Abstract. The convergence of the aforementioned quadrature rules for integrands possessing Holder-continuous derivatives of an appropriate order is proved to be uniform and not only pointwise. The rate of convergence is also established and an application to the numerical solution of singular integral equations is made.

Abstract. The convergence of the weighted Galerkin method (based on Chebyshcv or Jaeobi polynomials) for the direct numerical solution of one-dimensional, real Cauchy-type singular integral equations of the first and of the second kind on a finite interval is proved under sufficiently weak continuity assumptions for the kernels and the right-side functions of the integral equations. The convergence of the above method will be proved under sufficiently weak continuity assumptions for the kernels and the right-side functions of the integral equations and will be mainly based on the method used by Linz

No abstract

No abstract