Numerical quadrature for integrals involving oscillating functions - Denich, Eleonora; Novati, Paolo (Journal of Approximation Software, 2024)
This paper deals with the construction of a coupled Gaussian rule for weight functions involving powers, exponentials and trigonometric functions. Starting from a three term recursion for the moments, nodes and weights are computed by using the Chebyshev algorithm together with the Golub and Welsch method. An a posteriori approximation of the quadrature error by means of the generalized averaged Gaussian rules is also considered. Several numerical examples are provided.