Discrete Legendre Projection Methods for the Fredholm Integral Equations of the Second Kind

In this paper, we consider the discrete Galerkin and discrete collocation methods to solve the Fredholm integral equations of the second kind using Legendre polynomial bases. Using suffi-ciently accurate numerical quadrature rule, we obtain the error bounds for discrete Legendre solu-tions and iterated discrete Legendre solution for L² norm in both Legendre Galerkin and Legendre collocation method. We also obtain the superconvergence results for iterated Legendre Galerkin solution over Legendre Galerkin solution in L²-norm. Numerical example is presented to illustrate the theoretical results.