Conjugate symplecticity of second-order linear multi-step methods

doi:10.1016/j.cam.2006.02.042

	Conjugate symplecticity of second-order linear multi-step methods
	Feng, Quan-Dong ; Jiao, Yan-Dong ; Tang, Yi-Fa
	2007-06-01
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	203 期号:1 页码:6-14
摘要	We review the two different approaches for symplecticity of linear multi-step methods (LMSM) by Eirola and Sanz-Serna, Ge and Feng, and by Feng and Tang, Hairer and Leone, respectively, and give a numerical example between these two approaches. We prove that in the conjugate relation G(3)(lambda t) o G(1)(t) = G' o G(1)(lambda tau) with G(3)(tau) being LMSMs, if G(2)(tau) is symplectic, then the B-series error expansions of G(1)(tau), G(2)(tau) and G(3)(tau) of the form G(tau) (Z) = Sigma(+infinity)(i=0) (tau(i)/i!)Z(vertical bar i vertical bar) + tau(s+1) dA(1) + tau(s+2)A(2) + tau(s+3) A(3) + tau(s+4) A(4) + O(tau(s+5)) are equal to those of trapezoid, mid-point and Euler forward schemes up to a parameter theta (completely the same when theta = 1), respectively, this also partially solves a problern due to Hairer. In particular we indicate that the second-order symmetric leap-frog scheme Z(2) = Z(0) + 2 tau J(-1) del H(Z(1)) cannot be conjugate-symplectic via another LMSM. (c) 2006 Elsevier B.V. All rights reserved.
关键词	linear multi-step method step-transition operator B-series conjugate relation symplecticity
DOI	10.1016/j.cam.2006.02.042
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000245530900002
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/4346
专题	计算数学与科学工程计算研究所
通讯作者	Tang, Yi-Fa
作者单位	1.Chinese Acad Sci, LSEC, ICMSEC, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Chinese Acad Sci, Grad Sch, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Feng, Quan-Dong,Jiao, Yan-Dong,Tang, Yi-Fa. Conjugate symplecticity of second-order linear multi-step methods[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2007,203(1):6-14.
APA	Feng, Quan-Dong,Jiao, Yan-Dong,&Tang, Yi-Fa.(2007).Conjugate symplecticity of second-order linear multi-step methods.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,203(1),6-14.
MLA	Feng, Quan-Dong,et al."Conjugate symplecticity of second-order linear multi-step methods".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 203.1(2007):6-14.