Theory and Modern Applications
Table 15 Comparison of absolute errors for Example 8 ( \(\pmb{k=3}\) )
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 | 2.00943e−5 | 2.49095e−6 | 7.39087e−8 | 8.51470e−9 | 9.01484e−12 |
0.2 | 0.205291382243876 | 1.91219e−5 | 2.43795e−6 | 7.17544e−8 | 8.33840e−9 | 3.18067e−12 |
0.3 | 0.317687905980875 | 1.75163e−5 | 2.21871e−6 | 6.28094e−8 | 7.40476e−9 | 3.37537e−11 |
0.4 | 0.441387397450343 | 1.46803e−5 | 1.89551e−6 | 4.88112e−8 | 5.95511e−9 | 9.98910e−11 |
0.5 | 0.579559511251008 | 1.21171e−5 | 1.59113e−6 | 3.61323e−8 | 4.63996e−9 | 1.48223e−10 |
0.6 | 0.734970520367994 | 8.42905e−6 | 1.08465e−6 | 2.44077e−8 | 3.18752e−9 | 1.28915e−10 |
0.7 | 0.909981686939921 | 5.01234e−6 | 5.98191e−7 | 1.33754e−8 | 1.77942e−9 | 1.03023e−10 |
0.8 | 1.10657514524663 | 1.47814e−6 | 1.20797e−7 | 4.04928e−9 | 6.02002e−10 | 6.26907e−11 |
0.9 | 1.32639533423358 | 1.54737e−6 | 3.27982e−7 | 2.46634e−9 | 3.25944e−10 | 2.24953e−12 |