Análise do Método Multi-Passos com Transformada Diferencial Generalizada na Modelagem Fracionária
DOI:
https://doi.org/10.5540/tema.2019.020.01.133Keywords:
Cálculo Fracionário, Modelagem Fracionária, Método da Transformada Diferencial GeneralizadaAbstract
Apresenta-se uma análise crítica de uma técnica numérica que tem sido usada na resolução de equações diferenciais de ordem fracionária com derivadas de Caputo. Trata-se do método multi-passos com transformada diferencial generalizada. Verifica-se que a versão do método disponível na literatura produz soluções erradas a partir do segundo passo, isto é mostrado em aplicações aos modelos de Malthus e de Riccati. O problema é explicado em termos da não localidade da derivada de Caputo e das propriedades da transformada diferencial generalizada.References
R. C. Bassanezi, “Modelagem como estratégia metodológica no ensino da matemática,” in Boletim de Educação da SBMAC, (São Paulo), SBMAC, 1994.
R. F. Camargo and E. C. Oliveira, Cálculo fracionário. Editora Livraria da
Física, 2015.
L. K. B. Kuroda, A. V. Gomes, R. Tavoni, P. F. A. Mancera, N. Varalta,
and R. F. Camargo, “Unexpected behavior of Caputo fractional derivative,”
Computational and Applied Mathematics, vol. 36, no. 3, pp. 1173-1183, 2017.
V. S. Erturk, G. Zaman, and S. Momani, “A numeric-analytic method for
approximating a giving up smoking model containing fractional derivatives,” Computers and Mathematics with Applications, vol. 64, pp. 3065-3074, 2012.
A. H. Handam and A. A. Freihat, “A new analytic numeric method solution for fractional modified epidemiological model for computer viruses,” Applications and Applied Mathematics, vol. 10, pp. 919-936, 2015.
B. Ebenezer, K. Awuah-Werekoh, and J. Acquah, “Solution of HIV and malária coinfection model using MSGDTM,” Journal of Mathematics Research, vol. 7, pp. 181-193, 2015.
S. Arshad, A. Sohail, and S. Javed, “Dynamical study of fractional order tumor model,” International Journal of Computational Methods, vol. 12, pp. 1-12, 2015.
A. Freihat and S. Momani, “Application of multistep generalized diferential
transform method for the solutions of the fractional-order Chua's system,”
Computers and Mathematics with Applications, vol. 2012, pp. 1-12, 2012.
A. Momenzadeh and S. Sarv Ahrabi, “A comparison between numerical soluctions to fractional diferential equations: Adams-type predictor-corrector and multi-step generalized diferential transform method,” ArXiv e-prints, pp. 1-12, 2017.
L. K. B. Kuroda, A. Bruno-Alfonso, P. F. A. Mancera, and R. F. Camargo, “Aplicabilidade do método da transformada diferencial na modelagem fracionária,” (São José dos Campos), pp. 1-7, SBMAC, 2017.
L. K. B. Kuroda, “Cálculo fracionário aplicado em dinâmica tumoral: método da transformada diferencial generalizada,” Master's thesis, Instituto de Biociências, Universidade Estadual Paulista-UNESP, Botucatu, 2016.
Z. Odibat, C. Bertelle, M. Aziz-Alaoui, and G. H. E. Duchamp, “A Multi-
step diferential transform method and application to non-chaotic or Chaotic systems,” Applied Mathematical Sciences, vol. 12, pp. 1-15, 2010.
I. H. Abdel-Halim Hassan, “Application to diferential transformation method for solving systems of diferential equations,” Applied Mathematical Modelling, vol. 32, pp. 2552-2559, 2008.
F. Mirzaee, “Diferential transform method for solving linear and nonlinear systems of ordinary diferential equations,” Applied Mathematical Sciences, vol. 5, pp. 3465-3472, 2011.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish in this journal agree to the following terms:
Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.
Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
author. This is in accordance with the BOAI definition of open access
Intellectual Property
All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.