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An adaptive time-stepping fully discrete scheme for stochastic NLS equation: Strong convergence and numerical asymptotics

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  • Chen, Chuchu
  • Dang, Tonghe
  • Hong, Jialin

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.

Suggested Citation

  • Chen, Chuchu & Dang, Tonghe & Hong, Jialin, 2024. "An adaptive time-stepping fully discrete scheme for stochastic NLS equation: Strong convergence and numerical asymptotics," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:spapps:v:173:y:2024:i:c:s0304414924000796
    DOI: 10.1016/j.spa.2024.104373
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    References listed on IDEAS

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    1. Gautier, Eric, 2005. "Uniform large deviations for the nonlinear Schrodinger equation with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1904-1927, December.
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