Uniformly accurate time-splitting methods for the semiclassical linear Schr{\"o}dinger equation
Analysis of PDEs
2018-10-15 v2
Abstract
This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schr{\"o}dinger 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.
Cite
@article{arxiv.1601.04825,
title = {Uniformly accurate time-splitting methods for the semiclassical linear Schr{\"o}dinger equation},
author = {Philippe Chartier and Loïc Le Treust and Florian Méhats},
journal= {arXiv preprint arXiv:1601.04825},
year = {2018}
}