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Zbl 0593.65087
Sanz-Serna, J.M.; Verwer, J.G.
Conservative and nonconservative schemes for the solution of the nonlinear Schrödinger equation. (English)
[J] IMA J. Numer. Anal. 6, 25-42 (1986). ISSN 0272-4979; ISSN 1464-3642/e

Authors' summary: Five methods for the integration in time of a semidiscretization of the nonlinear Schrödinger equation are extensively tested. Three of them (a partly explicit scheme and two splitting procedures) are found to perform poorly. The reasons for their failure, including the so-called nonlinear blow-up, are analysed. We draw general conclusions on the advantages and drawbacks associated with the use of time-integrators which exactly conserve energy.
[Michael Sever (Jerusalem)]

MSC 2000:: *65Z05 Applications to physics
81Q05 Closed and approximate solutions to quantum-mechanical equations
65M06 Finite difference methods (IVP of PDE)
65M20 Method of lines (IVP of PDE)

Keywords: conservative schemes; nonconservative schemes; semidiscretization; nonlinear Schrödinger equation; explicit scheme; splitting; nonlinear blow-up; time-integrators

Cited in: Zbl 0702.65096

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