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Numerical Inverse Laplace Transform Methods

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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).

Stehfest Algorithm

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 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

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