Lax–Friedrichs Method

The Lax–Friedrichs method, named after Peter Lax and Kurt O. Friedrichs, is a numerical method for the solution of hyperbolic partial differential equations based on finite differences. The method can be described as the FTCS (forward in time, centered in space) scheme with an artificial viscosity term of 1/2. One can view the Lax–Friedrichs method as an alternative to Godunov's scheme, where one avoids solving a Riemann problem at each cell interface, at the expense of adding artificial viscosity.

Read more about Lax–Friedrichs MethodIllustration For A Linear Problem, Extensions To Nonlinear Problems, Stability and Accuracy

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Lax–Friedrichs Method - Stability and Accuracy
... This method is explicit and first order accurate in time and second order accurate in space provided are sufficiently-smooth functions ... Under these conditions, the method is stable if and only if the following condition is satisfied (A von Neumann stability analysis can show the ...

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