Convergence analysis for derivative dependent Fredholm-Hammerstein integral equations with Green's kernel

In this article, we consider a class of derivative dependent Fredholm-Hammerstein integral equations i.e., the integral equation, where the nonlinear function inside the integral sign is dependent on derivative and the kernel function is of Green's type. We propose the piecewise polynomial based Galerkin and iterated Galerkin methods to solve these type of derivative dependent Fredholm-Hammerstein integral equations. We discuss the convergence and error analysis of the proposed methods and also obtain the superconvergence results for iterated Galerkin approximations. Some numerical results are given to illustrate this improvement.