Comparison New Algorithm Modified Euler Based on Harmonic-Polygon Approach for Solving Ordinary Differential Equation

Abstract

There are many benefits to improve Euler scheme for solving the Ordinary Differential Equation problems. Among the benefits are simple implementation and low-cost computation. However, the problem of accuracy in the Euler scheme persuades scholar to use the complex method. Therefore, the main purpose of this research is to show the development of a new modified Euler scheme that improves the accuracy of the Polygon scheme in various step sizes. The implementation of the new scheme is by using the Polygon scheme and then Harmonic mean concept that is called the Harmonic-Polygon scheme. This Harmonic-Polygon scheme can provide new advantages more than the Euler scheme could offer by solving Ordinary Differential Equation problem. Four set of problems are solved via Harmonic-Polygon. Findings showed that new scheme or Harmonic-Polygon scheme can produced much better accuracy result.