Table 3 Maximum absolute error and rate of convergence of the proposed method for Example 4.2
\(\varepsilon \downarrow N \rightarrow\) | \(2^5\) | \(2^6\) | \(2^7\) | \(2^8\) | \(2^9\) | \(2^{10}\) |
|---|---|---|---|---|---|---|
\(2^{0}\) | 3.4992e–02 | 1.8983e–02 | 9.8939e–03 | 5.0518e–03 | 2.5526e–03 | 1.2831e–03 |
| Â | 0.8823e+00 | 0.9400e+00 | 0.9697e+00 | 0.9848e+00 | 0.9923e+00 | Â |
\(2^{-4}\) | 1.3018e–01 | 1.3971e–01 | 1.0548e–01 | 6.6102e–02 | 3.7290e–02 | 2.9853e–03 |
| Â | 0.1019e+00 | 0.4054e+00 | 0.6742e+00 | 0.8259e+00 | 0.9094e+00 | Â |
\(2^{-8}\) | 7.7364e–03 | 4.3025e–03 | 6.3198e–03 | 6.3217e–03 | 1.3572e–03 | 1.4234e–03 |
| Â | 0.8455e+00 | 0.5547e+00 | 0.7891e+00 | 0.8023e+00 | 0.9821e+00 | Â |
\(2^{-12}\) | 7.7206e–03 | 3.8803e–03 | 1.9451e–03 | 9.7376e–04 | 4.8817e–04 | 2.7002e–04 |
| Â | 0.9925e+00 | 0.9963e+00 | 0.9982e+00 | 0.9960e+00 | 0.9981e+00 | Â |
\(2^{-16}\) | 7.7206e–03 | 3.8803e–03 | 1.9451e–03 | 9.7376e–04 | 4.8718e–04 | 2.4367e–04 |
| Â | 0.9925e+00 | 0.9963e+00 | 0.9982e+00 | 0.9991e+00 | 0.9995e+00 | Â |
\(2^{-18}\) | 7.7206e–03 | 3.8803e–03 | 1.9451e–03 | 9.7376e–04 | 4.8718e–04 | 2.4367e–04 |
| Â | 0.9992e+00 | 0.9963e+00 | 0.9982e+00 | 0.9991e+00 | 0.9995e+00 | Â |
\(2^{-20}\) | 7.7206e–03 | 3.8803e–03 | 1.9451e–03 | 9.7376e–04 | 4.8718e–04 | 2.4367e–04 |
| Â | 0.9992e+00 | 0.9963e+00 | 0.9982e+00 | 0.9991e+00 | 0.9995e+00 | Â |