Parameter N Influence on the Fixed-Talbot Algorithm for the Laplace Transform Numerical Inversion

George Ricardo Libardi Calixto; Elisandra Konflanz Freitas; Juciara Alves Ferreira; Bárbara Denicol do Amaral Rodriguez; João Francisco Prolo Filho

doi:10.14295/vetor.v32i1.13754

Authors

George Ricardo Libardi Calixto Universidade Federal do Rio Grande
Elisandra Konflanz Freitas Universidade Federal do Rio Grande https://orcid.org/0000-0003-3176-6968
Juciara Alves Ferreira Universidade Federal do Rio Grande
Bárbara Denicol do Amaral Rodriguez Universidade Federal do Rio Grande https://orcid.org/0000-0001-8211-6418
João Francisco Prolo Filho Universidade Federal do Rio Grande

DOI:

https://doi.org/10.14295/vetor.v32i1.13754

Keywords:

Laplace Transform, Inverse Transform, Numerical Methods, Fixed-Talbot

Abstract

In this paper, Fixed-Talbot method computational aspects are explored for Laplace Transform numerical inversion and its efficiency in the treatment of a set of elementary functions of an exponential, oscillatory and logarithmic nature, based on the influence investigation of free parameter N. The numerical results are compared to the analytical solution while calculating the absolute error. The best value for N was determined in each studied function class, where the method presents satisfactory results. It was observed that increasing the number of terms in the summation for approximation (beyond the optimal value) doesn’t imply obtaining more refined results. In general, based on the data obtained, it was concluded that Fixed-Talbot method is efficient for the inversion of all classes of elementary functions evaluated in this article.

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