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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Error estimates at low regularity of splitting schemes for NLS
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by Alexander Ostermann, Frédéric Rousset and Katharina Schratz HTML | PDF
Math. Comp. 91 (2022), 169-182 Request permission

Abstract:

We study a filtered Lie splitting scheme for the cubic nonlinear Schrödinger equation. We establish error estimates at low regularity by using discrete Bourgain spaces. This allows us to handle data in $H^s$ with $0<s<1$ overcoming the standard stability restriction to smooth Sobolev spaces with index $s>1/2$ . More precisely, we prove convergence rates of order $\tau ^{s/2}$ in $L^2$ at this level of regularity.
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Additional Information
  • Alexander Ostermann
  • Affiliation: Department of Mathematics, University of Innsbruck, Technikerstr. 13, 6020 Innsbruck, Austria
  • MR Author ID: 134575
  • ORCID: 0000-0003-0194-2481
  • Email: alexander.ostermann@uibk.ac.at
  • Frédéric Rousset
  • Affiliation: Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d’Orsay (UMR 8628), 91405 Orsay Cedex, France
  • Email: frederic.rousset@universite-paris-saclay.fr
  • Katharina Schratz
  • Affiliation: LJLL (UMR 7598), Sorbonne Université, UPMC, 4 place Jussieu, 75005 Paris, France
  • MR Author ID: 990639
  • Email: katharina.schratz@sorbonne-universite.fr
  • Received by editor(s): December 27, 2020
  • Received by editor(s) in revised form: April 23, 2021
  • Published electronically: August 5, 2021
  • Additional Notes: The third author received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 850941).
  • © Copyright 2021 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 169-182
  • MSC (2020): Primary 65M12, 65M70, 35Q41
  • DOI: https://doi.org/10.1090/mcom/3676
  • MathSciNet review: 4350536