Theory and Modern Applications
Table 8 Comparison of absolute errors for Example 4 ( \(\pmb{k=3}\) )
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 | −0.0199006617063362 | 1.64143e−8 | 7.15543e−8 | 4.63072e−9 | 1.09733e−10 | 4.51913e−12 |
0.2 | −0.0784414263065627 | 4.26643e−7 | 7.99963e−8 | 7.54245e−9 | 8.38618e−11 | 2.46411e−11 |
0.3 | −0.172355392482105 | 1.45496e−6 | 1.90341e−7 | 3.52023e−8 | 4.66119e−10 | 5.31878e−10 |
0.4 | −0.296840010236547 | 7.54378e−6 | 7.77384e−7 | 8.52194e−8 | 1.55276e−10 | 1.16498e−9 |
0.5 | −0.44628710262842 | 7.18512e−6 | 1.12532e−6 | 1.07965e−7 | 6.28860e−10 | 1.47615e−9 |
0.6 | −0.614969399495921 | 1.65622e−5 | 1.03010e−7 | 1.82404e−7 | 7.06173e−9 | 1.72201e−9 |
0.7 | −0.797552239914736 | 2.32175e−5 | 6.06844e−7 | 2.25375e−7 | 1.22023e−8 | 1.80556e−9 |
0.8 | −0.989392483672214 | 2.86341e−5 | 1.40638e−6 | 2.44832e−7 | 1.51659e−8 | 1.67463e−9 |
0.9 | −1.18665369055547 | 3.30731e−5 | 2.31416e−6 | 2.41118e−7 | 1.67655e−8 | 1.39453e−9 |