Numerical analysis of some integral equations with singularities

Hdl Handle:
http://hdl.handle.net/10034/70394
Title:
Numerical analysis of some integral equations with singularities
Authors:
Thomas, Sophy M.
Abstract:
In this thesis we consider new approaches to the numerical solution of a class of Volterra integral equations, which contain a kernel with singularity of non-standard type. The kernel is singular in both arguments at the origin, resulting in multiple solutions, one of which is differentiable at the origin. We consider numerical methods to approximate any of the (infinitely many) solutions of the equation. We go on to show that the use of product integration over a short primary interval, combined with the careful use of extrapolation to improve the order, may be linked to any suitable standard method away from the origin. The resulting split-interval algorithm is shown to be reliable and flexible, capable of achieving good accuracy, with convergence to the one particular smooth solution.
Advisors:
Ford, Neville J.
Publisher:
University of Liverpool (Chester College of Higher Education)
Publication Date:
Apr-2006
URI:
http://hdl.handle.net/10034/70394
Type:
Thesis or dissertation
Language:
en
Sponsors:
Supported by a college bursary from the University of Chester.
Appears in Collections:
Theses

Full metadata record

DC FieldValue Language
dc.contributor.advisorFord, Neville J.en
dc.contributor.authorThomas, Sophy M.en
dc.date.accessioned2009-06-12T14:57:55Zen
dc.date.available2009-06-12T14:57:55Zen
dc.date.issued2006-04en
dc.identifieruk.bl.ethos.437510en
dc.identifier.urihttp://hdl.handle.net/10034/70394en
dc.description.abstractIn this thesis we consider new approaches to the numerical solution of a class of Volterra integral equations, which contain a kernel with singularity of non-standard type. The kernel is singular in both arguments at the origin, resulting in multiple solutions, one of which is differentiable at the origin. We consider numerical methods to approximate any of the (infinitely many) solutions of the equation. We go on to show that the use of product integration over a short primary interval, combined with the careful use of extrapolation to improve the order, may be linked to any suitable standard method away from the origin. The resulting split-interval algorithm is shown to be reliable and flexible, capable of achieving good accuracy, with convergence to the one particular smooth solution.en
dc.description.sponsorshipSupported by a college bursary from the University of Chester.en
dc.language.isoenen
dc.publisherUniversity of Liverpool (Chester College of Higher Education)en
dc.subjectintegral equationsen
dc.subjectVolterra integral equationsen
dc.titleNumerical analysis of some integral equations with singularitiesen
dc.typeThesis or dissertationen
dc.type.qualificationnamePhDen
dc.type.qualificationlevelDoctoralen
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