论文标题
过滤的用于求解PrandTL的integro-differention方程的插值
Filtered interpolation for solving Prandtl's integro-differential equations
论文作者
论文摘要
为了求解prandtl型方程，我们提出了一种基于Chebyshev节点的VP过滤插值的搭配 - 质量方法。在几个局部连续功能的Zygmund空间中证明了均匀的收敛性和稳定性。关于基于同一配置节点的Lagrange插值的经典方法，我们通过切断典型的日志因子来成功地重现L2情况的最佳收敛速率，而L2情况似乎不可避免地处理统一的规范。这样的改进不需要更大的计算工作。特别是我们提出了一种基于简单的2带宽线性系统的解决方案的快速算法，并证明，由于其尺寸趋于无穷大，因此条件数（在任何天然矩阵规范中）的序列趋向于有限的极限。
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.
