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Analogues of Kahan's method for higher order equations of higher degree

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. 175-189. ISBN 978-3-030-56999-0. E-ISBN 978-3-030-57000-2. (doi:10.1007/978-3-030-57000-2_9) (KAR id:81279)


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 order-preserving discretization schemes that are appropriate for certain systems of ordinary differential equations of higher order and higher degree.

Item Type: Book section
DOI/Identification number: 10.1007/978-3-030-57000-2_9
Projects: Cluster algebras with periodicity and discrete dynamics over finite fields
Uncontrolled keywords: Numerical Analysis; Mathematical Physics; Exactly Solvable and Integrable Systems
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Q Science > QA Mathematics (inc Computing science) > QA801 Analytic mechanics
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: Engineering and Physical Sciences Research Council (
Depositing User: Andrew Hone
Date Deposited: 16 May 2020 11:44 UTC
Last Modified: 12 Jul 2022 10:41 UTC
Resource URI: (The current URI for this page, for reference purposes)

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