Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 88, Issue 1, Pages -Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-021-01514-y
Keywords
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
Categories
Funding
- Swedish Research Council (VR) [2018-04443]
- FRO the mobility programs of the French Embassy/Institut francais de Suede
- INRIA Lille Nord-Europe
- Labex CEMPI [ANR-11-LABX-0007-01]
- Swedish Research Council [2018-04443] Funding Source: Swedish Research Council
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This article analyzes the convergence of the Lie-Trotter splitting scheme for the stochastic Manakov equation, proving that the strong order of the numerical approximation is 1/2 under globally Lipschitz nonlinear conditions. It demonstrates that the splitting scheme has a convergence order of 1/2 in probability and almost sure order 1/2- for cubic nonlinearities. Numerical experiments illustrate the results and efficiency of the scheme, while also investigating potential blowup of solutions for certain power-law nonlinearities.
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.
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