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Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime

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Abstract

The error behavior of exponential operator splitting methods for nonlinear Schrödinger equations in the semiclassical regime is studied. For the Lie and Strang splitting methods, the exact form of the local error is determined and the dependence on the semiclassical parameter is identified. This is enabled within a defect-based framework which also suggests asymptotically correct a posteriori local error estimators as the basis for adaptive time stepsize selection. Numerical examples substantiate and complement the theoretical investigations.

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Authors and Affiliations

  1. Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Wien, Austria

    Winfried Auzinger

  2. Institut für Mathematik, Leopold-Franzens Universität Innsbruck, Technikerstraße 13, 6020, Innsbruck, Austria

    Thomas Kassebacher & Mechthild Thalhammer

  3. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria

    Othmar Koch

Authors
  1. Winfried Auzinger
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  2. Thomas Kassebacher
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  3. Othmar Koch
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  4. Mechthild Thalhammer
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Correspondence to Thomas Kassebacher.

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Auzinger, W., Kassebacher, T., Koch, O. et al. Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime. Numer Algor 72, 1–35 (2016). https://doi.org/10.1007/s11075-015-0032-4

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  • DOI: https://doi.org/10.1007/s11075-015-0032-4

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