Extrapolation Using a Modified Projection Method

In [14], a new method based on projections onto a space of piecewise polynomials of degree ≤r − 1 has been shown to give a convergence of order 4r for second-kind integral equations. The size of the system of equations that must be solved, in implementing this method, remains the same as for the Galerkin/collocation method. In this article the solution obtained by the proposed method is shown to have an asymptotic series expansion which remains valid in the discrete version. The Richardson extrapolation can then be used to further improve the order of convergence to 4r + 2.