A High Accurate Approximation for a Galactic Newtonian Nonlinear Model Validated by Employing Observational Data
Keywords:
Perturbation method, nonlinear galactic model, flat rotation curves, approximated solutions.Abstract
This article proposes Perturbation Method (PM) to solve nonlinear problems. As case study PM is employed to provide a detailed study of a nonlinear galactic model. Our approach is rather elementary and seeks to explain as much detail as possible the material of this work.
In particular our solution gives rise qualitatively, to the known flat rotation curves. In fact, we compare the numerical solution and the obtained approximation by employing observational data proving the validity and high accuracy of the model under study.
References
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[2] Almudena Zurita Muñoz. “Curso Cosmología. Curvas de rotación y materia oscura en galaxias espirales.” Internet: http://www.ugr.es/~azurita/docencia/material_docente/cosmologia/cr_dm_clase_06.pdf , 2007 [Sep. 2015]
[3] T.L. Chow. Classical Mechanics. USA: John Wiley and Sons Inc., 1995.
[4] M.H. Holmes. Introduction to Perturbation Methods. New York: Springer-Verlag, 1995.
[5] U. Filobello-Niño, H. Vazquez-Leal, Y. Khan, A. Yildirim, V.M. Jimenez-Fernandez, A. L Herrera-May, R. Castañeda-Sheissa, and J. Cervantes-Perez. “Using Perturbation Method and Laplace-Padé Approximation to solve nonlinear problems.” Miskolc Mathematical Notes, vol. 14(1), pp. 89-101, 2013. ISSN: 1787-2405,
[6] U. Filobello-Niño, H. Vazquez-Leal, K. Boubaker, Y. Khan, A. Perez-Sesma, A. Sarmiento Reyes, V.M. Jimenez-Fernandez, A Diaz-Sanchez, A. Herrera-May, J. Sanchez-Orea and K. Pereyra-Castro. “Perturbation Method as a Powerful Tool to Solve Highly Nonlinear Problems: The Case of Gelfand,s Equation.” Asian Journal of Mathematics and Statistics, vol. 2013, pp. 7, 2013. DOI: 10.3923 /ajms.2013, ISSN 1994-5418, 2013.
[7] R. Resnick and D. Halliday. Física Vol. 1, USA: John Wiley and Sons, 1977.
[8] F. Mandl. Física Estadística. México: Editorial Limusa, S.A, 1979.
[9] Dennis Zill. A First Course in Differential Equations with Modeling Applications, USA: Brooks /Cole Cengage Learning, 10th Edition, 2012
[10] W. Enright, K. Jackson, S.A. Norsett, P. Thomsen. “Interpolants for Runge–Kutta formulas.” ACM Transactions on Mathematical Software (TOMS), vol. 12(3) pp. 193-218, 1986.
[11] E. Fehlberg. “Klassische Runge–Kutta–Formeln vierter und niedrigerer ordnung mit schrittweitenkontrolle und ihre anwendung auf Waermeleitungsprobleme.” Computing, vol. 6, pp. 61-71, 1970
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Published
2017-01-18
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Filobello-Nino, U., Vazquez-Leal, H., Sandoval-Hernandez, M., Perez-Sesma, J. A. A., Perez-Sesma, A., Sarmiento-Reyes, A., Jimenez-Fernandez, V. M., Huerta-Chua, J., Pereyra-Diaz, D., Castro-Gonzalez, F., Laguna-Camacho, J. R., Gasca-Herrera, A. E., Pretelin Canela, J. E., Palma-Grayeb, B. E., Cervantes-Perez, J., Sampieri-Gonzalez, C. E., Cuellar-Hernández, L., Hoyos-Reyes, C., Ruiz-Gomez, R., Contreras-Hernandez, A. D., Alvarez-Gasca, O., & Gonzalez-Martinez, F. J. (2017). A High Accurate Approximation for a Galactic Newtonian Nonlinear Model Validated by Employing Observational Data. American Scientific Research Journal for Engineering, Technology, and Sciences, 27(1), 139–150. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/1326
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