Superconvergent multi-Galerkin method for nonlinear Fredholm–Hammerstein integral equations

Abstract

In this paper, we apply the multi-Galerkin method with Kumar–Sloan technique to improve the superconvergence rates and find the numerical solution of non-linear Fredholm–Hammerstein integral equations for both smooth as well as the weakly singular kernels. Considering piecewise polynomial as basis function of the approximating subspace, we derive the improved superconvergence rates for multi-Galerkin method based on Kumar–Sloan approximations which are exactly the same superconvergence rates for the approximate solution as in the case of iterated multi-Galerkin method. We have shown improved superconvergence results without the need for iterated multi-Galerkin method. Theoretical results are verified using numerical examples.