# Courant-friederichs-lewy condition

From AMS Glossary

## Courant–Friederichs–Lewy condition

(Abbreviated CFL; also called Courant condition.) The property that a finite-difference approximation is formulated in such a way that it has access to the information that is required to determine the solution of the corresponding differential equation; violating this condition leads to a numerical instability.

As an example, suppose the solution to the differential equation is a wave traveling at speed

*c*. If a finite-difference approximation is only able to access information on its grid that is traveling at speeds less than*c*, it violates the CFL condition and it will not be able to approximate the solution of the differential equation.