Reversed-Series Solution to the Universal Kepler Equation

1997 ◽  
Vol 20 (6) ◽  
pp. 1276-1277 ◽  
Author(s):  
Andrew J. Staugler ◽  
David A. Chart ◽  
Robert G. Melton
Keyword(s):  
Series Solution ◽  
Kepler Equation

The Homotopy Perturbation Method for Accurate Orbits of the Planets in the Solar System: The Elliptical Kepler Equation

2017 ◽  
Vol 72 (10) ◽  
pp. 933-940
Author(s):  
Aisha Alshaery
Keyword(s):  
Solar System ◽  
Perturbation Method ◽  
Series Solution ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Accurate Solution ◽  
Homotopy Perturbation ◽  
Halley's Comet ◽  
The Mean ◽  
Kepler Equation

AbstractAccurate trajectories for the orbits of the planets in our solar system depends on obtaining an accurate solution for the elliptical Kepler equation. This equation is solved in this article using the homotopy perturbation method. Several properties of the periodicity of the obtained approximate solutions are introduced through some lemmas. Numerically, our calculations demonstrated the applicability of the obtained approximate solutions for all the planets in the solar system and also in the whole domain of eccentricity and mean anomaly. In the whole domain of the mean anomaly, 0≤M≤2π, and by using the different approximate solutions, the residuals were less than 4×10−17 for e∈[0, 0.06], 4×10−9 for e∈[0.06, 0.25], 3×10−8 for e∈[0.25, 0.40], 3×10−7 for e∈[0.40, 0.50], and 10−6 for e∈[0.50, 1.0]. Also, the approximate solutions were compared with the Bessel–Fourier series solution in the literature. In addition, the approximate homotopy solutions for the eccentric anomaly are used to show the convergence and periodicity of the approximate radial distances of Mercury and Pluto for three and five periods, respectively, as confirmation for some given lemmas. It has also been shown that the present analysis can be successfully applied to the orbit of Halley’s comet with a significant eccentricity.

SERIES SOLUTION FOR THE RADIATION-CONDUCTION INTERACTION ON UNSTEADY MHD FLOW

2011 ◽  
Vol 14 (10) ◽  
pp. 927-941 ◽  
Author(s):  
I. Ahmad ◽  
T. Javed ◽  
Tasawar Hayat ◽  
Muhammad Sajid
Keyword(s):  
Series Solution ◽  
Mhd Flow

Series solution of Laplace problems

2018 ◽  
Vol 60 ◽  
pp. 1
Author(s):  
Lloyd Nicholas Trefethen, FRS
Keyword(s):  
Series Solution

Optimal algebra and power series solution of fractional Black-Scholes pricing model

2021 ◽  
Vol 25 (8) ◽  
pp. 6075-6082
Author(s):  
Hemanta Mandal ◽  
B. Bira ◽  
D. Zeidan
Keyword(s):  
Power Series ◽  
Series Solution ◽  
Power Series Solution ◽  
Pricing Model ◽  
Black Scholes

Hybrid nanofluid flow over a stretched cylinder with the impact of homogeneous–heterogeneous reactions and Cattaneo–Christov heat flux: Series solution and numerical simulation

Heat Transfer ◽  
2021 ◽  
Author(s):  
Anthonysamy John Christopher ◽  
Nanjundan Magesh ◽  
Ramanahalli Jayadevamurthy Punith Gowda ◽  
Rangaswamy Naveen Kumar ◽  
Ravikumar Shashikala Varun Kumar
Keyword(s):  
Numerical Simulation ◽  
Heat Flux ◽  
Series Solution ◽  
Heterogeneous Reactions ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
The Impact

scholarly journals Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ming-Sheng Hu ◽  
Ravi P. Agarwal ◽  
Xiao-Jun Yang
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Series Solution ◽  
Differential Operators ◽  
Fractional Wave Equation ◽  
Local Fractional Calculus ◽  
Vibrating String ◽  
Fractional Differential ◽  
Fractional Differential Operators

We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag-Leffler function.

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