Sextic C 1-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.