Analysis of a splitting scheme for damped stochastic nonlinear Schrödinger equation with multiplicative noise

Jianbo Cui, Jialin Hong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)

Abstract

In this paper, we investigate the damped stochastic nonlinear Schrödinger (NLS) equation with multiplicative noise and its splitting-based approximation. When the damped effect is large enough, we prove that the solutions of both the damped stochastic NLS equation and the splitting scheme are exponentially stable and possess some exponential integrability. These properties show that the strong order of the scheme is 1 2 and independent of time. Additionally, we analyze the regularity of the Kolmogorov equation with respect to the stochastic NLS equation. As a consequence, the weak order of the scheme is shown to be 1 and independent of time.

Original languageEnglish
Pages (from-to)2045-2069
Number of pages25
JournalSIAM Journal on Numerical Analysis
Volume56
Issue number4
DOIs
Publication statusE-pub ahead of print - 10 Jul 2018

Keywords

  • Damped stochastic nonlinear Schrödinger equation
  • Exponential integrability
  • Kolmogorov equation
  • Strong order
  • Weak order

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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