Integration of Prandtl’s equation with the aid of quadrature formulae of Gauss type
Author:
Lazăr Dragoş
Journal:
Quart. Appl. Math. 52 (1994), 23-29
MSC:
Primary 65R20; Secondary 65D30, 76G25, 76M99
DOI:
https://doi.org/10.1090/qam/1262314
MathSciNet review:
MR1262314
Full-text PDF Free Access
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Abstract: The subject of this note is to present a method that can be used to integrate Prandtl’s equation by means of Gauss-type quadrature formulae.
N. I. Ioakimidis, A natural interpolation formula for Prandtl’s singular integrodifferential equation, Int. J. Numer. Methods Fluids 4, 283 (1984)
G. Monegato and V. Pennacchietti, Quadrature rules for Prandtl’s integral equation, Computing 37, 31 (1986)
N. I. Ioakimidis and P. S. Theocaris, On the numerical solution of singular integrodifferential equations, Quart. Appl. Math. 37, 325 (1979)
G. Monegato, On the weights of certain quadratures for the numerical evaluation of Cauchy principal value integrals and their derivatives, Numer. Math. 50, 273 (1987)
L. Dragos, Method of fundamental solutions. A novel theory of lifting surface in a subsonic flow, Arch. Mech. 35, 575 (1983)
K. W. Mangler, Improper integrals in theoretical aerodynamics, Br. Aero. Res. Council, R&M 2424 (1951)
Ch. Fox, A generalization of the Cauchy principal value, Canadian J. Math. 9, 110 (1957)
N. I. Muskhelishvili, Singular Integral Equations, P. Noordhoff, Groningen, 1953
Th. von Karman and J. M. Burgers, General aerodynamic theory-perfect fluids, in Aerodynamic Theory (Ed. W. F. Durand) vol. II, Springer, Berlin, 1935
N. I. Ioakimidis, A natural interpolation formula for Prandtl’s singular integrodifferential equation, Int. J. Numer. Methods Fluids 4, 283 (1984)
G. Monegato and V. Pennacchietti, Quadrature rules for Prandtl’s integral equation, Computing 37, 31 (1986)
N. I. Ioakimidis and P. S. Theocaris, On the numerical solution of singular integrodifferential equations, Quart. Appl. Math. 37, 325 (1979)
G. Monegato, On the weights of certain quadratures for the numerical evaluation of Cauchy principal value integrals and their derivatives, Numer. Math. 50, 273 (1987)
L. Dragos, Method of fundamental solutions. A novel theory of lifting surface in a subsonic flow, Arch. Mech. 35, 575 (1983)
K. W. Mangler, Improper integrals in theoretical aerodynamics, Br. Aero. Res. Council, R&M 2424 (1951)
Ch. Fox, A generalization of the Cauchy principal value, Canadian J. Math. 9, 110 (1957)
N. I. Muskhelishvili, Singular Integral Equations, P. Noordhoff, Groningen, 1953
Th. von Karman and J. M. Burgers, General aerodynamic theory-perfect fluids, in Aerodynamic Theory (Ed. W. F. Durand) vol. II, Springer, Berlin, 1935
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Article copyright:
© Copyright 1994
American Mathematical Society
