The application of a collocation method with respect to the Chebyshev nodes of second kind together with a Newton iteration to a class of nonlinear Cauchy singular integral equations is discussed. The investigation of the convergence of the Newton method is based on the stability of the respective c
Collocation Methods and Their Modifications for Cauchy Singular Integral Equations on the Interval
✍ Scribed by Alexander Rogozhin
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2004
- Tongue
- English
- Weight
- 222 KB
- Volume
- 1
- Category
- Article
- ISSN
- 1660-5446
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📜 SIMILAR VOLUMES
## Abstract We prove representations for the coefficient matrices of the linear systems which occur by applying certain collocation methods to Cauchy singular integral equations. These representations use fast discrete trigonometric transforms and give the possibility to design fast algorithms for
## Abstract Necessary and sufficient conditions for the stability of certain collocation methods applied to Cauchy singular integral equations on an interval are presented for weighted **L**__'__ norms. Moreover, the behavior of the approximation numbers, in particular their so‐called __k__ ‐splitt
This paper is devoted to the approximate solution of one-dimensional singular integral equations on a closed curve by spline collocation methods. As the main result we give conditions which are sufficient and in special cases also necessary for the convergence in SOBOLEV norms. The paper is organiz