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Numerische Mathematik

, Volume 136, Issue 1, pp 315–342 | Cite as

On Fourier time-splitting methods for nonlinear Schrödinger equations in the semi-classical limit II. Analytic regularity

  • Rémi CarlesEmail author
  • Clément Gallo
Article

Abstract

We consider the time discretization based on Lie-Trotter splitting, for the nonlinear Schrödinger equation, in the semi-classical limit, with initial data under the form of WKB states. We show that both the exact and the numerical solutions keep a WKB structure, on a time interval independent of the Planck constant. We prove error estimates, which show that the quadratic observables can be computed with a time step independent of the Planck constant. The functional framework is based on time-dependent analytic spaces, in order to overcome a previously encountered loss of regularity phenomenon.

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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institut Montpelliérain Alexander GrothendieckCNRS & Univ. MontpellierMontpellierFrance

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