Journal
JOURNAL OF COMPUTATIONAL MATHEMATICS
Volume 34, Issue 5, Pages 479-498Publisher
GLOBAL SCIENCE PRESS
DOI: 10.4208/jcm.1601-m2015-0265
Keywords
Hamiltonian systems; B-series; Energy-preserving method; Sixth order AVF method; Substitution law
Categories
Funding
- Jiangsu Collaborative Innovation Center for Climate Change
- National Natural Science Foundation of China [11271195, 41231173]
- Priority Academic Program Development of Jiangsu Higher Education Institutions
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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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