On the Numerical Solutions Based on a Novel Hybrid Method for Some VNDEs Problems

Stipan Podobnic^1,*, Barbara Charchekhandra²

¹Department of Mathematics, University of Rijeka, City of Rijeka, Croatia

²Jadavpur University, Department Of Mathematics, Kolkata, India

Emails: Stipanpod133@Uniri.hr; Charchekhandrabar32@yahoo.com

Abstract

This paper is devoted to find the solution of the Vanishing Neutral Differential Equations (VNDEs), where we review the ARCHI code for solving neutral differential equations, and then an improvement of this code will be presented in this paper to solve problems of VNDEs. This improvement is done by suggesting a new hybrid method of special interpolants with iteration procedure of RK method. We will analyze the convergence of the suggested new method by proving the following criteria

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

Keywords: Hybrid method; Numerical Solution; Convergence analysis; VDNE problem