Theory and Modern Applications
Table 6 Comparison of absolute errors for Example 3 ( \(\pmb{k=3}\) )
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 | 0.995037190209989 | 7.56440e−7 | 5.71715e−8 | 2.72876e−9 | 3.20637e−10 | 3.77395e−11 |
0.2 | 0.98058067569092 | 7.76980e−8 | 2.63566e−8 | 3.70661e−10 | 2.55319e−10 | 1.92960e−11 |
0.3 | 0.957826285221151 | 6.00860e−8 | 2.26763e−8 | 1.66112e−8 | 6.70535e−10 | 3.12874e−10 |
0.4 | 0.928476690885259 | 2.29220e−6 | 1.91073e−7 | 4.98419e−8 | 1.35278e−9 | 8.25356e−10 |
0.5 | 0.894427190999916 | 2.52812e−6 | 3.30368e−7 | 7.10777e−8 | 1.72866e−9 | 1.16419e−9 |
0.6 | 0.857492925712544 | 6.98583e−6 | 1.99788e−7 | 1.14244e−7 | 5.91857e−9 | 1.36581e−9 |
0.7 | 0.81923192051904 | 1.05020e−5 | 6.25059e−7 | 1.43766e−7 | 9.14354e−9 | 1.45891e−9 |
0.8 | 0.78086880944303 | 1.36172e−5 | 1.04964e−6 | 1.59582e−7 | 1.10759e−8 | 1.41417e−9 |
0.9 | 0.743294146247166 | 1.60925e−5 | 1.51021e−6 | 1.60847e−7 | 1.20134e−8 | 1.26230e−9 |