Gauss-Legendre quadrature for the evaluation of integrals involving the Hankel function

  • Authors:

  • David Elliott;Peter R. Johnston

  • Affiliations:

  • School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, Tasmania 7001, Australia;School of Science, Griffith University, Kessels Road, Nathan, Queensland 4111, Australia

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2008

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Abstract

The boundary integral method for the two dimensional Helmholtz equation requires the approximate evaluation of the integral @!"-"1^1g(x)H"0^(^1^)(@l(x-a)^2+b^2)dx, where g is a polynomial. In particular, Gauss-Legendre quadrature is considered when the source point is close to the interval of integration; that is -1=