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

doi:10.1137/17M1154904

	ANALYSIS OF A SPLITTING SCHEME FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION WITH MULTIPLICATIVE NOISE
	Cui, Jianbo 1; Hong, Jialin2
	2018
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	56 期号:4 页码:2045-2069
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.
关键词	damped stochastic nonlinear Schrodinger equation exponential integrability strong order weak order Kolmogorov equation
DOI	10.1137/17M1154904
语种	英语
资助项目	National Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[11290142]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000443291900004
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31150
专题	计算数学与科学工程计算研究所
通讯作者	Cui, Jianbo
作者单位	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
推荐引用方式 GB/T 7714	Cui, Jianbo,Hong, Jialin. ANALYSIS OF A SPLITTING SCHEME FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION WITH MULTIPLICATIVE NOISE[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2018,56(4):2045-2069.
APA	Cui, Jianbo,&Hong, Jialin.(2018).ANALYSIS OF A SPLITTING SCHEME FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION WITH MULTIPLICATIVE NOISE.SIAM JOURNAL ON NUMERICAL ANALYSIS,56(4),2045-2069.
MLA	Cui, Jianbo,et al."ANALYSIS OF A SPLITTING SCHEME FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION WITH MULTIPLICATIVE NOISE".SIAM JOURNAL ON NUMERICAL ANALYSIS 56.4(2018):2045-2069.