ABSTRACT
In the previous chapter we introduced several methods commonly used to obtain solutions of initial and boundary value problems to systems of ordinary differential equations. One of the tools we introduced was MATLAB’s ode45, a powerful numerical solver that is based on applying a finite difference approach to first discretize an ordinary differential equation and converting the underlying continuous problem to an algebraic problem, which we can then treat with matrix theory methods. In this chapter we will look at the details of finite difference methods to understand their scope of applicability. Although we will introduce finite difference methodology in the context of ordinary differential equations, one of our main goals is to prepare for applying these techniques to partial differential equations.
