2.5.1 Overshoot

**Figure 18:** Lax-Wendroff and Beam-Warming scheme.
$\includegraphics[width=8.0cm]{images/pde1d_solve_linadv_spikes_lax-wendroff_i200n20dt04.ps}$ $\includegraphics[width=8.0cm]{images/pde1d_solve_linadv_spikes_beam-warming_i200n20dt04.ps}$

Figure 18 shows the standard example after only $\bgroup\color{DEFcolor}$n$\egroup$ =20 time-steps for the Lax-Wendroff (Sect. 2.4.8) and the Beam-Warming scheme (Sect. 2.4.9) displaying overshooting post- and pre-shock oscillations.

This Gibb's phenomenon is closely related to overshoot of parabolic (or higher-order) interpolation schemes.