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arXiv · 1408.3183

Integral equation methods for the Yukawa-Beltrami equation on the sphere

Nilima Nigam·Mary-Catherine Kropinski·Bryan Quaife
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Abstract

An integral equation method for solving the Yukawa-Beltrami equation on a multiply-connected sub-manifold of the unit sphere is presented. A fundamental solution for the Yukawa-Beltrami operator is constructed. This fundamental solution can be represented by conical functions. Using a suitable representation formula, a Fredholm equation of the second kind with a compact integral operator needs to be solved. The discretization of this integral equation leads to a linear system whose condition number is bounded independent of the size of the system. Several numerical examples exploring the properties of this integral equation are presented.

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Nilima Nigam, Mary-Catherine Kropinski, Bryan Quaife. 2014-08-14. Integral equation methods for the Yukawa-Beltrami equation on the sphere. https://arxiv.org/abs/1408.3183

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