On the analytic solution of the lane-emden equation

1995 ◽  
Vol 8 (2) ◽  
pp. 161-181 ◽  
Author(s):  
G. Adomian ◽  
R. Rach ◽  
N. T. Shawagfeh
Keyword(s):  
Analytic Solution ◽  
Emden Equation

scholarly journals New Analytic Solution to the Lane-Emden Equation of Index 2

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
S. S. Motsa ◽  
S. Shateyi
Keyword(s):  
Analytical Methods ◽  
Initial Value Problems ◽  
Analytic Solution ◽  
Mathematical Physics ◽  
Numerical Results ◽  
Initial Value ◽  
Emden Equation ◽  
New Methods ◽  
Index 2 ◽  
Good Agreement

We present two new analytic methods that are used for solving initial value problems that model polytropic and stellar structures in astrophysics and mathematical physics. The applicability, effectiveness, and reliability of the methods are assessed on the Lane-Emden equation which is described by a second-order nonlinear differential equation. The results obtained in this work are also compared with numerical results of Horedt (1986) which are widely used as a benchmark for testing new methods of solution. Good agreement is observed between the present results and the numerical results. Comparison is also made between the proposed new methods and existing analytical methods and it is found that the new methods are more efficient and have several advantages over some of the existing analytical methods.

An Analytic Solution for the Noncoplanar P4P Problem with An Uncalibrated Camera

2011 ◽  
Vol 34 (4) ◽  
pp. 748-754 ◽  
Author(s):  
Yang GUO ◽  
Xiang-De ZHANG ◽  
Xin-He XU
Keyword(s):  
Analytic Solution ◽  
Uncalibrated Camera

On the convective diffusion under partial slip at wall

1989 ◽  
Vol 54 (4) ◽  
pp. 967-980 ◽  
Author(s):  
Ondřej Wein ◽  
Petr Kučera
Keyword(s):  
Mass Transfer ◽  
Numerical Solution ◽  
Analytic Solution ◽  
Convective Diffusion ◽  
Linear Velocity ◽  
Partial Slip ◽  
Accurate Calculation ◽  
Transfer Coefficients ◽  
Empirical Formulas ◽  
Mass Transfer Coefficients

Extended Leveque problem is studied for linear velocity profiles, vx(z) = u + qz. The existing analytic solution is reconsidered and shown to be inapplicable for the accurate calculation of mean mass-transfer coefficients. A numerical solution is reported and its accuracy is checked in detail. Simple but fairly accurate empirical formulas are suggested for the calculating of local and mean mass-transfer coefficients.

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