CourantFriedrichsLewyKriteriums
The Courant-Friedrichs-Lewy (CFL) condition is a crucial principle in the numerical solution of partial differential equations, particularly those involving wave propagation. It establishes a fundamental limit on the time step size that can be used in explicit numerical methods. Essentially, the CFL condition states that the domain of dependence of the numerical solution at a point must contain the domain of dependence of the true solution of the differential equation. If this condition is violated, numerical instabilities will arise, leading to erroneous and often unbounded results.
This condition arises because information travels at a finite speed in many physical phenomena described by
The precise form of the CFL condition depends on the specific numerical method and the differential equation