2.4.8 Lax-Wendroff scheme

Figure 15: Stencil and example for Lax-Wendroff scheme.

Figure 15: Lax-Wendroff scheme is $O \! \left( \Delta x^2 , \Delta t^2 \right)$ with flux

$$\textstyle f_{i+\frac{1}{2}}^n = \frac{1}{2} \left[ f \! \... ...lta x} \left[ \rho_{i+1}^n - \rho_{i}^n \right] \enspace .$$ (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.