NUMERICAL SOLUTIONS OF LINEAR SINGULAR INTEGRAL EQUATIONS BY MEANS OF TIKHONOV REGULARIZATION AND REPRODUCING KERNELS

Abstract. In this paper, a reproducing kernel method is proposed to per-form the analysis of different types of singular integral equations. We will be mostly interested in linear singular integral equations of Cauchy type which have functions as coefficients (for which an equation of Carleman type serves as a model). Anyway, due to the nature of our method we will be also able to study corresponding so-called discrete singular integral equations and in-verse source problems. All these include a new concept and method which provides practical and numerical solutions of very general linear singular in-tegral equations by combining the two theories of Tikhonov regularization and reproducing kernels. 1