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

摘要

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.