4.8 case 7

\(\tau =0.06\) sec, \(h=0.1\ \)ft\(,\) \(\frac {u\tau }{h}=\frac {2\times 0.06}{0.1}=1.2>1\)

Speed	Method	CPU time (sec)	RMSE	Animation (2D)	plots
U=2	Explicit FTCS	0.65	blows up	N/A blows up	HTML
	Explicit LAX	0.9	blows up	HTML
	Implicit FTCS	0.42	0.1531	HTML
	C-R	0.41	0.01244	HTML
U=t/20	Explicit FTCS	0.265	blows up	N/A blows up	HTML
	Explicit LAX	0.29	0.01389	HTML
	Implicit FTCS	0.36	0.0493	HTML
	C-R	0.36	0.01525	HTML

Notice that the CPU for the implicit method when speed is fixed is now higher than the CPU for the explicit methods. This can be explained as follows: since the time step now is larger than before, the number of times to solve \(Ax=b\) has been reduced. This made the implicit methods faster.

This implies that

Using a relatively large time step, implicit methods become faster than the explicit methods.