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Journal of Applied Mathematics
Volume 2004 (2004), Issue 6, Pages 479-494
http://dx.doi.org/10.1155/S1110757X04305024

Error bound analysis and singularly perturbed Abel-Volterra equations

The New York University in London, 6 Bedford Square, London WC1B 3RA, UK

Received 5 May 2003; Revised 16 June 2004

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Asymptotic solutions of nonlinear singularly perturbed Volterra integral equations with kernels possessing integrable singularity are investigated using singular perturbation methods and the Mellin transform technique. In particular, it is demonstrated that the formal approximation is asymptotically valid.