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Methods for the numerical solution of the nonlinear Schroedinger equation


Author: J. M. Sanz-Serna
Journal: Math. Comp. 43 (1984), 21-27
MSC: Primary 65M10
DOI: https://doi.org/10.1090/S0025-5718-1984-0744922-X
MathSciNet review: 744922
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Abstract: Optimal $ {L^2}$ rates of convergence are established for several fully-discrete schemes for the numerical solution of the nonlinear Schroedinger equation. Both finite differences and finite elements are considered for the discretization in space, while the integration in time is treated either by the leap-frog technique or by a modified Crank-Nicolson procedure, which generalizes the one suggested by Delfour, Fortin and Payne and possesses two useful conserved quantities.


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DOI: https://doi.org/10.1090/S0025-5718-1984-0744922-X
Article copyright: © Copyright 1984 American Mathematical Society