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    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.


    • K. Erikssonet al., Acta Numer. 4, 105 (1995). CrossrefGoogle Scholar
    • K.   Eriksson et al. , 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, . Google Scholar
    • J. Hoffman and C. Johnson, Encyclopedia of Computational Mechanics  (2004). Google Scholar
    • H.-O. Kreiss, Acta Numer. 1 (1991). Google Scholar
    • A. Logg, Automation of computational mathematical modeling, PhD thesis, Chalmers Univ. of Technology, 2004 . Google Scholar
    • A. Ruhe and D. Skoogh, Applied Parallel Computing — Large Scale Scientific and Industrial Problems, Lecture Notes in Computer Science, eds. B. Kågströmet al. (1988) pp. 491–502. Google Scholar
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