Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.437510
Title: Numerical analysis of some integral equations with singularities
Author: Thomas, Sophy Margaret
Awarding Body: University of Liverpool
Current Institution: University of Chester
Date of Award: 2006
Availability of Full Text:
Access through EThOS:
Access through Institution:
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.
Supervisor: Ford, Neville J. Sponsor: University of Chester
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.437510  DOI: Not available
Keywords: integral equations ; Volterra integral equations
Share: