Discrete cubic spline method for second-order boundary value problems

Abstract

In this paper, we use discrete cubic spline based on central differences to obtain approximate solution of a second-order boundary value problem. It is shown that the method is of order 4 if a parameter takes a specific value, else it is of order 2. Two numerical examples are included to illustrate our method as well as to compare the performance with other numerical methods proposed in the literature.

Keywords:

• discrete cubic spline
• central difference
• boundary value problem

2000 AMS Subject Classifications:

• 65D07
• 65L10

Acknowledgements

The authors would like to thank the referees for the comments which help to improve the paper.