2021/04/13 by Quispel, G. R. W., McLaren, D. I., Evripidou, C.
#34A05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #G.1.7 #J.2 #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2104.05951
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.