Local theory of projection methods for Cauchy singular integral equations on an interval

• Main Authors: Junghanns, P., U.Weber
• Language: English
• Published: Technische Universität Chemnitz 1998
• Subjects: info:eu-repo/classification/ddc/510; ddc:510; Cauchy singular integral equation; projection methods; stability; MSC 45E05; MSC 45L10
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801281; https://monarch.qucosa.de/id/qucosa%3A17504; https://monarch.qucosa.de/api/qucosa%3A17504/attachment/ATT-0/; https://monarch.qucosa.de/api/qucosa%3A17504/attachment/ATT-1/; https://monarch.qucosa.de/api/qucosa%3A17504/attachment/ATT-2/

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.