2.4.6 FTFS scheme

**Figure 12:** FTFS scheme: stencil diagram and (disastrous) test result.
$\includegraphics[width=8.0cm]{images/pde1d_stencil_0p.ps}$ $\includegraphics[width=8.0cm]{images/pde1d_solve_linadv_spikes_naive_i200n500dt04.ps}$

Figure 12 shows the stencil diagram and an example for the FTFS scheme with flux at $\bgroup\color{DEFcolor}$i+\frac{1}{2}$\egroup$

$\begin{displaymath} \textstyle f_{i+\frac{1}{2}}^n = f \! \left( \rho_{i+1}^n \right) \enspace . \end{displaymath}$

(109)