Exponential integrators for nonlinear Schrödinger equations with white noise dispersion (David Cohen, Umea)

29.03.2019 10:30

This presentation deals with the numerical integration in time of the nonlinear Schrödinger equation with power law nonlinearity and random dispersion. We introduce a new explicit exponential integrator for this purpose that integrates the noisy part of the equation exactly. We prove that this scheme is of mean-square order 1 and we draw consequences of this fact. We compare our exponential integrator with several other numerical methods from the literature. We finally propose a second exponential integrator, which is implicit and symmetric and, in contrast to the first one, preserves the L2-norm of the solution. This is a joint work with Guillaume Dujardin (INRIA Lille Nord Europe).

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Room 17, Séminaire d'analyse numérique

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