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Relaxation scheme for the nonlinear Schrödinger equation and Davey-Stewartson systems. (Schéma de relaxation pour l’équation de Schrödinger non linéaire et les systèmes de Davey et Stewartson.) (French. Abridged English version) Zbl 0911.65072
Summary: We introduce a new numerical scheme for the nonlinear Schrödinger equation and the Davey-Stewartson systems. This is a relaxation type scheme that avoids the resolution of nonlinear systems. We give convergence results for the semi-discrete version, locally in time for all data and globally in time for small data.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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