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Geometric and integrability properties of Kahan?s method: The preservation of certain quadratic integrals

Celledoni, Elena; McLaren, David; Owren, Brynjulf; Quispel, Reinout
Peer reviewed, Journal article
Accepted version
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URI
https://hdl.handle.net/11250/2651890
Date
2019
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  • Institutt for matematiske fag [1396]
  • Publikasjoner fra CRIStin - NTNU [19849]
Original version
10.1088/1751-8121/aafb1e
Abstract
Given a quadratic vector field on possessing a quadratic first integral depending on two of the independent variables, we give a constructive proof that Kahan's discretization method exactly preserves a nearby modified integral. Building on this result, we present a family of integrable quadratic vector fields (including the Euler top) whose Kahan discretization is a family of integrable maps.
Publisher
IOP
Journal
Journal of Physics A: Mathematical and Theoretical

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