Table 3 The residual errors and convergence rates of f 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. | \(\Vert Res({\mathbf{f}} )\Vert _{\infty }\) | Convergence rates | ||||
|---|---|---|---|---|---|---|
\(\xi = 0.25\) | \(\xi = 0.75\) | \(\xi = 1.00\) | \(\xi = 0.25\) | \(\xi = 0.75\) | \(\xi = 1.00\) | |
1 | \(2.14\times 10^{-2}\) | \(2.36\times 10^{-1}\) | \(3.72\times 10^{-1}\) | 1.14 | 1.00 | 0.98 |
2 | \(6.03\times 10^{-4}\) | \(1.43\times 10^{-2}\) | \(2.24\times 10^{-2}\) | 0.50 | 1.01 | 1.01 |
3 | \(1.05\times 10^{-5}\) | \(8.58\times 10^{-4}\) | \(1.43\times 10^{-3}\) | 1.53 | 1.00 | 1.00 |
4 | \(1.36\times 10^{-6}\) | \(5.04\times 10^{-5}\) | \(8.85\times 10^{-5}\) | 1.06 | 1.01 | 1.00 |
5 | \(5.95\times 10^{-8}\) | \(2.98\times 10^{-6}\) | \(5.52\times 10^{-6}\) | 0.97 | 1.02 | 1.00 |
6 | \(2.18\times 10^{-9}\) | \(1.70\times 10^{-7}\) | \(3.40\times 10^{-7}\) | 0.99 | 1.00 | 1.00 |
7 | \(8.84\times 10^{-11}\) | \(9.06\times 10^{-9}\) | \(2.07\times 10^{-8}\) | 0.95 | 1.00 | 1.00 |
8 | \(3.75\times 10^{-12}\) | \(4.85\times 10^{-10}\) | \(1.27\times 10^{-9}\) | 0.85 | 0.99 | 1.00 |