Lax-Wendroff Method: Periodic
Time:
Time Steps:
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 $$c=$$
$$\Delta x=$$
CFL =
H =
The time step $$\Delta t$$ is:
Time steps per period:
