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