Sextic spline collocation methods for nonlinear fifth-order boundary value problems

Abstract

In this paper, two sextic-spline collocation methods are developed and analysed for approximating solutions of nonlinear fifth-order boundary-value problems. The first method uses a spline interpolant and the second one is based on a spline quasi-interpolant, which are constructed from sextic splines. They are both proved to be second-order convergent. Numerical results confirm the order of convergence predicted by the analysis. It has been observed that the methods developed in this paper are better than the others given in the literature.

Keywords:

• fifth-order boundary-value problems
• collocation method
• sextic spline interpolant
• quasi-interpolant

2000 AMS Subject Classifications :

• 41A15
• 65D05
• 65D07
• 65D10

Acknowledgements

This research is supported by AI/182/08 and URAC-05.