Comparison of the absolute errors between the projected method and various collocation methods, for example 3 at t = 0.5
| x | An absolute error in [28] | An absolute error in [29] | An absolute error by our method for (α, β) = (0.5, 0.5) | An absolute error by our method for (α, β) = (0, 0) |
|---|---|---|---|---|
| 0.1 | 2.59 × 10−14 | 8.95 × 10−6 | 7.29 × 10−14 | 9.25 × 10−15 |
| 0.2 | 4.25 × 10−14 | 4.10 × 10−6 | 6.93 × 10−15 | 8.53 × 10−15 |
| 0.3 | 1.55 × 10−15 | 1.39 × 10−5 | 7.89 × 10−15 | 6.19 × 10−15 |
| 0.4 | 9.83 × 10−14 | 2.07 × 10−5 | 5.38 × 10−14 | 1.70 × 10−14 |
| 0.5 | 3.33 × 10−12 | 2.47 × 10−5 | 3.53 × 10−14 | 3.93 × 10−14 |
| 0.6 | 5.37 × 10−11 | 2.62 × 10−5 | 2.42 × 10−14 | 8.79 × 10−15 |
| 0.7 | 3.71 × 10−10 | 2.55 × 10−5 | 8.26 × 10−15 | 5.31 × 10−15 |
| 0.8 | 1.72 × 10−9 | 2.31 × 10−5 | 1.86 × 10−14 | 7.82 × 10−15 |
| 0.9 | 6.26 × 10−9 | 1.93 × 10−5 | 2.59 × 10−14 | 2.86 × 10−14 |
| An absolute error in [ | An absolute error in [ | An absolute error by our method for ( | An absolute error by our method for ( | |
|---|---|---|---|---|
| 0.1 | 2.59 × 10−14 | 8.95 × 10−6 | 7.29 × 10−14 | 9.25 × 10−15 |
| 0.2 | 4.25 × 10−14 | 4.10 × 10−6 | 6.93 × 10−15 | 8.53 × 10−15 |
| 0.3 | 1.55 × 10−15 | 1.39 × 10−5 | 7.89 × 10−15 | 6.19 × 10−15 |
| 0.4 | 9.83 × 10−14 | 2.07 × 10−5 | 5.38 × 10−14 | 1.70 × 10−14 |
| 0.5 | 3.33 × 10−12 | 2.47 × 10−5 | 3.53 × 10−14 | 3.93 × 10−14 |
| 0.6 | 5.37 × 10−11 | 2.62 × 10−5 | 2.42 × 10−14 | 8.79 × 10−15 |
| 0.7 | 3.71 × 10−10 | 2.55 × 10−5 | 8.26 × 10−15 | 5.31 × 10−15 |
| 0.8 | 1.72 × 10−9 | 2.31 × 10−5 | 1.86 × 10−14 | 7.82 × 10−15 |
| 0.9 | 6.26 × 10−9 | 1.93 × 10−5 | 2.59 × 10−14 | 2.86 × 10−14 |
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