A simple procedure for reducing numerical integration errors near singularities

Abstract Numerical integration of functions near singularity points presents a challenge to even advanced quadrature algorithms. Often it would be advantageous to have a simple technique with which to test the accuracy of these estimates. One such technique is described. It consists of subtracting an integrable complementary function from the original integrand, which reduces the curvature of the function to be integrated. This allows simpler numerical integration techniques to be employed for verification. In addition, the technique can be used directly to improve the accuracy of the baseline quadrature. The method provides a means of estimating the order of the functional singularity, which may be unknown.