Waveform relaxation of partial differential equations

In this paper, we investigate a numerical method for the construction of an optimal set of quadrature rules in the sense of Borges (Numer. Math. 67, 271–288, 1994) for two or three definite integrals with the same integrand and interval of integration, but with different weight functions, related to an arbitrary multi-index. The presented method is illustrated by numerical examples.