2.4.5 Donor cell (FTBS) scheme

**Figure 12:** Stencil and example for donor cell scheme.
$\includegraphics[width=8.0cm]{images/pde1d_stencil_m0.ps}$ $\includegraphics[width=8.0cm]{images/pde1d_solve_linadv_spikes_donor_i200n500dt04.ps}$

Figure 12: donor cell scheme (FTBS, 1st order upwind method, derived in Sect. 2.3.16), with flux

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

(113)

The result is wonderfully smooth but smeared out severely. Upwinding seems promising to achieve stability. However, the accuracy of the scheme has to be improved.