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

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 3-4 , 1987 , pp. 375 - 384
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

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