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Numerical inversion of the Laplace transform

Milovanović Gradimir V. (Faculty of Electronic Engineering - Department of Mathematics, Niš)
Cvetković Aleksandar S. (Faculty of Electronic Engineering - Department of Mathematics, Niš)

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 Műntz polynomials (see [1]), as well as the construction of the generalized Gaussian quadrature rules for the Műntz systems (see [2]). As an illustration of our method we consider an example with 100 real poles distributed uniformly on of the proposed method. 1 2 100. A numerical investigation shows the efficiency.

Keywords: Laplace transform, Bromwich integral, orthogonal polynomials, Gaussian quadrature formula