , eds.B. Kågström (1988) pp. 491–502. Google Scholar
| Remember to check out the Most Cited Articles! |
|---|
|
View our Mathematical Modelling books
|
