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Plane wave stability of some conservative schemes for the cubic Schrödinger equation

Published online by Cambridge University Press:  08 July 2009

Morten Dahlby  and
Brynjulf Owren
Morten Dahlby
Affiliation:
Department of Mathematical Sciences, NTNU, 7491 Trondheim, Norway. dahlby@math.ntnu.no; brynjulf.owren@math.ntnu.no
Brynjulf Owren
Affiliation:
Department of Mathematical Sciences, NTNU, 7491 Trondheim, Norway. dahlby@math.ntnu.no; brynjulf.owren@math.ntnu.no
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Abstract

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.

Keywords

Finite difference methodstabilityenergy conservationnonlinear Schrödinger equationlinearly implicit methods.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 4: Special issue on Numerical ODEs today , July 2009 , pp. 677 - 687
Copyright
© EDP Sciences, SMAI, 2009

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