This is a subroutine I used for my numerical simulations in my paper that was published in Applied Mathematical Modeling journal. Here is a link to the paper.
I developed this for the function in my paper; but, I could see a generalized form of this might come for finding the inverse Laplace transformation of a general function.
Note: This is not in useable form yet. Polishing of this source code for general purpose use is not done yet. This is just making a copy of all the files.