%0 Journal Article
%T Projection and multi-projection methods for second kind Volterra-Hammerstein integral equation
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Mandal, Moumita
%A Kant, Kapil
%A Nelakanti, Gnaneshwar
%D 2021
%\ 07/01/2021
%V 12
%N 2
%P 275-291
%! Projection and multi-projection methods for second kind Volterra-Hammerstein integral equation
%K Volterra-Hammerstein integral equations
%K Galerkin method
%K Multi-Galerkin method
%K Piecewise polynomials
%K Superconvergence rates
%R 10.22075/ijnaa.2020.18624.2026
%X 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 $mathcal O(h^{r})$ and $mathcal O(h^{2r}),$ respectively, for Galerkin and its iterated Galerkin methods in uniform norm, where $h, ~r$ denotes 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 $mathcal O(h^{3r})$ in the uniform norm. Numerical results are provided to demonstrate the theoretical results.
%U https://ijnaa.semnan.ac.ir/article_5039_941ca03a7b799e9881022c92340f39e6.pdf