Deducing properties of ODEs from their discretization

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...

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Authors: Quispel, G R W, McLaren, D I, Evripidou, C
Format: Article
Language:English
Subjects:
Discretization
Polynomials
Online Access:Get full text
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Summary: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.
ISSN:2331-8422