2.5.5 Modified equation for the FTBS scheme

A similar procedure gives the modified equation for the FTBS scheme

$$\frac{\partial \rho}{\partial t} + v_{} \frac{\partial \... ...ht) \frac{\partial^2 \rho}{{\partial x}^2} = 0 \enspace .$$ (129)

The coefficient of the additional diffusion term is negative if the CFL condition is fulfilled:

It describes diffusion, clearly seen in Fig. 12 (compare the example for the heat equation in Fig. 3).