Quadrature methods for integro-differential equations of Prandtl's type in weighted spaces of continuous functions

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. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

The paper discusses the approximate solution of Prandtl's type of integro-differential equations using quadrature methods with optimal Lagrange interpolation processes. It proves the stability and convergence of these methods in suitable weighted spaces of continuous functions. The method's efficiency has been validated through numerical experiments, including comparisons with other numerical procedures. As an application, the method has been successfully implemented to solve Prandtl's equation governing circulation air flow around the contour of elliptic or rectangular wing profiles.