A fourth-order numerical method for solving a class of derivative-dependent nonlinear singular boundary value problems

ABSTRACT

In this paper, a high-order numerical scheme based on quartic B-spline functions is proposed to solve derivative-dependent nonlinear singular boundary value problems. Convergence of the method is analysed. Five test problems are considered to illustrate the accuracy and efficiency of the method. The results obtained by present method are compared with those obtained by the uniform mesh cubic B-spline collocation (UCS) method [P. Roul and V.M.K. Prasad Goura, B-spline collocation methods and their convergence for a class of nonlinear derivative-dependent singular boundary value problems, Appl. Math. Comput. 341 (2019), pp. 428–450] and non-uniform mesh cubic B-spline collocation (NCS) method [P. Roul and V.M.K. Prasad Goura, B-spline collocation methods and their convergence for a class of nonlinear derivative-dependent singular boundary value problems, Appl. Math. Comput. 341 (2019), pp. 428–450]. The CPU time of proposed method is compared with that of the NCS method.

KEYWORDS:

• Boundary value problem
• B-spline function
• convergence analysis
• fourth-order accuracy
• Shallow membrane cap problem

2010 AMS SUBJECT CLASSIFICATIONS:

• 65L10
• 65L60
• 34B16

Acknowledgements

The first author gratefully acknowledges financial support from the CSIR, India in the form of project no.$25/(0286)/18/EMR-II$.

Disclosure statement

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

Additional information

Funding

The first author gratefully acknowledges financial support from the Council of Scientific and industrial research (CSIR), India in the form of project no. 25/(0286)/18/EMR-II.