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Numerical Algorithms

, Volume 72, Issue 1, pp 1–35 | Cite as

Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime

  • Winfried Auzinger
  • Thomas Kassebacher
  • Othmar Koch
  • Mechthild Thalhammer
Original Paper

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.

Keywords

Nonlinear Schrödinger equations Semiclassical regime Splitting methods Adaptive time integration Local error Convergence 

Mathematics Subject Classifications (2010)

65J10 65L05 65M12 65M15 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Winfried Auzinger
    • 1
  • Thomas Kassebacher
    • 2
  • Othmar Koch
    • 3
  • Mechthild Thalhammer
    • 2
  1. 1.Institute for Analysis and Scientific ComputingVienna University of TechnologyWienAustria
  2. 2.Institut für MathematikLeopold-Franzens Universität InnsbruckInnsbruckAustria
  3. 3.Faculty of MathematicsUniversity of ViennaWienAustria

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