Title: Projection and multi-projection methods for second kind Volterra-Hammerstein integral equation

Authors: M. Mandal, K. Kant and G. Nelakanti

Journal: International Journal of Nonlinear Analysis and Applications

Volume: In Press

Year: 2020

Publisher: Semnan University

Abstract: In this article, we discuss the piecewise polynomial based Galerkin method to approximate the solutions of second kind Volterra-Hammerstein integral equations. We discuss the convergence of the approximate solutions to the exact solutions and obtain the orders of convergence O(h^r ) and O(h^{2r} ), respectively, for Galerkin and its iterated Galerkin methods in uniform norm, where h, r denote the norm of the partition and smoothness of the kernel, respectively. We also obtain the superconvergence results for multi-Galerkin and iterated multi-Galerkin methods. We show that iterated multi-Galerkin method has the order of convergence O(h 3r ) in the uniform norm. Numerical results are provided to demonstrate the theoretical results.