U. Luther : Uniform Convergence of Polynomial Approximation Methods for Prandtl

Author(s) :

U. Luther

Title :

Uniform Convergence of Polynomial Approximation Methods for Prandtl

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 99-11, 1999

Mathematics Subject Classification :

45E05 [ Integral equations with kernels of Cauchy type ]

45L05 [ Theoretical approximation of solutions of integral equations ]

65R20 [ Integral equations (numerical methods) ]

41A05 [ Interpolation ]

Abstract :

We investigate weighted uniform convergence of collocation type methods for Prandtl's Integro-differential equation with the help of two scales of Besov spaces. The first scale is based on a weighted space of continuous functions, and the second one contains spaces of integrable functions. To prove stability and (almost) optimal convergence estimates, a general concept of modified collocation type methods is used, which is applicable to different kinds of approximation methods, like pure collocation methods and collocation-quadrature methods. The convergence results are obtained under very little assumptions on the right hand side of the equation, which allow weak singularities inside (-1,1).

Keywords :

Hypersingular integral equation, Weighted Besov spaces, Weighted spaces of continuous functions

Language :

english

Publication time :

12/1999