Using Modified Euler Method (MEM) for the Solution of some First Order Differential Equations with Initial Value Problems (IVPs).

Parker and Sochacki showed that a large class of ODE's could be converted to polynomial form using substitutions and using a system of equation. While this class of ODE's is dense in the analytic functions, it does not include all analytic functions. They also showed one can approximate the solution by a polynomial system and the resulting error bound when using these approximation. Differential equations can be solved using many methods that are generally accepted in mathematics. However, it is believed that one method is more accurate, efficient, sufficient and unique than the other. Thus; solutions of First Order Differential Equations (FODEs) with Initial Value Problems (IVPs) by Modified Euler Methods (MEM) will be exercised. Explicitly, numerical computational algorithm, convergence rate, approximation errors and uniqueness is of sensitive attention and concern.