Modified Jacobian Newton Iterative Method: Theory and Applications

Table 7

Numerical results for the 1D momentum equation wit𝜇=5 𝑣=0.001, initial conditio𝑢₀(𝑡)=𝑐_𝑛, and two iterations per time-step.

Δ𝑥	Δ𝑡	err𝐿1	errmax	𝜌𝐿1	𝜌max
1/10	1/20	0.0213	0.0495
1/20	1/20	0.0203	0.0470	0.0689	0.0746
1/40	1/20	0.0198	0.0457	0.0401	0.0402
1/80	1/20	0.0195	0.0450	0.0216	0.0209
1/10	1/40	0.0134	0.0312
1/20	1/40	0.0117	0.0271	0.1957	0.2009
1/40	1/40	0.0108	0.0249	0.1213	0.1211
1/80	1/40	0.0103	0.0238	0.0682	0.0674
1/10	1/80	0.0094	0.0217
1/20	1/80	0.0073	0.0169	0.3591	0.3641
1/40	1/80	0.0062	0.0143	0.2451	0.2448
1/80	1/80	0.0056	0.0129	0.1478	0.1469