Hone, A.N.W. and Quispel, G.R.W. (2020) Analogues of Kahan's method for higher order equations of higher degree. In: Shi, Y., ed. Asymptotic, Algebraic and Geometric Aspects of Integrable Systems In Honor of Nalini Joshi On Her 60th Birthday, TSIMF, Sanya, China, April 9–13, 2018. Springer Proceedings in Mathematics & Statistics . Springer, Cham, Switzerland, pp. 175189. ISBN 9783030569990. EISBN 9783030570002. (doi:10.1007/9783030570002_9) (KAR id:81279)
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Official URL: http://dx.doi.org/10.1007/9783030570002_9 
Abstract
Kahan introduced an explicit method of discretization for systems of first order differential equations with nonlinearities of degree at most two (quadratic vector fields). Kahan's method has attracted much interest due to the fact that it preserves many of the geometrical properties of the original continuous system. In particular, a large number of Hamiltonian systems of quadratic vector fields are known for which their Kahan discretization is a discrete integrable system. In this note, we introduce a special class of explicit orderpreserving discretization schemes that are appropriate for certain systems of ordinary differential equations of higher order and higher degree.
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