# 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} }

## 18 Citations

An Efficient Iterative Method for Solving the Elliptical Kepler’s Equation

- Physics, Mathematics
- 2021

In this paper, a numerical technique, based on Banach’s fixed point theorem, is proposed to obtain an approximate solution of the elliptical Kepler equation which is often used to describe the motion…

Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method

- MathematicsMathematical and Computational Applications
- 2019

The Ambartsumian delay equation is used in the theory of surface brightness in the Milky way. The Adomian decomposition method (ADM) is applied in this paper to solve this equation. Two canonical…

Solving Kepler's equation via nonlinear sequence transformations

- Mathematics
- 2021

Since more than three centuries Kepler’s equation continues to represents an important benchmark for testing new computational techniques. In the present paper, the classical Kapteyn series solution…

A novel exact solution for the fractional Ambartsumian equation

- Mathematics
- 2021

Fractional calculus (FC) is useful in studying physical phenomena with memory effect. In this paper, a fractional form of Ambartsumian equation is considered utilizing the Caputo fractional…

Exact Solution of Ambartsumian Delay Differential Equation and Comparison with Daftardar-Gejji and Jafari Approximate Method

- MathematicsMathematics
- 2018

The Ambartsumian equation, a linear differential equation involving a proportional delay term, is used in the theory of surface brightness in the Milky Way. In this paper, the Laplace-transform was…

Solution of Ambartsumian Delay Differential Equation with Conformable Derivative

- MathematicsMathematics
- 2019

This paper addresses the modelling of Ambartsumian equation using the conformable derivative as an application of the theory of surface brightness in astronomy. The homotopy perturbationmethod is…

Solution of Ambartsumian Delay Differential Equation in the q-Calculus

- Mathematics
- 2020

The Ambartsumian equation in view of the q-calculus is investigated in this paper. This equation is of practical interest in the theory of surface brightness in the Milky Way. Two approaches are…

Modification of Three Order Methods For Solving Satellite Orbital Equation in Elliptical Motion

- Physics
- 2020

Received: 26 / 1 /2020 Accepted: 3 / 5 / 2020 Available online: 6 / 6 / 2020 DOI: http://dx.doi.org/10.37652/JUAPS.2020.14.1.6 In the present study, a modification for iterative methods of three…

New Analytic Solution for Ambartsumian Equation

- Mathematics
- 2018

where is a further constant. Eq. (1) is called Ambartsumian equation which describes the surface brightness in Astronomy [1, 2]. Uniqueness and existence of this model has been investigated by Kato…

Development of analytical solution for a generalized Ambartsumian equation

- Mathematics
- 2020

Based on the conformable derivative, a generalized model of the Ambartsumian equation is analyzed in this paper. The solution is expressed as a power series of arbitrary powers. In addition, the…

## References

SHOWING 1-10 OF 29 REFERENCES

Bessel functions and Kepler's equation

- Physics, Geology
- 1992

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

- 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…

A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations

- MathematicsAppl. Math. Comput.
- 2011

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…

Adomian decomposition method for solving the Volterra integral form of the Lane-Emden equations with initial values and boundary conditions

- MathematicsAppl. Math. Comput.
- 2013

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…

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…

Analytical initial-guess-free solution to Kepler's transcendental equation using Boubaker Polynomials Expansion Scheme BPES

- Physics
- 2010

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

- Physics
- 1999

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…