Sextic C¹-spline collocation methods for solving delay differential equations

Abstract

In this paper, we propose a global collocation method for the numerical solution of the delay differential equations (DDEs). The method presented is based on sextic C ¹-splines s(x) as an approximation to the exact solution y(x) of the DDEs. Convergence results shows that the error bounds ‖ s ^j −y ^j ‖=O(h ⁶), j=0, 1, in the uniform norm. Moreover, the stability analysis properties of these methods have been studied. Numerical experiments will also be considered.

Keywords:

• delay differential equations
• sextic splines
• collocation methods
• stability analysis

2010 AMS Subject Classifications :

• 65L05
• 41A15
• 65D07
• 65L20

Acknowledgement

The authors are indebted to Professor S.E. El-Gendi for various valuable suggestions and constructive criticism.