dc.contributor.advisor Ford, Neville J. dc.contributor.author Thomas, Sophy M. * dc.date.accessioned 2009-06-12T14:57:55Z dc.date.available 2009-06-12T14:57:55Z dc.date.issued 2006-04 dc.identifier uk.bl.ethos.437510 dc.identifier.uri http://hdl.handle.net/10034/70394 dc.description.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. dc.description.sponsorship Supported by a college bursary from the University of Chester. en dc.language.iso en en dc.publisher University of Liverpool (Chester College of Higher Education) en dc.subject integral equations en dc.subject Volterra integral equations en dc.title Numerical analysis of some integral equations with singularities en dc.type Thesis or dissertation en dc.type.qualificationname PhD en dc.type.qualificationlevel Doctoral en html.description.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.
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