A new method for solving Hilbert type singular integral equations

A simple method for solving Hilbert type singular integral equations is proposed. Using the reproducing kernel as the basis of W21[0,2π], the singularity of the considered equation is removed skillfully. Since the problem is discussed in space W21[0,2π], which only require the absolute continuity of the considered function, our method is effective not only for smooth solutions, but also for non-smooth solutions. The final numerical examples show the efficiency of the proposed method.