1D Linear Advection

Lax-Wendroff Method: Finite Time

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 $$x=3$$ and that the wave starts at $$t=0$$ and ends at $$t=T$$.

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

Note the calculated step time $$\Delta t$$ and the number of time steps which should be a multiple of 10, or no more than 10.

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

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

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

The time step $$\Delta t$$ is:
The number of time steps is: