Error Analysis of Discrete Legendre Multi-Projection Methods for Nonlinear Fredholm Integral Equations

In this paper, polynomially-based discrete M-Galerkin and M-collocation methods are proposed to solve nonlinear Fredholm integral equation with a smooth kernel. Using suciently accurate numerical quadrature rule, we establish superconvergence results for the approximate and iterated approximate solutions of discrete Legendre M-Galerkin and M-collocation methods in both infinity and L-2-norm. Numerical examples are presented to illustrate the theoretical results.