2.2.9 Linear advection equation: crash

**Figure 4:** Euler scheme for advection equation.
$\includegraphics[width=8cm]{images/pde1d_solve_linadv_spikes_naive_i200n50dt01.ps}$ $\includegraphics[width=8cm]{images/pde1d_solve_linadv_spikes_naive_i200n10dt05.ps}$

Examples for ``spikes'' initial condition (red) and periodic boundaries are displayed in Fig. 4 for two time-steps $\bgroup\color{DEFcolor}$\Delta tv/\Delta x$\egroup$ =0.1, 0.5 after 50 or 10 steps, respectively (blue).

The growing oscillations render the scheme useless.