Improving the accuracy of the AVF method
arXiv:1308.1596
Abstract
The Average Vector Field (AVF) method is a B-series scheme of the second order. As a discrete gradient method it preserves exactly the energy integral for any canonical Hamiltonian system. We present and discuss two locally exact and energy-preserving modifications of the AVF method: AVF-LEX (of the third order) and AVF-SLEX (of the fourth order). Applications to spherically symmetric potentials are given, including a compact explicit expression for the AVF scheme for the Coulomb-Kepler problem.
17 pages plus 2 figures, presented at International Congress on Computational and Applied Mathematics (July 9-13, 2012, Gent, Belgium), Journal of Computational and Applied Mathematics, 2013