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A Stroboscopic Numerical Method for Highly Oscillatory Problems

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Numerical Analysis of Multiscale Computations

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 82))

Abstract

We suggest a method for the integration of highly oscillatory systems with a single high frequency. The new method may be seen as a purely numerical way of implementing the analytical technique of stroboscopic averaging. The technique may be easily implemented in combination with standard software and may be applied with variable step sizes. Numerical experiments show that the suggested algorithms may be substantially more efficient than standard numerical integrators.

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Acknowledgements

This research has been supported by ‘Acción Integrada entre España y Francia’ HF2008-0105. M.P. Calvo and J.M. Sanz-Serna are also supported by project MTM2007-63257 (Ministerio de Educación, España). A. Murua is also supported by projects MTM2007-61572 (Ministerio de Educación, España) and EHU08/43 (Universidad del País Vasco/Euskal Herriko Unibertsitatea).

Author information

Authors and Affiliations

  1. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid, Valladolid, Spain

    Mari Paz Calvo & Jesús María Sanz-Serna

  2. INRIA Rennes, ENS Cachan Bretagne, Campus Ker-Lann, av. Robert Schumann, 35170, Bruz, France

    Philippe Chartier

  3. Konputazio Zientziak eta A. A. Saila, Informatika Fakultatea, UPV/EHU, E–20018, Donostia–San Sebastián, Spain

    Ander Murua

Authors
  1. Mari Paz Calvo
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  2. Philippe Chartier
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  3. Ander Murua
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  4. Jesús María Sanz-Serna
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Corresponding author

Correspondence to Jesús María Sanz-Serna .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of Texas, University Station C 1200 1, Austin, 78712-0257, Texas, USA

    Björn Engquist

  2. Dept. Numerical Analysis &, Computer Science (NADA), Royal Institute of Technology (KTH), Lindstedtsvägen 3, Stockholm, 100 44, Sweden

    Olof Runborg

  3. , Department of Mathematics, University of Texas at Austin, University Station C1200 1, Austin, 78712-0257, Texas, USA

    Yen-Hsi R. Tsai

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Calvo, M.P., Chartier, P., Murua, A., Sanz-Serna, J.M. (2012). A Stroboscopic Numerical Method for Highly Oscillatory Problems. 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. https://doi.org/10.1007/978-3-642-21943-6_4

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