A note on a superconvergence result for the generalized airfoil equation

摘要

We obtain convergence results and error estimates for calculating linear functionals of solutions of a class of Cauchy singular integral equations via Galerkin's method. These results generalize the superconvergence estimates obtained by Miel [7], and involve extending the class of functionals, relaxing the smoothness conditions imposed, and determining the effects of quadrature errors in the numerical implementation of this method. In particular, it is shown that full superconvergence can be restored by evaluating the integrals sufficiently accurately.