Filtered interpolation for solving Prandtl’s integro-differential equations

In order to solve Prandtl-type equations we propose a collocation-quadrature method based on de la Vallée Poussin (briefly VP) filtered interpolation at Chebyshev nodes. Uniform convergence and stability are proved in couple of Hölder-Zygmund spaces locally continuous functions. With respect classical methods Lagrange the same collocation nodes, succeed reproducing optimal rates L2 case cut off typical log factor which seemed inevitable dealing with uniform norms. Such an improvement does not require greater computational effort. particular, fast algorithm solution simple 2-bandwidth linear system prove that, as its dimension tends infinity, sequence condition numbers (in any natural matrix norm) finite limit.