Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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: 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


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