1D Linear Advection

Lax-Wendroff Method: Periodic

Time Steps:

The Lax-Wendroff Method is:

\phi_i^{k+1}=\phi_i^k-\frac{c\Delta t}{2 \Delta x}(\phi_{i+1}^k-\phi_{i-1}^k)+\frac{c^2 \Delta t^2}{2\Delta x^2}(\phi_{i+1}^k-2\phi_i^k+\phi_{i+1}^k)

Assume that the domain is from $$x=0$$ to $$x=1$$ and that the wave has a period of $$\frac{1}{c}$$.

Choose the wave speed $$c$$, step size $$\Delta x$$, and the CFL number and the number of periods $$H$$.

Note the calculated step time $$\Delta t$$ and the number of time steps.

Click SOLVE to observe the initial condition in blue and the computed Lax-Wendroff solution in red.

Initial Condition: $$e^{-200(x - .5)^2}$$

Wave Speed $$c=$$
$$\Delta x=$$
H =

The time step $$\Delta t$$ is:
Time steps per period: