Laplace.jl

Numerical procedures to perform inverse Laplace transforms

Overview

Numerical implementations to numerically invert the Laplace transform

$$ \mathscr{L}^{-1} \{ \bar{f}(s) \} = f(t) = \frac{1}{2 \pi i} {\int_{\sigma - i \infty}^{\sigma + i \infty} \bar{f}(s) e^{st} \, ds} $$

Current algorithms

Real arguments

• Gaver-Stehfest method

Complex arguments

• Bromwich contour integration
  • Hyperbola
  • Fixed hyperbola (inversion at many time points)
  • Improved talbot