Approximate solution for the Lane-Emden equation of the second kind in a spherical annulus

Abstract

In this paper, we derive accurate approximate solution of Lane-Emden equation of the second kind in a spherical annulus geometry. The approximate solution is obtained by analytic arguments, and perturbation methods in terms of small and large radial distance parameter. The approximate solution is compared with the numerical solution. The approximate solution obtained is valid for all values of the radial distance parameter.Our best approximation has a maximum relative error in the dependent variable of 20%. In most cases it is much less than this value. This maximum error decreases as the radius of the annulus increases. Keywords: Lane-Emden equation, Spherical annulus, Approximate solutions, Thermal explosion