Show simple item record

dc.contributor.authorAoki, Yasunori 16:24:30 (GMT) 16:24:30 (GMT)
dc.description.abstractIn this thesis, we explore two important aspects of study of differential equations: analytical and computational aspects. We first consider a partial differential equation model for a static liquid surface (capillary surface). We prove through mathematical analyses that the solution of this mathematical model (the Laplace-Young equation) in a cusp domain can be bounded or unbounded depending on the boundary conditions. By utilizing the knowledge we have obtained about the singular behaviour of the solution through mathematical analysis, we then construct a numerical methodology to accurately approximate unbounded solutions of the Laplace-Young equation. Using this accurate numerical methodology, we explore some remaining open problems on singular solutions of the Laplace-Young equation. Lastly, we consider ordinary differential equation models used in the pharmaceutical industry and develop a numerical method for estimating model parameters from incomplete experimental data. With our numerical method, the parameter estimation can be done significantly faster and more robustly than with conventional methods.en
dc.publisherUniversity of Waterlooen
dc.subjectPartial Differential Equationsen
dc.subjectLaplace-Young Equationen
dc.subjectNumerical Approximationen
dc.titleStudy of Singular Capillary Surfaces and Development of the Cluster Newton Methoden
dc.typeDoctoral Thesisen
dc.subject.programApplied Mathematicsen Mathematicsen
uws-etd.degreeDoctor of Philosophyen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages