• Homotopy Continuation Method of Arbitrary Order of Convergence for Solving the Hyperbolic Form of Kepler’s Equation

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    • Keywords


      Homotopy method; hyperbolic Kepler’s equation; initial value problem; orbit determination.

    • Abstract


      In this paper, an efficient iterative method of arbitrary integer order of convergence ≥ 2 has been established for solving the hyperbolic form of Kepler’s equation. The method is of a dynamic nature in the sense that, moving 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. A property which avoids the critical situations between divergent and very slow convergent solutions that may exist in other numerical methods which depend on initial guess. Computational Package for digital implementation of the method is given and is applied to many case studies.

    • Author Affiliations


      M. A. Sharaf1 M. A. Banajh2 A. A. Alshaary2

      1. Department of Astronomy, Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia.
      2. Department of Mathematics, Girls College of Education, Jeddah, Saudi Arabia.
    • Dates

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