Parameter N Analysis on the Rational-Talbot Algorithm for Numerical Inversion of Laplace Transform

This article investigates the numerical inversion of the Laplace Transform by the Rational-Talbot method and analyzes the influence on the variation of the free parameter N established by the technique when applied to certain functions. The set of elementary functions, for which the method is tested...

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Published in:Vetor Vol. 31; no. 2; pp. 50 - 60
Main Authors: Freitas, Elisandra, Libardi Calixto, George Ricardo, Alves Ferreira, Juciara, Denicol do Amaral Rodriguez, Bárbara, Prolo Filho, João Francisco
Format: Journal Article
Language:English
Published: Universidade Federal do Rio Grande 17.12.2021
Subjects:
Laplace Transform
Numerical Inversion
Rational Approximation
ISSN:0102-7352, 2358-3452
Online Access:Get full text
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Abstract This article investigates the numerical inversion of the Laplace Transform by the Rational-Talbot method and analyzes the influence on the variation of the free parameter N established by the technique when applied to certain functions. The set of elementary functions, for which the method is tested, has exponential and oscillatory characteristics. Based on the results obtained, it was concluded that the Rational-Talbot method is e cient for the inversion of decreasing exponential functions. At the same time, to perform the inversion process effectively for trigonometric forms, the algorithm requires a greater amount of terms in the sum. For higher values of N, the technique works well. In fact, this is observed in inverting the functions transform, that combine trigonometric and polynomial factors. The method numerical results have a good precision for the treatment of decreasing exponential functions when multiplied by trigonometric functions.
AbstractList This article investigates the numerical inversion of the Laplace Transform by the Rational-Talbot method and analyzes the influence on the variation of the free parameter N established by the technique when applied to certain functions. The set of elementary functions, for which the method is tested, has exponential and oscillatory characteristics. Based on the results obtained, it was concluded that the Rational-Talbot method is e cient for the inversion of decreasing exponential functions. At the same time, to perform the inversion process effectively for trigonometric forms, the algorithm requires a greater amount of terms in the sum. For higher values of N, the technique works well. In fact, this is observed in inverting the functions transform, that combine trigonometric and polynomial factors. The method numerical results have a good precision for the treatment of decreasing exponential functions when multiplied by trigonometric functions.
Author Libardi Calixto, George Ricardo
Freitas, Elisandra
Denicol do Amaral Rodriguez, Bárbara
Alves Ferreira, Juciara
Prolo Filho, João Francisco
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Snippet This article investigates the numerical inversion of the Laplace Transform by the Rational-Talbot method and analyzes the influence on the variation of the...
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SubjectTerms Laplace Transform
Numerical Inversion
Rational Approximation
Title Parameter N Analysis on the Rational-Talbot Algorithm for Numerical Inversion of Laplace Transform
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