On Improving Euler Methods for Initial Value Problems

Euler introduced the famous Euler method in 1728. A s the simplest and the most analyzed numerical integration, it has become the stepping-s tone of numerical methods for solving Initial value Problems in Ordinary Differential Equations. There has been considerable efforts to improve on Euler method by increasing its order of accuracy. Recently, in [1], Abraham proposed a new improvement on Euler Method called M odified Improved Modified Euler Method. In this work, we investigate the basic prop erties of this new method vis-a-vis the older ones. Our analysis show that the method is converge nt to order 2 and stable when applied to autonomous Initial Value Problem. AMS MSC 2010 Classification: 65L05, 65L06.