Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method

1974/11/01 by F. Durbin · 1,144 citations
Computer Science · Engineering · Mathematics · #Algorithm #Applied mathematics #Computer science #Continuation #Electromagnetic Simulation and Numerical Methods #Exponential function #Geometry #Green's function for the three-variable Laplace equation #Inverse #Inverse Laplace transform #Inversion (geology) #Iterative Methods for Nonlinear Equations #Laplace transform #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Post's inversion formula #Series (stratigraphy)

paper · doi:10.1093/comjnl/17.4.371

published in The Computer Journal 17(4), 371-376 (Oxford University Press)

openalex publication_date 1974/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An accurate method is presented for the numerical inversion of Laplace transform, which is a natural continuation to Dubner and Abate's method. (Dubner and Abate, 1968). The advantages of this modified procedure are twofold: first, the error bound on the inverse f(t) becomes independent of t, instead of being exponential in t; second, and consequently, the trigonometric series obtained for f(t) in terms of F(s) is valid on the whole period 2T of the series. As it is proved, this error bound can be set arbitrarily small, and it is always possible to get good results, even in rather difficult cases. Particular implementations and numerical examples are presented.

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