Table 2 Comparison of the maximum absolute error of Example 5.1 of the proposed scheme and the result in [3]
\( \varepsilon \downarrow \) | N \( \rightarrow \) \( 2^5 \) | \( 2^6 \) | \(2^7 \) | \( 2^8 \) | \( 2^9 \) | \( 2^{10} \) |
|---|---|---|---|---|---|---|
Proposed scheme | ||||||
\( 2^{0} \) | 4.2307e-06 | 1.0587e-06 | 2.6468e-07 | 6.6170e-08 | 1.6505e-08 | 4.0694e-09 |
\( 2^{-4} \) | 2.9647e-05 | 7.5264e-06 | 1.8872e-06 | 4.7238e-07 | 1.1812e-07 | 2.9529e-08 |
\( 2^{-8} \) | 1.3865e-05 | 4.9014e-06 | 2.2887e-06 | 7.0094e-07 | 1.8356e-07 | 4.6429e-08 |
\(2^{-12}\) | 6.9416e-04 | 5.9134e-05 | 4.0396e-06 | 2.5841e-07 | 1.6151e-08 | 2.3062e-08 |
\( 2^{-16} \) | 4.0163e-03 | 1.2458e-03 | 1.8212e-04 | 1.5518e-05 | 1.0605e-06 | 6.7831e-08 |
Result in [3] | ||||||
\( 2^0 \) | 0.00343868 | 0.00198874 | 0.00110332 | 0.00060368 | 0.00030394 | 0.00015197 |
\( 2^{-4} \) | 0.01032126 | 0.00605257 | 0.00338123 | 0.00185003 | 0.00094445 | 0.00047551 |
\( 2^{-8} \) | 0.01125894 | 0.00660244 | 0.00368841 | 0.0020181 | 0.00103025 | 0.00051871 |
\( 2^{-12} \) | 0.011200979 | 0.00656845 | 0.00366942 | 0.00200771 | 0.00102495 | 0.00051604 |
\( 2^{-16}\) | 0.0112049 | 0.00657075 | 0.00367071 | 0.00200842 | 0.00102531 | 0.00051622 |