The Lax-Wendroff method is a single step method for evolving time dependent solutions governed by partial differential equations, in contrast to Runge-Kutta methods that need multiple stages per time step. We develop a flux reconstruction version of the method in combination with a Jacobian-free Lax-Wendroff procedure that is applicable to general hyperbolic conservation laws. The method is of collocation type, is quadrature free and can be cast in terms of matrix and vector operations. Special attention is paid to the construction of numerical flux, including for non-linear problems, resulting in higher CFL numbers than existing methods, which is shown through Fourier analysis and yielding uniform performance at all orders. Numerical results up to fifth order of accuracy for linear and non-linear problems are given to demonstrate the performance and accuracy of the method.

Lax-Wendroff 方法是用于演化由偏微分方程控制的时间相关解的单步方法，与每个时间步需要多个阶段的 Runge-Kutta 方法不同。我们结合适用于一般双曲守恒定律的无雅可比 Lax-Wendroff 程序开发了该方法的通量重建版本。该方法是搭配类型的，是无求积的，并且可以在矩阵和向量运算方面进行转换。特别注意数值通量的构建，包括非线性问题，导致比现有方法更高的 CFL 数，这通过傅里叶分析显示并在所有阶数上产生均匀的性能。