Modified Jacobian Newton Iterative Method: Theory and Applications

Table 12

Numerical results for the 2D momentum equation for the second component with𝜇=50,𝑣=(100,0.01)^𝑡, initial condition𝑢₀(𝑡)=𝑐_𝑛, and two iterations per time-step.

Δ𝑥=Δ𝑦	Δ𝑡	err𝐿1	errmax	𝜌𝐿1	𝜌max
		2nd c.	2nd c.	2nd c.	2nd c.
1/5	1/20	4.3543⋅10^−5	1.4944⋅10^−4
1/10	1/20	3.3673⋅10^−5	7.9483⋅10^−5	0.3708	0.9109
1/20	1/20	2.6026⋅10^−5	5.8697⋅10^−5	0.3717	0.4374
1/5	1/40	3.4961⋅10^−5	2.2384⋅10^−4
1/10	1/40	1.7944⋅10^−5	8.9509⋅10^−5	0.9622	1.3224
1/20	1/40	1.5956⋅10^−5	3.6902⋅10^−5	0.1695	1.2783
1/5	1/80	9.9887⋅10^−5	3.3905⋅10^−4
1/10	1/80	3.5572⋅10^−5	1.3625⋅10^−4	1.4896	1.3153
1/20	1/80	1.0557⋅10^−5	4.4096⋅10^−5	1.7525	1.6275