Theory and Modern Applications
Table 4 Absolute residuals for \(h=0.1\)
Method | t | VE | VFE | ||||
|---|---|---|---|---|---|---|---|
\(\vert \varepsilon_{1} \vert \) | \(\vert \varepsilon _{2} \vert \) | \(\vert \varepsilon_{3} \vert \) | \(\vert \varepsilon_{1} \vert \) | \(\vert \varepsilon_{2} \vert \) | \(\vert \varepsilon_{3} \vert \) | ||
RK−4 | 0.10 | 5.9E83 | 5.9E83 | 5.9E83 | 2.3E−01 | 1.3E00 | 1.6E02 |
4.00 | NaN | NaN | NaN | 8.0E−02 | 4.8E−02 | 5.5E00 | |
8.00 | NaN | NaN | NaN | 1.7E−02 | 3.6E−03 | 5.0E−01 | |
12.0 | NaN | NaN | NaN | 2.8E−03 | 3.4E−04 | 5.3E−02 | |
16.0 | NaN | NaN | NaN | 4.1E−04 | 3.1E−05 | 5.2E−03 | |
19.9 | NaN | NaN | NaN | 5.9E−05 | 3.04E−06 | 5.3E−04 | |
Euler | 0.10 | 0.0E00 | 0.0E00 | 3.8E03 | 2.1E−14 | 3.6E−15 | 1.6E02 |
4.00 | NaN | NaN | NaN | 2.8E−14 | 4.4E−16 | 4.5E00 | |
8.00 | NaN | NaN | NaN | 2.8E−14 | 6.9E−17 | 4.1E−01 | |
12.0 | NaN | NaN | NaN | 3.6E−14 | 0.0E00 | 4.1E−02 | |
16.0 | NaN | NaN | NaN | 2.1E−14 | 2.2E−19 | 3.8E−03 | |
19.9 | NaN | NaN | NaN | 7.1E−14 | 2.7E−20 | 3.6E−04 | |
NSFD | 0.10 | 6.0E02 | 6.0E02 | 6.4E02 | 9.8E−01 | 3.0E00 | 1.7E02 |
4.00 | 1.8E−01 | 2.6E−01 | 4.7E02 | 2.2E−01 | 1.7E−01 | 7.9E00 | |
8.00 | 1.1E−02 | 1.2E−02 | 4.7E02 | 4.3E−02 | 1.5E−02 | 8.5E−02 | |
12.0 | 8.5E−04 | 8.6E−03 | 4.8E02 | 7.1E−03 | 1.6E−03 | 9.8E−02 | |
16.0 | 7.4E−05 | 7.3E−05 | 4.8E02 | 1.1E−03 | 1.6E−04 | 1.1E−02 | |
19.9 | 7.1E−06 | 6.9E−06 | 4.8E02 | 1.7E−04 | 1.7E−05 | 1.7E−05 | |
EPA | 0.10 | 1.5E − 11 | 1.3E − 10 | 8.5E − 12 | 1.9E − 11 | 2.7E − 13 | 2.0E − 12 |
4.00 | 4.9E − 14 | 1.4E − 14 | 1.7E − 16 | 2.1E − 14 | 4.3E − 15 | 1.8E − 15 | |
8.00 | 2.8E − 14 | 7.1E − 15 | 8.6E − 16 | 1.8E − 14 | 2.9E − 15 | 1.2E − 15 | |
12.0 | 2.8E − 14 | 3.6E − 15 | 1.6E − 15 | 1.1E − 14 | 2.1E − 15 | 8.6E − 16 | |
16.0 | 6.8E − 15 | 5.3E − 15 | 1.9E − 15 | 1.8E − 14 | 1.6E − 15 | 6.7E − 16 | |
19.9 | 2.8E − 14 | 8.0E − 15 | 2.3E − 15 | 7.1E − 15 | 1.3E − 15 | 5.5E − 16 | |