Computing on Virtual Slow Manifolds of Fast Stochastic Systems

C. W. Gear,2 D. Givon and I. G. Kevrekidis
Department of Chemical Engineering,
Princeton University,
Princeton, NJ,
Received 10 January, 2010; accepted in revised form 20 March, 2010
Abstract: The persistently fast evolutionary behavior of certain differential systems may
have intrinsically slow features. We consider systems whose solution trajectories are slowly
changing distributions and assume that we do not have access to the equations of the
system, only to a simulator or legacy code that performs step-by-step time integration of
the system. We characterize the set of all possible instantaneous solutions by points on a
low-dimensional virtual slow manifold (VSM) and show how, when there is a sufficiently
large gap between the time scales of the fast and slow behaviors, we can restrict the
fast behavior observed numerically through simulation to the VSM and perform useful
computations more efficiently there.

c 2010 European Society of Computational Methods in Sciences and Engineering
Keywords: Projective Integration, Steady State, Legacy Codes, Equation Free
Mathematics Subject Classification: 65L05,65M99


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