An approximate short time Laplace transform inversion method

The "standard" numerical methods used for inverting the Laplace transform a re based on a regularization of an exact inversion formula. They are very s ensitive to noise in the Laplace transformed function. In this article we s uggest a different strategy. The inversion formula we use is an approximate one, but it is stable with respect to noise. The new approximate expressio n is obtained from a short time expansion of the Bromwich inversion formula . We show that this approximate result can be significantly improved when i terated, while remaining stable with respect to noise. The iterated method is exact for the class of functions of type E(m)e(aE). The method is applie d to a harmonic model of the stilbene molecule, to a truncated exponent ser ies, and to the flux-flux correlation function for the parabolic barrier. T hese examples demonstrate the utility of the method for application to prob lems of interest in molecular dynamics. (C) 2000 American Institute of Phys ics. [S0021- 9606(00)00835-7].