Strong convergence rate of splitting schemes for stochastic nonlinear Schrödinger equations

Jianbo Cui, Jialin Hong, Zhihui Liu, Weien Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

17 Citations (Scopus)

Abstract

In this paper, we show that solutions of stochastic nonlinear Schrödinger (NLS) equations can be approximated by solutions of coupled splitting systems. Based on these systems, we propose a new kind of fully discrete splitting schemes which possess algebraic strong convergence rates for stochastic NLS equations. Key ingredients of our approach are using the exponential integrability and stability of the corresponding splitting systems and numerical approximations. In particular, under very mild conditions, we derive the optimal strong convergence rate O(N −2[Formula presented] ) of the spectral splitting Crank–Nicolson scheme, where N and τ denote the dimension of the approximate space and the time step size, respectively.

Original languageEnglish
Pages (from-to)5625-5663
Number of pages39
JournalJournal of Differential Equations
Volume266
Issue number9
DOIs
Publication statusPublished - 15 Apr 2019
Externally publishedYes

Keywords

  • Exponential integrability
  • Non-monotone coefficients
  • Splitting scheme
  • Stochastic nonlinear Schrödinger equation
  • Strong convergence rate

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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