Quadratic B-spline collocation method for two-parameter singularly perturbed problem on exponentially graded mesh

ABSTRACT

In this article, we present a quadratic B-spline collocation method on an exponentially graded mesh for the solution of two-parameter singularly perturbed boundary value problems (TP-SPBVPs) whose solution exhibits twin boundary layers at both endpoints of the domain of consideration. The method is shown to be parameters uniformly convergent of order two. To verify the theoretical estimates and to show the better accuracy of the proposed method compared to the existing results, numerical experiments are presented for several test problems.

Keywords:

• Singularly perturbed problems
• two-parameter
• exponentially graded mesh
• quadratic B-spline collocation method
• error analysis

2010 Mathematics Subject Classifications:

• 65L10
• 65L50
• 65L70

Acknowledgements

The authors thank the reviewers for the their valuable suggestions for the improvement of the work. The first two authors thank National Board for Higher Mathematics, Department of Atomic Energy, Government of India, for the financial support under project No. 2/48(33)/2016 NBHM(R.P.)/R&DII/4533 dated 31 March 2017.

Disclosure statement

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

Additional information

Funding

This work was supported by National Board for Higher Mathematics [2/48(33)/2016 NBHM(R.P.)/R&DII/4533 dated 31 March 2017].