Convergence of the spline function for functional-differential equation of neutral type

Abstract

The existence, uniqueness and stability for the functional-differential equation of neutral type using spline of deficiency 3 with stepsize 3h spline function of degree four are presented in Ref. [1]. 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. Numerical examples are presented to illustrate the convergence of the method.

Keywords:

• Delay
• Ordinary differential equations
• Spline functions approximation
• Convergence and neutral type