A numerical method based on spline quasi-interpolating projectors for a class of Cauchy singular integral equations✩

This work presents a numerical method for a class of Cauchy singular integral equations. In particular, it is analyzed a collocation approach that relies on spline quasi-interpolating projectors, which are tailor-made with respect to the relevant features of the problem at hand. Theoretical estimates related to the convergence order of the method are provided, together with an analysis on the structure of the matrices appearing at the discretized level, which points out some propitious computational and spectral properties. Several numerical results are shown, validating the proposed error estimates.