Improving the accuracy of the AVF method

[摘要] 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. (C) 2013 Elsevier B.V. All rights reserved.

[发布日期] 2014-03-15

[效力级别]  Proceedings Paper

[关键词] Geometric numerical integration;Discrete gradient method;Average vector field method;Locally exact scheme;B-series;Hamiltonian systems