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 orderpreserving 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 N W 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/0000000197807369 
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