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A multiscale method for stiff ordinary differential equations with resonance
Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel.
Department of Mathematics, The University of Texas at Austin, Austin, USA.
Department of Mathematics, The University of Texas at Austin, Austin, USA.
2009 (English)In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 78, no 266, 929-956 p.Article in journal (Refereed) Published
Abstract [en]

A multiscale method for computing the effective behavior of a class of stiff and highly oscillatory ordinary differential equations (ODEs) is presented. The oscillations may be in resonance with one another and thereby generate hidden slow dynamics. The proposed method relies on correctly tracking a set of slow variables whose dynamics is closed up to perturbation, and is sufficient to approximate any variable and functional that are slow under the dynamics of the ODE. This set of variables is detected numerically as a preprocessing step in the numerical methods. Error and complexity estimates are obtained. The advantages of the method is demonstrated with a few examples, including a commonly studied problem of Fermi, Pasta, and Ulam.

Place, publisher, year, edition, pages
2009. Vol. 78, no 266, 929-956 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-72518OAI: oai:DiVA.org:kth-72518DiVA: diva2:487721
Note
In Memory of Germund Dahlquist. QC 20120507Available from: 2012-01-31 Created: 2012-01-31 Last updated: 2017-12-08Bibliographically approved

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