Asymptotic expansion of iterated Galerkin solution of Fredholm integral equations of the second kind with Green's kernel

Abstract

We consider a Fredholm integral equation of the second kind with kernel of the type of Green’s function. Iterated Galerkin method is applied to such an integral equation. For $r\ge 1$, a space of piecewise polynomials of degree $\le r-1$ with respect to a uniform partition is chosen to be the approximating space. We obtain an asymptotic expansion for the iterated Galerkin solution at the partition points. Richardson extrapolation is used to increase the order of convergence. A numerical example is considered to illustrate our theoretical results.