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Spectral integration and the numerical solution of two-point boundary value problems

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dc.contributor.advisor Reddy, Satish
dc.creator Norris, Gordon F.
dc.date.accessioned 2012-09-06T17:56:55Z
dc.date.available 2012-09-06T17:56:55Z
dc.date.copyright 1999-09-22
dc.date.issued 1999-09-22
dc.identifier.uri http://hdl.handle.net/1957/33271
dc.description Graduation date: 2000 en_US
dc.description.abstract Spectral integration methods have been introduced for constant-coefficient two-point boundary value problems by Greengard, and pseudospectral integration methods for Volterra integral equations have been investigated by Kauthen. This thesis presents an approach to variable-coefficient two-point boundary value problems which employs pseudospectral integration methods to solve an equivalent integral equation. This thesis covers three topics in the application of spectral integration methods to two-point boundary value problems. The first topic is the development of the spectral integration concept and a derivation of the spectral integration matrices. The derivation utilizes the discrete Chebyshev transform and leads to a stable algorithm for generating the integration matrices. Convergence theory for spectral integration of C[subscript k] and analytic functions is presented. Matrix-free implementations are discussed with an emphasis on computational efficiency. The second topic is the transformation of boundary value problems to equivalent Fredholm integral equations and discretization of the resulting integral equations. The discussion of boundary condition treatments includes Dirichlet, Neumann, and Robin type boundary conditions. The final topic is a numerical comparison of the spectral integration and spectral differentiation approaches to two-point boundary value problems. Numerical results are presented on the accuracy and efficiency of these two methods applied to a set of model problems. The main theoretical result of this thesis is a proof that the error in spectral integration of analytic functions decays exponentially with the number of discretization points N. It is demonstrated that spectrally accurate solutions to variable-coefficient boundary value problems can be obtained in O(NlogN) operations by the spectral integration method. Numerical examples show that spectral integration methods are competitive with spectral differentiation methods in terms of accuracy and efficiency. en_US
dc.language.iso en_US en_US
dc.subject.lcsh Boundary value problems en_US
dc.title Spectral integration and the numerical solution of two-point boundary value problems en_US
dc.type Thesis/Dissertation en_US
dc.degree.name Master of Science (M.S.) in Mathematics en_US
dc.degree.level Master's en_US
dc.degree.discipline Science en_US
dc.degree.grantor Oregon State University en_US
dc.description.digitization File scanned at 300 ppi (Monochrome) using ScandAll PRO 1.8.1 on a Fi-6770A in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR. en_US
dc.description.peerreview no en_us


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