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A natural interpolation formula for Prandtl's singular integrodifferential equation
Author(s) -
Ioakimidis N. I.
Publication year - 1984
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650040306
Subject(s) - mathematics , prandtl number , quadrature (astronomy) , nyström method , mathematical analysis , interpolation (computer graphics) , fredholm integral equation , integral equation , gaussian quadrature , classical mechanics , physics , heat transfer , motion (physics) , optics , thermodynamics
Prandtl's singular integrodifferential equation and related equations appear in problems of aerofoil and propeller theory in fluid mechanics. Here a natural interpolation formula for the approximation to the unknwon function of Prandtl's equation when this is solved numerically by the direct quadrature method, based on the Gauss‐ and Lobatto‐Chebyshev quadrature rules, is proposed. This interpolation formula is analogous to Nyström's natural interpolation formula for Fredholm integral equations of the second kind and the corresponding formula for singular integral equations. Numerical applications of the same formula are also made.