Ordinary Differential Equations

Differential equations arise in many areas of science and engineering when dealing with the modeling of problems which involve the change of some variable with respect to another. Most of these problems require the solution of an initial value problem (IVP). The IVP refers to the solution to a given differential equation that satisfies a given initial condition. There exist many situations where the differential equations that models the problem is difficult to solve exactly. For the solutions of those differential equations one has to resort to the methods for approximating the solution to the original problem. The initial value problem can be formulated as follows:

Given