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2.4.2 Naive FTCS scheme

Figure 9: Naive scheme: stencil diagram and (disastrous) test result.
\includegraphics[width=8.0cm]{images/} \includegraphics[width=8.0cm]{images/}
Figure 9: naive scheme (Euler scheme, FTCS, Sect. 2.2.9) from Eq. (92) with flux at \bgroup\color{DEFcolor}$i+\frac{1}{2}$\egroup
f_{i+\frac{1}{2}}^n = \frac{1}{2}
\left[ f \! ...
...\right) +
f \! \left( \rho_{i}^n \right)
\enspace .
\end{displaymath} (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.