In this paper, a numerical method, which is called the Laguerre collocation method, for the approximate solution of Lane–Emden type functional differential equations in terms of Laguerre polynomials are derived. The method is based on the matrix relations of Laguerre polynomials and their derivatives, and reduces the solution of the Lane–Emden type functional differential equation to the soluti...

A generator of Lie point symmetries admitted by a Lane–Emden equation of the second-kind for arbitrary shape factor k is used to determine invariant boundary conditions admitted by the equation. The generator of Lie point symmetries is then used to reduce the order of the Lane–Emden equation. A phase plane analysis of the reduced equation indicates that the stability of the invariant boundary c...

We compute multiprecision solutions of the Lane–Emden equation. This differential equation arises when introducing the well-known polytropic model into the equation of hydrostatic equilibrium for a nondistorted star. Since such multiprecision computations are time-consuming, we apply to this problem parallel programming techniques and thus the execution time of the computations is drastically r...

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.

We give the description of nonlinear nonautonomous ordinary differential equations of order n with a so-called reducible linear part. The group classification of generalized Emden-Fowler equations of the mentioned class is done. We have found such laws of the variation of f(x) that the equation admits one, two, or tree one-parameter Lie groups.

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 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.

By using critical point theory, some new sufficient conditions for the existence of at least 2N distinct solutions to boundary value problems of a discrete generalized Emden–Fowler equation are obtained. © 2009 Elsevier Ltd. All rights reserved.

The existence of a class of nonoscillatory solutions for a generalized Emden–Fowler differential equation is studied. Some analogies and discrepancies between the continuous and discrete case are also discussed. AMS subject classification: Primary 34C10, Secondary 34C15, 39A10.