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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.

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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada

    M. C. Kropinski & N. Nigam

  2. Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306, USA

    B. Quaife

Authors
  1. M. C. Kropinski
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  2. N. Nigam
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  3. B. Quaife
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Correspondence to B. Quaife.

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Communicated by: Alexander Barnett

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Kropinski, M.C., Nigam, N. & Quaife, B. Integral equation methods for the Yukawa-Beltrami equation on the sphere. Adv Comput Math 42, 469–488 (2016). https://doi.org/10.1007/s10444-015-9431-2

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  • DOI: https://doi.org/10.1007/s10444-015-9431-2

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