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. doi:10.1017/S0308210500018473. 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 | ||||
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| 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. | ||||
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| Issue or Number: | 3-4 | ||||
| DOI: | 10.1017/S0308210500018473 | ||||
| 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: | 15 Nov 2021 17:36 |
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