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Mixed Boundary-Value Problems in Potential Theory

Published online by Cambridge University Press:  20 January 2009

A. H. England
A. H. England
Affiliation:
Department of Theoretical Mechanics, University of Nottingham
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The problems associated with finding solutions of Laplace's equation subject to mixed boundary conditions have attracted much attention and, as a consequence, a variety of analytical techniques have been developed for the solution of such problems. Sneddon (1) has given a comprehensive account of these techniques. The object of this note is to draw attention to some simple orthogonal polynomial solutions to the most basic mixed boundary-value problems in two and threedimensional potential theory. These solutions have the advantage that most quantities of physical interest are easily evaluated in terms of known functions. Two-dimensional problems are considered in §2 and axially-symmetric three-dimensional problems in §3.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 2 , June 1979 , pp. 91 - 98
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

(1) Sneddon, I. N., Mixed Boundary Value Problems in Potential Theory (North-Holland, 1966).Google Scholar
(2) Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions (Dover, 1964).Google Scholar
(3) Erdogan, F., Gupta, G. D. and Cook, T. S., Numerical solution of singular integral equations, Mechanics of Fracture, Vol. 1 (Noordhoff, 1973, Ed. G. Sih), 368.Google Scholar
(4) Gladwell, G. M. L. and England, A. H., Quart. J. Mechs. Appl. Maths, 30 (1977), 175.Google Scholar
(5) Fox, L. and Parker, I. B., Chebyshev Polynomials in Numerical Analysis (Oxford, 1968).Google Scholar
(6) Tranter, C. J., Quart. J. Math. 1 (1950), 1.Google Scholar
(7) England, A. H. and Shail, R., Quart. J. Mechs. Appl. Maths. 30 (1977), 397.CrossRefGoogle Scholar
(8) Tricomi, F. G., Integral Equations (Interscience, 1957), §4.3.Google Scholar
(9) Pykhteev, G. N., Problems of Continuum Mechanics, S.I.A.M. (1961), 350.Google Scholar