We consider a finite section (Galerkin) and a collocation method for Cauchy singular
integral equations on the interval based on weighted Chebyshev polymoninals, where
the coefficients of the operator are piecewise continuous.
Stability conditions are derived using Banach algebra techniques, where
also the system case is mentioned. With the help of
appropriate Sobolev spaces a result on convergence rates is proved.
Computational aspects are discussed in order to develop
an effective algorithm. Numerical results, also
for a class of nonlinear singular integral equations,
are presented
