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

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