A new analytical solution of the hyperbolic Kepler equation using the Adomian decomposition method
@article{Ebaid2017ANA, title={A new analytical solution of the hyperbolic Kepler equation using the Adomian decomposition method}, author={Abdelhalim Ebaid and Randolph C. Rach and Essam R. El-Zahar}, journal={Acta Astronautica}, year={2017}, volume={138}, pages={1-9} }
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References
SHOWING 1-10 OF 37 REFERENCES
A Method Solving Kepler’s Equation for Hyperbolic Case
- Physics
- 1997
We developed a method to solve Kepler’s equation for the hyperboliccase. The solution interval is separated into three regions; F ≪ 1, F≈ 1, F ≫ 1. For the region F is large, we transformed the…
A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations
- MathematicsAppl. Math. Comput.
- 2011
Homotopy continuation method of arbitrary order of convergence for solving the hyperbolic form of Kepler’s equation
- Mathematics
- 2007
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…
Adomian decomposition method for solving the Volterra integral form of the Lane-Emden equations with initial values and boundary conditions
- MathematicsAppl. Math. Comput.
- 2013
A new simple method for the analytical solution of Kepler's equation
- Physics
- 1985
A new simple method for the closed-form solution of nonlinear algebraic and transcendental equations through integral formulae is proposed. This method is applied to the solution of the famous Kepler…
ALGEBRAIC COMPUTATION AND THE DECOMPOSITION METHOD
- Mathematics
- 1986
The decomposition method of Adomian, which was developed to solve nonlinear stochastic differential equations, has recently been generalized in a number of directions and is now applicable to wide…
Approximate Analytical Solution of a Nonlinear Boundary Value Problem and its Application in Fluid Mechanics
- Mathematics
- 2011
Although the decomposition method and its modified form were used during the last two decades by many authors to investigate various scientific models, a little attention was devoted for their…
Kepler's Iterative Solution to Kepler's Equation
- Physics, Geology
- 2000
The subject of this note is quite simple. In Astronomia nova 60, Kepler set out demonstrations and equations for finding the position of a planet moving in either an ellipse or a circle such that a…