Transformations for evaluating singular boundary element integrals
Journal of Computational and Applied Mathematics
An Efficient Algorithm for Solving the Generalized Airfoil Equation
Journal of Scientific Computing
A fast Petrov-Galerkin method for solving the generalized airfoil equation
Journal of Complexity
Numerical methods for Fredholm integral equations with singular right-hand sides
Advances in Computational Mathematics
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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.