# Courant–Friedrichs–Lewy condition

## Mathematical condition for convergence / From Wikipedia, the free encyclopedia

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In mathematics, the **convergence condition by Courant–Friedrichs–Lewy** is a necessary condition for convergence while solving certain partial differential equations (usually hyperbolic PDEs) numerically. It arises in the numerical analysis of explicit time integration schemes, when these are used for the numerical solution. As a consequence, the time step must be less than a certain upper bound, given a fixed spatial increment, in many explicit time-marching computer simulations; otherwise, the simulation produces incorrect or unstable results. The condition is named after Richard Courant, Kurt Friedrichs, and Hans Lewy who described it in their 1928 paper.^{[1]}