Courant Condition

The constant in the finite difference wave equation,

$$\frac{\rho}{T} \frac{1}{c^2} \frac{\Delta_t^2 }{\Delta_x^2 } = \frac{c^2}{c'^2}$$ (9)

where

$$c = \frac{ \rho}{ T }$$ (10)

and

$$c' = \frac{ \Delta_x}{ \Delta_t }$$ (11)

.

It can be shown that the Courant Condition, $c < c' = \Delta_x / \Delta_t$ limits constants values that allow stable solutions. More accuurate solutions will result from smaller $\Delta_x$ and $\Delta_t$ provided the Courrant Condition applies.