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NON-STANDARD DISCRETIZATIONS OF DIFFERENTIAL EQUATIONS

Towler, Kim (2015) NON-STANDARD DISCRETIZATIONS OF DIFFERENTIAL EQUATIONS. Doctor of Philosophy (PhD) thesis, University of Kent,. (KAR id:66665)

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Abstract

This thesis explores non-standard numerical integration methods for a range of

the preservation of various features when moving from the continuous system to a

by Hirota and Kimura (and also Kahan) [21, 32] will be presented along with

Mickens [40].

present a method for finding the most general forms of a non-standard scheme

this method have also been discovered through an alternative method by Roeger

Next we look at discretizing examples of 3-dimensional bi-Hamiltonian systems

method followed by the same method applied to the H´enon-Heiles case (ii) system.

Finally chapter 6 looks at systems with cubic vector fields and limit cycles with

First we look at a trimolecular system and then a Hamiltonian system that has a

quartic potential.

Item Type: Thesis (Doctor of Philosophy (PhD))
Thesis advisor: Hone, Andrew
Uncontrolled keywords: numerical integration, Kahan, Hirota, Kimura, Lotka-Volterra, non-standard discretizatons, Hamiltonian, symplectic
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
SWORD Depositor: System Moodle
Depositing User: System Moodle
Date Deposited: 09 Apr 2018 10:10 UTC
Last Modified: 06 Feb 2020 04:17 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/66665 (The current URI for this page, for reference purposes)
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