Theory and Modern Applications
Table 4 Comparison of absolute errors for Example 2 ( \(\pmb{k=3}\) )
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 | 0.990049833749168 | 2.08605e−4 | 5.07778e−7 | 4.15842e−7 | 2.78811e−9 | 2.71666e−9 |
0.2 | 0.960789439152323 | 2.21586e−4 | 5.87780e−7 | 4.10797e−7 | 2.80960e−9 | 2.51711e−9 |
0.3 | 0.913931185271228 | 5.48197e−5 | 1.20537e−6 | 1.38717e−7 | 4.74755e−9 | 9.86147e−10 |
0.4 | 0.852143788966211 | 1.92271e−5 | 1.45560e−6 | 2.03389e−8 | 5.53697e−9 | 1.07901e−10 |
0.5 | 0.778800783071405 | 3.85323e−5 | 1.36715e−6 | 5.24896e−8 | 5.19276e−9 | 8.98013e−11 |
0.6 | 0.697676326071031 | 2.41881e−5 | 1.19571e−6 | 4.21942e−8 | 4.19259e−9 | 4.05933e−11 |
0.7 | 0.612626394184416 | 1.59949e−5 | 1.01058e−6 | 3.36762e−8 | 3.38714e−9 | 1.56910e−11 |
0.8 | 0.527292424043049 | 9.22128e−6 | 5.95503e−7 | 2.06618e−8 | 2.03107e−9 | 3.88289e−11 |
0.9 | 0.444858066222941 | 3.14709e−6 | 2.04191e−7 | 7.61645e−9 | 7.32635e−10 | 6.69331e−11 |