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

Quoc T. Le Gia ()
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Quoc T. Le Gia: University of New South Wales

A chapter in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, pp 815-836 from Springer

Abstract: Abstract 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-72456-0_36

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DOI: 10.1007/978-3-319-72456-0_36

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