dc.contributor.advisor | Buono, Pietro-Luciano | |
dc.contributor.advisor | Van Veen, Lennaert | |
dc.contributor.author | Kovacic, Mitchell | |
dc.date.accessioned | 2013-09-27T19:59:03Z | |
dc.date.accessioned | 2022-03-29T17:05:57Z | |
dc.date.available | 2013-09-27T19:59:03Z | |
dc.date.available | 2022-03-29T17:05:57Z | |
dc.date.issued | 2013-08-01 | |
dc.identifier.uri | https://hdl.handle.net/10155/345 | |
dc.description.abstract | In this thesis we examine a recent animal aggregation model which describes the
evolution of two populations of animals moving on a 1-dimensional spatial domain
differing only by the direction they travel. The equations describing the evolution of
the populations is a hyperbolic, nonlocal partial di erential equation with periodic
boundary conditions [5].
We apply pseudo-spectral methods to numerically integrate initial states of the
populations given as small perturbations from a homogeneous steady state from which
bifurcations and dynamics have been studied from a linear and weakly nonlinear analysis
perspective [10, 11]. The existence of transcendental nonlinearities within the
equations makes this application of pseudo-spectral methods interestingly nontrivial
and simulations do display dynamics similar to those observed in Eftimie et al. [5].
Finally we apply matrix-free, pseudo-arclength continuation methods with consideration
given to symmetries within the model in an attempt to trace curves from
known states to more dynamically exotic regions of parameter space. The
ow operator
is used to condition the Newton systems arising from the continuation and to
allow for a matrix-free continuation algorithm [13]. However, unforeseen degeneracies
arise within the Newton system which necessitates further research in order to build
a robust continuation software. | en |
dc.description.sponsorship | University of Ontario Institute of Technology | en |
dc.language.iso | en | en |
dc.subject | Pseudo-spectral | en |
dc.subject | Continuation | en |
dc.subject | Matrix-free | en |
dc.subject | Aggregation | en |
dc.subject | Pseudo-arclength | en |
dc.title | On matrix-free pseudo-arclength continuation methods applied to a nonlocal partial differential equation in 1+1D with pseudo-spectral time-stepping | en |
dc.type | Thesis | en |
dc.degree.level | Master of Science (MSc) | en |
dc.degree.discipline | Modelling and Computational Science | en |