Análise Comparativa do Desempenho Numérico de Técnicas de Inversão da Transformada de Laplace aproximada por Série de Fourier
DOI:
https://doi.org/10.5902/2179460X66984Keywords:
Transformada de Laplace, Série de Fourier, Inversão NuméricaAbstract
Neste trabalho, um estudo comparativo entre três métodos numéricos para inversão da transformada de Laplace baseados na
expansão por Série de Fourier é apresentado. No processo, analisou-se o desempenho dos métodos propostos por Dubner e Abate
(1968), Durbin (1973) e Simon et al. (1972). Estes três métodos foram testados em um conjunto de funções elementares distintas, e
o seu desempenho quanto à precisão e esforço computacional foi checado. Em um estudo preliminar, baseado nos resultados
alcançados, pode-se concluir que os três métodos são capazes de inverter numericamente a transformada de Laplace para as
classes de funções selecionadas.
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References
Abate, J., Valkó, P. P. (2004). Multi-precision Laplace transform inversion. International Journal for Numerical Methods in Engineering, 60, 979–993.
do 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 Modelagem Computacional.
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 of Computacional 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 – 23.
Duffy, D. G. (1993). On the numerical inversion of Laplace transform: comparison of three new methods on characteristic problems 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. The Computer 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 da inversão numérica da transformada de Laplace aplicada a um problema de transporte. Revista Interdisciplinar de Pesquisa em Engenharia, 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. SIAM Journal 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 a um problema de transporte de soluto em um meio poroso. Dissertação (Mestrado), Universidade Federal do Rio Grande, Rio Grande, 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 methods for 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 labeled mitoses 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 Anniversary Volume, pp. 333 – 379.
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- 2022-07-14 (2)
- 2021-11-08 (1)
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