Table 1 Computative iterates and error of Algorithm 1 for the choices of different parameters \(\lambda = \frac{1}{3}\) and \(\alpha _{n} = \frac{1}{n+1}\), different initial points \(u_{1} = 0.2\), \(u_{1} = 0.5\) and the tolerance of error \(|u_{n+1} - u_{n}| < 10^{-6}\)
No. iter. | \(\lambda = \frac{1}{3}\) and \(\alpha _{n} = \frac{1}{n+1}\) | |||
|---|---|---|---|---|
\(u_{1} = 0.2\) | \(|u_{n+1} - u_{n}|\) | \(u_{1} = 0.5\) | \(|u_{n+1} - u_{n}|\) | |
1 | 0.2 | ⋯ | 0.5 | ⋯ |
2 | 0.429614 | 0.229614 | 0.646785 | 0.146785 |
3 | 0.589695 | 0.160081 | 0.744659 | 0.097874 |
10 | 0.962285 | 0.016117 | 0.976335 | 0.010127 |
15 | 0.993964 | 0.002721 | 0.996219 | 0.001705 |
20 | 0.999086 | 4.230861e−04 | 0.999428 | 2.649637e−04 |
25 | 0.999865 | 6.305888e−05 | 0.999916 | 3.948375e−05 |
30 | 0.999980 | 9.168267e−06 | 0.999987 | 5.740434e−06 |
31 | 0.999986 | 6.220992e−06 | 0.999991 | 3.895079e−06 |