ODE table
ODE table
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| problem | method | rtol | jac | scaled error (ours) | scaled error (SciPy 1.18.1) | nfev (+FD Jacobian) | nfev SciPy | njev | njev SciPy | steps | steps SciPy |
|---|---|---|---|---|---|---|---|---|---|---|---|
| decay | RK45 | 0.001 | false | 2.32 | 2.32 | 44 (+0) | 44 | 0 | 0 | 7 | 7 |
| decay | RK45 | 1e-06 | false | 1.27 | 1.27 | 140 (+0) | 140 | 0 | 0 | 23 | 23 |
| decay | RK45 | 1e-09 | false | 1.07 | 1.07 | 518 (+0) | 518 | 0 | 0 | 86 | 86 |
| decay | RK23 | 0.001 | false | 14.4 | 14.4 | 47 (+0) | 47 | 0 | 0 | 15 | 15 |
| decay | RK23 | 1e-06 | false | 7.63 | 7.63 | 461 (+0) | 461 | 0 | 0 | 153 | 153 |
| decay | RK23 | 1e-09 | false | 7.26 | 7.26 | 4577 (+0) | 4577 | 0 | 0 | 1525 | 1525 |
| decay | DOP853 | 0.001 | false | 0.0771 | 0.0771 | 50 (+0) | 50 | 0 | 0 | 4 | 4 |
| decay | DOP853 | 1e-06 | false | 0.221 | 0.221 | 86 (+0) | 86 | 0 | 0 | 7 | 7 |
| decay | DOP853 | 1e-09 | false | 0.274 | 0.274 | 170 (+0) | 170 | 0 | 0 | 14 | 14 |
| decay | Radau | 0.001 | false | 0.047 | 0.047 | 78 (+6) | 78 | 2 | 2 | 10 | 10 |
| decay | Radau | 1e-06 | false | 0.00948 | 0.00948 | 355 (+6) | 355 | 2 | 2 | 50 | 50 |
| decay | Radau | 1e-09 | false | 0.00132 | 0.00132 | 1954 (+6) | 1954 | 2 | 2 | 278 | 278 |
| decay | BDF | 0.001 | false | 2.61 | 2.61 | 54 (+3) | 54 | 1 | 1 | 26 | 26 |
| decay | BDF | 1e-06 | false | 10.4 | 10.4 | 132 (+3) | 132 | 1 | 1 | 65 | 65 |
| decay | BDF | 1e-09 | false | 38.4 | 38.4 | 346 (+3) | 346 | 1 | 1 | 172 | 172 |
| decay | LSODA | 0.001 | false | 2.32 | 2.67 | 44 (+0) | 39 | 0 | 0 | 7 | 19 |
| decay | LSODA | 1e-06 | false | 1.27 | 1.19 | 140 (+0) | 103 | 0 | 0 | 23 | 48 |
| decay | LSODA | 1e-09 | false | 0.274 | 6.32 | 170 (+0) | 147 | 0 | 0 | 14 | 71 |
| harmonic | RK45 | 0.001 | false | 9.2e+03 | 9.2e+03 | 218 (+0) | 218 | 0 | 0 | 36 | 36 |
| harmonic | RK45 | 1e-06 | false | 1.54e+03 | 1.54e+03 | 1130 (+0) | 1130 | 0 | 0 | 156 | 156 |
| harmonic | RK45 | 1e-09 | false | 360 | 360 | 3956 (+0) | 3956 | 0 | 0 | 631 | 631 |
| harmonic | RK23 | 0.001 | false | 5.87e+03 | 5.87e+03 | 494 (+0) | 494 | 0 | 0 | 124 | 124 |
| harmonic | RK23 | 1e-06 | false | 620 | 620 | 4205 (+0) | 4205 | 0 | 0 | 1342 | 1342 |
| harmonic | RK23 | 1e-09 | false | 60.1 | 60.1 | 41000 (+0) | 41000 | 0 | 0 | 13661 | 13661 |
| harmonic | DOP853 | 0.001 | false | 1.4e+03 | 1.4e+03 | 206 (+0) | 206 | 0 | 0 | 17 | 17 |
| harmonic | DOP853 | 1e-06 | false | 2.19e+03 | 2.19e+03 | 410 (+0) | 410 | 0 | 0 | 34 | 34 |
| harmonic | DOP853 | 1e-09 | false | 2.32e+03 | 2.32e+03 | 926 (+0) | 926 | 0 | 0 | 77 | 77 |
| harmonic | Radau | 0.001 | false | 26.7 | 26.7 | 414 (+4) | 414 | 2 | 2 | 58 | 58 |
| harmonic | Radau | 1e-06 | false | 0.742 | 0.739 | 2227 (+4) | 2227 | 2 | 2 | 317 | 317 |
| harmonic | Radau | 1e-09 | false | 0.0258 | 0.0266 | 12216 (+4) | 12356 | 2 | 2 | 1744 | 1764 |
| harmonic | BDF | 0.001 | false | 4.69e+03 | 4.69e+03 | 276 (+2) | 276 | 1 | 1 | 130 | 130 |
| harmonic | BDF | 1e-06 | false | 1.33e+04 | 1.33e+04 | 794 (+20) | 794 | 7 | 7 | 349 | 349 |
| harmonic | BDF | 1e-09 | false | 1.68e+04 | 1.68e+04 | 2099 (+8) | 2099 | 3 | 3 | 985 | 985 |
| harmonic | LSODA | 0.001 | false | 9.2e+03 | 2.25e+03 | 218 (+0) | 403 | 0 | 0 | 36 | 181 |
| harmonic | LSODA | 1e-06 | false | 1.54e+03 | 2.94e+03 | 1130 (+0) | 647 | 0 | 0 | 156 | 306 |
| harmonic | LSODA | 1e-09 | false | 2.32e+03 | 2.08e+03 | 926 (+0) | 940 | 0 | 0 | 77 | 462 |
| lotka | RK45 | 0.001 | false | 213 | 213 | 470 (+0) | 470 | 0 | 0 | 56 | 56 |
| lotka | RK45 | 1e-06 | false | 22.9 | 22.9 | 1394 (+0) | 1394 | 0 | 0 | 204 | 204 |
| lotka | RK45 | 1e-09 | false | 2.91 | 2.91 | 4802 (+0) | 4802 | 0 | 0 | 790 | 790 |
| lotka | RK23 | 0.001 | false | 128 | 128 | 593 (+0) | 593 | 0 | 0 | 170 | 170 |
| lotka | RK23 | 1e-06 | false | 118 | 118 | 5138 (+0) | 5138 | 0 | 0 | 1706 | 1706 |
| lotka | RK23 | 1e-09 | false | 116 | 116 | 51359 (+0) | 51359 | 0 | 0 | 17119 | 17119 |
| lotka | DOP853 | 0.001 | false | 1.31 | 1.31 | 638 (+0) | 638 | 0 | 0 | 35 | 35 |
| lotka | DOP853 | 1e-06 | false | 0.0921 | 0.0921 | 1082 (+0) | 1082 | 0 | 0 | 72 | 72 |
| lotka | DOP853 | 1e-09 | false | 0.87 | 0.87 | 2570 (+0) | 2570 | 0 | 0 | 172 | 172 |
| lotka | Radau | 0.001 | false | 1.32 | 1.32 | 1076 (+60) | 1076 | 30 | 30 | 126 | 126 |
| lotka | Radau | 1e-06 | false | 0.275 | 0.275 | 4883 (+88) | 4883 | 44 | 44 | 666 | 666 |
| lotka | Radau | 1e-09 | false | 0.0459 | 0.0459 | 25924 (+90) | 25924 | 45 | 45 | 3656 | 3656 |
| lotka | BDF | 0.001 | false | 85 | 85 | 639 (+29) | 639 | 10 | 10 | 240 | 240 |
| lotka | BDF | 1e-06 | false | 205 | 205 | 2050 (+11) | 2050 | 4 | 4 | 766 | 766 |
| lotka | BDF | 1e-09 | false | 571 | 571 | 6960 (+8) | 6960 | 3 | 3 | 2435 | 2435 |
| lotka | LSODA | 0.001 | false | 213 | 7.28 | 470 (+0) | 459 | 0 | 0 | 56 | 204 |
| lotka | LSODA | 1e-06 | false | 22.9 | 36.3 | 1394 (+0) | 927 | 0 | 0 | 204 | 432 |
| lotka | LSODA | 1e-09 | false | 0.87 | 53.7 | 2570 (+0) | 1683 | 0 | 0 | 172 | 799 |
| vdp1 | RK45 | 0.001 | false | 1.65e+03 | 1.65e+03 | 434 (+0) | 434 | 0 | 0 | 52 | 52 |
| vdp1 | RK45 | 1e-06 | false | 194 | 194 | 1436 (+0) | 1436 | 0 | 0 | 176 | 176 |
| vdp1 | RK45 | 1e-09 | false | 103 | 103 | 4370 (+0) | 4370 | 0 | 0 | 663 | 663 |
| vdp1 | RK23 | 0.001 | false | 118 | 118 | 503 (+0) | 503 | 0 | 0 | 130 | 130 |
| vdp1 | RK23 | 1e-06 | false | 54.8 | 54.8 | 4085 (+0) | 4085 | 0 | 0 | 1320 | 1320 |
| vdp1 | RK23 | 1e-09 | false | 36.5 | 36.5 | 39890 (+0) | 39890 | 0 | 0 | 13296 | 13296 |
| vdp1 | DOP853 | 0.001 | false | 4.87 | 4.87 | 578 (+0) | 578 | 0 | 0 | 35 | 35 |
| vdp1 | DOP853 | 1e-06 | false | 201 | 201 | 1070 (+0) | 1070 | 0 | 0 | 69 | 69 |
| vdp1 | DOP853 | 1e-09 | false | 3.65 | 3.65 | 2570 (+0) | 2570 | 0 | 0 | 158 | 158 |
| vdp1 | Radau | 0.001 | false | 13.4 | 13.4 | 967 (+44) | 967 | 22 | 22 | 104 | 104 |
| vdp1 | Radau | 0.001 | true | 20.2 | 20.2 | 941 (+0) | 941 | 22 | 22 | 102 | 102 |
| vdp1 | Radau | 1e-06 | false | 0.243 | 0.243 | 3767 (+86) | 3767 | 43 | 43 | 495 | 495 |
| vdp1 | Radau | 1e-06 | true | 0.179 | 0.179 | 3773 (+0) | 3773 | 41 | 41 | 498 | 498 |
| vdp1 | Radau | 1e-09 | false | 0.0419 | 0.0418 | 19891 (+90) | 19891 | 45 | 45 | 2762 | 2762 |
| vdp1 | Radau | 1e-09 | true | 0.0374 | 0.0376 | 19865 (+0) | 19865 | 44 | 44 | 2760 | 2760 |
| vdp1 | BDF | 0.001 | false | 336 | 336 | 646 (+35) | 646 | 12 | 12 | 215 | 215 |
| vdp1 | BDF | 0.001 | true | 265 | 265 | 626 (+0) | 626 | 13 | 13 | 213 | 213 |
| vdp1 | BDF | 1e-06 | false | 705 | 705 | 1646 (+2) | 1646 | 1 | 1 | 651 | 651 |
| vdp1 | BDF | 1e-06 | true | 728 | 728 | 1616 (+0) | 1616 | 1 | 1 | 666 | 666 |
| vdp1 | BDF | 1e-09 | false | 1.53e+03 | 1.53e+03 | 5347 (+2) | 5347 | 1 | 1 | 2043 | 2043 |
| vdp1 | BDF | 1e-09 | true | 1.38e+03 | 1.38e+03 | 5114 (+0) | 5114 | 1 | 1 | 2015 | 2015 |
| vdp1 | LSODA | 0.001 | false | 1.65e+03 | 16.9 | 434 (+0) | 509 | 0 | 0 | 52 | 223 |
| vdp1 | LSODA | 0.001 | true | 1.65e+03 | 16.9 | 434 (+0) | 509 | 0 | 0 | 52 | 223 |
| vdp1 | LSODA | 1e-06 | false | 194 | 248 | 1436 (+0) | 1100 | 0 | 0 | 176 | 502 |
| vdp1 | LSODA | 1e-06 | true | 194 | 248 | 1436 (+0) | 1100 | 0 | 0 | 176 | 502 |
| vdp1 | LSODA | 1e-09 | false | 3.65 | 153 | 2570 (+0) | 1879 | 0 | 3 | 158 | 896 |
| vdp1 | LSODA | 1e-09 | true | 3.65 | 224 | 2570 (+0) | 1883 | 0 | 5 | 158 | 910 |
| brusselator | RK45 | 0.001 | false | 4.53 | 4.54 | 362 (+0) | 362 | 0 | 0 | 46 | 46 |
| brusselator | RK45 | 1e-06 | false | 2.02 | 2.02 | 974 (+0) | 974 | 0 | 0 | 130 | 130 |
| brusselator | RK45 | 1e-09 | false | 1.91 | 1.91 | 2984 (+0) | 2984 | 0 | 0 | 474 | 474 |
| brusselator | RK23 | 0.001 | false | 9.09 | 9.09 | 323 (+0) | 323 | 0 | 0 | 78 | 78 |
| brusselator | RK23 | 1e-06 | false | 18.4 | 18.4 | 2267 (+0) | 2267 | 0 | 0 | 735 | 735 |
| brusselator | RK23 | 1e-09 | false | 20.2 | 20.2 | 22022 (+0) | 22022 | 0 | 0 | 7338 | 7338 |
| brusselator | DOP853 | 0.001 | false | 0.0323 | 0.0323 | 470 (+0) | 470 | 0 | 0 | 28 | 28 |
| brusselator | DOP853 | 1e-06 | false | 0.0267 | 0.0267 | 866 (+0) | 866 | 0 | 0 | 56 | 56 |
| brusselator | DOP853 | 1e-09 | false | 0.193 | 0.193 | 1886 (+0) | 1886 | 0 | 0 | 119 | 119 |
| brusselator | Radau | 0.001 | false | 0.112 | 0.112 | 718 (+44) | 718 | 22 | 22 | 71 | 71 |
| brusselator | Radau | 1e-06 | false | 0.0166 | 0.0166 | 2647 (+98) | 2647 | 49 | 49 | 338 | 338 |
| brusselator | Radau | 1e-09 | false | 0.00358 | 0.00358 | 12712 (+134) | 12712 | 67 | 67 | 1766 | 1766 |
| brusselator | BDF | 0.001 | false | 8.73 | 8.73 | 384 (+38) | 384 | 13 | 13 | 137 | 137 |
| brusselator | BDF | 1e-06 | false | 20.2 | 20.2 | 1253 (+5) | 1253 | 2 | 2 | 467 | 467 |
| brusselator | BDF | 1e-09 | false | 52.6 | 52.6 | 4090 (+5) | 4090 | 2 | 2 | 1459 | 1459 |
| brusselator | LSODA | 0.001 | false | 4.53 | 7.35 | 362 (+0) | 328 | 0 | 0 | 46 | 140 |
| brusselator | LSODA | 1e-06 | false | 2.02 | 10.5 | 974 (+0) | 647 | 0 | 0 | 130 | 300 |
| brusselator | LSODA | 1e-09 | false | 0.193 | 24.5 | 1886 (+0) | 1311 | 0 | 0 | 119 | 611 |
| arenstorf | RK45 | 0.001 | false | 1.11e+06 | 1.11e+06 | 644 (+0) | 644 | 0 | 0 | 76 | 76 |
| arenstorf | RK45 | 1e-06 | false | 1.72e+07 | 1.72e+07 | 1310 (+0) | 1310 | 0 | 0 | 179 | 179 |
| arenstorf | RK45 | 1e-09 | false | 3.25e+06 | 3.25e+06 | 4394 (+0) | 4394 | 0 | 0 | 706 | 706 |
| arenstorf | RK23 | 0.001 | false | 3.81e+05 | 3.81e+05 | 476 (+0) | 476 | 0 | 0 | 128 | 128 |
| arenstorf | RK23 | 1e-06 | false | 1.65e+07 | 1.65e+07 | 4619 (+0) | 4619 | 0 | 0 | 1482 | 1482 |
| arenstorf | RK23 | 1e-09 | false | 1.54e+07 | 1.54e+07 | 45086 (+0) | 45086 | 0 | 0 | 15021 | 15021 |
| arenstorf | DOP853 | 0.001 | false | 5.15e+05 | 5.15e+05 | 674 (+0) | 674 | 0 | 0 | 41 | 41 |
| arenstorf | DOP853 | 1e-06 | false | 5.44e+06 | 5.44e+06 | 1334 (+0) | 1334 | 0 | 0 | 79 | 79 |
| arenstorf | DOP853 | 1e-09 | false | 4.34e+06 | 4.68e+06 | 2678 (+0) | 2678 | 0 | 0 | 165 | 165 |
| arenstorf | Radau | 0.001 | false | 3.33e+05 | 3.33e+05 | 956 (+84) | 956 | 21 | 21 | 108 | 108 |
| arenstorf | Radau | 1e-06 | false | 5.73e+04 | 5.62e+04 | 4388 (+68) | 4394 | 17 | 21 | 561 | 561 |
| arenstorf | Radau | 1e-09 | false | 1.05e+04 | 1.08e+04 | 26163 (+24) | 26163 | 6 | 6 | 3199 | 3199 |
| arenstorf | BDF | 0.001 | false | 6.75e+05 | 6.75e+05 | 576 (+59) | 576 | 12 | 12 | 214 | 214 |
| arenstorf | BDF | 1e-06 | false | 1.08e+08 | 1.1e+08 | 1720 (+39) | 1712 | 8 | 8 | 722 | 721 |
| arenstorf | BDF | 1e-09 | false | 1.72e+08 | 1.72e+08 | 5109 (+29) | 5109 | 6 | 6 | 2197 | 2197 |
| arenstorf | LSODA | 0.001 | false | 1.11e+06 | 5.49e+05 | 644 (+0) | 613 | 0 | 14 | 76 | 287 |
| arenstorf | LSODA | 1e-06 | false | 1.72e+07 | 7e+07 | 1310 (+0) | 1310 | 0 | 0 | 179 | 603 |
| arenstorf | LSODA | 1e-09 | false | 4.34e+06 | 2.16e+07 | 2678 (+0) | 2169 | 0 | 0 | 165 | 1033 |
| vdp1000 | Radau | 0.001 | false | 0.0551 | 0.054 | 2837 (+194) | 2820 | 97 | 97 | 285 | 283 |
| vdp1000 | Radau | 0.001 | true | 0.0295 | 0.0483 | 2825 (+0) | 2849 | 99 | 99 | 282 | 285 |
| vdp1000 | Radau | 1e-06 | false | 0.0104 | 0.0112 | 10750 (+618) | 10767 | 309 | 309 | 1283 | 1285 |
| vdp1000 | Radau | 1e-06 | true | 0.00947 | 0.00947 | 10746 (+0) | 10746 | 306 | 306 | 1282 | 1282 |
| vdp1000 | BDF | 0.001 | false | 22 | 22 | 1880 (+305) | 1880 | 102 | 102 | 533 | 533 |
| vdp1000 | BDF | 0.001 | true | 16.6 | 16.6 | 1810 (+0) | 1810 | 98 | 98 | 526 | 526 |
| vdp1000 | BDF | 1e-06 | false | 22.3 | 22.3 | 5595 (+309) | 5595 | 103 | 103 | 1847 | 1847 |
| vdp1000 | BDF | 1e-06 | true | 20.3 | 22.3 | 5593 (+0) | 5595 | 102 | 103 | 1848 | 1847 |
| vdp1000 | LSODA | 0.001 | false | 15.3 | 12.4 | 2337 (+257) | 1803 | 87 | 130 | 384 | 727 |
| vdp1000 | LSODA | 0.001 | true | 15.3 | 12.4 | 2337 (+0) | 1543 | 87 | 130 | 384 | 727 |
| vdp1000 | LSODA | 1e-06 | false | 38.6 | 21.2 | 5618 (+308) | 3829 | 104 | 238 | 1073 | 1995 |
| vdp1000 | LSODA | 1e-06 | true | 38.6 | 23.7 | 5618 (+0) | 3206 | 104 | 214 | 1073 | 1852 |
| robertson | Radau | 0.0001 | false | 0.0172 | 0.0173 | 569 (+73) | 569 | 24 | 24 | 66 | 66 |
| robertson | Radau | 0.0001 | true | 0.0173 | 0.0173 | 569 (+0) | 569 | 24 | 24 | 66 | 66 |
| robertson | Radau | 1e-07 | false | 0.0288 | 0.0288 | 2319 (+116) | 2319 | 38 | 38 | 304 | 304 |
| robertson | Radau | 1e-07 | true | 0.0289 | 0.0289 | 2319 (+0) | 2319 | 38 | 38 | 304 | 304 |
| robertson | BDF | 0.0001 | false | 2.91 | 2.91 | 430 (+32) | 430 | 8 | 8 | 168 | 168 |
| robertson | BDF | 0.0001 | true | 2.91 | 2.91 | 430 (+0) | 430 | 8 | 8 | 168 | 168 |
| robertson | BDF | 1e-07 | false | 8.96 | 8.96 | 1324 (+40) | 1324 | 10 | 10 | 447 | 447 |
| robertson | BDF | 1e-07 | true | 8.96 | 8.96 | 1324 (+0) | 1324 | 10 | 10 | 447 | 447 |
| robertson | LSODA | 0.0001 | false | 2.87 | 2.6 | 564 (+27) | 358 | 7 | 35 | 174 | 191 |
| robertson | LSODA | 0.0001 | true | 2.87 | 2.6 | 564 (+0) | 253 | 7 | 35 | 174 | 191 |
| robertson | LSODA | 1e-07 | false | 8.97 | 0.607 | 1489 (+39) | 1195 | 10 | 83 | 399 | 606 |
| robertson | LSODA | 1e-07 | true | 8.97 | 3.22 | 1489 (+0) | 947 | 10 | 91 | 399 | 633 |
| hires | Radau | 0.001 | false | 0.0769 | 0.0769 | 465 (+161) | 465 | 20 | 20 | 43 | 43 |
| hires | Radau | 1e-06 | false | 0.0823 | 0.0823 | 1652 (+459) | 1652 | 57 | 57 | 183 | 183 |
| hires | BDF | 0.001 | false | 55.4 | 55.4 | 295 (+171) | 295 | 19 | 19 | 101 | 101 |
| hires | BDF | 1e-06 | false | 32.5 | 32.5 | 795 (+227) | 795 | 25 | 25 | 295 | 295 |
| hires | LSODA | 0.001 | false | 55.4 | 18.8 | 501 (+134) | 545 | 15 | 33 | 105 | 152 |
| hires | LSODA | 1e-06 | false | 40.5 | 11.3 | 1303 (+215) | 1141 | 24 | 41 | 306 | 454 |
| orego | Radau | 0.001 | false | 0.0704 | 0.136 | 2686 (+411) | 2704 | 137 | 137 | 233 | 233 |
| orego | Radau | 1e-06 | false | 0.0417 | 0.0415 | 9686 (+1185) | 9699 | 395 | 398 | 1059 | 1060 |
| orego | BDF | 0.001 | false | 32 | 32 | 1575 (+395) | 1575 | 99 | 99 | 464 | 464 |
| orego | BDF | 1e-06 | false | 47.5 | 56.9 | 4378 (+563) | 4402 | 141 | 143 | 1455 | 1457 |
| orego | LSODA | 0.001 | false | 2.8 | 4.32 | 2750 (+303) | 1656 | 77 | 128 | 529 | 652 |
| orego | LSODA | 1e-06 | false | 60.5 | 77.1 | 8300 (+408) | 4850 | 103 | 219 | 1610 | 2358 |
Created on by tannevaled
Modified on by tannevaled