Discretization of polynomial vector fields by polarization
Numerical Analysis
2016-02-17 v1 Exactly Solvable and Integrable Systems
Abstract
A novel integration method for quadratic vector fields was introduced by Kahan in 1993. Subsequently, it was shown that Kahan's method preserves a (modified) measure and energy when applied to quadratic Hamiltonian vector fields. Here we generalize Kahan's method to cubic resp. higher degree polynomial vector fields and show that the resulting discretization also preserves modified versions of the measure and energy when applied to cubic resp. higher degree polynomial Hamiltonian vector fields.
Cite
@article{arxiv.1506.03855,
title = {Discretization of polynomial vector fields by polarization},
author = {Elena Celledoni and Robert I. McLachlan and David I. McLaren and Brynjulf Owren and G. R. W. Quispel},
journal= {arXiv preprint arXiv:1506.03855},
year = {2016}
}