The successive approximations method for the airfoil equation
The successive approximations method for the solution of Fredholm equations of the second kind is applied in this paper, for the first time, and after an appropriate modification, to the airfoil equation [\textit{F. G. Tricomi}, Integral Equations (1957; Zbl 0078.094)]. Rather than giving just one more method for the solution of this equation, the aim of the paper is to show that a modification of the successive approximations method may be applied to the direct solution of some Cauchy type singular integral equations of the first kind. The numerical implementation of the method, by using Gaussian quadrature rules, is described in detail and applied to some simple cases. Numerical results verifying the accuracy and convergence of the method are displayed.
Cauchy type singular integral equations of the first kind
scientific article; zbMATH DE number 4083169