Non-polynomial sextic spline solution of singularly perturbed boundary-value problems

Abstract

In this paper, we develop a generalized scheme based on non-polynomial sextic spline for the numerical solution of second-order singularly perturbed two-point boundary-value problems. The proposed method is second, fourth- and sixth-order accurate. Convergence analysis of the fourth-order method is briefly discussed. We show that the approximate solution obtained by the proposed method is better than existing spline methods. Numerical examples are given to illustrate the efficiency of our methods.

Keywords:

• singularly perturbed boundary-value problems
• non-polynomial sextic spline
• boundary layers
• convergence analysis

2010 AMS Subject Classifications:

• 65L10
• 65L11

Acknowledgements

The authors are thankful to the DST, Govt. of India for providing financial support under the research project grant vide sanction no.100/IFD/13115/2010-11.