Integrating composed singularities using nonuniform subdivision and extrapolation

An approach to the computation of approximations to multidimensional integrals over an n-dimensional hyper-rectangular region, when the integrand has a composed singularity, is described. This approach is based on nested applications of a recently published nonuniform subdivision technique of the region of integration. The technique fits well to the subdivision strategy used in many adaptive algorithms. As in the noncomposed problems the technique results in good numerical stability properties. A two-dimensional experimental code is used to demonstrate the power of this approach.