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…
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