Journal of Engineering Mathematics

, Volume 5, Issue 1, pp 1-9

First online:

Gaussian quadrature formulas for the numerical integration of Bromwich's integral and the inversion of the laplace transform

  • R. PiessensAffiliated withInstitute for Applied Mathematics, University of Leuven

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An approximate formula for the inversion of the Laplace transformF(p) is studied. The formula is exact wheneverF(p) is a linear combination ofp −s+k ,k=0, 1, 2, ..., 2N−1, withs an arbitrary positive real number. The formula is derived from a gaussian integration formula for Bromwich's inversion integral.

A numerical example is given as illustration of the use of the approximate inversion formula.