Lax–Friedrichs method

Summary

The Lax–Friedrichs method is an explicit finite difference method for hyperbolic equations such as conservation laws. It replaces the value at the current point by the average of its two neighbours and then applies a centred difference of the flux. The averaging adds numerical viscosity, which makes the scheme stable under the Courant–Friedrichs–Lewy condition. It is first-order accurate and smears shocks, but it is simple and robust. See the definition.