Theory and Modern Applications
Table 1 The absolute errors of the presented algorithm I (\(E_{I}\)), algorithm II (\(E_{II}\)), and the numerical method of [45] for (31) with \(\alpha =0.1\), \(\nu =4\)
From: High order algorithms for numerical solution of fractional differential equations
| Â | Algorithm II | Algorithm I | Method of [45] | ||||
|---|---|---|---|---|---|---|---|
h | \(E_{II}\) | Ratio | CPU | \(E_{I}\) | Ratio | CPU | E |
1/5 | 3.5631e-06 | – | 0.0021 | 1.9302e-04 | – | 0.0015 | – |
1/10 | 1.3548e-07 | 4.71 | 0.0028 | 1.3809e-05 | 3.81 | 0.0044 | 3.64e-01 |
1/20 | 4.7060e-09 | 4.85 | 0.0062 | 9.4607e-07 | 3.87 | 0.0067 | 1.70e-01 |
1/40 | 1.9210e-10 | 4.61 | 0.0199 | 6.3530e-08 | 3.90 | 0.0180 | 7.13e-02 |