A collocation method for nonlinear Cauchy singular integral equations

The application of a collocation method with respect to the Chebyshev nodes of second kind together with a Newton iteration to a class of nonlinear Cauchy singular integral equations is discussed. The investigation of the convergence of the Newton method is based on the stability of the respective collocation method applied to linear Cauchy singular integral equations, which is proved by using Banach algebra techniques. Numerical results are presented.