Numerical solution of the generalized airfoil equation for an airfoil with a flap

SIAM Journal on Numerical Analysis

Volumn 34, Issue 6, 1997, Pages 2288-2305

  Monegato, G ^a   Sloan, I H ^b  

^a POLITECNICO DI TORINO   (Italy)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Collocation; Galerkin; Mellin convolution operator; Singular integral equations

Indexed keywords

EID: 0000346246     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142995295054     Document Type: Article

References (17)

1. D. BERTHOLD, W. HOPPE, AND B. SILBERMANN, A fast algorithm for solving the generalized airfoil equation. J. Comput. Appl. Math., 43 (1992), pp. 185-219.
2. S. R. BLAND, The two-dimensional oscillating airfoil in a wind tunnel in subsonic flow, SIAM J. Numer. Anal., 18 (1970), pp. 830-848.
3. J. ELSCHNER, On spline approximation for singular integral equations on an interval, Math. Nachr., 139 (1988), pp. 309-319.
4. J. ELSCHNER AND I. G. GRAHAM, An optimal order collocation method for first kind boundary integral equations on polygons, Numer. Math, 70 (1995), pp. 1-31.
5. J. A. FROMME AND M. A. GOLBERG, Numerical solution of a class of integral equations arising in two-dimensional aerodynamics, in Solution Methods for Integral Equations, M. A. Golberg, ed., Plenum Press, New York, 1979, pp. 109-167.
6. M. A. GOLBERG, Introduction to the numerical solution of Cauchy singular integral equations, in Numerical Solution of Integral Equations, M. A. Golberg, ed., Plenum Press, New York, 1990, pp. 183-308.
7. T. HARTMANN AND E. P. STEPHAN, Rates of convergence for collocation with Jacobi polynomials for the airfoil equation, J. Comput. Appl. Math., 51 (1994), pp. 179-191.
8. P. JUNGHANNS AND B. SILBERMANN, The Numerical Treatment of Singular Integral Equations by Means of Polynomial Approximations, preprint, P-MATH-35/86, AdW der DDR, Karl-Weierstrass-Institut für Math., Berlin, 1986.
9. P. JUNGHANNS, Product, integration for the generalized airfoil equation, in Beiträge zur Angewandten Analysis und Informatik, E. Schock, ed., Shaker Verlag, Aachen, 1994, pp. 171-188.
10. L. N. KARPENKO, The approximate solution of a singular integral equation by means of Jacobi polynomials, Prikl. Mat. Mekh., 30 (1966), pp. 564-569.
11. G. MONEGATO AND A. PALAMARA ORSI, Product formulas for Fredholm integral equations with rational kernel functions, in Numerical Integration III, H. Braess and G. Hämmerlin, eds., Internat. Ser. Numer. Math. 85, Birkhäuser, Basel, 1988, pp. 140-156.
12. G. MONEGATO AND P. LEPORA, On the numerical resolution of the generalized airfoil equation with Possio kernel, Numer. Math., 56 (1990), pp. 775-787.
13. G. MONEGATO AND S. PRÖSSDORF, Uniform convergence estimates for a collocation and discrete collocation method for the generalized airfoil equation, in Contribution to Numerical Mathematics, A. G. Agarwal, ed., World Scientific, Singapore, 1993. pp. 285-299. (See also the errata corrige in Internal Report 14, 1993, Dipartimento di Matematica, Politecnico di Torino, Italy.)
14. M. MORI, Quadrature formulas obtained by variable transformation and the DE-rule, J. Comput. Appl. Math., 12-13 (1985), pp. 119-130.
15. S. PRÖSSDORF AND B. SILBERMANN, Numerical Analysis for Integral and Related Operator Equations, Birkhäuser, Basel, 1991.
16. A. RATHSPELD, A quadrature method for a Cauchy singular integral equation with a fixed singularity. Seminar Analysis. Operator Equat. and Numer. Anal. 1985/86, Karl-Weierstrasse-Inst. Math., Akad. Wiss. DDR, Berlin, 1986, pp. 107-117.
17. F. G. TRICOMI, On the finite Hilbert transform, Quart. J. Math., 2 (1951), pp. 199-211.