2.4.10 Fromm scheme

**Figure 17:** Stencil and example for Fromm scheme.
$\includegraphics[width=8.0cm]{images/pde1d_stencil_mm0p.ps}$ $\includegraphics[width=8.0cm]{images/pde1d_solve_linadv_spikes_fromm_i200n500dt04.ps}$

Figure 17: Fromm scheme is $\bgroup\color{DEFcolor}$O \! \left( \Delta x^2 , \Delta t^2 \right)$\egroup$ with flux

$\begin{displaymath} \textstyle f_{i+\frac{1}{2}}^n = \frac{1}{2} \left( f_{\ma... ..._{\mathrm{Beam-Warming,} i+\frac{1}{2}}^n \right) \enspace . \end{displaymath}$

(118)

The result is smooth with some amount of overshoot. The initial shape of the spikes is recognizable. So far the best scheme, if the overshoot can be accepted.

See Sect. 2.6.6.