TY - JOUR
T1 - A Sixth Order Averaged Vector Field Method
AU - Li , Haochen
AU - Wang , Yushun
AU - Qin , Mengzhao
JO - Journal of Computational Mathematics
VL - 5
SP - 479
EP - 498
PY - 2016
DA - 2016/10
SN - 34
DO - http://doi.org/10.4208/jcm.1601-m2015-0265
UR - https://global-sci.org/intro/article_detail/jcm/9808.html
KW - Hamiltonian systems, B-series, Energy-preserving method, Sixth order AVF
method, Substitution law.
AB - <p style="text-align: justify;">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.</p>