Nystrom-Clenshaw-Curtis quadrature for integral equations with discontinuous kernels

A new highly accurate numerical approximation scheme based on a Gauss type Clenshaw-Curtis quadrature for Fredholm integral equations of the second kind x(t) + integral(a)(b) k(t, s)x(s)ds = y(t), 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. Relation to the singular value decomposition is indicated. Application to integro-differential Schrodinger equations with nonlocal potentials is given.