Plane wave stability of some conservative schemes for the cubic Schrödinger equation
Department of Mathematical Sciences,
NTNU, 7491 Trondheim, Norway. firstname.lastname@example.org; email@example.com
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.
Mathematics Subject Classification: 65M10 / 35Q55
Key words: Finite difference method / stability / energy conservation / nonlinear Schrödinger equation / linearly implicit methods.
© EDP Sciences, SMAI, 2009