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Consider a FV method as an approximation of the integral conservation law. Starting from the one-dimensional, scalar conservation equation $$u_t + f(u,\nabla u)_x =0,$$ with the definitions of the step sizes $\Delta x$ and $\Delta t$ t_n = n \Delta t,~~~x_i = i \Delta x,~~~x_{i+1/2}=\frac{1}{2}\left(x_i + x_{i+...