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arXiv · 1601.04825

Uniformly accurate time-splitting methods for the semiclassical linear Schr{\"o}dinger equation

Philippe Chartier·Loïc Le Treust·Florian Méhats
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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.

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Philippe Chartier, Loïc Le Treust, Florian Méhats. 2016-01-19. Uniformly accurate time-splitting methods for the semiclassical linear Schr{\"o}dinger equation. https://arxiv.org/abs/1601.04825

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