WIAS Preprint No. 625, (2000)

On polynomial collocation for Cauchy singular integral equations with fixed singularities



Authors

  • Junghanns, Peter
  • Rathsfeld, Andreas

2010 Mathematics Subject Classification

  • 45L10 65R20

Keywords

  • Cauchy singular integral equation, Mellin kernel, polynomial collocation, stability, convergence

Abstract

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.

Appeared in

  • Integral Equations and Operator Theory 43, 2002, pp. 155-176

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