A novel numerical approach and its convergence for numerical solution of nonlinear doubly singular boundary value problems

Abstract

This paper deals with two new recursive numerical schemes for the solution of a class of doubly singular two-point boundary value problems with different types of boundary conditions. We first transform the original problem into an equivalent integral equation to overcome the singular behaviour at the origin and then establish recursive schemes by employing Homotopy perturbation method for the solution of the resultant equation. We establish the convergence results of the new numerical methods. Four numerical examples are considered to demonstrate the efficiency and accuracy of the proposed methods. The present methods are shown their advantage over some existing methods (Chawla and Katti, 1982; Pandey and Singh, 2007; Pandey and Singh, 2004; Caglar et al., 2009; Kumar and Aziz, 2004; Khuri and Sayfy, 2010) developed for the solution of singular two-point boundary value problems. Moreover, the new methods are used to obtain the approximate solutions of the singular boundary value problems arising in various physical problems.