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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.

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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