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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. (2019) Analogues of Kahan's method for higher order equations of higher degree. In: Shi, Y., ed. Springer Proceedings in Mathematics & Statistics. Springer. (In press) (KAR id:81279)

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

Item Type: Book section
Projects: [UNSPECIFIED] 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: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew Hone
Date Deposited: 16 May 2020 11:44 UTC
Last Modified: 18 May 2020 14:09 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/81279 (The current URI for this page, for reference purposes)
Hone, A.N.W.: https://orcid.org/0000-0001-9780-7369
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