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Singular integral equations with logarithmic kernels

Published online by Cambridge University Press:  26 February 2010

L. W. Morland
L. W. Morland
Affiliation:
School of Mathematics and Physics, University of East Anglia.
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Summary

Closed form solutions are obtained for a class of singular integral equations of the first kind with difference kernels. The kernel function is the sum of a polynomial and a second polynomial multiplied by a logarithm, with the possible addition of a strong singularity. A wider class of kernels have approximate representations in one of the above forms, where, for a specified accuracy, the polynomial orders will depend on the range of any parameter present. For example, the modified Bessel function kernels K0(|γx|), K1(|γx|)sgn x in the interval |x| ≤ 2 can be so expressed using 16th order polynomials with a maximum error 10-5 for real γ in the range 0 < γ ≤ 4.

Type
Research Article
Information
Mathematika , Volume 17 , Issue 1 , June 1970 , pp. 47 - 56
Copyright
Copyright © University College London 1970

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