Discrete Legendre spectral projection methods for Fredholm–Hammerstein integral equations

In this paper we discuss the discrete Legendre Galerkin and discrete Legendre collocation methods for Fredholm–Hammerstein integral equations with smooth kernel. Using sufficiently accurate numerical quadrature rule, we obtain optimal convergence rates for both discrete Legendre Galerkin and discrete Legendre collocation solutions in both infinity and L2L2-norm. Numerical examples are given to illustrate the theoretical results.