Theory and Modern Applications
Table 3 Comparison of errors between the scheme (20) and the scheme given in [26]
From: An efficient numerical algorithm for solving the two-dimensional fractional cable equation
| Â | \(h_{x}=h_{y}=\tau \) | \(e_{2}(h,\tau)\) | \(e_{\infty }(h,\tau)\) | \(e_{2}(h,\tau)\) [26] | \(e_{\infty }(h,\tau)\) [26] |
|---|---|---|---|---|---|
\(\gamma _{1}=0.9\), \(\gamma _{2}=0.4\) | 1/5 | 4.8507e-3 | 9.7013e-3 | 2.7115e-2 | 5.3825e-2 |
1/10 | 1.2286e-3 | 2.4074e-3 | 1.0684e-2 | 2.1395e-2 | |
1/20 | 3.0928e-4 | 6.1511e-4 | 4.1439e-3 | 8.2895e-3 | |
1/30 | 1.3769e-4 | 2.7467e-4 | 2.3706e-3 | 4.7416e-3 | |
\(\gamma _{1}=0.6\), \(\gamma _{2}=0.8\) | 1/5 | 4.6336e-3 | 9.2673e-3 | 5.0394e-3 | 9.7966e-3 |
1/10 | 1.1881e-3 | 2.3281e-3 | 1.6070e-3 | 3.2412e-3 | |
1/20 | 3.0103e-4 | 5.9869e-4 | 5.0187e-4 | 1.0054e-3 | |
1/30 | 1.3436e-4 | 2.6804e-4 | 2.5264e-4 | 5.0562e-4 | |
\(\gamma _{1}=0.5\), \(\gamma _{2}=0.5\) | 1/5 | 4.4248e-3 | 8.8496e-3 | 1.9661e-2 | 3.8921e-2 |
1/10 | 1.1486e-3 | 2.2508e-3 | 7.2986e-3 | 1.4625e-2 | |
1/20 | 2.9324e-4 | 5.8320e-4 | 2.6612e-3 | 5.3241e-3 | |
1/30 | 1.3133e-4 | 2.6199e-4 | 1.4673e-3 | 2.9349e-3 |