Approximate Analytical Solutions Generalized Lane-Emden-Fowler Equations

Abstract

The work deals with a family of nonlinear differential equations of Lane–Emden–Fowler type. The original Lane–Emden equation was used to model the thermal behavior of spherical clouds of gas within the framework of classical thermodynamics. Slightly modified, it describes phase transitions in critical thermodynamic systems, cylindrical equilibrium shapes of lipid membranes and many other physical processes and phenomena. The aim of the present work is to obtain approximate analytical solutions of the regarded equations. The problem is formulated in terms of nonlinear Volterra integral equations of the second kind. The solutions are sought by He's homotopy perturbation technique, as series expansion in the independent variable, and by Picard's method of successive approximations.