Richardson extrapolation based on superconvergent Nyström and degenerate kernel methods

For computing the approximated solution of a second kind integral equation with a smooth kernel, we investigate in this paper the Richardson extrapolation using superconvergent Nyström and degenerate kernel methods based on interpolatory projection onto the space of (discontinuous) piecewise polynomials of degree ≤ r - 1 . We obtain asymptotic series expansions for the approximate solutions and we show that the order of convergence 4 r in the interpolation at Gauss points can be improved to 4 r + 2 . We illustrate the improvement of the order of convergence by numerical experiments.