On polynomial collocation for Cauchy singular integral equations with fixed singularities
- Junghanns, Peter
- Rathsfeld, Andreas
2010 Mathematics Subject Classification
- 45L10 65R20
- Cauchy singular integral equation, Mellin kernel, polynomial collocation, stability, convergence
In this paper we consider a polynomial collocation method for the numerical solution of Cauchy singular integral equations with fixed singularities over the interval, where the fixed singularities are supposed to be of Mellin convolution type. For the stability and convergence of this method in weighted L2 spaces, we derive necessary and sufficient conditions.
- Integral Equations and Operator Theory 43, 2002, pp. 155-176