Figure 4

Figure 4: Semi-discrete spectrum for the advection equation and freezing boundary conditions [Eqs. (10.1View Equation, 10.2View Equation, 10.3View Equation], a Chebyshev collocation method, and numerical injection of the boundary condition. The number of collocation points is (from left to right) N = 20,40,60. The scheme passes the von Neumann condition (no positive real component in the spectrum). In fact, as discussed in the body of the text, the method can be shown to actually be numerically stable.