Jansson, Johan; Johnson, Claes; Logg, Anders Computational modeling of dynamical systems. (English) Zbl 1160.65351 Math. Models Methods Appl. Sci. 15, No. 3, 471-481 (2005). 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. Cited in 1 Document MSC: 65P99 Numerical problems in dynamical systems 70-08 Computational methods for problems pertaining to mechanics of particles and systems Keywords:Modeling; dynamical system; reduced model; automation PDFBibTeX XMLCite \textit{J. Jansson} et al., Math. Models Methods Appl. Sci. 15, No. 3, 471--481 (2005; Zbl 1160.65351) Full Text: DOI arXiv 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 [4] Kreiss H.-O., Acta Numer. pp 1– [5] A. Ruhe and D. Skoogh, Applied Parallel Computing – Large Scale Scientific and Industrial Problems, Lecture Notes in Computer Science, eds. B. Kågström (1988) pp. 491–502. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.