2.4.2 Naive FTCS scheme

Figure 8: Naive scheme: stencil diagram and (disastrous) test result.

Figure 8 shows the stencil diagram and an example for the naive scheme (Euler scheme, FTCS) from Eq. (114) with flux at $i+\frac{1}{2}$

$$\textstyle f_{i+\frac{1}{2}}^n = \frac{1}{2} \left[ f \! ... ...\right) + f \! \left( \rho_{i}^n \right) \right] \enspace .$$ (105)