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A reversible multiscale integration method
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: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 7, no 3, 595-610 p.Article in journal (Refereed) Published
Abstract [en]

A multiscale, time reversible method for computing the effective slow behavior of systems of highly oscillatory ordinary differential equations is presented. The proposed method relies on correctly tracking a set of slow variables that is sufficient to approximate any variable and functional that are slow under the dynamics of the system. The algorithm follows the framework of the heterogeneous multiscale method. The notion of time reversibility in the multiple time-scale setting is discussed. The algorithm requires nontrivial matching between the microscopic state variables and the macroscopic slow ones. Numerical examples show the efficiency of the multiscale method and the advantages of time reversibility.

Place, publisher, year, edition, pages
Duke University Press, 2009. Vol. 7, no 3, 595-610 p.
Keyword [en]
Multiscale methods, highly oscillatory ordinary differential equations, reversible methods
National Category
URN: urn:nbn:se:kth:diva-72335ISI: 000271568500004OAI: diva2:487507
QC 20120201Available from: 2012-01-31 Created: 2012-01-31 Last updated: 2012-02-01Bibliographically approved

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Engquist, Björn
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