Integrability properties of Kahan's method
Exactly Solvable and Integrable Systems
2015-06-19 v1 Numerical Analysis
Abstract
We present several novel examples of integrable quadratic vector fields for which Kahan's discretization method preserves integrability. Our examples include generalized Suslov and Ishii systems, Nambu systems, Riccati systems, and the first Painlev\'e equation. We also discuss how Manin transformations arise in Kahan discretizations of certain vector fields.
Keywords
Cite
@article{arxiv.1405.3740,
title = {Integrability properties of Kahan's method},
author = {Elena Celledoni and Robert I McLachlan and David I McLaren and Brynjulf Owren and G R W Quispel},
journal= {arXiv preprint arXiv:1405.3740},
year = {2015}
}