THE NUMERICAL INVERSION OF THE LAPLACE TRANSFORM IN REPRODUCING KERNEL HILBERT SPACES

Abstract

In this paper we have converted the Laplace transform into an integral equation of the first kind of convolution type, which is an ill-posed problem and used a statistical regularization method to solve it. The method is applied to three examples taken from Rodriguez and Seatzu [1993]. It gives a good approximation to the true solution and compares well with the method given by Rodriguez and Seatzu [1993]. The results are shown in the Table and the diagrams.