On a quadrature formula for the direct value of the normal derivative of a simple layer potential in a 3D case

The improved quadrature formula for the direct value of the normal derivative of a simple layer potential with smooth density is derived for a wide class of smooth surfaces. Novel quadrature formula provides higher accuracy of computations than usual formula. The derived quadrature formula can be used for numerical solving of boundary value problems for equations of mathematical physics by the method of boundary integral equations.