Table 3
Comparative analysis of all methods, including the splitting, explicit, and PIROCK methods with varying tolerances.
| No. steps | ![$\[\overline{\Delta t}\]$](/articles/aa/full_html/2025/03/aa52351-24/aa52351-24-eq41.png){kind=small} |
FD evals | FA evals | FR evals | smax | CPU time/step (s) | Tot. time (s) | |
|---|---|---|---|---|---|---|---|---|
| splitting | 821 974 | 5.7 × 10−7 | 2 465 922 | 2 465 922 | 4 109 870 | 0 | 2 × 10−1 | 1.71 × 105 |
| explicit | 1 103 531 | 4.59 × 10−7 | 3 310 593 | 3 310 593 | 3 310 593 | 0 | 9 × 10−2 | 9.8 × 104 |
| PIR. (10−2) | 3306 | 1.486 × 10−4 | 38 516 | 9918 | 18 701 425 | 8 | 1.45 | 3.75 × 103 |
| PIR. (10−5) | 12 217 | 4.8 × 10−5 | 106 808 | 36 660 | 67 199 808 | 5 | 5.7 × 10−1 | 6.67 × 103 |
Notes. Comparison of the number of steps, average timestep value (![$\[\overline{\Delta t}\]$](/articles/aa/full_html/2025/03/aa52351-24/aa52351-24-eq42.png){kind=small}
), function evaluations for the FD, FA and FR terms, the maximum number of stages s, the average CPU time per step for each case, and the total computational time. The calculations were executed utilizing 28 Intel Broadwell processors integrated into the Pleiades cluster, consisting of the 14-core E5-2680v4 model operating at a clock speed of 2.4 GHz.
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