An algorithm for the approximate solution of integral equations of Mellin type

Summary.

The cruciform crack problem of elasticity gives rise to an integral equation of the second kind on [0,1] whose kernel has a fixed singularity at (0,0). We introduce a transformation of [0,1] onto itself such that an arbitrary number of derivatives vanish at the end points 0 and 1. If the transformed kernel is dominated near the origin by a Mellin kernel then we have given conditions under which the use of a modified Euler-Maclaurin quadrature rule and the Nyström method gives an approximate solution which converges to the exact solution of the original equation. The method is illustrated with a numerical example.