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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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References

Carslaw, H. S.Jaeger, J. C., Condution of heat in solids, 2nd ed. (Oxford, Clarendon Press)Google Scholar
Clenshaw, C. W., 1962, N.P.L. Mathematical Tables, 5 (London, H.M.S.O.).Google Scholar
Erdélyi, A., 1953, Higher transcendental functions, II (New York, McGraw-Hill).Google Scholar
Morland, L. W., 1967, Quart. J. Mech. Appl. Math., 20, 1, p. 74.Google Scholar
Morland, L. W., 1968, Quart. Appl. Math., 25, 4, p. 363.Google Scholar
Stewartson, K., 1963, Proc. Roy. Soc. A, 277, p. 107.Google Scholar
Tricomi, F. G., 1957, Integral equations (New York, Interscience).Google Scholar
Watson, G. N., 1944, Theory of Bessel functions, 2nd ed. (Cambridge, University Press).Google Scholar