Table 1 Maximum absolute error and rate of convergence of the proposed method for Example 4.1
\(\varepsilon \downarrow N \rightarrow\) | \(2^5\) | \(2^6\) | \(2^7\) | \(2^8\) | \(2^9\) | \(2^{10}\) |
|---|---|---|---|---|---|---|
\(2^{0}\) | 1.3116e–02 | 6.9097e–03 | 3.5442e–03 | 1.7946e–03 | 9.0298e–04 | 4.5291e–04 |
| Â | 0.9246e+00 | 0.9631e+00 | 0.9817e+00 | 0.9908e+00 | 0.9954e+00 | Â |
\(2^{-4}\) | 1.3387e–02 | 7.4664e–03 | 3.9318e–03 | 2.0162e–03 | 1.0207e–03 | 5.1355e–04 |
| Â | 0.8424e+00 | 0.9252e+00 | 0.9635e+00 | 0.9820e+00 | 0.9909e+00 | Â |
\(2^{-8}\) | 1.7334e–03 | 2.3379e–03 | 3.9174e–03 | 5.2115e–03 | 5.1020e–03 | 3.7144e–03 |
| Â | 0.4316e+00 | 0.7446e+00 | 0.4118e+00 | 0.0306e+00 | 0.4590e+00 | Â |
\(2^{-12}\) | 1.9236e–03 | 9.0871e–04 | 3.9685e–04 | 7.3668e–04 | 2.1274e–03 | 4.4521e–03 |
| Â | 1.0819e+00 | 1.1952e+00 | 0.8924e+00 | 1.5299e+00 | 1.0653e+00 | Â |
\(2^{-16}\) | 1.9236e–03 | 9.0871e–04 | 3.9685e–04 | 7.3668e–04 | 2.1274e–03 | 4.4521e–03 |
| Â | 1.0819e+00 | 1.1952e+00 | 0.8924e+00 | 1.5299e+00 | 1.0653e+00 | Â |
\(2^{-18}\) | 1.9236e–03 | 9.0871e–04 | 3.9685e–04 | 7.3668e–04 | 2.1274e–03 | 4.4521e–03 |
| Â | 1.0819e+00 | 1.1952e+00 | 0.8924e+00 | 1.5299e+00 | 1.0653e+00 | Â |
\(2^{-20}\) | 1.9236e–03 | 9.0871e–04 | 3.9685e–04 | 7.3668e–04 | 2.1274e–03 | 4.4521e–03 |
| Â | 1.0819e+00 | 1.1952e+00 | 0.8924e+00 | 1.5299e+00 | 1.0653e+00 | Â |