Accurate analytical periodic solution of the elliptical Kepler equation using the Adomian decomposition method

@article{Alshaery2017AccurateAP,
  title={Accurate analytical periodic solution of the elliptical Kepler equation using the Adomian decomposition method},
  author={Aisha Abdu Alshaery and Abdelhalim Ebaid},
  journal={Acta Astronautica},
  year={2017},
  volume={140},
  pages={27-33}
}
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References

SHOWING 1-10 OF 29 REFERENCES
Bessel functions and Kepler's equation
2. KEPLER'S EQUATION. After years of work, Johannes Kepler announced three laws of planetary motion early in the seventeenth century. Kepler's three laws state that the planets move in elliptical
Kepler's Iterative Solution to Kepler's Equation
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
A new simple method for the analytical solution of Kepler's equation
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
Approximate Analytical Solution of a Nonlinear Boundary Value Problem and its Application in Fluid Mechanics
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
ALGEBRAIC COMPUTATION AND THE DECOMPOSITION METHOD
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
Analytical initial-guess-free solution to Kepler's transcendental equation using Boubaker Polynomials Expansion Scheme BPES
An analytical initial-guess-free solution to the Kepler problem is proposed. The resolution protocol allows, oppositely to initial-guess methods, the determination of the real root of Kepler's
Chaotic behaviour in the newton iterative function associated with kepler's equation
The chaotic behaviour observed when Newton's method is used to solve Kepler's equation is analysed using methods borrowed from chaos theory. The result of the analysis is compared with previous
...
1
2
3
...