S. AMINI AND LH. SLOAN ABSTRACT. We study the uniform convergence of collocation methods for integral equations on the half line, where the integral operator is a compact perturbation of a Wiener-Hopf operator. We prove that the collocation and the iterated collocation solutions converge to the exact solution with optimal orders of convergence, provided the meshes are appropriately graded to take account of the asymptotic behavior of the solution. As a consequence of the analysis similar optimal convergence results are proved for the case of boundary integral equations on polygonal domains.