Table 6 Comparison of maximum absolute errors and orders of convergence for Example 3
\(\varepsilon \downarrow N \to\) | 64 | 128 | 256 | 512 | 1024 | 2048 |
|---|---|---|---|---|---|---|
Present method | ||||||
\(10^{ - \,1}\) | 1.5804e−07 | 9.5736e−09 | 6.0110e−10 | 3.8343e−11 | 2.4281e−12 | 1.7421e−13 |
4.0101 | 3.9934 | 3.9706 | 3.9811 | 3.8009 | ||
\(10^{ - \,2}\) | 4.4426e−06 | 2.8574e−07 | 1.8107e−08 | 1.1394e−09 | 7.1458e−11 | 4.4797e−12 |
3.9586 | 3.9801 | 3.9902 | 3.9950 | 3.9956 | ||
\(10^{ - \,3}\) | 3.8440e−04 | 2.6622e−05 | 1.7427e−06 | 1.1132e−07 | 7.0321e−09 | 4.4198e−10 |
3.8519 | 3.9332 | 3.9685 | 3.9846 | 3.9919 | ||
\(10^{ - \,4}\) | 4.6569e−04 | 5.9110e−05 | 6.6270e−06 | 6.8198e−07 | 1.0174e−07 | 2.3644e−08 |
2.9779 | 3.1570 | 3.2806 | 2.7448 | 2.1053 | ||
Result in ref. [15] | ||||||
\(10^{ - \,1}\) | 3.208e−04 | 7.957e−05 | 2.005e−05 | 5.007e−06 | 1.252e−06 | 3.131e−07 |
2.01 | 1.99 | 2.00 | 2.00 | 2.00 | ||
\(10^{ - \,2}\) | 4.066e−04 | 1.017e−04 | 2.544e−05 | 6.359e−06 | 1.590e−06 | 3.975e−07 |
2.00 | 2.00 | 2.00 | 2.00 | 2.00 | ||
\(10^{ - \,3}\) | 3.998e−04 | 1.003e−04 | 2.509e−05 | 6.274e−06 | 1.569e−06 | 3.922e−07 |
1.99 | 2.00 | 2.00 | 2.00 | 2.00 | ||
\(10^{ - \,4}\) | 3.859e−04 | 9.938e−05 | 2.504e−05 | 6.271e−06 | 1.568e−06 | 3.922e−07 |
1.96 | 1.99 | 2.00 | 2.00 | 2.00 | ||