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Quantum Simulation

Energy preserving methods for nonlinear Schrödinger equations

arXiv
Authors: Christophe Besse, Stephane Descombes, Guillaume Dujardin, Ingrid Lacroix-Violet

Year

2018

Paper ID

22746

Status

Preprint

Abstract Read

~2 min

Abstract Words

120

Citations

N/A

Abstract

This paper is concerned with the numerical integration in time of nonlinear Schrödinger equations using different methods preserving the energy or a discrete analog of it. The Crank-Nicolson method is a well known method of order 2 but is fully implicit and one may prefer a linearly implicit method like the relaxation method introduced in [10] for the cubic nonlinear Schr{ö}dinger equation. This method is also an energy preserving method and numerical simulations have shown that its order is 2. In this paper we give a rigorous proof of the order of this relaxation method and propose a generalized version that allows to deal with general power law nonlinearites. Numerical simulations for different physical models show the efficiency of these methods.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • This paper is concerned with the numerical integration in time of nonlinear Schrödinger equations using different methods preserving the energy or a discrete analog of it.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1812.04890 [2] arXiv https://arxiv.org/abs/1812.04890 [3] Publisher https://arxiv.org/abs/1812.04890

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