Theory and Modern Applications
Table 16 Estimated derivative at the knots for Problem 4
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 | 0.895170749 | 0.895210345 | 3.96E-05 | −1.094837582 | −1.095793107 | 9.56E-04 |
0.2 | 0.781397247 | 0.781425109 | 2.79E-05 | −1.178735909 | −1.179911611 | 1.18E-03 |
0.3 | 0.659816282 | 0.659831 | 1.47E-05 | −1.250856696 | −1.251970569 | 1.11E-03 |
0.4 | 0.531642652 | 0.531655948 | 1.33E-05 | −1.310479336 | −1.311530475 | 1.05E-03 |
0.5 | 0.398157023 | 0.398173256 | 1.62E-05 | −1.3570081 | −1.358123365 | 1.12E-03 |
0.6 | 0.260693142 | 0.260703061 | 9.92E-06 | −1.389978088 | −1.39128053 | 1.30E-03 |
0.7 | 0.1206245 | 0.120610969 | 1.35E-05 | −1.409059875 | −1.4105613 | 1.50E-03 |
0.8 | −0.020649382 | −0.020696212 | 4.68E-05 | −1.4140628 | −1.415582332 | 1.52E-03 |
0.9 | −0.161716941 | −0.161777672 | 6.07E-05 | −1.406046855 | −1.406046855 | 1.11E-03 |