A quadrature formula for integrals with nearby singularities

The purpose of this paper is to propose a new quadrature formula for integrals with nearby singularities. In the boundary element method, the integrands of nearby singular boundary integrals vary drastically with the distance between the field and the source point. Especially, field variables and their derivatives at a field point near a boundary cannot be computed accurately. In the present paper a quadrature formula for l-isolated singularities near the integration interval, based on Lagrange interpolatory polynomials, is obtained. The error estimation of the proposed formula is also given. Quadrature formulas for regular and singular integrals with conjugate poles are derived. Numerical examples are given and the proposed quadrature rules present the expected polynomial accuracy