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Volterra integral equations and a new Gronwall inequality (Part II: The nonlinear case)

Norbury, J. and Stuart, A. M. (1987) Volterra integral equations and a new Gronwall inequality (Part II: The nonlinear case). Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 106 (3-4). pp. 375-384. ISSN 0308-2105. https://resolver.caltech.edu/CaltechAUTHORS:20170612-135043115

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Abstract

We consider nonlinear singular Volterra integral equations of the second kind. We generalise the transformation method introduced in Part I of this paper [6] to cope with both the nonlinearity and slightly more general singular kernels. We also consider a particular class of nonlinear equation for which the solution behaviour is known. Using this a priori knowledge, we propose a modification of the transformation technique which results in a numerical method with good asymptotic stability properties. Applying the general theory of Part I of this paper, we prove convergence of this scheme.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/S0308210500018485DOIArticle
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-ii-the-nonlinear-case/ACA918ED054623F934C5053B6D32101FPublisherArticle
Additional Information:© 1987 Royal Society of Edinburgh. MS received 8 July 1986. Revised MS received 11 February 1987. 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 StuartJ2
Issue or Number:3-4
Record Number:CaltechAUTHORS:20170612-135043115
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170612-135043115
Official Citation:Norbury, J., & Stuart, A. (1987). Volterra integral equations and a new Gronwall inequality (Part II: The nonlinear case). Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 106(3-4), 375-384. doi:10.1017/S0308210500018485
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78117
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 Jun 2017 21:10
Last Modified:03 Oct 2019 18:05

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