Modified Jacobian Newton Iterative Method: Theory and Applications

Table 11

Numerical results for the 2D momentum equation for the first 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
		1st c.	1st c.	1st c.	1st c.
1/5	1/20	1.5438⋅10^−5	3.4309⋅10^−5
1/10	1/20	4.9141⋅10^−6	1.0522⋅10^−5	1.6515	1.7052
1/20	1/20	1.5506⋅10^−6	2.9160⋅10^−6	1.6641	1.8513
1/5	1/40	2.8839⋅10^−5	5.5444⋅10^−5
1/10	1/40	1.3790⋅10^−5	2.3806⋅10^−5	1.0645	1.2197
1/20	1/40	3.8495⋅10^−6	6.8075⋅10^−6	1.8408	1.8061
1/5	1/80	3.1295⋅10^−5	5.5073⋅10^−5
1/10	1/80	1.7722⋅10^−5	2.6822⋅10^−5	0.8204	1.0379
1/20	1/80	7.6640⋅10^−6	1.1356⋅10^−5	1.2094	1.2400