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The method of fundamental solutions applied to boundary value problems on the surface of a sphere

Alves, Carlos J. S.; Antunes, Pedro R. S.

Computers and Mathematics with Applications, 75 (7) (2018), 2365-2373

In this work we propose using the method of fundamental solutions (MFS) to solve boundary value problems for the Helmholtz-Beltrami equation on a sphere. We prove density and convergence results that justify the proposed MFS approximation. Several numerical examples are considered to illustrate the good performance of the method.