International Astronomy and Astrophysics Research Journal

Solving Differenced Kepler’s Equation Using Homotopic Continuation Method

H. H. Selim *

National Research Institute of Astronomy and Geophysics, Helwan, Cairo, Egypt.

*Author to whom correspondence should be addressed.

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Abstract

this paper deals with convergent ≥ 2 of arbitrary order through an effective iterative method, it is formulated to solve difference Kepler equation. This formulation with a dynamical aspect, where go from one iterative model to another one using more instruction. Where, the more important hint that, it is not need any prior information of initial guesses and keep away from the critical situations between divergent to the very slow convergent solutios, which may exist in another numerical method that depends on the initial guesses. Finally, copmuted algorithm and numerical example for the method are gevin.

Keywords: Initial value problem, differenced Kepler's equation, homotopy continuation method, space dynamics, mathematical astronomy

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