# CFL stability condition (1D FDTD)

The **CFL stability condition** limits the time step relative to grid spacing and wave speed. For a one-dimensional lossless medium, information must not travel farther than one grid interval in a single step:

$$
\frac{c_{\max}\Delta t}{\Delta x}\leq1
$$

Here $c_{\max}$ is the fastest wave speed in the domain. FDTD OpenMP defines its Courant number using the vacuum speed $c_0$ and derives the time step as:

$$
S=\frac{c_0\Delta t}{\Delta x},\qquad \Delta t=\frac{S\Delta x}{c_0}
$$

The defaults are $S = 0.5$ and $\Delta x = 0.01$ metres. Changing either through the simulation setters recomputes $\Delta t$ and the [[fdtd-openmp-update-coefficients|update coefficients]].

The implementation stores the requested Courant number without enforcing a stability bound. Choosing a suitable value remains the caller's responsibility. If materials permit propagation faster than $c_0$, the vacuum condition $S \leq 1$ alone is insufficient.

Stability also differs from accuracy. A stable simulation can still have substantial numerical dispersion when the grid contains too few samples per wavelength.