Numerical solutions of a boundary value problem on the sphere using radial basis functions
Numerical Analysis
2016-10-21 v2
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 (RBF). The error analysis between the exact solution and the approximation is provided. Numerical experiments are presented to confirm theoretical estimates.
Cite
@article{arxiv.1402.3353,
title = {Numerical solutions of a boundary value problem on the sphere using radial basis functions},
author = {Quoc Thong Le Gia},
journal= {arXiv preprint arXiv:1402.3353},
year = {2016}
}