Quadrature rules for Prandtl's integral equation
We construct an interpolatory quadrature formula of the type \[ \int^{1}_{-1}f'(x)/(y-x)dx\approx \sum^{n}_{i=1}w_{ni}(y)f(x_{ni}), \] where \(f(x)=(1- x)^{\alpha}(1+x)^{\beta}f_ 0(x)\), \(\alpha,\beta >0\), and \(\{x_{ni}\}\) are the n zeros of the n-th degree Chebyshev polynomial of the first kind, \(T_ n(x)\). We also give a convergence result and examine the behavior of the quantity \(\sum^{n}_{i=1}| w_{ni}(y)|\) as \(n\to \infty\).
scientific article; zbMATH DE number 3921809
scientific article