Plane wave stability of some conservative schemes for the cubic Schrödinger equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 4, p. 677-687

The plane wave stability properties of the conservative schemes of Besse [SIAM J. Numer. Anal. 42 (2004) 934-952] and Fei et al. [Appl. Math. Comput. 71 (1995) 165-177] for the cubic Schrödinger equation are analysed. Although the two methods possess many of the same conservation properties, we show that their stability behaviour is very different. An energy preserving generalisation of the Fei method with improved stability is presented.

DOI : https://doi.org/10.1051/m2an/2009022
Classification:  65M10,  35Q55
Keywords: finite difference method, stability, energy conservation, nonlinear Schrödinger equation, linearly implicit methods
@article{M2AN_2009__43_4_677_0,
author = {Dahlby, Morten and Owren, Brynjulf},
title = {Plane wave stability of some conservative schemes for the cubic Schr\"odinger equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {43},
number = {4},
year = {2009},
pages = {677-687},
doi = {10.1051/m2an/2009022},
zbl = {1167.65449},
mrnumber = {2542871},
language = {en},
url = {http://www.numdam.org/item/M2AN_2009__43_4_677_0}
}

Dahlby, Morten; Owren, Brynjulf. Plane wave stability of some conservative schemes for the cubic Schrödinger equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 4, pp. 677-687. doi : 10.1051/m2an/2009022. http://www.numdam.org/item/M2AN_2009__43_4_677_0/

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