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Journal Articles Stochastics and Partial Differential Equations: Analysis and Computations Year : 2017

Exponential integrators for nonlinear Schrödinger equations with white noise dispersion

Abstract

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 $L 2-norm$ of the solution.
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Dates and versions

hal-01403036 , version 1 (25-11-2016)

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David Cohen, Guillaume Dujardin. Exponential integrators for nonlinear Schrödinger equations with white noise dispersion. Stochastics and Partial Differential Equations: Analysis and Computations, 2017, pp.592-613. ⟨10.1007/s40072-017-0098-1⟩. ⟨hal-01403036⟩
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