The Product Midpoint Rule for Abel-Type Integral Equations of the First Kind with Perturbed Data

We consider the regularizing properties of the product midpoint rule for the stable solution of Abel-type integral equations of the first kind with perturbed right-hand sides. The impact of continuity and smoothness properties of solutions on the convergence rates is described in detailed manner by using a scale of Holder spaces. In addition, correcting starting weights are introduced to get rid of undesirable initial conditions. The proof of the inverse stability of the quadrature weights relies on Banach algebra techniques. Finally, numerical results are presented.