Theory and Modern Applications
Table 5 Pointwise absolute errors in the maximum norm and computed rates of convergence versus the number of sub-intervals N in Example 4.2 as we set \(\alpha _{1} = 0.4\), \(\alpha _{2} = 1.7\), \(h=0.01\), \(m=10\) and no Tol
N | Newton’s method | Halley’s method | ||||||
|---|---|---|---|---|---|---|---|---|
\(s_{0}=0.2\) | \(s_{0}=1.0\) | \(s_{0}=0.2\) | \(s_{0}=1.0\) | |||||
Max. error | Rate | Max. error | Rate | Max. error | Rate | Max. error | Rate | |
10 | 1.10E−03 | – | 1.10E−03 | – | 5.65E−05 | – | 5.65E−05 | – |
20 | 4.05E−04 | 1.434 | 4.05E−04 | 1.434 | 1.71E−05 | 1.725 | 1.71E−05 | 1.725 |
40 | 1.19E−04 | 1.765 | 1.19E−04 | 1.765 | 2.82E−06 | 2.599 | 2.82E−06 | 2.599 |
80 | 3.21E−05 | 1.893 | 3.21E−05 | 1.893 | 3.99E−07 | 2.824 | 3.99E−07 | 2.824 |
160 | 8.32E−06 | 1.949 | 8.32E−06 | 1.949 | 5.29E−08 | 2.913 | 5.29E−08 | 2.913 |
320 | 2.12E−06 | 1.974 | 2.12E−06 | 1.974 | 6.84E−09 | 2.952 | 6.84E−09 | 2.952 |