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 |
|
|
