In this chapter, we describe two numerical finite difference methods which are used for solving differential equations, e.g., the Euler method and Euler-Cromer method. The emphasis here is on algorithm errors, and an explanation of what is meant by the “order” of the error. We show that the Euler method introduces an error of order 2, denoted as \( \mathscr {O}(2),\) while the latter presents errors of order \(\mathscr {O}(3)\). We finish the chapter by applying the methods to two important physical problems: the physics of the pendulum and the physics of descending parachutes.