Homotopy perturbation method based on Green function for solving non-linear singular boundary value problems

Abstract

Non-linear singular two-point boundary value problems arise in many branches of applied mathematics and physics such as gas dynamics, biology science, etc. In this paper, we present a high-accurate method to solve a class of this type equations by using Homotopy perturbation method(HPM) based on Green function. Some examples from physical model problems are given and the results reveal that the method is very effective and convenient in solving equations with singularity, where the convergence of the result is observed. The advantage of this method is employed to present a reliable framework to overcome the singularity behavior at the point x = 0 for all models.