Haar wavelet approximate solutions for the generalized Lane-Emden equations arising in astrophysics

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 polytropic fluid which models the thermal behavior of a spherical cloud of gas acting under the mutual attraction of its molecules and subject to the classical laws of thermodynamics. The proposed method is based on the quasi-linearization approximation and replacement of an unknown function through a truncated series of Haar wavelet series of the function. The method is shown to be very reliable and easy to capture the solutions of generalized nonlinear singular Lane-Emden equations. The applicability of the method is shown by numerical tests on various cases of the generalized Lane-Emden equation and solutions are also reported in the neighborhood of a singular point. (C) 2013 Elsevier B.V. All rights reserved.