Table 4 Comparison of the maximum absolute error of Example 5.1 of the proposed scheme and the result in Example 5.2
\( \varepsilon \downarrow \) | N \( \rightarrow \) \( 2^5 \) | \( 2^6 \) | \( 2^7 \) | \( 2^8 \) | \( 2^9 \) | \( 2^{10} \) |
|---|---|---|---|---|---|---|
Proposed scheme | ||||||
\( 2^{0} \) | 1.4021e-05 | 3.5078e-06 | 8.7725e-07 | 2.1932e-07 | 5.4820e-08 | 1.3692e-08 |
\( 2^{-2} \) | 4.0894e-05 | 1.0233e-05 | 2.5588e-06 | 6.3973e-07 | 1.5993e-07 | 3.9962e-08 |
\( 2^{-4} \) | 8.3355e-05 | 2.0870e-05 | 5.2203e-06 | 1.3052e-06 | 3.2632e-07 | 8.1577e-08 |
\(2^{-6}\) | 1.3785e-04 | 3.4622e-05 | 8.6671e-06 | 2.1673e-06 | 5.4188e-07 | 1.3547e-07 |
\( 2^{-8} \) | 2.0102e-04 | 5.1032e-05 | 1.2800e-05 | 3.2036e-06 | 8.0104e-07 | 2.0027e-07 |
Result in [9] | ||||||
\( 2^{0} \) | 0.02882363 | 0.00729132 | 0.00183933 | 0.00046239 | 0.00011608 | 0.00002906 |
\( 2^{-2} \) | 0.02860477 | 0.00725102 | 0.0018317 | 0.00046143 | 0.00015067 | 0.00003785 |
\( 2^{-4} \) | 0.04001304 | 0.01015697 | 0.00257469 | 0.00065085 | 0.0001643 | 0.00004139 |
\( 2^{-6} \) | 0.04331213 | 0.01100204 | 0.00279084 | 0.00070696 | 0.00017896 | 0.00004527 |
\( 2^{-8} \) | 0.04342876 | 0.01104697 | 0.00280418 | 0.00071231 | 0.00018094 | 0.00004593 |