A novel approach based on mixed exponential compact finite difference and OHA methods for solving a class of nonlinear singular boundary value problems

Abstract

This work aims to find the numerical solution to a class of nonlinear singular boundary value problems (SBVPs). The considered problem has a singularity at x = 0. We introduce a computational technique comprising an optimal homotopy analysis (OHA) approach and exponential compact finite difference method (ECFDM) to solve this SBVPs. In this technique, the domain of the problem $I=[0,1]$ is divided into two subintervals as $I=I_1\cup I_2=[0,\xi ]\cup [\xi ,1]$ (the point $x=\xi$ is chosen sufficiently close to the singularity). In interval $I_1$, we employ the OHA scheme to overcome the singularity. In interval $I_2$, an ECFDM is designed to solve the resultant boundary value problem (BVP). Convergence analysis of the ECFDM is discussed. Furthermore, numerical experiments are performed to confirm the theoretical claims. The proposed ECFDM is shown to be fourth-order convergence.

Keywords:

• Singular boundary value problems
• OHA method
• high-order exponential compact difference scheme
• convergence analysis
• isothermal gas sphere
• thermal explosion in a cylindrical vessel

2010 AMS Subject Classifications:

• 65L10
• 65L60
• 34B16

Acknowledgments

The authors are very grateful to the anonymous referee for his insightful comments and suggestions.

Disclosure statement

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

Additional information

Funding

The authors also thankfully acknowledge the financial support provided by Council of Scientific and Industrial Research (CSIR), New Delhi, India in the form of project no. 25(0286)/18/EMR-II.