By the semi-inverse method, a variational principle is obtained for the Lane–Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method. 2002 Elsevier Science Inc. All rights reserved.

In this article Differential Transformation Method (DTMs) is considered to find exact and approximate solutions of singular Initial Value Problems (IVPs) of the Lane-Emden type in second-order Ordinary Differential Equations (ODEs). The method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series so...

where r is a constant, models the thermal behaviour of a spherical cloud of gas acting under the mutual attraction of its molecules and subject to the classical laws of thermodynamics. This equation was proposed by Lane (1) (see also (3)) and studied in detail by Emden (2). Fowler (4; 5) considered a generalization of Eq. (1), called Emden-Fowler equation (6), where the last term is replaced by...

The perturbation method is applied to numerical solution of the Lane-Emden Equation (LEE)of arbitrary index n, and the global parameters of polytropes are found as function of polytropic index n.

In this paper‎, ‎numerical solution of‎ ‎general Lane-Emden equation via collocation method based on‎ ‎Double Exponential DE transformation is considered‎. ‎The‎ ‎method converts equation to the nonlinear Volterra integral‎ ‎equation‎. ‎Numerical examples show the accuracy of the method.‎ ‎Also‎, ‎some remarks with respect to run-time‎, computational cost‎ ‎and implementation are discussed.