Homotopy Continuation Method of Arbitrary Order of Convergence for the Two-Body Universal Initial Value Problem

Authors: Sharaf M.A.¹; Sharaf A.A.²

Source: Celestial Mechanics and Dynamical Astronomy, Volume 86, Number 4, August 2003 , pp. 351-362(12)

Publisher: Springer

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Abstract:

In this paper, an efficient iterative method of arbitrary positive integer order of convergence 2 will be established for the two-body universal initial value problem. The method is of dynamic nature in the sense that, on going from one iterative scheme to the subsequent one, only additional instruction is needed. Moreover, which is the most important, the method does not need any a priori knowledge of the initial guess. A property which avoids the critical situations between divergent to very slow convergent solutions, that may exist in other numerical methods which depend on initial guess. Some applications of the method are also given.

Keywords: universal initial value problem; universal Kepler’s equation; homotopy continuation techniques

Language: English

Document Type: Research article

Affiliations: 1: Department of Astronomy, Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia, e-mail: sharaf_adel@hotmail.com 2: Department of Computer Science, Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia, e-mail: amrsh@aucegypt.edu

Publication date: 2003-08-01