Assessment

After looking at the results of the last project you should feel rather dissatisfied with the Euler algorithm. As it uses a linear approximation of the function to step outward, it requires a small step size to achieve high accuracy. A small step size means a large number of steps which leads to roundoff errors and instabilities. It is therefore not recommended for industrial use. However, Euler's rule does have the advantage of being self started, that is, you need only know to start your march into the unknown and consequently it is often used to start some of the more sophisticated algorithms.