Polynomially based multi-projection methods for Fredholm integral equations of the second kind

In this paper, we propose a multi-projection and iterated multi-projection methods for Fredholm integral equations of the second kind with a smooth kernel using polynomial bases. We obtain super-convergence rates for the approximate solutions, more precisely, we prove that in M-Galerkin and M-collocation methods not only iterative solution un′ approximates the exact solution u in the supremum norm with the order of convergence n-4k, but also the derivatives of un′ approximate the corresponding derivatives of u in the supremum norm with the same order of convergence, n being the degree of polynomial approximation and k being the smoothness of the kernel.