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Exponential integrators for nonlinear Schrödinger equations with white noise dispersion
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Department of Mathematics, University of Innsbruck, Innsbruck, Austria.ORCID iD: 0000-0001-6490-1957
2017 (English)In: Stochastics and Partial Differential Equations: Analysis and Computations, ISSN 2194-0401, Vol. 5, no 4, 592-613 p.Article in journal (Refereed) Published
Abstract [en]

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'>L 2  L2-norm of the solution.

Place, publisher, year, edition, pages
New York: Springer, 2017. Vol. 5, no 4, 592-613 p.
Keyword [en]
Stochastic partial differential equations, Nonlinear Schrödinger equation, White noise dispersion, Numerical methods, Geometric numerical integration, Exponential integrators, Mean-square convergence
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-137244DOI: 10.1007/s40072-017-0098-1OAI: oai:DiVA.org:umu-137244DiVA: diva2:1117092
Funder
Swedish Research Council, 2013-4562
Available from: 2017-06-28 Created: 2017-06-28 Last updated: 2017-11-30Bibliographically approved

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