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Solutions of certain finite difference equations connected with Laplace's equation

Published online by Cambridge University Press:  24 October 2008

K. F. Sander
K. F. Sander
Affiliation:
Engineering LaboratoryUniversity of Cambridge
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Abstract

The familiar difference equations approximating to Laplace's equation are investigated for exact solutions. Solutions corresponding to the electrostatic potentials for line dipole, point and ring charges are obtained analytically.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 1 , January 1962 , pp. 38 - 51
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

* We write j for √– 1.

* Hildebrand, F. B.Introduction to numerical analysis, Ch. 8 (New York, 1956).Google Scholar

* Since the equation involves H(ρ – 1), this means that H(ρ) exists for ρ > – ½.