Volume 34, Issue 5
A Sixth Order Averaged Vector Field Method

J. Comp. Math., 34 (2016), pp. 479-498.

Published online: 2016-10

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• 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.

• Keywords

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

65D15 65L05 65L70 65P10.

lihaochen_bjut@sina.com (Haochen Li)

wangyushun@njnu.edu.cn (Yushun Wang)

qmz@lsec.cc.ac.cn (Mengzhao Qin)

• BibTex
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@Article{JCM-34-479, author = {Li , Haochen and Wang , Yushun and Qin , Mengzhao }, title = {A Sixth Order Averaged Vector Field Method}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {5}, pages = {479--498}, 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.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1601-m2015-0265}, url = {http://global-sci.org/intro/article_detail/jcm/9808.html} }
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 KW - B-series KW - Energy-preserving method KW - Sixth order AVF method KW - Substitution law AB - 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.
Haochen Li , Yushun Wang & Mengzhao Qin . (2020). A Sixth Order Averaged Vector Field Method. Journal of Computational Mathematics. 34 (5). 479-498. doi:10.4208/jcm.1601-m2015-0265
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