Evaluation of the Convergence Interval of the Fixed Talbot Algorithm for Numerical Inversion of the Laplace Transform Applied to Solving the Wave Equation

Iago Henrique Teixeira Marcolino; Felipe Matheus Mendes Barbosa; Leslie Darien Pérez-Fernández; Camila Pinto da Costa

doi:10.63595/vetor.v35i2.18363

Authors

Iago Henrique Teixeira Marcolino Universidade Federal de Pelotas
Felipe Matheus Mendes Barbosa Universidade Federal de Pelotas https://orcid.org/0009-0005-1490-2026
Leslie Darien Pérez-Fernández Universidade Federal de Pelotas https://orcid.org/0000-0002-4452-264X
Camila Pinto da Costa Universidade Federal de Pelotas

DOI:

https://doi.org/10.63595/vetor.v35i2.18363

Keywords:

Inverse Laplace Transform, Numerical Convergence, Parameter Values, Fixed Talbot Algorithm

Abstract

This work examines the numerical inversion of the Laplace Transform via Fixed Talbot in an initial-boundary value problem for the wave equation. Although various numerical methods exist for the numerical inversion of the Laplace transform, the Fixed Talbot method shows the best performance based on previous tests. In the Talbot algorithm, it is necessary to adjust the parameters M and N to ensure convergence of the method; previous studies suggest a sufficient condition for convergence when the M/N ratio is within the interval (5, 19). To investigate the suggested convergence interval, the numerical inversion of the Laplace transform via Fixed Talbot was applied to an initial-boundary value problem for the wave equation, and a comparison was made between the numerical and exact solutions through the maximum absolute error. The results suggest the conservation of the proposed convergence interval for this type of partial differential equation.

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