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 3h 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.