Symplectic integrator for nonlinear high order Schrodinger equation with a trapped term | |
Kong, Linghua1; Hong, Jialin2; Wang, Lan1; Fu, Fangfang1 | |
刊名 | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS |
2009-09-15 | |
卷号 | 231期号:2页码:664-679 |
关键词 | Schrodinger equation Symplectic scheme Conservation law Trapped term |
ISSN号 | 0377-0427 |
DOI | 10.1016/j.cam.2009.04.023 |
英文摘要 | 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. |
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 |
语种 | 英语 |
出版者 | ELSEVIER SCIENCE BV |
WOS记录号 | WOS:000268515000016 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/7281] |
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. |
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