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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2019

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

Résumé

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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Dates et versions

hal-01257753 , version 1 (18-01-2016)
hal-01257753 , version 2 (11-10-2018)
hal-01257753 , version 3 (26-08-2020)

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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, 2019, 53 (2), pp.443-473. ⟨10.1051/m2an/2018060⟩. ⟨hal-01257753v3⟩
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