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On the solution of some axisymmetric boundary value problems by means of integral equations, II: further problems for a circular disc and a spherical cap

Published online by Cambridge University Press:  26 February 2010

W. D. Collins
W. D. Collins
Affiliation:
King's College, Newcastle upon Tyne
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Extract

Green and Zerna [1] have given a method of determining the electrostatic potential due to a circular disc maintained at a given axisymmetric potential, their method depending on the solution of a Volterra integral equation of the first kind and being a generalization of a method given by Love [2] for the determination of the electrostatic potential due to two equal co-axial circular discs maintained at constant potentials. In a recent paper [3], henceforth referred to as Part I, the author applied this method to the corresponding problem for a hollow spherical cap and also to the determination of the Stokes' stream-functions for perfect fluid flows past a cap and a disc. The method consists of expressing the potential as the real part of a complex integral of a real variable t, the integrand involving an unknown function g(t). The boundary condition on the disc or cap gives a Volterra integral equation of the first kind for g(t), it being possible to solve this equation and hence determine the potential by integration.

Type
Research Article
Information
Mathematika , Volume 6 , Issue 2 , December 1959 , pp. 120 - 133
Copyright
Copyright © University College London 1959

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References

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