Symplectic integrator for nonlinear high order Schrodinger equation with a trapped term

doi:10.1016/j.cam.2009.04.023

	Symplectic integrator for nonlinear high order Schrodinger equation with a trapped term
	Kong, Linghua 1; Hong, Jialin2 ; Wang, Lan 1; Fu, Fangfang 1
	2009-09-15
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	231 期号:2 页码:664-679
摘要	In the manuscript, we discuss the symplectic integrator for the numerical solution of a kind of high order Schrodinger equation with trapped terms. The Hamiltonian formulism is discovered for it. We first discretize the Hamiltonian system in space to reduce it to a finite-dimensional one. Then the symplectic midpoint scheme is applied to the temporal discretization. The symplectic scheme we devise is of second order accuracy in time and 21th order accuracy in space. It is proved that it preserves the charge of the original equation veraciously. The energy is not preserved explicitly for the exception of the linear case. However, after some computation, the energy transit formula in the temporal direction is obtained. In the numerical part, we compare our scheme with some existing schemes, including the leap frog scheme and the energy-preserving scheme. From the numerical evidence, we find that our numerical schemes are efficient and available. The numerical results are consistent with the theoretical analysis. (C) 2009 Elsevier B.V. All rights reserved.
关键词	Schrodinger equation Symplectic scheme Conservation law Trapped term
DOI	10.1016/j.cam.2009.04.023
语种	英语
资助项目	provincial natural science foundation of Jiangxi[2008GQS0054] ; foundation of department of education Jiangxi province[GJJ09147] ; Doctor Foundation of Jiangxi Normal University[2057] ; Young Growth Foundation of Jiangxi Normal University[2390] ; State Key Laboratory of Scientific and Engineering Computing, CAS ; Director Innovation Foundation of ICMSEC and AMSS ; Foundation of CAS ; NNSFC[19971089] ; NNSFC[10371128] ; NNSFC[60771054] ; Special Funds for Major State Basic Research Projects of China[2005CB321701] ; Innovation Foundation of Jiangxi Normal University
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000268515000016
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/7282
专题	计算数学与科学工程计算研究所
通讯作者	Kong, Linghua
作者单位	1.Jiangxi Normal Univ, Sch Math & Informat Sci, Nanchang 330022, Jiangxi, Peoples R China 2.Chinese Acad Sci, AMSS, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Kong, Linghua,Hong, Jialin,Wang, Lan,et al. Symplectic integrator for nonlinear high order Schrodinger equation with a trapped term[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2009,231(2):664-679.
APA	Kong, Linghua,Hong, Jialin,Wang, Lan,&Fu, Fangfang.(2009).Symplectic integrator for nonlinear high order Schrodinger equation with a trapped term.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,231(2),664-679.
MLA	Kong, Linghua,et al."Symplectic integrator for nonlinear high order Schrodinger equation with a trapped term".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 231.2(2009):664-679.