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

翻译：Gaus-Legendre 二次曲线和 roapezoide 规则是分析函数数字集成的有力工具。 但是,对于几乎单一的问题,这些标准方法变得令人无法接受地缓慢。 当已知附近奇点的位置时,我们讨论并概括了改善这些图案的一些现有方法。 我们最后对粘度流动的某些近乎单一的表面元件进行了应用。