Centroidal-Polygon: Solving First Order Ordinary Differential Equation using Centroidal mean to improve Euler Method

Abstract

Euler method is one of the oldest and simplest numerical techniques to solve mathematical problems. However, the Euler method lacks accuracy compared to other methods such as the Runge-Kutta and the Adam Bashforth. This research proposed a new scheme by enhancing the Euler method using centroidal mean, i.e. combining the Euler method and the mean concept. In this research, the proposed scheme would be used to improve the accuracy of the first order Ordinary Differential Equation (ODE). The enhanced Euler method was used based on the improved Euler method, which is a midpoint method. To analyse the accuracy of the proposed scheme and the existing schemes, SCILAB 6.0 software was used to compare the results of different step sizes. This research compared the proposed scheme with the Polygon scheme by Zul Zamri and the Harmonic-Polygon scheme by Nurhafizah. By using Centroidal-Polygon as the proposed scheme, more accurate results were yielded. However, the scheme was limited to some of the linear and non-linear equations only.