ABSTRACT
To illustrate the unstable behavior ofthe FTCS method applied to the convection equation, the solution to the convection problem presented in Section 11.1 is presented in Figure 11.8 for LU = 0.1 cm with M = 0.5 s, for which c = u M/LU = (0.1 )(0.5)/0.1 = 0.5. The solution is presented at times from 1.0 to 5.0 s and at 10.0 s. The amplitude of the solution increases in an unstable manner as the wave propagates to the right. Solutions for larger values of c are not shown because they are totally unrealistic. All of the other examples in this chapter are solved with LU = 0.05 cm and I1t = 0.25 s. For the FTCS method, that combination, for which c = 0.5 as in the present example, goes unstable more rapidly, so the results could not be illustrated in the figure.
