Métodos iterativos aplicados a la ecuación de Kepler

  1. Diloné Alvarado, Manuel Aurelio
Supervised by:
  1. José Manuel Gutiérrez Jiménez Director

Defence university: Universidad de La Rioja

Fecha de defensa: 18 July 2013

Committee:
  1. Sergio Amat Plata Chair
  2. Víctor Lanchares Barrasa Secretary
  3. Alicia Cordero Barbero Committee member
  4. Jesús Francisco Palacián Subiela Committee member
  5. María Jesús Rubio Committee member

Type: Thesis

Abstract

In this thesis we join two exciting areas such as astronomy, consisting of Kepler's equation, and numerical analysis, represented by iterative methods of solving equations. We investigate the behavior of a point methods (such as Newton's method, Halley's method, Chebyshev's method, super-Halley's method and Danby's method) and multipoint methods (such as the secant's method, bisection's method and Yun-Petkovic's method) when applied under certain initial conditions, Kepler's equation. Moreover, the cycles are characterized superatractives of period 2, which appear when applying Newton's method to the Kepler's equation, and ended with the characterization of the values of eccentricity, for which, semilocal convergence theories of Kantorovich, Gutierrez, Smale and Wang-Zhao, ensure Kepler's equation has a solution.