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

The cruciform crack problem ofelasticity gives rise to an integral equation of the secondkind 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 numberof derivatives vanish at theend points 0 and 1. If the transformed kernelis dominated near the origin by a Mellin kernel then we have given conditions under which the use of amodified Euler-Maclaurin quadrature rule and theNyström method gives an approximate solutionwhich converges to the exact solution of theoriginal equation. The method is illustrated with a numerical example. © 1995, Springer-Verlag Berlin Heidelberg. All rights reserved.