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Gauss-Legendre quadrature and the trapezoidal rule are powerful tools fornumerical integration of analytic functions. For nearly singular problems,however, these standard methods become unacceptably slow. We discuss andgeneralize some existing methods for improving on these schemes when thelocation of the nearby singularity is known. We conclude with an application tosome nearly singular surface integrals of viscous flow.

Decomposition and conformal mapping techniques for the quadrature of nearly singular integrals