Collocation for Cauchy singular integral equations

Abstract

The paper is concerned with the stability of collocation methods for Cauchy singular integral equations with piecewise continuous coefficients on an interval, where these methods look for an approximate solution of the form μ(x)pn(x) with a Jacobi weight μ(x) and a polynomial pn(x). Here, the Chebyshev weight μ(x)=1-x1+x and collocation with respect to Chebyshev nodes of first and fourth kind are considered.