Theory and Modern Applications
Table 14 Comparison of absolute errors for Example 8 ( \(\pmb{k=2}\) )
x | Exact solution | Absolute error M  = 3 | Absolute error M  = 4 | Absolute error M  = 5 | Absolute error M  = 6 | Absolute error M  = 7 |
|---|---|---|---|---|---|---|
0.1 | 0.100665339016074 | 1.99905e−4 | 2.28846e−5 | 1.72044e−6 | 4.80911e−7 | 5.02872e−8 |
0.2 | 0.205291382243876 | 1.91458e−4 | 2.34563e−5 | 1.63517e−6 | 4.79635e−7 | 4.89559e−8 |
0.3 | 0.317687905980875 | 1.67910e−4 | 2.28553e−5 | 1.57308e−6 | 4.65931e−7 | 4.71142e−8 |
0.4 | 0.441387397450343 | 1.61539e−4 | 2.17240e−5 | 1.47290e−6 | 4.39266e−7 | 4.45112e−8 |
0.5 | 0.579559511251008 | 1.51975e−4 | 2.13789e−5 | 1.36356e−6 | 4.18131e−7 | 4.14292e−8 |
0.6 | 0.734970520367994 | 9.83797e−5 | 1.29024e−5 | 9.77157e−7 | 2.95283e−7 | 2.86342e−8 |
0.7 | 0.909981686939921 | 4.84761e−5 | 5.13638e−6 | 6.43969e−7 | 1.71463e−7 | 1.62533e−8 |
0.8 | 1.10657514524663 | 7.88980e−6 | 1.98660e−6 | 2.77744e−7 | 5.15655e−8 | 4.25484e−9 |
0.9 | 1.32639533423358 | 3.47573e−5 | 7.91713e−6 | 5.42440e−8 | 5.87647e−8 | 6.74598e−9 |