Fairbairn, AI and Kelmanson, MA (2015) Computable theoretical error bounds for Nyström methods for 1-D Fredholm integral equations of the second kind. In: Harris, P, (ed.) Proceedings of the 10th UK Conference on Boundary Integral Methods. 10th UK Conference on Boundary Integral Methods, 13-14 Jul 2015, University of Brighton. University of Brighton ISBN 1910172057
Abstract
New expressions for computable error bounds are derived for Nyström method approximate solutions of one-dimensional second-kind Fredholm integral equations. The bounds are computed using only the numerical solution, and so require no a priori knowledge of the exact solution. The analysis is implemented on test problems with both well-behaved and “Runge-phenomenon” solutions, and the computed predictions are shown to be in impressive quantitative agreement with the true errors obtained from known exact solutions of the test problems. For independent computational validation, both Lagrange and barycentric interpolation are employed on grids with both regularly spaced nodes and those located at the roots or extrema of orthogonal polynomials. For independent theoretical validation, asymptotic estimates are derived for the convergence rates of the observed computational errors.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 Sep 2015 13:07 |
Last Modified: | 16 Nov 2016 10:39 |
Status: | Published |
Publisher: | University of Brighton |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:90237 |