Homotopy Continuation Method of Arbitrary Order of Convergence for Solving Differenced Hyperbolic Kepler's Equation

Abstract

In this paper, an efficient iterative method of arbitrary integer order of >=2 will be established for the solution of differenced hyperbolic convergent Kepler's equation. 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 priori knowledge of the initial guess. Aproperty which avoids the critical situations between divergent to very slow convergent solutios, that may exist in other numberical methods which depend on initial guess. Computeational package for digital implementation of the method is given.