Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation

Numerical approach of two-derivative Runge-Kutta type method with three-stage fifth-order (TDRKT3(5)) is developed and proposed for solving a special type of third-order delay dif-ferential equations (DDEs) with constant delay. An algorithm based on Newton interpolation and hybrid with the TDRKT method is built to approximate the solution of third-order DDEs. In this paper, three-stage fifth-order called TDRKT3(5) method with single third derivative and multiple evaluations of the fourth derivative is highlighted to solve third-order pantograph type delay differ-ential equations directly with the aid of the Newton interpolation method. Stability analysis of TDRKT3(5) method is investigated. The numerical experiments illustrate high efficiency and valid-ity of the new method for solving a special class of third-order DDEs and some future works are recommended by extending proposed method to solve fractional and singularly perturbed delay dif-ferential equations. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).