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

Published online by Cambridge University Press:  14 November 2011

J. Norbury  and
A. M. Stuart
J. Norbury
Affiliation:
Mathematical Institute, Oxford University, 24–29 St Giles, Oxford OX1 3LB, U.K.
A. M. Stuart
Affiliation:
Oxford University Computing Laboratory, 8–11 Keble Road, Oxford OX1 3QD, U.K.
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Synopsis

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.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 3-4 , 1987 , pp. 361 - 373
Copyright
Copyright © Royal Society of Edinburgh 1987

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