Advances in Computational Mathematics

, Volume 42, Issue 2, pp 469–488 | Cite as

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

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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.

Keywords

Yukawa-Beltrami boundary value problems Integral equations 

Mathematics Subject Classification (2010)

35J25 45B05 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of Scientific ComputingFlorida State UniversityTallahasseeUSA

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