New high order symplectic integrators via generating functions with its application in many-body problem

doi:10.1007/s10543-019-00785-0

	New high order symplectic integrators via generating functions with its application in many-body problem
	Tu, Xiongbiao 1,2; Murua, Ander 3; Tang, Yifa 1,2
刊名	BIT NUMERICAL MATHEMATICS
	2019-11-21
页码	27
关键词	High order Separable Hamiltonian Quadratic
ISSN号	0006-3835
DOI	10.1007/s10543-019-00785-0
英文摘要	A new family of high order one-step symplectic integration schemes for separable Hamiltonian systems with Hamiltonians of the form T(p)+U(q) is presented. The new integration methods are defined in terms of an explicitly defined generating function (of the third kind). They are implicit in q (but explicit in p and the internal states), and require the evaluation of the gradients of T(p) and U(q) and the actions of their Hessians on vectors (the later being relatively cheap in the case of many-body problems). A time-symmetric symplectic method is constructed that has order 10 when applied to Hamiltonian systems with quadratic kinetic energy T(p). It is shown by numerical experiments that the new methods have the expected order of convergence.
资助项目	National Natural Science Foundation of China[11771438] ; Ministerio de Economia y Competitividad (Spain) ; AEI/the Department of Education of the Basque Government through the Consolidated Research Group MATHMODE[MTM2016-77660-P] ; AEI/the Department of Education of the Basque Government through the Consolidated Research Group MATHMODE[IT1294-19]
WOS研究方向	Computer Science ; Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000497830800001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50316]
专题	中国科学院数学与系统科学研究院
通讯作者	Tu, Xiongbiao
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Univ Basque Country, Informat Fak, Konputazio Zientziak & AA Saila, E-20018 Donostia San Sebastian, Spain
推荐引用方式 GB/T 7714	Tu, Xiongbiao,Murua, Ander,Tang, Yifa. New high order symplectic integrators via generating functions with its application in many-body problem[J]. BIT NUMERICAL MATHEMATICS,2019:27.
APA	Tu, Xiongbiao,Murua, Ander,&Tang, Yifa.(2019).New high order symplectic integrators via generating functions with its application in many-body problem.BIT NUMERICAL MATHEMATICS,27.
MLA	Tu, Xiongbiao,et al."New high order symplectic integrators via generating functions with its application in many-body problem".BIT NUMERICAL MATHEMATICS (2019):27.