Oscillatory Systems with Three Separated Time Scales: Analysis and Computation

  • Gil Ariel
  • Björn Engquist
  • Yen-Hsi Richard Tsai
Conference paper

DOI: 10.1007/978-3-642-21943-6_2

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 82)
Cite this paper as:
Ariel G., Engquist B., Tsai YH.R. (2012) Oscillatory Systems with Three Separated Time Scales: Analysis and Computation. In: Engquist B., Runborg O., Tsai YH. (eds) Numerical Analysis of Multiscale Computations. Lecture Notes in Computational Science and Engineering, vol 82. Springer, Berlin, Heidelberg

Abstract

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gil Ariel
    • 1
  • Björn Engquist
    • 2
  • Yen-Hsi Richard Tsai
    • 2
  1. 1.Bar-Ilan UniversityRamat GanIsrael
  2. 2.Department of Mathematics and Institute for Computational Engineering and Sciences (ICES)The University of Texas at AustinAustinUSA

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