Volume 53, Number 2, March-April 2019
|Page(s)||443 - 473|
|Published online||24 April 2019|
Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation
Univ Rennes, INRIA, CNRS, IRMAR - UMR 6625, 35000, Rennes, France
Aix Marseille Univ, CNRS, Central Marseille, I2M, Marseille, France
Univ Rennes, CNRS, IRMAR - UMR 6625, 35000, Rennes, France
* Corresponding author: firstname.lastname@example.org
Accepted: 3 October 2018
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.
Mathematics Subject Classification: 35Q55 / 35F21 / 65M99 / 76A02 / 76Y05 / 81Q20 / 82D50
Key words: Schrödinger equation / semiclassical limit / numerical simulation / uniformly accurate / Madelung transform / splitting schemes
© EDP Sciences, SMAI 2019
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