Oscillatory systems with three separated time scales: Analysis and computation

Gil Ariel, Björn Engquist, Yen Hsi Richard Tsai

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations


We study a few interesting issues that occur in multiscale modeling and computation for oscillatory dynamical systems that involve three or more separated scales. A new type of slow variables which do not formally have bounded derivatives emerge from averaging in the fastest time scale. We present a few systems which have such new slow variables and discuss their characterization. The examples motivate a numerical multiscale algorithm that uses nested tiers of integrators which numerically solve the oscillatory system on different time scales. The communication between the scales follows the framework of the Heterogeneous Multiscale Method. The method’s accuracy and efficiency are evaluated and its applicability is demonstrated by examples.

Original languageEnglish
Title of host publicationNumerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009
EditorsOlof Runborg, Bjorn Engquist, Yen-Hsi R. Tsai
PublisherSpringer Verlag
Number of pages23
ISBN (Print)9783642219429
StatePublished - 2012
EventWorkshop on Numerical Analysis and Multiscale Computations, 2009 - Banff, Canada
Duration: 6 Dec 200911 Dec 2009

Publication series

NameLecture Notes in Computational Science and Engineering
ISSN (Print)1439-7358


ConferenceWorkshop on Numerical Analysis and Multiscale Computations, 2009

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2012.


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