Lane-Emden equation


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Lane-Emden equation

[′lān ′em·dən i‚kwā·zhən]
(astrophysics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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It has been successfully applied in the numerical solution of the generalized Lane-Emden equation [41], which is a highly nonlinear singular differential equation, in the numerical solution of higher-order regular differential equations [42], in approximate solution of the nonlinear fractional KdV-Burgers equation [43], in construct and predict the solitary pattern solutions for nonlinear time-fractional dispersive PDEs [44], and in predicting and representing the multiplicity of solutions to boundary value problems of fractional order [45].
In [12], the equation that models oxygen diffusion in a spherical cell, including nonlinear absorption kinetics, is solved by transforming the Lane-Emden equation into its equivalent Volterra integral form, then Adomian decomposition was employed to solve the nonlinear Fredholm-Volterra integral.
In Section 3, a brief description of Lane-Emden equation is presented.
Furthermore, by choosing r = 0 and k = 2, we get the standard Lane-Emden equation
For f (x,y) = [y.sup.n], g(x) = 0 and [alpha] = 2 the problem (1.1) is the standard Lane-Emden equation.
[11] Ramos J.I., Series approach to the Lane-Emden equation and Comparison with the homotopy Perturbation method", doi j.chaos:10:10-16 (2006).
We should remark that (28) is similar in form to the Lane-Emden equation of the first kind which has been considered in the literature [26-29].
Moreover, it has been recently observed that the density profiles of dark matter halos are often modeled by the isothermal Lane-Emden equation with suitable boundary conditions at the origin [2].
In the context of poly trope models this presents the problem that the central value of the potential cannot be used, as in the Lane-Emden equation. We can however impose the polytropic condition from (24) onto numerical solutions to iteratively solve the problem.
Consider a Lane-Emden equation of the second kind in [1].
Van Gorder, "Jacobi rational-Gauss collocation method for Lane-Emden equations of astrophysical significance," Nonlinear Analysis: Modelling and Control.