https://github.com/roliveira/nilt

Numerical Inverse Laplace Transform Methods
https://github.com/roliveira/nilt

algorithm benchmarks laplace-transform numerical-methods

Last synced: 4 days ago
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Numerical Inverse Laplace Transform Methods

• Host: GitHub
• URL: https://github.com/roliveira/nilt
• Owner: roliveira
• License: mit
• Created: 2021-09-10T19:24:17.000Z (over 3 years ago)
• Default Branch: main
• Last Pushed: 2024-08-28T15:29:26.000Z (5 months ago)
• Last Synced: 2024-08-28T17:11:38.243Z (5 months ago)
• Topics: algorithm, benchmarks, laplace-transform, numerical-methods
• Language: C++
• Homepage:
• Size: 19.5 KB
• Stars: 7
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Numerical Inverse Laplace Transform Methods

This repository is used to benchmark different algorithms for the numerical Laplace Transform Inversion. This work was partly developed in [Oliveira, R. (2021)](https://doi.org/10.25560/92253).

## Stehfest Algorithm

The algorithm described in [Stehfest, H. (1970)](https://doi.org/10.1145/361953.361969) is implemented in `StehfestAlgorithm` class. To exemplify the results, the entries entry for `f(t) = 1/sqrt(PI*t)` in Table 1 of the original paper are obtained by numerically inverting the Laplace Transform of `F(s) = 1/sqrt(s)` and are listed 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 |

## References

- 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