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Fleur McDonald

Doctor of Philosophy, (Mathematics)
Study Completed: 2013
College of Sciences


Thesis Title
Travelling Wave Solutions of Multisymplectic Discretisations of Wave Equations

Read article at Massey Research Online: MRO icon

Symplectic integrators are computer methods for approximating the solutions of equations while preserving their geometric features. Miss McDonald’s research looks to extend this idea to wave equations, which describe universal phenomena of waves in sound, light, and fluids, using numerical methods known as multisymplectic integrators. She does this by looking at a class of equations which possess travelling wave solutions and seeing how well these travelling wave solutions are preserved by multisymplectic methods. She uses two approaches to answer this question – numerical results and backward error analysis. From these two approaches she concluded that travelling wave solutions are preserved by multisymplectic integrators.

Distinguished Professor Robert McLachlan
Associate Professor Bruce Van Brunt