convergenceanalysisoftheformalenergiesofsymplecticmethodsforhamiltoniansystems

	convergenceanalysisoftheformalenergiesofsymplecticmethodsforhamiltoniansystems
	Zhang Ruili; Tang Yifa; Zhu Beibei; Tu Xiongbiao; Zhao Yue
	2016
发表期刊	sciencechinamathematics
ISSN	1674-7283
卷号	59 期号:2 页码:379
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
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/41462
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.