An Alternating-Direction Sinc-Galerkin method for elliptic problems on finite and infinite domains

dc.contributor.advisorChairperson, Graduate Committee: Kenneth L. Bowersen
dc.contributor.authorAlonso, Nicomedes, IIIen
dc.description.abstractAlternating-Direction Implicit (ADI) schemes are a class of very efficient algorithms for the numerical solution of differential equations. Sinc-Galerkin schemes employ a sinc basis to produce exponentially accurate approximate solutions to differential equations even in the presence of singularities. In this dissertation we begin with a broad overview of sinc methods for problems posed on both finite and infinite, one- and two-dimensional domains. We then present a variety of finite difference methods that lead to the introduction of a new Alternating-Direction Sinc-Galerkin scheme based on the classic ADI scheme for a linear matrix system. We note that when a Sinc-Galerkin method is used to solve a Poisson equation, the resulting matrix system is a Sylvester equation. We discuss ADI model problems in general and then prove that when a symmetric Sinc-Galerkin method is employed, the resulting Sylvester equation can be classified as an ADI model problem. Finally, we derive our Alternating-Direction Sinc-Galerkin (ADSG) method to solve this resulting Sylvester equation, specifying the use of a constant iteration parameter to avoid costly eigen-value computations. We end by applying ADSG to a variety of problems, comparing its performance to the standard technique that uses the Kronecker product, the Kronecker sum, and the concatenation operator.en
dc.publisherMontana State University - Bozeman, College of Letters & Scienceen
dc.rights.holderCopyright 2009 by Nicomedes Alonso IIIen
dc.subject.lcshGalerkin methodsen
dc.subject.lcshDifferential equationsen
dc.subject.lcshKronecker productsen
dc.subject.lcshPoisson's equationen
dc.titleAn Alternating-Direction Sinc-Galerkin method for elliptic problems on finite and infinite domainsen
thesis.catalog.ckey1428180en, Graduate Committee: John Lund; Jack D. Dockery; Mark C. Pernarowski; Lisa Davisen Sciences.en


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