On improvement of the iterated Galerkin solution of the second kind integral equations

For a second kind integral equation with a kernel which is less smooth along the diagonal, an approximate solution obtained by using a method proposed by the author in an earlier paper, is shown to have a higher rate of convergence than the iterated Galerkin solution. The projection is chosen to be either the orthogonal projection or an interpolatory projection onto a space of piecewise polynomials. The size of the system of equations that needs to be solved, in order to compute the proposed solution, remains the same as in the Galerkin method. The improvement of the proposed solution is illustrated by a numerical example.