Abstract
This paper is devoted to the computation of the spectrum of the finite Laplace transform (FLT) and its applications. For this purpose, we give two different practical methods. The first one uses a discretization of the FLT. The second one is based on the Gaussian quadrature method. The spectrum of the FLT is then used to invert the Laplace transform of time limited functions as well as the Laplace transform of essentially time limited functions. Several numerical results are given to illustrate the results of this work.