A modified homotopy perturbation method coupled with the Fourier transform for nonlinear and singular Lane–Emden equations

Abstract

In the present work the modified homotopy perturbation method (HPM), incorporating He’s polynomial into the HPM, combined with the Fourier transform, is used to solve the nonlinear and singular Lane–Emden equations. The closed form solutions, where the exact solutions exist, and the series form solutions, where the exact solutions do not exist, are obtained. Thereafter, the Pade approximant is used to provide the trend of monotonic convergence. Moreover, the concept of equilibrium, which arises from the nature of Lane–Emden differential equations when the space coordinate approaches infinity x→∞, is shown by the monotonic approach of the results toward a constant value.