Lax-Wendroff method

The Lax-Wendroff method, named after Peter Lax and Burton Wendroff, is a finite difference method for solving hyperbolic partial differential equations. It is second-order accurate in both space and time and is an explicit time integration scheme, meaning that the function defining the governing equation is evaluated at the current time. In the linear case, with a constant coefficient, the scheme has a simple closed form, and it extends to the general non-linear case in several ways, including a conservative form that uses the Jacobian matrix of the flux. To avoid evaluating the Jacobian, the Richtmyer two-step version first computes the flux at half time steps and half grid points and then uses those values to advance a full step. MacCormack's method is another method of the same type, using forward differencing followed by backward differencing.