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Kirkup, S.M. and Henwood, D.J. (1986) Practical Numerical Methods for the Integration of Functions of One Variable with an End Point Singularity. Report M.11, Department of Mathematics, Statistics and Operational Research, Brighton Polytechnic, Brighton.

has been cited by the following article:

• TITLE: Quadrature Rules for Functions with a Mid-Point Logarithmic Singularity in the Boundary Element Method Based on the x = tp Substitution

  AUTHORS: Stephen M. Kirkup, Javad Yazdani, George Papazafeiropoulos

  KEYWORDS: Boundary Element Method, Singular Integral, Numerical Integration

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.9 No.4, December 16, 2019

  ABSTRACT: Quadrature rules for evaluating singular integrals that typically occur in the boundary element method (BEM) for two-dimensional and axisymmetric three-dimensional problems are considered. This paper focuses on the numerical integration of the functions on the standard domain [-1, 1], with a logarithmic singularity at the centre. The substitution x = tp, where p (≥ 3) is an odd integer is given particular attention, as this returns a regular integral and the domain unchanged. Gauss-Legendre quadrature rules are applied to the transformed integrals for a number of values of p. It is shown that a high value for p typically gives more accurate results.