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A method of deriving quadrature rules has been developed which gives nodesand weights for a Gaussian-type rule which integrates functions of the form:f(x,y,t) = a(x,y,t)/((x-t)^2+y^2) + b(x,y,t)/([(x-t)^2+y^2]^{1/2}) +c(x,y,t)\log[(x-t)^2+y^2]^{1/2} + d(x,y,t), without having to explicitlyanalyze the singularities of $f(x,y,t)$ or separate it into its components. Themethod extends previous work on a similar technique for the evaluation ofCauchy principal value or Hadamard finite part integrals, in the case when$y\equiv0$. The method is tested by evaluating standard reference integrals andits error is found to be comparable to machine precision in the best case.

Numerical quadratures for near-singular and near-hypersingular integrals in boundary element methods