An effective approach for solving a class of nonlinear singular boundary value problems arising in different physical phenomena

Abstract

In this article, an effective computational technique is developed to get an analytical approximation to the solution of a class of two-point nonlinear singular boundary value problems arising in different physical models. The proposed approach consists of two steps. Firstly, formulate an integral operator by involving Green's function, and then, the Halpern's fixed-point method is implemented to the obtained integral operator to establish the desired iterative technique. The convergence of this approach is also discussed. To show the efficiency of our approach, various numerical examples are considered. The main advantages of the proposed method over existing methods are that the proposed method does not require Adomian polynomials to handle the nonlinearity, solves the problem without using the Lagrange multipliers and constrained variations and takes both endpoints of the interval into consideration. Further, the proposed method tackles the problems without requiring linearization, discretization, and perturbation assumptions, unlike other semi-analytical methods.

Keywords:

• Singular boundary value problem
• Iterative method
• Green's function
• Analytic approximation
• Lane-Emden type

2010 AMS SUBJECT CLASSIFICATIONS:

• 34B16
• 65L10
• 65L60

Acknowledgments

The research work was supported by Indian Institute of Technology Kharagpur, India. The author is greatly indebted to Prof. R. K. Pandey for excellent guidance. The author thanks the reviewers for their valuable suggestions and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).