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Computational modeling of dynamical systems. (English) Zbl 1160.65351

Summary: 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.

MSC:

65P99 Numerical problems in dynamical systems
70-08 Computational methods for problems pertaining to mechanics of particles and systems
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References:

[1] DOI: 10.1017/S0962492900002531 · doi:10.1017/S0962492900002531
[2] Eriksson K., Computational Differential Equations (1996) · Zbl 0946.65049
[3] Hoffman J., Encyclopedia of Computational Mechanics
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