Table 1 The values of \(\{x_{n}\}\) and \(\{y_{n}\}\) with initial values \(x_{1}=10\), \(y_{1}=8\) in Example 5.1
n | \(x_{n}\) | \(y_{n}\) | \(\|x_{n+1}-x_{n} \|\) | \(\|y_{n+1}-y_{n}\|\) |
|---|---|---|---|---|
1 | 10 | 8 | – | – |
2 | 5.83889 | 4.84877 | 4.16111E+00 | 3.15123E+00 |
3 | 3.77942 | 3.18014 | 2.05946E+00 | 1.66863E+00 |
4 | 2.59307 | 2.21325 | 1.18635E+00 | 9.66891E-01 |
5 | 1.88283 | 1.64025 | 7.10245E-01 | 5.72994E-01 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
21 | 1.00012 | 1.00002 | 8.54581E-05 | 1.56096E-05 |
22 | 1.00007 | 1.00001 | 4.93196E-05 | 8.15171E-06 |
23 | 1.00004 | 1.00000 | 2.84787E-05 | 4.25928E-06 |
24 | 1.00002 | 1.00000 | 1.64526E-05 | 2.22654E-06 |
25 | 1.00001 | 1.00000 | 9.50912E-06 | 1.16443E-06 |