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dc.contributor.advisorIserles, Arieh
dc.contributor.authorRamos, Alberto Gil Couto Pimentel
dc.date.accessioned2016-08-08T15:00:49Z
dc.date.available2016-08-08T15:00:49Z
dc.date.issued2016-06-28
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/256997
dc.description.abstractThe subject matter of this dissertation is the design, analysis and practical implementation of a new numerical method to approximate the eigenvalues and eigenfunctions of regular Sturm–Liouville problems, given in Liouville’s normal form, defined on compact intervals, with self-adjoint separated boundary conditions. These are classical problems in computational mathematics which lie on the interface between numerical analysis and spectral theory, with important applications in physics and chemistry, not least in the approximation of energy levels and wave functions of quantum systems. Because of their great importance, many numerical algorithms have been proposed over the years which span a vast and diverse repertoire of techniques. When compared with previous approaches, the principal advantage of the numerical method proposed in this dissertation is that it is accompanied by error bounds which: (i) hold uniformly over the entire eigenvalue range, and, (ii) can attain arbitrary high-order. This dissertation is composed of two parts, aggregated according to the regularity of the potential function. First, in the main part of this thesis, this work considers the truncation, discretization, practical implementation and MATLAB software, of the new approach for the classical setting with continuous and piecewise analytic potentials (Ramos and Iserles, 2015; Ramos, 2015a,b,c). Later, towards the end, this work touches upon an extension of the new ideas that enabled the truncation of the new approach, but instead for the general setting with absolutely integrable potentials (Ramos, 2014).en
dc.language.isoenen
dc.subjectNumerical methoden
dc.subjectEigenvaluesen
dc.subjectEigenfunctionsen
dc.subjectRegular Sturm–Liouville problemsen
dc.subjectSelf-adjoint separated boundary conditionsen
dc.subjectContinuous and piecewise analytic potentialsen
dc.subjectAbsolutely integrable potentialsen
dc.subjectUniformen
dc.subjectHigh-orderen
dc.subjectFer expansionsen
dc.subjectFer streamersen
dc.subjectLie-algebraic techniquesen
dc.subjectMultivariate oscillatory quadratureen
dc.subjectReduced Hall basisen
dc.subjectMATLABen
dc.subjectLiouville’s normal formen
dc.titleNumerical solution of Sturm–Liouville problems via Fer streamersen
dc.typeThesisen
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridgeen
dc.publisher.departmentDepartment of Applied Mathematics and Theoretical Physicsen
dc.publisher.departmentHomerton Collegeen
dc.identifier.doi10.17863/CAM.431


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