Improving the accuracy of the AVF method

Authors:
Jan L. Cieliński
Affiliations:
-
Venue:
Journal of Computational and Applied Mathematics
Year:
2014

Citing 5
Cited 0

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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.