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Lie-Trotter Splitti...
Lie-Trotter Splitting for the Nonlinear Stochastic Manakov System
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- Berg, André (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Cohen, David (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg,Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden
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- Dujardin, G. (author)
- Université de Lille,University of Lille,Univ. Lille, Inria, CNRS, UMR 8524 - Laboratoire Paul Painlevé, Villeneuve-d’Ascq, France
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(creator_code:org_t)
- 2021-05-22
- 2021
- English.
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In: Journal of Scientific Computing. - : Springer Science and Business Media LLC. - 0885-7474 .- 1573-7691. ; 88:1
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Abstract
Subject headings
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- This article analyses the convergence of the Lie-Trotter splitting scheme for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefringent optical fibers. First, we prove that the strong order of the numerical approximation is 1/2 if the nonlinear term in the system is globally Lipschitz. Then, we show that the splitting scheme has convergence order 1/2 in probability and almost sure order 1/2- in the case of a cubic nonlinearity. We provide several numerical experiments illustrating the aforementioned results and the efficiency of the Lie-Trotter splitting scheme. Finally, we numerically investigate the possible blowup of solutions for some power-law nonlinearities.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- Stochastic partial differential equations
- Stochastic Manakov equation
- Coupled system of stochastic nonlinear Schrodinger equations
- Numerical
- schemes
- Splitting scheme
- Lie-Trotter scheme
- Strong convergence
- Convergence in probability
- Almost sure convergence
- Convergence rates
- Blowup
- polarization mode dispersion
- schrodinger-equation
- optical-fibers
- diffusion
- Mathematics
- Convergence rates
Publication and Content Type
- ref (subject category)
- art (subject category)
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