Stability of collocation for weakly singular Volterra equations

For Abel integral equations of the second kind, we investigatethe stability of the collocation method with polynomial splines.We characterize the stability domain in terms of the eigenvaluesof the power series, which arises from the method employed.Furthermore, we prove strong stability and provide a rigorousdiscussion of the boundary of the stability region. A few examplesare considered in more depth and numerical illustrations aregiven.