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Numerical inversion of Laplace transforms of probability distributions. (English) Zbl 0821.65085
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)

MSC:
65R10 Numerical methods for integral transforms
44A10 Laplace transform
Software:
UBASIC
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