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 a couple of Hölder-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 and cut 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.

为了解决Prandtl型方程，我们提出了一种基于切比雪夫节点上的de laValléePoussin（简称VP）滤波插值的搭配正交方法。在几个局部连续函数的Hölder-Zygmund空间中证明了一致的收敛性和稳定性。关于在相同配置节点上基于Lagrange插值的经典方法，我们成功地再现了L ²情况的最优收敛速度并切断了典型对数似乎不可避免地要处理统一规范的因素。这种改进不需要更多的计算工作。特别是，我们基于简单的2带宽线性系统的解决方案提出了一种快速算法，并证明了随着其维数趋于无穷大，条件编号的序列（在任何自然矩阵范数中）都趋于有限的极限。