Table 2 Computative iterates and error of Algorithm 1 for the choices of different parameters \(\lambda = \frac{1}{3}\) and \(\alpha _{n} = \frac{1}{(n+1)^{3/2}}\), different initial points \(u_{1} = 0.2\) and \(u_{1} = 0.5\), with the stoping criterion \(|u_{n+1} - u_{n}| < 10^{-6}\)
No. iter. | \(\lambda = \frac{1}{3}\) and \(\alpha _{n} = \frac{1}{(n+1)^{3/2}}\) | |||
|---|---|---|---|---|
\(u_{1} = 0.2\) | \(|u_{n+1} - u_{n}|\) | \(u_{1} = 0.5\) | \(|u_{n+1} - u_{n}|\) | |
1 | 0.2 | ⋯ | 0.5 | ⋯ |
2 | 0.401851 | 0.201851 | 0.641811 | 0.141811 |
3 | 0.558448 | 0.156596 | 0.742398 | 0.100587 |
10 | 0.964051 | 0.016800 | 0.980325 | 0.009279 |
15 | 0.994939 | 0.002457 | 0.997246 | 0.001339 |
20 | 0.999309 | 3.391089e−04 | 0.999624 | 1.844173e−04 |
25 | 0.999907 | 4.593534e−05 | 0.999949 | 2.497333e−05 |
30 | 0.999987 | 6.170685e−06 | 0.999993 | 3.354629e−06 |
31 | 0.999991 | 4.127541e−06 | 0.999995 | 2.243889e−06 |