The criteria for stability of the FTCS numerical scheme for the heat equation is given by:

The stability criteria for the Forward Time Centered Space (FTCS) numerical scheme applied to the heat equation can be expressed in terms of the time step $\Delta t$, grid spacing $\Delta x$, and the thermal diffusivity $D$.

Stability Criterion

For the FTCS scheme to be stable, the following condition must hold:

$\frac{D \Delta t}{(\Delta x)^2} \leq \frac{1}{2}$

Explanation of the Terms

• $D$ = Thermal diffusivity of the material (constant specific to the problem)
• $\Delta t$ = Time step of the numerical scheme
• $\Delta x$ = Grid spacing in the spatial discretization

Final Answer

The FTCS scheme is stable if:

$\Delta t \leq \frac{(\Delta x)^2}{2D}$