Superconvergence of Legendre spectral approximation methods for nonlinear Volterra integral equations

This article explores the application of Kumar-Sloan technique based Legendre spectral Galerkin, collocation and multi-Galerkin methods to solve non-linear Volterra Hammerstein integral equations, and demonstrate significant advancements in superconvergence results in both infinity as well as L 2 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.