Deducing properties of ODEs from their discretization
Classical Analysis and ODEs
2021-04-14 v1 Numerical Analysis
Mathematical Physics
math.MP
Numerical Analysis
Abstract
We show that some hard to detect properties of quadratic ODEs (eg certain preserved integrals and measures) can be deduced more or less algorithmically from their Kahan discretization, using Darboux Polynomials (DPs). Somewhat similar results hold for ODEs of higher degree/order using certain other birational discretization methods.
Cite
@article{arxiv.2104.05951,
title = {Deducing properties of ODEs from their discretization},
author = {G. R. W. Quispel and D. I. McLaren and C. Evripidou},
journal= {arXiv preprint arXiv:2104.05951},
year = {2021}
}
Comments
5 pages