Approximated exponential integrators for the stochastic Manakov equation
Preprint, 2021

This article presents and analyses an exponential integrator for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefringent optical fibers. We first prove that the strong order of the numerical approximation is 1/2 if the nonlinear term in the system is globally Lipschitz-continuous. Then, we use this fact to prove that the exponential integrator has convergence order 1/2 in probability and almost sure order 1/2, in the case of the cubic nonlinear coupling which is relevant in optical fibers. Finally, we present several numerical experiments in order to support our theoretical findings and to illustrate the efficiency of the exponential integrator as well as a modified version of it.


Andre Berg

Umeå universitet

David Cohen

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Guillaume Dujardin

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

Numerisk analys och simulering av PDE med slumpmässig dispersion

Vetenskapsrådet (VR) (2018-04443), 2019-01-01 -- 2022-12-31.



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