On the regularization of the first kind integral equation with analytical kernel of logarithmic type

We study regularization methods for the integral equation of the first kind with analytical kernel of logarithmic type. The problem is severely ill-posed. In [1] a logarithmic type convergence rate for the Tikhonov regularized solution was proved. Here we are concerned with numerical aspects of the solution. First we consider the selfregularization of the problem by using projection methods in the sense of [9].Then we will see that the Tikhonov regularization of such methods is in accordance with a discretized version of the Tikhonov regularized solution in [1]. Finally, we describe numerical experiments being in a good agreement with the theoretical results