This paper is dedicated to a general numerical approach to inverse Laplace transforms based on the Post Inversion Formula, which is a theoretical equivalent to the inverse Laplace transform. Though most approaches are too computationally intensive to be of practical use, we introduce an efficient algorithm to compute it based on the Parker-Sochacki method (PSM). This paper also contains some example MATLAB code and algorithm analysis.
Zhang, Qinmao, "Inverse Laplace Transform and Post Inversion Formula" (2016). Mathematical Sciences Technical Reports (MSTR). 162.