Numerical Solution of Delay Differential Equations with Heronian Implicit Runge-Kutta Method

In recent years, there has been growing interest in the numerical solution of Delay Differential Equations (DDEs). This is due to the fact that DDEs provides a good means of modelling many phenomena in diverse application fields ranging from physical sciences, economy, medicine, education to electrodynamics. Hence, the increased attention in the numerical solutions to such problems becomes a necessity. The purpose of this study is to present a numerical method that uses a polynomial interpolating function when solving DDEs. In this paper, Heronian Implicit Runge-Kutta method is considered for the solution of DDEs while the delay term is being estimated with the aid of Hermite Interpolation of the third order. The Stability analysis of this method is considered, and its efficiency is represented and compared with some numerical examples. It is evident from the obtained results of the numerical examples that this numerical method alongside the polynomial interpolating function, which was used to approximate the delay term, is suitable for solving DDEs.