Exponential integrators for nonlinear Schrödinger equations with white noise dispersion
Artikel i vetenskaplig tidskrift, 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.

White noise dispersion

Geometric numerical integration

Stochastic partial differential equations

Mean-square convergence

Exponential integrators

Nonlinear Schrödinger equation

Numerical methods


David Cohen

University of Innsbruck

Umeå universitet

Guillaume Dujardin

Institut National de Recherche en Informatique et en Automatique (INRIA)

Lille I: Universite des Sciences et Technologies de Lille

Stochastics and Partial Differential Equations: Analysis and Computations

2194-0401 (ISSN)

Vol. 5 4 592-613





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