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ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion

An Erratum to this article was published on 10 June 2013

Abstract

A software package for numerical inversion of Laplace transforms computable everywhere on the real axis is described. Besides the function to invert the user has only to provide the numerical value (even if it is an approximate value) of the abscissa of convergence and the accuracy required for the inverse function. The software provides a controlled accuracy, i.e. it dynamically computes the so-called maximum attainable accuracy such that numerical results are provided within the greatest value between the user’s required accuracy and the maximum attainable accuracy. This is done because the intrinsic ill posedness of the real inversion problem sometime may prevent to reach the desired accuracy. The method implemented is based on a Laguerre polynomial series expansion of the inverse function and belongs to the class of polynomial-type methods of inversion of the Laplace transform, formally characterized as Collocation methods (C-methods).

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Correspondence to Luisa D’Amore.

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D’Amore, L., Campagna, R., Mele, V. et al. ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion. Numer Algor 63, 187–211 (2013). https://doi.org/10.1007/s11075-012-9636-0

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  • DOI: https://doi.org/10.1007/s11075-012-9636-0

Keywords

  • Inverse ill-posed problems
  • Laplace transform real inversion
  • Numerical regularization
  • Collocation methods
  • Laguerre series expansion