Symplectic properties of multistep Runge-Kutta methods

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	Symplectic properties of multistep Runge-Kutta methods
	Xiao, AG ; Tang, YF
	2002-11-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	44 期号:10-11 页码:1329-1338
摘要	We investigate the symplecticity of multistep Runge-Kutta methods,. (MRKMs) as general linear methods (GLMs) for Hamiltonian systems in accordance with the definition due to Bochev and Scovel [1], Eirola and Sanz-Serna [2], and Hairer and Leone [3,4]. We present a necessary and sufficient condition for an MRKM to be symplectic, and show that many typical high-order MRKMs cannot be symplectic unless they degenerate into one-step Runge-Kutta methods (RKMs). We also show that the order of any symplectic two-step RKM is at most 2. We conjecture that there exist order barriers for symplectic MRKMs, and more generally, for symplectic GLMs. (C) 2002 Elsevier Science Ltd. All rights reserved.
关键词	Hamiltonian system multistep Runge-Kutta method symplecticity
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000179530800006
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17565
专题	中国科学院数学与系统科学研究院
通讯作者	Tang, YF
作者单位	1.Acad Sinica, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China 2.Xiangtan Univ, Dept Math, Xiangtan 411105, Peoples R China
推荐引用方式 GB/T 7714	Xiao, AG,Tang, YF. Symplectic properties of multistep Runge-Kutta methods[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2002,44(10-11):1329-1338.
APA	Xiao, AG,&Tang, YF.(2002).Symplectic properties of multistep Runge-Kutta methods.COMPUTERS & MATHEMATICS WITH APPLICATIONS,44(10-11),1329-1338.
MLA	Xiao, AG,et al."Symplectic properties of multistep Runge-Kutta methods".COMPUTERS & MATHEMATICS WITH APPLICATIONS 44.10-11(2002):1329-1338.