Theory and Modern Applications
Table 9 Estimated derivative at the knots for Problem 2
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 | 0.983602117 | 0.98281753 | 7.85E-04 | −0.342603 | −0.343649394 | 1.05E-03 |
0.2 | 0.928266096 | 0.926699063 | 1.57E-03 | −0.781698 | −0.778719955 | 2.98E-03 |
0.3 | 0.823413873 | 0.821456892 | 1.96E-03 | −1.336360 | −1.326123469 | 1.02E-02 |
0.4 | 0.656402867 | 0.654651884 | 1.75E-03 | −2.028882 | −2.009976683 | 1.89E-02 |
0.5 | 0.412180318 | 0.41124837 | 9.32E-04 | −2.885262 | −2.858093594 | 2.72E-02 |
0.6 | 0.072884752 | 0.073216249 | 3.31E-04 | −3.935777 | −3.902548831 | 3.32E-02 |
0.7 | −0.382613014 | −0.380927289 | 1.69E-03 | −5.215620 | −5.180321935 | 3.53E-02 |
0.8 | −0.979238009 | −0.97664507 | 2.59E-03 | −6.765644 | −6.734033684 | 3.16E-02 |
0.9 | −1.746318209 | −1.743986109 | 2.33E-03 | −8.633207 | −8.612787083 | 2.04E-02 |