Lax–Wendroff method

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The Lax–Wendroff method, named after Peter Lax and Burton Wendroff, is a numerical method for the solution of hyperbolic partial differential equations, based on finite differences. It is second-order accurate in both space and time.

Suppose one has an equation of the following form:

where x and t are independent variables, and the initial state, ƒ(x, 0) is given.

The first step in the Lax–Wendroff method calculates values for ƒ(x, t) at half time steps, t_n + 1/2 and half grid points, x_i + 1/2. In the second step values at t_n + 1 are calculated using the data for t_n and t_n + 1/2.

First (Lax) step:

Second step:

This method can be further applied to some systems of partial differential equations.

[edit] References

• P.D Lax; B. Wendroff (1960). "Systems of conservation laws". Commun. Pure Appl Math. 13: 217–237. doi:10.1002/cpa.3160130205. 
• Michael J. Thompson, An Introduction to Astrophysical Fluid Dynamics, Imperial College Press, London, 2006.

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