 An adaptive time-stepping fully discrete scheme for stochastic NLS equation: Strong convergence and numerical asymptoticsChuchu Chen, Tonghe Dang and Jialin Hong Stochastic Processes and their Applications, 2024, vol. 173, issue C Abstract: In this paper, we propose and analyze an adaptive time-stepping fully discrete scheme which possesses the optimal strong convergence order for the stochastic nonlinear Schrödinger equation with multiplicative noise. Based on the splitting skill and the adaptive strategy, the H1-exponential integrability of the numerical solution is obtained, which is a key ingredient to derive the strong convergence order. We show that the proposed scheme converges strongly with orders 12 in time and 2 in space. To investigate the numerical asymptotic behavior, we establish the large deviation principle for the numerical solution. This is the first result on the study of the large deviation principle for the numerical scheme of stochastic partial differential equations with superlinearly growing drift. And as a byproduct, the error of the masses between the numerical and exact solutions is finally obtained. Keywords: Stochastic nonlinear Schrödinger equation; Adaptive time-stepping fully discrete scheme; Strong convergence; Large deviation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:173:y:2024:i:c:s0304414924000796 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2024.104373 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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