Theory and Modern Applications
Table 2 Comparison of absolute errors for Example 1 ( \(\pmb{k=3}\) )
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 | 0.00995004165278026 | 6.09766e−6 | 1.01327e−6 | 4.46956e−9 | 3.95315e−10 | 5.99699e−13 |
0.2 | 0.0392026631136497 | 7.11910e−6 | 1.19433e−6 | 5.22659e−9 | 4.73386e−10 | 5.69475e−13 |
0.3 | 0.0859802840213046 | 6.96418e−6 | 1.22938e−6 | 5.14196e−9 | 5.02232e−10 | 4.70207e−13 |
0.4 | 0.147369759040462 | 6.72907e−6 | 1.21170e−6 | 4.73782e−9 | 5.05799e−10 | 3.83082e−13 |
0.5 | 0.219395640472593 | 5.82617e−6 | 1.18534e−6 | 4.30528e−9 | 4.92414e−10 | 3.16524e−13 |
0.6 | 0.297120821367484 | 4.41211e−6 | 9.85413e−7 | 3.52994e−9 | 4.11916e−10 | 3.36841e−13 |
0.7 | 0.374772671769399 | 3.86910e−6 | 7.96955e−7 | 2.86759e−9 | 3.31169e−10 | 3.66096e−13 |
0.8 | 0.445892293982186 | 2.27080e−6 | 5.61629e−7 | 1.81250e−9 | 2.28235e−10 | 3.48554e−13 |
0.9 | 0.503504074299238 | 1.73623e−6 | 2.78002e−7 | 9.55841e−10 | 1.18077e−10 | 1.97952e−13 |