Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime

Winfried Auzinger, Harald Hofstätter, Othmar Koch, Karolina Kropielnicka and Pranav Singh

Applied Mathematics and Computation, 2019, vol. 362, issue C, -

Abstract: Time dependent Schrödinger equations with conservative force field commonly constitute a major challenge in the numerical approximation, especially when they are analysed in the semiclassical regime. Extremely high oscillations originate from the semiclassical parameter, and call for appropriate methods. We propose to employ a combination of asymptotic Zassenhaus splitting with time adaptivity. While the former turns the disadvantage of the semiclassical parameter into an advantage, leading to highly efficient methods with low error constants, the latter enables to choose an optimal time step and to speed up the calculations when the oscillations subside. We support the results with numerical examples.

Keywords: Numerical time integration; Time adaptivity; Splitting schemes; Asymptotic splittings (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319305338
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:362:y:2019:i:c:8

DOI: 10.1016/j.amc.2019.06.064

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().