NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME

doi:10.1137/16M1079099

	NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME
	Hong, Jialin1 ; Wang, Xu 1; Zhang, Liying 2
	2017
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	55 期号:1 页码:305-327
摘要	We consider a finite dimensional approximation of the stochastic nonlinear Schrodinger equation driven by multiplicative noise, which is derived by applying a symplectic method to the original equation in spatial direction. Both the unique ergodicity and the charge conservation law for this finite dimensional approximation are obtained on the unit sphere. To simulate the ergodic limit over long time for the finite dimensional approximation, we discretize it further in the temporal direction to obtain a fully discrete scheme, which inherits not only the stochastic multi-symplecticity and charge conservation law of the original equation but also the unique ergodicity of the finite dimensional approximation. The temporal average of the fully discrete numerical solution is proved to converge to the ergodic limit with order 1 with respect to the time step for a fixed spatial step. Numerical experiments verify our theoretical results on charge conservation, ergodicity, and weak convergence.
关键词	stochastic Schriidinger equation multiplicative noise unique ergodicity multisymplectic scheme weak error
DOI	10.1137/16M1079099
语种	英语
资助项目	National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[11290142] ; National Natural Science Foundation of China[11601514]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000396683300014
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/24833
专题	计算数学与科学工程计算研究所
通讯作者	Wang, Xu
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China 2.China Univ Min & Technol, Coll Sci, Dept Math, Beijing 100083, Peoples R China
推荐引用方式 GB/T 7714	Hong, Jialin,Wang, Xu,Zhang, Liying. NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2017,55(1):305-327.
APA	Hong, Jialin,Wang, Xu,&Zhang, Liying.(2017).NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME.SIAM JOURNAL ON NUMERICAL ANALYSIS,55(1),305-327.
MLA	Hong, Jialin,et al."NUMERICAL ANALYSIS ON ERGODIC LIMIT OF APPROXIMATIONS FOR STOCHASTIC NLS EQUATION VIA MULTI-SYMPLECTIC SCHEME".SIAM JOURNAL ON NUMERICAL ANALYSIS 55.1(2017):305-327.