A new method for solving Hilbert type singular integral equations

Abstract

Abstract A simple method for solving Hilbert type singular integral equations is proposed. Using the reproducing kernel as the basis of W 2 1 [ 0 , 2 π ] , the singularity of the considered equation is removed skillfully. Since the problem is discussed in space W 2 1 [ 0 , 2 π ] , 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.