The Numerical Solution and the Convergence Analysis of the Hybrid Method between the Special Insertion and the Iterative Method

This paper devoted to find the solution of the Vanishing Neutral Differential Equations (VNDEs). After having reviewed the ARCHI code, which was originally written by Paul with the aim of solving neutral differential equations, an improvement of this code will be presented in this paper to solve problems of VNDEs. This improvement is done by suggesting a hybrid method of special interpolants with iteration procedure of RK method. We will analyze the convergence of the suggested hybrid method. We conclude that the criteria of convergence for this method is:

and when , we have , that is the solution is convergent and the derivative of the solution is also convergent for VNDEs.