Modified Jacobian Newton Iterative Method: Theory and Applications

Table 8

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

Δ𝑥	Δ𝑡	err𝐿1	errmax	𝜌𝐿1	𝜌max
1/10	1/20	0.0180	0.0435
1/20	1/20	0.0120	0.0276	0.5867	0.6550
1/40	1/20	0.0095	0.0227	0.3311	0.2870
1/80	1/20	0.0085	0.0208	0.1706	0.1231
1/10	1/40	0.0172	0.0459
1/20	1/40	0.0125	0.0305	0.4652	0.5884
1/40	1/40	0.0108	0.0253	0.2366	0.2698
1/80	1/40	0.0097	0.0235	0.1191	0.1111
1/10	1/80	0.0166	0.0475
1/20	1/80	0.0132	0.0338	0.3327	0.4917
1/40	1/80	0.0119	0.0280	0.1640	0.2734
1/80	1/80	0.0112	0.0265	0.0802	0.0779