An efficient semi-numerical technique for solving nonlinear singular boundary value problems arising in various physical models

Abstract

An efficient semi-numerical method is proposed for solving nonlinear singular boundary value problems (BVPs) arising in various physical models. We proposed a modification of the Adomian decomposition method (ADM). The technique depends on transforming the BVPs to Fredholm integral equations before establishing the recursive scheme for the solution components of a specific solution. The major advantage of the proposed method over the classical ADM or modified ADM is that it provides not only better numerical results but also avoids unnecessary computation for determining the unknown parameters. Moreover, the proposed technique overcomes the singularity issue at the origin $x=0$. Furthermore, the convergence analysis of the proposed method is established. Two singular examples are examined to demonstrate the accuracy, applicability, and generality of the proposed method.

Keywords:

• singular boundary value problems
• Adomian decomposition method
• approximations
• Emden–Fowler equation
• Green's function

2010 AMS Subject Classifications:

• 34B05
• 34B15
• 34B16
• 34B18
• 34B27

Disclosure statement

The authors declare that there is no conflict of interests regarding the publication of this paper.