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

Haochen Li, Yushun Wang & Mengzhao Qin

DOI: 10.4208/jcm.1601-m2015-0265

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.

  • AMS Subject Headings

65D15, 65L05, 65L70, 65P10.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lihaochen_bjut@sina.com (Haochen Li)

wangyushun@njnu.edu.cn (Yushun Wang)

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

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-479, author = {Li , HaochenWang , 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, B-series, Energy-preserving method, Sixth order AVF method, 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.

Li , HaochenWang , Yushun and Qin , Mengzhao. (2016). 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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