The numerical solution of a fredholm integral equation with a singular kernel

An analysis is presented of a Fredholm integral equation of the second kind with a weakly singular kernel. The equation results from a mixed boundary value problem that describes a crack in an inhomogeneous elastic solid. The singularity in the kernel is dealt with by a numerical procedure known as product integration. The solution of the integral equation allows one to solve for the field quantities that are relevant to the boundary value problem. In terms of the field quantities, fracture parameters are calculated and the effect of material inhomogeneity upon crack stability is analyzed.