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.