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