Abstract
The Lane-Emden equations have been used to model some phenomena in astrophysics, such as mathematical physics and stellar structure theory. In addition, the Lane-Emden equation is a central equation in the theory of stellar structures. In this paper, we introduce the Lane-Emden differential equations. A special second order Lane-Emden differential equation is solved by He’s variational iteration, adomian decomposition method, homotopy analysis method, homotopy perturbation method, and finite difference method respectively. The results obtained are compared with each other and it is analyzed which method gives more reliable results and is more useful than the others.
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