In Figure 9.18 both exact and numerical solutions of problem (9.47) at time t = 5 are shown. The...

In Figure 9.18 both exact and numerical solutions of problem
(9.47) at time t = 5 are shown. The latter are computed by the
Lax-Wendroff (9.57) and upwind (9.59) schemes, using the same data of Exercise
9.13. By knowing that the CFL number is 0.8 and that we have used Δt
= 5.e − 3, comment on the dissipation and dispersion coefficients that we
have obtained.

Exercise 9.13

Solve problem (9.47) with initial datum and
boundary condition Use both Lax-Wendroff (9.57) and upwind
(9.59) schemes. Set the CFL number equal to 0.5. Verify experimentally that the
Lax-Wendroff scheme is second-order accurate with respect to Δ and
Δt, while the upwind scheme is first-order accurate. To evaluate
the error use the norm