COLLOCATION METHOD FOR SINGULAR INTEGRAL-EQUATIONS ON HOLDER SPACES

The classical polynomial collocation method is considered for a class of Cauchy singular integral equations with variable coefficients on a bounded interval. This method is naturally extended to the case of a n on-zero index of the underlying Fredholm operator. This is done by usi ng the structure of the kernel and a complement of the image of this o perator. For the extended method we directly obtain error bounds in th e norm of the weighted Holder spaces. As an illustration, some numeric al results are given.