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An efficient computational algorithm for the initial value problem associated with the universal Y functions
Author(s) -
Sharaf M. A.,
Saad A. S.,
Fadak M. A.
Publication year - 2016
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.201512300
Subject(s) - initial value problem , continuation , algorithm , iterative method , mathematics , integer (computer science) , homotopy , space (punctuation) , value (mathematics) , computer science , sequence (biology) , order (exchange) , mathematical analysis , pure mathematics , statistics , programming language , operating system , finance , biology , economics , genetics
In the present paper, an efficient iterative method of arbitrary integer order of convergent ≥2 based on the homotopy continuation techniques for the solution of the initial value problem of space dynamics using the universal Y functions is presented. The method is of dynamic nature in the sense that, ongoing from one iterative scheme to the subsequent one, only additional instruction is needed. Most importantly, the method does not need any prior knowledge of the initial guess. This is 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 guesses. A computational package for digital implementation of the method is given, together with numerical applications for elliptic, hyperbolic, and parabolic orbits. The accuracy of the results for all orbits is O(10 –16 ). (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)