Solving ordinary differential equations (ODES) and delay differential equations (DDES) using Nakashima’s 2 stages 4Th order Pseudo-Runge-Kutta method

Abstract

The aim of this research is to investigate numerically the problem on solving Delay Differential Equations (DDEs) using Nakashima’s 2 Stages 4th Order Pseudo-Runge-Kutta Method. This research also discussed the problem on solving Ordinary Differential Equations (ODEs) using the same method. In this research, we also developed the algorithm of Nakashima’s 2 Stages 4th Order Pseudo-Runge-Kutta Method and the algorithm of Nakashima’s 2 Stages 4th Order Pseudo-Runge-Kutta Method incorporated with Hermite Interpolation. Finally, we apply this method to a real life problem and we choose Food-Limited Model. In this research, we use Mathematica 7 software and Microsoft Excel to conduct the calculation.