Published January 1987
| public
Journal Article
Volterra integral equations and a new Gronwall inequality (Part II: The nonlinear case)
- Creators
- Norbury, J.
- Stuart, A. M.
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.
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.Additional details
- Eprint ID
- 78117
- DOI
- 10.1017/S0308210500018485
- Resolver ID
- CaltechAUTHORS:20170612-135043115
- Science and Engineering Research Council (SERC)
- Created
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2017-06-12Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
- Other Numbering System Name
- Andrew Stuart
- Other Numbering System Identifier
- J2