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2.4.8 Lax-Wendroff scheme

Figure 15: Stencil and example for Lax-Wendroff scheme.
\includegraphics[width=8.0cm]{images/} \includegraphics[width=8.0cm]{images/}
Figure 15: Lax-Wendroff scheme is \bgroup\color{DEFcolor}$O \! \left( \Delta x^2 , \Delta t^2 \right)$\egroup with flux
f_{i+\frac{1}{2}}^n = \frac{1}{2} \left[ f \! \...
...lta x}
\left[ \rho_{i+1}^n -
\enspace .
\end{displaymath} (116)
The result is smooth with considerable overshoot (that does not much grow with time anymore). This second order scheme might be useful for more regular initial conditions.