4.4 Case 3

In this case, we slightly make the time step longer than before. We start to see the instability of FTCS.

\(\tau =0.0013\) sec, \(h=0.1\ \)ft\(,\) \(\frac {u\tau }{h}=0.026\leq 1\) for fixed \(u\)

Speed	Method	CPU time (sec)	RMSE	Animation (2D)	plots
U=2	Explicit FTCS	1.9	0.0494	HTML	HTML
	Explicit LAX	2.78	0.01125	HTML
	Implicit FTCS	3.7	0.01245	HTML
	C-R	3.9	0.01128	HTML
U=t/20	Explicit FTCS	2.0	0.00365	HTML	HTML
	Explicit LAX	2.9	0.00331	HTML
	Implicit FTCS	5.56	0.00346	HTML
	C-R	6	0.00331	HTML

For explicit FTCS, The solution now starting to show instability at 25 minutes. Lax remained stable since CFL is satisfied. Explicit FTCS is becoming less accurate as well. Explicit Lax is most accurate at this time step.