Abate, Joseph; Whitt, Ward Numerical inversion of Laplace transforms of probability distributions. (English) Zbl 0821.65085 ORSA J. Comput. 7, No. 1, 36-43 (1995). For the numerical inversion of the Laplace transform \(\widehat f(s)\), the authors use two methods. The first approximates the inversion formula \(f(t) = (2/ \pi) e^{at} \int^ \infty_ 0 \text{Re} (\widehat f(a + iu) \cos (ut)du\) by means of the trapezoidal rule, and improves the result by means of Poisson’s summation formula and Euler’s summation technique. The second method follows D. L. Jagerman [Bell. Syst. Tech. J. 61, 1995-2002 (1982; Zbl 0496.65064)], uses the Post-Widder inversion formula, also Poisson’s summation and an acceleration of convergence due to H. Stehfest [Algorithm 368. Numerical inversion of Laplace transform, Commun. ACM 13, 479-490, erratum 624 (1970)]. Implementations of the methods are given in UBASIC. Reviewer: L.Berg (Rostock) Cited in 2 ReviewsCited in 172 Documents MSC: 65R10 Numerical methods for integral transforms 44A10 Laplace transform Keywords:numerical inversion; Laplace transform; inversion formula; Poisson’s summation formula; Euler’s summation technique; Post-Widder inversion formula; acceleration of convergence Citations:Zbl 0496.65064 Software:UBASIC PDFBibTeX XMLCite \textit{J. Abate} and \textit{W. Whitt}, ORSA J. Comput. 7, No. 1, 36--43 (1995; Zbl 0821.65085) Full Text: DOI Link