On the numerical evaluation of certain 2-D singular integrals

Abstract

The problem of approximating certain two-dimensional Cauchy principal value integrals is here considered, product integration formulas with multiple nodes are presented and the behaviour of the remainder is analyzed. Next a particular class of cubature rules is generated, having the peculiar property that the set of the nodes holds fixed while their multiplicities vary. Some numerical examples of application of the latter rules are also provided.