Research Article
Solving Nonstiff Higher Order Odes Using Variable Order Step Size Backward Difference Directly
Table 4
Comparison between the 1PBDVSO, DI, B1, and D1 methods for solving Problem
2.
| | TOL | MTD | STEPS | FS | MAXE | AVER | TIME
(total) |
| | 10−2 | D1
B1
DI
1PBDVSO | 135
134
96
173 | 0
0
0
0 | 4.83764 (−2)
2.63945 (−2)
4.99681 (−3)
1.01436 (−4) | 3.21705 (−2)
2.14665 (−2)
2.47698 (−3)
8.58874 (−5) | 6621
4358
1961
3218 |
| | 10−3 | D1
B1
DI
1PBDVSO | 175
121
157
162 | 1
0
0
0 | 8.81849 (−3)
3.90401 (−2)
6.91170 (−5)
2.40484 (−3) | 5.48179 (−3)
1.65274 (−2)
4.87625 (−5)
1.71894 (−3) | 8294
3896
2890
3005 |
| | 10−4 | D1
B1
DI
1PBDVSO | 233
173
141
142 | 2
0
0
0 | 2.85719 (−3)
1.44401 (−3)
1.79264 (−4)
2.60404 (−4) | 1.39202 (−3)
9.91992 (−4)
1.19952 (−4)
1.89056 (−4) | 11684
5520
2622
2635 |
| | 10−5 | D1
B1
DI
1PBDVSO | 226
263
238
237 | 1
2
0
0 | 3.05429 (−4)
1.97450 (−4)
5.14212 (−6)
1.03862 (−5) | 1.22401 (−4)
5.02997 (−5)
3.89969 (−6)
8.18350 (−6) | 11095
8492
4137
4268 |
| | 10−6 | D1
B1
DI
1PBDVSO | 337
262
214
218 | 1
0
0
0 | 1.12897 (−5)
6.52399 (−5)
1.18826 (−5)
1.56415 (−6) | 5.53620 (−6)
2.34931 (−5)
9.01852 (−6)
1.09680 (−6) | 16060
8429
3766
3941 |
| | 10−7 | D1
B1
DI
1PBDVSO | 421
337
368
370 | 2
0
0
0 | 4.00671 (−7)
1.70966 (−6)
1.79221 (−7)
2.75078 (−7) | 4.00671 (−7)
1.05119 (−6)
1.35202 (−7)
1.91969 (−7) | 19735
10899
6213
6584 |
| | 10−8 | D1
B1
DI
1PBDVSO | 610
523
335
336 | 4
3
1
0 | 3.05239 (−7)
4.90321 (−8)
3.11508 (−8)
3.64286 (−8) | 2.22380 (−7)
3.52515 (−8)
2.58590 (−8)
1.21667 (−8) | 29060
16840
5641
5996 |
| | 10−9 | D1
B1
DI
1PBDVSO | 534
555
578
575 | 2
5
1
0 | 4.96195 (−8)
9.16995 (−8)
1.20539 (−8)
3.80099 (−9) | 1.71145 (−8)
5.35093 (−8)
9.25523 (−9)
2.95718 (−9) | 25234
17610
9347
10114 |
| | 10−10 | D1
B1
DI
1PBDVSO | 800
671
516
517 | 2
4
0
0 | 2.12904 (−10)
8.63683 (−10)
8.37294 (−10)
3.30834 (−9) | 1.21736 (−10)
3.89440 (−10)
6.51148 (−10)
2.52921 (−9) | 38235
21617
8541
9011 |
|
|
