Modified Jacobian Newton Iterative Method: Theory and Applications

Table 6

Numerical results for the mixed convection-diffusion and Burgers equation with viscosit𝜇=5, initial conditio𝑢₀(𝑡)=𝑐_𝑛, and two iterations per time-step.

Δ𝑥=Δ𝑦	Δ𝑡	err𝐿1	errmax	𝜌𝐿1	𝜌max
1/5	1/20	1.3166⋅10^−5	2.9819⋅10^−5
1/10	1/20	5.6944⋅10^−6	1.3541⋅10^−5	1.2092	1.1389
1/20	1/20	1.6986⋅10^−6	4.5816⋅10^−6	1.7452	1.5634
1/40	1/20	7.8145⋅10^−7	2.0413⋅10^−6	1.1201	1.1663
1/5	1/40	1.4425⋅10^−5	3.2036⋅10^−5
1/10	1/40	7.2343⋅10^−6	1.5762⋅10^−5	0.9957	1.0233
1/20	1/40	3.0776⋅10^−6	6.7999⋅10^−6	1.2330	1.2129
1/40	1/40	9.8650⋅10^−7	2.3352⋅10^−6	1.6414	1.5420