ABSTRACT
As demonstrated in Example 11.9, the Law-Wendroff one-step method is an efficient and accurate method for solving the linear wave equation. For nonlinear POEs and systems of POEs, however, the method becomes quite compJicated. The complications arise in the replacement of the second-order time derivatives ftt and gtt in terms of spatial derivatives by differentiating the governing partial differential equations. The simple result obtained in Eq. (11.93) no longer applies. Consequently, the Lax-Wendroff one-step method is not used very often. More efficient methods, such as the Lax-Wendroff two-step method presented in Section 11.5.2 and the MacCormack method presented in Section 11.5.3 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 complex for nonlinear POEs, and thus considerably more efficient.
