Fairbairn, AI and Kelmanson, MA (2017) An exponentially convergent Volterra-Fredholm method for integro-differential equations. In: Chappell, DJ, (ed.) Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11),. UKBIM 11, 10-11 Jul 2017, Nottingham, UK. Nottingham Trent University: Publications ISBN 9780993111297
Abstract
Extending the authors’ recent work [15] on the explicit computation of error bounds for Nystrom solvers applied to one-dimensional Fredholm integro-differential equations (FIDEs), presented herein is a study of the errors incurred by first transforming (as in, e.g., [21]) the FIDE into a hybrid Volterra-Fredholm integral equation (VFIE). The VFIE is solved via a novel approach that utilises N-node Gauss-Legendre interpolation and quadrature for its Volterra and Fredholm components respectively: this results in numerical solutions whose error converges to zero exponentially with N, the rate of convergence being confirmed via large-
N asymptotics. Not only is the exponential rate inherently far superior
to the algebraic rate achieved in [21], but also it is demonstrated, via diverse test problems, to improve dramatically on even the exponential rate achieved in [15] via direct Nystrom discretisation of the original FIDE; this improvement is confirmed theoretically.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | (c) 2017, The Authors. This is an author produced version of a paper published in Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11) by Nottingham Trent University: Publications. |
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: | 13 Jul 2017 14:29 |
Last Modified: | 08 May 2018 14:14 |
Published Version: | http://irep.ntu.ac.uk/id/eprint/31463 |
Status: | Published |
Publisher: | Nottingham Trent University: Publications |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:118991 |