The discrete sloan iterate for the generalized airfoil equation

Abstract

We have defined and established the superconvergence of the Sloan iterate obtained from a polynomial Galerkin approximation for solving the generalized airfoil equation. When all the integrals involved are evaluated by using Gaussian quadratures with the same number of nodes as basis elements, the resulting discrete Sloan iterate becomes the Nyström approximation obtained by using the same rules. From this it follows that the discrete Sloan iterate v̂ n and the discrete Galerkin approximation v n agree at the quadrature nodes. Thus v̂ n converges no faster locally than v n . For practical purposes, computational superconvergence does not occur.