Application of Euler Method (EM) for the Solution of Some First Order Differential Equations with Initial Value Problems (IVP’s)

Abstract

The attempt to solve problems in science and technology, gradually led to mathematical model. Mathematical models involves equations in which functions and derivatives play important roles. However the theoretical development of this branch of mathematics – Ordinary differential Equations (ODE) has its origin rooted in a small number of mathematical problems. Therefore, Differential Equations (DE) can be solved using many methods that are generally accepted in mathematics. However, it is believed that one method should be more accurate, efficient, sufficient and unique than the other. Thus; solutions of First order Differential Equations (FOD’s) with initial value problems (IVP’s) by Euler Method (EM) will be of central concern. However, numeric computational algorithm, convergence rate, approximation errors and uniqueness will be seriously inspected and to ascertain Euler Method modification requirements in order to be more stable and reliable over other methods for the FODE’s with IVP’s