Modified Jacobian Newton Iterative Method: Theory and Applications

Table 9

Numerical results for the 1D momentum equation wit𝜇=50 𝑣=0.1, initial conditio𝑢₀(𝑡)=𝑐_𝑛, and two iterations per time-step.

Δ𝑥	Δ𝑡	err𝐿1	errmax	𝜌𝐿1	𝜌max
1/10	1/20	2.7352⋅10^−6	6.4129⋅10^−6
1/20	1/20	2.3320⋅10^−6	5.4284⋅10^−6	0.2301	0.2404
1/40	1/20	2.1144⋅10^−6	4.9247⋅10^−6	0.1413	0.1405
1/80	1/20	2.0021⋅10^−6	4.6614⋅10^−6	0.0787	0.0793
1/10	1/40	2.1711⋅10^−6	5.2875⋅10^−6
1/20	1/40	1.7001⋅10^−6	4.1292⋅10^−6	0.3528	0.3567
1/40	1/40	1.4388⋅10^−6	3.4979⋅10^−6	0.2408	0.2394
1/80	1/40	1.3023⋅10^−6	3.1694⋅10^−6	0.1438	0.1423
1/10	1/80	1.6788⋅10^−6	4.1163⋅10^−6
1/20	1/80	1.1870⋅10^−6	2.9138⋅10^−6	0.5001	0.4984
1/40	1/80	9.1123⋅10^−7	2.2535⋅10^−6	0.3814	0.3707
1/80	1/80	7.6585⋅10^−7	1.9025⋅10^−6	0.2507	0.2443