Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation

Philippe Chartier 1, 2 Loïc Le Treust 3, 4 Florian Méhats 2, 1, 5
1 MINGUS - Multi-scale numerical geometric schemes
IRMAR - Institut de Recherche Mathématique de Rennes, ENS Rennes - École normale supérieure - Rennes, Inria Rennes – Bretagne Atlantique
Abstract : This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schrödinger equation in the semiclassical limit. We specifically analyse the convergence behavior of the first-order splitting. Our main result is a proof of uniform accuracy. We illustrate the properties of our methods with simulations.
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Submitted on : Thursday, October 11, 2018 - 6:28:25 PM
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Philippe Chartier, Loïc Le Treust, Florian Méhats. Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2019, 53 (2), pp.443-473. ⟨10.1051/m2an/2018060 ⟩. ⟨hal-01257753v2⟩

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