High Accuracy Method for Integral Equations with Discontinuous Kernels

whose kernel k(t, s) is either discontinuous or not smooth along the main diagonal, is presented. This scheme is of spectral accuracy when k(t, s) is infinitely differentiable away from the diagonal t = s, and is also applicable when k(t, s) is singular along the boundary, and at isolated points on the main diagonal. The corresponding composite rule is described. Application to integro-differential Schroedinger equations with non-local potentials is given.