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 Holder-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 log m factor which seemed inevitable to have dealing with 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.