the objective of this paper is applying the well-known exact operational matrices (eoms) idea for solving the emden-fowler equations, illustrating the superiority of eoms over ordinary operational matrices (ooms). up to now, a few studies have been conducted on eoms ; but the solved differential equations did not have high-degree nonlinearity and the reported results could not strongly show the...

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order Emden-Fowler delay dynamic equations rxΔ Δ t p t x τ t 0 on a time scale T; here γ is a quotient of odd positive integers with r and p as real-valued positive rd-continuous functions defined on T. Our results in this paper not only extend the results given in Agarwal et al. 2005 , Akin-...

We analyze the stability of Newtonian polytropic static fluid spheres, described by the Lane-Emden equation. In the general case of arbitrary polytropic indices the Lane-Emden equation is a non-linear second order ordinary differential equation. By introducing a set of new variables, the Lane-Emden equation can be reduced to an autonomous system of two ordinary differential equations, which in ...

Lane-Emden equation is a nonlinear singular equation that plays an important role in the astrophysics. In this paper, we have applied the collocation method based on rational Chebyshev functions to solve Lane-Emden type equations. The method reduces solving the nonlinear ordinary differential equation to solving a system of nonlinear algebraic equations. The comparison of the results with the o...

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...

This paper provides a technique to investigate the solutions of generalized nonlinear singular Lane–Emden equations of first and second kinds by using a Haar wavelet quasi-linearization approach. The Lane–Emden equation is widely studied and is treated as a challenging equation in the theory of stellar structure for the gravitational potential of a self gravitating, spherically symmetric polytr...

The Lane-Emden equation has been used to model several phenomenas in theoretical physics, mathematical physics and astrophysics such as the theory of stellar structure. This study is an attempt to utilize the collocation method with the Rational Chebyshev of Second Kind function (RSC) to solve the Lane-Emden equation over the semi-infinit interval [0,+∞). According to well-known results and com...

Polytropic models play a very important role in galactic dynamics and in the theory of stellar structure and evolution. However, in general, the solution of the Lane-Emden equation can not be given analytically but only numerically. In this paper we give a good analytic approximate solution of the Lane-Emden equation. This approximation is very good for any finite polytropic index n and for the...

In this paper, a numerical method based on the hybrid of the quasilinearization method (QLM) and the collocation method is suggested for solving wellknown nonlinear Lane-Emden-type equations as singular initial value problems, which model many phenomena in mathematical physics and astrophysics. First, by using the QLM method, the nonlinear ordinary differential equation is converted into a sequ...

Abstract. In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden type nonlinear oscillator equation with linear forcing, ẍ+αxẋ+βx+γx = 0,which preserves the form of the time independent integral, conservative Hamiltonian and the equation of motion. Generalizing this transformation we prove the existence of non...