2020/05/11 by André Berg, David Cohen, Berg, André +3
Economics, Econometrics and Finance · Engineering · Mathematics · #65C30. 65C50. 65J08. 60H15. 60M15. 60-08. 35Q55 #Differential Equations and Numerical Methods #Extremum Seeking Control Systems #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2005.04978
openalex publication_date 2020/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.