Quadrature methods for integro-differential equations of Prandtl's type\n in weighted spaces of continuous functions

2020/08/01 by Maria Carmela De Bonis, Donatella Occorsio, De Bonis, Maria Carmela +1
Mathematics · Engineering · Environmental Science · #Differential Equations and Numerical Methods #Aerodynamics and Fluid Dynamics Research #Wind and Air Flow Studies

paper · pdf · doi:10.48550/arxiv.2008.00294

Abstract

The paper deals with the approximate solution of integro-differential\nequations of Prandtl's type. Quadrature methods involving ``optimal'' Lagrange\ninterpolation processes are proposed and conditions under which they are stable\nand convergent in suitable weighted spaces of continuous functions are proved.\n The efficiency of the method has been tested by some numerical experiments,\nsome of them including comparisons with other numerical procedures. In\nparticular, as an application, we have implemented the method for solving\nPrandtl's equation governing the circulation air flow along the contour of a\nplane wing profile, in the case of elliptic or rectangular wing-shape.\n

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