Theory and Modern Applications
Table 1 Coefficients of extended cubic basis \(E_{i}(x)\) and its derivatives at different knots
From: Extended cubic B-splines in the numerical solution of time fractional telegraph equation
\(x_{i}\) | \(x_{i+1}\) | \(x_{i+2}\) | \(x_{i+3}\) | \(x_{i+4}\) | else | |
|---|---|---|---|---|---|---|
\(E_{i}(x)\) | 0 | \(\frac{4-\lambda }{24}\) | \(\frac{8+\lambda }{12}\) | \(\frac{4-\lambda }{24}\) | 0 | 0 |
\(E^{\prime }_{i}(x)\) | 0 | \(\frac{1}{2h}\) | 0 | \(\frac{-1}{2h}\) | 0 | 0 |
\(E^{\prime \prime }_{i}(x)\) | 0 | \(\frac{2+\lambda }{2h^{2}}\) | \(-\frac{2+\lambda }{h^{2}}\) | \(\frac{2+\lambda }{2h^{2}}\) | 0 | 0 |