In this paper we qualitatively study radial solutions of the semilinear elliptic equation $\Delta u + u^n = 0$ with $u(0)=1$ and $u'(0)=0$ on positive real line, called Emden-Fowler or Lane-Emden equation. This is great importance in Newtonian astrophysics constant $n$ polytropic index. By introducing a set new variables, can be written as an autonomous system two ordinary differential equation...

Orthogonal functions and polynomials have been used by many authors for solving various problems. The main idea of using orthogonal basis is that a problem reduces to solving a system of linear or nonlinear algebraic equations by truncated series of orthogonal basis functions for solution of problem and using the operational matrices. Here we use Legendre wavelets basis on interval [0, 1]. Some...

We propose a numerical method for solving nonlinear initial-value problems of Lane-Emden type. The method is based upon nonclassical Gauss-Radau collocation points, and weighted interpolation. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced on arbitrary intervals. Then they are utilized to reduce the computation of nonlinear initial-value...

Abstract The purpose of this paper is to analyze the conformally flat spherically symmetric fluid distribution with generalized polytropic equations state. We have developed two different framework for definitions polytropes. frameworks development modified Lane–Emden equation are presented both cases. condition used calculate anisotropy factor which transform considered systems into consistent...

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalisations is given. As a first result we obtain t-dependent constants of the motion for particular instances of Emden equations by means of some of their particular solutions. Previously known results are recovered from t...

Here, a simple method to determine the rate of convergence of Adomian decomposition method is introduced. The proposed method is used to compare between the rate of convergence of standard and modified (proposed by Wazwaz [A.M. Wazwaz, A new method for solving singular initial value problems in the second-order ordinary differential equations, Appl. Math. Comput. 128 (2002) 45–57]) Adomian meth...

We analyze the effects of modified gravity on specific heats electrons and ions, Debye temperature, crystallization process, cooling mechanism in white dwarfs. derive Lane-Emden-Chandrasekhar equation relate it to process equations for Palatini $f(R)$ gravity. Moreover, first time literature, we show that model plays a crucial role not only mass size dwarf, but also affects their internal prope...

The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of the proof to partial differential equations is straight forward. The method, whose mathematical basis in physics was discussed recently by one of the present ...