Semilocal convergence of Whittaker's Method applied to the Kepler Equation

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Published: 2022-08-06

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Abstract

In this project the semilocal convergence of the Whittaker method is studied, in it the Kepler equation is characterized, in order to know which values of the eccentricity (e) of said method has convergence and to determine the intervals of existence and uniqueness of solution for the aforementioned equation.

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Keywords:
Kepler's Equation, Whittaker's Method, Semilocal Convergence, Eccentricity, Intervals of Existence, Uniqueness of Solution

Article Details

Author Biographies

José Miguel Gómez Guzmán, Universidad Tecnológica Del Cibao Oriental (UTECO), Dominican Repúblic

revistas.academicas@uteco.edu.do

Manuel Aurelio Diloné, Universidad Tecnológica Del Cibao Oriental - UTECO Dominican Repúblic

revistas.academicas@uteco.edu.do

How to Cite

Gómez Guzmán, J. M., & Aurelio Diloné, M. (2022). Semilocal convergence of Whittaker’s Method applied to the Kepler Equation. Revista Científica El Capacho, 11(1), 22-33. https://doi.org/10.63796/capacho.2022.v11i11.94

References

Argyros, I.K., Cho, Y.J. and Hilout, On the semilocal convergence of the Halley method using recurrent functions S. J. Appl. Math. Comput. (2011) 37: 221.

Bernardo Cascales, El teorema del Punto Fijo Universidad de MURCIA, La Manga, 2012

E. Kobal, Notice concerned with the calculation of roots of numerical equations,

Monatsh. Math. 02 (2002) pp. 331-332.

Francisco Israel Chicharro López, Análisis dinámico y aplicaciones de métodos iterativos de resolución ecuaciones no lineales, Universitat Politécnica de Valencia, España mayo de 2017

G.S. Salehov and M. A. Mertvetsova, On the convergence of some iterative processes, Izv. Kazansk. Phil. ANSSSR. Ser. Phiz-Matem. i Techn. Vol. 5, (1954), 77-108.

J. Gerlach, Accelerated convergence in Newton's Method, SIAM Review, Vol. 36,(1994), 272-276.

J. M. Gutiérrez, El método de Newton en espacios de Banach, Tesis doctoral, Universidad de La Rioja. Logroño, España, 1995.

J. S. Frame, A variation of Newton's method. American Mathematical Monthly, vol. 51 (1944) 36-38.

Kollerstrom, N., Thomas Simpson and Newton method of approximation: An enduring myth. The British Journal for the History of Science, Vol. 25 No. 4 ( 1992 ) , 347 - 354 . doi:10.1017/S0007087400029150

Manuel Aurelio Diloné Alvarado, Métodos iterativos aplicado a la ecuación de Kepler, Universidad de la Rioja, Servicio de Publicaciones, (2013).

M. A. Diloné, J. M. Gutiérrez and E. Vera's, Semilocal Convergence Newton Method Applied to Kepler Equation: New Results, British Journal of Mathematics & Computer Science 21(3): 1-13, 2017.

M.A. Hernandez Verón, An acceleration procedure of the Whittaker method by means of convexity, Univ. u Novom Sadu, Zb. Rad. Prirod.- Mat. Fak. Ser. Mat., 20 (1990), 1, 27-38.

P. Colwell: Solving Kepler's equation over three centuries, Willmann-Bell, EEUU, 1993.

S. Raluca: The semilocal convergence of the convex acceleration of

Whittaker's method, Scientific Studies and Research. Series Mathematics and Informatics. Vol. 22, (2012), 117-124.

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