Comparative analysis of the numerical performance of Laplace transform inversion techniques approximated by Fourier series

Authors

DOI:

https://doi.org/10.5902/2179460X66984

Keywords:

Laplace transform, Fourier Series, Numerical inversion

Abstract

In this work, a comparative study between three numerical methods for Laplace transform inversion based on Fourier seriesexpansion is presented. In the process, the performance of the methods proposed by Dubner e Abate (1968), Durbin (1973) andSimon et al.(1972) was analyzed. These three methods weretested on a set of distinct elementary functions, and their performancein terms of precision and computational effort was checked. In a preliminary study, based on the results achieved, it can beconcluded that the three methods are capable to invert numerically the Laplace transform for these classes of selected functions.

Downloads

Download data is not yet available.

Author Biographies

Juciara Alves Ferreira, Universidade Federal do Rio Grande, Rio Grande, RS

É graduada em Matemática Aplicada (2017), possui mestrado em Modelagem Computacional (2021) e atualmente é aluna do curso de Matemática Licenciatura pela Universidade Federal do Rio do Grande - FURG.

 

OBS. O link do lattes não foi disponibilizado deve a indisponibilidade da plataforma no momento da submissão.

Bárbara Denicol do Amaral Rodriguez, Universidade Federal do Rio Grande, Rio Grande, RS

Possui Bacharelado em Matemática Aplicada e Computacional (2000), Mestrado em Matemática Aplicada e Computacional (2003) e Doutorado em Engenharia Mecânica (2007), todos pela Universidade Federal do Rio Grande do Sul – UFRGS. Atualmente é professora Associada II – DE e docente permanente do Programa de Pós-Graduação em Modelagem Computacional e do Mestrado Profissional em Matemática em Rede Nacional na Universidade Federal do Rio Grande – FURG. Atua nas áreas de Matemática Aplicada, Engenharia e Ensino de Matemática: no desenvolvimento de métodos analíticos para resolução de problemas de transporte de partículas, técnicas e resolução de problemas a partir da transformada de Laplace e no estudo de metodologias alternativas de ensino e aprendizagem no Ensino Superior.

João Francisco Prolo Filho, Universidade Federal do Rio Grande, Rio Grande, RS

Possui graduação em Matemática Aplicada e Computacional pela Universidade Federal do Rio Grande do Sul – UFRGS (2004), mestrado (2007) e doutorado (2012) em Matemática Aplicada pela Universidade Federal do Rio Grande do Sul – UFRGS. Atualmente é Professor Associado 1 – DE na Universidade Federal do Rio Grande e é professor colaborador no Programa de Pós-Graduação em Engenharia Oceânica. Atua nas áreas de Matemática Aplicada e Engenharia: no desenvolvimento de métodos analíticos para resolução de problemas de transporte de nêutrons, transferência radiativa e dinâmica de gases rarefeitos; desenvolvimento de técnicas e resolução de problemas a partir da transformada de Laplace.

References

ABATE, J., VALKÓ, P. P. (2004). Multi-precision Laplace transform inversion. International Journal for Numerical Methods inEngineering, 60, 979–993.

AMARAL, G. C. M. (2016). Análise comparativa do desempenho numérico de técnicas de inversão da transformada de Laplace.Dissertação (Mestrado), Universidade Federal do Rio Grande, Rio Grande, Programa de Pós-Graduação em ModelagemComputacional.

COHEN, A. M. (2007). Numerical methods for Laplace transform inversion. Springer Science+Business Media, LLC, New York.

CRUMP, K. S. (1976). Numerical inversion of the Laplace transform using a Fourier series approximation. Journal ACM, 23(1), 89–96.

DAVIES, B., MARTIN, B. (1979). Numerical inversion of the Laplace transform: a survey and comparison of methods. Journal ofComputacional Physics, 33, 1 –32.

DUBNER, H., ABATE, J. (1968). Numerical inversion of Laplace transform by relating them to the finite Fourier cosine transform.Journal ACM, 15, 115 –123.

DUFFY, D. G. (1993). On the numerical inversion of Laplace transform: comparison of three new methods on characteristicproblems from applications. Transactions on Mathematical Software, 19, 333–359.

DURBIN, F. (1973). Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method. TheComputer Journal, 17(14), 371 –376.

FERREIRA, J., CALIXTO, G. R. L., KONFLANZ, E., DO AMARAL RODRIGUEZ, B. D., FILHO, J. F. P. (2021). Aspectos computacionais dainversão numérica da transformada de Laplace aplicada a um problema de transporte. Revista Interdisciplinar de Pesquisa emEngenharia, 1, 1–18.

FRANSOZI, L. (2015). Modelagem matemática do tempo de vida de baterias de Lítio íon polímero através de modelos híbridos.Dissertação (Mestrado), Universidade Regional do Noroeste do Estado do Rio Grande do Sul, Ijuí, Departamento de Ciências Exatas e Engenharias.

HOOG, F. R. D., KNIGHT, J. H., STOKES, A. N. (1982). An Improved Method for Numerical Inversion of Laplace Transforms. SIAMJournal on Scientific and Statistical Computing, 3(3), 357 –366.

PILATTI, C. (2019). Análise comparativa do desempenho numérico de técnicas de inversão da transformada de Laplace aplicados aum problema de transporte de soluto em um meio poroso. Dissertação (Mestrado), Universidade Federal do Rio Grande, RioGrande, Programa de Pós-Graduação em Modelagem Computacional.

PILLATI, C., DO AMARAL RODRIGUEZ, B. D., FILHO, J. F. P. (2019). Performance analysis of Stehfest and power series expansion methodsfor solution to diffusive and advective transport problems. Defect and Diffusion Forum, 396, 99 –108.

SIMON, R. M., STROOT, M. T., WEISS, G. H. (1972). Numerical inversion of Laplace transform with application to percetage labeledmitoses experiments. Computers and Biomedical Research, 5, 596 –607.

STROUD, K., BOOTH, D. J. (2003). Advanced Engineering Mathematics, 4º edn. Palgrave Macmilan, New York.

WYNN, P. (1967). Transformations to accelerate the convergence of Fourier series. Em: Gertrude Blanch AnniversaryVolume, pp.333 –379.

Downloads

Published

2021-11-08 — Updated on 2022-07-14

Versions

How to Cite

Ferreira, J. A., Rodriguez, B. D. do A., & Prolo Filho, J. F. (2022). Comparative analysis of the numerical performance of Laplace transform inversion techniques approximated by Fourier series. Ciência E Natura, 43, e8. https://doi.org/10.5902/2179460X66984 (Original work published November 8, 2021)

Issue

Vol. 43 (2021): Special Edition: X ERMAC RS

Section

Special Edition

License

Copyright (c) 2021 Ciência e Natura

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

To access the DECLARATION AND TRANSFER OF COPYRIGHT AUTHOR’S DECLARATION AND COPYRIGHT LICENSE click here.

 

Ethical Guidelines for Journal Publication

The Ciência e Natura journal is committed to ensuring ethics in publication and quality of articles. 

Conformance to standards of ethical behavior is therefore expected of all parties involved: Authors, Editors, Reviewers, and the Publisher.

In particular, 

Authors: Authors should present an objective discussion of the significance of research work as well as sufficient detail and references to permit others to replicate the experiments. Fraudulent or knowingly inaccurate statements constitute unethical behavior and are unacceptable. Review Articles should also be objective, comprehensive, and accurate accounts of the state of the art. The Authors should ensure that their work is entirely original works, and if the work and/or words of others have been used, this has been appropriately acknowledged. Plagiarism in all its forms constitutes unethical publishing behavior and is unacceptable. Submitting the same manuscript to more than one journal concurrently constitutes unethical publishing behavior and is unacceptable. Authors should not submit articles describing essentially the same research to more than one journal. The corresponding Author should ensure that there is a full consensus of all Co-authors in approving the final version of the paper and its submission for publication.

Editors: Editors should evaluate manuscripts exclusively on the basis of their academic merit. An Editor must not use unpublished information in the editor's own research without the express written consent of the Author. Editors should take reasonable responsive measures when ethical complaints have been presented concerning a submitted manuscript or published paper.

Reviewers: Any manuscripts received for review must be treated as confidential documents. Privileged information or ideas obtained through peer review must be kept confidential and not used for personal advantage. Reviewers should be conducted objectively, and observations should be formulated clearly with supporting arguments, so that Authors can use them for improving the paper. Any selected Reviewer who feels unqualified to review the research reported in a manuscript or knows that its prompt review will be impossible should notify the Editor and excuse himself from the review process. Reviewers should not consider manuscripts in which they have conflicts of interest resulting from competitive, collaborative, or other relationships or connections with any of the authors, companies, or institutions connected to the papers.

Most read articles by the same author(s)