Modified Jacobian Newton Iterative Method: Theory and Applications

Table 10

Numerical results for the 2D momentum equation with𝜇=2,𝑣=(1,1)^𝑡, initial condition𝑢₀(𝑡)=𝑐_𝑛, and two iterations per time-step.

Δ𝑥=Δ𝑦	Δ𝑡	err𝐿1	errmax	𝜌𝐿1	𝜌max	err𝐿1	errmax	𝜌𝐿1	𝜌max
		1st c.	1st c.	1st c.	1st c.	2nd c.	2nd c.	2nd c.	2nd c.
1/5	1/20	0.0027	0.0112			0.0145	0.0321
1/10	1/20	0.0016	0.0039	0.7425	1.5230	0.0033	0.0072	2.1526	2.1519
1/20	1/20	0.0007	0.0022	1.2712	0.8597	0.0021	0.0042	0.6391	0.7967
1/5	1/40	0.0045	0.0148			0.0288	0.0601
1/10	1/40	0.0032	0.0088	0.5124	0.7497	0.0125	0.0239	1.2012	1.3341
1/20	1/40	0.0014	0.0034	1.1693	1.3764	0.0029	0.0054	2.1263	2.1325
1/5	1/80	0.0136	0.0425			0.0493	0.1111
1/10	1/80	0.0080	0.0241	0.7679	0.8197	0.0278	0.0572	0.8285	0.9579
1/20	1/80	0.0039	0.0113	1.0166	1.0872	0.0115	0.0231	1.2746	1.3058