Theory and Modern Applications
Table 7 Comparison of absolute errors for Example 4 ( \(\pmb{k=2}\) )
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 | −0.0199006617063362 | 7.12293e−5 | 4.60723e−6 | 1.03881e−6 | 1.97866e−9 | 9.02739e−9 |
0.2 | −0.0784414263065627 | 1.66987e−6 | 6.19572e−7 | 6.99131e−7 | 1.51682e−8 | 1.68836e−9 |
0.3 | −0.172355392482105 | 1.21751e−4 | 1.76275e−6 | 3.42269e−7 | 2.01945e−8 | 6.31737e−9 |
0.4 | −0.296840010236547 | 2.74878e−5 | 1.49126e−6 | 1.06726e−6 | 5.07048e−9 | 9.34269e−9 |
0.5 | −0.44628710262842 | 1.06032e−5 | 2.81301e−6 | 4.23783e−8 | 4.20504e−8 | 1.76553e−10 |
0.6 | −0.614969399495921 | 2.72115e−4 | 1.79133e−5 | 8.97718e−6 | 5.75857e−7 | 1.78242e−7 |
0.7 | −0.797552239914736 | 4.58685e−4 | 2.48304e−5 | 1.45806e−5 | 9.99011e−7 | 2.95038e−7 |
0.8 | −0.989392483672214 | 5.79446e−4 | 2.95584e−5 | 1.83900e−5 | 1.27201e−6 | 3.69959e−7 |
0.9 | −1.18665369055547 | 6.57413e−4 | 3.25099e−5 | 2.04445e−5 | 1.43231e−6 | 4.14540e−7 |