This repository is used to benchmark different algorithms for the numerical Laplace Transform Inversion. This work was partly developed in Oliveira, R. (2021).
The algorithm described in Stehfest, H. (1970) is implemented in StehfestAlgorithm class. To exemplify the results, the entries entry for f(t) = 1/sqrt(PI*t) in Table 1 of the paper is obtained by numerically inverting the Laplace Transform of F(s) = 1/sqrt(s) and is reproduced below:
| t | fa(t) | fn(t) | err |
|---|---|---|---|
| 1 | 0.564189583548 | 0.564186508758 | 5.44992307092e-06 |
| 2 | 0.398942280401 | 0.398939582368 | 6.76296805803e-06 |
| 3 | 0.325735007935 | 0.325734581605 | 1.3088245455e-06 |
| 4 | 0.282094791774 | 0.282093254379 | 5.44992307092e-06 |
| 5 | 0.252313252202 | 0.252312282254 | 3.84421978257e-06 |
| 6 | 0.230329432981 | 0.230329170603 | 1.13914346481e-06 |
| 7 | 0.213243618623 | 0.213243982566 | 1.70670322864e-06 |
| 8 | 0.199471140201 | 0.199469791184 | 6.76296805803e-06 |
| 9 | 0.188063194516 | 0.188063264428 | 3.71747548209e-07 |
| 10 | 0.178412411615 | 0.178411614082 | 4.47016807695e-06 |
- Rodolfo Oliveira. 2021. Modelling of reactive transport in porous media using continuous time random walks. PhD Thesis (Mar. 2021). https://doi.org/10.25560/92253
- Harald Stehfest. 1970. Algorithm 368: Numerical inversion of Laplace transforms [D5]. Commun. ACM 13, 1 (Jan. 1970), 47–49. https://doi.org/10.1145/361953.361969