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.
Mots-clés : 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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {677--687},
publisher = {EDP-Sciences},
volume = {43},
number = {4},
year = {2009},
doi = {10.1051/m2an/2009022},
mrnumber = {2542871},
zbl = {1167.65449},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2009022/}
}
TY - JOUR AU - Dahlby, Morten AU - Owren, Brynjulf TI - Plane wave stability of some conservative schemes for the cubic Schrödinger equation JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 677 EP - 687 VL - 43 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2009022/ DO - 10.1051/m2an/2009022 LA - en ID - M2AN_2009__43_4_677_0 ER -
%0 Journal Article %A Dahlby, Morten %A Owren, Brynjulf %T Plane wave stability of some conservative schemes for the cubic Schrödinger equation %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 677-687 %V 43 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2009022/ %R 10.1051/m2an/2009022 %G en %F M2AN_2009__43_4_677_0
Dahlby, Morten; Owren, Brynjulf. Plane wave stability of some conservative schemes for the cubic Schrödinger equation. ESAIM: Modélisation mathématique et analyse numérique, Special issue on Numerical ODEs today, Tome 43 (2009) no. 4, pp. 677-687. doi : 10.1051/m2an/2009022. http://archive.numdam.org/articles/10.1051/m2an/2009022/
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