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Solution Methods for Integral Equations pp 147–167Cite as

Numerical Solution of a Class of Integral Equations Arising in Two-Dimensional Aerodynamics—The Problem of Flaps

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Part of the book series: Mathematical Concepts and Methods in Science and Engineering ((MCSENG,volume 18))

Abstract

Bland’s collocation method is extended to calculate aerodynamic forces on airfoils with flaps. This requires the solution of Cauchy singular integral equations with discontinuous right-hand sides. Straightforward application of collocation is shown to yield slow convergence, of order 1/N. Examination of a variety of methods that have been proposed to accelerate convergence leads us to select a simple form of extrapolation as an effective means of achieving engineering accuracy. Numerical results are presented supporting these assertions.

This work was supported by NASA Grant NSG-2140.

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Authors and Affiliations

  1. University of Nevada at Las Vegas, Las Vegas, Nevada, USA

    J. A. Fromme (Associate Professor of Mathematics) & M. A. Golberg (Professor of Mathematics)

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  1. J. A. Fromme
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  2. M. A. Golberg
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  1. Department of Mathematics, University of Nevada at Las Vegas, Las Vegas, Nevada, USA

    Michael A. Golberg

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Fromme, J.A., Golberg, M.A. (1979). Numerical Solution of a Class of Integral Equations Arising in Two-Dimensional Aerodynamics—The Problem of Flaps. In: Golberg, M.A. (eds) Solution Methods for Integral Equations. Mathematical Concepts and Methods in Science and Engineering, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1466-1_5

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