History tracking ability of hybrid second and fourth orders runge-kutta in solving delay differential equations

Abstract

This paper presents numerical solution for Delay Differential Equations systems to identify frequent discontinuities which occur after and sometimes before the initial solution. The Runge-Kutta methods have been chosen because they are well-established methods and can be modified to handle discontinuities by means of mapping of past values. The state system of the problem is first discretized before the method is applied to find the solution. Our objective is to develop a scheme for solving delay differential equations using hybrid second and fourth order of Runge-Kutta methods. The results have been compared with the result from Matlab routine dde23 which used second and third order of Runge-Kutta methods. Our numerical scheme is able to successfully handle discontinuities in the system and produces results with acceptable error.