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Computational modeling of dynamical systems

Journal article
Authors Johan Jansson
Claes Johnson
Anders Logg
Published in Mathematical Models and Methods in Applied Sciences
Volume 15
Issue 3
Pages 471-481
ISSN 0218-2025
Publication year 2005
Published at Department of Mathematical Sciences
Department of Mathematical Sciences, Mathematics
Pages 471-481
Language en
Links dx.doi.org/10.1142/S021820250500043...
Keywords Automation , Dynamical system , Modeling , Reduced model
Subject categories Mathematics, Computational Mathematics

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. © World Scientific Publishing Company.

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