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
On Spline Approximation for Singular Integral Equations on an Interval
β Scribed by Johannes Elschner
- Publisher
- John Wiley and Sons
- Year
- 1988
- Tongue
- English
- Weight
- 559 KB
- Volume
- 139
- Category
- Article
- ISSN
- 0025-584X
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π SIMILAR VOLUMES
## Abstract A class of nonlinear singular integral equations of Cauchy type on a finite interval is transformed to an equivalent class of (discontinuous) boundary value problems for holomorphic functions in the complex unit disk. Using recent results on the solvability of explicit RiemannβHilbert p
The classical polynomial collocation method is considered for a class of Cauchy singular integral equations with variable coefficients on a bounded interval. This method is naturally extended to the case of a non-zero index of the underlying Fredholm operator. This is done by using the structure of
## Abstract An approximation method for a wide class of twoβdimensional integral equations is proposed. The method is based on using a special function system. Orthonormality and good interaction with fundamental integral operators arising in partial differential equations are remarkable properties