Integral Equations and Operator Theory

, Volume 7, Issue 4, pp 536–560

A spline collocation method for singular integral equations with piecewise continuous coefficients

  • Siegfried Prößdorf
  • Andreas Rathsfeld
Article

DOI: 10.1007/BF01238865

Cite this article as:
Prößdorf, S. & Rathsfeld, A. Integr equ oper theory (1984) 7: 536. doi:10.1007/BF01238865

Abstract

We consider the collocation method with piecewise linear trial functions for systems of singular integral equations with Cauchy kernel and piecewise continuous coefficients. Necessary and sufficient conditions for the stability in L2 are given. The results are obtained in the case of a closed Ljapunov curve as well as in the case of an interval. The proof of the main theorem is based on a modification of the Banach algebra technique established in the local principle by Gohberg and Krupnik [2]. Our results extend those obtained by Prößdorf and Schmidt [9, 10] from the case of continuous coefficients and unit circle to the case of piecewise continuous coefficients.

Copyright information

© Birkhäuser Verlag 1984

Authors and Affiliations

  • Siegfried Prößdorf
    • 1
  • Andreas Rathsfeld
    • 1
  1. 1.Institut für MathematikAkademie der Wissenschaften der DDRBerlinDDR