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Volterra integral equations and a new Gronwall inequality (Part I: The linear case)

Norbury, J. and Stuart, A. M. (1987) Volterra integral equations and a new Gronwall inequality (Part I: The linear case). Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 106 (3-4). pp. 361-373. ISSN 0308-2105. https://resolver.caltech.edu/CaltechAUTHORS:20170612-131130001

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Abstract

We present a generalisation of the continuous Gronwall inequality and show its use in bounding solutions of discrete inequalities of a form that arise when analysing the convergence of product integration methods for Volterra integral equations. We then use these ideas to prove convergence of a numerical method which is effective in approximating Volterra integral equations of the second kind with weakly singular kernels.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/S0308210500018473DOIArticle
https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/volterra-integral-equations-and-a-new-gronwall-inequality-part-i-the-linear-case/D4B84BA2D0CFF988F6D72D4B9273A7BAPublisherArticle
Additional Information:© 1987 Royal Society of Edinburgh. MS received 8 July 1986. Revised MS received 11 February 1987. Published online: 14 November 2011. The second author is grateful to the Science and Engineering Research Council for financial support.
Funders:
Funding AgencyGrant Number
Science and Engineering Research Council (SERC)UNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ1
Issue or Number:3-4
Record Number:CaltechAUTHORS:20170612-131130001
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170612-131130001
Official Citation:Norbury, J., & Stuart, A. (1987). Volterra integral equations and a new Gronwall inequality (Part I: The linear case). Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 106(3-4), 361-373. doi:10.1017/S0308210500018473
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78111
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 Jun 2017 20:55
Last Modified:03 Oct 2019 18:05

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