End-point corrected trapezoidal quadrature rules for singular functions
Vladimir Abramovich Rokhlin · Computers & Mathematics with Applications · 1990
A group of quadrature formulae for end-point singular functions is presented generalizing classical end-point corrected trapezoidal quadrature rules. The actual values of the end-point corrections are obtained for each singularity as a solution of a system of linear algebraic equations. The algorithm is applicable to a wide class of monotonic singularities and does not require that an analytical expression for the singularity be known; only the knowledge of its first several moments and the ability to evaluate it on the interval of integration are needed.