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

•Integro-differential equations of Prandtl’s type in weighted uniform norms.•A collocation-quadrature method based on Lagrange projection at Jacobi zeros.•Study of stability, convergence and conditioning of the final linear systems.•Error estimates in weighted Zygmund norms.•Numerical experiments fo...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 393; p. 125721
Main Authors De Bonis, Maria Carmela, Occorsio, Donatella
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.03.2021
Subjects
Hypersingular integral equation
Lagrange interpolation
Prandtl’s integral equation
Quadrature method
Quadrature method
65R20
Lagrange interpolation
Hypersingular integral equation
45E05
Prandtl’s integral equation
41A05
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Summary:•Integro-differential equations of Prandtl’s type in weighted uniform norms.•A collocation-quadrature method based on Lagrange projection at Jacobi zeros.•Study of stability, convergence and conditioning of the final linear systems.•Error estimates in weighted Zygmund norms.•Numerical experiments for Prandtl’s equation for two different wing-shapes. The paper deals with the approximate solution of integro-differential equations of Prandtl’s type. Quadrature methods involving “optimal” Lagrange interpolation processes are proposed and conditions under which they are stable and convergent in suitable weighted spaces of continuous functions are proved. The efficiency of the method has been tested by some numerical experiments, some of them including comparisons with other numerical procedures. In particular, as an application, we have implemented the method for solving Prandtl’s equation governing the circulation air flow along the contour of a plane wing profile, in the case of elliptic or rectangular wing-shape.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2020.125721