Fairbairn, AI and Kelmanson, MA (2018) Error analysis of a spectrally accurate Volterra-transformation method for solving 1-D Fredholm integro-differential equations. International Journal of Mechanical Sciences, 144. pp. 382-391. ISSN 0020-7403
Abstract
Spectrally accurate a priori error estimates for Nyström-method approximate solutions of one-dimensional Fredholm integro-differential equations (FIDEs) are obtained indirectly by transforming the FIDE into a hybrid Volterra-Fredholm integral equation (VFIE), which is solved via a novel approach that utilises N-node Gauss-Legendre interpolation and quadrature for its Volterra and Fredholm components respectively. Errors in the numerical solutions of the VFIE converge to zero exponentially with N, the rate of convergence being confirmed via large-N asymptotics. Not only is the exponential rate far superior to the algebraic rate achieved in previous literature [29] but also it is demonstrated, via diverse test problems, to improve dramatically on even the exponential rate achieved in the approach [21] of direct Nyström discretisation of the original FIDE; this improvement is confirmed theoretically.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Elsevier Ltd. This is an author produced version of a paper published in International Journal of Mechanical Sciences. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Integro-ordinary differential equations; Error bounds; Spectral Collocation and related methods |
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: | 09 May 2018 11:21 |
Last Modified: | 05 May 2019 00:43 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.ijmecsci.2018.04.052 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:130518 |
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