Table 1
Integration performances for all the examples in Section 3.
| Example | Tolerance | Runtime (ms) |
|---|---|---|
| (1) | 10−8 | 77.5 ± 3.6 |
| 10−11 | 202 ± 22 | |
| 10−13 | 405 ± 28 | |
| (2) | 10−8 | 2.41 ± 0.23 |
| 10−11 | 5.28 ± 0.49 | |
| 10−13 | 9.3 ± 2.5 | |
| (3) | 10−8 | 1.97 ± 0.04 |
| 10−11 | 2.96 ± 0.17 | |
| 10−13 | 4.19 ± 0.08 | |
| (4) | 10−8 | 8.6 ± 0.5 |
| 10−11 | 31.1 ± 1.9 | |
| 10−13 | 74.8 ± 0.5 | |
| (5) | 10−8 | 17.5 ± 0.47 |
| 10−11 | 39.1 ± 3.1 | |
| 10−13 | 97.8 ± 1.6 | |
| (6) | 10−8 | 7.75 ± 0.40 |
| 10−11 | 26.3 ± 3.2 | |
| 10−13 | 61.4 ± 1.6 | |
| (7) | 10−8 | 18.5 ± 0.7 |
| 10−11 | 50.5 ± 4.1 | |
| 10−13 | 110.0 ± 3.4 | |
Notes. The examples considered correspond to: (1) Precessing orbit shown in Fig. 5; (2) Unstable circular orbit in Fig. 7 (left panel); (3) Stable circular orbit in Fig. 7 (right panel); (4) Plunging null geodesic with r0 = 2.1M in Fig. 9; (5) Unstable photon orbit with r0 = 3M in Fig. 9; (6) Escaping null geodesic with r0 = 6M in Fig. 9; (7) radially infalling geodesic in Fig. 13.
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