A Sixth Order Averaged Vector Field Method

Authors

  • Haochen Li Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Jiangsu, 210023, China
  • Yushun Wang Jiangsu Key Laboratory for NSLSCS, Jiangsu Collaborative Innovation Center of Biomedial Functional Materials, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, Jiangsu, China
  • Mengzhao Qin Lsec, Academy of Mathematics and System Sciences, Chinese Academy of Science, PoBox 2719, Beijing, China

DOI:

https://doi.org/10.4208/jcm.1601-m2015-0265

Keywords:

Hamiltonian systems, B-series, Energy-preserving method, Sixth order AVF method, Substitution law.

Abstract

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 experiments are presented to demonstrate the accuracy and the energy-preserving property of the sixth order AVF method.

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Published

2018-08-22

Issue

Vol. 34 No. 5 (2016)

Section

Articles