A Program for the Numerical Inversion of the Laplace Transform

A program is given that numerically inverts a given Laplace transform for discrete times specified by the user, and (most of the time) to within a specified absolute error. The computation is adaptive in that the program decides whether to compute a given point by integrating the Bromwich integral or to interpolate the point from the set of those already computed by integrating the Bromwich integral. If the integration is performed, it is done by accelerating partial sums to the limit, with the partial sums obtained by Gaussian quadrature with error control. Three examples, including two in which the transform is not the quotient of polynomials, indicate that the reliability of the program is good.