More on the weeks method for the numerical inversion of the Laplace transform

Summary Most of the numerical methods for the inversion of the Laplace Transform require the values of several incidental parameters. Generally, these parameters are related to the properties of the algorithm and to the analytical properties of the Laplace Transform functionF(s).One of the most promising inversion methods, the Weeks methods, computes the inverse functionf(t) as a series expansion of Laguerre functions involving two parameters, usually denoted by andb. In this paper we characterize the optimal choiceb_opt ofb, which maximizes the rate of convergence of the series, in terms of the location of the singularities ofF(s).