The fact that the truncation error, e.g. (Δx)ⁿ , must decay as Δx tends towards zero, is referred to as the consistency condition.

According to the Lax-Richtmyer theorem, a finite-difference scheme converges if and only if it is consistent and stable.

Von Neumann analysis yields only a necessary condition for the stability of a finite-difference scheme, so that further analysis is required to arrive at a sufficient condition.

A finite-difference scheme that is consistent must be either conditionally or unconditionally stable.