Theory and Modern Applications
Table 12 Comparison of absolute errors for Example 5.2 with \(\pmb{\eta=7.5}\) and \(\pmb{\eta=10.0}\)
From: A new approach for one-dimensional sine-Gordon equation
τ | AE RKM η = 7.5 | AE MHPM η = 7.5 [29] | AE ADM η = 7.5 [29] | AE RKM η = 10.0 | AE MHPM η = 10.0 [29] | AE ADM η = 10.0 [29] |
|---|---|---|---|---|---|---|
0.02 | 4.2E − 16 | 2.88750E − 14 | 2.88750E − 14 | 5.1E − 18 | 1.59700E − 17 | 1.59700E − 17 |
0.04 | 3.9E − 15 | 2.31000E − 13 | 2.31000E − 13 | 6.3E − 17 | 1.27763E − 16 | 1.27763E − 16 |
0.06 | 9.6E − 15 | 7.79626E − 13 | 7.79626E − 13 | 2.5E − 17 | 4.31201E − 16 | 4.31201E − 16 |
0.08 | 9.2E − 15 | 1.84800E − 12 | 1.84800E − 12 | 7.9E − 16 | 1.02210E − 15 | 1.02210E − 15 |
0.1 | 8.5E − 15 | 3.60939E − 12 | 3.60939E − 12 | 2.7E − 16 | 1.99629E − 15 | 1.99629E − 15 |
0.3 | 2.5E − 13 | 9.74833E − 11 | 9.74833E − 11 | 9.9E − 16 | 5.39165E − 14 | 5.39165E − 14 |