On spline regularized inversion of noisy Laplace transforms

Abstract

In this paper we have converted the Laplace transform to an integral equation of the first kind of convolution type, which is an ill-posed problem and used the spline regularization method to solve it. Inversion of perturbed Laplace transforms also plays an important role in system theory. The method is applied to several test examples taken from [1–3, 8, 11, 22]. It gives a good approximation to the true solution and compares well with the methods discussed in [1–3, 8, 11, 22]. The results are shown in Table 1 and respective diagrams.