Research Article
Solving Nonstiff Higher Order Odes Using Variable Order Step Size Backward Difference Directly
Table 3
Comparison between the 1PBDVSO, DI, B1, and D1 methods for solving Problem
1.
| TOL | MTD | STEPS | FS | MAXE | AVER | TIME (total) |
| 10−2 | D1 B1 DI 1PBDVSO | 113 89 76 71 | 5 3 1 0 | 8.80309 (−2) 2.07488 (−1) 8.78700 (−2) 1.17774 (−1) | 1.19400 (−1) 6.87734 (−2) 2.56159 (−2) 1.70700 (−2) | 2078 1628 969 969 |
| 10−3 | D1 B1 DI 1PBDVSO | 146 111 85 79 | 7 0 2 1 | 2.68984 (−2) 3.05138 (−2) 2.12907 (−2) 1.81903 (−2) | 5.25240 (−2) 6.28779 (−3) 9.00022 (−3) 6.05764 (−3) | 2560 2071 1135 1063 |
| 10−4 | D1 B1 DI 1PBDVSO | 151 170 94 149 | 2 1 1 0 | 4.30130 (−3) 5.37539 (−4) 4.25614 (−3) 1.97342 (−5) | 5.45887 (−3) 1.06165 (−4) 1.53472 (−3) 5.05592 (−6) | 3024 3169 1284 1951 |
| 10−5 | D1 B1 DI 1PBDVSO | 218 200 161 160 | 1 7 0 0 | 1.84329 (−5) 4.40121 (−4) 6.68588 (−4) 1.83864 (−5) | 1.33438 (−5) 1.37204 (−4) 2.70629 (−4) 6.47215 (−6) | 3860 3652 2094 2080 |
| 10−6 | D1 B1 DI 1PBDVSO | 275 121 179 176 | 3 0 1 0 | 1.80685 (−6) 1.38184 (−5) 3.15166 (−4) 5.88468 (−6) | 1.81711 (−6) 2.65555 (−6) 1.29162 (−4) 2.26518 (−6) | 5227 4077 2294 2272 |
| 10−7 | D1 B1 DI 1PBDVSO | 219 330 193 197 | 9 0 1 0 | 4.47927 (−6) 1.06409 (−7) 1.44784 (−4) 2.58941 (−7) | 7.17250 (−6) 6.01321 (−8) 5.87351 (−5) 9.00261 (−8) | 5413 6257 2502 2513 |
| 10−8 | D1 B1 DI 1PBDVSO | 348 287 205 209 | 2 2 0 0 | 3.49871 (−8) 4.59227 (−7) 6.69118 (−5) 6.96499 (−8) | 2.75009 (−8) 1.19307 (−7) 2.76364 (−5) 2.35911 (−8) | 6310 5367 8665 2664 |
| 10−9 | D1 B1 DI 1PBDVSO | 260 424 226 225 | 7 0 0 0 | 2.68246 (−8) 4.48526 (−10) 3.11980 (−5) 1.87994 (−9) | 1.79939 (−8) 1.44218 (−10) 1.25997 (−5) 4.25589 (−10) | 8633 8271 2944 2851 |
| 10−10 | D1 B1 DI 1PBDVSO | 526 475 370 248 | 9 10 0 0 | 3.45300 (−9) 7.88269 (−9) 1.44822 (−7) 4.13390 (−9) | 2.61398 (−9) 1.39352 (−9) 5.81042 (−8) 8.63144 (−10) | 9866 8822 4639 3109 |
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