Table 3 Comparison of the methods under consideration on the basis of absolute errors and CPU time for the stiff Problem 3 with different number of steps (n)
n | Method | ME_u | ME_v | LE_u | LE_v | CPU time |
|---|---|---|---|---|---|---|
216 | \(\mathrm{POBM} _{5}\) | 5.919e–07 | 5.919e–07 | 1.852e–17 | 1.949e–19 | 1.322e+00 |
\(\mathrm{RPOBM} _{5}\) | 5.919e–07 | 5.919e–07 | 1.852e–17 | 1.949e–19 | 1.057e+00 | |
\(\mathrm{BHSM} _{5}\) | 1.917e–05 | 1.917e–05 | 6.320e–16 | 6.653e–18 | 7.299e–01 | |
\(\mathrm{Sahi} _{6}\) | 3.468e–05 | 3.468e–05 | 4.494e–14 | 4.730e–16 | 2.074e+00 | |
Radau I5 | 3.468e–05 | 3.468e–05 | 1.185e–15 | 1.247e–17 | 1.270e+00 | |
1296 | \(\mathrm{POBM} _{5}\) | 1.232e–11 | 1.232e–11 | 3.969e–22 | 4.177e–24 | 7.689e+00 |
\(\mathrm{RPOBM} _{5}\) | 1.232e–11 | 1.232e–11 | 3.969e–22 | 4.177e–24 | 6.723e+00 | |
\(\mathrm{BHSM} _{5}\) | 4.197e–10 | 4.197e–10 | 1.300e–20 | 1.426e–22 | 2.474e+00 | |
\(\mathrm{Sahi} _{6}\) | 3.821e–09 | 3.821e–09 | 5.763e–18 | 6.067e–20 | 7.311e+00 | |
Radau I5 | 1.362e–09 | 1.362e–09 | 2.540e–20 | 2.674e–22 | 4.044e+00 | |
7776 | \(\mathrm{POBM} _{5}\) | 2.639e–16 | 2.639e–16 | 8.506e–27 | 8.954e–29 | 4.876e+01 |
\(\mathrm{RPOBM} _{5}\) | 2.639e–16 | 2.639e–16 | 8.506e–27 | 8.954e–29 | 3.723e+01 | |
\(\mathrm{BHSM} _{5}\) | 9.010e–15 | 9.010e–15 | 2.903e–25 | 3.056e–27 | 1.450e+01 | |
\(\mathrm{Sahi} _{6}\) | 4.809e–13 | 4.809e–13 | 7.409e–22 | 7.798e–24 | 4.061e+01 | |
Radau I5 | 3.811e–14 | 3.811e–14 | 5.444e–25 | 5.730e–27 | 2.482e+01 |