Exponential integrators for nonlinear Schrödinger equations with white noise dispersion
Journal article, 2017

This article 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.

Nonlinear Schrödinger equation

Exponential integrators

Mean-square convergence

White noise dispersion

Geometric numerical integration

Stochastic partial differential equations

Numerical methods


David Cohen

University of Innsbruck

Umeå University

Guillaume Dujardin

Inria Lille Nord Europe

Lille 1 University of Science and Technology

Stochastics and Partial Differential Equations: Analysis and Computations

2194-0401 (ISSN)

Vol. 5 4 592-613

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