Globally conservative properties and error estimation of a multi-symplectic scheme for Schrodinger equations with variable coefficients

doi:10.1016/j.apnum.2005.06.006

	Globally conservative properties and error estimation of a multi-symplectic scheme for Schrodinger equations with variable coefficients
	Hong, JL; Liu, Y ; Munthe-Kaas, H ; Zanna, A
	2006-06-01
发表期刊	APPLIED NUMERICAL MATHEMATICS
ISSN	0168-9274
卷号	56 期号:6 页码:814-843
摘要	Based on the multi-symplecticity of the Schrodinger equations with variable coefficients, we give a multisymplectic numerical scheme, and investigate some conservative properties and error estimation of it. We show that the scheme satisfies discrete normal conservation law corresponding to one possessed by the original equation. and propose global energy transit formulae in temporal direction. We also discuss some discrete properties corresponding to energy conservation laws of the original equations. In numerical experiments, the comparisons with modified Goldberg scheme and Modified Crank-Nicolson scheme are given to illustrate some properties of the multi-symplectic scheme in the numerical implementation, and the global energy transit is monitored due to the scheme does not preserve energy conservation law. Our numerical experiments show the match between theoretical and corresponding numerical results. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.
关键词	Schrodinger equations conservation laws error estimation global energy transit multi-symplectic integrators
DOI	10.1016/j.apnum.2005.06.006
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000237135600005
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/3513
专题	计算数学与科学工程计算研究所
通讯作者	Hong, JL
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China 2.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China 3.Inst Informat, N-5020 Bergen, Norway
推荐引用方式 GB/T 7714	Hong, JL,Liu, Y,Munthe-Kaas, H,et al. Globally conservative properties and error estimation of a multi-symplectic scheme for Schrodinger equations with variable coefficients[J]. APPLIED NUMERICAL MATHEMATICS,2006,56(6):814-843.
APA	Hong, JL,Liu, Y,Munthe-Kaas, H,&Zanna, A.(2006).Globally conservative properties and error estimation of a multi-symplectic scheme for Schrodinger equations with variable coefficients.APPLIED NUMERICAL MATHEMATICS,56(6),814-843.
MLA	Hong, JL,et al."Globally conservative properties and error estimation of a multi-symplectic scheme for Schrodinger equations with variable coefficients".APPLIED NUMERICAL MATHEMATICS 56.6(2006):814-843.