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BIT Numerical Mathematics

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29-06-2020

Asymptotic preserving trigonometric integrators for the quantum Zakharov system

Authors: Simon Baumstark, Katharina Schratz

Published in: BIT Numerical Mathematics | Issue 1/2021

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Abstract

We present a new class of asymptotic preserving trigonometric integrators for the quantum Zakharov system. Their convergence holds in the strong quantum regime \(\vartheta = 1\) as well as in the classical regime \(\vartheta \rightarrow 0\) without imposing any step size restrictions. Moreover, the new schemes are asymptotic preserving and converge to the classical Zakharov system in the limit \(\vartheta \rightarrow 0\) uniformly in the time discretization parameter. Numerical experiments underline the favorable error behavior of the new schemes with first- and second-order time convergence uniformly in \(\vartheta \), first-order asymptotic convergence in \(\vartheta \) and long time structure preservation properties.

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Title: Asymptotic preserving trigonometric integrators for the quantum Zakharov system
Authors: Simon Baumstark
Katharina Schratz
Publication date: 29-06-2020
Publisher: Springer Netherlands
Published in: BIT Numerical Mathematics / Issue 1/2021
Print ISSN: 0006-3835
Electronic ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-020-00815-2

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