Table 4 The residual errors and convergence rates of g when \(\lambda = 0.5, M = 2, c = 0.5, Sc = \gamma = 1, Pr = 1.5\)
From: On a bivariate spectral relaxation method for unsteady magneto-hydrodynamic flow in porous media
Iter. | \(\Vert Res({\mathbf{g}} )\Vert _{\infty }\) | Convergence Rates | ||||
|---|---|---|---|---|---|---|
\(\xi = 0.25\) | \(\xi = 0.75\) | \(\xi = 1.00\) | \(\xi = 0.25\) | \(\xi = 0.75\) | \(\xi = 1.00\) | |
1 | \(4.17\times 10^{-3}\) | \(4.93\times 10^{-2}\) | \(7.83\times 10^{-2}\) | 0.94 | 1.01 | 0.99 |
2 | \(4.96\times 10^{-5}\) | \(1.40\times 10^{-3}\) | \(2.21\times 10^{-3}\) | 0.75 | 1.03 | 1.04 |
3 | \(7.66\times 10^{-7}\) | \(3.81\times 10^{-5}\) | \(6.39\times 10^{-5}\) | 1.26 | 1.13 | 1.18 |
4 | \(3.38\times 10^{-8}\) | \(9.21\times 10^{-7}\) | \(1.58\times 10^{-6}\) | 1.07 | 0.76 | 0.56 |
5 | \(6.56\times 10^{-10}\) | \(1.38\times 10^{-8}\) | \(2.01\times 10^{-8}\) | 0.83 | 0.68 | 0.92 |
6 | \(9.49\times 10^{-12}\) | \(5.75\times 10^{-10}\) | \(1.78\times 10^{-9}\) | 1.00 | 1.27 | 1.18 |
7 | \(2.82\times 10^{-13}\) | \(6.58\times 10^{-11}\) | \(1.93\times 10^{-10}\) | 0.89 | 1.08 | 1.04 |
8 | \(8.39\times 10^{-15}\) | \(4.19\times 10^{-12}\) | \(1.39\times 10^{-11}\) | 0.95 | 1.00 | 1.00 |