LAUSR

In this paper, we consider the Legendre Galerkin and Legendre collocation methods for solving the Fredholm–Hammerstein integral equation with weakly singular kernels. We evaluate the convergence rates for both the methods in both $$L^2$$L2 and infinity-norm. To improve the convergence rates, iterated Legendre Galerkin and iterated Legendre collocation methods have been considered. We prove that iterated Legendre Galerkin methods converge faster than Legendre Galerkin methods in both $$L^2$$L2 and infinity-norm. Numerical examples are presented to validate the theoretical estimate.