On the numerical solution of the generalized Prandtl equation using variation-diminishing splines

Convergence results are proved for Cauchy principal value integrals of the Schoenberg variation-diminishing splines and its first derivative. The use of such splines in the numerical solution of the Prandtl and generalized Prandtl integral equations is proposed. A Nystrِm-type method and a modified Nystrِm method are used and compared computationally.