The paper deals with the approximate solution of integro-differential equations of Prandtl's type. Quadrature methods involving ``optimal'' Lagrange interpolation processes are proposed and conditions under which they are stable and convergent in suitable weighted spaces of continuous functions are proved. The efficiency of the method has been tested by some numerical experiments, some of them including comparisons with other numerical procedures. In particular, as an application, we have implemented the method for solving Prandtl's equation governing the circulation air flow along the contour of a plane wing profile, in the case of elliptic or rectangular wing-shape.

中文翻译：

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连续函数加权空间中Prandtl型积分微分方程的求积方法

本文研究了Prandtl型积分微分方程的近似解。提出了涉及“最佳”拉格朗日插值过程的正交方法，并证明了它们在连续函数的合适加权空间中稳定和收敛的条件。该方法的效率已经通过一些数值实验进行了测试，其中一些包括与其他数值程序的比较。特别是，作为一个应用，我们已经实现了求解 Prandtl 方程的方法，该方程控制沿平面机翼轮廓轮廓的循环气流，在椭圆或矩形机翼形状的情况下。