University of Hertfordshire

By the same authors

The Numerical Inversion of the Laplace Transform in a Multi-Precision Environment.

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Original languageEnglish
Number of pages16
JournalJournal of Applied Mathematics and Physics
Volume13
Issue5
DOIs
Publication statusPublished - 23 May 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 [1].
Because the numerical inversion of the Laplace transform is a perturbed problem [2], [9], and [11], 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 which exist in transforming the data from the Laplace 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.
Keywords: Laplace transform; Perturbation; Numerical Inversion; Multi-precision; Stehfest;
Talbot.

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