A collocation method for the generalized airfoil equation for an airfoil with a flap

摘要

We are concerned with the numerical solution of the generalized airfoil equation for an airfoil with a flap by means of global algebraic polynomial approximants. This problem has been considered in a recent paper by Monegato and Sloan [SIAM J. Numer. Anal., 34 (1997), pp. 2288-2305], where the authors proved the stability and convergence of a Galerkin method based on high order polynomials. They also presented very promising numerical results for the corresponding collocation method but left the theoretical results of stability and convergence as an open problem. We have succeeded in proving the stability and convergence properties of this collocation method by slightly modifying it in the neighborhood of the flap. The rate of convergence we have derived for our collocation method is very similar to that of the above Galerkin method. [References: 25]