Parametric quintic spline solution of third-order boundary value problems

Abstract

In this paper, we develop parametric quintic spline function to approximate the solution of third-order boundary value problems of the form u″′=f(x, u), a≤x≤b, subject to the boundary conditions u(a)=k ₁, u′(a)=k ₂ and u(b)=k ₃. The class of methods are second-, fourth- and sixth-order accurate. End equations of the splines are derived and truncation error is given. Three numerical examples are presented to illustrate the practical use of our methods as well as their accuracies when compared with some existing spline function methods. It is shown that the new methods give approximations, which are better than those produced by other methods.

Keywords:

• third-order boundary value problems
• parametric quintic splines
• end conditions

2000 AMS Subject Classification:

• 65L10

Acknowledgements

The authors would like to thank the referees for their useful and constructive comments.