Optimal error estimate of a compact scheme for nonlinear Schrodinger equation

doi:10.1016/j.apnum.2017.05.004

	Optimal error estimate of a compact scheme for nonlinear Schrodinger equation
	Hong, Jialin1 ; Ji, Lihai 2; Kong, Linghua 3; Wang, Tingchun 4
	2017-10-01
发表期刊	APPLIED NUMERICAL MATHEMATICS
ISSN	0168-9274
卷号	120 页码:68-81
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.
关键词	Nonlinear Schrodinger equation Compact scheme Symplectic scheme Energy conservation Optimal error estimate
DOI	10.1016/j.apnum.2017.05.004
语种	英语
资助项目	NNSFC[11571181] ; NNSFC[91530118] ; NNSFC[11471310] ; NNSFC[91630312] ; NNSFC[11021101] ; NNSFC[11290142] ; NNSFC[11601032]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000406575200005
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26288
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.