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https://doi.org/10.1145/155743.155788

has been cited by the following article:

• TITLE: The Numerical Inversion of the Laplace Transform in a Multi-Precision Environment

  AUTHORS: Colin L. Defreitas, Steve J. Kane

  KEYWORDS: Laplace Transform, Perturbation, Numerical Inversion, Multi-Precision, Stehfest, Talbot

  JOURNAL NAME: Applied Mathematics, Vol.13 No.5, May 23, 2022

  ABSTRACT: This paper examines the performance of five algorithms for numerically inverting the Laplace transform, in standard, 16-digit and multi-precision environments. The algorithms are taken from three of the four main classes of numerical methods used to invert the Laplace transform. Because the numerical inversion of the Laplace transform is a perturbed problem, rounding errors which are generated in numerical approximations can adversely affect the accurate reconstruction of the inverse transform. This paper demonstrates that working in a multi-precision environment can substantially reduce these errors and the resulting perturbations exist in transforming the data from the s-space into the time domain and in so doing overcome the main drawback of numerically inverting the Laplace transform. Our main finding is that both the Talbot and the accelerated Gaver functionals perform considerably better in a multi-precision environment increasing the advantages of using Laplace transform methods over time-stepping procedures in solving diffusion and more generally parabolic partial differential equations.