Legendre Spectral Solution of Weakly Singular Hammerstein Integral Equations

In this paper, polynomially based projection-type and the modified Galerkin-type methods for approximating the solution of Hammerstein integral equations with a weakly singular kernel are proposed. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of the proposed methods and that of superconvergence of the iterated method are analyzed. A numerical example is given to illustrate the theoretical estimates.