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Exponential integra...
Exponential integrators for nonlinear Schrödinger equations with white noise dispersion
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- Cohen, David (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Department of Mathematics, University of Innsbruck, Innsbruck, Austria,University of Innsbruck,Umeå University
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- Dujardin, Guillaume (författare)
- Institut National de Recherche en Informatique et en Automatique (INRIA),Lille I: Universite des Sciences et Technologies de Lille (USTL),Lille 1 University of Science and Technology (USTL)
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(creator_code:org_t)
- 2017-04-20
- 2017
- Engelska.
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Ingår i: Stochastics and Partial Differential Equations: Analysis and Computations. - New York : Springer. - 2194-0401 .- 2194-041X. ; 5:4, s. 592-613
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Stochastic partial differential equations
- Nonlinear Schrödinger equation
- White noise dispersion
- Numerical methods
- Geometric numerical integration
- Exponential integrators
- Mean-square convergence
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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