Theory and Modern Applications
Table 1 Comparison of absolute errors for Example 1 ( \(\pmb{k=2}\) )
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 | 0.00995004165278026 | 5.05015e−5 | 1.15174e−5 | 1.67248e−7 | 1.94092e−8 | 2.04877e−10 |
0.2 | 0.0392026631136497 | 6.99671e−5 | 1.49598e−5 | 2.08568e−7 | 2.37033e−8 | 2.44321e−10 |
0.3 | 0.0859802840213046 | 8.61420e−5 | 1.65555e−5 | 2.27808e−7 | 2.59825e−8 | 2.64413e−10 |
0.4 | 0.147369759040462 | 8.52543e−5 | 1.74995e−5 | 2.42605e−7 | 2.71268e−8 | 2.74407e−10 |
0.5 | 0.219395640472593 | 8.52773e−5 | 1.84611e−5 | 2.42878e−7 | 2.80195e−8 | 2.76631e−10 |
0.6 | 0.297120821367484 | 5.87600e−5 | 1.39445e−5 | 1.76695e−7 | 2.15210e−8 | 2.10918e−10 |
0.7 | 0.374772671769399 | 3.90650e−5 | 1.02566e−5 | 1.41817e−7 | 1.58798e−8 | 1.56994e−10 |
0.8 | 0.445892293982186 | 4.85804e−5 | 6.65266e−6 | 9.25693e−8 | 1.04099e−8 | 1.06686e−10 |
0.9 | 0.503504074299238 | 2.34107e−5 | 3.09612e−6 | 5.98109e−8 | 4.99262e−9 | 5.71941e−11 |