Fairbairn, AI and Kelmanson, MA (2019) A priori Nyström-method error bounds in approximate solutions of 1-D Fredholm integro-differential equations. International Journal of Mechanical Sciences, 150. pp. 755-766. ISSN 0020-7403
Abstract
A novel procedure is proposed for the a priori computation of error bounds for the ubiquitous Nyström solver applied to one-dimensional Fredholm integro-differential equations. The distinctive feature of the new approach is that the bounds are computed not only to spectral accuracy, but also explicitly, and in terms of only the numerical solution itself. Details are given of both the error analysis and its numerical implementation, and a corroborative asymptotic theory is developed in order to yield independent predictions of the convergence rates expected from Nyström discretisations of increasing order. All theory is first convincingly validated on a proof-of-concept continuous-kernel test problem whose solution is a priori known. The method is then applied to a novel integro-differential-equation formulation of a static, fourth-order, Euler-Bernoulli beam-deflection boundary-value problem in which the flexural rigidity varies along the beam, and for which no exact solution is attainable; in this case, validation of the resulting discontinuous-kernel approach is achieved using an asymptotic solution derived on the (realistic) assumption that variations in the cross-section of the beam occur on spatial scales an order of magnitude less than the beam’s length and width. Potential limitations of the new approach are discussed.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Elsevier Ltd. All rights reserved. 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; Numerical approximation of solutions |
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: | 18 Sep 2018 08:48 |
Last Modified: | 06 Nov 2019 01:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.ijmecsci.2018.09.021 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:135784 |
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Filename: Fairbairn and Kelmanson 2018 - revised.pdf
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