Convergence Of The Spline Function For Delay Dynamic System

The existence, uniqueness and stability for delay dynamic system using spline of deficiency 3 with stepsize 3 h spline function of degree four are presented in El-Safty, et al . (Existence, uniqueness and stability of the spline function for delay controlled dynamic system - Intern. J. Computer Math. , 77, 629-640, 2000). In this paper we extend the study to the convergence of our proposed spline method. We prove that, if the local error is of order p , then the global error is of order p as well and is a five order accurate. Numerical examples are presented to illustrative the convergence of the method.

Keywords:

• Delay Ordinary Differential Equations
• Spline Functions Approximation And Convergence