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Optimal error estimate of a compact scheme for nonlinear Schrodinger equation
Hong, Jialin1; Ji, Lihai2; Kong, Linghua3; Wang, Tingchun4
2017-10-01
Source PublicationAPPLIED NUMERICAL MATHEMATICS
ISSN0168-9274
Volume120Pages:68-81
AbstractIt has been pointed out in literature that the symplectic scheme of a nonlinear Hamiltonian system can not preserve the total energy in the discrete sense Ge and Marsden (1988)[10]. Moreover, due to the difficulty in obtaining a priori estimate of the numerical solution, it is very hard to establish the optimal error bound of the symplectic scheme without any restrictions on the grid ratios. In this paper, we develop and analyze a compact scheme for solving nonlinear Schrodinger equation. We introduce a cut-off technique for proving optimal L-infinity error estimate for the compact scheme. We show that the convergence of the compact scheme is of second order in time and of fourth order in space. Meanwhile, we define a new type of energy functional by using a recursion relationship, and then prove that the compact scheme is mass and energy-conserved, symplectic-conserved, unconditionally stable and can be computed efficiently. Numerical experiments confirm well the theoretical analysis results. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.
KeywordNonlinear Schrodinger equation Compact scheme Symplectic scheme Energy conservation Optimal error estimate
DOI10.1016/j.apnum.2017.05.004
Language英语
Funding ProjectNNSFC[11571181] ; NNSFC[91530118] ; NNSFC[11471310] ; NNSFC[91630312] ; NNSFC[11021101] ; NNSFC[11290142] ; NNSFC[11601032]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000406575200005
PublisherELSEVIER SCIENCE BV
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26288
Collection计算数学与科学工程计算研究所
Corresponding AuthorWang, Tingchun
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
2.Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China
3.Jiangxi Normal Univ, Sch Math & Informat Sci, Nanchang 330022, Jiangxi, Peoples R China
4.Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Jiangsu, Peoples R China
Recommended Citation
GB/T 7714
Hong, Jialin,Ji, Lihai,Kong, Linghua,et al. Optimal error estimate of a compact scheme for nonlinear Schrodinger equation[J]. APPLIED NUMERICAL MATHEMATICS,2017,120:68-81.
APA Hong, Jialin,Ji, Lihai,Kong, Linghua,&Wang, Tingchun.(2017).Optimal error estimate of a compact scheme for nonlinear Schrodinger equation.APPLIED NUMERICAL MATHEMATICS,120,68-81.
MLA Hong, Jialin,et al."Optimal error estimate of a compact scheme for nonlinear Schrodinger equation".APPLIED NUMERICAL MATHEMATICS 120(2017):68-81.
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