Translational addition theorems for spherical Laplacian functions and their application to boundary-value problems

Authors:
Ioan R. Ciric and Kumara S. C. M. Kotuwage

Journal:
Quart. Appl. Math. **72** (2014), 613-623

MSC (2010):
Primary 35A99, 35A09, 65N99

DOI:
https://doi.org/10.1090/S0033-569X-2014-01342-6

Published electronically:
June 11, 2014

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Abstract | References | Similar Articles | Additional Information

Abstract: General translational addition theorems are presented for spherical scalar Laplacian functions, and their application to boundary value problems is illustrated. By these theorems, the eigenfunction solutions in a system of spherical coordinates are expressed in terms of the spherical coordinates in another system, translated with respect to the first one. This allows for a rigorous analytic solution to be obtained for Laplacian and Poissonian fields in the presence of arbitrary configurations of spheres by imposing the exact boundary conditions. Complete formulations and solutions are presented for systems of electrically charged spheres and for arrays of perfect conductor spheres in external electric and magnetic fields. Illustrative computation examples are given for three-sphere systems. Numerical results of specified accuracy are generated, which are useful for validating various approximate numerical methods.

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Additional Information

**Ioan R. Ciric**

Affiliation:
Department of Electrical and Computer Engineering, The University of Manitoba, Canada

Email:
Ioan.Ciric@ad.umanitoba.ca

**Kumara S. C. M. Kotuwage**

Affiliation:
Department of Electrical and Computer Engineering, The University of Manitoba, Canada

Email:
mksckumara@gmail.com

DOI:
https://doi.org/10.1090/S0033-569X-2014-01342-6

Received by editor(s):
August 1, 2012

Published electronically:
June 11, 2014

Article copyright:
© Copyright 2014
Brown University