Virtual slow manifolds: The fast stochastic case

C. W. Gear, D. Givon, I. G. Kevrekidis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The persistently fast evolutionary behavior of certain differential systems may have intrinsically slow features. We consider fast stochastic 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-wise 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 important computations there.

Original languageEnglish (US)
Title of host publicationNumerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009
Pages17-20
Number of pages4
DOIs
StatePublished - Nov 26 2009
EventInternational Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 - Rethymno, Crete, Greece
Duration: Sep 18 2009Sep 22 2009

Publication series

NameAIP Conference Proceedings
Volume1168
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

OtherInternational Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009
CountryGreece
CityRethymno, Crete
Period9/18/099/22/09

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Keywords

  • Equation Free
  • Legacy Codes
  • Projective Integration
  • Steady State

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    Gear, C. W., Givon, D., & Kevrekidis, I. G. (2009). Virtual slow manifolds: The fast stochastic case. In Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 (pp. 17-20). (AIP Conference Proceedings; Vol. 1168). https://doi.org/10.1063/1.3241421