The PDE.

  The partial differential equation governing this problem for s(x,t) is the convection equation or ``one-way wave equation'',  

$$\d st + u \d sx = 0$$ (6)

It is an example of a hyperbolic equation. Unlike the parabolic heat equation of the previous section, it allows singular solutions.

The one way wave equation also arises in much more general one-dimensional unsteady hyperbolic problems by using standard mathematical simplifications. For that reason, it is a very important equation in the analysis of numerical schemes.