Theory and Modern Applications
Table 13 Estimated derivative at the knots for Problem 3
z | Exact \(w^{(1)} ( z ) \) | Cubic B-spline \(w^{(1)} ( z ) \) | Absolute error of \(w^{(1)} ( z ) \) | Exact \(w^{(2)} ( z ) \) | Cubic B-spline \(w^{(2)} ( z ) \) | Absolute error of \(w^{(2)} ( z ) \) |
|---|---|---|---|---|---|---|
0.1 | 0.01944 | 0.01511998 | 4.32E-03 | 0.297 | 0.302399605 | 5.40E-03 |
0.2 | 0.04608 | 0.040319947 | 5.76E-03 | 0.192 | 0.201599732 | 9.60E-03 |
0.3 | 0.05292 | 0.047879937 | 5.04E-03 | −0.063 | −0.050399929 | 1.26E-02 |
0.4 | 0.03456 | 0.031679959 | 2.88E-03 | −0.288 | −0.273599629 | 1.44E-02 |
0.5 | 0 | 1.81884E-09 | 1.82E-09 | −0.375 | −0.359999523 | 1.50E-02 |
0.6 | −0.03456 | −0.031679957 | 2.88E-03 | −0.288 | −0.273599656 | 1.44E-02 |
0.7 | −0.05292 | −0.047879938 | 5.04E-03 | −0.063 | −0.050399959 | 1.26E-02 |
0.8 | −0.04608 | −0.040319949 | 5.76E-03 | 0.192 | 0.201599729 | 9.60E-03 |
0.9 | −0.01944 | −0.015119981 | 4.32E-03 | 0.297 | 0.302399629 | 5.40E-03 |