B-spline collocation for two dimensional, time-dependent, parabolic PDEs

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dc.contributor.advisor Muir, Paul
dc.creator Li, Zhi
dc.date.accessioned 2013-08-21T15:35:17Z
dc.date.available 2013-08-21T15:35:17Z
dc.date.issued 2012
dc.identifier.other QA377 L489 2012
dc.identifier.uri http://library2.smu.ca/xmlui/handle/01/25070
dc.description vi, 177 leaves : ill. ; 29 cm. en_CA
dc.description Includes abstract and appendices.
dc.description Includes bibliographical references (leaves 82-88).
dc.description.abstract In this thesis, we consider B-spline collocation algorithms for solving two-dimensional in space, time-dependent parabolic partial differential equations (PDEs), defined over a rectangular region. We propose two ways to solve the problem: (i) The Method of Surfaces: Discretizing the problem in one of the spatial domains, we obtain a system of one-dimensional parabolic PDEs, which is then solved using a one-dimensional PDE system solver. (ii) Two-dimensional B-spline collocation: The numerical solution is represented as a bi-variate piecewise polynomial with unknown time-dependent coefficients. These coefficients are determined by requiring the numerical solution to satisfy the PDE at a number of points within the spatial domain, i.e., we collocate simultaneously in both spatial dimensions. This leads to an approximation of the PDE by a large system of time-dependent differential algebraic equations (DAEs), which we then solve using a high quality DAE solver. en_CA
dc.description.provenance Submitted by Dianne MacPhee (dianne.macphee@smu.ca) on 2013-08-21T15:35:17Z No. of bitstreams: 0 en
dc.description.provenance Made available in DSpace on 2013-08-21T15:35:17Z (GMT). No. of bitstreams: 0 Previous issue date: 2012 en
dc.language.iso en en_CA
dc.publisher Halifax, N.S. : Saint Mary's University en_CA
dc.subject.lcc QA377
dc.subject.lcsh Differential equations, Partial -- Numerical solutions
dc.subject.lcsh Differential equations, Parabolic -- Numerical solutions
dc.subject.lcsh Algorithms
dc.title B-spline collocation for two dimensional, time-dependent, parabolic PDEs en_CA
dc.type Text en_CA
thesis.degree.name Master of Science in Applied Science
thesis.degree.level Masters
thesis.degree.discipline Mathematics and Computing Science
thesis.degree.grantor Saint Mary's University (Halifax, N.S.)
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