Theory and Modern Applications
Table 5 Estimated derivative at the knots for Problem 1
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 | −0.110517092 | −0.11074035 | 2.23E-04 | −1.21568801 | −1.214807005 | 8.81E-04 |
0.2 | −0.244280552 | −0.244660538 | 3.80E-04 | −1.46568331 | −1.463596755 | 2.09E-03 |
0.3 | −0.404957642 | −0.405399753 | 4.42E-04 | −1.75481645 | −1.751187536 | 3.63E-03 |
0.4 | −0.596729879 | −0.59711663 | 3.87E-04 | −2.088554577 | −2.083150017 | 5.40E-03 |
0.5 | −0.824360635 | −0.824568788 | 2.08E-04 | −2.473081906 | −2.465893125 | 7.19E-03 |
0.6 | −1.09327128 | −1.093201278 | 7.00E-05 | −2.915390081 | −2.906756682 | 8.63E-03 |
0.7 | −1.409626895 | −1.40924466 | 3.82E-04 | −3.423379603 | −3.414110953 | 9.27E-03 |
0.8 | −1.780432743 | −1.779823367 | 6.09E-04 | −4.005973671 | −3.997463193 | 8.51E-03 |
0.9 | −2.2136428 | −2.213075086 | 5.68E-04 | −4.673245911 | −4.66757119 | 5.67E-03 |