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Boundary value problems on the unit sphere arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Robust numerical methods play an important role in solving these problems. In this article, we construct numerical solutions to a boundary value problem defined on a spherical sub-domain (with a sufficiently smooth boundary) using radial basis functions (RBFs). The error analysis between the exact solution and the approximation is provided. Numerical experiments are presented to confirm theoretical estimates.

Numerical Solutions of a Boundary Value Problem on the Sphere Using Radial Basis Functions