The successive approximations method for the airfoil equation

摘要

The successive approximations (or Neumann iterations) method for the solution of Fredholm integral equations of the second kind is applied here for the first time, after an appropriate modification, to a Cauchy-type singular integral equation of the first kind, the airfoil equation. The convergence of the method is investigated and three simple applications are made. The numerical implementation of the method (by using Gaussian quadrature rules) is also described in detail and numerical results verifying the accuracy and convergence of the method are displayed.