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P. Junghanns; U.Weber : Local theory of projection methods for Cauchy singular integral equations on an interval

P. Junghanns; U.Weber : Local theory of projection methods for Cauchy singular integral equations on an interval


Author(s) :
P. Junghanns; U.Weber
Title :
Local theory of projection methods for Cauchy singular integral equations on an interval
Electronic source :
[gzipped ps-file] 108 kB
Preprint series
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 97-25, 1997
Published in :
Boundary Integral Methods,
Appeared in :
Boundary Integral Methods
Mathematics Subject Classification :
45E05 [ Integral equations with kernels of Cauchy type ]
45L10 [ Numerical approximation of solutions of integral equations ]
Abstract :
We consider a finite section (Galerkin) and a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polymoninals, where the coefficients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra techniques, where also the system case is mentioned. With the help of appropriate Sobolev spaces a result on convergence rates is proved. Computational aspects are discussed in order to develop an effective algorithm. Numerical results, also for a class of nonlinear singular integral equations, are presented.
Keywords :
Cauchy singular integral equation, projection methods, stability
Language :
english
Publication time :
12/1997

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