Richardson extrapolation of iterated discrete Galerkin solution for two-dimensional Fredholm integral equations

Abstract

In this paper, we study the numerical solution of two-dimensional Fredholm integral equation by discrete Galerkin and iterated discrete Galerkin method. We are able to derive an asymptotic error expansion of the iterated discrete Galerkin solution. This expansion covers arbitrarily high powers of the discretization parameters if the solution of the integral equation is smooth. The expansion gives rise to Richardson-type extrapolation schemes which rapidly improve the original rate of the convergence. Numerical experiments confirm our theoretical results.