ANALYSIS OF A SPLITTING SCHEME FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION WITH MULTIPLICATIVE NOISE

被引：28

作者：

Cui, Jianbo ^{[1
]}

Hong, Jialin ^{[2
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2018年 / 56卷 / 04期

基金：

中国国家自然科学基金;

关键词：

damped stochastic nonlinear Schrodinger equation; exponential integrability; strong order; weak order; Kolmogorov equation; PARTIAL-DIFFERENTIAL-EQUATIONS; CONVERGENCE; APPROXIMATIONS; WHITE; DRIVEN; ORDER;

D O I：

10.1137/17M1154904

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the damped stochastic nonlinear Schrodinger (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.

引用

页码：2045 / 2069

页数：25

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