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Optimal error estimate of a compact scheme for nonlinear Schrodinger equation

文献类型：期刊论文

作者Hong, Jialin1; Ji, Lihai2; Kong, Linghua3; Wang, Tingchun4
刊名APPLIED NUMERICAL MATHEMATICS
出版日期2017-10-01
卷号120页码:68-81
关键词Nonlinear Schrodinger equation Compact scheme Symplectic scheme Energy conservation Optimal error estimate
ISSN号0168-9274
DOI10.1016/j.apnum.2017.05.004
英文摘要It 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.
资助项目NNSFC[11571181] ; NNSFC[91530118] ; NNSFC[11471310] ; NNSFC[91630312] ; NNSFC[11021101] ; NNSFC[11290142] ; NNSFC[11601032]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000406575200005
出版者ELSEVIER SCIENCE BV
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/26287]  
专题计算数学与科学工程计算研究所
通讯作者Wang, Tingchun
作者单位1.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
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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