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The Lax-Wendroff one-step method is an efficient and accurate method for solving the linear convection equation. For nonlinear PDEs and systems of PDEs, however, the method becomes quite complicate~. The complications arise in the replacement of the second-order time derivative fll in terms of space derivatives by differentiating the governing partial differential equation. The simple result obtained in Eq. (11.34) no longer applies. Consequently, the Lax-Wendroff one-step method is not used very often. More efficient methods, such as the Lax-Wendrofftwo-step method and the MacCormack method are generally used for nonlinear equations and systems of equations. These methods have the same general features as the Lax-Wendroff one-step method, but they are considerably less complicated for nonlinear PDEs, and thus considerably more efficient.