A numerical method for the generalized airfoil equation based on the de la Vallée Poussin interpolation

The authors consider the generalized airfoil equation in some weighted Hölder-Zygmund spaces with uniform norms. Using a projection method based on the de la Vallée Poussin interpolation, they reproduce the estimates of the L2 case by cutting off the typical extra logm factor which seemed inevitable to have dealing with the uniform norm, because of the unboundedness of the Lebesgue constants. The better convergence estimates do not produce a greater computational effort: the proposed numerical procedure leads to solve a simple tridiagonal linear system, the condition number of which tends to a finite limit as the dimension of the system tends to infinity, whatever natural matrix norm is considered. Several numerical tests are given.