L2 error estimates of collocation methods for solving certain singular integral equations

In this paper, we propose some special collocation schemes for solving Hilbert type singular and hypersingular integral equations on a circle, based on the superconvergence of quadrature rules for evaluating the corresponding singular integrals. With the aid of spectral analysis, the optimal and suboptimal L2 error estimates are established in a unified framework. At last, several numerical examples are provided to confirm the theoretical analysis.