Superconvergence Results for Weakly Singular Fredholm–Hammerstein Integral Equations. (4th April 2019) - Mandal, Moumita; Nelakanti, Gnaneshwar
Abstract: In this article, we consider the multi-Galerkin method for solving the Fredholm–Hammerstein integral equations with weakly singular kernels, using piecewise polynomial bases. We show that multi-Galerkin method has order of convergence O ( h r + α ) for the algebraic kernel, whereas for logarithmic kernel, it converges with the order O (   log     h   h r + 1 ) in uniform norm, where h is the norm of the partition and r is the smoothness of the solution. We also discuss the iterated multi-Galerkin method. We prove that iterated multi-Galerkin method has order of convergence O ( h r + 2 α ) for the algebraic kernel and for logarithmic kernel, it has order of convergence of order O ( (   log     h ) 2   h r + 2 ) in uniform norm. Numerical examples are given to illustrate the theoretical results.