Preliminaries

This section will illustrate the derivation and the numerical solution of a special hyperbolic PDE, the Wave Equation.

$$\frac{\partial^2 y(x,t)}{\partial t^2} = c^2 \frac{ \partial^2 y(x,t)}{\partial x^2}$$ (1)

This PDE describes waves on a string. It is an example often seen in Freshman’s Physics or in more advanced mechanics courses.

In this course, we will naturally compare the numerical approach to solve the Wave Equation to that to solve the Heat Transfer equation. There are many common aspects between these algorithms.