Laplace transform is a useful mathematical tool that one must be familiar with, while doing applied work. It is widely used in Queueing models where probability distributions are characterized in terms of transforms. Inverting a Laplace transform to get to the probability distribution is an essential task in Queueing theory. For textbook examples and simple Markovian models, one might be fortunate to find convenient forms for LT inversion. However for most of the real life situations, a practitioner needs to know a way to numerically invert LT.

The paper titled,``Numerical Inversion of Laplace Transforms of Probability Distributions'', written by Joseph Abate and Ward Whitt gives two methods.

I have rewritten the algorithm given in the paper in R  for Euler method_,_ and have verified the code for some basic textbook examples of inverse Laplace transforms. The following is the link to my document :

Inverse Laplace Transform in R