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

Ciric, Ioan; Kotuwage, Kumara

doi:10.1090/S0033-569X-2014-01342-6

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
MathSciNet review: 3291817
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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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