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Multivariate quadrature of a singular integrand

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Abstract

Consider an integral with a point singularity in its integrand, such as ρ−α or \(\log \rho \). We introduceand discuss two methods for approximating such integrals, in both two and three dimensions. The methods are first introduced using the unit disk as the quadrature region, and then, they are extended to other regions and to three dimensions. The error behavior of the numerical integration for singular points near to the boundary is examined.

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Authors and Affiliations

  1. University of Iowa, Iowa City, USA

    Kendall Atkinson

  2. California State University San Marcos, San Marcos, USA

    David Chien & Olaf Hansen

Authors
  1. Kendall Atkinson
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  2. David Chien
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  3. Olaf Hansen
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Correspondence to David Chien.

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Communicated by: Zydrunas Gimbutas

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Atkinson, K., Chien, D. & Hansen, O. Multivariate quadrature of a singular integrand. Adv Comput Math 47, 44 (2021). https://doi.org/10.1007/s10444-021-09869-4

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  • DOI: https://doi.org/10.1007/s10444-021-09869-4

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