An Elegant Perturbation Solution For The Lane-Emden Equation Of The Second Kind

Perturbation solutions are obtained for the Lane-Emden equation of the second kind which describe Bonnor-Ebert gas spheres. In particular, we employ the field-theoretic perturbative procedure due to Bender et al. to obtain analytical solutions to the nonlinear initial value problem. We find that the method allows one to construct perturbation solutions which converge rapidly to the true solutions in many cases, as it allows one to more accurately represent the influence of nonlinear terms in the linearized equations. The rapid convergence of the method results in qualitatively accurate solutions in relatively few iterations. © 2010 Elsevier B.V. All rights reserved