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ANALYSIS OF A SPLITTING SCHEME FOR DAMPED STOCHASTIC NONLINEAR SCHRODINGER EQUATION WITH MULTIPLICATIVE NOISE
Cui, Jianbo1; Hong, Jialin2
2018
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume56Issue:4Pages:2045-2069
AbstractIn 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.
Keyworddamped stochastic nonlinear Schrodinger equation exponential integrability strong order weak order Kolmogorov equation
DOI10.1137/17M1154904
Language英语
Funding ProjectNational Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[91530118] ; National Natural Science Foundation of China[11290142]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000443291900004
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31150
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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