Superconvergence of Legendre Spectral Approximation Methods for Nonlinear Volterra Integral Equations

This paper explores the application of Kumar–Sloan technique-based Legendre spectral Galerkin, collocation and multi-Galerkin methods to solve nonlinear Volterra–Hammerstein integral equations, and demonstrate significant advancements in superconvergence results in both infinity as well as [Formula: see text] norms. It is concluded that without going to the iterated versions, we obtain the improved superconvergence rates for Legendre spectral Galerkin, collocation and multi-Galerkin methods as higher as that of Legendre spectral iterated Galerkin, iterated collocation and iterated multi-Galerkin methods. Numerical results are given to show the efficiency of the proposed technique.