Numerical inversion of the Laplace transform

Abstract

We give a short account on the methods for numerical inversion of the Laplace transform and also propose a new method. Our method is inspired and motivated from a problem of the evaluation of the Müntz polynomials (see [1]), as well as the construction of the generalized Gaussian quadrature rules for the Müntz systems (see [2]). As an illustration of our method we consider an example with 100 real poles distributed uniformly on ¢ ¡ 1£ 2¤ 100¥. A numerical investigation shows the efficiency of the proposed method.

Calculation of the channel discharge function for the generalized lightning traveling current source return stroke model

“…In such cases we must use some methods for its approximative computation for a given t > 0. Different methods for numerical inversion of the Laplace transform were described in several papers [11], [35], [16], [1], [2], [36], [26], [38], [14], [10], [37], which include Fourier series expansions, Laguerre and Puiseux expansions, a combination of Gaver functionals, different deformations of the Bromwich contour, as well as a method based on Müntz systems (see [24], [25]). By determining the values f 1 (t ν ) on a particular discrete set T = {t ν } ν , we are able to obtain an approximation formula, usually interpolation (cf.…”

“…where to (26) and using Cauchy's integral formula, we can get the corresponding approximation of i(t) at t = nh.…”

Harmonic Analysis via an Integral Equation: An Application to Dengue Transmission

“…If the Laplace inverse is not straight forward, one would try Bromwich contour integrals [8,9]. Definition 5.…”

Investigation on Transient Responses of a Piezoelectric Crack by using Durbin and Zhao Methods for Numerical Inversion of Laplace Transforms

“…Numerous studies are related to the numerical inversion of the Laplace transform obtained using the Fourier series [6][7][8][9][10]. There have also been numerous crucial studies and reviews related to the numerical inversion of Laplace transform [11][12][13][14][15][16][17][18][19][20][21].…”