Preservation of phase space structure in symplectic integration : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Palmerston North, New Zealand

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Title

Preservation of phase space structure in symplectic integration : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Palmerston North, New Zealand

Content partner

Massey University

Collection

Massey Research Online

Description

This thesis concerns the study of geometric numerical integrators and how they preserve phase space structures of Hamiltonian ordinary differential equations. We examine the invariant sets of differential equations and investigate which numerical integrators preserve these sets, and under what conditions. We prove that when periodic orbits of Hamiltonian differential equations are discretized by a symplectic integrator they are preserved in the numerical solution when the integrator step size...

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Format

Research paper

Research format

Thesis

Thesis level

Doctoral

Date created

2009

Creator

O'Neale, Dion Robert James

URL

https://hdl.handle.net/10179/1127

Related subjects

Geometric integrator / Differential equations / Mathematical Sciences / Mathematics / Differential, difference and integral equations

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