Improving the Improved Modified Euler Method for Better Performance on Autonomous Initial Value Problems

The purpose of this paper was to propose a modification that would lead to a much improved approximation technique for the computation of the numerical solutions of initial value problems, particularly the autonomous type. The method that has been improved upon is our Improved Modified Euler method. By the simple modification effected, a much better performance was achieved, not just for the autonomous problem, but for the non-autonomous problem as well. The new method was also shown to be of order 2.