convergenceanalysisoftheformalenergiesofsymplecticmethodsforhamiltoniansystems

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	convergenceanalysisoftheformalenergiesofsymplecticmethodsforhamiltoniansystems
	Zhang Ruili; Tang Yifa; Zhu Beibei; Tu Xiongbiao; Zhao Yue
刊名	sciencechinamathematics
	2016
卷号	59 期号:2 页码:379
ISSN号	1674-7283
英文摘要	Based on Feng's theory of formal vector fields and formal flows, we study the convergence problem of the formal energies of symplectic methods for Hamiltonian systems and give the clear growth of the coefficients in the formal energies. With the help of B-series and Bernoulli functions, we prove that in the formal energy of the mid-point rule, the coefficient sequence of the merging products of an arbitrarily given rooted tree and the bushy trees of height 1 (whose subtrees are vertices), approaches 0 as the number of branches goes to oo; in the opposite direction, the coefficient sequence of the bushy trees of height m (m ≥ 2), whose subtrees are all tall trees, approaches oo at large speed as the number of branches goes to +oo. The conclusion extends successfully to the modified differential equations of other Runge-Kutta methods. This disproves a conjecture given by Tang et al. (2002), and implies:(1) in the inequality of estimate given by Benettin and Giorgilli (1994) for the terms of the modified formal vector fields, the high order of the upper bound is reached in numerous cases; (2) the formal energies/formal vector fields are nonconvergent in general case.
语种	英语
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/41461]
专题	计算数学与科学工程计算研究所
作者单位	中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Zhang Ruili,Tang Yifa,Zhu Beibei,et al. convergenceanalysisoftheformalenergiesofsymplecticmethodsforhamiltoniansystems[J]. sciencechinamathematics,2016,59(2):379.
APA	Zhang Ruili,Tang Yifa,Zhu Beibei,Tu Xiongbiao,&Zhao Yue.(2016).convergenceanalysisoftheformalenergiesofsymplecticmethodsforhamiltoniansystems.sciencechinamathematics,59(2),379.
MLA	Zhang Ruili,et al."convergenceanalysisoftheformalenergiesofsymplecticmethodsforhamiltoniansystems".sciencechinamathematics 59.2(2016):379.