Efficient continuous Runge-Kutta methods for asymptotically correct defect control

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dc.contributor.advisor Muir, Paul
dc.creator Drfoun, Hanan
dc.date.accessioned 2017-10-19T14:29:55Z
dc.date.available 2017-10-19T14:29:55Z
dc.date.issued 2017
dc.identifier.other QA379 D74 2017
dc.identifier.uri http://library2.smu.ca/handle/01/27162
dc.description xii, 124 leaves : coloured illustrations ; 29 cm
dc.description Includes abstract.
dc.description Includes bibliographical references (leaves 120-124).
dc.description.abstract Mono-Implicit Runge-Kutta (MIRK) methods and continuous MIRK (CMIRK) methods, are used in the numerical solution of boundary value ordinary differential equations (ODEs). One way of assessing the quality of the numerical solution is to estimate its maximum defect, which is the amount by which the solution fails to satisfy the ODE. The standard approach is to perform two point sampling of the defect on each subinterval of a mesh which partitions the problem domain to estimate the maximum defect. However, the location of the maximum defect on each subinterval typically varies from subinterval to subinterval, and from problem to problem. Thus sampling at only two points typically leads to an underestimate of the maximum defect. In this thesis, we will derive a new class of CMIRK interpolants for which the location of the maximum defect on each subinterval is the same over all subintervals and problems. en_CA
dc.language.iso en en_CA
dc.publisher Halifax, N.S. : Saint Mary's University
dc.subject.lcc QA379
dc.subject.lcsh Runge-Kutta formulas
dc.subject.lcsh Boundary value problems -- Asymptotic theory
dc.subject.lcsh Differential equations -- Numerical solutions
dc.title Efficient continuous Runge-Kutta methods for asymptotically correct defect control
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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