Inversion of the Laplace Transform Using the Gaver-Stehfest Algorithm
Stehfest  derived an algorithm for the numerical inversion of Laplace transforms. This Demonstration applies this algorithm to determine the inverse Laplace transforms of four test functions . The inverse functions and corresponding test functions are the following:[more]
1. with ,
2. with , where is Euler's constant,
3. with ,
4. with .
You can vary the parameters and . The blue curve shows the exact inverse and the red dots, the numerically calculated data using the Gaver–Stehfest algorithm.[less]
 H. Stehfest, "Algorithm 368: Numerical Inversion of Laplace Transform," Communications of the ACM, 13(1), 1970 pp. 47–49. doi: 10.1145/361953.361969.