2.4.2 Naive FTCS scheme

Figure 9: Naive scheme: stencil diagram and (disastrous) test result.

Figure 9: naive scheme (Euler scheme, FTCS, Sect. 2.2.9) from Eq. (92) with flux at $i+\frac{1}{2}$

$$\textstyle f_{i+\frac{1}{2}}^n = \frac{1}{2} \left[ f \! ... ...\right) + f \! \left( \rho_{i}^n \right) \right] \enspace .$$ (110)

The oscillations already seen in Fig. 4 grow exponentially. After some time the numerical result does not have the faintest resemblance to true solution.