A SIXTH ORDER AVERAGED VECTOR FIELD METHOD  

作　　者：Haochen Li Yushun Wang Mengzhao Qin 

机构地区：[1]Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Jiangsu, 210023, China [2]Lsec, Academy of Mathematics and System Sciences, Chinese Academy of Science, PoBox 2719, Beijing, China

出　　处：《Journal of Computational Mathematics》2016年第5期479-498,共20页计算数学（英文）

摘　　要：In this paper, based on the theory of rooted trees and B-series, we propose the concrete formulas of the substitution law for the trees of order = 5. With the help of the new substitution law, we derive a B-series integrator extending the averaged vector field （AVF） methods for general Hamiltonian system to higher order. The new integrator turns out to be order of six and exactly preserves energy for Hamiltonian systems. Numerical exper- iments are presented to demonstrate the accuracy and the energy-preserving property of the sixth order AVF method.In this paper, based on the theory of rooted trees and B-series, we propose the concrete formulas of the substitution law for the trees of order = 5. With the help of the new substitution law, we derive a B-series integrator extending the averaged vector field （AVF） methods for general Hamiltonian system to higher order. The new integrator turns out to be order of six and exactly preserves energy for Hamiltonian systems. Numerical exper- iments are presented to demonstrate the accuracy and the energy-preserving property of the sixth order AVF method.

关 键 词：Hamiltonian systems B-SERIES Energy=preserving method Sixth order AVFmethod Substitution law. 

分 类 号：O[理学]