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.

White noise dispersion

Geometric numerical integration

Stochastic partial differential equations

Mean-square convergence

Exponential integrators

Nonlinear Schrödinger equation

Numerical methods

Author

David Cohen

University of Innsbruck

Umeå University

Guillaume Dujardin

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

Lille 1 University of Science and Technology

Stochastics and Partial Differential Equations: Analysis and Computations

2194-0401 (ISSN)

Vol. 5 4 592-613

Subject Categories

Mathematics

DOI

10.1007/s40072-017-0098-1

More information

Latest update

9/25/2023