Implementation of Weeks' method for the inverse Laplace transform problem

The authors are presently involved in constructing a software package for the numerical inversion of the Laplace transform. In this report we describe one item. This obtains approximations for f(t) when numerical values of the Laplace transform function F(s) = Integral from 0 to infinity of f(t)e/sup -st/ dt Re s > sigma/sub 0/ are available for all complex s in the form of a user supplied subprogram. The user also supplies the numerical value of sigma/sub 0/ or an upper bound on sigma/sub 0/ and an accuracy parameter; sigma/sub 0/ is known as the Laplace transform convergence abscissa.